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--- /dev/null
+++ b/14UlXIZzwE4.txt
@@ -0,0 +1,6331 @@
+align:start position:0%
+ 
+morning everyone welcome to 609 5i
+
+ align:start position:0%
+morning everyone welcome to 609 5i
+ 
+
+ align:start position:0%
+morning everyone welcome to 609 5i
+thanks for registering for this class
+
+ align:start position:0%
+thanks for registering for this class
+ 
+
+ align:start position:0%
+thanks for registering for this class
+hope you like it
+
+ align:start position:0%
+hope you like it
+ 
+
+ align:start position:0%
+hope you like it
+my name is stringy David us I'm a
+
+ align:start position:0%
+my name is stringy David us I'm a
+ 
+
+ align:start position:0%
+my name is stringy David us I'm a
+professor of computer science at MIT
+
+ align:start position:0%
+professor of computer science at MIT
+ 
+
+ align:start position:0%
+professor of computer science at MIT
+obviously and I've been teaching at MIT
+
+ align:start position:0%
+obviously and I've been teaching at MIT
+ 
+
+ align:start position:0%
+obviously and I've been teaching at MIT
+for 430 years so I've been at it for a
+
+ align:start position:0%
+for 430 years so I've been at it for a
+ 
+
+ align:start position:0%
+for 430 years so I've been at it for a
+while
+
+ align:start position:0%
+while
+ 
+
+ align:start position:0%
+while
+the reason I'm teaching this IP class is
+
+ align:start position:0%
+the reason I'm teaching this IP class is
+ 
+
+ align:start position:0%
+the reason I'm teaching this IP class is
+because I want to try out this this way
+
+ align:start position:0%
+because I want to try out this this way
+ 
+
+ align:start position:0%
+because I want to try out this this way
+of teaching programming that starts with
+
+ align:start position:0%
+of teaching programming that starts with
+ 
+
+ align:start position:0%
+of teaching programming that starts with
+the recreational world of mathematical
+
+ align:start position:0%
+the recreational world of mathematical
+ 
+
+ align:start position:0%
+the recreational world of mathematical
+puzzles algorithmic puzzles and I want
+
+ align:start position:0%
+puzzles algorithmic puzzles and I want
+ 
+
+ align:start position:0%
+puzzles algorithmic puzzles and I want
+to connect it up to to writing programs
+
+ align:start position:0%
+to connect it up to to writing programs
+ 
+
+ align:start position:0%
+to connect it up to to writing programs
+and I have taught this material before
+
+ align:start position:0%
+and I have taught this material before
+ 
+
+ align:start position:0%
+and I have taught this material before
+in six double oh nine that I think some
+
+ align:start position:0%
+in six double oh nine that I think some
+ 
+
+ align:start position:0%
+in six double oh nine that I think some
+of you are registered for but but I
+
+ align:start position:0%
+of you are registered for but but I
+ 
+
+ align:start position:0%
+of you are registered for but but I
+wanted to teach it in a in a more
+
+ align:start position:0%
+wanted to teach it in a in a more
+ 
+
+ align:start position:0%
+wanted to teach it in a in a more
+interactive informal setting and I
+
+ align:start position:0%
+interactive informal setting and I
+ 
+
+ align:start position:0%
+interactive informal setting and I
+should mention that I wrote a book on
+
+ align:start position:0%
+should mention that I wrote a book on
+ 
+
+ align:start position:0%
+should mention that I wrote a book on
+this which is a book that's recommended
+
+ align:start position:0%
+this which is a book that's recommended
+ 
+
+ align:start position:0%
+this which is a book that's recommended
+or not required for six double O nine
+
+ align:start position:0%
+or not required for six double O nine
+ 
+
+ align:start position:0%
+or not required for six double O nine
+and so you might see this in the MIT
+
+ align:start position:0%
+and so you might see this in the MIT
+ 
+
+ align:start position:0%
+and so you might see this in the MIT
+press bookstore and other places and
+
+ align:start position:0%
+press bookstore and other places and
+ 
+
+ align:start position:0%
+press bookstore and other places and
+most of the material I'm gonna cover
+
+ align:start position:0%
+most of the material I'm gonna cover
+ 
+
+ align:start position:0%
+most of the material I'm gonna cover
+here is from the book but I don't want
+
+ align:start position:0%
+here is from the book but I don't want
+ 
+
+ align:start position:0%
+here is from the book but I don't want
+you to read the book because I want you
+
+ align:start position:0%
+you to read the book because I want you
+ 
+
+ align:start position:0%
+you to read the book because I want you
+to listen to my explanations for the
+
+ align:start position:0%
+to listen to my explanations for the
+ 
+
+ align:start position:0%
+to listen to my explanations for the
+puzzles and try and think of the the
+
+ align:start position:0%
+puzzles and try and think of the the
+ 
+
+ align:start position:0%
+puzzles and try and think of the the
+solutions yourself and and then
+
+ align:start position:0%
+solutions yourself and and then
+ 
+
+ align:start position:0%
+solutions yourself and and then
+obviously I do some one decoding a knot
+
+ align:start position:0%
+obviously I do some one decoding a knot
+ 
+
+ align:start position:0%
+obviously I do some one decoding a knot
+during lecture but offline and I'll show
+
+ align:start position:0%
+during lecture but offline and I'll show
+ 
+
+ align:start position:0%
+during lecture but offline and I'll show
+you some solutions to the puzzles and
+
+ align:start position:0%
+you some solutions to the puzzles and
+ 
+
+ align:start position:0%
+you some solutions to the puzzles and
+there'll be some exercises so if I don't
+
+ align:start position:0%
+there'll be some exercises so if I don't
+ 
+
+ align:start position:0%
+there'll be some exercises so if I don't
+want to spend a whole lot of time on
+
+ align:start position:0%
+want to spend a whole lot of time on
+ 
+
+ align:start position:0%
+want to spend a whole lot of time on
+logistics I this is an IEP class as I
+
+ align:start position:0%
+logistics I this is an IEP class as I
+ 
+
+ align:start position:0%
+logistics I this is an IEP class as I
+mentioned I'd like this to be informal
+
+ align:start position:0%
+mentioned I'd like this to be informal
+ 
+
+ align:start position:0%
+mentioned I'd like this to be informal
+and relaxed so we meet every day for two
+
+ align:start position:0%
+and relaxed so we meet every day for two
+ 
+
+ align:start position:0%
+and relaxed so we meet every day for two
+weeks we have the holiday coming up on
+
+ align:start position:0%
+weeks we have the holiday coming up on
+ 
+
+ align:start position:0%
+weeks we have the holiday coming up on
+Monday so we'll have nine total lectures
+
+ align:start position:0%
+Monday so we'll have nine total lectures
+ 
+
+ align:start position:0%
+Monday so we'll have nine total lectures
+roughly for an hour might spill over but
+
+ align:start position:0%
+roughly for an hour might spill over but
+ 
+
+ align:start position:0%
+roughly for an hour might spill over but
+hopefully you'll you'll be okay with it
+
+ align:start position:0%
+hopefully you'll you'll be okay with it
+ 
+
+ align:start position:0%
+hopefully you'll you'll be okay with it
+because you don't have you know another
+
+ align:start position:0%
+because you don't have you know another
+ 
+
+ align:start position:0%
+because you don't have you know another
+class to go to at noon and if you do
+
+ align:start position:0%
+class to go to at noon and if you do
+ 
+
+ align:start position:0%
+class to go to at noon and if you do
+yeah well let me know and I'll give you
+
+ align:start position:0%
+yeah well let me know and I'll give you
+ 
+
+ align:start position:0%
+yeah well let me know and I'll give you
+that five minutes of
+
+ align:start position:0%
+that five minutes of
+ 
+
+ align:start position:0%
+that five minutes of
+overflow personally at some at a time of
+
+ align:start position:0%
+overflow personally at some at a time of
+ 
+
+ align:start position:0%
+overflow personally at some at a time of
+your choosing but hopefully I'll keep
+
+ align:start position:0%
+your choosing but hopefully I'll keep
+ 
+
+ align:start position:0%
+your choosing but hopefully I'll keep
+keep on time so I and in terms of work I
+
+ align:start position:0%
+keep on time so I and in terms of work I
+ 
+
+ align:start position:0%
+keep on time so I and in terms of work I
+mean this is a pass/fail it's it's a
+
+ align:start position:0%
+mean this is a pass/fail it's it's a
+ 
+
+ align:start position:0%
+mean this is a pass/fail it's it's a
+four credit class I know some of you may
+
+ align:start position:0%
+four credit class I know some of you may
+ 
+
+ align:start position:0%
+four credit class I know some of you may
+be listeners but some of you are
+
+ align:start position:0%
+be listeners but some of you are
+ 
+
+ align:start position:0%
+be listeners but some of you are
+registered for it so I'll have to assign
+
+ align:start position:0%
+registered for it so I'll have to assign
+ 
+
+ align:start position:0%
+registered for it so I'll have to assign
+you a grade so there will be some
+
+ align:start position:0%
+you a grade so there will be some
+ 
+
+ align:start position:0%
+you a grade so there will be some
+exercises and I'm gonna make it very
+
+ align:start position:0%
+exercises and I'm gonna make it very
+ 
+
+ align:start position:0%
+exercises and I'm gonna make it very
+simple you little that the exercise is
+
+ align:start position:0%
+simple you little that the exercise is
+ 
+
+ align:start position:0%
+simple you little that the exercise is
+up on the website
+
+ align:start position:0%
+up on the website
+ 
+
+ align:start position:0%
+up on the website
+there'll be do you know two days from
+
+ align:start position:0%
+there'll be do you know two days from
+ 
+
+ align:start position:0%
+there'll be do you know two days from
+when I put them up and you'll have
+
+ align:start position:0%
+when I put them up and you'll have
+ 
+
+ align:start position:0%
+when I put them up and you'll have
+options in terms of whether to do a
+
+ align:start position:0%
+options in terms of whether to do a
+ 
+
+ align:start position:0%
+options in terms of whether to do a
+really simple exercise that's you know
+
+ align:start position:0%
+really simple exercise that's you know
+ 
+
+ align:start position:0%
+really simple exercise that's you know
+probably going to take about a five
+
+ align:start position:0%
+probably going to take about a five
+ 
+
+ align:start position:0%
+probably going to take about a five
+minutes or do something harder right and
+
+ align:start position:0%
+minutes or do something harder right and
+ 
+
+ align:start position:0%
+minutes or do something harder right and
+for each of the puzzles there's a two or
+
+ align:start position:0%
+for each of the puzzles there's a two or
+ 
+
+ align:start position:0%
+for each of the puzzles there's a two or
+three exercises and you get to do all of
+
+ align:start position:0%
+three exercises and you get to do all of
+ 
+
+ align:start position:0%
+three exercises and you get to do all of
+them if you want you can choose to do
+
+ align:start position:0%
+them if you want you can choose to do
+ 
+
+ align:start position:0%
+them if you want you can choose to do
+one or the other
+
+ align:start position:0%
+one or the other
+ 
+
+ align:start position:0%
+one or the other
+alright I'm gonna have office hours
+
+ align:start position:0%
+alright I'm gonna have office hours
+ 
+
+ align:start position:0%
+alright I'm gonna have office hours
+every day from one to two I don't plan
+
+ align:start position:0%
+every day from one to two I don't plan
+ 
+
+ align:start position:0%
+every day from one to two I don't plan
+on putting solutions up to the exercises
+
+ align:start position:0%
+on putting solutions up to the exercises
+ 
+
+ align:start position:0%
+on putting solutions up to the exercises
+the solutions to the to the puzzles
+
+ align:start position:0%
+the solutions to the to the puzzles
+ 
+
+ align:start position:0%
+the solutions to the to the puzzles
+themselves they'll be shown mostly in
+
+ align:start position:0%
+themselves they'll be shown mostly in
+ 
+
+ align:start position:0%
+themselves they'll be shown mostly in
+lecture and and put up on the seller
+
+ align:start position:0%
+lecture and and put up on the seller
+ 
+
+ align:start position:0%
+lecture and and put up on the seller
+website but the solutions to the
+
+ align:start position:0%
+website but the solutions to the
+ 
+
+ align:start position:0%
+website but the solutions to the
+exercises I'm not gonna put up but if
+
+ align:start position:0%
+exercises I'm not gonna put up but if
+ 
+
+ align:start position:0%
+exercises I'm not gonna put up but if
+you ever get stuck well that's what
+
+ align:start position:0%
+you ever get stuck well that's what
+ 
+
+ align:start position:0%
+you ever get stuck well that's what
+office hours are for and if you can't
+
+ align:start position:0%
+office hours are for and if you can't
+ 
+
+ align:start position:0%
+office hours are for and if you can't
+solve the exercises I'll help you solve
+
+ align:start position:0%
+solve the exercises I'll help you solve
+ 
+
+ align:start position:0%
+solve the exercises I'll help you solve
+them alright so did that without further
+
+ align:start position:0%
+them alright so did that without further
+ 
+
+ align:start position:0%
+them alright so did that without further
+ado let's let's dive in and talk about
+
+ align:start position:0%
+ado let's let's dive in and talk about
+ 
+
+ align:start position:0%
+ado let's let's dive in and talk about
+talk about puzzles and solving puzzles
+
+ align:start position:0%
+talk about puzzles and solving puzzles
+ 
+
+ align:start position:0%
+talk about puzzles and solving puzzles
+using algorithms and then and then
+
+ align:start position:0%
+using algorithms and then and then
+ 
+
+ align:start position:0%
+using algorithms and then and then
+programs I'd really like this to be
+
+ align:start position:0%
+programs I'd really like this to be
+ 
+
+ align:start position:0%
+programs I'd really like this to be
+interactive so the police ask questions
+
+ align:start position:0%
+interactive so the police ask questions
+ 
+
+ align:start position:0%
+interactive so the police ask questions
+and suggest solutions that I haven't
+
+ align:start position:0%
+and suggest solutions that I haven't
+ 
+
+ align:start position:0%
+and suggest solutions that I haven't
+taught off you know that'd be great in
+
+ align:start position:0%
+taught off you know that'd be great in
+ 
+
+ align:start position:0%
+taught off you know that'd be great in
+my second edition you know whenever that
+
+ align:start position:0%
+my second edition you know whenever that
+ 
+
+ align:start position:0%
+my second edition you know whenever that
+is you'll get credit for that alright so
+
+ align:start position:0%
+is you'll get credit for that alright so
+ 
+
+ align:start position:0%
+is you'll get credit for that alright so
+the first puzzle I I tried to have I
+
+ align:start position:0%
+the first puzzle I I tried to have I
+ 
+
+ align:start position:0%
+the first puzzle I I tried to have I
+don't know funny
+
+ align:start position:0%
+don't know funny
+ 
+
+ align:start position:0%
+don't know funny
+titles for all of these puzzles
+
+ align:start position:0%
+titles for all of these puzzles
+ 
+
+ align:start position:0%
+titles for all of these puzzles
+intriguing and so the first puzzle is
+
+ align:start position:0%
+intriguing and so the first puzzle is
+ 
+
+ align:start position:0%
+intriguing and so the first puzzle is
+called you will all confirm it this is
+
+ align:start position:0%
+called you will all confirm it this is
+ 
+
+ align:start position:0%
+called you will all confirm it this is
+really a warm-up puzzle as you'll see I
+
+ align:start position:0%
+really a warm-up puzzle as you'll see I
+ 
+
+ align:start position:0%
+really a warm-up puzzle as you'll see I
+mean this is true for any class things
+
+ align:start position:0%
+mean this is true for any class things
+ 
+
+ align:start position:0%
+mean this is true for any class things
+are going to get more complicated as we
+
+ align:start position:0%
+are going to get more complicated as we
+ 
+
+ align:start position:0%
+are going to get more complicated as we
+go along so if you'll probably do ten or
+
+ align:start position:0%
+go along so if you'll probably do ten or
+ 
+
+ align:start position:0%
+go along so if you'll probably do ten or
+twelve puzzles in the next two weeks
+
+ align:start position:0%
+twelve puzzles in the next two weeks
+ 
+
+ align:start position:0%
+twelve puzzles in the next two weeks
+and by the end you're going to see
+
+ align:start position:0%
+and by the end you're going to see
+ 
+
+ align:start position:0%
+and by the end you're going to see
+things like memorization and dynamic
+
+ align:start position:0%
+things like memorization and dynamic
+ 
+
+ align:start position:0%
+things like memorization and dynamic
+programming and things like that but
+
+ align:start position:0%
+programming and things like that but
+ 
+
+ align:start position:0%
+programming and things like that but
+towards the end of next week and if you
+
+ align:start position:0%
+towards the end of next week and if you
+ 
+
+ align:start position:0%
+towards the end of next week and if you
+don't know what those mean well that's
+
+ align:start position:0%
+don't know what those mean well that's
+ 
+
+ align:start position:0%
+don't know what those mean well that's
+great because you're hopefully you know
+
+ align:start position:0%
+great because you're hopefully you know
+ 
+
+ align:start position:0%
+great because you're hopefully you know
+you will know by the by the end of the
+
+ align:start position:0%
+you will know by the by the end of the
+ 
+
+ align:start position:0%
+you will know by the by the end of the
+two weeks and a lot of these things are
+
+ align:start position:0%
+two weeks and a lot of these things are
+ 
+
+ align:start position:0%
+two weeks and a lot of these things are
+algorithmic insights are insights that
+
+ align:start position:0%
+algorithmic insights are insights that
+ 
+
+ align:start position:0%
+algorithmic insights are insights that
+will help you in course six classes for
+
+ align:start position:0%
+will help you in course six classes for
+ 
+
+ align:start position:0%
+will help you in course six classes for
+sure and you know perhaps even if you
+
+ align:start position:0%
+sure and you know perhaps even if you
+ 
+
+ align:start position:0%
+sure and you know perhaps even if you
+follow a career outside of outside of
+
+ align:start position:0%
+follow a career outside of outside of
+ 
+
+ align:start position:0%
+follow a career outside of outside of
+course six all right so this particular
+
+ align:start position:0%
+course six all right so this particular
+ 
+
+ align:start position:0%
+course six all right so this particular
+puzzle is as I said a fairly simple
+
+ align:start position:0%
+puzzle is as I said a fairly simple
+ 
+
+ align:start position:0%
+puzzle is as I said a fairly simple
+puzzle at least to describe and the
+
+ align:start position:0%
+puzzle at least to describe and the
+ 
+
+ align:start position:0%
+puzzle at least to describe and the
+setting is as follows so you're a
+
+ align:start position:0%
+setting is as follows so you're a
+ 
+
+ align:start position:0%
+setting is as follows so you're a
+gatekeeper at a baseball game we'll just
+
+ align:start position:0%
+gatekeeper at a baseball game we'll just
+ 
+
+ align:start position:0%
+gatekeeper at a baseball game we'll just
+call it a baseball game because baseball
+
+ align:start position:0%
+call it a baseball game because baseball
+ 
+
+ align:start position:0%
+call it a baseball game because baseball
+players wear caps and you know that's
+
+ align:start position:0%
+players wear caps and you know that's
+ 
+
+ align:start position:0%
+players wear caps and you know that's
+most people are watching games with caps
+
+ align:start position:0%
+most people are watching games with caps
+ 
+
+ align:start position:0%
+most people are watching games with caps
+on and so you're a gate keeper and
+
+ align:start position:0%
+on and so you're a gate keeper and
+ 
+
+ align:start position:0%
+on and so you're a gate keeper and
+there's a bunch of people standing in
+
+ align:start position:0%
+there's a bunch of people standing in
+ 
+
+ align:start position:0%
+there's a bunch of people standing in
+line let's just say each of them knows
+
+ align:start position:0%
+line let's just say each of them knows
+ 
+
+ align:start position:0%
+line let's just say each of them knows
+their number and this is Python so the
+
+ align:start position:0%
+their number and this is Python so the
+ 
+
+ align:start position:0%
+their number and this is Python so the
+number starts at zero okay as opposed to
+
+ align:start position:0%
+number starts at zero okay as opposed to
+ 
+
+ align:start position:0%
+number starts at zero okay as opposed to
+one and there's there's a whole bunch of
+
+ align:start position:0%
+one and there's there's a whole bunch of
+ 
+
+ align:start position:0%
+one and there's there's a whole bunch of
+people standing in line ready to get in
+
+ align:start position:0%
+people standing in line ready to get in
+ 
+
+ align:start position:0%
+people standing in line ready to get in
+and they they all have caps and some of
+
+ align:start position:0%
+and they they all have caps and some of
+ 
+
+ align:start position:0%
+and they they all have caps and some of
+them you know wearing their caps for
+
+ align:start position:0%
+them you know wearing their caps for
+ 
+
+ align:start position:0%
+them you know wearing their caps for
+words so with the with the I guess what
+
+ align:start position:0%
+words so with the with the I guess what
+ 
+
+ align:start position:0%
+words so with the with the I guess what
+do you call it what's the front of the
+
+ align:start position:0%
+do you call it what's the front of the
+ 
+
+ align:start position:0%
+do you call it what's the front of the
+cap called the shape the the thing that
+
+ align:start position:0%
+cap called the shape the the thing that
+ 
+
+ align:start position:0%
+cap called the shape the the thing that
+gives you shape you know up front and so
+
+ align:start position:0%
+gives you shape you know up front and so
+ 
+
+ align:start position:0%
+gives you shape you know up front and so
+we just we just say let me try and draw
+
+ align:start position:0%
+we just we just say let me try and draw
+ 
+
+ align:start position:0%
+we just we just say let me try and draw
+this out so said this person is wearing
+
+ align:start position:0%
+this out so said this person is wearing
+ 
+
+ align:start position:0%
+this out so said this person is wearing
+his cap like that and and this lady here
+
+ align:start position:0%
+his cap like that and and this lady here
+ 
+
+ align:start position:0%
+his cap like that and and this lady here
+is is wearing her cap like this
+
+ align:start position:0%
+is is wearing her cap like this
+ 
+
+ align:start position:0%
+is is wearing her cap like this
+alright so that's four words and that's
+
+ align:start position:0%
+alright so that's four words and that's
+ 
+
+ align:start position:0%
+alright so that's four words and that's
+backwards okay so you're your job here
+
+ align:start position:0%
+backwards okay so you're your job here
+ 
+
+ align:start position:0%
+backwards okay so you're your job here
+is straight forward you can only let all
+
+ align:start position:0%
+is straight forward you can only let all
+ 
+
+ align:start position:0%
+is straight forward you can only let all
+of these people in into line in sorry
+
+ align:start position:0%
+of these people in into line in sorry
+ 
+
+ align:start position:0%
+of these people in into line in sorry
+into the stadium that were in line if
+
+ align:start position:0%
+into the stadium that were in line if
+ 
+
+ align:start position:0%
+into the stadium that were in line if
+they all
+
+ align:start position:0%
+they all
+ 
+
+ align:start position:0%
+they all
+conform okay so so they all have to wear
+
+ align:start position:0%
+conform okay so so they all have to wear
+ 
+
+ align:start position:0%
+conform okay so so they all have to wear
+their caps in a particular orientation
+
+ align:start position:0%
+their caps in a particular orientation
+ 
+
+ align:start position:0%
+their caps in a particular orientation
+and you don't particularly care which
+
+ align:start position:0%
+and you don't particularly care which
+ 
+
+ align:start position:0%
+and you don't particularly care which
+one all right
+
+ align:start position:0%
+one all right
+ 
+
+ align:start position:0%
+one all right
+and so they all have to be forwards you
+
+ align:start position:0%
+and so they all have to be forwards you
+ 
+
+ align:start position:0%
+and so they all have to be forwards you
+know all let's say you know 13 of them
+
+ align:start position:0%
+know all let's say you know 13 of them
+ 
+
+ align:start position:0%
+know all let's say you know 13 of them
+are they all have to be backwards right
+
+ align:start position:0%
+are they all have to be backwards right
+ 
+
+ align:start position:0%
+are they all have to be backwards right
+now all of them know their position on
+
+ align:start position:0%
+now all of them know their position on
+ 
+
+ align:start position:0%
+now all of them know their position on
+the line all right so this person knows
+
+ align:start position:0%
+the line all right so this person knows
+ 
+
+ align:start position:0%
+the line all right so this person knows
+that his position is zero this lady here
+
+ align:start position:0%
+that his position is zero this lady here
+ 
+
+ align:start position:0%
+that his position is zero this lady here
+knows that her position is one etc etc
+
+ align:start position:0%
+knows that her position is one etc etc
+ 
+
+ align:start position:0%
+knows that her position is one etc etc
+right and so so obviously you'd like to
+
+ align:start position:0%
+right and so so obviously you'd like to
+ 
+
+ align:start position:0%
+right and so so obviously you'd like to
+minimize the amount of work that you do
+
+ align:start position:0%
+minimize the amount of work that you do
+ 
+
+ align:start position:0%
+minimize the amount of work that you do
+and you could certainly choose let's say
+
+ align:start position:0%
+and you could certainly choose let's say
+ 
+
+ align:start position:0%
+and you could certainly choose let's say
+you want everyone to be forwards you
+
+ align:start position:0%
+you want everyone to be forwards you
+ 
+
+ align:start position:0%
+you want everyone to be forwards you
+could say hey lady in position one flip
+
+ align:start position:0%
+could say hey lady in position one flip
+ 
+
+ align:start position:0%
+could say hey lady in position one flip
+your cap right oh I should mention
+
+ align:start position:0%
+your cap right oh I should mention
+ 
+
+ align:start position:0%
+your cap right oh I should mention
+something that is important so people
+
+ align:start position:0%
+something that is important so people
+ 
+
+ align:start position:0%
+something that is important so people
+have a different definition of forwards
+
+ align:start position:0%
+have a different definition of forwards
+ 
+
+ align:start position:0%
+have a different definition of forwards
+and backwards you know that it's it's
+
+ align:start position:0%
+and backwards you know that it's it's
+ 
+
+ align:start position:0%
+and backwards you know that it's it's
+sort of what's natural and what's
+
+ align:start position:0%
+sort of what's natural and what's
+ 
+
+ align:start position:0%
+sort of what's natural and what's
+unnatural to them so so it's we think
+
+ align:start position:0%
+unnatural to them so so it's we think
+ 
+
+ align:start position:0%
+unnatural to them so so it's we think
+that this person has his cap on forwards
+
+ align:start position:0%
+that this person has his cap on forwards
+ 
+
+ align:start position:0%
+that this person has his cap on forwards
+you know before all you know he thinks
+
+ align:start position:0%
+you know before all you know he thinks
+ 
+
+ align:start position:0%
+you know before all you know he thinks
+he's got his cap on backwards or
+
+ align:start position:0%
+he's got his cap on backwards or
+ 
+
+ align:start position:0%
+he's got his cap on backwards or
+vice-versa
+
+ align:start position:0%
+vice-versa
+ 
+
+ align:start position:0%
+vice-versa
+right so you can it assume that the
+
+ align:start position:0%
+right so you can it assume that the
+ 
+
+ align:start position:0%
+right so you can it assume that the
+definition of forwards and backwards is
+
+ align:start position:0%
+definition of forwards and backwards is
+ 
+
+ align:start position:0%
+definition of forwards and backwards is
+identical for all of the people in line
+
+ align:start position:0%
+identical for all of the people in line
+ 
+
+ align:start position:0%
+identical for all of the people in line
+and and and really is the same as your
+
+ align:start position:0%
+and and and really is the same as your
+ 
+
+ align:start position:0%
+and and and really is the same as your
+definition I mean if it seems kind of
+
+ align:start position:0%
+definition I mean if it seems kind of
+ 
+
+ align:start position:0%
+definition I mean if it seems kind of
+unreasonable hey I mean this is a puzzle
+
+ align:start position:0%
+unreasonable hey I mean this is a puzzle
+ 
+
+ align:start position:0%
+unreasonable hey I mean this is a puzzle
+ok so so so let's let's let's not argue
+
+ align:start position:0%
+ok so so so let's let's let's not argue
+ 
+
+ align:start position:0%
+ok so so so let's let's let's not argue
+about that we can argue about other
+
+ align:start position:0%
+about that we can argue about other
+ 
+
+ align:start position:0%
+about that we can argue about other
+things like how to write Python programs
+
+ align:start position:0%
+things like how to write Python programs
+ 
+
+ align:start position:0%
+things like how to write Python programs
+properly so so what you have to do now
+
+ align:start position:0%
+properly so so what you have to do now
+ 
+
+ align:start position:0%
+properly so so what you have to do now
+is you have to call out commands that
+
+ align:start position:0%
+is you have to call out commands that
+ 
+
+ align:start position:0%
+is you have to call out commands that
+correspond to saying person in position
+
+ align:start position:0%
+correspond to saying person in position
+ 
+
+ align:start position:0%
+correspond to saying person in position
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+flip your cap right that's all you can
+
+ align:start position:0%
+flip your cap right that's all you can
+ 
+
+ align:start position:0%
+flip your cap right that's all you can
+say you can just say flip your cap right
+
+ align:start position:0%
+say you can just say flip your cap right
+ 
+
+ align:start position:0%
+say you can just say flip your cap right
+and you can obviously see how these caps
+
+ align:start position:0%
+and you can obviously see how these caps
+ 
+
+ align:start position:0%
+and you can obviously see how these caps
+are oriented and you can ask let's say
+
+ align:start position:0%
+are oriented and you can ask let's say
+ 
+
+ align:start position:0%
+are oriented and you can ask let's say
+that you had something like that I'm
+
+ align:start position:0%
+that you had something like that I'm
+ 
+
+ align:start position:0%
+that you had something like that I'm
+just making this up as I go along in
+
+ align:start position:0%
+just making this up as I go along in
+ 
+
+ align:start position:0%
+just making this up as I go along in
+terms of I'm not going to draw all the
+
+ align:start position:0%
+terms of I'm not going to draw all the
+ 
+
+ align:start position:0%
+terms of I'm not going to draw all the
+caps here but this is what it looks like
+
+ align:start position:0%
+caps here but this is what it looks like
+ 
+
+ align:start position:0%
+caps here but this is what it looks like
+and so you see in according to you you
+
+ align:start position:0%
+and so you see in according to you you
+ 
+
+ align:start position:0%
+and so you see in according to you you
+know UCF the
+
+ align:start position:0%
+know UCF the
+ 
+
+ align:start position:0%
+know UCF the
+be in terms of forwards and backwards
+
+ align:start position:0%
+be in terms of forwards and backwards
+ 
+
+ align:start position:0%
+be in terms of forwards and backwards
+and let's say you decide that you want
+
+ align:start position:0%
+and let's say you decide that you want
+ 
+
+ align:start position:0%
+and let's say you decide that you want
+everyone to have their their cap on
+
+ align:start position:0%
+everyone to have their their cap on
+ 
+
+ align:start position:0%
+everyone to have their their cap on
+forwards then you would you could say a
+
+ align:start position:0%
+forwards then you would you could say a
+ 
+
+ align:start position:0%
+forwards then you would you could say a
+person in position one flip your cap
+
+ align:start position:0%
+person in position one flip your cap
+ 
+
+ align:start position:0%
+person in position one flip your cap
+with person in position to flip your cap
+
+ align:start position:0%
+with person in position to flip your cap
+ 
+
+ align:start position:0%
+with person in position to flip your cap
+and then person whose position for 7 etc
+
+ align:start position:0%
+and then person whose position for 7 etc
+ 
+
+ align:start position:0%
+and then person whose position for 7 etc
+right and you want to make it easier on
+
+ align:start position:0%
+right and you want to make it easier on
+ 
+
+ align:start position:0%
+right and you want to make it easier on
+yourself because people do know their
+
+ align:start position:0%
+yourself because people do know their
+ 
+
+ align:start position:0%
+yourself because people do know their
+indices their positions in line and so
+
+ align:start position:0%
+indices their positions in line and so
+ 
+
+ align:start position:0%
+indices their positions in line and so
+you can say to save yourself some
+
+ align:start position:0%
+you can say to save yourself some
+ 
+
+ align:start position:0%
+you can say to save yourself some
+trouble you could say people in
+
+ align:start position:0%
+trouble you could say people in
+ 
+
+ align:start position:0%
+trouble you could say people in
+positions 1 through 2 and the
+
+ align:start position:0%
+positions 1 through 2 and the
+ 
+
+ align:start position:0%
+positions 1 through 2 and the
+implication is that it's inclusive flip
+
+ align:start position:0%
+implication is that it's inclusive flip
+ 
+
+ align:start position:0%
+implication is that it's inclusive flip
+your caps right and so that takes care
+
+ align:start position:0%
+your caps right and so that takes care
+ 
+
+ align:start position:0%
+your caps right and so that takes care
+of these two and perhaps you know eight
+
+ align:start position:0%
+of these two and perhaps you know eight
+ 
+
+ align:start position:0%
+of these two and perhaps you know eight
+here and nine you know had their caps on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+backwards and you could say are people
+
+ align:start position:0%
+backwards and you could say are people
+ 
+
+ align:start position:0%
+backwards and you could say are people
+in positions seven through nine flip
+
+ align:start position:0%
+in positions seven through nine flip
+ 
+
+ align:start position:0%
+in positions seven through nine flip
+your caps right so in this particular
+
+ align:start position:0%
+your caps right so in this particular
+ 
+
+ align:start position:0%
+your caps right so in this particular
+example assuming that things ended with
+
+ align:start position:0%
+example assuming that things ended with
+ 
+
+ align:start position:0%
+example assuming that things ended with
+ten people in line zero through nine you
+
+ align:start position:0%
+ten people in line zero through nine you
+ 
+
+ align:start position:0%
+ten people in line zero through nine you
+could get away with three commands you
+
+ align:start position:0%
+could get away with three commands you
+ 
+
+ align:start position:0%
+could get away with three commands you
+could say one through two and the
+
+ align:start position:0%
+could say one through two and the
+ 
+
+ align:start position:0%
+could say one through two and the
+implication as I said this this is
+
+ align:start position:0%
+implication as I said this this is
+ 
+
+ align:start position:0%
+implication as I said this this is
+inclusive flip and then you could say
+
+ align:start position:0%
+inclusive flip and then you could say
+ 
+
+ align:start position:0%
+inclusive flip and then you could say
+four flip and then you could say is
+
+ align:start position:0%
+four flip and then you could say is
+ 
+
+ align:start position:0%
+four flip and then you could say is
+seven through nine flip okay and if you
+
+ align:start position:0%
+seven through nine flip okay and if you
+ 
+
+ align:start position:0%
+seven through nine flip okay and if you
+did it the other way you could also say
+
+ align:start position:0%
+did it the other way you could also say
+ 
+
+ align:start position:0%
+did it the other way you could also say
+person that 0 flip and so this would go
+
+ align:start position:0%
+person that 0 flip and so this would go
+ 
+
+ align:start position:0%
+person that 0 flip and so this would go
+backwards person eight three flip
+
+ align:start position:0%
+backwards person eight three flip
+ 
+
+ align:start position:0%
+backwards person eight three flip
+obviously you can't say zero through
+
+ align:start position:0%
+obviously you can't say zero through
+ 
+
+ align:start position:0%
+obviously you can't say zero through
+three because that would be wrong and
+
+ align:start position:0%
+three because that would be wrong and
+ 
+
+ align:start position:0%
+three because that would be wrong and
+and then you could you could say five
+
+ align:start position:0%
+and then you could you could say five
+ 
+
+ align:start position:0%
+and then you could you could say five
+through five through six year so you
+
+ align:start position:0%
+through five through six year so you
+ 
+
+ align:start position:0%
+through five through six year so you
+would get three three commands in that
+
+ align:start position:0%
+would get three three commands in that
+ 
+
+ align:start position:0%
+would get three three commands in that
+case as well but if in fact for
+
+ align:start position:0%
+case as well but if in fact for
+ 
+
+ align:start position:0%
+case as well but if in fact for
+argument's sake let's just say that I'm
+
+ align:start position:0%
+argument's sake let's just say that I'm
+ 
+
+ align:start position:0%
+argument's sake let's just say that I'm
+gonna just turn this into ten and put it
+
+ align:start position:0%
+gonna just turn this into ten and put it
+ 
+
+ align:start position:0%
+gonna just turn this into ten and put it
+put an F down here then
+
+ align:start position:0%
+put an F down here then
+ 
+
+ align:start position:0%
+put an F down here then
+these three commands would still work if
+
+ align:start position:0%
+these three commands would still work if
+ 
+
+ align:start position:0%
+these three commands would still work if
+you wanted to focus on the on the bees
+
+ align:start position:0%
+you wanted to focus on the on the bees
+ 
+
+ align:start position:0%
+you wanted to focus on the on the bees
+on the backwards people and make make
+
+ align:start position:0%
+on the backwards people and make make
+ 
+
+ align:start position:0%
+on the backwards people and make make
+them go forwards but if you wanted to
+
+ align:start position:0%
+them go forwards but if you wanted to
+ 
+
+ align:start position:0%
+them go forwards but if you wanted to
+make all of the forward people go
+
+ align:start position:0%
+make all of the forward people go
+ 
+
+ align:start position:0%
+make all of the forward people go
+backwards you would need one two three
+
+ align:start position:0%
+backwards you would need one two three
+ 
+
+ align:start position:0%
+backwards you would need one two three
+four four commands alright so so in this
+
+ align:start position:0%
+four four commands alright so so in this
+ 
+
+ align:start position:0%
+four four commands alright so so in this
+particular case you're better off doing
+
+ align:start position:0%
+particular case you're better off doing
+ 
+
+ align:start position:0%
+particular case you're better off doing
+that as opposed to doing four commands
+
+ align:start position:0%
+that as opposed to doing four commands
+ 
+
+ align:start position:0%
+that as opposed to doing four commands
+alright so first straightforward
+
+ align:start position:0%
+alright so first straightforward
+ 
+
+ align:start position:0%
+alright so first straightforward
+question is manat talking about code yet
+
+ align:start position:0%
+question is manat talking about code yet
+ 
+
+ align:start position:0%
+question is manat talking about code yet
+I'm algorithmically you know just in
+
+ align:start position:0%
+I'm algorithmically you know just in
+ 
+
+ align:start position:0%
+I'm algorithmically you know just in
+terms of pseudocode and I'm happy with
+
+ align:start position:0%
+terms of pseudocode and I'm happy with
+ 
+
+ align:start position:0%
+terms of pseudocode and I'm happy with
+English how would you determine the
+
+ align:start position:0%
+English how would you determine the
+ 
+
+ align:start position:0%
+English how would you determine the
+minimum set of commands given a
+
+ align:start position:0%
+minimum set of commands given a
+ 
+
+ align:start position:0%
+minimum set of commands given a
+particular set of people there's an
+
+ align:start position:0%
+particular set of people there's an
+ 
+
+ align:start position:0%
+particular set of people there's an
+arbitrary set of people you want to make
+
+ align:start position:0%
+arbitrary set of people you want to make
+ 
+
+ align:start position:0%
+arbitrary set of people you want to make
+sure that you have the absolute minimum
+
+ align:start position:0%
+sure that you have the absolute minimum
+ 
+
+ align:start position:0%
+sure that you have the absolute minimum
+set of commands and you're going to have
+
+ align:start position:0%
+set of commands and you're going to have
+ 
+
+ align:start position:0%
+set of commands and you're going to have
+to use these intervals so you definitely
+
+ align:start position:0%
+to use these intervals so you definitely
+ 
+
+ align:start position:0%
+to use these intervals so you definitely
+want to look for all the contiguous
+
+ align:start position:0%
+want to look for all the contiguous
+ 
+
+ align:start position:0%
+want to look for all the contiguous
+intervals because obviously if you say
+
+ align:start position:0%
+intervals because obviously if you say
+ 
+
+ align:start position:0%
+intervals because obviously if you say
+one followed and and and then that's a
+
+ align:start position:0%
+one followed and and and then that's a
+ 
+
+ align:start position:0%
+one followed and and and then that's a
+separate command and you say two and
+
+ align:start position:0%
+separate command and you say two and
+ 
+
+ align:start position:0%
+separate command and you say two and
+that's a separate command you end up
+
+ align:start position:0%
+that's a separate command you end up
+ 
+
+ align:start position:0%
+that's a separate command you end up
+having more commands than necessary
+
+ align:start position:0%
+having more commands than necessary
+ 
+
+ align:start position:0%
+having more commands than necessary
+right so so anyone want to tell me I I
+
+ align:start position:0%
+right so so anyone want to tell me I I
+ 
+
+ align:start position:0%
+right so so anyone want to tell me I I
+guess roughly in in terms of pseudocode
+
+ align:start position:0%
+guess roughly in in terms of pseudocode
+ 
+
+ align:start position:0%
+guess roughly in in terms of pseudocode
+how this would work yeah go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through them and then whatever the
+
+ align:start position:0%
+through them and then whatever the
+ 
+
+ align:start position:0%
+through them and then whatever the
+second one so if you have whatever the
+
+ align:start position:0%
+second one so if you have whatever the
+ 
+
+ align:start position:0%
+second one so if you have whatever the
+second group is if it's ever beat those
+
+ align:start position:0%
+second group is if it's ever beat those
+ 
+
+ align:start position:0%
+second group is if it's ever beat those
+are the ones that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from what you pass through
+
+ align:start position:0%
+from what you pass through
+ 
+
+ align:start position:0%
+from what you pass through
+whatever you just tell them sounds good
+
+ align:start position:0%
+whatever you just tell them sounds good
+ 
+
+ align:start position:0%
+whatever you just tell them sounds good
+do you have anything to add to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's good good excellent so both of
+
+ align:start position:0%
+that's good good excellent so both of
+ 
+
+ align:start position:0%
+that's good good excellent so both of
+you had it right so let me explain what
+
+ align:start position:0%
+you had it right so let me explain what
+ 
+
+ align:start position:0%
+you had it right so let me explain what
+these two gentleman what was your name
+
+ align:start position:0%
+these two gentleman what was your name
+ 
+
+ align:start position:0%
+these two gentleman what was your name
+you're not sure what yours fatty
+
+ align:start position:0%
+you're not sure what yours fatty
+ 
+
+ align:start position:0%
+you're not sure what yours fatty
+so Canara and fatty said so so basically
+
+ align:start position:0%
+so Canara and fatty said so so basically
+ 
+
+ align:start position:0%
+so Canara and fatty said so so basically
+this is as I said the natural algorithm
+
+ align:start position:0%
+this is as I said the natural algorithm
+ 
+
+ align:start position:0%
+this is as I said the natural algorithm
+that you would use the natural algorithm
+
+ align:start position:0%
+that you would use the natural algorithm
+ 
+
+ align:start position:0%
+that you would use the natural algorithm
+would be that you walk through this list
+
+ align:start position:0%
+would be that you walk through this list
+ 
+
+ align:start position:0%
+would be that you walk through this list
+and you start computing what I would
+
+ align:start position:0%
+and you start computing what I would
+ 
+
+ align:start position:0%
+and you start computing what I would
+call you call it group Skinner but I'd
+
+ align:start position:0%
+call you call it group Skinner but I'd
+ 
+
+ align:start position:0%
+call you call it group Skinner but I'd
+call them intervals right and an
+
+ align:start position:0%
+call them intervals right and an
+ 
+
+ align:start position:0%
+call them intervals right and an
+interval this is something that is
+
+ align:start position:0%
+interval this is something that is
+ 
+
+ align:start position:0%
+interval this is something that is
+unbroken
+
+ align:start position:0%
+unbroken
+ 
+
+ align:start position:0%
+unbroken
+it's a contiguous it's a contiguous set
+
+ align:start position:0%
+it's a contiguous it's a contiguous set
+ 
+
+ align:start position:0%
+it's a contiguous it's a contiguous set
+of people who all have their caps in the
+
+ align:start position:0%
+of people who all have their caps in the
+ 
+
+ align:start position:0%
+of people who all have their caps in the
+same orientation you know be it forward
+
+ align:start position:0%
+same orientation you know be it forward
+ 
+
+ align:start position:0%
+same orientation you know be it forward
+or backwards and what you would do in
+
+ align:start position:0%
+or backwards and what you would do in
+ 
+
+ align:start position:0%
+or backwards and what you would do in
+this case is you would you would compute
+
+ align:start position:0%
+this case is you would you would compute
+ 
+
+ align:start position:0%
+this case is you would you would compute
+the you'd say I want to look at the
+
+ align:start position:0%
+the you'd say I want to look at the
+ 
+
+ align:start position:0%
+the you'd say I want to look at the
+forward intervals and the forward
+
+ align:start position:0%
+forward intervals and the forward
+ 
+
+ align:start position:0%
+forward intervals and the forward
+intervals would be zero zero because
+
+ align:start position:0%
+intervals would be zero zero because
+ 
+
+ align:start position:0%
+intervals would be zero zero because
+that would essentially what you have in
+
+ align:start position:0%
+that would essentially what you have in
+ 
+
+ align:start position:0%
+that would essentially what you have in
+here and going through that list you
+
+ align:start position:0%
+here and going through that list you
+ 
+
+ align:start position:0%
+here and going through that list you
+would get you would also say I'm gonna
+
+ align:start position:0%
+would get you would also say I'm gonna
+ 
+
+ align:start position:0%
+would get you would also say I'm gonna
+be computing the backward intervals and
+
+ align:start position:0%
+be computing the backward intervals and
+ 
+
+ align:start position:0%
+be computing the backward intervals and
+in this case you discover one two as the
+
+ align:start position:0%
+in this case you discover one two as the
+ 
+
+ align:start position:0%
+in this case you discover one two as the
+backward backwards interval so I'm gonna
+
+ align:start position:0%
+backward backwards interval so I'm gonna
+ 
+
+ align:start position:0%
+backward backwards interval so I'm gonna
+write them out like that and in general
+
+ align:start position:0%
+write them out like that and in general
+ 
+
+ align:start position:0%
+write them out like that and in general
+in the mathematical notation when you
+
+ align:start position:0%
+in the mathematical notation when you
+ 
+
+ align:start position:0%
+in the mathematical notation when you
+put square brackets these are closed
+
+ align:start position:0%
+put square brackets these are closed
+ 
+
+ align:start position:0%
+put square brackets these are closed
+intervals right so so zero is included
+
+ align:start position:0%
+intervals right so so zero is included
+ 
+
+ align:start position:0%
+intervals right so so zero is included
+and we're going to see a puzzle where
+
+ align:start position:0%
+and we're going to see a puzzle where
+ 
+
+ align:start position:0%
+and we're going to see a puzzle where
+you might see something a little bit
+
+ align:start position:0%
+you might see something a little bit
+ 
+
+ align:start position:0%
+you might see something a little bit
+different so I wanted to point that out
+
+ align:start position:0%
+different so I wanted to point that out
+ 
+
+ align:start position:0%
+different so I wanted to point that out
+so one two are both inside this interval
+
+ align:start position:0%
+so one two are both inside this interval
+ 
+
+ align:start position:0%
+so one two are both inside this interval
+and these two you would generate as you
+
+ align:start position:0%
+and these two you would generate as you
+ 
+
+ align:start position:0%
+and these two you would generate as you
+would you would go through the list and
+
+ align:start position:0%
+would you would go through the list and
+ 
+
+ align:start position:0%
+would you would go through the list and
+then you would generate three three over
+
+ align:start position:0%
+then you would generate three three over
+ 
+
+ align:start position:0%
+then you would generate three three over
+here and then you would generate four
+
+ align:start position:0%
+here and then you would generate four
+ 
+
+ align:start position:0%
+here and then you would generate four
+yep that's right just for up I'm sorry
+
+ align:start position:0%
+yep that's right just for up I'm sorry
+ 
+
+ align:start position:0%
+yep that's right just for up I'm sorry
+for four over here if you want to call
+
+ align:start position:0%
+for four over here if you want to call
+ 
+
+ align:start position:0%
+for four over here if you want to call
+it in an interval you could represent
+
+ align:start position:0%
+it in an interval you could represent
+ 
+
+ align:start position:0%
+it in an interval you could represent
+this differently and there's nothing
+
+ align:start position:0%
+this differently and there's nothing
+ 
+
+ align:start position:0%
+this differently and there's nothing
+that's stopping you in Python to have
+
+ align:start position:0%
+that's stopping you in Python to have
+ 
+
+ align:start position:0%
+that's stopping you in Python to have
+these it's slightly more complicated
+
+ align:start position:0%
+these it's slightly more complicated
+ 
+
+ align:start position:0%
+these it's slightly more complicated
+representation where you just have zero
+
+ align:start position:0%
+representation where you just have zero
+ 
+
+ align:start position:0%
+representation where you just have zero
+here as a number and if it's just a
+
+ align:start position:0%
+here as a number and if it's just a
+ 
+
+ align:start position:0%
+here as a number and if it's just a
+number then it represents an interval of
+
+ align:start position:0%
+number then it represents an interval of
+ 
+
+ align:start position:0%
+number then it represents an interval of
+length one but let's just be uniform
+
+ align:start position:0%
+length one but let's just be uniform
+ 
+
+ align:start position:0%
+length one but let's just be uniform
+about this you
+
+ align:start position:0%
+about this you
+ 
+
+ align:start position:0%
+about this you
+usually when you have special cases and
+
+ align:start position:0%
+usually when you have special cases and
+ 
+
+ align:start position:0%
+usually when you have special cases and
+if you do things heterogeneous Lee then
+
+ align:start position:0%
+if you do things heterogeneous Lee then
+ 
+
+ align:start position:0%
+if you do things heterogeneous Lee then
+you have more code to write right it
+
+ align:start position:0%
+you have more code to write right it
+ 
+
+ align:start position:0%
+you have more code to write right it
+might get more efficient but there's
+
+ align:start position:0%
+might get more efficient but there's
+ 
+
+ align:start position:0%
+might get more efficient but there's
+usually more more code to write so you
+
+ align:start position:0%
+usually more more code to write so you
+ 
+
+ align:start position:0%
+usually more more code to write so you
+do for four here and then you'd go up
+
+ align:start position:0%
+do for four here and then you'd go up
+ 
+
+ align:start position:0%
+do for four here and then you'd go up
+and and then you'd have five comma six
+
+ align:start position:0%
+and and then you'd have five comma six
+ 
+
+ align:start position:0%
+and and then you'd have five comma six
+and then you would do seven comma I'm
+
+ align:start position:0%
+and then you would do seven comma I'm
+ 
+
+ align:start position:0%
+and then you would do seven comma I'm
+sorry five at seven comma nine right so
+
+ align:start position:0%
+sorry five at seven comma nine right so
+ 
+
+ align:start position:0%
+sorry five at seven comma nine right so
+this is the first time you actually have
+
+ align:start position:0%
+this is the first time you actually have
+ 
+
+ align:start position:0%
+this is the first time you actually have
+something interesting in the sense that
+
+ align:start position:0%
+something interesting in the sense that
+ 
+
+ align:start position:0%
+something interesting in the sense that
+the interval has a representation that
+
+ align:start position:0%
+the interval has a representation that
+ 
+
+ align:start position:0%
+the interval has a representation that
+only has two numbers in it whereas you
+
+ align:start position:0%
+only has two numbers in it whereas you
+ 
+
+ align:start position:0%
+only has two numbers in it whereas you
+actually have three people in that
+
+ align:start position:0%
+actually have three people in that
+ 
+
+ align:start position:0%
+actually have three people in that
+interval right and obviously this could
+
+ align:start position:0%
+interval right and obviously this could
+ 
+
+ align:start position:0%
+interval right and obviously this could
+be arbitrarily large in the context of
+
+ align:start position:0%
+be arbitrarily large in the context of
+ 
+
+ align:start position:0%
+be arbitrarily large in the context of
+people getting into a baseball game and
+
+ align:start position:0%
+people getting into a baseball game and
+ 
+
+ align:start position:0%
+people getting into a baseball game and
+so seven through nine and then finally
+
+ align:start position:0%
+so seven through nine and then finally
+ 
+
+ align:start position:0%
+so seven through nine and then finally
+here ten through ten right and so now
+
+ align:start position:0%
+here ten through ten right and so now
+ 
+
+ align:start position:0%
+here ten through ten right and so now
+you go ahead and you count and you
+
+ align:start position:0%
+you go ahead and you count and you
+ 
+
+ align:start position:0%
+you go ahead and you count and you
+realize that there's four intervals here
+
+ align:start position:0%
+realize that there's four intervals here
+ 
+
+ align:start position:0%
+realize that there's four intervals here
+and three intervals here and then you
+
+ align:start position:0%
+and three intervals here and then you
+ 
+
+ align:start position:0%
+and three intervals here and then you
+say I'm gonna go ahead and go with with
+
+ align:start position:0%
+say I'm gonna go ahead and go with with
+ 
+
+ align:start position:0%
+say I'm gonna go ahead and go with with
+the backwards and asking the the people
+
+ align:start position:0%
+the backwards and asking the the people
+ 
+
+ align:start position:0%
+the backwards and asking the the people
+who are well according to you backwards
+
+ align:start position:0%
+who are well according to you backwards
+ 
+
+ align:start position:0%
+who are well according to you backwards
+to flip their caps so we're all good all
+
+ align:start position:0%
+to flip their caps so we're all good all
+ 
+
+ align:start position:0%
+to flip their caps so we're all good all
+right so so I'm gonna show you code that
+
+ align:start position:0%
+right so so I'm gonna show you code that
+ 
+
+ align:start position:0%
+right so so I'm gonna show you code that
+that implements exactly this algorithm
+
+ align:start position:0%
+that implements exactly this algorithm
+ 
+
+ align:start position:0%
+that implements exactly this algorithm
+and while you see the code I want you to
+
+ align:start position:0%
+and while you see the code I want you to
+ 
+
+ align:start position:0%
+and while you see the code I want you to
+think about this harder question on this
+
+ align:start position:0%
+think about this harder question on this
+ 
+
+ align:start position:0%
+think about this harder question on this
+code is going to do exactly what we
+
+ align:start position:0%
+code is going to do exactly what we
+ 
+
+ align:start position:0%
+code is going to do exactly what we
+described it's going to go compute all
+
+ align:start position:0%
+described it's going to go compute all
+ 
+
+ align:start position:0%
+described it's going to go compute all
+of these things and it good is going to
+
+ align:start position:0%
+of these things and it good is going to
+ 
+
+ align:start position:0%
+of these things and it good is going to
+make a pass through the entire as you
+
+ align:start position:0%
+make a pass through the entire as you
+ 
+
+ align:start position:0%
+make a pass through the entire as you
+can imagine it's going to make a pass
+
+ align:start position:0%
+can imagine it's going to make a pass
+ 
+
+ align:start position:0%
+can imagine it's going to make a pass
+through this entire Python list or the
+
+ align:start position:0%
+through this entire Python list or the
+ 
+
+ align:start position:0%
+through this entire Python list or the
+set of this group of people there's a
+
+ align:start position:0%
+set of this group of people there's a
+ 
+
+ align:start position:0%
+set of this group of people there's a
+queue of people and it's going to do
+
+ align:start position:0%
+queue of people and it's going to do
+ 
+
+ align:start position:0%
+queue of people and it's going to do
+this computation then it's going to say
+
+ align:start position:0%
+this computation then it's going to say
+ 
+
+ align:start position:0%
+this computation then it's going to say
+4 is greater than 3 and and then it's
+
+ align:start position:0%
+4 is greater than 3 and and then it's
+ 
+
+ align:start position:0%
+4 is greater than 3 and and then it's
+going to go through and start calling
+
+ align:start position:0%
+going to go through and start calling
+ 
+
+ align:start position:0%
+going to go through and start calling
+out commands for each of the backward
+
+ align:start position:0%
+out commands for each of the backward
+ 
+
+ align:start position:0%
+out commands for each of the backward
+intervals so in some sense it's going to
+
+ align:start position:0%
+intervals so in some sense it's going to
+ 
+
+ align:start position:0%
+intervals so in some sense it's going to
+make two passes over the the list all
+
+ align:start position:0%
+make two passes over the the list all
+ 
+
+ align:start position:0%
+make two passes over the the list all
+right so the first pass is to get all of
+
+ align:start position:0%
+right so the first pass is to get all of
+ 
+
+ align:start position:0%
+right so the first pass is to get all of
+the intervals together then there's a
+
+ align:start position:0%
+the intervals together then there's a
+ 
+
+ align:start position:0%
+the intervals together then there's a
+check and then the second pass is to
+
+ align:start position:0%
+check and then the second pass is to
+ 
+
+ align:start position:0%
+check and then the second pass is to
+take those those back those backward
+
+ align:start position:0%
+take those those back those backward
+ 
+
+ align:start position:0%
+take those those back those backward
+intervals in this case and call out
+
+ align:start position:0%
+intervals in this case and call out
+ 
+
+ align:start position:0%
+intervals in this case and call out
+those commands all right so that's what
+
+ align:start position:0%
+those commands all right so that's what
+ 
+
+ align:start position:0%
+those commands all right so that's what
+I mean by two passes
+
+ align:start position:0%
+I mean by two passes
+ 
+
+ align:start position:0%
+I mean by two passes
+yeah brilliant brilliant
+
+ align:start position:0%
+yeah brilliant brilliant
+ 
+
+ align:start position:0%
+yeah brilliant brilliant
+you okay so so I was going to say if you
+
+ align:start position:0%
+you okay so so I was going to say if you
+ 
+
+ align:start position:0%
+you okay so so I was going to say if you
+didn't understand what ganado said
+
+ align:start position:0%
+didn't understand what ganado said
+ 
+
+ align:start position:0%
+didn't understand what ganado said
+wonderful because then you can you can
+
+ align:start position:0%
+wonderful because then you can you can
+ 
+
+ align:start position:0%
+wonderful because then you can you can
+you can you know think about the
+
+ align:start position:0%
+you can you know think about the
+ 
+
+ align:start position:0%
+you can you know think about the
+question I'm going to ask and ignore
+
+ align:start position:0%
+question I'm going to ask and ignore
+ 
+
+ align:start position:0%
+question I'm going to ask and ignore
+what he said and and and then we'll
+
+ align:start position:0%
+what he said and and and then we'll
+ 
+
+ align:start position:0%
+what he said and and and then we'll
+we'll get to the I guess the the more
+
+ align:start position:0%
+we'll get to the I guess the the more
+ 
+
+ align:start position:0%
+we'll get to the I guess the the more
+efficient code but what I was going to
+
+ align:start position:0%
+efficient code but what I was going to
+ 
+
+ align:start position:0%
+efficient code but what I was going to
+ask was is there a way that I'm looking
+
+ align:start position:0%
+ask was is there a way that I'm looking
+ 
+
+ align:start position:0%
+ask was is there a way that I'm looking
+at this and I'm just going and I'm gonna
+
+ align:start position:0%
+at this and I'm just going and I'm gonna
+ 
+
+ align:start position:0%
+at this and I'm just going and I'm gonna
+just start calling out by the moment I
+
+ align:start position:0%
+just start calling out by the moment I
+ 
+
+ align:start position:0%
+just start calling out by the moment I
+see that there's an interval okay the
+
+ align:start position:0%
+see that there's an interval okay the
+ 
+
+ align:start position:0%
+see that there's an interval okay the
+moment I see there's this like this is
+
+ align:start position:0%
+moment I see there's this like this is
+ 
+
+ align:start position:0%
+moment I see there's this like this is
+an interval and and I'm gonna make a
+
+ align:start position:0%
+an interval and and I'm gonna make a
+ 
+
+ align:start position:0%
+an interval and and I'm gonna make a
+call with respect to whether I'm going
+
+ align:start position:0%
+call with respect to whether I'm going
+ 
+
+ align:start position:0%
+call with respect to whether I'm going
+to call all the command or not all right
+
+ align:start position:0%
+to call all the command or not all right
+ 
+
+ align:start position:0%
+to call all the command or not all right
+and I'm going to do this in one pass
+
+ align:start position:0%
+and I'm going to do this in one pass
+ 
+
+ align:start position:0%
+and I'm going to do this in one pass
+through this through this array okay I
+
+ align:start position:0%
+through this through this array okay I
+ 
+
+ align:start position:0%
+through this through this array okay I
+want to do this in one pass through the
+
+ align:start position:0%
+want to do this in one pass through the
+ 
+
+ align:start position:0%
+want to do this in one pass through the
+array I want to look at this and I say I
+
+ align:start position:0%
+array I want to look at this and I say I
+ 
+
+ align:start position:0%
+array I want to look at this and I say I
+see the interval 0 0 all right is is
+
+ align:start position:0%
+see the interval 0 0 all right is is
+ 
+
+ align:start position:0%
+see the interval 0 0 all right is is
+that going to be something that I need
+
+ align:start position:0%
+that going to be something that I need
+ 
+
+ align:start position:0%
+that going to be something that I need
+to worry about in terms of that person
+
+ align:start position:0%
+to worry about in terms of that person
+ 
+
+ align:start position:0%
+to worry about in terms of that person
+having to flip the his cap and then I
+
+ align:start position:0%
+having to flip the his cap and then I
+ 
+
+ align:start position:0%
+having to flip the his cap and then I
+see BB and I say oh the interval is 1
+
+ align:start position:0%
+see BB and I say oh the interval is 1
+ 
+
+ align:start position:0%
+see BB and I say oh the interval is 1
+comma 2 is that is that something I'm
+
+ align:start position:0%
+comma 2 is that is that something I'm
+ 
+
+ align:start position:0%
+comma 2 is that is that something I'm
+gonna have to deal with in terms of a
+
+ align:start position:0%
+gonna have to deal with in terms of a
+ 
+
+ align:start position:0%
+gonna have to deal with in terms of a
+command right and so someone else other
+
+ align:start position:0%
+command right and so someone else other
+ 
+
+ align:start position:0%
+command right and so someone else other
+than you not wrote I tell me if there's
+
+ align:start position:0%
+than you not wrote I tell me if there's
+ 
+
+ align:start position:0%
+than you not wrote I tell me if there's
+a there's a one pass algorithm and
+
+ align:start position:0%
+a there's a one pass algorithm and
+ 
+
+ align:start position:0%
+a there's a one pass algorithm and
+explain to me of why you can do this in
+
+ align:start position:0%
+explain to me of why you can do this in
+ 
+
+ align:start position:0%
+explain to me of why you can do this in
+one pass through the array and just in
+
+ align:start position:0%
+one pass through the array and just in
+ 
+
+ align:start position:0%
+one pass through the array and just in
+terms of code I'll preview this the
+
+ align:start position:0%
+terms of code I'll preview this the
+ 
+
+ align:start position:0%
+terms of code I'll preview this the
+first algorithm it needs according to my
+
+ align:start position:0%
+first algorithm it needs according to my
+ 
+
+ align:start position:0%
+first algorithm it needs according to my
+coding which is in grade 26 lines of
+
+ align:start position:0%
+coding which is in grade 26 lines of
+ 
+
+ align:start position:0%
+coding which is in grade 26 lines of
+code the second one needs eight lines of
+
+ align:start position:0%
+code the second one needs eight lines of
+ 
+
+ align:start position:0%
+code the second one needs eight lines of
+code alright so yeah go ahead
+
+ align:start position:0%
+code alright so yeah go ahead
+ 
+
+ align:start position:0%
+code alright so yeah go ahead
+how do you see the president rule there
+
+ align:start position:0%
+how do you see the president rule there
+ 
+
+ align:start position:0%
+how do you see the president rule there
+rule you know the second interval at the
+
+ align:start position:0%
+rule you know the second interval at the
+ 
+
+ align:start position:0%
+rule you know the second interval at the
+very least is gonna have the same number
+
+ align:start position:0%
+very least is gonna have the same number
+ 
+
+ align:start position:0%
+very least is gonna have the same number
+of like commands as the first one so you
+
+ align:start position:0%
+of like commands as the first one so you
+ 
+
+ align:start position:0%
+of like commands as the first one so you
+might as well always go at the second
+
+ align:start position:0%
+might as well always go at the second
+ 
+
+ align:start position:0%
+might as well always go at the second
+one so once you've identified what type
+
+ align:start position:0%
+one so once you've identified what type
+ 
+
+ align:start position:0%
+one so once you've identified what type
+the first interval is you iterate
+
+ align:start position:0%
+the first interval is you iterate
+ 
+
+ align:start position:0%
+the first interval is you iterate
+through the list see like and once you
+
+ align:start position:0%
+through the list see like and once you
+ 
+
+ align:start position:0%
+through the list see like and once you
+identify the person second intervals
+
+ align:start position:0%
+identify the person second intervals
+ 
+
+ align:start position:0%
+identify the person second intervals
+iterate through every type of the second
+
+ align:start position:0%
+iterate through every type of the second
+ 
+
+ align:start position:0%
+iterate through every type of the second
+interval and do a command for that Kevin
+
+ align:start position:0%
+interval and do a command for that Kevin
+ 
+
+ align:start position:0%
+interval and do a command for that Kevin
+so so you had it right and and kevin has
+
+ align:start position:0%
+so so you had it right and and kevin has
+ 
+
+ align:start position:0%
+so so you had it right and and kevin has
+it right as well so the observation here
+
+ align:start position:0%
+it right as well so the observation here
+ 
+
+ align:start position:0%
+it right as well so the observation here
+is actually the if I it was said a
+
+ align:start position:0%
+is actually the if I it was said a
+ 
+
+ align:start position:0%
+is actually the if I it was said a
+little bit differently by Kevin but I'm
+
+ align:start position:0%
+little bit differently by Kevin but I'm
+ 
+
+ align:start position:0%
+little bit differently by Kevin but I'm
+gonna say it a little bit differently
+
+ align:start position:0%
+gonna say it a little bit differently
+ 
+
+ align:start position:0%
+gonna say it a little bit differently
+and the observation is simply that that
+
+ align:start position:0%
+and the observation is simply that that
+ 
+
+ align:start position:0%
+and the observation is simply that that
+if you look at the very first
+
+ align:start position:0%
+if you look at the very first
+ 
+
+ align:start position:0%
+if you look at the very first
+orientation right the the very first
+
+ align:start position:0%
+orientation right the the very first
+ 
+
+ align:start position:0%
+orientation right the the very first
+orientation is something which at best
+
+ align:start position:0%
+orientation is something which at best
+ 
+
+ align:start position:0%
+orientation is something which at best
+is is going to do hat is going to be a
+
+ align:start position:0%
+is is going to do hat is going to be a
+ 
+
+ align:start position:0%
+is is going to do hat is going to be a
+tie right so if you if you had it ending
+
+ align:start position:0%
+tie right so if you if you had it ending
+ 
+
+ align:start position:0%
+tie right so if you if you had it ending
+at with 10 people 0 through 9 right then
+
+ align:start position:0%
+at with 10 people 0 through 9 right then
+ 
+
+ align:start position:0%
+at with 10 people 0 through 9 right then
+the number of forward intervals is the
+
+ align:start position:0%
+the number of forward intervals is the
+ 
+
+ align:start position:0%
+the number of forward intervals is the
+same as the number of backwards
+
+ align:start position:0%
+same as the number of backwards
+ 
+
+ align:start position:0%
+same as the number of backwards
+intervals okay and if you went here
+
+ align:start position:0%
+intervals okay and if you went here
+ 
+
+ align:start position:0%
+intervals okay and if you went here
+obviously the number of forward
+
+ align:start position:0%
+obviously the number of forward
+ 
+
+ align:start position:0%
+obviously the number of forward
+intervals is greater than the number of
+
+ align:start position:0%
+intervals is greater than the number of
+ 
+
+ align:start position:0%
+intervals is greater than the number of
+backwards intervals so you really only
+
+ align:start position:0%
+backwards intervals so you really only
+ 
+
+ align:start position:0%
+backwards intervals so you really only
+have to look at the first person in line
+
+ align:start position:0%
+have to look at the first person in line
+ 
+
+ align:start position:0%
+have to look at the first person in line
+to determine not to determine the
+
+ align:start position:0%
+to determine not to determine the
+ 
+
+ align:start position:0%
+to determine not to determine the
+intervals because you see the first
+
+ align:start position:0%
+intervals because you see the first
+ 
+
+ align:start position:0%
+intervals because you see the first
+person in line you have no idea what the
+
+ align:start position:0%
+person in line you have no idea what the
+ 
+
+ align:start position:0%
+person in line you have no idea what the
+intervals are that are coming after
+
+ align:start position:0%
+intervals are that are coming after
+ 
+
+ align:start position:0%
+intervals are that are coming after
+right I mean you can't you have to
+
+ align:start position:0%
+right I mean you can't you have to
+ 
+
+ align:start position:0%
+right I mean you can't you have to
+generate those intervals so you have to
+
+ align:start position:0%
+generate those intervals so you have to
+ 
+
+ align:start position:0%
+generate those intervals so you have to
+make your pass through the array but the
+
+ align:start position:0%
+make your pass through the array but the
+ 
+
+ align:start position:0%
+make your pass through the array but the
+first person in line gives it away in
+
+ align:start position:0%
+first person in line gives it away in
+ 
+
+ align:start position:0%
+first person in line gives it away in
+terms of what the final result is going
+
+ align:start position:0%
+terms of what the final result is going
+ 
+
+ align:start position:0%
+terms of what the final result is going
+to be with respect to your decision as
+
+ align:start position:0%
+to be with respect to your decision as
+ 
+
+ align:start position:0%
+to be with respect to your decision as
+to what set of commands you what set of
+
+ align:start position:0%
+to what set of commands you what set of
+ 
+
+ align:start position:0%
+to what set of commands you what set of
+commands you're going to call up right
+
+ align:start position:0%
+commands you're going to call up right
+ 
+
+ align:start position:0%
+commands you're going to call up right
+and so because this is an F you you you
+
+ align:start position:0%
+and so because this is an F you you you
+ 
+
+ align:start position:0%
+and so because this is an F you you you
+you basically say I'm gonna go and I'm
+
+ align:start position:0%
+you basically say I'm gonna go and I'm
+ 
+
+ align:start position:0%
+you basically say I'm gonna go and I'm
+going to make the people with the with
+
+ align:start position:0%
+going to make the people with the with
+ 
+
+ align:start position:0%
+going to make the people with the with
+the bees flip their flip their caps
+
+ align:start position:0%
+the bees flip their flip their caps
+ 
+
+ align:start position:0%
+the bees flip their flip their caps
+alright and that's that's a small
+
+ align:start position:0%
+alright and that's that's a small
+ 
+
+ align:start position:0%
+alright and that's that's a small
+observation in in terms of I it's inside
+
+ align:start position:0%
+observation in in terms of I it's inside
+ 
+
+ align:start position:0%
+observation in in terms of I it's inside
+but obviously
+
+ align:start position:0%
+but obviously
+ 
+
+ align:start position:0%
+but obviously
+it's potent in the sense that it's going
+
+ align:start position:0%
+it's potent in the sense that it's going
+ 
+
+ align:start position:0%
+it's potent in the sense that it's going
+to give you a one pass algorithm versus
+
+ align:start position:0%
+to give you a one pass algorithm versus
+ 
+
+ align:start position:0%
+to give you a one pass algorithm versus
+a two pass algorithm and as I mentioned
+
+ align:start position:0%
+a two pass algorithm and as I mentioned
+ 
+
+ align:start position:0%
+a two pass algorithm and as I mentioned
+it's going to give you a substantial
+
+ align:start position:0%
+it's going to give you a substantial
+ 
+
+ align:start position:0%
+it's going to give you a substantial
+reduction in the amount of code that you
+
+ align:start position:0%
+reduction in the amount of code that you
+ 
+
+ align:start position:0%
+reduction in the amount of code that you
+write all right
+
+ align:start position:0%
+write all right
+ 
+
+ align:start position:0%
+write all right
+um so I'm gonna show you a bunch of code
+
+ align:start position:0%
+um so I'm gonna show you a bunch of code
+ 
+
+ align:start position:0%
+um so I'm gonna show you a bunch of code
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+right so this is usually hard this is
+
+ align:start position:0%
+right so this is usually hard this is
+ 
+
+ align:start position:0%
+right so this is usually hard this is
+going to go by the way this this entire
+
+ align:start position:0%
+going to go by the way this this entire
+ 
+
+ align:start position:0%
+going to go by the way this this entire
+class and this is kind of my way of
+
+ align:start position:0%
+class and this is kind of my way of
+ 
+
+ align:start position:0%
+class and this is kind of my way of
+teaching at least this type of material
+
+ align:start position:0%
+teaching at least this type of material
+ 
+
+ align:start position:0%
+teaching at least this type of material
+that's algorithmic and has data
+
+ align:start position:0%
+that's algorithmic and has data
+ 
+
+ align:start position:0%
+that's algorithmic and has data
+structures and so on Internet I like
+
+ align:start position:0%
+structures and so on Internet I like
+ 
+
+ align:start position:0%
+structures and so on Internet I like
+explaining to people what they're going
+
+ align:start position:0%
+explaining to people what they're going
+ 
+
+ align:start position:0%
+explaining to people what they're going
+to see in the code without having to
+
+ align:start position:0%
+to see in the code without having to
+ 
+
+ align:start position:0%
+to see in the code without having to
+deal with Python syntax and you know
+
+ align:start position:0%
+deal with Python syntax and you know
+ 
+
+ align:start position:0%
+deal with Python syntax and you know
+worrying about whether it's while loops
+
+ align:start position:0%
+worrying about whether it's while loops
+ 
+
+ align:start position:0%
+worrying about whether it's while loops
+or for loops and things like that and
+
+ align:start position:0%
+or for loops and things like that and
+ 
+
+ align:start position:0%
+or for loops and things like that and
+tuples or arrays and things like that
+
+ align:start position:0%
+tuples or arrays and things like that
+ 
+
+ align:start position:0%
+tuples or arrays and things like that
+right so let's let's get into that good
+
+ align:start position:0%
+right so let's let's get into that good
+ 
+
+ align:start position:0%
+right so let's let's get into that good
+all right so the naive algorithm first
+
+ align:start position:0%
+all right so the naive algorithm first
+ 
+
+ align:start position:0%
+all right so the naive algorithm first
+okay so what you see here is an input so
+
+ align:start position:0%
+okay so what you see here is an input so
+ 
+
+ align:start position:0%
+okay so what you see here is an input so
+caps is is simply an input Python list
+
+ align:start position:0%
+caps is is simply an input Python list
+ 
+
+ align:start position:0%
+caps is is simply an input Python list
+that has as you can see from our
+
+ align:start position:0%
+that has as you can see from our
+ 
+
+ align:start position:0%
+that has as you can see from our
+examples the FS and the B's right and so
+
+ align:start position:0%
+examples the FS and the B's right and so
+ 
+
+ align:start position:0%
+examples the FS and the B's right and so
+f is for words and B is backwards and
+
+ align:start position:0%
+f is for words and B is backwards and
+ 
+
+ align:start position:0%
+f is for words and B is backwards and
+there's a couple of different Python
+
+ align:start position:0%
+there's a couple of different Python
+ 
+
+ align:start position:0%
+there's a couple of different Python
+lists so you can run them with different
+
+ align:start position:0%
+lists so you can run them with different
+ 
+
+ align:start position:0%
+lists so you can run them with different
+things and you know all of this
+
+ align:start position:0%
+things and you know all of this
+ 
+
+ align:start position:0%
+things and you know all of this
+hopefully is not at all surprising to
+
+ align:start position:0%
+hopefully is not at all surprising to
+ 
+
+ align:start position:0%
+hopefully is not at all surprising to
+you because we went through all of this
+
+ align:start position:0%
+you because we went through all of this
+ 
+
+ align:start position:0%
+you because we went through all of this
+in terms of the pseudocode right so the
+
+ align:start position:0%
+in terms of the pseudocode right so the
+ 
+
+ align:start position:0%
+in terms of the pseudocode right so the
+first initialization and I can just
+
+ align:start position:0%
+first initialization and I can just
+ 
+
+ align:start position:0%
+first initialization and I can just
+highlight that to make it easy so that's
+
+ align:start position:0%
+highlight that to make it easy so that's
+ 
+
+ align:start position:0%
+highlight that to make it easy so that's
+initialization and this part here the
+
+ align:start position:0%
+initialization and this part here the
+ 
+
+ align:start position:0%
+initialization and this part here the
+comment sort of gives it away is you're
+
+ align:start position:0%
+comment sort of gives it away is you're
+ 
+
+ align:start position:0%
+comment sort of gives it away is you're
+you're making a pass through the array
+
+ align:start position:0%
+you're making a pass through the array
+ 
+
+ align:start position:0%
+you're making a pass through the array
+computing the computing the intervals
+
+ align:start position:0%
+computing the computing the intervals
+ 
+
+ align:start position:0%
+computing the computing the intervals
+right and so so how do you actually get
+
+ align:start position:0%
+right and so so how do you actually get
+ 
+
+ align:start position:0%
+right and so so how do you actually get
+the intervals and there's one line of
+
+ align:start position:0%
+the intervals and there's one line of
+ 
+
+ align:start position:0%
+the intervals and there's one line of
+code that that does that I know by the
+
+ align:start position:0%
+code that that does that I know by the
+ 
+
+ align:start position:0%
+code that that does that I know by the
+way there's any questions about Python
+
+ align:start position:0%
+way there's any questions about Python
+ 
+
+ align:start position:0%
+way there's any questions about Python
+syntax you know just don't feel shy just
+
+ align:start position:0%
+syntax you know just don't feel shy just
+ 
+
+ align:start position:0%
+syntax you know just don't feel shy just
+just tell me ask me ask me a question
+
+ align:start position:0%
+just tell me ask me ask me a question
+ 
+
+ align:start position:0%
+just tell me ask me ask me a question
+and I'm happy to explain it I mean if
+
+ align:start position:0%
+and I'm happy to explain it I mean if
+ 
+
+ align:start position:0%
+and I'm happy to explain it I mean if
+I'm I don't want explain things that you
+
+ align:start position:0%
+I'm I don't want explain things that you
+ 
+
+ align:start position:0%
+I'm I don't want explain things that you
+all know obviously but if anyone of you
+
+ align:start position:0%
+all know obviously but if anyone of you
+ 
+
+ align:start position:0%
+all know obviously but if anyone of you
+doesn't know any particular thing please
+
+ align:start position:0%
+doesn't know any particular thing please
+ 
+
+ align:start position:0%
+doesn't know any particular thing please
+don't feel shy syntax is something that
+
+ align:start position:0%
+don't feel shy syntax is something that
+ 
+
+ align:start position:0%
+don't feel shy syntax is something that
+sometimes you even forget I mean I tend
+
+ align:start position:0%
+sometimes you even forget I mean I tend
+ 
+
+ align:start position:0%
+sometimes you even forget I mean I tend
+to forget things um so this thing here
+
+ align:start position:0%
+to forget things um so this thing here
+ 
+
+ align:start position:0%
+to forget things um so this thing here
+is is essentially something that that
+
+ align:start position:0%
+is is essentially something that that
+ 
+
+ align:start position:0%
+is is essentially something that that
+decides on when the what the intervals
+
+ align:start position:0%
+decides on when the what the intervals
+ 
+
+ align:start position:0%
+decides on when the what the intervals
+are and in the insight here is simple
+
+ align:start position:0%
+are and in the insight here is simple
+ 
+
+ align:start position:0%
+are and in the insight here is simple
+and you know that this interval ended
+
+ align:start position:0%
+and you know that this interval ended
+ 
+
+ align:start position:0%
+and you know that this interval ended
+when you see something here that is
+
+ align:start position:0%
+when you see something here that is
+ 
+
+ align:start position:0%
+when you see something here that is
+different from what the previous one is
+
+ align:start position:0%
+different from what the previous one is
+ 
+
+ align:start position:0%
+different from what the previous one is
+right so that's when you know so you
+
+ align:start position:0%
+right so that's when you know so you
+ 
+
+ align:start position:0%
+right so that's when you know so you
+generate the interval right you generate
+
+ align:start position:0%
+generate the interval right you generate
+ 
+
+ align:start position:0%
+generate the interval right you generate
+the interval when you you go and find
+
+ align:start position:0%
+the interval when you you go and find
+ 
+
+ align:start position:0%
+the interval when you you go and find
+something that is different from the
+
+ align:start position:0%
+something that is different from the
+ 
+
+ align:start position:0%
+something that is different from the
+current location that you're pointing to
+
+ align:start position:0%
+current location that you're pointing to
+ 
+
+ align:start position:0%
+current location that you're pointing to
+right so that's really what's going on
+
+ align:start position:0%
+right so that's really what's going on
+ 
+
+ align:start position:0%
+right so that's really what's going on
+out here you're in in this line you say
+
+ align:start position:0%
+out here you're in in this line you say
+ 
+
+ align:start position:0%
+out here you're in in this line you say
+you're setting a start here start is
+
+ align:start position:0%
+you're setting a start here start is
+ 
+
+ align:start position:0%
+you're setting a start here start is
+your counter and remember start is
+
+ align:start position:0%
+your counter and remember start is
+ 
+
+ align:start position:0%
+your counter and remember start is
+getting set again here
+
+ align:start position:0%
+getting set again here
+ 
+
+ align:start position:0%
+getting set again here
+initially it was set to zero and if you
+
+ align:start position:0%
+initially it was set to zero and if you
+ 
+
+ align:start position:0%
+initially it was set to zero and if you
+ever get to the point where you're
+
+ align:start position:0%
+ever get to the point where you're
+ 
+
+ align:start position:0%
+ever get to the point where you're
+looking at I it's the next thing you're
+
+ align:start position:0%
+looking at I it's the next thing you're
+ 
+
+ align:start position:0%
+looking at I it's the next thing you're
+looking at and if cap start which is the
+
+ align:start position:0%
+looking at and if cap start which is the
+ 
+
+ align:start position:0%
+looking at and if cap start which is the
+start of the interval is different from
+
+ align:start position:0%
+start of the interval is different from
+ 
+
+ align:start position:0%
+start of the interval is different from
+I it meant that the interval that began
+
+ align:start position:0%
+I it meant that the interval that began
+ 
+
+ align:start position:0%
+I it meant that the interval that began
+with start ended okay
+
+ align:start position:0%
+with start ended okay
+ 
+
+ align:start position:0%
+with start ended okay
+and so you essentially say well that
+
+ align:start position:0%
+and so you essentially say well that
+ 
+
+ align:start position:0%
+and so you essentially say well that
+that needs to end at I minus one because
+
+ align:start position:0%
+that needs to end at I minus one because
+ 
+
+ align:start position:0%
+that needs to end at I minus one because
+obviously cap start is different from
+
+ align:start position:0%
+obviously cap start is different from
+ 
+
+ align:start position:0%
+obviously cap start is different from
+cap size so this is the end of the
+
+ align:start position:0%
+cap size so this is the end of the
+ 
+
+ align:start position:0%
+cap size so this is the end of the
+interval right here all right and this
+
+ align:start position:0%
+interval right here all right and this
+ 
+
+ align:start position:0%
+interval right here all right and this
+particular thing is our interval is is
+
+ align:start position:0%
+particular thing is our interval is is
+ 
+
+ align:start position:0%
+particular thing is our interval is is
+is something that includes both these
+
+ align:start position:0%
+is something that includes both these
+ 
+
+ align:start position:0%
+is something that includes both these
+two numbers so it's not exactly that but
+
+ align:start position:0%
+two numbers so it's not exactly that but
+ 
+
+ align:start position:0%
+two numbers so it's not exactly that but
+it also includes where it might go
+
+ align:start position:0%
+it also includes where it might go
+ 
+
+ align:start position:0%
+it also includes where it might go
+it also includes whether this is an F or
+
+ align:start position:0%
+it also includes whether this is an F or
+ 
+
+ align:start position:0%
+it also includes whether this is an F or
+not so each of these things has I'm not
+
+ align:start position:0%
+not so each of these things has I'm not
+ 
+
+ align:start position:0%
+not so each of these things has I'm not
+gonna write it out for all of those
+
+ align:start position:0%
+gonna write it out for all of those
+ 
+
+ align:start position:0%
+gonna write it out for all of those
+things but I has the the orientation
+
+ align:start position:0%
+things but I has the the orientation
+ 
+
+ align:start position:0%
+things but I has the the orientation
+inside of it so that's what you have out
+
+ align:start position:0%
+inside of it so that's what you have out
+ 
+
+ align:start position:0%
+inside of it so that's what you have out
+here that's why we have three of these
+
+ align:start position:0%
+here that's why we have three of these
+ 
+
+ align:start position:0%
+here that's why we have three of these
+in this tuple right this is a tuple
+
+ align:start position:0%
+in this tuple right this is a tuple
+ 
+
+ align:start position:0%
+in this tuple right this is a tuple
+because it's got round brackets around
+
+ align:start position:0%
+because it's got round brackets around
+ 
+
+ align:start position:0%
+because it's got round brackets around
+it um I could have made it I could have
+
+ align:start position:0%
+it um I could have made it I could have
+ 
+
+ align:start position:0%
+it um I could have made it I could have
+made it a list if I wanted and so that's
+
+ align:start position:0%
+made it a list if I wanted and so that's
+ 
+
+ align:start position:0%
+made it a list if I wanted and so that's
+essentially what we have here and now
+
+ align:start position:0%
+essentially what we have here and now
+ 
+
+ align:start position:0%
+essentially what we have here and now
+here's what happens in this particular
+
+ align:start position:0%
+here's what happens in this particular
+ 
+
+ align:start position:0%
+here's what happens in this particular
+piece of code when you get to the end
+
+ align:start position:0%
+piece of code when you get to the end
+ 
+
+ align:start position:0%
+piece of code when you get to the end
+and you fall off the end so if you if
+
+ align:start position:0%
+and you fall off the end so if you if
+ 
+
+ align:start position:0%
+and you fall off the end so if you if
+you just end then this code essentially
+
+ align:start position:0%
+you just end then this code essentially
+ 
+
+ align:start position:0%
+you just end then this code essentially
+it skips over and doesn't it doesn't
+
+ align:start position:0%
+it skips over and doesn't it doesn't
+ 
+
+ align:start position:0%
+it skips over and doesn't it doesn't
+actually put in the last interval right
+
+ align:start position:0%
+actually put in the last interval right
+ 
+
+ align:start position:0%
+actually put in the last interval right
+because you don't see something when you
+
+ align:start position:0%
+because you don't see something when you
+ 
+
+ align:start position:0%
+because you don't see something when you
+come up here and you're off the end of
+
+ align:start position:0%
+come up here and you're off the end of
+ 
+
+ align:start position:0%
+come up here and you're off the end of
+the array you fall off the edge of the
+
+ align:start position:0%
+the array you fall off the edge of the
+ 
+
+ align:start position:0%
+the array you fall off the edge of the
+array you don't see a B that is
+
+ align:start position:0%
+array you don't see a B that is
+ 
+
+ align:start position:0%
+array you don't see a B that is
+different from F right so so this the if
+
+ align:start position:0%
+different from F right so so this the if
+ 
+
+ align:start position:0%
+different from F right so so this the if
+you just wrote that code so something
+
+ align:start position:0%
+you just wrote that code so something
+ 
+
+ align:start position:0%
+you just wrote that code so something
+that I'd say in many people would could
+
+ align:start position:0%
+that I'd say in many people would could
+ 
+
+ align:start position:0%
+that I'd say in many people would could
+would have a would have a quote bug
+
+ align:start position:0%
+would have a would have a quote bug
+ 
+
+ align:start position:0%
+would have a would have a quote bug
+where they won't add this part of the
+
+ align:start position:0%
+where they won't add this part of the
+ 
+
+ align:start position:0%
+where they won't add this part of the
+code here because I didn't realize this
+
+ align:start position:0%
+code here because I didn't realize this
+ 
+
+ align:start position:0%
+code here because I didn't realize this
+particular point that I made which and
+
+ align:start position:0%
+particular point that I made which and
+ 
+
+ align:start position:0%
+particular point that I made which and
+so that last interval doesn't get added
+
+ align:start position:0%
+so that last interval doesn't get added
+ 
+
+ align:start position:0%
+so that last interval doesn't get added
+in right and so you have a bit more code
+
+ align:start position:0%
+in right and so you have a bit more code
+ 
+
+ align:start position:0%
+in right and so you have a bit more code
+here that decides on the last interval
+
+ align:start position:0%
+here that decides on the last interval
+ 
+
+ align:start position:0%
+here that decides on the last interval
+and and then you count and then you go
+
+ align:start position:0%
+and and then you count and then you go
+ 
+
+ align:start position:0%
+and and then you count and then you go
+ahead and call the commands all right so
+
+ align:start position:0%
+ahead and call the commands all right so
+ 
+
+ align:start position:0%
+ahead and call the commands all right so
+this all looks good yeah very good with
+
+ align:start position:0%
+this all looks good yeah very good with
+ 
+
+ align:start position:0%
+this all looks good yeah very good with
+this is there a way that I could somehow
+
+ align:start position:0%
+this is there a way that I could somehow
+ 
+
+ align:start position:0%
+this is there a way that I could somehow
+eliminate these four lines of code which
+
+ align:start position:0%
+eliminate these four lines of code which
+ 
+
+ align:start position:0%
+eliminate these four lines of code which
+is a little bit annoying and and just do
+
+ align:start position:0%
+is a little bit annoying and and just do
+ 
+
+ align:start position:0%
+is a little bit annoying and and just do
+things in their rate how could i with a
+
+ align:start position:0%
+things in their rate how could i with a
+ 
+
+ align:start position:0%
+things in their rate how could i with a
+little trick I could eliminate those
+
+ align:start position:0%
+little trick I could eliminate those
+ 
+
+ align:start position:0%
+little trick I could eliminate those
+four lines of code I mean I might III
+
+ align:start position:0%
+four lines of code I mean I might III
+ 
+
+ align:start position:0%
+four lines of code I mean I might III
+need a little bit more you know quote
+
+ align:start position:0%
+need a little bit more you know quote
+ 
+
+ align:start position:0%
+need a little bit more you know quote
+pre-processing but how I eliminate that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+someone else I'll get you yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can have an extra check wasn't it
+
+ align:start position:0%
+you can have an extra check wasn't it
+ 
+
+ align:start position:0%
+you can have an extra check wasn't it
+Tanisha
+
+ align:start position:0%
+Tanisha
+ 
+
+ align:start position:0%
+Tanisha
+so Kanishka says that before you reach
+
+ align:start position:0%
+so Kanishka says that before you reach
+ 
+
+ align:start position:0%
+so Kanishka says that before you reach
+the end of the array you are or when you
+
+ align:start position:0%
+the end of the array you are or when you
+ 
+
+ align:start position:0%
+the end of the array you are or when you
+reach the end of the array you go ahead
+
+ align:start position:0%
+reach the end of the array you go ahead
+ 
+
+ align:start position:0%
+reach the end of the array you go ahead
+and and and and do a check that you've
+
+ align:start position:0%
+and and and and do a check that you've
+ 
+
+ align:start position:0%
+and and and and do a check that you've
+reached the end and generate the
+
+ align:start position:0%
+reached the end and generate the
+ 
+
+ align:start position:0%
+reached the end and generate the
+interval inside of it it just kind of
+
+ align:start position:0%
+interval inside of it it just kind of
+ 
+
+ align:start position:0%
+interval inside of it it just kind of
+like moving this code inside of it right
+
+ align:start position:0%
+like moving this code inside of it right
+ 
+
+ align:start position:0%
+like moving this code inside of it right
+so that's that's reasonable I'm not sure
+
+ align:start position:0%
+so that's that's reasonable I'm not sure
+ 
+
+ align:start position:0%
+so that's that's reasonable I'm not sure
+that's going to be as good as the way
+
+ align:start position:0%
+that's going to be as good as the way
+ 
+
+ align:start position:0%
+that's going to be as good as the way
+I'm that I want and which average which
+
+ align:start position:0%
+I'm that I want and which average which
+ 
+
+ align:start position:0%
+I'm that I want and which average which
+I coded think about pre-processing think
+
+ align:start position:0%
+I coded think about pre-processing think
+ 
+
+ align:start position:0%
+I coded think about pre-processing think
+about taking the array yeah okay all
+
+ align:start position:0%
+about taking the array yeah okay all
+ 
+
+ align:start position:0%
+about taking the array yeah okay all
+right this how many chemins do we have
+
+ align:start position:0%
+right this how many chemins do we have
+ 
+
+ align:start position:0%
+right this how many chemins do we have
+here okay so so so I you could you could
+
+ align:start position:0%
+here okay so so so I you could you could
+ 
+
+ align:start position:0%
+here okay so so so I you could you could
+do this
+
+ align:start position:0%
+do this
+ 
+
+ align:start position:0%
+do this
+right so let me let me show you
+
+ align:start position:0%
+right so let me let me show you
+ 
+
+ align:start position:0%
+right so let me let me show you
+something that's a little bit more so
+
+ align:start position:0%
+something that's a little bit more so
+ 
+
+ align:start position:0%
+something that's a little bit more so
+that was a 26 lines of code and so this
+
+ align:start position:0%
+that was a 26 lines of code and so this
+ 
+
+ align:start position:0%
+that was a 26 lines of code and so this
+says this is the line that's interesting
+
+ align:start position:0%
+says this is the line that's interesting
+ 
+
+ align:start position:0%
+says this is the line that's interesting
+so I had F and B right and so I don't
+
+ align:start position:0%
+so I had F and B right and so I don't
+ 
+
+ align:start position:0%
+so I had F and B right and so I don't
+want to add F for be there but you know
+
+ align:start position:0%
+want to add F for be there but you know
+ 
+
+ align:start position:0%
+want to add F for be there but you know
+what is what is convenient to do as it
+
+ align:start position:0%
+what is what is convenient to do as it
+ 
+
+ align:start position:0%
+what is what is convenient to do as it
+turns out is to just have something that
+
+ align:start position:0%
+turns out is to just have something that
+ 
+
+ align:start position:0%
+turns out is to just have something that
+essentially says there's an ending point
+
+ align:start position:0%
+essentially says there's an ending point
+ 
+
+ align:start position:0%
+essentially says there's an ending point
+so you have an exclusive end to their a
+
+ align:start position:0%
+so you have an exclusive end to their a
+ 
+
+ align:start position:0%
+so you have an exclusive end to their a
+that is actually that not something that
+
+ align:start position:0%
+that is actually that not something that
+ 
+
+ align:start position:0%
+that is actually that not something that
+would crash if you try to access it
+
+ align:start position:0%
+would crash if you try to access it
+ 
+
+ align:start position:0%
+would crash if you try to access it
+right you've added you had n people in
+
+ align:start position:0%
+right you've added you had n people in
+ 
+
+ align:start position:0%
+right you've added you had n people in
+line and now you have effectively in n
+
+ align:start position:0%
+line and now you have effectively in n
+ 
+
+ align:start position:0%
+line and now you have effectively in n
+plus 1 people in line but that n plus 1
+
+ align:start position:0%
+plus 1 people in line but that n plus 1
+ 
+
+ align:start position:0%
+plus 1 people in line but that n plus 1
+person is a dummy right or you know you
+
+ align:start position:0%
+person is a dummy right or you know you
+ 
+
+ align:start position:0%
+person is a dummy right or you know you
+can call them end and and then if you do
+
+ align:start position:0%
+can call them end and and then if you do
+ 
+
+ align:start position:0%
+can call them end and and then if you do
+that then that's it
+
+ align:start position:0%
+that then that's it
+ 
+
+ align:start position:0%
+that then that's it
+the previous code works right yeah you
+
+ align:start position:0%
+the previous code works right yeah you
+ 
+
+ align:start position:0%
+the previous code works right yeah you
+can just remove those four lines and
+
+ align:start position:0%
+can just remove those four lines and
+ 
+
+ align:start position:0%
+can just remove those four lines and
+you'll all just work right because your
+
+ align:start position:0%
+you'll all just work right because your
+ 
+
+ align:start position:0%
+you'll all just work right because your
+F or your B is not equal to end right so
+
+ align:start position:0%
+F or your B is not equal to end right so
+ 
+
+ align:start position:0%
+F or your B is not equal to end right so
+the the whatever you had at the end I'm
+
+ align:start position:0%
+the the whatever you had at the end I'm
+ 
+
+ align:start position:0%
+the the whatever you had at the end I'm
+sorry I'm overloading terms here
+
+ align:start position:0%
+sorry I'm overloading terms here
+ 
+
+ align:start position:0%
+sorry I'm overloading terms here
+whatever you had at the at the at the
+
+ align:start position:0%
+whatever you had at the at the at the
+ 
+
+ align:start position:0%
+whatever you had at the at the at the
+last element whether it was a it was a B
+
+ align:start position:0%
+last element whether it was a it was a B
+ 
+
+ align:start position:0%
+last element whether it was a it was a B
+which because it ended here or F when
+
+ align:start position:0%
+which because it ended here or F when
+ 
+
+ align:start position:0%
+which because it ended here or F when
+you equate that to E and D you're going
+
+ align:start position:0%
+you equate that to E and D you're going
+ 
+
+ align:start position:0%
+you equate that to E and D you're going
+to get an inequality and so that last
+
+ align:start position:0%
+to get an inequality and so that last
+ 
+
+ align:start position:0%
+to get an inequality and so that last
+interval gets generated okay so it's a
+
+ align:start position:0%
+interval gets generated okay so it's a
+ 
+
+ align:start position:0%
+interval gets generated okay so it's a
+small optimization Tony Hoare was a very
+
+ align:start position:0%
+small optimization Tony Hoare was a very
+ 
+
+ align:start position:0%
+small optimization Tony Hoare was a very
+famous computer scientist said that
+
+ align:start position:0%
+famous computer scientist said that
+ 
+
+ align:start position:0%
+famous computer scientist said that
+inside every program there's
+
+ align:start position:0%
+inside every program there's
+ 
+
+ align:start position:0%
+inside every program there's
+smaller program waiting to get out okay
+
+ align:start position:0%
+smaller program waiting to get out okay
+ 
+
+ align:start position:0%
+smaller program waiting to get out okay
+so so this is kind of one of the themes
+
+ align:start position:0%
+so so this is kind of one of the themes
+ 
+
+ align:start position:0%
+so so this is kind of one of the themes
+that I'd like to to harp on in this
+
+ align:start position:0%
+that I'd like to to harp on in this
+ 
+
+ align:start position:0%
+that I'd like to to harp on in this
+class which is it's nice to write
+
+ align:start position:0%
+class which is it's nice to write
+ 
+
+ align:start position:0%
+class which is it's nice to write
+compact code usually if you can write
+
+ align:start position:0%
+compact code usually if you can write
+ 
+
+ align:start position:0%
+compact code usually if you can write
+compact code there's fewer fewer bugs in
+
+ align:start position:0%
+compact code there's fewer fewer bugs in
+ 
+
+ align:start position:0%
+compact code there's fewer fewer bugs in
+it and you don't want to go overboard
+
+ align:start position:0%
+it and you don't want to go overboard
+ 
+
+ align:start position:0%
+it and you don't want to go overboard
+you don't want too many subtleties but
+
+ align:start position:0%
+you don't want too many subtleties but
+ 
+
+ align:start position:0%
+you don't want too many subtleties but
+it's nice to ride compact code and so
+
+ align:start position:0%
+it's nice to ride compact code and so
+ 
+
+ align:start position:0%
+it's nice to ride compact code and so
+this is a little bit more compact and
+
+ align:start position:0%
+this is a little bit more compact and
+ 
+
+ align:start position:0%
+this is a little bit more compact and
+and then finally here's the one pass
+
+ align:start position:0%
+and then finally here's the one pass
+ 
+
+ align:start position:0%
+and then finally here's the one pass
+algorithm right so the whole thing I
+
+ align:start position:0%
+algorithm right so the whole thing I
+ 
+
+ align:start position:0%
+algorithm right so the whole thing I
+said the please conform one pass is the
+
+ align:start position:0%
+said the please conform one pass is the
+ 
+
+ align:start position:0%
+said the please conform one pass is the
+is the the smarter algorithm that
+
+ align:start position:0%
+is the the smarter algorithm that
+ 
+
+ align:start position:0%
+is the the smarter algorithm that
+essentially says I look if I just look
+
+ align:start position:0%
+essentially says I look if I just look
+ 
+
+ align:start position:0%
+essentially says I look if I just look
+at the very first thing I'm going to I'm
+
+ align:start position:0%
+at the very first thing I'm going to I'm
+ 
+
+ align:start position:0%
+at the very first thing I'm going to I'm
+gonna be able to skip that and then move
+
+ align:start position:0%
+gonna be able to skip that and then move
+ 
+
+ align:start position:0%
+gonna be able to skip that and then move
+on right so this is fairly complicated I
+
+ align:start position:0%
+on right so this is fairly complicated I
+ 
+
+ align:start position:0%
+on right so this is fairly complicated I
+mean it's it do I you know the algorithm
+
+ align:start position:0%
+mean it's it do I you know the algorithm
+ 
+
+ align:start position:0%
+mean it's it do I you know the algorithm
+trying to map that to this code is
+
+ align:start position:0%
+trying to map that to this code is
+ 
+
+ align:start position:0%
+trying to map that to this code is
+non-trivial so we'll spend a minute or
+
+ align:start position:0%
+non-trivial so we'll spend a minute or
+ 
+
+ align:start position:0%
+non-trivial so we'll spend a minute or
+two on it right but here's here's how
+
+ align:start position:0%
+two on it right but here's here's how
+ 
+
+ align:start position:0%
+two on it right but here's here's how
+this works
+
+ align:start position:0%
+this works
+ 
+
+ align:start position:0%
+this works
+right and by the way just to make sure
+
+ align:start position:0%
+right and by the way just to make sure
+ 
+
+ align:start position:0%
+right and by the way just to make sure
+so I've repeated things here so the
+
+ align:start position:0%
+so I've repeated things here so the
+ 
+
+ align:start position:0%
+so I've repeated things here so the
+first the optimized algorithm for that
+
+ align:start position:0%
+first the optimized algorithm for that
+ 
+
+ align:start position:0%
+first the optimized algorithm for that
+particular example produce these first
+
+ align:start position:0%
+particular example produce these first
+ 
+
+ align:start position:0%
+particular example produce these first
+three commands and then the the one pass
+
+ align:start position:0%
+three commands and then the the one pass
+ 
+
+ align:start position:0%
+three commands and then the the one pass
+algorithm produce exactly the same
+
+ align:start position:0%
+algorithm produce exactly the same
+ 
+
+ align:start position:0%
+algorithm produce exactly the same
+commands right so this is good to do
+
+ align:start position:0%
+commands right so this is good to do
+ 
+
+ align:start position:0%
+commands right so this is good to do
+it's always nice to have a couple of
+
+ align:start position:0%
+it's always nice to have a couple of
+ 
+
+ align:start position:0%
+it's always nice to have a couple of
+different ways of solving a problem
+
+ align:start position:0%
+different ways of solving a problem
+ 
+
+ align:start position:0%
+different ways of solving a problem
+because then you can you can verify
+
+ align:start position:0%
+because then you can you can verify
+ 
+
+ align:start position:0%
+because then you can you can verify
+things right anyway so so this piece of
+
+ align:start position:0%
+things right anyway so so this piece of
+ 
+
+ align:start position:0%
+things right anyway so so this piece of
+code is essentially something that does
+
+ align:start position:0%
+code is essentially something that does
+ 
+
+ align:start position:0%
+code is essentially something that does
+the similar trick to what we had before
+
+ align:start position:0%
+the similar trick to what we had before
+ 
+
+ align:start position:0%
+the similar trick to what we had before
+in terms of adding I to the to the
+
+ align:start position:0%
+in terms of adding I to the to the
+ 
+
+ align:start position:0%
+in terms of adding I to the to the
+original list adding an element but
+
+ align:start position:0%
+original list adding an element but
+ 
+
+ align:start position:0%
+original list adding an element but
+we're not using E and D here we're
+
+ align:start position:0%
+we're not using E and D here we're
+ 
+
+ align:start position:0%
+we're not using E and D here we're
+actually saying I what what we want to
+
+ align:start position:0%
+actually saying I what what we want to
+ 
+
+ align:start position:0%
+actually saying I what what we want to
+do because we're going to go ahead and
+
+ align:start position:0%
+do because we're going to go ahead and
+ 
+
+ align:start position:0%
+do because we're going to go ahead and
+skip this anyway you know if you're
+
+ align:start position:0%
+skip this anyway you know if you're
+ 
+
+ align:start position:0%
+skip this anyway you know if you're
+going to skip the F so we whatever that
+
+ align:start position:0%
+going to skip the F so we whatever that
+ 
+
+ align:start position:0%
+going to skip the F so we whatever that
+is we could just sort of add up here
+
+ align:start position:0%
+is we could just sort of add up here
+ 
+
+ align:start position:0%
+is we could just sort of add up here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+that's that makes it easy you don't have
+
+ align:start position:0%
+that's that makes it easy you don't have
+ 
+
+ align:start position:0%
+that's that makes it easy you don't have
+to worry about what the what the actual
+
+ align:start position:0%
+to worry about what the what the actual
+ 
+
+ align:start position:0%
+to worry about what the what the actual
+characters are and and cooking up this e
+
+ align:start position:0%
+characters are and and cooking up this e
+ 
+
+ align:start position:0%
+characters are and and cooking up this e
+and D which is different from the F for
+
+ align:start position:0%
+and D which is different from the F for
+ 
+
+ align:start position:0%
+and D which is different from the F for
+the B because you know hey it's possible
+
+ align:start position:0%
+the B because you know hey it's possible
+ 
+
+ align:start position:0%
+the B because you know hey it's possible
+that that that people might use whatever
+
+ align:start position:0%
+that that that people might use whatever
+ 
+
+ align:start position:0%
+that that that people might use whatever
+they want to represent a forward cap or
+
+ align:start position:0%
+they want to represent a forward cap or
+ 
+
+ align:start position:0%
+they want to represent a forward cap or
+a backward cap so this is very clean you
+
+ align:start position:0%
+a backward cap so this is very clean you
+ 
+
+ align:start position:0%
+a backward cap so this is very clean you
+go ahead and put exactly that over here
+
+ align:start position:0%
+go ahead and put exactly that over here
+ 
+
+ align:start position:0%
+go ahead and put exactly that over here
+you know you're gonna skip that interval
+
+ align:start position:0%
+you know you're gonna skip that interval
+ 
+
+ align:start position:0%
+you know you're gonna skip that interval
+because of the you want to skip the
+
+ align:start position:0%
+because of the you want to skip the
+ 
+
+ align:start position:0%
+because of the you want to skip the
+first the first interval effectively
+
+ align:start position:0%
+first the first interval effectively
+ 
+
+ align:start position:0%
+first the first interval effectively
+because that medalta them allows you to
+
+ align:start position:0%
+because that medalta them allows you to
+ 
+
+ align:start position:0%
+because that medalta them allows you to
+do and then this part here is is doing
+
+ align:start position:0%
+do and then this part here is is doing
+ 
+
+ align:start position:0%
+do and then this part here is is doing
+what we had before
+
+ align:start position:0%
+what we had before
+ 
+
+ align:start position:0%
+what we had before
+we're not even generating the intervals
+
+ align:start position:0%
+we're not even generating the intervals
+ 
+
+ align:start position:0%
+we're not even generating the intervals
+we're just directly making the commands
+
+ align:start position:0%
+we're just directly making the commands
+ 
+
+ align:start position:0%
+we're just directly making the commands
+right so there's no tuples in terms of
+
+ align:start position:0%
+right so there's no tuples in terms of
+ 
+
+ align:start position:0%
+right so there's no tuples in terms of
+the tuples and depending of the
+
+ align:start position:0%
+the tuples and depending of the
+ 
+
+ align:start position:0%
+the tuples and depending of the
+intervals data structure that we had
+
+ align:start position:0%
+intervals data structure that we had
+ 
+
+ align:start position:0%
+intervals data structure that we had
+it's all it's all gone I'm just going to
+
+ align:start position:0%
+it's all it's all gone I'm just going to
+ 
+
+ align:start position:0%
+it's all it's all gone I'm just going to
+go ahead and and fire off these commands
+
+ align:start position:0%
+go ahead and and fire off these commands
+ 
+
+ align:start position:0%
+go ahead and and fire off these commands
+right and those commands are are they're
+
+ align:start position:0%
+right and those commands are are they're
+ 
+
+ align:start position:0%
+right and those commands are are they're
+written in kind of a funny way right
+
+ align:start position:0%
+written in kind of a funny way right
+ 
+
+ align:start position:0%
+written in kind of a funny way right
+because I I'm going to go ahead and if I
+
+ align:start position:0%
+because I I'm going to go ahead and if I
+ 
+
+ align:start position:0%
+because I I'm going to go ahead and if I
+wanted to print these things out you'd
+
+ align:start position:0%
+wanted to print these things out you'd
+ 
+
+ align:start position:0%
+wanted to print these things out you'd
+have to do this in this funny way if
+
+ align:start position:0%
+have to do this in this funny way if
+ 
+
+ align:start position:0%
+have to do this in this funny way if
+you're willing to wait and collect up
+
+ align:start position:0%
+you're willing to wait and collect up
+ 
+
+ align:start position:0%
+you're willing to wait and collect up
+the intervals you could certainly do
+
+ align:start position:0%
+the intervals you could certainly do
+ 
+
+ align:start position:0%
+the intervals you could certainly do
+that right but this is absolutely the
+
+ align:start position:0%
+that right but this is absolutely the
+ 
+
+ align:start position:0%
+that right but this is absolutely the
+most compact code that I could think of
+
+ align:start position:0%
+most compact code that I could think of
+ 
+
+ align:start position:0%
+most compact code that I could think of
+and I'm printing a command in two
+
+ align:start position:0%
+and I'm printing a command in two
+ 
+
+ align:start position:0%
+and I'm printing a command in two
+different parts right I'm printing the
+
+ align:start position:0%
+different parts right I'm printing the
+ 
+
+ align:start position:0%
+different parts right I'm printing the
+first part of the command that says
+
+ align:start position:0%
+first part of the command that says
+ 
+
+ align:start position:0%
+first part of the command that says
+people in positions and that's the start
+
+ align:start position:0%
+people in positions and that's the start
+ 
+
+ align:start position:0%
+people in positions and that's the start
+of the interval I write and I'm just
+
+ align:start position:0%
+of the interval I write and I'm just
+ 
+
+ align:start position:0%
+of the interval I write and I'm just
+using a Python constructor this is this
+
+ align:start position:0%
+using a Python constructor this is this
+ 
+
+ align:start position:0%
+using a Python constructor this is this
+E&D here is is something that the print
+
+ align:start position:0%
+E&D here is is something that the print
+ 
+
+ align:start position:0%
+E&D here is is something that the print
+command can recognize and this simply
+
+ align:start position:0%
+command can recognize and this simply
+ 
+
+ align:start position:0%
+command can recognize and this simply
+says don't give me a newline I want to
+
+ align:start position:0%
+says don't give me a newline I want to
+ 
+
+ align:start position:0%
+says don't give me a newline I want to
+print it exactly as you saw from when I
+
+ align:start position:0%
+print it exactly as you saw from when I
+ 
+
+ align:start position:0%
+print it exactly as you saw from when I
+ran the code the printing was exactly
+
+ align:start position:0%
+ran the code the printing was exactly
+ 
+
+ align:start position:0%
+ran the code the printing was exactly
+the same as the original algorithm right
+
+ align:start position:0%
+the same as the original algorithm right
+ 
+
+ align:start position:0%
+the same as the original algorithm right
+and so this e and E simply says don't
+
+ align:start position:0%
+and so this e and E simply says don't
+ 
+
+ align:start position:0%
+and so this e and E simply says don't
+print a new line at the end of of people
+
+ align:start position:0%
+print a new line at the end of of people
+ 
+
+ align:start position:0%
+print a new line at the end of of people
+and positions you know whatever this
+
+ align:start position:0%
+and positions you know whatever this
+ 
+
+ align:start position:0%
+and positions you know whatever this
+number is call it seven and and you
+
+ align:start position:0%
+number is call it seven and and you
+ 
+
+ align:start position:0%
+number is call it seven and and you
+don't print a new line and then you go
+
+ align:start position:0%
+don't print a new line and then you go
+ 
+
+ align:start position:0%
+don't print a new line and then you go
+you have it space here because you
+
+ align:start position:0%
+you have it space here because you
+ 
+
+ align:start position:0%
+you have it space here because you
+didn't print a new line or or a space
+
+ align:start position:0%
+didn't print a new line or or a space
+ 
+
+ align:start position:0%
+didn't print a new line or or a space
+and you go through I minus one which is
+
+ align:start position:0%
+and you go through I minus one which is
+ 
+
+ align:start position:0%
+and you go through I minus one which is
+exactly the same as we had before you
+
+ align:start position:0%
+exactly the same as we had before you
+ 
+
+ align:start position:0%
+exactly the same as we had before you
+only discovered that
+
+ align:start position:0%
+only discovered that
+ 
+
+ align:start position:0%
+only discovered that
+at the end of an interval and after you
+
+ align:start position:0%
+at the end of an interval and after you
+ 
+
+ align:start position:0%
+at the end of an interval and after you
+see the person that comes after the
+
+ align:start position:0%
+see the person that comes after the
+ 
+
+ align:start position:0%
+see the person that comes after the
+interval right so you have to go back to
+
+ align:start position:0%
+interval right so you have to go back to
+ 
+
+ align:start position:0%
+interval right so you have to go back to
+I minus one so this makes sense any
+
+ align:start position:0%
+I minus one so this makes sense any
+ 
+
+ align:start position:0%
+I minus one so this makes sense any
+questions about this code yeah plus
+
+ align:start position:0%
+questions about this code yeah plus
+ 
+
+ align:start position:0%
+questions about this code yeah plus
+there is a concatenation and you have
+
+ align:start position:0%
+there is a concatenation and you have
+ 
+
+ align:start position:0%
+there is a concatenation and you have
+two lists caps as a list and when you
+
+ align:start position:0%
+two lists caps as a list and when you
+ 
+
+ align:start position:0%
+two lists caps as a list and when you
+use a plus operator in Python the you
+
+ align:start position:0%
+use a plus operator in Python the you
+ 
+
+ align:start position:0%
+use a plus operator in Python the you
+you can only add things that are of the
+
+ align:start position:0%
+you can only add things that are of the
+ 
+
+ align:start position:0%
+you can only add things that are of the
+same type okay and so caps is a is a
+
+ align:start position:0%
+same type okay and so caps is a is a
+ 
+
+ align:start position:0%
+same type okay and so caps is a is a
+list and caps 0 is an element of the
+
+ align:start position:0%
+list and caps 0 is an element of the
+ 
+
+ align:start position:0%
+list and caps 0 is an element of the
+list and so you need to make it a list
+
+ align:start position:0%
+list and so you need to make it a list
+ 
+
+ align:start position:0%
+list and so you need to make it a list
+in order to use the plus operator you
+
+ align:start position:0%
+in order to use the plus operator you
+ 
+
+ align:start position:0%
+in order to use the plus operator you
+dis also other things you could do using
+
+ align:start position:0%
+dis also other things you could do using
+ 
+
+ align:start position:0%
+dis also other things you could do using
+a pen for example right so you could
+
+ align:start position:0%
+a pen for example right so you could
+ 
+
+ align:start position:0%
+a pen for example right so you could
+take that line and you can do caps tour
+
+ align:start position:0%
+take that line and you can do caps tour
+ 
+
+ align:start position:0%
+take that line and you can do caps tour
+the pen cap zero right and you wouldn't
+
+ align:start position:0%
+the pen cap zero right and you wouldn't
+ 
+
+ align:start position:0%
+the pen cap zero right and you wouldn't
+need all of the square brackets but you
+
+ align:start position:0%
+need all of the square brackets but you
+ 
+
+ align:start position:0%
+need all of the square brackets but you
+know that's just neither here or not
+
+ align:start position:0%
+know that's just neither here or not
+ 
+
+ align:start position:0%
+know that's just neither here or not
+there but I was no obviously not
+
+ align:start position:0%
+there but I was no obviously not
+ 
+
+ align:start position:0%
+there but I was no obviously not
+answering your question so go ahead yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but it's ok because I remember the
+
+ align:start position:0%
+but but it's ok because I remember the
+ 
+
+ align:start position:0%
+but but it's ok because I remember the
+if statement and is is going to skip the
+
+ align:start position:0%
+if statement and is is going to skip the
+ 
+
+ align:start position:0%
+if statement and is is going to skip the
+this one too so if I had two F's in the
+
+ align:start position:0%
+this one too so if I had two F's in the
+ 
+
+ align:start position:0%
+this one too so if I had two F's in the
+beginning I think your question is what
+
+ align:start position:0%
+beginning I think your question is what
+ 
+
+ align:start position:0%
+beginning I think your question is what
+would happen if I had two F's or three
+
+ align:start position:0%
+would happen if I had two F's or three
+ 
+
+ align:start position:0%
+would happen if I had two F's or three
+FS in the beginning right so I'm going
+
+ align:start position:0%
+FS in the beginning right so I'm going
+ 
+
+ align:start position:0%
+FS in the beginning right so I'm going
+to go ahead and first thing I'm going to
+
+ align:start position:0%
+to go ahead and first thing I'm going to
+ 
+
+ align:start position:0%
+to go ahead and first thing I'm going to
+do is I'm going to put an F at the end
+
+ align:start position:0%
+do is I'm going to put an F at the end
+ 
+
+ align:start position:0%
+do is I'm going to put an F at the end
+here and then maybe there's a bunch of
+
+ align:start position:0%
+here and then maybe there's a bunch of
+ 
+
+ align:start position:0%
+here and then maybe there's a bunch of
+stuff but then the nice thing is that
+
+ align:start position:0%
+stuff but then the nice thing is that
+ 
+
+ align:start position:0%
+stuff but then the nice thing is that
+I'll skip this f2 because because the
+
+ align:start position:0%
+I'll skip this f2 because because the
+ 
+
+ align:start position:0%
+I'll skip this f2 because because the
+not equal to on is not going to is not
+
+ align:start position:0%
+not equal to on is not going to is not
+ 
+
+ align:start position:0%
+not equal to on is not going to is not
+going to fire right right the next line
+
+ align:start position:0%
+going to fire right right the next line
+ 
+
+ align:start position:0%
+going to fire right right the next line
+the caps I not equal to I minus one this
+
+ align:start position:0%
+the caps I not equal to I minus one this
+ 
+
+ align:start position:0%
+the caps I not equal to I minus one this
+is this is going to be equal to so I'm
+
+ align:start position:0%
+is this is going to be equal to so I'm
+ 
+
+ align:start position:0%
+is this is going to be equal to so I'm
+going to go ahead and go to the next
+
+ align:start position:0%
+going to go ahead and go to the next
+ 
+
+ align:start position:0%
+going to go ahead and go to the next
+iteration of the loop that makes sense
+
+ align:start position:0%
+iteration of the loop that makes sense
+ 
+
+ align:start position:0%
+iteration of the loop that makes sense
+did people understand fadis question
+
+ align:start position:0%
+did people understand fadis question
+ 
+
+ align:start position:0%
+did people understand fadis question
+right it was a good question right so
+
+ align:start position:0%
+right it was a good question right so
+ 
+
+ align:start position:0%
+right it was a good question right so
+the question was you I you skipped the
+
+ align:start position:0%
+the question was you I you skipped the
+ 
+
+ align:start position:0%
+the question was you I you skipped the
+first one but what is making you skip
+
+ align:start position:0%
+first one but what is making you skip
+ 
+
+ align:start position:0%
+first one but what is making you skip
+this one because you want to skip the
+
+ align:start position:0%
+this one because you want to skip the
+ 
+
+ align:start position:0%
+this one because you want to skip the
+first interval correct and so that if
+
+ align:start position:0%
+first interval correct and so that if
+ 
+
+ align:start position:0%
+first interval correct and so that if
+statement is making you do that alright
+
+ align:start position:0%
+statement is making you do that alright
+ 
+
+ align:start position:0%
+statement is making you do that alright
+good so as you can see even a fairly
+
+ align:start position:0%
+good so as you can see even a fairly
+ 
+
+ align:start position:0%
+good so as you can see even a fairly
+straightforward puzzle this is
+
+ align:start position:0%
+straightforward puzzle this is
+ 
+
+ align:start position:0%
+straightforward puzzle this is
+the simplest puzzle we're going to do
+
+ align:start position:0%
+the simplest puzzle we're going to do
+ 
+
+ align:start position:0%
+the simplest puzzle we're going to do
+here right is the first one you know and
+
+ align:start position:0%
+here right is the first one you know and
+ 
+
+ align:start position:0%
+here right is the first one you know and
+there's nuances associated with how you
+
+ align:start position:0%
+there's nuances associated with how you
+ 
+
+ align:start position:0%
+there's nuances associated with how you
+solve it but also how you code it right
+
+ align:start position:0%
+solve it but also how you code it right
+ 
+
+ align:start position:0%
+solve it but also how you code it right
+and this is kind of I said you know my
+
+ align:start position:0%
+and this is kind of I said you know my
+ 
+
+ align:start position:0%
+and this is kind of I said you know my
+this was my Eureka moment you know a few
+
+ align:start position:0%
+this was my Eureka moment you know a few
+ 
+
+ align:start position:0%
+this was my Eureka moment you know a few
+years ago but I said I think the way you
+
+ align:start position:0%
+years ago but I said I think the way you
+ 
+
+ align:start position:0%
+years ago but I said I think the way you
+want to teach programming is is is at
+
+ align:start position:0%
+want to teach programming is is is at
+ 
+
+ align:start position:0%
+want to teach programming is is is at
+least some some aspects of programming
+
+ align:start position:0%
+least some some aspects of programming
+ 
+
+ align:start position:0%
+least some some aspects of programming
+is in this fashion right anyway good so
+
+ align:start position:0%
+is in this fashion right anyway good so
+ 
+
+ align:start position:0%
+is in this fashion right anyway good so
+we're done with this any questions about
+
+ align:start position:0%
+we're done with this any questions about
+ 
+
+ align:start position:0%
+we're done with this any questions about
+this puzzle all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/1ItXXlqK6eE.txt b/1ItXXlqK6eE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8545447461b2e24a4e02c347b6757b44ec84f7b8
--- /dev/null
+++ b/1ItXXlqK6eE.txt
@@ -0,0 +1,9056 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a this is just one person's
+
+ align:start position:0%
+so this is a this is just one person's
+ 
+
+ align:start position:0%
+so this is a this is just one person's
+rendition of a Gollum a Gollum is sort
+
+ align:start position:0%
+rendition of a Gollum a Gollum is sort
+ 
+
+ align:start position:0%
+rendition of a Gollum a Gollum is sort
+of uh the slave uh Rabbi low and U of
+
+ align:start position:0%
+of uh the slave uh Rabbi low and U of
+ 
+
+ align:start position:0%
+of uh the slave uh Rabbi low and U of
+Prague and it's a tale of uh
+
+ align:start position:0%
+Prague and it's a tale of uh
+ 
+
+ align:start position:0%
+Prague and it's a tale of uh
+a an individual made out of clay a a
+
+ align:start position:0%
+a an individual made out of clay a a
+ 
+
+ align:start position:0%
+a an individual made out of clay a a
+automaton made out of clay to carry out
+
+ align:start position:0%
+automaton made out of clay to carry out
+ 
+
+ align:start position:0%
+automaton made out of clay to carry out
+the the duties but it uh gets out of
+
+ align:start position:0%
+the the duties but it uh gets out of
+ 
+
+ align:start position:0%
+the the duties but it uh gets out of
+control while a good Rabbi is uh uh at
+
+ align:start position:0%
+control while a good Rabbi is uh uh at
+ 
+
+ align:start position:0%
+control while a good Rabbi is uh uh at
+uh Sho and uh nobody knows how to stop
+
+ align:start position:0%
+uh Sho and uh nobody knows how to stop
+ 
+
+ align:start position:0%
+uh Sho and uh nobody knows how to stop
+the thing so it's kind of uh running
+
+ align:start position:0%
+the thing so it's kind of uh running
+ 
+
+ align:start position:0%
+the thing so it's kind of uh running
+around a muuk and this is a problem and
+
+ align:start position:0%
+around a muuk and this is a problem and
+ 
+
+ align:start position:0%
+around a muuk and this is a problem and
+uh only only the rabbi knows how to shut
+
+ align:start position:0%
+uh only only the rabbi knows how to shut
+ 
+
+ align:start position:0%
+uh only only the rabbi knows how to shut
+it down um and so uh this is a kind of a
+
+ align:start position:0%
+it down um and so uh this is a kind of a
+ 
+
+ align:start position:0%
+it down um and so uh this is a kind of a
+a dominant metaphor for this book is
+
+ align:start position:0%
+a dominant metaphor for this book is
+ 
+
+ align:start position:0%
+a dominant metaphor for this book is
+this this concept of this this
+
+ align:start position:0%
+this this concept of this this
+ 
+
+ align:start position:0%
+this this concept of this this
+mechanical entity that that we create
+
+ align:start position:0%
+mechanical entity that that we create
+ 
+
+ align:start position:0%
+mechanical entity that that we create
+for our
+
+ align:start position:0%
+for our
+ 
+
+ align:start position:0%
+for our
+own to improve our
+
+ align:start position:0%
+own to improve our
+ 
+
+ align:start position:0%
+own to improve our
+lives but uh you know improve our lives
+
+ align:start position:0%
+lives but uh you know improve our lives
+ 
+
+ align:start position:0%
+lives but uh you know improve our lives
+through doing the chores and you know
+
+ align:start position:0%
+through doing the chores and you know
+ 
+
+ align:start position:0%
+through doing the chores and you know
+bringing the water up and all these
+
+ align:start position:0%
+bringing the water up and all these
+ 
+
+ align:start position:0%
+bringing the water up and all these
+sorts of things but it's not as simple
+
+ align:start position:0%
+sorts of things but it's not as simple
+ 
+
+ align:start position:0%
+sorts of things but it's not as simple
+as just making a lot of these things and
+
+ align:start position:0%
+as just making a lot of these things and
+ 
+
+ align:start position:0%
+as just making a lot of these things and
+just hoping that you know they'll all go
+
+ align:start position:0%
+just hoping that you know they'll all go
+ 
+
+ align:start position:0%
+just hoping that you know they'll all go
+out and do uh or intending that they'll
+
+ align:start position:0%
+out and do uh or intending that they'll
+ 
+
+ align:start position:0%
+out and do uh or intending that they'll
+go out and do everything that we intend
+
+ align:start position:0%
+go out and do everything that we intend
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+
+ align:start position:0%
+go out and do everything that we intend
+them to do but nothing else because
+
+ align:start position:0%
+them to do but nothing else because
+ 
+
+ align:start position:0%
+them to do but nothing else because
+there are there are tremend mendous
+
+ align:start position:0%
+there are there are tremend mendous
+ 
+
+ align:start position:0%
+there are there are tremend mendous
+impacts through the use of mechanical
+
+ align:start position:0%
+impacts through the use of mechanical
+ 
+
+ align:start position:0%
+impacts through the use of mechanical
+devices and and not just mechanical in
+
+ align:start position:0%
+devices and and not just mechanical in
+ 
+
+ align:start position:0%
+devices and and not just mechanical in
+the sense of uh the traditional sense of
+
+ align:start position:0%
+the sense of uh the traditional sense of
+ 
+
+ align:start position:0%
+the sense of uh the traditional sense of
+machine as Laura says here the the
+
+ align:start position:0%
+machine as Laura says here the the
+ 
+
+ align:start position:0%
+machine as Laura says here the the
+concept of machine is
+
+ align:start position:0%
+concept of machine is
+ 
+
+ align:start position:0%
+concept of machine is
+changing the processing of information
+
+ align:start position:0%
+changing the processing of information
+ 
+
+ align:start position:0%
+changing the processing of information
+is a mechanical
+
+ align:start position:0%
+is a mechanical
+ 
+
+ align:start position:0%
+is a mechanical
+process and so machines are beginning to
+
+ align:start position:0%
+process and so machines are beginning to
+ 
+
+ align:start position:0%
+process and so machines are beginning to
+be thought of or have long been thought
+
+ align:start position:0%
+be thought of or have long been thought
+ 
+
+ align:start position:0%
+be thought of or have long been thought
+of In wier's Time as uh also devices
+
+ align:start position:0%
+of In wier's Time as uh also devices
+ 
+
+ align:start position:0%
+of In wier's Time as uh also devices
+which are
+
+ align:start position:0%
+which are
+ 
+
+ align:start position:0%
+which are
+electronic and primarily uh working
+
+ align:start position:0%
+electronic and primarily uh working
+ 
+
+ align:start position:0%
+electronic and primarily uh working
+through electronic uh uh
+
+ align:start position:0%
+through electronic uh uh
+ 
+
+ align:start position:0%
+through electronic uh uh
+systems okay so uh this is a little
+
+ align:start position:0%
+systems okay so uh this is a little
+ 
+
+ align:start position:0%
+systems okay so uh this is a little
+essay uh that he wrote it's a very
+
+ align:start position:0%
+essay uh that he wrote it's a very
+ 
+
+ align:start position:0%
+essay uh that he wrote it's a very
+yeasty little book it's got lots and
+
+ align:start position:0%
+yeasty little book it's got lots and
+ 
+
+ align:start position:0%
+yeasty little book it's got lots and
+lots of little topics in it it's not
+
+ align:start position:0%
+lots of little topics in it it's not
+ 
+
+ align:start position:0%
+lots of little topics in it it's not
+meant as a uh uh technical although as
+
+ align:start position:0%
+meant as a uh uh technical although as
+ 
+
+ align:start position:0%
+meant as a uh uh technical although as
+as La said there there are some things
+
+ align:start position:0%
+as La said there there are some things
+ 
+
+ align:start position:0%
+as La said there there are some things
+in it that are uh uh
+
+ align:start position:0%
+in it that are uh uh
+ 
+
+ align:start position:0%
+in it that are uh uh
+conceptually uh a little more a little
+
+ align:start position:0%
+conceptually uh a little more a little
+ 
+
+ align:start position:0%
+conceptually uh a little more a little
+beyond the average readers um but the
+
+ align:start position:0%
+beyond the average readers um but the
+ 
+
+ align:start position:0%
+beyond the average readers um but the
+book itself is really just trying to
+
+ align:start position:0%
+book itself is really just trying to
+ 
+
+ align:start position:0%
+book itself is really just trying to
+talk a little bit about technology in
+
+ align:start position:0%
+talk a little bit about technology in
+ 
+
+ align:start position:0%
+talk a little bit about technology in
+the world that we're creating through it
+
+ align:start position:0%
+the world that we're creating through it
+ 
+
+ align:start position:0%
+the world that we're creating through it
+and uh weiner was a deeply uh he was a
+
+ align:start position:0%
+and uh weiner was a deeply uh he was a
+ 
+
+ align:start position:0%
+and uh weiner was a deeply uh he was a
+thinking person who thought deeply about
+
+ align:start position:0%
+thinking person who thought deeply about
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+
+ align:start position:0%
+thinking person who thought deeply about
+uh a whole range of things and
+
+ align:start position:0%
+uh a whole range of things and
+ 
+
+ align:start position:0%
+uh a whole range of things and
+um uh he's a uh uh
+
+ align:start position:0%
+um uh he's a uh uh
+ 
+
+ align:start position:0%
+um uh he's a uh uh
+a key person in the creation of the
+
+ align:start position:0%
+a key person in the creation of the
+ 
+
+ align:start position:0%
+a key person in the creation of the
+field of
+
+ align:start position:0%
+field of
+ 
+
+ align:start position:0%
+field of
+cybernetics uh his book
+
+ align:start position:0%
+cybernetics uh his book
+ 
+
+ align:start position:0%
+cybernetics uh his book
+cybernetics uh which is
+
+ align:start position:0%
+cybernetics uh which is
+ 
+
+ align:start position:0%
+cybernetics uh which is
+uh uh a the subtitle you can see control
+
+ align:start position:0%
+uh uh a the subtitle you can see control
+ 
+
+ align:start position:0%
+uh uh a the subtitle you can see control
+and communication in the animal and the
+
+ align:start position:0%
+and communication in the animal and the
+ 
+
+ align:start position:0%
+and communication in the animal and the
+Machine so the concept that we can
+
+ align:start position:0%
+Machine so the concept that we can
+ 
+
+ align:start position:0%
+Machine so the concept that we can
+transfer certain sorts of understandings
+
+ align:start position:0%
+transfer certain sorts of understandings
+ 
+
+ align:start position:0%
+transfer certain sorts of understandings
+we get from one location to another
+
+ align:start position:0%
+we get from one location to another
+ 
+
+ align:start position:0%
+we get from one location to another
+location is Central here and so we can
+
+ align:start position:0%
+location is Central here and so we can
+ 
+
+ align:start position:0%
+location is Central here and so we can
+learn we can learn about Mechanical
+
+ align:start position:0%
+learn we can learn about Mechanical
+ 
+
+ align:start position:0%
+learn we can learn about Mechanical
+Devices by studying biological entities
+
+ align:start position:0%
+Devices by studying biological entities
+ 
+
+ align:start position:0%
+Devices by studying biological entities
+and we can learn about biological
+
+ align:start position:0%
+and we can learn about biological
+ 
+
+ align:start position:0%
+and we can learn about biological
+entities by studying mechanical
+
+ align:start position:0%
+entities by studying mechanical
+ 
+
+ align:start position:0%
+entities by studying mechanical
+devices and the notion of how organisms
+
+ align:start position:0%
+devices and the notion of how organisms
+ 
+
+ align:start position:0%
+devices and the notion of how organisms
+control themselves can tell us lots and
+
+ align:start position:0%
+control themselves can tell us lots and
+ 
+
+ align:start position:0%
+control themselves can tell us lots and
+lots of things about how mechanical
+
+ align:start position:0%
+lots of things about how mechanical
+ 
+
+ align:start position:0%
+lots of things about how mechanical
+devices uh can be controlled
+
+ align:start position:0%
+devices uh can be controlled
+ 
+
+ align:start position:0%
+devices uh can be controlled
+and can also be
+
+ align:start position:0%
+and can also be
+ 
+
+ align:start position:0%
+and can also be
+self-regulating so these are these are
+
+ align:start position:0%
+self-regulating so these are these are
+ 
+
+ align:start position:0%
+self-regulating so these are these are
+areas that U are of of prime importance
+
+ align:start position:0%
+areas that U are of of prime importance
+ 
+
+ align:start position:0%
+areas that U are of of prime importance
+to him and that's sort of in the
+
+ align:start position:0%
+to him and that's sort of in the
+ 
+
+ align:start position:0%
+to him and that's sort of in the
+background of his thinking here is this
+
+ align:start position:0%
+background of his thinking here is this
+ 
+
+ align:start position:0%
+background of his thinking here is this
+whole question of U uh cybernetics and
+
+ align:start position:0%
+whole question of U uh cybernetics and
+ 
+
+ align:start position:0%
+whole question of U uh cybernetics and
+cybernetic
+
+ align:start position:0%
+cybernetic
+ 
+
+ align:start position:0%
+cybernetic
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+uh so U as Laura said the uh he he
+
+ align:start position:0%
+uh so U as Laura said the uh he he
+ 
+
+ align:start position:0%
+uh so U as Laura said the uh he he
+mentions it's a part of the scientist uh
+
+ align:start position:0%
+mentions it's a part of the scientist uh
+ 
+
+ align:start position:0%
+mentions it's a part of the scientist uh
+this is from page five to entertain
+
+ align:start position:0%
+this is from page five to entertain
+ 
+
+ align:start position:0%
+this is from page five to entertain
+heretical and forbidden opinions
+
+ align:start position:0%
+heretical and forbidden opinions
+ 
+
+ align:start position:0%
+heretical and forbidden opinions
+experimentally I mean weer has a sense
+
+ align:start position:0%
+experimentally I mean weer has a sense
+ 
+
+ align:start position:0%
+experimentally I mean weer has a sense
+of humor so some of this is he he he
+
+ align:start position:0%
+of humor so some of this is he he he
+ 
+
+ align:start position:0%
+of humor so some of this is he he he
+says this you know for impact and he's
+
+ align:start position:0%
+says this you know for impact and he's
+ 
+
+ align:start position:0%
+says this you know for impact and he's
+also aware that you know it's it's
+
+ align:start position:0%
+also aware that you know it's it's
+ 
+
+ align:start position:0%
+also aware that you know it's it's
+there's there's a element of humor
+
+ align:start position:0%
+there's there's a element of humor
+ 
+
+ align:start position:0%
+there's there's a element of humor
+behind this but uh the fact is that most
+
+ align:start position:0%
+behind this but uh the fact is that most
+ 
+
+ align:start position:0%
+behind this but uh the fact is that most
+people as he says when you say how
+
+ align:start position:0%
+people as he says when you say how
+ 
+
+ align:start position:0%
+people as he says when you say how
+machines and and humans or organisms
+
+ align:start position:0%
+machines and and humans or organisms
+ 
+
+ align:start position:0%
+machines and and humans or organisms
+alike just say oh you you can't talk
+
+ align:start position:0%
+alike just say oh you you can't talk
+ 
+
+ align:start position:0%
+alike just say oh you you can't talk
+about these two they just you know don't
+
+ align:start position:0%
+about these two they just you know don't
+ 
+
+ align:start position:0%
+about these two they just you know don't
+they're entirely different uh uh Realms
+
+ align:start position:0%
+they're entirely different uh uh Realms
+ 
+
+ align:start position:0%
+they're entirely different uh uh Realms
+and any comparison is going to be
+
+ align:start position:0%
+and any comparison is going to be
+ 
+
+ align:start position:0%
+and any comparison is going to be
+superficial and so uh and and sometimes
+
+ align:start position:0%
+superficial and so uh and and sometimes
+ 
+
+ align:start position:0%
+superficial and so uh and and sometimes
+people make these statements on sort of
+
+ align:start position:0%
+people make these statements on sort of
+ 
+
+ align:start position:0%
+people make these statements on sort of
+religious grounds and so that's why he
+
+ align:start position:0%
+religious grounds and so that's why he
+ 
+
+ align:start position:0%
+religious grounds and so that's why he
+says uh entertain heral well in
+
+ align:start position:0%
+says uh entertain heral well in
+ 
+
+ align:start position:0%
+says uh entertain heral well in
+science uh I mean heresy doesn't really
+
+ align:start position:0%
+science uh I mean heresy doesn't really
+ 
+
+ align:start position:0%
+science uh I mean heresy doesn't really
+have a whole lot lot of meaning in
+
+ align:start position:0%
+have a whole lot lot of meaning in
+ 
+
+ align:start position:0%
+have a whole lot lot of meaning in
+science if if there's a theory to be
+
+ align:start position:0%
+science if if there's a theory to be
+ 
+
+ align:start position:0%
+science if if there's a theory to be
+considered uh then it it should be
+
+ align:start position:0%
+considered uh then it it should be
+ 
+
+ align:start position:0%
+considered uh then it it should be
+considered but uh in in traditional uh
+
+ align:start position:0%
+considered but uh in in traditional uh
+ 
+
+ align:start position:0%
+considered but uh in in traditional uh
+religious Frameworks sometimes uh uh
+
+ align:start position:0%
+religious Frameworks sometimes uh uh
+ 
+
+ align:start position:0%
+religious Frameworks sometimes uh uh
+suggesting things such as Evolution or
+
+ align:start position:0%
+suggesting things such as Evolution or
+ 
+
+ align:start position:0%
+suggesting things such as Evolution or
+the similarity between humans and
+
+ align:start position:0%
+the similarity between humans and
+ 
+
+ align:start position:0%
+the similarity between humans and
+machines can be seen as a a heretical
+
+ align:start position:0%
+machines can be seen as a a heretical
+ 
+
+ align:start position:0%
+machines can be seen as a a heretical
+notion and he says if we allow heresy to
+
+ align:start position:0%
+notion and he says if we allow heresy to
+ 
+
+ align:start position:0%
+notion and he says if we allow heresy to
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+dictate what we study we're not going to
+
+ align:start position:0%
+dictate what we study we're not going to
+ 
+
+ align:start position:0%
+dictate what we study we're not going to
+get very far because you know we'll just
+
+ align:start position:0%
+get very far because you know we'll just
+ 
+
+ align:start position:0%
+get very far because you know we'll just
+have to take a lot off the table and say
+
+ align:start position:0%
+have to take a lot off the table and say
+ 
+
+ align:start position:0%
+have to take a lot off the table and say
+oh that's just you know it's heretical
+
+ align:start position:0%
+oh that's just you know it's heretical
+ 
+
+ align:start position:0%
+oh that's just you know it's heretical
+to consider that so yes Darwin uh
+
+ align:start position:0%
+to consider that so yes Darwin uh
+ 
+
+ align:start position:0%
+to consider that so yes Darwin uh
+Darwin's work by some uh by some uh
+
+ align:start position:0%
+Darwin's work by some uh by some uh
+ 
+
+ align:start position:0%
+Darwin's work by some uh by some uh
+thinkers was seen as heresy or or uh
+
+ align:start position:0%
+thinkers was seen as heresy or or uh
+ 
+
+ align:start position:0%
+thinkers was seen as heresy or or uh
+sort of irreligious and
+
+ align:start position:0%
+sort of irreligious and
+ 
+
+ align:start position:0%
+sort of irreligious and
+against um the whole concept of uh
+
+ align:start position:0%
+against um the whole concept of uh
+ 
+
+ align:start position:0%
+against um the whole concept of uh
+religion you you remember deia and Hume
+
+ align:start position:0%
+religion you you remember deia and Hume
+ 
+
+ align:start position:0%
+religion you you remember deia and Hume
+and what he said you know we should not
+
+ align:start position:0%
+and what he said you know we should not
+ 
+
+ align:start position:0%
+and what he said you know we should not
+consider these things we shouldn't even
+
+ align:start position:0%
+consider these things we shouldn't even
+ 
+
+ align:start position:0%
+consider these things we shouldn't even
+be talking about these questions because
+
+ align:start position:0%
+be talking about these questions because
+ 
+
+ align:start position:0%
+be talking about these questions because
+it's it's sacrilegious we should simply
+
+ align:start position:0%
+it's it's sacrilegious we should simply
+ 
+
+ align:start position:0%
+it's it's sacrilegious we should simply
+accept that the Creator made the world
+
+ align:start position:0%
+accept that the Creator made the world
+ 
+
+ align:start position:0%
+accept that the Creator made the world
+and the world is a is a wonderful
+
+ align:start position:0%
+and the world is a is a wonderful
+ 
+
+ align:start position:0%
+and the world is a is a wonderful
+marvelous place it's uh mysterious how
+
+ align:start position:0%
+marvelous place it's uh mysterious how
+ 
+
+ align:start position:0%
+marvelous place it's uh mysterious how
+it came into existence and to begin to
+
+ align:start position:0%
+it came into existence and to begin to
+ 
+
+ align:start position:0%
+it came into existence and to begin to
+reason about it and to think about it
+
+ align:start position:0%
+reason about it and to think about it
+ 
+
+ align:start position:0%
+reason about it and to think about it
+and to believe that we can understand it
+
+ align:start position:0%
+and to believe that we can understand it
+ 
+
+ align:start position:0%
+and to believe that we can understand it
+uh its Origins and principles is pushing
+
+ align:start position:0%
+uh its Origins and principles is pushing
+ 
+
+ align:start position:0%
+uh its Origins and principles is pushing
+us into the realm of the Creator and so
+
+ align:start position:0%
+us into the realm of the Creator and so
+ 
+
+ align:start position:0%
+us into the realm of the Creator and so
+um that's to me his point whereas you
+
+ align:start position:0%
+um that's to me his point whereas you
+ 
+
+ align:start position:0%
+um that's to me his point whereas you
+remember cleanthes is you
+
+ align:start position:0%
+remember cleanthes is you
+ 
+
+ align:start position:0%
+remember cleanthes is you
+know we can do it uh because these
+
+ align:start position:0%
+know we can do it uh because these
+ 
+
+ align:start position:0%
+know we can do it uh because these
+mechanical things that we find out about
+
+ align:start position:0%
+mechanical things that we find out about
+ 
+
+ align:start position:0%
+mechanical things that we find out about
+the the universe the world are things
+
+ align:start position:0%
+the the universe the world are things
+ 
+
+ align:start position:0%
+the the universe the world are things
+that uh simply
+
+ align:start position:0%
+that uh simply
+ 
+
+ align:start position:0%
+that uh simply
+prove the uh Glory of of God because
+
+ align:start position:0%
+prove the uh Glory of of God because
+ 
+
+ align:start position:0%
+prove the uh Glory of of God because
+they're so complex and so beautiful and
+
+ align:start position:0%
+they're so complex and so beautiful and
+ 
+
+ align:start position:0%
+they're so complex and so beautiful and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+intricate so why not study the
+
+ align:start position:0%
+intricate so why not study the
+ 
+
+ align:start position:0%
+intricate so why not study the
+mechanical World in order to go from
+
+ align:start position:0%
+mechanical World in order to go from
+ 
+
+ align:start position:0%
+mechanical World in order to go from
+nature up to Nature's
+
+ align:start position:0%
+nature up to Nature's
+ 
+
+ align:start position:0%
+nature up to Nature's
+God and then finally we have felo who
+
+ align:start position:0%
+God and then finally we have felo who
+ 
+
+ align:start position:0%
+God and then finally we have felo who
+sort of plays The Devil's Advocate and
+
+ align:start position:0%
+sort of plays The Devil's Advocate and
+ 
+
+ align:start position:0%
+sort of plays The Devil's Advocate and
+he says well as long as we're looking at
+
+ align:start position:0%
+he says well as long as we're looking at
+ 
+
+ align:start position:0%
+he says well as long as we're looking at
+this uh beautiful wonderful place uh
+
+ align:start position:0%
+this uh beautiful wonderful place uh
+ 
+
+ align:start position:0%
+this uh beautiful wonderful place uh
+let's note that it's not exactly as
+
+ align:start position:0%
+let's note that it's not exactly as
+ 
+
+ align:start position:0%
+let's note that it's not exactly as
+perfect as uh an he thinks it is uh
+
+ align:start position:0%
+perfect as uh an he thinks it is uh
+ 
+
+ align:start position:0%
+perfect as uh an he thinks it is uh
+things survive yes but just barely and
+
+ align:start position:0%
+things survive yes but just barely and
+ 
+
+ align:start position:0%
+things survive yes but just barely and
+there's a great deal of suffering and a
+
+ align:start position:0%
+there's a great deal of suffering and a
+ 
+
+ align:start position:0%
+there's a great deal of suffering and a
+lot of catastrophes and it's not all
+
+ align:start position:0%
+lot of catastrophes and it's not all
+ 
+
+ align:start position:0%
+lot of catastrophes and it's not all
+made in any sense uh of of the word
+
+ align:start position:0%
+made in any sense uh of of the word
+ 
+
+ align:start position:0%
+made in any sense uh of of the word
+Perfection that everybody would agree on
+
+ align:start position:0%
+Perfection that everybody would agree on
+ 
+
+ align:start position:0%
+Perfection that everybody would agree on
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so that's the uh that's kind of the
+
+ align:start position:0%
+so so that's the uh that's kind of the
+ 
+
+ align:start position:0%
+so so that's the uh that's kind of the
+entree into this work he wants to weer
+
+ align:start position:0%
+entree into this work he wants to weer
+ 
+
+ align:start position:0%
+entree into this work he wants to weer
+wants to talk about humans and
+
+ align:start position:0%
+wants to talk about humans and
+ 
+
+ align:start position:0%
+wants to talk about humans and
+machines and he wants wants to talk
+
+ align:start position:0%
+machines and he wants wants to talk
+ 
+
+ align:start position:0%
+machines and he wants wants to talk
+about some of the ways in which they're
+
+ align:start position:0%
+about some of the ways in which they're
+ 
+
+ align:start position:0%
+about some of the ways in which they're
+parallel and to find ways in which we
+
+ align:start position:0%
+parallel and to find ways in which we
+ 
+
+ align:start position:0%
+parallel and to find ways in which we
+can learn from the two regimes by
+
+ align:start position:0%
+can learn from the two regimes by
+ 
+
+ align:start position:0%
+can learn from the two regimes by
+comparing them and studying them so uh
+
+ align:start position:0%
+comparing them and studying them so uh
+ 
+
+ align:start position:0%
+comparing them and studying them so uh
+that's his uh that's his his proposition
+
+ align:start position:0%
+that's his uh that's his his proposition
+ 
+
+ align:start position:0%
+that's his uh that's his his proposition
+but he has a lot of warnings along the
+
+ align:start position:0%
+but he has a lot of warnings along the
+ 
+
+ align:start position:0%
+but he has a lot of warnings along the
+way so this is not just to say oh
+
+ align:start position:0%
+way so this is not just to say oh
+ 
+
+ align:start position:0%
+way so this is not just to say oh
+machines are these wonderful devices and
+
+ align:start position:0%
+machines are these wonderful devices and
+ 
+
+ align:start position:0%
+machines are these wonderful devices and
+the more we have the the better it is
+
+ align:start position:0%
+the more we have the the better it is
+ 
+
+ align:start position:0%
+the more we have the the better it is
+and we should just
+
+ align:start position:0%
+and we should just
+ 
+
+ align:start position:0%
+and we should just
+continue uh without worry uh he's he's
+
+ align:start position:0%
+continue uh without worry uh he's he's
+ 
+
+ align:start position:0%
+continue uh without worry uh he's he's
+actually looking at the other side and
+
+ align:start position:0%
+actually looking at the other side and
+ 
+
+ align:start position:0%
+actually looking at the other side and
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+well yes our machines are incredible
+
+ align:start position:0%
+well yes our machines are incredible
+ 
+
+ align:start position:0%
+well yes our machines are incredible
+creations and they have made it possible
+
+ align:start position:0%
+creations and they have made it possible
+ 
+
+ align:start position:0%
+creations and they have made it possible
+for us to survive but we have to be
+
+ align:start position:0%
+for us to survive but we have to be
+ 
+
+ align:start position:0%
+for us to survive but we have to be
+aware that they need they need to be
+
+ align:start position:0%
+aware that they need they need to be
+ 
+
+ align:start position:0%
+aware that they need they need to be
+controlled we need to understand them we
+
+ align:start position:0%
+controlled we need to understand them we
+ 
+
+ align:start position:0%
+controlled we need to understand them we
+have to understand their impacts and we
+
+ align:start position:0%
+have to understand their impacts and we
+ 
+
+ align:start position:0%
+have to understand their impacts and we
+can't just expect to keep using them
+
+ align:start position:0%
+can't just expect to keep using them
+ 
+
+ align:start position:0%
+can't just expect to keep using them
+without thinking that uh you know there
+
+ align:start position:0%
+without thinking that uh you know there
+ 
+
+ align:start position:0%
+without thinking that uh you know there
+going to be some costs there are costs
+
+ align:start position:0%
+going to be some costs there are costs
+ 
+
+ align:start position:0%
+going to be some costs there are costs
+and that's what he's
+
+ align:start position:0%
+and that's what he's
+ 
+
+ align:start position:0%
+and that's what he's
+uh okay so the three points U as Laur
+
+ align:start position:0%
+uh okay so the three points U as Laur
+ 
+
+ align:start position:0%
+uh okay so the three points U as Laur
+mentioned uh machines that
+
+ align:start position:0%
+mentioned uh machines that
+ 
+
+ align:start position:0%
+mentioned uh machines that
+learn machines that reproduce themselves
+
+ align:start position:0%
+learn machines that reproduce themselves
+ 
+
+ align:start position:0%
+learn machines that reproduce themselves
+are two
+
+ align:start position:0%
+are two
+ 
+
+ align:start position:0%
+are two
+concepts and uh machines that perform
+
+ align:start position:0%
+concepts and uh machines that perform
+ 
+
+ align:start position:0%
+concepts and uh machines that perform
+coordinately with man these are his key
+
+ align:start position:0%
+coordinately with man these are his key
+ 
+
+ align:start position:0%
+coordinately with man these are his key
+points of uh uh
+
+ align:start position:0%
+points of uh uh
+ 
+
+ align:start position:0%
+points of uh uh
+discussion what does learning imply in
+
+ align:start position:0%
+discussion what does learning imply in
+ 
+
+ align:start position:0%
+discussion what does learning imply in
+the way we usually use the
+
+ align:start position:0%
+the way we usually use the
+ 
+
+ align:start position:0%
+the way we usually use the
+word in terms of uh
+
+ align:start position:0%
+word in terms of uh
+ 
+
+ align:start position:0%
+word in terms of uh
+mental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+activity I mean don't we normally think
+
+ align:start position:0%
+activity I mean don't we normally think
+ 
+
+ align:start position:0%
+activity I mean don't we normally think
+of learning as some kind of mental
+
+ align:start position:0%
+of learning as some kind of mental
+ 
+
+ align:start position:0%
+of learning as some kind of mental
+activity certainly in in the case of the
+
+ align:start position:0%
+activity certainly in in the case of the
+ 
+
+ align:start position:0%
+activity certainly in in the case of the
+individual don't we I mean you're
+
+ align:start position:0%
+individual don't we I mean you're
+ 
+
+ align:start position:0%
+individual don't we I mean you're
+learning you're taking 1801 or 801 or
+
+ align:start position:0%
+learning you're taking 1801 or 801 or
+ 
+
+ align:start position:0%
+learning you're taking 1801 or 801 or
+802 or whatever you're taking uh I mean
+
+ align:start position:0%
+802 or whatever you're taking uh I mean
+ 
+
+ align:start position:0%
+802 or whatever you're taking uh I mean
+your learning is up here isn't it
+
+ align:start position:0%
+your learning is up here isn't it
+ 
+
+ align:start position:0%
+your learning is up here isn't it
+so what kind of stretch is it to say
+
+ align:start position:0%
+so what kind of stretch is it to say
+ 
+
+ align:start position:0%
+so what kind of stretch is it to say
+that you know there's this thing called
+
+ align:start position:0%
+that you know there's this thing called
+ 
+
+ align:start position:0%
+that you know there's this thing called
+philogenetic
+
+ align:start position:0%
+philogenetic
+ 
+
+ align:start position:0%
+philogenetic
+learning I think maybe he's referring to
+
+ align:start position:0%
+learning I think maybe he's referring to
+ 
+
+ align:start position:0%
+learning I think maybe he's referring to
+the type of learning um where like the
+
+ align:start position:0%
+the type of learning um where like the
+ 
+
+ align:start position:0%
+the type of learning um where like the
+knowledge is taken on persists in to
+
+ align:start position:0%
+knowledge is taken on persists in to
+ 
+
+ align:start position:0%
+knowledge is taken on persists in to
+like future Generations because what we
+
+ align:start position:0%
+like future Generations because what we
+ 
+
+ align:start position:0%
+like future Generations because what we
+learn as individuals unless we somehow
+
+ align:start position:0%
+learn as individuals unless we somehow
+ 
+
+ align:start position:0%
+learn as individuals unless we somehow
+have an impact on society is kind of
+
+ align:start position:0%
+have an impact on society is kind of
+ 
+
+ align:start position:0%
+have an impact on society is kind of
+irrelevant because eventually if it's
+
+ align:start position:0%
+irrelevant because eventually if it's
+ 
+
+ align:start position:0%
+irrelevant because eventually if it's
+just in our minds we're going to die and
+
+ align:start position:0%
+just in our minds we're going to die and
+ 
+
+ align:start position:0%
+just in our minds we're going to die and
+there's going to be no like learning of
+
+ align:start position:0%
+there's going to be no like learning of
+ 
+
+ align:start position:0%
+there's going to be no like learning of
+the species so it's what we learn as a
+
+ align:start position:0%
+the species so it's what we learn as a
+ 
+
+ align:start position:0%
+the species so it's what we learn as a
+species and what we communicate to
+
+ align:start position:0%
+species and what we communicate to
+ 
+
+ align:start position:0%
+species and what we communicate to
+others and gets passed on I guess that
+
+ align:start position:0%
+others and gets passed on I guess that
+ 
+
+ align:start position:0%
+others and gets passed on I guess that
+he's talking about in the sense of like
+
+ align:start position:0%
+he's talking about in the sense of like
+ 
+
+ align:start position:0%
+he's talking about in the sense of like
+philogenetic learning okay there are a
+
+ align:start position:0%
+philogenetic learning okay there are a
+ 
+
+ align:start position:0%
+philogenetic learning okay there are a
+lot of parallels here that you're you're
+
+ align:start position:0%
+lot of parallels here that you're you're
+ 
+
+ align:start position:0%
+lot of parallels here that you're you're
+bringing up uh yes
+
+ align:start position:0%
+bringing up uh yes
+ 
+
+ align:start position:0%
+bringing up uh yes
+Craig like in like in a fum there's not
+
+ align:start position:0%
+Craig like in like in a fum there's not
+ 
+
+ align:start position:0%
+Craig like in like in a fum there's not
+one spe one entity that's learning it's
+
+ align:start position:0%
+one spe one entity that's learning it's
+ 
+
+ align:start position:0%
+one spe one entity that's learning it's
+kind of taken as a whole class kind of
+
+ align:start position:0%
+kind of taken as a whole class kind of
+ 
+
+ align:start position:0%
+kind of taken as a whole class kind of
+Shifting towards the towards new trend
+
+ align:start position:0%
+Shifting towards the towards new trend
+ 
+
+ align:start position:0%
+Shifting towards the towards new trend
+and so there's not there it's not like
+
+ align:start position:0%
+and so there's not there it's not like
+ 
+
+ align:start position:0%
+and so there's not there it's not like
+something's actually getting smarter
+
+ align:start position:0%
+something's actually getting smarter
+ 
+
+ align:start position:0%
+something's actually getting smarter
+it's just through trial and a that okay
+
+ align:start position:0%
+it's just through trial and a that okay
+ 
+
+ align:start position:0%
+it's just through trial and a that okay
+mutations are working better it sort of
+
+ align:start position:0%
+mutations are working better it sort of
+ 
+
+ align:start position:0%
+mutations are working better it sort of
+goes back to the ship metaphor you know
+
+ align:start position:0%
+goes back to the ship metaphor you know
+ 
+
+ align:start position:0%
+goes back to the ship metaphor you know
+somebody learned how to make a very
+
+ align:start position:0%
+somebody learned how to make a very
+ 
+
+ align:start position:0%
+somebody learned how to make a very
+complicated clipper ship that you know
+
+ align:start position:0%
+complicated clipper ship that you know
+ 
+
+ align:start position:0%
+complicated clipper ship that you know
+you can send out across the oceans and
+
+ align:start position:0%
+you can send out across the oceans and
+ 
+
+ align:start position:0%
+you can send out across the oceans and
+uh go off to
+
+ align:start position:0%
+uh go off to
+ 
+
+ align:start position:0%
+uh go off to
+wherever uh that learning process some
+
+ align:start position:0%
+wherever uh that learning process some
+ 
+
+ align:start position:0%
+wherever uh that learning process some
+how got
+
+ align:start position:0%
+how got
+ 
+
+ align:start position:0%
+how got
+expressed in the physical object of the
+
+ align:start position:0%
+expressed in the physical object of the
+ 
+
+ align:start position:0%
+expressed in the physical object of the
+ship the ship is a kind of a A Treatise
+
+ align:start position:0%
+ship the ship is a kind of a A Treatise
+ 
+
+ align:start position:0%
+ship the ship is a kind of a A Treatise
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+will of based on the learning of many
+
+ align:start position:0%
+will of based on the learning of many
+ 
+
+ align:start position:0%
+will of based on the learning of many
+many different individuals that went
+
+ align:start position:0%
+many different individuals that went
+ 
+
+ align:start position:0%
+many different individuals that went
+into the creation of this this very
+
+ align:start position:0%
+into the creation of this this very
+ 
+
+ align:start position:0%
+into the creation of this this very
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+organism Charles I think the learning
+
+ align:start position:0%
+organism Charles I think the learning
+ 
+
+ align:start position:0%
+organism Charles I think the learning
+that that he's referring to here has
+
+ align:start position:0%
+that that he's referring to here has
+ 
+
+ align:start position:0%
+that that he's referring to here has
+more to do with the learning of babies
+
+ align:start position:0%
+more to do with the learning of babies
+ 
+
+ align:start position:0%
+more to do with the learning of babies
+than the learning that we do in school
+
+ align:start position:0%
+than the learning that we do in school
+ 
+
+ align:start position:0%
+than the learning that we do in school
+like now like for babies just getting to
+
+ align:start position:0%
+like now like for babies just getting to
+ 
+
+ align:start position:0%
+like now like for babies just getting to
+know the world it's like they'll try
+
+ align:start position:0%
+know the world it's like they'll try
+ 
+
+ align:start position:0%
+know the world it's like they'll try
+something and like that's where the
+
+ align:start position:0%
+something and like that's where the
+ 
+
+ align:start position:0%
+something and like that's where the
+parents role is it's like if they do
+
+ align:start position:0%
+parents role is it's like if they do
+ 
+
+ align:start position:0%
+parents role is it's like if they do
+something that's they're not supposed to
+
+ align:start position:0%
+something that's they're not supposed to
+ 
+
+ align:start position:0%
+something that's they're not supposed to
+do then they get I guess they may get
+
+ align:start position:0%
+do then they get I guess they may get
+ 
+
+ align:start position:0%
+do then they get I guess they may get
+punished and then so they know by trial
+
+ align:start position:0%
+punished and then so they know by trial
+ 
+
+ align:start position:0%
+punished and then so they know by trial
+error what not to do and what you can do
+
+ align:start position:0%
+error what not to do and what you can do
+ 
+
+ align:start position:0%
+error what not to do and what you can do
+and so in terms of like a in terms of
+
+ align:start position:0%
+and so in terms of like a in terms of
+ 
+
+ align:start position:0%
+and so in terms of like a in terms of
+like a whole race or like whole species
+
+ align:start position:0%
+like a whole race or like whole species
+ 
+
+ align:start position:0%
+like a whole race or like whole species
+if you think about every single
+
+ align:start position:0%
+if you think about every single
+ 
+
+ align:start position:0%
+if you think about every single
+individual as a new idea then you have
+
+ align:start position:0%
+individual as a new idea then you have
+ 
+
+ align:start position:0%
+individual as a new idea then you have
+all these new ideas that like they're
+
+ align:start position:0%
+all these new ideas that like they're
+ 
+
+ align:start position:0%
+all these new ideas that like they're
+just trying to figure their way around
+
+ align:start position:0%
+just trying to figure their way around
+ 
+
+ align:start position:0%
+just trying to figure their way around
+the world and whichever new ideas don't
+
+ align:start position:0%
+the world and whichever new ideas don't
+ 
+
+ align:start position:0%
+the world and whichever new ideas don't
+work don't get passed on and the new
+
+ align:start position:0%
+work don't get passed on and the new
+ 
+
+ align:start position:0%
+work don't get passed on and the new
+ideas that do work become like become
+
+ align:start position:0%
+ideas that do work become like become
+ 
+
+ align:start position:0%
+ideas that do work become like become
+like just knowledge right like you know
+
+ align:start position:0%
+like just knowledge right like you know
+ 
+
+ align:start position:0%
+like just knowledge right like you know
+it's right and then so you follow it's
+
+ align:start position:0%
+it's right and then so you follow it's
+ 
+
+ align:start position:0%
+it's right and then so you follow it's
+kind of like science you try this it's
+
+ align:start position:0%
+kind of like science you try this it's
+ 
+
+ align:start position:0%
+kind of like science you try this it's
+not right you try this this is right
+
+ align:start position:0%
+not right you try this this is right
+ 
+
+ align:start position:0%
+not right you try this this is right
+then I take my next step further and the
+
+ align:start position:0%
+then I take my next step further and the
+ 
+
+ align:start position:0%
+then I take my next step further and the
+next step further in this sense would
+
+ align:start position:0%
+next step further in this sense would
+ 
+
+ align:start position:0%
+next step further in this sense would
+just be the yeah
+
+ align:start position:0%
+just be the yeah
+ 
+
+ align:start position:0%
+just be the yeah
+uh any other yes Devin we can raise the
+
+ align:start position:0%
+uh any other yes Devin we can raise the
+ 
+
+ align:start position:0%
+uh any other yes Devin we can raise the
+level of abstraction though and we can
+
+ align:start position:0%
+level of abstraction though and we can
+ 
+
+ align:start position:0%
+level of abstraction though and we can
+as in any field of engineering draw a
+
+ align:start position:0%
+as in any field of engineering draw a
+ 
+
+ align:start position:0%
+as in any field of engineering draw a
+black box around anything whether it be
+
+ align:start position:0%
+black box around anything whether it be
+ 
+
+ align:start position:0%
+black box around anything whether it be
+a human being or a society or whatever
+
+ align:start position:0%
+a human being or a society or whatever
+ 
+
+ align:start position:0%
+a human being or a society or whatever
+you want and you know there's that
+
+ align:start position:0%
+you want and you know there's that
+ 
+
+ align:start position:0%
+you want and you know there's that
+there's that adage that the definition
+
+ align:start position:0%
+there's that adage that the definition
+ 
+
+ align:start position:0%
+there's that adage that the definition
+of irrationality is continually doing
+
+ align:start position:0%
+of irrationality is continually doing
+ 
+
+ align:start position:0%
+of irrationality is continually doing
+the same thing expecting different
+
+ align:start position:0%
+the same thing expecting different
+ 
+
+ align:start position:0%
+the same thing expecting different
+results so when you think of something
+
+ align:start position:0%
+results so when you think of something
+ 
+
+ align:start position:0%
+results so when you think of something
+like a function which Maps a bunch of
+
+ align:start position:0%
+like a function which Maps a bunch of
+ 
+
+ align:start position:0%
+like a function which Maps a bunch of
+inputs to a bunch of outputs no matter
+
+ align:start position:0%
+inputs to a bunch of outputs no matter
+ 
+
+ align:start position:0%
+inputs to a bunch of outputs no matter
+what you do you always give the same
+
+ align:start position:0%
+what you do you always give the same
+ 
+
+ align:start position:0%
+what you do you always give the same
+it's always going to give you the same
+
+ align:start position:0%
+it's always going to give you the same
+ 
+
+ align:start position:0%
+it's always going to give you the same
+result but the difference in any kind of
+
+ align:start position:0%
+result but the difference in any kind of
+ 
+
+ align:start position:0%
+result but the difference in any kind of
+Learning System whether it be a film or
+
+ align:start position:0%
+Learning System whether it be a film or
+ 
+
+ align:start position:0%
+Learning System whether it be a film or
+an individual is that as you give it a
+
+ align:start position:0%
+an individual is that as you give it a
+ 
+
+ align:start position:0%
+an individual is that as you give it a
+Time series you know you throw all this
+
+ align:start position:0%
+Time series you know you throw all this
+ 
+
+ align:start position:0%
+Time series you know you throw all this
+data information experiences at it it
+
+ align:start position:0%
+data information experiences at it it
+ 
+
+ align:start position:0%
+data information experiences at it it
+will slowly fine-tune its performance
+
+ align:start position:0%
+will slowly fine-tune its performance
+ 
+
+ align:start position:0%
+will slowly fine-tune its performance
+over time so that the outputs will
+
+ align:start position:0%
+over time so that the outputs will
+ 
+
+ align:start position:0%
+over time so that the outputs will
+change and hopefully stabilize and
+
+ align:start position:0%
+change and hopefully stabilize and
+ 
+
+ align:start position:0%
+change and hopefully stabilize and
+that's where the learning comes in and I
+
+ align:start position:0%
+that's where the learning comes in and I
+ 
+
+ align:start position:0%
+that's where the learning comes in and I
+think what he's getting out there is
+
+ align:start position:0%
+think what he's getting out there is
+ 
+
+ align:start position:0%
+think what he's getting out there is
+that that same kind of idea of a black
+
+ align:start position:0%
+that that same kind of idea of a black
+ 
+
+ align:start position:0%
+that that same kind of idea of a black
+box with input and output where the
+
+ align:start position:0%
+box with input and output where the
+ 
+
+ align:start position:0%
+box with input and output where the
+output is being fine-tuned as a result
+
+ align:start position:0%
+output is being fine-tuned as a result
+ 
+
+ align:start position:0%
+output is being fine-tuned as a result
+of the the relationships between the
+
+ align:start position:0%
+of the the relationships between the
+ 
+
+ align:start position:0%
+of the the relationships between the
+inputs is a general idea it's not just
+
+ align:start position:0%
+inputs is a general idea it's not just
+ 
+
+ align:start position:0%
+inputs is a general idea it's not just
+about people and it it it scales
+
+ align:start position:0%
+about people and it it it scales
+ 
+
+ align:start position:0%
+about people and it it it scales
+infinitely well and that's one of the
+
+ align:start position:0%
+infinitely well and that's one of the
+ 
+
+ align:start position:0%
+infinitely well and that's one of the
+the remarkable things about cybernetics
+
+ align:start position:0%
+the remarkable things about cybernetics
+ 
+
+ align:start position:0%
+the remarkable things about cybernetics
+as a field yeah yeah well put yeah yeah
+
+ align:start position:0%
+as a field yeah yeah well put yeah yeah
+ 
+
+ align:start position:0%
+as a field yeah yeah well put yeah yeah
+there there's this this this process of
+
+ align:start position:0%
+there there's this this this process of
+ 
+
+ align:start position:0%
+there there's this this this process of
+learning that is iterative and all these
+
+ align:start position:0%
+learning that is iterative and all these
+ 
+
+ align:start position:0%
+learning that is iterative and all these
+iterative uh the the the power of
+
+ align:start position:0%
+iterative uh the the the power of
+ 
+
+ align:start position:0%
+iterative uh the the the power of
+darwinian natural selection as an idea
+
+ align:start position:0%
+darwinian natural selection as an idea
+ 
+
+ align:start position:0%
+darwinian natural selection as an idea
+is this constant con this concept of the
+
+ align:start position:0%
+is this constant con this concept of the
+ 
+
+ align:start position:0%
+is this constant con this concept of the
+constant input and output which in the
+
+ align:start position:0%
+constant input and output which in the
+ 
+
+ align:start position:0%
+constant input and output which in the
+case of an individual organism is simply
+
+ align:start position:0%
+case of an individual organism is simply
+ 
+
+ align:start position:0%
+case of an individual organism is simply
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+reproduction reproduction passing on of
+
+ align:start position:0%
+reproduction reproduction passing on of
+ 
+
+ align:start position:0%
+reproduction reproduction passing on of
+uh certain kinds of uh traits remember
+
+ align:start position:0%
+uh certain kinds of uh traits remember
+ 
+
+ align:start position:0%
+uh certain kinds of uh traits remember
+Unity of type and also the fact that
+
+ align:start position:0%
+Unity of type and also the fact that
+ 
+
+ align:start position:0%
+Unity of type and also the fact that
+there is variation which these two facts
+
+ align:start position:0%
+there is variation which these two facts
+ 
+
+ align:start position:0%
+there is variation which these two facts
+uh uh weiner mentions in in the book as
+
+ align:start position:0%
+uh uh weiner mentions in in the book as
+ 
+
+ align:start position:0%
+uh uh weiner mentions in in the book as
+Salient points in evolution and so u in
+
+ align:start position:0%
+Salient points in evolution and so u in
+ 
+
+ align:start position:0%
+Salient points in evolution and so u in
+philogyny the expression of the learning
+
+ align:start position:0%
+philogyny the expression of the learning
+ 
+
+ align:start position:0%
+philogyny the expression of the learning
+takes what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well physical features of the organism I
+
+ align:start position:0%
+well physical features of the organism I
+ 
+
+ align:start position:0%
+well physical features of the organism I
+mean the uh the adaptability of uh say
+
+ align:start position:0%
+mean the uh the adaptability of uh say
+ 
+
+ align:start position:0%
+mean the uh the adaptability of uh say
+an organ an
+
+ align:start position:0%
+an organ an
+ 
+
+ align:start position:0%
+an organ an
+organism in terms of the eye eyesight I
+
+ align:start position:0%
+organism in terms of the eye eyesight I
+ 
+
+ align:start position:0%
+organism in terms of the eye eyesight I
+mean that's so when he when he's talking
+
+ align:start position:0%
+mean that's so when he when he's talking
+ 
+
+ align:start position:0%
+mean that's so when he when he's talking
+about phenetic learning he's really
+
+ align:start position:0%
+about phenetic learning he's really
+ 
+
+ align:start position:0%
+about phenetic learning he's really
+talking about that that kind of process
+
+ align:start position:0%
+talking about that that kind of process
+ 
+
+ align:start position:0%
+talking about that that kind of process
+that delivers a a a higher and higher
+
+ align:start position:0%
+that delivers a a a higher and higher
+ 
+
+ align:start position:0%
+that delivers a a a higher and higher
+functioning eye and its interaction with
+
+ align:start position:0%
+functioning eye and its interaction with
+ 
+
+ align:start position:0%
+functioning eye and its interaction with
+the environment becomes uh more and more
+
+ align:start position:0%
+the environment becomes uh more and more
+ 
+
+ align:start position:0%
+the environment becomes uh more and more
+refined and so it's a physical
+
+ align:start position:0%
+refined and so it's a physical
+ 
+
+ align:start position:0%
+refined and so it's a physical
+expression back to the ship it's it's an
+
+ align:start position:0%
+expression back to the ship it's it's an
+ 
+
+ align:start position:0%
+expression back to the ship it's it's an
+expression of of of physical
+
+ align:start position:0%
+expression of of of physical
+ 
+
+ align:start position:0%
+expression of of of physical
+interaction with
+
+ align:start position:0%
+interaction with
+ 
+
+ align:start position:0%
+interaction with
+environment in a a space a
+
+ align:start position:0%
+environment in a a space a
+ 
+
+ align:start position:0%
+environment in a a space a
+niche and higher higher levels of
+
+ align:start position:0%
+niche and higher higher levels of
+ 
+
+ align:start position:0%
+niche and higher higher levels of
+performance there would be in wier's
+
+ align:start position:0%
+performance there would be in wier's
+ 
+
+ align:start position:0%
+performance there would be in wier's
+terms philogenetic learning this is what
+
+ align:start position:0%
+terms philogenetic learning this is what
+ 
+
+ align:start position:0%
+terms philogenetic learning this is what
+delivers these complex organisms that
+
+ align:start position:0%
+delivers these complex organisms that
+ 
+
+ align:start position:0%
+delivers these complex organisms that
+are adapted to their
+
+ align:start position:0%
+are adapted to their
+ 
+
+ align:start position:0%
+are adapted to their
+environments okay so all this is based
+
+ align:start position:0%
+environments okay so all this is based
+ 
+
+ align:start position:0%
+environments okay so all this is based
+on this this kind of darwinian iteration
+
+ align:start position:0%
+on this this kind of darwinian iteration
+ 
+
+ align:start position:0%
+on this this kind of darwinian iteration
+process of U basically information out
+
+ align:start position:0%
+process of U basically information out
+ 
+
+ align:start position:0%
+process of U basically information out
+information in and information out um
+
+ align:start position:0%
+information in and information out um
+ 
+
+ align:start position:0%
+information in and information out um
+and a certain amount of change taking
+
+ align:start position:0%
+and a certain amount of change taking
+ 
+
+ align:start position:0%
+and a certain amount of change taking
+place and the new
+
+ align:start position:0%
+place and the new
+ 
+
+ align:start position:0%
+place and the new
+entity that has inherited the
+
+ align:start position:0%
+entity that has inherited the
+ 
+
+ align:start position:0%
+entity that has inherited the
+information of the last the parent
+
+ align:start position:0%
+information of the last the parent
+ 
+
+ align:start position:0%
+information of the last the parent
+entity either functions better uh or it
+
+ align:start position:0%
+entity either functions better uh or it
+ 
+
+ align:start position:0%
+entity either functions better uh or it
+doesn't but uh it's it's basically going
+
+ align:start position:0%
+doesn't but uh it's it's basically going
+ 
+
+ align:start position:0%
+doesn't but uh it's it's basically going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+tested each generation is going to be
+
+ align:start position:0%
+tested each generation is going to be
+ 
+
+ align:start position:0%
+tested each generation is going to be
+tested for the ability to uh survive and
+
+ align:start position:0%
+tested for the ability to uh survive and
+ 
+
+ align:start position:0%
+tested for the ability to uh survive and
+so this is a model that he's using for
+
+ align:start position:0%
+so this is a model that he's using for
+ 
+
+ align:start position:0%
+so this is a model that he's using for
+for uh machine learning too when he
+
+ align:start position:0%
+for uh machine learning too when he
+ 
+
+ align:start position:0%
+for uh machine learning too when he
+talks about machine
+
+ align:start position:0%
+talks about machine
+ 
+
+ align:start position:0%
+talks about machine
+learning and he talks about as or
+
+ align:start position:0%
+learning and he talks about as or
+ 
+
+ align:start position:0%
+learning and he talks about as or
+mentioned uh in terms of
+
+ align:start position:0%
+mentioned uh in terms of
+ 
+
+ align:start position:0%
+mentioned uh in terms of
+tic-tac-toe these little systems that uh
+
+ align:start position:0%
+tic-tac-toe these little systems that uh
+ 
+
+ align:start position:0%
+tic-tac-toe these little systems that uh
+can be uh played with a with a a
+
+ align:start position:0%
+can be uh played with a with a a
+ 
+
+ align:start position:0%
+can be uh played with a with a a
+computer and can actually be
+
+ align:start position:0%
+computer and can actually be
+ 
+
+ align:start position:0%
+computer and can actually be
+U uh subject to
+
+ align:start position:0%
+U uh subject to
+ 
+
+ align:start position:0%
+U uh subject to
+Improvement they get better
+
+ align:start position:0%
+Improvement they get better
+ 
+
+ align:start position:0%
+Improvement they get better
+and so there's a what he calls a
+
+ align:start position:0%
+and so there's a what he calls a
+ 
+
+ align:start position:0%
+and so there's a what he calls a
+Criterion of Merit that
+
+ align:start position:0%
+Criterion of Merit that
+ 
+
+ align:start position:0%
+Criterion of Merit that
+actually is a uh element in the
+
+ align:start position:0%
+actually is a uh element in the
+ 
+
+ align:start position:0%
+actually is a uh element in the
+selection process and as this uh
+
+ align:start position:0%
+selection process and as this uh
+ 
+
+ align:start position:0%
+selection process and as this uh
+improves it becomes uh the the the form
+
+ align:start position:0%
+improves it becomes uh the the the form
+ 
+
+ align:start position:0%
+improves it becomes uh the the the form
+that gets uh
+
+ align:start position:0%
+that gets uh
+ 
+
+ align:start position:0%
+that gets uh
+transmitted and so this this sort of
+
+ align:start position:0%
+transmitted and so this this sort of
+ 
+
+ align:start position:0%
+transmitted and so this this sort of
+process is uh is is
+
+ align:start position:0%
+process is uh is is
+ 
+
+ align:start position:0%
+process is uh is is
+key all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so all right and he also brings up this
+
+ align:start position:0%
+so all right and he also brings up this
+ 
+
+ align:start position:0%
+so all right and he also brings up this
+question of uh how
+
+ align:start position:0%
+question of uh how
+ 
+
+ align:start position:0%
+question of uh how
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+are bio our biological or organisms and
+
+ align:start position:0%
+are bio our biological or organisms and
+ 
+
+ align:start position:0%
+are bio our biological or organisms and
+uh mechanical
+
+ align:start position:0%
+uh mechanical
+ 
+
+ align:start position:0%
+uh mechanical
+processes and his uh one of his one of
+
+ align:start position:0%
+processes and his uh one of his one of
+ 
+
+ align:start position:0%
+processes and his uh one of his one of
+his major points is that U at the level
+
+ align:start position:0%
+his major points is that U at the level
+ 
+
+ align:start position:0%
+his major points is that U at the level
+of reproduction
+
+ align:start position:0%
+of reproduction
+ 
+
+ align:start position:0%
+of reproduction
+what is human reproduction what is any
+
+ align:start position:0%
+what is human reproduction what is any
+ 
+
+ align:start position:0%
+what is human reproduction what is any
+kind of biological
+
+ align:start position:0%
+kind of biological
+ 
+
+ align:start position:0%
+kind of biological
+reproduction it's I mean of course he
+
+ align:start position:0%
+reproduction it's I mean of course he
+ 
+
+ align:start position:0%
+reproduction it's I mean of course he
+knows a lot more you can see you know
+
+ align:start position:0%
+knows a lot more you can see you know
+ 
+
+ align:start position:0%
+knows a lot more you can see you know
+what's happened mle has been there you
+
+ align:start position:0%
+what's happened mle has been there you
+ 
+
+ align:start position:0%
+what's happened mle has been there you
+know and and you know he's way down the
+
+ align:start position:0%
+know and and you know he's way down the
+ 
+
+ align:start position:0%
+know and and you know he's way down the
+line now here from
+
+ align:start position:0%
+line now here from
+ 
+
+ align:start position:0%
+line now here from
+Darwin uh it's well known that uh
+
+ align:start position:0%
+Darwin uh it's well known that uh
+ 
+
+ align:start position:0%
+Darwin uh it's well known that uh
+there's a whole process taking place
+
+ align:start position:0%
+there's a whole process taking place
+ 
+
+ align:start position:0%
+there's a whole process taking place
+here and for all intents and purposes
+
+ align:start position:0%
+here and for all intents and purposes
+ 
+
+ align:start position:0%
+here and for all intents and purposes
+it's primarily a process of uh pattern
+
+ align:start position:0%
+it's primarily a process of uh pattern
+ 
+
+ align:start position:0%
+it's primarily a process of uh pattern
+and pattern superimposition on other
+
+ align:start position:0%
+and pattern superimposition on other
+ 
+
+ align:start position:0%
+and pattern superimposition on other
+uh and and the creation of new patterns
+
+ align:start position:0%
+uh and and the creation of new patterns
+ 
+
+ align:start position:0%
+uh and and the creation of new patterns
+from old patterns so he says here on
+
+ align:start position:0%
+from old patterns so he says here on
+ 
+
+ align:start position:0%
+from old patterns so he says here on
+page uh
+
+ align:start position:0%
+page uh
+ 
+
+ align:start position:0%
+page uh
+28 behind all this fantastically complex
+
+ align:start position:0%
+28 behind all this fantastically complex
+ 
+
+ align:start position:0%
+28 behind all this fantastically complex
+concatenation of processes he's talking
+
+ align:start position:0%
+concatenation of processes he's talking
+ 
+
+ align:start position:0%
+concatenation of processes he's talking
+about biological reproduction here lies
+
+ align:start position:0%
+about biological reproduction here lies
+ 
+
+ align:start position:0%
+about biological reproduction here lies
+one very simple fact that in the
+
+ align:start position:0%
+one very simple fact that in the
+ 
+
+ align:start position:0%
+one very simple fact that in the
+presence of a suitable nutritive
+
+ align:start position:0%
+presence of a suitable nutritive
+ 
+
+ align:start position:0%
+presence of a suitable nutritive
+nutritive uh medium of nucleic acids and
+
+ align:start position:0%
+nutritive uh medium of nucleic acids and
+ 
+
+ align:start position:0%
+nutritive uh medium of nucleic acids and
+amino acids a molecule of a gene
+
+ align:start position:0%
+amino acids a molecule of a gene
+ 
+
+ align:start position:0%
+amino acids a molecule of a gene
+consisting itself of a high specific
+
+ align:start position:0%
+consisting itself of a high specific
+ 
+
+ align:start position:0%
+consisting itself of a high specific
+combination of amino acids and nucleic
+
+ align:start position:0%
+combination of amino acids and nucleic
+ 
+
+ align:start position:0%
+combination of amino acids and nucleic
+acids can cause the medium to lay itself
+
+ align:start position:0%
+acids can cause the medium to lay itself
+ 
+
+ align:start position:0%
+acids can cause the medium to lay itself
+down into other molecules which either
+
+ align:start position:0%
+down into other molecules which either
+ 
+
+ align:start position:0%
+down into other molecules which either
+are molecules of the same gene or of
+
+ align:start position:0%
+are molecules of the same gene or of
+ 
+
+ align:start position:0%
+are molecules of the same gene or of
+other genes differing from it by
+
+ align:start position:0%
+other genes differing from it by
+ 
+
+ align:start position:0%
+other genes differing from it by
+relatively slight
+
+ align:start position:0%
+relatively slight
+ 
+
+ align:start position:0%
+relatively slight
+variations so there's a basically a
+
+ align:start position:0%
+variations so there's a basically a
+ 
+
+ align:start position:0%
+variations so there's a basically a
+pattern uh process of repetition and
+
+ align:start position:0%
+pattern uh process of repetition and
+ 
+
+ align:start position:0%
+pattern uh process of repetition and
+replication at the core at the center of
+
+ align:start position:0%
+replication at the core at the center of
+ 
+
+ align:start position:0%
+replication at the core at the center of
+biological
+
+ align:start position:0%
+biological
+ 
+
+ align:start position:0%
+biological
+reproduction what do you think think of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that sound like
+
+ align:start position:0%
+that sound like
+ 
+
+ align:start position:0%
+that sound like
+machine well well you know there are
+
+ align:start position:0%
+machine well well you know there are
+ 
+
+ align:start position:0%
+machine well well you know there are
+other things in the book that make us
+
+ align:start position:0%
+other things in the book that make us
+ 
+
+ align:start position:0%
+other things in the book that make us
+you know sound like uh we should be
+
+ align:start position:0%
+you know sound like uh we should be
+ 
+
+ align:start position:0%
+you know sound like uh we should be
+Beyond machines too but you know at at
+
+ align:start position:0%
+Beyond machines too but you know at at
+ 
+
+ align:start position:0%
+Beyond machines too but you know at at
+the heart at the heart you know we we
+
+ align:start position:0%
+the heart at the heart you know we we
+ 
+
+ align:start position:0%
+the heart at the heart you know we we
+again this is in the spirit of Norbert
+
+ align:start position:0%
+again this is in the spirit of Norbert
+ 
+
+ align:start position:0%
+again this is in the spirit of Norbert
+weiner we we need to put aside our our
+
+ align:start position:0%
+weiner we we need to put aside our our
+ 
+
+ align:start position:0%
+weiner we we need to put aside our our
+biases and our and you know if we really
+
+ align:start position:0%
+biases and our and you know if we really
+ 
+
+ align:start position:0%
+biases and our and you know if we really
+want to understand something it's not to
+
+ align:start position:0%
+want to understand something it's not to
+ 
+
+ align:start position:0%
+want to understand something it's not to
+say that that's
+
+ align:start position:0%
+say that that's
+ 
+
+ align:start position:0%
+say that that's
+all but at least understand that at at
+
+ align:start position:0%
+all but at least understand that at at
+ 
+
+ align:start position:0%
+all but at least understand that at at
+the core that you know there are certain
+
+ align:start position:0%
+the core that you know there are certain
+ 
+
+ align:start position:0%
+the core that you know there are certain
+kinds of patterns and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similarities uh I mean we could say wow
+
+ align:start position:0%
+similarities uh I mean we could say wow
+ 
+
+ align:start position:0%
+similarities uh I mean we could say wow
+you know this is this is making us into
+
+ align:start position:0%
+you know this is this is making us into
+ 
+
+ align:start position:0%
+you know this is this is making us into
+let's let's just forget about this field
+
+ align:start position:0%
+let's let's just forget about this field
+ 
+
+ align:start position:0%
+let's let's just forget about this field
+go away and you know make better cars or
+
+ align:start position:0%
+go away and you know make better cars or
+ 
+
+ align:start position:0%
+go away and you know make better cars or
+something you know but here we are I
+
+ align:start position:0%
+something you know but here we are I
+ 
+
+ align:start position:0%
+something you know but here we are I
+don't I've never understood every time
+
+ align:start position:0%
+don't I've never understood every time
+ 
+
+ align:start position:0%
+don't I've never understood every time
+the seg I don't what's the problem with
+
+ align:start position:0%
+the seg I don't what's the problem with
+ 
+
+ align:start position:0%
+the seg I don't what's the problem with
+being a machine what's the where's the
+
+ align:start position:0%
+being a machine what's the where's the
+ 
+
+ align:start position:0%
+being a machine what's the where's the
+where's the real breakdown I mean I
+
+ align:start position:0%
+where's the real breakdown I mean I
+ 
+
+ align:start position:0%
+where's the real breakdown I mean I
+guess I'm pretty naive in that I didn't
+
+ align:start position:0%
+guess I'm pretty naive in that I didn't
+ 
+
+ align:start position:0%
+guess I'm pretty naive in that I didn't
+grow up in a religious household and I
+
+ align:start position:0%
+grow up in a religious household and I
+ 
+
+ align:start position:0%
+grow up in a religious household and I
+wasn't surrounded by religious people so
+
+ align:start position:0%
+wasn't surrounded by religious people so
+ 
+
+ align:start position:0%
+wasn't surrounded by religious people so
+for me it's hard for me to grasp exactly
+
+ align:start position:0%
+for me it's hard for me to grasp exactly
+ 
+
+ align:start position:0%
+for me it's hard for me to grasp exactly
+what what that influence means because
+
+ align:start position:0%
+what what that influence means because
+ 
+
+ align:start position:0%
+what what that influence means because
+if you're a machine you know there's
+
+ align:start position:0%
+if you're a machine you know there's
+ 
+
+ align:start position:0%
+if you're a machine you know there's
+still the human use of human beings
+
+ align:start position:0%
+still the human use of human beings
+ 
+
+ align:start position:0%
+still the human use of human beings
+you're not being devalued in any way I
+
+ align:start position:0%
+you're not being devalued in any way I
+ 
+
+ align:start position:0%
+you're not being devalued in any way I
+don't I don't see what I'm just curious
+
+ align:start position:0%
+don't I don't see what I'm just curious
+ 
+
+ align:start position:0%
+don't I don't see what I'm just curious
+to get other people's perspective on
+
+ align:start position:0%
+to get other people's perspective on
+ 
+
+ align:start position:0%
+to get other people's perspective on
+that good question good question well I
+
+ align:start position:0%
+that good question good question well I
+ 
+
+ align:start position:0%
+that good question good question well I
+think that um it's like the machines
+
+ align:start position:0%
+think that um it's like the machines
+ 
+
+ align:start position:0%
+think that um it's like the machines
+that we've all grown up knowing don't
+
+ align:start position:0%
+that we've all grown up knowing don't
+ 
+
+ align:start position:0%
+that we've all grown up knowing don't
+have a mind of their own and so they're
+
+ align:start position:0%
+have a mind of their own and so they're
+ 
+
+ align:start position:0%
+have a mind of their own and so they're
+mindless and like maybe if you can say
+
+ align:start position:0%
+mindless and like maybe if you can say
+ 
+
+ align:start position:0%
+mindless and like maybe if you can say
+that oh they function and they come
+
+ align:start position:0%
+that oh they function and they come
+ 
+
+ align:start position:0%
+that oh they function and they come
+alive but then if you say that they're
+
+ align:start position:0%
+alive but then if you say that they're
+ 
+
+ align:start position:0%
+alive but then if you say that they're
+alive their life is basically
+
+ align:start position:0%
+alive their life is basically
+ 
+
+ align:start position:0%
+alive their life is basically
+meaningless because it's it's hasn't got
+
+ align:start position:0%
+meaningless because it's it's hasn't got
+ 
+
+ align:start position:0%
+meaningless because it's it's hasn't got
+any freedom of its own and so like just
+
+ align:start position:0%
+any freedom of its own and so like just
+ 
+
+ align:start position:0%
+any freedom of its own and so like just
+I think it's just growing up with
+
+ align:start position:0%
+I think it's just growing up with
+ 
+
+ align:start position:0%
+I think it's just growing up with
+technology like that and you are afraid
+
+ align:start position:0%
+technology like that and you are afraid
+ 
+
+ align:start position:0%
+technology like that and you are afraid
+that if your life is just like that of a
+
+ align:start position:0%
+that if your life is just like that of a
+ 
+
+ align:start position:0%
+that if your life is just like that of a
+machine that we have today which are our
+
+ align:start position:0%
+machine that we have today which are our
+ 
+
+ align:start position:0%
+machine that we have today which are our
+machines are rather rudimentary then
+
+ align:start position:0%
+machines are rather rudimentary then
+ 
+
+ align:start position:0%
+machines are rather rudimentary then
+like our lives would just be meaningless
+
+ align:start position:0%
+like our lives would just be meaningless
+ 
+
+ align:start position:0%
+like our lives would just be meaningless
+and that's a that's like a pretty
+
+ align:start position:0%
+and that's a that's like a pretty
+ 
+
+ align:start position:0%
+and that's a that's like a pretty
+terrifying concept to Grass interesting
+
+ align:start position:0%
+terrifying concept to Grass interesting
+ 
+
+ align:start position:0%
+terrifying concept to Grass interesting
+good points yeah okay uh kind of going
+
+ align:start position:0%
+good points yeah okay uh kind of going
+ 
+
+ align:start position:0%
+good points yeah okay uh kind of going
+off that I think uh machines lack
+
+ align:start position:0%
+off that I think uh machines lack
+ 
+
+ align:start position:0%
+off that I think uh machines lack
+the like element of life I mean that's
+
+ align:start position:0%
+the like element of life I mean that's
+ 
+
+ align:start position:0%
+the like element of life I mean that's
+not obviously not a great way of saying
+
+ align:start position:0%
+not obviously not a great way of saying
+ 
+
+ align:start position:0%
+not obviously not a great way of saying
+it but they don't have
+
+ align:start position:0%
+it but they don't have
+ 
+
+ align:start position:0%
+it but they don't have
+uh they they're artificial there
+
+ align:start position:0%
+uh they they're artificial there
+ 
+
+ align:start position:0%
+uh they they're artificial there
+everything I in an ideal machine would
+
+ align:start position:0%
+everything I in an ideal machine would
+ 
+
+ align:start position:0%
+everything I in an ideal machine would
+give you this response all the time when
+
+ align:start position:0%
+give you this response all the time when
+ 
+
+ align:start position:0%
+give you this response all the time when
+you put this stimulus or give it this
+
+ align:start position:0%
+you put this stimulus or give it this
+ 
+
+ align:start position:0%
+you put this stimulus or give it this
+question or whatever it's going to give
+
+ align:start position:0%
+question or whatever it's going to give
+ 
+
+ align:start position:0%
+question or whatever it's going to give
+you the same thing each time for the
+
+ align:start position:0%
+you the same thing each time for the
+ 
+
+ align:start position:0%
+you the same thing each time for the
+same uh stimulus whereas a human I I say
+
+ align:start position:0%
+same uh stimulus whereas a human I I say
+ 
+
+ align:start position:0%
+same uh stimulus whereas a human I I say
+hi today you say hi tomorrow you say hey
+
+ align:start position:0%
+hi today you say hi tomorrow you say hey
+ 
+
+ align:start position:0%
+hi today you say hi tomorrow you say hey
+the next day you say hello it's got that
+
+ align:start position:0%
+the next day you say hello it's got that
+ 
+
+ align:start position:0%
+the next day you say hello it's got that
+degree of variability or one day if
+
+ align:start position:0%
+degree of variability or one day if
+ 
+
+ align:start position:0%
+degree of variability or one day if
+you're pissed off of you might ignore me
+
+ align:start position:0%
+you're pissed off of you might ignore me
+ 
+
+ align:start position:0%
+you're pissed off of you might ignore me
+and just blow me off completely and I
+
+ align:start position:0%
+and just blow me off completely and I
+ 
+
+ align:start position:0%
+and just blow me off completely and I
+think uh the idea of being a machine and
+
+ align:start position:0%
+think uh the idea of being a machine and
+ 
+
+ align:start position:0%
+think uh the idea of being a machine and
+taking away that Humanity of it is
+
+ align:start position:0%
+taking away that Humanity of it is
+ 
+
+ align:start position:0%
+taking away that Humanity of it is
+distasteful some people and that's why I
+
+ align:start position:0%
+distasteful some people and that's why I
+ 
+
+ align:start position:0%
+distasteful some people and that's why I
+don't think it necessarily has to do
+
+ align:start position:0%
+don't think it necessarily has to do
+ 
+
+ align:start position:0%
+don't think it necessarily has to do
+with religion it's just personally I
+
+ align:start position:0%
+with religion it's just personally I
+ 
+
+ align:start position:0%
+with religion it's just personally I
+wouldn't want to be so just set stone so
+
+ align:start position:0%
+wouldn't want to be so just set stone so
+ 
+
+ align:start position:0%
+wouldn't want to be so just set stone so
+artificial so you do this I do this you
+
+ align:start position:0%
+artificial so you do this I do this you
+ 
+
+ align:start position:0%
+artificial so you do this I do this you
+do this I do this you do this I do this
+
+ align:start position:0%
+do this I do this you do this I do this
+ 
+
+ align:start position:0%
+do this I do this you do this I do this
+I'd rather have I think it's more
+
+ align:start position:0%
+I'd rather have I think it's more
+ 
+
+ align:start position:0%
+I'd rather have I think it's more
+appealing to have the degree of
+
+ align:start position:0%
+appealing to have the degree of
+ 
+
+ align:start position:0%
+appealing to have the degree of
+variability rather than just uh I'm just
+
+ align:start position:0%
+variability rather than just uh I'm just
+ 
+
+ align:start position:0%
+variability rather than just uh I'm just
+going through my program this stimulus
+
+ align:start position:0%
+going through my program this stimulus
+ 
+
+ align:start position:0%
+going through my program this stimulus
+means I have these three options this
+
+ align:start position:0%
+means I have these three options this
+ 
+
+ align:start position:0%
+means I have these three options this
+one is this this one is this this I'll
+
+ align:start position:0%
+one is this this one is this this I'll
+ 
+
+ align:start position:0%
+one is this this one is this this I'll
+select this one rather than being able
+
+ align:start position:0%
+select this one rather than being able
+ 
+
+ align:start position:0%
+select this one rather than being able
+to do whatever I want with it good point
+
+ align:start position:0%
+to do whatever I want with it good point
+ 
+
+ align:start position:0%
+to do whatever I want with it good point
+yeah I think the problem religious
+
+ align:start position:0%
+yeah I think the problem religious
+ 
+
+ align:start position:0%
+yeah I think the problem religious
+people have with it is that essentially
+
+ align:start position:0%
+people have with it is that essentially
+ 
+
+ align:start position:0%
+people have with it is that essentially
+I think a lot of religions say that you
+
+ align:start position:0%
+I think a lot of religions say that you
+ 
+
+ align:start position:0%
+I think a lot of religions say that you
+know humans are not just a body they're
+
+ align:start position:0%
+know humans are not just a body they're
+ 
+
+ align:start position:0%
+know humans are not just a body they're
+body and a soul and when you can reduce
+
+ align:start position:0%
+body and a soul and when you can reduce
+ 
+
+ align:start position:0%
+body and a soul and when you can reduce
+a human down into all these little
+
+ align:start position:0%
+a human down into all these little
+ 
+
+ align:start position:0%
+a human down into all these little
+mechanical bits and that's all that it
+
+ align:start position:0%
+mechanical bits and that's all that it
+ 
+
+ align:start position:0%
+mechanical bits and that's all that it
+is it's kind of saying that humans don't
+
+ align:start position:0%
+is it's kind of saying that humans don't
+ 
+
+ align:start position:0%
+is it's kind of saying that humans don't
+have that extra spiritual bit that we're
+
+ align:start position:0%
+have that extra spiritual bit that we're
+ 
+
+ align:start position:0%
+have that extra spiritual bit that we're
+just purely machine and I think that's
+
+ align:start position:0%
+just purely machine and I think that's
+ 
+
+ align:start position:0%
+just purely machine and I think that's
+what starts to bother people because
+
+ align:start position:0%
+what starts to bother people because
+ 
+
+ align:start position:0%
+what starts to bother people because
+then they say do we have a conscience or
+
+ align:start position:0%
+then they say do we have a conscience or
+ 
+
+ align:start position:0%
+then they say do we have a conscience or
+is it all mechanical is there are we
+
+ align:start position:0%
+is it all mechanical is there are we
+ 
+
+ align:start position:0%
+is it all mechanical is there are we
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+like is there meaning in life as opposed
+
+ align:start position:0%
+like is there meaning in life as opposed
+ 
+
+ align:start position:0%
+like is there meaning in life as opposed
+to is it just some kind of iterative uh
+
+ align:start position:0%
+to is it just some kind of iterative uh
+ 
+
+ align:start position:0%
+to is it just some kind of iterative uh
+replicant uh process that uh has no
+
+ align:start position:0%
+replicant uh process that uh has no
+ 
+
+ align:start position:0%
+replicant uh process that uh has no
+deeper
+
+ align:start position:0%
+deeper
+ 
+
+ align:start position:0%
+deeper
+meaning and humans of
+
+ align:start position:0%
+meaning and humans of
+ 
+
+ align:start position:0%
+meaning and humans of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+they thirst for some you know for
+
+ align:start position:0%
+they thirst for some you know for
+ 
+
+ align:start position:0%
+they thirst for some you know for
+meaning in their lives
+
+ align:start position:0%
+meaning in their lives
+ 
+
+ align:start position:0%
+meaning in their lives
+but you know there may be ways in which
+
+ align:start position:0%
+but you know there may be ways in which
+ 
+
+ align:start position:0%
+but you know there may be ways in which
+you know these are I mean to say that at
+
+ align:start position:0%
+you know these are I mean to say that at
+ 
+
+ align:start position:0%
+you know these are I mean to say that at
+the core things are
+
+ align:start position:0%
+the core things are
+ 
+
+ align:start position:0%
+the core things are
+mechanical is not necessarily to take
+
+ align:start position:0%
+mechanical is not necessarily to take
+ 
+
+ align:start position:0%
+mechanical is not necessarily to take
+away you know the the ability of people
+
+ align:start position:0%
+away you know the the ability of people
+ 
+
+ align:start position:0%
+away you know the the ability of people
+to find Value in their their lives and
+
+ align:start position:0%
+to find Value in their their lives and
+ 
+
+ align:start position:0%
+to find Value in their their lives and
+you know we're very complicated
+
+ align:start position:0%
+you know we're very complicated
+ 
+
+ align:start position:0%
+you know we're very complicated
+entities but at the core here as he's
+
+ align:start position:0%
+entities but at the core here as he's
+ 
+
+ align:start position:0%
+entities but at the core here as he's
+pointing out there there's some kind of
+
+ align:start position:0%
+pointing out there there's some kind of
+ 
+
+ align:start position:0%
+pointing out there there's some kind of
+mechanical process that basically shows
+
+ align:start position:0%
+mechanical process that basically shows
+ 
+
+ align:start position:0%
+mechanical process that basically shows
+that you know there are a lot of
+
+ align:start position:0%
+that you know there are a lot of
+ 
+
+ align:start position:0%
+that you know there are a lot of
+parallels at certain levels between
+
+ align:start position:0%
+parallels at certain levels between
+ 
+
+ align:start position:0%
+parallels at certain levels between
+humans and
+
+ align:start position:0%
+humans and
+ 
+
+ align:start position:0%
+humans and
+machines and what is the purpose of
+
+ align:start position:0%
+machines and what is the purpose of
+ 
+
+ align:start position:0%
+machines and what is the purpose of
+trying to search for
+
+ align:start position:0%
+trying to search for
+ 
+
+ align:start position:0%
+trying to search for
+this the cyberneticist says well we can
+
+ align:start position:0%
+this the cyberneticist says well we can
+ 
+
+ align:start position:0%
+this the cyberneticist says well we can
+learn from this process we can learn
+
+ align:start position:0%
+learn from this process we can learn
+ 
+
+ align:start position:0%
+learn from this process we can learn
+something about all kinds of
+
+ align:start position:0%
+something about all kinds of
+ 
+
+ align:start position:0%
+something about all kinds of
+phenomena in the physical
+
+ align:start position:0%
+phenomena in the physical
+ 
+
+ align:start position:0%
+phenomena in the physical
+world and we can learn things about
+
+ align:start position:0%
+world and we can learn things about
+ 
+
+ align:start position:0%
+world and we can learn things about
+humans too so there's the knowledge gen
+
+ align:start position:0%
+humans too so there's the knowledge gen
+ 
+
+ align:start position:0%
+humans too so there's the knowledge gen
+the person in search of knowledge wants
+
+ align:start position:0%
+the person in search of knowledge wants
+ 
+
+ align:start position:0%
+the person in search of knowledge wants
+to understand more
+
+ align:start position:0%
+to understand more
+ 
+
+ align:start position:0%
+to understand more
+deeply the mechanical processes at the
+
+ align:start position:0%
+deeply the mechanical processes at the
+ 
+
+ align:start position:0%
+deeply the mechanical processes at the
+heart of all phenomena whether
+
+ align:start position:0%
+heart of all phenomena whether
+ 
+
+ align:start position:0%
+heart of all phenomena whether
+mechanical machines or
+
+ align:start position:0%
+mechanical machines or
+ 
+
+ align:start position:0%
+mechanical machines or
+humans but then a lot of it depends as
+
+ align:start position:0%
+humans but then a lot of it depends as
+ 
+
+ align:start position:0%
+humans but then a lot of it depends as
+Dev says how how far you want to go in
+
+ align:start position:0%
+Dev says how how far you want to go in
+ 
+
+ align:start position:0%
+Dev says how how far you want to go in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+abstraction and where you want to take
+
+ align:start position:0%
+abstraction and where you want to take
+ 
+
+ align:start position:0%
+abstraction and where you want to take
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+but uh certainly he's for his purposes
+
+ align:start position:0%
+but uh certainly he's for his purposes
+ 
+
+ align:start position:0%
+but uh certainly he's for his purposes
+he's laying down something some very
+
+ align:start position:0%
+he's laying down something some very
+ 
+
+ align:start position:0%
+he's laying down something some very
+important principles here other thoughts
+
+ align:start position:0%
+important principles here other thoughts
+ 
+
+ align:start position:0%
+important principles here other thoughts
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+this yeah so yeah kind of along with was
+
+ align:start position:0%
+this yeah so yeah kind of along with was
+ 
+
+ align:start position:0%
+this yeah so yeah kind of along with was
+saying and like you were saying how
+
+ align:start position:0%
+saying and like you were saying how
+ 
+
+ align:start position:0%
+saying and like you were saying how
+people have sort of like people have a
+
+ align:start position:0%
+people have sort of like people have a
+ 
+
+ align:start position:0%
+people have sort of like people have a
+thirst for a finding a meaning of life
+
+ align:start position:0%
+thirst for a finding a meaning of life
+ 
+
+ align:start position:0%
+thirst for a finding a meaning of life
+finding a meaning to their lives and I
+
+ align:start position:0%
+finding a meaning to their lives and I
+ 
+
+ align:start position:0%
+finding a meaning to their lives and I
+think that like with computers the thing
+
+ align:start position:0%
+think that like with computers the thing
+ 
+
+ align:start position:0%
+think that like with computers the thing
+is that we know everything about them
+
+ align:start position:0%
+is that we know everything about them
+ 
+
+ align:start position:0%
+is that we know everything about them
+they're so complex so beautiful in terms
+
+ align:start position:0%
+they're so complex so beautiful in terms
+ 
+
+ align:start position:0%
+they're so complex so beautiful in terms
+of what we have created so far but like
+
+ align:start position:0%
+of what we have created so far but like
+ 
+
+ align:start position:0%
+of what we have created so far but like
+we know every single thing about them
+
+ align:start position:0%
+we know every single thing about them
+ 
+
+ align:start position:0%
+we know every single thing about them
+and there's no there's no magic in there
+
+ align:start position:0%
+and there's no there's no magic in there
+ 
+
+ align:start position:0%
+and there's no there's no magic in there
+like if we found a computer and we
+
+ align:start position:0%
+like if we found a computer and we
+ 
+
+ align:start position:0%
+like if we found a computer and we
+learned how to use it without
+
+ align:start position:0%
+learned how to use it without
+ 
+
+ align:start position:0%
+learned how to use it without
+understanding how it worked there would
+
+ align:start position:0%
+understanding how it worked there would
+ 
+
+ align:start position:0%
+understanding how it worked there would
+be some some sense of magic in there and
+
+ align:start position:0%
+be some some sense of magic in there and
+ 
+
+ align:start position:0%
+be some some sense of magic in there and
+I think it's that sense that like the
+
+ align:start position:0%
+I think it's that sense that like the
+ 
+
+ align:start position:0%
+I think it's that sense that like the
+more science develops like the more we
+
+ align:start position:0%
+more science develops like the more we
+ 
+
+ align:start position:0%
+more science develops like the more we
+know about how we work the more the L
+
+ align:start position:0%
+know about how we work the more the L
+ 
+
+ align:start position:0%
+know about how we work the more the L
+less like un the less mystery there is
+
+ align:start position:0%
+less like un the less mystery there is
+ 
+
+ align:start position:0%
+less like un the less mystery there is
+in there and like since ancient times
+
+ align:start position:0%
+in there and like since ancient times
+ 
+
+ align:start position:0%
+in there and like since ancient times
+people have been kind of relying on this
+
+ align:start position:0%
+people have been kind of relying on this
+ 
+
+ align:start position:0%
+people have been kind of relying on this
+mystery there like this mysterious and
+
+ align:start position:0%
+mystery there like this mysterious and
+ 
+
+ align:start position:0%
+mystery there like this mysterious and
+unknown um like Factor like how life
+
+ align:start position:0%
+unknown um like Factor like how life
+ 
+
+ align:start position:0%
+unknown um like Factor like how life
+works is so complex we don't understand
+
+ align:start position:0%
+works is so complex we don't understand
+ 
+
+ align:start position:0%
+works is so complex we don't understand
+it it must be God and maybe there's
+
+ align:start position:0%
+it it must be God and maybe there's
+ 
+
+ align:start position:0%
+it it must be God and maybe there's
+Heaven maybe there's hell the more
+
+ align:start position:0%
+Heaven maybe there's hell the more
+ 
+
+ align:start position:0%
+Heaven maybe there's hell the more
+science advances the less of that there
+
+ align:start position:0%
+science advances the less of that there
+ 
+
+ align:start position:0%
+science advances the less of that there
+is less room there is for that and so I
+
+ align:start position:0%
+is less room there is for that and so I
+ 
+
+ align:start position:0%
+is less room there is for that and so I
+think that's why we don't want like to
+
+ align:start position:0%
+think that's why we don't want like to
+ 
+
+ align:start position:0%
+think that's why we don't want like to
+associate ourselves with like machines
+
+ align:start position:0%
+associate ourselves with like machines
+ 
+
+ align:start position:0%
+associate ourselves with like machines
+cuz like we know every single thing
+
+ align:start position:0%
+cuz like we know every single thing
+ 
+
+ align:start position:0%
+cuz like we know every single thing
+about them and if eventually maybe
+
+ align:start position:0%
+about them and if eventually maybe
+ 
+
+ align:start position:0%
+about them and if eventually maybe
+that's what science is going to do to
+
+ align:start position:0%
+that's what science is going to do to
+ 
+
+ align:start position:0%
+that's what science is going to do to
+humans like we'll know every single
+
+ align:start position:0%
+humans like we'll know every single
+ 
+
+ align:start position:0%
+humans like we'll know every single
+thing about how humans work and all the
+
+ align:start position:0%
+thing about how humans work and all the
+ 
+
+ align:start position:0%
+thing about how humans work and all the
+possibilities there are and then that
+
+ align:start position:0%
+possibilities there are and then that
+ 
+
+ align:start position:0%
+possibilities there are and then that
+would leave no space for like
+
+ align:start position:0%
+would leave no space for like
+ 
+
+ align:start position:0%
+would leave no space for like
+spiritualism I mean keep keep in mind
+
+ align:start position:0%
+spiritualism I mean keep keep in mind
+ 
+
+ align:start position:0%
+spiritualism I mean keep keep in mind
+he's at this he's at the core of
+
+ align:start position:0%
+he's at this he's at the core of
+ 
+
+ align:start position:0%
+he's at this he's at the core of
+cybernetics so he's you know he's one of
+
+ align:start position:0%
+cybernetics so he's you know he's one of
+ 
+
+ align:start position:0%
+cybernetics so he's you know he's one of
+the key people in the field not the only
+
+ align:start position:0%
+the key people in the field not the only
+ 
+
+ align:start position:0%
+the key people in the field not the only
+one but uh he's a really important
+
+ align:start position:0%
+one but uh he's a really important
+ 
+
+ align:start position:0%
+one but uh he's a really important
+thinker um they do have a pretty big
+
+ align:start position:0%
+thinker um they do have a pretty big
+ 
+
+ align:start position:0%
+thinker um they do have a pretty big
+exhibit I think at the MIT Museum when I
+
+ align:start position:0%
+exhibit I think at the MIT Museum when I
+ 
+
+ align:start position:0%
+exhibit I think at the MIT Museum when I
+went last year when I came here on
+
+ align:start position:0%
+went last year when I came here on
+ 
+
+ align:start position:0%
+went last year when I came here on
+cybernetics and how they're like trying
+
+ align:start position:0%
+cybernetics and how they're like trying
+ 
+
+ align:start position:0%
+cybernetics and how they're like trying
+to build this robot they can actually
+
+ align:start position:0%
+to build this robot they can actually
+ 
+
+ align:start position:0%
+to build this robot they can actually
+see and like people are trying to make
+
+ align:start position:0%
+see and like people are trying to make
+ 
+
+ align:start position:0%
+see and like people are trying to make
+human machines a little weird but yeah
+
+ align:start position:0%
+human machines a little weird but yeah
+ 
+
+ align:start position:0%
+human machines a little weird but yeah
+so what is the why why why do you think
+
+ align:start position:0%
+so what is the why why why do you think
+ 
+
+ align:start position:0%
+so what is the why why why do you think
+that is why is it why why are we trying
+
+ align:start position:0%
+that is why is it why why are we trying
+ 
+
+ align:start position:0%
+that is why is it why why are we trying
+to what's driving you know all this new
+
+ align:start position:0%
+to what's driving you know all this new
+ 
+
+ align:start position:0%
+to what's driving you know all this new
+knowledge and machine learning and all
+
+ align:start position:0%
+knowledge and machine learning and all
+ 
+
+ align:start position:0%
+knowledge and machine learning and all
+the and and the effort to create uh sort
+
+ align:start position:0%
+the and and the effort to create uh sort
+ 
+
+ align:start position:0%
+the and and the effort to create uh sort
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+uh higher and higher
+
+ align:start position:0%
+uh higher and higher
+ 
+
+ align:start position:0%
+uh higher and higher
+functioning uh computational devices and
+
+ align:start position:0%
+functioning uh computational devices and
+ 
+
+ align:start position:0%
+functioning uh computational devices and
+to merge them with physical devices what
+
+ align:start position:0%
+to merge them with physical devices what
+ 
+
+ align:start position:0%
+to merge them with physical devices what
+is it want to say laziness it's not that
+
+ align:start position:0%
+is it want to say laziness it's not that
+ 
+
+ align:start position:0%
+is it want to say laziness it's not that
+because we can get them to do it for
+
+ align:start position:0%
+because we can get them to do it for
+ 
+
+ align:start position:0%
+because we can get them to do it for
+us I think it's a search for
+
+ align:start position:0%
+us I think it's a search for
+ 
+
+ align:start position:0%
+us I think it's a search for
+understanding the why we're trying to
+
+ align:start position:0%
+understanding the why we're trying to
+ 
+
+ align:start position:0%
+understanding the why we're trying to
+make uh something that can think the way
+
+ align:start position:0%
+make uh something that can think the way
+ 
+
+ align:start position:0%
+make uh something that can think the way
+a human does because especially in high
+
+ align:start position:0%
+a human does because especially in high
+ 
+
+ align:start position:0%
+a human does because especially in high
+highend uh mathematics and uh physics
+
+ align:start position:0%
+highend uh mathematics and uh physics
+ 
+
+ align:start position:0%
+highend uh mathematics and uh physics
+they use complex models to Model A even
+
+ align:start position:0%
+they use complex models to Model A even
+ 
+
+ align:start position:0%
+they use complex models to Model A even
+more complex system if we we obviously
+
+ align:start position:0%
+more complex system if we we obviously
+ 
+
+ align:start position:0%
+more complex system if we we obviously
+clearly don't understand the brain very
+
+ align:start position:0%
+clearly don't understand the brain very
+ 
+
+ align:start position:0%
+clearly don't understand the brain very
+well at all in terms of cognition and
+
+ align:start position:0%
+well at all in terms of cognition and
+ 
+
+ align:start position:0%
+well at all in terms of cognition and
+thought and way other things but if we
+
+ align:start position:0%
+thought and way other things but if we
+ 
+
+ align:start position:0%
+thought and way other things but if we
+can create a program say
+
+ align:start position:0%
+can create a program say
+ 
+
+ align:start position:0%
+can create a program say
+that moderately closely mimics what's
+
+ align:start position:0%
+that moderately closely mimics what's
+ 
+
+ align:start position:0%
+that moderately closely mimics what's
+what a human can do we can say all right
+
+ align:start position:0%
+what a human can do we can say all right
+ 
+
+ align:start position:0%
+what a human can do we can say all right
+well we don't know exactly how it works
+
+ align:start position:0%
+well we don't know exactly how it works
+ 
+
+ align:start position:0%
+well we don't know exactly how it works
+but this is a really good baseline or a
+
+ align:start position:0%
+but this is a really good baseline or a
+ 
+
+ align:start position:0%
+but this is a really good baseline or a
+rough estimate if how it works so that's
+
+ align:start position:0%
+rough estimate if how it works so that's
+ 
+
+ align:start position:0%
+rough estimate if how it works so that's
+how we're trying to understand cognition
+
+ align:start position:0%
+how we're trying to understand cognition
+ 
+
+ align:start position:0%
+how we're trying to understand cognition
+humans
+
+ align:start position:0%
+humans
+ 
+
+ align:start position:0%
+humans
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+natural quers for knowledge more and
+
+ align:start position:0%
+natural quers for knowledge more and
+ 
+
+ align:start position:0%
+natural quers for knowledge more and
+more deeper understanding of the world
+
+ align:start position:0%
+more deeper understanding of the world
+ 
+
+ align:start position:0%
+more deeper understanding of the world
+and La yeah I think it's some of it's
+
+ align:start position:0%
+and La yeah I think it's some of it's
+ 
+
+ align:start position:0%
+and La yeah I think it's some of it's
+like just basic curiosity of humans and
+
+ align:start position:0%
+like just basic curiosity of humans and
+ 
+
+ align:start position:0%
+like just basic curiosity of humans and
+also it's like why do humans clim as as
+
+ align:start position:0%
+also it's like why do humans clim as as
+ 
+
+ align:start position:0%
+also it's like why do humans clim as as
+they can right so I think it's just
+
+ align:start position:0%
+they can right so I think it's just
+ 
+
+ align:start position:0%
+they can right so I think it's just
+humans can get farther and farther and
+
+ align:start position:0%
+humans can get farther and farther and
+ 
+
+ align:start position:0%
+humans can get farther and farther and
+see how much they can
+
+ align:start position:0%
+see how much they can
+ 
+
+ align:start position:0%
+see how much they can
+do yeah I mean if if if you're in a
+
+ align:start position:0%
+do yeah I mean if if if you're in a
+ 
+
+ align:start position:0%
+do yeah I mean if if if you're in a
+specific area of inquiry um deeper and
+
+ align:start position:0%
+specific area of inquiry um deeper and
+ 
+
+ align:start position:0%
+specific area of inquiry um deeper and
+deeper under understanding of it is is
+
+ align:start position:0%
+deeper under understanding of it is is
+ 
+
+ align:start position:0%
+deeper under understanding of it is is
+it's it's a natural human
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impulse uh well according to weer there
+
+ align:start position:0%
+impulse uh well according to weer there
+ 
+
+ align:start position:0%
+impulse uh well according to weer there
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+other there are other drives
+
+ align:start position:0%
+other there are other drives
+ 
+
+ align:start position:0%
+other there are other drives
+um um I mean wier's tremendously
+
+ align:start position:0%
+um um I mean wier's tremendously
+ 
+
+ align:start position:0%
+um um I mean wier's tremendously
+upset by nuclear
+
+ align:start position:0%
+upset by nuclear
+ 
+
+ align:start position:0%
+upset by nuclear
+uh uh the technology that led to nuclear
+
+ align:start position:0%
+uh uh the technology that led to nuclear
+ 
+
+ align:start position:0%
+uh uh the technology that led to nuclear
+weapons this this deeply profoundly
+
+ align:start position:0%
+weapons this this deeply profoundly
+ 
+
+ align:start position:0%
+weapons this this deeply profoundly
+upset
+
+ align:start position:0%
+upset
+ 
+
+ align:start position:0%
+upset
+him because he was worried that um in in
+
+ align:start position:0%
+him because he was worried that um in in
+ 
+
+ align:start position:0%
+him because he was worried that um in in
+creating these entities the control of
+
+ align:start position:0%
+creating these entities the control of
+ 
+
+ align:start position:0%
+creating these entities the control of
+them they had simply rais the level and
+
+ align:start position:0%
+them they had simply rais the level and
+ 
+
+ align:start position:0%
+them they had simply rais the level and
+challenge of
+
+ align:start position:0%
+challenge of
+ 
+
+ align:start position:0%
+challenge of
+controlling them and put this challenge
+
+ align:start position:0%
+controlling them and put this challenge
+ 
+
+ align:start position:0%
+controlling them and put this challenge
+in front of humans and he was he was
+
+ align:start position:0%
+in front of humans and he was he was
+ 
+
+ align:start position:0%
+in front of humans and he was he was
+very very concerned about the human
+
+ align:start position:0%
+very very concerned about the human
+ 
+
+ align:start position:0%
+very very concerned about the human
+ability to stand up to to that um demand
+
+ align:start position:0%
+ability to stand up to to that um demand
+ 
+
+ align:start position:0%
+ability to stand up to to that um demand
+of uh of
+
+ align:start position:0%
+of uh of
+ 
+
+ align:start position:0%
+of uh of
+control so uh weiner did not work on
+
+ align:start position:0%
+control so uh weiner did not work on
+ 
+
+ align:start position:0%
+control so uh weiner did not work on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+technology uh uh my understanding is
+
+ align:start position:0%
+technology uh uh my understanding is
+ 
+
+ align:start position:0%
+technology uh uh my understanding is
+that he was invited to and cult and and
+
+ align:start position:0%
+that he was invited to and cult and and
+ 
+
+ align:start position:0%
+that he was invited to and cult and and
+cultivated and refused
+
+ align:start position:0%
+cultivated and refused
+ 
+
+ align:start position:0%
+cultivated and refused
+to uh and partly because of his
+
+ align:start position:0%
+to uh and partly because of his
+ 
+
+ align:start position:0%
+to uh and partly because of his
+understanding of uh the problems of
+
+ align:start position:0%
+understanding of uh the problems of
+ 
+
+ align:start position:0%
+understanding of uh the problems of
+control and how do you control these
+
+ align:start position:0%
+control and how do you control these
+ 
+
+ align:start position:0%
+control and how do you control these
+things when you create them so at the at
+
+ align:start position:0%
+things when you create them so at the at
+ 
+
+ align:start position:0%
+things when you create them so at the at
+the core of this of this book is this
+
+ align:start position:0%
+the core of this of this book is this
+ 
+
+ align:start position:0%
+the core of this of this book is this
+terrible problem of the control of uh
+
+ align:start position:0%
+terrible problem of the control of uh
+ 
+
+ align:start position:0%
+terrible problem of the control of uh
+technologies that uh were probably
+
+ align:start position:0%
+technologies that uh were probably
+ 
+
+ align:start position:0%
+technologies that uh were probably
+exhilarating to develop at you know at a
+
+ align:start position:0%
+exhilarating to develop at you know at a
+ 
+
+ align:start position:0%
+exhilarating to develop at you know at a
+theoretical
+
+ align:start position:0%
+theoretical
+ 
+
+ align:start position:0%
+theoretical
+level I mean to solve the problems and
+
+ align:start position:0%
+level I mean to solve the problems and
+ 
+
+ align:start position:0%
+level I mean to solve the problems and
+to create the entity was a huge rush for
+
+ align:start position:0%
+to create the entity was a huge rush for
+ 
+
+ align:start position:0%
+to create the entity was a huge rush for
+a lot of people who were incredibly
+
+ align:start position:0%
+a lot of people who were incredibly
+ 
+
+ align:start position:0%
+a lot of people who were incredibly
+bright
+
+ align:start position:0%
+bright
+ 
+
+ align:start position:0%
+bright
+talented and at the top of their fields
+
+ align:start position:0%
+talented and at the top of their fields
+ 
+
+ align:start position:0%
+talented and at the top of their fields
+and yet to create it once it's created
+
+ align:start position:0%
+and yet to create it once it's created
+ 
+
+ align:start position:0%
+and yet to create it once it's created
+you have to control
+
+ align:start position:0%
+you have to control
+ 
+
+ align:start position:0%
+you have to control
+it so that's why these little Tales of
+
+ align:start position:0%
+it so that's why these little Tales of
+ 
+
+ align:start position:0%
+it so that's why these little Tales of
+you know this uh you know the The
+
+ align:start position:0%
+you know this uh you know the The
+ 
+
+ align:start position:0%
+you know this uh you know the The
+Sorcerer's Apprentice and the monkeyy
+
+ align:start position:0%
+Sorcerer's Apprentice and the monkeyy
+ 
+
+ align:start position:0%
+Sorcerer's Apprentice and the monkeyy
+Paw keep coming back up in this
+
+ align:start position:0%
+Paw keep coming back up in this
+ 
+
+ align:start position:0%
+Paw keep coming back up in this
+piece and this is not he's he's not
+
+ align:start position:0%
+piece and this is not he's he's not
+ 
+
+ align:start position:0%
+piece and this is not he's he's not
+raising this
+
+ align:start position:0%
+raising this
+ 
+
+ align:start position:0%
+raising this
+from you know he's not against but he's
+
+ align:start position:0%
+from you know he's not against but he's
+ 
+
+ align:start position:0%
+from you know he's not against but he's
+not raising this from a humanistic point
+
+ align:start position:0%
+not raising this from a humanistic point
+ 
+
+ align:start position:0%
+not raising this from a humanistic point
+view so much as from a technical point
+
+ align:start position:0%
+view so much as from a technical point
+ 
+
+ align:start position:0%
+view so much as from a technical point
+of view of the control of the things
+
+ align:start position:0%
+of view of the control of the things
+ 
+
+ align:start position:0%
+of view of the control of the things
+that you create I mean who thought that
+
+ align:start position:0%
+that you create I mean who thought that
+ 
+
+ align:start position:0%
+that you create I mean who thought that
+uh at at that time that you know we
+
+ align:start position:0%
+uh at at that time that you know we
+ 
+
+ align:start position:0%
+uh at at that time that you know we
+would be dealing with uh a world of uh
+
+ align:start position:0%
+would be dealing with uh a world of uh
+ 
+
+ align:start position:0%
+would be dealing with uh a world of uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+proliferating uh Atomic uh
+
+ align:start position:0%
+proliferating uh Atomic uh
+ 
+
+ align:start position:0%
+proliferating uh Atomic uh
+Weaponry uh you know almost 70 years
+
+ align:start position:0%
+Weaponry uh you know almost 70 years
+ 
+
+ align:start position:0%
+Weaponry uh you know almost 70 years
+later with you know this technology you
+
+ align:start position:0%
+later with you know this technology you
+ 
+
+ align:start position:0%
+later with you know this technology you
+know a lot of different
+
+ align:start position:0%
+know a lot of different
+ 
+
+ align:start position:0%
+know a lot of different
+people uh made use of
+
+ align:start position:0%
+people uh made use of
+ 
+
+ align:start position:0%
+people uh made use of
+it and so the nuclear club club grew and
+
+ align:start position:0%
+it and so the nuclear club club grew and
+ 
+
+ align:start position:0%
+it and so the nuclear club club grew and
+uh he was aware of this set of
+
+ align:start position:0%
+uh he was aware of this set of
+ 
+
+ align:start position:0%
+uh he was aware of this set of
+problems and but this is not what people
+
+ align:start position:0%
+problems and but this is not what people
+ 
+
+ align:start position:0%
+problems and but this is not what people
+were thinking about when they were
+
+ align:start position:0%
+were thinking about when they were
+ 
+
+ align:start position:0%
+were thinking about when they were
+creating the original technology so
+
+ align:start position:0%
+creating the original technology so
+ 
+
+ align:start position:0%
+creating the original technology so
+that's that's that's a deep problem it's
+
+ align:start position:0%
+that's that's that's a deep problem it's
+ 
+
+ align:start position:0%
+that's that's that's a deep problem it's
+just you know what are the impacts what
+
+ align:start position:0%
+just you know what are the impacts what
+ 
+
+ align:start position:0%
+just you know what are the impacts what
+are going to be the costs I mean other
+
+ align:start position:0%
+are going to be the costs I mean other
+ 
+
+ align:start position:0%
+are going to be the costs I mean other
+examples he brings up in the in the book
+
+ align:start position:0%
+examples he brings up in the in the book
+ 
+
+ align:start position:0%
+examples he brings up in the in the book
+uh I didn't we didn't read the whole
+
+ align:start position:0%
+uh I didn't we didn't read the whole
+ 
+
+ align:start position:0%
+uh I didn't we didn't read the whole
+book but later in the book he he brings
+
+ align:start position:0%
+book but later in the book he he brings
+ 
+
+ align:start position:0%
+book but later in the book he he brings
+up even things like
+
+ align:start position:0%
+up even things like
+ 
+
+ align:start position:0%
+up even things like
+healthcare I mean we can create
+
+ align:start position:0%
+healthcare I mean we can create
+ 
+
+ align:start position:0%
+healthcare I mean we can create
+tremendous medical
+
+ align:start position:0%
+tremendous medical
+ 
+
+ align:start position:0%
+tremendous medical
+Technologies but how do we deal with the
+
+ align:start position:0%
+Technologies but how do we deal with the
+ 
+
+ align:start position:0%
+Technologies but how do we deal with the
+you know the the population explosions
+
+ align:start position:0%
+you know the the population explosions
+ 
+
+ align:start position:0%
+you know the the population explosions
+or the extension of populations he's not
+
+ align:start position:0%
+or the extension of populations he's not
+ 
+
+ align:start position:0%
+or the extension of populations he's not
+saying we shouldn't do them but what he
+
+ align:start position:0%
+saying we shouldn't do them but what he
+ 
+
+ align:start position:0%
+saying we shouldn't do them but what he
+is he's he's saying you know as you
+
+ align:start position:0%
+is he's he's saying you know as you
+ 
+
+ align:start position:0%
+is he's he's saying you know as you
+apply all these different Technologies
+
+ align:start position:0%
+apply all these different Technologies
+ 
+
+ align:start position:0%
+apply all these different Technologies
+you're going to have other other
+
+ align:start position:0%
+you're going to have other other
+ 
+
+ align:start position:0%
+you're going to have other other
+problems that you're going to have to to
+
+ align:start position:0%
+problems that you're going to have to to
+ 
+
+ align:start position:0%
+problems that you're going to have to to
+solve and you know it's it's it's it's
+
+ align:start position:0%
+solve and you know it's it's it's it's
+ 
+
+ align:start position:0%
+solve and you know it's it's it's it's
+it's a complex set of
+
+ align:start position:0%
+it's a complex set of
+ 
+
+ align:start position:0%
+it's a complex set of
+questions I mean no no one would uh
+
+ align:start position:0%
+questions I mean no no one would uh
+ 
+
+ align:start position:0%
+questions I mean no no one would uh
+certainly not weer would say well you
+
+ align:start position:0%
+certainly not weer would say well you
+ 
+
+ align:start position:0%
+certainly not weer would say well you
+shouldn't you know uh improve uh you
+
+ align:start position:0%
+shouldn't you know uh improve uh you
+ 
+
+ align:start position:0%
+shouldn't you know uh improve uh you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+uh delivery uh birth deliveries among
+
+ align:start position:0%
+uh delivery uh birth deliveries among
+ 
+
+ align:start position:0%
+uh delivery uh birth deliveries among
+all the pop I mean he would be you know
+
+ align:start position:0%
+all the pop I mean he would be you know
+ 
+
+ align:start position:0%
+all the pop I mean he would be you know
+he's a he's a definitely a a Humane
+
+ align:start position:0%
+he's a he's a definitely a a Humane
+ 
+
+ align:start position:0%
+he's a he's a definitely a a Humane
+individual who would be
+
+ align:start position:0%
+individual who would be
+ 
+
+ align:start position:0%
+individual who would be
+for all technologies that could improve
+
+ align:start position:0%
+for all technologies that could improve
+ 
+
+ align:start position:0%
+for all technologies that could improve
+human conditions
+
+ align:start position:0%
+human conditions
+ 
+
+ align:start position:0%
+human conditions
+but what he's saying is there going to
+
+ align:start position:0%
+but what he's saying is there going to
+ 
+
+ align:start position:0%
+but what he's saying is there going to
+be a lot of other challenges that are
+
+ align:start position:0%
+be a lot of other challenges that are
+ 
+
+ align:start position:0%
+be a lot of other challenges that are
+going to come along with
+
+ align:start position:0%
+going to come along with
+ 
+
+ align:start position:0%
+going to come along with
+these and so you know so then he uh okay
+
+ align:start position:0%
+these and so you know so then he uh okay
+ 
+
+ align:start position:0%
+these and so you know so then he uh okay
+so he says there are certain there are
+
+ align:start position:0%
+so he says there are certain there are
+ 
+
+ align:start position:0%
+so he says there are certain there are
+certain types of individuals he calls
+
+ align:start position:0%
+certain types of individuals he calls
+ 
+
+ align:start position:0%
+certain types of individuals he calls
+Gadget worshippers who he he does uh uh
+
+ align:start position:0%
+Gadget worshippers who he he does uh uh
+ 
+
+ align:start position:0%
+Gadget worshippers who he he does uh uh
+he does fault and these are people uh he
+
+ align:start position:0%
+he does fault and these are people uh he
+ 
+
+ align:start position:0%
+he does fault and these are people uh he
+says uh a person infatuated with the
+
+ align:start position:0%
+says uh a person infatuated with the
+ 
+
+ align:start position:0%
+says uh a person infatuated with the
+amplica amplification of power and
+
+ align:start position:0%
+amplica amplification of power and
+ 
+
+ align:start position:0%
+amplica amplification of power and
+control through
+
+ align:start position:0%
+control through
+ 
+
+ align:start position:0%
+control through
+technology as well as the transfer of
+
+ align:start position:0%
+technology as well as the transfer of
+ 
+
+ align:start position:0%
+technology as well as the transfer of
+human functions to machines and
+
+ align:start position:0%
+human functions to machines and
+ 
+
+ align:start position:0%
+human functions to machines and
+unquestioning
+
+ align:start position:0%
+unquestioning
+ 
+
+ align:start position:0%
+unquestioning
+servitude so what is this gadget
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worshipper
+
+ align:start position:0%
+worshipper
+ 
+
+ align:start position:0%
+worshipper
+why is it why does it emerge in this
+
+ align:start position:0%
+why is it why does it emerge in this
+ 
+
+ align:start position:0%
+why is it why does it emerge in this
+little book what's he talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about well certainly at at a certain
+
+ align:start position:0%
+about well certainly at at a certain
+ 
+
+ align:start position:0%
+about well certainly at at a certain
+level uh the
+
+ align:start position:0%
+level uh the
+ 
+
+ align:start position:0%
+level uh the
+uses of technology to gain personal
+
+ align:start position:0%
+uses of technology to gain personal
+ 
+
+ align:start position:0%
+uses of technology to gain personal
+ends and to to
+
+ align:start position:0%
+ends and to to
+ 
+
+ align:start position:0%
+ends and to to
+control other people um and it's it's
+
+ align:start position:0%
+control other people um and it's it's
+ 
+
+ align:start position:0%
+control other people um and it's it's
+his it's his argument that there are
+
+ align:start position:0%
+his it's his argument that there are
+ 
+
+ align:start position:0%
+his it's his argument that there are
+certain people who are attracted to
+
+ align:start position:0%
+certain people who are attracted to
+ 
+
+ align:start position:0%
+certain people who are attracted to
+this some people are attracted to you
+
+ align:start position:0%
+this some people are attracted to you
+ 
+
+ align:start position:0%
+this some people are attracted to you
+know power through the manipulation of
+
+ align:start position:0%
+know power through the manipulation of
+ 
+
+ align:start position:0%
+know power through the manipulation of
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+technology and that these are people who
+
+ align:start position:0%
+technology and that these are people who
+ 
+
+ align:start position:0%
+technology and that these are people who
+are uh a
+
+ align:start position:0%
+are uh a
+ 
+
+ align:start position:0%
+are uh a
+problem because uh there is
+
+ align:start position:0%
+problem because uh there is
+ 
+
+ align:start position:0%
+problem because uh there is
+is in inherent in some kind
+
+ align:start position:0%
+is in inherent in some kind
+ 
+
+ align:start position:0%
+is in inherent in some kind
+of uh in in some way in technology this
+
+ align:start position:0%
+of uh in in some way in technology this
+ 
+
+ align:start position:0%
+of uh in in some way in technology this
+this promise of
+
+ align:start position:0%
+this promise of
+ 
+
+ align:start position:0%
+this promise of
+control and that's going to
+
+ align:start position:0%
+control and that's going to
+ 
+
+ align:start position:0%
+control and that's going to
+draw many different types of people what
+
+ align:start position:0%
+draw many different types of people what
+ 
+
+ align:start position:0%
+draw many different types of people what
+one type he talks about as the gadget
+
+ align:start position:0%
+one type he talks about as the gadget
+ 
+
+ align:start position:0%
+one type he talks about as the gadget
+worshipper he says on page 54 it is the
+
+ align:start position:0%
+worshipper he says on page 54 it is the
+ 
+
+ align:start position:0%
+worshipper he says on page 54 it is the
+desire to avoid the personal
+
+ align:start position:0%
+desire to avoid the personal
+ 
+
+ align:start position:0%
+desire to avoid the personal
+responsibility for a dangerous or
+
+ align:start position:0%
+responsibility for a dangerous or
+ 
+
+ align:start position:0%
+responsibility for a dangerous or
+disastrous decision by placing the
+
+ align:start position:0%
+disastrous decision by placing the
+ 
+
+ align:start position:0%
+disastrous decision by placing the
+responsibility elsewhere on chance on
+
+ align:start position:0%
+responsibility elsewhere on chance on
+ 
+
+ align:start position:0%
+responsibility elsewhere on chance on
+human superiors in their policies which
+
+ align:start position:0%
+human superiors in their policies which
+ 
+
+ align:start position:0%
+human superiors in their policies which
+one cannot question or on a mechanical
+
+ align:start position:0%
+one cannot question or on a mechanical
+ 
+
+ align:start position:0%
+one cannot question or on a mechanical
+device which one cannot fully understand
+
+ align:start position:0%
+device which one cannot fully understand
+ 
+
+ align:start position:0%
+device which one cannot fully understand
+but which is has a presumed
+
+ align:start position:0%
+but which is has a presumed
+ 
+
+ align:start position:0%
+but which is has a presumed
+objectivity so this he identifies as the
+
+ align:start position:0%
+objectivity so this he identifies as the
+ 
+
+ align:start position:0%
+objectivity so this he identifies as the
+motive of Gadget
+
+ align:start position:0%
+motive of Gadget
+ 
+
+ align:start position:0%
+motive of Gadget
+worshippers and
+
+ align:start position:0%
+worshippers and
+ 
+
+ align:start position:0%
+worshippers and
+um they would be uh people who are
+
+ align:start position:0%
+um they would be uh people who are
+ 
+
+ align:start position:0%
+um they would be uh people who are
+interested in
+
+ align:start position:0%
+interested in
+ 
+
+ align:start position:0%
+interested in
+making the types of technologies that
+
+ align:start position:0%
+making the types of technologies that
+ 
+
+ align:start position:0%
+making the types of technologies that
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+uh give them power over other
+
+ align:start position:0%
+uh give them power over other
+ 
+
+ align:start position:0%
+uh give them power over other
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+um I'm not I mean I'm not sure exactly
+
+ align:start position:0%
+um I'm not I mean I'm not sure exactly
+ 
+
+ align:start position:0%
+um I'm not I mean I'm not sure exactly
+what he's talking about here I think
+
+ align:start position:0%
+what he's talking about here I think
+ 
+
+ align:start position:0%
+what he's talking about here I think
+he's talking mainly about military
+
+ align:start position:0%
+he's talking mainly about military
+ 
+
+ align:start position:0%
+he's talking mainly about military
+Technologies and things of that sort but
+
+ align:start position:0%
+Technologies and things of that sort but
+ 
+
+ align:start position:0%
+Technologies and things of that sort but
+uh uh you know uh it probably applies to
+
+ align:start position:0%
+uh uh you know uh it probably applies to
+ 
+
+ align:start position:0%
+uh uh you know uh it probably applies to
+many different
+
+ align:start position:0%
+many different
+ 
+
+ align:start position:0%
+many different
+regimes um and that's
+
+ align:start position:0%
+regimes um and that's
+ 
+
+ align:start position:0%
+regimes um and that's
+why this leads them into this whole
+
+ align:start position:0%
+why this leads them into this whole
+ 
+
+ align:start position:0%
+why this leads them into this whole
+discussion of magic what is the
+
+ align:start position:0%
+discussion of magic what is the
+ 
+
+ align:start position:0%
+discussion of magic what is the
+attraction of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+magic fig yeah okay we can't figure it
+
+ align:start position:0%
+magic fig yeah okay we can't figure it
+ 
+
+ align:start position:0%
+magic fig yeah okay we can't figure it
+out what does magic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do why do people want magic Mak life
+
+ align:start position:0%
+do why do people want magic Mak life
+ 
+
+ align:start position:0%
+do why do people want magic Mak life
+easier okay magic makes life easier okay
+
+ align:start position:0%
+easier okay magic makes life easier okay
+ 
+
+ align:start position:0%
+easier okay magic makes life easier okay
+but isn't there some deeper motive human
+
+ align:start position:0%
+but isn't there some deeper motive human
+ 
+
+ align:start position:0%
+but isn't there some deeper motive human
+motive why have humans always
+
+ align:start position:0%
+motive why have humans always
+ 
+
+ align:start position:0%
+motive why have humans always
+entertained the worlds of magic and I
+
+ align:start position:0%
+entertained the worlds of magic and I
+ 
+
+ align:start position:0%
+entertained the worlds of magic and I
+mean what is it that attracts humans to
+
+ align:start position:0%
+mean what is it that attracts humans to
+ 
+
+ align:start position:0%
+mean what is it that attracts humans to
+Magic David uh well maybe some people
+
+ align:start position:0%
+Magic David uh well maybe some people
+ 
+
+ align:start position:0%
+Magic David uh well maybe some people
+think it sort of suspense to laws of
+
+ align:start position:0%
+think it sort of suspense to laws of
+ 
+
+ align:start position:0%
+think it sort of suspense to laws of
+nature sort of it sort of gives like
+
+ align:start position:0%
+nature sort of it sort of gives like
+ 
+
+ align:start position:0%
+nature sort of it sort of gives like
+humans that illusion of control okay the
+
+ align:start position:0%
+humans that illusion of control okay the
+ 
+
+ align:start position:0%
+humans that illusion of control okay the
+power magic is is power unquestioning
+
+ align:start position:0%
+power magic is is power unquestioning
+ 
+
+ align:start position:0%
+power magic is is power unquestioning
+power and it's there just you know when
+
+ align:start position:0%
+power and it's there just you know when
+ 
+
+ align:start position:0%
+power and it's there just you know when
+you turn the
+
+ align:start position:0%
+you turn the
+ 
+
+ align:start position:0%
+you turn the
+switch so magic is always uh you know it
+
+ align:start position:0%
+switch so magic is always uh you know it
+ 
+
+ align:start position:0%
+switch so magic is always uh you know it
+it's it's attractive in in some sense uh
+
+ align:start position:0%
+it's it's attractive in in some sense uh
+ 
+
+ align:start position:0%
+it's it's attractive in in some sense uh
+maybe not to everybody but uh certainly
+
+ align:start position:0%
+maybe not to everybody but uh certainly
+ 
+
+ align:start position:0%
+maybe not to everybody but uh certainly
+the idea of using magic to enrich
+
+ align:start position:0%
+the idea of using magic to enrich
+ 
+
+ align:start position:0%
+the idea of using magic to enrich
+yourself or to gain power over other
+
+ align:start position:0%
+yourself or to gain power over other
+ 
+
+ align:start position:0%
+yourself or to gain power over other
+people is an old
+
+ align:start position:0%
+people is an old
+ 
+
+ align:start position:0%
+people is an old
+concept and and and and an old U human
+
+ align:start position:0%
+concept and and and and an old U human
+ 
+
+ align:start position:0%
+concept and and and and an old U human
+endeavor and he's arguing here through
+
+ align:start position:0%
+endeavor and he's arguing here through
+ 
+
+ align:start position:0%
+endeavor and he's arguing here through
+this gadget worshipper
+
+ align:start position:0%
+this gadget worshipper
+ 
+
+ align:start position:0%
+this gadget worshipper
+metaphor that
+
+ align:start position:0%
+metaphor that
+ 
+
+ align:start position:0%
+metaphor that
+in some ways Technologies also offer us
+
+ align:start position:0%
+in some ways Technologies also offer us
+ 
+
+ align:start position:0%
+in some ways Technologies also offer us
+a kind of a magical solution to
+
+ align:start position:0%
+a kind of a magical solution to
+ 
+
+ align:start position:0%
+a kind of a magical solution to
+problems they can and you know gaining
+
+ align:start position:0%
+problems they can and you know gaining
+ 
+
+ align:start position:0%
+problems they can and you know gaining
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+power is is is
+
+ align:start position:0%
+power is is is
+ 
+
+ align:start position:0%
+power is is is
+attractive
+
+ align:start position:0%
+attractive
+ 
+
+ align:start position:0%
+attractive
+um so and and it also tells us something
+
+ align:start position:0%
+um so and and it also tells us something
+ 
+
+ align:start position:0%
+um so and and it also tells us something
+about the nature of some of these uh
+
+ align:start position:0%
+about the nature of some of these uh
+ 
+
+ align:start position:0%
+about the nature of some of these uh
+Technologies so then uh he launches into
+
+ align:start position:0%
+Technologies so then uh he launches into
+ 
+
+ align:start position:0%
+Technologies so then uh he launches into
+the sourcers of Apprentice what's the
+
+ align:start position:0%
+the sourcers of Apprentice what's the
+ 
+
+ align:start position:0%
+the sourcers of Apprentice what's the
+story of the Sorcerers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Apprentice Chris did you get
+
+ align:start position:0%
+Apprentice Chris did you get
+ 
+
+ align:start position:0%
+Apprentice Chris did you get
+that this the monkeys PA oh the monkey P
+
+ align:start position:0%
+that this the monkeys PA oh the monkey P
+ 
+
+ align:start position:0%
+that this the monkeys PA oh the monkey P
+what about uh he he talks about the
+
+ align:start position:0%
+what about uh he he talks about the
+ 
+
+ align:start position:0%
+what about uh he he talks about the
+Sour's Apprentice first did
+
+ align:start position:0%
+Sour's Apprentice first did
+ 
+
+ align:start position:0%
+Sour's Apprentice first did
+anybody you know the story don't you
+
+ align:start position:0%
+anybody you know the story don't you
+ 
+
+ align:start position:0%
+anybody you know the story don't you
+yeah I for exactly what that goes but
+
+ align:start position:0%
+yeah I for exactly what that goes but
+ 
+
+ align:start position:0%
+yeah I for exactly what that goes but
+the The Apprentice goes and you know
+
+ align:start position:0%
+the The Apprentice goes and you know
+ 
+
+ align:start position:0%
+the The Apprentice goes and you know
+experimenting and makes some kind of
+
+ align:start position:0%
+experimenting and makes some kind of
+ 
+
+ align:start position:0%
+experimenting and makes some kind of
+disastrous mistake that goes running a
+
+ align:start position:0%
+disastrous mistake that goes running a
+ 
+
+ align:start position:0%
+disastrous mistake that goes running a
+mu and eventually the the sorcerer has
+
+ align:start position:0%
+mu and eventually the the sorcerer has
+ 
+
+ align:start position:0%
+mu and eventually the the sorcerer has
+to come back and kind of scold and slap
+
+ align:start position:0%
+to come back and kind of scold and slap
+ 
+
+ align:start position:0%
+to come back and kind of scold and slap
+across and wheel everything back in and
+
+ align:start position:0%
+across and wheel everything back in and
+ 
+
+ align:start position:0%
+across and wheel everything back in and
+great if you saw if you saw Disney uh
+
+ align:start position:0%
+great if you saw if you saw Disney uh
+ 
+
+ align:start position:0%
+great if you saw if you saw Disney uh
+Disney had a version of the sorcery the
+
+ align:start position:0%
+Disney had a version of the sorcery the
+ 
+
+ align:start position:0%
+Disney had a version of the sorcery the
+princess I think I gave you a link in
+
+ align:start position:0%
+princess I think I gave you a link in
+ 
+
+ align:start position:0%
+princess I think I gave you a link in
+maybe in the syllabus to this little
+
+ align:start position:0%
+maybe in the syllabus to this little
+ 
+
+ align:start position:0%
+maybe in the syllabus to this little
+cartoon but it was uh the broom and uh
+
+ align:start position:0%
+cartoon but it was uh the broom and uh
+ 
+
+ align:start position:0%
+cartoon but it was uh the broom and uh
+the sorcerer knew how to get the broom
+
+ align:start position:0%
+the sorcerer knew how to get the broom
+ 
+
+ align:start position:0%
+the sorcerer knew how to get the broom
+to go down and fetch water bring it up
+
+ align:start position:0%
+to go down and fetch water bring it up
+ 
+
+ align:start position:0%
+to go down and fetch water bring it up
+and uh he had certain language that he
+
+ align:start position:0%
+and uh he had certain language that he
+ 
+
+ align:start position:0%
+and uh he had certain language that he
+uh he spoke and the broom would spring
+
+ align:start position:0%
+uh he spoke and the broom would spring
+ 
+
+ align:start position:0%
+uh he spoke and the broom would spring
+into action and go fetch the water and
+
+ align:start position:0%
+into action and go fetch the water and
+ 
+
+ align:start position:0%
+into action and go fetch the water and
+the the impre but he also knew how to
+
+ align:start position:0%
+the the impre but he also knew how to
+ 
+
+ align:start position:0%
+the the impre but he also knew how to
+stop the broom so he's away one day and
+
+ align:start position:0%
+stop the broom so he's away one day and
+ 
+
+ align:start position:0%
+stop the broom so he's away one day and
+The
+
+ align:start position:0%
+The
+ 
+
+ align:start position:0%
+The
+Apprentice oh The Apprentice yeah you
+
+ align:start position:0%
+Apprentice oh The Apprentice yeah you
+ 
+
+ align:start position:0%
+Apprentice oh The Apprentice yeah you
+you may have seen the Mickey Mouse
+
+ align:start position:0%
+you may have seen the Mickey Mouse
+ 
+
+ align:start position:0%
+you may have seen the Mickey Mouse
+version Mickey M you know uh the The
+
+ align:start position:0%
+version Mickey M you know uh the The
+ 
+
+ align:start position:0%
+version Mickey M you know uh the The
+Apprentice uh knows how to start the
+
+ align:start position:0%
+Apprentice uh knows how to start the
+ 
+
+ align:start position:0%
+Apprentice uh knows how to start the
+broom and so the broom goes down and
+
+ align:start position:0%
+broom and so the broom goes down and
+ 
+
+ align:start position:0%
+broom and so the broom goes down and
+starts bringing up uh the water but he
+
+ align:start position:0%
+starts bringing up uh the water but he
+ 
+
+ align:start position:0%
+starts bringing up uh the water but he
+doesn't know how to stop it so it you
+
+ align:start position:0%
+doesn't know how to stop it so it you
+ 
+
+ align:start position:0%
+doesn't know how to stop it so it you
+know keeps it keeps going and everything
+
+ align:start position:0%
+know keeps it keeps going and everything
+ 
+
+ align:start position:0%
+know keeps it keeps going and everything
+is getting you know everything is
+
+ align:start position:0%
+is getting you know everything is
+ 
+
+ align:start position:0%
+is getting you know everything is
+getting flooded and uh it's it's out of
+
+ align:start position:0%
+getting flooded and uh it's it's out of
+ 
+
+ align:start position:0%
+getting flooded and uh it's it's out of
+control so it goes back to that that old
+
+ align:start position:0%
+control so it goes back to that that old
+ 
+
+ align:start position:0%
+control so it goes back to that that old
+story of the gollum you know the thing
+
+ align:start position:0%
+story of the gollum you know the thing
+ 
+
+ align:start position:0%
+story of the gollum you know the thing
+that's out of
+
+ align:start position:0%
+that's out of
+ 
+
+ align:start position:0%
+that's out of
+control and you know we know how to
+
+ align:start position:0%
+control and you know we know how to
+ 
+
+ align:start position:0%
+control and you know we know how to
+start it we don't quite know how to shut
+
+ align:start position:0%
+start it we don't quite know how to shut
+ 
+
+ align:start position:0%
+start it we don't quite know how to shut
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+down and you know are there any are
+
+ align:start position:0%
+down and you know are there any are
+ 
+
+ align:start position:0%
+down and you know are there any are
+there any examples of that in modern
+
+ align:start position:0%
+there any examples of that in modern
+ 
+
+ align:start position:0%
+there any examples of that in modern
+technology I mean I don't have anything
+
+ align:start position:0%
+technology I mean I don't have anything
+ 
+
+ align:start position:0%
+technology I mean I don't have anything
+specific in mind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but well maybe our automobiles
+
+ align:start position:0%
+but well maybe our automobiles
+ 
+
+ align:start position:0%
+but well maybe our automobiles
+are I mean you think how could we shut
+
+ align:start position:0%
+are I mean you think how could we shut
+ 
+
+ align:start position:0%
+are I mean you think how could we shut
+down you know the systems that we built
+
+ align:start position:0%
+down you know the systems that we built
+ 
+
+ align:start position:0%
+down you know the systems that we built
+there are many systems we could not shut
+
+ align:start position:0%
+there are many systems we could not shut
+ 
+
+ align:start position:0%
+there are many systems we could not shut
+down and they may be you know they may
+
+ align:start position:0%
+down and they may be you know they may
+ 
+
+ align:start position:0%
+down and they may be you know they may
+not necessarily be taking us in the
+
+ align:start position:0%
+not necessarily be taking us in the
+ 
+
+ align:start position:0%
+not necessarily be taking us in the
+right direction I mean that's not the
+
+ align:start position:0%
+right direction I mean that's not the
+ 
+
+ align:start position:0%
+right direction I mean that's not the
+say that uh we should uh abandon them
+
+ align:start position:0%
+say that uh we should uh abandon them
+ 
+
+ align:start position:0%
+say that uh we should uh abandon them
+immediately or that they were the wrong
+
+ align:start position:0%
+immediately or that they were the wrong
+ 
+
+ align:start position:0%
+immediately or that they were the wrong
+things to create but you know are there
+
+ align:start position:0%
+things to create but you know are there
+ 
+
+ align:start position:0%
+things to create but you know are there
+not areas that we've developed
+
+ align:start position:0%
+not areas that we've developed
+ 
+
+ align:start position:0%
+not areas that we've developed
+technologically that we now are
+
+ align:start position:0%
+technologically that we now are
+ 
+
+ align:start position:0%
+technologically that we now are
+beginning to wonder you know how long
+
+ align:start position:0%
+beginning to wonder you know how long
+ 
+
+ align:start position:0%
+beginning to wonder you know how long
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+this and and how do we stop it well it's
+
+ align:start position:0%
+this and and how do we stop it well it's
+ 
+
+ align:start position:0%
+this and and how do we stop it well it's
+not quite as easy as just shut it down
+
+ align:start position:0%
+not quite as easy as just shut it down
+ 
+
+ align:start position:0%
+not quite as easy as just shut it down
+but uh you know there are plenty of
+
+ align:start position:0%
+but uh you know there are plenty of
+ 
+
+ align:start position:0%
+but uh you know there are plenty of
+technological areas yeah uh that saying
+
+ align:start position:0%
+technological areas yeah uh that saying
+ 
+
+ align:start position:0%
+technological areas yeah uh that saying
+uh how do we stop it made me think of uh
+
+ align:start position:0%
+uh how do we stop it made me think of uh
+ 
+
+ align:start position:0%
+uh how do we stop it made me think of uh
+the cars uh the Toyota cars that
+
+ align:start position:0%
+the cars uh the Toyota cars that
+ 
+
+ align:start position:0%
+the cars uh the Toyota cars that
+wouldn't stop right right the
+
+ align:start position:0%
+wouldn't stop right right the
+ 
+
+ align:start position:0%
+wouldn't stop right right the
+on what people try to stop them and uh
+
+ align:start position:0%
+on what people try to stop them and uh
+ 
+
+ align:start position:0%
+on what people try to stop them and uh
+that's obviously not really a great
+
+ align:start position:0%
+that's obviously not really a great
+ 
+
+ align:start position:0%
+that's obviously not really a great
+example but it is example of uh
+
+ align:start position:0%
+example but it is example of uh
+ 
+
+ align:start position:0%
+example but it is example of uh
+technology and all right it's doing what
+
+ align:start position:0%
+technology and all right it's doing what
+ 
+
+ align:start position:0%
+technology and all right it's doing what
+we told to but now we
+
+ align:start position:0%
+we told to but now we
+ 
+
+ align:start position:0%
+we told to but now we
+don't yes we could manually open the
+
+ align:start position:0%
+don't yes we could manually open the
+ 
+
+ align:start position:0%
+don't yes we could manually open the
+engine and like start disconnecting
+
+ align:start position:0%
+engine and like start disconnecting
+ 
+
+ align:start position:0%
+engine and like start disconnecting
+things till it turns off but it's not
+
+ align:start position:0%
+things till it turns off but it's not
+ 
+
+ align:start position:0%
+things till it turns off but it's not
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+reasonable option okay the same way if
+
+ align:start position:0%
+reasonable option okay the same way if
+ 
+
+ align:start position:0%
+reasonable option okay the same way if
+like computer starts malfunction we can
+
+ align:start position:0%
+like computer starts malfunction we can
+ 
+
+ align:start position:0%
+like computer starts malfunction we can
+unplug it yeah but I mean what does that
+
+ align:start position:0%
+unplug it yeah but I mean what does that
+ 
+
+ align:start position:0%
+unplug it yeah but I mean what does that
+do for us yeah yeah so uh I mean again
+
+ align:start position:0%
+do for us yeah yeah so uh I mean again
+ 
+
+ align:start position:0%
+do for us yeah yeah so uh I mean again
+this is a this is I mean he's trying to
+
+ align:start position:0%
+this is a this is I mean he's trying to
+ 
+
+ align:start position:0%
+this is a this is I mean he's trying to
+get people he's not saying these you
+
+ align:start position:0%
+get people he's not saying these you
+ 
+
+ align:start position:0%
+get people he's not saying these you
+know Technologies are he's just trying
+
+ align:start position:0%
+know Technologies are he's just trying
+ 
+
+ align:start position:0%
+know Technologies are he's just trying
+to get people to think more deeply about
+
+ align:start position:0%
+to get people to think more deeply about
+ 
+
+ align:start position:0%
+to get people to think more deeply about
+what they're involved in and not simply
+
+ align:start position:0%
+what they're involved in and not simply
+ 
+
+ align:start position:0%
+what they're involved in and not simply
+look at the surface but to probe the
+
+ align:start position:0%
+look at the surface but to probe the
+ 
+
+ align:start position:0%
+look at the surface but to probe the
+deeper impact and
+
+ align:start position:0%
+deeper impact and
+ 
+
+ align:start position:0%
+deeper impact and
+meaning and and to also design when they
+
+ align:start position:0%
+meaning and and to also design when they
+ 
+
+ align:start position:0%
+meaning and and to also design when they
+do design to design more
+
+ align:start position:0%
+do design to design more
+ 
+
+ align:start position:0%
+do design to design more
+thoroughly so that you
+
+ align:start position:0%
+thoroughly so that you
+ 
+
+ align:start position:0%
+thoroughly so that you
+know possible problems are
+
+ align:start position:0%
+know possible problems are
+ 
+
+ align:start position:0%
+know possible problems are
+anticipated even so it's unlikely that
+
+ align:start position:0%
+anticipated even so it's unlikely that
+ 
+
+ align:start position:0%
+anticipated even so it's unlikely that
+all the problems will
+
+ align:start position:0%
+all the problems will
+ 
+
+ align:start position:0%
+all the problems will
+be okay so the monkeys paw again uh the
+
+ align:start position:0%
+be okay so the monkeys paw again uh the
+ 
+
+ align:start position:0%
+be okay so the monkeys paw again uh the
+whole tale of uh now the
+
+ align:start position:0%
+whole tale of uh now the
+ 
+
+ align:start position:0%
+whole tale of uh now the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh so what is the uh what is the
+
+ align:start position:0%
+uh so what is the uh what is the
+ 
+
+ align:start position:0%
+uh so what is the uh what is the
+monkey's
+
+ align:start position:0%
+monkey's
+ 
+
+ align:start position:0%
+monkey's
+paw he says here on page
+
+ align:start position:0%
+paw he says here on page
+ 
+
+ align:start position:0%
+paw he says here on page
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um in this tale an English working
+
+ align:start position:0%
+um in this tale an English working
+ 
+
+ align:start position:0%
+um in this tale an English working
+family is sitting down to dinner in its
+
+ align:start position:0%
+family is sitting down to dinner in its
+ 
+
+ align:start position:0%
+family is sitting down to dinner in its
+kitchen the sun leaves to work at a fa
+
+ align:start position:0%
+kitchen the sun leaves to work at a fa
+ 
+
+ align:start position:0%
+kitchen the sun leaves to work at a fa
+Factory and the old parents listen to
+
+ align:start position:0%
+Factory and the old parents listen to
+ 
+
+ align:start position:0%
+Factory and the old parents listen to
+the tales of their
+
+ align:start position:0%
+the tales of their
+ 
+
+ align:start position:0%
+the tales of their
+guest a sergeant major backed from
+
+ align:start position:0%
+guest a sergeant major backed from
+ 
+
+ align:start position:0%
+guest a sergeant major backed from
+service in the Indian army he tells them
+
+ align:start position:0%
+service in the Indian army he tells them
+ 
+
+ align:start position:0%
+service in the Indian army he tells them
+of Indian magic and shows them a dried
+
+ align:start position:0%
+of Indian magic and shows them a dried
+ 
+
+ align:start position:0%
+of Indian magic and shows them a dried
+monkeyy paw which he tells them is a
+
+ align:start position:0%
+monkeyy paw which he tells them is a
+ 
+
+ align:start position:0%
+monkeyy paw which he tells them is a
+Talisman which has been been endowed by
+
+ align:start position:0%
+Talisman which has been been endowed by
+ 
+
+ align:start position:0%
+Talisman which has been been endowed by
+an Indian holy man with the virtue of
+
+ align:start position:0%
+an Indian holy man with the virtue of
+ 
+
+ align:start position:0%
+an Indian holy man with the virtue of
+giving three wishes to each of three
+
+ align:start position:0%
+giving three wishes to each of three
+ 
+
+ align:start position:0%
+giving three wishes to each of three
+successive
+
+ align:start position:0%
+successive
+ 
+
+ align:start position:0%
+successive
+owners this he says was to prove the
+
+ align:start position:0%
+owners this he says was to prove the
+ 
+
+ align:start position:0%
+owners this he says was to prove the
+Folly of defying
+
+ align:start position:0%
+Folly of defying
+ 
+
+ align:start position:0%
+Folly of defying
+fate important to remember this that
+
+ align:start position:0%
+fate important to remember this that
+ 
+
+ align:start position:0%
+fate important to remember this that
+phrase there the Folly of defying
+
+ align:start position:0%
+phrase there the Folly of defying
+ 
+
+ align:start position:0%
+phrase there the Folly of defying
+fate he says that he does not know what
+
+ align:start position:0%
+fate he says that he does not know what
+ 
+
+ align:start position:0%
+fate he says that he does not know what
+were the first two wishes wishes of the
+
+ align:start position:0%
+were the first two wishes wishes of the
+ 
+
+ align:start position:0%
+were the first two wishes wishes of the
+first owner but that the last one was
+
+ align:start position:0%
+first owner but that the last one was
+ 
+
+ align:start position:0%
+first owner but that the last one was
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+death This should have told him
+
+ align:start position:0%
+death This should have told him
+ 
+
+ align:start position:0%
+death This should have told him
+something he self was the second owner
+
+ align:start position:0%
+something he self was the second owner
+ 
+
+ align:start position:0%
+something he self was the second owner
+but his experiences were too terrible to
+
+ align:start position:0%
+but his experiences were too terrible to
+ 
+
+ align:start position:0%
+but his experiences were too terrible to
+relate he's about to cast the p a Coal
+
+ align:start position:0%
+relate he's about to cast the p a Coal
+ 
+
+ align:start position:0%
+relate he's about to cast the p a Coal
+Fire when his host retrieves it and
+
+ align:start position:0%
+Fire when his host retrieves it and
+ 
+
+ align:start position:0%
+Fire when his host retrieves it and
+despite all the sergeant major can do
+
+ align:start position:0%
+despite all the sergeant major can do
+ 
+
+ align:start position:0%
+despite all the sergeant major can do
+wishes for 200
+
+ align:start position:0%
+wishes for 200
+ 
+
+ align:start position:0%
+wishes for 200
+lb shortly thereafter there is a knock
+
+ align:start position:0%
+lb shortly thereafter there is a knock
+ 
+
+ align:start position:0%
+lb shortly thereafter there is a knock
+at the door a very solemn gentleman is
+
+ align:start position:0%
+at the door a very solemn gentleman is
+ 
+
+ align:start position:0%
+at the door a very solemn gentleman is
+there from the company which has
+
+ align:start position:0%
+there from the company which has
+ 
+
+ align:start position:0%
+there from the company which has
+employed his son as gently as he can he
+
+ align:start position:0%
+employed his son as gently as he can he
+ 
+
+ align:start position:0%
+employed his son as gently as he can he
+breaks the news that the son has been
+
+ align:start position:0%
+breaks the news that the son has been
+ 
+
+ align:start position:0%
+breaks the news that the son has been
+killed in an accident at the
+
+ align:start position:0%
+killed in an accident at the
+ 
+
+ align:start position:0%
+killed in an accident at the
+factory without recognizing any
+
+ align:start position:0%
+factory without recognizing any
+ 
+
+ align:start position:0%
+factory without recognizing any
+responsibility in the matter the company
+
+ align:start position:0%
+responsibility in the matter the company
+ 
+
+ align:start position:0%
+responsibility in the matter the company
+offers its sympathy and 200b as a as a
+
+ align:start position:0%
+offers its sympathy and 200b as a as a
+ 
+
+ align:start position:0%
+offers its sympathy and 200b as a as a
+solatium as a compensation the parents
+
+ align:start position:0%
+solatium as a compensation the parents
+ 
+
+ align:start position:0%
+solatium as a compensation the parents
+are distracted and at the mother's
+
+ align:start position:0%
+are distracted and at the mother's
+ 
+
+ align:start position:0%
+are distracted and at the mother's
+suggestion they wish the sun Back Again
+
+ align:start position:0%
+suggestion they wish the sun Back Again
+ 
+
+ align:start position:0%
+suggestion they wish the sun Back Again
+by now it is dark without a dark windy
+
+ align:start position:0%
+by now it is dark without a dark windy
+ 
+
+ align:start position:0%
+by now it is dark without a dark windy
+night again there is a knocking at the
+
+ align:start position:0%
+night again there is a knocking at the
+ 
+
+ align:start position:0%
+night again there is a knocking at the
+door somehow the parents know that it is
+
+ align:start position:0%
+door somehow the parents know that it is
+ 
+
+ align:start position:0%
+door somehow the parents know that it is
+their son but not in the flesh the story
+
+ align:start position:0%
+their son but not in the flesh the story
+ 
+
+ align:start position:0%
+their son but not in the flesh the story
+ends with the third wish that the ghost
+
+ align:start position:0%
+ends with the third wish that the ghost
+ 
+
+ align:start position:0%
+ends with the third wish that the ghost
+should go
+
+ align:start position:0%
+should go
+ 
+
+ align:start position:0%
+should go
+away the theme of all these Tales is the
+
+ align:start position:0%
+away the theme of all these Tales is the
+ 
+
+ align:start position:0%
+away the theme of all these Tales is the
+danger of magic this seems to lie in the
+
+ align:start position:0%
+danger of magic this seems to lie in the
+ 
+
+ align:start position:0%
+danger of magic this seems to lie in the
+fact that the operation of magic is
+
+ align:start position:0%
+fact that the operation of magic is
+ 
+
+ align:start position:0%
+fact that the operation of magic is
+singularly literal minded which Laura
+
+ align:start position:0%
+singularly literal minded which Laura
+ 
+
+ align:start position:0%
+singularly literal minded which Laura
+mentioned and that if it grants you
+
+ align:start position:0%
+mentioned and that if it grants you
+ 
+
+ align:start position:0%
+mentioned and that if it grants you
+anything at all it grants you uh it
+
+ align:start position:0%
+anything at all it grants you uh it
+ 
+
+ align:start position:0%
+anything at all it grants you uh it
+grants what you ask for not what you
+
+ align:start position:0%
+grants what you ask for not what you
+ 
+
+ align:start position:0%
+grants what you ask for not what you
+should have asked for or what you
+
+ align:start position:0%
+should have asked for or what you
+ 
+
+ align:start position:0%
+should have asked for or what you
+intend so this is his uh tale and he you
+
+ align:start position:0%
+intend so this is his uh tale and he you
+ 
+
+ align:start position:0%
+intend so this is his uh tale and he you
+know again he's uh using this to uh to
+
+ align:start position:0%
+know again he's uh using this to uh to
+ 
+
+ align:start position:0%
+know again he's uh using this to uh to
+suggest yes that there are many things
+
+ align:start position:0%
+suggest yes that there are many things
+ 
+
+ align:start position:0%
+suggest yes that there are many things
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh we we can
+
+ align:start position:0%
+uh we we can
+ 
+
+ align:start position:0%
+uh we we can
+develop and uh they may not be what we
+
+ align:start position:0%
+develop and uh they may not be what we
+ 
+
+ align:start position:0%
+develop and uh they may not be what we
+thought they would
+
+ align:start position:0%
+thought they would
+ 
+
+ align:start position:0%
+thought they would
+be his argument that
+
+ align:start position:0%
+be his argument that
+ 
+
+ align:start position:0%
+be his argument that
+uh sorcery is um uh is is in some ways
+
+ align:start position:0%
+uh sorcery is um uh is is in some ways
+ 
+
+ align:start position:0%
+uh sorcery is um uh is is in some ways
+science is similar in some ways to
+
+ align:start position:0%
+science is similar in some ways to
+ 
+
+ align:start position:0%
+science is similar in some ways to
+sorcery I mean sorcery is Magic science
+
+ align:start position:0%
+sorcery I mean sorcery is Magic science
+ 
+
+ align:start position:0%
+sorcery I mean sorcery is Magic science
+is not Magic
+
+ align:start position:0%
+is not Magic
+ 
+
+ align:start position:0%
+is not Magic
+but there are certain kinds of power
+
+ align:start position:0%
+but there are certain kinds of power
+ 
+
+ align:start position:0%
+but there are certain kinds of power
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+are uh delivered
+
+ align:start position:0%
+are uh delivered
+ 
+
+ align:start position:0%
+are uh delivered
+through the applications of Science and
+
+ align:start position:0%
+through the applications of Science and
+ 
+
+ align:start position:0%
+through the applications of Science and
+again his his he's not a he's not a lite
+
+ align:start position:0%
+again his his he's not a he's not a lite
+ 
+
+ align:start position:0%
+again his his he's not a he's not a lite
+or a I mean he's at the core of a lot of
+
+ align:start position:0%
+or a I mean he's at the core of a lot of
+ 
+
+ align:start position:0%
+or a I mean he's at the core of a lot of
+but what he what he is saying is uh we
+
+ align:start position:0%
+but what he what he is saying is uh we
+ 
+
+ align:start position:0%
+but what he what he is saying is uh we
+need to think about these the people who
+
+ align:start position:0%
+need to think about these the people who
+ 
+
+ align:start position:0%
+need to think about these the people who
+develop it need to take some kind of uh
+
+ align:start position:0%
+develop it need to take some kind of uh
+ 
+
+ align:start position:0%
+develop it need to take some kind of uh
+role in thinking about what it's
+
+ align:start position:0%
+role in thinking about what it's
+ 
+
+ align:start position:0%
+role in thinking about what it's
+applications will be and what it social
+
+ align:start position:0%
+applications will be and what it social
+ 
+
+ align:start position:0%
+applications will be and what it social
+impact will be uh they can't simply they
+
+ align:start position:0%
+impact will be uh they can't simply they
+ 
+
+ align:start position:0%
+impact will be uh they can't simply they
+shouldn't
+
+ align:start position:0%
+shouldn't
+ 
+
+ align:start position:0%
+shouldn't
+simply be the technical people who say
+
+ align:start position:0%
+simply be the technical people who say
+ 
+
+ align:start position:0%
+simply be the technical people who say
+well it's somebody else's problem I
+
+ align:start position:0%
+well it's somebody else's problem I
+ 
+
+ align:start position:0%
+well it's somebody else's problem I
+develop it but you know it's not my
+
+ align:start position:0%
+develop it but you know it's not my
+ 
+
+ align:start position:0%
+develop it but you know it's not my
+problem to control it uh he he he's
+
+ align:start position:0%
+problem to control it uh he he he's
+ 
+
+ align:start position:0%
+problem to control it uh he he he's
+saying that this
+
+ align:start position:0%
+saying that this
+ 
+
+ align:start position:0%
+saying that this
+responsibility extends to the people who
+
+ align:start position:0%
+responsibility extends to the people who
+ 
+
+ align:start position:0%
+responsibility extends to the people who
+make it who make the make the
+
+ align:start position:0%
+make it who make the make the
+ 
+
+ align:start position:0%
+make it who make the make the
+Technologies so so his uh
+
+ align:start position:0%
+Technologies so so his uh
+ 
+
+ align:start position:0%
+Technologies so so his uh
+I mean his message is is also deals with
+
+ align:start position:0%
+I mean his message is is also deals with
+ 
+
+ align:start position:0%
+I mean his message is is also deals with
+simply the fact that uh
+
+ align:start position:0%
+simply the fact that uh
+ 
+
+ align:start position:0%
+simply the fact that uh
+automization you know we are automize
+
+ align:start position:0%
+automization you know we are automize
+ 
+
+ align:start position:0%
+automization you know we are automize
+everything I mean for many many reasons
+
+ align:start position:0%
+everything I mean for many many reasons
+ 
+
+ align:start position:0%
+everything I mean for many many reasons
+I mean we interact now with all kinds of
+
+ align:start position:0%
+I mean we interact now with all kinds of
+ 
+
+ align:start position:0%
+I mean we interact now with all kinds of
+devices and all kinds of processes have
+
+ align:start position:0%
+devices and all kinds of processes have
+ 
+
+ align:start position:0%
+devices and all kinds of processes have
+been
+
+ align:start position:0%
+been
+ 
+
+ align:start position:0%
+been
+automated a goal-seeking mechanism will
+
+ align:start position:0%
+automated a goal-seeking mechanism will
+ 
+
+ align:start position:0%
+automated a goal-seeking mechanism will
+not necessarily seek our goals unless we
+
+ align:start position:0%
+not necessarily seek our goals unless we
+ 
+
+ align:start position:0%
+not necessarily seek our goals unless we
+design it for that purpose and in that
+
+ align:start position:0%
+design it for that purpose and in that
+ 
+
+ align:start position:0%
+design it for that purpose and in that
+designing we must foresee all the steps
+
+ align:start position:0%
+designing we must foresee all the steps
+ 
+
+ align:start position:0%
+designing we must foresee all the steps
+of the process process for which it is
+
+ align:start position:0%
+of the process process for which it is
+ 
+
+ align:start position:0%
+of the process process for which it is
+designed that's what I was just
+
+ align:start position:0%
+designed that's what I was just
+ 
+
+ align:start position:0%
+designed that's what I was just
+mentioning the penalties for errors of
+
+ align:start position:0%
+mentioning the penalties for errors of
+ 
+
+ align:start position:0%
+mentioning the penalties for errors of
+foresight will be enormously increased
+
+ align:start position:0%
+foresight will be enormously increased
+ 
+
+ align:start position:0%
+foresight will be enormously increased
+as automization comes into its full use
+
+ align:start position:0%
+as automization comes into its full use
+ 
+
+ align:start position:0%
+as automization comes into its full use
+so this is this is again a concern from
+
+ align:start position:0%
+so this is this is again a concern from
+ 
+
+ align:start position:0%
+so this is this is again a concern from
+somebody who's at the core of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process and this this is also my
+
+ align:start position:0%
+process and this this is also my
+ 
+
+ align:start position:0%
+process and this this is also my
+favorite quote the world of the future
+
+ align:start position:0%
+favorite quote the world of the future
+ 
+
+ align:start position:0%
+favorite quote the world of the future
+will be in ever more demanding struggle
+
+ align:start position:0%
+will be in ever more demanding struggle
+ 
+
+ align:start position:0%
+will be in ever more demanding struggle
+against the limitations of our
+
+ align:start position:0%
+against the limitations of our
+ 
+
+ align:start position:0%
+against the limitations of our
+intelligence not a comfortable hammock
+
+ align:start position:0%
+intelligence not a comfortable hammock
+ 
+
+ align:start position:0%
+intelligence not a comfortable hammock
+in which we can lie down to be waited
+
+ align:start position:0%
+in which we can lie down to be waited
+ 
+
+ align:start position:0%
+in which we can lie down to be waited
+upon by our robot
+
+ align:start position:0%
+upon by our robot
+ 
+
+ align:start position:0%
+upon by our robot
+slaves so he foresaw the weak link here
+
+ align:start position:0%
+slaves so he foresaw the weak link here
+ 
+
+ align:start position:0%
+slaves so he foresaw the weak link here
+as the human
+
+ align:start position:0%
+as the human
+ 
+
+ align:start position:0%
+as the human
+link the ability of humans to kind of
+
+ align:start position:0%
+link the ability of humans to kind of
+ 
+
+ align:start position:0%
+link the ability of humans to kind of
+keep up with what's happening and to
+
+ align:start position:0%
+keep up with what's happening and to
+ 
+
+ align:start position:0%
+keep up with what's happening and to
+understand and control it and to use it
+
+ align:start position:0%
+understand and control it and to use it
+ 
+
+ align:start position:0%
+understand and control it and to use it
+wisely Jake I think that's really kind
+
+ align:start position:0%
+wisely Jake I think that's really kind
+ 
+
+ align:start position:0%
+wisely Jake I think that's really kind
+of his whole point overall is that uh
+
+ align:start position:0%
+of his whole point overall is that uh
+ 
+
+ align:start position:0%
+of his whole point overall is that uh
+the limiting factor is our ability to
+
+ align:start position:0%
+the limiting factor is our ability to
+ 
+
+ align:start position:0%
+the limiting factor is our ability to
+convey to our machines or robots or
+
+ align:start position:0%
+convey to our machines or robots or
+ 
+
+ align:start position:0%
+convey to our machines or robots or
+artificial intelligence or software what
+
+ align:start position:0%
+artificial intelligence or software what
+ 
+
+ align:start position:0%
+artificial intelligence or software what
+exactly you want from it and that's
+
+ align:start position:0%
+exactly you want from it and that's
+ 
+
+ align:start position:0%
+exactly you want from it and that's
+that's the why
+
+ align:start position:0%
+that's the why
+ 
+
+ align:start position:0%
+that's the why
+there's however many different
+
+ align:start position:0%
+there's however many different
+ 
+
+ align:start position:0%
+there's however many different
+programming languages there's different
+
+ align:start position:0%
+programming languages there's different
+ 
+
+ align:start position:0%
+programming languages there's different
+ways to program a different certain
+
+ align:start position:0%
+ways to program a different certain
+ 
+
+ align:start position:0%
+ways to program a different certain
+program there's so much variability
+
+ align:start position:0%
+program there's so much variability
+ 
+
+ align:start position:0%
+program there's so much variability
+because there is no perfect and exact
+
+ align:start position:0%
+because there is no perfect and exact
+ 
+
+ align:start position:0%
+because there is no perfect and exact
+way to make it do exactly what we want
+
+ align:start position:0%
+way to make it do exactly what we want
+ 
+
+ align:start position:0%
+way to make it do exactly what we want
+we have to kind of use work throughs
+
+ align:start position:0%
+we have to kind of use work throughs
+ 
+
+ align:start position:0%
+we have to kind of use work throughs
+work arounds and different things to try
+
+ align:start position:0%
+work arounds and different things to try
+ 
+
+ align:start position:0%
+work arounds and different things to try
+try to get what we want there's no way
+
+ align:start position:0%
+try to get what we want there's no way
+ 
+
+ align:start position:0%
+try to get what we want there's no way
+to you can't just tell a computer do
+
+ align:start position:0%
+to you can't just tell a computer do
+ 
+
+ align:start position:0%
+to you can't just tell a computer do
+this and have it come up with the way to
+
+ align:start position:0%
+this and have it come up with the way to
+ 
+
+ align:start position:0%
+this and have it come up with the way to
+do you to say take this step this step
+
+ align:start position:0%
+do you to say take this step this step
+ 
+
+ align:start position:0%
+do you to say take this step this step
+if this and that the case is this case
+
+ align:start position:0%
+if this and that the case is this case
+ 
+
+ align:start position:0%
+if this and that the case is this case
+this case this case else and all sorts
+
+ align:start position:0%
+this case this case else and all sorts
+ 
+
+ align:start position:0%
+this case this case else and all sorts
+of other things try to get what we want
+
+ align:start position:0%
+of other things try to get what we want
+ 
+
+ align:start position:0%
+of other things try to get what we want
+there's no way to just say do it and
+
+ align:start position:0%
+there's no way to just say do it and
+ 
+
+ align:start position:0%
+there's no way to just say do it and
+have to get done yeah yeah that's where
+
+ align:start position:0%
+have to get done yeah yeah that's where
+ 
+
+ align:start position:0%
+have to get done yeah yeah that's where
+the challenge is TR so that's the
+
+ align:start position:0%
+the challenge is TR so that's the
+ 
+
+ align:start position:0%
+the challenge is TR so that's the
+challenge of design is is to understand
+
+ align:start position:0%
+challenge of design is is to understand
+ 
+
+ align:start position:0%
+challenge of design is is to understand
+the design design and to see how its
+
+ align:start position:0%
+the design design and to see how its
+ 
+
+ align:start position:0%
+the design design and to see how its
+expression is ultimately going to
+
+ align:start position:0%
+expression is ultimately going to
+ 
+
+ align:start position:0%
+expression is ultimately going to
+ultimately take place and the full range
+
+ align:start position:0%
+ultimately take place and the full range
+ 
+
+ align:start position:0%
+ultimately take place and the full range
+of things because there are many many
+
+ align:start position:0%
+of things because there are many many
+ 
+
+ align:start position:0%
+of things because there are many many
+things that have been designed with
+
+ align:start position:0%
+things that have been designed with
+ 
+
+ align:start position:0%
+things that have been designed with
+perfectly wonderful intentions and uh
+
+ align:start position:0%
+perfectly wonderful intentions and uh
+ 
+
+ align:start position:0%
+perfectly wonderful intentions and uh
+that have turned out not to really work
+
+ align:start position:0%
+that have turned out not to really work
+ 
+
+ align:start position:0%
+that have turned out not to really work
+the way that we uh the designers
+
+ align:start position:0%
+the way that we uh the designers
+ 
+
+ align:start position:0%
+the way that we uh the designers
+intended them to even though they had
+
+ align:start position:0%
+intended them to even though they had
+ 
+
+ align:start position:0%
+intended them to even though they had
+the best of
+
+ align:start position:0%
+the best of
+ 
+
+ align:start position:0%
+the best of
+intentions so that's that's a big and
+
+ align:start position:0%
+intentions so that's that's a big and
+ 
+
+ align:start position:0%
+intentions so that's that's a big and
+especially as Things become more and
+
+ align:start position:0%
+especially as Things become more and
+ 
+
+ align:start position:0%
+especially as Things become more and
+more powerful and as Computing really
+
+ align:start position:0%
+more powerful and as Computing really
+ 
+
+ align:start position:0%
+more powerful and as Computing really
+magnifies our
+
+ align:start position:0%
+magnifies our
+ 
+
+ align:start position:0%
+magnifies our
+power um you know we are definitely in a
+
+ align:start position:0%
+power um you know we are definitely in a
+ 
+
+ align:start position:0%
+power um you know we are definitely in a
+in a more complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+World okay you see some of these
+
+ align:start position:0%
+World okay you see some of these
+ 
+
+ align:start position:0%
+World okay you see some of these
+environments we we we live in you know
+
+ align:start position:0%
+environments we we we live in you know
+ 
+
+ align:start position:0%
+environments we we we live in you know
+can you imagine being in the Space
+
+ align:start position:0%
+can you imagine being in the Space
+ 
+
+ align:start position:0%
+can you imagine being in the Space
+Capsule and going off to uh you know the
+
+ align:start position:0%
+Capsule and going off to uh you know the
+ 
+
+ align:start position:0%
+Capsule and going off to uh you know the
+moon it's like trying to you know some
+
+ align:start position:0%
+moon it's like trying to you know some
+ 
+
+ align:start position:0%
+moon it's like trying to you know some
+of you may have seen the the film
+
+ align:start position:0%
+of you may have seen the the film
+ 
+
+ align:start position:0%
+of you may have seen the the film
+U uh you know just just trying to
+
+ align:start position:0%
+U uh you know just just trying to
+ 
+
+ align:start position:0%
+U uh you know just just trying to
+be uh aware of what's happening in that
+
+ align:start position:0%
+be uh aware of what's happening in that
+ 
+
+ align:start position:0%
+be uh aware of what's happening in that
+kind of a system I mean humans have
+
+ align:start position:0%
+kind of a system I mean humans have
+ 
+
+ align:start position:0%
+kind of a system I mean humans have
+really uh put a a tremendous challenge
+
+ align:start position:0%
+really uh put a a tremendous challenge
+ 
+
+ align:start position:0%
+really uh put a a tremendous challenge
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+themselves okay so uh he's uh you know
+
+ align:start position:0%
+themselves okay so uh he's uh you know
+ 
+
+ align:start position:0%
+themselves okay so uh he's uh you know
+this is a great little book uh you know
+
+ align:start position:0%
+this is a great little book uh you know
+ 
+
+ align:start position:0%
+this is a great little book uh you know
+when you get some time I hope you're
+
+ align:start position:0%
+when you get some time I hope you're
+ 
+
+ align:start position:0%
+when you get some time I hope you're
+saving some of these books that uh you
+
+ align:start position:0%
+saving some of these books that uh you
+ 
+
+ align:start position:0%
+saving some of these books that uh you
+have the links and things of that sort
+
+ align:start position:0%
+have the links and things of that sort
+ 
+
+ align:start position:0%
+have the links and things of that sort
+because it's definitely worth revisiting
+
+ align:start position:0%
+because it's definitely worth revisiting
+ 
+
+ align:start position:0%
+because it's definitely worth revisiting
+this book it's a wonderful little book
+
+ align:start position:0%
+this book it's a wonderful little book
+ 
+
+ align:start position:0%
+this book it's a wonderful little book
+uh and U in some ways uh it was his his
+
+ align:start position:0%
+uh and U in some ways uh it was his his
+ 
+
+ align:start position:0%
+uh and U in some ways uh it was his his
+swans song his message to the world of
+
+ align:start position:0%
+swans song his message to the world of
+ 
+
+ align:start position:0%
+swans song his message to the world of
+uh from you know his accumulated
+
+ align:start position:0%
+uh from you know his accumulated
+ 
+
+ align:start position:0%
+uh from you know his accumulated
+wisdom uh and uh you know a life of uh
+
+ align:start position:0%
+wisdom uh and uh you know a life of uh
+ 
+
+ align:start position:0%
+wisdom uh and uh you know a life of uh
+incredible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+achievement
\ No newline at end of file
diff --git a/1_dMnMLbIok.txt b/1_dMnMLbIok.txt
new file mode 100644
index 0000000000000000000000000000000000000000..992938650fd155fc8275a607663371c0ea89b99a
--- /dev/null
+++ b/1_dMnMLbIok.txt
@@ -0,0 +1,3179 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK, let's start.
+
+So we are going to change
+perspective again and think
+
+in terms of lattice models.
+
+So for the first
+part of this course,
+
+I was trying to change
+your perspective
+
+from thinking in terms of
+microscopic degrees of freedom
+
+to a statistical field.
+
+Now we are going to go back
+and try to build pictures
+
+around things that
+look more microscopic.
+
+Typically, in many solid
+state configurations,
+
+we are dealing with transitions
+that take place on a lattice.
+
+For example, imagine a square
+lattice, which is easy to draw,
+
+but there could be all kinds
+of cubic and more complex
+
+lattices.
+
+And then, at each
+side of this lattice,
+
+you may have one microscopic
+degrees of freedom
+
+that is ultimately participating
+in the ordering and the phase
+
+transition that
+you have in mind.
+
+Could, for example,
+be a spin, or it
+
+could be one atom
+in a binary mixture.
+
+And what you would like to do
+is to construct a partition
+
+function, again, by summing
+over all degrees of freedom.
+
+And we need some
+kind of Hamiltonian.
+
+And what we are going
+to assume governs
+
+that Hamiltonian is the analog
+of this locality assumption
+
+that we have in
+statistical field theories.
+
+That is, we are going
+to assume that one
+
+of our degrees of
+freedom essentially
+
+talks to a small
+neighborhood around it.
+
+And the simplest
+neighborhood would
+
+be to basically talk to
+the nearest neighbor.
+
+So if I, for example,
+assign index i
+
+to each side of
+the lattice, let's
+
+say I have some variable at each
+side that could be something.
+
+Let's call it SI.
+
+Then my partition
+function would be
+
+obtained by summing
+over all configurations.
+
+And the weight I'm going to
+assume in terms of this lattice
+
+picture to be a sum
+over interactions
+
+that exist between
+pairs of sides.
+
+So that's already an assumption
+that it's a pairwise thing.
+
+And I'm going to use this
+symbol ij with an angular
+
+bracket along it,
+around it, to indicate
+
+the sum over nearest neighbors.
+
+And there is some
+function of the variables
+
+that live on these neighbors.
+
+So basically, in the
+picture that I have drawn,
+
+interactions exist only between
+the places that you see lines.
+
+So that this pin
+does not interact
+
+with this pin, this
+pin, or this pin,
+
+but it interacts
+with these four pins,
+
+to which it is near neighbor.
+
+Now clearly, the form
+of the interaction
+
+has to be dictated by
+your degrees of freedom.
+
+And the idea of
+this representation,
+
+as opposed to the previous
+statistical field theory
+
+that we had, is that in
+several important instances,
+
+you may want to know not only
+what these universal properties
+
+are, but also, let's say, the
+explicit temperature or phase
+
+diagram of the system as a
+function of external parameters
+
+as well as temperature.
+
+And if you have some idea of
+how your microscopic degrees
+
+of freedom interact
+with each other,
+
+you should be able to solve
+this kind of partition function,
+
+get the singularities,
+et cetera.
+
+So let's look at some simple
+versions of this construction
+
+and gradually discuss
+the kinds of things
+
+that we could do with it.
+
+So some simple models.
+
+The simplest one
+is the Ising model
+
+where the variable that
+you have at each side
+
+has two possibilities.
+
+So it's a binary variable in
+the context of a binary alloy.
+
+It could be, let's
+say, atom A or atom
+
+B that is occupying
+a particular site.
+
+There are also cases
+where there will be some--
+
+if this is a surface and
+you're absorbing particles
+
+on top of it, there could be
+a particle sitting here or not
+
+sitting here.
+
+So that would be also another
+example of a binary variable.
+
+So you could indicate that by
+empty or occupied, zero or one.
+
+But let's indicate it by
+plus or minus one as the two
+
+possible values
+that you can have.
+
+Now, if I look at the
+analog of the interaction
+
+that I have between two
+sites that are neighboring
+
+each other, what
+can I write down?
+
+Well, the most general
+thing that I can write down
+
+is, first of all, a
+constant I can put,
+
+such as shift of energy.
+
+There could be a linear
+term in-- let's put
+
+all of these with minus signs.
+
+Sigma i and sigma j.
+
+I assume that it is symmetric
+with respect to the two sides.
+
+For reasons to become
+apparent shortly,
+
+I will divide by z, which
+is the coordination number.
+
+How many bonds per side?
+
+And then the next
+term that I can
+
+put is something like
+j sigma i sigma j.
+
+And actually, I can't
+put anything else.
+
+Because if you s of this as
+a power series in sigma i
+
+and sigma j, and sigma
+has only two values,
+
+it will terminate here.
+
+Because any higher power of
+sigma is either one or sigma
+
+itself.
+
+So another way of writing
+this is that the partition
+
+function of the Ising model is
+obtained by summing over all 2
+
+to the n configurations
+that I have.
+
+If I have a lattice
+of n sides, each side
+
+can have two possibilities of
+a kind of Hamiltonian, which
+
+is basically some constant
+plus h sum over i sigma i kind
+
+of field that prefers one
+side or the other side.
+
+So it is an analog of a magnetic
+field in this binary system.
+
+And basically, I convert it from
+a description that is overall
+
+balanced to a description
+overall sides.
+
+And that's why I had put the
+coordination number there.
+
+It's kind of a
+matter of convention.
+
+And then a term that
+prefers neighboring sites
+
+to be aligned as
+long as k positive.
+
+So that's one
+example of a model.
+
+Another model that
+we will also look at
+
+is what I started to
+draw at the beginning.
+
+That is, at each site,
+you have a vector.
+
+And again, going in terms of
+the pictures that we had before,
+
+let's imagine that we have a
+vector that has n components.
+
+So SI is something
+that is in RN.
+
+And I will assume that the
+magnitude of this vector
+
+is one.
+
+So essentially,
+imagine that you have
+
+a unit vector, and each
+site that can rotate.
+
+So if n equals to one, you
+have essentially one component
+
+vector.
+
+Its square has to
+be one, so the two
+
+values that it can have
+are plus one and minus one.
+
+So the n equals to one case
+is the Ising model again.
+
+So this ON is a
+generalization of the Ising
+
+model to multiple components.
+
+n equals to two corresponds
+to a unit vector
+
+that can take any angle
+in two dimensions.
+
+And that is usually
+given the name xy model.
+
+n equals to three is
+something that maybe you
+
+want to use to describe
+magnetic ions in this lattice.
+
+And classically, the direction
+of this ion could be anywhere.
+
+The spin of the
+ion can be anywhere
+
+on the surface of a sphere.
+
+So that's three
+components, and this model
+
+is sometimes called
+the Heisenberg model.
+
+Yes.
+
+AUDIENCE: In the
+Ising model, what's
+
+the correspondence between g
+hat h hat j hat and g, h, and k?
+
+PROFESSOR: Minus beta.
+
+Yeah.
+
+So maybe I should have written.
+
+In order to take this-- if I
+think of this as energy pair
+
+bond, then in order to
+get the Boltzmann weight,
+
+I have to put a minus beta.
+
+So I would have said
+that this g, for example,
+
+is minus beta g hat.
+
+k is minus beta j hat.
+
+And h is minus beta h hat.
+
+So I should have
+emphasized that.
+
+What I meant by b--
+actually, I wrote
+
+b-- so what I should have
+done here to be consistent,
+
+let's write this as minus beta.
+
+Thank you.
+
+That was important.
+
+If I described these b's
+as being energies, then
+
+minus beta times
+that will be what
+
+will go in the Boltzmann factor.
+
+OK
+
+So whereas these were examples
+that we had more or less seen
+
+their continuum version in
+the Landau-Ginzburg model,
+
+there are other symmetries
+that get broken.
+
+And things for which
+we didn't discuss
+
+what the corresponding
+statistical field theory is.
+
+A commonly used case
+pertains to something
+
+that's called a Potts model.
+
+Where at each side
+you have a variable,
+
+let's call it SI,
+that takes q values,
+
+one, two, three,
+all the way to q.
+
+And I can write
+what would appear
+
+in the exponent
+minus beta h to be
+
+a sum over nearest neighbors.
+
+And I can give some kind of
+an interaction parameter here,
+
+but a delta si sj.
+
+So basically, what it says is
+that on each side of a lattice,
+
+you put a number.
+
+Could be one, two,
+three, up to q.
+
+And if two neighbors are
+the same, they like it,
+
+and they gain some
+kind of a weight.
+
+That is, if k is positive,
+encourages that to happen.
+
+If the two neighbors
+are different,
+
+then it doesn't matter.
+
+You don't gain energy,
+but you don't really
+
+care as to which one it is.
+
+The underlying symmetry that
+this has is permutation.
+
+Basically, if you were to
+permute all of these indices
+
+consistently across the
+lattice in any particular way,
+
+the energy would not change.
+
+So permutation symmetry
+is what underlies this.
+
+And again, if I look at the
+case of two, then at each side,
+
+let's say I have one or two.
+
+And one one and two two are
+things that gain energy.
+
+One two or two one don't.
+
+Clearly it is the same
+as the Ising model.
+
+So q equals to two is another
+way of writing the Ising model.
+
+Q equals to three is something
+that we haven't seen.
+
+So at each site, there
+are three possibilities.
+
+Actually, when I started at MIT
+as a graduate student in 1979,
+
+the project that I had
+to do related to the q
+
+equals to three Potts model.
+
+Where did it come from?
+
+Well, at that time,
+people were looking
+
+at surface of graphite,
+which as you know,
+
+has this hexagonal structure.
+
+And then you can
+absorb molecules
+
+on top of that, such as,
+for example, krypton.
+
+And krypton would
+want to come and sit
+
+in the center of one
+of these hexagons.
+
+But its size was such
+that once it sat there,
+
+you couldn't occupy
+any of these sides.
+
+So the next one would have
+to go, let's say, over here.
+
+Now, it is possible to
+subdivide this set of hexagons
+
+into three sub lattices.
+
+One, two, three, one,
+two, three, et cetera.
+
+Actually, I drew
+this one incorrectly.
+
+It would be sitting here.
+
+And what happens is that
+basically the agile particles
+
+would order by occupying one of
+three equivalent sublattices.
+
+So the way that that order
+got destroyed was then
+
+described by the q equals to
+three Potts universality class.
+
+You can think of
+something like q
+
+equals to four that would
+have a symmetry of a tetragon.
+
+And so some structure that
+is like a tetragon getting,
+
+let's say, distorted in
+some particular direction
+
+would then have four equivalent
+directions, et cetera.
+
+So there's a whole set of other
+types of universality classes
+
+and symmetry breakings that
+we did not discuss before.
+
+And I just want
+to emphasize that
+
+what we discussed before does
+not cover all possible symmetry
+
+breakings.
+
+It was just supposed to
+show you an important class
+
+and the technology
+to deal with that.
+
+But again, in this
+particular system,
+
+let's say you really wanted
+to know at what temperature
+
+the phase transition occurs,
+as well as what potential phase
+
+diagrams and
+critical behavior is.
+
+And then you would
+say, well, even
+
+if I could construct a
+statistical field theory
+
+and analyze it in
+two dimensions,
+
+and we've seen how
+hard it is to go
+
+below some other
+critical dimension,
+
+it doesn't tell me things about
+phase diagrams, et cetera.
+
+So maybe trying to understand
+and deal with this lattice
+
+model itself would tell
+us more information.
+
+Although about quantities that
+are not necessarily inverse.
+
+Depending on your
+microscopic model,
+
+you may try to introduce
+more complicated systems,
+
+such as inspired by quantum
+mechanics, you can think
+
+of something that
+I'll call a spin S
+
+model in which your SI
+takes values from minus s,
+
+minus s plus 1, all
+the way to plus s.
+
+There's 2s plus 1 possibilities.
+
+And you can think of this
+as components of, say,
+
+a quantum spin of s
+along the zed axis.
+
+Write some kind of
+Hamiltonian for this.
+
+But as long as you deal
+with things classically,
+
+it turns out that
+this kind of system
+
+will not really have different
+universality from the Ising
+
+model.
+
+So let's say we have
+this lattice model.
+
+Then what can we do?
+
+So in the next
+set of lectures, I
+
+will describe some tools for
+dealing with these models.
+
+One set of approaches, the
+one that we will start today,
+
+has to do with the position
+space renormalization group.
+
+That is the approach
+that we were following
+
+for renormalization previously.
+
+Dealt with going
+to Fourier space.
+
+We had this sphere,
+hyper sphere.
+
+And then we were basically
+eliminating modes
+
+at the edge of this
+sphere in Fourier space.
+
+We started actually by
+describing the process
+
+in real space.
+
+So we will see
+that in some cases,
+
+it is possible to do a
+renormalization group directly
+
+on these lattice models.
+
+Second thing is, it turns out
+that as combinatorial problems,
+
+some, but a very small
+subset of these models,
+
+are susceptible to
+exact solutions.
+
+Turns out that practically
+all models in one dimension,
+
+as we will start today,
+one can solve exactly.
+
+But there's one
+prominent case, which
+
+is the two dimensionalizing
+model that one can also
+
+solve exactly.
+
+And it's a very
+interesting solution
+
+that we will also examine in, I
+don't know, a couple of weeks.
+
+Finally, there are
+approximate schemes
+
+that people have evolved for
+studying these problems, where
+
+you have series expansions
+starting from limits, where
+
+you know what is happening.
+
+And one simple
+example would be to go
+
+to very high temperatures.
+
+And at high temperatures,
+essentially every degree
+
+of freedom does what it wants.
+
+So it's essentially a
+zero dimensional problem
+
+that you can solve.
+
+And then you can start treating
+interactions perturbatively.
+
+So this is kind of
+similar to the expansions
+
+that we had developed in 8
+333, the virial expansions,
+
+et cetera, about
+the ideal gas limit.
+
+But now done on a system
+that is a lattice,
+
+and going to
+sufficiently high order
+
+that you can say something
+about the phase transition.
+
+There is another extreme.
+
+In these systems, typically
+the zero temperature state
+
+is trivial.
+
+It is perfectly ordered.
+
+Let's say all the
+spins are aligned.
+
+And then you can start
+expanding in excitations
+
+around that state and
+see whether eventually,
+
+by including more
+and more excitations,
+
+you can see the phase transition
+out of the ordered state.
+
+And something that is actually
+probably the most common use
+
+of these models, but I
+won't cover in class,
+
+is to put them on the computer
+and do some kind of a Monte
+
+Carlo simulation,
+which is essentially
+
+a numerical way of trying to
+generate configurations that
+
+are governed by this weight.
+
+And by changing the temperature
+as it appears in that weight,
+
+whether or not one can,
+in the simulation, see
+
+the phase transition happen.
+
+So that's the change
+in perspective
+
+that I want you to have.
+
+So the first thing
+that we're going to do
+
+is to do the number one here,
+to do the position space
+
+renormalization group of
+one dimensional Ising model.
+
+And the procedure that
+I describe for you
+
+is sufficiently general
+that in fact you
+
+can apply to any other
+one dimensional model,
+
+as long as you only have these
+nearest neighbor interactions.
+
+So here you have a lattice
+that is one dimensional.
+
+So you have a set
+of sites one, two.
+
+At some point, you have i,
+i minus one, i plus one.
+
+Let's say we call
+the last one n.
+
+So there are n sites.
+
+There are going to be 2 to
+the n possible configurations.
+
+And your task is given
+that at each site,
+
+there's a variable
+that is binary.
+
+You want to calculate a
+partition function, which
+
+is a sum over all these 2
+to the n configurations.
+
+Of a weight that is
+this e to the sum
+
+over i B, the interaction
+that couples SI and SI plus 1.
+
+Maybe I should have
+called this e hat.
+
+And B is the thing that has
+minus beta absorbed in it.
+
+So notice that basically, the
+way that I have written it,
+
+one is interacting with two.
+
+i minus one is
+interacting with i.
+
+i is interacting
+with i plus one.
+
+So I wrote the nearest
+neighbor interaction
+
+in this particular fashion.
+
+We may or may not worry
+about the last spin,
+
+whether I want to
+finish the series here,
+
+or sometimes I will use
+periodic boundary condition
+
+and bring it back and couple
+it to the first one, where
+
+I have a ring.
+
+So that's another possibility.
+
+Doesn't really matter all
+that much at this stage.
+
+So this runs for i
+going from one to n.
+
+There are n degrees of freedom.
+
+Now, renormalization
+group is a procedure
+
+by which I get rid of
+some degrees of freedom.
+
+So previously, I have
+emphasized that what we did
+
+was some kind of an averaging.
+
+So we said that
+let's say I could
+
+do some averaging of
+three sites and call
+
+some kind of a representative
+of those three.
+
+Let's say that we
+want to do a RG
+
+by a factor of b equals to two.
+
+So then maybe you say that
+I will pick sigma i prime
+
+and u sigma i to be sigma i
+plus sigma i plus 1 over 2,
+
+doing some kind of an average.
+
+The problem with this choice
+is that if the two spins are
+
+both pluses, I will get plus.
+
+If they're both minuses,
+I will get minus.
+
+If there is one plus and
+one minus, I will get zero.
+
+Why that is not
+nice is that that
+
+changes the structure
+of the theory.
+
+So I started with
+binary variables.
+
+I do this rescaling.
+
+If I choose this scheme, I will
+have three variables per site.
+
+But I can insist upon keeping
+two variables per site, as long
+
+as I do everything
+consistently and precisely.
+
+So maybe I can say that
+when this occurs, where
+
+the two sites are different,
+and the average would be zero,
+
+I choose as tiebreaker
+the left one.
+
+So then I will
+have plus or minus.
+
+Now you can convince
+yourself that if I do this,
+
+and I choose always the
+left one as tiebreaker,
+
+the story is the same as
+just keeping the left one.
+
+So essentially, this kind of
+averaging with a tiebreaker
+
+is equivalent to getting
+rid of every other spin.
+
+And so essentially
+what I can do is
+
+to say that I call
+a sigma i prime.
+
+Now, in the new listing that I
+have, this thing is no longer,
+
+let's say, the tenth one.
+
+It becomes the fifth one because
+I removed half of things.
+
+So sigma i prime is
+really sigma 2i minus 1.
+
+So basically, all the odd ones
+I will call to be my new spins.
+
+All the even ones I want to
+get rid of, I'll call them SI.
+
+So this is just a
+renaming of the variables.
+
+I did some handwaving
+to justify.
+
+Effectivity, all I did
+was I broke this sum
+
+into two sets of sums, but
+I call sigma i prime and SI.
+
+And each one of
+them the index i,
+
+rather than running from
+1 to n in this new set,
+
+the index i runs
+from 1 to n over 2.
+
+So what I have said,
+agian, is very trivial.
+
+I've said that the
+original sum, I
+
+bring over as a sum over
+the odd spin, whose names
+
+I have changed, and a
+sum over even spins,
+
+whose names I have called SI.
+
+And I have an interaction,
+which I can write as sum over i,
+
+essentially running
+from 1 to n over 2.
+
+I start with the interaction
+that involves sigma i
+
+prime with si because
+now each sigma i
+
+prime is acting with
+an s on one side.
+
+And then there's
+another interaction,
+
+which is SI, and the next.
+
+So essentially, I rename
+things, and I regrouped bonds.
+
+And the sum that was n terms
+now n over 2 pairs of terms.
+
+Nothing significant.
+
+But the point is
+that over here, I
+
+can rewrite this as a
+sum over sigma i prime.
+
+And this is a product over
+terms where within each term,
+
+I can sum over the spin that
+is sitting between two spins
+
+that I'm keeping.
+
+So I'm getting rid of this spin
+that sits between spin sigma
+
+i prime and sigma
+i plus 1 prime.
+
+Now, once I perform
+this sum over SI here,
+
+then what I will
+get is some function
+
+that depends on sigma i prime
+and sigma i plus 1 prime.
+
+And I can choose to
+write that function as e
+
+to the b prime sigma i
+prime sigma i plus 1 prime.
+
+And hence, the
+partition function
+
+after removing every
+other spin is the same
+
+as the partition function that
+I have for the remaining spins
+
+weighted with this b prime.
+
+So you can see that I took the
+original partition function
+
+and recast it in
+precisely the same form
+
+after removing half of
+the degrees of freedom.
+
+Now, the original b
+for the Ising model
+
+is going to be parameterized
+by g, h, and k.
+
+So the b prime I
+did parameterize.
+
+So this, let's say, emphasizes
+parameterized by g, h, k.
+
+I can similarly
+parameterize this
+
+by g prime, h prime, k prime.
+
+And how do I know that?
+
+Because when I was
+writing this, I
+
+emphasized that this is
+the most general form
+
+that I can write down.
+
+There is nothing else
+other than this form
+
+that I can write down for this.
+
+So what I have essentially is
+that this e to the b prime,
+
+which is e to the g prime plus
+h prime sigma i prime plus sigma
+
+i plus 1 prime plus k
+prime sigma i prime sigma
+
+i plus 1 prime involves
+these three parameters,
+
+is obtained by summing over SI.
+
+Let me just call it s being
+minus plus 1 of e to the g plus
+
+h sigma 1 sigma i prime plus
+SI plus k sigma i prime SI
+
+plus g plus kh sigma SI plus
+sigma i plus 1 prime plus k SI
+
+sigma i plus 1.
+
+So it's an implicit
+equation that
+
+relates g prime, h prime,
+k prime, to g, h, and k.
+
+And in particular, just
+to make the writing
+
+of this thing explicit more
+clearly, I will give names.
+
+I will call e to the k to
+the x, e to the h to by,
+
+e to the g to bz.
+
+And here, similarly,
+I will write x prime e
+
+to the k prime, y
+prime e to the h prime,
+
+and z prime is e to the g prime.
+
+So now I just have
+to make a table.
+
+I have sigma i prime
+sigma i plus 1 prime.
+
+And here also I can
+have values of s.
+
+And the simplest possibility
+here is I have plus plus.
+
+Actually, let's put
+this number further out.
+
+So if both the sigma
+primes are plus,
+
+what do I have on
+the left hand side?
+
+I have e to the g
+prime, which is z prime.
+
+e to the 2h prime, which
+is y prime squared.
+
+e to the k prime,
+which is x prime.
+
+What do I have on
+the left hand side?
+
+On the left hand side, I
+have two possible things
+
+that I can put.
+
+I can put s to be either
+plus or s to be minus,
+
+and I have to sum over
+those two possibilities.
+
+You can see that in all
+cases, I have e to the 2g.
+
+That's a trivial thing.
+
+So I will always
+have a z squared.
+
+Irrespective of s, I
+have two factors of e
+
+to the h sigma prime.
+
+OK, you know what happened?
+
+I should've used--
+since I was using
+
+b, this factor of h over 2.
+
+So I really should have
+put here an h prime over 2,
+
+and I should have
+put here an h over 2
+
+and h over 2 because the field
+that was residing on the sites,
+
+I am dividing half of it
+to the right and half of it
+
+to the left bond.
+
+And since I'm writing things
+in terms of the bonds,
+
+that's how I should go.
+
+So what I have here actually
+is now one factor of i prime.
+
+That's better.
+
+Now, what I have on
+the right is similarly
+
+one factor of y
+from the h's that
+
+go with sigma 1
+prime, sigma 2 prime.
+
+And then if s is
+plus, then you can
+
+see that I will get two
+factors of e to the k
+
+because both bonds
+will be satisfied.
+
+Both bonds will be plus plus.
+
+So I will get x squared,
+and the contribution
+
+to the h of the
+intermediate bond s
+
+is going to be 1e to the h.
+
+So I will get x squared y.
+
+Whereas if I put it the
+intermediate sign for s
+
+to be minus 1, then I have
+two pluses at the end.
+
+The one in the middle is minus.
+
+So I would have two
+dissatisfied factors of e
+
+to the k becoming
+e to the minus k.
+
+So it's x to the minus 2.
+
+And the field also
+will give a factor of e
+
+to the minus h or y inverse.
+
+So there are four
+possibilities here.
+
+The next one is minus minus.
+
+z prime will stay the way it is.
+
+The field has switched sign.
+
+So this becomes y prime inverse.
+
+But since both of them
+are minus-- minus,
+
+minus-- the k factor
+is satisfied and happy.
+
+Gives me x prime because
+it's e to the plus k.
+
+On the right hand side, I
+will always get the z squared.
+
+The first factor
+becomes the inverse.
+
+Now, s plus 1 is a
+plus site, plus spin,
+
+that is sandwiched
+between two minus spins.
+
+So there are two unhappy bonds.
+
+This gives me x to the minus 2.
+
+Why the spin is pointing in
+the direction of the field.
+
+So there's the y here.
+
+And here I will get x
+squared and y inverse
+
+because now I have
+three negative signs.
+
+So all the k's are happy.
+
+There's the next one,
+which is plus and minus.
+
+Plus and minus, we can see that
+the contribution to the field
+
+vanishes.
+
+Because sigma i prime and plus
+sigma i plus 1 prime are zero.
+
+I will still get z,
+the contribution,
+
+because plus and minus,
+the bond between them
+
+gives me e to the minus k prime.
+
+I have here z squared.
+
+There is no overall contribution
+of y for the same reason
+
+that there was nothing here.
+
+But from s, I will get a
+factor of y plus y inverse.
+
+And there's no
+contribution for x
+
+because I have a
+plus and a minus.
+
+And if the spin is either
+plus or minus in the middle,
+
+there will be one satisfied
+and one dissatisfied bond.
+
+Again, by symmetry,
+the other configuration
+
+is exactly the same.
+
+So while I had four
+configuration, and hence
+
+four things to match, the
+last two are the same.
+
+And that's consistent
+with my having
+
+three variables, x prime, y
+prime, and z prime, to solve.
+
+So there are three equations
+and three variables.
+
+Now, to solve these equations,
+we can do several things.
+
+Let's, for example, multiply
+all four equations together.
+
+What do we get on
+the left hand side?
+
+There are two x's, two
+inverse x's, y, and inverse y,
+
+but four factors of z.
+
+So I get z prime to
+the fourth factor.
+
+On the other side, I
+will get z to the eight,
+
+and then the product
+of those four factors.
+
+I can divide one, equation
+one, by equation two.
+
+What do I get?
+
+The x's cancel.
+
+The x's cancel.
+
+So I will get y prime squared.
+
+On the other side,
+divide these two.
+
+I will get y squared.
+
+x squared y plus x
+squared y inverse,
+
+x minus 2y plus x2 minus--
+yeah, x2 y inverse.
+
+And finally, to get the equation
+for x prime, what I can do
+
+is I can multiply 1 and
+2, divide by 3 and 4.
+
+And if I do that, on
+the left hand side
+
+I will get x prime
+to the fourth.
+
+And on the right
+hand side, I will
+
+get x squared y plus x
+to the minus 2 y inverse
+
+x minus 2y x squared y inverse
+divided by y plus y inverse
+
+squared.
+
+So I can take the log of
+these equations, if you like,
+
+to get the recurrence
+relations for the parameters.
+
+For example, taking the
+log of that equation,
+
+you can see that I
+will get g prime.
+
+From here, I would get
+2g plus some function.
+
+There's some delta g
+that depends on k and h.
+
+If I do the same
+thing here, you can
+
+see that I will
+get an h prime that
+
+is h plus some function
+from the log of this
+
+that depends on k and h.
+
+And finally, I will get k
+prime some function of k and h.
+
+This parameter g is
+not that important.
+
+It's basically an
+overall constant.
+
+The way that we started
+it, we certainly
+
+don't expect it to modify
+phase diagrams, et cetera.
+
+And you can see that it never
+affects the equations that
+
+govern h and k, the
+two parameters that
+
+give the relative weight of
+different configurations.
+
+Whether you are in a ferromagnet
+or a disordered state
+
+is governed by these
+two parameters.
+
+And indeed, we can ignore this.
+
+Essentially, what it amounts to
+is as follows, that every time
+
+I remove some of the
+spins, I gradually
+
+build a contribution
+to my free energy.
+
+Because clearly, once
+I have integrated out
+
+over all of the energies, what I
+will have will be the partition
+
+function.
+
+Its log would be
+the free energy.
+
+And actually, we encountered
+exactly the same thing
+
+when we were doing
+momentum space RG.
+
+There was always, as a
+result of the integration,
+
+some contribution that I
+call delta f that I never
+
+looked at because, OK, it's
+part of the free energy
+
+but does not govern
+the relative weights
+
+of the different configurations.
+
+So these are really
+the two things
+
+that we need to focus on.
+
+Now, if we did things
+correctly and these
+
+are correct equations, had
+I started in the subspace
+
+where h equals to zero,
+which had up-down symmetries,
+
+I could have changed all of
+my sigmas to minus sigma,
+
+and for h equals to zero, the
+energy would not have changed.
+
+So a check that we
+did things correctly
+
+is that if h equals to zero,
+then h prime has to be zero.
+
+So let's see.
+
+If h equals to zero
+or y is equal to one,
+
+well if y is equal
+to one, you can
+
+see that those two factors in
+the numerator and denominator
+
+are exactly the same.
+
+And so y prime stays to one.
+
+So this check has
+been performed.
+
+So if I am on h equals to
+zero on the subspace that
+
+has symmetry, then I have only
+one parameter, this k or x.
+
+And so on this space, the
+recursion relation that I have
+
+is that x prime
+to the fourth is x
+
+squared plus x to
+the minus 2 squared.
+
+I think I made a mistake here.
+
+No, it's correct.
+
+y plus y inverse.
+
+OK, but y is one.
+
+So this is divided by
+2 squared, which is 4.
+
+But let me double check
+so that I don't go-- yeah.
+
+So this is correct.
+
+So I can write it in terms
+of x being e to the k.
+
+So what I have here
+is e to the 4k prime.
+
+I have here e to the 2k plus e
+to the minus 2k divided by 2,
+
+which is hyperbolic
+cosine of 2k, squared.
+
+So what I will get is k
+prime is 1/2 log hyperbolic
+
+cosine of 2k.
+
+Now, k is a parameter
+that we are changing.
+
+As we make k stronger,
+presumably things
+
+are more coupled to each
+other and should go more
+
+towards order.
+
+As k goes towards zero,
+basically the spins
+
+are independent.
+
+They can do whatever they like.
+
+So it kind of makes
+sense that there
+
+should be a fixed point at
+zero corresponding to zero
+
+correlation length.
+
+And let's check that.
+
+So if k is going to zero--
+it's very small-- then
+
+k prime is 1/2 log hyperbolic
+cosine of a small number,
+
+is roughly 1 plus that
+small number squared over 2.
+
+There's a series like that.
+
+Log of 1 plus a small
+number is a small number.
+
+So this becomes 4k
+squared over 2 over 2.
+
+It's k squared.
+
+So it says that if I, let's say,
+start with a k that is 1/10,
+
+my k prime would be
+1/100 and then 1/10,000.
+
+So basically, this
+is a fixed point
+
+that attracts everything to it.
+
+Essentially, what
+it says is you may
+
+have some weak
+amount of coupling.
+
+As you go and look at the spins
+that are further and further
+
+apart, the effective coupling
+between them is going to zero.
+
+And the spins that
+are further apart
+
+don't care about each other.
+
+They do whatever they like.
+
+So that all makes
+physical sense.
+
+Well, we are really
+interested in this other end.
+
+What happens at k
+going to infinity?
+
+We can kind of look
+at this equation.
+
+Or actually, look at this
+equation, also doesn't matter.
+
+But here, maybe it's clearer.
+
+So I have e to the 4k prime.
+
+And this is going to
+be dominated by this.
+
+This is e to the 2k.
+
+e to the minus 2k is very small.
+
+So it's going to
+be approximately
+
+e to the 4k divided by 4.
+
+So what I have out here
+is that k is very large.
+
+k prime is roughly
+k, but then smaller
+
+by a factor that
+is 1/2 of log 2.
+
+So we try to take two spins that
+are next to each other, couple
+
+them with a very strong k.
+
+Let's say a million,
+10 million, whatever.
+
+And then I look at spins
+that are too further apart.
+
+They're still very strongly
+coupled, but slightly less.
+
+It's a million minus log 2.
+
+So it very, very gradually
+starts to move away from here.
+
+But then as it kind of goes
+further, it kind of speeds up.
+
+What it says is that it is true.
+
+At infinity, you
+have a fixed point.
+
+But that fixed
+point is unstable.
+
+And even if you have very
+strong but finite coupling,
+
+because things are finite, as
+you go further and further out,
+
+the spins become less
+and less correlated.
+
+This, again, is another
+indication of the statement
+
+that a one dimensional
+system will not order.
+
+So one thing that you
+can do to sort of make
+
+this look slightly better, since
+we have the interval from zero
+
+to infinity, is to
+change variables.
+
+I can ask what does
+tang of k prime do?
+
+So tang k prime is e to the
+2k prime minus 1 divided by
+
+e to the 2k prime plus 1.
+
+You write e to the 2k's
+in terms of this variable.
+
+At the end of the day,
+a little bit of algebra,
+
+you can convince yourself
+that the recursion relation
+
+for tang k has a
+very simple form.
+
+The new tang k is simply the
+square of the old tang k.
+
+If I plot things as
+a function of tang k
+
+that runs between zero
+and one, that fixed point
+
+that was at infinity
+gets mapped into one,
+
+and the flow is
+always towards here.
+
+There is no other
+fixed point in between.
+
+Previously, it wasn't
+clear from the way
+
+that I had written whether
+potentially there's
+
+other fixed points
+along the k-axis.
+
+If you write it as t
+prime tang is t squared,
+
+where t stands for tang,
+clearly the only fixed points
+
+are at zero and one.
+
+But now this also
+allows us to ask
+
+what happens if
+you also introduce
+
+the field direction,
+h, in this space.
+
+Now, one thing to
+check is that if you
+
+start with k equals to zero,
+that is independent spins,
+
+you look at the equation here.
+
+k equals to 0 corresponds
+to x equals to one.
+
+This factor drops out.
+
+You see y prime is equal to y.
+
+So if you have no
+coupling, there
+
+is no reason why the
+magnetic field should change.
+
+So essentially, this entire line
+corresponds to fixed points.
+
+Every point here
+is a fixed point.
+
+And we can show
+that, essentially,
+
+if you start along
+field zero, you go here.
+
+If you start along different
+values of the field,
+
+you basically go to
+someplace along this line.
+
+And all of these flows
+originate, if you go and plot
+
+them, from back here
+at this fixed point
+
+that we identified before
+at h equals to zero.
+
+So in order to find out what is
+happening along that direction,
+
+all we need to do is to go and
+look at x going to infinity.
+
+With x going to
+infinity, you can
+
+see that y prime squared, the
+equation that we have for y,
+
+y prime squared is y squared.
+
+And then there's this fraction.
+
+Clearly, the terms that are
+proportional to x squared
+
+will overwhelm
+those proportional
+
+to x to the minus 2.
+
+So I will get a
+y and a y inverse
+
+from the numerator
+and denominator.
+
+And so this goes
+like y to the fourth.
+
+Which means that in the vicinity
+of this point, what you have is
+
+that h prime is 2h.
+
+So this, again, is
+irrelevant direction.
+
+And here, you are flowing
+in this direction.
+
+And the combination
+of these two really
+
+justifies the kind of flows
+that I had shown you before.
+
+So essentially, in the
+one dimensional model,
+
+you can start with any
+microscopic set of k and h's
+
+that you want.
+
+As you rescale, you essentially
+go to independent spins
+
+with an effective
+magnetic field.
+
+So let's say we start with
+very close to this fixed point.
+
+So we had a very
+large value of k.
+
+I expect if I have
+a large value of k,
+
+neighboring spins are
+really close to each other.
+
+I have to go very far before,
+if I have a patch of pluses,
+
+I can go over to a
+patch of minuses.
+
+So there's a large
+correlation length
+
+in the vicinity of this point.
+
+And that correlation
+length is a function
+
+of our parameters k and h.
+
+Now, the point is that
+the recursion relation
+
+that I have for k does not look
+like the type of recursions
+
+that I had before.
+
+This one is fine because I can
+think of this as my usual h
+
+prime is b to the yh h, where
+here I'm clearly dealing
+
+with a b equals to two, and so
+I can read off my yh to be one.
+
+But the recursion
+relation that I have for k
+
+is not of that form.
+
+But who said that I
+choose k as the variable
+
+that I put over here?
+
+I have been doing all of
+these manipulations going
+
+from k to x, et cetera.
+
+One thing that behaves
+nicely, you can see,
+
+is a variable if I
+call e to the minus k
+
+prime is square root
+of 2 e to the minus k.
+
+At k equals to infinity,
+this is something
+
+that goes to zero on both ends.
+
+But if its k is
+large but not finite,
+
+it says that on
+the rescaling, it
+
+changes by a factor of root 2.
+
+So if I say, well,
+what is c as a function
+
+of the magnetic field,
+rather than writing k,
+
+I will write it as
+e to the minus k.
+
+It's just another way
+of writing things.
+
+Well, I know that under
+one step of RG, all
+
+my length scales have
+shrunk by a factor of two.
+
+So this is twice the c that
+I should write down with 2h
+
+and root 2 e to the minus k.
+
+So I just related the
+correlation length
+
+before and after one
+step of RG, starting
+
+from very close to this point.
+
+And for these two
+factors, 2 and root 2,
+
+I use the results that
+I have over there.
+
+And this I can keep doing.
+
+I can keep iterating this.
+
+After l steps of
+RG, this becomes 2
+
+to the l, c of 2
+to the lh, and 2
+
+to the l over 2
+e to the minus k.
+
+I iterate this sufficiently
+so that I have moved away
+
+from this fixed point, where
+everything is very strongly
+
+correlated.
+
+And so that means
+I move, let's say,
+
+until this number is something
+that is of the order of one.
+
+Could be 2.
+
+Could be 1/2.
+
+I really don't care.
+
+But the number of
+iterations, the number
+
+of rescalings by a
+factor of two that I
+
+have to do in order to achieve
+this, is when 2 to the l
+
+is of the order of e to the k.
+
+e to the 2k, sorry.
+
+And if I do that, I
+find that c should
+
+be e to the 2k some
+function of h e to the 2k.
+
+So let's say I am
+at h equals to zero.
+
+And I make the strength of the
+interaction between neighbors
+
+stronger and stronger.
+
+If I asked you, how does
+the correlation length,
+
+how does the size of the patches
+that are all plus and minus
+
+change as k becomes
+stronger and stronger?
+
+Well, RG tells you that
+it goes in this fashion.
+
+In the problem
+set that you have,
+
+you will solve the problem
+exactly by a different method
+
+and get exactly this form.
+
+What else?
+
+Well, we said that one of the
+characteristics of a system
+
+is that the free
+energy has a singular
+
+part as a function
+of the variables
+
+that we have that is related
+to the correlation length
+
+to the power d.
+
+In this case, we
+have d equals to one.
+
+So the statement is
+that the singular part
+
+of the free energy, as you
+approach infinite coupling
+
+strength, behaves
+as e to the minus 2k
+
+some other function
+of h, e to the 2k.
+
+Once you have a
+function such as this,
+
+you can take two
+derivatives with respect
+
+to the field to get
+the susceptibility.
+
+So the susceptibility would
+go like two derivatives
+
+of the free energy with
+respect to the field.
+
+You can see that each derivative
+brings forth a factor of e
+
+to the 2k.
+
+So two derivatives will bring
+a factor of e to the 2k,
+
+if I evaluate it at
+h equals to zero.
+
+So the statement is that
+if I'm at zero field,
+
+and I put on a small
+infinitesimal magnetic field,
+
+it tends to overturn
+all of the spins
+
+in the direction of the field.
+
+And the further you are
+close to k to infinity,
+
+there are larger responses
+that you would see.
+
+The susceptibility
+of the response
+
+diverges as k goes to infinity.
+
+So in some sense, this model
+does not have phase transition,
+
+but it demonstrates some
+signatures of the phase
+
+transition, such as
+diverging correlation length
+
+and diverging
+susceptibility if you
+
+go to very, very strong
+nearest neighbor coupling.
+
+There is one other
+relationship that we had.
+
+That is, the susceptibility
+is an integral
+
+in d dimension over
+the correlation length,
+
+which we could say
+in one dimension--
+
+well, actually, let's
+write it in d dimension.
+
+e to the minus x
+over c divided by x.
+
+We introduce an exponent,
+eta, to describe
+
+the decay of correlations.
+
+So this would generally behave
+like c to the 2 minus eta.
+
+Now, in this case, we see that
+both the correlation length
+
+and susceptibility diverge with
+the same behavior, e to the 2k.
+
+They're proportional
+to each other.
+
+So that immediately
+tells me that for the one
+
+dimensional system
+that we are looking at,
+
+eta is equal to one.
+
+And if I substitute back
+here, so eta is one,
+
+the dimension is one,
+and the two cancels.
+
+Essentially, it says that
+the correlation length
+
+in one dimension have a
+pure exponential decay.
+
+They don't have this
+sub leading power load
+
+that you would have
+in higher dimensions.
+
+So when you do
+things exactly, you
+
+will also be able
+to verify that.
+
+So all of the predictions
+of this position space
+
+RG method that we can carry out
+in this one dimensional example
+
+very easily, you can
+also calculate and obtain
+
+through the method that
+is called transfer matrix,
+
+and is the subject
+of the problem set
+
+that was posted yesterday.
+
+Also, you can see that
+this approach will
+
+work for any system
+in one dimension.
+
+All I really need to ensure is
+that the b that I write down
+
+is sufficiently
+general to include
+
+all possible interactions that
+I can write between two spins.
+
+Because if I have some
+subset of those interactions,
+
+and then I do this procedure
+that I have over here
+
+and then take the
+log, there's no reason
+
+why that would not
+generate all things that
+
+are consistent with symmetry.
+
+So you really have to
+put all possible terms,
+
+and then you will get
+all possible terms here,
+
+and there would be a recursion
+relation that would relate.
+
+You can do this very easily, for
+example, for the Potts model.
+
+For the continuous spin systems,
+it becomes more difficult.
+
+Now let's say briefly as to why
+we can solve things exactly,
+
+let's say, for the one
+dimensionalizing model
+
+by this procedure.
+
+But this procedure we cannot
+do in higher dimensions.
+
+So let's, for example, think
+that we have a square lattice.
+
+Just generalize what we
+had to two dimensions.
+
+And let's say that we want
+to eliminate this spin
+
+and-- well, let's see,
+what's the best way?
+
+Yeah, we want to eliminate
+a checkerboard of spins.
+
+So we want to eliminate
+half of the spins.
+
+Let's say the white
+squares on a checkerboard.
+
+And if I were to eliminate these
+spins, like I did over here,
+
+I should be able to
+generate interactions
+
+among spins that are left over.
+
+So you say, fine.
+
+Let's pick these four spins.
+
+Sigma 1, sigma 2,
+sigma 3, sigma 4,
+
+that are connected
+to this spin, s,
+
+that is sitting in the middle,
+that I have to eliminate.
+
+So let's also stay
+in the space where
+
+h equals to zero,
+just for simplicity.
+
+So the result of
+eliminating that is
+
+I have to do a sum over s.
+
+I have e to the-- let's say
+the original interaction is k,
+
+and s is coupled by these bonds
+to sigma 1, sigma 2, sigma 3,
+
+sigma 4.
+
+Now, summing over the
+two possible values of s
+
+is very simple.
+
+It just gives me e to
+the k times the sum plus
+
+e to the minus k, that sum.
+
+So it's the same thing as 2
+hyperbolic cosine of k, sigma
+
+1 plus sigma 2 plus
+sigma 3 plus sigma 4.
+
+We say good.
+
+I had something like
+that, and I took a log
+
+so that I got the k prime.
+
+So maybe I'll do something
+like a recasting of this,
+
+and maybe a recasting of this
+will give me some constant,
+
+will give me some
+kind of a k prime,
+
+and then I will have sigma
+1, sigma 2, sigma 2, sigma 3,
+
+sigma 3, sigma 4,
+sigma 4, sigma 1.
+
+But you immediately see that
+that cannot be the entire
+
+story.
+
+Because there is really
+no ordering among sigma 1,
+
+sigma 2, sigma 3, sigma 4.
+
+So clearly, because of
+the symmetries of this,
+
+you will generate also sigma 1
+sigma 3 plus sigma 2 sigma 4.
+
+That is, eliminating this
+spin will generate for you
+
+interactions among
+these, but also
+
+interactions that go like this.
+
+And in fact, if you
+do it carefully,
+
+you'll find that you will also
+generate an interaction that
+
+is product of all four spins.
+
+You will generate something
+that involves all of the force.
+
+So basically, because
+of the way of geometry,
+
+et cetera, that you have
+in higher dimensions,
+
+there is no trick that
+is analogous to what
+
+we could do in one dimension
+where you would eliminate
+
+some subset of spins and not
+generate longer and longer
+
+range interactions, interactions
+that you did not have.
+
+You could say, OK, I
+will start including
+
+all of these
+interactions and then
+
+have a higher, larger
+parameter space.
+
+But then you do
+something else, you'll
+
+find that you need to
+include further and further
+
+neighboring interactions.
+
+So unless you do some kind of
+termination or approximation,
+
+which we will do
+next time, then there
+
+is no way to do this exactly
+in higher dimensions.
+
+AUDIENCE: Question.
+
+PROFESSOR: Yes.
+
+AUDIENCE: I mean, are you
+putting any sort of weight
+
+on the fact that, for
+example, sigma 1 and sigma 3
+
+are farther apart than
+sigma 1 and sigma 2,
+
+or are we using taxi cab
+distances on this lattice?
+
+PROFESSOR: Well, we are
+thinking of an original model
+
+that we would like
+to solve, in which
+
+I have specified that
+things are coupled only
+
+to nearest neighbors.
+
+So the ones that correspond
+to sigma 1, sigma 3,
+
+are next nearest neighbors.
+
+They're certainly farther
+apart on the lattice.
+
+You could say, well,
+there's some justification,
+
+if these are ions
+and they have spins,
+
+to have some weaker interaction
+that goes across here.
+
+There has to be some
+notion of space.
+
+I don't want to couple everybody
+to everybody else equivalently.
+
+But if I include this,
+then I have further more
+
+complicated Hamiltonian.
+
+And when I do RG,
+I will generate
+
+an even more
+complicated Hamiltonian.
+
+Yes.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Question is, suppose
+I have a square lattice.
+
+Let's go here.
+
+And the suggestion
+is, why don't I
+
+eliminate all of
+the spins over here,
+
+maybe all of the
+spins over here?
+
+So the problem is that I
+will generate interactions
+
+that not only go like this, but
+interactions that go like this.
+
+So the idea of what happens is
+that imagine that there's these
+
+spins that you're eliminating.
+
+As long as there's paths that
+connect the spins that you're
+
+eliminating to any
+other spin, you
+
+will generate that
+kind of couple.
+
+Again, the reason that the
+one dimensional model works
+
+is also related to
+its exact solvability
+
+by this transfer matrix method.
+
+So I will briefly mention
+that in the last five minutes.
+
+So for one dimensional
+models, the partition function
+
+is a sum over whatever
+degree of freedom you have.
+
+Could be Ising, Potts,
+xy, doesn't matter.
+
+But the point is
+that the interaction
+
+is a sum of bonds that connect
+one site to the next site.
+
+I can write this as a product of
+e to the b of SI and SI plus 1.
+
+Now, I can regard
+this entity-- let's
+
+say I have the Potts
+model q values.
+
+This is q possible values.
+
+This is q possible values.
+
+So there are q squared possible
+values of the interaction.
+
+And there is q squared
+possible values
+
+of this Boltzmann weight.
+
+I can regard that
+as a matrix, but I
+
+can write in this fashion.
+
+And so what you
+have over there, you
+
+can see is effectively you have
+s1, ts2, s2, ts3, and so forth.
+
+And if I use periodic boundary
+condition like the one
+
+that I indicated there so
+that the last one is connected
+
+to the first one, and then I
+do a sum over all of these s's,
+
+this is just the
+product of two matrices.
+
+So this is going to become, when
+I sum over s2, s1 t squared s3
+
+and so forth.
+
+You can see that
+the end result is
+
+trace of the matrix t
+raised to the power of n.
+
+Now, the trace you can
+calculate in any representation
+
+of the matrix.
+
+If you manage to find
+the representation where
+
+t is diagonal, then
+the trace would
+
+be sum over alpha
+lambda alpha to the n,
+
+where these lambdas are the
+eigenvalues of this matrix.
+
+And if n is very large,
+the thermodynamic
+
+limit that we are
+interested, it will
+
+be dominated by the
+largest eigenvalue.
+
+Now, if I write this for
+something like Potts model
+
+or any of the spin models that
+I had indicated over there,
+
+you can see that all
+elements of this matrix
+
+being these Boltzmann
+weights are plus, positive.
+
+Now, there's a theorem called
+Frobenius's theorem, which
+
+states that if you have a
+matrix, all of its eigenvalues
+
+are positive, then the largest
+eigenvalues is non-degenerate.
+
+So what that means is that if
+this matrix is characterized
+
+by a set of parameters, like
+our k's, et cetera, and I
+
+change that parameter,
+k, well the eigenvalue
+
+is obtained by looking
+at a single matrix.
+
+It doesn't know
+anything about that.
+
+The only way that the
+eigenvalue can become singular
+
+is if two eigenvalues
+cross each other.
+
+And since Frobenius's
+theorem does not allow that,
+
+you conclude that this
+largest eigenvalue
+
+has to be a perfectly nice
+analytical function of all
+
+of the parameters that go into
+constructing this Hamiltonian.
+
+And that's a mathematical way
+of saying that there is no phase
+
+transition for one dimensional
+model because you cannot have
+
+a crossing of eigenvalues, and
+there is no singularity that
+
+can take place.
+
+Now, an interesting then
+question or caveat to that
+
+comes from the very question
+that was asked over here.
+
+What if I have, let's say,
+a two dimensional model,
+
+and I regard it essentially
+as a complicated one
+
+dimensional model in
+which I have a complicated
+
+multi-variable
+thing over one side,
+
+and then I can go through this
+exact same procedure over here
+
+also?
+
+And then I would have to
+diagonalize this huge matrix.
+
+So if this is l, it would be a
+2 to the l by 2 to the l matrix.
+
+And you may naively
+think that, again,
+
+according to
+Frobenius's theorem,
+
+there should be no
+phase transition.
+
+Now, this is exactly what
+Lars Onsager did in order
+
+to solve the two
+dimensionalizing model.
+
+He constructed this matrix
+and was clever enough
+
+to diagonalize it and show
+that in the limit of l going
+
+to infinity, then the
+Frobenius's theorem
+
+can and will be violated.
+
+And so that's something
+that we will also
+
+discuss in some of
+our future lectures.
+
+Yes.
+
+AUDIENCE: But it won't
+be violated in the one
+
+dimensional case, even
+if n goes to infinity?
+
+PROFESSOR: Yeah, because
+n only appears over here.
+
+Lambda max is a perfectly
+analytic function.
\ No newline at end of file
diff --git a/1eXWDepLpNU.txt b/1eXWDepLpNU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e527f88bf6de1e2c900ede79c6f5eb706b10c66c
--- /dev/null
+++ b/1eXWDepLpNU.txt
@@ -0,0 +1,11603 @@
+align:start position:0%
+ 
+okay so where were we last time we had
+
+ align:start position:0%
+okay so where were we last time we had
+ 
+
+ align:start position:0%
+okay so where were we last time we had
+started we had talked about started a
+
+ align:start position:0%
+started we had talked about started a
+ 
+
+ align:start position:0%
+started we had talked about started a
+general conversation about
+
+ align:start position:0%
+general conversation about
+ 
+
+ align:start position:0%
+general conversation about
+estimation and um we had seen a couple
+
+ align:start position:0%
+estimation and um we had seen a couple
+ 
+
+ align:start position:0%
+estimation and um we had seen a couple
+of different examples of estimators that
+
+ align:start position:0%
+of different examples of estimators that
+ 
+
+ align:start position:0%
+of different examples of estimators that
+seem to have kind of just like we just
+
+ align:start position:0%
+seem to have kind of just like we just
+ 
+
+ align:start position:0%
+seem to have kind of just like we just
+thought of them off the top of our head
+
+ align:start position:0%
+thought of them off the top of our head
+ 
+
+ align:start position:0%
+thought of them off the top of our head
+and both estimators remember this was uh
+
+ align:start position:0%
+and both estimators remember this was uh
+ 
+
+ align:start position:0%
+and both estimators remember this was uh
+we were estimating Theta in a zero in a
+
+ align:start position:0%
+we were estimating Theta in a zero in a
+ 
+
+ align:start position:0%
+we were estimating Theta in a zero in a
+uniform zero Theta distribution and both
+
+ align:start position:0%
+uniform zero Theta distribution and both
+ 
+
+ align:start position:0%
+uniform zero Theta distribution and both
+estimators seemed quite reasonable and
+
+ align:start position:0%
+estimators seemed quite reasonable and
+ 
+
+ align:start position:0%
+estimators seemed quite reasonable and
+so then the next obvious question is
+
+ align:start position:0%
+so then the next obvious question is
+ 
+
+ align:start position:0%
+so then the next obvious question is
+well how do we know which one to use how
+
+ align:start position:0%
+well how do we know which one to use how
+ 
+
+ align:start position:0%
+well how do we know which one to use how
+do we decide between estimators if we
+
+ align:start position:0%
+do we decide between estimators if we
+ 
+
+ align:start position:0%
+do we decide between estimators if we
+have more than one estimator available
+
+ align:start position:0%
+have more than one estimator available
+ 
+
+ align:start position:0%
+have more than one estimator available
+okay and last time we saw the first
+
+ align:start position:0%
+okay and last time we saw the first
+ 
+
+ align:start position:0%
+okay and last time we saw the first
+Criterion that that one might want to
+
+ align:start position:0%
+Criterion that that one might want to
+ 
+
+ align:start position:0%
+Criterion that that one might want to
+use to uh choose among estimators and
+
+ align:start position:0%
+use to uh choose among estimators and
+ 
+
+ align:start position:0%
+use to uh choose among estimators and
+that was unbiased unbiasedness okay so
+
+ align:start position:0%
+that was unbiased unbiasedness okay so
+ 
+
+ align:start position:0%
+that was unbiased unbiasedness okay so
+an estimator is unbiased for Theta if
+
+ align:start position:0%
+an estimator is unbiased for Theta if
+ 
+
+ align:start position:0%
+an estimator is unbiased for Theta if
+the expectation of the estimator is
+
+ align:start position:0%
+the expectation of the estimator is
+ 
+
+ align:start position:0%
+the expectation of the estimator is
+equal to the parameter we're trying to
+
+ align:start position:0%
+equal to the parameter we're trying to
+ 
+
+ align:start position:0%
+equal to the parameter we're trying to
+estimate for all values of the parameter
+
+ align:start position:0%
+estimate for all values of the parameter
+ 
+
+ align:start position:0%
+estimate for all values of the parameter
+all possible values of the parameter
+
+ align:start position:0%
+all possible values of the parameter
+ 
+
+ align:start position:0%
+all possible values of the parameter
+okay and then I drew a picture and I
+
+ align:start position:0%
+okay and then I drew a picture and I
+ 
+
+ align:start position:0%
+okay and then I drew a picture and I
+said that here is so remember an
+
+ align:start position:0%
+said that here is so remember an
+ 
+
+ align:start position:0%
+said that here is so remember an
+estimator is a function of random
+
+ align:start position:0%
+estimator is a function of random
+ 
+
+ align:start position:0%
+estimator is a function of random
+variables so it itself is a random Vari
+
+ align:start position:0%
+variables so it itself is a random Vari
+ 
+
+ align:start position:0%
+variables so it itself is a random Vari
+aable so it has a distribution so we can
+
+ align:start position:0%
+aable so it has a distribution so we can
+ 
+
+ align:start position:0%
+aable so it has a distribution so we can
+talk about characteristics of that
+
+ align:start position:0%
+talk about characteristics of that
+ 
+
+ align:start position:0%
+talk about characteristics of that
+distribution here is a particular
+
+ align:start position:0%
+distribution here is a particular
+ 
+
+ align:start position:0%
+distribution here is a particular
+distribution of an estimator Theta hat
+
+ align:start position:0%
+distribution of an estimator Theta hat
+ 
+
+ align:start position:0%
+distribution of an estimator Theta hat
+and this one I've drawn so that it's
+
+ align:start position:0%
+and this one I've drawn so that it's
+ 
+
+ align:start position:0%
+and this one I've drawn so that it's
+unbiased here's a particular
+
+ align:start position:0%
+unbiased here's a particular
+ 
+
+ align:start position:0%
+unbiased here's a particular
+distribution of a different Theta hat
+
+ align:start position:0%
+distribution of a different Theta hat
+ 
+
+ align:start position:0%
+distribution of a different Theta hat
+say and I've drawn it so it's biased
+
+ align:start position:0%
+say and I've drawn it so it's biased
+ 
+
+ align:start position:0%
+say and I've drawn it so it's biased
+okay so the expectation for that the
+
+ align:start position:0%
+okay so the expectation for that the
+ 
+
+ align:start position:0%
+okay so the expectation for that the
+second uh estimator over there is not
+
+ align:start position:0%
+second uh estimator over there is not
+ 
+
+ align:start position:0%
+second uh estimator over there is not
+equal to Theta so it's a biased
+
+ align:start position:0%
+equal to Theta so it's a biased
+ 
+
+ align:start position:0%
+equal to Theta so it's a biased
+estimator okay so let's see an example
+
+ align:start position:0%
+estimator okay so let's see an example
+ 
+
+ align:start position:0%
+estimator okay so let's see an example
+so we've seen this particular estimator
+
+ align:start position:0%
+so we've seen this particular estimator
+ 
+
+ align:start position:0%
+so we've seen this particular estimator
+before remember this is uh uniform the
+
+ align:start position:0%
+before remember this is uh uniform the
+ 
+
+ align:start position:0%
+before remember this is uh uniform the
+the random sample is uniform zero Theta
+
+ align:start position:0%
+the random sample is uniform zero Theta
+ 
+
+ align:start position:0%
+the random sample is uniform zero Theta
+and we came up with the idea that we
+
+ align:start position:0%
+and we came up with the idea that we
+ 
+
+ align:start position:0%
+and we came up with the idea that we
+could just get you know compute the
+
+ align:start position:0%
+could just get you know compute the
+ 
+
+ align:start position:0%
+could just get you know compute the
+sample mean from from that random sample
+
+ align:start position:0%
+sample mean from from that random sample
+ 
+
+ align:start position:0%
+sample mean from from that random sample
+multiply it by two and that would be a
+
+ align:start position:0%
+multiply it by two and that would be a
+ 
+
+ align:start position:0%
+multiply it by two and that would be a
+reasonable estimator for Theta hat or
+
+ align:start position:0%
+reasonable estimator for Theta hat or
+ 
+
+ align:start position:0%
+reasonable estimator for Theta hat or
+for Theta
+
+ align:start position:0%
+for Theta
+ 
+
+ align:start position:0%
+for Theta
+sorry um so let's see if this one is in
+
+ align:start position:0%
+sorry um so let's see if this one is in
+ 
+
+ align:start position:0%
+sorry um so let's see if this one is in
+fact biased or
+
+ align:start position:0%
+fact biased or
+ 
+
+ align:start position:0%
+fact biased or
+unbiased well we can just compute the
+
+ align:start position:0%
+unbiased well we can just compute the
+ 
+
+ align:start position:0%
+unbiased well we can just compute the
+expectation by using the properties of
+
+ align:start position:0%
+expectation by using the properties of
+ 
+
+ align:start position:0%
+expectation by using the properties of
+expectation that we saw a few lectures
+
+ align:start position:0%
+expectation that we saw a few lectures
+ 
+
+ align:start position:0%
+expectation that we saw a few lectures
+ago so we don't have to we don't have to
+
+ align:start position:0%
+ago so we don't have to we don't have to
+ 
+
+ align:start position:0%
+ago so we don't have to we don't have to
+sort of go back to the definition of
+
+ align:start position:0%
+sort of go back to the definition of
+ 
+
+ align:start position:0%
+sort of go back to the definition of
+expectation we just say well the
+
+ align:start position:0%
+expectation we just say well the
+ 
+
+ align:start position:0%
+expectation we just say well the
+expectation of theta hat is equal to by
+
+ align:start position:0%
+expectation of theta hat is equal to by
+ 
+
+ align:start position:0%
+expectation of theta hat is equal to by
+properties of expectation we can pull
+
+ align:start position:0%
+properties of expectation we can pull
+ 
+
+ align:start position:0%
+properties of expectation we can pull
+out the two and the 1 over n from the uh
+
+ align:start position:0%
+out the two and the 1 over n from the uh
+ 
+
+ align:start position:0%
+out the two and the 1 over n from the uh
+from the expectation and from the
+
+ align:start position:0%
+from the expectation and from the
+ 
+
+ align:start position:0%
+from the expectation and from the
+summation
+
+ align:start position:0%
+summation
+ 
+
+ align:start position:0%
+summation
+okay and then we put we plug in the uh
+
+ align:start position:0%
+okay and then we put we plug in the uh
+ 
+
+ align:start position:0%
+okay and then we put we plug in the uh
+the expectation of X subi which is just
+
+ align:start position:0%
+the expectation of X subi which is just
+ 
+
+ align:start position:0%
+the expectation of X subi which is just
+equal to Theta over 2 everyone knows
+
+ align:start position:0%
+equal to Theta over 2 everyone knows
+ 
+
+ align:start position:0%
+equal to Theta over 2 everyone knows
+where that came from right okay and then
+
+ align:start position:0%
+where that came from right okay and then
+ 
+
+ align:start position:0%
+where that came from right okay and then
+we just sort of do this summation and we
+
+ align:start position:0%
+we just sort of do this summation and we
+ 
+
+ align:start position:0%
+we just sort of do this summation and we
+get the twos cancel and we get that this
+
+ align:start position:0%
+get the twos cancel and we get that this
+ 
+
+ align:start position:0%
+get the twos cancel and we get that this
+is equal to Theta okay so unbiased
+
+ align:start position:0%
+is equal to Theta okay so unbiased
+ 
+
+ align:start position:0%
+is equal to Theta okay so unbiased
+estimator so that's a good thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay how about our other estimate
+
+ align:start position:0%
+right okay how about our other estimate
+ 
+
+ align:start position:0%
+right okay how about our other estimate
+so the other option that we had talked
+
+ align:start position:0%
+so the other option that we had talked
+ 
+
+ align:start position:0%
+so the other option that we had talked
+about was just using the nth order
+
+ align:start position:0%
+about was just using the nth order
+ 
+
+ align:start position:0%
+about was just using the nth order
+statistic and that also seemed
+
+ align:start position:0%
+statistic and that also seemed
+ 
+
+ align:start position:0%
+statistic and that also seemed
+reasonable right so let's see uh what we
+
+ align:start position:0%
+reasonable right so let's see uh what we
+ 
+
+ align:start position:0%
+reasonable right so let's see uh what we
+can say about whether this one is biased
+
+ align:start position:0%
+can say about whether this one is biased
+ 
+
+ align:start position:0%
+can say about whether this one is biased
+or unbiased any uh any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guesses become more unbiased as you take
+
+ align:start position:0%
+guesses become more unbiased as you take
+ 
+
+ align:start position:0%
+guesses become more unbiased as you take
+as n
+
+ align:start position:0%
+as n
+ 
+
+ align:start position:0%
+as n
+increases so you you you have kind of
+
+ align:start position:0%
+increases so you you you have kind of
+ 
+
+ align:start position:0%
+increases so you you you have kind of
+the right intuition but you haven't
+
+ align:start position:0%
+the right intuition but you haven't
+ 
+
+ align:start position:0%
+the right intuition but you haven't
+expressed it in the right way so BAS
+
+ align:start position:0%
+expressed it in the right way so BAS
+ 
+
+ align:start position:0%
+expressed it in the right way so BAS
+basically what what's happening is that
+
+ align:start position:0%
+basically what what's happening is that
+ 
+
+ align:start position:0%
+basically what what's happening is that
+the it it it it will be biased we're
+
+ align:start position:0%
+the it it it it will be biased we're
+ 
+
+ align:start position:0%
+the it it it it will be biased we're
+going to see that and the amount of the
+
+ align:start position:0%
+going to see that and the amount of the
+ 
+
+ align:start position:0%
+going to see that and the amount of the
+bias is going to get smaller as in gets
+
+ align:start position:0%
+bias is going to get smaller as in gets
+ 
+
+ align:start position:0%
+bias is going to get smaller as in gets
+larger okay so and do you want to do you
+
+ align:start position:0%
+larger okay so and do you want to do you
+ 
+
+ align:start position:0%
+larger okay so and do you want to do you
+want to share your intuition for why
+
+ align:start position:0%
+want to share your intuition for why
+ 
+
+ align:start position:0%
+want to share your intuition for why
+it's biased we talked about it last time
+
+ align:start position:0%
+it's biased we talked about it last time
+ 
+
+ align:start position:0%
+it's biased we talked about it last time
+if you take more draws then the
+
+ align:start position:0%
+if you take more draws then the
+ 
+
+ align:start position:0%
+if you take more draws then the
+probability that the highest draws
+
+ align:start position:0%
+probability that the highest draws
+ 
+
+ align:start position:0%
+probability that the highest draws
+closest to feta increases that's right
+
+ align:start position:0%
+closest to feta increases that's right
+ 
+
+ align:start position:0%
+closest to feta increases that's right
+that's right so we're getting so this
+
+ align:start position:0%
+that's right so we're getting so this
+ 
+
+ align:start position:0%
+that's right so we're getting so this
+estimator is sort of getting close but
+
+ align:start position:0%
+estimator is sort of getting close but
+ 
+
+ align:start position:0%
+estimator is sort of getting close but
+it's but it's always going to be biased
+
+ align:start position:0%
+it's but it's always going to be biased
+ 
+
+ align:start position:0%
+it's but it's always going to be biased
+in for a finite sample
+
+ align:start position:0%
+in for a finite sample
+ 
+
+ align:start position:0%
+in for a finite sample
+because always that the nth order
+
+ align:start position:0%
+because always that the nth order
+ 
+
+ align:start position:0%
+because always that the nth order
+statistic is always less than or equal
+
+ align:start position:0%
+statistic is always less than or equal
+ 
+
+ align:start position:0%
+statistic is always less than or equal
+to Theta it's never greater than Theta
+
+ align:start position:0%
+to Theta it's never greater than Theta
+ 
+
+ align:start position:0%
+to Theta it's never greater than Theta
+it's always less than or equal to Theta
+
+ align:start position:0%
+it's always less than or equal to Theta
+ 
+
+ align:start position:0%
+it's always less than or equal to Theta
+and it's equal to Theta with zero
+
+ align:start position:0%
+and it's equal to Theta with zero
+ 
+
+ align:start position:0%
+and it's equal to Theta with zero
+probability okay so that's sort of the
+
+ align:start position:0%
+probability okay so that's sort of the
+ 
+
+ align:start position:0%
+probability okay so that's sort of the
+the way that you know that this is going
+
+ align:start position:0%
+the way that you know that this is going
+ 
+
+ align:start position:0%
+the way that you know that this is going
+to be a biased estimator the intuition I
+
+ align:start position:0%
+to be a biased estimator the intuition I
+ 
+
+ align:start position:0%
+to be a biased estimator the intuition I
+guess that I use okay so let's verify
+
+ align:start position:0%
+guess that I use okay so let's verify
+ 
+
+ align:start position:0%
+guess that I use okay so let's verify
+this okay we're not we can't just use
+
+ align:start position:0%
+this okay we're not we can't just use
+ 
+
+ align:start position:0%
+this okay we're not we can't just use
+the properties of uh expectation like we
+
+ align:start position:0%
+the properties of uh expectation like we
+ 
+
+ align:start position:0%
+the properties of uh expectation like we
+did on the last slide to calculate the
+
+ align:start position:0%
+did on the last slide to calculate the
+ 
+
+ align:start position:0%
+did on the last slide to calculate the
+uh the expectation of this estimator and
+
+ align:start position:0%
+uh the expectation of this estimator and
+ 
+
+ align:start position:0%
+uh the expectation of this estimator and
+so we're going to do it directly using
+
+ align:start position:0%
+so we're going to do it directly using
+ 
+
+ align:start position:0%
+so we're going to do it directly using
+the definition of
+
+ align:start position:0%
+the definition of
+ 
+
+ align:start position:0%
+the definition of
+expectation and in order to do that we
+
+ align:start position:0%
+expectation and in order to do that we
+ 
+
+ align:start position:0%
+expectation and in order to do that we
+first need the PDF of the inth order
+
+ align:start position:0%
+first need the PDF of the inth order
+ 
+
+ align:start position:0%
+first need the PDF of the inth order
+statistic well we've seen that before so
+
+ align:start position:0%
+statistic well we've seen that before so
+ 
+
+ align:start position:0%
+statistic well we've seen that before so
+we'll just go back to previous uh
+
+ align:start position:0%
+we'll just go back to previous uh
+ 
+
+ align:start position:0%
+we'll just go back to previous uh
+lecture and recall that this is the sort
+
+ align:start position:0%
+lecture and recall that this is the sort
+ 
+
+ align:start position:0%
+lecture and recall that this is the sort
+of General um that's the general formula
+
+ align:start position:0%
+of General um that's the general formula
+ 
+
+ align:start position:0%
+of General um that's the general formula
+for the PDF of the nth order statistic
+
+ align:start position:0%
+for the PDF of the nth order statistic
+ 
+
+ align:start position:0%
+for the PDF of the nth order statistic
+from some distribution F okay now we
+
+ align:start position:0%
+from some distribution F okay now we
+ 
+
+ align:start position:0%
+from some distribution F okay now we
+have a specific distribution here zero
+
+ align:start position:0%
+have a specific distribution here zero
+ 
+
+ align:start position:0%
+have a specific distribution here zero
+uniform uh sorry uniform zero Theta so
+
+ align:start position:0%
+uniform uh sorry uniform zero Theta so
+ 
+
+ align:start position:0%
+uniform uh sorry uniform zero Theta so
+we'll plug in that a specific uh PDF
+
+ align:start position:0%
+we'll plug in that a specific uh PDF
+ 
+
+ align:start position:0%
+we'll plug in that a specific uh PDF
+plug in the uniform PDF here and the
+
+ align:start position:0%
+plug in the uniform PDF here and the
+ 
+
+ align:start position:0%
+plug in the uniform PDF here and the
+uniform CDF here and then we get
+
+ align:start position:0%
+uniform CDF here and then we get
+ 
+
+ align:start position:0%
+uniform CDF here and then we get
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay and then it just simplifies to this
+
+ align:start position:0%
+okay and then it just simplifies to this
+ 
+
+ align:start position:0%
+okay and then it just simplifies to this
+okay so now we have the PDF of the nth
+
+ align:start position:0%
+okay so now we have the PDF of the nth
+ 
+
+ align:start position:0%
+okay so now we have the PDF of the nth
+order statistic we'll be able to
+
+ align:start position:0%
+order statistic we'll be able to
+ 
+
+ align:start position:0%
+order statistic we'll be able to
+calculate its expectation with
+
+ align:start position:0%
+calculate its expectation with
+ 
+
+ align:start position:0%
+calculate its expectation with
+that okay and so what we did is I just
+
+ align:start position:0%
+that okay and so what we did is I just
+ 
+
+ align:start position:0%
+that okay and so what we did is I just
+took the PDF from the previous slide and
+
+ align:start position:0%
+took the PDF from the previous slide and
+ 
+
+ align:start position:0%
+took the PDF from the previous slide and
+plugged it into the definition of
+
+ align:start position:0%
+plugged it into the definition of
+ 
+
+ align:start position:0%
+plugged it into the definition of
+expectation remember the expectation of
+
+ align:start position:0%
+expectation remember the expectation of
+ 
+
+ align:start position:0%
+expectation remember the expectation of
+a random variable is just equal to
+
+ align:start position:0%
+a random variable is just equal to
+ 
+
+ align:start position:0%
+a random variable is just equal to
+that's continuous it's just equal to the
+
+ align:start position:0%
+that's continuous it's just equal to the
+ 
+
+ align:start position:0%
+that's continuous it's just equal to the
+integral of x times the PDF so that's
+
+ align:start position:0%
+integral of x times the PDF so that's
+ 
+
+ align:start position:0%
+integral of x times the PDF so that's
+exactly what I did there I solved the
+
+ align:start position:0%
+exactly what I did there I solved the
+ 
+
+ align:start position:0%
+exactly what I did there I solved the
+integral and
+
+ align:start position:0%
+integral and
+ 
+
+ align:start position:0%
+integral and
+um you know just a couple of steps of
+
+ align:start position:0%
+um you know just a couple of steps of
+ 
+
+ align:start position:0%
+um you know just a couple of steps of
+math later I get that it's equal to n
+
+ align:start position:0%
+math later I get that it's equal to n
+ 
+
+ align:start position:0%
+math later I get that it's equal to n
+over n + 1 *
+
+ align:start position:0%
+over n + 1 *
+ 
+
+ align:start position:0%
+over n + 1 *
+Theta okay so not only is our intuition
+
+ align:start position:0%
+Theta okay so not only is our intuition
+ 
+
+ align:start position:0%
+Theta okay so not only is our intuition
+that um the bi that it's biased is
+
+ align:start position:0%
+that um the bi that it's biased is
+ 
+
+ align:start position:0%
+that um the bi that it's biased is
+confirmed here but also our intuition
+
+ align:start position:0%
+confirmed here but also our intuition
+ 
+
+ align:start position:0%
+confirmed here but also our intuition
+that the bias is going down as the
+
+ align:start position:0%
+that the bias is going down as the
+ 
+
+ align:start position:0%
+that the bias is going down as the
+sample size is getting bigger is also
+
+ align:start position:0%
+sample size is getting bigger is also
+ 
+
+ align:start position:0%
+sample size is getting bigger is also
+confirmed
+
+ align:start position:0%
+confirmed
+ 
+
+ align:start position:0%
+confirmed
+okay does this make
+
+ align:start position:0%
+okay does this make
+ 
+
+ align:start position:0%
+okay does this make
+sense okay so so having an unb estimator
+
+ align:start position:0%
+sense okay so so having an unb estimator
+ 
+
+ align:start position:0%
+sense okay so so having an unb estimator
+is great is that the only thing we care
+
+ align:start position:0%
+is great is that the only thing we care
+ 
+
+ align:start position:0%
+is great is that the only thing we care
+about I think you guess that the answer
+
+ align:start position:0%
+about I think you guess that the answer
+ 
+
+ align:start position:0%
+about I think you guess that the answer
+is probably no it's not the only thing
+
+ align:start position:0%
+is probably no it's not the only thing
+ 
+
+ align:start position:0%
+is probably no it's not the only thing
+we care about oh so yeah I guess this is
+
+ align:start position:0%
+we care about oh so yeah I guess this is
+ 
+
+ align:start position:0%
+we care about oh so yeah I guess this is
+what I already said not surprising the
+
+ align:start position:0%
+what I already said not surprising the
+ 
+
+ align:start position:0%
+what I already said not surprising the
+estimator always be less than or equal
+
+ align:start position:0%
+estimator always be less than or equal
+ 
+
+ align:start position:0%
+estimator always be less than or equal
+to Theta
+
+ align:start position:0%
+to Theta
+ 
+
+ align:start position:0%
+to Theta
+okay oh sorry before we get to the
+
+ align:start position:0%
+okay oh sorry before we get to the
+ 
+
+ align:start position:0%
+okay oh sorry before we get to the
+second Criterion I just want to give uh
+
+ align:start position:0%
+second Criterion I just want to give uh
+ 
+
+ align:start position:0%
+second Criterion I just want to give uh
+give you a couple of
+
+ align:start position:0%
+give you a couple of
+ 
+
+ align:start position:0%
+give you a couple of
+useful um
+
+ align:start position:0%
+useful um
+ 
+
+ align:start position:0%
+useful um
+results about sort of unbiased
+
+ align:start position:0%
+results about sort of unbiased
+ 
+
+ align:start position:0%
+results about sort of unbiased
+estimators so the first uh result is
+
+ align:start position:0%
+estimators so the first uh result is
+ 
+
+ align:start position:0%
+estimators so the first uh result is
+that if we have a sample mean for an IID
+
+ align:start position:0%
+that if we have a sample mean for an IID
+ 
+
+ align:start position:0%
+that if we have a sample mean for an IID
+sample then that sample mean is an
+
+ align:start position:0%
+sample then that sample mean is an
+ 
+
+ align:start position:0%
+sample then that sample mean is an
+unbiased estimator for the population
+
+ align:start position:0%
+unbiased estimator for the population
+ 
+
+ align:start position:0%
+unbiased estimator for the population
+mean okay the the mean of the underlying
+
+ align:start position:0%
+mean okay the the mean of the underlying
+ 
+
+ align:start position:0%
+mean okay the the mean of the underlying
+population okay so that's always going
+
+ align:start position:0%
+population okay so that's always going
+ 
+
+ align:start position:0%
+population okay so that's always going
+to be true the the uh you know for an
+
+ align:start position:0%
+to be true the the uh you know for an
+ 
+
+ align:start position:0%
+to be true the the uh you know for an
+IID sample the sample mean is unbiased
+
+ align:start position:0%
+IID sample the sample mean is unbiased
+ 
+
+ align:start position:0%
+IID sample the sample mean is unbiased
+for the population mean now we all we
+
+ align:start position:0%
+for the population mean now we all we
+ 
+
+ align:start position:0%
+for the population mean now we all we
+actually already knew this we didn't use
+
+ align:start position:0%
+actually already knew this we didn't use
+ 
+
+ align:start position:0%
+actually already knew this we didn't use
+the word unbiased but remember when we
+
+ align:start position:0%
+the word unbiased but remember when we
+ 
+
+ align:start position:0%
+the word unbiased but remember when we
+introduced samp LE mean we calculated
+
+ align:start position:0%
+introduced samp LE mean we calculated
+ 
+
+ align:start position:0%
+introduced samp LE mean we calculated
+the expectation of the sample mean you
+
+ align:start position:0%
+the expectation of the sample mean you
+ 
+
+ align:start position:0%
+the expectation of the sample mean you
+guys remember that calculation okay we
+
+ align:start position:0%
+guys remember that calculation okay we
+ 
+
+ align:start position:0%
+guys remember that calculation okay we
+calculated the expectation the sample
+
+ align:start position:0%
+calculated the expectation the sample
+ 
+
+ align:start position:0%
+calculated the expectation the sample
+mean and it was equal to Mu the the
+
+ align:start position:0%
+mean and it was equal to Mu the the
+ 
+
+ align:start position:0%
+mean and it was equal to Mu the the
+underlying mean or the population mean
+
+ align:start position:0%
+underlying mean or the population mean
+ 
+
+ align:start position:0%
+underlying mean or the population mean
+so in fact we already knew
+
+ align:start position:0%
+so in fact we already knew
+ 
+
+ align:start position:0%
+so in fact we already knew
+that another result that we haven't seen
+
+ align:start position:0%
+that another result that we haven't seen
+ 
+
+ align:start position:0%
+that another result that we haven't seen
+before because I haven't even defined uh
+
+ align:start position:0%
+before because I haven't even defined uh
+ 
+
+ align:start position:0%
+before because I haven't even defined uh
+what a sample variance is but it's a
+
+ align:start position:0%
+what a sample variance is but it's a
+ 
+
+ align:start position:0%
+what a sample variance is but it's a
+useful result nonetheless is that if we
+
+ align:start position:0%
+useful result nonetheless is that if we
+ 
+
+ align:start position:0%
+useful result nonetheless is that if we
+have an IID sample and we com compute
+
+ align:start position:0%
+have an IID sample and we com compute
+ 
+
+ align:start position:0%
+have an IID sample and we com compute
+this estimator here it's called the
+
+ align:start position:0%
+this estimator here it's called the
+ 
+
+ align:start position:0%
+this estimator here it's called the
+sample variance this is going to be
+
+ align:start position:0%
+sample variance this is going to be
+ 
+
+ align:start position:0%
+sample variance this is going to be
+unbiased for the population
+
+ align:start position:0%
+unbiased for the population
+ 
+
+ align:start position:0%
+unbiased for the population
+variance
+
+ align:start position:0%
+variance
+ 
+
+ align:start position:0%
+variance
+okay so I I am leaving out the proof of
+
+ align:start position:0%
+okay so I I am leaving out the proof of
+ 
+
+ align:start position:0%
+okay so I I am leaving out the proof of
+that it's a little it's kind of a little
+
+ align:start position:0%
+that it's a little it's kind of a little
+ 
+
+ align:start position:0%
+that it's a little it's kind of a little
+fussy a bit of a fussy proof and I don't
+
+ align:start position:0%
+fussy a bit of a fussy proof and I don't
+ 
+
+ align:start position:0%
+fussy a bit of a fussy proof and I don't
+think it's very instructive but if
+
+ align:start position:0%
+think it's very instructive but if
+ 
+
+ align:start position:0%
+think it's very instructive but if
+anyone's interested happy to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you yep before we move on I I wanted to
+
+ align:start position:0%
+you yep before we move on I I wanted to
+ 
+
+ align:start position:0%
+you yep before we move on I I wanted to
+ask a question about this the sample
+
+ align:start position:0%
+ask a question about this the sample
+ 
+
+ align:start position:0%
+ask a question about this the sample
+mean for an i sample is unbi population
+
+ align:start position:0%
+mean for an i sample is unbi population
+ 
+
+ align:start position:0%
+mean for an i sample is unbi population
+me um does the fact that it's unbiased
+
+ align:start position:0%
+me um does the fact that it's unbiased
+ 
+
+ align:start position:0%
+me um does the fact that it's unbiased
+mean that you're getting the actual
+
+ align:start position:0%
+mean that you're getting the actual
+ 
+
+ align:start position:0%
+mean that you're getting the actual
+population mean when you do the sample
+
+ align:start position:0%
+population mean when you do the sample
+ 
+
+ align:start position:0%
+population mean when you do the sample
+mean or no I don't think that's happen
+
+ align:start position:0%
+mean or no I don't think that's happen
+ 
+
+ align:start position:0%
+mean or no I don't think that's happen
+no so what it means is that the sample
+
+ align:start position:0%
+no so what it means is that the sample
+ 
+
+ align:start position:0%
+no so what it means is that the sample
+mean has a
+
+ align:start position:0%
+mean has a
+ 
+
+ align:start position:0%
+mean has a
+distribution and that distribution the
+
+ align:start position:0%
+distribution and that distribution the
+ 
+
+ align:start position:0%
+distribution and that distribution the
+expectation of that distribution is the
+
+ align:start position:0%
+expectation of that distribution is the
+ 
+
+ align:start position:0%
+expectation of that distribution is the
+population mean okay
+
+ align:start position:0%
+population mean okay
+ 
+
+ align:start position:0%
+population mean okay
+so here there's some distribution maybe
+
+ align:start position:0%
+so here there's some distribution maybe
+ 
+
+ align:start position:0%
+so here there's some distribution maybe
+it's uniform maybe it's
+
+ align:start position:0%
+it's uniform maybe it's
+ 
+
+ align:start position:0%
+it's uniform maybe it's
+normal whatever there's some
+
+ align:start position:0%
+normal whatever there's some
+ 
+
+ align:start position:0%
+normal whatever there's some
+distribution that governs that that that
+
+ align:start position:0%
+distribution that governs that that that
+ 
+
+ align:start position:0%
+distribution that governs that that that
+our random sample is governed by okay a
+
+ align:start position:0%
+our random sample is governed by okay a
+ 
+
+ align:start position:0%
+our random sample is governed by okay a
+random sample is drawn by or drawn from
+
+ align:start position:0%
+random sample is drawn by or drawn from
+ 
+
+ align:start position:0%
+random sample is drawn by or drawn from
+okay and then we get a random sample we
+
+ align:start position:0%
+okay and then we get a random sample we
+ 
+
+ align:start position:0%
+okay and then we get a random sample we
+compute the sample mean and the the
+
+ align:start position:0%
+compute the sample mean and the the
+ 
+
+ align:start position:0%
+compute the sample mean and the the
+distribution of the sample mean so if we
+
+ align:start position:0%
+distribution of the sample mean so if we
+ 
+
+ align:start position:0%
+distribution of the sample mean so if we
+think of the sample mean as a an
+
+ align:start position:0%
+think of the sample mean as a an
+ 
+
+ align:start position:0%
+think of the sample mean as a an
+estimator it's going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be it's it's going to have expect
+
+ align:start position:0%
+be it's it's going to have expect
+ 
+
+ align:start position:0%
+be it's it's going to have expect
+expectation sample mean any
+
+ align:start position:0%
+expectation sample mean any
+ 
+
+ align:start position:0%
+expectation sample mean any
+particular realization of that estimator
+
+ align:start position:0%
+particular realization of that estimator
+ 
+
+ align:start position:0%
+particular realization of that estimator
+so like if we have when we have the the
+
+ align:start position:0%
+so like if we have when we have the the
+ 
+
+ align:start position:0%
+so like if we have when we have the the
+numbers you know the realizations for
+
+ align:start position:0%
+numbers you know the realizations for
+ 
+
+ align:start position:0%
+numbers you know the realizations for
+the um random sample and we plug them in
+
+ align:start position:0%
+the um random sample and we plug them in
+ 
+
+ align:start position:0%
+the um random sample and we plug them in
+to the function for the estimator then
+
+ align:start position:0%
+to the function for the estimator then
+ 
+
+ align:start position:0%
+to the function for the estimator then
+basically what we're doing is we're
+
+ align:start position:0%
+basically what we're doing is we're
+ 
+
+ align:start position:0%
+basically what we're doing is we're
+getting some realization from this
+
+ align:start position:0%
+getting some realization from this
+ 
+
+ align:start position:0%
+getting some realization from this
+distribution so it's it depending on how
+
+ align:start position:0%
+distribution so it's it depending on how
+ 
+
+ align:start position:0%
+distribution so it's it depending on how
+tightly distributed it is around the the
+
+ align:start position:0%
+tightly distributed it is around the the
+ 
+
+ align:start position:0%
+tightly distributed it is around the the
+the population mean it could be you know
+
+ align:start position:0%
+the population mean it could be you know
+ 
+
+ align:start position:0%
+the population mean it could be you know
+it could very close to this with high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay questions about this so these
+
+ align:start position:0%
+okay okay questions about this so these
+ 
+
+ align:start position:0%
+okay okay questions about this so these
+are just two sort of useful facts that
+
+ align:start position:0%
+are just two sort of useful facts that
+ 
+
+ align:start position:0%
+are just two sort of useful facts that
+we'll refer to uh in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+future okay so now uh is unbiasedness
+
+ align:start position:0%
+future okay so now uh is unbiasedness
+ 
+
+ align:start position:0%
+future okay so now uh is unbiasedness
+all we care about in an estimator okay
+
+ align:start position:0%
+all we care about in an estimator okay
+ 
+
+ align:start position:0%
+all we care about in an estimator okay
+the answer is no so uh in particular
+
+ align:start position:0%
+the answer is no so uh in particular
+ 
+
+ align:start position:0%
+the answer is no so uh in particular
+there are other aspects of distributions
+
+ align:start position:0%
+there are other aspects of distributions
+ 
+
+ align:start position:0%
+there are other aspects of distributions
+of the estimators that we might care
+
+ align:start position:0%
+of the estimators that we might care
+ 
+
+ align:start position:0%
+of the estimators that we might care
+about we might care about I just alluded
+
+ align:start position:0%
+about we might care about I just alluded
+ 
+
+ align:start position:0%
+about we might care about I just alluded
+to this how tightly distributed it is
+
+ align:start position:0%
+to this how tightly distributed it is
+ 
+
+ align:start position:0%
+to this how tightly distributed it is
+around the unknown parameter okay we
+
+ align:start position:0%
+around the unknown parameter okay we
+ 
+
+ align:start position:0%
+around the unknown parameter okay we
+could have an estimator that has a very
+
+ align:start position:0%
+could have an estimator that has a very
+ 
+
+ align:start position:0%
+could have an estimator that has a very
+diffuse distribution and that estimator
+
+ align:start position:0%
+diffuse distribution and that estimator
+ 
+
+ align:start position:0%
+diffuse distribution and that estimator
+even if its expectation is is the the um
+
+ align:start position:0%
+even if its expectation is is the the um
+ 
+
+ align:start position:0%
+even if its expectation is is the the um
+parameter that we're trying to estimate
+
+ align:start position:0%
+parameter that we're trying to estimate
+ 
+
+ align:start position:0%
+parameter that we're trying to estimate
+even if that's its expectation in other
+
+ align:start position:0%
+even if that's its expectation in other
+ 
+
+ align:start position:0%
+even if that's its expectation in other
+words even if it's unbiased might not be
+
+ align:start position:0%
+words even if it's unbiased might not be
+ 
+
+ align:start position:0%
+words even if it's unbiased might not be
+very useful to us if it has lots of
+
+ align:start position:0%
+very useful to us if it has lots of
+ 
+
+ align:start position:0%
+very useful to us if it has lots of
+probability far away from the real print
+
+ align:start position:0%
+probability far away from the real print
+ 
+
+ align:start position:0%
+probability far away from the real print
+okay and that's what efficiency is about
+
+ align:start position:0%
+okay and that's what efficiency is about
+ 
+
+ align:start position:0%
+okay and that's what efficiency is about
+so given two unbiased estimators Theta 1
+
+ align:start position:0%
+so given two unbiased estimators Theta 1
+ 
+
+ align:start position:0%
+so given two unbiased estimators Theta 1
+hat and Theta 2 hat Theta 1 Hat is more
+
+ align:start position:0%
+hat and Theta 2 hat Theta 1 Hat is more
+ 
+
+ align:start position:0%
+hat and Theta 2 hat Theta 1 Hat is more
+efficient than Theta 2 hat if for a
+
+ align:start position:0%
+efficient than Theta 2 hat if for a
+ 
+
+ align:start position:0%
+efficient than Theta 2 hat if for a
+given sample size the variance of theta
+
+ align:start position:0%
+given sample size the variance of theta
+ 
+
+ align:start position:0%
+given sample size the variance of theta
+1 Hat is less than the variance of theta
+
+ align:start position:0%
+1 Hat is less than the variance of theta
+ 
+
+ align:start position:0%
+1 Hat is less than the variance of theta
+2 hat okay so let me show you a
+
+ align:start position:0%
+2 hat okay so let me show you a
+ 
+
+ align:start position:0%
+2 hat okay so let me show you a
+picture so here we have two unbiased
+
+ align:start position:0%
+picture so here we have two unbiased
+ 
+
+ align:start position:0%
+picture so here we have two unbiased
+estimators we have an efficient one
+
+ align:start position:0%
+estimators we have an efficient one
+ 
+
+ align:start position:0%
+estimators we have an efficient one
+whose distribution is pretty tightly
+
+ align:start position:0%
+whose distribution is pretty tightly
+ 
+
+ align:start position:0%
+whose distribution is pretty tightly
+distributed or concentrated around the
+
+ align:start position:0%
+distributed or concentrated around the
+ 
+
+ align:start position:0%
+distributed or concentrated around the
+unknown parameter and we have an
+
+ align:start position:0%
+unknown parameter and we have an
+ 
+
+ align:start position:0%
+unknown parameter and we have an
+inefficient one whose distribution is
+
+ align:start position:0%
+inefficient one whose distribution is
+ 
+
+ align:start position:0%
+inefficient one whose distribution is
+much more spread out and we're going to
+
+ align:start position:0%
+much more spread out and we're going to
+ 
+
+ align:start position:0%
+much more spread out and we're going to
+we're going to prefer the efficient
+
+ align:start position:0%
+we're going to prefer the efficient
+ 
+
+ align:start position:0%
+we're going to prefer the efficient
+estimator
+
+ align:start position:0%
+estimator
+ 
+
+ align:start position:0%
+estimator
+okay is that clear to everyone why we
+
+ align:start position:0%
+okay is that clear to everyone why we
+ 
+
+ align:start position:0%
+okay is that clear to everyone why we
+prefer
+
+ align:start position:0%
+prefer
+ 
+
+ align:start position:0%
+prefer
+okay okay so note that this definition
+
+ align:start position:0%
+okay okay so note that this definition
+ 
+
+ align:start position:0%
+okay okay so note that this definition
+has defined efficiency here just for
+
+ align:start position:0%
+has defined efficiency here just for
+ 
+
+ align:start position:0%
+has defined efficiency here just for
+unbiased estimators the notion of
+
+ align:start position:0%
+unbiased estimators the notion of
+ 
+
+ align:start position:0%
+unbiased estimators the notion of
+efficiency is broader than that so it
+
+ align:start position:0%
+efficiency is broader than that so it
+ 
+
+ align:start position:0%
+efficiency is broader than that so it
+can exist for sort of broader classes of
+
+ align:start position:0%
+can exist for sort of broader classes of
+ 
+
+ align:start position:0%
+can exist for sort of broader classes of
+estimators as well I'm not going to give
+
+ align:start position:0%
+estimators as well I'm not going to give
+ 
+
+ align:start position:0%
+estimators as well I'm not going to give
+you a formal definition but just think
+
+ align:start position:0%
+you a formal definition but just think
+ 
+
+ align:start position:0%
+you a formal definition but just think
+that if an estimator has a larger
+
+ align:start position:0%
+that if an estimator has a larger
+ 
+
+ align:start position:0%
+that if an estimator has a larger
+variance it's less efficient than an
+
+ align:start position:0%
+variance it's less efficient than an
+ 
+
+ align:start position:0%
+variance it's less efficient than an
+estimator with a smaller variance okay
+
+ align:start position:0%
+estimator with a smaller variance okay
+ 
+
+ align:start position:0%
+estimator with a smaller variance okay
+and we typically Define that in CL in
+
+ align:start position:0%
+and we typically Define that in CL in
+ 
+
+ align:start position:0%
+and we typically Define that in CL in
+different classes of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+estimators
+
+ align:start position:0%
+estimators
+ 
+
+ align:start position:0%
+estimators
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so fine suppose we have an efficient
+
+ align:start position:0%
+so fine suppose we have an efficient
+ 
+
+ align:start position:0%
+so fine suppose we have an efficient
+estimator and uh or you know an
+
+ align:start position:0%
+estimator and uh or you know an
+ 
+
+ align:start position:0%
+estimator and uh or you know an
+estimator has a small variance and then
+
+ align:start position:0%
+estimator has a small variance and then
+ 
+
+ align:start position:0%
+estimator has a small variance and then
+we have another estimator it has a
+
+ align:start position:0%
+we have another estimator it has a
+ 
+
+ align:start position:0%
+we have another estimator it has a
+larger variance uh but it's unbiased
+
+ align:start position:0%
+larger variance uh but it's unbiased
+ 
+
+ align:start position:0%
+larger variance uh but it's unbiased
+okay so sorry the first one is biased
+
+ align:start position:0%
+okay so sorry the first one is biased
+ 
+
+ align:start position:0%
+okay so sorry the first one is biased
+has a small variance the second one is
+
+ align:start position:0%
+has a small variance the second one is
+ 
+
+ align:start position:0%
+has a small variance the second one is
+unbiased and has a large variance how do
+
+ align:start position:0%
+unbiased and has a large variance how do
+ 
+
+ align:start position:0%
+unbiased and has a large variance how do
+we know which one to choose well there's
+
+ align:start position:0%
+we know which one to choose well there's
+ 
+
+ align:start position:0%
+we know which one to choose well there's
+no right answer okay so there's no
+
+ align:start position:0%
+no right answer okay so there's no
+ 
+
+ align:start position:0%
+no right answer okay so there's no
+there's no I'm you know I can't sort of
+
+ align:start position:0%
+there's no I'm you know I can't sort of
+ 
+
+ align:start position:0%
+there's no I'm you know I can't sort of
+tell you the theorem that says well you
+
+ align:start position:0%
+tell you the theorem that says well you
+ 
+
+ align:start position:0%
+tell you the theorem that says well you
+always need to choose this estimator
+
+ align:start position:0%
+always need to choose this estimator
+ 
+
+ align:start position:0%
+always need to choose this estimator
+over over the other one uh but there
+
+ align:start position:0%
+over over the other one uh but there
+ 
+
+ align:start position:0%
+over over the other one uh but there
+might be uh there might be sort of um
+
+ align:start position:0%
+might be uh there might be sort of um
+ 
+
+ align:start position:0%
+might be uh there might be sort of um
+other aside from just kind of picking
+
+ align:start position:0%
+other aside from just kind of picking
+ 
+
+ align:start position:0%
+other aside from just kind of picking
+your favorite estimator there might be
+
+ align:start position:0%
+your favorite estimator there might be
+ 
+
+ align:start position:0%
+your favorite estimator there might be
+kind of a more uh routinized way to
+
+ align:start position:0%
+kind of a more uh routinized way to
+ 
+
+ align:start position:0%
+kind of a more uh routinized way to
+trade off bias and efficiency in
+
+ align:start position:0%
+trade off bias and efficiency in
+ 
+
+ align:start position:0%
+trade off bias and efficiency in
+estimation and one way to do this is um
+
+ align:start position:0%
+estimation and one way to do this is um
+ 
+
+ align:start position:0%
+estimation and one way to do this is um
+minimum or is u mean square error okay
+
+ align:start position:0%
+minimum or is u mean square error okay
+ 
+
+ align:start position:0%
+minimum or is u mean square error okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um I'm going to Define mean square error
+
+ align:start position:0%
+um I'm going to Define mean square error
+ 
+
+ align:start position:0%
+um I'm going to Define mean square error
+as the expectation of theta hat minus
+
+ align:start position:0%
+as the expectation of theta hat minus
+ 
+
+ align:start position:0%
+as the expectation of theta hat minus
+Theta Square squar okay and that can be
+
+ align:start position:0%
+Theta Square squar okay and that can be
+ 
+
+ align:start position:0%
+Theta Square squar okay and that can be
+Rewritten as the variance of theta hat
+
+ align:start position:0%
+Rewritten as the variance of theta hat
+ 
+
+ align:start position:0%
+Rewritten as the variance of theta hat
+so we can think of that basically is the
+
+ align:start position:0%
+so we can think of that basically is the
+ 
+
+ align:start position:0%
+so we can think of that basically is the
+efficiency a measure of the efficiency
+
+ align:start position:0%
+efficiency a measure of the efficiency
+ 
+
+ align:start position:0%
+efficiency a measure of the efficiency
+of the estimator plus the expectation of
+
+ align:start position:0%
+of the estimator plus the expectation of
+ 
+
+ align:start position:0%
+of the estimator plus the expectation of
+theta hat minus Theta quantity squared
+
+ align:start position:0%
+theta hat minus Theta quantity squared
+ 
+
+ align:start position:0%
+theta hat minus Theta quantity squared
+and that is uh in fact the bias that is
+
+ align:start position:0%
+and that is uh in fact the bias that is
+ 
+
+ align:start position:0%
+and that is uh in fact the bias that is
+you know sort of this difference here is
+
+ align:start position:0%
+you know sort of this difference here is
+ 
+
+ align:start position:0%
+you know sort of this difference here is
+defined as the bias so the so that last
+
+ align:start position:0%
+defined as the bias so the so that last
+ 
+
+ align:start position:0%
+defined as the bias so the so that last
+term is the bias squared okay okay so
+
+ align:start position:0%
+term is the bias squared okay okay so
+ 
+
+ align:start position:0%
+term is the bias squared okay okay so
+for unbiased estimators that quantity is
+
+ align:start position:0%
+for unbiased estimators that quantity is
+ 
+
+ align:start position:0%
+for unbiased estimators that quantity is
+going to be zero for biased estimators
+
+ align:start position:0%
+going to be zero for biased estimators
+ 
+
+ align:start position:0%
+going to be zero for biased estimators
+it's going to be positive okay so mean
+
+ align:start position:0%
+it's going to be positive okay so mean
+ 
+
+ align:start position:0%
+it's going to be positive okay so mean
+square error is a way to to uh you know
+
+ align:start position:0%
+square error is a way to to uh you know
+ 
+
+ align:start position:0%
+square error is a way to to uh you know
+sort of trade off bias and efficiency
+
+ align:start position:0%
+sort of trade off bias and efficiency
+ 
+
+ align:start position:0%
+sort of trade off bias and efficiency
+you can choose a estimator that is the
+
+ align:start position:0%
+you can choose a estimator that is the
+ 
+
+ align:start position:0%
+you can choose a estimator that is the
+minimum mean squared error estimator and
+
+ align:start position:0%
+minimum mean squared error estimator and
+ 
+
+ align:start position:0%
+minimum mean squared error estimator and
+then that sort of allows you know
+
+ align:start position:0%
+then that sort of allows you know
+ 
+
+ align:start position:0%
+then that sort of allows you know
+basically allows this explicit trade-off
+
+ align:start position:0%
+basically allows this explicit trade-off
+ 
+
+ align:start position:0%
+basically allows this explicit trade-off
+between bias and
+
+ align:start position:0%
+between bias and
+ 
+
+ align:start position:0%
+between bias and
+efficiency okay
+
+ align:start position:0%
+efficiency okay
+ 
+
+ align:start position:0%
+efficiency okay
+um so I should point out it is a
+
+ align:start position:0%
+um so I should point out it is a
+ 
+
+ align:start position:0%
+um so I should point out it is a
+reasonable way to trade off bias and
+
+ align:start position:0%
+reasonable way to trade off bias and
+ 
+
+ align:start position:0%
+reasonable way to trade off bias and
+efficiency it's not the only one and
+
+ align:start position:0%
+efficiency it's not the only one and
+ 
+
+ align:start position:0%
+efficiency it's not the only one and
+like I said it's not you know there's no
+
+ align:start position:0%
+like I said it's not you know there's no
+ 
+
+ align:start position:0%
+like I said it's not you know there's no
+right answer when it comes to choosing
+
+ align:start position:0%
+right answer when it comes to choosing
+ 
+
+ align:start position:0%
+right answer when it comes to choosing
+among estimators uh that you know that
+
+ align:start position:0%
+among estimators uh that you know that
+ 
+
+ align:start position:0%
+among estimators uh that you know that
+have sort of that are not dominated in
+
+ align:start position:0%
+have sort of that are not dominated in
+ 
+
+ align:start position:0%
+have sort of that are not dominated in
+in all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways okay and I'll finally mention uh
+
+ align:start position:0%
+ways okay and I'll finally mention uh
+ 
+
+ align:start position:0%
+ways okay and I'll finally mention uh
+one additional
+
+ align:start position:0%
+one additional
+ 
+
+ align:start position:0%
+one additional
+Criterion um Thea uh sorry Theta hat is
+
+ align:start position:0%
+Criterion um Thea uh sorry Theta hat is
+ 
+
+ align:start position:0%
+Criterion um Thea uh sorry Theta hat is
+a consistent estimator for Theta if the
+
+ align:start position:0%
+a consistent estimator for Theta if the
+ 
+
+ align:start position:0%
+a consistent estimator for Theta if the
+following is true you take the absolute
+
+ align:start position:0%
+following is true you take the absolute
+ 
+
+ align:start position:0%
+following is true you take the absolute
+value the absolute difference between uh
+
+ align:start position:0%
+value the absolute difference between uh
+ 
+
+ align:start position:0%
+value the absolute difference between uh
+Theta and Theta
+
+ align:start position:0%
+Theta and Theta
+ 
+
+ align:start position:0%
+Theta and Theta
+hat and the probability of that absolute
+
+ align:start position:0%
+hat and the probability of that absolute
+ 
+
+ align:start position:0%
+hat and the probability of that absolute
+difference being less than some uh small
+
+ align:start position:0%
+difference being less than some uh small
+ 
+
+ align:start position:0%
+difference being less than some uh small
+uh number Delta goes to one as n goes to
+
+ align:start position:0%
+uh number Delta goes to one as n goes to
+ 
+
+ align:start position:0%
+uh number Delta goes to one as n goes to
+Infinity okay so practically speak
+
+ align:start position:0%
+Infinity okay so practically speak
+ 
+
+ align:start position:0%
+Infinity okay so practically speak
+speaking what does this mean well first
+
+ align:start position:0%
+speaking what does this mean well first
+ 
+
+ align:start position:0%
+speaking what does this mean well first
+of all let me draw you a
+
+ align:start position:0%
+of all let me draw you a
+ 
+
+ align:start position:0%
+of all let me draw you a
+picture okay so uh this is what a
+
+ align:start position:0%
+picture okay so uh this is what a
+ 
+
+ align:start position:0%
+picture okay so uh this is what a
+consistent estimator looks like as n
+
+ align:start position:0%
+consistent estimator looks like as n
+ 
+
+ align:start position:0%
+consistent estimator looks like as n
+goes to Infinity so basically you have a
+
+ align:start position:0%
+goes to Infinity so basically you have a
+ 
+
+ align:start position:0%
+goes to Infinity so basically you have a
+consistent estimator I've drawn this one
+
+ align:start position:0%
+consistent estimator I've drawn this one
+ 
+
+ align:start position:0%
+consistent estimator I've drawn this one
+to be unbiased for all in it doesn't
+
+ align:start position:0%
+to be unbiased for all in it doesn't
+ 
+
+ align:start position:0%
+to be unbiased for all in it doesn't
+have to be unbiased but that that's just
+
+ align:start position:0%
+have to be unbiased but that that's just
+ 
+
+ align:start position:0%
+have to be unbiased but that that's just
+the way I drew the picture here so
+
+ align:start position:0%
+the way I drew the picture here so
+ 
+
+ align:start position:0%
+the way I drew the picture here so
+basically you have an estimator and it
+
+ align:start position:0%
+basically you have an estimator and it
+ 
+
+ align:start position:0%
+basically you have an estimator and it
+has a distribution and as n uh goes to
+
+ align:start position:0%
+has a distribution and as n uh goes to
+ 
+
+ align:start position:0%
+has a distribution and as n uh goes to
+Infinity the distribution is getting
+
+ align:start position:0%
+Infinity the distribution is getting
+ 
+
+ align:start position:0%
+Infinity the distribution is getting
+more and more concentrated ated around
+
+ align:start position:0%
+more and more concentrated ated around
+ 
+
+ align:start position:0%
+more and more concentrated ated around
+the true parameter and in fact in the
+
+ align:start position:0%
+the true parameter and in fact in the
+ 
+
+ align:start position:0%
+the true parameter and in fact in the
+limit um it collapses to a single point
+
+ align:start position:0%
+limit um it collapses to a single point
+ 
+
+ align:start position:0%
+limit um it collapses to a single point
+at the true parameter as n goes to
+
+ align:start position:0%
+at the true parameter as n goes to
+ 
+
+ align:start position:0%
+at the true parameter as n goes to
+Infinity okay so this is what um what's
+
+ align:start position:0%
+Infinity okay so this is what um what's
+ 
+
+ align:start position:0%
+Infinity okay so this is what um what's
+known as a consistent
+
+ align:start position:0%
+known as a consistent
+ 
+
+ align:start position:0%
+known as a consistent
+estimator so let me just emphasize I've
+
+ align:start position:0%
+estimator so let me just emphasize I've
+ 
+
+ align:start position:0%
+estimator so let me just emphasize I've
+drawn this picture um you know for an
+
+ align:start position:0%
+drawn this picture um you know for an
+ 
+
+ align:start position:0%
+drawn this picture um you know for an
+estimator that's unbiased a consistent
+
+ align:start position:0%
+estimator that's unbiased a consistent
+ 
+
+ align:start position:0%
+estimator that's unbiased a consistent
+estimator doesn't have to be unbiased I
+
+ align:start position:0%
+estimator doesn't have to be unbiased I
+ 
+
+ align:start position:0%
+estimator doesn't have to be unbiased I
+could have drawn you know all of these
+
+ align:start position:0%
+could have drawn you know all of these
+ 
+
+ align:start position:0%
+could have drawn you know all of these
+distributions having bias but the bias
+
+ align:start position:0%
+distributions having bias but the bias
+ 
+
+ align:start position:0%
+distributions having bias but the bias
+is going to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so I have in the interest of time I
+
+ align:start position:0%
+okay so I have in the interest of time I
+ 
+
+ align:start position:0%
+okay so I have in the interest of time I
+I haven't uh included these examples on
+
+ align:start position:0%
+I haven't uh included these examples on
+ 
+
+ align:start position:0%
+I haven't uh included these examples on
+um you know in the lecture notes but I
+
+ align:start position:0%
+um you know in the lecture notes but I
+ 
+
+ align:start position:0%
+um you know in the lecture notes but I
+will tell you in case you're curious
+
+ align:start position:0%
+will tell you in case you're curious
+ 
+
+ align:start position:0%
+will tell you in case you're curious
+that the two estimators that we looked
+
+ align:start position:0%
+that the two estimators that we looked
+ 
+
+ align:start position:0%
+that the two estimators that we looked
+at for the uniform zero Theta um uh
+
+ align:start position:0%
+at for the uniform zero Theta um uh
+ 
+
+ align:start position:0%
+at for the uniform zero Theta um uh
+random sample uh the unbiased estimator
+
+ align:start position:0%
+random sample uh the unbiased estimator
+ 
+
+ align:start position:0%
+random sample uh the unbiased estimator
+the one that was two times the sample
+
+ align:start position:0%
+the one that was two times the sample
+ 
+
+ align:start position:0%
+the one that was two times the sample
+mean uh was much less efficient than the
+
+ align:start position:0%
+mean uh was much less efficient than the
+ 
+
+ align:start position:0%
+mean uh was much less efficient than the
+biased estimator the one that the the
+
+ align:start position:0%
+biased estimator the one that the the
+ 
+
+ align:start position:0%
+biased estimator the one that the the
+nth order statistic okay and so in that
+
+ align:start position:0%
+nth order statistic okay and so in that
+ 
+
+ align:start position:0%
+nth order statistic okay and so in that
+in in that case you might want to choose
+
+ align:start position:0%
+in in that case you might want to choose
+ 
+
+ align:start position:0%
+in in that case you might want to choose
+the inth order statistic just because
+
+ align:start position:0%
+the inth order statistic just because
+ 
+
+ align:start position:0%
+the inth order statistic just because
+it's you know for um you know reasonably
+
+ align:start position:0%
+it's you know for um you know reasonably
+ 
+
+ align:start position:0%
+it's you know for um you know reasonably
+sized random sample uh it's just its
+
+ align:start position:0%
+sized random sample uh it's just its
+ 
+
+ align:start position:0%
+sized random sample uh it's just its
+distribution is going to be much more
+
+ align:start position:0%
+distribution is going to be much more
+ 
+
+ align:start position:0%
+distribution is going to be much more
+tightly distributed around uh you know
+
+ align:start position:0%
+tightly distributed around uh you know
+ 
+
+ align:start position:0%
+tightly distributed around uh you know
+near Theta than two times the random s
+
+ align:start position:0%
+near Theta than two times the random s
+ 
+
+ align:start position:0%
+near Theta than two times the random s
+or two times the sample
+
+ align:start position:0%
+or two times the sample
+ 
+
+ align:start position:0%
+or two times the sample
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so the criteria that I've gone
+
+ align:start position:0%
+okay okay so the criteria that I've gone
+ 
+
+ align:start position:0%
+okay okay so the criteria that I've gone
+through these they're probably the most
+
+ align:start position:0%
+through these they're probably the most
+ 
+
+ align:start position:0%
+through these they're probably the most
+important reasons for choosing one
+
+ align:start position:0%
+important reasons for choosing one
+ 
+
+ align:start position:0%
+important reasons for choosing one
+estimator over another um but they're
+
+ align:start position:0%
+estimator over another um but they're
+ 
+
+ align:start position:0%
+estimator over another um but they're
+they don't necessarily have to be the
+
+ align:start position:0%
+they don't necessarily have to be the
+ 
+
+ align:start position:0%
+they don't necessarily have to be the
+only considerations so sometimes
+
+ align:start position:0%
+only considerations so sometimes
+ 
+
+ align:start position:0%
+only considerations so sometimes
+estimators can be really difficult ult
+
+ align:start position:0%
+estimators can be really difficult ult
+ 
+
+ align:start position:0%
+estimators can be really difficult ult
+to compute like they can be uh used you
+
+ align:start position:0%
+to compute like they can be uh used you
+ 
+
+ align:start position:0%
+to compute like they can be uh used you
+know sort of hours of computer time or
+
+ align:start position:0%
+know sort of hours of computer time or
+ 
+
+ align:start position:0%
+know sort of hours of computer time or
+something like that and so you might
+
+ align:start position:0%
+something like that and so you might
+ 
+
+ align:start position:0%
+something like that and so you might
+choose an estimator just based on sort
+
+ align:start position:0%
+choose an estimator just based on sort
+ 
+
+ align:start position:0%
+choose an estimator just based on sort
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+computational Simplicity um and that's
+
+ align:start position:0%
+computational Simplicity um and that's
+ 
+
+ align:start position:0%
+computational Simplicity um and that's
+not an unreasonable thing to do you
+
+ align:start position:0%
+not an unreasonable thing to do you
+ 
+
+ align:start position:0%
+not an unreasonable thing to do you
+might also choose an estimator based on
+
+ align:start position:0%
+might also choose an estimator based on
+ 
+
+ align:start position:0%
+might also choose an estimator based on
+how robust it is what do I mean by
+
+ align:start position:0%
+how robust it is what do I mean by
+ 
+
+ align:start position:0%
+how robust it is what do I mean by
+robust well basically an estimator is
+
+ align:start position:0%
+robust well basically an estimator is
+ 
+
+ align:start position:0%
+robust well basically an estimator is
+robust if it still will do a decent job
+
+ align:start position:0%
+robust if it still will do a decent job
+ 
+
+ align:start position:0%
+robust if it still will do a decent job
+perform well for for estimating the
+
+ align:start position:0%
+perform well for for estimating the
+ 
+
+ align:start position:0%
+perform well for for estimating the
+unknown parameter even if some of your
+
+ align:start position:0%
+unknown parameter even if some of your
+ 
+
+ align:start position:0%
+unknown parameter even if some of your
+assumptions underlying assumptions are
+
+ align:start position:0%
+assumptions underlying assumptions are
+ 
+
+ align:start position:0%
+assumptions underlying assumptions are
+incorrect so for instance let's suppose
+
+ align:start position:0%
+incorrect so for instance let's suppose
+ 
+
+ align:start position:0%
+incorrect so for instance let's suppose
+that we um let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose that we want to estimate
+
+ align:start position:0%
+suppose that we want to estimate
+ 
+
+ align:start position:0%
+suppose that we want to estimate
+mu and we think
+
+ align:start position:0%
+mu and we think
+ 
+
+ align:start position:0%
+mu and we think
+that the random sample is drawn from a
+
+ align:start position:0%
+that the random sample is drawn from a
+ 
+
+ align:start position:0%
+that the random sample is drawn from a
+distribution that looks like this okay
+
+ align:start position:0%
+distribution that looks like this okay
+ 
+
+ align:start position:0%
+distribution that looks like this okay
+but in fact it's drawn from a
+
+ align:start position:0%
+but in fact it's drawn from a
+ 
+
+ align:start position:0%
+but in fact it's drawn from a
+distribution that looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's this is still the mean mu is
+
+ align:start position:0%
+so it's this is still the mean mu is
+ 
+
+ align:start position:0%
+so it's this is still the mean mu is
+still the mean of this distribution but
+
+ align:start position:0%
+still the mean of this distribution but
+ 
+
+ align:start position:0%
+still the mean of this distribution but
+uh We've assumed that um you know we're
+
+ align:start position:0%
+uh We've assumed that um you know we're
+ 
+
+ align:start position:0%
+uh We've assumed that um you know we're
+drawing from this distribution when in
+
+ align:start position:0%
+drawing from this distribution when in
+ 
+
+ align:start position:0%
+drawing from this distribution when in
+Factor we're drawing from that one a
+
+ align:start position:0%
+Factor we're drawing from that one a
+ 
+
+ align:start position:0%
+Factor we're drawing from that one a
+robust estimator will still do a good
+
+ align:start position:0%
+robust estimator will still do a good
+ 
+
+ align:start position:0%
+robust estimator will still do a good
+job of estimating me even if our
+
+ align:start position:0%
+job of estimating me even if our
+ 
+
+ align:start position:0%
+job of estimating me even if our
+assumptions about the underlying
+
+ align:start position:0%
+assumptions about the underlying
+ 
+
+ align:start position:0%
+assumptions about the underlying
+distribution are wrong okay and so uh
+
+ align:start position:0%
+distribution are wrong okay and so uh
+ 
+
+ align:start position:0%
+distribution are wrong okay and so uh
+sometimes we choose estimators that are
+
+ align:start position:0%
+sometimes we choose estimators that are
+ 
+
+ align:start position:0%
+sometimes we choose estimators that are
+robust to uh different assumptions if we
+
+ align:start position:0%
+robust to uh different assumptions if we
+ 
+
+ align:start position:0%
+robust to uh different assumptions if we
+don't have a good you know if we don't
+
+ align:start position:0%
+don't have a good you know if we don't
+ 
+
+ align:start position:0%
+don't have a good you know if we don't
+have a lot of confidence about our
+
+ align:start position:0%
+have a lot of confidence about our
+ 
+
+ align:start position:0%
+have a lot of confidence about our
+underlying
+
+ align:start position:0%
+underlying
+ 
+
+ align:start position:0%
+underlying
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+okay oh and um yeah so I guess this is
+
+ align:start position:0%
+okay oh and um yeah so I guess this is
+ 
+
+ align:start position:0%
+okay oh and um yeah so I guess this is
+an example of a robust estimator that we
+
+ align:start position:0%
+an example of a robust estimator that we
+ 
+
+ align:start position:0%
+an example of a robust estimator that we
+talked about last time briefly it turns
+
+ align:start position:0%
+talked about last time briefly it turns
+ 
+
+ align:start position:0%
+talked about last time briefly it turns
+out that the two times the sample median
+
+ align:start position:0%
+out that the two times the sample median
+ 
+
+ align:start position:0%
+out that the two times the sample median
+estimator from the uniform example um
+
+ align:start position:0%
+estimator from the uniform example um
+ 
+
+ align:start position:0%
+estimator from the uniform example um
+has will have less bias than the two
+
+ align:start position:0%
+has will have less bias than the two
+ 
+
+ align:start position:0%
+has will have less bias than the two
+times the sample mean estimator uh if
+
+ align:start position:0%
+times the sample mean estimator uh if
+ 
+
+ align:start position:0%
+times the sample mean estimator uh if
+we've misspecified the tail
+
+ align:start position:0%
+we've misspecified the tail
+ 
+
+ align:start position:0%
+we've misspecified the tail
+probabilities in that uniform
+
+ align:start position:0%
+probabilities in that uniform
+ 
+
+ align:start position:0%
+probabilities in that uniform
+example okay so that's an example of a
+
+ align:start position:0%
+example okay so that's an example of a
+ 
+
+ align:start position:0%
+example okay so that's an example of a
+an estimator that um you know might be
+
+ align:start position:0%
+an estimator that um you know might be
+ 
+
+ align:start position:0%
+an estimator that um you know might be
+might actually not be as good as the
+
+ align:start position:0%
+might actually not be as good as the
+ 
+
+ align:start position:0%
+might actually not be as good as the
+other two estimators we saw in terms of
+
+ align:start position:0%
+other two estimators we saw in terms of
+ 
+
+ align:start position:0%
+other two estimators we saw in terms of
+bias and efficiency but might have this
+
+ align:start position:0%
+bias and efficiency but might have this
+ 
+
+ align:start position:0%
+bias and efficiency but might have this
+other property of robustness that could
+
+ align:start position:0%
+other property of robustness that could
+ 
+
+ align:start position:0%
+other property of robustness that could
+come in handy at some
+
+ align:start position:0%
+come in handy at some
+ 
+
+ align:start position:0%
+come in handy at some
+point yes those tail probabilities be
+
+ align:start position:0%
+point yes those tail probabilities be
+ 
+
+ align:start position:0%
+point yes those tail probabilities be
+be like underestimated or overestimated
+
+ align:start position:0%
+be like underestimated or overestimated
+ 
+
+ align:start position:0%
+be like underestimated or overestimated
+for that to POS or does it not matter
+
+ align:start position:0%
+for that to POS or does it not matter
+ 
+
+ align:start position:0%
+for that to POS or does it not matter
+well robust so robustness is basically
+
+ align:start position:0%
+well robust so robustness is basically
+ 
+
+ align:start position:0%
+well robust so robustness is basically
+just a a um it's just a um kind of a
+
+ align:start position:0%
+just a a um it's just a um kind of a
+ 
+
+ align:start position:0%
+just a a um it's just a um kind of a
+property of an estimator that says it's
+
+ align:start position:0%
+property of an estimator that says it's
+ 
+
+ align:start position:0%
+property of an estimator that says it's
+still performs well if your assumptions
+
+ align:start position:0%
+still performs well if your assumptions
+ 
+
+ align:start position:0%
+still performs well if your assumptions
+are incorrect and and it and it could be
+
+ align:start position:0%
+are incorrect and and it and it could be
+ 
+
+ align:start position:0%
+are incorrect and and it and it could be
+it could be that the estimator could
+
+ align:start position:0%
+it could be that the estimator could
+ 
+
+ align:start position:0%
+it could be that the estimator could
+only uh is only robust to miss
+
+ align:start position:0%
+only uh is only robust to miss
+ 
+
+ align:start position:0%
+only uh is only robust to miss
+specifications in One Direction and not
+
+ align:start position:0%
+specifications in One Direction and not
+ 
+
+ align:start position:0%
+specifications in One Direction and not
+the other direction that's possible but
+
+ align:start position:0%
+the other direction that's possible but
+ 
+
+ align:start position:0%
+the other direction that's possible but
+you know just the the sort of general
+
+ align:start position:0%
+you know just the the sort of general
+ 
+
+ align:start position:0%
+you know just the the sort of general
+definition of robust is just that that
+
+ align:start position:0%
+definition of robust is just that that
+ 
+
+ align:start position:0%
+definition of robust is just that that
+it's um not sensitive to the second part
+
+ align:start position:0%
+it's um not sensitive to the second part
+ 
+
+ align:start position:0%
+it's um not sensitive to the second part
+of this of the slide is it's showing
+
+ align:start position:0%
+of this of the slide is it's showing
+ 
+
+ align:start position:0%
+of this of the slide is it's showing
+that that's just an example of what
+
+ align:start position:0%
+that that's just an example of what
+ 
+
+ align:start position:0%
+that that's just an example of what
+could happen yeah it's not necessarily
+
+ align:start position:0%
+could happen yeah it's not necessarily
+ 
+
+ align:start position:0%
+could happen yeah it's not necessarily
+always true exactly that's right yep yes
+
+ align:start position:0%
+always true exactly that's right yep yes
+ 
+
+ align:start position:0%
+always true exactly that's right yep yes
+in that example what would be the
+
+ align:start position:0%
+in that example what would be the
+ 
+
+ align:start position:0%
+in that example what would be the
+um the wrong distribution that wee we
+
+ align:start position:0%
+um the wrong distribution that wee we
+ 
+
+ align:start position:0%
+um the wrong distribution that wee we
+so let's suppose so the we came up with
+
+ align:start position:0%
+so let's suppose so the we came up with
+ 
+
+ align:start position:0%
+so let's suppose so the we came up with
+this two times the sample median
+
+ align:start position:0%
+this two times the sample median
+ 
+
+ align:start position:0%
+this two times the sample median
+estimator in the uniform 0 to Theta
+
+ align:start position:0%
+estimator in the uniform 0 to Theta
+ 
+
+ align:start position:0%
+estimator in the uniform 0 to Theta
+example so let's suppose instead of
+
+ align:start position:0%
+example so let's suppose instead of
+ 
+
+ align:start position:0%
+example so let's suppose instead of
+uniform 0 to Theta let's
+
+ align:start position:0%
+uniform 0 to Theta let's
+ 
+
+ align:start position:0%
+uniform 0 to Theta let's
+suppose the um the distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was look like that
+
+ align:start position:0%
+was look like that
+ 
+
+ align:start position:0%
+was look like that
+instead then um and and we carried
+
+ align:start position:0%
+instead then um and and we carried
+ 
+
+ align:start position:0%
+instead then um and and we carried
+through all of the analysis of the
+
+ align:start position:0%
+through all of the analysis of the
+ 
+
+ align:start position:0%
+through all of the analysis of the
+estimator as if this were the
+
+ align:start position:0%
+estimator as if this were the
+ 
+
+ align:start position:0%
+estimator as if this were the
+distribution then if we use the two
+
+ align:start position:0%
+distribution then if we use the two
+ 
+
+ align:start position:0%
+distribution then if we use the two
+times the sample median estimator we're
+
+ align:start position:0%
+times the sample median estimator we're
+ 
+
+ align:start position:0%
+times the sample median estimator we're
+probably uh going to do a better job
+
+ align:start position:0%
+probably uh going to do a better job
+ 
+
+ align:start position:0%
+probably uh going to do a better job
+estimating I I would have to sort of
+
+ align:start position:0%
+estimating I I would have to sort of
+ 
+
+ align:start position:0%
+estimating I I would have to sort of
+work it out to be sure but um in that
+
+ align:start position:0%
+work it out to be sure but um in that
+ 
+
+ align:start position:0%
+work it out to be sure but um in that
+example we're almost certainly going to
+
+ align:start position:0%
+example we're almost certainly going to
+ 
+
+ align:start position:0%
+example we're almost certainly going to
+do a better job of estimating Theta with
+
+ align:start position:0%
+do a better job of estimating Theta with
+ 
+
+ align:start position:0%
+do a better job of estimating Theta with
+the two times the median estimator than
+
+ align:start position:0%
+the two times the median estimator than
+ 
+
+ align:start position:0%
+the two times the median estimator than
+the two times the sample mean
+
+ align:start position:0%
+the two times the sample mean
+ 
+
+ align:start position:0%
+the two times the sample mean
+estimator
+
+ align:start position:0%
+estimator
+ 
+
+ align:start position:0%
+estimator
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so now we know at least
+
+ align:start position:0%
+okay okay so now we know at least
+ 
+
+ align:start position:0%
+okay okay so now we know at least
+roughly speaking how to figure out if an
+
+ align:start position:0%
+roughly speaking how to figure out if an
+ 
+
+ align:start position:0%
+roughly speaking how to figure out if an
+estimator is good once we have one okay
+
+ align:start position:0%
+estimator is good once we have one okay
+ 
+
+ align:start position:0%
+estimator is good once we have one okay
+so we have lots of different criteria to
+
+ align:start position:0%
+so we have lots of different criteria to
+ 
+
+ align:start position:0%
+so we have lots of different criteria to
+consider um and you know some some good
+
+ align:start position:0%
+consider um and you know some some good
+ 
+
+ align:start position:0%
+consider um and you know some some good
+guidelines but how do we get an
+
+ align:start position:0%
+guidelines but how do we get an
+ 
+
+ align:start position:0%
+guidelines but how do we get an
+estimator in the first place okay so the
+
+ align:start position:0%
+estimator in the first place okay so the
+ 
+
+ align:start position:0%
+estimator in the first place okay so the
+example that I went over in class A
+
+ align:start position:0%
+example that I went over in class A
+ 
+
+ align:start position:0%
+example that I went over in class A
+couple lectures ago
+
+ align:start position:0%
+couple lectures ago
+ 
+
+ align:start position:0%
+couple lectures ago
+uh we just kind of dreamed dreamed them
+
+ align:start position:0%
+uh we just kind of dreamed dreamed them
+ 
+
+ align:start position:0%
+uh we just kind of dreamed dreamed them
+up off the top of our head right which
+
+ align:start position:0%
+up off the top of our head right which
+ 
+
+ align:start position:0%
+up off the top of our head right which
+you know is is it turns out can
+
+ align:start position:0%
+you know is is it turns out can
+ 
+
+ align:start position:0%
+you know is is it turns out can
+sometimes result in in quite reasonable
+
+ align:start position:0%
+sometimes result in in quite reasonable
+ 
+
+ align:start position:0%
+sometimes result in in quite reasonable
+estimators but it might be a little
+
+ align:start position:0%
+estimators but it might be a little
+ 
+
+ align:start position:0%
+estimators but it might be a little
+comforting to know that you don't always
+
+ align:start position:0%
+comforting to know that you don't always
+ 
+
+ align:start position:0%
+comforting to know that you don't always
+just have to be able to dream things up
+
+ align:start position:0%
+just have to be able to dream things up
+ 
+
+ align:start position:0%
+just have to be able to dream things up
+off the top of your head okay so there
+
+ align:start position:0%
+off the top of your head okay so there
+ 
+
+ align:start position:0%
+off the top of your head okay so there
+are two main Frameworks for deriving
+
+ align:start position:0%
+are two main Frameworks for deriving
+ 
+
+ align:start position:0%
+are two main Frameworks for deriving
+estimators one is called the method of
+
+ align:start position:0%
+estimators one is called the method of
+ 
+
+ align:start position:0%
+estimators one is called the method of
+moments and the uh second is called
+
+ align:start position:0%
+moments and the uh second is called
+ 
+
+ align:start position:0%
+moments and the uh second is called
+maximum likelihood estimation okay and
+
+ align:start position:0%
+maximum likelihood estimation okay and
+ 
+
+ align:start position:0%
+maximum likelihood estimation okay and
+in fact we've seen examples of both so
+
+ align:start position:0%
+in fact we've seen examples of both so
+ 
+
+ align:start position:0%
+in fact we've seen examples of both so
+two times the sample mean uh in the
+
+ align:start position:0%
+two times the sample mean uh in the
+ 
+
+ align:start position:0%
+two times the sample mean uh in the
+uniform example is a method of moments
+
+ align:start position:0%
+uniform example is a method of moments
+ 
+
+ align:start position:0%
+uniform example is a method of moments
+estimator and uh the um nth order
+
+ align:start position:0%
+estimator and uh the um nth order
+ 
+
+ align:start position:0%
+estimator and uh the um nth order
+statistic in that same in the uniform
+
+ align:start position:0%
+statistic in that same in the uniform
+ 
+
+ align:start position:0%
+statistic in that same in the uniform
+zero Theta distribution is a maximum
+
+ align:start position:0%
+zero Theta distribution is a maximum
+ 
+
+ align:start position:0%
+zero Theta distribution is a maximum
+likelihood estimator
+
+ align:start position:0%
+likelihood estimator
+ 
+
+ align:start position:0%
+likelihood estimator
+okay and then as I said before a third
+
+ align:start position:0%
+okay and then as I said before a third
+ 
+
+ align:start position:0%
+okay and then as I said before a third
+framework you can think of is to just
+
+ align:start position:0%
+framework you can think of is to just
+ 
+
+ align:start position:0%
+framework you can think of is to just
+come up with something clever off the
+
+ align:start position:0%
+come up with something clever off the
+ 
+
+ align:start position:0%
+come up with something clever off the
+top of your head and that sometimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+okay okay so let me just give you um
+
+ align:start position:0%
+okay okay so let me just give you um
+ 
+
+ align:start position:0%
+okay okay so let me just give you um
+sort of sketch out what the method of
+
+ align:start position:0%
+sort of sketch out what the method of
+ 
+
+ align:start position:0%
+sort of sketch out what the method of
+moments um uh framework for deriving
+
+ align:start position:0%
+moments um uh framework for deriving
+ 
+
+ align:start position:0%
+moments um uh framework for deriving
+estimators is give you an example of one
+
+ align:start position:0%
+estimators is give you an example of one
+ 
+
+ align:start position:0%
+estimators is give you an example of one
+uh and then do the same for maximum
+
+ align:start position:0%
+uh and then do the same for maximum
+ 
+
+ align:start position:0%
+uh and then do the same for maximum
+likelihood okay so the method of moments
+
+ align:start position:0%
+likelihood okay so the method of moments
+ 
+
+ align:start position:0%
+likelihood okay so the method of moments
+um was developed in in 1894 by Carl
+
+ align:start position:0%
+um was developed in in 1894 by Carl
+ 
+
+ align:start position:0%
+um was developed in in 1894 by Carl
+Pearson that many many people consider
+
+ align:start position:0%
+Pearson that many many people consider
+ 
+
+ align:start position:0%
+Pearson that many many people consider
+to be the father of mathematical
+
+ align:start position:0%
+to be the father of mathematical
+ 
+
+ align:start position:0%
+to be the father of mathematical
+statistics um there's a picture of them
+
+ align:start position:0%
+statistics um there's a picture of them
+ 
+
+ align:start position:0%
+statistics um there's a picture of them
+um and first to tell you what the method
+
+ align:start position:0%
+um and first to tell you what the method
+ 
+
+ align:start position:0%
+um and first to tell you what the method
+of moments uh what method of moments
+
+ align:start position:0%
+of moments uh what method of moments
+ 
+
+ align:start position:0%
+of moments uh what method of moments
+estimation is I've got to define a
+
+ align:start position:0%
+estimation is I've got to define a
+ 
+
+ align:start position:0%
+estimation is I've got to define a
+couple of things so I've got to define
+
+ align:start position:0%
+couple of things so I've got to define
+ 
+
+ align:start position:0%
+couple of things so I've got to define
+population moments and I've got to
+
+ align:start position:0%
+population moments and I've got to
+ 
+
+ align:start position:0%
+population moments and I've got to
+define sample
+
+ align:start position:0%
+define sample
+ 
+
+ align:start position:0%
+define sample
+moments okay so a population moment
+
+ align:start position:0%
+moments okay so a population moment
+ 
+
+ align:start position:0%
+moments okay so a population moment
+we've we've already seen we haven't used
+
+ align:start position:0%
+we've we've already seen we haven't used
+ 
+
+ align:start position:0%
+we've we've already seen we haven't used
+the terminology population moment but uh
+
+ align:start position:0%
+the terminology population moment but uh
+ 
+
+ align:start position:0%
+the terminology population moment but uh
+we've already seen uh the first
+
+ align:start position:0%
+we've already seen uh the first
+ 
+
+ align:start position:0%
+we've already seen uh the first
+population moment about the origin which
+
+ align:start position:0%
+population moment about the origin which
+ 
+
+ align:start position:0%
+population moment about the origin which
+is just the expectation okay the second
+
+ align:start position:0%
+is just the expectation okay the second
+ 
+
+ align:start position:0%
+is just the expectation okay the second
+population moment about the origin is is
+
+ align:start position:0%
+population moment about the origin is is
+ 
+
+ align:start position:0%
+population moment about the origin is is
+the expectation of X squar third
+
+ align:start position:0%
+the expectation of X squar third
+ 
+
+ align:start position:0%
+the expectation of X squar third
+population moment expectation of X cubed
+
+ align:start position:0%
+population moment expectation of X cubed
+ 
+
+ align:start position:0%
+population moment expectation of X cubed
+okay so for any distribution we can just
+
+ align:start position:0%
+okay so for any distribution we can just
+ 
+
+ align:start position:0%
+okay so for any distribution we can just
+you know we can calculate these as
+
+ align:start position:0%
+you know we can calculate these as
+ 
+
+ align:start position:0%
+you know we can calculate these as
+functions of the parameters or we can
+
+ align:start position:0%
+functions of the parameters or we can
+ 
+
+ align:start position:0%
+functions of the parameters or we can
+look them up on Wikipedia or we can look
+
+ align:start position:0%
+look them up on Wikipedia or we can look
+ 
+
+ align:start position:0%
+look them up on Wikipedia or we can look
+them up in the back of our statistics
+
+ align:start position:0%
+them up in the back of our statistics
+ 
+
+ align:start position:0%
+them up in the back of our statistics
+book or whatever um but you know we can
+
+ align:start position:0%
+book or whatever um but you know we can
+ 
+
+ align:start position:0%
+book or whatever um but you know we can
+we can get uh sort of the population
+
+ align:start position:0%
+we can get uh sort of the population
+ 
+
+ align:start position:0%
+we can get uh sort of the population
+moments as functions of the parameters
+
+ align:start position:0%
+moments as functions of the parameters
+ 
+
+ align:start position:0%
+moments as functions of the parameters
+of the distributions okay so what's the
+
+ align:start position:0%
+of the distributions okay so what's the
+ 
+
+ align:start position:0%
+of the distributions okay so what's the
+as a function of of parameters of the
+
+ align:start position:0%
+as a function of of parameters of the
+ 
+
+ align:start position:0%
+as a function of of parameters of the
+distribution what's the first population
+
+ align:start position:0%
+distribution what's the first population
+ 
+
+ align:start position:0%
+distribution what's the first population
+moment of a normal
+
+ align:start position:0%
+moment of a normal
+ 
+
+ align:start position:0%
+moment of a normal
+distribution mu how about of a pan does
+
+ align:start position:0%
+distribution mu how about of a pan does
+ 
+
+ align:start position:0%
+distribution mu how about of a pan does
+anyone remember that Lambda Lambda how
+
+ align:start position:0%
+anyone remember that Lambda Lambda how
+ 
+
+ align:start position:0%
+anyone remember that Lambda Lambda how
+about of a
+
+ align:start position:0%
+about of a
+ 
+
+ align:start position:0%
+about of a
+uniform
+
+ align:start position:0%
+uniform
+ 
+
+ align:start position:0%
+uniform
+z uh to
+
+ align:start position:0%
+z uh to
+ 
+
+ align:start position:0%
+z uh to
+Theta Theta over two right okay so you
+
+ align:start position:0%
+Theta Theta over two right okay so you
+ 
+
+ align:start position:0%
+Theta Theta over two right okay so you
+guys get the idea the sample moments are
+
+ align:start position:0%
+guys get the idea the sample moments are
+ 
+
+ align:start position:0%
+guys get the idea the sample moments are
+just we've seen obviously the first
+
+ align:start position:0%
+just we've seen obviously the first
+ 
+
+ align:start position:0%
+just we've seen obviously the first
+sample moment uh it's just the sample
+
+ align:start position:0%
+sample moment uh it's just the sample
+ 
+
+ align:start position:0%
+sample moment uh it's just the sample
+mean okay the second sample moment is
+
+ align:start position:0%
+mean okay the second sample moment is
+ 
+
+ align:start position:0%
+mean okay the second sample moment is
+the same thing but uh we're going to
+
+ align:start position:0%
+the same thing but uh we're going to
+ 
+
+ align:start position:0%
+the same thing but uh we're going to
+square all of the um the observations
+
+ align:start position:0%
+square all of the um the observations
+ 
+
+ align:start position:0%
+square all of the um the observations
+instead and and so forth you have a
+
+ align:start position:0%
+instead and and so forth you have a
+ 
+
+ align:start position:0%
+instead and and so forth you have a
+question going back to the sample
+
+ align:start position:0%
+question going back to the sample
+ 
+
+ align:start position:0%
+question going back to the sample
+variance that you showed us that was
+
+ align:start position:0%
+variance that you showed us that was
+ 
+
+ align:start position:0%
+variance that you showed us that was
+divided by nus one so is there any like
+
+ align:start position:0%
+divided by nus one so is there any like
+ 
+
+ align:start position:0%
+divided by nus one so is there any like
+inconsistent or like how do you
+
+ align:start position:0%
+inconsistent or like how do you
+ 
+
+ align:start position:0%
+inconsistent or like how do you
+reconcile the fact that the sample
+
+ align:start position:0%
+reconcile the fact that the sample
+ 
+
+ align:start position:0%
+reconcile the fact that the sample
+moments um so the S so the the the
+
+ align:start position:0%
+moments um so the S so the the the
+ 
+
+ align:start position:0%
+moments um so the S so the the the
+sample moment that I showed you was not
+
+ align:start position:0%
+sample moment that I showed you was not
+ 
+
+ align:start position:0%
+sample moment that I showed you was not
+a sample M well first of all uh the it
+
+ align:start position:0%
+a sample M well first of all uh the it
+ 
+
+ align:start position:0%
+a sample M well first of all uh the it
+it was not about the origin it was about
+
+ align:start position:0%
+it was not about the origin it was about
+ 
+
+ align:start position:0%
+it was not about the origin it was about
+the mean so I'm defining sample moments
+
+ align:start position:0%
+the mean so I'm defining sample moments
+ 
+
+ align:start position:0%
+the mean so I'm defining sample moments
+here as I I left I left it out but I
+
+ align:start position:0%
+here as I I left I left it out but I
+ 
+
+ align:start position:0%
+here as I I left I left it out but I
+should have said sample moments about
+
+ align:start position:0%
+should have said sample moments about
+ 
+
+ align:start position:0%
+should have said sample moments about
+the origin so there are two different
+
+ align:start position:0%
+the origin so there are two different
+ 
+
+ align:start position:0%
+the origin so there are two different
+types of moments for a dist sample
+
+ align:start position:0%
+types of moments for a dist sample
+ 
+
+ align:start position:0%
+types of moments for a dist sample
+moments for a distribution one is about
+
+ align:start position:0%
+moments for a distribution one is about
+ 
+
+ align:start position:0%
+moments for a distribution one is about
+the mean and one's about the origin
+
+ align:start position:0%
+the mean and one's about the origin
+ 
+
+ align:start position:0%
+the mean and one's about the origin
+these ones are about the origin and the
+
+ align:start position:0%
+these ones are about the origin and the
+ 
+
+ align:start position:0%
+these ones are about the origin and the
+other thing is that I to be honest I'm
+
+ align:start position:0%
+other thing is that I to be honest I'm
+ 
+
+ align:start position:0%
+other thing is that I to be honest I'm
+not sure the sample
+
+ align:start position:0%
+not sure the sample
+ 
+
+ align:start position:0%
+not sure the sample
+variance uh may
+
+ align:start position:0%
+variance uh may
+ 
+
+ align:start position:0%
+variance uh may
+not I I believe that actually the
+
+ align:start position:0%
+not I I believe that actually the
+ 
+
+ align:start position:0%
+not I I believe that actually the
+definition of the second sample moment
+
+ align:start position:0%
+definition of the second sample moment
+ 
+
+ align:start position:0%
+definition of the second sample moment
+about the mean is one over n it's not 1
+
+ align:start position:0%
+about the mean is one over n it's not 1
+ 
+
+ align:start position:0%
+about the mean is one over n it's not 1
+over n minus one so the sample variance
+
+ align:start position:0%
+over n minus one so the sample variance
+ 
+
+ align:start position:0%
+over n minus one so the sample variance
+is defined differently than the second
+
+ align:start position:0%
+is defined differently than the second
+ 
+
+ align:start position:0%
+is defined differently than the second
+sample moment about the mean and the
+
+ align:start position:0%
+sample moment about the mean and the
+ 
+
+ align:start position:0%
+sample moment about the mean and the
+reason why is that the second sample
+
+ align:start position:0%
+reason why is that the second sample
+ 
+
+ align:start position:0%
+reason why is that the second sample
+moment about the mean is actually a
+
+ align:start position:0%
+moment about the mean is actually a
+ 
+
+ align:start position:0%
+moment about the mean is actually a
+biased estimator of the variance so it's
+
+ align:start position:0%
+biased estimator of the variance so it's
+ 
+
+ align:start position:0%
+biased estimator of the variance so it's
+um yeah thanks for thanks for asking
+
+ align:start position:0%
+um yeah thanks for thanks for asking
+ 
+
+ align:start position:0%
+um yeah thanks for thanks for asking
+that question but yeah there's a no no
+
+ align:start position:0%
+that question but yeah there's a no no
+ 
+
+ align:start position:0%
+that question but yeah there's a no no
+inconsistency Okay so we've got these
+
+ align:start position:0%
+inconsistency Okay so we've got these
+ 
+
+ align:start position:0%
+inconsistency Okay so we've got these
+population moments these you can just
+
+ align:start position:0%
+population moments these you can just
+ 
+
+ align:start position:0%
+population moments these you can just
+think of these as like functions of the
+
+ align:start position:0%
+think of these as like functions of the
+ 
+
+ align:start position:0%
+think of these as like functions of the
+parameters okay and then we've got the
+
+ align:start position:0%
+parameters okay and then we've got the
+ 
+
+ align:start position:0%
+parameters okay and then we've got the
+sample moments and we're going to use
+
+ align:start position:0%
+sample moments and we're going to use
+ 
+
+ align:start position:0%
+sample moments and we're going to use
+those together to derve
+
+ align:start position:0%
+those together to derve
+ 
+
+ align:start position:0%
+those together to derve
+estimators okay so to estimate a
+
+ align:start position:0%
+estimators okay so to estimate a
+ 
+
+ align:start position:0%
+estimators okay so to estimate a
+parameter we equate the first population
+
+ align:start position:0%
+parameter we equate the first population
+ 
+
+ align:start position:0%
+parameter we equate the first population
+moment which is as I said a function of
+
+ align:start position:0%
+moment which is as I said a function of
+ 
+
+ align:start position:0%
+moment which is as I said a function of
+the parameter to the first sample moment
+
+ align:start position:0%
+the parameter to the first sample moment
+ 
+
+ align:start position:0%
+the parameter to the first sample moment
+and then we just solve for the parameter
+
+ align:start position:0%
+and then we just solve for the parameter
+ 
+
+ align:start position:0%
+and then we just solve for the parameter
+so let's do a quick
+
+ align:start position:0%
+so let's do a quick
+ 
+
+ align:start position:0%
+so let's do a quick
+example so this is an example we've
+
+ align:start position:0%
+example so this is an example we've
+ 
+
+ align:start position:0%
+example so this is an example we've
+already seen uh the first population
+
+ align:start position:0%
+already seen uh the first population
+ 
+
+ align:start position:0%
+already seen uh the first population
+moment expectation of X of a uniform 0
+
+ align:start position:0%
+moment expectation of X of a uniform 0
+ 
+
+ align:start position:0%
+moment expectation of X of a uniform 0
+to Theta is just Theta over 2 and the
+
+ align:start position:0%
+to Theta is just Theta over 2 and the
+ 
+
+ align:start position:0%
+to Theta is just Theta over 2 and the
+first sample moment is just 1/ n * the
+
+ align:start position:0%
+first sample moment is just 1/ n * the
+ 
+
+ align:start position:0%
+first sample moment is just 1/ n * the
+sum of the X's so we equate those two
+
+ align:start position:0%
+sum of the X's so we equate those two
+ 
+
+ align:start position:0%
+sum of the X's so we equate those two
+things we have to now stick a hat on the
+
+ align:start position:0%
+things we have to now stick a hat on the
+ 
+
+ align:start position:0%
+things we have to now stick a hat on the
+Theta because it's uh once we once we
+
+ align:start position:0%
+Theta because it's uh once we once we
+ 
+
+ align:start position:0%
+Theta because it's uh once we once we
+equate the sample moment and the
+
+ align:start position:0%
+equate the sample moment and the
+ 
+
+ align:start position:0%
+equate the sample moment and the
+population moment now now we're solving
+
+ align:start position:0%
+population moment now now we're solving
+ 
+
+ align:start position:0%
+population moment now now we're solving
+for an estimator not the parameter we
+
+ align:start position:0%
+for an estimator not the parameter we
+ 
+
+ align:start position:0%
+for an estimator not the parameter we
+stick a hat on on it and then we solve
+
+ align:start position:0%
+stick a hat on on it and then we solve
+ 
+
+ align:start position:0%
+stick a hat on on it and then we solve
+for Theta hat
+
+ align:start position:0%
+for Theta hat
+ 
+
+ align:start position:0%
+for Theta hat
+okay so that's exactly the estimator we
+
+ align:start position:0%
+okay so that's exactly the estimator we
+ 
+
+ align:start position:0%
+okay so that's exactly the estimator we
+saw before and this is just exhibiting
+
+ align:start position:0%
+saw before and this is just exhibiting
+ 
+
+ align:start position:0%
+saw before and this is just exhibiting
+that it is in fact a method of moments
+
+ align:start position:0%
+that it is in fact a method of moments
+ 
+
+ align:start position:0%
+that it is in fact a method of moments
+estimator okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what if you have more than one parameter
+
+ align:start position:0%
+what if you have more than one parameter
+ 
+
+ align:start position:0%
+what if you have more than one parameter
+estimate so for instance what if you
+
+ align:start position:0%
+estimate so for instance what if you
+ 
+
+ align:start position:0%
+estimate so for instance what if you
+have a normal distribution and you want
+
+ align:start position:0%
+have a normal distribution and you want
+ 
+
+ align:start position:0%
+have a normal distribution and you want
+an estimate of both the mean and the um
+
+ align:start position:0%
+an estimate of both the mean and the um
+ 
+
+ align:start position:0%
+an estimate of both the mean and the um
+the variance from the the normal
+
+ align:start position:0%
+the variance from the the normal
+ 
+
+ align:start position:0%
+the variance from the the normal
+distribution or you have like a binomial
+
+ align:start position:0%
+distribution or you have like a binomial
+ 
+
+ align:start position:0%
+distribution or you have like a binomial
+distribution you want n and p or
+
+ align:start position:0%
+distribution you want n and p or
+ 
+
+ align:start position:0%
+distribution you want n and p or
+something like that well um no problem
+
+ align:start position:0%
+something like that well um no problem
+ 
+
+ align:start position:0%
+something like that well um no problem
+so the method of moments can accommodate
+
+ align:start position:0%
+so the method of moments can accommodate
+ 
+
+ align:start position:0%
+so the method of moments can accommodate
+that you just use as many sample and
+
+ align:start position:0%
+that you just use as many sample and
+ 
+
+ align:start position:0%
+that you just use as many sample and
+population moments as necessary so each
+
+ align:start position:0%
+population moments as necessary so each
+ 
+
+ align:start position:0%
+population moments as necessary so each
+pair of you know sort of a sample moment
+
+ align:start position:0%
+pair of you know sort of a sample moment
+ 
+
+ align:start position:0%
+pair of you know sort of a sample moment
+and a population moment each one of
+
+ align:start position:0%
+and a population moment each one of
+ 
+
+ align:start position:0%
+and a population moment each one of
+those is called a moment
+
+ align:start position:0%
+those is called a moment
+ 
+
+ align:start position:0%
+those is called a moment
+condition and then if you have K
+
+ align:start position:0%
+condition and then if you have K
+ 
+
+ align:start position:0%
+condition and then if you have K
+parameters to estimate you just have K
+
+ align:start position:0%
+parameters to estimate you just have K
+ 
+
+ align:start position:0%
+parameters to estimate you just have K
+moment conditions and then uh that
+
+ align:start position:0%
+moment conditions and then uh that
+ 
+
+ align:start position:0%
+moment conditions and then uh that
+basically means you'll have K equations
+
+ align:start position:0%
+basically means you'll have K equations
+ 
+
+ align:start position:0%
+basically means you'll have K equations
+in K unknowns the K unknowns being the
+
+ align:start position:0%
+in K unknowns the K unknowns being the
+ 
+
+ align:start position:0%
+in K unknowns the K unknowns being the
+all of the parameter with hats on them
+
+ align:start position:0%
+all of the parameter with hats on them
+ 
+
+ align:start position:0%
+all of the parameter with hats on them
+you're you're solving for estimators for
+
+ align:start position:0%
+you're you're solving for estimators for
+ 
+
+ align:start position:0%
+you're you're solving for estimators for
+all those parameters and so then you
+
+ align:start position:0%
+all those parameters and so then you
+ 
+
+ align:start position:0%
+all those parameters and so then you
+just solve those K moment conditions for
+
+ align:start position:0%
+just solve those K moment conditions for
+ 
+
+ align:start position:0%
+just solve those K moment conditions for
+the K PR or for the K
+
+ align:start position:0%
+the K PR or for the K
+ 
+
+ align:start position:0%
+the K PR or for the K
+estimators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so second framework uh the
+
+ align:start position:0%
+okay okay so second framework uh the
+ 
+
+ align:start position:0%
+okay okay so second framework uh the
+idea for maximum likelihood estimation
+
+ align:start position:0%
+idea for maximum likelihood estimation
+ 
+
+ align:start position:0%
+idea for maximum likelihood estimation
+has been around for a very long time and
+
+ align:start position:0%
+has been around for a very long time and
+ 
+
+ align:start position:0%
+has been around for a very long time and
+uh if you try to sort of figure out what
+
+ align:start position:0%
+uh if you try to sort of figure out what
+ 
+
+ align:start position:0%
+uh if you try to sort of figure out what
+its origin is it's really a little
+
+ align:start position:0%
+its origin is it's really a little
+ 
+
+ align:start position:0%
+its origin is it's really a little
+unclear I think that um uh a lot of um
+
+ align:start position:0%
+unclear I think that um uh a lot of um
+ 
+
+ align:start position:0%
+unclear I think that um uh a lot of um
+sort of historians of Statistics would
+
+ align:start position:0%
+sort of historians of Statistics would
+ 
+
+ align:start position:0%
+sort of historians of Statistics would
+attribute the idea to lrange in the
+
+ align:start position:0%
+attribute the idea to lrange in the
+ 
+
+ align:start position:0%
+attribute the idea to lrange in the
+1770s um but it probably the basic idea
+
+ align:start position:0%
+1770s um but it probably the basic idea
+ 
+
+ align:start position:0%
+1770s um but it probably the basic idea
+probably predated that uh and sort of
+
+ align:start position:0%
+probably predated that uh and sort of
+ 
+
+ align:start position:0%
+probably predated that uh and sort of
+the analytics like proving that maximum
+
+ align:start position:0%
+the analytics like proving that maximum
+ 
+
+ align:start position:0%
+the analytics like proving that maximum
+likelihood estimation was a reasonable
+
+ align:start position:0%
+likelihood estimation was a reasonable
+ 
+
+ align:start position:0%
+likelihood estimation was a reasonable
+thing to do uh that that sort of came
+
+ align:start position:0%
+thing to do uh that that sort of came
+ 
+
+ align:start position:0%
+thing to do uh that that sort of came
+much later around 1930 with ra Fischer
+
+ align:start position:0%
+much later around 1930 with ra Fischer
+ 
+
+ align:start position:0%
+much later around 1930 with ra Fischer
+okay and there's those guys you can
+
+ align:start position:0%
+okay and there's those guys you can
+ 
+
+ align:start position:0%
+okay and there's those guys you can
+probably figure out which one is from
+
+ align:start position:0%
+probably figure out which one is from
+ 
+
+ align:start position:0%
+probably figure out which one is from
+1770s and which one's from the
+
+ align:start position:0%
+1770s and which one's from the
+ 
+
+ align:start position:0%
+1770s and which one's from the
+1930s okay so what is a maximum likel
+
+ align:start position:0%
+1930s okay so what is a maximum likel
+ 
+
+ align:start position:0%
+1930s okay so what is a maximum likel
+Hood estimator well it's the value Theta
+
+ align:start position:0%
+Hood estimator well it's the value Theta
+ 
+
+ align:start position:0%
+Hood estimator well it's the value Theta
+hat which most likely would have
+
+ align:start position:0%
+hat which most likely would have
+ 
+
+ align:start position:0%
+hat which most likely would have
+generated The observed
+
+ align:start position:0%
+generated The observed
+ 
+
+ align:start position:0%
+generated The observed
+sample okay that's why it's called
+
+ align:start position:0%
+sample okay that's why it's called
+ 
+
+ align:start position:0%
+sample okay that's why it's called
+maximum
+
+ align:start position:0%
+maximum
+ 
+
+ align:start position:0%
+maximum
+likelihood okay so what exactly does
+
+ align:start position:0%
+likelihood okay so what exactly does
+ 
+
+ align:start position:0%
+likelihood okay so what exactly does
+this mean how do we how do we find
+
+ align:start position:0%
+this mean how do we how do we find
+ 
+
+ align:start position:0%
+this mean how do we how do we find
+it okay so let's think of it this way so
+
+ align:start position:0%
+it okay so let's think of it this way so
+ 
+
+ align:start position:0%
+it okay so let's think of it this way so
+this is not sort of this is just U
+
+ align:start position:0%
+this is not sort of this is just U
+ 
+
+ align:start position:0%
+this is not sort of this is just U
+motivation this is not exactly this is
+
+ align:start position:0%
+motivation this is not exactly this is
+ 
+
+ align:start position:0%
+motivation this is not exactly this is
+not in in fact how you find a maximum
+
+ align:start position:0%
+not in in fact how you find a maximum
+ 
+
+ align:start position:0%
+not in in fact how you find a maximum
+likelihood estimator but this is going
+
+ align:start position:0%
+likelihood estimator but this is going
+ 
+
+ align:start position:0%
+likelihood estimator but this is going
+to serve as motivation okay so let's
+
+ align:start position:0%
+to serve as motivation okay so let's
+ 
+
+ align:start position:0%
+to serve as motivation okay so let's
+suppose we have a random sample
+
+ align:start position:0%
+suppose we have a random sample
+ 
+
+ align:start position:0%
+suppose we have a random sample
+and we uh want and we know that our
+
+ align:start position:0%
+and we uh want and we know that our
+ 
+
+ align:start position:0%
+and we uh want and we know that our
+random sample is from some particular
+
+ align:start position:0%
+random sample is from some particular
+ 
+
+ align:start position:0%
+random sample is from some particular
+distribution but we don't know which
+
+ align:start position:0%
+distribution but we don't know which
+ 
+
+ align:start position:0%
+distribution but we don't know which
+member or some particular family of
+
+ align:start position:0%
+member or some particular family of
+ 
+
+ align:start position:0%
+member or some particular family of
+distributions but don't know which
+
+ align:start position:0%
+distributions but don't know which
+ 
+
+ align:start position:0%
+distributions but don't know which
+member it is so in other words we know
+
+ align:start position:0%
+member it is so in other words we know
+ 
+
+ align:start position:0%
+member it is so in other words we know
+it has a beta distribution but we don't
+
+ align:start position:0%
+it has a beta distribution but we don't
+ 
+
+ align:start position:0%
+it has a beta distribution but we don't
+know what the parameter of the beta
+
+ align:start position:0%
+know what the parameter of the beta
+ 
+
+ align:start position:0%
+know what the parameter of the beta
+distribution is or we know it's a normal
+
+ align:start position:0%
+distribution is or we know it's a normal
+ 
+
+ align:start position:0%
+distribution is or we know it's a normal
+distribution but we don't know what mu
+
+ align:start position:0%
+distribution but we don't know what mu
+ 
+
+ align:start position:0%
+distribution but we don't know what mu
+and sigma squ are okay so you can think
+
+ align:start position:0%
+and sigma squ are okay so you can think
+ 
+
+ align:start position:0%
+and sigma squ are okay so you can think
+of being able to create a histogram with
+
+ align:start position:0%
+of being able to create a histogram with
+ 
+
+ align:start position:0%
+of being able to create a histogram with
+our random sample okay and this is sort
+
+ align:start position:0%
+our random sample okay and this is sort
+ 
+
+ align:start position:0%
+our random sample okay and this is sort
+of the empirical counterpart of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PDF on the other side you can think of
+
+ align:start position:0%
+PDF on the other side you can think of
+ 
+
+ align:start position:0%
+PDF on the other side you can think of
+taking this family of distributions that
+
+ align:start position:0%
+taking this family of distributions that
+ 
+
+ align:start position:0%
+taking this family of distributions that
+we're assuming or that we know that our
+
+ align:start position:0%
+we're assuming or that we know that our
+ 
+
+ align:start position:0%
+we're assuming or that we know that our
+uh random sample has come from and
+
+ align:start position:0%
+uh random sample has come from and
+ 
+
+ align:start position:0%
+uh random sample has come from and
+varying the parameter or parameters in
+
+ align:start position:0%
+varying the parameter or parameters in
+ 
+
+ align:start position:0%
+varying the parameter or parameters in
+that distribution that family of
+
+ align:start position:0%
+that distribution that family of
+ 
+
+ align:start position:0%
+that distribution that family of
+distributions and we get sort of all
+
+ align:start position:0%
+distributions and we get sort of all
+ 
+
+ align:start position:0%
+distributions and we get sort of all
+kinds of different possibilities here
+
+ align:start position:0%
+kinds of different possibilities here
+ 
+
+ align:start position:0%
+kinds of different possibilities here
+and presumably we get a Continuum of
+
+ align:start position:0%
+and presumably we get a Continuum of
+ 
+
+ align:start position:0%
+and presumably we get a Continuum of
+possibilities I've just drawn what is
+
+ align:start position:0%
+possibilities I've just drawn what is
+ 
+
+ align:start position:0%
+possibilities I've just drawn what is
+this I've drawn five different
+
+ align:start position:0%
+this I've drawn five different
+ 
+
+ align:start position:0%
+this I've drawn five different
+possibilities here but you know we have
+
+ align:start position:0%
+possibilities here but you know we have
+ 
+
+ align:start position:0%
+possibilities here but you know we have
+sort of an infinite number of
+
+ align:start position:0%
+sort of an infinite number of
+ 
+
+ align:start position:0%
+sort of an infinite number of
+possibilities as we vary the parameter
+
+ align:start position:0%
+possibilities as we vary the parameter
+ 
+
+ align:start position:0%
+possibilities as we vary the parameter
+or parameters of these distribut ions
+
+ align:start position:0%
+or parameters of these distribut ions
+ 
+
+ align:start position:0%
+or parameters of these distribut ions
+okay so where did we get these well as I
+
+ align:start position:0%
+okay so where did we get these well as I
+ 
+
+ align:start position:0%
+okay so where did we get these well as I
+said we're assuming a particular family
+
+ align:start position:0%
+said we're assuming a particular family
+ 
+
+ align:start position:0%
+said we're assuming a particular family
+and then just varying the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters so how do we choose which one
+
+ align:start position:0%
+parameters so how do we choose which one
+ 
+
+ align:start position:0%
+parameters so how do we choose which one
+of those well just sort of intuitively
+
+ align:start position:0%
+of those well just sort of intuitively
+ 
+
+ align:start position:0%
+of those well just sort of intuitively
+or graphically we want to choose the one
+
+ align:start position:0%
+or graphically we want to choose the one
+ 
+
+ align:start position:0%
+or graphically we want to choose the one
+that sort of fits our histogram the best
+
+ align:start position:0%
+that sort of fits our histogram the best
+ 
+
+ align:start position:0%
+that sort of fits our histogram the best
+right okay so that's what we
+
+ align:start position:0%
+right okay so that's what we
+ 
+
+ align:start position:0%
+right okay so that's what we
+do we choose the the member of the
+
+ align:start position:0%
+do we choose the the member of the
+ 
+
+ align:start position:0%
+do we choose the the member of the
+family of distributions that's most
+
+ align:start position:0%
+family of distributions that's most
+ 
+
+ align:start position:0%
+family of distributions that's most
+likely to have produced our data so if
+
+ align:start position:0%
+likely to have produced our data so if
+ 
+
+ align:start position:0%
+likely to have produced our data so if
+we chose a member of the family whose
+
+ align:start position:0%
+we chose a member of the family whose
+ 
+
+ align:start position:0%
+we chose a member of the family whose
+shape was much different than our
+
+ align:start position:0%
+shape was much different than our
+ 
+
+ align:start position:0%
+shape was much different than our
+histogram that it's unlikely that it
+
+ align:start position:0%
+histogram that it's unlikely that it
+ 
+
+ align:start position:0%
+histogram that it's unlikely that it
+would that that parameter would have
+
+ align:start position:0%
+would that that parameter would have
+ 
+
+ align:start position:0%
+would that that parameter would have
+produced the data that we saw okay the
+
+ align:start position:0%
+produced the data that we saw okay the
+ 
+
+ align:start position:0%
+produced the data that we saw okay the
+one that fits our histogram most closely
+
+ align:start position:0%
+one that fits our histogram most closely
+ 
+
+ align:start position:0%
+one that fits our histogram most closely
+that's the one that's most likely to
+
+ align:start position:0%
+that's the one that's most likely to
+ 
+
+ align:start position:0%
+that's the one that's most likely to
+have given rise to our
+
+ align:start position:0%
+have given rise to our
+ 
+
+ align:start position:0%
+have given rise to our
+data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so Theta half the our maximum
+
+ align:start position:0%
+okay so Theta half the our maximum
+ 
+
+ align:start position:0%
+okay so Theta half the our maximum
+likelihood estimator is the value of the
+
+ align:start position:0%
+likelihood estimator is the value of the
+ 
+
+ align:start position:0%
+likelihood estimator is the value of the
+parameter associated with this
+
+ align:start position:0%
+parameter associated with this
+ 
+
+ align:start position:0%
+parameter associated with this
+particular best fit member of the family
+
+ align:start position:0%
+particular best fit member of the family
+ 
+
+ align:start position:0%
+particular best fit member of the family
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+distributions okay so is that is that
+
+ align:start position:0%
+distributions okay so is that is that
+ 
+
+ align:start position:0%
+distributions okay so is that is that
+sort of concept
+
+ align:start position:0%
+sort of concept
+ 
+
+ align:start position:0%
+sort of concept
+clear even if you don't know how to find
+
+ align:start position:0%
+clear even if you don't know how to find
+ 
+
+ align:start position:0%
+clear even if you don't know how to find
+that yet
+
+ align:start position:0%
+that yet
+ 
+
+ align:start position:0%
+that yet
+okay okay so conceptually makes sense at
+
+ align:start position:0%
+okay okay so conceptually makes sense at
+ 
+
+ align:start position:0%
+okay okay so conceptually makes sense at
+least I hope it
+
+ align:start position:0%
+least I hope it
+ 
+
+ align:start position:0%
+least I hope it
+does operationally how do we go about
+
+ align:start position:0%
+does operationally how do we go about
+ 
+
+ align:start position:0%
+does operationally how do we go about
+this how do we find the one one of a
+
+ align:start position:0%
+this how do we find the one one of a
+ 
+
+ align:start position:0%
+this how do we find the one one of a
+bunch of PDFs that's most likely to have
+
+ align:start position:0%
+bunch of PDFs that's most likely to have
+ 
+
+ align:start position:0%
+bunch of PDFs that's most likely to have
+produced our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data well the key is that we have to
+
+ align:start position:0%
+data well the key is that we have to
+ 
+
+ align:start position:0%
+data well the key is that we have to
+think about the joint PDF of our data in
+
+ align:start position:0%
+think about the joint PDF of our data in
+ 
+
+ align:start position:0%
+think about the joint PDF of our data in
+a somewhat different way okay so we we
+
+ align:start position:0%
+a somewhat different way okay so we we
+ 
+
+ align:start position:0%
+a somewhat different way okay so we we
+know how to if we have a random sample
+
+ align:start position:0%
+know how to if we have a random sample
+ 
+
+ align:start position:0%
+know how to if we have a random sample
+we know how to get the joint PDF of that
+
+ align:start position:0%
+we know how to get the joint PDF of that
+ 
+
+ align:start position:0%
+we know how to get the joint PDF of that
+random sample okay we're just it's just
+
+ align:start position:0%
+random sample okay we're just it's just
+ 
+
+ align:start position:0%
+random sample okay we're just it's just
+the product of the individual PD FS of
+
+ align:start position:0%
+the product of the individual PD FS of
+ 
+
+ align:start position:0%
+the product of the individual PD FS of
+all of the the random variables in our
+
+ align:start position:0%
+all of the the random variables in our
+ 
+
+ align:start position:0%
+all of the the random variables in our
+random sample okay now we think of this
+
+ align:start position:0%
+random sample okay now we think of this
+ 
+
+ align:start position:0%
+random sample okay now we think of this
+joint PDF as the function of the
+
+ align:start position:0%
+joint PDF as the function of the
+ 
+
+ align:start position:0%
+joint PDF as the function of the
+parameters now okay we'd always sort of
+
+ align:start position:0%
+parameters now okay we'd always sort of
+ 
+
+ align:start position:0%
+parameters now okay we'd always sort of
+taken the parameters as given they were
+
+ align:start position:0%
+taken the parameters as given they were
+ 
+
+ align:start position:0%
+taken the parameters as given they were
+just sort of constants in our function
+
+ align:start position:0%
+just sort of constants in our function
+ 
+
+ align:start position:0%
+just sort of constants in our function
+that we sort of took as given now we
+
+ align:start position:0%
+that we sort of took as given now we
+ 
+
+ align:start position:0%
+that we sort of took as given now we
+think of that joint PDF as a function of
+
+ align:start position:0%
+think of that joint PDF as a function of
+ 
+
+ align:start position:0%
+think of that joint PDF as a function of
+those parameters and we're going to
+
+ align:start position:0%
+those parameters and we're going to
+ 
+
+ align:start position:0%
+those parameters and we're going to
+maximize that distrib or that joint PDF
+
+ align:start position:0%
+maximize that distrib or that joint PDF
+ 
+
+ align:start position:0%
+maximize that distrib or that joint PDF
+over the possible values of the pr
+
+ align:start position:0%
+over the possible values of the pr
+ 
+
+ align:start position:0%
+over the possible values of the pr
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+okay okay yes of course and we we'll
+
+ align:start position:0%
+okay okay yes of course and we we'll
+ 
+
+ align:start position:0%
+okay okay yes of course and we we'll
+we'll see a couple of examples as well
+
+ align:start position:0%
+we'll see a couple of examples as well
+ 
+
+ align:start position:0%
+we'll see a couple of examples as well
+but I'm happy to go over this because
+
+ align:start position:0%
+but I'm happy to go over this because
+ 
+
+ align:start position:0%
+but I'm happy to go over this because
+it's a little it's a little subtle it's
+
+ align:start position:0%
+it's a little it's a little subtle it's
+ 
+
+ align:start position:0%
+it's a little it's a little subtle it's
+a little confusing um so basically what
+
+ align:start position:0%
+a little confusing um so basically what
+ 
+
+ align:start position:0%
+a little confusing um so basically what
+we do actually let me go to the next
+
+ align:start position:0%
+we do actually let me go to the next
+ 
+
+ align:start position:0%
+we do actually let me go to the next
+slide yes okay so in other words what we
+
+ align:start position:0%
+slide yes okay so in other words what we
+ 
+
+ align:start position:0%
+slide yes okay so in other words what we
+do is we take the joint PDF of our
+
+ align:start position:0%
+do is we take the joint PDF of our
+ 
+
+ align:start position:0%
+do is we take the joint PDF of our
+random sample we're going to call it
+
+ align:start position:0%
+random sample we're going to call it
+ 
+
+ align:start position:0%
+random sample we're going to call it
+instead of calling it ad joint PDF we're
+
+ align:start position:0%
+instead of calling it ad joint PDF we're
+ 
+
+ align:start position:0%
+instead of calling it ad joint PDF we're
+now going to call it a likelihood
+
+ align:start position:0%
+now going to call it a likelihood
+ 
+
+ align:start position:0%
+now going to call it a likelihood
+function okay that's just suggestive to
+
+ align:start position:0%
+function okay that's just suggestive to
+ 
+
+ align:start position:0%
+function okay that's just suggestive to
+us that we have to think of it in a
+
+ align:start position:0%
+us that we have to think of it in a
+ 
+
+ align:start position:0%
+us that we have to think of it in a
+different way it's exactly the same
+
+ align:start position:0%
+different way it's exactly the same
+ 
+
+ align:start position:0%
+different way it's exactly the same
+thing the likelihood function is the
+
+ align:start position:0%
+thing the likelihood function is the
+ 
+
+ align:start position:0%
+thing the likelihood function is the
+joint PDF of a random sample how do we
+
+ align:start position:0%
+joint PDF of a random sample how do we
+ 
+
+ align:start position:0%
+joint PDF of a random sample how do we
+get this likelihood function well we
+
+ align:start position:0%
+get this likelihood function well we
+ 
+
+ align:start position:0%
+get this likelihood function well we
+just take the product of the individual
+
+ align:start position:0%
+just take the product of the individual
+ 
+
+ align:start position:0%
+just take the product of the individual
+PDFs of all of the guys in our random
+
+ align:start position:0%
+PDFs of all of the guys in our random
+ 
+
+ align:start position:0%
+PDFs of all of the guys in our random
+sample right you guys remember that so
+
+ align:start position:0%
+sample right you guys remember that so
+ 
+
+ align:start position:0%
+sample right you guys remember that so
+these are a what's a random sample it's
+
+ align:start position:0%
+these are a what's a random sample it's
+ 
+
+ align:start position:0%
+these are a what's a random sample it's
+independent identically distributed
+
+ align:start position:0%
+independent identically distributed
+ 
+
+ align:start position:0%
+independent identically distributed
+random variables to get the joint
+
+ align:start position:0%
+random variables to get the joint
+ 
+
+ align:start position:0%
+random variables to get the joint
+distribution of independent identically
+
+ align:start position:0%
+distribution of independent identically
+ 
+
+ align:start position:0%
+distribution of independent identically
+distributed random variables you just
+
+ align:start position:0%
+distributed random variables you just
+ 
+
+ align:start position:0%
+distributed random variables you just
+take their their distribution and you
+
+ align:start position:0%
+take their their distribution and you
+ 
+
+ align:start position:0%
+take their their distribution and you
+multiply them together because they're
+
+ align:start position:0%
+multiply them together because they're
+ 
+
+ align:start position:0%
+multiply them together because they're
+independent okay so this is the joint
+
+ align:start position:0%
+independent okay so this is the joint
+ 
+
+ align:start position:0%
+independent okay so this is the joint
+PDF of our random sample we're going to
+
+ align:start position:0%
+PDF of our random sample we're going to
+ 
+
+ align:start position:0%
+PDF of our random sample we're going to
+re label that the likelihood function
+
+ align:start position:0%
+re label that the likelihood function
+ 
+
+ align:start position:0%
+re label that the likelihood function
+and we're going to think of the
+
+ align:start position:0%
+and we're going to think of the
+ 
+
+ align:start position:0%
+and we're going to think of the
+likelihood function as being a function
+
+ align:start position:0%
+likelihood function as being a function
+ 
+
+ align:start position:0%
+likelihood function as being a function
+of theta given the data as as opposed to
+
+ align:start position:0%
+of theta given the data as as opposed to
+ 
+
+ align:start position:0%
+of theta given the data as as opposed to
+the other way around and then we're
+
+ align:start position:0%
+the other way around and then we're
+ 
+
+ align:start position:0%
+the other way around and then we're
+going to map maximize that likelihood
+
+ align:start position:0%
+going to map maximize that likelihood
+ 
+
+ align:start position:0%
+going to map maximize that likelihood
+function with respect to these
+
+ align:start position:0%
+function with respect to these
+ 
+
+ align:start position:0%
+function with respect to these
+parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+okay okay so like I said I will I have a
+
+ align:start position:0%
+okay okay so like I said I will I have a
+ 
+
+ align:start position:0%
+okay okay so like I said I will I have a
+couple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples okay and this actually just
+
+ align:start position:0%
+examples okay and this actually just
+ 
+
+ align:start position:0%
+examples okay and this actually just
+emphasizes what we said before so we've
+
+ align:start position:0%
+emphasizes what we said before so we've
+ 
+
+ align:start position:0%
+emphasizes what we said before so we've
+got this likelihood function we just
+
+ align:start position:0%
+got this likelihood function we just
+ 
+
+ align:start position:0%
+got this likelihood function we just
+maximize it over all possible values of
+
+ align:start position:0%
+maximize it over all possible values of
+ 
+
+ align:start position:0%
+maximize it over all possible values of
+theta and the one thing to keep in mind
+
+ align:start position:0%
+theta and the one thing to keep in mind
+ 
+
+ align:start position:0%
+theta and the one thing to keep in mind
+I don't for this class you don't really
+
+ align:start position:0%
+I don't for this class you don't really
+ 
+
+ align:start position:0%
+I don't for this class you don't really
+have to worry about this but when you if
+
+ align:start position:0%
+have to worry about this but when you if
+ 
+
+ align:start position:0%
+have to worry about this but when you if
+you go out of this class and you
+
+ align:start position:0%
+you go out of this class and you
+ 
+
+ align:start position:0%
+you go out of this class and you
+encounter uh maximum likelihood in the
+
+ align:start position:0%
+encounter uh maximum likelihood in the
+ 
+
+ align:start position:0%
+encounter uh maximum likelihood in the
+larger world then you're going to have
+
+ align:start position:0%
+larger world then you're going to have
+ 
+
+ align:start position:0%
+larger world then you're going to have
+to realize that a lot of times what we
+
+ align:start position:0%
+to realize that a lot of times what we
+ 
+
+ align:start position:0%
+to realize that a lot of times what we
+do instead of maximizing the likelihood
+
+ align:start position:0%
+do instead of maximizing the likelihood
+ 
+
+ align:start position:0%
+do instead of maximizing the likelihood
+function is we maximize the log
+
+ align:start position:0%
+function is we maximize the log
+ 
+
+ align:start position:0%
+function is we maximize the log
+likelihood function so that's a
+
+ align:start position:0%
+likelihood function so that's a
+ 
+
+ align:start position:0%
+likelihood function so that's a
+perfectly fine thing to do the whatever
+
+ align:start position:0%
+perfectly fine thing to do the whatever
+ 
+
+ align:start position:0%
+perfectly fine thing to do the whatever
+maximizes the likelihood function is
+
+ align:start position:0%
+maximizes the likelihood function is
+ 
+
+ align:start position:0%
+maximizes the likelihood function is
+going to maximize any monotonic
+
+ align:start position:0%
+going to maximize any monotonic
+ 
+
+ align:start position:0%
+going to maximize any monotonic
+transformation of the likelihood
+
+ align:start position:0%
+transformation of the likelihood
+ 
+
+ align:start position:0%
+transformation of the likelihood
+function so it's fine to take a log the
+
+ align:start position:0%
+function so it's fine to take a log the
+ 
+
+ align:start position:0%
+function so it's fine to take a log the
+reason we do it is computationally it
+
+ align:start position:0%
+reason we do it is computationally it
+ 
+
+ align:start position:0%
+reason we do it is computationally it
+just is much easier typically to
+
+ align:start position:0%
+just is much easier typically to
+ 
+
+ align:start position:0%
+just is much easier typically to
+maximize the log likelihood function
+
+ align:start position:0%
+maximize the log likelihood function
+ 
+
+ align:start position:0%
+maximize the log likelihood function
+okay so you sort of go out into the
+
+ align:start position:0%
+okay so you sort of go out into the
+ 
+
+ align:start position:0%
+okay so you sort of go out into the
+broader world you will encounter log
+
+ align:start position:0%
+broader world you will encounter log
+ 
+
+ align:start position:0%
+broader world you will encounter log
+likelihood functions not likelihood
+
+ align:start position:0%
+likelihood functions not likelihood
+ 
+
+ align:start position:0%
+likelihood functions not likelihood
+functions and that's why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so uh it's good practice um I'm not
+
+ align:start position:0%
+okay so uh it's good practice um I'm not
+ 
+
+ align:start position:0%
+okay so uh it's good practice um I'm not
+necessarily saying you guys have to do
+
+ align:start position:0%
+necessarily saying you guys have to do
+ 
+
+ align:start position:0%
+necessarily saying you guys have to do
+it but it's good practice If you're sort
+
+ align:start position:0%
+it but it's good practice If you're sort
+ 
+
+ align:start position:0%
+it but it's good practice If you're sort
+of interested in in this kind of um you
+
+ align:start position:0%
+of interested in in this kind of um you
+ 
+
+ align:start position:0%
+of interested in in this kind of um you
+know in these kinds of techniques to
+
+ align:start position:0%
+know in these kinds of techniques to
+ 
+
+ align:start position:0%
+know in these kinds of techniques to
+take uh to write down some joint PDFs uh
+
+ align:start position:0%
+take uh to write down some joint PDFs uh
+ 
+
+ align:start position:0%
+take uh to write down some joint PDFs uh
+maybe take the logs to make computation
+
+ align:start position:0%
+maybe take the logs to make computation
+ 
+
+ align:start position:0%
+maybe take the logs to make computation
+easier take the derivative with respect
+
+ align:start position:0%
+easier take the derivative with respect
+ 
+
+ align:start position:0%
+easier take the derivative with respect
+to Theta set the derivatives equal to
+
+ align:start position:0%
+to Theta set the derivatives equal to
+ 
+
+ align:start position:0%
+to Theta set the derivatives equal to
+zero solve for the maximum likelihood
+
+ align:start position:0%
+zero solve for the maximum likelihood
+ 
+
+ align:start position:0%
+zero solve for the maximum likelihood
+estimators um you certainly can do that
+
+ align:start position:0%
+estimators um you certainly can do that
+ 
+
+ align:start position:0%
+estimators um you certainly can do that
+we're not going to do it here okay what
+
+ align:start position:0%
+we're not going to do it here okay what
+ 
+
+ align:start position:0%
+we're not going to do it here okay what
+I'm going to do instead is I'm going to
+
+ align:start position:0%
+I'm going to do instead is I'm going to
+ 
+
+ align:start position:0%
+I'm going to do instead is I'm going to
+do a couple of examples that are both
+
+ align:start position:0%
+do a couple of examples that are both
+ 
+
+ align:start position:0%
+do a couple of examples that are both
+unusual in that they can't can't be
+
+ align:start position:0%
+unusual in that they can't can't be
+ 
+
+ align:start position:0%
+unusual in that they can't can't be
+solved this way because their Maxim
+
+ align:start position:0%
+solved this way because their Maxim
+ 
+
+ align:start position:0%
+solved this way because their Maxim
+their Maxima are not at a point where
+
+ align:start position:0%
+their Maxima are not at a point where
+ 
+
+ align:start position:0%
+their Maxima are not at a point where
+the likelihood function is
+
+ align:start position:0%
+the likelihood function is
+ 
+
+ align:start position:0%
+the likelihood function is
+differentiable but then also don't we
+
+ align:start position:0%
+differentiable but then also don't we
+ 
+
+ align:start position:0%
+differentiable but then also don't we
+don't have to sort of get bogged down
+
+ align:start position:0%
+don't have to sort of get bogged down
+ 
+
+ align:start position:0%
+don't have to sort of get bogged down
+with all the computation so I think
+
+ align:start position:0%
+with all the computation so I think
+ 
+
+ align:start position:0%
+with all the computation so I think
+they're kind of easier examples to to
+
+ align:start position:0%
+they're kind of easier examples to to
+ 
+
+ align:start position:0%
+they're kind of easier examples to to
+show you I think
+
+ align:start position:0%
+show you I think
+ 
+
+ align:start position:0%
+show you I think
+okay so do we guess what do we think the
+
+ align:start position:0%
+okay so do we guess what do we think the
+ 
+
+ align:start position:0%
+okay so do we guess what do we think the
+PDFs are going to be and then we do good
+
+ align:start position:0%
+PDFs are going to be and then we do good
+ 
+
+ align:start position:0%
+PDFs are going to be and then we do good
+question so the question was do we guess
+
+ align:start position:0%
+question so the question was do we guess
+ 
+
+ align:start position:0%
+question so the question was do we guess
+what the PDF is so sometimes we may
+
+ align:start position:0%
+what the PDF is so sometimes we may
+ 
+
+ align:start position:0%
+what the PDF is so sometimes we may
+know when why do we know I don't know
+
+ align:start position:0%
+know when why do we know I don't know
+ 
+
+ align:start position:0%
+know when why do we know I don't know
+maybe we're engineers and we've sort of
+
+ align:start position:0%
+maybe we're engineers and we've sort of
+ 
+
+ align:start position:0%
+maybe we're engineers and we've sort of
+worked in uh you know sort of a
+
+ align:start position:0%
+worked in uh you know sort of a
+ 
+
+ align:start position:0%
+worked in uh you know sort of a
+particular field for our entire careers
+
+ align:start position:0%
+particular field for our entire careers
+ 
+
+ align:start position:0%
+particular field for our entire careers
+and we know that the you know sort of
+
+ align:start position:0%
+and we know that the you know sort of
+ 
+
+ align:start position:0%
+and we know that the you know sort of
+random draws from this par you know like
+
+ align:start position:0%
+random draws from this par you know like
+ 
+
+ align:start position:0%
+random draws from this par you know like
+from some random event that happens uh
+
+ align:start position:0%
+from some random event that happens uh
+ 
+
+ align:start position:0%
+from some random event that happens uh
+with this particular machine always has
+
+ align:start position:0%
+with this particular machine always has
+ 
+
+ align:start position:0%
+with this particular machine always has
+an exponential distribution and we just
+
+ align:start position:0%
+an exponential distribution and we just
+ 
+
+ align:start position:0%
+an exponential distribution and we just
+don't know what the parameter is but we
+
+ align:start position:0%
+don't know what the parameter is but we
+ 
+
+ align:start position:0%
+don't know what the parameter is but we
+know you know we just know from vast
+
+ align:start position:0%
+know you know we just know from vast
+ 
+
+ align:start position:0%
+know you know we just know from vast
+years of experience it's going to be
+
+ align:start position:0%
+years of experience it's going to be
+ 
+
+ align:start position:0%
+years of experience it's going to be
+exponential IAL or maybe we have a
+
+ align:start position:0%
+exponential IAL or maybe we have a
+ 
+
+ align:start position:0%
+exponential IAL or maybe we have a
+theoretical reason to believe that there
+
+ align:start position:0%
+theoretical reason to believe that there
+ 
+
+ align:start position:0%
+theoretical reason to believe that there
+is a particular distribution that's
+
+ align:start position:0%
+is a particular distribution that's
+ 
+
+ align:start position:0%
+is a particular distribution that's
+giving rise to um the random sample or
+
+ align:start position:0%
+giving rise to um the random sample or
+ 
+
+ align:start position:0%
+giving rise to um the random sample or
+sometimes we just guess so it's it it
+
+ align:start position:0%
+sometimes we just guess so it's it it
+ 
+
+ align:start position:0%
+sometimes we just guess so it's it it
+just depends a lot on the problem
+
+ align:start position:0%
+just depends a lot on the problem
+ 
+
+ align:start position:0%
+just depends a lot on the problem
+whether how confident we are about the
+
+ align:start position:0%
+whether how confident we are about the
+ 
+
+ align:start position:0%
+whether how confident we are about the
+the distribution the underlying
+
+ align:start position:0%
+the distribution the underlying
+ 
+
+ align:start position:0%
+the distribution the underlying
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+so okay so I said we we'll do a couple
+
+ align:start position:0%
+so okay so I said we we'll do a couple
+ 
+
+ align:start position:0%
+so okay so I said we we'll do a couple
+of examples but I'm going to do ones
+
+ align:start position:0%
+of examples but I'm going to do ones
+ 
+
+ align:start position:0%
+of examples but I'm going to do ones
+that don't involve the standard you know
+
+ align:start position:0%
+that don't involve the standard you know
+ 
+
+ align:start position:0%
+that don't involve the standard you know
+sort of taking the log of the likelihood
+
+ align:start position:0%
+sort of taking the log of the likelihood
+ 
+
+ align:start position:0%
+sort of taking the log of the likelihood
+function uh setting uh you know sort of
+
+ align:start position:0%
+function uh setting uh you know sort of
+ 
+
+ align:start position:0%
+function uh setting uh you know sort of
+taking derivative with respect to Theta
+
+ align:start position:0%
+taking derivative with respect to Theta
+ 
+
+ align:start position:0%
+taking derivative with respect to Theta
+setting the derivative equal to zero Etc
+
+ align:start position:0%
+setting the derivative equal to zero Etc
+ 
+
+ align:start position:0%
+setting the derivative equal to zero Etc
+I'm going to do some kind of
+
+ align:start position:0%
+I'm going to do some kind of
+ 
+
+ align:start position:0%
+I'm going to do some kind of
+non-standard examples
+
+ align:start position:0%
+non-standard examples
+ 
+
+ align:start position:0%
+non-standard examples
+instead okay so back
+
+ align:start position:0%
+instead okay so back
+ 
+
+ align:start position:0%
+instead okay so back
+to uh this sort of uniform zero Theta
+
+ align:start position:0%
+to uh this sort of uniform zero Theta
+ 
+
+ align:start position:0%
+to uh this sort of uniform zero Theta
+example remember what the maximum
+
+ align:start position:0%
+example remember what the maximum
+ 
+
+ align:start position:0%
+example remember what the maximum
+likelihood estimator from
+
+ align:start position:0%
+likelihood estimator from
+ 
+
+ align:start position:0%
+likelihood estimator from
+um uh what the sorry remember what the I
+
+ align:start position:0%
+um uh what the sorry remember what the I
+ 
+
+ align:start position:0%
+um uh what the sorry remember what the I
+told you I didn't show you obviously but
+
+ align:start position:0%
+told you I didn't show you obviously but
+ 
+
+ align:start position:0%
+told you I didn't show you obviously but
+remember what the maximum likelihood
+
+ align:start position:0%
+remember what the maximum likelihood
+ 
+
+ align:start position:0%
+remember what the maximum likelihood
+estimator for this
+
+ align:start position:0%
+estimator for this
+ 
+
+ align:start position:0%
+estimator for this
+is It's the nth order
+
+ align:start position:0%
+is It's the nth order
+ 
+
+ align:start position:0%
+is It's the nth order
+statistic that's the that's the uh
+
+ align:start position:0%
+statistic that's the that's the uh
+ 
+
+ align:start position:0%
+statistic that's the that's the uh
+expectation of of that estimator but so
+
+ align:start position:0%
+expectation of of that estimator but so
+ 
+
+ align:start position:0%
+expectation of of that estimator but so
+the the maximum likelihood estimator I
+
+ align:start position:0%
+the the maximum likelihood estimator I
+ 
+
+ align:start position:0%
+the the maximum likelihood estimator I
+just said it verbally it wasn't on the
+
+ align:start position:0%
+just said it verbally it wasn't on the
+ 
+
+ align:start position:0%
+just said it verbally it wasn't on the
+slide but I said that that in fact it's
+
+ align:start position:0%
+slide but I said that that in fact it's
+ 
+
+ align:start position:0%
+slide but I said that that in fact it's
+the the nth order
+
+ align:start position:0%
+the the nth order
+ 
+
+ align:start position:0%
+the the nth order
+statistic okay or I think I did okay so
+
+ align:start position:0%
+statistic okay or I think I did okay so
+ 
+
+ align:start position:0%
+statistic okay or I think I did okay so
+so let's figure that out let's verify
+
+ align:start position:0%
+so let's figure that out let's verify
+ 
+
+ align:start position:0%
+so let's figure that out let's verify
+that in fact that is the maximum
+
+ align:start position:0%
+that in fact that is the maximum
+ 
+
+ align:start position:0%
+that in fact that is the maximum
+likelihood estimator okay so what do we
+
+ align:start position:0%
+likelihood estimator okay so what do we
+ 
+
+ align:start position:0%
+likelihood estimator okay so what do we
+do we first have to write down the
+
+ align:start position:0%
+do we first have to write down the
+ 
+
+ align:start position:0%
+do we first have to write down the
+likelihood function how do we get the
+
+ align:start position:0%
+likelihood function how do we get the
+ 
+
+ align:start position:0%
+likelihood function how do we get the
+likelihood function it's just the joint
+
+ align:start position:0%
+likelihood function it's just the joint
+ 
+
+ align:start position:0%
+likelihood function it's just the joint
+PDF of our random sample okay so we have
+
+ align:start position:0%
+PDF of our random sample okay so we have
+ 
+
+ align:start position:0%
+PDF of our random sample okay so we have
+each of our each of the
+
+ align:start position:0%
+each of our each of the
+ 
+
+ align:start position:0%
+each of our each of the
+individual members of the random sample
+
+ align:start position:0%
+individual members of the random sample
+ 
+
+ align:start position:0%
+individual members of the random sample
+has this distribution one over Theta for
+
+ align:start position:0%
+has this distribution one over Theta for
+ 
+
+ align:start position:0%
+has this distribution one over Theta for
+X in Zer to Theta and zero
+
+ align:start position:0%
+X in Zer to Theta and zero
+ 
+
+ align:start position:0%
+X in Zer to Theta and zero
+otherwise okay everyone agrees to
+
+ align:start position:0%
+otherwise okay everyone agrees to
+ 
+
+ align:start position:0%
+otherwise okay everyone agrees to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so let's think back to the definition of
+
+ align:start position:0%
+so let's think back to the definition of
+ 
+
+ align:start position:0%
+so let's think back to the definition of
+the maximum likelihood
+
+ align:start position:0%
+the maximum likelihood
+ 
+
+ align:start position:0%
+the maximum likelihood
+estimator it being the parameter that's
+
+ align:start position:0%
+estimator it being the parameter that's
+ 
+
+ align:start position:0%
+estimator it being the parameter that's
+most likely to have given rise to the
+
+ align:start position:0%
+most likely to have given rise to the
+ 
+
+ align:start position:0%
+most likely to have given rise to the
+sample that we observed
+
+ align:start position:0%
+sample that we observed
+ 
+
+ align:start position:0%
+sample that we observed
+okay why so I say here I claim here that
+
+ align:start position:0%
+okay why so I say here I claim here that
+ 
+
+ align:start position:0%
+okay why so I say here I claim here that
+we obviously would not pick any Theta
+
+ align:start position:0%
+we obviously would not pick any Theta
+ 
+
+ align:start position:0%
+we obviously would not pick any Theta
+hat less than the nth order statistic
+
+ align:start position:0%
+hat less than the nth order statistic
+ 
+
+ align:start position:0%
+hat less than the nth order statistic
+why is that given the definition of the
+
+ align:start position:0%
+why is that given the definition of the
+ 
+
+ align:start position:0%
+why is that given the definition of the
+maximum likelihood
+
+ align:start position:0%
+maximum likelihood
+ 
+
+ align:start position:0%
+maximum likelihood
+estimator um Wella is maximum so
+
+ align:start position:0%
+estimator um Wella is maximum so
+ 
+
+ align:start position:0%
+estimator um Wella is maximum so
+there's like a greater value that shows
+
+ align:start position:0%
+there's like a greater value that shows
+ 
+
+ align:start position:0%
+there's like a greater value that shows
+up in the random sample it can't it
+
+ align:start position:0%
+up in the random sample it can't it
+ 
+
+ align:start position:0%
+up in the random sample it can't it
+cannot have happened right it's it's a
+
+ align:start position:0%
+cannot have happened right it's it's a
+ 
+
+ align:start position:0%
+cannot have happened right it's it's a
+probability zero event so let me just
+
+ align:start position:0%
+probability zero event so let me just
+ 
+
+ align:start position:0%
+probability zero event so let me just
+draw a quick picture to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+illustrate okay so here's our
+
+ align:start position:0%
+illustrate okay so here's our
+ 
+
+ align:start position:0%
+illustrate okay so here's our
+distribution Theta is
+
+ align:start position:0%
+distribution Theta is
+ 
+
+ align:start position:0%
+distribution Theta is
+unknown if we were to choose so so we
+
+ align:start position:0%
+unknown if we were to choose so so we
+ 
+
+ align:start position:0%
+unknown if we were to choose so so we
+have you know sort of a random sample
+
+ align:start position:0%
+have you know sort of a random sample
+ 
+
+ align:start position:0%
+have you know sort of a random sample
+chosen from this the entire random
+
+ align:start position:0%
+chosen from this the entire random
+ 
+
+ align:start position:0%
+chosen from this the entire random
+sample has to be less than Theta okay
+
+ align:start position:0%
+sample has to be less than Theta okay
+ 
+
+ align:start position:0%
+sample has to be less than Theta okay
+just just has to be I mean that's how
+
+ align:start position:0%
+just just has to be I mean that's how
+ 
+
+ align:start position:0%
+just just has to be I mean that's how
+that's how the problem is set up so
+
+ align:start position:0%
+that's how the problem is set up so
+ 
+
+ align:start position:0%
+that's how the problem is set up so
+let's suppose we
+
+ align:start position:0%
+let's suppose we
+ 
+
+ align:start position:0%
+let's suppose we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+or actually maybe what I'll do is erase
+
+ align:start position:0%
+or actually maybe what I'll do is erase
+ 
+
+ align:start position:0%
+or actually maybe what I'll do is erase
+this part and we
+
+ align:start position:0%
+this part and we
+ 
+
+ align:start position:0%
+this part and we
+have an nth order statistic we would
+
+ align:start position:0%
+have an nth order statistic we would
+ 
+
+ align:start position:0%
+have an nth order statistic we would
+never choose a guess for Theta below the
+
+ align:start position:0%
+never choose a guess for Theta below the
+ 
+
+ align:start position:0%
+never choose a guess for Theta below the
+nth order statistic because that would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggest a situation like this that we
+
+ align:start position:0%
+suggest a situation like this that we
+ 
+
+ align:start position:0%
+suggest a situation like this that we
+know can't happen Okay does everyone
+
+ align:start position:0%
+know can't happen Okay does everyone
+ 
+
+ align:start position:0%
+know can't happen Okay does everyone
+understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so Theta always has to be at least
+
+ align:start position:0%
+that so Theta always has to be at least
+ 
+
+ align:start position:0%
+that so Theta always has to be at least
+as big as the anthor
+
+ align:start position:0%
+as big as the anthor
+ 
+
+ align:start position:0%
+as big as the anthor
+statistic or Theta
+
+ align:start position:0%
+statistic or Theta
+ 
+
+ align:start position:0%
+statistic or Theta
+hat okay so now we've got the PDF of
+
+ align:start position:0%
+hat okay so now we've got the PDF of
+ 
+
+ align:start position:0%
+hat okay so now we've got the PDF of
+each individual guy in the random sample
+
+ align:start position:0%
+each individual guy in the random sample
+ 
+
+ align:start position:0%
+each individual guy in the random sample
+from that since we know that they're
+
+ align:start position:0%
+from that since we know that they're
+ 
+
+ align:start position:0%
+from that since we know that they're
+independent we can write down the
+
+ align:start position:0%
+independent we can write down the
+ 
+
+ align:start position:0%
+independent we can write down the
+likelihood function which is also the
+
+ align:start position:0%
+likelihood function which is also the
+ 
+
+ align:start position:0%
+likelihood function which is also the
+The Joint PDF of the random sample so
+
+ align:start position:0%
+The Joint PDF of the random sample so
+ 
+
+ align:start position:0%
+The Joint PDF of the random sample so
+that's just remember it's the product of
+
+ align:start position:0%
+that's just remember it's the product of
+ 
+
+ align:start position:0%
+that's just remember it's the product of
+all of the individual PDFs so it's just
+
+ align:start position:0%
+all of the individual PDFs so it's just
+ 
+
+ align:start position:0%
+all of the individual PDFs so it's just
+one over Theta raised to the n for all X
+
+ align:start position:0%
+one over Theta raised to the n for all X
+ 
+
+ align:start position:0%
+one over Theta raised to the n for all X
+or for X subis in this interval and it's
+
+ align:start position:0%
+or for X subis in this interval and it's
+ 
+
+ align:start position:0%
+or for X subis in this interval and it's
+going to be zero otherwise
+
+ align:start position:0%
+going to be zero otherwise
+ 
+
+ align:start position:0%
+going to be zero otherwise
+okay now we can actually restate this um
+
+ align:start position:0%
+okay now we can actually restate this um
+ 
+
+ align:start position:0%
+okay now we can actually restate this um
+condition here instead of saying
+
+ align:start position:0%
+condition here instead of saying
+ 
+
+ align:start position:0%
+condition here instead of saying
+XI in 0 to Theta for IAL 1 to n we can
+
+ align:start position:0%
+XI in 0 to Theta for IAL 1 to n we can
+ 
+
+ align:start position:0%
+XI in 0 to Theta for IAL 1 to n we can
+just say
+
+ align:start position:0%
+just say
+ 
+
+ align:start position:0%
+just say
+instead we can just say instead that's
+
+ align:start position:0%
+instead we can just say instead that's
+ 
+
+ align:start position:0%
+instead we can just say instead that's
+the same as the nth order statistic
+
+ align:start position:0%
+the same as the nth order statistic
+ 
+
+ align:start position:0%
+the same as the nth order statistic
+being less than
+
+ align:start position:0%
+being less than
+ 
+
+ align:start position:0%
+being less than
+Theta okay just equivalent it's an
+
+ align:start position:0%
+Theta okay just equivalent it's an
+ 
+
+ align:start position:0%
+Theta okay just equivalent it's an
+equivalent statement you can say all of
+
+ align:start position:0%
+equivalent statement you can say all of
+ 
+
+ align:start position:0%
+equivalent statement you can say all of
+the X's are in zero in in in the
+
+ align:start position:0%
+the X's are in zero in in in the
+ 
+
+ align:start position:0%
+the X's are in zero in in in the
+interval zero to Theta or the biggest X
+
+ align:start position:0%
+interval zero to Theta or the biggest X
+ 
+
+ align:start position:0%
+interval zero to Theta or the biggest X
+is less than Theta okay so we can say we
+
+ align:start position:0%
+is less than Theta okay so we can say we
+ 
+
+ align:start position:0%
+is less than Theta okay so we can say we
+can say it like that
+
+ align:start position:0%
+can say it like that
+ 
+
+ align:start position:0%
+can say it like that
+instead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so what is the value that
+
+ align:start position:0%
+okay and so what is the value that
+ 
+
+ align:start position:0%
+okay and so what is the value that
+maximizes this likelihood function it is
+
+ align:start position:0%
+maximizes this likelihood function it is
+ 
+
+ align:start position:0%
+maximizes this likelihood function it is
+in fact the anth order
+
+ align:start position:0%
+in fact the anth order
+ 
+
+ align:start position:0%
+in fact the anth order
+statistic so
+
+ align:start position:0%
+statistic so
+ 
+
+ align:start position:0%
+statistic so
+graphically let me show you it might not
+
+ align:start position:0%
+graphically let me show you it might not
+ 
+
+ align:start position:0%
+graphically let me show you it might not
+be 100% clear when you see it in this
+
+ align:start position:0%
+be 100% clear when you see it in this
+ 
+
+ align:start position:0%
+be 100% clear when you see it in this
+form I hope when I show you graphically
+
+ align:start position:0%
+form I hope when I show you graphically
+ 
+
+ align:start position:0%
+form I hope when I show you graphically
+it will become more clear okay why is it
+
+ align:start position:0%
+it will become more clear okay why is it
+ 
+
+ align:start position:0%
+it will become more clear okay why is it
+that the that this function is maximized
+
+ align:start position:0%
+that the that this function is maximized
+ 
+
+ align:start position:0%
+that the that this function is maximized
+at the nth order statistic so this
+
+ align:start position:0%
+at the nth order statistic so this
+ 
+
+ align:start position:0%
+at the nth order statistic so this
+likelihood function is equal to zero for
+
+ align:start position:0%
+likelihood function is equal to zero for
+ 
+
+ align:start position:0%
+likelihood function is equal to zero for
+all values up until the nth order
+
+ align:start position:0%
+all values up until the nth order
+ 
+
+ align:start position:0%
+all values up until the nth order
+statistic okay think of the likelihood
+
+ align:start position:0%
+statistic okay think of the likelihood
+ 
+
+ align:start position:0%
+statistic okay think of the likelihood
+function think of this now instead of
+
+ align:start position:0%
+function think of this now instead of
+ 
+
+ align:start position:0%
+function think of this now instead of
+being a joint PDF of the random sample
+
+ align:start position:0%
+being a joint PDF of the random sample
+ 
+
+ align:start position:0%
+being a joint PDF of the random sample
+this is a function of theta okay so
+
+ align:start position:0%
+this is a function of theta okay so
+ 
+
+ align:start position:0%
+this is a function of theta okay so
+basically what it's saying is this the
+
+ align:start position:0%
+basically what it's saying is this the
+ 
+
+ align:start position:0%
+basically what it's saying is this the
+function is equal to this if Theta is
+
+ align:start position:0%
+function is equal to this if Theta is
+ 
+
+ align:start position:0%
+function is equal to this if Theta is
+greater than the nth order statistic and
+
+ align:start position:0%
+greater than the nth order statistic and
+ 
+
+ align:start position:0%
+greater than the nth order statistic and
+it's equal to zero otherwise so for any
+
+ align:start position:0%
+it's equal to zero otherwise so for any
+ 
+
+ align:start position:0%
+it's equal to zero otherwise so for any
+values of theta less than the norder
+
+ align:start position:0%
+values of theta less than the norder
+ 
+
+ align:start position:0%
+values of theta less than the norder
+statistic this function is equal to zero
+
+ align:start position:0%
+statistic this function is equal to zero
+ 
+
+ align:start position:0%
+statistic this function is equal to zero
+okay so off to the left it's equal to
+
+ align:start position:0%
+okay so off to the left it's equal to
+ 
+
+ align:start position:0%
+okay so off to the left it's equal to
+zero then starting at the nth or
+
+ align:start position:0%
+zero then starting at the nth or
+ 
+
+ align:start position:0%
+zero then starting at the nth or
+statistic let me flip back again it's
+
+ align:start position:0%
+statistic let me flip back again it's
+ 
+
+ align:start position:0%
+statistic let me flip back again it's
+just equal to 1 over Theta to the n so
+
+ align:start position:0%
+just equal to 1 over Theta to the n so
+ 
+
+ align:start position:0%
+just equal to 1 over Theta to the n so
+when we graph it in Theta space like
+
+ align:start position:0%
+when we graph it in Theta space like
+ 
+
+ align:start position:0%
+when we graph it in Theta space like
+this we get that it's equal to zero
+
+ align:start position:0%
+this we get that it's equal to zero
+ 
+
+ align:start position:0%
+this we get that it's equal to zero
+until you get to the anth order
+
+ align:start position:0%
+until you get to the anth order
+ 
+
+ align:start position:0%
+until you get to the anth order
+statistic then it jumps up to one over
+
+ align:start position:0%
+statistic then it jumps up to one over
+ 
+
+ align:start position:0%
+statistic then it jumps up to one over
+Theta to the n and then it you know as
+
+ align:start position:0%
+Theta to the n and then it you know as
+ 
+
+ align:start position:0%
+Theta to the n and then it you know as
+it declines as Theta gets gets larger
+
+ align:start position:0%
+it declines as Theta gets gets larger
+ 
+
+ align:start position:0%
+it declines as Theta gets gets larger
+okay so this is maximized at the inth
+
+ align:start position:0%
+okay so this is maximized at the inth
+ 
+
+ align:start position:0%
+okay so this is maximized at the inth
+order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statistic okay
+
+ align:start position:0%
+statistic okay
+ 
+
+ align:start position:0%
+statistic okay
+questions does this make
+
+ align:start position:0%
+questions does this make
+ 
+
+ align:start position:0%
+questions does this make
+sense and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than n yeah yeah exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah because it's just the sample
+
+ align:start position:0%
+yeah yeah because it's just the sample
+ 
+
+ align:start position:0%
+yeah yeah because it's just the sample
+size oh I guess the other thing I want
+
+ align:start position:0%
+size oh I guess the other thing I want
+ 
+
+ align:start position:0%
+size oh I guess the other thing I want
+to say about is you can probably see now
+
+ align:start position:0%
+to say about is you can probably see now
+ 
+
+ align:start position:0%
+to say about is you can probably see now
+by looking at the picture why uh we
+
+ align:start position:0%
+by looking at the picture why uh we
+ 
+
+ align:start position:0%
+by looking at the picture why uh we
+didn't solve this by writing down the
+
+ align:start position:0%
+didn't solve this by writing down the
+ 
+
+ align:start position:0%
+didn't solve this by writing down the
+likelihood function taking the uh
+
+ align:start position:0%
+likelihood function taking the uh
+ 
+
+ align:start position:0%
+likelihood function taking the uh
+derivative with respect to Theta setting
+
+ align:start position:0%
+derivative with respect to Theta setting
+ 
+
+ align:start position:0%
+derivative with respect to Theta setting
+the derivative equal to zero Etc because
+
+ align:start position:0%
+the derivative equal to zero Etc because
+ 
+
+ align:start position:0%
+the derivative equal to zero Etc because
+in fact it's not differentiable at the
+
+ align:start position:0%
+in fact it's not differentiable at the
+ 
+
+ align:start position:0%
+in fact it's not differentiable at the
+max so if we had tried to do that we
+
+ align:start position:0%
+max so if we had tried to do that we
+ 
+
+ align:start position:0%
+max so if we had tried to do that we
+would have run into some trouble
+
+ align:start position:0%
+would have run into some trouble
+ 
+
+ align:start position:0%
+would have run into some trouble
+okay okay second
+
+ align:start position:0%
+okay okay second
+ 
+
+ align:start position:0%
+okay okay second
+example let uh xabi uh be IID uniform Z
+
+ align:start position:0%
+example let uh xabi uh be IID uniform Z
+ 
+
+ align:start position:0%
+example let uh xabi uh be IID uniform Z
+or sorry Theta minus 12 to Theta +2 so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we again have a uniform
+
+ align:start position:0%
+here we again have a uniform
+ 
+
+ align:start position:0%
+here we again have a uniform
+distribution it's not the length of the
+
+ align:start position:0%
+distribution it's not the length of the
+ 
+
+ align:start position:0%
+distribution it's not the length of the
+interval that's unknown we know that the
+
+ align:start position:0%
+interval that's unknown we know that the
+ 
+
+ align:start position:0%
+interval that's unknown we know that the
+interval is length one it's just the
+
+ align:start position:0%
+interval is length one it's just the
+ 
+
+ align:start position:0%
+interval is length one it's just the
+location of the interval that's unknown
+
+ align:start position:0%
+location of the interval that's unknown
+ 
+
+ align:start position:0%
+location of the interval that's unknown
+so the parameter Theta is determining
+
+ align:start position:0%
+so the parameter Theta is determining
+ 
+
+ align:start position:0%
+so the parameter Theta is determining
+the location of this interval okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is Theta -2 up to Theta +
+
+ align:start position:0%
+so this is Theta -2 up to Theta +
+ 
+
+ align:start position:0%
+so this is Theta -2 up to Theta +
+12 okay so this is is our our uh uniform
+
+ align:start position:0%
+12 okay so this is is our our uh uniform
+ 
+
+ align:start position:0%
+12 okay so this is is our our uh uniform
+distribution we're interested in
+
+ align:start position:0%
+distribution we're interested in
+ 
+
+ align:start position:0%
+distribution we're interested in
+estimating the unknown parameter Theta
+
+ align:start position:0%
+estimating the unknown parameter Theta
+ 
+
+ align:start position:0%
+estimating the unknown parameter Theta
+the unknown parameter Theta just
+
+ align:start position:0%
+the unknown parameter Theta just
+ 
+
+ align:start position:0%
+the unknown parameter Theta just
+determines the location of this interval
+
+ align:start position:0%
+determines the location of this interval
+ 
+
+ align:start position:0%
+determines the location of this interval
+okay and since the interval is is uh
+
+ align:start position:0%
+okay and since the interval is is uh
+ 
+
+ align:start position:0%
+okay and since the interval is is uh
+length one then the PDF is always equal
+
+ align:start position:0%
+length one then the PDF is always equal
+ 
+
+ align:start position:0%
+length one then the PDF is always equal
+to one uh in the interval of zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otherwise so let's write down the
+
+ align:start position:0%
+otherwise so let's write down the
+ 
+
+ align:start position:0%
+otherwise so let's write down the
+likelihood function well this one we
+
+ align:start position:0%
+likelihood function well this one we
+ 
+
+ align:start position:0%
+likelihood function well this one we
+have to be a little clever about we have
+
+ align:start position:0%
+have to be a little clever about we have
+ 
+
+ align:start position:0%
+have to be a little clever about we have
+to sort of think about it um when we
+
+ align:start position:0%
+to sort of think about it um when we
+ 
+
+ align:start position:0%
+to sort of think about it um when we
+write it down so obviously the
+
+ align:start position:0%
+write it down so obviously the
+ 
+
+ align:start position:0%
+write it down so obviously the
+likelihood fun so one raed to the nth
+
+ align:start position:0%
+likelihood fun so one raed to the nth
+ 
+
+ align:start position:0%
+likelihood fun so one raed to the nth
+power is just equal to one but then we
+
+ align:start position:0%
+power is just equal to one but then we
+ 
+
+ align:start position:0%
+power is just equal to one but then we
+have what we have to be clever about is
+
+ align:start position:0%
+have what we have to be clever about is
+ 
+
+ align:start position:0%
+have what we have to be clever about is
+these uh bounds here okay and so let me
+
+ align:start position:0%
+these uh bounds here okay and so let me
+ 
+
+ align:start position:0%
+these uh bounds here okay and so let me
+go through uh the explanation of how we
+
+ align:start position:0%
+go through uh the explanation of how we
+ 
+
+ align:start position:0%
+go through uh the explanation of how we
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+those okay so we're writing them in ter
+
+ align:start position:0%
+those okay so we're writing them in ter
+ 
+
+ align:start position:0%
+those okay so we're writing them in ter
+in terms of order statistics okay and
+
+ align:start position:0%
+in terms of order statistics okay and
+ 
+
+ align:start position:0%
+in terms of order statistics okay and
+let me just point out that actually once
+
+ align:start position:0%
+let me just point out that actually once
+ 
+
+ align:start position:0%
+let me just point out that actually once
+once I convince you that these bounds
+
+ align:start position:0%
+once I convince you that these bounds
+ 
+
+ align:start position:0%
+once I convince you that these bounds
+are correct which I hope to do in just a
+
+ align:start position:0%
+are correct which I hope to do in just a
+ 
+
+ align:start position:0%
+are correct which I hope to do in just a
+moment then the maximum likelihood
+
+ align:start position:0%
+moment then the maximum likelihood
+ 
+
+ align:start position:0%
+moment then the maximum likelihood
+estimator is going to be any value in
+
+ align:start position:0%
+estimator is going to be any value in
+ 
+
+ align:start position:0%
+estimator is going to be any value in
+that uh interval because any value in
+
+ align:start position:0%
+that uh interval because any value in
+ 
+
+ align:start position:0%
+that uh interval because any value in
+this interval maximizes the likelihood
+
+ align:start position:0%
+this interval maximizes the likelihood
+ 
+
+ align:start position:0%
+this interval maximizes the likelihood
+function okay it's just flat over that
+
+ align:start position:0%
+function okay it's just flat over that
+ 
+
+ align:start position:0%
+function okay it's just flat over that
+interval it's equal to one so any value
+
+ align:start position:0%
+interval it's equal to one so any value
+ 
+
+ align:start position:0%
+interval it's equal to one so any value
+in that interval is going to maximize
+
+ align:start position:0%
+in that interval is going to maximize
+ 
+
+ align:start position:0%
+in that interval is going to maximize
+the likelihood
+
+ align:start position:0%
+the likelihood
+ 
+
+ align:start position:0%
+the likelihood
+function okay so now I just have to
+
+ align:start position:0%
+function okay so now I just have to
+ 
+
+ align:start position:0%
+function okay so now I just have to
+convince you that these uh that this
+
+ align:start position:0%
+convince you that these uh that this
+ 
+
+ align:start position:0%
+convince you that these uh that this
+sort of condition is
+
+ align:start position:0%
+sort of condition is
+ 
+
+ align:start position:0%
+sort of condition is
+correct okay so let's look at this one
+
+ align:start position:0%
+correct okay so let's look at this one
+ 
+
+ align:start position:0%
+correct okay so let's look at this one
+graphically so let's suppose we've got a
+
+ align:start position:0%
+graphically so let's suppose we've got a
+ 
+
+ align:start position:0%
+graphically so let's suppose we've got a
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+sample the interval that the the
+
+ align:start position:0%
+sample the interval that the the
+ 
+
+ align:start position:0%
+sample the interval that the the
+underlying distribution is has you know
+
+ align:start position:0%
+underlying distribution is has you know
+ 
+
+ align:start position:0%
+underlying distribution is has you know
+a uniform where the interval is length
+
+ align:start position:0%
+a uniform where the interval is length
+ 
+
+ align:start position:0%
+a uniform where the interval is length
+one and it's centered at Theta and it's
+
+ align:start position:0%
+one and it's centered at Theta and it's
+ 
+
+ align:start position:0%
+one and it's centered at Theta and it's
+got to be here somewhere okay this is
+
+ align:start position:0%
+got to be here somewhere okay this is
+ 
+
+ align:start position:0%
+got to be here somewhere okay this is
+our random sample so it's got to sort of
+
+ align:start position:0%
+our random sample so it's got to sort of
+ 
+
+ align:start position:0%
+our random sample so it's got to sort of
+all of these uh observations have to
+
+ align:start position:0%
+all of these uh observations have to
+ 
+
+ align:start position:0%
+all of these uh observations have to
+live in that interval okay it's got to
+
+ align:start position:0%
+live in that interval okay it's got to
+ 
+
+ align:start position:0%
+live in that interval okay it's got to
+Encompass all the data so what are the
+
+ align:start position:0%
+Encompass all the data so what are the
+ 
+
+ align:start position:0%
+Encompass all the data so what are the
+possibilities well the interval could be
+
+ align:start position:0%
+possibilities well the interval could be
+ 
+
+ align:start position:0%
+possibilities well the interval could be
+there could be there could be there
+
+ align:start position:0%
+there could be there could be there
+ 
+
+ align:start position:0%
+there could be there could be there
+could be
+
+ align:start position:0%
+could be
+ 
+
+ align:start position:0%
+could be
+there and in fact all there's a whole
+
+ align:start position:0%
+there and in fact all there's a whole
+ 
+
+ align:start position:0%
+there and in fact all there's a whole
+Continuum right and all of those
+
+ align:start position:0%
+Continuum right and all of those
+ 
+
+ align:start position:0%
+Continuum right and all of those
+possibilities are equally
+
+ align:start position:0%
+possibilities are equally
+ 
+
+ align:start position:0%
+possibilities are equally
+likely
+
+ align:start position:0%
+likely
+ 
+
+ align:start position:0%
+likely
+okay can it be there no no way right
+
+ align:start position:0%
+okay can it be there no no way right
+ 
+
+ align:start position:0%
+okay can it be there no no way right
+because if it's if it's over here then
+
+ align:start position:0%
+because if it's if it's over here then
+ 
+
+ align:start position:0%
+because if it's if it's over here then
+these these happen these occurred with
+
+ align:start position:0%
+these these happen these occurred with
+ 
+
+ align:start position:0%
+these these happen these occurred with
+probability zero or they couldn't they
+
+ align:start position:0%
+probability zero or they couldn't they
+ 
+
+ align:start position:0%
+probability zero or they couldn't they
+couldn't occur
+
+ align:start position:0%
+couldn't occur
+ 
+
+ align:start position:0%
+couldn't occur
+okay likewise can't be there okay so I
+
+ align:start position:0%
+okay likewise can't be there okay so I
+ 
+
+ align:start position:0%
+okay likewise can't be there okay so I
+think I've convinced you that there's
+
+ align:start position:0%
+think I've convinced you that there's
+ 
+
+ align:start position:0%
+think I've convinced you that there's
+sort of a range of different
+
+ align:start position:0%
+sort of a range of different
+ 
+
+ align:start position:0%
+sort of a range of different
+possibilities that for the location of
+
+ align:start position:0%
+possibilities that for the location of
+ 
+
+ align:start position:0%
+possibilities that for the location of
+this interval of length one and the only
+
+ align:start position:0%
+this interval of length one and the only
+ 
+
+ align:start position:0%
+this interval of length one and the only
+question is how do we um how do we
+
+ align:start position:0%
+question is how do we um how do we
+ 
+
+ align:start position:0%
+question is how do we um how do we
+express what that range is okay
+
+ align:start position:0%
+express what that range is okay
+ 
+
+ align:start position:0%
+express what that range is okay
+well the Theta can be at most 1/2 above
+
+ align:start position:0%
+well the Theta can be at most 1/2 above
+ 
+
+ align:start position:0%
+well the Theta can be at most 1/2 above
+the first order
+
+ align:start position:0%
+the first order
+ 
+
+ align:start position:0%
+the first order
+statistic okay let me just flip back so
+
+ align:start position:0%
+statistic okay let me just flip back so
+ 
+
+ align:start position:0%
+statistic okay let me just flip back so
+over here is the first order statistic
+
+ align:start position:0%
+over here is the first order statistic
+ 
+
+ align:start position:0%
+over here is the first order statistic
+okay we know that the the left edge of
+
+ align:start position:0%
+okay we know that the the left edge of
+ 
+
+ align:start position:0%
+okay we know that the the left edge of
+the interval can't be any higher than
+
+ align:start position:0%
+the interval can't be any higher than
+ 
+
+ align:start position:0%
+the interval can't be any higher than
+the first order statistic so therefore
+
+ align:start position:0%
+the first order statistic so therefore
+ 
+
+ align:start position:0%
+the first order statistic so therefore
+Theta can't be any higher than 1/2 above
+
+ align:start position:0%
+Theta can't be any higher than 1/2 above
+ 
+
+ align:start position:0%
+Theta can't be any higher than 1/2 above
+that okay then the same reasoning goes
+
+ align:start position:0%
+that okay then the same reasoning goes
+ 
+
+ align:start position:0%
+that okay then the same reasoning goes
+with the nth order statistic
+
+ align:start position:0%
+with the nth order statistic
+ 
+
+ align:start position:0%
+with the nth order statistic
+oops Theta can be at most 1/ half below
+
+ align:start position:0%
+oops Theta can be at most 1/ half below
+ 
+
+ align:start position:0%
+oops Theta can be at most 1/ half below
+the enth order statistic it can't be any
+
+ align:start position:0%
+the enth order statistic it can't be any
+ 
+
+ align:start position:0%
+the enth order statistic it can't be any
+further down or we're going to start
+
+ align:start position:0%
+further down or we're going to start
+ 
+
+ align:start position:0%
+further down or we're going to start
+missing the observations at the top
+
+ align:start position:0%
+missing the observations at the top
+ 
+
+ align:start position:0%
+missing the observations at the top
+okay and so that gives us a you know
+
+ align:start position:0%
+okay and so that gives us a you know
+ 
+
+ align:start position:0%
+okay and so that gives us a you know
+sort of a a little region in which Theta
+
+ align:start position:0%
+sort of a a little region in which Theta
+ 
+
+ align:start position:0%
+sort of a a little region in which Theta
+can live and all the values in Theta in
+
+ align:start position:0%
+can live and all the values in Theta in
+ 
+
+ align:start position:0%
+can live and all the values in Theta in
+that little region in that window are
+
+ align:start position:0%
+that little region in that window are
+ 
+
+ align:start position:0%
+that little region in that window are
+equally likely because we wrote down the
+
+ align:start position:0%
+equally likely because we wrote down the
+ 
+
+ align:start position:0%
+equally likely because we wrote down the
+likelihood functions it's just equal to
+
+ align:start position:0%
+likelihood functions it's just equal to
+ 
+
+ align:start position:0%
+likelihood functions it's just equal to
+one in that region okay so in fact if
+
+ align:start position:0%
+one in that region okay so in fact if
+ 
+
+ align:start position:0%
+one in that region okay so in fact if
+you you know
+
+ align:start position:0%
+you you know
+ 
+
+ align:start position:0%
+you you know
+I can flip back if you want but this is
+
+ align:start position:0%
+I can flip back if you want but this is
+ 
+
+ align:start position:0%
+I can flip back if you want but this is
+in fact uh the the condition that I had
+
+ align:start position:0%
+in fact uh the the condition that I had
+ 
+
+ align:start position:0%
+in fact uh the the condition that I had
+on the likelihood function okay so let
+
+ align:start position:0%
+on the likelihood function okay so let
+ 
+
+ align:start position:0%
+on the likelihood function okay so let
+me just okay that Theta is in the nth
+
+ align:start position:0%
+me just okay that Theta is in the nth
+ 
+
+ align:start position:0%
+me just okay that Theta is in the nth
+order statistic minus
+
+ align:start position:0%
+order statistic minus
+ 
+
+ align:start position:0%
+order statistic minus
+one2 a to up to the first order
+
+ align:start position:0%
+one2 a to up to the first order
+ 
+
+ align:start position:0%
+one2 a to up to the first order
+statistic plus 1/2 there should be sort
+
+ align:start position:0%
+statistic plus 1/2 there should be sort
+ 
+
+ align:start position:0%
+statistic plus 1/2 there should be sort
+of an overlap and that the overlap of
+
+ align:start position:0%
+of an overlap and that the overlap of
+ 
+
+ align:start position:0%
+of an overlap and that the overlap of
+those two um you know sort of conditions
+
+ align:start position:0%
+those two um you know sort of conditions
+ 
+
+ align:start position:0%
+those two um you know sort of conditions
+uh gives us the region where Theta
+
+ align:start position:0%
+uh gives us the region where Theta
+ 
+
+ align:start position:0%
+uh gives us the region where Theta
+live does that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense yes
+
+ align:start position:0%
+sense yes
+ 
+
+ align:start position:0%
+sense yes
+okay okay so maximum likelihood
+
+ align:start position:0%
+okay okay so maximum likelihood
+ 
+
+ align:start position:0%
+okay okay so maximum likelihood
+estimators are you know it's sort of
+
+ align:start position:0%
+estimators are you know it's sort of
+ 
+
+ align:start position:0%
+estimators are you know it's sort of
+it's a very popular framework for uh
+
+ align:start position:0%
+it's a very popular framework for uh
+ 
+
+ align:start position:0%
+it's a very popular framework for uh
+deriving
+
+ align:start position:0%
+deriving
+ 
+
+ align:start position:0%
+deriving
+estimators and they and part of it is
+
+ align:start position:0%
+estimators and they and part of it is
+ 
+
+ align:start position:0%
+estimators and they and part of it is
+because they have some very favorable
+
+ align:start position:0%
+because they have some very favorable
+ 
+
+ align:start position:0%
+because they have some very favorable
+properties well part of it is because
+
+ align:start position:0%
+properties well part of it is because
+ 
+
+ align:start position:0%
+properties well part of it is because
+they're kind of always available if
+
+ align:start position:0%
+they're kind of always available if
+ 
+
+ align:start position:0%
+they're kind of always available if
+you're willing to take a stand like make
+
+ align:start position:0%
+you're willing to take a stand like make
+ 
+
+ align:start position:0%
+you're willing to take a stand like make
+an assumption about what the underlying
+
+ align:start position:0%
+an assumption about what the underlying
+ 
+
+ align:start position:0%
+an assumption about what the underlying
+distribution is then you can write down
+
+ align:start position:0%
+distribution is then you can write down
+ 
+
+ align:start position:0%
+distribution is then you can write down
+a maximum likelihood estimator okay of
+
+ align:start position:0%
+a maximum likelihood estimator okay of
+ 
+
+ align:start position:0%
+a maximum likelihood estimator okay of
+course that's also true for a method of
+
+ align:start position:0%
+course that's also true for a method of
+ 
+
+ align:start position:0%
+course that's also true for a method of
+moments estimator but uh you know sort
+
+ align:start position:0%
+moments estimator but uh you know sort
+ 
+
+ align:start position:0%
+moments estimator but uh you know sort
+of Maximum likelihood estimators are you
+
+ align:start position:0%
+of Maximum likelihood estimators are you
+ 
+
+ align:start position:0%
+of Maximum likelihood estimators are you
+know sort of available uh you know if
+
+ align:start position:0%
+know sort of available uh you know if
+ 
+
+ align:start position:0%
+know sort of available uh you know if
+you're sort of willing to write down a a
+
+ align:start position:0%
+you're sort of willing to write down a a
+ 
+
+ align:start position:0%
+you're sort of willing to write down a a
+distribution of the underlying um
+
+ align:start position:0%
+distribution of the underlying um
+ 
+
+ align:start position:0%
+distribution of the underlying um
+data but it they also have some very
+
+ align:start position:0%
+data but it they also have some very
+ 
+
+ align:start position:0%
+data but it they also have some very
+favorable properties so if your
+
+ align:start position:0%
+favorable properties so if your
+ 
+
+ align:start position:0%
+favorable properties so if your
+assumptions are correct so this is all
+
+ align:start position:0%
+assumptions are correct so this is all
+ 
+
+ align:start position:0%
+assumptions are correct so this is all
+assuming that you haven't made a mistake
+
+ align:start position:0%
+assuming that you haven't made a mistake
+ 
+
+ align:start position:0%
+assuming that you haven't made a mistake
+in sort of assuming the underlying
+
+ align:start position:0%
+in sort of assuming the underlying
+ 
+
+ align:start position:0%
+in sort of assuming the underlying
+distribution then the maximum likelihood
+
+ align:start position:0%
+distribution then the maximum likelihood
+ 
+
+ align:start position:0%
+distribution then the maximum likelihood
+estimator is going to have the following
+
+ align:start position:0%
+estimator is going to have the following
+ 
+
+ align:start position:0%
+estimator is going to have the following
+properties if there is an efficient
+
+ align:start position:0%
+properties if there is an efficient
+ 
+
+ align:start position:0%
+properties if there is an efficient
+estimator in a class of consistent
+
+ align:start position:0%
+estimator in a class of consistent
+ 
+
+ align:start position:0%
+estimator in a class of consistent
+estimators maximum likelihood estimation
+
+ align:start position:0%
+estimators maximum likelihood estimation
+ 
+
+ align:start position:0%
+estimators maximum likelihood estimation
+will produce it okay so that tells you
+
+ align:start position:0%
+will produce it okay so that tells you
+ 
+
+ align:start position:0%
+will produce it okay so that tells you
+right there you don't have to check for
+
+ align:start position:0%
+right there you don't have to check for
+ 
+
+ align:start position:0%
+right there you don't have to check for
+the efficiency of your estimator um if
+
+ align:start position:0%
+the efficiency of your estimator um if
+ 
+
+ align:start position:0%
+the efficiency of your estimator um if
+you're using maximum likelihood you know
+
+ align:start position:0%
+you're using maximum likelihood you know
+ 
+
+ align:start position:0%
+you're using maximum likelihood you know
+it's it's going to have it's going to
+
+ align:start position:0%
+it's it's going to have it's going to
+ 
+
+ align:start position:0%
+it's it's going to have it's going to
+have that a good property in that
+
+ align:start position:0%
+have that a good property in that
+ 
+
+ align:start position:0%
+have that a good property in that
+respect
+
+ align:start position:0%
+respect
+ 
+
+ align:start position:0%
+respect
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um also there is a central limit theorem
+
+ align:start position:0%
+um also there is a central limit theorem
+ 
+
+ align:start position:0%
+um also there is a central limit theorem
+type um result having to do with a
+
+ align:start position:0%
+type um result having to do with a
+ 
+
+ align:start position:0%
+type um result having to do with a
+maximum likelihood estimators so under
+
+ align:start position:0%
+maximum likelihood estimators so under
+ 
+
+ align:start position:0%
+maximum likelihood estimators so under
+certain regularity conditions if uh you
+
+ align:start position:0%
+certain regularity conditions if uh you
+ 
+
+ align:start position:0%
+certain regularity conditions if uh you
+know sort of the maximum likelihood
+
+ align:start position:0%
+know sort of the maximum likelihood
+ 
+
+ align:start position:0%
+know sort of the maximum likelihood
+estimator is not on some boundary of
+
+ align:start position:0%
+estimator is not on some boundary of
+ 
+
+ align:start position:0%
+estimator is not on some boundary of
+some space or something like that then
+
+ align:start position:0%
+some space or something like that then
+ 
+
+ align:start position:0%
+some space or something like that then
+uh asymptotically sort of as your um
+
+ align:start position:0%
+uh asymptotically sort of as your um
+ 
+
+ align:start position:0%
+uh asymptotically sort of as your um
+sample size is getting bigger and bigger
+
+ align:start position:0%
+sample size is getting bigger and bigger
+ 
+
+ align:start position:0%
+sample size is getting bigger and bigger
+maximum likelihood estimators are going
+
+ align:start position:0%
+maximum likelihood estimators are going
+ 
+
+ align:start position:0%
+maximum likelihood estimators are going
+to have a normal or approximately normal
+
+ align:start position:0%
+to have a normal or approximately normal
+ 
+
+ align:start position:0%
+to have a normal or approximately normal
+distribution so just like we had the
+
+ align:start position:0%
+distribution so just like we had the
+ 
+
+ align:start position:0%
+distribution so just like we had the
+central limit theorem for the sample
+
+ align:start position:0%
+central limit theorem for the sample
+ 
+
+ align:start position:0%
+central limit theorem for the sample
+mean there's a central limit theorem
+
+ align:start position:0%
+mean there's a central limit theorem
+ 
+
+ align:start position:0%
+mean there's a central limit theorem
+like result for maximum likelihood
+
+ align:start position:0%
+like result for maximum likelihood
+ 
+
+ align:start position:0%
+like result for maximum likelihood
+estimators and that's uh that can be
+
+ align:start position:0%
+estimators and that's uh that can be
+ 
+
+ align:start position:0%
+estimators and that's uh that can be
+very uh useful for inference which we'll
+
+ align:start position:0%
+very uh useful for inference which we'll
+ 
+
+ align:start position:0%
+very uh useful for inference which we'll
+see after spring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+break so does this mean that uh maximum
+
+ align:start position:0%
+break so does this mean that uh maximum
+ 
+
+ align:start position:0%
+break so does this mean that uh maximum
+likelihood estimation is always the
+
+ align:start position:0%
+likelihood estimation is always the
+ 
+
+ align:start position:0%
+likelihood estimation is always the
+right thing to do okay well well uh no
+
+ align:start position:0%
+right thing to do okay well well uh no
+ 
+
+ align:start position:0%
+right thing to do okay well well uh no
+in fact
+
+ align:start position:0%
+in fact
+ 
+
+ align:start position:0%
+in fact
+so in we saw an example where uh where
+
+ align:start position:0%
+so in we saw an example where uh where
+ 
+
+ align:start position:0%
+so in we saw an example where uh where
+you know even given that our you know
+
+ align:start position:0%
+you know even given that our you know
+ 
+
+ align:start position:0%
+you know even given that our you know
+our assumptions were correct the maximum
+
+ align:start position:0%
+our assumptions were correct the maximum
+ 
+
+ align:start position:0%
+our assumptions were correct the maximum
+likelihood estimator was biased okay so
+
+ align:start position:0%
+likelihood estimator was biased okay so
+ 
+
+ align:start position:0%
+likelihood estimator was biased okay so
+that was the example where we were
+
+ align:start position:0%
+that was the example where we were
+ 
+
+ align:start position:0%
+that was the example where we were
+estimating Theta from the uniform zero
+
+ align:start position:0%
+estimating Theta from the uniform zero
+ 
+
+ align:start position:0%
+estimating Theta from the uniform zero
+Theta distribution um and our maximum
+
+ align:start position:0%
+Theta distribution um and our maximum
+ 
+
+ align:start position:0%
+Theta distribution um and our maximum
+likelihood uh estimator for any finite
+
+ align:start position:0%
+likelihood uh estimator for any finite
+ 
+
+ align:start position:0%
+likelihood uh estimator for any finite
+sample size was going to be biased okay
+
+ align:start position:0%
+sample size was going to be biased okay
+ 
+
+ align:start position:0%
+sample size was going to be biased okay
+now in fact in that particular example
+
+ align:start position:0%
+now in fact in that particular example
+ 
+
+ align:start position:0%
+now in fact in that particular example
+we could fix the bias because the bias
+
+ align:start position:0%
+we could fix the bias because the bias
+ 
+
+ align:start position:0%
+we could fix the bias because the bias
+is a function of N and we know how big
+
+ align:start position:0%
+is a function of N and we know how big
+ 
+
+ align:start position:0%
+is a function of N and we know how big
+our sample size is so we can actually
+
+ align:start position:0%
+our sample size is so we can actually
+ 
+
+ align:start position:0%
+our sample size is so we can actually
+undo that bias um but in in there are
+
+ align:start position:0%
+undo that bias um but in in there are
+ 
+
+ align:start position:0%
+undo that bias um but in in there are
+lots of examples where you don't know
+
+ align:start position:0%
+lots of examples where you don't know
+ 
+
+ align:start position:0%
+lots of examples where you don't know
+the size of the bias and so you can't
+
+ align:start position:0%
+the size of the bias and so you can't
+ 
+
+ align:start position:0%
+the size of the bias and so you can't
+always undo it okay so they can be
+
+ align:start position:0%
+always undo it okay so they can be
+ 
+
+ align:start position:0%
+always undo it okay so they can be
+biased and we saw an example and
+
+ align:start position:0%
+biased and we saw an example and
+ 
+
+ align:start position:0%
+biased and we saw an example and
+sometimes we just you know we're we're
+
+ align:start position:0%
+sometimes we just you know we're we're
+ 
+
+ align:start position:0%
+sometimes we just you know we're we're
+not interested in biased
+
+ align:start position:0%
+not interested in biased
+ 
+
+ align:start position:0%
+not interested in biased
+estimators they might be difficult to
+
+ align:start position:0%
+estimators they might be difficult to
+ 
+
+ align:start position:0%
+estimators they might be difficult to
+compute and then um finally they can be
+
+ align:start position:0%
+compute and then um finally they can be
+ 
+
+ align:start position:0%
+compute and then um finally they can be
+sensitive to incorrect assumptions about
+
+ align:start position:0%
+sensitive to incorrect assumptions about
+ 
+
+ align:start position:0%
+sensitive to incorrect assumptions about
+the underlying distribution so um and
+
+ align:start position:0%
+the underlying distribution so um and
+ 
+
+ align:start position:0%
+the underlying distribution so um and
+more so than other estimators so the the
+
+ align:start position:0%
+more so than other estimators so the the
+ 
+
+ align:start position:0%
+more so than other estimators so the the
+method of moments uh estimators tend to
+
+ align:start position:0%
+method of moments uh estimators tend to
+ 
+
+ align:start position:0%
+method of moments uh estimators tend to
+be more robust to uh sort of um the
+
+ align:start position:0%
+be more robust to uh sort of um the
+ 
+
+ align:start position:0%
+be more robust to uh sort of um the
+underlying assumptions because they rely
+
+ align:start position:0%
+underlying assumptions because they rely
+ 
+
+ align:start position:0%
+underlying assumptions because they rely
+less so the maximum likelihood
+
+ align:start position:0%
+less so the maximum likelihood
+ 
+
+ align:start position:0%
+less so the maximum likelihood
+estimators really rely on the entire
+
+ align:start position:0%
+estimators really rely on the entire
+ 
+
+ align:start position:0%
+estimators really rely on the entire
+shape of the distribution of the random
+
+ align:start position:0%
+shape of the distribution of the random
+ 
+
+ align:start position:0%
+shape of the distribution of the random
+sample Le the method of moments
+
+ align:start position:0%
+sample Le the method of moments
+ 
+
+ align:start position:0%
+sample Le the method of moments
+estimators don't they just rely on the
+
+ align:start position:0%
+estimators don't they just rely on the
+ 
+
+ align:start position:0%
+estimators don't they just rely on the
+moments and so you can imagine just kind
+
+ align:start position:0%
+moments and so you can imagine just kind
+ 
+
+ align:start position:0%
+moments and so you can imagine just kind
+of intuitively that something that
+
+ align:start position:0%
+of intuitively that something that
+ 
+
+ align:start position:0%
+of intuitively that something that
+relies on the entire shape of a
+
+ align:start position:0%
+relies on the entire shape of a
+ 
+
+ align:start position:0%
+relies on the entire shape of a
+distribution if you're if you're wrong
+
+ align:start position:0%
+distribution if you're if you're wrong
+ 
+
+ align:start position:0%
+distribution if you're if you're wrong
+about that shape of a distribution you
+
+ align:start position:0%
+about that shape of a distribution you
+ 
+
+ align:start position:0%
+about that shape of a distribution you
+know it might be sensitive that
+
+ align:start position:0%
+know it might be sensitive that
+ 
+
+ align:start position:0%
+know it might be sensitive that
+something can go wrong and that's in
+
+ align:start position:0%
+something can go wrong and that's in
+ 
+
+ align:start position:0%
+something can go wrong and that's in
+general true maximum likelihood
+
+ align:start position:0%
+general true maximum likelihood
+ 
+
+ align:start position:0%
+general true maximum likelihood
+estimators can be sensitive to incorrect
+
+ align:start position:0%
+estimators can be sensitive to incorrect
+ 
+
+ align:start position:0%
+estimators can be sensitive to incorrect
+assumptions about the underlying
+
+ align:start position:0%
+assumptions about the underlying
+ 
+
+ align:start position:0%
+assumptions about the underlying
+distributions okay questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay so I would like to just go
+
+ align:start position:0%
+no okay so I would like to just go
+ 
+
+ align:start position:0%
+no okay so I would like to just go
+through um a a summary of what we've
+
+ align:start position:0%
+through um a a summary of what we've
+ 
+
+ align:start position:0%
+through um a a summary of what we've
+done so far this semester and uh feel
+
+ align:start position:0%
+done so far this semester and uh feel
+ 
+
+ align:start position:0%
+done so far this semester and uh feel
+free to chime in with questions um
+
+ align:start position:0%
+free to chime in with questions um
+ 
+
+ align:start position:0%
+free to chime in with questions um
+and you know ask about if you have
+
+ align:start position:0%
+and you know ask about if you have
+ 
+
+ align:start position:0%
+and you know ask about if you have
+questions about the exam you know sort
+
+ align:start position:0%
+questions about the exam you know sort
+ 
+
+ align:start position:0%
+questions about the exam you know sort
+of relative to this you know what you
+
+ align:start position:0%
+of relative to this you know what you
+ 
+
+ align:start position:0%
+of relative to this you know what you
+might be responsible for on the exam I'm
+
+ align:start position:0%
+might be responsible for on the exam I'm
+ 
+
+ align:start position:0%
+might be responsible for on the exam I'm
+happy to answer those questions
+
+ align:start position:0%
+happy to answer those questions
+ 
+
+ align:start position:0%
+happy to answer those questions
+okay so we started out uh this semester
+
+ align:start position:0%
+okay so we started out uh this semester
+ 
+
+ align:start position:0%
+okay so we started out uh this semester
+with uh some probability Basics okay so
+
+ align:start position:0%
+with uh some probability Basics okay so
+ 
+
+ align:start position:0%
+with uh some probability Basics okay so
+uh we introduced the concept of
+
+ align:start position:0%
+uh we introduced the concept of
+ 
+
+ align:start position:0%
+uh we introduced the concept of
+probability and talked about simple
+
+ align:start position:0%
+probability and talked about simple
+ 
+
+ align:start position:0%
+probability and talked about simple
+sample spaces independent events
+
+ align:start position:0%
+sample spaces independent events
+ 
+
+ align:start position:0%
+sample spaces independent events
+conditional probabilities and base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rule and in some sense that was kind
+
+ align:start position:0%
+Rule and in some sense that was kind
+ 
+
+ align:start position:0%
+Rule and in some sense that was kind
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+of foundation for uh you know sort of
+
+ align:start position:0%
+of foundation for uh you know sort of
+ 
+
+ align:start position:0%
+of foundation for uh you know sort of
+going on and and studying probability
+
+ align:start position:0%
+going on and and studying probability
+ 
+
+ align:start position:0%
+going on and and studying probability
+with the kind of mathematical construct
+
+ align:start position:0%
+with the kind of mathematical construct
+ 
+
+ align:start position:0%
+with the kind of mathematical construct
+of the the random variable but do note
+
+ align:start position:0%
+of the the random variable but do note
+ 
+
+ align:start position:0%
+of the the random variable but do note
+that uh we didn't study the sort of uh
+
+ align:start position:0%
+that uh we didn't study the sort of uh
+ 
+
+ align:start position:0%
+that uh we didn't study the sort of uh
+we didn't study base rule in the context
+
+ align:start position:0%
+we didn't study base rule in the context
+ 
+
+ align:start position:0%
+we didn't study base rule in the context
+of um random variables you can you can
+
+ align:start position:0%
+of um random variables you can you can
+ 
+
+ align:start position:0%
+of um random variables you can you can
+actually um sort of formulate a Baye
+
+ align:start position:0%
+actually um sort of formulate a Baye
+ 
+
+ align:start position:0%
+actually um sort of formulate a Baye
+rule using random variables which we
+
+ align:start position:0%
+rule using random variables which we
+ 
+
+ align:start position:0%
+rule using random variables which we
+didn't do uh but it's sort of a Bas Ru
+
+ align:start position:0%
+didn't do uh but it's sort of a Bas Ru
+ 
+
+ align:start position:0%
+didn't do uh but it's sort of a Bas Ru
+is a very important concept um that you
+
+ align:start position:0%
+is a very important concept um that you
+ 
+
+ align:start position:0%
+is a very important concept um that you
+know sort of aside from uh you know Pro
+
+ align:start position:0%
+know sort of aside from uh you know Pro
+ 
+
+ align:start position:0%
+know sort of aside from uh you know Pro
+I guess sort of the the one concept that
+
+ align:start position:0%
+I guess sort of the the one concept that
+ 
+
+ align:start position:0%
+I guess sort of the the one concept that
+we covered in the beginning that wasn't
+
+ align:start position:0%
+we covered in the beginning that wasn't
+ 
+
+ align:start position:0%
+we covered in the beginning that wasn't
+sort of just foundation for the rest of
+
+ align:start position:0%
+sort of just foundation for the rest of
+ 
+
+ align:start position:0%
+sort of just foundation for the rest of
+what we're doing
+
+ align:start position:0%
+what we're doing
+ 
+
+ align:start position:0%
+what we're doing
+okay then we introduced uh random
+
+ align:start position:0%
+okay then we introduced uh random
+ 
+
+ align:start position:0%
+okay then we introduced uh random
+variables and uh we defined what a
+
+ align:start position:0%
+variables and uh we defined what a
+ 
+
+ align:start position:0%
+variables and uh we defined what a
+random variable was we discussed ways to
+
+ align:start position:0%
+random variable was we discussed ways to
+ 
+
+ align:start position:0%
+random variable was we discussed ways to
+represent distribution so a probability
+
+ align:start position:0%
+represent distribution so a probability
+ 
+
+ align:start position:0%
+represent distribution so a probability
+function a probability density function
+
+ align:start position:0%
+function a probability density function
+ 
+
+ align:start position:0%
+function a probability density function
+so those were kind of
+
+ align:start position:0%
+so those were kind of
+ 
+
+ align:start position:0%
+so those were kind of
+analogous uh sort of things but one was
+
+ align:start position:0%
+analogous uh sort of things but one was
+ 
+
+ align:start position:0%
+analogous uh sort of things but one was
+for discrete random variables and one
+
+ align:start position:0%
+for discrete random variables and one
+ 
+
+ align:start position:0%
+for discrete random variables and one
+was for continuous random variables and
+
+ align:start position:0%
+was for continuous random variables and
+ 
+
+ align:start position:0%
+was for continuous random variables and
+then we also talked about how the same
+
+ align:start position:0%
+then we also talked about how the same
+ 
+
+ align:start position:0%
+then we also talked about how the same
+information in PFS and PDFs can be
+
+ align:start position:0%
+information in PFS and PDFs can be
+ 
+
+ align:start position:0%
+information in PFS and PDFs can be
+embodied in a CDF okay and that's the
+
+ align:start position:0%
+embodied in a CDF okay and that's the
+ 
+
+ align:start position:0%
+embodied in a CDF okay and that's the
+definition of a CDF is the same for both
+
+ align:start position:0%
+definition of a CDF is the same for both
+ 
+
+ align:start position:0%
+definition of a CDF is the same for both
+uh continuous and discrete random
+
+ align:start position:0%
+uh continuous and discrete random
+ 
+
+ align:start position:0%
+uh continuous and discrete random
+variables and um then we also covered
+
+ align:start position:0%
+variables and um then we also covered
+ 
+
+ align:start position:0%
+variables and um then we also covered
+sort of the random variable analogues to
+
+ align:start position:0%
+sort of the random variable analogues to
+ 
+
+ align:start position:0%
+sort of the random variable analogues to
+the sort of stuff we covered in
+
+ align:start position:0%
+the sort of stuff we covered in
+ 
+
+ align:start position:0%
+the sort of stuff we covered in
+probability Basics so we talked about we
+
+ align:start position:0%
+probability Basics so we talked about we
+ 
+
+ align:start position:0%
+probability Basics so we talked about we
+had talked about independent events then
+
+ align:start position:0%
+had talked about independent events then
+ 
+
+ align:start position:0%
+had talked about independent events then
+we talked about independent random
+
+ align:start position:0%
+we talked about independent random
+ 
+
+ align:start position:0%
+we talked about independent random
+variables we talked about conditional
+
+ align:start position:0%
+variables we talked about conditional
+ 
+
+ align:start position:0%
+variables we talked about conditional
+probabilities then talked about
+
+ align:start position:0%
+probabilities then talked about
+ 
+
+ align:start position:0%
+probabilities then talked about
+conditional PDFs
+
+ align:start position:0%
+conditional PDFs
+ 
+
+ align:start position:0%
+conditional PDFs
+okay and then uh then Esther uh covered
+
+ align:start position:0%
+okay and then uh then Esther uh covered
+ 
+
+ align:start position:0%
+okay and then uh then Esther uh covered
+some um sort of um I don't know
+
+ align:start position:0%
+some um sort of um I don't know
+ 
+
+ align:start position:0%
+some um sort of um I don't know
+empirical counterparts to some of the
+
+ align:start position:0%
+empirical counterparts to some of the
+ 
+
+ align:start position:0%
+empirical counterparts to some of the
+things that we had been talking about
+
+ align:start position:0%
+things that we had been talking about
+ 
+
+ align:start position:0%
+things that we had been talking about
+theoretically in class so she talked
+
+ align:start position:0%
+theoretically in class so she talked
+ 
+
+ align:start position:0%
+theoretically in class so she talked
+about both a histogram defined what a
+
+ align:start position:0%
+about both a histogram defined what a
+ 
+
+ align:start position:0%
+about both a histogram defined what a
+histogram was showed us some nice
+
+ align:start position:0%
+histogram was showed us some nice
+ 
+
+ align:start position:0%
+histogram was showed us some nice
+examples and then also talked about um
+
+ align:start position:0%
+examples and then also talked about um
+ 
+
+ align:start position:0%
+examples and then also talked about um
+uh kernel density estimate and sort of
+
+ align:start position:0%
+uh kernel density estimate and sort of
+ 
+
+ align:start position:0%
+uh kernel density estimate and sort of
+what the difference between a histogram
+
+ align:start position:0%
+what the difference between a histogram
+ 
+
+ align:start position:0%
+what the difference between a histogram
+and a kernel density estimate is um and
+
+ align:start position:0%
+and a kernel density estimate is um and
+ 
+
+ align:start position:0%
+and a kernel density estimate is um and
+showed us some pictures of those as
+
+ align:start position:0%
+showed us some pictures of those as
+ 
+
+ align:start position:0%
+showed us some pictures of those as
+well and uh sort of uh you know we saw
+
+ align:start position:0%
+well and uh sort of uh you know we saw
+ 
+
+ align:start position:0%
+well and uh sort of uh you know we saw
+lots of examples that we hope gave you
+
+ align:start position:0%
+lots of examples that we hope gave you
+ 
+
+ align:start position:0%
+lots of examples that we hope gave you
+kind of a sense for how these
+
+ align:start position:0%
+kind of a sense for how these
+ 
+
+ align:start position:0%
+kind of a sense for how these
+theoretical you know objects function
+
+ align:start position:0%
+theoretical you know objects function
+ 
+
+ align:start position:0%
+theoretical you know objects function
+and what information they tell us and
+
+ align:start position:0%
+and what information they tell us and
+ 
+
+ align:start position:0%
+and what information they tell us and
+how to interpret them um then we started
+
+ align:start position:0%
+how to interpret them um then we started
+ 
+
+ align:start position:0%
+how to interpret them um then we started
+talking about functions of random
+
+ align:start position:0%
+talking about functions of random
+ 
+
+ align:start position:0%
+talking about functions of random
+variables so we saw some basic
+
+ align:start position:0%
+variables so we saw some basic
+ 
+
+ align:start position:0%
+variables so we saw some basic
+strategies or I guess actually one basic
+
+ align:start position:0%
+strategies or I guess actually one basic
+ 
+
+ align:start position:0%
+strategies or I guess actually one basic
+strategy for figuring out the
+
+ align:start position:0%
+strategy for figuring out the
+ 
+
+ align:start position:0%
+strategy for figuring out the
+distribution of a function of random
+
+ align:start position:0%
+distribution of a function of random
+ 
+
+ align:start position:0%
+distribution of a function of random
+variables and then I also did I went
+
+ align:start position:0%
+variables and then I also did I went
+ 
+
+ align:start position:0%
+variables and then I also did I went
+through several important examples and
+
+ align:start position:0%
+through several important examples and
+ 
+
+ align:start position:0%
+through several important examples and
+um so I think it it's useful to go back
+
+ align:start position:0%
+um so I think it it's useful to go back
+ 
+
+ align:start position:0%
+um so I think it it's useful to go back
+and sort of be comfortable with the
+
+ align:start position:0%
+and sort of be comfortable with the
+ 
+
+ align:start position:0%
+and sort of be comfortable with the
+examples so what were some of the
+
+ align:start position:0%
+examples so what were some of the
+ 
+
+ align:start position:0%
+examples so what were some of the
+examples that we went through well we
+
+ align:start position:0%
+examples that we went through well we
+ 
+
+ align:start position:0%
+examples that we went through well we
+did a sort of the um probability
+
+ align:start position:0%
+did a sort of the um probability
+ 
+
+ align:start position:0%
+did a sort of the um probability
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+transformation and we did uh convolution
+
+ align:start position:0%
+transformation and we did uh convolution
+ 
+
+ align:start position:0%
+transformation and we did uh convolution
+we did linear transformations of Rand
+
+ align:start position:0%
+we did linear transformations of Rand
+ 
+
+ align:start position:0%
+we did linear transformations of Rand
+variables we did order
+
+ align:start position:0%
+variables we did order
+ 
+
+ align:start position:0%
+variables we did order
+statistics maybe that's it I'm not sure
+
+ align:start position:0%
+statistics maybe that's it I'm not sure
+ 
+
+ align:start position:0%
+statistics maybe that's it I'm not sure
+maybe there's one more I don't know
+
+ align:start position:0%
+maybe there's one more I don't know
+ 
+
+ align:start position:0%
+maybe there's one more I don't know
+those are sort of uh those are all
+
+ align:start position:0%
+those are sort of uh those are all
+ 
+
+ align:start position:0%
+those are sort of uh those are all
+important examples and all things that
+
+ align:start position:0%
+important examples and all things that
+ 
+
+ align:start position:0%
+important examples and all things that
+we sort of have drawn on since and we'll
+
+ align:start position:0%
+we sort of have drawn on since and we'll
+ 
+
+ align:start position:0%
+we sort of have drawn on since and we'll
+continue to draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on then we sort of introduced uh moments
+
+ align:start position:0%
+on then we sort of introduced uh moments
+ 
+
+ align:start position:0%
+on then we sort of introduced uh moments
+of distributions so we defined uh mean
+
+ align:start position:0%
+of distributions so we defined uh mean
+ 
+
+ align:start position:0%
+of distributions so we defined uh mean
+variance we defined a few couple other
+
+ align:start position:0%
+variance we defined a few couple other
+ 
+
+ align:start position:0%
+variance we defined a few couple other
+uh but we mostly focused on the mean and
+
+ align:start position:0%
+uh but we mostly focused on the mean and
+ 
+
+ align:start position:0%
+uh but we mostly focused on the mean and
+variance and then in addition to
+
+ align:start position:0%
+variance and then in addition to
+ 
+
+ align:start position:0%
+variance and then in addition to
+learning how to or expectation if you'd
+
+ align:start position:0%
+learning how to or expectation if you'd
+ 
+
+ align:start position:0%
+learning how to or expectation if you'd
+rather expectation and variance in
+
+ align:start position:0%
+rather expectation and variance in
+ 
+
+ align:start position:0%
+rather expectation and variance in
+addition to sort of learning how to
+
+ align:start position:0%
+addition to sort of learning how to
+ 
+
+ align:start position:0%
+addition to sort of learning how to
+directly compute the expectation and
+
+ align:start position:0%
+directly compute the expectation and
+ 
+
+ align:start position:0%
+directly compute the expectation and
+variance uh given the distribution of a
+
+ align:start position:0%
+variance uh given the distribution of a
+ 
+
+ align:start position:0%
+variance uh given the distribution of a
+random variable we also learned a lot of
+
+ align:start position:0%
+random variable we also learned a lot of
+ 
+
+ align:start position:0%
+random variable we also learned a lot of
+techniques and properties to help
+
+ align:start position:0%
+techniques and properties to help
+ 
+
+ align:start position:0%
+techniques and properties to help
+compute moments of functions of random
+
+ align:start position:0%
+compute moments of functions of random
+ 
+
+ align:start position:0%
+compute moments of functions of random
+variables so you have uh you have a
+
+ align:start position:0%
+variables so you have uh you have a
+ 
+
+ align:start position:0%
+variables so you have uh you have a
+random variable maybe you know its
+
+ align:start position:0%
+random variable maybe you know its
+ 
+
+ align:start position:0%
+random variable maybe you know its
+moments
+
+ align:start position:0%
+moments
+ 
+
+ align:start position:0%
+moments
+uh but what you're really concerned with
+
+ align:start position:0%
+uh but what you're really concerned with
+ 
+
+ align:start position:0%
+uh but what you're really concerned with
+is a function of that random variable do
+
+ align:start position:0%
+is a function of that random variable do
+ 
+
+ align:start position:0%
+is a function of that random variable do
+you have to figure out how that function
+
+ align:start position:0%
+you have to figure out how that function
+ 
+
+ align:start position:0%
+you have to figure out how that function
+is distributed and then compute the
+
+ align:start position:0%
+is distributed and then compute the
+ 
+
+ align:start position:0%
+is distributed and then compute the
+moments directly you can do that usually
+
+ align:start position:0%
+moments directly you can do that usually
+ 
+
+ align:start position:0%
+moments directly you can do that usually
+you don't often times we can just uh
+
+ align:start position:0%
+you don't often times we can just uh
+ 
+
+ align:start position:0%
+you don't often times we can just uh
+rely on like properties of expectation
+
+ align:start position:0%
+rely on like properties of expectation
+ 
+
+ align:start position:0%
+rely on like properties of expectation
+properties of variance properties of
+
+ align:start position:0%
+properties of variance properties of
+ 
+
+ align:start position:0%
+properties of variance properties of
+co-variance Etc um to figure out the the
+
+ align:start position:0%
+co-variance Etc um to figure out the the
+ 
+
+ align:start position:0%
+co-variance Etc um to figure out the the
+characteristics of distributions of
+
+ align:start position:0%
+characteristics of distributions of
+ 
+
+ align:start position:0%
+characteristics of distributions of
+functions of Random variabl
+
+ align:start position:0%
+functions of Random variabl
+ 
+
+ align:start position:0%
+functions of Random variabl
+okay then uh Esther went through uh a
+
+ align:start position:0%
+okay then uh Esther went through uh a
+ 
+
+ align:start position:0%
+okay then uh Esther went through uh a
+whole lecture discussing special
+
+ align:start position:0%
+whole lecture discussing special
+ 
+
+ align:start position:0%
+whole lecture discussing special
+distributions and uh these are all
+
+ align:start position:0%
+distributions and uh these are all
+ 
+
+ align:start position:0%
+distributions and uh these are all
+distributions that are useful they
+
+ align:start position:0%
+distributions that are useful they
+ 
+
+ align:start position:0%
+distributions that are useful they
+distributions that will re-enter your
+
+ align:start position:0%
+distributions that will re-enter your
+ 
+
+ align:start position:0%
+distributions that will re-enter your
+life at some point in high probability I
+
+ align:start position:0%
+life at some point in high probability I
+ 
+
+ align:start position:0%
+life at some point in high probability I
+would say um they uh they distributions
+
+ align:start position:0%
+would say um they uh they distributions
+ 
+
+ align:start position:0%
+would say um they uh they distributions
+that we will continue to discuss
+
+ align:start position:0%
+that we will continue to discuss
+ 
+
+ align:start position:0%
+that we will continue to discuss
+throughout the semester and so it's good
+
+ align:start position:0%
+throughout the semester and so it's good
+ 
+
+ align:start position:0%
+throughout the semester and so it's good
+if you sort of have some level of
+
+ align:start position:0%
+if you sort of have some level of
+ 
+
+ align:start position:0%
+if you sort of have some level of
+comfort with them we're not interested
+
+ align:start position:0%
+comfort with them we're not interested
+ 
+
+ align:start position:0%
+comfort with them we're not interested
+in having you memorize PDFs of special
+
+ align:start position:0%
+in having you memorize PDFs of special
+ 
+
+ align:start position:0%
+in having you memorize PDFs of special
+distributions we're not interested in
+
+ align:start position:0%
+distributions we're not interested in
+ 
+
+ align:start position:0%
+distributions we're not interested in
+having you memorize the uh the
+
+ align:start position:0%
+having you memorize the uh the
+ 
+
+ align:start position:0%
+having you memorize the uh the
+expectation and the variance of special
+
+ align:start position:0%
+expectation and the variance of special
+ 
+
+ align:start position:0%
+expectation and the variance of special
+distributions um sometimes that just
+
+ align:start position:0%
+distributions um sometimes that just
+ 
+
+ align:start position:0%
+distributions um sometimes that just
+happens because you use them so much but
+
+ align:start position:0%
+happens because you use them so much but
+ 
+
+ align:start position:0%
+happens because you use them so much but
+um so on the exam so if you feel
+
+ align:start position:0%
+um so on the exam so if you feel
+ 
+
+ align:start position:0%
+um so on the exam so if you feel
+comfortable you can sort of write them
+
+ align:start position:0%
+comfortable you can sort of write them
+ 
+
+ align:start position:0%
+comfortable you can sort of write them
+out on your your page of notes that you
+
+ align:start position:0%
+out on your your page of notes that you
+ 
+
+ align:start position:0%
+out on your your page of notes that you
+bring in but we'll also provide things
+
+ align:start position:0%
+bring in but we'll also provide things
+ 
+
+ align:start position:0%
+bring in but we'll also provide things
+like that on the exam okay
+
+ align:start position:0%
+like that on the exam okay
+ 
+
+ align:start position:0%
+like that on the exam okay
+um and then finally uh in the last
+
+ align:start position:0%
+um and then finally uh in the last
+ 
+
+ align:start position:0%
+um and then finally uh in the last
+couple of lectures we started talking
+
+ align:start position:0%
+couple of lectures we started talking
+ 
+
+ align:start position:0%
+couple of lectures we started talking
+about estimation so we started our
+
+ align:start position:0%
+about estimation so we started our
+ 
+
+ align:start position:0%
+about estimation so we started our
+segue
+
+ align:start position:0%
+segue
+ 
+
+ align:start position:0%
+segue
+into um estimation in some sense was the
+
+ align:start position:0%
+into um estimation in some sense was the
+ 
+
+ align:start position:0%
+into um estimation in some sense was the
+central limit theorem so we've been
+
+ align:start position:0%
+central limit theorem so we've been
+ 
+
+ align:start position:0%
+central limit theorem so we've been
+talking about functions of random
+
+ align:start position:0%
+talking about functions of random
+ 
+
+ align:start position:0%
+talking about functions of random
+variables and we introduced a a special
+
+ align:start position:0%
+variables and we introduced a a special
+ 
+
+ align:start position:0%
+variables and we introduced a a special
+particularly useful function of random
+
+ align:start position:0%
+particularly useful function of random
+ 
+
+ align:start position:0%
+particularly useful function of random
+variables called the sample mean and we
+
+ align:start position:0%
+variables called the sample mean and we
+ 
+
+ align:start position:0%
+variables called the sample mean and we
+computed what the expect
+
+ align:start position:0%
+computed what the expect
+ 
+
+ align:start position:0%
+computed what the expect
+of that that function was what the
+
+ align:start position:0%
+of that that function was what the
+ 
+
+ align:start position:0%
+of that that function was what the
+expectation of the sample mean is we
+
+ align:start position:0%
+expectation of the sample mean is we
+ 
+
+ align:start position:0%
+expectation of the sample mean is we
+computed what the variance of that
+
+ align:start position:0%
+computed what the variance of that
+ 
+
+ align:start position:0%
+computed what the variance of that
+sample mean was but we wanted to know
+
+ align:start position:0%
+sample mean was but we wanted to know
+ 
+
+ align:start position:0%
+sample mean was but we wanted to know
+even more about its characteristics and
+
+ align:start position:0%
+even more about its characteristics and
+ 
+
+ align:start position:0%
+even more about its characteristics and
+how it was distributed and the central
+
+ align:start position:0%
+how it was distributed and the central
+ 
+
+ align:start position:0%
+how it was distributed and the central
+limit themm told us that the C Central
+
+ align:start position:0%
+limit themm told us that the C Central
+ 
+
+ align:start position:0%
+limit themm told us that the C Central
+limit them had this sort of remarkable
+
+ align:start position:0%
+limit them had this sort of remarkable
+ 
+
+ align:start position:0%
+limit them had this sort of remarkable
+result that no matter what kind of
+
+ align:start position:0%
+result that no matter what kind of
+ 
+
+ align:start position:0%
+result that no matter what kind of
+distribution you're drawing from and
+
+ align:start position:0%
+distribution you're drawing from and
+ 
+
+ align:start position:0%
+distribution you're drawing from and
+Computing the sample mean of if your
+
+ align:start position:0%
+Computing the sample mean of if your
+ 
+
+ align:start position:0%
+Computing the sample mean of if your
+sample size is big enough from that
+
+ align:start position:0%
+sample size is big enough from that
+ 
+
+ align:start position:0%
+sample size is big enough from that
+crazy
+
+ align:start position:0%
+crazy
+ 
+
+ align:start position:0%
+crazy
+distribution uh then the sample mean is
+
+ align:start position:0%
+distribution uh then the sample mean is
+ 
+
+ align:start position:0%
+distribution uh then the sample mean is
+have approximately a normal distribution
+
+ align:start position:0%
+have approximately a normal distribution
+ 
+
+ align:start position:0%
+have approximately a normal distribution
+okay and that's just super
+
+ align:start position:0%
+okay and that's just super
+ 
+
+ align:start position:0%
+okay and that's just super
+useful um the the full usefulness of it
+
+ align:start position:0%
+useful um the the full usefulness of it
+ 
+
+ align:start position:0%
+useful um the the full usefulness of it
+has not occurred to you yet because we
+
+ align:start position:0%
+has not occurred to you yet because we
+ 
+
+ align:start position:0%
+has not occurred to you yet because we
+haven't gotten to inference but uh we
+
+ align:start position:0%
+haven't gotten to inference but uh we
+ 
+
+ align:start position:0%
+haven't gotten to inference but uh we
+will after spring break get to inference
+
+ align:start position:0%
+will after spring break get to inference
+ 
+
+ align:start position:0%
+will after spring break get to inference
+and then you will know okay so we talked
+
+ align:start position:0%
+and then you will know okay so we talked
+ 
+
+ align:start position:0%
+and then you will know okay so we talked
+about the central we talked about the
+
+ align:start position:0%
+about the central we talked about the
+ 
+
+ align:start position:0%
+about the central we talked about the
+sample mean so that's that's kind of the
+
+ align:start position:0%
+sample mean so that's that's kind of the
+ 
+
+ align:start position:0%
+sample mean so that's that's kind of the
+most important estimator that we talked
+
+ align:start position:0%
+most important estimator that we talked
+ 
+
+ align:start position:0%
+most important estimator that we talked
+about we talked about the central limit
+
+ align:start position:0%
+about we talked about the central limit
+ 
+
+ align:start position:0%
+about we talked about the central limit
+theem which told us some important facts
+
+ align:start position:0%
+theem which told us some important facts
+ 
+
+ align:start position:0%
+theem which told us some important facts
+about the the how the sample mean
+
+ align:start position:0%
+about the the how the sample mean
+ 
+
+ align:start position:0%
+about the the how the sample mean
+behaved uh we had sort of a general
+
+ align:start position:0%
+behaved uh we had sort of a general
+ 
+
+ align:start position:0%
+behaved uh we had sort of a general
+discussion um about estimation and then
+
+ align:start position:0%
+discussion um about estimation and then
+ 
+
+ align:start position:0%
+discussion um about estimation and then
+the last two topics we covered these are
+
+ align:start position:0%
+the last two topics we covered these are
+ 
+
+ align:start position:0%
+the last two topics we covered these are
+topics that we will not test you on on
+
+ align:start position:0%
+topics that we will not test you on on
+ 
+
+ align:start position:0%
+topics that we will not test you on on
+the exam the last two topics we covered
+
+ align:start position:0%
+the exam the last two topics we covered
+ 
+
+ align:start position:0%
+the exam the last two topics we covered
+were criteria for assessing estimators
+
+ align:start position:0%
+were criteria for assessing estimators
+ 
+
+ align:start position:0%
+were criteria for assessing estimators
+so whether an estimator is unbiased
+
+ align:start position:0%
+so whether an estimator is unbiased
+ 
+
+ align:start position:0%
+so whether an estimator is unbiased
+whether it's efficient whether it's a
+
+ align:start position:0%
+whether it's efficient whether it's a
+ 
+
+ align:start position:0%
+whether it's efficient whether it's a
+minimum me squared error estimator
+
+ align:start position:0%
+minimum me squared error estimator
+ 
+
+ align:start position:0%
+minimum me squared error estimator
+whether it's consistent um and then we
+
+ align:start position:0%
+whether it's consistent um and then we
+ 
+
+ align:start position:0%
+whether it's consistent um and then we
+also talked about uh Frameworks for
+
+ align:start position:0%
+also talked about uh Frameworks for
+ 
+
+ align:start position:0%
+also talked about uh Frameworks for
+deriving estimators um method of moments
+
+ align:start position:0%
+deriving estimators um method of moments
+ 
+
+ align:start position:0%
+deriving estimators um method of moments
+estimation and maximum likelihood
+
+ align:start position:0%
+estimation and maximum likelihood
+ 
+
+ align:start position:0%
+estimation and maximum likelihood
+estimation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
\ No newline at end of file
diff --git a/2N0OXAiX-BM.txt b/2N0OXAiX-BM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1261208cc0a89b137ec031568dd07a0c8233de24
--- /dev/null
+++ b/2N0OXAiX-BM.txt
@@ -0,0 +1,3419 @@
+align:start position:0%
+ 
+a new way of thinking about this is
+
+ align:start position:0%
+a new way of thinking about this is
+ 
+
+ align:start position:0%
+a new way of thinking about this is
+based on integral equations so it's a
+
+ align:start position:0%
+based on integral equations so it's a
+ 
+
+ align:start position:0%
+based on integral equations so it's a
+nice method of it's less complicated
+
+ align:start position:0%
+nice method of it's less complicated
+ 
+
+ align:start position:0%
+nice method of it's less complicated
+than it seems and it leads to some
+
+ align:start position:0%
+than it seems and it leads to some
+ 
+
+ align:start position:0%
+than it seems and it leads to some
+expressions for the scattering amplitude
+
+ align:start position:0%
+expressions for the scattering amplitude
+ 
+
+ align:start position:0%
+expressions for the scattering amplitude
+we'll find another formula for this
+
+ align:start position:0%
+we'll find another formula for this
+ 
+
+ align:start position:0%
+we'll find another formula for this
+quantity f of K of theta when we cannot
+
+ align:start position:0%
+quantity f of K of theta when we cannot
+ 
+
+ align:start position:0%
+quantity f of K of theta when we cannot
+calculate it with phase shifts but phase
+
+ align:start position:0%
+calculate it with phase shifts but phase
+ 
+
+ align:start position:0%
+calculate it with phase shifts but phase
+shifts is very powerful if your prompt
+
+ align:start position:0%
+shifts is very powerful if your prompt
+ 
+
+ align:start position:0%
+shifts is very powerful if your prompt
+has spherical symmetry it's it's
+
+ align:start position:0%
+has spherical symmetry it's it's
+ 
+
+ align:start position:0%
+has spherical symmetry it's it's
+probably the first thing you try because
+
+ align:start position:0%
+probably the first thing you try because
+ 
+
+ align:start position:0%
+probably the first thing you try because
+there's nothing to prevent you from
+
+ align:start position:0%
+there's nothing to prevent you from
+ 
+
+ align:start position:0%
+there's nothing to prevent you from
+finding a solution in that case ok so
+
+ align:start position:0%
+finding a solution in that case ok so
+ 
+
+ align:start position:0%
+finding a solution in that case ok so
+integral equations so integral
+
+ align:start position:0%
+integral equations so integral
+ 
+
+ align:start position:0%
+integral equations so integral
+scattering equation scattering so what
+
+ align:start position:0%
+scattering equation scattering so what
+ 
+
+ align:start position:0%
+scattering equation scattering so what
+are we solving we're solving minus H
+
+ align:start position:0%
+are we solving we're solving minus H
+ 
+
+ align:start position:0%
+are we solving we're solving minus H
+squared over 2m laplacian plus V of R a
+
+ align:start position:0%
+squared over 2m laplacian plus V of R a
+ 
+
+ align:start position:0%
+squared over 2m laplacian plus V of R a
+potential that is not necessarily
+
+ align:start position:0%
+potential that is not necessarily
+ 
+
+ align:start position:0%
+potential that is not necessarily
+spherical equals or acts on apps ifr to
+
+ align:start position:0%
+spherical equals or acts on apps ifr to
+ 
+
+ align:start position:0%
+spherical equals or acts on apps ifr to
+give you h squared K squared over 2m psy
+
+ align:start position:0%
+give you h squared K squared over 2m psy
+ 
+
+ align:start position:0%
+give you h squared K squared over 2m psy
+of our so it's an equation for
+
+ align:start position:0%
+of our so it's an equation for
+ 
+
+ align:start position:0%
+of our so it's an equation for
+eigenstates the sharing their equation
+
+ align:start position:0%
+eigenstates the sharing their equation
+ 
+
+ align:start position:0%
+eigenstates the sharing their equation
+right it's good it's nice and this is
+
+ align:start position:0%
+right it's good it's nice and this is
+ 
+
+ align:start position:0%
+right it's good it's nice and this is
+what we've been solving we've been
+
+ align:start position:0%
+what we've been solving we've been
+ 
+
+ align:start position:0%
+what we've been solving we've been
+solving it for some particular cases the
+
+ align:start position:0%
+solving it for some particular cases the
+ 
+
+ align:start position:0%
+solving it for some particular cases the
+case of physical interest for us was
+
+ align:start position:0%
+case of physical interest for us was
+ 
+
+ align:start position:0%
+case of physical interest for us was
+when there was a plane wave coming in
+
+ align:start position:0%
+when there was a plane wave coming in
+ 
+
+ align:start position:0%
+when there was a plane wave coming in
+from infinity and a spherical wave going
+
+ align:start position:0%
+from infinity and a spherical wave going
+ 
+
+ align:start position:0%
+from infinity and a spherical wave going
+out at infinity now I
+
+ align:start position:0%
+out at infinity now I
+ 
+
+ align:start position:0%
+out at infinity now I
+this moment is probably convenient to
+
+ align:start position:0%
+this moment is probably convenient to
+ 
+
+ align:start position:0%
+this moment is probably convenient to
+clean up the units from this equation a
+
+ align:start position:0%
+clean up the units from this equation a
+ 
+
+ align:start position:0%
+clean up the units from this equation a
+little so I'll use a notation in which V
+
+ align:start position:0%
+little so I'll use a notation in which V
+ 
+
+ align:start position:0%
+little so I'll use a notation in which V
+of R is equal to H squared over 2m u of
+
+ align:start position:0%
+of R is equal to H squared over 2m u of
+ 
+
+ align:start position:0%
+of R is equal to H squared over 2m u of
+r u still reminds you of a potential I
+
+ align:start position:0%
+r u still reminds you of a potential I
+ 
+
+ align:start position:0%
+r u still reminds you of a potential I
+think and it's a good thing it's a
+
+ align:start position:0%
+think and it's a good thing it's a
+ 
+
+ align:start position:0%
+think and it's a good thing it's a
+definition of U of our it's definition
+
+ align:start position:0%
+definition of U of our it's definition
+ 
+
+ align:start position:0%
+definition of U of our it's definition
+and in that way I could get rid of the H
+
+ align:start position:0%
+and in that way I could get rid of the H
+ 
+
+ align:start position:0%
+and in that way I could get rid of the H
+bars in the Schrodinger equation and
+
+ align:start position:0%
+bars in the Schrodinger equation and
+ 
+
+ align:start position:0%
+bars in the Schrodinger equation and
+what do we get we get minus laplacian
+
+ align:start position:0%
+what do we get we get minus laplacian
+ 
+
+ align:start position:0%
+what do we get we get minus laplacian
+plus u of r acting on Phi of R is equal
+
+ align:start position:0%
+plus u of r acting on Phi of R is equal
+ 
+
+ align:start position:0%
+plus u of r acting on Phi of R is equal
+to K squared acting on so far ok that
+
+ align:start position:0%
+to K squared acting on so far ok that
+ 
+
+ align:start position:0%
+to K squared acting on so far ok that
+looks nice
+
+ align:start position:0%
+looks nice
+ 
+
+ align:start position:0%
+looks nice
+it probably is nicer if you put it in a
+
+ align:start position:0%
+it probably is nicer if you put it in a
+ 
+
+ align:start position:0%
+it probably is nicer if you put it in a
+way that the left hand side is kind of a
+
+ align:start position:0%
+way that the left hand side is kind of a
+ 
+
+ align:start position:0%
+way that the left hand side is kind of a
+nice simple operator and the right hand
+
+ align:start position:0%
+nice simple operator and the right hand
+ 
+
+ align:start position:0%
+nice simple operator and the right hand
+side involves a potential so I will move
+
+ align:start position:0%
+side involves a potential so I will move
+ 
+
+ align:start position:0%
+side involves a potential so I will move
+it along so that I can pass the nablus
+
+ align:start position:0%
+it along so that I can pass the nablus
+ 
+
+ align:start position:0%
+it along so that I can pass the nablus
+squared to the ripe and then make that
+
+ align:start position:0%
+squared to the ripe and then make that
+ 
+
+ align:start position:0%
+squared to the ripe and then make that
+the left hand side so this will be
+
+ align:start position:0%
+the left hand side so this will be
+ 
+
+ align:start position:0%
+the left hand side so this will be
+laplacian squared plus K squared on psy
+
+ align:start position:0%
+laplacian squared plus K squared on psy
+ 
+
+ align:start position:0%
+laplacian squared plus K squared on psy
+of r is equal to u of r sy afar okay so
+
+ align:start position:0%
+of r is equal to u of r sy afar okay so
+ 
+
+ align:start position:0%
+of r is equal to u of r sy afar okay so
+with written with we've done nothing so
+
+ align:start position:0%
+with written with we've done nothing so
+ 
+
+ align:start position:0%
+with written with we've done nothing so
+far
+
+ align:start position:0%
+far
+ 
+
+ align:start position:0%
+far
+except put the equation in a way that
+
+ align:start position:0%
+except put the equation in a way that
+ 
+
+ align:start position:0%
+except put the equation in a way that
+stimulates our thinking we kind of think
+
+ align:start position:0%
+stimulates our thinking we kind of think
+ 
+
+ align:start position:0%
+stimulates our thinking we kind of think
+of the right-hand side as a source and
+
+ align:start position:0%
+of the right-hand side as a source and
+ 
+
+ align:start position:0%
+of the right-hand side as a source and
+the left hand side as
+
+ align:start position:0%
+the left hand side as
+ 
+
+ align:start position:0%
+the left hand side as
+kind of the equation you want to solve
+
+ align:start position:0%
+kind of the equation you want to solve
+ 
+
+ align:start position:0%
+kind of the equation you want to solve
+sometimes you have an equation like that
+
+ align:start position:0%
+sometimes you have an equation like that
+ 
+
+ align:start position:0%
+sometimes you have an equation like that
+and you can get this zero here well
+
+ align:start position:0%
+and you can get this zero here well
+ 
+
+ align:start position:0%
+and you can get this zero here well
+that's when the potential is zero but
+
+ align:start position:0%
+that's when the potential is zero but
+ 
+
+ align:start position:0%
+that's when the potential is zero but
+sometimes there's a bit of potential so
+
+ align:start position:0%
+sometimes there's a bit of potential so
+ 
+
+ align:start position:0%
+sometimes there's a bit of potential so
+the solution feeds back into this
+
+ align:start position:0%
+the solution feeds back into this
+ 
+
+ align:start position:0%
+the solution feeds back into this
+whenever you have an equation of this
+
+ align:start position:0%
+whenever you have an equation of this
+ 
+
+ align:start position:0%
+whenever you have an equation of this
+form some nice operator so this we call
+
+ align:start position:0%
+form some nice operator so this we call
+ 
+
+ align:start position:0%
+form some nice operator so this we call
+nice operator acting on sigh giving you
+
+ align:start position:0%
+nice operator acting on sigh giving you
+ 
+
+ align:start position:0%
+nice operator acting on sigh giving you
+something that depends on side that
+
+ align:start position:0%
+something that depends on side that
+ 
+
+ align:start position:0%
+something that depends on side that
+maybe it's not that nice or not that
+
+ align:start position:0%
+maybe it's not that nice or not that
+ 
+
+ align:start position:0%
+maybe it's not that nice or not that
+simple we can try to solve this using a
+
+ align:start position:0%
+simple we can try to solve this using a
+ 
+
+ align:start position:0%
+simple we can try to solve this using a
+greens function
+
+ align:start position:0%
+greens function
+ 
+
+ align:start position:0%
+greens function
+that's what greens functions are good
+
+ align:start position:0%
+that's what greens functions are good
+ 
+
+ align:start position:0%
+that's what greens functions are good
+for so let's try to use the greens
+
+ align:start position:0%
+for so let's try to use the greens
+ 
+
+ align:start position:0%
+for so let's try to use the greens
+function so what is a greens function it
+
+ align:start position:0%
+function so what is a greens function it
+ 
+
+ align:start position:0%
+function so what is a greens function it
+is basically a way of understanding what
+
+ align:start position:0%
+is basically a way of understanding what
+ 
+
+ align:start position:0%
+is basically a way of understanding what
+this operator is so nice operator must
+
+ align:start position:0%
+this operator is so nice operator must
+ 
+
+ align:start position:0%
+this operator is so nice operator must
+have a greens function so what is your
+
+ align:start position:0%
+have a greens function so what is your
+ 
+
+ align:start position:0%
+have a greens function so what is your
+greens function here it's called G and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we say it's depends on R minus R prime R
+
+ align:start position:0%
+we say it's depends on R minus R prime R
+ 
+
+ align:start position:0%
+we say it's depends on R minus R prime R
+prime is an arbitrary point so far but
+
+ align:start position:0%
+prime is an arbitrary point so far but
+ 
+
+ align:start position:0%
+prime is an arbitrary point so far but
+here is what it does it's it's basically
+
+ align:start position:0%
+here is what it does it's it's basically
+ 
+
+ align:start position:0%
+here is what it does it's it's basically
+a solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you want this greens function to be
+
+ align:start position:0%
+you want this greens function to be
+ 
+
+ align:start position:0%
+you want this greens function to be
+almost zero except they're not quite
+
+ align:start position:0%
+almost zero except they're not quite
+ 
+
+ align:start position:0%
+almost zero except they're not quite
+equal to zero you want it to be equal to
+
+ align:start position:0%
+equal to zero you want it to be equal to
+ 
+
+ align:start position:0%
+equal to zero you want it to be equal to
+a delta function so so that's the
+
+ align:start position:0%
+a delta function so so that's the
+ 
+
+ align:start position:0%
+a delta function so so that's the
+definition of the greens function is
+
+ align:start position:0%
+definition of the greens function is
+ 
+
+ align:start position:0%
+definition of the greens function is
+that thing which is the solution of a
+
+ align:start position:0%
+that thing which is the solution of a
+ 
+
+ align:start position:0%
+that thing which is the solution of a
+similar equation when you have the nice
+
+ align:start position:0%
+similar equation when you have the nice
+ 
+
+ align:start position:0%
+similar equation when you have the nice
+operator acting on the greens function
+
+ align:start position:0%
+operator acting on the greens function
+ 
+
+ align:start position:0%
+operator acting on the greens function
+being just a delta function it's almost
+
+ align:start position:0%
+being just a delta function it's almost
+ 
+
+ align:start position:0%
+being just a delta function it's almost
+saying that the greens function is the
+
+ align:start position:0%
+saying that the greens function is the
+ 
+
+ align:start position:0%
+saying that the greens function is the
+thing that solves that equation with
+
+ align:start position:0%
+thing that solves that equation with
+ 
+
+ align:start position:0%
+thing that solves that equation with
+zero on the right hand side except that
+
+ align:start position:0%
+zero on the right hand side except that
+ 
+
+ align:start position:0%
+zero on the right hand side except that
+it's not really zero it's a source in
+
+ align:start position:0%
+it's not really zero it's a source in
+ 
+
+ align:start position:0%
+it's not really zero it's a source in
+the right hand side it's a delta
+
+ align:start position:0%
+the right hand side it's a delta
+ 
+
+ align:start position:0%
+the right hand side it's a delta
+function at this point so you would say
+
+ align:start position:0%
+function at this point so you would say
+ 
+
+ align:start position:0%
+function at this point so you would say
+maybe okay I don't know that why would I
+
+ align:start position:0%
+maybe okay I don't know that why would I
+ 
+
+ align:start position:0%
+maybe okay I don't know that why would I
+care about this equation you care for
+
+ align:start position:0%
+care about this equation you care for
+ 
+
+ align:start position:0%
+care about this equation you care for
+two reasons the first reason is that
+
+ align:start position:0%
+two reasons the first reason is that
+ 
+
+ align:start position:0%
+two reasons the first reason is that
+this equation is easier to solve than
+
+ align:start position:0%
+this equation is easier to solve than
+ 
+
+ align:start position:0%
+this equation is easier to solve than
+this one doesn't involve the potential
+
+ align:start position:0%
+this one doesn't involve the potential
+ 
+
+ align:start position:0%
+this one doesn't involve the potential
+which is complicated it just involves a
+
+ align:start position:0%
+which is complicated it just involves a
+ 
+
+ align:start position:0%
+which is complicated it just involves a
+delta function so we can have this G and
+
+ align:start position:0%
+delta function so we can have this G and
+ 
+
+ align:start position:0%
+delta function so we can have this G and
+solve it once because it doesn't involve
+
+ align:start position:0%
+solve it once because it doesn't involve
+ 
+
+ align:start position:0%
+solve it once because it doesn't involve
+the potential and then the great thing
+
+ align:start position:0%
+the potential and then the great thing
+ 
+
+ align:start position:0%
+the potential and then the great thing
+about this equation is that it allows
+
+ align:start position:0%
+about this equation is that it allows
+ 
+
+ align:start position:0%
+about this equation is that it allows
+you to write a solution for the top
+
+ align:start position:0%
+you to write a solution for the top
+ 
+
+ align:start position:0%
+you to write a solution for the top
+equation without having to do any work
+
+ align:start position:0%
+equation without having to do any work
+ 
+
+ align:start position:0%
+equation without having to do any work
+anymore once you have the greens
+
+ align:start position:0%
+anymore once you have the greens
+ 
+
+ align:start position:0%
+anymore once you have the greens
+function you're done so let's assume you
+
+ align:start position:0%
+function you're done so let's assume you
+ 
+
+ align:start position:0%
+function you're done so let's assume you
+have the greens function how would you
+
+ align:start position:0%
+have the greens function how would you
+ 
+
+ align:start position:0%
+have the greens function how would you
+write the solution for this equation so
+
+ align:start position:0%
+write the solution for this equation so
+ 
+
+ align:start position:0%
+write the solution for this equation so
+the idea is superposition basically
+
+ align:start position:0%
+the idea is superposition basically
+ 
+
+ align:start position:0%
+the idea is superposition basically
+and we'll do it using that so our aim is
+
+ align:start position:0%
+and we'll do it using that so our aim is
+ 
+
+ align:start position:0%
+and we'll do it using that so our aim is
+to use this greens function if we had it
+
+ align:start position:0%
+to use this greens function if we had it
+ 
+
+ align:start position:0%
+to use this greens function if we had it
+to write a solution for this equation so
+
+ align:start position:0%
+to write a solution for this equation so
+ 
+
+ align:start position:0%
+to write a solution for this equation so
+here is the claim you write sine of X is
+
+ align:start position:0%
+here is the claim you write sine of X is
+ 
+
+ align:start position:0%
+here is the claim you write sine of X is
+it going to be given by a beginning one
+
+ align:start position:0%
+it going to be given by a beginning one
+ 
+
+ align:start position:0%
+it going to be given by a beginning one
+size zero of X that is going to be a
+
+ align:start position:0%
+size zero of X that is going to be a
+ 
+
+ align:start position:0%
+size zero of X that is going to be a
+funny one this one solves laplacian plus
+
+ align:start position:0%
+funny one this one solves laplacian plus
+ 
+
+ align:start position:0%
+funny one this one solves laplacian plus
+K squared on size zero of X or R is
+
+ align:start position:0%
+K squared on size zero of X or R is
+ 
+
+ align:start position:0%
+K squared on size zero of X or R is
+equal to zero so whenever you have an
+
+ align:start position:0%
+equal to zero so whenever you have an
+ 
+
+ align:start position:0%
+equal to zero so whenever you have an
+equation of this form you can add any a
+
+ align:start position:0%
+equation of this form you can add any a
+ 
+
+ align:start position:0%
+equation of this form you can add any a
+solution anything that this killed by
+
+ align:start position:0%
+solution anything that this killed by
+ 
+
+ align:start position:0%
+solution anything that this killed by
+this can be added to whatever solution
+
+ align:start position:0%
+this can be added to whatever solution
+ 
+
+ align:start position:0%
+this can be added to whatever solution
+you have so let's assume that we have a
+
+ align:start position:0%
+you have so let's assume that we have a
+ 
+
+ align:start position:0%
+you have so let's assume that we have a
+solution of this form size zero of this
+
+ align:start position:0%
+solution of this form size zero of this
+ 
+
+ align:start position:0%
+solution of this form size zero of this
+form now here I'll add one more thing
+
+ align:start position:0%
+form now here I'll add one more thing
+ 
+
+ align:start position:0%
+form now here I'll add one more thing
+the important part is going to be an
+
+ align:start position:0%
+the important part is going to be an
+ 
+
+ align:start position:0%
+the important part is going to be an
+integral over our prime here is the
+
+ align:start position:0%
+integral over our prime here is the
+ 
+
+ align:start position:0%
+integral over our prime here is the
+superposition I'm going to think of this
+
+ align:start position:0%
+superposition I'm going to think of this
+ 
+
+ align:start position:0%
+superposition I'm going to think of this
+potential you are far as kind of
+
+ align:start position:0%
+potential you are far as kind of
+ 
+
+ align:start position:0%
+potential you are far as kind of
+existing at every point R prime so I'm
+
+ align:start position:0%
+existing at every point R prime so I'm
+ 
+
+ align:start position:0%
+existing at every point R prime so I'm
+going to write the solution as a
+
+ align:start position:0%
+going to write the solution as a
+ 
+
+ align:start position:0%
+going to write the solution as a
+superposition that involves the greens
+
+ align:start position:0%
+superposition that involves the greens
+ 
+
+ align:start position:0%
+superposition that involves the greens
+function so this will be G of R minus R
+
+ align:start position:0%
+function so this will be G of R minus R
+ 
+
+ align:start position:0%
+function so this will be G of R minus R
+prime times u of r prime times
+
+ align:start position:0%
+prime times u of r prime times
+ 
+
+ align:start position:0%
+prime times u of r prime times
+sy of R Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I claim that this is equivalent to this
+
+ align:start position:0%
+I claim that this is equivalent to this
+ 
+
+ align:start position:0%
+I claim that this is equivalent to this
+equation that we have that this side
+
+ align:start position:0%
+equation that we have that this side
+ 
+
+ align:start position:0%
+equation that we have that this side
+provides more than equivalent
+
+ align:start position:0%
+provides more than equivalent
+ 
+
+ align:start position:0%
+provides more than equivalent
+I think the precise way to say this
+
+ align:start position:0%
+I think the precise way to say this
+ 
+
+ align:start position:0%
+I think the precise way to say this
+provides a solution of this equation the
+
+ align:start position:0%
+provides a solution of this equation the
+ 
+
+ align:start position:0%
+provides a solution of this equation the
+way I've written so let's try it
+
+ align:start position:0%
+way I've written so let's try it
+ 
+
+ align:start position:0%
+way I've written so let's try it
+suppose I calculate laplacian plus K
+
+ align:start position:0%
+suppose I calculate laplacian plus K
+ 
+
+ align:start position:0%
+suppose I calculate laplacian plus K
+squared on side effects here okay the
+
+ align:start position:0%
+squared on side effects here okay the
+ 
+
+ align:start position:0%
+squared on side effects here okay the
+first term it's already zero so
+
+ align:start position:0%
+first term it's already zero so
+ 
+
+ align:start position:0%
+first term it's already zero so
+laplacian plus K squared on size zero is
+
+ align:start position:0%
+laplacian plus K squared on size zero is
+ 
+
+ align:start position:0%
+laplacian plus K squared on size zero is
+already zero and then I come here and I
+
+ align:start position:0%
+already zero and then I come here and I
+ 
+
+ align:start position:0%
+already zero and then I come here and I
+say ok I'm a laplacian I care about our
+
+ align:start position:0%
+say ok I'm a laplacian I care about our
+ 
+
+ align:start position:0%
+say ok I'm a laplacian I care about our
+because I'm a depression I don't care
+
+ align:start position:0%
+because I'm a depression I don't care
+ 
+
+ align:start position:0%
+because I'm a depression I don't care
+about our prime so I come in here and I
+
+ align:start position:0%
+about our prime so I come in here and I
+ 
+
+ align:start position:0%
+about our prime so I come in here and I
+ignore our prime ignore our prime I
+
+ align:start position:0%
+ignore our prime ignore our prime I
+ 
+
+ align:start position:0%
+ignore our prime ignore our prime I
+cannot ignore this thing so we have plus
+
+ align:start position:0%
+cannot ignore this thing so we have plus
+ 
+
+ align:start position:0%
+cannot ignore this thing so we have plus
+integral D our prime laplacian plus K
+
+ align:start position:0%
+integral D our prime laplacian plus K
+ 
+
+ align:start position:0%
+integral D our prime laplacian plus K
+squared acting on G of our minus R prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times U of R Prime sy of our prime and
+
+ align:start position:0%
+times U of R Prime sy of our prime and
+ 
+
+ align:start position:0%
+times U of R Prime sy of our prime and
+now because the greens function was
+
+ align:start position:0%
+now because the greens function was
+ 
+
+ align:start position:0%
+now because the greens function was
+designed to give you a delta of R minus
+
+ align:start position:0%
+designed to give you a delta of R minus
+ 
+
+ align:start position:0%
+designed to give you a delta of R minus
+R prime this is an integral that can be
+
+ align:start position:0%
+R prime this is an integral that can be
+ 
+
+ align:start position:0%
+R prime this is an integral that can be
+done the integral over R Prime and just
+
+ align:start position:0%
+done the integral over R Prime and just
+ 
+
+ align:start position:0%
+done the integral over R Prime and just
+set the rest of the integrand at the
+
+ align:start position:0%
+set the rest of the integrand at the
+ 
+
+ align:start position:0%
+set the rest of the integrand at the
+point R because you integrate over R
+
+ align:start position:0%
+point R because you integrate over R
+ 
+
+ align:start position:0%
+point R because you integrate over R
+Prime and this Delta function fires when
+
+ align:start position:0%
+Prime and this Delta function fires when
+ 
+
+ align:start position:0%
+Prime and this Delta function fires when
+our R
+
+ align:start position:0%
+our R
+ 
+
+ align:start position:0%
+our R
+is equal to R so this gives me you of
+
+ align:start position:0%
+is equal to R so this gives me you of
+ 
+
+ align:start position:0%
+is equal to R so this gives me you of
+our sigh of our and that is the equation
+
+ align:start position:0%
+our sigh of our and that is the equation
+ 
+
+ align:start position:0%
+our sigh of our and that is the equation
+I wanted to solve the question that we
+
+ align:start position:0%
+I wanted to solve the question that we
+ 
+
+ align:start position:0%
+I wanted to solve the question that we
+have here so we have turned the problem
+
+ align:start position:0%
+have here so we have turned the problem
+ 
+
+ align:start position:0%
+have here so we have turned the problem
+this cannot be called the solution
+
+ align:start position:0%
+this cannot be called the solution
+ 
+
+ align:start position:0%
+this cannot be called the solution
+because we have not solved it we have
+
+ align:start position:0%
+because we have not solved it we have
+ 
+
+ align:start position:0%
+because we have not solved it we have
+turned the problem into a different kind
+
+ align:start position:0%
+turned the problem into a different kind
+ 
+
+ align:start position:0%
+turned the problem into a different kind
+of problem we it might even seem that
+
+ align:start position:0%
+of problem we it might even seem that
+ 
+
+ align:start position:0%
+of problem we it might even seem that
+we've made the problem worse by turning
+
+ align:start position:0%
+we've made the problem worse by turning
+ 
+
+ align:start position:0%
+we've made the problem worse by turning
+this into an integral equation there's
+
+ align:start position:0%
+this into an integral equation there's
+ 
+
+ align:start position:0%
+this into an integral equation there's
+no derivatives here but the function
+
+ align:start position:0%
+no derivatives here but the function
+ 
+
+ align:start position:0%
+no derivatives here but the function
+that you're looking for appears outside
+
+ align:start position:0%
+that you're looking for appears outside
+ 
+
+ align:start position:0%
+that you're looking for appears outside
+and inside the integral so these things
+
+ align:start position:0%
+and inside the integral so these things
+ 
+
+ align:start position:0%
+and inside the integral so these things
+are called integral equations and and
+
+ align:start position:0%
+are called integral equations and and
+ 
+
+ align:start position:0%
+are called integral equations and and
+the power of an integral equation is the
+
+ align:start position:0%
+the power of an integral equation is the
+ 
+
+ align:start position:0%
+the power of an integral equation is the
+insight it can give you once you have an
+
+ align:start position:0%
+insight it can give you once you have an
+ 
+
+ align:start position:0%
+insight it can give you once you have an
+idea of what the green's function is and
+
+ align:start position:0%
+idea of what the green's function is and
+ 
+
+ align:start position:0%
+idea of what the green's function is and
+also it's a good place to do a recursive
+
+ align:start position:0%
+also it's a good place to do a recursive
+ 
+
+ align:start position:0%
+also it's a good place to do a recursive
+approximations in that you can
+
+ align:start position:0%
+approximations in that you can
+ 
+
+ align:start position:0%
+approximations in that you can
+essentially begin and say ok i know the
+
+ align:start position:0%
+essentially begin and say ok i know the
+ 
+
+ align:start position:0%
+essentially begin and say ok i know the
+wave function is this plus that but
+
+ align:start position:0%
+wave function is this plus that but
+ 
+
+ align:start position:0%
+wave function is this plus that but
+maybe if in some sense i can think of
+
+ align:start position:0%
+maybe if in some sense i can think of
+ 
+
+ align:start position:0%
+maybe if in some sense i can think of
+this thing as the leading solution i
+
+ align:start position:0%
+this thing as the leading solution i
+ 
+
+ align:start position:0%
+this thing as the leading solution i
+could substitute the living solution in
+
+ align:start position:0%
+could substitute the living solution in
+ 
+
+ align:start position:0%
+could substitute the living solution in
+here and try to make an approximation
+
+ align:start position:0%
+here and try to make an approximation
+ 
+
+ align:start position:0%
+here and try to make an approximation
+that's gonna give you a nice
+
+ align:start position:0%
+that's gonna give you a nice
+ 
+
+ align:start position:0%
+that's gonna give you a nice
+approximation the born approximation
+
+ align:start position:0%
+approximation the born approximation
+ 
+
+ align:start position:0%
+approximation the born approximation
+we'll see that soon now that should be
+
+ align:start position:0%
+we'll see that soon now that should be
+ 
+
+ align:start position:0%
+we'll see that soon now that should be
+upside ours I think I'm using R so I
+
+ align:start position:0%
+upside ours I think I'm using R so I
+ 
+
+ align:start position:0%
+upside ours I think I'm using R so I
+please so ours and ours yeah no no
+
+ align:start position:0%
+please so ours and ours yeah no no
+ 
+
+ align:start position:0%
+please so ours and ours yeah no no
+difference at this moment ok so the next
+
+ align:start position:0%
+difference at this moment ok so the next
+ 
+
+ align:start position:0%
+difference at this moment ok so the next
+step is solving for the greens function
+
+ align:start position:0%
+step is solving for the greens function
+ 
+
+ align:start position:0%
+step is solving for the greens function
+we need the greens function otherwise we
+
+ align:start position:0%
+we need the greens function otherwise we
+ 
+
+ align:start position:0%
+we need the greens function otherwise we
+cannot make progress with this equation
+
+ align:start position:0%
+cannot make progress with this equation
+ 
+
+ align:start position:0%
+cannot make progress with this equation
+so I'm gonna do a simple solution of the
+
+ align:start position:0%
+so I'm gonna do a simple solution of the
+ 
+
+ align:start position:0%
+so I'm gonna do a simple solution of the
+greens function basically by doing a
+
+ align:start position:0%
+greens function basically by doing a
+ 
+
+ align:start position:0%
+greens function basically by doing a
+couple of checks and saying that is the
+
+ align:start position:0%
+couple of checks and saying that is the
+ 
+
+ align:start position:0%
+couple of checks and saying that is the
+answer we're interested in and and there
+
+ align:start position:0%
+answer we're interested in and and there
+ 
+
+ align:start position:0%
+answer we're interested in and and there
+are several possible greens functions
+
+ align:start position:0%
+are several possible greens functions
+ 
+
+ align:start position:0%
+are several possible greens functions
+and depending on the problem you're
+
+ align:start position:0%
+and depending on the problem you're
+ 
+
+ align:start position:0%
+and depending on the problem you're
+solving you choose the right greens
+
+ align:start position:0%
+solving you choose the right greens
+ 
+
+ align:start position:0%
+solving you choose the right greens
+function and we'll choose the one that
+
+ align:start position:0%
+function and we'll choose the one that
+ 
+
+ align:start position:0%
+function and we'll choose the one that
+is suitable for us now this is a
+
+ align:start position:0%
+is suitable for us now this is a
+ 
+
+ align:start position:0%
+is suitable for us now this is a
+something that can be done the general
+
+ align:start position:0%
+something that can be done the general
+ 
+
+ align:start position:0%
+something that can be done the general
+solutions can be obtained by contour
+
+ align:start position:0%
+solutions can be obtained by contour
+ 
+
+ align:start position:0%
+solutions can be obtained by contour
+integration and there are all kinds of
+
+ align:start position:0%
+integration and there are all kinds of
+ 
+
+ align:start position:0%
+integration and there are all kinds of
+nice methods to do this but in fact in
+
+ align:start position:0%
+nice methods to do this but in fact in
+ 
+
+ align:start position:0%
+nice methods to do this but in fact in
+this case it's really simple you don't
+
+ align:start position:0%
+this case it's really simple you don't
+ 
+
+ align:start position:0%
+this case it's really simple you don't
+need any of those complicated things you
+
+ align:start position:0%
+need any of those complicated things you
+ 
+
+ align:start position:0%
+need any of those complicated things you
+can just pretty much write the solution
+
+ align:start position:0%
+can just pretty much write the solution
+ 
+
+ align:start position:0%
+can just pretty much write the solution
+so that's what I'm gonna do so what do
+
+ align:start position:0%
+so that's what I'm gonna do so what do
+ 
+
+ align:start position:0%
+so that's what I'm gonna do so what do
+we need for the greens function so we
+
+ align:start position:0%
+we need for the greens function so we
+ 
+
+ align:start position:0%
+we need for the greens function so we
+have a greens function that depends on R
+
+ align:start position:0%
+have a greens function that depends on R
+ 
+
+ align:start position:0%
+have a greens function that depends on R
+minus R prime okay and so it depends on
+
+ align:start position:0%
+minus R prime okay and so it depends on
+ 
+
+ align:start position:0%
+minus R prime okay and so it depends on
+a vector so let me simplify the matter
+
+ align:start position:0%
+a vector so let me simplify the matter
+ 
+
+ align:start position:0%
+a vector so let me simplify the matter
+by saying okay since it depends on a
+
+ align:start position:0%
+by saying okay since it depends on a
+ 
+
+ align:start position:0%
+by saying okay since it depends on a
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+I'll just first calculate what is G of
+
+ align:start position:0%
+I'll just first calculate what is G of
+ 
+
+ align:start position:0%
+I'll just first calculate what is G of
+are the greens function of R when the
+
+ align:start position:0%
+are the greens function of R when the
+ 
+
+ align:start position:0%
+are the greens function of R when the
+vector is R or you can think it's when
+
+ align:start position:0%
+vector is R or you can think it's when
+ 
+
+ align:start position:0%
+vector is R or you can think it's when
+our prime is equal to zero whatever I
+
+ align:start position:0%
+our prime is equal to zero whatever I
+ 
+
+ align:start position:0%
+our prime is equal to zero whatever I
+find for G of our this one is obtained
+
+ align:start position:0%
+find for G of our this one is obtained
+ 
+
+ align:start position:0%
+find for G of our this one is obtained
+by whatever I find here put in instead R
+
+ align:start position:0%
+by whatever I find here put in instead R
+ 
+
+ align:start position:0%
+by whatever I find here put in instead R
+minus R prime so GFR is enough for what
+
+ align:start position:0%
+minus R prime so GFR is enough for what
+ 
+
+ align:start position:0%
+minus R prime so GFR is enough for what
+we want to do so it should have
+
+ align:start position:0%
+we want to do so it should have
+ 
+
+ align:start position:0%
+we want to do so it should have
+laplacian
+
+ align:start position:0%
+laplacian
+ 
+
+ align:start position:0%
+laplacian
+plus K squared on G of our should be
+
+ align:start position:0%
+plus K squared on G of our should be
+ 
+
+ align:start position:0%
+plus K squared on G of our should be
+four not 4pi it's Delta of our okay so
+
+ align:start position:0%
+four not 4pi it's Delta of our okay so
+ 
+
+ align:start position:0%
+four not 4pi it's Delta of our okay so
+we've looked at that in fact at the
+
+ align:start position:0%
+we've looked at that in fact at the
+ 
+
+ align:start position:0%
+we've looked at that in fact at the
+beginning of this course not of this
+
+ align:start position:0%
+beginning of this course not of this
+ 
+
+ align:start position:0%
+beginning of this course not of this
+course of the discussion of scattering
+
+ align:start position:0%
+course of the discussion of scattering
+ 
+
+ align:start position:0%
+course of the discussion of scattering
+we looked at this equation in fact we
+
+ align:start position:0%
+we looked at this equation in fact we
+ 
+
+ align:start position:0%
+we looked at this equation in fact we
+wanted to solve it when the right-hand
+
+ align:start position:0%
+wanted to solve it when the right-hand
+ 
+
+ align:start position:0%
+wanted to solve it when the right-hand
+side was 0 to find solutions of the
+
+ align:start position:0%
+side was 0 to find solutions of the
+ 
+
+ align:start position:0%
+side was 0 to find solutions of the
+Schrodinger equation and we found that
+
+ align:start position:0%
+Schrodinger equation and we found that
+ 
+
+ align:start position:0%
+Schrodinger equation and we found that
+this G's could be of the form e to the I
+
+ align:start position:0%
+this G's could be of the form e to the I
+ 
+
+ align:start position:0%
+this G's could be of the form e to the I
+K R plus minus IKr over R those were the
+
+ align:start position:0%
+K R plus minus IKr over R those were the
+ 
+
+ align:start position:0%
+K R plus minus IKr over R those were the
+spherical waves that solved this
+
+ align:start position:0%
+spherical waves that solved this
+ 
+
+ align:start position:0%
+spherical waves that solved this
+equation with zero potential those are
+
+ align:start position:0%
+equation with zero potential those are
+ 
+
+ align:start position:0%
+equation with zero potential those are
+our solutions now it's easy to see that
+
+ align:start position:0%
+our solutions now it's easy to see that
+ 
+
+ align:start position:0%
+our solutions now it's easy to see that
+laplacian plus K squared on this g that
+
+ align:start position:0%
+laplacian plus K squared on this g that
+ 
+
+ align:start position:0%
+laplacian plus K squared on this g that
+has a plus or minus is equal to zero for
+
+ align:start position:0%
+has a plus or minus is equal to zero for
+ 
+
+ align:start position:0%
+has a plus or minus is equal to zero for
+our different from zero the formulas for
+
+ align:start position:0%
+our different from zero the formulas for
+ 
+
+ align:start position:0%
+our different from zero the formulas for
+the laplacian that you can use for are
+
+ align:start position:0%
+the laplacian that you can use for are
+ 
+
+ align:start position:0%
+the laplacian that you can use for are
+different from zero you can check that
+
+ align:start position:0%
+different from zero you can check that
+ 
+
+ align:start position:0%
+different from zero you can check that
+is true it's easy you can use that
+
+ align:start position:0%
+is true it's easy you can use that
+ 
+
+ align:start position:0%
+is true it's easy you can use that
+formula for example that the laplacian
+
+ align:start position:0%
+formula for example that the laplacian
+ 
+
+ align:start position:0%
+formula for example that the laplacian
+is 1 over R the second should be partial
+
+ align:start position:0%
+is 1 over R the second should be partial
+ 
+
+ align:start position:0%
+is 1 over R the second should be partial
+this second the R squared R subside like
+
+ align:start position:0%
+this second the R squared R subside like
+ 
+
+ align:start position:0%
+this second the R squared R subside like
+that that formula in one 30 seconds you
+
+ align:start position:0%
+that that formula in one 30 seconds you
+ 
+
+ align:start position:0%
+that that formula in one 30 seconds you
+can see that that works for are
+
+ align:start position:0%
+can see that that works for are
+ 
+
+ align:start position:0%
+can see that that works for are
+different from zero but then there's
+
+ align:start position:0%
+different from zero but then there's
+ 
+
+ align:start position:0%
+different from zero but then there's
+also a formula that you know that
+
+ align:start position:0%
+also a formula that you know that
+ 
+
+ align:start position:0%
+also a formula that you know that
+laplacian of 1 over R from
+
+ align:start position:0%
+laplacian of 1 over R from
+ 
+
+ align:start position:0%
+laplacian of 1 over R from
+electromagnetism is minus 4pi times the
+
+ align:start position:0%
+electromagnetism is minus 4pi times the
+ 
+
+ align:start position:0%
+electromagnetism is minus 4pi times the
+delta function of r this comes from
+
+ align:start position:0%
+delta function of r this comes from
+ 
+
+ align:start position:0%
+delta function of r this comes from
+poissons equation in electromagnetism so
+
+ align:start position:0%
+poissons equation in electromagnetism so
+ 
+
+ align:start position:0%
+poissons equation in electromagnetism so
+that's saying of laplacian of the
+
+ align:start position:0%
+that's saying of laplacian of the
+ 
+
+ align:start position:0%
+that's saying of laplacian of the
+potential is the charge density is the
+
+ align:start position:0%
+potential is the charge density is the
+ 
+
+ align:start position:0%
+potential is the charge density is the
+potential for a charge the charges at R
+
+ align:start position:0%
+potential for a charge the charges at R
+ 
+
+ align:start position:0%
+potential for a charge the charges at R
+equals 0 is a singularity it's something
+
+ align:start position:0%
+equals 0 is a singularity it's something
+ 
+
+ align:start position:0%
+equals 0 is a singularity it's something
+you study so here if I put a minus 1
+
+ align:start position:0%
+you study so here if I put a minus 1
+ 
+
+ align:start position:0%
+you study so here if I put a minus 1
+over 4 PI 4G plus minus a minus 1 over 4
+
+ align:start position:0%
+over 4 PI 4G plus minus a minus 1 over 4
+ 
+
+ align:start position:0%
+over 4 PI 4G plus minus a minus 1 over 4
+pi the laplacian of this whole thing is
+
+ align:start position:0%
+pi the laplacian of this whole thing is
+ 
+
+ align:start position:0%
+pi the laplacian of this whole thing is
+zero but when you approach zero the
+
+ align:start position:0%
+zero but when you approach zero the
+ 
+
+ align:start position:0%
+zero but when you approach zero the
+laplacian of this function this function
+
+ align:start position:0%
+laplacian of this function this function
+ 
+
+ align:start position:0%
+laplacian of this function this function
+approaches just 1 over R as R goes to 0
+
+ align:start position:0%
+approaches just 1 over R as R goes to 0
+ 
+
+ align:start position:0%
+approaches just 1 over R as R goes to 0
+this goes to 1 and the laplacian of 1
+
+ align:start position:0%
+this goes to 1 and the laplacian of 1
+ 
+
+ align:start position:0%
+this goes to 1 and the laplacian of 1
+over r gives you this minus 4 pi cancels
+
+ align:start position:0%
+over r gives you this minus 4 pi cancels
+ 
+
+ align:start position:0%
+over r gives you this minus 4 pi cancels
+with that and it will give you a delta
+
+ align:start position:0%
+with that and it will give you a delta
+ 
+
+ align:start position:0%
+with that and it will give you a delta
+function so the delta function will
+
+ align:start position:0%
+function so the delta function will
+ 
+
+ align:start position:0%
+function so the delta function will
+arise correctly from this quantity so
+
+ align:start position:0%
+arise correctly from this quantity so
+ 
+
+ align:start position:0%
+arise correctly from this quantity so
+i've argued without solving this
+
+ align:start position:0%
+i've argued without solving this
+ 
+
+ align:start position:0%
+i've argued without solving this
+equation that this does give you a
+
+ align:start position:0%
+equation that this does give you a
+ 
+
+ align:start position:0%
+equation that this does give you a
+solution of the greens for the greens
+
+ align:start position:0%
+solution of the greens for the greens
+ 
+
+ align:start position:0%
+solution of the greens for the greens
+function its laplacian plus K squared is
+
+ align:start position:0%
+function its laplacian plus K squared is
+ 
+
+ align:start position:0%
+function its laplacian plus K squared is
+0 away from 0 and as you approach 0 it
+
+ align:start position:0%
+0 away from 0 and as you approach 0 it
+ 
+
+ align:start position:0%
+0 away from 0 and as you approach 0 it
+has a bright singularity to give a delta
+
+ align:start position:0%
+has a bright singularity to give a delta
+ 
+
+ align:start position:0%
+has a bright singularity to give a delta
+function so this is your greens function
+
+ align:start position:0%
+function so this is your greens function
+ 
+
+ align:start position:0%
+function so this is your greens function
+as I said many ways to derive it if you
+
+ align:start position:0%
+as I said many ways to derive it if you
+ 
+
+ align:start position:0%
+as I said many ways to derive it if you
+want see griffiths see other ways in
+
+ align:start position:0%
+want see griffiths see other ways in
+ 
+
+ align:start position:0%
+want see griffiths see other ways in
+which it can be done then you can also
+
+ align:start position:0%
+which it can be done then you can also
+ 
+
+ align:start position:0%
+which it can be done then you can also
+check this by doing properly the vector
+
+ align:start position:0%
+check this by doing properly the vector
+ 
+
+ align:start position:0%
+check this by doing properly the vector
+calculus you can take a laplacian as
+
+ align:start position:0%
+calculus you can take a laplacian as
+ 
+
+ align:start position:0%
+calculus you can take a laplacian as
+divergence of the gradient and calculate
+
+ align:start position:0%
+divergence of the gradient and calculate
+ 
+
+ align:start position:0%
+divergence of the gradient and calculate
+every step and it's it's fun to do it as
+
+ align:start position:0%
+every step and it's it's fun to do it as
+ 
+
+ align:start position:0%
+every step and it's it's fun to do it as
+well you check that this works oh this
+
+ align:start position:0%
+well you check that this works oh this
+ 
+
+ align:start position:0%
+well you check that this works oh this
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+and now we have to make choices and our
+
+ align:start position:0%
+and now we have to make choices and our
+ 
+
+ align:start position:0%
+and now we have to make choices and our
+choices are going to be adjusted to the
+
+ align:start position:0%
+choices are going to be adjusted to the
+ 
+
+ align:start position:0%
+choices are going to be adjusted to the
+problem we're trying to solve we're
+
+ align:start position:0%
+problem we're trying to solve we're
+ 
+
+ align:start position:0%
+problem we're trying to solve we're
+trying to solve a scattering problem and
+
+ align:start position:0%
+trying to solve a scattering problem and
+ 
+
+ align:start position:0%
+trying to solve a scattering problem and
+sighs zero represents a solution and
+
+ align:start position:0%
+sighs zero represents a solution and
+ 
+
+ align:start position:0%
+sighs zero represents a solution and
+from the way we thought of our waves we
+
+ align:start position:0%
+from the way we thought of our waves we
+ 
+
+ align:start position:0%
+from the way we thought of our waves we
+had sigh we'll eat to the I KZ plus F of
+
+ align:start position:0%
+had sigh we'll eat to the I KZ plus F of
+ 
+
+ align:start position:0%
+had sigh we'll eat to the I KZ plus F of
+theta and Phi e to the IKr over R so
+
+ align:start position:0%
+theta and Phi e to the IKr over R so
+ 
+
+ align:start position:0%
+theta and Phi e to the IKr over R so
+it's reasonable to try to set and we're
+
+ align:start position:0%
+it's reasonable to try to set and we're
+ 
+
+ align:start position:0%
+it's reasonable to try to set and we're
+going to find solutions by serving size
+
+ align:start position:0%
+going to find solutions by serving size
+ 
+
+ align:start position:0%
+going to find solutions by serving size
+zero to be e to the i kz it does solve
+
+ align:start position:0%
+zero to be e to the i kz it does solve
+ 
+
+ align:start position:0%
+zero to be e to the i kz it does solve
+the equation laplacian square plus K
+
+ align:start position:0%
+the equation laplacian square plus K
+ 
+
+ align:start position:0%
+the equation laplacian square plus K
+squared equals zero and then we're going
+
+ align:start position:0%
+squared equals zero and then we're going
+ 
+
+ align:start position:0%
+squared equals zero and then we're going
+to set the greens function to be G plus
+
+ align:start position:0%
+to set the greens function to be G plus
+ 
+
+ align:start position:0%
+to set the greens function to be G plus
+with a plus here because we want
+
+ align:start position:0%
+with a plus here because we want
+ 
+
+ align:start position:0%
+with a plus here because we want
+solutions of the type e to the IKr we've
+
+ align:start position:0%
+solutions of the type e to the IKr we've
+ 
+
+ align:start position:0%
+solutions of the type e to the IKr we've
+already decided those were the solutions
+
+ align:start position:0%
+already decided those were the solutions
+ 
+
+ align:start position:0%
+already decided those were the solutions
+we need and a greens function with a
+
+ align:start position:0%
+we need and a greens function with a
+ 
+
+ align:start position:0%
+we need and a greens function with a
+plus in there it's gonna generate that
+
+ align:start position:0%
+plus in there it's gonna generate that
+ 
+
+ align:start position:0%
+plus in there it's gonna generate that
+so those are fine you could have chosen
+
+ align:start position:0%
+so those are fine you could have chosen
+ 
+
+ align:start position:0%
+so those are fine you could have chosen
+another thing here an arbitrary solution
+
+ align:start position:0%
+another thing here an arbitrary solution
+ 
+
+ align:start position:0%
+another thing here an arbitrary solution
+and you could have chosen and G minus as
+
+ align:start position:0%
+and you could have chosen and G minus as
+ 
+
+ align:start position:0%
+and you could have chosen and G minus as
+well and you would get a solution of the
+
+ align:start position:0%
+well and you would get a solution of the
+ 
+
+ align:start position:0%
+well and you would get a solution of the
+Schrodinger equation it would not have
+
+ align:start position:0%
+Schrodinger equation it would not have
+ 
+
+ align:start position:0%
+Schrodinger equation it would not have
+much to do with a solution we're trying
+
+ align:start position:0%
+much to do with a solution we're trying
+ 
+
+ align:start position:0%
+much to do with a solution we're trying
+to get so let's show that this gives us
+
+ align:start position:0%
+to get so let's show that this gives us
+ 
+
+ align:start position:0%
+to get so let's show that this gives us
+this kind of solution we want to get and
+
+ align:start position:0%
+this kind of solution we want to get and
+ 
+
+ align:start position:0%
+this kind of solution we want to get and
+gives us already a formula for the
+
+ align:start position:0%
+gives us already a formula for the
+ 
+
+ align:start position:0%
+gives us already a formula for the
+scattering amplitude so let's let's do
+
+ align:start position:0%
+scattering amplitude so let's let's do
+ 
+
+ align:start position:0%
+scattering amplitude so let's let's do
+that for that we just need to write what
+
+ align:start position:0%
+that for that we just need to write what
+ 
+
+ align:start position:0%
+that for that we just need to write what
+the greens function is and approximate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it will be a first step okay so what
+
+ align:start position:0%
+so it will be a first step okay so what
+ 
+
+ align:start position:0%
+so it will be a first step okay so what
+do we have
+
+ align:start position:0%
+do we have
+ 
+
+ align:start position:0%
+do we have
+sigh of our is equal to e to the i ka
+
+ align:start position:0%
+sigh of our is equal to e to the i ka
+ 
+
+ align:start position:0%
+sigh of our is equal to e to the i ka
+I'm writing up this top equation but we
+
+ align:start position:0%
+I'm writing up this top equation but we
+ 
+
+ align:start position:0%
+I'm writing up this top equation but we
+now write it with the right boundary
+
+ align:start position:0%
+now write it with the right boundary
+ 
+
+ align:start position:0%
+now write it with the right boundary
+conditions which correspond to upsize
+
+ align:start position:0%
+conditions which correspond to upsize
+ 
+
+ align:start position:0%
+conditions which correspond to upsize
+zero and a particularly greens function
+
+ align:start position:0%
+zero and a particularly greens function
+ 
+
+ align:start position:0%
+zero and a particularly greens function
+the cube are prime G of R minus R prime
+
+ align:start position:0%
+the cube are prime G of R minus R prime
+ 
+
+ align:start position:0%
+the cube are prime G of R minus R prime
+u of our prime all those are vectors and
+
+ align:start position:0%
+u of our prime all those are vectors and
+ 
+
+ align:start position:0%
+u of our prime all those are vectors and
+sy of our prime all those are vectors
+
+ align:start position:0%
+sy of our prime all those are vectors
+ 
+
+ align:start position:0%
+sy of our prime all those are vectors
+except G which is pretty in that it is
+
+ align:start position:0%
+except G which is pretty in that it is
+ 
+
+ align:start position:0%
+except G which is pretty in that it is
+spherically symmetric this G plus minus
+
+ align:start position:0%
+spherically symmetric this G plus minus
+ 
+
+ align:start position:0%
+spherically symmetric this G plus minus
+of our just depends on the magnitude of
+
+ align:start position:0%
+of our just depends on the magnitude of
+ 
+
+ align:start position:0%
+of our just depends on the magnitude of
+R which is very nice okay so a couple of
+
+ align:start position:0%
+R which is very nice okay so a couple of
+ 
+
+ align:start position:0%
+R which is very nice okay so a couple of
+things that we can do here and most
+
+ align:start position:0%
+things that we can do here and most
+ 
+
+ align:start position:0%
+things that we can do here and most
+everybody would do let's G plus of R
+
+ align:start position:0%
+everybody would do let's G plus of R
+ 
+
+ align:start position:0%
+everybody would do let's G plus of R
+minus R prime is equal to minus 1 over 4
+
+ align:start position:0%
+minus R prime is equal to minus 1 over 4
+ 
+
+ align:start position:0%
+minus R prime is equal to minus 1 over 4
+pi e to the I K length of our minus R
+
+ align:start position:0%
+pi e to the I K length of our minus R
+ 
+
+ align:start position:0%
+pi e to the I K length of our minus R
+prime that's what this is supposed to be
+
+ align:start position:0%
+prime that's what this is supposed to be
+ 
+
+ align:start position:0%
+prime that's what this is supposed to be
+over length of our minus R prime
+
+ align:start position:0%
+over length of our minus R prime
+ 
+
+ align:start position:0%
+over length of our minus R prime
+remember I said to you that whenever we
+
+ align:start position:0%
+remember I said to you that whenever we
+ 
+
+ align:start position:0%
+remember I said to you that whenever we
+had G of r then to get the one we need
+
+ align:start position:0%
+had G of r then to get the one we need
+ 
+
+ align:start position:0%
+had G of r then to get the one we need
+we'll just have to replace the r by r
+
+ align:start position:0%
+we'll just have to replace the r by r
+ 
+
+ align:start position:0%
+we'll just have to replace the r by r
+minus r prime and here this little r or
+
+ align:start position:0%
+minus r prime and here this little r or
+ 
+
+ align:start position:0%
+minus r prime and here this little r or
+r without the vector is the magnitude of
+
+ align:start position:0%
+r without the vector is the magnitude of
+ 
+
+ align:start position:0%
+r without the vector is the magnitude of
+this vector so we've put the magnitude
+
+ align:start position:0%
+this vector so we've put the magnitude
+ 
+
+ align:start position:0%
+this vector so we've put the magnitude
+of those vectors there now people look
+
+ align:start position:0%
+of those vectors there now people look
+ 
+
+ align:start position:0%
+of those vectors there now people look
+for approximations in here so here is
+
+ align:start position:0%
+for approximations in here so here is
+ 
+
+ align:start position:0%
+for approximations in here so here is
+what we need to do imagine you are the
+
+ align:start position:0%
+what we need to do imagine you are the
+ 
+
+ align:start position:0%
+what we need to do imagine you are the
+origin here is a potential and you have
+
+ align:start position:0%
+origin here is a potential and you have
+ 
+
+ align:start position:0%
+origin here is a potential and you have
+your system of coordinates you are
+
+ align:start position:0%
+your system of coordinates you are
+ 
+
+ align:start position:0%
+your system of coordinates you are
+integrating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over places where the potential exists
+
+ align:start position:0%
+over places where the potential exists
+ 
+
+ align:start position:0%
+over places where the potential exists
+so the r-prime that you're integrating
+
+ align:start position:0%
+so the r-prime that you're integrating
+ 
+
+ align:start position:0%
+so the r-prime that you're integrating
+remains inside the range of the
+
+ align:start position:0%
+remains inside the range of the
+ 
+
+ align:start position:0%
+remains inside the range of the
+potential here is zero and then there's
+
+ align:start position:0%
+potential here is zero and then there's
+ 
+
+ align:start position:0%
+potential here is zero and then there's
+an R which is where you are looking at
+
+ align:start position:0%
+an R which is where you are looking at
+ 
+
+ align:start position:0%
+an R which is where you are looking at
+and there's an angle between these two
+
+ align:start position:0%
+and there's an angle between these two
+ 
+
+ align:start position:0%
+and there's an angle between these two
+maybe I should I mean make the angle a
+
+ align:start position:0%
+maybe I should I mean make the angle a
+ 
+
+ align:start position:0%
+maybe I should I mean make the angle a
+little bigger smaller I mean R and if in
+
+ align:start position:0%
+little bigger smaller I mean R and if in
+ 
+
+ align:start position:0%
+little bigger smaller I mean R and if in
+general we look always far enough this
+
+ align:start position:0%
+general we look always far enough this
+ 
+
+ align:start position:0%
+general we look always far enough this
+is an exact solution but we might as
+
+ align:start position:0%
+is an exact solution but we might as
+ 
+
+ align:start position:0%
+is an exact solution but we might as
+well considering consider looking at
+
+ align:start position:0%
+well considering consider looking at
+ 
+
+ align:start position:0%
+well considering consider looking at
+size that are located far from the
+
+ align:start position:0%
+size that are located far from the
+ 
+
+ align:start position:0%
+size that are located far from the
+potential so we have the idea of what
+
+ align:start position:0%
+potential so we have the idea of what
+ 
+
+ align:start position:0%
+potential so we have the idea of what
+should we do with this terms one thing
+
+ align:start position:0%
+should we do with this terms one thing
+ 
+
+ align:start position:0%
+should we do with this terms one thing
+you can do is to say that in the
+
+ align:start position:0%
+you can do is to say that in the
+ 
+
+ align:start position:0%
+you can do is to say that in the
+denominator here R minus R prime is good
+
+ align:start position:0%
+denominator here R minus R prime is good
+ 
+
+ align:start position:0%
+denominator here R minus R prime is good
+enough to set it to R in the denominator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for the numerator however it's a lot
+
+ align:start position:0%
+and for the numerator however it's a lot
+ 
+
+ align:start position:0%
+and for the numerator however it's a lot
+more sensitive because you have a K here
+
+ align:start position:0%
+more sensitive because you have a K here
+ 
+
+ align:start position:0%
+more sensitive because you have a K here
+and depending on whether K is large or
+
+ align:start position:0%
+and depending on whether K is large or
+ 
+
+ align:start position:0%
+and depending on whether K is large or
+small that small difference in our minus
+
+ align:start position:0%
+small that small difference in our minus
+ 
+
+ align:start position:0%
+small that small difference in our minus
+R prime if you're estimating this and
+
+ align:start position:0%
+R prime if you're estimating this and
+ 
+
+ align:start position:0%
+R prime if you're estimating this and
+you make an error comparable with the
+
+ align:start position:0%
+you make an error comparable with the
+ 
+
+ align:start position:0%
+you make an error comparable with the
+wavelength of your particle you make a
+
+ align:start position:0%
+wavelength of your particle you make a
+ 
+
+ align:start position:0%
+wavelength of your particle you make a
+big mistake if you're far away you're a
+
+ align:start position:0%
+big mistake if you're far away you're a
+ 
+
+ align:start position:0%
+big mistake if you're far away you're a
+hundred times farther than the range of
+
+ align:start position:0%
+hundred times farther than the range of
+ 
+
+ align:start position:0%
+hundred times farther than the range of
+the potential here you're making a 1
+
+ align:start position:0%
+the potential here you're making a 1
+ 
+
+ align:start position:0%
+the potential here you're making a 1
+percent error no problem but if you're
+
+ align:start position:0%
+percent error no problem but if you're
+ 
+
+ align:start position:0%
+percent error no problem but if you're
+making a 1 percent error in the estimate
+
+ align:start position:0%
+making a 1 percent error in the estimate
+ 
+
+ align:start position:0%
+making a 1 percent error in the estimate
+of this that might be still comparable
+
+ align:start position:0%
+of this that might be still comparable
+ 
+
+ align:start position:0%
+of this that might be still comparable
+to the wavelength of this K so you have
+
+ align:start position:0%
+to the wavelength of this K so you have
+ 
+
+ align:start position:0%
+to the wavelength of this K so you have
+to be a lot more careful in the face
+
+ align:start position:0%
+to be a lot more careful in the face
+ 
+
+ align:start position:0%
+to be a lot more careful in the face
+than you have to be on the other one so
+
+ align:start position:0%
+than you have to be on the other one so
+ 
+
+ align:start position:0%
+than you have to be on the other one so
+on the face for the number for the face
+
+ align:start position:0%
+on the face for the number for the face
+ 
+
+ align:start position:0%
+on the face for the number for the face
+face
+
+ align:start position:0%
+face
+ 
+
+ align:start position:0%
+face
+we will take our - our prime equal to R
+
+ align:start position:0%
+we will take our - our prime equal to R
+ 
+
+ align:start position:0%
+we will take our - our prime equal to R
+minus n R Prime
+
+ align:start position:0%
+minus n R Prime
+ 
+
+ align:start position:0%
+minus n R Prime
+so what is n n is a unit vector in this
+
+ align:start position:0%
+so what is n n is a unit vector in this
+ 
+
+ align:start position:0%
+so what is n n is a unit vector in this
+direction and indeed approximately the
+
+ align:start position:0%
+direction and indeed approximately the
+ 
+
+ align:start position:0%
+direction and indeed approximately the
+this distance here is approximately
+
+ align:start position:0%
+this distance here is approximately
+ 
+
+ align:start position:0%
+this distance here is approximately
+equal to the distance R minus the
+
+ align:start position:0%
+equal to the distance R minus the
+ 
+
+ align:start position:0%
+equal to the distance R minus the
+projection of our prime into this one so
+
+ align:start position:0%
+projection of our prime into this one so
+ 
+
+ align:start position:0%
+projection of our prime into this one so
+that is your approximate distance so
+
+ align:start position:0%
+that is your approximate distance so
+ 
+
+ align:start position:0%
+that is your approximate distance so
+here is the final formula we're gonna
+
+ align:start position:0%
+here is the final formula we're gonna
+ 
+
+ align:start position:0%
+here is the final formula we're gonna
+write today I'm running out of time
+
+ align:start position:0%
+write today I'm running out of time
+ 
+
+ align:start position:0%
+write today I'm running out of time
+but that's what we wanted to end up with
+
+ align:start position:0%
+but that's what we wanted to end up with
+ 
+
+ align:start position:0%
+but that's what we wanted to end up with
+so here is what we get so g + of R minus
+
+ align:start position:0%
+so here is what we get so g + of R minus
+ 
+
+ align:start position:0%
+so here is what we get so g + of R minus
+R prime has become minus 1 over 4 PI R
+
+ align:start position:0%
+R prime has become minus 1 over 4 PI R
+ 
+
+ align:start position:0%
+R prime has become minus 1 over 4 PI R
+the denominator is R there's an e to the
+
+ align:start position:0%
+the denominator is R there's an e to the
+ 
+
+ align:start position:0%
+the denominator is R there's an e to the
+IKr and then e to the minus I K and R
+
+ align:start position:0%
+IKr and then e to the minus I K and R
+ 
+
+ align:start position:0%
+IKr and then e to the minus I K and R
+Prime so that's and the arrows are
+
+ align:start position:0%
+Prime so that's and the arrows are
+ 
+
+ align:start position:0%
+Prime so that's and the arrows are
+crucial here if I don't put an arrow
+
+ align:start position:0%
+crucial here if I don't put an arrow
+ 
+
+ align:start position:0%
+crucial here if I don't put an arrow
+somewhere it probably means something so
+
+ align:start position:0%
+somewhere it probably means something so
+ 
+
+ align:start position:0%
+somewhere it probably means something so
+I of R is equal to e to the i kz + minus
+
+ align:start position:0%
+I of R is equal to e to the i kz + minus
+ 
+
+ align:start position:0%
+I of R is equal to e to the i kz + minus
+1 over 4 pi r the integral over R prime
+
+ align:start position:0%
+1 over 4 pi r the integral over R prime
+ 
+
+ align:start position:0%
+1 over 4 pi r the integral over R prime
+doesn't care about this the cube R prime
+
+ align:start position:0%
+doesn't care about this the cube R prime
+ 
+
+ align:start position:0%
+doesn't care about this the cube R prime
+e to the minus I K and dot R prime times
+
+ align:start position:0%
+e to the minus I K and dot R prime times
+ 
+
+ align:start position:0%
+e to the minus I K and dot R prime times
+U of our prime of CI of our prime all
+
+ align:start position:0%
+U of our prime of CI of our prime all
+ 
+
+ align:start position:0%
+U of our prime of CI of our prime all
+that x let me take the our out into the
+
+ align:start position:0%
+that x let me take the our out into the
+ 
+
+ align:start position:0%
+that x let me take the our out into the
+I K R over
+
+ align:start position:0%
+I K R over
+ 
+
+ align:start position:0%
+I K R over
+are so look at what we've obtained I
+
+ align:start position:0%
+are so look at what we've obtained I
+ 
+
+ align:start position:0%
+are so look at what we've obtained I
+just rewrote finally this expression for
+
+ align:start position:0%
+just rewrote finally this expression for
+ 
+
+ align:start position:0%
+just rewrote finally this expression for
+the greens function over there with the
+
+ align:start position:0%
+the greens function over there with the
+ 
+
+ align:start position:0%
+the greens function over there with the
+integral over our prime and the greens
+
+ align:start position:0%
+integral over our prime and the greens
+ 
+
+ align:start position:0%
+integral over our prime and the greens
+function here you have this quantity in
+
+ align:start position:0%
+function here you have this quantity in
+ 
+
+ align:start position:0%
+function here you have this quantity in
+brackets this quantity in brackets here
+
+ align:start position:0%
+brackets this quantity in brackets here
+ 
+
+ align:start position:0%
+brackets this quantity in brackets here
+is nothing but the F of theta phi of the
+
+ align:start position:0%
+is nothing but the F of theta phi of the
+ 
+
+ align:start position:0%
+is nothing but the F of theta phi of the
+scattering amplitude you have this equal
+
+ align:start position:0%
+scattering amplitude you have this equal
+ 
+
+ align:start position:0%
+scattering amplitude you have this equal
+to that plus e to the IKr over R so
+
+ align:start position:0%
+to that plus e to the IKr over R so
+ 
+
+ align:start position:0%
+to that plus e to the IKr over R so
+we'll continue that next time and finish
+
+ align:start position:0%
+we'll continue that next time and finish
+ 
+
+ align:start position:0%
+we'll continue that next time and finish
+up with scattering crowding the first
+
+ align:start position:0%
+up with scattering crowding the first
+ 
+
+ align:start position:0%
+up with scattering crowding the first
+half of the next lecture
\ No newline at end of file
diff --git a/2Op3QLzMgSY.txt b/2Op3QLzMgSY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2d063943a275ceb338ca889abcdc5f582de49e34
--- /dev/null
+++ b/2Op3QLzMgSY.txt
@@ -0,0 +1,3219 @@
+[MUSIC PLAYING]
+
+PROFESSOR: I'd like to
+welcome you to this
+
+course on computer science.
+
+Actually, that's a terrible
+way to start.
+
+Computer science is a terrible
+name for this business.
+
+First of all, it's
+not a science.
+
+It might be engineering or it
+might be art, but we'll
+
+actually see that computer
+so-called science actually has
+
+a lot in common with magic,
+and we'll see
+
+that in this course.
+
+So it's not a science.
+
+It's also not really very
+much about computers.
+
+And it's not about computers in
+the same sense that physics
+
+is not really about particle
+accelerators, and biology is
+
+not really about microscopes
+and petri dishes.
+
+And it's not about computers
+in the same sense that
+
+geometry is not really about
+using surveying instruments.
+
+In fact, there's a lot of
+commonality between computer
+
+science and geometry.
+
+Geometry, first of all,
+is another subject
+
+with a lousy name.
+
+The name comes from Gaia,
+meaning the Earth, and metron,
+
+meaning to measure.
+
+Geometry originally
+meant measuring
+
+the Earth or surveying.
+
+And the reason for that was
+that, thousands of years ago,
+
+the Egyptian priesthood
+developed the rudiments of
+
+geometry in order to figure
+out how to restore the
+
+boundaries of fields that were
+destroyed in the annual
+
+flooding of the Nile.
+
+And to the Egyptians who did
+that, geometry really was the
+
+use of surveying instruments.
+
+Now, the reason that we think
+computer science is about
+
+computers is pretty much the
+same reason that the Egyptians
+
+thought geometry was about
+surveying instruments.
+
+And that is, when some field
+is just getting started and
+
+you don't really understand it
+very well, it's very easy to
+
+confuse the essence of what
+you're doing with the tools
+
+that you use.
+
+And indeed, on some absolute
+scale of things, we probably
+
+know less about the essence of
+computer science than the
+
+ancient Egyptians really
+knew about geometry.
+
+Well, what do I mean by the
+essence of computer science?
+
+What do I mean by the
+essence of geometry?
+
+See, it's certainly true that
+these Egyptians went off and
+
+used surveying instruments, but
+when we look back on them
+
+after a couple of thousand
+years, we say, gee, what they
+
+were doing, the important stuff
+they were doing, was to
+
+begin to formalize notions about
+space and time, to start
+
+a way of talking about
+mathematical truths formally.
+
+That led to the axiomatic
+method.
+
+That led to sort of all of
+modern mathematics, figuring
+
+out a way to talk precisely
+about so-called declarative
+
+knowledge, what is true.
+
+Well, similarly, I think in the
+future people will look
+
+back and say, yes, those
+primitives in the 20th century
+
+were fiddling around with
+these gadgets called
+
+computers, but really what they
+were doing is starting to
+
+learn how to formalize
+intuitions about process, how
+
+to do things, starting to
+develop a way to talk
+
+precisely about how-to
+knowledge, as opposed to
+
+geometry that talks about
+what is true.
+
+Let me give you an
+example of that.
+
+Let's take a look.
+
+Here is a piece of mathematics
+that says what
+
+a square root is.
+
+The square root of X is the
+number Y, such that Y squared
+
+is equal to X and Y
+is greater than 0.
+
+Now, that's a fine piece of
+mathematics, but just telling
+
+you what a square root is
+doesn't really say anything
+
+about how you might go
+out and find one.
+
+So let's contrast that with a
+piece of imperative knowledge,
+
+how you might go out and
+find a square root.
+
+This, in fact, also comes
+from Egypt, not
+
+ancient, ancient Egypt.
+
+This is an algorithm due to
+Heron of Alexandria, called
+
+how to find a square root
+by successive averaging.
+
+And what it says is that, in
+order to find a square root,
+
+you make a guess, you
+improve that guess--
+
+and the way you improve the
+guess is to average the guess
+
+and X over the guess, and we'll
+talk a little bit later
+
+about why that's a reasonable
+thing--
+
+and you keep improving the guess
+until it's good enough.
+
+That's a method.
+
+That's how to do something
+as opposed to declarative
+
+knowledge that says what
+you're looking for.
+
+That's a process.
+
+Well, what's a process
+in general?
+
+It's kind of hard to say.
+
+You can think of it as like a
+magical spirit that sort of
+
+lives in the computer
+and does something.
+
+And the thing that directs a
+process is a pattern of rules
+
+called a procedure.
+
+So procedures are the spells,
+if you like, that control
+
+these magical spirits that
+are the processes.
+
+I guess you know everyone needs
+a magical language, and
+
+sorcerers, real sorcerers, use
+ancient Arcadian or Sumerian
+
+or Babylonian or whatever.
+
+We're going to conjure our
+spirits in a magical language
+
+called Lisp, which is a language
+designed for talking
+
+about, for casting the spells
+that are procedures to direct
+
+the processes.
+
+Now, it's very easy
+to learn Lisp.
+
+In fact, in a few minutes,
+I'm going to teach you,
+
+essentially, all of Lisp.
+
+I'm going to teach you,
+essentially, all of the rules.
+
+And you shouldn't find that
+particularly surprising.
+
+That's sort of like saying it's
+very easy to learn the
+
+rules of chess.
+
+And indeed, in a few minutes,
+you can tell somebody the
+
+rules of chess.
+
+But of course, that's very
+different from saying you
+
+understand the implications of
+those rules and how to use
+
+those rules to become a
+masterful chess player.
+
+Well, Lisp is the same way.
+
+We're going to state the rules
+in a few minutes, and it'll be
+
+very easy to see.
+
+But what's really hard is going
+to be the implications
+
+of those rules, how you exploit
+those rules to be a
+
+master programmer.
+
+And the implications of those
+rules are going to take us
+
+the, well, the whole rest of
+the subject and, of course,
+
+way beyond.
+
+OK, so in computer science,
+we're in the business of
+
+formalizing this sort of how-to
+imperative knowledge,
+
+how to do stuff.
+
+And the real issues of computer
+science are, of
+
+course, not telling people
+how to do square roots.
+
+Because if that was
+all it was, there
+
+wouldn't be no big deal.
+
+The real problems come when we
+try to build very, very large
+
+systems, computer programs that
+are thousands of pages
+
+long, so long that nobody can
+really hold them in their
+
+heads all at once.
+
+And the only reason that that's
+possible is because
+
+there are techniques for
+controlling the complexity of
+
+these large systems. And these
+techniques that are
+
+controlling complexity
+are what this
+
+course is really about.
+
+And in some sense, that's
+really what
+
+computer science is about.
+
+Now, that may seem like a very
+strange thing to say.
+
+Because after all, a lot of
+people besides computer
+
+scientists deal with controlling
+complexity.
+
+A large airliner is an extremely
+complex system, and
+
+the aeronautical engineers who
+design that are dealing with
+
+immense complexity.
+
+But there's a difference
+between that kind of
+
+complexity and what we deal
+with in computer science.
+
+And that is that computer
+science, in some
+
+sense, isn't real.
+
+You see, when an engineer is
+designing a physical system,
+
+that's made out of real parts.
+
+The engineers who worry about
+that have to address problems
+
+of tolerance and approximation
+and noise in the system.
+
+So for example, as an electrical
+engineer, I can go
+
+off and easily build a one-stage
+amplifier or a
+
+two-stage amplifier, and I can
+imagine cascading a lot of
+
+them to build a million-stage
+amplifier.
+
+But it's ridiculous to build
+such a thing, because long
+
+before the millionth stage,
+the thermal noise in those
+
+components way at the beginning
+is going to get
+
+amplified and make the whole
+thing meaningless.
+
+Computer science deals with
+idealized components.
+
+We know as much as we want about
+these little program and
+
+data pieces that we're fitting
+things together.
+
+We don't have to worry
+about tolerance.
+
+And that means that, in building
+a large program,
+
+there's not all that much
+difference between what I can
+
+build and what I can imagine,
+because the parts are these
+
+abstract entities that I
+know as much as I want.
+
+I know about them as precisely
+as I'd like.
+
+So as opposed to other kinds
+of engineering, where the
+
+constraints on what you can
+build are the constraints of
+
+physical systems, the
+constraints of physics and
+
+noise and approximation, the
+constraints imposed in
+
+building large software systems
+are the limitations of
+
+our own minds.
+
+So in that sense, computer
+science is like an abstract
+
+form of engineering.
+
+It's the kind of engineering
+where you ignore the
+
+constraints that are
+imposed by reality.
+
+Well, what are some of
+these techniques?
+
+They're not special to
+computer science.
+
+First technique, which is used
+in all of engineering, is a
+
+kind of abstraction called
+black-box abstraction.
+
+Take something and build
+a box about it.
+
+Let's see, for example, if we
+looked at that square root
+
+method, I might want to take
+that and build a box.
+
+That sort of says, to find the
+square root of X. And that
+
+might be a whole complicated
+set of rules.
+
+And that might end up being a
+kind of thing where I can put
+
+in, say, 36 and say, what's
+the square root of 36?
+
+And out comes six.
+
+And the important thing is that
+I'd like to design that
+
+so that if George comes along
+and would like to compute,
+
+say, the square root of A plus
+the square root of B, he can
+
+take this thing and use it as
+a module without having to
+
+look inside and build something
+that looks like
+
+this, like an A and a B and a
+square root box and another
+
+square root box and then
+something that adds that would
+
+put out the answer.
+
+And you can see, just from the
+fact that I want to do that,
+
+is from George's point of view,
+the internals of what's
+
+in here should not
+be important.
+
+So for instance, it shouldn't
+matter that, when I wrote
+
+this, I said I want to find the
+square root of X. I could
+
+have said the square root of Y,
+or the square root of A, or
+
+anything at all.
+
+That's the fundamental notion of
+putting something in a box
+
+using black-box abstraction
+to suppress detail.
+
+And the reason for that is you
+want to go off and build
+
+bigger boxes.
+
+Now, there's another reason
+for doing black-box
+
+abstraction other than you want
+to suppress detail for
+
+building bigger boxes.
+
+Sometimes you want to say that
+your way of doing something,
+
+your how-to method, is an
+instance of a more general
+
+thing, and you'd like your
+language to be able to express
+
+that generality.
+
+Let me show you another example
+
+sticking with square roots.
+
+Let's go back and take another
+look at that slide with the
+
+square root algorithm on it.
+
+Remember what that says.
+
+That says, in order to do
+something, I make a guess, and
+
+I improve that guess,
+and I sort of keep
+
+improving that guess.
+
+So there's the general strategy
+of, I'm looking for
+
+something, and the way
+I find it is that I
+
+keep improving it.
+
+Now, that's a particular case
+of another kind of strategy
+
+for finding a fixed point
+of something.
+
+So you have a fixed point
+of a function.
+
+A fixed point of a function
+is something, is a value.
+
+A fixed point of a function F is
+a value Y, such that F of Y
+
+equals Y. And the way I might do
+that is start with a guess.
+
+And then if I want something
+that doesn't change when I
+
+keep applying F, is I'll keep
+applying F over and over until
+
+that result doesn't
+change very much.
+
+So there's a general strategy.
+
+And then, for example, to
+compute the square root of X,
+
+I can try and find a fixed point
+of the function which
+
+takes Y to the average of X/Y.
+And the idea that is that if I
+
+really had Y equal to the square
+root of X, then Y and
+
+X/Y would be the same value.
+
+They'd both be the square root
+of X, because X over the
+
+square root of X is the
+square root of X.
+
+And so the average if Y were
+equal to the square of X, then
+
+the average wouldn't change.
+
+So the square root of X
+is a fixed point of
+
+that particular function.
+
+Now, what I'd like to have,
+I'd like to express the
+
+general strategy for finding
+fixed points.
+
+So what I might imagine doing,
+is to find, is to be able to
+
+use my language to define a box
+that says "fixed point,"
+
+just like I could make a box
+that says "square root." And
+
+I'd like to be able to express
+this in my language.
+
+So I'd like to express not only
+the imperative how-to
+
+knowledge of a particular thing
+like square root, but
+
+I'd like to be able to express
+the imperative knowledge of
+
+how to do a general thing like
+how to find fixed point.
+
+And in fact, let's go back and
+look at that slide again.
+
+See, not only is this a piece
+of imperative knowledge, how
+
+to find a fixed point, but
+over here on the bottom,
+
+there's another piece of
+imperative knowledge which
+
+says, one way to compute square
+root is to apply this
+
+general fixed point method.
+
+So I'd like to also
+be able to express
+
+that imperative knowledge.
+
+What would that look like?
+
+That would say, this fixed point
+box is such that if I
+
+input to it the function that
+takes Y to the average of Y
+
+and X/Y, then what should come
+out of that fixed point box is
+
+a method for finding
+square roots.
+
+So in these boxes we're
+building, we're not only
+
+building boxes that you input
+numbers and output numbers,
+
+we're going to be building in
+boxes that, in effect, compute
+
+methods like finding
+square root.
+
+And my take is their inputs
+functions, like Y goes to the
+
+average of Y and X/Y. The reason
+we want to do that, the
+
+reason this is a procedure, will
+end up being a procedure,
+
+as we'll see, whose value is
+another procedure, the reason
+
+we want to do that is because
+procedures are going to be our
+
+ways of talking about imperative
+knowledge.
+
+And the way to make that very
+powerful is to be able to talk
+
+about other kinds
+of knowledge.
+
+So here is a procedure that, in
+effect, talks about another
+
+procedure, a general strategy
+that itself talks about
+
+general strategies.
+
+Well, our first topic in this
+course-- there'll be three
+
+major topics-- will be black-box
+abstraction.
+
+Let's look at that in a little
+bit more detail.
+
+What we're going to do is we
+will start out talking about
+
+how Lisp is built up out
+of primitive objects.
+
+What does the language
+supply with us?
+
+And we'll see that there are
+primitive procedures and
+
+primitive data.
+
+Then we're going to see, how do
+you take those primitives
+
+and combine them to make more
+complicated things, means of
+
+combination?
+
+And what we'll see is that
+there are ways of putting
+
+things together, putting
+primitive procedures together
+
+to make more complicated
+procedures.
+
+And we'll see how to put
+primitive data together to
+
+make compound data.
+
+Then we'll say, well, having
+made those compounds things,
+
+how do you abstract them?
+
+How do you put those black boxes
+around them so you can
+
+use them as components in
+more complex things?
+
+And we'll see that's done by
+defining procedures and a
+
+technique for dealing with
+compound data called data
+
+abstraction.
+
+And then, what's maybe the most
+important thing, is going
+
+from just the rules to how
+does an expert work?
+
+How do you express common
+patterns of doing things, like
+
+saying, well, there's a general
+method of fixed point
+
+and square root is a particular
+case of that?
+
+And we're going to use--
+
+I've already hinted at it--
+something called higher-order
+
+procedures, namely procedures
+whose inputs and outputs are
+
+themselves procedures.
+
+And then we'll also see
+something very interesting.
+
+We'll see, as we go further and
+further on and become more
+
+abstract, there'll be very--
+
+well, the line between what we
+consider to be data and what
+
+we consider to be procedures
+is going to blur at an
+
+incredible rate.
+
+Well, that's our first
+subject, black-box
+
+abstraction.
+
+Let's look at the
+second topic.
+
+I can introduce it like this.
+
+See, suppose I want to
+express the idea--
+
+remember, we're talking
+about ideas--
+
+suppose I want to express the
+idea that I can take something
+
+and multiply it by the sum
+of two other things.
+
+So for example, I might say,
+if I had one and three and
+
+multiply that by two,
+I get eight.
+
+But I'm talking about the
+general idea of what's called
+
+linear combination, that you
+can add two things and
+
+multiply them by
+something else.
+
+It's very easy when I think
+about it for numbers, but
+
+suppose I also want to use that
+same idea to think about,
+
+I could add two vectors, a1 and
+a2, and then scale them by
+
+some factor x and get
+another vector.
+
+Or I might say, I want to think
+about a1 and a2 as being
+
+polynomials, and I might want
+to add those two polynomials
+
+and then multiply them by two to
+get a more complicated one.
+
+Or a1 and a2 might be electrical
+signals, and I
+
+might want to think about
+summing those two electrical
+
+signals and then putting the
+whole thing through an
+
+amplifier, multiplying
+it by some
+
+factor of two or something.
+
+The idea is I want to
+think about the
+
+general notion of that.
+
+Now, if our language is going
+to be good language for
+
+expressing those kind of general
+ideas, if I really,
+
+really can do that, I'd like to
+be able to say I'm going to
+
+multiply by x the sum of a1 and
+a2, and I'd like that to
+
+express the general idea of all
+different kinds of things
+
+that a1 and a2 could be.
+
+Now, if you think about that,
+there's a problem, because
+
+after all, the actual primitive
+operations that go
+
+on in the machine are obviously
+going to be
+
+different if I'm adding two
+numbers than if I'm adding two
+
+polynomials, or if I'm adding
+the representation of two
+
+electrical signals
+or wave forms.
+
+Somewhere, there has to be the
+knowledge of the kinds of
+
+various things that you
+can add and the
+
+ways of adding them.
+
+Now, to construct such a system,
+the question is, where
+
+do I put that knowledge?
+
+How do I think about
+the different kinds
+
+of choices I have?
+
+And if tomorrow George comes up
+with a new kind of object
+
+that might be added and
+multiplied, how do I add
+
+George's new object to the
+system without screwing up
+
+everything that was
+already there?
+
+Well, that's going to be the
+second big topic, the way of
+
+controlling that kind
+of complexity.
+
+And the way you do that is by
+establishing conventional
+
+interfaces, agreed upon ways of
+plugging things together.
+
+Just like in electrical
+engineering, people have
+
+standard impedances for
+connectors, and then you know
+
+if you build something with
+one of those standard
+
+impedances, you can plug it
+together with something else.
+
+So that's going to be our
+second large topic,
+
+conventional interfaces.
+
+What we're going to see is,
+first, we're going to talk
+
+about the problem of generic
+operations, which is the one I
+
+alluded to, things like "plus"
+that have to work with all
+
+different kinds of data.
+
+So we talk about generic
+operations.
+
+Then we're going to talk about
+really large-scale structures.
+
+How do you put together very
+large programs that model the
+
+kinds of complex systems
+in the real world that
+
+you'd like to model?
+
+And what we're going to see
+is that there are two very
+
+important metaphors for putting
+together such systems.
+
+One is called object-oriented
+programming, where you sort of
+
+think of your system as a kind
+of society full of little
+
+things that interact by sending
+
+information between them.
+
+And then the second one is
+operations on aggregates,
+
+called streams, where you think
+of a large system put
+
+together kind of like a signal
+processing engineer puts
+
+together a large electrical
+system.
+
+That's going to be
+our second topic.
+
+Now, the third thing we're going
+to come to, the third
+
+basic technique for controlling
+complexity, is
+
+making new languages.
+
+Because sometimes, when you're
+sort of overwhelmed by the
+
+complexity of a design, the
+way that you control that
+
+complexity is to pick a
+new design language.
+
+And the purpose of the new
+design language will be to
+
+highlight different aspects
+of the system.
+
+It will suppress some kinds of
+details and emphasize other
+
+kinds of details.
+
+This is going to be the most
+magical part of the course.
+
+We're going to start out by
+actually looking at the
+
+technology for building new
+computer languages.
+
+The first thing we're going to
+do is actually build in Lisp.
+
+We're going to express in Lisp
+the process of interpreting
+
+Lisp itself.
+
+And that's going to be a very
+sort of self-circular thing.
+
+There's a little mystical
+symbol that
+
+has to do with that.
+
+The process of interpreting Lisp
+is sort of a giant wheel
+
+of two processes, apply and
+eval, which sort of constantly
+
+reduce expressions
+to each other.
+
+Then we're going to see all
+sorts of other magical things.
+
+Here's another magical symbol.
+
+This is sort of the Y operator,
+which is, in some
+
+sense, the expression
+of infinity inside
+
+our procedural language.
+
+We'll take a look at that.
+
+In any case, this section
+of the course is called
+
+Metalinguistic Abstraction,
+abstracting by talking about
+
+how you construct
+new languages.
+
+As I said, we're going to start
+out by looking at the
+
+process of interpretation.
+
+We're going to look
+at this apply-eval
+
+loop, and build Lisp.
+
+Then, just to show you that this
+is very general, we're
+
+going to use exactly the same
+technology to build a very
+
+different kind of language, a
+so-called logic programming
+
+language, where you don't really
+talk about procedures
+
+at all that have inputs
+and outputs.
+
+What you do is talk about
+relations between things.
+
+And then finally, we're going
+to talk about how you
+
+implement these things very
+concretely on the very
+
+simplest kind of machines.
+
+We'll see something like this.
+
+This is a picture of a chip,
+which is the Lisp interpreter
+
+that we will be talking about
+then in hardware.
+
+Well, there's an outline of the
+course, three big topics.
+
+Black-box abstraction,
+conventional interfaces,
+
+metalinguistic abstraction.
+
+Now, let's take a break now and
+then we'll get started.
+
+[MUSIC PLAYING]
+
+Let's actually start in
+learning Lisp now.
+
+Actually, we'll start out by
+learning something much more
+
+important, maybe the very most
+important thing in this
+
+course, which is not Lisp, in
+particular, of course, but
+
+rather a general framework for
+thinking about languages that
+
+I already alluded to.
+
+When somebody tells you they're
+going to show you a
+
+language, what you should say
+is, what I'd like you to tell
+
+me is what are the primitive
+elements?
+
+What does the language
+come with?
+
+Then, what are the ways you
+put those together?
+
+What are the means
+of combination?
+
+What are the things that allow
+you to take these primitive
+
+elements and build bigger
+things out of them?
+
+What are the ways of putting
+things together?
+
+And then, what are the
+means of abstraction?
+
+How do we take those complicated
+things and draw
+
+those boxes around them?
+
+How do we name them so that we
+can now use them as if they
+
+were primitive elements
+in making still
+
+more complex things?
+
+And so on, and so
+on, and so on.
+
+So when someone says to you,
+gee, I have a great new
+
+computer language, you don't
+say, how many characters does
+
+it take to invert a matrix?
+
+It's irrelevant.
+
+What you say is, if the language
+did not come with
+
+matrices built in or with
+something else built in, how
+
+could I then build that thing?
+
+What are the means of
+combination which would allow
+
+me to do that?
+
+And then, what are the means of
+abstraction which allow me
+
+then to use those as elements
+in making more complicated
+
+things yet?
+
+Well, we're going to see that
+Lisp has some primitive data
+
+and some primitive procedures.
+
+In fact, let's really start.
+
+And here's a piece of
+primitive data in
+
+Lisp, number three.
+
+Actually, if I'm being very
+pedantic, that's not the
+
+number three.
+
+That's some symbol that
+represents Plato's concept of
+
+the number three.
+
+And here's another.
+
+Here's some more primitive
+data in Lisp, 17.4.
+
+Or actually, some representation
+of 17.4.
+
+And here's another one, five.
+
+Here's another primitive
+object that's
+
+built in Lisp, addition.
+
+Actually, to use the same kind
+of pedantic-- this is a name
+
+for the primitive method
+of adding things.
+
+Just like this is a name for
+Plato's number three, this is
+
+a name for Plato's concept
+of how you add things.
+
+So those are some primitive
+elements.
+
+I can put them together.
+
+I can say, gee, what's the sum
+of three and 17.4 and five?
+
+And the way I do that is to
+say, let's apply the sum
+
+operator to these
+three numbers.
+
+And I should get,
+what? eight, 17.
+
+25.4.
+
+So I should be able to ask Lisp
+what the value of this
+
+is, and it will return 25.4.
+
+Let's introduce some names.
+
+This thing that I typed is
+called a combination.
+
+And a combination consists,
+in general,
+
+of applying an operator--
+
+so this is an operator--
+
+to some operands.
+
+These are the operands.
+
+And of course, I can make
+more complex things.
+
+The reason I can get complexity
+out of this is
+
+because the operands themselves,
+in general, can be
+
+combinations.
+
+So for instance, I could say,
+what is the sum of three and
+
+the product of five and
+six and eight and two?
+
+And I should get-- let's see--
+
+30, 40, 43.
+
+So Lisp should tell
+me that that's 43.
+
+Forming combinations is the
+basic needs of combination
+
+that we'll be looking at.
+
+And then, well, you see
+some syntax here.
+
+Lisp uses what's called prefix
+notation, which means that the
+
+operator is written to the
+left of the operands.
+
+It's just a convention.
+
+And notice, it's fully
+parenthesized.
+
+And the parentheses make it
+completely unambiguous.
+
+So by looking at this, I can see
+that there's the operator,
+
+and there are one, two,
+three, four operands.
+
+And I can see that the second
+operand here is itself some
+
+combination that has one
+operator and two operands.
+
+Parentheses in Lisp are a little
+bit, or are very unlike
+
+parentheses in conventional
+mathematics.
+
+In mathematics, we sort of use
+them to mean grouping, and it
+
+sort of doesn't hurt if
+sometimes you leave out
+
+parentheses if people
+understand
+
+that that's a group.
+
+And in general, it doesn't
+hurt if you put in extra
+
+parentheses, because that
+maybe makes the
+
+grouping more distinct.
+
+Lisp is not like that.
+
+In Lisp, you cannot leave out
+parentheses, and you cannot
+
+put in extra parentheses,
+because putting in parentheses
+
+always means, exactly and
+precisely, this is a
+
+combination which has
+meaning, applying
+
+operators to operands.
+
+And if I left this out, if I
+left those parentheses out, it
+
+would mean something else.
+
+In fact, the way to think about
+this, is really what I'm
+
+doing when I write something
+like this is writing a tree.
+
+So this combination is a tree
+that has a plus and then a
+
+thee and then a something else
+and an eight and a two.
+
+And then this something else
+here is itself a little
+
+subtree that has a star
+and a five and a six.
+
+And the way to think of that
+is, really, what's going on
+
+are we're writing these trees,
+and parentheses are just a way
+
+to write this two-dimensional
+structure as a linear
+
+character string.
+
+Because at least when Lisp first
+started and people had
+
+teletypes or punch cards or
+whatever, this was more
+
+convenient.
+
+Maybe if Lisp started today,
+the syntax of Lisp
+
+would look like that.
+
+Well, let's look at
+what that actually
+
+looks like on the computer.
+
+Here I have a Lisp interaction
+set up.
+
+There's a editor.
+
+And on the top, I'm going to
+type some values and ask Lisp
+
+what they are.
+
+So for instance, I can say
+to Lisp, what's the
+
+value of that symbol?
+
+That's three.
+
+And I ask Lisp to evaluate it.
+
+And there you see Lisp has
+returned on the bottom, and
+
+said, oh yeah, that's three.
+
+Or I can say, what's the sum of
+three and four and eight?
+
+What's that combination?
+
+And ask Lisp to evaluate it.
+
+That's 15.
+
+Or I can type in something
+more complicated.
+
+I can say, what's the sum of the
+product of three and the
+
+sum of seven and 19.5?
+
+And you'll notice here that Lisp
+has something built in
+
+that helps me keep track of
+all these parentheses.
+
+Watch as I type the next closed
+parentheses, which is
+
+going to close the combination
+starting with the star.
+
+The opening one will flash.
+
+Here, I'll rub those out
+and do it again.
+
+Type close, and you see
+that closes the plus.
+
+Close again, that
+closes the star.
+
+Now I'm back to the sum, and
+maybe I'm going to add that
+
+all to four.
+
+That closes the plus.
+
+Now I have a complete
+combination, and I can ask
+
+Lisp for the value of that.
+
+That kind of paren balancing is
+something that's built into
+
+a lot of Lisp systems to help
+you keep track, because it is
+
+kind of hard just by hand doing
+all these parentheses.
+
+There's another kind of
+convention for keeping track
+
+of parentheses.
+
+Let me write another complicated
+combination.
+
+Let's take the sum of the
+product of three and five and
+
+add that to something.
+
+And now what I'm going to do is
+I'm going to indent so that
+
+the operands are written
+vertically.
+
+Which the sum of that and
+the product of 47 and--
+
+let's say the product
+of 47 with a
+
+difference of 20 and 6.8.
+
+That means subtract
+6.8 from 20.
+
+And then you see the
+parentheses close.
+
+Close the minus.
+
+Close the star.
+
+And now let's get another
+operator.
+
+You see the Lisp editor here
+is indenting to the right
+
+position automatically to
+help me keep track.
+
+I'll do that again.
+
+I'll close that last
+parentheses again.
+
+You see it balances the plus.
+
+Now I can say, what's
+the value of that?
+
+So those two things, indenting
+to the right level, which is
+
+called pretty printing, and
+flashing parentheses, are two
+
+things that a lot of Lisp
+systems have built in to help
+
+you keep track.
+
+And you should learn
+how to use them.
+
+Well, those are the
+primitives.
+
+There's a means of
+combination.
+
+Now let's go up to the
+means of abstraction.
+
+I'd like to be able to take
+the idea that I do some
+
+combination like this, and
+abstract it and give it a
+
+simple name, so I can use
+that as an element.
+
+And I do that in Lisp with
+"define." So I can say, for
+
+example, define A to be the
+product of five and five.
+
+And now I could say, for
+example, to Lisp, what is the
+
+product of A and A?
+
+And this should be 25, and
+this should be 625.
+
+And then, crucial thing,
+I can now use A--
+
+here I've used it in
+a combination--
+
+but I could use that in other
+more complicated things that I
+
+name in turn.
+
+So I could say, define B to be
+the sum of, we'll say, A and
+
+the product of five and A.
+And then close the plus.
+
+Let's take a look at that
+on the computer and
+
+see how that looks.
+
+So I'll just type what
+I wrote on the board.
+
+I could say, define A to be the
+product of five and five.
+
+And I'll tell that to Lisp.
+
+And notice what Lisp responded
+there with
+
+was an A in the bottom.
+
+In general, when you type in
+a definition in Lisp, it
+
+responds with the symbol
+being defined.
+
+Now I could say to Lisp, what
+is the product of A and A?
+
+And it says that's 625.
+
+I can define B to be the sum of
+A and the product of five
+
+and A. Close a paren
+closes the star.
+
+Close the plus.
+
+Close the "define." Lisp says,
+OK, B, there on the bottom.
+
+And now I can say to Lisp,
+what's the value of B?
+
+And I can say something more
+complicated, like what's the
+
+sum of A and the quotient
+of B and five?
+
+That slash is divide, another
+primitive operator.
+
+I've divided B by five,
+added it to A. Lisp
+
+says, OK, that's 55.
+
+So there's what it looks like.
+
+There's the basic means
+of defining something.
+
+It's the simplest kind of
+naming, but it's not really
+
+very powerful.
+
+See, what I'd really
+like to name--
+
+remember, we're talking about
+general methods--
+
+I'd like to name, oh, the
+general idea that, for
+
+example, I could multiply five
+by five, or six by six, or
+
+1,001 by 1,001, 1,001.7
+by 1,001.7.
+
+I'd like to be able to name
+the general idea of
+
+multiplying something
+by itself.
+
+Well, you know what that is.
+
+That's called squaring.
+
+And the way I can do that in
+Lisp is I can say, define to
+
+square something x, multiply
+x by itself.
+
+And then having done that,
+I could say to Lisp, for
+
+example, what's the
+square of 10?
+
+And Lisp will say 100.
+
+So now let's actually look at
+that a little more closely.
+
+Right, there's the definition
+of square.
+
+To square something, multiply
+it by itself.
+
+You see this x here.
+
+That x is kind of a pronoun,
+which is the something that
+
+I'm going to square.
+
+And what I do with it
+is I multiply x, I
+
+multiply it by itself.
+
+OK.
+
+So there's the notation for
+defining a procedure.
+
+Actually, this is a little bit
+confusing, because this is
+
+sort of how I might
+use square.
+
+And I say square root of x or
+square root of 10, but it's
+
+not making it very clear that
+I'm actually naming something.
+
+So let me write this definition
+in another way that
+
+makes it a little
+bit more clear
+
+that I'm naming something.
+
+I'll say, "define" square to
+be lambda of x times xx.
+
+Here, I'm naming something
+square, just like over here,
+
+I'm naming something A. The
+thing that I'm naming square--
+
+here, the thing I named A was
+the value of this combination.
+
+Here, the thing that I'm naming
+square is this thing
+
+that begins with lambda, and
+lambda is Lisp's way of saying
+
+make a procedure.
+
+Let's look at that more
+closely on the slide.
+
+The way I read that definition
+is to say, I define square to
+
+be make a procedure--
+
+that's what the lambda is--
+
+make a procedure with
+an argument named x.
+
+And what it does is return
+the results of
+
+multiplying x by itself.
+
+Now, in general, we're going to
+be using this top form of
+
+defining, just because it's a
+little bit more convenient.
+
+But don't lose sight of the fact
+that it's really this.
+
+In fact, as far as the Lisp
+interpreter's concerned,
+
+there's no difference between
+typing this to it and typing
+
+this to it.
+
+And there's a word for that,
+sort of syntactic sugar.
+
+What syntactic sugar means,
+it's having somewhat more
+
+convenient surface forms
+for typing something.
+
+So this is just really syntactic
+sugar for this
+
+underlying Greek thing
+with the lambda.
+
+And the reason you should
+remember that is don't forget
+
+that, when I write something
+like this, I'm
+
+really naming something.
+
+I'm naming something square,
+and the something that I'm
+
+naming square is a procedure
+that's getting constructed.
+
+Well, let's look at that
+on the computer, too.
+
+So I'll come and I'll say,
+define square of
+
+x to be times xx.
+
+Now I'll tell Lisp that.
+
+It says "square." See, I've
+named something "square." Now,
+
+having done that, I can
+ask Lisp for, what's
+
+the square of 1,001?
+
+Or in general, I could say,
+what's the square of the sum
+
+of five and seven?
+
+The square of 12's 144.
+
+Or I can use square itself
+as an element in some
+
+combination.
+
+I can say, what's the sum of
+the square of three and the
+
+square of four?
+
+nine and 16 is 25.
+
+Or I can use square as an
+element in some much more
+
+complicated thing.
+
+I can say, what's the square
+of, the sqare of,
+
+the square of 1,001?
+
+And there's the square of the
+square of the square of 1,001.
+
+Or I can say to Lisp, what
+is square itself?
+
+What's the value of that?
+
+And Lisp returns some
+conventional way of telling me
+
+that that's a procedure.
+
+It says, "compound procedure
+square." Remember, the value
+
+of square is this procedure, and
+the thing with the stars
+
+and the brackets are just Lisp's
+conventional way of
+
+describing that.
+
+Let's look at two more
+examples of defining.
+
+Here are two more procedures.
+
+I can define the average of x
+and y to be the sum of x and y
+
+divided by two.
+
+Or having had average and mean
+square, having had average and
+
+square, I can use that to talk
+about the mean square of
+
+something, which is the average
+of the square of x and
+
+the square of y.
+
+So for example, having done
+that, I could say, what's the
+
+mean square of two and three?
+
+And I should get the
+average of four and
+
+nine, which is 6.5.
+
+The key thing here is that,
+having defined square, I can
+
+use it as if it were
+primitive.
+
+So if we look here on the
+slide, if I look at mean
+
+square, the person defining mean
+square doesn't have to
+
+know, at this point, whether
+square was something built
+
+into the language or
+whether it was a
+
+procedure that was defined.
+
+And that's a key thing in Lisp,
+that you do not make
+
+arbitrary distinctions between
+things that happen to be
+
+primitive in the language
+and things that
+
+happen to be built in.
+
+A person using that shouldn't
+even have to know.
+
+So the things you construct get
+used with all the power
+
+and flexibility as if they
+were primitives.
+
+In fact, you can drive that
+home by looking on the
+
+computer one more time.
+
+We talked about plus.
+
+And in fact, if I come here on
+the computer screen and say,
+
+what is the value of plus?
+
+Notice what Lisp types out.
+
+On the bottom there, it typed
+out, "compound procedure
+
+plus." Because, in this system,
+it turns out that the
+
+addition operator is itself
+a compound procedure.
+
+And if I didn't just type that
+in, you'd never know that, and
+
+it wouldn't make any
+difference anyway.
+
+We don't care.
+
+It's below the level of
+the abstraction that
+
+we're dealing with.
+
+So the key thing is you cannot
+tell, should not be able to
+
+tell, in general, the difference
+between things that
+
+are built in and things
+that are compound.
+
+Why is that?
+
+Because the things that are
+compound have an abstraction
+
+wrapper wrapped around them.
+
+We've seen almost all the
+elements of Lisp now.
+
+There's only one more we have to
+look at, and that is how to
+
+make a case analysis.
+
+Let me show you what I mean.
+
+We might want to think about the
+mathematical definition of
+
+the absolute value functions.
+
+I might say the absolute value
+of x is the function which has
+
+the property that it's
+negative of x.
+
+For x less than zero, it's
+zero for x equal to zero.
+
+And it's x for x greater
+than zero.
+
+And Lisp has a way of making
+case analyses.
+
+Let me define for you
+absolute value.
+
+Say define the absolute value
+of x is conditional.
+
+This means case analysis,
+COND.
+
+If x is less than zero, the
+answer is negate x.
+
+What I've written here
+is a clause.
+
+This whole thing is a
+conditional clause,
+
+and it has two parts.
+
+This part here is a predicate
+or a condition.
+
+That's a condition.
+
+And the condition is expressed
+by something called a
+
+predicate, and a predicate in
+Lisp is some sort of thing
+
+that returns either
+true or false.
+
+And you see Lisp has a
+primitive procedure,
+
+less-than, that tests whether
+something is true or false.
+
+And the other part of a clause
+is an action or a thing to do,
+
+in the case where that's true.
+
+And here, what I'm doing
+is negating x.
+
+The negation operator, the
+minus sign in Lisp is
+
+a little bit funny.
+
+If there's two or more
+arguments, if there's two
+
+arguments it subtracts the
+second one from the first, and
+
+we saw that.
+
+And if there's one argument,
+it negates it.
+
+So this corresponds to that.
+
+And then there's another
+COND clause.
+
+It says, in the case where
+x is equal to zero,
+
+the answer is zero.
+
+And in the case where x
+is greater than zero,
+
+the answer is x.
+
+Close that clause.
+
+Close the COND.
+
+Close the definition.
+
+And there's the definition
+of absolute value.
+
+And you see it's the case
+analysis that looks very much
+
+like the case analysis you
+use in mathematics.
+
+There's a somewhat different
+way of writing a restricted
+
+case analysis.
+
+Often, you have a case analysis
+where you only have
+
+one case, where you test
+something, and then depending
+
+on whether it's true or false,
+you do something.
+
+And here's another definition of
+absolute value which looks
+
+almost the same, which says,
+if x is less than zero, the
+
+result is negate x.
+
+Otherwise, the answer is x.
+
+And we'll be using "if" a lot.
+
+But again, the thing to remember
+is that this form of
+
+absolute value that you're
+looking at here, and then this
+
+one over here that I wrote
+on the board, are
+
+essentially the same.
+
+And "if" and COND are--
+
+well, whichever way
+you like it.
+
+You can think of COND as
+syntactic sugar for "if," or
+
+you can think of "if" as
+syntactic sugar for COND, and
+
+it doesn't make any
+difference.
+
+The person implementing a Lisp
+system will pick one and
+
+implement the other
+in terms of that.
+
+And it doesn't matter
+which one you pick.
+
+Why don't we break now, and
+then take some questions.
+
+How come sometimes when I write
+define, I put an open
+
+paren here and say, define open
+paren something or other,
+
+and sometimes when
+I write this, I
+
+don't put an open paren?
+
+The answer is, this particular
+form of "define," where you
+
+say define some expression, is
+this very special thing for
+
+defining procedures.
+
+But again, what it really means
+is I'm defining this
+
+symbol, square, to be that.
+
+So the way you should think
+about it is what "define" does
+
+is you write "define," and the
+second thing you write is the
+
+symbol here-- no open paren--
+
+the symbol you're defining and
+what you're defining it to be.
+
+That's like here
+and like here.
+
+That's sort of the basic way
+you use "define." And then,
+
+there's this special syntactic
+trick which allows you to
+
+define procedures that
+look like this.
+
+So the difference is, it's
+whether or not you're defining
+
+a procedure.
+
+[MUSIC PLAYING]
+
+Well, believe it or not, you
+actually now know enough Lisp
+
+to write essentially any
+numerical procedure that you'd
+
+write in a language like FORTRAN
+or Basic or whatever,
+
+or, essentially, any
+other language.
+
+And you're probably saying,
+that's not believable, because
+
+you know that these languages
+have things like "for
+
+statements," and "do until
+while" or something.
+
+But we don't really
+need any of that.
+
+In fact, we're not going
+to use any of
+
+that in this course.
+
+Let me show you.
+
+Again, looking back at square
+root, let's go back to this
+
+square root algorithm of
+Heron of Alexandria.
+
+Remember what that said.
+
+It said, to find an
+approximation to the square
+
+root of X, you make a guess,
+you improve that guess by
+
+averaging the guess and
+X over the guess.
+
+You keep improving that until
+the guess is good enough.
+
+I already alluded to the idea.
+
+The idea is that, if the initial
+guess that you took
+
+was actually equal to the square
+root of X, then G here
+
+would be equal to X/G.
+
+So if you hit the square
+root, averaging them
+
+wouldn't change it.
+
+If the G that you picked was
+larger than the square root of
+
+X, then X/G will be smaller than
+the square root of X, so
+
+that when you average
+G and X/G, you get
+
+something in between.
+
+So if you pick a G that's
+too small, your
+
+answer will be too large.
+
+If you pick a G that's too
+large, if your G is larger
+
+than the square root of X and
+X/G will be smaller than the
+
+square root of X.
+
+So averaging always gives you
+something in between.
+
+And then, it's not quite
+trivial, but it's possible to
+
+show that, in fact, if G misses
+the square root of X by
+
+a little bit, the average of G
+and X/G will actually keep
+
+getting closer to the square
+root of X. So if you keep
+
+doing this enough, you'll
+eventually get as
+
+close as you want.
+
+And then there's another fact,
+that you can always start out
+
+this process by using 1
+as an initial guess.
+
+And it'll always converge to
+the square root of X. So
+
+that's this method of successive
+averaging due to
+
+Heron of Alexandria.
+
+Let's write it in Lisp.
+
+Well, the central idea is, what
+does it mean to try a
+
+guess for the square
+root of X?
+
+Let's write that.
+
+So we'll say, define to try a
+guess for the square root of
+
+X, what do we do?
+
+We'll say, if the guess is good
+enough to be a guess for
+
+the square root of X,
+then, as an answer,
+
+we'll take the guess.
+
+Otherwise, we will try
+the improved guess.
+
+We'll improve that guess for
+the square root of X, and
+
+we'll try that as a guess for
+the square root of X. Close
+
+the "try." Close the "if." Close
+the "define." So that's
+
+how we try a guess.
+
+And then, the next part of the
+process said, in order to
+
+compute square roots, we'll
+say, define to compute the
+
+square root of X, we will try
+one as a guess for the square
+
+root of X. Well, we have to
+define a couple more things.
+
+We have to say, how is
+a guess good enough?
+
+And how do we improve a guess?
+
+So let's look at that.
+
+The algorithm to improve a guess
+for the square root of
+
+X, we average--
+
+that was the algorithm--
+
+we average the guess with
+the quotient of
+
+dividing X by the guess.
+
+That's how we improve a guess.
+
+And to tell whether a guess is
+good enough, well, we have to
+
+decide something.
+
+This is supposed to be a guess
+for the square root of X, so
+
+one possible thing you can do
+is say, when you take that
+
+guess and square it, do you get
+something very close to X?
+
+So one way to say that is to
+say, I square the guess,
+
+subtract X from that, and see if
+the absolute value of that
+
+whole thing is less than some
+small number, which depends on
+
+my purposes.
+
+So there's a complete procedure
+for how to compute
+
+the square root of X. Let's look
+at the structure of that
+
+a little bit.
+
+I have the whole thing.
+
+I have the notion of how to
+compute a square root.
+
+That's some kind of module.
+
+That's some kind of black box.
+
+It's defined in terms of how to
+try a guess for the square
+
+root of X.
+
+"Try" is defined in terms of,
+well, telling whether
+
+something is good enough
+and telling
+
+how to improve something.
+
+So good enough.
+
+"Try" is defined in terms of
+"good enough" and "improve."
+
+And let's see what
+else I fill in.
+
+Well, I'll go down this tree.
+
+"Good enough" was defined
+in terms of
+
+absolute value, and square.
+
+And improve was defined in
+terms of something called
+
+averaging and then some other
+primitive operator.
+
+Square root's defined in terms
+of "try." "Try" is defined in
+
+terms of "good enough"
+and "improve,"
+
+but also "try" itself.
+
+So "try" is also defined in
+terms of how to try itself.
+
+Well, that may give you some
+problems. Your high school
+
+geometry teacher probably told
+you that it's naughty to try
+
+and define things in terms of
+themselves, because it doesn't
+
+make sense.
+
+But that's false.
+
+Sometimes it makes perfect
+sense to define things in
+
+terms of themselves.
+
+And this is the case.
+
+And we can look at that.
+
+We could write down what this
+means, and say, suppose I
+
+asked Lisp what the square
+root of two is.
+
+What's the square root
+of two mean?
+
+Well, that means I try one
+as a guess for the
+
+square root of two.
+
+Now I look.
+
+I say, gee, is one a good enough
+guess for the square
+
+root of two?
+
+And that depends on the test
+that "good enough" does.
+
+And in this case, "good enough"
+will say, no, one is
+
+not a good enough guess for
+the square root of two.
+
+So that will reduce to saying,
+I have to try an improved--
+
+improve one as a guess for the
+square root of two, and try
+
+that as a guess for the
+square root of two.
+
+Improving one as a guess for the
+square root of two means I
+
+average one and two
+divided by one.
+
+So this is going
+to be average.
+
+This piece here will be the
+average of one and the
+
+quotient of two by one.
+
+That's this piece here.
+
+And this is 1.5.
+
+So this square root of two
+reduces to trying one for the
+
+square root of two, which
+reduces to trying 1.5 as a
+
+guess for the square
+root of two.
+
+So that makes sense.
+
+Let's look at the rest
+of the process.
+
+If I try 1.5, that reduces.
+
+1.5 turns out to be not good
+enough as a guess for the
+
+square root of two.
+
+So that reduces to trying the
+average of 1.5 and two divided
+
+by 1.5 as a guess for the
+square root of two.
+
+That average turns
+out to be 1.333.
+
+So this whole thing reduces to
+trying 1.333 as a guess for
+
+the square root of two.
+
+And then so on.
+
+That reduces to another called
+a "good enough," 1.4
+
+something or other.
+
+And then it keeps going until
+the process finally stops with
+
+something that "good enough"
+thinks is good enough, which,
+
+in this case, is 1.4142
+something or other.
+
+So the process makes
+perfect sense.
+
+This, by the way, is called
+a recursive definition.
+
+And the ability to make
+recursive definitions is a
+
+source of incredible power.
+
+And as you can already see I've
+hinted at, it's the thing
+
+that effectively allows you to
+do these infinite computations
+
+that go on until something is
+true, without having any other
+
+constricts other than the
+ability to call a procedure.
+
+Well, let's see, there's
+one more thing.
+
+Let me show you a variant of
+this definition of square root
+
+here on the slide.
+
+Here's sort of the same thing.
+
+What I've done here is packaged
+the definitions of
+
+"improve" and "good enough"
+and "try" inside "square
+
+root." So, in effect, what
+I've done is I've built a
+
+square root box.
+
+So I've built a box that's the
+square root procedure that
+
+someone can use.
+
+They might put in 36
+and get out six.
+
+And then, packaged inside this
+box are the definitions of
+
+"try" and "good enough"
+and "improve."
+
+So they're hidden
+inside this box.
+
+And the reason for doing that
+is that, if someone's using
+
+this square root, if George is
+using this square root, George
+
+probably doesn't care very much
+that, when I implemented
+
+square root, I had things inside
+there called "try" and
+
+"good enough" and "improve." And
+in fact, Harry might have
+
+a cube root procedure that has
+"try" and "good enough" and
+
+"improve." And in order to not
+get the whole system confused,
+
+it'd be good for Harry to
+package his internal
+
+procedures inside his
+cube root procedure.
+
+Well, this is called block
+structure, this particular way
+
+of packaging internals inside
+of a definition.
+
+And let's go back and look
+at the slide again.
+
+The way to read this kind of
+procedure is to say, to define
+
+"square root," well, inside that
+definition, I'll have the
+
+definition of an "improve" and
+the definition of "good
+
+enough" and the definition of
+"try." And then, subject to
+
+those definitions, the way I do
+square root is to try one.
+
+And notice here, I don't have to
+say one as a guess for the
+
+square root of X, because since
+it's all inside the
+
+square root, it sort of
+has this X known.
+
+Let me summarize.
+
+We started out with the idea
+that what we're going to be
+
+doing is expressing imperative
+knowledge.
+
+And in fact, here's a slide
+that summarizes the way we
+
+looked at Lisp.
+
+We started out by looking at
+some primitive elements in
+
+addition and multiplication,
+some predicates for testing
+
+whether something is less-than
+or something's equal.
+
+And in fact, we saw really
+sneakily in the system we're
+
+actually using, these aren't
+actually primitives, but it
+
+doesn't matter.
+
+What matters is we're going
+to use them as if they're
+
+primitives.
+
+We're not going to
+look inside.
+
+We also have some primitive
+data and some numbers.
+
+We saw some means of
+composition, means of
+
+combination, the basic one being
+composing functions and
+
+building combinations with
+operators and operands.
+
+And there were some other
+things, like COND and "if" and
+
+"define." But the main thing
+about "define," in particular,
+
+was that it was the means
+of abstraction.
+
+It was the way that
+we name things.
+
+You can also see from this slide
+not only where we've
+
+been, but holes we
+have to fill in.
+
+At some point, we'll have to
+talk about how you combine
+
+primitive data to get compound
+data, and how you abstract
+
+data so you can use large
+globs of data as
+
+if they were primitive.
+
+So that's where we're going.
+
+But before we do that, for the
+next couple of lectures we're
+
+going to be talking about, first
+of all, how it is that
+
+you make a link between these
+procedures we write and the
+
+processes that happen
+in the machine.
+
+And then, how it is that you
+start using the power of Lisp
+
+to talk not only about these
+individual little
+
+computations, but about general
+conventional methods
+
+of doing things.
+
+OK, are there any questions?
+
+AUDIENCE: Yes.
+
+If we defined A using
+parentheses instead of as we
+
+did, what would be
+the difference?
+
+PROFESSOR: If I wrote this, if
+I wrote that, what I would be
+
+doing is defining a procedure
+named A. In this case, a
+
+procedure of no arguments,
+which, when I ran it, would
+
+give me back five times five.
+
+AUDIENCE: Right.
+
+I mean, you come up with the
+same thing, except for you
+
+really got a different--
+
+PROFESSOR: Right.
+
+And the difference would
+be, in the old one--
+
+Let me be a little
+bit clearer here.
+
+Let's call this A, like here.
+
+And pretend here, just for
+contrast, I wrote, define D to
+
+be the product of
+five and five.
+
+And the difference between
+those, let's think about
+
+interactions with the
+Lisp interpreter.
+
+I could type in A and Lisp
+would return 25.
+
+I could type in D, if I just
+typed in D, Lisp would return
+
+compound procedure D, because
+that's what it is.
+
+It's a procedure.
+
+I could run D. I could say,
+what's the value of running D?
+
+Here is a combination
+with no operands.
+
+I see there are no operands.
+
+I didn't put any after D. And
+it would say, oh, that's 25.
+
+Or I could say, just for
+completeness, if I typed in,
+
+what's the value of running A?
+
+I get an error.
+
+The error would be the same
+one as over there.
+
+It'd be the error would say,
+sorry, 25, which is the value
+
+of A, is not an operator that
+I can apply to something.
\ No newline at end of file
diff --git a/2fjZhoifOiM.txt b/2fjZhoifOiM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8c3e8da2cabd77ceb41eeb6b285829e9e3d6eeff
--- /dev/null
+++ b/2fjZhoifOiM.txt
@@ -0,0 +1,4202 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare@mit.edu.
+
+PROFESSOR: Any issues with
+the project so far?
+
+Have you gotten your
+repositories set up and the
+
+compiler works and all this?
+
+So I'm glad to see a
+lot of people are
+
+getting a early start.
+
+In fact, if you haven't, a lot
+of other people in the class
+
+are getting an early start
+so you're behind already.
+
+So go there, get the project
+started, because these
+
+performance projects can
+run for long time.
+
+And in fact, last year a lot of
+people asking, when is my
+
+project done?
+
+Because a lot of times when you
+have a project there's a
+
+certain set of--
+
+we ask you to implement.
+
+Once that's implemented,
+the project is over.
+
+But when is a performance
+project done?
+
+And the only answer I L when the
+deadline comes because you
+
+can always shave 10% here,
+you can get a better data
+
+structure, you can
+keep like kind of
+
+tweaking for a long time.
+
+And a lot of you will do.
+
+In fact, to give you a warning,
+last year, the
+
+performance difference between
+the best project won, versus
+
+the worst one, even the worst
+one got about 50% better than
+
+the code we gave.
+
+But the best one got 1,000x
+better than the worst one
+
+because they figured out right
+data structures, they changed
+
+algorithms, they did some
+precomputation, they did a lot
+
+of cool stuff, and so there's
+a lot to get if you do this
+
+project right.
+
+So just don't be happy if you
+just got 10%, 50%, and say,
+
+yeah, I got some performance.
+
+Think carefully.
+
+There's a lot of room in
+this project for you to
+
+gain, so work hard.
+
+I'm not saying this
+yields 1,000x.
+
+I don't know.
+
+I haven't exactly seen all the
+things you can do, but there
+
+could be a huge thing
+you can win.
+
+So think through not just small,
+low hanging fruit, but
+
+there could be interesting
+things you can do that can
+
+have impact.
+
+So today what I am going to do
+is talk a little bit about
+
+basics of performance
+engineering.
+
+Kind of things you guys
+would probably
+
+know, rules to follow.
+
+So to start that if you look at
+performance engineering, it
+
+can fit into a couple
+of classes.
+
+One is you want to get a maximum
+out of the compiler
+
+you have, the processor you
+have, the system you have, you
+
+want them running efficiently.
+
+So if you look at the matrix
+multiple examples we did this
+
+in the first class it's saying,
+OK, we have a system,
+
+we have this very well known
+algorithm, very long piece of
+
+code, and we want to get the
+best out of that thing, how do
+
+you go about doing that?
+
+That's mainly the focus there.
+
+Then when you we looked at
+the bithacking stuff that
+
+Professor Leiserson did last
+time, it's mainly about really
+
+changing the algorithms.
+
+We basically said, OK, look, if
+we're thinking about this
+
+as bits there might be
+fundamental different ways to
+
+approach this problem.
+
+By doing that we can actually
+get really good performance.
+
+OK, we'll be doing
+more of that.
+
+Today we are going to focus on
+this two middle criteria.
+
+What we are going to do is we
+are going to stay within the
+
+spirit of the program
+that was given.
+
+Even though we are going to
+change the program a little
+
+bit, we are not going to
+fundamentally change what the
+
+program does.
+
+So the same computations would
+be done basically on the same
+
+day but what we will do is we
+will change certain aspects
+
+how it's being done to gain some
+performance advantages.
+
+So the nice thing about this
+one is you don't have to
+
+really understand the algorithm,
+you don't have to
+
+understand lot of what's going
+on in, what's implementation.
+
+This is more--
+
+you can do this as a
+mechanism sub out.
+
+The unfortunate thing is there's
+not theory in these
+
+type of engineering.
+
+There's not something we
+can prove, here's the
+
+optimal you can do.
+
+[UNINTELLIGIBLE] nice there.
+
+So normally performance
+programming basically knows
+
+that you need to understand
+everything that's in modern
+
+performance.
+
+That means all the way from high
+level algorithms, every
+
+layer in the systems, the
+compiler, the hardware, the
+
+disks, all those things can
+impact performance.
+
+So it's normally when in
+performance to understand
+
+everything that
+[UNINTELLIGIBLE].
+
+This is very different from
+a lot of what you
+
+guys are used to.
+
+It is staying within
+one layer.
+
+You say, OK, this is my
+layer, I don't care
+
+what's on any of it.
+
+I don't know care much about--
+
+I'm going to work on that.
+
+And the thing that normally
+comes and bite you is the
+
+other layers that you just
+take for granted.
+
+In performance it's basically
+going through end to end.
+
+That's the normal thing.
+
+And normally, if you are an
+experienced performance
+
+engineer, you know when
+the problems show up.
+
+And you can kind of have a basic
+understanding, here are
+
+the kind of places where they
+have performance problems.
+
+And so a good performance this
+is where experience comes in.
+
+So instead of saying looking at
+the code and say I have no
+
+idea what's going on, you can
+say, let me think about this,
+
+this is where normally
+something goes wrong.
+
+And then you have to have the
+skill to zoom in and identify
+
+the problem fast.
+
+And most of performance
+engineering is basically a
+
+good dose of common sense.
+
+So have kind of a good
+person who can
+
+do really good debugging.
+
+Is you have kind of a built in
+algorithm how do you go about
+
+doing something.
+
+And a lot of times you know
+your strengths, kind of
+
+mistakes you make, you look at
+those things first, and the
+
+same way performance engineering
+there has to be
+
+kind of a back of your
+head algorithm.
+
+And hopefully at the end of
+this class you're going to
+
+develop that.
+
+And in this lecture what I'm
+trying to do is come up with a
+
+set of rules, that kind of
+patterns that occur regularly,
+
+mistakes lot of people make,
+and that can have a
+
+substantial performance impact,
+or performance gain if
+
+you do that.
+
+If you have done the design
+patterns lectures in 005, yes,
+
+you do, you will see
+some similar ideas.
+
+What you're doing is kind of
+say, OK, here's a bunch of
+
+patterns in there,
+what we can do.
+
+So what I'm doing is I am
+following some very
+
+interesting set of rules that
+was developed by this guy
+
+named John Bentley.
+
+He wrote a book called
+Programming Pearls, I guess.
+
+It's a very old book, last
+published in 1990.
+
+It talks about a lot of the
+small, interesting things you
+
+can do to get really
+good performance.
+
+It's out of print.
+
+This is probably one
+reason to probably
+
+go to library probably.
+
+Libraries have this copy but you
+can't get it on Amazon or
+
+online so that's unfortunate.
+
+But what I'm going to do is
+I'm going to kind of read
+
+through it and some of these
+rules, modified to suit the
+
+current program and practices.
+
+So he looked at it and said
+there are basically two kinds
+
+of things you can do,
+we can modify data,
+
+you can modify code.
+
+And then went down more into
+details, if you modify data
+
+you can do three things.
+
+You can pay one against other,
+you can pay by space and gain
+
+time, you can pay from time and
+gain space, and there's
+
+sometimes, if you're lucky, you
+have a win-win situation
+
+when you can get both space
+and time advantage.
+
+So let's go through a couple
+of those things.
+
+So if you [UNINTELLIGIBLE]
+
+by space for time, there
+are four things.
+
+I'm going to go through all
+this four data structure
+
+augmentation, storing
+precomputed results, caching,
+
+and lazy evaluation.
+
+So what's data structure
+augmentation?
+
+So here what you want to do is
+you have a data structure that
+
+you keep the data.
+
+You add some extra information
+to your data structures.
+
+That can mean the common
+operations run much quicker.
+
+OK?
+
+And when this is good, because
+what do you want to do is this
+
+adding this information
+has a clear benefit.
+
+Calculating additional
+information has to
+
+be cheap and easy.
+
+So you don't want a situation
+where we have this
+
+information, you've spent all
+this time calculating this
+
+additional information and
+you're not using it that much,
+
+or the use doesn't give you
+that much advantage.
+
+So you have amortize
+the cost in here.
+
+And then also keeping that
+information current can't be
+
+too difficult, because
+sometimes you can add
+
+information into a data
+structure that makes it very
+
+hard to make sure that that
+information is kept up to
+
+date, and then you're spending
+more time and you're
+
+[UNINTELLIGIBLE]
+
+that.
+
+So a couple of quick
+examples in here.
+
+Something like if you have a
+single link list, if you are
+
+doing a lot of deletion it's a
+very expensive proposition
+
+because you might had to walk
+through the entire list to
+
+delete an element.
+
+But if you are in a doubly
+linked list, a division
+
+operation is basically
+order one instead of
+
+[UNINTELLIGIBLE].
+
+So suddenly you realize, I'm
+doing a lot of deletions,
+
+suddenly I can say I'm adding
+this additional information to
+
+my link list, I'm maintaining
+point as to both directions,
+
+make this one operation
+run much faster.
+
+This is a very classic example
+of adding additional
+
+information.
+
+Another one is what we call
+reference counting.
+
+So assume I have objects
+somewhere and I want to figure
+
+out who points to me.
+
+In terms of garbage collection
+you want to see if anybody
+
+points to me.
+
+The normal way to do that is
+look for every other thing
+
+saying is anybody pointing to
+that person, had to walk
+
+through every possible object
+out there to find if anybody's
+
+pointing to this object.
+
+That's what normal garbage
+garbage collectors do.
+
+But there's something
+easier, what you
+
+call reference counting.
+
+That means if each object keep
+a count on the amount of
+
+pointing coming to itself then
+to ask that question, is this
+
+really true?
+
+And you look and say,
+OK, what's my count?
+
+If there's count to zero
+nobody's pointing to me.
+
+But of course every time you
+point to that object to update
+
+the counter, every time you
+point away or take away an
+
+object that points you have to
+subtract the counters, you had
+
+to keep that information
+additional.
+
+But by doing that discussion
+about asking whether anybody
+
+points to you becomes a
+very trivial question.
+
+So here's a case you add a
+little bit more information
+
+and that makes some questions,
+some things you want to know
+
+trivial and very easy to do,
+and you have to figure out
+
+where the [UNINTELLIGIBLE]
+
+is.
+
+So here's one interesting
+thing.
+
+Go a little bit further,
+one thing you can do is
+
+precompute, result
+and storage.
+
+What you are doing is you want
+some calc computation and
+
+instead of every time you want
+that in recalculating it, say,
+
+OK, I'm going to compute them
+early and I'm going to store
+
+it somewhere, and then every
+time I want then I
+
+just do a look up.
+
+So when is this going
+to be useful?
+
+So this is--
+
+the rest of my slides are going
+to have this kind of
+
+form, I'm going to give you a
+problem, tell you when it's
+
+going to be useful, and
+use some examples.
+
+First of all, the function you
+are calculating has to be
+
+somewhat expensive, otherwise if
+it is just a simple single
+
+operation look up is probably
+too slow to compile.
+
+And the function has to be very
+heavily used, because if
+
+you are calling it many, many
+times it's worth storing it.
+
+Another very important
+thing is the argument
+
+space has to be small.
+
+You might be asking for calling
+the function millions
+
+and millions of time, but every
+time you call you give a
+
+different set of arguments.
+
+If the arguments are very large
+it can be many, many
+
+things here, and then it's not
+easy to store everything.
+
+And it might take more time to
+find all the solutions for all
+
+the arguments.
+
+So if the arguments
+have to be small.
+
+And of, course, a couple
+additional things, results
+
+only depends on the arguments.
+
+So assume the function results
+actually look time of day to
+
+the computation.
+
+OK, that doesn't work, because
+then every time you call the
+
+function, you get different
+result.
+
+That doesn't work that much.
+
+And functions shouldn't
+have side effects.
+
+What that means is if you call
+the function, if it is
+
+modifying some global variable,
+global state.
+
+OK.
+
+Then if you keep the call, if
+you don't call the function
+
+that might not happen, so you
+want to make sure that this
+
+function is something can not
+call and give the results and
+
+the state of the system
+won't change.
+
+And another interesting, nice
+thing to have is function
+
+determinants, that means every
+time you call the function you
+
+get the same four arguments,
+you get the same results.
+
+So this is a long list.
+
+Some of the things I will go,
+so for an example, OK, so
+
+instead of me getting there
+getting all the things I want,
+
+you [INAUDIBLE]
+
+when I give a prescription like
+the thing, what kind of
+
+things can I do in this way
+that might be helpful?
+
+Can anybody come up with
+an interesting example?
+
+[UNINTELLIGIBLE]
+
+would precompute and save.
+
+AUDIENCE: Anytime you do
+dynamic programming.
+
+PROFESSOR: Anytime you
+dynamic program.
+
+This is dynamic programming,
+it's a very good way, later we
+
+probably go get a little
+bit into that.
+
+Where you precompute
+and save results.
+
+OK, that's very sophisticated
+answer.
+
+Good.
+
+Any other things you
+can think of?
+
+That's almost a meta answer
+that's in that class of things
+
+you can do.
+
+Any problem there that you have
+encountered that you'd
+
+rather precompute and save that
+would be a big, big win.
+
+AUDIENCE: Operations with large
+primes that [INAUDIBLE].
+
+PROFESSOR: Operations with?
+
+AUDIENCE: Large primes.
+
+PROFESSOR: Large primes,
+operations in
+
+large primes, yes.
+
+If you are doing that,
+especially if this fits into
+
+this argument space
+small apart.
+
+If the large primes are, any
+large primes then you might
+
+not call it multiple times.
+
+So here I want to give you kind
+of a template that what
+
+happens here.
+
+So what you want to do is at
+initialization time I get this
+
+function initialized, what I
+do is I precompute for all
+
+arguments what the results are
+stored at, and then every time
+
+you go apply the function I
+just basically, instead of
+
+calling the function, I just
+look at this table.
+
+OK.
+
+So then would this
+be a bad idea?
+
+AUDIENCE: Because you know this
+early ahead of time you
+
+know that you're going to be
+calling the function for all
+
+of your arguments.
+
+PROFESSOR: So if the argument
+space is very large or if you
+
+don't call the function that
+many times, or as I said, it
+
+might only call for very small
+number of arguments,
+
+[UNINTELLIGIBLE]
+
+this might not be a good idea.
+
+OK?
+
+So we will go.
+
+As we improve, you'll see some
+other things that actually
+
+address that.
+
+So here's an interesting way of
+doing a use case in here.
+
+So what I have here is
+Pascal's Triangle.
+
+How many people know
+Pascal's Triangle?
+
+OK, good, so I don't have
+to explain that.
+
+So here is a simple computation
+
+for Pascal's Triangle.
+
+So what I'm doing is in order
+to calculate this value I am
+
+calling these two values
+and adding that.
+
+OK?
+
+But the problem is that this
+will call- so it kind of call
+
+exponentially more and
+more doing that.
+
+So you'd say exponential
+rhythm.
+
+However, what I can do in
+Pascal's Triangle is I can
+
+basically compute it at the
+beginning by storing the
+
+previous role, or previous set
+of values in and then previous
+
+role, and every time I'm calling
+I just basically have
+
+to look up the two elements
+in the previous role.
+
+Trying to get my mouse, OK.
+
+Only have to look at the two
+elements on the previous role.
+
+I added up, I will never have
+to compute beyond that.
+
+So, in fact, by just doing
+this one I have taken
+
+exponential algorithm to
+basically lead a path through
+
+the data, basically.
+
+This actually become a square,
+because if you have some
+
+depth, I had to do i squared--
+
+become a square, pass
+through the data.
+
+If I'm looking for n, I
+don't know how to do
+
+exponential look up.
+
+Everybody saw this?
+
+So this is a nice way, simple
+way I'm just doing a simple
+
+storing this data, however in
+here I had to calculate, I
+
+need to know how much maximum
+of that, and calculate and I
+
+just look up.
+
+And here the [UNINTELLIGIBLE]
+
+if you calculate a little bit
+extra, who cares, I'm OK.
+
+And another interesting
+thing is Fibonnaci.
+
+And again, here, if you do
+keeping the previous value, in
+
+here, you're actually changing
+from exponential algorithm, to
+
+in here basically a linear
+calculation.
+
+OK?
+
+So this is almost an algorithmic
+change here.
+
+I kind of lied when
+I said it's just a
+
+data structure change.
+
+But just a simple data structure
+change made an
+
+algorithm difference.
+
+So the other interesting thing
+you can do is caching.
+
+So what that means is if you
+have a heavily used function
+
+you can keep some number of
+previous basically results
+
+from calling that function.
+
+This has a lot of caveats
+so let's go
+
+through this carefully.
+
+Again the function has to be
+expensive, otherwise it's not
+
+worth doing all that work.
+
+Functions have to be heavily
+used, otherwise you're
+
+calculating and if you don't
+reuse it it's not worth doing
+
+all the worth.
+
+Here the arguments space can be
+large, OK, because you are
+
+not calculating everything, you
+can have a large argument
+
+space, and that's OK.
+
+And then there's another thing
+called temporal locality.
+
+Anybody knows what temporal
+locality means?
+
+OK what.
+
+AUDIENCE: The same arguments are
+called [UNINTELLIGIBLE].
+
+PROFESSOR: Yeah, so a lot of
+times we realize that if you
+
+go into the caching and
+stuff like that.
+
+We really get into that in
+hardware when you talk about
+
+hardware lecture.
+
+So what happens is yes, we have
+observed that if I have a
+
+set of arguments and if I
+calculate most of the times I
+
+will have the same arguments
+very quickly time-wise.
+
+So if I calculate something,
+then for a short time I might
+
+reuse those arguments again and
+again, so that's called
+
+temporal locality.
+
+So caching works when there's a
+very good temporal locality.
+
+And then there's two other
+things we want to do because
+
+we won't have hash function that
+means because a lot of
+
+arguments from that we only get
+one value to look up where
+
+I store my cache, have to have
+a hash function, but to
+
+calculate it by argument.
+
+Sometimes if the arguments are
+too complicated you might not
+
+be able to calculate a good
+hash function and the hash
+
+function has to be good.
+
+What do you mean by a
+good hash function?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, no
+[UNINTELLIGIBLE].
+
+That means they tend to be
+a good distribution.
+
+So given most of the arguments
+it shouldn't be ending up as
+
+the same value again, so you
+should have good distribution
+
+when you call with different
+arguments.
+
+And the final results only
+depend on the arguments that's
+
+again otherwise you have a
+problem and the function
+
+[UNINTELLIGIBLE]
+
+if your [UNINTELLIGIBLE]
+this important.
+
+And there's another thing
+called coherence.
+
+So what that means
+is I keep some
+
+precalculated values in here.
+
+And sometime this if results
+are only dependent on the
+
+arguments you don't have
+that much of an issue.
+
+But sometimes you might in the
+situation that the results are
+
+dependent on the arguments and
+some other things like the
+
+time of the day or whatever.
+
+And if you want full coherence,
+what you want to
+
+make sure is--
+
+many of you know that the
+results might be varied.
+
+I need to understand
+that, I need to
+
+invalidate all the cache.
+
+And suddenly the data or the
+user changed so that thing I
+
+memorized only works for User
+A, now went to User B, the
+
+results are wrong and I had to
+get rid of all the results.
+
+Or there are some cases where
+you could say, yeah, little
+
+bit of things I can tolerate,
+like for example, a really far
+
+fetched example is something
+like if you're looking at a
+
+web page on a search.
+
+OK, you don't have a good
+guarantee that all the web
+
+pages in the world are
+in that search.
+
+If you're a little bit late
+getting a new web
+
+page, then you're OK.
+
+So you can do tolerate
+sometimes, a lot of times, if
+
+you can tolerate these kind of
+things you can have huge
+
+performance impact.
+
+You don't have to be exact.
+
+So some of these projects we
+look we look at these kind of
+
+ideas, of tolerate a little bit
+of a slack and getting a
+
+good performance out of that.
+
+So here's the kind of code, I
+put a lot of code in my slides
+
+because not I won't explain
+everything but since these
+
+online if you want to figure out
+what the right template is
+
+you can look at it.
+
+I have no idea why this
+is moving on me.
+
+OK, OK, here we go.
+
+So what you first have to say
+is every time you cache a
+
+value you have to know, I had
+to know old arguments and
+
+results, I had to store that,
+and then I'm keeping this many
+
+precomputed values in here.
+
+And so every time I call the
+function with arguments first
+
+I have to see I had to get the
+get the has with these
+
+arguments because that might be
+the place, this buffer disk
+
+just might be the place I have
+stored a previously computed
+
+[UNINTELLIGIBLE].
+
+Then you say, OK look, is my
+[UNINTELLIGIBLE] stored, has
+
+the same argument.
+
+If that means I already have
+that precomputed, at that
+
+point I just return it, I
+have no issue in there.
+
+Otherwise you're to call the
+function because I haven't
+
+stored it, and then I will go
+about storing the value
+
+because I calculated I need a
+storage because the next time
+
+I call these arguments I want
+to get the same results, and
+
+then I return the result.
+
+OK.
+
+Is this kind of clear, how
+this caching works?
+
+OK, what's a good place for
+caching versus precomputing?
+
+Any idea what can make a good
+scenario where actually
+
+caching can have a big impact?
+
+You have heard a lot of things
+that have the word cache
+
+associated with it, and you can
+say, OK, what that means.
+
+AUDIENCE: Web browsing.
+
+PROFESSOR: Web browsing OK, you
+web browse actually that's
+
+a cache, because there's a good
+probability that if you
+
+look at a page and you might be
+refreshing that page or you
+
+might be looking at that page,
+so a lot of times what you do
+
+is you keep a copy locally, and
+the next time you ask for
+
+that and if you have a local
+copy you can give
+
+that local copy back.
+
+And then of course there's some
+issues about how to make
+
+the local companies stay, the
+coherence issues and stuff
+
+like that it can get complicated
+but that's a
+
+situation where actually
+you can use caching.
+
+So finally, in this category,
+we are going to talk about
+
+lazy evaluation.
+
+So lazy evaluation means
+basically a lot of times you
+
+might ask for value but you
+might not really need it at
+
+that point.
+
+Just keep the computation to the
+side without doing it and
+
+then do the computations only
+when you really, really need
+
+the result.
+
+So basically this is useful, a
+lot of times you might try to
+
+compute a lot of values but
+only a certain of that
+
+actually is used.
+
+And at that point you just
+basically further that
+
+calculation and only use it
+when it's actually done.
+
+The nice part is when can be
+done in a function call, and
+
+also results can be calculated
+kind of incrementally.
+
+And also, the arguments or
+what's needed to calculate the
+
+results can be nicely packaged
+up so it can be
+
+recalculated later.
+
+So here what you do here is in
+the precomputing is something
+
+like precomputing but you don't
+precompute early, at the
+
+beginning nothing
+is precomputed.
+
+When you only ask to apply a
+function then if there's no
+
+precomputed value you'll
+recompute, otherwise you just
+
+return the value.
+
+So if you compare this one
+Pascal's Triangle beforehand I
+
+just computed, there's a bunch
+of values in here and kept it.
+
+OK assuming OK up to
+PDMAX I will have
+
+the results in there.
+
+But you might not do that.
+
+PDMAX might be very large and
+you might be looking only for
+
+small Pascal Triangle.
+
+So instead of doing that, what
+you can do is you can do this
+
+way, you can keep the array for
+results, assume everything
+
+is normally in [UNINTELLIGIBLE]
+
+global array.
+
+and then what happens is you
+look at the results if the
+
+results is greater than zero we
+are what you're looking at,
+
+that means, ah-ha.
+
+I have calculated it.
+
+I have a new value, I
+just iterated it.
+
+I'm happy.
+
+Otherwise I will call Pascal
+by recalculating values
+
+because I don't have the
+current results.
+
+And once I get it
+I will store it.
+
+Once I get the value I will
+basically, I will calculate
+
+the Pascal, I will store it and
+I will return the value.
+
+So what that means is this value
+of the Pascal yx will be
+
+only calculated once fully, and
+afterward every other time
+
+you lose that you actually
+use the previous one.
+
+This works very nice, this works
+both very nice about
+
+precomputation but you don't
+pay that extra overhead.
+
+So you are doing the minimum
+amount of computation.
+
+You can never exceed the
+computation of the normal
+
+computation.
+
+So if you only ask for Pascal
+very small one, that's exactly
+
+the work we [UNINTELLIGIBLE]
+do.
+
+But it will also really use this
+kind of exponential blow
+
+up that happens in the
+normal computation.
+
+So this is kind of the you can
+have the cake and eat it too
+
+in this work.
+
+OK good.
+
+So now let's switch from space
+for time, for time for space.
+
+OK?
+
+So here, one thing you can do
+is if you have a huge amount
+
+of data what you can do is you
+can store the data in some
+
+kind of reduced form and then
+what you can do is then you
+
+can get a big compression of
+data basically and then as you
+
+need the data you can do some
+more computation to get the
+
+data you want.
+
+So what you're doing is you are
+really reducing the space
+
+you need but now you are paying
+by time to get access
+
+to that data.
+
+So this is why [UNINTELLIGIBLE]
+
+storage is at a premium.
+
+If you look at systems before
+1980s everybody had to do it
+
+because storage was a premium
+and all the memory and disk
+
+space was so complicated
+everything got
+
+compacted in there.
+
+Now, most your laptop and
+desktops, you don't care, you
+
+have enough space.
+
+However, if you got things
+like embedded devices and
+
+things like that, this still
+becomes a issue.
+
+Or if you have a very large data
+set it becomes an issue.
+
+And what you can do is by
+compressing, drastically
+
+reduce the data size.
+
+And you can do it in different
+ways, sometimes you
+
+can do it in batch.
+
+That means you keep the data
+compressed, expand it all, and
+
+process, hopefully you
+have room for that.
+
+Or sometimes if you don't have
+room you do it by streams,
+
+that means you're looking at a
+small amount of data expanded,
+
+work at it and then either throw
+it or again compress it
+
+and put it back in.
+
+And hardest thing is if you
+actually do random access.
+
+That means you'll randomly go
+to some data, expand and
+
+understand that sometimes
+there's some complications.
+
+So there are a bunch of packing
+methods and some
+
+simplest things are use
+a small data size.
+
+So right now you're dealing with
+64 bit words, you can say
+
+wait a minute, why does this
+data only need 8 bits?
+
+Why do you keep storing
+everything 64-bit if my data
+
+maximum can be only 0 to 256.
+
+I can use 8 bits.
+
+Or I can look at that and I
+can use small data size,
+
+that's something.
+
+And a lot of people realize a
+lot of data we are storing are
+
+just zeros.
+
+There are many different data
+structures, you have huge data
+
+structures and most
+of it's zeroes.
+
+And eliminating zeroes in many
+instances can you get a long
+
+way in many, many, many
+data storage.
+
+And something like LZ77
+eliminates repetition.
+
+So a lot of times what you
+find in there you have
+
+repetitive patterns you can
+eliminate that and then, of
+
+course, you can go into a
+lot more complicated.
+
+heavy-weight compression.
+
+So to just give you a feel for
+what compression is like I
+
+found this cute animation so
+I will show it to you.
+
+So here is the input stream, but
+it has this corrector LA,
+
+and then it has some notion
+about how much a repetition it
+
+has, corrector O and 0 3.
+
+So what happens if it's
+just a character?
+
+It will get taken in, so these
+two correctors go.
+
+Now these two forces from the
+point I point in here go to
+
+inwards, and repeat
+it four times.
+
+What that means is basically in
+here it will get repeated
+
+four times because that 2 4.
+
+So that means instead of having
+these four correctors
+
+in there, what it had was it had
+two things, and then all
+
+get repeated three times and
+then it'd get shifted in here.
+
+So instead of having ten
+correctors before, we had 2,
+
+3, 4, 5, 6, 7.
+
+Seven, out of seven correctors
+you compress you stored
+
+information off ten correctors
+because of repetition.
+
+OK, so this is a very simple
+scheme that people use to do
+
+this LZ77 compression.
+
+More complicated thing you can
+do a lot of times is build an
+
+interpreter.
+
+What that means is you have some
+complex data, instead of
+
+storing the data you have a
+summary of the data stored.
+
+OK.
+
+And then what you can do is
+you can do this abstract
+
+representation.
+
+I mean you were already
+tested.
+
+Like, for example, you
+[UNINTELLIGIBLE]
+
+exactly doing that.
+
+What you do is you start off
+storing all the beats of
+
+machine instructions.
+
+You store it in abstraction
+called add register names or
+
+something like in smd.
+
+What that means is you're
+building a very simple
+
+abstraction which that would be
+more complex sometimes to
+
+store than the actual data.
+
+So in here, things like if you
+look at a java byte cord,
+
+that's a nice interpreter.
+
+So instead of storing all this
+complex instructions you
+
+interpret, you stored some
+higher level set of
+
+instructions, that byte code,
+that is much more compressed
+
+and that you run you map it into
+the machine instructions.
+
+There's a lot of advantages
+other than just compressing
+
+storage, it's a nice
+abstraction, you can change it
+
+at the highly level easily.
+
+OK, so those are something that
+you can do, you give up
+
+one thing for the other.
+
+And if you're lucky you can have
+the cake and eat it too.
+
+Which is you get both space
+and time at the same time.
+
+So we looked at it in last
+lecture sometime.
+
+This is bithack.
+
+Bithacks kind of gave you that
+because instead of having 64
+
+bit word to represent you got
+64 of them into one big
+
+stream, if you're only
+representing zeroes and ones.
+
+And by doing that you get a lot
+more compressed storage.
+
+Also now you can operate that
+entire 64 in parallel.
+
+We can generalize it a little
+bit, so instead of just doing
+
+64 Boolean, sometimes you can
+do in a 64 bit word, you can
+
+store two 32 bit words,
+or four 16 bit words,
+
+so eight 8 bit words.
+
+OK.
+
+In [UNINTELLIGIBLE]
+
+is called a Memex
+SSE extensions.
+
+Normally it's called SIMDs, a
+single instruction multiple
+
+data, because what you do to
+that, all the bits, are the
+
+same thing for everybody.
+
+So if you're adding you're
+doing same add
+
+for both of the data.
+
+And because of that you
+basically going to get both
+
+the compression.
+
+Because now for 64 bit you are
+keeping two thing, or four
+
+things, or eight things.
+
+Also, now you're operating.
+
+In a single operation you can
+get the same operation
+
+happening to all the data.
+
+So you're getting both storage
+and fast operations in here.
+
+Of course if you only look at
+one you have to do a little
+
+bit more work, you take it out
+of that data word, so if
+
+you're just looking at
+[UNINTELLIGIBLE]
+
+thing can be expensive.
+
+So when is it viable?
+
+You'll do the same operations
+all the data.
+
+OK, if each day you do something
+different it's not
+
+that great and items can be
+stored in contiguous memory,
+
+so when you load you can say I'm
+getting nice in one word,
+
+if I'm getting two 32 bit, so
+four 16 bit, so I can do that.
+
+And you don't end up picking
+each operations and doing
+
+individual things too much.
+
+So if you are to pick each
+individual elements a lot,
+
+then you have to actually now
+pick apart that word and that
+
+can be multiple operations
+and expensive.
+
+So here's a simple example.
+
+This, I think, from after last
+bithacks class, this is a
+
+little bit, you probably know,
+can come up with enough
+
+examples here.
+
+What I'm doing is I'm doing
+a Battleship board game.
+
+So you represent the board, and
+the interesting thing in
+
+this board is to know whether
+that location has something or
+
+not, it's empty or full, that's
+all I need to know.
+
+And so normally if I do this
+board game I can have two
+
+boards in here.
+
+But what I'm doing is having
+this overlap calculations,
+
+saying of the two boards,
+how many things overlap.
+
+I can just have each location
+represented by integer, but
+
+then only the representing one
+value is not good enough.
+
+One thing I can do is I can just
+put each row into one 64
+
+bit word, and then instead of
+doing the two loops I can, in
+
+one loop, I can just do the
+ending off each row, and I get
+
+the result.
+
+So after the the bithack
+lecture, this should be kind
+
+of trivial.
+
+OK, everybody get it?
+
+Anybody have questions so far?
+
+Are we all on the same page?
+
+OK, good.
+
+There's a lot of blank faces so
+I want to help, I'll start
+
+asking more questions
+or something.
+
+OK, so that's modifying data.
+
+Now we're going to modifying
+code, where you will change
+
+the programs to actually get
+performance and that can be
+
+done in loops, logic rules,
+procedures, expression, and
+
+parallelism rules.
+
+When we get to parallelism rules
+we will actually do a
+
+lot more on them in future
+lectures, but I just want to
+
+address some basic stuff now.
+
+Bunch of different loop rules.
+
+I will go each of them
+individually.
+
+So first of all, why loops?
+
+Why do you think loops
+are so important?
+
+OK, somebody who hasn't
+answered the question.
+
+Why is loops so important?
+
+Why are we like really focused
+on loops all of the time?
+
+Anyone want to answer
+here, this side?
+
+OK.
+
+AUDIENCE: [INAUDIBLE] in terms
+of maintainability,
+
+[INAUDIBLE]?
+
+PROFESSOR: Yeah, so loops
+give you a nice, simple
+
+abstractions it's easier to
+maintain instead of having
+
+multiple computed times.
+
+Yes, instead of having same
+thing repeated millions of
+
+times for the same thing, if I
+write a loop, it's much more
+
+concise representation.
+
+That's why I think we do a lot
+of loops, because it makes
+
+programs easier.
+
+In fact, assume this word,
+loops didn't exist, OK?
+
+If loops doesn't exist that
+means you're going at each
+
+instruction get executed
+only one time.
+
+If you have a 3 gigahertz
+machine that requires even if
+
+you do one instruction per cycle
+in 32 bit instruction
+
+you need 12 gigabytes of
+instruction per second, if you
+
+only execute one instruction
+once.
+
+That means if you have 100
+gigabyte disk full of a
+
+program you go through each
+instruction the entire 100
+
+gigabytes in 8 seconds.
+
+OK.
+
+Of course this can never be
+done, that means you cannot
+
+feed 100 gigabytes into the
+processor in 8 seconds.
+
+That won't work because of
+the disk access time,
+
+caches, and all those.
+
+Even if it is doable, what
+that means is the entire
+
+reason your Pentium is running
+at 3 gigahertz and actually
+
+showing like it's running as 3
+gigahertz is because you are
+
+using instructions
+many, many times.
+
+You have loops that run
+millions of times.
+
+If you don't have loops you
+can use whatever the data
+
+machine you build in '004 and
+that probably as fast you
+
+could get because of this
+instruction thing.
+
+So loops are critical, and
+loops are what makes our
+
+programs run fast.
+
+Repeated execution of same
+instruction again
+
+and again and again.
+
+OK.
+
+So in the world, in that sense,
+if you think about
+
+this, unless there are some
+instruction that's run
+
+millions of times, you can
+never keep this ferocious
+
+beast's appetite full because
+there will always be new
+
+instructions.
+
+So because of that looking at
+loops, if you want to get good
+
+performance just looking at the
+most important loops, the
+
+inner loops, and just doing only
+that we'll probably get
+
+you most of way in
+many, many cases.
+
+And basically I could even say
+99 of the program execution
+
+time is in 10% of the code,
+even, more than
+
+that in many cases.
+
+Because otherwise
+[UNINTELLIGIBLE]
+
+back of the envelope calcuation
+you can do, you
+
+realize how much code you need
+to feed the beast to keep it
+
+active otherwise.
+
+So first loop optimization,
+loop and
+
+invariant code motion.
+
+So normally in a loop you run
+millions of times, and if you
+
+do the same thing millions of
+times and get the same results
+
+you are just doing useless
+computation.
+
+And so here the key thing is
+most of the time the compiler,
+
+a good compiler will
+come help you.
+
+So in this class you're
+not trying
+
+to replace the compiler.
+
+We, as humans, we want to the
+least amount of work.
+
+The compilers [UNINTELLIGIBLE]
+dumb things sitting in there,
+
+it can do most of
+the hard work.
+
+The key thing is first
+trying to get the
+
+compiler to do the work.
+
+Only do things yourself if
+the compiler cannot do.
+
+So most of the time compiler,
+if it can analyze the code,
+
+and prove the results are the
+same in each iteration, it's
+
+going to get rid of it, it
+will do that for you.
+
+But there are cases it's not
+possible because sometimes the
+
+computation might be too costly
+and also there might be
+
+cases the computation is too
+cheap if you hoist it out, you
+
+have to keep the results in
+some [UNINTELLIGIBLE]
+
+and if you keep too many things
+in too many registers,
+
+that cost might be
+too expensive.
+
+So there might be case that you
+might not do, but most of
+
+the time what happens
+because the
+
+compiler can't do anything.
+
+So here's a good example.
+
+I'm doing, I don't know why I
+did that, but square root and
+
+take exponential off that.
+
+Compiler look at that
+as functions.
+
+I have no idea what the function
+are most of the time.
+
+The compiler can't tell what
+each function does because the
+
+function call.
+
+It can do any arbitrary thing as
+far as the compiler knows.
+
+It says, OK, function call,
+I don't know what happened
+
+inside so I'm just giving up and
+I'm just leaving it, but
+
+you, on the other hand, knows
+that the square root function,
+
+exponential function doesn't
+have any what you call the
+
+side effects.
+
+That means those functions
+doesn't go
+
+changing anything else.
+
+It just calculates
+[UNINTELLIGIBLE] the value,
+
+you'll know this basically
+calculate the same value again
+
+and again and you can just
+basically take it out, do it
+
+twice, happy.
+
+So lot of times make sure
+the compiler can do it.
+
+If the compiler cannot do then
+you have to go in and
+
+interfere at that point.
+
+So here's another interesting
+thing the compilers cannot do.
+
+A lot of times you're going
+through this array or data
+
+structure looking
+for some value.
+
+OK, once you've found the value,
+you will say OK, found
+
+it, I return.
+
+OK.
+
+Normally what that means is when
+you're going to add it,
+
+there's two things.
+
+First of all you had to test
+whether you found the value
+
+that you're trying to exit.
+
+Second, you have to make sure
+that you don't overrun on the
+
+data structure, you're
+not overrunning that.
+
+you have to make sure you're not
+at the end of that because
+
+that value might not
+be in that area.
+
+If that's the case, you run
+to the end of that.
+
+So pretend I don't find it.
+
+So you do two tests.
+
+One thing you can do is you
+start doing the two test at
+
+the end of that array, how about
+you add the value you
+
+are testing for?
+
+So you know when you reach to
+the end you will always find
+
+the value because you
+added there, so you
+
+know it's there already.
+
+So by doing that you can reuse
+the test by just looking for
+
+the value because now when it
+comes to the end, you don't
+
+have to do anymore tests because
+the value you're
+
+looking is already there and
+you found that, you go out.
+
+But you should be able to add
+that value to the end of that.
+
+So what you do is this is your
+normal test that's what you're
+
+doing is you're, if I can get my
+mouse, you're going through
+
+this array, looking
+for a value.
+
+A value I return otherwise
+I return minus 1 in here.
+
+Now I do two tests.
+
+I do this test to make
+sure that I'm not at
+
+the end of the array.
+
+I'm [UNINTELLIGIBLE] this one.
+
+So, in fact, [UNINTELLIGIBLE]
+
+loop I just can put the two
+tests next to each other so
+
+this is what you're doing.
+
+But instead of doing that one
+thing I can do is put that at
+
+the end of the array, after
+all the data that I care
+
+about, I can put the value I'm
+looking for and then I just
+
+only do one test.
+
+I check for that value.
+
+So if you find the real
+value in the area, at
+
+that point I'm done.
+
+Or I ran out of the array, and
+after I ran out the real data
+
+I just found the value because
+I, myself, put it there.
+
+And so I have to find it, and
+the minute I find it, if I
+
+realize that's the case I say,
+OK, that's the value I put and
+
+I [UNINTELLIGIBLE].
+
+Here I have done something
+which is not really good
+
+programming practice.
+
+Can anybody put your 005
+hat and say, that's bad
+
+programming?
+
+AUDIENCE: You modified
+[INAUDIBLE].
+
+PROFESSOR: I modified
+my input array.
+
+I know.
+
+That's not that great.
+
+I mean if I did it really well,
+if I want to make sure
+
+what I should have done is kept
+the old value of the n
+
+and at the end, it back
+so it looks the
+
+pristine thing I got.
+
+I mean, if I was really careful
+I would have done
+
+that, and then my invariant that
+my input array haven't
+
+changed would hold nicely.
+because here I have mucked
+
+with my input array.
+
+So even though you are
+constantly doing performance
+
+programming you should still
+have a good eye for doing good
+
+correct programming and keeping
+nice programming
+
+variants around than mucking
+it all over the place.
+
+So if you wonder putting a new
+hat in here, you should still
+
+have the 005 hat, at
+least partially.
+
+What else can we do?
+
+A lot of times what you find
+is we have these loops, and
+
+loops have a couple
+of features.
+
+First of all, you have to keep
+checking the loop condition,
+
+that's expensive.
+
+And if the loop body is very
+small, the compiler doesn't
+
+have that much opportunity to
+do anything useful in the
+
+body, just basically
+compile as is.
+
+So one thing you want to do is
+if the loop bodies are too
+
+small and the number of
+iterations is small, you want
+
+to unroll the loop.
+
+So in here, instead of doing
+this calculation again and
+
+again, I want to actually do a
+computation unrolled, and this
+
+gives you two things.
+
+First of all I get rid of
+this disk, so I actually
+
+[UNINTELLIGIBLE] in here.
+
+And second, this computation can
+be done much faster, the
+
+compiler can do this much
+faster than this one.
+
+Do you see why?
+
+Can anybody see why this
+computation would happen much
+
+faster than this doing in
+the loop iteration?
+
+AUDIENCE: Because you don't have
+to write the final result
+
+of the variable until all
+the numbers [INAUDIBLE]?
+
+PROFESSOR: So that's
+one thing.
+
+Even the final results in the
+register what happens in here?
+
+So that's a good assertion
+but that's not
+
+exactly what's back there.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK, he got 90%
+of the way there.
+
+First of all here I
+had increment i.
+
+And I have it check
+[UNINTELLIGIBLE]
+
+the loop condition.
+
+That's another point in here.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: The one on right
+can be run in parallel.
+
+In here I am doing
+sum equals--
+
+some plus A I, so that means
+I have to calculate
+
+[UNINTELLIGIBLE].
+
+Once that is done and we get the
+results only then I can go
+
+add the two, only then
+I can add day three.
+
+So the last [UNINTELLIGIBLE]
+
+using, you can show 16
+instructions at every cycle.
+
+OK what six things you
+can do in here?
+
+Nothing.
+
+Because you're just waiting.
+
+You're twiddling your thumb for
+the first one to finish,
+
+to do that.
+
+In here, you can say, look, I
+don't have to add A1A to it.
+
+I can just do these things
+in parallel.
+
+The first cycle I can
+add is 0 to A of 1.
+
+that's one instruction
+2 3 2 4 5 3 6 7.
+
+I can add all those things
+together as a tree.
+
+I can do tree addition instead
+of one after another, that can
+
+happen in one go.
+
+And I can get a six editions
+done and then the next
+
+instruction I add the
+[UNINTELLIGIBLE] and at the
+
+later stages do not have too
+much to do but I could get a
+
+lot of [UNINTELLIGIBLE].
+
+So the compiler can actually
+[UNINTELLIGIBLE]
+
+all of that.
+
+So that works very nicely if
+I have small number of
+
+iterations.
+
+But if you have a large number
+of iterations, you can still
+
+do some stuff.
+
+So in here what you can do is
+it goes to one and you can
+
+say, OK, I don't know.
+
+I don't know how to unroll fully
+because I don't know
+
+what n is, but I can
+unroll partially.
+
+So here what I can do is say,
+look, I have been running it n
+
+times, I will unroll
+my loop four times.
+
+OK.
+
+So I at least get enough
+of unrolling here.
+
+That way you can choose.
+
+That is, you unroll enough that
+the meshing can get busy.
+
+It's not just crawling.
+
+And then I haven't blown up my
+code like crazy in here.
+
+And of course you had to clean
+up and then you have to know
+
+how many full iterations.
+
+So how do you choose
+how much to unroll?
+
+What impacts my number
+of unrolls?
+
+I unroll four times.
+
+You can get greedy, and say, I'm
+going to unroll 8 times,
+
+16, 32, 64, 128.
+
+Because a lot of time these are
+not zero-sum some gains.
+
+Some stuff impact
+some other way.
+
+So what should I use normally
+for my amount of
+
+iterations to unroll?
+
+Anybody want to take
+a guess what helps?
+
+AUDIENCE: It's probably the
+number [UNINTELLIGIBLE].
+
+PROFESSOR: OK, so in one sense
+you can look and say number of
+
+instructions I can execute in
+one cycle, that's a good thing
+
+to keep, unroll enough to
+keep the process of
+
+[UNINTELLIGIBLE] most
+of the time.
+
+But sometimes we can say oh
+that's hard to figure that one
+
+out, I don't know that because
+I'm at the compiler.
+
+I'm at high level.
+
+I don't know what happens
+at low level.
+
+I'm going to unroll
+1,000 times.
+
+So why shouldn't I unroll
+a huge amount?
+
+What happens if I
+unroll too much?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: You might--
+
+AUDIENCE: You might
+to be [INAUDIBLE].
+
+PROFESSOR: OK, define
+it more closely.
+
+What do you mean?
+
+AUDIENCE: Perhaps there's
+some [UNINTELLIGIBLE].
+
+PROFESSOR: That's the one
+interesting thing.
+
+Assume your number
+of iterations
+
+are not always millions.
+
+Sometimes you might
+[UNINTELLIGIBLE]
+
+hundred times, or 200 times.
+
+So if you unroll 500 times,
+you would never get to the
+
+unroll loop.
+
+You end up in this
+clean up loop.
+
+And so clean up loop, of course,
+is not unrolled and so
+
+you're back to your
+square one.
+
+And so a lot of times if you
+unroll too much and if your
+
+number of iterations doesn't
+fit so you end up in here,
+
+that's not good.
+
+Another thing is when you unroll
+loop here there's a
+
+huge amount of instructions
+now.
+
+That instructions might be too
+much, it might not fit in the
+
+cache, it might just overwhelm
+the memory system.
+
+So you have already now created
+a loop that doesn't
+
+fit in the instruction cache
+and that's not good either.
+
+So that will limit down roll, so
+don't get too greedy, just
+
+sometimes these are the things
+you kind of play with in the
+
+problems you're looking
+at and some of it is
+
+architecture dependent.
+
+Some of them are things like
+too much unroll where the
+
+number of iterations not that
+high is problem dependent.
+
+Another thing you can do there
+are many places if you have
+
+two different very same looking
+loops we can put them
+
+together into one loop and that
+gives [UNINTELLIGIBLE]
+
+all the loop tests and stuff
+and also the array access.
+
+At least done once, so
+that can give you
+
+a benefit in here.
+
+Here's interesting one.
+
+Here you have this weird loop
+that the j loop run from I to
+
+J in minus I, I to n minus I.
+How can I improve this one?
+
+Can anybody tell me what
+might happen in here?
+
+So I have outer loop I goes from
+0 to N, inner loop goes
+
+from I to N minus
+I. What happen?
+
+Somebody's getting it.
+
+OK.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yes, what happens is
+because what the loop is at
+
+the beginning you're going from
+basically 0 to N, and
+
+then the lower bound is going
+like this, upper bound is
+
+going like this.
+
+After N over 2, this is
+N, N over 2, there's
+
+no iterations left.
+
+OK, you're trading and trading
+and trading and after it
+
+iterates, so you're running
+outer loop, N over 2 to end
+
+with nothing running
+on the inner loop.
+
+And so if you have this kind
+of funky loops you can just
+
+look at it a little bit careful
+and say, wait a
+
+minute, that's not useful.
+
+So therefore I can just get rid
+of this new situations.
+
+And then sort of free
+trading to nothing.
+
+So that's loops rules.
+
+Loops are very important.
+
+also you can do a lot of
+interesting logic rules.
+
+So first of all, can anybody
+shout out what each of these
+
+things can be done?
+
+Square root of x
+greater than 0.
+
+Square of [UNINTELLIGIBLE]
+
+zero, sorry.
+
+x [UNINTELLIGIBLE].
+
+Actually, not [UNINTELLIGIBLE]
+
+sorry.
+
+x not equal to zero.
+
+Because x squared of
+x squared non-zero.
+
+OK.
+
+Here's something your compiler
+probably doesn't know about
+
+the transformation.
+
+We can do that.
+
+How about the next one?
+
+How can I get to input
+the next one?
+
+Square root of base climb,
+looking at the distance
+
+between x and Y and AB.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Eliminate
+the square root.
+
+It doesn't help anything you
+do except do too much
+
+computation.
+
+OK, next one.
+
+Yeah, I can basically multiply
+and then do take a one
+
+[UNINTELLIGIBLE]
+
+final one.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: One.
+
+OK, and then you should go and
+find that program who wrote
+
+that, but believe me you'll
+find these kind of code
+
+sitting somewhere because you
+didn't think through, you just
+
+start writing and suddenly you
+have this kind of nice axiom.
+
+So when do that this is
+something compiler can do, of
+
+for these kind of patterns.
+
+That was a stupid mistake but
+a lot of other things are
+
+things that a compiler cannot do
+but you know more than the
+
+compiler does.
+
+OK.
+
+Other interesting thing in
+here is if you're looking
+
+something like [UNINTELLIGIBLE]
+
+increasing function- OK, let
+me look at this carefully.
+
+OK, this is very similar to what
+we talked before with the
+
+[INAUDIBLE]
+
+ending.
+
+So one thing you can do is I can
+put the cut off at the end
+
+and then I don't have to take
+check both the bounds and
+
+basically [UNINTELLIGIBLE]
+
+through something.
+
+Basically this is the
+[UNINTELLIGIBLE]
+
+check we did done a little
+bit differently.
+
+OK.
+
+And here's another interesting
+thing.
+
+Reordering test.
+
+So what can you do here?
+
+What do I do here?
+
+I'm looking at is, I am looking
+at two different a
+
+circles, see whether they
+are [UNINTELLIGIBLE]
+
+in here.
+
+This is expensive test because
+I had to do something in a
+
+square root and check
+whether it's less
+
+than or equal to radius.
+
+So here's what I had to do.
+
+How can I make this faster?
+
+What's the [UNINTELLIGIBLE]
+in here?
+
+So assume I have this bunch of
+balls running around in my
+
+graphics program.
+
+I want to make sure that the
+balls haven't collided.
+
+They are actually moving with no
+collision with other balls
+
+and I'm doing this test.
+
+What's a good [UNINTELLIGIBLE]
+in here?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: So he's getting there
+because most of the time
+
+what happens is if you're
+looking at two balls collision
+
+most times these balls are
+farther apart and if you just
+
+found the square around the
+ball, testing these two
+
+squares are colliding
+it's very cheap, OK?
+
+And then if the squares are all
+happy, then and only then
+
+you might want to check
+if actually all the
+
+balls are all happening.
+
+OK and by doing this square test
+you can do very expensive
+
+operations in here.
+
+You can basically do some very
+simple thing, in fact I have
+
+even reduced it more by just
+doing first doing the x side
+
+and then if x is
+[UNINTELLIGIBLE]
+
+I don't even have to check for
+Y. And only if those two
+
+checks fail that I realize,
+look, the square might be now
+
+there's a good chance it's
+actually the color id.
+
+And there's a really good chance
+most of the test, after
+
+doing the first two things,
+will be done.
+
+You'll never have to go through
+this very expensive
+
+operations.
+
+So here's something you have a
+little bit of intuition on
+
+what's going on out there in
+the problem, and use that
+
+intuition to look like more
+work, but in reality really
+
+reduce the amount of work you
+had to do because the test is
+
+very expensive.
+
+OK, here what I have done, OK
+this is a little bit of a
+
+contrived example, what I want
+to do is assume I have
+
+basically a 4 bit word
+in here, OK.
+
+And I am checking- this would be
+8 I think, so I have 8 bit
+
+word in here.
+
+OK, I'm checking whether the
+8 bit word is a palindrome.
+
+So the way I check the word is a
+palindrome is first of all I
+
+set up some bits in here,
+bit masks, OK?
+
+And I have a bit mask
+for the two ends.
+
+I said, OK, these two are same,
+then these two same,
+
+these two same, these two same,
+I just kind of go down
+
+the bit mask.
+
+Did everybody see
+how this work?
+
+And then in these two I kind
+of shift my bit mask to the
+
+side, these two, basically
+shifting.
+
+So I'm checking the most two
+bits are the same, the next
+
+two bits are the same, next two
+bits are the same, going
+
+on [UNINTELLIGIBLE].
+
+OK, so every time I do that
+I have [UNINTELLIGIBLE]
+
+this bit mask do this operation
+and stuff like that.
+
+Assume I am checking whether
+my [UNINTELLIGIBLE]
+
+correctors.
+
+If I call this a lot of
+times what can I do?
+
+Kind of out of the
+box thinking.
+
+So the one thing is if I am only
+looking for correctors,
+
+how many different correctors
+are there?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, because all the
+correctors in everything I
+
+look up, I have 8 bits,
+two to date.
+
+What's two to date?
+
+[UNINTELLIGIBLE].
+
+OK, so you have 256
+possibilities in here, OK.
+
+So I'm doing this to 256 why
+don't I precompute and store?
+
+So if I just calculate for 256
+different possibilities, we
+
+see the palindrome or not, I
+just store a bit for each of
+
+them, saying it's a palindrome
+or not, and then my palindrome
+
+test is very simple.
+
+I just look up my look up table
+and say, hey, is this a
+
+palindrome, no?
+
+Yes?
+
+No?
+
+Done.
+
+So if I'm doing this computation
+a lot of times I
+
+suddenly realize I can
+precompute the kind of things
+
+we did before.
+
+I am very safe, I can do that.
+
+So sometimes you have this
+programs that has very
+
+complicated control structures
+but when you look at this here
+
+you realize [UNINTELLIGIBLE]
+
+use multiple times in here.
+
+There's S1, if v S2, else S3.
+
+S4 again, if v S5.
+
+And so there re a lot of
+conditions going on in here.
+
+And something like that you can
+sometimes look at that and
+
+say, like OK, look, because
+my conditions are simple.
+
+I mean in here, I only do one,
+I just do that one and I will
+
+create the path depending
+on what the
+
+Boolean expressions are.
+
+And even if you have two or
+three conditions you can
+
+create a couple of parts
+depending on that.
+
+So I'm replicating some
+stuff, like S1 is in
+
+both, S4 is in both.
+
+So I have expanded my code a
+lot, but now instead of having
+
+this spaghetti code that my
+compiler and my architecture
+
+is going to stop all the time
+because [UNINTELLIGIBLE]
+
+prediction and stuff, as
+Professor Leiserson pointed
+
+out, can have issues.
+
+I created this nice single
+branch, lot of code to
+
+execute, lot of chances for
+my compiler to do a lot of
+
+optimization.
+
+I can say things like that.
+
+And compiler can do it most of
+the time and sometimes you
+
+might want to help
+the compiler.
+
+Procedure rules.
+
+So one interesting thing is a
+lot of times when you have a
+
+lot of small procedure calls.
+
+A couple of things.
+
+OK, let me ask you, what's the
+problem with having a lot of
+
+small procedure calls?
+
+You cause a lot of small methods
+all over the place.
+
+What's the problem with
+small methods?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: [UNINTELLIGIBLE]
+
+yes, because every time you do
+a method call you have to
+
+basically go change everything
+[UNINTELLIGIBLE], put it back
+
+in memory, stack, and
+then go do that.
+
+I have a basically calling
+[UNINTELLIGIBLE]
+
+expensive part.
+
+OK, so if I'm doing a very
+small thing your calling
+
+context might have a lot more
+than overhead than what the
+
+procedure does, method does.
+
+What else?
+
+What's a more subtle thing
+that can happen?
+
+So if you're thinking more, I'm
+a compiler guy so I think
+
+like compilers, what would the
+compiler do at this point?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Compiler
+[UNINTELLIGIBLE]
+
+oops, barrier, I have no idea
+what's happening in here.
+
+I had retrieved this
+as just bit stop.
+
+I will do a bunch of things
+above that, I will do a bunch
+
+things below that.
+
+But I can't go through that kind
+of thing, so the compiler
+
+basically treats that as, I
+can't touch that barrier.
+
+And that [UNINTELLIGIBLE] means
+the amount of stuff that
+
+the compiler can do is
+[UNINTELLIGIBLE].
+
+So one way to do that
+is basically inline.
+
+On a max function, it's pretty
+simple to inline.
+
+Basically you can define a macro
+that the CE front end
+
+will go inline for you.
+
+So this is simple.
+
+Or you can define inline method
+in here and put it in
+
+the same file, and then we will
+tell the compiler, look,
+
+go and try doing inline
+listening, and by doing that
+
+we are forcing the compiler, or
+telling it the ability to
+
+inline, and they're not only
+getting rid of the overhead of
+
+the method calls, but also
+you're letting the compiler a
+
+lot more opportunity to go and
+do something interesting.
+
+So here's something you'll
+find in many
+
+streaming type programs.
+
+What you do is you run through
+a loop, reading through a
+
+bunch of data, do
+some processing
+
+and writing it back.
+
+And then you want to get the
+data you wrote back, read it
+
+again, do some processing
+and write it back.
+
+The problem in that this one
+is the first loop which
+
+stretches through all data.
+
+So by the time I'm done with the
+first loop I have written
+
+all the data and the thing I
+wrote early is probably all
+
+the way down in my
+cache hierarchy.
+
+Because I wrote a huge amount
+and it doesn't count it in my
+
+cache so it goes down, down,
+down, and the next guy has to
+
+read it all the way
+from bottom up.
+
+So [UNINTELLIGIBLE]
+
+means instead of doing that what
+you can do is run for a
+
+small amount of data.
+
+So don't run the entire
+data set.
+
+Run a small amount of data,
+write it into a buffer in the
+
+middle that we know sit in the
+cache, and the disk guys picks
+
+up the buffer and finish it
+up and write it back.
+
+So by keeping the data in the
+buffers what they have done is
+
+between these two I actually
+had some nice locality.
+
+I can keep the data up.
+
+So as we go into memory systems
+and stuff like that
+
+these kind of patterns
+come up a lot.
+
+Ah ha.
+
+Tail recursion elimination.
+
+So here there are many functions
+that the last thing
+
+you do is call itself.
+
+OK?
+
+This is pretty expensive because
+what normally happens
+
+is when you call a function you
+set up a calling contest,
+
+you do all this context
+[UNINTELLIGIBLE]
+
+put things into the stack and
+go, but you don't need to keep
+
+instead because you're basically
+done with the
+
+previous guy.
+
+You're just calling just to
+go create another stack.
+
+In a lot of these cases you can
+reformulate the problem
+
+into nice loop that has
+no function calls.
+
+So, in here, when you're doing
+factorial, you can actually
+
+formulate the factorial in a way
+that you don't have to do
+
+a function call.
+
+So a lot of times if you end
+up in a situation that the
+
+last thing you do in some part
+is the call itself and if
+
+you're not doing anything
+afterwards, you can always end
+
+up in a situation where you
+don't know how do that, you
+
+can actually convert it into
+[UNINTELLIGIBLE] loop.
+
+And by doing this I got rid of
+all my calling overhead and
+
+stuff that I'm just starting
+a nice tight loop.
+
+OK?
+
+So if you have patterns that
+look like that you can think,
+
+OK, look, this is nice,
+I thought through
+
+[UNINTELLIGIBLE].
+
+I got this there.
+
+But now I can [UNINTELLIGIBLE]
+transform it to more iterative
+
+way of executing.
+
+In many cases you will find
+a way of doing that.
+
+OK, then there are a bunch
+of expression rules.
+
+So a lot of times you have this
+computation that if you
+
+think carefully you can let
+the preprocessor do in
+
+something like calculate
+something like that, if I know
+
+what [UNINTELLIGIBLE] are, stuff
+like that, I can just
+
+put it in as a constant and
+voila I don't even have to pay
+
+any cost to compute it because
+by the time it's compiled all
+
+the computing is done.
+
+And there are a lot of good
+cases you can just get rid of
+
+work by giving it to
+the preprocessor.
+
+I'm just calling sin(a) and
+sin(a) twice in here, and the
+
+sin(a) squared I just basically,
+the compiler
+
+probably won't know that the
+sine every time you give it
+
+the same number, you give it
+the same same input, it's a
+
+function, I think the compiler
+doesn't know that, and this is
+
+something you probably have
+to do for the compiler.
+
+Especially when you know the
+function has no side effects.
+
+This is a little bit more funky,
+so assume I do two
+
+similar computations, you might
+want to do them together
+
+as a single computation that
+gives the compiler more
+
+opportunity, but that means you
+relay the function like a
+
+sine, cosine, s of 1 function.
+
+It's a little bit of funky thing
+that in this list of
+
+interesting things to do.
+
+But I put it there because there
+might be cases you might
+
+find that's interesting, like if
+you're doing taking min and
+
+max, it might be calling
+min and max separated.
+
+You might be able to
+call it together.
+
+So the last set of rules
+is parallelism rules.
+
+Of course, we are going to visit
+parallelism like crazy
+
+in this class, but today we will
+just go through some very
+
+high level stuff to give you a
+little bit of feel for what
+
+can be done.
+
+So I have this rule,
+this program.
+
+So what's wrong with
+this program?
+
+Why would this program
+run very slow?
+
+Can anybody tell me?
+
+Why can't, in this program, I
+can't do the full utilization
+
+of my machine.
+
+The problem in this program is
+every iteration until this
+
+condition is calculated I can't
+start calculating this.
+
+And so every iteration I had
+of it, this is finished,
+
+condition calculated,
+and [UNINTELLIGIBLE]
+
+and new calculate that.
+
+And once that's done, you go
+to the next iteration.
+
+We go to next iteration.
+
+So by doing this I can't
+do too much work.
+
+On the other hand, if I can
+unroll the loop like two times
+
+and have two different
+conditions, now I can do this
+
+condition and these conditions,
+and these two can
+
+be done in parallel and when
+these two get resolved I can
+
+do these two operations.
+
+So instead of doing xmax, I'm
+operating two different
+
+variables and at the end
+I can resolve that.
+
+So what I'm doing is
+I'm calculating
+
+two things in there.
+
+And they go to four things,
+whatever, to
+
+keep the machine busy.
+
+And each of them can be
+calculated independently.
+
+OK, so I can get parallelism
+and at the end of the day I
+
+can do that to help when I'm
+summing something or whatever.
+
+Do you see this?
+
+So to get the six instruction
+issued at a time, something
+
+like that will give you more
+abilities because there's more
+
+things that can run
+in parallel.
+
+So most of the time it will be
+good to see whether you can
+
+eliminate these kind of chains
+like here xmax is a chain
+
+because xmax--
+
+until the previous is calculated
+I can't calculate
+
+the next one, until that so I
+have this chain that until
+
+this is calculated I can't do
+this, until this is done I
+
+can't do the next iteration, so
+xmax is kind of keeping me
+
+very sequential.
+
+By doing that I have two
+things I can calculate.
+
+So other interesting things is
+if you are doing through this
+
+kind of data structure
+link list.
+
+Sometimes if you have I believe
+the bypass have
+
+another point that points couple
+of things ahead then I
+
+can keep multiple of
+them going on.
+
+So I can do sort of waiting
+for the next one I can
+
+basically switch two elements,
+do that so the next one I can
+
+get some parallelism in here so
+I can do things like that.
+
+So to get some basic parallel
+performance going on.
+
+And this is basic kind of a
+little bit of a data structure
+
+augmentation.
+
+You add additional data
+make it run faster.
+
+And you want to get all
+your loops vectorized.
+
+That means you want to run
+things like assembly
+
+instruction.
+
+If you're using 32 bits, you
+want to put a couple of them
+
+together, run in
+one SIMD unit.
+
+But I don't want any of
+you guys to go write
+
+assembly to do this.
+
+It's going to be a big pain to
+write all the SIMD assembly.
+
+We are not talking about
+assembly but most the
+
+compiler, [UNINTELLIGIBLE]
+compiler is somewhat
+
+good at doing it.
+
+So what this means is you're
+kind of really nudge the
+
+compiler, look at bunch of
+compiler frags to get the
+
+compiler to do it.
+
+Sometimes it's--
+
+when we go more into it, we'll
+figure out how we can do it
+
+looking at given the right flags
+to compiler, sometimes
+
+chaining the program a
+little bit makes it
+
+easier for the compiler.
+
+So sometimes just wrestling with
+the compiler, that's much
+
+more easier, believe me, than
+trying to do it by yourself.
+
+By doing that you can get some
+interesting performance.
+
+And we will talk a lot more
+about this coarse grain
+
+parallelism and we have a bunch
+of lectures on that.
+
+Trying to figure out how to get
+multicores, each core do
+
+something parallel, and get
+all your [UNINTELLIGIBLE]
+
+in the machine working
+for at a given time
+
+then only one guy.
+
+And so here's an interesting
+situation.
+
+So I have this problem here.
+
+Can I run this parallel?
+
+So what I'm doing is I'm doing
+these two loops and I'm adding
+
+all the elements of
+an array to total.
+
+Is this parallel?
+
+Can I run anything or any of
+these things parallel?
+
+Somebody says, yes, no,
+whatever, what do you think?
+
+Take a stand.
+
+OK, what do you think?
+
+AUDIENCE: I think yes.
+
+PROFESSOR: Somebody
+says yes, good.
+
+Yes, takers, no takers.
+
+Yes, everybody says yes.
+
+[UNINTELLIGIBLE]
+
+is parallel.
+
+But look at here, what happens
+is previous total is needed to
+
+calculate the next total, so how
+can I run this parallel?
+
+AUDIENCE: [INAUDIBLE]
+
+for loop jumps every two.
+
+PROFESSOR: OK, so she's somewhat
+onto it, so let me
+
+show you what we can do.
+
+One thing you can do is instead
+of calculating one
+
+total for each basically
+column, you can
+
+calculate its own total.
+
+OK?
+
+So what happens is so for this
+i's row, j's column.
+
+So for each row, so each row
+gets a different total, a temp
+
+total, and so what that means
+is you can calculate all the
+
+columns total separately.
+
+You can total all the columns,
+and then total up those values
+
+to get the full total.
+
+So totalling up columns can be
+done parallel because now all
+
+of these things can be done
+parallel because it's
+
+totalling up two different,
+multiple different values.
+
+So it's kind of what she said
+but you do it for each row
+
+separately.
+
+And so here's something, you
+made the program a little bit
+
+more complicated.
+
+Actually for a sequence it run a
+little bit slower but at the
+
+end of the day you actually
+get the program
+
+parallelizable.
+
+So a lot of times when you're
+parallelizing is to also
+
+looking at that algorithm little
+bit changes to the
+
+program that at the beginning
+might look like you're slowing
+
+down the program but ending
+up getting good parallel
+
+performance.
+
+So a lot of parallelism
+looks like this.
+
+So here's the entire list of
+things we talked about.
+
+It's out there so you can go
+look at them and see if you
+
+understand them better.
+
+And I'm leaving you with this
+example that I'm not going to
+
+have time to go through. which
+is my program of a traveling
+
+salesman problem.
+
+So what you're doing is you're
+looking at a way for a
+
+tradesman to travel to
+all of the city's
+
+with a minimum cost.
+
+Of course the minimum shortest
+thing is exponential algorithm
+
+so you don't do that.
+
+There's a good heuristic, that
+the greedy heuristic every
+
+time you go to the city you go
+to the cheapest city that's
+
+not visited and you just jump
+around and that's seem to be
+
+pretty good heuristic.
+
+And so I call this up, and I
+will go to the end and then
+
+just finish it up.
+
+Oops, I went too far.
+
+So what I did was I have eight
+different stages basically,
+
+each stage I did some changes
+and then I got this program to
+
+run about five times faster
+than from where I started.
+
+So you will see at each
+stage what I did.
+
+So this is basically out of the
+menu of things I showed
+
+you I found an instance I can
+do and in this program I got
+
+five times faster.
+
+This is more normal than the
+300 [UNINTELLIGIBLE]
+
+I got [UNINTELLIGIBLE]
+
+and that's a real extreme
+case, but enjoy
+
+looking at this code.
\ No newline at end of file
diff --git a/2oooMpS_3vg.txt b/2oooMpS_3vg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c0243ef55695b28e6f65cdefea8f03f401072f83
--- /dev/null
+++ b/2oooMpS_3vg.txt
@@ -0,0 +1,13267 @@
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+
+ align:start position:0%
+do a little primer on climate science
+and a very little primer on the science
+
+ align:start position:0%
+and a very little primer on the science
+ 
+
+ align:start position:0%
+and a very little primer on the science
+and a primer on the
+
+ align:start position:0%
+and a primer on the
+ 
+
+ align:start position:0%
+and a primer on the
+policy uh this could easily take more
+
+ align:start position:0%
+policy uh this could easily take more
+ 
+
+ align:start position:0%
+policy uh this could easily take more
+than a semester but we'll do it in an
+
+ align:start position:0%
+than a semester but we'll do it in an
+ 
+
+ align:start position:0%
+than a semester but we'll do it in an
+hour and a half so
+
+ align:start position:0%
+hour and a half so
+ 
+
+ align:start position:0%
+hour and a half so
+uh what I'm going to mostly do is do
+
+ align:start position:0%
+uh what I'm going to mostly do is do
+ 
+
+ align:start position:0%
+uh what I'm going to mostly do is do
+what economists often do which is to say
+
+ align:start position:0%
+what economists often do which is to say
+ 
+
+ align:start position:0%
+what economists often do which is to say
+well let's suppose we have a zar let's
+
+ align:start position:0%
+well let's suppose we have a zar let's
+ 
+
+ align:start position:0%
+well let's suppose we have a zar let's
+suppose we have have a zar who can who
+
+ align:start position:0%
+suppose we have have a zar who can who
+ 
+
+ align:start position:0%
+suppose we have have a zar who can who
+can set policy what would the Zar do
+
+ align:start position:0%
+can set policy what would the Zar do
+ 
+
+ align:start position:0%
+can set policy what would the Zar do
+about climate let's assume it it's not
+
+ align:start position:0%
+about climate let's assume it it's not
+ 
+
+ align:start position:0%
+about climate let's assume it it's not
+it's it's a modern Zar not a denist zar
+
+ align:start position:0%
+it's it's a modern Zar not a denist zar
+ 
+
+ align:start position:0%
+it's it's a modern Zar not a denist zar
+um I'm going to argue and try to
+
+ align:start position:0%
+um I'm going to argue and try to
+ 
+
+ align:start position:0%
+um I'm going to argue and try to
+indicate to you why even for a zar this
+
+ align:start position:0%
+indicate to you why even for a zar this
+ 
+
+ align:start position:0%
+indicate to you why even for a zar this
+would be a hard problem this is the
+
+ align:start position:0%
+would be a hard problem this is the
+ 
+
+ align:start position:0%
+would be a hard problem this is the
+hardest public policy problem I've ever
+
+ align:start position:0%
+hardest public policy problem I've ever
+ 
+
+ align:start position:0%
+hardest public policy problem I've ever
+come near um
+
+ align:start position:0%
+come near um
+ 
+
+ align:start position:0%
+come near um
+so today we have AAR to Wednesday and
+
+ align:start position:0%
+so today we have AAR to Wednesday and
+ 
+
+ align:start position:0%
+so today we have AAR to Wednesday and
+Friday uh we don't it's like the real
+
+ align:start position:0%
+Friday uh we don't it's like the real
+ 
+
+ align:start position:0%
+Friday uh we don't it's like the real
+world and we will go through a
+
+ align:start position:0%
+world and we will go through a
+ 
+
+ align:start position:0%
+world and we will go through a
+negotiation in which you will be on as
+
+ align:start position:0%
+negotiation in which you will be on as
+ 
+
+ align:start position:0%
+negotiation in which you will be on as
+you know on teams we'll talk a little
+
+ align:start position:0%
+you know on teams we'll talk a little
+ 
+
+ align:start position:0%
+you know on teams we'll talk a little
+bit about that at the end because we're
+
+ align:start position:0%
+bit about that at the end because we're
+ 
+
+ align:start position:0%
+bit about that at the end because we're
+going to have to do some adjustments you
+
+ align:start position:0%
+going to have to do some adjustments you
+ 
+
+ align:start position:0%
+going to have to do some adjustments you
+all want to be rich countries you can't
+
+ align:start position:0%
+all want to be rich countries you can't
+ 
+
+ align:start position:0%
+all want to be rich countries you can't
+all be rich countries some of you have
+
+ align:start position:0%
+all be rich countries some of you have
+ 
+
+ align:start position:0%
+all be rich countries some of you have
+to be poor uh it's like life um all
+
+ align:start position:0%
+to be poor uh it's like life um all
+ 
+
+ align:start position:0%
+to be poor uh it's like life um all
+right so so let me do a a very little
+
+ align:start position:0%
+right so so let me do a a very little
+ 
+
+ align:start position:0%
+right so so let me do a a very little
+bit of background on the science and
+
+ align:start position:0%
+bit of background on the science and
+ 
+
+ align:start position:0%
+bit of background on the science and
+then talk about why it's a hard policy
+
+ align:start position:0%
+then talk about why it's a hard policy
+ 
+
+ align:start position:0%
+then talk about why it's a hard policy
+problem um
+
+ align:start position:0%
+problem um
+ 
+
+ align:start position:0%
+problem um
+you've probably seen this graph uh this
+
+ align:start position:0%
+you've probably seen this graph uh this
+ 
+
+ align:start position:0%
+you've probably seen this graph uh this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+from uh uh NASA global temperatures are
+
+ align:start position:0%
+from uh uh NASA global temperatures are
+ 
+
+ align:start position:0%
+from uh uh NASA global temperatures are
+rising if you look if you look at the
+
+ align:start position:0%
+rising if you look if you look at the
+ 
+
+ align:start position:0%
+rising if you look if you look at the
+last few years it looks like a Slowdown
+
+ align:start position:0%
+last few years it looks like a Slowdown
+ 
+
+ align:start position:0%
+last few years it looks like a Slowdown
+this has been much debated the latest
+
+ align:start position:0%
+this has been much debated the latest
+ 
+
+ align:start position:0%
+this has been much debated the latest
+evidence suggests this is because of
+
+ align:start position:0%
+evidence suggests this is because of
+ 
+
+ align:start position:0%
+evidence suggests this is because of
+linia conditions in the Pacific which
+
+ align:start position:0%
+linia conditions in the Pacific which
+ 
+
+ align:start position:0%
+linia conditions in the Pacific which
+tend to lower the temperature um and
+
+ align:start position:0%
+tend to lower the temperature um and
+ 
+
+ align:start position:0%
+tend to lower the temperature um and
+solar radiation is at a minimum in its
+
+ align:start position:0%
+solar radiation is at a minimum in its
+ 
+
+ align:start position:0%
+solar radiation is at a minimum in its
+cycle
+
+ align:start position:0%
+cycle
+ 
+
+ align:start position:0%
+cycle
+those who follow these things closely
+
+ align:start position:0%
+those who follow these things closely
+ 
+
+ align:start position:0%
+those who follow these things closely
+expect when we go to El Nino conditions
+
+ align:start position:0%
+expect when we go to El Nino conditions
+ 
+
+ align:start position:0%
+expect when we go to El Nino conditions
+in the Pacific that we will break
+
+ align:start position:0%
+in the Pacific that we will break
+ 
+
+ align:start position:0%
+in the Pacific that we will break
+previous records nine of the 10 warmest
+
+ align:start position:0%
+previous records nine of the 10 warmest
+ 
+
+ align:start position:0%
+previous records nine of the 10 warmest
+years on record have been in this
+
+ align:start position:0%
+years on record have been in this
+ 
+
+ align:start position:0%
+years on record have been in this
+Century so if you smooth and you see
+
+ align:start position:0%
+Century so if you smooth and you see
+ 
+
+ align:start position:0%
+Century so if you smooth and you see
+there's a lot of variability year to
+
+ align:start position:0%
+there's a lot of variability year to
+ 
+
+ align:start position:0%
+there's a lot of variability year to
+year if you smooth the trend is
+
+ align:start position:0%
+year if you smooth the trend is
+ 
+
+ align:start position:0%
+year if you smooth the trend is
+reasonably
+
+ align:start position:0%
+reasonably
+ 
+
+ align:start position:0%
+reasonably
+clear that's
+
+ align:start position:0%
+clear that's
+ 
+
+ align:start position:0%
+clear that's
+data this is
+
+ align:start position:0%
+data this is
+ 
+
+ align:start position:0%
+data this is
+inference there's strong evidence backed
+
+ align:start position:0%
+inference there's strong evidence backed
+ 
+
+ align:start position:0%
+inference there's strong evidence backed
+by theory that human activity has a lot
+
+ align:start position:0%
+by theory that human activity has a lot
+ 
+
+ align:start position:0%
+by theory that human activity has a lot
+to to do with this this
+
+ align:start position:0%
+to to do with this this
+ 
+
+ align:start position:0%
+to to do with this this
+is uh Global Greenhouse emissions by gas
+
+ align:start position:0%
+is uh Global Greenhouse emissions by gas
+ 
+
+ align:start position:0%
+is uh Global Greenhouse emissions by gas
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+2004 you'll see on the right CO2 from
+
+ align:start position:0%
+2004 you'll see on the right CO2 from
+ 
+
+ align:start position:0%
+2004 you'll see on the right CO2 from
+fossil fuel use is a big contributor not
+
+ align:start position:0%
+fossil fuel use is a big contributor not
+ 
+
+ align:start position:0%
+fossil fuel use is a big contributor not
+the only
+
+ align:start position:0%
+the only
+ 
+
+ align:start position:0%
+the only
+contributor uh I think CO2 other is
+
+ align:start position:0%
+contributor uh I think CO2 other is
+ 
+
+ align:start position:0%
+contributor uh I think CO2 other is
+probably cement manufacturer this is
+
+ align:start position:0%
+probably cement manufacturer this is
+ 
+
+ align:start position:0%
+probably cement manufacturer this is
+land use deforestation biomass
+
+ align:start position:0%
+land use deforestation biomass
+ 
+
+ align:start position:0%
+land use deforestation biomass
+Agriculture and so forth methane nitrous
+
+ align:start position:0%
+Agriculture and so forth methane nitrous
+ 
+
+ align:start position:0%
+Agriculture and so forth methane nitrous
+oxide which is a a nasty Long Live gas
+
+ align:start position:0%
+oxide which is a a nasty Long Live gas
+ 
+
+ align:start position:0%
+oxide which is a a nasty Long Live gas
+largely comes from
+
+ align:start position:0%
+largely comes from
+ 
+
+ align:start position:0%
+largely comes from
+agriculture U methane comes of course
+
+ align:start position:0%
+agriculture U methane comes of course
+ 
+
+ align:start position:0%
+agriculture U methane comes of course
+from a variety of sources and then there
+
+ align:start position:0%
+from a variety of sources and then there
+ 
+
+ align:start position:0%
+from a variety of sources and then there
+are a bunch of long live very potent but
+
+ align:start position:0%
+are a bunch of long live very potent but
+ 
+
+ align:start position:0%
+are a bunch of long live very potent but
+very small very low concentration gases
+
+ align:start position:0%
+very small very low concentration gases
+ 
+
+ align:start position:0%
+very small very low concentration gases
+this is by
+
+ align:start position:0%
+this is by
+ 
+
+ align:start position:0%
+this is by
+sector and again you can see an awful
+
+ align:start position:0%
+sector and again you can see an awful
+ 
+
+ align:start position:0%
+sector and again you can see an awful
+lot of this is human activity obviously
+
+ align:start position:0%
+lot of this is human activity obviously
+ 
+
+ align:start position:0%
+lot of this is human activity obviously
+but generating electricity manufacturing
+
+ align:start position:0%
+but generating electricity manufacturing
+ 
+
+ align:start position:0%
+but generating electricity manufacturing
+transportation and again you get land
+
+ align:start position:0%
+transportation and again you get land
+ 
+
+ align:start position:0%
+transportation and again you get land
+use and Forestry so it's a it's a rain
+
+ align:start position:0%
+use and Forestry so it's a it's a rain
+ 
+
+ align:start position:0%
+use and Forestry so it's a it's a rain
+this is later data but it doesn't show
+
+ align:start position:0%
+this is later data but it doesn't show
+ 
+
+ align:start position:0%
+this is later data but it doesn't show
+it by gas
+
+ align:start position:0%
+it by gas
+ 
+
+ align:start position:0%
+it by gas
+um there are a wide variety of
+
+ align:start position:0%
+um there are a wide variety of
+ 
+
+ align:start position:0%
+um there are a wide variety of
+activities involved that that emit heat
+
+ align:start position:0%
+activities involved that that emit heat
+ 
+
+ align:start position:0%
+activities involved that that emit heat
+trapping gases
+
+ align:start position:0%
+trapping gases
+ 
+
+ align:start position:0%
+trapping gases
+um and uh again there's there's evidence
+
+ align:start position:0%
+um and uh again there's there's evidence
+ 
+
+ align:start position:0%
+um and uh again there's there's evidence
+there's theory that suggests that this
+
+ align:start position:0%
+there's theory that suggests that this
+ 
+
+ align:start position:0%
+there's theory that suggests that this
+is really a driver the changes in solar
+
+ align:start position:0%
+is really a driver the changes in solar
+ 
+
+ align:start position:0%
+is really a driver the changes in solar
+radiation the El Nino La n is not uh big
+
+ align:start position:0%
+radiation the El Nino La n is not uh big
+ 
+
+ align:start position:0%
+radiation the El Nino La n is not uh big
+enough yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+largely you also lose soil carbon uh if
+
+ align:start position:0%
+largely you also lose soil carbon uh if
+ 
+
+ align:start position:0%
+largely you also lose soil carbon uh if
+you if you cultivate and till the soil
+
+ align:start position:0%
+you if you cultivate and till the soil
+ 
+
+ align:start position:0%
+you if you cultivate and till the soil
+uh you'll lose you'll you'll you you'll
+
+ align:start position:0%
+uh you'll lose you'll you'll you you'll
+ 
+
+ align:start position:0%
+uh you'll lose you'll you'll you you'll
+have an effect you'll reduce what's
+
+ align:start position:0%
+have an effect you'll reduce what's
+ 
+
+ align:start position:0%
+have an effect you'll reduce what's
+stored in the soil so it's mostly
+
+ align:start position:0%
+stored in the soil so it's mostly
+ 
+
+ align:start position:0%
+stored in the soil so it's mostly
+deforestation but it can also be just
+
+ align:start position:0%
+deforestation but it can also be just
+ 
+
+ align:start position:0%
+deforestation but it can also be just
+agricultural
+
+ align:start position:0%
+agricultural
+ 
+
+ align:start position:0%
+agricultural
+practices um okay
+
+ align:start position:0%
+practices um okay
+ 
+
+ align:start position:0%
+practices um okay
+but for deforestation is crucial I'm
+
+ align:start position:0%
+but for deforestation is crucial I'm
+ 
+
+ align:start position:0%
+but for deforestation is crucial I'm
+going to we're going to talk mostly
+
+ align:start position:0%
+going to we're going to talk mostly
+ 
+
+ align:start position:0%
+going to we're going to talk mostly
+about CO2 from fossil fuels because
+
+ align:start position:0%
+about CO2 from fossil fuels because
+ 
+
+ align:start position:0%
+about CO2 from fossil fuels because
+that's where the policy action is and
+
+ align:start position:0%
+that's where the policy action is and
+ 
+
+ align:start position:0%
+that's where the policy action is and
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+deforestation um mostly
+
+ align:start position:0%
+deforestation um mostly
+ 
+
+ align:start position:0%
+deforestation um mostly
+because you can measure fossil fuel use
+
+ align:start position:0%
+because you can measure fossil fuel use
+ 
+
+ align:start position:0%
+because you can measure fossil fuel use
+relatively easily figuring out how
+
+ align:start position:0%
+relatively easily figuring out how
+ 
+
+ align:start position:0%
+relatively easily figuring out how
+agriculture generates nitrous oxide is
+
+ align:start position:0%
+agriculture generates nitrous oxide is
+ 
+
+ align:start position:0%
+agriculture generates nitrous oxide is
+harder much harder to measure but fuel
+
+ align:start position:0%
+harder much harder to measure but fuel
+ 
+
+ align:start position:0%
+harder much harder to measure but fuel
+use is rela relatively easy
+
+ align:start position:0%
+use is rela relatively easy
+ 
+
+ align:start position:0%
+use is rela relatively easy
+deforestation is relatively easy to
+
+ align:start position:0%
+deforestation is relatively easy to
+ 
+
+ align:start position:0%
+deforestation is relatively easy to
+measure so you can actually imagine
+
+ align:start position:0%
+measure so you can actually imagine
+ 
+
+ align:start position:0%
+measure so you can actually imagine
+agreements that might be enforceable so
+
+ align:start position:0%
+agreements that might be enforceable so
+ 
+
+ align:start position:0%
+agreements that might be enforceable so
+that's where the policy action is we
+
+ align:start position:0%
+that's where the policy action is we
+ 
+
+ align:start position:0%
+that's where the policy action is we
+also know whoops back we also know that
+
+ align:start position:0%
+also know whoops back we also know that
+ 
+
+ align:start position:0%
+also know whoops back we also know that
+there have been some clear impacts of
+
+ align:start position:0%
+there have been some clear impacts of
+ 
+
+ align:start position:0%
+there have been some clear impacts of
+climate change this is everybody's seen
+
+ align:start position:0%
+climate change this is everybody's seen
+ 
+
+ align:start position:0%
+climate change this is everybody's seen
+this this is a the change in sea ice in
+
+ align:start position:0%
+this this is a the change in sea ice in
+ 
+
+ align:start position:0%
+this this is a the change in sea ice in
+September of 79 to September of 2007 and
+
+ align:start position:0%
+September of 79 to September of 2007 and
+ 
+
+ align:start position:0%
+September of 79 to September of 2007 and
+obviously that continues and this is a
+
+ align:start position:0%
+obviously that continues and this is a
+ 
+
+ align:start position:0%
+obviously that continues and this is a
+projection and it can only be a
+
+ align:start position:0%
+projection and it can only be a
+ 
+
+ align:start position:0%
+projection and it can only be a
+projection for reasons I want to talk
+
+ align:start position:0%
+projection for reasons I want to talk
+ 
+
+ align:start position:0%
+projection for reasons I want to talk
+about of um days over
+
+ align:start position:0%
+about of um days over
+ 
+
+ align:start position:0%
+about of um days over
+100° and you see uh G there it gets hot
+
+ align:start position:0%
+100° and you see uh G there it gets hot
+ 
+
+ align:start position:0%
+100° and you see uh G there it gets hot
+in the desert but if in fact and the
+
+ align:start position:0%
+in the desert but if in fact and the
+ 
+
+ align:start position:0%
+in the desert but if in fact and the
+problem with this is is mainly uh human
+
+ align:start position:0%
+problem with this is is mainly uh human
+ 
+
+ align:start position:0%
+problem with this is is mainly uh human
+health people who are uh fragile in a
+
+ align:start position:0%
+health people who are uh fragile in a
+ 
+
+ align:start position:0%
+health people who are uh fragile in a
+variety of ways or who aren't air
+
+ align:start position:0%
+variety of ways or who aren't air
+ 
+
+ align:start position:0%
+variety of ways or who aren't air
+conditioned uh don't deal well with with
+
+ align:start position:0%
+conditioned uh don't deal well with with
+ 
+
+ align:start position:0%
+conditioned uh don't deal well with with
+large numbers of days over 100° it
+
+ align:start position:0%
+large numbers of days over 100° it
+ 
+
+ align:start position:0%
+large numbers of days over 100° it
+happened in Europe a couple of years ago
+
+ align:start position:0%
+happened in Europe a couple of years ago
+ 
+
+ align:start position:0%
+happened in Europe a couple of years ago
+there were a number of more than a
+
+ align:start position:0%
+there were a number of more than a
+ 
+
+ align:start position:0%
+there were a number of more than a
+number uh a fair number of deaths so
+
+ align:start position:0%
+number uh a fair number of deaths so
+ 
+
+ align:start position:0%
+number uh a fair number of deaths so
+these are obvious impacts if it gets
+
+ align:start position:0%
+these are obvious impacts if it gets
+ 
+
+ align:start position:0%
+these are obvious impacts if it gets
+warmer you have more hot days if it gets
+
+ align:start position:0%
+warmer you have more hot days if it gets
+ 
+
+ align:start position:0%
+warmer you have more hot days if it gets
+warmer the sea ice
+
+ align:start position:0%
+warmer the sea ice
+ 
+
+ align:start position:0%
+warmer the sea ice
+melts but that's a small part of the
+
+ align:start position:0%
+melts but that's a small part of the
+ 
+
+ align:start position:0%
+melts but that's a small part of the
+story is warming so why is this
+
+ align:start position:0%
+story is warming so why is this
+ 
+
+ align:start position:0%
+story is warming so why is this
+hard why is this a hard policy problem
+
+ align:start position:0%
+hard why is this a hard policy problem
+ 
+
+ align:start position:0%
+hard why is this a hard policy problem
+step reason one is the time
+
+ align:start position:0%
+step reason one is the time
+ 
+
+ align:start position:0%
+step reason one is the time
+scales and the time
+
+ align:start position:0%
+scales and the time
+ 
+
+ align:start position:0%
+scales and the time
+scales CO2 isn't doesn't come out of the
+
+ align:start position:0%
+scales CO2 isn't doesn't come out of the
+ 
+
+ align:start position:0%
+scales CO2 isn't doesn't come out of the
+atmosphere by simple exponential decay
+
+ align:start position:0%
+atmosphere by simple exponential decay
+ 
+
+ align:start position:0%
+atmosphere by simple exponential decay
+the process is complicated but if you
+
+ align:start position:0%
+the process is complicated but if you
+ 
+
+ align:start position:0%
+the process is complicated but if you
+think about a
+
+ align:start position:0%
+think about a
+ 
+
+ align:start position:0%
+think about a
+halflife you want to think about around
+
+ align:start position:0%
+halflife you want to think about around
+ 
+
+ align:start position:0%
+halflife you want to think about around
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+century if you can think of it in
+
+ align:start position:0%
+century if you can think of it in
+ 
+
+ align:start position:0%
+century if you can think of it in
+Half-Life
+
+ align:start position:0%
+Half-Life
+ 
+
+ align:start position:0%
+Half-Life
+terms not only does the stuff stay up
+
+ align:start position:0%
+terms not only does the stuff stay up
+ 
+
+ align:start position:0%
+terms not only does the stuff stay up
+there a long time but it takes a long
+
+ align:start position:0%
+there a long time but it takes a long
+ 
+
+ align:start position:0%
+there a long time but it takes a long
+time for its effects for the earth to be
+
+ align:start position:0%
+time for its effects for the earth to be
+ 
+
+ align:start position:0%
+time for its effects for the earth to be
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+equilibrium depending on you know how
+
+ align:start position:0%
+equilibrium depending on you know how
+ 
+
+ align:start position:0%
+equilibrium depending on you know how
+much Heat's coming in and and being
+
+ align:start position:0%
+much Heat's coming in and and being
+ 
+
+ align:start position:0%
+much Heat's coming in and and being
+trapped you got to warm the deep ocean
+
+ align:start position:0%
+trapped you got to warm the deep ocean
+ 
+
+ align:start position:0%
+trapped you got to warm the deep ocean
+the deep ocean is deep heat diffuses
+
+ align:start position:0%
+the deep ocean is deep heat diffuses
+ 
+
+ align:start position:0%
+the deep ocean is deep heat diffuses
+slowly so it's a it takes a while to
+
+ align:start position:0%
+slowly so it's a it takes a while to
+ 
+
+ align:start position:0%
+slowly so it's a it takes a while to
+warm so we're not an equilibrium now and
+
+ align:start position:0%
+warm so we're not an equilibrium now and
+ 
+
+ align:start position:0%
+warm so we're not an equilibrium now and
+the question of how far out of
+
+ align:start position:0%
+the question of how far out of
+ 
+
+ align:start position:0%
+the question of how far out of
+equilibrium we are is kind of a serious
+
+ align:start position:0%
+equilibrium we are is kind of a serious
+ 
+
+ align:start position:0%
+equilibrium we are is kind of a serious
+one um so even if you cut emissions
+
+ align:start position:0%
+one um so even if you cut emissions
+ 
+
+ align:start position:0%
+one um so even if you cut emissions
+sharply now warming would
+
+ align:start position:0%
+sharply now warming would
+ 
+
+ align:start position:0%
+sharply now warming would
+continue for
+
+ align:start position:0%
+continue for
+ 
+
+ align:start position:0%
+continue for
+decades given that we're not going to
+
+ align:start position:0%
+decades given that we're not going to
+ 
+
+ align:start position:0%
+decades given that we're not going to
+cut emission
+
+ align:start position:0%
+cut emission
+ 
+
+ align:start position:0%
+cut emission
+sharply we're dealing with centuries
+
+ align:start position:0%
+sharply we're dealing with centuries
+ 
+
+ align:start position:0%
+sharply we're dealing with centuries
+and in this literature people run out to
+
+ align:start position:0%
+and in this literature people run out to
+ 
+
+ align:start position:0%
+and in this literature people run out to
+2100 and typically out Beyond 2100 in
+
+ align:start position:0%
+2100 and typically out Beyond 2100 in
+ 
+
+ align:start position:0%
+2100 and typically out Beyond 2100 in
+thinking about a variety of
+
+ align:start position:0%
+thinking about a variety of
+ 
+
+ align:start position:0%
+thinking about a variety of
+things most human problems don't have
+
+ align:start position:0%
+things most human problems don't have
+ 
+
+ align:start position:0%
+things most human problems don't have
+time scales like that it means that
+
+ align:start position:0%
+time scales like that it means that
+ 
+
+ align:start position:0%
+time scales like that it means that
+actions taken today will affect your
+
+ align:start position:0%
+actions taken today will affect your
+ 
+
+ align:start position:0%
+actions taken today will affect your
+grandchildren that's not true in most
+
+ align:start position:0%
+grandchildren that's not true in most
+ 
+
+ align:start position:0%
+grandchildren that's not true in most
+areas of policy you can do tax policy
+
+ align:start position:0%
+areas of policy you can do tax policy
+ 
+
+ align:start position:0%
+areas of policy you can do tax policy
+Lots between now and the time your
+
+ align:start position:0%
+Lots between now and the time your
+ 
+
+ align:start position:0%
+Lots between now and the time your
+grandchildren vote but CO2 it's still
+
+ align:start position:0%
+grandchildren vote but CO2 it's still
+ 
+
+ align:start position:0%
+grandchildren vote but CO2 it's still
+going to be there the CO2 emitted today
+
+ align:start position:0%
+going to be there the CO2 emitted today
+ 
+
+ align:start position:0%
+going to be there the CO2 emitted today
+will still be there in large quantity
+
+ align:start position:0%
+will still be there in large quantity
+ 
+
+ align:start position:0%
+will still be there in large quantity
+when your grandchildren are walking
+
+ align:start position:0%
+when your grandchildren are walking
+ 
+
+ align:start position:0%
+when your grandchildren are walking
+around blaming you for it so if the Zar
+
+ align:start position:0%
+around blaming you for it so if the Zar
+ 
+
+ align:start position:0%
+around blaming you for it so if the Zar
+has to if we have a climate Zar he has
+
+ align:start position:0%
+has to if we have a climate Zar he has
+ 
+
+ align:start position:0%
+has to if we have a climate Zar he has
+to think about how to treat people not
+
+ align:start position:0%
+to think about how to treat people not
+ 
+
+ align:start position:0%
+to think about how to treat people not
+yet born because actions today will
+
+ align:start position:0%
+yet born because actions today will
+ 
+
+ align:start position:0%
+yet born because actions today will
+affect people not yet
+
+ align:start position:0%
+affect people not yet
+ 
+
+ align:start position:0%
+affect people not yet
+born I mean this is a typical example
+
+ align:start position:0%
+born I mean this is a typical example
+ 
+
+ align:start position:0%
+born I mean this is a typical example
+this is somebody's somebody's story of
+
+ align:start position:0%
+this is somebody's somebody's story of
+ 
+
+ align:start position:0%
+this is somebody's somebody's story of
+what gets flooded in Florida if you get
+
+ align:start position:0%
+what gets flooded in Florida if you get
+ 
+
+ align:start position:0%
+what gets flooded in Florida if you get
+about a meter sea level rise a meter
+
+ align:start position:0%
+about a meter sea level rise a meter
+ 
+
+ align:start position:0%
+about a meter sea level rise a meter
+your sea level rise is sort of order of
+
+ align:start position:0%
+your sea level rise is sort of order of
+ 
+
+ align:start position:0%
+your sea level rise is sort of order of
+magnitude what might happen in a
+
+ align:start position:0%
+magnitude what might happen in a
+ 
+
+ align:start position:0%
+magnitude what might happen in a
+century what's it worth today to prevent
+
+ align:start position:0%
+century what's it worth today to prevent
+ 
+
+ align:start position:0%
+century what's it worth today to prevent
+that in 2
+
+ align:start position:0%
+that in 2
+ 
+
+ align:start position:0%
+that in 2
+2112 uh for reference uh my mother lives
+
+ align:start position:0%
+2112 uh for reference uh my mother lives
+ 
+
+ align:start position:0%
+2112 uh for reference uh my mother lives
+there more or less so she's okay on the
+
+ align:start position:0%
+there more or less so she's okay on the
+ 
+
+ align:start position:0%
+there more or less so she's okay on the
+other hand she's 90 years old this
+
+ align:start position:0%
+other hand she's 90 years old this
+ 
+
+ align:start position:0%
+other hand she's 90 years old this
+doesn't apply to her um but it will
+
+ align:start position:0%
+doesn't apply to her um but it will
+ 
+
+ align:start position:0%
+doesn't apply to her um but it will
+apply potentially to great great
+
+ align:start position:0%
+apply potentially to great great
+ 
+
+ align:start position:0%
+apply potentially to great great
+grandchildren so
+
+ align:start position:0%
+grandchildren so
+ 
+
+ align:start position:0%
+grandchildren so
+time scales of a century or more are
+
+ align:start position:0%
+time scales of a century or more are
+ 
+
+ align:start position:0%
+time scales of a century or more are
+hard because you know you you want a
+
+ align:start position:0%
+hard because you know you you want a
+ 
+
+ align:start position:0%
+hard because you know you you want a
+discount but how do you do that this is
+
+ align:start position:0%
+discount but how do you do that this is
+ 
+
+ align:start position:0%
+discount but how do you do that this is
+a live controversy I'm not going to give
+
+ align:start position:0%
+a live controversy I'm not going to give
+ 
+
+ align:start position:0%
+a live controversy I'm not going to give
+you an answer economists have nasty
+
+ align:start position:0%
+you an answer economists have nasty
+ 
+
+ align:start position:0%
+you an answer economists have nasty
+arguments about this there are three
+
+ align:start position:0%
+arguments about this there are three
+ 
+
+ align:start position:0%
+arguments about this there are three
+ways you might want to think about
+
+ align:start position:0%
+ways you might want to think about
+ 
+
+ align:start position:0%
+ways you might want to think about
+it the obvious way to think about what
+
+ align:start position:0%
+it the obvious way to think about what
+ 
+
+ align:start position:0%
+it the obvious way to think about what
+am I going to do about a century from
+
+ align:start position:0%
+am I going to do about a century from
+ 
+
+ align:start position:0%
+am I going to do about a century from
+now is to just think about private
+
+ align:start position:0%
+now is to just think about private
+ 
+
+ align:start position:0%
+now is to just think about private
+sector well I could I could put it in a
+
+ align:start position:0%
+sector well I could I could put it in a
+ 
+
+ align:start position:0%
+sector well I could I could put it in a
+bank or I could invest in a business or
+
+ align:start position:0%
+bank or I could invest in a business or
+ 
+
+ align:start position:0%
+bank or I could invest in a business or
+I could invested in dealing with climate
+
+ align:start position:0%
+I could invested in dealing with climate
+ 
+
+ align:start position:0%
+I could invested in dealing with climate
+change I make that choice so if I I
+
+ align:start position:0%
+change I make that choice so if I I
+ 
+
+ align:start position:0%
+change I make that choice so if I I
+ought to be using the same kind of
+
+ align:start position:0%
+ought to be using the same kind of
+ 
+
+ align:start position:0%
+ought to be using the same kind of
+discounting in both decisions right
+
+ align:start position:0%
+discounting in both decisions right
+ 
+
+ align:start position:0%
+discounting in both decisions right
+because I don't want to I don't want to
+
+ align:start position:0%
+because I don't want to I don't want to
+ 
+
+ align:start position:0%
+because I don't want to I don't want to
+IM have an imbalance you missed the
+
+ align:start position:0%
+IM have an imbalance you missed the
+ 
+
+ align:start position:0%
+IM have an imbalance you missed the
+science you could have fixed it
+
+ align:start position:0%
+science you could have fixed it
+ 
+
+ align:start position:0%
+science you could have fixed it
+um this is Professor Solomon who has
+
+ align:start position:0%
+um this is Professor Solomon who has
+ 
+
+ align:start position:0%
+um this is Professor Solomon who has
+forgotten more about climate science
+
+ align:start position:0%
+forgotten more about climate science
+ 
+
+ align:start position:0%
+forgotten more about climate science
+than I could ever aspire to learn at any
+
+ align:start position:0%
+than I could ever aspire to learn at any
+ 
+
+ align:start position:0%
+than I could ever aspire to learn at any
+rate we're talking about policy and
+
+ align:start position:0%
+rate we're talking about policy and
+ 
+
+ align:start position:0%
+rate we're talking about policy and
+we're talking about discounting um and
+
+ align:start position:0%
+we're talking about discounting um and
+ 
+
+ align:start position:0%
+we're talking about discounting um and
+why why this is hard so one one school
+
+ align:start position:0%
+why why this is hard so one one school
+ 
+
+ align:start position:0%
+why why this is hard so one one school
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+thought uh says you got to use you got
+
+ align:start position:0%
+thought uh says you got to use you got
+ 
+
+ align:start position:0%
+thought uh says you got to use you got
+to use a um private sector discount
+
+ align:start position:0%
+to use a um private sector discount
+ 
+
+ align:start position:0%
+to use a um private sector discount
+rate and one reason this school of
+
+ align:start position:0%
+rate and one reason this school of
+ 
+
+ align:start position:0%
+rate and one reason this school of
+thought achieved prominence was the Army
+
+ align:start position:0%
+thought achieved prominence was the Army
+ 
+
+ align:start position:0%
+thought achieved prominence was the Army
+Corps of
+
+ align:start position:0%
+Corps of
+ 
+
+ align:start position:0%
+Corps of
+Engineers when deciding H whether or not
+
+ align:start position:0%
+Engineers when deciding H whether or not
+ 
+
+ align:start position:0%
+Engineers when deciding H whether or not
+to build dams always used a very low
+
+ align:start position:0%
+to build dams always used a very low
+ 
+
+ align:start position:0%
+to build dams always used a very low
+discount
+
+ align:start position:0%
+discount
+ 
+
+ align:start position:0%
+discount
+rate dams last a long time so if you use
+
+ align:start position:0%
+rate dams last a long time so if you use
+ 
+
+ align:start position:0%
+rate dams last a long time so if you use
+a very low discount rate Dam look pretty
+
+ align:start position:0%
+a very low discount rate Dam look pretty
+ 
+
+ align:start position:0%
+a very low discount rate Dam look pretty
+promising
+
+ align:start position:0%
+promising
+ 
+
+ align:start position:0%
+promising
+economically and it was a huge slog in
+
+ align:start position:0%
+economically and it was a huge slog in
+ 
+
+ align:start position:0%
+economically and it was a huge slog in
+the 50s and 60s to get the core of
+
+ align:start position:0%
+the 50s and 60s to get the core of
+ 
+
+ align:start position:0%
+the 50s and 60s to get the core of
+engineers to use a private sector rate
+
+ align:start position:0%
+engineers to use a private sector rate
+ 
+
+ align:start position:0%
+engineers to use a private sector rate
+to say you can build this kind of plant
+
+ align:start position:0%
+to say you can build this kind of plant
+ 
+
+ align:start position:0%
+to say you can build this kind of plant
+or you can build a dam you ought to use
+
+ align:start position:0%
+or you can build a dam you ought to use
+ 
+
+ align:start position:0%
+or you can build a dam you ought to use
+the same discount rate in both cases you
+
+ align:start position:0%
+the same discount rate in both cases you
+ 
+
+ align:start position:0%
+the same discount rate in both cases you
+ought to use a private sector rate to
+
+ align:start position:0%
+ought to use a private sector rate to
+ 
+
+ align:start position:0%
+ought to use a private sector rate to
+think about whether or not you build
+
+ align:start position:0%
+think about whether or not you build
+ 
+
+ align:start position:0%
+think about whether or not you build
+dams there's a second school of thought
+
+ align:start position:0%
+dams there's a second school of thought
+ 
+
+ align:start position:0%
+dams there's a second school of thought
+that says wait a minute this isn't
+
+ align:start position:0%
+that says wait a minute this isn't
+ 
+
+ align:start position:0%
+that says wait a minute this isn't
+really a private sector decision if you
+
+ align:start position:0%
+really a private sector decision if you
+ 
+
+ align:start position:0%
+really a private sector decision if you
+think about optimal growth Theory
+
+ align:start position:0%
+think about optimal growth Theory
+ 
+
+ align:start position:0%
+think about optimal growth Theory
+optimal growth Theory usually
+
+ align:start position:0%
+optimal growth Theory usually
+ 
+
+ align:start position:0%
+optimal growth Theory usually
+says let me not do more than wave my
+
+ align:start position:0%
+says let me not do more than wave my
+ 
+
+ align:start position:0%
+says let me not do more than wave my
+hands at that you usually says there's a
+
+ align:start position:0%
+hands at that you usually says there's a
+ 
+
+ align:start position:0%
+hands at that you usually says there's a
+there are two reasons you discount the
+
+ align:start position:0%
+there are two reasons you discount the
+ 
+
+ align:start position:0%
+there are two reasons you discount the
+future forget the private sector for the
+
+ align:start position:0%
+future forget the private sector for the
+ 
+
+ align:start position:0%
+future forget the private sector for the
+moment if you're doing everything
+
+ align:start position:0%
+moment if you're doing everything
+ 
+
+ align:start position:0%
+moment if you're doing everything
+optimally in the economy there are two
+
+ align:start position:0%
+optimally in the economy there are two
+ 
+
+ align:start position:0%
+optimally in the economy there are two
+reasons you discount the future one
+
+ align:start position:0%
+reasons you discount the future one
+ 
+
+ align:start position:0%
+reasons you discount the future one
+there might be a pure rate of time
+
+ align:start position:0%
+there might be a pure rate of time
+ 
+
+ align:start position:0%
+there might be a pure rate of time
+preference whatever that might
+
+ align:start position:0%
+preference whatever that might
+ 
+
+ align:start position:0%
+preference whatever that might
+mean and you value money you value
+
+ align:start position:0%
+mean and you value money you value
+ 
+
+ align:start position:0%
+mean and you value money you value
+benefits in the future less than
+
+ align:start position:0%
+benefits in the future less than
+ 
+
+ align:start position:0%
+benefits in the future less than
+benefits today because people people in
+
+ align:start position:0%
+benefits today because people people in
+ 
+
+ align:start position:0%
+benefits today because people people in
+the future will be
+
+ align:start position:0%
+the future will be
+ 
+
+ align:start position:0%
+the future will be
+richer and therefore being just a little
+
+ align:start position:0%
+richer and therefore being just a little
+ 
+
+ align:start position:0%
+richer and therefore being just a little
+bit quick with the hands uh uh income on
+
+ align:start position:0%
+bit quick with the hands uh uh income on
+ 
+
+ align:start position:0%
+bit quick with the hands uh uh income on
+the margin's worth less so if I were in
+
+ align:start position:0%
+the margin's worth less so if I were in
+ 
+
+ align:start position:0%
+the margin's worth less so if I were in
+the future and I were richer then a
+
+ align:start position:0%
+the future and I were richer then a
+ 
+
+ align:start position:0%
+the future and I were richer then a
+dollar's worth of benefit would be worth
+
+ align:start position:0%
+dollar's worth of benefit would be worth
+ 
+
+ align:start position:0%
+dollar's worth of benefit would be worth
+less to me then than it is now I'll take
+
+ align:start position:0%
+less to me then than it is now I'll take
+ 
+
+ align:start position:0%
+less to me then than it is now I'll take
+that into account I'll discount that
+
+ align:start position:0%
+that into account I'll discount that
+ 
+
+ align:start position:0%
+that into account I'll discount that
+second term because people will be
+
+ align:start position:0%
+second term because people will be
+ 
+
+ align:start position:0%
+second term because people will be
+wealthier says you make a judgment and
+
+ align:start position:0%
+wealthier says you make a judgment and
+ 
+
+ align:start position:0%
+wealthier says you make a judgment and
+their their formulas I won't trouble you
+
+ align:start position:0%
+their their formulas I won't trouble you
+ 
+
+ align:start position:0%
+their their formulas I won't trouble you
+their for formulas that say here's how
+
+ align:start position:0%
+their for formulas that say here's how
+ 
+
+ align:start position:0%
+their for formulas that say here's how
+you deal with that and then you you say
+
+ align:start position:0%
+you deal with that and then you you say
+ 
+
+ align:start position:0%
+you deal with that and then you you say
+well I have a preference we all have
+
+ align:start position:0%
+well I have a preference we all have
+ 
+
+ align:start position:0%
+well I have a preference we all have
+preference for today over tomorrow
+
+ align:start position:0%
+preference for today over tomorrow
+ 
+
+ align:start position:0%
+preference for today over tomorrow
+that's a pure rate of time
+
+ align:start position:0%
+that's a pure rate of time
+ 
+
+ align:start position:0%
+that's a pure rate of time
+preference the third approach that's
+
+ align:start position:0%
+preference the third approach that's
+ 
+
+ align:start position:0%
+preference the third approach that's
+come into the into the re literature
+
+ align:start position:0%
+come into the into the re literature
+ 
+
+ align:start position:0%
+come into the into the re literature
+recently says why do you have a pure
+
+ align:start position:0%
+recently says why do you have a pure
+ 
+
+ align:start position:0%
+recently says why do you have a pure
+rate of time preference what does that
+
+ align:start position:0%
+rate of time preference what does that
+ 
+
+ align:start position:0%
+rate of time preference what does that
+mean that discriminates between
+
+ align:start position:0%
+mean that discriminates between
+ 
+
+ align:start position:0%
+mean that discriminates between
+Generations a pure rate of time
+
+ align:start position:0%
+Generations a pure rate of time
+ 
+
+ align:start position:0%
+Generations a pure rate of time
+preference says even if my grandchildren
+
+ align:start position:0%
+preference says even if my grandchildren
+ 
+
+ align:start position:0%
+preference says even if my grandchildren
+are rich are no richer than I am
+
+ align:start position:0%
+are rich are no richer than I am
+ 
+
+ align:start position:0%
+are rich are no richer than I am
+uh I'm going to value a dollar to them
+
+ align:start position:0%
+uh I'm going to value a dollar to them
+ 
+
+ align:start position:0%
+uh I'm going to value a dollar to them
+less than a dollar to
+
+ align:start position:0%
+less than a dollar to
+ 
+
+ align:start position:0%
+less than a dollar to
+me that doesn't make moral
+
+ align:start position:0%
+me that doesn't make moral
+ 
+
+ align:start position:0%
+me that doesn't make moral
+sense so IID use a zero rate of pure
+
+ align:start position:0%
+sense so IID use a zero rate of pure
+ 
+
+ align:start position:0%
+sense so IID use a zero rate of pure
+time preference and then make a judgment
+
+ align:start position:0%
+time preference and then make a judgment
+ 
+
+ align:start position:0%
+time preference and then make a judgment
+if I if I can if I want to about how
+
+ align:start position:0%
+if I if I can if I want to about how
+ 
+
+ align:start position:0%
+if I if I can if I want to about how
+much richer they will be and how much
+
+ align:start position:0%
+much richer they will be and how much
+ 
+
+ align:start position:0%
+much richer they will be and how much
+that ought to matter when I think about
+
+ align:start position:0%
+that ought to matter when I think about
+ 
+
+ align:start position:0%
+that ought to matter when I think about
+benefits now I I I present this
+
+ align:start position:0%
+benefits now I I I present this
+ 
+
+ align:start position:0%
+benefits now I I I present this
+not those are very different
+
+ align:start position:0%
+not those are very different
+ 
+
+ align:start position:0%
+not those are very different
+positions and they have very different
+
+ align:start position:0%
+positions and they have very different
+ 
+
+ align:start position:0%
+positions and they have very different
+implications for how you think about the
+
+ align:start position:0%
+implications for how you think about the
+ 
+
+ align:start position:0%
+implications for how you think about the
+future and I have to tell you depending
+
+ align:start position:0%
+future and I have to tell you depending
+ 
+
+ align:start position:0%
+future and I have to tell you depending
+on on the day of the week and the
+
+ align:start position:0%
+on on the day of the week and the
+ 
+
+ align:start position:0%
+on on the day of the week and the
+weather I I myself vacillate but let me
+
+ align:start position:0%
+weather I I myself vacillate but let me
+ 
+
+ align:start position:0%
+weather I I myself vacillate but let me
+let me just give you the um the
+
+ align:start position:0%
+let me just give you the um the
+ 
+
+ align:start position:0%
+let me just give you the um the
+implications let's take rates to
+
+ align:start position:0%
+implications let's take rates to
+ 
+
+ align:start position:0%
+implications let's take rates to
+illustrate these 7% and 3% are used in
+
+ align:start position:0%
+illustrate these 7% and 3% are used in
+ 
+
+ align:start position:0%
+illustrate these 7% and 3% are used in
+federal government decision- making the
+
+ align:start position:0%
+federal government decision- making the
+ 
+
+ align:start position:0%
+federal government decision- making the
+7% you might think of as like a private
+
+ align:start position:0%
+7% you might think of as like a private
+ 
+
+ align:start position:0%
+7% you might think of as like a private
+sector rate the 3% gets down to that
+
+ align:start position:0%
+sector rate the 3% gets down to that
+ 
+
+ align:start position:0%
+sector rate the 3% gets down to that
+second category it's a pure rate of time
+
+ align:start position:0%
+second category it's a pure rate of time
+ 
+
+ align:start position:0%
+second category it's a pure rate of time
+preference plus an adjustment and and
+
+ align:start position:0%
+preference plus an adjustment and and
+ 
+
+ align:start position:0%
+preference plus an adjustment and and
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+1% was used in an influential report on
+
+ align:start position:0%
+1% was used in an influential report on
+ 
+
+ align:start position:0%
+1% was used in an influential report on
+climate change that takes the third
+
+ align:start position:0%
+climate change that takes the third
+ 
+
+ align:start position:0%
+climate change that takes the third
+position no pure rate of time preference
+
+ align:start position:0%
+position no pure rate of time preference
+ 
+
+ align:start position:0%
+position no pure rate of time preference
+no discrimination between
+
+ align:start position:0%
+no discrimination between
+ 
+
+ align:start position:0%
+no discrimination between
+Generations so let's let's uh apply that
+
+ align:start position:0%
+Generations so let's let's uh apply that
+ 
+
+ align:start position:0%
+Generations so let's let's uh apply that
+to a million dollars in 100
+
+ align:start position:0%
+to a million dollars in 100
+ 
+
+ align:start position:0%
+to a million dollars in 100
+years all right if I use 1% that million
+
+ align:start position:0%
+years all right if I use 1% that million
+ 
+
+ align:start position:0%
+years all right if I use 1% that million
+dollars in 100 years is worth 368
+
+ align:start position:0%
+dollars in 100 years is worth 368
+ 
+
+ align:start position:0%
+dollars in 100 years is worth 368
+$8,000 so I'd spend a fair amount
+
+ align:start position:0%
+$8,000 so I'd spend a fair amount
+ 
+
+ align:start position:0%
+$8,000 so I'd spend a fair amount
+wouldn't spend a million today but I'd
+
+ align:start position:0%
+wouldn't spend a million today but I'd
+ 
+
+ align:start position:0%
+wouldn't spend a million today but I'd
+spend a fair amount to avoid a million
+
+ align:start position:0%
+spend a fair amount to avoid a million
+ 
+
+ align:start position:0%
+spend a fair amount to avoid a million
+dollar worth of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Damages
+
+ align:start position:0%
+Damages
+ 
+
+ align:start position:0%
+Damages
+3% woo I wouldn't spend very much at all
+
+ align:start position:0%
+3% woo I wouldn't spend very much at all
+ 
+
+ align:start position:0%
+3% woo I wouldn't spend very much at all
+to avoid a million dollars worth of
+
+ align:start position:0%
+to avoid a million dollars worth of
+ 
+
+ align:start position:0%
+to avoid a million dollars worth of
+Damages and at
+
+ align:start position:0%
+Damages and at
+ 
+
+ align:start position:0%
+Damages and at
+7% we get what a guy who used to work
+
+ align:start position:0%
+7% we get what a guy who used to work
+ 
+
+ align:start position:0%
+7% we get what a guy who used to work
+for me called the magic ray gun you let
+
+ align:start position:0%
+for me called the magic ray gun you let
+ 
+
+ align:start position:0%
+for me called the magic ray gun you let
+me discount anything at 7%
+
+ align:start position:0%
+me discount anything at 7%
+ 
+
+ align:start position:0%
+me discount anything at 7%
+in the future it goes away it's it's a
+
+ align:start position:0%
+in the future it goes away it's it's a
+ 
+
+ align:start position:0%
+in the future it goes away it's it's a
+it's it's a
+
+ align:start position:0%
+it's it's a
+ 
+
+ align:start position:0%
+it's it's a
+disappearing disappearing function I
+
+ align:start position:0%
+disappearing disappearing function I
+ 
+
+ align:start position:0%
+disappearing disappearing function I
+would spend $9,000 today to avoid a
+
+ align:start position:0%
+would spend $9,000 today to avoid a
+ 
+
+ align:start position:0%
+would spend $9,000 today to avoid a
+million dollar worth of Damages in a 100
+
+ align:start position:0%
+million dollar worth of Damages in a 100
+ 
+
+ align:start position:0%
+million dollar worth of Damages in a 100
+years if I use that discount rate it
+
+ align:start position:0%
+years if I use that discount rate it
+ 
+
+ align:start position:0%
+years if I use that discount rate it
+matters a lot it matters a
+
+ align:start position:0%
+matters a lot it matters a
+ 
+
+ align:start position:0%
+matters a lot it matters a
+lot and there's no easy way to decide I
+
+ align:start position:0%
+lot and there's no easy way to decide I
+ 
+
+ align:start position:0%
+lot and there's no easy way to decide I
+think to decide among these views if you
+
+ align:start position:0%
+think to decide among these views if you
+ 
+
+ align:start position:0%
+think to decide among these views if you
+scratch most economists they come down
+
+ align:start position:0%
+scratch most economists they come down
+ 
+
+ align:start position:0%
+scratch most economists they come down
+here at 3%
+
+ align:start position:0%
+here at 3%
+ 
+
+ align:start position:0%
+here at 3%
+say but if you ask them well wait a
+
+ align:start position:0%
+say but if you ask them well wait a
+ 
+
+ align:start position:0%
+say but if you ask them well wait a
+minute aren't you crowding out private
+
+ align:start position:0%
+minute aren't you crowding out private
+ 
+
+ align:start position:0%
+minute aren't you crowding out private
+Investments they say oh well maybe maybe
+
+ align:start position:0%
+Investments they say oh well maybe maybe
+ 
+
+ align:start position:0%
+Investments they say oh well maybe maybe
+not and if you ask them well why are you
+
+ align:start position:0%
+not and if you ask them well why are you
+ 
+
+ align:start position:0%
+not and if you ask them well why are you
+discriminating against future
+
+ align:start position:0%
+discriminating against future
+ 
+
+ align:start position:0%
+discriminating against future
+generations with this pure rate of time
+
+ align:start position:0%
+generations with this pure rate of time
+ 
+
+ align:start position:0%
+generations with this pure rate of time
+preference where does that come
+
+ align:start position:0%
+preference where does that come
+ 
+
+ align:start position:0%
+preference where does that come
+from uh most people go well yeah that's
+
+ align:start position:0%
+from uh most people go well yeah that's
+ 
+
+ align:start position:0%
+from uh most people go well yeah that's
+a point so uh you can make Arguments for
+
+ align:start position:0%
+a point so uh you can make Arguments for
+ 
+
+ align:start position:0%
+a point so uh you can make Arguments for
+all three of these and they have very
+
+ align:start position:0%
+all three of these and they have very
+ 
+
+ align:start position:0%
+all three of these and they have very
+different implications the Zar will have
+
+ align:start position:0%
+different implications the Zar will have
+ 
+
+ align:start position:0%
+different implications the Zar will have
+to choose is this see the issue I hope
+
+ align:start position:0%
+to choose is this see the issue I hope
+ 
+
+ align:start position:0%
+to choose is this see the issue I hope
+if you're talking about five years 10
+
+ align:start position:0%
+if you're talking about five years 10
+ 
+
+ align:start position:0%
+if you're talking about five years 10
+years it doesn't matter that much if
+
+ align:start position:0%
+years it doesn't matter that much if
+ 
+
+ align:start position:0%
+years it doesn't matter that much if
+you're talking about a 100 years which
+
+ align:start position:0%
+you're talking about a 100 years which
+ 
+
+ align:start position:0%
+you're talking about a 100 years which
+we are here it does or
+
+ align:start position:0%
+we are here it does or
+ 
+
+ align:start position:0%
+we are here it does or
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+okay that's
+
+ align:start position:0%
+okay that's
+ 
+
+ align:start position:0%
+okay that's
+hard and it's hard for the Zar it's not
+
+ align:start position:0%
+hard and it's hard for the Zar it's not
+ 
+
+ align:start position:0%
+hard and it's hard for the Zar it's not
+just hard
+
+ align:start position:0%
+just hard
+ 
+
+ align:start position:0%
+just hard
+politically I think the reason so that's
+
+ align:start position:0%
+politically I think the reason so that's
+ 
+
+ align:start position:0%
+politically I think the reason so that's
+one reason why it's hard the Zar is
+
+ align:start position:0%
+one reason why it's hard the Zar is
+ 
+
+ align:start position:0%
+one reason why it's hard the Zar is
+willing to make sacrifices today for
+
+ align:start position:0%
+willing to make sacrifices today for
+ 
+
+ align:start position:0%
+willing to make sacrifices today for
+gener ations not yet B born or even
+
+ align:start position:0%
+gener ations not yet B born or even
+ 
+
+ align:start position:0%
+gener ations not yet B born or even
+thought
+
+ align:start position:0%
+thought
+ 
+
+ align:start position:0%
+thought
+of many other people who aren't as
+
+ align:start position:0%
+of many other people who aren't as
+ 
+
+ align:start position:0%
+of many other people who aren't as
+farsighted as the are may have trouble
+
+ align:start position:0%
+farsighted as the are may have trouble
+ 
+
+ align:start position:0%
+farsighted as the are may have trouble
+doing that or voting to do that that's a
+
+ align:start position:0%
+doing that or voting to do that that's a
+ 
+
+ align:start position:0%
+doing that or voting to do that that's a
+tough that's a tough trade-off right we
+
+ align:start position:0%
+tough that's a tough trade-off right we
+ 
+
+ align:start position:0%
+tough that's a tough trade-off right we
+could reduce emissions today sharply and
+
+ align:start position:0%
+could reduce emissions today sharply and
+ 
+
+ align:start position:0%
+could reduce emissions today sharply and
+it wouldn't make any it wouldn't make
+
+ align:start position:0%
+it wouldn't make any it wouldn't make
+ 
+
+ align:start position:0%
+it wouldn't make any it wouldn't make
+much difference to us might not make
+
+ align:start position:0%
+much difference to us might not make
+ 
+
+ align:start position:0%
+much difference to us might not make
+much difference to us might make some
+
+ align:start position:0%
+much difference to us might make some
+ 
+
+ align:start position:0%
+much difference to us might make some
+difference to our children might make a
+
+ align:start position:0%
+difference to our children might make a
+ 
+
+ align:start position:0%
+difference to our children might make a
+lot of difference to their children you
+
+ align:start position:0%
+lot of difference to their children you
+ 
+
+ align:start position:0%
+lot of difference to their children you
+can't even imagine having grandchildren
+
+ align:start position:0%
+can't even imagine having grandchildren
+ 
+
+ align:start position:0%
+can't even imagine having grandchildren
+at this point right am I right I hope uh
+
+ align:start position:0%
+at this point right am I right I hope uh
+ 
+
+ align:start position:0%
+at this point right am I right I hope uh
+uh but you
+
+ align:start position:0%
+uh but you
+ 
+
+ align:start position:0%
+uh but you
+will and so will
+
+ align:start position:0%
+will and so will
+ 
+
+ align:start position:0%
+will and so will
+they okay that's one reason why it's
+
+ align:start position:0%
+they okay that's one reason why it's
+ 
+
+ align:start position:0%
+they okay that's one reason why it's
+hard because it's hard to think in terms
+
+ align:start position:0%
+hard because it's hard to think in terms
+ 
+
+ align:start position:0%
+hard because it's hard to think in terms
+of a century when you're making
+
+ align:start position:0%
+of a century when you're making
+ 
+
+ align:start position:0%
+of a century when you're making
+decisions today or
+
+ align:start position:0%
+decisions today or
+ 
+
+ align:start position:0%
+decisions today or
+more a second reason why this is hard
+
+ align:start position:0%
+more a second reason why this is hard
+ 
+
+ align:start position:0%
+more a second reason why this is hard
+even for thear is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncertainty
+
+ align:start position:0%
+uncertainty
+ 
+
+ align:start position:0%
+uncertainty
+and one of the one of the things
+
+ align:start position:0%
+and one of the one of the things
+ 
+
+ align:start position:0%
+and one of the one of the things
+Professor Solomon and I have learned is
+
+ align:start position:0%
+Professor Solomon and I have learned is
+ 
+
+ align:start position:0%
+Professor Solomon and I have learned is
+you can't say uncertain in public
+
+ align:start position:0%
+you can't say uncertain in public
+ 
+
+ align:start position:0%
+you can't say uncertain in public
+discourse because uncertain to the
+
+ align:start position:0%
+discourse because uncertain to the
+ 
+
+ align:start position:0%
+discourse because uncertain to the
+public means my God I don't have a clue
+
+ align:start position:0%
+public means my God I don't have a clue
+ 
+
+ align:start position:0%
+public means my God I don't have a clue
+what uncertain means in this context is
+
+ align:start position:0%
+what uncertain means in this context is
+ 
+
+ align:start position:0%
+what uncertain means in this context is
+I may not know the probability
+
+ align:start position:0%
+I may not know the probability
+ 
+
+ align:start position:0%
+I may not know the probability
+distribution but there is a probability
+
+ align:start position:0%
+distribution but there is a probability
+ 
+
+ align:start position:0%
+distribution but there is a probability
+distribution it's not and it's not uh uh
+
+ align:start position:0%
+distribution it's not and it's not uh uh
+ 
+
+ align:start position:0%
+distribution it's not and it's not uh uh
+infinitely spread
+
+ align:start position:0%
+infinitely spread
+ 
+
+ align:start position:0%
+infinitely spread
+out if you think about elements of
+
+ align:start position:0%
+out if you think about elements of
+ 
+
+ align:start position:0%
+out if you think about elements of
+uncertainty what will the atmosphere
+
+ align:start position:0%
+uncertainty what will the atmosphere
+ 
+
+ align:start position:0%
+uncertainty what will the atmosphere
+look like in a hundred years if we don't
+
+ align:start position:0%
+look like in a hundred years if we don't
+ 
+
+ align:start position:0%
+look like in a hundred years if we don't
+do anything well you know that depends
+
+ align:start position:0%
+do anything well you know that depends
+ 
+
+ align:start position:0%
+do anything well you know that depends
+on population does China collapse does
+
+ align:start position:0%
+on population does China collapse does
+ 
+
+ align:start position:0%
+on population does China collapse does
+China not collapse it depends on future
+
+ align:start position:0%
+China not collapse it depends on future
+ 
+
+ align:start position:0%
+China not collapse it depends on future
+economic growth it depends on the mix of
+
+ align:start position:0%
+economic growth it depends on the mix of
+ 
+
+ align:start position:0%
+economic growth it depends on the mix of
+activity what happens to manufacturing
+
+ align:start position:0%
+activity what happens to manufacturing
+ 
+
+ align:start position:0%
+activity what happens to manufacturing
+versus Services it depends on new
+
+ align:start position:0%
+versus Services it depends on new
+ 
+
+ align:start position:0%
+versus Services it depends on new
+technologies somebody comes up with
+
+ align:start position:0%
+technologies somebody comes up with
+ 
+
+ align:start position:0%
+technologies somebody comes up with
+cheap storage the world moves to solar
+
+ align:start position:0%
+cheap storage the world moves to solar
+ 
+
+ align:start position:0%
+cheap storage the world moves to solar
+power it's a very different
+
+ align:start position:0%
+power it's a very different
+ 
+
+ align:start position:0%
+power it's a very different
+world um than if that doesn't happen
+
+ align:start position:0%
+world um than if that doesn't happen
+ 
+
+ align:start position:0%
+world um than if that doesn't happen
+those are all big uncertainties so we
+
+ align:start position:0%
+those are all big uncertainties so we
+ 
+
+ align:start position:0%
+those are all big uncertainties so we
+don't really know what emissions will
+
+ align:start position:0%
+don't really know what emissions will
+ 
+
+ align:start position:0%
+don't really know what emissions will
+look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like there are uncertainties about the
+
+ align:start position:0%
+like there are uncertainties about the
+ 
+
+ align:start position:0%
+like there are uncertainties about the
+climate system serious uncertainties
+
+ align:start position:0%
+climate system serious uncertainties
+ 
+
+ align:start position:0%
+climate system serious uncertainties
+about the climate system not that we
+
+ align:start position:0%
+about the climate system not that we
+ 
+
+ align:start position:0%
+about the climate system not that we
+don't know anything but as I mentioned
+
+ align:start position:0%
+don't know anything but as I mentioned
+ 
+
+ align:start position:0%
+don't know anything but as I mentioned
+there's this issue of how fast will the
+
+ align:start position:0%
+there's this issue of how fast will the
+ 
+
+ align:start position:0%
+there's this issue of how fast will the
+deep ocean warm there issues of
+
+ align:start position:0%
+deep ocean warm there issues of
+ 
+
+ align:start position:0%
+deep ocean warm there issues of
+irreversibilities and tipping points
+
+ align:start position:0%
+irreversibilities and tipping points
+ 
+
+ align:start position:0%
+irreversibilities and tipping points
+potentially did you want to talk about
+
+ align:start position:0%
+potentially did you want to talk about
+ 
+
+ align:start position:0%
+potentially did you want to talk about
+that and say a word about some of these
+
+ align:start position:0%
+that and say a word about some of these
+ 
+
+ align:start position:0%
+that and say a word about some of these
+uncertainties can I can I provoke you
+
+ align:start position:0%
+uncertainties can I can I provoke you
+ 
+
+ align:start position:0%
+uncertainties can I can I provoke you
+into a
+
+ align:start position:0%
+into a
+ 
+
+ align:start position:0%
+into a
+comment
+
+ align:start position:0%
+comment
+ 
+
+ align:start position:0%
+comment
+um possibly I guess I'm not quite sure
+
+ align:start position:0%
+um possibly I guess I'm not quite sure
+ 
+
+ align:start position:0%
+um possibly I guess I'm not quite sure
+where you want to go with it oh I just
+
+ align:start position:0%
+where you want to go with it oh I just
+ 
+
+ align:start position:0%
+where you want to go with it oh I just
+want to uh some uh some illustrative
+
+ align:start position:0%
+want to uh some uh some illustrative
+ 
+
+ align:start position:0%
+want to uh some uh some illustrative
+detail or some examples of things that
+
+ align:start position:0%
+detail or some examples of things that
+ 
+
+ align:start position:0%
+detail or some examples of things that
+might be a a concern or that might be
+
+ align:start position:0%
+might be a a concern or that might be
+ 
+
+ align:start position:0%
+might be a a concern or that might be
+nonlinearities or that might be like
+
+ align:start position:0%
+nonlinearities or that might be like
+ 
+
+ align:start position:0%
+nonlinearities or that might be like
+falling off a
+
+ align:start position:0%
+falling off a
+ 
+
+ align:start position:0%
+falling off a
+table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you want to take a second just take
+
+ align:start position:0%
+okay you want to take a second just take
+ 
+
+ align:start position:0%
+okay you want to take a second just take
+a second put I hate to wa waste of
+
+ align:start position:0%
+a second put I hate to wa waste of
+ 
+
+ align:start position:0%
+a second put I hate to wa waste of
+resource I I'll do my best um you know
+
+ align:start position:0%
+resource I I'll do my best um you know
+ 
+
+ align:start position:0%
+resource I I'll do my best um you know
+th this this issue of tipping points in
+
+ align:start position:0%
+th this this issue of tipping points in
+ 
+
+ align:start position:0%
+th this this issue of tipping points in
+my mind is actually a lot more difficult
+
+ align:start position:0%
+my mind is actually a lot more difficult
+ 
+
+ align:start position:0%
+my mind is actually a lot more difficult
+than the issue of of irreversibility the
+
+ align:start position:0%
+than the issue of of irreversibility the
+ 
+
+ align:start position:0%
+than the issue of of irreversibility the
+IR reversibility problem we can talk
+
+ align:start position:0%
+IR reversibility problem we can talk
+ 
+
+ align:start position:0%
+IR reversibility problem we can talk
+about a little bit more clearly um you
+
+ align:start position:0%
+about a little bit more clearly um you
+ 
+
+ align:start position:0%
+about a little bit more clearly um you
+know for
+
+ align:start position:0%
+know for
+ 
+
+ align:start position:0%
+know for
+example um if it were to be the case
+
+ align:start position:0%
+example um if it were to be the case
+ 
+
+ align:start position:0%
+example um if it were to be the case
+that Artic sea ice were to uh disappear
+
+ align:start position:0%
+that Artic sea ice were to uh disappear
+ 
+
+ align:start position:0%
+that Artic sea ice were to uh disappear
+you might imagine that uh that would be
+
+ align:start position:0%
+you might imagine that uh that would be
+ 
+
+ align:start position:0%
+you might imagine that uh that would be
+an irreversible process but I think
+
+ align:start position:0%
+an irreversible process but I think
+ 
+
+ align:start position:0%
+an irreversible process but I think
+we're finding more and more that it
+
+ align:start position:0%
+we're finding more and more that it
+ 
+
+ align:start position:0%
+we're finding more and more that it
+actually isn't even though we had very
+
+ align:start position:0%
+actually isn't even though we had very
+ 
+
+ align:start position:0%
+actually isn't even though we had very
+low Arctic SE ice in 2007 because we
+
+ align:start position:0%
+low Arctic SE ice in 2007 because we
+ 
+
+ align:start position:0%
+low Arctic SE ice in 2007 because we
+have such cold winter
+
+ align:start position:0%
+have such cold winter
+ 
+
+ align:start position:0%
+have such cold winter
+we have the ability to reform the sea
+
+ align:start position:0%
+we have the ability to reform the sea
+ 
+
+ align:start position:0%
+we have the ability to reform the sea
+ice because it's
+
+ align:start position:0%
+ice because it's
+ 
+
+ align:start position:0%
+ice because it's
+thin even when you have multi-year ice
+
+ align:start position:0%
+thin even when you have multi-year ice
+ 
+
+ align:start position:0%
+thin even when you have multi-year ice
+it's still relatively thin it's only a
+
+ align:start position:0%
+it's still relatively thin it's only a
+ 
+
+ align:start position:0%
+it's still relatively thin it's only a
+few years uh that matters but when we
+
+ align:start position:0%
+few years uh that matters but when we
+ 
+
+ align:start position:0%
+few years uh that matters but when we
+for example uh do something that causes
+
+ align:start position:0%
+for example uh do something that causes
+ 
+
+ align:start position:0%
+for example uh do something that causes
+a big dent in the Greenland ice sheet
+
+ align:start position:0%
+a big dent in the Greenland ice sheet
+ 
+
+ align:start position:0%
+a big dent in the Greenland ice sheet
+now you know that that truly is
+
+ align:start position:0%
+now you know that that truly is
+ 
+
+ align:start position:0%
+now you know that that truly is
+something that you could think about as
+
+ align:start position:0%
+something that you could think about as
+ 
+
+ align:start position:0%
+something that you could think about as
+irreversible it's going to take a very
+
+ align:start position:0%
+irreversible it's going to take a very
+ 
+
+ align:start position:0%
+irreversible it's going to take a very
+very long time so on human time scales
+
+ align:start position:0%
+very long time so on human time scales
+ 
+
+ align:start position:0%
+very long time so on human time scales
+it's essentially irreversible if you
+
+ align:start position:0%
+it's essentially irreversible if you
+ 
+
+ align:start position:0%
+it's essentially irreversible if you
+lose a big piece of the Greenland ice
+
+ align:start position:0%
+lose a big piece of the Greenland ice
+ 
+
+ align:start position:0%
+lose a big piece of the Greenland ice
+sheet is there a Tipping Point Beyond
+
+ align:start position:0%
+sheet is there a Tipping Point Beyond
+ 
+
+ align:start position:0%
+sheet is there a Tipping Point Beyond
+which the Greenland ice sheet might kind
+
+ align:start position:0%
+which the Greenland ice sheet might kind
+ 
+
+ align:start position:0%
+which the Greenland ice sheet might kind
+of suddenly fall apart is something
+
+ align:start position:0%
+of suddenly fall apart is something
+ 
+
+ align:start position:0%
+of suddenly fall apart is something
+that's been raised much more of a
+
+ align:start position:0%
+that's been raised much more of a
+ 
+
+ align:start position:0%
+that's been raised much more of a
+controversial issue it's
+
+ align:start position:0%
+controversial issue it's
+ 
+
+ align:start position:0%
+controversial issue it's
+conceivable but most scientists who
+
+ align:start position:0%
+conceivable but most scientists who
+ 
+
+ align:start position:0%
+conceivable but most scientists who
+study the ice would argue that it's more
+
+ align:start position:0%
+study the ice would argue that it's more
+ 
+
+ align:start position:0%
+study the ice would argue that it's more
+likely to be a slow process but it but
+
+ align:start position:0%
+likely to be a slow process but it but
+ 
+
+ align:start position:0%
+likely to be a slow process but it but
+it's possible and one of the things that
+
+ align:start position:0%
+it's possible and one of the things that
+ 
+
+ align:start position:0%
+it's possible and one of the things that
+that could be uh a Tipping Point for the
+
+ align:start position:0%
+that could be uh a Tipping Point for the
+ 
+
+ align:start position:0%
+that could be uh a Tipping Point for the
+Arctic that people have also talked
+
+ align:start position:0%
+Arctic that people have also talked
+ 
+
+ align:start position:0%
+Arctic that people have also talked
+about of course is methane release from
+
+ align:start position:0%
+about of course is methane release from
+ 
+
+ align:start position:0%
+about of course is methane release from
+um things like uh UND sea deposits of
+
+ align:start position:0%
+um things like uh UND sea deposits of
+ 
+
+ align:start position:0%
+um things like uh UND sea deposits of
+methane that are actually tied up in in
+
+ align:start position:0%
+methane that are actually tied up in in
+ 
+
+ align:start position:0%
+methane that are actually tied up in in
+uh formations called clathrates and also
+
+ align:start position:0%
+uh formations called clathrates and also
+ 
+
+ align:start position:0%
+uh formations called clathrates and also
+in permafrost which you're probably more
+
+ align:start position:0%
+in permafrost which you're probably more
+ 
+
+ align:start position:0%
+in permafrost which you're probably more
+familiar with so there there are ways to
+
+ align:start position:0%
+familiar with so there there are ways to
+ 
+
+ align:start position:0%
+familiar with so there there are ways to
+trigger things that in the Tipping Point
+
+ align:start position:0%
+trigger things that in the Tipping Point
+ 
+
+ align:start position:0%
+trigger things that in the Tipping Point
+framework usually involve ice because
+
+ align:start position:0%
+framework usually involve ice because
+ 
+
+ align:start position:0%
+framework usually involve ice because
+you know that and and you can sort of
+
+ align:start position:0%
+you know that and and you can sort of
+ 
+
+ align:start position:0%
+you know that and and you can sort of
+see why that would be it's either ice or
+
+ align:start position:0%
+see why that would be it's either ice or
+ 
+
+ align:start position:0%
+see why that would be it's either ice or
+it's not you know there's no there is no
+
+ align:start position:0%
+it's not you know there's no there is no
+ 
+
+ align:start position:0%
+it's not you know there's no there is no
+slow transition from from one to to
+
+ align:start position:0%
+slow transition from from one to to
+ 
+
+ align:start position:0%
+slow transition from from one to to
+another it's a real change of state so
+
+ align:start position:0%
+another it's a real change of state so
+ 
+
+ align:start position:0%
+another it's a real change of state so
+that's some ideas okay thank you thank
+
+ align:start position:0%
+that's some ideas okay thank you thank
+ 
+
+ align:start position:0%
+that's some ideas okay thank you thank
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+so that's hard thear has to think about
+
+ align:start position:0%
+so that's hard thear has to think about
+ 
+
+ align:start position:0%
+so that's hard thear has to think about
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+possibilities which we know something
+
+ align:start position:0%
+possibilities which we know something
+ 
+
+ align:start position:0%
+possibilities which we know something
+but we don't know we can't tell when
+
+ align:start position:0%
+but we don't know we can't tell when
+ 
+
+ align:start position:0%
+but we don't know we can't tell when
+that might occur if that might those
+
+ align:start position:0%
+that might occur if that might those
+ 
+
+ align:start position:0%
+that might occur if that might those
+things might
+
+ align:start position:0%
+things might
+ 
+
+ align:start position:0%
+things might
+occur
+
+ align:start position:0%
+occur
+ 
+
+ align:start position:0%
+occur
+even climate models models complex
+
+ align:start position:0%
+even climate models models complex
+ 
+
+ align:start position:0%
+even climate models models complex
+simulation models of the climate system
+
+ align:start position:0%
+simulation models of the climate system
+ 
+
+ align:start position:0%
+simulation models of the climate system
+and there are a number of them disagree
+
+ align:start position:0%
+and there are a number of them disagree
+ 
+
+ align:start position:0%
+and there are a number of them disagree
+on what happens
+
+ align:start position:0%
+on what happens
+ 
+
+ align:start position:0%
+on what happens
+regionally will it be wetter or
+
+ align:start position:0%
+regionally will it be wetter or
+ 
+
+ align:start position:0%
+regionally will it be wetter or
+drier well that matters a
+
+ align:start position:0%
+drier well that matters a
+ 
+
+ align:start position:0%
+drier well that matters a
+lot it matters a lot whether it'll be
+
+ align:start position:0%
+lot it matters a lot whether it'll be
+ 
+
+ align:start position:0%
+lot it matters a lot whether it'll be
+wetter or drier in particular
+
+ align:start position:0%
+wetter or drier in particular
+ 
+
+ align:start position:0%
+wetter or drier in particular
+areas um for well let me just say that
+
+ align:start position:0%
+areas um for well let me just say that
+ 
+
+ align:start position:0%
+areas um for well let me just say that
+it also we don't have good predictions
+
+ align:start position:0%
+it also we don't have good predictions
+ 
+
+ align:start position:0%
+it also we don't have good predictions
+for the impacts on Hurrican
+
+ align:start position:0%
+for the impacts on Hurrican
+ 
+
+ align:start position:0%
+for the impacts on Hurrican
+canes
+
+ align:start position:0%
+canes
+ 
+
+ align:start position:0%
+canes
+more more intense none of the above more
+
+ align:start position:0%
+more more intense none of the above more
+ 
+
+ align:start position:0%
+more more intense none of the above more
+water goes into the air because it's
+
+ align:start position:0%
+water goes into the air because it's
+ 
+
+ align:start position:0%
+water goes into the air because it's
+warmer it comes down how does it come
+
+ align:start position:0%
+warmer it comes down how does it come
+ 
+
+ align:start position:0%
+warmer it comes down how does it come
+down where does it come
+
+ align:start position:0%
+down where does it come
+ 
+
+ align:start position:0%
+down where does it come
+down very
+
+ align:start position:0%
+down very
+ 
+
+ align:start position:0%
+down very
+uncertain implications for regional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impacts Regional impacts will take us
+
+ align:start position:0%
+impacts Regional impacts will take us
+ 
+
+ align:start position:0%
+impacts Regional impacts will take us
+into new ground particularly for
+
+ align:start position:0%
+into new ground particularly for
+ 
+
+ align:start position:0%
+into new ground particularly for
+ecosystems we don't quite know how ecos
+
+ align:start position:0%
+ecosystems we don't quite know how ecos
+ 
+
+ align:start position:0%
+ecosystems we don't quite know how ecos
+systems will respond because we haven't
+
+ align:start position:0%
+systems will respond because we haven't
+ 
+
+ align:start position:0%
+systems will respond because we haven't
+done it and it's not a it's not an easy
+
+ align:start position:0%
+done it and it's not a it's not an easy
+ 
+
+ align:start position:0%
+done it and it's not a it's not an easy
+experiment so IM damages effects like
+
+ align:start position:0%
+experiment so IM damages effects like
+ 
+
+ align:start position:0%
+experiment so IM damages effects like
+rainfall are uncertain the implications
+
+ align:start position:0%
+rainfall are uncertain the implications
+ 
+
+ align:start position:0%
+rainfall are uncertain the implications
+of those effects are also
+
+ align:start position:0%
+of those effects are also
+ 
+
+ align:start position:0%
+of those effects are also
+uncertain and
+
+ align:start position:0%
+uncertain and
+ 
+
+ align:start position:0%
+uncertain and
+finally um there's little experience in
+
+ align:start position:0%
+finally um there's little experience in
+ 
+
+ align:start position:0%
+finally um there's little experience in
+sort of how do human civilizations react
+
+ align:start position:0%
+sort of how do human civilizations react
+ 
+
+ align:start position:0%
+sort of how do human civilizations react
+to large scale environmental changes of
+
+ align:start position:0%
+to large scale environmental changes of
+ 
+
+ align:start position:0%
+to large scale environmental changes of
+various kinds I've been seeing on Google
+
+ align:start position:0%
+various kinds I've been seeing on Google
+ 
+
+ align:start position:0%
+various kinds I've been seeing on Google
+News reference to small changes in
+
+ align:start position:0%
+News reference to small changes in
+ 
+
+ align:start position:0%
+News reference to small changes in
+rainfall being the likely culprit in the
+
+ align:start position:0%
+rainfall being the likely culprit in the
+ 
+
+ align:start position:0%
+rainfall being the likely culprit in the
+downfall of the Mayas maybe 20
+
+ align:start position:0%
+downfall of the Mayas maybe 20
+ 
+
+ align:start position:0%
+downfall of the Mayas maybe 20
+30% reductions not huge droughts
+
+ align:start position:0%
+30% reductions not huge droughts
+ 
+
+ align:start position:0%
+30% reductions not huge droughts
+sensitive enough are poor countries in
+
+ align:start position:0%
+sensitive enough are poor countries in
+ 
+
+ align:start position:0%
+sensitive enough are poor countries in
+the tropics that sensitive probably not
+
+ align:start position:0%
+the tropics that sensitive probably not
+ 
+
+ align:start position:0%
+the tropics that sensitive probably not
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+sensitive uh and finally the cost of
+
+ align:start position:0%
+sensitive uh and finally the cost of
+ 
+
+ align:start position:0%
+sensitive uh and finally the cost of
+emissions reductions are also
+
+ align:start position:0%
+emissions reductions are also
+ 
+
+ align:start position:0%
+emissions reductions are also
+uncertain so the Zar is going to have to
+
+ align:start position:0%
+uncertain so the Zar is going to have to
+ 
+
+ align:start position:0%
+uncertain so the Zar is going to have to
+deal with this and the Zar is going to
+
+ align:start position:0%
+deal with this and the Zar is going to
+ 
+
+ align:start position:0%
+deal with this and the Zar is going to
+have to deal with the fact that we will
+
+ align:start position:0%
+have to deal with the fact that we will
+ 
+
+ align:start position:0%
+have to deal with the fact that we will
+be learning as we go so this is I I now
+
+ align:start position:0%
+be learning as we go so this is I I now
+ 
+
+ align:start position:0%
+be learning as we go so this is I I now
+go to uh my favorite picture from the so
+
+ align:start position:0%
+go to uh my favorite picture from the so
+ 
+
+ align:start position:0%
+go to uh my favorite picture from the so
+you can't do cost benefit analysis
+
+ align:start position:0%
+you can't do cost benefit analysis
+ 
+
+ align:start position:0%
+you can't do cost benefit analysis
+because you don't know the cost and you
+
+ align:start position:0%
+because you don't know the cost and you
+ 
+
+ align:start position:0%
+because you don't know the cost and you
+don't know the
+
+ align:start position:0%
+don't know the
+ 
+
+ align:start position:0%
+don't know the
+benefits so thear can't just do the
+
+ align:start position:0%
+benefits so thear can't just do the
+ 
+
+ align:start position:0%
+benefits so thear can't just do the
+arithmetic because he doesn't know the
+
+ align:start position:0%
+arithmetic because he doesn't know the
+ 
+
+ align:start position:0%
+arithmetic because he doesn't know the
+costs or the benefits even if he could
+
+ align:start position:0%
+costs or the benefits even if he could
+ 
+
+ align:start position:0%
+costs or the benefits even if he could
+do the
+
+ align:start position:0%
+do the
+ 
+
+ align:start position:0%
+do the
+discounting a problem like this needs
+
+ align:start position:0%
+discounting a problem like this needs
+ 
+
+ align:start position:0%
+discounting a problem like this needs
+adaptive or iterative risk management
+
+ align:start position:0%
+adaptive or iterative risk management
+ 
+
+ align:start position:0%
+adaptive or iterative risk management
+and you can read that in the report of
+
+ align:start position:0%
+and you can read that in the report of
+ 
+
+ align:start position:0%
+and you can read that in the report of
+the committee on America's climate
+
+ align:start position:0%
+the committee on America's climate
+ 
+
+ align:start position:0%
+the committee on America's climate
+choices on which professor Solomon and I
+
+ align:start position:0%
+choices on which professor Solomon and I
+ 
+
+ align:start position:0%
+choices on which professor Solomon and I
+both served if you think about steering
+
+ align:start position:0%
+both served if you think about steering
+ 
+
+ align:start position:0%
+both served if you think about steering
+a ship in iceberg infested waters at
+
+ align:start position:0%
+a ship in iceberg infested waters at
+ 
+
+ align:start position:0%
+a ship in iceberg infested waters at
+night before
+
+ align:start position:0%
+night before
+ 
+
+ align:start position:0%
+night before
+radar uh I to avoid the Titanic it the
+
+ align:start position:0%
+radar uh I to avoid the Titanic it the
+ 
+
+ align:start position:0%
+radar uh I to avoid the Titanic it the
+the elements of what a sensible Skipper
+
+ align:start position:0%
+the elements of what a sensible Skipper
+ 
+
+ align:start position:0%
+the elements of what a sensible Skipper
+does are the elements of what the Zar
+
+ align:start position:0%
+does are the elements of what the Zar
+ 
+
+ align:start position:0%
+does are the elements of what the Zar
+would do to deal with climate you slow
+
+ align:start position:0%
+would do to deal with climate you slow
+ 
+
+ align:start position:0%
+would do to deal with climate you slow
+down good plan so you reduce
+
+ align:start position:0%
+down good plan so you reduce
+ 
+
+ align:start position:0%
+down good plan so you reduce
+emissions you don't quite know what the
+
+ align:start position:0%
+emissions you don't quite know what the
+ 
+
+ align:start position:0%
+emissions you don't quite know what the
+consequences are but you know more
+
+ align:start position:0%
+consequences are but you know more
+ 
+
+ align:start position:0%
+consequences are but you know more
+of of having more emissions or of going
+
+ align:start position:0%
+of of having more emissions or of going
+ 
+
+ align:start position:0%
+of of having more emissions or of going
+faster but you know they're probably not
+
+ align:start position:0%
+faster but you know they're probably not
+ 
+
+ align:start position:0%
+faster but you know they're probably not
+good on balance so you slow down you
+
+ align:start position:0%
+good on balance so you slow down you
+ 
+
+ align:start position:0%
+good on balance so you slow down you
+prepare for for something to happen you
+
+ align:start position:0%
+prepare for for something to happen you
+ 
+
+ align:start position:0%
+prepare for for something to happen you
+prepare to
+
+ align:start position:0%
+prepare to
+ 
+
+ align:start position:0%
+prepare to
+adapt you learn you station Lookouts you
+
+ align:start position:0%
+adapt you learn you station Lookouts you
+ 
+
+ align:start position:0%
+adapt you learn you station Lookouts you
+study the system you see what's going
+
+ align:start position:0%
+study the system you see what's going
+ 
+
+ align:start position:0%
+study the system you see what's going
+on you develop options new technologies
+
+ align:start position:0%
+on you develop options new technologies
+ 
+
+ align:start position:0%
+on you develop options new technologies
+geoengineering which I'll talk about
+
+ align:start position:0%
+geoengineering which I'll talk about
+ 
+
+ align:start position:0%
+geoengineering which I'll talk about
+briefly and you try to figure out a
+
+ align:start position:0%
+briefly and you try to figure out a
+ 
+
+ align:start position:0%
+briefly and you try to figure out a
+system that enables learning to affect
+
+ align:start position:0%
+system that enables learning to affect
+ 
+
+ align:start position:0%
+system that enables learning to affect
+decisions so you want to hear the
+
+ align:start position:0%
+decisions so you want to hear the
+ 
+
+ align:start position:0%
+decisions so you want to hear the
+Lookouts when they see something so
+
+ align:start position:0%
+Lookouts when they see something so
+ 
+
+ align:start position:0%
+Lookouts when they see something so
+that's the sort of thing the Zar is
+
+ align:start position:0%
+that's the sort of thing the Zar is
+ 
+
+ align:start position:0%
+that's the sort of thing the Zar is
+going to have to do because we don't
+
+ align:start position:0%
+going to have to do because we don't
+ 
+
+ align:start position:0%
+going to have to do because we don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+probabilities we don't know really
+
+ align:start position:0%
+probabilities we don't know really
+ 
+
+ align:start position:0%
+probabilities we don't know really
+models and studies of what's going to
+
+ align:start position:0%
+models and studies of what's going to
+ 
+
+ align:start position:0%
+models and studies of what's going to
+happen to the Greenland ice sheet but we
+
+ align:start position:0%
+happen to the Greenland ice sheet but we
+ 
+
+ align:start position:0%
+happen to the Greenland ice sheet but we
+don't know for sure we don't know for
+
+ align:start position:0%
+don't know for sure we don't know for
+ 
+
+ align:start position:0%
+don't know for sure we don't know for
+sure and we don't know for sure whether
+
+ align:start position:0%
+sure and we don't know for sure whether
+ 
+
+ align:start position:0%
+sure and we don't know for sure whether
+it's going to get wetter or drier in
+
+ align:start position:0%
+it's going to get wetter or drier in
+ 
+
+ align:start position:0%
+it's going to get wetter or drier in
+Ethiopia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just a word about
+
+ align:start position:0%
+so just a word about
+ 
+
+ align:start position:0%
+so just a word about
+adaptation the Zar will have to have to
+
+ align:start position:0%
+adaptation the Zar will have to have to
+ 
+
+ align:start position:0%
+adaptation the Zar will have to have to
+do some of
+
+ align:start position:0%
+do some of
+ 
+
+ align:start position:0%
+do some of
+this but as I said the small scale and
+
+ align:start position:0%
+this but as I said the small scale and
+ 
+
+ align:start position:0%
+this but as I said the small scale and
+we will adapt uh that that first line is
+
+ align:start position:0%
+we will adapt uh that that first line is
+ 
+
+ align:start position:0%
+we will adapt uh that that first line is
+one of my favorite statements about
+
+ align:start position:0%
+one of my favorite statements about
+ 
+
+ align:start position:0%
+one of my favorite statements about
+adaptation which is the default mode of
+
+ align:start position:0%
+adaptation which is the default mode of
+ 
+
+ align:start position:0%
+adaptation which is the default mode of
+adaptation is
+
+ align:start position:0%
+adaptation is
+ 
+
+ align:start position:0%
+adaptation is
+suffering so we'll adapt but the
+
+ align:start position:0%
+suffering so we'll adapt but the
+ 
+
+ align:start position:0%
+suffering so we'll adapt but the
+question is will we actually uh do any
+
+ align:start position:0%
+question is will we actually uh do any
+ 
+
+ align:start position:0%
+question is will we actually uh do any
+changes will we will we do any proactive
+
+ align:start position:0%
+changes will we will we do any proactive
+ 
+
+ align:start position:0%
+changes will we will we do any proactive
+adaptation um as I said problem one is
+
+ align:start position:0%
+adaptation um as I said problem one is
+ 
+
+ align:start position:0%
+adaptation um as I said problem one is
+that the the climate models differ and I
+
+ align:start position:0%
+that the the climate models differ and I
+ 
+
+ align:start position:0%
+that the the climate models differ and I
+will give you an example a colleague was
+
+ align:start position:0%
+will give you an example a colleague was
+ 
+
+ align:start position:0%
+will give you an example a colleague was
+called in by the government of Ethiopia
+
+ align:start position:0%
+called in by the government of Ethiopia
+ 
+
+ align:start position:0%
+called in by the government of Ethiopia
+some years ago and they said all right
+
+ align:start position:0%
+some years ago and they said all right
+ 
+
+ align:start position:0%
+some years ago and they said all right
+we believe there's going to be climate
+
+ align:start position:0%
+we believe there's going to be climate
+ 
+
+ align:start position:0%
+we believe there's going to be climate
+change what do we do half the climate
+
+ align:start position:0%
+change what do we do half the climate
+ 
+
+ align:start position:0%
+change what do we do half the climate
+models say it's going to get
+
+ align:start position:0%
+models say it's going to get
+ 
+
+ align:start position:0%
+models say it's going to get
+drier and half the climate models say
+
+ align:start position:0%
+drier and half the climate models say
+ 
+
+ align:start position:0%
+drier and half the climate models say
+it's going to get
+
+ align:start position:0%
+it's going to get
+ 
+
+ align:start position:0%
+it's going to get
+wetter how exactly do we prepare for
+
+ align:start position:0%
+wetter how exactly do we prepare for
+ 
+
+ align:start position:0%
+wetter how exactly do we prepare for
+this un certain
+
+ align:start position:0%
+this un certain
+ 
+
+ align:start position:0%
+this un certain
+future their answer was pave the
+
+ align:start position:0%
+future their answer was pave the
+ 
+
+ align:start position:0%
+future their answer was pave the
+roads because if it's drier okay you
+
+ align:start position:0%
+roads because if it's drier okay you
+ 
+
+ align:start position:0%
+roads because if it's drier okay you
+have paved roads if it's wetter a
+
+ align:start position:0%
+have paved roads if it's wetter a
+ 
+
+ align:start position:0%
+have paved roads if it's wetter a
+problem that Ethiopia traditionally has
+
+ align:start position:0%
+problem that Ethiopia traditionally has
+ 
+
+ align:start position:0%
+problem that Ethiopia traditionally has
+is that unpaved roads wash out when
+
+ align:start position:0%
+is that unpaved roads wash out when
+ 
+
+ align:start position:0%
+is that unpaved roads wash out when
+there's heavy rainfall and the whole
+
+ align:start position:0%
+there's heavy rainfall and the whole
+ 
+
+ align:start position:0%
+there's heavy rainfall and the whole
+process of getting food to Market breaks
+
+ align:start position:0%
+process of getting food to Market breaks
+ 
+
+ align:start position:0%
+process of getting food to Market breaks
+down so if it gets wetter you will
+
+ align:start position:0%
+down so if it gets wetter you will
+ 
+
+ align:start position:0%
+down so if it gets wetter you will
+really need paved
+
+ align:start position:0%
+really need paved
+ 
+
+ align:start position:0%
+really need paved
+roads and if it doesn't get wetter paved
+
+ align:start position:0%
+roads and if it doesn't get wetter paved
+ 
+
+ align:start position:0%
+roads and if it doesn't get wetter paved
+roads are not a bad thing to have
+
+ align:start position:0%
+roads are not a bad thing to have
+ 
+
+ align:start position:0%
+roads are not a bad thing to have
+they're going to be a lot of decisions
+
+ align:start position:0%
+they're going to be a lot of decisions
+ 
+
+ align:start position:0%
+they're going to be a lot of decisions
+like that a lot of people looking for
+
+ align:start position:0%
+like that a lot of people looking for
+ 
+
+ align:start position:0%
+like that a lot of people looking for
+robust policies the second problem of
+
+ align:start position:0%
+robust policies the second problem of
+ 
+
+ align:start position:0%
+robust policies the second problem of
+course is thear can't possibly make all
+
+ align:start position:0%
+course is thear can't possibly make all
+ 
+
+ align:start position:0%
+course is thear can't possibly make all
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+decisions they're going to be made at
+
+ align:start position:0%
+decisions they're going to be made at
+ 
+
+ align:start position:0%
+decisions they're going to be made at
+state and local levels a number of
+
+ align:start position:0%
+state and local levels a number of
+ 
+
+ align:start position:0%
+state and local levels a number of
+cities and states have now already and
+
+ align:start position:0%
+cities and states have now already and
+ 
+
+ align:start position:0%
+cities and states have now already and
+the US and certainly foreign countries
+
+ align:start position:0%
+the US and certainly foreign countries
+ 
+
+ align:start position:0%
+the US and certainly foreign countries
+have now processes in place to think
+
+ align:start position:0%
+have now processes in place to think
+ 
+
+ align:start position:0%
+have now processes in place to think
+about this to try to think about things
+
+ align:start position:0%
+about this to try to think about things
+ 
+
+ align:start position:0%
+about this to try to think about things
+as Ethiopia did what can we do that's
+
+ align:start position:0%
+as Ethiopia did what can we do that's
+ 
+
+ align:start position:0%
+as Ethiopia did what can we do that's
+robust if we're going to have a sea
+
+ align:start position:0%
+robust if we're going to have a sea
+ 
+
+ align:start position:0%
+robust if we're going to have a sea
+level rise how do we cope with that what
+
+ align:start position:0%
+level rise how do we cope with that what
+ 
+
+ align:start position:0%
+level rise how do we cope with that what
+do we need to do about hurricanes how do
+
+ align:start position:0%
+do we need to do about hurricanes how do
+ 
+
+ align:start position:0%
+do we need to do about hurricanes how do
+we change various policies awful lot of
+
+ align:start position:0%
+we change various policies awful lot of
+ 
+
+ align:start position:0%
+we change various policies awful lot of
+that is local awful lot of that has to
+
+ align:start position:0%
+that is local awful lot of that has to
+ 
+
+ align:start position:0%
+that is local awful lot of that has to
+be local and an awful lot of that's
+
+ align:start position:0%
+be local and an awful lot of that's
+ 
+
+ align:start position:0%
+be local and an awful lot of that's
+going to be in poor
+
+ align:start position:0%
+going to be in poor
+ 
+
+ align:start position:0%
+going to be in poor
+countries so adaptation will happen the
+
+ align:start position:0%
+countries so adaptation will happen the
+ 
+
+ align:start position:0%
+countries so adaptation will happen the
+Zar will try to do something about that
+
+ align:start position:0%
+Zar will try to do something about that
+ 
+
+ align:start position:0%
+Zar will try to do something about that
+but that one hopes is not enough or one
+
+ align:start position:0%
+but that one hopes is not enough or one
+ 
+
+ align:start position:0%
+but that one hopes is not enough or one
+doubts it will be enough to really get
+
+ align:start position:0%
+doubts it will be enough to really get
+ 
+
+ align:start position:0%
+doubts it will be enough to really get
+us smoothly new technology you guys are
+
+ align:start position:0%
+us smoothly new technology you guys are
+ 
+
+ align:start position:0%
+us smoothly new technology you guys are
+going to develop new technologies that's
+
+ align:start position:0%
+going to develop new technologies that's
+ 
+
+ align:start position:0%
+going to develop new technologies that's
+going to be terrific what's the Zar
+
+ align:start position:0%
+going to be terrific what's the Zar
+ 
+
+ align:start position:0%
+going to be terrific what's the Zar
+going to do about that well governments
+
+ align:start position:0%
+going to do about that well governments
+ 
+
+ align:start position:0%
+going to do about that well governments
+we come back to some of these issues but
+
+ align:start position:0%
+we come back to some of these issues but
+ 
+
+ align:start position:0%
+we come back to some of these issues but
+governments have a terrible record of
+
+ align:start position:0%
+governments have a terrible record of
+ 
+
+ align:start position:0%
+governments have a terrible record of
+pushing the development of Civilian
+
+ align:start position:0%
+pushing the development of Civilian
+ 
+
+ align:start position:0%
+pushing the development of Civilian
+Technologies military Technologies space
+
+ align:start position:0%
+Technologies military Technologies space
+ 
+
+ align:start position:0%
+Technologies military Technologies space
+Technologies where cost doesn't
+
+ align:start position:0%
+Technologies where cost doesn't
+ 
+
+ align:start position:0%
+Technologies where cost doesn't
+matter fine basic research fine getting
+
+ align:start position:0%
+matter fine basic research fine getting
+ 
+
+ align:start position:0%
+matter fine basic research fine getting
+stuff to Market at a reasonable price
+
+ align:start position:0%
+stuff to Market at a reasonable price
+ 
+
+ align:start position:0%
+stuff to Market at a reasonable price
+bad record so if you can't adapt and you
+
+ align:start position:0%
+bad record so if you can't adapt and you
+ 
+
+ align:start position:0%
+bad record so if you can't adapt and you
+can't solve it with
+
+ align:start position:0%
+can't solve it with
+ 
+
+ align:start position:0%
+can't solve it with
+technology um you got to reduce
+
+ align:start position:0%
+technology um you got to reduce
+ 
+
+ align:start position:0%
+technology um you got to reduce
+emissions why is reducing hard oh well
+
+ align:start position:0%
+emissions why is reducing hard oh well
+ 
+
+ align:start position:0%
+emissions why is reducing hard oh well
+let me first fossil fuels I'll just
+
+ align:start position:0%
+let me first fossil fuels I'll just
+ 
+
+ align:start position:0%
+let me first fossil fuels I'll just
+another thing you might think about
+
+ align:start position:0%
+another thing you might think about
+ 
+
+ align:start position:0%
+another thing you might think about
+doing and you've probably read about is
+
+ align:start position:0%
+doing and you've probably read about is
+ 
+
+ align:start position:0%
+doing and you've probably read about is
+geoengineering um the simplest way to
+
+ align:start position:0%
+geoengineering um the simplest way to
+ 
+
+ align:start position:0%
+geoengineering um the simplest way to
+think about that is artificial volcanoes
+
+ align:start position:0%
+think about that is artificial volcanoes
+ 
+
+ align:start position:0%
+think about that is artificial volcanoes
+you might put
+
+ align:start position:0%
+you might put
+ 
+
+ align:start position:0%
+you might put
+sulfate when Mount Pinatubo blew up uh
+
+ align:start position:0%
+sulfate when Mount Pinatubo blew up uh
+ 
+
+ align:start position:0%
+sulfate when Mount Pinatubo blew up uh
+as I understand it there was a
+
+ align:start position:0%
+as I understand it there was a
+ 
+
+ align:start position:0%
+as I understand it there was a
+discernable
+
+ align:start position:0%
+discernable
+ 
+
+ align:start position:0%
+discernable
+cooling small particles aerosols uh in
+
+ align:start position:0%
+cooling small particles aerosols uh in
+ 
+
+ align:start position:0%
+cooling small particles aerosols uh in
+the stratosphere reflect sunlight so why
+
+ align:start position:0%
+the stratosphere reflect sunlight so why
+ 
+
+ align:start position:0%
+the stratosphere reflect sunlight so why
+don't we just either burn more coal
+
+ align:start position:0%
+don't we just either burn more coal
+ 
+
+ align:start position:0%
+don't we just either burn more coal
+or take the 16-inch guns from
+
+ align:start position:0%
+or take the 16-inch guns from
+ 
+
+ align:start position:0%
+or take the 16-inch guns from
+battleships that aren't in use anymore
+
+ align:start position:0%
+battleships that aren't in use anymore
+ 
+
+ align:start position:0%
+battleships that aren't in use anymore
+turn them up and fire aerosols into the
+
+ align:start position:0%
+turn them up and fire aerosols into the
+ 
+
+ align:start position:0%
+turn them up and fire aerosols into the
+stratosphere uh this is a serious
+
+ align:start position:0%
+stratosphere uh this is a serious
+ 
+
+ align:start position:0%
+stratosphere uh this is a serious
+proposal to reflect
+
+ align:start position:0%
+proposal to reflect
+ 
+
+ align:start position:0%
+proposal to reflect
+sunlight well uh you might want to have
+
+ align:start position:0%
+sunlight well uh you might want to have
+ 
+
+ align:start position:0%
+sunlight well uh you might want to have
+that in your back pocket for emergencies
+
+ align:start position:0%
+that in your back pocket for emergencies
+ 
+
+ align:start position:0%
+that in your back pocket for emergencies
+but uh first of all if you have more CO2
+
+ align:start position:0%
+but uh first of all if you have more CO2
+ 
+
+ align:start position:0%
+but uh first of all if you have more CO2
+in the atmosphere the ocean becomes more
+
+ align:start position:0%
+in the atmosphere the ocean becomes more
+ 
+
+ align:start position:0%
+in the atmosphere the ocean becomes more
+acidic and creatures die doesn't solve
+
+ align:start position:0%
+acidic and creatures die doesn't solve
+ 
+
+ align:start position:0%
+acidic and creatures die doesn't solve
+that problem and second if you don't
+
+ align:start position:0%
+that problem and second if you don't
+ 
+
+ align:start position:0%
+that problem and second if you don't
+reduce emissions you got to keep doing
+
+ align:start position:0%
+reduce emissions you got to keep doing
+ 
+
+ align:start position:0%
+reduce emissions you got to keep doing
+more and more of that and that does not
+
+ align:start position:0%
+more and more of that and that does not
+ 
+
+ align:start position:0%
+more and more of that and that does not
+sound like a long-term Way Forward so
+
+ align:start position:0%
+sound like a long-term Way Forward so
+ 
+
+ align:start position:0%
+sound like a long-term Way Forward so
+CO2 is where the policy focus is because
+
+ align:start position:0%
+CO2 is where the policy focus is because
+ 
+
+ align:start position:0%
+CO2 is where the policy focus is because
+as we saw from those earlier graphs it's
+
+ align:start position:0%
+as we saw from those earlier graphs it's
+ 
+
+ align:start position:0%
+as we saw from those earlier graphs it's
+it's quite important it lasts a long
+
+ align:start position:0%
+it's quite important it lasts a long
+ 
+
+ align:start position:0%
+it's quite important it lasts a long
+time we can measure fossil fuel use
+
+ align:start position:0%
+time we can measure fossil fuel use
+ 
+
+ align:start position:0%
+time we can measure fossil fuel use
+pretty easily think about countries that
+
+ align:start position:0%
+pretty easily think about countries that
+ 
+
+ align:start position:0%
+pretty easily think about countries that
+import all their oil
+
+ align:start position:0%
+import all their oil
+ 
+
+ align:start position:0%
+import all their oil
+um you can measure Imports pretty easily
+
+ align:start position:0%
+um you can measure Imports pretty easily
+ 
+
+ align:start position:0%
+um you can measure Imports pretty easily
+at the ports where they happen you may
+
+ align:start position:0%
+at the ports where they happen you may
+ 
+
+ align:start position:0%
+at the ports where they happen you may
+be wrong plus or minus inventory
+
+ align:start position:0%
+be wrong plus or minus inventory
+ 
+
+ align:start position:0%
+be wrong plus or minus inventory
+accumulation but it's not easy to carry
+
+ align:start position:0%
+accumulation but it's not easy to carry
+ 
+
+ align:start position:0%
+accumulation but it's not easy to carry
+in not cheap to carry inventories of
+
+ align:start position:0%
+in not cheap to carry inventories of
+ 
+
+ align:start position:0%
+in not cheap to carry inventories of
+crude oil and refined product so it's
+
+ align:start position:0%
+crude oil and refined product so it's
+ 
+
+ align:start position:0%
+crude oil and refined product so it's
+not in terms of internationally
+
+ align:start position:0%
+not in terms of internationally
+ 
+
+ align:start position:0%
+not in terms of internationally
+enforceable agreements fossil fuel is
+
+ align:start position:0%
+enforceable agreements fossil fuel is
+ 
+
+ align:start position:0%
+enforceable agreements fossil fuel is
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+easy compared to anything else you want
+
+ align:start position:0%
+easy compared to anything else you want
+ 
+
+ align:start position:0%
+easy compared to anything else you want
+to think
+
+ align:start position:0%
+to think
+ 
+
+ align:start position:0%
+to think
+about uh another reason you focus on it
+
+ align:start position:0%
+about uh another reason you focus on it
+ 
+
+ align:start position:0%
+about uh another reason you focus on it
+as we talked about uh last week not only
+
+ align:start position:0%
+as we talked about uh last week not only
+ 
+
+ align:start position:0%
+as we talked about uh last week not only
+does it involve durable assets that can
+
+ align:start position:0%
+does it involve durable assets that can
+ 
+
+ align:start position:0%
+does it involve durable assets that can
+last a long time that are expensive and
+
+ align:start position:0%
+last a long time that are expensive and
+ 
+
+ align:start position:0%
+last a long time that are expensive and
+thus expensive to replace
+
+ align:start position:0%
+thus expensive to replace
+ 
+
+ align:start position:0%
+thus expensive to replace
+early um but they're all these other
+
+ align:start position:0%
+early um but they're all these other
+ 
+
+ align:start position:0%
+early um but they're all these other
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+dependencies that keep you down a path
+
+ align:start position:0%
+dependencies that keep you down a path
+ 
+
+ align:start position:0%
+dependencies that keep you down a path
+so that if you want to so the energy
+
+ align:start position:0%
+so that if you want to so the energy
+ 
+
+ align:start position:0%
+so that if you want to so the energy
+system is a slow ship to turn and if you
+
+ align:start position:0%
+system is a slow ship to turn and if you
+ 
+
+ align:start position:0%
+system is a slow ship to turn and if you
+need to turn it because its impacts last
+
+ align:start position:0%
+need to turn it because its impacts last
+ 
+
+ align:start position:0%
+need to turn it because its impacts last
+100 years
+
+ align:start position:0%
+100 years
+ 
+
+ align:start position:0%
+100 years
+and if you can turn it because you can
+
+ align:start position:0%
+and if you can turn it because you can
+ 
+
+ align:start position:0%
+and if you can turn it because you can
+monitor and enforce that's a logical
+
+ align:start position:0%
+monitor and enforce that's a logical
+ 
+
+ align:start position:0%
+monitor and enforce that's a logical
+place to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+focus why is that problem hard why is it
+
+ align:start position:0%
+focus why is that problem hard why is it
+ 
+
+ align:start position:0%
+focus why is that problem hard why is it
+hard to to change emissions well we
+
+ align:start position:0%
+hard to to change emissions well we
+ 
+
+ align:start position:0%
+hard to to change emissions well we
+talked about that this
+
+ align:start position:0%
+talked about that this
+ 
+
+ align:start position:0%
+talked about that this
+is some of some colorcoded not very well
+
+ align:start position:0%
+is some of some colorcoded not very well
+ 
+
+ align:start position:0%
+is some of some colorcoded not very well
+colorcoded Emissions trajectories on the
+
+ align:start position:0%
+colorcoded Emissions trajectories on the
+ 
+
+ align:start position:0%
+colorcoded Emissions trajectories on the
+left um matched with atmospheric CO2
+
+ align:start position:0%
+left um matched with atmospheric CO2
+ 
+
+ align:start position:0%
+left um matched with atmospheric CO2
+concentrations on the right and matched
+
+ align:start position:0%
+concentrations on the right and matched
+ 
+
+ align:start position:0%
+concentrations on the right and matched
+down here
+
+ align:start position:0%
+down here
+ 
+
+ align:start position:0%
+down here
+except for the really aggressive
+
+ align:start position:0%
+except for the really aggressive
+ 
+
+ align:start position:0%
+except for the really aggressive
+reduction scenario matched with uh
+
+ align:start position:0%
+reduction scenario matched with uh
+ 
+
+ align:start position:0%
+reduction scenario matched with uh
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+increases uh so the world runs on fossil
+
+ align:start position:0%
+increases uh so the world runs on fossil
+ 
+
+ align:start position:0%
+increases uh so the world runs on fossil
+fuels to a first approximation you saw
+
+ align:start position:0%
+fuels to a first approximation you saw
+ 
+
+ align:start position:0%
+fuels to a first approximation you saw
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+those um uh Lawrence Livermore graphs
+
+ align:start position:0%
+those um uh Lawrence Livermore graphs
+ 
+
+ align:start position:0%
+those um uh Lawrence Livermore graphs
+of sources of fuel sources of energy
+
+ align:start position:0%
+of sources of fuel sources of energy
+ 
+
+ align:start position:0%
+of sources of fuel sources of energy
+most of it's fossil the world runs on
+
+ align:start position:0%
+most of it's fossil the world runs on
+ 
+
+ align:start position:0%
+most of it's fossil the world runs on
+fossil fuels big emission cuts are
+
+ align:start position:0%
+fossil fuels big emission cuts are
+ 
+
+ align:start position:0%
+fossil fuels big emission cuts are
+needed if you're going to reduce
+
+ align:start position:0%
+needed if you're going to reduce
+ 
+
+ align:start position:0%
+needed if you're going to reduce
+temperature take the you might think of
+
+ align:start position:0%
+temperature take the you might think of
+ 
+
+ align:start position:0%
+temperature take the you might think of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+orange kind of as an estimate of
+
+ align:start position:0%
+orange kind of as an estimate of
+ 
+
+ align:start position:0%
+orange kind of as an estimate of
+businesses usual maybe somebody's
+
+ align:start position:0%
+businesses usual maybe somebody's
+ 
+
+ align:start position:0%
+businesses usual maybe somebody's
+estimate the blue then is a pretty
+
+ align:start position:0%
+estimate the blue then is a pretty
+ 
+
+ align:start position:0%
+estimate the blue then is a pretty
+aggressive cut but look what and the
+
+ align:start position:0%
+aggressive cut but look what and the
+ 
+
+ align:start position:0%
+aggressive cut but look what and the
+blue relative to the orange at the end
+
+ align:start position:0%
+blue relative to the orange at the end
+ 
+
+ align:start position:0%
+blue relative to the orange at the end
+of the century has a pretty big impact
+
+ align:start position:0%
+of the century has a pretty big impact
+ 
+
+ align:start position:0%
+of the century has a pretty big impact
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+atmospheric uh uh concentrations but the
+
+ align:start position:0%
+atmospheric uh uh concentrations but the
+ 
+
+ align:start position:0%
+atmospheric uh uh concentrations but the
+temperature still goes up the
+
+ align:start position:0%
+temperature still goes up the
+ 
+
+ align:start position:0%
+temperature still goes up the
+temperature still goes up substantially
+
+ align:start position:0%
+temperature still goes up substantially
+ 
+
+ align:start position:0%
+temperature still goes up substantially
+that's a 2 degree or is that a 3 degree
+
+ align:start position:0%
+that's a 2 degree or is that a 3 degree
+ 
+
+ align:start position:0%
+that's a 2 degree or is that a 3 degree
+increase in temperature temperature 3° C
+
+ align:start position:0%
+increase in temperature temperature 3° C
+ 
+
+ align:start position:0%
+increase in temperature temperature 3° C
+Fahrenheit increase in temperature uh
+
+ align:start position:0%
+Fahrenheit increase in temperature uh
+ 
+
+ align:start position:0%
+Fahrenheit increase in temperature uh
+the orange much bigger but that's a big
+
+ align:start position:0%
+the orange much bigger but that's a big
+ 
+
+ align:start position:0%
+the orange much bigger but that's a big
+change right if you're going from here
+
+ align:start position:0%
+change right if you're going from here
+ 
+
+ align:start position:0%
+change right if you're going from here
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+here China's not getting rich burning
+
+ align:start position:0%
+here China's not getting rich burning
+ 
+
+ align:start position:0%
+here China's not getting rich burning
+coal on that on the blue path we're not
+
+ align:start position:0%
+coal on that on the blue path we're not
+ 
+
+ align:start position:0%
+coal on that on the blue path we're not
+uh increasing our energy at all probably
+
+ align:start position:0%
+uh increasing our energy at all probably
+ 
+
+ align:start position:0%
+uh increasing our energy at all probably
+Europe is cutting back even farther to
+
+ align:start position:0%
+Europe is cutting back even farther to
+ 
+
+ align:start position:0%
+Europe is cutting back even farther to
+get to that blue path that's a big
+
+ align:start position:0%
+get to that blue path that's a big
+ 
+
+ align:start position:0%
+get to that blue path that's a big
+deal that's so if it's the easiest thing
+
+ align:start position:0%
+deal that's so if it's the easiest thing
+ 
+
+ align:start position:0%
+deal that's so if it's the easiest thing
+to do and it's an important thing to do
+
+ align:start position:0%
+to do and it's an important thing to do
+ 
+
+ align:start position:0%
+to do and it's an important thing to do
+it's a big deal so that's one reason why
+
+ align:start position:0%
+it's a big deal so that's one reason why
+ 
+
+ align:start position:0%
+it's a big deal so that's one reason why
+it's hard is we live on fossil fuels so
+
+ align:start position:0%
+it's hard is we live on fossil fuels so
+ 
+
+ align:start position:0%
+it's hard is we live on fossil fuels so
+if you're going to cut the use of fossil
+
+ align:start position:0%
+if you're going to cut the use of fossil
+ 
+
+ align:start position:0%
+if you're going to cut the use of fossil
+fuels emissions from fossil
+
+ align:start position:0%
+fuels emissions from fossil
+ 
+
+ align:start position:0%
+fuels emissions from fossil
+fuels it's emissions from fossil fuels
+
+ align:start position:0%
+fuels it's emissions from fossil fuels
+ 
+
+ align:start position:0%
+fuels it's emissions from fossil fuels
+uh you can do some fuel switching you
+
+ align:start position:0%
+uh you can do some fuel switching you
+ 
+
+ align:start position:0%
+uh you can do some fuel switching you
+can do some efficiency you can do some
+
+ align:start position:0%
+can do some efficiency you can do some
+ 
+
+ align:start position:0%
+can do some efficiency you can do some
+this that and the other but you will
+
+ align:start position:0%
+this that and the other but you will
+ 
+
+ align:start position:0%
+this that and the other but you will
+have to do a
+
+ align:start position:0%
+have to do a
+ 
+
+ align:start position:0%
+have to do a
+lot new technologies will be essential
+
+ align:start position:0%
+lot new technologies will be essential
+ 
+
+ align:start position:0%
+lot new technologies will be essential
+but they may or may not appear in
+
+ align:start position:0%
+but they may or may not appear in
+ 
+
+ align:start position:0%
+but they may or may not appear in
+time okay okay so that's a big deal so
+
+ align:start position:0%
+time okay okay so that's a big deal so
+ 
+
+ align:start position:0%
+time okay okay so that's a big deal so
+we all go to bicycles that's great we
+
+ align:start position:0%
+we all go to bicycles that's great we
+ 
+
+ align:start position:0%
+we all go to bicycles that's great we
+can do that we can emulate the Dutch and
+
+ align:start position:0%
+can do that we can emulate the Dutch and
+ 
+
+ align:start position:0%
+can do that we can emulate the Dutch and
+we can all bicycle to
+
+ align:start position:0%
+we can all bicycle to
+ 
+
+ align:start position:0%
+we can all bicycle to
+work but we're not the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem any projection of the future
+
+ align:start position:0%
+problem any projection of the future
+ 
+
+ align:start position:0%
+problem any projection of the future
+says the growth in emissions will come
+
+ align:start position:0%
+says the growth in emissions will come
+ 
+
+ align:start position:0%
+says the growth in emissions will come
+from countries that are now poor they
+
+ align:start position:0%
+from countries that are now poor they
+ 
+
+ align:start position:0%
+from countries that are now poor they
+have been growing more rapidly than
+
+ align:start position:0%
+have been growing more rapidly than
+ 
+
+ align:start position:0%
+have been growing more rapidly than
+countries that are now Rich for some
+
+ align:start position:0%
+countries that are now Rich for some
+ 
+
+ align:start position:0%
+countries that are now Rich for some
+time and all projections are they will
+
+ align:start position:0%
+time and all projections are they will
+ 
+
+ align:start position:0%
+time and all projections are they will
+continue to do so so this is from BP's
+
+ align:start position:0%
+continue to do so so this is from BP's
+ 
+
+ align:start position:0%
+continue to do so so this is from BP's
+energy Outlook if you look up to
+
+ align:start position:0%
+energy Outlook if you look up to
+ 
+
+ align:start position:0%
+energy Outlook if you look up to
+2020 1990 to 20110 you'll see oecd
+
+ align:start position:0%
+2020 1990 to 20110 you'll see oecd
+ 
+
+ align:start position:0%
+2020 1990 to 20110 you'll see oecd
+emissions rich country emissions pretty
+
+ align:start position:0%
+emissions rich country emissions pretty
+ 
+
+ align:start position:0%
+emissions rich country emissions pretty
+flat I mean they'd be up a bit but for
+
+ align:start position:0%
+flat I mean they'd be up a bit but for
+ 
+
+ align:start position:0%
+flat I mean they'd be up a bit but for
+the recession but not much but dramatic
+
+ align:start position:0%
+the recession but not much but dramatic
+ 
+
+ align:start position:0%
+the recession but not much but dramatic
+growth in the less rich countries
+
+ align:start position:0%
+growth in the less rich countries
+ 
+
+ align:start position:0%
+growth in the less rich countries
+derotic growth again for the world as a
+
+ align:start position:0%
+derotic growth again for the world as a
+ 
+
+ align:start position:0%
+derotic growth again for the world as a
+whole energy and co2 have grown less
+
+ align:start position:0%
+whole energy and co2 have grown less
+ 
+
+ align:start position:0%
+whole energy and co2 have grown less
+rapidly than GDP that
+
+ align:start position:0%
+rapidly than GDP that
+ 
+
+ align:start position:0%
+rapidly than GDP that
+declining we saw in the US is a general
+
+ align:start position:0%
+declining we saw in the US is a general
+ 
+
+ align:start position:0%
+declining we saw in the US is a general
+phenomenon
+
+ align:start position:0%
+phenomenon
+ 
+
+ align:start position:0%
+phenomenon
+but if you don't you know if you try to
+
+ align:start position:0%
+but if you don't you know if you try to
+ 
+
+ align:start position:0%
+but if you don't you know if you try to
+control Global emissions try to reduce
+
+ align:start position:0%
+control Global emissions try to reduce
+ 
+
+ align:start position:0%
+control Global emissions try to reduce
+Global emissions by reducing oecd
+
+ align:start position:0%
+Global emissions by reducing oecd
+ 
+
+ align:start position:0%
+Global emissions by reducing oecd
+emissions you see if if we go to Zero by
+
+ align:start position:0%
+emissions you see if if we go to Zero by
+ 
+
+ align:start position:0%
+emissions you see if if we go to Zero by
+2030 and and the non
+
+ align:start position:0%
+2030 and and the non
+ 
+
+ align:start position:0%
+2030 and and the non
+oec D proceeds on the track Global
+
+ align:start position:0%
+oec D proceeds on the track Global
+ 
+
+ align:start position:0%
+oec D proceeds on the track Global
+emissions will be up
+
+ align:start position:0%
+emissions will be up
+ 
+
+ align:start position:0%
+emissions will be up
+right just by
+
+ align:start position:0%
+right just by
+ 
+
+ align:start position:0%
+right just by
+I so yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sam policy changes the idea what those
+
+ align:start position:0%
+Sam policy changes the idea what those
+ 
+
+ align:start position:0%
+Sam policy changes the idea what those
+could be
+
+ align:start position:0%
+could be
+ 
+
+ align:start position:0%
+could be
+um you know you read the report and you
+
+ align:start position:0%
+um you know you read the report and you
+ 
+
+ align:start position:0%
+um you know you read the report and you
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+well what are they assuming they're
+
+ align:start position:0%
+well what are they assuming they're
+ 
+
+ align:start position:0%
+well what are they assuming they're
+assuming tightening restrictions in
+
+ align:start position:0%
+assuming tightening restrictions in
+ 
+
+ align:start position:0%
+assuming tightening restrictions in
+Europe they're assuming something in the
+
+ align:start position:0%
+Europe they're assuming something in the
+ 
+
+ align:start position:0%
+Europe they're assuming something in the
+US they're assuming uh continued
+
+ align:start position:0%
+US they're assuming uh continued
+ 
+
+ align:start position:0%
+US they're assuming uh continued
+efficiency increases they're not
+
+ align:start position:0%
+efficiency increases they're not
+ 
+
+ align:start position:0%
+efficiency increases they're not
+assuming the kind of global agreement
+
+ align:start position:0%
+assuming the kind of global agreement
+ 
+
+ align:start position:0%
+assuming the kind of global agreement
+you guys are going to negotiate
+
+ align:start position:0%
+you guys are going to negotiate
+ 
+
+ align:start position:0%
+you guys are going to negotiate
+Wednesday and Friday that's clear
+
+ align:start position:0%
+Wednesday and Friday that's clear
+ 
+
+ align:start position:0%
+Wednesday and Friday that's clear
+they're not assuming sort of a second
+
+ align:start position:0%
+they're not assuming sort of a second
+ 
+
+ align:start position:0%
+they're not assuming sort of a second
+Kyoto Protocol ratified by the whole
+
+ align:start position:0%
+Kyoto Protocol ratified by the whole
+ 
+
+ align:start position:0%
+Kyoto Protocol ratified by the whole
+world uh I think and it's an interesting
+
+ align:start position:0%
+world uh I think and it's an interesting
+ 
+
+ align:start position:0%
+world uh I think and it's an interesting
+assumption to assume that absent
+
+ align:start position:0%
+assumption to assume that absent
+ 
+
+ align:start position:0%
+assumption to assume that absent
+anything going on in these countries
+
+ align:start position:0%
+anything going on in these countries
+ 
+
+ align:start position:0%
+anything going on in these countries
+that these countries will continue I
+
+ align:start position:0%
+that these countries will continue I
+ 
+
+ align:start position:0%
+that these countries will continue I
+mean here they're showing a reduction a
+
+ align:start position:0%
+mean here they're showing a reduction a
+ 
+
+ align:start position:0%
+mean here they're showing a reduction a
+positive reduction in emissions here
+
+ align:start position:0%
+positive reduction in emissions here
+ 
+
+ align:start position:0%
+positive reduction in emissions here
+over that period so that that is and
+
+ align:start position:0%
+over that period so that that is and
+ 
+
+ align:start position:0%
+over that period so that that is and
+there's growth not huge growth but
+
+ align:start position:0%
+there's growth not huge growth but
+ 
+
+ align:start position:0%
+there's growth not huge growth but
+there's growth so they're assuming a
+
+ align:start position:0%
+there's growth so they're assuming a
+ 
+
+ align:start position:0%
+there's growth so they're assuming a
+tightening in the oecd continued
+
+ align:start position:0%
+tightening in the oecd continued
+ 
+
+ align:start position:0%
+tightening in the oecd continued
+efficiency increases
+
+ align:start position:0%
+efficiency increases
+ 
+
+ align:start position:0%
+efficiency increases
+here some I there some discussion of of
+
+ align:start position:0%
+here some I there some discussion of of
+ 
+
+ align:start position:0%
+here some I there some discussion of of
+China becoming a bit a bit less carbon
+
+ align:start position:0%
+China becoming a bit a bit less carbon
+ 
+
+ align:start position:0%
+China becoming a bit a bit less carbon
+intensive but but the main policy
+
+ align:start position:0%
+intensive but but the main policy
+ 
+
+ align:start position:0%
+intensive but but the main policy
+actions here and they do not assume a
+
+ align:start position:0%
+actions here and they do not assume a
+ 
+
+ align:start position:0%
+actions here and they do not assume a
+global
+
+ align:start position:0%
+global
+ 
+
+ align:start position:0%
+global
+agreement um it's a short description I
+
+ align:start position:0%
+agreement um it's a short description I
+ 
+
+ align:start position:0%
+agreement um it's a short description I
+invite you to read it it's about two
+
+ align:start position:0%
+invite you to read it it's about two
+ 
+
+ align:start position:0%
+invite you to read it it's about two
+pages see what see what you think they
+
+ align:start position:0%
+pages see what see what you think they
+ 
+
+ align:start position:0%
+pages see what see what you think they
+assume but that's how I get that's what
+
+ align:start position:0%
+assume but that's how I get that's what
+ 
+
+ align:start position:0%
+assume but that's how I get that's what
+I get out of it you can see there there
+
+ align:start position:0%
+I get out of it you can see there there
+ 
+
+ align:start position:0%
+I get out of it you can see there there
+continuing to assume for the world as a
+
+ align:start position:0%
+continuing to assume for the world as a
+ 
+
+ align:start position:0%
+continuing to assume for the world as a
+whole uh efficiency increases right the
+
+ align:start position:0%
+whole uh efficiency increases right the
+ 
+
+ align:start position:0%
+whole uh efficiency increases right the
+GDP grows much more rapidly than energy
+
+ align:start position:0%
+GDP grows much more rapidly than energy
+ 
+
+ align:start position:0%
+GDP grows much more rapidly than energy
+use and they're continuing to assume for
+
+ align:start position:0%
+use and they're continuing to assume for
+ 
+
+ align:start position:0%
+use and they're continuing to assume for
+the world as a whole decarbonization
+
+ align:start position:0%
+the world as a whole decarbonization
+ 
+
+ align:start position:0%
+the world as a whole decarbonization
+presumably presumably a switch out of
+
+ align:start position:0%
+presumably presumably a switch out of
+ 
+
+ align:start position:0%
+presumably presumably a switch out of
+coal into natural gas and Renewables I'd
+
+ align:start position:0%
+coal into natural gas and Renewables I'd
+ 
+
+ align:start position:0%
+coal into natural gas and Renewables I'd
+have to go back and check but I think
+
+ align:start position:0%
+have to go back and check but I think
+ 
+
+ align:start position:0%
+have to go back and check but I think
+that's part of the
+
+ align:start position:0%
+that's part of the
+ 
+
+ align:start position:0%
+that's part of the
+scenario anything else yeah how big is
+
+ align:start position:0%
+scenario anything else yeah how big is
+ 
+
+ align:start position:0%
+scenario anything else yeah how big is
+the impact of other emissions like
+
+ align:start position:0%
+the impact of other emissions like
+ 
+
+ align:start position:0%
+the impact of other emissions like
+methane I know that it keeps more
+
+ align:start position:0%
+methane I know that it keeps more
+ 
+
+ align:start position:0%
+methane I know that it keeps more
+heat methane uh has
+
+ align:start position:0%
+heat methane uh has
+ 
+
+ align:start position:0%
+heat methane uh has
+a the reason for not focusing on methane
+
+ align:start position:0%
+a the reason for not focusing on methane
+ 
+
+ align:start position:0%
+a the reason for not focusing on methane
+even though it it is a more potent heat
+
+ align:start position:0%
+even though it it is a more potent heat
+ 
+
+ align:start position:0%
+even though it it is a more potent heat
+trapping gas it doesn't stay in the
+
+ align:start position:0%
+trapping gas it doesn't stay in the
+ 
+
+ align:start position:0%
+trapping gas it doesn't stay in the
+atmosphere is long a so it's about 10
+
+ align:start position:0%
+atmosphere is long a so it's about 10
+ 
+
+ align:start position:0%
+atmosphere is long a so it's about 10
+year halflife by ballpark about 10 years
+
+ align:start position:0%
+year halflife by ballpark about 10 years
+ 
+
+ align:start position:0%
+year halflife by ballpark about 10 years
+uh and B it's harder to figure it has
+
+ align:start position:0%
+uh and B it's harder to figure it has
+ 
+
+ align:start position:0%
+uh and B it's harder to figure it has
+many sources so it's got natural gas
+
+ align:start position:0%
+many sources so it's got natural gas
+ 
+
+ align:start position:0%
+many sources so it's got natural gas
+leaks it's got got uh landfill
+
+ align:start position:0%
+leaks it's got got uh landfill
+ 
+
+ align:start position:0%
+leaks it's got got uh landfill
+decomposition it's got things rotting so
+
+ align:start position:0%
+decomposition it's got things rotting so
+ 
+
+ align:start position:0%
+decomposition it's got things rotting so
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+harder to control and in fact in 20
+
+ align:start position:0%
+harder to control and in fact in 20
+ 
+
+ align:start position:0%
+harder to control and in fact in 20
+years 30
+
+ align:start position:0%
+years 30
+ 
+
+ align:start position:0%
+years 30
+years uh less serious yeah please I
+
+ align:start position:0%
+years uh less serious yeah please I
+ 
+
+ align:start position:0%
+years uh less serious yeah please I
+think part of the confusion on methane
+
+ align:start position:0%
+think part of the confusion on methane
+ 
+
+ align:start position:0%
+think part of the confusion on methane
+is that although every molecule of
+
+ align:start position:0%
+is that although every molecule of
+ 
+
+ align:start position:0%
+is that although every molecule of
+methane is more potent than a molecule
+
+ align:start position:0%
+methane is more potent than a molecule
+ 
+
+ align:start position:0%
+methane is more potent than a molecule
+of CO2 there's a lot more CO2 in the
+
+ align:start position:0%
+of CO2 there's a lot more CO2 in the
+ 
+
+ align:start position:0%
+of CO2 there's a lot more CO2 in the
+atmosphere so actually CO2 doing three
+
+ align:start position:0%
+atmosphere so actually CO2 doing three
+ 
+
+ align:start position:0%
+atmosphere so actually CO2 doing three
+times more warming right now than the
+
+ align:start position:0%
+times more warming right now than the
+ 
+
+ align:start position:0%
+times more warming right now than the
+total of all the methane because there's
+
+ align:start position:0%
+total of all the methane because there's
+ 
+
+ align:start position:0%
+total of all the methane because there's
+so much more of it even though each
+
+ align:start position:0%
+so much more of it even though each
+ 
+
+ align:start position:0%
+so much more of it even though each
+methane molecule is a strong guy yeah I
+
+ align:start position:0%
+methane molecule is a strong guy yeah I
+ 
+
+ align:start position:0%
+methane molecule is a strong guy yeah I
+didn't do that yeah I didn't do that I
+
+ align:start position:0%
+didn't do that yeah I didn't do that I
+ 
+
+ align:start position:0%
+didn't do that yeah I didn't do that I
+should have done it I should have done
+
+ align:start position:0%
+should have done it I should have done
+ 
+
+ align:start position:0%
+should have done it I should have done
+it um yeah if you if you break
+
+ align:start position:0%
+it um yeah if you if you break
+ 
+
+ align:start position:0%
+it um yeah if you if you break
+down sources of anthropogenic warming
+
+ align:start position:0%
+down sources of anthropogenic warming
+ 
+
+ align:start position:0%
+down sources of anthropogenic warming
+CO2
+
+ align:start position:0%
+CO2
+ 
+
+ align:start position:0%
+CO2
+dominates when people get to talking
+
+ align:start position:0%
+dominates when people get to talking
+ 
+
+ align:start position:0%
+dominates when people get to talking
+about methane being an effective
+
+ align:start position:0%
+about methane being an effective
+ 
+
+ align:start position:0%
+about methane being an effective
+greenhouse gas it can get very confusing
+
+ align:start position:0%
+greenhouse gas it can get very confusing
+ 
+
+ align:start position:0%
+greenhouse gas it can get very confusing
+yeah yeah so for this we have the CO2
+
+ align:start position:0%
+yeah yeah so for this we have the CO2
+ 
+
+ align:start position:0%
+yeah yeah so for this we have the CO2
+emissions by the the
+
+ align:start position:0%
+emissions by the the
+ 
+
+ align:start position:0%
+emissions by the the
+oesd countries right yep but in term of
+
+ align:start position:0%
+oesd countries right yep but in term of
+ 
+
+ align:start position:0%
+oesd countries right yep but in term of
+population I think the O count we're
+
+ align:start position:0%
+population I think the O count we're
+ 
+
+ align:start position:0%
+population I think the O count we're
+going to come there we're going to break
+
+ align:start position:0%
+going to come there we're going to break
+ 
+
+ align:start position:0%
+going to come there we're going to break
+it down yes you are in terms of per
+
+ align:start position:0%
+it down yes you are in terms of per
+ 
+
+ align:start position:0%
+it down yes you are in terms of per
+capita the oecd countries are much
+
+ align:start position:0%
+capita the oecd countries are much
+ 
+
+ align:start position:0%
+capita the oecd countries are much
+higher but the only point to be made
+
+ align:start position:0%
+higher but the only point to be made
+ 
+
+ align:start position:0%
+higher but the only point to be made
+here is if you want this top graph to
+
+ align:start position:0%
+here is if you want this top graph to
+ 
+
+ align:start position:0%
+here is if you want this top graph to
+come down you're not going to get it all
+
+ align:start position:0%
+come down you're not going to get it all
+ 
+
+ align:start position:0%
+come down you're not going to get it all
+here and you got to do something up
+
+ align:start position:0%
+here and you got to do something up
+ 
+
+ align:start position:0%
+here and you got to do something up
+here somehow somehow um we will come to
+
+ align:start position:0%
+here somehow somehow um we will come to
+ 
+
+ align:start position:0%
+here somehow somehow um we will come to
+questions of fairness in about a half a
+
+ align:start position:0%
+questions of fairness in about a half a
+ 
+
+ align:start position:0%
+questions of fairness in about a half a
+second but uh so that's that's a
+
+ align:start position:0%
+second but uh so that's that's a
+ 
+
+ align:start position:0%
+second but uh so that's that's a
+reason you you're going to have to deal
+
+ align:start position:0%
+reason you you're going to have to deal
+ 
+
+ align:start position:0%
+reason you you're going to have to deal
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+growth and the growth is going to come
+
+ align:start position:0%
+growth and the growth is going to come
+ 
+
+ align:start position:0%
+growth and the growth is going to come
+from many from countries that are now
+
+ align:start position:0%
+from many from countries that are now
+ 
+
+ align:start position:0%
+from many from countries that are now
+poorer than the oecd
+
+ align:start position:0%
+poorer than the oecd
+ 
+
+ align:start position:0%
+poorer than the oecd
+countries the other reason let me just
+
+ align:start position:0%
+countries the other reason let me just
+ 
+
+ align:start position:0%
+countries the other reason let me just
+briefly
+
+ align:start position:0%
+briefly
+ 
+
+ align:start position:0%
+briefly
+do a little economics here as opposed to
+
+ align:start position:0%
+do a little economics here as opposed to
+ 
+
+ align:start position:0%
+do a little economics here as opposed to
+a little a little pseudo
+
+ align:start position:0%
+a little a little pseudo
+ 
+
+ align:start position:0%
+a little a little pseudo
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+suppose you want to reduce
+
+ align:start position:0%
+suppose you want to reduce
+ 
+
+ align:start position:0%
+suppose you want to reduce
+emissions say you want to Total
+
+ align:start position:0%
+emissions say you want to Total
+ 
+
+ align:start position:0%
+emissions say you want to Total
+reduction emissions uh from business as
+
+ align:start position:0%
+reduction emissions uh from business as
+ 
+
+ align:start position:0%
+reduction emissions uh from business as
+usual of capital
+
+ align:start position:0%
+usual of capital
+ 
+
+ align:start position:0%
+usual of capital
+r and you want to do it worldwide and
+
+ align:start position:0%
+r and you want to do it worldwide and
+ 
+
+ align:start position:0%
+r and you want to do it worldwide and
+the cost of getting reductions in
+
+ align:start position:0%
+the cost of getting reductions in
+ 
+
+ align:start position:0%
+the cost of getting reductions in
+country I is given by this cost function
+
+ align:start position:0%
+country I is given by this cost function
+ 
+
+ align:start position:0%
+country I is given by this cost function
+all right so the Zar cares about global
+
+ align:start position:0%
+all right so the Zar cares about global
+ 
+
+ align:start position:0%
+all right so the Zar cares about global
+cost so what the Zar is going to do is
+
+ align:start position:0%
+cost so what the Zar is going to do is
+ 
+
+ align:start position:0%
+cost so what the Zar is going to do is
+is reduce emissions he's going to
+
+ align:start position:0%
+is reduce emissions he's going to
+ 
+
+ align:start position:0%
+is reduce emissions he's going to
+minimize the total cost subject to this
+
+ align:start position:0%
+minimize the total cost subject to this
+ 
+
+ align:start position:0%
+minimize the total cost subject to this
+constraint and if if you recall or just
+
+ align:start position:0%
+constraint and if if you recall or just
+ 
+
+ align:start position:0%
+constraint and if if you recall or just
+use your intuition you're going to have
+
+ align:start position:0%
+use your intuition you're going to have
+ 
+
+ align:start position:0%
+use your intuition you're going to have
+to have the marginal cost the derivative
+
+ align:start position:0%
+to have the marginal cost the derivative
+ 
+
+ align:start position:0%
+to have the marginal cost the derivative
+of this function with respect to its
+
+ align:start position:0%
+of this function with respect to its
+ 
+
+ align:start position:0%
+of this function with respect to its
+argument equal across
+
+ align:start position:0%
+argument equal across
+ 
+
+ align:start position:0%
+argument equal across
+countries if not I can rearrange
+
+ align:start position:0%
+countries if not I can rearrange
+ 
+
+ align:start position:0%
+countries if not I can rearrange
+reductions in a way that'll lower cost
+
+ align:start position:0%
+reductions in a way that'll lower cost
+ 
+
+ align:start position:0%
+reductions in a way that'll lower cost
+I'll do a little more where marginal
+
+ align:start position:0%
+I'll do a little more where marginal
+ 
+
+ align:start position:0%
+I'll do a little more where marginal
+cost is low and a little less where
+
+ align:start position:0%
+cost is low and a little less where
+ 
+
+ align:start position:0%
+cost is low and a little less where
+marginal cost is high get the same
+
+ align:start position:0%
+marginal cost is high get the same
+ 
+
+ align:start position:0%
+marginal cost is high get the same
+reductions lower cost that's always true
+
+ align:start position:0%
+reductions lower cost that's always true
+ 
+
+ align:start position:0%
+reductions lower cost that's always true
+unless the marginal costs are equal well
+
+ align:start position:0%
+unless the marginal costs are equal well
+ 
+
+ align:start position:0%
+unless the marginal costs are equal well
+I I if marginal costs are going to be
+
+ align:start position:0%
+I I if marginal costs are going to be
+ 
+
+ align:start position:0%
+I I if marginal costs are going to be
+equal then unless it's really
+
+ align:start position:0%
+equal then unless it's really
+ 
+
+ align:start position:0%
+equal then unless it's really
+hard to reduce emissions in poor
+
+ align:start position:0%
+hard to reduce emissions in poor
+ 
+
+ align:start position:0%
+hard to reduce emissions in poor
+countries they have to play if we're
+
+ align:start position:0%
+countries they have to play if we're
+ 
+
+ align:start position:0%
+countries they have to play if we're
+going to reduce total cost that's not
+
+ align:start position:0%
+going to reduce total cost that's not
+ 
+
+ align:start position:0%
+going to reduce total cost that's not
+it's not a question of who pays for it
+
+ align:start position:0%
+it's not a question of who pays for it
+ 
+
+ align:start position:0%
+it's not a question of who pays for it
+it's a question of where it
+
+ align:start position:0%
+it's a question of where it
+ 
+
+ align:start position:0%
+it's a question of where it
+happens right doesn't say that that
+
+ align:start position:0%
+happens right doesn't say that that
+ 
+
+ align:start position:0%
+happens right doesn't say that that
+Bangladesh has to pay to reduce
+
+ align:start position:0%
+Bangladesh has to pay to reduce
+ 
+
+ align:start position:0%
+Bangladesh has to pay to reduce
+emissions in Bangladesh it says that
+
+ align:start position:0%
+emissions in Bangladesh it says that
+ 
+
+ align:start position:0%
+emissions in Bangladesh it says that
+emissions in Bangladesh will have to be
+
+ align:start position:0%
+emissions in Bangladesh will have to be
+ 
+
+ align:start position:0%
+emissions in Bangladesh will have to be
+reduced so there's separate questions
+
+ align:start position:0%
+reduced so there's separate questions
+ 
+
+ align:start position:0%
+reduced so there's separate questions
+but it says the poor will need to be
+
+ align:start position:0%
+but it says the poor will need to be
+ 
+
+ align:start position:0%
+but it says the poor will need to be
+involved this
+
+ align:start position:0%
+involved this
+ 
+
+ align:start position:0%
+involved this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um if you
+
+ align:start position:0%
+um if you
+ 
+
+ align:start position:0%
+um if you
+recall 1401 if you have a firm producing
+
+ align:start position:0%
+recall 1401 if you have a firm producing
+ 
+
+ align:start position:0%
+recall 1401 if you have a firm producing
+in multiple plants this is exactly the
+
+ align:start position:0%
+in multiple plants this is exactly the
+ 
+
+ align:start position:0%
+in multiple plants this is exactly the
+same exactly the same principle you want
+
+ align:start position:0%
+same exactly the same principle you want
+ 
+
+ align:start position:0%
+same exactly the same principle you want
+to equalize on the
+
+ align:start position:0%
+to equalize on the
+ 
+
+ align:start position:0%
+to equalize on the
+margin that means everybody normally it
+
+ align:start position:0%
+margin that means everybody normally it
+ 
+
+ align:start position:0%
+margin that means everybody normally it
+means everybody has to
+
+ align:start position:0%
+means everybody has to
+ 
+
+ align:start position:0%
+means everybody has to
+play there are two approaches that have
+
+ align:start position:0%
+play there are two approaches that have
+ 
+
+ align:start position:0%
+play there are two approaches that have
+been put on the table for this and we'll
+
+ align:start position:0%
+been put on the table for this and we'll
+ 
+
+ align:start position:0%
+been put on the table for this and we'll
+come back we'll come back to both of
+
+ align:start position:0%
+come back we'll come back to both of
+ 
+
+ align:start position:0%
+come back we'll come back to both of
+them The Parson at all piece on the
+
+ align:start position:0%
+them The Parson at all piece on the
+ 
+
+ align:start position:0%
+them The Parson at all piece on the
+reading list which is optional talks
+
+ align:start position:0%
+reading list which is optional talks
+ 
+
+ align:start position:0%
+reading list which is optional talks
+about talks about one of them you could
+
+ align:start position:0%
+about talks about one of them you could
+ 
+
+ align:start position:0%
+about talks about one of them you could
+say all right how
+
+ align:start position:0%
+say all right how
+ 
+
+ align:start position:0%
+say all right how
+about the Zar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+there's a price of $20 a ton for carbon
+
+ align:start position:0%
+there's a price of $20 a ton for carbon
+ 
+
+ align:start position:0%
+there's a price of $20 a ton for carbon
+emissions from fossil
+
+ align:start position:0%
+emissions from fossil
+ 
+
+ align:start position:0%
+emissions from fossil
+fuels the Zar doesn't like to do central
+
+ align:start position:0%
+fuels the Zar doesn't like to do central
+ 
+
+ align:start position:0%
+fuels the Zar doesn't like to do central
+planning uh he's learned that lesson but
+
+ align:start position:0%
+planning uh he's learned that lesson but
+ 
+
+ align:start position:0%
+planning uh he's learned that lesson but
+the Zar can Tinker with prices so he'll
+
+ align:start position:0%
+the Zar can Tinker with prices so he'll
+ 
+
+ align:start position:0%
+the Zar can Tinker with prices so he'll
+put a price of $20 a ton for
+
+ align:start position:0%
+put a price of $20 a ton for
+ 
+
+ align:start position:0%
+put a price of $20 a ton for
+emissions well that means everybody
+
+ align:start position:0%
+emissions well that means everybody
+ 
+
+ align:start position:0%
+emissions well that means everybody
+who's contemplating emissions is going
+
+ align:start position:0%
+who's contemplating emissions is going
+ 
+
+ align:start position:0%
+who's contemplating emissions is going
+to cut back until the cost of cutting
+
+ align:start position:0%
+to cut back until the cost of cutting
+ 
+
+ align:start position:0%
+to cut back until the cost of cutting
+back Rises to
+
+ align:start position:0%
+back Rises to
+ 
+
+ align:start position:0%
+back Rises to
+$20 and I'll get this marginal cost
+
+ align:start position:0%
+$20 and I'll get this marginal cost
+ 
+
+ align:start position:0%
+$20 and I'll get this marginal cost
+equality that
+
+ align:start position:0%
+equality that
+ 
+
+ align:start position:0%
+equality that
+way right so I just price the thing we
+
+ align:start position:0%
+way right so I just price the thing we
+ 
+
+ align:start position:0%
+way right so I just price the thing we
+talked about this earlier this is
+
+ align:start position:0%
+talked about this earlier this is
+ 
+
+ align:start position:0%
+talked about this earlier this is
+pricing the harm so I price the harm
+
+ align:start position:0%
+pricing the harm so I price the harm
+ 
+
+ align:start position:0%
+pricing the harm so I price the harm
+people cut back on the
+
+ align:start position:0%
+people cut back on the
+ 
+
+ align:start position:0%
+people cut back on the
+harm um it's a tax it'll show up as a
+
+ align:start position:0%
+harm um it's a tax it'll show up as a
+ 
+
+ align:start position:0%
+harm um it's a tax it'll show up as a
+tax on probably show up as a tax on
+
+ align:start position:0%
+tax on probably show up as a tax on
+ 
+
+ align:start position:0%
+tax on probably show up as a tax on
+fuel right tax much higher on coal than
+
+ align:start position:0%
+fuel right tax much higher on coal than
+ 
+
+ align:start position:0%
+fuel right tax much higher on coal than
+on natural gas but that's one way to do
+
+ align:start position:0%
+on natural gas but that's one way to do
+ 
+
+ align:start position:0%
+on natural gas but that's one way to do
+it and and and the Zar the Zar can do
+
+ align:start position:0%
+it and and and the Zar the Zar can do
+ 
+
+ align:start position:0%
+it and and and the Zar the Zar can do
+that the other way to do
+
+ align:start position:0%
+that the other way to do
+ 
+
+ align:start position:0%
+that the other way to do
+it that makes sense right that's easy we
+
+ align:start position:0%
+it that makes sense right that's easy we
+ 
+
+ align:start position:0%
+it that makes sense right that's easy we
+just price the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing the other way to do it is a little
+
+ align:start position:0%
+thing the other way to do it is a little
+ 
+
+ align:start position:0%
+thing the other way to do it is a little
+more convoluted but only a little more
+
+ align:start position:0%
+more convoluted but only a little more
+ 
+
+ align:start position:0%
+more convoluted but only a little more
+and we'll return to the equivalence
+
+ align:start position:0%
+and we'll return to the equivalence
+ 
+
+ align:start position:0%
+and we'll return to the equivalence
+later on
+
+ align:start position:0%
+later on
+ 
+
+ align:start position:0%
+later on
+is the our prints up statistic uh prints
+
+ align:start position:0%
+is the our prints up statistic uh prints
+ 
+
+ align:start position:0%
+is the our prints up statistic uh prints
+up certificates drops them from
+
+ align:start position:0%
+up certificates drops them from
+ 
+
+ align:start position:0%
+up certificates drops them from
+helicopters and
+
+ align:start position:0%
+helicopters and
+ 
+
+ align:start position:0%
+helicopters and
+says to emit a ton of CO2 you have to
+
+ align:start position:0%
+says to emit a ton of CO2 you have to
+ 
+
+ align:start position:0%
+says to emit a ton of CO2 you have to
+give me a
+
+ align:start position:0%
+give me a
+ 
+
+ align:start position:0%
+give me a
+certificate limited number number of
+
+ align:start position:0%
+certificate limited number number of
+ 
+
+ align:start position:0%
+certificate limited number number of
+certificates equal to the total amount
+
+ align:start position:0%
+certificates equal to the total amount
+ 
+
+ align:start position:0%
+certificates equal to the total amount
+of CO2 the Zar wants to
+
+ align:start position:0%
+of CO2 the Zar wants to
+ 
+
+ align:start position:0%
+of CO2 the Zar wants to
+permit you get a
+
+ align:start position:0%
+permit you get a
+ 
+
+ align:start position:0%
+permit you get a
+market right I go around looking for
+
+ align:start position:0%
+market right I go around looking for
+ 
+
+ align:start position:0%
+market right I go around looking for
+certificates I'm willing to pay 20 bucks
+
+ align:start position:0%
+certificates I'm willing to pay 20 bucks
+ 
+
+ align:start position:0%
+certificates I'm willing to pay 20 bucks
+for it I'm willing to pay some price the
+
+ align:start position:0%
+for it I'm willing to pay some price the
+ 
+
+ align:start position:0%
+for it I'm willing to pay some price the
+market will determine what price in this
+
+ align:start position:0%
+market will determine what price in this
+ 
+
+ align:start position:0%
+market will determine what price in this
+case if I fix a price the market will
+
+ align:start position:0%
+case if I fix a price the market will
+ 
+
+ align:start position:0%
+case if I fix a price the market will
+determine the
+
+ align:start position:0%
+determine the
+ 
+
+ align:start position:0%
+determine the
+quantity if I fix a quantity the market
+
+ align:start position:0%
+quantity if I fix a quantity the market
+ 
+
+ align:start position:0%
+quantity if I fix a quantity the market
+will determine the price but I can go
+
+ align:start position:0%
+will determine the price but I can go
+ 
+
+ align:start position:0%
+will determine the price but I can go
+either
+
+ align:start position:0%
+either
+ 
+
+ align:start position:0%
+either
+way and if thear knows all doesn't
+
+ align:start position:0%
+way and if thear knows all doesn't
+ 
+
+ align:start position:0%
+way and if thear knows all doesn't
+matter which way he
+
+ align:start position:0%
+matter which way he
+ 
+
+ align:start position:0%
+matter which way he
+goes we'll talk a little later I think
+
+ align:start position:0%
+goes we'll talk a little later I think
+ 
+
+ align:start position:0%
+goes we'll talk a little later I think
+about about when and where and how it
+
+ align:start position:0%
+about about when and where and how it
+ 
+
+ align:start position:0%
+about about when and where and how it
+might matter
+
+ align:start position:0%
+might matter
+ 
+
+ align:start position:0%
+might matter
+but that's what thear might that's what
+
+ align:start position:0%
+but that's what thear might that's what
+ 
+
+ align:start position:0%
+but that's what thear might that's what
+thear might want to do right do those
+
+ align:start position:0%
+thear might want to do right do those
+ 
+
+ align:start position:0%
+thear might want to do right do those
+make sort of top of the head sense as a
+
+ align:start position:0%
+make sort of top of the head sense as a
+ 
+
+ align:start position:0%
+make sort of top of the head sense as a
+way to do it without without having to
+
+ align:start position:0%
+way to do it without without having to
+ 
+
+ align:start position:0%
+way to do it without without having to
+do central
+
+ align:start position:0%
+do central
+ 
+
+ align:start position:0%
+do central
+planning for all the nations of the
+
+ align:start position:0%
+planning for all the nations of the
+ 
+
+ align:start position:0%
+planning for all the nations of the
+world but if you say it's $30 a ton or
+
+ align:start position:0%
+world but if you say it's $30 a ton or
+ 
+
+ align:start position:0%
+world but if you say it's $30 a ton or
+$40 a ton on for
+
+ align:start position:0%
+$40 a ton on for
+ 
+
+ align:start position:0%
+$40 a ton on for
+everybody and poor countries have to pay
+
+ align:start position:0%
+everybody and poor countries have to pay
+ 
+
+ align:start position:0%
+everybody and poor countries have to pay
+it how do they do that how do they do
+
+ align:start position:0%
+it how do they do that how do they do
+ 
+
+ align:start position:0%
+it how do they do that how do they do
+that so you know that they're going to
+
+ align:start position:0%
+that so you know that they're going to
+ 
+
+ align:start position:0%
+that so you know that they're going to
+have to do some
+
+ align:start position:0%
+have to do some
+ 
+
+ align:start position:0%
+have to do some
+reduction because if you think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it they're building buildings facilities
+
+ align:start position:0%
+it they're building buildings facilities
+ 
+
+ align:start position:0%
+it they're building buildings facilities
+Etc it's a lot cheaper to insulate a new
+
+ align:start position:0%
+Etc it's a lot cheaper to insulate a new
+ 
+
+ align:start position:0%
+Etc it's a lot cheaper to insulate a new
+house when it's being built to go back
+
+ align:start position:0%
+house when it's being built to go back
+ 
+
+ align:start position:0%
+house when it's being built to go back
+and and retrofit an old house it's a lot
+
+ align:start position:0%
+and and retrofit an old house it's a lot
+ 
+
+ align:start position:0%
+and and retrofit an old house it's a lot
+cheaper to make a new power plant
+
+ align:start position:0%
+cheaper to make a new power plant
+ 
+
+ align:start position:0%
+cheaper to make a new power plant
+efficient than to repower an old Power
+
+ align:start position:0%
+efficient than to repower an old Power
+ 
+
+ align:start position:0%
+efficient than to repower an old Power
+Plant so if the new if the poorer
+
+ align:start position:0%
+Plant so if the new if the poorer
+ 
+
+ align:start position:0%
+Plant so if the new if the poorer
+countries of the world are growing more
+
+ align:start position:0%
+countries of the world are growing more
+ 
+
+ align:start position:0%
+countries of the world are growing more
+rapidly they have a lot more relatively
+
+ align:start position:0%
+rapidly they have a lot more relatively
+ 
+
+ align:start position:0%
+rapidly they have a lot more relatively
+inexpensive investment
+
+ align:start position:0%
+inexpensive investment
+ 
+
+ align:start position:0%
+inexpensive investment
+opportunities they also may not have
+
+ align:start position:0%
+opportunities they also may not have
+ 
+
+ align:start position:0%
+opportunities they also may not have
+built Los Angeles yet so they're in a
+
+ align:start position:0%
+built Los Angeles yet so they're in a
+ 
+
+ align:start position:0%
+built Los Angeles yet so they're in a
+position to decide more easily on a
+
+ align:start position:0%
+position to decide more easily on a
+ 
+
+ align:start position:0%
+position to decide more easily on a
+different Urban
+
+ align:start position:0%
+different Urban
+ 
+
+ align:start position:0%
+different Urban
+structure less less spread out less
+
+ align:start position:0%
+structure less less spread out less
+ 
+
+ align:start position:0%
+structure less less spread out less
+reliant on cars so there are a set of
+
+ align:start position:0%
+reliant on cars so there are a set of
+ 
+
+ align:start position:0%
+reliant on cars so there are a set of
+choices that are being
+
+ align:start position:0%
+choices that are being
+ 
+
+ align:start position:0%
+choices that are being
+made there also if you look at retrofit
+
+ align:start position:0%
+made there also if you look at retrofit
+ 
+
+ align:start position:0%
+made there also if you look at retrofit
+options there's a lot of energy use
+
+ align:start position:0%
+options there's a lot of energy use
+ 
+
+ align:start position:0%
+options there's a lot of energy use
+now that is polluting as well as
+
+ align:start position:0%
+now that is polluting as well as
+ 
+
+ align:start position:0%
+now that is polluting as well as
+inefficient so modernizing some of the
+
+ align:start position:0%
+inefficient so modernizing some of the
+ 
+
+ align:start position:0%
+inefficient so modernizing some of the
+plants now uh will create a double
+
+ align:start position:0%
+plants now uh will create a double
+ 
+
+ align:start position:0%
+plants now uh will create a double
+benefit I you can do something besides
+
+ align:start position:0%
+benefit I you can do something besides
+ 
+
+ align:start position:0%
+benefit I you can do something besides
+little kerosene generators for instance
+
+ align:start position:0%
+little kerosene generators for instance
+ 
+
+ align:start position:0%
+little kerosene generators for instance
+for electricity in a lot of places you
+
+ align:start position:0%
+for electricity in a lot of places you
+ 
+
+ align:start position:0%
+for electricity in a lot of places you
+will not only save energy but you clean
+
+ align:start position:0%
+will not only save energy but you clean
+ 
+
+ align:start position:0%
+will not only save energy but you clean
+the air so there's a benefit to be had
+
+ align:start position:0%
+the air so there's a benefit to be had
+ 
+
+ align:start position:0%
+the air so there's a benefit to be had
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+bringing these countries
+
+ align:start position:0%
+bringing these countries
+ 
+
+ align:start position:0%
+bringing these countries
+closer uh to the
+
+ align:start position:0%
+closer uh to the
+ 
+
+ align:start position:0%
+closer uh to the
+frontier with what they already
+
+ align:start position:0%
+frontier with what they already
+ 
+
+ align:start position:0%
+frontier with what they already
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is a hard problem for the
+
+ align:start position:0%
+so this is a hard problem for the
+ 
+
+ align:start position:0%
+so this is a hard problem for the
+zar
+
+ align:start position:0%
+zar
+ 
+
+ align:start position:0%
+zar
+the Zar has to figure out how she's
+
+ align:start position:0%
+the Zar has to figure out how she's
+ 
+
+ align:start position:0%
+the Zar has to figure out how she's
+going to or the Zar Arena how she's
+
+ align:start position:0%
+going to or the Zar Arena how she's
+ 
+
+ align:start position:0%
+going to or the Zar Arena how she's
+going to deal with the distant future
+
+ align:start position:0%
+going to deal with the distant future
+ 
+
+ align:start position:0%
+going to deal with the distant future
+and great great
+
+ align:start position:0%
+and great great
+ 
+
+ align:start position:0%
+and great great
+grandchildren
+
+ align:start position:0%
+grandchildren
+ 
+
+ align:start position:0%
+grandchildren
+how to get to deal with uncertainty
+
+ align:start position:0%
+how to get to deal with uncertainty
+ 
+
+ align:start position:0%
+how to get to deal with uncertainty
+today and to learn to deal with it
+
+ align:start position:0%
+today and to learn to deal with it
+ 
+
+ align:start position:0%
+today and to learn to deal with it
+tomorrow as Learning
+
+ align:start position:0%
+tomorrow as Learning
+ 
+
+ align:start position:0%
+tomorrow as Learning
+Happens thear is going to have to figure
+
+ align:start position:0%
+Happens thear is going to have to figure
+ 
+
+ align:start position:0%
+Happens thear is going to have to figure
+out what if anything could be done about
+
+ align:start position:0%
+out what if anything could be done about
+ 
+
+ align:start position:0%
+out what if anything could be done about
+Technologies how to get people en a to
+
+ align:start position:0%
+Technologies how to get people en a to
+ 
+
+ align:start position:0%
+Technologies how to get people en a to
+adapt
+
+ align:start position:0%
+adapt
+ 
+
+ align:start position:0%
+adapt
+if the Zar focuses on fossil
+
+ align:start position:0%
+if the Zar focuses on fossil
+ 
+
+ align:start position:0%
+if the Zar focuses on fossil
+fuel the Zar has to make big changes and
+
+ align:start position:0%
+fuel the Zar has to make big changes and
+ 
+
+ align:start position:0%
+fuel the Zar has to make big changes and
+the Zar has to involve the
+
+ align:start position:0%
+the Zar has to involve the
+ 
+
+ align:start position:0%
+the Zar has to involve the
+poor the Zar has to involve the poor it
+
+ align:start position:0%
+poor the Zar has to involve the poor it
+ 
+
+ align:start position:0%
+poor the Zar has to involve the poor it
+can't be done by Rich countries if rich
+
+ align:start position:0%
+can't be done by Rich countries if rich
+ 
+
+ align:start position:0%
+can't be done by Rich countries if rich
+countries alone try to do it you know if
+
+ align:start position:0%
+countries alone try to do it you know if
+ 
+
+ align:start position:0%
+countries alone try to do it you know if
+you go back to something like this you
+
+ align:start position:0%
+you go back to something like this you
+ 
+
+ align:start position:0%
+you go back to something like this you
+want to slow growth in you want to
+
+ align:start position:0%
+want to slow growth in you want to
+ 
+
+ align:start position:0%
+want to slow growth in you want to
+eliminate growth in emissions by only
+
+ align:start position:0%
+eliminate growth in emissions by only
+ 
+
+ align:start position:0%
+eliminate growth in emissions by only
+the rich countries they'd have to go to
+
+ align:start position:0%
+the rich countries they'd have to go to
+ 
+
+ align:start position:0%
+the rich countries they'd have to go to
+zero to have a big impact it ain't going
+
+ align:start position:0%
+zero to have a big impact it ain't going
+ 
+
+ align:start position:0%
+zero to have a big impact it ain't going
+to happen so the poor need to be
+
+ align:start position:0%
+to happen so the poor need to be
+ 
+
+ align:start position:0%
+to happen so the poor need to be
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+involved and the first question that
+
+ align:start position:0%
+involved and the first question that
+ 
+
+ align:start position:0%
+involved and the first question that
+comes
+
+ align:start position:0%
+comes
+ 
+
+ align:start position:0%
+comes
+up already came up is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fair this is a missions per
+
+ align:start position:0%
+fair this is a missions per
+ 
+
+ align:start position:0%
+fair this is a missions per
+capita this is uh Annex 2 North America
+
+ align:start position:0%
+capita this is uh Annex 2 North America
+ 
+
+ align:start position:0%
+capita this is uh Annex 2 North America
+is US and Canada this is Australia New
+
+ align:start position:0%
+is US and Canada this is Australia New
+ 
+
+ align:start position:0%
+is US and Canada this is Australia New
+Zealand
+
+ align:start position:0%
+Zealand
+ 
+
+ align:start position:0%
+Zealand
+Japan uh EIT or economies in transition
+
+ align:start position:0%
+Japan uh EIT or economies in transition
+ 
+
+ align:start position:0%
+Japan uh EIT or economies in transition
+that's uh um Russia and Eastern Europe
+
+ align:start position:0%
+that's uh um Russia and Eastern Europe
+ 
+
+ align:start position:0%
+that's uh um Russia and Eastern Europe
+there's the Middle East Annex two Europe
+
+ align:start position:0%
+there's the Middle East Annex two Europe
+ 
+
+ align:start position:0%
+there's the Middle East Annex two Europe
+or Rich European countries China other
+
+ align:start position:0%
+or Rich European countries China other
+ 
+
+ align:start position:0%
+or Rich European countries China other
+countries Latin America the rest of Asia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Africa is it fair to involve
+
+ align:start position:0%
+Africa is it fair to involve
+ 
+
+ align:start position:0%
+Africa is it fair to involve
+them my golly that's you're going to go
+
+ align:start position:0%
+them my golly that's you're going to go
+ 
+
+ align:start position:0%
+them my golly that's you're going to go
+to you're going to go to Cambodia you
+
+ align:start position:0%
+to you're going to go to Cambodia you
+ 
+
+ align:start position:0%
+to you're going to go to Cambodia you
+remember I I put up the Cambodia energy
+
+ align:start position:0%
+remember I I put up the Cambodia energy
+ 
+
+ align:start position:0%
+remember I I put up the Cambodia energy
+diagram some while ago Cambodia Imports
+
+ align:start position:0%
+diagram some while ago Cambodia Imports
+ 
+
+ align:start position:0%
+diagram some while ago Cambodia Imports
+some oil and burns a lot of
+
+ align:start position:0%
+some oil and burns a lot of
+ 
+
+ align:start position:0%
+some oil and burns a lot of
+wood that's the Energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+System you know and they mostly ride
+
+ align:start position:0%
+System you know and they mostly ride
+ 
+
+ align:start position:0%
+System you know and they mostly ride
+motorbikes and you can't get them much
+
+ align:start position:0%
+motorbikes and you can't get them much
+ 
+
+ align:start position:0%
+motorbikes and you can't get them much
+smaller um than the ones they have so to
+
+ align:start position:0%
+smaller um than the ones they have so to
+ 
+
+ align:start position:0%
+smaller um than the ones they have so to
+ha this is an enormous
+
+ align:start position:0%
+ha this is an enormous
+ 
+
+ align:start position:0%
+ha this is an enormous
+disparity right North America is running
+
+ align:start position:0%
+disparity right North America is running
+ 
+
+ align:start position:0%
+disparity right North America is running
+I don't know 16 metric tons per capita
+
+ align:start position:0%
+I don't know 16 metric tons per capita
+ 
+
+ align:start position:0%
+I don't know 16 metric tons per capita
+Africa is running less than one big
+
+ align:start position:0%
+Africa is running less than one big
+ 
+
+ align:start position:0%
+Africa is running less than one big
+disparity huge disparity very different
+
+ align:start position:0%
+disparity huge disparity very different
+ 
+
+ align:start position:0%
+disparity huge disparity very different
+very different system so if you're going
+
+ align:start position:0%
+very different system so if you're going
+ 
+
+ align:start position:0%
+very different system so if you're going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+change you're going to look people in
+
+ align:start position:0%
+change you're going to look people in
+ 
+
+ align:start position:0%
+change you're going to look people in
+the face and those of you who want to be
+
+ align:start position:0%
+the face and those of you who want to be
+ 
+
+ align:start position:0%
+the face and those of you who want to be
+developing countries or developed
+
+ align:start position:0%
+developing countries or developed
+ 
+
+ align:start position:0%
+developing countries or developed
+countries on Wednesday and Friday you're
+
+ align:start position:0%
+countries on Wednesday and Friday you're
+ 
+
+ align:start position:0%
+countries on Wednesday and Friday you're
+going to look your poor brethren in the
+
+ align:start position:0%
+going to look your poor brethren in the
+ 
+
+ align:start position:0%
+going to look your poor brethren in the
+face and
+
+ align:start position:0%
+face and
+ 
+
+ align:start position:0%
+face and
+say you Latin America rest of Asia
+
+ align:start position:0%
+say you Latin America rest of Asia
+ 
+
+ align:start position:0%
+say you Latin America rest of Asia
+Africa boy you got to take steps we'll
+
+ align:start position:0%
+Africa boy you got to take steps we'll
+ 
+
+ align:start position:0%
+Africa boy you got to take steps we'll
+do what we
+
+ align:start position:0%
+do what we
+ 
+
+ align:start position:0%
+do what we
+can but you've got to take steps see we
+
+ align:start position:0%
+can but you've got to take steps see we
+ 
+
+ align:start position:0%
+can but you've got to take steps see we
+we have path dependence up here we're
+
+ align:start position:0%
+we have path dependence up here we're
+ 
+
+ align:start position:0%
+we have path dependence up here we're
+we're kind of stuck on a path and you
+
+ align:start position:0%
+we're kind of stuck on a path and you
+ 
+
+ align:start position:0%
+we're kind of stuck on a path and you
+know what are you going going to do
+
+ align:start position:0%
+know what are you going going to do
+ 
+
+ align:start position:0%
+know what are you going going to do
+um so fairness is also in you know one
+
+ align:start position:0%
+um so fairness is also in you know one
+ 
+
+ align:start position:0%
+um so fairness is also in you know one
+response might be yeah well let's look
+
+ align:start position:0%
+response might be yeah well let's look
+ 
+
+ align:start position:0%
+response might be yeah well let's look
+at let's look not per capita but you
+
+ align:start position:0%
+at let's look not per capita but you
+ 
+
+ align:start position:0%
+at let's look not per capita but you
+know you're you're low cause you're
+
+ align:start position:0%
+know you're you're low cause you're
+ 
+
+ align:start position:0%
+know you're you're low cause you're
+really really poor and we're really
+
+ align:start position:0%
+really really poor and we're really
+ 
+
+ align:start position:0%
+really really poor and we're really
+really sad about it but per dollar of
+
+ align:start position:0%
+really sad about it but per dollar of
+ 
+
+ align:start position:0%
+really sad about it but per dollar of
+GDP the differences are less
+
+ align:start position:0%
+GDP the differences are less
+ 
+
+ align:start position:0%
+GDP the differences are less
+Stark the winners now are the Middle
+
+ align:start position:0%
+Stark the winners now are the Middle
+ 
+
+ align:start position:0%
+Stark the winners now are the Middle
+East Soviet Union in Eastern Europe
+
+ align:start position:0%
+East Soviet Union in Eastern Europe
+ 
+
+ align:start position:0%
+East Soviet Union in Eastern Europe
+because those were really manufacturing
+
+ align:start position:0%
+because those were really manufacturing
+ 
+
+ align:start position:0%
+because those were really manufacturing
+intensive Technologies they ran on cheap
+
+ align:start position:0%
+intensive Technologies they ran on cheap
+ 
+
+ align:start position:0%
+intensive Technologies they ran on cheap
+Russian
+
+ align:start position:0%
+Russian
+ 
+
+ align:start position:0%
+Russian
+oil which was made available at low cost
+
+ align:start position:0%
+oil which was made available at low cost
+ 
+
+ align:start position:0%
+oil which was made available at low cost
+and Russian natural gas they still have
+
+ align:start position:0%
+and Russian natural gas they still have
+ 
+
+ align:start position:0%
+and Russian natural gas they still have
+an enormous amount of inefficient
+
+ align:start position:0%
+an enormous amount of inefficient
+ 
+
+ align:start position:0%
+an enormous amount of inefficient
+Capital stock
+
+ align:start position:0%
+Capital stock
+ 
+
+ align:start position:0%
+Capital stock
+running um and China which has a
+
+ align:start position:0%
+running um and China which has a
+ 
+
+ align:start position:0%
+running um and China which has a
+manufacturing intensive economy and uses
+
+ align:start position:0%
+manufacturing intensive economy and uses
+ 
+
+ align:start position:0%
+manufacturing intensive economy and uses
+a lot of
+
+ align:start position:0%
+a lot of
+ 
+
+ align:start position:0%
+a lot of
+coal so you know per unit of GDP
+
+ align:start position:0%
+coal so you know per unit of GDP
+ 
+
+ align:start position:0%
+coal so you know per unit of GDP
+Africa's right in there with everybody
+
+ align:start position:0%
+Africa's right in there with everybody
+ 
+
+ align:start position:0%
+Africa's right in there with everybody
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+they just happen to have not much GDP
+
+ align:start position:0%
+they just happen to have not much GDP
+ 
+
+ align:start position:0%
+they just happen to have not much GDP
+per capita so you say well you know per
+
+ align:start position:0%
+per capita so you say well you know per
+ 
+
+ align:start position:0%
+per capita so you say well you know per
+dollar of GDP we can make Cuts you can
+
+ align:start position:0%
+dollar of GDP we can make Cuts you can
+ 
+
+ align:start position:0%
+dollar of GDP we can make Cuts you can
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+cuts and one response might be yeah but
+
+ align:start position:0%
+cuts and one response might be yeah but
+ 
+
+ align:start position:0%
+cuts and one response might be yeah but
+we'd like our GDP to grow thank you very
+
+ align:start position:0%
+we'd like our GDP to grow thank you very
+ 
+
+ align:start position:0%
+we'd like our GDP to grow thank you very
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+so this is another nice example this is
+
+ align:start position:0%
+so this is another nice example this is
+ 
+
+ align:start position:0%
+so this is another nice example this is
+if you do the cumulative you do what's
+
+ align:start position:0%
+if you do the cumulative you do what's
+ 
+
+ align:start position:0%
+if you do the cumulative you do what's
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+air um which was the point professor
+
+ align:start position:0%
+air um which was the point professor
+ 
+
+ align:start position:0%
+air um which was the point professor
+Solomon was making if you do what's in
+
+ align:start position:0%
+Solomon was making if you do what's in
+ 
+
+ align:start position:0%
+Solomon was making if you do what's in
+the air this is just CO2 but it's co it
+
+ align:start position:0%
+the air this is just CO2 but it's co it
+ 
+
+ align:start position:0%
+the air this is just CO2 but it's co it
+shows cumulatively what's in the air
+
+ align:start position:0%
+shows cumulatively what's in the air
+ 
+
+ align:start position:0%
+shows cumulatively what's in the air
+now based on a model of the carbon cycle
+
+ align:start position:0%
+now based on a model of the carbon cycle
+ 
+
+ align:start position:0%
+now based on a model of the carbon cycle
+what's in the air now and where it came
+
+ align:start position:0%
+what's in the air now and where it came
+ 
+
+ align:start position:0%
+what's in the air now and where it came
+from Blue is the rich countries this
+
+ align:start position:0%
+from Blue is the rich countries this
+ 
+
+ align:start position:0%
+from Blue is the rich countries this
+this is kind of middle- inome developing
+
+ align:start position:0%
+this is kind of middle- inome developing
+ 
+
+ align:start position:0%
+this is kind of middle- inome developing
+countries and that's the very
+
+ align:start position:0%
+countries and that's the very
+ 
+
+ align:start position:0%
+countries and that's the very
+poor so in terms of who caused the
+
+ align:start position:0%
+poor so in terms of who caused the
+ 
+
+ align:start position:0%
+poor so in terms of who caused the
+problem it's not who who put the stuff
+
+ align:start position:0%
+problem it's not who who put the stuff
+ 
+
+ align:start position:0%
+problem it's not who who put the stuff
+in the air it's not China who's putting
+
+ align:start position:0%
+in the air it's not China who's putting
+ 
+
+ align:start position:0%
+in the air it's not China who's putting
+it in the air and who's growing yeah but
+
+ align:start position:0%
+it in the air and who's growing yeah but
+ 
+
+ align:start position:0%
+it in the air and who's growing yeah but
+who put it
+
+ align:start position:0%
+who put it
+ 
+
+ align:start position:0%
+who put it
+there it's
+
+ align:start position:0%
+there it's
+ 
+
+ align:start position:0%
+there it's
+us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay A little bit of of sort of how the
+
+ align:start position:0%
+okay A little bit of of sort of how the
+ 
+
+ align:start position:0%
+okay A little bit of of sort of how the
+international conversation on all of
+
+ align:start position:0%
+international conversation on all of
+ 
+
+ align:start position:0%
+international conversation on all of
+this has gone just by way of background
+
+ align:start position:0%
+this has gone just by way of background
+ 
+
+ align:start position:0%
+this has gone just by way of background
+and then we'll see what questions you
+
+ align:start position:0%
+and then we'll see what questions you
+ 
+
+ align:start position:0%
+and then we'll see what questions you
+have because I've gone through this much
+
+ align:start position:0%
+have because I've gone through this much
+ 
+
+ align:start position:0%
+have because I've gone through this much
+too rapidly um as I mentioned the
+
+ align:start position:0%
+too rapidly um as I mentioned the
+ 
+
+ align:start position:0%
+too rapidly um as I mentioned the
+framework convention on climate change
+
+ align:start position:0%
+framework convention on climate change
+ 
+
+ align:start position:0%
+framework convention on climate change
+was was um drafted in 1992 ratified by
+
+ align:start position:0%
+was was um drafted in 1992 ratified by
+ 
+
+ align:start position:0%
+was was um drafted in 1992 ratified by
+everybody there have been 17 conferences
+
+ align:start position:0%
+everybody there have been 17 conferences
+ 
+
+ align:start position:0%
+everybody there have been 17 conferences
+of the parties referred to as
+
+ align:start position:0%
+of the parties referred to as
+ 
+
+ align:start position:0%
+of the parties referred to as
+cops um large Gatherings of diplomats
+
+ align:start position:0%
+cops um large Gatherings of diplomats
+ 
+
+ align:start position:0%
+cops um large Gatherings of diplomats
+non-governmental organizations
+
+ align:start position:0%
+non-governmental organizations
+ 
+
+ align:start position:0%
+non-governmental organizations
+demonstrators hangers on um cocktail
+
+ align:start position:0%
+demonstrators hangers on um cocktail
+ 
+
+ align:start position:0%
+demonstrators hangers on um cocktail
+parties receptions
+
+ align:start position:0%
+parties receptions
+ 
+
+ align:start position:0%
+parties receptions
+there have been 17 of
+
+ align:start position:0%
+there have been 17 of
+ 
+
+ align:start position:0%
+there have been 17 of
+them you will be the
+
+ align:start position:0%
+them you will be the
+ 
+
+ align:start position:0%
+them you will be the
+18th um the third produced the Kyoto
+
+ align:start position:0%
+18th um the third produced the Kyoto
+ 
+
+ align:start position:0%
+18th um the third produced the Kyoto
+Protocol the framework convention
+
+ align:start position:0%
+Protocol the framework convention
+ 
+
+ align:start position:0%
+Protocol the framework convention
+divided the world into Annex one
+
+ align:start position:0%
+divided the world into Annex one
+ 
+
+ align:start position:0%
+divided the world into Annex one
+countries and everybody else Annex 2
+
+ align:start position:0%
+countries and everybody else Annex 2
+ 
+
+ align:start position:0%
+countries and everybody else Annex 2
+which was on some of those earlier
+
+ align:start position:0%
+which was on some of those earlier
+ 
+
+ align:start position:0%
+which was on some of those earlier
+graphs is a a subset of anex one it's
+
+ align:start position:0%
+graphs is a a subset of anex one it's
+ 
+
+ align:start position:0%
+graphs is a a subset of anex one it's
+the Richer Annex one
+
+ align:start position:0%
+the Richer Annex one
+ 
+
+ align:start position:0%
+the Richer Annex one
+countries the Kyoto Protocol
+
+ align:start position:0%
+countries the Kyoto Protocol
+ 
+
+ align:start position:0%
+countries the Kyoto Protocol
+called for Annex one countries
+
+ align:start position:0%
+called for Annex one countries
+ 
+
+ align:start position:0%
+called for Annex one countries
+only and by the way it's not all rich
+
+ align:start position:0%
+only and by the way it's not all rich
+ 
+
+ align:start position:0%
+only and by the way it's not all rich
+countries South Korea is not Annex one
+
+ align:start position:0%
+countries South Korea is not Annex one
+ 
+
+ align:start position:0%
+countries South Korea is not Annex one
+um Singapore is not Annex one uh Saudi
+
+ align:start position:0%
+um Singapore is not Annex one uh Saudi
+ 
+
+ align:start position:0%
+um Singapore is not Annex one uh Saudi
+Arabia is not Annex one and so forth so
+
+ align:start position:0%
+Arabia is not Annex one and so forth so
+ 
+
+ align:start position:0%
+Arabia is not Annex one and so forth so
+it's a industrialized
+
+ align:start position:0%
+it's a industrialized
+ 
+
+ align:start position:0%
+it's a industrialized
+countries o oecd roughly
+
+ align:start position:0%
+countries o oecd roughly
+ 
+
+ align:start position:0%
+countries o oecd roughly
+oecd Annex one
+
+ align:start position:0%
+oecd Annex one
+ 
+
+ align:start position:0%
+oecd Annex one
+countries uh were to make reductions
+
+ align:start position:0%
+countries uh were to make reductions
+ 
+
+ align:start position:0%
+countries uh were to make reductions
+there were negotiated reductions
+
+ align:start position:0%
+there were negotiated reductions
+ 
+
+ align:start position:0%
+there were negotiated reductions
+the rest of the world which I just said
+
+ align:start position:0%
+the rest of the world which I just said
+ 
+
+ align:start position:0%
+the rest of the world which I just said
+Has to participate if something's going
+
+ align:start position:0%
+Has to participate if something's going
+ 
+
+ align:start position:0%
+Has to participate if something's going
+to happen refus to even promise making
+
+ align:start position:0%
+to happen refus to even promise making
+ 
+
+ align:start position:0%
+to happen refus to even promise making
+promises in the
+
+ align:start position:0%
+promises in the
+ 
+
+ align:start position:0%
+promises in the
+future so there wasn't even a commitment
+
+ align:start position:0%
+future so there wasn't even a commitment
+ 
+
+ align:start position:0%
+future so there wasn't even a commitment
+to make a commitment they would not
+
+ align:start position:0%
+to make a commitment they would not
+ 
+
+ align:start position:0%
+to make a commitment they would not
+commit to
+
+ align:start position:0%
+commit to
+ 
+
+ align:start position:0%
+commit to
+commit uh and if you think about that
+
+ align:start position:0%
+commit uh and if you think about that
+ 
+
+ align:start position:0%
+commit uh and if you think about that
+that's really
+
+ align:start position:0%
+that's really
+ 
+
+ align:start position:0%
+that's really
+resisting um we'll be happy to come to
+
+ align:start position:0%
+resisting um we'll be happy to come to
+ 
+
+ align:start position:0%
+resisting um we'll be happy to come to
+these meetings but we do not now promise
+
+ align:start position:0%
+these meetings but we do not now promise
+ 
+
+ align:start position:0%
+these meetings but we do not now promise
+ever to commit to do anything unless of
+
+ align:start position:0%
+ever to commit to do anything unless of
+ 
+
+ align:start position:0%
+ever to commit to do anything unless of
+course it's paid for so the Kyoto
+
+ align:start position:0%
+course it's paid for so the Kyoto
+ 
+
+ align:start position:0%
+course it's paid for so the Kyoto
+Protocol called for anx1 countries to
+
+ align:start position:0%
+Protocol called for anx1 countries to
+ 
+
+ align:start position:0%
+Protocol called for anx1 countries to
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+reductions it was
+
+ align:start position:0%
+reductions it was
+ 
+
+ align:start position:0%
+reductions it was
+ratified by the members of the East
+
+ align:start position:0%
+ratified by the members of the East
+ 
+
+ align:start position:0%
+ratified by the members of the East
+European Union
+
+ align:start position:0%
+European Union
+ 
+
+ align:start position:0%
+European Union
+Japan Australia Canada uh lots of other
+
+ align:start position:0%
+Japan Australia Canada uh lots of other
+ 
+
+ align:start position:0%
+Japan Australia Canada uh lots of other
+folks uh we did
+
+ align:start position:0%
+folks uh we did
+ 
+
+ align:start position:0%
+folks uh we did
+not the history of that is roughly that
+
+ align:start position:0%
+not the history of that is roughly that
+ 
+
+ align:start position:0%
+not the history of that is roughly that
+uh President Clinton in the runup to
+
+ align:start position:0%
+uh President Clinton in the runup to
+ 
+
+ align:start position:0%
+uh President Clinton in the runup to
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+negotiations had a lot of there was a
+
+ align:start position:0%
+negotiations had a lot of there was a
+ 
+
+ align:start position:0%
+negotiations had a lot of there was a
+lot of noise in the air about how this
+
+ align:start position:0%
+lot of noise in the air about how this
+ 
+
+ align:start position:0%
+lot of noise in the air about how this
+will be free it'll be a great benefit to
+
+ align:start position:0%
+will be free it'll be a great benefit to
+ 
+
+ align:start position:0%
+will be free it'll be a great benefit to
+the US economy this will be fabulous we
+
+ align:start position:0%
+the US economy this will be fabulous we
+ 
+
+ align:start position:0%
+the US economy this will be fabulous we
+can reduce emissions it'll be no cost
+
+ align:start position:0%
+can reduce emissions it'll be no cost
+ 
+
+ align:start position:0%
+can reduce emissions it'll be no cost
+every Economist not working for the
+
+ align:start position:0%
+every Economist not working for the
+ 
+
+ align:start position:0%
+every Economist not working for the
+administration stood up and said well
+
+ align:start position:0%
+administration stood up and said well
+ 
+
+ align:start position:0%
+administration stood up and said well
+it's not going to cost that much money
+
+ align:start position:0%
+it's not going to cost that much money
+ 
+
+ align:start position:0%
+it's not going to cost that much money
+but it will
+
+ align:start position:0%
+but it will
+ 
+
+ align:start position:0%
+but it will
+cost Congress passed a resolution 95 to
+
+ align:start position:0%
+cost Congress passed a resolution 95 to
+ 
+
+ align:start position:0%
+cost Congress passed a resolution 95 to
+nothing saying we won't ratify anything
+
+ align:start position:0%
+nothing saying we won't ratify anything
+ 
+
+ align:start position:0%
+nothing saying we won't ratify anything
+that basically slightly different
+
+ align:start position:0%
+that basically slightly different
+ 
+
+ align:start position:0%
+that basically slightly different
+language that doesn't require the
+
+ align:start position:0%
+language that doesn't require the
+ 
+
+ align:start position:0%
+language that doesn't require the
+Chinese to do something now 95 to
+
+ align:start position:0%
+Chinese to do something now 95 to
+ 
+
+ align:start position:0%
+Chinese to do something now 95 to
+nothing
+
+ align:start position:0%
+nothing
+ 
+
+ align:start position:0%
+nothing
+so Al Gore went to Kyoto the US said
+
+ align:start position:0%
+so Al Gore went to Kyoto the US said
+ 
+
+ align:start position:0%
+so Al Gore went to Kyoto the US said
+this is fabulous we made an agreement
+
+ align:start position:0%
+this is fabulous we made an agreement
+ 
+
+ align:start position:0%
+this is fabulous we made an agreement
+the treaty was not sent to the senate
+
+ align:start position:0%
+the treaty was not sent to the senate
+ 
+
+ align:start position:0%
+the treaty was not sent to the senate
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+ratification uh and President George W
+
+ align:start position:0%
+ratification uh and President George W
+ 
+
+ align:start position:0%
+ratification uh and President George W
+bush uh formally declared the horse dead
+
+ align:start position:0%
+bush uh formally declared the horse dead
+ 
+
+ align:start position:0%
+bush uh formally declared the horse dead
+in 2001 when he said we're not going to
+
+ align:start position:0%
+in 2001 when he said we're not going to
+ 
+
+ align:start position:0%
+in 2001 when he said we're not going to
+play so the EU has established and again
+
+ align:start position:0%
+play so the EU has established and again
+ 
+
+ align:start position:0%
+play so the EU has established and again
+you can read The Parson at all article
+
+ align:start position:0%
+you can read The Parson at all article
+ 
+
+ align:start position:0%
+you can read The Parson at all article
+if you're interested in it established
+
+ align:start position:0%
+if you're interested in it established
+ 
+
+ align:start position:0%
+if you're interested in it established
+an emissions trading scheme they did
+
+ align:start position:0%
+an emissions trading scheme they did
+ 
+
+ align:start position:0%
+an emissions trading scheme they did
+these certificates Dro from the air that
+
+ align:start position:0%
+these certificates Dro from the air that
+ 
+
+ align:start position:0%
+these certificates Dro from the air that
+let you emit carbon dioxide I mean it's
+
+ align:start position:0%
+let you emit carbon dioxide I mean it's
+ 
+
+ align:start position:0%
+let you emit carbon dioxide I mean it's
+not a perfect system you'll see some
+
+ align:start position:0%
+not a perfect system you'll see some
+ 
+
+ align:start position:0%
+not a perfect system you'll see some
+glitches um but it may work and they may
+
+ align:start position:0%
+glitches um but it may work and they may
+ 
+
+ align:start position:0%
+glitches um but it may work and they may
+actually meet their
+
+ align:start position:0%
+actually meet their
+ 
+
+ align:start position:0%
+actually meet their
+commitments it doesn't appear anybody
+
+ align:start position:0%
+commitments it doesn't appear anybody
+ 
+
+ align:start position:0%
+commitments it doesn't appear anybody
+else will even those that ratified the
+
+ align:start position:0%
+else will even those that ratified the
+ 
+
+ align:start position:0%
+else will even those that ratified the
+treaty Australia is walking away I think
+
+ align:start position:0%
+treaty Australia is walking away I think
+ 
+
+ align:start position:0%
+treaty Australia is walking away I think
+Canada has walked away Japan Japan May
+
+ align:start position:0%
+Canada has walked away Japan Japan May
+ 
+
+ align:start position:0%
+Canada has walked away Japan Japan May
+because of of the incredible disaster
+
+ align:start position:0%
+because of of the incredible disaster
+ 
+
+ align:start position:0%
+because of of the incredible disaster
+they've gone through but would not have
+
+ align:start position:0%
+they've gone through but would not have
+ 
+
+ align:start position:0%
+they've gone through but would not have
+absent it um and may not since they now
+
+ align:start position:0%
+absent it um and may not since they now
+ 
+
+ align:start position:0%
+absent it um and may not since they now
+say that they will replace the nuclear
+
+ align:start position:0%
+say that they will replace the nuclear
+ 
+
+ align:start position:0%
+say that they will replace the nuclear
+plants with coal so we'll see but at any
+
+ align:start position:0%
+plants with coal so we'll see but at any
+ 
+
+ align:start position:0%
+plants with coal so we'll see but at any
+rate nothing will
+
+ align:start position:0%
+rate nothing will
+ 
+
+ align:start position:0%
+rate nothing will
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+the subsequent agreements H there was
+
+ align:start position:0%
+the subsequent agreements H there was
+ 
+
+ align:start position:0%
+the subsequent agreements H there was
+Copenhagen there was a lot of fuss
+
+ align:start position:0%
+Copenhagen there was a lot of fuss
+ 
+
+ align:start position:0%
+Copenhagen there was a lot of fuss
+around Copenhagen you'll see the runup
+
+ align:start position:0%
+around Copenhagen you'll see the runup
+ 
+
+ align:start position:0%
+around Copenhagen you'll see the runup
+discussed in The Economist reading you
+
+ align:start position:0%
+discussed in The Economist reading you
+ 
+
+ align:start position:0%
+discussed in The Economist reading you
+will see the most recent Doha discussed
+
+ align:start position:0%
+will see the most recent Doha discussed
+ 
+
+ align:start position:0%
+will see the most recent Doha discussed
+in the second very short Economist
+
+ align:start position:0%
+in the second very short Economist
+ 
+
+ align:start position:0%
+in the second very short Economist
+reading happened in
+
+ align:start position:0%
+reading happened in
+ 
+
+ align:start position:0%
+reading happened in
+December um there are no Global there's
+
+ align:start position:0%
+December um there are no Global there's
+ 
+
+ align:start position:0%
+December um there are no Global there's
+no Global agreement in
+
+ align:start position:0%
+no Global agreement in
+ 
+
+ align:start position:0%
+no Global agreement in
+place what happened in Doha and I uh
+
+ align:start position:0%
+place what happened in Doha and I uh
+ 
+
+ align:start position:0%
+place what happened in Doha and I uh
+it's on it's on my slides for for
+
+ align:start position:0%
+it's on it's on my slides for for
+ 
+
+ align:start position:0%
+it's on it's on my slides for for
+Wednesday but I'll tell you now what
+
+ align:start position:0%
+Wednesday but I'll tell you now what
+ 
+
+ align:start position:0%
+Wednesday but I'll tell you now what
+happened in
+
+ align:start position:0%
+happened in
+ 
+
+ align:start position:0%
+happened in
+Doha was basically the Europeans agreed
+
+ align:start position:0%
+Doha was basically the Europeans agreed
+ 
+
+ align:start position:0%
+Doha was basically the Europeans agreed
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+continue um there was a promise of money
+
+ align:start position:0%
+continue um there was a promise of money
+ 
+
+ align:start position:0%
+continue um there was a promise of money
+to go from the rich countries to the
+
+ align:start position:0%
+to go from the rich countries to the
+ 
+
+ align:start position:0%
+to go from the rich countries to the
+poor countries a much smaller promise
+
+ align:start position:0%
+poor countries a much smaller promise
+ 
+
+ align:start position:0%
+poor countries a much smaller promise
+than you will consider Wednesday and
+
+ align:start position:0%
+than you will consider Wednesday and
+ 
+
+ align:start position:0%
+than you will consider Wednesday and
+Friday but there was a promise we'll see
+
+ align:start position:0%
+Friday but there was a promise we'll see
+ 
+
+ align:start position:0%
+Friday but there was a promise we'll see
+if it's
+
+ align:start position:0%
+if it's
+ 
+
+ align:start position:0%
+if it's
+kept um
+
+ align:start position:0%
+kept um
+ 
+
+ align:start position:0%
+kept um
+and the developing World promised to
+
+ align:start position:0%
+and the developing World promised to
+ 
+
+ align:start position:0%
+and the developing World promised to
+consider making
+
+ align:start position:0%
+consider making
+ 
+
+ align:start position:0%
+consider making
+promises that is to say the refusal to
+
+ align:start position:0%
+promises that is to say the refusal to
+ 
+
+ align:start position:0%
+promises that is to say the refusal to
+commit ever to commit is off the table
+
+ align:start position:0%
+commit ever to commit is off the table
+ 
+
+ align:start position:0%
+commit ever to commit is off the table
+they now say they will consider in
+
+ align:start position:0%
+they now say they will consider in
+ 
+
+ align:start position:0%
+they now say they will consider in
+subsequent negotiations beginning in
+
+ align:start position:0%
+subsequent negotiations beginning in
+ 
+
+ align:start position:0%
+subsequent negotiations beginning in
+2015 participating in a global
+
+ align:start position:0%
+2015 participating in a global
+ 
+
+ align:start position:0%
+2015 participating in a global
+regime of some sort not fully spelled
+
+ align:start position:0%
+regime of some sort not fully spelled
+ 
+
+ align:start position:0%
+regime of some sort not fully spelled
+out so the poor countries as I say need
+
+ align:start position:0%
+out so the poor countries as I say need
+ 
+
+ align:start position:0%
+out so the poor countries as I say need
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+participate have managed to be excluded
+
+ align:start position:0%
+participate have managed to be excluded
+ 
+
+ align:start position:0%
+participate have managed to be excluded
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far the task you will face on Wednesday
+
+ align:start position:0%
+far the task you will face on Wednesday
+ 
+
+ align:start position:0%
+far the task you will face on Wednesday
+and Friday is to is to and I hope do it
+
+ align:start position:0%
+and Friday is to is to and I hope do it
+ 
+
+ align:start position:0%
+and Friday is to is to and I hope do it
+with a straight
+
+ align:start position:0%
+with a straight
+ 
+
+ align:start position:0%
+with a straight
+face uh is to make proposals that have
+
+ align:start position:0%
+face uh is to make proposals that have
+ 
+
+ align:start position:0%
+face uh is to make proposals that have
+some hope of being accepted when you go
+
+ align:start position:0%
+some hope of being accepted when you go
+ 
+
+ align:start position:0%
+some hope of being accepted when you go
+back to your
+
+ align:start position:0%
+back to your
+ 
+
+ align:start position:0%
+back to your
+capitals uh of emissions reductions that
+
+ align:start position:0%
+capitals uh of emissions reductions that
+ 
+
+ align:start position:0%
+capitals uh of emissions reductions that
+will get the job done globally okay I've
+
+ align:start position:0%
+will get the job done globally okay I've
+ 
+
+ align:start position:0%
+will get the job done globally okay I've
+covered a lot uh and I'm going to pause
+
+ align:start position:0%
+covered a lot uh and I'm going to pause
+ 
+
+ align:start position:0%
+covered a lot uh and I'm going to pause
+here I hate to quit this early but let
+
+ align:start position:0%
+here I hate to quit this early but let
+ 
+
+ align:start position:0%
+here I hate to quit this early but let
+me see if you have questions or
+
+ align:start position:0%
+me see if you have questions or
+ 
+
+ align:start position:0%
+me see if you have questions or
+comments how do we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this have you all read the brief
+
+ align:start position:0%
+this have you all read the brief
+ 
+
+ align:start position:0%
+this have you all read the brief
+briefing materials no they're they're up
+
+ align:start position:0%
+briefing materials no they're they're up
+ 
+
+ align:start position:0%
+briefing materials no they're they're up
+for Wednesday I guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah two degrees Celsius which is what
+
+ align:start position:0%
+yeah two degrees Celsius which is what
+ 
+
+ align:start position:0%
+yeah two degrees Celsius which is what
+we're working with because that's how
+
+ align:start position:0%
+we're working with because that's how
+ 
+
+ align:start position:0%
+we're working with because that's how
+the uh uh exercise was set is really
+
+ align:start position:0%
+the uh uh exercise was set is really
+ 
+
+ align:start position:0%
+the uh uh exercise was set is really
+ambitious at this
+
+ align:start position:0%
+ambitious at this
+ 
+
+ align:start position:0%
+ambitious at this
+stage I mean it is the co it is the goal
+
+ align:start position:0%
+stage I mean it is the co it is the goal
+ 
+
+ align:start position:0%
+stage I mean it is the co it is the goal
+that was adopted in Copenhagen
+
+ align:start position:0%
+that was adopted in Copenhagen
+ 
+
+ align:start position:0%
+that was adopted in Copenhagen
+um it's a very ambitious goal at this
+
+ align:start position:0%
+um it's a very ambitious goal at this
+ 
+
+ align:start position:0%
+um it's a very ambitious goal at this
+stage it might not have been so
+
+ align:start position:0%
+stage it might not have been so
+ 
+
+ align:start position:0%
+stage it might not have been so
+ambitious 20 years ago but now you know
+
+ align:start position:0%
+ambitious 20 years ago but now you know
+ 
+
+ align:start position:0%
+ambitious 20 years ago but now you know
+more stuff in the air stuff going to
+
+ align:start position:0%
+more stuff in the air stuff going to
+ 
+
+ align:start position:0%
+more stuff in the air stuff going to
+stay a long time steeper reductions
+
+ align:start position:0%
+stay a long time steeper reductions
+ 
+
+ align:start position:0%
+stay a long time steeper reductions
+called for yeah I mean who knows what
+
+ align:start position:0%
+called for yeah I mean who knows what
+ 
+
+ align:start position:0%
+called for yeah I mean who knows what
+it's going to take but it's not going to
+
+ align:start position:0%
+it's going to take but it's not going to
+ 
+
+ align:start position:0%
+it's going to take but it's not going to
+be a walk in the park it's going to be
+
+ align:start position:0%
+be a walk in the park it's going to be
+ 
+
+ align:start position:0%
+be a walk in the park it's going to be
+serious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+money it is it is but as they say in
+
+ align:start position:0%
+money it is it is but as they say in
+ 
+
+ align:start position:0%
+money it is it is but as they say in
+Washington you've got only a hundred of
+
+ align:start position:0%
+Washington you've got only a hundred of
+ 
+
+ align:start position:0%
+Washington you've got only a hundred of
+those percents to play
+
+ align:start position:0%
+those percents to play
+ 
+
+ align:start position:0%
+those percents to play
+with so less than 1% sounds
+
+ align:start position:0%
+with so less than 1% sounds
+ 
+
+ align:start position:0%
+with so less than 1% sounds
+small until you start saying what does
+
+ align:start position:0%
+small until you start saying what does
+ 
+
+ align:start position:0%
+small until you start saying what does
+that mean we don't do 1% of the
+
+ align:start position:0%
+that mean we don't do 1% of the
+ 
+
+ align:start position:0%
+that mean we don't do 1% of the
+household budget easy but 1% of moving
+
+ align:start position:0%
+household budget easy but 1% of moving
+ 
+
+ align:start position:0%
+household budget easy but 1% of moving
+1% of world GDP from purpose a to
+
+ align:start position:0%
+1% of world GDP from purpose a to
+ 
+
+ align:start position:0%
+1% of world GDP from purpose a to
+purpose B requires governments to do
+
+ align:start position:0%
+purpose B requires governments to do
+ 
+
+ align:start position:0%
+purpose B requires governments to do
+serious things deciding to cut back 1%
+
+ align:start position:0%
+serious things deciding to cut back 1%
+ 
+
+ align:start position:0%
+serious things deciding to cut back 1%
+yourself yeah you can do that it's
+
+ align:start position:0%
+yourself yeah you can do that it's
+ 
+
+ align:start position:0%
+yourself yeah you can do that it's
+nothing but deciding that us is going to
+
+ align:start position:0%
+nothing but deciding that us is going to
+ 
+
+ align:start position:0%
+nothing but deciding that us is going to
+increase spending on something by 1% a
+
+ align:start position:0%
+increase spending on something by 1% a
+ 
+
+ align:start position:0%
+increase spending on something by 1% a
+that's a big percent of government
+
+ align:start position:0%
+that's a big percent of government
+ 
+
+ align:start position:0%
+that's a big percent of government
+bigger percentage of government
+
+ align:start position:0%
+bigger percentage of government
+ 
+
+ align:start position:0%
+bigger percentage of government
+activity and B you're going to have to
+
+ align:start position:0%
+activity and B you're going to have to
+ 
+
+ align:start position:0%
+activity and B you're going to have to
+tax spend torque regulate do significant
+
+ align:start position:0%
+tax spend torque regulate do significant
+ 
+
+ align:start position:0%
+tax spend torque regulate do significant
+things so yeah it's only 1% of GDP and
+
+ align:start position:0%
+things so yeah it's only 1% of GDP and
+ 
+
+ align:start position:0%
+things so yeah it's only 1% of GDP and
+all the models say that's sort of the
+
+ align:start position:0%
+all the models say that's sort of the
+ 
+
+ align:start position:0%
+all the models say that's sort of the
+right order of magnitude for the kinds
+
+ align:start position:0%
+right order of magnitude for the kinds
+ 
+
+ align:start position:0%
+right order of magnitude for the kinds
+of things you'll need to do one maybe
+
+ align:start position:0%
+of things you'll need to do one maybe
+ 
+
+ align:start position:0%
+of things you'll need to do one maybe
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+but it's that that sounds easier than it
+
+ align:start position:0%
+but it's that that sounds easier than it
+ 
+
+ align:start position:0%
+but it's that that sounds easier than it
+is let me just say that another yeah
+
+ align:start position:0%
+is let me just say that another yeah
+ 
+
+ align:start position:0%
+is let me just say that another yeah
+David you talking about the Kyoto
+
+ align:start position:0%
+David you talking about the Kyoto
+ 
+
+ align:start position:0%
+David you talking about the Kyoto
+Protocol and how basically the EU is the
+
+ align:start position:0%
+Protocol and how basically the EU is the
+ 
+
+ align:start position:0%
+Protocol and how basically the EU is the
+only one who even has a chance of
+
+ align:start position:0%
+only one who even has a chance of
+ 
+
+ align:start position:0%
+only one who even has a chance of
+meeting what they promised what's been
+
+ align:start position:0%
+meeting what they promised what's been
+ 
+
+ align:start position:0%
+meeting what they promised what's been
+proposed to like kind of make sure that
+
+ align:start position:0%
+proposed to like kind of make sure that
+ 
+
+ align:start position:0%
+proposed to like kind of make sure that
+people actually meet what they said so
+
+ align:start position:0%
+people actually meet what they said so
+ 
+
+ align:start position:0%
+people actually meet what they said so
+that say I'm the EU and I spent all this
+
+ align:start position:0%
+that say I'm the EU and I spent all this
+ 
+
+ align:start position:0%
+that say I'm the EU and I spent all this
+money trying to control our CO2
+
+ align:start position:0%
+money trying to control our CO2
+ 
+
+ align:start position:0%
+money trying to control our CO2
+emissions we did our part and no one
+
+ align:start position:0%
+emissions we did our part and no one
+ 
+
+ align:start position:0%
+emissions we did our part and no one
+else did and it's really not going to
+
+ align:start position:0%
+else did and it's really not going to
+ 
+
+ align:start position:0%
+else did and it's really not going to
+make a difference well there's all this
+
+ align:start position:0%
+make a difference well there's all this
+ 
+
+ align:start position:0%
+make a difference well there's all this
+money and no one else did there's no
+
+ align:start position:0%
+money and no one else did there's no
+ 
+
+ align:start position:0%
+money and no one else did there's no
+enforcement mechanism um in in the
+
+ align:start position:0%
+enforcement mechanism um in in the
+ 
+
+ align:start position:0%
+enforcement mechanism um in in the
+protocol I don't know that the framework
+
+ align:start position:0%
+protocol I don't know that the framework
+ 
+
+ align:start position:0%
+protocol I don't know that the framework
+convention even allows for the
+
+ align:start position:0%
+convention even allows for the
+ 
+
+ align:start position:0%
+convention even allows for the
+possibility of an enforcement mechanism
+
+ align:start position:0%
+possibility of an enforcement mechanism
+ 
+
+ align:start position:0%
+possibility of an enforcement mechanism
+I'd have to go back and look
+
+ align:start position:0%
+I'd have to go back and look
+ 
+
+ align:start position:0%
+I'd have to go back and look
+um for simple International agreements
+
+ align:start position:0%
+um for simple International agreements
+ 
+
+ align:start position:0%
+um for simple International agreements
+it hasn't mattered much the Montreal
+
+ align:start position:0%
+it hasn't mattered much the Montreal
+ 
+
+ align:start position:0%
+it hasn't mattered much the Montreal
+protocol to phase out ozone depleting
+
+ align:start position:0%
+protocol to phase out ozone depleting
+ 
+
+ align:start position:0%
+protocol to phase out ozone depleting
+substances widely
+
+ align:start position:0%
+substances widely
+ 
+
+ align:start position:0%
+substances widely
+ratified not perfect there's some
+
+ align:start position:0%
+ratified not perfect there's some
+ 
+
+ align:start position:0%
+ratified not perfect there's some
+illegal manufacturing here and there
+
+ align:start position:0%
+illegal manufacturing here and there
+ 
+
+ align:start position:0%
+illegal manufacturing here and there
+but basically it's tiny so most
+
+ align:start position:0%
+but basically it's tiny so most
+ 
+
+ align:start position:0%
+but basically it's tiny so most
+governments can afford to just do it
+
+ align:start position:0%
+governments can afford to just do it
+ 
+
+ align:start position:0%
+governments can afford to just do it
+most countries can afford to do it it's
+
+ align:start position:0%
+most countries can afford to do it it's
+ 
+
+ align:start position:0%
+most countries can afford to do it it's
+a rich countries use those chemicals
+
+ align:start position:0%
+a rich countries use those chemicals
+ 
+
+ align:start position:0%
+a rich countries use those chemicals
+more than poor countries Rich chemicals
+
+ align:start position:0%
+more than poor countries Rich chemicals
+ 
+
+ align:start position:0%
+more than poor countries Rich chemicals
+can afford substit rich countries can
+
+ align:start position:0%
+can afford substit rich countries can
+ 
+
+ align:start position:0%
+can afford substit rich countries can
+afford substitutes not perfect but cheap
+
+ align:start position:0%
+afford substitutes not perfect but cheap
+ 
+
+ align:start position:0%
+afford substitutes not perfect but cheap
+this not so cheap and so no enforcement
+
+ align:start position:0%
+this not so cheap and so no enforcement
+ 
+
+ align:start position:0%
+this not so cheap and so no enforcement
+mechanism there either as far as I know
+
+ align:start position:0%
+mechanism there either as far as I know
+ 
+
+ align:start position:0%
+mechanism there either as far as I know
+I don't think there was in any case it
+
+ align:start position:0%
+I don't think there was in any case it
+ 
+
+ align:start position:0%
+I don't think there was in any case it
+wasn't was never seriously
+
+ align:start position:0%
+wasn't was never seriously
+ 
+
+ align:start position:0%
+wasn't was never seriously
+deployed here
+
+ align:start position:0%
+deployed here
+ 
+
+ align:start position:0%
+deployed here
+what would you do I mean the the
+
+ align:start position:0%
+what would you do I mean the the
+ 
+
+ align:start position:0%
+what would you do I mean the the
+Europeans were ready to go everybody was
+
+ align:start position:0%
+Europeans were ready to go everybody was
+ 
+
+ align:start position:0%
+Europeans were ready to go everybody was
+very excited Al Gore flew to Kyoto it
+
+ align:start position:0%
+very excited Al Gore flew to Kyoto it
+ 
+
+ align:start position:0%
+very excited Al Gore flew to Kyoto it
+was it was High Times and to say the US
+
+ align:start position:0%
+was it was High Times and to say the US
+ 
+
+ align:start position:0%
+was it was High Times and to say the US
+has always talked about monitoring no
+
+ align:start position:0%
+has always talked about monitoring no
+ 
+
+ align:start position:0%
+has always talked about monitoring no
+matter who the president's been we
+
+ align:start position:0%
+matter who the president's been we
+ 
+
+ align:start position:0%
+matter who the president's been we
+always talk about monitoring so in in
+
+ align:start position:0%
+always talk about monitoring so in in
+ 
+
+ align:start position:0%
+always talk about monitoring so in in
+these kinds of discussions nobody
+
+ align:start position:0%
+these kinds of discussions nobody
+ 
+
+ align:start position:0%
+these kinds of discussions nobody
+listens to as much now but we always say
+
+ align:start position:0%
+listens to as much now but we always say
+ 
+
+ align:start position:0%
+listens to as much now but we always say
+gee you ought to actually know if
+
+ align:start position:0%
+gee you ought to actually know if
+ 
+
+ align:start position:0%
+gee you ought to actually know if
+somebody's
+
+ align:start position:0%
+somebody's
+ 
+
+ align:start position:0%
+somebody's
+obeying the obeying the
+
+ align:start position:0%
+obeying the obeying the
+ 
+
+ align:start position:0%
+obeying the obeying the
+agreement um that's resisted by a lot of
+
+ align:start position:0%
+agreement um that's resisted by a lot of
+ 
+
+ align:start position:0%
+agreement um that's resisted by a lot of
+countries um so no and you can now
+
+ align:start position:0%
+countries um so no and you can now
+ 
+
+ align:start position:0%
+countries um so no and you can now
+imagine the beginnings of a European
+
+ align:start position:0%
+imagine the beginnings of a European
+ 
+
+ align:start position:0%
+imagine the beginnings of a European
+reaction wait a minute we're doing all
+
+ align:start position:0%
+reaction wait a minute we're doing all
+ 
+
+ align:start position:0%
+reaction wait a minute we're doing all
+this and what are all these other people
+
+ align:start position:0%
+this and what are all these other people
+ 
+
+ align:start position:0%
+this and what are all these other people
+doing they're smiling at us they're
+
+ align:start position:0%
+doing they're smiling at us they're
+ 
+
+ align:start position:0%
+doing they're smiling at us they're
+Al it it raises the cost of our heavy
+
+ align:start position:0%
+Al it it raises the cost of our heavy
+ 
+
+ align:start position:0%
+Al it it raises the cost of our heavy
+industry our energy intensive industry
+
+ align:start position:0%
+industry our energy intensive industry
+ 
+
+ align:start position:0%
+industry our energy intensive industry
+and wait a minute why are we doing this
+
+ align:start position:0%
+and wait a minute why are we doing this
+ 
+
+ align:start position:0%
+and wait a minute why are we doing this
+again because it's not going to have any
+
+ align:start position:0%
+again because it's not going to have any
+ 
+
+ align:start position:0%
+again because it's not going to have any
+effect right I mean Europe is a
+
+ align:start position:0%
+effect right I mean Europe is a
+ 
+
+ align:start position:0%
+effect right I mean Europe is a
+relatively relative to those big charts
+
+ align:start position:0%
+relatively relative to those big charts
+ 
+
+ align:start position:0%
+relatively relative to those big charts
+the kind of reductions that Europe's
+
+ align:start position:0%
+the kind of reductions that Europe's
+ 
+
+ align:start position:0%
+the kind of reductions that Europe's
+making are hard to
+
+ align:start position:0%
+making are hard to
+ 
+
+ align:start position:0%
+making are hard to
+see on the on the aggregate if I go back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to I go that's the one if I go back to
+
+ align:start position:0%
+to I go that's the one if I go back to
+ 
+
+ align:start position:0%
+to I go that's the one if I go back to
+this one you know Europe might be the
+
+ align:start position:0%
+this one you know Europe might be the
+ 
+
+ align:start position:0%
+this one you know Europe might be the
+width of this
+
+ align:start position:0%
+width of this
+ 
+
+ align:start position:0%
+width of this
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+at some cost so you could imagine the
+
+ align:start position:0%
+at some cost so you could imagine the
+ 
+
+ align:start position:0%
+at some cost so you could imagine the
+European public being less and less
+
+ align:start position:0%
+European public being less and less
+ 
+
+ align:start position:0%
+European public being less and less
+excited just as they've begun to phase
+
+ align:start position:0%
+excited just as they've begun to phase
+ 
+
+ align:start position:0%
+excited just as they've begun to phase
+down uh subsidies for renewable
+
+ align:start position:0%
+down uh subsidies for renewable
+ 
+
+ align:start position:0%
+down uh subsidies for renewable
+energy so yeah it's there's that's part
+
+ align:start position:0%
+energy so yeah it's there's that's part
+ 
+
+ align:start position:0%
+energy so yeah it's there's that's part
+of the problem the Zar can enforce we do
+
+ align:start position:0%
+of the problem the Zar can enforce we do
+ 
+
+ align:start position:0%
+of the problem the Zar can enforce we do
+not have a zar we do not have a zar so
+
+ align:start position:0%
+not have a zar we do not have a zar so
+ 
+
+ align:start position:0%
+not have a zar we do not have a zar so
+when the senate pass resolution saying
+
+ align:start position:0%
+when the senate pass resolution saying
+ 
+
+ align:start position:0%
+when the senate pass resolution saying
+they won't approve anything that doesn't
+
+ align:start position:0%
+they won't approve anything that doesn't
+ 
+
+ align:start position:0%
+they won't approve anything that doesn't
+Force China to also have emissions or
+
+ align:start position:0%
+Force China to also have emissions or
+ 
+
+ align:start position:0%
+Force China to also have emissions or
+emissions reductions didn't say force it
+
+ align:start position:0%
+emissions reductions didn't say force it
+ 
+
+ align:start position:0%
+emissions reductions didn't say force it
+that you can't use Force because none of
+
+ align:start position:0%
+that you can't use Force because none of
+ 
+
+ align:start position:0%
+that you can't use Force because none of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+agreements that unless it it requires
+
+ align:start position:0%
+agreements that unless it it requires
+ 
+
+ align:start position:0%
+agreements that unless it it requires
+which is to say that China signs on to
+
+ align:start position:0%
+which is to say that China signs on to
+ 
+
+ align:start position:0%
+which is to say that China signs on to
+something that says it will do X yeah
+
+ align:start position:0%
+something that says it will do X yeah
+ 
+
+ align:start position:0%
+something that says it will do X yeah
+but it doesn't specify that they have to
+
+ align:start position:0%
+but it doesn't specify that they have to
+ 
+
+ align:start position:0%
+but it doesn't specify that they have to
+actually be
+
+ align:start position:0%
+actually be
+ 
+
+ align:start position:0%
+actually be
+monitored oh I can't imagine I can't and
+
+ align:start position:0%
+monitored oh I can't imagine I can't and
+ 
+
+ align:start position:0%
+monitored oh I can't imagine I can't and
+you know this country's got a long a
+
+ align:start position:0%
+you know this country's got a long a
+ 
+
+ align:start position:0%
+you know this country's got a long a
+long history of strategic arms reduction
+
+ align:start position:0%
+long history of strategic arms reduction
+ 
+
+ align:start position:0%
+long history of strategic arms reduction
+do you remember well you wouldn't
+
+ align:start position:0%
+do you remember well you wouldn't
+ 
+
+ align:start position:0%
+do you remember well you wouldn't
+remember but you may have heard people
+
+ align:start position:0%
+remember but you may have heard people
+ 
+
+ align:start position:0%
+remember but you may have heard people
+say trust but verify we've always had
+
+ align:start position:0%
+say trust but verify we've always had
+ 
+
+ align:start position:0%
+say trust but verify we've always had
+that view internationally that we want
+
+ align:start position:0%
+that view internationally that we want
+ 
+
+ align:start position:0%
+that view internationally that we want
+to make sure if we're going to obey
+
+ align:start position:0%
+to make sure if we're going to obey
+ 
+
+ align:start position:0%
+to make sure if we're going to obey
+we're going to make sure other people do
+
+ align:start position:0%
+we're going to make sure other people do
+ 
+
+ align:start position:0%
+we're going to make sure other people do
+too at least monitor you may not be able
+
+ align:start position:0%
+too at least monitor you may not be able
+ 
+
+ align:start position:0%
+too at least monitor you may not be able
+to enforce so I can't see us signing
+
+ align:start position:0%
+to enforce so I can't see us signing
+ 
+
+ align:start position:0%
+to enforce so I can't see us signing
+something ratifying something that
+
+ align:start position:0%
+something ratifying something that
+ 
+
+ align:start position:0%
+something ratifying something that
+doesn't have at least monitoring
+
+ align:start position:0%
+doesn't have at least monitoring
+ 
+
+ align:start position:0%
+doesn't have at least monitoring
+Provisions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enforcement look at look at attempts to
+
+ align:start position:0%
+enforcement look at look at attempts to
+ 
+
+ align:start position:0%
+enforcement look at look at attempts to
+take action against Syria the world
+
+ align:start position:0%
+take action against Syria the world
+ 
+
+ align:start position:0%
+take action against Syria the world
+Community doesn't lightly enforce stuff
+
+ align:start position:0%
+Community doesn't lightly enforce stuff
+ 
+
+ align:start position:0%
+Community doesn't lightly enforce stuff
+but every so often Syria Iran something
+
+ align:start position:0%
+but every so often Syria Iran something
+ 
+
+ align:start position:0%
+but every so often Syria Iran something
+gets done but it doesn't get done easily
+
+ align:start position:0%
+gets done but it doesn't get done easily
+ 
+
+ align:start position:0%
+gets done but it doesn't get done easily
+doesn't get done automatically it's a
+
+ align:start position:0%
+doesn't get done automatically it's a
+ 
+
+ align:start position:0%
+doesn't get done automatically it's a
+big political deal David how is this not
+
+ align:start position:0%
+big political deal David how is this not
+ 
+
+ align:start position:0%
+big political deal David how is this not
+led to Stronger partnership laws in that
+
+ align:start position:0%
+led to Stronger partnership laws in that
+ 
+
+ align:start position:0%
+led to Stronger partnership laws in that
+you know I see it as a place where a
+
+ align:start position:0%
+you know I see it as a place where a
+ 
+
+ align:start position:0%
+you know I see it as a place where a
+more developed nation that has you know
+
+ align:start position:0%
+more developed nation that has you know
+ 
+
+ align:start position:0%
+more developed nation that has you know
+high technology inss like MIT could come
+
+ align:start position:0%
+high technology inss like MIT could come
+ 
+
+ align:start position:0%
+high technology inss like MIT could come
+in and talk to a place like Africa and
+
+ align:start position:0%
+in and talk to a place like Africa and
+ 
+
+ align:start position:0%
+in and talk to a place like Africa and
+there's already know a fair amount of
+
+ align:start position:0%
+there's already know a fair amount of
+ 
+
+ align:start position:0%
+there's already know a fair amount of
+infrastructure Investments that's made
+
+ align:start position:0%
+infrastructure Investments that's made
+ 
+
+ align:start position:0%
+infrastructure Investments that's made
+and you know a lot of it can be in the
+
+ align:start position:0%
+and you know a lot of it can be in the
+ 
+
+ align:start position:0%
+and you know a lot of it can be in the
+terms of low interest loans or or you
+
+ align:start position:0%
+terms of low interest loans or or you
+ 
+
+ align:start position:0%
+terms of low interest loans or or you
+provide experts and um help build up the
+
+ align:start position:0%
+provide experts and um help build up the
+ 
+
+ align:start position:0%
+provide experts and um help build up the
+infrastructure because your your cost is
+
+ align:start position:0%
+infrastructure because your your cost is
+ 
+
+ align:start position:0%
+infrastructure because your your cost is
+lower and you're developing something
+
+ align:start position:0%
+lower and you're developing something
+ 
+
+ align:start position:0%
+lower and you're developing something
+new you know you're fostering local here
+
+ align:start position:0%
+new you know you're fostering local here
+ 
+
+ align:start position:0%
+new you know you're fostering local here
+in the states by making that part of
+
+ align:start position:0%
+in the states by making that part of
+ 
+
+ align:start position:0%
+in the states by making that part of
+your avilable Global value but you're
+
+ align:start position:0%
+your avilable Global value but you're
+ 
+
+ align:start position:0%
+your avilable Global value but you're
+also helping internation how does that
+
+ align:start position:0%
+also helping internation how does that
+ 
+
+ align:start position:0%
+also helping internation how does that
+not happen well it it it happens to some
+
+ align:start position:0%
+not happen well it it it happens to some
+ 
+
+ align:start position:0%
+not happen well it it it happens to some
+extent there's a
+
+ align:start position:0%
+extent there's a
+ 
+
+ align:start position:0%
+extent there's a
+problem of of measurement right the
+
+ align:start position:0%
+problem of of measurement right the
+ 
+
+ align:start position:0%
+problem of of measurement right the
+European
+
+ align:start position:0%
+European
+ 
+
+ align:start position:0%
+European
+system the Kyoto the Kyoto Protocol
+
+ align:start position:0%
+system the Kyoto the Kyoto Protocol
+ 
+
+ align:start position:0%
+system the Kyoto the Kyoto Protocol
+provides
+
+ align:start position:0%
+provides
+ 
+
+ align:start position:0%
+provides
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+called Joint
+
+ align:start position:0%
+called Joint
+ 
+
+ align:start position:0%
+called Joint
+implementation well I forget the exact
+
+ align:start position:0%
+implementation well I forget the exact
+ 
+
+ align:start position:0%
+implementation well I forget the exact
+language the clean development mechanism
+
+ align:start position:0%
+language the clean development mechanism
+ 
+
+ align:start position:0%
+language the clean development mechanism
+CDM you can if you're a European
+
+ align:start position:0%
+CDM you can if you're a European
+ 
+
+ align:start position:0%
+CDM you can if you're a European
+company you can meet some of your
+
+ align:start position:0%
+company you can meet some of your
+ 
+
+ align:start position:0%
+company you can meet some of your
+obligations by in by reducing emissions
+
+ align:start position:0%
+obligations by in by reducing emissions
+ 
+
+ align:start position:0%
+obligations by in by reducing emissions
+in a poor country so you can go to
+
+ align:start position:0%
+in a poor country so you can go to
+ 
+
+ align:start position:0%
+in a poor country so you can go to
+China
+
+ align:start position:0%
+China
+ 
+
+ align:start position:0%
+China
+and do a deal bring in new technology do
+
+ align:start position:0%
+and do a deal bring in new technology do
+ 
+
+ align:start position:0%
+and do a deal bring in new technology do
+something that will reduce emissions
+
+ align:start position:0%
+something that will reduce emissions
+ 
+
+ align:start position:0%
+something that will reduce emissions
+and that will give you credit and that's
+
+ align:start position:0%
+and that will give you credit and that's
+ 
+
+ align:start position:0%
+and that will give you credit and that's
+exactly that kind of thinking can we
+
+ align:start position:0%
+exactly that kind of thinking can we
+ 
+
+ align:start position:0%
+exactly that kind of thinking can we
+even though China isn't
+
+ align:start position:0%
+even though China isn't
+ 
+
+ align:start position:0%
+even though China isn't
+participating it's still cheaper to do
+
+ align:start position:0%
+participating it's still cheaper to do
+ 
+
+ align:start position:0%
+participating it's still cheaper to do
+reductions there so let's find a way to
+
+ align:start position:0%
+reductions there so let's find a way to
+ 
+
+ align:start position:0%
+reductions there so let's find a way to
+give countries in Europe credit for
+
+ align:start position:0%
+give countries in Europe credit for
+ 
+
+ align:start position:0%
+give countries in Europe credit for
+reductions in
+
+ align:start position:0%
+reductions in
+ 
+
+ align:start position:0%
+reductions in
+China there are a couple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems well it all boils down to one
+
+ align:start position:0%
+problems well it all boils down to one
+ 
+
+ align:start position:0%
+problems well it all boils down to one
+problem really which is how do you
+
+ align:start position:0%
+problem really which is how do you
+ 
+
+ align:start position:0%
+problem really which is how do you
+measure it because it's you you you're
+
+ align:start position:0%
+measure it because it's you you you're
+ 
+
+ align:start position:0%
+measure it because it's you you you're
+reducing over what would have been so
+
+ align:start position:0%
+reducing over what would have been so
+ 
+
+ align:start position:0%
+reducing over what would have been so
+you modernize a
+
+ align:start position:0%
+you modernize a
+ 
+
+ align:start position:0%
+you modernize a
+factory so would that factory have been
+
+ align:start position:0%
+factory so would that factory have been
+ 
+
+ align:start position:0%
+factory so would that factory have been
+running forever with old technology or
+
+ align:start position:0%
+running forever with old technology or
+ 
+
+ align:start position:0%
+running forever with old technology or
+would it have been torn down or would it
+
+ align:start position:0%
+would it have been torn down or would it
+ 
+
+ align:start position:0%
+would it have been torn down or would it
+have been modernized anyway so either
+
+ align:start position:0%
+have been modernized anyway so either
+ 
+
+ align:start position:0%
+have been modernized anyway so either
+your real your real light on how you do
+
+ align:start position:0%
+your real your real light on how you do
+ 
+
+ align:start position:0%
+your real your real light on how you do
+this and you you don't impose real tough
+
+ align:start position:0%
+this and you you don't impose real tough
+ 
+
+ align:start position:0%
+this and you you don't impose real tough
+restrictions and then you're not getting
+
+ align:start position:0%
+restrictions and then you're not getting
+ 
+
+ align:start position:0%
+restrictions and then you're not getting
+real reductions or you you make it
+
+ align:start position:0%
+real reductions or you you make it
+ 
+
+ align:start position:0%
+real reductions or you you make it
+really hard to document in which case
+
+ align:start position:0%
+really hard to document in which case
+ 
+
+ align:start position:0%
+really hard to document in which case
+you kill the market so it's it happens
+
+ align:start position:0%
+you kill the market so it's it happens
+ 
+
+ align:start position:0%
+you kill the market so it's it happens
+and it happens to some extent the
+
+ align:start position:0%
+and it happens to some extent the
+ 
+
+ align:start position:0%
+and it happens to some extent the
+Europeans have gotten a little tired of
+
+ align:start position:0%
+Europeans have gotten a little tired of
+ 
+
+ align:start position:0%
+Europeans have gotten a little tired of
+it as I recall thinking that it's been a
+
+ align:start position:0%
+it as I recall thinking that it's been a
+ 
+
+ align:start position:0%
+it as I recall thinking that it's been a
+little too easy but
+
+ align:start position:0%
+little too easy but
+ 
+
+ align:start position:0%
+little too easy but
+um one of the features of the Waxman
+
+ align:start position:0%
+um one of the features of the Waxman
+ 
+
+ align:start position:0%
+um one of the features of the Waxman
+Mary bill in the
+
+ align:start position:0%
+Mary bill in the
+ 
+
+ align:start position:0%
+Mary bill in the
+US which was the KA trade bill that was
+
+ align:start position:0%
+US which was the KA trade bill that was
+ 
+
+ align:start position:0%
+US which was the KA trade bill that was
+was killed it allowed for
+
+ align:start position:0%
+was killed it allowed for
+ 
+
+ align:start position:0%
+was killed it allowed for
+that for it did it covered only fossil
+
+ align:start position:0%
+that for it did it covered only fossil
+ 
+
+ align:start position:0%
+that for it did it covered only fossil
+fuels but it it allowed companies to get
+
+ align:start position:0%
+fuels but it it allowed companies to get
+ 
+
+ align:start position:0%
+fuels but it it allowed companies to get
+credit for things done in
+
+ align:start position:0%
+credit for things done in
+ 
+
+ align:start position:0%
+credit for things done in
+agriculture so you could change land
+
+ align:start position:0%
+agriculture so you could change land
+ 
+
+ align:start position:0%
+agriculture so you could change land
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+and it it was it was a giveaway to
+
+ align:start position:0%
+and it it was it was a giveaway to
+ 
+
+ align:start position:0%
+and it it was it was a giveaway to
+agriculture basically because the
+
+ align:start position:0%
+agriculture basically because the
+ 
+
+ align:start position:0%
+agriculture basically because the
+standards were going to be pretty easy
+
+ align:start position:0%
+standards were going to be pretty easy
+ 
+
+ align:start position:0%
+standards were going to be pretty easy
+but it was that same notion that that I
+
+ align:start position:0%
+but it was that same notion that that I
+ 
+
+ align:start position:0%
+but it was that same notion that that I
+want to reach out Beyond places that I
+
+ align:start position:0%
+want to reach out Beyond places that I
+ 
+
+ align:start position:0%
+want to reach out Beyond places that I
+can price to give people
+
+ align:start position:0%
+can price to give people
+ 
+
+ align:start position:0%
+can price to give people
+incentives but it's really hard because
+
+ align:start position:0%
+incentives but it's really hard because
+ 
+
+ align:start position:0%
+incentives but it's really hard because
+you can measure what is emitted you can
+
+ align:start position:0%
+you can measure what is emitted you can
+ 
+
+ align:start position:0%
+you can measure what is emitted you can
+never measure what would have
+
+ align:start position:0%
+never measure what would have
+ 
+
+ align:start position:0%
+never measure what would have
+been we we you could see the same
+
+ align:start position:0%
+been we we you could see the same
+ 
+
+ align:start position:0%
+been we we you could see the same
+problem with forests if you think for
+
+ align:start position:0%
+problem with forests if you think for
+ 
+
+ align:start position:0%
+problem with forests if you think for
+just a minute if I pay you not to cut
+
+ align:start position:0%
+just a minute if I pay you not to cut
+ 
+
+ align:start position:0%
+just a minute if I pay you not to cut
+down a forest does that mean the guy
+
+ align:start position:0%
+down a forest does that mean the guy
+ 
+
+ align:start position:0%
+down a forest does that mean the guy
+across the street cuts his down to
+
+ align:start position:0%
+across the street cuts his down to
+ 
+
+ align:start position:0%
+across the street cuts his down to
+provide the
+
+ align:start position:0%
+provide the
+ 
+
+ align:start position:0%
+provide the
+timber or or what uh and you would never
+
+ align:start position:0%
+timber or or what uh and you would never
+ 
+
+ align:start position:0%
+timber or or what uh and you would never
+have cut it
+
+ align:start position:0%
+have cut it
+ 
+
+ align:start position:0%
+have cut it
+down um or you would have I you know so
+
+ align:start position:0%
+down um or you would have I you know so
+ 
+
+ align:start position:0%
+down um or you would have I you know so
+it's a natural it's a natural model if
+
+ align:start position:0%
+it's a natural it's a natural model if
+ 
+
+ align:start position:0%
+it's a natural it's a natural model if
+everybody was if there were a common
+
+ align:start position:0%
+everybody was if there were a common
+ 
+
+ align:start position:0%
+everybody was if there were a common
+regime a cap and trade or a tax regime
+
+ align:start position:0%
+regime a cap and trade or a tax regime
+ 
+
+ align:start position:0%
+regime a cap and trade or a tax regime
+that would happen automatically easily
+
+ align:start position:0%
+that would happen automatically easily
+ 
+
+ align:start position:0%
+that would happen automatically easily
+and you wouldn't have a measurement
+
+ align:start position:0%
+and you wouldn't have a measurement
+ 
+
+ align:start position:0%
+and you wouldn't have a measurement
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+it's just hard to do it without such a
+
+ align:start position:0%
+it's just hard to do it without such a
+ 
+
+ align:start position:0%
+it's just hard to do it without such a
+thing there us companies there's some
+
+ align:start position:0%
+thing there us companies there's some
+ 
+
+ align:start position:0%
+thing there us companies there's some
+sort of informal trading in carbon
+
+ align:start position:0%
+sort of informal trading in carbon
+ 
+
+ align:start position:0%
+sort of informal trading in carbon
+credits in the US and companies will do
+
+ align:start position:0%
+credits in the US and companies will do
+ 
+
+ align:start position:0%
+credits in the US and companies will do
+stuff like this and get and take credit
+
+ align:start position:0%
+stuff like this and get and take credit
+ 
+
+ align:start position:0%
+stuff like this and get and take credit
+for it perfectly fine activity it's it's
+
+ align:start position:0%
+for it perfectly fine activity it's it's
+ 
+
+ align:start position:0%
+for it perfectly fine activity it's it's
+it's uh uh socially responsible and all
+
+ align:start position:0%
+it's uh uh socially responsible and all
+ 
+
+ align:start position:0%
+it's uh uh socially responsible and all
+that but it's just hard to assess
+
+ align:start position:0%
+that but it's just hard to assess
+ 
+
+ align:start position:0%
+that but it's just hard to assess
+where's the developing Nation resistance
+
+ align:start position:0%
+where's the developing Nation resistance
+ 
+
+ align:start position:0%
+where's the developing Nation resistance
+like they're getting investment why
+
+ align:start position:0%
+like they're getting investment why
+ 
+
+ align:start position:0%
+like they're getting investment why
+would they not want besides the
+
+ align:start position:0%
+would they not want besides the
+ 
+
+ align:start position:0%
+would they not want besides the
+measurement problem I I would see it
+
+ align:start position:0%
+measurement problem I I would see it
+ 
+
+ align:start position:0%
+measurement problem I I would see it
+someone get foreign investment anyways
+
+ align:start position:0%
+someone get foreign investment anyways
+ 
+
+ align:start position:0%
+someone get foreign investment anyways
+and you take out full full page ads in
+
+ align:start position:0%
+and you take out full full page ads in
+ 
+
+ align:start position:0%
+and you take out full full page ads in
+the economy right well you know what
+
+ align:start position:0%
+the economy right well you know what
+ 
+
+ align:start position:0%
+the economy right well you know what
+they're worried about is I you guys got
+
+ align:start position:0%
+they're worried about is I you guys got
+ 
+
+ align:start position:0%
+they're worried about is I you guys got
+rich we want to get rich you guys got
+
+ align:start position:0%
+rich we want to get rich you guys got
+ 
+
+ align:start position:0%
+rich we want to get rich you guys got
+rich burning fossil fuel and you're
+
+ align:start position:0%
+rich burning fossil fuel and you're
+ 
+
+ align:start position:0%
+rich burning fossil fuel and you're
+telling
+
+ align:start position:0%
+telling
+ 
+
+ align:start position:0%
+telling
+us I assume I'm going to hear a bunch of
+
+ align:start position:0%
+us I assume I'm going to hear a bunch of
+ 
+
+ align:start position:0%
+us I assume I'm going to hear a bunch of
+this on Wednesday and Friday from the
+
+ align:start position:0%
+this on Wednesday and Friday from the
+ 
+
+ align:start position:0%
+this on Wednesday and Friday from the
+developing world you're telling us that
+
+ align:start position:0%
+developing world you're telling us that
+ 
+
+ align:start position:0%
+developing world you're telling us that
+you got to do
+
+ align:start position:0%
+you got to do
+ 
+
+ align:start position:0%
+you got to do
+that and you're now leaning on us the
+
+ align:start position:0%
+that and you're now leaning on us the
+ 
+
+ align:start position:0%
+that and you're now leaning on us the
+phrase the fear
+
+ align:start position:0%
+phrase the fear
+ 
+
+ align:start position:0%
+phrase the fear
+isn't that boatloads of investment will
+
+ align:start position:0%
+isn't that boatloads of investment will
+ 
+
+ align:start position:0%
+isn't that boatloads of investment will
+come in and modernize their Factory the
+
+ align:start position:0%
+come in and modernize their Factory the
+ 
+
+ align:start position:0%
+come in and modernize their Factory the
+fear is that you're going to raise the
+
+ align:start position:0%
+fear is that you're going to raise the
+ 
+
+ align:start position:0%
+fear is that you're going to raise the
+price of fuel to my poor people a lot of
+
+ align:start position:0%
+price of fuel to my poor people a lot of
+ 
+
+ align:start position:0%
+price of fuel to my poor people a lot of
+these countries subsidize
+
+ align:start position:0%
+these countries subsidize
+ 
+
+ align:start position:0%
+these countries subsidize
+fuel um and I don't want to take the
+
+ align:start position:0%
+fuel um and I don't want to take the
+ 
+
+ align:start position:0%
+fuel um and I don't want to take the
+political heat from something that
+
+ align:start position:0%
+political heat from something that
+ 
+
+ align:start position:0%
+political heat from something that
+restricts my ability to
+
+ align:start position:0%
+restricts my ability to
+ 
+
+ align:start position:0%
+restricts my ability to
+grow if you're telling me that the
+
+ align:start position:0%
+grow if you're telling me that the
+ 
+
+ align:start position:0%
+grow if you're telling me that the
+Europeans are going to come in and
+
+ align:start position:0%
+Europeans are going to come in and
+ 
+
+ align:start position:0%
+Europeans are going to come in and
+modernize my factories that's swell I
+
+ align:start position:0%
+modernize my factories that's swell I
+ 
+
+ align:start position:0%
+modernize my factories that's swell I
+love it if you're telling me that I have
+
+ align:start position:0%
+love it if you're telling me that I have
+ 
+
+ align:start position:0%
+love it if you're telling me that I have
+to change my policies
+
+ align:start position:0%
+to change my policies
+ 
+
+ align:start position:0%
+to change my policies
+in a way that might slow growth and keep
+
+ align:start position:0%
+in a way that might slow growth and keep
+ 
+
+ align:start position:0%
+in a way that might slow growth and keep
+my people poor I'm not real
+
+ align:start position:0%
+my people poor I'm not real
+ 
+
+ align:start position:0%
+my people poor I'm not real
+excited
+
+ align:start position:0%
+excited
+ 
+
+ align:start position:0%
+excited
+and you can say you know I've been
+
+ align:start position:0%
+and you can say you know I've been
+ 
+
+ align:start position:0%
+and you can say you know I've been
+talking about your grandchildren and
+
+ align:start position:0%
+talking about your grandchildren and
+ 
+
+ align:start position:0%
+talking about your grandchildren and
+great-grandchildren well I mean if your
+
+ align:start position:0%
+great-grandchildren well I mean if your
+ 
+
+ align:start position:0%
+great-grandchildren well I mean if your
+kids are starving today that's a pretty
+
+ align:start position:0%
+kids are starving today that's a pretty
+ 
+
+ align:start position:0%
+kids are starving today that's a pretty
+abstract
+
+ align:start position:0%
+abstract
+ 
+
+ align:start position:0%
+abstract
+argument that's real abstract
+
+ align:start position:0%
+argument that's real abstract
+ 
+
+ align:start position:0%
+argument that's real abstract
+so other comments reactions
+
+ align:start position:0%
+so other comments reactions
+ 
+
+ align:start position:0%
+so other comments reactions
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thoughts yeah um so mostly we've been
+
+ align:start position:0%
+thoughts yeah um so mostly we've been
+ 
+
+ align:start position:0%
+thoughts yeah um so mostly we've been
+talking about about greenhouse gases um
+
+ align:start position:0%
+talking about about greenhouse gases um
+ 
+
+ align:start position:0%
+talking about about greenhouse gases um
+is there any International discussion
+
+ align:start position:0%
+is there any International discussion
+ 
+
+ align:start position:0%
+is there any International discussion
+about other like climate changing forces
+
+ align:start position:0%
+about other like climate changing forces
+ 
+
+ align:start position:0%
+about other like climate changing forces
+like like black carbon or other like
+
+ align:start position:0%
+like like black carbon or other like
+ 
+
+ align:start position:0%
+like like black carbon or other like
+aerosols or is that not not that I'm
+
+ align:start position:0%
+aerosols or is that not not that I'm
+ 
+
+ align:start position:0%
+aerosols or is that not not that I'm
+aware of is there some okay say well I
+
+ align:start position:0%
+aware of is there some okay say well I
+ 
+
+ align:start position:0%
+aware of is there some okay say well I
+mean the state department just a few
+
+ align:start position:0%
+mean the state department just a few
+ 
+
+ align:start position:0%
+mean the state department just a few
+weeks ago announced that uh we would
+
+ align:start position:0%
+weeks ago announced that uh we would
+ 
+
+ align:start position:0%
+weeks ago announced that uh we would
+they will you
+
+ align:start position:0%
+they will you
+ 
+
+ align:start position:0%
+they will you
+want oh you didn't sign a release form
+
+ align:start position:0%
+want oh you didn't sign a release form
+ 
+
+ align:start position:0%
+want oh you didn't sign a release form
+but never mind I release
+
+ align:start position:0%
+but never mind I release
+ 
+
+ align:start position:0%
+but never mind I release
+you and everyone is released out there
+
+ align:start position:0%
+you and everyone is released out there
+ 
+
+ align:start position:0%
+you and everyone is released out there
+in television land okay just a few weeks
+
+ align:start position:0%
+in television land okay just a few weeks
+ 
+
+ align:start position:0%
+in television land okay just a few weeks
+ago the state department announced that
+
+ align:start position:0%
+ago the state department announced that
+ 
+
+ align:start position:0%
+ago the state department announced that
+uh we would be part of and I guess the
+
+ align:start position:0%
+uh we would be part of and I guess the
+ 
+
+ align:start position:0%
+uh we would be part of and I guess the
+leader of an effort to try to reduce
+
+ align:start position:0%
+leader of an effort to try to reduce
+ 
+
+ align:start position:0%
+leader of an effort to try to reduce
+emissions of soot and other shortlived
+
+ align:start position:0%
+emissions of soot and other shortlived
+ 
+
+ align:start position:0%
+emissions of soot and other shortlived
+gases um stuff like methane and
+
+ align:start position:0%
+gases um stuff like methane and
+ 
+
+ align:start position:0%
+gases um stuff like methane and
+tropospheric ozon as well so uh that's a
+
+ align:start position:0%
+tropospheric ozon as well so uh that's a
+ 
+
+ align:start position:0%
+tropospheric ozon as well so uh that's a
+voluntary program um but but there are
+
+ align:start position:0%
+voluntary program um but but there are
+ 
+
+ align:start position:0%
+voluntary program um but but there are
+movements in that direction and there is
+
+ align:start position:0%
+movements in that direction and there is
+ 
+
+ align:start position:0%
+movements in that direction and there is
+actually quite a bit of investment in um
+
+ align:start position:0%
+actually quite a bit of investment in um
+ 
+
+ align:start position:0%
+actually quite a bit of investment in um
+providing uh very much more efficient
+
+ align:start position:0%
+providing uh very much more efficient
+ 
+
+ align:start position:0%
+providing uh very much more efficient
+stoves to people in very poor uh
+
+ align:start position:0%
+stoves to people in very poor uh
+ 
+
+ align:start position:0%
+stoves to people in very poor uh
+countries uh so that they can avoid
+
+ align:start position:0%
+countries uh so that they can avoid
+ 
+
+ align:start position:0%
+countries uh so that they can avoid
+using things like dung and coal and
+
+ align:start position:0%
+using things like dung and coal and
+ 
+
+ align:start position:0%
+using things like dung and coal and
+stuff like that which generates an
+
+ align:start position:0%
+stuff like that which generates an
+ 
+
+ align:start position:0%
+stuff like that which generates an
+enormous amount of pollution so it has
+
+ align:start position:0%
+enormous amount of pollution so it has
+ 
+
+ align:start position:0%
+enormous amount of pollution so it has
+both a health benefit and an efficiency
+
+ align:start position:0%
+both a health benefit and an efficiency
+ 
+
+ align:start position:0%
+both a health benefit and an efficiency
+benit benefit and it also Cuts carbon a
+
+ align:start position:0%
+benit benefit and it also Cuts carbon a
+ 
+
+ align:start position:0%
+benit benefit and it also Cuts carbon a
+little bit but you know realistically
+
+ align:start position:0%
+little bit but you know realistically
+ 
+
+ align:start position:0%
+little bit but you know realistically
+the main motivation is much more
+
+ align:start position:0%
+the main motivation is much more
+ 
+
+ align:start position:0%
+the main motivation is much more
+grounded in
+
+ align:start position:0%
+grounded in
+ 
+
+ align:start position:0%
+grounded in
+soot I
+
+ align:start position:0%
+soot I
+ 
+
+ align:start position:0%
+soot I
+mean one reason not the main reason
+
+ align:start position:0%
+mean one reason not the main reason
+ 
+
+ align:start position:0%
+mean one reason not the main reason
+necessarily to be concerned with black
+
+ align:start position:0%
+necessarily to be concerned with black
+ 
+
+ align:start position:0%
+necessarily to be concerned with black
+carbon emissions is the effect on the
+
+ align:start position:0%
+carbon emissions is the effect on the
+ 
+
+ align:start position:0%
+carbon emissions is the effect on the
+reflectivity right you have a lot of sea
+
+ align:start position:0%
+reflectivity right you have a lot of sea
+ 
+
+ align:start position:0%
+reflectivity right you have a lot of sea
+ice ice tends to reflect black carbon
+
+ align:start position:0%
+ice ice tends to reflect black carbon
+ 
+
+ align:start position:0%
+ice ice tends to reflect black carbon
+tends to absorb so it does matter for
+
+ align:start position:0%
+tends to absorb so it does matter for
+ 
+
+ align:start position:0%
+tends to absorb so it does matter for
+climate but it also matters for what you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bree there are are lots of international
+
+ align:start position:0%
+Bree there are are lots of international
+ 
+
+ align:start position:0%
+Bree there are are lots of international
+environmental treaties most don't have
+
+ align:start position:0%
+environmental treaties most don't have
+ 
+
+ align:start position:0%
+environmental treaties most don't have
+anything to do with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+climate
\ No newline at end of file
diff --git a/3Mvzp5xvEXA.txt b/3Mvzp5xvEXA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..32d5b19635e443e8876286d26b2d4b9464b2c770
--- /dev/null
+++ b/3Mvzp5xvEXA.txt
@@ -0,0 +1,9467 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+so I'm going to talk today about a
+
+ align:start position:0%
+so I'm going to talk today about a
+ 
+
+ align:start position:0%
+so I'm going to talk today about a
+couple of things I had a hell of a time
+
+ align:start position:0%
+couple of things I had a hell of a time
+ 
+
+ align:start position:0%
+couple of things I had a hell of a time
+constructing a nice clean narrative arc
+
+ align:start position:0%
+constructing a nice clean narrative arc
+ 
+
+ align:start position:0%
+constructing a nice clean narrative arc
+through everything I wanted to say and
+
+ align:start position:0%
+through everything I wanted to say and
+ 
+
+ align:start position:0%
+through everything I wanted to say and
+so I finally just decided the hell with
+
+ align:start position:0%
+so I finally just decided the hell with
+ 
+
+ align:start position:0%
+so I finally just decided the hell with
+it I'm just gonna be honest there's
+
+ align:start position:0%
+it I'm just gonna be honest there's
+ 
+
+ align:start position:0%
+it I'm just gonna be honest there's
+several different pieces they don't make
+
+ align:start position:0%
+several different pieces they don't make
+ 
+
+ align:start position:0%
+several different pieces they don't make
+a narrative arc that's life I want to
+
+ align:start position:0%
+a narrative arc that's life I want to
+ 
+
+ align:start position:0%
+a narrative arc that's life I want to
+address what I see as a sort of
+
+ align:start position:0%
+address what I see as a sort of
+ 
+
+ align:start position:0%
+address what I see as a sort of
+macroscopic view of the organization of
+
+ align:start position:0%
+macroscopic view of the organization of
+ 
+
+ align:start position:0%
+macroscopic view of the organization of
+the human brain is giving us a kind of
+
+ align:start position:0%
+the human brain is giving us a kind of
+ 
+
+ align:start position:0%
+the human brain is giving us a kind of
+picture of what I'm going to call the
+
+ align:start position:0%
+picture of what I'm going to call the
+ 
+
+ align:start position:0%
+picture of what I'm going to call the
+architecture of human intelligence right
+
+ align:start position:0%
+architecture of human intelligence right
+ 
+
+ align:start position:0%
+architecture of human intelligence right
+we're trying to understand intelligence
+
+ align:start position:0%
+we're trying to understand intelligence
+ 
+
+ align:start position:0%
+we're trying to understand intelligence
+in this class and so I think the overall
+
+ align:start position:0%
+in this class and so I think the overall
+ 
+
+ align:start position:0%
+in this class and so I think the overall
+organization of the human brain in which
+
+ align:start position:0%
+organization of the human brain in which
+ 
+
+ align:start position:0%
+organization of the human brain in which
+we've made a lot of progress in the last
+
+ align:start position:0%
+we've made a lot of progress in the last
+ 
+
+ align:start position:0%
+we've made a lot of progress in the last
+20 years gives us a kind of macro
+
+ align:start position:0%
+20 years gives us a kind of macro
+ 
+
+ align:start position:0%
+20 years gives us a kind of macro
+picture of what the pieces of the system
+
+ align:start position:0%
+picture of what the pieces of the system
+ 
+
+ align:start position:0%
+picture of what the pieces of the system
+are so I'll talk about that and then
+
+ align:start position:0%
+are so I'll talk about that and then
+ 
+
+ align:start position:0%
+are so I'll talk about that and then
+also if I talk fast enough do a kind of
+
+ align:start position:0%
+also if I talk fast enough do a kind of
+ 
+
+ align:start position:0%
+also if I talk fast enough do a kind of
+whirlwind introduction through the basic
+
+ align:start position:0%
+whirlwind introduction through the basic
+ 
+
+ align:start position:0%
+whirlwind introduction through the basic
+methods of human cognitive neuroscience
+
+ align:start position:0%
+methods of human cognitive neuroscience
+ 
+
+ align:start position:0%
+methods of human cognitive neuroscience
+using face recognition as an example to
+
+ align:start position:0%
+using face recognition as an example to
+ 
+
+ align:start position:0%
+using face recognition as an example to
+illustrate what each of the methods can
+
+ align:start position:0%
+illustrate what each of the methods can
+ 
+
+ align:start position:0%
+illustrate what each of the methods can
+and cannot do so that's the agenda it's
+
+ align:start position:0%
+and cannot do so that's the agenda it's
+ 
+
+ align:start position:0%
+and cannot do so that's the agenda it's
+gonna be pretty basic so if you've heard
+
+ align:start position:0%
+gonna be pretty basic so if you've heard
+ 
+
+ align:start position:0%
+gonna be pretty basic so if you've heard
+me speak before you've probably heard a
+
+ align:start position:0%
+me speak before you've probably heard a
+ 
+
+ align:start position:0%
+me speak before you've probably heard a
+lot of this so anyway the key question
+
+ align:start position:0%
+lot of this so anyway the key question
+ 
+
+ align:start position:0%
+lot of this so anyway the key question
+we're trying to address in this course
+
+ align:start position:0%
+we're trying to address in this course
+ 
+
+ align:start position:0%
+we're trying to address in this course
+is how does the brain produce
+
+ align:start position:0%
+is how does the brain produce
+ 
+
+ align:start position:0%
+is how does the brain produce
+intelligent behavior and how may we be
+
+ align:start position:0%
+intelligent behavior and how may we be
+ 
+
+ align:start position:0%
+intelligent behavior and how may we be
+able to replicate that intelligence in
+
+ align:start position:0%
+able to replicate that intelligence in
+ 
+
+ align:start position:0%
+able to replicate that intelligence in
+machines ok so there's of course a
+
+ align:start position:0%
+machines ok so there's of course a
+ 
+
+ align:start position:0%
+machines ok so there's of course a
+million different ways to go at that
+
+ align:start position:0%
+million different ways to go at that
+ 
+
+ align:start position:0%
+million different ways to go at that
+question and you can go at it from a
+
+ align:start position:0%
+question and you can go at it from a
+ 
+
+ align:start position:0%
+question and you can go at it from a
+kind of computational angle a coding
+
+ align:start position:0%
+kind of computational angle a coding
+ 
+
+ align:start position:0%
+kind of computational angle a coding
+perspective from a fine-grained neural
+
+ align:start position:0%
+perspective from a fine-grained neural
+ 
+
+ align:start position:0%
+perspective from a fine-grained neural
+circuit perspective and I need to do
+
+ align:start position:0%
+circuit perspective and I need to do
+ 
+
+ align:start position:0%
+circuit perspective and I need to do
+something that's kind of in-between
+
+ align:start position:0%
+something that's kind of in-between
+ 
+
+ align:start position:0%
+something that's kind of in-between
+because those are the things we can
+
+ align:start position:0%
+because those are the things we can
+ 
+
+ align:start position:0%
+because those are the things we can
+approach in human brains and its really
+
+ align:start position:0%
+approach in human brains and its really
+ 
+
+ align:start position:0%
+approach in human brains and its really
+human intelligence we want to understand
+
+ align:start position:0%
+human intelligence we want to understand
+ 
+
+ align:start position:0%
+human intelligence we want to understand
+I'd say some of human intelligence is a
+
+ align:start position:0%
+I'd say some of human intelligence is a
+ 
+
+ align:start position:0%
+I'd say some of human intelligence is a
+lot of it is things that we share with
+
+ align:start position:0%
+lot of it is things that we share with
+ 
+
+ align:start position:0%
+lot of it is things that we share with
+animals but some of it is not and so I
+
+ align:start position:0%
+animals but some of it is not and so I
+ 
+
+ align:start position:0%
+animals but some of it is not and so I
+think it's important to be able to
+
+ align:start position:0%
+think it's important to be able to
+ 
+
+ align:start position:0%
+think it's important to be able to
+approach this not just from the
+
+ align:start position:0%
+approach this not just from the
+ 
+
+ align:start position:0%
+approach this not just from the
+perspectives of animal research
+
+ align:start position:0%
+perspectives of animal research
+ 
+
+ align:start position:0%
+perspectives of animal research
+magnificent as those methods are but to
+
+ align:start position:0%
+magnificent as those methods are but to
+ 
+
+ align:start position:0%
+magnificent as those methods are but to
+also see what we can learn about human
+
+ align:start position:0%
+also see what we can learn about human
+ 
+
+ align:start position:0%
+also see what we can learn about human
+brains
+
+ align:start position:0%
+brains
+ 
+
+ align:start position:0%
+brains
+okay so I'll talk a bit about the
+
+ align:start position:0%
+okay so I'll talk a bit about the
+ 
+
+ align:start position:0%
+okay so I'll talk a bit about the
+overall functional architecture of the
+
+ align:start position:0%
+overall functional architecture of the
+ 
+
+ align:start position:0%
+overall functional architecture of the
+human brain what are the basic pieces of
+
+ align:start position:0%
+human brain what are the basic pieces of
+ 
+
+ align:start position:0%
+human brain what are the basic pieces of
+the system and then I'll get into some
+
+ align:start position:0%
+the system and then I'll get into some
+ 
+
+ align:start position:0%
+the system and then I'll get into some
+some different methods and what they
+
+ align:start position:0%
+some different methods and what they
+ 
+
+ align:start position:0%
+some different methods and what they
+tell us about about face perception okay
+
+ align:start position:0%
+tell us about about face perception okay
+ 
+
+ align:start position:0%
+tell us about about face perception okay
+so at the most general level we can ask
+
+ align:start position:0%
+so at the most general level we can ask
+ 
+
+ align:start position:0%
+so at the most general level we can ask
+whether human intelligence as people
+
+ align:start position:0%
+whether human intelligence as people
+ 
+
+ align:start position:0%
+whether human intelligence as people
+have been asking for centuries actually
+
+ align:start position:0%
+have been asking for centuries actually
+ 
+
+ align:start position:0%
+have been asking for centuries actually
+whether human intelligence is the
+
+ align:start position:0%
+whether human intelligence is the
+ 
+
+ align:start position:0%
+whether human intelligence is the
+product of a bunch of very special
+
+ align:start position:0%
+product of a bunch of very special
+ 
+
+ align:start position:0%
+product of a bunch of very special
+purpose components each optimized to
+
+ align:start position:0%
+purpose components each optimized to
+ 
+
+ align:start position:0%
+purpose components each optimized to
+solve a specific problem kind of like
+
+ align:start position:0%
+solve a specific problem kind of like
+ 
+
+ align:start position:0%
+solve a specific problem kind of like
+this device here where you have a saw
+
+ align:start position:0%
+this device here where you have a saw
+ 
+
+ align:start position:0%
+this device here where you have a saw
+for cutting wood scissors for cutting
+
+ align:start position:0%
+for cutting wood scissors for cutting
+ 
+
+ align:start position:0%
+for cutting wood scissors for cutting
+paper saws don't work that well on paper
+
+ align:start position:0%
+paper saws don't work that well on paper
+ 
+
+ align:start position:0%
+paper saws don't work that well on paper
+and scissors don't work that well on
+
+ align:start position:0%
+and scissors don't work that well on
+ 
+
+ align:start position:0%
+and scissors don't work that well on
+wood or whether human intelligence is a
+
+ align:start position:0%
+wood or whether human intelligence is a
+ 
+
+ align:start position:0%
+wood or whether human intelligence is a
+product of some were kind of generic
+
+ align:start position:0%
+product of some were kind of generic
+ 
+
+ align:start position:0%
+product of some were kind of generic
+all-purpose computational power that
+
+ align:start position:0%
+all-purpose computational power that
+ 
+
+ align:start position:0%
+all-purpose computational power that
+makes us generically smart without
+
+ align:start position:0%
+makes us generically smart without
+ 
+
+ align:start position:0%
+makes us generically smart without
+optimizing us for any particular tasks
+
+ align:start position:0%
+optimizing us for any particular tasks
+ 
+
+ align:start position:0%
+optimizing us for any particular tasks
+and just to foreshadow the answer as in
+
+ align:start position:0%
+and just to foreshadow the answer as in
+ 
+
+ align:start position:0%
+and just to foreshadow the answer as in
+all questions in psychology the answer
+
+ align:start position:0%
+all questions in psychology the answer
+ 
+
+ align:start position:0%
+all questions in psychology the answer
+is both but we'll do that in some detail
+
+ align:start position:0%
+is both but we'll do that in some detail
+ 
+
+ align:start position:0%
+is both but we'll do that in some detail
+before we get into that who cares and
+
+ align:start position:0%
+before we get into that who cares and
+ 
+
+ align:start position:0%
+before we get into that who cares and
+I'd say first of all this kind of macro
+
+ align:start position:0%
+I'd say first of all this kind of macro
+ 
+
+ align:start position:0%
+I'd say first of all this kind of macro
+level question about functional
+
+ align:start position:0%
+level question about functional
+ 
+
+ align:start position:0%
+level question about functional
+components of the human mind and brain
+
+ align:start position:0%
+components of the human mind and brain
+ 
+
+ align:start position:0%
+components of the human mind and brain
+matters for a bunch of reasons first of
+
+ align:start position:0%
+matters for a bunch of reasons first of
+ 
+
+ align:start position:0%
+matters for a bunch of reasons first of
+all I just think it's one of the most
+
+ align:start position:0%
+all I just think it's one of the most
+ 
+
+ align:start position:0%
+all I just think it's one of the most
+basic questions we can ask about about
+
+ align:start position:0%
+basic questions we can ask about about
+ 
+
+ align:start position:0%
+basic questions we can ask about about
+ourselves about who we are is to ask
+
+ align:start position:0%
+ourselves about who we are is to ask
+ 
+
+ align:start position:0%
+ourselves about who we are is to ask
+what the basic pieces are of our minds
+
+ align:start position:0%
+what the basic pieces are of our minds
+ 
+
+ align:start position:0%
+what the basic pieces are of our minds
+second more pragmatically this kind of
+
+ align:start position:0%
+second more pragmatically this kind of
+ 
+
+ align:start position:0%
+second more pragmatically this kind of
+divide and conquer research strategy has
+
+ align:start position:0%
+divide and conquer research strategy has
+ 
+
+ align:start position:0%
+divide and conquer research strategy has
+been effective in lots of different
+
+ align:start position:0%
+been effective in lots of different
+ 
+
+ align:start position:0%
+been effective in lots of different
+fields that are trying to understand a
+
+ align:start position:0%
+fields that are trying to understand a
+ 
+
+ align:start position:0%
+fields that are trying to understand a
+complex system what do you do with this
+
+ align:start position:0%
+complex system what do you do with this
+ 
+
+ align:start position:0%
+complex system what do you do with this
+incredibly complex system where you just
+
+ align:start position:0%
+incredibly complex system where you just
+ 
+
+ align:start position:0%
+incredibly complex system where you just
+can't even figure out how to get started
+
+ align:start position:0%
+can't even figure out how to get started
+ 
+
+ align:start position:0%
+can't even figure out how to get started
+well one sensible way to get started is
+
+ align:start position:0%
+well one sensible way to get started is
+ 
+
+ align:start position:0%
+well one sensible way to get started is
+first figure out what its pieces are and
+
+ align:start position:0%
+first figure out what its pieces are and
+ 
+
+ align:start position:0%
+first figure out what its pieces are and
+then maybe try to figure out how each of
+
+ align:start position:0%
+then maybe try to figure out how each of
+ 
+
+ align:start position:0%
+then maybe try to figure out how each of
+the pieces work and then maybe someday
+
+ align:start position:0%
+the pieces work and then maybe someday
+ 
+
+ align:start position:0%
+the pieces work and then maybe someday
+maybe not in my lifetime figure out how
+
+ align:start position:0%
+maybe not in my lifetime figure out how
+ 
+
+ align:start position:0%
+maybe not in my lifetime figure out how
+they all work together in some
+
+ align:start position:0%
+they all work together in some
+ 
+
+ align:start position:0%
+they all work together in some
+coordinated fashion and third somewhat
+
+ align:start position:0%
+coordinated fashion and third somewhat
+ 
+
+ align:start position:0%
+coordinated fashion and third somewhat
+more subtly of course we want to know
+
+ align:start position:0%
+more subtly of course we want to know
+ 
+
+ align:start position:0%
+more subtly of course we want to know
+not just what the pieces are but what
+
+ align:start position:0%
+not just what the pieces are but what
+ 
+
+ align:start position:0%
+not just what the pieces are but what
+the computations that are performed in
+
+ align:start position:0%
+the computations that are performed in
+ 
+
+ align:start position:0%
+the computations that are performed in
+each of those pieces and what the
+
+ align:start position:0%
+each of those pieces and what the
+ 
+
+ align:start position:0%
+each of those pieces and what the
+representations extracted
+
+ align:start position:0%
+representations extracted
+ 
+
+ align:start position:0%
+representations extracted
+pease are and I think even just a
+
+ align:start position:0%
+pease are and I think even just a
+ 
+
+ align:start position:0%
+pease are and I think even just a
+functional characterization of the scope
+
+ align:start position:0%
+functional characterization of the scope
+ 
+
+ align:start position:0%
+functional characterization of the scope
+of a particular brain region already
+
+ align:start position:0%
+of a particular brain region already
+ 
+
+ align:start position:0%
+of a particular brain region already
+gives us some important clues about the
+
+ align:start position:0%
+gives us some important clues about the
+ 
+
+ align:start position:0%
+gives us some important clues about the
+kinds of computations that go on there
+
+ align:start position:0%
+kinds of computations that go on there
+ 
+
+ align:start position:0%
+kinds of computations that go on there
+right so if we find that there's a part
+
+ align:start position:0%
+right so if we find that there's a part
+ 
+
+ align:start position:0%
+right so if we find that there's a part
+of the brain that's primarily involved
+
+ align:start position:0%
+of the brain that's primarily involved
+ 
+
+ align:start position:0%
+of the brain that's primarily involved
+in face recognition not in reading
+
+ align:start position:0%
+in face recognition not in reading
+ 
+
+ align:start position:0%
+in face recognition not in reading
+visually presented words recognizing
+
+ align:start position:0%
+visually presented words recognizing
+ 
+
+ align:start position:0%
+visually presented words recognizing
+scenes or recognizing objects that
+
+ align:start position:0%
+scenes or recognizing objects that
+ 
+
+ align:start position:0%
+scenes or recognizing objects that
+already gives us some clues about the
+
+ align:start position:0%
+already gives us some clues about the
+ 
+
+ align:start position:0%
+already gives us some clues about the
+kinds of computations that would be
+
+ align:start position:0%
+kinds of computations that would be
+ 
+
+ align:start position:0%
+kinds of computations that would be
+appropriate for that scope of tasks
+
+ align:start position:0%
+appropriate for that scope of tasks
+ 
+
+ align:start position:0%
+appropriate for that scope of tasks
+right so if you tried to write the code
+
+ align:start position:0%
+right so if you tried to write the code
+ 
+
+ align:start position:0%
+right so if you tried to write the code
+to do that you'd be writing very
+
+ align:start position:0%
+to do that you'd be writing very
+ 
+
+ align:start position:0%
+to do that you'd be writing very
+different code if it only had to do face
+
+ align:start position:0%
+different code if it only had to do face
+ 
+
+ align:start position:0%
+different code if it only had to do face
+recognition versus if it also had to be
+
+ align:start position:0%
+recognition versus if it also had to be
+ 
+
+ align:start position:0%
+recognition versus if it also had to be
+able to recognize words and scenes and
+
+ align:start position:0%
+able to recognize words and scenes and
+ 
+
+ align:start position:0%
+able to recognize words and scenes and
+objects presented visually ok so that's
+
+ align:start position:0%
+objects presented visually ok so that's
+ 
+
+ align:start position:0%
+objects presented visually ok so that's
+my list of the main reasons and of
+
+ align:start position:0%
+my list of the main reasons and of
+ 
+
+ align:start position:0%
+my list of the main reasons and of
+course serve heaps of different ways to
+
+ align:start position:0%
+course serve heaps of different ways to
+ 
+
+ align:start position:0%
+course serve heaps of different ways to
+investigate this question and I'll
+
+ align:start position:0%
+investigate this question and I'll
+ 
+
+ align:start position:0%
+investigate this question and I'll
+mention some of those in the second half
+
+ align:start position:0%
+mention some of those in the second half
+ 
+
+ align:start position:0%
+mention some of those in the second half
+but I want to start with Spearman who
+
+ align:start position:0%
+but I want to start with Spearman who
+ 
+
+ align:start position:0%
+but I want to start with Spearman who
+published a paper in 1904 in the
+
+ align:start position:0%
+published a paper in 1904 in the
+ 
+
+ align:start position:0%
+published a paper in 1904 in the
+American Journal of Psychology this
+
+ align:start position:0%
+American Journal of Psychology this
+ 
+
+ align:start position:0%
+American Journal of Psychology this
+article was sandwiched between a
+
+ align:start position:0%
+article was sandwiched between a
+ 
+
+ align:start position:0%
+article was sandwiched between a
+discussion of the soul and an article on
+
+ align:start position:0%
+discussion of the soul and an article on
+ 
+
+ align:start position:0%
+discussion of the soul and an article on
+the psychology of the English sparrow
+
+ align:start position:0%
+the psychology of the English sparrow
+ 
+
+ align:start position:0%
+the psychology of the English sparrow
+and in this article Spearman did the
+
+ align:start position:0%
+and in this article Spearman did the
+ 
+
+ align:start position:0%
+and in this article Spearman did the
+following low-tech but fascinating thing
+
+ align:start position:0%
+following low-tech but fascinating thing
+ 
+
+ align:start position:0%
+following low-tech but fascinating thing
+he tested a whole bunch of kids in two
+
+ align:start position:0%
+he tested a whole bunch of kids in two
+ 
+
+ align:start position:0%
+he tested a whole bunch of kids in two
+different schools on a wide variety of
+
+ align:start position:0%
+different schools on a wide variety of
+ 
+
+ align:start position:0%
+different schools on a wide variety of
+different tasks and this included
+
+ align:start position:0%
+different tasks and this included
+ 
+
+ align:start position:0%
+different tasks and this included
+scholastic achievement type things he
+
+ align:start position:0%
+scholastic achievement type things he
+ 
+
+ align:start position:0%
+scholastic achievement type things he
+got exam grades from each student and a
+
+ align:start position:0%
+got exam grades from each student and a
+ 
+
+ align:start position:0%
+got exam grades from each student and a
+bunch of different classes and he
+
+ align:start position:0%
+bunch of different classes and he
+ 
+
+ align:start position:0%
+bunch of different classes and he
+measured a whole bunch of other kinds of
+
+ align:start position:0%
+measured a whole bunch of other kinds of
+ 
+
+ align:start position:0%
+measured a whole bunch of other kinds of
+psychological abilities including some
+
+ align:start position:0%
+psychological abilities including some
+ 
+
+ align:start position:0%
+psychological abilities including some
+very kind of psycho physical perceptual
+
+ align:start position:0%
+very kind of psycho physical perceptual
+ 
+
+ align:start position:0%
+very kind of psycho physical perceptual
+discrimination abilities how well could
+
+ align:start position:0%
+discrimination abilities how well could
+ 
+
+ align:start position:0%
+discrimination abilities how well could
+people discriminate the Bryton the
+
+ align:start position:0%
+people discriminate the Bryton the
+ 
+
+ align:start position:0%
+people discriminate the Bryton the
+loudness of two different tones the
+
+ align:start position:0%
+loudness of two different tones the
+ 
+
+ align:start position:0%
+loudness of two different tones the
+brightness of two different flashes of
+
+ align:start position:0%
+brightness of two different flashes of
+ 
+
+ align:start position:0%
+brightness of two different flashes of
+white the weight of two different pieces
+
+ align:start position:0%
+white the weight of two different pieces
+ 
+
+ align:start position:0%
+white the weight of two different pieces
+of stuff and what he found well before I
+
+ align:start position:0%
+of stuff and what he found well before I
+ 
+
+ align:start position:0%
+of stuff and what he found well before I
+tell you what he found what do you what
+
+ align:start position:0%
+tell you what he found what do you what
+ 
+
+ align:start position:0%
+tell you what he found what do you what
+would you expect with this should we
+
+ align:start position:0%
+would you expect with this should we
+ 
+
+ align:start position:0%
+would you expect with this should we
+expect a correlation between your
+
+ align:start position:0%
+expect a correlation between your
+ 
+
+ align:start position:0%
+expect a correlation between your
+ability to discriminate two different
+
+ align:start position:0%
+ability to discriminate two different
+ 
+
+ align:start position:0%
+ability to discriminate two different
+loudness ha's and say your math score in
+
+ align:start position:0%
+loudness ha's and say your math score in
+ 
+
+ align:start position:0%
+loudness ha's and say your math score in
+grade five on a math exam Germans main
+
+ align:start position:0%
+grade five on a math exam Germans main
+ 
+
+ align:start position:0%
+grade five on a math exam Germans main
+result is that most pairs of tasks were
+
+ align:start position:0%
+result is that most pairs of tasks were
+ 
+
+ align:start position:0%
+result is that most pairs of tasks were
+correlated with each other that is if
+
+ align:start position:0%
+correlated with each other that is if
+ 
+
+ align:start position:0%
+correlated with each other that is if
+you were good at one you're good at the
+
+ align:start position:0%
+you were good at one you're good at the
+ 
+
+ align:start position:0%
+you were good at one you're good at the
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+even tasks that seemingly have very
+
+ align:start position:0%
+even tasks that seemingly have very
+ 
+
+ align:start position:0%
+even tasks that seemingly have very
+little to do with each other and this is
+
+ align:start position:0%
+little to do with each other and this is
+ 
+
+ align:start position:0%
+little to do with each other and this is
+the basis of the whole idea of G which
+
+ align:start position:0%
+the basis of the whole idea of G which
+ 
+
+ align:start position:0%
+the basis of the whole idea of G which
+is the general factor which is what led
+
+ align:start position:0%
+is the general factor which is what led
+ 
+
+ align:start position:0%
+is the general factor which is what led
+to the whole idea of IQ and IQ testing
+
+ align:start position:0%
+to the whole idea of IQ and IQ testing
+ 
+
+ align:start position:0%
+to the whole idea of IQ and IQ testing
+and in America we're very uptight about
+
+ align:start position:0%
+and in America we're very uptight about
+ 
+
+ align:start position:0%
+and in America we're very uptight about
+the idea of IQ Brits don't seem to have
+
+ align:start position:0%
+the idea of IQ Brits don't seem to have
+ 
+
+ align:start position:0%
+the idea of IQ Brits don't seem to have
+a problem with this idea they're very
+
+ align:start position:0%
+a problem with this idea they're very
+ 
+
+ align:start position:0%
+a problem with this idea they're very
+enthusiastic about the idea and always
+
+ align:start position:0%
+enthusiastic about the idea and always
+ 
+
+ align:start position:0%
+enthusiastic about the idea and always
+have been but um they aside from all the
+
+ align:start position:0%
+have been but um they aside from all the
+ 
+
+ align:start position:0%
+have been but um they aside from all the
+social uses and misuses of IQ tests the
+
+ align:start position:0%
+social uses and misuses of IQ tests the
+ 
+
+ align:start position:0%
+social uses and misuses of IQ tests the
+point is there's actually a deep
+
+ align:start position:0%
+point is there's actually a deep
+ 
+
+ align:start position:0%
+point is there's actually a deep
+discovery about psychology that Spearman
+
+ align:start position:0%
+discovery about psychology that Spearman
+ 
+
+ align:start position:0%
+discovery about psychology that Spearman
+made from the fact that all of these
+
+ align:start position:0%
+made from the fact that all of these
+ 
+
+ align:start position:0%
+made from the fact that all of these
+tasks were correlated with each other he
+
+ align:start position:0%
+tasks were correlated with each other he
+ 
+
+ align:start position:0%
+tasks were correlated with each other he
+didn't know what it was kind of like
+
+ align:start position:0%
+didn't know what it was kind of like
+ 
+
+ align:start position:0%
+didn't know what it was kind of like
+Gregor Mendel inferring genes without
+
+ align:start position:0%
+Gregor Mendel inferring genes without
+ 
+
+ align:start position:0%
+Gregor Mendel inferring genes without
+knowing anything about molecular biology
+
+ align:start position:0%
+knowing anything about molecular biology
+ 
+
+ align:start position:0%
+knowing anything about molecular biology
+Spearman just inferred there's something
+
+ align:start position:0%
+Spearman just inferred there's something
+ 
+
+ align:start position:0%
+Spearman just inferred there's something
+general about the human intellect such
+
+ align:start position:0%
+general about the human intellect such
+ 
+
+ align:start position:0%
+general about the human intellect such
+that there are these strong correlations
+
+ align:start position:0%
+that there are these strong correlations
+ 
+
+ align:start position:0%
+that there are these strong correlations
+about town across tasks okay so that's G
+
+ align:start position:0%
+about town across tasks okay so that's G
+ 
+
+ align:start position:0%
+about town across tasks okay so that's G
+but less well known about Spearman's
+
+ align:start position:0%
+but less well known about Spearman's
+ 
+
+ align:start position:0%
+but less well known about Spearman's
+work as he also talked about the
+
+ align:start position:0%
+work as he also talked about the
+ 
+
+ align:start position:0%
+work as he also talked about the
+specific factor yes and s was the fact
+
+ align:start position:0%
+specific factor yes and s was the fact
+ 
+
+ align:start position:0%
+specific factor yes and s was the fact
+that although the broad result of his
+
+ align:start position:0%
+that although the broad result of his
+ 
+
+ align:start position:0%
+that although the broad result of his
+experiments was that most pairs of tasks
+
+ align:start position:0%
+experiments was that most pairs of tasks
+ 
+
+ align:start position:0%
+experiments was that most pairs of tasks
+were correlated there were some tasks
+
+ align:start position:0%
+were correlated there were some tasks
+ 
+
+ align:start position:0%
+were correlated there were some tasks
+that weren't so strongly correlated with
+
+ align:start position:0%
+that weren't so strongly correlated with
+ 
+
+ align:start position:0%
+that weren't so strongly correlated with
+others and that you could factor those
+
+ align:start position:0%
+others and that you could factor those
+ 
+
+ align:start position:0%
+others and that you could factor those
+out and discover some mental abilities
+
+ align:start position:0%
+out and discover some mental abilities
+ 
+
+ align:start position:0%
+out and discover some mental abilities
+that weren't just you know broadly
+
+ align:start position:0%
+that weren't just you know broadly
+ 
+
+ align:start position:0%
+that weren't just you know broadly
+shared across subjects and I think this
+
+ align:start position:0%
+shared across subjects and I think this
+ 
+
+ align:start position:0%
+shared across subjects and I think this
+is kind of foreshadows everything that
+
+ align:start position:0%
+is kind of foreshadows everything that
+ 
+
+ align:start position:0%
+is kind of foreshadows everything that
+we see with functional MRI there's a lot
+
+ align:start position:0%
+we see with functional MRI there's a lot
+ 
+
+ align:start position:0%
+we see with functional MRI there's a lot
+of specific essence and there's also
+
+ align:start position:0%
+of specific essence and there's also
+ 
+
+ align:start position:0%
+of specific essence and there's also
+some G and you can see those in
+
+ align:start position:0%
+some G and you can see those in
+ 
+
+ align:start position:0%
+some G and you can see those in
+different brain regions as I will detail
+
+ align:start position:0%
+different brain regions as I will detail
+ 
+
+ align:start position:0%
+different brain regions as I will detail
+next another method was invented by
+
+ align:start position:0%
+next another method was invented by
+ 
+
+ align:start position:0%
+next another method was invented by
+Franz Joseph gall and he argued that
+
+ align:start position:0%
+Franz Joseph gall and he argued that
+ 
+
+ align:start position:0%
+Franz Joseph gall and he argued that
+they're distinct mental faculties that
+
+ align:start position:0%
+they're distinct mental faculties that
+ 
+
+ align:start position:0%
+they're distinct mental faculties that
+live in different parts of the brain
+
+ align:start position:0%
+live in different parts of the brain
+ 
+
+ align:start position:0%
+live in different parts of the brain
+right which i think is more or less
+
+ align:start position:0%
+right which i think is more or less
+ 
+
+ align:start position:0%
+right which i think is more or less
+right as I'll argue but you know Paul
+
+ align:start position:0%
+right as I'll argue but you know Paul
+ 
+
+ align:start position:0%
+right as I'll argue but you know Paul
+lived in the 1700s and he didn't have an
+
+ align:start position:0%
+lived in the 1700s and he didn't have an
+ 
+
+ align:start position:0%
+lived in the 1700s and he didn't have an
+MRI machine so he did the best he could
+
+ align:start position:0%
+MRI machine so he did the best he could
+ 
+
+ align:start position:0%
+MRI machine so he did the best he could
+which wasn't so hot he invented the
+
+ align:start position:0%
+which wasn't so hot he invented the
+ 
+
+ align:start position:0%
+which wasn't so hot he invented the
+infamous method of phrenology he felt
+
+ align:start position:0%
+infamous method of phrenology he felt
+ 
+
+ align:start position:0%
+infamous method of phrenology he felt
+the bumps on the skull and tried to
+
+ align:start position:0%
+the bumps on the skull and tried to
+ 
+
+ align:start position:0%
+the bumps on the skull and tried to
+relate those to specific abilities of
+
+ align:start position:0%
+relate those to specific abilities of
+ 
+
+ align:start position:0%
+relate those to specific abilities of
+different individuals and from this
+
+ align:start position:0%
+different individuals and from this
+ 
+
+ align:start position:0%
+different individuals and from this
+inferred
+
+ align:start position:0%
+inferred
+ 
+
+ align:start position:0%
+inferred
+27 mental faculties my favorites are
+
+ align:start position:0%
+27 mental faculties my favorites are
+ 
+
+ align:start position:0%
+27 mental faculties my favorites are
+amativeness filial piety and veneration
+
+ align:start position:0%
+amativeness filial piety and veneration
+ 
+
+ align:start position:0%
+amativeness filial piety and veneration
+and so you know there's a kernel of the
+
+ align:start position:0%
+and so you know there's a kernel of the
+ 
+
+ align:start position:0%
+and so you know there's a kernel of the
+right idea but kind of the wrong method
+
+ align:start position:0%
+right idea but kind of the wrong method
+ 
+
+ align:start position:0%
+right idea but kind of the wrong method
+and another method that was a you know
+
+ align:start position:0%
+and another method that was a you know
+ 
+
+ align:start position:0%
+and another method that was a you know
+very early one was the method of
+
+ align:start position:0%
+very early one was the method of
+ 
+
+ align:start position:0%
+very early one was the method of
+studying the loss of specific mental
+
+ align:start position:0%
+studying the loss of specific mental
+ 
+
+ align:start position:0%
+studying the loss of specific mental
+abilities after brain damage and so
+
+ align:start position:0%
+abilities after brain damage and so
+ 
+
+ align:start position:0%
+abilities after brain damage and so
+florals whose often credited as being
+
+ align:start position:0%
+florals whose often credited as being
+ 
+
+ align:start position:0%
+florals whose often credited as being
+the first experimental neuroscientist
+
+ align:start position:0%
+the first experimental neuroscientist
+ 
+
+ align:start position:0%
+the first experimental neuroscientist
+went around making lesions in pigeons
+
+ align:start position:0%
+went around making lesions in pigeons
+ 
+
+ align:start position:0%
+went around making lesions in pigeons
+and rabbits and didn't and then testing
+
+ align:start position:0%
+and rabbits and didn't and then testing
+ 
+
+ align:start position:0%
+and rabbits and didn't and then testing
+them on various things and he didn't
+
+ align:start position:0%
+them on various things and he didn't
+ 
+
+ align:start position:0%
+them on various things and he didn't
+really find much difference in what
+
+ align:start position:0%
+really find much difference in what
+ 
+
+ align:start position:0%
+really find much difference in what
+parts of the brain he took out for their
+
+ align:start position:0%
+parts of the brain he took out for their
+ 
+
+ align:start position:0%
+parts of the brain he took out for their
+mental abilities maybe that's because he
+
+ align:start position:0%
+mental abilities maybe that's because he
+ 
+
+ align:start position:0%
+mental abilities maybe that's because he
+wasn't such a hot experimental you know
+
+ align:start position:0%
+wasn't such a hot experimental you know
+ 
+
+ align:start position:0%
+wasn't such a hot experimental you know
+he didn't have great experimental
+
+ align:start position:0%
+he didn't have great experimental
+ 
+
+ align:start position:0%
+he didn't have great experimental
+methods in any case he argued that all
+
+ align:start position:0%
+methods in any case he argued that all
+ 
+
+ align:start position:0%
+methods in any case he argued that all
+sensory and volitional faculties exist
+
+ align:start position:0%
+sensory and volitional faculties exist
+ 
+
+ align:start position:0%
+sensory and volitional faculties exist
+in the cerebral hemispheres and must be
+
+ align:start position:0%
+in the cerebral hemispheres and must be
+ 
+
+ align:start position:0%
+in the cerebral hemispheres and must be
+regarded as occupying concurrently the
+
+ align:start position:0%
+regarded as occupying concurrently the
+ 
+
+ align:start position:0%
+regarded as occupying concurrently the
+same seat in those structures right in
+
+ align:start position:0%
+same seat in those structures right in
+ 
+
+ align:start position:0%
+same seat in those structures right in
+other words everything is on top of
+
+ align:start position:0%
+other words everything is on top of
+ 
+
+ align:start position:0%
+other words everything is on top of
+everything else in the brain okay so
+
+ align:start position:0%
+everything else in the brain okay so
+ 
+
+ align:start position:0%
+everything else in the brain okay so
+that was a sort of you know dominant
+
+ align:start position:0%
+that was a sort of you know dominant
+ 
+
+ align:start position:0%
+that was a sort of you know dominant
+view for a while people thought gold was
+
+ align:start position:0%
+view for a while people thought gold was
+ 
+
+ align:start position:0%
+view for a while people thought gold was
+kind of a crackpot even though he wrote
+
+ align:start position:0%
+kind of a crackpot even though he wrote
+ 
+
+ align:start position:0%
+kind of a crackpot even though he wrote
+very popular books and went around here
+
+ align:start position:0%
+very popular books and went around here
+ 
+
+ align:start position:0%
+very popular books and went around here
+up giving popular lectures at huge
+
+ align:start position:0%
+up giving popular lectures at huge
+ 
+
+ align:start position:0%
+up giving popular lectures at huge
+numbers of people attended the
+
+ align:start position:0%
+numbers of people attended the
+ 
+
+ align:start position:0%
+numbers of people attended the
+respectable intellectual society didn't
+
+ align:start position:0%
+respectable intellectual society didn't
+ 
+
+ align:start position:0%
+respectable intellectual society didn't
+take him seriously in fact the whole
+
+ align:start position:0%
+take him seriously in fact the whole
+ 
+
+ align:start position:0%
+take him seriously in fact the whole
+idea of localization of function wasn't
+
+ align:start position:0%
+idea of localization of function wasn't
+ 
+
+ align:start position:0%
+idea of localization of function wasn't
+taken seriously until Paul Broca a
+
+ align:start position:0%
+taken seriously until Paul Broca a
+ 
+
+ align:start position:0%
+taken seriously until Paul Broca a
+member of the the French Academy stood
+
+ align:start position:0%
+member of the the French Academy stood
+ 
+
+ align:start position:0%
+member of the the French Academy stood
+up in front of the Society of
+
+ align:start position:0%
+up in front of the Society of
+ 
+
+ align:start position:0%
+up in front of the Society of
+anthropology in Paris in 1861 and
+
+ align:start position:0%
+anthropology in Paris in 1861 and
+ 
+
+ align:start position:0%
+anthropology in Paris in 1861 and
+announced that the left frontal lobe is
+
+ align:start position:0%
+announced that the left frontal lobe is
+ 
+
+ align:start position:0%
+announced that the left frontal lobe is
+the seat of speech and this was based on
+
+ align:start position:0%
+the seat of speech and this was based on
+ 
+
+ align:start position:0%
+the seat of speech and this was based on
+his patient tan whose brain is shown
+
+ align:start position:0%
+his patient tan whose brain is shown
+ 
+
+ align:start position:0%
+his patient tan whose brain is shown
+here tan was named tan because that was
+
+ align:start position:0%
+here tan was named tan because that was
+ 
+
+ align:start position:0%
+here tan was named tan because that was
+all he could say after damage to his
+
+ align:start position:0%
+all he could say after damage to his
+ 
+
+ align:start position:0%
+all he could say after damage to his
+left inferior frontal lobe and Broca
+
+ align:start position:0%
+left inferior frontal lobe and Broca
+ 
+
+ align:start position:0%
+left inferior frontal lobe and Broca
+pointed out that tan had lots of other
+
+ align:start position:0%
+pointed out that tan had lots of other
+ 
+
+ align:start position:0%
+pointed out that tan had lots of other
+mental faculties preserved and it was
+
+ align:start position:0%
+mental faculties preserved and it was
+ 
+
+ align:start position:0%
+mental faculties preserved and it was
+simply speech that was disrupted and
+
+ align:start position:0%
+simply speech that was disrupted and
+ 
+
+ align:start position:0%
+simply speech that was disrupted and
+from this was kind of one of the first
+
+ align:start position:0%
+from this was kind of one of the first
+ 
+
+ align:start position:0%
+from this was kind of one of the first
+respectable people to argue for
+
+ align:start position:0%
+respectable people to argue for
+ 
+
+ align:start position:0%
+respectable people to argue for
+localization of function okay so this
+
+ align:start position:0%
+localization of function okay so this
+ 
+
+ align:start position:0%
+localization of function okay so this
+this research program goes on and by the
+
+ align:start position:0%
+this research program goes on and by the
+ 
+
+ align:start position:0%
+this research program goes on and by the
+end of the 20th century there's pretty
+
+ align:start position:0%
+end of the 20th century there's pretty
+ 
+
+ align:start position:0%
+end of the 20th century there's pretty
+much agreement that basic sensory and
+
+ align:start position:0%
+much agreement that basic sensory and
+ 
+
+ align:start position:0%
+much agreement that basic sensory and
+motor functions do exhibit localization
+
+ align:start position:0%
+motor functions do exhibit localization
+ 
+
+ align:start position:0%
+motor functions do exhibit localization
+of function in the brain there are
+
+ align:start position:0%
+of function in the brain there are
+ 
+
+ align:start position:0%
+of function in the brain there are
+different regions for basic visual
+
+ align:start position:0%
+different regions for basic visual
+ 
+
+ align:start position:0%
+different regions for basic visual
+processing auditory
+
+ align:start position:0%
+processing auditory
+ 
+
+ align:start position:0%
+processing auditory
+processing and so forth and that was no
+
+ align:start position:0%
+processing and so forth and that was no
+ 
+
+ align:start position:0%
+processing and so forth and that was no
+longer controversial but the whole
+
+ align:start position:0%
+longer controversial but the whole
+ 
+
+ align:start position:0%
+longer controversial but the whole
+question of whether higher level mental
+
+ align:start position:0%
+question of whether higher level mental
+ 
+
+ align:start position:0%
+question of whether higher level mental
+functions were localized in distinct
+
+ align:start position:0%
+functions were localized in distinct
+ 
+
+ align:start position:0%
+functions were localized in distinct
+parts of the brain was controversial
+
+ align:start position:0%
+parts of the brain was controversial
+ 
+
+ align:start position:0%
+parts of the brain was controversial
+then and remains controversial now and
+
+ align:start position:0%
+then and remains controversial now and
+ 
+
+ align:start position:0%
+then and remains controversial now and
+so it method I'll focus on is functional
+
+ align:start position:0%
+so it method I'll focus on is functional
+ 
+
+ align:start position:0%
+so it method I'll focus on is functional
+MRI because I think it's played a huge
+
+ align:start position:0%
+MRI because I think it's played a huge
+ 
+
+ align:start position:0%
+MRI because I think it's played a huge
+role in addressing this question at this
+
+ align:start position:0%
+role in addressing this question at this
+ 
+
+ align:start position:0%
+role in addressing this question at this
+kind of macroscopic level and I think
+
+ align:start position:0%
+kind of macroscopic level and I think
+ 
+
+ align:start position:0%
+kind of macroscopic level and I think
+you guys know what an MRI machine is in
+
+ align:start position:0%
+you guys know what an MRI machine is in
+ 
+
+ align:start position:0%
+you guys know what an MRI machine is in
+case anybody's been on Mars for a while
+
+ align:start position:0%
+case anybody's been on Mars for a while
+ 
+
+ align:start position:0%
+case anybody's been on Mars for a while
+it the important part is it's measure is
+
+ align:start position:0%
+it the important part is it's measure is
+ 
+
+ align:start position:0%
+it the important part is it's measure is
+a very indirect measure of neural
+
+ align:start position:0%
+a very indirect measure of neural
+ 
+
+ align:start position:0%
+a very indirect measure of neural
+activity by way of a long causal chain
+
+ align:start position:0%
+activity by way of a long causal chain
+ 
+
+ align:start position:0%
+activity by way of a long causal chain
+neurons fire you incur metabolic cost
+
+ align:start position:0%
+neurons fire you incur metabolic cost
+ 
+
+ align:start position:0%
+neurons fire you incur metabolic cost
+and blood flow changes to that region
+
+ align:start position:0%
+and blood flow changes to that region
+ 
+
+ align:start position:0%
+and blood flow changes to that region
+blood flow increase more than
+
+ align:start position:0%
+blood flow increase more than
+ 
+
+ align:start position:0%
+blood flow increase more than
+compensates for oxygen use producing a
+
+ align:start position:0%
+compensates for oxygen use producing a
+ 
+
+ align:start position:0%
+compensates for oxygen use producing a
+local decrease rather than the expected
+
+ align:start position:0%
+local decrease rather than the expected
+ 
+
+ align:start position:0%
+local decrease rather than the expected
+increase in deoxyhemoglobin relative to
+
+ align:start position:0%
+increase in deoxyhemoglobin relative to
+ 
+
+ align:start position:0%
+increase in deoxyhemoglobin relative to
+oxyhemoglobin those two are magnetically
+
+ align:start position:0%
+oxyhemoglobin those two are magnetically
+ 
+
+ align:start position:0%
+oxyhemoglobin those two are magnetically
+different that's what the MRI machine
+
+ align:start position:0%
+different that's what the MRI machine
+ 
+
+ align:start position:0%
+different that's what the MRI machine
+detects it's very indirect so it's
+
+ align:start position:0%
+detects it's very indirect so it's
+ 
+
+ align:start position:0%
+detects it's very indirect so it's
+remarkable it works as well as it does
+
+ align:start position:0%
+remarkable it works as well as it does
+ 
+
+ align:start position:0%
+remarkable it works as well as it does
+and it's currently the best non-invasive
+
+ align:start position:0%
+and it's currently the best non-invasive
+ 
+
+ align:start position:0%
+and it's currently the best non-invasive
+method we have in humans in terms of
+
+ align:start position:0%
+method we have in humans in terms of
+ 
+
+ align:start position:0%
+method we have in humans in terms of
+both spatial and having both spatial
+
+ align:start position:0%
+both spatial and having both spatial
+ 
+
+ align:start position:0%
+both spatial and having both spatial
+while spatial resolution not temporal
+
+ align:start position:0%
+while spatial resolution not temporal
+ 
+
+ align:start position:0%
+while spatial resolution not temporal
+resolution okay so and many of you are
+
+ align:start position:0%
+resolution okay so and many of you are
+ 
+
+ align:start position:0%
+resolution okay so and many of you are
+already diving into the details of some
+
+ align:start position:0%
+already diving into the details of some
+ 
+
+ align:start position:0%
+already diving into the details of some
+of the data we collected but in case
+
+ align:start position:0%
+of the data we collected but in case
+ 
+
+ align:start position:0%
+of the data we collected but in case
+you're on other projects and are coming
+
+ align:start position:0%
+you're on other projects and are coming
+ 
+
+ align:start position:0%
+you're on other projects and are coming
+from other fields the basic format of
+
+ align:start position:0%
+from other fields the basic format of
+ 
+
+ align:start position:0%
+from other fields the basic format of
+the data in a typical functional MRI
+
+ align:start position:0%
+the data in a typical functional MRI
+ 
+
+ align:start position:0%
+the data in a typical functional MRI
+study is you have tens of thousands of
+
+ align:start position:0%
+study is you have tens of thousands of
+ 
+
+ align:start position:0%
+study is you have tens of thousands of
+three-dimensional pixels or voxels that
+
+ align:start position:0%
+three-dimensional pixels or voxels that
+ 
+
+ align:start position:0%
+three-dimensional pixels or voxels that
+you scan and those typically you sample
+
+ align:start position:0%
+you scan and those typically you sample
+ 
+
+ align:start position:0%
+you scan and those typically you sample
+a whole set once every two seconds or so
+
+ align:start position:0%
+a whole set once every two seconds or so
+ 
+
+ align:start position:0%
+a whole set once every two seconds or so
+you can push it and do it every second
+
+ align:start position:0%
+you can push it and do it every second
+ 
+
+ align:start position:0%
+you can push it and do it every second
+or less under special circumstances you
+
+ align:start position:0%
+or less under special circumstances you
+ 
+
+ align:start position:0%
+or less under special circumstances you
+can have more voxels by sampling at
+
+ align:start position:0%
+can have more voxels by sampling at
+ 
+
+ align:start position:0%
+can have more voxels by sampling at
+higher resolution but that's ballpark of
+
+ align:start position:0%
+higher resolution but that's ballpark of
+ 
+
+ align:start position:0%
+higher resolution but that's ballpark of
+the format of the kind of movie you can
+
+ align:start position:0%
+the format of the kind of movie you can
+ 
+
+ align:start position:0%
+the format of the kind of movie you can
+get of brain activity okay so a few
+
+ align:start position:0%
+get of brain activity okay so a few
+ 
+
+ align:start position:0%
+get of brain activity okay so a few
+things about the the method and its
+
+ align:start position:0%
+things about the the method and its
+ 
+
+ align:start position:0%
+things about the the method and its
+limitations because they're really
+
+ align:start position:0%
+limitations because they're really
+ 
+
+ align:start position:0%
+limitations because they're really
+important in terms of what you can learn
+
+ align:start position:0%
+important in terms of what you can learn
+ 
+
+ align:start position:0%
+important in terms of what you can learn
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+functional MRI and what you can't so
+
+ align:start position:0%
+functional MRI and what you can't so
+ 
+
+ align:start position:0%
+functional MRI and what you can't so
+first of all this is a timeline my
+
+ align:start position:0%
+first of all this is a timeline my
+ 
+
+ align:start position:0%
+first of all this is a timeline my
+x-axis even though it's invisible is
+
+ align:start position:0%
+x-axis even though it's invisible is
+ 
+
+ align:start position:0%
+x-axis even though it's invisible is
+time in seconds and so if you imagine
+
+ align:start position:0%
+time in seconds and so if you imagine
+ 
+
+ align:start position:0%
+time in seconds and so if you imagine
+looking at v1 and presenting a brief say
+
+ align:start position:0%
+looking at v1 and presenting a brief say
+ 
+
+ align:start position:0%
+looking at v1 and presenting a brief say
+tenth of a second high contrast flash of
+
+ align:start position:0%
+tenth of a second high contrast flash of
+ 
+
+ align:start position:0%
+tenth of a second high contrast flash of
+a checkerboard what we know from
+
+ align:start position:0%
+a checkerboard what we know from
+ 
+
+ align:start position:0%
+a checkerboard what we know from
+neurophysiology is that neurons fire
+
+ align:start position:0%
+neurophysiology is that neurons fire
+ 
+
+ align:start position:0%
+neurophysiology is that neurons fire
+within a hundred milliseconds of
+
+ align:start position:0%
+within a hundred milliseconds of
+ 
+
+ align:start position:0%
+within a hundred milliseconds of
+official onset the information gets
+
+ align:start position:0%
+official onset the information gets
+ 
+
+ align:start position:0%
+official onset the information gets
+right up there really fast the bold
+
+ align:start position:0%
+right up there really fast the bold
+ 
+
+ align:start position:0%
+right up there really fast the bold
+which stands for blood oxygenation level
+
+ align:start position:0%
+which stands for blood oxygenation level
+ 
+
+ align:start position:0%
+which stands for blood oxygenation level
+dependent or functional MRI response is
+
+ align:start position:0%
+dependent or functional MRI response is
+ 
+
+ align:start position:0%
+dependent or functional MRI response is
+way lagged behind this okay so the
+
+ align:start position:0%
+way lagged behind this okay so the
+ 
+
+ align:start position:0%
+way lagged behind this okay so the
+neurons are firing way over here in this
+
+ align:start position:0%
+neurons are firing way over here in this
+ 
+
+ align:start position:0%
+neurons are firing way over here in this
+graph essentially at time zero a tenth
+
+ align:start position:0%
+graph essentially at time zero a tenth
+ 
+
+ align:start position:0%
+graph essentially at time zero a tenth
+of a second but the MRI response is six
+
+ align:start position:0%
+of a second but the MRI response is six
+ 
+
+ align:start position:0%
+of a second but the MRI response is six
+seconds later okay
+
+ align:start position:0%
+seconds later okay
+ 
+
+ align:start position:0%
+seconds later okay
+so it's really slow and that has a bunch
+
+ align:start position:0%
+so it's really slow and that has a bunch
+ 
+
+ align:start position:0%
+so it's really slow and that has a bunch
+of implications about what we can and
+
+ align:start position:0%
+of implications about what we can and
+ 
+
+ align:start position:0%
+of implications about what we can and
+cannot learn from it so first of all
+
+ align:start position:0%
+cannot learn from it so first of all
+ 
+
+ align:start position:0%
+cannot learn from it so first of all
+because it's so slow we we can't resolve
+
+ align:start position:0%
+because it's so slow we we can't resolve
+ 
+
+ align:start position:0%
+because it's so slow we we can't resolve
+the steps and a computation for fast
+
+ align:start position:0%
+the steps and a computation for fast
+ 
+
+ align:start position:0%
+the steps and a computation for fast
+systems like vision and hearing and
+
+ align:start position:0%
+systems like vision and hearing and
+ 
+
+ align:start position:0%
+systems like vision and hearing and
+language understanding systems for which
+
+ align:start position:0%
+language understanding systems for which
+ 
+
+ align:start position:0%
+language understanding systems for which
+we have dedicated machinery that's
+
+ align:start position:0%
+we have dedicated machinery that's
+ 
+
+ align:start position:0%
+we have dedicated machinery that's
+highly efficient where you can recognize
+
+ align:start position:0%
+highly efficient where you can recognize
+ 
+
+ align:start position:0%
+highly efficient where you can recognize
+the gist of a scene within a quarter of
+
+ align:start position:0%
+the gist of a scene within a quarter of
+ 
+
+ align:start position:0%
+the gist of a scene within a quarter of
+a second of when it flashes on a screen
+
+ align:start position:0%
+a second of when it flashes on a screen
+ 
+
+ align:start position:0%
+a second of when it flashes on a screen
+in front of you that and and similarly
+
+ align:start position:0%
+in front of you that and and similarly
+ 
+
+ align:start position:0%
+in front of you that and and similarly
+you understand the meaning of a sentence
+
+ align:start position:0%
+you understand the meaning of a sentence
+ 
+
+ align:start position:0%
+you understand the meaning of a sentence
+so rapidly that you've already parsed
+
+ align:start position:0%
+so rapidly that you've already parsed
+ 
+
+ align:start position:0%
+so rapidly that you've already parsed
+much of the sentence you know well
+
+ align:start position:0%
+much of the sentence you know well
+ 
+
+ align:start position:0%
+much of the sentence you know well
+before the sentence is over
+
+ align:start position:0%
+before the sentence is over
+ 
+
+ align:start position:0%
+before the sentence is over
+right so these are extremely efficient
+
+ align:start position:0%
+right so these are extremely efficient
+ 
+
+ align:start position:0%
+right so these are extremely efficient
+rapid mental processes that means the
+
+ align:start position:0%
+rapid mental processes that means the
+ 
+
+ align:start position:0%
+rapid mental processes that means the
+component steps in those mental
+
+ align:start position:0%
+component steps in those mental
+ 
+
+ align:start position:0%
+component steps in those mental
+processes happen over ten or a few tens
+
+ align:start position:0%
+processes happen over ten or a few tens
+ 
+
+ align:start position:0%
+processes happen over ten or a few tens
+of milliseconds and we're off way off in
+
+ align:start position:0%
+of milliseconds and we're off way off in
+ 
+
+ align:start position:0%
+of milliseconds and we're off way off in
+temporal resolution with functional MRI
+
+ align:start position:0%
+temporal resolution with functional MRI
+ 
+
+ align:start position:0%
+temporal resolution with functional MRI
+all of those things are squashed
+
+ align:start position:0%
+all of those things are squashed
+ 
+
+ align:start position:0%
+all of those things are squashed
+together on top of each other that's a
+
+ align:start position:0%
+together on top of each other that's a
+ 
+
+ align:start position:0%
+together on top of each other that's a
+drag that's just life we can't see those
+
+ align:start position:0%
+drag that's just life we can't see those
+ 
+
+ align:start position:0%
+drag that's just life we can't see those
+individual component steps with
+
+ align:start position:0%
+individual component steps with
+ 
+
+ align:start position:0%
+individual component steps with
+functional MRI the second thing is that
+
+ align:start position:0%
+functional MRI the second thing is that
+ 
+
+ align:start position:0%
+functional MRI the second thing is that
+the spatial resolution it's the best
+
+ align:start position:0%
+the spatial resolution it's the best
+ 
+
+ align:start position:0%
+the spatial resolution it's the best
+that we have in humans non-invasively
+
+ align:start position:0%
+that we have in humans non-invasively
+ 
+
+ align:start position:0%
+that we have in humans non-invasively
+right now but it's absolutely awful
+
+ align:start position:0%
+right now but it's absolutely awful
+ 
+
+ align:start position:0%
+right now but it's absolutely awful
+compared to what you can do in animals
+
+ align:start position:0%
+compared to what you can do in animals
+ 
+
+ align:start position:0%
+compared to what you can do in animals
+so I miss Jim DeCarlo's talk yesterday
+
+ align:start position:0%
+so I miss Jim DeCarlo's talk yesterday
+ 
+
+ align:start position:0%
+so I miss Jim DeCarlo's talk yesterday
+but um but those methods are spectacular
+
+ align:start position:0%
+but um but those methods are spectacular
+ 
+
+ align:start position:0%
+but um but those methods are spectacular
+you can record from individual neurons
+
+ align:start position:0%
+you can record from individual neurons
+ 
+
+ align:start position:0%
+you can record from individual neurons
+record their precise activity with
+
+ align:start position:0%
+record their precise activity with
+ 
+
+ align:start position:0%
+record their precise activity with
+beautiful
+
+ align:start position:0%
+beautiful
+ 
+
+ align:start position:0%
+beautiful
+information in contrast functional MRI
+
+ align:start position:0%
+information in contrast functional MRI
+ 
+
+ align:start position:0%
+information in contrast functional MRI
+is like you know the dark ages we have
+
+ align:start position:0%
+is like you know the dark ages we have
+ 
+
+ align:start position:0%
+is like you know the dark ages we have
+typically hundreds of thousands of
+
+ align:start position:0%
+typically hundreds of thousands of
+ 
+
+ align:start position:0%
+typically hundreds of thousands of
+neurons in each voxel ok so the real
+
+ align:start position:0%
+neurons in each voxel ok so the real
+ 
+
+ align:start position:0%
+neurons in each voxel ok so the real
+miracle of functional MRI is we ever see
+
+ align:start position:0%
+miracle of functional MRI is we ever see
+ 
+
+ align:start position:0%
+miracle of functional MRI is we ever see
+anything at all rather than just garbage
+
+ align:start position:0%
+anything at all rather than just garbage
+ 
+
+ align:start position:0%
+anything at all rather than just garbage
+because you're summing over so many
+
+ align:start position:0%
+because you're summing over so many
+ 
+
+ align:start position:0%
+because you're summing over so many
+neurons at once and it's just a lucky
+
+ align:start position:0%
+neurons at once and it's just a lucky
+ 
+
+ align:start position:0%
+neurons at once and it's just a lucky
+fact of the organization of the human
+
+ align:start position:0%
+fact of the organization of the human
+ 
+
+ align:start position:0%
+fact of the organization of the human
+brain that you have clusterings of
+
+ align:start position:0%
+brain that you have clusterings of
+ 
+
+ align:start position:0%
+brain that you have clusterings of
+neurons with similar respond selectively
+
+ align:start position:0%
+neurons with similar respond selectively
+ 
+
+ align:start position:0%
+neurons with similar respond selectively
+''tis and similar functions at such a
+
+ align:start position:0%
+''tis and similar functions at such a
+ 
+
+ align:start position:0%
+''tis and similar functions at such a
+macro grain that you can see some stuff
+
+ align:start position:0%
+macro grain that you can see some stuff
+ 
+
+ align:start position:0%
+macro grain that you can see some stuff
+with functional MRI although you miss a
+
+ align:start position:0%
+with functional MRI although you miss a
+ 
+
+ align:start position:0%
+with functional MRI although you miss a
+lot as well the third important limit of
+
+ align:start position:0%
+lot as well the third important limit of
+ 
+
+ align:start position:0%
+lot as well the third important limit of
+functional MRI that comes out of just a
+
+ align:start position:0%
+functional MRI that comes out of just a
+ 
+
+ align:start position:0%
+functional MRI that comes out of just a
+consideration of what the method
+
+ align:start position:0%
+consideration of what the method
+ 
+
+ align:start position:0%
+consideration of what the method
+measures is that you can only really see
+
+ align:start position:0%
+measures is that you can only really see
+ 
+
+ align:start position:0%
+measures is that you can only really see
+differences between conditions with
+
+ align:start position:0%
+differences between conditions with
+ 
+
+ align:start position:0%
+differences between conditions with
+functional MRI the magnitude of the MRI
+
+ align:start position:0%
+functional MRI the magnitude of the MRI
+ 
+
+ align:start position:0%
+functional MRI the magnitude of the MRI
+response in a voxel at a time point is
+
+ align:start position:0%
+response in a voxel at a time point is
+ 
+
+ align:start position:0%
+response in a voxel at a time point is
+meaningless it might be you know 563 and
+
+ align:start position:0%
+meaningless it might be you know 563 and
+ 
+
+ align:start position:0%
+meaningless it might be you know 563 and
+that's all it means nothing right means
+
+ align:start position:0%
+that's all it means nothing right means
+ 
+
+ align:start position:0%
+that's all it means nothing right means
+nothing it's just the bright you know
+
+ align:start position:0%
+nothing it's just the bright you know
+ 
+
+ align:start position:0%
+nothing it's just the bright you know
+the intensity of the MRI signal the only
+
+ align:start position:0%
+the intensity of the MRI signal the only
+ 
+
+ align:start position:0%
+the intensity of the MRI signal the only
+way to make it mean something is to
+
+ align:start position:0%
+way to make it mean something is to
+ 
+
+ align:start position:0%
+way to make it mean something is to
+compare it to something else usually two
+
+ align:start position:0%
+compare it to something else usually two
+ 
+
+ align:start position:0%
+compare it to something else usually two
+different tasks or two different stimuli
+
+ align:start position:0%
+different tasks or two different stimuli
+ 
+
+ align:start position:0%
+different tasks or two different stimuli
+and so you can go far with that but it's
+
+ align:start position:0%
+and so you can go far with that but it's
+ 
+
+ align:start position:0%
+and so you can go far with that but it's
+important to realize you can't translate
+
+ align:start position:0%
+important to realize you can't translate
+ 
+
+ align:start position:0%
+important to realize you can't translate
+it into any kind of absolute measure of
+
+ align:start position:0%
+it into any kind of absolute measure of
+ 
+
+ align:start position:0%
+it into any kind of absolute measure of
+neural activity it's only a relative
+
+ align:start position:0%
+neural activity it's only a relative
+ 
+
+ align:start position:0%
+neural activity it's only a relative
+measure of strength of neural activity
+
+ align:start position:0%
+measure of strength of neural activity
+ 
+
+ align:start position:0%
+measure of strength of neural activity
+between two different two or more
+
+ align:start position:0%
+between two different two or more
+ 
+
+ align:start position:0%
+between two different two or more
+different conditions okay and the final
+
+ align:start position:0%
+different conditions okay and the final
+ 
+
+ align:start position:0%
+different conditions okay and the final
+you know deep limitation of functional
+
+ align:start position:0%
+you know deep limitation of functional
+ 
+
+ align:start position:0%
+you know deep limitation of functional
+MRI is that we don't we use this that's
+
+ align:start position:0%
+MRI is that we don't we use this that's
+ 
+
+ align:start position:0%
+MRI is that we don't we use this that's
+convenient phrase neural activity it's
+
+ align:start position:0%
+convenient phrase neural activity it's
+ 
+
+ align:start position:0%
+convenient phrase neural activity it's
+very convenient because it's extremely
+
+ align:start position:0%
+very convenient because it's extremely
+ 
+
+ align:start position:0%
+very convenient because it's extremely
+vague and fittingly so because we don't
+
+ align:start position:0%
+vague and fittingly so because we don't
+ 
+
+ align:start position:0%
+vague and fittingly so because we don't
+know exactly what kind of neural
+
+ align:start position:0%
+know exactly what kind of neural
+ 
+
+ align:start position:0%
+know exactly what kind of neural
+activity is driving the Bolton response
+
+ align:start position:0%
+activity is driving the Bolton response
+ 
+
+ align:start position:0%
+activity is driving the Bolton response
+it could be spikes or action potentials
+
+ align:start position:0%
+it could be spikes or action potentials
+ 
+
+ align:start position:0%
+it could be spikes or action potentials
+it could be synaptic synaptic activity
+
+ align:start position:0%
+it could be synaptic synaptic activity
+ 
+
+ align:start position:0%
+it could be synaptic synaptic activity
+that doesn't lead to spikes it could be
+
+ align:start position:0%
+that doesn't lead to spikes it could be
+ 
+
+ align:start position:0%
+that doesn't lead to spikes it could be
+tonic inhibition it could be all kinds
+
+ align:start position:0%
+tonic inhibition it could be all kinds
+ 
+
+ align:start position:0%
+tonic inhibition it could be all kinds
+of different things
+
+ align:start position:0%
+of different things
+ 
+
+ align:start position:0%
+of different things
+anything that's metabolically expensive
+
+ align:start position:0%
+anything that's metabolically expensive
+ 
+
+ align:start position:0%
+anything that's metabolically expensive
+is likely to increase the blood blood
+
+ align:start position:0%
+is likely to increase the blood blood
+ 
+
+ align:start position:0%
+is likely to increase the blood blood
+flow response in practice when people
+
+ align:start position:0%
+flow response in practice when people
+ 
+
+ align:start position:0%
+flow response in practice when people
+have looked at it it's very nicely
+
+ align:start position:0%
+have looked at it it's very nicely
+ 
+
+ align:start position:0%
+have looked at it it's very nicely
+correlated with firing rate right with
+
+ align:start position:0%
+correlated with firing rate right with
+ 
+
+ align:start position:0%
+correlated with firing rate right with
+some you know bumps and caveat so you
+
+ align:start position:0%
+some you know bumps and caveat so you
+ 
+
+ align:start position:0%
+some you know bumps and caveat so you
+can never be totally sure but there's
+
+ align:start position:0%
+can never be totally sure but there's
+ 
+
+ align:start position:0%
+can never be totally sure but there's
+it's a pretty good proxy for firing rate
+
+ align:start position:0%
+it's a pretty good proxy for firing rate
+ 
+
+ align:start position:0%
+it's a pretty good proxy for firing rate
+you just need to remember in the back of
+
+ align:start position:0%
+you just need to remember in the back of
+ 
+
+ align:start position:0%
+you just need to remember in the back of
+your mind that it could be other stuff
+
+ align:start position:0%
+your mind that it could be other stuff
+ 
+
+ align:start position:0%
+your mind that it could be other stuff
+to the final very important caveat is
+
+ align:start position:0%
+to the final very important caveat is
+ 
+
+ align:start position:0%
+to the final very important caveat is
+that functional MRI it like like you
+
+ align:start position:0%
+that functional MRI it like like you
+ 
+
+ align:start position:0%
+that functional MRI it like like you
+know most other methods where you're
+
+ align:start position:0%
+know most other methods where you're
+ 
+
+ align:start position:0%
+know most other methods where you're
+just recording neural activity in a
+
+ align:start position:0%
+just recording neural activity in a
+ 
+
+ align:start position:0%
+just recording neural activity in a
+variety of different ways you're just
+
+ align:start position:0%
+variety of different ways you're just
+ 
+
+ align:start position:0%
+variety of different ways you're just
+watching you're not intervening and that
+
+ align:start position:0%
+watching you're not intervening and that
+ 
+
+ align:start position:0%
+watching you're not intervening and that
+means you're not measuring the causal
+
+ align:start position:0%
+means you're not measuring the causal
+ 
+
+ align:start position:0%
+means you're not measuring the causal
+role of the things you measure and
+
+ align:start position:0%
+role of the things you measure and
+ 
+
+ align:start position:0%
+role of the things you measure and
+that's very important because it could
+
+ align:start position:0%
+that's very important because it could
+ 
+
+ align:start position:0%
+that's very important because it could
+be that everything you measure is just
+
+ align:start position:0%
+be that everything you measure is just
+ 
+
+ align:start position:0%
+be that everything you measure is just
+completely epi phenomenal and has
+
+ align:start position:0%
+completely epi phenomenal and has
+ 
+
+ align:start position:0%
+completely epi phenomenal and has
+absolutely nothing to do with behavior
+
+ align:start position:0%
+absolutely nothing to do with behavior
+ 
+
+ align:start position:0%
+absolutely nothing to do with behavior
+okay so in practice that's unlikely that
+
+ align:start position:0%
+okay so in practice that's unlikely that
+ 
+
+ align:start position:0%
+okay so in practice that's unlikely that
+you have all the systemic stuff for no
+
+ align:start position:0%
+you have all the systemic stuff for no
+ 
+
+ align:start position:0%
+you have all the systemic stuff for no
+reason but you need to kind of keep in
+
+ align:start position:0%
+reason but you need to kind of keep in
+ 
+
+ align:start position:0%
+reason but you need to kind of keep in
+mind that functional MRI is not affords
+
+ align:start position:0%
+mind that functional MRI is not affords
+ 
+
+ align:start position:0%
+mind that functional MRI is not affords
+no window at all into the causal role of
+
+ align:start position:0%
+no window at all into the causal role of
+ 
+
+ align:start position:0%
+no window at all into the causal role of
+different regions for that you need to
+
+ align:start position:0%
+different regions for that you need to
+ 
+
+ align:start position:0%
+different regions for that you need to
+complement it with other methods okay
+
+ align:start position:0%
+complement it with other methods okay
+ 
+
+ align:start position:0%
+complement it with other methods okay
+so despite all these limitations I think
+
+ align:start position:0%
+so despite all these limitations I think
+ 
+
+ align:start position:0%
+so despite all these limitations I think
+functional MRI has had a huge impact on
+
+ align:start position:0%
+functional MRI has had a huge impact on
+ 
+
+ align:start position:0%
+functional MRI has had a huge impact on
+the field and in admittedly unbiased but
+
+ align:start position:0%
+the field and in admittedly unbiased but
+ 
+
+ align:start position:0%
+the field and in admittedly unbiased but
+I think it's one of these things where
+
+ align:start position:0%
+I think it's one of these things where
+ 
+
+ align:start position:0%
+I think it's one of these things where
+as it happens you know we get so used to
+
+ align:start position:0%
+as it happens you know we get so used to
+ 
+
+ align:start position:0%
+as it happens you know we get so used to
+a result the minute it gets published it
+
+ align:start position:0%
+a result the minute it gets published it
+ 
+
+ align:start position:0%
+a result the minute it gets published it
+was like oh yeah right these when a
+
+ align:start position:0%
+was like oh yeah right these when a
+ 
+
+ align:start position:0%
+was like oh yeah right these when a
+little movement so what but I think it's
+
+ align:start position:0%
+little movement so what but I think it's
+ 
+
+ align:start position:0%
+little movement so what but I think it's
+important to step back so I made a bunch
+
+ align:start position:0%
+important to step back so I made a bunch
+ 
+
+ align:start position:0%
+important to step back so I made a bunch
+of pictures too to show you why I think
+
+ align:start position:0%
+of pictures too to show you why I think
+ 
+
+ align:start position:0%
+of pictures too to show you why I think
+this is important okay here is
+
+ align:start position:0%
+this is important okay here is
+ 
+
+ align:start position:0%
+this is important okay here is
+Penfield's map functional map of the
+
+ align:start position:0%
+Penfield's map functional map of the
+ 
+
+ align:start position:0%
+Penfield's map functional map of the
+human brain published in nineteen fifty
+
+ align:start position:0%
+human brain published in nineteen fifty
+ 
+
+ align:start position:0%
+human brain published in nineteen fifty
+seven year before I was born and he has
+
+ align:start position:0%
+seven year before I was born and he has
+ 
+
+ align:start position:0%
+seven year before I was born and he has
+six count'em six functional regions
+
+ align:start position:0%
+six count'em six functional regions
+ 
+
+ align:start position:0%
+six count'em six functional regions
+labeled in there you probably can't see
+
+ align:start position:0%
+labeled in there you probably can't see
+ 
+
+ align:start position:0%
+labeled in there you probably can't see
+them but it's the basic sensory and
+
+ align:start position:0%
+them but it's the basic sensory and
+ 
+
+ align:start position:0%
+them but it's the basic sensory and
+motor regions visual cortex auditory
+
+ align:start position:0%
+motor regions visual cortex auditory
+ 
+
+ align:start position:0%
+motor regions visual cortex auditory
+cortex motor cortex speech up here in
+
+ align:start position:0%
+cortex motor cortex speech up here in
+ 
+
+ align:start position:0%
+cortex motor cortex speech up here in
+Broca's area and then my favorite is
+
+ align:start position:0%
+Broca's area and then my favorite is
+ 
+
+ align:start position:0%
+Broca's area and then my favorite is
+this word that's his interpretive nice
+
+ align:start position:0%
+this word that's his interpretive nice
+ 
+
+ align:start position:0%
+this word that's his interpretive nice
+okay anyway this was based on electrical
+
+ align:start position:0%
+okay anyway this was based on electrical
+ 
+
+ align:start position:0%
+okay anyway this was based on electrical
+recording and stimulation in patients
+
+ align:start position:0%
+recording and stimulation in patients
+ 
+
+ align:start position:0%
+recording and stimulation in patients
+with epilepsy who were undergoing brain
+
+ align:start position:0%
+with epilepsy who were undergoing brain
+ 
+
+ align:start position:0%
+with epilepsy who were undergoing brain
+surgery actually a very powerful method
+
+ align:start position:0%
+surgery actually a very powerful method
+ 
+
+ align:start position:0%
+surgery actually a very powerful method
+but that's where it got him he published
+
+ align:start position:0%
+but that's where it got him he published
+ 
+
+ align:start position:0%
+but that's where it got him he published
+this near the end of his career and
+
+ align:start position:0%
+this near the end of his career and
+ 
+
+ align:start position:0%
+this near the end of his career and
+that's nice but it's pretty rudimentary
+
+ align:start position:0%
+that's nice but it's pretty rudimentary
+ 
+
+ align:start position:0%
+that's nice but it's pretty rudimentary
+okay now cut to 1990 immediately before
+
+ align:start position:0%
+okay now cut to 1990 immediately before
+ 
+
+ align:start position:0%
+okay now cut to 1990 immediately before
+the advent advent of functional MRI and
+
+ align:start position:0%
+the advent advent of functional MRI and
+ 
+
+ align:start position:0%
+the advent advent of functional MRI and
+I this is really crude the black
+
+ align:start position:0%
+I this is really crude the black
+ 
+
+ align:start position:0%
+I this is really crude the black
+outlines are the basic sensory and motor
+
+ align:start position:0%
+outlines are the basic sensory and motor
+ 
+
+ align:start position:0%
+outlines are the basic sensory and motor
+regions and I've added a couple of big
+
+ align:start position:0%
+regions and I've added a couple of big
+ 
+
+ align:start position:0%
+regions and I've added a couple of big
+colored blobs for regions that had been
+
+ align:start position:0%
+colored blobs for regions that had been
+ 
+
+ align:start position:0%
+colored blobs for regions that had been
+identified by studying patients with
+
+ align:start position:0%
+identified by studying patients with
+ 
+
+ align:start position:0%
+identified by studying patients with
+brain damage
+
+ align:start position:0%
+brain damage
+ 
+
+ align:start position:0%
+brain damage
+so you know even from broken Wernicke it
+
+ align:start position:0%
+so you know even from broken Wernicke it
+ 
+
+ align:start position:0%
+so you know even from broken Wernicke it
+was known that approximately these
+
+ align:start position:0%
+was known that approximately these
+ 
+
+ align:start position:0%
+was known that approximately these
+regions were involved in language
+
+ align:start position:0%
+regions were involved in language
+ 
+
+ align:start position:0%
+regions were involved in language
+because people with damage there lost
+
+ align:start position:0%
+because people with damage there lost
+ 
+
+ align:start position:0%
+because people with damage there lost
+their language abilities you get whacked
+
+ align:start position:0%
+their language abilities you get whacked
+ 
+
+ align:start position:0%
+their language abilities you get whacked
+in your parietal lobe you have weird
+
+ align:start position:0%
+in your parietal lobe you have weird
+ 
+
+ align:start position:0%
+in your parietal lobe you have weird
+attentional problems like neglecting the
+
+ align:start position:0%
+attentional problems like neglecting the
+ 
+
+ align:start position:0%
+attentional problems like neglecting the
+left half of space and stuff like that
+
+ align:start position:0%
+left half of space and stuff like that
+ 
+
+ align:start position:0%
+left half of space and stuff like that
+if you have damaged somewhere to the
+
+ align:start position:0%
+if you have damaged somewhere to the
+ 
+
+ align:start position:0%
+if you have damaged somewhere to the
+back end of the right hemisphere you
+
+ align:start position:0%
+back end of the right hemisphere you
+ 
+
+ align:start position:0%
+back end of the right hemisphere you
+might lose face recognition ability
+
+ align:start position:0%
+might lose face recognition ability
+ 
+
+ align:start position:0%
+might lose face recognition ability
+these things were known by around 1990
+
+ align:start position:0%
+these things were known by around 1990
+ 
+
+ align:start position:0%
+these things were known by around 1990
+not much else that's basically the
+
+ align:start position:0%
+not much else that's basically the
+ 
+
+ align:start position:0%
+not much else that's basically the
+functional map of the brain 1990 okay
+
+ align:start position:0%
+functional map of the brain 1990 okay
+ 
+
+ align:start position:0%
+functional map of the brain 1990 okay
+let's see may see if it probably seems
+
+ align:start position:0%
+let's see may see if it probably seems
+ 
+
+ align:start position:0%
+let's see may see if it probably seems
+like ancient history to a lot of you but
+
+ align:start position:0%
+like ancient history to a lot of you but
+ 
+
+ align:start position:0%
+like ancient history to a lot of you but
+not to me okay here we are today okay
+
+ align:start position:0%
+not to me okay here we are today okay
+ 
+
+ align:start position:0%
+not to me okay here we are today okay
+there's a lot of stuff we've learned
+
+ align:start position:0%
+there's a lot of stuff we've learned
+ 
+
+ align:start position:0%
+there's a lot of stuff we've learned
+right there are a lot of particular
+
+ align:start position:0%
+right there are a lot of particular
+ 
+
+ align:start position:0%
+right there are a lot of particular
+parts of the human brain which have been
+
+ align:start position:0%
+parts of the human brain which have been
+ 
+
+ align:start position:0%
+parts of the human brain which have been
+whose function has been characterized
+
+ align:start position:0%
+whose function has been characterized
+ 
+
+ align:start position:0%
+whose function has been characterized
+quite precisely not in the sense that we
+
+ align:start position:0%
+quite precisely not in the sense that we
+ 
+
+ align:start position:0%
+quite precisely not in the sense that we
+know the precise circuits in there or
+
+ align:start position:0%
+know the precise circuits in there or
+ 
+
+ align:start position:0%
+know the precise circuits in there or
+that we can very precisely characterize
+
+ align:start position:0%
+that we can very precisely characterize
+ 
+
+ align:start position:0%
+that we can very precisely characterize
+the representations or computations but
+
+ align:start position:0%
+the representations or computations but
+ 
+
+ align:start position:0%
+the representations or computations but
+to the it sense that we know that a
+
+ align:start position:0%
+to the it sense that we know that a
+ 
+
+ align:start position:0%
+to the it sense that we know that a
+region may be very selectively involved
+
+ align:start position:0%
+region may be very selectively involved
+ 
+
+ align:start position:0%
+region may be very selectively involved
+for example in thinking about what other
+
+ align:start position:0%
+for example in thinking about what other
+ 
+
+ align:start position:0%
+for example in thinking about what other
+people are thinking a totally remarkable
+
+ align:start position:0%
+people are thinking a totally remarkable
+ 
+
+ align:start position:0%
+people are thinking a totally remarkable
+result that Rebecca Saxe who discovered
+
+ align:start position:0%
+result that Rebecca Saxe who discovered
+ 
+
+ align:start position:0%
+result that Rebecca Saxe who discovered
+it will tell you about when she's here
+
+ align:start position:0%
+it will tell you about when she's here
+ 
+
+ align:start position:0%
+it will tell you about when she's here
+next week okay so that was completely
+
+ align:start position:0%
+next week okay so that was completely
+ 
+
+ align:start position:0%
+next week okay so that was completely
+unknown even 15 years ago let alone back
+
+ align:start position:0%
+unknown even 15 years ago let alone back
+ 
+
+ align:start position:0%
+unknown even 15 years ago let alone back
+in 1990 and likewise most of these other
+
+ align:start position:0%
+in 1990 and likewise most of these other
+ 
+
+ align:start position:0%
+in 1990 and likewise most of these other
+regions were known only in you know
+
+ align:start position:0%
+regions were known only in you know
+ 
+
+ align:start position:0%
+regions were known only in you know
+either known in the blurrier sense or
+
+ align:start position:0%
+either known in the blurrier sense or
+ 
+
+ align:start position:0%
+either known in the blurrier sense or
+not with this precision so I think even
+
+ align:start position:0%
+not with this precision so I think even
+ 
+
+ align:start position:0%
+not with this precision so I think even
+though this is very limited and it's
+
+ align:start position:0%
+though this is very limited and it's
+ 
+
+ align:start position:0%
+though this is very limited and it's
+kind of step 0 and trying to understand
+
+ align:start position:0%
+kind of step 0 and trying to understand
+ 
+
+ align:start position:0%
+kind of step 0 and trying to understand
+the human brain I think it's important
+
+ align:start position:0%
+the human brain I think it's important
+ 
+
+ align:start position:0%
+the human brain I think it's important
+progress and I think to push a little
+
+ align:start position:0%
+progress and I think to push a little
+ 
+
+ align:start position:0%
+progress and I think to push a little
+farther I'd like to see this as an
+
+ align:start position:0%
+farther I'd like to see this as an
+ 
+
+ align:start position:0%
+farther I'd like to see this as an
+admittedly very blurry but still a
+
+ align:start position:0%
+admittedly very blurry but still a
+ 
+
+ align:start position:0%
+admittedly very blurry but still a
+picture of the architecture of human
+
+ align:start position:0%
+picture of the architecture of human
+ 
+
+ align:start position:0%
+picture of the architecture of human
+intelligence what are the basic pieces
+
+ align:start position:0%
+intelligence what are the basic pieces
+ 
+
+ align:start position:0%
+intelligence what are the basic pieces
+what is it we have in here to work with
+
+ align:start position:0%
+what is it we have in here to work with
+ 
+
+ align:start position:0%
+what is it we have in here to work with
+when we think we have these basic pieces
+
+ align:start position:0%
+when we think we have these basic pieces
+ 
+
+ align:start position:0%
+when we think we have these basic pieces
+a bunch more that haven't been
+
+ align:start position:0%
+a bunch more that haven't been
+ 
+
+ align:start position:0%
+a bunch more that haven't been
+discovered yet
+
+ align:start position:0%
+discovered yet
+ 
+
+ align:start position:0%
+discovered yet
+and a lot more that we need to know
+
+ align:start position:0%
+and a lot more that we need to know
+ 
+
+ align:start position:0%
+and a lot more that we need to know
+about each of these and how they
+
+ align:start position:0%
+about each of these and how they
+ 
+
+ align:start position:0%
+about each of these and how they
+interact and all of that but you know a
+
+ align:start position:0%
+interact and all of that but you know a
+ 
+
+ align:start position:0%
+interact and all of that but you know a
+reasonable beginning ok all right so
+
+ align:start position:0%
+reasonable beginning ok all right so
+ 
+
+ align:start position:0%
+reasonable beginning ok all right so
+that's my story year ok for fun this is
+
+ align:start position:0%
+that's my story year ok for fun this is
+ 
+
+ align:start position:0%
+that's my story year ok for fun this is
+me with a bunch of functional regions
+
+ align:start position:0%
+me with a bunch of functional regions
+ 
+
+ align:start position:0%
+me with a bunch of functional regions
+identified in my brain and so the
+
+ align:start position:0%
+identified in my brain and so the
+ 
+
+ align:start position:0%
+identified in my brain and so the
+argument I'm making here is that the
+
+ align:start position:0%
+argument I'm making here is that the
+ 
+
+ align:start position:0%
+argument I'm making here is that the
+human mind and brain contain
+
+ align:start position:0%
+human mind and brain contain
+ 
+
+ align:start position:0%
+human mind and brain contain
+a set of highly specialized components
+
+ align:start position:0%
+a set of highly specialized components
+ 
+
+ align:start position:0%
+a set of highly specialized components
+each solving a different specific
+
+ align:start position:0%
+each solving a different specific
+ 
+
+ align:start position:0%
+each solving a different specific
+problem and that each of these regions
+
+ align:start position:0%
+problem and that each of these regions
+ 
+
+ align:start position:0%
+problem and that each of these regions
+is present in essentially every normal
+
+ align:start position:0%
+is present in essentially every normal
+ 
+
+ align:start position:0%
+is present in essentially every normal
+person it's just part of the basic
+
+ align:start position:0%
+person it's just part of the basic
+ 
+
+ align:start position:0%
+person it's just part of the basic
+architecture of the human mind and brain
+
+ align:start position:0%
+architecture of the human mind and brain
+ 
+
+ align:start position:0%
+architecture of the human mind and brain
+now this view is pretty simple but
+
+ align:start position:0%
+now this view is pretty simple but
+ 
+
+ align:start position:0%
+now this view is pretty simple but
+nonetheless it's often confused with a
+
+ align:start position:0%
+nonetheless it's often confused with a
+ 
+
+ align:start position:0%
+nonetheless it's often confused with a
+whole bunch of other things that people
+
+ align:start position:0%
+whole bunch of other things that people
+ 
+
+ align:start position:0%
+whole bunch of other things that people
+think are the same thing and that aren't
+
+ align:start position:0%
+think are the same thing and that aren't
+ 
+
+ align:start position:0%
+think are the same thing and that aren't
+so it's starting to drive me insane so
+
+ align:start position:0%
+so it's starting to drive me insane so
+ 
+
+ align:start position:0%
+so it's starting to drive me insane so
+I'm going to take five minutes and go
+
+ align:start position:0%
+I'm going to take five minutes and go
+ 
+
+ align:start position:0%
+I'm going to take five minutes and go
+through the things this does not mean
+
+ align:start position:0%
+through the things this does not mean
+ 
+
+ align:start position:0%
+through the things this does not mean
+and okay I hope this doesn't insult your
+
+ align:start position:0%
+and okay I hope this doesn't insult your
+ 
+
+ align:start position:0%
+and okay I hope this doesn't insult your
+intelligence but it's amazing how in the
+
+ align:start position:0%
+intelligence but it's amazing how in the
+ 
+
+ align:start position:0%
+intelligence but it's amazing how in the
+current literature in the field people
+
+ align:start position:0%
+current literature in the field people
+ 
+
+ align:start position:0%
+current literature in the field people
+conflate these things okay so I'm
+
+ align:start position:0%
+conflate these things okay so I'm
+ 
+
+ align:start position:0%
+conflate these things okay so I'm
+talking about functional specificity
+
+ align:start position:0%
+talking about functional specificity
+ 
+
+ align:start position:0%
+talking about functional specificity
+which is a question of whether this
+
+ align:start position:0%
+which is a question of whether this
+ 
+
+ align:start position:0%
+which is a question of whether this
+particular region right here is engaged
+
+ align:start position:0%
+particular region right here is engaged
+ 
+
+ align:start position:0%
+particular region right here is engaged
+in pretty selectively in just that
+
+ align:start position:0%
+in pretty selectively in just that
+ 
+
+ align:start position:0%
+in pretty selectively in just that
+particular mental process and not lots
+
+ align:start position:0%
+particular mental process and not lots
+ 
+
+ align:start position:0%
+particular mental process and not lots
+of other mental processes okay that's
+
+ align:start position:0%
+of other mental processes okay that's
+ 
+
+ align:start position:0%
+of other mental processes okay that's
+what I mean by functional specificity
+
+ align:start position:0%
+what I mean by functional specificity
+ 
+
+ align:start position:0%
+what I mean by functional specificity
+that's a different idea than anatomical
+
+ align:start position:0%
+that's a different idea than anatomical
+ 
+
+ align:start position:0%
+that's a different idea than anatomical
+specificity anatomical specificity would
+
+ align:start position:0%
+specificity anatomical specificity would
+ 
+
+ align:start position:0%
+specificity anatomical specificity would
+say is only this region that's involved
+
+ align:start position:0%
+say is only this region that's involved
+ 
+
+ align:start position:0%
+say is only this region that's involved
+and nothing else is involved that's a
+
+ align:start position:0%
+and nothing else is involved that's a
+ 
+
+ align:start position:0%
+and nothing else is involved that's a
+different question right how specific is
+
+ align:start position:0%
+different question right how specific is
+ 
+
+ align:start position:0%
+different question right how specific is
+this region versus are there other
+
+ align:start position:0%
+this region versus are there other
+ 
+
+ align:start position:0%
+this region versus are there other
+regions that do something similar also
+
+ align:start position:0%
+regions that do something similar also
+ 
+
+ align:start position:0%
+regions that do something similar also
+an interesting question but a different
+
+ align:start position:0%
+an interesting question but a different
+ 
+
+ align:start position:0%
+an interesting question but a different
+one okay
+
+ align:start position:0%
+one okay
+ 
+
+ align:start position:0%
+one okay
+I'm going to go through this fast so if
+
+ align:start position:0%
+I'm going to go through this fast so if
+ 
+
+ align:start position:0%
+I'm going to go through this fast so if
+any of it doesn't make sense just raise
+
+ align:start position:0%
+any of it doesn't make sense just raise
+ 
+
+ align:start position:0%
+any of it doesn't make sense just raise
+your hand and all explain it work okay
+
+ align:start position:0%
+your hand and all explain it work okay
+ 
+
+ align:start position:0%
+your hand and all explain it work okay
+yet another idea is the necessity of a
+
+ align:start position:0%
+yet another idea is the necessity of a
+ 
+
+ align:start position:0%
+yet another idea is the necessity of a
+brain region for a particular function
+
+ align:start position:0%
+brain region for a particular function
+ 
+
+ align:start position:0%
+brain region for a particular function
+that's actually what we really want to
+
+ align:start position:0%
+that's actually what we really want to
+ 
+
+ align:start position:0%
+that's actually what we really want to
+know what the functional specificity
+
+ align:start position:0%
+know what the functional specificity
+ 
+
+ align:start position:0%
+know what the functional specificity
+question is not just does it only
+
+ align:start position:0%
+question is not just does it only
+ 
+
+ align:start position:0%
+question is not just does it only
+turn-on when you do X but do you
+
+ align:start position:0%
+turn-on when you do X but do you
+ 
+
+ align:start position:0%
+turn-on when you do X but do you
+absolutely need it for X and so that's
+
+ align:start position:0%
+absolutely need it for X and so that's
+ 
+
+ align:start position:0%
+absolutely need it for X and so that's
+actually a central question that's
+
+ align:start position:0%
+actually a central question that's
+ 
+
+ align:start position:0%
+actually a central question that's
+that's closely connected to it's really
+
+ align:start position:0%
+that's closely connected to it's really
+ 
+
+ align:start position:0%
+that's closely connected to it's really
+part of functional specificity this is a
+
+ align:start position:0%
+part of functional specificity this is a
+ 
+
+ align:start position:0%
+part of functional specificity this is a
+causal question it's different from the
+
+ align:start position:0%
+causal question it's different from the
+ 
+
+ align:start position:0%
+causal question it's different from the
+question of sufficiency right it's a
+
+ align:start position:0%
+question of sufficiency right it's a
+ 
+
+ align:start position:0%
+question of sufficiency right it's a
+given rate brain region sufficient for a
+
+ align:start position:0%
+given rate brain region sufficient for a
+ 
+
+ align:start position:0%
+given rate brain region sufficient for a
+mental process well I think that's just
+
+ align:start position:0%
+mental process well I think that's just
+ 
+
+ align:start position:0%
+mental process well I think that's just
+kind of a wrongheaded question because
+
+ align:start position:0%
+kind of a wrongheaded question because
+ 
+
+ align:start position:0%
+kind of a wrongheaded question because
+nothing's ever sufficient it's just kind
+
+ align:start position:0%
+nothing's ever sufficient it's just kind
+ 
+
+ align:start position:0%
+nothing's ever sufficient it's just kind
+of a confused idea I mean what would
+
+ align:start position:0%
+of a confused idea I mean what would
+ 
+
+ align:start position:0%
+of a confused idea I mean what would
+that mean that would mean we excise my
+
+ align:start position:0%
+that mean that would mean we excise my
+ 
+
+ align:start position:0%
+that mean that would mean we excise my
+face area we put it in a dish keep all
+
+ align:start position:0%
+face area we put it in a dish keep all
+ 
+
+ align:start position:0%
+face area we put it in a dish keep all
+the neurons alive let's pretend we could
+
+ align:start position:0%
+the neurons alive let's pretend we could
+ 
+
+ align:start position:0%
+the neurons alive let's pretend we could
+do that I'm sure and Boyden could figure
+
+ align:start position:0%
+do that I'm sure and Boyden could figure
+ 
+
+ align:start position:0%
+do that I'm sure and Boyden could figure
+out how to do that in a weekend and so
+
+ align:start position:0%
+out how to do that in a weekend and so
+ 
+
+ align:start position:0%
+out how to do that in a weekend and so
+we have this thing alive in a dish can
+
+ align:start position:0%
+we have this thing alive in a dish can
+ 
+
+ align:start position:0%
+we have this thing alive in a dish can
+it do face recognition well of course
+
+ align:start position:0%
+it do face recognition well of course
+ 
+
+ align:start position:0%
+it do face recognition well of course
+not you've got to get the information in
+
+ align:start position:0%
+not you've got to get the information in
+ 
+
+ align:start position:0%
+not you've got to get the information in
+there in the right form Hadden if the
+
+ align:start position:0%
+there in the right form Hadden if the
+ 
+
+ align:start position:0%
+there in the right form Hadden if the
+information doesn't get out and inform
+
+ align:start position:0%
+information doesn't get out and inform
+ 
+
+ align:start position:0%
+information doesn't get out and inform
+the rest of a brain it's not doesn't
+
+ align:start position:0%
+the rest of a brain it's not doesn't
+ 
+
+ align:start position:0%
+the rest of a brain it's not doesn't
+how's a face person right so you need
+
+ align:start position:0%
+how's a face person right so you need
+ 
+
+ align:start position:0%
+how's a face person right so you need
+things to be connected up and that you
+
+ align:start position:0%
+things to be connected up and that you
+ 
+
+ align:start position:0%
+things to be connected up and that you
+need lots of other brain regions to be
+
+ align:start position:0%
+need lots of other brain regions to be
+ 
+
+ align:start position:0%
+need lots of other brain regions to be
+involved so let's distinguish whether
+
+ align:start position:0%
+involved so let's distinguish whether
+ 
+
+ align:start position:0%
+involved so let's distinguish whether
+this brain region is function specific
+
+ align:start position:0%
+this brain region is function specific
+ 
+
+ align:start position:0%
+this brain region is function specific
+for a process from whether it's
+
+ align:start position:0%
+for a process from whether it's
+ 
+
+ align:start position:0%
+for a process from whether it's
+sufficient for the whole process of
+
+ align:start position:0%
+sufficient for the whole process of
+ 
+
+ align:start position:0%
+sufficient for the whole process of
+course it's not sufficient okay all
+
+ align:start position:0%
+course it's not sufficient okay all
+ 
+
+ align:start position:0%
+course it's not sufficient okay all
+right I know you guys would never say
+
+ align:start position:0%
+right I know you guys would never say
+ 
+
+ align:start position:0%
+right I know you guys would never say
+anything so dominant okay a question of
+
+ align:start position:0%
+anything so dominant okay a question of
+ 
+
+ align:start position:0%
+anything so dominant okay a question of
+connectivity right so people often say
+
+ align:start position:0%
+connectivity right so people often say
+ 
+
+ align:start position:0%
+connectivity right so people often say
+oh well this this region is part of a
+
+ align:start position:0%
+oh well this this region is part of a
+ 
+
+ align:start position:0%
+oh well this this region is part of a
+network period my reaction is like duh
+
+ align:start position:0%
+network period my reaction is like duh
+ 
+
+ align:start position:0%
+network period my reaction is like duh
+of course it's part of a network
+
+ align:start position:0%
+of course it's part of a network
+ 
+
+ align:start position:0%
+of course it's part of a network
+everything's part of a network in no way
+
+ align:start position:0%
+everything's part of a network in no way
+ 
+
+ align:start position:0%
+everything's part of a network in no way
+does that engage with the question of
+
+ align:start position:0%
+does that engage with the question of
+ 
+
+ align:start position:0%
+does that engage with the question of
+whether that region is functionally
+
+ align:start position:0%
+whether that region is functionally
+ 
+
+ align:start position:0%
+whether that region is functionally
+specific right a functionally specific
+
+ align:start position:0%
+specific right a functionally specific
+ 
+
+ align:start position:0%
+specific right a functionally specific
+region of course is part of a network it
+
+ align:start position:0%
+region of course is part of a network it
+ 
+
+ align:start position:0%
+region of course is part of a network it
+talks to other brain regions those other
+
+ align:start position:0%
+talks to other brain regions those other
+ 
+
+ align:start position:0%
+talks to other brain regions those other
+brain regions may play an important role
+
+ align:start position:0%
+brain regions may play an important role
+ 
+
+ align:start position:0%
+brain regions may play an important role
+in its processing sure at the very least
+
+ align:start position:0%
+in its processing sure at the very least
+ 
+
+ align:start position:0%
+in its processing sure at the very least
+they're necessary for getting the
+
+ align:start position:0%
+they're necessary for getting the
+ 
+
+ align:start position:0%
+they're necessary for getting the
+information in and out and using it okay
+
+ align:start position:0%
+information in and out and using it okay
+ 
+
+ align:start position:0%
+information in and out and using it okay
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+the final thing that people confuse with
+
+ align:start position:0%
+the final thing that people confuse with
+ 
+
+ align:start position:0%
+the final thing that people confuse with
+functional specificity is an anus this
+
+ align:start position:0%
+functional specificity is an anus this
+ 
+
+ align:start position:0%
+functional specificity is an anus this
+is a very different concept right just
+
+ align:start position:0%
+is a very different concept right just
+ 
+
+ align:start position:0%
+is a very different concept right just
+because we have some particular part of
+
+ align:start position:0%
+because we have some particular part of
+ 
+
+ align:start position:0%
+because we have some particular part of
+the brain for which we make it really
+
+ align:start position:0%
+the brain for which we make it really
+ 
+
+ align:start position:0%
+the brain for which we make it really
+strong evidence that it's very
+
+ align:start position:0%
+strong evidence that it's very
+ 
+
+ align:start position:0%
+strong evidence that it's very
+specifically involved in mental process
+
+ align:start position:0%
+specifically involved in mental process
+ 
+
+ align:start position:0%
+specifically involved in mental process
+X that's cool that's important that's
+
+ align:start position:0%
+X that's cool that's important that's
+ 
+
+ align:start position:0%
+X that's cool that's important that's
+completely orthogonal to how it got
+
+ align:start position:0%
+completely orthogonal to how it got
+ 
+
+ align:start position:0%
+completely orthogonal to how it got
+wired up and whether it's innately
+
+ align:start position:0%
+wired up and whether it's innately
+ 
+
+ align:start position:0%
+wired up and whether it's innately
+specified in the genome that whole
+
+ align:start position:0%
+specified in the genome that whole
+ 
+
+ align:start position:0%
+specified in the genome that whole
+circuit or whether that circuit is
+
+ align:start position:0%
+circuit or whether that circuit is
+ 
+
+ align:start position:0%
+circuit or whether that circuit is
+instructed by experience over
+
+ align:start position:0%
+instructed by experience over
+ 
+
+ align:start position:0%
+instructed by experience over
+development or as in the usual case very
+
+ align:start position:0%
+development or as in the usual case very
+ 
+
+ align:start position:0%
+development or as in the usual case very
+complicated combinations of those two
+
+ align:start position:0%
+complicated combinations of those two
+ 
+
+ align:start position:0%
+complicated combinations of those two
+okay so just to remind you that
+
+ align:start position:0%
+okay so just to remind you that
+ 
+
+ align:start position:0%
+okay so just to remind you that
+functional specificity is a different
+
+ align:start position:0%
+functional specificity is a different
+ 
+
+ align:start position:0%
+functional specificity is a different
+question from an anus and one way you
+
+ align:start position:0%
+question from an anus and one way you
+ 
+
+ align:start position:0%
+question from an anus and one way you
+can see that very clearly is to consider
+
+ align:start position:0%
+can see that very clearly is to consider
+ 
+
+ align:start position:0%
+can see that very clearly is to consider
+the case of the visual word form area
+
+ align:start position:0%
+the case of the visual word form area
+ 
+
+ align:start position:0%
+the case of the visual word form area
+about which I'll show you some data in a
+
+ align:start position:0%
+about which I'll show you some data in a
+ 
+
+ align:start position:0%
+about which I'll show you some data in a
+moment the visual word form area
+
+ align:start position:0%
+moment the visual word form area
+ 
+
+ align:start position:0%
+moment the visual word form area
+responds selectively to words and letter
+
+ align:start position:0%
+responds selectively to words and letter
+ 
+
+ align:start position:0%
+responds selectively to words and letter
+strings in an orthography you know not
+
+ align:start position:0%
+strings in an orthography you know not
+ 
+
+ align:start position:0%
+strings in an orthography you know not
+an orthography you don't know it's very
+
+ align:start position:0%
+an orthography you don't know it's very
+ 
+
+ align:start position:0%
+an orthography you don't know it's very
+anatomically stereotyped mine is
+
+ align:start position:0%
+anatomically stereotyped mine is
+ 
+
+ align:start position:0%
+anatomically stereotyped mine is
+approximately right there and so is
+
+ align:start position:0%
+approximately right there and so is
+ 
+
+ align:start position:0%
+approximately right there and so is
+yours in your brain and it responds to
+
+ align:start position:0%
+yours in your brain and it responds to
+ 
+
+ align:start position:0%
+yours in your brain and it responds to
+orthographies you know if you can read
+
+ align:start position:0%
+orthographies you know if you can read
+ 
+
+ align:start position:0%
+orthographies you know if you can read
+Arabic and Hebrew yours also responds
+
+ align:start position:0%
+Arabic and Hebrew yours also responds
+ 
+
+ align:start position:0%
+Arabic and Hebrew yours also responds
+when you look at words in Arabic and
+
+ align:start position:0%
+when you look at words in Arabic and
+ 
+
+ align:start position:0%
+when you look at words in Arabic and
+Hebrew if you can't it doesn't or it
+
+ align:start position:0%
+Hebrew if you can't it doesn't or it
+ 
+
+ align:start position:0%
+Hebrew if you can't it doesn't or it
+responds a whole lot less okay so that's
+
+ align:start position:0%
+responds a whole lot less okay so that's
+ 
+
+ align:start position:0%
+responds a whole lot less okay so that's
+a function of your individual experience
+
+ align:start position:0%
+a function of your individual experience
+ 
+
+ align:start position:0%
+a function of your individual experience
+not your ancestors experience it has
+
+ align:start position:0%
+not your ancestors experience it has
+ 
+
+ align:start position:0%
+not your ancestors experience it has
+strong functional specificity and yet
+
+ align:start position:0%
+strong functional specificity and yet
+ 
+
+ align:start position:0%
+strong functional specificity and yet
+it's functional specificity is not
+
+ align:start position:0%
+it's functional specificity is not
+ 
+
+ align:start position:0%
+it's functional specificity is not
+innate so this idea that I'm taking out
+
+ align:start position:0%
+innate so this idea that I'm taking out
+ 
+
+ align:start position:0%
+innate so this idea that I'm taking out
+here's has become kind of unpopular it's
+
+ align:start position:0%
+here's has become kind of unpopular it's
+ 
+
+ align:start position:0%
+here's has become kind of unpopular it's
+very trendy to say oh of course we know
+
+ align:start position:0%
+very trendy to say oh of course we know
+ 
+
+ align:start position:0%
+very trendy to say oh of course we know
+the brain doesn't have specialized
+
+ align:start position:0%
+the brain doesn't have specialized
+ 
+
+ align:start position:0%
+the brain doesn't have specialized
+components so for example here's from a
+
+ align:start position:0%
+components so for example here's from a
+ 
+
+ align:start position:0%
+components so for example here's from a
+textbook Scotty tell unlike their
+
+ align:start position:0%
+textbook Scotty tell unlike their
+ 
+
+ align:start position:0%
+textbook Scotty tell unlike their
+phrenologist who believe this very
+
+ align:start position:0%
+phrenologist who believe this very
+ 
+
+ align:start position:0%
+phrenologist who believe this very
+stupid idea that very complex traits
+
+ align:start position:0%
+stupid idea that very complex traits
+ 
+
+ align:start position:0%
+stupid idea that very complex traits
+were associated with discrete brain
+
+ align:start position:0%
+were associated with discrete brain
+ 
+
+ align:start position:0%
+were associated with discrete brain
+regions modern researchers recognize
+
+ align:start position:0%
+regions modern researchers recognize
+ 
+
+ align:start position:0%
+regions modern researchers recognize
+that a single brain brain region may
+
+ align:start position:0%
+that a single brain brain region may
+ 
+
+ align:start position:0%
+that a single brain brain region may
+participate in more than one function
+
+ align:start position:0%
+participate in more than one function
+ 
+
+ align:start position:0%
+participate in more than one function
+well he built in the hedge word may so
+
+ align:start position:0%
+well he built in the hedge word may so
+ 
+
+ align:start position:0%
+well he built in the hedge word may so
+we can't really have a fight but you
+
+ align:start position:0%
+we can't really have a fight but you
+ 
+
+ align:start position:0%
+we can't really have a fight but you
+know he's trying to stake out this
+
+ align:start position:0%
+know he's trying to stake out this
+ 
+
+ align:start position:0%
+know he's trying to stake out this
+different view Lisa
+
+ align:start position:0%
+different view Lisa
+ 
+
+ align:start position:0%
+different view Lisa
+Feldman Barrett I haven't met her but
+
+ align:start position:0%
+Feldman Barrett I haven't met her but
+ 
+
+ align:start position:0%
+Feldman Barrett I haven't met her but
+she's driving me insane most recently by
+
+ align:start position:0%
+she's driving me insane most recently by
+ 
+
+ align:start position:0%
+she's driving me insane most recently by
+proclaiming all kinds of things in the
+
+ align:start position:0%
+proclaiming all kinds of things in the
+ 
+
+ align:start position:0%
+proclaiming all kinds of things in the
+New York Times just a few weeks ago
+
+ align:start position:0%
+New York Times just a few weeks ago
+ 
+
+ align:start position:0%
+New York Times just a few weeks ago
+quote in general the workings of the
+
+ align:start position:0%
+quote in general the workings of the
+ 
+
+ align:start position:0%
+quote in general the workings of the
+brain are not one-to-one whereby a given
+
+ align:start position:0%
+brain are not one-to-one whereby a given
+ 
+
+ align:start position:0%
+brain are not one-to-one whereby a given
+region has a distinct psychological
+
+ align:start position:0%
+region has a distinct psychological
+ 
+
+ align:start position:0%
+region has a distinct psychological
+purpose right well she's got Hedge words
+
+ align:start position:0%
+purpose right well she's got Hedge words
+ 
+
+ align:start position:0%
+purpose right well she's got Hedge words
+in general dive we all have hedge words
+
+ align:start position:0%
+in general dive we all have hedge words
+ 
+
+ align:start position:0%
+in general dive we all have hedge words
+but you know she's she's basically what
+
+ align:start position:0%
+but you know she's she's basically what
+ 
+
+ align:start position:0%
+but you know she's she's basically what
+she's reasoning from is the fact that
+
+ align:start position:0%
+she's reasoning from is the fact that
+ 
+
+ align:start position:0%
+she's reasoning from is the fact that
+her data suggests that specific emotions
+
+ align:start position:0%
+her data suggests that specific emotions
+ 
+
+ align:start position:0%
+her data suggests that specific emotions
+don't inhabit specific brain regions
+
+ align:start position:0%
+don't inhabit specific brain regions
+ 
+
+ align:start position:0%
+don't inhabit specific brain regions
+from the idea that the whole brain has
+
+ align:start position:0%
+from the idea that the whole brain has
+ 
+
+ align:start position:0%
+from the idea that the whole brain has
+no localization of function well that's
+
+ align:start position:0%
+no localization of function well that's
+ 
+
+ align:start position:0%
+no localization of function well that's
+idiotic
+
+ align:start position:0%
+idiotic
+ 
+
+ align:start position:0%
+idiotic
+it's just idiotic right okay so I hope
+
+ align:start position:0%
+it's just idiotic right okay so I hope
+ 
+
+ align:start position:0%
+it's just idiotic right okay so I hope
+that people will stop these fast and
+
+ align:start position:0%
+that people will stop these fast and
+ 
+
+ align:start position:0%
+that people will stop these fast and
+loose arguments but here's my favorite
+
+ align:start position:0%
+loose arguments but here's my favorite
+ 
+
+ align:start position:0%
+loose arguments but here's my favorite
+this old coot all I know this is gonna
+
+ align:start position:0%
+this old coot all I know this is gonna
+ 
+
+ align:start position:0%
+this old coot all I know this is gonna
+be on the web and here I am carrying on
+
+ align:start position:0%
+be on the web and here I am carrying on
+ 
+
+ align:start position:0%
+be on the web and here I am carrying on
+is if we have anyway whatever this guy
+
+ align:start position:0%
+is if we have anyway whatever this guy
+ 
+
+ align:start position:0%
+is if we have anyway whatever this guy
+cracks me up
+
+ align:start position:0%
+cracks me up
+ 
+
+ align:start position:0%
+cracks me up
+he's been publishing every year he
+
+ align:start position:0%
+he's been publishing every year he
+ 
+
+ align:start position:0%
+he's been publishing every year he
+publishes another book kind of going
+
+ align:start position:0%
+publishes another book kind of going
+ 
+
+ align:start position:0%
+publishes another book kind of going
+after function I'm right any studies
+
+ align:start position:0%
+after function I'm right any studies
+ 
+
+ align:start position:0%
+after function I'm right any studies
+using brain images that report single
+
+ align:start position:0%
+using brain images that report single
+ 
+
+ align:start position:0%
+using brain images that report single
+areas of activation exclusively
+
+ align:start position:0%
+areas of activation exclusively
+ 
+
+ align:start position:0%
+areas of activation exclusively
+associated with a particular cognitive
+
+ align:start position:0%
+associated with a particular cognitive
+ 
+
+ align:start position:0%
+associated with a particular cognitive
+process should be a priori considered to
+
+ align:start position:0%
+process should be a priori considered to
+ 
+
+ align:start position:0%
+process should be a priori considered to
+be artifacts of the arbitrary threshold
+
+ align:start position:0%
+be artifacts of the arbitrary threshold
+ 
+
+ align:start position:0%
+be artifacts of the arbitrary threshold
+set by the investigators and seriously
+
+ align:start position:0%
+set by the investigators and seriously
+ 
+
+ align:start position:0%
+set by the investigators and seriously
+questioned you go
+
+ align:start position:0%
+questioned you go
+ 
+
+ align:start position:0%
+questioned you go
+so anyway um that's fun anyway my point
+
+ align:start position:0%
+so anyway um that's fun anyway my point
+ 
+
+ align:start position:0%
+so anyway um that's fun anyway my point
+is just that we should engage in the
+
+ align:start position:0%
+is just that we should engage in the
+ 
+
+ align:start position:0%
+is just that we should engage in the
+data right this isn't like an ideology
+
+ align:start position:0%
+data right this isn't like an ideology
+ 
+
+ align:start position:0%
+data right this isn't like an ideology
+where we can just proclaim our opinions
+
+ align:start position:0%
+where we can just proclaim our opinions
+ 
+
+ align:start position:0%
+where we can just proclaim our opinions
+there are data that speak to it so let
+
+ align:start position:0%
+there are data that speak to it so let
+ 
+
+ align:start position:0%
+there are data that speak to it so let
+me show you some of mine okay so what
+
+ align:start position:0%
+me show you some of mine okay so what
+ 
+
+ align:start position:0%
+me show you some of mine okay so what
+would be evidence of functional
+
+ align:start position:0%
+would be evidence of functional
+ 
+
+ align:start position:0%
+would be evidence of functional
+specificity there are lots of ways of
+
+ align:start position:0%
+specificity there are lots of ways of
+ 
+
+ align:start position:0%
+specificity there are lots of ways of
+doing it the way I like to do it is
+
+ align:start position:0%
+doing it the way I like to do it is
+ 
+
+ align:start position:0%
+doing it the way I like to do it is
+something called a functional region of
+
+ align:start position:0%
+something called a functional region of
+ 
+
+ align:start position:0%
+something called a functional region of
+interest method the the problem is that
+
+ align:start position:0%
+interest method the the problem is that
+ 
+
+ align:start position:0%
+interest method the the problem is that
+although there are very systematic
+
+ align:start position:0%
+although there are very systematic
+ 
+
+ align:start position:0%
+although there are very systematic
+regularities in the functional
+
+ align:start position:0%
+regularities in the functional
+ 
+
+ align:start position:0%
+regularities in the functional
+organization of the brain each of these
+
+ align:start position:0%
+organization of the brain each of these
+ 
+
+ align:start position:0%
+organization of the brain each of these
+regions that I'm talking about is in
+
+ align:start position:0%
+regions that I'm talking about is in
+ 
+
+ align:start position:0%
+regions that I'm talking about is in
+approximately the same location in each
+
+ align:start position:0%
+approximately the same location in each
+ 
+
+ align:start position:0%
+approximately the same location in each
+normal subject their actual location
+
+ align:start position:0%
+normal subject their actual location
+ 
+
+ align:start position:0%
+normal subject their actual location
+varies a bit from subject to subject so
+
+ align:start position:0%
+varies a bit from subject to subject so
+ 
+
+ align:start position:0%
+varies a bit from subject to subject so
+if you do the standard thing of aligning
+
+ align:start position:0%
+if you do the standard thing of aligning
+ 
+
+ align:start position:0%
+if you do the standard thing of aligning
+brains and averaging across them you get
+
+ align:start position:0%
+brains and averaging across them you get
+ 
+
+ align:start position:0%
+brains and averaging across them you get
+a lot of mush and yet there isn't much
+
+ align:start position:0%
+a lot of mush and yet there isn't much
+ 
+
+ align:start position:0%
+a lot of mush and yet there isn't much
+mush in each subject individually and so
+
+ align:start position:0%
+mush in each subject individually and so
+ 
+
+ align:start position:0%
+mush in each subject individually and so
+to deal with that problem and to deal
+
+ align:start position:0%
+to deal with that problem and to deal
+ 
+
+ align:start position:0%
+to deal with that problem and to deal
+with a bunch of other problems we use
+
+ align:start position:0%
+with a bunch of other problems we use
+ 
+
+ align:start position:0%
+with a bunch of other problems we use
+something called a functional region of
+
+ align:start position:0%
+something called a functional region of
+ 
+
+ align:start position:0%
+something called a functional region of
+interest method and that means if you
+
+ align:start position:0%
+interest method and that means if you
+ 
+
+ align:start position:0%
+interest method and that means if you
+want to study a given region you find it
+
+ align:start position:0%
+want to study a given region you find it
+ 
+
+ align:start position:0%
+want to study a given region you find it
+in that subject individually and then
+
+ align:start position:0%
+in that subject individually and then
+ 
+
+ align:start position:0%
+in that subject individually and then
+once you've found it with a simple
+
+ align:start position:0%
+once you've found it with a simple
+ 
+
+ align:start position:0%
+once you've found it with a simple
+contrast you want to find a face region
+
+ align:start position:0%
+contrast you want to find a face region
+ 
+
+ align:start position:0%
+contrast you want to find a face region
+you find a region that responds more
+
+ align:start position:0%
+you find a region that responds more
+ 
+
+ align:start position:0%
+you find a region that responds more
+when people look at faces than when they
+
+ align:start position:0%
+when people look at faces than when they
+ 
+
+ align:start position:0%
+when people look at faces than when they
+look at objects now you found it in that
+
+ align:start position:0%
+look at objects now you found it in that
+ 
+
+ align:start position:0%
+look at objects now you found it in that
+subject it's these 85 voxels right there
+
+ align:start position:0%
+subject it's these 85 voxels right there
+ 
+
+ align:start position:0%
+subject it's these 85 voxels right there
+in that subject now we run a new
+
+ align:start position:0%
+in that subject now we run a new
+ 
+
+ align:start position:0%
+in that subject now we run a new
+experiment to test more interesting
+
+ align:start position:0%
+experiment to test more interesting
+ 
+
+ align:start position:0%
+experiment to test more interesting
+questions about it and we measure the
+
+ align:start position:0%
+questions about it and we measure the
+ 
+
+ align:start position:0%
+questions about it and we measure the
+response in those boxes okay that also
+
+ align:start position:0%
+response in those boxes okay that also
+ 
+
+ align:start position:0%
+response in those boxes okay that also
+has the advantage that the data you plot
+
+ align:start position:0%
+has the advantage that the data you plot
+ 
+
+ align:start position:0%
+has the advantage that the data you plot
+and look at it's independent of the way
+
+ align:start position:0%
+and look at it's independent of the way
+ 
+
+ align:start position:0%
+and look at it's independent of the way
+you found those voxels a very important
+
+ align:start position:0%
+you found those voxels a very important
+ 
+
+ align:start position:0%
+you found those voxels a very important
+problem in a lot of functional
+
+ align:start position:0%
+problem in a lot of functional
+ 
+
+ align:start position:0%
+problem in a lot of functional
+neuroimaging where people have non
+
+ align:start position:0%
+neuroimaging where people have non
+ 
+
+ align:start position:0%
+neuroimaging where people have non
+independent statistical problems with
+
+ align:start position:0%
+independent statistical problems with
+ 
+
+ align:start position:0%
+independent statistical problems with
+their data analysis if you have a
+
+ align:start position:0%
+their data analysis if you have a
+ 
+
+ align:start position:0%
+their data analysis if you have a
+functional region of interest that's
+
+ align:start position:0%
+functional region of interest that's
+ 
+
+ align:start position:0%
+functional region of interest that's
+localized independently of the data you
+
+ align:start position:0%
+localized independently of the data you
+ 
+
+ align:start position:0%
+localized independently of the data you
+look at in it you get out of that
+
+ align:start position:0%
+look at in it you get out of that
+ 
+
+ align:start position:0%
+look at in it you get out of that
+problem it's also a huge benefit because
+
+ align:start position:0%
+problem it's also a huge benefit because
+ 
+
+ align:start position:0%
+problem it's also a huge benefit because
+one of the central problems with
+
+ align:start position:0%
+one of the central problems with
+ 
+
+ align:start position:0%
+one of the central problems with
+functional brain imaging which i think
+
+ align:start position:0%
+functional brain imaging which i think
+ 
+
+ align:start position:0%
+functional brain imaging which i think
+has led to the fact that a large percent
+
+ align:start position:0%
+has led to the fact that a large percent
+ 
+
+ align:start position:0%
+has led to the fact that a large percent
+of the published neuroimaging findings
+
+ align:start position:0%
+of the published neuroimaging findings
+ 
+
+ align:start position:0%
+of the published neuroimaging findings
+are probably noise is that they're just
+
+ align:start position:0%
+are probably noise is that they're just
+ 
+
+ align:start position:0%
+are probably noise is that they're just
+too many degrees of freedom you have
+
+ align:start position:0%
+too many degrees of freedom you have
+ 
+
+ align:start position:0%
+too many degrees of freedom you have
+tens of thousands of voxels you have
+
+ align:start position:0%
+tens of thousands of voxels you have
+ 
+
+ align:start position:0%
+tens of thousands of voxels you have
+loads of different places to look and
+
+ align:start position:0%
+loads of different places to look and
+ 
+
+ align:start position:0%
+loads of different places to look and
+ways to analyze your data one of the
+
+ align:start position:0%
+ways to analyze your data one of the
+ 
+
+ align:start position:0%
+ways to analyze your data one of the
+things I love dearly about the
+
+ align:start position:0%
+things I love dearly about the
+ 
+
+ align:start position:0%
+things I love dearly about the
+functional region of interest method is
+
+ align:start position:0%
+functional region of interest method is
+ 
+
+ align:start position:0%
+functional region of interest method is
+that you tie your hands
+
+ align:start position:0%
+that you tie your hands
+ 
+
+ align:start position:0%
+that you tie your hands
+in a really good way right so you're
+
+ align:start position:0%
+in a really good way right so you're
+ 
+
+ align:start position:0%
+in a really good way right so you're
+you're specifying in advance exactly
+
+ align:start position:0%
+you're specifying in advance exactly
+ 
+
+ align:start position:0%
+you're specifying in advance exactly
+where you're gonna look and you specify
+
+ align:start position:0%
+where you're gonna look and you specify
+ 
+
+ align:start position:0%
+where you're gonna look and you specify
+exactly how you're going to quantify the
+
+ align:start position:0%
+exactly how you're going to quantify the
+ 
+
+ align:start position:0%
+exactly how you're going to quantify the
+response and so you have no degrees of
+
+ align:start position:0%
+response and so you have no degrees of
+ 
+
+ align:start position:0%
+response and so you have no degrees of
+freedom and that gives you a huge
+
+ align:start position:0%
+freedom and that gives you a huge
+ 
+
+ align:start position:0%
+freedom and that gives you a huge
+statistical advantage and it means
+
+ align:start position:0%
+statistical advantage and it means
+ 
+
+ align:start position:0%
+statistical advantage and it means
+you're less likely to be inadvertently
+
+ align:start position:0%
+you're less likely to be inadvertently
+ 
+
+ align:start position:0%
+you're less likely to be inadvertently
+publishing papers on noise okay so
+
+ align:start position:0%
+publishing papers on noise okay so
+ 
+
+ align:start position:0%
+publishing papers on noise okay so
+that's the function region of interest
+
+ align:start position:0%
+that's the function region of interest
+ 
+
+ align:start position:0%
+that's the function region of interest
+method here's just we've done loads of
+
+ align:start position:0%
+method here's just we've done loads of
+ 
+
+ align:start position:0%
+method here's just we've done loads of
+these experiments here's just from a
+
+ align:start position:0%
+these experiments here's just from a
+ 
+
+ align:start position:0%
+these experiments here's just from a
+current experiment in my lab being
+
+ align:start position:0%
+current experiment in my lab being
+ 
+
+ align:start position:0%
+current experiment in my lab being
+conducted by Zeynep Sagan she's actually
+
+ align:start position:0%
+conducted by Zeynep Sagan she's actually
+ 
+
+ align:start position:0%
+conducted by Zeynep Sagan she's actually
+looking at connectivity of different
+
+ align:start position:0%
+looking at connectivity of different
+ 
+
+ align:start position:0%
+looking at connectivity of different
+brain regions using a different method I
+
+ align:start position:0%
+brain regions using a different method I
+ 
+
+ align:start position:0%
+brain regions using a different method I
+probably won't have time to talk about
+
+ align:start position:0%
+probably won't have time to talk about
+ 
+
+ align:start position:0%
+probably won't have time to talk about
+it it's very cool but in the process
+
+ align:start position:0%
+it it's very cool but in the process
+ 
+
+ align:start position:0%
+it it's very cool but in the process
+she's run a whole bunch of functional
+
+ align:start position:0%
+she's run a whole bunch of functional
+ 
+
+ align:start position:0%
+she's run a whole bunch of functional
+localizers and so we can look in her
+
+ align:start position:0%
+localizers and so we can look in her
+ 
+
+ align:start position:0%
+localizers and so we can look in her
+data at the response of the fusiform
+
+ align:start position:0%
+data at the response of the fusiform
+ 
+
+ align:start position:0%
+data at the response of the fusiform
+face area to a whole bunch of different
+
+ align:start position:0%
+face area to a whole bunch of different
+ 
+
+ align:start position:0%
+face area to a whole bunch of different
+conditions ok so these are a bunch of
+
+ align:start position:0%
+conditions ok so these are a bunch of
+ 
+
+ align:start position:0%
+conditions ok so these are a bunch of
+auditory and language conditions so okay
+
+ align:start position:0%
+auditory and language conditions so okay
+ 
+
+ align:start position:0%
+auditory and language conditions so okay
+not too surprising it doesn't respond
+
+ align:start position:0%
+not too surprising it doesn't respond
+ 
+
+ align:start position:0%
+not too surprising it doesn't respond
+very much to those they're presented
+
+ align:start position:0%
+very much to those they're presented
+ 
+
+ align:start position:0%
+very much to those they're presented
+auditorily but these are all visual
+
+ align:start position:0%
+auditorily but these are all visual
+ 
+
+ align:start position:0%
+auditorily but these are all visual
+stimuli here the two yellow bars our
+
+ align:start position:0%
+stimuli here the two yellow bars our
+ 
+
+ align:start position:0%
+stimuli here the two yellow bars our
+faces this is line drawings of faces
+
+ align:start position:0%
+faces this is line drawings of faces
+ 
+
+ align:start position:0%
+faces this is line drawings of faces
+this is video clips color video clips of
+
+ align:start position:0%
+this is video clips color video clips of
+ 
+
+ align:start position:0%
+this is video clips color video clips of
+faces strong responses to both and all
+
+ align:start position:0%
+faces strong responses to both and all
+ 
+
+ align:start position:0%
+faces strong responses to both and all
+of these other conditions line drawings
+
+ align:start position:0%
+of these other conditions line drawings
+ 
+
+ align:start position:0%
+of these other conditions line drawings
+of objects movies of objects movies of
+
+ align:start position:0%
+of objects movies of objects movies of
+ 
+
+ align:start position:0%
+of objects movies of objects movies of
+scenes scrambled objects words scrambled
+
+ align:start position:0%
+scenes scrambled objects words scrambled
+ 
+
+ align:start position:0%
+scenes scrambled objects words scrambled
+words bodies all produce much lower
+
+ align:start position:0%
+words bodies all produce much lower
+ 
+
+ align:start position:0%
+words bodies all produce much lower
+responses okay so I would say this is
+
+ align:start position:0%
+responses okay so I would say this is
+ 
+
+ align:start position:0%
+responses okay so I would say this is
+pretty strong selectivity it's been
+
+ align:start position:0%
+pretty strong selectivity it's been
+ 
+
+ align:start position:0%
+pretty strong selectivity it's been
+tested against lots of alternatives only
+
+ align:start position:0%
+tested against lots of alternatives only
+ 
+
+ align:start position:0%
+tested against lots of alternatives only
+a tiny percent of which are shown here
+
+ align:start position:0%
+a tiny percent of which are shown here
+ 
+
+ align:start position:0%
+a tiny percent of which are shown here
+as I mentioned before it's present in
+
+ align:start position:0%
+as I mentioned before it's present in
+ 
+
+ align:start position:0%
+as I mentioned before it's present in
+more or less the same place in pretty
+
+ align:start position:0%
+more or less the same place in pretty
+ 
+
+ align:start position:0%
+more or less the same place in pretty
+much every normal subject I think it's
+
+ align:start position:0%
+much every normal subject I think it's
+ 
+
+ align:start position:0%
+much every normal subject I think it's
+just a basic piece of mental
+
+ align:start position:0%
+just a basic piece of mental
+ 
+
+ align:start position:0%
+just a basic piece of mental
+architecture now this is a very simple
+
+ align:start position:0%
+architecture now this is a very simple
+ 
+
+ align:start position:0%
+architecture now this is a very simple
+univariate measure we're just measuring
+
+ align:start position:0%
+univariate measure we're just measuring
+ 
+
+ align:start position:0%
+univariate measure we're just measuring
+the very crude thing of the overall
+
+ align:start position:0%
+the very crude thing of the overall
+ 
+
+ align:start position:0%
+the very crude thing of the overall
+magnitude of MRI response in that region
+
+ align:start position:0%
+magnitude of MRI response in that region
+ 
+
+ align:start position:0%
+magnitude of MRI response in that region
+to these conditions there are legitimate
+
+ align:start position:0%
+to these conditions there are legitimate
+ 
+
+ align:start position:0%
+to these conditions there are legitimate
+counter arguments to the simple-minded
+
+ align:start position:0%
+counter arguments to the simple-minded
+ 
+
+ align:start position:0%
+counter arguments to the simple-minded
+view I'm putting forth and we should
+
+ align:start position:0%
+view I'm putting forth and we should
+ 
+
+ align:start position:0%
+view I'm putting forth and we should
+consider them I think the most important
+
+ align:start position:0%
+consider them I think the most important
+ 
+
+ align:start position:0%
+consider them I think the most important
+one comes from pattern analysis methods
+
+ align:start position:0%
+one comes from pattern analysis methods
+ 
+
+ align:start position:0%
+one comes from pattern analysis methods
+which I will talk about if I get there
+
+ align:start position:0%
+which I will talk about if I get there
+ 
+
+ align:start position:0%
+which I will talk about if I get there
+and importantly these data don't tell us
+
+ align:start position:0%
+and importantly these data don't tell us
+ 
+
+ align:start position:0%
+and importantly these data don't tell us
+about the causal role of that region it
+
+ align:start position:0%
+about the causal role of that region it
+ 
+
+ align:start position:0%
+about the causal role of that region it
+will return to those however the point
+
+ align:start position:0%
+will return to those however the point
+ 
+
+ align:start position:0%
+will return to those however the point
+is before we blithely say it's not
+
+ align:start position:0%
+is before we blithely say it's not
+ 
+
+ align:start position:0%
+is before we blithely say it's not
+fashionable to talk about functional
+
+ align:start position:0%
+fashionable to talk about functional
+ 
+
+ align:start position:0%
+fashionable to talk about functional
+specificity we need counter arguments to
+
+ align:start position:0%
+specificity we need counter arguments to
+ 
+
+ align:start position:0%
+specificity we need counter arguments to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+like this okay they're pretty strong and
+
+ align:start position:0%
+like this okay they're pretty strong and
+ 
+
+ align:start position:0%
+like this okay they're pretty strong and
+that you know that's just one example to
+
+ align:start position:0%
+that you know that's just one example to
+ 
+
+ align:start position:0%
+that you know that's just one example to
+show you just a few others from santa's
+
+ align:start position:0%
+show you just a few others from santa's
+ 
+
+ align:start position:0%
+show you just a few others from santa's
+paper okay so this is what I just showed
+
+ align:start position:0%
+paper okay so this is what I just showed
+ 
+
+ align:start position:0%
+paper okay so this is what I just showed
+you but I'm in the same experiment we
+
+ align:start position:0%
+you but I'm in the same experiment we
+ 
+
+ align:start position:0%
+you but I'm in the same experiment we
+can look at other brain regions okay so
+
+ align:start position:0%
+can look at other brain regions okay so
+ 
+
+ align:start position:0%
+can look at other brain regions okay so
+that this is a bottom surface of the of
+
+ align:start position:0%
+that this is a bottom surface of the of
+ 
+
+ align:start position:0%
+that this is a bottom surface of the of
+the brain there so this is the occipital
+
+ align:start position:0%
+the brain there so this is the occipital
+ 
+
+ align:start position:0%
+the brain there so this is the occipital
+pole front of the head bottom of the
+
+ align:start position:0%
+pole front of the head bottom of the
+ 
+
+ align:start position:0%
+pole front of the head bottom of the
+temporal lobe that face area is the
+
+ align:start position:0%
+temporal lobe that face area is the
+ 
+
+ align:start position:0%
+temporal lobe that face area is the
+region in yellow in this subject this
+
+ align:start position:0%
+region in yellow in this subject this
+ 
+
+ align:start position:0%
+region in yellow in this subject this
+purple region is that visual word form
+
+ align:start position:0%
+purple region is that visual word form
+ 
+
+ align:start position:0%
+purple region is that visual word form
+area that I mentioned and here is its
+
+ align:start position:0%
+area that I mentioned and here is its
+ 
+
+ align:start position:0%
+area that I mentioned and here is its
+response magnitude across a whole bunch
+
+ align:start position:0%
+response magnitude across a whole bunch
+ 
+
+ align:start position:0%
+response magnitude across a whole bunch
+of subjects you localizing and then
+
+ align:start position:0%
+of subjects you localizing and then
+ 
+
+ align:start position:0%
+of subjects you localizing and then
+independently testing the purple bars
+
+ align:start position:0%
+independently testing the purple bars
+ 
+
+ align:start position:0%
+independently testing the purple bars
+are when sorry subjects are looking at
+
+ align:start position:0%
+are when sorry subjects are looking at
+ 
+
+ align:start position:0%
+are when sorry subjects are looking at
+visually presented words and again all
+
+ align:start position:0%
+visually presented words and again all
+ 
+
+ align:start position:0%
+visually presented words and again all
+these other conditions faces objects
+
+ align:start position:0%
+these other conditions faces objects
+ 
+
+ align:start position:0%
+these other conditions faces objects
+bodies scenes you know listening to
+
+ align:start position:0%
+bodies scenes you know listening to
+ 
+
+ align:start position:0%
+bodies scenes you know listening to
+words all of those things much lower
+
+ align:start position:0%
+words all of those things much lower
+ 
+
+ align:start position:0%
+words all of those things much lower
+response okay in the same experiment we
+
+ align:start position:0%
+response okay in the same experiment we
+ 
+
+ align:start position:0%
+response okay in the same experiment we
+can also look at a set of regions that
+
+ align:start position:0%
+can also look at a set of regions that
+ 
+
+ align:start position:0%
+can also look at a set of regions that
+respond to speech I mentioned those very
+
+ align:start position:0%
+respond to speech I mentioned those very
+ 
+
+ align:start position:0%
+respond to speech I mentioned those very
+briefly in my introduction a few days
+
+ align:start position:0%
+briefly in my introduction a few days
+ 
+
+ align:start position:0%
+briefly in my introduction a few days
+ago these are regions a number of people
+
+ align:start position:0%
+ago these are regions a number of people
+ 
+
+ align:start position:0%
+ago these are regions a number of people
+have found in this case what we they're
+
+ align:start position:0%
+have found in this case what we they're
+ 
+
+ align:start position:0%
+have found in this case what we they're
+immediately below or lateral to primary
+
+ align:start position:0%
+immediately below or lateral to primary
+ 
+
+ align:start position:0%
+immediately below or lateral to primary
+auditory cortex in humans interestingly
+
+ align:start position:0%
+auditory cortex in humans interestingly
+ 
+
+ align:start position:0%
+auditory cortex in humans interestingly
+situated right between primary auditory
+
+ align:start position:0%
+situated right between primary auditory
+ 
+
+ align:start position:0%
+situated right between primary auditory
+cortex and language sensitive regions
+
+ align:start position:0%
+cortex and language sensitive regions
+ 
+
+ align:start position:0%
+cortex and language sensitive regions
+right between is a set of regions that
+
+ align:start position:0%
+right between is a set of regions that
+ 
+
+ align:start position:0%
+right between is a set of regions that
+respond to the sounds of speech okay not
+
+ align:start position:0%
+respond to the sounds of speech okay not
+ 
+
+ align:start position:0%
+respond to the sounds of speech okay not
+to the content of language but the
+
+ align:start position:0%
+to the content of language but the
+ 
+
+ align:start position:0%
+to the content of language but the
+sounds of speech and so this is when
+
+ align:start position:0%
+sounds of speech and so this is when
+ 
+
+ align:start position:0%
+sounds of speech and so this is when
+people are just going to say this is
+
+ align:start position:0%
+people are just going to say this is
+ 
+
+ align:start position:0%
+people are just going to say this is
+when people are saying stuff like ba da
+
+ align:start position:0%
+when people are saying stuff like ba da
+ 
+
+ align:start position:0%
+when people are saying stuff like ba da
+da ba da cow so they're just lying in
+
+ align:start position:0%
+da ba da cow so they're just lying in
+ 
+
+ align:start position:0%
+da ba da cow so they're just lying in
+the scanner saying ba da da ba da da and
+
+ align:start position:0%
+the scanner saying ba da da ba da da and
+ 
+
+ align:start position:0%
+the scanner saying ba da da ba da da and
+here's when they're tapping their
+
+ align:start position:0%
+here's when they're tapping their
+ 
+
+ align:start position:0%
+here's when they're tapping their
+fingers in a systematic order here's
+
+ align:start position:0%
+fingers in a systematic order here's
+ 
+
+ align:start position:0%
+fingers in a systematic order here's
+when they're listening to sentences
+
+ align:start position:0%
+when they're listening to sentences
+ 
+
+ align:start position:0%
+when they're listening to sentences
+importantly this is when they're
+
+ align:start position:0%
+importantly this is when they're
+ 
+
+ align:start position:0%
+importantly this is when they're
+listening to Jabberwocky
+
+ align:start position:0%
+listening to Jabberwocky
+ 
+
+ align:start position:0%
+listening to Jabberwocky
+gobbledygook that's meaningless okay so
+
+ align:start position:0%
+gobbledygook that's meaningless okay so
+ 
+
+ align:start position:0%
+gobbledygook that's meaningless okay so
+no meaning but phonemes same response
+
+ align:start position:0%
+no meaning but phonemes same response
+ 
+
+ align:start position:0%
+no meaning but phonemes same response
+that's what tells us that this region is
+
+ align:start position:0%
+that's what tells us that this region is
+ 
+
+ align:start position:0%
+that's what tells us that this region is
+involved in processing the sounds of
+
+ align:start position:0%
+involved in processing the sounds of
+ 
+
+ align:start position:0%
+involved in processing the sounds of
+speech not the content of language and
+
+ align:start position:0%
+speech not the content of language and
+ 
+
+ align:start position:0%
+speech not the content of language and
+lo to everything else so other things
+
+ align:start position:0%
+lo to everything else so other things
+ 
+
+ align:start position:0%
+lo to everything else so other things
+moving outside of perceptual regions you
+
+ align:start position:0%
+moving outside of perceptual regions you
+ 
+
+ align:start position:0%
+moving outside of perceptual regions you
+might say okay fine perception is an
+
+ align:start position:0%
+might say okay fine perception is an
+ 
+
+ align:start position:0%
+might say okay fine perception is an
+inherently modular process there's
+
+ align:start position:0%
+inherently modular process there's
+ 
+
+ align:start position:0%
+inherently modular process there's
+different kinds of perceptual problems
+
+ align:start position:0%
+different kinds of perceptual problems
+ 
+
+ align:start position:0%
+different kinds of perceptual problems
+that make sense but high level cognition
+
+ align:start position:0%
+that make sense but high level cognition
+ 
+
+ align:start position:0%
+that make sense but high level cognition
+we wouldn't really have functional
+
+ align:start position:0%
+we wouldn't really have functional
+ 
+
+ align:start position:0%
+we wouldn't really have functional
+specificity for that but oh yes we do
+
+ align:start position:0%
+specificity for that but oh yes we do
+ 
+
+ align:start position:0%
+specificity for that but oh yes we do
+here are some language regions there's a
+
+ align:start position:0%
+here are some language regions there's a
+ 
+
+ align:start position:0%
+here are some language regions there's a
+bunch of them in the temporal and
+
+ align:start position:0%
+bunch of them in the temporal and
+ 
+
+ align:start position:0%
+bunch of them in the temporal and
+frontal lobe that have been known since
+
+ align:start position:0%
+frontal lobe that have been known since
+ 
+
+ align:start position:0%
+frontal lobe that have been known since
+wernicke and Broca but now with
+
+ align:start position:0%
+wernicke and Broca but now with
+ 
+
+ align:start position:0%
+wernicke and Broca but now with
+functional MRI we can identify them in
+
+ align:start position:0%
+functional MRI we can identify them in
+ 
+
+ align:start position:0%
+functional MRI we can identify them in
+individual subjects and go back and
+
+ align:start position:0%
+individual subjects and go back and
+ 
+
+ align:start position:0%
+individual subjects and go back and
+repeatedly query them and say are they
+
+ align:start position:0%
+repeatedly query them and say are they
+ 
+
+ align:start position:0%
+repeatedly query them and say are they
+involved in all of these other mental
+
+ align:start position:0%
+involved in all of these other mental
+ 
+
+ align:start position:0%
+involved in all of these other mental
+processes so this is now the response in
+
+ align:start position:0%
+processes so this is now the response in
+ 
+
+ align:start position:0%
+processes so this is now the response in
+a language region so identified here's a
+
+ align:start position:0%
+a language region so identified here's a
+ 
+
+ align:start position:0%
+a language region so identified here's a
+response when you're listening to
+
+ align:start position:0%
+response when you're listening to
+ 
+
+ align:start position:0%
+response when you're listening to
+sentences this is when you're listening
+
+ align:start position:0%
+sentences this is when you're listening
+ 
+
+ align:start position:0%
+sentences this is when you're listening
+to Jabberwocky
+
+ align:start position:0%
+to Jabberwocky
+ 
+
+ align:start position:0%
+to Jabberwocky
+nonsense strings here's when you're
+
+ align:start position:0%
+nonsense strings here's when you're
+ 
+
+ align:start position:0%
+nonsense strings here's when you're
+saying ba da da ba da da it's not just
+
+ align:start position:0%
+saying ba da da ba da da it's not just
+ 
+
+ align:start position:0%
+saying ba da da ba da da it's not just
+speech sounds here's when you're
+
+ align:start position:0%
+speech sounds here's when you're
+ 
+
+ align:start position:0%
+speech sounds here's when you're
+listening to synthetically decomposed
+
+ align:start position:0%
+listening to synthetically decomposed
+ 
+
+ align:start position:0%
+listening to synthetically decomposed
+speech sounds that are acoustically very
+
+ align:start position:0%
+speech sounds that are acoustically very
+ 
+
+ align:start position:0%
+speech sounds that are acoustically very
+similar to the Jabberwocky speech it's
+
+ align:start position:0%
+similar to the Jabberwocky speech it's
+ 
+
+ align:start position:0%
+similar to the Jabberwocky speech it's
+just not interested in those things it
+
+ align:start position:0%
+just not interested in those things it
+ 
+
+ align:start position:0%
+just not interested in those things it
+seems to be interested in something more
+
+ align:start position:0%
+seems to be interested in something more
+ 
+
+ align:start position:0%
+seems to be interested in something more
+like the meaning of a sentence and just
+
+ align:start position:0%
+like the meaning of a sentence and just
+ 
+
+ align:start position:0%
+like the meaning of a sentence and just
+to show you some other data we have on
+
+ align:start position:0%
+to show you some other data we have on
+ 
+
+ align:start position:0%
+to show you some other data we have on
+this this is data from F Federico who
+
+ align:start position:0%
+this this is data from F Federico who
+ 
+
+ align:start position:0%
+this this is data from F Federico who
+has tested this region now this is sort
+
+ align:start position:0%
+has tested this region now this is sort
+ 
+
+ align:start position:0%
+has tested this region now this is sort
+of roughly Broca's area on the main
+
+ align:start position:0%
+of roughly Broca's area on the main
+ 
+
+ align:start position:0%
+of roughly Broca's area on the main
+mental functions that people have argued
+
+ align:start position:0%
+mental functions that people have argued
+ 
+
+ align:start position:0%
+mental functions that people have argued
+overlap in the brain with language
+
+ align:start position:0%
+overlap in the brain with language
+ 
+
+ align:start position:0%
+overlap in the brain with language
+namely sorry this is probably hard to
+
+ align:start position:0%
+namely sorry this is probably hard to
+ 
+
+ align:start position:0%
+namely sorry this is probably hard to
+see here but arithmetic so we have
+
+ align:start position:0%
+see here but arithmetic so we have
+ 
+
+ align:start position:0%
+see here but arithmetic so we have
+difficult and easy mental arithmetic
+
+ align:start position:0%
+difficult and easy mental arithmetic
+ 
+
+ align:start position:0%
+difficult and easy mental arithmetic
+intact and scrambled music and pink a
+
+ align:start position:0%
+intact and scrambled music and pink a
+ 
+
+ align:start position:0%
+intact and scrambled music and pink a
+bunch of working memory tasks spatial
+
+ align:start position:0%
+bunch of working memory tasks spatial
+ 
+
+ align:start position:0%
+bunch of working memory tasks spatial
+working memory and verbal working memory
+
+ align:start position:0%
+working memory and verbal working memory
+ 
+
+ align:start position:0%
+working memory and verbal working memory
+and a bunch of cognitive control tasks
+
+ align:start position:0%
+and a bunch of cognitive control tasks
+ 
+
+ align:start position:0%
+and a bunch of cognitive control tasks
+just kind of a tension demanding tasks
+
+ align:start position:0%
+just kind of a tension demanding tasks
+ 
+
+ align:start position:0%
+just kind of a tension demanding tasks
+where you have to switch between tasks
+
+ align:start position:0%
+where you have to switch between tasks
+ 
+
+ align:start position:0%
+where you have to switch between tasks
+and stuff like that and here is a
+
+ align:start position:0%
+and stuff like that and here is a
+ 
+
+ align:start position:0%
+and stuff like that and here is a
+response profile in that region reading
+
+ align:start position:0%
+response profile in that region reading
+ 
+
+ align:start position:0%
+response profile in that region reading
+sentences reading non-word strings all
+
+ align:start position:0%
+sentences reading non-word strings all
+ 
+
+ align:start position:0%
+sentences reading non-word strings all
+of those other tasks both the difficult
+
+ align:start position:0%
+of those other tasks both the difficult
+ 
+
+ align:start position:0%
+of those other tasks both the difficult
+and the easy version no response at all
+
+ align:start position:0%
+and the easy version no response at all
+ 
+
+ align:start position:0%
+and the easy version no response at all
+that's extreme functional specificity
+
+ align:start position:0%
+that's extreme functional specificity
+ 
+
+ align:start position:0%
+that's extreme functional specificity
+right it's not that we've tested
+
+ align:start position:0%
+right it's not that we've tested
+ 
+
+ align:start position:0%
+right it's not that we've tested
+everything there's more to be done but
+
+ align:start position:0%
+everything there's more to be done but
+ 
+
+ align:start position:0%
+everything there's more to be done but
+the first pass Quarian of you know do
+
+ align:start position:0%
+the first pass Quarian of you know do
+ 
+
+ align:start position:0%
+the first pass Quarian of you know do
+those language regions engage in all of
+
+ align:start position:0%
+those language regions engage in all of
+ 
+
+ align:start position:0%
+those language regions engage in all of
+these other things that people thought
+
+ align:start position:0%
+these other things that people thought
+ 
+
+ align:start position:0%
+these other things that people thought
+might overlap with language the answer
+
+ align:start position:0%
+might overlap with language the answer
+ 
+
+ align:start position:0%
+might overlap with language the answer
+is no they don't
+
+ align:start position:0%
+is no they don't
+ 
+
+ align:start position:0%
+is no they don't
+right and interest and I think that's
+
+ align:start position:0%
+right and interest and I think that's
+ 
+
+ align:start position:0%
+right and interest and I think that's
+really deep and and interesting because
+
+ align:start position:0%
+really deep and and interesting because
+ 
+
+ align:start position:0%
+really deep and and interesting because
+it means that you know this this basic
+
+ align:start position:0%
+it means that you know this this basic
+ 
+
+ align:start position:0%
+it means that you know this this basic
+question that we all you know start
+
+ align:start position:0%
+question that we all you know start
+ 
+
+ align:start position:0%
+question that we all you know start
+asking ourselves when we're young is
+
+ align:start position:0%
+asking ourselves when we're young is
+ 
+
+ align:start position:0%
+asking ourselves when we're young is
+what is the relationship between
+
+ align:start position:0%
+what is the relationship between
+ 
+
+ align:start position:0%
+what is the relationship between
+language
+
+ align:start position:0%
+language
+ 
+
+ align:start position:0%
+language
+thought I know Liz disagrees with me
+
+ align:start position:0%
+thought I know Liz disagrees with me
+ 
+
+ align:start position:0%
+thought I know Liz disagrees with me
+somewhat on this that's because she's
+
+ align:start position:0%
+somewhat on this that's because she's
+ 
+
+ align:start position:0%
+somewhat on this that's because she's
+very articulate and she doesn't feel the
+
+ align:start position:0%
+very articulate and she doesn't feel the
+ 
+
+ align:start position:0%
+very articulate and she doesn't feel the
+difference between an idea and its
+
+ align:start position:0%
+difference between an idea and its
+ 
+
+ align:start position:0%
+difference between an idea and its
+articulation I'm less articulate it's
+
+ align:start position:0%
+articulation I'm less articulate it's
+ 
+
+ align:start position:0%
+articulation I'm less articulate it's
+very obvious to me they're different
+
+ align:start position:0%
+very obvious to me they're different
+ 
+
+ align:start position:0%
+very obvious to me they're different
+things you know it's not the only reason
+
+ align:start position:0%
+things you know it's not the only reason
+ 
+
+ align:start position:0%
+things you know it's not the only reason
+she has data too and it'd be fun to
+
+ align:start position:0%
+she has data too and it'd be fun to
+ 
+
+ align:start position:0%
+she has data too and it'd be fun to
+discuss but I think there's a vast gulf
+
+ align:start position:0%
+discuss but I think there's a vast gulf
+ 
+
+ align:start position:0%
+discuss but I think there's a vast gulf
+between the two and that all many
+
+ align:start position:0%
+between the two and that all many
+ 
+
+ align:start position:0%
+between the two and that all many
+different aspects of cognition can
+
+ align:start position:0%
+different aspects of cognition can
+ 
+
+ align:start position:0%
+different aspects of cognition can
+proceed just fine without language
+
+ align:start position:0%
+proceed just fine without language
+ 
+
+ align:start position:0%
+proceed just fine without language
+regions and actually the stronger
+
+ align:start position:0%
+regions and actually the stronger
+ 
+
+ align:start position:0%
+regions and actually the stronger
+evidence for that comes not from these
+
+ align:start position:0%
+evidence for that comes not from these
+ 
+
+ align:start position:0%
+evidence for that comes not from these
+functional MRI data striking as I think
+
+ align:start position:0%
+functional MRI data striking as I think
+ 
+
+ align:start position:0%
+functional MRI data striking as I think
+they are but from patient data so
+
+ align:start position:0%
+they are but from patient data so
+ 
+
+ align:start position:0%
+they are but from patient data so
+rosemary Varley and England has been
+
+ align:start position:0%
+rosemary Varley and England has been
+ 
+
+ align:start position:0%
+rosemary Varley and England has been
+testing patients with global aphasia
+
+ align:start position:0%
+testing patients with global aphasia
+ 
+
+ align:start position:0%
+testing patients with global aphasia
+this is this very tragic horrible thing
+
+ align:start position:0%
+this is this very tragic horrible thing
+ 
+
+ align:start position:0%
+this is this very tragic horrible thing
+that happens in patients who have
+
+ align:start position:0%
+that happens in patients who have
+ 
+
+ align:start position:0%
+that happens in patients who have
+massive left hemisphere strokes that
+
+ align:start position:0%
+massive left hemisphere strokes that
+ 
+
+ align:start position:0%
+massive left hemisphere strokes that
+pretty much take out essentially all of
+
+ align:start position:0%
+pretty much take out essentially all of
+ 
+
+ align:start position:0%
+pretty much take out essentially all of
+their language abilities those people
+
+ align:start position:0%
+their language abilities those people
+ 
+
+ align:start position:0%
+their language abilities those people
+she has shown are intact in their
+
+ align:start position:0%
+she has shown are intact in their
+ 
+
+ align:start position:0%
+she has shown are intact in their
+navigation abilities their arithmetic
+
+ align:start position:0%
+navigation abilities their arithmetic
+ 
+
+ align:start position:0%
+navigation abilities their arithmetic
+abilities their ability to solve logic
+
+ align:start position:0%
+abilities their ability to solve logic
+ 
+
+ align:start position:0%
+abilities their ability to solve logic
+problems their ability to think about
+
+ align:start position:0%
+problems their ability to think about
+ 
+
+ align:start position:0%
+problems their ability to think about
+what other people are thinking their
+
+ align:start position:0%
+what other people are thinking their
+ 
+
+ align:start position:0%
+what other people are thinking their
+ability to appreciate music and so on
+
+ align:start position:0%
+ability to appreciate music and so on
+ 
+
+ align:start position:0%
+ability to appreciate music and so on
+and so forth so I think there's really a
+
+ align:start position:0%
+and so forth so I think there's really a
+ 
+
+ align:start position:0%
+and so forth so I think there's really a
+very big difference between a major part
+
+ align:start position:0%
+very big difference between a major part
+ 
+
+ align:start position:0%
+very big difference between a major part
+of the system that you need to
+
+ align:start position:0%
+of the system that you need to
+ 
+
+ align:start position:0%
+of the system that you need to
+understand the meaning of a sentence and
+
+ align:start position:0%
+understand the meaning of a sentence and
+ 
+
+ align:start position:0%
+understand the meaning of a sentence and
+all of those other aspects of thought
+
+ align:start position:0%
+all of those other aspects of thought
+ 
+
+ align:start position:0%
+all of those other aspects of thought
+this is just showing you what I mean by
+
+ align:start position:0%
+this is just showing you what I mean by
+ 
+
+ align:start position:0%
+this is just showing you what I mean by
+functional specificity what the evidence
+
+ align:start position:0%
+functional specificity what the evidence
+ 
+
+ align:start position:0%
+functional specificity what the evidence
+what the basic first-order evidence is
+
+ align:start position:0%
+what the basic first-order evidence is
+ 
+
+ align:start position:0%
+what the basic first-order evidence is
+and these are just the regions that we
+
+ align:start position:0%
+and these are just the regions that we
+ 
+
+ align:start position:0%
+and these are just the regions that we
+happen to have in this study so I could
+
+ align:start position:0%
+happen to have in this study so I could
+ 
+
+ align:start position:0%
+happen to have in this study so I could
+make a new slide but for lots of other
+
+ align:start position:0%
+make a new slide but for lots of other
+ 
+
+ align:start position:0%
+make a new slide but for lots of other
+perceptual and cognitive functions
+
+ align:start position:0%
+perceptual and cognitive functions
+ 
+
+ align:start position:0%
+perceptual and cognitive functions
+people have found quite specific brain
+
+ align:start position:0%
+people have found quite specific brain
+ 
+
+ align:start position:0%
+people have found quite specific brain
+regions for perceiving bodies and scenes
+
+ align:start position:0%
+regions for perceiving bodies and scenes
+ 
+
+ align:start position:0%
+regions for perceiving bodies and scenes
+of course motion the area MT has been
+
+ align:start position:0%
+of course motion the area MT has been
+ 
+
+ align:start position:0%
+of course motion the area MT has been
+studied for a long time
+
+ align:start position:0%
+studied for a long time
+ 
+
+ align:start position:0%
+studied for a long time
+regions that are quite quite
+
+ align:start position:0%
+regions that are quite quite
+ 
+
+ align:start position:0%
+regions that are quite quite
+specifically involved in processing
+
+ align:start position:0%
+specifically involved in processing
+ 
+
+ align:start position:0%
+specifically involved in processing
+shape we've been studying color
+
+ align:start position:0%
+shape we've been studying color
+ 
+
+ align:start position:0%
+shape we've been studying color
+processing regions recently they're not
+
+ align:start position:0%
+processing regions recently they're not
+ 
+
+ align:start position:0%
+processing regions recently they're not
+as selective for color as some of these
+
+ align:start position:0%
+as selective for color as some of these
+ 
+
+ align:start position:0%
+as selective for color as some of these
+other regions but they're very
+
+ align:start position:0%
+other regions but they're very
+ 
+
+ align:start position:0%
+other regions but they're very
+anatomically consistent and things I
+
+ align:start position:0%
+anatomically consistent and things I
+ 
+
+ align:start position:0%
+anatomically consistent and things I
+mentioned before in my brief
+
+ align:start position:0%
+mentioned before in my brief
+ 
+
+ align:start position:0%
+mentioned before in my brief
+introduction regions that are
+
+ align:start position:0%
+introduction regions that are
+ 
+
+ align:start position:0%
+introduction regions that are
+specifically involved in processing
+
+ align:start position:0%
+specifically involved in processing
+ 
+
+ align:start position:0%
+specifically involved in processing
+pitch information and music information
+
+ align:start position:0%
+pitch information and music information
+ 
+
+ align:start position:0%
+pitch information and music information
+and as you'll hear next week from our
+
+ align:start position:0%
+and as you'll hear next week from our
+ 
+
+ align:start position:0%
+and as you'll hear next week from our
+Rebecca Saxe theory of mind or thinking
+
+ align:start position:0%
+Rebecca Saxe theory of mind or thinking
+ 
+
+ align:start position:0%
+Rebecca Saxe theory of mind or thinking
+about other people's thoughts and so
+
+ align:start position:0%
+about other people's thoughts and so
+ 
+
+ align:start position:0%
+about other people's thoughts and so
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+quite a litany of mental functions that
+
+ align:start position:0%
+quite a litany of mental functions that
+ 
+
+ align:start position:0%
+quite a litany of mental functions that
+have brain regions that are quite
+
+ align:start position:0%
+have brain regions that are quite
+ 
+
+ align:start position:0%
+have brain regions that are quite
+specifically engaged that mental
+
+ align:start position:0%
+specifically engaged that mental
+ 
+
+ align:start position:0%
+specifically engaged that mental
+function and each of these to varying
+
+ align:start position:0%
+function and each of these to varying
+ 
+
+ align:start position:0%
+function and each of these to varying
+degrees but to you know some appreciable
+
+ align:start position:0%
+degrees but to you know some appreciable
+ 
+
+ align:start position:0%
+degrees but to you know some appreciable
+degree have corroborating evidence from
+
+ align:start position:0%
+degree have corroborating evidence from
+ 
+
+ align:start position:0%
+degree have corroborating evidence from
+patients who have that specific deficit
+
+ align:start position:0%
+patients who have that specific deficit
+ 
+
+ align:start position:0%
+patients who have that specific deficit
+so that shows that each of these has is
+
+ align:start position:0%
+so that shows that each of these has is
+ 
+
+ align:start position:0%
+so that shows that each of these has is
+likely to be not only activated during
+
+ align:start position:0%
+likely to be not only activated during
+ 
+
+ align:start position:0%
+likely to be not only activated during
+but causally involved in its mental
+
+ align:start position:0%
+but causally involved in its mental
+ 
+
+ align:start position:0%
+but causally involved in its mental
+function and as I mentioned there are
+
+ align:start position:0%
+function and as I mentioned there are
+ 
+
+ align:start position:0%
+function and as I mentioned there are
+actually good counter arguments to some
+
+ align:start position:0%
+actually good counter arguments to some
+ 
+
+ align:start position:0%
+actually good counter arguments to some
+of the things I've been making that are
+
+ align:start position:0%
+of the things I've been making that are
+ 
+
+ align:start position:0%
+of the things I've been making that are
+worth discussing I think the pattern
+
+ align:start position:0%
+worth discussing I think the pattern
+ 
+
+ align:start position:0%
+worth discussing I think the pattern
+analysis data is the strongest oh and I
+
+ align:start position:0%
+analysis data is the strongest oh and I
+ 
+
+ align:start position:0%
+analysis data is the strongest oh and I
+do need to take a few more minutes just
+
+ align:start position:0%
+do need to take a few more minutes just
+ 
+
+ align:start position:0%
+do need to take a few more minutes just
+like five or something okay
+
+ align:start position:0%
+like five or something okay
+ 
+
+ align:start position:0%
+like five or something okay
+so all of that's to say so here's you
+
+ align:start position:0%
+so all of that's to say so here's you
+ 
+
+ align:start position:0%
+so all of that's to say so here's you
+know roughly where we are now there are
+
+ align:start position:0%
+know roughly where we are now there are
+ 
+
+ align:start position:0%
+know roughly where we are now there are
+counter arguments but loose talk about
+
+ align:start position:0%
+counter arguments but loose talk about
+ 
+
+ align:start position:0%
+counter arguments but loose talk about
+oh there's no localization of function
+
+ align:start position:0%
+oh there's no localization of function
+ 
+
+ align:start position:0%
+oh there's no localization of function
+in the brain you got engaged with this
+
+ align:start position:0%
+in the brain you got engaged with this
+ 
+
+ align:start position:0%
+in the brain you got engaged with this
+at first and give me a serious
+
+ align:start position:0%
+at first and give me a serious
+ 
+
+ align:start position:0%
+at first and give me a serious
+counter-argument right okay finally I
+
+ align:start position:0%
+counter-argument right okay finally I
+ 
+
+ align:start position:0%
+counter-argument right okay finally I
+want to say that though it's not that
+
+ align:start position:0%
+want to say that though it's not that
+ 
+
+ align:start position:0%
+want to say that though it's not that
+the whole brain is like this right there
+
+ align:start position:0%
+the whole brain is like this right there
+ 
+
+ align:start position:0%
+the whole brain is like this right there
+are it's there there big gray patches
+
+ align:start position:0%
+are it's there there big gray patches
+ 
+
+ align:start position:0%
+are it's there there big gray patches
+where we haven't figured out what it's
+
+ align:start position:0%
+where we haven't figured out what it's
+ 
+
+ align:start position:0%
+where we haven't figured out what it's
+doing but there are also substantial
+
+ align:start position:0%
+doing but there are also substantial
+ 
+
+ align:start position:0%
+doing but there are also substantial
+patches that are have already been shown
+
+ align:start position:0%
+patches that are have already been shown
+ 
+
+ align:start position:0%
+patches that are have already been shown
+to be in some sense the opposite of this
+
+ align:start position:0%
+to be in some sense the opposite of this
+ 
+
+ align:start position:0%
+to be in some sense the opposite of this
+region used in almost any difficult task
+
+ align:start position:0%
+region used in almost any difficult task
+ 
+
+ align:start position:0%
+region used in almost any difficult task
+you do at all and I think this is a very
+
+ align:start position:0%
+you do at all and I think this is a very
+ 
+
+ align:start position:0%
+you do at all and I think this is a very
+interesting part of the whole story of
+
+ align:start position:0%
+interesting part of the whole story of
+ 
+
+ align:start position:0%
+interesting part of the whole story of
+the architecture of intelligence so I'm
+
+ align:start position:0%
+the architecture of intelligence so I'm
+ 
+
+ align:start position:0%
+the architecture of intelligence so I'm
+going to take five minutes and tell you
+
+ align:start position:0%
+going to take five minutes and tell you
+ 
+
+ align:start position:0%
+going to take five minutes and tell you
+about it this work is primarily the work
+
+ align:start position:0%
+about it this work is primarily the work
+ 
+
+ align:start position:0%
+about it this work is primarily the work
+of John Duncan in England and he's been
+
+ align:start position:0%
+of John Duncan in England and he's been
+ 
+
+ align:start position:0%
+of John Duncan in England and he's been
+pointing out for about 15 years that
+
+ align:start position:0%
+pointing out for about 15 years that
+ 
+
+ align:start position:0%
+pointing out for about 15 years that
+there are regions in the frontal lobe
+
+ align:start position:0%
+there are regions in the frontal lobe
+ 
+
+ align:start position:0%
+there are regions in the frontal lobe
+shown here that are engaged in pretty
+
+ align:start position:0%
+shown here that are engaged in pretty
+ 
+
+ align:start position:0%
+shown here that are engaged in pretty
+much any difficult tasks you do anytime
+
+ align:start position:0%
+much any difficult tasks you do anytime
+ 
+
+ align:start position:0%
+much any difficult tasks you do anytime
+you increase the difficulty of a task
+
+ align:start position:0%
+you increase the difficulty of a task
+ 
+
+ align:start position:0%
+you increase the difficulty of a task
+whether it's perceptual or high-level
+
+ align:start position:0%
+whether it's perceptual or high-level
+ 
+
+ align:start position:0%
+whether it's perceptual or high-level
+cognitive those regions turn on
+
+ align:start position:0%
+cognitive those regions turn on
+ 
+
+ align:start position:0%
+cognitive those regions turn on
+differentially and so that's why he
+
+ align:start position:0%
+differentially and so that's why he
+ 
+
+ align:start position:0%
+differentially and so that's why he
+calls a multiple demand they respond to
+
+ align:start position:0%
+calls a multiple demand they respond to
+ 
+
+ align:start position:0%
+calls a multiple demand they respond to
+multiple different kinds of demand and
+
+ align:start position:0%
+multiple different kinds of demand and
+ 
+
+ align:start position:0%
+multiple different kinds of demand and
+so right Duncan argues that these
+
+ align:start position:0%
+so right Duncan argues that these
+ 
+
+ align:start position:0%
+so right Duncan argues that these
+regions are related to fluid
+
+ align:start position:0%
+regions are related to fluid
+ 
+
+ align:start position:0%
+regions are related to fluid
+intelligence
+
+ align:start position:0%
+intelligence
+ 
+
+ align:start position:0%
+intelligence
+so remember Spearman who I started with
+
+ align:start position:0%
+so remember Spearman who I started with
+ 
+
+ align:start position:0%
+so remember Spearman who I started with
+who talks about the the general factor
+
+ align:start position:0%
+who talks about the the general factor
+ 
+
+ align:start position:0%
+who talks about the the general factor
+gee well Duncan thinks that basically
+
+ align:start position:0%
+gee well Duncan thinks that basically
+ 
+
+ align:start position:0%
+gee well Duncan thinks that basically
+this is the seat of
+
+ align:start position:0%
+this is the seat of
+ 
+
+ align:start position:0%
+this is the seat of
+these regions here to oversimplify his
+
+ align:start position:0%
+these regions here to oversimplify his
+ 
+
+ align:start position:0%
+these regions here to oversimplify his
+argument evidence for that and one is
+
+ align:start position:0%
+argument evidence for that and one is
+ 
+
+ align:start position:0%
+argument evidence for that and one is
+well they're strongly activated when you
+
+ align:start position:0%
+well they're strongly activated when you
+ 
+
+ align:start position:0%
+well they're strongly activated when you
+do classic G loading tasks that's not
+
+ align:start position:0%
+do classic G loading tasks that's not
+ 
+
+ align:start position:0%
+do classic G loading tasks that's not
+that surprising they're activated in all
+
+ align:start position:0%
+that surprising they're activated in all
+ 
+
+ align:start position:0%
+that surprising they're activated in all
+different kinds of tasks more
+
+ align:start position:0%
+different kinds of tasks more
+ 
+
+ align:start position:0%
+different kinds of tasks more
+interestingly he did a large patient
+
+ align:start position:0%
+interestingly he did a large patient
+ 
+
+ align:start position:0%
+interestingly he did a large patient
+study where they found a eighty or so
+
+ align:start position:0%
+study where they found a eighty or so
+ 
+
+ align:start position:0%
+study where they found a eighty or so
+patients in their neuro psych patients
+
+ align:start position:0%
+patients in their neuro psych patients
+ 
+
+ align:start position:0%
+patients in their neuro psych patients
+in their patient database and they
+
+ align:start position:0%
+in their patient database and they
+ 
+
+ align:start position:0%
+in their patient database and they
+identified the Lok locus of the brain
+
+ align:start position:0%
+identified the Lok locus of the brain
+ 
+
+ align:start position:0%
+identified the Lok locus of the brain
+damaged in each of those patients and
+
+ align:start position:0%
+damaged in each of those patients and
+ 
+
+ align:start position:0%
+damaged in each of those patients and
+what they did was they measured post
+
+ align:start position:0%
+what they did was they measured post
+ 
+
+ align:start position:0%
+what they did was they measured post
+injury IQ they estimated from a variety
+
+ align:start position:0%
+injury IQ they estimated from a variety
+ 
+
+ align:start position:0%
+injury IQ they estimated from a variety
+of sources pre-injury IQ and they asked
+
+ align:start position:0%
+of sources pre-injury IQ and they asked
+ 
+
+ align:start position:0%
+of sources pre-injury IQ and they asked
+how much does your IQ go down after
+
+ align:start position:0%
+how much does your IQ go down after
+ 
+
+ align:start position:0%
+how much does your IQ go down after
+brain damage as a function of one the
+
+ align:start position:0%
+brain damage as a function of one the
+ 
+
+ align:start position:0%
+brain damage as a function of one the
+volume of tissue you lost in brain
+
+ align:start position:0%
+volume of tissue you lost in brain
+ 
+
+ align:start position:0%
+volume of tissue you lost in brain
+damage into the locus of tissue okay and
+
+ align:start position:0%
+damage into the locus of tissue okay and
+ 
+
+ align:start position:0%
+damage into the locus of tissue okay and
+basically what he finds is if you lose
+
+ align:start position:0%
+basically what he finds is if you lose
+ 
+
+ align:start position:0%
+basically what he finds is if you lose
+tissue in these regions your IQ goes
+
+ align:start position:0%
+tissue in these regions your IQ goes
+ 
+
+ align:start position:0%
+tissue in these regions your IQ goes
+down if you lose tissue elsewhere you
+
+ align:start position:0%
+down if you lose tissue elsewhere you
+ 
+
+ align:start position:0%
+down if you lose tissue elsewhere you
+may become paralyzed or aphasic or
+
+ align:start position:0%
+may become paralyzed or aphasic or
+ 
+
+ align:start position:0%
+may become paralyzed or aphasic or
+prosopagnosia
+
+ align:start position:0%
+prosopagnosia
+ 
+
+ align:start position:0%
+prosopagnosia
+you don't lose your your IQ does not go
+
+ align:start position:0%
+you don't lose your your IQ does not go
+ 
+
+ align:start position:0%
+you don't lose your your IQ does not go
+down okay in fact he made a kind of
+
+ align:start position:0%
+down okay in fact he made a kind of
+ 
+
+ align:start position:0%
+down okay in fact he made a kind of
+ghoulish calculation that you lose six
+
+ align:start position:0%
+ghoulish calculation that you lose six
+ 
+
+ align:start position:0%
+ghoulish calculation that you lose six
+and a half IQ points for every ten cubic
+
+ align:start position:0%
+and a half IQ points for every ten cubic
+ 
+
+ align:start position:0%
+and a half IQ points for every ten cubic
+centimeters of this region of cortex and
+
+ align:start position:0%
+centimeters of this region of cortex and
+ 
+
+ align:start position:0%
+centimeters of this region of cortex and
+almost nothing for for the rest of the
+
+ align:start position:0%
+almost nothing for for the rest of the
+ 
+
+ align:start position:0%
+almost nothing for for the rest of the
+brain so you know this is kind of crude
+
+ align:start position:0%
+brain so you know this is kind of crude
+ 
+
+ align:start position:0%
+brain so you know this is kind of crude
+it's you know it's very imperfect what
+
+ align:start position:0%
+it's you know it's very imperfect what
+ 
+
+ align:start position:0%
+it's you know it's very imperfect what
+you can get from patient study but I
+
+ align:start position:0%
+you can get from patient study but I
+ 
+
+ align:start position:0%
+you can get from patient study but I
+think it's intriguing and so his
+
+ align:start position:0%
+think it's intriguing and so his
+ 
+
+ align:start position:0%
+think it's intriguing and so his
+suggestion is that in addition to these
+
+ align:start position:0%
+suggestion is that in addition to these
+ 
+
+ align:start position:0%
+suggestion is that in addition to these
+highly specialized cortical regions that
+
+ align:start position:0%
+highly specialized cortical regions that
+ 
+
+ align:start position:0%
+highly specialized cortical regions that
+we use for these these particular
+
+ align:start position:0%
+we use for these these particular
+ 
+
+ align:start position:0%
+we use for these these particular
+important tasks we also have this kind
+
+ align:start position:0%
+important tasks we also have this kind
+ 
+
+ align:start position:0%
+important tasks we also have this kind
+of general-purpose machinery that makes
+
+ align:start position:0%
+of general-purpose machinery that makes
+ 
+
+ align:start position:0%
+of general-purpose machinery that makes
+us generically smart and I'm going to
+
+ align:start position:0%
+us generically smart and I'm going to
+ 
+
+ align:start position:0%
+us generically smart and I'm going to
+skip our own we've tested this more
+
+ align:start position:0%
+skip our own we've tested this more
+ 
+
+ align:start position:0%
+skip our own we've tested this more
+seriously he group analyses which I
+
+ align:start position:0%
+seriously he group analyses which I
+ 
+
+ align:start position:0%
+seriously he group analyses which I
+don't like we did it in collaboration
+
+ align:start position:0%
+don't like we did it in collaboration
+ 
+
+ align:start position:0%
+don't like we did it in collaboration
+with him with individual subject
+
+ align:start position:0%
+with him with individual subject
+ 
+
+ align:start position:0%
+with him with individual subject
+analyses the most precise measurements
+
+ align:start position:0%
+analyses the most precise measurements
+ 
+
+ align:start position:0%
+analyses the most precise measurements
+we could make and boy is he right I mean
+
+ align:start position:0%
+we could make and boy is he right I mean
+ 
+
+ align:start position:0%
+we could make and boy is he right I mean
+these even to the voxel you can find
+
+ align:start position:0%
+these even to the voxel you can find
+ 
+
+ align:start position:0%
+these even to the voxel you can find
+that these regions are engaged in seven
+
+ align:start position:0%
+that these regions are engaged in seven
+ 
+
+ align:start position:0%
+that these regions are engaged in seven
+or eight very very different kinds of
+
+ align:start position:0%
+or eight very very different kinds of
+ 
+
+ align:start position:0%
+or eight very very different kinds of
+cognitive demand all activate the same
+
+ align:start position:0%
+cognitive demand all activate the same
+ 
+
+ align:start position:0%
+cognitive demand all activate the same
+voxel differentially so the basic story
+
+ align:start position:0%
+voxel differentially so the basic story
+ 
+
+ align:start position:0%
+voxel differentially so the basic story
+I'm putting forth here without the whole
+
+ align:start position:0%
+I'm putting forth here without the whole
+ 
+
+ align:start position:0%
+I'm putting forth here without the whole
+second half of my talk I'm sorry about
+
+ align:start position:0%
+second half of my talk I'm sorry about
+ 
+
+ align:start position:0%
+second half of my talk I'm sorry about
+that is that
+
+ align:start position:0%
+that is that
+ 
+
+ align:start position:0%
+that is that
+is that the macroscale the architecture
+
+ align:start position:0%
+is that the macroscale the architecture
+ 
+
+ align:start position:0%
+is that the macroscale the architecture
+of human intelligence is that we have
+
+ align:start position:0%
+of human intelligence is that we have
+ 
+
+ align:start position:0%
+of human intelligence is that we have
+these special-purpose bits for a small
+
+ align:start position:0%
+these special-purpose bits for a small
+ 
+
+ align:start position:0%
+these special-purpose bits for a small
+issue of important mental functions not
+
+ align:start position:0%
+issue of important mental functions not
+ 
+
+ align:start position:0%
+issue of important mental functions not
+all of them innate maybe some of them in
+
+ align:start position:0%
+all of them innate maybe some of them in
+ 
+
+ align:start position:0%
+all of them innate maybe some of them in
+addition we have some general-purpose
+
+ align:start position:0%
+addition we have some general-purpose
+ 
+
+ align:start position:0%
+addition we have some general-purpose
+machinery there's loes work that we
+
+ align:start position:0%
+machinery there's loes work that we
+ 
+
+ align:start position:0%
+machinery there's loes work that we
+don't know from the precise computations
+
+ align:start position:0%
+don't know from the precise computations
+ 
+
+ align:start position:0%
+don't know from the precise computations
+that go on in these things to their
+
+ align:start position:0%
+that go on in these things to their
+ 
+
+ align:start position:0%
+that go on in these things to their
+connectivity to they you know the actual
+
+ align:start position:0%
+connectivity to they you know the actual
+ 
+
+ align:start position:0%
+connectivity to they you know the actual
+precise representations that you can see
+
+ align:start position:0%
+precise representations that you can see
+ 
+
+ align:start position:0%
+precise representations that you can see
+with the neural code if you could
+
+ align:start position:0%
+with the neural code if you could
+ 
+
+ align:start position:0%
+with the neural code if you could
+measure it which we can't in humans to
+
+ align:start position:0%
+measure it which we can't in humans to
+ 
+
+ align:start position:0%
+measure it which we can't in humans to
+the timing of these interactions which
+
+ align:start position:0%
+the timing of these interactions which
+ 
+
+ align:start position:0%
+the timing of these interactions which
+of them are uniquely human which of them
+
+ align:start position:0%
+of them are uniquely human which of them
+ 
+
+ align:start position:0%
+of them are uniquely human which of them
+are also present in monkeys and I don't
+
+ align:start position:0%
+are also present in monkeys and I don't
+ 
+
+ align:start position:0%
+are also present in monkeys and I don't
+have time to go find a slide but one of
+
+ align:start position:0%
+have time to go find a slide but one of
+ 
+
+ align:start position:0%
+have time to go find a slide but one of
+the things we've been doing recently is
+
+ align:start position:0%
+the things we've been doing recently is
+ 
+
+ align:start position:0%
+the things we've been doing recently is
+looking in the ventral visual pathway at
+
+ align:start position:0%
+looking in the ventral visual pathway at
+ 
+
+ align:start position:0%
+looking in the ventral visual pathway at
+the organization of face place and color
+
+ align:start position:0%
+the organization of face place and color
+ 
+
+ align:start position:0%
+the organization of face place and color
+selectivity and what we see is that as
+
+ align:start position:0%
+selectivity and what we see is that as
+ 
+
+ align:start position:0%
+selectivity and what we see is that as
+we as me and bevel Conway and Rosa Rosa
+
+ align:start position:0%
+we as me and bevel Conway and Rosa Rosa
+ 
+
+ align:start position:0%
+we as me and bevel Conway and Rosa Rosa
+later Sousa bevel and Rosa had
+
+ align:start position:0%
+later Sousa bevel and Rosa had
+ 
+
+ align:start position:0%
+later Sousa bevel and Rosa had
+previously shown that on the lateral
+
+ align:start position:0%
+previously shown that on the lateral
+ 
+
+ align:start position:0%
+previously shown that on the lateral
+surface in the monkey you have three
+
+ align:start position:0%
+surface in the monkey you have three
+ 
+
+ align:start position:0%
+surface in the monkey you have three
+bands of cell activity so it goes face
+
+ align:start position:0%
+bands of cell activity so it goes face
+ 
+
+ align:start position:0%
+bands of cell activity so it goes face
+selectivity color selectivity play
+
+ align:start position:0%
+selectivity color selectivity play
+ 
+
+ align:start position:0%
+selectivity color selectivity play
+selectivity and three bands on the side
+
+ align:start position:0%
+selectivity and three bands on the side
+ 
+
+ align:start position:0%
+selectivity and three bands on the side
+of the temporal lobe in monkeys we find
+
+ align:start position:0%
+of the temporal lobe in monkeys we find
+ 
+
+ align:start position:0%
+of the temporal lobe in monkeys we find
+is in humans you have exactly the same
+
+ align:start position:0%
+is in humans you have exactly the same
+ 
+
+ align:start position:0%
+is in humans you have exactly the same
+organization in the same order but it's
+
+ align:start position:0%
+organization in the same order but it's
+ 
+
+ align:start position:0%
+organization in the same order but it's
+rolled around on the ventral surface of
+
+ align:start position:0%
+rolled around on the ventral surface of
+ 
+
+ align:start position:0%
+rolled around on the ventral surface of
+the brain in the same order face color
+
+ align:start position:0%
+the brain in the same order face color
+ 
+
+ align:start position:0%
+the brain in the same order face color
+place on the bottom of the brain so we
+
+ align:start position:0%
+place on the bottom of the brain so we
+ 
+
+ align:start position:0%
+place on the bottom of the brain so we
+think that whole broad region is
+
+ align:start position:0%
+think that whole broad region is
+ 
+
+ align:start position:0%
+think that whole broad region is
+homologous between monkeys and humans it
+
+ align:start position:0%
+homologous between monkeys and humans it
+ 
+
+ align:start position:0%
+homologous between monkeys and humans it
+just rolled around on the bottom maybe
+
+ align:start position:0%
+just rolled around on the bottom maybe
+ 
+
+ align:start position:0%
+just rolled around on the bottom maybe
+it got pushed over something and that's
+
+ align:start position:0%
+it got pushed over something and that's
+ 
+
+ align:start position:0%
+it got pushed over something and that's
+not exactly a novel argument actually
+
+ align:start position:0%
+not exactly a novel argument actually
+ 
+
+ align:start position:0%
+not exactly a novel argument actually
+even Rick wrote a paper suggesting this
+
+ align:start position:0%
+even Rick wrote a paper suggesting this
+ 
+
+ align:start position:0%
+even Rick wrote a paper suggesting this
+a while back and I think we're starting
+
+ align:start position:0%
+a while back and I think we're starting
+ 
+
+ align:start position:0%
+a while back and I think we're starting
+to see those homologies and the reason
+
+ align:start position:0%
+to see those homologies and the reason
+ 
+
+ align:start position:0%
+to see those homologies and the reason
+that's important is that it means that
+
+ align:start position:0%
+that's important is that it means that
+ 
+
+ align:start position:0%
+that's important is that it means that
+all these questions we desperately want
+
+ align:start position:0%
+all these questions we desperately want
+ 
+
+ align:start position:0%
+all these questions we desperately want
+to answer about the you know causal
+
+ align:start position:0%
+to answer about the you know causal
+ 
+
+ align:start position:0%
+to answer about the you know causal
+world connectivity population codes
+
+ align:start position:0%
+world connectivity population codes
+ 
+
+ align:start position:0%
+world connectivity population codes
+interactions between regions development
+
+ align:start position:0%
+interactions between regions development
+ 
+
+ align:start position:0%
+interactions between regions development
+all of that that we can't answer very
+
+ align:start position:0%
+all of that that we can't answer very
+ 
+
+ align:start position:0%
+all of that that we can't answer very
+well in humans Fenric can answer in
+
+ align:start position:0%
+well in humans Fenric can answer in
+ 
+
+ align:start position:0%
+well in humans Fenric can answer in
+monkeys and after a break he will tell
+
+ align:start position:0%
+monkeys and after a break he will tell
+ 
+
+ align:start position:0%
+monkeys and after a break he will tell
+you about all of that right
+
+ align:start position:0%
+you about all of that right
+ 
+
+ align:start position:0%
+you about all of that right
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/3RGYj06NSTI.txt b/3RGYj06NSTI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b609135220e043fcea40a4e3d87db9940946f077
--- /dev/null
+++ b/3RGYj06NSTI.txt
@@ -0,0 +1,5427 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last lecture I did a fairly standard
+
+ align:start position:0%
+last lecture I did a fairly standard
+ 
+
+ align:start position:0%
+last lecture I did a fairly standard
+treatment of the harmonic oscillator
+
+ align:start position:0%
+treatment of the harmonic oscillator
+ 
+
+ align:start position:0%
+treatment of the harmonic oscillator
+which is not supposed to make you
+
+ align:start position:0%
+which is not supposed to make you
+ 
+
+ align:start position:0%
+which is not supposed to make you
+excited but just to see that you can do
+
+ align:start position:0%
+excited but just to see that you can do
+ 
+
+ align:start position:0%
+excited but just to see that you can do
+this and the the the path to the
+
+ align:start position:0%
+this and the the the path to the
+ 
+
+ align:start position:0%
+this and the the the path to the
+solution was to define dimensionless
+
+ align:start position:0%
+solution was to define dimensionless
+ 
+
+ align:start position:0%
+solution was to define dimensionless
+position coordinate and then you get a
+
+ align:start position:0%
+position coordinate and then you get a
+ 
+
+ align:start position:0%
+position coordinate and then you get a
+dimensionless Schrodinger equation and
+
+ align:start position:0%
+dimensionless Schrodinger equation and
+ 
+
+ align:start position:0%
+dimensionless Schrodinger equation and
+the solution of that involves two steps
+
+ align:start position:0%
+the solution of that involves two steps
+ 
+
+ align:start position:0%
+the solution of that involves two steps
+one is to insist that the function there
+
+ align:start position:0%
+one is to insist that the function there
+ 
+
+ align:start position:0%
+one is to insist that the function there
+was solutions to the this earlier
+
+ align:start position:0%
+was solutions to the this earlier
+ 
+
+ align:start position:0%
+was solutions to the this earlier
+equation have an exponentially damped
+
+ align:start position:0%
+equation have an exponentially damped
+ 
+
+ align:start position:0%
+equation have an exponentially damped
+form and then the Schrodinger equation
+
+ align:start position:0%
+form and then the Schrodinger equation
+ 
+
+ align:start position:0%
+form and then the Schrodinger equation
+is transformed into a new equation
+
+ align:start position:0%
+is transformed into a new equation
+ 
+
+ align:start position:0%
+is transformed into a new equation
+called the Hermit equation and you
+
+ align:start position:0%
+called the Hermit equation and you
+ 
+
+ align:start position:0%
+called the Hermit equation and you
+shouldn't get all excited about that the
+
+ align:start position:0%
+shouldn't get all excited about that the
+ 
+
+ align:start position:0%
+shouldn't get all excited about that the
+mathematicians take care of it and and
+
+ align:start position:0%
+mathematicians take care of it and and
+ 
+
+ align:start position:0%
+mathematicians take care of it and and
+so the solutions to this Hermit
+
+ align:start position:0%
+so the solutions to this Hermit
+ 
+
+ align:start position:0%
+so the solutions to this Hermit
+differential equation gives you a set of
+
+ align:start position:0%
+differential equation gives you a set of
+ 
+
+ align:start position:0%
+differential equation gives you a set of
+orthogonal and normalized wave functions
+
+ align:start position:0%
+orthogonal and normalized wave functions
+ 
+
+ align:start position:0%
+orthogonal and normalized wave functions
+they give you the energy levels
+
+ align:start position:0%
+they give you the energy levels
+ 
+
+ align:start position:0%
+they give you the energy levels
+expressed as a quantum number plus 1/2
+
+ align:start position:0%
+expressed as a quantum number plus 1/2
+ 
+
+ align:start position:0%
+expressed as a quantum number plus 1/2
+times constant the energy levels the
+
+ align:start position:0%
+times constant the energy levels the
+ 
+
+ align:start position:0%
+times constant the energy levels the
+with the quantum number V are even or
+
+ align:start position:0%
+with the quantum number V are even or
+ 
+
+ align:start position:0%
+with the quantum number V are even or
+odd and V and they're even or odd in
+
+ align:start position:0%
+odd and V and they're even or odd in
+ 
+
+ align:start position:0%
+odd and V and they're even or odd in
+sigh the evens v and corresponds to even
+
+ align:start position:0%
+sigh the evens v and corresponds to even
+ 
+
+ align:start position:0%
+sigh the evens v and corresponds to even
+sy v is the number of internal nodes and
+
+ align:start position:0%
+sy v is the number of internal nodes and
+ 
+
+ align:start position:0%
+sy v is the number of internal nodes and
+there are all sorts of things you can do
+
+ align:start position:0%
+there are all sorts of things you can do
+ 
+
+ align:start position:0%
+there are all sorts of things you can do
+to say well I expect if I know how to do
+
+ align:start position:0%
+to say well I expect if I know how to do
+ 
+
+ align:start position:0%
+to say well I expect if I know how to do
+certain things in classical mechanics
+
+ align:start position:0%
+certain things in classical mechanics
+ 
+
+ align:start position:0%
+certain things in classical mechanics
+they're going to come out pretty much
+
+ align:start position:0%
+they're going to come out pretty much
+ 
+
+ align:start position:0%
+they're going to come out pretty much
+the same way in quantum mechanics so
+
+ align:start position:0%
+the same way in quantum mechanics so
+ 
+
+ align:start position:0%
+the same way in quantum mechanics so
+that's the standard structure but more
+
+ align:start position:0%
+that's the standard structure but more
+ 
+
+ align:start position:0%
+that's the standard structure but more
+importantly I want you to have in your
+
+ align:start position:0%
+importantly I want you to have in your
+ 
+
+ align:start position:0%
+importantly I want you to have in your
+head the pictures of the wave functions
+
+ align:start position:0%
+head the pictures of the wave functions
+ 
+
+ align:start position:0%
+head the pictures of the wave functions
+the idea that
+
+ align:start position:0%
+the idea that
+ 
+
+ align:start position:0%
+the idea that
+is a zero-point energy and that that
+
+ align:start position:0%
+is a zero-point energy and that that
+ 
+
+ align:start position:0%
+is a zero-point energy and that that
+there's a reason for that that the wave
+
+ align:start position:0%
+there's a reason for that that the wave
+ 
+
+ align:start position:0%
+there's a reason for that that the wave
+functions have tails extending out into
+
+ align:start position:0%
+functions have tails extending out into
+ 
+
+ align:start position:0%
+functions have tails extending out into
+the non-classical or the four
+
+ align:start position:0%
+the non-classical or the four
+ 
+
+ align:start position:0%
+the non-classical or the four
+classically forbidden region and this
+
+ align:start position:0%
+classically forbidden region and this
+ 
+
+ align:start position:0%
+classically forbidden region and this
+turns out to be the beginning of
+
+ align:start position:0%
+turns out to be the beginning of
+ 
+
+ align:start position:0%
+turns out to be the beginning of
+tunneling you'll you'll be looking at
+
+ align:start position:0%
+tunneling you'll you'll be looking at
+ 
+
+ align:start position:0%
+tunneling you'll you'll be looking at
+tunneling more more specifically we also
+
+ align:start position:0%
+tunneling more more specifically we also
+ 
+
+ align:start position:0%
+tunneling more more specifically we also
+what I also want you to know how the
+
+ align:start position:0%
+what I also want you to know how the
+ 
+
+ align:start position:0%
+what I also want you to know how the
+spacing of nodes is and that involves
+
+ align:start position:0%
+spacing of nodes is and that involves
+ 
+
+ align:start position:0%
+spacing of nodes is and that involves
+generalization of the Dubrow idea that
+
+ align:start position:0%
+generalization of the Dubrow idea that
+ 
+
+ align:start position:0%
+generalization of the Dubrow idea that
+the wave length is H over P but if the
+
+ align:start position:0%
+the wave length is H over P but if the
+ 
+
+ align:start position:0%
+the wave length is H over P but if the
+potential is not constant then P is a
+
+ align:start position:0%
+potential is not constant then P is a
+ 
+
+ align:start position:0%
+potential is not constant then P is a
+function of X this is not the classical
+
+ align:start position:0%
+function of X this is not the classical
+ 
+
+ align:start position:0%
+function of X this is not the classical
+the quantum mechanical operator this is
+
+ align:start position:0%
+the quantum mechanical operator this is
+ 
+
+ align:start position:0%
+the quantum mechanical operator this is
+a function which provides you with a lot
+
+ align:start position:0%
+a function which provides you with a lot
+ 
+
+ align:start position:0%
+a function which provides you with a lot
+of inter
+
+ align:start position:0%
+of inter
+ 
+
+ align:start position:0%
+of inter
+intuition and then see if you know where
+
+ align:start position:0%
+intuition and then see if you know where
+ 
+
+ align:start position:0%
+intuition and then see if you know where
+the node spacings are and you know the
+
+ align:start position:0%
+the node spacings are and you know the
+ 
+
+ align:start position:0%
+the node spacings are and you know the
+anvil or the shape of the envelope you
+
+ align:start position:0%
+anvil or the shape of the envelope you
+ 
+
+ align:start position:0%
+anvil or the shape of the envelope you
+have basically everything you need to
+
+ align:start position:0%
+have basically everything you need to
+ 
+
+ align:start position:0%
+have basically everything you need to
+have a classical sense of what's going
+
+ align:start position:0%
+have a classical sense of what's going
+ 
+
+ align:start position:0%
+have a classical sense of what's going
+on and then I guess it's mostly hidden I
+
+ align:start position:0%
+on and then I guess it's mostly hidden I
+ 
+
+ align:start position:0%
+on and then I guess it's mostly hidden I
+did a little bit of semi-classical
+
+ align:start position:0%
+did a little bit of semi-classical
+ 
+
+ align:start position:0%
+did a little bit of semi-classical
+theory and I showed that if you
+
+ align:start position:0%
+theory and I showed that if you
+ 
+
+ align:start position:0%
+theory and I showed that if you
+integrate from the left turning point to
+
+ align:start position:0%
+integrate from the left turning point to
+ 
+
+ align:start position:0%
+integrate from the left turning point to
+the right turning point and a given
+
+ align:start position:0%
+the right turning point and a given
+ 
+
+ align:start position:0%
+the right turning point and a given
+energy of this momentum function you get
+
+ align:start position:0%
+energy of this momentum function you get
+ 
+
+ align:start position:0%
+energy of this momentum function you get
+h over two times the number of nodes and
+
+ align:start position:0%
+h over two times the number of nodes and
+ 
+
+ align:start position:0%
+h over two times the number of nodes and
+this is the semi-classical quantization
+
+ align:start position:0%
+this is the semi-classical quantization
+ 
+
+ align:start position:0%
+this is the semi-classical quantization
+it's incredibly important and it's it's
+
+ align:start position:0%
+it's incredibly important and it's it's
+ 
+
+ align:start position:0%
+it's incredibly important and it's it's
+useful either as an exact or an
+
+ align:start position:0%
+useful either as an exact or an
+ 
+
+ align:start position:0%
+useful either as an exact or an
+approximate result for all
+
+ align:start position:0%
+approximate result for all
+ 
+
+ align:start position:0%
+approximate result for all
+one-dimensional problems and so it tells
+
+ align:start position:0%
+one-dimensional problems and so it tells
+ 
+
+ align:start position:0%
+one-dimensional problems and so it tells
+you how to how to begin now before I
+
+ align:start position:0%
+you how to how to begin now before I
+ 
+
+ align:start position:0%
+you how to how to begin now before I
+start talking about what we're gonna do
+
+ align:start position:0%
+start talking about what we're gonna do
+ 
+
+ align:start position:0%
+start talking about what we're gonna do
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+I want to stress where we're going so
+
+ align:start position:0%
+I want to stress where we're going so
+ 
+
+ align:start position:0%
+I want to stress where we're going so
+we're going to be looking at some
+
+ align:start position:0%
+we're going to be looking at some
+ 
+
+ align:start position:0%
+we're going to be looking at some
+exactly solve problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we have the particle a box there
+
+ align:start position:0%
+and so we have the particle a box there
+ 
+
+ align:start position:0%
+and so we have the particle a box there
+not much oscillator hydrogen and yet to
+
+ align:start position:0%
+not much oscillator hydrogen and yet to
+ 
+
+ align:start position:0%
+not much oscillator hydrogen and yet to
+come and the rigid rotor now all of
+
+ align:start position:0%
+come and the rigid rotor now all of
+ 
+
+ align:start position:0%
+come and the rigid rotor now all of
+these problems have an infinite number
+
+ align:start position:0%
+these problems have an infinite number
+ 
+
+ align:start position:0%
+these problems have an infinite number
+of eigen functions an infinite number of
+
+ align:start position:0%
+of eigen functions an infinite number of
+ 
+
+ align:start position:0%
+of eigen functions an infinite number of
+energy levels and that's intimidating
+
+ align:start position:0%
+energy levels and that's intimidating
+ 
+
+ align:start position:0%
+energy levels and that's intimidating
+but it's true now this these infinite
+
+ align:start position:0%
+but it's true now this these infinite
+ 
+
+ align:start position:0%
+but it's true now this these infinite
+number of functions are explicit
+
+ align:start position:0%
+number of functions are explicit
+ 
+
+ align:start position:0%
+number of functions are explicit
+functions of the quantum number and so
+
+ align:start position:0%
+functions of the quantum number and so
+ 
+
+ align:start position:0%
+functions of the quantum number and so
+we have an infinite number but in order
+
+ align:start position:0%
+we have an infinite number but in order
+ 
+
+ align:start position:0%
+we have an infinite number but in order
+to describe systems we're going to be
+
+ align:start position:0%
+to describe systems we're going to be
+ 
+
+ align:start position:0%
+to describe systems we're going to be
+calculating integrals we're going to be
+
+ align:start position:0%
+calculating integrals we're going to be
+ 
+
+ align:start position:0%
+calculating integrals we're going to be
+calculating a lot of integrals between
+
+ align:start position:0%
+calculating a lot of integrals between
+ 
+
+ align:start position:0%
+calculating a lot of integrals between
+these infinite number of functions so we
+
+ align:start position:0%
+these infinite number of functions so we
+ 
+
+ align:start position:0%
+these infinite number of functions so we
+have an infinity squared of integrals
+
+ align:start position:0%
+have an infinity squared of integrals
+ 
+
+ align:start position:0%
+have an infinity squared of integrals
+well I shouldn't scare you because well
+
+ align:start position:0%
+well I shouldn't scare you because well
+ 
+
+ align:start position:0%
+well I shouldn't scare you because well
+you but I'm going to show you is that
+
+ align:start position:0%
+you but I'm going to show you is that
+ 
+
+ align:start position:0%
+you but I'm going to show you is that
+all of the integrals that we are going
+
+ align:start position:0%
+all of the integrals that we are going
+ 
+
+ align:start position:0%
+all of the integrals that we are going
+to encounter our explicit functions of
+
+ align:start position:0%
+to encounter our explicit functions of
+ 
+
+ align:start position:0%
+to encounter our explicit functions of
+the quantum numbers and they have rather
+
+ align:start position:0%
+the quantum numbers and they have rather
+ 
+
+ align:start position:0%
+the quantum numbers and they have rather
+relatively selection rules in other
+
+ align:start position:0%
+relatively selection rules in other
+ 
+
+ align:start position:0%
+relatively selection rules in other
+words which integrals are nonzero based
+
+ align:start position:0%
+words which integrals are nonzero based
+ 
+
+ align:start position:0%
+words which integrals are nonzero based
+on the difference in quantum numbers
+
+ align:start position:0%
+on the difference in quantum numbers
+ 
+
+ align:start position:0%
+on the difference in quantum numbers
+between the left-hand side and the
+
+ align:start position:0%
+between the left-hand side and the
+ 
+
+ align:start position:0%
+between the left-hand side and the
+right-hand side so we're collecting
+
+ align:start position:0%
+right-hand side so we're collecting
+ 
+
+ align:start position:0%
+right-hand side so we're collecting
+these things in order to calculate a
+
+ align:start position:0%
+these things in order to calculate a
+ 
+
+ align:start position:0%
+these things in order to calculate a
+whole bunch of stuff and I told you that
+
+ align:start position:0%
+whole bunch of stuff and I told you that
+ 
+
+ align:start position:0%
+whole bunch of stuff and I told you that
+this of course for use rather than
+
+ align:start position:0%
+this of course for use rather than
+ 
+
+ align:start position:0%
+this of course for use rather than
+philosophy or history and so if you
+
+ align:start position:0%
+philosophy or history and so if you
+ 
+
+ align:start position:0%
+philosophy or history and so if you
+encounter any quantum mechanical problem
+
+ align:start position:0%
+encounter any quantum mechanical problem
+ 
+
+ align:start position:0%
+encounter any quantum mechanical problem
+you'd like to be able to describe what
+
+ align:start position:0%
+you'd like to be able to describe what
+ 
+
+ align:start position:0%
+you'd like to be able to describe what
+you could observe with it and so if
+
+ align:start position:0%
+you could observe with it and so if
+ 
+
+ align:start position:0%
+you could observe with it and so if
+you're armed with the infinite number of
+
+ align:start position:0%
+you're armed with the infinite number of
+ 
+
+ align:start position:0%
+you're armed with the infinite number of
+energy levels and eigen solutions for
+
+ align:start position:0%
+energy levels and eigen solutions for
+ 
+
+ align:start position:0%
+energy levels and eigen solutions for
+our problem you can calculate any
+
+ align:start position:0%
+our problem you can calculate any
+ 
+
+ align:start position:0%
+our problem you can calculate any
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+so you define some property you're
+
+ align:start position:0%
+so you define some property you're
+ 
+
+ align:start position:0%
+so you define some property you're
+interested in there is a quantum
+
+ align:start position:0%
+interested in there is a quantum
+ 
+
+ align:start position:0%
+interested in there is a quantum
+mechanical operator that corresponds to
+
+ align:start position:0%
+mechanical operator that corresponds to
+ 
+
+ align:start position:0%
+mechanical operator that corresponds to
+that property and in order to be able to
+
+ align:start position:0%
+that property and in order to be able to
+ 
+
+ align:start position:0%
+that property and in order to be able to
+describe the observations of that
+
+ align:start position:0%
+describe the observations of that
+ 
+
+ align:start position:0%
+describe the observations of that
+property you need to calculate integrals
+
+ align:start position:0%
+property you need to calculate integrals
+ 
+
+ align:start position:0%
+property you need to calculate integrals
+of that operator well la-dee-da that's
+
+ align:start position:0%
+of that operator well la-dee-da that's
+ 
+
+ align:start position:0%
+of that operator well la-dee-da that's
+that should be intimidating but it's not
+
+ align:start position:0%
+that should be intimidating but it's not
+ 
+
+ align:start position:0%
+that should be intimidating but it's not
+because almost all of these integrals
+
+ align:start position:0%
+because almost all of these integrals
+ 
+
+ align:start position:0%
+because almost all of these integrals
+can be expressed as a simple constant
+
+ align:start position:0%
+can be expressed as a simple constant
+ 
+
+ align:start position:0%
+can be expressed as a simple constant
+times a function of the quantum numbers
+
+ align:start position:0%
+times a function of the quantum numbers
+ 
+
+ align:start position:0%
+times a function of the quantum numbers
+or the difference of quantum numbers and
+
+ align:start position:0%
+or the difference of quantum numbers and
+ 
+
+ align:start position:0%
+or the difference of quantum numbers and
+that's that that's a fantastic thing we
+
+ align:start position:0%
+that's that that's a fantastic thing we
+ 
+
+ align:start position:0%
+that's that that's a fantastic thing we
+can also so we have any operator we have
+
+ align:start position:0%
+can also so we have any operator we have
+ 
+
+ align:start position:0%
+can also so we have any operator we have
+supposed the Hamiltonian is an exactly
+
+ align:start position:0%
+supposed the Hamiltonian is an exactly
+ 
+
+ align:start position:0%
+supposed the Hamiltonian is an exactly
+solve problem plus something else which
+
+ align:start position:0%
+solve problem plus something else which
+ 
+
+ align:start position:0%
+solve problem plus something else which
+we'll call h1 and this is complicated
+
+ align:start position:0%
+we'll call h1 and this is complicated
+ 
+
+ align:start position:0%
+we'll call h1 and this is complicated
+this is a complexity in the or it's the
+
+ align:start position:0%
+this is a complexity in the or it's the
+ 
+
+ align:start position:0%
+this is a complexity in the or it's the
+reality in the problem and in order to
+
+ align:start position:0%
+reality in the problem and in order to
+ 
+
+ align:start position:0%
+reality in the problem and in order to
+to deal with this again you're going to
+
+ align:start position:0%
+to deal with this again you're going to
+ 
+
+ align:start position:0%
+to deal with this again you're going to
+need to calculate integrals of this
+
+ align:start position:0%
+need to calculate integrals of this
+ 
+
+ align:start position:0%
+need to calculate integrals of this
+operator and the last thing that's
+
+ align:start position:0%
+operator and the last thing that's
+ 
+
+ align:start position:0%
+operator and the last thing that's
+really great to be exciting is once we
+
+ align:start position:0%
+really great to be exciting is once we
+ 
+
+ align:start position:0%
+really great to be exciting is once we
+do the time and once we look at the
+
+ align:start position:0%
+do the time and once we look at the
+ 
+
+ align:start position:0%
+do the time and once we look at the
+time-dependent schrodinger equation
+
+ align:start position:0%
+time-dependent schrodinger equation
+ 
+
+ align:start position:0%
+time-dependent schrodinger equation
+we're going to get wave packets and
+
+ align:start position:0%
+we're going to get wave packets and
+ 
+
+ align:start position:0%
+we're going to get wave packets and
+these are functions of position and time
+
+ align:start position:0%
+these are functions of position and time
+ 
+
+ align:start position:0%
+these are functions of position and time
+and these wave packets are classical
+
+ align:start position:0%
+and these wave packets are classical
+ 
+
+ align:start position:0%
+and these wave packets are classical
+like localized objects that move
+
+ align:start position:0%
+like localized objects that move
+ 
+
+ align:start position:0%
+like localized objects that move
+following the Newton's equations of
+
+ align:start position:0%
+following the Newton's equations of
+ 
+
+ align:start position:0%
+following the Newton's equations of
+motion for the center of the wave packet
+
+ align:start position:0%
+motion for the center of the wave packet
+ 
+
+ align:start position:0%
+motion for the center of the wave packet
+and again there are a whole bunch of
+
+ align:start position:0%
+and again there are a whole bunch of
+ 
+
+ align:start position:0%
+and again there are a whole bunch of
+integrals you're going to need in order
+
+ align:start position:0%
+integrals you're going to need in order
+ 
+
+ align:start position:0%
+integrals you're going to need in order
+to do these things and so right now
+
+ align:start position:0%
+to do these things and so right now
+ 
+
+ align:start position:0%
+to do these things and so right now
+we're starting with the best problem for
+
+ align:start position:0%
+we're starting with the best problem for
+ 
+
+ align:start position:0%
+we're starting with the best problem for
+these integrals because the harmonic
+
+ align:start position:0%
+these integrals because the harmonic
+ 
+
+ align:start position:0%
+these integrals because the harmonic
+oscillator has so special properties and
+
+ align:start position:0%
+oscillator has so special properties and
+ 
+
+ align:start position:0%
+oscillator has so special properties and
+the lecture notes are incredibly tedious
+
+ align:start position:0%
+the lecture notes are incredibly tedious
+ 
+
+ align:start position:0%
+the lecture notes are incredibly tedious
+and they're mostly proofs and I'm going
+
+ align:start position:0%
+and they're mostly proofs and I'm going
+ 
+
+ align:start position:0%
+and they're mostly proofs and I'm going
+to try to go fast over the the the
+
+ align:start position:0%
+to try to go fast over the the the
+ 
+
+ align:start position:0%
+to try to go fast over the the the
+tedious stuff and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+give you the important ideas but since
+
+ align:start position:0%
+give you the important ideas but since
+ 
+
+ align:start position:0%
+give you the important ideas but since
+there is so important logic you should
+
+ align:start position:0%
+there is so important logic you should
+ 
+
+ align:start position:0%
+there is so important logic you should
+really look at these notes okay so what
+
+ align:start position:0%
+really look at these notes okay so what
+ 
+
+ align:start position:0%
+really look at these notes okay so what
+we're going to be doing today is we
+
+ align:start position:0%
+we're going to be doing today is we
+ 
+
+ align:start position:0%
+we're going to be doing today is we
+start with the coordinate momentum
+
+ align:start position:0%
+start with the coordinate momentum
+ 
+
+ align:start position:0%
+start with the coordinate momentum
+operators we're going to get the these
+
+ align:start position:0%
+operators we're going to get the these
+ 
+
+ align:start position:0%
+operators we're going to get the these
+operators in dimensionless form and then
+
+ align:start position:0%
+operators in dimensionless form and then
+ 
+
+ align:start position:0%
+operators in dimensionless form and then
+we're going to get these a and a dagger
+
+ align:start position:0%
+we're going to get these a and a dagger
+ 
+
+ align:start position:0%
+we're going to get these a and a dagger
+guys and this so this step is
+
+ align:start position:0%
+guys and this so this step is
+ 
+
+ align:start position:0%
+guys and this so this step is
+reminiscent of what I did at the
+
+ align:start position:0%
+reminiscent of what I did at the
+ 
+
+ align:start position:0%
+reminiscent of what I did at the
+beginning of the previous lecture and
+
+ align:start position:0%
+beginning of the previous lecture and
+ 
+
+ align:start position:0%
+beginning of the previous lecture and
+then this is magic because this magic
+
+ align:start position:0%
+then this is magic because this magic
+ 
+
+ align:start position:0%
+then this is magic because this magic
+enables you to just look at integrals
+
+ align:start position:0%
+enables you to just look at integrals
+ 
+
+ align:start position:0%
+enables you to just look at integrals
+and say I know that integral is zero or
+
+ align:start position:0%
+and say I know that integral is zero or
+ 
+
+ align:start position:0%
+and say I know that integral is zero or
+I know that area was not zero and with a
+
+ align:start position:0%
+I know that area was not zero and with a
+ 
+
+ align:start position:0%
+I know that area was not zero and with a
+little bit more effort maybe something
+
+ align:start position:0%
+little bit more effort maybe something
+ 
+
+ align:start position:0%
+little bit more effort maybe something
+that you put on the back of a postage
+
+ align:start position:0%
+that you put on the back of a postage
+ 
+
+ align:start position:0%
+that you put on the back of a postage
+stamp you can evaluate that integral not
+
+ align:start position:0%
+stamp you can evaluate that integral not
+ 
+
+ align:start position:0%
+stamp you can evaluate that integral not
+by knowing integral tables but by
+
+ align:start position:0%
+by knowing integral tables but by
+ 
+
+ align:start position:0%
+by knowing integral tables but by
+knowing the properties of these simple
+
+ align:start position:0%
+knowing the properties of these simple
+ 
+
+ align:start position:0%
+knowing the properties of these simple
+little a and a dagger and that's a
+
+ align:start position:0%
+little a and a dagger and that's a
+ 
+
+ align:start position:0%
+little a and a dagger and that's a
+fantastic thing and it's so fantastic
+
+ align:start position:0%
+fantastic thing and it's so fantastic
+ 
+
+ align:start position:0%
+fantastic thing and it's so fantastic
+that this is one of the reasons why
+
+ align:start position:0%
+that this is one of the reasons why
+ 
+
+ align:start position:0%
+that this is one of the reasons why
+almost all problems in quantum mechanics
+
+ align:start position:0%
+almost all problems in quantum mechanics
+ 
+
+ align:start position:0%
+almost all problems in quantum mechanics
+start with a harmonic oscillator
+
+ align:start position:0%
+start with a harmonic oscillator
+ 
+
+ align:start position:0%
+start with a harmonic oscillator
+approximation because there is so much
+
+ align:start position:0%
+approximation because there is so much
+ 
+
+ align:start position:0%
+approximation because there is so much
+you can do with this a and a dagger
+
+ align:start position:0%
+you can do with this a and a dagger
+ 
+
+ align:start position:0%
+you can do with this a and a dagger
+formalism now at the beginning I also
+
+ align:start position:0%
+formalism now at the beginning I also
+ 
+
+ align:start position:0%
+formalism now at the beginning I also
+told you that in quantum mechanics the
+
+ align:start position:0%
+told you that in quantum mechanics the
+ 
+
+ align:start position:0%
+told you that in quantum mechanics the
+important thing that contains everything
+
+ align:start position:0%
+important thing that contains everything
+ 
+
+ align:start position:0%
+important thing that contains everything
+we're allowed to know about a system is
+
+ align:start position:0%
+we're allowed to know about a system is
+ 
+
+ align:start position:0%
+we're allowed to know about a system is
+the wave function but I also told you we
+
+ align:start position:0%
+the wave function but I also told you we
+ 
+
+ align:start position:0%
+the wave function but I also told you we
+can never measure the wave function we
+
+ align:start position:0%
+can never measure the wave function we
+ 
+
+ align:start position:0%
+can never measure the wave function we
+can never experimentally determine it
+
+ align:start position:0%
+can never experimentally determine it
+ 
+
+ align:start position:0%
+can never experimentally determine it
+and so we need to be able to calculate
+
+ align:start position:0%
+and so we need to be able to calculate
+ 
+
+ align:start position:0%
+and so we need to be able to calculate
+what this wave function does as far as
+
+ align:start position:0%
+what this wave function does as far as
+ 
+
+ align:start position:0%
+what this wave function does as far as
+what we can observe and these aids in a
+
+ align:start position:0%
+what we can observe and these aids in a
+ 
+
+ align:start position:0%
+what we can observe and these aids in a
+daggers are really important than being
+
+ align:start position:0%
+daggers are really important than being
+ 
+
+ align:start position:0%
+daggers are really important than being
+able to do that okay so
+
+ align:start position:0%
+able to do that okay so
+ 
+
+ align:start position:0%
+able to do that okay so
+I'm going to start with covering what I
+
+ align:start position:0%
+I'm going to start with covering what I
+ 
+
+ align:start position:0%
+I'm going to start with covering what I
+did in the notes but I'm going to jump
+
+ align:start position:0%
+did in the notes but I'm going to jump
+ 
+
+ align:start position:0%
+did in the notes but I'm going to jump
+to final results at some point governed
+
+ align:start position:0%
+to final results at some point governed
+ 
+
+ align:start position:0%
+to final results at some point governed
+by the clock and so the first thing
+
+ align:start position:0%
+by the clock and so the first thing
+ 
+
+ align:start position:0%
+by the clock and so the first thing
+we're going to do is these and so what
+
+ align:start position:0%
+we're going to do is these and so what
+ 
+
+ align:start position:0%
+we're going to do is these and so what
+we do is we define the relationship
+
+ align:start position:0%
+we do is we define the relationship
+ 
+
+ align:start position:0%
+we do is we define the relationship
+between the ordinary position coordinate
+
+ align:start position:0%
+between the ordinary position coordinate
+ 
+
+ align:start position:0%
+between the ordinary position coordinate
+and this little twiddle means it's
+
+ align:start position:0%
+and this little twiddle means it's
+ 
+
+ align:start position:0%
+and this little twiddle means it's
+dimensionless and so we can write the
+
+ align:start position:0%
+dimensionless and so we can write the
+ 
+
+ align:start position:0%
+dimensionless and so we can write the
+inverse of that and that's the one we
+
+ align:start position:0%
+inverse of that and that's the one we
+ 
+
+ align:start position:0%
+inverse of that and that's the one we
+are going to want to well actually we go
+
+ align:start position:0%
+are going to want to well actually we go
+ 
+
+ align:start position:0%
+are going to want to well actually we go
+both ways okay and we do the same thing
+
+ align:start position:0%
+both ways okay and we do the same thing
+ 
+
+ align:start position:0%
+both ways okay and we do the same thing
+for the momentum P is equal to H bar mu
+
+ align:start position:0%
+for the momentum P is equal to H bar mu
+ 
+
+ align:start position:0%
+for the momentum P is equal to H bar mu
+Omega square root P twiddle and the
+
+ align:start position:0%
+Omega square root P twiddle and the
+ 
+
+ align:start position:0%
+Omega square root P twiddle and the
+inverse finally which I don't need to
+
+ align:start position:0%
+inverse finally which I don't need to
+ 
+
+ align:start position:0%
+inverse finally which I don't need to
+write and finally we get the Hamiltonian
+
+ align:start position:0%
+write and finally we get the Hamiltonian
+ 
+
+ align:start position:0%
+write and finally we get the Hamiltonian
+which is V squared or 2 mu plus 1/2 K x
+
+ align:start position:0%
+which is V squared or 2 mu plus 1/2 K x
+ 
+
+ align:start position:0%
+which is V squared or 2 mu plus 1/2 K x
+squared and we'll put that into these
+
+ align:start position:0%
+squared and we'll put that into these
+ 
+
+ align:start position:0%
+squared and we'll put that into these
+new units so we have H bar mu Omega over
+
+ align:start position:0%
+new units so we have H bar mu Omega over
+ 
+
+ align:start position:0%
+new units so we have H bar mu Omega over
+2 mu P twiddle squared plus K over 2 now
+
+ align:start position:0%
+2 mu P twiddle squared plus K over 2 now
+ 
+
+ align:start position:0%
+2 mu P twiddle squared plus K over 2 now
+this is all very tedious but the payoff
+
+ align:start position:0%
+this is all very tedious but the payoff
+ 
+
+ align:start position:0%
+this is all very tedious but the payoff
+is very soon K over 2 times H bar Omega
+
+ align:start position:0%
+is very soon K over 2 times H bar Omega
+ 
+
+ align:start position:0%
+is very soon K over 2 times H bar Omega
+x squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well isn't that interesting we we can
+
+ align:start position:0%
+well isn't that interesting we we can
+ 
+
+ align:start position:0%
+well isn't that interesting we we can
+combine week we can absorb a K over mu
+
+ align:start position:0%
+combine week we can absorb a K over mu
+ 
+
+ align:start position:0%
+combine week we can absorb a K over mu
+in Omega and so we get actually a big
+
+ align:start position:0%
+in Omega and so we get actually a big
+ 
+
+ align:start position:0%
+in Omega and so we get actually a big
+simplification we get H bar Omega over 2
+
+ align:start position:0%
+simplification we get H bar Omega over 2
+ 
+
+ align:start position:0%
+simplification we get H bar Omega over 2
+times P twiddle squared + x squared well
+
+ align:start position:0%
+times P twiddle squared + x squared well
+ 
+
+ align:start position:0%
+times P twiddle squared + x squared well
+that's it that looks simpler okay and so
+
+ align:start position:0%
+that's it that looks simpler okay and so
+ 
+
+ align:start position:0%
+that's it that looks simpler okay and so
+the next thing we do is it looks like a
+
+ align:start position:0%
+the next thing we do is it looks like a
+ 
+
+ align:start position:0%
+the next thing we do is it looks like a
+simple simple problem from algebra let's
+
+ align:start position:0%
+simple simple problem from algebra let's
+ 
+
+ align:start position:0%
+simple simple problem from algebra let's
+factor this now it's a little tricky
+
+ align:start position:0%
+factor this now it's a little tricky
+ 
+
+ align:start position:0%
+factor this now it's a little tricky
+because you know you know you can factor
+
+ align:start position:0%
+because you know you know you can factor
+ 
+
+ align:start position:0%
+because you know you know you can factor
+something in real terms if this is a
+
+ align:start position:0%
+something in real terms if this is a
+ 
+
+ align:start position:0%
+something in real terms if this is a
+minus sign but we are allowed to talk
+
+ align:start position:0%
+minus sign but we are allowed to talk
+ 
+
+ align:start position:0%
+minus sign but we are allowed to talk
+about complex quantities and so we can
+
+ align:start position:0%
+about complex quantities and so we can
+ 
+
+ align:start position:0%
+about complex quantities and so we can
+we can factor that and so this term the
+
+ align:start position:0%
+we can factor that and so this term the
+ 
+
+ align:start position:0%
+we can factor that and so this term the
+twiddle plus it's equal to IP little
+
+ align:start position:0%
+twiddle plus it's equal to IP little
+ 
+
+ align:start position:0%
+twiddle plus it's equal to IP little
+plus x times minus IP little plus X okay
+
+ align:start position:0%
+plus x times minus IP little plus X okay
+ 
+
+ align:start position:0%
+plus x times minus IP little plus X okay
+and you can work that out that IP times
+
+ align:start position:0%
+and you can work that out that IP times
+ 
+
+ align:start position:0%
+and you can work that out that IP times
+I minus I P is P squared and x times X
+
+ align:start position:0%
+I minus I P is P squared and x times X
+ 
+
+ align:start position:0%
+I minus I P is P squared and x times X
+is x squared and then we have these
+
+ align:start position:0%
+is x squared and then we have these
+ 
+
+ align:start position:0%
+is x squared and then we have these
+cross terms IP times X and x times minus
+
+ align:start position:0%
+cross terms IP times X and x times minus
+ 
+
+ align:start position:0%
+cross terms IP times X and x times minus
+IP looks they don't commute if this were
+
+ align:start position:0%
+IP looks they don't commute if this were
+ 
+
+ align:start position:0%
+IP looks they don't commute if this were
+algebra well they would go away but they
+
+ align:start position:0%
+algebra well they would go away but they
+ 
+
+ align:start position:0%
+algebra well they would go away but they
+don't and so what you end up getting is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P little squared plus X twiddle squared
+
+ align:start position:0%
+P little squared plus X twiddle squared
+ 
+
+ align:start position:0%
+P little squared plus X twiddle squared
+I dimes I'm gonna stop writing the
+
+ align:start position:0%
+I dimes I'm gonna stop writing the
+ 
+
+ align:start position:0%
+I dimes I'm gonna stop writing the
+twiddle so okay so we have this I want
+
+ align:start position:0%
+twiddle so okay so we have this I want
+ 
+
+ align:start position:0%
+twiddle so okay so we have this I want
+to make sure that I haven't sabotage
+
+ align:start position:0%
+to make sure that I haven't sabotage
+ 
+
+ align:start position:0%
+to make sure that I haven't sabotage
+myself that's going to be yeah that's
+
+ align:start position:0%
+myself that's going to be yeah that's
+ 
+
+ align:start position:0%
+myself that's going to be yeah that's
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay so we have something here that
+
+ align:start position:0%
+okay so we have something here that
+ 
+
+ align:start position:0%
+okay so we have something here that
+isn't zero it looks like I times the
+
+ align:start position:0%
+isn't zero it looks like I times the
+ 
+
+ align:start position:0%
+isn't zero it looks like I times the
+commutator of P twiddle with x12 well we
+
+ align:start position:0%
+commutator of P twiddle with x12 well we
+ 
+
+ align:start position:0%
+commutator of P twiddle with x12 well we
+can work that out because we know the
+
+ align:start position:0%
+can work that out because we know the
+ 
+
+ align:start position:0%
+can work that out because we know the
+commutator of P ordinary with X ordinary
+
+ align:start position:0%
+commutator of P ordinary with X ordinary
+ 
+
+ align:start position:0%
+commutator of P ordinary with X ordinary
+and so I did that and so we have this
+
+ align:start position:0%
+and so I did that and so we have this
+ 
+
+ align:start position:0%
+and so I did that and so we have this
+commutator P after some algebra we get
+
+ align:start position:0%
+commutator P after some algebra we get
+ 
+
+ align:start position:0%
+commutator P after some algebra we get
++1 a number a pure number no I want you
+
+ align:start position:0%
++1 a number a pure number no I want you
+ 
+
+ align:start position:0%
++1 a number a pure number no I want you
+to check my algebra so you just
+
+ align:start position:0%
+to check my algebra so you just
+ 
+
+ align:start position:0%
+to check my algebra so you just
+substitute in what this is in terms of
+
+ align:start position:0%
+substitute in what this is in terms of
+ 
+
+ align:start position:0%
+substitute in what this is in terms of
+ordinary P and the ordinary X use the
+
+ align:start position:0%
+ordinary P and the ordinary X use the
+ 
+
+ align:start position:0%
+ordinary P and the ordinary X use the
+commutator for ordinary X P which is IH
+
+ align:start position:0%
+commutator for ordinary X P which is IH
+ 
+
+ align:start position:0%
+commutator for ordinary X P which is IH
+bar and magically you get +1 so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's very strange and boring
+
+ align:start position:0%
+there's very strange and boring
+ 
+
+ align:start position:0%
+there's very strange and boring
+derivation says okay well it's okay and
+
+ align:start position:0%
+derivation says okay well it's okay and
+ 
+
+ align:start position:0%
+derivation says okay well it's okay and
+let's now give these two things names
+
+ align:start position:0%
+let's now give these two things names
+ 
+
+ align:start position:0%
+let's now give these two things names
+okay this guy we're going to call as a
+
+ align:start position:0%
+okay this guy we're going to call as a
+ 
+
+ align:start position:0%
+okay this guy we're going to call as a
+as a square root of two times a and this
+
+ align:start position:0%
+as a square root of two times a and this
+ 
+
+ align:start position:0%
+as a square root of two times a and this
+one is going to be the square root of
+
+ align:start position:0%
+one is going to be the square root of
+ 
+
+ align:start position:0%
+one is going to be the square root of
+two times a dagger so H is going to be H
+
+ align:start position:0%
+two times a dagger so H is going to be H
+ 
+
+ align:start position:0%
+two times a dagger so H is going to be H
+bar Omega over 2 times square root 2 a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared of 2 a dagger minus 1 remember
+
+ align:start position:0%
+squared of 2 a dagger minus 1 remember
+ 
+
+ align:start position:0%
+squared of 2 a dagger minus 1 remember
+when we factored it we got this extra
+
+ align:start position:0%
+when we factored it we got this extra
+ 
+
+ align:start position:0%
+when we factored it we got this extra
+term which was 1 and in order to make it
+
+ align:start position:0%
+term which was 1 and in order to make it
+ 
+
+ align:start position:0%
+term which was 1 and in order to make it
+correct we have to subtract it away ok
+
+ align:start position:0%
+correct we have to subtract it away ok
+ 
+
+ align:start position:0%
+correct we have to subtract it away ok
+and so this becomes H bar Omega Hey -
+
+ align:start position:0%
+and so this becomes H bar Omega Hey -
+ 
+
+ align:start position:0%
+and so this becomes H bar Omega Hey -
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+oh isn't that nice now we have the
+
+ align:start position:0%
+oh isn't that nice now we have the
+ 
+
+ align:start position:0%
+oh isn't that nice now we have the
+Hamiltonian expressed as a constant
+
+ align:start position:0%
+Hamiltonian expressed as a constant
+ 
+
+ align:start position:0%
+Hamiltonian expressed as a constant
+which we know is important because it's
+
+ align:start position:0%
+which we know is important because it's
+ 
+
+ align:start position:0%
+which we know is important because it's
+related to the energy levels and times
+
+ align:start position:0%
+related to the energy levels and times
+ 
+
+ align:start position:0%
+related to the energy levels and times
+these two little things which turn out
+
+ align:start position:0%
+these two little things which turn out
+ 
+
+ align:start position:0%
+these two little things which turn out
+to be the gift from God it's it's an
+
+ align:start position:0%
+to be the gift from God it's it's an
+ 
+
+ align:start position:0%
+to be the gift from God it's it's an
+incredible thing what these do okay so
+
+ align:start position:0%
+incredible thing what these do okay so
+ 
+
+ align:start position:0%
+incredible thing what these do okay so
+we have gone through some algebra and we
+
+ align:start position:0%
+we have gone through some algebra and we
+ 
+
+ align:start position:0%
+we have gone through some algebra and we
+know the relationship between a and the
+
+ align:start position:0%
+know the relationship between a and the
+ 
+
+ align:start position:0%
+know the relationship between a and the
+X and P twiddles
+
+ align:start position:0%
+X and P twiddles
+ 
+
+ align:start position:0%
+X and P twiddles
+and we can similarly for a dagger and we
+
+ align:start position:0%
+and we can similarly for a dagger and we
+ 
+
+ align:start position:0%
+and we can similarly for a dagger and we
+can go in the other direction and we
+
+ align:start position:0%
+can go in the other direction and we
+ 
+
+ align:start position:0%
+can go in the other direction and we
+know the commutator and now we're going
+
+ align:start position:0%
+know the commutator and now we're going
+ 
+
+ align:start position:0%
+know the commutator and now we're going
+to start doing some really
+
+ align:start position:0%
+to start doing some really
+ 
+
+ align:start position:0%
+to start doing some really
+great stuff okay well one thing we're
+
+ align:start position:0%
+great stuff okay well one thing we're
+ 
+
+ align:start position:0%
+great stuff okay well one thing we're
+going to want to know about is a hat a
+
+ align:start position:0%
+going to want to know about is a hat a
+ 
+
+ align:start position:0%
+going to want to know about is a hat a
+hat a dagger that commutator had and
+
+ align:start position:0%
+hat a dagger that commutator had and
+ 
+
+ align:start position:0%
+hat a dagger that commutator had and
+that turns out to be well I already did
+
+ align:start position:0%
+that turns out to be well I already did
+ 
+
+ align:start position:0%
+that turns out to be well I already did
+I already derived it it turns out to be
+
+ align:start position:0%
+I already derived it it turns out to be
+ 
+
+ align:start position:0%
+I already derived it it turns out to be
+plus one and as a result we can say
+
+ align:start position:0%
+plus one and as a result we can say
+ 
+
+ align:start position:0%
+plus one and as a result we can say
+things like this a a dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry so using this trick we can show we
+
+ align:start position:0%
+sorry so using this trick we can show we
+ 
+
+ align:start position:0%
+sorry so using this trick we can show we
+can always replace something like a a
+
+ align:start position:0%
+can always replace something like a a
+ 
+
+ align:start position:0%
+can always replace something like a a
+dagger by a dagger a + this commutator
+
+ align:start position:0%
+dagger by a dagger a + this commutator
+ 
+
+ align:start position:0%
+dagger by a dagger a + this commutator
+which is one and so we have this really
+
+ align:start position:0%
+which is one and so we have this really
+ 
+
+ align:start position:0%
+which is one and so we have this really
+neat way of reversing the order of the
+
+ align:start position:0%
+neat way of reversing the order of the
+ 
+
+ align:start position:0%
+neat way of reversing the order of the
+A's and a daggers so with this we're
+
+ align:start position:0%
+A's and a daggers so with this we're
+ 
+
+ align:start position:0%
+A's and a daggers so with this we're
+going to soon discover that a operating
+
+ align:start position:0%
+going to soon discover that a operating
+ 
+
+ align:start position:0%
+going to soon discover that a operating
+on the eigen function gives square root
+
+ align:start position:0%
+on the eigen function gives square root
+ 
+
+ align:start position:0%
+on the eigen function gives square root
+of V times psy.d - 1 + a dagger
+
+ align:start position:0%
+of V times psy.d - 1 + a dagger
+ 
+
+ align:start position:0%
+of V times psy.d - 1 + a dagger
+operating on this one wave function
+
+ align:start position:0%
+operating on this one wave function
+ 
+
+ align:start position:0%
+operating on this one wave function
+gives v + 1 square by V + 1 which is the
+
+ align:start position:0%
+gives v + 1 square by V + 1 which is the
+ 
+
+ align:start position:0%
+gives v + 1 square by V + 1 which is the
+reason these things are valuable because
+
+ align:start position:0%
+reason these things are valuable because
+ 
+
+ align:start position:0%
+reason these things are valuable because
+if you have any any eigenfunction you
+
+ align:start position:0%
+if you have any any eigenfunction you
+ 
+
+ align:start position:0%
+if you have any any eigenfunction you
+can get all of the others so suppose you
+
+ align:start position:0%
+can get all of the others so suppose you
+ 
+
+ align:start position:0%
+can get all of the others so suppose you
+have the lowest eigenfunction you apply
+
+ align:start position:0%
+have the lowest eigenfunction you apply
+ 
+
+ align:start position:0%
+have the lowest eigenfunction you apply
+a dagger on it as many times as you need
+
+ align:start position:0%
+a dagger on it as many times as you need
+ 
+
+ align:start position:0%
+a dagger on it as many times as you need
+to get to say the Vieth function so you
+
+ align:start position:0%
+to get to say the Vieth function so you
+ 
+
+ align:start position:0%
+to get to say the Vieth function so you
+don't actually you're not going to be
+
+ align:start position:0%
+don't actually you're not going to be
+ 
+
+ align:start position:0%
+don't actually you're not going to be
+evaluating integrals you're be going to
+
+ align:start position:0%
+evaluating integrals you're be going to
+ 
+
+ align:start position:0%
+evaluating integrals you're be going to
+be counting A's and a daggers and
+
+ align:start position:0%
+be counting A's and a daggers and
+ 
+
+ align:start position:0%
+be counting A's and a daggers and
+permuting them around and getting ones
+
+ align:start position:0%
+permuting them around and getting ones
+ 
+
+ align:start position:0%
+permuting them around and getting ones
+and stuff like that yes I didn't what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is to switch the order and
+
+ align:start position:0%
+okay so this is to switch the order and
+ 
+
+ align:start position:0%
+okay so this is to switch the order and
+I've done that and that then is no I
+
+ align:start position:0%
+I've done that and that then is no I
+ 
+
+ align:start position:0%
+I've done that and that then is no I
+think wait a second okay so we have a a
+
+ align:start position:0%
+think wait a second okay so we have a a
+ 
+
+ align:start position:0%
+think wait a second okay so we have a a
+dagger so that's a a a dagger minus a
+
+ align:start position:0%
+dagger so that's a a a dagger minus a
+ 
+
+ align:start position:0%
+dagger so that's a a a dagger minus a
+dagger a and that's oh yeah thank you
+
+ align:start position:0%
+dagger a and that's oh yeah thank you
+ 
+
+ align:start position:0%
+dagger a and that's oh yeah thank you
+it's very very easy to get lost and once
+
+ align:start position:0%
+it's very very easy to get lost and once
+ 
+
+ align:start position:0%
+it's very very easy to get lost and once
+you lost you can never be found because
+
+ align:start position:0%
+you lost you can never be found because
+ 
+
+ align:start position:0%
+you lost you can never be found because
+you've made a mistake that's built into
+
+ align:start position:0%
+you've made a mistake that's built into
+ 
+
+ align:start position:0%
+you've made a mistake that's built into
+your logic and you're never going to see
+
+ align:start position:0%
+your logic and you're never going to see
+ 
+
+ align:start position:0%
+your logic and you're never going to see
+it see it took me a couple of minutes to
+
+ align:start position:0%
+it see it took me a couple of minutes to
+ 
+
+ align:start position:0%
+it see it took me a couple of minutes to
+even accept that the the inside from ITA
+
+ align:start position:0%
+even accept that the the inside from ITA
+ 
+
+ align:start position:0%
+even accept that the the inside from ITA
+was sitting there calmly thinking and
+
+ align:start position:0%
+was sitting there calmly thinking and
+ 
+
+ align:start position:0%
+was sitting there calmly thinking and
+I'm trying to do several things in
+
+ align:start position:0%
+I'm trying to do several things in
+ 
+
+ align:start position:0%
+I'm trying to do several things in
+addition to think okay so we we can do
+
+ align:start position:0%
+addition to think okay so we we can do
+ 
+
+ align:start position:0%
+addition to think okay so we we can do
+things like this suppose we have sigh I
+
+ align:start position:0%
+things like this suppose we have sigh I
+ 
+
+ align:start position:0%
+things like this suppose we have sigh I
+can't use this notation yet so suppose
+
+ align:start position:0%
+can't use this notation yet so suppose
+ 
+
+ align:start position:0%
+can't use this notation yet so suppose
+we have Sai star V and we have a dagger
+
+ align:start position:0%
+we have Sai star V and we have a dagger
+ 
+
+ align:start position:0%
+we have Sai star V and we have a dagger
+a dagger a dagger high V prime DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are razing operators so this is
+
+ align:start position:0%
+these are razing operators so this is
+ 
+
+ align:start position:0%
+these are razing operators so this is
+going to take V the V prime to be prime
+
+ align:start position:0%
+going to take V the V prime to be prime
+ 
+
+ align:start position:0%
+going to take V the V prime to be prime
+plus three those who that's the only
+
+ align:start position:0%
+plus three those who that's the only
+ 
+
+ align:start position:0%
+plus three those who that's the only
+integral that's 0 not 0 and we get V
+
+ align:start position:0%
+integral that's 0 not 0 and we get V
+ 
+
+ align:start position:0%
+integral that's 0 not 0 and we get V
+prime plus 1 V prime plus 2 V prime plus
+
+ align:start position:0%
+prime plus 1 V prime plus 2 V prime plus
+ 
+
+ align:start position:0%
+prime plus 1 V prime plus 2 V prime plus
+3 square root as the constants and this
+
+ align:start position:0%
+3 square root as the constants and this
+ 
+
+ align:start position:0%
+3 square root as the constants and this
+would be so that you know instead of
+
+ align:start position:0%
+would be so that you know instead of
+ 
+
+ align:start position:0%
+would be so that you know instead of
+evaluating an integral looking at what
+
+ align:start position:0%
+evaluating an integral looking at what
+ 
+
+ align:start position:0%
+evaluating an integral looking at what
+the X's and peas are we we just have a
+
+ align:start position:0%
+the X's and peas are we we just have a
+ 
+
+ align:start position:0%
+the X's and peas are we we just have a
+little game we play okay so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have to prove some of the things I've
+
+ align:start position:0%
+we have to prove some of the things I've
+ 
+
+ align:start position:0%
+we have to prove some of the things I've
+said so we have eight and we're going to
+
+ align:start position:0%
+said so we have eight and we're going to
+ 
+
+ align:start position:0%
+said so we have eight and we're going to
+operate on a dagger sy V so what does
+
+ align:start position:0%
+operate on a dagger sy V so what does
+ 
+
+ align:start position:0%
+operate on a dagger sy V so what does
+the Hamiltonian do to this thing so what
+
+ align:start position:0%
+the Hamiltonian do to this thing so what
+ 
+
+ align:start position:0%
+the Hamiltonian do to this thing so what
+we're going to want to do is to the show
+
+ align:start position:0%
+we're going to want to do is to the show
+ 
+
+ align:start position:0%
+we're going to want to do is to the show
+that this thing is an eigen value eigen
+
+ align:start position:0%
+that this thing is an eigen value eigen
+ 
+
+ align:start position:0%
+that this thing is an eigen value eigen
+function V plus one and that's what
+
+ align:start position:0%
+function V plus one and that's what
+ 
+
+ align:start position:0%
+function V plus one and that's what
+we're going to get so let's just go
+
+ align:start position:0%
+we're going to get so let's just go
+ 
+
+ align:start position:0%
+we're going to get so let's just go
+through this so we have h-bar Omega a
+
+ align:start position:0%
+through this so we have h-bar Omega a
+ 
+
+ align:start position:0%
+through this so we have h-bar Omega a
+dagger A plus 1/2 times sy v so what I
+
+ align:start position:0%
+dagger A plus 1/2 times sy v so what I
+ 
+
+ align:start position:0%
+dagger A plus 1/2 times sy v so what I
+did is yeah I showed that the
+
+ align:start position:0%
+did is yeah I showed that the
+ 
+
+ align:start position:0%
+did is yeah I showed that the
+Hamiltonian oh yeah I did right here the
+
+ align:start position:0%
+Hamiltonian oh yeah I did right here the
+ 
+
+ align:start position:0%
+Hamiltonian oh yeah I did right here the
+Hamiltonian is H bar Omega
+
+ align:start position:0%
+Hamiltonian is H bar Omega
+ 
+
+ align:start position:0%
+Hamiltonian is H bar Omega
+a a dagger minus 1/2 or if we reverse
+
+ align:start position:0%
+a a dagger minus 1/2 or if we reverse
+ 
+
+ align:start position:0%
+a a dagger minus 1/2 or if we reverse
+these it's equal to H bar Omega a dagger
+
+ align:start position:0%
+these it's equal to H bar Omega a dagger
+ 
+
+ align:start position:0%
+these it's equal to H bar Omega a dagger
+A plus 1/2 so we can use either one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm using that one and so except I
+
+ align:start position:0%
+so I'm using that one and so except I
+ 
+
+ align:start position:0%
+so I'm using that one and so except I
+wanted a dagger here okay because we
+
+ align:start position:0%
+wanted a dagger here okay because we
+ 
+
+ align:start position:0%
+wanted a dagger here okay because we
+wanna show what the Hamiltonian does to
+
+ align:start position:0%
+wanna show what the Hamiltonian does to
+ 
+
+ align:start position:0%
+wanna show what the Hamiltonian does to
+this okay now we can pull an a dagger
+
+ align:start position:0%
+this okay now we can pull an a dagger
+ 
+
+ align:start position:0%
+this okay now we can pull an a dagger
+out to the right right because this the
+
+ align:start position:0%
+out to the right right because this the
+ 
+
+ align:start position:0%
+out to the right right because this the
+1/2 times a dagger well that the matter
+
+ align:start position:0%
+1/2 times a dagger well that the matter
+ 
+
+ align:start position:0%
+1/2 times a dagger well that the matter
+this a dagger a a dagger
+
+ align:start position:0%
+this a dagger a a dagger
+ 
+
+ align:start position:0%
+this a dagger a a dagger
+well we can pull this a dagger out so we
+
+ align:start position:0%
+well we can pull this a dagger out so we
+ 
+
+ align:start position:0%
+well we can pull this a dagger out so we
+have h-bar Omega a dagger is equal to a
+
+ align:start position:0%
+have h-bar Omega a dagger is equal to a
+ 
+
+ align:start position:0%
+have h-bar Omega a dagger is equal to a
+a dagger plus 1/2 sy V now we use our
+
+ align:start position:0%
+a dagger plus 1/2 sy V now we use our
+ 
+
+ align:start position:0%
+a dagger plus 1/2 sy V now we use our
+magic commutator trick to replace this
+
+ align:start position:0%
+magic commutator trick to replace this
+ 
+
+ align:start position:0%
+magic commutator trick to replace this
+by a dagger a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus one okay so now we have h-bar Omega
+
+ align:start position:0%
+plus one okay so now we have h-bar Omega
+ 
+
+ align:start position:0%
+plus one okay so now we have h-bar Omega
+a dagger and we have a dagger A plus
+
+ align:start position:0%
+a dagger and we have a dagger A plus
+ 
+
+ align:start position:0%
+a dagger and we have a dagger A plus
+three-halves 5e well this is e V Plus H
+
+ align:start position:0%
+three-halves 5e well this is e V Plus H
+ 
+
+ align:start position:0%
+three-halves 5e well this is e V Plus H
+bar Omega we've increased the number
+
+ align:start position:0%
+bar Omega we've increased the number
+ 
+
+ align:start position:0%
+bar Omega we've increased the number
+that started here here is e V that was
+
+ align:start position:0%
+that started here here is e V that was
+ 
+
+ align:start position:0%
+that started here here is e V that was
+evie plus 1 and so now we have no
+
+ align:start position:0%
+evie plus 1 and so now we have no
+ 
+
+ align:start position:0%
+evie plus 1 and so now we have no
+operators in here and we can stick the a
+
+ align:start position:0%
+operators in here and we can stick the a
+ 
+
+ align:start position:0%
+operators in here and we can stick the a
+dagger back here and so we have h bar
+
+ align:start position:0%
+dagger back here and so we have h bar
+ 
+
+ align:start position:0%
+dagger back here and so we have h bar
+omega e v plus 1 a dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what we have here we have an
+
+ align:start position:0%
+well what we have here we have an
+ 
+
+ align:start position:0%
+well what we have here we have an
+operator we have this function we have
+
+ align:start position:0%
+operator we have this function we have
+ 
+
+ align:start position:0%
+operator we have this function we have
+some constant times the same function so
+
+ align:start position:0%
+some constant times the same function so
+ 
+
+ align:start position:0%
+some constant times the same function so
+what we've shown is that this thing is
+
+ align:start position:0%
+what we've shown is that this thing is
+ 
+
+ align:start position:0%
+what we've shown is that this thing is
+an eigenfunction of the hamiltonian that
+
+ align:start position:0%
+an eigenfunction of the hamiltonian that
+ 
+
+ align:start position:0%
+an eigenfunction of the hamiltonian that
+belongs to the eigenvalue e v plus one
+
+ align:start position:0%
+belongs to the eigenvalue e v plus one
+ 
+
+ align:start position:0%
+belongs to the eigenvalue e v plus one
+we've increased the energy by one so
+
+ align:start position:0%
+we've increased the energy by one so
+ 
+
+ align:start position:0%
+we've increased the energy by one so
+what we have so so we can show that we
+
+ align:start position:0%
+what we have so so we can show that we
+ 
+
+ align:start position:0%
+what we have so so we can show that we
+apply a dagger to any function we
+
+ align:start position:0%
+apply a dagger to any function we
+ 
+
+ align:start position:0%
+apply a dagger to any function we
+increase its energy and we can do this
+
+ align:start position:0%
+increase its energy and we can do this
+ 
+
+ align:start position:0%
+increase its energy and we can do this
+forever we could also do a similar thing
+
+ align:start position:0%
+forever we could also do a similar thing
+ 
+
+ align:start position:0%
+forever we could also do a similar thing
+if we apply a to Saifee we can go down
+
+ align:start position:0%
+if we apply a to Saifee we can go down
+ 
+
+ align:start position:0%
+if we apply a to Saifee we can go down
+but at some point we run out of steam
+
+ align:start position:0%
+but at some point we run out of steam
+ 
+
+ align:start position:0%
+but at some point we run out of steam
+because we've gone gone to the lowest
+
+ align:start position:0%
+because we've gone gone to the lowest
+ 
+
+ align:start position:0%
+because we've gone gone to the lowest
+energy and if we go lower we get zero we
+
+ align:start position:0%
+energy and if we go lower we get zero we
+ 
+
+ align:start position:0%
+energy and if we go lower we get zero we
+get so a operating on sy min gives zero
+
+ align:start position:0%
+get so a operating on sy min gives zero
+ 
+
+ align:start position:0%
+get so a operating on sy min gives zero
+so we have this stack of energy levels
+
+ align:start position:0%
+so we have this stack of energy levels
+ 
+
+ align:start position:0%
+so we have this stack of energy levels
+and wave functions and we have the same
+
+ align:start position:0%
+and wave functions and we have the same
+ 
+
+ align:start position:0%
+and wave functions and we have the same
+stack being repeated as we go down but
+
+ align:start position:0%
+stack being repeated as we go down but
+ 
+
+ align:start position:0%
+stack being repeated as we go down but
+this one has an end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we bring back what a is and so a
+
+ align:start position:0%
+okay so we bring back what a is and so a
+ 
+
+ align:start position:0%
+okay so we bring back what a is and so a
+dive in is zero that's the equation we
+
+ align:start position:0%
+dive in is zero that's the equation we
+ 
+
+ align:start position:0%
+dive in is zero that's the equation we
+bring in what Amon is it's I mean but
+
+ align:start position:0%
+bring in what Amon is it's I mean but
+ 
+
+ align:start position:0%
+bring in what Amon is it's I mean but
+what a is and it's I P little X plus X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we do some algebra and what we end up
+
+ align:start position:0%
+so we do some algebra and what we end up
+ 
+
+ align:start position:0%
+so we do some algebra and what we end up
+with is a differential equation so I'm
+
+ align:start position:0%
+with is a differential equation so I'm
+ 
+
+ align:start position:0%
+with is a differential equation so I'm
+in the X is equal to again a little bit
+
+ align:start position:0%
+in the X is equal to again a little bit
+ 
+
+ align:start position:0%
+in the X is equal to again a little bit
+more algebra minus mu Omega over H bar
+
+ align:start position:0%
+more algebra minus mu Omega over H bar
+ 
+
+ align:start position:0%
+more algebra minus mu Omega over H bar
+times sine then so what function gives
+
+ align:start position:0%
+times sine then so what function gives
+ 
+
+ align:start position:0%
+times sine then so what function gives
+there's an X in here too so what
+
+ align:start position:0%
+there's an X in here too so what
+ 
+
+ align:start position:0%
+there's an X in here too so what
+function has a derivative which is the
+
+ align:start position:0%
+function has a derivative which is the
+ 
+
+ align:start position:0%
+function has a derivative which is the
+function you had started with times the
+
+ align:start position:0%
+function you had started with times the
+ 
+
+ align:start position:0%
+function you had started with times the
+variable times a constant okay and so
+
+ align:start position:0%
+variable times a constant okay and so
+ 
+
+ align:start position:0%
+variable times a constant okay and so
+the answer to that is that sigh men
+
+ align:start position:0%
+the answer to that is that sigh men
+ 
+
+ align:start position:0%
+the answer to that is that sigh men
+asked to have the form some
+
+ align:start position:0%
+asked to have the form some
+ 
+
+ align:start position:0%
+asked to have the form some
+normalization factor times e to the
+
+ align:start position:0%
+normalization factor times e to the
+ 
+
+ align:start position:0%
+normalization factor times e to the
+minus M Omega or mu Omega sorry you over
+
+ align:start position:0%
+minus M Omega or mu Omega sorry you over
+ 
+
+ align:start position:0%
+minus M Omega or mu Omega sorry you over
+to H bar x squared a Gaussian well had
+
+ align:start position:0%
+to H bar x squared a Gaussian well had
+ 
+
+ align:start position:0%
+to H bar x squared a Gaussian well had
+to be a Gaussian right we know when we
+
+ align:start position:0%
+to be a Gaussian right we know when we
+ 
+
+ align:start position:0%
+to be a Gaussian right we know when we
+did the algebra this we're going to get
+
+ align:start position:0%
+did the algebra this we're going to get
+ 
+
+ align:start position:0%
+did the algebra this we're going to get
+some function times a Gaussian but for
+
+ align:start position:0%
+some function times a Gaussian but for
+ 
+
+ align:start position:0%
+some function times a Gaussian but for
+the lowest function the hermite
+
+ align:start position:0%
+the lowest function the hermite
+ 
+
+ align:start position:0%
+the lowest function the hermite
+polynomial is one and all there is is a
+
+ align:start position:0%
+polynomial is one and all there is is a
+ 
+
+ align:start position:0%
+polynomial is one and all there is is a
+Gaussian and so it says well we found
+
+ align:start position:0%
+Gaussian and so it says well we found
+ 
+
+ align:start position:0%
+Gaussian and so it says well we found
+the lowest level
+
+ align:start position:0%
+the lowest level
+ 
+
+ align:start position:0%
+the lowest level
+and we can normalize it and so let's
+
+ align:start position:0%
+and we can normalize it and so let's
+ 
+
+ align:start position:0%
+and we can normalize it and so let's
+start over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we have found is Simon of X is
+
+ align:start position:0%
+so what we have found is Simon of X is
+ 
+
+ align:start position:0%
+so what we have found is Simon of X is
+equal to MU Omega over PI H bar to the
+
+ align:start position:0%
+equal to MU Omega over PI H bar to the
+ 
+
+ align:start position:0%
+equal to MU Omega over PI H bar to the
+1/4 power e to the minus u Omega over 2
+
+ align:start position:0%
+1/4 power e to the minus u Omega over 2
+ 
+
+ align:start position:0%
+1/4 power e to the minus u Omega over 2
+H bar expert well that's useful we knew
+
+ align:start position:0%
+H bar expert well that's useful we knew
+ 
+
+ align:start position:0%
+H bar expert well that's useful we knew
+that but this time we got it out of a
+
+ align:start position:0%
+that but this time we got it out of a
+ 
+
+ align:start position:0%
+that but this time we got it out of a
+completely different path and now we can
+
+ align:start position:0%
+completely different path and now we can
+ 
+
+ align:start position:0%
+completely different path and now we can
+get all higher V by a dagger a dagger
+
+ align:start position:0%
+get all higher V by a dagger a dagger
+ 
+
+ align:start position:0%
+get all higher V by a dagger a dagger
+etcetera so remember we don't care
+
+ align:start position:0%
+etcetera so remember we don't care
+ 
+
+ align:start position:0%
+etcetera so remember we don't care
+anything about what the function is we
+
+ align:start position:0%
+anything about what the function is we
+ 
+
+ align:start position:0%
+anything about what the function is we
+just know that we can bring it in and
+
+ align:start position:0%
+just know that we can bring it in and
+ 
+
+ align:start position:0%
+just know that we can bring it in and
+get rid of it as well because what we
+
+ align:start position:0%
+get rid of it as well because what we
+ 
+
+ align:start position:0%
+get rid of it as well because what we
+want is the values of integrals
+
+ align:start position:0%
+want is the values of integrals
+ 
+
+ align:start position:0%
+want is the values of integrals
+involving that function and some
+
+ align:start position:0%
+involving that function and some
+ 
+
+ align:start position:0%
+involving that function and some
+operator so but yeah we can have all of
+
+ align:start position:0%
+operator so but yeah we can have all of
+ 
+
+ align:start position:0%
+operator so but yeah we can have all of
+those functions and this is a way of
+
+ align:start position:0%
+those functions and this is a way of
+ 
+
+ align:start position:0%
+those functions and this is a way of
+generating all of the functions and so
+
+ align:start position:0%
+generating all of the functions and so
+ 
+
+ align:start position:0%
+generating all of the functions and so
+if we want to
+
+ align:start position:0%
+if we want to
+ 
+
+ align:start position:0%
+if we want to
+sigh V we would do a dagger the V power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divided by the dagger IV the what do you
+
+ align:start position:0%
+divided by the dagger IV the what do you
+ 
+
+ align:start position:0%
+divided by the dagger IV the what do you
+call this with an exclamation point
+
+ align:start position:0%
+call this with an exclamation point
+ 
+
+ align:start position:0%
+call this with an exclamation point
+factorial ha so we apply this operator
+
+ align:start position:0%
+factorial ha so we apply this operator
+ 
+
+ align:start position:0%
+factorial ha so we apply this operator
+that raises us to high at whatever level
+
+ align:start position:0%
+that raises us to high at whatever level
+ 
+
+ align:start position:0%
+that raises us to high at whatever level
+we want and starting from this Gaussian
+
+ align:start position:0%
+we want and starting from this Gaussian
+ 
+
+ align:start position:0%
+we want and starting from this Gaussian
+at the bottom and we have this
+
+ align:start position:0%
+at the bottom and we have this
+ 
+
+ align:start position:0%
+at the bottom and we have this
+normalization factor which cancels out
+
+ align:start position:0%
+normalization factor which cancels out
+ 
+
+ align:start position:0%
+normalization factor which cancels out
+at the fact the the stuff that you get
+
+ align:start position:0%
+at the fact the the stuff that you get
+ 
+
+ align:start position:0%
+at the fact the the stuff that you get
+by applying maybe ok so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there's some more logic in my notes
+
+ align:start position:0%
+now there's some more logic in my notes
+ 
+
+ align:start position:0%
+now there's some more logic in my notes
+and I don't want to do that but what
+
+ align:start position:0%
+and I don't want to do that but what
+ 
+
+ align:start position:0%
+and I don't want to do that but what
+we'd like to be able to show is that a
+
+ align:start position:0%
+we'd like to be able to show is that a
+ 
+
+ align:start position:0%
+we'd like to be able to show is that a
+dagger on side V gives some constant and
+
+ align:start position:0%
+dagger on side V gives some constant and
+ 
+
+ align:start position:0%
+dagger on side V gives some constant and
+the discuss that has some value we're
+
+ align:start position:0%
+the discuss that has some value we're
+ 
+
+ align:start position:0%
+the discuss that has some value we're
+going to evaluate what it is and
+
+ align:start position:0%
+going to evaluate what it is and
+ 
+
+ align:start position:0%
+going to evaluate what it is and
+similarly a side V gives DV and some
+
+ align:start position:0%
+similarly a side V gives DV and some
+ 
+
+ align:start position:0%
+similarly a side V gives DV and some
+constant V equal to V minus 1/2 okay we
+
+ align:start position:0%
+constant V equal to V minus 1/2 okay we
+ 
+
+ align:start position:0%
+constant V equal to V minus 1/2 okay we
+can derive those things and I'm not
+
+ align:start position:0%
+can derive those things and I'm not
+ 
+
+ align:start position:0%
+can derive those things and I'm not
+going to waste time deriving them I'm
+
+ align:start position:0%
+going to waste time deriving them I'm
+ 
+
+ align:start position:0%
+going to waste time deriving them I'm
+going to just give you the values but we
+
+ align:start position:0%
+going to just give you the values but we
+ 
+
+ align:start position:0%
+going to just give you the values but we
+already know that cv is square root of V
+
+ align:start position:0%
+already know that cv is square root of V
+ 
+
+ align:start position:0%
+already know that cv is square root of V
+plus 1/2 B plus 1 and DV and you can see
+
+ align:start position:0%
+plus 1/2 B plus 1 and DV and you can see
+ 
+
+ align:start position:0%
+plus 1/2 B plus 1 and DV and you can see
+the derivation of my notes I don't think
+
+ align:start position:0%
+the derivation of my notes I don't think
+ 
+
+ align:start position:0%
+the derivation of my notes I don't think
+going through them is going to be
+
+ align:start position:0%
+going through them is going to be
+ 
+
+ align:start position:0%
+going through them is going to be
+instructive and that's just going to be
+
+ align:start position:0%
+instructive and that's just going to be
+ 
+
+ align:start position:0%
+instructive and that's just going to be
+the ok so now we have something it's
+
+ align:start position:0%
+the ok so now we have something it's
+ 
+
+ align:start position:0%
+the ok so now we have something it's
+wonderful because everything you need to
+
+ align:start position:0%
+wonderful because everything you need to
+ 
+
+ align:start position:0%
+wonderful because everything you need to
+know about getting numbers concerning
+
+ align:start position:0%
+know about getting numbers concerning
+ 
+
+ align:start position:0%
+know about getting numbers concerning
+harmonic oscillator is obtained from
+
+ align:start position:0%
+harmonic oscillator is obtained from
+ 
+
+ align:start position:0%
+harmonic oscillator is obtained from
+these five equations a dagger on side V
+
+ align:start position:0%
+these five equations a dagger on side V
+ 
+
+ align:start position:0%
+these five equations a dagger on side V
+is V plus 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hey I'm IV is V sorry B minus 1 I've
+
+ align:start position:0%
+hey I'm IV is V sorry B minus 1 I've
+ 
+
+ align:start position:0%
+hey I'm IV is V sorry B minus 1 I've
+said this before but you know these are
+
+ align:start position:0%
+said this before but you know these are
+ 
+
+ align:start position:0%
+said this before but you know these are
+the most useful things you'll ever
+
+ align:start position:0%
+the most useful things you'll ever
+ 
+
+ align:start position:0%
+the most useful things you'll ever
+encounter we have this thing called a
+
+ align:start position:0%
+encounter we have this thing called a
+ 
+
+ align:start position:0%
+encounter we have this thing called a
+number operator and that number operator
+
+ align:start position:0%
+number operator and that number operator
+ 
+
+ align:start position:0%
+number operator and that number operator
+is a dagger at a and the number operator
+
+ align:start position:0%
+is a dagger at a and the number operator
+ 
+
+ align:start position:0%
+is a dagger at a and the number operator
+operating on side V gives V by V and so
+
+ align:start position:0%
+operating on side V gives V by V and so
+ 
+
+ align:start position:0%
+operating on side V gives V by V and so
+that's a kind of benign operator that it
+
+ align:start position:0%
+that's a kind of benign operator that it
+ 
+
+ align:start position:0%
+that's a kind of benign operator that it
+can suck up all sorts of come
+
+ align:start position:0%
+can suck up all sorts of come
+ 
+
+ align:start position:0%
+can suck up all sorts of come
+the factors of a dagger a because it
+
+ align:start position:0%
+the factors of a dagger a because it
+ 
+
+ align:start position:0%
+the factors of a dagger a because it
+just gives it a useful thing and then we
+
+ align:start position:0%
+just gives it a useful thing and then we
+ 
+
+ align:start position:0%
+just gives it a useful thing and then we
+have a dagger and this is one well you
+
+ align:start position:0%
+have a dagger and this is one well you
+ 
+
+ align:start position:0%
+have a dagger and this is one well you
+you sort of know it's going to be 1
+
+ align:start position:0%
+you sort of know it's going to be 1
+ 
+
+ align:start position:0%
+you sort of know it's going to be 1
+because a a dagger it gives an increase
+
+ align:start position:0%
+because a a dagger it gives an increase
+ 
+
+ align:start position:0%
+because a a dagger it gives an increase
+it gives V plus 1 and a and an a gives
+
+ align:start position:0%
+it gives V plus 1 and a and an a gives
+ 
+
+ align:start position:0%
+it gives V plus 1 and a and an a gives
+via B minus 1 so it's plus 1 not minus 1
+
+ align:start position:0%
+via B minus 1 so it's plus 1 not minus 1
+ 
+
+ align:start position:0%
+via B minus 1 so it's plus 1 not minus 1
+and you know that it's hardwired ok well
+
+ align:start position:0%
+and you know that it's hardwired ok well
+ 
+
+ align:start position:0%
+and you know that it's hardwired ok well
+I did it I got to the point where it
+
+ align:start position:0%
+I did it I got to the point where it
+ 
+
+ align:start position:0%
+I did it I got to the point where it
+starts to get interesting so we're going
+
+ align:start position:0%
+starts to get interesting so we're going
+ 
+
+ align:start position:0%
+starts to get interesting so we're going
+to be using this notation a dagger and a
+
+ align:start position:0%
+to be using this notation a dagger and a
+ 
+
+ align:start position:0%
+to be using this notation a dagger and a
+for all sorts of stuff and one sort of
+
+ align:start position:0%
+for all sorts of stuff and one sort of
+ 
+
+ align:start position:0%
+for all sorts of stuff and one sort of
+thing is transition intensities and
+
+ align:start position:0%
+thing is transition intensities and
+ 
+
+ align:start position:0%
+thing is transition intensities and
+selections so you have a harmonic
+
+ align:start position:0%
+selections so you have a harmonic
+ 
+
+ align:start position:0%
+selections so you have a harmonic
+oscillator monarch oscillator is say a
+
+ align:start position:0%
+oscillator monarch oscillator is say a
+ 
+
+ align:start position:0%
+oscillator monarch oscillator is say a
+diatomic molecule which is heteronuclear
+
+ align:start position:0%
+diatomic molecule which is heteronuclear
+ 
+
+ align:start position:0%
+diatomic molecule which is heteronuclear
+and so as the molecule vibrates you have
+
+ align:start position:0%
+and so as the molecule vibrates you have
+ 
+
+ align:start position:0%
+and so as the molecule vibrates you have
+a dipole moment which is oscillating and
+
+ align:start position:0%
+a dipole moment which is oscillating and
+ 
+
+ align:start position:0%
+a dipole moment which is oscillating and
+so any electric field oscillating
+
+ align:start position:0%
+so any electric field oscillating
+ 
+
+ align:start position:0%
+so any electric field oscillating
+electric field will grab a hold of that
+
+ align:start position:0%
+electric field will grab a hold of that
+ 
+
+ align:start position:0%
+electric field will grab a hold of that
+dipole moment and stretch or compress it
+
+ align:start position:0%
+dipole moment and stretch or compress it
+ 
+
+ align:start position:0%
+dipole moment and stretch or compress it
+especially if that field is in resonance
+
+ align:start position:0%
+especially if that field is in resonance
+ 
+
+ align:start position:0%
+especially if that field is in resonance
+with h-bar Omega and I'm gonna I've got
+
+ align:start position:0%
+with h-bar Omega and I'm gonna I've got
+ 
+
+ align:start position:0%
+with h-bar Omega and I'm gonna I've got
+some beautiful animations showing this
+
+ align:start position:0%
+some beautiful animations showing this
+ 
+
+ align:start position:0%
+some beautiful animations showing this
+but we can't do that until we have
+
+ align:start position:0%
+but we can't do that until we have
+ 
+
+ align:start position:0%
+but we can't do that until we have
+time-dependent quantum mechanics so we
+
+ align:start position:0%
+time-dependent quantum mechanics so we
+ 
+
+ align:start position:0%
+time-dependent quantum mechanics so we
+have a time-dependent radiation field
+
+ align:start position:0%
+have a time-dependent radiation field
+ 
+
+ align:start position:0%
+have a time-dependent radiation field
+which is going to interact with the
+
+ align:start position:0%
+which is going to interact with the
+ 
+
+ align:start position:0%
+which is going to interact with the
+dipole associated with the vibrating
+
+ align:start position:0%
+dipole associated with the vibrating
+ 
+
+ align:start position:0%
+dipole associated with the vibrating
+molecule and it's going to cause
+
+ align:start position:0%
+molecule and it's going to cause
+ 
+
+ align:start position:0%
+molecule and it's going to cause
+transitions and so we can write the
+
+ align:start position:0%
+transitions and so we can write the
+ 
+
+ align:start position:0%
+transitions and so we can write the
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+the quantum mechanical operator that
+
+ align:start position:0%
+the quantum mechanical operator that
+ 
+
+ align:start position:0%
+the quantum mechanical operator that
+causes the transitions this is the
+
+ align:start position:0%
+causes the transitions this is the
+ 
+
+ align:start position:0%
+causes the transitions this is the
+electric dipole moment operator as a
+
+ align:start position:0%
+electric dipole moment operator as a
+ 
+
+ align:start position:0%
+electric dipole moment operator as a
+function of coordinate and we can do a
+
+ align:start position:0%
+function of coordinate and we can do a
+ 
+
+ align:start position:0%
+function of coordinate and we can do a
+power series expansion of this and we
+
+ align:start position:0%
+power series expansion of this and we
+ 
+
+ align:start position:0%
+power series expansion of this and we
+have so we have u 0 the constant term
+
+ align:start position:0%
+have so we have u 0 the constant term
+ 
+
+ align:start position:0%
+have so we have u 0 the constant term
+the first derivative of the dipole with
+
+ align:start position:0%
+the first derivative of the dipole with
+ 
+
+ align:start position:0%
+the first derivative of the dipole with
+respect to X and the second derivative
+
+ align:start position:0%
+respect to X and the second derivative
+ 
+
+ align:start position:0%
+respect to X and the second derivative
+of the dipole with respect to X and so
+
+ align:start position:0%
+of the dipole with respect to X and so
+ 
+
+ align:start position:0%
+of the dipole with respect to X and so
+we have the X cofactor and the x squared
+
+ align:start position:0%
+we have the X cofactor and the x squared
+ 
+
+ align:start position:0%
+we have the X cofactor and the x squared
+cofactor and so this guy doesn't have
+
+ align:start position:0%
+cofactor and so this guy doesn't have
+ 
+
+ align:start position:0%
+cofactor and so this guy doesn't have
+any X on it it's a constant the only
+
+ align:start position:0%
+any X on it it's a constant the only
+ 
+
+ align:start position:0%
+any X on it it's a constant the only
+integrals involving the only integrals
+
+ align:start position:0%
+integrals involving the only integrals
+ 
+
+ align:start position:0%
+integrals involving the only integrals
+are Delta V V Prime following the
+
+ align:start position:0%
+are Delta V V Prime following the
+ 
+
+ align:start position:0%
+are Delta V V Prime following the
+selection will Delta V V prime so these
+
+ align:start position:0%
+selection will Delta V V prime so these
+ 
+
+ align:start position:0%
+selection will Delta V V prime so these
+integrals are zero unless V and V prime
+
+ align:start position:0%
+integrals are zero unless V and V prime
+ 
+
+ align:start position:0%
+integrals are zero unless V and V prime
+are the same and that that's as well
+
+ align:start position:0%
+are the same and that that's as well
+ 
+
+ align:start position:0%
+are the same and that that's as well
+there's an oscillating field is going to
+
+ align:start position:0%
+there's an oscillating field is going to
+ 
+
+ align:start position:0%
+there's an oscillating field is going to
+do anything Q to it it's just going to
+
+ align:start position:0%
+do anything Q to it it's just going to
+ 
+
+ align:start position:0%
+do anything Q to it it's just going to
+leave it in the same vibrational level
+
+ align:start position:0%
+leave it in the same vibrational level
+ 
+
+ align:start position:0%
+leave it in the same vibrational level
+but it might have a electric stark
+
+ align:start position:0%
+but it might have a electric stark
+ 
+
+ align:start position:0%
+but it might have a electric stark
+effect but that's something else okay so
+
+ align:start position:0%
+effect but that's something else okay so
+ 
+
+ align:start position:0%
+effect but that's something else okay so
+so this term does nothing as far as
+
+ align:start position:0%
+so this term does nothing as far as
+ 
+
+ align:start position:0%
+so this term does nothing as far as
+vibration is concerned this guy which is
+
+ align:start position:0%
+vibration is concerned this guy which is
+ 
+
+ align:start position:0%
+vibration is concerned this guy which is
+a plus a dagger as a selection of all
+
+ align:start position:0%
+a plus a dagger as a selection of all
+ 
+
+ align:start position:0%
+a plus a dagger as a selection of all
+Delta V of plus minus 1
+
+ align:start position:0%
+Delta V of plus minus 1
+ 
+
+ align:start position:0%
+Delta V of plus minus 1
+and this guy as a selection rule Delta V
+
+ align:start position:0%
+and this guy as a selection rule Delta V
+ 
+
+ align:start position:0%
+and this guy as a selection rule Delta V
+of plus and minus 2 and 0 so if we're
+
+ align:start position:0%
+of plus and minus 2 and 0 so if we're
+ 
+
+ align:start position:0%
+of plus and minus 2 and 0 so if we're
+interested in the intensities of
+
+ align:start position:0%
+interested in the intensities of
+ 
+
+ align:start position:0%
+interested in the intensities of
+vibrational transitions it says well
+
+ align:start position:0%
+vibrational transitions it says well
+ 
+
+ align:start position:0%
+vibrational transitions it says well
+this is the important term and it causes
+
+ align:start position:0%
+this is the important term and it causes
+ 
+
+ align:start position:0%
+this is the important term and it causes
+transitions changing the vibrational
+
+ align:start position:0%
+transitions changing the vibrational
+ 
+
+ align:start position:0%
+transitions changing the vibrational
+quantum number by one which is called
+
+ align:start position:0%
+quantum number by one which is called
+ 
+
+ align:start position:0%
+quantum number by one which is called
+the fundamental
+
+ align:start position:0%
+the fundamental
+ 
+
+ align:start position:0%
+the fundamental
+this gives rise to overtones so all of a
+
+ align:start position:0%
+this gives rise to overtones so all of a
+ 
+
+ align:start position:0%
+this gives rise to overtones so all of a
+sudden we're in real a real problem land
+
+ align:start position:0%
+sudden we're in real a real problem land
+ 
+
+ align:start position:0%
+sudden we're in real a real problem land
+where if we're looking at vibrational
+
+ align:start position:0%
+where if we're looking at vibrational
+ 
+
+ align:start position:0%
+where if we're looking at vibrational
+transitions in a molecule that this
+
+ align:start position:0%
+transitions in a molecule that this
+ 
+
+ align:start position:0%
+transitions in a molecule that this
+enables us to calculate what's important
+
+ align:start position:0%
+enables us to calculate what's important
+ 
+
+ align:start position:0%
+enables us to calculate what's important
+or to say these are the intensities I
+
+ align:start position:0%
+or to say these are the intensities I
+ 
+
+ align:start position:0%
+or to say these are the intensities I
+measure and these are the first and
+
+ align:start position:0%
+measure and these are the first and
+ 
+
+ align:start position:0%
+measure and these are the first and
+second derivative of the dipole moment
+
+ align:start position:0%
+second derivative of the dipole moment
+ 
+
+ align:start position:0%
+second derivative of the dipole moment
+operator is a function of you know clear
+
+ align:start position:0%
+operator is a function of you know clear
+ 
+
+ align:start position:0%
+operator is a function of you know clear
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+didn't that need okay I've gone so fast
+
+ align:start position:0%
+didn't that need okay I've gone so fast
+ 
+
+ align:start position:0%
+didn't that need okay I've gone so fast
+I'm a more or less at the end of my
+
+ align:start position:0%
+I'm a more or less at the end of my
+ 
+
+ align:start position:0%
+I'm a more or less at the end of my
+notes but I can Blair on for a while so
+
+ align:start position:0%
+notes but I can Blair on for a while so
+ 
+
+ align:start position:0%
+notes but I can Blair on for a while so
+suppose you have some integral involving
+
+ align:start position:0%
+suppose you have some integral involving
+ 
+
+ align:start position:0%
+suppose you have some integral involving
+an operator and the vibrational wave
+
+ align:start position:0%
+an operator and the vibrational wave
+ 
+
+ align:start position:0%
+an operator and the vibrational wave
+function so so we have sine V star some
+
+ align:start position:0%
+function so so we have sine V star some
+ 
+
+ align:start position:0%
+function so so we have sine V star some
+operator sorry V prime DX and we'd like
+
+ align:start position:0%
+operator sorry V prime DX and we'd like
+ 
+
+ align:start position:0%
+operator sorry V prime DX and we'd like
+to know how to focus our energies we're
+
+ align:start position:0%
+to know how to focus our energies we're
+ 
+
+ align:start position:0%
+to know how to focus our energies we're
+very busy people we don't want to
+
+ align:start position:0%
+very busy people we don't want to
+ 
+
+ align:start position:0%
+very busy people we don't want to
+evaluate integrals that come out to be
+
+ align:start position:0%
+evaluate integrals that come out to be
+ 
+
+ align:start position:0%
+evaluate integrals that come out to be
+zero we'd like to just know so if this
+
+ align:start position:0%
+zero we'd like to just know so if this
+ 
+
+ align:start position:0%
+zero we'd like to just know so if this
+operator is some function of X or
+
+ align:start position:0%
+operator is some function of X or
+ 
+
+ align:start position:0%
+operator is some function of X or
+function of P we'd have a power series
+
+ align:start position:0%
+function of P we'd have a power series
+ 
+
+ align:start position:0%
+function of P we'd have a power series
+expansion of the operator and we then
+
+ align:start position:0%
+expansion of the operator and we then
+ 
+
+ align:start position:0%
+expansion of the operator and we then
+know what the selection rules are so
+
+ align:start position:0%
+know what the selection rules are so
+ 
+
+ align:start position:0%
+know what the selection rules are so
+usually use it you look at the operator
+
+ align:start position:0%
+usually use it you look at the operator
+ 
+
+ align:start position:0%
+usually use it you look at the operator
+and you find that it is a function it's
+
+ align:start position:0%
+and you find that it is a function it's
+ 
+
+ align:start position:0%
+and you find that it is a function it's
+a linear quadratic cubic function of X
+
+ align:start position:0%
+a linear quadratic cubic function of X
+ 
+
+ align:start position:0%
+a linear quadratic cubic function of X
+the leading term is usually linear bang
+
+ align:start position:0%
+the leading term is usually linear bang
+ 
+
+ align:start position:0%
+the leading term is usually linear bang
+you have a delta V of +1 selection rule
+
+ align:start position:0%
+you have a delta V of +1 selection rule
+ 
+
+ align:start position:0%
+you have a delta V of +1 selection rule
+or if someone has bothered to actually
+
+ align:start position:0%
+or if someone has bothered to actually
+ 
+
+ align:start position:0%
+or if someone has bothered to actually
+convert the operator to some form that's
+
+ align:start position:0%
+convert the operator to some form that's
+ 
+
+ align:start position:0%
+convert the operator to some form that's
+the operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this this might have some form a dagger
+
+ align:start position:0%
+this this might have some form a dagger
+ 
+
+ align:start position:0%
+this this might have some form a dagger
+cubed times some constant okay so if the
+
+ align:start position:0%
+cubed times some constant okay so if the
+ 
+
+ align:start position:0%
+cubed times some constant okay so if the
+operator looks like a dagger cubed we
+
+ align:start position:0%
+operator looks like a dagger cubed we
+ 
+
+ align:start position:0%
+operator looks like a dagger cubed we
+know that the selection rule is V 2 V
+
+ align:start position:0%
+know that the selection rule is V 2 V
+ 
+
+ align:start position:0%
+know that the selection rule is V 2 V
+plus 3 and we know that the matrix on
+
+ align:start position:0%
+plus 3 and we know that the matrix on
+ 
+
+ align:start position:0%
+plus 3 and we know that the matrix on
+the integral is V plus 1 times V plus 2
+
+ align:start position:0%
+the integral is V plus 1 times V plus 2
+ 
+
+ align:start position:0%
+the integral is V plus 1 times V plus 2
+times V plus 3 square root of that and
+
+ align:start position:0%
+times V plus 3 square root of that and
+ 
+
+ align:start position:0%
+times V plus 3 square root of that and
+the constant so there's a huge number of
+
+ align:start position:0%
+the constant so there's a huge number of
+ 
+
+ align:start position:0%
+the constant so there's a huge number of
+problems that instead of being pages and
+
+ align:start position:0%
+problems that instead of being pages and
+ 
+
+ align:start position:0%
+problems that instead of being pages and
+pages of algebra are just reduced to
+
+ align:start position:0%
+pages of algebra are just reduced to
+ 
+
+ align:start position:0%
+pages of algebra are just reduced to
+something that you can tell by
+
+ align:start position:0%
+something that you can tell by
+ 
+
+ align:start position:0%
+something that you can tell by
+inspection so one of the the tricks is
+
+ align:start position:0%
+inspection so one of the the tricks is
+ 
+
+ align:start position:0%
+inspection so one of the the tricks is
+we have an operator like x squared or X
+
+ align:start position:0%
+we have an operator like x squared or X
+ 
+
+ align:start position:0%
+we have an operator like x squared or X
+cubed what we want to do is write this
+
+ align:start position:0%
+cubed what we want to do is write this
+ 
+
+ align:start position:0%
+cubed what we want to do is write this
+in terms of a squared a dagger squared
+
+ align:start position:0%
+in terms of a squared a dagger squared
+ 
+
+ align:start position:0%
+in terms of a squared a dagger squared
+and maybe some combination of a dagger a
+
+ align:start position:0%
+and maybe some combination of a dagger a
+ 
+
+ align:start position:0%
+and maybe some combination of a dagger a
+so we want to take the a dagger A's with
+
+ align:start position:0%
+so we want to take the a dagger A's with
+ 
+
+ align:start position:0%
+so we want to take the a dagger A's with
+the a a daggers and combine them using
+
+ align:start position:0%
+the a a daggers and combine them using
+ 
+
+ align:start position:0%
+the a a daggers and combine them using
+the commutation rule and then we have
+
+ align:start position:0%
+the commutation rule and then we have
+ 
+
+ align:start position:0%
+the commutation rule and then we have
+expressed this in this maximally simple
+
+ align:start position:0%
+expressed this in this maximally simple
+ 
+
+ align:start position:0%
+expressed this in this maximally simple
+form and then you just apply a squared
+
+ align:start position:0%
+form and then you just apply a squared
+ 
+
+ align:start position:0%
+form and then you just apply a squared
+apply a dagger squared and you apply
+
+ align:start position:0%
+apply a dagger squared and you apply
+ 
+
+ align:start position:0%
+apply a dagger squared and you apply
+this and you've got the value of the
+
+ align:start position:0%
+this and you've got the value of the
+ 
+
+ align:start position:0%
+this and you've got the value of the
+integral so if you're a busy person and
+
+ align:start position:0%
+integral so if you're a busy person and
+ 
+
+ align:start position:0%
+integral so if you're a busy person and
+you want to actually calculate stuff you
+
+ align:start position:0%
+you want to actually calculate stuff you
+ 
+
+ align:start position:0%
+you want to actually calculate stuff you
+want to know how to reduce operators
+
+ align:start position:0%
+want to know how to reduce operators
+ 
+
+ align:start position:0%
+want to know how to reduce operators
+usually expressed as some power of the
+
+ align:start position:0%
+usually expressed as some power of the
+ 
+
+ align:start position:0%
+usually expressed as some power of the
+coordinate or the momentum into a sum of
+
+ align:start position:0%
+coordinate or the momentum into a sum of
+ 
+
+ align:start position:0%
+coordinate or the momentum into a sum of
+terms involving these organized products
+
+ align:start position:0%
+terms involving these organized products
+ 
+
+ align:start position:0%
+terms involving these organized products
+of A's and a daggers and you're going to
+
+ align:start position:0%
+of A's and a daggers and you're going to
+ 
+
+ align:start position:0%
+of A's and a daggers and you're going to
+be absolutely shocked at how
+
+ align:start position:0%
+be absolutely shocked at how
+ 
+
+ align:start position:0%
+be absolutely shocked at how
+perturbation theory which leads to
+
+ align:start position:0%
+perturbation theory which leads to
+ 
+
+ align:start position:0%
+perturbation theory which leads to
+basically all of the formulas in
+
+ align:start position:0%
+basically all of the formulas in
+ 
+
+ align:start position:0%
+basically all of the formulas in
+spectroscopy
+
+ align:start position:0%
+spectroscopy
+ 
+
+ align:start position:0%
+spectroscopy
+it's an ugly theory but it reduces
+
+ align:start position:0%
+it's an ugly theory but it reduces
+ 
+
+ align:start position:0%
+it's an ugly theory but it reduces
+everything to things that you can just
+
+ align:start position:0%
+everything to things that you can just
+ 
+
+ align:start position:0%
+everything to things that you can just
+write down at the speed of your pen or
+
+ align:start position:0%
+write down at the speed of your pen or
+ 
+
+ align:start position:0%
+write down at the speed of your pen or
+pencil and and that's a fantastic thing
+
+ align:start position:0%
+pencil and and that's a fantastic thing
+ 
+
+ align:start position:0%
+pencil and and that's a fantastic thing
+so you can't do this with the particle
+
+ align:start position:0%
+so you can't do this with the particle
+ 
+
+ align:start position:0%
+so you can't do this with the particle
+in a box you can't do this with a
+
+ align:start position:0%
+in a box you can't do this with a
+ 
+
+ align:start position:0%
+in a box you can't do this with a
+hydrogen atom you can't do this with a
+
+ align:start position:0%
+hydrogen atom you can't do this with a
+ 
+
+ align:start position:0%
+hydrogen atom you can't do this with a
+rigid rope well you can do some of this
+
+ align:start position:0%
+rigid rope well you can do some of this
+ 
+
+ align:start position:0%
+rigid rope well you can do some of this
+with a rigid rotor but the harmonic
+
+ align:start position:0%
+with a rigid rotor but the harmonic
+ 
+
+ align:start position:0%
+with a rigid rotor but the harmonic
+oscillator is so ubiquitous because
+
+ align:start position:0%
+oscillator is so ubiquitous because
+ 
+
+ align:start position:0%
+oscillator is so ubiquitous because
+every one-dimensional problem is
+
+ align:start position:0%
+every one-dimensional problem is
+ 
+
+ align:start position:0%
+every one-dimensional problem is
+harmonic at the bottom and so you can
+
+ align:start position:0%
+harmonic at the bottom and so you can
+ 
+
+ align:start position:0%
+harmonic at the bottom and so you can
+use it and then you can put in the
+
+ align:start position:0%
+use it and then you can put in the
+ 
+
+ align:start position:0%
+use it and then you can put in the
+corrections but also because you want to
+
+ align:start position:0%
+corrections but also because you want to
+ 
+
+ align:start position:0%
+corrections but also because you want to
+describe dynamics you almost always use
+
+ align:start position:0%
+describe dynamics you almost always use
+ 
+
+ align:start position:0%
+describe dynamics you almost always use
+the harmonic oscillator because not only
+
+ align:start position:0%
+the harmonic oscillator because not only
+ 
+
+ align:start position:0%
+the harmonic oscillator because not only
+do you know the integrals but you know
+
+ align:start position:0%
+do you know the integrals but you know
+ 
+
+ align:start position:0%
+do you know the integrals but you know
+there's only a few normally you're going
+
+ align:start position:0%
+there's only a few normally you're going
+ 
+
+ align:start position:0%
+there's only a few normally you're going
+to be summing over an infinite number of
+
+ align:start position:0%
+to be summing over an infinite number of
+ 
+
+ align:start position:0%
+to be summing over an infinite number of
+quantum numbers and that takes time and
+
+ align:start position:0%
+quantum numbers and that takes time and
+ 
+
+ align:start position:0%
+quantum numbers and that takes time and
+it takes judgment to say well only
+
+ align:start position:0%
+it takes judgment to say well only
+ 
+
+ align:start position:0%
+it takes judgment to say well only
+certain of these are important but for
+
+ align:start position:0%
+certain of these are important but for
+ 
+
+ align:start position:0%
+certain of these are important but for
+the harmonic oscillator this sums are
+
+ align:start position:0%
+the harmonic oscillator this sums are
+ 
+
+ align:start position:0%
+the harmonic oscillator this sums are
+finite all of these things are wonderful
+
+ align:start position:0%
+finite all of these things are wonderful
+ 
+
+ align:start position:0%
+finite all of these things are wonderful
+and that's why whenever you look at a
+
+ align:start position:0%
+and that's why whenever you look at a
+ 
+
+ align:start position:0%
+and that's why whenever you look at a
+theory you're going to discover that
+
+ align:start position:0%
+theory you're going to discover that
+ 
+
+ align:start position:0%
+theory you're going to discover that
+hidden in there is the harmonic
+
+ align:start position:0%
+hidden in there is the harmonic
+ 
+
+ align:start position:0%
+hidden in there is the harmonic
+oscillator approximation because then
+
+ align:start position:0%
+oscillator approximation because then
+ 
+
+ align:start position:0%
+oscillator approximation because then
+everything is doable in no effort and
+
+ align:start position:0%
+everything is doable in no effort and
+ 
+
+ align:start position:0%
+everything is doable in no effort and
+sometimes when you look at a paper like
+
+ align:start position:0%
+sometimes when you look at a paper like
+ 
+
+ align:start position:0%
+sometimes when you look at a paper like
+that it doesn't show you the
+
+ align:start position:0%
+that it doesn't show you the
+ 
+
+ align:start position:0%
+that it doesn't show you the
+intermediate steps because everybody
+
+ align:start position:0%
+intermediate steps because everybody
+ 
+
+ align:start position:0%
+intermediate steps because everybody
+knows what a harmonic oscillator does
+
+ align:start position:0%
+knows what a harmonic oscillator does
+ 
+
+ align:start position:0%
+knows what a harmonic oscillator does
+and there's also a lot of insight
+
+ align:start position:0%
+and there's also a lot of insight
+ 
+
+ align:start position:0%
+and there's also a lot of insight
+because you know something like this
+
+ align:start position:0%
+because you know something like this
+ 
+
+ align:start position:0%
+because you know something like this
+this is an odd symmetry term this is an
+
+ align:start position:0%
+this is an odd symmetry term this is an
+ 
+
+ align:start position:0%
+this is an odd symmetry term this is an
+even symmetry term and there are all
+
+ align:start position:0%
+even symmetry term and there are all
+ 
+
+ align:start position:0%
+even symmetry term and there are all
+sorts of things that have to do with are
+
+ align:start position:0%
+sorts of things that have to do with are
+ 
+
+ align:start position:0%
+sorts of things that have to do with are
+you conserving symmetry or changing
+
+ align:start position:0%
+you conserving symmetry or changing
+ 
+
+ align:start position:0%
+you conserving symmetry or changing
+symmetry and sometimes there's the issue
+
+ align:start position:0%
+symmetry and sometimes there's the issue
+ 
+
+ align:start position:0%
+symmetry and sometimes there's the issue
+is how does the molecule spontaneously
+
+ align:start position:0%
+is how does the molecule spontaneously
+ 
+
+ align:start position:0%
+is how does the molecule spontaneously
+change symmetry by doing something
+
+ align:start position:0%
+change symmetry by doing something
+ 
+
+ align:start position:0%
+change symmetry by doing something
+interacting with a field or or hat
+
+ align:start position:0%
+interacting with a field or or hat
+ 
+
+ align:start position:0%
+interacting with a field or or hat
+interacting with some feature of the
+
+ align:start position:0%
+interacting with some feature of the
+ 
+
+ align:start position:0%
+interacting with some feature of the
+potential surface so this is a place
+
+ align:start position:0%
+potential surface so this is a place
+ 
+
+ align:start position:0%
+potential surface so this is a place
+where it's labor-saving and insight
+
+ align:start position:0%
+where it's labor-saving and insight
+ 
+
+ align:start position:0%
+where it's labor-saving and insight
+generating and it's really amazing
+
+ align:start position:0%
+generating and it's really amazing
+ 
+
+ align:start position:0%
+generating and it's really amazing
+so maybe you know maybe I've bored you
+
+ align:start position:0%
+so maybe you know maybe I've bored you
+ 
+
+ align:start position:0%
+so maybe you know maybe I've bored you
+with this but this is you know this is
+
+ align:start position:0%
+with this but this is you know this is
+ 
+
+ align:start position:0%
+with this but this is you know this is
+the beginning of almost every Theory the
+
+ align:start position:0%
+the beginning of almost every Theory the
+ 
+
+ align:start position:0%
+the beginning of almost every Theory the
+you'll encounter just because of the
+
+ align:start position:0%
+you'll encounter just because of the
+ 
+
+ align:start position:0%
+you'll encounter just because of the
+simplicity of the A's and a daggers okay
+
+ align:start position:0%
+simplicity of the A's and a daggers okay
+ 
+
+ align:start position:0%
+simplicity of the A's and a daggers okay
+I'm done
+
+ align:start position:0%
+I'm done
+ 
+
+ align:start position:0%
+I'm done
+thank you
\ No newline at end of file
diff --git a/40Sum5KfG1Q.txt b/40Sum5KfG1Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..69add805f5c57ef829b51be370d9a784d7a04e51
--- /dev/null
+++ b/40Sum5KfG1Q.txt
@@ -0,0 +1,8355 @@
+align:start position:0%
+ 
+now at the time that um that Watson and
+
+ align:start position:0%
+now at the time that um that Watson and
+ 
+
+ align:start position:0%
+now at the time that um that Watson and
+C figured out the the structure of DNA
+
+ align:start position:0%
+C figured out the the structure of DNA
+ 
+
+ align:start position:0%
+C figured out the the structure of DNA
+you know it was sort of obvious that
+
+ align:start position:0%
+you know it was sort of obvious that
+ 
+
+ align:start position:0%
+you know it was sort of obvious that
+since the two strands are complimentary
+
+ align:start position:0%
+since the two strands are complimentary
+ 
+
+ align:start position:0%
+since the two strands are complimentary
+you could see how it replicated and they
+
+ align:start position:0%
+you could see how it replicated and they
+ 
+
+ align:start position:0%
+you could see how it replicated and they
+also uh got a they could see that
+
+ align:start position:0%
+also uh got a they could see that
+ 
+
+ align:start position:0%
+also uh got a they could see that
+somehow the information must be encoded
+
+ align:start position:0%
+somehow the information must be encoded
+ 
+
+ align:start position:0%
+somehow the information must be encoded
+in the sequence of of uh of um letters
+
+ align:start position:0%
+in the sequence of of uh of um letters
+ 
+
+ align:start position:0%
+in the sequence of of uh of um letters
+down the the strands of of the DNA but
+
+ align:start position:0%
+down the the strands of of the DNA but
+ 
+
+ align:start position:0%
+down the the strands of of the DNA but
+it wasn't obvious what the code was how
+
+ align:start position:0%
+it wasn't obvious what the code was how
+ 
+
+ align:start position:0%
+it wasn't obvious what the code was how
+it was arranged how it worked and in in
+
+ align:start position:0%
+it was arranged how it worked and in in
+ 
+
+ align:start position:0%
+it was arranged how it worked and in in
+principle uh it was anything you could
+
+ align:start position:0%
+principle uh it was anything you could
+ 
+
+ align:start position:0%
+principle uh it was anything you could
+do with with four letters and so I had I
+
+ align:start position:0%
+do with with four letters and so I had I
+ 
+
+ align:start position:0%
+do with with four letters and so I had I
+pointed out the other day this is sort
+
+ align:start position:0%
+pointed out the other day this is sort
+ 
+
+ align:start position:0%
+pointed out the other day this is sort
+of a four-letter
+
+ align:start position:0%
+of a four-letter
+ 
+
+ align:start position:0%
+of a four-letter
+alphabet and I think it's useful to
+
+ align:start position:0%
+alphabet and I think it's useful to
+ 
+
+ align:start position:0%
+alphabet and I think it's useful to
+think of it this way with uh a g c and T
+
+ align:start position:0%
+think of it this way with uh a g c and T
+ 
+
+ align:start position:0%
+think of it this way with uh a g c and T
+and RNA is also being a
+
+ align:start position:0%
+and RNA is also being a
+ 
+
+ align:start position:0%
+and RNA is also being a
+four-letter
+
+ align:start position:0%
+four-letter
+ 
+
+ align:start position:0%
+four-letter
+alphabet but proteins are actually a
+
+ align:start position:0%
+alphabet but proteins are actually a
+ 
+
+ align:start position:0%
+alphabet but proteins are actually a
+20l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alphabet because there are 20 different
+
+ align:start position:0%
+alphabet because there are 20 different
+ 
+
+ align:start position:0%
+alphabet because there are 20 different
+amino
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acids and so somehow uh since one of the
+
+ align:start position:0%
+acids and so somehow uh since one of the
+ 
+
+ align:start position:0%
+acids and so somehow uh since one of the
+key things that the DNA had to do it was
+
+ align:start position:0%
+key things that the DNA had to do it was
+ 
+
+ align:start position:0%
+key things that the DNA had to do it was
+it somehow had to encode uh the the
+
+ align:start position:0%
+it somehow had to encode uh the the
+ 
+
+ align:start position:0%
+it somehow had to encode uh the the
+information for making the the proteins
+
+ align:start position:0%
+information for making the the proteins
+ 
+
+ align:start position:0%
+information for making the the proteins
+and it was there was a lot of work on
+
+ align:start position:0%
+and it was there was a lot of work on
+ 
+
+ align:start position:0%
+and it was there was a lot of work on
+protein biosynthesis at the time and it
+
+ align:start position:0%
+protein biosynthesis at the time and it
+ 
+
+ align:start position:0%
+protein biosynthesis at the time and it
+looked pretty complicated uh people had
+
+ align:start position:0%
+looked pretty complicated uh people had
+ 
+
+ align:start position:0%
+looked pretty complicated uh people had
+found that RNA seemed to be important
+
+ align:start position:0%
+found that RNA seemed to be important
+ 
+
+ align:start position:0%
+found that RNA seemed to be important
+cells that were making lots of protein
+
+ align:start position:0%
+cells that were making lots of protein
+ 
+
+ align:start position:0%
+cells that were making lots of protein
+had lots of RNA in them and another
+
+ align:start position:0%
+had lots of RNA in them and another
+ 
+
+ align:start position:0%
+had lots of RNA in them and another
+thing they noticed was if you looked in
+
+ align:start position:0%
+thing they noticed was if you looked in
+ 
+
+ align:start position:0%
+thing they noticed was if you looked in
+eukariotic cells the DNA stayed in the
+
+ align:start position:0%
+eukariotic cells the DNA stayed in the
+ 
+
+ align:start position:0%
+eukariotic cells the DNA stayed in the
+nucleus but the proteins were were out
+
+ align:start position:0%
+nucleus but the proteins were were out
+ 
+
+ align:start position:0%
+nucleus but the proteins were were out
+most of them were out in the cytoplasm
+
+ align:start position:0%
+most of them were out in the cytoplasm
+ 
+
+ align:start position:0%
+most of them were out in the cytoplasm
+and the evidence was that they they were
+
+ align:start position:0%
+and the evidence was that they they were
+ 
+
+ align:start position:0%
+and the evidence was that they they were
+made out in the cytoplasm so somehow the
+
+ align:start position:0%
+made out in the cytoplasm so somehow the
+ 
+
+ align:start position:0%
+made out in the cytoplasm so somehow the
+information had to get out of the
+
+ align:start position:0%
+information had to get out of the
+ 
+
+ align:start position:0%
+information had to get out of the
+nucleus where the DNA was
+
+ align:start position:0%
+nucleus where the DNA was
+ 
+
+ align:start position:0%
+nucleus where the DNA was
+and uh into the cytoplasm and
+
+ align:start position:0%
+and uh into the cytoplasm and
+ 
+
+ align:start position:0%
+and uh into the cytoplasm and
+biochemists were breaking cells open and
+
+ align:start position:0%
+biochemists were breaking cells open and
+ 
+
+ align:start position:0%
+biochemists were breaking cells open and
+trying to make cellular extracts that
+
+ align:start position:0%
+trying to make cellular extracts that
+ 
+
+ align:start position:0%
+trying to make cellular extracts that
+would synthesize proteins and I think
+
+ align:start position:0%
+would synthesize proteins and I think
+ 
+
+ align:start position:0%
+would synthesize proteins and I think
+it's fair to say at the time that it
+
+ align:start position:0%
+it's fair to say at the time that it
+ 
+
+ align:start position:0%
+it's fair to say at the time that it
+looked extremely
+
+ align:start position:0%
+looked extremely
+ 
+
+ align:start position:0%
+looked extremely
+complicated and so thinking about how
+
+ align:start position:0%
+complicated and so thinking about how
+ 
+
+ align:start position:0%
+complicated and so thinking about how
+DNA encoded information got translated
+
+ align:start position:0%
+DNA encoded information got translated
+ 
+
+ align:start position:0%
+DNA encoded information got translated
+in proteins was was a was a very complex
+
+ align:start position:0%
+in proteins was was a was a very complex
+ 
+
+ align:start position:0%
+in proteins was was a was a very complex
+uh issue but then actually there was a
+
+ align:start position:0%
+uh issue but then actually there was a
+ 
+
+ align:start position:0%
+uh issue but then actually there was a
+very interesting development that that
+
+ align:start position:0%
+very interesting development that that
+ 
+
+ align:start position:0%
+very interesting development that that
+uh had a strong influence in Watson and
+
+ align:start position:0%
+uh had a strong influence in Watson and
+ 
+
+ align:start position:0%
+uh had a strong influence in Watson and
+Crick and led to them getting crick in
+
+ align:start position:0%
+Crick and led to them getting crick in
+ 
+
+ align:start position:0%
+Crick and led to them getting crick in
+particular getting a a key insight into
+
+ align:start position:0%
+particular getting a a key insight into
+ 
+
+ align:start position:0%
+particular getting a a key insight into
+the nature of this coding problem
+
+ align:start position:0%
+the nature of this coding problem
+ 
+
+ align:start position:0%
+the nature of this coding problem
+there's a physicist uh George gaml Who
+
+ align:start position:0%
+there's a physicist uh George gaml Who
+ 
+
+ align:start position:0%
+there's a physicist uh George gaml Who
+some of you know he proposed The Big
+
+ align:start position:0%
+some of you know he proposed The Big
+ 
+
+ align:start position:0%
+some of you know he proposed The Big
+Bang Theory and very strong theoretical
+
+ align:start position:0%
+Bang Theory and very strong theoretical
+ 
+
+ align:start position:0%
+Bang Theory and very strong theoretical
+physicist and he wrote a letter to
+
+ align:start position:0%
+physicist and he wrote a letter to
+ 
+
+ align:start position:0%
+physicist and he wrote a letter to
+Watson and Crick he thought he'd figured
+
+ align:start position:0%
+Watson and Crick he thought he'd figured
+ 
+
+ align:start position:0%
+Watson and Crick he thought he'd figured
+out the basis of the of the genetic code
+
+ align:start position:0%
+out the basis of the of the genetic code
+ 
+
+ align:start position:0%
+out the basis of the of the genetic code
+and his idea was you had these sequences
+
+ align:start position:0%
+and his idea was you had these sequences
+ 
+
+ align:start position:0%
+and his idea was you had these sequences
+of AG C's and T's and so every
+
+ align:start position:0%
+of AG C's and T's and so every
+ 
+
+ align:start position:0%
+of AG C's and T's and so every
+everywhere that there was was and the
+
+ align:start position:0%
+everywhere that there was was and the
+ 
+
+ align:start position:0%
+everywhere that there was was and the
+two bases came together there were sort
+
+ align:start position:0%
+two bases came together there were sort
+ 
+
+ align:start position:0%
+two bases came together there were sort
+of like a little different shaped hole
+
+ align:start position:0%
+of like a little different shaped hole
+ 
+
+ align:start position:0%
+of like a little different shaped hole
+so his idea was the amino acids would
+
+ align:start position:0%
+so his idea was the amino acids would
+ 
+
+ align:start position:0%
+so his idea was the amino acids would
+stick into these little holes and he had
+
+ align:start position:0%
+stick into these little holes and he had
+ 
+
+ align:start position:0%
+stick into these little holes and he had
+a theory showing that you could encode
+
+ align:start position:0%
+a theory showing that you could encode
+ 
+
+ align:start position:0%
+a theory showing that you could encode
+the sequence of proteins by having the
+
+ align:start position:0%
+the sequence of proteins by having the
+ 
+
+ align:start position:0%
+the sequence of proteins by having the
+the side chains of the amino acids stick
+
+ align:start position:0%
+the side chains of the amino acids stick
+ 
+
+ align:start position:0%
+the side chains of the amino acids stick
+into these little holes along the DNA
+
+ align:start position:0%
+into these little holes along the DNA
+ 
+
+ align:start position:0%
+into these little holes along the DNA
+now that turned out to be a number of
+
+ align:start position:0%
+now that turned out to be a number of
+ 
+
+ align:start position:0%
+now that turned out to be a number of
+problems with that it didn't take into
+
+ align:start position:0%
+problems with that it didn't take into
+ 
+
+ align:start position:0%
+problems with that it didn't take into
+account the involvement of RNA which was
+
+ align:start position:0%
+account the involvement of RNA which was
+ 
+
+ align:start position:0%
+account the involvement of RNA which was
+sort of there was quite a bit of
+
+ align:start position:0%
+sort of there was quite a bit of
+ 
+
+ align:start position:0%
+sort of there was quite a bit of
+evidence for and more importantly it
+
+ align:start position:0%
+evidence for and more importantly it
+ 
+
+ align:start position:0%
+evidence for and more importantly it
+didn't take into account the the the
+
+ align:start position:0%
+didn't take into account the the the
+ 
+
+ align:start position:0%
+didn't take into account the the the
+structure of the side chains of the
+
+ align:start position:0%
+structure of the side chains of the
+ 
+
+ align:start position:0%
+structure of the side chains of the
+amino acids which you guys have been
+
+ align:start position:0%
+amino acids which you guys have been
+ 
+
+ align:start position:0%
+amino acids which you guys have been
+exposed to but it had a very profound
+
+ align:start position:0%
+exposed to but it had a very profound
+ 
+
+ align:start position:0%
+exposed to but it had a very profound
+influence on Watson and C they read this
+
+ align:start position:0%
+influence on Watson and C they read this
+ 
+
+ align:start position:0%
+influence on Watson and C they read this
+letter they immediately realized the
+
+ align:start position:0%
+letter they immediately realized the
+ 
+
+ align:start position:0%
+letter they immediately realized the
+idea was wrong they went out and had a
+
+ align:start position:0%
+idea was wrong they went out and had a
+ 
+
+ align:start position:0%
+idea was wrong they went out and had a
+lunch at a pub decided that gamow had
+
+ align:start position:0%
+lunch at a pub decided that gamow had
+ 
+
+ align:start position:0%
+lunch at a pub decided that gamow had
+had actually thought there were 25 amino
+
+ align:start position:0%
+had actually thought there were 25 amino
+ 
+
+ align:start position:0%
+had actually thought there were 25 amino
+acids but they realized some of them
+
+ align:start position:0%
+acids but they realized some of them
+ 
+
+ align:start position:0%
+acids but they realized some of them
+were just sort of special ones that were
+
+ align:start position:0%
+were just sort of special ones that were
+ 
+
+ align:start position:0%
+were just sort of special ones that were
+modified only in particular proteins and
+
+ align:start position:0%
+modified only in particular proteins and
+ 
+
+ align:start position:0%
+modified only in particular proteins and
+there were really 20 amino acids that
+
+ align:start position:0%
+there were really 20 amino acids that
+ 
+
+ align:start position:0%
+there were really 20 amino acids that
+were found universally in nature in
+
+ align:start position:0%
+were found universally in nature in
+ 
+
+ align:start position:0%
+were found universally in nature in
+amino acids and what they crick in
+
+ align:start position:0%
+amino acids and what they crick in
+ 
+
+ align:start position:0%
+amino acids and what they crick in
+particular realized was that maybe
+
+ align:start position:0%
+particular realized was that maybe
+ 
+
+ align:start position:0%
+particular realized was that maybe
+instead of having to think about protein
+
+ align:start position:0%
+instead of having to think about protein
+ 
+
+ align:start position:0%
+instead of having to think about protein
+synthesis through this very complex ex
+
+ align:start position:0%
+synthesis through this very complex ex
+ 
+
+ align:start position:0%
+synthesis through this very complex ex
+set of extracts and mixtures the
+
+ align:start position:0%
+set of extracts and mixtures the
+ 
+
+ align:start position:0%
+set of extracts and mixtures the
+biochemist was would work on that he
+
+ align:start position:0%
+biochemist was would work on that he
+ 
+
+ align:start position:0%
+biochemist was would work on that he
+could think about it at a purely
+
+ align:start position:0%
+could think about it at a purely
+ 
+
+ align:start position:0%
+could think about it at a purely
+theoretical level which basically is up
+
+ align:start position:0%
+theoretical level which basically is up
+ 
+
+ align:start position:0%
+theoretical level which basically is up
+at this kind of level that if you have a
+
+ align:start position:0%
+at this kind of level that if you have a
+ 
+
+ align:start position:0%
+at this kind of level that if you have a
+molecule that has four letters and it's
+
+ align:start position:0%
+molecule that has four letters and it's
+ 
+
+ align:start position:0%
+molecule that has four letters and it's
+going to be encoding proteins how does
+
+ align:start position:0%
+going to be encoding proteins how does
+ 
+
+ align:start position:0%
+going to be encoding proteins how does
+it do it can I work out sort of the
+
+ align:start position:0%
+it do it can I work out sort of the
+ 
+
+ align:start position:0%
+it do it can I work out sort of the
+basis or a possible theory for that
+
+ align:start position:0%
+basis or a possible theory for that
+ 
+
+ align:start position:0%
+basis or a possible theory for that
+could happen without actually knowing
+
+ align:start position:0%
+could happen without actually knowing
+ 
+
+ align:start position:0%
+could happen without actually knowing
+all of the biochemical details so Crick
+
+ align:start position:0%
+all of the biochemical details so Crick
+ 
+
+ align:start position:0%
+all of the biochemical details so Crick
+made a couple of
+
+ align:start position:0%
+made a couple of
+ 
+
+ align:start position:0%
+made a couple of
+simplifying uh
+
+ align:start position:0%
+simplifying uh
+ 
+
+ align:start position:0%
+simplifying uh
+assumptions one was that the DNA only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determined the linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence of amino
+
+ align:start position:0%
+sequence of amino
+ 
+
+ align:start position:0%
+sequence of amino
+acids
+
+ align:start position:0%
+acids
+ 
+
+ align:start position:0%
+acids
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+protein that all this information about
+
+ align:start position:0%
+protein that all this information about
+ 
+
+ align:start position:0%
+protein that all this information about
+the three-dimensional stuff came from
+
+ align:start position:0%
+the three-dimensional stuff came from
+ 
+
+ align:start position:0%
+the three-dimensional stuff came from
+the properties of the of the uh linear
+
+ align:start position:0%
+the properties of the of the uh linear
+ 
+
+ align:start position:0%
+the properties of the of the uh linear
+sequence once it was made and I think
+
+ align:start position:0%
+sequence once it was made and I think
+ 
+
+ align:start position:0%
+sequence once it was made and I think
+you've hopefully have enough
+
+ align:start position:0%
+you've hopefully have enough
+ 
+
+ align:start position:0%
+you've hopefully have enough
+understanding of hydrophobic and other
+
+ align:start position:0%
+understanding of hydrophobic and other
+ 
+
+ align:start position:0%
+understanding of hydrophobic and other
+sorts of interactions that would cause a
+
+ align:start position:0%
+sorts of interactions that would cause a
+ 
+
+ align:start position:0%
+sorts of interactions that would cause a
+a linear sequence of amino acids to take
+
+ align:start position:0%
+a linear sequence of amino acids to take
+ 
+
+ align:start position:0%
+a linear sequence of amino acids to take
+up a particular confirmation and the
+
+ align:start position:0%
+up a particular confirmation and the
+ 
+
+ align:start position:0%
+up a particular confirmation and the
+other thing he just he uh assumption he
+
+ align:start position:0%
+other thing he just he uh assumption he
+ 
+
+ align:start position:0%
+other thing he just he uh assumption he
+made that it must be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Universal
+
+ align:start position:0%
+Universal
+ 
+
+ align:start position:0%
+Universal
+and it would be hard to see how life
+
+ align:start position:0%
+and it would be hard to see how life
+ 
+
+ align:start position:0%
+and it would be hard to see how life
+could have started if there wasn't some
+
+ align:start position:0%
+could have started if there wasn't some
+ 
+
+ align:start position:0%
+could have started if there wasn't some
+kind of of uh code that was Universal
+
+ align:start position:0%
+kind of of uh code that was Universal
+ 
+
+ align:start position:0%
+kind of of uh code that was Universal
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+organisms and if you start from those
+
+ align:start position:0%
+organisms and if you start from those
+ 
+
+ align:start position:0%
+organisms and if you start from those
+kind of considerations then what you can
+
+ align:start position:0%
+kind of considerations then what you can
+ 
+
+ align:start position:0%
+kind of considerations then what you can
+see is you can't just have a onetoone
+
+ align:start position:0%
+see is you can't just have a onetoone
+ 
+
+ align:start position:0%
+see is you can't just have a onetoone
+correspondence between a letter in the
+
+ align:start position:0%
+correspondence between a letter in the
+ 
+
+ align:start position:0%
+correspondence between a letter in the
+MEO in the uh nucleic acid alphabet and
+
+ align:start position:0%
+MEO in the uh nucleic acid alphabet and
+ 
+
+ align:start position:0%
+MEO in the uh nucleic acid alphabet and
+a letter down here if a stood for
+
+ align:start position:0%
+a letter down here if a stood for
+ 
+
+ align:start position:0%
+a letter down here if a stood for
+veiling that would be fine but you could
+
+ align:start position:0%
+veiling that would be fine but you could
+ 
+
+ align:start position:0%
+veiling that would be fine but you could
+only have code for four me acids that
+
+ align:start position:0%
+only have code for four me acids that
+ 
+
+ align:start position:0%
+only have code for four me acids that
+way so if you had onel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words in
+
+ align:start position:0%
+words in
+ 
+
+ align:start position:0%
+words in
+DNA there are four possibilities and so
+
+ align:start position:0%
+DNA there are four possibilities and so
+ 
+
+ align:start position:0%
+DNA there are four possibilities and so
+you could only make four if you had two
+
+ align:start position:0%
+you could only make four if you had two
+ 
+
+ align:start position:0%
+you could only make four if you had two
+two letter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words then you'd have 16 possibilities
+
+ align:start position:0%
+words then you'd have 16 possibilities
+ 
+
+ align:start position:0%
+words then you'd have 16 possibilities
+still not enough for uh all the amino
+
+ align:start position:0%
+still not enough for uh all the amino
+ 
+
+ align:start position:0%
+still not enough for uh all the amino
+acids if you had three-letter word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you could do 64 and there'd be in
+
+ align:start position:0%
+then you could do 64 and there'd be in
+ 
+
+ align:start position:0%
+then you could do 64 and there'd be in
+principle that would be all you need it
+
+ align:start position:0%
+principle that would be all you need it
+ 
+
+ align:start position:0%
+principle that would be all you need it
+doesn't rule out there couldn't be five
+
+ align:start position:0%
+doesn't rule out there couldn't be five
+ 
+
+ align:start position:0%
+doesn't rule out there couldn't be five
+or six seven letter words or if you
+
+ align:start position:0%
+or six seven letter words or if you
+ 
+
+ align:start position:0%
+or six seven letter words or if you
+think about this as they were thinking
+
+ align:start position:0%
+think about this as they were thinking
+ 
+
+ align:start position:0%
+think about this as they were thinking
+about it at the time uh even if it were
+
+ align:start position:0%
+about it at the time uh even if it were
+ 
+
+ align:start position:0%
+about it at the time uh even if it were
+let's say a three-letter word is it a
+
+ align:start position:0%
+let's say a three-letter word is it a
+ 
+
+ align:start position:0%
+let's say a three-letter word is it a
+code where you have one word then the
+
+ align:start position:0%
+code where you have one word then the
+ 
+
+ align:start position:0%
+code where you have one word then the
+next word the next word or could it be
+
+ align:start position:0%
+next word the next word or could it be
+ 
+
+ align:start position:0%
+next word the next word or could it be
+an overlapping word and what about
+
+ align:start position:0%
+an overlapping word and what about
+ 
+
+ align:start position:0%
+an overlapping word and what about
+punctuation and maybe another thing you
+
+ align:start position:0%
+punctuation and maybe another thing you
+ 
+
+ align:start position:0%
+punctuation and maybe another thing you
+can see if it's agct da d da there's a
+
+ align:start position:0%
+can see if it's agct da d da there's a
+ 
+
+ align:start position:0%
+can see if it's agct da d da there's a
+frame of reference problem because if
+
+ align:start position:0%
+frame of reference problem because if
+ 
+
+ align:start position:0%
+frame of reference problem because if
+I'm going to read them in groups of
+
+ align:start position:0%
+I'm going to read them in groups of
+ 
+
+ align:start position:0%
+I'm going to read them in groups of
+three if I start here I'll get one word
+
+ align:start position:0%
+three if I start here I'll get one word
+ 
+
+ align:start position:0%
+three if I start here I'll get one word
+but if I start one letter over the next
+
+ align:start position:0%
+but if I start one letter over the next
+ 
+
+ align:start position:0%
+but if I start one letter over the next
+group of three won't be the same so
+
+ align:start position:0%
+group of three won't be the same so
+ 
+
+ align:start position:0%
+group of three won't be the same so
+somehow there would have to be uh a
+
+ align:start position:0%
+somehow there would have to be uh a
+ 
+
+ align:start position:0%
+somehow there would have to be uh a
+starting point and so these are the sort
+
+ align:start position:0%
+starting point and so these are the sort
+ 
+
+ align:start position:0%
+starting point and so these are the sort
+of considerations that they that uh they
+
+ align:start position:0%
+of considerations that they that uh they
+ 
+
+ align:start position:0%
+of considerations that they that uh they
+had to take
+
+ align:start position:0%
+had to take
+ 
+
+ align:start position:0%
+had to take
+into uh account and and in fact Watson
+
+ align:start position:0%
+into uh account and and in fact Watson
+ 
+
+ align:start position:0%
+into uh account and and in fact Watson
+and uh excuse me uh Francis Crick and
+
+ align:start position:0%
+and uh excuse me uh Francis Crick and
+ 
+
+ align:start position:0%
+and uh excuse me uh Francis Crick and
+another scientist uh um Sydney brener
+
+ align:start position:0%
+another scientist uh um Sydney brener
+ 
+
+ align:start position:0%
+another scientist uh um Sydney brener
+and some others other scientists worked
+
+ align:start position:0%
+and some others other scientists worked
+ 
+
+ align:start position:0%
+and some others other scientists worked
+out a very elegant uh genetic experiment
+
+ align:start position:0%
+out a very elegant uh genetic experiment
+ 
+
+ align:start position:0%
+out a very elegant uh genetic experiment
+that that demonstrated that it was a
+
+ align:start position:0%
+that that demonstrated that it was a
+ 
+
+ align:start position:0%
+that that demonstrated that it was a
+three-letter
+
+ align:start position:0%
+three-letter
+ 
+
+ align:start position:0%
+three-letter
+code and I don't have the um the time to
+
+ align:start position:0%
+code and I don't have the um the time to
+ 
+
+ align:start position:0%
+code and I don't have the um the time to
+go into it in this course if you take a
+
+ align:start position:0%
+go into it in this course if you take a
+ 
+
+ align:start position:0%
+go into it in this course if you take a
+genetics course it's a it's a very
+
+ align:start position:0%
+genetics course it's a it's a very
+ 
+
+ align:start position:0%
+genetics course it's a it's a very
+beautiful experiment um the principle of
+
+ align:start position:0%
+beautiful experiment um the principle of
+ 
+
+ align:start position:0%
+beautiful experiment um the principle of
+the thing which I could show you rather
+
+ align:start position:0%
+the thing which I could show you rather
+ 
+
+ align:start position:0%
+the thing which I could show you rather
+easily is if you're writing a a
+
+ align:start position:0%
+easily is if you're writing a a
+ 
+
+ align:start position:0%
+easily is if you're writing a a
+three-letter word a three thing where
+
+ align:start position:0%
+three-letter word a three thing where
+ 
+
+ align:start position:0%
+three-letter word a three thing where
+you're reading in three-letter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words something like this the cat ran
+
+ align:start position:0%
+words something like this the cat ran
+ 
+
+ align:start position:0%
+words something like this the cat ran
+out and I don't
+
+ align:start position:0%
+out and I don't
+ 
+
+ align:start position:0%
+out and I don't
+know ate the rat or something like that
+
+ align:start position:0%
+know ate the rat or something like that
+ 
+
+ align:start position:0%
+know ate the rat or something like that
+and these were all just continuously run
+
+ align:start position:0%
+and these were all just continuously run
+ 
+
+ align:start position:0%
+and these were all just continuously run
+together not not separated out but I put
+
+ align:start position:0%
+together not not separated out but I put
+ 
+
+ align:start position:0%
+together not not separated out but I put
+them out here as you can see the
+
+ align:start position:0%
+them out here as you can see the
+ 
+
+ align:start position:0%
+them out here as you can see the
+three-letter words if you lost one
+
+ align:start position:0%
+three-letter words if you lost one
+ 
+
+ align:start position:0%
+three-letter words if you lost one
+letter then it would change to sort of
+
+ align:start position:0%
+letter then it would change to sort of
+ 
+
+ align:start position:0%
+letter then it would change to sort of
+gibberish you'd get uh stuff that looked
+
+ align:start position:0%
+gibberish you'd get uh stuff that looked
+ 
+
+ align:start position:0%
+gibberish you'd get uh stuff that looked
+like like this and if you uh put one one
+
+ align:start position:0%
+like like this and if you uh put one one
+ 
+
+ align:start position:0%
+like like this and if you uh put one one
+in you'd have the same problem but if
+
+ align:start position:0%
+in you'd have the same problem but if
+ 
+
+ align:start position:0%
+in you'd have the same problem but if
+you were to take
+
+ align:start position:0%
+you were to take
+ 
+
+ align:start position:0%
+you were to take
+out either take out three letters or put
+
+ align:start position:0%
+out either take out three letters or put
+ 
+
+ align:start position:0%
+out either take out three letters or put
+in three letters then even though
+
+ align:start position:0%
+in three letters then even though
+ 
+
+ align:start position:0%
+in three letters then even though
+there'd be a little mess in here
+
+ align:start position:0%
+there'd be a little mess in here
+ 
+
+ align:start position:0%
+there'd be a little mess in here
+somewhere say I took out two more of
+
+ align:start position:0%
+somewhere say I took out two more of
+ 
+
+ align:start position:0%
+somewhere say I took out two more of
+these what we would now from then on
+
+ align:start position:0%
+these what we would now from then on
+ 
+
+ align:start position:0%
+these what we would now from then on
+we'd have but the rest of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it would now makes sense again and they
+
+ align:start position:0%
+it would now makes sense again and they
+ 
+
+ align:start position:0%
+it would now makes sense again and they
+did this sort of experiment genetically
+
+ align:start position:0%
+did this sort of experiment genetically
+ 
+
+ align:start position:0%
+did this sort of experiment genetically
+they managed to figure out there were
+
+ align:start position:0%
+they managed to figure out there were
+ 
+
+ align:start position:0%
+they managed to figure out there were
+two kinds of mutations they could get in
+
+ align:start position:0%
+two kinds of mutations they could get in
+ 
+
+ align:start position:0%
+two kinds of mutations they could get in
+a particular way some were putting in a
+
+ align:start position:0%
+a particular way some were putting in a
+ 
+
+ align:start position:0%
+a particular way some were putting in a
+letter some were taking out a letter and
+
+ align:start position:0%
+letter some were taking out a letter and
+ 
+
+ align:start position:0%
+letter some were taking out a letter and
+they didn't know at the time whether
+
+ align:start position:0%
+they didn't know at the time whether
+ 
+
+ align:start position:0%
+they didn't know at the time whether
+they're adding or deleting but they
+
+ align:start position:0%
+they're adding or deleting but they
+ 
+
+ align:start position:0%
+they're adding or deleting but they
+could tell they were in the opposite
+
+ align:start position:0%
+could tell they were in the opposite
+ 
+
+ align:start position:0%
+could tell they were in the opposite
+directions and then they found if they
+
+ align:start position:0%
+directions and then they found if they
+ 
+
+ align:start position:0%
+directions and then they found if they
+took three of one class like three that
+
+ align:start position:0%
+took three of one class like three that
+ 
+
+ align:start position:0%
+took three of one class like three that
+would delete a letter and put them all
+
+ align:start position:0%
+would delete a letter and put them all
+ 
+
+ align:start position:0%
+would delete a letter and put them all
+together then things would more or less
+
+ align:start position:0%
+together then things would more or less
+ 
+
+ align:start position:0%
+together then things would more or less
+work or if they put three that stuck in
+
+ align:start position:0%
+work or if they put three that stuck in
+ 
+
+ align:start position:0%
+work or if they put three that stuck in
+an extra letter then everything would
+
+ align:start position:0%
+an extra letter then everything would
+ 
+
+ align:start position:0%
+an extra letter then everything would
+more or less work so there was a genetic
+
+ align:start position:0%
+more or less work so there was a genetic
+ 
+
+ align:start position:0%
+more or less work so there was a genetic
+proof of the uh three-letter part of the
+
+ align:start position:0%
+proof of the uh three-letter part of the
+ 
+
+ align:start position:0%
+proof of the uh three-letter part of the
+code before it was figured out exactly
+
+ align:start position:0%
+code before it was figured out exactly
+ 
+
+ align:start position:0%
+code before it was figured out exactly
+uh how the code
+
+ align:start position:0%
+uh how the code
+ 
+
+ align:start position:0%
+uh how the code
+itself itself worked and so going from
+
+ align:start position:0%
+itself itself worked and so going from
+ 
+
+ align:start position:0%
+itself itself worked and so going from
+this um sort of
+
+ align:start position:0%
+this um sort of
+ 
+
+ align:start position:0%
+this um sort of
+theoretical uh insight into the the code
+
+ align:start position:0%
+theoretical uh insight into the the code
+ 
+
+ align:start position:0%
+theoretical uh insight into the the code
+to actually figuring out how proteins
+
+ align:start position:0%
+to actually figuring out how proteins
+ 
+
+ align:start position:0%
+to actually figuring out how proteins
+were made uh was was still was still
+
+ align:start position:0%
+were made uh was was still was still
+ 
+
+ align:start position:0%
+were made uh was was still was still
+quite a lot of stuff that had to to
+
+ align:start position:0%
+quite a lot of stuff that had to to
+ 
+
+ align:start position:0%
+quite a lot of stuff that had to to
+happen and one was
+
+ align:start position:0%
+happen and one was
+ 
+
+ align:start position:0%
+happen and one was
+the the concept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of messenger RNA as I said there had
+
+ align:start position:0%
+of messenger RNA as I said there had
+ 
+
+ align:start position:0%
+of messenger RNA as I said there had
+been quite a lot of evidence that RNA
+
+ align:start position:0%
+been quite a lot of evidence that RNA
+ 
+
+ align:start position:0%
+been quite a lot of evidence that RNA
+was somehow involved in protein
+
+ align:start position:0%
+was somehow involved in protein
+ 
+
+ align:start position:0%
+was somehow involved in protein
+synthesis because cells that made a lot
+
+ align:start position:0%
+synthesis because cells that made a lot
+ 
+
+ align:start position:0%
+synthesis because cells that made a lot
+of protein made a lot of RNA and it
+
+ align:start position:0%
+of protein made a lot of RNA and it
+ 
+
+ align:start position:0%
+of protein made a lot of RNA and it
+seemed to be um in the right sort of
+
+ align:start position:0%
+seemed to be um in the right sort of
+ 
+
+ align:start position:0%
+seemed to be um in the right sort of
+place in the in the cell uh for the
+
+ align:start position:0%
+place in the in the cell uh for the
+ 
+
+ align:start position:0%
+place in the in the cell uh for the
+proteins to be made so the idea emerged
+
+ align:start position:0%
+proteins to be made so the idea emerged
+ 
+
+ align:start position:0%
+proteins to be made so the idea emerged
+that RNA was somehow a carrier of
+
+ align:start position:0%
+that RNA was somehow a carrier of
+ 
+
+ align:start position:0%
+that RNA was somehow a carrier of
+information from the DNA
+
+ align:start position:0%
+information from the DNA
+ 
+
+ align:start position:0%
+information from the DNA
+to the cytoplasm so it would uh carry uh
+
+ align:start position:0%
+to the cytoplasm so it would uh carry uh
+ 
+
+ align:start position:0%
+to the cytoplasm so it would uh carry uh
+could serve as a template for making
+
+ align:start position:0%
+could serve as a template for making
+ 
+
+ align:start position:0%
+could serve as a template for making
+proteins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so the idea was to cop that the cell
+
+ align:start position:0%
+so so the idea was to cop that the cell
+ 
+
+ align:start position:0%
+so so the idea was to cop that the cell
+copied the sequence of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+portion of the DNA and we'd probably
+
+ align:start position:0%
+portion of the DNA and we'd probably
+ 
+
+ align:start position:0%
+portion of the DNA and we'd probably
+think of this as a gene right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um into RNA and the
+
+ align:start position:0%
+um into RNA and the
+ 
+
+ align:start position:0%
+um into RNA and the
+RNA would go into the cytoplasm that's
+
+ align:start position:0%
+RNA would go into the cytoplasm that's
+ 
+
+ align:start position:0%
+RNA would go into the cytoplasm that's
+the part outside the
+
+ align:start position:0%
+the part outside the
+ 
+
+ align:start position:0%
+the part outside the
+nucleus and then it would
+
+ align:start position:0%
+nucleus and then it would
+ 
+
+ align:start position:0%
+nucleus and then it would
+serve as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+template for protein
+
+ align:start position:0%
+template for protein
+ 
+
+ align:start position:0%
+template for protein
+synthesis because of this
+
+ align:start position:0%
+synthesis because of this
+ 
+
+ align:start position:0%
+synthesis because of this
+this thought that if you had a cell like
+
+ align:start position:0%
+this thought that if you had a cell like
+ 
+
+ align:start position:0%
+this thought that if you had a cell like
+this with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleus and the DNA and here that if a
+
+ align:start position:0%
+nucleus and the DNA and here that if a
+ 
+
+ align:start position:0%
+nucleus and the DNA and here that if a
+piece of
+
+ align:start position:0%
+piece of
+ 
+
+ align:start position:0%
+piece of
+RNA were to go out into the cytoplasm
+
+ align:start position:0%
+RNA were to go out into the cytoplasm
+ 
+
+ align:start position:0%
+RNA were to go out into the cytoplasm
+and have those properties it would be
+
+ align:start position:0%
+and have those properties it would be
+ 
+
+ align:start position:0%
+and have those properties it would be
+functioning more or less as a messenger
+
+ align:start position:0%
+functioning more or less as a messenger
+ 
+
+ align:start position:0%
+functioning more or less as a messenger
+that would be carrying the genetic
+
+ align:start position:0%
+that would be carrying the genetic
+ 
+
+ align:start position:0%
+that would be carrying the genetic
+information from inside the nucleus out
+
+ align:start position:0%
+information from inside the nucleus out
+ 
+
+ align:start position:0%
+information from inside the nucleus out
+into the cytoplasm and so the term uh
+
+ align:start position:0%
+into the cytoplasm and so the term uh
+ 
+
+ align:start position:0%
+into the cytoplasm and so the term uh
+began to be used of a a messenger RNA
+
+ align:start position:0%
+began to be used of a a messenger RNA
+ 
+
+ align:start position:0%
+began to be used of a a messenger RNA
+and and so over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I'll put an MR RNA to to indicate
+
+ align:start position:0%
+here I'll put an MR RNA to to indicate
+ 
+
+ align:start position:0%
+here I'll put an MR RNA to to indicate
+uh that now one thing you can also see
+
+ align:start position:0%
+uh that now one thing you can also see
+ 
+
+ align:start position:0%
+uh that now one thing you can also see
+is we've talked about the structure of
+
+ align:start position:0%
+is we've talked about the structure of
+ 
+
+ align:start position:0%
+is we've talked about the structure of
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+um of DNA and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RNA and it's essentially the same with
+
+ align:start position:0%
+RNA and it's essentially the same with
+ 
+
+ align:start position:0%
+RNA and it's essentially the same with
+one this is the nucleotide which is the
+
+ align:start position:0%
+one this is the nucleotide which is the
+ 
+
+ align:start position:0%
+one this is the nucleotide which is the
+fundamental uh building
+
+ align:start position:0%
+fundamental uh building
+ 
+
+ align:start position:0%
+fundamental uh building
+block of DNA and if you recall in DNA
+
+ align:start position:0%
+block of DNA and if you recall in DNA
+ 
+
+ align:start position:0%
+block of DNA and if you recall in DNA
+there's a hydroxy excuse me a hydrogen
+
+ align:start position:0%
+there's a hydroxy excuse me a hydrogen
+ 
+
+ align:start position:0%
+there's a hydroxy excuse me a hydrogen
+there but in
+
+ align:start position:0%
+there but in
+ 
+
+ align:start position:0%
+there but in
+RNA there is this extra uh
+
+ align:start position:0%
+RNA there is this extra uh
+ 
+
+ align:start position:0%
+RNA there is this extra uh
+hydroxy this is one one prime two Prime
+
+ align:start position:0%
+hydroxy this is one one prime two Prime
+ 
+
+ align:start position:0%
+hydroxy this is one one prime two Prime
+3 Prime 4 Prime excuse me one let's just
+
+ align:start position:0%
+3 Prime 4 Prime excuse me one let's just
+ 
+
+ align:start position:0%
+3 Prime 4 Prime excuse me one let's just
+leave it like this for the moment 1 2 3
+
+ align:start position:0%
+leave it like this for the moment 1 2 3
+ 
+
+ align:start position:0%
+leave it like this for the moment 1 2 3
+four five and so this uh the um DNA as
+
+ align:start position:0%
+four five and so this uh the um DNA as
+ 
+
+ align:start position:0%
+four five and so this uh the um DNA as
+we heard was um deoxy ribon acid because
+
+ align:start position:0%
+we heard was um deoxy ribon acid because
+ 
+
+ align:start position:0%
+we heard was um deoxy ribon acid because
+it's missing this but other than that uh
+
+ align:start position:0%
+it's missing this but other than that uh
+ 
+
+ align:start position:0%
+it's missing this but other than that uh
+the backbones are are are similar so and
+
+ align:start position:0%
+the backbones are are are similar so and
+ 
+
+ align:start position:0%
+the backbones are are are similar so and
+the the letters are almost the same the
+
+ align:start position:0%
+the the letters are almost the same the
+ 
+
+ align:start position:0%
+the the letters are almost the same the
+a the G and the C are exactly the same
+
+ align:start position:0%
+a the G and the C are exactly the same
+ 
+
+ align:start position:0%
+a the G and the C are exactly the same
+bases in DNA and RNA the only difference
+
+ align:start position:0%
+bases in DNA and RNA the only difference
+ 
+
+ align:start position:0%
+bases in DNA and RNA the only difference
+is with the T and the and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uracil so this
+
+ align:start position:0%
+uracil so this
+ 
+
+ align:start position:0%
+uracil so this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+this is thyine which is found in
+
+ align:start position:0%
+this is thyine which is found in
+ 
+
+ align:start position:0%
+this is thyine which is found in
+DNA and this is our this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uracil which is found
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in uh found in RNA so the base pairing
+
+ align:start position:0%
+in uh found in RNA so the base pairing
+ 
+
+ align:start position:0%
+in uh found in RNA so the base pairing
+is over on this part of the molecule so
+
+ align:start position:0%
+is over on this part of the molecule so
+ 
+
+ align:start position:0%
+is over on this part of the molecule so
+whether or not you have a methyl group
+
+ align:start position:0%
+whether or not you have a methyl group
+ 
+
+ align:start position:0%
+whether or not you have a methyl group
+doesn't really change the base pairing
+
+ align:start position:0%
+doesn't really change the base pairing
+ 
+
+ align:start position:0%
+doesn't really change the base pairing
+and so this process of copying
+
+ align:start position:0%
+and so this process of copying
+ 
+
+ align:start position:0%
+and so this process of copying
+information in DNA uh to uh me to
+
+ align:start position:0%
+information in DNA uh to uh me to
+ 
+
+ align:start position:0%
+information in DNA uh to uh me to
+information that's in RNA was seen as
+
+ align:start position:0%
+information that's in RNA was seen as
+ 
+
+ align:start position:0%
+information that's in RNA was seen as
+it's essentially the same kind of
+
+ align:start position:0%
+it's essentially the same kind of
+ 
+
+ align:start position:0%
+it's essentially the same kind of
+language but it's just sort of like
+
+ align:start position:0%
+language but it's just sort of like
+ 
+
+ align:start position:0%
+language but it's just sort of like
+taking somebody's word processor file
+
+ align:start position:0%
+taking somebody's word processor file
+ 
+
+ align:start position:0%
+taking somebody's word processor file
+and writing out long hand uh you'd be
+
+ align:start position:0%
+and writing out long hand uh you'd be
+ 
+
+ align:start position:0%
+and writing out long hand uh you'd be
+transcribing the information
+
+ align:start position:0%
+transcribing the information
+ 
+
+ align:start position:0%
+transcribing the information
+but it would be the same essentially the
+
+ align:start position:0%
+but it would be the same essentially the
+ 
+
+ align:start position:0%
+but it would be the same essentially the
+same kind of information in essentially
+
+ align:start position:0%
+same kind of information in essentially
+ 
+
+ align:start position:0%
+same kind of information in essentially
+the same the same form so this is known
+
+ align:start position:0%
+the same the same form so this is known
+ 
+
+ align:start position:0%
+the same the same form so this is known
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transcription I'll take just one very
+
+ align:start position:0%
+transcription I'll take just one very
+ 
+
+ align:start position:0%
+transcription I'll take just one very
+brief thing some of you may wonder why
+
+ align:start position:0%
+brief thing some of you may wonder why
+ 
+
+ align:start position:0%
+brief thing some of you may wonder why
+did nature do it this way Why didn't it
+
+ align:start position:0%
+did nature do it this way Why didn't it
+ 
+
+ align:start position:0%
+did nature do it this way Why didn't it
+just use
+
+ align:start position:0%
+just use
+ 
+
+ align:start position:0%
+just use
+uracil in DNA so as a very brief aside
+
+ align:start position:0%
+uracil in DNA so as a very brief aside
+ 
+
+ align:start position:0%
+uracil in DNA so as a very brief aside
+uh there we I think we understand
+
+ align:start position:0%
+uh there we I think we understand
+ 
+
+ align:start position:0%
+uh there we I think we understand
+pretty much what why it does it and that
+
+ align:start position:0%
+pretty much what why it does it and that
+ 
+
+ align:start position:0%
+pretty much what why it does it and that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+citadine has this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um structure this is so this is C which
+
+ align:start position:0%
+um structure this is so this is C which
+ 
+
+ align:start position:0%
+um structure this is so this is C which
+is found in DNA but it undergoes uh all
+
+ align:start position:0%
+is found in DNA but it undergoes uh all
+ 
+
+ align:start position:0%
+is found in DNA but it undergoes uh all
+all of your um DNA is is a chemical and
+
+ align:start position:0%
+all of your um DNA is is a chemical and
+ 
+
+ align:start position:0%
+all of your um DNA is is a chemical and
+it's it's able to undergo spontaneous
+
+ align:start position:0%
+it's it's able to undergo spontaneous
+ 
+
+ align:start position:0%
+it's it's able to undergo spontaneous
+kinds of damage uh in fact we have in a
+
+ align:start position:0%
+kinds of damage uh in fact we have in a
+ 
+
+ align:start position:0%
+kinds of damage uh in fact we have in a
+every one of our cells uh every day
+
+ align:start position:0%
+every one of our cells uh every day
+ 
+
+ align:start position:0%
+every one of our cells uh every day
+10,000 times in any given cell a base
+
+ align:start position:0%
+10,000 times in any given cell a base
+ 
+
+ align:start position:0%
+10,000 times in any given cell a base
+falls off totally just leaving a the
+
+ align:start position:0%
+falls off totally just leaving a the
+ 
+
+ align:start position:0%
+falls off totally just leaving a the
+deoxy ribos sitting there and the cells
+
+ align:start position:0%
+deoxy ribos sitting there and the cells
+ 
+
+ align:start position:0%
+deoxy ribos sitting there and the cells
+have to fix it up and we have DNA repair
+
+ align:start position:0%
+have to fix it up and we have DNA repair
+ 
+
+ align:start position:0%
+have to fix it up and we have DNA repair
+systems that do that but another very
+
+ align:start position:0%
+systems that do that but another very
+ 
+
+ align:start position:0%
+systems that do that but another very
+common kind of of thing that that
+
+ align:start position:0%
+common kind of of thing that that
+ 
+
+ align:start position:0%
+common kind of of thing that that
+happens is that uh this nh2 group
+
+ align:start position:0%
+happens is that uh this nh2 group
+ 
+
+ align:start position:0%
+happens is that uh this nh2 group
+deaminates
+
+ align:start position:0%
+deaminates
+ 
+
+ align:start position:0%
+deaminates
+and if you do that if if a c happens to
+
+ align:start position:0%
+and if you do that if if a c happens to
+ 
+
+ align:start position:0%
+and if you do that if if a c happens to
+deaminate in DNA it gives you a
+
+ align:start position:0%
+deaminate in DNA it gives you a
+ 
+
+ align:start position:0%
+deaminate in DNA it gives you a
+uracil and if that ever happens the cell
+
+ align:start position:0%
+uracil and if that ever happens the cell
+ 
+
+ align:start position:0%
+uracil and if that ever happens the cell
+is actually able to tell that the uh
+
+ align:start position:0%
+is actually able to tell that the uh
+ 
+
+ align:start position:0%
+is actually able to tell that the uh
+that something went wrong because urell
+
+ align:start position:0%
+that something went wrong because urell
+ 
+
+ align:start position:0%
+that something went wrong because urell
+is not supposed to be in DNA and there
+
+ align:start position:0%
+is not supposed to be in DNA and there
+ 
+
+ align:start position:0%
+is not supposed to be in DNA and there
+are repair systems that constantly scan
+
+ align:start position:0%
+are repair systems that constantly scan
+ 
+
+ align:start position:0%
+are repair systems that constantly scan
+the DNA and take out take out any
+
+ align:start position:0%
+the DNA and take out take out any
+ 
+
+ align:start position:0%
+the DNA and take out take out any
+uracils that that are in
+
+ align:start position:0%
+uracils that that are in
+ 
+
+ align:start position:0%
+uracils that that are in
+there and the reason that if if uh it
+
+ align:start position:0%
+there and the reason that if if uh it
+ 
+
+ align:start position:0%
+there and the reason that if if uh it
+actually used thyine instead of using
+
+ align:start position:0%
+actually used thyine instead of using
+ 
+
+ align:start position:0%
+actually used thyine instead of using
+thyine it used uracil then the cell
+
+ align:start position:0%
+thyine it used uracil then the cell
+ 
+
+ align:start position:0%
+thyine it used uracil then the cell
+wouldn't know whether the osell got
+
+ align:start position:0%
+wouldn't know whether the osell got
+ 
+
+ align:start position:0%
+wouldn't know whether the osell got
+there because it was supposed to be
+
+ align:start position:0%
+there because it was supposed to be
+ 
+
+ align:start position:0%
+there because it was supposed to be
+there as part of the sequence or whether
+
+ align:start position:0%
+there as part of the sequence or whether
+ 
+
+ align:start position:0%
+there as part of the sequence or whether
+it had Arisen by uh deamination of a of
+
+ align:start position:0%
+it had Arisen by uh deamination of a of
+ 
+
+ align:start position:0%
+it had Arisen by uh deamination of a of
+a citadine it's a minor point but there
+
+ align:start position:0%
+a citadine it's a minor point but there
+ 
+
+ align:start position:0%
+a citadine it's a minor point but there
+is I think we do have an understanding
+
+ align:start position:0%
+is I think we do have an understanding
+ 
+
+ align:start position:0%
+is I think we do have an understanding
+as to why there's thyine in DNA and
+
+ align:start position:0%
+as to why there's thyine in DNA and
+ 
+
+ align:start position:0%
+as to why there's thyine in DNA and
+uracil in in RNA this isn't isn't such a
+
+ align:start position:0%
+uracil in in RNA this isn't isn't such a
+ 
+
+ align:start position:0%
+uracil in in RNA this isn't isn't such a
+worry in uh in
+
+ align:start position:0%
+worry in uh in
+ 
+
+ align:start position:0%
+worry in uh in
+RNA okay but anyway um so there's still
+
+ align:start position:0%
+RNA okay but anyway um so there's still
+ 
+
+ align:start position:0%
+RNA okay but anyway um so there's still
+a really big problem here though that
+
+ align:start position:0%
+a really big problem here though that
+ 
+
+ align:start position:0%
+a really big problem here though that
+that Watson and Crick and others were
+
+ align:start position:0%
+that Watson and Crick and others were
+ 
+
+ align:start position:0%
+that Watson and Crick and others were
+grappling with and it has to do as I say
+
+ align:start position:0%
+grappling with and it has to do as I say
+ 
+
+ align:start position:0%
+grappling with and it has to do as I say
+with this fact that the information up
+
+ align:start position:0%
+with this fact that the information up
+ 
+
+ align:start position:0%
+with this fact that the information up
+here is uh the first in DNA and RNA it's
+
+ align:start position:0%
+here is uh the first in DNA and RNA it's
+ 
+
+ align:start position:0%
+here is uh the first in DNA and RNA it's
+written as a sequence of uh of letters
+
+ align:start position:0%
+written as a sequence of uh of letters
+ 
+
+ align:start position:0%
+written as a sequence of uh of letters
+if you will chemical letters but there
+
+ align:start position:0%
+if you will chemical letters but there
+ 
+
+ align:start position:0%
+if you will chemical letters but there
+are only four letters in the DNA
+
+ align:start position:0%
+are only four letters in the DNA
+ 
+
+ align:start position:0%
+are only four letters in the DNA
+alphabet and essentially the same four
+
+ align:start position:0%
+alphabet and essentially the same four
+ 
+
+ align:start position:0%
+alphabet and essentially the same four
+letters in the RNA alphabet however the
+
+ align:start position:0%
+letters in the RNA alphabet however the
+ 
+
+ align:start position:0%
+letters in the RNA alphabet however the
+protein language has got a totally
+
+ align:start position:0%
+protein language has got a totally
+ 
+
+ align:start position:0%
+protein language has got a totally
+different alphabet so uh we it's somehow
+
+ align:start position:0%
+different alphabet so uh we it's somehow
+ 
+
+ align:start position:0%
+different alphabet so uh we it's somehow
+like sort of translating now from
+
+ align:start position:0%
+like sort of translating now from
+ 
+
+ align:start position:0%
+like sort of translating now from
+English to Japanese or something like
+
+ align:start position:0%
+English to Japanese or something like
+ 
+
+ align:start position:0%
+English to Japanese or something like
+that some really fundamental change had
+
+ align:start position:0%
+that some really fundamental change had
+ 
+
+ align:start position:0%
+that some really fundamental change had
+to happen because it was a real
+
+ align:start position:0%
+to happen because it was a real
+ 
+
+ align:start position:0%
+to happen because it was a real
+conversion from one kind of language to
+
+ align:start position:0%
+conversion from one kind of language to
+ 
+
+ align:start position:0%
+conversion from one kind of language to
+another and so this process is known as
+
+ align:start position:0%
+another and so this process is known as
+ 
+
+ align:start position:0%
+another and so this process is known as
+as translation that's going from
+
+ align:start position:0%
+as translation that's going from
+ 
+
+ align:start position:0%
+as translation that's going from
+information that's written using a
+
+ align:start position:0%
+information that's written using a
+ 
+
+ align:start position:0%
+information that's written using a
+four-letter nucleic acid uh alphabet to
+
+ align:start position:0%
+four-letter nucleic acid uh alphabet to
+ 
+
+ align:start position:0%
+four-letter nucleic acid uh alphabet to
+information that's written using a 20l
+
+ align:start position:0%
+information that's written using a 20l
+ 
+
+ align:start position:0%
+information that's written using a 20l
+uh amino acid alphabet and uh Crick on
+
+ align:start position:0%
+uh amino acid alphabet and uh Crick on
+ 
+
+ align:start position:0%
+uh amino acid alphabet and uh Crick on
+Purely theoretical grounds figured well
+
+ align:start position:0%
+Purely theoretical grounds figured well
+ 
+
+ align:start position:0%
+Purely theoretical grounds figured well
+if you're going from one language to
+
+ align:start position:0%
+if you're going from one language to
+ 
+
+ align:start position:0%
+if you're going from one language to
+another what do you need you need a
+
+ align:start position:0%
+another what do you need you need a
+ 
+
+ align:start position:0%
+another what do you need you need a
+translator and what's a translator a
+
+ align:start position:0%
+translator and what's a translator a
+ 
+
+ align:start position:0%
+translator and what's a translator a
+translator is someone who speaks both
+
+ align:start position:0%
+translator is someone who speaks both
+ 
+
+ align:start position:0%
+translator is someone who speaks both
+languages so his idea was that if there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was I'm going to just separate out let's
+
+ align:start position:0%
+was I'm going to just separate out let's
+ 
+
+ align:start position:0%
+was I'm going to just separate out let's
+say this is the messenger RNA and I just
+
+ align:start position:0%
+say this is the messenger RNA and I just
+ 
+
+ align:start position:0%
+say this is the messenger RNA and I just
+for for um Clarity here have spaced out
+
+ align:start position:0%
+for for um Clarity here have spaced out
+ 
+
+ align:start position:0%
+for for um Clarity here have spaced out
+the three-letter words so we can see
+
+ align:start position:0%
+the three-letter words so we can see
+ 
+
+ align:start position:0%
+the three-letter words so we can see
+them these would be three like g a c or
+
+ align:start position:0%
+them these would be three like g a c or
+ 
+
+ align:start position:0%
+them these would be three like g a c or
+something like that in the uh in the RNA
+
+ align:start position:0%
+something like that in the uh in the RNA
+ 
+
+ align:start position:0%
+something like that in the uh in the RNA
+that there would be some kind of
+
+ align:start position:0%
+that there would be some kind of
+ 
+
+ align:start position:0%
+that there would be some kind of
+translator and his idea was that it
+
+ align:start position:0%
+translator and his idea was that it
+ 
+
+ align:start position:0%
+translator and his idea was that it
+would be something that had a particular
+
+ align:start position:0%
+would be something that had a particular
+ 
+
+ align:start position:0%
+would be something that had a particular
+amino acid at one end and it had the
+
+ align:start position:0%
+amino acid at one end and it had the
+ 
+
+ align:start position:0%
+amino acid at one end and it had the
+complimentary nucleotides at the other
+
+ align:start position:0%
+complimentary nucleotides at the other
+ 
+
+ align:start position:0%
+complimentary nucleotides at the other
+end so it could if you will read the
+
+ align:start position:0%
+end so it could if you will read the
+ 
+
+ align:start position:0%
+end so it could if you will read the
+genetic code that was written in the in
+
+ align:start position:0%
+genetic code that was written in the in
+ 
+
+ align:start position:0%
+genetic code that was written in the in
+the r using the the nucleic acid uh
+
+ align:start position:0%
+the r using the the nucleic acid uh
+ 
+
+ align:start position:0%
+the r using the the nucleic acid uh
+alphabet but it would also be speaking
+
+ align:start position:0%
+alphabet but it would also be speaking
+ 
+
+ align:start position:0%
+alphabet but it would also be speaking
+the amino acid uh language got the idea
+
+ align:start position:0%
+the amino acid uh language got the idea
+ 
+
+ align:start position:0%
+the amino acid uh language got the idea
+so this is this the idea was that this
+
+ align:start position:0%
+so this is this the idea was that this
+ 
+
+ align:start position:0%
+so this is this the idea was that this
+would be he they used the words adapter
+
+ align:start position:0%
+would be he they used the words adapter
+ 
+
+ align:start position:0%
+would be he they used the words adapter
+or a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+translator so that was on basically
+
+ align:start position:0%
+translator so that was on basically
+ 
+
+ align:start position:0%
+translator so that was on basically
+theoretical grounds that if you had to
+
+ align:start position:0%
+theoretical grounds that if you had to
+ 
+
+ align:start position:0%
+theoretical grounds that if you had to
+go from a four-letter language to a
+
+ align:start position:0%
+go from a four-letter language to a
+ 
+
+ align:start position:0%
+go from a four-letter language to a
+20-letter language you needed some kind
+
+ align:start position:0%
+20-letter language you needed some kind
+ 
+
+ align:start position:0%
+20-letter language you needed some kind
+of translator or adapter now at that
+
+ align:start position:0%
+of translator or adapter now at that
+ 
+
+ align:start position:0%
+of translator or adapter now at that
+same time that these considerations are
+
+ align:start position:0%
+same time that these considerations are
+ 
+
+ align:start position:0%
+same time that these considerations are
+going on biochemist began to find a
+
+ align:start position:0%
+going on biochemist began to find a
+ 
+
+ align:start position:0%
+going on biochemist began to find a
+class of small uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rnas that had an amino
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attached and so there were entities that
+
+ align:start position:0%
+attached and so there were entities that
+ 
+
+ align:start position:0%
+attached and so there were entities that
+had just the sort of properties that
+
+ align:start position:0%
+had just the sort of properties that
+ 
+
+ align:start position:0%
+had just the sort of properties that
+that cricet envisioned you need from
+
+ align:start position:0%
+that cricet envisioned you need from
+ 
+
+ align:start position:0%
+that cricet envisioned you need from
+theoretical uh considerations these were
+
+ align:start position:0%
+theoretical uh considerations these were
+ 
+
+ align:start position:0%
+theoretical uh considerations these were
+given the name
+
+ align:start position:0%
+given the name
+ 
+
+ align:start position:0%
+given the name
+transfer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rnas or trnas as they're usually
+
+ align:start position:0%
+rnas or trnas as they're usually
+ 
+
+ align:start position:0%
+rnas or trnas as they're usually
+referred to uh now and I've told you
+
+ align:start position:0%
+referred to uh now and I've told you
+ 
+
+ align:start position:0%
+referred to uh now and I've told you
+that RNA a uh has since it's got nucleic
+
+ align:start position:0%
+that RNA a uh has since it's got nucleic
+ 
+
+ align:start position:0%
+that RNA a uh has since it's got nucleic
+acid bases if you have a single strand
+
+ align:start position:0%
+acid bases if you have a single strand
+ 
+
+ align:start position:0%
+acid bases if you have a single strand
+of of of uh either an RNA or a DNA and
+
+ align:start position:0%
+of of of uh either an RNA or a DNA and
+ 
+
+ align:start position:0%
+of of of uh either an RNA or a DNA and
+you don't have a complimentary double
+
+ align:start position:0%
+you don't have a complimentary double
+ 
+
+ align:start position:0%
+you don't have a complimentary double
+strand then if there are complimentary
+
+ align:start position:0%
+strand then if there are complimentary
+ 
+
+ align:start position:0%
+strand then if there are complimentary
+sequences they can come together and uh
+
+ align:start position:0%
+sequences they can come together and uh
+ 
+
+ align:start position:0%
+sequences they can come together and uh
+and pair just the same way that
+
+ align:start position:0%
+and pair just the same way that
+ 
+
+ align:start position:0%
+and pair just the same way that
+complimentary sequences can come
+
+ align:start position:0%
+complimentary sequences can come
+ 
+
+ align:start position:0%
+complimentary sequences can come
+together in in uh in DNA and in the case
+
+ align:start position:0%
+together in in uh in DNA and in the case
+ 
+
+ align:start position:0%
+together in in uh in DNA and in the case
+of trnas once we once the sequence of
+
+ align:start position:0%
+of trnas once we once the sequence of
+ 
+
+ align:start position:0%
+of trnas once we once the sequence of
+these were determined they um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops have to here we go um they would
+
+ align:start position:0%
+oops have to here we go um they would
+ 
+
+ align:start position:0%
+oops have to here we go um they would
+they Fold It Up in into a Cloverleaf
+
+ align:start position:0%
+they Fold It Up in into a Cloverleaf
+ 
+
+ align:start position:0%
+they Fold It Up in into a Cloverleaf
+shape and the amino acid is attached up
+
+ align:start position:0%
+shape and the amino acid is attached up
+ 
+
+ align:start position:0%
+shape and the amino acid is attached up
+at the three prime end of the chain up
+
+ align:start position:0%
+at the three prime end of the chain up
+ 
+
+ align:start position:0%
+at the three prime end of the chain up
+here what's known as the acceptor part
+
+ align:start position:0%
+here what's known as the acceptor part
+ 
+
+ align:start position:0%
+here what's known as the acceptor part
+of the molecule and down here is so
+
+ align:start position:0%
+of the molecule and down here is so
+ 
+
+ align:start position:0%
+of the molecule and down here is so
+that's that corresponds to this part up
+
+ align:start position:0%
+that's that corresponds to this part up
+ 
+
+ align:start position:0%
+that's that corresponds to this part up
+here and here are here is what's known
+
+ align:start position:0%
+here and here are here is what's known
+ 
+
+ align:start position:0%
+here and here are here is what's known
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+anticodon the each of these three-letter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words and nucleic acid language is G is
+
+ align:start position:0%
+words and nucleic acid language is G is
+ 
+
+ align:start position:0%
+words and nucleic acid language is G is
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+codon and so something that had a
+
+ align:start position:0%
+codon and so something that had a
+ 
+
+ align:start position:0%
+codon and so something that had a
+complementary sequence to a codon was
+
+ align:start position:0%
+complementary sequence to a codon was
+ 
+
+ align:start position:0%
+complementary sequence to a codon was
+called an anticodon so if it's um g g G
+
+ align:start position:0%
+called an anticodon so if it's um g g G
+ 
+
+ align:start position:0%
+called an anticodon so if it's um g g G
+is the codon then
+
+ align:start position:0%
+is the codon then
+ 
+
+ align:start position:0%
+is the codon then
+CCC would be the would be the uh
+
+ align:start position:0%
+CCC would be the would be the uh
+ 
+
+ align:start position:0%
+CCC would be the would be the uh
+anti-codon now this is just a schematic
+
+ align:start position:0%
+anti-codon now this is just a schematic
+ 
+
+ align:start position:0%
+anti-codon now this is just a schematic
+as you can see it shows where the um uh
+
+ align:start position:0%
+as you can see it shows where the um uh
+ 
+
+ align:start position:0%
+as you can see it shows where the um uh
+where the
+
+ align:start position:0%
+where the
+ 
+
+ align:start position:0%
+where the
+um uh hydrogen bonds are that form the
+
+ align:start position:0%
+um uh hydrogen bonds are that form the
+ 
+
+ align:start position:0%
+um uh hydrogen bonds are that form the
+stuff when the crystal structures were
+
+ align:start position:0%
+stuff when the crystal structures were
+ 
+
+ align:start position:0%
+stuff when the crystal structures were
+done first crystal structure of TRNA was
+
+ align:start position:0%
+done first crystal structure of TRNA was
+ 
+
+ align:start position:0%
+done first crystal structure of TRNA was
+actually done by Alex Rich who's in the
+
+ align:start position:0%
+actually done by Alex Rich who's in the
+ 
+
+ align:start position:0%
+actually done by Alex Rich who's in the
+biology department at MIT and he was in
+
+ align:start position:0%
+biology department at MIT and he was in
+ 
+
+ align:start position:0%
+biology department at MIT and he was in
+this picture I showed you talking to to
+
+ align:start position:0%
+this picture I showed you talking to to
+ 
+
+ align:start position:0%
+this picture I showed you talking to to
+Matt mes
+
+ align:start position:0%
+Matt mes
+ 
+
+ align:start position:0%
+Matt mes
+and we although we can't see this
+
+ align:start position:0%
+and we although we can't see this
+ 
+
+ align:start position:0%
+and we although we can't see this
+terribly well maybe you could hit the
+
+ align:start position:0%
+terribly well maybe you could hit the
+ 
+
+ align:start position:0%
+terribly well maybe you could hit the
+lights there um the crystal structure
+
+ align:start position:0%
+lights there um the crystal structure
+ 
+
+ align:start position:0%
+lights there um the crystal structure
+showed that that the the molecule had a
+
+ align:start position:0%
+showed that that the the molecule had a
+ 
+
+ align:start position:0%
+showed that that the the molecule had a
+didn't look like a clover leaf as in
+
+ align:start position:0%
+didn't look like a clover leaf as in
+ 
+
+ align:start position:0%
+didn't look like a clover leaf as in
+there it had more this shape and I'll
+
+ align:start position:0%
+there it had more this shape and I'll
+ 
+
+ align:start position:0%
+there it had more this shape and I'll
+show you this more clearly in this
+
+ align:start position:0%
+show you this more clearly in this
+ 
+
+ align:start position:0%
+show you this more clearly in this
+picture I showed you this little part of
+
+ align:start position:0%
+picture I showed you this little part of
+ 
+
+ align:start position:0%
+picture I showed you this little part of
+the of the thing when I was showing you
+
+ align:start position:0%
+the of the thing when I was showing you
+ 
+
+ align:start position:0%
+the of the thing when I was showing you
+how an RNA could form up could form
+
+ align:start position:0%
+how an RNA could form up could form
+ 
+
+ align:start position:0%
+how an RNA could form up could form
+where for example if you copy us the the
+
+ align:start position:0%
+where for example if you copy us the the
+ 
+
+ align:start position:0%
+where for example if you copy us the the
+gene encoding and TRNA and for example
+
+ align:start position:0%
+gene encoding and TRNA and for example
+ 
+
+ align:start position:0%
+gene encoding and TRNA and for example
+the the green SE sequence here in green
+
+ align:start position:0%
+the the green SE sequence here in green
+ 
+
+ align:start position:0%
+the the green SE sequence here in green
+is complimentary to the sequence here or
+
+ align:start position:0%
+is complimentary to the sequence here or
+ 
+
+ align:start position:0%
+is complimentary to the sequence here or
+the sequence here in in sort of blue or
+
+ align:start position:0%
+the sequence here in in sort of blue or
+ 
+
+ align:start position:0%
+the sequence here in in sort of blue or
+purple is complimentary to the sequence
+
+ align:start position:0%
+purple is complimentary to the sequence
+ 
+
+ align:start position:0%
+purple is complimentary to the sequence
+here that what can happen then if you
+
+ align:start position:0%
+here that what can happen then if you
+ 
+
+ align:start position:0%
+here that what can happen then if you
+allow a single strand uh RNA like this
+
+ align:start position:0%
+allow a single strand uh RNA like this
+ 
+
+ align:start position:0%
+allow a single strand uh RNA like this
+to fold up ther thermodynamically it
+
+ align:start position:0%
+to fold up ther thermodynamically it
+ 
+
+ align:start position:0%
+to fold up ther thermodynamically it
+will then go to the lower energy state
+
+ align:start position:0%
+will then go to the lower energy state
+ 
+
+ align:start position:0%
+will then go to the lower energy state
+which is involves being able to make
+
+ align:start position:0%
+which is involves being able to make
+ 
+
+ align:start position:0%
+which is involves being able to make
+these hydrogen bonds and I think you can
+
+ align:start position:0%
+these hydrogen bonds and I think you can
+ 
+
+ align:start position:0%
+these hydrogen bonds and I think you can
+sort of see the Clover Leaf here's one
+
+ align:start position:0%
+sort of see the Clover Leaf here's one
+ 
+
+ align:start position:0%
+sort of see the Clover Leaf here's one
+of the leaves the other's down here and
+
+ align:start position:0%
+of the leaves the other's down here and
+ 
+
+ align:start position:0%
+of the leaves the other's down here and
+the others it's a little bit distorted
+
+ align:start position:0%
+the others it's a little bit distorted
+ 
+
+ align:start position:0%
+the others it's a little bit distorted
+here and the reason is cuz I'm going to
+
+ align:start position:0%
+here and the reason is cuz I'm going to
+ 
+
+ align:start position:0%
+here and the reason is cuz I'm going to
+continue now to show you how this
+
+ align:start position:0%
+continue now to show you how this
+ 
+
+ align:start position:0%
+continue now to show you how this
+structure once you get to the Clover
+
+ align:start position:0%
+structure once you get to the Clover
+ 
+
+ align:start position:0%
+structure once you get to the Clover
+Leaf then it folds
+
+ align:start position:0%
+Leaf then it folds
+ 
+
+ align:start position:0%
+Leaf then it folds
+up to make other kinds of interactions
+
+ align:start position:0%
+up to make other kinds of interactions
+ 
+
+ align:start position:0%
+up to make other kinds of interactions
+and it takes that shape with the TR
+
+ align:start position:0%
+and it takes that shape with the TR
+ 
+
+ align:start position:0%
+and it takes that shape with the TR
+going on at this end and the anticodon
+
+ align:start position:0%
+going on at this end and the anticodon
+ 
+
+ align:start position:0%
+going on at this end and the anticodon
+being down here and what's happening now
+
+ align:start position:0%
+being down here and what's happening now
+ 
+
+ align:start position:0%
+being down here and what's happening now
+they've morphed on the Vandal surfaces
+
+ align:start position:0%
+they've morphed on the Vandal surfaces
+ 
+
+ align:start position:0%
+they've morphed on the Vandal surfaces
+so you can see what this would look like
+
+ align:start position:0%
+so you can see what this would look like
+ 
+
+ align:start position:0%
+so you can see what this would look like
+three-dimensional shape the TR the the
+
+ align:start position:0%
+three-dimensional shape the TR the the
+ 
+
+ align:start position:0%
+three-dimensional shape the TR the the
+amino acid would be attached at that end
+
+ align:start position:0%
+amino acid would be attached at that end
+ 
+
+ align:start position:0%
+amino acid would be attached at that end
+and there there is the anti-codon that
+
+ align:start position:0%
+and there there is the anti-codon that
+ 
+
+ align:start position:0%
+and there there is the anti-codon that
+would be able to recognize the codon in
+
+ align:start position:0%
+would be able to recognize the codon in
+ 
+
+ align:start position:0%
+would be able to recognize the codon in
+the in the RNA I mean it the physical
+
+ align:start position:0%
+the in the RNA I mean it the physical
+ 
+
+ align:start position:0%
+the in the RNA I mean it the physical
+reality is pretty close to this
+
+ align:start position:0%
+reality is pretty close to this
+ 
+
+ align:start position:0%
+reality is pretty close to this
+simple uh simple little depiction
+
+ align:start position:0%
+simple uh simple little depiction
+ 
+
+ align:start position:0%
+simple uh simple little depiction
+here okay so once this
+
+ align:start position:0%
+here okay so once this
+ 
+
+ align:start position:0%
+here okay so once this
+uh this uh basic Paradigm had been had
+
+ align:start position:0%
+uh this uh basic Paradigm had been had
+ 
+
+ align:start position:0%
+uh this uh basic Paradigm had been had
+been straightened
+
+ align:start position:0%
+been straightened
+ 
+
+ align:start position:0%
+been straightened
+out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gave rise then to this this idea then
+
+ align:start position:0%
+gave rise then to this this idea then
+ 
+
+ align:start position:0%
+gave rise then to this this idea then
+putting it all together that the
+
+ align:start position:0%
+putting it all together that the
+ 
+
+ align:start position:0%
+putting it all together that the
+information in DNA that a portion of it
+
+ align:start position:0%
+information in DNA that a portion of it
+ 
+
+ align:start position:0%
+information in DNA that a portion of it
+was would be copied into RNA and that
+
+ align:start position:0%
+was would be copied into RNA and that
+ 
+
+ align:start position:0%
+was would be copied into RNA and that
+would go out into the cytoplasm and then
+
+ align:start position:0%
+would go out into the cytoplasm and then
+ 
+
+ align:start position:0%
+would go out into the cytoplasm and then
+in the cytoplasm these translators the
+
+ align:start position:0%
+in the cytoplasm these translators the
+ 
+
+ align:start position:0%
+in the cytoplasm these translators the
+trnas would be able to decode the uh
+
+ align:start position:0%
+trnas would be able to decode the uh
+ 
+
+ align:start position:0%
+trnas would be able to decode the uh
+read the the nucleic acid information
+
+ align:start position:0%
+read the the nucleic acid information
+ 
+
+ align:start position:0%
+read the the nucleic acid information
+and use that to determine the linear
+
+ align:start position:0%
+and use that to determine the linear
+ 
+
+ align:start position:0%
+and use that to determine the linear
+order of amino acids
+
+ align:start position:0%
+order of amino acids
+ 
+
+ align:start position:0%
+order of amino acids
+uh in a protein uh Crick when he came up
+
+ align:start position:0%
+uh in a protein uh Crick when he came up
+ 
+
+ align:start position:0%
+uh in a protein uh Crick when he came up
+with this gave this the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term the central
+
+ align:start position:0%
+term the central
+ 
+
+ align:start position:0%
+term the central
+dogma and it's a word that still people
+
+ align:start position:0%
+dogma and it's a word that still people
+ 
+
+ align:start position:0%
+dogma and it's a word that still people
+still use this term to apply to this
+
+ align:start position:0%
+still use this term to apply to this
+ 
+
+ align:start position:0%
+still use this term to apply to this
+this idea of information flow going from
+
+ align:start position:0%
+this idea of information flow going from
+ 
+
+ align:start position:0%
+this idea of information flow going from
+DNA to RNA and protein is still used to
+
+ align:start position:0%
+DNA to RNA and protein is still used to
+ 
+
+ align:start position:0%
+DNA to RNA and protein is still used to
+this day there's actually a a sort of
+
+ align:start position:0%
+this day there's actually a a sort of
+ 
+
+ align:start position:0%
+this day there's actually a a sort of
+little twist to that because at the time
+
+ align:start position:0%
+little twist to that because at the time
+ 
+
+ align:start position:0%
+little twist to that because at the time
+that Crick proposed the term he actually
+
+ align:start position:0%
+that Crick proposed the term he actually
+ 
+
+ align:start position:0%
+that Crick proposed the term he actually
+thought the word dogma meant uh an idea
+
+ align:start position:0%
+thought the word dogma meant uh an idea
+ 
+
+ align:start position:0%
+thought the word dogma meant uh an idea
+for which there is not reasonable
+
+ align:start position:0%
+for which there is not reasonable
+ 
+
+ align:start position:0%
+for which there is not reasonable
+evidence but he was sort of amused years
+
+ align:start position:0%
+evidence but he was sort of amused years
+ 
+
+ align:start position:0%
+evidence but he was sort of amused years
+later to realize that a more reasonable
+
+ align:start position:0%
+later to realize that a more reasonable
+ 
+
+ align:start position:0%
+later to realize that a more reasonable
+definition of Dogma is sort of something
+
+ align:start position:0%
+definition of Dogma is sort of something
+ 
+
+ align:start position:0%
+definition of Dogma is sort of something
+that a True Believer cannot doubt and so
+
+ align:start position:0%
+that a True Believer cannot doubt and so
+ 
+
+ align:start position:0%
+that a True Believer cannot doubt and so
+he kind of
+
+ align:start position:0%
+he kind of
+ 
+
+ align:start position:0%
+he kind of
+accidentally made an assertion that he
+
+ align:start position:0%
+accidentally made an assertion that he
+ 
+
+ align:start position:0%
+accidentally made an assertion that he
+was right but fortunately he was right
+
+ align:start position:0%
+was right but fortunately he was right
+ 
+
+ align:start position:0%
+was right but fortunately he was right
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the next big job though in working in
+
+ align:start position:0%
+the next big job though in working in
+ 
+
+ align:start position:0%
+the next big job though in working in
+working this out was to crack the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code and it's fine to know that it's a
+
+ align:start position:0%
+code and it's fine to know that it's a
+ 
+
+ align:start position:0%
+code and it's fine to know that it's a
+three-letter code and it's fine to know
+
+ align:start position:0%
+three-letter code and it's fine to know
+ 
+
+ align:start position:0%
+three-letter code and it's fine to know
+it goes into RNA and and uh then the
+
+ align:start position:0%
+it goes into RNA and and uh then the
+ 
+
+ align:start position:0%
+it goes into RNA and and uh then the
+TRNA translated but if you can't can't
+
+ align:start position:0%
+TRNA translated but if you can't can't
+ 
+
+ align:start position:0%
+TRNA translated but if you can't can't
+if you can't crack the code then you
+
+ align:start position:0%
+if you can't crack the code then you
+ 
+
+ align:start position:0%
+if you can't crack the code then you
+have no idea what any of the
+
+ align:start position:0%
+have no idea what any of the
+ 
+
+ align:start position:0%
+have no idea what any of the
+information uh means it was sort of like
+
+ align:start position:0%
+information uh means it was sort of like
+ 
+
+ align:start position:0%
+information uh means it was sort of like
+before the Rosetta Stone when they could
+
+ align:start position:0%
+before the Rosetta Stone when they could
+ 
+
+ align:start position:0%
+before the Rosetta Stone when they could
+look at the higher hieroglyphics in the
+
+ align:start position:0%
+look at the higher hieroglyphics in the
+ 
+
+ align:start position:0%
+look at the higher hieroglyphics in the
+Egyptian tombs and they could see there
+
+ align:start position:0%
+Egyptian tombs and they could see there
+ 
+
+ align:start position:0%
+Egyptian tombs and they could see there
+was a lot of information and there were
+
+ align:start position:0%
+was a lot of information and there were
+ 
+
+ align:start position:0%
+was a lot of information and there were
+symbols and so on but they didn't know
+
+ align:start position:0%
+symbols and so on but they didn't know
+ 
+
+ align:start position:0%
+symbols and so on but they didn't know
+what it meant until finally they got
+
+ align:start position:0%
+what it meant until finally they got
+ 
+
+ align:start position:0%
+what it meant until finally they got
+something that allowed them to relate it
+
+ align:start position:0%
+something that allowed them to relate it
+ 
+
+ align:start position:0%
+something that allowed them to relate it
+to a language they didn't know and they
+
+ align:start position:0%
+to a language they didn't know and they
+ 
+
+ align:start position:0%
+to a language they didn't know and they
+were able to work out the principles so
+
+ align:start position:0%
+were able to work out the principles so
+ 
+
+ align:start position:0%
+were able to work out the principles so
+somehow uh scientists had then to crack
+
+ align:start position:0%
+somehow uh scientists had then to crack
+ 
+
+ align:start position:0%
+somehow uh scientists had then to crack
+the code and there were two
+
+ align:start position:0%
+the code and there were two
+ 
+
+ align:start position:0%
+the code and there were two
+um uh two scientists who played uh a
+
+ align:start position:0%
+um uh two scientists who played uh a
+ 
+
+ align:start position:0%
+um uh two scientists who played uh a
+really big role one was
+
+ align:start position:0%
+really big role one was
+ 
+
+ align:start position:0%
+really big role one was
+Marshall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nurenberg who was at NIH and it's in
+
+ align:start position:0%
+nurenberg who was at NIH and it's in
+ 
+
+ align:start position:0%
+nurenberg who was at NIH and it's in
+fact still at NIH and the other one was
+
+ align:start position:0%
+fact still at NIH and the other one was
+ 
+
+ align:start position:0%
+fact still at NIH and the other one was
+an MI scientist who's on the same floor
+
+ align:start position:0%
+an MI scientist who's on the same floor
+ 
+
+ align:start position:0%
+an MI scientist who's on the same floor
+as me and MIT Goen uh corana and they
+
+ align:start position:0%
+as me and MIT Goen uh corana and they
+ 
+
+ align:start position:0%
+as me and MIT Goen uh corana and they
+used two different approaches but
+
+ align:start position:0%
+used two different approaches but
+ 
+
+ align:start position:0%
+used two different approaches but
+between these two approaches the the
+
+ align:start position:0%
+between these two approaches the the
+ 
+
+ align:start position:0%
+between these two approaches the the
+genetic code was was cracked and what um
+
+ align:start position:0%
+genetic code was was cracked and what um
+ 
+
+ align:start position:0%
+genetic code was was cracked and what um
+nerenberg did
+
+ align:start position:0%
+nerenberg did
+ 
+
+ align:start position:0%
+nerenberg did
+was to take a protein
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+synthesizing extract that he knew needed
+
+ align:start position:0%
+synthesizing extract that he knew needed
+ 
+
+ align:start position:0%
+synthesizing extract that he knew needed
+RNA in order to work so that would
+
+ align:start position:0%
+RNA in order to work so that would
+ 
+
+ align:start position:0%
+RNA in order to work so that would
+wasn't a surprise at this point because
+
+ align:start position:0%
+wasn't a surprise at this point because
+ 
+
+ align:start position:0%
+wasn't a surprise at this point because
+people were thinking the RNA would be
+
+ align:start position:0%
+people were thinking the RNA would be
+ 
+
+ align:start position:0%
+people were thinking the RNA would be
+the message and what at that point the
+
+ align:start position:0%
+the message and what at that point the
+ 
+
+ align:start position:0%
+the message and what at that point the
+the ability to make uh synthesize uh
+
+ align:start position:0%
+the ability to make uh synthesize uh
+ 
+
+ align:start position:0%
+the ability to make uh synthesize uh
+nucleic acids was quite limited compared
+
+ align:start position:0%
+nucleic acids was quite limited compared
+ 
+
+ align:start position:0%
+nucleic acids was quite limited compared
+to what we do now and so there were
+
+ align:start position:0%
+to what we do now and so there were
+ 
+
+ align:start position:0%
+to what we do now and so there were
+different ways of making them uh
+
+ align:start position:0%
+different ways of making them uh
+ 
+
+ align:start position:0%
+different ways of making them uh
+sometimes you could do it enzymatically
+
+ align:start position:0%
+sometimes you could do it enzymatically
+ 
+
+ align:start position:0%
+sometimes you could do it enzymatically
+but what nernberg for example was able
+
+ align:start position:0%
+but what nernberg for example was able
+ 
+
+ align:start position:0%
+but what nernberg for example was able
+to make was polyu so this was an RNA
+
+ align:start position:0%
+to make was polyu so this was an RNA
+ 
+
+ align:start position:0%
+to make was polyu so this was an RNA
+that was just u u u u u u u u and then
+
+ align:start position:0%
+that was just u u u u u u u u and then
+ 
+
+ align:start position:0%
+that was just u u u u u u u u and then
+what he did was he set up 20 reactions
+
+ align:start position:0%
+what he did was he set up 20 reactions
+ 
+
+ align:start position:0%
+what he did was he set up 20 reactions
+and in every reaction he put some of
+
+ align:start position:0%
+and in every reaction he put some of
+ 
+
+ align:start position:0%
+and in every reaction he put some of
+this extract he put polyu and he put 19
+
+ align:start position:0%
+this extract he put polyu and he put 19
+ 
+
+ align:start position:0%
+this extract he put polyu and he put 19
+of the of the amino acids that were um
+
+ align:start position:0%
+of the of the amino acids that were um
+ 
+
+ align:start position:0%
+of the of the amino acids that were um
+unlabeled and then only one amino acid
+
+ align:start position:0%
+unlabeled and then only one amino acid
+ 
+
+ align:start position:0%
+unlabeled and then only one amino acid
+that had radio label in it so he ran
+
+ align:start position:0%
+that had radio label in it so he ran
+ 
+
+ align:start position:0%
+that had radio label in it so he ran
+these 20 reactions and he waited to see
+
+ align:start position:0%
+these 20 reactions and he waited to see
+ 
+
+ align:start position:0%
+these 20 reactions and he waited to see
+could he get any in any of these did he
+
+ align:start position:0%
+could he get any in any of these did he
+ 
+
+ align:start position:0%
+could he get any in any of these did he
+get uh protein made that would have been
+
+ align:start position:0%
+get uh protein made that would have been
+ 
+
+ align:start position:0%
+get uh protein made that would have been
+Co by the polyu and what he ended up
+
+ align:start position:0%
+Co by the polyu and what he ended up
+ 
+
+ align:start position:0%
+Co by the polyu and what he ended up
+with was polyphenol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alanine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which you may recall when we were
+
+ align:start position:0%
+which you may recall when we were
+ 
+
+ align:start position:0%
+which you may recall when we were
+talking
+
+ align:start position:0%
+talking
+ 
+
+ align:start position:0%
+talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+structures of amino acids there's the
+
+ align:start position:0%
+structures of amino acids there's the
+ 
+
+ align:start position:0%
+structures of amino acids there's the
+basic backbone and
+
+ align:start position:0%
+basic backbone and
+ 
+
+ align:start position:0%
+basic backbone and
+the polyphenol is the one that has if
+
+ align:start position:0%
+the polyphenol is the one that has if
+ 
+
+ align:start position:0%
+the polyphenol is the one that has if
+you will a Benzene ring hanging off off
+
+ align:start position:0%
+you will a Benzene ring hanging off off
+ 
+
+ align:start position:0%
+you will a Benzene ring hanging off off
+the end and so what that meant was that
+
+ align:start position:0%
+the end and so what that meant was that
+ 
+
+ align:start position:0%
+the end and so what that meant was that
+uuu
+
+ align:start position:0%
+uuu
+ 
+
+ align:start position:0%
+uuu
+must
+
+ align:start position:0%
+must
+ 
+
+ align:start position:0%
+must
+code for fee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or pheny alanine and if it's
+
+ align:start position:0%
+or pheny alanine and if it's
+ 
+
+ align:start position:0%
+or pheny alanine and if it's
+uu in the RNA that must
+
+ align:start position:0%
+uu in the RNA that must
+ 
+
+ align:start position:0%
+uu in the RNA that must
+mean that the DNA that encodes
+
+ align:start position:0%
+mean that the DNA that encodes
+ 
+
+ align:start position:0%
+mean that the DNA that encodes
+this must
+
+ align:start position:0%
+this must
+ 
+
+ align:start position:0%
+this must
+have must have that sequence a AA and
+
+ align:start position:0%
+have must have that sequence a AA and
+ 
+
+ align:start position:0%
+have must have that sequence a AA and
+TTT and you can see that one of the two
+
+ align:start position:0%
+TTT and you can see that one of the two
+ 
+
+ align:start position:0%
+TTT and you can see that one of the two
+two strands of the DNA since T base pair
+
+ align:start position:0%
+two strands of the DNA since T base pair
+ 
+
+ align:start position:0%
+two strands of the DNA since T base pair
+is the same as urine one of the strands
+
+ align:start position:0%
+is the same as urine one of the strands
+ 
+
+ align:start position:0%
+is the same as urine one of the strands
+in the the DNA is going to have the same
+
+ align:start position:0%
+in the the DNA is going to have the same
+ 
+
+ align:start position:0%
+in the the DNA is going to have the same
+sequence as one of the strands in the in
+
+ align:start position:0%
+sequence as one of the strands in the in
+ 
+
+ align:start position:0%
+sequence as one of the strands in the in
+the RNA now I'll just tell you one brief
+
+ align:start position:0%
+the RNA now I'll just tell you one brief
+ 
+
+ align:start position:0%
+the RNA now I'll just tell you one brief
+little anecdote I heard uh Marshall
+
+ align:start position:0%
+little anecdote I heard uh Marshall
+ 
+
+ align:start position:0%
+little anecdote I heard uh Marshall
+nberg talk at this this uh meeting they
+
+ align:start position:0%
+nberg talk at this this uh meeting they
+ 
+
+ align:start position:0%
+nberg talk at this this uh meeting they
+had to celebrate the 50th anniversary of
+
+ align:start position:0%
+had to celebrate the 50th anniversary of
+ 
+
+ align:start position:0%
+had to celebrate the 50th anniversary of
+discovery of DNA and um he posed
+
+ align:start position:0%
+discovery of DNA and um he posed
+ 
+
+ align:start position:0%
+discovery of DNA and um he posed
+something that I never thought about in
+
+ align:start position:0%
+something that I never thought about in
+ 
+
+ align:start position:0%
+something that I never thought about in
+my years of teaching this but might
+
+ align:start position:0%
+my years of teaching this but might
+ 
+
+ align:start position:0%
+my years of teaching this but might
+occur to you guys if we put it up a
+
+ align:start position:0%
+occur to you guys if we put it up a
+ 
+
+ align:start position:0%
+occur to you guys if we put it up a
+problem Set uh you all know something
+
+ align:start position:0%
+problem Set uh you all know something
+ 
+
+ align:start position:0%
+problem Set uh you all know something
+that Benzene is nothing but sort of
+
+ align:start position:0%
+that Benzene is nothing but sort of
+ 
+
+ align:start position:0%
+that Benzene is nothing but sort of
+these uh this is I call even referred to
+
+ align:start position:0%
+these uh this is I call even referred to
+ 
+
+ align:start position:0%
+these uh this is I call even referred to
+it as a as a Benzene ring it's a very
+
+ align:start position:0%
+it as a as a Benzene ring it's a very
+ 
+
+ align:start position:0%
+it as a as a Benzene ring it's a very
+organic kind of solvent so if we put on
+
+ align:start position:0%
+organic kind of solvent so if we put on
+ 
+
+ align:start position:0%
+organic kind of solvent so if we put on
+a problem set if you made polyphenol
+
+ align:start position:0%
+a problem set if you made polyphenol
+ 
+
+ align:start position:0%
+a problem set if you made polyphenol
+alanine would you expect this to be
+
+ align:start position:0%
+alanine would you expect this to be
+ 
+
+ align:start position:0%
+alanine would you expect this to be
+soluble in
+
+ align:start position:0%
+soluble in
+ 
+
+ align:start position:0%
+soluble in
+water this is very very hydrophobic very
+
+ align:start position:0%
+water this is very very hydrophobic very
+ 
+
+ align:start position:0%
+water this is very very hydrophobic very
+very water hating and your answer would
+
+ align:start position:0%
+very water hating and your answer would
+ 
+
+ align:start position:0%
+very water hating and your answer would
+be correct if you said no I wouldn't
+
+ align:start position:0%
+be correct if you said no I wouldn't
+ 
+
+ align:start position:0%
+be correct if you said no I wouldn't
+expect polyphenol alanine to be soluble
+
+ align:start position:0%
+expect polyphenol alanine to be soluble
+ 
+
+ align:start position:0%
+expect polyphenol alanine to be soluble
+in water in fact if we were in a protein
+
+ align:start position:0%
+in water in fact if we were in a protein
+ 
+
+ align:start position:0%
+in water in fact if we were in a protein
+we would expect it to probably be in the
+
+ align:start position:0%
+we would expect it to probably be in the
+ 
+
+ align:start position:0%
+we would expect it to probably be in the
+core where all the hydrophobic
+
+ align:start position:0%
+core where all the hydrophobic
+ 
+
+ align:start position:0%
+core where all the hydrophobic
+interactions the water hating Parts
+
+ align:start position:0%
+interactions the water hating Parts
+ 
+
+ align:start position:0%
+interactions the water hating Parts
+would go so Marshall nberg said when in
+
+ align:start position:0%
+would go so Marshall nberg said when in
+ 
+
+ align:start position:0%
+would go so Marshall nberg said when in
+his talk well he had he showed that he
+
+ align:start position:0%
+his talk well he had he showed that he
+ 
+
+ align:start position:0%
+his talk well he had he showed that he
+had Radioactive fanine in he still had
+
+ align:start position:0%
+had Radioactive fanine in he still had
+ 
+
+ align:start position:0%
+had Radioactive fanine in he still had
+to prove chemically that he had
+
+ align:start position:0%
+to prove chemically that he had
+ 
+
+ align:start position:0%
+to prove chemically that he had
+polyphenol alanine but he wasn't much of
+
+ align:start position:0%
+polyphenol alanine but he wasn't much of
+ 
+
+ align:start position:0%
+polyphenol alanine but he wasn't much of
+a biochemist so he walked down to the
+
+ align:start position:0%
+a biochemist so he walked down to the
+ 
+
+ align:start position:0%
+a biochemist so he walked down to the
+lab just below him at NI at NIH and
+
+ align:start position:0%
+lab just below him at NI at NIH and
+ 
+
+ align:start position:0%
+lab just below him at NI at NIH and
+walked in the door and saw the first
+
+ align:start position:0%
+walked in the door and saw the first
+ 
+
+ align:start position:0%
+walked in the door and saw the first
+person he said saw and said how do you
+
+ align:start position:0%
+person he said saw and said how do you
+ 
+
+ align:start position:0%
+person he said saw and said how do you
+um uh how do you solubilize polyphenol
+
+ align:start position:0%
+um uh how do you solubilize polyphenol
+ 
+
+ align:start position:0%
+um uh how do you solubilize polyphenol
+alanine let's make sure I got this right
+
+ align:start position:0%
+alanine let's make sure I got this right
+ 
+
+ align:start position:0%
+alanine let's make sure I got this right
+and the guy said oh you just take 33%
+
+ align:start position:0%
+and the guy said oh you just take 33%
+ 
+
+ align:start position:0%
+and the guy said oh you just take 33%
+hydrobromic acid and glacial acetic acid
+
+ align:start position:0%
+hydrobromic acid and glacial acetic acid
+ 
+
+ align:start position:0%
+hydrobromic acid and glacial acetic acid
+and and it works so he went back
+
+ align:start position:0%
+and and it works so he went back
+ 
+
+ align:start position:0%
+and and it works so he went back
+upstairs and dissolved it turned out it
+
+ align:start position:0%
+upstairs and dissolved it turned out it
+ 
+
+ align:start position:0%
+upstairs and dissolved it turned out it
+it dissolved in that he went on to
+
+ align:start position:0%
+it dissolved in that he went on to
+ 
+
+ align:start position:0%
+it dissolved in that he went on to
+characterize it and he said it didn't
+
+ align:start position:0%
+characterize it and he said it didn't
+ 
+
+ align:start position:0%
+characterize it and he said it didn't
+occur to him or he didn't learn till
+
+ align:start position:0%
+occur to him or he didn't learn till
+ 
+
+ align:start position:0%
+occur to him or he didn't learn till
+about 15 or 20 years later that he just
+
+ align:start position:0%
+about 15 or 20 years later that he just
+ 
+
+ align:start position:0%
+about 15 or 20 years later that he just
+walked up to the only person in the
+
+ align:start position:0%
+walked up to the only person in the
+ 
+
+ align:start position:0%
+walked up to the only person in the
+world who knew how to solubilize
+
+ align:start position:0%
+world who knew how to solubilize
+ 
+
+ align:start position:0%
+world who knew how to solubilize
+polyphenol
+
+ align:start position:0%
+polyphenol
+ 
+
+ align:start position:0%
+polyphenol
+by total coincidence this guy who we
+
+ align:start position:0%
+by total coincidence this guy who we
+ 
+
+ align:start position:0%
+by total coincidence this guy who we
+talked to had been working away trying
+
+ align:start position:0%
+talked to had been working away trying
+ 
+
+ align:start position:0%
+talked to had been working away trying
+to figure out a way and had come with
+
+ align:start position:0%
+to figure out a way and had come with
+ 
+
+ align:start position:0%
+to figure out a way and had come with
+this odd mix of hydrobromic acid and in
+
+ align:start position:0%
+this odd mix of hydrobromic acid and in
+ 
+
+ align:start position:0%
+this odd mix of hydrobromic acid and in
+glacial AIC and he just inste of you
+
+ align:start position:0%
+glacial AIC and he just inste of you
+ 
+
+ align:start position:0%
+glacial AIC and he just inste of you
+know all the places in the world he
+
+ align:start position:0%
+know all the places in the world he
+ 
+
+ align:start position:0%
+know all the places in the world he
+walked up to the one person who knew and
+
+ align:start position:0%
+walked up to the one person who knew and
+ 
+
+ align:start position:0%
+walked up to the one person who knew and
+and got the answer so the other part of
+
+ align:start position:0%
+and got the answer so the other part of
+ 
+
+ align:start position:0%
+and got the answer so the other part of
+the story then involves uh Goin K who I
+
+ align:start position:0%
+the story then involves uh Goin K who I
+ 
+
+ align:start position:0%
+the story then involves uh Goin K who I
+mentioned when I telling you initially
+
+ align:start position:0%
+mentioned when I telling you initially
+ 
+
+ align:start position:0%
+mentioned when I telling you initially
+about the the Nobel laurates at um at at
+
+ align:start position:0%
+about the the Nobel laurates at um at at
+ 
+
+ align:start position:0%
+about the the Nobel laurates at um at at
+uh MIT and Goin is a brilliant organic
+
+ align:start position:0%
+uh MIT and Goin is a brilliant organic
+ 
+
+ align:start position:0%
+uh MIT and Goin is a brilliant organic
+chemist he synthesized DNA uh you know
+
+ align:start position:0%
+chemist he synthesized DNA uh you know
+ 
+
+ align:start position:0%
+chemist he synthesized DNA uh you know
+there was a point where a whole issue of
+
+ align:start position:0%
+there was a point where a whole issue of
+ 
+
+ align:start position:0%
+there was a point where a whole issue of
+a journal came out that was nothing but
+
+ align:start position:0%
+a journal came out that was nothing but
+ 
+
+ align:start position:0%
+a journal came out that was nothing but
+his Labs work on synthesizing uh DNA
+
+ align:start position:0%
+his Labs work on synthesizing uh DNA
+ 
+
+ align:start position:0%
+his Labs work on synthesizing uh DNA
+well he was good at nucleic acids and
+
+ align:start position:0%
+well he was good at nucleic acids and
+ 
+
+ align:start position:0%
+well he was good at nucleic acids and
+one of the strategies that they could
+
+ align:start position:0%
+one of the strategies that they could
+ 
+
+ align:start position:0%
+one of the strategies that they could
+use chemically was they would make
+
+ align:start position:0%
+use chemically was they would make
+ 
+
+ align:start position:0%
+use chemically was they would make
+something like a d nucleotide like ca
+
+ align:start position:0%
+something like a d nucleotide like ca
+ 
+
+ align:start position:0%
+something like a d nucleotide like ca
+and then they were able to polymerize
+
+ align:start position:0%
+and then they were able to polymerize
+ 
+
+ align:start position:0%
+and then they were able to polymerize
+that to make a piece of RNA so they
+
+ align:start position:0%
+that to make a piece of RNA so they
+ 
+
+ align:start position:0%
+that to make a piece of RNA so they
+could make an
+
+ align:start position:0%
+could make an
+ 
+
+ align:start position:0%
+could make an
+RNA that had the sequence C c a c a c a
+
+ align:start position:0%
+RNA that had the sequence C c a c a c a
+ 
+
+ align:start position:0%
+RNA that had the sequence C c a c a c a
+c a and so on and what you can see from
+
+ align:start position:0%
+c a and so on and what you can see from
+ 
+
+ align:start position:0%
+c a and so on and what you can see from
+that is that there
+
+ align:start position:0%
+that is that there
+ 
+
+ align:start position:0%
+that is that there
+are two different codons in that one is
+
+ align:start position:0%
+are two different codons in that one is
+ 
+
+ align:start position:0%
+are two different codons in that one is
+uh CAC and the other is ACA and the
+
+ align:start position:0%
+uh CAC and the other is ACA and the
+ 
+
+ align:start position:0%
+uh CAC and the other is ACA and the
+reason he made it was he was
+
+ align:start position:0%
+reason he made it was he was
+ 
+
+ align:start position:0%
+reason he made it was he was
+synthesizing it by
+
+ align:start position:0%
+synthesizing it by
+ 
+
+ align:start position:0%
+synthesizing it by
+polymerizing um nucleotides so in these
+
+ align:start position:0%
+polymerizing um nucleotides so in these
+ 
+
+ align:start position:0%
+polymerizing um nucleotides so in these
+same kind of experiments there was
+
+ align:start position:0%
+same kind of experiments there was
+ 
+
+ align:start position:0%
+same kind of experiments there was
+describing before what they found this
+
+ align:start position:0%
+describing before what they found this
+ 
+
+ align:start position:0%
+describing before what they found this
+synthesized was alternating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+histadine and thine and it took you
+
+ align:start position:0%
+histadine and thine and it took you
+ 
+
+ align:start position:0%
+histadine and thine and it took you
+can't tell from that experiment alone
+
+ align:start position:0%
+can't tell from that experiment alone
+ 
+
+ align:start position:0%
+can't tell from that experiment alone
+one of those is must be U histadine and
+
+ align:start position:0%
+one of those is must be U histadine and
+ 
+
+ align:start position:0%
+one of those is must be U histadine and
+one of them must be thine but you can't
+
+ align:start position:0%
+one of them must be thine but you can't
+ 
+
+ align:start position:0%
+one of them must be thine but you can't
+tell from that experiment so more
+
+ align:start position:0%
+tell from that experiment so more
+ 
+
+ align:start position:0%
+tell from that experiment so more
+experiments were needed and what was
+
+ align:start position:0%
+experiments were needed and what was
+ 
+
+ align:start position:0%
+experiments were needed and what was
+learned from that experiment in that
+
+ align:start position:0%
+learned from that experiment in that
+ 
+
+ align:start position:0%
+learned from that experiment in that
+case was that CAC corresponded to
+
+ align:start position:0%
+case was that CAC corresponded to
+ 
+
+ align:start position:0%
+case was that CAC corresponded to
+histadine and ACA
+
+ align:start position:0%
+histadine and ACA
+ 
+
+ align:start position:0%
+histadine and ACA
+corresponded to to three andine so these
+
+ align:start position:0%
+corresponded to to three andine so these
+ 
+
+ align:start position:0%
+corresponded to to three andine so these
+kind of experiments were then uh put
+
+ align:start position:0%
+kind of experiments were then uh put
+ 
+
+ align:start position:0%
+kind of experiments were then uh put
+together to give what's known as the
+
+ align:start position:0%
+together to give what's known as the
+ 
+
+ align:start position:0%
+together to give what's known as the
+genetic code which is the three-letter
+
+ align:start position:0%
+genetic code which is the three-letter
+ 
+
+ align:start position:0%
+genetic code which is the three-letter
+words encoded in DNA that encode the
+
+ align:start position:0%
+words encoded in DNA that encode the
+ 
+
+ align:start position:0%
+words encoded in DNA that encode the
+sequence amino acids and proteins and
+
+ align:start position:0%
+sequence amino acids and proteins and
+ 
+
+ align:start position:0%
+sequence amino acids and proteins and
+there's it's usually displayed as a
+
+ align:start position:0%
+there's it's usually displayed as a
+ 
+
+ align:start position:0%
+there's it's usually displayed as a
+table and you read it in this way that
+
+ align:start position:0%
+table and you read it in this way that
+ 
+
+ align:start position:0%
+table and you read it in this way that
+this is the this thing over here is the
+
+ align:start position:0%
+this is the this thing over here is the
+ 
+
+ align:start position:0%
+this is the this thing over here is the
+first base in the codon across the top
+
+ align:start position:0%
+first base in the codon across the top
+ 
+
+ align:start position:0%
+first base in the codon across the top
+is the second base in the codon and down
+
+ align:start position:0%
+is the second base in the codon and down
+ 
+
+ align:start position:0%
+is the second base in the codon and down
+over here is the third base so if we go
+
+ align:start position:0%
+over here is the third base so if we go
+ 
+
+ align:start position:0%
+over here is the third base so if we go
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um uh c as the first say the one for
+
+ align:start position:0%
+um uh c as the first say the one for
+ 
+
+ align:start position:0%
+um uh c as the first say the one for
+histadine we're just showing you C is
+
+ align:start position:0%
+histadine we're just showing you C is
+ 
+
+ align:start position:0%
+histadine we're just showing you C is
+the first letter a is the second letter
+
+ align:start position:0%
+the first letter a is the second letter
+ 
+
+ align:start position:0%
+the first letter a is the second letter
+so this is the box that's going to we're
+
+ align:start position:0%
+so this is the box that's going to we're
+ 
+
+ align:start position:0%
+so this is the box that's going to we're
+going to be looking at and if C is the
+
+ align:start position:0%
+going to be looking at and if C is the
+ 
+
+ align:start position:0%
+going to be looking at and if C is the
+third letter we can see it encodes
+
+ align:start position:0%
+third letter we can see it encodes
+ 
+
+ align:start position:0%
+third letter we can see it encodes
+histadine or a c come back to
+
+ align:start position:0%
+histadine or a c come back to
+ 
+
+ align:start position:0%
+histadine or a c come back to
+a uh then uh the a is certainly three
+
+ align:start position:0%
+a uh then uh the a is certainly three
+ 
+
+ align:start position:0%
+a uh then uh the a is certainly three
+but you can also see something else here
+
+ align:start position:0%
+but you can also see something else here
+ 
+
+ align:start position:0%
+but you can also see something else here
+and that is because there were 6 four
+
+ align:start position:0%
+and that is because there were 6 four
+ 
+
+ align:start position:0%
+and that is because there were 6 four
+possibilities uh with this three-letter
+
+ align:start position:0%
+possibilities uh with this three-letter
+ 
+
+ align:start position:0%
+possibilities uh with this three-letter
+word the code is what's known as
+
+ align:start position:0%
+word the code is what's known as
+ 
+
+ align:start position:0%
+word the code is what's known as
+degenerate that is there you there are
+
+ align:start position:0%
+degenerate that is there you there are
+ 
+
+ align:start position:0%
+degenerate that is there you there are
+more words in the in the uh genetic code
+
+ align:start position:0%
+more words in the in the uh genetic code
+ 
+
+ align:start position:0%
+more words in the in the uh genetic code
+than are needed to specify the
+
+ align:start position:0%
+than are needed to specify the
+ 
+
+ align:start position:0%
+than are needed to specify the
+um the number of amino acids that have
+
+ align:start position:0%
+um the number of amino acids that have
+ 
+
+ align:start position:0%
+um the number of amino acids that have
+to be coded so just want to make a
+
+ align:start position:0%
+to be coded so just want to make a
+ 
+
+ align:start position:0%
+to be coded so just want to make a
+couple of of points about this so the
+
+ align:start position:0%
+couple of of points about this so the
+ 
+
+ align:start position:0%
+couple of of points about this so the
+genetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's degenerate there are 61 codons that
+
+ align:start position:0%
+it's degenerate there are 61 codons that
+ 
+
+ align:start position:0%
+it's degenerate there are 61 codons that
+correspond
+
+ align:start position:0%
+correspond
+ 
+
+ align:start position:0%
+correspond
+to an amino acid and that means that
+
+ align:start position:0%
+to an amino acid and that means that
+ 
+
+ align:start position:0%
+to an amino acid and that means that
+some and think threein is a good example
+
+ align:start position:0%
+some and think threein is a good example
+ 
+
+ align:start position:0%
+some and think threein is a good example
+there's more than one word in the
+
+ align:start position:0%
+there's more than one word in the
+ 
+
+ align:start position:0%
+there's more than one word in the
+genetic code that means uh thine there
+
+ align:start position:0%
+genetic code that means uh thine there
+ 
+
+ align:start position:0%
+genetic code that means uh thine there
+were three codons for which there was no
+
+ align:start position:0%
+were three codons for which there was no
+ 
+
+ align:start position:0%
+were three codons for which there was no
+corresponding amino
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+and those mean stop and that would make
+
+ align:start position:0%
+and those mean stop and that would make
+ 
+
+ align:start position:0%
+and those mean stop and that would make
+sense because if you're reading down a
+
+ align:start position:0%
+sense because if you're reading down a
+ 
+
+ align:start position:0%
+sense because if you're reading down a
+nucleic acid piece of RNA at some point
+
+ align:start position:0%
+nucleic acid piece of RNA at some point
+ 
+
+ align:start position:0%
+nucleic acid piece of RNA at some point
+you'd have to end the protein and so
+
+ align:start position:0%
+you'd have to end the protein and so
+ 
+
+ align:start position:0%
+you'd have to end the protein and so
+there are actually three that are that
+
+ align:start position:0%
+there are actually three that are that
+ 
+
+ align:start position:0%
+there are actually three that are that
+are used for that
+
+ align:start position:0%
+are used for that
+ 
+
+ align:start position:0%
+are used for that
+purpose and know there's some small
+
+ align:start position:0%
+purpose and know there's some small
+ 
+
+ align:start position:0%
+purpose and know there's some small
+variation on this uh in in
+
+ align:start position:0%
+variation on this uh in in
+ 
+
+ align:start position:0%
+variation on this uh in in
+nature there's usually one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops one amino acid that's used for
+
+ align:start position:0%
+oops one amino acid that's used for
+ 
+
+ align:start position:0%
+oops one amino acid that's used for
+starting a protein and that's methine
+
+ align:start position:0%
+starting a protein and that's methine
+ 
+
+ align:start position:0%
+starting a protein and that's methine
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+a right there now some of this stuff
+
+ align:start position:0%
+a right there now some of this stuff
+ 
+
+ align:start position:0%
+a right there now some of this stuff
+probably sounds like it's been around
+
+ align:start position:0%
+probably sounds like it's been around
+ 
+
+ align:start position:0%
+probably sounds like it's been around
+forever and that's certainly true of
+
+ align:start position:0%
+forever and that's certainly true of
+ 
+
+ align:start position:0%
+forever and that's certainly true of
+some of the stuff you hear in in um in
+
+ align:start position:0%
+some of the stuff you hear in in um in
+ 
+
+ align:start position:0%
+some of the stuff you hear in in um in
+your chemistry and math physics courses
+
+ align:start position:0%
+your chemistry and math physics courses
+ 
+
+ align:start position:0%
+your chemistry and math physics courses
+just want to drive you home when I was
+
+ align:start position:0%
+just want to drive you home when I was
+ 
+
+ align:start position:0%
+just want to drive you home when I was
+in undergrad Watson's first book called
+
+ align:start position:0%
+in undergrad Watson's first book called
+ 
+
+ align:start position:0%
+in undergrad Watson's first book called
+the molecular biology of the Gene and
+
+ align:start position:0%
+the molecular biology of the Gene and
+ 
+
+ align:start position:0%
+the molecular biology of the Gene and
+come out so I was when I was your age
+
+ align:start position:0%
+come out so I was when I was your age
+ 
+
+ align:start position:0%
+come out so I was when I was your age
+and I realized I look ancient but you
+
+ align:start position:0%
+and I realized I look ancient but you
+ 
+
+ align:start position:0%
+and I realized I look ancient but you
+know I'm still at least I'm still here
+
+ align:start position:0%
+know I'm still at least I'm still here
+ 
+
+ align:start position:0%
+know I'm still at least I'm still here
+um uh when I uh when I was an undergrad
+
+ align:start position:0%
+um uh when I uh when I was an undergrad
+ 
+
+ align:start position:0%
+um uh when I uh when I was an undergrad
+I had Watson's book this was the genetic
+
+ align:start position:0%
+I had Watson's book this was the genetic
+ 
+
+ align:start position:0%
+I had Watson's book this was the genetic
+code that was in the book the genetic
+
+ align:start position:0%
+code that was in the book the genetic
+ 
+
+ align:start position:0%
+code that was in the book the genetic
+code as of May 1965 and you'll notice
+
+ align:start position:0%
+code as of May 1965 and you'll notice
+ 
+
+ align:start position:0%
+code as of May 1965 and you'll notice
+there are a bunch of there gaps in here
+
+ align:start position:0%
+there are a bunch of there gaps in here
+ 
+
+ align:start position:0%
+there are a bunch of there gaps in here
+and all the things that are underlined
+
+ align:start position:0%
+and all the things that are underlined
+ 
+
+ align:start position:0%
+and all the things that are underlined
+were things that for which there was a
+
+ align:start position:0%
+were things that for which there was a
+ 
+
+ align:start position:0%
+were things that for which there was a
+tentative assignment so although you may
+
+ align:start position:0%
+tentative assignment so although you may
+ 
+
+ align:start position:0%
+tentative assignment so although you may
+take this think that it's been knowledge
+
+ align:start position:0%
+take this think that it's been knowledge
+ 
+
+ align:start position:0%
+take this think that it's been knowledge
+that's been around forever it was still
+
+ align:start position:0%
+that's been around forever it was still
+ 
+
+ align:start position:0%
+that's been around forever it was still
+you know was in wasn't even complete in
+
+ align:start position:0%
+you know was in wasn't even complete in
+ 
+
+ align:start position:0%
+you know was in wasn't even complete in
+the textbook when I was when I was an
+
+ align:start position:0%
+the textbook when I was when I was an
+ 
+
+ align:start position:0%
+the textbook when I was when I was an
+undergrad
+
+ align:start position:0%
+undergrad
+ 
+
+ align:start position:0%
+undergrad
+okay okay so one of the things then
+
+ align:start position:0%
+okay okay so one of the things then
+ 
+
+ align:start position:0%
+okay okay so one of the things then
+that's important to think about uh the
+
+ align:start position:0%
+that's important to think about uh the
+ 
+
+ align:start position:0%
+that's important to think about uh the
+nucleic acid stuff there's there's this
+
+ align:start position:0%
+nucleic acid stuff there's there's this
+ 
+
+ align:start position:0%
+nucleic acid stuff there's there's this
+is the basis of how U proteins are coded
+
+ align:start position:0%
+is the basis of how U proteins are coded
+ 
+
+ align:start position:0%
+is the basis of how U proteins are coded
+in the DNA but everything else has to be
+
+ align:start position:0%
+in the DNA but everything else has to be
+ 
+
+ align:start position:0%
+in the DNA but everything else has to be
+there too and the genetic
+
+ align:start position:0%
+there too and the genetic
+ 
+
+ align:start position:0%
+there too and the genetic
+code that's what we've been talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+universal but there are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+languages written in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DNA that are not
+
+ align:start position:0%
+DNA that are not
+ 
+
+ align:start position:0%
+DNA that are not
+Universal and one of them was that
+
+ align:start position:0%
+Universal and one of them was that
+ 
+
+ align:start position:0%
+Universal and one of them was that
+little example I gave you with an origin
+
+ align:start position:0%
+little example I gave you with an origin
+ 
+
+ align:start position:0%
+little example I gave you with an origin
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+replication eoli only starts DNA
+
+ align:start position:0%
+replication eoli only starts DNA
+ 
+
+ align:start position:0%
+replication eoli only starts DNA
+replication at one very particular point
+
+ align:start position:0%
+replication at one very particular point
+ 
+
+ align:start position:0%
+replication at one very particular point
+in its chromosome so it is a particular
+
+ align:start position:0%
+in its chromosome so it is a particular
+ 
+
+ align:start position:0%
+in its chromosome so it is a particular
+sequence of DNA it's actually about 250
+
+ align:start position:0%
+sequence of DNA it's actually about 250
+ 
+
+ align:start position:0%
+sequence of DNA it's actually about 250
+nucleotides long so you could think of
+
+ align:start position:0%
+nucleotides long so you could think of
+ 
+
+ align:start position:0%
+nucleotides long so you could think of
+that as a language it's a like starting
+
+ align:start position:0%
+that as a language it's a like starting
+ 
+
+ align:start position:0%
+that as a language it's a like starting
+DNA a chromosome replication language
+
+ align:start position:0%
+DNA a chromosome replication language
+ 
+
+ align:start position:0%
+DNA a chromosome replication language
+it's only got one word in it and the
+
+ align:start position:0%
+it's only got one word in it and the
+ 
+
+ align:start position:0%
+it's only got one word in it and the
+word is 250 nucleotides BL another place
+
+ align:start position:0%
+word is 250 nucleotides BL another place
+ 
+
+ align:start position:0%
+word is 250 nucleotides BL another place
+that's very important and that is if
+
+ align:start position:0%
+that's very important and that is if
+ 
+
+ align:start position:0%
+that's very important and that is if
+you're going to make an RNA copy if
+
+ align:start position:0%
+you're going to make an RNA copy if
+ 
+
+ align:start position:0%
+you're going to make an RNA copy if
+you're going to do
+
+ align:start position:0%
+you're going to do
+ 
+
+ align:start position:0%
+you're going to do
+transcription of a piece of
+
+ align:start position:0%
+transcription of a piece of
+ 
+
+ align:start position:0%
+transcription of a piece of
+DNA
+
+ align:start position:0%
+DNA
+ 
+
+ align:start position:0%
+DNA
+and this is the I'll call this the
+
+ align:start position:0%
+and this is the I'll call this the
+ 
+
+ align:start position:0%
+and this is the I'll call this the
+coding
+
+ align:start position:0%
+coding
+ 
+
+ align:start position:0%
+coding
+sequence this would be the sequence of
+
+ align:start position:0%
+sequence this would be the sequence of
+ 
+
+ align:start position:0%
+sequence this would be the sequence of
+three-letter words that would specify
+
+ align:start position:0%
+three-letter words that would specify
+ 
+
+ align:start position:0%
+three-letter words that would specify
+the amino acid of the of the protein if
+
+ align:start position:0%
+the amino acid of the of the protein if
+ 
+
+ align:start position:0%
+the amino acid of the of the protein if
+you were going to make an RNA copy of
+
+ align:start position:0%
+you were going to make an RNA copy of
+ 
+
+ align:start position:0%
+you were going to make an RNA copy of
+that you would have to somewhere have
+
+ align:start position:0%
+that you would have to somewhere have
+ 
+
+ align:start position:0%
+that you would have to somewhere have
+something here that's a sequence up here
+
+ align:start position:0%
+something here that's a sequence up here
+ 
+
+ align:start position:0%
+something here that's a sequence up here
+that means start
+
+ align:start position:0%
+that means start
+ 
+
+ align:start position:0%
+that means start
+transcription
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one at the end some other sequence
+
+ align:start position:0%
+and one at the end some other sequence
+ 
+
+ align:start position:0%
+and one at the end some other sequence
+of of uh letters in the nucleic acid
+
+ align:start position:0%
+of of uh letters in the nucleic acid
+ 
+
+ align:start position:0%
+of of uh letters in the nucleic acid
+that would mean stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transcription this is
+
+ align:start position:0%
+transcription this is
+ 
+
+ align:start position:0%
+transcription this is
+given the technical term it's referred
+
+ align:start position:0%
+given the technical term it's referred
+ 
+
+ align:start position:0%
+given the technical term it's referred
+to as a
+
+ align:start position:0%
+to as a
+ 
+
+ align:start position:0%
+to as a
+promoter the stop
+
+ align:start position:0%
+promoter the stop
+ 
+
+ align:start position:0%
+promoter the stop
+one is referred to as a as a
+
+ align:start position:0%
+one is referred to as a as a
+ 
+
+ align:start position:0%
+one is referred to as a as a
+terminator and these uh will say more
+
+ align:start position:0%
+terminator and these uh will say more
+ 
+
+ align:start position:0%
+terminator and these uh will say more
+about this cuz one of the thing the
+
+ align:start position:0%
+about this cuz one of the thing the
+ 
+
+ align:start position:0%
+about this cuz one of the thing the
+beauties of having this system of
+
+ align:start position:0%
+beauties of having this system of
+ 
+
+ align:start position:0%
+beauties of having this system of
+getting uh making an RNA copy is it
+
+ align:start position:0%
+getting uh making an RNA copy is it
+ 
+
+ align:start position:0%
+getting uh making an RNA copy is it
+provides a beautiful point of Regulation
+
+ align:start position:0%
+provides a beautiful point of Regulation
+ 
+
+ align:start position:0%
+provides a beautiful point of Regulation
+because the cell can determine whether
+
+ align:start position:0%
+because the cell can determine whether
+ 
+
+ align:start position:0%
+because the cell can determine whether
+or not it's going to make a particular
+
+ align:start position:0%
+or not it's going to make a particular
+ 
+
+ align:start position:0%
+or not it's going to make a particular
+protein by whether or not it chooses to
+
+ align:start position:0%
+protein by whether or not it chooses to
+ 
+
+ align:start position:0%
+protein by whether or not it chooses to
+make the um make make the protein or not
+
+ align:start position:0%
+make the um make make the protein or not
+ 
+
+ align:start position:0%
+make the um make make the protein or not
+and so U having this RNA intermediate
+
+ align:start position:0%
+and so U having this RNA intermediate
+ 
+
+ align:start position:0%
+and so U having this RNA intermediate
+and being able to control transcription
+
+ align:start position:0%
+and being able to control transcription
+ 
+
+ align:start position:0%
+and being able to control transcription
+is a really important part of the whole
+
+ align:start position:0%
+is a really important part of the whole
+ 
+
+ align:start position:0%
+is a really important part of the whole
+regulation that makes
+
+ align:start position:0%
+regulation that makes
+ 
+
+ align:start position:0%
+regulation that makes
+uh that makes life U possible the
+
+ align:start position:0%
+uh that makes life U possible the
+ 
+
+ align:start position:0%
+uh that makes life U possible the
+transcription is carried out by an
+
+ align:start position:0%
+transcription is carried out by an
+ 
+
+ align:start position:0%
+transcription is carried out by an
+enzyme that's known as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RNA polymerase and let me make one more
+
+ align:start position:0%
+RNA polymerase and let me make one more
+ 
+
+ align:start position:0%
+RNA polymerase and let me make one more
+point just I was
+
+ align:start position:0%
+point just I was
+ 
+
+ align:start position:0%
+point just I was
+this these promoters and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Terminators are not
+
+ align:start position:0%
+Terminators are not
+ 
+
+ align:start position:0%
+Terminators are not
+Universal so when we talk about
+
+ align:start position:0%
+Universal so when we talk about
+ 
+
+ align:start position:0%
+Universal so when we talk about
+recombinant D a little bit in the course
+
+ align:start position:0%
+recombinant D a little bit in the course
+ 
+
+ align:start position:0%
+recombinant D a little bit in the course
+if I take a mouse Gene and I put it in
+
+ align:start position:0%
+if I take a mouse Gene and I put it in
+ 
+
+ align:start position:0%
+if I take a mouse Gene and I put it in
+eoli even though the genetic code is the
+
+ align:start position:0%
+eoli even though the genetic code is the
+ 
+
+ align:start position:0%
+eoli even though the genetic code is the
+same we might have all the same sequence
+
+ align:start position:0%
+same we might have all the same sequence
+ 
+
+ align:start position:0%
+same we might have all the same sequence
+of amino acids specified you won't get
+
+ align:start position:0%
+of amino acids specified you won't get
+ 
+
+ align:start position:0%
+of amino acids specified you won't get
+the RNA made because the thing the
+
+ align:start position:0%
+the RNA made because the thing the
+ 
+
+ align:start position:0%
+the RNA made because the thing the
+sequences that say start transcription
+
+ align:start position:0%
+sequences that say start transcription
+ 
+
+ align:start position:0%
+sequences that say start transcription
+and stop transcription are different
+
+ align:start position:0%
+and stop transcription are different
+ 
+
+ align:start position:0%
+and stop transcription are different
+between a mouse and a bacterium even
+
+ align:start position:0%
+between a mouse and a bacterium even
+ 
+
+ align:start position:0%
+between a mouse and a bacterium even
+though the genetic code is the same so
+
+ align:start position:0%
+though the genetic code is the same so
+ 
+
+ align:start position:0%
+though the genetic code is the same so
+you can kind of see from first
+
+ align:start position:0%
+you can kind of see from first
+ 
+
+ align:start position:0%
+you can kind of see from first
+principles if you're doing recombinant
+
+ align:start position:0%
+principles if you're doing recombinant
+ 
+
+ align:start position:0%
+principles if you're doing recombinant
+DNA and you wanted to express the most
+
+ align:start position:0%
+DNA and you wanted to express the most
+ 
+
+ align:start position:0%
+DNA and you wanted to express the most
+protein in coli you would have to fiddle
+
+ align:start position:0%
+protein in coli you would have to fiddle
+ 
+
+ align:start position:0%
+protein in coli you would have to fiddle
+around with the sequences up here and
+
+ align:start position:0%
+around with the sequences up here and
+ 
+
+ align:start position:0%
+around with the sequences up here and
+the sequences down there the parts that
+
+ align:start position:0%
+the sequences down there the parts that
+ 
+
+ align:start position:0%
+the sequences down there the parts that
+are are not
+
+ align:start position:0%
+are are not
+ 
+
+ align:start position:0%
+are are not
+Universal guys with me okay so what what
+
+ align:start position:0%
+Universal guys with me okay so what what
+ 
+
+ align:start position:0%
+Universal guys with me okay so what what
+what does an RNA uh polymerase do it
+
+ align:start position:0%
+what does an RNA uh polymerase do it
+ 
+
+ align:start position:0%
+what does an RNA uh polymerase do it
+sort it recognizes this this sequence
+
+ align:start position:0%
+sort it recognizes this this sequence
+ 
+
+ align:start position:0%
+sort it recognizes this this sequence
+and then it teases the strands apart to
+
+ align:start position:0%
+and then it teases the strands apart to
+ 
+
+ align:start position:0%
+and then it teases the strands apart to
+make a little bubble like
+
+ align:start position:0%
+make a little bubble like
+ 
+
+ align:start position:0%
+make a little bubble like
+this so let's say a t a g c ta a so the
+
+ align:start position:0%
+this so let's say a t a g c ta a so the
+ 
+
+ align:start position:0%
+this so let's say a t a g c ta a so the
+other strand then would be t a t
+
+ align:start position:0%
+other strand then would be t a t
+ 
+
+ align:start position:0%
+other strand then would be t a t
+CG ta and then RNA plas
+
+ align:start position:0%
+CG ta and then RNA plas
+ 
+
+ align:start position:0%
+CG ta and then RNA plas
+unlike um a DNA plase can begin a chain
+
+ align:start position:0%
+unlike um a DNA plase can begin a chain
+ 
+
+ align:start position:0%
+unlike um a DNA plase can begin a chain
+denovo remember an important thing about
+
+ align:start position:0%
+denovo remember an important thing about
+ 
+
+ align:start position:0%
+denovo remember an important thing about
+DNA plases was they had to have a primer
+
+ align:start position:0%
+DNA plases was they had to have a primer
+ 
+
+ align:start position:0%
+DNA plases was they had to have a primer
+Terminus to get started that was why
+
+ align:start position:0%
+Terminus to get started that was why
+ 
+
+ align:start position:0%
+Terminus to get started that was why
+they had to use those okazaki fragments
+
+ align:start position:0%
+they had to use those okazaki fragments
+ 
+
+ align:start position:0%
+they had to use those okazaki fragments
+so this is DNA this would be five Prime
+
+ align:start position:0%
+so this is DNA this would be five Prime
+ 
+
+ align:start position:0%
+so this is DNA this would be five Prime
+three prime three prime and five Prime
+
+ align:start position:0%
+three prime three prime and five Prime
+ 
+
+ align:start position:0%
+three prime three prime and five Prime
+and it will what an RNA ply can do it
+
+ align:start position:0%
+and it will what an RNA ply can do it
+ 
+
+ align:start position:0%
+and it will what an RNA ply can do it
+uses D ATP D
+
+ align:start position:0%
+uses D ATP D
+ 
+
+ align:start position:0%
+uses D ATP D
+GTP
+
+ align:start position:0%
+GTP
+ 
+
+ align:start position:0%
+GTP
+dctp and the UTP it uses triphosphates
+
+ align:start position:0%
+dctp and the UTP it uses triphosphates
+ 
+
+ align:start position:0%
+dctp and the UTP it uses triphosphates
+excuse me not not get rid of the excuse
+
+ align:start position:0%
+excuse me not not get rid of the excuse
+ 
+
+ align:start position:0%
+excuse me not not get rid of the excuse
+me my mistake no no Deoxys here of
+
+ align:start position:0%
+me my mistake no no Deoxys here of
+ 
+
+ align:start position:0%
+me my mistake no no Deoxys here of
+course this is RNA uses ATP GTP CTP and
+
+ align:start position:0%
+course this is RNA uses ATP GTP CTP and
+ 
+
+ align:start position:0%
+course this is RNA uses ATP GTP CTP and
+uh and UTP as the substrates so it uses
+
+ align:start position:0%
+uh and UTP as the substrates so it uses
+ 
+
+ align:start position:0%
+uh and UTP as the substrates so it uses
+triphosphates just the same way DNA
+
+ align:start position:0%
+triphosphates just the same way DNA
+ 
+
+ align:start position:0%
+triphosphates just the same way DNA
+polymerases do and then it's able to
+
+ align:start position:0%
+polymerases do and then it's able to
+ 
+
+ align:start position:0%
+polymerases do and then it's able to
+start a chain d o and it
+
+ align:start position:0%
+start a chain d o and it
+ 
+
+ align:start position:0%
+start a chain d o and it
+synthesizes the
+
+ align:start position:0%
+synthesizes the
+ 
+
+ align:start position:0%
+synthesizes the
+RNA in a five Prime to three prime
+
+ align:start position:0%
+RNA in a five Prime to three prime
+ 
+
+ align:start position:0%
+RNA in a five Prime to three prime
+Direction the same direction that a
+
+ align:start position:0%
+Direction the same direction that a
+ 
+
+ align:start position:0%
+Direction the same direction that a
+strand of DNA is made by DNA polymerase
+
+ align:start position:0%
+strand of DNA is made by DNA polymerase
+ 
+
+ align:start position:0%
+strand of DNA is made by DNA polymerase
+so it would copy here and so it would
+
+ align:start position:0%
+so it would copy here and so it would
+ 
+
+ align:start position:0%
+so it would copy here and so it would
+put in an a opposite a t and then
+
+ align:start position:0%
+put in an a opposite a t and then
+ 
+
+ align:start position:0%
+put in an a opposite a t and then
+because it's R A it will put in a u
+
+ align:start position:0%
+because it's R A it will put in a u
+ 
+
+ align:start position:0%
+because it's R A it will put in a u
+opposite an A and then an a g c a and u
+
+ align:start position:0%
+opposite an A and then an a g c a and u
+ 
+
+ align:start position:0%
+opposite an A and then an a g c a and u
+and so on so
+
+ align:start position:0%
+and so on so
+ 
+
+ align:start position:0%
+and so on so
+this right here is the
+
+ align:start position:0%
+this right here is the
+ 
+
+ align:start position:0%
+this right here is the
+beginning of the RNA that's being
+
+ align:start position:0%
+beginning of the RNA that's being
+ 
+
+ align:start position:0%
+beginning of the RNA that's being
+synthesized by the uh RNA
+
+ align:start position:0%
+synthesized by the uh RNA
+ 
+
+ align:start position:0%
+synthesized by the uh RNA
+polymerase this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strand it's known as the transcribed
+
+ align:start position:0%
+strand it's known as the transcribed
+ 
+
+ align:start position:0%
+strand it's known as the transcribed
+Strand and by default then that one is
+
+ align:start position:0%
+Strand and by default then that one is
+ 
+
+ align:start position:0%
+Strand and by default then that one is
+the non-transcribed Strand what you can
+
+ align:start position:0%
+the non-transcribed Strand what you can
+ 
+
+ align:start position:0%
+the non-transcribed Strand what you can
+see by doing this it's making in RNA the
+
+ align:start position:0%
+see by doing this it's making in RNA the
+ 
+
+ align:start position:0%
+see by doing this it's making in RNA the
+same sequences up here except that
+
+ align:start position:0%
+same sequences up here except that
+ 
+
+ align:start position:0%
+same sequences up here except that
+everywhere there's a there's no u in the
+
+ align:start position:0%
+everywhere there's a there's no u in the
+ 
+
+ align:start position:0%
+everywhere there's a there's no u in the
+in the uh
+
+ align:start position:0%
+in the uh
+ 
+
+ align:start position:0%
+in the uh
+DNA so the final thing then is how the
+
+ align:start position:0%
+DNA so the final thing then is how the
+ 
+
+ align:start position:0%
+DNA so the final thing then is how the
+how this information gets all put
+
+ align:start position:0%
+how this information gets all put
+ 
+
+ align:start position:0%
+how this information gets all put
+together to make
+
+ align:start position:0%
+together to make
+ 
+
+ align:start position:0%
+together to make
+proteins and protein synthesis is done
+
+ align:start position:0%
+proteins and protein synthesis is done
+ 
+
+ align:start position:0%
+proteins and protein synthesis is done
+by an amazing machine known as a
+
+ align:start position:0%
+by an amazing machine known as a
+ 
+
+ align:start position:0%
+by an amazing machine known as a
+ribosome it's made up of some
+
+ align:start position:0%
+ribosome it's made up of some
+ 
+
+ align:start position:0%
+ribosome it's made up of some
+special large
+
+ align:start position:0%
+special large
+ 
+
+ align:start position:0%
+special large
+rnas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called R
+
+ align:start position:0%
+called R
+ 
+
+ align:start position:0%
+called R
+rnas some proteins as well these are
+
+ align:start position:0%
+rnas some proteins as well these are
+ 
+
+ align:start position:0%
+rnas some proteins as well these are
+make up the ribosome and then it needs a
+
+ align:start position:0%
+make up the ribosome and then it needs a
+ 
+
+ align:start position:0%
+make up the ribosome and then it needs a
+messenger
+
+ align:start position:0%
+messenger
+ 
+
+ align:start position:0%
+messenger
+RNA uh and it needs the
+
+ align:start position:0%
+RNA uh and it needs the
+ 
+
+ align:start position:0%
+RNA uh and it needs the
+various trnas Each of which carries uh
+
+ align:start position:0%
+various trnas Each of which carries uh
+ 
+
+ align:start position:0%
+various trnas Each of which carries uh
+an amino acid that's appropriate to its
+
+ align:start position:0%
+an amino acid that's appropriate to its
+ 
+
+ align:start position:0%
+an amino acid that's appropriate to its
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+anticodon and the in very briefly sort
+
+ align:start position:0%
+anticodon and the in very briefly sort
+ 
+
+ align:start position:0%
+anticodon and the in very briefly sort
+of the way this is and you can see this
+
+ align:start position:0%
+of the way this is and you can see this
+ 
+
+ align:start position:0%
+of the way this is and you can see this
+in in your
+
+ align:start position:0%
+in in your
+ 
+
+ align:start position:0%
+in in your
+textbook what the ribosome does is it
+
+ align:start position:0%
+textbook what the ribosome does is it
+ 
+
+ align:start position:0%
+textbook what the ribosome does is it
+takes it's sort of a let's consider this
+
+ align:start position:0%
+takes it's sort of a let's consider this
+ 
+
+ align:start position:0%
+takes it's sort of a let's consider this
+is the messenger RNA a I'm just going to
+
+ align:start position:0%
+is the messenger RNA a I'm just going to
+ 
+
+ align:start position:0%
+is the messenger RNA a I'm just going to
+take three codons
+
+ align:start position:0%
+take three codons
+ 
+
+ align:start position:0%
+take three codons
+here and this messenger and I threads
+
+ align:start position:0%
+here and this messenger and I threads
+ 
+
+ align:start position:0%
+here and this messenger and I threads
+into the the ribosome and I'll sort of
+
+ align:start position:0%
+into the the ribosome and I'll sort of
+ 
+
+ align:start position:0%
+into the the ribosome and I'll sort of
+show a kind of a it's able to recognize
+
+ align:start position:0%
+show a kind of a it's able to recognize
+ 
+
+ align:start position:0%
+show a kind of a it's able to recognize
+the first codon and the second codeon
+
+ align:start position:0%
+the first codon and the second codeon
+ 
+
+ align:start position:0%
+the first codon and the second codeon
+remember of course there's no spacing
+
+ align:start position:0%
+remember of course there's no spacing
+ 
+
+ align:start position:0%
+remember of course there's no spacing
+like this in the RNA and then in the
+
+ align:start position:0%
+like this in the RNA and then in the
+ 
+
+ align:start position:0%
+like this in the RNA and then in the
+context of this large uh Factory it's
+
+ align:start position:0%
+context of this large uh Factory it's
+ 
+
+ align:start position:0%
+context of this large uh Factory it's
+able to find the TRNA that has amino
+
+ align:start position:0%
+able to find the TRNA that has amino
+ 
+
+ align:start position:0%
+able to find the TRNA that has amino
+acid one and the the anticodon that
+
+ align:start position:0%
+acid one and the the anticodon that
+ 
+
+ align:start position:0%
+acid one and the the anticodon that
+would correspond to this the TR that has
+
+ align:start position:0%
+would correspond to this the TR that has
+ 
+
+ align:start position:0%
+would correspond to this the TR that has
+the next amino acid attached and its
+
+ align:start position:0%
+the next amino acid attached and its
+ 
+
+ align:start position:0%
+the next amino acid attached and its
+anticodon so you can see what's happened
+
+ align:start position:0%
+anticodon so you can see what's happened
+ 
+
+ align:start position:0%
+anticodon so you can see what's happened
+that it's been able to order the first
+
+ align:start position:0%
+that it's been able to order the first
+ 
+
+ align:start position:0%
+that it's been able to order the first
+amino acid coded by that codon and put
+
+ align:start position:0%
+amino acid coded by that codon and put
+ 
+
+ align:start position:0%
+amino acid coded by that codon and put
+it physically right next to the the um
+
+ align:start position:0%
+it physically right next to the the um
+ 
+
+ align:start position:0%
+it physically right next to the the um
+the next amino acid that's coded here
+
+ align:start position:0%
+the next amino acid that's coded here
+ 
+
+ align:start position:0%
+the next amino acid that's coded here
+and then it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+catalyzes the formation of a peptide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bond what happens when that does is the
+
+ align:start position:0%
+bond what happens when that does is the
+ 
+
+ align:start position:0%
+bond what happens when that does is the
+way this amino acid is joined to the
+
+ align:start position:0%
+way this amino acid is joined to the
+ 
+
+ align:start position:0%
+way this amino acid is joined to the
+TRNA there's energy energ stored in that
+
+ align:start position:0%
+TRNA there's energy energ stored in that
+ 
+
+ align:start position:0%
+TRNA there's energy energ stored in that
+Bond and so thermodynamically that was
+
+ align:start position:0%
+Bond and so thermodynamically that was
+ 
+
+ align:start position:0%
+Bond and so thermodynamically that was
+that allows this Bond formation to go
+
+ align:start position:0%
+that allows this Bond formation to go
+ 
+
+ align:start position:0%
+that allows this Bond formation to go
+and now you end up essentially with this
+
+ align:start position:0%
+and now you end up essentially with this
+ 
+
+ align:start position:0%
+and now you end up essentially with this
+and what happens now is everything
+
+ align:start position:0%
+and what happens now is everything
+ 
+
+ align:start position:0%
+and what happens now is everything
+clicks over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so you could think of it as this
+
+ align:start position:0%
+one so you could think of it as this
+ 
+
+ align:start position:0%
+one so you could think of it as this
+this whole RNA shifts over one so the
+
+ align:start position:0%
+this whole RNA shifts over one so the
+ 
+
+ align:start position:0%
+this whole RNA shifts over one so the
+the one that used to be here is now
+
+ align:start position:0%
+the one that used to be here is now
+ 
+
+ align:start position:0%
+the one that used to be here is now
+sticking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outside here's part of the
+
+ align:start position:0%
+outside here's part of the
+ 
+
+ align:start position:0%
+outside here's part of the
+ribosome here's the next codon
+
+ align:start position:0%
+ribosome here's the next codon
+ 
+
+ align:start position:0%
+ribosome here's the next codon
+this what we have here is the TRNA it's
+
+ align:start position:0%
+this what we have here is the TRNA it's
+ 
+
+ align:start position:0%
+this what we have here is the TRNA it's
+got amino acid 2 joined to amino acid
+
+ align:start position:0%
+got amino acid 2 joined to amino acid
+ 
+
+ align:start position:0%
+got amino acid 2 joined to amino acid
+one the next codon specifies the next
+
+ align:start position:0%
+one the next codon specifies the next
+ 
+
+ align:start position:0%
+one the next codon specifies the next
+amino acid which is three and the and
+
+ align:start position:0%
+amino acid which is three and the and
+ 
+
+ align:start position:0%
+amino acid which is three and the and
+the process is then able to to go on
+
+ align:start position:0%
+the process is then able to to go on
+ 
+
+ align:start position:0%
+the process is then able to to go on
+like that now the r the structure of the
+
+ align:start position:0%
+like that now the r the structure of the
+ 
+
+ align:start position:0%
+like that now the r the structure of the
+ribosome the crystal structure of the
+
+ align:start position:0%
+ribosome the crystal structure of the
+ 
+
+ align:start position:0%
+ribosome the crystal structure of the
+ribosome was just finished and I guess
+
+ align:start position:0%
+ribosome was just finished and I guess
+ 
+
+ align:start position:0%
+ribosome was just finished and I guess
+we've got as many lights out as we can
+
+ align:start position:0%
+we've got as many lights out as we can
+ 
+
+ align:start position:0%
+we've got as many lights out as we can
+do right now um it's absolutely
+
+ align:start position:0%
+do right now um it's absolutely
+ 
+
+ align:start position:0%
+do right now um it's absolutely
+remarkable it's mostly
+
+ align:start position:0%
+remarkable it's mostly
+ 
+
+ align:start position:0%
+remarkable it's mostly
+RNA uh this is the gray stuff and the
+
+ align:start position:0%
+RNA uh this is the gray stuff and the
+ 
+
+ align:start position:0%
+RNA uh this is the gray stuff and the
+blue stuff are two huge rnas that are
+
+ align:start position:0%
+blue stuff are two huge rnas that are
+ 
+
+ align:start position:0%
+blue stuff are two huge rnas that are
+all folded up in three-dimensional space
+
+ align:start position:0%
+all folded up in three-dimensional space
+ 
+
+ align:start position:0%
+all folded up in three-dimensional space
+and these things that are sort of stuck
+
+ align:start position:0%
+and these things that are sort of stuck
+ 
+
+ align:start position:0%
+and these things that are sort of stuck
+on the outside these purple things here
+
+ align:start position:0%
+on the outside these purple things here
+ 
+
+ align:start position:0%
+on the outside these purple things here
+or the the dark blue things here that
+
+ align:start position:0%
+or the the dark blue things here that
+ 
+
+ align:start position:0%
+or the the dark blue things here that
+sort of look like cherries stuck on the
+
+ align:start position:0%
+sort of look like cherries stuck on the
+ 
+
+ align:start position:0%
+sort of look like cherries stuck on the
+outside of a cake those are proteins so
+
+ align:start position:0%
+outside of a cake those are proteins so
+ 
+
+ align:start position:0%
+outside of a cake those are proteins so
+most of this is RNA Big Balls of RNA
+
+ align:start position:0%
+most of this is RNA Big Balls of RNA
+ 
+
+ align:start position:0%
+most of this is RNA Big Balls of RNA
+with proteins kind of decor ating the
+
+ align:start position:0%
+with proteins kind of decor ating the
+ 
+
+ align:start position:0%
+with proteins kind of decor ating the
+outside the messenger RNA is a green
+
+ align:start position:0%
+outside the messenger RNA is a green
+ 
+
+ align:start position:0%
+outside the messenger RNA is a green
+thing that snakes through there's the
+
+ align:start position:0%
+thing that snakes through there's the
+ 
+
+ align:start position:0%
+thing that snakes through there's the
+messenger RNA see it's snaking through
+
+ align:start position:0%
+messenger RNA see it's snaking through
+ 
+
+ align:start position:0%
+messenger RNA see it's snaking through
+and maybe you can recognize in the
+
+ align:start position:0%
+and maybe you can recognize in the
+ 
+
+ align:start position:0%
+and maybe you can recognize in the
+middle this this TRNA uh there's an
+
+ align:start position:0%
+middle this this TRNA uh there's an
+ 
+
+ align:start position:0%
+middle this this TRNA uh there's an
+orange one and a yellow one those
+
+ align:start position:0%
+orange one and a yellow one those
+ 
+
+ align:start position:0%
+orange one and a yellow one those
+correspond to the t two TRNA I depicted
+
+ align:start position:0%
+correspond to the t two TRNA I depicted
+ 
+
+ align:start position:0%
+correspond to the t two TRNA I depicted
+here and I'm just going to see if I can
+
+ align:start position:0%
+here and I'm just going to see if I can
+ 
+
+ align:start position:0%
+here and I'm just going to see if I can
+stop this at a there's a there's a
+
+ align:start position:0%
+stop this at a there's a there's a
+ 
+
+ align:start position:0%
+stop this at a there's a there's a
+Viewpoint I'd like you to see uh when it
+
+ align:start position:0%
+Viewpoint I'd like you to see uh when it
+ 
+
+ align:start position:0%
+Viewpoint I'd like you to see uh when it
+comes around again here in just a sec
+
+ align:start position:0%
+comes around again here in just a sec
+ 
+
+ align:start position:0%
+comes around again here in just a sec
+I'll see if I can catch it there right
+
+ align:start position:0%
+I'll see if I can catch it there right
+ 
+
+ align:start position:0%
+I'll see if I can catch it there right
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+this is the here's one of the trnas in
+
+ align:start position:0%
+this is the here's one of the trnas in
+ 
+
+ align:start position:0%
+this is the here's one of the trnas in
+yellow and its end is right there and
+
+ align:start position:0%
+yellow and its end is right there and
+ 
+
+ align:start position:0%
+yellow and its end is right there and
+there's the other TRNA and its end is
+
+ align:start position:0%
+there's the other TRNA and its end is
+ 
+
+ align:start position:0%
+there's the other TRNA and its end is
+right there so this corresponds to the
+
+ align:start position:0%
+right there so this corresponds to the
+ 
+
+ align:start position:0%
+right there so this corresponds to the
+point at which there's going to be an
+
+ align:start position:0%
+point at which there's going to be an
+ 
+
+ align:start position:0%
+point at which there's going to be an
+amino acid formed and it's going to be
+
+ align:start position:0%
+amino acid formed and it's going to be
+ 
+
+ align:start position:0%
+amino acid formed and it's going to be
+catalyze something's going to catalyze
+
+ align:start position:0%
+catalyze something's going to catalyze
+ 
+
+ align:start position:0%
+catalyze something's going to catalyze
+the formation of that Bond well the next
+
+ align:start position:0%
+the formation of that Bond well the next
+ 
+
+ align:start position:0%
+the formation of that Bond well the next
+picture sort of shows uh what happens if
+
+ align:start position:0%
+picture sort of shows uh what happens if
+ 
+
+ align:start position:0%
+picture sort of shows uh what happens if
+you pull that apart and what you'll see
+
+ align:start position:0%
+you pull that apart and what you'll see
+ 
+
+ align:start position:0%
+you pull that apart and what you'll see
+is that here's the end of one end of the
+
+ align:start position:0%
+is that here's the end of one end of the
+ 
+
+ align:start position:0%
+is that here's the end of one end of the
+TRNA there's the other end and there's
+
+ align:start position:0%
+TRNA there's the other end and there's
+ 
+
+ align:start position:0%
+TRNA there's the other end and there's
+nothing near it except for
+
+ align:start position:0%
+nothing near it except for
+ 
+
+ align:start position:0%
+nothing near it except for
+RNA so RNA is actually
+
+ align:start position:0%
+RNA so RNA is actually
+ 
+
+ align:start position:0%
+RNA so RNA is actually
+catalyzing the formation of the peptide
+
+ align:start position:0%
+catalyzing the formation of the peptide
+ 
+
+ align:start position:0%
+catalyzing the formation of the peptide
+bond another way to say
+
+ align:start position:0%
+bond another way to say
+ 
+
+ align:start position:0%
+bond another way to say
+that would be that the
+
+ align:start position:0%
+that would be that the
+ 
+
+ align:start position:0%
+that would be that the
+ribosome which is the protein
+
+ align:start position:0%
+ribosome which is the protein
+ 
+
+ align:start position:0%
+ribosome which is the protein
+synthesizing the factory is
+
+ align:start position:0%
+synthesizing the factory is
+ 
+
+ align:start position:0%
+synthesizing the factory is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+ribos remember I said most of the
+
+ align:start position:0%
+ribos remember I said most of the
+ 
+
+ align:start position:0%
+ribos remember I said most of the
+chemical reactions that are that need
+
+ align:start position:0%
+chemical reactions that are that need
+ 
+
+ align:start position:0%
+chemical reactions that are that need
+catalysts are carried out out by
+
+ align:start position:0%
+catalysts are carried out out by
+ 
+
+ align:start position:0%
+catalysts are carried out out by
+proteins but there are a few that are
+
+ align:start position:0%
+proteins but there are a few that are
+ 
+
+ align:start position:0%
+proteins but there are a few that are
+carried out by by RNA where RNA is the
+
+ align:start position:0%
+carried out by by RNA where RNA is the
+ 
+
+ align:start position:0%
+carried out by by RNA where RNA is the
+Catalyst and
+
+ align:start position:0%
+Catalyst and
+ 
+
+ align:start position:0%
+Catalyst and
+remarkably the formation of the bond
+
+ align:start position:0%
+remarkably the formation of the bond
+ 
+
+ align:start position:0%
+remarkably the formation of the bond
+which is at the heart of protein which
+
+ align:start position:0%
+which is at the heart of protein which
+ 
+
+ align:start position:0%
+which is at the heart of protein which
+are so important for all life is
+
+ align:start position:0%
+are so important for all life is
+ 
+
+ align:start position:0%
+are so important for all life is
+character is is U catalyzed by protein
+
+ align:start position:0%
+character is is U catalyzed by protein
+ 
+
+ align:start position:0%
+character is is U catalyzed by protein
+if you look at what makes proteins what
+
+ align:start position:0%
+if you look at what makes proteins what
+ 
+
+ align:start position:0%
+if you look at what makes proteins what
+what do you see you see huge balls of
+
+ align:start position:0%
+what do you see you see huge balls of
+ 
+
+ align:start position:0%
+what do you see you see huge balls of
+RNA a messenger in our RNA threading
+
+ align:start position:0%
+RNA a messenger in our RNA threading
+ 
+
+ align:start position:0%
+RNA a messenger in our RNA threading
+through two trnas and the enzyme
+
+ align:start position:0%
+through two trnas and the enzyme
+ 
+
+ align:start position:0%
+through two trnas and the enzyme
+activity or the catalytic activi is
+
+ align:start position:0%
+activity or the catalytic activi is
+ 
+
+ align:start position:0%
+activity or the catalytic activi is
+encoded by the RNA as well as I said
+
+ align:start position:0%
+encoded by the RNA as well as I said
+ 
+
+ align:start position:0%
+encoded by the RNA as well as I said
+people think possibly there was an RNA
+
+ align:start position:0%
+people think possibly there was an RNA
+ 
+
+ align:start position:0%
+people think possibly there was an RNA
+world that preceded our present day
+
+ align:start position:0%
+world that preceded our present day
+ 
+
+ align:start position:0%
+world that preceded our present day
+world with DNA RNA and protein and who
+
+ align:start position:0%
+world with DNA RNA and protein and who
+ 
+
+ align:start position:0%
+world with DNA RNA and protein and who
+knows but this sort of look at a
+
+ align:start position:0%
+knows but this sort of look at a
+ 
+
+ align:start position:0%
+knows but this sort of look at a
+ribosome could at least make you see
+
+ align:start position:0%
+ribosome could at least make you see
+ 
+
+ align:start position:0%
+ribosome could at least make you see
+that that's a plausible explanation that
+
+ align:start position:0%
+that that's a plausible explanation that
+ 
+
+ align:start position:0%
+that that's a plausible explanation that
+RNA might have been running the show for
+
+ align:start position:0%
+RNA might have been running the show for
+ 
+
+ align:start position:0%
+RNA might have been running the show for
+a while before anything else got
+
+ align:start position:0%
+a while before anything else got
+ 
+
+ align:start position:0%
+a while before anything else got
+involved anyway we'll see you on Friday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
\ No newline at end of file
diff --git a/49Ro2zf9hAc.txt b/49Ro2zf9hAc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2f7d340e1403cf0d61ec0bae6ef6147bb241d865
--- /dev/null
+++ b/49Ro2zf9hAc.txt
@@ -0,0 +1,10572 @@
+align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+last time we
+
+ align:start position:0%
+last time we
+ 
+
+ align:start position:0%
+last time we
+were talking about sequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i introduced the notion of a limit
+
+ align:start position:0%
+and i introduced the notion of a limit
+ 
+
+ align:start position:0%
+and i introduced the notion of a limit
+of a sequence um
+
+ align:start position:0%
+of a sequence um
+ 
+
+ align:start position:0%
+of a sequence um
+so we say that
+
+ align:start position:0%
+so we say that
+ 
+
+ align:start position:0%
+so we say that
+x n converges to x if for all epsilon
+
+ align:start position:0%
+x n converges to x if for all epsilon
+ 
+
+ align:start position:0%
+x n converges to x if for all epsilon
+positive there exists an m a natural
+
+ align:start position:0%
+positive there exists an m a natural
+ 
+
+ align:start position:0%
+positive there exists an m a natural
+number such that for all little n bigger
+
+ align:start position:0%
+number such that for all little n bigger
+ 
+
+ align:start position:0%
+number such that for all little n bigger
+than or equal to capital m we have x of
+
+ align:start position:0%
+than or equal to capital m we have x of
+ 
+
+ align:start position:0%
+than or equal to capital m we have x of
+n minus x is less than epsilon so what
+
+ align:start position:0%
+n minus x is less than epsilon so what
+ 
+
+ align:start position:0%
+n minus x is less than epsilon so what
+this definition says
+
+ align:start position:0%
+this definition says
+ 
+
+ align:start position:0%
+this definition says
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+given any little bit of tolerance as
+
+ align:start position:0%
+given any little bit of tolerance as
+ 
+
+ align:start position:0%
+given any little bit of tolerance as
+long as i go far enough out in the
+
+ align:start position:0%
+long as i go far enough out in the
+ 
+
+ align:start position:0%
+long as i go far enough out in the
+sequence the entries are getting within
+
+ align:start position:0%
+sequence the entries are getting within
+ 
+
+ align:start position:0%
+sequence the entries are getting within
+that tolerance to x okay and when we
+
+ align:start position:0%
+that tolerance to x okay and when we
+ 
+
+ align:start position:0%
+that tolerance to x okay and when we
+when x n converges to x we'll write x is
+
+ align:start position:0%
+when x n converges to x we'll write x is
+ 
+
+ align:start position:0%
+when x n converges to x we'll write x is
+equal to the limit as n goes to infinity
+
+ align:start position:0%
+equal to the limit as n goes to infinity
+ 
+
+ align:start position:0%
+equal to the limit as n goes to infinity
+of x sub n or
+
+ align:start position:0%
+of x sub n or
+ 
+
+ align:start position:0%
+of x sub n or
+using this notation x sub n
+
+ align:start position:0%
+using this notation x sub n
+ 
+
+ align:start position:0%
+using this notation x sub n
+arrow x
+
+ align:start position:0%
+arrow x
+ 
+
+ align:start position:0%
+arrow x
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so i've said before that if you ever
+
+ align:start position:0%
+and so i've said before that if you ever
+ 
+
+ align:start position:0%
+and so i've said before that if you ever
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+a reasonable
+
+ align:start position:0%
+a reasonable
+ 
+
+ align:start position:0%
+a reasonable
+reasonably complicated or interesting
+
+ align:start position:0%
+reasonably complicated or interesting
+ 
+
+ align:start position:0%
+reasonably complicated or interesting
+definition you should try to come up
+
+ align:start position:0%
+definition you should try to come up
+ 
+
+ align:start position:0%
+definition you should try to come up
+with examples
+
+ align:start position:0%
+with examples
+ 
+
+ align:start position:0%
+with examples
+and negate it so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the end of last time we saw a few
+
+ align:start position:0%
+the end of last time we saw a few
+ 
+
+ align:start position:0%
+the end of last time we saw a few
+examples of
+
+ align:start position:0%
+examples of
+ 
+
+ align:start position:0%
+examples of
+at least one example of a convergent
+
+ align:start position:0%
+at least one example of a convergent
+ 
+
+ align:start position:0%
+at least one example of a convergent
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+um let's negate this uh definition
+
+ align:start position:0%
+um let's negate this uh definition
+ 
+
+ align:start position:0%
+um let's negate this uh definition
+because then we'll also come up with an
+
+ align:start position:0%
+because then we'll also come up with an
+ 
+
+ align:start position:0%
+because then we'll also come up with an
+example of a sequence which does not
+
+ align:start position:0%
+example of a sequence which does not
+ 
+
+ align:start position:0%
+example of a sequence which does not
+converge
+
+ align:start position:0%
+converge
+ 
+
+ align:start position:0%
+converge
+and so the negation of this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition is that xn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does not converge to x what does this
+
+ align:start position:0%
+does not converge to x what does this
+ 
+
+ align:start position:0%
+does not converge to x what does this
+mean so this is the actual negation part
+
+ align:start position:0%
+mean so this is the actual negation part
+ 
+
+ align:start position:0%
+mean so this is the actual negation part
+if there exists
+
+ align:start position:0%
+if there exists
+ 
+
+ align:start position:0%
+if there exists
+an epsilon positive so whenever we
+
+ align:start position:0%
+an epsilon positive so whenever we
+ 
+
+ align:start position:0%
+an epsilon positive so whenever we
+negate a4 all it becomes there exists
+
+ align:start position:0%
+negate a4 all it becomes there exists
+ 
+
+ align:start position:0%
+negate a4 all it becomes there exists
+and whenever we negate there exists it
+
+ align:start position:0%
+and whenever we negate there exists it
+ 
+
+ align:start position:0%
+and whenever we negate there exists it
+becomes a for all
+
+ align:start position:0%
+becomes a for all
+ 
+
+ align:start position:0%
+becomes a for all
+so there exists some bad epsilon zero
+
+ align:start position:0%
+so there exists some bad epsilon zero
+ 
+
+ align:start position:0%
+so there exists some bad epsilon zero
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+natural numbers in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+in n bigger than or equal to m
+
+ align:start position:0%
+in n bigger than or equal to m
+ 
+
+ align:start position:0%
+in n bigger than or equal to m
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x n minus x is bigger than or equal to
+
+ align:start position:0%
+x n minus x is bigger than or equal to
+ 
+
+ align:start position:0%
+x n minus x is bigger than or equal to
+this bad
+
+ align:start position:0%
+this bad
+ 
+
+ align:start position:0%
+this bad
+epsilon naught and distance
+
+ align:start position:0%
+epsilon naught and distance
+ 
+
+ align:start position:0%
+epsilon naught and distance
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we have a picture that goes along
+
+ align:start position:0%
+so we have a picture that goes along
+ 
+
+ align:start position:0%
+so we have a picture that goes along
+with convergence we can have a picture
+
+ align:start position:0%
+with convergence we can have a picture
+ 
+
+ align:start position:0%
+with convergence we can have a picture
+that goes along with
+
+ align:start position:0%
+that goes along with
+ 
+
+ align:start position:0%
+that goes along with
+a sequence not converging to x so this
+
+ align:start position:0%
+a sequence not converging to x so this
+ 
+
+ align:start position:0%
+a sequence not converging to x so this
+means if i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go out within this bad epsilon knot
+
+ align:start position:0%
+go out within this bad epsilon knot
+ 
+
+ align:start position:0%
+go out within this bad epsilon knot
+and if i go
+
+ align:start position:0%
+and if i go
+ 
+
+ align:start position:0%
+and if i go
+arbitrarily out in the sequence i can
+
+ align:start position:0%
+arbitrarily out in the sequence i can
+ 
+
+ align:start position:0%
+arbitrarily out in the sequence i can
+always find an element x sub n which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not in that interval
+
+ align:start position:0%
+not in that interval
+ 
+
+ align:start position:0%
+not in that interval
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and we use this negation to prove a
+
+ align:start position:0%
+and we use this negation to prove a
+ 
+
+ align:start position:0%
+and we use this negation to prove a
+certain sequence does not converge to x
+
+ align:start position:0%
+certain sequence does not converge to x
+ 
+
+ align:start position:0%
+certain sequence does not converge to x
+but let's go back
+
+ align:start position:0%
+but let's go back
+ 
+
+ align:start position:0%
+but let's go back
+to another example of a sequence which
+
+ align:start position:0%
+to another example of a sequence which
+ 
+
+ align:start position:0%
+to another example of a sequence which
+does converge
+
+ align:start position:0%
+does converge
+ 
+
+ align:start position:0%
+does converge
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again how does the proof go you have to
+
+ align:start position:0%
+again how does the proof go you have to
+ 
+
+ align:start position:0%
+again how does the proof go you have to
+verify
+
+ align:start position:0%
+verify
+ 
+
+ align:start position:0%
+verify
+the definition of the limit i mean
+
+ align:start position:0%
+the definition of the limit i mean
+ 
+
+ align:start position:0%
+the definition of the limit i mean
+there's nothing else that we have to use
+
+ align:start position:0%
+there's nothing else that we have to use
+ 
+
+ align:start position:0%
+there's nothing else that we have to use
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+so let epsilon be positive
+
+ align:start position:0%
+so let epsilon be positive
+ 
+
+ align:start position:0%
+so let epsilon be positive
+and now off to the side over here i'm
+
+ align:start position:0%
+and now off to the side over here i'm
+ 
+
+ align:start position:0%
+and now off to the side over here i'm
+going to do a little bit of work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to show you how exactly
+
+ align:start position:0%
+to show you how exactly
+ 
+
+ align:start position:0%
+to show you how exactly
+in practice one would find such a
+
+ align:start position:0%
+in practice one would find such a
+ 
+
+ align:start position:0%
+in practice one would find such a
+capital m or choose a capital m to get
+
+ align:start position:0%
+capital m or choose a capital m to get
+ 
+
+ align:start position:0%
+capital m or choose a capital m to get
+that um 1 over n squared plus 30 n plus
+
+ align:start position:0%
+that um 1 over n squared plus 30 n plus
+ 
+
+ align:start position:0%
+that um 1 over n squared plus 30 n plus
+1 would be less than epsilon
+
+ align:start position:0%
+1 would be less than epsilon
+ 
+
+ align:start position:0%
+1 would be less than epsilon
+for n bigger than or equal to capital m
+
+ align:start position:0%
+for n bigger than or equal to capital m
+ 
+
+ align:start position:0%
+for n bigger than or equal to capital m
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+typically how this works is
+
+ align:start position:0%
+typically how this works is
+ 
+
+ align:start position:0%
+typically how this works is
+unlike in calculus where you have some
+
+ align:start position:0%
+unlike in calculus where you have some
+ 
+
+ align:start position:0%
+unlike in calculus where you have some
+inequality that you want to
+
+ align:start position:0%
+inequality that you want to
+ 
+
+ align:start position:0%
+inequality that you want to
+get and then you solve for n
+
+ align:start position:0%
+get and then you solve for n
+ 
+
+ align:start position:0%
+get and then you solve for n
+in analysis what's great is that you can
+
+ align:start position:0%
+in analysis what's great is that you can
+ 
+
+ align:start position:0%
+in analysis what's great is that you can
+replace that
+
+ align:start position:0%
+replace that
+ 
+
+ align:start position:0%
+replace that
+thing you want to make small by
+
+ align:start position:0%
+thing you want to make small by
+ 
+
+ align:start position:0%
+thing you want to make small by
+something simpler and then solve that
+
+ align:start position:0%
+something simpler and then solve that
+ 
+
+ align:start position:0%
+something simpler and then solve that
+inequality what do i mean so i want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do i want to do i want to find m
+
+ align:start position:0%
+what do i want to do i want to find m
+ 
+
+ align:start position:0%
+what do i want to do i want to find m
+so that if
+
+ align:start position:0%
+so that if
+ 
+
+ align:start position:0%
+so that if
+m is bigger than or equal to m then
+
+ align:start position:0%
+m is bigger than or equal to m then
+ 
+
+ align:start position:0%
+m is bigger than or equal to m then
+so i'm saying the limit is 0 so i want
+
+ align:start position:0%
+so i'm saying the limit is 0 so i want
+ 
+
+ align:start position:0%
+so i'm saying the limit is 0 so i want
+to show
+
+ align:start position:0%
+to show
+ 
+
+ align:start position:0%
+to show
+1 over n squared plus 30 n
+
+ align:start position:0%
+1 over n squared plus 30 n
+ 
+
+ align:start position:0%
+1 over n squared plus 30 n
+plus 1
+
+ align:start position:0%
+plus 1
+ 
+
+ align:start position:0%
+plus 1
+is less than epsilon okay
+
+ align:start position:0%
+is less than epsilon okay
+ 
+
+ align:start position:0%
+is less than epsilon okay
+now i could try to solve this inequality
+
+ align:start position:0%
+now i could try to solve this inequality
+ 
+
+ align:start position:0%
+now i could try to solve this inequality
+for n
+
+ align:start position:0%
+for n
+ 
+
+ align:start position:0%
+for n
+but this is a quadratic function and
+
+ align:start position:0%
+but this is a quadratic function and
+ 
+
+ align:start position:0%
+but this is a quadratic function and
+imagine i put a
+
+ align:start position:0%
+imagine i put a
+ 
+
+ align:start position:0%
+imagine i put a
+20 there
+
+ align:start position:0%
+20 there
+ 
+
+ align:start position:0%
+20 there
+so i can't exactly solve exactly for n
+
+ align:start position:0%
+so i can't exactly solve exactly for n
+ 
+
+ align:start position:0%
+so i can't exactly solve exactly for n
+uh to guarantee this
+
+ align:start position:0%
+uh to guarantee this
+ 
+
+ align:start position:0%
+uh to guarantee this
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+what's great about analysis is that i
+
+ align:start position:0%
+what's great about analysis is that i
+ 
+
+ align:start position:0%
+what's great about analysis is that i
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+i don't have to work
+
+ align:start position:0%
+i don't have to work
+ 
+
+ align:start position:0%
+i don't have to work
+that hard
+
+ align:start position:0%
+that hard
+ 
+
+ align:start position:0%
+that hard
+i could start with this thing which i
+
+ align:start position:0%
+i could start with this thing which i
+ 
+
+ align:start position:0%
+i could start with this thing which i
+want to bound by epsilon
+
+ align:start position:0%
+want to bound by epsilon
+ 
+
+ align:start position:0%
+want to bound by epsilon
+replace it by something bigger and then
+
+ align:start position:0%
+replace it by something bigger and then
+ 
+
+ align:start position:0%
+replace it by something bigger and then
+find capital m so that that bigger thing
+
+ align:start position:0%
+find capital m so that that bigger thing
+ 
+
+ align:start position:0%
+find capital m so that that bigger thing
+is less than epsilon so what do i mean
+
+ align:start position:0%
+is less than epsilon so what do i mean
+ 
+
+ align:start position:0%
+is less than epsilon so what do i mean
+so let's start with this thing one over
+
+ align:start position:0%
+so let's start with this thing one over
+ 
+
+ align:start position:0%
+so let's start with this thing one over
+n squared
+
+ align:start position:0%
+n squared
+ 
+
+ align:start position:0%
+n squared
+plus 30 n
+
+ align:start position:0%
+plus 30 n
+ 
+
+ align:start position:0%
+plus 30 n
+plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this one is only making things bigger
+
+ align:start position:0%
+so this one is only making things bigger
+ 
+
+ align:start position:0%
+so this one is only making things bigger
+i'm going to do this very slowly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is less than or equal to this
+
+ align:start position:0%
+this is less than or equal to this
+ 
+
+ align:start position:0%
+this is less than or equal to this
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+for this i've just added 1 to the
+
+ align:start position:0%
+for this i've just added 1 to the
+ 
+
+ align:start position:0%
+for this i've just added 1 to the
+denominator and 1 over n squared plus 30
+
+ align:start position:0%
+denominator and 1 over n squared plus 30
+ 
+
+ align:start position:0%
+denominator and 1 over n squared plus 30
+n this certainly looks a little bit
+
+ align:start position:0%
+n this certainly looks a little bit
+ 
+
+ align:start position:0%
+n this certainly looks a little bit
+simpler to solve for n less than epsilon
+
+ align:start position:0%
+simpler to solve for n less than epsilon
+ 
+
+ align:start position:0%
+simpler to solve for n less than epsilon
+but i can make it even simpler by
+
+ align:start position:0%
+but i can make it even simpler by
+ 
+
+ align:start position:0%
+but i can make it even simpler by
+dropping the n squared because n squared
+
+ align:start position:0%
+dropping the n squared because n squared
+ 
+
+ align:start position:0%
+dropping the n squared because n squared
+is positive so that's only making the
+
+ align:start position:0%
+is positive so that's only making the
+ 
+
+ align:start position:0%
+is positive so that's only making the
+bottom bigger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i have 1 over 30 n and this is
+
+ align:start position:0%
+okay so i have 1 over 30 n and this is
+ 
+
+ align:start position:0%
+okay so i have 1 over 30 n and this is
+certainly less than or equal to 1 over n
+
+ align:start position:0%
+certainly less than or equal to 1 over n
+ 
+
+ align:start position:0%
+certainly less than or equal to 1 over n
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+what does this
+
+ align:start position:0%
+what does this
+ 
+
+ align:start position:0%
+what does this
+computation show this shows that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if one over n is less than epsilon then
+
+ align:start position:0%
+if one over n is less than epsilon then
+ 
+
+ align:start position:0%
+if one over n is less than epsilon then
+this implies that
+
+ align:start position:0%
+this implies that
+ 
+
+ align:start position:0%
+this implies that
+one over n squared plus 30 n
+
+ align:start position:0%
+one over n squared plus 30 n
+ 
+
+ align:start position:0%
+one over n squared plus 30 n
+plus one is less than epsilon
+
+ align:start position:0%
+plus one is less than epsilon
+ 
+
+ align:start position:0%
+plus one is less than epsilon
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right if this thing is less than
+
+ align:start position:0%
+all right if this thing is less than
+ 
+
+ align:start position:0%
+all right if this thing is less than
+epsilon then by this string of
+
+ align:start position:0%
+epsilon then by this string of
+ 
+
+ align:start position:0%
+epsilon then by this string of
+inequalities this thing will be less
+
+ align:start position:0%
+inequalities this thing will be less
+ 
+
+ align:start position:0%
+inequalities this thing will be less
+than epsilon so we choose capital m
+
+ align:start position:0%
+than epsilon so we choose capital m
+ 
+
+ align:start position:0%
+than epsilon so we choose capital m
+so that we get this
+
+ align:start position:0%
+so that we get this
+ 
+
+ align:start position:0%
+so that we get this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now when we actually write the proof
+
+ align:start position:0%
+now when we actually write the proof
+ 
+
+ align:start position:0%
+now when we actually write the proof
+it'll look something like this but the
+
+ align:start position:0%
+it'll look something like this but the
+ 
+
+ align:start position:0%
+it'll look something like this but the
+you know actual style of the proof is is
+
+ align:start position:0%
+you know actual style of the proof is is
+ 
+
+ align:start position:0%
+you know actual style of the proof is is
+a little bit
+
+ align:start position:0%
+a little bit
+ 
+
+ align:start position:0%
+a little bit
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+and if you didn't see this it would just
+
+ align:start position:0%
+and if you didn't see this it would just
+ 
+
+ align:start position:0%
+and if you didn't see this it would just
+seem like i pulled this capital m out of
+
+ align:start position:0%
+seem like i pulled this capital m out of
+ 
+
+ align:start position:0%
+seem like i pulled this capital m out of
+nowhere
+
+ align:start position:0%
+nowhere
+ 
+
+ align:start position:0%
+nowhere
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but this is the thinking that goes
+
+ align:start position:0%
+but this is the thinking that goes
+ 
+
+ align:start position:0%
+but this is the thinking that goes
+behind it so let epsilon be positive now
+
+ align:start position:0%
+behind it so let epsilon be positive now
+ 
+
+ align:start position:0%
+behind it so let epsilon be positive now
+i'll tell you how to choose capital m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose m
+
+ align:start position:0%
+choose m
+ 
+
+ align:start position:0%
+choose m
+natural number
+
+ align:start position:0%
+natural number
+ 
+
+ align:start position:0%
+natural number
+so that so we wanted for all n bigger
+
+ align:start position:0%
+so that so we wanted for all n bigger
+ 
+
+ align:start position:0%
+so that so we wanted for all n bigger
+than or equal to capital m one over n is
+
+ align:start position:0%
+than or equal to capital m one over n is
+ 
+
+ align:start position:0%
+than or equal to capital m one over n is
+less than epsilon so
+
+ align:start position:0%
+less than epsilon so
+ 
+
+ align:start position:0%
+less than epsilon so
+uh this will certainly be true if n is
+
+ align:start position:0%
+uh this will certainly be true if n is
+ 
+
+ align:start position:0%
+uh this will certainly be true if n is
+bigger than or equal to m capital m so
+
+ align:start position:0%
+bigger than or equal to m capital m so
+ 
+
+ align:start position:0%
+bigger than or equal to m capital m so
+that one over capital m is less than
+
+ align:start position:0%
+that one over capital m is less than
+ 
+
+ align:start position:0%
+that one over capital m is less than
+epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason we can choose capital m
+
+ align:start position:0%
+and the reason we can choose capital m
+ 
+
+ align:start position:0%
+and the reason we can choose capital m
+like this again where is this coming
+
+ align:start position:0%
+like this again where is this coming
+ 
+
+ align:start position:0%
+like this again where is this coming
+from it's coming from the archimedean uh
+
+ align:start position:0%
+from it's coming from the archimedean uh
+ 
+
+ align:start position:0%
+from it's coming from the archimedean uh
+property of the real numbers
+
+ align:start position:0%
+property of the real numbers
+ 
+
+ align:start position:0%
+property of the real numbers
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we've chosen capital m now we need to
+
+ align:start position:0%
+we've chosen capital m now we need to
+ 
+
+ align:start position:0%
+we've chosen capital m now we need to
+show that this capital m works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then for all
+
+ align:start position:0%
+then for all
+ 
+
+ align:start position:0%
+then for all
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+bigger than or equal to capital m
+
+ align:start position:0%
+bigger than or equal to capital m
+ 
+
+ align:start position:0%
+bigger than or equal to capital m
+if i look at
+
+ align:start position:0%
+if i look at
+ 
+
+ align:start position:0%
+if i look at
+1 over n squared plus 30 n
+
+ align:start position:0%
+1 over n squared plus 30 n
+ 
+
+ align:start position:0%
+1 over n squared plus 30 n
+plus 1 minus 0 my proposed limit
+
+ align:start position:0%
+plus 1 minus 0 my proposed limit
+ 
+
+ align:start position:0%
+plus 1 minus 0 my proposed limit
+this is equal to 1 over n squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus 1.
+
+ align:start position:0%
+plus 1.
+ 
+
+ align:start position:0%
+plus 1.
+and this is less than or equal to if i
+
+ align:start position:0%
+and this is less than or equal to if i
+ 
+
+ align:start position:0%
+and this is less than or equal to if i
+drop n squared and 1
+
+ align:start position:0%
+drop n squared and 1
+ 
+
+ align:start position:0%
+drop n squared and 1
+30 n which is less than or equal to 1
+
+ align:start position:0%
+30 n which is less than or equal to 1
+ 
+
+ align:start position:0%
+30 n which is less than or equal to 1
+over n
+
+ align:start position:0%
+over n
+ 
+
+ align:start position:0%
+over n
+which is less than or equal to 1 over
+
+ align:start position:0%
+which is less than or equal to 1 over
+ 
+
+ align:start position:0%
+which is less than or equal to 1 over
+capital m which is less than epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so something of a non-example
+
+ align:start position:0%
+so so something of a non-example
+ 
+
+ align:start position:0%
+so so something of a non-example
+um let's show that the sequence
+
+ align:start position:0%
+um let's show that the sequence
+ 
+
+ align:start position:0%
+um let's show that the sequence
+minus one to the n
+
+ align:start position:0%
+minus one to the n
+ 
+
+ align:start position:0%
+minus one to the n
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+dnc does not converge
+
+ align:start position:0%
+dnc does not converge
+ 
+
+ align:start position:0%
+dnc does not converge
+not democratic national committee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does not converge
+
+ align:start position:0%
+does not converge
+ 
+
+ align:start position:0%
+does not converge
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so this is just the sequence um
+
+ align:start position:0%
+so this is just the sequence um
+ 
+
+ align:start position:0%
+so this is just the sequence um
+minus one one minus one one minus one
+
+ align:start position:0%
+minus one one minus one one minus one
+ 
+
+ align:start position:0%
+minus one one minus one one minus one
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+okay so we have to show it does not
+
+ align:start position:0%
+okay so we have to show it does not
+ 
+
+ align:start position:0%
+okay so we have to show it does not
+converge meaning for every x and r we'll
+
+ align:start position:0%
+converge meaning for every x and r we'll
+ 
+
+ align:start position:0%
+converge meaning for every x and r we'll
+show that x n does not converge to x
+
+ align:start position:0%
+show that x n does not converge to x
+ 
+
+ align:start position:0%
+show that x n does not converge to x
+using the
+
+ align:start position:0%
+using the
+ 
+
+ align:start position:0%
+using the
+negation of the definition all right
+
+ align:start position:0%
+negation of the definition all right
+ 
+
+ align:start position:0%
+negation of the definition all right
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let x be an r and what do we want to
+
+ align:start position:0%
+let x be an r and what do we want to
+ 
+
+ align:start position:0%
+let x be an r and what do we want to
+show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus 1 to the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does not converge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we'll use this definition so
+
+ align:start position:0%
+okay and we'll use this definition so
+ 
+
+ align:start position:0%
+okay and we'll use this definition so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this definition means we need to find a
+
+ align:start position:0%
+this definition means we need to find a
+ 
+
+ align:start position:0%
+this definition means we need to find a
+bad epsilon naught
+
+ align:start position:0%
+bad epsilon naught
+ 
+
+ align:start position:0%
+bad epsilon naught
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's the the kind of thinking that
+
+ align:start position:0%
+and here's the the kind of thinking that
+ 
+
+ align:start position:0%
+and here's the the kind of thinking that
+goes along with this
+
+ align:start position:0%
+goes along with this
+ 
+
+ align:start position:0%
+goes along with this
+there's one there's minus one
+
+ align:start position:0%
+there's one there's minus one
+ 
+
+ align:start position:0%
+there's one there's minus one
+this sequence just keeps alternating
+
+ align:start position:0%
+this sequence just keeps alternating
+ 
+
+ align:start position:0%
+this sequence just keeps alternating
+right so so intuitively there's no way
+
+ align:start position:0%
+right so so intuitively there's no way
+ 
+
+ align:start position:0%
+right so so intuitively there's no way
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh every element of the sequence can be
+
+ align:start position:0%
+uh every element of the sequence can be
+ 
+
+ align:start position:0%
+uh every element of the sequence can be
+getting or every entry in the sequence
+
+ align:start position:0%
+getting or every entry in the sequence
+ 
+
+ align:start position:0%
+getting or every entry in the sequence
+can be getting close to some single x
+
+ align:start position:0%
+can be getting close to some single x
+ 
+
+ align:start position:0%
+can be getting close to some single x
+so what's the idea the idea is that the
+
+ align:start position:0%
+so what's the idea the idea is that the
+ 
+
+ align:start position:0%
+so what's the idea the idea is that the
+distance between
+
+ align:start position:0%
+distance between
+ 
+
+ align:start position:0%
+distance between
+these two guys
+
+ align:start position:0%
+these two guys
+ 
+
+ align:start position:0%
+these two guys
+is always two
+
+ align:start position:0%
+is always two
+ 
+
+ align:start position:0%
+is always two
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so somehow
+
+ align:start position:0%
+so somehow
+ 
+
+ align:start position:0%
+so somehow
+um the distance between
+
+ align:start position:0%
+um the distance between
+ 
+
+ align:start position:0%
+um the distance between
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+every entry or
+
+ align:start position:0%
+every entry or
+ 
+
+ align:start position:0%
+every entry or
+basically some entry has to be within
+
+ align:start position:0%
+basically some entry has to be within
+ 
+
+ align:start position:0%
+basically some entry has to be within
+distance uh if it's if this is within
+
+ align:start position:0%
+distance uh if it's if this is within
+ 
+
+ align:start position:0%
+distance uh if it's if this is within
+distance one
+
+ align:start position:0%
+distance one
+ 
+
+ align:start position:0%
+distance one
+say to a given x
+
+ align:start position:0%
+say to a given x
+ 
+
+ align:start position:0%
+say to a given x
+then this will be greater than or equal
+
+ align:start position:0%
+then this will be greater than or equal
+ 
+
+ align:start position:0%
+then this will be greater than or equal
+to one in distance to x
+
+ align:start position:0%
+to one in distance to x
+ 
+
+ align:start position:0%
+to one in distance to x
+okay so you can imagine x is over here
+
+ align:start position:0%
+okay so you can imagine x is over here
+ 
+
+ align:start position:0%
+okay so you can imagine x is over here
+minus one is within distance one to x
+
+ align:start position:0%
+minus one is within distance one to x
+ 
+
+ align:start position:0%
+minus one is within distance one to x
+but then one would be
+
+ align:start position:0%
+but then one would be
+ 
+
+ align:start position:0%
+but then one would be
+greater than distance one
+
+ align:start position:0%
+greater than distance one
+ 
+
+ align:start position:0%
+greater than distance one
+uh to x
+
+ align:start position:0%
+uh to x
+ 
+
+ align:start position:0%
+uh to x
+okay so our bad epsilon naught
+
+ align:start position:0%
+okay so our bad epsilon naught
+ 
+
+ align:start position:0%
+okay so our bad epsilon naught
+was going to be one as we'll see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let epsilon not equals one that's our
+
+ align:start position:0%
+let epsilon not equals one that's our
+ 
+
+ align:start position:0%
+let epsilon not equals one that's our
+bad epsilon so now we have to show for
+
+ align:start position:0%
+bad epsilon so now we have to show for
+ 
+
+ align:start position:0%
+bad epsilon so now we have to show for
+all capital m and natural number there
+
+ align:start position:0%
+all capital m and natural number there
+ 
+
+ align:start position:0%
+all capital m and natural number there
+exists a little n bigger than or equal
+
+ align:start position:0%
+exists a little n bigger than or equal
+ 
+
+ align:start position:0%
+exists a little n bigger than or equal
+to capital m so that
+
+ align:start position:0%
+to capital m so that
+ 
+
+ align:start position:0%
+to capital m so that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we have that inequality so
+
+ align:start position:0%
+we have that inequality so
+ 
+
+ align:start position:0%
+we have that inequality so
+let m be a natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number then what do we see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so then this says there exists an n
+
+ align:start position:0%
+uh so then this says there exists an n
+ 
+
+ align:start position:0%
+uh so then this says there exists an n
+greater than or equal to capital m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i will show that n is in fact either
+
+ align:start position:0%
+and i will show that n is in fact either
+ 
+
+ align:start position:0%
+and i will show that n is in fact either
+capital m or capital n plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then two
+
+ align:start position:0%
+then two
+ 
+
+ align:start position:0%
+then two
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the distance between
+
+ align:start position:0%
+the distance between
+ 
+
+ align:start position:0%
+the distance between
+minus one to the m and minus 1 to the n
+
+ align:start position:0%
+minus one to the m and minus 1 to the n
+ 
+
+ align:start position:0%
+minus one to the m and minus 1 to the n
+plus 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is less than or equal to now using the
+
+ align:start position:0%
+is less than or equal to now using the
+ 
+
+ align:start position:0%
+is less than or equal to now using the
+triangle inequality i add and subtract x
+
+ align:start position:0%
+triangle inequality i add and subtract x
+ 
+
+ align:start position:0%
+triangle inequality i add and subtract x
+and then use the triangle inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i have the sum of two numbers is
+
+ align:start position:0%
+so i have the sum of two numbers is
+ 
+
+ align:start position:0%
+so i have the sum of two numbers is
+bigger than or equal to two
+
+ align:start position:0%
+bigger than or equal to two
+ 
+
+ align:start position:0%
+bigger than or equal to two
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the only way that can happen is if
+
+ align:start position:0%
+and the only way that can happen is if
+ 
+
+ align:start position:0%
+and the only way that can happen is if
+one of these numbers is bigger than or
+
+ align:start position:0%
+one of these numbers is bigger than or
+ 
+
+ align:start position:0%
+one of these numbers is bigger than or
+equal to one if both of these numbers
+
+ align:start position:0%
+equal to one if both of these numbers
+ 
+
+ align:start position:0%
+equal to one if both of these numbers
+are less than one
+
+ align:start position:0%
+are less than one
+ 
+
+ align:start position:0%
+are less than one
+then the sum is less than two and i
+
+ align:start position:0%
+then the sum is less than two and i
+ 
+
+ align:start position:0%
+then the sum is less than two and i
+would have two is less than two that's
+
+ align:start position:0%
+would have two is less than two that's
+ 
+
+ align:start position:0%
+would have two is less than two that's
+not possible so one of these numbers has
+
+ align:start position:0%
+not possible so one of these numbers has
+ 
+
+ align:start position:0%
+not possible so one of these numbers has
+to be bigger than or equal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore i could take n equal to
+
+ align:start position:0%
+and therefore i could take n equal to
+ 
+
+ align:start position:0%
+and therefore i could take n equal to
+capital m uh if this is bigger than or
+
+ align:start position:0%
+capital m uh if this is bigger than or
+ 
+
+ align:start position:0%
+capital m uh if this is bigger than or
+equal to one or if this is bigger than
+
+ align:start position:0%
+equal to one or if this is bigger than
+ 
+
+ align:start position:0%
+equal to one or if this is bigger than
+or equal to one i k i take little n to
+
+ align:start position:0%
+or equal to one i k i take little n to
+ 
+
+ align:start position:0%
+or equal to one i k i take little n to
+be capital n plus one so that's the end
+
+ align:start position:0%
+be capital n plus one so that's the end
+ 
+
+ align:start position:0%
+be capital n plus one so that's the end
+of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alrighty so that's uh
+
+ align:start position:0%
+alrighty so that's uh
+ 
+
+ align:start position:0%
+alrighty so that's uh
+that's good for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples for now
+
+ align:start position:0%
+examples for now
+ 
+
+ align:start position:0%
+examples for now
+let's prove a
+
+ align:start position:0%
+let's prove a
+ 
+
+ align:start position:0%
+let's prove a
+general theorem about convergent
+
+ align:start position:0%
+general theorem about convergent
+ 
+
+ align:start position:0%
+general theorem about convergent
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+namely that if i have a convergent
+
+ align:start position:0%
+namely that if i have a convergent
+ 
+
+ align:start position:0%
+namely that if i have a convergent
+sequence then it's bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me just give you a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quick reminder
+
+ align:start position:0%
+quick reminder
+ 
+
+ align:start position:0%
+quick reminder
+about what being bounded means for a
+
+ align:start position:0%
+about what being bounded means for a
+ 
+
+ align:start position:0%
+about what being bounded means for a
+sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i.e
+
+ align:start position:0%
+i.e
+ 
+
+ align:start position:0%
+i.e
+exists some number such that
+
+ align:start position:0%
+exists some number such that
+ 
+
+ align:start position:0%
+exists some number such that
+for all n
+
+ align:start position:0%
+for all n
+ 
+
+ align:start position:0%
+for all n
+x n is less than or equal to capital b
+
+ align:start position:0%
+x n is less than or equal to capital b
+ 
+
+ align:start position:0%
+x n is less than or equal to capital b
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now as
+
+ align:start position:0%
+now as
+ 
+
+ align:start position:0%
+now as
+um beginning students of math
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+what types of questions should we start
+
+ align:start position:0%
+what types of questions should we start
+ 
+
+ align:start position:0%
+what types of questions should we start
+asking ourselves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of those so one of the types
+
+ align:start position:0%
+one of those so one of the types
+ 
+
+ align:start position:0%
+one of those so one of the types
+or a type of question that we should ask
+
+ align:start position:0%
+or a type of question that we should ask
+ 
+
+ align:start position:0%
+or a type of question that we should ask
+when we come across a theorem
+
+ align:start position:0%
+when we come across a theorem
+ 
+
+ align:start position:0%
+when we come across a theorem
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+you know a one-way street meaning if
+
+ align:start position:0%
+you know a one-way street meaning if
+ 
+
+ align:start position:0%
+you know a one-way street meaning if
+something happens and something else
+
+ align:start position:0%
+something happens and something else
+ 
+
+ align:start position:0%
+something happens and something else
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+is does the converse hold namely if i
+
+ align:start position:0%
+is does the converse hold namely if i
+ 
+
+ align:start position:0%
+is does the converse hold namely if i
+assume x sub n is a bounded sequence
+
+ align:start position:0%
+assume x sub n is a bounded sequence
+ 
+
+ align:start position:0%
+assume x sub n is a bounded sequence
+does this imply that xn is convergent
+
+ align:start position:0%
+does this imply that xn is convergent
+ 
+
+ align:start position:0%
+does this imply that xn is convergent
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if somebody if you ever hear the
+
+ align:start position:0%
+so if somebody if you ever hear the
+ 
+
+ align:start position:0%
+so if somebody if you ever hear the
+words does the converse hold that's what
+
+ align:start position:0%
+words does the converse hold that's what
+ 
+
+ align:start position:0%
+words does the converse hold that's what
+they mean
+
+ align:start position:0%
+they mean
+ 
+
+ align:start position:0%
+they mean
+now for this statement this is false
+
+ align:start position:0%
+now for this statement this is false
+ 
+
+ align:start position:0%
+now for this statement this is false
+if xn is bounded implies xn is
+
+ align:start position:0%
+if xn is bounded implies xn is
+ 
+
+ align:start position:0%
+if xn is bounded implies xn is
+convergent that's false because we have
+
+ align:start position:0%
+convergent that's false because we have
+ 
+
+ align:start position:0%
+convergent that's false because we have
+an example right there of a bounded
+
+ align:start position:0%
+an example right there of a bounded
+ 
+
+ align:start position:0%
+an example right there of a bounded
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+this sequence here minus 1 to the n is
+
+ align:start position:0%
+this sequence here minus 1 to the n is
+ 
+
+ align:start position:0%
+this sequence here minus 1 to the n is
+bounded since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean an absolute value this equals 1
+
+ align:start position:0%
+i mean an absolute value this equals 1
+ 
+
+ align:start position:0%
+i mean an absolute value this equals 1
+for all n so we could take b equals 1.
+
+ align:start position:0%
+for all n so we could take b equals 1.
+ 
+
+ align:start position:0%
+for all n so we could take b equals 1.
+so minus one to the n is a bounded
+
+ align:start position:0%
+so minus one to the n is a bounded
+ 
+
+ align:start position:0%
+so minus one to the n is a bounded
+sequence which is not convergent so the
+
+ align:start position:0%
+sequence which is not convergent so the
+ 
+
+ align:start position:0%
+sequence which is not convergent so the
+converse does not hold
+
+ align:start position:0%
+converse does not hold
+ 
+
+ align:start position:0%
+converse does not hold
+okay so let's prove
+
+ align:start position:0%
+okay so let's prove
+ 
+
+ align:start position:0%
+okay so let's prove
+the theorem and let me draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little picture to go along with it
+
+ align:start position:0%
+a little picture to go along with it
+ 
+
+ align:start position:0%
+a little picture to go along with it
+of kind of what's going on
+
+ align:start position:0%
+of kind of what's going on
+ 
+
+ align:start position:0%
+of kind of what's going on
+um so here's zero
+
+ align:start position:0%
+um so here's zero
+ 
+
+ align:start position:0%
+um so here's zero
+let's imagine
+
+ align:start position:0%
+let's imagine
+ 
+
+ align:start position:0%
+let's imagine
+let me make this picture a little bit
+
+ align:start position:0%
+let me make this picture a little bit
+ 
+
+ align:start position:0%
+let me make this picture a little bit
+bigger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before i go into the proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let x be the limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is not the proof yet this is
+
+ align:start position:0%
+so this is not the proof yet this is
+ 
+
+ align:start position:0%
+so this is not the proof yet this is
+just uh
+
+ align:start position:0%
+just uh
+ 
+
+ align:start position:0%
+just uh
+more discussion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if this x sub n is converging to x
+
+ align:start position:0%
+so if this x sub n is converging to x
+ 
+
+ align:start position:0%
+so if this x sub n is converging to x
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+let's say i go out distance 1
+
+ align:start position:0%
+let's say i go out distance 1
+ 
+
+ align:start position:0%
+let's say i go out distance 1
+to x
+
+ align:start position:0%
+to x
+ 
+
+ align:start position:0%
+to x
+then all of the x of n's eventually have
+
+ align:start position:0%
+then all of the x of n's eventually have
+ 
+
+ align:start position:0%
+then all of the x of n's eventually have
+to land in
+
+ align:start position:0%
+to land in
+ 
+
+ align:start position:0%
+to land in
+this strip here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+x sub n
+
+ align:start position:0%
+x sub n
+ 
+
+ align:start position:0%
+x sub n
+and bigger than or equal to some capital
+
+ align:start position:0%
+and bigger than or equal to some capital
+ 
+
+ align:start position:0%
+and bigger than or equal to some capital
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i know that they're all within
+
+ align:start position:0%
+so i know that they're all within
+ 
+
+ align:start position:0%
+so i know that they're all within
+distance one to x so an absolute value
+
+ align:start position:0%
+distance one to x so an absolute value
+ 
+
+ align:start position:0%
+distance one to x so an absolute value
+they'd be bounded by
+
+ align:start position:0%
+they'd be bounded by
+ 
+
+ align:start position:0%
+they'd be bounded by
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+let's say for this picture it'd be x
+
+ align:start position:0%
+let's say for this picture it'd be x
+ 
+
+ align:start position:0%
+let's say for this picture it'd be x
+plus one but um if this was over there
+
+ align:start position:0%
+plus one but um if this was over there
+ 
+
+ align:start position:0%
+plus one but um if this was over there
+capital it would be the absolute value
+
+ align:start position:0%
+capital it would be the absolute value
+ 
+
+ align:start position:0%
+capital it would be the absolute value
+of x plus one
+
+ align:start position:0%
+of x plus one
+ 
+
+ align:start position:0%
+of x plus one
+so that takes care of all x sub n's with
+
+ align:start position:0%
+so that takes care of all x sub n's with
+ 
+
+ align:start position:0%
+so that takes care of all x sub n's with
+n bigger than or equal to m and then
+
+ align:start position:0%
+n bigger than or equal to m and then
+ 
+
+ align:start position:0%
+n bigger than or equal to m and then
+there's only finitely many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guys to deal with
+
+ align:start position:0%
+guys to deal with
+ 
+
+ align:start position:0%
+guys to deal with
+maybe there's a bigger one out here x of
+
+ align:start position:0%
+maybe there's a bigger one out here x of
+ 
+
+ align:start position:0%
+maybe there's a bigger one out here x of
+m minus one
+
+ align:start position:0%
+m minus one
+ 
+
+ align:start position:0%
+m minus one
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to deal with and and
+
+ align:start position:0%
+to deal with and and
+ 
+
+ align:start position:0%
+to deal with and and
+that's how we define our our number is
+
+ align:start position:0%
+that's how we define our our number is
+ 
+
+ align:start position:0%
+that's how we define our our number is
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+absolute value of x plus one uh plus
+
+ align:start position:0%
+absolute value of x plus one uh plus
+ 
+
+ align:start position:0%
+absolute value of x plus one uh plus
+these finite the absolute value of these
+
+ align:start position:0%
+these finite the absolute value of these
+ 
+
+ align:start position:0%
+these finite the absolute value of these
+finitely many and then that would be
+
+ align:start position:0%
+finitely many and then that would be
+ 
+
+ align:start position:0%
+finitely many and then that would be
+something that's bigger than or equal to
+
+ align:start position:0%
+something that's bigger than or equal to
+ 
+
+ align:start position:0%
+something that's bigger than or equal to
+every element in the sequence so how
+
+ align:start position:0%
+every element in the sequence so how
+ 
+
+ align:start position:0%
+every element in the sequence so how
+does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the picture that goes with it how
+
+ align:start position:0%
+that's the picture that goes with it how
+ 
+
+ align:start position:0%
+that's the picture that goes with it how
+do we write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we take that picture to proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose xn converges to x that's our
+
+ align:start position:0%
+suppose xn converges to x that's our
+ 
+
+ align:start position:0%
+suppose xn converges to x that's our
+assumption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there exists a natural number m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+all n bigger than or equal to capital m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x sub n minus x is within distance one
+
+ align:start position:0%
+x sub n minus x is within distance one
+ 
+
+ align:start position:0%
+x sub n minus x is within distance one
+our x of n is within distance one to x
+
+ align:start position:0%
+our x of n is within distance one to x
+ 
+
+ align:start position:0%
+our x of n is within distance one to x
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+for all n bigger than or equal to
+
+ align:start position:0%
+for all n bigger than or equal to
+ 
+
+ align:start position:0%
+for all n bigger than or equal to
+capital m if we look at the absolute
+
+ align:start position:0%
+capital m if we look at the absolute
+ 
+
+ align:start position:0%
+capital m if we look at the absolute
+value of x sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+add and subtract x
+
+ align:start position:0%
+add and subtract x
+ 
+
+ align:start position:0%
+add and subtract x
+and now use the triangle inequality this
+
+ align:start position:0%
+and now use the triangle inequality this
+ 
+
+ align:start position:0%
+and now use the triangle inequality this
+is less than or equal to absolute value
+
+ align:start position:0%
+is less than or equal to absolute value
+ 
+
+ align:start position:0%
+is less than or equal to absolute value
+of x sub n minus x
+
+ align:start position:0%
+of x sub n minus x
+ 
+
+ align:start position:0%
+of x sub n minus x
+plus the absolute value of x equals one
+
+ align:start position:0%
+plus the absolute value of x equals one
+ 
+
+ align:start position:0%
+plus the absolute value of x equals one
+plus x
+
+ align:start position:0%
+plus x
+ 
+
+ align:start position:0%
+plus x
+okay so for all
+
+ align:start position:0%
+okay so for all
+ 
+
+ align:start position:0%
+okay so for all
+entries in the sequence past this point
+
+ align:start position:0%
+entries in the sequence past this point
+ 
+
+ align:start position:0%
+entries in the sequence past this point
+capital m
+
+ align:start position:0%
+capital m
+ 
+
+ align:start position:0%
+capital m
+they're bounded in absolute value by one
+
+ align:start position:0%
+they're bounded in absolute value by one
+ 
+
+ align:start position:0%
+they're bounded in absolute value by one
+plus x that's just a number okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just have to take care of the
+
+ align:start position:0%
+we just have to take care of the
+ 
+
+ align:start position:0%
+we just have to take care of the
+one up to capital m minus one guys we
+
+ align:start position:0%
+one up to capital m minus one guys we
+ 
+
+ align:start position:0%
+one up to capital m minus one guys we
+just have to find a number bigger than
+
+ align:start position:0%
+just have to find a number bigger than
+ 
+
+ align:start position:0%
+just have to find a number bigger than
+those guys
+
+ align:start position:0%
+those guys
+ 
+
+ align:start position:0%
+those guys
+and this number
+
+ align:start position:0%
+and this number
+ 
+
+ align:start position:0%
+and this number
+and we'll have found a b so then let's
+
+ align:start position:0%
+and we'll have found a b so then let's
+ 
+
+ align:start position:0%
+and we'll have found a b so then let's
+take b to be
+
+ align:start position:0%
+take b to be
+ 
+
+ align:start position:0%
+take b to be
+x sub 1
+
+ align:start position:0%
+x sub 1
+ 
+
+ align:start position:0%
+x sub 1
+plus x sub 2 plus
+
+ align:start position:0%
+plus x sub 2 plus
+ 
+
+ align:start position:0%
+plus x sub 2 plus
+x sub
+
+ align:start position:0%
+x sub
+ 
+
+ align:start position:0%
+x sub
+capital m minus 1
+
+ align:start position:0%
+capital m minus 1
+ 
+
+ align:start position:0%
+capital m minus 1
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+for all n a natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the absolute value of x of n is less
+
+ align:start position:0%
+the absolute value of x of n is less
+ 
+
+ align:start position:0%
+the absolute value of x of n is less
+than or equal to b right because if n is
+
+ align:start position:0%
+than or equal to b right because if n is
+ 
+
+ align:start position:0%
+than or equal to b right because if n is
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+capital m then its absolute value is
+
+ align:start position:0%
+capital m then its absolute value is
+ 
+
+ align:start position:0%
+capital m then its absolute value is
+bounded by one of these its absolute
+
+ align:start position:0%
+bounded by one of these its absolute
+ 
+
+ align:start position:0%
+bounded by one of these its absolute
+value is equal to one of these and
+
+ align:start position:0%
+value is equal to one of these and
+ 
+
+ align:start position:0%
+value is equal to one of these and
+therefore less than or equal to
+
+ align:start position:0%
+therefore less than or equal to
+ 
+
+ align:start position:0%
+therefore less than or equal to
+uh one of these plus some non-negative
+
+ align:start position:0%
+uh one of these plus some non-negative
+ 
+
+ align:start position:0%
+uh one of these plus some non-negative
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+and if n is bigger than or equal to
+
+ align:start position:0%
+and if n is bigger than or equal to
+ 
+
+ align:start position:0%
+and if n is bigger than or equal to
+capital m then we have this bound that
+
+ align:start position:0%
+capital m then we have this bound that
+ 
+
+ align:start position:0%
+capital m then we have this bound that
+we use
+
+ align:start position:0%
+we use
+ 
+
+ align:start position:0%
+we use
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and this number is certainly less than
+
+ align:start position:0%
+and this number is certainly less than
+ 
+
+ align:start position:0%
+and this number is certainly less than
+or equal to capital b again because
+
+ align:start position:0%
+or equal to capital b again because
+ 
+
+ align:start position:0%
+or equal to capital b again because
+it's this number plus the sum of
+
+ align:start position:0%
+it's this number plus the sum of
+ 
+
+ align:start position:0%
+it's this number plus the sum of
+non-negative numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in general there's no like easy
+
+ align:start position:0%
+now in general there's no like easy
+ 
+
+ align:start position:0%
+now in general there's no like easy
+like easily checkable
+
+ align:start position:0%
+like easily checkable
+ 
+
+ align:start position:0%
+like easily checkable
+criterion for a sequence to converge
+
+ align:start position:0%
+criterion for a sequence to converge
+ 
+
+ align:start position:0%
+criterion for a sequence to converge
+all we can do is verify the definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there are some sequences which are
+
+ align:start position:0%
+but there are some sequences which are
+ 
+
+ align:start position:0%
+but there are some sequences which are
+you can easily check
+
+ align:start position:0%
+you can easily check
+ 
+
+ align:start position:0%
+you can easily check
+or or figure out if they converge just
+
+ align:start position:0%
+or or figure out if they converge just
+ 
+
+ align:start position:0%
+or or figure out if they converge just
+by telling if
+
+ align:start position:0%
+by telling if
+ 
+
+ align:start position:0%
+by telling if
+if they're bounded those are what are
+
+ align:start position:0%
+if they're bounded those are what are
+ 
+
+ align:start position:0%
+if they're bounded those are what are
+called monotone sequences
+
+ align:start position:0%
+called monotone sequences
+ 
+
+ align:start position:0%
+called monotone sequences
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is in some sense the class of
+
+ align:start position:0%
+so this is in some sense the class of
+ 
+
+ align:start position:0%
+so this is in some sense the class of
+sequences that does kind of satisfy the
+
+ align:start position:0%
+sequences that does kind of satisfy the
+ 
+
+ align:start position:0%
+sequences that does kind of satisfy the
+converse of that theorem i stated a
+
+ align:start position:0%
+converse of that theorem i stated a
+ 
+
+ align:start position:0%
+converse of that theorem i stated a
+minute ago
+
+ align:start position:0%
+minute ago
+ 
+
+ align:start position:0%
+minute ago
+so sequence
+
+ align:start position:0%
+so sequence
+ 
+
+ align:start position:0%
+so sequence
+x of n is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monotone increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all natural numbers little n
+
+ align:start position:0%
+for all natural numbers little n
+ 
+
+ align:start position:0%
+for all natural numbers little n
+x of n is less than or equal to x of n
+
+ align:start position:0%
+x of n is less than or equal to x of n
+ 
+
+ align:start position:0%
+x of n is less than or equal to x of n
+plus one so this means that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x of one is less than or equal to x sub
+
+ align:start position:0%
+x of one is less than or equal to x sub
+ 
+
+ align:start position:0%
+x of one is less than or equal to x sub
+two is less than or equal to x sub three
+
+ align:start position:0%
+two is less than or equal to x sub three
+ 
+
+ align:start position:0%
+two is less than or equal to x sub three
+and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence is monotone decreasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we have the other inequalities so
+
+ align:start position:0%
+if we have the other inequalities so
+ 
+
+ align:start position:0%
+if we have the other inequalities so
+things are getting
+
+ align:start position:0%
+things are getting
+ 
+
+ align:start position:0%
+things are getting
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+x sub n is bigger than or equal to x of
+
+ align:start position:0%
+x sub n is bigger than or equal to x of
+ 
+
+ align:start position:0%
+x sub n is bigger than or equal to x of
+n plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we have
+
+ align:start position:0%
+and if we have
+ 
+
+ align:start position:0%
+and if we have
+a sequence which is monotone increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or monotone decreasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's one or the other
+
+ align:start position:0%
+so it's one or the other
+ 
+
+ align:start position:0%
+so it's one or the other
+you say xn is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monotone or monotonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you know it's simple enough to uh come
+
+ align:start position:0%
+you know it's simple enough to uh come
+ 
+
+ align:start position:0%
+you know it's simple enough to uh come
+up with examples of sequences which are
+
+ align:start position:0%
+up with examples of sequences which are
+ 
+
+ align:start position:0%
+up with examples of sequences which are
+monotone increasing monotone decreasing
+
+ align:start position:0%
+monotone increasing monotone decreasing
+ 
+
+ align:start position:0%
+monotone increasing monotone decreasing
+or neither so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one over n so this is just
+
+ align:start position:0%
+one over n so this is just
+ 
+
+ align:start position:0%
+one over n so this is just
+one one-half
+
+ align:start position:0%
+one one-half
+ 
+
+ align:start position:0%
+one one-half
+third
+
+ align:start position:0%
+third
+ 
+
+ align:start position:0%
+third
+fourth
+
+ align:start position:0%
+fourth
+ 
+
+ align:start position:0%
+fourth
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monotone decreasing
+
+ align:start position:0%
+monotone decreasing
+ 
+
+ align:start position:0%
+monotone decreasing
+and if i
+
+ align:start position:0%
+and if i
+ 
+
+ align:start position:0%
+and if i
+take minus
+
+ align:start position:0%
+take minus
+ 
+
+ align:start position:0%
+take minus
+uh the sequence then i get that reverses
+
+ align:start position:0%
+uh the sequence then i get that reverses
+ 
+
+ align:start position:0%
+uh the sequence then i get that reverses
+basically all of the inequalities and i
+
+ align:start position:0%
+basically all of the inequalities and i
+ 
+
+ align:start position:0%
+basically all of the inequalities and i
+get a monotone increasing one so then
+
+ align:start position:0%
+get a monotone increasing one so then
+ 
+
+ align:start position:0%
+get a monotone increasing one so then
+this is minus one minus a half
+
+ align:start position:0%
+this is minus one minus a half
+ 
+
+ align:start position:0%
+this is minus one minus a half
+minus the third minus the fourth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monotone increasing and then something
+
+ align:start position:0%
+monotone increasing and then something
+ 
+
+ align:start position:0%
+monotone increasing and then something
+that's not is we've already
+
+ align:start position:0%
+that's not is we've already
+ 
+
+ align:start position:0%
+that's not is we've already
+come across that minus one to the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so
+
+ align:start position:0%
+okay and so
+ 
+
+ align:start position:0%
+okay and so
+the theorem about monotone sequences is
+
+ align:start position:0%
+the theorem about monotone sequences is
+ 
+
+ align:start position:0%
+the theorem about monotone sequences is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that there's a simpler criterion than
+
+ align:start position:0%
+that there's a simpler criterion than
+ 
+
+ align:start position:0%
+that there's a simpler criterion than
+the definition for
+
+ align:start position:0%
+the definition for
+ 
+
+ align:start position:0%
+the definition for
+determining when they're convergent or
+
+ align:start position:0%
+determining when they're convergent or
+ 
+
+ align:start position:0%
+determining when they're convergent or
+if you like
+
+ align:start position:0%
+if you like
+ 
+
+ align:start position:0%
+if you like
+they satisfy the converse of this
+
+ align:start position:0%
+they satisfy the converse of this
+ 
+
+ align:start position:0%
+they satisfy the converse of this
+theorem up here
+
+ align:start position:0%
+theorem up here
+ 
+
+ align:start position:0%
+theorem up here
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monotonic sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is bounded okay so we proved a minute
+
+ align:start position:0%
+it is bounded okay so we proved a minute
+ 
+
+ align:start position:0%
+it is bounded okay so we proved a minute
+ago that convergent sequences are
+
+ align:start position:0%
+ago that convergent sequences are
+ 
+
+ align:start position:0%
+ago that convergent sequences are
+bounded so for monotonic sequences
+
+ align:start position:0%
+bounded so for monotonic sequences
+ 
+
+ align:start position:0%
+bounded so for monotonic sequences
+converse holds
+
+ align:start position:0%
+converse holds
+ 
+
+ align:start position:0%
+converse holds
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's do the proof of this i'm gonna
+
+ align:start position:0%
+so let's do the proof of this i'm gonna
+ 
+
+ align:start position:0%
+so let's do the proof of this i'm gonna
+do the proof for monotone increasing
+
+ align:start position:0%
+do the proof for monotone increasing
+ 
+
+ align:start position:0%
+do the proof for monotone increasing
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+sequences and as an exercise i'll leave
+
+ align:start position:0%
+sequences and as an exercise i'll leave
+ 
+
+ align:start position:0%
+sequences and as an exercise i'll leave
+it to you to do the proof for monotone
+
+ align:start position:0%
+it to you to do the proof for monotone
+ 
+
+ align:start position:0%
+it to you to do the proof for monotone
+decreasing sequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose x of n is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a monotone
+
+ align:start position:0%
+a monotone
+ 
+
+ align:start position:0%
+a monotone
+increasing sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's two
+
+ align:start position:0%
+so there's two
+ 
+
+ align:start position:0%
+so there's two
+directions to prove convergence
+
+ align:start position:0%
+directions to prove convergence
+ 
+
+ align:start position:0%
+directions to prove convergence
+if and only if bounded
+
+ align:start position:0%
+if and only if bounded
+ 
+
+ align:start position:0%
+if and only if bounded
+so we have one direction
+
+ align:start position:0%
+so we have one direction
+ 
+
+ align:start position:0%
+so we have one direction
+meaning
+
+ align:start position:0%
+meaning
+ 
+
+ align:start position:0%
+meaning
+convergence implies bounded this is just
+
+ align:start position:0%
+convergence implies bounded this is just
+ 
+
+ align:start position:0%
+convergence implies bounded this is just
+the previous theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where we proved that every convergent
+
+ align:start position:0%
+where we proved that every convergent
+ 
+
+ align:start position:0%
+where we proved that every convergent
+sequence is bounded not just monotonic
+
+ align:start position:0%
+sequence is bounded not just monotonic
+ 
+
+ align:start position:0%
+sequence is bounded not just monotonic
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the meat is in proving the converse
+
+ align:start position:0%
+the meat is in proving the converse
+ 
+
+ align:start position:0%
+the meat is in proving the converse
+direction and in fact we'll be able to
+
+ align:start position:0%
+direction and in fact we'll be able to
+ 
+
+ align:start position:0%
+direction and in fact we'll be able to
+pick out uh what the limit is of this
+
+ align:start position:0%
+pick out uh what the limit is of this
+ 
+
+ align:start position:0%
+pick out uh what the limit is of this
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose x of n is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded
+
+ align:start position:0%
+bounded
+ 
+
+ align:start position:0%
+bounded
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if i look at the set of entries
+
+ align:start position:0%
+then if i look at the set of entries
+ 
+
+ align:start position:0%
+then if i look at the set of entries
+okay so not the sequence but if i look
+
+ align:start position:0%
+okay so not the sequence but if i look
+ 
+
+ align:start position:0%
+okay so not the sequence but if i look
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+the set
+
+ align:start position:0%
+the set
+ 
+
+ align:start position:0%
+the set
+of values
+
+ align:start position:0%
+of values
+ 
+
+ align:start position:0%
+of values
+that this uh sequence takes so x sub n
+
+ align:start position:0%
+that this uh sequence takes so x sub n
+ 
+
+ align:start position:0%
+that this uh sequence takes so x sub n
+and it's a natural number this is now a
+
+ align:start position:0%
+and it's a natural number this is now a
+ 
+
+ align:start position:0%
+and it's a natural number this is now a
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+subset of the real numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a bounded set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaning it's bounded above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and below because there exists some
+
+ align:start position:0%
+and below because there exists some
+ 
+
+ align:start position:0%
+and below because there exists some
+capital b so that
+
+ align:start position:0%
+capital b so that
+ 
+
+ align:start position:0%
+capital b so that
+x sub n is
+
+ align:start position:0%
+x sub n is
+ 
+
+ align:start position:0%
+x sub n is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+an absolute value less than or equal to
+
+ align:start position:0%
+an absolute value less than or equal to
+ 
+
+ align:start position:0%
+an absolute value less than or equal to
+capital b for all n so that means x sub
+
+ align:start position:0%
+capital b for all n so that means x sub
+ 
+
+ align:start position:0%
+capital b for all n so that means x sub
+n is between b and minus b
+
+ align:start position:0%
+n is between b and minus b
+ 
+
+ align:start position:0%
+n is between b and minus b
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+what's the picture again that goes with
+
+ align:start position:0%
+what's the picture again that goes with
+ 
+
+ align:start position:0%
+what's the picture again that goes with
+this so we have these x sub n's
+
+ align:start position:0%
+this so we have these x sub n's
+ 
+
+ align:start position:0%
+this so we have these x sub n's
+one x sub two x three we know that they
+
+ align:start position:0%
+one x sub two x three we know that they
+ 
+
+ align:start position:0%
+one x sub two x three we know that they
+cannot go past a certain
+
+ align:start position:0%
+cannot go past a certain
+ 
+
+ align:start position:0%
+cannot go past a certain
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+uh and they're
+
+ align:start position:0%
+uh and they're
+ 
+
+ align:start position:0%
+uh and they're
+steadily increasing but they can't
+
+ align:start position:0%
+steadily increasing but they can't
+ 
+
+ align:start position:0%
+steadily increasing but they can't
+keep
+
+ align:start position:0%
+keep
+ 
+
+ align:start position:0%
+keep
+strictly
+
+ align:start position:0%
+strictly
+ 
+
+ align:start position:0%
+strictly
+they can't increase without bound so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+not only that they're bounded by
+
+ align:start position:0%
+not only that they're bounded by
+ 
+
+ align:start position:0%
+not only that they're bounded by
+uh some
+
+ align:start position:0%
+uh some
+ 
+
+ align:start position:0%
+uh some
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+x which i'll define to be the supremum
+
+ align:start position:0%
+x which i'll define to be the supremum
+ 
+
+ align:start position:0%
+x which i'll define to be the supremum
+of this set
+
+ align:start position:0%
+of this set
+ 
+
+ align:start position:0%
+of this set
+and these guys are just getting in in
+
+ align:start position:0%
+and these guys are just getting in in
+ 
+
+ align:start position:0%
+and these guys are just getting in in
+essence so this is a picture i mean
+
+ align:start position:0%
+essence so this is a picture i mean
+ 
+
+ align:start position:0%
+essence so this is a picture i mean
+me trying to explain to you what's going
+
+ align:start position:0%
+me trying to explain to you what's going
+ 
+
+ align:start position:0%
+me trying to explain to you what's going
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+if x is the
+
+ align:start position:0%
+if x is the
+ 
+
+ align:start position:0%
+if x is the
+soup of this
+
+ align:start position:0%
+soup of this
+ 
+
+ align:start position:0%
+soup of this
+set of entries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then what do i know about x sub n
+
+ align:start position:0%
+then what do i know about x sub n
+ 
+
+ align:start position:0%
+then what do i know about x sub n
+i mean x
+
+ align:start position:0%
+i mean x
+ 
+
+ align:start position:0%
+i mean x
+is that if i go a little bit to the left
+
+ align:start position:0%
+is that if i go a little bit to the left
+ 
+
+ align:start position:0%
+is that if i go a little bit to the left
+of x so let me draw this again
+
+ align:start position:0%
+of x so let me draw this again
+ 
+
+ align:start position:0%
+of x so let me draw this again
+so okay so let me uh let me back up a
+
+ align:start position:0%
+so okay so let me uh let me back up a
+ 
+
+ align:start position:0%
+so okay so let me uh let me back up a
+minute here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since the set is bounded in r
+
+ align:start position:0%
+so since the set is bounded in r
+ 
+
+ align:start position:0%
+so since the set is bounded in r
+it has a supremum in r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what i claim is that this supremum
+
+ align:start position:0%
+and what i claim is that this supremum
+ 
+
+ align:start position:0%
+and what i claim is that this supremum
+is in fact the limit of this sequence
+
+ align:start position:0%
+is in fact the limit of this sequence
+ 
+
+ align:start position:0%
+is in fact the limit of this sequence
+okay this is a supremum of a set
+
+ align:start position:0%
+okay this is a supremum of a set
+ 
+
+ align:start position:0%
+okay this is a supremum of a set
+i'm saying it's the limit of the
+
+ align:start position:0%
+i'm saying it's the limit of the
+ 
+
+ align:start position:0%
+i'm saying it's the limit of the
+sequence so what's the what's the
+
+ align:start position:0%
+sequence so what's the what's the
+ 
+
+ align:start position:0%
+sequence so what's the what's the
+thinking here
+
+ align:start position:0%
+thinking here
+ 
+
+ align:start position:0%
+thinking here
+um so x is the supremum of all the
+
+ align:start position:0%
+um so x is the supremum of all the
+ 
+
+ align:start position:0%
+um so x is the supremum of all the
+entries in x sub n so nothing's ever
+
+ align:start position:0%
+entries in x sub n so nothing's ever
+ 
+
+ align:start position:0%
+entries in x sub n so nothing's ever
+going to be bigger than
+
+ align:start position:0%
+going to be bigger than
+ 
+
+ align:start position:0%
+going to be bigger than
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+some tolerance x plus epsilon so we just
+
+ align:start position:0%
+some tolerance x plus epsilon so we just
+ 
+
+ align:start position:0%
+some tolerance x plus epsilon so we just
+need to worry about what's to the left
+
+ align:start position:0%
+need to worry about what's to the left
+ 
+
+ align:start position:0%
+need to worry about what's to the left
+of it
+
+ align:start position:0%
+of it
+ 
+
+ align:start position:0%
+of it
+and we need to find a capital number m
+
+ align:start position:0%
+and we need to find a capital number m
+ 
+
+ align:start position:0%
+and we need to find a capital number m
+so that all the x of n's are in this
+
+ align:start position:0%
+so that all the x of n's are in this
+ 
+
+ align:start position:0%
+so that all the x of n's are in this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+interval here
+
+ align:start position:0%
+interval here
+ 
+
+ align:start position:0%
+interval here
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we're trying to show that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're trying to show that the extra
+
+ align:start position:0%
+we're trying to show that the extra
+ 
+
+ align:start position:0%
+we're trying to show that the extra
+bends converge to x the supremum of this
+
+ align:start position:0%
+bends converge to x the supremum of this
+ 
+
+ align:start position:0%
+bends converge to x the supremum of this
+guy so let's walk through this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by this picture so x is the supremum
+
+ align:start position:0%
+by this picture so x is the supremum
+ 
+
+ align:start position:0%
+by this picture so x is the supremum
+nothing's bigger
+
+ align:start position:0%
+nothing's bigger
+ 
+
+ align:start position:0%
+nothing's bigger
+than x so all of the x of n's are to the
+
+ align:start position:0%
+than x so all of the x of n's are to the
+ 
+
+ align:start position:0%
+than x so all of the x of n's are to the
+left of x plus epsilon so now we just
+
+ align:start position:0%
+left of x plus epsilon so now we just
+ 
+
+ align:start position:0%
+left of x plus epsilon so now we just
+need to worry about x minus epsilon
+
+ align:start position:0%
+need to worry about x minus epsilon
+ 
+
+ align:start position:0%
+need to worry about x minus epsilon
+now since x is the supremum of this set
+
+ align:start position:0%
+now since x is the supremum of this set
+ 
+
+ align:start position:0%
+now since x is the supremum of this set
+x minus epsilon can't be an upper bound
+
+ align:start position:0%
+x minus epsilon can't be an upper bound
+ 
+
+ align:start position:0%
+x minus epsilon can't be an upper bound
+for the set of entries of x sub n so
+
+ align:start position:0%
+for the set of entries of x sub n so
+ 
+
+ align:start position:0%
+for the set of entries of x sub n so
+that means there has to exist some
+
+ align:start position:0%
+that means there has to exist some
+ 
+
+ align:start position:0%
+that means there has to exist some
+x sub m
+
+ align:start position:0%
+x sub m
+ 
+
+ align:start position:0%
+x sub m
+so that it's bigger than x minus epsilon
+
+ align:start position:0%
+so that it's bigger than x minus epsilon
+ 
+
+ align:start position:0%
+so that it's bigger than x minus epsilon
+but now this is where we use the fact
+
+ align:start position:0%
+but now this is where we use the fact
+ 
+
+ align:start position:0%
+but now this is where we use the fact
+that this is a monotone increasing
+
+ align:start position:0%
+that this is a monotone increasing
+ 
+
+ align:start position:0%
+that this is a monotone increasing
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+because then if n is bigger than or
+
+ align:start position:0%
+because then if n is bigger than or
+ 
+
+ align:start position:0%
+because then if n is bigger than or
+equal to capital m then x sub n is
+
+ align:start position:0%
+equal to capital m then x sub n is
+ 
+
+ align:start position:0%
+equal to capital m then x sub n is
+strictly to the right of
+
+ align:start position:0%
+strictly to the right of
+ 
+
+ align:start position:0%
+strictly to the right of
+x sub m or it's equal to x sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and still less than or equal to x
+
+ align:start position:0%
+and still less than or equal to x
+ 
+
+ align:start position:0%
+and still less than or equal to x
+because x is the supremum of all the
+
+ align:start position:0%
+because x is the supremum of all the
+ 
+
+ align:start position:0%
+because x is the supremum of all the
+entries
+
+ align:start position:0%
+entries
+ 
+
+ align:start position:0%
+entries
+so then for n bigger than or equal to
+
+ align:start position:0%
+so then for n bigger than or equal to
+ 
+
+ align:start position:0%
+so then for n bigger than or equal to
+capital m they all have to lie in this
+
+ align:start position:0%
+capital m they all have to lie in this
+ 
+
+ align:start position:0%
+capital m they all have to lie in this
+interval and that's why the
+
+ align:start position:0%
+interval and that's why the
+ 
+
+ align:start position:0%
+interval and that's why the
+sequence converges to the supremum of
+
+ align:start position:0%
+sequence converges to the supremum of
+ 
+
+ align:start position:0%
+sequence converges to the supremum of
+this set so we're using
+
+ align:start position:0%
+this set so we're using
+ 
+
+ align:start position:0%
+this set so we're using
+um in a crucial way this the fact that
+
+ align:start position:0%
+um in a crucial way this the fact that
+ 
+
+ align:start position:0%
+um in a crucial way this the fact that
+this uh sequence is monotonic increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to prove this claim let epsilon be
+
+ align:start position:0%
+so to prove this claim let epsilon be
+ 
+
+ align:start position:0%
+so to prove this claim let epsilon be
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since x minus epsilon is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an upper bound for
+
+ align:start position:0%
+an upper bound for
+ 
+
+ align:start position:0%
+an upper bound for
+this set x sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists an m naught
+
+ align:start position:0%
+there exists an m naught
+ 
+
+ align:start position:0%
+there exists an m naught
+natural number so that
+
+ align:start position:0%
+natural number so that
+ 
+
+ align:start position:0%
+natural number so that
+x of n minus epsilon is less than x sub
+
+ align:start position:0%
+x of n minus epsilon is less than x sub
+ 
+
+ align:start position:0%
+x of n minus epsilon is less than x sub
+m naught
+
+ align:start position:0%
+m naught
+ 
+
+ align:start position:0%
+m naught
+is less than or equal to x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m to be this m naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+for all n bigger than or equal to m we
+
+ align:start position:0%
+for all n bigger than or equal to m we
+ 
+
+ align:start position:0%
+for all n bigger than or equal to m we
+have x sub n
+
+ align:start position:0%
+have x sub n
+ 
+
+ align:start position:0%
+have x sub n
+minus epsilon which is less than x sub
+
+ align:start position:0%
+minus epsilon which is less than x sub
+ 
+
+ align:start position:0%
+minus epsilon which is less than x sub
+m naught and because n is bigger than or
+
+ align:start position:0%
+m naught and because n is bigger than or
+ 
+
+ align:start position:0%
+m naught and because n is bigger than or
+equal to capital m and this is a
+
+ align:start position:0%
+equal to capital m and this is a
+ 
+
+ align:start position:0%
+equal to capital m and this is a
+monotone increasing sequence x sub m
+
+ align:start position:0%
+monotone increasing sequence x sub m
+ 
+
+ align:start position:0%
+monotone increasing sequence x sub m
+naught is less than or equal to x sub n
+
+ align:start position:0%
+naught is less than or equal to x sub n
+ 
+
+ align:start position:0%
+naught is less than or equal to x sub n
+and because x is a supremum of
+
+ align:start position:0%
+and because x is a supremum of
+ 
+
+ align:start position:0%
+and because x is a supremum of
+of um
+
+ align:start position:0%
+of um
+ 
+
+ align:start position:0%
+of um
+the set of all entries of this sequence
+
+ align:start position:0%
+the set of all entries of this sequence
+ 
+
+ align:start position:0%
+the set of all entries of this sequence
+this is less than or equal to x
+
+ align:start position:0%
+this is less than or equal to x
+ 
+
+ align:start position:0%
+this is less than or equal to x
+which is less than
+
+ align:start position:0%
+which is less than
+ 
+
+ align:start position:0%
+which is less than
+x plus epsilon
+
+ align:start position:0%
+x plus epsilon
+ 
+
+ align:start position:0%
+x plus epsilon
+or to summarize so this should not be x
+
+ align:start position:0%
+or to summarize so this should not be x
+ 
+
+ align:start position:0%
+or to summarize so this should not be x
+sub n that should be x minus epsilon
+
+ align:start position:0%
+sub n that should be x minus epsilon
+ 
+
+ align:start position:0%
+sub n that should be x minus epsilon
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+x minus epsilon is less than x of n is
+
+ align:start position:0%
+x minus epsilon is less than x of n is
+ 
+
+ align:start position:0%
+x minus epsilon is less than x of n is
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+x plus epsilon and that's the same as
+
+ align:start position:0%
+x plus epsilon and that's the same as
+ 
+
+ align:start position:0%
+x plus epsilon and that's the same as
+showing the absolute value of x of n
+
+ align:start position:0%
+showing the absolute value of x of n
+ 
+
+ align:start position:0%
+showing the absolute value of x of n
+minus x is less than epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now what's the change for
+
+ align:start position:0%
+now what's the change for
+ 
+
+ align:start position:0%
+now what's the change for
+monotone decreasing is that
+
+ align:start position:0%
+monotone decreasing is that
+ 
+
+ align:start position:0%
+monotone decreasing is that
+we'll be able to identify
+
+ align:start position:0%
+we'll be able to identify
+ 
+
+ align:start position:0%
+we'll be able to identify
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+limit of the sequence as being the imph
+
+ align:start position:0%
+limit of the sequence as being the imph
+ 
+
+ align:start position:0%
+limit of the sequence as being the imph
+the enthemum of this set
+
+ align:start position:0%
+the enthemum of this set
+ 
+
+ align:start position:0%
+the enthemum of this set
+all right but i'll leave that to you as
+
+ align:start position:0%
+all right but i'll leave that to you as
+ 
+
+ align:start position:0%
+all right but i'll leave that to you as
+an exercise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's use this real quick to uh prove
+
+ align:start position:0%
+so let's use this real quick to uh prove
+ 
+
+ align:start position:0%
+so let's use this real quick to uh prove
+the limit of a
+
+ align:start position:0%
+the limit of a
+ 
+
+ align:start position:0%
+the limit of a
+little bit more interesting sequence
+
+ align:start position:0%
+little bit more interesting sequence
+ 
+
+ align:start position:0%
+little bit more interesting sequence
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+you know one over
+
+ align:start position:0%
+you know one over
+ 
+
+ align:start position:0%
+you know one over
+this one which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's reasonably interesting i guess but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know typically in math we just don't
+
+ align:start position:0%
+you know typically in math we just don't
+ 
+
+ align:start position:0%
+you know typically in math we just don't
+prove
+
+ align:start position:0%
+prove
+ 
+
+ align:start position:0%
+prove
+theorems for the sake of proving
+
+ align:start position:0%
+theorems for the sake of proving
+ 
+
+ align:start position:0%
+theorems for the sake of proving
+theorems
+
+ align:start position:0%
+theorems
+ 
+
+ align:start position:0%
+theorems
+typically there's some concrete
+
+ align:start position:0%
+typically there's some concrete
+ 
+
+ align:start position:0%
+typically there's some concrete
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+reason we do things
+
+ align:start position:0%
+reason we do things
+ 
+
+ align:start position:0%
+reason we do things
+there's some concrete sequence we're
+
+ align:start position:0%
+there's some concrete sequence we're
+ 
+
+ align:start position:0%
+there's some concrete sequence we're
+trying to prove converges or
+
+ align:start position:0%
+trying to prove converges or
+ 
+
+ align:start position:0%
+trying to prove converges or
+has a certain property
+
+ align:start position:0%
+has a certain property
+ 
+
+ align:start position:0%
+has a certain property
+or doesn't have a certain property
+
+ align:start position:0%
+or doesn't have a certain property
+ 
+
+ align:start position:0%
+or doesn't have a certain property
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so kind of the basic one is
+
+ align:start position:0%
+so kind of the basic one is
+ 
+
+ align:start position:0%
+so kind of the basic one is
+if you like a geometric sequence so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a positive number between zero and
+
+ align:start position:0%
+is a positive number between zero and
+ 
+
+ align:start position:0%
+is a positive number between zero and
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we'll prove that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this sequence c to the n is convergent
+
+ align:start position:0%
+this sequence c to the n is convergent
+ 
+
+ align:start position:0%
+this sequence c to the n is convergent
+and it converges to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll prove as c if c is bigger than
+
+ align:start position:0%
+and we'll prove as c if c is bigger than
+ 
+
+ align:start position:0%
+and we'll prove as c if c is bigger than
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the sequence c to the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is unbounded in particular it can't
+
+ align:start position:0%
+is unbounded in particular it can't
+ 
+
+ align:start position:0%
+is unbounded in particular it can't
+converge
+
+ align:start position:0%
+converge
+ 
+
+ align:start position:0%
+converge
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's do um
+
+ align:start position:0%
+so let's do um
+ 
+
+ align:start position:0%
+so let's do um
+let's go in reverse order let's prove
+
+ align:start position:0%
+let's go in reverse order let's prove
+ 
+
+ align:start position:0%
+let's go in reverse order let's prove
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+if c is bigger than one then this thing
+
+ align:start position:0%
+if c is bigger than one then this thing
+ 
+
+ align:start position:0%
+if c is bigger than one then this thing
+is unbounded
+
+ align:start position:0%
+is unbounded
+ 
+
+ align:start position:0%
+is unbounded
+it doesn't require one but it's shorter
+
+ align:start position:0%
+it doesn't require one but it's shorter
+ 
+
+ align:start position:0%
+it doesn't require one but it's shorter
+than one and we can go ahead and do it
+
+ align:start position:0%
+than one and we can go ahead and do it
+ 
+
+ align:start position:0%
+than one and we can go ahead and do it
+um and we'll use this fact that we
+
+ align:start position:0%
+um and we'll use this fact that we
+ 
+
+ align:start position:0%
+um and we'll use this fact that we
+proved um i think in the first lecture
+
+ align:start position:0%
+proved um i think in the first lecture
+ 
+
+ align:start position:0%
+proved um i think in the first lecture
+uh or first or second lecture using
+
+ align:start position:0%
+uh or first or second lecture using
+ 
+
+ align:start position:0%
+uh or first or second lecture using
+induction
+
+ align:start position:0%
+induction
+ 
+
+ align:start position:0%
+induction
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what does it mean to show something is
+
+ align:start position:0%
+what does it mean to show something is
+ 
+
+ align:start position:0%
+what does it mean to show something is
+unbounded again we get to use our
+
+ align:start position:0%
+unbounded again we get to use our
+ 
+
+ align:start position:0%
+unbounded again we get to use our
+negation skills
+
+ align:start position:0%
+negation skills
+ 
+
+ align:start position:0%
+negation skills
+it means that so what do we want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+uh b
+
+ align:start position:0%
+uh b
+ 
+
+ align:start position:0%
+uh b
+bigger than or equal to zero
+
+ align:start position:0%
+bigger than or equal to zero
+ 
+
+ align:start position:0%
+bigger than or equal to zero
+there exist an n
+
+ align:start position:0%
+there exist an n
+ 
+
+ align:start position:0%
+there exist an n
+natural number
+
+ align:start position:0%
+natural number
+ 
+
+ align:start position:0%
+natural number
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+c to the n is
+
+ align:start position:0%
+c to the n is
+ 
+
+ align:start position:0%
+c to the n is
+bigger than b
+
+ align:start position:0%
+bigger than b
+ 
+
+ align:start position:0%
+bigger than b
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now how are we going to find this
+
+ align:start position:0%
+okay now how are we going to find this
+ 
+
+ align:start position:0%
+okay now how are we going to find this
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+this seems like a complicated thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's replace it by something simpler
+
+ align:start position:0%
+let's replace it by something simpler
+ 
+
+ align:start position:0%
+let's replace it by something simpler
+again this is analysis which means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get to use our wits and try to
+
+ align:start position:0%
+we get to use our wits and try to
+ 
+
+ align:start position:0%
+we get to use our wits and try to
+replace complicated things by simpler
+
+ align:start position:0%
+replace complicated things by simpler
+ 
+
+ align:start position:0%
+replace complicated things by simpler
+things and work with the simpler things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me do a little bit of again this
+
+ align:start position:0%
+so let me do a little bit of again this
+ 
+
+ align:start position:0%
+so let me do a little bit of again this
+is off to the side kind of how would one
+
+ align:start position:0%
+is off to the side kind of how would one
+ 
+
+ align:start position:0%
+is off to the side kind of how would one
+thing through this
+
+ align:start position:0%
+thing through this
+ 
+
+ align:start position:0%
+thing through this
+if you look at c to the n remember we
+
+ align:start position:0%
+if you look at c to the n remember we
+ 
+
+ align:start position:0%
+if you look at c to the n remember we
+have this inequality from
+
+ align:start position:0%
+have this inequality from
+ 
+
+ align:start position:0%
+have this inequality from
+uh infinite time ago that
+
+ align:start position:0%
+uh infinite time ago that
+ 
+
+ align:start position:0%
+uh infinite time ago that
+one that as long as x is bigger than or
+
+ align:start position:0%
+one that as long as x is bigger than or
+ 
+
+ align:start position:0%
+one that as long as x is bigger than or
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus 1 then i get 1 plus x to the n
+
+ align:start position:0%
+minus 1 then i get 1 plus x to the n
+ 
+
+ align:start position:0%
+minus 1 then i get 1 plus x to the n
+is bigger than 1 plus n times x
+
+ align:start position:0%
+is bigger than 1 plus n times x
+ 
+
+ align:start position:0%
+is bigger than 1 plus n times x
+okay for all natural numbers n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that means c to the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is equal to 1 plus c minus 1
+
+ align:start position:0%
+which is equal to 1 plus c minus 1
+ 
+
+ align:start position:0%
+which is equal to 1 plus c minus 1
+to the n so this is my x is bigger than
+
+ align:start position:0%
+to the n so this is my x is bigger than
+ 
+
+ align:start position:0%
+to the n so this is my x is bigger than
+or equal to
+
+ align:start position:0%
+or equal to
+ 
+
+ align:start position:0%
+or equal to
+1 plus n times c minus 1
+
+ align:start position:0%
+1 plus n times c minus 1
+ 
+
+ align:start position:0%
+1 plus n times c minus 1
+which is bigger than or equal to n times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c minus 1.
+
+ align:start position:0%
+c minus 1.
+ 
+
+ align:start position:0%
+c minus 1.
+you see so if i want to make if i want
+
+ align:start position:0%
+you see so if i want to make if i want
+ 
+
+ align:start position:0%
+you see so if i want to make if i want
+to make this big it suffices to make
+
+ align:start position:0%
+to make this big it suffices to make
+ 
+
+ align:start position:0%
+to make this big it suffices to make
+this big
+
+ align:start position:0%
+this big
+ 
+
+ align:start position:0%
+this big
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's how that's what i'll do
+
+ align:start position:0%
+so that's how that's what i'll do
+ 
+
+ align:start position:0%
+so that's how that's what i'll do
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let n be a natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+n is bigger than
+
+ align:start position:0%
+n is bigger than
+ 
+
+ align:start position:0%
+n is bigger than
+b over c minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then now this we did off to the side
+
+ align:start position:0%
+then now this we did off to the side
+ 
+
+ align:start position:0%
+then now this we did off to the side
+we'll just put in the proof now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and c to the n equals 1 plus
+
+ align:start position:0%
+and c to the n equals 1 plus
+ 
+
+ align:start position:0%
+and c to the n equals 1 plus
+1 minus c
+
+ align:start position:0%
+1 minus c
+ 
+
+ align:start position:0%
+1 minus c
+to the n
+
+ align:start position:0%
+to the n
+ 
+
+ align:start position:0%
+to the n
+is bigger than or equal to 1 plus n
+
+ align:start position:0%
+is bigger than or equal to 1 plus n
+ 
+
+ align:start position:0%
+is bigger than or equal to 1 plus n
+times c minus 1 which is bigger than or
+
+ align:start position:0%
+times c minus 1 which is bigger than or
+ 
+
+ align:start position:0%
+times c minus 1 which is bigger than or
+equal to n
+
+ align:start position:0%
+equal to n
+ 
+
+ align:start position:0%
+equal to n
+times c minus 1 which is
+
+ align:start position:0%
+times c minus 1 which is
+ 
+
+ align:start position:0%
+times c minus 1 which is
+bigger than b
+
+ align:start position:0%
+bigger than b
+ 
+
+ align:start position:0%
+bigger than b
+over c minus 1 times c minus 1 equals b
+
+ align:start position:0%
+over c minus 1 times c minus 1 equals b
+ 
+
+ align:start position:0%
+over c minus 1 times c minus 1 equals b
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's prove uh
+
+ align:start position:0%
+okay so now let's prove uh
+ 
+
+ align:start position:0%
+okay so now let's prove uh
+the first claim that if c is between
+
+ align:start position:0%
+the first claim that if c is between
+ 
+
+ align:start position:0%
+the first claim that if c is between
+zero and one then the limit as n goes to
+
+ align:start position:0%
+zero and one then the limit as n goes to
+ 
+
+ align:start position:0%
+zero and one then the limit as n goes to
+infinity of c to the n equals zero
+
+ align:start position:0%
+infinity of c to the n equals zero
+ 
+
+ align:start position:0%
+infinity of c to the n equals zero
+so first i want to prove uh the
+
+ align:start position:0%
+so first i want to prove uh the
+ 
+
+ align:start position:0%
+so first i want to prove uh the
+following claim that we in fact have a
+
+ align:start position:0%
+following claim that we in fact have a
+ 
+
+ align:start position:0%
+following claim that we in fact have a
+decreasing sequence
+
+ align:start position:0%
+decreasing sequence
+ 
+
+ align:start position:0%
+decreasing sequence
+uh which is bounded below by
+
+ align:start position:0%
+uh which is bounded below by
+ 
+
+ align:start position:0%
+uh which is bounded below by
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+zero so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all n 0 is less than c to the n is
+
+ align:start position:0%
+for all n 0 is less than c to the n is
+ 
+
+ align:start position:0%
+for all n 0 is less than c to the n is
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+i should say c to the n plus 1
+
+ align:start position:0%
+i should say c to the n plus 1
+ 
+
+ align:start position:0%
+i should say c to the n plus 1
+is less than c to the n
+
+ align:start position:0%
+is less than c to the n
+ 
+
+ align:start position:0%
+is less than c to the n
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the proof of this claim is a very
+
+ align:start position:0%
+so the proof of this claim is a very
+ 
+
+ align:start position:0%
+so the proof of this claim is a very
+simple induction argument so we'll do
+
+ align:start position:0%
+simple induction argument so we'll do
+ 
+
+ align:start position:0%
+simple induction argument so we'll do
+this by induction so we have the base
+
+ align:start position:0%
+this by induction so we have the base
+ 
+
+ align:start position:0%
+this by induction so we have the base
+case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n equals one
+
+ align:start position:0%
+n equals one
+ 
+
+ align:start position:0%
+n equals one
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we are assuming that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c is between zero and one
+
+ align:start position:0%
+c is between zero and one
+ 
+
+ align:start position:0%
+c is between zero and one
+and if i multiply through by c
+
+ align:start position:0%
+and if i multiply through by c
+ 
+
+ align:start position:0%
+and if i multiply through by c
+i conclude that zero is less than c
+
+ align:start position:0%
+i conclude that zero is less than c
+ 
+
+ align:start position:0%
+i conclude that zero is less than c
+squared is less than c
+
+ align:start position:0%
+squared is less than c
+ 
+
+ align:start position:0%
+squared is less than c
+and that's the n equals one case
+
+ align:start position:0%
+and that's the n equals one case
+ 
+
+ align:start position:0%
+and that's the n equals one case
+and the inductive step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean is essentially the same proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 is less than c
+
+ align:start position:0%
+0 is less than c
+ 
+
+ align:start position:0%
+0 is less than c
+to the n plus 1 is less than c to the m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then multiplying through by c
+
+ align:start position:0%
+then multiplying through by c
+ 
+
+ align:start position:0%
+then multiplying through by c
+we get that
+
+ align:start position:0%
+we get that
+ 
+
+ align:start position:0%
+we get that
+0 is less than c to the m
+
+ align:start position:0%
+0 is less than c to the m
+ 
+
+ align:start position:0%
+0 is less than c to the m
+plus 2 is less than
+
+ align:start position:0%
+plus 2 is less than
+ 
+
+ align:start position:0%
+plus 2 is less than
+c to the n plus one which is n equals n
+
+ align:start position:0%
+c to the n plus one which is n equals n
+ 
+
+ align:start position:0%
+c to the n plus one which is n equals n
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+okay here we're using
+
+ align:start position:0%
+okay here we're using
+ 
+
+ align:start position:0%
+okay here we're using
+uh this fact here okay that c is
+
+ align:start position:0%
+uh this fact here okay that c is
+ 
+
+ align:start position:0%
+uh this fact here okay that c is
+positive so it doesn't flip the
+
+ align:start position:0%
+positive so it doesn't flip the
+ 
+
+ align:start position:0%
+positive so it doesn't flip the
+inequalities
+
+ align:start position:0%
+inequalities
+ 
+
+ align:start position:0%
+inequalities
+so i can multiply through and preserve
+
+ align:start position:0%
+so i can multiply through and preserve
+ 
+
+ align:start position:0%
+so i can multiply through and preserve
+the inequalities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+this shows that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this sequence is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monotone
+
+ align:start position:0%
+monotone
+ 
+
+ align:start position:0%
+monotone
+decreasing and it's bounded below by
+
+ align:start position:0%
+decreasing and it's bounded below by
+ 
+
+ align:start position:0%
+decreasing and it's bounded below by
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+and in fact bounded because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because c to the n an absolute value
+
+ align:start position:0%
+because c to the n an absolute value
+ 
+
+ align:start position:0%
+because c to the n an absolute value
+these are all positive it's equal to c
+
+ align:start position:0%
+these are all positive it's equal to c
+ 
+
+ align:start position:0%
+these are all positive it's equal to c
+to the n
+
+ align:start position:0%
+to the n
+ 
+
+ align:start position:0%
+to the n
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+c to the n is less than c to the n minus
+
+ align:start position:0%
+c to the n is less than c to the n minus
+ 
+
+ align:start position:0%
+c to the n is less than c to the n minus
+1 which is less than c to the n minus 2
+
+ align:start position:0%
+1 which is less than c to the n minus 2
+ 
+
+ align:start position:0%
+1 which is less than c to the n minus 2
+so on and so on
+
+ align:start position:0%
+so on and so on
+ 
+
+ align:start position:0%
+so on and so on
+which is less than c
+
+ align:start position:0%
+which is less than c
+ 
+
+ align:start position:0%
+which is less than c
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh it's bounded
+
+ align:start position:0%
+uh it's bounded
+ 
+
+ align:start position:0%
+uh it's bounded
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i guess i could have built that into
+
+ align:start position:0%
+i guess i could have built that into
+ 
+
+ align:start position:0%
+i guess i could have built that into
+this inequality and proved that as well
+
+ align:start position:0%
+this inequality and proved that as well
+ 
+
+ align:start position:0%
+this inequality and proved that as well
+but um that's okay
+
+ align:start position:0%
+but um that's okay
+ 
+
+ align:start position:0%
+but um that's okay
+so it has a limit so by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the previous theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a limit
+
+ align:start position:0%
+has a limit
+ 
+
+ align:start position:0%
+has a limit
+and i'll call it l
+
+ align:start position:0%
+and i'll call it l
+ 
+
+ align:start position:0%
+and i'll call it l
+and now what i want to show is that l is
+
+ align:start position:0%
+and now what i want to show is that l is
+ 
+
+ align:start position:0%
+and now what i want to show is that l is
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how we'll do that is
+
+ align:start position:0%
+and how we'll do that is
+ 
+
+ align:start position:0%
+and how we'll do that is
+um one of uh
+
+ align:start position:0%
+um one of uh
+ 
+
+ align:start position:0%
+um one of uh
+these analysis tricks where are not
+
+ align:start position:0%
+these analysis tricks where are not
+ 
+
+ align:start position:0%
+these analysis tricks where are not
+really tricks but rather than show is l
+
+ align:start position:0%
+really tricks but rather than show is l
+ 
+
+ align:start position:0%
+really tricks but rather than show is l
+is directly equal to 0 we'll show that
+
+ align:start position:0%
+is directly equal to 0 we'll show that
+ 
+
+ align:start position:0%
+is directly equal to 0 we'll show that
+the absolute value of l is less than
+
+ align:start position:0%
+the absolute value of l is less than
+ 
+
+ align:start position:0%
+the absolute value of l is less than
+epsilon for every epsilon positive and
+
+ align:start position:0%
+epsilon for every epsilon positive and
+ 
+
+ align:start position:0%
+epsilon for every epsilon positive and
+therefore it has to be zero because it's
+
+ align:start position:0%
+therefore it has to be zero because it's
+ 
+
+ align:start position:0%
+therefore it has to be zero because it's
+just a fixed number
+
+ align:start position:0%
+just a fixed number
+ 
+
+ align:start position:0%
+just a fixed number
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let epsilon be positive again we're
+
+ align:start position:0%
+so let epsilon be positive again we're
+ 
+
+ align:start position:0%
+so let epsilon be positive again we're
+going to show that the absolute value of
+
+ align:start position:0%
+going to show that the absolute value of
+ 
+
+ align:start position:0%
+going to show that the absolute value of
+l which is just a fixed number is less
+
+ align:start position:0%
+l which is just a fixed number is less
+ 
+
+ align:start position:0%
+l which is just a fixed number is less
+than epsilon
+
+ align:start position:0%
+than epsilon
+ 
+
+ align:start position:0%
+than epsilon
+and therefore capital
+
+ align:start position:0%
+and therefore capital
+ 
+
+ align:start position:0%
+and therefore capital
+l has to be zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+since this sequence converges
+
+ align:start position:0%
+since this sequence converges
+ 
+
+ align:start position:0%
+since this sequence converges
+an m a natural number
+
+ align:start position:0%
+an m a natural number
+ 
+
+ align:start position:0%
+an m a natural number
+such that for all n
+
+ align:start position:0%
+such that for all n
+ 
+
+ align:start position:0%
+such that for all n
+bigger than or equal to capital m
+
+ align:start position:0%
+bigger than or equal to capital m
+ 
+
+ align:start position:0%
+bigger than or equal to capital m
+c to the n minus l
+
+ align:start position:0%
+c to the n minus l
+ 
+
+ align:start position:0%
+c to the n minus l
+is less than
+
+ align:start position:0%
+is less than
+ 
+
+ align:start position:0%
+is less than
+1 minus c times epsilon
+
+ align:start position:0%
+1 minus c times epsilon
+ 
+
+ align:start position:0%
+1 minus c times epsilon
+over 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now maybe you're wondering
+
+ align:start position:0%
+now maybe you're wondering
+ 
+
+ align:start position:0%
+now maybe you're wondering
+why i chose uh why why didn't i just use
+
+ align:start position:0%
+why i chose uh why why didn't i just use
+ 
+
+ align:start position:0%
+why i chose uh why why didn't i just use
+epsilon here well in the end
+
+ align:start position:0%
+epsilon here well in the end
+ 
+
+ align:start position:0%
+epsilon here well in the end
+it's just going to come out to
+
+ align:start position:0%
+it's just going to come out to
+ 
+
+ align:start position:0%
+it's just going to come out to
+this being less than epsilon an absolute
+
+ align:start position:0%
+this being less than epsilon an absolute
+ 
+
+ align:start position:0%
+this being less than epsilon an absolute
+value otherwise i would have come out
+
+ align:start position:0%
+value otherwise i would have come out
+ 
+
+ align:start position:0%
+value otherwise i would have come out
+with less than epsilon times some number
+
+ align:start position:0%
+with less than epsilon times some number
+ 
+
+ align:start position:0%
+with less than epsilon times some number
+and i did away with that number by
+
+ align:start position:0%
+and i did away with that number by
+ 
+
+ align:start position:0%
+and i did away with that number by
+choosing a different number here
+
+ align:start position:0%
+choosing a different number here
+ 
+
+ align:start position:0%
+choosing a different number here
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now we compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if i look at
+
+ align:start position:0%
+that if i look at
+ 
+
+ align:start position:0%
+that if i look at
+1 minus c times the absolute value of l
+
+ align:start position:0%
+1 minus c times the absolute value of l
+ 
+
+ align:start position:0%
+1 minus c times the absolute value of l
+this is equal to l minus c times l
+
+ align:start position:0%
+this is equal to l minus c times l
+ 
+
+ align:start position:0%
+this is equal to l minus c times l
+and this is less than or equal to
+
+ align:start position:0%
+and this is less than or equal to
+ 
+
+ align:start position:0%
+and this is less than or equal to
+l minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c to the capital m
+
+ align:start position:0%
+c to the capital m
+ 
+
+ align:start position:0%
+c to the capital m
+plus uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's put a plus one plus c to the m
+
+ align:start position:0%
+let's put a plus one plus c to the m
+ 
+
+ align:start position:0%
+let's put a plus one plus c to the m
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+minus c to the l
+
+ align:start position:0%
+minus c to the l
+ 
+
+ align:start position:0%
+minus c to the l
+and by the triangle inequality this is
+
+ align:start position:0%
+and by the triangle inequality this is
+ 
+
+ align:start position:0%
+and by the triangle inequality this is
+less than or equal to l minus c to the
+
+ align:start position:0%
+less than or equal to l minus c to the
+ 
+
+ align:start position:0%
+less than or equal to l minus c to the
+n plus one plus
+
+ align:start position:0%
+n plus one plus
+ 
+
+ align:start position:0%
+n plus one plus
+now c to the n plus 1 minus c to the l
+
+ align:start position:0%
+now c to the n plus 1 minus c to the l
+ 
+
+ align:start position:0%
+now c to the n plus 1 minus c to the l
+so i can pull out a c which is positive
+
+ align:start position:0%
+so i can pull out a c which is positive
+ 
+
+ align:start position:0%
+so i can pull out a c which is positive
+so i can get
+
+ align:start position:0%
+so i can get
+ 
+
+ align:start position:0%
+so i can get
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+n plus 1 is bigger than m
+
+ align:start position:0%
+n plus 1 is bigger than m
+ 
+
+ align:start position:0%
+n plus 1 is bigger than m
+so it satisfies this inequality
+
+ align:start position:0%
+so it satisfies this inequality
+ 
+
+ align:start position:0%
+so it satisfies this inequality
+and so does this one
+
+ align:start position:0%
+and so does this one
+ 
+
+ align:start position:0%
+and so does this one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and therefore this is less than
+
+ align:start position:0%
+and therefore this is less than
+ 
+
+ align:start position:0%
+and therefore this is less than
+epsilon over two times one minus c
+
+ align:start position:0%
+epsilon over two times one minus c
+ 
+
+ align:start position:0%
+epsilon over two times one minus c
+plus c times
+
+ align:start position:0%
+plus c times
+ 
+
+ align:start position:0%
+plus c times
+epsilon over two times one minus c and
+
+ align:start position:0%
+epsilon over two times one minus c and
+ 
+
+ align:start position:0%
+epsilon over two times one minus c and
+this is less than so c is less than 1 so
+
+ align:start position:0%
+this is less than so c is less than 1 so
+ 
+
+ align:start position:0%
+this is less than so c is less than 1 so
+this whole thing is less than epsilon
+
+ align:start position:0%
+this whole thing is less than epsilon
+ 
+
+ align:start position:0%
+this whole thing is less than epsilon
+over 2 times 1 minus c plus another
+
+ align:start position:0%
+over 2 times 1 minus c plus another
+ 
+
+ align:start position:0%
+over 2 times 1 minus c plus another
+epsilon over 2 so i get epsilon over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times 1 minus c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and thus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the absolute value of l is less than
+
+ align:start position:0%
+the absolute value of l is less than
+ 
+
+ align:start position:0%
+the absolute value of l is less than
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+and since epsilon was arbitrary that
+
+ align:start position:0%
+and since epsilon was arbitrary that
+ 
+
+ align:start position:0%
+and since epsilon was arbitrary that
+implies the absolute value of l is equal
+
+ align:start position:0%
+implies the absolute value of l is equal
+ 
+
+ align:start position:0%
+implies the absolute value of l is equal
+to zero ie
+
+ align:start position:0%
+to zero ie
+ 
+
+ align:start position:0%
+to zero ie
+l is equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's a
+
+ align:start position:0%
+okay so that's a
+ 
+
+ align:start position:0%
+okay so that's a
+very concrete
+
+ align:start position:0%
+very concrete
+ 
+
+ align:start position:0%
+very concrete
+um application of some of these theorems
+
+ align:start position:0%
+um application of some of these theorems
+ 
+
+ align:start position:0%
+um application of some of these theorems
+we've been proving which is really
+
+ align:start position:0%
+we've been proving which is really
+ 
+
+ align:start position:0%
+we've been proving which is really
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+i think the only real reason one proves
+
+ align:start position:0%
+i think the only real reason one proves
+ 
+
+ align:start position:0%
+i think the only real reason one proves
+theorems is
+
+ align:start position:0%
+theorems is
+ 
+
+ align:start position:0%
+theorems is
+you typically have a
+
+ align:start position:0%
+you typically have a
+ 
+
+ align:start position:0%
+you typically have a
+concrete
+
+ align:start position:0%
+concrete
+ 
+
+ align:start position:0%
+concrete
+example of something in mind that you
+
+ align:start position:0%
+example of something in mind that you
+ 
+
+ align:start position:0%
+example of something in mind that you
+want to study
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in order to study it
+
+ align:start position:0%
+but in order to study it
+ 
+
+ align:start position:0%
+but in order to study it
+often requires some
+
+ align:start position:0%
+often requires some
+ 
+
+ align:start position:0%
+often requires some
+general machinery
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i.e theorems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so now we'll
+
+ align:start position:0%
+all right so now we'll
+ 
+
+ align:start position:0%
+all right so now we'll
+talk a little bit about sequences
+
+ align:start position:0%
+talk a little bit about sequences
+ 
+
+ align:start position:0%
+talk a little bit about sequences
+obtained from
+
+ align:start position:0%
+obtained from
+ 
+
+ align:start position:0%
+obtained from
+other sequences um
+
+ align:start position:0%
+other sequences um
+ 
+
+ align:start position:0%
+other sequences um
+so these are called subsequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or sequence is obtained from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a single sequence
+
+ align:start position:0%
+a single sequence
+ 
+
+ align:start position:0%
+a single sequence
+so what do i mean by this let me give
+
+ align:start position:0%
+so what do i mean by this let me give
+ 
+
+ align:start position:0%
+so what do i mean by this let me give
+you the the precise definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we start off with
+
+ align:start position:0%
+so we start off with
+ 
+
+ align:start position:0%
+so we start off with
+a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a increasing sequence of integers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n sub k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me just say what what this means
+
+ align:start position:0%
+let me just say what what this means
+ 
+
+ align:start position:0%
+let me just say what what this means
+rather than write out the word and then
+
+ align:start position:0%
+rather than write out the word and then
+ 
+
+ align:start position:0%
+rather than write out the word and then
+say what it means
+
+ align:start position:0%
+say what it means
+ 
+
+ align:start position:0%
+say what it means
+so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sequence of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+natural numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which are strictly increasing n sub 1 is
+
+ align:start position:0%
+which are strictly increasing n sub 1 is
+ 
+
+ align:start position:0%
+which are strictly increasing n sub 1 is
+less than n sub 2 is less than n sub 3
+
+ align:start position:0%
+less than n sub 2 is less than n sub 3
+ 
+
+ align:start position:0%
+less than n sub 2 is less than n sub 3
+and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the new sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x sub
+
+ align:start position:0%
+x sub
+ 
+
+ align:start position:0%
+x sub
+n sub k so now the index is not n
+
+ align:start position:0%
+n sub k so now the index is not n
+ 
+
+ align:start position:0%
+n sub k so now the index is not n
+but the index is k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is called a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the original sequence x sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so how should you view
+
+ align:start position:0%
+all right so how should you view
+ 
+
+ align:start position:0%
+all right so how should you view
+subsequences of a sequence
+
+ align:start position:0%
+subsequences of a sequence
+ 
+
+ align:start position:0%
+subsequences of a sequence
+you should think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that i line up all the entries of x of
+
+ align:start position:0%
+that i line up all the entries of x of
+ 
+
+ align:start position:0%
+that i line up all the entries of x of
+my original sequence x sub n
+
+ align:start position:0%
+my original sequence x sub n
+ 
+
+ align:start position:0%
+my original sequence x sub n
+and then i just start
+
+ align:start position:0%
+and then i just start
+ 
+
+ align:start position:0%
+and then i just start
+uh picking entries
+
+ align:start position:0%
+uh picking entries
+ 
+
+ align:start position:0%
+uh picking entries
+out of the sequence so
+
+ align:start position:0%
+out of the sequence so
+ 
+
+ align:start position:0%
+out of the sequence so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but every time i make a choice i have to
+
+ align:start position:0%
+but every time i make a choice i have to
+ 
+
+ align:start position:0%
+but every time i make a choice i have to
+move to the right and make another
+
+ align:start position:0%
+move to the right and make another
+ 
+
+ align:start position:0%
+move to the right and make another
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+okay that's that's
+
+ align:start position:0%
+okay that's that's
+ 
+
+ align:start position:0%
+okay that's that's
+what i was just saying there expresses
+
+ align:start position:0%
+what i was just saying there expresses
+ 
+
+ align:start position:0%
+what i was just saying there expresses
+this condition that um
+
+ align:start position:0%
+this condition that um
+ 
+
+ align:start position:0%
+this condition that um
+this sequence of natural numbers is
+
+ align:start position:0%
+this sequence of natural numbers is
+ 
+
+ align:start position:0%
+this sequence of natural numbers is
+increasing so i pick an entry in the
+
+ align:start position:0%
+increasing so i pick an entry in the
+ 
+
+ align:start position:0%
+increasing so i pick an entry in the
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+that's going to be my first guy
+
+ align:start position:0%
+that's going to be my first guy
+ 
+
+ align:start position:0%
+that's going to be my first guy
+the first element of my new subsequence
+
+ align:start position:0%
+the first element of my new subsequence
+ 
+
+ align:start position:0%
+the first element of my new subsequence
+and then i move to the right
+
+ align:start position:0%
+and then i move to the right
+ 
+
+ align:start position:0%
+and then i move to the right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+maybe i pick the next one maybe i pick
+
+ align:start position:0%
+maybe i pick the next one maybe i pick
+ 
+
+ align:start position:0%
+maybe i pick the next one maybe i pick
+one three down i pick that one and then
+
+ align:start position:0%
+one three down i pick that one and then
+ 
+
+ align:start position:0%
+one three down i pick that one and then
+i move to the right of that one
+
+ align:start position:0%
+i move to the right of that one
+ 
+
+ align:start position:0%
+i move to the right of that one
+and pick a new one
+
+ align:start position:0%
+and pick a new one
+ 
+
+ align:start position:0%
+and pick a new one
+and then i move to the right of that one
+
+ align:start position:0%
+and then i move to the right of that one
+ 
+
+ align:start position:0%
+and then i move to the right of that one
+and pick another one
+
+ align:start position:0%
+and pick another one
+ 
+
+ align:start position:0%
+and pick another one
+okay so if you want to generate a
+
+ align:start position:0%
+okay so if you want to generate a
+ 
+
+ align:start position:0%
+okay so if you want to generate a
+subsequence from an original sequence
+
+ align:start position:0%
+subsequence from an original sequence
+ 
+
+ align:start position:0%
+subsequence from an original sequence
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+how do you think about this again line
+
+ align:start position:0%
+how do you think about this again line
+ 
+
+ align:start position:0%
+how do you think about this again line
+them all up start picking entries but
+
+ align:start position:0%
+them all up start picking entries but
+ 
+
+ align:start position:0%
+them all up start picking entries but
+every time you pick an entry you have to
+
+ align:start position:0%
+every time you pick an entry you have to
+ 
+
+ align:start position:0%
+every time you pick an entry you have to
+move to the right and pick in order to
+
+ align:start position:0%
+move to the right and pick in order to
+ 
+
+ align:start position:0%
+move to the right and pick in order to
+pick your next entry
+
+ align:start position:0%
+pick your next entry
+ 
+
+ align:start position:0%
+pick your next entry
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me give you some examples and
+
+ align:start position:0%
+so let me give you some examples and
+ 
+
+ align:start position:0%
+so let me give you some examples and
+non-examples
+
+ align:start position:0%
+non-examples
+ 
+
+ align:start position:0%
+non-examples
+so for example if
+
+ align:start position:0%
+so for example if
+ 
+
+ align:start position:0%
+so for example if
+our sequence our original sequence is
+
+ align:start position:0%
+our sequence our original sequence is
+ 
+
+ align:start position:0%
+our sequence our original sequence is
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+two three four five
+
+ align:start position:0%
+two three four five
+ 
+
+ align:start position:0%
+two three four five
+six
+
+ align:start position:0%
+six
+ 
+
+ align:start position:0%
+six
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+what would be examples of some
+
+ align:start position:0%
+what would be examples of some
+ 
+
+ align:start position:0%
+what would be examples of some
+subsequences
+
+ align:start position:0%
+subsequences
+ 
+
+ align:start position:0%
+subsequences
+the odd numbers 1 3
+
+ align:start position:0%
+the odd numbers 1 3
+ 
+
+ align:start position:0%
+the odd numbers 1 3
+five seven
+
+ align:start position:0%
+five seven
+ 
+
+ align:start position:0%
+five seven
+nine and so on
+
+ align:start position:0%
+nine and so on
+ 
+
+ align:start position:0%
+nine and so on
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you see how i'm taking the original
+
+ align:start position:0%
+you see how i'm taking the original
+ 
+
+ align:start position:0%
+you see how i'm taking the original
+sequence so this is
+
+ align:start position:0%
+sequence so this is
+ 
+
+ align:start position:0%
+sequence so this is
+x sub n i'm taking
+
+ align:start position:0%
+x sub n i'm taking
+ 
+
+ align:start position:0%
+x sub n i'm taking
+i'm just picking entries from the
+
+ align:start position:0%
+i'm just picking entries from the
+ 
+
+ align:start position:0%
+i'm just picking entries from the
+original sequence but every time i pick
+
+ align:start position:0%
+original sequence but every time i pick
+ 
+
+ align:start position:0%
+original sequence but every time i pick
+an entry i i move to the right and pick
+
+ align:start position:0%
+an entry i i move to the right and pick
+ 
+
+ align:start position:0%
+an entry i i move to the right and pick
+a new one so i picked one now i get to
+
+ align:start position:0%
+a new one so i picked one now i get to
+ 
+
+ align:start position:0%
+a new one so i picked one now i get to
+choose anything to the right of that i
+
+ align:start position:0%
+choose anything to the right of that i
+ 
+
+ align:start position:0%
+choose anything to the right of that i
+pick three now i have to choose i can
+
+ align:start position:0%
+pick three now i have to choose i can
+ 
+
+ align:start position:0%
+pick three now i have to choose i can
+choose anything to the right of that
+
+ align:start position:0%
+choose anything to the right of that
+ 
+
+ align:start position:0%
+choose anything to the right of that
+so in the language of this definition
+
+ align:start position:0%
+so in the language of this definition
+ 
+
+ align:start position:0%
+so in the language of this definition
+the increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence of integers is just the odd
+
+ align:start position:0%
+sequence of integers is just the odd
+ 
+
+ align:start position:0%
+sequence of integers is just the odd
+integers so
+
+ align:start position:0%
+integers so
+ 
+
+ align:start position:0%
+integers so
+2k minus 1. so here
+
+ align:start position:0%
+2k minus 1. so here
+ 
+
+ align:start position:0%
+2k minus 1. so here
+x of n is equal to just n
+
+ align:start position:0%
+x of n is equal to just n
+ 
+
+ align:start position:0%
+x of n is equal to just n
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i could pick
+
+ align:start position:0%
+i could pick
+ 
+
+ align:start position:0%
+i could pick
+another subsequence would be uh the
+
+ align:start position:0%
+another subsequence would be uh the
+ 
+
+ align:start position:0%
+another subsequence would be uh the
+sequence of even numbers 2 4 6
+
+ align:start position:0%
+sequence of even numbers 2 4 6
+ 
+
+ align:start position:0%
+sequence of even numbers 2 4 6
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+10.
+
+ align:start position:0%
+10.
+ 
+
+ align:start position:0%
+10.
+all right this is a subsequence of this
+
+ align:start position:0%
+all right this is a subsequence of this
+ 
+
+ align:start position:0%
+all right this is a subsequence of this
+original sequence here the increasing
+
+ align:start position:0%
+original sequence here the increasing
+ 
+
+ align:start position:0%
+original sequence here the increasing
+sequence of integers is 2k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i could pick uh
+
+ align:start position:0%
+i could pick uh
+ 
+
+ align:start position:0%
+i could pick uh
+the subsequence could be the sequence of
+
+ align:start position:0%
+the subsequence could be the sequence of
+ 
+
+ align:start position:0%
+the subsequence could be the sequence of
+prime numbers 2 3
+
+ align:start position:0%
+prime numbers 2 3
+ 
+
+ align:start position:0%
+prime numbers 2 3
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+7 11
+
+ align:start position:0%
+7 11
+ 
+
+ align:start position:0%
+7 11
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so i don't have a general formula
+
+ align:start position:0%
+yeah so i don't have a general formula
+ 
+
+ align:start position:0%
+yeah so i don't have a general formula
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+good luck finding one
+
+ align:start position:0%
+good luck finding one
+ 
+
+ align:start position:0%
+good luck finding one
+but we'll just write this as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kth prime number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what would
+
+ align:start position:0%
+now what would
+ 
+
+ align:start position:0%
+now what would
+not be an example so these are examples
+
+ align:start position:0%
+not be an example so these are examples
+ 
+
+ align:start position:0%
+not be an example so these are examples
+of subsequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not examples of subsequences would be
+
+ align:start position:0%
+not examples of subsequences would be
+ 
+
+ align:start position:0%
+not examples of subsequences would be
+for example the sequence 1 1 1 1
+
+ align:start position:0%
+for example the sequence 1 1 1 1
+ 
+
+ align:start position:0%
+for example the sequence 1 1 1 1
+1. this is not a subsequence of this
+
+ align:start position:0%
+1. this is not a subsequence of this
+ 
+
+ align:start position:0%
+1. this is not a subsequence of this
+original sequence okay
+
+ align:start position:0%
+original sequence okay
+ 
+
+ align:start position:0%
+original sequence okay
+remember i have i have a sequence of
+
+ align:start position:0%
+remember i have i have a sequence of
+ 
+
+ align:start position:0%
+remember i have i have a sequence of
+natural numbers which is increasing
+
+ align:start position:0%
+natural numbers which is increasing
+ 
+
+ align:start position:0%
+natural numbers which is increasing
+and x sub n sub k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means that this new sequence is obtained
+
+ align:start position:0%
+means that this new sequence is obtained
+ 
+
+ align:start position:0%
+means that this new sequence is obtained
+from the old one by picking entries by
+
+ align:start position:0%
+from the old one by picking entries by
+ 
+
+ align:start position:0%
+from the old one by picking entries by
+picking an entry moving to the right
+
+ align:start position:0%
+picking an entry moving to the right
+ 
+
+ align:start position:0%
+picking an entry moving to the right
+picking the next entry moving to the
+
+ align:start position:0%
+picking the next entry moving to the
+ 
+
+ align:start position:0%
+picking the next entry moving to the
+right and picking the next entry
+
+ align:start position:0%
+right and picking the next entry
+ 
+
+ align:start position:0%
+right and picking the next entry
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+in order to get this sequence from this
+
+ align:start position:0%
+in order to get this sequence from this
+ 
+
+ align:start position:0%
+in order to get this sequence from this
+one i just stay on the first entry and
+
+ align:start position:0%
+one i just stay on the first entry and
+ 
+
+ align:start position:0%
+one i just stay on the first entry and
+keep picking it but that's
+
+ align:start position:0%
+keep picking it but that's
+ 
+
+ align:start position:0%
+keep picking it but that's
+not how a subsequence is defined
+
+ align:start position:0%
+not how a subsequence is defined
+ 
+
+ align:start position:0%
+not how a subsequence is defined
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here if you like this would mean n
+
+ align:start position:0%
+so here if you like this would mean n
+ 
+
+ align:start position:0%
+so here if you like this would mean n
+sub k
+
+ align:start position:0%
+sub k
+ 
+
+ align:start position:0%
+sub k
+is equal to one
+
+ align:start position:0%
+is equal to one
+ 
+
+ align:start position:0%
+is equal to one
+for all k and this is not a strictly
+
+ align:start position:0%
+for all k and this is not a strictly
+ 
+
+ align:start position:0%
+for all k and this is not a strictly
+increasing sequence of natural numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh or one one
+
+ align:start position:0%
+uh or one one
+ 
+
+ align:start position:0%
+uh or one one
+three three
+
+ align:start position:0%
+three three
+ 
+
+ align:start position:0%
+three three
+five five and so on that's also not so
+
+ align:start position:0%
+five five and so on that's also not so
+ 
+
+ align:start position:0%
+five five and so on that's also not so
+these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+subsequences of the original sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i hope that's clear um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i'm not saying i want to emphasize this
+
+ align:start position:0%
+i'm not saying i want to emphasize this
+ 
+
+ align:start position:0%
+i'm not saying i want to emphasize this
+i'm not saying
+
+ align:start position:0%
+i'm not saying
+ 
+
+ align:start position:0%
+i'm not saying
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the number you pick
+
+ align:start position:0%
+the number you pick
+ 
+
+ align:start position:0%
+the number you pick
+time has to be different from the number
+
+ align:start position:0%
+time has to be different from the number
+ 
+
+ align:start position:0%
+time has to be different from the number
+you picked
+
+ align:start position:0%
+you picked
+ 
+
+ align:start position:0%
+you picked
+before meaning the value
+
+ align:start position:0%
+before meaning the value
+ 
+
+ align:start position:0%
+before meaning the value
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you couldn't have one one one one as
+
+ align:start position:0%
+you couldn't have one one one one as
+ 
+
+ align:start position:0%
+you couldn't have one one one one as
+a subsequence of this guy because one is
+
+ align:start position:0%
+a subsequence of this guy because one is
+ 
+
+ align:start position:0%
+a subsequence of this guy because one is
+only in the first entry you can't keep
+
+ align:start position:0%
+only in the first entry you can't keep
+ 
+
+ align:start position:0%
+only in the first entry you can't keep
+picking
+
+ align:start position:0%
+picking
+ 
+
+ align:start position:0%
+picking
+one entry you have to pick an entry and
+
+ align:start position:0%
+one entry you have to pick an entry and
+ 
+
+ align:start position:0%
+one entry you have to pick an entry and
+move to the next
+
+ align:start position:0%
+move to the next
+ 
+
+ align:start position:0%
+move to the next
+entry or the or one after that and pick
+
+ align:start position:0%
+entry or the or one after that and pick
+ 
+
+ align:start position:0%
+entry or the or one after that and pick
+that entry
+
+ align:start position:0%
+that entry
+ 
+
+ align:start position:0%
+that entry
+to obtain your sequence but that doesn't
+
+ align:start position:0%
+to obtain your sequence but that doesn't
+ 
+
+ align:start position:0%
+to obtain your sequence but that doesn't
+necessarily mean
+
+ align:start position:0%
+necessarily mean
+ 
+
+ align:start position:0%
+necessarily mean
+that those
+
+ align:start position:0%
+that those
+ 
+
+ align:start position:0%
+that those
+actual numbers in those entries have to
+
+ align:start position:0%
+actual numbers in those entries have to
+ 
+
+ align:start position:0%
+actual numbers in those entries have to
+be different so for example if i look at
+
+ align:start position:0%
+be different so for example if i look at
+ 
+
+ align:start position:0%
+be different so for example if i look at
+the sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus 1 1
+
+ align:start position:0%
+minus 1 1
+ 
+
+ align:start position:0%
+minus 1 1
+minus 1
+
+ align:start position:0%
+minus 1
+ 
+
+ align:start position:0%
+minus 1
+minus 1.
+
+ align:start position:0%
+minus 1.
+ 
+
+ align:start position:0%
+minus 1.
+1 meaning x of n is equal to minus 1 to
+
+ align:start position:0%
+1 meaning x of n is equal to minus 1 to
+ 
+
+ align:start position:0%
+1 meaning x of n is equal to minus 1 to
+the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then a perfectly good subsequence is
+
+ align:start position:0%
+then a perfectly good subsequence is
+ 
+
+ align:start position:0%
+then a perfectly good subsequence is
+given by
+
+ align:start position:0%
+given by
+ 
+
+ align:start position:0%
+given by
+minus 1 minus 1 minus 1
+
+ align:start position:0%
+minus 1 minus 1 minus 1
+ 
+
+ align:start position:0%
+minus 1 minus 1 minus 1
+minus one
+
+ align:start position:0%
+minus one
+ 
+
+ align:start position:0%
+minus one
+where okay so it looks like i'm just
+
+ align:start position:0%
+where okay so it looks like i'm just
+ 
+
+ align:start position:0%
+where okay so it looks like i'm just
+picking one of the entries but really
+
+ align:start position:0%
+picking one of the entries but really
+ 
+
+ align:start position:0%
+picking one of the entries but really
+i'm not here
+
+ align:start position:0%
+i'm not here
+ 
+
+ align:start position:0%
+i'm not here
+the increasing sequence of what i'm
+
+ align:start position:0%
+the increasing sequence of what i'm
+ 
+
+ align:start position:0%
+the increasing sequence of what i'm
+doing here to get this new sequence i
+
+ align:start position:0%
+doing here to get this new sequence i
+ 
+
+ align:start position:0%
+doing here to get this new sequence i
+pick the first entry then i pick the
+
+ align:start position:0%
+pick the first entry then i pick the
+ 
+
+ align:start position:0%
+pick the first entry then i pick the
+third then i pick the fifth then i pick
+
+ align:start position:0%
+third then i pick the fifth then i pick
+ 
+
+ align:start position:0%
+third then i pick the fifth then i pick
+the seventh so
+
+ align:start position:0%
+the seventh so
+ 
+
+ align:start position:0%
+the seventh so
+n sub k equals two k minus one
+
+ align:start position:0%
+n sub k equals two k minus one
+ 
+
+ align:start position:0%
+n sub k equals two k minus one
+all right so all the actual numbers
+
+ align:start position:0%
+all right so all the actual numbers
+ 
+
+ align:start position:0%
+all right so all the actual numbers
+appearing in the sequence are the same
+
+ align:start position:0%
+appearing in the sequence are the same
+ 
+
+ align:start position:0%
+appearing in the sequence are the same
+but i'm actually picking
+
+ align:start position:0%
+but i'm actually picking
+ 
+
+ align:start position:0%
+but i'm actually picking
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+entries from the original sequence
+
+ align:start position:0%
+entries from the original sequence
+ 
+
+ align:start position:0%
+entries from the original sequence
+all right where they appear so this is
+
+ align:start position:0%
+all right where they appear so this is
+ 
+
+ align:start position:0%
+all right where they appear so this is
+also fine so is one one one one one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is nk equals two times k so these
+
+ align:start position:0%
+this is nk equals two times k so these
+ 
+
+ align:start position:0%
+this is nk equals two times k so these
+are all good sub uh sub sequences so
+
+ align:start position:0%
+are all good sub uh sub sequences so
+ 
+
+ align:start position:0%
+are all good sub uh sub sequences so
+these were subsequences of
+
+ align:start position:0%
+these were subsequences of
+ 
+
+ align:start position:0%
+these were subsequences of
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+of the original sequence
+
+ align:start position:0%
+of the original sequence
+ 
+
+ align:start position:0%
+of the original sequence
+these are subsequences of
+
+ align:start position:0%
+these are subsequences of
+ 
+
+ align:start position:0%
+these are subsequences of
+uh this sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so from a given sequence we
+
+ align:start position:0%
+all right so from a given sequence we
+ 
+
+ align:start position:0%
+all right so from a given sequence we
+obtain
+
+ align:start position:0%
+obtain
+ 
+
+ align:start position:0%
+obtain
+a new we we can obtain new sequences
+
+ align:start position:0%
+a new we we can obtain new sequences
+ 
+
+ align:start position:0%
+a new we we can obtain new sequences
+from this uh original sequence
+
+ align:start position:0%
+from this uh original sequence
+ 
+
+ align:start position:0%
+from this uh original sequence
+in this way
+
+ align:start position:0%
+in this way
+ 
+
+ align:start position:0%
+in this way
+so a natural question is to ask
+
+ align:start position:0%
+so a natural question is to ask
+ 
+
+ align:start position:0%
+so a natural question is to ask
+how does
+
+ align:start position:0%
+how does
+ 
+
+ align:start position:0%
+how does
+going from a sequence to a subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know of not react but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behave with respect to limits okay if
+
+ align:start position:0%
+behave with respect to limits okay if
+ 
+
+ align:start position:0%
+behave with respect to limits okay if
+the original sequence converges to a
+
+ align:start position:0%
+the original sequence converges to a
+ 
+
+ align:start position:0%
+the original sequence converges to a
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+does a subsequence or does every
+
+ align:start position:0%
+does a subsequence or does every
+ 
+
+ align:start position:0%
+does a subsequence or does every
+subsequence converge to that limit as
+
+ align:start position:0%
+subsequence converge to that limit as
+ 
+
+ align:start position:0%
+subsequence converge to that limit as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+and this shouldn't come as a surprise
+
+ align:start position:0%
+and this shouldn't come as a surprise
+ 
+
+ align:start position:0%
+and this shouldn't come as a surprise
+that that it does because
+
+ align:start position:0%
+that that it does because
+ 
+
+ align:start position:0%
+that that it does because
+you know all of the elements of the
+
+ align:start position:0%
+you know all of the elements of the
+ 
+
+ align:start position:0%
+you know all of the elements of the
+sequence are getting close all the
+
+ align:start position:0%
+sequence are getting close all the
+ 
+
+ align:start position:0%
+sequence are getting close all the
+entries of the sequence are getting
+
+ align:start position:0%
+entries of the sequence are getting
+ 
+
+ align:start position:0%
+entries of the sequence are getting
+close to a given number
+
+ align:start position:0%
+close to a given number
+ 
+
+ align:start position:0%
+close to a given number
+and a subsequence is just if you like
+
+ align:start position:0%
+and a subsequence is just if you like
+ 
+
+ align:start position:0%
+and a subsequence is just if you like
+picking certain ones along the way
+
+ align:start position:0%
+picking certain ones along the way
+ 
+
+ align:start position:0%
+picking certain ones along the way
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+certainly if i'm in a subsequence then
+
+ align:start position:0%
+certainly if i'm in a subsequence then
+ 
+
+ align:start position:0%
+certainly if i'm in a subsequence then
+as long as i'm far enough out in the
+
+ align:start position:0%
+as long as i'm far enough out in the
+ 
+
+ align:start position:0%
+as long as i'm far enough out in the
+subsequence i'll be close to that limit
+
+ align:start position:0%
+subsequence i'll be close to that limit
+ 
+
+ align:start position:0%
+subsequence i'll be close to that limit
+as well all right so if you didn't get
+
+ align:start position:0%
+as well all right so if you didn't get
+ 
+
+ align:start position:0%
+as well all right so if you didn't get
+all that rambling um
+
+ align:start position:0%
+all that rambling um
+ 
+
+ align:start position:0%
+all that rambling um
+i'll
+
+ align:start position:0%
+i'll
+ 
+
+ align:start position:0%
+i'll
+go ahead and state the theorem and prove
+
+ align:start position:0%
+go ahead and state the theorem and prove
+ 
+
+ align:start position:0%
+go ahead and state the theorem and prove
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xn is a sequence which converges
+
+ align:start position:0%
+xn is a sequence which converges
+ 
+
+ align:start position:0%
+xn is a sequence which converges
+to x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and x of n sub k is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subsequence of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x of n
+
+ align:start position:0%
+x of n
+ 
+
+ align:start position:0%
+x of n
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh the subsequence converges to x as
+
+ align:start position:0%
+uh the subsequence converges to x as
+ 
+
+ align:start position:0%
+uh the subsequence converges to x as
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit as k goes to infinity of x sub n
+
+ align:start position:0%
+limit as k goes to infinity of x sub n
+ 
+
+ align:start position:0%
+limit as k goes to infinity of x sub n
+sub k
+
+ align:start position:0%
+sub k
+ 
+
+ align:start position:0%
+sub k
+equals x
+
+ align:start position:0%
+equals x
+ 
+
+ align:start position:0%
+equals x
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+um let me just start off by making a
+
+ align:start position:0%
+um let me just start off by making a
+ 
+
+ align:start position:0%
+um let me just start off by making a
+simple observation based on the fact
+
+ align:start position:0%
+simple observation based on the fact
+ 
+
+ align:start position:0%
+simple observation based on the fact
+that this increasing sequence
+
+ align:start position:0%
+that this increasing sequence
+ 
+
+ align:start position:0%
+that this increasing sequence
+that the n sub k's are an increasing
+
+ align:start position:0%
+that the n sub k's are an increasing
+ 
+
+ align:start position:0%
+that the n sub k's are an increasing
+sequence of natural numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n sub 1 is bigger than or equal to 1 is
+
+ align:start position:0%
+n sub 1 is bigger than or equal to 1 is
+ 
+
+ align:start position:0%
+n sub 1 is bigger than or equal to 1 is
+less than n sub 2 is less than n sub 3.
+
+ align:start position:0%
+less than n sub 2 is less than n sub 3.
+ 
+
+ align:start position:0%
+less than n sub 2 is less than n sub 3.
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+this implies that
+
+ align:start position:0%
+this implies that
+ 
+
+ align:start position:0%
+this implies that
+for all k
+
+ align:start position:0%
+for all k
+ 
+
+ align:start position:0%
+for all k
+natural number
+
+ align:start position:0%
+natural number
+ 
+
+ align:start position:0%
+natural number
+n sub k
+
+ align:start position:0%
+n sub k
+ 
+
+ align:start position:0%
+n sub k
+is bigger than or equal to k
+
+ align:start position:0%
+is bigger than or equal to k
+ 
+
+ align:start position:0%
+is bigger than or equal to k
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so this is not so hard to believe
+
+ align:start position:0%
+um so this is not so hard to believe
+ 
+
+ align:start position:0%
+um so this is not so hard to believe
+because n sub 1 has to be at least
+
+ align:start position:0%
+because n sub 1 has to be at least
+ 
+
+ align:start position:0%
+because n sub 1 has to be at least
+bigger than one n sub 2 has to be at
+
+ align:start position:0%
+bigger than one n sub 2 has to be at
+ 
+
+ align:start position:0%
+bigger than one n sub 2 has to be at
+least bigger than n sub 1 so it's either
+
+ align:start position:0%
+least bigger than n sub 1 so it's either
+ 
+
+ align:start position:0%
+least bigger than n sub 1 so it's either
+n sub 1 plus 1 or bigger
+
+ align:start position:0%
+n sub 1 plus 1 or bigger
+ 
+
+ align:start position:0%
+n sub 1 plus 1 or bigger
+and therefore you know you get by a
+
+ align:start position:0%
+and therefore you know you get by a
+ 
+
+ align:start position:0%
+and therefore you know you get by a
+simple induction argument which i'll
+
+ align:start position:0%
+simple induction argument which i'll
+ 
+
+ align:start position:0%
+simple induction argument which i'll
+leave to you you can prove that for all
+
+ align:start position:0%
+leave to you you can prove that for all
+ 
+
+ align:start position:0%
+leave to you you can prove that for all
+k a natural number
+
+ align:start position:0%
+k a natural number
+ 
+
+ align:start position:0%
+k a natural number
+n sub k is bigger than or equal to k
+
+ align:start position:0%
+n sub k is bigger than or equal to k
+ 
+
+ align:start position:0%
+n sub k is bigger than or equal to k
+the induct on uh k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we want to prove that this sequence
+
+ align:start position:0%
+so we want to prove that this sequence
+ 
+
+ align:start position:0%
+so we want to prove that this sequence
+converges to x and we're going to do
+
+ align:start position:0%
+converges to x and we're going to do
+ 
+
+ align:start position:0%
+converges to x and we're going to do
+that using the only means we have so
+
+ align:start position:0%
+that using the only means we have so
+ 
+
+ align:start position:0%
+that using the only means we have so
+this is just some arbitrary subsequence
+
+ align:start position:0%
+this is just some arbitrary subsequence
+ 
+
+ align:start position:0%
+this is just some arbitrary subsequence
+of x sub n all we have is the definition
+
+ align:start position:0%
+of x sub n all we have is the definition
+ 
+
+ align:start position:0%
+of x sub n all we have is the definition
+to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to now prove this so we
+
+ align:start position:0%
+so we're going to now prove this so we
+ 
+
+ align:start position:0%
+so we're going to now prove this so we
+have to show for all epsilon positive
+
+ align:start position:0%
+have to show for all epsilon positive
+ 
+
+ align:start position:0%
+have to show for all epsilon positive
+blah blah blah so the first thing we
+
+ align:start position:0%
+blah blah blah so the first thing we
+ 
+
+ align:start position:0%
+blah blah blah so the first thing we
+have to do is let epsilon be positive
+
+ align:start position:0%
+have to do is let epsilon be positive
+ 
+
+ align:start position:0%
+have to do is let epsilon be positive
+now we'll use the fact that x sub n
+
+ align:start position:0%
+now we'll use the fact that x sub n
+ 
+
+ align:start position:0%
+now we'll use the fact that x sub n
+converges to x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sub x n converges to x
+
+ align:start position:0%
+sub x n converges to x
+ 
+
+ align:start position:0%
+sub x n converges to x
+there exists a natural number
+
+ align:start position:0%
+there exists a natural number
+ 
+
+ align:start position:0%
+there exists a natural number
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+such that for all n bigger than or equal
+
+ align:start position:0%
+such that for all n bigger than or equal
+ 
+
+ align:start position:0%
+such that for all n bigger than or equal
+to m naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x sub n minus x absolute value is less
+
+ align:start position:0%
+x sub n minus x absolute value is less
+ 
+
+ align:start position:0%
+x sub n minus x absolute value is less
+than epsilon
+
+ align:start position:0%
+than epsilon
+ 
+
+ align:start position:0%
+than epsilon
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this m sub not we'll choose for our
+
+ align:start position:0%
+this m sub not we'll choose for our
+ 
+
+ align:start position:0%
+this m sub not we'll choose for our
+subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose m to equal m sub naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we need to show that this capital
+
+ align:start position:0%
+so now we need to show that this capital
+ 
+
+ align:start position:0%
+so now we need to show that this capital
+m works for our subsequence meaning if k
+
+ align:start position:0%
+m works for our subsequence meaning if k
+ 
+
+ align:start position:0%
+m works for our subsequence meaning if k
+is bigger than or equal to capital m
+
+ align:start position:0%
+is bigger than or equal to capital m
+ 
+
+ align:start position:0%
+is bigger than or equal to capital m
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+x of n sub k minus x is uh
+
+ align:start position:0%
+x of n sub k minus x is uh
+ 
+
+ align:start position:0%
+x of n sub k minus x is uh
+an absolute value less than epsilon but
+
+ align:start position:0%
+an absolute value less than epsilon but
+ 
+
+ align:start position:0%
+an absolute value less than epsilon but
+this just follows from from this fact
+
+ align:start position:0%
+this just follows from from this fact
+ 
+
+ align:start position:0%
+this just follows from from this fact
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+then if k
+
+ align:start position:0%
+then if k
+ 
+
+ align:start position:0%
+then if k
+is bigger than or equal to m this
+
+ align:start position:0%
+is bigger than or equal to m this
+ 
+
+ align:start position:0%
+is bigger than or equal to m this
+implies
+
+ align:start position:0%
+implies
+ 
+
+ align:start position:0%
+implies
+by this inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n sub k is bigger than or equal to m
+
+ align:start position:0%
+n sub k is bigger than or equal to m
+ 
+
+ align:start position:0%
+n sub k is bigger than or equal to m
+which remember is equal to m sub naught
+
+ align:start position:0%
+which remember is equal to m sub naught
+ 
+
+ align:start position:0%
+which remember is equal to m sub naught
+so n sub k is some integer
+
+ align:start position:0%
+so n sub k is some integer
+ 
+
+ align:start position:0%
+so n sub k is some integer
+so natural number bigger than or equal
+
+ align:start position:0%
+so natural number bigger than or equal
+ 
+
+ align:start position:0%
+so natural number bigger than or equal
+to m sub naught
+
+ align:start position:0%
+to m sub naught
+ 
+
+ align:start position:0%
+to m sub naught
+so that implies by this inequality that
+
+ align:start position:0%
+so that implies by this inequality that
+ 
+
+ align:start position:0%
+so that implies by this inequality that
+x of n sub k
+
+ align:start position:0%
+x of n sub k
+ 
+
+ align:start position:0%
+x of n sub k
+minus x an absolute value is less than
+
+ align:start position:0%
+minus x an absolute value is less than
+ 
+
+ align:start position:0%
+minus x an absolute value is less than
+epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
\ No newline at end of file
diff --git a/4EcVts56MCU.txt b/4EcVts56MCU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a331305c3329d1adca787bbf584544b2c0340938
--- /dev/null
+++ b/4EcVts56MCU.txt
@@ -0,0 +1,1171 @@
+align:start position:0%
+ 
+why does shape matter
+
+ align:start position:0%
+why does shape matter
+ 
+
+ align:start position:0%
+why does shape matter
+i told you shape mattered in the very
+
+ align:start position:0%
+i told you shape mattered in the very
+ 
+
+ align:start position:0%
+i told you shape mattered in the very
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+but why does it matter right let's say
+
+ align:start position:0%
+but why does it matter right let's say
+ 
+
+ align:start position:0%
+but why does it matter right let's say
+isn't it just important to know what the
+
+ align:start position:0%
+isn't it just important to know what the
+ 
+
+ align:start position:0%
+isn't it just important to know what the
+chemistry is
+
+ align:start position:0%
+chemistry is
+ 
+
+ align:start position:0%
+chemistry is
+and not the actual shape why does the
+
+ align:start position:0%
+and not the actual shape why does the
+ 
+
+ align:start position:0%
+and not the actual shape why does the
+shape matter and so i thought i would
+
+ align:start position:0%
+shape matter and so i thought i would
+ 
+
+ align:start position:0%
+shape matter and so i thought i would
+give you an example
+
+ align:start position:0%
+give you an example
+ 
+
+ align:start position:0%
+give you an example
+of that um with smell
+
+ align:start position:0%
+of that um with smell
+ 
+
+ align:start position:0%
+of that um with smell
+and and i yeah right
+
+ align:start position:0%
+and and i yeah right
+ 
+
+ align:start position:0%
+and and i yeah right
+exactly and i actually think we should
+
+ align:start position:0%
+exactly and i actually think we should
+ 
+
+ align:start position:0%
+exactly and i actually think we should
+do this more often i
+
+ align:start position:0%
+do this more often i
+ 
+
+ align:start position:0%
+do this more often i
+you know i feel like this is inspiring
+
+ align:start position:0%
+you know i feel like this is inspiring
+ 
+
+ align:start position:0%
+you know i feel like this is inspiring
+we talk about stopping and smelling the
+
+ align:start position:0%
+we talk about stopping and smelling the
+ 
+
+ align:start position:0%
+we talk about stopping and smelling the
+flowers
+
+ align:start position:0%
+flowers
+ 
+
+ align:start position:0%
+flowers
+but do we actually do it and look at
+
+ align:start position:0%
+but do we actually do it and look at
+ 
+
+ align:start position:0%
+but do we actually do it and look at
+that they've got
+
+ align:start position:0%
+that they've got
+ 
+
+ align:start position:0%
+that they've got
+you know one armor on the other this is
+
+ align:start position:0%
+you know one armor on the other this is
+ 
+
+ align:start position:0%
+you know one armor on the other this is
+a moment
+
+ align:start position:0%
+a moment
+ 
+
+ align:start position:0%
+a moment
+you can't share this moment on instagram
+
+ align:start position:0%
+you can't share this moment on instagram
+ 
+
+ align:start position:0%
+you can't share this moment on instagram
+you have to put your phone down and be
+
+ align:start position:0%
+you have to put your phone down and be
+ 
+
+ align:start position:0%
+you have to put your phone down and be
+there to have this moment
+
+ align:start position:0%
+there to have this moment
+ 
+
+ align:start position:0%
+there to have this moment
+and i highly encourage you to be
+
+ align:start position:0%
+and i highly encourage you to be
+ 
+
+ align:start position:0%
+and i highly encourage you to be
+inspired by this
+
+ align:start position:0%
+inspired by this
+ 
+
+ align:start position:0%
+inspired by this
+now smell and taste are actually related
+
+ align:start position:0%
+now smell and taste are actually related
+ 
+
+ align:start position:0%
+now smell and taste are actually related
+and smell is um
+
+ align:start position:0%
+and smell is um
+ 
+
+ align:start position:0%
+and smell is um
+you know it's actually a fascinating
+
+ align:start position:0%
+you know it's actually a fascinating
+ 
+
+ align:start position:0%
+you know it's actually a fascinating
+thing it we can smell about ten thousand
+
+ align:start position:0%
+thing it we can smell about ten thousand
+ 
+
+ align:start position:0%
+thing it we can smell about ten thousand
+uh different smells um
+
+ align:start position:0%
+uh different smells um
+ 
+
+ align:start position:0%
+uh different smells um
+it's remarkable uh a dog can smell
+
+ align:start position:0%
+it's remarkable uh a dog can smell
+ 
+
+ align:start position:0%
+it's remarkable uh a dog can smell
+between ten and a hundred thousand times
+
+ align:start position:0%
+between ten and a hundred thousand times
+ 
+
+ align:start position:0%
+between ten and a hundred thousand times
+more right so if you if you do the
+
+ align:start position:0%
+more right so if you if you do the
+ 
+
+ align:start position:0%
+more right so if you if you do the
+analogy that people do with vision
+
+ align:start position:0%
+analogy that people do with vision
+ 
+
+ align:start position:0%
+analogy that people do with vision
+we can see a third of a mile dog could
+
+ align:start position:0%
+we can see a third of a mile dog could
+ 
+
+ align:start position:0%
+we can see a third of a mile dog could
+see about 3 000 miles
+
+ align:start position:0%
+see about 3 000 miles
+ 
+
+ align:start position:0%
+see about 3 000 miles
+right that's pretty cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the question is why do we smell how
+
+ align:start position:0%
+but the question is why do we smell how
+ 
+
+ align:start position:0%
+but the question is why do we smell how
+do we smell
+
+ align:start position:0%
+do we smell
+ 
+
+ align:start position:0%
+do we smell
+how do we taste and it turns out that
+
+ align:start position:0%
+how do we taste and it turns out that
+ 
+
+ align:start position:0%
+how do we taste and it turns out that
+the way that we distinguish from one
+
+ align:start position:0%
+the way that we distinguish from one
+ 
+
+ align:start position:0%
+the way that we distinguish from one
+smell
+
+ align:start position:0%
+smell
+ 
+
+ align:start position:0%
+smell
+or in one taste in another has to do
+
+ align:start position:0%
+or in one taste in another has to do
+ 
+
+ align:start position:0%
+or in one taste in another has to do
+with the shape of the molecule
+
+ align:start position:0%
+with the shape of the molecule
+ 
+
+ align:start position:0%
+with the shape of the molecule
+and so just like a key right in it with
+
+ align:start position:0%
+and so just like a key right in it with
+ 
+
+ align:start position:0%
+and so just like a key right in it with
+a key there's not
+
+ align:start position:0%
+a key there's not
+ 
+
+ align:start position:0%
+a key there's not
+it's all the same material it's the same
+
+ align:start position:0%
+it's all the same material it's the same
+ 
+
+ align:start position:0%
+it's all the same material it's the same
+chemistry in the key but the shape
+
+ align:start position:0%
+chemistry in the key but the shape
+ 
+
+ align:start position:0%
+chemistry in the key but the shape
+is different that can unlock the door or
+
+ align:start position:0%
+is different that can unlock the door or
+ 
+
+ align:start position:0%
+is different that can unlock the door or
+not that is literally how
+
+ align:start position:0%
+not that is literally how
+ 
+
+ align:start position:0%
+not that is literally how
+our receptor cells work for taste and
+
+ align:start position:0%
+our receptor cells work for taste and
+ 
+
+ align:start position:0%
+our receptor cells work for taste and
+smell
+
+ align:start position:0%
+smell
+ 
+
+ align:start position:0%
+smell
+um this is a cartoon i found that i kind
+
+ align:start position:0%
+um this is a cartoon i found that i kind
+ 
+
+ align:start position:0%
+um this is a cartoon i found that i kind
+of like see okay
+
+ align:start position:0%
+of like see okay
+ 
+
+ align:start position:0%
+of like see okay
+shapes circles squares
+
+ align:start position:0%
+shapes circles squares
+ 
+
+ align:start position:0%
+shapes circles squares
+right uh okay and some shapes come in
+
+ align:start position:0%
+right uh okay and some shapes come in
+ 
+
+ align:start position:0%
+right uh okay and some shapes come in
+and they make happiness
+
+ align:start position:0%
+and they make happiness
+ 
+
+ align:start position:0%
+and they make happiness
+happiness flowers and stuff cheat i
+
+ align:start position:0%
+happiness flowers and stuff cheat i
+ 
+
+ align:start position:0%
+happiness flowers and stuff cheat i
+don't know is cheese happy it looks
+
+ align:start position:0%
+don't know is cheese happy it looks
+ 
+
+ align:start position:0%
+don't know is cheese happy it looks
+neutral
+
+ align:start position:0%
+neutral
+ 
+
+ align:start position:0%
+neutral
+i would get happy with cheese but anyway
+
+ align:start position:0%
+i would get happy with cheese but anyway
+ 
+
+ align:start position:0%
+i would get happy with cheese but anyway
+uh fish for some reason but you know it
+
+ align:start position:0%
+uh fish for some reason but you know it
+ 
+
+ align:start position:0%
+uh fish for some reason but you know it
+depends
+
+ align:start position:0%
+depends
+ 
+
+ align:start position:0%
+depends
+and but it's shape dependent now the
+
+ align:start position:0%
+and but it's shape dependent now the
+ 
+
+ align:start position:0%
+and but it's shape dependent now the
+thing is taste works that way too so
+
+ align:start position:0%
+thing is taste works that way too so
+ 
+
+ align:start position:0%
+thing is taste works that way too so
+this is what's happening in your tongue
+
+ align:start position:0%
+this is what's happening in your tongue
+ 
+
+ align:start position:0%
+this is what's happening in your tongue
+you've got these these uh these taste
+
+ align:start position:0%
+you've got these these uh these taste
+ 
+
+ align:start position:0%
+you've got these these uh these taste
+buds we've all heard
+
+ align:start position:0%
+buds we've all heard
+ 
+
+ align:start position:0%
+buds we've all heard
+the word taste bud right but what is
+
+ align:start position:0%
+the word taste bud right but what is
+ 
+
+ align:start position:0%
+the word taste bud right but what is
+really going on
+
+ align:start position:0%
+really going on
+ 
+
+ align:start position:0%
+really going on
+what is really going on is a combination
+
+ align:start position:0%
+what is really going on is a combination
+ 
+
+ align:start position:0%
+what is really going on is a combination
+of chemistry
+
+ align:start position:0%
+of chemistry
+ 
+
+ align:start position:0%
+of chemistry
+and shape recognition um so
+
+ align:start position:0%
+and shape recognition um so
+ 
+
+ align:start position:0%
+and shape recognition um so
+so the taste bud if you look at the
+
+ align:start position:0%
+so the taste bud if you look at the
+ 
+
+ align:start position:0%
+so the taste bud if you look at the
+taste bud that's inside of the little
+
+ align:start position:0%
+taste bud that's inside of the little
+ 
+
+ align:start position:0%
+taste bud that's inside of the little
+these little pores inside your tongue
+
+ align:start position:0%
+these little pores inside your tongue
+ 
+
+ align:start position:0%
+these little pores inside your tongue
+there's a blow up of it
+
+ align:start position:0%
+there's a blow up of it
+ 
+
+ align:start position:0%
+there's a blow up of it
+and so this is what the surface of your
+
+ align:start position:0%
+and so this is what the surface of your
+ 
+
+ align:start position:0%
+and so this is what the surface of your
+tongue looks like and there's a little
+
+ align:start position:0%
+tongue looks like and there's a little
+ 
+
+ align:start position:0%
+tongue looks like and there's a little
+pore
+
+ align:start position:0%
+pore
+ 
+
+ align:start position:0%
+pore
+and there's little filters in there that
+
+ align:start position:0%
+and there's little filters in there that
+ 
+
+ align:start position:0%
+and there's little filters in there that
+help certain molecules you know kind of
+
+ align:start position:0%
+help certain molecules you know kind of
+ 
+
+ align:start position:0%
+help certain molecules you know kind of
+get in there
+
+ align:start position:0%
+get in there
+ 
+
+ align:start position:0%
+get in there
+and what happens when they get in there
+
+ align:start position:0%
+and what happens when they get in there
+ 
+
+ align:start position:0%
+and what happens when they get in there
+well what happens is you've got these
+
+ align:start position:0%
+well what happens is you've got these
+ 
+
+ align:start position:0%
+well what happens is you've got these
+taste receptor cells
+
+ align:start position:0%
+taste receptor cells
+ 
+
+ align:start position:0%
+taste receptor cells
+that are like lock key pairs they
+
+ align:start position:0%
+that are like lock key pairs they
+ 
+
+ align:start position:0%
+that are like lock key pairs they
+actually only look at like the circle or
+
+ align:start position:0%
+actually only look at like the circle or
+ 
+
+ align:start position:0%
+actually only look at like the circle or
+the diamond and they can tell you which
+
+ align:start position:0%
+the diamond and they can tell you which
+ 
+
+ align:start position:0%
+the diamond and they can tell you which
+one is which
+
+ align:start position:0%
+one is which
+ 
+
+ align:start position:0%
+one is which
+and that's a major part of how we
+
+ align:start position:0%
+and that's a major part of how we
+ 
+
+ align:start position:0%
+and that's a major part of how we
+distinguish from one shape
+
+ align:start position:0%
+distinguish from one shape
+ 
+
+ align:start position:0%
+distinguish from one shape
+uh to another and it's actually so um
+
+ align:start position:0%
+uh to another and it's actually so um
+ 
+
+ align:start position:0%
+uh to another and it's actually so um
+uh it's it's it goes back a long way why
+
+ align:start position:0%
+uh it's it's it goes back a long way why
+ 
+
+ align:start position:0%
+uh it's it's it goes back a long way why
+because shape and smell are are
+
+ align:start position:0%
+because shape and smell are are
+ 
+
+ align:start position:0%
+because shape and smell are are
+literally uh survival they are literally
+
+ align:start position:0%
+literally uh survival they are literally
+ 
+
+ align:start position:0%
+literally uh survival they are literally
+like you can
+
+ align:start position:0%
+like you can
+ 
+
+ align:start position:0%
+like you can
+you know if you taste something and it's
+
+ align:start position:0%
+you know if you taste something and it's
+ 
+
+ align:start position:0%
+you know if you taste something and it's
+and it and it
+
+ align:start position:0%
+and it and it
+ 
+
+ align:start position:0%
+and it and it
+tastes poisonous don't eat it you live
+
+ align:start position:0%
+tastes poisonous don't eat it you live
+ 
+
+ align:start position:0%
+tastes poisonous don't eat it you live
+right so it is it is a very emotional
+
+ align:start position:0%
+right so it is it is a very emotional
+ 
+
+ align:start position:0%
+right so it is it is a very emotional
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+to smell and taste because it is
+
+ align:start position:0%
+to smell and taste because it is
+ 
+
+ align:start position:0%
+to smell and taste because it is
+actually coupled to
+
+ align:start position:0%
+actually coupled to
+ 
+
+ align:start position:0%
+actually coupled to
+to your very survival and democracy
+
+ align:start position:0%
+to your very survival and democracy
+ 
+
+ align:start position:0%
+to your very survival and democracy
+himself democritus
+
+ align:start position:0%
+himself democritus
+ 
+
+ align:start position:0%
+himself democritus
+democr our friend democritus said that
+
+ align:start position:0%
+democr our friend democritus said that
+ 
+
+ align:start position:0%
+democr our friend democritus said that
+shape
+
+ align:start position:0%
+shape
+ 
+
+ align:start position:0%
+shape
+must be involved he thought that because
+
+ align:start position:0%
+must be involved he thought that because
+ 
+
+ align:start position:0%
+must be involved he thought that because
+things that taste bitter
+
+ align:start position:0%
+things that taste bitter
+ 
+
+ align:start position:0%
+things that taste bitter
+are sharp that the bitter molecules were
+
+ align:start position:0%
+are sharp that the bitter molecules were
+ 
+
+ align:start position:0%
+are sharp that the bitter molecules were
+sharp
+
+ align:start position:0%
+sharp
+ 
+
+ align:start position:0%
+sharp
+they must have sharpness to them and
+
+ align:start position:0%
+they must have sharpness to them and
+ 
+
+ align:start position:0%
+they must have sharpness to them and
+like like shards of glass
+
+ align:start position:0%
+like like shards of glass
+ 
+
+ align:start position:0%
+like like shards of glass
+that's how he imagined it and the sweet
+
+ align:start position:0%
+that's how he imagined it and the sweet
+ 
+
+ align:start position:0%
+that's how he imagined it and the sweet
+molecules were sort of these soft
+
+ align:start position:0%
+molecules were sort of these soft
+ 
+
+ align:start position:0%
+molecules were sort of these soft
+fluffy spheres right but that's not that
+
+ align:start position:0%
+fluffy spheres right but that's not that
+ 
+
+ align:start position:0%
+fluffy spheres right but that's not that
+far
+
+ align:start position:0%
+far
+ 
+
+ align:start position:0%
+far
+off from being sort of what happens
+
+ align:start position:0%
+off from being sort of what happens
+ 
+
+ align:start position:0%
+off from being sort of what happens
+a little bit but when we look at like
+
+ align:start position:0%
+a little bit but when we look at like
+ 
+
+ align:start position:0%
+a little bit but when we look at like
+you know glucose and and quinine we say
+
+ align:start position:0%
+you know glucose and and quinine we say
+ 
+
+ align:start position:0%
+you know glucose and and quinine we say
+okay those are very
+
+ align:start position:0%
+okay those are very
+ 
+
+ align:start position:0%
+okay those are very
+different chemistries so it might not be
+
+ align:start position:0%
+different chemistries so it might not be
+ 
+
+ align:start position:0%
+different chemistries so it might not be
+as obvious
+
+ align:start position:0%
+as obvious
+ 
+
+ align:start position:0%
+as obvious
+why one of them tastes so different than
+
+ align:start position:0%
+why one of them tastes so different than
+ 
+
+ align:start position:0%
+why one of them tastes so different than
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+but check out this example this is the
+
+ align:start position:0%
+but check out this example this is the
+ 
+
+ align:start position:0%
+but check out this example this is the
+same molecule the carbonic molecule
+
+ align:start position:0%
+same molecule the carbonic molecule
+ 
+
+ align:start position:0%
+same molecule the carbonic molecule
+that is called an enantiomer which means
+
+ align:start position:0%
+that is called an enantiomer which means
+ 
+
+ align:start position:0%
+that is called an enantiomer which means
+that it has
+
+ align:start position:0%
+that it has
+ 
+
+ align:start position:0%
+that it has
+handedness it's the exact same chemical
+
+ align:start position:0%
+handedness it's the exact same chemical
+ 
+
+ align:start position:0%
+handedness it's the exact same chemical
+formula and the exact same structure
+
+ align:start position:0%
+formula and the exact same structure
+ 
+
+ align:start position:0%
+formula and the exact same structure
+except for one is like this and one is
+
+ align:start position:0%
+except for one is like this and one is
+ 
+
+ align:start position:0%
+except for one is like this and one is
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+that's handedness right and that
+
+ align:start position:0%
+that's handedness right and that
+ 
+
+ align:start position:0%
+that's handedness right and that
+difference makes one of them taste and
+
+ align:start position:0%
+difference makes one of them taste and
+ 
+
+ align:start position:0%
+difference makes one of them taste and
+smell like experiment and the other like
+
+ align:start position:0%
+smell like experiment and the other like
+ 
+
+ align:start position:0%
+smell like experiment and the other like
+caraway seeds
+
+ align:start position:0%
+caraway seeds
+ 
+
+ align:start position:0%
+caraway seeds
+right it's incredible it's entire it
+
+ align:start position:0%
+right it's incredible it's entire it
+ 
+
+ align:start position:0%
+right it's incredible it's entire it
+means that in our tongues in our noses
+
+ align:start position:0%
+means that in our tongues in our noses
+ 
+
+ align:start position:0%
+means that in our tongues in our noses
+we must have
+
+ align:start position:0%
+we must have
+ 
+
+ align:start position:0%
+we must have
+chiral uh the ability to to determine
+
+ align:start position:0%
+chiral uh the ability to to determine
+ 
+
+ align:start position:0%
+chiral uh the ability to to determine
+the chirality
+
+ align:start position:0%
+the chirality
+ 
+
+ align:start position:0%
+the chirality
+it's pretty cool right so shape is
+
+ align:start position:0%
+it's pretty cool right so shape is
+ 
+
+ align:start position:0%
+it's pretty cool right so shape is
+critical and this is one example of why
+
+ align:start position:0%
+critical and this is one example of why
+ 
+
+ align:start position:0%
+critical and this is one example of why
+this is one example why okay
+
+ align:start position:0%
+this is one example why okay
+ 
+
+ align:start position:0%
+this is one example why okay
+you
\ No newline at end of file
diff --git a/4OinSH6sAUo.txt b/4OinSH6sAUo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..177c93543c42b4fc8a582cb9e11c66724c3a34a5
--- /dev/null
+++ b/4OinSH6sAUo.txt
@@ -0,0 +1,4415 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: So I want to begin
+by reviewing a little bit what
+
+I said last time in terms
+of this overview lecture.
+
+And then we'll finish
+the overview lecture.
+
+So summary of last lecture
+is actually on five slides.
+
+It's not all on this one slide.
+
+We started by talking about the
+standard Big Bang, by which I
+
+mean the Big Bang without
+thinking about inflation.
+
+And I pointed out that
+it really describes
+
+only the aftermath of a bang.
+
+It begins with the
+description of the universe
+
+as a hot, dense soup of
+particles which more or less
+
+uniformly fills the
+entire available space,
+
+and the entire system
+is already expanding.
+
+Cosmic inflation is a prequel
+to the conventional Big Bang
+
+story.
+
+It describes how
+repulsive gravity, which
+
+in the context of
+general relativity,
+
+can happen as a consequence
+of negative pressure.
+
+This repulsive
+gravity could have
+
+driven a tiny patch
+of the early universe
+
+into a gigantic burst of
+exponential expansion.
+
+And our visible
+universe would then
+
+be the aftermath of that event.
+
+As this happened, the
+total energy of this patch
+
+would be very small and
+could even be identically 0.
+
+And the way that's possible
+is caused by the fact
+
+that the gravitational
+field that fills the space
+
+has a negative
+contribution to the energy.
+
+And as far as we can tell
+in our real universe,
+
+there are about
+equal to each other.
+
+They could cancel each other
+exactly as far as we can tell.
+
+So the total energy
+could in fact
+
+be exactly zero,
+which is what allows
+
+one to build a huge
+universe starting
+
+from either nothing
+or almost nothing.
+
+Inflation.
+
+The next item is
+evidence for inflation.
+
+Why do we think there's
+at least a good chance
+
+that our universe
+underwent inflation?
+
+And I pointed out three items.
+
+The first was that inflation
+could explain the large scale
+
+uniformity that we
+observe in the universe
+
+and that large
+scale uniformity is
+
+seen most clearly in the
+cosmic microwave background
+
+radiation, which is observed
+to be uniform to one
+
+part in $100,000, that is same
+intensity all across the sky
+
+no matter what direction
+you look, once you account
+
+for the Earth's motion,
+to an accuracy of one part
+
+in 100,000.
+
+Secondly, inflation can explain
+a rather remarkable fact
+
+about this quantity
+omega, where omega
+
+is defined as the actual
+mass density of the universe
+
+rho divided by rho critical,
+the critical mass density which
+
+is the density that would make
+the universe precisely flat.
+
+The statement that that
+ratio is equal to 1 we know
+
+is accurate to about 15
+decimal places at one second
+
+after the Big Bang.
+
+And prior to inflation,
+we didn't really
+
+have any explanation
+for that at all.
+
+But inflation
+drives omega to one
+
+and gives us an explanation
+for why, therefore,
+
+started out so
+extraordinarily close to 1.
+
+And in fact, it
+makes a prediction.
+
+We'd expect that if
+inflation is right,
+
+omega should still be one today.
+
+And we now have measured omega
+to be 1.0010 plus or minus
+
+0.0065, which I
+think is fabulous.
+
+Finally, inflation
+gives an explanation
+
+for the inhomogeneities
+that we see in the universe.
+
+It explains them as
+quantum fluctuations which
+
+happened during the inflationary
+process and, most importantly
+
+really, as inflation was
+ending, the quantum fluctuations
+
+cause inflation to go
+on for a little bit
+
+longer in some
+regions than others.
+
+And that sets up
+these inhomogeneities.
+
+Today, we can see
+these inhomogeneities
+
+most accurately.
+
+inhomogeneities, of course, are
+huge at the level of galaxies,
+
+so they're obvious.
+
+But it's hard to connect
+them to the early universe.
+
+So we can make our most
+precise comparison between what
+
+we observe and theories
+of the early universe
+
+by making careful observations
+of the cosmic background
+
+radiation itself, which has
+these ripples in the intensity,
+
+It is not quite uniform.
+
+There really are ripples at the
+level of one part in 100,000,
+
+which can now be observed.
+
+And inflation makes
+a clear prediction
+
+for the spectrum
+of those ripples,
+
+how the intensity should
+vary with wavelength.
+
+And I showed you this graph last
+time from the Planck satellite.
+
+The agreement between the
+prediction and the theory
+
+is really marvelous.
+
+So we'll be coming back to that
+near the end of the course.
+
+Finally, in the last
+lecture, I began
+
+to talk about inflation and
+the possible implications
+
+for a multiverse, the idea that
+our universe might be embedded
+
+in a much larger
+thing consisting
+
+of many universes, which
+we call a multiverse.
+
+And the key point is that
+most inflation models
+
+tend to become eternal.
+
+And that is once inflation
+starts, it never stops.
+
+And the reason for
+that, basically,
+
+is that the metastable
+material, this repulsive gravity
+
+material that's causing
+the inflation, decays,
+
+but it also
+exponentially expands.
+
+And for typical models,
+the exponential expansion
+
+completely overpowers the decay.
+
+So even though it's an
+unstable material that decays,
+
+the total volume of it actually
+increases exponentially
+
+with time rather than decreases.
+
+Decays happen however,
+and wherever decay happen,
+
+it forms what we call
+a pocket universe.
+
+We would be living in one
+of those pocket universes.
+
+And the number of
+pocket universes
+
+grows exponentially with time as
+the whole system grows and goes
+
+on, as far as we
+can tell, forever.
+
+And that is the picture
+of the multiverse
+
+that inflation tends to lead to.
+
+Finally, this is my
+last summary slide
+
+and then we'll
+start new material.
+
+At the very end of
+lecture, I talked
+
+about a problem, which is very
+important in our present day
+
+thinking about
+physics and cosmology,
+
+and that is the nightmare that
+this discovery of dark energy
+
+leads to.
+
+What was discovered
+at about 1998
+
+is that the expansion
+of the universe
+
+is not slowing down under
+the influence of gravity
+
+as one might expect,
+but Instead, it's
+
+actually accelerating.
+
+The universe is expanding
+faster and faster.
+
+And that indicates
+that space today
+
+is filled with some repulsive
+gravity material, which
+
+we call the dark energy.
+
+And the simplest interpretation
+of the dark energy
+
+is that it simply vacuum energy,
+the energy of empty space.
+
+Space does have an
+energy density that
+
+have exactly the
+properties that we observe,
+
+so it seems natural to
+draw that connection.
+
+Vacuum energy, at first,
+might seem surprising.
+
+If a vacuum's empty, why should
+it have any mass density?
+
+But in a quantum field theory,
+it's really not surprising
+
+because in a quantum
+field theory,
+
+the vacuum is really not empty.
+
+In a quantum field
+theory, there's
+
+no such thing as
+actual emptiness.
+
+Instead, in the vacuum, one has
+constant quantum fluctuations
+
+of fields.
+
+And in our current theory
+of particle physics,
+
+the standard model
+of particle physics,
+
+there's even one particular
+field called the Higgs field,
+
+which has a non-zero
+mean value in the vacuum
+
+besides fluctuations.
+
+So the vacuum is a
+very complicated state.
+
+What makes it the
+vacuum is simply
+
+that it's alleged to be the
+state of lowest possible energy
+
+density, but that
+doesn't have to be zero
+
+and doesn't even
+look like there's
+
+any reason why it
+should be zero.
+
+So there's no problem
+buying the fact
+
+that maybe the vacuum does
+have a non-zero energy density.
+
+The problem comes
+about though when
+
+we try to understand the
+magnitude of this vacuum
+
+energy.
+
+If it was going to have
+a vacuum energy density,
+
+we'd expect it to be
+vastly larger than what
+
+is observed in the
+form of the expansion
+
+acceleration of the universe.
+
+So a typical order of magnitude
+in the particle physics
+
+model for the vacuum
+energy is, in fact,
+
+about a full 120
+orders of magnitude
+
+larger than the
+number that's implied
+
+by the acceleration
+of the universe.
+
+So that is a big problem.
+
+I began to talk about a possible
+resolution to that problem.
+
+It's only a possible resolution.
+
+Nobody has really
+settled on this.
+
+But there's a
+possible resolution
+
+which comes out
+of String theory,
+
+and in particular
+from this idea, which
+
+is called the landscape
+of String theory.
+
+Most String theorists believe
+that String theory has
+
+no unique vacuum,
+but instead, there's
+
+a colossal number, perhaps
+something like 10 to the 500,
+
+different metastable
+states, which
+
+even though they are metastable,
+are incredibly long-lived,
+
+long-lived compared to the age
+of the universe as we know it.
+
+So any one of these 10 to
+the 500 different states
+
+could serve as effectively
+the vacuum for one
+
+of these pocket universes.
+
+And the different
+pocket universes
+
+would presumably fill the
+whole set of possible vacua
+
+in the landscape, giving reality
+to all these possibilities
+
+that come about
+in String theory.
+
+And in particular, each
+different type of vacuum
+
+would have its own
+vacuum energy density.
+
+And because there are
+both positive and negative
+
+contributions-- I think I
+didn't read that out loud--
+
+but there are both positive
+and negative contributions
+
+that arise in quantum
+field theories.
+
+So the vacuum energy
+of a typical state
+
+could be either
+positive or negative.
+
+And what we would
+expect of these 10
+
+to the 500 different
+vacua is that they
+
+would have a range
+of energy densities
+
+that would range from something
+like minus 10 to the 120
+
+to plus 10 to the 120
+times the observed value.
+
+So the observed value
+would be in there,
+
+but would be an incredibly
+small fraction of the universes.
+
+Yes?
+
+AUDIENCE: Does this mean that
+so many pocket universes could
+
+be closed and opened as well
+in terms of their geometry?
+
+Or--
+
+PROFESSOR: They're
+actually predicted
+
+to be open due to complications
+about how they form,
+
+which I'm not going to go into.
+
+But they should all be open, but
+very close to flat for the ones
+
+that under a lot of inflation.
+
+So they'd be
+indistinguishable from flat,
+
+but technically, they'd be open.
+
+Yes?
+
+AUDIENCE: Is the minus 10 to
+the 120 plus 10 to the 120 just
+
+chosen because we're off
+520 orders of magnitude,
+
+or is it predicted
+somewhere else?
+
+PROFESSOR: Well,
+when we say we're off
+
+by 120 orders of magnitude,
+the more precise statement
+
+is that the estimate of what
+a typical range of the energy
+
+should be is 10 to 120
+times the observed value.
+
+So this is basically just
+a restatement of that.
+
+And you might
+wonder why I didn't
+
+put 5 times 10 to the
+120, but in fact, the 120
+
+itself is only accurate
+to within a few orders
+
+of magnitude, so 5
+times that wouldn't
+
+have made any difference
+in the way one
+
+actually interprets
+those numbers.
+
+10 to the 123 is probably
+slightly more accurate number
+
+actually.
+
+But this is good enough
+for our purposes.
+
+Yes?
+
+AUDIENCE: Just a
+general question
+
+about inflation properties.
+
+We think of attractive
+gravity as driving
+
+the motion of objects
+through space.
+
+So why do we think
+of repulsive gravity
+
+like to drive the
+expanse of space itself?
+
+PROFESSOR: Well, for one
+thing, it does actually
+
+behave differently.
+
+Repulsive gravity,
+repulsive gravity
+
+that appears in
+general relativity,
+
+is not just ordinary gravity
+with the opposite sign.
+
+Ordinary gravity
+has the property
+
+that if I have two objects to
+attract each other with a force
+
+proportional to the
+masses of those objects.
+
+This repulsive
+gravity is actually
+
+an effect caused by the negative
+pressure in the space between.
+
+So if I have two
+objects, they will
+
+start to accelerate apart
+by the amount that's
+
+totally independent
+of the masses.
+
+This is not really the
+masses that's causing it.
+
+So the whole force was
+completely different,
+
+so we can't really
+just compare them.
+
+In either case, when
+everything is moving apart,
+
+it's really a
+matter of viewpoint
+
+when you think of the
+whole space as expanding
+
+or whether you think
+of the particles
+
+as moving through space.
+
+In relativity, there's no
+way to put a needle on space,
+
+put a pen in it and
+say this is stationary.
+
+So we really can't say that
+the space is moving or not.
+
+In cosmology, we usually
+find that the simpler picture
+
+and the one that we
+will generally use
+
+is that space expands
+with the matter.
+
+It gives a much
+simpler description
+
+of how things behave.
+
+Good question.
+
+Yes?
+
+AUDIENCE: I have a question
+going back a few slides.
+
+PROFESSOR: Sure, you
+want me to go back.
+
+AUDIENCE: How the energy
+of the early universe
+
+seemed to be close to zero.
+
+Are there theoretical
+models that would explain
+
+or that would say it
+should be exactly 0?
+
+PROFESSOR: Yeah, there are.
+
+I didn't mention it.
+
+But if the universe is closed,
+which is a possibility.
+
+Even if it's very nearly flat,
+it could still be closed.
+
+If it were closed, it would
+have exactly zero energy.
+
+Yes?
+
+AUDIENCE: So the
+cosmic background,
+
+microwave background,
+picks ups that it's
+
+pretty similar in all
+directions once correct for it.
+
+And this leads to the thought
+that the cosmological principle
+
+all over the universe
+is pretty identical.
+
+Is it possible that
+we are actually
+
+located in just a smaller
+like circular pathway
+
+and it may be different
+than [? allowed. ?]
+
+And there's many
+of these patches,
+
+so we-- there's actually
+like a speckled form.
+
+PROFESSOR: OK.
+
+So if you didn't
+hear the question,
+
+I was asked if it's possible
+that the universe is not
+
+really homogeneous on
+a very large scales,
+
+but really speckled, just
+that speckles are large
+
+and our speckle might
+look very different
+
+from other speckles
+that are far away.
+
+And that was the question.
+
+And the answer is certainly
+if the multiverse picture
+
+is right.
+
+That is exactly the case
+that's being predicted.
+
+These other pocket
+universes could
+
+be viewed as other
+speckles in your language,
+
+and they'd be very different
+from what we've observed.
+
+So inflation actually
+changes one's attitude
+
+about this particular question.
+
+Back in the old days,
+before inflation,
+
+the uniformity of the
+universe had no explanation,
+
+so it became a postulate.
+
+And nobody postulates
+that something
+
+is uniform on that scale.
+
+If you are going to
+make a postulate,
+
+you just postulate that
+the universe is uniform.
+
+So that was the postulate
+that was in use.
+
+But now that we think of the
+homogeneity of the universe
+
+as being generated by a
+dynamical process, inflation,
+
+then, it's a natural
+question to ask,
+
+what is the scale
+of the homogeneity
+
+that that generates.
+
+And it's certainly
+a scale that's
+
+much larger than
+what we can observe.
+
+So we don't really expect
+to see inhomogeneity
+
+as caused by different
+pockets of inflation,
+
+but the model seems to
+make it very plausible that
+
+is what we would see if
+we could see far enough.
+
+Any other questions while
+we're on a little break here?
+
+Yes?
+
+AUDIENCE: If the
+universe is expanding,
+
+then I think like we are
+expanding as well, so how can
+
+we observe the change
+from a distance,
+
+in particular everything
+is increasing scale?
+
+PROFESSOR: OK.
+
+That's a very good question.
+
+The question was if the
+universe is expanding,
+
+then the universe is everything.
+
+So everything is expanding.
+
+And if everything's expanding,
+when you compare things
+
+with rulers, they
+have the same length.
+
+So how would you even observe
+that everything was expanding?
+
+And the answer to
+that is that when
+
+we say the universe
+is expanding,
+
+we're not really saying that
+everything is expanding.
+
+When we say the
+universe is expanding,
+
+we really are saying that the
+galaxies are getting further
+
+apart from each other,
+but individual atoms
+
+are not getting bigger.
+
+The length of a
+ruler, determined
+
+by the number of atoms
+and how those atoms move
+
+to ground state, does not
+expand with the universe.
+
+So the expansion is
+now partially driven
+
+by the repulsive
+gravity that exists
+
+now, which is causing the
+universe to accelerate.
+
+But most of the expansion is
+really just a residual velocity
+
+from the Big Bang,
+whatever caused it then.
+
+I would assert inflation.
+
+And it's just a matter
+of coasting outward, not
+
+being pulled outward,
+and that coasting outward
+
+does not cause
+atoms to get bigger.
+
+Yes?
+
+AUDIENCE: Is the current
+idea that the expansion,
+
+like the acceleration,
+is indefinite or are we
+
+going to reach a stop point?
+
+PROFESSOR: OK.
+
+What will be the ultimate
+future, I'm being asked here.
+
+And the answer, as you might
+guess, is nobody really knows.
+
+But in the context of the kind
+of models I'm talking about,
+
+there is a pretty
+definite answer,
+
+which is that our
+pocket universe--
+
+I'll answer at the level
+of our pocket universe
+
+and I'll answer at the level
+of the multiverse as a hole.
+
+At the level of our
+pocket universe,
+
+our pocket universe
+will thin out.
+
+Life will eventually
+become impossible
+
+because matter density
+will be too low.
+
+It will probably decay.
+
+Our vacuum is probably
+not absolutely stable.
+
+Very few things 2
+String theory are,
+
+if something like String
+theory is the right theory.
+
+But even though it
+will be decaying,
+
+it will be expanding still
+faster than it decays.
+
+So the decay will cause
+holes in our universe.
+
+It will become
+like Swiss cheese.
+
+But the universe, as
+a whole, will just
+
+go on exponentially
+expanding, perhaps
+
+forever, as far as
+we can tell, forever.
+
+The multiverse is a
+more vibrant object.
+
+The multiverse,
+as I always said,
+
+would continue to generate
+new pocket universes forever.
+
+So the multiverse
+would forever be alive
+
+even though each pocket
+universe in the multiverse
+
+would form at some time
+and then ultimately die,
+
+die of thinning out
+into nothingness.
+
+Yes?
+
+AUDIENCE: Just to add to that.
+
+Do you believe that maybe
+it's a cyclic process?
+
+So it expand and decay and
+then come back [? yet again ?]
+
+and then happen all over again?
+
+PROFESSOR: OK.
+
+The question is could it
+be a cyclic process that
+
+expands, reaches maximum,
+comes back and crunches,
+
+and expands again.
+
+That is certainly a
+possibility, and there
+
+is some people who
+take it very seriously.
+
+I don't see any evidence for it.
+
+And furthermore, there
+never really was and still
+
+really isn't a reasonable
+theory of the bounce
+
+that would have to be
+a part of that theory.
+
+Yeah?
+
+AUDIENCE: But would it be
+the expansion overtaking
+
+the decay in our own vacuum
+that our universe exists
+
+in, our own little pocket
+vacuums of ultimate decay
+
+within our system create more
+little pocket universes--
+
+[INTERPOSING VOICES]
+
+PROFESSOR: Within.
+
+Yes.
+
+Yeah, that's correct.
+
+They would not be a big fraction
+of the volume of our universe,
+
+but, yes.
+
+The pieces in our universe
+that might decay in the future
+
+would produce new
+pocket universes.
+
+Most of them would be very low
+energy pocket universes that
+
+would presumably not create
+life, but some of them
+
+could nonetheless have a high
+enough energy to create life.
+
+So we would expect
+new, thriving universes
+
+to appear out of our
+own pocket universe
+
+as it reaches this
+expansion death.
+
+Yes?
+
+AUDIENCE: What does
+distinguishes different vacua
+
+besides the
+cosmological constant?
+
+PROFESSOR: The question
+is what distinguishes
+
+the different vacua besides
+the cosmological constant.
+
+And the answer is that they can
+distinguish in many, many ways.
+
+What fundamentally
+distinguishes them
+
+is the rearrangement
+of the innards
+
+within the space, maybe a little
+bit more precise without trying
+
+to get into details
+which I probably
+
+don't understand either.
+
+But what's going on is that
+String theory fundamentally
+
+says that space has nine
+dimensions, not the three
+
+that we observe.
+
+And the way the
+nine becomes three
+
+is that the extra
+dimensions get twisted up
+
+into tiny little knots, so
+they occupy too small a length
+
+to ever be seen.
+
+But there are many
+different ways
+
+of twisting up those
+extra dimensions,
+
+and that's really what leads
+to these very large numbers
+
+of possible vacua.
+
+The extra dimensions are
+twisted up differently.
+
+So that means that as
+far as the low energy
+
+physics in these
+different vacua--
+
+practically everything
+could be different,
+
+even the dimension of
+space could be different.
+
+You could have different numbers
+of dimensions compactified.
+
+And the whole particle
+spectrum would
+
+be different because what we
+view as a particle is really
+
+just the fluctuation of vacuum.
+
+And if you have a different
+structure to the vacuum itself,
+
+the kinds of particles
+that exist in it
+
+could be totally different.
+
+So the physics inside
+these pocket universe
+
+could look tremendously
+different from what
+
+we observe even though
+that we're predicating
+
+the whole description
+on the idea
+
+that, ultimately, it's
+the same laws of physics
+
+that apply everywhere.
+
+Other questions?
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: OK.
+
+I think you're asking about
+if we have a small patch, then
+
+that goes inflation and the rest
+doesn't, how does the patch end
+
+up dominating because
+it started out
+
+with just a small
+fraction of the particles.
+
+Doesn't it still have the same
+small fraction of particles?
+
+Is that what you're asking?
+
+AUDIENCE: Well, I guess.
+
+If you start out with the
+smooth particles being
+
+the excessive matter,
+and one of the particles
+
+behaves and the other
+two particles [INAUDIBLE]
+
+even if it's still
+just two particles?
+
+PROFESSOR: Right.
+
+It isn't the number of
+particles conserved, basically,
+
+as all this happens, is I
+think what you're asking.
+
+AUDIENCE: Well, even if it
+eventually [? is called ?]
+
+expanded wave because the
+second part will [INAUDIBLE]
+
+PROFESSOR: Well, let's see.
+
+I'm having a little
+trouble hearing you.
+
+But let me make a definite--
+let me make a broader statement,
+
+and you can tell
+me if I've answered
+
+what you're asking about or not.
+
+When one of these
+patches undergoes
+
+the exponential
+expansion of inflation,
+
+the energy is really
+not very well described
+
+as particles at all.
+
+It's really described
+in terms of fields.
+
+And fields sometimes behave
+like particles, but not always.
+
+And in this case-- in principle,
+there's a particle description
+
+too, but it's not
+nearly as obvious
+
+as the field description.
+
+So you have energy stored in
+fields and the region grows.
+
+The energy stored
+in those fields
+
+actually increases
+as the region goes.
+
+The energy density remains
+approximately constant.
+
+And that sounds like
+it would violate
+
+the conservation of energy,
+but we discussed the fact
+
+that what saves
+conservation of energy
+
+and allows this to happen in
+spite of conservation of energy
+
+is that as the
+region expands, it
+
+is filled by a gravitational
+field, which is now occupying
+
+a larger and larger volume, and
+that gravitational field has
+
+a negative energy density.
+
+So the total energy, which
+is what has to be conserved,
+
+remains very small
+and perhaps zero,
+
+and the region can
+grow without limit
+
+while still having this very
+small or zero total energy.
+
+Then, eventually it
+decays and when it decays,
+
+it produces new particles,
+and the colossal number
+
+of new particles, and
+those would be the stuff
+
+that we would be made out of.
+
+And that number is vastly larger
+than the number of particles
+
+that may have been
+in this region
+
+when the inflation started.
+
+Yes?
+
+AUDIENCE: So does the emergence
+of [INAUDIBLE] just purely
+
+a conservation of energy?
+
+Like, what do you need to
+make these [? an organism ?],
+
+the negative energy,
+zero [INAUDIBLE] I guess.
+
+PROFESSOR: Are you saying
+the conservation of energy
+
+maybe controls the whole
+show, and that this is really
+
+the only thing consistent
+with conservation of energy?
+
+I think that's probably
+an exaggeration
+
+because if nothing happened,
+that would conserve energy too.
+
+So I think one needs more than
+just the conservation of energy
+
+to be able to describe how the
+universe is going to evolve.
+
+OK.
+
+Let me continue.
+
+Get back to the beginning
+there, back to the end.
+
+OK.
+
+So I just finished talking about
+the landscape of String theory
+
+and how it offers all
+these possible vacua.
+
+So in particular, and this is
+now the new stuff, if there
+
+are 10 to the 500 vacua of
+String theory, for example.
+
+We don't really know the number,
+but something crazy like that.
+
+And if only one part in
+10 to the 120 of them
+
+have this very small energy,
+thus the energy densities
+
+are spread from plus
+10 to the 120 times
+
+what we observe to minus 10 to
+the 120 times what we observe.
+
+That would mean that
+what we observed
+
+would be a narrow slice in the
+middle there occupying about 10
+
+to the minus 120th of the
+length of that spread.
+
+We would then expect--
+and all this, of course,
+
+is very crude estimates.
+
+It's not really the
+numbers that's important,
+
+it's whether or not
+you believe the ideas.
+
+But we'd expect then that
+about 10 to the minus 120
+
+of the different vacua would
+have an acceptably low vacuum
+
+energy density.
+
+But that's still a
+colossal number because 10
+
+to the minus 120
+times 10 to the 500--
+
+you add the exponents--
+is 10 to the 380.
+
+So we would still predict
+that even though they'd
+
+be very rare, there might be
+10 to the 380 different kinds
+
+of vacua, all which would
+have a vacuum energy density
+
+as well as what we observe.
+
+So there's no problem finding,
+in the landscape, vacua
+
+whose energy density is
+as low as what we observe.
+
+But then there's the question
+if they're so incredibly rare,
+
+wouldn't it take
+a miracle for us
+
+to be living in one of these
+incredibly unusual vacua
+
+with such an extraordinarily
+low vacuum energy density.
+
+That then leads to
+what is sometimes
+
+called Anthropic considerations
+or perhaps a selection effect.
+
+And to see how that works and
+make it sound not as crazy
+
+as it might sound
+otherwise, I want
+
+to begin by giving an example
+where I think one could really
+
+say that this effect happens.
+
+And that is suppose we just
+look at our own position
+
+in our own visible
+universe and look at,
+
+for example, the mass density.
+
+Where we're actually
+living is incredibly
+
+unusual in many ways, but one
+of the ways we could talk about,
+
+which is just simple
+and quantitative,
+
+is the mass density.
+
+The mass density of the
+things around this room
+
+is on the order of one gram per
+centimeter cubed give or take
+
+a factor of 10.
+
+The factor of 10 is
+not very important
+
+for I'm talking about here.
+
+The point is that
+the average mass
+
+density of the universe, the
+visible universe, is about 10
+
+to the minus 30 grams
+per centimeter cubed.
+
+It's really unbelievable
+how empty the universe is.
+
+It's actually a far lower mass
+density than is possible for us
+
+to achieve in laboratories
+on Earth with the best vacua
+
+that we can make in
+our laboratories.
+
+So where we're living
+has a mass density of 10
+
+to the 30 times the average
+of the visible universe.
+
+So we're not living in a typical
+place in our visible universe.
+
+We're living in an
+extraordinarily atypical place
+
+within our visible universe.
+
+And we can ask how
+would we explain that.
+
+Is it just a matter
+of chance that we're
+
+living in a place that's
+such a high mass density?
+
+Doesn't seem very likely
+if it's a matter of chance.
+
+Is it luck?
+
+Is it divine
+providence, whatever?
+
+I think most of us would admit
+that it's probably a selection
+
+effect.
+
+That that's where life happens.
+
+Life doesn't happen throughout
+most of the visible universe,
+
+but in these rare
+places, like the surface
+
+of our planet, which is
+special in more ways than just
+
+the mass density, but
+the mass density alone
+
+is enough to make it
+extraordinarily special.
+
+We're off by a factor
+of 10 to the 30
+
+from the average
+of our environment.
+
+So if we're willing
+to explain why
+
+we live in such an unusual place
+within our visible universe
+
+and explain that as simply
+a requirement for life,
+
+then it doesn't seem to be such
+a stretch to maybe imagine--
+
+and it was Steve Weinberg who
+first emphasized this in 1987.
+
+Certainly not the
+first person to say it,
+
+but the first person to
+say it and have people
+
+sometimes believe him.
+
+He pointed out that may be the
+low energy-- the low vacuum
+
+energy density could be
+explained the same way.
+
+If we're not living
+in a typical place
+
+within our visible
+universe, there's
+
+no reason for similar
+ideas to expect
+
+that we should be living
+in a typical place
+
+in the multiverse.
+
+Maybe only a small fraction
+of these different types
+
+of pocket universe's
+can support life.
+
+And maybe the only
+way to have life
+
+is to have a very small value
+for the vacuum energy density.
+
+And there is some
+physics behind that.
+
+Remember this vacuum energy
+density drives expansion--
+
+acceleration, I should say.
+
+So if the vacuum energy density
+were significantly larger
+
+than what we
+observe, the universe
+
+would accelerate
+incredibly rapidly
+
+and would fly apart
+before there'd
+
+be any time for anything
+interesting to happen
+
+like galaxies forming.
+
+Weinberg based his arguments
+here on the assumption
+
+that galaxies are a
+necessity for life.
+
+Yes?
+
+AUDIENCE: So that's
+what I was going to ask.
+
+Why do we assume that our
+universe is the only one that
+
+could have like-- why couldn't
+just all the multi-universes
+
+have like--
+
+PROFESSOR: Right.
+
+Right.
+
+Well, that's OK.
+
+That is what I am talking about.
+
+I'm trying to answer it.
+
+So if the vacuum energy density
+were significantly larger
+
+than what we observe,
+the universes
+
+would fly apart so fast
+that there could never
+
+be galaxies and therefore
+never planets, none of things
+
+that we think of as being
+associated with life as we know
+
+it.
+
+Conversely, if the vacuum energy
+density were negative, but had
+
+a magnitude large compared
+to what we observed,
+
+that would be a large negative
+acceleration, an implosion.
+
+And those universes would
+just implode, collapse,
+
+in an incredibly short amount
+of time, much too fast for life,
+
+of any type that we
+know of, to form.
+
+So there is a physical argument
+which suggests that life only
+
+forms when the vacuum
+energy density is very low.
+
+And Weinberg and his
+collaborators-- and this
+
+is the same Steve Weinberg who
+wrote the First Three Minutes
+
+that we're reading-- calculated
+what the requirements would
+
+be for galaxy formation.
+
+And they decided that, within
+about a factor of 5 or so,
+
+the vacuum energy
+density would have
+
+to be about the same as
+what we observe or less
+
+in order for galaxies to form.
+
+So it seems like a
+possible explanation.
+
+It's certainly not a generally
+accepted explanation.
+
+These things are very
+controversial one.
+
+I guess that's, in
+fact, what I was
+
+going to talk about
+on my next slide.
+
+Some physicists by this
+selection effect idea.
+
+I tend to buy it.
+
+But a number of physicists
+regard it as totally
+
+ridiculous, saying you
+could explain anything
+
+if you except
+arguments like that.
+
+And there's some truth to that.
+
+You can explain a lot
+of things if you're
+
+willing to just say,
+well, maybe that's needed
+
+for life to happen.
+
+So because of that, I would
+say that these selection effect
+
+arguments or anthropic
+arguments should always
+
+be viewed as the
+arguments of last resort.
+
+That is, unless we
+actually understand
+
+the landscape of
+String theory, which
+
+we do not in detail,
+and once we actually
+
+understand what it
+takes to create life,
+
+we really can't do more than
+give plausibility arguments
+
+to justify these
+anthropic explanations.
+
+But these anthropic
+arguments do sound sensible.
+
+I think there's nothing
+illogical about them,
+
+and they could very well be the
+explanations for some things.
+
+As I pointed out, I think it
+is the explanation for why
+
+we are living in
+such an unusual place
+
+within our own visible universe.
+
+And it means that these
+selection effect arguments
+
+become very attractive when the
+search for more deterministic
+
+explanations have failed.
+
+And in the case of trying to
+explain the very small vacuum
+
+energy density, I think
+other attempts have failed.
+
+We don't have any calculational,
+deterministic understanding
+
+for why the vacuum energy
+should be so small.
+
+So is it time to accept this
+explanation of last resort
+
+that the vacuum energy
+density is small
+
+because it has to be
+for life to the evolve?
+
+Your guess is as good as mine.
+
+I don't really know.
+
+But I would say that, in the
+case of the vacuum energy
+
+density, people have
+been trying very, very
+
+hard for quite a
+few years now to try
+
+to find a particle physics
+explanation for why the vacuum
+
+energy has to be small, and
+nobody's really found anything
+
+that anybody has found-- that
+any large number of people
+
+have found to be acceptable.
+
+So it is certainly a
+very serious problem.
+
+And I think it is
+time to take seriously
+
+the argument of last resort,
+that maybe it's that way only
+
+because in the parts of the
+multiverse where it's not
+
+that way, nobody lives there.
+
+So I would say it's
+hard to deny, as of now,
+
+that the selection
+effect explanation is
+
+the most plausible of
+any explanation that
+
+is known at the present time.
+
+To summarize things--
+I'm actually done now,
+
+but let me just
+summarize what I said
+
+to remind you where we're at.
+
+I've argued that the
+inflationary paradigm
+
+is in great shape.
+
+It explains the large
+scale uniformity.
+
+It predicts the mass
+density of the universe
+
+to better than about 1% accuracy
+and explains the ripples
+
+that we see in the cosmic
+background radiation,
+
+explaining them as a result
+of quantum fluctuations
+
+that took place in the
+very early universe.
+
+The picture leads
+to three ideas that
+
+at least point towards
+the idea of a multiverse.
+
+It certainly doesn't prove that
+we're living in a multiverse.
+
+But the three ideas that
+point in that direction
+
+are, first of all, the
+statement that almost
+
+all inflationary models
+lead to this feature
+
+of eternal inflation, that
+the exponential expansion
+
+of the inflating material,
+generally speaking,
+
+out runs the decay
+of that material
+
+so that the volume grows
+exponentially forever.
+
+Second point is that, in 1998,
+the astronomers discovered
+
+this rather amazing fact
+that the universe is not
+
+slowing down as it expands,
+but in fact, is accelerating.
+
+And that indicates
+that there has
+
+to be some peculiar material
+in the universe other than what
+
+we already knew was here,
+and that peculiar material is
+
+called the dark energy.
+
+And we don't have any simple
+interpretation of what it is,
+
+but it seems to most
+likely be vacuum energy.
+
+And if it is, it
+leads immediately
+
+to the important
+question of can we
+
+understand why it has
+a value that it has.
+
+It seems to be much smaller
+than what we would expect.
+
+And then three, the
+String theorists
+
+give us an interesting
+way out here.
+
+The String theorists tell
+us that maybe there's
+
+not unique vacuum to
+the laws of physics,
+
+but maybe there's a
+huge number, which
+
+seems to be in fact what
+String theory predicts.
+
+And if there is, then of
+the many different vacua
+
+you expect there to be,
+in fact perhaps even
+
+a large number, that would have
+this very small vacuum energy
+
+density, a tiny fraction of
+the total different vacua,
+
+but nonetheless a
+large number of vacua
+
+that would have this property.
+
+And then this
+selection effect idea
+
+can provide a
+possible explanation
+
+for why we are living in one of
+those very unusual vacua which
+
+has this incredibly tiny
+vacuum energy density.
+
+So finally, I'd
+just like to close
+
+with a little sociological
+discussion here.
+
+Do physicists really
+take this seriously?
+
+And I'd like to tell you about
+a conversation that took place
+
+at a conference a few years ago.
+
+Starting with Martin Rees, who I
+don't know if you know the name
+
+or not, but he's an Astronomer
+Royal of Great Britain,
+
+former president
+of Royal Society,
+
+former master of
+Trinity College as well,
+
+a very distinguished person,
+nice guy, too, by the way.
+
+And he said that
+he is sufficiently
+
+confident in the multiverse
+to bet his dog's life on it.
+
+Andrei Linde, from Stanford,
+a real enthusiastic person
+
+about the multiverse, one of the
+founders of inflation as well,
+
+said that he's so
+confident that he
+
+would bet his own life on it.
+
+Steve Weinberg was not
+at this conference,
+
+but he wrote an article
+commenting on this discussion
+
+later which became known.
+
+And I always considered
+Steve Weinberg
+
+the voice of reason,
+which is why we're
+
+reading the First Three Minutes.
+
+And he said that I have
+just enough confidence
+
+in the multiverse to
+bet-- guess what's
+
+coming-- the lives of both
+Andrei Linde and Martin Rees'
+
+dog.
+
+That's it for the
+summary, or the overview.
+
+Anymore overview type
+questions before we get back
+
+to the beginning, actual
+beginning of the class?
+
+Yes?
+
+AUDIENCE: You said-- so
+selection effect argument says
+
+that it's because life
+exists within these certain
+
+constraints, omega being one
+and low energy larger than it
+
+generally is allowed, that
+life could exist in this way.
+
+But we're considering
+carbon-based life.
+
+What if there's some
+other [INAUDIBLE] life
+
+forms out there that gives
+us different energies
+
+and radiation and
+stuff like that?
+
+PROFESSOR: Yeah, what
+you're pointing toward
+
+is certainly a severe weakness
+of these selection effect
+
+arguments, that we really know
+about carbon-based life, life
+
+that's like us, and we can
+talk about what conditions
+
+are needed to make life
+like us, but maybe there's
+
+life that's totally
+different from us
+
+that we don't know
+anything about that
+
+might be able to
+live under totally
+
+different circumstances.
+
+That is a real weakness.
+
+However, I would argue-- and
+this is also controversial.
+
+Not everybody would agree
+with what I'm about to say.
+
+But I would argue that if
+we're willing to explain
+
+the unusual features of
+the piece of the universe
+
+that we live in by
+selection effect arguments--
+
+the fact I used, the
+example is simply
+
+that we're living a place
+where the mass density is
+
+10 to the 30 times
+larger than the mean.
+
+If we're willing to use the
+anthropic arguments to explain
+
+that, then I think all those
+same issues arise there also.
+
+If life was really teem--
+if the universe was really
+
+teeming with a different
+kind of life that
+
+thrived in vacua,
+then we'd be much more
+
+likely to be one of them,
+extremely unusual creatures
+
+living on the
+surfaces of planets.
+
+So I think it's a
+possible weakness
+
+that one has to
+keep in mind, but I
+
+don't think it should
+stop us from using
+
+those arguments completely.
+
+But it is certainly a
+cause for skepticism.
+
+Yes?
+
+AUDIENCE: Isn't the point
+of the selection principle
+
+just the fact that exist--
+the universe selected for us.
+
+Does it matter for the general
+of just for like carbon-based
+
+[? organisms? ?] Is the fact
+that we exist [INAUDIBLE]
+
+that we've been selected
+for [INAUDIBLE]?
+
+PROFESSOR: You're
+asking about, I
+
+think, how peculiar
+to carbon-based life
+
+should we expect these selection
+effect arguments to be.
+
+AUDIENCE: Doesn't the selection
+affect where [INAUDIBLE]?
+
+PROFESSOR: Now that's
+an important point,
+
+and certainly one that's not
+settled among philosophers,
+
+probabilist,
+physicists, or anybody.
+
+What you're asking-- if
+I'm summarizing it right--
+
+is when we're thinking
+of the selection effects,
+
+should we may be only talk
+about carbon-based life
+
+because, after all, we know
+that we are carbon-based life.
+
+So what does it matter if
+there's other kinds of life
+
+out there?
+
+That's one way of
+looking at it, certainly.
+
+Or, maybe we should think
+about all kinds of life.
+
+That's something
+else that people say.
+
+The problem I would--
+I tend to be by the way
+
+the kind of person that thinks
+that all life is relevant,
+
+not just carbon-based life.
+
+Because we happen
+to be carbon-based,
+
+and we happen to
+have fingernails
+
+that have a certain
+length, and we
+
+happen to have hair
+that's a certain length
+
+or a certain
+thickness, does that
+
+mean we should only
+think of those things
+
+as being relevant
+when we're thinking
+
+about selection effects?
+
+And I would say
+that they're not.
+
+If our hair had a
+different thicknesses,
+
+we would still be able to
+make measurements and so on.
+
+So from my point
+of view, when one
+
+thinks about these issues
+of selection effects,
+
+one should precondition
+only on the elements that
+
+are necessary to ask the
+question in the first place.
+
+And what I would like to
+think-- and as I point out,
+
+this is controversial,
+not everybody
+
+agrees with me-- is that
+a good theory should
+
+be a theory in which you could
+say that most of the people who
+
+ask this particular question
+will get the answer that we
+
+say.
+
+If only a tiny fraction of
+people who ask that question
+
+will get that answer, but
+that same tiny fraction
+
+happens to have hair
+of a certain color
+
+and you have hair
+of that color, to me
+
+that's still not an explanation
+because you don't know why you
+
+have hair of that
+color or why you're
+
+living in such an unusual place.
+
+OK that strikes up a
+lot of conversations.
+
+Yes?
+
+AUDIENCE: You
+mentioned last time
+
+that the different
+pocket universes
+
+that comprise the multiverse
+are disconnected from each other
+
+though they start out as patches
+within the preceding vacua.
+
+What starts to disconnect
+them fundamentally
+
+from the vacuum
+which they formed?
+
+PROFESSOR: The question is
+what is it that separates these
+
+different pocket universe's.
+
+If they start out all
+in the same space,
+
+don't they remain all
+in the same space?
+
+And the answer is they do, but
+the space they started out in
+
+was expanding at
+a very rapid rate.
+
+So in most cases,
+but not all actually,
+
+two pocket universes will
+form far enough apart
+
+from each other
+that they will never
+
+touch each other as they grow
+because the space in between
+
+will expand to fast to
+ever allow them to meet.
+
+However, collisions
+of pocket universities
+
+will occur if two pocket
+universes form close enough
+
+to each other, the expansion
+of space in between
+
+will not be enough to keep them
+apart, and they will glide.
+
+How frequent one should
+think of that as being
+
+is an incredibly tough
+question to which
+
+nobody knows the answer.
+
+There are actually--
+at least there
+
+is at least one
+astronomical paper
+
+in the literature by
+a group of astronomers
+
+who have looked for possible
+signs of a collision of bubbles
+
+in our past.
+
+They did not find
+anything definitive.
+
+But it is something
+to think about,
+
+and it's something people
+are thinking about.
+
+There really are
+quite a few papers
+
+about collisions of
+bubbles in the literature.
+
+Yes?
+
+AUDIENCE: How long
+is long-lived?
+
+So if the energy density was
+too large and too negative
+
+would that still
+be long-lived if it
+
+were to collide upon itself?
+
+PROFESSOR: Talking about the
+lifetime of these universes
+
+that I said would
+collapse very quickly.
+
+How quickly do I mean?
+
+AUDIENCE: Like the
+metastable long-lived.
+
+PROFESSOR: I used
+the word long-lived
+
+at least twice in what I've
+talked about-- I talked
+
+about the long-lived
+metastable vacua.
+
+And there, by long-lived
+I mean anything
+
+that's long compared to the age
+of our universe since the Big
+
+Bang.
+
+Long means long
+compared to 10 to the 10
+
+years in that context.
+
+I also said that if the
+vacuum energy of a universe
+
+were large and negative, it
+would very rapidly collapse.
+
+That could be as fast as
+10 to the minus 20 seconds.
+
+It could be very fast
+depending on how large
+
+the cosmological constant was.
+
+Yes?
+
+AUDIENCE: So I have read
+that there's an effect such
+
+that if you're vacuum
+can be seen differently
+
+by different observers.
+
+For example, inertial--
+there's something
+
+that I read in effect it says
+that if one inertial observer
+
+sees vacuum, another
+observer that's
+
+accelerating with
+respect to that observer
+
+would see like a number
+of particles [INAUDIBLE]
+
+a warm gas.
+
+So how much of the effect we
+observe are due to the fact
+
+that perhaps we believe the
+universe is accelerating,
+
+and we're accelerating perhaps
+with respect to some vacuum
+
+and we're just observing that.
+
+That's just a fact of our
+motion not necessarily the--
+
+PROFESSOR: You're
+touching on something
+
+that is in fact very confusing.
+
+What is your name?
+
+AUDIENCE: Hani.
+
+PROFESSOR: Hani?
+
+What Hani said was
+that he had heard--
+
+and this is correct--
+that if one had simply
+
+a region of ordinary
+vacuum-- and I am now
+
+going to talk about
+special [INAUDIBLE] vacuum.
+
+You don't even need relativity.
+
+You don't general relativity,
+you just need this.
+
+If you had an accelerating
+observer moving
+
+through that vacuum, the
+accelerating observer
+
+would not see something
+that looked like vacuum,
+
+but rather would see particles
+that in fact would look
+
+like they had a finite
+temperature which you can
+
+calculate, a temperature that's
+determined by the acceleration.
+
+So the question is,
+how much of what
+
+we see should we think
+of as really being there
+
+and how much might be caused
+just by our own motion.
+
+And there's not a terribly
+great answer to that question
+
+that I know of except that we--
+when these questions come up,
+
+we tend to just
+adopt the philosophy
+
+that an observer
+who's freely moving,
+
+which really means moving
+with the gravitational field,
+
+a geodesic observer as the
+word phrase is sometimes used,
+
+essentially defines what
+you might call reality
+
+and then if you calculate what
+accelerating observers might
+
+see in terms of that reality.
+
+And we are almost
+geodesic observers.
+
+The Earth is exerting a
+force on our feet, which
+
+violates that a little bit,
+but by the overall cosmic scale
+
+of things where
+the speed of light
+
+is what determines
+what's significant,
+
+we are essentially inertial
+or geodesic observers.
+
+Yes, Aviv?
+
+Aviv first and then
+the one in front.
+
+AUDIENCE: So I'm wondering
+about the philosophical approach
+
+to this discussion and why
+the very-- by the definition,
+
+we can't possibly
+observe another universe.
+
+And so maybe we
+have a theory that
+
+makes a lot of great
+predictions like inflation.
+
+But it may also make
+predictions about multiverse.
+
+We can't possibly empirically
+determine whether that's true
+
+or not, so a
+nonfalsifiable question.
+
+And so I feel like
+[INAUDIBLE] who [INAUDIBLE]
+
+essentially never
+going to be answered.
+
+And if we're going to
+be strict empiricists,
+
+should we not be concerned
+with this question?
+
+PROFESSOR: The question is if we
+could never see another pocket
+
+universe, is it even
+a valid question
+
+to discuss whether
+or not they exist,
+
+a valid scientific question.
+
+That is also a question
+which is generally
+
+debated in the community, and
+people have taken both sides.
+
+There certainly is
+a point of view,
+
+which I think I
+tend to take, which
+
+is that we never really
+insist that every aspect
+
+of our theories can be tested.
+
+If you think about any theory,
+even Newtonian gravity,
+
+you can certainly
+imagine implications
+
+of Newtonian
+gravity that you can
+
+calculate that
+nobody's ever measured.
+
+So I think in practice we
+tend to accept theories
+
+when they have made enough
+measurements that we've tested
+
+so that the theory
+becomes persuasive.
+
+And when that happens, I think
+we should, at the same time,
+
+take seriously whatever
+those words mean,
+
+the implications that the theory
+has for things that cannot be
+
+directly tested.
+
+As far as the other
+pocket universes,
+
+some people think
+it's important,
+
+and maybe I do too,
+that even though it's
+
+highly unlikely, incredibly
+unlikely, unbelievably unlikely
+
+that we'll ever acquire
+direct observational evidence
+
+for another pocket universe,
+it's not really in principle
+
+impossible because of the fact
+that pocket universes can,
+
+in principle, collide.
+
+So we could, in principle,
+describe with evidence
+
+that our universe has had
+contact with another pocket
+
+universe in the past.
+
+Yes.
+
+AUDIENCE: What
+determines the stability
+
+of a particular vacuum state?
+
+Is it simply things with higher
+vacuum energies are less stable
+
+and things with lower vacuum
+energies are more stable?
+
+PROFESSOR: The question
+is what determines
+
+the stability of
+the different vacua.
+
+Is it simply that
+higher energy ones
+
+are more unstable and lower
+energy ones are more stable
+
+or is it more
+complicated than that?
+
+And the answer,
+as far as I know,
+
+is that there is a trend
+for higher energy ones
+
+to be more unstable and lower
+energy ones to be more stable.
+
+But it's not as simple as that.
+
+There are also wide
+variations that
+
+are independent of
+the energy density.
+
+AUDIENCE: If the one
+that we're living in
+
+is incredibly is really
+ridiculously close to zero
+
+in a city that seems to make
+it incredibly unlikely that we
+
+would pay anything else I soon
+
+PROFESSOR: Right.
+
+The question is if
+our universe has
+
+such has such a
+small energy density
+
+relative to the average.
+
+Wouldn't that mean
+that we should also
+
+expect to be much more
+long-lived than average?
+
+And the answer is I guess so.
+
+But as far as the effect
+on the Swiss cheese
+
+picture that I described
+for the ultimate future,
+
+it doesn't change the
+words that I used.
+
+It just changes how frequent
+those decays would be.
+
+But since the future of
+this pocket universe,
+
+if this picture is
+right, will be infinite,
+
+decays will happen no matter
+how small the probability is.
+
+An infinite number of
+decays will happen in fact.
+
+OK we should probably
+go on now even
+
+if there are more questions.
+
+We have a whole term to
+discuss things like this.
+
+The next thing I
+want to do is handle
+
+some housekeeping details.
+
+I'd like to arrange
+office hours.
+
+And the problem sets
+are due on Friday,
+
+so what [? Tsingtao ?]
+and I thought
+
+was that a good time
+for office hours
+
+would be on Wednesdays
+and Thursdays.
+
+One of us on each of those days.
+
+It turns out that I can't
+really do Thursdays,
+
+so one of us on
+each of those days
+
+ends up meaning
+that I'll probably
+
+be having office
+hours on Wednesdays.
+
+This is all
+provisional depending
+
+on how it works with you folks.
+
+And [? Tsingtao ?]
+will probably be
+
+having office
+hours on Thursdays.
+
+Generally speaking, if one
+wants to have an office
+
+hour that most
+people can come to,
+
+I think it should be
+in the late afternoon.
+
+So maybe we'll start by
+discussing my office hours
+
+since it comes before
+[? Tsingtao's, ?] Wednesday
+
+versus Thursday.
+
+So on Wednesday, I
+can do an office hour
+
+in the late, normal afternoon,
+which might mean 4:00 to 5:00
+
+I think after five some
+people have sports activities
+
+and things.
+
+We're told to try to
+avoid those hours.
+
+So 4:00 to 5:00 would be
+a reasonable possibility
+
+for my office hour on Wednesday.
+
+If that doesn't
+work, I could stay
+
+and have the office
+hour in the evening.
+
+That's actually what
+I did two years ago.
+
+I had an office hour
+from 7:30 to 8:30.
+
+It was also
+Wednesdays-- I forget.
+
+But it was in the evening,
+and that's a possibility.
+
+So let me ask if I have my
+office hour from 4:00 to 5:00
+
+on Wednesdays, how
+many of you who
+
+might be interested in coming
+would not be able to come?
+
+1, 2, 3, 4, 5, 6,
+7, 8, 9, 10, 11, 12.
+
+A significant number, but
+most of you can come at least.
+
+Let me ask the corresponding
+question for the evening.
+
+Suppose I made the office
+hour from 7:30 to 8:30
+
+in the evening on Wednesdays.
+
+In that case, how many of
+you who might want to come
+
+would not be able to come?
+
+1, 2, 3 5, 6, so it's a smaller
+number, but not vastly smaller.
+
+OK I think I'll do it in
+the evening for the benefit
+
+of the difference
+between those two groups.
+
+And the evening also has
+the little slight advantage
+
+that it can be a little more
+open-ended if people still
+
+have questions after
+the normal time is over.
+
+So I will make my office hour on
+Wednesday's from 7:30 to 8:30.
+
+Is that particular hour as good
+an hour as any on Wednesday
+
+evening.
+
+Would people want to
+move it earlier or later?
+
+Any suggestions for moving
+it earlier or later?
+
+AUDIENCE: I know people have
+sports til technically at least
+
+7:00, but if it's 6:30 to
+7:30 might be a little--
+
+PROFESSOR: 6:30?
+
+You'll be starting at 6--
+starting at 6:30 versus-- 6:30
+
+to 7:30, starting at 6:30.
+
+Well, I'd be happy
+to do that, but I
+
+suspect we might run
+into problems with people
+
+who have sport
+activities, but let's see.
+
+How many of you would
+be inconvenienced
+
+if I started at 6:30
+instead of 7:30?
+
+3, 4, 5, 6, a number.
+
+So I think we'll honor
+that and start at 7:30.
+
+I assume 7 is also a bit of
+a problem for those people.
+
+We'll say 7:30.
+
+Now, I have to announce
+that this week is going
+
+to unfortunately have to be
+an exception because I already
+
+have plans for Wednesday night.
+
+So for this week, I
+think the best thing--
+
+the only possible
+thing, probably
+
+the best-- it's almost
+the only possible thing
+
+would be 4:00 to
+5:00 on Wednesday.
+
+Wednesday's bit tomorrow.
+
+I'll send you all an email
+when I find a room for that.
+
+I think I'll probably
+not have it in my office,
+
+but maybe it will
+be in my office.
+
+Comment up there?
+
+AUDIENCE: Oh, I was just
+going to ask where, but you--
+
+PROFESSOR: Where?
+
+OK, I guess then the
+fourth option's my office.
+
+I was hoping to put
+a sign of my office
+
+if we're someplace
+other than my office.
+
+So should put this
+on the board too.
+
+Tomorrow 4:00 to 5:00 PM.
+
+So be at my office
+or I'll send email.
+
+Yes?
+
+AUDIENCE: How will we be turning
+in the Thursday problem set?
+
+PROFESSOR: We're going
+to talk about that now.
+
+For Thursday, for
+[? Tsingtao, ?] I remember
+
+you had some constraints.
+
+So what was possible?
+
+TSINGTAO: Yeah.
+
+So I usually leave
+around 7:00 PM,
+
+so I have appointment
+[? meeting ?],
+
+and today is probably
+not very good at 4:00 PM.
+
+PROFESSOR: So 4:00 to 5:00 is a
+possibility for [? Tsingtao ?]
+
+on Thursday, and I
+guess later than that.
+
+But should be over by
+5:00-- by 7:00 either
+
+or do you want it to
+be over before then.
+
+TSINGTAO: Oh, 6:00 to 7:002
+Oh, 6:00 to 7:002 I guess.
+
+PROFESSOR: 6:00 to
+7:00 would be OK?
+
+TSINGTAO: Yeah, that's OK.
+
+PROFESSOR: OK, so let's
+start with 4:00 to 5:00.
+
+If [? Tsingtao ?] was to have
+an office hour from 4:00 to 5:00
+
+on Thursdays, how many of you
+think you might want to go
+
+would be unable to?
+
+Wow, tons!
+
+OK, that seems more than
+half of you I think.
+
+So I guess we try to avoid that.
+
+This impact's probably
+an athletic region,
+
+but maybe we'll have to do that
+for lack of an alternative.
+
+Suppose it were 5:00 to 6:00.
+
+How many of you who would be
+interesting in coming-- who
+
+might be interesting
+in coming, I should say
+
+I guess because it'll
+vary from week to week--
+
+but how many of you
+who think you might
+
+be interested in
+coming would not
+
+be able to come from 5:00
+to 6:00 on Thursdays.
+
+OK, a small group.
+
+1, 2, 3, 4, 5, 6, 7.
+
+Looks to me like 7.
+
+And let's say, I
+said 4:00-- That
+
+was at 6:00-- that
+was 5:00 to 6:00.
+
+So maybe we should next try 5:30
+to 6:30 in smaller increments
+
+here.
+
+If we're 5:30 to
+6:30, how many of you
+
+would not be able to come?
+
+Looks like pretty
+much the same people.
+
+And if it were 6:00 to
+7:00, how many of you
+
+would not be able to come?
+
+Same people, I think it is
+literally the same people.
+
+OK.
+
+So it looks like 4:00
+to 5:00 is very bad.
+
+And all other times
+are about equivalent.
+
+So I think if all other
+times are bad equivalently,
+
+we probably might as well
+make it 5:00 to 6:00.
+
+And that way
+[? Tsingtao ?] can get off
+
+to an earliest possible start
+to wherever he's going at 7:00,
+
+and it also means a little
+more flexibility in the end
+
+if there are more questions.
+
+AUDIENCE: Where is that located?
+
+PROFESSOR: That
+also, I think, will
+
+require us to get a room
+which will be announced.
+
+So I will try to
+arrange rooms tomorrow
+
+morning and send
+it by email, and I
+
+guess I'll post it on
+the website as well.
+
+Any other organizational--
+and questions
+
+limited to organizational
+questions now?
+
+Get back to physics later.
+
+Any organizational
+questions before we
+
+start on Doppler shifts?
+
+Yes?
+
+AUDIENCE: If I can't make
+a single office hour,
+
+how should I field questions
+when I have questions?
+
+PROFESSOR: A good question.
+
+Yeah, there may be some
+people, and apparently there is
+
+at least one who cannot
+make either of these times,
+
+even though we tried
+to optimize things.
+
+So by all means,
+don't feel like you
+
+don't have a channel
+for questions.
+
+If you have a question,
+send an email to
+
+either me, or
+[? Tsingtao, ?] or both.
+
+And we'll either answer
+it together with you
+
+or answer you by email depending
+on what the question is
+
+and what seems useful.
+
+And that goes for everybody.
+
+In that case, if
+everybody's on board,
+
+we will now start the actual
+material for the term.
+
+Well, the overview
+is an overview
+
+of the material for the term,
+but not at the standard pace
+
+and the standard
+level of detail.
+
+So what I want to
+talk about this week--
+
+and I guess I'll only get
+to start today and finish
+
+on Thursday-- I had
+planned to tell you
+
+everything you need to know
+for the problem set by today,
+
+but that's not going to happen.
+
+So I don't-- if people complain,
+we could consider postponing
+
+the due date of the problem
+set, so consider that an option.
+
+But probably you could
+do the problem set anyway
+
+because it is all
+described in lecture notes.
+
+But if any of you have
+difficulties meeting
+
+that deadline, it will be a
+somewhat flexible deadline
+
+this week because of
+the fact that I'm not
+
+covering the material
+today as I had planned.
+
+And I'll admit that's not
+necessarily a good thing
+
+to do in terms of problem set.
+
+So we're going to begin
+the course, in principle,
+
+by talking about Hubble's law,
+although Hubble's law will
+
+rapidly lead us to the
+question of the Doppler shift,
+
+which is what I'll
+mainly be talking
+
+about for the rest of today
+and for most of Thursday.
+
+Hubble's law itself
+is a simple equation
+
+that v is equal to h r,
+where v is the recession
+
+velocity of any typical galaxy.
+
+Hubble's law is
+not an exact law,
+
+so individual galaxies will
+deviate from Hubble's law.
+
+But in principle,
+Hubble's law tells you
+
+what the recession velocity
+is of a galaxy, at least
+
+to reasonable accuracy.
+
+Where h is what is often
+called Hubble's constant.
+
+Sometimes, it is called
+the Hubble parameter.
+
+I like actually-- it's called
+the Hubble expansion rate.
+
+The problem with calling
+Hubble's constant
+
+is that it's not
+really a constant
+
+over the lifetime
+of the universe.
+
+It's a constant over the
+lifetime of an astronomer,
+
+but not a constant over the
+lifetime of the universe?
+
+And we'll be talking about
+universes, not astronomers,
+
+at least for the most part.
+
+And even over history,
+it's not a constant
+
+because the estimate
+of Hubble's constant
+
+has actually changed by a
+factor of about 10 or so
+
+since Hubble's
+original estimate.
+
+And the r that appears here
+is the distance to the galaxy.
+
+And if you look at the lecture
+notes from two years ago,
+
+they start out by saying
+that Hubble's law was
+
+discovered by Hubble in 1929.
+
+When I looked at that
+first sentence in my notes,
+
+and when I started to
+revise them for this year,
+
+I realized that I heard
+that that statement has
+
+become controversial.
+
+Almost everything in
+cosmology is controversial,
+
+so even that statement
+is controversial.
+
+There are claims
+that Lemaitre really
+
+deserves credit for Hubble's
+law rather than Hubble.
+
+And there's some
+validity to that claim.
+
+There's also some
+[? intrigued ?] that happens,
+
+if you want to read about this.
+
+It was discovered by
+several of-- I think
+
+amateur historians I think is
+what they are often referred
+
+to in the press-- that we know
+mainly of Lemaitre's work-- we
+
+being the Western speaking,
+the Western English speaking
+
+world-- know mainly
+of a Lemaitre's work
+
+through a 1931 translation
+in a 1927 paper
+
+he wrote about the
+foundations of cosmology.
+
+And it turned out that several
+significant seeming paragraphs
+
+in the 1927 French
+article somehow
+
+didn't make it to the 1931
+English translation, paragraphs
+
+about the Hubble constant.
+
+And for a while, that
+seemed like dirty play
+
+and there were accusations that
+Hubble, or friends of Hubble,
+
+had suppressed those
+paragraphs when
+
+the article was translated.
+
+The truth finally was
+discovered a couple years ago
+
+by a physicist named Mario Livio
+who actually was on the Daily
+
+Show a couple nights
+ago by the way.
+
+He has a book out now, not about
+this, but about other things.
+
+But anyway, he
+discovered by going
+
+through the archives of the
+monthly notices of astronomy,
+
+which is where the article
+was published in English.
+
+And turned out it
+was Lemaitre himself
+
+he removed those paragraphs.
+
+The paragraphs basically
+gave a numerical estimate
+
+of the Hubble constant, but by
+1931 Hubble's papered already
+
+been published, so Lemaitre
+felt that it was only
+
+a less accurate estimate
+of the same quantity
+
+that Hubble had estimated, so he
+cut it out of his translation.
+
+What certainly is
+true is that Lemaitre
+
+knew about Hubble's law
+on theoretical grounds.
+
+Lemaitre was building a model
+of an expanding universe.
+
+I don't know if he is
+really the first person
+
+to know that an expanding
+universe model gave rise
+
+to a linear relationship
+between velocity and distance,
+
+but he certainly did know about
+it and understood Hubble's law
+
+and give an estimate
+of it based on data.
+
+What he did not
+do, however, is try
+
+to use data to actually
+show that there
+
+was a linear relationship.
+
+What Lemaitre did,
+in those paragraphs
+
+that were not
+translated, was simply
+
+to look at a large
+group of galaxies,
+
+figure an average value for
+v and an average value of r
+
+and determine h from
+dividing those two averages.
+
+And he admitted
+that there was not
+
+really good enough data to tell
+if the relationship is linear
+
+or not.
+
+I think it is definitely
+fair to say that Hubble
+
+is the person who deserves
+credit for arguing first really
+
+with a fairly weak argument,
+but then got stronger over time,
+
+that there really is
+astronomical evidence
+
+for this linear relationship
+between velocity and distance.
+
+So probably it will continue
+to be called Hubble's law.
+
+If you look in
+Wikipedia, it tells you
+
+either one is acceptable
+at the moment,
+
+but Wikipedia articles
+change rapidly,
+
+so we'll see what
+it says next year.
+
+It's also mentioned
+that we should probably
+
+root for Lemaitre since
+Lemaitre, it turns out-- well,
+
+he was a Belgian priest,
+it was often described,
+
+but he was also an MIT
+student, had a Ph.D. for MIT,
+
+which he received in 1927.
+
+You can actually
+read his thesis.
+
+When I was writing
+my [INAUDIBLE] book,
+
+I remember going
+to the MIT archives
+
+and actually picking up
+his thesis and reading it.
+
+It's not that well-written
+actually, but it's interesting.
+
+Although he got
+his Ph.D. from MIT,
+
+it also turns out that
+he did most of his work
+
+down Mass Ave at the
+Harvard College Observatory,
+
+but the Harvard
+College Observatory
+
+did not give degrees
+in those days.
+
+It was just an observatory.
+
+So he wanted to get a
+degree, so he signed up
+
+at MIT for the Ph.D.
+Program and wrote a thesis,
+
+received a Ph.D.
+
+Onward, what I really
+want to talk about
+
+is, after mentioning
+Hubble's law--
+
+so Hubble's law as an indication
+that the universe is expanding.
+
+And we'll talk more about the
+history of all this later,
+
+and it actually is very
+well-described in Steve
+
+Weinberg's book.
+
+But initially, Einstein
+proposed a model
+
+of the universe that was
+static, and it was really
+
+Hubble who convinced
+Einstein that observationally
+
+the universe does not appear
+to be static, but does
+
+appear instead to obey
+this expansion law.
+
+So that gave rise to the theory
+of the expanding universe.
+
+But what I want to
+talk about today
+
+is how one measures the
+v that appears here.
+
+There's also a big
+discussion about how
+
+one measures r, the distance.
+
+And that is, I think, rather
+well-done in Steve Weinberg's
+
+book, and I'm going to
+pretty much leave it
+
+to your reading of
+Steve Weinberg's book
+
+to learn about how distances to
+distant galaxies are estimated.
+
+Roughly-speaking,
+I might just say
+
+that they are estimated
+by finding objects
+
+in those distant galaxies
+whose brightnesses you think
+
+you know, by one
+means or another.
+
+And a complicated story
+is what objects are there
+
+in brightnesses
+we think we know.
+
+But once you find an
+object whose brightness
+
+you think you know, those
+go by the general name
+
+of standard candles,
+a standard candle
+
+being an object whose
+brightness you know,
+
+then you can tell
+how far the object is
+
+by how bright it appears.
+
+And that becomes a very
+straightforward way
+
+of estimating distances,
+and that is the only way
+
+we really have of estimating
+distances of distant galaxies.
+
+So it's a much longer story than
+what I just said, and you'll
+
+read about it in
+Weinberg's book.
+
+The velocity is measured
+by the Doppler shift,
+
+and that's what lecture
+notes one are mainly about,
+
+and that's what I'll be
+talking about for the remaining
+
+few minutes of today's class.
+
+And what we want to do in the
+course of this set of lecture
+
+notes, this week of
+class I guess it will be,
+
+is understand how to
+calculate the Doppler
+
+shift both non-relativistically
+and relativistically,
+
+and we'll just work out the
+primary cases of observer
+
+stationary source moving, source
+stationary observer moving,
+
+and all in a line, for
+both the relativistic and
+
+non-relativistic cases.
+
+So I think I'll launch into
+the first calculation, which
+
+you might even have
+time to finish.
+
+I'd like to consider
+a case where
+
+the observer is stationary
+and the source is moving,
+
+which is normally how we
+think of the distant galaxies.
+
+We work in our own reference
+frame, so we're stationary,
+
+the galaxy is moving.
+
+How do we calculate
+this redshift
+
+I should say at the
+asset here, however--
+
+I don't know if I said
+it in the lecture notes--
+
+that the cosmological
+redshift is actually
+
+a little bit different from what
+we're calculating this week.
+
+This week, we're calculating
+the special relativity redshift.
+
+But cosmology is not controlled
+by special relativity
+
+because special relativity
+does not describe gravity,
+
+and gravity plays a
+major role in cosmology.
+
+So the cosmological redshift,
+we will talk about a little
+
+later in the course,
+in a more precise way.
+
+But for now, we, like Hubble--
+Hubble didn't know any better--
+
+are ignoring gravity, which
+is OK for the nearby stars,
+
+and the further away they
+are, the more important
+
+these gravitational influences
+are, and ignoring gravity one
+
+could just use special
+relativity or even
+
+Newtonian kinematics
+to calculate
+
+the relationship between
+v and the redshift.
+
+And that's what we'll
+be talking about.
+
+So the first problem that
+we want to talk about--
+
+and I guess I'll just set it up
+and that's as far as we get--
+
+will be a problem where there's
+a source of radiation, which
+
+is moving to the right in our
+diagram with a velocity, v,
+
+and an observer
+who is stationary.
+
+Now of course, all these are
+frame dependent statements,
+
+but we're working
+in a frame where
+
+the observer is stationary.
+
+And we're also going to assume
+for the non-relativistic case,
+
+that the air-- we'll be talking
+about sound waves-- but the air
+
+is stationary in this frame.
+
+So the frame of backboard is not
+only the frame of the observer,
+
+but it's also the
+frame of the air
+
+when we're talking about the
+non-relativistic sound wave
+
+calculation.
+
+So to define our
+notation, we're going
+
+to let u be equal the
+velocity of the sound wave.
+
+And that would normally be
+measured relative to the air,
+
+but the air will be at
+rest in this picture,
+
+so u will be the velocity
+of the sound wave
+
+relative to the diagram.
+
+v is the velocity of the
+source already shown.
+
+And we'll be interested
+in two time periods,
+
+delta t sub s where
+s stands for source,
+
+which will be the period of
+the wave at the source, which
+
+is the same as talking
+about the period of the wave
+
+as it would be
+measured by the source.
+
+And delta t sub
+O-- that's supposed
+
+to be a capital O, not a zero.
+
+It is the period of the wave
+at the observer or as observed.
+
+And the important point, which
+is maybe obvious qualitatively,
+
+is that these two times,
+or time intervals,
+
+will not be equal to each other.
+
+And the reason, basically,
+is that because the source is
+
+moving-- and I've defined
+positive v the way
+
+astronomers would as moving away
+from us-- because the source is
+
+moving away from us,
+each successive wave that
+
+goes from the source to us has
+to travel a little bit further.
+
+And that means that each wave
+crest is slightly delayed
+
+from when it would
+have gotten here
+
+if everything were stationary.
+
+And if you delay
+each wave crest,
+
+it means the time
+between crests is larger.
+
+And that means
+that we expect here
+
+that delta t sub O will be
+larger than delta t sub s
+
+because of this extra distance
+that each wave crest has
+
+to travel.
+
+And what we'll be
+doing next time--
+
+I think I will just
+leave the calculations
+
+for next time-- is
+calculating that.
+
+And then doing the same
+thing for the case where
+
+the observers moving and
+the source is stationary,
+
+and then talking a little
+bit about special relativity,
+
+and then repeating
+both calculations
+
+with a special relativity
+situation where
+
+we'll be talking about light
+rays and velocities that
+
+might be comparable
+to the speed of light.
+
+So see you folks on
+Thursday, but maybe I'll
+
+see some of you at my
+office hour tomorrow.
+
+And I will send an email about
+where exactly that office
+
+hour will take place.
\ No newline at end of file
diff --git a/50Tla309i7o.txt b/50Tla309i7o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c4767bdc9d04b403f11ba62739545255624cd54b
--- /dev/null
+++ b/50Tla309i7o.txt
@@ -0,0 +1,1651 @@
+align:start position:0%
+ 
+next is this phenomenon that when you
+
+ align:start position:0%
+next is this phenomenon that when you
+ 
+
+ align:start position:0%
+next is this phenomenon that when you
+have a wave packet and it moves it can
+
+ align:start position:0%
+have a wave packet and it moves it can
+ 
+
+ align:start position:0%
+have a wave packet and it moves it can
+change shape and get distorted and that
+
+ align:start position:0%
+change shape and get distorted and that
+ 
+
+ align:start position:0%
+change shape and get distorted and that
+is a very nice phenomenon that takes
+
+ align:start position:0%
+is a very nice phenomenon that takes
+ 
+
+ align:start position:0%
+is a very nice phenomenon that takes
+place in general and causes the
+
+ align:start position:0%
+place in general and causes the
+ 
+
+ align:start position:0%
+place in general and causes the
+technological complications and it's
+
+ align:start position:0%
+technological complications and it's
+ 
+
+ align:start position:0%
+technological complications and it's
+conceptually interesting so let's let's
+
+ align:start position:0%
+conceptually interesting so let's let's
+ 
+
+ align:start position:0%
+conceptually interesting so let's let's
+discuss it so it's still wave packets
+
+ align:start position:0%
+discuss it so it's still wave packets
+ 
+
+ align:start position:0%
+discuss it so it's still wave packets
+but now we have to go back and an add
+
+ align:start position:0%
+but now we have to go back and an add
+ 
+
+ align:start position:0%
+but now we have to go back and an add
+some time to it so shape changes so we
+
+ align:start position:0%
+some time to it so shape changes so we
+ 
+
+ align:start position:0%
+some time to it so shape changes so we
+had a sigh of X and T is equal 1 over
+
+ align:start position:0%
+had a sigh of X and T is equal 1 over
+ 
+
+ align:start position:0%
+had a sigh of X and T is equal 1 over
+square root of 2 pi v ke e to the ikx e
+
+ align:start position:0%
+square root of 2 pi v ke e to the ikx e
+ 
+
+ align:start position:0%
+square root of 2 pi v ke e to the ikx e
+to the minus I Omega of K T and what did
+
+ align:start position:0%
+to the minus I Omega of K T and what did
+ 
+
+ align:start position:0%
+to the minus I Omega of K T and what did
+we do with this to analyze how it
+
+ align:start position:0%
+we do with this to analyze how it
+ 
+
+ align:start position:0%
+we do with this to analyze how it
+propagates we expanded Omega of K as
+
+ align:start position:0%
+propagates we expanded Omega of K as
+ 
+
+ align:start position:0%
+propagates we expanded Omega of K as
+Omega of K naught which again this
+
+ align:start position:0%
+Omega of K naught which again this
+ 
+
+ align:start position:0%
+Omega of K naught which again this
+quantity centered and peaks around K
+
+ align:start position:0%
+quantity centered and peaks around K
+ 
+
+ align:start position:0%
+quantity centered and peaks around K
+naught plus K minus K naught times the
+
+ align:start position:0%
+naught plus K minus K naught times the
+ 
+
+ align:start position:0%
+naught plus K minus K naught times the
+Omega DK at K naught plus one-half K
+
+ align:start position:0%
+Omega DK at K naught plus one-half K
+ 
+
+ align:start position:0%
+Omega DK at K naught plus one-half K
+minus K naught squared the second Omega
+
+ align:start position:0%
+minus K naught squared the second Omega
+ 
+
+ align:start position:0%
+minus K naught squared the second Omega
+DK squared at k naught and it might seem
+
+ align:start position:0%
+DK squared at k naught and it might seem
+ 
+
+ align:start position:0%
+DK squared at k naught and it might seem
+that this goes on forever and what did
+
+ align:start position:0%
+that this goes on forever and what did
+ 
+
+ align:start position:0%
+that this goes on forever and what did
+we do before we looked at this thing and
+
+ align:start position:0%
+we do before we looked at this thing and
+ 
+
+ align:start position:0%
+we do before we looked at this thing and
+we did the integral with this term and
+
+ align:start position:0%
+we did the integral with this term and
+ 
+
+ align:start position:0%
+we did the integral with this term and
+nor the next and with this term we
+
+ align:start position:0%
+nor the next and with this term we
+ 
+
+ align:start position:0%
+nor the next and with this term we
+discovered that the profile moves with
+
+ align:start position:0%
+discovered that the profile moves with
+ 
+
+ align:start position:0%
+discovered that the profile moves with
+this velocity the group velocity now we
+
+ align:start position:0%
+this velocity the group velocity now we
+ 
+
+ align:start position:0%
+this velocity the group velocity now we
+want to go back and at least get an idea
+
+ align:start position:0%
+want to go back and at least get an idea
+ 
+
+ align:start position:0%
+want to go back and at least get an idea
+of how this term could change the result
+
+ align:start position:0%
+of how this term could change the result
+ 
+
+ align:start position:0%
+of how this term could change the result
+and it would change the result by
+
+ align:start position:0%
+and it would change the result by
+ 
+
+ align:start position:0%
+and it would change the result by
+deforming the shape of the packet so it
+
+ align:start position:0%
+deforming the shape of the packet so it
+ 
+
+ align:start position:0%
+deforming the shape of the packet so it
+is of interest to know for example how
+
+ align:start position:0%
+is of interest to know for example how
+ 
+
+ align:start position:0%
+is of interest to know for example how
+long you have to wait before your packet
+
+ align:start position:0%
+long you have to wait before your packet
+ 
+
+ align:start position:0%
+long you have to wait before your packet
+gets overly deformed or how do you
+
+ align:start position:0%
+gets overly deformed or how do you
+ 
+
+ align:start position:0%
+gets overly deformed or how do you
+evolve a packet so we need to recall
+
+ align:start position:0%
+evolve a packet so we need to recall
+ 
+
+ align:start position:0%
+evolve a packet so we need to recall
+this derivative so the Omega the K is
+
+ align:start position:0%
+this derivative so the Omega the K is
+ 
+
+ align:start position:0%
+this derivative so the Omega the K is
+the same as the EDP by multiplying by H
+
+ align:start position:0%
+the same as the EDP by multiplying by H
+ 
+
+ align:start position:0%
+the same as the EDP by multiplying by H
+bar and this you remember was P over m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the EDP is P over m and is equal to H
+
+ align:start position:0%
+the EDP is P over m and is equal to H
+ 
+
+ align:start position:0%
+the EDP is P over m and is equal to H
+Bar K over m so the second Omega the K
+
+ align:start position:0%
+Bar K over m so the second Omega the K
+ 
+
+ align:start position:0%
+Bar K over m so the second Omega the K
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+I must differentiate the first
+
+ align:start position:0%
+I must differentiate the first
+ 
+
+ align:start position:0%
+I must differentiate the first
+derivative with respect to K so I
+
+ align:start position:0%
+derivative with respect to K so I
+ 
+
+ align:start position:0%
+derivative with respect to K so I
+differentiate the first derivative with
+
+ align:start position:0%
+differentiate the first derivative with
+ 
+
+ align:start position:0%
+differentiate the first derivative with
+respect to K now I get just H bar over m
+
+ align:start position:0%
+respect to K now I get just H bar over m
+ 
+
+ align:start position:0%
+respect to K now I get just H bar over m
+which is quite nice and the third
+
+ align:start position:0%
+which is quite nice and the third
+ 
+
+ align:start position:0%
+which is quite nice and the third
+derivative the three Omega the case cube
+
+ align:start position:0%
+derivative the three Omega the case cube
+ 
+
+ align:start position:0%
+derivative the three Omega the case cube
+is zero and therefore I didn't have to
+
+ align:start position:0%
+is zero and therefore I didn't have to
+ 
+
+ align:start position:0%
+is zero and therefore I didn't have to
+worry about these terms the serious
+
+ align:start position:0%
+worry about these terms the serious
+ 
+
+ align:start position:0%
+worry about these terms the serious
+terminates the Taylor series terminates
+
+ align:start position:0%
+terminates the Taylor series terminates
+ 
+
+ align:start position:0%
+terminates the Taylor series terminates
+for mr. yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is it that we get well this term
+
+ align:start position:0%
+so what is it that we get well this term
+ 
+
+ align:start position:0%
+so what is it that we get well this term
+is roughly then 1/2 K minus K naught
+
+ align:start position:0%
+is roughly then 1/2 K minus K naught
+ 
+
+ align:start position:0%
+is roughly then 1/2 K minus K naught
+squared times H bar over m and we can go
+
+ align:start position:0%
+squared times H bar over m and we can go
+ 
+
+ align:start position:0%
+squared times H bar over m and we can go
+back to the integral that we're trying
+
+ align:start position:0%
+back to the integral that we're trying
+ 
+
+ align:start position:0%
+back to the integral that we're trying
+to do we don't do it again or not by any
+
+ align:start position:0%
+to do we don't do it again or not by any
+ 
+
+ align:start position:0%
+to do we don't do it again or not by any
+means but just observe what's going on
+
+ align:start position:0%
+means but just observe what's going on
+ 
+
+ align:start position:0%
+means but just observe what's going on
+there and we have an e to the minus I
+
+ align:start position:0%
+there and we have an e to the minus I
+ 
+
+ align:start position:0%
+there and we have an e to the minus I
+Omega of K T that we did take into
+
+ align:start position:0%
+Omega of K T that we did take into
+ 
+
+ align:start position:0%
+Omega of K T that we did take into
+account but the term that we're dropping
+
+ align:start position:0%
+account but the term that we're dropping
+ 
+
+ align:start position:0%
+account but the term that we're dropping
+now is a term that is minus I Omega of K
+
+ align:start position:0%
+now is a term that is minus I Omega of K
+ 
+
+ align:start position:0%
+now is a term that is minus I Omega of K
+well whatever we have here 1/2 K minus K
+
+ align:start position:0%
+well whatever we have here 1/2 K minus K
+ 
+
+ align:start position:0%
+well whatever we have here 1/2 K minus K
+naught squared H bar over m t that's the
+
+ align:start position:0%
+naught squared H bar over m t that's the
+ 
+
+ align:start position:0%
+naught squared H bar over m t that's the
+face that we ignored before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now we'll just say that we expect
+
+ align:start position:0%
+but now we'll just say that we expect
+ 
+
+ align:start position:0%
+but now we'll just say that we expect
+therefore that the shape doesn't change
+
+ align:start position:0%
+therefore that the shape doesn't change
+ 
+
+ align:start position:0%
+therefore that the shape doesn't change
+as long as we can ignore this face and
+
+ align:start position:0%
+as long as we can ignore this face and
+ 
+
+ align:start position:0%
+as long as we can ignore this face and
+this face would start changing shape of
+
+ align:start position:0%
+this face would start changing shape of
+ 
+
+ align:start position:0%
+this face would start changing shape of
+the object so so our statement is going
+
+ align:start position:0%
+the object so so our statement is going
+ 
+
+ align:start position:0%
+the object so so our statement is going
+to be that we have no shape so let's
+
+ align:start position:0%
+to be that we have no shape so let's
+ 
+
+ align:start position:0%
+to be that we have no shape so let's
+imagine you started with a packet that
+
+ align:start position:0%
+imagine you started with a packet that
+ 
+
+ align:start position:0%
+imagine you started with a packet that
+some time T equals zero and then you let
+
+ align:start position:0%
+some time T equals zero and then you let
+ 
+
+ align:start position:0%
+some time T equals zero and then you let
+time go by well there's some numbers
+
+ align:start position:0%
+time go by well there's some numbers
+ 
+
+ align:start position:0%
+time go by well there's some numbers
+here and time is increasing at some
+
+ align:start position:0%
+here and time is increasing at some
+ 
+
+ align:start position:0%
+here and time is increasing at some
+point this face is going to become
+
+ align:start position:0%
+point this face is going to become
+ 
+
+ align:start position:0%
+point this face is going to become
+unknowable and it's going to start
+
+ align:start position:0%
+unknowable and it's going to start
+ 
+
+ align:start position:0%
+unknowable and it's going to start
+affecting everything but we have no
+
+ align:start position:0%
+affecting everything but we have no
+ 
+
+ align:start position:0%
+affecting everything but we have no
+shape change or no appreciable shape
+
+ align:start position:0%
+shape change or no appreciable shape
+ 
+
+ align:start position:0%
+shape change or no appreciable shape
+change as long as this quantity is much
+
+ align:start position:0%
+change as long as this quantity is much
+ 
+
+ align:start position:0%
+change as long as this quantity is much
+less than 1 so as long as say K minus K
+
+ align:start position:0%
+less than 1 so as long as say K minus K
+ 
+
+ align:start position:0%
+less than 1 so as long as say K minus K
+naught squared H bar over m absolute
+
+ align:start position:0%
+naught squared H bar over m absolute
+ 
+
+ align:start position:0%
+naught squared H bar over m absolute
+value of T is much less than 1 no shape
+
+ align:start position:0%
+value of T is much less than 1 no shape
+ 
+
+ align:start position:0%
+value of T is much less than 1 no shape
+change now it's convenient to write it
+
+ align:start position:0%
+change now it's convenient to write it
+ 
+
+ align:start position:0%
+change now it's convenient to write it
+in terms of things that are more
+
+ align:start position:0%
+in terms of things that are more
+ 
+
+ align:start position:0%
+in terms of things that are more
+familiar so we should estimate this
+
+ align:start position:0%
+familiar so we should estimate this
+ 
+
+ align:start position:0%
+familiar so we should estimate this
+thing now we're doing estimates in a
+
+ align:start position:0%
+thing now we're doing estimates in a
+ 
+
+ align:start position:0%
+thing now we're doing estimates in a
+very direct and rough way here but look
+
+ align:start position:0%
+very direct and rough way here but look
+ 
+
+ align:start position:0%
+very direct and rough way here but look
+your integrals are around K naught and
+
+ align:start position:0%
+your integrals are around K naught and
+ 
+
+ align:start position:0%
+your integrals are around K naught and
+as you remember they just extend a
+
+ align:start position:0%
+as you remember they just extend a
+ 
+
+ align:start position:0%
+as you remember they just extend a
+little bit because it has some width so
+
+ align:start position:0%
+little bit because it has some width so
+ 
+
+ align:start position:0%
+little bit because it has some width so
+K minus K not as soon as you do the
+
+ align:start position:0%
+K minus K not as soon as you do the
+ 
+
+ align:start position:0%
+K minus K not as soon as you do the
+interval over k you're basically
+
+ align:start position:0%
+interval over k you're basically
+ 
+
+ align:start position:0%
+interval over k you're basically
+saying this thing is about the size of
+
+ align:start position:0%
+saying this thing is about the size of
+ 
+
+ align:start position:0%
+saying this thing is about the size of
+the uncertainty in case so I'll put here
+
+ align:start position:0%
+the uncertainty in case so I'll put here
+ 
+
+ align:start position:0%
+the uncertainty in case so I'll put here
+Delta K squared then you have H bar t
+
+ align:start position:0%
+Delta K squared then you have H bar t
+ 
+
+ align:start position:0%
+Delta K squared then you have H bar t
+over m much less than 1 now H bar times
+
+ align:start position:0%
+over m much less than 1 now H bar times
+ 
+
+ align:start position:0%
+over m much less than 1 now H bar times
+Delta K is Delta P so this equation is
+
+ align:start position:0%
+Delta K is Delta P so this equation is
+ 
+
+ align:start position:0%
+Delta K is Delta P so this equation is
+also of the form Delta P squared T over
+
+ align:start position:0%
+also of the form Delta P squared T over
+ 
+
+ align:start position:0%
+also of the form Delta P squared T over
+H bar m much less than 1 there are
+
+ align:start position:0%
+H bar m much less than 1 there are
+ 
+
+ align:start position:0%
+H bar m much less than 1 there are
+several forms of this equation with this
+
+ align:start position:0%
+several forms of this equation with this
+ 
+
+ align:start position:0%
+several forms of this equation with this
+kind of noise so this is a particularly
+
+ align:start position:0%
+kind of noise so this is a particularly
+ 
+
+ align:start position:0%
+kind of noise so this is a particularly
+nice form so if you know the uncertainty
+
+ align:start position:0%
+nice form so if you know the uncertainty
+ 
+
+ align:start position:0%
+nice form so if you know the uncertainty
+in momentum of your packet or wave
+
+ align:start position:0%
+in momentum of your packet or wave
+ 
+
+ align:start position:0%
+in momentum of your packet or wave
+packet you know up to what time you can
+
+ align:start position:0%
+packet you know up to what time you can
+ 
+
+ align:start position:0%
+packet you know up to what time you can
+wait and there's no big deformation of
+
+ align:start position:0%
+wait and there's no big deformation of
+ 
+
+ align:start position:0%
+wait and there's no big deformation of
+this wave packet another thing you can
+
+ align:start position:0%
+this wave packet another thing you can
+ 
+
+ align:start position:0%
+this wave packet another thing you can
+do is involved in certainty in X because
+
+ align:start position:0%
+do is involved in certainty in X because
+ 
+
+ align:start position:0%
+do is involved in certainty in X because
+well Delta P Delta X is equal to H bar
+
+ align:start position:0%
+well Delta P Delta X is equal to H bar
+ 
+
+ align:start position:0%
+well Delta P Delta X is equal to H bar
+so we can do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so with delta P times Delta X equal
+
+ align:start position:0%
+and so with delta P times Delta X equal
+ 
+
+ align:start position:0%
+and so with delta P times Delta X equal
+to about h-bar you can write T less than
+
+ align:start position:0%
+to about h-bar you can write T less than
+ 
+
+ align:start position:0%
+to about h-bar you can write T less than
+h-bar over m over Delta P squared which
+
+ align:start position:0%
+h-bar over m over Delta P squared which
+ 
+
+ align:start position:0%
+h-bar over m over Delta P squared which
+would be H squared Delta x squared you
+
+ align:start position:0%
+would be H squared Delta x squared you
+ 
+
+ align:start position:0%
+would be H squared Delta x squared you
+think I'm getting it right yep so T much
+
+ align:start position:0%
+think I'm getting it right yep so T much
+ 
+
+ align:start position:0%
+think I'm getting it right yep so T much
+less than M over H bar Delta x squared
+
+ align:start position:0%
+less than M over H bar Delta x squared
+ 
+
+ align:start position:0%
+less than M over H bar Delta x squared
+that's another way you could write this
+
+ align:start position:0%
+that's another way you could write this
+ 
+
+ align:start position:0%
+that's another way you could write this
+inequality there is one way to write
+
+ align:start position:0%
+inequality there is one way to write
+ 
+
+ align:start position:0%
+inequality there is one way to write
+inequality that you can intuitively feel
+
+ align:start position:0%
+inequality that you can intuitively feel
+ 
+
+ align:start position:0%
+inequality that you can intuitively feel
+you understand what's happening and take
+
+ align:start position:0%
+you understand what's happening and take
+ 
+
+ align:start position:0%
+you understand what's happening and take
+this form a from a write it as Delta P P
+
+ align:start position:0%
+this form a from a write it as Delta P P
+ 
+
+ align:start position:0%
+this form a from a write it as Delta P P
+over m less than h-bar over Delta P and
+
+ align:start position:0%
+over m less than h-bar over Delta P and
+ 
+
+ align:start position:0%
+over m less than h-bar over Delta P and
+H bar over Delta P is Delta X okay you
+
+ align:start position:0%
+H bar over Delta P is Delta X okay you
+ 
+
+ align:start position:0%
+H bar over Delta P is Delta X okay you
+go Delta P over m t less than or equal
+
+ align:start position:0%
+go Delta P over m t less than or equal
+ 
+
+ align:start position:0%
+go Delta P over m t less than or equal
+much less I'm sorry
+
+ align:start position:0%
+much less I'm sorry
+ 
+
+ align:start position:0%
+much less I'm sorry
+much less than Delta X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think this is understandable you see
+
+ align:start position:0%
+I think this is understandable you see
+ 
+
+ align:start position:0%
+I think this is understandable you see
+why why does the packet change shape the
+
+ align:start position:0%
+why why does the packet change shape the
+ 
+
+ align:start position:0%
+why why does the packet change shape the
+reason it changes shape is because the
+
+ align:start position:0%
+reason it changes shape is because the
+ 
+
+ align:start position:0%
+reason it changes shape is because the
+group velocity is not the same for all
+
+ align:start position:0%
+group velocity is not the same for all
+ 
+
+ align:start position:0%
+group velocity is not the same for all
+the frequencies the packet mostly moves
+
+ align:start position:0%
+the frequencies the packet mostly moves
+ 
+
+ align:start position:0%
+the frequencies the packet mostly moves
+with K naught and we ever rated the
+
+ align:start position:0%
+with K naught and we ever rated the
+ 
+
+ align:start position:0%
+with K naught and we ever rated the
+group velocity in K naught but if it
+
+ align:start position:0%
+group velocity in K naught but if it
+ 
+
+ align:start position:0%
+group velocity in K naught but if it
+would have a definite velocity would
+
+ align:start position:0%
+would have a definite velocity would
+ 
+
+ align:start position:0%
+would have a definite velocity would
+have a definite velocity would have a
+
+ align:start position:0%
+have a definite velocity would have a
+ 
+
+ align:start position:0%
+have a definite velocity would have a
+definite momentum but that's not
+
+ align:start position:0%
+definite momentum but that's not
+ 
+
+ align:start position:0%
+definite momentum but that's not
+possible these things have uncertainty
+
+ align:start position:0%
+possible these things have uncertainty
+ 
+
+ align:start position:0%
+possible these things have uncertainty
+in momentum and they have uncertainty in
+
+ align:start position:0%
+in momentum and they have uncertainty in
+ 
+
+ align:start position:0%
+in momentum and they have uncertainty in
+K that we use it to ride it so different
+
+ align:start position:0%
+K that we use it to ride it so different
+ 
+
+ align:start position:0%
+K that we use it to ride it so different
+parts of the wave can move with
+
+ align:start position:0%
+parts of the wave can move with
+ 
+
+ align:start position:0%
+parts of the wave can move with
+different velocities different group
+
+ align:start position:0%
+different velocities different group
+ 
+
+ align:start position:0%
+different velocities different group
+velocities the group velocity you have a
+
+ align:start position:0%
+velocities the group velocity you have a
+ 
+
+ align:start position:0%
+velocities the group velocity you have a
+later that K naught but some part of the
+
+ align:start position:0%
+later that K naught but some part of the
+ 
+
+ align:start position:0%
+later that K naught but some part of the
+packet is is propagating with group
+
+ align:start position:0%
+packet is is propagating with group
+ 
+
+ align:start position:0%
+packet is is propagating with group
+velocities that are near K naught but
+
+ align:start position:0%
+velocities that are near K naught but
+ 
+
+ align:start position:0%
+velocities that are near K naught but
+not exactly there so you have a
+
+ align:start position:0%
+not exactly there so you have a
+ 
+
+ align:start position:0%
+not exactly there so you have a
+dispersion in the velocity which is an
+
+ align:start position:0%
+dispersion in the velocity which is an
+ 
+
+ align:start position:0%
+dispersion in the velocity which is an
+uncertainty in the velocity or an
+
+ align:start position:0%
+uncertainty in the velocity or an
+ 
+
+ align:start position:0%
+uncertainty in the velocity or an
+uncertainty in the momentum think the
+
+ align:start position:0%
+uncertainty in the momentum think the
+ 
+
+ align:start position:0%
+uncertainty in the momentum think the
+momentum divided by mass is velocity so
+
+ align:start position:0%
+momentum divided by mass is velocity so
+ 
+
+ align:start position:0%
+momentum divided by mass is velocity so
+here it is an uncertainty in the
+
+ align:start position:0%
+here it is an uncertainty in the
+ 
+
+ align:start position:0%
+here it is an uncertainty in the
+velocity and if you multiply the
+
+ align:start position:0%
+velocity and if you multiply the
+ 
+
+ align:start position:0%
+velocity and if you multiply the
+uncertainty in the velocity times this
+
+ align:start position:0%
+uncertainty in the velocity times this
+ 
+
+ align:start position:0%
+uncertainty in the velocity times this
+time that you can wait then the change
+
+ align:start position:0%
+time that you can wait then the change
+ 
+
+ align:start position:0%
+time that you can wait then the change
+in shape is not much
+
+ align:start position:0%
+in shape is not much
+ 
+
+ align:start position:0%
+in shape is not much
+if those is this product which is the
+
+ align:start position:0%
+if those is this product which is the
+ 
+
+ align:start position:0%
+if those is this product which is the
+difference of how one part moves with
+
+ align:start position:0%
+difference of how one part moves with
+ 
+
+ align:start position:0%
+difference of how one part moves with
+respect to the other difference of
+
+ align:start position:0%
+respect to the other difference of
+ 
+
+ align:start position:0%
+respect to the other difference of
+relative time is still smaller than the
+
+ align:start position:0%
+relative time is still smaller than the
+ 
+
+ align:start position:0%
+relative time is still smaller than the
+sort of uncertainty that controls the
+
+ align:start position:0%
+sort of uncertainty that controls the
+ 
+
+ align:start position:0%
+sort of uncertainty that controls the
+shape of the packet so the packet has a
+
+ align:start position:0%
+shape of the packet so the packet has a
+ 
+
+ align:start position:0%
+shape of the packet so the packet has a
+delta X a delta X and as long as this
+
+ align:start position:0%
+delta X a delta X and as long as this
+ 
+
+ align:start position:0%
+delta X a delta X and as long as this
+part the left part of the packet and the
+
+ align:start position:0%
+part the left part of the packet and the
+ 
+
+ align:start position:0%
+part the left part of the packet and the
+top of the packet the diff
+
+ align:start position:0%
+top of the packet the diff
+ 
+
+ align:start position:0%
+top of the packet the diff
+of velocities times the time it just
+
+ align:start position:0%
+of velocities times the time it just
+ 
+
+ align:start position:0%
+of velocities times the time it just
+still compared to Delta X is small then
+
+ align:start position:0%
+still compared to Delta X is small then
+ 
+
+ align:start position:0%
+still compared to Delta X is small then
+that the thing doesn't change much so I
+
+ align:start position:0%
+that the thing doesn't change much so I
+ 
+
+ align:start position:0%
+that the thing doesn't change much so I
+think this is one neat way of seeing
+
+ align:start position:0%
+think this is one neat way of seeing
+ 
+
+ align:start position:0%
+think this is one neat way of seeing
+what an equation that you sometimes use
+
+ align:start position:0%
+what an equation that you sometimes use
+ 
+
+ align:start position:0%
+what an equation that you sometimes use
+in this form sometimes use in this form
+
+ align:start position:0%
+in this form sometimes use in this form
+ 
+
+ align:start position:0%
+in this form sometimes use in this form
+it's just things that you can use in
+
+ align:start position:0%
+it's just things that you can use in
+ 
+
+ align:start position:0%
+it's just things that you can use in
+different ways so for example I will not
+
+ align:start position:0%
+different ways so for example I will not
+ 
+
+ align:start position:0%
+different ways so for example I will not
+well I can do this a little exercise
+
+ align:start position:0%
+well I can do this a little exercise
+ 
+
+ align:start position:0%
+well I can do this a little exercise
+exercise if you have Delta X equals 10
+
+ align:start position:0%
+exercise if you have Delta X equals 10
+ 
+
+ align:start position:0%
+exercise if you have Delta X equals 10
+to the minus 10 meters that's atomic
+
+ align:start position:0%
+to the minus 10 meters that's atomic
+ 
+
+ align:start position:0%
+to the minus 10 meters that's atomic
+size for an electron what is the how
+
+ align:start position:0%
+size for an electron what is the how
+ 
+
+ align:start position:0%
+size for an electron what is the how
+long does it remain localized so you
+
+ align:start position:0%
+long does it remain localized so you
+ 
+
+ align:start position:0%
+long does it remain localized so you
+have an electron and you produce a party
+
+ align:start position:0%
+have an electron and you produce a party
+ 
+
+ align:start position:0%
+have an electron and you produce a party
+then localize it to the size of an atom
+
+ align:start position:0%
+then localize it to the size of an atom
+ 
+
+ align:start position:0%
+then localize it to the size of an atom
+how long can you wait before this
+
+ align:start position:0%
+how long can you wait before this
+ 
+
+ align:start position:0%
+how long can you wait before this
+electron is just all over the room
+
+ align:start position:0%
+electron is just all over the room
+ 
+
+ align:start position:0%
+electron is just all over the room
+well we when we say this T and we say
+
+ align:start position:0%
+well we when we say this T and we say
+ 
+
+ align:start position:0%
+well we when we say this T and we say
+this time we're basically saying that
+
+ align:start position:0%
+this time we're basically saying that
+ 
+
+ align:start position:0%
+this time we're basically saying that
+it's roughly still there maybe grew 20%
+
+ align:start position:0%
+it's roughly still there maybe grew 20%
+ 
+
+ align:start position:0%
+it's roughly still there maybe grew 20%
+30% but what's the rough time that you
+
+ align:start position:0%
+30% but what's the rough time that you
+ 
+
+ align:start position:0%
+30% but what's the rough time that you
+can expect that it stays there so in
+
+ align:start position:0%
+can expect that it stays there so in
+ 
+
+ align:start position:0%
+can expect that it stays there so in
+this case we can use just this formula
+
+ align:start position:0%
+this case we can use just this formula
+ 
+
+ align:start position:0%
+this case we can use just this formula
+and we say the time could be
+
+ align:start position:0%
+and we say the time could be
+ 
+
+ align:start position:0%
+and we say the time could be
+approximately m over H bar Delta x
+
+ align:start position:0%
+approximately m over H bar Delta x
+ 
+
+ align:start position:0%
+approximately m over H bar Delta x
+squared it's fun to see the numbers you
+
+ align:start position:0%
+squared it's fun to see the numbers you
+ 
+
+ align:start position:0%
+squared it's fun to see the numbers you
+would calculate it with MC squared over
+
+ align:start position:0%
+would calculate it with MC squared over
+ 
+
+ align:start position:0%
+would calculate it with MC squared over
+H bar C times Delta X
+
+ align:start position:0%
+H bar C times Delta X
+ 
+
+ align:start position:0%
+H bar C times Delta X
+oversee this squared the answer is about
+
+ align:start position:0%
+oversee this squared the answer is about
+ 
+
+ align:start position:0%
+oversee this squared the answer is about
+10 to the minus 16 seconds not much this
+
+ align:start position:0%
+10 to the minus 16 seconds not much this
+ 
+
+ align:start position:0%
+10 to the minus 16 seconds not much this
+this is kind of a practical issue in
+
+ align:start position:0%
+this is kind of a practical issue in
+ 
+
+ align:start position:0%
+this is kind of a practical issue in
+accelerators as well particle physics
+
+ align:start position:0%
+accelerators as well particle physics
+ 
+
+ align:start position:0%
+accelerators as well particle physics
+accelerators they conserve bunches a
+
+ align:start position:0%
+accelerators they conserve bunches a
+ 
+
+ align:start position:0%
+accelerators they conserve bunches a
+little bunch of protons in the LHC it's
+
+ align:start position:0%
+little bunch of protons in the LHC it's
+ 
+
+ align:start position:0%
+little bunch of protons in the LHC it's
+a little cylinder in which the wave
+
+ align:start position:0%
+a little cylinder in which the wave
+ 
+
+ align:start position:0%
+a little cylinder in which the wave
+functions of the protons are all
+
+ align:start position:0%
+functions of the protons are all
+ 
+
+ align:start position:0%
+functions of the protons are all
+collimated very thin short a couple of
+
+ align:start position:0%
+collimated very thin short a couple of
+ 
+
+ align:start position:0%
+collimated very thin short a couple of
+centimeters short and after going around
+
+ align:start position:0%
+centimeters short and after going around
+ 
+
+ align:start position:0%
+centimeters short and after going around
+many times around accelerator they
+
+ align:start position:0%
+many times around accelerator they
+ 
+
+ align:start position:0%
+many times around accelerator they
+always have to be compressed and kept
+
+ align:start position:0%
+always have to be compressed and kept
+ 
+
+ align:start position:0%
+always have to be compressed and kept
+back sent back to shape because just of
+
+ align:start position:0%
+back sent back to shape because just of
+ 
+
+ align:start position:0%
+back sent back to shape because just of
+diffusion these things just propagate
+
+ align:start position:0%
+diffusion these things just propagate
+ 
+
+ align:start position:0%
+diffusion these things just propagate
+and so it's a rather important thing
\ No newline at end of file
diff --git a/50oEJs-HZHQ.txt b/50oEJs-HZHQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c974fb9fd7d5b4051c11d6aed1eee3f74caaed0d
--- /dev/null
+++ b/50oEJs-HZHQ.txt
@@ -0,0 +1,8363 @@
+align:start position:0%
+ 
+last time we started talking about Ross
+
+ align:start position:0%
+last time we started talking about Ross
+ 
+
+ align:start position:0%
+last time we started talking about Ross
+theorem and we showed a Fourier analytic
+
+ align:start position:0%
+theorem and we showed a Fourier analytic
+ 
+
+ align:start position:0%
+theorem and we showed a Fourier analytic
+proof of Ross theorem in the finite
+
+ align:start position:0%
+proof of Ross theorem in the finite
+ 
+
+ align:start position:0%
+proof of Ross theorem in the finite
+field model so roster in F 3 to the N
+
+ align:start position:0%
+field model so roster in F 3 to the N
+ 
+
+ align:start position:0%
+field model so roster in F 3 to the N
+and I want you today show you how to
+
+ align:start position:0%
+and I want you today show you how to
+ 
+
+ align:start position:0%
+and I want you today show you how to
+modify that proof to work in integers
+
+ align:start position:0%
+modify that proof to work in integers
+ 
+
+ align:start position:0%
+modify that proof to work in integers
+and this will be basically Ross original
+
+ align:start position:0%
+and this will be basically Ross original
+ 
+
+ align:start position:0%
+and this will be basically Ross original
+proof office theorem so what we'll prove
+
+ align:start position:0%
+proof office theorem so what we'll prove
+ 
+
+ align:start position:0%
+proof office theorem so what we'll prove
+today is the statement that the size of
+
+ align:start position:0%
+today is the statement that the size of
+ 
+
+ align:start position:0%
+today is the statement that the size of
+the largest three ap3 subset of 1 to n
+
+ align:start position:0%
+the largest three ap3 subset of 1 to n
+ 
+
+ align:start position:0%
+the largest three ap3 subset of 1 to n
+is at most and divided by log log n ok
+
+ align:start position:0%
+is at most and divided by log log n ok
+ 
+
+ align:start position:0%
+is at most and divided by log log n ok
+so we'll proof a bound of this form the
+
+ align:start position:0%
+so we'll proof a bound of this form the
+ 
+
+ align:start position:0%
+so we'll proof a bound of this form the
+strategy of this proof will be very
+
+ align:start position:0%
+strategy of this proof will be very
+ 
+
+ align:start position:0%
+strategy of this proof will be very
+similar to the one that we have from
+
+ align:start position:0%
+similar to the one that we have from
+ 
+
+ align:start position:0%
+similar to the one that we have from
+last time so let me review for you what
+
+ align:start position:0%
+last time so let me review for you what
+ 
+
+ align:start position:0%
+last time so let me review for you what
+is the strategy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from last time the proof had three
+
+ align:start position:0%
+so from last time the proof had three
+ 
+
+ align:start position:0%
+so from last time the proof had three
+main steps in the first step we observed
+
+ align:start position:0%
+main steps in the first step we observed
+ 
+
+ align:start position:0%
+main steps in the first step we observed
+that if you are in a three AP three set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists a large Fourier
+
+ align:start position:0%
+then there exists a large Fourier
+ 
+
+ align:start position:0%
+then there exists a large Fourier
+coefficient from this Fourier
+
+ align:start position:0%
+coefficient from this Fourier
+ 
+
+ align:start position:0%
+coefficient from this Fourier
+coefficient we were able to extract a
+
+ align:start position:0%
+coefficient we were able to extract a
+ 
+
+ align:start position:0%
+coefficient we were able to extract a
+large subspace where there's a density
+
+ align:start position:0%
+large subspace where there's a density
+ 
+
+ align:start position:0%
+large subspace where there's a density
+increment I want to modify that strategy
+
+ align:start position:0%
+increment I want to modify that strategy
+ 
+
+ align:start position:0%
+increment I want to modify that strategy
+so that we can work in the integers
+
+ align:start position:0%
+so that we can work in the integers
+ 
+
+ align:start position:0%
+so that we can work in the integers
+unlike in f2 to the M where things were
+
+ align:start position:0%
+unlike in f2 to the M where things were
+ 
+
+ align:start position:0%
+unlike in f2 to the M where things were
+fairly nice and clean and because you
+
+ align:start position:0%
+fairly nice and clean and because you
+ 
+
+ align:start position:0%
+fairly nice and clean and because you
+have subspaces you can you know take a
+
+ align:start position:0%
+have subspaces you can you know take a
+ 
+
+ align:start position:0%
+have subspaces you can you know take a
+Fourier coefficient pass down to a
+
+ align:start position:0%
+Fourier coefficient pass down to a
+ 
+
+ align:start position:0%
+Fourier coefficient pass down to a
+subspace there's no subspaces there are
+
+ align:start position:0%
+subspace there's no subspaces there are
+ 
+
+ align:start position:0%
+subspace there's no subspaces there are
+no subspaces in integers so we'll have
+
+ align:start position:0%
+no subspaces in integers so we'll have
+ 
+
+ align:start position:0%
+no subspaces in integers so we'll have
+to do something slightly different but
+
+ align:start position:0%
+to do something slightly different but
+ 
+
+ align:start position:0%
+to do something slightly different but
+in the same spirit so you'll find a
+
+ align:start position:0%
+in the same spirit so you'll find a
+ 
+
+ align:start position:0%
+in the same spirit so you'll find a
+large Fourier coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we will find that there's density
+
+ align:start position:0%
+and we will find that there's density
+ 
+
+ align:start position:0%
+and we will find that there's density
+increment when you restrict not to
+
+ align:start position:0%
+increment when you restrict not to
+ 
+
+ align:start position:0%
+increment when you restrict not to
+subspaces but what could play the role
+
+ align:start position:0%
+subspaces but what could play the role
+ 
+
+ align:start position:0%
+subspaces but what could play the role
+of subspaces when it comes to the
+
+ align:start position:0%
+of subspaces when it comes to the
+ 
+
+ align:start position:0%
+of subspaces when it comes to the
+integers so I want something which looks
+
+ align:start position:0%
+integers so I want something which looks
+ 
+
+ align:start position:0%
+integers so I want something which looks
+like a smaller version of the original
+
+ align:start position:0%
+like a smaller version of the original
+ 
+
+ align:start position:0%
+like a smaller version of the original
+space so instead of open integers if we
+
+ align:start position:0%
+space so instead of open integers if we
+ 
+
+ align:start position:0%
+space so instead of open integers if we
+restrict to a sub progression so to a
+
+ align:start position:0%
+restrict to a sub progression so to a
+ 
+
+ align:start position:0%
+restrict to a sub progression so to a
+smaller arithmetic progression and we'll
+
+ align:start position:0%
+smaller arithmetic progression and we'll
+ 
+
+ align:start position:0%
+smaller arithmetic progression and we'll
+show that you can restrict to a sub
+
+ align:start position:0%
+show that you can restrict to a sub
+ 
+
+ align:start position:0%
+show that you can restrict to a sub
+progression where you can obtain density
+
+ align:start position:0%
+progression where you can obtain density
+ 
+
+ align:start position:0%
+progression where you can obtain density
+increment or restrict integers to
+
+ align:start position:0%
+increment or restrict integers to
+ 
+
+ align:start position:0%
+increment or restrict integers to
+something smaller and then same as last
+
+ align:start position:0%
+something smaller and then same as last
+ 
+
+ align:start position:0%
+something smaller and then same as last
+time we can iterate this inner increment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to obtain the conclusion that you have
+
+ align:start position:0%
+to obtain the conclusion that you have
+ 
+
+ align:start position:0%
+to obtain the conclusion that you have
+an upper bound on the size of this 383
+
+ align:start position:0%
+an upper bound on the size of this 383
+ 
+
+ align:start position:0%
+an upper bound on the size of this 383
+set okay so that's the strategy so you
+
+ align:start position:0%
+set okay so that's the strategy so you
+ 
+
+ align:start position:0%
+set okay so that's the strategy so you
+see the same strategy as the one we did
+
+ align:start position:0%
+see the same strategy as the one we did
+ 
+
+ align:start position:0%
+see the same strategy as the one we did
+last time and many of the ingredients
+
+ align:start position:0%
+last time and many of the ingredients
+ 
+
+ align:start position:0%
+last time and many of the ingredients
+will have parallels but the execution
+
+ align:start position:0%
+will have parallels but the execution
+ 
+
+ align:start position:0%
+will have parallels but the execution
+will be slightly different especially in
+
+ align:start position:0%
+will be slightly different especially in
+ 
+
+ align:start position:0%
+will be slightly different especially in
+the second step where because we no
+
+ align:start position:0%
+the second step where because we no
+ 
+
+ align:start position:0%
+the second step where because we no
+longer have subspaces which are nice and
+
+ align:start position:0%
+longer have subspaces which are nice and
+ 
+
+ align:start position:0%
+longer have subspaces which are nice and
+clean so that's why we started with a
+
+ align:start position:0%
+clean so that's why we started with a
+ 
+
+ align:start position:0%
+clean so that's why we started with a
+finite fuel model just to show how
+
+ align:start position:0%
+finite fuel model just to show how
+ 
+
+ align:start position:0%
+finite fuel model just to show how
+things work in a slightly easier setting
+
+ align:start position:0%
+things work in a slightly easier setting
+ 
+
+ align:start position:0%
+things work in a slightly easier setting
+and today we'll see how to do the same
+
+ align:start position:0%
+and today we'll see how to do the same
+ 
+
+ align:start position:0%
+and today we'll see how to do the same
+kind of strategy here where there's
+
+ align:start position:0%
+kind of strategy here where there's
+ 
+
+ align:start position:0%
+kind of strategy here where there's
+going to be a bit more work but not too
+
+ align:start position:0%
+going to be a bit more work but not too
+ 
+
+ align:start position:0%
+going to be a bit more work but not too
+much more bit more work so before we
+
+ align:start position:0%
+much more bit more work so before we
+ 
+
+ align:start position:0%
+much more bit more work so before we
+start any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so last time I used the proof
+
+ align:start position:0%
+all right so last time I used the proof
+ 
+
+ align:start position:0%
+all right so last time I used the proof
+of rostrum as an excuse to introduce
+
+ align:start position:0%
+of rostrum as an excuse to introduce
+ 
+
+ align:start position:0%
+of rostrum as an excuse to introduce
+Fourier analysis and we're gonna see
+
+ align:start position:0%
+Fourier analysis and we're gonna see
+ 
+
+ align:start position:0%
+Fourier analysis and we're gonna see
+basically the same kind of Fourier
+
+ align:start position:0%
+basically the same kind of Fourier
+ 
+
+ align:start position:0%
+basically the same kind of Fourier
+analysis but it's going to take on a
+
+ align:start position:0%
+analysis but it's going to take on a
+ 
+
+ align:start position:0%
+analysis but it's going to take on a
+slightly different form because we're
+
+ align:start position:0%
+slightly different form because we're
+ 
+
+ align:start position:0%
+slightly different form because we're
+not working at three to the N I work
+
+ align:start position:0%
+not working at three to the N I work
+ 
+
+ align:start position:0%
+not working at three to the N I work
+working inside the integers and there's
+
+ align:start position:0%
+working inside the integers and there's
+ 
+
+ align:start position:0%
+working inside the integers and there's
+a general theory of Fourier analysis on
+
+ align:start position:0%
+a general theory of Fourier analysis on
+ 
+
+ align:start position:0%
+a general theory of Fourier analysis on
+the group abelian groups I don't want to
+
+ align:start position:0%
+the group abelian groups I don't want to
+ 
+
+ align:start position:0%
+the group abelian groups I don't want to
+go into that theory because it's I want
+
+ align:start position:0%
+go into that theory because it's I want
+ 
+
+ align:start position:0%
+go into that theory because it's I want
+to focus on the specific case but the
+
+ align:start position:0%
+to focus on the specific case but the
+ 
+
+ align:start position:0%
+to focus on the specific case but the
+points are given in a median group you
+
+ align:start position:0%
+points are given in a median group you
+ 
+
+ align:start position:0%
+points are given in a median group you
+always have a dual group do group of
+
+ align:start position:0%
+always have a dual group do group of
+ 
+
+ align:start position:0%
+always have a dual group do group of
+characters and they play the role of
+
+ align:start position:0%
+characters and they play the role of
+ 
+
+ align:start position:0%
+characters and they play the role of
+Fourier transform specifically in the
+
+ align:start position:0%
+Fourier transform specifically in the
+ 
+
+ align:start position:0%
+Fourier transform specifically in the
+case of Z we have the following Fourier
+
+ align:start position:0%
+case of Z we have the following Fourier
+ 
+
+ align:start position:0%
+case of Z we have the following Fourier
+transform so the dual group of Z turns
+
+ align:start position:0%
+transform so the dual group of Z turns
+ 
+
+ align:start position:0%
+transform so the dual group of Z turns
+out to be a torus so real numbers mod
+
+ align:start position:0%
+out to be a torus so real numbers mod
+ 
+
+ align:start position:0%
+out to be a torus so real numbers mod
+one and the Fourier transform it's the
+
+ align:start position:0%
+one and the Fourier transform it's the
+ 
+
+ align:start position:0%
+one and the Fourier transform it's the
+finest follows starting with a function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the integers if you like let's say it's
+
+ align:start position:0%
+the integers if you like let's say it's
+ 
+
+ align:start position:0%
+the integers if you like let's say it's
+finally supported just to make our lives
+
+ align:start position:0%
+finally supported just to make our lives
+ 
+
+ align:start position:0%
+finally supported just to make our lives
+a bit easier don't have to deal with
+
+ align:start position:0%
+a bit easier don't have to deal with
+ 
+
+ align:start position:0%
+a bit easier don't have to deal with
+technicalities but in general the
+
+ align:start position:0%
+technicalities but in general the
+ 
+
+ align:start position:0%
+technicalities but in general the
+following formula holds we have this
+
+ align:start position:0%
+following formula holds we have this
+ 
+
+ align:start position:0%
+following formula holds we have this
+Fourier transform defined by setting F
+
+ align:start position:0%
+Fourier transform defined by setting F
+ 
+
+ align:start position:0%
+Fourier transform defined by setting F
+hat of theta to be the following some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where this e is somewhat standard
+
+ align:start position:0%
+where this e is somewhat standard
+ 
+
+ align:start position:0%
+where this e is somewhat standard
+notation additive combinatorics it's e
+
+ align:start position:0%
+notation additive combinatorics it's e
+ 
+
+ align:start position:0%
+notation additive combinatorics it's e
+to the 2 pi I so it goes a fraction T
+
+ align:start position:0%
+to the 2 pi I so it goes a fraction T
+ 
+
+ align:start position:0%
+to the 2 pi I so it goes a fraction T
+around the complex unit circle okay so
+
+ align:start position:0%
+around the complex unit circle okay so
+ 
+
+ align:start position:0%
+around the complex unit circle okay so
+that's the Fourier transform on the
+
+ align:start position:0%
+that's the Fourier transform on the
+ 
+
+ align:start position:0%
+that's the Fourier transform on the
+integers you might have seen this before
+
+ align:start position:0%
+integers you might have seen this before
+ 
+
+ align:start position:0%
+integers you might have seen this before
+under a different name this is usually
+
+ align:start position:0%
+under a different name this is usually
+ 
+
+ align:start position:0%
+under a different name this is usually
+called for you serious you know the
+
+ align:start position:0%
+called for you serious you know the
+ 
+
+ align:start position:0%
+called for you serious you know the
+notation may be slightly different okay
+
+ align:start position:0%
+notation may be slightly different okay
+ 
+
+ align:start position:0%
+notation may be slightly different okay
+so that's that's always see today and
+
+ align:start position:0%
+so that's that's always see today and
+ 
+
+ align:start position:0%
+so that's that's always see today and
+this Fourier transform plays the same
+
+ align:start position:0%
+this Fourier transform plays the same
+ 
+
+ align:start position:0%
+this Fourier transform plays the same
+role as the Fourier transform from last
+
+ align:start position:0%
+role as the Fourier transform from last
+ 
+
+ align:start position:0%
+role as the Fourier transform from last
+time which was on the group F 3 to the M
+
+ align:start position:0%
+time which was on the group F 3 to the M
+ 
+
+ align:start position:0%
+time which was on the group F 3 to the M
+and just as in the last time we had a
+
+ align:start position:0%
+and just as in the last time we had a
+ 
+
+ align:start position:0%
+and just as in the last time we had a
+number of important identities and will
+
+ align:start position:0%
+number of important identities and will
+ 
+
+ align:start position:0%
+number of important identities and will
+have the same kinds of identities so let
+
+ align:start position:0%
+have the same kinds of identities so let
+ 
+
+ align:start position:0%
+have the same kinds of identities so let
+me remind you what they are and the
+
+ align:start position:0%
+me remind you what they are and the
+ 
+
+ align:start position:0%
+me remind you what they are and the
+proofs are all basically the same so I
+
+ align:start position:0%
+proofs are all basically the same so I
+ 
+
+ align:start position:0%
+proofs are all basically the same so I
+won't show you the proofs I've had 0 is
+
+ align:start position:0%
+won't show you the proofs I've had 0 is
+ 
+
+ align:start position:0%
+won't show you the proofs I've had 0 is
+simply the sum of over the domain we
+
+ align:start position:0%
+simply the sum of over the domain we
+ 
+
+ align:start position:0%
+simply the sum of over the domain we
+have this plancherel possible identity
+
+ align:start position:0%
+have this plancherel possible identity
+ 
+
+ align:start position:0%
+have this plancherel possible identity
+which tells us that if you look at the
+
+ align:start position:0%
+which tells us that if you look at the
+ 
+
+ align:start position:0%
+which tells us that if you look at the
+inner product by linear form in the
+
+ align:start position:0%
+inner product by linear form in the
+ 
+
+ align:start position:0%
+inner product by linear form in the
+physical space it equals to the inner
+
+ align:start position:0%
+physical space it equals to the inner
+ 
+
+ align:start position:0%
+physical space it equals to the inner
+product in the Fourier space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the physical space now use some in
+
+ align:start position:0%
+in the physical space now use some in
+ 
+
+ align:start position:0%
+in the physical space now use some in
+the frequency space you take integral
+
+ align:start position:0%
+the frequency space you take integral
+ 
+
+ align:start position:0%
+the frequency space you take integral
+over the torus or the circle in this
+
+ align:start position:0%
+over the torus or the circle in this
+ 
+
+ align:start position:0%
+over the torus or the circle in this
+case it's a one dimensional tourism
+
+ align:start position:0%
+case it's a one dimensional tourism
+ 
+
+ align:start position:0%
+case it's a one dimensional tourism
+there's also the Fourier inversion
+
+ align:start position:0%
+there's also the Fourier inversion
+ 
+
+ align:start position:0%
+there's also the Fourier inversion
+formula which now says that f of X is
+
+ align:start position:0%
+formula which now says that f of X is
+ 
+
+ align:start position:0%
+formula which now says that f of X is
+equal to F hat of theta G of X theta
+
+ align:start position:0%
+equal to F hat of theta G of X theta
+ 
+
+ align:start position:0%
+equal to F hat of theta G of X theta
+you can't equate theta from zero to one
+
+ align:start position:0%
+you can't equate theta from zero to one
+ 
+
+ align:start position:0%
+you can't equate theta from zero to one
+on the torus circle and third and
+
+ align:start position:0%
+on the torus circle and third and
+ 
+
+ align:start position:0%
+on the torus circle and third and
+finally there was this identity last
+
+ align:start position:0%
+finally there was this identity last
+ 
+
+ align:start position:0%
+finally there was this identity last
+time that related sweet home arithmetic
+
+ align:start position:0%
+time that related sweet home arithmetic
+ 
+
+ align:start position:0%
+time that related sweet home arithmetic
+progressions to the Fourier transform
+
+ align:start position:0%
+progressions to the Fourier transform
+ 
+
+ align:start position:0%
+progressions to the Fourier transform
+okay so this last one was slightly not
+
+ align:start position:0%
+okay so this last one was slightly not
+ 
+
+ align:start position:0%
+okay so this last one was slightly not
+asked I mean it's not as standard as the
+
+ align:start position:0%
+asked I mean it's not as standard as the
+ 
+
+ align:start position:0%
+asked I mean it's not as standard as the
+first several which are standard for
+
+ align:start position:0%
+first several which are standard for
+ 
+
+ align:start position:0%
+first several which are standard for
+your identities but this one will be
+
+ align:start position:0%
+your identities but this one will be
+ 
+
+ align:start position:0%
+your identities but this one will be
+useful to us so the identity relating
+
+ align:start position:0%
+useful to us so the identity relating
+ 
+
+ align:start position:0%
+useful to us so the identity relating
+the Fourier transform the three a piece
+
+ align:start position:0%
+the Fourier transform the three a piece
+ 
+
+ align:start position:0%
+the Fourier transform the three a piece
+now has the following form okay so if we
+
+ align:start position:0%
+now has the following form okay so if we
+ 
+
+ align:start position:0%
+now has the following form okay so if we
+define lambda of F and G and H to be the
+
+ align:start position:0%
+define lambda of F and G and H to be the
+ 
+
+ align:start position:0%
+define lambda of F and G and H to be the
+following sum which sums over all three
+
+ align:start position:0%
+following sum which sums over all three
+ 
+
+ align:start position:0%
+following sum which sums over all three
+a piece in the integers then one can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write this expression in terms of the
+
+ align:start position:0%
+write this expression in terms of the
+ 
+
+ align:start position:0%
+write this expression in terms of the
+Fourier transform as follows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so compared to this formula to the one
+
+ align:start position:0%
+so compared to this formula to the one
+ 
+
+ align:start position:0%
+so compared to this formula to the one
+that we saw from last time it's the same
+
+ align:start position:0%
+that we saw from last time it's the same
+ 
+
+ align:start position:0%
+that we saw from last time it's the same
+formula there are different domains
+
+ align:start position:0%
+formula there are different domains
+ 
+
+ align:start position:0%
+formula there are different domains
+where you're summing or integrating or
+
+ align:start position:0%
+where you're summing or integrating or
+ 
+
+ align:start position:0%
+where you're summing or integrating or
+it's the same formula and the proof is
+
+ align:start position:0%
+it's the same formula and the proof is
+ 
+
+ align:start position:0%
+it's the same formula and the proof is
+the same go look at the proof it's the
+
+ align:start position:0%
+the same go look at the proof it's the
+ 
+
+ align:start position:0%
+the same go look at the proof it's the
+same proof okay so these are the key
+
+ align:start position:0%
+same proof okay so these are the key
+ 
+
+ align:start position:0%
+same proof okay so these are the key
+Fourier things that we'll use and then
+
+ align:start position:0%
+Fourier things that we'll use and then
+ 
+
+ align:start position:0%
+Fourier things that we'll use and then
+we'll try to follow our nose with the
+
+ align:start position:0%
+we'll try to follow our nose with the
+ 
+
+ align:start position:0%
+we'll try to follow our nose with the
+same as a proof as last time and see
+
+ align:start position:0%
+same as a proof as last time and see
+ 
+
+ align:start position:0%
+same as a proof as last time and see
+where we can get so let me introduce one
+
+ align:start position:0%
+where we can get so let me introduce one
+ 
+
+ align:start position:0%
+where we can get so let me introduce one
+more notation so I'll write lambda sub 3
+
+ align:start position:0%
+more notation so I'll write lambda sub 3
+ 
+
+ align:start position:0%
+more notation so I'll write lambda sub 3
+of F to be lambda of F F F three times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well at this point if you
+
+ align:start position:0%
+okay well at this point if you
+ 
+
+ align:start position:0%
+okay well at this point if you
+understood the lecture from last time
+
+ align:start position:0%
+understood the lecture from last time
+ 
+
+ align:start position:0%
+understood the lecture from last time
+none of anything I've said so far should
+
+ align:start position:0%
+none of anything I've said so far should
+ 
+
+ align:start position:0%
+none of anything I've said so far should
+be surprising we are working integers so
+
+ align:start position:0%
+be surprising we are working integers so
+ 
+
+ align:start position:0%
+be surprising we are working integers so
+we should look at the corresponding
+
+ align:start position:0%
+we should look at the corresponding
+ 
+
+ align:start position:0%
+we should look at the corresponding
+Fourier transform in integers and if we
+
+ align:start position:0%
+Fourier transform in integers and if we
+ 
+
+ align:start position:0%
+Fourier transform in integers and if we
+follow your nose this is all the things
+
+ align:start position:0%
+follow your nose this is all the things
+ 
+
+ align:start position:0%
+follow your nose this is all the things
+that we're going to use okay so what was
+
+ align:start position:0%
+that we're going to use okay so what was
+ 
+
+ align:start position:0%
+that we're going to use okay so what was
+one of the first things we mentioned
+
+ align:start position:0%
+one of the first things we mentioned
+ 
+
+ align:start position:0%
+one of the first things we mentioned
+regarding the Fourier transform from
+
+ align:start position:0%
+regarding the Fourier transform from
+ 
+
+ align:start position:0%
+regarding the Fourier transform from
+last time after this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's do a counting lemma so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what should a counting lemma say what
+
+ align:start position:0%
+what should a counting lemma say what
+ 
+
+ align:start position:0%
+what should a counting lemma say what
+the spirit of the counting lemma is that
+
+ align:start position:0%
+the spirit of the counting lemma is that
+ 
+
+ align:start position:0%
+the spirit of the counting lemma is that
+if you have two functions that are close
+
+ align:start position:0%
+if you have two functions that are close
+ 
+
+ align:start position:0%
+if you have two functions that are close
+to each other and how close means
+
+ align:start position:0%
+to each other and how close means
+ 
+
+ align:start position:0%
+to each other and how close means
+closing for you then their corresponding
+
+ align:start position:0%
+closing for you then their corresponding
+ 
+
+ align:start position:0%
+closing for you then their corresponding
+number of three peas should be similar
+
+ align:start position:0%
+number of three peas should be similar
+ 
+
+ align:start position:0%
+number of three peas should be similar
+so so that's what we want to say indeed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the County lemma for us will say that
+
+ align:start position:0%
+so the County lemma for us will say that
+ 
+
+ align:start position:0%
+so the County lemma for us will say that
+if F and G are functions on Z and such
+
+ align:start position:0%
+if F and G are functions on Z and such
+ 
+
+ align:start position:0%
+if F and G are functions on Z and such
+that they're l2 norms are both bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by this M sum of the squared absolute
+
+ align:start position:0%
+by this M sum of the squared absolute
+ 
+
+ align:start position:0%
+by this M sum of the squared absolute
+value entries are both bounded then the
+
+ align:start position:0%
+value entries are both bounded then the
+ 
+
+ align:start position:0%
+value entries are both bounded then the
+difference of their three applicants
+
+ align:start position:0%
+difference of their three applicants
+ 
+
+ align:start position:0%
+difference of their three applicants
+should not be so different from each
+
+ align:start position:0%
+should not be so different from each
+ 
+
+ align:start position:0%
+should not be so different from each
+other if F and G are closing for you and
+
+ align:start position:0%
+other if F and G are closing for you and
+ 
+
+ align:start position:0%
+other if F and G are closing for you and
+that means if all the Fourier
+
+ align:start position:0%
+that means if all the Fourier
+ 
+
+ align:start position:0%
+that means if all the Fourier
+coefficients of F minus G are small then
+
+ align:start position:0%
+coefficients of F minus G are small then
+ 
+
+ align:start position:0%
+coefficients of F minus G are small then
+lambda 3 FF which considers three AP
+
+ align:start position:0%
+lambda 3 FF which considers three AP
+ 
+
+ align:start position:0%
+lambda 3 FF which considers three AP
+counting F is close to that of G okay
+
+ align:start position:0%
+counting F is close to that of G okay
+ 
+
+ align:start position:0%
+counting F is close to that of G okay
+same kind of three AP counting lama from
+
+ align:start position:0%
+same kind of three AP counting lama from
+ 
+
+ align:start position:0%
+same kind of three AP counting lama from
+last time so let's prove it as with
+
+ align:start position:0%
+last time so let's prove it as with
+ 
+
+ align:start position:0%
+last time so let's prove it as with
+accounting lemma proofs you've seen
+
+ align:start position:0%
+accounting lemma proofs you've seen
+ 
+
+ align:start position:0%
+accounting lemma proofs you've seen
+several times already in this course we
+
+ align:start position:0%
+several times already in this course we
+ 
+
+ align:start position:0%
+several times already in this course we
+will prove it by first writing this
+
+ align:start position:0%
+will prove it by first writing this
+ 
+
+ align:start position:0%
+will prove it by first writing this
+difference as a telescoping sum the
+
+ align:start position:0%
+difference as a telescoping sum the
+ 
+
+ align:start position:0%
+difference as a telescoping sum the
+first term being F minus G F and then G
+
+ align:start position:0%
+first term being F minus G F and then G
+ 
+
+ align:start position:0%
+first term being F minus G F and then G
+of F minus G F the lambda G G minus G
+
+ align:start position:0%
+of F minus G F the lambda G G minus G
+ 
+
+ align:start position:0%
+of F minus G F the lambda G G minus G
+and we would like to show that each of
+
+ align:start position:0%
+and we would like to show that each of
+ 
+
+ align:start position:0%
+and we would like to show that each of
+these terms is small if F minus G has
+
+ align:start position:0%
+these terms is small if F minus G has
+ 
+
+ align:start position:0%
+these terms is small if F minus G has
+small fourier coefficients so let's
+
+ align:start position:0%
+small fourier coefficients so let's
+ 
+
+ align:start position:0%
+small fourier coefficients so let's
+found the first term so let me bound
+
+ align:start position:0%
+found the first term so let me bound
+ 
+
+ align:start position:0%
+found the first term so let me bound
+this first term using the 3 AP identity
+
+ align:start position:0%
+this first term using the 3 AP identity
+ 
+
+ align:start position:0%
+this first term using the 3 AP identity
+relating through AP to Fourier
+
+ align:start position:0%
+relating through AP to Fourier
+ 
+
+ align:start position:0%
+relating through AP to Fourier
+coefficients we can write this lambda as
+
+ align:start position:0%
+coefficients we can write this lambda as
+ 
+
+ align:start position:0%
+coefficients we can write this lambda as
+the following integral over Fourier
+
+ align:start position:0%
+the following integral over Fourier
+ 
+
+ align:start position:0%
+the following integral over Fourier
+coefficients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now let me okay so what was the
+
+ align:start position:0%
+and now let me okay so what was the
+ 
+
+ align:start position:0%
+and now let me okay so what was the
+trick last time so we said let's pull
+
+ align:start position:0%
+trick last time so we said let's pull
+ 
+
+ align:start position:0%
+trick last time so we said let's pull
+out one of these guys and then use
+
+ align:start position:0%
+out one of these guys and then use
+ 
+
+ align:start position:0%
+out one of these guys and then use
+triangle inequality on the remaining
+
+ align:start position:0%
+triangle inequality on the remaining
+ 
+
+ align:start position:0%
+triangle inequality on the remaining
+factors so we'll do that so far so good
+
+ align:start position:0%
+factors so we'll do that so far so good
+ 
+
+ align:start position:0%
+factors so we'll do that so far so good
+and now you see this integral by Cauchy
+
+ align:start position:0%
+and now you see this integral by Cauchy
+ 
+
+ align:start position:0%
+and now you see this integral by Cauchy
+Schwarz Cauchy Schwarz the fast first
+
+ align:start position:0%
+Schwarz Cauchy Schwarz the fast first
+ 
+
+ align:start position:0%
+Schwarz Cauchy Schwarz the fast first
+factor you got this L to sum this L to
+
+ align:start position:0%
+factor you got this L to sum this L to
+ 
+
+ align:start position:0%
+factor you got this L to sum this L to
+integral and then you apply Cauchy
+
+ align:start position:0%
+integral and then you apply Cauchy
+ 
+
+ align:start position:0%
+integral and then you apply Cauchy
+Schwarz to the second factor now what do
+
+ align:start position:0%
+Schwarz to the second factor now what do
+ 
+
+ align:start position:0%
+Schwarz to the second factor now what do
+we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so yeah so you see in l2 or Fourier
+
+ align:start position:0%
+okay so yeah so you see in l2 or Fourier
+ 
+
+ align:start position:0%
+okay so yeah so you see in l2 or Fourier
+the first automatic reaction should be
+
+ align:start position:0%
+the first automatic reaction should be
+ 
+
+ align:start position:0%
+the first automatic reaction should be
+to use plan Tyrell or Percival so apply
+
+ align:start position:0%
+to use plan Tyrell or Percival so apply
+ 
+
+ align:start position:0%
+to use plan Tyrell or Percival so apply
+apply plan to RL identity to each of
+
+ align:start position:0%
+apply plan to RL identity to each of
+ 
+
+ align:start position:0%
+apply plan to RL identity to each of
+these factors we find that each of those
+
+ align:start position:0%
+these factors we find that each of those
+ 
+
+ align:start position:0%
+these factors we find that each of those
+factors is equal to this L to some in
+
+ align:start position:0%
+factors is equal to this L to some in
+ 
+
+ align:start position:0%
+factors is equal to this L to some in
+the physical space this square root the
+
+ align:start position:0%
+the physical space this square root the
+ 
+
+ align:start position:0%
+the physical space this square root the
+same thing screwed again okay and then
+
+ align:start position:0%
+same thing screwed again okay and then
+ 
+
+ align:start position:0%
+same thing screwed again okay and then
+we find that because there was a
+
+ align:start position:0%
+we find that because there was a
+ 
+
+ align:start position:0%
+we find that because there was a
+hypothesis in the hypothesis towards a
+
+ align:start position:0%
+hypothesis in the hypothesis towards a
+ 
+
+ align:start position:0%
+hypothesis in the hypothesis towards a
+pound and on this the sum of squares and
+
+ align:start position:0%
+pound and on this the sum of squares and
+ 
+
+ align:start position:0%
+pound and on this the sum of squares and
+similarly with the other two terms okay
+
+ align:start position:0%
+similarly with the other two terms okay
+ 
+
+ align:start position:0%
+similarly with the other two terms okay
+so that proves the county memo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay great
+
+ align:start position:0%
+okay great
+ 
+
+ align:start position:0%
+okay great
+so the question its last time we had a
+
+ align:start position:0%
+so the question its last time we had a
+ 
+
+ align:start position:0%
+so the question its last time we had a
+counting lemma that looked slightly
+
+ align:start position:0%
+counting lemma that looked slightly
+ 
+
+ align:start position:0%
+counting lemma that looked slightly
+different but I claimed they're all
+
+ align:start position:0%
+different but I claimed they're all
+ 
+
+ align:start position:0%
+different but I claimed they're all
+really the same counting lemma they're
+
+ align:start position:0%
+really the same counting lemma they're
+ 
+
+ align:start position:0%
+really the same counting lemma they're
+all the same proofs if you run this
+
+ align:start position:0%
+all the same proofs if you run this
+ 
+
+ align:start position:0%
+all the same proofs if you run this
+proof it won't work if you take what we
+
+ align:start position:0%
+proof it won't work if you take what we
+ 
+
+ align:start position:0%
+proof it won't work if you take what we
+did last time it's the same kind of
+
+ align:start position:0%
+did last time it's the same kind of
+ 
+
+ align:start position:0%
+did last time it's the same kind of
+proofs so last time we had a counting
+
+ align:start position:0%
+proofs so last time we had a counting
+ 
+
+ align:start position:0%
+proofs so last time we had a counting
+number where we had the same FF
+
+ align:start position:0%
+number where we had the same FF
+ 
+
+ align:start position:0%
+number where we had the same FF
+essentially well now I have allow you to
+
+ align:start position:0%
+essentially well now I have allow you to
+ 
+
+ align:start position:0%
+essentially well now I have allow you to
+essentially take three different things
+
+ align:start position:0%
+essentially take three different things
+ 
+
+ align:start position:0%
+essentially take three different things
+and okay so both in both cases you're
+
+ align:start position:0%
+and okay so both in both cases you're
+ 
+
+ align:start position:0%
+and okay so both in both cases you're
+running through this calculation but
+
+ align:start position:0%
+running through this calculation but
+ 
+
+ align:start position:0%
+running through this calculation but
+they look slightly different I agree it
+
+ align:start position:0%
+they look slightly different I agree it
+ 
+
+ align:start position:0%
+they look slightly different I agree it
+doesn't look exactly the same but if you
+
+ align:start position:0%
+doesn't look exactly the same but if you
+ 
+
+ align:start position:0%
+doesn't look exactly the same but if you
+think about what's involved in the proof
+
+ align:start position:0%
+think about what's involved in the proof
+ 
+
+ align:start position:0%
+think about what's involved in the proof
+they're the same proofs any more
+
+ align:start position:0%
+they're the same proofs any more
+ 
+
+ align:start position:0%
+they're the same proofs any more
+questions all right so now we have this
+
+ align:start position:0%
+questions all right so now we have this
+ 
+
+ align:start position:0%
+questions all right so now we have this
+County lemma so let's start our proof of
+
+ align:start position:0%
+County lemma so let's start our proof of
+ 
+
+ align:start position:0%
+County lemma so let's start our proof of
+Roth's theorem in the integers as with
+
+ align:start position:0%
+Roth's theorem in the integers as with
+ 
+
+ align:start position:0%
+Roth's theorem in the integers as with
+last time there will be three steps as
+
+ align:start position:0%
+last time there will be three steps as
+ 
+
+ align:start position:0%
+last time there will be three steps as
+mentioned up there okay in the first
+
+ align:start position:0%
+mentioned up there okay in the first
+ 
+
+ align:start position:0%
+mentioned up there okay in the first
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+let us show that if you are three AP
+
+ align:start position:0%
+let us show that if you are three AP
+ 
+
+ align:start position:0%
+let us show that if you are three AP
+free then we can obtain a density a
+
+ align:start position:0%
+free then we can obtain a density a
+ 
+
+ align:start position:0%
+free then we can obtain a density a
+large Fourier coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this course it's this counting
+
+ align:start position:0%
+so in this course it's this counting
+ 
+
+ align:start position:0%
+so in this course it's this counting
+number we actually saw just basically
+
+ align:start position:0%
+number we actually saw just basically
+ 
+
+ align:start position:0%
+number we actually saw just basically
+this kind of proof for the first time
+
+ align:start position:0%
+this kind of proof for the first time
+ 
+
+ align:start position:0%
+this kind of proof for the first time
+when we discussed graph counting lemma
+
+ align:start position:0%
+when we discussed graph counting lemma
+ 
+
+ align:start position:0%
+when we discussed graph counting lemma
+back in the chapter on samurai deist
+
+ align:start position:0%
+back in the chapter on samurai deist
+ 
+
+ align:start position:0%
+back in the chapter on samurai deist
+regularity lemma and sure they all look
+
+ align:start position:0%
+regularity lemma and sure they all look
+ 
+
+ align:start position:0%
+regularity lemma and sure they all look
+literally not exactly the same but
+
+ align:start position:0%
+literally not exactly the same but
+ 
+
+ align:start position:0%
+literally not exactly the same but
+they're all really the same kind of
+
+ align:start position:0%
+they're all really the same kind of
+ 
+
+ align:start position:0%
+they're all really the same kind of
+proofs I'm showing you the same thing in
+
+ align:start position:0%
+proofs I'm showing you the same thing in
+ 
+
+ align:start position:0%
+proofs I'm showing you the same thing in
+many different guises but they're all
+
+ align:start position:0%
+many different guises but they're all
+ 
+
+ align:start position:0%
+many different guises but they're all
+the same proofs so if you are a set free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm ice with last time I'm going to call
+
+ align:start position:0%
+I'm ice with last time I'm going to call
+ 
+
+ align:start position:0%
+I'm ice with last time I'm going to call
+alpha the density of a now inside this
+
+ align:start position:0%
+alpha the density of a now inside this
+ 
+
+ align:start position:0%
+alpha the density of a now inside this
+progression this length end progression
+
+ align:start position:0%
+progression this length end progression
+ 
+
+ align:start position:0%
+progression this length end progression
+and suppose n is large enough so the
+
+ align:start position:0%
+and suppose n is large enough so the
+ 
+
+ align:start position:0%
+and suppose n is large enough so the
+conclusion now is that there exists some
+
+ align:start position:0%
+conclusion now is that there exists some
+ 
+
+ align:start position:0%
+conclusion now is that there exists some
+theta such that if you look at this sum
+
+ align:start position:0%
+theta such that if you look at this sum
+ 
+
+ align:start position:0%
+theta such that if you look at this sum
+over here as I sum over both integers
+
+ align:start position:0%
+over here as I sum over both integers
+ 
+
+ align:start position:0%
+over here as I sum over both integers
+actually I mean do the sum only from one
+
+ align:start position:0%
+actually I mean do the sum only from one
+ 
+
+ align:start position:0%
+actually I mean do the sum only from one
+to uppercase n I claim that it's saying
+
+ align:start position:0%
+to uppercase n I claim that it's saying
+ 
+
+ align:start position:0%
+to uppercase n I claim that it's saying
+what this title says if you are 383 and
+
+ align:start position:0%
+what this title says if you are 383 and
+ 
+
+ align:start position:0%
+what this title says if you are 383 and
+this end is large enough relative to the
+
+ align:start position:0%
+this end is large enough relative to the
+ 
+
+ align:start position:0%
+this end is large enough relative to the
+density you think of this density alpha
+
+ align:start position:0%
+density you think of this density alpha
+ 
+
+ align:start position:0%
+density you think of this density alpha
+is a constant then I can find a large
+
+ align:start position:0%
+is a constant then I can find a large
+ 
+
+ align:start position:0%
+is a constant then I can find a large
+Fourier coefficient you know there's a
+
+ align:start position:0%
+Fourier coefficient you know there's a
+ 
+
+ align:start position:0%
+Fourier coefficient you know there's a
+small difference and this is related to
+
+ align:start position:0%
+small difference and this is related to
+ 
+
+ align:start position:0%
+small difference and this is related to
+what you were asking earlier between how
+
+ align:start position:0%
+what you were asking earlier between how
+ 
+
+ align:start position:0%
+what you were asking earlier between how
+we set things up now versus will happen
+
+ align:start position:0%
+we set things up now versus will happen
+ 
+
+ align:start position:0%
+we set things up now versus will happen
+last time so last time we just look
+
+ align:start position:0%
+last time so last time we just look
+ 
+
+ align:start position:0%
+last time so last time we just look
+for a Fourier coefficient corresponding
+
+ align:start position:0%
+for a Fourier coefficient corresponding
+ 
+
+ align:start position:0%
+for a Fourier coefficient corresponding
+in tune non zero are now I'm not
+
+ align:start position:0%
+in tune non zero are now I'm not
+ 
+
+ align:start position:0%
+in tune non zero are now I'm not
+restricting non zero but I don't start
+
+ align:start position:0%
+restricting non zero but I don't start
+ 
+
+ align:start position:0%
+restricting non zero but I don't start
+with an indicator function I start with
+
+ align:start position:0%
+with an indicator function I start with
+ 
+
+ align:start position:0%
+with an indicator function I start with
+the demeaned indicator function I take
+
+ align:start position:0%
+the demeaned indicator function I take
+ 
+
+ align:start position:0%
+the demeaned indicator function I take
+out a me so that the zeroth coefficient
+
+ align:start position:0%
+out a me so that the zeroth coefficient
+ 
+
+ align:start position:0%
+out a me so that the zeroth coefficient
+so to speak which corresponds to the
+
+ align:start position:0%
+so to speak which corresponds to the
+ 
+
+ align:start position:0%
+so to speak which corresponds to the
+mean is already zero so you don't get to
+
+ align:start position:0%
+mean is already zero so you don't get to
+ 
+
+ align:start position:0%
+mean is already zero so you don't get to
+use that for your coefficient so if you
+
+ align:start position:0%
+use that for your coefficient so if you
+ 
+
+ align:start position:0%
+use that for your coefficient so if you
+didn't do this if you just try to do
+
+ align:start position:0%
+didn't do this if you just try to do
+ 
+
+ align:start position:0%
+didn't do this if you just try to do
+this last time and you can also do the
+
+ align:start position:0%
+this last time and you can also do the
+ 
+
+ align:start position:0%
+this last time and you can also do the
+exactly the same setup but if you don't
+
+ align:start position:0%
+exactly the same setup but if you don't
+ 
+
+ align:start position:0%
+exactly the same setup but if you don't
+be mean it then if you don't have this
+
+ align:start position:0%
+be mean it then if you don't have this
+ 
+
+ align:start position:0%
+be mean it then if you don't have this
+term then this statement is trivially
+
+ align:start position:0%
+term then this statement is trivially
+ 
+
+ align:start position:0%
+term then this statement is trivially
+true because I can take theta equal to
+
+ align:start position:0%
+true because I can take theta equal to
+ 
+
+ align:start position:0%
+true because I can take theta equal to
+zero that's but I don't want I want to I
+
+ align:start position:0%
+zero that's but I don't want I want to I
+ 
+
+ align:start position:0%
+zero that's but I don't want I want to I
+want an actual significant Fourier
+
+ align:start position:0%
+want an actual significant Fourier
+ 
+
+ align:start position:0%
+want an actual significant Fourier
+improvement so I take I do this demean
+
+ align:start position:0%
+improvement so I take I do this demean
+ 
+
+ align:start position:0%
+improvement so I take I do this demean
+and then I consider its Fourier
+
+ align:start position:0%
+and then I consider its Fourier
+ 
+
+ align:start position:0%
+and then I consider its Fourier
+coefficient okay any questions about the
+
+ align:start position:0%
+coefficient okay any questions about the
+ 
+
+ align:start position:0%
+coefficient okay any questions about the
+statement yeah so this demeaning is
+
+ align:start position:0%
+statement yeah so this demeaning is
+ 
+
+ align:start position:0%
+statement yeah so this demeaning is
+really important alright so that's
+
+ align:start position:0%
+really important alright so that's
+ 
+
+ align:start position:0%
+really important alright so that's
+something that's a very common technique
+
+ align:start position:0%
+something that's a very common technique
+ 
+
+ align:start position:0%
+something that's a very common technique
+whenever you do these kinds of analyses
+
+ align:start position:0%
+whenever you do these kinds of analyses
+ 
+
+ align:start position:0%
+whenever you do these kinds of analyses
+let's make sure you're okay so that
+
+ align:start position:0%
+let's make sure you're okay so that
+ 
+
+ align:start position:0%
+let's make sure you're okay so that
+you're so you're looking at functions
+
+ align:start position:0%
+you're so you're looking at functions
+ 
+
+ align:start position:0%
+you're so you're looking at functions
+with mean zero we have the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+information about 3p counts in a because
+
+ align:start position:0%
+information about 3p counts in a because
+ 
+
+ align:start position:0%
+information about 3p counts in a because
+a is 3 P 3 so what is the value of
+
+ align:start position:0%
+a is 3 P 3 so what is the value of
+ 
+
+ align:start position:0%
+a is 3 P 3 so what is the value of
+lambda sub 3 of the indicator of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lambda of three if you look at the
+
+ align:start position:0%
+lambda of three if you look at the
+ 
+
+ align:start position:0%
+lambda of three if you look at the
+expression it basically sums over all 3
+
+ align:start position:0%
+expression it basically sums over all 3
+ 
+
+ align:start position:0%
+expression it basically sums over all 3
+a piece but a has no 3 a piece except
+
+ align:start position:0%
+a piece but a has no 3 a piece except
+ 
+
+ align:start position:0%
+a piece but a has no 3 a piece except
+for the trivial ones so you only
+
+ align:start position:0%
+for the trivial ones so you only
+ 
+
+ align:start position:0%
+for the trivial ones so you only
+consider the trivial 3 a piece which has
+
+ align:start position:0%
+consider the trivial 3 a piece which has
+ 
+
+ align:start position:0%
+consider the trivial 3 a piece which has
+size exactly the size of a which is
+
+ align:start position:0%
+size exactly the size of a which is
+ 
+
+ align:start position:0%
+size exactly the size of a which is
+alpha N from trivial
+
+ align:start position:0%
+alpha N from trivial
+ 
+
+ align:start position:0%
+alpha N from trivial
+3a please on the other hand what do we
+
+ align:start position:0%
+3a please on the other hand what do we
+ 
+
+ align:start position:0%
+3a please on the other hand what do we
+know about lambda 3 of this interval
+
+ align:start position:0%
+know about lambda 3 of this interval
+ 
+
+ align:start position:0%
+know about lambda 3 of this interval
+from 1 to n ok so how many 3 a piece are
+
+ align:start position:0%
+from 1 to n ok so how many 3 a piece are
+ 
+
+ align:start position:0%
+from 1 to n ok so how many 3 a piece are
+there roughly it's going to be about N
+
+ align:start position:0%
+there roughly it's going to be about N
+ 
+
+ align:start position:0%
+there roughly it's going to be about N
+squared over 2 at least n squared over 2
+
+ align:start position:0%
+squared over 2 at least n squared over 2
+ 
+
+ align:start position:0%
+squared over 2 at least n squared over 2
+because to generate a 3 AP I just have
+
+ align:start position:0%
+because to generate a 3 AP I just have
+ 
+
+ align:start position:0%
+because to generate a 3 AP I just have
+to pick a first term and the third term
+
+ align:start position:0%
+to pick a first term and the third term
+ 
+
+ align:start position:0%
+to pick a first term and the third term
+and I'm okay as long as they're the same
+
+ align:start position:0%
+and I'm okay as long as they're the same
+ 
+
+ align:start position:0%
+and I'm okay as long as they're the same
+parity then you have a 3 so same parity
+
+ align:start position:0%
+parity then you have a 3 so same parity
+ 
+
+ align:start position:0%
+parity then you have a 3 so same parity
+cuts you down by half so you have at
+
+ align:start position:0%
+cuts you down by half so you have at
+ 
+
+ align:start position:0%
+cuts you down by half so you have at
+least n squared over 2 3 a piece so now
+
+ align:start position:0%
+least n squared over 2 3 a piece so now
+ 
+
+ align:start position:0%
+least n squared over 2 3 a piece so now
+let's look at how to apply the counting
+
+ align:start position:0%
+let's look at how to apply the counting
+ 
+
+ align:start position:0%
+let's look at how to apply the counting
+lemma to this setting so we have the
+
+ align:start position:0%
+lemma to this setting so we have the
+ 
+
+ align:start position:0%
+lemma to this setting so we have the
+counting lemma up there where I now want
+
+ align:start position:0%
+counting lemma up there where I now want
+ 
+
+ align:start position:0%
+counting lemma up there where I now want
+to apply it so apply counting to on one
+
+ align:start position:0%
+to apply it so apply counting to on one
+ 
+
+ align:start position:0%
+to apply it so apply counting to on one
+hand the indicator function of a so so
+
+ align:start position:0%
+hand the indicator function of a so so
+ 
+
+ align:start position:0%
+hand the indicator function of a so so
+we get a count 3 piecing a but also
+
+ align:start position:0%
+we get a count 3 piecing a but also
+ 
+
+ align:start position:0%
+we get a count 3 piecing a but also
+compared to the normalized indicator on
+
+ align:start position:0%
+compared to the normalized indicator on
+ 
+
+ align:start position:0%
+compared to the normalized indicator on
+the interval okay so maybe this is a
+
+ align:start position:0%
+the interval okay so maybe this is a
+ 
+
+ align:start position:0%
+the interval okay so maybe this is a
+good point for me to pause and remind
+
+ align:start position:0%
+good point for me to pause and remind
+ 
+
+ align:start position:0%
+good point for me to pause and remind
+you that the spirit of this whole proof
+
+ align:start position:0%
+you that the spirit of this whole proof
+ 
+
+ align:start position:0%
+you that the spirit of this whole proof
+is understanding structure versus pseudo
+
+ align:start position:0%
+is understanding structure versus pseudo
+ 
+
+ align:start position:0%
+is understanding structure versus pseudo
+randomness as was was with the case last
+
+ align:start position:0%
+randomness as was was with the case last
+ 
+
+ align:start position:0%
+randomness as was was with the case last
+time so we want to understand in what
+
+ align:start position:0%
+time so we want to understand in what
+ 
+
+ align:start position:0%
+time so we want to understand in what
+ways is a pseudo random and here pseudo
+
+ align:start position:0%
+ways is a pseudo random and here pseudo
+ 
+
+ align:start position:0%
+ways is a pseudo random and here pseudo
+random just as what last time means
+
+ align:start position:0%
+random just as what last time means
+ 
+
+ align:start position:0%
+random just as what last time means
+having small Fourier coefficients being
+
+ align:start position:0%
+having small Fourier coefficients being
+ 
+
+ align:start position:0%
+having small Fourier coefficients being
+for a uniform if a pseudo random which
+
+ align:start position:0%
+for a uniform if a pseudo random which
+ 
+
+ align:start position:0%
+for a uniform if a pseudo random which
+here means F and G are close to each
+
+ align:start position:0%
+here means F and G are close to each
+ 
+
+ align:start position:0%
+here means F and G are close to each
+other that's what being school rehna
+
+ align:start position:0%
+other that's what being school rehna
+ 
+
+ align:start position:0%
+other that's what being school rehna
+means then the county line I will tell
+
+ align:start position:0%
+means then the county line I will tell
+ 
+
+ align:start position:0%
+means then the county line I will tell
+us the F and G should have
+
+ align:start position:0%
+us the F and G should have
+ 
+
+ align:start position:0%
+us the F and G should have
+a peek house but a has basically no AP
+
+ align:start position:0%
+a peek house but a has basically no AP
+ 
+
+ align:start position:0%
+a peek house but a has basically no AP
+account so they should not be close to
+
+ align:start position:0%
+account so they should not be close to
+ 
+
+ align:start position:0%
+account so they should not be close to
+each other so so that's right so that's
+
+ align:start position:0%
+each other so so that's right so that's
+ 
+
+ align:start position:0%
+each other so so that's right so that's
+the strategy to show that a is not
+
+ align:start position:0%
+the strategy to show that a is not
+ 
+
+ align:start position:0%
+the strategy to show that a is not
+pseudo-random in this sense and thereby
+
+ align:start position:0%
+pseudo-random in this sense and thereby
+ 
+
+ align:start position:0%
+pseudo-random in this sense and thereby
+extracting a large Fourier coefficient
+
+ align:start position:0%
+extracting a large Fourier coefficient
+ 
+
+ align:start position:0%
+extracting a large Fourier coefficient
+so we apply counting to these two
+
+ align:start position:0%
+so we apply counting to these two
+ 
+
+ align:start position:0%
+so we apply counting to these two
+functions and we obtain that so this
+
+ align:start position:0%
+functions and we obtain that so this
+ 
+
+ align:start position:0%
+functions and we obtain that so this
+quantity which corresponds to lambda 3
+
+ align:start position:0%
+quantity which corresponds to lambda 3
+ 
+
+ align:start position:0%
+quantity which corresponds to lambda 3
+of G minus alpha n difference is upper
+
+ align:start position:0%
+of G minus alpha n difference is upper
+ 
+
+ align:start position:0%
+of G minus alpha n difference is upper
+bounded by the using the counting lemma
+
+ align:start position:0%
+bounded by the using the counting lemma
+ 
+
+ align:start position:0%
+bounded by the using the counting lemma
+we find that their difference is upper
+
+ align:start position:0%
+we find that their difference is upper
+ 
+
+ align:start position:0%
+we find that their difference is upper
+bounded by the following quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+namely you look at the difference
+
+ align:start position:0%
+namely you look at the difference
+ 
+
+ align:start position:0%
+namely you look at the difference
+between F and G and evaluate us maximum
+
+ align:start position:0%
+between F and G and evaluate us maximum
+ 
+
+ align:start position:0%
+between F and G and evaluate us maximum
+Fourier coefficient so if a is
+
+ align:start position:0%
+Fourier coefficient so if a is
+ 
+
+ align:start position:0%
+Fourier coefficient so if a is
+pseudo-random meaning that for a uniform
+
+ align:start position:0%
+pseudo-random meaning that for a uniform
+ 
+
+ align:start position:0%
+pseudo-random meaning that for a uniform
+this L infinity norm is small then I
+
+ align:start position:0%
+this L infinity norm is small then I
+ 
+
+ align:start position:0%
+this L infinity norm is small then I
+should expect lots and lots of 3a
+
+ align:start position:0%
+should expect lots and lots of 3a
+ 
+
+ align:start position:0%
+should expect lots and lots of 3a
+piecing it but because that is not the
+
+ align:start position:0%
+piecing it but because that is not the
+ 
+
+ align:start position:0%
+piecing it but because that is not the
+case we should be able to conclude that
+
+ align:start position:0%
+case we should be able to conclude that
+ 
+
+ align:start position:0%
+case we should be able to conclude that
+there is some large Fourier coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so thus rearranging the equation above
+
+ align:start position:0%
+so thus rearranging the equation above
+ 
+
+ align:start position:0%
+so thus rearranging the equation above
+we have that ok so we have this
+
+ align:start position:0%
+we have that ok so we have this
+ 
+
+ align:start position:0%
+we have that ok so we have this
+expression here and now we are ok so let
+
+ align:start position:0%
+expression here and now we are ok so let
+ 
+
+ align:start position:0%
+expression here and now we are ok so let
+me simplify this expression slightly and
+
+ align:start position:0%
+me simplify this expression slightly and
+ 
+
+ align:start position:0%
+me simplify this expression slightly and
+now we're using that and it's
+
+ align:start position:0%
+now we're using that and it's
+ 
+
+ align:start position:0%
+now we're using that and it's
+sufficiently large so where n is
+
+ align:start position:0%
+sufficiently large so where n is
+ 
+
+ align:start position:0%
+sufficiently large so where n is
+sufficiently large so this quantity is
+
+ align:start position:0%
+sufficiently large so this quantity is
+ 
+
+ align:start position:0%
+sufficiently large so this quantity is
+at least a tenth of alpha squared n and
+
+ align:start position:0%
+at least a tenth of alpha squared n and
+ 
+
+ align:start position:0%
+at least a tenth of alpha squared n and
+that's the conclusion all right so
+
+ align:start position:0%
+that's the conclusion all right so
+ 
+
+ align:start position:0%
+that's the conclusion all right so
+that's the conclusion of this step here
+
+ align:start position:0%
+that's the conclusion of this step here
+ 
+
+ align:start position:0%
+that's the conclusion of this step here
+what is this mean this means there
+
+ align:start position:0%
+what is this mean this means there
+ 
+
+ align:start position:0%
+what is this mean this means there
+exists some theta so that the Fourier
+
+ align:start position:0%
+exists some theta so that the Fourier
+ 
+
+ align:start position:0%
+exists some theta so that the Fourier
+coefficient at theta is at least the
+
+ align:start position:0%
+coefficient at theta is at least the
+ 
+
+ align:start position:0%
+coefficient at theta is at least the
+claimed quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions so that finishes step one
+
+ align:start position:0%
+any questions so that finishes step one
+ 
+
+ align:start position:0%
+any questions so that finishes step one
+so now let me go on to step two in step
+
+ align:start position:0%
+so now let me go on to step two in step
+ 
+
+ align:start position:0%
+so now let me go on to step two in step
+two we wish to show that if you have a
+
+ align:start position:0%
+two we wish to show that if you have a
+ 
+
+ align:start position:0%
+two we wish to show that if you have a
+large for your coefficient then one can
+
+ align:start position:0%
+large for your coefficient then one can
+ 
+
+ align:start position:0%
+large for your coefficient then one can
+obtain a density increment so last time
+
+ align:start position:0%
+obtain a density increment so last time
+ 
+
+ align:start position:0%
+obtain a density increment so last time
+we were working in a finite field vector
+
+ align:start position:0%
+we were working in a finite field vector
+ 
+
+ align:start position:0%
+we were working in a finite field vector
+space a fourier coefficient which is a
+
+ align:start position:0%
+space a fourier coefficient which is a
+ 
+
+ align:start position:0%
+space a fourier coefficient which is a
+dual vector corresponds to some
+
+ align:start position:0%
+dual vector corresponds to some
+ 
+
+ align:start position:0%
+dual vector corresponds to some
+hyperplane and having a large fourier
+
+ align:start position:0%
+hyperplane and having a large fourier
+ 
+
+ align:start position:0%
+hyperplane and having a large fourier
+coefficient then implies that the
+
+ align:start position:0%
+coefficient then implies that the
+ 
+
+ align:start position:0%
+coefficient then implies that the
+density of a on the co set of those
+
+ align:start position:0%
+density of a on the co set of those
+ 
+
+ align:start position:0%
+density of a on the co set of those
+hyper planes must be not all close to
+
+ align:start position:0%
+hyper planes must be not all close to
+ 
+
+ align:start position:0%
+hyper planes must be not all close to
+each other so one of the hyper planes
+
+ align:start position:0%
+each other so one of the hyper planes
+ 
+
+ align:start position:0%
+each other so one of the hyper planes
+must have significantly higher density
+
+ align:start position:0%
+must have significantly higher density
+ 
+
+ align:start position:0%
+must have significantly higher density
+than the rest okay so we want to do
+
+ align:start position:0%
+than the rest okay so we want to do
+ 
+
+ align:start position:0%
+than the rest okay so we want to do
+something similar here except we run
+
+ align:start position:0%
+something similar here except we run
+ 
+
+ align:start position:0%
+something similar here except we run
+into this technical difficulty where
+
+ align:start position:0%
+into this technical difficulty where
+ 
+
+ align:start position:0%
+into this technical difficulty where
+there are no subspaces anymore right so
+
+ align:start position:0%
+there are no subspaces anymore right so
+ 
+
+ align:start position:0%
+there are no subspaces anymore right so
+the Fourier character namely
+
+ align:start position:0%
+the Fourier character namely
+ 
+
+ align:start position:0%
+the Fourier character namely
+corresponding to this theta is just a
+
+ align:start position:0%
+corresponding to this theta is just a
+ 
+
+ align:start position:0%
+corresponding to this theta is just a
+real number it doesn't divide up your
+
+ align:start position:0%
+real number it doesn't divide up your
+ 
+
+ align:start position:0%
+real number it doesn't divide up your
+space doesn't divide up you one two and
+
+ align:start position:0%
+space doesn't divide up you one two and
+ 
+
+ align:start position:0%
+space doesn't divide up you one two and
+very nice thing to sub chunks but we
+
+ align:start position:0%
+very nice thing to sub chunks but we
+ 
+
+ align:start position:0%
+very nice thing to sub chunks but we
+still want to use this data to chop up
+
+ align:start position:0%
+still want to use this data to chop up
+ 
+
+ align:start position:0%
+still want to use this data to chop up
+one to n into smaller spaces so that we
+
+ align:start position:0%
+one to n into smaller spaces so that we
+ 
+
+ align:start position:0%
+one to n into smaller spaces so that we
+can iterate and do density increment all
+
+ align:start position:0%
+can iterate and do density increment all
+ 
+
+ align:start position:0%
+can iterate and do density increment all
+right so let's see what we can do
+
+ align:start position:0%
+right so let's see what we can do
+ 
+
+ align:start position:0%
+right so let's see what we can do
+so given this data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we would like to do is to partition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one through n into sub progressions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so chop up one to n into sub a
+
+ align:start position:0%
+okay so chop up one to n into sub a
+ 
+
+ align:start position:0%
+okay so chop up one to n into sub a
+piece such that if you evaluate so this
+
+ align:start position:0%
+piece such that if you evaluate so this
+ 
+
+ align:start position:0%
+piece such that if you evaluate so this
+data is fixed so on each sub ap this
+
+ align:start position:0%
+data is fixed so on each sub ap this
+ 
+
+ align:start position:0%
+data is fixed so on each sub ap this
+function here is roughly constant on
+
+ align:start position:0%
+function here is roughly constant on
+ 
+
+ align:start position:0%
+function here is roughly constant on
+each of your parts last time we had this
+
+ align:start position:0%
+each of your parts last time we had this
+ 
+
+ align:start position:0%
+each of your parts last time we had this
+for a character and then we chopped it
+
+ align:start position:0%
+for a character and then we chopped it
+ 
+
+ align:start position:0%
+for a character and then we chopped it
+up using these three hyperplanes
+
+ align:start position:0%
+up using these three hyperplanes
+ 
+
+ align:start position:0%
+up using these three hyperplanes
+and on each hyperplane the 48 character
+
+ align:start position:0%
+and on each hyperplane the 48 character
+ 
+
+ align:start position:0%
+and on each hyperplane the 48 character
+is literally constant that's what we
+
+ align:start position:0%
+is literally constant that's what we
+ 
+
+ align:start position:0%
+is literally constant that's what we
+worked with and now you cannot get them
+
+ align:start position:0%
+worked with and now you cannot get them
+ 
+
+ align:start position:0%
+worked with and now you cannot get them
+to be exactly constant but the next best
+
+ align:start position:0%
+to be exactly constant but the next best
+ 
+
+ align:start position:0%
+to be exactly constant but the next best
+thing we can hope for is to get this
+
+ align:start position:0%
+thing we can hope for is to get this
+ 
+
+ align:start position:0%
+thing we can hope for is to get this
+fourier character to be roughly constant
+
+ align:start position:0%
+fourier character to be roughly constant
+ 
+
+ align:start position:0%
+fourier character to be roughly constant
+okay so we're going to do some
+
+ align:start position:0%
+okay so we're going to do some
+ 
+
+ align:start position:0%
+okay so we're going to do some
+partitioning that allows us to achieve
+
+ align:start position:0%
+partitioning that allows us to achieve
+ 
+
+ align:start position:0%
+partitioning that allows us to achieve
+this characteristic and let me give you
+
+ align:start position:0%
+this characteristic and let me give you
+ 
+
+ align:start position:0%
+this characteristic and let me give you
+some intuition about why this is true
+
+ align:start position:0%
+some intuition about why this is true
+ 
+
+ align:start position:0%
+some intuition about why this is true
+and this is not exactly a surprise in
+
+ align:start position:0%
+and this is not exactly a surprise in
+ 
+
+ align:start position:0%
+and this is not exactly a surprise in
+fact the intuition is just that if you
+
+ align:start position:0%
+fact the intuition is just that if you
+ 
+
+ align:start position:0%
+fact the intuition is just that if you
+look at what this function behaves like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's going on here you are on the
+
+ align:start position:0%
+so what's going on here you are on the
+ 
+
+ align:start position:0%
+so what's going on here you are on the
+unit circle and you are jumping by theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you just keep jumping by theta and so
+
+ align:start position:0%
+so you just keep jumping by theta and so
+ 
+
+ align:start position:0%
+so you just keep jumping by theta and so
+on and I want to show that I can chop up
+
+ align:start position:0%
+on and I want to show that I can chop up
+ 
+
+ align:start position:0%
+on and I want to show that I can chop up
+my progression into a bunch of almost
+
+ align:start position:0%
+my progression into a bunch of almost
+ 
+
+ align:start position:0%
+my progression into a bunch of almost
+periodic pieces where in each part
+
+ align:start position:0%
+periodic pieces where in each part
+ 
+
+ align:start position:0%
+periodic pieces where in each part
+I'm staying inside a small arc and so in
+
+ align:start position:0%
+I'm staying inside a small arc and so in
+ 
+
+ align:start position:0%
+I'm staying inside a small arc and so in
+the extreme case of this where it is
+
+ align:start position:0%
+the extreme case of this where it is
+ 
+
+ align:start position:0%
+the extreme case of this where it is
+very easy to see is if X is some
+
+ align:start position:0%
+very easy to see is if X is some
+ 
+
+ align:start position:0%
+very easy to see is if X is some
+rational number
+
+ align:start position:0%
+rational number
+ 
+
+ align:start position:0%
+rational number
+a overbeat with be fairly small then we
+
+ align:start position:0%
+a overbeat with be fairly small then we
+ 
+
+ align:start position:0%
+a overbeat with be fairly small then we
+can so then this character is actually
+
+ align:start position:0%
+can so then this character is actually
+ 
+
+ align:start position:0%
+can so then this character is actually
+constant a piece with common different
+
+ align:start position:0%
+constant a piece with common different
+ 
+
+ align:start position:0%
+constant a piece with common different
+speed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I so theta theta thank you theta 2 pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if theta is some rational with some
+
+ align:start position:0%
+if theta is some rational with some
+ 
+
+ align:start position:0%
+if theta is some rational with some
+small denominator so then you are
+
+ align:start position:0%
+small denominator so then you are
+ 
+
+ align:start position:0%
+small denominator so then you are
+literally jumping in periodic steps on
+
+ align:start position:0%
+literally jumping in periodic steps on
+ 
+
+ align:start position:0%
+literally jumping in periodic steps on
+the unit circle so if you partition and
+
+ align:start position:0%
+the unit circle so if you partition and
+ 
+
+ align:start position:0%
+the unit circle so if you partition and
+according to the exact same periods you
+
+ align:start position:0%
+according to the exact same periods you
+ 
+
+ align:start position:0%
+according to the exact same periods you
+have you have that this character is
+
+ align:start position:0%
+have you have that this character is
+ 
+
+ align:start position:0%
+have you have that this character is
+exactly constant on each of your
+
+ align:start position:0%
+exactly constant on each of your
+ 
+
+ align:start position:0%
+exactly constant on each of your
+progressions now in general the theta
+
+ align:start position:0%
+progressions now in general the theta
+ 
+
+ align:start position:0%
+progressions now in general the theta
+you get out of that proof might not have
+
+ align:start position:0%
+you get out of that proof might not have
+ 
+
+ align:start position:0%
+you get out of that proof might not have
+this very nice form but we can at least
+
+ align:start position:0%
+this very nice form but we can at least
+ 
+
+ align:start position:0%
+this very nice form but we can at least
+approximately achieve the desired effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so to achieve approximately girth
+
+ align:start position:0%
+okay so to achieve approximately girth
+ 
+
+ align:start position:0%
+okay so to achieve approximately girth
+desired effect what we'll do is to find
+
+ align:start position:0%
+desired effect what we'll do is to find
+ 
+
+ align:start position:0%
+desired effect what we'll do is to find
+something so that B times theta is not
+
+ align:start position:0%
+something so that B times theta is not
+ 
+
+ align:start position:0%
+something so that B times theta is not
+quite an integer but very close to an
+
+ align:start position:0%
+quite an integer but very close to an
+ 
+
+ align:start position:0%
+quite an integer but very close to an
+integer okay so this probably many of
+
+ align:start position:0%
+integer okay so this probably many of
+ 
+
+ align:start position:0%
+integer okay so this probably many of
+you seen before it's a classic
+
+ align:start position:0%
+you seen before it's a classic
+ 
+
+ align:start position:0%
+you seen before it's a classic
+pigeonhole type result so if you have
+
+ align:start position:0%
+pigeonhole type result so if you have
+ 
+
+ align:start position:0%
+pigeonhole type result so if you have
+think of a real number and a delta kind
+
+ align:start position:0%
+think of a real number and a delta kind
+ 
+
+ align:start position:0%
+think of a real number and a delta kind
+of a tolerance then there exists a
+
+ align:start position:0%
+of a tolerance then there exists a
+ 
+
+ align:start position:0%
+of a tolerance then there exists a
+positive integer T at most one over
+
+ align:start position:0%
+positive integer T at most one over
+ 
+
+ align:start position:0%
+positive integer T at most one over
+delta such that the times theta is very
+
+ align:start position:0%
+delta such that the times theta is very
+ 
+
+ align:start position:0%
+delta such that the times theta is very
+close to an integer so this norm here is
+
+ align:start position:0%
+close to an integer so this norm here is
+ 
+
+ align:start position:0%
+close to an integer so this norm here is
+distance to the closest integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright alright so the proof here is by
+
+ align:start position:0%
+alright alright so the proof here is by
+ 
+
+ align:start position:0%
+alright alright so the proof here is by
+pigeonhole principle so if we let M be 1
+
+ align:start position:0%
+pigeonhole principle so if we let M be 1
+ 
+
+ align:start position:0%
+pigeonhole principle so if we let M be 1
+over Delta round down and consider the
+
+ align:start position:0%
+over Delta round down and consider the
+ 
+
+ align:start position:0%
+over Delta round down and consider the
+numbers 0 theta 2 theta 3 data and so on
+
+ align:start position:0%
+numbers 0 theta 2 theta 3 data and so on
+ 
+
+ align:start position:0%
+numbers 0 theta 2 theta 3 data and so on
+- M theta so by pigeonhole there exists
+
+ align:start position:0%
+- M theta so by pigeonhole there exists
+ 
+
+ align:start position:0%
+- M theta so by pigeonhole there exists
+I theta J theta some two different terms
+
+ align:start position:0%
+I theta J theta some two different terms
+ 
+
+ align:start position:0%
+I theta J theta some two different terms
+of the sequence such that they differ by
+
+ align:start position:0%
+of the sequence such that they differ by
+ 
+
+ align:start position:0%
+of the sequence such that they differ by
+less than most Delta in their fractional
+
+ align:start position:0%
+less than most Delta in their fractional
+ 
+
+ align:start position:0%
+less than most Delta in their fractional
+parts so now I'll take T to be
+
+ align:start position:0%
+parts so now I'll take T to be
+ 
+
+ align:start position:0%
+parts so now I'll take T to be
+difference between I and J ok so even
+
+ align:start position:0%
+difference between I and J ok so even
+ 
+
+ align:start position:0%
+difference between I and J ok so even
+though you don't have exactly rational
+
+ align:start position:0%
+though you don't have exactly rational
+ 
+
+ align:start position:0%
+though you don't have exactly rational
+we have approximately ratio so this is a
+
+ align:start position:0%
+we have approximately ratio so this is a
+ 
+
+ align:start position:0%
+we have approximately ratio so this is a
+it's a simple rational approximation
+
+ align:start position:0%
+it's a simple rational approximation
+ 
+
+ align:start position:0%
+it's a simple rational approximation
+statement and using this operational
+
+ align:start position:0%
+statement and using this operational
+ 
+
+ align:start position:0%
+statement and using this operational
+approximation we can now kind of try to
+
+ align:start position:0%
+approximation we can now kind of try to
+ 
+
+ align:start position:0%
+approximation we can now kind of try to
+do the intuition here pretending that
+
+ align:start position:0%
+do the intuition here pretending that
+ 
+
+ align:start position:0%
+do the intuition here pretending that
+we're working with rational numbers so
+
+ align:start position:0%
+we're working with rational numbers so
+ 
+
+ align:start position:0%
+we're working with rational numbers so
+if we take a tie between 0 & 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta irrational and suppose and it's
+
+ align:start position:0%
+theta irrational and suppose and it's
+ 
+
+ align:start position:0%
+theta irrational and suppose and it's
+large enough okay so here C means there
+
+ align:start position:0%
+large enough okay so here C means there
+ 
+
+ align:start position:0%
+large enough okay so here C means there
+exist some sufficiently large some
+
+ align:start position:0%
+exist some sufficiently large some
+ 
+
+ align:start position:0%
+exist some sufficiently large some
+constant C such that the statement is
+
+ align:start position:0%
+constant C such that the statement is
+ 
+
+ align:start position:0%
+constant C such that the statement is
+true so suppose think million yeah that
+
+ align:start position:0%
+true so suppose think million yeah that
+ 
+
+ align:start position:0%
+true so suppose think million yeah that
+should be fine so then there exists so
+
+ align:start position:0%
+should be fine so then there exists so
+ 
+
+ align:start position:0%
+should be fine so then there exists so
+then one can partition one to n into sub
+
+ align:start position:0%
+then one can partition one to n into sub
+ 
+
+ align:start position:0%
+then one can partition one to n into sub
+ApS which will call P I and each having
+
+ align:start position:0%
+ApS which will call P I and each having
+ 
+
+ align:start position:0%
+ApS which will call P I and each having
+length between cube root of n and twice
+
+ align:start position:0%
+length between cube root of n and twice
+ 
+
+ align:start position:0%
+length between cube root of n and twice
+the cube root of n such that this
+
+ align:start position:0%
+the cube root of n such that this
+ 
+
+ align:start position:0%
+the cube root of n such that this
+character that we want to stay roughly
+
+ align:start position:0%
+character that we want to stay roughly
+ 
+
+ align:start position:0%
+character that we want to stay roughly
+constant indeed does not change very
+
+ align:start position:0%
+constant indeed does not change very
+ 
+
+ align:start position:0%
+constant indeed does not change very
+much if you look at two terms in the
+
+ align:start position:0%
+much if you look at two terms in the
+ 
+
+ align:start position:0%
+much if you look at two terms in the
+same AP in the same sub AP then the
+
+ align:start position:0%
+same AP in the same sub AP then the
+ 
+
+ align:start position:0%
+same AP in the same sub AP then the
+value of this character each P sub I is
+
+ align:start position:0%
+value of this character each P sub I is
+ 
+
+ align:start position:0%
+value of this character each P sub I is
+roughly the same so they don't vary by
+
+ align:start position:0%
+roughly the same so they don't vary by
+ 
+
+ align:start position:0%
+roughly the same so they don't vary by
+more than Etta on each P I right so here
+
+ align:start position:0%
+more than Etta on each P I right so here
+ 
+
+ align:start position:0%
+more than Etta on each P I right so here
+we're partitioning this one to n into a
+
+ align:start position:0%
+we're partitioning this one to n into a
+ 
+
+ align:start position:0%
+we're partitioning this one to n into a
+sub a piece so that this guy here stays
+
+ align:start position:0%
+sub a piece so that this guy here stays
+ 
+
+ align:start position:0%
+sub a piece so that this guy here stays
+roughly constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions alright so think
+
+ align:start position:0%
+okay any questions alright so think
+ 
+
+ align:start position:0%
+okay any questions alright so think
+about how you might prove this let's
+
+ align:start position:0%
+about how you might prove this let's
+ 
+
+ align:start position:0%
+about how you might prove this let's
+take a quick break so you see we are
+
+ align:start position:0%
+take a quick break so you see we are
+ 
+
+ align:start position:0%
+take a quick break so you see we are
+basically following the same strategy as
+
+ align:start position:0%
+basically following the same strategy as
+ 
+
+ align:start position:0%
+basically following the same strategy as
+a proof from last time but this second
+
+ align:start position:0%
+a proof from last time but this second
+ 
+
+ align:start position:0%
+a proof from last time but this second
+step which we're all right now needs to
+
+ align:start position:0%
+step which we're all right now needs to
+ 
+
+ align:start position:0%
+step which we're all right now needs to
+be somewhat modified because you cannot
+
+ align:start position:0%
+be somewhat modified because you cannot
+ 
+
+ align:start position:0%
+be somewhat modified because you cannot
+cut this space up into pieces where your
+
+ align:start position:0%
+cut this space up into pieces where your
+ 
+
+ align:start position:0%
+cut this space up into pieces where your
+character is constant if they're roughly
+
+ align:start position:0%
+character is constant if they're roughly
+ 
+
+ align:start position:0%
+character is constant if they're roughly
+constant then we're good to go so that's
+
+ align:start position:0%
+constant then we're good to go so that's
+ 
+
+ align:start position:0%
+constant then we're good to go so that's
+what we're doing now so let's prove the
+
+ align:start position:0%
+what we're doing now so let's prove the
+ 
+
+ align:start position:0%
+what we're doing now so let's prove the
+statement up there so let's prove this
+
+ align:start position:0%
+statement up there so let's prove this
+ 
+
+ align:start position:0%
+statement up there so let's prove this
+statement over here
+
+ align:start position:0%
+statement over here
+ 
+
+ align:start position:0%
+statement over here
+so using we find that there exists some
+
+ align:start position:0%
+so using we find that there exists some
+ 
+
+ align:start position:0%
+so using we find that there exists some
+D okay so write down some number for now
+
+ align:start position:0%
+D okay so write down some number for now
+ 
+
+ align:start position:0%
+D okay so write down some number for now
+don't worry about any more come up short
+
+ align:start position:0%
+don't worry about any more come up short
+ 
+
+ align:start position:0%
+don't worry about any more come up short
+you why I write this specific quantity
+
+ align:start position:0%
+you why I write this specific quantity
+ 
+
+ align:start position:0%
+you why I write this specific quantity
+so there exist some D just not too big
+
+ align:start position:0%
+so there exist some D just not too big
+ 
+
+ align:start position:0%
+so there exist some D just not too big
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d theta is very close to an integer so
+
+ align:start position:0%
+d theta is very close to an integer so
+ 
+
+ align:start position:0%
+d theta is very close to an integer so
+now I'm merely applying for excellent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so given such D and so how big is
+
+ align:start position:0%
+okay so given such D and so how big is
+ 
+
+ align:start position:0%
+okay so given such D and so how big is
+this T you see that because I assumed
+
+ align:start position:0%
+this T you see that because I assumed
+ 
+
+ align:start position:0%
+this T you see that because I assumed
+that n is sufficiently large if we
+
+ align:start position:0%
+that n is sufficiently large if we
+ 
+
+ align:start position:0%
+that n is sufficiently large if we
+choose that seed large enough T is at
+
+ align:start position:0%
+choose that seed large enough T is at
+ 
+
+ align:start position:0%
+choose that seed large enough T is at
+most root n so given such T which is at
+
+ align:start position:0%
+most root n so given such T which is at
+ 
+
+ align:start position:0%
+most root n so given such T which is at
+most root n you can partition 1 to n
+
+ align:start position:0%
+most root n you can partition 1 to n
+ 
+
+ align:start position:0%
+most root n you can partition 1 to n
+into sub progressions with common
+
+ align:start position:0%
+into sub progressions with common
+ 
+
+ align:start position:0%
+into sub progressions with common
+difference D essentially look at residue
+
+ align:start position:0%
+difference D essentially look at residue
+ 
+
+ align:start position:0%
+difference D essentially look at residue
+classes mod T so they're all going to
+
+ align:start position:0%
+classes mod T so they're all going to
+ 
+
+ align:start position:0%
+classes mod T so they're all going to
+have length by basically and over D and
+
+ align:start position:0%
+have length by basically and over D and
+ 
+
+ align:start position:0%
+have length by basically and over D and
+I chopped them up a little bit further
+
+ align:start position:0%
+I chopped them up a little bit further
+ 
+
+ align:start position:0%
+I chopped them up a little bit further
+to get so a piece of lengths between
+
+ align:start position:0%
+to get so a piece of lengths between
+ 
+
+ align:start position:0%
+to get so a piece of lengths between
+cube root of N and twice cube root of N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm going to make sure that all of my
+
+ align:start position:0%
+so I'm going to make sure that all of my
+ 
+
+ align:start position:0%
+so I'm going to make sure that all of my
+ApS are roughly the same length and now
+
+ align:start position:0%
+ApS are roughly the same length and now
+ 
+
+ align:start position:0%
+ApS are roughly the same length and now
+inside each sub progression let me call
+
+ align:start position:0%
+inside each sub progression let me call
+ 
+
+ align:start position:0%
+inside each sub progression let me call
+the sub progression P prime sub
+
+ align:start position:0%
+the sub progression P prime sub
+ 
+
+ align:start position:0%
+the sub progression P prime sub
+progression P let's look at how much
+
+ align:start position:0%
+progression P let's look at how much
+ 
+
+ align:start position:0%
+progression P let's look at how much
+this character value can vary inside
+
+ align:start position:0%
+this character value can vary inside
+ 
+
+ align:start position:0%
+this character value can vary inside
+this progression so we how much can this
+
+ align:start position:0%
+this progression so we how much can this
+ 
+
+ align:start position:0%
+this progression so we how much can this
+can this very well because theta is such
+
+ align:start position:0%
+can this very well because theta is such
+ 
+
+ align:start position:0%
+can this very well because theta is such
+that D times theta is very close to an
+
+ align:start position:0%
+that D times theta is very close to an
+ 
+
+ align:start position:0%
+that D times theta is very close to an
+integer and the length of each
+
+ align:start position:0%
+integer and the length of each
+ 
+
+ align:start position:0%
+integer and the length of each
+progression is not too large here I want
+
+ align:start position:0%
+progression is not too large here I want
+ 
+
+ align:start position:0%
+progression is not too large here I want
+some control on the length so we find
+
+ align:start position:0%
+some control on the length so we find
+ 
+
+ align:start position:0%
+some control on the length so we find
+that the maximum variation is at most
+
+ align:start position:0%
+that the maximum variation is at most
+ 
+
+ align:start position:0%
+that the maximum variation is at most
+the size of P the length of P times so
+
+ align:start position:0%
+the size of P the length of P times so
+ 
+
+ align:start position:0%
+the size of P the length of P times so
+this that difference over there all of
+
+ align:start position:0%
+this that difference over there all of
+ 
+
+ align:start position:0%
+this that difference over there all of
+these are exponential so I can shift
+
+ align:start position:0%
+these are exponential so I can shift
+ 
+
+ align:start position:0%
+these are exponential so I can shift
+them well the length of P is at most
+
+ align:start position:0%
+them well the length of P is at most
+ 
+
+ align:start position:0%
+them well the length of P is at most
+twice cube root of n and okay so what is
+
+ align:start position:0%
+twice cube root of n and okay so what is
+ 
+
+ align:start position:0%
+twice cube root of n and okay so what is
+this quantity so the point is that if
+
+ align:start position:0%
+this quantity so the point is that if
+ 
+
+ align:start position:0%
+this quantity so the point is that if
+this fractional part here is very close
+
+ align:start position:0%
+this fractional part here is very close
+ 
+
+ align:start position:0%
+this fractional part here is very close
+to an integer then e to that number you
+
+ align:start position:0%
+to an integer then e to that number you
+ 
+
+ align:start position:0%
+to an integer then e to that number you
+to the 2pi times that item number should
+
+ align:start position:0%
+to the 2pi times that item number should
+ 
+
+ align:start position:0%
+to the 2pi times that item number should
+be very close to one because what's
+
+ align:start position:0%
+be very close to one because what's
+ 
+
+ align:start position:0%
+be very close to one because what's
+happening here this is the distance
+
+ align:start position:0%
+happening here this is the distance
+ 
+
+ align:start position:0%
+happening here this is the distance
+between those two points on a circle
+
+ align:start position:0%
+between those two points on a circle
+ 
+
+ align:start position:0%
+between those two points on a circle
+which is and most bounded by the length
+
+ align:start position:0%
+which is and most bounded by the length
+ 
+
+ align:start position:0%
+which is and most bounded by the length
+of the arc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so court length and most out of the
+
+ align:start position:0%
+okay so court length and most out of the
+ 
+
+ align:start position:0%
+okay so court length and most out of the
+arc so now you put everything here
+
+ align:start position:0%
+arc so now you put everything here
+ 
+
+ align:start position:0%
+arc so now you put everything here
+together and applying the bound that we
+
+ align:start position:0%
+together and applying the bound that we
+ 
+
+ align:start position:0%
+together and applying the bound that we
+got D theta so this is the reason for
+
+ align:start position:0%
+got D theta so this is the reason for
+ 
+
+ align:start position:0%
+got D theta so this is the reason for
+choosing that we are number up there we
+
+ align:start position:0%
+choosing that we are number up there we
+ 
+
+ align:start position:0%
+choosing that we are number up there we
+find that variation within each
+
+ align:start position:0%
+find that variation within each
+ 
+
+ align:start position:0%
+find that variation within each
+progression is at most eight so
+
+ align:start position:0%
+progression is at most eight so
+ 
+
+ align:start position:0%
+progression is at most eight so
+variation of this character within each
+
+ align:start position:0%
+variation of this character within each
+ 
+
+ align:start position:0%
+variation of this character within each
+progression it's not very large and that
+
+ align:start position:0%
+progression it's not very large and that
+ 
+
+ align:start position:0%
+progression it's not very large and that
+that's the claim any questions so this
+
+ align:start position:0%
+that's the claim any questions so this
+ 
+
+ align:start position:0%
+that's the claim any questions so this
+is the analogous claim to the one that
+
+ align:start position:0%
+is the analogous claim to the one that
+ 
+
+ align:start position:0%
+is the analogous claim to the one that
+we have the one that we used last time
+
+ align:start position:0%
+we have the one that we used last time
+ 
+
+ align:start position:0%
+we have the one that we used last time
+where we said that the character is
+
+ align:start position:0%
+where we said that the character is
+ 
+
+ align:start position:0%
+where we said that the character is
+constant on each cosine of the
+
+ align:start position:0%
+constant on each cosine of the
+ 
+
+ align:start position:0%
+constant on each cosine of the
+hyperplane not exactly constant but
+
+ align:start position:0%
+hyperplane not exactly constant but
+ 
+
+ align:start position:0%
+hyperplane not exactly constant but
+almost good enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so the goal of step two is to
+
+ align:start position:0%
+all right so the goal of step two is to
+ 
+
+ align:start position:0%
+all right so the goal of step two is to
+show an energy so a density increment
+
+ align:start position:0%
+show an energy so a density increment
+ 
+
+ align:start position:0%
+show an energy so a density increment
+that if you have a large Fourier
+
+ align:start position:0%
+that if you have a large Fourier
+ 
+
+ align:start position:0%
+that if you have a large Fourier
+coefficient then we want to claim that
+
+ align:start position:0%
+coefficient then we want to claim that
+ 
+
+ align:start position:0%
+coefficient then we want to claim that
+the density goes up significantly on
+
+ align:start position:0%
+the density goes up significantly on
+ 
+
+ align:start position:0%
+the density goes up significantly on
+some sub progression and the next part
+
+ align:start position:0%
+some sub progression and the next part
+ 
+
+ align:start position:0%
+some sub progression and the next part
+the next lemma will get us to that goal
+
+ align:start position:0%
+the next lemma will get us to that goal
+ 
+
+ align:start position:0%
+the next lemma will get us to that goal
+and this part is very similar to the one
+
+ align:start position:0%
+and this part is very similar to the one
+ 
+
+ align:start position:0%
+and this part is very similar to the one
+that we saw from last time but with this
+
+ align:start position:0%
+that we saw from last time but with this
+ 
+
+ align:start position:0%
+that we saw from last time but with this
+new partition in - density alpha and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exist some progression sub progression I
+
+ align:start position:0%
+exist some progression sub progression I
+ 
+
+ align:start position:0%
+exist some progression sub progression I
+just mean that I'm starting with
+
+ align:start position:0%
+just mean that I'm starting with
+ 
+
+ align:start position:0%
+just mean that I'm starting with
+original progression 1 to N and I'm
+
+ align:start position:0%
+original progression 1 to N and I'm
+ 
+
+ align:start position:0%
+original progression 1 to N and I'm
+zooming in to some sub progression with
+
+ align:start position:0%
+zooming in to some sub progression with
+ 
+
+ align:start position:0%
+zooming in to some sub progression with
+the length of P fairly long so the
+
+ align:start position:0%
+the length of P fairly long so the
+ 
+
+ align:start position:0%
+the length of P fairly long so the
+length appears at least cube root of N
+
+ align:start position:0%
+length appears at least cube root of N
+ 
+
+ align:start position:0%
+length appears at least cube root of N
+and such that a when restricted to this
+
+ align:start position:0%
+and such that a when restricted to this
+ 
+
+ align:start position:0%
+and such that a when restricted to this
+sub progression has a density increment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so originally the density of a is alpha
+
+ align:start position:0%
+so originally the density of a is alpha
+ 
+
+ align:start position:0%
+so originally the density of a is alpha
+so we're zooming into some sub
+
+ align:start position:0%
+so we're zooming into some sub
+ 
+
+ align:start position:0%
+so we're zooming into some sub
+progression P with a pretty long sub
+
+ align:start position:0%
+progression P with a pretty long sub
+ 
+
+ align:start position:0%
+progression P with a pretty long sub
+progression where the density goes up
+
+ align:start position:0%
+progression where the density goes up
+ 
+
+ align:start position:0%
+progression where the density goes up
+significantly from a to essentially a
+
+ align:start position:0%
+significantly from a to essentially a
+ 
+
+ align:start position:0%
+significantly from a to essentially a
+from alpha to roughly alpha plus alpha
+
+ align:start position:0%
+from alpha to roughly alpha plus alpha
+ 
+
+ align:start position:0%
+from alpha to roughly alpha plus alpha
+squared okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we start with a 383 set so
+
+ align:start position:0%
+all right so we start with a 383 set so
+ 
+
+ align:start position:0%
+all right so we start with a 383 set so
+from step one there exists some data
+
+ align:start position:0%
+from step one there exists some data
+ 
+
+ align:start position:0%
+from step one there exists some data
+with large code so a corresponds to a
+
+ align:start position:0%
+with large code so a corresponds to a
+ 
+
+ align:start position:0%
+with large code so a corresponds to a
+large Fourier coefficient so this sum
+
+ align:start position:0%
+large Fourier coefficient so this sum
+ 
+
+ align:start position:0%
+large Fourier coefficient so this sum
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now we use okay so step one this
+
+ align:start position:0%
+and now we use okay so step one this
+ 
+
+ align:start position:0%
+and now we use okay so step one this
+consequence and from this data now we
+
+ align:start position:0%
+consequence and from this data now we
+ 
+
+ align:start position:0%
+consequence and from this data now we
+apply the lemma up there too so we apply
+
+ align:start position:0%
+apply the lemma up there too so we apply
+ 
+
+ align:start position:0%
+apply the lemma up there too so we apply
+lemma where let's say ha being alpha
+
+ align:start position:0%
+lemma where let's say ha being alpha
+ 
+
+ align:start position:0%
+lemma where let's say ha being alpha
+squared over 30 the exact constants are
+
+ align:start position:0%
+squared over 30 the exact constants are
+ 
+
+ align:start position:0%
+squared over 30 the exact constants are
+not so important when we apply the lemma
+
+ align:start position:0%
+not so important when we apply the lemma
+ 
+
+ align:start position:0%
+not so important when we apply the lemma
+to partition and into a bunch of sub
+
+ align:start position:0%
+to partition and into a bunch of sub
+ 
+
+ align:start position:0%
+to partition and into a bunch of sub
+progressions which we'll call p1 through
+
+ align:start position:0%
+progressions which we'll call p1 through
+ 
+
+ align:start position:0%
+progressions which we'll call p1 through
+p8 and each of these progressions have
+
+ align:start position:0%
+p8 and each of these progressions have
+ 
+
+ align:start position:0%
+p8 and each of these progressions have
+length between cube root of n and twice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want to understand what happens to
+
+ align:start position:0%
+and I want to understand what happens to
+ 
+
+ align:start position:0%
+and I want to understand what happens to
+the density of a when restricted to
+
+ align:start position:0%
+the density of a when restricted to
+ 
+
+ align:start position:0%
+the density of a when restricted to
+these progressions so starting with this
+
+ align:start position:0%
+these progressions so starting with this
+ 
+
+ align:start position:0%
+these progressions so starting with this
+inequality over here which suggests to
+
+ align:start position:0%
+inequality over here which suggests to
+ 
+
+ align:start position:0%
+inequality over here which suggests to
+us that there must be some deviation so
+
+ align:start position:0%
+us that there must be some deviation so
+ 
+
+ align:start position:0%
+us that there must be some deviation so
+starting starting with what we saw and
+
+ align:start position:0%
+starting starting with what we saw and
+ 
+
+ align:start position:0%
+starting starting with what we saw and
+now inside each progression this the X
+
+ align:start position:0%
+now inside each progression this the X
+ 
+
+ align:start position:0%
+now inside each progression this the X
+theta is roughly constant so if you
+
+ align:start position:0%
+theta is roughly constant so if you
+ 
+
+ align:start position:0%
+theta is roughly constant so if you
+pretend them as actually constant I can
+
+ align:start position:0%
+pretend them as actually constant I can
+ 
+
+ align:start position:0%
+pretend them as actually constant I can
+break up this Sun depending on where the
+
+ align:start position:0%
+break up this Sun depending on where the
+ 
+
+ align:start position:0%
+break up this Sun depending on where the
+XS lie so I from 1 okay and let me sum
+
+ align:start position:0%
+XS lie so I from 1 okay and let me sum
+ 
+
+ align:start position:0%
+XS lie so I from 1 okay and let me sum
+inside each progression okay so by
+
+ align:start position:0%
+inside each progression okay so by
+ 
+
+ align:start position:0%
+inside each progression okay so by
+triangle inequality
+
+ align:start position:0%
+triangle inequality
+ 
+
+ align:start position:0%
+triangle inequality
+I can upper bound the first sum by where
+
+ align:start position:0%
+I can upper bound the first sum by where
+ 
+
+ align:start position:0%
+I can upper bound the first sum by where
+I now cut some into progression by
+
+ align:start position:0%
+I now cut some into progression by
+ 
+
+ align:start position:0%
+I now cut some into progression by
+progression and on each progression this
+
+ align:start position:0%
+progression and on each progression this
+ 
+
+ align:start position:0%
+progression and on each progression this
+character is roughly constant so let me
+
+ align:start position:0%
+character is roughly constant so let me
+ 
+
+ align:start position:0%
+character is roughly constant so let me
+take out the maximum possible deviations
+
+ align:start position:0%
+take out the maximum possible deviations
+ 
+
+ align:start position:0%
+take out the maximum possible deviations
+from them being constant so upper bound
+
+ align:start position:0%
+from them being constant so upper bound
+ 
+
+ align:start position:0%
+from them being constant so upper bound
+again you find that we can essentially
+
+ align:start position:0%
+again you find that we can essentially
+ 
+
+ align:start position:0%
+again you find that we can essentially
+pretend so if each exponential is
+
+ align:start position:0%
+pretend so if each exponential is
+ 
+
+ align:start position:0%
+pretend so if each exponential is
+constant on each sub progression then I
+
+ align:start position:0%
+constant on each sub progression then I
+ 
+
+ align:start position:0%
+constant on each sub progression then I
+- well just have this sum here but I
+
+ align:start position:0%
+- well just have this sum here but I
+ 
+
+ align:start position:0%
+- well just have this sum here but I
+lose a little bit because it's not
+
+ align:start position:0%
+lose a little bit because it's not
+ 
+
+ align:start position:0%
+lose a little bit because it's not
+exactly constants almost constant so I
+
+ align:start position:0%
+exactly constants almost constant so I
+ 
+
+ align:start position:0%
+exactly constants almost constant so I
+lose a little bit and that little bit is
+
+ align:start position:0%
+lose a little bit and that little bit is
+ 
+
+ align:start position:0%
+lose a little bit and that little bit is
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+lose that little bit of a tub and so on
+
+ align:start position:0%
+lose that little bit of a tub and so on
+ 
+
+ align:start position:0%
+lose that little bit of a tub and so on
+each progression P I you lose almost
+
+ align:start position:0%
+each progression P I you lose almost
+ 
+
+ align:start position:0%
+each progression P I you lose almost
+something that's essentially of a square
+
+ align:start position:0%
+something that's essentially of a square
+ 
+
+ align:start position:0%
+something that's essentially of a square
+times the length of P i okay now you see
+
+ align:start position:0%
+times the length of P i okay now you see
+ 
+
+ align:start position:0%
+times the length of P i okay now you see
+I've chosen the error parameter so that
+
+ align:start position:0%
+I've chosen the error parameter so that
+ 
+
+ align:start position:0%
+I've chosen the error parameter so that
+everything I've lost is no not so much
+
+ align:start position:0%
+everything I've lost is no not so much
+ 
+
+ align:start position:0%
+everything I've lost is no not so much
+more than the initial bound I began with
+
+ align:start position:0%
+more than the initial bound I began with
+ 
+
+ align:start position:0%
+more than the initial bound I began with
+so in particular we see that even if we
+
+ align:start position:0%
+so in particular we see that even if we
+ 
+
+ align:start position:0%
+so in particular we see that even if we
+have pretended that the characters were
+
+ align:start position:0%
+have pretended that the characters were
+ 
+
+ align:start position:0%
+have pretended that the characters were
+constant on each progression we would
+
+ align:start position:0%
+constant on each progression we would
+ 
+
+ align:start position:0%
+constant on each progression we would
+have still obtained some lower bound on
+
+ align:start position:0%
+have still obtained some lower bound on
+ 
+
+ align:start position:0%
+have still obtained some lower bound on
+the total deviation okay and what is
+
+ align:start position:0%
+the total deviation okay and what is
+ 
+
+ align:start position:0%
+the total deviation okay and what is
+this quantity over here or you see I'm
+
+ align:start position:0%
+this quantity over here or you see I'm
+ 
+
+ align:start position:0%
+this quantity over here or you see I'm
+restricting each some to each sub
+
+ align:start position:0%
+restricting each some to each sub
+ 
+
+ align:start position:0%
+restricting each some to each sub
+progression but this sum here even
+
+ align:start position:0%
+progression but this sum here even
+ 
+
+ align:start position:0%
+progression but this sum here even
+though it's the sum but it's really
+
+ align:start position:0%
+though it's the sum but it's really
+ 
+
+ align:start position:0%
+though it's the sum but it's really
+counting how many elements of a are in
+
+ align:start position:0%
+counting how many elements of a are in
+ 
+
+ align:start position:0%
+counting how many elements of a are in
+that progression so this sum over here
+
+ align:start position:0%
+that progression so this sum over here
+ 
+
+ align:start position:0%
+that progression so this sum over here
+is the same thing okay so let me write
+
+ align:start position:0%
+is the same thing okay so let me write
+ 
+
+ align:start position:0%
+is the same thing okay so let me write
+it Newport
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so what we have so the left-hand side
+
+ align:start position:0%
+so so what we have so the left-hand side
+ 
+
+ align:start position:0%
+so so what we have so the left-hand side
+over there is this quantity here we see
+
+ align:start position:0%
+over there is this quantity here we see
+ 
+
+ align:start position:0%
+over there is this quantity here we see
+that the right-hand side even though you
+
+ align:start position:0%
+that the right-hand side even though you
+ 
+
+ align:start position:0%
+that the right-hand side even though you
+have that sum it is really just counting
+
+ align:start position:0%
+have that sum it is really just counting
+ 
+
+ align:start position:0%
+have that sum it is really just counting
+how many elements of a are in each
+
+ align:start position:0%
+how many elements of a are in each
+ 
+
+ align:start position:0%
+how many elements of a are in each
+progression versus how many you should
+
+ align:start position:0%
+progression versus how many you should
+ 
+
+ align:start position:0%
+progression versus how many you should
+expect based on the overall density of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that should look similar to what we
+
+ align:start position:0%
+so that should look similar to what we
+ 
+
+ align:start position:0%
+so that should look similar to what we
+got last time I know the intuition
+
+ align:start position:0%
+got last time I know the intuition
+ 
+
+ align:start position:0%
+got last time I know the intuition
+should be that well if the average
+
+ align:start position:0%
+should be that well if the average
+ 
+
+ align:start position:0%
+should be that well if the average
+deviation is large then one of them one
+
+ align:start position:0%
+deviation is large then one of them one
+ 
+
+ align:start position:0%
+deviation is large then one of them one
+of these terms should have the density
+
+ align:start position:0%
+of these terms should have the density
+ 
+
+ align:start position:0%
+of these terms should have the density
+increment if you try to do the next step
+
+ align:start position:0%
+increment if you try to do the next step
+ 
+
+ align:start position:0%
+increment if you try to do the next step
+somewhat naively you run into an issue
+
+ align:start position:0%
+somewhat naively you run into an issue
+ 
+
+ align:start position:0%
+somewhat naively you run into an issue
+because it could be here you have K
+
+ align:start position:0%
+because it could be here you have K
+ 
+
+ align:start position:0%
+because it could be here you have K
+terms it could be that you have all the
+
+ align:start position:0%
+terms it could be that you have all the
+ 
+
+ align:start position:0%
+terms it could be that you have all the
+densities except for one going up only
+
+ align:start position:0%
+densities except for one going up only
+ 
+
+ align:start position:0%
+densities except for one going up only
+slightly and one density dropping
+
+ align:start position:0%
+slightly and one density dropping
+ 
+
+ align:start position:0%
+slightly and one density dropping
+dramatically in which case you might not
+
+ align:start position:0%
+dramatically in which case you might not
+ 
+
+ align:start position:0%
+dramatically in which case you might not
+have a significant density increment
+
+ align:start position:0%
+have a significant density increment
+ 
+
+ align:start position:0%
+have a significant density increment
+right so we want to show that on some
+
+ align:start position:0%
+right so we want to show that on some
+ 
+
+ align:start position:0%
+right so we want to show that on some
+progression the density increases
+
+ align:start position:0%
+progression the density increases
+ 
+
+ align:start position:0%
+progression the density increases
+significantly so far from this
+
+ align:start position:0%
+significantly so far from this
+ 
+
+ align:start position:0%
+significantly so far from this
+inequality we just know that there is
+
+ align:start position:0%
+inequality we just know that there is
+ 
+
+ align:start position:0%
+inequality we just know that there is
+some sub progression where the density
+
+ align:start position:0%
+some sub progression where the density
+ 
+
+ align:start position:0%
+some sub progression where the density
+changes significantly but of course the
+
+ align:start position:0%
+changes significantly but of course the
+ 
+
+ align:start position:0%
+changes significantly but of course the
+overall density the average density
+
+ align:start position:0%
+overall density the average density
+ 
+
+ align:start position:0%
+overall density the average density
+should remain constant so if some goes
+
+ align:start position:0%
+should remain constant so if some goes
+ 
+
+ align:start position:0%
+should remain constant so if some goes
+up others must go down but if you just
+
+ align:start position:0%
+up others must go down but if you just
+ 
+
+ align:start position:0%
+up others must go down but if you just
+try to do an averaging argument you have
+
+ align:start position:0%
+try to do an averaging argument you have
+ 
+
+ align:start position:0%
+try to do an averaging argument you have
+to be careful so so there was a trick
+
+ align:start position:0%
+to be careful so so there was a trick
+ 
+
+ align:start position:0%
+to be careful so so there was a trick
+last time which we didn't really mean
+
+ align:start position:0%
+last time which we didn't really mean
+ 
+
+ align:start position:0%
+last time which we didn't really mean
+last time but now now it's much more you
+
+ align:start position:0%
+last time but now now it's much more you
+ 
+
+ align:start position:0%
+last time but now now it's much more you
+more useful where I want to show that if
+
+ align:start position:0%
+more useful where I want to show that if
+ 
+
+ align:start position:0%
+more useful where I want to show that if
+this holds then some P I sees a large
+
+ align:start position:0%
+this holds then some P I sees a large
+ 
+
+ align:start position:0%
+this holds then some P I sees a large
+and it sees a large density increment
+
+ align:start position:0%
+and it sees a large density increment
+ 
+
+ align:start position:0%
+and it sees a large density increment
+and to do that let me rewrite this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the following so I keep the same
+
+ align:start position:0%
+as the following so I keep the same
+ 
+
+ align:start position:0%
+as the following so I keep the same
+expression and I add a term which is the
+
+ align:start position:0%
+expression and I add a term which is the
+ 
+
+ align:start position:0%
+expression and I add a term which is the
+same thing but without the absolute
+
+ align:start position:0%
+same thing but without the absolute
+ 
+
+ align:start position:0%
+same thing but without the absolute
+value okay so you see these guys stay
+
+ align:start position:0%
+value okay so you see these guys stay
+ 
+
+ align:start position:0%
+value okay so you see these guys stay
+total to zero so adding that term it
+
+ align:start position:0%
+total to zero so adding that term it
+ 
+
+ align:start position:0%
+total to zero so adding that term it
+doesn't change my expression but now the
+
+ align:start position:0%
+doesn't change my expression but now the
+ 
+
+ align:start position:0%
+doesn't change my expression but now the
+summon is always non-negative so it's
+
+ align:start position:0%
+summon is always non-negative so it's
+ 
+
+ align:start position:0%
+summon is always non-negative so it's
+either zero or twice this number
+
+ align:start position:0%
+either zero or twice this number
+ 
+
+ align:start position:0%
+either zero or twice this number
+depending on the sign of okay so
+
+ align:start position:0%
+depending on the sign of okay so
+ 
+
+ align:start position:0%
+depending on the sign of okay so
+comparing left hand side right hand side
+
+ align:start position:0%
+comparing left hand side right hand side
+ 
+
+ align:start position:0%
+comparing left hand side right hand side
+we see that there must be some I so
+
+ align:start position:0%
+we see that there must be some I so
+ 
+
+ align:start position:0%
+we see that there must be some I so
+hence this sum I such that the left hand
+
+ align:start position:0%
+hence this sum I such that the left hand
+ 
+
+ align:start position:0%
+hence this sum I such that the left hand
+side the ice term on the left hand side
+
+ align:start position:0%
+side the ice term on the left hand side
+ 
+
+ align:start position:0%
+side the ice term on the left hand side
+is less than or equal to the ice term on
+
+ align:start position:0%
+is less than or equal to the ice term on
+ 
+
+ align:start position:0%
+is less than or equal to the ice term on
+the right hand side and in particular
+
+ align:start position:0%
+the right hand side and in particular
+ 
+
+ align:start position:0%
+the right hand side and in particular
+that term should be positive so it
+
+ align:start position:0%
+that term should be positive so it
+ 
+
+ align:start position:0%
+that term should be positive so it
+implies okay so how can how can you get
+
+ align:start position:0%
+implies okay so how can how can you get
+ 
+
+ align:start position:0%
+implies okay so how can how can you get
+this inequality with it in pies simply
+
+ align:start position:0%
+this inequality with it in pies simply
+ 
+
+ align:start position:0%
+this inequality with it in pies simply
+that the restriction of a to this pie is
+
+ align:start position:0%
+that the restriction of a to this pie is
+ 
+
+ align:start position:0%
+that the restriction of a to this pie is
+at least alpha plus alpha squared over
+
+ align:start position:0%
+at least alpha plus alpha squared over
+ 
+
+ align:start position:0%
+at least alpha plus alpha squared over
+40 times so this claim here just says
+
+ align:start position:0%
+40 times so this claim here just says
+ 
+
+ align:start position:0%
+40 times so this claim here just says
+that on the ice progression there's a
+
+ align:start position:0%
+that on the ice progression there's a
+ 
+
+ align:start position:0%
+that on the ice progression there's a
+significant energy increment if it's
+
+ align:start position:0%
+significant energy increment if it's
+ 
+
+ align:start position:0%
+significant energy increment if it's
+worth decrement that term could have
+
+ align:start position:0%
+worth decrement that term could have
+ 
+
+ align:start position:0%
+worth decrement that term could have
+been zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this achieves what we were
+
+ align:start position:0%
+okay so this achieves what we were
+ 
+
+ align:start position:0%
+okay so this achieves what we were
+looking for in step two namely to find
+
+ align:start position:0%
+looking for in step two namely to find
+ 
+
+ align:start position:0%
+looking for in step two namely to find
+that there's a density increment on some
+
+ align:start position:0%
+that there's a density increment on some
+ 
+
+ align:start position:0%
+that there's a density increment on some
+long sub progression now we can go to
+
+ align:start position:0%
+long sub progression now we can go to
+ 
+
+ align:start position:0%
+long sub progression now we can go to
+step three which is basically the same
+
+ align:start position:0%
+step three which is basically the same
+ 
+
+ align:start position:0%
+step three which is basically the same
+as we saw last time
+
+ align:start position:0%
+as we saw last time
+ 
+
+ align:start position:0%
+as we saw last time
+where now we want to iterate this
+
+ align:start position:0%
+where now we want to iterate this
+ 
+
+ align:start position:0%
+where now we want to iterate this
+density increment okay so it's basically
+
+ align:start position:0%
+density increment okay so it's basically
+ 
+
+ align:start position:0%
+density increment okay so it's basically
+the same argument as last time you start
+
+ align:start position:0%
+the same argument as last time you start
+ 
+
+ align:start position:0%
+the same argument as last time you start
+with density alpha and each step in the
+
+ align:start position:0%
+with density alpha and each step in the
+ 
+
+ align:start position:0%
+with density alpha and each step in the
+integration the density goes up quite a
+
+ align:start position:0%
+integration the density goes up quite a
+ 
+
+ align:start position:0%
+integration the density goes up quite a
+bit and we want to control the total
+
+ align:start position:0%
+bit and we want to control the total
+ 
+
+ align:start position:0%
+bit and we want to control the total
+number of steps knowing that the final
+
+ align:start position:0%
+number of steps knowing that the final
+ 
+
+ align:start position:0%
+number of steps knowing that the final
+density at most one always okay so how
+
+ align:start position:0%
+density at most one always okay so how
+ 
+
+ align:start position:0%
+density at most one always okay so how
+many steps can you take so this was the
+
+ align:start position:0%
+many steps can you take so this was the
+ 
+
+ align:start position:0%
+many steps can you take so this was the
+same argument that we saw last time you
+
+ align:start position:0%
+same argument that we saw last time you
+ 
+
+ align:start position:0%
+same argument that we saw last time you
+see that starting with alpha or not
+
+ align:start position:0%
+see that starting with alpha or not
+ 
+
+ align:start position:0%
+see that starting with alpha or not
+alpha if doubles after certain number of
+
+ align:start position:0%
+alpha if doubles after certain number of
+ 
+
+ align:start position:0%
+alpha if doubles after certain number of
+steps we double after okay so how many
+
+ align:start position:0%
+steps we double after okay so how many
+ 
+
+ align:start position:0%
+steps we double after okay so how many
+steps do you need well I want to get
+
+ align:start position:0%
+steps do you need well I want to get
+ 
+
+ align:start position:0%
+steps do you need well I want to get
+from alpha 2 to alpha so I need at most
+
+ align:start position:0%
+from alpha 2 to alpha so I need at most
+ 
+
+ align:start position:0%
+from alpha 2 to alpha so I need at most
+alpha over 40 steps ok so last time I
+
+ align:start position:0%
+alpha over 40 steps ok so last time I
+ 
+
+ align:start position:0%
+alpha over 40 steps ok so last time I
+was slightly sloppy and so there's a
+
+ align:start position:0%
+was slightly sloppy and so there's a
+ 
+
+ align:start position:0%
+was slightly sloppy and so there's a
+basically a floor up or floor down
+
+ align:start position:0%
+basically a floor up or floor down
+ 
+
+ align:start position:0%
+basically a floor up or floor down
+sitting up or down situation but I
+
+ align:start position:0%
+sitting up or down situation but I
+ 
+
+ align:start position:0%
+sitting up or down situation but I
+should add a plus one yeah
+
+ align:start position:0%
+should add a plus one yeah
+ 
+
+ align:start position:0%
+should add a plus one yeah
+40 40 over alpha so you double after at
+
+ align:start position:0%
+40 40 over alpha so you double after at
+ 
+
+ align:start position:0%
+40 40 over alpha so you double after at
+most that many steps and then now you
+
+ align:start position:0%
+most that many steps and then now you
+ 
+
+ align:start position:0%
+most that many steps and then now you
+are at density at least 2 alpha so we
+
+ align:start position:0%
+are at density at least 2 alpha so we
+ 
+
+ align:start position:0%
+are at density at least 2 alpha so we
+double after at most 20 over alpha steps
+
+ align:start position:0%
+double after at most 20 over alpha steps
+ 
+
+ align:start position:0%
+double after at most 20 over alpha steps
+and so on and we double at most
+
+ align:start position:0%
+and so on and we double at most
+ 
+
+ align:start position:0%
+and so on and we double at most
+basically log sub 2 of 1 over alpha
+
+ align:start position:0%
+basically log sub 2 of 1 over alpha
+ 
+
+ align:start position:0%
+basically log sub 2 of 1 over alpha
+times okay so anyway putting everything
+
+ align:start position:0%
+times okay so anyway putting everything
+ 
+
+ align:start position:0%
+times okay so anyway putting everything
+together we see that the total number of
+
+ align:start position:0%
+together we see that the total number of
+ 
+
+ align:start position:0%
+together we see that the total number of
+steps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes and most on the order of 1 over
+
+ align:start position:0%
+yes and most on the order of 1 over
+ 
+
+ align:start position:0%
+yes and most on the order of 1 over
+alpha when you stop you can only stop
+
+ align:start position:0%
+alpha when you stop you can only stop
+ 
+
+ align:start position:0%
+alpha when you stop you can only stop
+for one reason because in the so so in
+
+ align:start position:0%
+for one reason because in the so so in
+ 
+
+ align:start position:0%
+for one reason because in the so so in
+step 1
+
+ align:start position:0%
+step 1
+ 
+
+ align:start position:0%
+step 1
+remember the iteration said that the
+
+ align:start position:0%
+remember the iteration said that the
+ 
+
+ align:start position:0%
+remember the iteration said that the
+process terminates process can always go
+
+ align:start position:0%
+process terminates process can always go
+ 
+
+ align:start position:0%
+process terminates process can always go
+on and it terminates if the length 2 now
+
+ align:start position:0%
+on and it terminates if the length 2 now
+ 
+
+ align:start position:0%
+on and it terminates if the length 2 now
+a step I so let ni be the length of the
+
+ align:start position:0%
+a step I so let ni be the length of the
+ 
+
+ align:start position:0%
+a step I so let ni be the length of the
+progression that step I is at most C
+
+ align:start position:0%
+progression that step I is at most C
+ 
+
+ align:start position:0%
+progression that step I is at most C
+times alpha I to the minus 12 provided
+
+ align:start position:0%
+times alpha I to the minus 12 provided
+ 
+
+ align:start position:0%
+times alpha I to the minus 12 provided
+that n is large enough you can always
+
+ align:start position:0%
+that n is large enough you can always
+ 
+
+ align:start position:0%
+that n is large enough you can always
+pass to a sub progression and here you
+
+ align:start position:0%
+pass to a sub progression and here you
+ 
+
+ align:start position:0%
+pass to a sub progression and here you
+know when you pass the sub progression
+
+ align:start position:0%
+know when you pass the sub progression
+ 
+
+ align:start position:0%
+know when you pass the sub progression
+of course you can read label that sub
+
+ align:start position:0%
+of course you can read label that sub
+ 
+
+ align:start position:0%
+of course you can read label that sub
+progression and it's now 1 through n I
+
+ align:start position:0%
+progression and it's now 1 through n I
+ 
+
+ align:start position:0%
+progression and it's now 1 through n I
+so I can it's all the progressions are
+
+ align:start position:0%
+so I can it's all the progressions are
+ 
+
+ align:start position:0%
+so I can it's all the progressions are
+basically the same as the first set of
+
+ align:start position:0%
+basically the same as the first set of
+ 
+
+ align:start position:0%
+basically the same as the first set of
+positive integers prefix of the positive
+
+ align:start position:0%
+positive integers prefix of the positive
+ 
+
+ align:start position:0%
+positive integers prefix of the positive
+integers so when we stop a step I you
+
+ align:start position:0%
+integers so when we stop a step I you
+ 
+
+ align:start position:0%
+integers so when we stop a step I you
+must have n sub I being
+
+ align:start position:0%
+must have n sub I being
+ 
+
+ align:start position:0%
+must have n sub I being
+most this quantity over here which is at
+
+ align:start position:0%
+most this quantity over here which is at
+ 
+
+ align:start position:0%
+most this quantity over here which is at
+most C times the initial density raised
+
+ align:start position:0%
+most C times the initial density raised
+ 
+
+ align:start position:0%
+most C times the initial density raised
+to this minus 12 so therefore the
+
+ align:start position:0%
+to this minus 12 so therefore the
+ 
+
+ align:start position:0%
+to this minus 12 so therefore the
+initial length n of the space is bounded
+
+ align:start position:0%
+initial length n of the space is bounded
+ 
+
+ align:start position:0%
+initial length n of the space is bounded
+by each time we went down by a cube root
+
+ align:start position:0%
+by each time we went down by a cube root
+ 
+
+ align:start position:0%
+by each time we went down by a cube root
+at most right so you find if you stop a
+
+ align:start position:0%
+at most right so you find if you stop a
+ 
+
+ align:start position:0%
+at most right so you find if you stop a
+step I then the initial length is at
+
+ align:start position:0%
+step I then the initial length is at
+ 
+
+ align:start position:0%
+step I then the initial length is at
+most n sub I to the 3 times 3 to the
+
+ align:start position:0%
+most n sub I to the 3 times 3 to the
+ 
+
+ align:start position:0%
+most n sub I to the 3 times 3 to the
+power of I each time you're doing a cube
+
+ align:start position:0%
+power of I each time you're doing a cube
+ 
+
+ align:start position:0%
+power of I each time you're doing a cube
+root okay so you put everything together
+
+ align:start position:0%
+root okay so you put everything together
+ 
+
+ align:start position:0%
+root okay so you put everything together
+that most time in the iterations when
+
+ align:start position:0%
+that most time in the iterations when
+ 
+
+ align:start position:0%
+that most time in the iterations when
+you stop the length is at most this so
+
+ align:start position:0%
+you stop the length is at most this so
+ 
+
+ align:start position:0%
+you stop the length is at most this so
+you put them together and then you find
+
+ align:start position:0%
+you put them together and then you find
+ 
+
+ align:start position:0%
+you put them together and then you find
+that the n must be at most double
+
+ align:start position:0%
+that the n must be at most double
+ 
+
+ align:start position:0%
+that the n must be at most double
+exponential in 1 over the density in
+
+ align:start position:0%
+exponential in 1 over the density in
+ 
+
+ align:start position:0%
+exponential in 1 over the density in
+other words density is at most 1 over
+
+ align:start position:0%
+other words density is at most 1 over
+ 
+
+ align:start position:0%
+other words density is at most 1 over
+log log n which is what we claimed in
+
+ align:start position:0%
+log log n which is what we claimed in
+ 
+
+ align:start position:0%
+log log n which is what we claimed in
+Ross theorem okay so that finishes the
+
+ align:start position:0%
+Ross theorem okay so that finishes the
+ 
+
+ align:start position:0%
+Ross theorem okay so that finishes the
+proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+any questions so the message here is
+
+ align:start position:0%
+any questions so the message here is
+ 
+
+ align:start position:0%
+any questions so the message here is
+that it's the same proof as last time
+
+ align:start position:0%
+that it's the same proof as last time
+ 
+
+ align:start position:0%
+that it's the same proof as last time
+but we need to do a bit more work and
+
+ align:start position:0%
+but we need to do a bit more work and
+ 
+
+ align:start position:0%
+but we need to do a bit more work and
+none of this work is difficult but
+
+ align:start position:0%
+none of this work is difficult but
+ 
+
+ align:start position:0%
+none of this work is difficult but
+they're more technical and that's often
+
+ align:start position:0%
+they're more technical and that's often
+ 
+
+ align:start position:0%
+they're more technical and that's often
+a theme that you see in additive
+
+ align:start position:0%
+a theme that you see in additive
+ 
+
+ align:start position:0%
+a theme that you see in additive
+combinatorics this is part of the reason
+
+ align:start position:0%
+combinatorics this is part of the reason
+ 
+
+ align:start position:0%
+combinatorics this is part of the reason
+why the finite field model is a really
+
+ align:start position:0%
+why the finite field model is a really
+ 
+
+ align:start position:0%
+why the finite field model is a really
+nice playground because there are things
+
+ align:start position:0%
+nice playground because there are things
+ 
+
+ align:start position:0%
+nice playground because there are things
+tend to be often cleaner but the ideas
+
+ align:start position:0%
+tend to be often cleaner but the ideas
+ 
+
+ align:start position:0%
+tend to be often cleaner but the ideas
+are often similar or the same ideas not
+
+ align:start position:0%
+are often similar or the same ideas not
+ 
+
+ align:start position:0%
+are often similar or the same ideas not
+always next lecture we'll see you one
+
+ align:start position:0%
+always next lecture we'll see you one
+ 
+
+ align:start position:0%
+always next lecture we'll see you one
+technique where there's a dramatic
+
+ align:start position:0%
+technique where there's a dramatic
+ 
+
+ align:start position:0%
+technique where there's a dramatic
+difference between the finite field
+
+ align:start position:0%
+difference between the finite field
+ 
+
+ align:start position:0%
+difference between the finite field
+vector space and over the integers but
+
+ align:start position:0%
+vector space and over the integers but
+ 
+
+ align:start position:0%
+vector space and over the integers but
+for many things in additive
+
+ align:start position:0%
+for many things in additive
+ 
+
+ align:start position:0%
+for many things in additive
+combinatorics define a fuel vector space
+
+ align:start position:0%
+combinatorics define a fuel vector space
+ 
+
+ align:start position:0%
+combinatorics define a fuel vector space
+is just a nicer place to be in to try
+
+ align:start position:0%
+is just a nicer place to be in to try
+ 
+
+ align:start position:0%
+is just a nicer place to be in to try
+all your ideas and techniques what let
+
+ align:start position:0%
+all your ideas and techniques what let
+ 
+
+ align:start position:0%
+all your ideas and techniques what let
+me comment on some analogies between
+
+ align:start position:0%
+me comment on some analogies between
+ 
+
+ align:start position:0%
+me comment on some analogies between
+these two approaches and compare the
+
+ align:start position:0%
+these two approaches and compare the
+ 
+
+ align:start position:0%
+these two approaches and compare the
+bounds so on one hand so we saw last
+
+ align:start position:0%
+bounds so on one hand so we saw last
+ 
+
+ align:start position:0%
+bounds so on one hand so we saw last
+time is proof in FP to the end now the
+
+ align:start position:0%
+time is proof in FP to the end now the
+ 
+
+ align:start position:0%
+time is proof in FP to the end now the
+integers inside this interval of length
+
+ align:start position:0%
+integers inside this interval of length
+ 
+
+ align:start position:0%
+integers inside this interval of length
+so let me write uppercase and in both
+
+ align:start position:0%
+so let me write uppercase and in both
+ 
+
+ align:start position:0%
+so let me write uppercase and in both
+cases to be the size of the overall
+
+ align:start position:0%
+cases to be the size of the overall
+ 
+
+ align:start position:0%
+cases to be the size of the overall
+ambient space so what kind of bounds do
+
+ align:start position:0%
+ambient space so what kind of bounds do
+ 
+
+ align:start position:0%
+ambient space so what kind of bounds do
+we get in both situations so last time
+
+ align:start position:0%
+we get in both situations so last time
+ 
+
+ align:start position:0%
+we get in both situations so last time
+for in F 3 to the end we got a bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is of the order and over log n
+
+ align:start position:0%
+which is of the order and over log n
+ 
+
+ align:start position:0%
+which is of the order and over log n
+whereas today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pound is somewhat worse a little bit
+
+ align:start position:0%
+pound is somewhat worse a little bit
+ 
+
+ align:start position:0%
+pound is somewhat worse a little bit
+worse now we lose an extra lock so where
+
+ align:start position:0%
+worse now we lose an extra lock so where
+ 
+
+ align:start position:0%
+worse now we lose an extra lock so where
+do we lose an extra lock in this
+
+ align:start position:0%
+do we lose an extra lock in this
+ 
+
+ align:start position:0%
+do we lose an extra lock in this
+argument so where does these two
+
+ align:start position:0%
+argument so where does these two
+ 
+
+ align:start position:0%
+argument so where does these two
+argument where do these two arguments
+
+ align:start position:0%
+argument where do these two arguments
+ 
+
+ align:start position:0%
+argument where do these two arguments
+differ qualitatively okay so you're
+
+ align:start position:0%
+differ qualitatively okay so you're
+ 
+
+ align:start position:0%
+differ qualitatively okay so you're
+dividing by so here in each iteration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over here your size of the iteration I
+
+ align:start position:0%
+over here your size of the iteration I
+ 
+
+ align:start position:0%
+over here your size of the iteration I
+mean iteration the size of the space
+
+ align:start position:0%
+mean iteration the size of the space
+ 
+
+ align:start position:0%
+mean iteration the size of the space
+goes down by a factor three whereas over
+
+ align:start position:0%
+goes down by a factor three whereas over
+ 
+
+ align:start position:0%
+goes down by a factor three whereas over
+here it could go down by a cube root and
+
+ align:start position:0%
+here it could go down by a cube root and
+ 
+
+ align:start position:0%
+here it could go down by a cube root and
+that's that's precisely right so that
+
+ align:start position:0%
+that's that's precisely right so that
+ 
+
+ align:start position:0%
+that's that's precisely right so that
+explains for this extra lock in the
+
+ align:start position:0%
+explains for this extra lock in the
+ 
+
+ align:start position:0%
+explains for this extra lock in the
+bounds so while this is a great analogy
+
+ align:start position:0%
+bounds so while this is a great analogy
+ 
+
+ align:start position:0%
+bounds so while this is a great analogy
+it's not a perfect analogy you see there
+
+ align:start position:0%
+it's not a perfect analogy you see there
+ 
+
+ align:start position:0%
+it's not a perfect analogy you see there
+is a divergence here between the two
+
+ align:start position:0%
+is a divergence here between the two
+ 
+
+ align:start position:0%
+is a divergence here between the two
+situations and so then you might ask is
+
+ align:start position:0%
+situations and so then you might ask is
+ 
+
+ align:start position:0%
+situations and so then you might ask is
+there some way to avoid the loss this
+
+ align:start position:0%
+there some way to avoid the loss this
+ 
+
+ align:start position:0%
+there some way to avoid the loss this
+extra log factor loss over here is there
+
+ align:start position:0%
+extra log factor loss over here is there
+ 
+
+ align:start position:0%
+extra log factor loss over here is there
+some way to carry out the strategy that
+
+ align:start position:0%
+some way to carry out the strategy that
+ 
+
+ align:start position:0%
+some way to carry out the strategy that
+we did last time in a way that is much
+
+ align:start position:0%
+we did last time in a way that is much
+ 
+
+ align:start position:0%
+we did last time in a way that is much
+more faithful to that strategy of
+
+ align:start position:0%
+more faithful to that strategy of
+ 
+
+ align:start position:0%
+more faithful to that strategy of
+passing down to subspaces so here we
+
+ align:start position:0%
+passing down to subspaces so here we
+ 
+
+ align:start position:0%
+passing down to subspaces so here we
+pass two progressions and because we
+
+ align:start position:0%
+pass two progressions and because we
+ 
+
+ align:start position:0%
+pass two progressions and because we
+have do this extra you know pigeonhole
+
+ align:start position:0%
+have do this extra you know pigeonhole
+ 
+
+ align:start position:0%
+have do this extra you know pigeonhole
+type argument it was somewhat lost we
+
+ align:start position:0%
+type argument it was somewhat lost we
+ 
+
+ align:start position:0%
+type argument it was somewhat lost we
+lost a power which translated into this
+
+ align:start position:0%
+lost a power which translated into this
+ 
+
+ align:start position:0%
+lost a power which translated into this
+extra log so it turns out there there is
+
+ align:start position:0%
+extra log so it turns out there there is
+ 
+
+ align:start position:0%
+extra log so it turns out there there is
+some way to do this so let me just
+
+ align:start position:0%
+some way to do this so let me just
+ 
+
+ align:start position:0%
+some way to do this so let me just
+briefly mention what's the idea that is
+
+ align:start position:0%
+briefly mention what's the idea that is
+ 
+
+ align:start position:0%
+briefly mention what's the idea that is
+involved so last time we went down from
+
+ align:start position:0%
+involved so last time we went down from
+ 
+
+ align:start position:0%
+involved so last time we went down from
+so the main objects that we were passing
+
+ align:start position:0%
+so the main objects that we were passing
+ 
+
+ align:start position:0%
+so the main objects that we were passing
+or start with a vector space and passed
+
+ align:start position:0%
+or start with a vector space and passed
+ 
+
+ align:start position:0%
+or start with a vector space and passed
+down to a subspace which is also a
+
+ align:start position:0%
+down to a subspace which is also a
+ 
+
+ align:start position:0%
+down to a subspace which is also a
+vector space so you can define subspaces
+
+ align:start position:0%
+vector space so you can define subspaces
+ 
+
+ align:start position:0%
+vector space so you can define subspaces
+in a street the end by the following so
+
+ align:start position:0%
+in a street the end by the following so
+ 
+
+ align:start position:0%
+in a street the end by the following so
+I can start with some set of characters
+
+ align:start position:0%
+I can start with some set of characters
+ 
+
+ align:start position:0%
+I can start with some set of characters
+you and I define as some set of
+
+ align:start position:0%
+you and I define as some set of
+ 
+
+ align:start position:0%
+you and I define as some set of
+characters s and I define u sub s to be
+
+ align:start position:0%
+characters s and I define u sub s to be
+ 
+
+ align:start position:0%
+characters s and I define u sub s to be
+basically the orthogonal complement of s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok so this is a subspace and these were
+
+ align:start position:0%
+ok so this is a subspace and these were
+ 
+
+ align:start position:0%
+ok so this is a subspace and these were
+the kind of subspaces that we saw last
+
+ align:start position:0%
+the kind of subspaces that we saw last
+ 
+
+ align:start position:0%
+the kind of subspaces that we saw last
+time because the SS or the ARS that came
+
+ align:start position:0%
+time because the SS or the ARS that came
+ 
+
+ align:start position:0%
+time because the SS or the ARS that came
+out of the proof last time every time we
+
+ align:start position:0%
+out of the proof last time every time we
+ 
+
+ align:start position:0%
+out of the proof last time every time we
+saw bond we throw it in we cut down to a
+
+ align:start position:0%
+saw bond we throw it in we cut down to a
+ 
+
+ align:start position:0%
+saw bond we throw it in we cut down to a
+smaller subspace and we repeat but the
+
+ align:start position:0%
+smaller subspace and we repeat but the
+ 
+
+ align:start position:0%
+smaller subspace and we repeat but the
+progressions they don't really look like
+
+ align:start position:0%
+progressions they don't really look like
+ 
+
+ align:start position:0%
+progressions they don't really look like
+this alright so the question is is there
+
+ align:start position:0%
+this alright so the question is is there
+ 
+
+ align:start position:0%
+this alright so the question is is there
+some way to do this argument so that you
+
+ align:start position:0%
+some way to do this argument so that you
+ 
+
+ align:start position:0%
+some way to do this argument so that you
+end up with progressions and look like
+
+ align:start position:0%
+end up with progressions and look like
+ 
+
+ align:start position:0%
+end up with progressions and look like
+that and it turns out there is a way and
+
+ align:start position:0%
+that and it turns out there is a way and
+ 
+
+ align:start position:0%
+that and it turns out there is a way and
+there are these objects which will see
+
+ align:start position:0%
+there are these objects which will see
+ 
+
+ align:start position:0%
+there are these objects which will see
+more later in this course called poor
+
+ align:start position:0%
+more later in this course called poor
+ 
+
+ align:start position:0%
+more later in this course called poor
+sets okay so they were used by poor gain
+
+ align:start position:0%
+sets okay so they were used by poor gain
+ 
+
+ align:start position:0%
+sets okay so they were used by poor gain
+to mimic this machine an argument that
+
+ align:start position:0%
+to mimic this machine an argument that
+ 
+
+ align:start position:0%
+to mimic this machine an argument that
+we saw last time more faithfully into
+
+ align:start position:0%
+we saw last time more faithfully into
+ 
+
+ align:start position:0%
+we saw last time more faithfully into
+the integers where we're going to come
+
+ align:start position:0%
+the integers where we're going to come
+ 
+
+ align:start position:0%
+the integers where we're going to come
+up with some set of integers that
+
+ align:start position:0%
+up with some set of integers that
+ 
+
+ align:start position:0%
+up with some set of integers that
+resemble the much closed more closely
+
+ align:start position:0%
+resemble the much closed more closely
+ 
+
+ align:start position:0%
+resemble the much closed more closely
+resemble this notion of subspaces
+
+ align:start position:0%
+resemble this notion of subspaces
+ 
+
+ align:start position:0%
+resemble this notion of subspaces
+in the finite field setting and for this
+
+ align:start position:0%
+in the finite field setting and for this
+ 
+
+ align:start position:0%
+in the finite field setting and for this
+it's much easier to work inside a group
+
+ align:start position:0%
+it's much easier to work inside a group
+ 
+
+ align:start position:0%
+it's much easier to work inside a group
+so instead of working in the integers
+
+ align:start position:0%
+so instead of working in the integers
+ 
+
+ align:start position:0%
+so instead of working in the integers
+let's work inside Z mod and Z so we can
+
+ align:start position:0%
+let's work inside Z mod and Z so we can
+ 
+
+ align:start position:0%
+let's work inside Z mod and Z so we can
+do Fourier transform in Z mod NZ so the
+
+ align:start position:0%
+do Fourier transform in Z mod NZ so the
+ 
+
+ align:start position:0%
+do Fourier transform in Z mod NZ so the
+discrete Fourier analysis here so in Z
+
+ align:start position:0%
+discrete Fourier analysis here so in Z
+ 
+
+ align:start position:0%
+discrete Fourier analysis here so in Z
+mod NZ we define so given an S let's
+
+ align:start position:0%
+mod NZ we define so given an S let's
+ 
+
+ align:start position:0%
+mod NZ we define so given an S let's
+define the spore set to be the set of
+
+ align:start position:0%
+define the spore set to be the set of
+ 
+
+ align:start position:0%
+define the spore set to be the set of
+elements of NZ such that if you look at
+
+ align:start position:0%
+elements of NZ such that if you look at
+ 
+
+ align:start position:0%
+elements of NZ such that if you look at
+what really is supposed to resemble this
+
+ align:start position:0%
+what really is supposed to resemble this
+ 
+
+ align:start position:0%
+what really is supposed to resemble this
+this thing over here if this quantity is
+
+ align:start position:0%
+this thing over here if this quantity is
+ 
+
+ align:start position:0%
+this thing over here if this quantity is
+small for all s so we put that element
+
+ align:start position:0%
+small for all s so we put that element
+ 
+
+ align:start position:0%
+small for all s so we put that element
+into the spore set so these sets they
+
+ align:start position:0%
+into the spore set so these sets they
+ 
+
+ align:start position:0%
+into the spore set so these sets they
+they function much more like subspaces
+
+ align:start position:0%
+they function much more like subspaces
+ 
+
+ align:start position:0%
+they function much more like subspaces
+so there are the analogy of subspaces
+
+ align:start position:0%
+so there are the analogy of subspaces
+ 
+
+ align:start position:0%
+so there are the analogy of subspaces
+inside G mod n Z which n is prime has no
+
+ align:start position:0%
+inside G mod n Z which n is prime has no
+ 
+
+ align:start position:0%
+inside G mod n Z which n is prime has no
+subgroups it has no natural subspace
+
+ align:start position:0%
+subgroups it has no natural subspace
+ 
+
+ align:start position:0%
+subgroups it has no natural subspace
+structure but by looking at these four
+
+ align:start position:0%
+structure but by looking at these four
+ 
+
+ align:start position:0%
+structure but by looking at these four
+sets they provide a natural way to set
+
+ align:start position:0%
+sets they provide a natural way to set
+ 
+
+ align:start position:0%
+sets they provide a natural way to set
+up this argument so that you can but
+
+ align:start position:0%
+up this argument so that you can but
+ 
+
+ align:start position:0%
+up this argument so that you can but
+with much more technicalities repeat
+
+ align:start position:0%
+with much more technicalities repeat
+ 
+
+ align:start position:0%
+with much more technicalities repeat
+this kind of arguments more similar to
+
+ align:start position:0%
+this kind of arguments more similar to
+ 
+
+ align:start position:0%
+this kind of arguments more similar to
+last time but passing not subspaces but
+
+ align:start position:0%
+last time but passing not subspaces but
+ 
+
+ align:start position:0%
+last time but passing not subspaces but
+to poor sets and and then with quite a
+
+ align:start position:0%
+to poor sets and and then with quite a
+ 
+
+ align:start position:0%
+to poor sets and and then with quite a
+bit of extra work one can obtain bounds
+
+ align:start position:0%
+bit of extra work one can obtain bounds
+ 
+
+ align:start position:0%
+bit of extra work one can obtain bounds
+of the quantity and over poly block so
+
+ align:start position:0%
+of the quantity and over poly block so
+ 
+
+ align:start position:0%
+of the quantity and over poly block so
+the current best bound I mentioned last
+
+ align:start position:0%
+the current best bound I mentioned last
+ 
+
+ align:start position:0%
+the current best bound I mentioned last
+time this of this type was just through
+
+ align:start position:0%
+time this of this type was just through
+ 
+
+ align:start position:0%
+time this of this type was just through
+further refinements of this technique
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the last thing I want to mention today
+
+ align:start position:0%
+the last thing I want to mention today
+ 
+
+ align:start position:0%
+the last thing I want to mention today
+is so far we've been talking about three
+
+ align:start position:0%
+is so far we've been talking about three
+ 
+
+ align:start position:0%
+is so far we've been talking about three
+APs
+
+ align:start position:0%
+APs
+ 
+
+ align:start position:0%
+APs
+so what about four term arithmetic
+
+ align:start position:0%
+so what about four term arithmetic
+ 
+
+ align:start position:0%
+so what about four term arithmetic
+progressions doing any of the things
+
+ align:start position:0%
+progressions doing any of the things
+ 
+
+ align:start position:0%
+progressions doing any of the things
+that we talked about here
+
+ align:start position:0%
+that we talked about here
+ 
+
+ align:start position:0%
+that we talked about here
+work for for a piece and there's an
+
+ align:start position:0%
+work for for a piece and there's an
+ 
+
+ align:start position:0%
+work for for a piece and there's an
+analogy to be made here compared to what
+
+ align:start position:0%
+analogy to be made here compared to what
+ 
+
+ align:start position:0%
+analogy to be made here compared to what
+we discussed with graphs or so you grasp
+
+ align:start position:0%
+we discussed with graphs or so you grasp
+ 
+
+ align:start position:0%
+we discussed with graphs or so you grasp
+from kind of triangle counting them on a
+
+ align:start position:0%
+from kind of triangle counting them on a
+ 
+
+ align:start position:0%
+from kind of triangle counting them on a
+triangle remove all mm and then we said
+
+ align:start position:0%
+triangle remove all mm and then we said
+ 
+
+ align:start position:0%
+triangle remove all mm and then we said
+that the proof for a piece we will need
+
+ align:start position:0%
+that the proof for a piece we will need
+ 
+
+ align:start position:0%
+that the proof for a piece we will need
+the hypergraph version the simplex
+
+ align:start position:0%
+the hypergraph version the simplex
+ 
+
+ align:start position:0%
+the hypergraph version the simplex
+removal lemma hypergraph regularity
+
+ align:start position:0%
+removal lemma hypergraph regularity
+ 
+
+ align:start position:0%
+removal lemma hypergraph regularity
+lemma and now it's much more difficult
+
+ align:start position:0%
+lemma and now it's much more difficult
+ 
+
+ align:start position:0%
+lemma and now it's much more difficult
+and that analogy carries two and the
+
+ align:start position:0%
+and that analogy carries two and the
+ 
+
+ align:start position:0%
+and that analogy carries two and the
+same kind of difficulties that come up
+
+ align:start position:0%
+same kind of difficulties that come up
+ 
+
+ align:start position:0%
+same kind of difficulties that come up
+so it can be done but you need something
+
+ align:start position:0%
+so it can be done but you need something
+ 
+
+ align:start position:0%
+so it can be done but you need something
+more and the main message I want you to
+
+ align:start position:0%
+more and the main message I want you to
+ 
+
+ align:start position:0%
+more and the main message I want you to
+take away is that for a piece well we
+
+ align:start position:0%
+take away is that for a piece well we
+ 
+
+ align:start position:0%
+take away is that for a piece well we
+had a counting memo that says that
+
+ align:start position:0%
+had a counting memo that says that
+ 
+
+ align:start position:0%
+had a counting memo that says that
+Fourier coefficients and Fourier
+
+ align:start position:0%
+Fourier coefficients and Fourier
+ 
+
+ align:start position:0%
+Fourier coefficients and Fourier
+transform controls 3 MP caps it turns
+
+ align:start position:0%
+transform controls 3 MP caps it turns
+ 
+
+ align:start position:0%
+transform controls 3 MP caps it turns
+out the same is not true for foil please
+
+ align:start position:0%
+out the same is not true for foil please
+ 
+
+ align:start position:0%
+out the same is not true for foil please
+so for you that's not let me give you
+
+ align:start position:0%
+so for you that's not let me give you
+ 
+
+ align:start position:0%
+so for you that's not let me give you
+some okay so in fact in the homework for
+
+ align:start position:0%
+some okay so in fact in the homework for
+ 
+
+ align:start position:0%
+some okay so in fact in the homework for
+this week there is a specific example of
+
+ align:start position:0%
+this week there is a specific example of
+ 
+
+ align:start position:0%
+this week there is a specific example of
+a set where it has uniformly small
+
+ align:start position:0%
+a set where it has uniformly small
+ 
+
+ align:start position:0%
+a set where it has uniformly small
+Fourier coefficients but that's a wrong
+
+ align:start position:0%
+Fourier coefficients but that's a wrong
+ 
+
+ align:start position:0%
+Fourier coefficients but that's a wrong
+number of 40-piece so the following it
+
+ align:start position:0%
+number of 40-piece so the following it
+ 
+
+ align:start position:0%
+number of 40-piece so the following it
+is true ok so it is true that you have
+
+ align:start position:0%
+is true ok so it is true that you have
+ 
+
+ align:start position:0%
+is true ok so it is true that you have
+some readies theorem in let's just talk
+
+ align:start position:0%
+some readies theorem in let's just talk
+ 
+
+ align:start position:0%
+some readies theorem in let's just talk
+about the finite field setting where
+
+ align:start position:0%
+about the finite field setting where
+ 
+
+ align:start position:0%
+about the finite field setting where
+things are bit easier to discuss so it
+
+ align:start position:0%
+things are bit easier to discuss so it
+ 
+
+ align:start position:0%
+things are bit easier to discuss so it
+is true that the size of the biggest
+
+ align:start position:0%
+is true that the size of the biggest
+ 
+
+ align:start position:0%
+is true that the size of the biggest
+subset of F 5 to the N is a tiny
+
+ align:start position:0%
+subset of F 5 to the N is a tiny
+ 
+
+ align:start position:0%
+subset of F 5 to the N is a tiny
+fraction it's a little one fraction with
+
+ align:start position:0%
+fraction it's a little one fraction with
+ 
+
+ align:start position:0%
+fraction it's a little one fraction with
+the entire space I use f5 here because
+
+ align:start position:0%
+the entire space I use f5 here because
+ 
+
+ align:start position:0%
+the entire space I use f5 here because
+if I set F 3 it doesn't make sense to
+
+ align:start position:0%
+if I set F 3 it doesn't make sense to
+ 
+
+ align:start position:0%
+if I set F 3 it doesn't make sense to
+talk about four ATP's so at five but it
+
+ align:start position:0%
+talk about four ATP's so at five but it
+ 
+
+ align:start position:0%
+talk about four ATP's so at five but it
+doesn't really matter which specific
+
+ align:start position:0%
+doesn't really matter which specific
+ 
+
+ align:start position:0%
+doesn't really matter which specific
+field so you can prove this using
+
+ align:start position:0%
+field so you can prove this using
+ 
+
+ align:start position:0%
+field so you can prove this using
+hypergraph removal say
+
+ align:start position:0%
+hypergraph removal say
+ 
+
+ align:start position:0%
+hypergraph removal say
+proof verbatim that we saw earlier if
+
+ align:start position:0%
+proof verbatim that we saw earlier if
+ 
+
+ align:start position:0%
+proof verbatim that we saw earlier if
+you have hypergraph removal but if you
+
+ align:start position:0%
+you have hypergraph removal but if you
+ 
+
+ align:start position:0%
+you have hypergraph removal but if you
+want to try to prove it using Fourier
+
+ align:start position:0%
+want to try to prove it using Fourier
+ 
+
+ align:start position:0%
+want to try to prove it using Fourier
+analysis or it doesn't work quite using
+
+ align:start position:0%
+analysis or it doesn't work quite using
+ 
+
+ align:start position:0%
+analysis or it doesn't work quite using
+the same strategy but in fact there is a
+
+ align:start position:0%
+the same strategy but in fact there is a
+ 
+
+ align:start position:0%
+the same strategy but in fact there is a
+modification that would allow you to to
+
+ align:start position:0%
+modification that would allow you to to
+ 
+
+ align:start position:0%
+modification that would allow you to to
+make it work but you need an extension
+
+ align:start position:0%
+make it work but you need an extension
+ 
+
+ align:start position:0%
+make it work but you need an extension
+of Fourier analysis and it was known as
+
+ align:start position:0%
+of Fourier analysis and it was known as
+ 
+
+ align:start position:0%
+of Fourier analysis and it was known as
+higher order for your analysis which was
+
+ align:start position:0%
+higher order for your analysis which was
+ 
+
+ align:start position:0%
+higher order for your analysis which was
+an important development in modern
+
+ align:start position:0%
+an important development in modern
+ 
+
+ align:start position:0%
+an important development in modern
+additive combinatorics that initially
+
+ align:start position:0%
+additive combinatorics that initially
+ 
+
+ align:start position:0%
+additive combinatorics that initially
+arose in Gao versus work where he gave a
+
+ align:start position:0%
+arose in Gao versus work where he gave a
+ 
+
+ align:start position:0%
+arose in Gao versus work where he gave a
+new proof of samurais theorem so towers
+
+ align:start position:0%
+new proof of samurais theorem so towers
+ 
+
+ align:start position:0%
+new proof of samurais theorem so towers
+didn't work in this setting he worked in
+
+ align:start position:0%
+didn't work in this setting he worked in
+ 
+
+ align:start position:0%
+didn't work in this setting he worked in
+integers but many of the ideas
+
+ align:start position:0%
+integers but many of the ideas
+ 
+
+ align:start position:0%
+integers but many of the ideas
+originated from from his paper and then
+
+ align:start position:0%
+originated from from his paper and then
+ 
+
+ align:start position:0%
+originated from from his paper and then
+subsequently developed lots of people in
+
+ align:start position:0%
+subsequently developed lots of people in
+ 
+
+ align:start position:0%
+subsequently developed lots of people in
+various settings I just want to give you
+
+ align:start position:0%
+various settings I just want to give you
+ 
+
+ align:start position:0%
+various settings I just want to give you
+one specific statement what this higher
+
+ align:start position:0%
+one specific statement what this higher
+ 
+
+ align:start position:0%
+one specific statement what this higher
+order Fourier analysis looks like it's a
+
+ align:start position:0%
+order Fourier analysis looks like it's a
+ 
+
+ align:start position:0%
+order Fourier analysis looks like it's a
+fancy term and you know statements often
+
+ align:start position:0%
+fancy term and you know statements often
+ 
+
+ align:start position:0%
+fancy term and you know statements often
+get very technical but I just want to
+
+ align:start position:0%
+get very technical but I just want to
+ 
+
+ align:start position:0%
+get very technical but I just want to
+give you one concrete thing to take away
+
+ align:start position:0%
+give you one concrete thing to take away
+ 
+
+ align:start position:0%
+give you one concrete thing to take away
+all right so for for a piece higher
+
+ align:start position:0%
+all right so for for a piece higher
+ 
+
+ align:start position:0%
+all right so for for a piece higher
+order for analysis roughly it also goes
+
+ align:start position:0%
+order for analysis roughly it also goes
+ 
+
+ align:start position:0%
+order for analysis roughly it also goes
+by the name of quadratic for urinalysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me give you a very specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instance of the theorem and this can be
+
+ align:start position:0%
+instance of the theorem and this can be
+ 
+
+ align:start position:0%
+instance of the theorem and this can be
+sometimes called an inverse theorem for
+
+ align:start position:0%
+sometimes called an inverse theorem for
+ 
+
+ align:start position:0%
+sometimes called an inverse theorem for
+quadratic for you analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose okay so for every Delta there
+
+ align:start position:0%
+suppose okay so for every Delta there
+ 
+
+ align:start position:0%
+suppose okay so for every Delta there
+exists some C such that following is
+
+ align:start position:0%
+exists some C such that following is
+ 
+
+ align:start position:0%
+exists some C such that following is
+true if a is a subset F Phi to the N
+
+ align:start position:0%
+true if a is a subset F Phi to the N
+ 
+
+ align:start position:0%
+true if a is a subset F Phi to the N
+with density alpha and such that it's so
+
+ align:start position:0%
+with density alpha and such that it's so
+ 
+
+ align:start position:0%
+with density alpha and such that it's so
+now lambda sub four so this is the for
+
+ align:start position:0%
+now lambda sub four so this is the for
+ 
+
+ align:start position:0%
+now lambda sub four so this is the for
+AP density so similar to three a people
+
+ align:start position:0%
+AP density so similar to three a people
+ 
+
+ align:start position:0%
+AP density so similar to three a people
+now you write four terms the for AP
+
+ align:start position:0%
+now you write four terms the for AP
+ 
+
+ align:start position:0%
+now you write four terms the for AP
+density of a differs from
+
+ align:start position:0%
+density of a differs from
+ 
+
+ align:start position:0%
+density of a differs from
+alpha to the fourth by a significant
+
+ align:start position:0%
+alpha to the fourth by a significant
+ 
+
+ align:start position:0%
+alpha to the fourth by a significant
+amount okay so for three a piece then we
+
+ align:start position:0%
+amount okay so for three a piece then we
+ 
+
+ align:start position:0%
+amount okay so for three a piece then we
+said that now a has a large Fourier
+
+ align:start position:0%
+said that now a has a large Fourier
+ 
+
+ align:start position:0%
+said that now a has a large Fourier
+coefficient so for okay
+
+ align:start position:0%
+coefficient so for okay
+ 
+
+ align:start position:0%
+coefficient so for okay
+four for a piece that may not be true
+
+ align:start position:0%
+four for a piece that may not be true
+ 
+
+ align:start position:0%
+four for a piece that may not be true
+but the following is true so then there
+
+ align:start position:0%
+but the following is true so then there
+ 
+
+ align:start position:0%
+but the following is true so then there
+exists a nonzero quadratic polynomial F
+
+ align:start position:0%
+exists a nonzero quadratic polynomial F
+ 
+
+ align:start position:0%
+exists a nonzero quadratic polynomial F
+in n variables over a five such that the
+
+ align:start position:0%
+in n variables over a five such that the
+ 
+
+ align:start position:0%
+in n variables over a five such that the
+indicator function of a correlates with
+
+ align:start position:0%
+indicator function of a correlates with
+ 
+
+ align:start position:0%
+indicator function of a correlates with
+this quadratic exponential face so free
+
+ align:start position:0%
+this quadratic exponential face so free
+ 
+
+ align:start position:0%
+this quadratic exponential face so free
+analysis the conclusion that we got from
+
+ align:start position:0%
+analysis the conclusion that we got from
+ 
+
+ align:start position:0%
+analysis the conclusion that we got from
+counting lemma is that you have some
+
+ align:start position:0%
+counting lemma is that you have some
+ 
+
+ align:start position:0%
+counting lemma is that you have some
+linear function f such that this
+
+ align:start position:0%
+linear function f such that this
+ 
+
+ align:start position:0%
+linear function f such that this
+quantity is large this large Fourier
+
+ align:start position:0%
+quantity is large this large Fourier
+ 
+
+ align:start position:0%
+quantity is large this large Fourier
+coefficient okay so that is not true for
+
+ align:start position:0%
+coefficient okay so that is not true for
+ 
+
+ align:start position:0%
+coefficient okay so that is not true for
+for a piece but what is true is that now
+
+ align:start position:0%
+for a piece but what is true is that now
+ 
+
+ align:start position:0%
+for a piece but what is true is that now
+you can look at quadratic exponential
+
+ align:start position:0%
+you can look at quadratic exponential
+ 
+
+ align:start position:0%
+you can look at quadratic exponential
+faces and then this true so that's the
+
+ align:start position:0%
+faces and then this true so that's the
+ 
+
+ align:start position:0%
+faces and then this true so that's the
+content of higher order for you I mean
+
+ align:start position:0%
+content of higher order for you I mean
+ 
+
+ align:start position:0%
+content of higher order for you I mean
+that's the example of higher order
+
+ align:start position:0%
+that's the example of higher order
+ 
+
+ align:start position:0%
+that's the example of higher order
+Fourier analysis and you can imagine
+
+ align:start position:0%
+Fourier analysis and you can imagine
+ 
+
+ align:start position:0%
+Fourier analysis and you can imagine
+with this type of result and with quite
+
+ align:start position:0%
+with this type of result and with quite
+ 
+
+ align:start position:0%
+with this type of result and with quite
+a bit of more work you can try to follow
+
+ align:start position:0%
+a bit of more work you can try to follow
+ 
+
+ align:start position:0%
+a bit of more work you can try to follow
+a similar density increment strategy to
+
+ align:start position:0%
+a similar density increment strategy to
+ 
+
+ align:start position:0%
+a similar density increment strategy to
+prove similarities theorem for for a
+
+ align:start position:0%
+prove similarities theorem for for a
+ 
+
+ align:start position:0%
+prove similarities theorem for for a
+piece
\ No newline at end of file
diff --git a/56iFMY8QW2k.txt b/56iFMY8QW2k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ad404a4f064305ae336fa92bbc69fa21f66caf4
--- /dev/null
+++ b/56iFMY8QW2k.txt
@@ -0,0 +1,12371 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer high quality educational
+
+ align:start position:0%
+to offer high quality educational
+ 
+
+ align:start position:0%
+to offer high quality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu uh now today we're going to
+
+ align:start position:0%
+ocw.mit.edu uh now today we're going to
+ 
+
+ align:start position:0%
+ocw.mit.edu uh now today we're going to
+talk about random walks and in
+
+ align:start position:0%
+talk about random walks and in
+ 
+
+ align:start position:0%
+talk about random walks and in
+particular we're going to look at a
+
+ align:start position:0%
+particular we're going to look at a
+ 
+
+ align:start position:0%
+particular we're going to look at a
+classic phenomenon known as gamblers
+
+ align:start position:0%
+classic phenomenon known as gamblers
+ 
+
+ align:start position:0%
+classic phenomenon known as gamblers
+ruin uh it's a great way to end the term
+
+ align:start position:0%
+ruin uh it's a great way to end the term
+ 
+
+ align:start position:0%
+ruin uh it's a great way to end the term
+because the solution requires several of
+
+ align:start position:0%
+because the solution requires several of
+ 
+
+ align:start position:0%
+because the solution requires several of
+the techniques that we've developed
+
+ align:start position:0%
+the techniques that we've developed
+ 
+
+ align:start position:0%
+the techniques that we've developed
+since the midterm so it's actually a
+
+ align:start position:0%
+since the midterm so it's actually a
+ 
+
+ align:start position:0%
+since the midterm so it's actually a
+good review we'll review recurrences
+
+ align:start position:0%
+good review we'll review recurrences
+ 
+
+ align:start position:0%
+good review we'll review recurrences
+we'll review a lot of probability laws
+
+ align:start position:0%
+we'll review a lot of probability laws
+ 
+
+ align:start position:0%
+we'll review a lot of probability laws
+and it's uh it's actually a nice problem
+
+ align:start position:0%
+and it's uh it's actually a nice problem
+ 
+
+ align:start position:0%
+and it's uh it's actually a nice problem
+to look at it's it's another example
+
+ align:start position:0%
+to look at it's it's another example
+ 
+
+ align:start position:0%
+to look at it's it's another example
+where you get a non-intuitive solution
+
+ align:start position:0%
+where you get a non-intuitive solution
+ 
+
+ align:start position:0%
+where you get a non-intuitive solution
+using probability and if you like to
+
+ align:start position:0%
+using probability and if you like to
+ 
+
+ align:start position:0%
+using probability and if you like to
+gamble it's really good that you look at
+
+ align:start position:0%
+gamble it's really good that you look at
+ 
+
+ align:start position:0%
+gamble it's really good that you look at
+this problem before you go to Vegas or
+
+ align:start position:0%
+this problem before you go to Vegas or
+ 
+
+ align:start position:0%
+this problem before you go to Vegas or
+down to Foxwood
+
+ align:start position:0%
+down to Foxwood
+ 
+
+ align:start position:0%
+down to Foxwood
+now in the gambler's ruin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem you start with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$1 and we're going to do a simplified
+
+ align:start position:0%
+$1 and we're going to do a simplified
+ 
+
+ align:start position:0%
+$1 and we're going to do a simplified
+version where in each bet you win a
+
+ align:start position:0%
+version where in each bet you win a
+ 
+
+ align:start position:0%
+version where in each bet you win a
+dollar or you lose a dollar now these
+
+ align:start position:0%
+dollar or you lose a dollar now these
+ 
+
+ align:start position:0%
+dollar or you lose a dollar now these
+days there's not many bets in a casino
+
+ align:start position:0%
+days there's not many bets in a casino
+ 
+
+ align:start position:0%
+days there's not many bets in a casino
+for a dollar it's more like like 10
+
+ align:start position:0%
+for a dollar it's more like like 10
+ 
+
+ align:start position:0%
+for a dollar it's more like like 10
+bucks but just to make it simple for
+
+ align:start position:0%
+bucks but just to make it simple for
+ 
+
+ align:start position:0%
+bucks but just to make it simple for
+counting we're going to assume that each
+
+ align:start position:0%
+counting we're going to assume that each
+ 
+
+ align:start position:0%
+counting we're going to assume that each
+bet you win a dollar with probability
+
+ align:start position:0%
+bet you win a dollar with probability
+ 
+
+ align:start position:0%
+bet you win a dollar with probability
+p and you
+
+ align:start position:0%
+p and you
+ 
+
+ align:start position:0%
+p and you
+lose a
+
+ align:start position:0%
+lose a
+ 
+
+ align:start position:0%
+lose a
+dollar with
+
+ align:start position:0%
+dollar with
+ 
+
+ align:start position:0%
+dollar with
+probability one minus
+
+ align:start position:0%
+probability one minus
+ 
+
+ align:start position:0%
+probability one minus
+p and in this version we're going to
+
+ align:start position:0%
+p and in this version we're going to
+ 
+
+ align:start position:0%
+p and in this version we're going to
+assume you keep
+
+ align:start position:0%
+assume you keep
+ 
+
+ align:start position:0%
+assume you keep
+playing until one of two things happens
+
+ align:start position:0%
+playing until one of two things happens
+ 
+
+ align:start position:0%
+playing until one of two things happens
+you get ahead by MLL or you lose all the
+
+ align:start position:0%
+you get ahead by MLL or you lose all the
+ 
+
+ align:start position:0%
+you get ahead by MLL or you lose all the
+money you came with all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nll so you play
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+until you
+
+ align:start position:0%
+until you
+ 
+
+ align:start position:0%
+until you
+win M more net M plus or you
+
+ align:start position:0%
+win M more net M plus or you
+ 
+
+ align:start position:0%
+win M more net M plus or you
+lose
+
+ align:start position:0%
+lose
+ 
+
+ align:start position:0%
+lose
+n and that's where you go broke you run
+
+ align:start position:0%
+n and that's where you go broke you run
+ 
+
+ align:start position:0%
+n and that's where you go broke you run
+out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+money and we're going to assume you
+
+ align:start position:0%
+money and we're going to assume you
+ 
+
+ align:start position:0%
+money and we're going to assume you
+don't Bor borrow anything from the
+
+ align:start position:0%
+don't Bor borrow anything from the
+ 
+
+ align:start position:0%
+don't Bor borrow anything from the
+house all right and we're going to look
+
+ align:start position:0%
+house all right and we're going to look
+ 
+
+ align:start position:0%
+house all right and we're going to look
+at the
+
+ align:start position:0%
+at the
+ 
+
+ align:start position:0%
+at the
+probability that you come out a winner
+
+ align:start position:0%
+probability that you come out a winner
+ 
+
+ align:start position:0%
+probability that you come out a winner
+versus going home broke that you you
+
+ align:start position:0%
+versus going home broke that you you
+ 
+
+ align:start position:0%
+versus going home broke that you you
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+MLL now the game we're going to
+
+ align:start position:0%
+MLL now the game we're going to
+ 
+
+ align:start position:0%
+MLL now the game we're going to
+analyze is roulette but the technique
+
+ align:start position:0%
+analyze is roulette but the technique
+ 
+
+ align:start position:0%
+analyze is roulette but the technique
+works for any of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them how many people have played
+
+ align:start position:0%
+them how many people have played
+ 
+
+ align:start position:0%
+them how many people have played
+roulette before some form or another
+
+ align:start position:0%
+roulette before some form or another
+ 
+
+ align:start position:0%
+roulette before some form or another
+okay so this is the game where there's
+
+ align:start position:0%
+okay so this is the game where there's
+ 
+
+ align:start position:0%
+okay so this is the game where there's
+the ball that goes around on the dish
+
+ align:start position:0%
+the ball that goes around on the dish
+ 
+
+ align:start position:0%
+the ball that goes around on the dish
+and you spin the wheel and there's 36
+
+ align:start position:0%
+and you spin the wheel and there's 36
+ 
+
+ align:start position:0%
+and you spin the wheel and there's 36
+numbers uh from 1 to 36 half of them are
+
+ align:start position:0%
+numbers uh from 1 to 36 half of them are
+ 
+
+ align:start position:0%
+numbers uh from 1 to 36 half of them are
+red half are black and then there's the
+
+ align:start position:0%
+red half are black and then there's the
+ 
+
+ align:start position:0%
+red half are black and then there's the
+zero and the double zero that are
+
+ align:start position:0%
+zero and the double zero that are
+ 
+
+ align:start position:0%
+zero and the double zero that are
+green and we're going to look at the
+
+ align:start position:0%
+green and we're going to look at the
+ 
+
+ align:start position:0%
+green and we're going to look at the
+version where you just bet on red are
+
+ align:start position:0%
+version where you just bet on red are
+ 
+
+ align:start position:0%
+version where you just bet on red are
+black and you win if the ball lands in a
+
+ align:start position:0%
+black and you win if the ball lands in a
+ 
+
+ align:start position:0%
+black and you win if the ball lands in a
+slot that's red and there's 18 of those
+
+ align:start position:0%
+slot that's red and there's 18 of those
+ 
+
+ align:start position:0%
+slot that's red and there's 18 of those
+and you lose
+
+ align:start position:0%
+and you lose
+ 
+
+ align:start position:0%
+and you lose
+otherwise so in this case the
+
+ align:start position:0%
+otherwise so in this case the
+ 
+
+ align:start position:0%
+otherwise so in this case the
+probability of winning
+
+ align:start position:0%
+probability of winning
+ 
+
+ align:start position:0%
+probability of winning
+p is there's 18 ch CH es to win and it's
+
+ align:start position:0%
+p is there's 18 ch CH es to win and it's
+ 
+
+ align:start position:0%
+p is there's 18 ch CH es to win and it's
+not 36 total it's 38 total because of
+
+ align:start position:0%
+not 36 total it's 38 total because of
+ 
+
+ align:start position:0%
+not 36 total it's 38 total because of
+the zero and the double zero all right
+
+ align:start position:0%
+the zero and the double zero all right
+ 
+
+ align:start position:0%
+the zero and the double zero all right
+so this is a 919 chance of winning and a
+
+ align:start position:0%
+so this is a 919 chance of winning and a
+ 
+
+ align:start position:0%
+so this is a 919 chance of winning and a
+1019 chance of
+
+ align:start position:0%
+1019 chance of
+ 
+
+ align:start position:0%
+1019 chance of
+losing and so this is a game that has a
+
+ align:start position:0%
+losing and so this is a game that has a
+ 
+
+ align:start position:0%
+losing and so this is a game that has a
+chance of winning of about
+
+ align:start position:0%
+chance of winning of about
+ 
+
+ align:start position:0%
+chance of winning of about
+47% so it's almost a fair game it's not
+
+ align:start position:0%
+47% so it's almost a fair game it's not
+ 
+
+ align:start position:0%
+47% so it's almost a fair game it's not
+50/50 and that's because the casino's
+
+ align:start position:0%
+50/50 and that's because the casino's
+ 
+
+ align:start position:0%
+50/50 and that's because the casino's
+got to make some money I mean they they
+
+ align:start position:0%
+got to make some money I mean they they
+ 
+
+ align:start position:0%
+got to make some money I mean they they
+have the big facility they're giving
+
+ align:start position:0%
+have the big facility they're giving
+ 
+
+ align:start position:0%
+have the big facility they're giving
+free drinks and all the rest so they got
+
+ align:start position:0%
+free drinks and all the rest so they got
+ 
+
+ align:start position:0%
+free drinks and all the rest so they got
+to make money somehow and they make
+
+ align:start position:0%
+to make money somehow and they make
+ 
+
+ align:start position:0%
+to make money somehow and they make
+money on this bet because you know
+
+ align:start position:0%
+money on this bet because you know
+ 
+
+ align:start position:0%
+money on this bet because you know
+they're going to make uh three cents you
+
+ align:start position:0%
+they're going to make uh three cents you
+ 
+
+ align:start position:0%
+they're going to make uh three cents you
+know on the dollar here you're going to
+
+ align:start position:0%
+know on the dollar here you're going to
+ 
+
+ align:start position:0%
+know on the dollar here you're going to
+wager and then you're going to come back
+
+ align:start position:0%
+wager and then you're going to come back
+ 
+
+ align:start position:0%
+wager and then you're going to come back
+with with
+
+ align:start position:0%
+with with
+ 
+
+ align:start position:0%
+with with
+47% and people generally are fine with
+
+ align:start position:0%
+47% and people generally are fine with
+ 
+
+ align:start position:0%
+47% and people generally are fine with
+that they don't expect to have the odds
+
+ align:start position:0%
+that they don't expect to have the odds
+ 
+
+ align:start position:0%
+that they don't expect to have the odds
+in their favor when you're gambling in a
+
+ align:start position:0%
+in their favor when you're gambling in a
+ 
+
+ align:start position:0%
+in their favor when you're gambling in a
+casino now in an effort to sort of come
+
+ align:start position:0%
+casino now in an effort to sort of come
+ 
+
+ align:start position:0%
+casino now in an effort to sort of come
+home a winner the way people do that
+
+ align:start position:0%
+home a winner the way people do that
+ 
+
+ align:start position:0%
+home a winner the way people do that
+knowing that the odds are a little
+
+ align:start position:0%
+knowing that the odds are a little
+ 
+
+ align:start position:0%
+knowing that the odds are a little
+against them is they might put more
+
+ align:start position:0%
+against them is they might put more
+ 
+
+ align:start position:0%
+against them is they might put more
+money in their pocket coming in than
+
+ align:start position:0%
+money in their pocket coming in than
+ 
+
+ align:start position:0%
+money in their pocket coming in than
+they expect to win so often you'll see
+
+ align:start position:0%
+they expect to win so often you'll see
+ 
+
+ align:start position:0%
+they expect to win so often you'll see
+people come in to the casino with a goal
+
+ align:start position:0%
+people come in to the casino with a goal
+ 
+
+ align:start position:0%
+people come in to the casino with a goal
+of winning a
+
+ align:start position:0%
+of winning a
+ 
+
+ align:start position:0%
+of winning a
+hundred but they start with a thousand
+
+ align:start position:0%
+hundred but they start with a thousand
+ 
+
+ align:start position:0%
+hundred but they start with a thousand
+in their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pocket so they're willing to risk a
+
+ align:start position:0%
+pocket so they're willing to risk a
+ 
+
+ align:start position:0%
+pocket so they're willing to risk a
+th000 bucks and but they're going to
+
+ align:start position:0%
+th000 bucks and but they're going to
+ 
+
+ align:start position:0%
+th000 bucks and but they're going to
+quit happy if they get up a
+
+ align:start position:0%
+quit happy if they get up a
+ 
+
+ align:start position:0%
+quit happy if they get up a
+hundred
+
+ align:start position:0%
+hundred
+ 
+
+ align:start position:0%
+hundred
+okay so you're going to go home with
+
+ align:start position:0%
+okay so you're going to go home with
+ 
+
+ align:start position:0%
+okay so you're going to go home with
+$1,100 or you're going home with zero in
+
+ align:start position:0%
+$1,100 or you're going home with zero in
+ 
+
+ align:start position:0%
+$1,100 or you're going home with zero in
+this case and you came with a
+
+ align:start position:0%
+this case and you came with a
+ 
+
+ align:start position:0%
+this case and you came with a
+th000 and this means that you're at
+
+ align:start position:0%
+th000 and this means that you're at
+ 
+
+ align:start position:0%
+th000 and this means that you're at
+least the thinking goes this means that
+
+ align:start position:0%
+least the thinking goes this means that
+ 
+
+ align:start position:0%
+least the thinking goes this means that
+you're more likely to go home happy if
+
+ align:start position:0%
+you're more likely to go home happy if
+ 
+
+ align:start position:0%
+you're more likely to go home happy if
+you quit when you get up by a hundred
+
+ align:start position:0%
+you quit when you get up by a hundred
+ 
+
+ align:start position:0%
+you quit when you get up by a hundred
+you're more likely to land there because
+
+ align:start position:0%
+you're more likely to land there because
+ 
+
+ align:start position:0%
+you're more likely to land there because
+it's almost a fair game than you are to
+
+ align:start position:0%
+it's almost a fair game than you are to
+ 
+
+ align:start position:0%
+it's almost a fair game than you are to
+lose all
+
+ align:start position:0%
+lose all
+ 
+
+ align:start position:0%
+lose all
+thousand that's the thinking anyway in
+
+ align:start position:0%
+thousand that's the thinking anyway in
+ 
+
+ align:start position:0%
+thousand that's the thinking anyway in
+fact my mother-in-law plays roulette red
+
+ align:start position:0%
+fact my mother-in-law plays roulette red
+ 
+
+ align:start position:0%
+fact my mother-in-law plays roulette red
+and black and she follows the
+
+ align:start position:0%
+and black and she follows the
+ 
+
+ align:start position:0%
+and black and she follows the
+strategy you know and she claims that
+
+ align:start position:0%
+strategy you know and she claims that
+ 
+
+ align:start position:0%
+strategy you know and she claims that
+she does this for for that reason that
+
+ align:start position:0%
+she does this for for that reason that
+ 
+
+ align:start position:0%
+she does this for for that reason that
+she almost always wins you know she goes
+
+ align:start position:0%
+she almost always wins you know she goes
+ 
+
+ align:start position:0%
+she almost always wins you know she goes
+home happy almost always and that's the
+
+ align:start position:0%
+home happy almost always and that's the
+ 
+
+ align:start position:0%
+home happy almost always and that's the
+important thing here uh and it does
+
+ align:start position:0%
+important thing here uh and it does
+ 
+
+ align:start position:0%
+important thing here uh and it does
+sound reasonable because after all we're
+
+ align:start position:0%
+sound reasonable because after all we're
+ 
+
+ align:start position:0%
+sound reasonable because after all we're
+LED is almost a fair
+
+ align:start position:0%
+LED is almost a fair
+ 
+
+ align:start position:0%
+LED is almost a fair
+game so what do you think how many
+
+ align:start position:0%
+game so what do you think how many
+ 
+
+ align:start position:0%
+game so what do you think how many
+people think she's right that she almost
+
+ align:start position:0%
+people think she's right that she almost
+ 
+
+ align:start position:0%
+people think she's right that she almost
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+wins anybody I have sort of set it up
+
+ align:start position:0%
+wins anybody I have sort of set it up
+ 
+
+ align:start position:0%
+wins anybody I have sort of set it up
+it's my mother-in-law after all so
+
+ align:start position:0%
+it's my mother-in-law after all so
+ 
+
+ align:start position:0%
+it's my mother-in-law after all so
+probably she's going to be wrong you
+
+ align:start position:0%
+probably she's going to be wrong you
+ 
+
+ align:start position:0%
+probably she's going to be wrong you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+uh well how many people think it's
+
+ align:start position:0%
+uh well how many people think it's
+ 
+
+ align:start position:0%
+uh well how many people think it's
+better than a 50% chance you win a 100
+
+ align:start position:0%
+better than a 50% chance you win a 100
+ 
+
+ align:start position:0%
+better than a 50% chance you win a 100
+before you lose a
+
+ align:start position:0%
+before you lose a
+ 
+
+ align:start position:0%
+before you lose a
+thousand that's that's probably more 50
+
+ align:start position:0%
+thousand that's that's probably more 50
+ 
+
+ align:start position:0%
+thousand that's that's probably more 50
+there's a how many people think you're
+
+ align:start position:0%
+there's a how many people think you're
+ 
+
+ align:start position:0%
+there's a how many people think you're
+more likely to lose a thousand bucks
+
+ align:start position:0%
+more likely to lose a thousand bucks
+ 
+
+ align:start position:0%
+more likely to lose a thousand bucks
+before you win a
+
+ align:start position:0%
+before you win a
+ 
+
+ align:start position:0%
+before you win a
+hundred wow okay so you've been to 604
+
+ align:start position:0%
+hundred wow okay so you've been to 604
+ 
+
+ align:start position:0%
+hundred wow okay so you've been to 604
+too long now okay what about this how
+
+ align:start position:0%
+too long now okay what about this how
+ 
+
+ align:start position:0%
+too long now okay what about this how
+many people think you're more likely to
+
+ align:start position:0%
+many people think you're more likely to
+ 
+
+ align:start position:0%
+many people think you're more likely to
+lose
+
+ align:start position:0%
+lose
+ 
+
+ align:start position:0%
+lose
+$10,000 than to win a hundred
+
+ align:start position:0%
+$10,000 than to win a hundred
+ 
+
+ align:start position:0%
+$10,000 than to win a hundred
+all right how many people think you're
+
+ align:start position:0%
+all right how many people think you're
+ 
+
+ align:start position:0%
+all right how many people think you're
+more likely to lose a million
+
+ align:start position:0%
+more likely to lose a million
+ 
+
+ align:start position:0%
+more likely to lose a million
+dollars well a bunch of you still think
+
+ align:start position:0%
+dollars well a bunch of you still think
+ 
+
+ align:start position:0%
+dollars well a bunch of you still think
+that okay well you're right in fact it
+
+ align:start position:0%
+that okay well you're right in fact it
+ 
+
+ align:start position:0%
+that okay well you're right in fact it
+is almost certain you will go broke no
+
+ align:start position:0%
+is almost certain you will go broke no
+ 
+
+ align:start position:0%
+is almost certain you will go broke no
+matter how much money you bring before
+
+ align:start position:0%
+matter how much money you bring before
+ 
+
+ align:start position:0%
+matter how much money you bring before
+you win
+
+ align:start position:0%
+you win
+ 
+
+ align:start position:0%
+you win
+$100 okay in fact we're going to prove
+
+ align:start position:0%
+$100 okay in fact we're going to prove
+ 
+
+ align:start position:0%
+$100 okay in fact we're going to prove
+today that the probability that you win
+
+ align:start position:0%
+today that the probability that you win
+ 
+
+ align:start position:0%
+today that the probability that you win
+$100
+
+ align:start position:0%
+$100
+ 
+
+ align:start position:0%
+$100
+before losing a hundred million if you
+
+ align:start position:0%
+before losing a hundred million if you
+ 
+
+ align:start position:0%
+before losing a hundred million if you
+stayed long enough that takes a
+
+ align:start position:0%
+stayed long enough that takes a
+ 
+
+ align:start position:0%
+stayed long enough that takes a
+while the chance you go home a winner is
+
+ align:start position:0%
+while the chance you go home a winner is
+ 
+
+ align:start position:0%
+while the chance you go home a winner is
+less than 1
+
+ align:start position:0%
+less than 1
+ 
+
+ align:start position:0%
+less than 1
+37,6
+
+ align:start position:0%
+37,6
+ 
+
+ align:start position:0%
+37,6
+48 you have no chance to go home
+
+ align:start position:0%
+48 you have no chance to go home
+ 
+
+ align:start position:0%
+48 you have no chance to go home
+happy so you know my mother-in-law is
+
+ align:start position:0%
+happy so you know my mother-in-law is
+ 
+
+ align:start position:0%
+happy so you know my mother-in-law is
+telling me the story about how she
+
+ align:start position:0%
+telling me the story about how she
+ 
+
+ align:start position:0%
+telling me the story about how she
+always goes home happy and I'm saying no
+
+ align:start position:0%
+always goes home happy and I'm saying no
+ 
+
+ align:start position:0%
+always goes home happy and I'm saying no
+no wait a minute you can't you never
+
+ align:start position:0%
+no wait a minute you can't you never
+ 
+
+ align:start position:0%
+no wait a minute you can't you never
+went home Happy let's be honest right it
+
+ align:start position:0%
+went home Happy let's be honest right it
+ 
+
+ align:start position:0%
+went home Happy let's be honest right it
+can't be she goes no no no no it's true
+
+ align:start position:0%
+can't be she goes no no no no it's true
+ 
+
+ align:start position:0%
+can't be she goes no no no no it's true
+and I go no look look there's a
+
+ align:start position:0%
+and I go no look look there's a
+ 
+
+ align:start position:0%
+and I go no look look there's a
+mathematical proof I have a proof I can
+
+ align:start position:0%
+mathematical proof I have a proof I can
+ 
+
+ align:start position:0%
+mathematical proof I have a proof I can
+show you my proof very unlikely you go
+
+ align:start position:0%
+show you my proof very unlikely you go
+ 
+
+ align:start position:0%
+show you my proof very unlikely you go
+home a winter you know so somehow she's
+
+ align:start position:0%
+home a winter you know so somehow she's
+ 
+
+ align:start position:0%
+home a winter you know so somehow she's
+not very impressed with the mathematical
+
+ align:start position:0%
+not very impressed with the mathematical
+ 
+
+ align:start position:0%
+not very impressed with the mathematical
+proof you know and she keeps insisting
+
+ align:start position:0%
+proof you know and she keeps insisting
+ 
+
+ align:start position:0%
+proof you know and she keeps insisting
+and I keep trying to show her the proof
+
+ align:start position:0%
+and I keep trying to show her the proof
+ 
+
+ align:start position:0%
+and I keep trying to show her the proof
+and uh anyway I hope I'll have more luck
+
+ align:start position:0%
+and uh anyway I hope I'll have more luck
+ 
+
+ align:start position:0%
+and uh anyway I hope I'll have more luck
+with you guys today in showing you the
+
+ align:start position:0%
+with you guys today in showing you the
+ 
+
+ align:start position:0%
+with you guys today in showing you the
+proof that the chance you go home happy
+
+ align:start position:0%
+proof that the chance you go home happy
+ 
+
+ align:start position:0%
+proof that the chance you go home happy
+here is very very small now in the end I
+
+ align:start position:0%
+here is very very small now in the end I
+ 
+
+ align:start position:0%
+here is very very small now in the end I
+didn't convince her but uh we'll we'll
+
+ align:start position:0%
+didn't convince her but uh we'll we'll
+ 
+
+ align:start position:0%
+didn't convince her but uh we'll we'll
+see how we do here
+
+ align:start position:0%
+see how we do here
+ 
+
+ align:start position:0%
+see how we do here
+today now in order to see why this
+
+ align:start position:0%
+today now in order to see why this
+ 
+
+ align:start position:0%
+today now in order to see why this
+probability is so stunningly small we
+
+ align:start position:0%
+probability is so stunningly small we
+ 
+
+ align:start position:0%
+probability is so stunningly small we
+just never guess it's it's that low
+
+ align:start position:0%
+just never guess it's it's that low
+ 
+
+ align:start position:0%
+just never guess it's it's that low
+we've got to learn about random walks
+
+ align:start position:0%
+we've got to learn about random walks
+ 
+
+ align:start position:0%
+we've got to learn about random walks
+and they come up in all sorts of
+
+ align:start position:0%
+and they come up in all sorts of
+ 
+
+ align:start position:0%
+and they come up in all sorts of
+applications in fact uh you know page
+
+ align:start position:0%
+applications in fact uh you know page
+ 
+
+ align:start position:0%
+applications in fact uh you know page
+rank you know they got Google started
+
+ align:start position:0%
+rank you know they got Google started
+ 
+
+ align:start position:0%
+rank you know they got Google started
+it's all based on a random walk through
+
+ align:start position:0%
+it's all based on a random walk through
+ 
+
+ align:start position:0%
+it's all based on a random walk through
+the web or through the links on web
+
+ align:start position:0%
+the web or through the links on web
+ 
+
+ align:start position:0%
+the web or through the links on web
+pages on that graph uh now for the
+
+ align:start position:0%
+pages on that graph uh now for the
+ 
+
+ align:start position:0%
+pages on that graph uh now for the
+gambling problem we're going to look at
+
+ align:start position:0%
+gambling problem we're going to look at
+ 
+
+ align:start position:0%
+gambling problem we're going to look at
+a very special case probably the
+
+ align:start position:0%
+a very special case probably the
+ 
+
+ align:start position:0%
+a very special case probably the
+simplest case of Random walk and that's
+
+ align:start position:0%
+simplest case of Random walk and that's
+ 
+
+ align:start position:0%
+simplest case of Random walk and that's
+a one-dimensional random walk in a
+
+ align:start position:0%
+a one-dimensional random walk in a
+ 
+
+ align:start position:0%
+a one-dimensional random walk in a
+one-dimensional random walk there's some
+
+ align:start position:0%
+one-dimensional random walk there's some
+ 
+
+ align:start position:0%
+one-dimensional random walk there's some
+value say the number of dollars you've
+
+ align:start position:0%
+value say the number of dollars you've
+ 
+
+ align:start position:0%
+value say the number of dollars you've
+got you know in your pocket and this
+
+ align:start position:0%
+got you know in your pocket and this
+ 
+
+ align:start position:0%
+got you know in your pocket and this
+value can go up or go down or stay the
+
+ align:start position:0%
+value can go up or go down or stay the
+ 
+
+ align:start position:0%
+value can go up or go down or stay the
+same each time you do something like
+
+ align:start position:0%
+same each time you do something like
+ 
+
+ align:start position:0%
+same each time you do something like
+make a bet and each of these happens
+
+ align:start position:0%
+make a bet and each of these happens
+ 
+
+ align:start position:0%
+make a bet and each of these happens
+with a certain
+
+ align:start position:0%
+with a certain
+ 
+
+ align:start position:0%
+with a certain
+probability now in this case you either
+
+ align:start position:0%
+probability now in this case you either
+ 
+
+ align:start position:0%
+probability now in this case you either
+go up by one or you go down by one and
+
+ align:start position:0%
+go up by one or you go down by one and
+ 
+
+ align:start position:0%
+go up by one or you go down by one and
+you can't stay the same every bet you
+
+ align:start position:0%
+you can't stay the same every bet you
+ 
+
+ align:start position:0%
+you can't stay the same every bet you
+win a buck or you lose lose a buck so
+
+ align:start position:0%
+win a buck or you lose lose a buck so
+ 
+
+ align:start position:0%
+win a buck or you lose lose a buck so
+it's really a special case and we can
+
+ align:start position:0%
+it's really a special case and we can
+ 
+
+ align:start position:0%
+it's really a special case and we can
+diagram it as follows so we can put time
+
+ align:start position:0%
+diagram it as follows so we can put time
+ 
+
+ align:start position:0%
+diagram it as follows so we can put time
+or the number of bets on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis and we can put the number of
+
+ align:start position:0%
+axis and we can put the number of
+ 
+
+ align:start position:0%
+axis and we can put the number of
+dollars on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis now in this case we start with
+
+ align:start position:0%
+axis now in this case we start with
+ 
+
+ align:start position:0%
+axis now in this case we start with
+n and we might win the first bet so we
+
+ align:start position:0%
+n and we might win the first bet so we
+ 
+
+ align:start position:0%
+n and we might win the first bet so we
+go to n plus one we might lose lose a
+
+ align:start position:0%
+go to n plus one we might lose lose a
+ 
+
+ align:start position:0%
+go to n plus one we might lose lose a
+bit might lose again could win the next
+
+ align:start position:0%
+bit might lose again could win the next
+ 
+
+ align:start position:0%
+bit might lose again could win the next
+one lose win lose lose so this
+
+ align:start position:0%
+one lose win lose lose so this
+ 
+
+ align:start position:0%
+one lose win lose lose so this
+corresponds to a string win lose lose
+
+ align:start position:0%
+corresponds to a string win lose lose
+ 
+
+ align:start position:0%
+corresponds to a string win lose lose
+lose lose win lose win lose
+
+ align:start position:0%
+lose lose win lose win lose
+ 
+
+ align:start position:0%
+lose lose win lose win lose
+lose
+
+ align:start position:0%
+lose
+ 
+
+ align:start position:0%
+lose
+lose okay and when we win we go up a
+
+ align:start position:0%
+lose okay and when we win we go up a
+ 
+
+ align:start position:0%
+lose okay and when we win we go up a
+dollar and we lose we go down a dollar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's called onedimensional because
+
+ align:start position:0%
+and it's called onedimensional because
+ 
+
+ align:start position:0%
+and it's called onedimensional because
+there's just one thing that's changing
+
+ align:start position:0%
+there's just one thing that's changing
+ 
+
+ align:start position:0%
+there's just one thing that's changing
+you're going up and down there now the
+
+ align:start position:0%
+you're going up and down there now the
+ 
+
+ align:start position:0%
+you're going up and down there now the
+probability of going up is
+
+ align:start position:0%
+probability of going up is
+ 
+
+ align:start position:0%
+probability of going up is
+p and that's no matter what happened
+
+ align:start position:0%
+p and that's no matter what happened
+ 
+
+ align:start position:0%
+p and that's no matter what happened
+before it's a memoryless independent
+
+ align:start position:0%
+before it's a memoryless independent
+ 
+
+ align:start position:0%
+before it's a memoryless independent
+system the probability you win your I
+
+ align:start position:0%
+system the probability you win your I
+ 
+
+ align:start position:0%
+system the probability you win your I
+bet has nothing to do is totally
+
+ align:start position:0%
+bet has nothing to do is totally
+ 
+
+ align:start position:0%
+bet has nothing to do is totally
+independent mutually independent of all
+
+ align:start position:0%
+independent mutually independent of all
+ 
+
+ align:start position:0%
+independent mutually independent of all
+the other bets that took place
+
+ align:start position:0%
+the other bets that took place
+ 
+
+ align:start position:0%
+the other bets that took place
+before all right so let's write that
+
+ align:start position:0%
+before all right so let's write that
+ 
+
+ align:start position:0%
+before all right so let's write that
+down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the probability of an up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+move is p the probability of a Down
+
+ align:start position:0%
+move is p the probability of a Down
+ 
+
+ align:start position:0%
+move is p the probability of a Down
+move is 1 minus p and these are mutually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent of past
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moves now when you have a random walk
+
+ align:start position:0%
+moves now when you have a random walk
+ 
+
+ align:start position:0%
+moves now when you have a random walk
+with a moves are mutually independent it
+
+ align:start position:0%
+with a moves are mutually independent it
+ 
+
+ align:start position:0%
+with a moves are mutually independent it
+has a special name it's called a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Martingale you know there's not all
+
+ align:start position:0%
+Martingale you know there's not all
+ 
+
+ align:start position:0%
+Martingale you know there's not all
+random walks don't have to have mutually
+
+ align:start position:0%
+random walks don't have to have mutually
+ 
+
+ align:start position:0%
+random walks don't have to have mutually
+independent steps like say you're
+
+ align:start position:0%
+independent steps like say you're
+ 
+
+ align:start position:0%
+independent steps like say you're
+looking about winning and losing a
+
+ align:start position:0%
+looking about winning and losing a
+ 
+
+ align:start position:0%
+looking about winning and losing a
+baseball game in a series we looked at a
+
+ align:start position:0%
+baseball game in a series we looked at a
+ 
+
+ align:start position:0%
+baseball game in a series we looked at a
+scenario where if you lost yesterday
+
+ align:start position:0%
+scenario where if you lost yesterday
+ 
+
+ align:start position:0%
+scenario where if you lost yesterday
+you're feeling lousy more likely to lose
+
+ align:start position:0%
+you're feeling lousy more likely to lose
+ 
+
+ align:start position:0%
+you're feeling lousy more likely to lose
+today not true in the gambling case here
+
+ align:start position:0%
+today not true in the gambling case here
+ 
+
+ align:start position:0%
+today not true in the gambling case here
+it's mutually independent and that's the
+
+ align:start position:0%
+it's mutually independent and that's the
+ 
+
+ align:start position:0%
+it's mutually independent and that's the
+only case we're going to study for
+
+ align:start position:0%
+only case we're going to study for
+ 
+
+ align:start position:0%
+only case we're going to study for
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+walks
+
+ align:start position:0%
+walks
+ 
+
+ align:start position:0%
+walks
+now if p is not a
+
+ align:start position:0%
+now if p is not a
+ 
+
+ align:start position:0%
+now if p is not a
+half the random walk is said to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+biased and that's what happens in the
+
+ align:start position:0%
+biased and that's what happens in the
+ 
+
+ align:start position:0%
+biased and that's what happens in the
+casino it's biased in favor of the
+
+ align:start position:0%
+casino it's biased in favor of the
+ 
+
+ align:start position:0%
+casino it's biased in favor of the
+house if P equals a
+
+ align:start position:0%
+house if P equals a
+ 
+
+ align:start position:0%
+house if P equals a
+half then the random walk is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unbiased
+
+ align:start position:0%
+unbiased
+ 
+
+ align:start position:0%
+unbiased
+now in this particular case that we're
+
+ align:start position:0%
+now in this particular case that we're
+ 
+
+ align:start position:0%
+now in this particular case that we're
+looking at we have boundaries on the
+
+ align:start position:0%
+looking at we have boundaries on the
+ 
+
+ align:start position:0%
+looking at we have boundaries on the
+random walk there's a boundary at zero
+
+ align:start position:0%
+random walk there's a boundary at zero
+ 
+
+ align:start position:0%
+random walk there's a boundary at zero
+because you go home broke if you lost
+
+ align:start position:0%
+because you go home broke if you lost
+ 
+
+ align:start position:0%
+because you go home broke if you lost
+everything if the random walk ever hits
+
+ align:start position:0%
+everything if the random walk ever hits
+ 
+
+ align:start position:0%
+everything if the random walk ever hits
+zero dollars you're done and we're also
+
+ align:start position:0%
+zero dollars you're done and we're also
+ 
+
+ align:start position:0%
+zero dollars you're done and we're also
+going to put a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary at n plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M okay so I'm going to have a
+
+ align:start position:0%
+M okay so I'm going to have a
+ 
+
+ align:start position:0%
+M okay so I'm going to have a
+boundary here
+
+ align:start position:0%
+boundary here
+ 
+
+ align:start position:0%
+boundary here
+so that if I win MLL here I stop and I
+
+ align:start position:0%
+so that if I win MLL here I stop and I
+ 
+
+ align:start position:0%
+so that if I win MLL here I stop and I
+go home happy if the random walk ever
+
+ align:start position:0%
+go home happy if the random walk ever
+ 
+
+ align:start position:0%
+go home happy if the random walk ever
+goes here then I
+
+ align:start position:0%
+goes here then I
+ 
+
+ align:start position:0%
+goes here then I
+stop those are called boundary
+
+ align:start position:0%
+stop those are called boundary
+ 
+
+ align:start position:0%
+stop those are called boundary
+conditions for the
+
+ align:start position:0%
+conditions for the
+ 
+
+ align:start position:0%
+conditions for the
+walk and what we want to do is analyze
+
+ align:start position:0%
+walk and what we want to do is analyze
+ 
+
+ align:start position:0%
+walk and what we want to do is analyze
+the probability that we hit that top
+
+ align:start position:0%
+the probability that we hit that top
+ 
+
+ align:start position:0%
+the probability that we hit that top
+boundary before we hit the bottom
+
+ align:start position:0%
+boundary before we hit the bottom
+ 
+
+ align:start position:0%
+boundary before we hit the bottom
+boundary so we're going to Define that
+
+ align:start position:0%
+boundary so we're going to Define that
+ 
+
+ align:start position:0%
+boundary so we're going to Define that
+event to be W star
+
+ align:start position:0%
+event to be W star
+ 
+
+ align:start position:0%
+event to be W star
+W star is the
+
+ align:start position:0%
+W star is the
+ 
+
+ align:start position:0%
+W star is the
+event that the random walk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hits T which is n plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M
+
+ align:start position:0%
+M
+ 
+
+ align:start position:0%
+M
+before it hits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero in other words you go home happy
+
+ align:start position:0%
+zero in other words you go home happy
+ 
+
+ align:start position:0%
+zero in other words you go home happy
+without going
+
+ align:start position:0%
+without going
+ 
+
+ align:start position:0%
+without going
+broke let's also Define d to be the
+
+ align:start position:0%
+broke let's also Define d to be the
+ 
+
+ align:start position:0%
+broke let's also Define d to be the
+number number of dollars at the start
+
+ align:start position:0%
+number number of dollars at the start
+ 
+
+ align:start position:0%
+number number of dollars at the start
+and this is just going to be n in our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case we're interested
+
+ align:start position:0%
+case we're interested
+ 
+
+ align:start position:0%
+case we're interested
+in call it X subn is the
+
+ align:start position:0%
+in call it X subn is the
+ 
+
+ align:start position:0%
+in call it X subn is the
+probability that we go home
+
+ align:start position:0%
+probability that we go home
+ 
+
+ align:start position:0%
+probability that we go home
+Happy given we started with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n all right that's a function of n so
+
+ align:start position:0%
+n all right that's a function of n so
+ 
+
+ align:start position:0%
+n all right that's a function of n so
+we'll make a variable called xn and we
+
+ align:start position:0%
+we'll make a variable called xn and we
+ 
+
+ align:start position:0%
+we'll make a variable called xn and we
+want to know what that probability is
+
+ align:start position:0%
+want to know what that probability is
+ 
+
+ align:start position:0%
+want to know what that probability is
+and of course the more you come with
+
+ align:start position:0%
+and of course the more you come with
+ 
+
+ align:start position:0%
+and of course the more you come with
+you'd think it's a higher chance of
+
+ align:start position:0%
+you'd think it's a higher chance of
+ 
+
+ align:start position:0%
+you'd think it's a higher chance of
+winning the more you have in your pocket
+
+ align:start position:0%
+winning the more you have in your pocket
+ 
+
+ align:start position:0%
+winning the more you have in your pocket
+because you can play for more so the
+
+ align:start position:0%
+because you can play for more so the
+ 
+
+ align:start position:0%
+because you can play for more so the
+goal is to figure this
+
+ align:start position:0%
+goal is to figure this
+ 
+
+ align:start position:0%
+goal is to figure this
+out now to do this we could use the tree
+
+ align:start position:0%
+out now to do this we could use the tree
+ 
+
+ align:start position:0%
+out now to do this we could use the tree
+method but it gets pretty
+
+ align:start position:0%
+method but it gets pretty
+ 
+
+ align:start position:0%
+method but it gets pretty
+complicated because the sample space is
+
+ align:start position:0%
+complicated because the sample space is
+ 
+
+ align:start position:0%
+complicated because the sample space is
+the sample space of all one law
+
+ align:start position:0%
+the sample space of all one law
+ 
+
+ align:start position:0%
+the sample space of all one law
+sequences and how big is that sample
+
+ align:start position:0%
+sequences and how big is that sample
+ 
+
+ align:start position:0%
+sequences and how big is that sample
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinite I could play Forever all right
+
+ align:start position:0%
+infinite I could play Forever all right
+ 
+
+ align:start position:0%
+infinite I could play Forever all right
+now it turns out the probability of
+
+ align:start position:0%
+now it turns out the probability of
+ 
+
+ align:start position:0%
+now it turns out the probability of
+playing forever is zero and we won't
+
+ align:start position:0%
+playing forever is zero and we won't
+ 
+
+ align:start position:0%
+playing forever is zero and we won't
+prove that but there are an infinite
+
+ align:start position:0%
+prove that but there are an infinite
+ 
+
+ align:start position:0%
+prove that but there are an infinite
+number of sample points so doing the
+
+ align:start position:0%
+number of sample points so doing the
+ 
+
+ align:start position:0%
+number of sample points so doing the
+tree methods a little complicated when
+
+ align:start position:0%
+tree methods a little complicated when
+ 
+
+ align:start position:0%
+tree methods a little complicated when
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+infinite um so what we're going to do is
+
+ align:start position:0%
+infinite um so what we're going to do is
+ 
+
+ align:start position:0%
+infinite um so what we're going to do is
+use some of the theorems we proved over
+
+ align:start position:0%
+use some of the theorems we proved over
+ 
+
+ align:start position:0%
+use some of the theorems we proved over
+the last few weeks and set up a
+
+ align:start position:0%
+the last few weeks and set up a
+ 
+
+ align:start position:0%
+the last few weeks and set up a
+recurrence to find this
+
+ align:start position:0%
+recurrence to find this
+ 
+
+ align:start position:0%
+recurrence to find this
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I'm going to tell you what the
+
+ align:start position:0%
+now I'm going to tell you what the
+ 
+
+ align:start position:0%
+now I'm going to tell you what the
+recurrence is and then prove that that's
+
+ align:start position:0%
+recurrence is and then prove that that's
+ 
+
+ align:start position:0%
+recurrence is and then prove that that's
+right so I
+
+ align:start position:0%
+right so I
+ 
+
+ align:start position:0%
+right so I
+claim that
+
+ align:start position:0%
+claim that
+ 
+
+ align:start position:0%
+claim that
+xn is zero zero probability if we start
+
+ align:start position:0%
+xn is zero zero probability if we start
+ 
+
+ align:start position:0%
+xn is zero zero probability if we start
+with n with zero
+
+ align:start position:0%
+with n with zero
+ 
+
+ align:start position:0%
+with n with zero
+dollars it's one if we start with
+
+ align:start position:0%
+dollars it's one if we start with
+ 
+
+ align:start position:0%
+dollars it's one if we start with
+t and it's p * X x n
+
+ align:start position:0%
+t and it's p * X x n
+ 
+
+ align:start position:0%
+t and it's p * X x n
+-1 + 1 - P xn +
+
+ align:start position:0%
+-1 + 1 - P xn +
+ 
+
+ align:start position:0%
+-1 + 1 - P xn +
+1 if we start with
+
+ align:start position:0%
+1 if we start with
+ 
+
+ align:start position:0%
+1 if we start with
+between um zero and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T all right so that's what I claim xn is
+
+ align:start position:0%
+T all right so that's what I claim xn is
+ 
+
+ align:start position:0%
+T all right so that's what I claim xn is
+and it's of course a recursion that I've
+
+ align:start position:0%
+and it's of course a recursion that I've
+ 
+
+ align:start position:0%
+and it's of course a recursion that I've
+set up here so let's see why that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case Okay so let's check the zero case
+
+ align:start position:0%
+case Okay so let's check the zero case
+ 
+
+ align:start position:0%
+case Okay so let's check the zero case
+x0 is the probability we go home a
+
+ align:start position:0%
+x0 is the probability we go home a
+ 
+
+ align:start position:0%
+x0 is the probability we go home a
+winner given we started with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 right why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah you you started broke you
+
+ align:start position:0%
+that yeah you you started broke you
+ 
+
+ align:start position:0%
+that yeah you you started broke you
+never get off the ground because you
+
+ align:start position:0%
+never get off the ground because you
+ 
+
+ align:start position:0%
+never get off the ground because you
+quit as soon as you have zero dollars so
+
+ align:start position:0%
+quit as soon as you have zero dollars so
+ 
+
+ align:start position:0%
+quit as soon as you have zero dollars so
+you have no chance
+
+ align:start position:0%
+you have no chance
+ 
+
+ align:start position:0%
+you have no chance
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+win because you're broke to
+
+ align:start position:0%
+win because you're broke to
+ 
+
+ align:start position:0%
+win because you're broke to
+start right let's check the next case
+
+ align:start position:0%
+start right let's check the next case
+ 
+
+ align:start position:0%
+start right let's check the next case
+XT case n equals T is the probability
+
+ align:start position:0%
+XT case n equals T is the probability
+ 
+
+ align:start position:0%
+XT case n equals T is the probability
+you go home a winner given that you
+
+ align:start position:0%
+you go home a winner given that you
+ 
+
+ align:start position:0%
+you go home a winner given that you
+started with t
+
+ align:start position:0%
+started with t
+ 
+
+ align:start position:0%
+started with t
+do why is that
+
+ align:start position:0%
+do why is that
+ 
+
+ align:start position:0%
+do why is that
+one why is that certain sort of from the
+
+ align:start position:0%
+one why is that certain sort of from the
+ 
+
+ align:start position:0%
+one why is that certain sort of from the
+definition you already have your money
+
+ align:start position:0%
+definition you already have your money
+ 
+
+ align:start position:0%
+definition you already have your money
+you already hit the top boundary because
+
+ align:start position:0%
+you already hit the top boundary because
+ 
+
+ align:start position:0%
+you already hit the top boundary because
+you started there remember you quit and
+
+ align:start position:0%
+you started there remember you quit and
+ 
+
+ align:start position:0%
+you started there remember you quit and
+you're happy go home happy if you hit
+
+ align:start position:0%
+you're happy go home happy if you hit
+ 
+
+ align:start position:0%
+you're happy go home happy if you hit
+T all right so you're guaranteed to go
+
+ align:start position:0%
+T all right so you're guaranteed to go
+ 
+
+ align:start position:0%
+T all right so you're guaranteed to go
+home happy because you never make any
+
+ align:start position:0%
+home happy because you never make any
+ 
+
+ align:start position:0%
+home happy because you never make any
+bets you started with all the money you
+
+ align:start position:0%
+bets you started with all the money you
+ 
+
+ align:start position:0%
+bets you started with all the money you
+needed to go home happy all right then
+
+ align:start position:0%
+needed to go home happy all right then
+ 
+
+ align:start position:0%
+needed to go home happy all right then
+we have the interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case where you start with between zero
+
+ align:start position:0%
+case where you start with between zero
+ 
+
+ align:start position:0%
+case where you start with between zero
+and T and now you're going to make some
+
+ align:start position:0%
+and T and now you're going to make some
+ 
+
+ align:start position:0%
+and T and now you're going to make some
+bets and then xn is the probability just
+
+ align:start position:0%
+bets and then xn is the probability just
+ 
+
+ align:start position:0%
+bets and then xn is the probability just
+the definition of going home Happy
+
+ align:start position:0%
+the definition of going home Happy
+ 
+
+ align:start position:0%
+the definition of going home Happy
+I.E winning T having T dollars if you
+
+ align:start position:0%
+I.E winning T having T dollars if you
+ 
+
+ align:start position:0%
+I.E winning T having T dollars if you
+start with
+
+ align:start position:0%
+start with
+ 
+
+ align:start position:0%
+start with
+n now there's two cases to analyze this
+
+ align:start position:0%
+n now there's two cases to analyze this
+ 
+
+ align:start position:0%
+n now there's two cases to analyze this
+based on what happens in the first bet
+
+ align:start position:0%
+based on what happens in the first bet
+ 
+
+ align:start position:0%
+based on what happens in the first bet
+you could win it or you could lose it
+
+ align:start position:0%
+you could win it or you could lose it
+ 
+
+ align:start position:0%
+you could win it or you could lose it
+and then we're going to
+
+ align:start position:0%
+and then we're going to
+ 
+
+ align:start position:0%
+and then we're going to
+recurse so we're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Define e to be the
+
+ align:start position:0%
+Define e to be the
+ 
+
+ align:start position:0%
+Define e to be the
+event that you win the first
+
+ align:start position:0%
+event that you win the first
+ 
+
+ align:start position:0%
+event that you win the first
+bet
+
+ align:start position:0%
+bet
+ 
+
+ align:start position:0%
+bet
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+ebar is the
+
+ align:start position:0%
+ebar is the
+ 
+
+ align:start position:0%
+ebar is the
+event that you lose the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bet all right now by the theorem of
+
+ align:start position:0%
+bet all right now by the theorem of
+ 
+
+ align:start position:0%
+bet all right now by the theorem of
+total probability which we did in
+
+ align:start position:0%
+total probability which we did in
+ 
+
+ align:start position:0%
+total probability which we did in
+recitation maybe a couple weeks ago we
+
+ align:start position:0%
+recitation maybe a couple weeks ago we
+ 
+
+ align:start position:0%
+recitation maybe a couple weeks ago we
+can rewrite this depending on whether e
+
+ align:start position:0%
+can rewrite this depending on whether e
+ 
+
+ align:start position:0%
+can rewrite this depending on whether e
+happened or the complement of
+
+ align:start position:0%
+happened or the complement of
+ 
+
+ align:start position:0%
+happened or the complement of
+happened and you get that the
+
+ align:start position:0%
+happened and you get that the
+ 
+
+ align:start position:0%
+happened and you get that the
+probability is simply the probab of
+
+ align:start position:0%
+probability is simply the probab of
+ 
+
+ align:start position:0%
+probability is simply the probab of
+going home
+
+ align:start position:0%
+going home
+ 
+
+ align:start position:0%
+going home
+happy and winning the first bet times
+
+ align:start position:0%
+happy and winning the first bet times
+ 
+
+ align:start position:0%
+happy and winning the first bet times
+the probab whoops and I got to put the
+
+ align:start position:0%
+the probab whoops and I got to put the
+ 
+
+ align:start position:0%
+the probab whoops and I got to put the
+conditioning in that doesn't go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away so I'm breaking into two cases the
+
+ align:start position:0%
+away so I'm breaking into two cases the
+ 
+
+ align:start position:0%
+away so I'm breaking into two cases the
+first one is you win the first bet given
+
+ align:start position:0%
+first one is you win the first bet given
+ 
+
+ align:start position:0%
+first one is you win the first bet given
+D equals
+
+ align:start position:0%
+D equals
+ 
+
+ align:start position:0%
+D equals
+n and the case where you lose the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bet given equal
+
+ align:start position:0%
+bet given equal
+ 
+
+ align:start position:0%
+bet given equal
+n any questions
+
+ align:start position:0%
+n any questions
+ 
+
+ align:start position:0%
+n any questions
+here probability of going home Happy
+
+ align:start position:0%
+here probability of going home Happy
+ 
+
+ align:start position:0%
+here probability of going home Happy
+given you start
+
+ align:start position:0%
+given you start
+ 
+
+ align:start position:0%
+given you start
+with1 is the probability of going home
+
+ align:start position:0%
+with1 is the probability of going home
+ 
+
+ align:start position:0%
+with1 is the probability of going home
+happy and winning the first bet
+
+ align:start position:0%
+happy and winning the first bet
+ 
+
+ align:start position:0%
+happy and winning the first bet
+oops Yeah uh given D equals n plus the
+
+ align:start position:0%
+oops Yeah uh given D equals n plus the
+ 
+
+ align:start position:0%
+oops Yeah uh given D equals n plus the
+probability of going home happy and
+
+ align:start position:0%
+probability of going home happy and
+ 
+
+ align:start position:0%
+probability of going home happy and
+losing the first bet given D equals n
+
+ align:start position:0%
+losing the first bet given D equals n
+ 
+
+ align:start position:0%
+losing the first bet given D equals n
+just those are the two
+
+ align:start position:0%
+just those are the two
+ 
+
+ align:start position:0%
+just those are the two
+cases now I can use the definition of
+
+ align:start position:0%
+cases now I can use the definition of
+ 
+
+ align:start position:0%
+cases now I can use the definition of
+conditional probability to rewrite
+
+ align:start position:0%
+conditional probability to rewrite
+ 
+
+ align:start position:0%
+conditional probability to rewrite
+these this is the probability we got two
+
+ align:start position:0%
+these this is the probability we got two
+ 
+
+ align:start position:0%
+these this is the probability we got two
+events that the first one
+
+ align:start position:0%
+events that the first one
+ 
+
+ align:start position:0%
+events that the first one
+happens given D equals
+
+ align:start position:0%
+happens given D equals
+ 
+
+ align:start position:0%
+happens given D equals
+n times the probability the second one
+
+ align:start position:0%
+n times the probability the second one
+ 
+
+ align:start position:0%
+n times the probability the second one
+happens given that the first one
+
+ align:start position:0%
+happens given that the first one
+ 
+
+ align:start position:0%
+happens given that the first one
+happened and D equals
+
+ align:start position:0%
+happened and D equals
+ 
+
+ align:start position:0%
+happened and D equals
+n all right this is just the definition
+
+ align:start position:0%
+n all right this is just the definition
+ 
+
+ align:start position:0%
+n all right this is just the definition
+of conditional probability when I got an
+
+ align:start position:0%
+of conditional probability when I got an
+ 
+
+ align:start position:0%
+of conditional probability when I got an
+intersection of events here the
+
+ align:start position:0%
+intersection of events here the
+ 
+
+ align:start position:0%
+intersection of events here the
+probability of both happening is the
+
+ align:start position:0%
+probability of both happening is the
+ 
+
+ align:start position:0%
+probability of both happening is the
+probability of the first happening times
+
+ align:start position:0%
+probability of the first happening times
+ 
+
+ align:start position:0%
+probability of the first happening times
+the probability of the second happening
+
+ align:start position:0%
+the probability of the second happening
+ 
+
+ align:start position:0%
+the probability of the second happening
+given that the first happened and of
+
+ align:start position:0%
+given that the first happened and of
+ 
+
+ align:start position:0%
+given that the first happened and of
+course everything is in this universe of
+
+ align:start position:0%
+course everything is in this universe of
+ 
+
+ align:start position:0%
+course everything is in this universe of
+D equals
+
+ align:start position:0%
+D equals
+ 
+
+ align:start position:0%
+D equals
+n all right so I've used it in a little
+
+ align:start position:0%
+n all right so I've used it in a little
+ 
+
+ align:start position:0%
+n all right so I've used it in a little
+Just A Different Twist from when we had
+
+ align:start position:0%
+Just A Different Twist from when we had
+ 
+
+ align:start position:0%
+Just A Different Twist from when we had
+it before same thing over here this now
+
+ align:start position:0%
+it before same thing over here this now
+ 
+
+ align:start position:0%
+it before same thing over here this now
+is the probability of e Prime given D
+
+ align:start position:0%
+is the probability of e Prime given D
+ 
+
+ align:start position:0%
+is the probability of e Prime given D
+equals n times the probability of w star
+
+ align:start position:0%
+equals n times the probability of w star
+ 
+
+ align:start position:0%
+equals n times the probability of w star
+winning going home Happy
+
+ align:start position:0%
+winning going home Happy
+ 
+
+ align:start position:0%
+winning going home Happy
+given that you lost the first bet and D
+
+ align:start position:0%
+given that you lost the first bet and D
+ 
+
+ align:start position:0%
+given that you lost the first bet and D
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+that's D equals n
+
+ align:start position:0%
+that's D equals n
+ 
+
+ align:start position:0%
+that's D equals n
+there right so it looks like it's gotten
+
+ align:start position:0%
+there right so it looks like it's gotten
+ 
+
+ align:start position:0%
+there right so it looks like it's gotten
+more complicated but now we can start
+
+ align:start position:0%
+more complicated but now we can start
+ 
+
+ align:start position:0%
+more complicated but now we can start
+simplifying what's the probability of
+
+ align:start position:0%
+simplifying what's the probability of
+ 
+
+ align:start position:0%
+simplifying what's the probability of
+winning the first bet given that you
+
+ align:start position:0%
+winning the first bet given that you
+ 
+
+ align:start position:0%
+winning the first bet given that you
+started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with1
+
+ align:start position:0%
+with1
+ 
+
+ align:start position:0%
+with1
+P in fact does this have anything to do
+
+ align:start position:0%
+P in fact does this have anything to do
+ 
+
+ align:start position:0%
+P in fact does this have anything to do
+with the probability of winning the
+
+ align:start position:0%
+with the probability of winning the
+ 
+
+ align:start position:0%
+with the probability of winning the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+bet no this is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P okay uh um now what about this
+
+ align:start position:0%
+P okay uh um now what about this
+ 
+
+ align:start position:0%
+P okay uh um now what about this
+thing I am conditioning on winning the
+
+ align:start position:0%
+thing I am conditioning on winning the
+ 
+
+ align:start position:0%
+thing I am conditioning on winning the
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bet
+
+ align:start position:0%
+bet
+ 
+
+ align:start position:0%
+bet
+given and I start with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nll okay what's another way of
+
+ align:start position:0%
+nll okay what's another way of
+ 
+
+ align:start position:0%
+nll okay what's another way of
+expressing I won the first bet and I
+
+ align:start position:0%
+expressing I won the first bet and I
+ 
+
+ align:start position:0%
+expressing I won the first bet and I
+started with
+
+ align:start position:0%
+started with
+ 
+
+ align:start position:0%
+started with
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+yeah I now have n Plus $ going
+
+ align:start position:0%
+yeah I now have n Plus $ going
+ 
+
+ align:start position:0%
+yeah I now have n Plus $ going
+forward and because I have a Martingale
+
+ align:start position:0%
+forward and because I have a Martingale
+ 
+
+ align:start position:0%
+forward and because I have a Martingale
+and everything is mutually independent
+
+ align:start position:0%
+and everything is mutually independent
+ 
+
+ align:start position:0%
+and everything is mutually independent
+it's like the world starts all over
+
+ align:start position:0%
+it's like the world starts all over
+ 
+
+ align:start position:0%
+it's like the world starts all over
+again I'm now in a state with n plus1
+
+ align:start position:0%
+again I'm now in a state with n plus1
+ 
+
+ align:start position:0%
+again I'm now in a state with n plus1
+and I want to know the
+
+ align:start position:0%
+and I want to know the
+ 
+
+ align:start position:0%
+and I want to know the
+probability that I go home Happy doesn't
+
+ align:start position:0%
+probability that I go home Happy doesn't
+ 
+
+ align:start position:0%
+probability that I go home Happy doesn't
+matter how I got the N
+
+ align:start position:0%
+matter how I got the N
+ 
+
+ align:start position:0%
+matter how I got the N
+plus1 it's just going forward I got n
+
+ align:start position:0%
+plus1 it's just going forward I got n
+ 
+
+ align:start position:0%
+plus1 it's just going forward I got n
+plus1 in my pocket I want to the
+
+ align:start position:0%
+plus1 in my pocket I want to the
+ 
+
+ align:start position:0%
+plus1 in my pocket I want to the
+probably to go and home happy so I reset
+
+ align:start position:0%
+probably to go and home happy so I reset
+ 
+
+ align:start position:0%
+probably to go and home happy so I reset
+to D equals n
+
+ align:start position:0%
+to D equals n
+ 
+
+ align:start position:0%
+to D equals n
+plus1
+
+ align:start position:0%
+plus1
+ 
+
+ align:start position:0%
+plus1
+okay so I replace this with that because
+
+ align:start position:0%
+okay so I replace this with that because
+ 
+
+ align:start position:0%
+okay so I replace this with that because
+however long it took me to get there and
+
+ align:start position:0%
+however long it took me to get there and
+ 
+
+ align:start position:0%
+however long it took me to get there and
+all that stuff doesn't matter for this
+
+ align:start position:0%
+all that stuff doesn't matter for this
+ 
+
+ align:start position:0%
+all that stuff doesn't matter for this
+analysis it's all mutually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent okay probability of losing
+
+ align:start position:0%
+independent okay probability of losing
+ 
+
+ align:start position:0%
+independent okay probability of losing
+the first bet given that I started with
+
+ align:start position:0%
+the first bet given that I started with
+ 
+
+ align:start position:0%
+the first bet given that I started with
+N1 one minus P doesn't matter how much I
+
+ align:start position:0%
+N1 one minus P doesn't matter how much I
+ 
+
+ align:start position:0%
+N1 one minus P doesn't matter how much I
+started with and here I'm I want to know
+
+ align:start position:0%
+started with and here I'm I want to know
+ 
+
+ align:start position:0%
+started with and here I'm I want to know
+the probability of going home
+
+ align:start position:0%
+the probability of going home
+ 
+
+ align:start position:0%
+the probability of going home
+Happy
+
+ align:start position:0%
+Happy
+ 
+
+ align:start position:0%
+Happy
+given well if I lost the first bet and I
+
+ align:start position:0%
+given well if I lost the first bet and I
+ 
+
+ align:start position:0%
+given well if I lost the first bet and I
+started with n what have I
+
+ align:start position:0%
+started with n what have I
+ 
+
+ align:start position:0%
+started with n what have I
+got n minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay and doesn't matter how I got to
+
+ align:start position:0%
+one okay and doesn't matter how I got to
+ 
+
+ align:start position:0%
+one okay and doesn't matter how I got to
+n minus
+
+ align:start position:0%
+n minus
+ 
+
+ align:start position:0%
+n minus
+one okay well now this is going to get
+
+ align:start position:0%
+one okay well now this is going to get
+ 
+
+ align:start position:0%
+one okay well now this is going to get
+really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simple what's another name for that
+
+ align:start position:0%
+simple what's another name for that
+ 
+
+ align:start position:0%
+simple what's another name for that
+expression xn +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and another name for this
+
+ align:start position:0%
+one and another name for this
+ 
+
+ align:start position:0%
+one and another name for this
+expression xn minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay so we Prov that xn equals pxn +
+
+ align:start position:0%
+one okay so we Prov that xn equals pxn +
+ 
+
+ align:start position:0%
+one okay so we Prov that xn equals pxn +
+1 + 1 - pxn minus one and that's what I
+
+ align:start position:0%
+1 + 1 - pxn minus one and that's what I
+ 
+
+ align:start position:0%
+1 + 1 - pxn minus one and that's what I
+claimed was true so we finished the
+
+ align:start position:0%
+claimed was true so we finished the
+ 
+
+ align:start position:0%
+claimed was true so we finished the
+proof any
+
+ align:start position:0%
+proof any
+ 
+
+ align:start position:0%
+proof any
+questions did I screw it
+
+ align:start position:0%
+questions did I screw it
+ 
+
+ align:start position:0%
+questions did I screw it
+up I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim probability of winning
+
+ align:start position:0%
+claim probability of winning
+ 
+
+ align:start position:0%
+claim probability of winning
+so let's see let's see if I have it
+
+ align:start position:0%
+so let's see let's see if I have it
+ 
+
+ align:start position:0%
+so let's see let's see if I have it
+wrong in here might screwed it up
+
+ align:start position:0%
+wrong in here might screwed it up
+ 
+
+ align:start position:0%
+wrong in here might screwed it up
+because I think I proved it's n+ one
+
+ align:start position:0%
+because I think I proved it's n+ one
+ 
+
+ align:start position:0%
+because I think I proved it's n+ one
+right yep sure enough I think this is a
+
+ align:start position:0%
+right yep sure enough I think this is a
+ 
+
+ align:start position:0%
+right yep sure enough I think this is a
+plus one that's a minus one yeah always
+
+ align:start position:0%
+plus one that's a minus one yeah always
+ 
+
+ align:start position:0%
+plus one that's a minus one yeah always
+good to check that you proved what you
+
+ align:start position:0%
+good to check that you proved what you
+ 
+
+ align:start position:0%
+good to check that you proved what you
+said you were going to prove so what I
+
+ align:start position:0%
+said you were going to prove so what I
+ 
+
+ align:start position:0%
+said you were going to prove so what I
+said I needed to change this that's what
+
+ align:start position:0%
+said I needed to change this that's what
+ 
+
+ align:start position:0%
+said I needed to change this that's what
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proved
+
+ align:start position:0%
+proved
+ 
+
+ align:start position:0%
+proved
+okay any other questions that was a
+
+ align:start position:0%
+okay any other questions that was a
+ 
+
+ align:start position:0%
+okay any other questions that was a
+pretty important
+
+ align:start position:0%
+pretty important
+ 
+
+ align:start position:0%
+pretty important
+question all right
+
+ align:start position:0%
+question all right
+ 
+
+ align:start position:0%
+question all right
+so we have a recurrence for xn now it's
+
+ align:start position:0%
+so we have a recurrence for xn now it's
+ 
+
+ align:start position:0%
+so we have a recurrence for xn now it's
+a little funny looking at first because
+
+ align:start position:0%
+a little funny looking at first because
+ 
+
+ align:start position:0%
+a little funny looking at first because
+normally with recurrences xn would
+
+ align:start position:0%
+normally with recurrences xn would
+ 
+
+ align:start position:0%
+normally with recurrences xn would
+depend on x sub I that are smaller I are
+
+ align:start position:0%
+depend on x sub I that are smaller I are
+ 
+
+ align:start position:0%
+depend on x sub I that are smaller I are
+smaller than n so it looks a little
+
+ align:start position:0%
+smaller than n so it looks a little
+ 
+
+ align:start position:0%
+smaller than n so it looks a little
+wacky but is that a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem I can just solve for xn plus one
+
+ align:start position:0%
+problem I can just solve for xn plus one
+ 
+
+ align:start position:0%
+problem I can just solve for xn plus one
+just subtract this and put it over there
+
+ align:start position:0%
+just subtract this and put it over there
+ 
+
+ align:start position:0%
+just subtract this and put it over there
+all right so let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so if I bring if I solve for
+
+ align:start position:0%
+that okay so if I bring if I solve for
+ 
+
+ align:start position:0%
+that okay so if I bring if I solve for
+xn plus one up there or put pxn plus1 on
+
+ align:start position:0%
+xn plus one up there or put pxn plus1 on
+ 
+
+ align:start position:0%
+xn plus one up there or put pxn plus1 on
+its own side I get P xn + 1
+
+ align:start position:0%
+its own side I get P xn + 1
+ 
+
+ align:start position:0%
+its own side I get P xn + 1
+-
+
+ align:start position:0%
+-
+ 
+
+ align:start position:0%
+-
+xn + 1 -
+
+ align:start position:0%
+xn + 1 -
+ 
+
+ align:start position:0%
+xn + 1 -
+P xn - one equals 0 and I know that x0
+
+ align:start position:0%
+P xn - one equals 0 and I know that x0
+ 
+
+ align:start position:0%
+P xn - one equals 0 and I know that x0
+is0 and I know that XT equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 now what type of recurrence is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this linear good so it's a linear
+
+ align:start position:0%
+this linear good so it's a linear
+ 
+
+ align:start position:0%
+this linear good so it's a linear
+recurrence and what type of linear
+
+ align:start position:0%
+recurrence and what type of linear
+ 
+
+ align:start position:0%
+recurrence and what type of linear
+recurrence is it
+
+ align:start position:0%
+recurrence is it
+ 
+
+ align:start position:0%
+recurrence is it
+homogeneous that's the best case simple
+
+ align:start position:0%
+homogeneous that's the best case simple
+ 
+
+ align:start position:0%
+homogeneous that's the best case simple
+case that's good the boundy conditions
+
+ align:start position:0%
+case that's good the boundy conditions
+ 
+
+ align:start position:0%
+case that's good the boundy conditions
+are a little weird because the
+
+ align:start position:0%
+are a little weird because the
+ 
+
+ align:start position:0%
+are a little weird because the
+recurrences we all saw before you know
+
+ align:start position:0%
+recurrences we all saw before you know
+ 
+
+ align:start position:0%
+recurrences we all saw before you know
+if we had two boundary conditions it
+
+ align:start position:0%
+if we had two boundary conditions it
+ 
+
+ align:start position:0%
+if we had two boundary conditions it
+would be x0 and X1 here it's x0 and XT
+
+ align:start position:0%
+would be x0 and X1 here it's x0 and XT
+ 
+
+ align:start position:0%
+would be x0 and X1 here it's x0 and XT
+but all you need or two doesn't matter
+
+ align:start position:0%
+but all you need or two doesn't matter
+ 
+
+ align:start position:0%
+but all you need or two doesn't matter
+where they
+
+ align:start position:0%
+where they
+ 
+
+ align:start position:0%
+where they
+are all right so how do I solve that
+
+ align:start position:0%
+are all right so how do I solve that
+ 
+
+ align:start position:0%
+are all right so how do I solve that
+thing what's the next thing I uh
+
+ align:start position:0%
+thing what's the next thing I uh
+ 
+
+ align:start position:0%
+thing what's the next thing I uh
+do what is
+
+ align:start position:0%
+do what is
+ 
+
+ align:start position:0%
+do what is
+it characteristic equation and what do
+
+ align:start position:0%
+it characteristic equation and what do
+ 
+
+ align:start position:0%
+it characteristic equation and what do
+you do with that
+
+ align:start position:0%
+you do with that
+ 
+
+ align:start position:0%
+you do with that
+equation solve it get the roots this
+
+ align:start position:0%
+equation solve it get the roots this
+ 
+
+ align:start position:0%
+equation solve it get the roots this
+will be good practice for the the final
+
+ align:start position:0%
+will be good practice for the the final
+ 
+
+ align:start position:0%
+will be good practice for the the final
+because you'll probably have to do
+
+ align:start position:0%
+because you'll probably have to do
+ 
+
+ align:start position:0%
+because you'll probably have to do
+something like this all right so that's
+
+ align:start position:0%
+something like this all right so that's
+ 
+
+ align:start position:0%
+something like this all right so that's
+the characteristic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation and what's the order of this
+
+ align:start position:0%
+equation and what's the order of this
+ 
+
+ align:start position:0%
+equation and what's the order of this
+equation the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degree it's going to be it's going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be me two right I'm gonna have PR squar
+
+ align:start position:0%
+be me two right I'm gonna have PR squar
+ 
+
+ align:start position:0%
+be me two right I'm gonna have PR squar
+minus r + 1 - p is zero that's my
+
+ align:start position:0%
+minus r + 1 - p is zero that's my
+ 
+
+ align:start position:0%
+minus r + 1 - p is zero that's my
+characteristic
+
+ align:start position:0%
+characteristic
+ 
+
+ align:start position:0%
+characteristic
+equation all right remember that so I
+
+ align:start position:0%
+equation all right remember that so I
+ 
+
+ align:start position:0%
+equation all right remember that so I
+make this be the constant term then I
+
+ align:start position:0%
+make this be the constant term then I
+ 
+
+ align:start position:0%
+make this be the constant term then I
+have the first order term then the
+
+ align:start position:0%
+have the first order term then the
+ 
+
+ align:start position:0%
+have the first order term then the
+second order
+
+ align:start position:0%
+second order
+ 
+
+ align:start position:0%
+second order
+term all right now I solve
+
+ align:start position:0%
+term all right now I solve
+ 
+
+ align:start position:0%
+term all right now I solve
+it and that's easy for a second order
+
+ align:start position:0%
+it and that's easy for a second order
+ 
+
+ align:start position:0%
+it and that's easy for a second order
+equation one plus or minus the square Ro
+
+ align:start position:0%
+equation one plus or minus the square Ro
+ 
+
+ align:start position:0%
+equation one plus or minus the square Ro
+TK of 1
+
+ align:start position:0%
+TK of 1
+ 
+
+ align:start position:0%
+TK of 1
+- 4 4 P 1 minus
+
+ align:start position:0%
+- 4 4 P 1 minus
+ 
+
+ align:start position:0%
+- 4 4 P 1 minus
+p over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p all right let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so this is one plus or minus
+
+ align:start position:0%
+that okay so this is one plus or minus
+ 
+
+ align:start position:0%
+that okay so this is one plus or minus
+Square < TK of 1 - 4 p + 4 p ^
+
+ align:start position:0%
+Square < TK of 1 - 4 p + 4 p ^
+ 
+
+ align:start position:0%
+Square < TK of 1 - 4 p + 4 p ^
+2 over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p just using the quadratic formula and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simplifying and it works out really
+
+ align:start position:0%
+simplifying and it works out really
+ 
+
+ align:start position:0%
+simplifying and it works out really
+nicely because that is the square root
+
+ align:start position:0%
+nicely because that is the square root
+ 
+
+ align:start position:0%
+nicely because that is the square root
+this is just 1 minus 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p^2 so that's 1 plus or minus 1 - 2 p
+
+ align:start position:0%
+p^2 so that's 1 plus or minus 1 - 2 p
+ 
+
+ align:start position:0%
+p^2 so that's 1 plus or minus 1 - 2 p
+over 2
+
+ align:start position:0%
+over 2
+ 
+
+ align:start position:0%
+over 2
+p and that
+
+ align:start position:0%
+p and that
+ 
+
+ align:start position:0%
+p and that
+is 2 - 2 p over 2
+
+ align:start position:0%
+is 2 - 2 p over 2
+ 
+
+ align:start position:0%
+is 2 - 2 p over 2
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+or let's see one minus one cancels then
+
+ align:start position:0%
+or let's see one minus one cancels then
+ 
+
+ align:start position:0%
+or let's see one minus one cancels then
+one then minus minus 2 p is 2 p over 2 p
+
+ align:start position:0%
+one then minus minus 2 p is 2 p over 2 p
+ 
+
+ align:start position:0%
+one then minus minus 2 p is 2 p over 2 p
+so the answers the roots
+
+ align:start position:0%
+so the answers the roots
+ 
+
+ align:start position:0%
+so the answers the roots
+are divide by two on this one I get 1
+
+ align:start position:0%
+are divide by two on this one I get 1
+ 
+
+ align:start position:0%
+are divide by two on this one I get 1
+minus p over p and
+
+ align:start position:0%
+minus p over p and
+ 
+
+ align:start position:0%
+minus p over p and
+one those are the
+
+ align:start position:0%
+one those are the
+ 
+
+ align:start position:0%
+one those are the
+roots
+
+ align:start position:0%
+roots
+ 
+
+ align:start position:0%
+roots
+okay are these roots Ro
+
+ align:start position:0%
+okay are these roots Ro
+ 
+
+ align:start position:0%
+okay are these roots Ro
+different do I have the case of a double
+
+ align:start position:0%
+different do I have the case of a double
+ 
+
+ align:start position:0%
+different do I have the case of a double
+root or the roots always
+
+ align:start position:0%
+root or the roots always
+ 
+
+ align:start position:0%
+root or the roots always
+different yeah they're usually different
+
+ align:start position:0%
+different yeah they're usually different
+ 
+
+ align:start position:0%
+different yeah they're usually different
+what's the case where these roots are
+
+ align:start position:0%
+what's the case where these roots are
+ 
+
+ align:start position:0%
+what's the case where these roots are
+the same 0 five which is sort of an
+
+ align:start position:0%
+the same 0 five which is sort of an
+ 
+
+ align:start position:0%
+the same 0 five which is sort of an
+interesting case in this game right
+
+ align:start position:0%
+interesting case in this game right
+ 
+
+ align:start position:0%
+interesting case in this game right
+because if P equals a half we have an
+
+ align:start position:0%
+because if P equals a half we have an
+ 
+
+ align:start position:0%
+because if P equals a half we have an
+unbiased random walk you got a fair game
+
+ align:start position:0%
+unbiased random walk you got a fair game
+ 
+
+ align:start position:0%
+unbiased random walk you got a fair game
+and so it says right away well maybe the
+
+ align:start position:0%
+and so it says right away well maybe the
+ 
+
+ align:start position:0%
+and so it says right away well maybe the
+result is going to be different for a
+
+ align:start position:0%
+result is going to be different for a
+ 
+
+ align:start position:0%
+result is going to be different for a
+fair game than the game we're playing in
+
+ align:start position:0%
+fair game than the game we're playing in
+ 
+
+ align:start position:0%
+fair game than the game we're playing in
+the casino where it's where it's
+
+ align:start position:0%
+the casino where it's where it's
+ 
+
+ align:start position:0%
+the casino where it's where it's
+biased okay so let's look at the casino
+
+ align:start position:0%
+biased okay so let's look at the casino
+ 
+
+ align:start position:0%
+biased okay so let's look at the casino
+game where p is not a half then the
+
+ align:start position:0%
+game where p is not a half then the
+ 
+
+ align:start position:0%
+game where p is not a half then the
+roots are
+
+ align:start position:0%
+roots are
+ 
+
+ align:start position:0%
+roots are
+different later we'll go back and
+
+ align:start position:0%
+different later we'll go back and
+ 
+
+ align:start position:0%
+different later we'll go back and
+analyze the case when the roots are the
+
+ align:start position:0%
+analyze the case when the roots are the
+ 
+
+ align:start position:0%
+analyze the case when the roots are the
+same for the fair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game all right so if p is not a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half then we can solve for
+
+ align:start position:0%
+half then we can solve for
+ 
+
+ align:start position:0%
+half then we can solve for
+xn xn is some
+
+ align:start position:0%
+xn xn is some
+ 
+
+ align:start position:0%
+xn xn is some
+constant times the first root to the N
+
+ align:start position:0%
+constant times the first root to the N
+ 
+
+ align:start position:0%
+constant times the first root to the N
+power plus a constant times the second
+
+ align:start position:0%
+power plus a constant times the second
+ 
+
+ align:start position:0%
+power plus a constant times the second
+root to the nth power remember that's
+
+ align:start position:0%
+root to the nth power remember that's
+ 
+
+ align:start position:0%
+root to the nth power remember that's
+how it works for any linear homogeneous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence okay and that's
+
+ align:start position:0%
+recurrence okay and that's
+ 
+
+ align:start position:0%
+recurrence okay and that's
+easy because the second root was one
+
+ align:start position:0%
+easy because the second root was one
+ 
+
+ align:start position:0%
+easy because the second root was one
+this is just plus b one to the N is is
+
+ align:start position:0%
+this is just plus b one to the N is is
+ 
+
+ align:start position:0%
+this is just plus b one to the N is is
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+how do I figure out what A and B
+
+ align:start position:0%
+how do I figure out what A and B
+ 
+
+ align:start position:0%
+how do I figure out what A and B
+are boundary conditions very good okay
+
+ align:start position:0%
+are boundary conditions very good okay
+ 
+
+ align:start position:0%
+are boundary conditions very good okay
+so let's look at the boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the first boundary condition is
+
+ align:start position:0%
+okay so the first boundary condition is
+ 
+
+ align:start position:0%
+okay so the first boundary condition is
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+zero so we have 0 equals
+
+ align:start position:0%
+zero so we have 0 equals
+ 
+
+ align:start position:0%
+zero so we have 0 equals
+x0 plugging in there oops I forgot the N
+
+ align:start position:0%
+x0 plugging in there oops I forgot the N
+ 
+
+ align:start position:0%
+x0 plugging in there oops I forgot the N
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+here plugging in n equals z well this to
+
+ align:start position:0%
+here plugging in n equals z well this to
+ 
+
+ align:start position:0%
+here plugging in n equals z well this to
+the zero is just one that is a plus
+
+ align:start position:0%
+the zero is just one that is a plus
+ 
+
+ align:start position:0%
+the zero is just one that is a plus
+b that means that b equals minus
+
+ align:start position:0%
+b that means that b equals minus
+ 
+
+ align:start position:0%
+b that means that b equals minus
+a then the second boundary condition is
+
+ align:start position:0%
+a then the second boundary condition is
+ 
+
+ align:start position:0%
+a then the second boundary condition is
+1 = X
+
+ align:start position:0%
+1 = X
+ 
+
+ align:start position:0%
+1 = X
+subt and that is a 1 - p over P to the
+
+ align:start position:0%
+subt and that is a 1 - p over P to the
+ 
+
+ align:start position:0%
+subt and that is a 1 - p over P to the
+t plus b but B was minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a and now I can solve for a all right so
+
+ align:start position:0%
+a and now I can solve for a all right so
+ 
+
+ align:start position:0%
+a and now I can solve for a all right so
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+a equal 1
+
+ align:start position:0%
+a equal 1
+ 
+
+ align:start position:0%
+a equal 1
+over 1 - p
+
+ align:start position:0%
+over 1 - p
+ 
+
+ align:start position:0%
+over 1 - p
+P the T
+
+ align:start position:0%
+P the T
+ 
+
+ align:start position:0%
+P the T
+-1 and B isga A -1 over 1 - p p the T
+
+ align:start position:0%
+-1 and B isga A -1 over 1 - p p the T
+ 
+
+ align:start position:0%
+-1 and B isga A -1 over 1 - p p the T
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one all right then I plug those back in
+
+ align:start position:0%
+one all right then I plug those back in
+ 
+
+ align:start position:0%
+one all right then I plug those back in
+to the formula for
+
+ align:start position:0%
+to the formula for
+ 
+
+ align:start position:0%
+to the formula for
+xn all right so I take here's my
+
+ align:start position:0%
+xn all right so I take here's my
+ 
+
+ align:start position:0%
+xn all right so I take here's my
+constant a I multiply that times 1 - p
+
+ align:start position:0%
+constant a I multiply that times 1 - p
+ 
+
+ align:start position:0%
+constant a I multiply that times 1 - p
+over P to the N plus I add this in
+
+ align:start position:0%
+over P to the N plus I add this in
+ 
+
+ align:start position:0%
+over P to the N plus I add this in
+all right so this means that the
+
+ align:start position:0%
+all right so this means that the
+ 
+
+ align:start position:0%
+all right so this means that the
+probability of going home a
+
+ align:start position:0%
+probability of going home a
+ 
+
+ align:start position:0%
+probability of going home a
+winner is 1 minus p over P to the
+
+ align:start position:0%
+winner is 1 minus p over P to the
+ 
+
+ align:start position:0%
+winner is 1 minus p over P to the
+N over that thing 1 - p over P to the T
+
+ align:start position:0%
+N over that thing 1 - p over P to the T
+ 
+
+ align:start position:0%
+N over that thing 1 - p over P to the T
+minus 1 plus the B term which really is
+
+ align:start position:0%
+minus 1 plus the B term which really is
+ 
+
+ align:start position:0%
+minus 1 plus the B term which really is
+a minus term here is well it's just
+
+ align:start position:0%
+a minus term here is well it's just
+ 
+
+ align:start position:0%
+a minus term here is well it's just
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one put that on top here
+
+ align:start position:0%
+one put that on top here
+ 
+
+ align:start position:0%
+one put that on top here
+okay now that sort of looks messy
+
+ align:start position:0%
+okay now that sort of looks messy
+ 
+
+ align:start position:0%
+okay now that sort of looks messy
+um but there's a simplification to get
+
+ align:start position:0%
+um but there's a simplification to get
+ 
+
+ align:start position:0%
+um but there's a simplification to get
+an upper bound that's very
+
+ align:start position:0%
+an upper bound that's very
+ 
+
+ align:start position:0%
+an upper bound that's very
+close in particular if you have an bias
+
+ align:start position:0%
+close in particular if you have an bias
+ 
+
+ align:start position:0%
+close in particular if you have an bias
+game against you so if p is less than a
+
+ align:start position:0%
+game against you so if p is less than a
+ 
+
+ align:start position:0%
+game against you so if p is less than a
+half as it is in
+
+ align:start position:0%
+half as it is in
+ 
+
+ align:start position:0%
+half as it is in
+roulette then this is a number bigger
+
+ align:start position:0%
+roulette then this is a number bigger
+ 
+
+ align:start position:0%
+roulette then this is a number bigger
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+one that means that 1 minus p over p is
+
+ align:start position:0%
+one that means that 1 minus p over p is
+ 
+
+ align:start position:0%
+one that means that 1 minus p over p is
+bigger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so this is bigger than one this is
+
+ align:start position:0%
+one so this is bigger than one this is
+ 
+
+ align:start position:0%
+one so this is bigger than one this is
+bigger than one t is the upper limit
+
+ align:start position:0%
+bigger than one t is the upper limit
+ 
+
+ align:start position:0%
+bigger than one t is the upper limit
+it's n plus M so I've got a bigger
+
+ align:start position:0%
+it's n plus M so I've got a bigger
+ 
+
+ align:start position:0%
+it's n plus M so I've got a bigger
+number down here than I do here so I got
+
+ align:start position:0%
+number down here than I do here so I got
+ 
+
+ align:start position:0%
+number down here than I do here so I got
+an overall it's a fraction less than one
+
+ align:start position:0%
+an overall it's a fraction less than one
+ 
+
+ align:start position:0%
+an overall it's a fraction less than one
+and when you have a fraction less than
+
+ align:start position:0%
+and when you have a fraction less than
+ 
+
+ align:start position:0%
+and when you have a fraction less than
+one if you add one to the numerator and
+
+ align:start position:0%
+one if you add one to the numerator and
+ 
+
+ align:start position:0%
+one if you add one to the numerator and
+the denominator it gets closer to one
+
+ align:start position:0%
+the denominator it gets closer to one
+ 
+
+ align:start position:0%
+the denominator it gets closer to one
+gets
+
+ align:start position:0%
+gets
+ 
+
+ align:start position:0%
+gets
+bigger all right so this is upper
+
+ align:start position:0%
+bigger all right so this is upper
+ 
+
+ align:start position:0%
+bigger all right so this is upper
+bounded by just adding one to each of
+
+ align:start position:0%
+bounded by just adding one to each of
+ 
+
+ align:start position:0%
+bounded by just adding one to each of
+these it's upper bounded by this over
+
+ align:start position:0%
+these it's upper bounded by this over
+ 
+
+ align:start position:0%
+these it's upper bounded by this over
+that which is 1us p/ P to the N minus
+
+ align:start position:0%
+that which is 1us p/ P to the N minus
+ 
+
+ align:start position:0%
+that which is 1us p/ P to the N minus
+t and t is just n plus M so this
+
+ align:start position:0%
+t and t is just n plus M so this
+ 
+
+ align:start position:0%
+t and t is just n plus M so this
+equals well why don't I turn it upside
+
+ align:start position:0%
+equals well why don't I turn it upside
+ 
+
+ align:start position:0%
+equals well why don't I turn it upside
+down make it P over 1 minus P to get a
+
+ align:start position:0%
+down make it P over 1 minus P to get a
+ 
+
+ align:start position:0%
+down make it P over 1 minus P to get a
+fraction it's less than one T minus n
+
+ align:start position:0%
+fraction it's less than one T minus n
+ 
+
+ align:start position:0%
+fraction it's less than one T minus n
+and that equals p over 1 minus P to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m and this is how much you're trying to
+
+ align:start position:0%
+m and this is how much you're trying to
+ 
+
+ align:start position:0%
+m and this is how much you're trying to
+get ahead $100 in the case of my
+
+ align:start position:0%
+get ahead $100 in the case of my
+ 
+
+ align:start position:0%
+get ahead $100 in the case of my
+mother-in-law
+
+ align:start position:0%
+mother-in-law
+ 
+
+ align:start position:0%
+mother-in-law
+say okay so what we've proved let me
+
+ align:start position:0%
+say okay so what we've proved let me
+ 
+
+ align:start position:0%
+say okay so what we've proved let me
+State what we've proved is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem so we prove
+
+ align:start position:0%
+theorem so we prove
+ 
+
+ align:start position:0%
+theorem so we prove
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if p is less than a half if you're
+
+ align:start position:0%
+if p is less than a half if you're
+ 
+
+ align:start position:0%
+if p is less than a half if you're
+likely to more likely to lose a bet than
+
+ align:start position:0%
+likely to more likely to lose a bet than
+ 
+
+ align:start position:0%
+likely to more likely to lose a bet than
+win
+
+ align:start position:0%
+win
+ 
+
+ align:start position:0%
+win
+it then the
+
+ align:start position:0%
+it then the
+ 
+
+ align:start position:0%
+it then the
+probability that you win
+
+ align:start position:0%
+probability that you win
+ 
+
+ align:start position:0%
+probability that you win
+MLL before you lose
+
+ align:start position:0%
+MLL before you lose
+ 
+
+ align:start position:0%
+MLL before you lose
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+dollars is at most p over 1 minus P to
+
+ align:start position:0%
+dollars is at most p over 1 minus P to
+ 
+
+ align:start position:0%
+dollars is at most p over 1 minus P to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+m that's what we just
+
+ align:start position:0%
+m that's what we just
+ 
+
+ align:start position:0%
+m that's what we just
+proved
+
+ align:start position:0%
+proved
+ 
+
+ align:start position:0%
+proved
+and so now you can plug in values for
+
+ align:start position:0%
+and so now you can plug in values for
+ 
+
+ align:start position:0%
+and so now you can plug in values for
+example for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roulette P equal
+
+ align:start position:0%
+roulette P equal
+ 
+
+ align:start position:0%
+roulette P equal
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+9/19 which means that P over 1 minus
+
+ align:start position:0%
+9/19 which means that P over 1 minus
+ 
+
+ align:start position:0%
+9/19 which means that P over 1 minus
+P well that's going to be
+
+ align:start position:0%
+P well that's going to be
+ 
+
+ align:start position:0%
+P well that's going to be
+9/9 over
+
+ align:start position:0%
+9/9 over
+ 
+
+ align:start position:0%
+9/9 over
+109 which is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9/10 all right and if M the amount you
+
+ align:start position:0%
+9/10 all right and if M the amount you
+ 
+
+ align:start position:0%
+9/10 all right and if M the amount you
+want to win is $100
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and N is $1,000 that's what you start
+
+ align:start position:0%
+and N is $1,000 that's what you start
+ 
+
+ align:start position:0%
+and N is $1,000 that's what you start
+with and are you're willing to
+
+ align:start position:0%
+with and are you're willing to
+ 
+
+ align:start position:0%
+with and are you're willing to
+lose well the probability you win you go
+
+ align:start position:0%
+lose well the probability you win you go
+ 
+
+ align:start position:0%
+lose well the probability you win you go
+home
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happy that you w star or that you win
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$100 is less than or equal to
+
+ align:start position:0%
+$100 is less than or equal to
+ 
+
+ align:start position:0%
+$100 is less than or equal to
+9/10 raised to the m which is
+
+ align:start position:0%
+9/10 raised to the m which is
+ 
+
+ align:start position:0%
+9/10 raised to the m which is
+100 so it's 9/10 to the 100 and that
+
+ align:start position:0%
+100 so it's 9/10 to the 100 and that
+ 
+
+ align:start position:0%
+100 so it's 9/10 to the 100 and that
+turns out to be less than one and 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+7,648 which is where that answer came
+
+ align:start position:0%
+7,648 which is where that answer came
+ 
+
+ align:start position:0%
+7,648 which is where that answer came
+from now you can see why my
+
+ align:start position:0%
+from now you can see why my
+ 
+
+ align:start position:0%
+from now you can see why my
+mother-in-law may have gotten lost
+
+ align:start position:0%
+mother-in-law may have gotten lost
+ 
+
+ align:start position:0%
+mother-in-law may have gotten lost
+somewhere here you know in the
+
+ align:start position:0%
+somewhere here you know in the
+ 
+
+ align:start position:0%
+somewhere here you know in the
+calculations but this is a proof that
+
+ align:start position:0%
+calculations but this is a proof that
+ 
+
+ align:start position:0%
+calculations but this is a proof that
+the chance you win a 100 bucks before
+
+ align:start position:0%
+the chance you win a 100 bucks before
+ 
+
+ align:start position:0%
+the chance you win a 100 bucks before
+you lose a th000 bucks is is very very
+
+ align:start position:0%
+you lose a th000 bucks is is very very
+ 
+
+ align:start position:0%
+you lose a th000 bucks is is very very
+small now do you see why the answer is
+
+ align:start position:0%
+small now do you see why the answer is
+ 
+
+ align:start position:0%
+small now do you see why the answer is
+no better than if you came with a
+
+ align:start position:0%
+no better than if you came with a
+ 
+
+ align:start position:0%
+no better than if you came with a
+million dollars in your
+
+ align:start position:0%
+million dollars in your
+ 
+
+ align:start position:0%
+million dollars in your
+pocket say you came with n equals a
+
+ align:start position:0%
+pocket say you came with n equals a
+ 
+
+ align:start position:0%
+pocket say you came with n equals a
+million
+
+ align:start position:0%
+million
+ 
+
+ align:start position:0%
+million
+dollars why is the answer not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changing yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you're already in a really deep
+
+ align:start position:0%
+yeah you're already in a really deep
+ 
+
+ align:start position:0%
+yeah you're already in a really deep
+hole Ah that's the intuition that's
+
+ align:start position:0%
+hole Ah that's the intuition that's
+ 
+
+ align:start position:0%
+hole Ah that's the intuition that's
+right and we're going to get to that in
+
+ align:start position:0%
+right and we're going to get to that in
+ 
+
+ align:start position:0%
+right and we're going to get to that in
+a minute I want to know from the
+
+ align:start position:0%
+a minute I want to know from the
+ 
+
+ align:start position:0%
+a minute I want to know from the
+formula why is it no difference if I
+
+ align:start position:0%
+formula why is it no difference if I
+ 
+
+ align:start position:0%
+formula why is it no difference if I
+come with thousand versus a million
+
+ align:start position:0%
+come with thousand versus a million
+ 
+
+ align:start position:0%
+come with thousand versus a million
+dollars
+
+ align:start position:0%
+dollars
+ 
+
+ align:start position:0%
+dollars
+yeah yeah the formula has nothing to do
+
+ align:start position:0%
+yeah yeah the formula has nothing to do
+ 
+
+ align:start position:0%
+yeah yeah the formula has nothing to do
+with end you could come with A1 trillion
+
+ align:start position:0%
+with end you could come with A1 trillion
+ 
+
+ align:start position:0%
+with end you could come with A1 trillion
+dollar in your
+
+ align:start position:0%
+dollar in your
+ 
+
+ align:start position:0%
+dollar in your
+wallet and it doesn't improve this bound
+
+ align:start position:0%
+wallet and it doesn't improve this bound
+ 
+
+ align:start position:0%
+wallet and it doesn't improve this bound
+this bound only depends on what you're
+
+ align:start position:0%
+this bound only depends on what you're
+ 
+
+ align:start position:0%
+this bound only depends on what you're
+trying to win not on how much you came
+
+ align:start position:0%
+trying to win not on how much you came
+ 
+
+ align:start position:0%
+trying to win not on how much you came
+with so no matter how much you come with
+
+ align:start position:0%
+with so no matter how much you come with
+ 
+
+ align:start position:0%
+with so no matter how much you come with
+the chance you win a 100 bucks before
+
+ align:start position:0%
+the chance you win a 100 bucks before
+ 
+
+ align:start position:0%
+the chance you win a 100 bucks before
+you lose everything is at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+137,000 now we can plug in some other
+
+ align:start position:0%
+137,000 now we can plug in some other
+ 
+
+ align:start position:0%
+137,000 now we can plug in some other
+values just for
+
+ align:start position:0%
+values just for
+ 
+
+ align:start position:0%
+values just for
+fun you know different values of M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know if you thought 1 and 37,000 was
+
+ align:start position:0%
+you know if you thought 1 and 37,000 was
+ 
+
+ align:start position:0%
+you know if you thought 1 and 37,000 was
+unlikely the chance of winning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$1,000 or a th000 bets
+
+ align:start position:0%
+$1,000 or a th000 bets
+ 
+
+ align:start position:0%
+$1,000 or a th000 bets
+worth before you're broke well that's
+
+ align:start position:0%
+worth before you're broke well that's
+ 
+
+ align:start position:0%
+worth before you're broke well that's
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+9/10 to the
+
+ align:start position:0%
+9/10 to the
+ 
+
+ align:start position:0%
+9/10 to the
+Thousand that's less
+
+ align:start position:0%
+Thousand that's less
+ 
+
+ align:start position:0%
+Thousand that's less
+than 2 * 10-
+
+ align:start position:0%
+than 2 * 10-
+ 
+
+ align:start position:0%
+than 2 * 10-
+46 really really really unlikely even
+
+ align:start position:0%
+46 really really really unlikely even
+ 
+
+ align:start position:0%
+46 really really really unlikely even
+winning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$10 is not
+
+ align:start position:0%
+$10 is not
+ 
+
+ align:start position:0%
+$10 is not
+likely this just plug in the numbers
+
+ align:start position:0%
+likely this just plug in the numbers
+ 
+
+ align:start position:0%
+likely this just plug in the numbers
+probability you win $10 betting a dollar
+
+ align:start position:0%
+probability you win $10 betting a dollar
+ 
+
+ align:start position:0%
+probability you win $10 betting a dollar
+at a
+
+ align:start position:0%
+at a
+ 
+
+ align:start position:0%
+at a
+time is less than 9/10 to the 10th
+
+ align:start position:0%
+time is less than 9/10 to the 10th
+ 
+
+ align:start position:0%
+time is less than 9/10 to the 10th
+power that's less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+35 you can come to the casino with $10
+
+ align:start position:0%
+35 you can come to the casino with $10
+ 
+
+ align:start position:0%
+35 you can come to the casino with $10
+million bet a dollar at a
+
+ align:start position:0%
+million bet a dollar at a
+ 
+
+ align:start position:0%
+million bet a dollar at a
+time and you quit if you just get up 10
+
+ align:start position:0%
+time and you quit if you just get up 10
+ 
+
+ align:start position:0%
+time and you quit if you just get up 10
+bets get up $10 the chance you get up
+
+ align:start position:0%
+bets get up $10 the chance you get up
+ 
+
+ align:start position:0%
+bets get up $10 the chance you get up
+$10 before you lose 10 million how about
+
+ align:start position:0%
+$10 before you lose 10 million how about
+ 
+
+ align:start position:0%
+$10 before you lose 10 million how about
+one and three you're twice as likely to
+
+ align:start position:0%
+one and three you're twice as likely to
+ 
+
+ align:start position:0%
+one and three you're twice as likely to
+lose $10 million as you are to win 10
+
+ align:start position:0%
+lose $10 million as you are to win 10
+ 
+
+ align:start position:0%
+lose $10 million as you are to win 10
+that just weird right because it's
+
+ align:start position:0%
+that just weird right because it's
+ 
+
+ align:start position:0%
+that just weird right because it's
+almost a fair game it's almost 50/50 any
+
+ align:start position:0%
+almost a fair game it's almost 50/50 any
+ 
+
+ align:start position:0%
+almost a fair game it's almost 50/50 any
+questions about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis that's I don't I find that
+
+ align:start position:0%
+analysis that's I don't I find that
+ 
+
+ align:start position:0%
+analysis that's I don't I find that
+shocking right you know just the
+
+ align:start position:0%
+shocking right you know just the
+ 
+
+ align:start position:0%
+shocking right you know just the
+intuition would seem to say otherwise so
+
+ align:start position:0%
+intuition would seem to say otherwise so
+ 
+
+ align:start position:0%
+intuition would seem to say otherwise so
+I guess there's a moral here if you're
+
+ align:start position:0%
+I guess there's a moral here if you're
+ 
+
+ align:start position:0%
+I guess there's a moral here if you're
+going to gamble learn how to count cards
+
+ align:start position:0%
+going to gamble learn how to count cards
+ 
+
+ align:start position:0%
+going to gamble learn how to count cards
+in blackjack or some game where you can
+
+ align:start position:0%
+in blackjack or some game where you can
+ 
+
+ align:start position:0%
+in blackjack or some game where you can
+make it even because even in a game
+
+ align:start position:0%
+make it even because even in a game
+ 
+
+ align:start position:0%
+make it even because even in a game
+where it's pretty close you're doomed
+
+ align:start position:0%
+where it's pretty close you're doomed
+ 
+
+ align:start position:0%
+where it's pretty close you're doomed
+you know you're just never going to go
+
+ align:start position:0%
+you know you're just never going to go
+ 
+
+ align:start position:0%
+you know you're just never going to go
+home
+
+ align:start position:0%
+home
+ 
+
+ align:start position:0%
+home
+happy all right now if you can have a
+
+ align:start position:0%
+happy all right now if you can have a
+ 
+
+ align:start position:0%
+happy all right now if you can have a
+fair game the world changes much better
+
+ align:start position:0%
+fair game the world changes much better
+ 
+
+ align:start position:0%
+fair game the world changes much better
+circumstance so actually let's do this
+
+ align:start position:0%
+circumstance so actually let's do this
+ 
+
+ align:start position:0%
+circumstance so actually let's do this
+same analysis for a fair game because
+
+ align:start position:0%
+same analysis for a fair game because
+ 
+
+ align:start position:0%
+same analysis for a fair game because
+that's where our intuition really comes
+
+ align:start position:0%
+that's where our intuition really comes
+ 
+
+ align:start position:0%
+that's where our intuition really comes
+from because we're thinking of this game
+
+ align:start position:0%
+from because we're thinking of this game
+ 
+
+ align:start position:0%
+from because we're thinking of this game
+as almost fair and in a fair game the
+
+ align:start position:0%
+as almost fair and in a fair game the
+ 
+
+ align:start position:0%
+as almost fair and in a fair game the
+answer is going to be very different and
+
+ align:start position:0%
+answer is going to be very different and
+ 
+
+ align:start position:0%
+answer is going to be very different and
+it all goes back to the recurrence and
+
+ align:start position:0%
+it all goes back to the recurrence and
+ 
+
+ align:start position:0%
+it all goes back to the recurrence and
+the roots of the characteristic equation
+
+ align:start position:0%
+the roots of the characteristic equation
+ 
+
+ align:start position:0%
+the roots of the characteristic equation
+because in a fair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game p is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half and then you have a double root 1 -
+
+ align:start position:0%
+half and then you have a double root 1 -
+ 
+
+ align:start position:0%
+half and then you have a double root 1 -
+a half over half equals 1 and that means
+
+ align:start position:0%
+a half over half equals 1 and that means
+ 
+
+ align:start position:0%
+a half over half equals 1 and that means
+a double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+root at
+
+ align:start position:0%
+root at
+ 
+
+ align:start position:0%
+root at
+one and that changes everything so let's
+
+ align:start position:0%
+one and that changes everything so let's
+ 
+
+ align:start position:0%
+one and that changes everything so let's
+let's go through now and do all this
+
+ align:start position:0%
+let's go through now and do all this
+ 
+
+ align:start position:0%
+let's go through now and do all this
+analysis uh in the case of a fair
+
+ align:start position:0%
+analysis uh in the case of a fair
+ 
+
+ align:start position:0%
+analysis uh in the case of a fair
+game and this will give us practice with
+
+ align:start position:0%
+game and this will give us practice with
+ 
+
+ align:start position:0%
+game and this will give us practice with
+double roots and recurrences because as
+
+ align:start position:0%
+double roots and recurrences because as
+ 
+
+ align:start position:0%
+double roots and recurrences because as
+you see now it does
+
+ align:start position:0%
+you see now it does
+ 
+
+ align:start position:0%
+you see now it does
+happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's figure out the chance that we go
+
+ align:start position:0%
+let's figure out the chance that we go
+ 
+
+ align:start position:0%
+let's figure out the chance that we go
+home a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+winner okay so let's see in this case we
+
+ align:start position:0%
+winner okay so let's see in this case we
+ 
+
+ align:start position:0%
+winner okay so let's see in this case we
+know the
+
+ align:start position:0%
+know the
+ 
+
+ align:start position:0%
+know the
+roots can anybody tell me what formula
+
+ align:start position:0%
+roots can anybody tell me what formula
+ 
+
+ align:start position:0%
+roots can anybody tell me what formula
+we're going to use for the
+
+ align:start position:0%
+we're going to use for the
+ 
+
+ align:start position:0%
+we're going to use for the
+solution got a double root at one so
+
+ align:start position:0%
+solution got a double root at one so
+ 
+
+ align:start position:0%
+solution got a double root at one so
+there's going to be a one to the end
+
+ align:start position:0%
+there's going to be a one to the end
+ 
+
+ align:start position:0%
+there's going to be a one to the end
+here I don't just put a constant a in
+
+ align:start position:0%
+here I don't just put a constant a in
+ 
+
+ align:start position:0%
+here I don't just put a constant a in
+front what do I do with a double
+
+ align:start position:0%
+front what do I do with a double
+ 
+
+ align:start position:0%
+front what do I do with a double
+root what is it n a n not quite a n you
+
+ align:start position:0%
+root what is it n a n not quite a n you
+ 
+
+ align:start position:0%
+root what is it n a n not quite a n you
+got an A N
+
+ align:start position:0%
+got an A N
+ 
+
+ align:start position:0%
+got an A N
+here plus b that's what you do for a
+
+ align:start position:0%
+here plus b that's what you do for a
+ 
+
+ align:start position:0%
+here plus b that's what you do for a
+double root because you you make a
+
+ align:start position:0%
+double root because you you make a
+ 
+
+ align:start position:0%
+double root because you you make a
+first-degree polinomial in N here so we
+
+ align:start position:0%
+first-degree polinomial in N here so we
+ 
+
+ align:start position:0%
+first-degree polinomial in N here so we
+plug that in the roots at one so it's
+
+ align:start position:0%
+plug that in the roots at one so it's
+ 
+
+ align:start position:0%
+plug that in the roots at one so it's
+really easy the solution is really easy
+
+ align:start position:0%
+really easy the solution is really easy
+ 
+
+ align:start position:0%
+really easy the solution is really easy
+now no messy powers or anything it's
+
+ align:start position:0%
+now no messy powers or anything it's
+ 
+
+ align:start position:0%
+now no messy powers or anything it's
+just a n plus
+
+ align:start position:0%
+just a n plus
+ 
+
+ align:start position:0%
+just a n plus
+b and I can figure out a and B from the
+
+ align:start position:0%
+b and I can figure out a and B from the
+ 
+
+ align:start position:0%
+b and I can figure out a and B from the
+boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions all right x0 is
+
+ align:start position:0%
+conditions all right x0 is
+ 
+
+ align:start position:0%
+conditions all right x0 is
+zero x0 is just
+
+ align:start position:0%
+zero x0 is just
+ 
+
+ align:start position:0%
+zero x0 is just
+B because it's a * Z goes away and that
+
+ align:start position:0%
+B because it's a * Z goes away and that
+ 
+
+ align:start position:0%
+B because it's a * Z goes away and that
+means the b equals zero this is getting
+
+ align:start position:0%
+means the b equals zero this is getting
+ 
+
+ align:start position:0%
+means the b equals zero this is getting
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+simple one is
+
+ align:start position:0%
+simple one is
+ 
+
+ align:start position:0%
+simple one is
+XT and that's a plus b but B was zero
+
+ align:start position:0%
+XT and that's a plus b but B was zero
+ 
+
+ align:start position:0%
+XT and that's a plus b but B was zero
+that's a 1 a * 1 + B that's just
+
+ align:start position:0%
+that's a 1 a * 1 + B that's just
+ 
+
+ align:start position:0%
+that's a 1 a * 1 + B that's just
+a it means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aals oh I didn't do that oh a n good n's
+
+ align:start position:0%
+aals oh I didn't do that oh a n good n's
+ 
+
+ align:start position:0%
+aals oh I didn't do that oh a n good n's
+not one n's T so it's a t plus b this is
+
+ align:start position:0%
+not one n's T so it's a t plus b this is
+ 
+
+ align:start position:0%
+not one n's T so it's a t plus b this is
+a t here so a t equals 1 that means a is
+
+ align:start position:0%
+a t here so a t equals 1 that means a is
+ 
+
+ align:start position:0%
+a t here so a t equals 1 that means a is
+1 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T all right that means
+
+ align:start position:0%
+T all right that means
+ 
+
+ align:start position:0%
+T all right that means
+that X
+
+ align:start position:0%
+that X
+ 
+
+ align:start position:0%
+that X
+n is n / T and T is the total the top
+
+ align:start position:0%
+n is n / T and T is the total the top
+ 
+
+ align:start position:0%
+n is n / T and T is the total the top
+limit is n plus M because you quit if
+
+ align:start position:0%
+limit is n plus M because you quit if
+ 
+
+ align:start position:0%
+limit is n plus M because you quit if
+you get ahead M dollars this is just now
+
+ align:start position:0%
+you get ahead M dollars this is just now
+ 
+
+ align:start position:0%
+you get ahead M dollars this is just now
+n over n +
+
+ align:start position:0%
+n over n +
+ 
+
+ align:start position:0%
+n over n +
+m all right
+
+ align:start position:0%
+m all right
+ 
+
+ align:start position:0%
+m all right
+so let's write that down it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem if p is a half right you have a
+
+ align:start position:0%
+theorem if p is a half right you have a
+ 
+
+ align:start position:0%
+theorem if p is a half right you have a
+fair game
+
+ align:start position:0%
+fair game
+ 
+
+ align:start position:0%
+fair game
+then the
+
+ align:start position:0%
+then the
+ 
+
+ align:start position:0%
+then the
+probability you win
+
+ align:start position:0%
+probability you win
+ 
+
+ align:start position:0%
+probability you win
+M before you
+
+ align:start position:0%
+M before you
+ 
+
+ align:start position:0%
+M before you
+lose
+
+ align:start position:0%
+lose
+ 
+
+ align:start position:0%
+lose
+n is just n Over N plus
+
+ align:start position:0%
+n is just n Over N plus
+ 
+
+ align:start position:0%
+n is just n Over N plus
+M and this might fit the intuition
+
+ align:start position:0%
+M and this might fit the intuition
+ 
+
+ align:start position:0%
+M and this might fit the intuition
+better all right so for the
+
+ align:start position:0%
+better all right so for the
+ 
+
+ align:start position:0%
+better all right so for the
+Mother-in-law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strategy if m is 100
+
+ align:start position:0%
+strategy if m is 100
+ 
+
+ align:start position:0%
+strategy if m is 100
+and N is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th what's the probability you win you go
+
+ align:start position:0%
+th what's the probability you win you go
+ 
+
+ align:start position:0%
+th what's the probability you win you go
+home a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+winner
+
+ align:start position:0%
+winner
+ 
+
+ align:start position:0%
+winner
+yeah, over a
+
+ align:start position:0%
+yeah, over a
+ 
+
+ align:start position:0%
+yeah, over a
+th000 plus
+
+ align:start position:0%
+th000 plus
+ 
+
+ align:start position:0%
+th000 plus
+100,000 over 1100 is 10 over
+
+ align:start position:0%
+100,000 over 1100 is 10 over
+ 
+
+ align:start position:0%
+100,000 over 1100 is 10 over
+11 so she does go home happy most of the
+
+ align:start position:0%
+11 so she does go home happy most of the
+ 
+
+ align:start position:0%
+11 so she does go home happy most of the
+time 10 out of 11 Knights if she's
+
+ align:start position:0%
+time 10 out of 11 Knights if she's
+ 
+
+ align:start position:0%
+time 10 out of 11 Knights if she's
+playing a fair
+
+ align:start position:0%
+playing a fair
+ 
+
+ align:start position:0%
+playing a fair
+game all right any
+
+ align:start position:0%
+game all right any
+ 
+
+ align:start position:0%
+game all right any
+questions about that so the trouble we
+
+ align:start position:0%
+questions about that so the trouble we
+ 
+
+ align:start position:0%
+questions about that so the trouble we
+get into
+
+ align:start position:0%
+get into
+ 
+
+ align:start position:0%
+get into
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+that the fair game results match our
+
+ align:start position:0%
+that the fair game results match our
+ 
+
+ align:start position:0%
+that the fair game results match our
+intuition you know if you're 10 times as
+
+ align:start position:0%
+intuition you know if you're 10 times as
+ 
+
+ align:start position:0%
+intuition you know if you're 10 times as
+likely you have 10 times as much money
+
+ align:start position:0%
+likely you have 10 times as much money
+ 
+
+ align:start position:0%
+likely you have 10 times as much money
+in a fair game you'd expect to go home
+
+ align:start position:0%
+in a fair game you'd expect to go home
+ 
+
+ align:start position:0%
+in a fair game you'd expect to go home
+Happy 10 out of 11 nights that makes a
+
+ align:start position:0%
+Happy 10 out of 11 nights that makes a
+ 
+
+ align:start position:0%
+Happy 10 out of 11 nights that makes a
+lot of sense you you go home Happy 10
+
+ align:start position:0%
+lot of sense you you go home Happy 10
+ 
+
+ align:start position:0%
+lot of sense you you go home Happy 10
+and then you lose
+
+ align:start position:0%
+and then you lose
+ 
+
+ align:start position:0%
+and then you lose
+the 11th that's a 10:1 ratio which is
+
+ align:start position:0%
+the 11th that's a 10:1 ratio which is
+ 
+
+ align:start position:0%
+the 11th that's a 10:1 ratio which is
+the money brought into the
+
+ align:start position:0%
+the money brought into the
+ 
+
+ align:start position:0%
+the money brought into the
+game the trouble we get into is the fair
+
+ align:start position:0%
+game the trouble we get into is the fair
+ 
+
+ align:start position:0%
+game the trouble we get into is the fair
+game is very close to the real game
+
+ align:start position:0%
+game is very close to the real game
+ 
+
+ align:start position:0%
+game is very close to the real game
+instead of 5050 it's
+
+ align:start position:0%
+instead of 5050 it's
+ 
+
+ align:start position:0%
+instead of 5050 it's
+4753 and so our intuition says the
+
+ align:start position:0%
+4753 and so our intuition says the
+ 
+
+ align:start position:0%
+4753 and so our intuition says the
+results the probability of going home
+
+ align:start position:0%
+results the probability of going home
+ 
+
+ align:start position:0%
+results the probability of going home
+happy in the fair game should be close
+
+ align:start position:0%
+happy in the fair game should be close
+ 
+
+ align:start position:0%
+happy in the fair game should be close
+to the probability of going home happy
+
+ align:start position:0%
+to the probability of going home happy
+ 
+
+ align:start position:0%
+to the probability of going home happy
+in the real game and that's not true
+
+ align:start position:0%
+in the real game and that's not true
+ 
+
+ align:start position:0%
+in the real game and that's not true
+there's a discontinuity here because of
+
+ align:start position:0%
+there's a discontinuity here because of
+ 
+
+ align:start position:0%
+there's a discontinuity here because of
+the double rout and the character
+
+ align:start position:0%
+the double rout and the character
+ 
+
+ align:start position:0%
+the double rout and the character
+completely changes so instead of being
+
+ align:start position:0%
+completely changes so instead of being
+ 
+
+ align:start position:0%
+completely changes so instead of being
+close to 10 out of 11 you're down there
+
+ align:start position:0%
+close to 10 out of 11 you're down there
+ 
+
+ align:start position:0%
+close to 10 out of 11 you're down there
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+137,000 completely different
+
+ align:start position:0%
+137,000 completely different
+ 
+
+ align:start position:0%
+137,000 completely different
+Behavior
+
+ align:start position:0%
+Behavior
+ 
+
+ align:start position:0%
+Behavior
+okay any
+
+ align:start position:0%
+okay any
+ 
+
+ align:start position:0%
+okay any
+questions all right so let me give you
+
+ align:start position:0%
+questions all right so let me give you
+ 
+
+ align:start position:0%
+questions all right so let me give you
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+idea like one and then you kind of do
+
+ align:start position:0%
+idea like one and then you kind of do
+ 
+
+ align:start position:0%
+idea like one and then you kind of do
+that repeatedly ah now if I did m equal
+
+ align:start position:0%
+that repeatedly ah now if I did m equal
+ 
+
+ align:start position:0%
+that repeatedly ah now if I did m equal
+1 I could use that as enough for bound
+
+ align:start position:0%
+1 I could use that as enough for bound
+ 
+
+ align:start position:0%
+1 I could use that as enough for bound
+and it's not so interesting but say 90%
+
+ align:start position:0%
+and it's not so interesting but say 90%
+ 
+
+ align:start position:0%
+and it's not so interesting but say 90%
+um but I would actually go plug it back
+
+ align:start position:0%
+um but I would actually go plug it back
+ 
+
+ align:start position:0%
+um but I would actually go plug it back
+in here so this would be n plus one and
+
+ align:start position:0%
+in here so this would be n plus one and
+ 
+
+ align:start position:0%
+in here so this would be n plus one and
+it would depend how much money I brought
+
+ align:start position:0%
+it would depend how much money I brought
+ 
+
+ align:start position:0%
+it would depend how much money I brought
+but there is a pretty good chance I go
+
+ align:start position:0%
+but there is a pretty good chance I go
+ 
+
+ align:start position:0%
+but there is a pretty good chance I go
+home a winner for n equals one oh sorry
+
+ align:start position:0%
+home a winner for n equals one oh sorry
+ 
+
+ align:start position:0%
+home a winner for n equals one oh sorry
+m equals one right because I got a
+
+ align:start position:0%
+m equals one right because I got a
+ 
+
+ align:start position:0%
+m equals one right because I got a
+pretty good chance that I either 47%
+
+ align:start position:0%
+pretty good chance that I either 47%
+ 
+
+ align:start position:0%
+pretty good chance that I either 47%
+chance I win the first time then I go
+
+ align:start position:0%
+chance I win the first time then I go
+ 
+
+ align:start position:0%
+chance I win the first time then I go
+home happy if I lost the first time now
+
+ align:start position:0%
+home happy if I lost the first time now
+ 
+
+ align:start position:0%
+home happy if I lost the first time now
+I just got to win twice and I might win
+
+ align:start position:0%
+I just got to win twice and I might win
+ 
+
+ align:start position:0%
+I just got to win twice and I might win
+twice in a row that'll happen about 20%
+
+ align:start position:0%
+twice in a row that'll happen about 20%
+ 
+
+ align:start position:0%
+twice in a row that'll happen about 20%
+of the time if I lose that I I got to
+
+ align:start position:0%
+of the time if I lose that I I got to
+ 
+
+ align:start position:0%
+of the time if I lose that I I got to
+win three in a row that'll happen around
+
+ align:start position:0%
+win three in a row that'll happen around
+ 
+
+ align:start position:0%
+win three in a row that'll happen around
+10% of the time so I got 10 plus 20 plus
+
+ align:start position:0%
+10% of the time so I got 10 plus 20 plus
+ 
+
+ align:start position:0%
+10% of the time so I got 10 plus 20 plus
+almost 50 most of the time I'm going to
+
+ align:start position:0%
+almost 50 most of the time I'm going to
+ 
+
+ align:start position:0%
+almost 50 most of the time I'm going to
+go home happy if I just have to get
+
+ align:start position:0%
+go home happy if I just have to get
+ 
+
+ align:start position:0%
+go home happy if I just have to get
+ahead by
+
+ align:start position:0%
+ahead by
+ 
+
+ align:start position:0%
+ahead by
+one but it doesn't take much more than
+
+ align:start position:0%
+one but it doesn't take much more than
+ 
+
+ align:start position:0%
+one but it doesn't take much more than
+one before you're not likely to go home
+
+ align:start position:0%
+one before you're not likely to go home
+ 
+
+ align:start position:0%
+one before you're not likely to go home
+Happy getting a head 10 is not going to
+
+ align:start position:0%
+Happy getting a head 10 is not going to
+ 
+
+ align:start position:0%
+Happy getting a head 10 is not going to
+happen very likely now you want to
+
+ align:start position:0%
+happen very likely now you want to
+ 
+
+ align:start position:0%
+happen very likely now you want to
+recurse on
+
+ align:start position:0%
+recurse on
+ 
+
+ align:start position:0%
+recurse on
+that you know I'm pretty likely to get
+
+ align:start position:0%
+that you know I'm pretty likely to get
+ 
+
+ align:start position:0%
+that you know I'm pretty likely to get
+head by
+
+ align:start position:0%
+head by
+ 
+
+ align:start position:0%
+head by
+one well okay get ahead by one now I'm
+
+ align:start position:0%
+one well okay get ahead by one now I'm
+ 
+
+ align:start position:0%
+one well okay get ahead by one now I'm
+pretty likely to do it again all right I
+
+ align:start position:0%
+pretty likely to do it again all right I
+ 
+
+ align:start position:0%
+pretty likely to do it again all right I
+did it again now I'm pretty likely to do
+
+ align:start position:0%
+did it again now I'm pretty likely to do
+ 
+
+ align:start position:0%
+did it again now I'm pretty likely to do
+it again and there's this thing called
+
+ align:start position:0%
+it again and there's this thing called
+ 
+
+ align:start position:0%
+it again and there's this thing called
+induction that we worried a lot about so
+
+ align:start position:0%
+induction that we worried a lot about so
+ 
+
+ align:start position:0%
+induction that we worried a lot about so
+by induction we're likely to go home
+
+ align:start position:0%
+by induction we're likely to go home
+ 
+
+ align:start position:0%
+by induction we're likely to go home
+happy with 10 no no because every time
+
+ align:start position:0%
+happy with 10 no no because every time
+ 
+
+ align:start position:0%
+happy with 10 no no because every time
+you don't get there you're dead right so
+
+ align:start position:0%
+you don't get there you're dead right so
+ 
+
+ align:start position:0%
+you don't get there you're dead right so
+you had a little chance of dying and not
+
+ align:start position:0%
+you had a little chance of dying and not
+ 
+
+ align:start position:0%
+you had a little chance of dying and not
+reaching one and a little chance of
+
+ align:start position:0%
+reaching one and a little chance of
+ 
+
+ align:start position:0%
+reaching one and a little chance of
+dying and not going from one to two and
+
+ align:start position:0%
+dying and not going from one to two and
+ 
+
+ align:start position:0%
+dying and not going from one to two and
+you add up all those chances of dying
+
+ align:start position:0%
+you add up all those chances of dying
+ 
+
+ align:start position:0%
+you add up all those chances of dying
+and your toast because that'll be adding
+
+ align:start position:0%
+and your toast because that'll be adding
+ 
+
+ align:start position:0%
+and your toast because that'll be adding
+up to everything pretty
+
+ align:start position:0%
+up to everything pretty
+ 
+
+ align:start position:0%
+up to everything pretty
+much all right so that's a good question
+
+ align:start position:0%
+much all right so that's a good question
+ 
+
+ align:start position:0%
+much all right so that's a good question
+if you're likely to win get up by one
+
+ align:start position:0%
+if you're likely to win get up by one
+ 
+
+ align:start position:0%
+if you're likely to win get up by one
+why aren't you likely to get up by 10
+
+ align:start position:0%
+why aren't you likely to get up by 10
+ 
+
+ align:start position:0%
+why aren't you likely to get up by 10
+yeah it doesn't work that way that's a
+
+ align:start position:0%
+yeah it doesn't work that way that's a
+ 
+
+ align:start position:0%
+yeah it doesn't work that way that's a
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+question let me show you the phenomenon
+
+ align:start position:0%
+question let me show you the phenomenon
+ 
+
+ align:start position:0%
+question let me show you the phenomenon
+that's going on
+
+ align:start position:0%
+that's going on
+ 
+
+ align:start position:0%
+that's going on
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh as to why it works out this way when
+
+ align:start position:0%
+uh as to why it works out this way when
+ 
+
+ align:start position:0%
+uh as to why it works out this way when
+we had the math so we looked at it that
+
+ align:start position:0%
+we had the math so we looked at it that
+ 
+
+ align:start position:0%
+we had the math so we looked at it that
+way and we noticed that one case is a
+
+ align:start position:0%
+way and we noticed that one case is a
+ 
+
+ align:start position:0%
+way and we noticed that one case is a
+double root and the other case isn't and
+
+ align:start position:0%
+double root and the other case isn't and
+ 
+
+ align:start position:0%
+double root and the other case isn't and
+that exponential in the case where you
+
+ align:start position:0%
+that exponential in the case where you
+ 
+
+ align:start position:0%
+that exponential in the case where you
+didn't have that second root at one
+
+ align:start position:0%
+didn't have that second root at one
+ 
+
+ align:start position:0%
+didn't have that second root at one
+makes an enormous difference
+
+ align:start position:0%
+makes an enormous difference
+ 
+
+ align:start position:0%
+makes an enormous difference
+you know qualitatively we can draw the
+
+ align:start position:0%
+you know qualitatively we can draw the
+ 
+
+ align:start position:0%
+you know qualitatively we can draw the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+cases so in the case of an unbiased or
+
+ align:start position:0%
+cases so in the case of an unbiased or
+ 
+
+ align:start position:0%
+cases so in the case of an unbiased or
+fair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game if we track what's going on over
+
+ align:start position:0%
+game if we track what's going on over
+ 
+
+ align:start position:0%
+game if we track what's going on over
+time and we start with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nll sort of this is our
+
+ align:start position:0%
+nll sort of this is our
+ 
+
+ align:start position:0%
+nll sort of this is our
+Baseline and here's our Target T is n
+
+ align:start position:0%
+Baseline and here's our Target T is n
+ 
+
+ align:start position:0%
+Baseline and here's our Target T is n
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+M and so we quit if we ever get here and
+
+ align:start position:0%
+M and so we quit if we ever get here and
+ 
+
+ align:start position:0%
+M and so we quit if we ever get here and
+we quit if we ever hit the bottom and we
+
+ align:start position:0%
+we quit if we ever hit the bottom and we
+ 
+
+ align:start position:0%
+we quit if we ever hit the bottom and we
+got a random walk you know it's going
+
+ align:start position:0%
+got a random walk you know it's going
+ 
+
+ align:start position:0%
+got a random walk you know it's going
+around you know there's just doing this
+
+ align:start position:0%
+around you know there's just doing this
+ 
+
+ align:start position:0%
+around you know there's just doing this
+kind of stuff and eventually it's going
+
+ align:start position:0%
+kind of stuff and eventually it's going
+ 
+
+ align:start position:0%
+kind of stuff and eventually it's going
+to hit one of these
+
+ align:start position:0%
+to hit one of these
+ 
+
+ align:start position:0%
+to hit one of these
+boundaries and if we're if m is small
+
+ align:start position:0%
+boundaries and if we're if m is small
+ 
+
+ align:start position:0%
+boundaries and if we're if m is small
+compared to
+
+ align:start position:0%
+compared to
+ 
+
+ align:start position:0%
+compared to
+n we're more likely to hit this boundary
+
+ align:start position:0%
+n we're more likely to hit this boundary
+ 
+
+ align:start position:0%
+n we're more likely to hit this boundary
+and in fact the chance we hit this
+
+ align:start position:0%
+and in fact the chance we hit this
+ 
+
+ align:start position:0%
+and in fact the chance we hit this
+boundary first is the like the ratio of
+
+ align:start position:0%
+boundary first is the like the ratio of
+ 
+
+ align:start position:0%
+boundary first is the like the ratio of
+these sizes it's n over the total is a
+
+ align:start position:0%
+these sizes it's n over the total is a
+ 
+
+ align:start position:0%
+these sizes it's n over the total is a
+chance that we hit that one
+
+ align:start position:0%
+chance that we hit that one
+ 
+
+ align:start position:0%
+chance that we hit that one
+first now in the bias
+
+ align:start position:0%
+first now in the bias
+ 
+
+ align:start position:0%
+first now in the bias
+case picture looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different so in the bias case
+
+ align:start position:0%
+different so in the bias case
+ 
+
+ align:start position:0%
+different so in the bias case
+draw it
+
+ align:start position:0%
+draw it
+ 
+
+ align:start position:0%
+draw it
+here so this is now
+
+ align:start position:0%
+here so this is now
+ 
+
+ align:start position:0%
+here so this is now
+biased and we're going to assume it's
+
+ align:start position:0%
+biased and we're going to assume it's
+ 
+
+ align:start position:0%
+biased and we're going to assume it's
+downward biased you're more likely to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lose so you start at n and you got your
+
+ align:start position:0%
+lose so you start at n and you got your
+ 
+
+ align:start position:0%
+lose so you start at n and you got your
+boundary up here at
+
+ align:start position:0%
+boundary up here at
+ 
+
+ align:start position:0%
+boundary up here at
+tal n plus
+
+ align:start position:0%
+tal n plus
+ 
+
+ align:start position:0%
+tal n plus
+M time is going this
+
+ align:start position:0%
+M time is going this
+ 
+
+ align:start position:0%
+M time is going this
+way the problem is you got
+
+ align:start position:0%
+way the problem is you got
+ 
+
+ align:start position:0%
+way the problem is you got
+a downward sort of
+
+ align:start position:0%
+a downward sort of
+ 
+
+ align:start position:0%
+a downward sort of
+Baseline
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you expect to lose a little bit
+
+ align:start position:0%
+because you expect to lose a little bit
+ 
+
+ align:start position:0%
+because you expect to lose a little bit
+each time and so you're taking these
+
+ align:start position:0%
+each time and so you're taking these
+ 
+
+ align:start position:0%
+each time and so you're taking these
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+walk and you
+
+ align:start position:0%
+walk and you
+ 
+
+ align:start position:0%
+walk and you
+Collide here
+
+ align:start position:0%
+Collide here
+ 
+
+ align:start position:0%
+Collide here
+and these things are known as the the
+
+ align:start position:0%
+and these things are known as the the
+ 
+
+ align:start position:0%
+and these things are known as the the
+swings this is known as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drift and the drift downward is 1 minus
+
+ align:start position:0%
+drift and the drift downward is 1 minus
+ 
+
+ align:start position:0%
+drift and the drift downward is 1 minus
+2p that's what you expect expect to lose
+
+ align:start position:0%
+2p that's what you expect expect to lose
+ 
+
+ align:start position:0%
+2p that's what you expect expect to lose
+if you did the expected loss on each bet
+
+ align:start position:0%
+if you did the expected loss on each bet
+ 
+
+ align:start position:0%
+if you did the expected loss on each bet
+one minus 2p because you're going to not
+
+ align:start position:0%
+one minus 2p because you're going to not
+ 
+
+ align:start position:0%
+one minus 2p because you're going to not
+be a fair game this one has that has
+
+ align:start position:0%
+be a fair game this one has that has
+ 
+
+ align:start position:0%
+be a fair game this one has that has
+zero drift up there it stays steady and
+
+ align:start position:0%
+zero drift up there it stays steady and
+ 
+
+ align:start position:0%
+zero drift up there it stays steady and
+in random
+
+ align:start position:0%
+in random
+ 
+
+ align:start position:0%
+in random
+walks
+
+ align:start position:0%
+walks
+ 
+
+ align:start position:0%
+walks
+drift
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outweighs the
+
+ align:start position:0%
+outweighs the
+ 
+
+ align:start position:0%
+outweighs the
+swings these are the swings here and
+
+ align:start position:0%
+swings these are the swings here and
+ 
+
+ align:start position:0%
+swings these are the swings here and
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+random the drift is deterministic it's
+
+ align:start position:0%
+random the drift is deterministic it's
+ 
+
+ align:start position:0%
+random the drift is deterministic it's
+steadily going down and so almost always
+
+ align:start position:0%
+steadily going down and so almost always
+ 
+
+ align:start position:0%
+steadily going down and so almost always
+in a random walk the drift totally takes
+
+ align:start position:0%
+in a random walk the drift totally takes
+ 
+
+ align:start position:0%
+in a random walk the drift totally takes
+over the swings the swings are small
+
+ align:start position:0%
+over the swings the swings are small
+ 
+
+ align:start position:0%
+over the swings the swings are small
+compared to what you're losing on a
+
+ align:start position:0%
+compared to what you're losing on a
+ 
+
+ align:start position:0%
+compared to what you're losing on a
+steady
+
+ align:start position:0%
+steady
+ 
+
+ align:start position:0%
+steady
+basis all right and that's why the
+
+ align:start position:0%
+basis all right and that's why the
+ 
+
+ align:start position:0%
+basis all right and that's why the
+you're so much more likely to lose when
+
+ align:start position:0%
+you're so much more likely to lose when
+ 
+
+ align:start position:0%
+you're so much more likely to lose when
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+the uh drift
+
+ align:start position:0%
+the uh drift
+ 
+
+ align:start position:0%
+the uh drift
+downward all right just as an example
+
+ align:start position:0%
+downward all right just as an example
+ 
+
+ align:start position:0%
+downward all right just as an example
+maybe putting some numbers around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the swings are the same in both
+
+ align:start position:0%
+that the swings are the same in both
+ 
+
+ align:start position:0%
+that the swings are the same in both
+cases so let's give you a some
+
+ align:start position:0%
+cases so let's give you a some
+ 
+
+ align:start position:0%
+cases so let's give you a some
+qualification for how big the swings
+
+ align:start position:0%
+qualification for how big the swings
+ 
+
+ align:start position:0%
+qualification for how big the swings
+tend to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be and sort of do that with standard
+
+ align:start position:0%
+be and sort of do that with standard
+ 
+
+ align:start position:0%
+be and sort of do that with standard
+deviation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation after X bets or X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps the amount you've drifted or the
+
+ align:start position:0%
+steps the amount you've drifted or the
+ 
+
+ align:start position:0%
+steps the amount you've drifted or the
+expected
+
+ align:start position:0%
+expected
+ 
+
+ align:start position:0%
+expected
+losses 1 minus 2p
+
+ align:start position:0%
+losses 1 minus 2p
+ 
+
+ align:start position:0%
+losses 1 minus 2p
+X and that's maybe we should just
+
+ align:start position:0%
+X and that's maybe we should just
+ 
+
+ align:start position:0%
+X and that's maybe we should just
+understand why this is a case the
+
+ align:start position:0%
+understand why this is a case the
+ 
+
+ align:start position:0%
+understand why this is a case the
+expected return on a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bet is one with probability p and minus
+
+ align:start position:0%
+bet is one with probability p and minus
+ 
+
+ align:start position:0%
+bet is one with probability p and minus
+one with probability one minus
+
+ align:start position:0%
+one with probability one minus
+ 
+
+ align:start position:0%
+one with probability one minus
+p and so that
+
+ align:start position:0%
+p and so that
+ 
+
+ align:start position:0%
+p and so that
+is I get that
+
+ align:start position:0%
+is I get that
+ 
+
+ align:start position:0%
+is I get that
+right I think that's
+
+ align:start position:0%
+right I think that's
+ 
+
+ align:start position:0%
+right I think that's
+right oh is that oh expected loss I'm
+
+ align:start position:0%
+right oh is that oh expected loss I'm
+ 
+
+ align:start position:0%
+right oh is that oh expected loss I'm
+measuring the drift downward instead of
+
+ align:start position:0%
+measuring the drift downward instead of
+ 
+
+ align:start position:0%
+measuring the drift downward instead of
+expected return let's do the loss
+
+ align:start position:0%
+expected return let's do the loss
+ 
+
+ align:start position:0%
+expected return let's do the loss
+because that's the drift as a downward
+
+ align:start position:0%
+because that's the drift as a downward
+ 
+
+ align:start position:0%
+because that's the drift as a downward
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+so the expected loss now you lose a
+
+ align:start position:0%
+so the expected loss now you lose a
+ 
+
+ align:start position:0%
+so the expected loss now you lose a
+dollar with one minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p and you gain a dollar which is
+
+ align:start position:0%
+p and you gain a dollar which is
+ 
+
+ align:start position:0%
+p and you gain a dollar which is
+negative loss with probability
+
+ align:start position:0%
+negative loss with probability
+ 
+
+ align:start position:0%
+negative loss with probability
+p and so you get 1 minus P minus p is 1
+
+ align:start position:0%
+p and so you get 1 minus P minus p is 1
+ 
+
+ align:start position:0%
+p and so you get 1 minus P minus p is 1
+minus 2 p so that's your expected loss
+
+ align:start position:0%
+minus 2 p so that's your expected loss
+ 
+
+ align:start position:0%
+minus 2 p so that's your expected loss
+your expected winnings are the negative
+
+ align:start position:0%
+your expected winnings are the negative
+ 
+
+ align:start position:0%
+your expected winnings are the negative
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+that so after X steps you expect to
+
+ align:start position:0%
+that so after X steps you expect to
+ 
+
+ align:start position:0%
+that so after X steps you expect to
+lose well just add up the linearity of
+
+ align:start position:0%
+lose well just add up the linearity of
+ 
+
+ align:start position:0%
+lose well just add up the linearity of
+expectation you expect to lose this much
+
+ align:start position:0%
+expectation you expect to lose this much
+ 
+
+ align:start position:0%
+expectation you expect to lose this much
+x times so that's your expected drift
+
+ align:start position:0%
+x times so that's your expected drift
+ 
+
+ align:start position:0%
+x times so that's your expected drift
+you've expected to lose that
+
+ align:start position:0%
+you've expected to lose that
+ 
+
+ align:start position:0%
+you've expected to lose that
+much now the swing and we won't prove
+
+ align:start position:0%
+much now the swing and we won't prove
+ 
+
+ align:start position:0%
+much now the swing and we won't prove
+this the swing is expected to be square
+
+ align:start position:0%
+this the swing is expected to be square
+ 
+
+ align:start position:0%
+this the swing is expected to be square
+root of x times a constant so I've used
+
+ align:start position:0%
+root of x times a constant so I've used
+ 
+
+ align:start position:0%
+root of x times a constant so I've used
+the Theta notation here and the constant
+
+ align:start position:0%
+the Theta notation here and the constant
+ 
+
+ align:start position:0%
+the Theta notation here and the constant
+is small if I take X consecutive bets
+
+ align:start position:0%
+is small if I take X consecutive bets
+ 
+
+ align:start position:0%
+is small if I take X consecutive bets
+for a
+
+ align:start position:0%
+for a
+ 
+
+ align:start position:0%
+for a
+dollar I'm very likely to be about
+
+ align:start position:0%
+dollar I'm very likely to be about
+ 
+
+ align:start position:0%
+dollar I'm very likely to be about
+square root of x off of the expected
+
+ align:start position:0%
+square root of x off of the expected
+ 
+
+ align:start position:0%
+square root of x off of the expected
+drift and you can see that this is
+
+ align:start position:0%
+drift and you can see that this is
+ 
+
+ align:start position:0%
+drift and you can see that this is
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+root that is linear so this totally
+
+ align:start position:0%
+root that is linear so this totally
+ 
+
+ align:start position:0%
+root that is linear so this totally
+dominates that so the swings are
+
+ align:start position:0%
+dominates that so the swings are
+ 
+
+ align:start position:0%
+dominates that so the swings are
+generally not enough to save you and so
+
+ align:start position:0%
+generally not enough to save you and so
+ 
+
+ align:start position:0%
+generally not enough to save you and so
+you're just going to cruise downward and
+
+ align:start position:0%
+you're just going to cruise downward and
+ 
+
+ align:start position:0%
+you're just going to cruise downward and
+crash almost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surely okay any
+
+ align:start position:0%
+surely okay any
+ 
+
+ align:start position:0%
+surely okay any
+questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so we figured out the
+
+ align:start position:0%
+okay all right so we figured out the
+ 
+
+ align:start position:0%
+okay all right so we figured out the
+probability of winning MLL before going
+
+ align:start position:0%
+probability of winning MLL before going
+ 
+
+ align:start position:0%
+probability of winning MLL before going
+broke that's that's done with
+
+ align:start position:0%
+broke that's that's done with
+ 
+
+ align:start position:0%
+broke that's that's done with
+um now this means it's logical conclude
+
+ align:start position:0%
+um now this means it's logical conclude
+ 
+
+ align:start position:0%
+um now this means it's logical conclude
+you're likely to go home broke in an
+
+ align:start position:0%
+you're likely to go home broke in an
+ 
+
+ align:start position:0%
+you're likely to go home broke in an
+unfair
+
+ align:start position:0%
+unfair
+ 
+
+ align:start position:0%
+unfair
+game um actually before we do that
+
+ align:start position:0%
+game um actually before we do that
+ 
+
+ align:start position:0%
+game um actually before we do that
+there's one other case we got to rule
+
+ align:start position:0%
+there's one other case we got to rule
+ 
+
+ align:start position:0%
+there's one other case we got to rule
+out we proved you're likely not to go
+
+ align:start position:0%
+out we proved you're likely not to go
+ 
+
+ align:start position:0%
+out we proved you're likely not to go
+home a winner does that necessarily mean
+
+ align:start position:0%
+home a winner does that necessarily mean
+ 
+
+ align:start position:0%
+home a winner does that necessarily mean
+you're likely to go broke I've been
+
+ align:start position:0%
+you're likely to go broke I've been
+ 
+
+ align:start position:0%
+you're likely to go broke I've been
+saying that but is there's some other
+
+ align:start position:0%
+saying that but is there's some other
+ 
+
+ align:start position:0%
+saying that but is there's some other
+thing we should
+
+ align:start position:0%
+thing we should
+ 
+
+ align:start position:0%
+thing we should
+check let one way you might not go home
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broke what is it you don't go home and
+
+ align:start position:0%
+broke what is it you don't go home and
+ 
+
+ align:start position:0%
+broke what is it you don't go home and
+why would you not go
+
+ align:start position:0%
+why would you not go
+ 
+
+ align:start position:0%
+why would you not go
+home yeah playing forever you're playing
+
+ align:start position:0%
+home yeah playing forever you're playing
+ 
+
+ align:start position:0%
+home yeah playing forever you're playing
+forever all right we didn't rule out
+
+ align:start position:0%
+forever all right we didn't rule out
+ 
+
+ align:start position:0%
+forever all right we didn't rule out
+that case that you're playing forever
+
+ align:start position:0%
+that case that you're playing forever
+ 
+
+ align:start position:0%
+that case that you're playing forever
+but it turns out if you did the same
+
+ align:start position:0%
+but it turns out if you did the same
+ 
+
+ align:start position:0%
+but it turns out if you did the same
+analysis you could analyze the
+
+ align:start position:0%
+analysis you could analyze the
+ 
+
+ align:start position:0%
+analysis you could analyze the
+probability of going home broke and when
+
+ align:start position:0%
+probability of going home broke and when
+ 
+
+ align:start position:0%
+probability of going home broke and when
+you add it to the probabil of going home
+
+ align:start position:0%
+you add it to the probabil of going home
+ 
+
+ align:start position:0%
+you add it to the probabil of going home
+a winner it adds to one which means the
+
+ align:start position:0%
+a winner it adds to one which means the
+ 
+
+ align:start position:0%
+a winner it adds to one which means the
+probability of playing forever is
+
+ align:start position:0%
+probability of playing forever is
+ 
+
+ align:start position:0%
+probability of playing forever is
+zero now there are sample points where
+
+ align:start position:0%
+zero now there are sample points where
+ 
+
+ align:start position:0%
+zero now there are sample points where
+you play forever but when you add up all
+
+ align:start position:0%
+you play forever but when you add up all
+ 
+
+ align:start position:0%
+you play forever but when you add up all
+those sample points if their probability
+
+ align:start position:0%
+those sample points if their probability
+ 
+
+ align:start position:0%
+those sample points if their probability
+is zero we ignore them and we say it
+
+ align:start position:0%
+is zero we ignore them and we say it
+ 
+
+ align:start position:0%
+is zero we ignore them and we say it
+can't happen now we're bordering on
+
+ align:start position:0%
+can't happen now we're bordering on
+ 
+
+ align:start position:0%
+can't happen now we're bordering on
+philosophy here okay because there is a
+
+ align:start position:0%
+philosophy here okay because there is a
+ 
+
+ align:start position:0%
+philosophy here okay because there is a
+sample point you could win lose win lose
+
+ align:start position:0%
+sample point you could win lose win lose
+ 
+
+ align:start position:0%
+sample point you could win lose win lose
+win lose forever but because you add
+
+ align:start position:0%
+win lose forever but because you add
+ 
+
+ align:start position:0%
+win lose forever but because you add
+them all up at zero measure Theory and
+
+ align:start position:0%
+them all up at zero measure Theory and
+ 
+
+ align:start position:0%
+them all up at zero measure Theory and
+some math we're not going to get into
+
+ align:start position:0%
+some math we're not going to get into
+ 
+
+ align:start position:0%
+some math we're not going to get into
+tells you it doesn't happen all right
+
+ align:start position:0%
+tells you it doesn't happen all right
+ 
+
+ align:start position:0%
+tells you it doesn't happen all right
+it's probability one you're a winner or
+
+ align:start position:0%
+it's probability one you're a winner or
+ 
+
+ align:start position:0%
+it's probability one you're a winner or
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+loser
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um all right so I'm not gonna not going
+
+ align:start position:0%
+um all right so I'm not gonna not going
+ 
+
+ align:start position:0%
+um all right so I'm not gonna not going
+to prove that that the probability you
+
+ align:start position:0%
+to prove that that the probability you
+ 
+
+ align:start position:0%
+to prove that that the probability you
+play Forever is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero all right but let's look at how
+
+ align:start position:0%
+zero all right but let's look at how
+ 
+
+ align:start position:0%
+zero all right but let's look at how
+long you play
+
+ align:start position:0%
+long you play
+ 
+
+ align:start position:0%
+long you play
+how long does it take you to go home one
+
+ align:start position:0%
+how long does it take you to go home one
+ 
+
+ align:start position:0%
+how long does it take you to go home one
+way or another go
+
+ align:start position:0%
+way or another go
+ 
+
+ align:start position:0%
+way or another go
+broke and uh to do this we're going to
+
+ align:start position:0%
+broke and uh to do this we're going to
+ 
+
+ align:start position:0%
+broke and uh to do this we're going to
+set up another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence so we know eventually we hit
+
+ align:start position:0%
+recurrence so we know eventually we hit
+ 
+
+ align:start position:0%
+recurrence so we know eventually we hit
+a boundary I want to know how many bets
+
+ align:start position:0%
+a boundary I want to know how many bets
+ 
+
+ align:start position:0%
+a boundary I want to know how many bets
+does it take to hit the
+
+ align:start position:0%
+does it take to hit the
+ 
+
+ align:start position:0%
+does it take to hit the
+boundary how long do we get to play
+
+ align:start position:0%
+boundary how long do we get to play
+ 
+
+ align:start position:0%
+boundary how long do we get to play
+before we go home on
+
+ align:start position:0%
+before we go home on
+ 
+
+ align:start position:0%
+before we go home on
+unhappy so the S will be the number of
+
+ align:start position:0%
+unhappy so the S will be the number of
+ 
+
+ align:start position:0%
+unhappy so the S will be the number of
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+until we hit a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary and I want to know the expected
+
+ align:start position:0%
+boundary and I want to know the expected
+ 
+
+ align:start position:0%
+boundary and I want to know the expected
+number I'll call it Isa here is the
+
+ align:start position:0%
+number I'll call it Isa here is the
+ 
+
+ align:start position:0%
+number I'll call it Isa here is the
+expected value of s given that I start
+
+ align:start position:0%
+expected value of s given that I start
+ 
+
+ align:start position:0%
+expected value of s given that I start
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n i mean the reason you could think
+
+ align:start position:0%
+n i mean the reason you could think
+ 
+
+ align:start position:0%
+n i mean the reason you could think
+about this is you know we know we're
+
+ align:start position:0%
+about this is you know we know we're
+ 
+
+ align:start position:0%
+about this is you know we know we're
+going to go home broke pretty pretty
+
+ align:start position:0%
+going to go home broke pretty pretty
+ 
+
+ align:start position:0%
+going to go home broke pretty pretty
+likely do we at least have some fun in
+
+ align:start position:0%
+likely do we at least have some fun in
+ 
+
+ align:start position:0%
+likely do we at least have some fun in
+the meantime do we get a lot of gambling
+
+ align:start position:0%
+the meantime do we get a lot of gambling
+ 
+
+ align:start position:0%
+the meantime do we get a lot of gambling
+in in free drinks or whatever before
+
+ align:start position:0%
+in in free drinks or whatever before
+ 
+
+ align:start position:0%
+in in free drinks or whatever before
+we're we're killed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here now this also has a recurrence and
+
+ align:start position:0%
+here now this also has a recurrence and
+ 
+
+ align:start position:0%
+here now this also has a recurrence and
+I'm going to show you what it is then
+
+ align:start position:0%
+I'm going to show you what it is then
+ 
+
+ align:start position:0%
+I'm going to show you what it is then
+prove that that's correct so I claim
+
+ align:start position:0%
+prove that that's correct so I claim
+ 
+
+ align:start position:0%
+prove that that's correct so I claim
+that the expected number of steps given
+
+ align:start position:0%
+that the expected number of steps given
+ 
+
+ align:start position:0%
+that the expected number of steps given
+we start with nll is well zero if we
+
+ align:start position:0%
+we start with nll is well zero if we
+ 
+
+ align:start position:0%
+we start with nll is well zero if we
+start with no
+
+ align:start position:0%
+start with no
+ 
+
+ align:start position:0%
+start with no
+money because we already broke it's zero
+
+ align:start position:0%
+money because we already broke it's zero
+ 
+
+ align:start position:0%
+money because we already broke it's zero
+if we
+
+ align:start position:0%
+if we
+ 
+
+ align:start position:0%
+if we
+start with T
+
+ align:start position:0%
+start with T
+ 
+
+ align:start position:0%
+start with T
+because then we just go home Happy
+
+ align:start position:0%
+because then we just go home Happy
+ 
+
+ align:start position:0%
+because then we just go home Happy
+there's no bets because we've already
+
+ align:start position:0%
+there's no bets because we've already
+ 
+
+ align:start position:0%
+there's no bets because we've already
+hit the upper
+
+ align:start position:0%
+hit the upper
+ 
+
+ align:start position:0%
+hit the upper
+boundary and the interesting case will
+
+ align:start position:0%
+boundary and the interesting case will
+ 
+
+ align:start position:0%
+boundary and the interesting case will
+be it's 1 + P
+
+ align:start position:0%
+be it's 1 + P
+ 
+
+ align:start position:0%
+be it's 1 + P
+* e
+
+ align:start position:0%
+* e
+ 
+
+ align:start position:0%
+* e
+nus1 + 1 -
+
+ align:start position:0%
+nus1 + 1 -
+ 
+
+ align:start position:0%
+nus1 + 1 -
+P up n + one 1 minus p e n minus one if
+
+ align:start position:0%
+P up n + one 1 minus p e n minus one if
+ 
+
+ align:start position:0%
+P up n + one 1 minus p e n minus one if
+we start with between zero and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+okay so let's prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that actually the
+
+ align:start position:0%
+that actually the
+ 
+
+ align:start position:0%
+that actually the
+proof is exactly the same as the last
+
+ align:start position:0%
+proof is exactly the same as the last
+ 
+
+ align:start position:0%
+proof is exactly the same as the last
+one so I don't think I need to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it all right the proof is is pretty
+
+ align:start position:0%
+it all right the proof is is pretty
+ 
+
+ align:start position:0%
+it all right the proof is is pretty
+simple because we look at two cases you
+
+ align:start position:0%
+simple because we look at two cases you
+ 
+
+ align:start position:0%
+simple because we look at two cases you
+win the first
+
+ align:start position:0%
+win the first
+ 
+
+ align:start position:0%
+win the first
+bet happens with probability p and then
+
+ align:start position:0%
+bet happens with probability p and then
+ 
+
+ align:start position:0%
+bet happens with probability p and then
+you're starting with n plus1 over again
+
+ align:start position:0%
+you're starting with n plus1 over again
+ 
+
+ align:start position:0%
+you're starting with n plus1 over again
+or you lose the first bet happens with
+
+ align:start position:0%
+or you lose the first bet happens with
+ 
+
+ align:start position:0%
+or you lose the first bet happens with
+probability one minus p and you're
+
+ align:start position:0%
+probability one minus p and you're
+ 
+
+ align:start position:0%
+probability one minus p and you're
+starting over with n minus $1 now same
+
+ align:start position:0%
+starting over with n minus $1 now same
+ 
+
+ align:start position:0%
+starting over with n minus $1 now same
+as last time in fact this whole
+
+ align:start position:0%
+as last time in fact this whole
+ 
+
+ align:start position:0%
+as last time in fact this whole
+recurrence is identical to last time
+
+ align:start position:0%
+recurrence is identical to last time
+ 
+
+ align:start position:0%
+recurrence is identical to last time
+except for one
+
+ align:start position:0%
+except for one
+ 
+
+ align:start position:0%
+except for one
+thing what's the one thing that's
+
+ align:start position:0%
+thing what's the one thing that's
+ 
+
+ align:start position:0%
+thing what's the one thing that's
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+now what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it you
+
+ align:start position:0%
+it you
+ 
+
+ align:start position:0%
+it you
+have so
+
+ align:start position:0%
+have so
+ 
+
+ align:start position:0%
+have so
+it's that's
+
+ align:start position:0%
+it's that's
+ 
+
+ align:start position:0%
+it's that's
+different there's another difference
+
+ align:start position:0%
+different there's another difference
+ 
+
+ align:start position:0%
+different there's another difference
+that's one difference that's going to
+
+ align:start position:0%
+that's one difference that's going to
+ 
+
+ align:start position:0%
+that's one difference that's going to
+make it inhomogeneous that's sort of a
+
+ align:start position:0%
+make it inhomogeneous that's sort of a
+ 
+
+ align:start position:0%
+make it inhomogeneous that's sort of a
+pain what's the other difference from
+
+ align:start position:0%
+pain what's the other difference from
+ 
+
+ align:start position:0%
+pain what's the other difference from
+last time this part's the same
+
+ align:start position:0%
+last time this part's the same
+ 
+
+ align:start position:0%
+last time this part's the same
+otherwise what is it boundary conditions
+
+ align:start position:0%
+otherwise what is it boundary conditions
+ 
+
+ align:start position:0%
+otherwise what is it boundary conditions
+that was a one before now it's a
+
+ align:start position:0%
+that was a one before now it's a
+ 
+
+ align:start position:0%
+that was a one before now it's a
+zero okay so I little change here and I
+
+ align:start position:0%
+zero okay so I little change here and I
+ 
+
+ align:start position:0%
+zero okay so I little change here and I
+added a one here uh but that's going to
+
+ align:start position:0%
+added a one here uh but that's going to
+ 
+
+ align:start position:0%
+added a one here uh but that's going to
+make it a pretty different answer so
+
+ align:start position:0%
+make it a pretty different answer so
+ 
+
+ align:start position:0%
+make it a pretty different answer so
+let's see what the recurrence is I'll
+
+ align:start position:0%
+let's see what the recurrence is I'll
+ 
+
+ align:start position:0%
+let's see what the recurrence is I'll
+rearrange rearrange terms here to put it
+
+ align:start position:0%
+rearrange rearrange terms here to put it
+ 
+
+ align:start position:0%
+rearrange rearrange terms here to put it
+into recurrence
+
+ align:start position:0%
+into recurrence
+ 
+
+ align:start position:0%
+into recurrence
+I get p e subn + 1 minus e n + 1- p n
+
+ align:start position:0%
+I get p e subn + 1 minus e n + 1- p n
+ 
+
+ align:start position:0%
+I get p e subn + 1 minus e n + 1- p n
+minus one equals minus1 not zero and the
+
+ align:start position:0%
+minus one equals minus1 not zero and the
+ 
+
+ align:start position:0%
+minus one equals minus1 not zero and the
+boundary conditions are e0 is zero and e
+
+ align:start position:0%
+boundary conditions are e0 is zero and e
+ 
+
+ align:start position:0%
+boundary conditions are e0 is zero and e
+t is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay what's the first thing you do when
+
+ align:start position:0%
+okay what's the first thing you do when
+ 
+
+ align:start position:0%
+okay what's the first thing you do when
+you have an inhomogeneous linear
+
+ align:start position:0%
+you have an inhomogeneous linear
+ 
+
+ align:start position:0%
+you have an inhomogeneous linear
+recurrence solve the homogeneous
+
+ align:start position:0%
+recurrence solve the homogeneous
+ 
+
+ align:start position:0%
+recurrence solve the homogeneous
+one and the answer there well it's the
+
+ align:start position:0%
+one and the answer there well it's the
+ 
+
+ align:start position:0%
+one and the answer there well it's the
+same as before this is the part we
+
+ align:start position:0%
+same as before this is the part we
+ 
+
+ align:start position:0%
+same as before this is the part we
+analyzed and we'll do it for the case
+
+ align:start position:0%
+analyzed and we'll do it for the case
+ 
+
+ align:start position:0%
+analyzed and we'll do it for the case
+when p is not a half so the unfair
+
+ align:start position:0%
+when p is not a half so the unfair
+ 
+
+ align:start position:0%
+when p is not a half so the unfair
+game so the homogeneous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution Isen just from before same
+
+ align:start position:0%
+solution Isen just from before same
+ 
+
+ align:start position:0%
+solution Isen just from before same
+thing 1 - p over P to the N plus b and
+
+ align:start position:0%
+thing 1 - p over P to the N plus b and
+ 
+
+ align:start position:0%
+thing 1 - p over P to the N plus b and
+this is the case with two roots P does
+
+ align:start position:0%
+this is the case with two roots P does
+ 
+
+ align:start position:0%
+this is the case with two roots P does
+not equal a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half what's the next thing you
+
+ align:start position:0%
+half what's the next thing you
+ 
+
+ align:start position:0%
+half what's the next thing you
+do for in homogeneous
+
+ align:start position:0%
+do for in homogeneous
+ 
+
+ align:start position:0%
+do for in homogeneous
+recurrence are we plugging in boundary
+
+ align:start position:0%
+recurrence are we plugging in boundary
+ 
+
+ align:start position:0%
+recurrence are we plugging in boundary
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+yet no so what do I do
+
+ align:start position:0%
+yet no so what do I do
+ 
+
+ align:start position:0%
+yet no so what do I do
+next particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution and what's my first
+
+ align:start position:0%
+solution and what's my first
+ 
+
+ align:start position:0%
+solution and what's my first
+guess with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here what do I guess for
+
+ align:start position:0%
+here what do I guess for
+ 
+
+ align:start position:0%
+here what do I guess for
+n I'm trying to guess something that
+
+ align:start position:0%
+n I'm trying to guess something that
+ 
+
+ align:start position:0%
+n I'm trying to guess something that
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+that so what do I
+
+ align:start position:0%
+that so what do I
+ 
+
+ align:start position:0%
+that so what do I
+guess constant yeah something just
+
+ align:start position:0%
+guess constant yeah something just
+ 
+
+ align:start position:0%
+guess constant yeah something just
+that's a scalar I'll just guess a
+
+ align:start position:0%
+that's a scalar I'll just guess a
+ 
+
+ align:start position:0%
+that's a scalar I'll just guess a
+constant and if I plug a constant a into
+
+ align:start position:0%
+constant and if I plug a constant a into
+ 
+
+ align:start position:0%
+constant and if I plug a constant a into
+here it's going to f
+
+ align:start position:0%
+here it's going to f
+ 
+
+ align:start position:0%
+here it's going to f
+CU I'll just get pull the A out I'll get
+
+ align:start position:0%
+CU I'll just get pull the A out I'll get
+ 
+
+ align:start position:0%
+CU I'll just get pull the A out I'll get
+p minus1 plus one minus p is zero and
+
+ align:start position:0%
+p minus1 plus one minus p is zero and
+ 
+
+ align:start position:0%
+p minus1 plus one minus p is zero and
+Zer doesn't equal minus one so it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fails so I guess again what do I guess
+
+ align:start position:0%
+fails so I guess again what do I guess
+ 
+
+ align:start position:0%
+fails so I guess again what do I guess
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+time a n plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b all right and I don't think I'll drag
+
+ align:start position:0%
+b all right and I don't think I'll drag
+ 
+
+ align:start position:0%
+b all right and I don't think I'll drag
+you through all the uh algebra for that
+
+ align:start position:0%
+you through all the uh algebra for that
+ 
+
+ align:start position:0%
+you through all the uh algebra for that
+but it works
+
+ align:start position:0%
+but it works
+ 
+
+ align:start position:0%
+but it works
+works and when you do it you find
+
+ align:start position:0%
+works and when you do it you find
+ 
+
+ align:start position:0%
+works and when you do it you find
+that a is min-1 over 2 p minus one and B
+
+ align:start position:0%
+that a is min-1 over 2 p minus one and B
+ 
+
+ align:start position:0%
+that a is min-1 over 2 p minus one and B
+could be anything
+
+ align:start position:0%
+could be anything
+ 
+
+ align:start position:0%
+could be anything
+so let me just rewrite this as 1 over 1
+
+ align:start position:0%
+so let me just rewrite this as 1 over 1
+ 
+
+ align:start position:0%
+so let me just rewrite this as 1 over 1
+minus 2 p and B can be anything so we'll
+
+ align:start position:0%
+minus 2 p and B can be anything so we'll
+ 
+
+ align:start position:0%
+minus 2 p and B can be anything so we'll
+set b equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero all right so we've got our
+
+ align:start position:0%
+zero all right so we've got our
+ 
+
+ align:start position:0%
+zero all right so we've got our
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+solution it's not hard to go compute
+
+ align:start position:0%
+solution it's not hard to go compute
+ 
+
+ align:start position:0%
+solution it's not hard to go compute
+that you just plug it plug it back in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solve okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we add them together to get the
+
+ align:start position:0%
+so now we add them together to get the
+ 
+
+ align:start position:0%
+so now we add them together to get the
+general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution this is a n plus b b was zero
+
+ align:start position:0%
+solution this is a n plus b b was zero
+ 
+
+ align:start position:0%
+solution this is a n plus b b was zero
+and here's a as 1 over 1 -
+
+ align:start position:0%
+and here's a as 1 over 1 -
+ 
+
+ align:start position:0%
+and here's a as 1 over 1 -
+2p and now what do we
+
+ align:start position:0%
+2p and now what do we
+ 
+
+ align:start position:0%
+2p and now what do we
+do to finish I got my general solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I adding up the homogeneous in the
+
+ align:start position:0%
+here I adding up the homogeneous in the
+ 
+
+ align:start position:0%
+here I adding up the homogeneous in the
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+solution plug in the boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions all right I'm not going to
+
+ align:start position:0%
+conditions all right I'm not going to
+ 
+
+ align:start position:0%
+conditions all right I'm not going to
+drag you through solving this case but
+
+ align:start position:0%
+drag you through solving this case but
+ 
+
+ align:start position:0%
+drag you through solving this case but
+I'm going to show you the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer = n over 1 -
+
+ align:start position:0%
+answer = n over 1 -
+ 
+
+ align:start position:0%
+answer = n over 1 -
+2p oops minus t the upper boundary over
+
+ align:start position:0%
+2p oops minus t the upper boundary over
+ 
+
+ align:start position:0%
+2p oops minus t the upper boundary over
+1 - 2
+
+ align:start position:0%
+1 - 2
+ 
+
+ align:start position:0%
+1 - 2
+p Time 1 - p over P the
+
+ align:start position:0%
+p Time 1 - p over P the
+ 
+
+ align:start position:0%
+p Time 1 - p over P the
+nus1
+
+ align:start position:0%
+nus1
+ 
+
+ align:start position:0%
+nus1
+over 1us p over P to the T minus one so
+
+ align:start position:0%
+over 1us p over P to the T minus one so
+ 
+
+ align:start position:0%
+over 1us p over P to the T minus one so
+actually this looks a little familiar
+
+ align:start position:0%
+actually this looks a little familiar
+ 
+
+ align:start position:0%
+actually this looks a little familiar
+from the last time when we did this
+
+ align:start position:0%
+from the last time when we did this
+ 
+
+ align:start position:0%
+from the last time when we did this
+recurrence figuring out the probability
+
+ align:start position:0%
+recurrence figuring out the probability
+ 
+
+ align:start position:0%
+recurrence figuring out the probability
+we go home a winner here this is the
+
+ align:start position:0%
+we go home a winner here this is the
+ 
+
+ align:start position:0%
+we go home a winner here this is the
+expected number of steps to hit a
+
+ align:start position:0%
+expected number of steps to hit a
+ 
+
+ align:start position:0%
+expected number of steps to hit a
+boundary to go
+
+ align:start position:0%
+boundary to go
+ 
+
+ align:start position:0%
+boundary to go
+home if we plug in the values it's a
+
+ align:start position:0%
+home if we plug in the values it's a
+ 
+
+ align:start position:0%
+home if we plug in the values it's a
+little hairy but you can compute
+
+ align:start position:0%
+little hairy but you can compute
+ 
+
+ align:start position:0%
+little hairy but you can compute
+it so for example if m is
+
+ align:start position:0%
+it so for example if m is
+ 
+
+ align:start position:0%
+it so for example if m is
+100 N is a
+
+ align:start position:0%
+100 N is a
+ 
+
+ align:start position:0%
+100 N is a
+th000 t would be 1100 in that
+
+ align:start position:0%
+th000 t would be 1100 in that
+ 
+
+ align:start position:0%
+th000 t would be 1100 in that
+case p is
+
+ align:start position:0%
+case p is
+ 
+
+ align:start position:0%
+case p is
+9/19 playing
+
+ align:start position:0%
+9/19 playing
+ 
+
+ align:start position:0%
+9/19 playing
+roulette then the expected number of
+
+ align:start position:0%
+roulette then the expected number of
+ 
+
+ align:start position:0%
+roulette then the expected number of
+bets
+
+ align:start position:0%
+bets
+ 
+
+ align:start position:0%
+bets
+before you have to go
+
+ align:start position:0%
+before you have to go
+ 
+
+ align:start position:0%
+before you have to go
+home
+
+ align:start position:0%
+home
+ 
+
+ align:start position:0%
+home
+is 1900 from this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+0.56 from that
+
+ align:start position:0%
+0.56 from that
+ 
+
+ align:start position:0%
+0.56 from that
+part okay so actually 19,000 sorry so
+
+ align:start position:0%
+part okay so actually 19,000 sorry so
+ 
+
+ align:start position:0%
+part okay so actually 19,000 sorry so
+it's very close to
+
+ align:start position:0%
+it's very close to
+ 
+
+ align:start position:0%
+it's very close to
+19,000 bets you got to
+
+ align:start position:0%
+19,000 bets you got to
+ 
+
+ align:start position:0%
+19,000 bets you got to
+make all right so it takes a long time
+
+ align:start position:0%
+make all right so it takes a long time
+ 
+
+ align:start position:0%
+make all right so it takes a long time
+to lose a th000 bucks and it sort of
+
+ align:start position:0%
+to lose a th000 bucks and it sort of
+ 
+
+ align:start position:0%
+to lose a th000 bucks and it sort of
+comes very close to the answer you would
+
+ align:start position:0%
+comes very close to the answer you would
+ 
+
+ align:start position:0%
+comes very close to the answer you would
+have guessed without thinking and
+
+ align:start position:0%
+have guessed without thinking and
+ 
+
+ align:start position:0%
+have guessed without thinking and
+solving the recurrence if you expect to
+
+ align:start position:0%
+solving the recurrence if you expect to
+ 
+
+ align:start position:0%
+solving the recurrence if you expect to
+lose one minus 2 p every
+
+ align:start position:0%
+lose one minus 2 p every
+ 
+
+ align:start position:0%
+lose one minus 2 p every
+bet and you want to know how long the
+
+ align:start position:0%
+bet and you want to know how long the
+ 
+
+ align:start position:0%
+bet and you want to know how long the
+expected time to lose n doll you might
+
+ align:start position:0%
+expected time to lose n doll you might
+ 
+
+ align:start position:0%
+expected time to lose n doll you might
+well have said I think it's going to be
+
+ align:start position:0%
+well have said I think it's going to be
+ 
+
+ align:start position:0%
+well have said I think it's going to be
+n over the amount I lose every
+
+ align:start position:0%
+n over the amount I lose every
+ 
+
+ align:start position:0%
+n over the amount I lose every
+time that would be wrong
+
+ align:start position:0%
+time that would be wrong
+ 
+
+ align:start position:0%
+time that would be wrong
+technically because you'd have left off
+
+ align:start position:0%
+technically because you'd have left off
+ 
+
+ align:start position:0%
+technically because you'd have left off
+this nasty thing but this nasty thing
+
+ align:start position:0%
+this nasty thing but this nasty thing
+ 
+
+ align:start position:0%
+this nasty thing but this nasty thing
+doesn't make much of a real difference
+
+ align:start position:0%
+doesn't make much of a real difference
+ 
+
+ align:start position:0%
+doesn't make much of a real difference
+because it goes to zero really fast for
+
+ align:start position:0%
+because it goes to zero really fast for
+ 
+
+ align:start position:0%
+because it goes to zero really fast for
+any numbers like 100 and a thousand
+
+ align:start position:0%
+any numbers like 100 and a thousand
+ 
+
+ align:start position:0%
+any numbers like 100 and a thousand
+makes no difference at all so the
+
+ align:start position:0%
+makes no difference at all so the
+ 
+
+ align:start position:0%
+makes no difference at all so the
+intuition in that case comes out to be
+
+ align:start position:0%
+intuition in that case comes out to be
+ 
+
+ align:start position:0%
+intuition in that case comes out to be
+pretty close even though technically
+
+ align:start position:0%
+pretty close even though technically
+ 
+
+ align:start position:0%
+pretty close even though technically
+it's not exactly
+
+ align:start position:0%
+it's not exactly
+ 
+
+ align:start position:0%
+it's not exactly
+right now to see why this goes to
+
+ align:start position:0%
+right now to see why this goes to
+ 
+
+ align:start position:0%
+right now to see why this goes to
+zero if T equals n plus M here this is n
+
+ align:start position:0%
+zero if T equals n plus M here this is n
+ 
+
+ align:start position:0%
+zero if T equals n plus M here this is n
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+M and your upper limit say goes to
+
+ align:start position:0%
+M and your upper limit say goes to
+ 
+
+ align:start position:0%
+M and your upper limit say goes to
+Infinity it's 100 in this case then that
+
+ align:start position:0%
+Infinity it's 100 in this case then that
+ 
+
+ align:start position:0%
+Infinity it's 100 in this case then that
+just zooms to zero and you're only left
+
+ align:start position:0%
+just zooms to zero and you're only left
+ 
+
+ align:start position:0%
+just zooms to zero and you're only left
+with that which means that we can use
+
+ align:start position:0%
+with that which means that we can use
+ 
+
+ align:start position:0%
+with that which means that we can use
+ASM totic notation
+
+ align:start position:0%
+ASM totic notation
+ 
+
+ align:start position:0%
+ASM totic notation
+here to sort of characterize the
+
+ align:start position:0%
+here to sort of characterize the
+ 
+
+ align:start position:0%
+here to sort of characterize the
+expected number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bets and it's totally dominated by the
+
+ align:start position:0%
+bets and it's totally dominated by the
+ 
+
+ align:start position:0%
+bets and it's totally dominated by the
+drift so as M goes to
+
+ align:start position:0%
+drift so as M goes to
+ 
+
+ align:start position:0%
+drift so as M goes to
+Infinity the expected time to live here
+
+ align:start position:0%
+Infinity the expected time to live here
+ 
+
+ align:start position:0%
+Infinity the expected time to live here
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Tilda n/ 1 - 2p if you've got
+
+ align:start position:0%
+Tilda n/ 1 - 2p if you've got
+ 
+
+ align:start position:0%
+Tilda n/ 1 - 2p if you've got
+n losing one minus 2 p every time then
+
+ align:start position:0%
+n losing one minus 2 p every time then
+ 
+
+ align:start position:0%
+n losing one minus 2 p every time then
+you last for n over one minus 2p
+
+ align:start position:0%
+you last for n over one minus 2p
+ 
+
+ align:start position:0%
+you last for n over one minus 2p
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+okay now actually what situation in
+
+ align:start position:0%
+okay now actually what situation in
+ 
+
+ align:start position:0%
+okay now actually what situation in
+words does m going to infinity mean say
+
+ align:start position:0%
+words does m going to infinity mean say
+ 
+
+ align:start position:0%
+words does m going to infinity mean say
+I set M to be
+
+ align:start position:0%
+I set M to be
+ 
+
+ align:start position:0%
+I set M to be
+Infinity what what what is that kind of
+
+ align:start position:0%
+Infinity what what what is that kind of
+ 
+
+ align:start position:0%
+Infinity what what what is that kind of
+game if M's Infinity how long am I
+
+ align:start position:0%
+game if M's Infinity how long am I
+ 
+
+ align:start position:0%
+game if M's Infinity how long am I
+playing now yeah now you're playing for
+
+ align:start position:0%
+playing now yeah now you're playing for
+ 
+
+ align:start position:0%
+playing now yeah now you're playing for
+as long as it takes you to lose all of
+
+ align:start position:0%
+as long as it takes you to lose all of
+ 
+
+ align:start position:0%
+as long as it takes you to lose all of
+your money yes all right because there
+
+ align:start position:0%
+your money yes all right because there
+ 
+
+ align:start position:0%
+your money yes all right because there
+is no stopping condition up here going
+
+ align:start position:0%
+is no stopping condition up here going
+ 
+
+ align:start position:0%
+is no stopping condition up here going
+home happy I'm going to play Forever or
+
+ align:start position:0%
+home happy I'm going to play Forever or
+ 
+
+ align:start position:0%
+home happy I'm going to play Forever or
+until I lose
+
+ align:start position:0%
+until I lose
+ 
+
+ align:start position:0%
+until I lose
+everything and this says how long you
+
+ align:start position:0%
+everything and this says how long you
+ 
+
+ align:start position:0%
+everything and this says how long you
+expect to
+
+ align:start position:0%
+expect to
+ 
+
+ align:start position:0%
+expect to
+play all right it's a little less than n
+
+ align:start position:0%
+play all right it's a little less than n
+ 
+
+ align:start position:0%
+play all right it's a little less than n
+over one minus
+
+ align:start position:0%
+over one minus
+ 
+
+ align:start position:0%
+over one minus
+2p uh so if you play until you go broke
+
+ align:start position:0%
+2p uh so if you play until you go broke
+ 
+
+ align:start position:0%
+2p uh so if you play until you go broke
+that's how long you expect to play
+
+ align:start position:0%
+that's how long you expect to play
+ 
+
+ align:start position:0%
+that's how long you expect to play
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um so that's that sort of makes sense in
+
+ align:start position:0%
+um so that's that sort of makes sense in
+ 
+
+ align:start position:0%
+um so that's that sort of makes sense in
+that scenario that's not one where it
+
+ align:start position:0%
+that scenario that's not one where it
+ 
+
+ align:start position:0%
+that scenario that's not one where it
+surprises You by
+
+ align:start position:0%
+surprises You by
+ 
+
+ align:start position:0%
+surprises You by
+intuition it is interesting to consider
+
+ align:start position:0%
+intuition it is interesting to consider
+ 
+
+ align:start position:0%
+intuition it is interesting to consider
+the case of a fair game because there's
+
+ align:start position:0%
+the case of a fair game because there's
+ 
+
+ align:start position:0%
+the case of a fair game because there's
+a something that's non-intuitive that
+
+ align:start position:0%
+a something that's non-intuitive that
+ 
+
+ align:start position:0%
+a something that's non-intuitive that
+happens there so in a fair game p is a
+
+ align:start position:0%
+happens there so in a fair game p is a
+ 
+
+ align:start position:0%
+happens there so in a fair game p is a
+half now if I plug in a half
+
+ align:start position:0%
+half now if I plug in a half
+ 
+
+ align:start position:0%
+half now if I plug in a half
+here well I divide by
+
+ align:start position:0%
+here well I divide by
+ 
+
+ align:start position:0%
+here well I divide by
+zero I expect to play forever let's see
+
+ align:start position:0%
+zero I expect to play forever let's see
+ 
+
+ align:start position:0%
+zero I expect to play forever let's see
+if that really I that's not a good way
+
+ align:start position:0%
+if that really I that's not a good way
+ 
+
+ align:start position:0%
+if that really I that's not a good way
+to do the analysis that you get to a
+
+ align:start position:0%
+to do the analysis that you get to a
+ 
+
+ align:start position:0%
+to do the analysis that you get to a
+divide by zero let's actually go back
+
+ align:start position:0%
+divide by zero let's actually go back
+ 
+
+ align:start position:0%
+divide by zero let's actually go back
+and look at this for the case when p is
+
+ align:start position:0%
+and look at this for the case when p is
+ 
+
+ align:start position:0%
+and look at this for the case when p is
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half and see what happens in a fair game
+
+ align:start position:0%
+half and see what happens in a fair game
+ 
+
+ align:start position:0%
+half and see what happens in a fair game
+how long you expect to play in a fair
+
+ align:start position:0%
+how long you expect to play in a fair
+ 
+
+ align:start position:0%
+how long you expect to play in a fair
+game then the homogeneous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution is the simple case e is a n
+
+ align:start position:0%
+solution is the simple case e is a n
+ 
+
+ align:start position:0%
+solution is the simple case e is a n
+plus b you got a double root at
+
+ align:start position:0%
+plus b you got a double root at
+ 
+
+ align:start position:0%
+plus b you got a double root at
+one which we don't have to worry about
+
+ align:start position:0%
+one which we don't have to worry about
+ 
+
+ align:start position:0%
+one which we don't have to worry about
+one the
+
+ align:start position:0%
+one the
+ 
+
+ align:start position:0%
+one the
+N when you do your particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution you'll
+
+ align:start position:0%
+solution you'll
+ 
+
+ align:start position:0%
+solution you'll
+try a single
+
+ align:start position:0%
+try a single
+ 
+
+ align:start position:0%
+try a single
+scaler and it fails actually use lower
+
+ align:start position:0%
+scaler and it fails actually use lower
+ 
+
+ align:start position:0%
+scaler and it fails actually use lower
+case a
+
+ align:start position:0%
+case a
+ 
+
+ align:start position:0%
+case a
+fails you will then
+
+ align:start position:0%
+fails you will then
+ 
+
+ align:start position:0%
+fails you will then
+try a degree 1
+
+ align:start position:0%
+try a degree 1
+ 
+
+ align:start position:0%
+try a degree 1
+polom and that will fail what are you
+
+ align:start position:0%
+polom and that will fail what are you
+ 
+
+ align:start position:0%
+polom and that will fail what are you
+going to try
+
+ align:start position:0%
+going to try
+ 
+
+ align:start position:0%
+going to try
+next second degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polinomial and that will
+
+ align:start position:0%
+polinomial and that will
+ 
+
+ align:start position:0%
+polinomial and that will
+work okay and the answer you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get when you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is that I'll put the answer here it
+
+ align:start position:0%
+that is that I'll put the answer here it
+ 
+
+ align:start position:0%
+that is that I'll put the answer here it
+turns out that a is minus one and B and
+
+ align:start position:0%
+turns out that a is minus one and B and
+ 
+
+ align:start position:0%
+turns out that a is minus one and B and
+C can be zero so it's just going to be
+
+ align:start position:0%
+C can be zero so it's just going to be
+ 
+
+ align:start position:0%
+C can be zero so it's just going to be
+minus n^2 for the particular
+
+ align:start position:0%
+minus n^2 for the particular
+ 
+
+ align:start position:0%
+minus n^2 for the particular
+solution that means your general
+
+ align:start position:0%
+solution that means your general
+ 
+
+ align:start position:0%
+solution that means your general
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+is a n + B minus n
+
+ align:start position:0%
+is a n + B minus n
+ 
+
+ align:start position:0%
+is a n + B minus n
+2 now you do your boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition all right you have e0 is
+
+ align:start position:0%
+condition all right you have e0 is
+ 
+
+ align:start position:0%
+condition all right you have e0 is
+zero plug in zero for n that's equal to
+
+ align:start position:0%
+zero plug in zero for n that's equal to
+ 
+
+ align:start position:0%
+zero plug in zero for n that's equal to
+B so B is zero that's
+
+ align:start position:0%
+B so B is zero that's
+ 
+
+ align:start position:0%
+B so B is zero that's
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+e is zero and I plug in t here I get a t
+
+ align:start position:0%
+e is zero and I plug in t here I get a t
+ 
+
+ align:start position:0%
+e is zero and I plug in t here I get a t
+b is 0 minus
+
+ align:start position:0%
+b is 0 minus
+ 
+
+ align:start position:0%
+b is 0 minus
+t^2 so I solve for a here that means
+
+ align:start position:0%
+t^2 so I solve for a here that means
+ 
+
+ align:start position:0%
+t^2 so I solve for a here that means
+that a equals
+
+ align:start position:0%
+that a equals
+ 
+
+ align:start position:0%
+that a equals
+T A t^2 minus t^2 is z a has to be
+
+ align:start position:0%
+T A t^2 minus t^2 is z a has to be
+ 
+
+ align:start position:0%
+T A t^2 minus t^2 is z a has to be
+T so that means
+
+ align:start position:0%
+T so that means
+ 
+
+ align:start position:0%
+T so that means
+that en
+
+ align:start position:0%
+that en
+ 
+
+ align:start position:0%
+that en
+n is
+
+ align:start position:0%
+n is
+ 
+
+ align:start position:0%
+n is
+TN minus n^
+
+ align:start position:0%
+TN minus n^
+ 
+
+ align:start position:0%
+TN minus n^
+2 now T is the number is the upper bound
+
+ align:start position:0%
+2 now T is the number is the upper bound
+ 
+
+ align:start position:0%
+2 now T is the number is the upper bound
+is just n plus
+
+ align:start position:0%
+is just n plus
+ 
+
+ align:start position:0%
+is just n plus
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+n + m * N - n^ 2 this gets really simple
+
+ align:start position:0%
+n + m * N - n^ 2 this gets really simple
+ 
+
+ align:start position:0%
+n + m * N - n^ 2 this gets really simple
+the n s cancels I just get n
+
+ align:start position:0%
+the n s cancels I just get n
+ 
+
+ align:start position:0%
+the n s cancels I just get n
+m that says if you're playing a fair
+
+ align:start position:0%
+m that says if you're playing a fair
+ 
+
+ align:start position:0%
+m that says if you're playing a fair
+game until you win M or lose n you
+
+ align:start position:0%
+game until you win M or lose n you
+ 
+
+ align:start position:0%
+game until you win M or lose n you
+expect to play for NM
+
+ align:start position:0%
+expect to play for NM
+ 
+
+ align:start position:0%
+expect to play for NM
+steps which is really nice this is p is
+
+ align:start position:0%
+steps which is really nice this is p is
+ 
+
+ align:start position:0%
+steps which is really nice this is p is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+half very
+
+ align:start position:0%
+half very
+ 
+
+ align:start position:0%
+half very
+clean uh
+
+ align:start position:0%
+clean uh
+ 
+
+ align:start position:0%
+clean uh
+now if you let M be equal to Infinity
+
+ align:start position:0%
+now if you let M be equal to Infinity
+ 
+
+ align:start position:0%
+now if you let M be equal to Infinity
+you're going to expect to play
+
+ align:start position:0%
+you're going to expect to play
+ 
+
+ align:start position:0%
+you're going to expect to play
+forever so with a fair game if you play
+
+ align:start position:0%
+forever so with a fair game if you play
+ 
+
+ align:start position:0%
+forever so with a fair game if you play
+until you're broke the expected number
+
+ align:start position:0%
+until you're broke the expected number
+ 
+
+ align:start position:0%
+until you're broke the expected number
+of bets is
+
+ align:start position:0%
+of bets is
+ 
+
+ align:start position:0%
+of bets is
+infinite that's nice you just you you're
+
+ align:start position:0%
+infinite that's nice you just you you're
+ 
+
+ align:start position:0%
+infinite that's nice you just you you're
+you can play Forever is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation um
+
+ align:start position:0%
+expectation um
+ 
+
+ align:start position:0%
+expectation um
+now here's the weird thing if you expect
+
+ align:start position:0%
+now here's the weird thing if you expect
+ 
+
+ align:start position:0%
+now here's the weird thing if you expect
+to play Forever does that mean you're
+
+ align:start position:0%
+to play Forever does that mean you're
+ 
+
+ align:start position:0%
+to play Forever does that mean you're
+not likely to go home broke
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you expect to play for with you expect
+
+ align:start position:0%
+you expect to play for with you expect
+ 
+
+ align:start position:0%
+you expect to play for with you expect
+to play Forever and as long as you're
+
+ align:start position:0%
+to play Forever and as long as you're
+ 
+
+ align:start position:0%
+to play Forever and as long as you're
+playing you're not going home
+
+ align:start position:0%
+playing you're not going home
+ 
+
+ align:start position:0%
+playing you're not going home
+broke now you know there's some chance
+
+ align:start position:0%
+broke now you know there's some chance
+ 
+
+ align:start position:0%
+broke now you know there's some chance
+of going home broke because you might
+
+ align:start position:0%
+of going home broke because you might
+ 
+
+ align:start position:0%
+of going home broke because you might
+just lose every bet not
+
+ align:start position:0%
+just lose every bet not
+ 
+
+ align:start position:0%
+just lose every bet not
+likely all right
+
+ align:start position:0%
+likely all right
+ 
+
+ align:start position:0%
+likely all right
+um here's the weird thing the
+
+ align:start position:0%
+um here's the weird thing the
+ 
+
+ align:start position:0%
+um here's the weird thing the
+probability you go home broke if you
+
+ align:start position:0%
+probability you go home broke if you
+ 
+
+ align:start position:0%
+probability you go home broke if you
+play until you go broke is
+
+ align:start position:0%
+play until you go broke is
+ 
+
+ align:start position:0%
+play until you go broke is
+one you will go home broke it's just
+
+ align:start position:0%
+one you will go home broke it's just
+ 
+
+ align:start position:0%
+one you will go home broke it's just
+that it takes you expected infinite
+
+ align:start position:0%
+that it takes you expected infinite
+ 
+
+ align:start position:0%
+that it takes you expected infinite
+amount of time to do it sort of one of
+
+ align:start position:0%
+amount of time to do it sort of one of
+ 
+
+ align:start position:0%
+amount of time to do it sort of one of
+these weird things in a fair game so
+
+ align:start position:0%
+these weird things in a fair game so
+ 
+
+ align:start position:0%
+these weird things in a fair game so
+here we've got we prove that the
+
+ align:start position:0%
+here we've got we prove that the
+ 
+
+ align:start position:0%
+here we've got we prove that the
+expected number of bets is NM if M's
+
+ align:start position:0%
+expected number of bets is NM if M's
+ 
+
+ align:start position:0%
+expected number of bets is NM if M's
+infinite that becomes an imponent number
+
+ align:start position:0%
+infinite that becomes an imponent number
+ 
+
+ align:start position:0%
+infinite that becomes an imponent number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+bets but one more theorem
+
+ align:start position:0%
+bets but one more theorem
+ 
+
+ align:start position:0%
+bets but one more theorem
+here this one's a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surprising this theorem is called quit
+
+ align:start position:0%
+surprising this theorem is called quit
+ 
+
+ align:start position:0%
+surprising this theorem is called quit
+while you were
+
+ align:start position:0%
+while you were
+ 
+
+ align:start position:0%
+while you were
+ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nll and it's a fair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game and you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+play until you go
+
+ align:start position:0%
+play until you go
+ 
+
+ align:start position:0%
+play until you go
+broke
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the probability that you do go
+
+ align:start position:0%
+then the probability that you do go
+ 
+
+ align:start position:0%
+then the probability that you do go
+broke as opposed to playing forever is
+
+ align:start position:0%
+broke as opposed to playing forever is
+ 
+
+ align:start position:0%
+broke as opposed to playing forever is
+one it's a certainty you'll go broke
+
+ align:start position:0%
+one it's a certainty you'll go broke
+ 
+
+ align:start position:0%
+one it's a certainty you'll go broke
+even though it expects expect you expect
+
+ align:start position:0%
+even though it expects expect you expect
+ 
+
+ align:start position:0%
+even though it expects expect you expect
+to take it an infinite amount of time
+
+ align:start position:0%
+to take it an infinite amount of time
+ 
+
+ align:start position:0%
+to take it an infinite amount of time
+all right so let's prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the proof is by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contradiction assume it's not
+
+ align:start position:0%
+contradiction assume it's not
+ 
+
+ align:start position:0%
+contradiction assume it's not
+true and that means that you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assuming that there exists some number
+
+ align:start position:0%
+assuming that there exists some number
+ 
+
+ align:start position:0%
+assuming that there exists some number
+of dollars
+
+ align:start position:0%
+of dollars
+ 
+
+ align:start position:0%
+of dollars
+that you can start
+
+ align:start position:0%
+that you can start
+ 
+
+ align:start position:0%
+that you can start
+with and some Epsilon bigger than
+
+ align:start position:0%
+with and some Epsilon bigger than
+ 
+
+ align:start position:0%
+with and some Epsilon bigger than
+zero such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+probability that you lose the
+
+ align:start position:0%
+probability that you lose the
+ 
+
+ align:start position:0%
+probability that you lose the
+N which case you're going home
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broke let me yeah let me write it
+
+ align:start position:0%
+broke let me yeah let me write it
+ 
+
+ align:start position:0%
+broke let me yeah let me write it
+probability to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broke
+
+ align:start position:0%
+broke
+ 
+
+ align:start position:0%
+broke
+is at most one minus
+
+ align:start position:0%
+is at most one minus
+ 
+
+ align:start position:0%
+is at most one minus
+Epsilon in other words if the theorem is
+
+ align:start position:0%
+Epsilon in other words if the theorem is
+ 
+
+ align:start position:0%
+Epsilon in other words if the theorem is
+not true there exists some amount of
+
+ align:start position:0%
+not true there exists some amount of
+ 
+
+ align:start position:0%
+not true there exists some amount of
+money you can start with such that the
+
+ align:start position:0%
+money you can start with such that the
+ 
+
+ align:start position:0%
+money you can start with such that the
+chance you go broke is less than one
+
+ align:start position:0%
+chance you go broke is less than one
+ 
+
+ align:start position:0%
+chance you go broke is less than one
+less than one minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon okay now that means that for all
+
+ align:start position:0%
+Epsilon okay now that means that for all
+ 
+
+ align:start position:0%
+Epsilon okay now that means that for all
+M where you might possibly stop but
+
+ align:start position:0%
+M where you might possibly stop but
+ 
+
+ align:start position:0%
+M where you might possibly stop but
+you're not going to the probability you
+
+ align:start position:0%
+you're not going to the probability you
+ 
+
+ align:start position:0%
+you're not going to the probability you
+lose n before you win
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m is at most 1us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon okay because we're saying the
+
+ align:start position:0%
+Epsilon okay because we're saying the
+ 
+
+ align:start position:0%
+Epsilon okay because we're saying the
+probability you lose n no matter what is
+
+ align:start position:0%
+probability you lose n no matter what is
+ 
+
+ align:start position:0%
+probability you lose n no matter what is
+at most at so it's certainly less than
+
+ align:start position:0%
+at most at so it's certainly less than
+ 
+
+ align:start position:0%
+at most at so it's certainly less than
+oneus Epsilon that you lose n before you
+
+ align:start position:0%
+oneus Epsilon that you lose n before you
+ 
+
+ align:start position:0%
+oneus Epsilon that you lose n before you
+win M
+
+ align:start position:0%
+win M
+ 
+
+ align:start position:0%
+win M
+doll and we know what that probability
+
+ align:start position:0%
+doll and we know what that probability
+ 
+
+ align:start position:0%
+doll and we know what that probability
+is this probability is just M over n
+
+ align:start position:0%
+is this probability is just M over n
+ 
+
+ align:start position:0%
+is this probability is just M over n
+plus M we proved that
+
+ align:start position:0%
+plus M we proved that
+ 
+
+ align:start position:0%
+plus M we proved that
+earlier so that has to be less than 1us
+
+ align:start position:0%
+earlier so that has to be less than 1us
+ 
+
+ align:start position:0%
+earlier so that has to be less than 1us
+Epsilon for all
+
+ align:start position:0%
+Epsilon for all
+ 
+
+ align:start position:0%
+Epsilon for all
+M and now I just multiply
+
+ align:start position:0%
+M and now I just multiply
+ 
+
+ align:start position:0%
+M and now I just multiply
+through for all
+
+ align:start position:0%
+through for all
+ 
+
+ align:start position:0%
+through for all
+M that means that m is less than or
+
+ align:start position:0%
+M that means that m is less than or
+ 
+
+ align:start position:0%
+M that means that m is less than or
+equal to 1us Epsilon n +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m all right then we'll solve
+
+ align:start position:0%
+m all right then we'll solve
+ 
+
+ align:start position:0%
+m all right then we'll solve
+oops solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay so just multiply this out so for
+
+ align:start position:0%
+okay so just multiply this out so for
+ 
+
+ align:start position:0%
+okay so just multiply this out so for
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M less than equal to n plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M um minus Epsilon M minus Epsilon M and
+
+ align:start position:0%
+M um minus Epsilon M minus Epsilon M and
+ 
+
+ align:start position:0%
+M um minus Epsilon M minus Epsilon M and
+now pull the M terms out
+
+ align:start position:0%
+now pull the M terms out
+ 
+
+ align:start position:0%
+now pull the M terms out
+here I get for all M Epsilon m is less
+
+ align:start position:0%
+here I get for all M Epsilon m is less
+ 
+
+ align:start position:0%
+here I get for all M Epsilon m is less
+than or equal to 1 - Epsilon
+
+ align:start position:0%
+than or equal to 1 - Epsilon
+ 
+
+ align:start position:0%
+than or equal to 1 - Epsilon
+n that means for all m m is smaller than
+
+ align:start position:0%
+n that means for all m m is smaller than
+ 
+
+ align:start position:0%
+n that means for all m m is smaller than
+1 - Epsilon Epsilon *
+
+ align:start position:0%
+1 - Epsilon Epsilon *
+ 
+
+ align:start position:0%
+1 - Epsilon Epsilon *
+n and that can't be true it's not true
+
+ align:start position:0%
+n and that can't be true it's not true
+ 
+
+ align:start position:0%
+n and that can't be true it's not true
+that for all M this is less than that
+
+ align:start position:0%
+that for all M this is less than that
+ 
+
+ align:start position:0%
+that for all M this is less than that
+because these are fixed
+
+ align:start position:0%
+because these are fixed
+ 
+
+ align:start position:0%
+because these are fixed
+values that's a
+
+ align:start position:0%
+values that's a
+ 
+
+ align:start position:0%
+values that's a
+contradiction all right so we've proved
+
+ align:start position:0%
+contradiction all right so we've proved
+ 
+
+ align:start position:0%
+contradiction all right so we've proved
+that if you keep playing until you're
+
+ align:start position:0%
+that if you keep playing until you're
+ 
+
+ align:start position:0%
+that if you keep playing until you're
+broke you will go broke with probability
+
+ align:start position:0%
+broke you will go broke with probability
+ 
+
+ align:start position:0%
+broke you will go broke with probability
+one so even if you're playing a fair
+
+ align:start position:0%
+one so even if you're playing a fair
+ 
+
+ align:start position:0%
+one so even if you're playing a fair
+game quit while you're ahead because if
+
+ align:start position:0%
+game quit while you're ahead because if
+ 
+
+ align:start position:0%
+game quit while you're ahead because if
+you don't you're going to go broke the
+
+ align:start position:0%
+you don't you're going to go broke the
+ 
+
+ align:start position:0%
+you don't you're going to go broke the
+swings will eventually catch up with you
+
+ align:start position:0%
+swings will eventually catch up with you
+ 
+
+ align:start position:0%
+swings will eventually catch up with you
+so if we draw the graph here see why
+
+ align:start position:0%
+so if we draw the graph here see why
+ 
+
+ align:start position:0%
+so if we draw the graph here see why
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true all right if I have time going this
+
+ align:start position:0%
+true all right if I have time going this
+ 
+
+ align:start position:0%
+true all right if I have time going this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+all right and I start with n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doll my Baseline is here the drift is
+
+ align:start position:0%
+doll my Baseline is here the drift is
+ 
+
+ align:start position:0%
+doll my Baseline is here the drift is
+zero I'm going to have
+
+ align:start position:0%
+zero I'm going to have
+ 
+
+ align:start position:0%
+zero I'm going to have
+swings I might have some really big high
+
+ align:start position:0%
+swings I might have some really big high
+ 
+
+ align:start position:0%
+swings I might have some really big high
+swings but it doesn't matter because
+
+ align:start position:0%
+swings but it doesn't matter because
+ 
+
+ align:start position:0%
+swings but it doesn't matter because
+eventually I'm going to get a really bad
+
+ align:start position:0%
+eventually I'm going to get a really bad
+ 
+
+ align:start position:0%
+eventually I'm going to get a really bad
+swing and I'm G to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broke okay now if you ever play a game
+
+ align:start position:0%
+broke okay now if you ever play a game
+ 
+
+ align:start position:0%
+broke okay now if you ever play a game
+where you're likely to be winning each
+
+ align:start position:0%
+where you're likely to be winning each
+ 
+
+ align:start position:0%
+where you're likely to be winning each
+time and the drift goes up
+
+ align:start position:0%
+time and the drift goes up
+ 
+
+ align:start position:0%
+time and the drift goes up
+that's a good game to play obviously it
+
+ align:start position:0%
+that's a good game to play obviously it
+ 
+
+ align:start position:0%
+that's a good game to play obviously it
+just keeps getting better and that's a
+
+ align:start position:0%
+just keeps getting better and that's a
+ 
+
+ align:start position:0%
+just keeps getting better and that's a
+whole math change
+
+ align:start position:0%
+whole math change
+ 
+
+ align:start position:0%
+whole math change
+there okay uh so that's it uh remember
+
+ align:start position:0%
+there okay uh so that's it uh remember
+ 
+
+ align:start position:0%
+there okay uh so that's it uh remember
+we have the ice cream study session
+
+ align:start position:0%
+we have the ice cream study session
+ 
+
+ align:start position:0%
+we have the ice cream study session
+Monday so come to that if you'd like uh
+
+ align:start position:0%
+Monday so come to that if you'd like uh
+ 
+
+ align:start position:0%
+Monday so come to that if you'd like uh
+and definitely come to the final on
+
+ align:start position:0%
+and definitely come to the final on
+ 
+
+ align:start position:0%
+and definitely come to the final on
+Tuesday and uh thanks for your hard work
+
+ align:start position:0%
+Tuesday and uh thanks for your hard work
+ 
+
+ align:start position:0%
+Tuesday and uh thanks for your hard work
+and being such a great class this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year
\ No newline at end of file
diff --git a/5gI1aF81Saw.txt b/5gI1aF81Saw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f80ca3675c5ff74e0985828cf373e405dfc5e66b
--- /dev/null
+++ b/5gI1aF81Saw.txt
@@ -0,0 +1,347 @@
+Actually, the title is
+interesting.
+
+It is Materials of Equilibrium.
+A lot of people who look at the
+
+content would think of this as,
+you know, this comes out of a
+
+course that used to be called
+Thermodynamics of Materials
+
+which is a standard staple of
+students who would do graduate
+
+materials education.
+Almost everybody would have
+
+this as a requirement.
+We deliberately changed the
+
+title to Materials of
+Equilibrium to make it something
+
+broader.
+We really wanted it to be
+
+Standard Classical
+Thermodynamics,
+
+which is what we do,
+but wanted to broaden that into
+
+sort of modern metrics to
+understand and study the
+
+energetics of the materials.
+What we do is we essentially
+
+teach, first of all,
+we teach three large segments.
+
+One is classical
+thermodynamics.
+
+And the idea is that people
+need to see the general frame in
+
+which you can set up an energy
+description for materials.
+
+How they react with their
+environment.
+
+How they react with other
+systems.
+
+So we wanted to teach them
+first the general framework in
+
+which to study energetics of
+materials.
+
+And the reason we want it that
+general is because
+
+thermodynamics really has
+evolved from being a science
+
+with a fixed application in
+material science that would have
+
+been used for studying
+metallurgy.
+
+You know, making steel,
+refining of ores and things
+
+like that.
+Very standard sort of
+
+application so that you could
+almost teach through the
+
+applications.
+Now thermodynamics has much
+
+more evolved to a much broader
+range of applications and
+
+materials.
+People use it on polymers.
+
+People use it on thin films.
+People use it in biology.
+
+So we couldn't just teach
+through applications anymore
+
+because there were too many.
+And we don't know where it
+
+might go next.
+So, because of that,
+
+I feel it real important to
+teach the generic framework so
+
+that a student can go with this
+and whatever they meet in their
+
+research apply it.
+So that is about six weeks of
+
+lecturing.
+After that, since
+
+thermodynamics is a macroscopic
+description of materials,
+
+I would teach statistical
+mechanics, which is the science
+
+that teaches you how to relate
+microscopic details,
+
+atomic level details to the
+thermodynamics.
+
+[UNINTELLIGIBLE PHRASE]
+titanium and another aluminum.
+
+So that is the second piece.
+And then the third piece is
+
+essentially taking all that and
+making it more applied.
+
+So now we say we are going to
+study solutions of materials.
+
+We are going to study thin
+films of materials.
+
+We may study now polymer
+mixtures.
+
+So those are the essential
+three pieces.
+
+And so there is an enormous
+emphasis on understanding the
+
+concepts behind what we teach.
+Because of that,
+
+for example,
+I do not assign homeworks on a
+
+weekly basis.
+I feel that the time over which
+
+things have to sink in is longer
+than a week in many cases.
+
+So we have sets of assignments
+that go on the Web.
+
+Students do not have to turn
+them in.
+
+A week later the solution is
+gone so they can work on this at
+
+their own pace.
+Well, the way we evaluate the
+
+students is in a very classical
+sense.
+
+We have two mid-term exams.
+The first one is purely on
+
+classical thermodynamics so it
+would be the first block of the
+
+lecture, the course.
+And there is a second mid-term
+
+which largely covers statistical
+mechanics and some classical
+
+thermodynamics.
+And then there is a
+
+comprehensive file.
+And, actually,
+
+the comprehensive file is
+weighted for half of the grade,
+
+so it is a very extensive
+weighting.
+
+And, again, that comes back to
+the idea that I feel,
+
+you know, this is a difficult
+subject, thermodynamics,
+
+and students need sufficient
+dwell time on it.
+
+So I feel that I can only
+really evaluate them in the end
+
+whether they understand it.
+If it were up to me,
+
+I would probably put even more
+emphasis on the final.
+
+And so, the final is
+comprehensive.
+
+It covers the whole course,
+and also the integration
+
+between the different sections.
+So 3.20 Energetics of Materials
+
+is a required course for all our
+incoming DMSE students.
+
+So they would take it typically
+in their first semester at MIT.
+
+It is a recommended course for
+master students.
+
+Masters can also take a
+shortened version of it.
+
+But typically what we see is
+that most of the students in
+
+Material Science will take that
+course in their first semester.
+
+And the reason it is taken in
+the first semester is there are
+
+a lot of other classes that
+build on it.
+
+You could see this course
+really as the kind of basic
+
+description of how materials
+evolve, what their equilibrium
+
+states are, how they interact
+with their environment so other
+
+classes that talk about phase
+transformations between
+
+materials or mechanical
+behavior, the relation between
+
+mechanical properties and
+processing would all build on
+
+this course.
+It makes sense that it is
+
+taught early.
+So the course has a thermal
+
+help email list which gets
+logged now.
+
+That started,
+we always had a thermal help
+
+email, and those emails would
+get distributed to the staff in
+
+the class.
+And whoever felt they could
+
+answer the question would pick
+it up and cc everybody so we
+
+knew it was answered.
+And then we had a creative TA
+
+who said, you know,
+we have all these really
+
+interesting answers to questions
+and we really should aggregate
+
+this.
+And so, that is how the log got
+
+started.
+And now you can actually look
+
+online and look at the questions
+that were asked other years,
+
+the answers that were given.
+And the students find that very
+
+useful.
+Thermodynamics is a difficult
+
+subject.
+It is one that is extremely
+
+difficult to learn in one
+setting, you know,
+
+and in one pass through the
+material.
+
+You know, it is not like taking
+a course in PowerPoint or
+
+something where you learn facts.
+Thermodynamics is more about
+
+assembling the facts in a
+continuous framework.
+
+And it took me many years to do
+that.
+
+So maybe my advice is to not
+give up.
+
+It is a tough subject,
+but it is one of these subjects
+
+that once you get it you wonder
+why it was so hard.
\ No newline at end of file
diff --git a/5jrZ_AxAb5s.txt b/5jrZ_AxAb5s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..703ce70b791f5356f1d3d0878550a23562297dce
--- /dev/null
+++ b/5jrZ_AxAb5s.txt
@@ -0,0 +1,259 @@
+align:start position:0%
+ 
+so in the end I would like to conclude
+
+ align:start position:0%
+so in the end I would like to conclude
+ 
+
+ align:start position:0%
+so in the end I would like to conclude
+it like this that there is a military
+
+ align:start position:0%
+it like this that there is a military
+ 
+
+ align:start position:0%
+it like this that there is a military
+there is no military solution to the
+
+ align:start position:0%
+there is no military solution to the
+ 
+
+ align:start position:0%
+there is no military solution to the
+terrorism however with a well thought
+
+ align:start position:0%
+terrorism however with a well thought
+ 
+
+ align:start position:0%
+terrorism however with a well thought
+out limited and accurately executed
+
+ align:start position:0%
+out limited and accurately executed
+ 
+
+ align:start position:0%
+out limited and accurately executed
+action could fulfill the short-term
+
+ align:start position:0%
+action could fulfill the short-term
+ 
+
+ align:start position:0%
+action could fulfill the short-term
+goals a more comprehensive and a policy
+
+ align:start position:0%
+goals a more comprehensive and a policy
+ 
+
+ align:start position:0%
+goals a more comprehensive and a policy
+oriented approach is essential to
+
+ align:start position:0%
+oriented approach is essential to
+ 
+
+ align:start position:0%
+oriented approach is essential to
+address this problem there's a need to
+
+ align:start position:0%
+address this problem there's a need to
+ 
+
+ align:start position:0%
+address this problem there's a need to
+understand why the public opinion in the
+
+ align:start position:0%
+understand why the public opinion in the
+ 
+
+ align:start position:0%
+understand why the public opinion in the
+Muslim countries is against United
+
+ align:start position:0%
+Muslim countries is against United
+ 
+
+ align:start position:0%
+Muslim countries is against United
+States it's important to note that
+
+ align:start position:0%
+States it's important to note that
+ 
+
+ align:start position:0%
+States it's important to note that
+majority of the people though they are
+
+ align:start position:0%
+majority of the people though they are
+ 
+
+ align:start position:0%
+majority of the people though they are
+not supportive of US policies but they
+
+ align:start position:0%
+not supportive of US policies but they
+ 
+
+ align:start position:0%
+not supportive of US policies but they
+are not for the terrorism so
+
+ align:start position:0%
+are not for the terrorism so
+ 
+
+ align:start position:0%
+are not for the terrorism so
+particularly in the Middle East their
+
+ align:start position:0%
+particularly in the Middle East their
+ 
+
+ align:start position:0%
+particularly in the Middle East their
+policy largely people criticize this
+
+ align:start position:0%
+policy largely people criticize this
+ 
+
+ align:start position:0%
+policy largely people criticize this
+policy but they are not supporting
+
+ align:start position:0%
+policy but they are not supporting
+ 
+
+ align:start position:0%
+policy but they are not supporting
+terrorist at large there are very few
+
+ align:start position:0%
+terrorist at large there are very few
+ 
+
+ align:start position:0%
+terrorist at large there are very few
+who support terrorism against us and
+
+ align:start position:0%
+who support terrorism against us and
+ 
+
+ align:start position:0%
+who support terrorism against us and
+another thing I would like to point out
+
+ align:start position:0%
+another thing I would like to point out
+ 
+
+ align:start position:0%
+another thing I would like to point out
+is that that it is certainly not the
+
+ align:start position:0%
+is that that it is certainly not the
+ 
+
+ align:start position:0%
+is that that it is certainly not the
+democracy and Freedom the people most of
+
+ align:start position:0%
+democracy and Freedom the people most of
+ 
+
+ align:start position:0%
+democracy and Freedom the people most of
+the people over here thinks that it's a
+
+ align:start position:0%
+the people over here thinks that it's a
+ 
+
+ align:start position:0%
+the people over here thinks that it's a
+democracy and freedom which they don't
+
+ align:start position:0%
+democracy and freedom which they don't
+ 
+
+ align:start position:0%
+democracy and freedom which they don't
+like about us it's certainly other
+
+ align:start position:0%
+like about us it's certainly other
+ 
+
+ align:start position:0%
+like about us it's certainly other
+things they are worried about and
+
+ align:start position:0%
+things they are worried about and
+ 
+
+ align:start position:0%
+things they are worried about and
+there's need to reach out to the public
+
+ align:start position:0%
+there's need to reach out to the public
+ 
+
+ align:start position:0%
+there's need to reach out to the public
+instead of just focusing on their rulers
+
+ align:start position:0%
+instead of just focusing on their rulers
+ 
+
+ align:start position:0%
+instead of just focusing on their rulers
+which are not Democratic set up so
+
+ align:start position:0%
+which are not Democratic set up so
+ 
+
+ align:start position:0%
+which are not Democratic set up so
+there's a difference between the rulers
+
+ align:start position:0%
+there's a difference between the rulers
+ 
+
+ align:start position:0%
+there's a difference between the rulers
+in the Muslim world and the General
+
+ align:start position:0%
+in the Muslim world and the General
+ 
+
+ align:start position:0%
+in the Muslim world and the General
+Public
\ No newline at end of file
diff --git a/5lO7gBJEzH4.txt b/5lO7gBJEzH4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..40386a54da7c67426e4c555ff0f59711fd7c6796
--- /dev/null
+++ b/5lO7gBJEzH4.txt
@@ -0,0 +1,4159 @@
+PROFESSOR: Today, we are
+talking about the local behavior
+
+of a crease pattern.
+
+So you take some crease
+pattern for some flat folding--
+
+we're thinking about
+flat foldability.
+
+This is a foldability question.
+
+I give you a crease
+pattern like this.
+
+I want to know, does it fold
+flat, like this one does.
+
+And we're studying
+what happens locally
+
+right around a single vertex.
+
+So I didn't mention
+graph terminology.
+
+It's probably useful
+to mention that.
+
+These corners-- where all the
+edges come together-- those
+
+are vertices.
+
+These triangles-- or in
+general, some regions
+
+divided by the
+creases-- we call faces.
+
+If we just sort of imagine
+cutting a little disk
+
+around that vertex and
+seeing how it behaves,
+
+we get a nice circular piece of
+paper with some crease pattern.
+
+And we want to understand when
+those things fold flat and when
+
+they don't.
+
+Sometimes they do,
+sometimes they don't.
+
+This is kind of like a one
+dimensional folding problem.
+
+So let me write some
+stuff about that.
+
+So we get what we call single
+vertex crease patterns.
+
+So something like--
+this is the example
+
+I have made-- just
+something like that.
+
+That should be flat foldable.
+
+So we think of having
+a disk of paper.
+
+It doesn't really
+matter, but it's
+
+going to be easier
+to reason about
+
+and think about a disk of paper.
+
+Really, we just mean some small
+region around that vertex.
+
+There's obviously one vertex
+in the crease pattern.
+
+Let's say we have n creases
+emanating from one vertex.
+
+This pattern is
+going to be defined
+
+by some sequence of angles.
+
+In general, theta
+1 up to theta n.
+
+If there are n creases, there
+will be n angles between them,
+
+say in clockwise order.
+
+And let's see.
+
+When we fold this thing
+flat-- like in this picture--
+
+we take this disk.
+
+We fold it along all
+of those creases.
+
+What I'd like to
+focus on is what
+
+happens to the
+boundary of the paper.
+
+So there's this outer circle.
+
+The boundary is a circle.
+
+And locally, if you look
+at one of these creases,
+
+it's like folding the
+circle in half onto itself.
+
+And when you make all of these
+creases, if you're successful,
+
+you end up folding the circle
+onto a portion of the circle.
+
+So if you look at
+this boundary-- which
+
+is a little hard to see.
+
+Why don't I trace it?
+
+It's going to do
+something like this.
+
+So this is what the 3D
+thing looks like blown up
+
+a little bit-- and I changed
+the angles a little bit.
+
+But this is what a flat
+folding would look like.
+
+And I'm really just
+focusing on how
+
+the circle maps
+around this circle.
+
+So a flat folding of a disk also
+folds a circle onto a circle.
+
+So we have a flat folding on one
+of these single vertex crease
+
+patterns, we get a folding
+of a circle onto a circle.
+
+This is nice, because
+circles are one dimensional.
+
+And last class, we talked about
+folding one dimensional line
+
+segments.
+
+A circle is just a little
+bit more complicated.
+
+It's different topology.
+
+But we can use a lot
+of the same mindset,
+
+at least, as we did for folding
+line segments onto the line.
+
+In particular, you can see,
+yeah, this is kind of circular.
+
+But you could also imagine
+unrolling it a little bit
+
+and making it straight.
+
+Something like this.
+
+So that it lies on
+a straight line,
+
+if you just unroll that circle.
+
+So you also get a folding
+of a circle in some sense
+
+onto a line by unrolling.
+
+Now, at this point, I want to
+mention a slight issue here.
+
+I mean for this
+unrolling to work--
+
+if you're taking a circle
+like this-- in particular,
+
+you must make at least one
+fold for this to be possible.
+
+Because right now, if I
+haven't folded anything,
+
+I just have a big circle,
+I can't unroll circle
+
+onto a line.
+
+I haven't collapsed it.
+
+Yet here, I've made
+it small enough
+
+that it only occupies a
+portion of the entire circle.
+
+And so I can unroll it.
+
+So this is true, as long as
+I make at least one fold.
+
+OK.
+
+Technically, I need to
+assume another thing, which
+
+is that this thing came
+from a flat piece of paper.
+
+I said there were these angles.
+
+And what I intended to mean is
+that the sum of those angles
+
+is 360 degrees, as it is
+in a flat piece of paper.
+
+But I'm not always going
+to require this assumption.
+
+It's what we care
+about for thinking
+
+about a crease pattern
+of a flat piece of paper
+
+and we look at each vertex.
+
+This will be true.
+
+But when we reason about these
+single vertex crease patterns,
+
+it's really useful to think
+about, sort of in the middle,
+
+this could get smaller.
+
+So for example, you have
+a pattern like this.
+
+Let's say I just take these
+two creases on the bottom
+
+and I fold a crimp.
+
+Because I know a cramp is
+kind of a good thing to do.
+
+So now I have what's
+called a cone of paper.
+
+The sum of the angles--
+there's two angles here,
+
+this one and this one.
+
+Each one looks like
+270-- no, not 270, 135?
+
+In total, it's 270.
+
+So the total angle there
+is now less than 360.
+
+This is what we
+call a convex cone.
+
+So if you relax this
+constraint to allow less than
+
+or equal to 360, then
+we get a convex cone.
+
+And today, I only want to talk
+about flat paper and convex
+
+cones.
+
+We need this for the
+induction, essentially--
+
+for proving things
+about the flat case.
+
+In the textbook-- if you look
+at this chapter on single vertex
+
+crease patterns-- we
+also prove or study
+
+the case where the sum of the
+angles is greater than 360,
+
+which you could never
+make from flat paper.
+
+But hey, it's fun
+to think about.
+
+It's a natural generalization.
+
+And all the things
+that we do here,
+
+you can generalize
+to that situation.
+
+It's just a little bit harder.
+
+So what does it take to
+fold a circle onto a line?
+
+In this situation
+of a convex cone,
+
+where we make at least
+one fold, our folding
+
+is going to lie along a
+portion of the circle.
+
+We can unroll it
+a little bit, get
+
+something lying on
+a straight line.
+
+It's kind of like folding a line
+segment onto a straight line,
+
+if it was flat folding of one
+dimensional pieces of paper.
+
+But there's a lot
+of differences.
+
+I mean, they are similar.
+
+But a lot of the things
+we proved last time
+
+do not hold in the
+case of circular paper.
+
+So I have a bunch of them here.
+
+So one problem-- you
+may recall before,
+
+if we had a line segment and
+we put an arbitrary crease
+
+pattern, then we could just
+assign a mountain valley
+
+assignment, alternating
+mountain valley.
+
+And that would always
+fold flat, no collisions.
+
+OK.
+
+In this world of having a
+circular piece of paper,
+
+that's no longer true.
+
+For example, if you have
+this kind of crease pattern
+
+on a circle or in
+the disk, it would
+
+look like this,
+those two creases.
+
+You can't fold that thing flat.
+
+It's not going to work.
+
+We'll see exactly what
+you need to forbid
+
+for that to make sense.
+
+Another example is
+something like this.
+
+I mean, if I tried to draw this
+in the line, what's happening
+
+is I have a short segment and
+then I have a long segment.
+
+So the problem is
+those ends don't meet.
+
+But even when the ends
+meet-- like in this picture,
+
+imagine these are
+vertically aligned--
+
+if I do this alternating
+mountain valley pattern--
+
+mountain valley assignment--
+I can't join these ends
+
+and make a circle, because that
+would collide with everything.
+
+So this thing actually
+does have a flat folding
+
+starting from a circle.
+
+And I'm not going to try
+to un-map it to a circle.
+
+It does fold, but not like that.
+
+Not with that alternating
+mountain valley pattern.
+
+There are other annoying things.
+
+Let me tell you one
+more on the proof side.
+
+Last time, we had
+a lemma that said,
+
+if your crease
+pattern is mingling--
+
+which still is a
+meaningful notion here--
+
+then you have a crimp, or
+an end fold in that case.
+
+Here, of course, we
+don't have any end folds.
+
+Here, we also do not
+get this implication.
+
+Mingling does not imply
+the existence of a crimp.
+
+And where the proof breaks
+down is if you have-- so
+
+if you remember, our
+parentheses from last time--
+
+we had this kind of pattern.
+
+And we said, well, you
+keep going and either
+
+on the left side, you have
+a beginning open paren
+
+or on the right side you have
+a closing round parenthesis.
+
+In either case, you've
+got an end fold.
+
+Now, this can actually
+happen in a circle.
+
+And so you have
+nothing you can do.
+
+So you could have this pattern.
+
+There would be no crimp.
+
+And probably, in that case,
+you would not be flat foldable,
+
+but in particular,
+this implication fails.
+
+So we have to do more work.
+
+But we're going to get
+the same kind of result
+
+that, in linear
+time, we can tell
+
+whether one of these
+things folds flat.
+
+So that's good news.
+
+So last time, telling whether
+a crease pattern folded flat
+
+was trivial.
+
+The answer was always yes.
+
+And now, it's not so trivial.
+
+So let's start
+with characterizing
+
+crease patterns that fold flat.
+
+Then we will go to mountain
+valley patterns that fold flat.
+
+It'd be great if I
+could just say that,
+
+but I mean here, of
+course, single vertex.
+
+So I give you one of
+these sequence of angles.
+
+Let's say it sums
+to 360 or less.
+
+When is it going to
+be flat foldable?
+
+And the answer is very simple.
+
+Let me write it down.
+
+This thing is going to be
+flat foldable if and only
+
+if the sum of the odd
+angles is equal to the sum
+
+of the even angles.
+
+And, yeah, I'm implicitly
+assuming and requiring
+
+here that n is even.
+
+That's something we'll prove.
+
+So n is actually even and
+minus 1 is going be odd.
+
+And if you happen
+to have started
+
+with a flat piece of paper--
+for the sum of all these things
+
+is 360-- then of course, if
+you have them evenly divided,
+
+this sum will be 180 degrees.
+
+But if you started with the
+convex cone, it'll be smaller.
+
+For this reason, a lot of
+people-- or some people
+
+call this the 180 degree
+property, or the pie property--
+
+if you like to think in
+radians instead of degrees.
+
+And we can do a
+little example here.
+
+This guy-- this crease pattern--
+has a 90 degree angle here.
+
+And it has a 90 degree
+angle down here.
+
+So the sum of those two is 180.
+
+Those are alternating angles,
+different parity classes.
+
+This is 45.
+
+This is the complement, 135.
+
+And those also sum
+to 180, of course.
+
+One does only if the other does.
+
+So it's flat foldable.
+
+We're golden.
+
+Something like this
+is bad, because I
+
+mean it's an even number.
+
+But the odd angles do not equal
+the sum of the even angles.
+
+One's clearly bigger.
+
+And this is a general property.
+
+This is also called
+Kawasaki's theorem
+
+or Kawasaki-Justin's theorem.
+
+They proved it in 1989.
+
+This is pretty
+much the beginning
+
+of origami mathematics.
+
+So let's prove it.
+
+There's two things to prove.
+
+One is that any flat
+foldable crease pattern
+
+has this property,
+which is pretty easy.
+
+And the other, which
+is a little bit harder,
+
+is that if you
+have this property,
+
+you really are flat foldable.
+
+That's the full
+characterization.
+
+So let's start with
+the easy direction.
+
+If you're flat foldable,
+you must have that sum.
+
+OK.
+
+So it's all about thinking
+what happens at a crease.
+
+So we're thinking
+about the boundary
+
+of this piece of paper.
+
+We're thinking about the circle.
+
+And what's happening on
+the circle as you travel,
+
+say counterclockwise
+for some amount
+
+of time, that would
+be first angle.
+
+Then you make a fold.
+
+It's either a
+mountain or valley.
+
+At this point, we don't care.
+
+Either way, you turn around--
+maybe you turn around this way,
+
+or you turn around this way.
+
+But in terms as your
+travel along a circle--
+
+so we went theta 1
+counterclockwise.
+
+Now we're going to
+go theta 2 clockwise;
+
+then we're going to go theta
+3 counterclockwise, and so on.
+
+We keep alternating
+back and forth.
+
+It's much easier to
+think drawn a line.
+
+So we go to the right, theta 1.
+
+Then we go to the left, theta 2.
+
+Then we go to the
+right, theta 3.
+
+And I don't know about
+the layering here.
+
+I'm just drawing it in
+terms of horizontal travel.
+
+The y-coordinate means nothing.
+
+In order for this thing
+to be a flat folding--
+
+to be a valid folding
+of a circle of paper--
+
+these guys have to have
+the same x-coordinate.
+
+So I don't know-- I mean,
+the y-coordinates, they also
+
+have to work out.
+
+But we're not thinking
+about the y-coordinates.
+
+We're just thinking
+about x travel.
+
+We've got to get
+back to where we
+
+started if we're
+folding a circle.
+
+That's it.
+
+So how much total travel
+do we do, in a sign sense?
+
+How much do we go right?
+
+Well, we go theta
+1 to the right.
+
+Then we go theta 2
+to the left, which
+
+is like going negative
+theta 2 to the right.
+
+And then we go through
+theta 3 to the right.
+
+Then we go negative
+theta 4 to the right.
+
+And you add up this alternating
+summation that must equal 0.
+
+The other thing that I should
+say is that n has to be even.
+
+This is maybe obvious
+at this point.
+
+But we're supposed to alternate.
+
+Every time we hit a crease,
+we have to change direction.
+
+And so in the end, it's
+important that after theta 4,
+
+we change direction
+to visit theta 1.
+
+If they were aligned-- like
+if theta 4 went over here
+
+and then theta 5 went
+like that, and there
+
+was an odd number of
+creases, this would be bad.
+
+Even though they're lined
+up, there's no crease here.
+
+You just went straight
+from theta 5 theta 1.
+
+You're supposed to change
+direction every crease.
+
+So also, n is even to
+alternate directions.
+
+Question?
+
+AUDIENCE: Oh, no.
+
+You already--
+
+PROFESSOR: All right, good.
+
+Clear?
+
+This is pretty easy, once you
+realize the angles correspond
+
+to x-coordinates in
+this linear space.
+
+So why is this enough?
+
+In order to show
+that this property is
+
+enough for flat
+foldability, we need
+
+to actually worry about the
+stacking order of these edges.
+
+We need to worry about
+the y-coordinates.
+
+We need to make sure that
+they can avoid collision
+
+with some mountain
+valley assignment.
+
+The good news is we're free
+to use whatever mountains
+
+and valleys we want.
+
+We can stack things
+however we want.
+
+We just need to find
+some valid state.
+
+And our intuition, from
+the one dimensional case,
+
+was we should try alternating
+mountains and valleys.
+
+That seemed like a good thing.
+
+It avoided collisions for
+an open piece of paper--
+
+for a line segment.
+
+Of course, we know
+that's not enough.
+
+Here-- somewhere--
+I drew this example.
+
+So it's alternating
+in the middle,
+
+and then that last
+crease is a problem.
+
+But that's all we need to fix.
+
+It turns out it's not so hard.
+
+So we have a nice circle.
+
+What I'd like to do
+is cut that circle.
+
+So here, I sort of cut
+it and thought about it
+
+as a line segment and
+then I wanted to rejoin.
+
+OK.
+
+I'm going to be careful
+about where I cut it.
+
+OK, I want to cut at an
+extreme left or extreme right.
+
+It doesn't matter.
+
+We can see here the cut
+ended up being in the middle.
+
+That's bad.
+
+So how do I fix it?
+
+What does extreme mean?
+
+How do I tell--
+given a circle, it's
+
+a little hard to say
+what extreme means,
+
+because it's circular.
+
+But if I take a
+picture like this,
+
+I've already drawn it
+with nice x-coordinates--
+
+I don't know about the
+y-coordinates yet-- I say,
+
+oh that's bad.
+
+My cut point ended
+up being non-extreme.
+
+Well, this is extreme.
+
+So cut here instead.
+
+So what that means is
+redraw this picture
+
+with this being the cut point.
+
+So maybe, this is the beginning.
+
+So we go like that again
+and now we wrap around.
+
+So now we have this segment.
+
+And now we have this segment.
+
+And lo and behold,
+it remained extreme.
+
+And this is always true.
+
+You can do this sort
+of cut and rejoin
+
+the ends that were
+messed up before.
+
+And you'll preserve
+the x-coordinates.
+
+The x-coordinates
+aren't changing
+
+when you do this kind
+of transformation.
+
+So there's a clear leftmost
+and there's a clear rightmost.
+
+You pick either one,
+you cut there instead.
+
+And now we have
+this nice property
+
+that it's easy to join
+the ends, because it's
+
+as far left as you can go.
+
+There can't be anything
+that penetrates,
+
+because that would
+be farther left.
+
+Let me write down some
+words corresponding to that.
+
+So once we cut at
+this extreme crease,
+
+you can fold this
+1D segment just
+
+like we used to be able to.
+
+So we can fold it flat
+using the accordion fold,
+
+alternating mountain and valley.
+
+We know that works.
+
+And then all we need to show
+is that the two ends can join.
+
+Those ends are the two
+copies of the cut crease
+
+that we did in this first step.
+
+We need two things.
+
+One is that they are
+aligned and that's
+
+where we need this condition--
+that the sum of the odd angles
+
+equals the sum of even angles,
+which is the same as saying
+
+the alternating sum
+is equal to zero.
+
+That tells us that
+whatever we do,
+
+the x-coordinates are
+lined up at the end.
+
+So they are aligned by the
+assumption that we made here.
+
+And you can join
+without crossing.
+
+So this is a statement
+about y-coordinates.
+
+And we know it's OK, because
+it's at the left extreme.
+
+So by this choice
+of the proper cut,
+
+there could be other things
+that come right to the boundary
+
+here, but that's considered OK.
+
+That's not crossing,
+that just touching.
+
+Nothing can go farther
+left because it
+
+was the left extreme.
+
+That's the end of the proof.
+
+Any questions about that?
+
+That's Kawasaki's
+theorem-- Kawasaki-Justin.
+
+I would mention just for fun--
+this is sort of classic--
+
+if you allow one of
+these-- a non-convex cone,
+
+where you have more than
+360 degrees of material--
+
+this statement is not true.
+
+And there's one other
+situation which can happen,
+
+which is that the alternating
+sum of angles is not zero,
+
+but it's plus or minus
+360 degrees, which is fun.
+
+And you can see examples
+of that in the book.
+
+All right.
+
+So obviously, if
+you want to tell
+
+whether a crease pattern-- or a
+single vertex is flat foldable,
+
+you just compute this
+thing in linear time
+
+and you know yes or no.
+
+So crease patterns
+are pretty easy-- just
+
+have one extra condition.
+
+What about mountain
+valley assignments?
+
+Last time, we looked at
+mountain valley assignments
+
+and we showed that crimps
+and end folds were always
+
+enough to fold any mountain
+valley assignment that's
+
+out there.
+
+That will continue
+to be true here,
+
+except now we don't
+have end folds.
+
+Now, it's crimps all the way.
+
+What does it mean?
+
+So that is the flat foldable
+mountain valley patterns.
+
+We're going to prove
+that crimps are enough,
+
+but before we get
+there, I need a bunch
+
+of sort of warm up facts about
+valid mountain valley patterns.
+
+The first thing is just
+counting mountains and valleys.
+
+So even if you play with a
+simple example like this one,
+
+you see it as three
+mountains and one valley
+
+or three valleys
+and one mountain.
+
+In fact, if you have
+a degree 4 vertex,
+
+with four creases
+emanating from that point,
+
+those are your only choices.
+
+You could try, for example,
+making it all valleys,
+
+and it-- I mean,
+you can't do it.
+
+It's hard to demonstrate.
+
+You could try making it two
+mountains and two valleys.
+
+Maybe I try to do
+mountain mountain here
+
+and then somehow this is going
+to be valley valley there.
+
+It's no good.
+
+But what's happening here is
+that the number of mountains
+
+and the number valleys
+must differ by exactly two.
+
+It doesn't matter who's bigger.
+
+So the difference could be
+plus 2 or minus 2, because you
+
+can always flip over and negate
+that difference, swapping
+
+mountains for valleys.
+
+But they always have to
+differ by exactly two.
+
+Why is that?
+
+Well, this is--
+yeah, we're again
+
+going to think of a
+picture like this.
+
+We have horizontal travel
+according to the theta i's.
+
+We're also going to think
+about the vertical picture.
+
+If this thing is flat
+foldable-- so I'm assuming,
+
+it's flat foldable--
+then this must happen.
+
+This is called Maekawa's
+theorem, by the way.
+
+It was proved by Jun Maekawa
+in 1986-- a little earlier.
+
+Also proved by Jacques
+Justin around the same time--
+
+back before we were good at
+internet and communication
+
+and whatnot.
+
+And there were little pockets
+of mathematical origamists
+
+and they found each
+other basically
+
+in '89, when there was the-- '89
+was the first origami science
+
+math and education
+conference-- started
+
+bringing these people together.
+
+The last one was this summer.
+
+Right.
+
+So why is this true?
+
+I don't know.
+
+A flat folding looks
+like something.
+
+It has no crossings.
+
+It has-- the horizontal
+travel, we understand.
+
+It ends up back
+where it started.
+
+There's also some notion of
+layers and vertical travel,
+
+which is a little
+tricky to think about.
+
+But the one thing that's
+easy to think about-- I
+
+mean, this forms
+essentially a polygon.
+
+It's like a really
+squashed polygon.
+
+And these vertical segments are
+actually really just points.
+
+OK, imagine.
+
+That's just where
+you turn around.
+
+So it's like a polygon,
+just stretched or squashed
+
+down onto a line.
+
+And we know some
+things about polygons.
+
+OK, as an end
+vertex polygon-- you
+
+know that the sum of
+the interior angles
+
+is-- whatever it is.
+
+I always get confused
+with that formula.
+
+So I don't like
+to think about it.
+
+But one thing we-- an
+easier way to think
+
+about that same statement
+is just think about how much
+
+turning the polygon does.
+
+So you start here, you
+turn right 180 degrees,
+
+you turn left 180 degrees,
+you turn left 180, right 180,
+
+right 180, right 180.
+
+How much is it in total?
+
+Oh gosh, do I have to add?
+
+No.
+
+It's so simple.
+
+It's 360.
+
+Right?
+
+Just, if you think about
+if you're going around
+
+in a circle, any polygon-- not
+just flat-- but anything in two
+
+dimensions, the total amount
+of turning you do is 360.
+
+Or if you count backwards,
+it's negative 360.
+
+So this is the key--
+something you should all
+
+know about polygons.
+
+If you look at sum of the turn
+angles-- how much turning you
+
+do at each vertex--
+that will always
+
+be plus or minus
+360 in any polygon.
+
+This is equivalent to the sum
+of the interior angles being,
+
+whatever, pi times n minus
+2, which I don't remember.
+
+But this is much
+easier to remember.
+
+And it's useful, because we
+can map mountains and valleys
+
+to left and right turns.
+
+As I said, every time
+this is a valley,
+
+it was a left turn by 180.
+
+Every time it was a mountain,
+it was a right turn by 180.
+
+So valleys, mountains,
+right turns--
+
+so I'm going to think
+of that as negative 180.
+
+Now, of course technically, it
+could be the other way around.
+
+It could be this is
+negative, this is positive.
+
+But I already have a
+plus and minus here.
+
+So it's symmetric.
+
+So if we sum up the
+turn angles-- which
+
+we know is supposed to
+be plus or minus 360--
+
+the sum of the turn angles
+is going to be-- we're
+
+going to have 180 for
+each valley, so 180
+
+times the number of valleys.
+
+And we're going to have
+negative 180 for each mountain.
+
+And so the 180's factor out.
+
+And this thing is supposed to
+equal 360-- plus or minus 360.
+
+How could that be?
+
+Well, the number of valleys
+minus number of mountains
+
+should be either 2-- for
+plus 360-- or negative 2--
+
+for minus 360.
+
+So that proves the theorem.
+
+And that's why, in a degree
+4 vertex, one of them
+
+has to be 3, the
+other one has to be 1.
+
+There's no other option,
+because the total number is 4.
+
+It's the only way to
+get the difference
+
+to be plus or minus 2.
+
+So that's kind of nice.
+
+But it's not enough,
+unfortunately.
+
+If I gave you a mountain
+valley pattern that
+
+satisfies this
+condition, it still
+
+might not be flat foldable.
+
+That's maybe no surprise.
+
+It's not like we had
+such a simple test
+
+for the one dimensional
+case, which should be easier.
+
+We had to give an algorithm.
+
+We said repeatedly
+crimp and end fold.
+
+If you get stuck,
+the answer is no.
+
+If you don't get stuck,
+you folded it great.
+
+I love this eraser--
+increases entropy.
+
+Let me tell you one case
+that is easy to think about.
+
+Because it's nice.
+
+It reduces directly to
+the one dimensional case.
+
+And that's what I
+call the generic case.
+
+Generic is this very convenient
+term we use in mathematics.
+
+It's actually really
+tricky to define.
+
+So I'd like to not
+define it, if I can.
+
+But maybe I should.
+
+The simple version, which
+is not quite enough,
+
+is to say that all of the
+angles in the crease pattern
+
+are different.
+
+OK, here, for example,
+two of them are the same.
+
+There's two 90 degree angles.
+
+This is not generic.
+
+It's just easier to draw.
+
+But in general, I
+mean, you imagine,
+
+you just draw some random thing.
+
+None of those lengths
+are going to be the same.
+
+Yeah, the alternating
+sum is zero.
+
+But that's it.
+
+And that's what I--
+the generic case
+
+is that is the only thing that
+holds true about these angles.
+
+You can take the
+alternating sum.
+
+That equals zero.
+
+If you take some alternating sum
+of some subset of the angles,
+
+that will not equal zero.
+
+If you take a random example,
+this is going to be true.
+
+OK, just bear with me.
+
+Suppose never any two
+angles are the same.
+
+Then look at the
+globally smallest crease,
+
+so globally smallest theta.
+
+Say it's theta i.
+
+So the picture is theta i,
+theta i minus 1, theta i plus 1.
+
+And what do we know
+if it's globally
+
+smallest and none of
+the values are equal?
+
+Then we know that
+these two are bigger.
+
+No big surprise.
+
+Think about what happens if
+this is small, these are bigger,
+
+and you try to make these both
+valleys or both mountains,
+
+that's, of course, bad.
+
+This is one of the
+situations we had
+
+in the one dimensional case.
+
+I mean, really,
+this is a circle,
+
+but I can think just locally
+about what's happening here.
+
+So in this situation, one
+of these must be a mountain
+
+and the other must be a valley.
+
+I don't know which
+order they are,
+
+but I know they're different.
+
+And then I know I can
+apply one of these crimps.
+
+Incidentally, the word crimp,
+Jason Koo was asking about,
+
+like, why do you call
+it crimp and not pleat?
+
+Probably, I should
+call it pleat.
+
+But it's crimp in my mind.
+
+It's been crimp in
+my mind since 1998
+
+when we wrote the 1D paper.
+
+It was before I knew the word
+pleat, so that's my excuse.
+
+So pleat or crimp,
+take your pick.
+
+Crimp is usually
+many pleats together.
+
+That's crimping.
+
+Cool.
+
+So crimps, we kind of like.
+
+Why do we like crimps?
+
+We proved, in the one
+dimensional case last time,
+
+that if you make a crimp
+and your original thing
+
+was flat foldable, the new
+thing will be flat foldable.
+
+Good news is, that
+is still true.
+
+I told you, all these
+things were no longer
+
+true in the circular case.
+
+It's still true in
+the circular case.
+
+Should I tell you--
+
+Let me just remind you-- the
+same proof works-- remind you
+
+what the proof looked like.
+
+We had a crimp, and we're
+hoping to fold that first.
+
+We know at some point,
+these creases get folded.
+
+But there may be
+other junk in here,
+
+or maybe other junk in here.
+
+We'd like to get
+rid of that junk.
+
+And so what we did
+is move this junk up
+
+to here, which was always safe.
+
+We moved this junk down to here.
+
+And that was still a folded
+state-- a flat folded state.
+
+OK, remember all this stuff.
+
+Therefore, we could have
+folded the crimp first.
+
+And then we have a flat folding
+in this situation, where
+
+this paper is effectively
+glued together, which means,
+
+it was safe to fold this
+crimp and glue these
+
+together and never
+touch them again.
+
+So that is still true
+in the circular case.
+
+That proof didn't really assume
+anything about the paper.
+
+Would even work for
+like tree shaped
+
+paper or something weird.
+
+So if we can find a crimp, which
+we can in the generic case,
+
+then you just make a crimp,
+make a crimp, repeat.
+
+If you ever get stuck, you know
+that the original thing was not
+
+flat foldable, because the thing
+you have is not flat foldable.
+
+Why?
+
+If there's no cramp
+in the generic case,
+
+that means you have two valleys
+around the smallest angle,
+
+and that's clearly bad.
+
+So-- I'm not writing
+a lot of details here.
+
+Is that clear?
+
+If I have an angle
+that's surrounded
+
+by strictly larger
+angles, I know
+
+there must be one
+mountain and one valley.
+
+Then I can safely make
+a crimp and repeat.
+
+The trouble comes in when
+these angles are equal.
+
+We never had to
+think about angles
+
+being equal in the
+one dimensional case.
+
+It didn't matter much.
+
+We just said, oh, you know,
+it's safe to make a crimp,
+
+as long as this was greater
+than or equal to this
+
+and this was greater
+than or equal to this.
+
+That is still true; it's
+safe to make a crimp.
+
+But how do we know
+that there is a crimp?
+
+How do we know that there's a
+mountain followed by valley?
+
+We don't.
+
+I mean, if they're equal,
+this would be all right.
+
+That's two valleys is valid if
+these three angles are equal.
+
+But I claim still somewhere
+there's got to be a crimp.
+
+There's no longer a notion of
+the globally smallest angle,
+
+because some of them are equal.
+
+We've got to find that
+crimp, but it's out there.
+
+So we just need to
+prove that it exists.
+
+So to do that, we're going
+to generalize this theorem--
+
+Meakawa-Justin-- that number
+of mountains minus number
+
+of valleys is plus or minus 2.
+
+That's true, and
+it's a statement
+
+about the sum of all the
+angles-- all of the creases.
+
+What I'd like is something
+a little bit more localized.
+
+And in particular,
+we're going to think
+
+about when I have a whole
+bunch of angles that are equal,
+
+how many mountains and
+valleys can there be in there.
+
+So it's what I
+call local counts.
+
+So while everything I said
+so far is pretty classic,
+
+this result was proved
+in 2001 by Tom Hall,
+
+so much more recent,
+over a decade later.
+
+So let's think about
+k equal angles.
+
+And I want that to be a maximal
+sequence of equal angles,
+
+so the ones right after and
+right before are different.
+
+And furthermore,
+I'm going to assume
+
+that they're bigger--
+strictly larger angles.
+
+OK, so something like that.
+
+A bunch of equal
+angles-- k of them--
+
+bigger angles on either side.
+
+This almost always exists.
+
+I should mention-- so I'm
+going to say something
+
+about this situation.
+
+But this situation should exist,
+because I take the smallest
+
+angle out there and then
+I see how many friends
+
+it has that are all equal.
+
+If it's the smallest angle--
+or it's one of the smallest
+
+angles-- then the
+ones surrounding
+
+it are going to be bigger--
+unless all the angles are
+
+equal.
+
+So there's one case, which
+we'll worry about later.
+
+It's very easy.
+
+All the angles are equal.
+
+In fact, I could tell you
+how to worry about that.
+
+If all the angles are
+equal, then everything
+
+is crimpable as long as we can
+find a switch between mountain
+
+and valley-- somewhere.
+
+And because the number
+of mountains and valleys
+
+is plus or minus 2, there's
+got to be-- so they're almost
+
+in equal balance-- there's
+got to be a valley.
+
+It can't be all valleys,
+can't be all mountains.
+
+So somewhere,
+there's a transition
+
+between mountain and valley.
+
+So you get a crimp out of that.
+
+But otherwise, if they're
+not all equal-- let's
+
+think about k equal angles
+surrounded by two larger guys.
+
+Forgot how technical this is.
+
+All right.
+
+Then I want to look at
+the number of mountains
+
+and the number valleys among
+these k plus one creases,
+
+so within that range.
+
+It's going to be 0, if k is odd.
+
+And it's going to be plus
+or minus 1, if k is even.
+
+It's not plus or minus 2.
+
+Intuitively, plus or minus 2 is
+when you go all the way around.
+
+Here, we're just
+looking at a segment--
+
+a portion of the entire circle.
+
+Remember, this is actually
+a circle somewhere.
+
+And this corresponds
+to, in the odd case,
+
+you're going to be going in
+the same direction afterwards.
+
+In the even case,
+you're going to have
+
+turned around but
+not a full circle.
+
+So it's going to
+be plus or minus 1.
+
+There's a lot of
+ways to prove this.
+
+One way is to think
+about convex cones.
+
+So if k is even, and you
+fold this thing-- let's see,
+
+one, two, three, four,
+five, six-- equal angles.
+
+And then there's
+the two longer guys.
+
+They may not be the
+same length, but that's
+
+what you get in the even case.
+
+So what I'd like to do is
+just, in order to just reduce
+
+to things that we've already
+thought about-- I mean,
+
+you could talk about
+turn angles again,
+
+or you could just say, hey,
+I know Maekawa's theorem.
+
+So as long as I could make
+this into a circle, which
+
+I can do by adding
+that stuff, now I
+
+have a nice circular--
+it's a flat folded state.
+
+There's no crossings
+here, presumably
+
+because this did something.
+
+I don't actually know
+that it's zigzagging.
+
+It might do other stuff.
+
+But it's not going to
+cross what I just added.
+
+So the number of mountains
+minus number of valleys,
+
+in total here, must
+be plus or minus 2.
+
+I only added one
+crease-- this one.
+
+So that's going to make
+it either plus or minus 1
+
+or plus or minus 3.
+
+If you think about
+it a little bit,
+
+it has to be plus or minus 1.
+
+And hopefully, that's
+what I wrote here, yes.
+
+Because I mean, really, we're
+thinking about turn angles
+
+again, I'm afraid.
+
+Can't totally reduce it.
+
+We just turned around here.
+
+And we were about to
+finish the circle, which
+
+would make it plus or minus 2.
+
+Before we finish the circle,
+it's plus or minus 1.
+
+k is odd.
+
+Again, this might go
+like that, whatever.
+
+But, because it's an
+odd number, these guys
+
+are going in the same direction.
+
+And so the total turn
+angle here must be 0.
+
+And one way to see that is to
+extend it into a full polygon.
+
+You know that it's plus or
+minus 2 for this whole thing.
+
+And I added two guys
+in the same direction.
+
+If I remove them, it's going
+to go down to plus or minus 0.
+
+That was a bit hand wavy.
+
+But do you buy that?
+
+AUDIENCE: [INAUDIBLE]
+plus or minus 0?
+
+PROFESSOR: Plus or
+minus 0 is 0, yeah.
+
+You went from 2 down
+to zero, because you
+
+remove two identical guys.
+
+So let me tie this all
+together, because there's
+
+so many little cases.
+
+So I want to know what
+mountain valley patterns are
+
+flat foldable, single
+vertex, m/v patterns.
+
+I claim there is a crimp.
+
+If it's flat foldable,
+there has to be a crimp
+
+that you can find to do.
+
+Remember, a crimp
+was where this length
+
+was less than or equal to
+this length and less than
+
+or equal to this length.
+
+And one of these was m.
+
+One of them was v. That was
+the definition of a crimp.
+
+I claim such a
+thing always exists.
+
+The proof is two parts.
+
+If all the angles are equal,
+we know that these conditions
+
+are always satisfied,
+because everything is equal.
+
+So we just need to
+find an m followed by v
+
+or a v followed by an m.
+
+And by Maekawa's theorem, we
+know it's not all m's or all
+
+v's.
+
+So somewhere, there has to be
+a transition from m to v's.
+
+So just use that lemma
+theorem or the count property.
+
+Otherwise, if they're
+not all equal,
+
+then I can apply this
+local counts result,
+
+take the smallest angle-- take
+one instance of the smallest
+
+angle.
+
+There could be many of them.
+
+Find all of its neighboring
+friends that are equal.
+
+Then I know that the next
+angles before and after
+
+have to be strictly bigger.
+
+Then I know that the number of
+mountains and valleys in here--
+
+if I look at the
+difference and it's
+
+0, that means the
+number of mountains
+
+equals the number of valleys.
+
+Therefore, there's
+at least one of each.
+
+And therefore, there's a
+transition from mountain
+
+to valley in there.
+
+Because the transition
+from mountain to valley--
+
+like right here,
+that's a valid crimp.
+
+This guy's bigger;
+this guy's equal.
+
+This would also be
+a fine transition,
+
+because everybody's equal.
+
+This would also be
+a fine transition.
+
+Any transition from
+mountain to valley in here,
+
+I've got a crimp.
+
+The even case is a little-- I
+got to think a little bit more.
+
+k is even.
+
+k plus 1, which is the number
+of creases here, is odd.
+
+And the difference between
+mountains and valleys
+
+among those k plus one
+creases is plus or minus 1.
+
+Think about it for second.
+
+That means there's, again, at
+least one mountain and at least
+
+one valley.
+
+Because k, to be even,
+has to be at least 2.
+
+We've got to have at
+least three things.
+
+So there's going to be at
+least one of one and two
+
+of the other, in fact.
+
+And I just need one mountain and
+one valley somewhere in there.
+
+And then I know there has to
+be a transition from mountain
+
+to valley.
+
+Otherwise, use local counts.
+
+And in either case, we
+get either a mountain
+
+to valley transition or a
+valley to mountain transition.
+
+And I get it in such a way
+that these inequalities
+
+on the lengths hold.
+
+So in other words,
+that it's a crimp.
+
+Therefore, any flat foldable,
+single vertex, mountain valley
+
+pattern has a crimp.
+
+Make it.
+
+And as I was arguing
+here, just like last time,
+
+that crimp will still--
+after you do the crimp,
+
+you'll still be flat
+foldable, so repeat.
+
+Cook until done is
+how I like to put it.
+
+Question.
+
+AUDIENCE: What about the trivial
+case of just folding a circle
+
+in half?
+
+PROFESSOR: The trivial case
+of folding a circle in half.
+
+All right.
+
+That's a good question.
+
+It's kind of a technicality.
+
+One version would be to
+say, that's zero vertices.
+
+That doesn't count.
+
+And we're thinking
+about one vertex.
+
+And as soon as
+you think about it
+
+as one vertex, which is
+fine, then you actually
+
+have two creases there.
+
+So it's two creases.
+
+And hopefully, this works.
+
+Oh, I see what you're saying.
+
+It's not a crimp.
+
+That's a good point.
+
+AUDIENCE: But then
+it's flat foldable.
+
+PROFESSOR: It is flat foldable,
+and yet, there's no crimp.
+
+Damn it.
+
+All right.
+
+Sorry?
+
+AUDIENCE: But it follows
+Maekawa's, right?
+
+PROFESSOR: Yeah.
+
+So I made a slight mistake here.
+
+I said if all the
+angles are equal,
+
+then Maekawa says there's
+at least one of each.
+
+That's not true when n equals 2.
+
+Then there's two of one
+and zero of the other.
+
+As long as you have more than
+two creases, then this is true.
+
+That's enough.
+
+So you have to handle
+this as a special case.
+
+AUDIENCE: At the end
+of your algorithm,
+
+you're always left
+with two of the same--
+
+PROFESSOR: That's true.
+
+This is an important
+special case to remember,
+
+because this will be
+the final picture.
+
+After you do a sequence of
+crimps, this is the good case.
+
+If your thing is
+flat foldable, you
+
+will always end up with that.
+
+AUDIENCE: That's a
+case where everything
+
+is the same, smallest.
+
+PROFESSOR: It's another example
+where all the angles are equal.
+
+So that's why this
+is the situation.
+
+It's either Maekawa and
+you get a cramp here,
+
+because n is greater than 2.
+
+And here, I should say,
+if n is greater than 2,
+
+then this is true.
+
+Of course the n equals 2
+case, it looks like that.
+
+And it had better be both
+valleys or both mountains.
+
+Otherwise, it's not going
+to be flat foldable.
+
+I forgot about that.
+
+I should add it in the notes.
+
+But it's in the textbook, right.
+
+AUDIENCE: At the end
+of the algorithm,
+
+it's not going to be a circle.
+
+It's going to be a cone.
+
+PROFESSOR: That's true.
+
+It won't actually
+look like this.
+
+At the end of the algorithm,
+it's going to be a cone.
+
+The two angles will be equal,
+because of Kawasaki's theorem.
+
+And they should still be both
+mountains or both valleys.
+
+But it's going to be--
+we can see it right here.
+
+So I apply my crimp,
+and now I have a cone,
+
+and there's two angles.
+
+There's one here, which
+has been fused together.
+
+And there's one here,
+which is the original.
+
+They're equal.
+
+And it's two mountains
+or two valleys,
+
+if I turned it upside down.
+
+And then it finishes.
+
+So that's the algorithm
+in action-- two steps.
+
+First you find this crimp here.
+
+This is actually the
+globally smallest angle.
+
+It's surrounded
+by bigger angles.
+
+So it's really easy.
+
+Then I have a cone with
+two equal angles, which
+
+is what has to
+happen at the end.
+
+And then I'm done.
+
+Good?
+
+AUDIENCE: Is that the
+only way to do it?
+
+PROFESSOR: This is
+what always happens.
+
+Oh, is this the only way
+to flat fold these things?
+
+No.
+
+There are other--
+yes, one of the two.
+
+I think it depends
+what you're counting.
+
+If you're counting mountain
+valley assignments-- I mean,
+
+if you just want to know,
+can every mountain valley
+
+assignment be
+folded by crimping.
+
+Then the answer is yes.
+
+That's what we proved.
+
+But if you want to get
+every possible folded state,
+
+crimps are not
+going to be enough.
+
+The reason they're not enough is
+because we're using this thing.
+
+So, hey, here's some
+hypothetical folded state.
+
+We can rip it out and make
+the crimp has been done.
+
+But then there's a
+folded state you're not
+
+able to reach by crimping.
+
+We need to work that into an
+actual example, where crimping
+
+forbids you from reaching
+some folded state.
+
+But I'm pretty sure one
+exists because of this.
+
+AUDIENCE: Could that
+be more like spirals?
+
+PROFESSOR: Yeah, maybe some
+kind of spiraling thing.
+
+AUDIENCE: Well, layering
+takes into account--
+
+PROFESSOR: Right.
+
+What we're missing here is
+getting all the possible layer
+
+stacking orders.
+
+So we're just trying to match
+a mountain valley assignment.
+
+We're not going to match
+a target layer ordering,
+
+because we simplified
+the layer orders in order
+
+to make crimps possible.
+
+So crimps won't get you
+some of the folded states.
+
+But one thing you can
+play with over here--
+
+that has been played
+with by Tom Hall--
+
+is if I give you
+a crease pattern,
+
+how many flat foldable
+mountain valley
+
+assignments does it have?
+
+OK, we have this nice linear
+time algorithm to tell you
+
+whether a particular
+one is doable.
+
+How many are there?
+
+And there is-- if
+you work through all
+
+of the things I've shown you
+in a little bit more detail,
+
+you can recover-- this
+was finding a crimp.
+
+But you can actually
+look at what
+
+are all the crimps
+that are possible
+
+and actually count how
+many different ways
+
+there are to fold.
+
+How many crimps you can do.
+
+And then given those
+crimps, how many crimps you
+
+can go after that.
+
+And in the same linear
+time kind of algorithm,
+
+you can figure out how many
+different mountain valley
+
+patterns are flat foldable.
+
+That takes a little
+bit more care.
+
+I will tell you the extremes.
+
+How small could the number of
+flat foldable mountain valley
+
+assignments be for a
+given crease pattern?
+
+Well, do you have
+any guesses when?
+
+When do I have the least
+choice of where to make crimps?
+
+Yeah.
+
+AUDIENCE: We have three angles.
+
+PROFESSOR: For general n.
+
+Sorry.
+
+But, yeah, three angles
+or, I guess, two angles.
+
+We really can't do any--
+I don't have any choice.
+
+But for general n,
+how should I disperse
+
+the theta i's in
+order to make there
+
+be very few possible crimps?
+
+AUDIENCE: When there are
+only two transitions.
+
+PROFESSOR: When there
+are only two transitions
+
+between mountains and valleys.
+
+All the mountains are together.
+
+All the valleys are together.
+
+That's right, if I was asking
+a question about mountains
+
+and valleys.
+
+But I was asking a
+question about theta i's.
+
+So I want to count how many
+mountain valley patterns there
+
+are-- mountain valley
+assignments that
+
+are flat foldable for
+a given crease pattern.
+
+AUDIENCE: So if you
+have a bunch of angles,
+
+consecutive theta
+i's are increasing?
+
+PROFESSOR: All the angles
+are consecutive increasing.
+
+Yeah, that pretty much works.
+
+In fact, what I need
+is the generic case,
+
+where all angles are
+different and they never
+
+become equal by folding,
+which is what generic means.
+
+So then there was only
+really one crimp I could do,
+
+which is the globally
+smallest angle.
+
+So actually, I still
+have two choices.
+
+I could do mountain then
+valley or valley then mountain.
+
+But I only have two
+choices for that crimp.
+
+Then I will have two
+choices for the next crimp,
+
+two choices for the next crimp.
+
+In general, I get 2 to the
+n possible mountain valley
+
+assignments for
+the generic case.
+
+OK, what about,
+what's the opposite,
+
+where I get as much
+choice as possible?
+
+AUDIENCE: Isn't 2 to the n every
+mountain valley assignment?
+
+PROFESSOR: Yes, 2 to the
+n-- no-- 2 to the n over 2.
+
+Thank you.
+
+Right.
+
+There are 2 to the n conceivable
+mountain valley assignments.
+
+It can't be that big.
+
+Every time I do a crimp, I
+eat two creases, not one.
+
+That's what I forgot.
+
+Good.
+
+It's still pretty big though.
+
+It's like square root of
+all the possible things you
+
+could imagine are
+indeed feasible.
+
+What, from 2 to the n
+to 2 to the n over 2.
+
+When would I get the
+most choice in crimping?
+
+AUDIENCE: All angles are equal.
+
+PROFESSOR: All angles are equal.
+
+That's the opposite extreme.
+
+And in this case--
+a little messier.
+
+When all the angles are
+equal, the only property
+
+you need-- and you can
+see that from the proof--
+
+the only property you
+need is that the number
+
+mountains minus
+the number valleys
+
+is plus or minus
+2, and n is even.
+
+As long as you have
+that, we showed here,
+
+you're going to
+have-- on alternation
+
+from mountain valley-- that's
+a valid crimp, because all
+
+the angles are equal.
+
+And you keep going.
+
+So it's just, how do you
+disperse that many-- how
+
+do I disperse n over
+2 minus 1 mountains
+
+among n different positions.
+
+That's what this represents.
+
+And positions, how do I pick
+n over 2 minus 1 of them
+
+to be mountains.
+
+Or it could be n over 2
+minus 1 of them are valleys.
+
+And that's this factor of 2.
+
+So it could have more
+mountains or more valleys.
+
+And then you somehow
+place those among those.
+
+And if you don't
+know this notation,
+
+that's just what it means.
+
+If you want to know
+using other notation,
+
+it's like this, n over
+2 minus 1 factorial,
+
+over 2 plus 1 factorial.
+
+If you don't know factorials,
+I'll tell you about them later.
+
+Cool.
+
+So that's kind of the end of
+the single vertex situation.
+
+Yeah, I think I'll mention one
+interesting open question here,
+
+which I would love to
+explore maybe in our problem
+
+session-- which looks like it'll
+be Mondays at 5:00, I think.
+
+This is one vertex, and we
+went through all this work
+
+to solve a single
+vertex situation.
+
+And it's interesting,
+as we'll see,
+
+to think about locally
+how each vertex behaves.
+
+But you would think, if
+you have a crease pattern
+
+with two vertices, it
+shouldn't be that much harder.
+
+So here we have linear time.
+
+How quickly can you tell
+whether a two vertex crease
+
+pattern is flat foldable?
+
+As far as I know, no one
+has looked at that problem.
+
+Surely, we can do
+it in quadratic time
+
+but maybe even
+linear time, I think.
+
+It can't be that hard, I think.
+
+In general, if I have a
+small number of vertices--
+
+say k vertices-- much
+smaller than n creases,
+
+is there-- for the
+algorithms people-- is there
+
+fixed parameter
+tractable algorithm in k?
+
+Or can I get something--
+even getting something like n
+
+to some function of
+k, would be progress.
+
+I think this should be doable.
+
+But ideally, we
+get a running time
+
+that's exponential
+in k and linear in n.
+
+That would be my hope.
+
+Why do I say it has
+to be exponential?
+
+Because in general,
+if I give you
+
+a crease pattern with n
+vertices-- lots of vertices--
+
+this problem is
+NP-complete, which
+
+is-- there's not going
+to be a polynomial time
+
+algorithm for it.
+
+Nothing good.
+
+We will prove that
+next Wednesday.
+
+So I'll hold off on
+that a little bit.
+
+But for two vertices,
+how hard could it be?
+
+All right.
+
+I want to talk about
+one related topic.
+
+And then we will go
+to origami design
+
+and do a little bit
+on the tree method.
+
+But before we get
+there, I want to talk
+
+about local foldability,
+which is a cool topic.
+
+People tend to forget about it.
+
+I really like it.
+
+I think it would make
+a cool project also.
+
+It's a nice algorithm.
+
+It goes back to Bern
+and Hayes, 1996.
+
+So it's also right
+at the beginning
+
+of origami mathematics.
+
+And it's this idea,
+all right, I give you
+
+a crease pattern now
+arbitrarily many vertices.
+
+And if I ask you,
+does it fold flat?
+
+That's NP-complete--
+intractable-- same paper.
+
+But what if I ask you just
+to give me a mountain valley
+
+assignment that might fold flat?
+
+Well, that's also NP-complete.
+
+But if you actually
+want it to fold flat,
+
+this is really the same problem.
+
+But if I ask you, give me a
+mountain valley assignment,
+
+so that if I checked
+every vertex according
+
+to this algorithm, at least
+every vertex folds flat.
+
+That would seem nice.
+
+Definitely, I have to find a
+mountain valley assignment that
+
+satisfies these
+conditions, that as I
+
+do successive crimps,
+every vertex-- if I cut out
+
+the vertex separately,
+it would fold flat.
+
+This is the notion
+of local foldability.
+
+And there's a linear
+time algorithm
+
+to give you a mountain valley
+assignment that ought to work,
+
+in that at each vertex it works.
+
+It still may not work globally
+for some other reason.
+
+But it's pretty good.
+
+I think this would be,
+actually, pretty practical.
+
+I think in a lot of real
+world origami settings--
+
+when you're doing
+flat folding anyway--
+
+locally foldable is going to be
+enough to be globally foldable.
+
+That's a guess.
+
+I don't know if it's true.
+
+Consistent mountain
+valley assignment,
+
+if there is one, so that each
+vertex locally folds flat.
+
+Let me try to concoct a
+small example that's relevant
+
+here-- got to think.
+
+Yes, I think that works.
+
+All right, here we go.
+
+I think this is in the textbook.
+
+I remember drawing it
+in the past three years
+
+ago or whatever.
+
+So here's a crease pattern
+on a square or whatever.
+
+AUDIENCE: The top
+one should have--
+
+PROFESSOR: Yes, it
+should have this.
+
+Thank you.
+
+So this satisfies
+Kawasaki's theorem--
+
+that was the hard part--
+because these angles sum to 180.
+
+And it's symmetric all around.
+
+OK, these angles
+are the smallest.
+
+They are 60 degrees.
+
+This is an equilateral triangle.
+
+So we have this-- not
+quite the generic case,
+
+but we have the
+smallest angle is
+
+surrounded by two larger angles.
+
+Therefore, one of
+these is a mountain;
+
+the other is a valley.
+
+That means that
+these two creases
+
+have to have different
+assignments-- I'm
+
+going to write a not equal sign.
+
+One of these is a mountain,
+and the other is a valley.
+
+They can't be the same.
+
+Also, these two
+cannot be the same.
+
+Also, these two
+cannot be the same.
+
+That's not possible.
+
+Because I've got three,
+it has to alternate.
+
+You can alternate three times.
+
+You can only alternative
+at even number of times.
+
+Two of these are mountains.
+
+One is valley.
+
+And then you've got a problem.
+
+OK, so this thing is
+not flat foldable.
+
+And this algorithm
+will tell you that.
+
+Because it will say,
+hey, I can't even
+
+find a mountain
+valley assignment
+
+that could possibly
+fold each vertex flat.
+
+So this is a nice algorithm.
+
+At least, it will detect
+annoying situations like that.
+
+So in order to solve
+this, we're going to use--
+
+and I'm just going to sketch
+how this algorithm works--
+
+we're going to use this
+characterization and this idea
+
+that we can really find all
+possible mountain valley
+
+assignments just by trying all
+the possible crimp sequences.
+
+Now, there are
+exponentially many.
+
+So it's not like I'm actually
+going to try them all.
+
+But I need to explore that
+space of candidate crimps
+
+and see what happens.
+
+So the idea is kind of crazy.
+
+The beginning of
+the algorithm is
+
+fold each vertex flat-- somehow.
+
+I don't care how.
+
+Just pick a crimp, do it.
+
+Pick a crimp, do it--
+separately for each vertex.
+
+They're not going
+to be compatible.
+
+And don't look at the mountain
+valley assignment you get.
+
+But look at the crimping
+sequence you get.
+
+So here, let's do
+a little example--
+
+a non-trivial example.
+
+So here, we have the peace sign,
+and these two angles are equal.
+
+They're smallest.
+
+I could crimp this
+angle first, or I
+
+could crimp this angle first.
+
+I have a choice.
+
+So I'll draw both of them.
+
+If I crimp this angle
+first, I know these guys
+
+are paired up in the sense
+that they must be not equal--
+
+one's mountain and one's valley.
+
+After I do that crimp-- just
+like in the real example
+
+I had-- this angle
+will equal that angle.
+
+And these two guys must
+have equal assignments.
+
+They must be both
+mountain or both valley.
+
+In this situation,
+these two guys
+
+are not equal, if I
+crimp this pair first.
+
+And these two guys must
+be equal-- equal now
+
+in the sense of being
+mountain or valley.
+
+OK, so there are still
+exponentially many
+
+possibilities in how to do this.
+
+But just pick one-- pick one
+of these ways of pairing up.
+
+You're going to pair up
+each of the n creases
+
+into n over 2 pairs.
+
+And they're going to have some
+not equal and equal signs.
+
+So now, if you imagine
+the general picture,
+
+like here, for example, I
+might get-- in this pattern,
+
+I would be forced
+to get not equals
+
+and these guys paired up.
+
+And in general, I want to
+look at these kinds of cycles.
+
+If I come into a vertex--
+here's a vertex--
+
+it's paired up with somebody.
+
+So if I come in here,
+I can go out somewhere.
+
+And I come to this vertex,
+it's paired with somebody.
+
+So I'm going to just-- I
+can keep wandering around.
+
+And in general, there will
+be a bunch of these paths
+
+that you can follow.
+
+What could the paths do?
+
+They either close up on
+themselves-- maybe things
+
+are paired up in such a way
+that you make a return trip.
+
+Or it could be some other path.
+
+Let me draw a dotted path.
+
+It could come in
+here, and maybe it
+
+gets paired up with this guy.
+
+Maybe it goes off to infinity.
+
+It reaches the
+boundary of the paper.
+
+Those are the two possibilities.
+
+You get paths, which
+go off to the edge--
+
+off to infinity on either end.
+
+Or you could get cycles.
+
+The cycles are the problem.
+
+Because whenever I have a cycle,
+I have a parity constraint.
+
+For example, when
+they're all not equals,
+
+the length of the
+cycle must be even.
+
+If there were-- what's
+the general statement?
+
+It's like the
+parity of the cycle,
+
+which is whether
+it's even or odd,
+
+should be equal to the parity of
+the number of not equal signs.
+
+Something like that.
+
+I've got a sheet here.
+
+Great, I just said
+"parity problems."
+
+It's something like that.
+
+It's either the
+parity of the cycle
+
+should equal the parity
+of the number of equals
+
+or the parity of the
+number of not equals.
+
+I think, number of equals.
+
+Anyway, one of the two.
+
+And you can just check.
+
+I mean, you're forced.
+
+If I say, OK, let's
+make this mountain,
+
+then this is either
+equals or not equals.
+
+It'll tell me whether this
+is mountain or valley.
+
+Just walk around the cycle.
+
+Either you get a
+contradiction or you don't.
+
+If you get a contradiction,
+we have a problem.
+
+How could we possibly
+fix the problem?
+
+Well, when we made-- you
+look at each of these cramps.
+
+I mean, in fact, you could
+look at each of these vertices
+
+separately.
+
+But you think about one of
+these crimps and say, well,
+
+could I have done
+it another way?
+
+Sometimes, there are crimps
+that have other equal choices.
+
+Maybe, there are a
+bunch of equal angles.
+
+And I could have done
+a different pairing.
+
+What happens when I try
+a different pairing?
+
+Well, instead of this
+being in one cycle
+
+and, let's say, this
+being in another cycle,
+
+if I pair these guys
+up instead, I'll
+
+end up merging those two
+cycles into one bigger thing.
+
+It could be a path or a cycle.
+
+And the algorithm says, just
+keep doing those cycle merges.
+
+And if you get stuck, your
+thing is not locally foldable.
+
+That's the hard part to prove.
+
+Otherwise, you will find
+one of these patterns
+
+that you can actually
+resolve mountains and valleys
+
+all the way through.
+
+So let's say, so start with some
+folding-- say local folding,
+
+whatever.
+
+I'm going to say with some
+pairing of creases at vertices.
+
+And merge two paths or
+cycles whenever possible.
+
+And when I say merge,
+I mean whenever
+
+you have-- what are the possible
+things you could possibly
+
+merge-- when you have at some
+point during the algorithm
+
+a bunch of equal angles, you
+have a choice which of these
+
+you crimp.
+
+Obviously, the mountain valley
+assignment is not fixed.
+
+You can crimp any of them.
+
+You picked one of
+them, and it's sort
+
+of merging whatever this
+thing is attached to,
+
+to whatever this
+thing is attached to.
+
+If there's something else that's
+disconnected from that thing,
+
+I want you to instead
+merge two of them that
+
+combines two different
+connected components-- two
+
+paths or cycles.
+
+Merging means I decrease
+the total number
+
+of paths or cycles.
+
+I combine two into one.
+
+Whenever that's possible, do it.
+
+You can prove that
+if you have parity
+
+problem in the
+merge thing, you had
+
+to have had a parity
+problem originally.
+
+And merging can only
+fix parity problems.
+
+That's the claim, and that's
+what I will not prove.
+
+Once you know that-- and it
+doesn't matter in what order
+
+or how you choose to merge-- you
+just merge as much as possible.
+
+And either the resulting
+thing is OK or not.
+
+And accordingly, you will
+tell whether this thing
+
+is locally foldable.
+
+Sorry, I want to move
+on to other things.
+
+But I think this would be a fun
+thing to actually implement.
+
+It's an easy algorithm.
+
+And it's, I think, a pretty good
+test it for problems like this
+
+that prevent flat foldability.
+
+So let's move on from
+foldability to origami design.
+
+So a bit of a big transition.
+
+And we're going to talk
+about origami design
+
+a lot more next class also
+but just start it off today.
+
+And the particular
+algorithm for origami design
+
+I want to talk about is
+called the tree method.
+
+This is probably
+the oldest algorithm
+
+for origami design,
+in that people
+
+have been thinking about it and
+developing it for many years
+
+through this period called
+the Bug Wars, when people were
+
+trying to design more and
+more complicated insects.
+
+It's like, well, I can make
+an insect with six legs.
+
+Oh yeah, well I can make
+a spider with eight legs.
+
+Oh yeah, well I can make
+an insect-- a beetle that
+
+has wings and horns and there's
+thorns on the horns-- you know,
+
+all these crazy things.
+
+During that time,
+there were a lot
+
+of people thinking
+about how do I
+
+make more and more
+complicated-- especially, more
+
+limbs in my creatures
+and very precise
+
+arrangements of those
+limbs, let's say.
+
+And that is what the tree
+method deals with and was really
+
+formalized by Robert Lang,
+who published a paper in '96,
+
+describing it as a sort
+of complete algorithm.
+
+And it's still
+not known for sure
+
+that that algorithm
+always works.
+
+But that's what
+we've been working
+
+on-- me and Marty and Rob Lang--
+for the last four years or so.
+
+And soon, we will
+publish that thing
+
+and prove that this
+thing always works.
+
+But I'm going to describe the
+algorithm without the proof
+
+that it works.
+
+And what it does--
+I'll tell you its goal
+
+from a mathematical perspective.
+
+So it's interested in
+practical origami design.
+
+So we're going to start from
+a square piece of paper.
+
+It would also work
+for triangular pieces
+
+of paper or anything convex.
+
+But squares are what
+people usually care about.
+
+Sometimes it's used
+for rectangles also.
+
+The idea is I give to
+you a stick figure.
+
+So that's formally,
+it's a tree--
+
+a graph without any cycles.
+
+It's a metric tree, meaning
+that I put lengths on the edges.
+
+I know this length-- this
+edge length-- is maybe
+
+twice as long as this one.
+
+So I really draw it with
+edge lengths in mind.
+
+Then what I want
+you to do is find
+
+some folding of a
+piece of paper--
+
+I should really be looking
+at what I'm trying to match.
+
+So here, here, this
+goes down, such
+
+that I want to find some folding
+of a square paper-- in fact,
+
+the smallest square
+possible, so that when
+
+I project-- like
+this-- vertically,
+
+the projection of that folding
+is exactly that metric tree.
+
+And this is called a
+uniaxial-- this thing is
+
+called a uniaxial base.
+
+Let me tell you a little bit
+why it's called a uniaxial base.
+
+We're thinking about what
+are called origami bases.
+
+These there like the
+beginning of origami models.
+
+And most classic
+origami models--
+
+like more than 60 years ago--
+start from one of these bases.
+
+You've got waterbomb base on
+the top left, preliminary base,
+
+fish base, bird base
+windmill base, and frog base.
+
+I can't remember them all.
+
+I have a little example here.
+
+This is the waterbomb base.
+
+So it's just very
+simple crease pattern.
+
+And why this is useful
+is, it gives you
+
+sort of four flaps of
+paper to work with.
+
+Maybe you make one
+of them the head
+
+and the other two wings
+and the back one a tail,
+
+if you're making a crane.
+
+If doesn't actually
+start not from this space
+
+but from the other one.
+
+But the same idea.
+
+If you're folding a
+crane, one of these
+
+would be the head, the
+other tail, and two wings.
+
+This is great if you're
+making a four flap animal.
+
+And if you think
+about its projection--
+
+and it's easier to think
+about in this other picture--
+
+the projection of this
+thing is a four limbed star.
+
+You can see it's a plus sign.
+
+All of them are the same length.
+
+And so this is
+actually something
+
+you can get out of
+the tree method.
+
+You just give that
+as your input.
+
+You will get this 3D thing
+and this crease pattern
+
+as your origami-- as the output.
+
+Let me show you the
+program in action.
+
+So Robert Lang
+implemented this thing.
+
+It's called tree maker.
+
+It's freely available, open
+source, all that good stuff.
+
+And I'm not an expert at
+using it, so bear with me.
+
+But if we wanted to say,
+I would like that star.
+
+OK, now, I drew it obviously
+not with all the lengths equal,
+
+but it's ignoring the
+lengths that I drew.
+
+And they're actually
+specified here.
+
+So all the lengths here
+are supposed to be 1.
+
+And then I say, OK, optimize.
+
+And then make a crease pattern.
+
+And then show me
+the crease pattern.
+
+And there it is, exactly
+the crease pattern
+
+I made, although actually I can
+see from the mountain valley
+
+assignment-- because
+this is not really--
+
+this is not flat origami.
+
+It made it this way.
+
+So it's flat.
+
+Of course, the projection is
+the same-- still four limbs.
+
+And so it's dashes for valleys
+and solid lines for mountains.
+
+But you can make
+anything you want.
+
+So let's say we want to
+make-- I don't know-- a lizard
+
+or something.
+
+So the blue lines are the tree.
+
+So here's-- can I do this?
+
+Yes, there we go.
+
+So here, I have a forearm,
+a head, a foreleg,
+
+another forearm, a body segment,
+tail, and two hind legs.
+
+Maybe I want to make that.
+
+So I say optimize and then
+make a crease pattern, and then
+
+boom.
+
+You fold that, and it will
+have exactly that projection.
+
+And assuming it did a
+reasonable job at computation,
+
+this will be the best
+way to fold this thing.
+
+And it's the
+smallest square that
+
+matches exactly that shape.
+
+You get the best scale
+factor between the size
+
+of your piece of paper
+and the target shape.
+
+But actually, doing
+that optimization--
+
+the first step I
+did-- is NP-complete.
+
+So it's not going
+to do it perfectly,
+
+and we'll prove that Wednesday.
+
+But the heuristics
+are pretty good.
+
+AUDIENCE: It finds a local.
+
+PROFESSOR: It finds
+a local minimum,
+
+and often it finds
+a pretty good one.
+
+And sometimes you can coax it
+to find better ones, but, yeah.
+
+It's not perfect, but
+hey, it's NP-complete.
+
+So you can't do it.
+
+This actually shows you what it
+would look like in x-ray view.
+
+And then you can say,
+oh, that was nice,
+
+but let's-- where is
+my-- yeah, that was good.
+
+But maybe I really
+wanted the head segment
+
+to be shorter length of 0.5.
+
+And then I wanted the
+tail to be really long.
+
+And then you can optimize that
+and find a crease pattern.
+
+And it'll complain.
+
+Because it's having trouble.
+
+Oh, dear.
+
+Demo effect.
+
+I should have tried
+this example before.
+
+It's not-- oh, gosh.
+
+It's one of these annoying ones.
+
+I should say-- I should add
+some feature like maybe a strain
+
+split something, add a
+little bit, maybe do that
+
+and-- there we go.
+
+I cheated, and I'll explain
+how I cheated last time.
+
+But if sometimes the
+particular method
+
+fails but you can fix it by
+adding in another tiny limb
+
+off the edge somewhere--
+and of course, you
+
+can then get rid of that at
+the end when you're folding,
+
+it only makes the
+problem slightly harder.
+
+And it'll still find a folding.
+
+But we'll talk about
+that next time.
+
+And I'm way out of time,
+so we will stop there.
\ No newline at end of file
diff --git a/5uygC4oJvCI.txt b/5uygC4oJvCI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d018c0ee6f3a8ff2ff6bce1faf224255c584ef76
--- /dev/null
+++ b/5uygC4oJvCI.txt
@@ -0,0 +1,9667 @@
+align:start position:0%
+ 
+so so um so remember what has been
+
+ align:start position:0%
+so so um so remember what has been
+ 
+
+ align:start position:0%
+so so um so remember what has been
+happening to the US economy as as as
+
+ align:start position:0%
+happening to the US economy as as as
+ 
+
+ align:start position:0%
+happening to the US economy as as as
+economy and and it happens similarly
+
+ align:start position:0%
+economy and and it happens similarly
+ 
+
+ align:start position:0%
+economy and and it happens similarly
+with a few lcks and leads and and
+
+ align:start position:0%
+with a few lcks and leads and and
+ 
+
+ align:start position:0%
+with a few lcks and leads and and
+differences in sizes but around the
+
+ align:start position:0%
+differences in sizes but around the
+ 
+
+ align:start position:0%
+differences in sizes but around the
+world in most economies around the world
+
+ align:start position:0%
+world in most economies around the world
+ 
+
+ align:start position:0%
+world in most economies around the world
+as the economy began to reopen from
+
+ align:start position:0%
+as the economy began to reopen from
+ 
+
+ align:start position:0%
+as the economy began to reopen from
+covid H we had a situation where we had
+
+ align:start position:0%
+covid H we had a situation where we had
+ 
+
+ align:start position:0%
+covid H we had a situation where we had
+sort of too much demand for Supply the
+
+ align:start position:0%
+sort of too much demand for Supply the
+ 
+
+ align:start position:0%
+sort of too much demand for Supply the
+the potential output using the
+
+ align:start position:0%
+the potential output using the
+ 
+
+ align:start position:0%
+the potential output using the
+terminology you'll have in the ISL NPC
+
+ align:start position:0%
+terminology you'll have in the ISL NPC
+ 
+
+ align:start position:0%
+terminology you'll have in the ISL NPC
+model was slow in picking up because we
+
+ align:start position:0%
+model was slow in picking up because we
+ 
+
+ align:start position:0%
+model was slow in picking up because we
+still had lots of bottlenecks in the
+
+ align:start position:0%
+still had lots of bottlenecks in the
+ 
+
+ align:start position:0%
+still had lots of bottlenecks in the
+supply chains and and in different
+
+ align:start position:0%
+supply chains and and in different
+ 
+
+ align:start position:0%
+supply chains and and in different
+sectors of the economy H some people
+
+ align:start position:0%
+sectors of the economy H some people
+ 
+
+ align:start position:0%
+sectors of the economy H some people
+didn't didn't want to come back to work
+
+ align:start position:0%
+didn't didn't want to come back to work
+ 
+
+ align:start position:0%
+didn't didn't want to come back to work
+to the labor force for a while and and
+
+ align:start position:0%
+to the labor force for a while and and
+ 
+
+ align:start position:0%
+to the labor force for a while and and
+and so on so so the supply side was very
+
+ align:start position:0%
+and so on so so the supply side was very
+ 
+
+ align:start position:0%
+and so on so so the supply side was very
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+impair ER not as impair as in the middle
+
+ align:start position:0%
+impair ER not as impair as in the middle
+ 
+
+ align:start position:0%
+impair ER not as impair as in the middle
+of the covid in 2020 say but it's still
+
+ align:start position:0%
+of the covid in 2020 say but it's still
+ 
+
+ align:start position:0%
+of the covid in 2020 say but it's still
+in pair while
+
+ align:start position:0%
+in pair while
+ 
+
+ align:start position:0%
+in pair while
+demand was very strong because people
+
+ align:start position:0%
+demand was very strong because people
+ 
+
+ align:start position:0%
+demand was very strong because people
+were fed up of being staying at home
+
+ align:start position:0%
+were fed up of being staying at home
+ 
+
+ align:start position:0%
+were fed up of being staying at home
+they had saved a lot during the the
+
+ align:start position:0%
+they had saved a lot during the the
+ 
+
+ align:start position:0%
+they had saved a lot during the the
+covid recession and they wanted to spend
+
+ align:start position:0%
+covid recession and they wanted to spend
+ 
+
+ align:start position:0%
+covid recession and they wanted to spend
+okay and there had been lots of fiscal
+
+ align:start position:0%
+okay and there had been lots of fiscal
+ 
+
+ align:start position:0%
+okay and there had been lots of fiscal
+support and monetary policy support and
+
+ align:start position:0%
+support and monetary policy support and
+ 
+
+ align:start position:0%
+support and monetary policy support and
+so on so people feel wealthy and felt
+
+ align:start position:0%
+so on so people feel wealthy and felt
+ 
+
+ align:start position:0%
+so on so people feel wealthy and felt
+rich
+
+ align:start position:0%
+rich
+ 
+
+ align:start position:0%
+rich
+and and so they want to spend you know
+
+ align:start position:0%
+and and so they want to spend you know
+ 
+
+ align:start position:0%
+and and so they want to spend you know
+if is there's a big demand but Supply is
+
+ align:start position:0%
+if is there's a big demand but Supply is
+ 
+
+ align:start position:0%
+if is there's a big demand but Supply is
+not there that is starts introducing
+
+ align:start position:0%
+not there that is starts introducing
+ 
+
+ align:start position:0%
+not there that is starts introducing
+inflationary pressures that's say we
+
+ align:start position:0%
+inflationary pressures that's say we
+ 
+
+ align:start position:0%
+inflationary pressures that's say we
+have a a negative output a positive
+
+ align:start position:0%
+have a a negative output a positive
+ 
+
+ align:start position:0%
+have a a negative output a positive
+output Gap output above potential output
+
+ align:start position:0%
+output Gap output above potential output
+ 
+
+ align:start position:0%
+output Gap output above potential output
+that puts immediately inflationary
+
+ align:start position:0%
+that puts immediately inflationary
+ 
+
+ align:start position:0%
+that puts immediately inflationary
+pressure that's what we learn from the
+
+ align:start position:0%
+pressure that's what we learn from the
+ 
+
+ align:start position:0%
+pressure that's what we learn from the
+Philips curve and all that
+
+ align:start position:0%
+Philips curve and all that
+ 
+
+ align:start position:0%
+Philips curve and all that
+okay and now for a while the the the FED
+
+ align:start position:0%
+okay and now for a while the the the FED
+ 
+
+ align:start position:0%
+okay and now for a while the the the FED
+um did not want to react to this because
+
+ align:start position:0%
+um did not want to react to this because
+ 
+
+ align:start position:0%
+um did not want to react to this because
+they thought that this was going to be
+
+ align:start position:0%
+they thought that this was going to be
+ 
+
+ align:start position:0%
+they thought that this was going to be
+mostly a temporary phenomenon that
+
+ align:start position:0%
+mostly a temporary phenomenon that
+ 
+
+ align:start position:0%
+mostly a temporary phenomenon that
+Supply would recover pretty rapidly and
+
+ align:start position:0%
+Supply would recover pretty rapidly and
+ 
+
+ align:start position:0%
+Supply would recover pretty rapidly and
+that you know people would after taking
+
+ align:start position:0%
+that you know people would after taking
+ 
+
+ align:start position:0%
+that you know people would after taking
+one trip well they wouldn't want to take
+
+ align:start position:0%
+one trip well they wouldn't want to take
+ 
+
+ align:start position:0%
+one trip well they wouldn't want to take
+a second one fiscal support was winding
+
+ align:start position:0%
+a second one fiscal support was winding
+ 
+
+ align:start position:0%
+a second one fiscal support was winding
+down and so on so they thought this
+
+ align:start position:0%
+down and so on so they thought this
+ 
+
+ align:start position:0%
+down and so on so they thought this
+would go away and they didn't want to
+
+ align:start position:0%
+would go away and they didn't want to
+ 
+
+ align:start position:0%
+would go away and they didn't want to
+sort of cool off the economy because
+
+ align:start position:0%
+sort of cool off the economy because
+ 
+
+ align:start position:0%
+sort of cool off the economy because
+they thought they didn't want to fight a
+
+ align:start position:0%
+they thought they didn't want to fight a
+ 
+
+ align:start position:0%
+they thought they didn't want to fight a
+temporary fight now as a result of new
+
+ align:start position:0%
+temporary fight now as a result of new
+ 
+
+ align:start position:0%
+temporary fight now as a result of new
+shocks the war and things like that but
+
+ align:start position:0%
+shocks the war and things like that but
+ 
+
+ align:start position:0%
+shocks the war and things like that but
+also that the initial call was not right
+
+ align:start position:0%
+also that the initial call was not right
+ 
+
+ align:start position:0%
+also that the initial call was not right
+was incorrect that there was a lot of
+
+ align:start position:0%
+was incorrect that there was a lot of
+ 
+
+ align:start position:0%
+was incorrect that there was a lot of
+inertia in demand and and and and that
+
+ align:start position:0%
+inertia in demand and and and and that
+ 
+
+ align:start position:0%
+inertia in demand and and and and that
+that pickup in demand sort of lasted a
+
+ align:start position:0%
+that pickup in demand sort of lasted a
+ 
+
+ align:start position:0%
+that pickup in demand sort of lasted a
+lot longer than I expected H is that
+
+ align:start position:0%
+lot longer than I expected H is that
+ 
+
+ align:start position:0%
+lot longer than I expected H is that
+that inflation really began to rise and
+
+ align:start position:0%
+that inflation really began to rise and
+ 
+
+ align:start position:0%
+that inflation really began to rise and
+the Fed was really CAU what is called
+
+ align:start position:0%
+the Fed was really CAU what is called
+ 
+
+ align:start position:0%
+the Fed was really CAU what is called
+behind the curve know they needed to
+
+ align:start position:0%
+behind the curve know they needed to
+ 
+
+ align:start position:0%
+behind the curve know they needed to
+they were they should have started at
+
+ align:start position:0%
+they were they should have started at
+ 
+
+ align:start position:0%
+they were they should have started at
+least Expos it's easy to see it that way
+
+ align:start position:0%
+least Expos it's easy to see it that way
+ 
+
+ align:start position:0%
+least Expos it's easy to see it that way
+they should have remember what you have
+
+ align:start position:0%
+they should have remember what you have
+ 
+
+ align:start position:0%
+they should have remember what you have
+if you have an a situation where output
+
+ align:start position:0%
+if you have an a situation where output
+ 
+
+ align:start position:0%
+if you have an a situation where output
+is above potential output the interest
+
+ align:start position:0%
+is above potential output the interest
+ 
+
+ align:start position:0%
+is above potential output the interest
+rate is supposed to be rising so the FED
+
+ align:start position:0%
+rate is supposed to be rising so the FED
+ 
+
+ align:start position:0%
+rate is supposed to be rising so the FED
+is supposed to be increasing the
+
+ align:start position:0%
+is supposed to be increasing the
+ 
+
+ align:start position:0%
+is supposed to be increasing the
+interest rate but it didn't for a while
+
+ align:start position:0%
+interest rate but it didn't for a while
+ 
+
+ align:start position:0%
+interest rate but it didn't for a while
+assuming that the forces that were
+
+ align:start position:0%
+assuming that the forces that were
+ 
+
+ align:start position:0%
+assuming that the forces that were
+bringing potential output down and
+
+ align:start position:0%
+bringing potential output down and
+ 
+
+ align:start position:0%
+bringing potential output down and
+demand up were so transitory when they
+
+ align:start position:0%
+demand up were so transitory when they
+ 
+
+ align:start position:0%
+demand up were so transitory when they
+discovered that wasn't the case they had
+
+ align:start position:0%
+discovered that wasn't the case they had
+ 
+
+ align:start position:0%
+discovered that wasn't the case they had
+to start catching up as a result of that
+
+ align:start position:0%
+to start catching up as a result of that
+ 
+
+ align:start position:0%
+to start catching up as a result of that
+they began to hike interest very very
+
+ align:start position:0%
+they began to hike interest very very
+ 
+
+ align:start position:0%
+they began to hike interest very very
+rapidly okay and the unusually rapidly
+
+ align:start position:0%
+rapidly okay and the unusually rapidly
+ 
+
+ align:start position:0%
+rapidly okay and the unusually rapidly
+for economy like the US and the reason
+
+ align:start position:0%
+for economy like the US and the reason
+ 
+
+ align:start position:0%
+for economy like the US and the reason
+there are many reasons why why policy
+
+ align:start position:0%
+there are many reasons why why policy
+ 
+
+ align:start position:0%
+there are many reasons why why policy
+makers especially monetary policy makers
+
+ align:start position:0%
+makers especially monetary policy makers
+ 
+
+ align:start position:0%
+makers especially monetary policy makers
+prefer to be gradualist meaning to move
+
+ align:start position:0%
+prefer to be gradualist meaning to move
+ 
+
+ align:start position:0%
+prefer to be gradualist meaning to move
+things in smaller steps rather than in
+
+ align:start position:0%
+things in smaller steps rather than in
+ 
+
+ align:start position:0%
+things in smaller steps rather than in
+one big Bank ER especially in the way up
+
+ align:start position:0%
+one big Bank ER especially in the way up
+ 
+
+ align:start position:0%
+one big Bank ER especially in the way up
+no if if it is to cut rates they're very
+
+ align:start position:0%
+no if if it is to cut rates they're very
+ 
+
+ align:start position:0%
+no if if it is to cut rates they're very
+willing to be very aggressive in cutting
+
+ align:start position:0%
+willing to be very aggressive in cutting
+ 
+
+ align:start position:0%
+willing to be very aggressive in cutting
+rates but racing rates is something they
+
+ align:start position:0%
+rates but racing rates is something they
+ 
+
+ align:start position:0%
+rates but racing rates is something they
+tend to be reluctant to do very very
+
+ align:start position:0%
+tend to be reluctant to do very very
+ 
+
+ align:start position:0%
+tend to be reluctant to do very very
+rapidly and one of the main reasons
+
+ align:start position:0%
+rapidly and one of the main reasons
+ 
+
+ align:start position:0%
+rapidly and one of the main reasons
+they're reluctant to do that very
+
+ align:start position:0%
+they're reluctant to do that very
+ 
+
+ align:start position:0%
+they're reluctant to do that very
+rapidly is because something may break
+
+ align:start position:0%
+rapidly is because something may break
+ 
+
+ align:start position:0%
+rapidly is because something may break
+in the process and there are certain
+
+ align:start position:0%
+in the process and there are certain
+ 
+
+ align:start position:0%
+in the process and there are certain
+things are very important if they break
+
+ align:start position:0%
+things are very important if they break
+ 
+
+ align:start position:0%
+things are very important if they break
+there are certain other things are not
+
+ align:start position:0%
+there are certain other things are not
+ 
+
+ align:start position:0%
+there are certain other things are not
+very important if they break but one of
+
+ align:start position:0%
+very important if they break but one of
+ 
+
+ align:start position:0%
+very important if they break but one of
+the things that is very important if
+
+ align:start position:0%
+the things that is very important if
+ 
+
+ align:start position:0%
+the things that is very important if
+they break is Banks okay and and and
+
+ align:start position:0%
+they break is Banks okay and and and
+ 
+
+ align:start position:0%
+they break is Banks okay and and and
+that's typically where you get run into
+
+ align:start position:0%
+that's typically where you get run into
+ 
+
+ align:start position:0%
+that's typically where you get run into
+trouble when there is episodes of very
+
+ align:start position:0%
+trouble when there is episodes of very
+ 
+
+ align:start position:0%
+trouble when there is episodes of very
+fast hikes in rates now because the US
+
+ align:start position:0%
+fast hikes in rates now because the US
+ 
+
+ align:start position:0%
+fast hikes in rates now because the US
+banking sector especially the large
+
+ align:start position:0%
+banking sector especially the large
+ 
+
+ align:start position:0%
+banking sector especially the large
+Banks were sort of very resilient they
+
+ align:start position:0%
+Banks were sort of very resilient they
+ 
+
+ align:start position:0%
+Banks were sort of very resilient they
+had lot of capital and so on there
+
+ align:start position:0%
+had lot of capital and so on there
+ 
+
+ align:start position:0%
+had lot of capital and so on there
+wasn't a lot of concern that that would
+
+ align:start position:0%
+wasn't a lot of concern that that would
+ 
+
+ align:start position:0%
+wasn't a lot of concern that that would
+be an issue in the US because again the
+
+ align:start position:0%
+be an issue in the US because again the
+ 
+
+ align:start position:0%
+be an issue in the US because again the
+the big Banks look very healthy uh
+
+ align:start position:0%
+the big Banks look very healthy uh
+ 
+
+ align:start position:0%
+the big Banks look very healthy uh
+deposits were flowing out of big Banks
+
+ align:start position:0%
+deposits were flowing out of big Banks
+ 
+
+ align:start position:0%
+deposits were flowing out of big Banks
+but it was happening all at a normal
+
+ align:start position:0%
+but it was happening all at a normal
+ 
+
+ align:start position:0%
+but it was happening all at a normal
+Pace it's normal that deposits go out of
+
+ align:start position:0%
+Pace it's normal that deposits go out of
+ 
+
+ align:start position:0%
+Pace it's normal that deposits go out of
+the banking sector when interest rates
+
+ align:start position:0%
+the banking sector when interest rates
+ 
+
+ align:start position:0%
+the banking sector when interest rates
+are to rise uh but there was no sign of
+
+ align:start position:0%
+are to rise uh but there was no sign of
+ 
+
+ align:start position:0%
+are to rise uh but there was no sign of
+major trouble well that changed a month
+
+ align:start position:0%
+major trouble well that changed a month
+ 
+
+ align:start position:0%
+major trouble well that changed a month
+ago as you well know and something broke
+
+ align:start position:0%
+ago as you well know and something broke
+ 
+
+ align:start position:0%
+ago as you well know and something broke
+finally no and that the major episode
+
+ align:start position:0%
+finally no and that the major episode
+ 
+
+ align:start position:0%
+finally no and that the major episode
+there was the Silicon Valley Bank know
+
+ align:start position:0%
+there was the Silicon Valley Bank know
+ 
+
+ align:start position:0%
+there was the Silicon Valley Bank know
+we Al saw a big bank bank run there and
+
+ align:start position:0%
+we Al saw a big bank bank run there and
+ 
+
+ align:start position:0%
+we Al saw a big bank bank run there and
+eventually that bank collapsed and since
+
+ align:start position:0%
+eventually that bank collapsed and since
+ 
+
+ align:start position:0%
+eventually that bank collapsed and since
+then things have looked a little more
+
+ align:start position:0%
+then things have looked a little more
+ 
+
+ align:start position:0%
+then things have looked a little more
+complicated so here you have for example
+
+ align:start position:0%
+complicated so here you have for example
+ 
+
+ align:start position:0%
+complicated so here you have for example
+a a Commercial Bank deposits as I said
+
+ align:start position:0%
+a a Commercial Bank deposits as I said
+ 
+
+ align:start position:0%
+a a Commercial Bank deposits as I said
+as I said as the FED began to hike so
+
+ align:start position:0%
+as I said as the FED began to hike so
+ 
+
+ align:start position:0%
+as I said as the FED began to hike so
+focus on the red line the FED began to
+
+ align:start position:0%
+focus on the red line the FED began to
+ 
+
+ align:start position:0%
+focus on the red line the FED began to
+hike rates then H deposits began to
+
+ align:start position:0%
+hike rates then H deposits began to
+ 
+
+ align:start position:0%
+hike rates then H deposits began to
+people began to move their money out of
+
+ align:start position:0%
+people began to move their money out of
+ 
+
+ align:start position:0%
+people began to move their money out of
+deposit into US treasuries money market
+
+ align:start position:0%
+deposit into US treasuries money market
+ 
+
+ align:start position:0%
+deposit into US treasuries money market
+funds things of that kind that was
+
+ align:start position:0%
+funds things of that kind that was
+ 
+
+ align:start position:0%
+funds things of that kind that was
+normal okay and that didn't lead to a
+
+ align:start position:0%
+normal okay and that didn't lead to a
+ 
+
+ align:start position:0%
+normal okay and that didn't lead to a
+big cut in lending which is what you
+
+ align:start position:0%
+big cut in lending which is what you
+ 
+
+ align:start position:0%
+big cut in lending which is what you
+worried about when when Banks lose
+
+ align:start position:0%
+worried about when when Banks lose
+ 
+
+ align:start position:0%
+worried about when when Banks lose
+funding but things began to change quite
+
+ align:start position:0%
+funding but things began to change quite
+ 
+
+ align:start position:0%
+funding but things began to change quite
+rapidly well in the second half of 2022
+
+ align:start position:0%
+rapidly well in the second half of 2022
+ 
+
+ align:start position:0%
+rapidly well in the second half of 2022
+this was perceived felt mostly by large
+
+ align:start position:0%
+this was perceived felt mostly by large
+ 
+
+ align:start position:0%
+this was perceived felt mostly by large
+Banks and when deposits decline
+
+ align:start position:0%
+Banks and when deposits decline
+ 
+
+ align:start position:0%
+Banks and when deposits decline
+gradually in large Banks that's not such
+
+ align:start position:0%
+gradually in large Banks that's not such
+ 
+
+ align:start position:0%
+gradually in large Banks that's not such
+a big issue because deposits are not the
+
+ align:start position:0%
+a big issue because deposits are not the
+ 
+
+ align:start position:0%
+a big issue because deposits are not the
+only funding source that that big banks
+
+ align:start position:0%
+only funding source that that big banks
+ 
+
+ align:start position:0%
+only funding source that that big banks
+have they have many other sources of
+
+ align:start position:0%
+have they have many other sources of
+ 
+
+ align:start position:0%
+have they have many other sources of
+funding H but then things that's what
+
+ align:start position:0%
+funding H but then things that's what
+ 
+
+ align:start position:0%
+funding H but then things that's what
+happens this year things accelerated
+
+ align:start position:0%
+happens this year things accelerated
+ 
+
+ align:start position:0%
+happens this year things accelerated
+very very quickly H this year and so
+
+ align:start position:0%
+very very quickly H this year and so
+ 
+
+ align:start position:0%
+very very quickly H this year and so
+this is different this is a different
+
+ align:start position:0%
+this is different this is a different
+ 
+
+ align:start position:0%
+this is different this is a different
+animal from this sort of very controlled
+
+ align:start position:0%
+animal from this sort of very controlled
+ 
+
+ align:start position:0%
+animal from this sort of very controlled
+decline in deposits as interest we're
+
+ align:start position:0%
+decline in deposits as interest we're
+ 
+
+ align:start position:0%
+decline in deposits as interest we're
+hiking this is a very sharp decline in
+
+ align:start position:0%
+hiking this is a very sharp decline in
+ 
+
+ align:start position:0%
+hiking this is a very sharp decline in
+deposits okay uh so that's a problem
+
+ align:start position:0%
+deposits okay uh so that's a problem
+ 
+
+ align:start position:0%
+deposits okay uh so that's a problem
+because that that's an avoid
+
+ align:start position:0%
+because that that's an avoid
+ 
+
+ align:start position:0%
+because that that's an avoid
+will hit lending okay so that's when to
+
+ align:start position:0%
+will hit lending okay so that's when to
+ 
+
+ align:start position:0%
+will hit lending okay so that's when to
+show up in terms of the moldes we have
+
+ align:start position:0%
+show up in terms of the moldes we have
+ 
+
+ align:start position:0%
+show up in terms of the moldes we have
+had if you were to use your ISL MPC
+
+ align:start position:0%
+had if you were to use your ISL MPC
+ 
+
+ align:start position:0%
+had if you were to use your ISL MPC
+model it would show up as an increas in
+
+ align:start position:0%
+model it would show up as an increas in
+ 
+
+ align:start position:0%
+model it would show up as an increas in
+X remember we had premium and stuff like
+
+ align:start position:0%
+X remember we had premium and stuff like
+ 
+
+ align:start position:0%
+X remember we had premium and stuff like
+that well that's a way you probably
+
+ align:start position:0%
+that well that's a way you probably
+ 
+
+ align:start position:0%
+that well that's a way you probably
+could model what is happening right
+
+ align:start position:0%
+could model what is happening right
+ 
+
+ align:start position:0%
+could model what is happening right
+now now one of the big as I said before
+
+ align:start position:0%
+now now one of the big as I said before
+ 
+
+ align:start position:0%
+now now one of the big as I said before
+these are in different Scala so a small
+
+ align:start position:0%
+these are in different Scala so a small
+ 
+
+ align:start position:0%
+these are in different Scala so a small
+Bank deposits on the left large Banks
+
+ align:start position:0%
+Bank deposits on the left large Banks
+ 
+
+ align:start position:0%
+Bank deposits on the left large Banks
+deposit on the on the right
+
+ align:start position:0%
+deposit on the on the right
+ 
+
+ align:start position:0%
+deposit on the on the right
+as I said before through most of of this
+
+ align:start position:0%
+as I said before through most of of this
+ 
+
+ align:start position:0%
+as I said before through most of of this
+episode in which deposits were declining
+
+ align:start position:0%
+episode in which deposits were declining
+ 
+
+ align:start position:0%
+episode in which deposits were declining
+in the in the banking
+
+ align:start position:0%
+in the in the banking
+ 
+
+ align:start position:0%
+in the in the banking
+sector it was mostly a phenomenon that
+
+ align:start position:0%
+sector it was mostly a phenomenon that
+ 
+
+ align:start position:0%
+sector it was mostly a phenomenon that
+was that that affected large Banks and
+
+ align:start position:0%
+was that that affected large Banks and
+ 
+
+ align:start position:0%
+was that that affected large Banks and
+it was very grad okay but what happened
+
+ align:start position:0%
+it was very grad okay but what happened
+ 
+
+ align:start position:0%
+it was very grad okay but what happened
+since a month ago is essentially small
+
+ align:start position:0%
+since a month ago is essentially small
+ 
+
+ align:start position:0%
+since a month ago is essentially small
+and mediumsized Banks experien a very
+
+ align:start position:0%
+and mediumsized Banks experien a very
+ 
+
+ align:start position:0%
+and mediumsized Banks experien a very
+large running deposits part of that went
+
+ align:start position:0%
+large running deposits part of that went
+ 
+
+ align:start position:0%
+large running deposits part of that went
+to money market us treasuries and and
+
+ align:start position:0%
+to money market us treasuries and and
+ 
+
+ align:start position:0%
+to money market us treasuries and and
+part of it you don't see different scale
+
+ align:start position:0%
+part of it you don't see different scale
+ 
+
+ align:start position:0%
+part of it you don't see different scale
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+but it went actually to large Banks it
+
+ align:start position:0%
+but it went actually to large Banks it
+ 
+
+ align:start position:0%
+but it went actually to large Banks it
+was relocation it's called that's called
+
+ align:start position:0%
+was relocation it's called that's called
+ 
+
+ align:start position:0%
+was relocation it's called that's called
+flight to Quality okay now even if if if
+
+ align:start position:0%
+flight to Quality okay now even if if if
+ 
+
+ align:start position:0%
+flight to Quality okay now even if if if
+this has been a full relocation of of H
+
+ align:start position:0%
+this has been a full relocation of of H
+ 
+
+ align:start position:0%
+this has been a full relocation of of H
+deposits from large bank to from small
+
+ align:start position:0%
+deposits from large bank to from small
+ 
+
+ align:start position:0%
+deposits from large bank to from small
+Banks to large Banks and so no deposit
+
+ align:start position:0%
+Banks to large Banks and so no deposit
+ 
+
+ align:start position:0%
+Banks to large Banks and so no deposit
+would have declined in the whole banking
+
+ align:start position:0%
+would have declined in the whole banking
+ 
+
+ align:start position:0%
+would have declined in the whole banking
+sector that would have consequences for
+
+ align:start position:0%
+sector that would have consequences for
+ 
+
+ align:start position:0%
+sector that would have consequences for
+the economy because these type of banks
+
+ align:start position:0%
+the economy because these type of banks
+ 
+
+ align:start position:0%
+the economy because these type of banks
+don't lend to the same type of
+
+ align:start position:0%
+don't lend to the same type of
+ 
+
+ align:start position:0%
+don't lend to the same type of
+people small Banks small especially
+
+ align:start position:0%
+people small Banks small especially
+ 
+
+ align:start position:0%
+people small Banks small especially
+Regional Banks lend a lot to people that
+
+ align:start position:0%
+Regional Banks lend a lot to people that
+ 
+
+ align:start position:0%
+Regional Banks lend a lot to people that
+to businesses and people that do not
+
+ align:start position:0%
+to businesses and people that do not
+ 
+
+ align:start position:0%
+to businesses and people that do not
+have other sources of funding they tend
+
+ align:start position:0%
+have other sources of funding they tend
+ 
+
+ align:start position:0%
+have other sources of funding they tend
+to be small businesses and so on the
+
+ align:start position:0%
+to be small businesses and so on the
+ 
+
+ align:start position:0%
+to be small businesses and so on the
+only way they can get borrow is either
+
+ align:start position:0%
+only way they can get borrow is either
+ 
+
+ align:start position:0%
+only way they can get borrow is either
+from the family or from a bank but they
+
+ align:start position:0%
+from the family or from a bank but they
+ 
+
+ align:start position:0%
+from the family or from a bank but they
+cannot issue bonds and things like that
+
+ align:start position:0%
+cannot issue bonds and things like that
+ 
+
+ align:start position:0%
+cannot issue bonds and things like that
+no and so they don't have other sources
+
+ align:start position:0%
+no and so they don't have other sources
+ 
+
+ align:start position:0%
+no and so they don't have other sources
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+funding and so that's the problem
+
+ align:start position:0%
+funding and so that's the problem
+ 
+
+ align:start position:0%
+funding and so that's the problem
+because what you see here is naturally
+
+ align:start position:0%
+because what you see here is naturally
+ 
+
+ align:start position:0%
+because what you see here is naturally
+when you start seeing deposits going out
+
+ align:start position:0%
+when you start seeing deposits going out
+ 
+
+ align:start position:0%
+when you start seeing deposits going out
+there have been also H losses
+
+ align:start position:0%
+there have been also H losses
+ 
+
+ align:start position:0%
+there have been also H losses
+experienced by the Banks because they
+
+ align:start position:0%
+experienced by the Banks because they
+ 
+
+ align:start position:0%
+experienced by the Banks because they
+had to recognize the losses in the asset
+
+ align:start position:0%
+had to recognize the losses in the asset
+ 
+
+ align:start position:0%
+had to recognize the losses in the asset
+side once they lost deposit is that they
+
+ align:start position:0%
+side once they lost deposit is that they
+ 
+
+ align:start position:0%
+side once they lost deposit is that they
+had to cut lending and you can see here
+
+ align:start position:0%
+had to cut lending and you can see here
+ 
+
+ align:start position:0%
+had to cut lending and you can see here
+what has been happening to lending large
+
+ align:start position:0%
+what has been happening to lending large
+ 
+
+ align:start position:0%
+what has been happening to lending large
+Banks they began to slow down here but
+
+ align:start position:0%
+Banks they began to slow down here but
+ 
+
+ align:start position:0%
+Banks they began to slow down here but
+it's a gradual slow down you have seen a
+
+ align:start position:0%
+it's a gradual slow down you have seen a
+ 
+
+ align:start position:0%
+it's a gradual slow down you have seen a
+very sharp decline in lending over the
+
+ align:start position:0%
+very sharp decline in lending over the
+ 
+
+ align:start position:0%
+very sharp decline in lending over the
+last three or four weeks okay so we're
+
+ align:start position:0%
+last three or four weeks okay so we're
+ 
+
+ align:start position:0%
+last three or four weeks okay so we're
+in the early phases what we like to call
+
+ align:start position:0%
+in the early phases what we like to call
+ 
+
+ align:start position:0%
+in the early phases what we like to call
+as described as a credit crunch okay and
+
+ align:start position:0%
+as described as a credit crunch okay and
+ 
+
+ align:start position:0%
+as described as a credit crunch okay and
+um now that's a the problem as I said
+
+ align:start position:0%
+um now that's a the problem as I said
+ 
+
+ align:start position:0%
+um now that's a the problem as I said
+before because those
+
+ align:start position:0%
+before because those
+ 
+
+ align:start position:0%
+before because those
+banks these Banks Banks in Gray here are
+
+ align:start position:0%
+banks these Banks Banks in Gray here are
+ 
+
+ align:start position:0%
+banks these Banks Banks in Gray here are
+the banks that lend primarily to small
+
+ align:start position:0%
+the banks that lend primarily to small
+ 
+
+ align:start position:0%
+the banks that lend primarily to small
+and medium-sized businesses okay so you
+
+ align:start position:0%
+and medium-sized businesses okay so you
+ 
+
+ align:start position:0%
+and medium-sized businesses okay so you
+see here the share of
+
+ align:start position:0%
+see here the share of
+ 
+
+ align:start position:0%
+see here the share of
+commercial H and Industrial loans by
+
+ align:start position:0%
+commercial H and Industrial loans by
+ 
+
+ align:start position:0%
+commercial H and Industrial loans by
+Bank size H and this is loans to small
+
+ align:start position:0%
+Bank size H and this is loans to small
+ 
+
+ align:start position:0%
+Bank size H and this is loans to small
+businesses loan to larger business these
+
+ align:start position:0%
+businesses loan to larger business these
+ 
+
+ align:start position:0%
+businesses loan to larger business these
+are the banks that are in grade before
+
+ align:start position:0%
+are the banks that are in grade before
+ 
+
+ align:start position:0%
+are the banks that are in grade before
+below $250 billion and you see that that
+
+ align:start position:0%
+below $250 billion and you see that that
+ 
+
+ align:start position:0%
+below $250 billion and you see that that
+they have a large share of loans to
+
+ align:start position:0%
+they have a large share of loans to
+ 
+
+ align:start position:0%
+they have a large share of loans to
+small businesses okay so those sectors
+
+ align:start position:0%
+small businesses okay so those sectors
+ 
+
+ align:start position:0%
+small businesses okay so those sectors
+are going to suff suffer a lot so
+
+ align:start position:0%
+are going to suff suffer a lot so
+ 
+
+ align:start position:0%
+are going to suff suffer a lot so
+there's going to be a a contraction in
+
+ align:start position:0%
+there's going to be a a contraction in
+ 
+
+ align:start position:0%
+there's going to be a a contraction in
+the economy and it's going to be very
+
+ align:start position:0%
+the economy and it's going to be very
+ 
+
+ align:start position:0%
+the economy and it's going to be very
+concentrated on the small businesses
+
+ align:start position:0%
+concentrated on the small businesses
+ 
+
+ align:start position:0%
+concentrated on the small businesses
+mediumsized businesses and so on and
+
+ align:start position:0%
+mediumsized businesses and so on and
+ 
+
+ align:start position:0%
+mediumsized businesses and so on and
+again it's more problematic a
+
+ align:start position:0%
+again it's more problematic a
+ 
+
+ align:start position:0%
+again it's more problematic a
+contraction in lending to those
+
+ align:start position:0%
+contraction in lending to those
+ 
+
+ align:start position:0%
+contraction in lending to those
+businesses because they don't have
+
+ align:start position:0%
+businesses because they don't have
+ 
+
+ align:start position:0%
+businesses because they don't have
+alternative sources of funding that's it
+
+ align:start position:0%
+alternative sources of funding that's it
+ 
+
+ align:start position:0%
+alternative sources of funding that's it
+okay it's either return earnings the
+
+ align:start position:0%
+okay it's either return earnings the
+ 
+
+ align:start position:0%
+okay it's either return earnings the
+family if it is really really small or H
+
+ align:start position:0%
+family if it is really really small or H
+ 
+
+ align:start position:0%
+family if it is really really small or H
+ER
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Banks again big corporations these guys
+
+ align:start position:0%
+Banks again big corporations these guys
+ 
+
+ align:start position:0%
+Banks again big corporations these guys
+probably have are borrowing from 10
+
+ align:start position:0%
+probably have are borrowing from 10
+ 
+
+ align:start position:0%
+probably have are borrowing from 10
+different banks and and and they have
+
+ align:start position:0%
+different banks and and and they have
+ 
+
+ align:start position:0%
+different banks and and and they have
+issued corporate bonds and and they even
+
+ align:start position:0%
+issued corporate bonds and and they even
+ 
+
+ align:start position:0%
+issued corporate bonds and and they even
+have commercial paper this a entirely
+
+ align:start position:0%
+have commercial paper this a entirely
+ 
+
+ align:start position:0%
+have commercial paper this a entirely
+different life when you live here than
+
+ align:start position:0%
+different life when you live here than
+ 
+
+ align:start position:0%
+different life when you live here than
+when you live
+
+ align:start position:0%
+when you live
+ 
+
+ align:start position:0%
+when you live
+here H if you look by sectors that also
+
+ align:start position:0%
+here H if you look by sectors that also
+ 
+
+ align:start position:0%
+here H if you look by sectors that also
+is going to have implications for
+
+ align:start position:0%
+is going to have implications for
+ 
+
+ align:start position:0%
+is going to have implications for
+sectors so this is going to be clearly
+
+ align:start position:0%
+sectors so this is going to be clearly
+ 
+
+ align:start position:0%
+sectors so this is going to be clearly
+contractionary but it's not going to be
+
+ align:start position:0%
+contractionary but it's not going to be
+ 
+
+ align:start position:0%
+contractionary but it's not going to be
+equally contractionary it will depend on
+
+ align:start position:0%
+equally contractionary it will depend on
+ 
+
+ align:start position:0%
+equally contractionary it will depend on
+the composition of your sectors and not
+
+ align:start position:0%
+the composition of your sectors and not
+ 
+
+ align:start position:0%
+the composition of your sectors and not
+all sectors have the same share of small
+
+ align:start position:0%
+all sectors have the same share of small
+ 
+
+ align:start position:0%
+all sectors have the same share of small
+businesses and and and mediumsized
+
+ align:start position:0%
+businesses and and and mediumsized
+ 
+
+ align:start position:0%
+businesses and and and mediumsized
+businesses you see here the construction
+
+ align:start position:0%
+businesses you see here the construction
+ 
+
+ align:start position:0%
+businesses you see here the construction
+services a very large share most of the
+
+ align:start position:0%
+services a very large share most of the
+ 
+
+ align:start position:0%
+services a very large share most of the
+more than half of the businesses in
+
+ align:start position:0%
+more than half of the businesses in
+ 
+
+ align:start position:0%
+more than half of the businesses in
+construction are really small or
+
+ align:start position:0%
+construction are really small or
+ 
+
+ align:start position:0%
+construction are really small or
+mediumsized businesses okay H big
+
+ align:start position:0%
+mediumsized businesses okay H big
+ 
+
+ align:start position:0%
+mediumsized businesses okay H big
+contract with utilities where sort of
+
+ align:start position:0%
+contract with utilities where sort of
+ 
+
+ align:start position:0%
+contract with utilities where sort of
+they are all big businesses and so on
+
+ align:start position:0%
+they are all big businesses and so on
+ 
+
+ align:start position:0%
+they are all big businesses and so on
+okay so so big dispersion and so this is
+
+ align:start position:0%
+okay so so big dispersion and so this is
+ 
+
+ align:start position:0%
+okay so so big dispersion and so this is
+going to be a contraction is going to be
+
+ align:start position:0%
+going to be a contraction is going to be
+ 
+
+ align:start position:0%
+going to be a contraction is going to be
+very felt is felt very strongly here at
+
+ align:start position:0%
+very felt is felt very strongly here at
+ 
+
+ align:start position:0%
+very felt is felt very strongly here at
+the top
+
+ align:start position:0%
+the top
+ 
+
+ align:start position:0%
+the top
+okay so that's what is happening right
+
+ align:start position:0%
+okay so that's what is happening right
+ 
+
+ align:start position:0%
+okay so that's what is happening right
+now and from the point of view of the
+
+ align:start position:0%
+now and from the point of view of the
+ 
+
+ align:start position:0%
+now and from the point of view of the
+aggregate essentially where we have gone
+
+ align:start position:0%
+aggregate essentially where we have gone
+ 
+
+ align:start position:0%
+aggregate essentially where we have gone
+is from a path like this to a path like
+
+ align:start position:0%
+is from a path like this to a path like
+ 
+
+ align:start position:0%
+is from a path like this to a path like
+that so the economy was overheating so
+
+ align:start position:0%
+that so the economy was overheating so
+ 
+
+ align:start position:0%
+that so the economy was overheating so
+we need to slow down the economy there's
+
+ align:start position:0%
+we need to slow down the economy there's
+ 
+
+ align:start position:0%
+we need to slow down the economy there's
+no way around that output was above
+
+ align:start position:0%
+no way around that output was above
+ 
+
+ align:start position:0%
+no way around that output was above
+potential output that was causing
+
+ align:start position:0%
+potential output that was causing
+ 
+
+ align:start position:0%
+potential output that was causing
+inflationary pressure we needed to bring
+
+ align:start position:0%
+inflationary pressure we needed to bring
+ 
+
+ align:start position:0%
+inflationary pressure we needed to bring
+this stuff down and the economy was
+
+ align:start position:0%
+this stuff down and the economy was
+ 
+
+ align:start position:0%
+this stuff down and the economy was
+slowing down but it was happening at
+
+ align:start position:0%
+slowing down but it was happening at
+ 
+
+ align:start position:0%
+slowing down but it was happening at
+sort of a very slow pace and that was a
+
+ align:start position:0%
+sort of a very slow pace and that was a
+ 
+
+ align:start position:0%
+sort of a very slow pace and that was a
+bit exas exasperating for the FED but it
+
+ align:start position:0%
+bit exas exasperating for the FED but it
+ 
+
+ align:start position:0%
+bit exas exasperating for the FED but it
+was happening very very slowly among
+
+ align:start position:0%
+was happening very very slowly among
+ 
+
+ align:start position:0%
+was happening very very slowly among
+other things because of the balance
+
+ align:start position:0%
+other things because of the balance
+ 
+
+ align:start position:0%
+other things because of the balance
+sheets of the household sector and
+
+ align:start position:0%
+sheets of the household sector and
+ 
+
+ align:start position:0%
+sheets of the household sector and
+corporations in general was so very
+
+ align:start position:0%
+corporations in general was so very
+ 
+
+ align:start position:0%
+corporations in general was so very
+healthy but now things are accelerating
+
+ align:start position:0%
+healthy but now things are accelerating
+ 
+
+ align:start position:0%
+healthy but now things are accelerating
+very quickly because once you produce
+
+ align:start position:0%
+very quickly because once you produce
+ 
+
+ align:start position:0%
+very quickly because once you produce
+credit CR credit constraints and things
+
+ align:start position:0%
+credit CR credit constraints and things
+ 
+
+ align:start position:0%
+credit CR credit constraints and things
+like that like that so of the same
+
+ align:start position:0%
+like that like that so of the same
+ 
+
+ align:start position:0%
+like that like that so of the same
+declines in wealth that we were
+
+ align:start position:0%
+declines in wealth that we were
+ 
+
+ align:start position:0%
+declines in wealth that we were
+experienced before that were dragging
+
+ align:start position:0%
+experienced before that were dragging
+ 
+
+ align:start position:0%
+experienced before that were dragging
+aggregate demand down have a much larger
+
+ align:start position:0%
+aggregate demand down have a much larger
+ 
+
+ align:start position:0%
+aggregate demand down have a much larger
+effect and so we're changing from some a
+
+ align:start position:0%
+effect and so we're changing from some a
+ 
+
+ align:start position:0%
+effect and so we're changing from some a
+world that look like that to world it's
+
+ align:start position:0%
+world that look like that to world it's
+ 
+
+ align:start position:0%
+world that look like that to world it's
+going to look a lot more like this and
+
+ align:start position:0%
+going to look a lot more like this and
+ 
+
+ align:start position:0%
+going to look a lot more like this and
+that's tricky for the central bank
+
+ align:start position:0%
+that's tricky for the central bank
+ 
+
+ align:start position:0%
+that's tricky for the central bank
+because now the FED needs to before
+
+ align:start position:0%
+because now the FED needs to before
+ 
+
+ align:start position:0%
+because now the FED needs to before
+there was no way around they had to hike
+
+ align:start position:0%
+there was no way around they had to hike
+ 
+
+ align:start position:0%
+there was no way around they had to hike
+interest rate H because the main problem
+
+ align:start position:0%
+interest rate H because the main problem
+ 
+
+ align:start position:0%
+interest rate H because the main problem
+was inflation now they know that as they
+
+ align:start position:0%
+was inflation now they know that as they
+ 
+
+ align:start position:0%
+was inflation now they know that as they
+hike interest rate they still need to
+
+ align:start position:0%
+hike interest rate they still need to
+ 
+
+ align:start position:0%
+hike interest rate they still need to
+hike interest rate I think unless it is
+
+ align:start position:0%
+hike interest rate I think unless it is
+ 
+
+ align:start position:0%
+hike interest rate I think unless it is
+a big mess ER because inflation is still
+
+ align:start position:0%
+a big mess ER because inflation is still
+ 
+
+ align:start position:0%
+a big mess ER because inflation is still
+way above their target ER but they have
+
+ align:start position:0%
+way above their target ER but they have
+ 
+
+ align:start position:0%
+way above their target ER but they have
+to be very worried that this stuff
+
+ align:start position:0%
+to be very worried that this stuff
+ 
+
+ align:start position:0%
+to be very worried that this stuff
+doesn't become to
+
+ align:start position:0%
+doesn't become to
+ 
+
+ align:start position:0%
+doesn't become to
+steep the things get to be very
+
+ align:start position:0%
+steep the things get to be very
+ 
+
+ align:start position:0%
+steep the things get to be very
+nonlinear when the financial sector is
+
+ align:start position:0%
+nonlinear when the financial sector is
+ 
+
+ align:start position:0%
+nonlinear when the financial sector is
+involved and and so probably that means
+
+ align:start position:0%
+involved and and so probably that means
+ 
+
+ align:start position:0%
+involved and and so probably that means
+that on net they already did it in the
+
+ align:start position:0%
+that on net they already did it in the
+ 
+
+ align:start position:0%
+that on net they already did it in the
+previous meeting everyone anticipated 50
+
+ align:start position:0%
+previous meeting everyone anticipated 50
+ 
+
+ align:start position:0%
+previous meeting everyone anticipated 50
+basis points of hikes once svb happened
+
+ align:start position:0%
+basis points of hikes once svb happened
+ 
+
+ align:start position:0%
+basis points of hikes once svb happened
+the bets went down dramatically and the
+
+ align:start position:0%
+the bets went down dramatically and the
+ 
+
+ align:start position:0%
+the bets went down dramatically and the
+realization went down to 25 basis points
+
+ align:start position:0%
+realization went down to 25 basis points
+ 
+
+ align:start position:0%
+realization went down to 25 basis points
+and so that's where we are H now now if
+
+ align:start position:0%
+and so that's where we are H now now if
+ 
+
+ align:start position:0%
+and so that's where we are H now now if
+everything works as
+
+ align:start position:0%
+everything works as
+ 
+
+ align:start position:0%
+everything works as
+plan and more or less that's a forecast
+
+ align:start position:0%
+plan and more or less that's a forecast
+ 
+
+ align:start position:0%
+plan and more or less that's a forecast
+at this moment there isn't any panic and
+
+ align:start position:0%
+at this moment there isn't any panic and
+ 
+
+ align:start position:0%
+at this moment there isn't any panic and
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+is that we're going to experience not a
+
+ align:start position:0%
+is that we're going to experience not a
+ 
+
+ align:start position:0%
+is that we're going to experience not a
+technically a recession but significant
+
+ align:start position:0%
+technically a recession but significant
+ 
+
+ align:start position:0%
+technically a recession but significant
+slowdown in in in the next quarters or
+
+ align:start position:0%
+slowdown in in in the next quarters or
+ 
+
+ align:start position:0%
+slowdown in in in the next quarters or
+so okay so that that's that's what that
+
+ align:start position:0%
+so okay so that that's that's what that
+ 
+
+ align:start position:0%
+so okay so that that's that's what that
+sort of the consensus expecting to to
+
+ align:start position:0%
+sort of the consensus expecting to to
+ 
+
+ align:start position:0%
+sort of the consensus expecting to to
+see H as a result of all these combined
+
+ align:start position:0%
+see H as a result of all these combined
+ 
+
+ align:start position:0%
+see H as a result of all these combined
+forces the effect that it still needs to
+
+ align:start position:0%
+forces the effect that it still needs to
+ 
+
+ align:start position:0%
+forces the effect that it still needs to
+tighten because of aggregate demand
+
+ align:start position:0%
+tighten because of aggregate demand
+ 
+
+ align:start position:0%
+tighten because of aggregate demand
+reasons and the very negative effect of
+
+ align:start position:0%
+reasons and the very negative effect of
+ 
+
+ align:start position:0%
+reasons and the very negative effect of
+the credit crunch especially on certain
+
+ align:start position:0%
+the credit crunch especially on certain
+ 
+
+ align:start position:0%
+the credit crunch especially on certain
+parts of the economy okay but that's
+
+ align:start position:0%
+parts of the economy okay but that's
+ 
+
+ align:start position:0%
+parts of the economy okay but that's
+what if everything again it works as
+
+ align:start position:0%
+what if everything again it works as
+ 
+
+ align:start position:0%
+what if everything again it works as
+plan means things continue to go Fairly
+
+ align:start position:0%
+plan means things continue to go Fairly
+ 
+
+ align:start position:0%
+plan means things continue to go Fairly
+smoothly H then it's certainly not going
+
+ align:start position:0%
+smoothly H then it's certainly not going
+ 
+
+ align:start position:0%
+smoothly H then it's certainly not going
+to be a a good year for economic
+
+ align:start position:0%
+to be a a good year for economic
+ 
+
+ align:start position:0%
+to be a a good year for economic
+activity ER but it shouldn't be a
+
+ align:start position:0%
+activity ER but it shouldn't be a
+ 
+
+ align:start position:0%
+activity ER but it shouldn't be a
+disaster either and that's sort of where
+
+ align:start position:0%
+disaster either and that's sort of where
+ 
+
+ align:start position:0%
+disaster either and that's sort of where
+we are at and and the tension is well if
+
+ align:start position:0%
+we are at and and the tension is well if
+ 
+
+ align:start position:0%
+we are at and and the tension is well if
+the financial crisis sort
+
+ align:start position:0%
+the financial crisis sort
+ 
+
+ align:start position:0%
+the financial crisis sort
+of leaks into the larger Banks then then
+
+ align:start position:0%
+of leaks into the larger Banks then then
+ 
+
+ align:start position:0%
+of leaks into the larger Banks then then
+these numbers are going to get a lot
+
+ align:start position:0%
+these numbers are going to get a lot
+ 
+
+ align:start position:0%
+these numbers are going to get a lot
+worse of course but that's that's that's
+
+ align:start position:0%
+worse of course but that's that's that's
+ 
+
+ align:start position:0%
+worse of course but that's that's that's
+a concern at the moment but uh but it
+
+ align:start position:0%
+a concern at the moment but uh but it
+ 
+
+ align:start position:0%
+a concern at the moment but uh but it
+doesn't seem like the central scenario
+
+ align:start position:0%
+doesn't seem like the central scenario
+ 
+
+ align:start position:0%
+doesn't seem like the central scenario
+now there are also some good news
+
+ align:start position:0%
+now there are also some good news
+ 
+
+ align:start position:0%
+now there are also some good news
+happening because remember that the
+
+ align:start position:0%
+happening because remember that the
+ 
+
+ align:start position:0%
+happening because remember that the
+problem we have the problem you have
+
+ align:start position:0%
+problem we have the problem you have
+ 
+
+ align:start position:0%
+problem we have the problem you have
+comes from two sides one side is too
+
+ align:start position:0%
+comes from two sides one side is too
+ 
+
+ align:start position:0%
+comes from two sides one side is too
+much demand and that the FED can affect
+
+ align:start position:0%
+much demand and that the FED can affect
+ 
+
+ align:start position:0%
+much demand and that the FED can affect
+very quickly that's that's what it's
+
+ align:start position:0%
+very quickly that's that's what it's
+ 
+
+ align:start position:0%
+very quickly that's that's what it's
+doing by hiking interest rate not as
+
+ align:start position:0%
+doing by hiking interest rate not as
+ 
+
+ align:start position:0%
+doing by hiking interest rate not as
+quickly as they would like but still
+
+ align:start position:0%
+quickly as they would like but still
+ 
+
+ align:start position:0%
+quickly as they would like but still
+they they have an impact on that but the
+
+ align:start position:0%
+they they have an impact on that but the
+ 
+
+ align:start position:0%
+they they have an impact on that but the
+other problem was aggregate supply and
+
+ align:start position:0%
+other problem was aggregate supply and
+ 
+
+ align:start position:0%
+other problem was aggregate supply and
+in particular is that the labor market
+
+ align:start position:0%
+in particular is that the labor market
+ 
+
+ align:start position:0%
+in particular is that the labor market
+look very tight and remember when we did
+
+ align:start position:0%
+look very tight and remember when we did
+ 
+
+ align:start position:0%
+look very tight and remember when we did
+the Philips curve and all that the labor
+
+ align:start position:0%
+the Philips curve and all that the labor
+ 
+
+ align:start position:0%
+the Philips curve and all that the labor
+market is very critical in all that
+
+ align:start position:0%
+market is very critical in all that
+ 
+
+ align:start position:0%
+market is very critical in all that
+process of generating inflation and so
+
+ align:start position:0%
+process of generating inflation and so
+ 
+
+ align:start position:0%
+process of generating inflation and so
+on that's a reason you sort of try to
+
+ align:start position:0%
+on that's a reason you sort of try to
+ 
+
+ align:start position:0%
+on that's a reason you sort of try to
+generate more unemployment essentially
+
+ align:start position:0%
+generate more unemployment essentially
+ 
+
+ align:start position:0%
+generate more unemployment essentially
+to lower wage pressure because that
+
+ align:start position:0%
+to lower wage pressure because that
+ 
+
+ align:start position:0%
+to lower wage pressure because that
+means less pressure on prices and so on
+
+ align:start position:0%
+means less pressure on prices and so on
+ 
+
+ align:start position:0%
+means less pressure on prices and so on
+so forth and one of the problems is that
+
+ align:start position:0%
+so forth and one of the problems is that
+ 
+
+ align:start position:0%
+so forth and one of the problems is that
+again looks is very nice in principle
+
+ align:start position:0%
+again looks is very nice in principle
+ 
+
+ align:start position:0%
+again looks is very nice in principle
+that we have very low unemployment rate
+
+ align:start position:0%
+that we have very low unemployment rate
+ 
+
+ align:start position:0%
+that we have very low unemployment rate
+but it's very difficult to sort of lower
+
+ align:start position:0%
+but it's very difficult to sort of lower
+ 
+
+ align:start position:0%
+but it's very difficult to sort of lower
+wage pressure If unemployment is so low
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+having said this and this is the part
+
+ align:start position:0%
+having said this and this is the part
+ 
+
+ align:start position:0%
+having said this and this is the part
+that I say is sort of Fairly good news
+
+ align:start position:0%
+that I say is sort of Fairly good news
+ 
+
+ align:start position:0%
+that I say is sort of Fairly good news
+having said this in the mod we simplify
+
+ align:start position:0%
+having said this in the mod we simplify
+ 
+
+ align:start position:0%
+having said this in the mod we simplify
+things and we just put an employment as
+
+ align:start position:0%
+things and we just put an employment as
+ 
+
+ align:start position:0%
+things and we just put an employment as
+the only variable that could adjust and
+
+ align:start position:0%
+the only variable that could adjust and
+ 
+
+ align:start position:0%
+the only variable that could adjust and
+that was important for wages as aside
+
+ align:start position:0%
+that was important for wages as aside
+ 
+
+ align:start position:0%
+that was important for wages as aside
+from some institutional things in
+
+ align:start position:0%
+from some institutional things in
+ 
+
+ align:start position:0%
+from some institutional things in
+practice there are many other indicators
+
+ align:start position:0%
+practice there are many other indicators
+ 
+
+ align:start position:0%
+practice there are many other indicators
+and really what really matters is
+
+ align:start position:0%
+and really what really matters is
+ 
+
+ align:start position:0%
+and really what really matters is
+employment what happens we took as a
+
+ align:start position:0%
+employment what happens we took as a
+ 
+
+ align:start position:0%
+employment what happens we took as a
+fixed n we took a fixed the
+
+ align:start position:0%
+fixed n we took a fixed the
+ 
+
+ align:start position:0%
+fixed n we took a fixed the
+participation rate and that's the reason
+
+ align:start position:0%
+participation rate and that's the reason
+ 
+
+ align:start position:0%
+participation rate and that's the reason
+unemployment was the variable summarize
+
+ align:start position:0%
+unemployment was the variable summarize
+ 
+
+ align:start position:0%
+unemployment was the variable summarize
+everything but what really puts pressure
+
+ align:start position:0%
+everything but what really puts pressure
+ 
+
+ align:start position:0%
+everything but what really puts pressure
+on labor market is shortage of workers
+
+ align:start position:0%
+on labor market is shortage of workers
+ 
+
+ align:start position:0%
+on labor market is shortage of workers
+if you have an unemployment rate that is
+
+ align:start position:0%
+if you have an unemployment rate that is
+ 
+
+ align:start position:0%
+if you have an unemployment rate that is
+constant but there are lots of workers
+
+ align:start position:0%
+constant but there are lots of workers
+ 
+
+ align:start position:0%
+constant but there are lots of workers
+have coming into the labor force and
+
+ align:start position:0%
+have coming into the labor force and
+ 
+
+ align:start position:0%
+have coming into the labor force and
+that's not doesn't put as much pressure
+
+ align:start position:0%
+that's not doesn't put as much pressure
+ 
+
+ align:start position:0%
+that's not doesn't put as much pressure
+on on wages and therefore less pressure
+
+ align:start position:0%
+on on wages and therefore less pressure
+ 
+
+ align:start position:0%
+on on wages and therefore less pressure
+on inflation and this is exactly what we
+
+ align:start position:0%
+on inflation and this is exactly what we
+ 
+
+ align:start position:0%
+on inflation and this is exactly what we
+beginning to see in the US economy and I
+
+ align:start position:0%
+beginning to see in the US economy and I
+ 
+
+ align:start position:0%
+beginning to see in the US economy and I
+think that's very good news it gives us
+
+ align:start position:0%
+think that's very good news it gives us
+ 
+
+ align:start position:0%
+think that's very good news it gives us
+hope that this inflationary process may
+
+ align:start position:0%
+hope that this inflationary process may
+ 
+
+ align:start position:0%
+hope that this inflationary process may
+come down a little faster so this is
+
+ align:start position:0%
+come down a little faster so this is
+ 
+
+ align:start position:0%
+come down a little faster so this is
+labor market participation remember so
+
+ align:start position:0%
+labor market participation remember so
+ 
+
+ align:start position:0%
+labor market participation remember so
+this unemployment number
+
+ align:start position:0%
+this unemployment number
+ 
+
+ align:start position:0%
+this unemployment number
+spike a lot but it under represented how
+
+ align:start position:0%
+spike a lot but it under represented how
+ 
+
+ align:start position:0%
+spike a lot but it under represented how
+much contraction there was in labor in
+
+ align:start position:0%
+much contraction there was in labor in
+ 
+
+ align:start position:0%
+much contraction there was in labor in
+employment and so on because many people
+
+ align:start position:0%
+employment and so on because many people
+ 
+
+ align:start position:0%
+employment and so on because many people
+simply exit the labor force and those
+
+ align:start position:0%
+simply exit the labor force and those
+ 
+
+ align:start position:0%
+simply exit the labor force and those
+remember we don't count as an employed
+
+ align:start position:0%
+remember we don't count as an employed
+ 
+
+ align:start position:0%
+remember we don't count as an employed
+okay and so that happened it was a very
+
+ align:start position:0%
+okay and so that happened it was a very
+ 
+
+ align:start position:0%
+okay and so that happened it was a very
+sharp decline in the in the labor force
+
+ align:start position:0%
+sharp decline in the in the labor force
+ 
+
+ align:start position:0%
+sharp decline in the in the labor force
+in the labor participation rate so
+
+ align:start position:0%
+in the labor participation rate so
+ 
+
+ align:start position:0%
+in the labor participation rate so
+decline in the labor force and then that
+
+ align:start position:0%
+decline in the labor force and then that
+ 
+
+ align:start position:0%
+decline in the labor force and then that
+recovery is one of the things that
+
+ align:start position:0%
+recovery is one of the things that
+ 
+
+ align:start position:0%
+recovery is one of the things that
+happened much slower than the FED
+
+ align:start position:0%
+happened much slower than the FED
+ 
+
+ align:start position:0%
+happened much slower than the FED
+anticipated and that was part of the
+
+ align:start position:0%
+anticipated and that was part of the
+ 
+
+ align:start position:0%
+anticipated and that was part of the
+mistake is they thought that this was
+
+ align:start position:0%
+mistake is they thought that this was
+ 
+
+ align:start position:0%
+mistake is they thought that this was
+going to come back quickly and that for
+
+ align:start position:0%
+going to come back quickly and that for
+ 
+
+ align:start position:0%
+going to come back quickly and that for
+potential output was going to rise very
+
+ align:start position:0%
+potential output was going to rise very
+ 
+
+ align:start position:0%
+potential output was going to rise very
+quickly and it didn't that was one of
+
+ align:start position:0%
+quickly and it didn't that was one of
+ 
+
+ align:start position:0%
+quickly and it didn't that was one of
+the the the mistakes the forast mistakes
+
+ align:start position:0%
+the the the mistakes the forast mistakes
+ 
+
+ align:start position:0%
+the the the mistakes the forast mistakes
+but now it's clearly it's coming back to
+
+ align:start position:0%
+but now it's clearly it's coming back to
+ 
+
+ align:start position:0%
+but now it's clearly it's coming back to
+levels that are sort of more consistent
+
+ align:start position:0%
+levels that are sort of more consistent
+ 
+
+ align:start position:0%
+levels that are sort of more consistent
+with historical
+
+ align:start position:0%
+with historical
+ 
+
+ align:start position:0%
+with historical
+levels if you look at the employment to
+
+ align:start position:0%
+levels if you look at the employment to
+ 
+
+ align:start position:0%
+levels if you look at the employment to
+population ratio also big decline for
+
+ align:start position:0%
+population ratio also big decline for
+ 
+
+ align:start position:0%
+population ratio also big decline for
+similar reasons but if you look at
+
+ align:start position:0%
+similar reasons but if you look at
+ 
+
+ align:start position:0%
+similar reasons but if you look at
+employment to population ratio today is
+
+ align:start position:0%
+employment to population ratio today is
+ 
+
+ align:start position:0%
+employment to population ratio today is
+clearly sort of getting back to the
+
+ align:start position:0%
+clearly sort of getting back to the
+ 
+
+ align:start position:0%
+clearly sort of getting back to the
+trend it had before okay so so that's
+
+ align:start position:0%
+trend it had before okay so so that's
+ 
+
+ align:start position:0%
+trend it had before okay so so that's
+that's very good news in the sense that
+
+ align:start position:0%
+that's very good news in the sense that
+ 
+
+ align:start position:0%
+that's very good news in the sense that
+even if unemployment doesn't move a lot
+
+ align:start position:0%
+even if unemployment doesn't move a lot
+ 
+
+ align:start position:0%
+even if unemployment doesn't move a lot
+this sort of reduces well it's good for
+
+ align:start position:0%
+this sort of reduces well it's good for
+ 
+
+ align:start position:0%
+this sort of reduces well it's good for
+output expands and so on but it also
+
+ align:start position:0%
+output expands and so on but it also
+ 
+
+ align:start position:0%
+output expands and so on but it also
+lowers the pre inflationary pressures in
+
+ align:start position:0%
+lowers the pre inflationary pressures in
+ 
+
+ align:start position:0%
+lowers the pre inflationary pressures in
+the economy and another component that
+
+ align:start position:0%
+the economy and another component that
+ 
+
+ align:start position:0%
+the economy and another component that
+actually that that I think I mentioned a
+
+ align:start position:0%
+actually that that I think I mentioned a
+ 
+
+ align:start position:0%
+actually that that I think I mentioned a
+couple of times in in the lecture but is
+
+ align:start position:0%
+couple of times in in the lecture but is
+ 
+
+ align:start position:0%
+couple of times in in the lecture but is
+immigration in in a market like the us a
+
+ align:start position:0%
+immigration in in a market like the us a
+ 
+
+ align:start position:0%
+immigration in in a market like the us a
+lot of the labor forces comes from
+
+ align:start position:0%
+lot of the labor forces comes from
+ 
+
+ align:start position:0%
+lot of the labor forces comes from
+immigration okay and and that stopped
+
+ align:start position:0%
+immigration okay and and that stopped
+ 
+
+ align:start position:0%
+immigration okay and and that stopped
+for a while for a variety of reasons but
+
+ align:start position:0%
+for a while for a variety of reasons but
+ 
+
+ align:start position:0%
+for a while for a variety of reasons but
+certainly Co had a a big effect so so
+
+ align:start position:0%
+certainly Co had a a big effect so so
+ 
+
+ align:start position:0%
+certainly Co had a a big effect so so
+that meant sort of about
+
+ align:start position:0%
+that meant sort of about
+ 
+
+ align:start position:0%
+that meant sort of about
+500,000 less people a year coming into
+
+ align:start position:0%
+500,000 less people a year coming into
+ 
+
+ align:start position:0%
+500,000 less people a year coming into
+the US Labor Force and that has big
+
+ align:start position:0%
+the US Labor Force and that has big
+ 
+
+ align:start position:0%
+the US Labor Force and that has big
+impacts especially in some sectors of
+
+ align:start position:0%
+impacts especially in some sectors of
+ 
+
+ align:start position:0%
+impacts especially in some sectors of
+the economy okay lots of and and that's
+
+ align:start position:0%
+the economy okay lots of and and that's
+ 
+
+ align:start position:0%
+the economy okay lots of and and that's
+clearly being fixed now okay we may have
+
+ align:start position:0%
+clearly being fixed now okay we may have
+ 
+
+ align:start position:0%
+clearly being fixed now okay we may have
+other problems people may fight for
+
+ align:start position:0%
+other problems people may fight for
+ 
+
+ align:start position:0%
+other problems people may fight for
+political reasons and the SS whatever
+
+ align:start position:0%
+political reasons and the SS whatever
+ 
+
+ align:start position:0%
+political reasons and the SS whatever
+but from the point of view of macro this
+
+ align:start position:0%
+but from the point of view of macro this
+ 
+
+ align:start position:0%
+but from the point of view of macro this
+is certainly helping okay and in fact if
+
+ align:start position:0%
+is certainly helping okay and in fact if
+ 
+
+ align:start position:0%
+is certainly helping okay and in fact if
+you look at where the wage pressure is
+
+ align:start position:0%
+you look at where the wage pressure is
+ 
+
+ align:start position:0%
+you look at where the wage pressure is
+really coming from in the US economy is
+
+ align:start position:0%
+really coming from in the US economy is
+ 
+
+ align:start position:0%
+really coming from in the US economy is
+coming from those sectors where sort of
+
+ align:start position:0%
+coming from those sectors where sort of
+ 
+
+ align:start position:0%
+coming from those sectors where sort of
+immigrants play a big role you know um
+
+ align:start position:0%
+immigrants play a big role you know um
+ 
+
+ align:start position:0%
+immigrants play a big role you know um
+accommodation Food Services stuff like
+
+ align:start position:0%
+accommodation Food Services stuff like
+ 
+
+ align:start position:0%
+accommodation Food Services stuff like
+that you see that there sort of wages
+
+ align:start position:0%
+that you see that there sort of wages
+ 
+
+ align:start position:0%
+that you see that there sort of wages
+Rose pretty dramatically because there
+
+ align:start position:0%
+Rose pretty dramatically because there
+ 
+
+ align:start position:0%
+Rose pretty dramatically because there
+was a massive shortage there for two
+
+ align:start position:0%
+was a massive shortage there for two
+ 
+
+ align:start position:0%
+was a massive shortage there for two
+reasons one people didn't want to go
+
+ align:start position:0%
+reasons one people didn't want to go
+ 
+
+ align:start position:0%
+reasons one people didn't want to go
+back to those sectors to work close
+
+ align:start position:0%
+back to those sectors to work close
+ 
+
+ align:start position:0%
+back to those sectors to work close
+contact and stuff like that and the
+
+ align:start position:0%
+contact and stuff like that and the
+ 
+
+ align:start position:0%
+contact and stuff like that and the
+other one is that the important flow of
+
+ align:start position:0%
+other one is that the important flow of
+ 
+
+ align:start position:0%
+other one is that the important flow of
+supply of workers into that had sort of
+
+ align:start position:0%
+supply of workers into that had sort of
+ 
+
+ align:start position:0%
+supply of workers into that had sort of
+slowed down quite dramatically okay so
+
+ align:start position:0%
+slowed down quite dramatically okay so
+ 
+
+ align:start position:0%
+slowed down quite dramatically okay so
+that's where we're at and as a result of
+
+ align:start position:0%
+that's where we're at and as a result of
+ 
+
+ align:start position:0%
+that's where we're at and as a result of
+all these good forces despite the fact
+
+ align:start position:0%
+all these good forces despite the fact
+ 
+
+ align:start position:0%
+all these good forces despite the fact
+that we have very low
+
+ align:start position:0%
+that we have very low
+ 
+
+ align:start position:0%
+that we have very low
+unemployment you can see that wage
+
+ align:start position:0%
+unemployment you can see that wage
+ 
+
+ align:start position:0%
+unemployment you can see that wage
+pressure is beginning to decline in the
+
+ align:start position:0%
+pressure is beginning to decline in the
+ 
+
+ align:start position:0%
+pressure is beginning to decline in the
+US okay so it was very high there but
+
+ align:start position:0%
+US okay so it was very high there but
+ 
+
+ align:start position:0%
+US okay so it was very high there but
+those numbers are very distorted by
+
+ align:start position:0%
+those numbers are very distorted by
+ 
+
+ align:start position:0%
+those numbers are very distorted by
+composition effects and stuff like that
+
+ align:start position:0%
+composition effects and stuff like that
+ 
+
+ align:start position:0%
+composition effects and stuff like that
+but these were the numbers that were
+
+ align:start position:0%
+but these were the numbers that were
+ 
+
+ align:start position:0%
+but these were the numbers that were
+very worrisome I mean with wage
+
+ align:start position:0%
+very worrisome I mean with wage
+ 
+
+ align:start position:0%
+very worrisome I mean with wage
+inflation of 6% it's going to be very
+
+ align:start position:0%
+inflation of 6% it's going to be very
+ 
+
+ align:start position:0%
+inflation of 6% it's going to be very
+difficult to bring inflation to 2% down
+
+ align:start position:0%
+difficult to bring inflation to 2% down
+ 
+
+ align:start position:0%
+difficult to bring inflation to 2% down
+you need much lower wag inflation but
+
+ align:start position:0%
+you need much lower wag inflation but
+ 
+
+ align:start position:0%
+you need much lower wag inflation but
+you see that that is beginning to
+
+ align:start position:0%
+you see that that is beginning to
+ 
+
+ align:start position:0%
+you see that that is beginning to
+decline 2% is still too high for a
+
+ align:start position:0%
+decline 2% is still too high for a
+ 
+
+ align:start position:0%
+decline 2% is still too high for a
+steady state if you want to go back to
+
+ align:start position:0%
+steady state if you want to go back to
+ 
+
+ align:start position:0%
+steady state if you want to go back to
+2% inflation rate because you can have
+
+ align:start position:0%
+2% inflation rate because you can have
+ 
+
+ align:start position:0%
+2% inflation rate because you can have
+an increase in real wage but that has to
+
+ align:start position:0%
+an increase in real wage but that has to
+ 
+
+ align:start position:0%
+an increase in real wage but that has to
+be more or less aligned with the rate of
+
+ align:start position:0%
+be more or less aligned with the rate of
+ 
+
+ align:start position:0%
+be more or less aligned with the rate of
+growth of
+
+ align:start position:0%
+growth of
+ 
+
+ align:start position:0%
+growth of
+productivity which is much lower than
+
+ align:start position:0%
+productivity which is much lower than
+ 
+
+ align:start position:0%
+productivity which is much lower than
+that I mean at best it's 1% one and a
+
+ align:start position:0%
+that I mean at best it's 1% one and a
+ 
+
+ align:start position:0%
+that I mean at best it's 1% one and a
+half sometimes but so you could live
+
+ align:start position:0%
+half sometimes but so you could live
+ 
+
+ align:start position:0%
+half sometimes but so you could live
+with three and a half% weight real
+
+ align:start position:0%
+with three and a half% weight real
+ 
+
+ align:start position:0%
+with three and a half% weight real
+nominal wage growth but four four and a
+
+ align:start position:0%
+nominal wage growth but four four and a
+ 
+
+ align:start position:0%
+nominal wage growth but four four and a
+half it's it's a bit too much
+
+ align:start position:0%
+half it's it's a bit too much
+ 
+
+ align:start position:0%
+half it's it's a bit too much
+okay anyway so that's a that's that's
+
+ align:start position:0%
+okay anyway so that's a that's that's
+ 
+
+ align:start position:0%
+okay anyway so that's a that's that's
+the state of economy any questions about
+
+ align:start position:0%
+the state of economy any questions about
+ 
+
+ align:start position:0%
+the state of economy any questions about
+the state of economy open questions
+
+ align:start position:0%
+the state of economy open questions
+ 
+
+ align:start position:0%
+the state of economy open questions
+no no you're happy with it I'm fine good
+
+ align:start position:0%
+no no you're happy with it I'm fine good
+ 
+
+ align:start position:0%
+no no you're happy with it I'm fine good
+okay good so so what I want to next is
+
+ align:start position:0%
+okay good so so what I want to next is
+ 
+
+ align:start position:0%
+okay good so so what I want to next is
+so this was a summary and I all that I
+
+ align:start position:0%
+so this was a summary and I all that I
+ 
+
+ align:start position:0%
+so this was a summary and I all that I
+did here I did close economy economics
+
+ align:start position:0%
+did here I did close economy economics
+ 
+
+ align:start position:0%
+did here I did close economy economics
+okay all the my description I didn't
+
+ align:start position:0%
+okay all the my description I didn't
+ 
+
+ align:start position:0%
+okay all the my description I didn't
+need to tell you what was happening in
+
+ align:start position:0%
+need to tell you what was happening in
+ 
+
+ align:start position:0%
+need to tell you what was happening in
+the rest of the world and so on that
+
+ align:start position:0%
+the rest of the world and so on that
+ 
+
+ align:start position:0%
+the rest of the world and so on that
+would have been a lot harder to do if if
+
+ align:start position:0%
+would have been a lot harder to do if if
+ 
+
+ align:start position:0%
+would have been a lot harder to do if if
+if this was Singapore for example
+
+ align:start position:0%
+if this was Singapore for example
+ 
+
+ align:start position:0%
+if this was Singapore for example
+because Singapore depends a lot on the
+
+ align:start position:0%
+because Singapore depends a lot on the
+ 
+
+ align:start position:0%
+because Singapore depends a lot on the
+rest of the world and it's very
+
+ align:start position:0%
+rest of the world and it's very
+ 
+
+ align:start position:0%
+rest of the world and it's very
+difficult to tell a story that just
+
+ align:start position:0%
+difficult to tell a story that just
+ 
+
+ align:start position:0%
+difficult to tell a story that just
+depends on what happen in Singapore the
+
+ align:start position:0%
+depends on what happen in Singapore the
+ 
+
+ align:start position:0%
+depends on what happen in Singapore the
+US is pretty unique in that you can tell
+
+ align:start position:0%
+US is pretty unique in that you can tell
+ 
+
+ align:start position:0%
+US is pretty unique in that you can tell
+most of the story based on what happens
+
+ align:start position:0%
+most of the story based on what happens
+ 
+
+ align:start position:0%
+most of the story based on what happens
+in the US most not all but most of the
+
+ align:start position:0%
+in the US most not all but most of the
+ 
+
+ align:start position:0%
+in the US most not all but most of the
+story and that's what I just did almost
+
+ align:start position:0%
+story and that's what I just did almost
+ 
+
+ align:start position:0%
+story and that's what I just did almost
+anywhere else you need to think about
+
+ align:start position:0%
+anywhere else you need to think about
+ 
+
+ align:start position:0%
+anywhere else you need to think about
+even if you're in Japan big economy and
+
+ align:start position:0%
+even if you're in Japan big economy and
+ 
+
+ align:start position:0%
+even if you're in Japan big economy and
+so on effects will play a big role and
+
+ align:start position:0%
+so on effects will play a big role and
+ 
+
+ align:start position:0%
+so on effects will play a big role and
+so when you describe the state of the
+
+ align:start position:0%
+so when you describe the state of the
+ 
+
+ align:start position:0%
+so when you describe the state of the
+economy you're going to be talking about
+
+ align:start position:0%
+economy you're going to be talking about
+ 
+
+ align:start position:0%
+economy you're going to be talking about
+the Yen very high very low or
+
+ align:start position:0%
+the Yen very high very low or
+ 
+
+ align:start position:0%
+the Yen very high very low or
+not here you don't worry much about the
+
+ align:start position:0%
+not here you don't worry much about the
+ 
+
+ align:start position:0%
+not here you don't worry much about the
+dollar but the US is very unique on
+
+ align:start position:0%
+dollar but the US is very unique on
+ 
+
+ align:start position:0%
+dollar but the US is very unique on
+that I think no other country in the
+
+ align:start position:0%
+that I think no other country in the
+ 
+
+ align:start position:0%
+that I think no other country in the
+world has that that feature okay so now
+
+ align:start position:0%
+world has that that feature okay so now
+ 
+
+ align:start position:0%
+world has that that feature okay so now
+we're going to open up the economy and
+
+ align:start position:0%
+we're going to open up the economy and
+ 
+
+ align:start position:0%
+we're going to open up the economy and
+again perhaps it's it's the least
+
+ align:start position:0%
+again perhaps it's it's the least
+ 
+
+ align:start position:0%
+again perhaps it's it's the least
+important for the us but anywhere else
+
+ align:start position:0%
+important for the us but anywhere else
+ 
+
+ align:start position:0%
+important for the us but anywhere else
+is tremendously important more so it's
+
+ align:start position:0%
+is tremendously important more so it's
+ 
+
+ align:start position:0%
+is tremendously important more so it's
+becoming increasingly important for the
+
+ align:start position:0%
+becoming increasingly important for the
+ 
+
+ align:start position:0%
+becoming increasingly important for the
+US it has been becoming increasingly
+
+ align:start position:0%
+US it has been becoming increasingly
+ 
+
+ align:start position:0%
+US it has been becoming increasingly
+important for the US now we're in the
+
+ align:start position:0%
+important for the US now we're in the
+ 
+
+ align:start position:0%
+important for the US now we're in the
+middle of a de globalization mess we
+
+ align:start position:0%
+middle of a de globalization mess we
+ 
+
+ align:start position:0%
+middle of a de globalization mess we
+shall see where we end up so there has
+
+ align:start position:0%
+shall see where we end up so there has
+ 
+
+ align:start position:0%
+shall see where we end up so there has
+been a bit of a reversion of a very
+
+ align:start position:0%
+been a bit of a reversion of a very
+ 
+
+ align:start position:0%
+been a bit of a reversion of a very
+strong Trend towards integrating the
+
+ align:start position:0%
+strong Trend towards integrating the
+ 
+
+ align:start position:0%
+strong Trend towards integrating the
+economies of the world through many
+
+ align:start position:0%
+economies of the world through many
+ 
+
+ align:start position:0%
+economies of the world through many
+different channels and so I want to talk
+
+ align:start position:0%
+different channels and so I want to talk
+ 
+
+ align:start position:0%
+different channels and so I want to talk
+about what are the key variables in the
+
+ align:start position:0%
+about what are the key variables in the
+ 
+
+ align:start position:0%
+about what are the key variables in the
+when you integrate an economy to the
+
+ align:start position:0%
+when you integrate an economy to the
+ 
+
+ align:start position:0%
+when you integrate an economy to the
+rest of the world and and and things of
+
+ align:start position:0%
+rest of the world and and and things of
+ 
+
+ align:start position:0%
+rest of the world and and and things of
+that kind H I'm going to start with some
+
+ align:start position:0%
+that kind H I'm going to start with some
+ 
+
+ align:start position:0%
+that kind H I'm going to start with some
+definitions what are variables are we're
+
+ align:start position:0%
+definitions what are variables are we're
+ 
+
+ align:start position:0%
+definitions what are variables are we're
+going to be talking about that we
+
+ align:start position:0%
+going to be talking about that we
+ 
+
+ align:start position:0%
+going to be talking about that we
+weren't talking about up to now so one
+
+ align:start position:0%
+weren't talking about up to now so one
+ 
+
+ align:start position:0%
+weren't talking about up to now so one
+of the things that's going to be very
+
+ align:start position:0%
+of the things that's going to be very
+ 
+
+ align:start position:0%
+of the things that's going to be very
+important in an open economy exchange
+
+ align:start position:0%
+important in an open economy exchange
+ 
+
+ align:start position:0%
+important in an open economy exchange
+rate okay and here I'm giv you I'm going
+
+ align:start position:0%
+rate okay and here I'm giv you I'm going
+ 
+
+ align:start position:0%
+rate okay and here I'm giv you I'm going
+to Define things very formally later on
+
+ align:start position:0%
+to Define things very formally later on
+ 
+
+ align:start position:0%
+to Define things very formally later on
+but but but here you see an
+
+ align:start position:0%
+but but but here you see an
+ 
+
+ align:start position:0%
+but but but here you see an
+example of the US dollar Visa the main
+
+ align:start position:0%
+example of the US dollar Visa the main
+ 
+
+ align:start position:0%
+example of the US dollar Visa the main
+trading partners the US trades with many
+
+ align:start position:0%
+trading partners the US trades with many
+ 
+
+ align:start position:0%
+trading partners the US trades with many
+different parts of the world and there's
+
+ align:start position:0%
+different parts of the world and there's
+ 
+
+ align:start position:0%
+different parts of the world and there's
+an bilateral effects between those
+
+ align:start position:0%
+an bilateral effects between those
+ 
+
+ align:start position:0%
+an bilateral effects between those
+things and this measure here is
+
+ align:start position:0%
+things and this measure here is
+ 
+
+ align:start position:0%
+things and this measure here is
+something that weights by the amount of
+
+ align:start position:0%
+something that weights by the amount of
+ 
+
+ align:start position:0%
+something that weights by the amount of
+trade that we have with different
+
+ align:start position:0%
+trade that we have with different
+ 
+
+ align:start position:0%
+trade that we have with different
+economies of the world trace the
+
+ align:start position:0%
+economies of the world trace the
+ 
+
+ align:start position:0%
+economies of the world trace the
+different effects and says well is the
+
+ align:start position:0%
+different effects and says well is the
+ 
+
+ align:start position:0%
+different effects and says well is the
+dollar strong weak or whatever
+
+ align:start position:0%
+dollar strong weak or whatever
+ 
+
+ align:start position:0%
+dollar strong weak or whatever
+this is a matter of convention there's
+
+ align:start position:0%
+this is a matter of convention there's
+ 
+
+ align:start position:0%
+this is a matter of convention there's
+many ways you can no there are two ways
+
+ align:start position:0%
+many ways you can no there are two ways
+ 
+
+ align:start position:0%
+many ways you can no there are two ways
+in which you can do it but we're going
+
+ align:start position:0%
+in which you can do it but we're going
+ 
+
+ align:start position:0%
+in which you can do it but we're going
+to do it the following way what this
+
+ align:start position:0%
+to do it the following way what this
+ 
+
+ align:start position:0%
+to do it the following way what this
+effects will reflect is the price of the
+
+ align:start position:0%
+effects will reflect is the price of the
+ 
+
+ align:start position:0%
+effects will reflect is the price of the
+domestic currency in foreign currency
+
+ align:start position:0%
+domestic currency in foreign currency
+ 
+
+ align:start position:0%
+domestic currency in foreign currency
+terms so that means when this goes up
+
+ align:start position:0%
+terms so that means when this goes up
+ 
+
+ align:start position:0%
+terms so that means when this goes up
+means the dollar was becoming very
+
+ align:start position:0%
+means the dollar was becoming very
+ 
+
+ align:start position:0%
+means the dollar was becoming very
+expensive okay and that's a that's a
+
+ align:start position:0%
+expensive okay and that's a that's a
+ 
+
+ align:start position:0%
+expensive okay and that's a that's a
+very sharp I I'll get back to it but we
+
+ align:start position:0%
+very sharp I I'll get back to it but we
+ 
+
+ align:start position:0%
+very sharp I I'll get back to it but we
+call that an appreciation of the
+
+ align:start position:0%
+call that an appreciation of the
+ 
+
+ align:start position:0%
+call that an appreciation of the
+currency okay so here the the dollar was
+
+ align:start position:0%
+currency okay so here the the dollar was
+ 
+
+ align:start position:0%
+currency okay so here the the dollar was
+becoming very expensive in terms of
+
+ align:start position:0%
+becoming very expensive in terms of
+ 
+
+ align:start position:0%
+becoming very expensive in terms of
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+currencies the opposite happened sort of
+
+ align:start position:0%
+currencies the opposite happened sort of
+ 
+
+ align:start position:0%
+currencies the opposite happened sort of
+starting the second half of 2022 and now
+
+ align:start position:0%
+starting the second half of 2022 and now
+ 
+
+ align:start position:0%
+starting the second half of 2022 and now
+we have some had some Cycles here during
+
+ align:start position:0%
+we have some had some Cycles here during
+ 
+
+ align:start position:0%
+we have some had some Cycles here during
+this year but that's sort of that's
+
+ align:start position:0%
+this year but that's sort of that's
+ 
+
+ align:start position:0%
+this year but that's sort of that's
+going to be a very important variable
+
+ align:start position:0%
+going to be a very important variable
+ 
+
+ align:start position:0%
+going to be a very important variable
+the FX we call it the FX exchange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate another variable that we haven't
+
+ align:start position:0%
+rate another variable that we haven't
+ 
+
+ align:start position:0%
+rate another variable that we haven't
+talked about but but that is going to be
+
+ align:start position:0%
+talked about but but that is going to be
+ 
+
+ align:start position:0%
+talked about but but that is going to be
+important here is is and and that
+
+ align:start position:0%
+important here is is and and that
+ 
+
+ align:start position:0%
+important here is is and and that
+politicians argue a lot about it for
+
+ align:start position:0%
+politicians argue a lot about it for
+ 
+
+ align:start position:0%
+politicians argue a lot about it for
+with the wrong arguments but but but
+
+ align:start position:0%
+with the wrong arguments but but but
+ 
+
+ align:start position:0%
+with the wrong arguments but but but
+they do ER is the trades balance trade
+
+ align:start position:0%
+they do ER is the trades balance trade
+ 
+
+ align:start position:0%
+they do ER is the trades balance trade
+trade balance of goods and services of
+
+ align:start position:0%
+trade balance of goods and services of
+ 
+
+ align:start position:0%
+trade balance of goods and services of
+goods and services so this the trade
+
+ align:start position:0%
+goods and services so this the trade
+ 
+
+ align:start position:0%
+goods and services so this the trade
+balance of goods and services is simply
+
+ align:start position:0%
+balance of goods and services is simply
+ 
+
+ align:start position:0%
+balance of goods and services is simply
+a er um the difference between the
+
+ align:start position:0%
+a er um the difference between the
+ 
+
+ align:start position:0%
+a er um the difference between the
+exports so what a country sells to the
+
+ align:start position:0%
+exports so what a country sells to the
+ 
+
+ align:start position:0%
+exports so what a country sells to the
+rest of the world versus its import that
+
+ align:start position:0%
+rest of the world versus its import that
+ 
+
+ align:start position:0%
+rest of the world versus its import that
+is how much it buys from the rest of the
+
+ align:start position:0%
+is how much it buys from the rest of the
+ 
+
+ align:start position:0%
+is how much it buys from the rest of the
+world okay so this is monthly data for
+
+ align:start position:0%
+world okay so this is monthly data for
+ 
+
+ align:start position:0%
+world okay so this is monthly data for
+the US
+
+ align:start position:0%
+the US
+ 
+
+ align:start position:0%
+the US
+the US nowadays sort of runs a deficit a
+
+ align:start position:0%
+the US nowadays sort of runs a deficit a
+ 
+
+ align:start position:0%
+the US nowadays sort of runs a deficit a
+trade balance deficit of the order of 7
+
+ align:start position:0%
+trade balance deficit of the order of 7
+ 
+
+ align:start position:0%
+trade balance deficit of the order of 7
+70 billion dollars a
+
+ align:start position:0%
+70 billion dollars a
+ 
+
+ align:start position:0%
+70 billion dollars a
+month that means it exports to the rest
+
+ align:start position:0%
+month that means it exports to the rest
+ 
+
+ align:start position:0%
+month that means it exports to the rest
+of the world about S no 70 billion
+
+ align:start position:0%
+of the world about S no 70 billion
+ 
+
+ align:start position:0%
+of the world about S no 70 billion
+dollar less than it Imports sorry sorry
+
+ align:start position:0%
+dollar less than it Imports sorry sorry
+ 
+
+ align:start position:0%
+dollar less than it Imports sorry sorry
+yeah seven less than it Imports perfect
+
+ align:start position:0%
+yeah seven less than it Imports perfect
+ 
+
+ align:start position:0%
+yeah seven less than it Imports perfect
+okay you have seen that this is
+
+ align:start position:0%
+okay you have seen that this is
+ 
+
+ align:start position:0%
+okay you have seen that this is
+pretty H sustained
+
+ align:start position:0%
+pretty H sustained
+ 
+
+ align:start position:0%
+pretty H sustained
+actually here look pretty balanced but
+
+ align:start position:0%
+actually here look pretty balanced but
+ 
+
+ align:start position:0%
+actually here look pretty balanced but
+but but but the US on on on average has
+
+ align:start position:0%
+but but but the US on on on average has
+ 
+
+ align:start position:0%
+but but but the US on on on average has
+a situation like that okay the US tends
+
+ align:start position:0%
+a situation like that okay the US tends
+ 
+
+ align:start position:0%
+a situation like that okay the US tends
+to export less than it Imports and then
+
+ align:start position:0%
+to export less than it Imports and then
+ 
+
+ align:start position:0%
+to export less than it Imports and then
+that's when politicians get all very
+
+ align:start position:0%
+that's when politicians get all very
+ 
+
+ align:start position:0%
+that's when politicians get all very
+worked out and said you know this is
+
+ align:start position:0%
+worked out and said you know this is
+ 
+
+ align:start position:0%
+worked out and said you know this is
+unfair competition from the rest of the
+
+ align:start position:0%
+unfair competition from the rest of the
+ 
+
+ align:start position:0%
+unfair competition from the rest of the
+world and so on so forth I think in
+
+ align:start position:0%
+world and so on so forth I think in
+ 
+
+ align:start position:0%
+world and so on so forth I think in
+general has very little to do with that
+
+ align:start position:0%
+general has very little to do with that
+ 
+
+ align:start position:0%
+general has very little to do with that
+it has to do that with the fact that the
+
+ align:start position:0%
+it has to do that with the fact that the
+ 
+
+ align:start position:0%
+it has to do that with the fact that the
+US likes to save less than the rest of
+
+ align:start position:0%
+US likes to save less than the rest of
+ 
+
+ align:start position:0%
+US likes to save less than the rest of
+the world and and but but let me not get
+
+ align:start position:0%
+the world and and but but let me not get
+ 
+
+ align:start position:0%
+the world and and but but let me not get
+into that and think much later in the
+
+ align:start position:0%
+into that and think much later in the
+ 
+
+ align:start position:0%
+into that and think much later in the
+course but anyway that's the situation
+
+ align:start position:0%
+course but anyway that's the situation
+ 
+
+ align:start position:0%
+course but anyway that's the situation
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+US this is obviously a blep that has to
+
+ align:start position:0%
+US this is obviously a blep that has to
+ 
+
+ align:start position:0%
+US this is obviously a blep that has to
+do with covid and so on but you see that
+
+ align:start position:0%
+do with covid and so on but you see that
+ 
+
+ align:start position:0%
+do with covid and so on but you see that
+we're now more or less back to to where
+
+ align:start position:0%
+we're now more or less back to to where
+ 
+
+ align:start position:0%
+we're now more or less back to to where
+we were before this was a period
+
+ align:start position:0%
+we were before this was a period
+ 
+
+ align:start position:0%
+we were before this was a period
+actually of lots of global political
+
+ align:start position:0%
+actually of lots of global political
+ 
+
+ align:start position:0%
+actually of lots of global political
+tension because it had one counterpart
+
+ align:start position:0%
+tension because it had one counterpart
+ 
+
+ align:start position:0%
+tension because it had one counterpart
+that was very big it was
+
+ align:start position:0%
+that was very big it was
+ 
+
+ align:start position:0%
+that was very big it was
+China okay and it is called the the time
+
+ align:start position:0%
+China okay and it is called the the time
+ 
+
+ align:start position:0%
+China okay and it is called the the time
+of the global
+
+ align:start position:0%
+of the global
+ 
+
+ align:start position:0%
+of the global
+imbalances and that the US was learning
+
+ align:start position:0%
+imbalances and that the US was learning
+ 
+
+ align:start position:0%
+imbalances and that the US was learning
+very large trade deficits and then China
+
+ align:start position:0%
+very large trade deficits and then China
+ 
+
+ align:start position:0%
+very large trade deficits and then China
+in particular was running very large
+
+ align:start position:0%
+in particular was running very large
+ 
+
+ align:start position:0%
+in particular was running very large
+trade surpluses and and so there were
+
+ align:start position:0%
+trade surpluses and and so there were
+ 
+
+ align:start position:0%
+trade surpluses and and so there were
+lots of political quarters because of
+
+ align:start position:0%
+lots of political quarters because of
+ 
+
+ align:start position:0%
+lots of political quarters because of
+that here you have a so obviously the US
+
+ align:start position:0%
+that here you have a so obviously the US
+ 
+
+ align:start position:0%
+that here you have a so obviously the US
+has many many trading partners and with
+
+ align:start position:0%
+has many many trading partners and with
+ 
+
+ align:start position:0%
+has many many trading partners and with
+respect to many of them it has very
+
+ align:start position:0%
+respect to many of them it has very
+ 
+
+ align:start position:0%
+respect to many of them it has very
+large deficits so on net and here are
+
+ align:start position:0%
+large deficits so on net and here are
+ 
+
+ align:start position:0%
+large deficits so on net and here are
+the main I rank the the 10 main net
+
+ align:start position:0%
+the main I rank the the 10 main net
+ 
+
+ align:start position:0%
+the main I rank the the 10 main net
+deficits for the us so I don't know when
+
+ align:start position:0%
+deficits for the us so I don't know when
+ 
+
+ align:start position:0%
+deficits for the us so I don't know when
+was this but anyway it looks like that
+
+ align:start position:0%
+was this but anyway it looks like that
+ 
+
+ align:start position:0%
+was this but anyway it looks like that
+sort of for the
+
+ align:start position:0%
+sort of for the
+ 
+
+ align:start position:0%
+sort of for the
+last eight or so
+
+ align:start position:0%
+last eight or so
+ 
+
+ align:start position:0%
+last eight or so
+years remove Co it looks more or less
+
+ align:start position:0%
+years remove Co it looks more or less
+ 
+
+ align:start position:0%
+years remove Co it looks more or less
+like this all the time and you see that
+
+ align:start position:0%
+like this all the time and you see that
+ 
+
+ align:start position:0%
+like this all the time and you see that
+the US indeed large
+
+ align:start position:0%
+the US indeed large
+ 
+
+ align:start position:0%
+the US indeed large
+large exports to China about $153
+
+ align:start position:0%
+large exports to China about $153
+ 
+
+ align:start position:0%
+large exports to China about $153
+billion a year and it Imports about 536
+
+ align:start position:0%
+billion a year and it Imports about 536
+ 
+
+ align:start position:0%
+billion a year and it Imports about 536
+billions a year so the net deficit is$
+
+ align:start position:0%
+billions a year so the net deficit is$
+ 
+
+ align:start position:0%
+billions a year so the net deficit is$
+380 billion dollar a year and that's the
+
+ align:start position:0%
+380 billion dollar a year and that's the
+ 
+
+ align:start position:0%
+380 billion dollar a year and that's the
+reason this is a big political thing
+
+ align:start position:0%
+reason this is a big political thing
+ 
+
+ align:start position:0%
+reason this is a big political thing
+okay because it sounds
+
+ align:start position:0%
+okay because it sounds
+ 
+
+ align:start position:0%
+okay because it sounds
+like a big deficit but there are other
+
+ align:start position:0%
+like a big deficit but there are other
+ 
+
+ align:start position:0%
+like a big deficit but there are other
+countries with respect to Mexico 130
+
+ align:start position:0%
+countries with respect to Mexico 130
+ 
+
+ align:start position:0%
+countries with respect to Mexico 130
+billion and so on the US exports a lot
+
+ align:start position:0%
+billion and so on the US exports a lot
+ 
+
+ align:start position:0%
+billion and so on the US exports a lot
+more to
+
+ align:start position:0%
+more to
+ 
+
+ align:start position:0%
+more to
+Mexico ER Vietnam a lot of what happens
+
+ align:start position:0%
+Mexico ER Vietnam a lot of what happens
+ 
+
+ align:start position:0%
+Mexico ER Vietnam a lot of what happens
+from Vietnam is really Chinese exports
+
+ align:start position:0%
+from Vietnam is really Chinese exports
+ 
+
+ align:start position:0%
+from Vietnam is really Chinese exports
+in this guys but but uh but there you
+
+ align:start position:0%
+in this guys but but uh but there you
+ 
+
+ align:start position:0%
+in this guys but but uh but there you
+see it okay there are many others
+
+ align:start position:0%
+see it okay there are many others
+ 
+
+ align:start position:0%
+see it okay there are many others
+Germany is always a a problem but uh a
+
+ align:start position:0%
+Germany is always a a problem but uh a
+ 
+
+ align:start position:0%
+Germany is always a a problem but uh a
+problem for somebody that his deficit as
+
+ align:start position:0%
+problem for somebody that his deficit as
+ 
+
+ align:start position:0%
+problem for somebody that his deficit as
+a problem
+
+ align:start position:0%
+a problem
+ 
+
+ align:start position:0%
+a problem
+uh and so on okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now that's a on the good side this is
+
+ align:start position:0%
+now that's a on the good side this is
+ 
+
+ align:start position:0%
+now that's a on the good side this is
+this is this what I was saying here is
+
+ align:start position:0%
+this is this what I was saying here is
+ 
+
+ align:start position:0%
+this is this what I was saying here is
+that you know one sense of openness is
+
+ align:start position:0%
+that you know one sense of openness is
+ 
+
+ align:start position:0%
+that you know one sense of openness is
+on the goods and services Market that
+
+ align:start position:0%
+on the goods and services Market that
+ 
+
+ align:start position:0%
+on the goods and services Market that
+you buy goods from the rest of the world
+
+ align:start position:0%
+you buy goods from the rest of the world
+ 
+
+ align:start position:0%
+you buy goods from the rest of the world
+the rest of the world buys goods from
+
+ align:start position:0%
+the rest of the world buys goods from
+ 
+
+ align:start position:0%
+the rest of the world buys goods from
+you sometimes these things are balanced
+
+ align:start position:0%
+you sometimes these things are balanced
+ 
+
+ align:start position:0%
+you sometimes these things are balanced
+sometimes they're not H when at the
+
+ align:start position:0%
+sometimes they're not H when at the
+ 
+
+ align:start position:0%
+sometimes they're not H when at the
+aggre level they're not balance for a
+
+ align:start position:0%
+aggre level they're not balance for a
+ 
+
+ align:start position:0%
+aggre level they're not balance for a
+very long period of time unless you're
+
+ align:start position:0%
+very long period of time unless you're
+ 
+
+ align:start position:0%
+very long period of time unless you're
+the US that often causes problems ER um
+
+ align:start position:0%
+the US that often causes problems ER um
+ 
+
+ align:start position:0%
+the US that often causes problems ER um
+but at the bilateral level if you look
+
+ align:start position:0%
+but at the bilateral level if you look
+ 
+
+ align:start position:0%
+but at the bilateral level if you look
+at any country we'll have situations
+
+ align:start position:0%
+at any country we'll have situations
+ 
+
+ align:start position:0%
+at any country we'll have situations
+like this some country where they export
+
+ align:start position:0%
+like this some country where they export
+ 
+
+ align:start position:0%
+like this some country where they export
+a lot to and import very little from and
+
+ align:start position:0%
+a lot to and import very little from and
+ 
+
+ align:start position:0%
+a lot to and import very little from and
+vice versa but that's the way the US
+
+ align:start position:0%
+vice versa but that's the way the US
+ 
+
+ align:start position:0%
+vice versa but that's the way the US
+looks another sense of openness which is
+
+ align:start position:0%
+looks another sense of openness which is
+ 
+
+ align:start position:0%
+looks another sense of openness which is
+very important is financial openness no
+
+ align:start position:0%
+very important is financial openness no
+ 
+
+ align:start position:0%
+very important is financial openness no
+meaning that you can also buy or save
+
+ align:start position:0%
+meaning that you can also buy or save
+ 
+
+ align:start position:0%
+meaning that you can also buy or save
+using foreign assets or domestic assets
+
+ align:start position:0%
+using foreign assets or domestic assets
+ 
+
+ align:start position:0%
+using foreign assets or domestic assets
+okay so you can buy a foreign asset
+
+ align:start position:0%
+okay so you can buy a foreign asset
+ 
+
+ align:start position:0%
+okay so you can buy a foreign asset
+perhaps not directly or most of you
+
+ align:start position:0%
+perhaps not directly or most of you
+ 
+
+ align:start position:0%
+perhaps not directly or most of you
+directly but you can do it through a
+
+ align:start position:0%
+directly but you can do it through a
+ 
+
+ align:start position:0%
+directly but you can do it through a
+broker and so on you can buy foreign
+
+ align:start position:0%
+broker and so on you can buy foreign
+ 
+
+ align:start position:0%
+broker and so on you can buy foreign
+assets or and foreigners buy lots of us
+
+ align:start position:0%
+assets or and foreigners buy lots of us
+ 
+
+ align:start position:0%
+assets or and foreigners buy lots of us
+assets okay that's a sense of openness
+
+ align:start position:0%
+assets okay that's a sense of openness
+ 
+
+ align:start position:0%
+assets okay that's a sense of openness
+in financial markets that you can buy
+
+ align:start position:0%
+in financial markets that you can buy
+ 
+
+ align:start position:0%
+in financial markets that you can buy
+you're not stuck with your own your
+
+ align:start position:0%
+you're not stuck with your own your
+ 
+
+ align:start position:0%
+you're not stuck with your own your
+country's financial asset you can also
+
+ align:start position:0%
+country's financial asset you can also
+ 
+
+ align:start position:0%
+country's financial asset you can also
+invest in other Count's Financial assets
+
+ align:start position:0%
+invest in other Count's Financial assets
+ 
+
+ align:start position:0%
+invest in other Count's Financial assets
+and vice
+
+ align:start position:0%
+and vice
+ 
+
+ align:start position:0%
+and vice
+versa those things probably you how I
+
+ align:start position:0%
+versa those things probably you how I
+ 
+
+ align:start position:0%
+versa those things probably you how I
+mean you notice trade openness a lot
+
+ align:start position:0%
+mean you notice trade openness a lot
+ 
+
+ align:start position:0%
+mean you notice trade openness a lot
+more probably than financial openness no
+
+ align:start position:0%
+more probably than financial openness no
+ 
+
+ align:start position:0%
+more probably than financial openness no
+because you're all the time buying
+
+ align:start position:0%
+because you're all the time buying
+ 
+
+ align:start position:0%
+because you're all the time buying
+imported goods and stuff like that
+
+ align:start position:0%
+imported goods and stuff like that
+ 
+
+ align:start position:0%
+imported goods and stuff like that
+H while you probably not involving lot
+
+ align:start position:0%
+H while you probably not involving lot
+ 
+
+ align:start position:0%
+H while you probably not involving lot
+of transactions of international
+
+ align:start position:0%
+of transactions of international
+ 
+
+ align:start position:0%
+of transactions of international
+financial instruments and so on but they
+
+ align:start position:0%
+financial instruments and so on but they
+ 
+
+ align:start position:0%
+financial instruments and so on but they
+are very large okay so if Pension funds
+
+ align:start position:0%
+are very large okay so if Pension funds
+ 
+
+ align:start position:0%
+are very large okay so if Pension funds
+and so on they're all involved in very
+
+ align:start position:0%
+and so on they're all involved in very
+ 
+
+ align:start position:0%
+and so on they're all involved in very
+large transactions in fact transactions
+
+ align:start position:0%
+large transactions in fact transactions
+ 
+
+ align:start position:0%
+large transactions in fact transactions
+in financial markets are an order of
+
+ align:start position:0%
+in financial markets are an order of
+ 
+
+ align:start position:0%
+in financial markets are an order of
+magnitude larger than transactions in
+
+ align:start position:0%
+magnitude larger than transactions in
+ 
+
+ align:start position:0%
+magnitude larger than transactions in
+the Goods Market very large and here you
+
+ align:start position:0%
+the Goods Market very large and here you
+ 
+
+ align:start position:0%
+the Goods Market very large and here you
+have an example of a
+
+ align:start position:0%
+have an example of a
+ 
+
+ align:start position:0%
+have an example of a
+by origin the the the you know foreign
+
+ align:start position:0%
+by origin the the the you know foreign
+ 
+
+ align:start position:0%
+by origin the the the you know foreign
+Holdings of us
+
+ align:start position:0%
+Holdings of us
+ 
+
+ align:start position:0%
+Holdings of us
+assets and this is in in in billions
+
+ align:start position:0%
+assets and this is in in in billions
+ 
+
+ align:start position:0%
+assets and this is in in in billions
+so these guys here this is China and
+
+ align:start position:0%
+so these guys here this is China and
+ 
+
+ align:start position:0%
+so these guys here this is China and
+Canada so have the largest and the UK
+
+ align:start position:0%
+Canada so have the largest and the UK
+ 
+
+ align:start position:0%
+Canada so have the largest and the UK
+those have sort of you know in the order
+
+ align:start position:0%
+those have sort of you know in the order
+ 
+
+ align:start position:0%
+those have sort of you know in the order
+of $2
+
+ align:start position:0%
+of $2
+ 
+
+ align:start position:0%
+of $2
+trillion of us assets they're
+
+ align:start position:0%
+trillion of us assets they're
+ 
+
+ align:start position:0%
+trillion of us assets they're
+holding Japan should be here also L A
+
+ align:start position:0%
+holding Japan should be here also L A
+ 
+
+ align:start position:0%
+holding Japan should be here also L A
+there there it is
+
+ align:start position:0%
+there there it is
+ 
+
+ align:start position:0%
+there there it is
+yeah now in these two countries
+
+ align:start position:0%
+yeah now in these two countries
+ 
+
+ align:start position:0%
+yeah now in these two countries
+here a lot of those Holdings
+
+ align:start position:0%
+here a lot of those Holdings
+ 
+
+ align:start position:0%
+here a lot of those Holdings
+actually well particularly in China more
+
+ align:start position:0%
+actually well particularly in China more
+ 
+
+ align:start position:0%
+actually well particularly in China more
+than than in Japan in China is a little
+
+ align:start position:0%
+than than in Japan in China is a little
+ 
+
+ align:start position:0%
+than than in Japan in China is a little
+less than than Japan
+
+ align:start position:0%
+less than than Japan
+ 
+
+ align:start position:0%
+less than than Japan
+Japan they save a lot so they need to
+
+ align:start position:0%
+Japan they save a lot so they need to
+ 
+
+ align:start position:0%
+Japan they save a lot so they need to
+buy lots of financial assets and the US
+
+ align:start position:0%
+buy lots of financial assets and the US
+ 
+
+ align:start position:0%
+buy lots of financial assets and the US
+is as the main producer of financial
+
+ align:start position:0%
+is as the main producer of financial
+ 
+
+ align:start position:0%
+is as the main producer of financial
+Assets in the world so they save a lot
+
+ align:start position:0%
+Assets in the world so they save a lot
+ 
+
+ align:start position:0%
+Assets in the world so they save a lot
+on that but also the central bank
+
+ align:start position:0%
+on that but also the central bank
+ 
+
+ align:start position:0%
+on that but also the central bank
+because of currency intervention and so
+
+ align:start position:0%
+because of currency intervention and so
+ 
+
+ align:start position:0%
+because of currency intervention and so
+on buys lots of us
+
+ align:start position:0%
+on buys lots of us
+ 
+
+ align:start position:0%
+on buys lots of us
+treasuries China this is mostly the
+
+ align:start position:0%
+treasuries China this is mostly the
+ 
+
+ align:start position:0%
+treasuries China this is mostly the
+Central Bank buying US treasuries
+
+ align:start position:0%
+Central Bank buying US treasuries
+ 
+
+ align:start position:0%
+Central Bank buying US treasuries
+foreign reserves okay large amount of
+
+ align:start position:0%
+foreign reserves okay large amount of
+ 
+
+ align:start position:0%
+foreign reserves okay large amount of
+reserves Canada is private sector
+
+ align:start position:0%
+reserves Canada is private sector
+ 
+
+ align:start position:0%
+reserves Canada is private sector
+Pension funds and so on for but you see
+
+ align:start position:0%
+Pension funds and so on for but you see
+ 
+
+ align:start position:0%
+Pension funds and so on for but you see
+Brazilians also buy lots of assets from
+
+ align:start position:0%
+Brazilians also buy lots of assets from
+ 
+
+ align:start position:0%
+Brazilians also buy lots of assets from
+the US again central banks play big
+
+ align:start position:0%
+the US again central banks play big
+ 
+
+ align:start position:0%
+the US again central banks play big
+roles in all this Australia is less the
+
+ align:start position:0%
+roles in all this Australia is less the
+ 
+
+ align:start position:0%
+roles in all this Australia is less the
+Central Bank much more private sector UK
+
+ align:start position:0%
+Central Bank much more private sector UK
+ 
+
+ align:start position:0%
+Central Bank much more private sector UK
+is all private sector and so
+
+ align:start position:0%
+is all private sector and so
+ 
+
+ align:start position:0%
+is all private sector and so
+on and then Europe okay but point of
+
+ align:start position:0%
+on and then Europe okay but point of
+ 
+
+ align:start position:0%
+on and then Europe okay but point of
+that picture is that there's lots of
+
+ align:start position:0%
+that picture is that there's lots of
+ 
+
+ align:start position:0%
+that picture is that there's lots of
+countries in the world resent of
+
+ align:start position:0%
+countries in the world resent of
+ 
+
+ align:start position:0%
+countries in the world resent of
+different countries in the world that
+
+ align:start position:0%
+different countries in the world that
+ 
+
+ align:start position:0%
+different countries in the world that
+buy us Financial assets and in big
+
+ align:start position:0%
+buy us Financial assets and in big
+ 
+
+ align:start position:0%
+buy us Financial assets and in big
+amounts
+
+ align:start position:0%
+amounts
+ 
+
+ align:start position:0%
+amounts
+okay I don't know what the total number
+
+ align:start position:0%
+okay I don't know what the total number
+ 
+
+ align:start position:0%
+okay I don't know what the total number
+today is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably actually let me not make up
+
+ align:start position:0%
+probably actually let me not make up
+ 
+
+ align:start position:0%
+probably actually let me not make up
+that number you may find it
+
+ align:start position:0%
+that number you may find it
+ 
+
+ align:start position:0%
+that number you may find it
+um but it is certainly in
+
+ align:start position:0%
+um but it is certainly in
+ 
+
+ align:start position:0%
+um but it is certainly in
+the2 trillion dollar or something like
+
+ align:start position:0%
+the2 trillion dollar or something like
+ 
+
+ align:start position:0%
+the2 trillion dollar or something like
+that of H assets held us assets held by
+
+ align:start position:0%
+that of H assets held us assets held by
+ 
+
+ align:start position:0%
+that of H assets held us assets held by
+foreigners you can check it and tell me
+
+ align:start position:0%
+foreigners you can check it and tell me
+ 
+
+ align:start position:0%
+foreigners you can check it and tell me
+it's probably
+
+ align:start position:0%
+it's probably
+ 
+
+ align:start position:0%
+it's probably
+more here's the other way around us
+
+ align:start position:0%
+more here's the other way around us
+ 
+
+ align:start position:0%
+more here's the other way around us
+residents Holdings of foreign assets
+
+ align:start position:0%
+residents Holdings of foreign assets
+ 
+
+ align:start position:0%
+residents Holdings of foreign assets
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+ER you see us
+
+ align:start position:0%
+ER you see us
+ 
+
+ align:start position:0%
+ER you see us
+us residents hold lots of Canadian
+
+ align:start position:0%
+us residents hold lots of Canadian
+ 
+
+ align:start position:0%
+us residents hold lots of Canadian
+assets okay and mostly developed
+
+ align:start position:0%
+assets okay and mostly developed
+ 
+
+ align:start position:0%
+assets okay and mostly developed
+economies but you have India China and
+
+ align:start position:0%
+economies but you have India China and
+ 
+
+ align:start position:0%
+economies but you have India China and
+so on lots of Latino American
+
+ align:start position:0%
+so on lots of Latino American
+ 
+
+ align:start position:0%
+so on lots of Latino American
+assets and so on okay so the US is so
+
+ align:start position:0%
+assets and so on okay so the US is so
+ 
+
+ align:start position:0%
+assets and so on okay so the US is so
+it's not only that the rest of the world
+
+ align:start position:0%
+it's not only that the rest of the world
+ 
+
+ align:start position:0%
+it's not only that the rest of the world
+demands us asset but us
+
+ align:start position:0%
+demands us asset but us
+ 
+
+ align:start position:0%
+demands us asset but us
+residents perhaps not directly most of
+
+ align:start position:0%
+residents perhaps not directly most of
+ 
+
+ align:start position:0%
+residents perhaps not directly most of
+you but indirectly demand lots of
+
+ align:start position:0%
+you but indirectly demand lots of
+ 
+
+ align:start position:0%
+you but indirectly demand lots of
+foreign assets okay um there are some
+
+ align:start position:0%
+foreign assets okay um there are some
+ 
+
+ align:start position:0%
+foreign assets okay um there are some
+very fascinating facts that happen here
+
+ align:start position:0%
+very fascinating facts that happen here
+ 
+
+ align:start position:0%
+very fascinating facts that happen here
+because the type of assets that
+
+ align:start position:0%
+because the type of assets that
+ 
+
+ align:start position:0%
+because the type of assets that
+foreigners tend to demand from the US
+
+ align:start position:0%
+foreigners tend to demand from the US
+ 
+
+ align:start position:0%
+foreigners tend to demand from the US
+are very different from the ones that
+
+ align:start position:0%
+are very different from the ones that
+ 
+
+ align:start position:0%
+are very different from the ones that
+us er um demands from the rest of the
+
+ align:start position:0%
+us er um demands from the rest of the
+ 
+
+ align:start position:0%
+us er um demands from the rest of the
+world ER in fact one of the things that
+
+ align:start position:0%
+world ER in fact one of the things that
+ 
+
+ align:start position:0%
+world ER in fact one of the things that
+that the reasons the US can afford
+
+ align:start position:0%
+that the reasons the US can afford
+ 
+
+ align:start position:0%
+that the reasons the US can afford
+running those chronic trade
+
+ align:start position:0%
+running those chronic trade
+ 
+
+ align:start position:0%
+running those chronic trade
+deficits is because it tends to get much
+
+ align:start position:0%
+deficits is because it tends to get much
+ 
+
+ align:start position:0%
+deficits is because it tends to get much
+higher Returns on the asset it buys
+
+ align:start position:0%
+higher Returns on the asset it buys
+ 
+
+ align:start position:0%
+higher Returns on the asset it buys
+abroad than foreigners get on the assets
+
+ align:start position:0%
+abroad than foreigners get on the assets
+ 
+
+ align:start position:0%
+abroad than foreigners get on the assets
+they buy in the US and the difference
+
+ align:start position:0%
+they buy in the US and the difference
+ 
+
+ align:start position:0%
+they buy in the US and the difference
+allows you to find sort of systematic
+
+ align:start position:0%
+allows you to find sort of systematic
+ 
+
+ align:start position:0%
+allows you to find sort of systematic
+trade deficits and the reason for that
+
+ align:start position:0%
+trade deficits and the reason for that
+ 
+
+ align:start position:0%
+trade deficits and the reason for that
+is a lot of the US assets that for buy
+
+ align:start position:0%
+is a lot of the US assets that for buy
+ 
+
+ align:start position:0%
+is a lot of the US assets that for buy
+they do it for safety reasons they're
+
+ align:start position:0%
+they do it for safety reasons they're
+ 
+
+ align:start position:0%
+they do it for safety reasons they're
+buying us treasure it's very safe
+
+ align:start position:0%
+buying us treasure it's very safe
+ 
+
+ align:start position:0%
+buying us treasure it's very safe
+instrument just in case there is a big
+
+ align:start position:0%
+instrument just in case there is a big
+ 
+
+ align:start position:0%
+instrument just in case there is a big
+mess they they want to have those assets
+
+ align:start position:0%
+mess they they want to have those assets
+ 
+
+ align:start position:0%
+mess they they want to have those assets
+so it's it's almost for insurance reason
+
+ align:start position:0%
+so it's it's almost for insurance reason
+ 
+
+ align:start position:0%
+so it's it's almost for insurance reason
+ER the US Treasures are sort of
+
+ align:start position:0%
+ER the US Treasures are sort of
+ 
+
+ align:start position:0%
+ER the US Treasures are sort of
+perceived as the main safe Assets in the
+
+ align:start position:0%
+perceived as the main safe Assets in the
+ 
+
+ align:start position:0%
+perceived as the main safe Assets in the
+world okay so they they hold it for for
+
+ align:start position:0%
+world okay so they they hold it for for
+ 
+
+ align:start position:0%
+world okay so they they hold it for for
+that reason while the US mostly hold
+
+ align:start position:0%
+that reason while the US mostly hold
+ 
+
+ align:start position:0%
+that reason while the US mostly hold
+assets abroad for a you know risky
+
+ align:start position:0%
+assets abroad for a you know risky
+ 
+
+ align:start position:0%
+assets abroad for a you know risky
+Investments either foreign direct
+
+ align:start position:0%
+Investments either foreign direct
+ 
+
+ align:start position:0%
+Investments either foreign direct
+investment or Equity stuff like that and
+
+ align:start position:0%
+investment or Equity stuff like that and
+ 
+
+ align:start position:0%
+investment or Equity stuff like that and
+typically most fixed income investments
+
+ align:start position:0%
+typically most fixed income investments
+ 
+
+ align:start position:0%
+typically most fixed income investments
+in the US a lot of it a lot of what you
+
+ align:start position:0%
+in the US a lot of it a lot of what you
+ 
+
+ align:start position:0%
+in the US a lot of it a lot of what you
+see here is just us resident reaching
+
+ align:start position:0%
+see here is just us resident reaching
+ 
+
+ align:start position:0%
+see here is just us resident reaching
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+yield
+
+ align:start position:0%
+yield
+ 
+
+ align:start position:0%
+yield
+Brazilian Sovereign bonds equivalence of
+
+ align:start position:0%
+Brazilian Sovereign bonds equivalence of
+ 
+
+ align:start position:0%
+Brazilian Sovereign bonds equivalence of
+the US treasuries you know give you 9%
+
+ align:start position:0%
+the US treasuries you know give you 9%
+ 
+
+ align:start position:0%
+the US treasuries you know give you 9%
+10% it's a lot higher than the US tends
+
+ align:start position:0%
+10% it's a lot higher than the US tends
+ 
+
+ align:start position:0%
+10% it's a lot higher than the US tends
+to give H 14% even now and so on so so
+
+ align:start position:0%
+to give H 14% even now and so on so so
+ 
+
+ align:start position:0%
+to give H 14% even now and so on so so
+so net the US tends to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has less Assets in the rest of the world
+
+ align:start position:0%
+has less Assets in the rest of the world
+ 
+
+ align:start position:0%
+has less Assets in the rest of the world
+than foreigners have of the US and it
+
+ align:start position:0%
+than foreigners have of the US and it
+ 
+
+ align:start position:0%
+than foreigners have of the US and it
+still makes sufficiently more return
+
+ align:start position:0%
+still makes sufficiently more return
+ 
+
+ align:start position:0%
+still makes sufficiently more return
+higher return on average on an asset it
+
+ align:start position:0%
+higher return on average on an asset it
+ 
+
+ align:start position:0%
+higher return on average on an asset it
+holds from the rest of the world that it
+
+ align:start position:0%
+holds from the rest of the world that it
+ 
+
+ align:start position:0%
+holds from the rest of the world that it
+has a surplus which which it can Finance
+
+ align:start position:0%
+has a surplus which which it can Finance
+ 
+
+ align:start position:0%
+has a surplus which which it can Finance
+the trade deficit This is complicated
+
+ align:start position:0%
+the trade deficit This is complicated
+ 
+
+ align:start position:0%
+the trade deficit This is complicated
+you don't need to know the details but I
+
+ align:start position:0%
+you don't need to know the details but I
+ 
+
+ align:start position:0%
+you don't need to know the details but I
+to tell you what the kind of things are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happening so so there's three senses in
+
+ align:start position:0%
+happening so so there's three senses in
+ 
+
+ align:start position:0%
+happening so so there's three senses in
+which you can have a a and of of
+
+ align:start position:0%
+which you can have a a and of of
+ 
+
+ align:start position:0%
+which you can have a a and of of
+openness the two that I have described
+
+ align:start position:0%
+openness the two that I have described
+ 
+
+ align:start position:0%
+openness the two that I have described
+implicitly already Goods in Goods Market
+
+ align:start position:0%
+implicitly already Goods in Goods Market
+ 
+
+ align:start position:0%
+implicitly already Goods in Goods Market
+that you can
+
+ align:start position:0%
+that you can
+ 
+
+ align:start position:0%
+that you can
+buy foreign goods and you can sell Goods
+
+ align:start position:0%
+buy foreign goods and you can sell Goods
+ 
+
+ align:start position:0%
+buy foreign goods and you can sell Goods
+to the rest of the world and the second
+
+ align:start position:0%
+to the rest of the world and the second
+ 
+
+ align:start position:0%
+to the rest of the world and the second
+one is financial markets which is what I
+
+ align:start position:0%
+one is financial markets which is what I
+ 
+
+ align:start position:0%
+one is financial markets which is what I
+just described you can choose between
+
+ align:start position:0%
+just described you can choose between
+ 
+
+ align:start position:0%
+just described you can choose between
+domestic and foreign assets the main
+
+ align:start position:0%
+domestic and foreign assets the main
+ 
+
+ align:start position:0%
+domestic and foreign assets the main
+impediments to the forers typically are
+
+ align:start position:0%
+impediments to the forers typically are
+ 
+
+ align:start position:0%
+impediments to the forers typically are
+tariffs and quotas and you have heard a
+
+ align:start position:0%
+tariffs and quotas and you have heard a
+ 
+
+ align:start position:0%
+tariffs and quotas and you have heard a
+lot about tariffs and so on these days
+
+ align:start position:0%
+lot about tariffs and so on these days
+ 
+
+ align:start position:0%
+lot about tariffs and so on these days
+ER the main impediment for financial
+
+ align:start position:0%
+ER the main impediment for financial
+ 
+
+ align:start position:0%
+ER the main impediment for financial
+Market is what is called Capital
+
+ align:start position:0%
+Market is what is called Capital
+ 
+
+ align:start position:0%
+Market is what is called Capital
+controls very rarely develop economies
+
+ align:start position:0%
+controls very rarely develop economies
+ 
+
+ align:start position:0%
+controls very rarely develop economies
+impose Capital
+
+ align:start position:0%
+impose Capital
+ 
+
+ align:start position:0%
+impose Capital
+controls but emerging markets do it
+
+ align:start position:0%
+controls but emerging markets do it
+ 
+
+ align:start position:0%
+controls but emerging markets do it
+regularly okay H limit the amount of
+
+ align:start position:0%
+regularly okay H limit the amount of
+ 
+
+ align:start position:0%
+regularly okay H limit the amount of
+especially Capital outflows when lots of
+
+ align:start position:0%
+especially Capital outflows when lots of
+ 
+
+ align:start position:0%
+especially Capital outflows when lots of
+capitalist Le in the country they try to
+
+ align:start position:0%
+capitalist Le in the country they try to
+ 
+
+ align:start position:0%
+capitalist Le in the country they try to
+stop you from doing more of that and and
+
+ align:start position:0%
+stop you from doing more of that and and
+ 
+
+ align:start position:0%
+stop you from doing more of that and and
+they sometimes do it in the way in
+
+ align:start position:0%
+they sometimes do it in the way in
+ 
+
+ align:start position:0%
+they sometimes do it in the way in
+because they they want to avoid the
+
+ align:start position:0%
+because they they want to avoid the
+ 
+
+ align:start position:0%
+because they they want to avoid the
+micro instability that comes from the
+
+ align:start position:0%
+micro instability that comes from the
+ 
+
+ align:start position:0%
+micro instability that comes from the
+big reversal of capital flows so they
+
+ align:start position:0%
+big reversal of capital flows so they
+ 
+
+ align:start position:0%
+big reversal of capital flows so they
+don't let lots of capital flow in during
+
+ align:start position:0%
+don't let lots of capital flow in during
+ 
+
+ align:start position:0%
+don't let lots of capital flow in during
+the boom just to prevent
+
+ align:start position:0%
+the boom just to prevent
+ 
+
+ align:start position:0%
+the boom just to prevent
+a reversal later on that's capital
+
+ align:start position:0%
+a reversal later on that's capital
+ 
+
+ align:start position:0%
+a reversal later on that's capital
+controls and there's a third way of
+
+ align:start position:0%
+controls and there's a third way of
+ 
+
+ align:start position:0%
+controls and there's a third way of
+opening to the rest of the world H which
+
+ align:start position:0%
+opening to the rest of the world H which
+ 
+
+ align:start position:0%
+opening to the rest of the world H which
+is Factor markets okay which is that
+
+ align:start position:0%
+is Factor markets okay which is that
+ 
+
+ align:start position:0%
+is Factor markets okay which is that
+firms can choose location I mean some
+
+ align:start position:0%
+firms can choose location I mean some
+ 
+
+ align:start position:0%
+firms can choose location I mean some
+plants we're seeing you know Japanese
+
+ align:start position:0%
+plants we're seeing you know Japanese
+ 
+
+ align:start position:0%
+plants we're seeing you know Japanese
+plants that that that do not export
+
+ align:start position:0%
+plants that that that do not export
+ 
+
+ align:start position:0%
+plants that that that do not export
+Toyotas from directly from
+
+ align:start position:0%
+Toyotas from directly from
+ 
+
+ align:start position:0%
+Toyotas from directly from
+from from Japan they have the plant here
+
+ align:start position:0%
+from from Japan they have the plant here
+ 
+
+ align:start position:0%
+from from Japan they have the plant here
+either in Canada or somewhere in the US
+
+ align:start position:0%
+either in Canada or somewhere in the US
+ 
+
+ align:start position:0%
+either in Canada or somewhere in the US
+and they sell locally so that's that's
+
+ align:start position:0%
+and they sell locally so that's that's
+ 
+
+ align:start position:0%
+and they sell locally so that's that's
+relocation of factors of production
+
+ align:start position:0%
+relocation of factors of production
+ 
+
+ align:start position:0%
+relocation of factors of production
+Japanese Capital that relocates to some
+
+ align:start position:0%
+Japanese Capital that relocates to some
+ 
+
+ align:start position:0%
+Japanese Capital that relocates to some
+place in Canada or in the US and labor
+
+ align:start position:0%
+place in Canada or in the US and labor
+ 
+
+ align:start position:0%
+place in Canada or in the US and labor
+you can also have workers that move from
+
+ align:start position:0%
+you can also have workers that move from
+ 
+
+ align:start position:0%
+you can also have workers that move from
+one place to the other that's another
+
+ align:start position:0%
+one place to the other that's another
+ 
+
+ align:start position:0%
+one place to the other that's another
+form of openness no free Capital free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free Factor mobility in this part of the
+
+ align:start position:0%
+free Factor mobility in this part of the
+ 
+
+ align:start position:0%
+free Factor mobility in this part of the
+course we're not going to talk about
+
+ align:start position:0%
+course we're not going to talk about
+ 
+
+ align:start position:0%
+course we're not going to talk about
+this okay we're going to just we're
+
+ align:start position:0%
+this okay we're going to just we're
+ 
+
+ align:start position:0%
+this okay we're going to just we're
+going to focus in the on these
+
+ align:start position:0%
+going to focus in the on these
+ 
+
+ align:start position:0%
+going to focus in the on these
+two the first we're going to look at is
+
+ align:start position:0%
+two the first we're going to look at is
+ 
+
+ align:start position:0%
+two the first we're going to look at is
+going to be a model of the Goods Market
+
+ align:start position:0%
+going to be a model of the Goods Market
+ 
+
+ align:start position:0%
+going to be a model of the Goods Market
+and that's going to be very much H like
+
+ align:start position:0%
+and that's going to be very much H like
+ 
+
+ align:start position:0%
+and that's going to be very much H like
+the islm but with an open economy and
+
+ align:start position:0%
+the islm but with an open economy and
+ 
+
+ align:start position:0%
+the islm but with an open economy and
+then we're going to bring in interest
+
+ align:start position:0%
+then we're going to bring in interest
+ 
+
+ align:start position:0%
+then we're going to bring in interest
+rate but now on you which is what
+
+ align:start position:0%
+rate but now on you which is what
+ 
+
+ align:start position:0%
+rate but now on you which is what
+remember what we did in the closed
+
+ align:start position:0%
+remember what we did in the closed
+ 
+
+ align:start position:0%
+remember what we did in the closed
+economy first we look at the Goods
+
+ align:start position:0%
+economy first we look at the Goods
+ 
+
+ align:start position:0%
+economy first we look at the Goods
+Market then we look at interest rate
+
+ align:start position:0%
+Market then we look at interest rate
+ 
+
+ align:start position:0%
+Market then we look at interest rate
+determination that was our LM and then
+
+ align:start position:0%
+determination that was our LM and then
+ 
+
+ align:start position:0%
+determination that was our LM and then
+we put the things together we came up
+
+ align:start position:0%
+we put the things together we came up
+ 
+
+ align:start position:0%
+we put the things together we came up
+with slm here the tricky thing is that
+
+ align:start position:0%
+with slm here the tricky thing is that
+ 
+
+ align:start position:0%
+with slm here the tricky thing is that
+there's not only one interest rate there
+
+ align:start position:0%
+there's not only one interest rate there
+ 
+
+ align:start position:0%
+there's not only one interest rate there
+are really two you have to decide
+
+ align:start position:0%
+are really two you have to decide
+ 
+
+ align:start position:0%
+are really two you have to decide
+between the domestic and foreign
+
+ align:start position:0%
+between the domestic and foreign
+ 
+
+ align:start position:0%
+between the domestic and foreign
+interest rate and then there's an
+
+ align:start position:0%
+interest rate and then there's an
+ 
+
+ align:start position:0%
+interest rate and then there's an
+exchange rate in between which will also
+
+ align:start position:0%
+exchange rate in between which will also
+ 
+
+ align:start position:0%
+exchange rate in between which will also
+affect so that's the reason it's going
+
+ align:start position:0%
+affect so that's the reason it's going
+ 
+
+ align:start position:0%
+affect so that's the reason it's going
+to get a little more complicated because
+
+ align:start position:0%
+to get a little more complicated because
+ 
+
+ align:start position:0%
+to get a little more complicated because
+you're going to be having two different
+
+ align:start position:0%
+you're going to be having two different
+ 
+
+ align:start position:0%
+you're going to be having two different
+prices two different Goods you can buy
+
+ align:start position:0%
+prices two different Goods you can buy
+ 
+
+ align:start position:0%
+prices two different Goods you can buy
+you can going to have also two different
+
+ align:start position:0%
+you can going to have also two different
+ 
+
+ align:start position:0%
+you can going to have also two different
+assets you can buy okay and the effects
+
+ align:start position:0%
+assets you can buy okay and the effects
+ 
+
+ align:start position:0%
+assets you can buy okay and the effects
+is going to affect all those things if
+
+ align:start position:0%
+is going to affect all those things if
+ 
+
+ align:start position:0%
+is going to affect all those things if
+when whenever I say FS I mean thechange
+
+ align:start position:0%
+when whenever I say FS I mean thechange
+ 
+
+ align:start position:0%
+when whenever I say FS I mean thechange
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+okay forign exchange that's the reason
+
+ align:start position:0%
+okay forign exchange that's the reason
+ 
+
+ align:start position:0%
+okay forign exchange that's the reason
+sometimes called
+
+ align:start position:0%
+sometimes called
+ 
+
+ align:start position:0%
+sometimes called
+FX now one thing that happens er er is
+
+ align:start position:0%
+FX now one thing that happens er er is
+ 
+
+ align:start position:0%
+FX now one thing that happens er er is
+that because economies are so integrated
+
+ align:start position:0%
+that because economies are so integrated
+ 
+
+ align:start position:0%
+that because economies are so integrated
+in in goods and financial markets is
+
+ align:start position:0%
+in in goods and financial markets is
+ 
+
+ align:start position:0%
+in in goods and financial markets is
+that bus business Cycles tend to be
+
+ align:start position:0%
+that bus business Cycles tend to be
+ 
+
+ align:start position:0%
+that bus business Cycles tend to be
+especially large one large large ones
+
+ align:start position:0%
+especially large one large large ones
+ 
+
+ align:start position:0%
+especially large one large large ones
+tend to be very synchronized around the
+
+ align:start position:0%
+tend to be very synchronized around the
+ 
+
+ align:start position:0%
+tend to be very synchronized around the
+world you see here Emerging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Markets sorry yeah this is the world
+
+ align:start position:0%
+Markets sorry yeah this is the world
+ 
+
+ align:start position:0%
+Markets sorry yeah this is the world
+that's that's emerging markets and
+
+ align:start position:0%
+that's that's emerging markets and
+ 
+
+ align:start position:0%
+that's that's emerging markets and
+that's advanced
+
+ align:start position:0%
+that's advanced
+ 
+
+ align:start position:0%
+that's advanced
+economies you can see the kind of things
+
+ align:start position:0%
+economies you can see the kind of things
+ 
+
+ align:start position:0%
+economies you can see the kind of things
+we discuss in the growth section which
+
+ align:start position:0%
+we discuss in the growth section which
+ 
+
+ align:start position:0%
+we discuss in the growth section which
+is these countries tend to grow faster
+
+ align:start position:0%
+is these countries tend to grow faster
+ 
+
+ align:start position:0%
+is these countries tend to grow faster
+than these countries because they're
+
+ align:start position:0%
+than these countries because they're
+ 
+
+ align:start position:0%
+than these countries because they're
+catching up okay that's the reason
+
+ align:start position:0%
+catching up okay that's the reason
+ 
+
+ align:start position:0%
+catching up okay that's the reason
+they're called emerging you know H but
+
+ align:start position:0%
+they're called emerging you know H but
+ 
+
+ align:start position:0%
+they're called emerging you know H but
+at the level of business cycle they're
+
+ align:start position:0%
+at the level of business cycle they're
+ 
+
+ align:start position:0%
+at the level of business cycle they're
+very synchronized I mean the 2008 2009
+
+ align:start position:0%
+very synchronized I mean the 2008 2009
+ 
+
+ align:start position:0%
+very synchronized I mean the 2008 2009
+recession was a recession
+
+ align:start position:0%
+recession was a recession
+ 
+
+ align:start position:0%
+recession was a recession
+globally this one doesn't have covid but
+
+ align:start position:0%
+globally this one doesn't have covid but
+ 
+
+ align:start position:0%
+globally this one doesn't have covid but
+but well Co naturally was very
+
+ align:start position:0%
+but well Co naturally was very
+ 
+
+ align:start position:0%
+but well Co naturally was very
+synchronized around the world but big
+
+ align:start position:0%
+synchronized around the world but big
+ 
+
+ align:start position:0%
+synchronized around the world but big
+the the point I'm making here is that
+
+ align:start position:0%
+the the point I'm making here is that
+ 
+
+ align:start position:0%
+the the point I'm making here is that
+once you're very integrated to the rest
+
+ align:start position:0%
+once you're very integrated to the rest
+ 
+
+ align:start position:0%
+once you're very integrated to the rest
+of the world you're Al exposed to a new
+
+ align:start position:0%
+of the world you're Al exposed to a new
+ 
+
+ align:start position:0%
+of the world you're Al exposed to a new
+source of shocks it may help you in many
+
+ align:start position:0%
+source of shocks it may help you in many
+ 
+
+ align:start position:0%
+source of shocks it may help you in many
+instances but you're also exposed to
+
+ align:start position:0%
+instances but you're also exposed to
+ 
+
+ align:start position:0%
+instances but you're also exposed to
+things that come
+
+ align:start position:0%
+things that come
+ 
+
+ align:start position:0%
+things that come
+from the rest of the world and the
+
+ align:start position:0%
+from the rest of the world and the
+ 
+
+ align:start position:0%
+from the rest of the world and the
+evidence is that business Cycles are
+
+ align:start position:0%
+evidence is that business Cycles are
+ 
+
+ align:start position:0%
+evidence is that business Cycles are
+very synchronized it's very difficult
+
+ align:start position:0%
+very synchronized it's very difficult
+ 
+
+ align:start position:0%
+very synchronized it's very difficult
+for the rest of the world to be immune
+
+ align:start position:0%
+for the rest of the world to be immune
+ 
+
+ align:start position:0%
+for the rest of the world to be immune
+to us recession for example it's very
+
+ align:start position:0%
+to us recession for example it's very
+ 
+
+ align:start position:0%
+to us recession for example it's very
+easy for the US to be immune to an
+
+ align:start position:0%
+easy for the US to be immune to an
+ 
+
+ align:start position:0%
+easy for the US to be immune to an
+Argentinian recession that's that's a
+
+ align:start position:0%
+Argentinian recession that's that's a
+ 
+
+ align:start position:0%
+Argentinian recession that's that's a
+different story but but but when things
+
+ align:start position:0%
+different story but but but when things
+ 
+
+ align:start position:0%
+different story but but but when things
+are large invol the large economies
+
+ align:start position:0%
+are large invol the large economies
+ 
+
+ align:start position:0%
+are large invol the large economies
+typically that will leak into the rest
+
+ align:start position:0%
+typically that will leak into the rest
+ 
+
+ align:start position:0%
+typically that will leak into the rest
+of the world China has sort of changed a
+
+ align:start position:0%
+of the world China has sort of changed a
+ 
+
+ align:start position:0%
+of the world China has sort of changed a
+little bit the composition used to be
+
+ align:start position:0%
+little bit the composition used to be
+ 
+
+ align:start position:0%
+little bit the composition used to be
+the case that that was always the case
+
+ align:start position:0%
+the case that that was always the case
+ 
+
+ align:start position:0%
+the case that that was always the case
+the if the us sankk then everyone sank
+
+ align:start position:0%
+the if the us sankk then everyone sank
+ 
+
+ align:start position:0%
+the if the us sankk then everyone sank
+and and and and the and now you have
+
+ align:start position:0%
+and and and and the and now you have
+ 
+
+ align:start position:0%
+and and and and the and now you have
+China which stabilizes it's a difference
+
+ align:start position:0%
+China which stabilizes it's a difference
+ 
+
+ align:start position:0%
+China which stabilizes it's a difference
+it's not completely
+
+ align:start position:0%
+it's not completely
+ 
+
+ align:start position:0%
+it's not completely
+correlated with with the US and so that
+
+ align:start position:0%
+correlated with with the US and so that
+ 
+
+ align:start position:0%
+correlated with with the US and so that
+has been stabilizing actually for many
+
+ align:start position:0%
+has been stabilizing actually for many
+ 
+
+ align:start position:0%
+has been stabilizing actually for many
+especially commodity producing economies
+
+ align:start position:0%
+especially commodity producing economies
+ 
+
+ align:start position:0%
+especially commodity producing economies
+and so on but it's still the case big
+
+ align:start position:0%
+and so on but it's still the case big
+ 
+
+ align:start position:0%
+and so on but it's still the case big
+mess is a big mess everywhere if the
+
+ align:start position:0%
+mess is a big mess everywhere if the
+ 
+
+ align:start position:0%
+mess is a big mess everywhere if the
+economies were close there would be no
+
+ align:start position:0%
+economies were close there would be no
+ 
+
+ align:start position:0%
+economies were close there would be no
+reason unless you have some saw you know
+
+ align:start position:0%
+reason unless you have some saw you know
+ 
+
+ align:start position:0%
+reason unless you have some saw you know
+shock covid even if the economies were
+
+ align:start position:0%
+shock covid even if the economies were
+ 
+
+ align:start position:0%
+shock covid even if the economies were
+completely closed would have been a mess
+
+ align:start position:0%
+completely closed would have been a mess
+ 
+
+ align:start position:0%
+completely closed would have been a mess
+because you know it's as long as the
+
+ align:start position:0%
+because you know it's as long as the
+ 
+
+ align:start position:0%
+because you know it's as long as the
+virus spread then it's a mess regardless
+
+ align:start position:0%
+virus spread then it's a mess regardless
+ 
+
+ align:start position:0%
+virus spread then it's a mess regardless
+but that's not the case here this
+
+ align:start position:0%
+but that's not the case here this
+ 
+
+ align:start position:0%
+but that's not the case here this
+recession was caused by a financial
+
+ align:start position:0%
+recession was caused by a financial
+ 
+
+ align:start position:0%
+recession was caused by a financial
+shock in the
+
+ align:start position:0%
+shock in the
+ 
+
+ align:start position:0%
+shock in the
+US okay and still the whole econ the the
+
+ align:start position:0%
+US okay and still the whole econ the the
+ 
+
+ align:start position:0%
+US okay and still the whole econ the the
+global economy as a whole suffer a lot
+
+ align:start position:0%
+global economy as a whole suffer a lot
+ 
+
+ align:start position:0%
+global economy as a whole suffer a lot
+so Things become very synchronized
+
+ align:start position:0%
+so Things become very synchronized
+ 
+
+ align:start position:0%
+so Things become very synchronized
+because of
+
+ align:start position:0%
+because of
+ 
+
+ align:start position:0%
+because of
+that another thing that has been
+
+ align:start position:0%
+that another thing that has been
+ 
+
+ align:start position:0%
+that another thing that has been
+happening is that
+
+ align:start position:0%
+happening is that
+ 
+
+ align:start position:0%
+happening is that
+everywhere again still we shall see
+
+ align:start position:0%
+everywhere again still we shall see
+ 
+
+ align:start position:0%
+everywhere again still we shall see
+where we end up after this covid things
+
+ align:start position:0%
+where we end up after this covid things
+ 
+
+ align:start position:0%
+where we end up after this covid things
+there was a slight reversion of that but
+
+ align:start position:0%
+there was a slight reversion of that but
+ 
+
+ align:start position:0%
+there was a slight reversion of that but
+everywhere even the US which one of the
+
+ align:start position:0%
+everywhere even the US which one of the
+ 
+
+ align:start position:0%
+everywhere even the US which one of the
+closest economies in the world one of
+
+ align:start position:0%
+closest economies in the world one of
+ 
+
+ align:start position:0%
+closest economies in the world one of
+the closest of the significant economies
+
+ align:start position:0%
+the closest of the significant economies
+ 
+
+ align:start position:0%
+the closest of the significant economies
+ER there has been a sort of there was a
+
+ align:start position:0%
+ER there has been a sort of there was a
+ 
+
+ align:start position:0%
+ER there has been a sort of there was a
+steady Trend rise towards higher
+
+ align:start position:0%
+steady Trend rise towards higher
+ 
+
+ align:start position:0%
+steady Trend rise towards higher
+integration to the rest of the world
+
+ align:start position:0%
+integration to the rest of the world
+ 
+
+ align:start position:0%
+integration to the rest of the world
+okay and the same is happening in
+
+ align:start position:0%
+okay and the same is happening in
+ 
+
+ align:start position:0%
+okay and the same is happening in
+financial markets it's just an order of
+
+ align:start position:0%
+financial markets it's just an order of
+ 
+
+ align:start position:0%
+financial markets it's just an order of
+magnitude larger but but you see here in
+
+ align:start position:0%
+magnitude larger but but you see here in
+ 
+
+ align:start position:0%
+magnitude larger but but you see here in
+the US you see that imports and exports
+
+ align:start position:0%
+the US you see that imports and exports
+ 
+
+ align:start position:0%
+the US you see that imports and exports
+as a share of GDP they were both Rising
+
+ align:start position:0%
+as a share of GDP they were both Rising
+ 
+
+ align:start position:0%
+as a share of GDP they were both Rising
+ing over time here shows you what I
+
+ align:start position:0%
+ing over time here shows you what I
+ 
+
+ align:start position:0%
+ing over time here shows you what I
+showed you before which is the deficit
+
+ align:start position:0%
+showed you before which is the deficit
+ 
+
+ align:start position:0%
+showed you before which is the deficit
+chronic deficit that the US has had but
+
+ align:start position:0%
+chronic deficit that the US has had but
+ 
+
+ align:start position:0%
+chronic deficit that the US has had but
+still even exports have been rising for
+
+ align:start position:0%
+still even exports have been rising for
+ 
+
+ align:start position:0%
+still even exports have been rising for
+a while
+
+ align:start position:0%
+a while
+ 
+
+ align:start position:0%
+a while
+now this number here you know that about
+
+ align:start position:0%
+now this number here you know that about
+ 
+
+ align:start position:0%
+now this number here you know that about
+the 20% of the US produced Goods 15% of
+
+ align:start position:0%
+the 20% of the US produced Goods 15% of
+ 
+
+ align:start position:0%
+the 20% of the US produced Goods 15% of
+GDP the US has about 15% of of of GDP in
+
+ align:start position:0%
+GDP the US has about 15% of of of GDP in
+ 
+
+ align:start position:0%
+GDP the US has about 15% of of of GDP in
+Imports and in exports some people use
+
+ align:start position:0%
+Imports and in exports some people use
+ 
+
+ align:start position:0%
+Imports and in exports some people use
+that the sum for example of Imports plus
+
+ align:start position:0%
+that the sum for example of Imports plus
+ 
+
+ align:start position:0%
+that the sum for example of Imports plus
+exports over GDP as a measure of
+
+ align:start position:0%
+exports over GDP as a measure of
+ 
+
+ align:start position:0%
+exports over GDP as a measure of
+openness how open is an economy and it's
+
+ align:start position:0%
+openness how open is an economy and it's
+ 
+
+ align:start position:0%
+openness how open is an economy and it's
+okay for comparisons but it's clearly
+
+ align:start position:0%
+okay for comparisons but it's clearly
+ 
+
+ align:start position:0%
+okay for comparisons but it's clearly
+underestimate how open economies really
+
+ align:start position:0%
+underestimate how open economies really
+ 
+
+ align:start position:0%
+underestimate how open economies really
+are I mean many of the goods that are
+
+ align:start position:0%
+are I mean many of the goods that are
+ 
+
+ align:start position:0%
+are I mean many of the goods that are
+considered that that the US does not
+
+ align:start position:0%
+considered that that the US does not
+ 
+
+ align:start position:0%
+considered that that the US does not
+import are produced domestically so they
+
+ align:start position:0%
+import are produced domestically so they
+ 
+
+ align:start position:0%
+import are produced domestically so they
+don't count as part of imports or
+
+ align:start position:0%
+don't count as part of imports or
+ 
+
+ align:start position:0%
+don't count as part of imports or
+anything their price is really
+
+ align:start position:0%
+anything their price is really
+ 
+
+ align:start position:0%
+anything their price is really
+determined by International
+
+ align:start position:0%
+determined by International
+ 
+
+ align:start position:0%
+determined by International
+competition okay the price of a of a
+
+ align:start position:0%
+competition okay the price of a of a
+ 
+
+ align:start position:0%
+competition okay the price of a of a
+Ford is very different with foreign
+
+ align:start position:0%
+Ford is very different with foreign
+ 
+
+ align:start position:0%
+Ford is very different with foreign
+compe I that not so we don't count the
+
+ align:start position:0%
+compe I that not so we don't count the
+ 
+
+ align:start position:0%
+compe I that not so we don't count the
+fors produced here as Imports or
+
+ align:start position:0%
+fors produced here as Imports or
+ 
+
+ align:start position:0%
+fors produced here as Imports or
+anything or and if would be part of the
+
+ align:start position:0%
+anything or and if would be part of the
+ 
+
+ align:start position:0%
+anything or and if would be part of the
+nontradable not tradeable it wouldn't
+
+ align:start position:0%
+nontradable not tradeable it wouldn't
+ 
+
+ align:start position:0%
+nontradable not tradeable it wouldn't
+part of this measure of openness but
+
+ align:start position:0%
+part of this measure of openness but
+ 
+
+ align:start position:0%
+part of this measure of openness but
+it's clear that the price and even the
+
+ align:start position:0%
+it's clear that the price and even the
+ 
+
+ align:start position:0%
+it's clear that the price and even the
+quality is being affected by exposure to
+
+ align:start position:0%
+quality is being affected by exposure to
+ 
+
+ align:start position:0%
+quality is being affected by exposure to
+International competition okay so there
+
+ align:start position:0%
+International competition okay so there
+ 
+
+ align:start position:0%
+International competition okay so there
+are very few sectors that are not really
+
+ align:start position:0%
+are very few sectors that are not really
+ 
+
+ align:start position:0%
+are very few sectors that are not really
+exposed to International competitions
+
+ align:start position:0%
+exposed to International competitions
+ 
+
+ align:start position:0%
+exposed to International competitions
+yeah haircuts they're not I mean you
+
+ align:start position:0%
+yeah haircuts they're not I mean you
+ 
+
+ align:start position:0%
+yeah haircuts they're not I mean you
+know you're not going to unless you
+
+ align:start position:0%
+know you're not going to unless you
+ 
+
+ align:start position:0%
+know you're not going to unless you
+leave sort of at
+
+ align:start position:0%
+leave sort of at
+ 
+
+ align:start position:0%
+leave sort of at
+some country you know County at the
+
+ align:start position:0%
+some country you know County at the
+ 
+
+ align:start position:0%
+some country you know County at the
+border of with Canada and there is a
+
+ align:start position:0%
+border of with Canada and there is a
+ 
+
+ align:start position:0%
+border of with Canada and there is a
+town right on the side that that's
+
+ align:start position:0%
+town right on the side that that's
+ 
+
+ align:start position:0%
+town right on the side that that's
+that's that's not going to happen
+
+ align:start position:0%
+that's that's not going to happen
+ 
+
+ align:start position:0%
+that's that's not going to happen
+but okay so trend is upward and and and
+
+ align:start position:0%
+but okay so trend is upward and and and
+ 
+
+ align:start position:0%
+but okay so trend is upward and and and
+uh even more so than than those numbers
+
+ align:start position:0%
+uh even more so than than those numbers
+ 
+
+ align:start position:0%
+uh even more so than than those numbers
+suggest if you look across the world and
+
+ align:start position:0%
+suggest if you look across the world and
+ 
+
+ align:start position:0%
+suggest if you look across the world and
+here is what I show you before is what I
+
+ align:start position:0%
+here is what I show you before is what I
+ 
+
+ align:start position:0%
+here is what I show you before is what I
+said before is the US
+
+ align:start position:0%
+said before is the US
+ 
+
+ align:start position:0%
+said before is the US
+actually it's is certainly look very
+
+ align:start position:0%
+actually it's is certainly look very
+ 
+
+ align:start position:0%
+actually it's is certainly look very
+close relative to others if you look at
+
+ align:start position:0%
+close relative to others if you look at
+ 
+
+ align:start position:0%
+close relative to others if you look at
+across large
+
+ align:start position:0%
+across large
+ 
+
+ align:start position:0%
+across large
+economies Japan which is also a very
+
+ align:start position:0%
+economies Japan which is also a very
+ 
+
+ align:start position:0%
+economies Japan which is also a very
+close economy for a variety of reasons
+
+ align:start position:0%
+close economy for a variety of reasons
+ 
+
+ align:start position:0%
+close economy for a variety of reasons
+is still more open than the US UK little
+
+ align:start position:0%
+is still more open than the US UK little
+ 
+
+ align:start position:0%
+is still more open than the US UK little
+Chile here but you know one thing that
+
+ align:start position:0%
+Chile here but you know one thing that
+ 
+
+ align:start position:0%
+Chile here but you know one thing that
+this shows this Dimension here shows is
+
+ align:start position:0%
+this shows this Dimension here shows is
+ 
+
+ align:start position:0%
+this shows this Dimension here shows is
+that the smaller you are the more open
+
+ align:start position:0%
+that the smaller you are the more open
+ 
+
+ align:start position:0%
+that the smaller you are the more open
+you're likely to be and it makes sense
+
+ align:start position:0%
+you're likely to be and it makes sense
+ 
+
+ align:start position:0%
+you're likely to be and it makes sense
+it's harder to produce all the goods if
+
+ align:start position:0%
+it's harder to produce all the goods if
+ 
+
+ align:start position:0%
+it's harder to produce all the goods if
+you have you know a small
+
+ align:start position:0%
+you have you know a small
+ 
+
+ align:start position:0%
+you have you know a small
+country and and and so so so that's
+
+ align:start position:0%
+country and and and so so so that's
+ 
+
+ align:start position:0%
+country and and and so so so that's
+that's a pattern the smaller you are
+
+ align:start position:0%
+that's a pattern the smaller you are
+ 
+
+ align:start position:0%
+that's a pattern the smaller you are
+controlling for a variety of
+
+ align:start position:0%
+controlling for a variety of
+ 
+
+ align:start position:0%
+controlling for a variety of
+factors ER you tend to be more open you
+
+ align:start position:0%
+factors ER you tend to be more open you
+ 
+
+ align:start position:0%
+factors ER you tend to be more open you
+need to Import and Export more import
+
+ align:start position:0%
+need to Import and Export more import
+ 
+
+ align:start position:0%
+need to Import and Export more import
+more in particular uh now that pattern
+
+ align:start position:0%
+more in particular uh now that pattern
+ 
+
+ align:start position:0%
+more in particular uh now that pattern
+is disrupted when you look in this
+
+ align:start position:0%
+is disrupted when you look in this
+ 
+
+ align:start position:0%
+is disrupted when you look in this
+direction no so this all these
+
+ align:start position:0%
+direction no so this all these
+ 
+
+ align:start position:0%
+direction no so this all these
+countries ER which are clearly much
+
+ align:start position:0%
+countries ER which are clearly much
+ 
+
+ align:start position:0%
+countries ER which are clearly much
+larger than Chile in terms of GDP and on
+
+ align:start position:0%
+larger than Chile in terms of GDP and on
+ 
+
+ align:start position:0%
+larger than Chile in terms of GDP and on
+ER have very high export ratios why do
+
+ align:start position:0%
+ER have very high export ratios why do
+ 
+
+ align:start position:0%
+ER have very high export ratios why do
+you think that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case exactly they're in Europe so so you
+
+ align:start position:0%
+case exactly they're in Europe so so you
+ 
+
+ align:start position:0%
+case exactly they're in Europe so so you
+know this Europe is very special Europe
+
+ align:start position:0%
+know this Europe is very special Europe
+ 
+
+ align:start position:0%
+know this Europe is very special Europe
+as a whole is as close as the US so if
+
+ align:start position:0%
+as a whole is as close as the US so if
+ 
+
+ align:start position:0%
+as a whole is as close as the US so if
+you look at the whole area together but
+
+ align:start position:0%
+you look at the whole area together but
+ 
+
+ align:start position:0%
+you look at the whole area together but
+but there is lots of intra Europe
+
+ align:start position:0%
+but there is lots of intra Europe
+ 
+
+ align:start position:0%
+but there is lots of intra Europe
+exports and imports especially in the
+
+ align:start position:0%
+exports and imports especially in the
+ 
+
+ align:start position:0%
+exports and imports especially in the
+Euro Zone I mean you have lots of things
+
+ align:start position:0%
+Euro Zone I mean you have lots of things
+ 
+
+ align:start position:0%
+Euro Zone I mean you have lots of things
+you have the same currency you just you
+
+ align:start position:0%
+you have the same currency you just you
+ 
+
+ align:start position:0%
+you have the same currency you just you
+know it's it's right next door so so so
+
+ align:start position:0%
+know it's it's right next door so so so
+ 
+
+ align:start position:0%
+know it's it's right next door so so so
+they're very open but they're very open
+
+ align:start position:0%
+they're very open but they're very open
+ 
+
+ align:start position:0%
+they're very open but they're very open
+within Europe not so much with the rest
+
+ align:start position:0%
+within Europe not so much with the rest
+ 
+
+ align:start position:0%
+within Europe not so much with the rest
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+world but this does a differ shate intra
+
+ align:start position:0%
+world but this does a differ shate intra
+ 
+
+ align:start position:0%
+world but this does a differ shate intra
+Europe exports and imports versus total
+
+ align:start position:0%
+Europe exports and imports versus total
+ 
+
+ align:start position:0%
+Europe exports and imports versus total
+and that's the reason you see these
+
+ align:start position:0%
+and that's the reason you see these
+ 
+
+ align:start position:0%
+and that's the reason you see these
+numbers are very very large but even
+
+ align:start position:0%
+numbers are very very large but even
+ 
+
+ align:start position:0%
+numbers are very very large but even
+here within here you see that the
+
+ align:start position:0%
+here within here you see that the
+ 
+
+ align:start position:0%
+here within here you see that the
+smaller countries tend to be very open
+
+ align:start position:0%
+smaller countries tend to be very open
+ 
+
+ align:start position:0%
+smaller countries tend to be very open
+much more open than than than bigger
+
+ align:start position:0%
+much more open than than than bigger
+ 
+
+ align:start position:0%
+much more open than than than bigger
+countries
+
+ align:start position:0%
+countries
+ 
+
+ align:start position:0%
+countries
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so H as as I said so
+
+ align:start position:0%
+good so H as as I said so
+ 
+
+ align:start position:0%
+good so H as as I said so
+terminology um this picture looks very
+
+ align:start position:0%
+terminology um this picture looks very
+ 
+
+ align:start position:0%
+terminology um this picture looks very
+similar to the picture I show you
+
+ align:start position:0%
+similar to the picture I show you
+ 
+
+ align:start position:0%
+similar to the picture I show you
+earlier on but it's not there it was a
+
+ align:start position:0%
+earlier on but it's not there it was a
+ 
+
+ align:start position:0%
+earlier on but it's not there it was a
+trade weighted H dollar and here is just
+
+ align:start position:0%
+trade weighted H dollar and here is just
+ 
+
+ align:start position:0%
+trade weighted H dollar and here is just
+one particular bilateral exchange rate
+
+ align:start position:0%
+one particular bilateral exchange rate
+ 
+
+ align:start position:0%
+one particular bilateral exchange rate
+which is the dollar yen exchange rate
+
+ align:start position:0%
+which is the dollar yen exchange rate
+ 
+
+ align:start position:0%
+which is the dollar yen exchange rate
+what happens is is when the dollar
+
+ align:start position:0%
+what happens is is when the dollar
+ 
+
+ align:start position:0%
+what happens is is when the dollar
+appreciates typically appreciates
+
+ align:start position:0%
+appreciates typically appreciates
+ 
+
+ align:start position:0%
+appreciates typically appreciates
+against everything and so on that's the
+
+ align:start position:0%
+against everything and so on that's the
+ 
+
+ align:start position:0%
+against everything and so on that's the
+reason the pictures look very similar
+
+ align:start position:0%
+reason the pictures look very similar
+ 
+
+ align:start position:0%
+reason the pictures look very similar
+but this was pretty dramatic you know
+
+ align:start position:0%
+but this was pretty dramatic you know
+ 
+
+ align:start position:0%
+but this was pretty dramatic you know
+there was a very sharp appreciation of
+
+ align:start position:0%
+there was a very sharp appreciation of
+ 
+
+ align:start position:0%
+there was a very sharp appreciation of
+the of the dollar of well strike what I
+
+ align:start position:0%
+the of the dollar of well strike what I
+ 
+
+ align:start position:0%
+the of the dollar of well strike what I
+said I'm so anyways this is the pattern
+
+ align:start position:0%
+said I'm so anyways this is the pattern
+ 
+
+ align:start position:0%
+said I'm so anyways this is the pattern
+of the number of yens per dollars
+
+ align:start position:0%
+of the number of yens per dollars
+ 
+
+ align:start position:0%
+of the number of yens per dollars
+meaning meaning that's we decided that
+
+ align:start position:0%
+meaning meaning that's we decided that
+ 
+
+ align:start position:0%
+meaning meaning that's we decided that
+that's the way we're going to find the
+
+ align:start position:0%
+that's the way we're going to find the
+ 
+
+ align:start position:0%
+that's the way we're going to find the
+exchange this the price of the domestic
+
+ align:start position:0%
+exchange this the price of the domestic
+ 
+
+ align:start position:0%
+exchange this the price of the domestic
+currency in terms of foreign currency so
+
+ align:start position:0%
+currency in terms of foreign currency so
+ 
+
+ align:start position:0%
+currency in terms of foreign currency so
+the price of the US dollar goes up up
+
+ align:start position:0%
+the price of the US dollar goes up up
+ 
+
+ align:start position:0%
+the price of the US dollar goes up up
+when they pay you more yens per dollar
+
+ align:start position:0%
+when they pay you more yens per dollar
+ 
+
+ align:start position:0%
+when they pay you more yens per dollar
+okay and and it went up very rapidly
+
+ align:start position:0%
+okay and and it went up very rapidly
+ 
+
+ align:start position:0%
+okay and and it went up very rapidly
+from close to 100 to 150 that was
+
+ align:start position:0%
+from close to 100 to 150 that was
+ 
+
+ align:start position:0%
+from close to 100 to 150 that was
+massive there were massive interventions
+
+ align:start position:0%
+massive there were massive interventions
+ 
+
+ align:start position:0%
+massive there were massive interventions
+here because it was clear that this was
+
+ align:start position:0%
+here because it was clear that this was
+ 
+
+ align:start position:0%
+here because it was clear that this was
+getting totally out of hand but but uh
+
+ align:start position:0%
+getting totally out of hand but but uh
+ 
+
+ align:start position:0%
+getting totally out of hand but but uh
+but any so that was okay and we
+
+ align:start position:0%
+but any so that was okay and we
+ 
+
+ align:start position:0%
+but any so that was okay and we
+say in this case so when a currency
+
+ align:start position:0%
+say in this case so when a currency
+ 
+
+ align:start position:0%
+say in this case so when a currency
+gains in value we call that in terms of
+
+ align:start position:0%
+gains in value we call that in terms of
+ 
+
+ align:start position:0%
+gains in value we call that in terms of
+other currencies there's no sense of a
+
+ align:start position:0%
+other currencies there's no sense of a
+ 
+
+ align:start position:0%
+other currencies there's no sense of a
+currency gaining value in terms of
+
+ align:start position:0%
+currency gaining value in terms of
+ 
+
+ align:start position:0%
+currency gaining value in terms of
+nothing it has to be in terms of other
+
+ align:start position:0%
+nothing it has to be in terms of other
+ 
+
+ align:start position:0%
+nothing it has to be in terms of other
+currency that's what an exchange itate
+
+ align:start position:0%
+currency that's what an exchange itate
+ 
+
+ align:start position:0%
+currency that's what an exchange itate
+is we say that the currency is
+
+ align:start position:0%
+is we say that the currency is
+ 
+
+ align:start position:0%
+is we say that the currency is
+appreciating okay so in this case is the
+
+ align:start position:0%
+appreciating okay so in this case is the
+ 
+
+ align:start position:0%
+appreciating okay so in this case is the
+nominal exchange rate so it's dollars
+
+ align:start position:0%
+nominal exchange rate so it's dollars
+ 
+
+ align:start position:0%
+nominal exchange rate so it's dollars
+per dollars when the
+
+ align:start position:0%
+per dollars when the
+ 
+
+ align:start position:0%
+per dollars when the
+dollar when the dollar is going up here
+
+ align:start position:0%
+dollar when the dollar is going up here
+ 
+
+ align:start position:0%
+dollar when the dollar is going up here
+we say the dollar is appreciating
+
+ align:start position:0%
+we say the dollar is appreciating
+ 
+
+ align:start position:0%
+we say the dollar is appreciating
+relative to the Japanese Yen okay that
+
+ align:start position:0%
+relative to the Japanese Yen okay that
+ 
+
+ align:start position:0%
+relative to the Japanese Yen okay that
+means the dollar is becoming more
+
+ align:start position:0%
+means the dollar is becoming more
+ 
+
+ align:start position:0%
+means the dollar is becoming more
+expensive they have to give you more
+
+ align:start position:0%
+expensive they have to give you more
+ 
+
+ align:start position:0%
+expensive they have to give you more
+yens per dollar you can look at it from
+
+ align:start position:0%
+yens per dollar you can look at it from
+ 
+
+ align:start position:0%
+yens per dollar you can look at it from
+the point of view of Japan and then the
+
+ align:start position:0%
+the point of view of Japan and then the
+ 
+
+ align:start position:0%
+the point of view of Japan and then the
+picture would look the other way around
+
+ align:start position:0%
+picture would look the other way around
+ 
+
+ align:start position:0%
+picture would look the other way around
+and it says in this same picture I know
+
+ align:start position:0%
+and it says in this same picture I know
+ 
+
+ align:start position:0%
+and it says in this same picture I know
+that the Japanese yen is
+
+ align:start position:0%
+that the Japanese yen is
+ 
+
+ align:start position:0%
+that the Japanese yen is
+depreciating relative to the US dollar
+
+ align:start position:0%
+depreciating relative to the US dollar
+ 
+
+ align:start position:0%
+depreciating relative to the US dollar
+okay so depreciation is when your
+
+ align:start position:0%
+okay so depreciation is when your
+ 
+
+ align:start position:0%
+okay so depreciation is when your
+currency loses value appreciation is
+
+ align:start position:0%
+currency loses value appreciation is
+ 
+
+ align:start position:0%
+currency loses value appreciation is
+when your currency gains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value a k i mean if I tell you unless
+
+ align:start position:0%
+value a k i mean if I tell you unless
+ 
+
+ align:start position:0%
+value a k i mean if I tell you unless
+you sort of more or less knows the
+
+ align:start position:0%
+you sort of more or less knows the
+ 
+
+ align:start position:0%
+you sort of more or less knows the
+prices in the different places if I tell
+
+ align:start position:0%
+prices in the different places if I tell
+ 
+
+ align:start position:0%
+prices in the different places if I tell
+you that that that the Japanese
+
+ align:start position:0%
+you that that that the Japanese
+ 
+
+ align:start position:0%
+you that that that the Japanese
+ER the US buys 1030
+
+ align:start position:0%
+ER the US buys 1030
+ 
+
+ align:start position:0%
+ER the US buys 1030
+Japanese Yen you can tell me and then I
+
+ align:start position:0%
+Japanese Yen you can tell me and then I
+ 
+
+ align:start position:0%
+Japanese Yen you can tell me and then I
+ask you where would you like to buy your
+
+ align:start position:0%
+ask you where would you like to buy your
+ 
+
+ align:start position:0%
+ask you where would you like to buy your
+car and assume that the car is the same
+
+ align:start position:0%
+car and assume that the car is the same
+ 
+
+ align:start position:0%
+car and assume that the car is the same
+quality no transport cost and so on and
+
+ align:start position:0%
+quality no transport cost and so on and
+ 
+
+ align:start position:0%
+quality no transport cost and so on and
+I tell you look the Japanese yen is give
+
+ align:start position:0%
+I tell you look the Japanese yen is give
+ 
+
+ align:start position:0%
+I tell you look the Japanese yen is give
+you you you for each dollar you get 120
+
+ align:start position:0%
+you you you for each dollar you get 120
+ 
+
+ align:start position:0%
+you you you for each dollar you get 120
+130 Japanese Y where do you want to buy
+
+ align:start position:0%
+130 Japanese Y where do you want to buy
+ 
+
+ align:start position:0%
+130 Japanese Y where do you want to buy
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cars that's the right answer you have no
+
+ align:start position:0%
+cars that's the right answer you have no
+ 
+
+ align:start position:0%
+cars that's the right answer you have no
+clue that doesn't tell you anything know
+
+ align:start position:0%
+clue that doesn't tell you anything know
+ 
+
+ align:start position:0%
+clue that doesn't tell you anything know
+it tells you the the the nominal
+
+ align:start position:0%
+it tells you the the the nominal
+ 
+
+ align:start position:0%
+it tells you the the the nominal
+exchanger tells you the relative value
+
+ align:start position:0%
+exchanger tells you the relative value
+ 
+
+ align:start position:0%
+exchanger tells you the relative value
+of of currencies
+
+ align:start position:0%
+of of currencies
+ 
+
+ align:start position:0%
+of of currencies
+but to make the decision of where you
+
+ align:start position:0%
+but to make the decision of where you
+ 
+
+ align:start position:0%
+but to make the decision of where you
+buy your car you need to know which car
+
+ align:start position:0%
+buy your car you need to know which car
+ 
+
+ align:start position:0%
+buy your car you need to know which car
+is more expensive and that's for that's
+
+ align:start position:0%
+is more expensive and that's for that's
+ 
+
+ align:start position:0%
+is more expensive and that's for that's
+not enough to know the the the the the
+
+ align:start position:0%
+not enough to know the the the the the
+ 
+
+ align:start position:0%
+not enough to know the the the the the
+the exchange the nominal exchange you
+
+ align:start position:0%
+the exchange the nominal exchange you
+ 
+
+ align:start position:0%
+the exchange the nominal exchange you
+need to know what is the price of the
+
+ align:start position:0%
+need to know what is the price of the
+ 
+
+ align:start position:0%
+need to know what is the price of the
+car in each place in its own currency
+
+ align:start position:0%
+car in each place in its own currency
+ 
+
+ align:start position:0%
+car in each place in its own currency
+and then I'm going to use exchange rate
+
+ align:start position:0%
+and then I'm going to use exchange rate
+ 
+
+ align:start position:0%
+and then I'm going to use exchange rate
+to translate them into some common
+
+ align:start position:0%
+to translate them into some common
+ 
+
+ align:start position:0%
+to translate them into some common
+currency suppose I tell you now that H
+
+ align:start position:0%
+currency suppose I tell you now that H
+ 
+
+ align:start position:0%
+currency suppose I tell you now that H
+the the price of of of the they do the
+
+ align:start position:0%
+the the price of of of the they do the
+ 
+
+ align:start position:0%
+the the price of of of the they do the
+opposite experiment they say look the
+
+ align:start position:0%
+opposite experiment they say look the
+ 
+
+ align:start position:0%
+opposite experiment they say look the
+price of a of a of a the same car in
+
+ align:start position:0%
+price of a of a of a the same car in
+ 
+
+ align:start position:0%
+price of a of a of a the same car in
+Japan
+
+ align:start position:0%
+Japan
+ 
+
+ align:start position:0%
+Japan
+is um
+
+ align:start position:0%
+is um
+ 
+
+ align:start position:0%
+is um
+150,000
+
+ align:start position:0%
+150,000
+ 
+
+ align:start position:0%
+150,000
+Yen well there you all have to lots of
+
+ align:start position:0%
+Yen well there you all have to lots of
+ 
+
+ align:start position:0%
+Yen well there you all have to lots of
+zeros
+
+ align:start position:0%
+zeros
+ 
+
+ align:start position:0%
+zeros
+but 150,000 Y and and in the US is500
+
+ align:start position:0%
+but 150,000 Y and and in the US is500
+ 
+
+ align:start position:0%
+but 150,000 Y and and in the US is500
+this a used car something
+
+ align:start position:0%
+this a used car something
+ 
+
+ align:start position:0%
+this a used car something
+$1,500 and and then I ask you a question
+
+ align:start position:0%
+$1,500 and and then I ask you a question
+ 
+
+ align:start position:0%
+$1,500 and and then I ask you a question
+where do you want to buy your
+
+ align:start position:0%
+where do you want to buy your
+ 
+
+ align:start position:0%
+where do you want to buy your
+car you can't answer either because you
+
+ align:start position:0%
+car you can't answer either because you
+ 
+
+ align:start position:0%
+car you can't answer either because you
+don't know how to compare unless I give
+
+ align:start position:0%
+don't know how to compare unless I give
+ 
+
+ align:start position:0%
+don't know how to compare unless I give
+you the nominal exchanges as well you
+
+ align:start position:0%
+you the nominal exchanges as well you
+ 
+
+ align:start position:0%
+you the nominal exchanges as well you
+don't know how to compare those 150,000
+
+ align:start position:0%
+don't know how to compare those 150,000
+ 
+
+ align:start position:0%
+don't know how to compare those 150,000
+yens for versus the 50 $100 so you need
+
+ align:start position:0%
+yens for versus the 50 $100 so you need
+ 
+
+ align:start position:0%
+yens for versus the 50 $100 so you need
+both and that concept that captures both
+
+ align:start position:0%
+both and that concept that captures both
+ 
+
+ align:start position:0%
+both and that concept that captures both
+is what is called the real exchange rate
+
+ align:start position:0%
+is what is called the real exchange rate
+ 
+
+ align:start position:0%
+is what is called the real exchange rate
+the real exchange is design for that to
+
+ align:start position:0%
+the real exchange is design for that to
+ 
+
+ align:start position:0%
+the real exchange is design for that to
+capture where you're going to do your
+
+ align:start position:0%
+capture where you're going to do your
+ 
+
+ align:start position:0%
+capture where you're going to do your
+imports and exports okay and it's a
+
+ align:start position:0%
+imports and exports okay and it's a
+ 
+
+ align:start position:0%
+imports and exports okay and it's a
+relative pricing of two not currencies
+
+ align:start position:0%
+relative pricing of two not currencies
+ 
+
+ align:start position:0%
+relative pricing of two not currencies
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+Goods okay so that's what the real
+
+ align:start position:0%
+Goods okay so that's what the real
+ 
+
+ align:start position:0%
+Goods okay so that's what the real
+exchange is is the price of domestic
+
+ align:start position:0%
+exchange is is the price of domestic
+ 
+
+ align:start position:0%
+exchange is is the price of domestic
+Goods relative to foreign Goods how many
+
+ align:start position:0%
+Goods relative to foreign Goods how many
+ 
+
+ align:start position:0%
+Goods relative to foreign Goods how many
+japanese cars you give me for one car us
+
+ align:start position:0%
+japanese cars you give me for one car us
+ 
+
+ align:start position:0%
+japanese cars you give me for one car us
+car that's a real exchange rate which is
+
+ align:start position:0%
+car that's a real exchange rate which is
+ 
+
+ align:start position:0%
+car that's a real exchange rate which is
+different from the nominal exchange
+
+ align:start position:0%
+different from the nominal exchange
+ 
+
+ align:start position:0%
+different from the nominal exchange
+rate now it's related to the nominal
+
+ align:start position:0%
+rate now it's related to the nominal
+ 
+
+ align:start position:0%
+rate now it's related to the nominal
+exchange rate and it happens that in
+
+ align:start position:0%
+exchange rate and it happens that in
+ 
+
+ align:start position:0%
+exchange rate and it happens that in
+practice a lot of the volatility of that
+
+ align:start position:0%
+practice a lot of the volatility of that
+ 
+
+ align:start position:0%
+practice a lot of the volatility of that
+price is as result of the volatility of
+
+ align:start position:0%
+price is as result of the volatility of
+ 
+
+ align:start position:0%
+price is as result of the volatility of
+the nominal exchange but this let me and
+
+ align:start position:0%
+the nominal exchange but this let me and
+ 
+
+ align:start position:0%
+the nominal exchange but this let me and
+this with this I will stop so let me
+
+ align:start position:0%
+this with this I will stop so let me
+ 
+
+ align:start position:0%
+this with this I will stop so let me
+call Epsilon the real exchange rate and
+
+ align:start position:0%
+call Epsilon the real exchange rate and
+ 
+
+ align:start position:0%
+call Epsilon the real exchange rate and
+let me let me see how we're going to get
+
+ align:start position:0%
+let me let me see how we're going to get
+ 
+
+ align:start position:0%
+let me let me see how we're going to get
+to that expression here so what want to
+
+ align:start position:0%
+to that expression here so what want to
+ 
+
+ align:start position:0%
+to that expression here so what want to
+compare here is the relative value of
+
+ align:start position:0%
+compare here is the relative value of
+ 
+
+ align:start position:0%
+compare here is the relative value of
+two goods because that's what will
+
+ align:start position:0%
+two goods because that's what will
+ 
+
+ align:start position:0%
+two goods because that's what will
+matter for my my consumption decision or
+
+ align:start position:0%
+matter for my my consumption decision or
+ 
+
+ align:start position:0%
+matter for my my consumption decision or
+my purchase decision
+
+ align:start position:0%
+my purchase decision
+ 
+
+ align:start position:0%
+my purchase decision
+so suppose we're talking about this car
+
+ align:start position:0%
+so suppose we're talking about this car
+ 
+
+ align:start position:0%
+so suppose we're talking about this car
+and suppose I know that the price of a
+
+ align:start position:0%
+and suppose I know that the price of a
+ 
+
+ align:start position:0%
+and suppose I know that the price of a
+of of of the car in the US is
+
+ align:start position:0%
+of of of the car in the US is
+ 
+
+ align:start position:0%
+of of of the car in the US is
+p okay and now I want to compare it with
+
+ align:start position:0%
+p okay and now I want to compare it with
+ 
+
+ align:start position:0%
+p okay and now I want to compare it with
+the with well do I buy it here or do I
+
+ align:start position:0%
+the with well do I buy it here or do I
+ 
+
+ align:start position:0%
+the with well do I buy it here or do I
+buy it in Japan for that um I'm going to
+
+ align:start position:0%
+buy it in Japan for that um I'm going to
+ 
+
+ align:start position:0%
+buy it in Japan for that um I'm going to
+have to I I'm going to have to compare
+
+ align:start position:0%
+have to I I'm going to have to compare
+ 
+
+ align:start position:0%
+have to I I'm going to have to compare
+them in the same currency so the first
+
+ align:start position:0%
+them in the same currency so the first
+ 
+
+ align:start position:0%
+them in the same currency so the first
+thing I'm going to do is I'm going to
+
+ align:start position:0%
+thing I'm going to do is I'm going to
+ 
+
+ align:start position:0%
+thing I'm going to do is I'm going to
+translate my US dollar price for to
+
+ align:start position:0%
+translate my US dollar price for to
+ 
+
+ align:start position:0%
+translate my US dollar price for to
+Japanese dollar to to Yen pricing okay
+
+ align:start position:0%
+Japanese dollar to to Yen pricing okay
+ 
+
+ align:start position:0%
+Japanese dollar to to Yen pricing okay
+so say the the the I'm going to have
+
+ align:start position:0%
+so say the the the I'm going to have
+ 
+
+ align:start position:0%
+so say the the the I'm going to have
+simpler numbers than the one there
+
+ align:start position:0%
+simpler numbers than the one there
+ 
+
+ align:start position:0%
+simpler numbers than the one there
+supposed to the car in the US cost
+
+ align:start position:0%
+supposed to the car in the US cost
+ 
+
+ align:start position:0%
+supposed to the car in the US cost
+$10,000 suppose that for each dollar you
+
+ align:start position:0%
+$10,000 suppose that for each dollar you
+ 
+
+ align:start position:0%
+$10,000 suppose that for each dollar you
+get 10 Yen then then $10,000 time 10
+
+ align:start position:0%
+get 10 Yen then then $10,000 time 10
+ 
+
+ align:start position:0%
+get 10 Yen then then $10,000 time 10
+that means it's $ 100,000 Yen so the us
+
+ align:start position:0%
+that means it's $ 100,000 Yen so the us
+ 
+
+ align:start position:0%
+that means it's $ 100,000 Yen so the us
+if I buy the car in the US I pay 100,000
+
+ align:start position:0%
+if I buy the car in the US I pay 100,000
+ 
+
+ align:start position:0%
+if I buy the car in the US I pay 100,000
+Yen and so now ah sorry this was not
+
+ align:start position:0%
+Yen and so now ah sorry this was not
+ 
+
+ align:start position:0%
+Yen and so now ah sorry this was not
+Japan in this example it's the UK well
+
+ align:start position:0%
+Japan in this example it's the UK well
+ 
+
+ align:start position:0%
+Japan in this example it's the UK well
+the same story okay and it's even
+
+ align:start position:0%
+the same story okay and it's even
+ 
+
+ align:start position:0%
+the same story okay and it's even
+simpler ER is say
+
+ align:start position:0%
+simpler ER is say
+ 
+
+ align:start position:0%
+simpler ER is say
+then then the the car in the US cost
+
+ align:start position:0%
+then then the the car in the US cost
+ 
+
+ align:start position:0%
+then then the the car in the US cost
+$10,000 and the The Exchange each dollar
+
+ align:start position:0%
+$10,000 and the The Exchange each dollar
+ 
+
+ align:start position:0%
+$10,000 and the The Exchange each dollar
+buys 80 cents of 80 cents of of pounds
+
+ align:start position:0%
+buys 80 cents of 80 cents of of pounds
+ 
+
+ align:start position:0%
+buys 80 cents of 80 cents of of pounds
+so that means 8,000 pound so the US car
+
+ align:start position:0%
+so that means 8,000 pound so the US car
+ 
+
+ align:start position:0%
+so that means 8,000 pound so the US car
+is is cost
+
+ align:start position:0%
+is is cost
+ 
+
+ align:start position:0%
+is is cost
+8,000 now I compare it with a car in the
+
+ align:start position:0%
+8,000 now I compare it with a car in the
+ 
+
+ align:start position:0%
+8,000 now I compare it with a car in the
+UK say the same car and the ratio of
+
+ align:start position:0%
+UK say the same car and the ratio of
+ 
+
+ align:start position:0%
+UK say the same car and the ratio of
+these two things is what we call the
+
+ align:start position:0%
+these two things is what we call the
+ 
+
+ align:start position:0%
+these two things is what we call the
+real exchange rate so it's the price of
+
+ align:start position:0%
+real exchange rate so it's the price of
+ 
+
+ align:start position:0%
+real exchange rate so it's the price of
+the domestic Good Times the exchange
+
+ align:start position:0%
+the domestic Good Times the exchange
+ 
+
+ align:start position:0%
+the domestic Good Times the exchange
+rate divided by the foreign price and
+
+ align:start position:0%
+rate divided by the foreign price and
+ 
+
+ align:start position:0%
+rate divided by the foreign price and
+that's a real exchange so if the if the
+
+ align:start position:0%
+that's a real exchange so if the if the
+ 
+
+ align:start position:0%
+that's a real exchange so if the if the
+if the price in the of the of the car in
+
+ align:start position:0%
+if the price in the of the of the car in
+ 
+
+ align:start position:0%
+if the price in the of the of the car in
+the UK was $9,000 and I could buy the
+
+ align:start position:0%
+the UK was $9,000 and I could buy the
+ 
+
+ align:start position:0%
+the UK was $9,000 and I could buy the
+car in the US for $8,000 I would
+
+ align:start position:0%
+car in the US for $8,000 I would
+ 
+
+ align:start position:0%
+car in the US for $8,000 I would
+probably buy it in the US in practice
+
+ align:start position:0%
+probably buy it in the US in practice
+ 
+
+ align:start position:0%
+probably buy it in the US in practice
+there are difference between the two car
+
+ align:start position:0%
+there are difference between the two car
+ 
+
+ align:start position:0%
+there are difference between the two car
+on but that tells you that's the kind of
+
+ align:start position:0%
+on but that tells you that's the kind of
+ 
+
+ align:start position:0%
+on but that tells you that's the kind of
+thing that the real exchange means is a
+
+ align:start position:0%
+thing that the real exchange means is a
+ 
+
+ align:start position:0%
+thing that the real exchange means is a
+relative price of goods okay but the way
+
+ align:start position:0%
+relative price of goods okay but the way
+ 
+
+ align:start position:0%
+relative price of goods okay but the way
+to go from that is you have to multiply
+
+ align:start position:0%
+to go from that is you have to multiply
+ 
+
+ align:start position:0%
+to go from that is you have to multiply
+the nominal exchange rate times the
+
+ align:start position:0%
+the nominal exchange rate times the
+ 
+
+ align:start position:0%
+the nominal exchange rate times the
+price because that converts it into the
+
+ align:start position:0%
+price because that converts it into the
+ 
+
+ align:start position:0%
+price because that converts it into the
+same currency as the price and then you
+
+ align:start position:0%
+same currency as the price and then you
+ 
+
+ align:start position:0%
+same currency as the price and then you
+can compare them that's
+
+ align:start position:0%
+can compare them that's
+ 
+
+ align:start position:0%
+can compare them that's
+idea so let let's stop here and we're
+
+ align:start position:0%
+idea so let let's stop here and we're
+ 
+
+ align:start position:0%
+idea so let let's stop here and we're
+going to continue talking about open
+
+ align:start position:0%
+going to continue talking about open
+ 
+
+ align:start position:0%
+going to continue talking about open
+economy next week so next on Wednesday
+
+ align:start position:0%
+economy next week so next on Wednesday
+ 
+
+ align:start position:0%
+economy next week so next on Wednesday
+what I'm going to do is a review of of H
+
+ align:start position:0%
+what I'm going to do is a review of of H
+ 
+
+ align:start position:0%
+what I'm going to do is a review of of H
+ISL MPC and and and growth
\ No newline at end of file
diff --git a/68XZ_P9MKM8.txt b/68XZ_P9MKM8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..037d31a086732f09e5b0d20cafe2fb6f4798f163
--- /dev/null
+++ b/68XZ_P9MKM8.txt
@@ -0,0 +1,13819 @@
+align:start position:0%
+ 
+To participate in this next exercise,
+
+ align:start position:0%
+To participate in this next exercise,
+ 
+
+ align:start position:0%
+To participate in this next exercise,
+you'll have to grab um one of these uh
+
+ align:start position:0%
+you'll have to grab um one of these uh
+ 
+
+ align:start position:0%
+you'll have to grab um one of these uh
+uh index cards that are on the table
+
+ align:start position:0%
+uh index cards that are on the table
+ 
+
+ align:start position:0%
+uh index cards that are on the table
+that correspond to a particular
+
+ align:start position:0%
+that correspond to a particular
+ 
+
+ align:start position:0%
+that correspond to a particular
+technology. It looks like film, radio,
+
+ align:start position:0%
+technology. It looks like film, radio,
+ 
+
+ align:start position:0%
+technology. It looks like film, radio,
+and television are amongst the remaining
+
+ align:start position:0%
+and television are amongst the remaining
+ 
+
+ align:start position:0%
+and television are amongst the remaining
+ones. Um and you'll get in small groups
+
+ align:start position:0%
+ones. Um and you'll get in small groups
+ 
+
+ align:start position:0%
+ones. Um and you'll get in small groups
+um and uh work on those. Here's what I'd
+
+ align:start position:0%
+um and uh work on those. Here's what I'd
+ 
+
+ align:start position:0%
+um and uh work on those. Here's what I'd
+like you to do. Find the other people
+
+ align:start position:0%
+like you to do. Find the other people
+ 
+
+ align:start position:0%
+like you to do. Find the other people
+who have the same card as you. Um, uh,
+
+ align:start position:0%
+who have the same card as you. Um, uh,
+ 
+
+ align:start position:0%
+who have the same card as you. Um, uh,
+discuss what you learned from the
+
+ align:start position:0%
+discuss what you learned from the
+ 
+
+ align:start position:0%
+discuss what you learned from the
+readings, anything that sort of stands
+
+ align:start position:0%
+readings, anything that sort of stands
+ 
+
+ align:start position:0%
+readings, anything that sort of stands
+out to you, comes to your mind. But then
+
+ align:start position:0%
+out to you, comes to your mind. But then
+ 
+
+ align:start position:0%
+out to you, comes to your mind. But then
+I want you to make a chart, which you
+
+ align:start position:0%
+I want you to make a chart, which you
+ 
+
+ align:start position:0%
+I want you to make a chart, which you
+can do on the whiteboard or on our um,
+
+ align:start position:0%
+can do on the whiteboard or on our um,
+ 
+
+ align:start position:0%
+can do on the whiteboard or on our um,
+blue pieces of paper there. Um, that uh,
+
+ align:start position:0%
+blue pieces of paper there. Um, that uh,
+ 
+
+ align:start position:0%
+blue pieces of paper there. Um, that uh,
+that capture sort of three key ideas.
+
+ align:start position:0%
+that capture sort of three key ideas.
+ 
+
+ align:start position:0%
+that capture sort of three key ideas.
+First of all, who are all of the
+
+ align:start position:0%
+First of all, who are all of the
+ 
+
+ align:start position:0%
+First of all, who are all of the
+stakeholders who are involved in the
+
+ align:start position:0%
+stakeholders who are involved in the
+ 
+
+ align:start position:0%
+stakeholders who are involved in the
+implementation of this technology? One
+
+ align:start position:0%
+implementation of this technology? One
+ 
+
+ align:start position:0%
+implementation of this technology? One
+of the things that I think Larry Cubin
+
+ align:start position:0%
+of the things that I think Larry Cubin
+ 
+
+ align:start position:0%
+of the things that I think Larry Cubin
+is particularly wonderful at um is
+
+ align:start position:0%
+is particularly wonderful at um is
+ 
+
+ align:start position:0%
+is particularly wonderful at um is
+giving you a sense of all of the
+
+ align:start position:0%
+giving you a sense of all of the
+ 
+
+ align:start position:0%
+giving you a sense of all of the
+different hands that touch a technology
+
+ align:start position:0%
+different hands that touch a technology
+ 
+
+ align:start position:0%
+different hands that touch a technology
+making its way into a school and all the
+
+ align:start position:0%
+making its way into a school and all the
+ 
+
+ align:start position:0%
+making its way into a school and all the
+different hands that touch a technology
+
+ align:start position:0%
+different hands that touch a technology
+ 
+
+ align:start position:0%
+different hands that touch a technology
+when it's in the school. This is
+
+ align:start position:0%
+when it's in the school. This is
+ 
+
+ align:start position:0%
+when it's in the school. This is
+incredibly important for understanding
+
+ align:start position:0%
+incredibly important for understanding
+ 
+
+ align:start position:0%
+incredibly important for understanding
+how technologies actually get used um in
+
+ align:start position:0%
+how technologies actually get used um in
+ 
+
+ align:start position:0%
+how technologies actually get used um in
+in sort of a lot of times in like
+
+ align:start position:0%
+in sort of a lot of times in like
+ 
+
+ align:start position:0%
+in sort of a lot of times in like
+canonical design. And I think this comes
+
+ align:start position:0%
+canonical design. And I think this comes
+ 
+
+ align:start position:0%
+canonical design. And I think this comes
+up in sort of software engineering
+
+ align:start position:0%
+up in sort of software engineering
+ 
+
+ align:start position:0%
+up in sort of software engineering
+classes and things like this idea that
+
+ align:start position:0%
+classes and things like this idea that
+ 
+
+ align:start position:0%
+classes and things like this idea that
+like there's a programmer and a user and
+
+ align:start position:0%
+like there's a programmer and a user and
+ 
+
+ align:start position:0%
+like there's a programmer and a user and
+the user is like one person who's
+
+ align:start position:0%
+the user is like one person who's
+ 
+
+ align:start position:0%
+the user is like one person who's
+sitting at a keyboard with their fingers
+
+ align:start position:0%
+sitting at a keyboard with their fingers
+ 
+
+ align:start position:0%
+sitting at a keyboard with their fingers
+on the keyboard and like that's the
+
+ align:start position:0%
+on the keyboard and like that's the
+ 
+
+ align:start position:0%
+on the keyboard and like that's the
+person you need to pay attention to. And
+
+ align:start position:0%
+person you need to pay attention to. And
+ 
+
+ align:start position:0%
+person you need to pay attention to. And
+that like two-part model of like
+
+ align:start position:0%
+that like two-part model of like
+ 
+
+ align:start position:0%
+that like two-part model of like
+designer and user totally breaks down in
+
+ align:start position:0%
+designer and user totally breaks down in
+ 
+
+ align:start position:0%
+designer and user totally breaks down in
+schools. Um there are lots of people who
+
+ align:start position:0%
+schools. Um there are lots of people who
+ 
+
+ align:start position:0%
+schools. Um there are lots of people who
+are very different who could be
+
+ align:start position:0%
+are very different who could be
+ 
+
+ align:start position:0%
+are very different who could be
+considered users of technology in
+
+ align:start position:0%
+considered users of technology in
+ 
+
+ align:start position:0%
+considered users of technology in
+schools. Um, another thing that's that
+
+ align:start position:0%
+schools. Um, another thing that's that
+ 
+
+ align:start position:0%
+schools. Um, another thing that's that
+Larry Cubin does really well is he he he
+
+ align:start position:0%
+Larry Cubin does really well is he he he
+ 
+
+ align:start position:0%
+Larry Cubin does really well is he he he
+helps us pay attention to how these
+
+ align:start position:0%
+helps us pay attention to how these
+ 
+
+ align:start position:0%
+helps us pay attention to how these
+people have what I'll call different
+
+ align:start position:0%
+people have what I'll call different
+ 
+
+ align:start position:0%
+people have what I'll call different
+interests. By interests, I don't mean
+
+ align:start position:0%
+interests. By interests, I don't mean
+ 
+
+ align:start position:0%
+interests. By interests, I don't mean
+curiosities. I mean like incentives,
+
+ align:start position:0%
+curiosities. I mean like incentives,
+ 
+
+ align:start position:0%
+curiosities. I mean like incentives,
+stakes, sort of how a political
+
+ align:start position:0%
+stakes, sort of how a political
+ 
+
+ align:start position:0%
+stakes, sort of how a political
+scientist might use the word interest.
+
+ align:start position:0%
+scientist might use the word interest.
+ 
+
+ align:start position:0%
+scientist might use the word interest.
+Um, all of these different stakeholders
+
+ align:start position:0%
+Um, all of these different stakeholders
+ 
+
+ align:start position:0%
+Um, all of these different stakeholders
+are rewarded for different kinds of
+
+ align:start position:0%
+are rewarded for different kinds of
+ 
+
+ align:start position:0%
+are rewarded for different kinds of
+things. Um, they also have what we'll
+
+ align:start position:0%
+things. Um, they also have what we'll
+ 
+
+ align:start position:0%
+things. Um, they also have what we'll
+call disinterests or disincentives. they
+
+ align:start position:0%
+call disinterests or disincentives. they
+ 
+
+ align:start position:0%
+call disinterests or disincentives. they
+are also trying to avoid or will be
+
+ align:start position:0%
+are also trying to avoid or will be
+ 
+
+ align:start position:0%
+are also trying to avoid or will be
+punished for different kinds of things.
+
+ align:start position:0%
+punished for different kinds of things.
+ 
+
+ align:start position:0%
+punished for different kinds of things.
+Um so for the technology that you that
+
+ align:start position:0%
+Um so for the technology that you that
+ 
+
+ align:start position:0%
+Um so for the technology that you that
+you picked a card of and are talking
+
+ align:start position:0%
+you picked a card of and are talking
+ 
+
+ align:start position:0%
+you picked a card of and are talking
+with your colleagues about think of all
+
+ align:start position:0%
+with your colleagues about think of all
+ 
+
+ align:start position:0%
+with your colleagues about think of all
+of the different people who you think
+
+ align:start position:0%
+of the different people who you think
+ 
+
+ align:start position:0%
+of the different people who you think
+could be considered stakeholders in the
+
+ align:start position:0%
+could be considered stakeholders in the
+ 
+
+ align:start position:0%
+could be considered stakeholders in the
+implementation of this thing. What and
+
+ align:start position:0%
+implementation of this thing. What and
+ 
+
+ align:start position:0%
+implementation of this thing. What and
+then for each of those stakeholders come
+
+ align:start position:0%
+then for each of those stakeholders come
+ 
+
+ align:start position:0%
+then for each of those stakeholders come
+up with like a couple of their interests
+
+ align:start position:0%
+up with like a couple of their interests
+ 
+
+ align:start position:0%
+up with like a couple of their interests
+and a couple of their disinterests or
+
+ align:start position:0%
+and a couple of their disinterests or
+ 
+
+ align:start position:0%
+and a couple of their disinterests or
+disincentives or things that punish them
+
+ align:start position:0%
+disincentives or things that punish them
+ 
+
+ align:start position:0%
+disincentives or things that punish them
+or those kinds of things. Does that as a
+
+ align:start position:0%
+or those kinds of things. Does that as a
+ 
+
+ align:start position:0%
+or those kinds of things. Does that as a
+general exercise make sense? Um, and the
+
+ align:start position:0%
+general exercise make sense? Um, and the
+ 
+
+ align:start position:0%
+general exercise make sense? Um, and the
+thing that we're trying to do together
+
+ align:start position:0%
+thing that we're trying to do together
+ 
+
+ align:start position:0%
+thing that we're trying to do together
+is around we want to we want to try to
+
+ align:start position:0%
+is around we want to we want to try to
+ 
+
+ align:start position:0%
+is around we want to we want to try to
+recreate the world around these
+
+ align:start position:0%
+recreate the world around these
+ 
+
+ align:start position:0%
+recreate the world around these
+technologies. That's what I think Larry
+
+ align:start position:0%
+technologies. That's what I think Larry
+ 
+
+ align:start position:0%
+technologies. That's what I think Larry
+Cuban is so fabulous at, um, is saying
+
+ align:start position:0%
+Cuban is so fabulous at, um, is saying
+ 
+
+ align:start position:0%
+Cuban is so fabulous at, um, is saying
+like, yep, a television set is going to
+
+ align:start position:0%
+like, yep, a television set is going to
+ 
+
+ align:start position:0%
+like, yep, a television set is going to
+roll into a but it's going to roll into
+
+ align:start position:0%
+roll into a but it's going to roll into
+ 
+
+ align:start position:0%
+roll into a but it's going to roll into
+a classroom and into a school and into a
+
+ align:start position:0%
+a classroom and into a school and into a
+ 
+
+ align:start position:0%
+a classroom and into a school and into a
+community and there's all these people
+
+ align:start position:0%
+community and there's all these people
+ 
+
+ align:start position:0%
+community and there's all these people
+who are part of that. Um, that's what we
+
+ align:start position:0%
+who are part of that. Um, that's what we
+ 
+
+ align:start position:0%
+who are part of that. Um, that's what we
+really need to get out here. I'll tell
+
+ align:start position:0%
+really need to get out here. I'll tell
+ 
+
+ align:start position:0%
+really need to get out here. I'll tell
+the last thing I'll tell you before I
+
+ align:start position:0%
+the last thing I'll tell you before I
+ 
+
+ align:start position:0%
+the last thing I'll tell you before I
+cut you loose um, is Larry Cuban has a
+
+ align:start position:0%
+cut you loose um, is Larry Cuban has a
+ 
+
+ align:start position:0%
+cut you loose um, is Larry Cuban has a
+totally fascinating history himself. He
+
+ align:start position:0%
+totally fascinating history himself. He
+ 
+
+ align:start position:0%
+totally fascinating history himself. He
+was a social studies teacher in the 50s
+
+ align:start position:0%
+was a social studies teacher in the 50s
+ 
+
+ align:start position:0%
+was a social studies teacher in the 50s
+and 60s. Then he was a school principal.
+
+ align:start position:0%
+and 60s. Then he was a school principal.
+ 
+
+ align:start position:0%
+and 60s. Then he was a school principal.
+Then he was a superintendent. He was
+
+ align:start position:0%
+Then he was a superintendent. He was
+ 
+
+ align:start position:0%
+Then he was a superintendent. He was
+actually the superintendent in
+
+ align:start position:0%
+actually the superintendent in
+ 
+
+ align:start position:0%
+actually the superintendent in
+Arlington, Virginia. Um which is where
+
+ align:start position:0%
+Arlington, Virginia. Um which is where
+ 
+
+ align:start position:0%
+Arlington, Virginia. Um which is where
+my wife went to school. So when my wife
+
+ align:start position:0%
+my wife went to school. So when my wife
+ 
+
+ align:start position:0%
+my wife went to school. So when my wife
+was an elementary school student, um uh
+
+ align:start position:0%
+was an elementary school student, um uh
+ 
+
+ align:start position:0%
+was an elementary school student, um uh
+her her superintendent at the time was
+
+ align:start position:0%
+her her superintendent at the time was
+ 
+
+ align:start position:0%
+her her superintendent at the time was
+Larry Cuban. Um and are Arlington,
+
+ align:start position:0%
+Larry Cuban. Um and are Arlington,
+ 
+
+ align:start position:0%
+Larry Cuban. Um and are Arlington,
+Virginia. Fairfax. Close enough. Yeah.
+
+ align:start position:0%
+Virginia. Fairfax. Close enough. Yeah.
+ 
+
+ align:start position:0%
+Virginia. Fairfax. Close enough. Yeah.
+Yeah. Um and it was only after he had
+
+ align:start position:0%
+Yeah. Um and it was only after he had
+ 
+
+ align:start position:0%
+Yeah. Um and it was only after he had
+like a pretty distinguished career as a
+
+ align:start position:0%
+like a pretty distinguished career as a
+ 
+
+ align:start position:0%
+like a pretty distinguished career as a
+teacher, a principal, a superintendent
+
+ align:start position:0%
+teacher, a principal, a superintendent
+ 
+
+ align:start position:0%
+teacher, a principal, a superintendent
+that he went to Stanford. Um got his
+
+ align:start position:0%
+that he went to Stanford. Um got his
+ 
+
+ align:start position:0%
+that he went to Stanford. Um got his
+dissertation. um became a historian of
+
+ align:start position:0%
+dissertation. um became a historian of
+ 
+
+ align:start position:0%
+dissertation. um became a historian of
+education and then eventually a a
+
+ align:start position:0%
+education and then eventually a a
+ 
+
+ align:start position:0%
+education and then eventually a a
+history of education professor out
+
+ align:start position:0%
+history of education professor out
+ 
+
+ align:start position:0%
+history of education professor out
+there. Um so he's someone who's like
+
+ align:start position:0%
+there. Um so he's someone who's like
+ 
+
+ align:start position:0%
+there. Um so he's someone who's like
+extremely well read as I'm sure you got
+
+ align:start position:0%
+extremely well read as I'm sure you got
+ 
+
+ align:start position:0%
+extremely well read as I'm sure you got
+a sense of and things like that, but he
+
+ align:start position:0%
+a sense of and things like that, but he
+ 
+
+ align:start position:0%
+a sense of and things like that, but he
+also just deeply understands the kinds
+
+ align:start position:0%
+also just deeply understands the kinds
+ 
+
+ align:start position:0%
+also just deeply understands the kinds
+of things that make schools tick and
+
+ align:start position:0%
+of things that make schools tick and
+ 
+
+ align:start position:0%
+of things that make schools tick and
+make the people inside schools tick.
+
+ align:start position:0%
+make the people inside schools tick.
+ 
+
+ align:start position:0%
+make the people inside schools tick.
+Does this exercise make sense? Find the
+
+ align:start position:0%
+Does this exercise make sense? Find the
+ 
+
+ align:start position:0%
+Does this exercise make sense? Find the
+people with your cards. Move yourselves
+
+ align:start position:0%
+people with your cards. Move yourselves
+ 
+
+ align:start position:0%
+people with your cards. Move yourselves
+around. Make this little chart either on
+
+ align:start position:0%
+around. Make this little chart either on
+ 
+
+ align:start position:0%
+around. Make this little chart either on
+the board or on these blue pieces of
+
+ align:start position:0%
+the board or on these blue pieces of
+ 
+
+ align:start position:0%
+the board or on these blue pieces of
+paper. Ready? Go.
+
+ align:start position:0%
+paper. Ready? Go.
+ 
+
+ align:start position:0%
+paper. Ready? Go.
+That's a little bit th those things are
+
+ align:start position:0%
+That's a little bit th those things are
+ 
+
+ align:start position:0%
+That's a little bit th those things are
+those things are hugely important you
+
+ align:start position:0%
+those things are hugely important you
+ 
+
+ align:start position:0%
+those things are hugely important you
+know like like what like where does
+
+ align:start position:0%
+know like like what like where does
+ 
+
+ align:start position:0%
+know like like what like where does
+teaching actually happen like there's
+
+ align:start position:0%
+teaching actually happen like there's
+ 
+
+ align:start position:0%
+teaching actually happen like there's
+some human being you know who like needs
+
+ align:start position:0%
+some human being you know who like needs
+ 
+
+ align:start position:0%
+some human being you know who like needs
+to go to the bathroom and needs to eat
+
+ align:start position:0%
+to go to the bathroom and needs to eat
+ 
+
+ align:start position:0%
+to go to the bathroom and needs to eat
+and I mean he has that great quote in
+
+ align:start position:0%
+and I mean he has that great quote in
+ 
+
+ align:start position:0%
+and I mean he has that great quote in
+there it's not about film but television
+
+ align:start position:0%
+there it's not about film but television
+ 
+
+ align:start position:0%
+there it's not about film but television
+that they found that they're more likely
+
+ align:start position:0%
+that they found that they're more likely
+ 
+
+ align:start position:0%
+that they found that they're more likely
+to use television in the afternoon than
+
+ align:start position:0%
+to use television in the afternoon than
+ 
+
+ align:start position:0%
+to use television in the afternoon than
+in the mornings. Um and it and it all
+
+ align:start position:0%
+in the mornings. Um and it and it all
+ 
+
+ align:start position:0%
+in the mornings. Um and it and it all
+it's all like biology and culture like
+
+ align:start position:0%
+it's all like biology and culture like
+ 
+
+ align:start position:0%
+it's all like biology and culture like
+our brains work better in the morning.
+
+ align:start position:0%
+our brains work better in the morning.
+ 
+
+ align:start position:0%
+our brains work better in the morning.
+We're all a little flagging by the
+
+ align:start position:0%
+We're all a little flagging by the
+ 
+
+ align:start position:0%
+We're all a little flagging by the
+afternoon. Those kinds of things. Um,
+
+ align:start position:0%
+afternoon. Those kinds of things. Um,
+ 
+
+ align:start position:0%
+afternoon. Those kinds of things. Um,
+and so yeah, I think that like anybody
+
+ align:start position:0%
+and so yeah, I think that like anybody
+ 
+
+ align:start position:0%
+and so yeah, I think that like anybody
+who's building a technology has to think
+
+ align:start position:0%
+who's building a technology has to think
+ 
+
+ align:start position:0%
+who's building a technology has to think
+to themselves like, you know, what are
+
+ align:start position:0%
+to themselves like, you know, what are
+ 
+
+ align:start position:0%
+to themselves like, you know, what are
+you? Yeah. Yeah. What like what are the
+
+ align:start position:0%
+you? Yeah. Yeah. What like what are the
+ 
+
+ align:start position:0%
+you? Yeah. Yeah. What like what are the
+variations in a teacher's day? Like when
+
+ align:start position:0%
+variations in a teacher's day? Like when
+ 
+
+ align:start position:0%
+variations in a teacher's day? Like when
+do they have more energy or less energy?
+
+ align:start position:0%
+do they have more energy or less energy?
+ 
+
+ align:start position:0%
+do they have more energy or less energy?
+How does it fit into those kinds of
+
+ align:start position:0%
+How does it fit into those kinds of
+ 
+
+ align:start position:0%
+How does it fit into those kinds of
+cycles and things like that? Like those
+
+ align:start position:0%
+cycles and things like that? Like those
+ 
+
+ align:start position:0%
+cycles and things like that? Like those
+are every bit as real as you know the
+
+ align:start position:0%
+are every bit as real as you know the
+ 
+
+ align:start position:0%
+are every bit as real as you know the
+test score goals that we have or
+
+ align:start position:0%
+test score goals that we have or
+ 
+
+ align:start position:0%
+test score goals that we have or
+anything else.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is really good. This is really
+
+ align:start position:0%
+This is really good. This is really
+ 
+
+ align:start position:0%
+This is really good. This is really
+good. Take a few more minutes. Take a
+
+ align:start position:0%
+good. Take a few more minutes. Take a
+ 
+
+ align:start position:0%
+good. Take a few more minutes. Take a
+few more minutes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We're trying to think about interest for
+
+ align:start position:0%
+We're trying to think about interest for
+ 
+
+ align:start position:0%
+We're trying to think about interest for
+schools for producers. Sure. So, if
+
+ align:start position:0%
+schools for producers. Sure. So, if
+ 
+
+ align:start position:0%
+schools for producers. Sure. So, if
+you're a school, so if you're a school,
+
+ align:start position:0%
+you're a school, so if you're a school,
+ 
+
+ align:start position:0%
+you're a school, so if you're a school,
+what would make you go, h I'm not sure I
+
+ align:start position:0%
+what would make you go, h I'm not sure I
+ 
+
+ align:start position:0%
+what would make you go, h I'm not sure I
+want to do anything with films. It's so
+
+ align:start position:0%
+want to do anything with films. It's so
+ 
+
+ align:start position:0%
+want to do anything with films. It's so
+it's 1913. Um, silent films, you know,
+
+ align:start position:0%
+it's 1913. Um, silent films, you know,
+ 
+
+ align:start position:0%
+it's 1913. Um, silent films, you know,
+started coming out in earnest around the
+
+ align:start position:0%
+started coming out in earnest around the
+ 
+
+ align:start position:0%
+started coming out in earnest around the
+turn of the century. There's a handful
+
+ align:start position:0%
+turn of the century. There's a handful
+ 
+
+ align:start position:0%
+turn of the century. There's a handful
+of people um one, you know, the most
+
+ align:start position:0%
+of people um one, you know, the most
+ 
+
+ align:start position:0%
+of people um one, you know, the most
+prominent of them is Thomas Edison. You
+
+ align:start position:0%
+prominent of them is Thomas Edison. You
+ 
+
+ align:start position:0%
+prominent of them is Thomas Edison. You
+know, a guy invents a light bulb. Um and
+
+ align:start position:0%
+know, a guy invents a light bulb. Um and
+ 
+
+ align:start position:0%
+know, a guy invents a light bulb. Um and
+he gets in front of Congress and he
+
+ align:start position:0%
+he gets in front of Congress and he
+ 
+
+ align:start position:0%
+he gets in front of Congress and he
+says, you know, he's first in 1913, he
+
+ align:start position:0%
+says, you know, he's first in 1913, he
+ 
+
+ align:start position:0%
+says, you know, he's first in 1913, he
+says, I mean, I'll read the other quote,
+
+ align:start position:0%
+says, I mean, I'll read the other quote,
+ 
+
+ align:start position:0%
+says, I mean, I'll read the other quote,
+but he says, um, in a decade, textbooks
+
+ align:start position:0%
+but he says, um, in a decade, textbooks
+ 
+
+ align:start position:0%
+but he says, um, in a decade, textbooks
+will be replaced by film strips. That's
+
+ align:start position:0%
+will be replaced by film strips. That's
+ 
+
+ align:start position:0%
+will be replaced by film strips. That's
+how powerful this new technology is
+
+ align:start position:0%
+how powerful this new technology is
+ 
+
+ align:start position:0%
+how powerful this new technology is
+going to be. Um, if you're a school
+
+ align:start position:0%
+going to be. Um, if you're a school
+ 
+
+ align:start position:0%
+going to be. Um, if you're a school
+principal, what would be some things
+
+ align:start position:0%
+principal, what would be some things
+ 
+
+ align:start position:0%
+principal, what would be some things
+that make you go, you're pretty smart,
+
+ align:start position:0%
+that make you go, you're pretty smart,
+ 
+
+ align:start position:0%
+that make you go, you're pretty smart,
+Thomas, but I'm not so sure about this
+
+ align:start position:0%
+Thomas, but I'm not so sure about this
+ 
+
+ align:start position:0%
+Thomas, but I'm not so sure about this
+one?
+
+ align:start position:0%
+one?
+ 
+
+ align:start position:0%
+one?
+Maybe if they just put a bunch of money
+
+ align:start position:0%
+Maybe if they just put a bunch of money
+ 
+
+ align:start position:0%
+Maybe if they just put a bunch of money
+into textbooks. Sure. So yeah, they have
+
+ align:start position:0%
+into textbooks. Sure. So yeah, they have
+ 
+
+ align:start position:0%
+into textbooks. Sure. So yeah, they have
+an entire infrastructure built around
+
+ align:start position:0%
+an entire infrastructure built around
+ 
+
+ align:start position:0%
+an entire infrastructure built around
+the existing technologies. They h they
+
+ align:start position:0%
+the existing technologies. They h they
+ 
+
+ align:start position:0%
+the existing technologies. They h they
+have shelves on the wall. They have
+
+ align:start position:0%
+have shelves on the wall. They have
+ 
+
+ align:start position:0%
+have shelves on the wall. They have
+libraries full of books. Every one of
+
+ align:start position:0%
+libraries full of books. Every one of
+ 
+
+ align:start position:0%
+libraries full of books. Every one of
+their teachers has been trained to teach
+
+ align:start position:0%
+their teachers has been trained to teach
+ 
+
+ align:start position:0%
+their teachers has been trained to teach
+with textbooks. And not a single one of
+
+ align:start position:0%
+with textbooks. And not a single one of
+ 
+
+ align:start position:0%
+with textbooks. And not a single one of
+their teachers in you know when these
+
+ align:start position:0%
+their teachers in you know when these
+ 
+
+ align:start position:0%
+their teachers in you know when these
+things are first introduced has ever
+
+ align:start position:0%
+things are first introduced has ever
+ 
+
+ align:start position:0%
+things are first introduced has ever
+been in a class as a student learning
+
+ align:start position:0%
+been in a class as a student learning
+ 
+
+ align:start position:0%
+been in a class as a student learning
+from a film. So you have this huge
+
+ align:start position:0%
+from a film. So you have this huge
+ 
+
+ align:start position:0%
+from a film. So you have this huge
+inherent conservatism in the system. So
+
+ align:start position:0%
+inherent conservatism in the system. So
+ 
+
+ align:start position:0%
+inherent conservatism in the system. So
+that could be one. What would be what
+
+ align:start position:0%
+that could be one. What would be what
+ 
+
+ align:start position:0%
+that could be one. What would be what
+would be some others?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean, yeah. I mean, I I guess it's
+
+ align:start position:0%
+I mean, yeah. I mean, I I guess it's
+ 
+
+ align:start position:0%
+I mean, yeah. I mean, I I guess it's
+kind of adding on to that, but like
+
+ align:start position:0%
+kind of adding on to that, but like
+ 
+
+ align:start position:0%
+kind of adding on to that, but like
+integrating it into like a classroom
+
+ align:start position:0%
+integrating it into like a classroom
+ 
+
+ align:start position:0%
+integrating it into like a classroom
+setting, like how how would they even
+
+ align:start position:0%
+setting, like how how would they even
+ 
+
+ align:start position:0%
+setting, like how how would they even
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+uh integrate into like even even if
+
+ align:start position:0%
+uh integrate into like even even if
+ 
+
+ align:start position:0%
+uh integrate into like even even if
+they're like completely on board like
+
+ align:start position:0%
+they're like completely on board like
+ 
+
+ align:start position:0%
+they're like completely on board like
+like what how would they even integrate
+
+ align:start position:0%
+like what how would they even integrate
+ 
+
+ align:start position:0%
+like what how would they even integrate
+it into a classroom? What for films?
+
+ align:start position:0%
+it into a classroom? What for films?
+ 
+
+ align:start position:0%
+it into a classroom? What for films?
+What would be what would be some of the
+
+ align:start position:0%
+What would be what would be some of the
+ 
+
+ align:start position:0%
+What would be what would be some of the
+challenges of integration?
+
+ align:start position:0%
+challenges of integration?
+ 
+
+ align:start position:0%
+challenges of integration?
+Um like
+
+ align:start position:0%
+Um like
+ 
+
+ align:start position:0%
+Um like
+the technology that you would need to
+
+ align:start position:0%
+the technology that you would need to
+ 
+
+ align:start position:0%
+the technology that you would need to
+like uh put into a classroom or like to
+
+ align:start position:0%
+like uh put into a classroom or like to
+ 
+
+ align:start position:0%
+like uh put into a classroom or like to
+a school. Say tell me specifically for
+
+ align:start position:0%
+a school. Say tell me specifically for
+ 
+
+ align:start position:0%
+a school. Say tell me specifically for
+films what some of that technology might
+
+ align:start position:0%
+films what some of that technology might
+ 
+
+ align:start position:0%
+films what some of that technology might
+be. Um I mean like isn't I I don't think
+
+ align:start position:0%
+be. Um I mean like isn't I I don't think
+ 
+
+ align:start position:0%
+be. Um I mean like isn't I I don't think
+like the the projectors in like back
+
+ align:start position:0%
+like the the projectors in like back
+ 
+
+ align:start position:0%
+like the the projectors in like back
+then could like fit into like a
+
+ align:start position:0%
+then could like fit into like a
+ 
+
+ align:start position:0%
+then could like fit into like a
+classroom. Oh, they so they could I mean
+
+ align:start position:0%
+classroom. Oh, they so they could I mean
+ 
+
+ align:start position:0%
+classroom. Oh, they so they could I mean
+you know like they're they're portable
+
+ align:start position:0%
+you know like they're they're portable
+ 
+
+ align:start position:0%
+you know like they're they're portable
+enough but they're big. They're these
+
+ align:start position:0%
+enough but they're big. They're these
+ 
+
+ align:start position:0%
+enough but they're big. They're these
+like big lumbering machines for which
+
+ align:start position:0%
+like big lumbering machines for which
+ 
+
+ align:start position:0%
+like big lumbering machines for which
+the rooms are like if you have if you
+
+ align:start position:0%
+the rooms are like if you have if you
+ 
+
+ align:start position:0%
+the rooms are like if you have if you
+have a classroom like let's say you have
+
+ align:start position:0%
+have a classroom like let's say you have
+ 
+
+ align:start position:0%
+have a classroom like let's say you have
+a big population growth and so you're
+
+ align:start position:0%
+a big population growth and so you're
+ 
+
+ align:start position:0%
+a big population growth and so you're
+you're you built you you know someone in
+
+ align:start position:0%
+you're you built you you know someone in
+ 
+
+ align:start position:0%
+you're you built you you know someone in
+the 1850s built a school and it was 12
+
+ align:start position:0%
+the 1850s built a school and it was 12
+ 
+
+ align:start position:0%
+the 1850s built a school and it was 12
+kids per classroom and now you're
+
+ align:start position:0%
+kids per classroom and now you're
+ 
+
+ align:start position:0%
+kids per classroom and now you're
+putting 18 kids per classroom in there.
+
+ align:start position:0%
+putting 18 kids per classroom in there.
+ 
+
+ align:start position:0%
+putting 18 kids per classroom in there.
+Like a totally legitimate reason would
+
+ align:start position:0%
+Like a totally legitimate reason would
+ 
+
+ align:start position:0%
+Like a totally legitimate reason would
+be there is not space in this room to
+
+ align:start position:0%
+be there is not space in this room to
+ 
+
+ align:start position:0%
+be there is not space in this room to
+physically move this machine. Like what
+
+ align:start position:0%
+physically move this machine. Like what
+ 
+
+ align:start position:0%
+physically move this machine. Like what
+are some other sort of what else do you
+
+ align:start position:0%
+are some other sort of what else do you
+ 
+
+ align:start position:0%
+are some other sort of what else do you
+need for films as a technology to be
+
+ align:start position:0%
+need for films as a technology to be
+ 
+
+ align:start position:0%
+need for films as a technology to be
+able to be implemented? Do you need a
+
+ align:start position:0%
+able to be implemented? Do you need a
+ 
+
+ align:start position:0%
+able to be implemented? Do you need a
+giant projector? You're going to put
+
+ align:start position:0%
+giant projector? You're going to put
+ 
+
+ align:start position:0%
+giant projector? You're going to put
+thing on wheels. What else do you need?
+
+ align:start position:0%
+thing on wheels. What else do you need?
+ 
+
+ align:start position:0%
+thing on wheels. What else do you need?
+A place to actually project it onto.
+
+ align:start position:0%
+A place to actually project it onto.
+ 
+
+ align:start position:0%
+A place to actually project it onto.
+Okay, good. You're going to have to go
+
+ align:start position:0%
+Okay, good. You're going to have to go
+ 
+
+ align:start position:0%
+Okay, good. You're going to have to go
+to all your classrooms and you're going
+
+ align:start position:0%
+to all your classrooms and you're going
+ 
+
+ align:start position:0%
+to all your classrooms and you're going
+to have to install screens at the front
+
+ align:start position:0%
+to have to install screens at the front
+ 
+
+ align:start position:0%
+to have to install screens at the front
+of the room. Like not the hugest
+
+ align:start position:0%
+of the room. Like not the hugest
+ 
+
+ align:start position:0%
+of the room. Like not the hugest
+challenge, but also not free, you know,
+
+ align:start position:0%
+challenge, but also not free, you know,
+ 
+
+ align:start position:0%
+challenge, but also not free, you know,
+not like like so who's going to do these
+
+ align:start position:0%
+not like like so who's going to do these
+ 
+
+ align:start position:0%
+not like like so who's going to do these
+things? Um, you know, the uh the films
+
+ align:start position:0%
+things? Um, you know, the uh the films
+ 
+
+ align:start position:0%
+things? Um, you know, the uh the films
+also came on these like huge reels. Um,
+
+ align:start position:0%
+also came on these like huge reels. Um,
+ 
+
+ align:start position:0%
+also came on these like huge reels. Um,
+you know, it wasn't just like, you know,
+
+ align:start position:0%
+you know, it wasn't just like, you know,
+ 
+
+ align:start position:0%
+you know, it wasn't just like, you know,
+pick your YouTube channel and play like
+
+ align:start position:0%
+pick your YouTube channel and play like
+ 
+
+ align:start position:0%
+pick your YouTube channel and play like
+where in your building are you going to
+
+ align:start position:0%
+where in your building are you going to
+ 
+
+ align:start position:0%
+where in your building are you going to
+keep a library of film reels? Who's
+
+ align:start position:0%
+keep a library of film reels? Who's
+ 
+
+ align:start position:0%
+keep a library of film reels? Who's
+going to organize those libraries of
+
+ align:start position:0%
+going to organize those libraries of
+ 
+
+ align:start position:0%
+going to organize those libraries of
+film reels? Like um you know if you have
+
+ align:start position:0%
+film reels? Like um you know if you have
+ 
+
+ align:start position:0%
+film reels? Like um you know if you have
+four elementary schools in an or four
+
+ align:start position:0%
+four elementary schools in an or four
+ 
+
+ align:start position:0%
+four elementary schools in an or four
+elementary classroom like let's say have
+
+ align:start position:0%
+elementary classroom like let's say have
+ 
+
+ align:start position:0%
+elementary classroom like let's say have
+four first grades, are you going to buy
+
+ align:start position:0%
+four first grades, are you going to buy
+ 
+
+ align:start position:0%
+four first grades, are you going to buy
+four copies of this film so that
+
+ align:start position:0%
+four copies of this film so that
+ 
+
+ align:start position:0%
+four copies of this film so that
+everyone can watch it at the same time?
+
+ align:start position:0%
+everyone can watch it at the same time?
+ 
+
+ align:start position:0%
+everyone can watch it at the same time?
+If not, how are you going to like
+
+ align:start position:0%
+If not, how are you going to like
+ 
+
+ align:start position:0%
+If not, how are you going to like
+physically organize and move like this
+
+ align:start position:0%
+physically organize and move like this
+ 
+
+ align:start position:0%
+physically organize and move like this
+giant reel from one space to another?
+
+ align:start position:0%
+giant reel from one space to another?
+ 
+
+ align:start position:0%
+giant reel from one space to another?
+Those are all those are all you know you
+
+ align:start position:0%
+Those are all those are all you know you
+ 
+
+ align:start position:0%
+Those are all those are all you know you
+could imagine the principal being like
+
+ align:start position:0%
+could imagine the principal being like
+ 
+
+ align:start position:0%
+could imagine the principal being like
+but how are we but how are we but how
+
+ align:start position:0%
+but how are we but how are we but how
+ 
+
+ align:start position:0%
+but how are we but how are we but how
+are we but how are we and all this stuff
+
+ align:start position:0%
+are we but how are we and all this stuff
+ 
+
+ align:start position:0%
+are we but how are we and all this stuff
+costs money. Um, so those are all kinds
+
+ align:start position:0%
+costs money. Um, so those are all kinds
+ 
+
+ align:start position:0%
+costs money. Um, so those are all kinds
+of, you know, like like, you know,
+
+ align:start position:0%
+of, you know, like like, you know,
+ 
+
+ align:start position:0%
+of, you know, like like, you know,
+Thomas Edison is here telling you that
+
+ align:start position:0%
+Thomas Edison is here telling you that
+ 
+
+ align:start position:0%
+Thomas Edison is here telling you that
+you're going to get 100% efficient
+
+ align:start position:0%
+you're going to get 100% efficient
+ 
+
+ align:start position:0%
+you're going to get 100% efficient
+learning through this thing, which is
+
+ align:start position:0%
+learning through this thing, which is
+ 
+
+ align:start position:0%
+learning through this thing, which is
+the potential gains, which you no one
+
+ align:start position:0%
+the potential gains, which you no one
+ 
+
+ align:start position:0%
+the potential gains, which you no one
+has any evidence for because it hasn't
+
+ align:start position:0%
+has any evidence for because it hasn't
+ 
+
+ align:start position:0%
+has any evidence for because it hasn't
+happened yet. But you've got to think to
+
+ align:start position:0%
+happened yet. But you've got to think to
+ 
+
+ align:start position:0%
+happened yet. But you've got to think to
+yourself like like what are all these
+
+ align:start position:0%
+yourself like like what are all these
+ 
+
+ align:start position:0%
+yourself like like what are all these
+costs? What are all these material
+
+ align:start position:0%
+costs? What are all these material
+ 
+
+ align:start position:0%
+costs? What are all these material
+changes? Yeah. So think about how you
+
+ align:start position:0%
+changes? Yeah. So think about how you
+ 
+
+ align:start position:0%
+changes? Yeah. So think about how you
+can articulate some of those things. But
+
+ align:start position:0%
+can articulate some of those things. But
+ 
+
+ align:start position:0%
+can articulate some of those things. But
+good like when you really get like, you
+
+ align:start position:0%
+good like when you really get like, you
+ 
+
+ align:start position:0%
+good like when you really get like, you
+know, for to to do this exercise, well,
+
+ align:start position:0%
+know, for to to do this exercise, well,
+ 
+
+ align:start position:0%
+know, for to to do this exercise, well,
+you have to like what exactly is this
+
+ align:start position:0%
+you have to like what exactly is this
+ 
+
+ align:start position:0%
+you have to like what exactly is this
+technology? Like like even physically,
+
+ align:start position:0%
+technology? Like like even physically,
+ 
+
+ align:start position:0%
+technology? Like like even physically,
+what does it require? How many of these
+
+ align:start position:0%
+what does it require? How many of these
+ 
+
+ align:start position:0%
+what does it require? How many of these
+things do you need to buy? How much do
+
+ align:start position:0%
+things do you need to buy? How much do
+ 
+
+ align:start position:0%
+things do you need to buy? How much do
+they cost? All that kind of stuff. How
+
+ align:start position:0%
+they cost? All that kind of stuff. How
+ 
+
+ align:start position:0%
+they cost? All that kind of stuff. How
+reusable are they? Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. This is really good. Why don't we
+
+ align:start position:0%
+okay. This is really good. Why don't we
+ 
+
+ align:start position:0%
+okay. This is really good. Why don't we
+take a break here? Um, go ahead and you
+
+ align:start position:0%
+take a break here? Um, go ahead and you
+ 
+
+ align:start position:0%
+take a break here? Um, go ahead and you
+can sit back down to the seats that you
+
+ align:start position:0%
+can sit back down to the seats that you
+ 
+
+ align:start position:0%
+can sit back down to the seats that you
+were at. Um, I think everyone's written
+
+ align:start position:0%
+were at. Um, I think everyone's written
+ 
+
+ align:start position:0%
+were at. Um, I think everyone's written
+kind of broadly enough um that we'll be
+
+ align:start position:0%
+kind of broadly enough um that we'll be
+ 
+
+ align:start position:0%
+kind of broadly enough um that we'll be
+able to see from a
+
+ align:start position:0%
+able to see from a
+ 
+
+ align:start position:0%
+able to see from a
+distance. But yeah, really good. Really
+
+ align:start position:0%
+distance. But yeah, really good. Really
+ 
+
+ align:start position:0%
+distance. But yeah, really good. Really
+good. Now I need to find a little spot
+
+ align:start position:0%
+good. Now I need to find a little spot
+ 
+
+ align:start position:0%
+good. Now I need to find a little spot
+for me to um
+
+ align:start position:0%
+for me to um
+ 
+
+ align:start position:0%
+for me to um
+everyone's last minute notes. Every
+
+ align:start position:0%
+everyone's last minute notes. Every
+ 
+
+ align:start position:0%
+everyone's last minute notes. Every
+Yeah. Yeah. Now is your chance to put
+
+ align:start position:0%
+Yeah. Yeah. Now is your chance to put
+ 
+
+ align:start position:0%
+Yeah. Yeah. Now is your chance to put
+the final the final few things up there.
+
+ align:start position:0%
+the final the final few things up there.
+ 
+
+ align:start position:0%
+the final the final few things up there.
+Um good. So every What was the minimum
+
+ align:start position:0%
+Um good. So every What was the minimum
+ 
+
+ align:start position:0%
+Um good. So every What was the minimum
+number of stakeholders people came up
+
+ align:start position:0%
+number of stakeholders people came up
+ 
+
+ align:start position:0%
+number of stakeholders people came up
+with? Um these guys are the winners with
+
+ align:start position:0%
+with? Um these guys are the winners with
+ 
+
+ align:start position:0%
+with? Um these guys are the winners with
+the longest list. Let's just read it out
+
+ align:start position:0%
+the longest list. Let's just read it out
+ 
+
+ align:start position:0%
+the longest list. Let's just read it out
+loud. Co. Oh no. The state admin,
+
+ align:start position:0%
+loud. Co. Oh no. The state admin,
+ 
+
+ align:start position:0%
+loud. Co. Oh no. The state admin,
+parents, teachers, students,
+
+ align:start position:0%
+parents, teachers, students,
+ 
+
+ align:start position:0%
+parents, teachers, students,
+corporations, manufacturers, edtech
+
+ align:start position:0%
+corporations, manufacturers, edtech
+ 
+
+ align:start position:0%
+corporations, manufacturers, edtech
+investors, developers, policy makers.
+
+ align:start position:0%
+investors, developers, policy makers.
+ 
+
+ align:start position:0%
+investors, developers, policy makers.
+Great. So, just as a starting point, I
+
+ align:start position:0%
+Great. So, just as a starting point, I
+ 
+
+ align:start position:0%
+Great. So, just as a starting point, I
+mean, there are some other ones that
+
+ align:start position:0%
+mean, there are some other ones that
+ 
+
+ align:start position:0%
+mean, there are some other ones that
+showed up around here, studios,
+
+ align:start position:0%
+showed up around here, studios,
+ 
+
+ align:start position:0%
+showed up around here, studios,
+broadcasters, the FCC, um, that sort of
+
+ align:start position:0%
+broadcasters, the FCC, um, that sort of
+ 
+
+ align:start position:0%
+broadcasters, the FCC, um, that sort of
+different psychologists. Yeah, there are
+
+ align:start position:0%
+different psychologists. Yeah, there are
+ 
+
+ align:start position:0%
+different psychologists. Yeah, there are
+a lot of people who have something at
+
+ align:start position:0%
+a lot of people who have something at
+ 
+
+ align:start position:0%
+a lot of people who have something at
+stake in these decisions. They're
+
+ align:start position:0%
+stake in these decisions. They're
+ 
+
+ align:start position:0%
+stake in these decisions. They're
+complex, multihuman kinds of decisions.
+
+ align:start position:0%
+complex, multihuman kinds of decisions.
+ 
+
+ align:start position:0%
+complex, multihuman kinds of decisions.
+So, that's a good start. Um, let me just
+
+ align:start position:0%
+So, that's a good start. Um, let me just
+ 
+
+ align:start position:0%
+So, that's a good start. Um, let me just
+read. Um, so given how complex these
+
+ align:start position:0%
+read. Um, so given how complex these
+ 
+
+ align:start position:0%
+read. Um, so given how complex these
+things are, why are folks so
+
+ align:start position:0%
+things are, why are folks so
+ 
+
+ align:start position:0%
+things are, why are folks so
+enthusiastic about it? Let's ask Thomas
+
+ align:start position:0%
+enthusiastic about it? Let's ask Thomas
+ 
+
+ align:start position:0%
+enthusiastic about it? Let's ask Thomas
+Edison. Um, what does Thomas Edison
+
+ align:start position:0%
+Edison. Um, what does Thomas Edison
+ 
+
+ align:start position:0%
+Edison. Um, what does Thomas Edison
+think about this? I believe that the
+
+ align:start position:0%
+think about this? I believe that the
+ 
+
+ align:start position:0%
+think about this? I believe that the
+motion picture is destined to
+
+ align:start position:0%
+motion picture is destined to
+ 
+
+ align:start position:0%
+motion picture is destined to
+revolutionize our educational system and
+
+ align:start position:0%
+revolutionize our educational system and
+ 
+
+ align:start position:0%
+revolutionize our educational system and
+that in a few years it will supplant
+
+ align:start position:0%
+that in a few years it will supplant
+ 
+
+ align:start position:0%
+that in a few years it will supplant
+largely if not entirely the use of
+
+ align:start position:0%
+largely if not entirely the use of
+ 
+
+ align:start position:0%
+largely if not entirely the use of
+textbooks. I should say that on the
+
+ align:start position:0%
+textbooks. I should say that on the
+ 
+
+ align:start position:0%
+textbooks. I should say that on the
+average we get about 2% efficiency out
+
+ align:start position:0%
+average we get about 2% efficiency out
+ 
+
+ align:start position:0%
+average we get about 2% efficiency out
+of school books as they are written
+
+ align:start position:0%
+of school books as they are written
+ 
+
+ align:start position:0%
+of school books as they are written
+today. You're laughing. Why are you
+
+ align:start position:0%
+today. You're laughing. Why are you
+ 
+
+ align:start position:0%
+today. You're laughing. Why are you
+laughing? Thomas Edison is just here
+
+ align:start position:0%
+laughing? Thomas Edison is just here
+ 
+
+ align:start position:0%
+laughing? Thomas Edison is just here
+making up. He doesn't 2% that
+
+ align:start position:0%
+making up. He doesn't 2% that
+ 
+
+ align:start position:0%
+making up. He doesn't 2% that
+doesn't mean a thing. He was good at
+
+ align:start position:0%
+doesn't mean a thing. He was good at
+ 
+
+ align:start position:0%
+doesn't mean a thing. He was good at
+light bulbs. He wasn't maybe as good at
+
+ align:start position:0%
+light bulbs. He wasn't maybe as good at
+ 
+
+ align:start position:0%
+light bulbs. He wasn't maybe as good at
+this. Um, the education of the future as
+
+ align:start position:0%
+this. Um, the education of the future as
+ 
+
+ align:start position:0%
+this. Um, the education of the future as
+I see it will be conducted through the
+
+ align:start position:0%
+I see it will be conducted through the
+ 
+
+ align:start position:0%
+I see it will be conducted through the
+medium of the motion picture where it
+
+ align:start position:0%
+medium of the motion picture where it
+ 
+
+ align:start position:0%
+medium of the motion picture where it
+should be possible to obtain 100%
+
+ align:start position:0%
+should be possible to obtain 100%
+ 
+
+ align:start position:0%
+should be possible to obtain 100%
+efficiency. Thomas Edison 1922. Um,
+
+ align:start position:0%
+efficiency. Thomas Edison 1922. Um,
+ 
+
+ align:start position:0%
+efficiency. Thomas Edison 1922. Um,
+you'll read a couple of other quotes
+
+ align:start position:0%
+you'll read a couple of other quotes
+ 
+
+ align:start position:0%
+you'll read a couple of other quotes
+that I have from Thomas Edison. One of
+
+ align:start position:0%
+that I have from Thomas Edison. One of
+ 
+
+ align:start position:0%
+that I have from Thomas Edison. One of
+them is in here in in failure to disrupt
+
+ align:start position:0%
+them is in here in in failure to disrupt
+ 
+
+ align:start position:0%
+them is in here in in failure to disrupt
+when you read that. But in 1913, he went
+
+ align:start position:0%
+when you read that. But in 1913, he went
+ 
+
+ align:start position:0%
+when you read that. But in 1913, he went
+in front of Congress and said in 10
+
+ align:start position:0%
+in front of Congress and said in 10
+ 
+
+ align:start position:0%
+in front of Congress and said in 10
+years the textbook will entire will be
+
+ align:start position:0%
+years the textbook will entire will be
+ 
+
+ align:start position:0%
+years the textbook will entire will be
+entirely replaced by um film strips. And
+
+ align:start position:0%
+entirely replaced by um film strips. And
+ 
+
+ align:start position:0%
+entirely replaced by um film strips. And
+then he went back 10 years later in 1923
+
+ align:start position:0%
+then he went back 10 years later in 1923
+ 
+
+ align:start position:0%
+then he went back 10 years later in 1923
+and he said in 20 years textbooks will
+
+ align:start position:0%
+and he said in 20 years textbooks will
+ 
+
+ align:start position:0%
+and he said in 20 years textbooks will
+be entirely replaced by film strips. Um
+
+ align:start position:0%
+be entirely replaced by film strips. Um
+ 
+
+ align:start position:0%
+be entirely replaced by film strips. Um
+I think you can find many similar kinds
+
+ align:start position:0%
+I think you can find many similar kinds
+ 
+
+ align:start position:0%
+I think you can find many similar kinds
+of arguments that are made today. Um I
+
+ align:start position:0%
+of arguments that are made today. Um I
+ 
+
+ align:start position:0%
+of arguments that are made today. Um I
+think you will not have a hard time um
+
+ align:start position:0%
+think you will not have a hard time um
+ 
+
+ align:start position:0%
+think you will not have a hard time um
+finding people who tell you that the
+
+ align:start position:0%
+finding people who tell you that the
+ 
+
+ align:start position:0%
+finding people who tell you that the
+oldfashioned techniques are only 2%
+
+ align:start position:0%
+oldfashioned techniques are only 2%
+ 
+
+ align:start position:0%
+oldfashioned techniques are only 2%
+efficient but the new ones will be 100%
+
+ align:start position:0%
+efficient but the new ones will be 100%
+ 
+
+ align:start position:0%
+efficient but the new ones will be 100%
+efficient. Um so that's the promise. the
+
+ align:start position:0%
+efficient. Um so that's the promise. the
+ 
+
+ align:start position:0%
+efficient. Um so that's the promise. the
+promise is that we could do
+
+ align:start position:0%
+promise is that we could do
+ 
+
+ align:start position:0%
+promise is that we could do
+substantially better than we're doing
+
+ align:start position:0%
+substantially better than we're doing
+ 
+
+ align:start position:0%
+substantially better than we're doing
+right now if we if we think about
+
+ align:start position:0%
+right now if we if we think about
+ 
+
+ align:start position:0%
+right now if we if we think about
+implementing all of these uh different
+
+ align:start position:0%
+implementing all of these uh different
+ 
+
+ align:start position:0%
+implementing all of these uh different
+kinds of technologies. Um so an
+
+ align:start position:0%
+kinds of technologies. Um so an
+ 
+
+ align:start position:0%
+kinds of technologies. Um so an
+intuition that you can develop um is
+
+ align:start position:0%
+intuition that you can develop um is
+ 
+
+ align:start position:0%
+intuition that you can develop um is
+that this is this is a century old
+
+ align:start position:0%
+that this is this is a century old
+ 
+
+ align:start position:0%
+that this is this is a century old
+enterprise. Um for the last 100 110
+
+ align:start position:0%
+enterprise. Um for the last 100 110
+ 
+
+ align:start position:0%
+enterprise. Um for the last 100 110
+years people have thought how can we
+
+ align:start position:0%
+years people have thought how can we
+ 
+
+ align:start position:0%
+years people have thought how can we
+take analog technologies and eventually
+
+ align:start position:0%
+take analog technologies and eventually
+ 
+
+ align:start position:0%
+take analog technologies and eventually
+digital technologies bring them into
+
+ align:start position:0%
+digital technologies bring them into
+ 
+
+ align:start position:0%
+digital technologies bring them into
+schools to improve learning. Um there
+
+ align:start position:0%
+schools to improve learning. Um there
+ 
+
+ align:start position:0%
+schools to improve learning. Um there
+are millions of people who work on
+
+ align:start position:0%
+are millions of people who work on
+ 
+
+ align:start position:0%
+are millions of people who work on
+education. Many of them are very very
+
+ align:start position:0%
+education. Many of them are very very
+ 
+
+ align:start position:0%
+education. Many of them are very very
+smart. Um from the earliest, you know,
+
+ align:start position:0%
+smart. Um from the earliest, you know,
+ 
+
+ align:start position:0%
+smart. Um from the earliest, you know,
+you read a little bit about um uh
+
+ align:start position:0%
+you read a little bit about um uh
+ 
+
+ align:start position:0%
+you read a little bit about um uh
+personal computers kind of from the 70s
+
+ align:start position:0%
+personal computers kind of from the 70s
+ 
+
+ align:start position:0%
+personal computers kind of from the 70s
+and 80s, the Apple 2 plus kind of the
+
+ align:start position:0%
+and 80s, the Apple 2 plus kind of the
+ 
+
+ align:start position:0%
+and 80s, the Apple 2 plus kind of the
+generation of computers that I grew up
+
+ align:start position:0%
+generation of computers that I grew up
+ 
+
+ align:start position:0%
+generation of computers that I grew up
+with, but that's actually like 20 years
+
+ align:start position:0%
+with, but that's actually like 20 years
+ 
+
+ align:start position:0%
+with, but that's actually like 20 years
+into the game. Um from the moment people
+
+ align:start position:0%
+into the game. Um from the moment people
+ 
+
+ align:start position:0%
+into the game. Um from the moment people
+built computers the size of this room,
+
+ align:start position:0%
+built computers the size of this room,
+ 
+
+ align:start position:0%
+built computers the size of this room,
+um computer scientists, educators,
+
+ align:start position:0%
+um computer scientists, educators,
+ 
+
+ align:start position:0%
+um computer scientists, educators,
+learning scientists partnered together
+
+ align:start position:0%
+learning scientists partnered together
+ 
+
+ align:start position:0%
+learning scientists partnered together
+to try to figure out if there's some way
+
+ align:start position:0%
+to try to figure out if there's some way
+ 
+
+ align:start position:0%
+to try to figure out if there's some way
+to use computers to teach people. So, so
+
+ align:start position:0%
+to use computers to teach people. So, so
+ 
+
+ align:start position:0%
+to use computers to teach people. So, so
+just compute, you know, not even all
+
+ align:start position:0%
+just compute, you know, not even all
+ 
+
+ align:start position:0%
+just compute, you know, not even all
+these other radio, film, other things.
+
+ align:start position:0%
+these other radio, film, other things.
+ 
+
+ align:start position:0%
+these other radio, film, other things.
+Computing alone is like a 70-year
+
+ align:start position:0%
+Computing alone is like a 70-year
+ 
+
+ align:start position:0%
+Computing alone is like a 70-year
+enterprise of trying to improve schools.
+
+ align:start position:0%
+enterprise of trying to improve schools.
+ 
+
+ align:start position:0%
+enterprise of trying to improve schools.
+There are lots of things that we've
+
+ align:start position:0%
+There are lots of things that we've
+ 
+
+ align:start position:0%
+There are lots of things that we've
+tried and learned in 70 years. So, one
+
+ align:start position:0%
+tried and learned in 70 years. So, one
+ 
+
+ align:start position:0%
+tried and learned in 70 years. So, one
+intuition that I hope you will take away
+
+ align:start position:0%
+intuition that I hope you will take away
+ 
+
+ align:start position:0%
+intuition that I hope you will take away
+from this class is that when you're
+
+ align:start position:0%
+from this class is that when you're
+ 
+
+ align:start position:0%
+from this class is that when you're
+thinking about an education technology
+
+ align:start position:0%
+thinking about an education technology
+ 
+
+ align:start position:0%
+thinking about an education technology
+problem of any form or type, about a
+
+ align:start position:0%
+problem of any form or type, about a
+ 
+
+ align:start position:0%
+problem of any form or type, about a
+design problem, an implementation
+
+ align:start position:0%
+design problem, an implementation
+ 
+
+ align:start position:0%
+design problem, an implementation
+problem, a policy problem, you should
+
+ align:start position:0%
+problem, a policy problem, you should
+ 
+
+ align:start position:0%
+problem, a policy problem, you should
+think to yourself, we probably have done
+
+ align:start position:0%
+think to yourself, we probably have done
+ 
+
+ align:start position:0%
+think to yourself, we probably have done
+something like this before. Um there is
+
+ align:start position:0%
+something like this before. Um there is
+ 
+
+ align:start position:0%
+something like this before. Um there is
+nothing that is so new, so utterly
+
+ align:start position:0%
+nothing that is so new, so utterly
+ 
+
+ align:start position:0%
+nothing that is so new, so utterly
+different that there aren't like cognate
+
+ align:start position:0%
+different that there aren't like cognate
+ 
+
+ align:start position:0%
+different that there aren't like cognate
+examples that could help us think
+
+ align:start position:0%
+examples that could help us think
+ 
+
+ align:start position:0%
+examples that could help us think
+through whatever these challenges are.
+
+ align:start position:0%
+through whatever these challenges are.
+ 
+
+ align:start position:0%
+through whatever these challenges are.
+Um let's think about a couple of these
+
+ align:start position:0%
+Um let's think about a couple of these
+ 
+
+ align:start position:0%
+Um let's think about a couple of these
+stakeholders. Which stakeholders seem to
+
+ align:start position:0%
+stakeholders. Which stakeholders seem to
+ 
+
+ align:start position:0%
+stakeholders. Which stakeholders seem to
+appear pretty much in all of them?
+
+ align:start position:0%
+appear pretty much in all of them?
+ 
+
+ align:start position:0%
+appear pretty much in all of them?
+What's who's who seem to be sort of
+
+ align:start position:0%
+What's who's who seem to be sort of
+ 
+
+ align:start position:0%
+What's who's who seem to be sort of
+universal stakeholders?
+
+ align:start position:0%
+universal stakeholders?
+ 
+
+ align:start position:0%
+universal stakeholders?
+Teachers. Teachers. Let's start with
+
+ align:start position:0%
+Teachers. Teachers. Let's start with
+ 
+
+ align:start position:0%
+Teachers. Teachers. Let's start with
+them because they're the best. Um I I
+
+ align:start position:0%
+them because they're the best. Um I I
+ 
+
+ align:start position:0%
+them because they're the best. Um I I
+love teachers. I would I mean definitely
+
+ align:start position:0%
+love teachers. I would I mean definitely
+ 
+
+ align:start position:0%
+love teachers. I would I mean definitely
+one of the reasons why I do what I do is
+
+ align:start position:0%
+one of the reasons why I do what I do is
+ 
+
+ align:start position:0%
+one of the reasons why I do what I do is
+I just think teachers are great.
+
+ align:start position:0%
+I just think teachers are great.
+ 
+
+ align:start position:0%
+I just think teachers are great.
+Um what what kinds of things get
+
+ align:start position:0%
+Um what what kinds of things get
+ 
+
+ align:start position:0%
+Um what what kinds of things get
+teachers excited? What what what if if
+
+ align:start position:0%
+teachers excited? What what what if if
+ 
+
+ align:start position:0%
+teachers excited? What what what if if
+you're if you're if you want to get a
+
+ align:start position:0%
+you're if you're if you want to get a
+ 
+
+ align:start position:0%
+you're if you're if you want to get a
+teacher using education technology, what
+
+ align:start position:0%
+teacher using education technology, what
+ 
+
+ align:start position:0%
+teacher using education technology, what
+are the what are the felt needs that
+
+ align:start position:0%
+are the what are the felt needs that
+ 
+
+ align:start position:0%
+are the what are the felt needs that
+they have that are going to be really
+
+ align:start position:0%
+they have that are going to be really
+ 
+
+ align:start position:0%
+they have that are going to be really
+important to them? This is one that I
+
+ align:start position:0%
+important to them? This is one that I
+ 
+
+ align:start position:0%
+important to them? This is one that I
+think will be pretty consistent across a
+
+ align:start position:0%
+think will be pretty consistent across a
+ 
+
+ align:start position:0%
+think will be pretty consistent across a
+bunch of these, but we can see if there
+
+ align:start position:0%
+bunch of these, but we can see if there
+ 
+
+ align:start position:0%
+bunch of these, but we can see if there
+are differences, too. Reducing their
+
+ align:start position:0%
+are differences, too. Reducing their
+ 
+
+ align:start position:0%
+are differences, too. Reducing their
+workload. Okay, good. I love it.
+
+ align:start position:0%
+workload. Okay, good. I love it.
+ 
+
+ align:start position:0%
+workload. Okay, good. I love it.
+reducing
+
+ align:start position:0%
+reducing
+ 
+
+ align:start position:0%
+reducing
+workload. Why is that so important to
+
+ align:start position:0%
+workload. Why is that so important to
+ 
+
+ align:start position:0%
+workload. Why is that so important to
+teachers?
+
+ align:start position:0%
+teachers?
+ 
+
+ align:start position:0%
+teachers?
+It's because they have so much they have
+
+ align:start position:0%
+It's because they have so much they have
+ 
+
+ align:start position:0%
+It's because they have so much they have
+so much to do. These are not people who
+
+ align:start position:0%
+so much to do. These are not people who
+ 
+
+ align:start position:0%
+so much to do. These are not people who
+spend a bunch of time like sitting
+
+ align:start position:0%
+spend a bunch of time like sitting
+ 
+
+ align:start position:0%
+spend a bunch of time like sitting
+around waiting for the phone to ring or
+
+ align:start position:0%
+around waiting for the phone to ring or
+ 
+
+ align:start position:0%
+around waiting for the phone to ring or
+something like that. Um teacher workload
+
+ align:start position:0%
+something like that. Um teacher workload
+ 
+
+ align:start position:0%
+something like that. Um teacher workload
+in the United States is actually in
+
+ align:start position:0%
+in the United States is actually in
+ 
+
+ align:start position:0%
+in the United States is actually in
+certain ways like much higher than other
+
+ align:start position:0%
+certain ways like much higher than other
+ 
+
+ align:start position:0%
+certain ways like much higher than other
+comparable OECD countries. So O is the
+
+ align:start position:0%
+comparable OECD countries. So O is the
+ 
+
+ align:start position:0%
+comparable OECD countries. So O is the
+organization of economic cooperative
+
+ align:start position:0%
+organization of economic cooperative
+ 
+
+ align:start position:0%
+organization of economic cooperative
+development something like that. It's
+
+ align:start position:0%
+development something like that. It's
+ 
+
+ align:start position:0%
+development something like that. It's
+like rich countries 30 or 40 rich
+
+ align:start position:0%
+like rich countries 30 or 40 rich
+ 
+
+ align:start position:0%
+like rich countries 30 or 40 rich
+countries. Um, American teachers
+
+ align:start position:0%
+countries. Um, American teachers
+ 
+
+ align:start position:0%
+countries. Um, American teachers
+compared to our colleagues in other
+
+ align:start position:0%
+compared to our colleagues in other
+ 
+
+ align:start position:0%
+compared to our colleagues in other
+countries spend more time in front of
+
+ align:start position:0%
+countries spend more time in front of
+ 
+
+ align:start position:0%
+countries spend more time in front of
+students actually directly teaching than
+
+ align:start position:0%
+students actually directly teaching than
+ 
+
+ align:start position:0%
+students actually directly teaching than
+in many other places. Um, so many other
+
+ align:start position:0%
+in many other places. Um, so many other
+ 
+
+ align:start position:0%
+in many other places. Um, so many other
+countries in the world like a full-time
+
+ align:start position:0%
+countries in the world like a full-time
+ 
+
+ align:start position:0%
+countries in the world like a full-time
+licensed teacher would have more
+
+ align:start position:0%
+licensed teacher would have more
+ 
+
+ align:start position:0%
+licensed teacher would have more
+collaborative planning time, more
+
+ align:start position:0%
+collaborative planning time, more
+ 
+
+ align:start position:0%
+collaborative planning time, more
+grading time, other kinds of things like
+
+ align:start position:0%
+grading time, other kinds of things like
+ 
+
+ align:start position:0%
+grading time, other kinds of things like
+that. So, US teachers compared to their
+
+ align:start position:0%
+that. So, US teachers compared to their
+ 
+
+ align:start position:0%
+that. So, US teachers compared to their
+colleagues around the world are like
+
+ align:start position:0%
+colleagues around the world are like
+ 
+
+ align:start position:0%
+colleagues around the world are like
+behind the ball on having time anyway.
+
+ align:start position:0%
+behind the ball on having time anyway.
+ 
+
+ align:start position:0%
+behind the ball on having time anyway.
+Um, reducing workload is something they
+
+ align:start position:0%
+Um, reducing workload is something they
+ 
+
+ align:start position:0%
+Um, reducing workload is something they
+care about. What else do they care
+
+ align:start position:0%
+care about. What else do they care
+ 
+
+ align:start position:0%
+care about. What else do they care
+about? Like it has to spark the students
+
+ align:start position:0%
+about? Like it has to spark the students
+ 
+
+ align:start position:0%
+about? Like it has to spark the students
+interest. Good. So, they don't want kids
+
+ align:start position:0%
+interest. Good. So, they don't want kids
+ 
+
+ align:start position:0%
+interest. Good. So, they don't want kids
+to be bored.
+
+ align:start position:0%
+to be bored.
+ 
+
+ align:start position:0%
+to be bored.
+um that one of their one of their core
+
+ align:start position:0%
+um that one of their one of their core
+ 
+
+ align:start position:0%
+um that one of their one of their core
+interests is how am I going to keep
+
+ align:start position:0%
+interests is how am I going to keep
+ 
+
+ align:start position:0%
+interests is how am I going to keep
+these folks motivated? How am I going to
+
+ align:start position:0%
+these folks motivated? How am I going to
+ 
+
+ align:start position:0%
+these folks motivated? How am I going to
+keep them learning? What else do they
+
+ align:start position:0%
+keep them learning? What else do they
+ 
+
+ align:start position:0%
+keep them learning? What else do they
+care about? They care about it being of
+
+ align:start position:0%
+care about? They care about it being of
+ 
+
+ align:start position:0%
+care about? They care about it being of
+actually good quality. Okay, good. So,
+
+ align:start position:0%
+actually good quality. Okay, good. So,
+ 
+
+ align:start position:0%
+actually good quality. Okay, good. So,
+like it's really important that learning
+
+ align:start position:0%
+like it's really important that learning
+ 
+
+ align:start position:0%
+like it's really important that learning
+goes up, that quality is high, um that
+
+ align:start position:0%
+goes up, that quality is high, um that
+ 
+
+ align:start position:0%
+goes up, that quality is high, um that
+that you know that that uh teachers take
+
+ align:start position:0%
+that you know that that uh teachers take
+ 
+
+ align:start position:0%
+that you know that that uh teachers take
+their professionalism very very
+
+ align:start position:0%
+their professionalism very very
+ 
+
+ align:start position:0%
+their professionalism very very
+seriously and that you know and and
+
+ align:start position:0%
+seriously and that you know and and
+ 
+
+ align:start position:0%
+seriously and that you know and and
+they're held accountable in various
+
+ align:start position:0%
+they're held accountable in various
+ 
+
+ align:start position:0%
+they're held accountable in various
+kinds of ways. Um, and this could be
+
+ align:start position:0%
+kinds of ways. Um, and this could be
+ 
+
+ align:start position:0%
+kinds of ways. Um, and this could be
+different across different kinds of
+
+ align:start position:0%
+different across different kinds of
+ 
+
+ align:start position:0%
+different across different kinds of
+teachers. Um, so in the United States,
+
+ align:start position:0%
+teachers. Um, so in the United States,
+ 
+
+ align:start position:0%
+teachers. Um, so in the United States,
+we primaril we we we test in in certain
+
+ align:start position:0%
+we primaril we we we test in in certain
+ 
+
+ align:start position:0%
+we primaril we we we test in in certain
+kinds of ways. We test like way more
+
+ align:start position:0%
+kinds of ways. We test like way more
+ 
+
+ align:start position:0%
+kinds of ways. We test like way more
+than every other country does. There's
+
+ align:start position:0%
+than every other country does. There's
+ 
+
+ align:start position:0%
+than every other country does. There's
+no country that tests all of their
+
+ align:start position:0%
+no country that tests all of their
+ 
+
+ align:start position:0%
+no country that tests all of their
+students every year, third to eighth
+
+ align:start position:0%
+students every year, third to eighth
+ 
+
+ align:start position:0%
+students every year, third to eighth
+grade, in both reading and math. Most
+
+ align:start position:0%
+grade, in both reading and math. Most
+ 
+
+ align:start position:0%
+grade, in both reading and math. Most
+other countries are like if you test
+
+ align:start position:0%
+other countries are like if you test
+ 
+
+ align:start position:0%
+other countries are like if you test
+them in the third grade, you probably
+
+ align:start position:0%
+them in the third grade, you probably
+ 
+
+ align:start position:0%
+them in the third grade, you probably
+wait a couple years to like, you know, I
+
+ align:start position:0%
+wait a couple years to like, you know, I
+ 
+
+ align:start position:0%
+wait a couple years to like, you know, I
+mean, you give them like but you give
+
+ align:start position:0%
+mean, you give them like but you give
+ 
+
+ align:start position:0%
+mean, you give them like but you give
+them assessments or exams or whatever,
+
+ align:start position:0%
+them assessments or exams or whatever,
+ 
+
+ align:start position:0%
+them assessments or exams or whatever,
+but you don't give them like big
+
+ align:start position:0%
+but you don't give them like big
+ 
+
+ align:start position:0%
+but you don't give them like big
+national tests. Um and so if you are a
+
+ align:start position:0%
+national tests. Um and so if you are a
+ 
+
+ align:start position:0%
+national tests. Um and so if you are a
+teacher of reading or of math, um your
+
+ align:start position:0%
+teacher of reading or of math, um your
+ 
+
+ align:start position:0%
+teacher of reading or of math, um your
+test scores are scrutinized in a way
+
+ align:start position:0%
+test scores are scrutinized in a way
+ 
+
+ align:start position:0%
+test scores are scrutinized in a way
+that a science teacher, art teacher, a
+
+ align:start position:0%
+that a science teacher, art teacher, a
+ 
+
+ align:start position:0%
+that a science teacher, art teacher, a
+health teacher, other kinds of teachers
+
+ align:start position:0%
+health teacher, other kinds of teachers
+ 
+
+ align:start position:0%
+health teacher, other kinds of teachers
+are not similarly scrutinized. Um so
+
+ align:start position:0%
+are not similarly scrutinized. Um so
+ 
+
+ align:start position:0%
+are not similarly scrutinized. Um so
+within the you know there could be
+
+ align:start position:0%
+within the you know there could be
+ 
+
+ align:start position:0%
+within the you know there could be
+different kinds of incentives. One of
+
+ align:start position:0%
+different kinds of incentives. One of
+ 
+
+ align:start position:0%
+different kinds of incentives. One of
+the things I always enjoyed about being
+
+ align:start position:0%
+the things I always enjoyed about being
+ 
+
+ align:start position:0%
+the things I always enjoyed about being
+a history teacher is that there there
+
+ align:start position:0%
+a history teacher is that there there
+ 
+
+ align:start position:0%
+a history teacher is that there there
+were never really tests that I were
+
+ align:start position:0%
+were never really tests that I were
+ 
+
+ align:start position:0%
+were never really tests that I were
+preparing my students for. um in the
+
+ align:start position:0%
+preparing my students for. um in the
+ 
+
+ align:start position:0%
+preparing my students for. um in the
+same way I taught in private school, but
+
+ align:start position:0%
+same way I taught in private school, but
+ 
+
+ align:start position:0%
+same way I taught in private school, but
+even my math teacher colleagues like
+
+ align:start position:0%
+even my math teacher colleagues like
+ 
+
+ align:start position:0%
+even my math teacher colleagues like
+felt like they were preparing students
+
+ align:start position:0%
+felt like they were preparing students
+ 
+
+ align:start position:0%
+felt like they were preparing students
+for the SAT, for the APs, things like
+
+ align:start position:0%
+for the SAT, for the APs, things like
+ 
+
+ align:start position:0%
+for the SAT, for the APs, things like
+that. That was never really my concern.
+
+ align:start position:0%
+that. That was never really my concern.
+ 
+
+ align:start position:0%
+that. That was never really my concern.
+Um as a result, like I had to spend less
+
+ align:start position:0%
+Um as a result, like I had to spend less
+ 
+
+ align:start position:0%
+Um as a result, like I had to spend less
+time thinking to myself, this new thing
+
+ align:start position:0%
+time thinking to myself, this new thing
+ 
+
+ align:start position:0%
+time thinking to myself, this new thing
+I'm bringing in this classroom, is this
+
+ align:start position:0%
+I'm bringing in this classroom, is this
+ 
+
+ align:start position:0%
+I'm bringing in this classroom, is this
+going to prepare people for some kind of
+
+ align:start position:0%
+going to prepare people for some kind of
+ 
+
+ align:start position:0%
+going to prepare people for some kind of
+nearly universal testing experiences?
+
+ align:start position:0%
+nearly universal testing experiences?
+ 
+
+ align:start position:0%
+nearly universal testing experiences?
+Like my math teacher colleagues always
+
+ align:start position:0%
+Like my math teacher colleagues always
+ 
+
+ align:start position:0%
+Like my math teacher colleagues always
+had to be thinking about that. I could
+
+ align:start position:0%
+had to be thinking about that. I could
+ 
+
+ align:start position:0%
+had to be thinking about that. I could
+be like, well, you know, Tibetan
+
+ align:start position:0%
+be like, well, you know, Tibetan
+ 
+
+ align:start position:0%
+be like, well, you know, Tibetan
+Buddhism isn't on the test, but it's
+
+ align:start position:0%
+Buddhism isn't on the test, but it's
+ 
+
+ align:start position:0%
+Buddhism isn't on the test, but it's
+awesome. Let's study it. Um you know, so
+
+ align:start position:0%
+awesome. Let's study it. Um you know, so
+ 
+
+ align:start position:0%
+awesome. Let's study it. Um you know, so
+so that's different. Good. other kinds
+
+ align:start position:0%
+so that's different. Good. other kinds
+ 
+
+ align:start position:0%
+so that's different. Good. other kinds
+of things. Yeah. Tai and then Sabrina.
+
+ align:start position:0%
+of things. Yeah. Tai and then Sabrina.
+ 
+
+ align:start position:0%
+of things. Yeah. Tai and then Sabrina.
+Um accessibility and like inclusion. So
+
+ align:start position:0%
+Um accessibility and like inclusion. So
+ 
+
+ align:start position:0%
+Um accessibility and like inclusion. So
+making sure that like no one's left out
+
+ align:start position:0%
+making sure that like no one's left out
+ 
+
+ align:start position:0%
+making sure that like no one's left out
+from your diverse group of learners from
+
+ align:start position:0%
+from your diverse group of learners from
+ 
+
+ align:start position:0%
+from your diverse group of learners from
+any technology.
+
+ align:start position:0%
+any technology.
+ 
+
+ align:start position:0%
+any technology.
+Yeah. Um and that would not be a
+
+ align:start position:0%
+Yeah. Um and that would not be a
+ 
+
+ align:start position:0%
+Yeah. Um and that would not be a
+universal concern across these decades.
+
+ align:start position:0%
+universal concern across these decades.
+ 
+
+ align:start position:0%
+universal concern across these decades.
+um that you know um uh it would it would
+
+ align:start position:0%
+um that you know um uh it would it would
+ 
+
+ align:start position:0%
+um that you know um uh it would it would
+have been considered much more common to
+
+ align:start position:0%
+have been considered much more common to
+ 
+
+ align:start position:0%
+have been considered much more common to
+say like certain people have totally
+
+ align:start position:0%
+say like certain people have totally
+ 
+
+ align:start position:0%
+say like certain people have totally
+unsolvable learning disabilities and
+
+ align:start position:0%
+unsolvable learning disabilities and
+ 
+
+ align:start position:0%
+unsolvable learning disabilities and
+society should tend to their welfare in
+
+ align:start position:0%
+society should tend to their welfare in
+ 
+
+ align:start position:0%
+society should tend to their welfare in
+some other kind of way in the 30s and
+
+ align:start position:0%
+some other kind of way in the 30s and
+ 
+
+ align:start position:0%
+some other kind of way in the 30s and
+40s and 50s and then somewhere in the
+
+ align:start position:0%
+40s and 50s and then somewhere in the
+ 
+
+ align:start position:0%
+40s and 50s and then somewhere in the
+middle of the 20th century we passed um
+
+ align:start position:0%
+middle of the 20th century we passed um
+ 
+
+ align:start position:0%
+middle of the 20th century we passed um
+the Americans with Disabilities Act um
+
+ align:start position:0%
+the Americans with Disabilities Act um
+ 
+
+ align:start position:0%
+the Americans with Disabilities Act um
+which which totally transformed our
+
+ align:start position:0%
+which which totally transformed our
+ 
+
+ align:start position:0%
+which which totally transformed our
+thoughts and in fact you know created a
+
+ align:start position:0%
+thoughts and in fact you know created a
+ 
+
+ align:start position:0%
+thoughts and in fact you know created a
+federal right for people to have um you
+
+ align:start position:0%
+federal right for people to have um you
+ 
+
+ align:start position:0%
+federal right for people to have um you
+know a a way of being a fair and
+
+ align:start position:0%
+know a a way of being a fair and
+ 
+
+ align:start position:0%
+know a a way of being a fair and
+appropriate public education Um, and I
+
+ align:start position:0%
+appropriate public education Um, and I
+ 
+
+ align:start position:0%
+appropriate public education Um, and I
+would also just say educa, like as
+
+ align:start position:0%
+would also just say educa, like as
+ 
+
+ align:start position:0%
+would also just say educa, like as
+society has gotten more interested in
+
+ align:start position:0%
+society has gotten more interested in
+ 
+
+ align:start position:0%
+society has gotten more interested in
+values of inclusion generally, um, what
+
+ align:start position:0%
+values of inclusion generally, um, what
+ 
+
+ align:start position:0%
+values of inclusion generally, um, what
+people would have worried about with
+
+ align:start position:0%
+people would have worried about with
+ 
+
+ align:start position:0%
+people would have worried about with
+inclusion with personal computers in the
+
+ align:start position:0%
+inclusion with personal computers in the
+ 
+
+ align:start position:0%
+inclusion with personal computers in the
+1980s is very different for what they
+
+ align:start position:0%
+1980s is very different for what they
+ 
+
+ align:start position:0%
+1980s is very different for what they
+would be worried about with the
+
+ align:start position:0%
+would be worried about with the
+ 
+
+ align:start position:0%
+would be worried about with the
+computers that are getting in front of
+
+ align:start position:0%
+computers that are getting in front of
+ 
+
+ align:start position:0%
+computers that are getting in front of
+their students right now. That's a great
+
+ align:start position:0%
+their students right now. That's a great
+ 
+
+ align:start position:0%
+their students right now. That's a great
+one. I'm going to say being able to
+
+ align:start position:0%
+one. I'm going to say being able to
+ 
+
+ align:start position:0%
+one. I'm going to say being able to
+track student progress.
+
+ align:start position:0%
+track student progress.
+ 
+
+ align:start position:0%
+track student progress.
+Track
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+progress
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assessment. Good. Yeah. I mean, actually
+
+ align:start position:0%
+assessment. Good. Yeah. I mean, actually
+ 
+
+ align:start position:0%
+assessment. Good. Yeah. I mean, actually
+interesting over this uh century, you
+
+ align:start position:0%
+interesting over this uh century, you
+ 
+
+ align:start position:0%
+interesting over this uh century, you
+know, um some of the earliest
+
+ align:start position:0%
+know, um some of the earliest
+ 
+
+ align:start position:0%
+know, um some of the earliest
+technologies had nothing to do with
+
+ align:start position:0%
+technologies had nothing to do with
+ 
+
+ align:start position:0%
+technologies had nothing to do with
+that, radio and film, but one of the
+
+ align:start position:0%
+that, radio and film, but one of the
+ 
+
+ align:start position:0%
+that, radio and film, but one of the
+very earliest ones you read about um
+
+ align:start position:0%
+very earliest ones you read about um
+ 
+
+ align:start position:0%
+very earliest ones you read about um
+physical teaching machines. Um uh and
+
+ align:start position:0%
+physical teaching machines. Um uh and
+ 
+
+ align:start position:0%
+physical teaching machines. Um uh and
+hopefully you got I mean you saw some
+
+ align:start position:0%
+hopefully you got I mean you saw some
+ 
+
+ align:start position:0%
+hopefully you got I mean you saw some
+pictures um I was just actually looking
+
+ align:start position:0%
+pictures um I was just actually looking
+ 
+
+ align:start position:0%
+pictures um I was just actually looking
+today there was a Sydney Pressie is one
+
+ align:start position:0%
+today there was a Sydney Pressie is one
+ 
+
+ align:start position:0%
+today there was a Sydney Pressie is one
+of the people who Audrey Waters writes
+
+ align:start position:0%
+of the people who Audrey Waters writes
+ 
+
+ align:start position:0%
+of the people who Audrey Waters writes
+about. Um and there's somebody on
+
+ align:start position:0%
+about. Um and there's somebody on
+ 
+
+ align:start position:0%
+about. Um and there's somebody on
+YouTube who had posted this like
+
+ align:start position:0%
+YouTube who had posted this like
+ 
+
+ align:start position:0%
+YouTube who had posted this like
+fabulous two-minute clip of him
+
+ align:start position:0%
+fabulous two-minute clip of him
+ 
+
+ align:start position:0%
+fabulous two-minute clip of him
+demonstrating one of his teacher
+
+ align:start position:0%
+demonstrating one of his teacher
+ 
+
+ align:start position:0%
+demonstrating one of his teacher
+machines and unfortunately that account
+
+ align:start position:0%
+machines and unfortunately that account
+ 
+
+ align:start position:0%
+machines and unfortunately that account
+was deleted before this year's class. Um
+
+ align:start position:0%
+was deleted before this year's class. Um
+ 
+
+ align:start position:0%
+was deleted before this year's class. Um
+may maybe I'll send you a version of it
+
+ align:start position:0%
+may maybe I'll send you a version of it
+ 
+
+ align:start position:0%
+may maybe I'll send you a version of it
+later. The only version of the video
+
+ align:start position:0%
+later. The only version of the video
+ 
+
+ align:start position:0%
+later. The only version of the video
+still exists is one in which a nand
+
+ align:start position:0%
+still exists is one in which a nand
+ 
+
+ align:start position:0%
+still exists is one in which a nand
+augur wall's voice is superimposed of
+
+ align:start position:0%
+augur wall's voice is superimposed of
+ 
+
+ align:start position:0%
+augur wall's voice is superimposed of
+it. Um, so somebody took an audio clip
+
+ align:start position:0%
+it. Um, so somebody took an audio clip
+ 
+
+ align:start position:0%
+it. Um, so somebody took an audio clip
+of Anand Agarwal talking about the
+
+ align:start position:0%
+of Anand Agarwal talking about the
+ 
+
+ align:start position:0%
+of Anand Agarwal talking about the
+capacities of Edex. Um, and played the
+
+ align:start position:0%
+capacities of Edex. Um, and played the
+ 
+
+ align:start position:0%
+capacities of Edex. Um, and played the
+audio over Sydney Pressy demonstrating
+
+ align:start position:0%
+audio over Sydney Pressy demonstrating
+ 
+
+ align:start position:0%
+audio over Sydney Pressy demonstrating
+the teaching machine. Um, and uh, it's a
+
+ align:start position:0%
+the teaching machine. Um, and uh, it's a
+ 
+
+ align:start position:0%
+the teaching machine. Um, and uh, it's a
+little too close for comfort even though
+
+ align:start position:0%
+little too close for comfort even though
+ 
+
+ align:start position:0%
+little too close for comfort even though
+it's a century apart. Um, but teaching
+
+ align:start position:0%
+it's a century apart. Um, but teaching
+ 
+
+ align:start position:0%
+it's a century apart. Um, but teaching
+machines, they were kind of like
+
+ align:start position:0%
+machines, they were kind of like
+ 
+
+ align:start position:0%
+machines, they were kind of like
+typewriters. Um, they had these four
+
+ align:start position:0%
+typewriters. Um, they had these four
+ 
+
+ align:start position:0%
+typewriters. Um, they had these four
+keys that were on them and so they would
+
+ align:start position:0%
+keys that were on them and so they would
+ 
+
+ align:start position:0%
+keys that were on them and so they would
+display one question at a time. Um, it
+
+ align:start position:0%
+display one question at a time. Um, it
+ 
+
+ align:start position:0%
+display one question at a time. Um, it
+was like pre-cantron technology, you
+
+ align:start position:0%
+was like pre-cantron technology, you
+ 
+
+ align:start position:0%
+was like pre-cantron technology, you
+know, and then there would be one of
+
+ align:start position:0%
+know, and then there would be one of
+ 
+
+ align:start position:0%
+know, and then there would be one of
+four possible answers. Um, in one of the
+
+ align:start position:0%
+four possible answers. Um, in one of the
+ 
+
+ align:start position:0%
+four possible answers. Um, in one of the
+earliest versions, it had a little like
+
+ align:start position:0%
+earliest versions, it had a little like
+ 
+
+ align:start position:0%
+earliest versions, it had a little like
+bank of mints in the back of them and so
+
+ align:start position:0%
+bank of mints in the back of them and so
+ 
+
+ align:start position:0%
+bank of mints in the back of them and so
+when you press the right button, like a
+
+ align:start position:0%
+when you press the right button, like a
+ 
+
+ align:start position:0%
+when you press the right button, like a
+little candy or something would roll out
+
+ align:start position:0%
+little candy or something would roll out
+ 
+
+ align:start position:0%
+little candy or something would roll out
+and give you like a little behaviorist
+
+ align:start position:0%
+and give you like a little behaviorist
+ 
+
+ align:start position:0%
+and give you like a little behaviorist
+positive, um, reinforcement kinds of
+
+ align:start position:0%
+positive, um, reinforcement kinds of
+ 
+
+ align:start position:0%
+positive, um, reinforcement kinds of
+things. Um, but one, you know, one of
+
+ align:start position:0%
+things. Um, but one, you know, one of
+ 
+
+ align:start position:0%
+things. Um, but one, you know, one of
+the main virtues of it was like, oh man,
+
+ align:start position:0%
+the main virtues of it was like, oh man,
+ 
+
+ align:start position:0%
+the main virtues of it was like, oh man,
+if we could get enough people these
+
+ align:start position:0%
+if we could get enough people these
+ 
+
+ align:start position:0%
+if we could get enough people these
+things, um, then we could like assess
+
+ align:start position:0%
+things, um, then we could like assess
+ 
+
+ align:start position:0%
+things, um, then we could like assess
+their progress almost constantly. We'd
+
+ align:start position:0%
+their progress almost constantly. We'd
+ 
+
+ align:start position:0%
+their progress almost constantly. We'd
+know exactly where they are. So, so this
+
+ align:start position:0%
+know exactly where they are. So, so this
+ 
+
+ align:start position:0%
+know exactly where they are. So, so this
+idea of track, you
+
+ align:start position:0%
+idea of track, you
+ 
+
+ align:start position:0%
+idea of track, you
+know, tracking student progress is
+
+ align:start position:0%
+know, tracking student progress is
+ 
+
+ align:start position:0%
+know, tracking student progress is
+something that's like particularly
+
+ align:start position:0%
+something that's like particularly
+ 
+
+ align:start position:0%
+something that's like particularly
+urgently concerned in our datadriven
+
+ align:start position:0%
+urgently concerned in our datadriven
+ 
+
+ align:start position:0%
+urgently concerned in our datadriven
+world, but was still something that
+
+ align:start position:0%
+world, but was still something that
+ 
+
+ align:start position:0%
+world, but was still something that
+people were interested in a century ago.
+
+ align:start position:0%
+people were interested in a century ago.
+ 
+
+ align:start position:0%
+people were interested in a century ago.
+Um, what are what are some of the I'll
+
+ align:start position:0%
+Um, what are what are some of the I'll
+ 
+
+ align:start position:0%
+Um, what are what are some of the I'll
+just put them under here. What are some
+
+ align:start position:0%
+just put them under here. What are some
+ 
+
+ align:start position:0%
+just put them under here. What are some
+of the the the would be disincentives
+
+ align:start position:0%
+of the the the would be disincentives
+ 
+
+ align:start position:0%
+of the the the would be disincentives
+for teachers? What are some things that
+
+ align:start position:0%
+for teachers? What are some things that
+ 
+
+ align:start position:0%
+for teachers? What are some things that
+if you were trying to get teachers to
+
+ align:start position:0%
+if you were trying to get teachers to
+ 
+
+ align:start position:0%
+if you were trying to get teachers to
+adopt new technologies would be the
+
+ align:start position:0%
+adopt new technologies would be the
+ 
+
+ align:start position:0%
+adopt new technologies would be the
+sorts of things that would be barriers
+
+ align:start position:0%
+sorts of things that would be barriers
+ 
+
+ align:start position:0%
+sorts of things that would be barriers
+for them? Complexity. Why complexity? A
+
+ align:start position:0%
+for them? Complexity. Why complexity? A
+ 
+
+ align:start position:0%
+for them? Complexity. Why complexity? A
+lot of there's there's uh some teachers
+
+ align:start position:0%
+lot of there's there's uh some teachers
+ 
+
+ align:start position:0%
+lot of there's there's uh some teachers
+who are more able to adapt to new
+
+ align:start position:0%
+who are more able to adapt to new
+ 
+
+ align:start position:0%
+who are more able to adapt to new
+technologies and some teachers who just
+
+ align:start position:0%
+technologies and some teachers who just
+ 
+
+ align:start position:0%
+technologies and some teachers who just
+cannot understand how certain
+
+ align:start position:0%
+cannot understand how certain
+ 
+
+ align:start position:0%
+cannot understand how certain
+technologies might work. Yeah. So I so I
+
+ align:start position:0%
+technologies might work. Yeah. So I so I
+ 
+
+ align:start position:0%
+technologies might work. Yeah. So I so I
+think I think that aptitude is right. I
+
+ align:start position:0%
+think I think that aptitude is right. I
+ 
+
+ align:start position:0%
+think I think that aptitude is right. I
+also many like if you go into teaching
+
+ align:start position:0%
+also many like if you go into teaching
+ 
+
+ align:start position:0%
+also many like if you go into teaching
+there probably probably two things that
+
+ align:start position:0%
+there probably probably two things that
+ 
+
+ align:start position:0%
+there probably probably two things that
+really drive you. One is you love the
+
+ align:start position:0%
+really drive you. One is you love the
+ 
+
+ align:start position:0%
+really drive you. One is you love the
+content that you teach. That's more true
+
+ align:start position:0%
+content that you teach. That's more true
+ 
+
+ align:start position:0%
+content that you teach. That's more true
+for secondary educators than for early
+
+ align:start position:0%
+for secondary educators than for early
+ 
+
+ align:start position:0%
+for secondary educators than for early
+elementary educators but probably true
+
+ align:start position:0%
+elementary educators but probably true
+ 
+
+ align:start position:0%
+elementary educators but probably true
+for them. And you probably love people.
+
+ align:start position:0%
+for them. And you probably love people.
+ 
+
+ align:start position:0%
+for them. And you probably love people.
+um very difficult to be a teacher if you
+
+ align:start position:0%
+um very difficult to be a teacher if you
+ 
+
+ align:start position:0%
+um very difficult to be a teacher if you
+don't find people especially young
+
+ align:start position:0%
+don't find people especially young
+ 
+
+ align:start position:0%
+don't find people especially young
+people pretty engaging. the kinds of
+
+ align:start position:0%
+people pretty engaging. the kinds of
+ 
+
+ align:start position:0%
+people pretty engaging. the kinds of
+folks who find people engaging, they
+
+ align:start position:0%
+folks who find people engaging, they
+ 
+
+ align:start position:0%
+folks who find people engaging, they
+might just find tech, it's not 100%
+
+ align:start position:0%
+might just find tech, it's not 100%
+ 
+
+ align:start position:0%
+might just find tech, it's not 100%
+overlap, but there just technology is
+
+ align:start position:0%
+overlap, but there just technology is
+ 
+
+ align:start position:0%
+overlap, but there just technology is
+less engaging. Like they didn't want to
+
+ align:start position:0%
+less engaging. Like they didn't want to
+ 
+
+ align:start position:0%
+less engaging. Like they didn't want to
+spend their life sitting in front of a
+
+ align:start position:0%
+spend their life sitting in front of a
+ 
+
+ align:start position:0%
+spend their life sitting in front of a
+computer typing itself. They wanted to
+
+ align:start position:0%
+computer typing itself. They wanted to
+ 
+
+ align:start position:0%
+computer typing itself. They wanted to
+be interacting with people.
+
+ align:start position:0%
+be interacting with people.
+ 
+
+ align:start position:0%
+be interacting with people.
+Um, but the other thing I would say is
+
+ align:start position:0%
+Um, but the other thing I would say is
+ 
+
+ align:start position:0%
+Um, but the other thing I would say is
+that there are many educators who spend
+
+ align:start position:0%
+that there are many educators who spend
+ 
+
+ align:start position:0%
+that there are many educators who spend
+a lot of time polishing their craft and
+
+ align:start position:0%
+a lot of time polishing their craft and
+ 
+
+ align:start position:0%
+a lot of time polishing their craft and
+are good at teaching the way they're
+
+ align:start position:0%
+are good at teaching the way they're
+ 
+
+ align:start position:0%
+are good at teaching the way they're
+teaching right now and have been
+
+ align:start position:0%
+teaching right now and have been
+ 
+
+ align:start position:0%
+teaching right now and have been
+teaching for the last decade. And so
+
+ align:start position:0%
+teaching for the last decade. And so
+ 
+
+ align:start position:0%
+teaching for the last decade. And so
+when they see a new piece of technology
+
+ align:start position:0%
+when they see a new piece of technology
+ 
+
+ align:start position:0%
+when they see a new piece of technology
+come in, they're thinking to themselves,
+
+ align:start position:0%
+come in, they're thinking to themselves,
+ 
+
+ align:start position:0%
+come in, they're thinking to themselves,
+is this thing really going to be better
+
+ align:start position:0%
+is this thing really going to be better
+ 
+
+ align:start position:0%
+is this thing really going to be better
+than the thing that I've been doing and
+
+ align:start position:0%
+than the thing that I've been doing and
+ 
+
+ align:start position:0%
+than the thing that I've been doing and
+got good at for a while, um, you know,
+
+ align:start position:0%
+got good at for a while, um, you know,
+ 
+
+ align:start position:0%
+got good at for a while, um, you know,
+what am I g what am I I'm going to have
+
+ align:start position:0%
+what am I g what am I I'm going to have
+ 
+
+ align:start position:0%
+what am I g what am I I'm going to have
+to lose something when I integrate this
+
+ align:start position:0%
+to lose something when I integrate this
+ 
+
+ align:start position:0%
+to lose something when I integrate this
+new thing? Like like any technology
+
+ align:start position:0%
+new thing? Like like any technology
+ 
+
+ align:start position:0%
+new thing? Like like any technology
+adoption involves loss. Any change
+
+ align:start position:0%
+adoption involves loss. Any change
+ 
+
+ align:start position:0%
+adoption involves loss. Any change
+involves loss. You got to give something
+
+ align:start position:0%
+involves loss. You got to give something
+ 
+
+ align:start position:0%
+involves loss. You got to give something
+up. Um, I think giving up it may be
+
+ align:start position:0%
+up. Um, I think giving up it may be
+ 
+
+ align:start position:0%
+up. Um, I think giving up it may be
+pretty good. Um, a lot I think a lot of
+
+ align:start position:0%
+pretty good. Um, a lot I think a lot of
+ 
+
+ align:start position:0%
+pretty good. Um, a lot I think a lot of
+people think that older teachers because
+
+ align:start position:0%
+people think that older teachers because
+ 
+
+ align:start position:0%
+people think that older teachers because
+are are less likely to adopt
+
+ align:start position:0%
+are are less likely to adopt
+ 
+
+ align:start position:0%
+are are less likely to adopt
+technologies because they're not
+
+ align:start position:0%
+technologies because they're not
+ 
+
+ align:start position:0%
+technologies because they're not
+technology fluent. But having worked
+
+ align:start position:0%
+technology fluent. But having worked
+ 
+
+ align:start position:0%
+technology fluent. But having worked
+with many many teachers, I'm really
+
+ align:start position:0%
+with many many teachers, I'm really
+ 
+
+ align:start position:0%
+with many many teachers, I'm really
+convinced that there's no relationship
+
+ align:start position:0%
+convinced that there's no relationship
+ 
+
+ align:start position:0%
+convinced that there's no relationship
+between age and technology adoption.
+
+ align:start position:0%
+between age and technology adoption.
+ 
+
+ align:start position:0%
+between age and technology adoption.
+There are young teachers that are super
+
+ align:start position:0%
+There are young teachers that are super
+ 
+
+ align:start position:0%
+There are young teachers that are super
+interested and there are young teachers
+
+ align:start position:0%
+interested and there are young teachers
+ 
+
+ align:start position:0%
+interested and there are young teachers
+who hate it. There are old teachers who
+
+ align:start position:0%
+who hate it. There are old teachers who
+ 
+
+ align:start position:0%
+who hate it. There are old teachers who
+are like, I'm pretty good at what I do.
+
+ align:start position:0%
+are like, I'm pretty good at what I do.
+ 
+
+ align:start position:0%
+are like, I'm pretty good at what I do.
+And there are old teachers who are old
+
+ align:start position:0%
+And there are old teachers who are old
+ 
+
+ align:start position:0%
+And there are old teachers who are old
+teachers because they've spent the last
+
+ align:start position:0%
+teachers because they've spent the last
+ 
+
+ align:start position:0%
+teachers because they've spent the last
+20 years going, it's really fun to try
+
+ align:start position:0%
+20 years going, it's really fun to try
+ 
+
+ align:start position:0%
+20 years going, it's really fun to try
+new things. It's really fun to try to
+
+ align:start position:0%
+new things. It's really fun to try to
+ 
+
+ align:start position:0%
+new things. It's really fun to try to
+get better. What was one of your
+
+ align:start position:0%
+get better. What was one of your
+ 
+
+ align:start position:0%
+get better. What was one of your
+disincentives, Sabrina? uh student
+
+ align:start position:0%
+disincentives, Sabrina? uh student
+ 
+
+ align:start position:0%
+disincentives, Sabrina? uh student
+distraction.
+
+ align:start position:0%
+distraction.
+ 
+
+ align:start position:0%
+distraction.
+Great. And obviously some of these
+
+ align:start position:0%
+Great. And obviously some of these
+ 
+
+ align:start position:0%
+Great. And obviously some of these
+technologies are more akin to that than
+
+ align:start position:0%
+technologies are more akin to that than
+ 
+
+ align:start position:0%
+technologies are more akin to that than
+others. Like if you're playing a film
+
+ align:start position:0%
+others. Like if you're playing a film
+ 
+
+ align:start position:0%
+others. Like if you're playing a film
+strip or something like that, like you
+
+ align:start position:0%
+strip or something like that, like you
+ 
+
+ align:start position:0%
+strip or something like that, like you
+probably have kids attention or things
+
+ align:start position:0%
+probably have kids attention or things
+ 
+
+ align:start position:0%
+probably have kids attention or things
+like that. Um but uh certainly as we get
+
+ align:start position:0%
+like that. Um but uh certainly as we get
+ 
+
+ align:start position:0%
+like that. Um but uh certainly as we get
+into computers, any anything in which
+
+ align:start position:0%
+into computers, any anything in which
+ 
+
+ align:start position:0%
+into computers, any anything in which
+you know the the attention is where
+
+ align:start position:0%
+you know the the attention is where
+ 
+
+ align:start position:0%
+you know the the attention is where
+where each student is responsible for
+
+ align:start position:0%
+where each student is responsible for
+ 
+
+ align:start position:0%
+where each student is responsible for
+their own attention um is something that
+
+ align:start position:0%
+their own attention um is something that
+ 
+
+ align:start position:0%
+their own attention um is something that
+that uh can can raise concerns for
+
+ align:start position:0%
+that uh can can raise concerns for
+ 
+
+ align:start position:0%
+that uh can can raise concerns for
+teachers because kids like to be attend
+
+ align:start position:0%
+teachers because kids like to be attend
+ 
+
+ align:start position:0%
+teachers because kids like to be attend
+to all kinds of things. What what other
+
+ align:start position:0%
+to all kinds of things. What what other
+ 
+
+ align:start position:0%
+to all kinds of things. What what other
+things would be disincentives like
+
+ align:start position:0%
+things would be disincentives like
+ 
+
+ align:start position:0%
+things would be disincentives like
+teacher displacement like they feel like
+
+ align:start position:0%
+teacher displacement like they feel like
+ 
+
+ align:start position:0%
+teacher displacement like they feel like
+they're being replaced? Yep. Um so
+
+ align:start position:0%
+they're being replaced? Yep. Um so
+ 
+
+ align:start position:0%
+they're being replaced? Yep. Um so
+teachers are a profession um you know
+
+ align:start position:0%
+teachers are a profession um you know
+ 
+
+ align:start position:0%
+teachers are a profession um you know
+that that protects their job security
+
+ align:start position:0%
+that that protects their job security
+ 
+
+ align:start position:0%
+that that protects their job security
+with a license and things like that like
+
+ align:start position:0%
+with a license and things like that like
+ 
+
+ align:start position:0%
+with a license and things like that like
+lots of other professions do like
+
+ align:start position:0%
+lots of other professions do like
+ 
+
+ align:start position:0%
+lots of other professions do like
+doctors and pharmacists and lawyers and
+
+ align:start position:0%
+doctors and pharmacists and lawyers and
+ 
+
+ align:start position:0%
+doctors and pharmacists and lawyers and
+all kinds of people. Um and uh yeah and
+
+ align:start position:0%
+all kinds of people. Um and uh yeah and
+ 
+
+ align:start position:0%
+all kinds of people. Um and uh yeah and
+yeah but most professionals are not
+
+ align:start position:0%
+yeah but most professionals are not
+ 
+
+ align:start position:0%
+yeah but most professionals are not
+super enthusiastic about technology that
+
+ align:start position:0%
+super enthusiastic about technology that
+ 
+
+ align:start position:0%
+super enthusiastic about technology that
+has the capacity to replace the
+
+ align:start position:0%
+has the capacity to replace the
+ 
+
+ align:start position:0%
+has the capacity to replace the
+functions that they're doing.
+
+ align:start position:0%
+functions that they're doing.
+ 
+
+ align:start position:0%
+functions that they're doing.
+Um, good. Let's think about some of
+
+ align:start position:0%
+Um, good. Let's think about some of
+ 
+
+ align:start position:0%
+Um, good. Let's think about some of
+these other um, so, so this is a good
+
+ align:start position:0%
+these other um, so, so this is a good
+ 
+
+ align:start position:0%
+these other um, so, so this is a good
+one. So, so again, we could think about
+
+ align:start position:0%
+one. So, so again, we could think about
+ 
+
+ align:start position:0%
+one. So, so again, we could think about
+anytime a new technology is being
+
+ align:start position:0%
+anytime a new technology is being
+ 
+
+ align:start position:0%
+anytime a new technology is being
+introduced, is it going to reduce
+
+ align:start position:0%
+introduced, is it going to reduce
+ 
+
+ align:start position:0%
+introduced, is it going to reduce
+workload? Is it going to spark interest?
+
+ align:start position:0%
+workload? Is it going to spark interest?
+ 
+
+ align:start position:0%
+workload? Is it going to spark interest?
+Will it spark interest in the first
+
+ align:start position:0%
+Will it spark interest in the first
+ 
+
+ align:start position:0%
+Will it spark interest in the first
+three weeks of this new technology being
+
+ align:start position:0%
+three weeks of this new technology being
+ 
+
+ align:start position:0%
+three weeks of this new technology being
+here, will it spark interest two years
+
+ align:start position:0%
+here, will it spark interest two years
+ 
+
+ align:start position:0%
+here, will it spark interest two years
+after the technology has been
+
+ align:start position:0%
+after the technology has been
+ 
+
+ align:start position:0%
+after the technology has been
+introduced? Is it going to be of high
+
+ align:start position:0%
+introduced? Is it going to be of high
+ 
+
+ align:start position:0%
+introduced? Is it going to be of high
+quality? Do I have control over the
+
+ align:start position:0%
+quality? Do I have control over the
+ 
+
+ align:start position:0%
+quality? Do I have control over the
+quality? Um, accessible inclusion, is it
+
+ align:start position:0%
+quality? Um, accessible inclusion, is it
+ 
+
+ align:start position:0%
+quality? Um, accessible inclusion, is it
+going to improve learning? Will it be
+
+ align:start position:0%
+going to improve learning? Will it be
+ 
+
+ align:start position:0%
+going to improve learning? Will it be
+able to track assessment? Is it too
+
+ align:start position:0%
+able to track assessment? Is it too
+ 
+
+ align:start position:0%
+able to track assessment? Is it too
+complex? Will it like distract my
+
+ align:start position:0%
+complex? Will it like distract my
+ 
+
+ align:start position:0%
+complex? Will it like distract my
+students? Is it going to displace
+
+ align:start position:0%
+students? Is it going to displace
+ 
+
+ align:start position:0%
+students? Is it going to displace
+essential functions that I perform? Um,
+
+ align:start position:0%
+essential functions that I perform? Um,
+ 
+
+ align:start position:0%
+essential functions that I perform? Um,
+those are like that is a good set of
+
+ align:start position:0%
+those are like that is a good set of
+ 
+
+ align:start position:0%
+those are like that is a good set of
+questions that you could ask, you know,
+
+ align:start position:0%
+questions that you could ask, you know,
+ 
+
+ align:start position:0%
+questions that you could ask, you know,
+that Cuban does ask in some ways of
+
+ align:start position:0%
+that Cuban does ask in some ways of
+ 
+
+ align:start position:0%
+that Cuban does ask in some ways of
+radio and film and television and
+
+ align:start position:0%
+radio and film and television and
+ 
+
+ align:start position:0%
+radio and film and television and
+teaching machines and computers. Um, and
+
+ align:start position:0%
+teaching machines and computers. Um, and
+ 
+
+ align:start position:0%
+teaching machines and computers. Um, and
+you could ask them of AI and Khan
+
+ align:start position:0%
+you could ask them of AI and Khan
+ 
+
+ align:start position:0%
+you could ask them of AI and Khan
+Academy and I civics and anything else
+
+ align:start position:0%
+Academy and I civics and anything else
+ 
+
+ align:start position:0%
+Academy and I civics and anything else
+that comes along. Like these are all
+
+ align:start position:0%
+that comes along. Like these are all
+ 
+
+ align:start position:0%
+that comes along. Like these are all
+still good questions to ask. Um, let's
+
+ align:start position:0%
+still good questions to ask. Um, let's
+ 
+
+ align:start position:0%
+still good questions to ask. Um, let's
+try to hit now a bunch of these other
+
+ align:start position:0%
+try to hit now a bunch of these other
+ 
+
+ align:start position:0%
+try to hit now a bunch of these other
+stakeholders. Um, who are who are some
+
+ align:start position:0%
+stakeholders. Um, who are who are some
+ 
+
+ align:start position:0%
+stakeholders. Um, who are who are some
+of the stakeholders that surprised you?
+
+ align:start position:0%
+of the stakeholders that surprised you?
+ 
+
+ align:start position:0%
+of the stakeholders that surprised you?
+Who are the ones that you were like,
+
+ align:start position:0%
+Who are the ones that you were like,
+ 
+
+ align:start position:0%
+Who are the ones that you were like,
+"Whoa, I wouldn't have thought of this
+
+ align:start position:0%
+"Whoa, I wouldn't have thought of this
+ 
+
+ align:start position:0%
+"Whoa, I wouldn't have thought of this
+in terms of education
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technology, weird ones or unique ones."
+
+ align:start position:0%
+technology, weird ones or unique ones."
+ 
+
+ align:start position:0%
+technology, weird ones or unique ones."
+I mean, I thought like my group was the
+
+ align:start position:0%
+I mean, I thought like my group was the
+ 
+
+ align:start position:0%
+I mean, I thought like my group was the
+teacher machines and it was like the
+
+ align:start position:0%
+teacher machines and it was like the
+ 
+
+ align:start position:0%
+teacher machines and it was like the
+psychologists that like come up with the
+
+ align:start position:0%
+psychologists that like come up with the
+ 
+
+ align:start position:0%
+psychologists that like come up with the
+ideas um that go into how these
+
+ align:start position:0%
+ideas um that go into how these
+ 
+
+ align:start position:0%
+ideas um that go into how these
+technologies are or what they're based
+
+ align:start position:0%
+technologies are or what they're based
+ 
+
+ align:start position:0%
+technologies are or what they're based
+on. Um like I guess I never just never
+
+ align:start position:0%
+on. Um like I guess I never just never
+ 
+
+ align:start position:0%
+on. Um like I guess I never just never
+really thought like oh like you know it
+
+ align:start position:0%
+really thought like oh like you know it
+ 
+
+ align:start position:0%
+really thought like oh like you know it
+is the people who like thought of
+
+ align:start position:0%
+is the people who like thought of
+ 
+
+ align:start position:0%
+is the people who like thought of
+constructivism and like situated
+
+ align:start position:0%
+constructivism and like situated
+ 
+
+ align:start position:0%
+constructivism and like situated
+learning that has then sparked this
+
+ align:start position:0%
+learning that has then sparked this
+ 
+
+ align:start position:0%
+learning that has then sparked this
+interest in everything else. Um and so
+
+ align:start position:0%
+interest in everything else. Um and so
+ 
+
+ align:start position:0%
+interest in everything else. Um and so
+it's like people have ideas but all of
+
+ align:start position:0%
+it's like people have ideas but all of
+ 
+
+ align:start position:0%
+it's like people have ideas but all of
+that initially stemmed from these like
+
+ align:start position:0%
+that initially stemmed from these like
+ 
+
+ align:start position:0%
+that initially stemmed from these like
+two thoughts of learning. Good. Yeah. So
+
+ align:start position:0%
+two thoughts of learning. Good. Yeah. So
+ 
+
+ align:start position:0%
+two thoughts of learning. Good. Yeah. So
+so so people have ideas about what good
+
+ align:start position:0%
+so so people have ideas about what good
+ 
+
+ align:start position:0%
+so so people have ideas about what good
+teaching and learning should be like.
+
+ align:start position:0%
+teaching and learning should be like.
+ 
+
+ align:start position:0%
+teaching and learning should be like.
+Those ideas are in some ways they seem
+
+ align:start position:0%
+Those ideas are in some ways they seem
+ 
+
+ align:start position:0%
+Those ideas are in some ways they seem
+pretty universal because we can find
+
+ align:start position:0%
+pretty universal because we can find
+ 
+
+ align:start position:0%
+pretty universal because we can find
+them going back through history but
+
+ align:start position:0%
+them going back through history but
+ 
+
+ align:start position:0%
+them going back through history but
+they're als they're always being
+
+ align:start position:0%
+they're als they're always being
+ 
+
+ align:start position:0%
+they're als they're always being
+reinterpreted updated things like that.
+
+ align:start position:0%
+reinterpreted updated things like that.
+ 
+
+ align:start position:0%
+reinterpreted updated things like that.
+Um Sydney Pressie is in this moment
+
+ align:start position:0%
+Um Sydney Pressie is in this moment
+ 
+
+ align:start position:0%
+Um Sydney Pressie is in this moment
+where behaviorism is an incredibly
+
+ align:start position:0%
+where behaviorism is an incredibly
+ 
+
+ align:start position:0%
+where behaviorism is an incredibly
+prominent set of you know set of ideas.
+
+ align:start position:0%
+prominent set of you know set of ideas.
+ 
+
+ align:start position:0%
+prominent set of you know set of ideas.
+This behaviorism you're probably all
+
+ align:start position:0%
+This behaviorism you're probably all
+ 
+
+ align:start position:0%
+This behaviorism you're probably all
+familiar with of you know you uh punish
+
+ align:start position:0%
+familiar with of you know you uh punish
+ 
+
+ align:start position:0%
+familiar with of you know you uh punish
+people when they do things wrong and you
+
+ align:start position:0%
+people when they do things wrong and you
+ 
+
+ align:start position:0%
+people when they do things wrong and you
+reward them when you do things right and
+
+ align:start position:0%
+reward them when you do things right and
+ 
+
+ align:start position:0%
+reward them when you do things right and
+you condition their behavior that way.
+
+ align:start position:0%
+you condition their behavior that way.
+ 
+
+ align:start position:0%
+you condition their behavior that way.
+Um and so he creates a physical machine
+
+ align:start position:0%
+Um and so he creates a physical machine
+ 
+
+ align:start position:0%
+Um and so he creates a physical machine
+that embodies those ideas. Um there you
+
+ align:start position:0%
+that embodies those ideas. Um there you
+ 
+
+ align:start position:0%
+that embodies those ideas. Um there you
+know and then you know Seymour Papert
+
+ align:start position:0%
+know and then you know Seymour Papert
+ 
+
+ align:start position:0%
+know and then you know Seymour Papert
+will come along um and be like oh man
+
+ align:start position:0%
+will come along um and be like oh man
+ 
+
+ align:start position:0%
+will come along um and be like oh man
+why can't we learn math the way that
+
+ align:start position:0%
+why can't we learn math the way that
+ 
+
+ align:start position:0%
+why can't we learn math the way that
+like kids who go to visit France learn
+
+ align:start position:0%
+like kids who go to visit France learn
+ 
+
+ align:start position:0%
+like kids who go to visit France learn
+French? um why can't we make a thing
+
+ align:start position:0%
+French? um why can't we make a thing
+ 
+
+ align:start position:0%
+French? um why can't we make a thing
+which is math land? I bet logo could be
+
+ align:start position:0%
+which is math land? I bet logo could be
+ 
+
+ align:start position:0%
+which is math land? I bet logo could be
+like math land. He has a set he have a
+
+ align:start position:0%
+like math land. He has a set he have a
+ 
+
+ align:start position:0%
+like math land. He has a set he have a
+set of ideas about what good teaching
+
+ align:start position:0%
+set of ideas about what good teaching
+ 
+
+ align:start position:0%
+set of ideas about what good teaching
+and learning looks like and he
+
+ align:start position:0%
+and learning looks like and he
+ 
+
+ align:start position:0%
+and learning looks like and he
+incorporates those ideas. Um and they
+
+ align:start position:0%
+incorporates those ideas. Um and they
+ 
+
+ align:start position:0%
+incorporates those ideas. Um and they
+and people become partisans of these
+
+ align:start position:0%
+and people become partisans of these
+ 
+
+ align:start position:0%
+and people become partisans of these
+ideas. Um you know probably the most
+
+ align:start position:0%
+ideas. Um you know probably the most
+ 
+
+ align:start position:0%
+ideas. Um you know probably the most
+prominent partisan of education
+
+ align:start position:0%
+prominent partisan of education
+ 
+
+ align:start position:0%
+prominent partisan of education
+technology in the United States today is
+
+ align:start position:0%
+technology in the United States today is
+ 
+
+ align:start position:0%
+technology in the United States today is
+Salon. Um who's someone who like had a
+
+ align:start position:0%
+Salon. Um who's someone who like had a
+ 
+
+ align:start position:0%
+Salon. Um who's someone who like had a
+very particular idea like a like clear
+
+ align:start position:0%
+very particular idea like a like clear
+ 
+
+ align:start position:0%
+very particular idea like a like clear
+vision of what personalized learning
+
+ align:start position:0%
+vision of what personalized learning
+ 
+
+ align:start position:0%
+vision of what personalized learning
+would look like. you know, he had he had
+
+ align:start position:0%
+would look like. you know, he had he had
+ 
+
+ align:start position:0%
+would look like. you know, he had he had
+I don't know if you know about his his
+
+ align:start position:0%
+I don't know if you know about his his
+ 
+
+ align:start position:0%
+I don't know if you know about his his
+personal experience, but he was like a
+
+ align:start position:0%
+personal experience, but he was like a
+ 
+
+ align:start position:0%
+personal experience, but he was like a
+hedge fund person or something like that
+
+ align:start position:0%
+hedge fund person or something like that
+ 
+
+ align:start position:0%
+hedge fund person or something like that
+and his uh um niece was having trouble
+
+ align:start position:0%
+and his uh um niece was having trouble
+ 
+
+ align:start position:0%
+and his uh um niece was having trouble
+with math and he started tutoring his
+
+ align:start position:0%
+with math and he started tutoring his
+ 
+
+ align:start position:0%
+with math and he started tutoring his
+niece in math and he put like did it
+
+ align:start position:0%
+niece in math and he put like did it
+ 
+
+ align:start position:0%
+niece in math and he put like did it
+over videos and so he put the videos
+
+ align:start position:0%
+over videos and so he put the videos
+ 
+
+ align:start position:0%
+over videos and so he put the videos
+online, people started watching them. He
+
+ align:start position:0%
+online, people started watching them. He
+ 
+
+ align:start position:0%
+online, people started watching them. He
+go, "Wow, what if every person could
+
+ align:start position:0%
+go, "Wow, what if every person could
+ 
+
+ align:start position:0%
+go, "Wow, what if every person could
+have this little like personalized
+
+ align:start position:0%
+have this little like personalized
+ 
+
+ align:start position:0%
+have this little like personalized
+tutor?" Um what if each person could
+
+ align:start position:0%
+tutor?" Um what if each person could
+ 
+
+ align:start position:0%
+tutor?" Um what if each person could
+sort of study math at their own
+
+ align:start position:0%
+sort of study math at their own
+ 
+
+ align:start position:0%
+sort of study math at their own
+individual pace? Um, and then he built
+
+ align:start position:0%
+individual pace? Um, and then he built
+ 
+
+ align:start position:0%
+individual pace? Um, and then he built
+this whole enterprise and continues to,
+
+ align:start position:0%
+this whole enterprise and continues to,
+ 
+
+ align:start position:0%
+this whole enterprise and continues to,
+you know, he he's incredibly
+
+ align:start position:0%
+you know, he he's incredibly
+ 
+
+ align:start position:0%
+you know, he he's incredibly
+enthusiastic about AI right now because
+
+ align:start position:0%
+enthusiastic about AI right now because
+ 
+
+ align:start position:0%
+enthusiastic about AI right now because
+like, oh man, instead of just having me
+
+ align:start position:0%
+like, oh man, instead of just having me
+ 
+
+ align:start position:0%
+like, oh man, instead of just having me
+record um a tutor for each person, like
+
+ align:start position:0%
+record um a tutor for each person, like
+ 
+
+ align:start position:0%
+record um a tutor for each person, like
+what if the GPT can like generate
+
+ align:start position:0%
+what if the GPT can like generate
+ 
+
+ align:start position:0%
+what if the GPT can like generate
+personalized text related to each
+
+ align:start position:0%
+personalized text related to each
+ 
+
+ align:start position:0%
+personalized text related to each
+individual person or something like
+
+ align:start position:0%
+individual person or something like
+ 
+
+ align:start position:0%
+individual person or something like
+that. Um, and those ideas, you know,
+
+ align:start position:0%
+that. Um, and those ideas, you know,
+ 
+
+ align:start position:0%
+that. Um, and those ideas, you know,
+they're it's it's not like they're just
+
+ align:start position:0%
+they're it's it's not like they're just
+ 
+
+ align:start position:0%
+they're it's it's not like they're just
+dropped in the world. They're advocated
+
+ align:start position:0%
+dropped in the world. They're advocated
+ 
+
+ align:start position:0%
+dropped in the world. They're advocated
+for. Um, did you all see the New York
+
+ align:start position:0%
+for. Um, did you all see the New York
+ 
+
+ align:start position:0%
+for. Um, did you all see the New York
+Time was it New York Times or Washington
+
+ align:start position:0%
+Time was it New York Times or Washington
+ 
+
+ align:start position:0%
+Time was it New York Times or Washington
+Post? Somebody wrote an op-ed about um
+
+ align:start position:0%
+Post? Somebody wrote an op-ed about um
+ 
+
+ align:start position:0%
+Post? Somebody wrote an op-ed about um
+about Salon and AI. It was either in the
+
+ align:start position:0%
+about Salon and AI. It was either in the
+ 
+
+ align:start position:0%
+about Salon and AI. It was either in the
+Washington Post or the New York Times,
+
+ align:start position:0%
+Washington Post or the New York Times,
+ 
+
+ align:start position:0%
+Washington Post or the New York Times,
+but it was basically something like this
+
+ align:start position:0%
+but it was basically something like this
+ 
+
+ align:start position:0%
+but it was basically something like this
+is the first AI that your kid will love
+
+ align:start position:0%
+is the first AI that your kid will love
+ 
+
+ align:start position:0%
+is the first AI that your kid will love
+or something like that. And it's
+
+ align:start position:0%
+or something like that. And it's
+ 
+
+ align:start position:0%
+or something like that. And it's
+basically just a sort of celebratory
+
+ align:start position:0%
+basically just a sort of celebratory
+ 
+
+ align:start position:0%
+basically just a sort of celebratory
+piece of of Kot MIGO. Um good. So, so
+
+ align:start position:0%
+piece of of Kot MIGO. Um good. So, so
+ 
+
+ align:start position:0%
+piece of of Kot MIGO. Um good. So, so
+that's an unusual group, you know, and
+
+ align:start position:0%
+that's an unusual group, you know, and
+ 
+
+ align:start position:0%
+that's an unusual group, you know, and
+and those groups um they I mean today
+
+ align:start position:0%
+and those groups um they I mean today
+ 
+
+ align:start position:0%
+and those groups um they I mean today
+they like, you know, like Saw Khan goes
+
+ align:start position:0%
+they like, you know, like Saw Khan goes
+ 
+
+ align:start position:0%
+they like, you know, like Saw Khan goes
+on the Today Show and tells people what
+
+ align:start position:0%
+on the Today Show and tells people what
+ 
+
+ align:start position:0%
+on the Today Show and tells people what
+he thinks. He goes to investor
+
+ align:start position:0%
+he thinks. He goes to investor
+ 
+
+ align:start position:0%
+he thinks. He goes to investor
+conferences and tells people what he
+
+ align:start position:0%
+conferences and tells people what he
+ 
+
+ align:start position:0%
+conferences and tells people what he
+thinks. He goes to schools, you know,
+
+ align:start position:0%
+thinks. He goes to schools, you know,
+ 
+
+ align:start position:0%
+thinks. He goes to schools, you know,
+Harvard and MIT bringing him in every
+
+ align:start position:0%
+Harvard and MIT bringing him in every
+ 
+
+ align:start position:0%
+Harvard and MIT bringing him in every
+couple years and things like that. So
+
+ align:start position:0%
+couple years and things like that. So
+ 
+
+ align:start position:0%
+couple years and things like that. So
+these folks advocate for their ideas. Um
+
+ align:start position:0%
+these folks advocate for their ideas. Um
+ 
+
+ align:start position:0%
+these folks advocate for their ideas. Um
+they're not, you know, the ideas the
+
+ align:start position:0%
+they're not, you know, the ideas the
+ 
+
+ align:start position:0%
+they're not, you know, the ideas the
+ideas don't fall from the sky. There's a
+
+ align:start position:0%
+ideas don't fall from the sky. There's a
+ 
+
+ align:start position:0%
+ideas don't fall from the sky. There's a
+stakeholder who is advancing those
+
+ align:start position:0%
+stakeholder who is advancing those
+ 
+
+ align:start position:0%
+stakeholder who is advancing those
+ideas. Who are some who are some other
+
+ align:start position:0%
+ideas. Who are some who are some other
+ 
+
+ align:start position:0%
+ideas. Who are some who are some other
+stakeholders that seem important? Um, I
+
+ align:start position:0%
+stakeholders that seem important? Um, I
+ 
+
+ align:start position:0%
+stakeholders that seem important? Um, I
+thought it was weird that you could
+
+ align:start position:0%
+thought it was weird that you could
+ 
+
+ align:start position:0%
+thought it was weird that you could
+think about like manufacturers and I
+
+ align:start position:0%
+think about like manufacturers and I
+ 
+
+ align:start position:0%
+think about like manufacturers and I
+mean like like the people who produce
+
+ align:start position:0%
+mean like like the people who produce
+ 
+
+ align:start position:0%
+mean like like the people who produce
+transistors which is like TSMC and ASML
+
+ align:start position:0%
+transistors which is like TSMC and ASML
+ 
+
+ align:start position:0%
+transistors which is like TSMC and ASML
+because if a bunch of schools across
+
+ align:start position:0%
+because if a bunch of schools across
+ 
+
+ align:start position:0%
+because if a bunch of schools across
+America all of a sudden need like
+
+ align:start position:0%
+America all of a sudden need like
+ 
+
+ align:start position:0%
+America all of a sudden need like
+thousands and thousands of iPads and you
+
+ align:start position:0%
+thousands and thousands of iPads and you
+ 
+
+ align:start position:0%
+thousands and thousands of iPads and you
+have like this big backlog request on
+
+ align:start position:0%
+have like this big backlog request on
+ 
+
+ align:start position:0%
+have like this big backlog request on
+like M2 chips or whatever is in them
+
+ align:start position:0%
+like M2 chips or whatever is in them
+ 
+
+ align:start position:0%
+like M2 chips or whatever is in them
+right now and then someone like TSMC the
+
+ align:start position:0%
+right now and then someone like TSMC the
+ 
+
+ align:start position:0%
+right now and then someone like TSMC the
+only people who really produce
+
+ align:start position:0%
+only people who really produce
+ 
+
+ align:start position:0%
+only people who really produce
+transistors has this huge float and they
+
+ align:start position:0%
+transistors has this huge float and they
+ 
+
+ align:start position:0%
+transistors has this huge float and they
+make a lot of money. Yeah. Yeah. that
+
+ align:start position:0%
+make a lot of money. Yeah. Yeah. that
+ 
+
+ align:start position:0%
+make a lot of money. Yeah. Yeah. that
+that that that people become, you know,
+
+ align:start position:0%
+that that that people become, you know,
+ 
+
+ align:start position:0%
+that that that people become, you know,
+that those folks then organize
+
+ align:start position:0%
+that those folks then organize
+ 
+
+ align:start position:0%
+that those folks then organize
+themselves into trade groups um and they
+
+ align:start position:0%
+themselves into trade groups um and they
+ 
+
+ align:start position:0%
+themselves into trade groups um and they
+go to, you know, they they how do they
+
+ align:start position:0%
+go to, you know, they they how do they
+ 
+
+ align:start position:0%
+go to, you know, they they how do they
+how do they advance their interests?
+
+ align:start position:0%
+how do they advance their interests?
+ 
+
+ align:start position:0%
+how do they advance their interests?
+They do things like um give some of
+
+ align:start position:0%
+They do things like um give some of
+ 
+
+ align:start position:0%
+They do things like um give some of
+their materials away for schools,
+
+ align:start position:0%
+their materials away for schools,
+ 
+
+ align:start position:0%
+their materials away for schools,
+demonstration, they create training
+
+ align:start position:0%
+demonstration, they create training
+ 
+
+ align:start position:0%
+demonstration, they create training
+programs for their materials and share
+
+ align:start position:0%
+programs for their materials and share
+ 
+
+ align:start position:0%
+programs for their materials and share
+them. Um they have sales and marketing
+
+ align:start position:0%
+them. Um they have sales and marketing
+ 
+
+ align:start position:0%
+them. Um they have sales and marketing
+people that go around and get people
+
+ align:start position:0%
+people that go around and get people
+ 
+
+ align:start position:0%
+people that go around and get people
+advanced about that. Um they like
+
+ align:start position:0%
+advanced about that. Um they like
+ 
+
+ align:start position:0%
+advanced about that. Um they like
+sponsor conferences. they, you know,
+
+ align:start position:0%
+sponsor conferences. they, you know,
+ 
+
+ align:start position:0%
+sponsor conferences. they, you know,
+what maybe that they're not even
+
+ align:start position:0%
+what maybe that they're not even
+ 
+
+ align:start position:0%
+what maybe that they're not even
+directly advertising for. They're
+
+ align:start position:0%
+directly advertising for. They're
+ 
+
+ align:start position:0%
+directly advertising for. They're
+they're just, you know, their presence
+
+ align:start position:0%
+they're just, you know, their presence
+ 
+
+ align:start position:0%
+they're just, you know, their presence
+to try to encourage teachers and other
+
+ align:start position:0%
+to try to encourage teachers and other
+ 
+
+ align:start position:0%
+to try to encourage teachers and other
+sorts of groups to to be behind it. Um,
+
+ align:start position:0%
+sorts of groups to to be behind it. Um,
+ 
+
+ align:start position:0%
+sorts of groups to to be behind it. Um,
+you know, uh, we spend an enormous
+
+ align:start position:0%
+you know, uh, we spend an enormous
+ 
+
+ align:start position:0%
+you know, uh, we spend an enormous
+amount of money on education every year
+
+ align:start position:0%
+amount of money on education every year
+ 
+
+ align:start position:0%
+amount of money on education every year
+in the United States and lot, you know,
+
+ align:start position:0%
+in the United States and lot, you know,
+ 
+
+ align:start position:0%
+in the United States and lot, you know,
+the the biggest chunk of that money goes
+
+ align:start position:0%
+the the biggest chunk of that money goes
+ 
+
+ align:start position:0%
+the the biggest chunk of that money goes
+to pay the salaries of the people who do
+
+ align:start position:0%
+to pay the salaries of the people who do
+ 
+
+ align:start position:0%
+to pay the salaries of the people who do
+stuff and another big chunk of that
+
+ align:start position:0%
+stuff and another big chunk of that
+ 
+
+ align:start position:0%
+stuff and another big chunk of that
+money goes to heating and air
+
+ align:start position:0%
+money goes to heating and air
+ 
+
+ align:start position:0%
+money goes to heating and air
+conditioning, you know, for which there
+
+ align:start position:0%
+conditioning, you know, for which there
+ 
+
+ align:start position:0%
+conditioning, you know, for which there
+are people who are selling those things.
+
+ align:start position:0%
+are people who are selling those things.
+ 
+
+ align:start position:0%
+are people who are selling those things.
+Um but you know basically the third
+
+ align:start position:0%
+Um but you know basically the third
+ 
+
+ align:start position:0%
+Um but you know basically the third
+biggest bucket after those two is the
+
+ align:start position:0%
+biggest bucket after those two is the
+ 
+
+ align:start position:0%
+biggest bucket after those two is the
+stuff we buy in schools to help people
+
+ align:start position:0%
+stuff we buy in schools to help people
+ 
+
+ align:start position:0%
+stuff we buy in schools to help people
+learn. Um and so um uh yeah there there
+
+ align:start position:0%
+learn. Um and so um uh yeah there there
+ 
+
+ align:start position:0%
+learn. Um and so um uh yeah there there
+are advocates who are you know the folks
+
+ align:start position:0%
+are advocates who are you know the folks
+ 
+
+ align:start position:0%
+are advocates who are you know the folks
+who are not neutral in these things. Um
+
+ align:start position:0%
+who are not neutral in these things. Um
+ 
+
+ align:start position:0%
+who are not neutral in these things. Um
+there are ways you know Apple computer
+
+ align:start position:0%
+there are ways you know Apple computer
+ 
+
+ align:start position:0%
+there are ways you know Apple computer
+has been particularly prominent over the
+
+ align:start position:0%
+has been particularly prominent over the
+ 
+
+ align:start position:0%
+has been particularly prominent over the
+last bunch of years and trying to craft
+
+ align:start position:0%
+last bunch of years and trying to craft
+ 
+
+ align:start position:0%
+last bunch of years and trying to craft
+a vision of itself as a company um that
+
+ align:start position:0%
+a vision of itself as a company um that
+ 
+
+ align:start position:0%
+a vision of itself as a company um that
+has a particular role inside colleges,
+
+ align:start position:0%
+has a particular role inside colleges,
+ 
+
+ align:start position:0%
+has a particular role inside colleges,
+universities, schools those kinds of
+
+ align:start position:0%
+universities, schools those kinds of
+ 
+
+ align:start position:0%
+universities, schools those kinds of
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+I think something that surprised me, but
+
+ align:start position:0%
+I think something that surprised me, but
+ 
+
+ align:start position:0%
+I think something that surprised me, but
+maybe it's not that surprising, was like
+
+ align:start position:0%
+maybe it's not that surprising, was like
+ 
+
+ align:start position:0%
+maybe it's not that surprising, was like
+government government as a whole and
+
+ align:start position:0%
+government government as a whole and
+ 
+
+ align:start position:0%
+government government as a whole and
+like eludism between governments because
+
+ align:start position:0%
+like eludism between governments because
+ 
+
+ align:start position:0%
+like eludism between governments because
+uh in the class we took last semester
+
+ align:start position:0%
+uh in the class we took last semester
+ 
+
+ align:start position:0%
+uh in the class we took last semester
+like in education. We talked a lot about
+
+ align:start position:0%
+like in education. We talked a lot about
+ 
+
+ align:start position:0%
+like in education. We talked a lot about
+like Americanism and how like it's so
+
+ align:start position:0%
+like Americanism and how like it's so
+ 
+
+ align:start position:0%
+like Americanism and how like it's so
+linked with education and I know it's
+
+ align:start position:0%
+linked with education and I know it's
+ 
+
+ align:start position:0%
+linked with education and I know it's
+such a big thing to be like oh like this
+
+ align:start position:0%
+such a big thing to be like oh like this
+ 
+
+ align:start position:0%
+such a big thing to be like oh like this
+country has like the biggest amount like
+
+ align:start position:0%
+country has like the biggest amount like
+ 
+
+ align:start position:0%
+country has like the biggest amount like
+the highest SAT score on average or like
+
+ align:start position:0%
+the highest SAT score on average or like
+ 
+
+ align:start position:0%
+the highest SAT score on average or like
+this many people academy or something
+
+ align:start position:0%
+this many people academy or something
+ 
+
+ align:start position:0%
+this many people academy or something
+like that. So sometimes it really is
+
+ align:start position:0%
+like that. So sometimes it really is
+ 
+
+ align:start position:0%
+like that. So sometimes it really is
+just like governments competing against
+
+ align:start position:0%
+just like governments competing against
+ 
+
+ align:start position:0%
+just like governments competing against
+each other and trying to see like who's
+
+ align:start position:0%
+each other and trying to see like who's
+ 
+
+ align:start position:0%
+each other and trying to see like who's
+the best of the best. Great. And in the
+
+ align:start position:0%
+the best of the best. Great. And in the
+ 
+
+ align:start position:0%
+the best of the best. Great. And in the
+United States when we talk about
+
+ align:start position:0%
+United States when we talk about
+ 
+
+ align:start position:0%
+United States when we talk about
+government actors, what are all the
+
+ align:start position:0%
+government actors, what are all the
+ 
+
+ align:start position:0%
+government actors, what are all the
+different possible government actors we
+
+ align:start position:0%
+different possible government actors we
+ 
+
+ align:start position:0%
+different possible government actors we
+might be thinking about?
+
+ align:start position:0%
+might be thinking about?
+ 
+
+ align:start position:0%
+might be thinking about?
+Education. So there's a US Department of
+
+ align:start position:0%
+Education. So there's a US Department of
+ 
+
+ align:start position:0%
+Education. So there's a US Department of
+Education. Who else is there?
+
+ align:start position:0%
+Education. Who else is there?
+ 
+
+ align:start position:0%
+Education. Who else is there?
+So local boards of education. So there's
+
+ align:start position:0%
+So local boards of education. So there's
+ 
+
+ align:start position:0%
+So local boards of education. So there's
+local boards of education. So a very un
+
+ align:start position:0%
+local boards of education. So a very un
+ 
+
+ align:start position:0%
+local boards of education. So a very un
+unusual thing about the United States
+
+ align:start position:0%
+unusual thing about the United States
+ 
+
+ align:start position:0%
+unusual thing about the United States
+Department of Education is it is or the
+
+ align:start position:0%
+Department of Education is it is or the
+ 
+
+ align:start position:0%
+Department of Education is it is or the
+United States education system is it's
+
+ align:start position:0%
+United States education system is it's
+ 
+
+ align:start position:0%
+United States education system is it's
+extremely decentralized. There are
+
+ align:start position:0%
+extremely decentralized. There are
+ 
+
+ align:start position:0%
+extremely decentralized. There are
+130,000 schools and there are 13,000
+
+ align:start position:0%
+130,000 schools and there are 13,000
+ 
+
+ align:start position:0%
+130,000 schools and there are 13,000
+school districts. The modal elected
+
+ align:start position:0%
+school districts. The modal elected
+ 
+
+ align:start position:0%
+school districts. The modal elected
+official in the United States is a
+
+ align:start position:0%
+official in the United States is a
+ 
+
+ align:start position:0%
+official in the United States is a
+schoolboard member. There are more if if
+
+ align:start position:0%
+schoolboard member. There are more if if
+ 
+
+ align:start position:0%
+schoolboard member. There are more if if
+you are if you're an elected official in
+
+ align:start position:0%
+you are if you're an elected official in
+ 
+
+ align:start position:0%
+you are if you're an elected official in
+the United States, the thing you are
+
+ align:start position:0%
+the United States, the thing you are
+ 
+
+ align:start position:0%
+the United States, the thing you are
+most likely to be is a schoolboard
+
+ align:start position:0%
+most likely to be is a schoolboard
+ 
+
+ align:start position:0%
+most likely to be is a schoolboard
+member. Um and you know um schoolboard
+
+ align:start position:0%
+member. Um and you know um schoolboard
+ 
+
+ align:start position:0%
+member. Um and you know um schoolboard
+members are interesting stakeholders.
+
+ align:start position:0%
+members are interesting stakeholders.
+ 
+
+ align:start position:0%
+members are interesting stakeholders.
+They are um well and they range from
+
+ align:start position:0%
+They are um well and they range from
+ 
+
+ align:start position:0%
+They are um well and they range from
+community to communities. In lots of
+
+ align:start position:0%
+community to communities. In lots of
+ 
+
+ align:start position:0%
+community to communities. In lots of
+communities, they're just like a
+
+ align:start position:0%
+communities, they're just like a
+ 
+
+ align:start position:0%
+communities, they're just like a
+community member who's particularly
+
+ align:start position:0%
+community member who's particularly
+ 
+
+ align:start position:0%
+community member who's particularly
+interested in education. Um but there
+
+ align:start position:0%
+interested in education. Um but there
+ 
+
+ align:start position:0%
+interested in education. Um but there
+are also um people who are looking to um
+
+ align:start position:0%
+are also um people who are looking to um
+ 
+
+ align:start position:0%
+are also um people who are looking to um
+you know, it's an entry point for people
+
+ align:start position:0%
+you know, it's an entry point for people
+ 
+
+ align:start position:0%
+you know, it's an entry point for people
+who are interested in political careers.
+
+ align:start position:0%
+who are interested in political careers.
+ 
+
+ align:start position:0%
+who are interested in political careers.
+Lots of people who you are schoolboard
+
+ align:start position:0%
+Lots of people who you are schoolboard
+ 
+
+ align:start position:0%
+Lots of people who you are schoolboard
+members go to be on state reps and other
+
+ align:start position:0%
+members go to be on state reps and other
+ 
+
+ align:start position:0%
+members go to be on state reps and other
+kinds of things like that. This is a
+
+ align:start position:0%
+kinds of things like that. This is a
+ 
+
+ align:start position:0%
+kinds of things like that. This is a
+particularly um sort of fakened moment
+
+ align:start position:0%
+particularly um sort of fakened moment
+ 
+
+ align:start position:0%
+particularly um sort of fakened moment
+for people who are politically who are
+
+ align:start position:0%
+for people who are politically who are
+ 
+
+ align:start position:0%
+for people who are politically who are
+who are politically ambitious to pursue
+
+ align:start position:0%
+who are politically ambitious to pursue
+ 
+
+ align:start position:0%
+who are politically ambitious to pursue
+those ambitious uh through the school
+
+ align:start position:0%
+those ambitious uh through the school
+ 
+
+ align:start position:0%
+those ambitious uh through the school
+system. Um especially uh in the American
+
+ align:start position:0%
+system. Um especially uh in the American
+ 
+
+ align:start position:0%
+system. Um especially uh in the American
+right um where where reform of schools
+
+ align:start position:0%
+right um where where reform of schools
+ 
+
+ align:start position:0%
+right um where where reform of schools
+has become like a way to get kind of
+
+ align:start position:0%
+has become like a way to get kind of
+ 
+
+ align:start position:0%
+has become like a way to get kind of
+attention within the political party and
+
+ align:start position:0%
+attention within the political party and
+ 
+
+ align:start position:0%
+attention within the political party and
+things like that. Um, and uh, and yeah,
+
+ align:start position:0%
+things like that. Um, and uh, and yeah,
+ 
+
+ align:start position:0%
+things like that. Um, and uh, and yeah,
+there's all there's all kinds of towns
+
+ align:start position:0%
+there's all there's all kinds of towns
+ 
+
+ align:start position:0%
+there's all there's all kinds of towns
+across the country where, you know, and
+
+ align:start position:0%
+across the country where, you know, and
+ 
+
+ align:start position:0%
+across the country where, you know, and
+I think you get some of this is like
+
+ align:start position:0%
+I think you get some of this is like
+ 
+
+ align:start position:0%
+I think you get some of this is like
+some school board is like, you know,
+
+ align:start position:0%
+some school board is like, you know,
+ 
+
+ align:start position:0%
+some school board is like, you know,
+what would be really great is film
+
+ align:start position:0%
+what would be really great is film
+ 
+
+ align:start position:0%
+what would be really great is film
+strips. Like, let's go big on film
+
+ align:start position:0%
+strips. Like, let's go big on film
+ 
+
+ align:start position:0%
+strips. Like, let's go big on film
+strips. Um, you know, what would be
+
+ align:start position:0%
+strips. Um, you know, what would be
+ 
+
+ align:start position:0%
+strips. Um, you know, what would be
+really great is like closed circuit
+
+ align:start position:0%
+really great is like closed circuit
+ 
+
+ align:start position:0%
+really great is like closed circuit
+television. Um, wouldn't that be a
+
+ align:start position:0%
+television. Um, wouldn't that be a
+ 
+
+ align:start position:0%
+television. Um, wouldn't that be a
+useful thing to have? You know, and so
+
+ align:start position:0%
+useful thing to have? You know, and so
+ 
+
+ align:start position:0%
+useful thing to have? You know, and so
+it's it's not even like it's not the
+
+ align:start position:0%
+it's it's not even like it's not the
+ 
+
+ align:start position:0%
+it's it's not even like it's not the
+teachers, it's not the superintendent,
+
+ align:start position:0%
+teachers, it's not the superintendent,
+ 
+
+ align:start position:0%
+teachers, it's not the superintendent,
+it's not the people who are sort of in
+
+ align:start position:0%
+it's not the people who are sort of in
+ 
+
+ align:start position:0%
+it's not the people who are sort of in
+the schools, it's like some community
+
+ align:start position:0%
+the schools, it's like some community
+ 
+
+ align:start position:0%
+the schools, it's like some community
+members who are like, "Let's do it."
+
+ align:start position:0%
+members who are like, "Let's do it."
+ 
+
+ align:start position:0%
+members who are like, "Let's do it."
+um uh you know I in uh in the United
+
+ align:start position:0%
+um uh you know I in uh in the United
+ 
+
+ align:start position:0%
+um uh you know I in uh in the United
+States today there probably two versions
+
+ align:start position:0%
+States today there probably two versions
+ 
+
+ align:start position:0%
+States today there probably two versions
+of that is there are definitely school
+
+ align:start position:0%
+of that is there are definitely school
+ 
+
+ align:start position:0%
+of that is there are definitely school
+boards whose identity is sort of shaped
+
+ align:start position:0%
+boards whose identity is sort of shaped
+ 
+
+ align:start position:0%
+boards whose identity is sort of shaped
+around like being a cutting edge school
+
+ align:start position:0%
+around like being a cutting edge school
+ 
+
+ align:start position:0%
+around like being a cutting edge school
+like in a bunch of the affluent suburban
+
+ align:start position:0%
+like in a bunch of the affluent suburban
+ 
+
+ align:start position:0%
+like in a bunch of the affluent suburban
+towns around Boston you know like Wells
+
+ align:start position:0%
+towns around Boston you know like Wells
+ 
+
+ align:start position:0%
+towns around Boston you know like Wells
+Lee Newton like they want to be thought
+
+ align:start position:0%
+Lee Newton like they want to be thought
+ 
+
+ align:start position:0%
+Lee Newton like they want to be thought
+of as having like really great cutting
+
+ align:start position:0%
+of as having like really great cutting
+ 
+
+ align:start position:0%
+of as having like really great cutting
+edge forward thinking schools you know
+
+ align:start position:0%
+edge forward thinking schools you know
+ 
+
+ align:start position:0%
+edge forward thinking schools you know
+Newton spent $200 million or something
+
+ align:start position:0%
+Newton spent $200 million or something
+ 
+
+ align:start position:0%
+Newton spent $200 million or something
+like that on the last high school that
+
+ align:start position:0%
+like that on the last high school that
+ 
+
+ align:start position:0%
+like that on the last high school that
+they built um and so it can be you know
+
+ align:start position:0%
+they built um and so it can be you know
+ 
+
+ align:start position:0%
+they built um and so it can be you know
+a way they become a schoolboard member
+
+ align:start position:0%
+a way they become a schoolboard member
+ 
+
+ align:start position:0%
+a way they become a schoolboard member
+is like I'm going to help the school
+
+ align:start position:0%
+is like I'm going to help the school
+ 
+
+ align:start position:0%
+is like I'm going to help the school
+system modernize and embrace technology
+
+ align:start position:0%
+system modernize and embrace technology
+ 
+
+ align:start position:0%
+system modernize and embrace technology
+and things like that. There can also be
+
+ align:start position:0%
+and things like that. There can also be
+ 
+
+ align:start position:0%
+and things like that. There can also be
+the opposite. There can also be people
+
+ align:start position:0%
+the opposite. There can also be people
+ 
+
+ align:start position:0%
+the opposite. There can also be people
+who come in um the most common is like
+
+ align:start position:0%
+who come in um the most common is like
+ 
+
+ align:start position:0%
+who come in um the most common is like
+people who work for the technology
+
+ align:start position:0%
+people who work for the technology
+ 
+
+ align:start position:0%
+people who work for the technology
+industry who are like you have no idea
+
+ align:start position:0%
+industry who are like you have no idea
+ 
+
+ align:start position:0%
+industry who are like you have no idea
+how much surveillance is built into this
+
+ align:start position:0%
+how much surveillance is built into this
+ 
+
+ align:start position:0%
+how much surveillance is built into this
+technology. Um all the time when I talk
+
+ align:start position:0%
+technology. Um all the time when I talk
+ 
+
+ align:start position:0%
+technology. Um all the time when I talk
+to you know principles or
+
+ align:start position:0%
+to you know principles or
+ 
+
+ align:start position:0%
+to you know principles or
+superintendents who are being like we're
+
+ align:start position:0%
+superintendents who are being like we're
+ 
+
+ align:start position:0%
+superintendents who are being like we're
+kind of having a hard time you know
+
+ align:start position:0%
+kind of having a hard time you know
+ 
+
+ align:start position:0%
+kind of having a hard time you know
+helping parents understand why these
+
+ align:start position:0%
+helping parents understand why these
+ 
+
+ align:start position:0%
+helping parents understand why these
+things would be useful. It's like
+
+ align:start position:0%
+things would be useful. It's like
+ 
+
+ align:start position:0%
+things would be useful. It's like
+someone who works for Google or
+
+ align:start position:0%
+someone who works for Google or
+ 
+
+ align:start position:0%
+someone who works for Google or
+Microsoft or something like that, you
+
+ align:start position:0%
+Microsoft or something like that, you
+ 
+
+ align:start position:0%
+Microsoft or something like that, you
+know, who like who knows the
+
+ align:start position:0%
+know, who like who knows the
+ 
+
+ align:start position:0%
+know, who like who knows the
+surveillance capacity of these tools and
+
+ align:start position:0%
+surveillance capacity of these tools and
+ 
+
+ align:start position:0%
+surveillance capacity of these tools and
+is concerned about it. Um, yeah, I just
+
+ align:start position:0%
+is concerned about it. Um, yeah, I just
+ 
+
+ align:start position:0%
+is concerned about it. Um, yeah, I just
+kind of like an anecdote that I used to
+
+ align:start position:0%
+kind of like an anecdote that I used to
+ 
+
+ align:start position:0%
+kind of like an anecdote that I used to
+work in edtech and educational
+
+ align:start position:0%
+work in edtech and educational
+ 
+
+ align:start position:0%
+work in edtech and educational
+publishing and I worked on mostly
+
+ align:start position:0%
+publishing and I worked on mostly
+ 
+
+ align:start position:0%
+publishing and I worked on mostly
+products for the state of Florida and
+
+ align:start position:0%
+products for the state of Florida and
+ 
+
+ align:start position:0%
+products for the state of Florida and
+like really showed how much power some
+
+ align:start position:0%
+like really showed how much power some
+ 
+
+ align:start position:0%
+like really showed how much power some
+of these districts have like the because
+
+ align:start position:0%
+of these districts have like the because
+ 
+
+ align:start position:0%
+of these districts have like the because
+the school board would make a decision
+
+ align:start position:0%
+the school board would make a decision
+ 
+
+ align:start position:0%
+the school board would make a decision
+like every several times or one or two
+
+ align:start position:0%
+like every several times or one or two
+ 
+
+ align:start position:0%
+like every several times or one or two
+districts in Florida would some say they
+
+ align:start position:0%
+districts in Florida would some say they
+ 
+
+ align:start position:0%
+districts in Florida would some say they
+need something and that would change the
+
+ align:start position:0%
+need something and that would change the
+ 
+
+ align:start position:0%
+need something and that would change the
+entire road map for a product that's
+
+ align:start position:0%
+entire road map for a product that's
+ 
+
+ align:start position:0%
+entire road map for a product that's
+used nationally. So it's like you have a
+
+ align:start position:0%
+used nationally. So it's like you have a
+ 
+
+ align:start position:0%
+used nationally. So it's like you have a
+couple people in Florida who are like we
+
+ align:start position:0%
+couple people in Florida who are like we
+ 
+
+ align:start position:0%
+couple people in Florida who are like we
+really need this thing and suddenly it's
+
+ align:start position:0%
+really need this thing and suddenly it's
+ 
+
+ align:start position:0%
+really need this thing and suddenly it's
+like kids in Arkansas are also are
+
+ align:start position:0%
+like kids in Arkansas are also are
+ 
+
+ align:start position:0%
+like kids in Arkansas are also are
+learning differently. So I would this is
+
+ align:start position:0%
+learning differently. So I would this is
+ 
+
+ align:start position:0%
+learning differently. So I would this is
+in this is definitely still true. It's
+
+ align:start position:0%
+in this is definitely still true. It's
+ 
+
+ align:start position:0%
+in this is definitely still true. It's
+breaking down a little bit because of
+
+ align:start position:0%
+breaking down a little bit because of
+ 
+
+ align:start position:0%
+breaking down a little bit because of
+the capacity for sort of a web
+
+ align:start position:0%
+the capacity for sort of a web
+ 
+
+ align:start position:0%
+the capacity for sort of a web
+publishing and custom publication but
+
+ align:start position:0%
+publishing and custom publication but
+ 
+
+ align:start position:0%
+publishing and custom publication but
+for a big chunk of what you might I
+
+ align:start position:0%
+for a big chunk of what you might I
+ 
+
+ align:start position:0%
+for a big chunk of what you might I
+don't know the latter third of the 20th
+
+ align:start position:0%
+don't know the latter third of the 20th
+ 
+
+ align:start position:0%
+don't know the latter third of the 20th
+century the first 10 years of the 21st
+
+ align:start position:0%
+century the first 10 years of the 21st
+ 
+
+ align:start position:0%
+century the first 10 years of the 21st
+century um basic you know like somebody
+
+ align:start position:0%
+century um basic you know like somebody
+ 
+
+ align:start position:0%
+century um basic you know like somebody
+publishers would publish a US history
+
+ align:start position:0%
+publishers would publish a US history
+ 
+
+ align:start position:0%
+publishers would publish a US history
+book um how do they decide what to make
+
+ align:start position:0%
+book um how do they decide what to make
+ 
+
+ align:start position:0%
+book um how do they decide what to make
+of a US history book um you say well
+
+ align:start position:0%
+of a US history book um you say well
+ 
+
+ align:start position:0%
+of a US history book um you say well
+like what are the most important states
+
+ align:start position:0%
+like what are the most important states
+ 
+
+ align:start position:0%
+like what are the most important states
+to sell this history book
+
+ align:start position:0%
+to sell this history book
+ 
+
+ align:start position:0%
+to sell this history book
+in Florida is one of them what are the
+
+ align:start position:0%
+in Florida is one of them what are the
+ 
+
+ align:start position:0%
+in Florida is one of them what are the
+other ones You can name them.
+
+ align:start position:0%
+other ones You can name them.
+ 
+
+ align:start position:0%
+other ones You can name them.
+California,
+
+ align:start position:0%
+California,
+ 
+
+ align:start position:0%
+California,
+Texas, New York, California, Texas, New
+
+ align:start position:0%
+Texas, New York, California, Texas, New
+ 
+
+ align:start position:0%
+Texas, New York, California, Texas, New
+York, Florida. Um those are like four of
+
+ align:start position:0%
+York, Florida. Um those are like four of
+ 
+
+ align:start position:0%
+York, Florida. Um those are like four of
+the most important states just by
+
+ align:start position:0%
+the most important states just by
+ 
+
+ align:start position:0%
+the most important states just by
+population. Um so now you got to think
+
+ align:start position:0%
+population. Um so now you got to think
+ 
+
+ align:start position:0%
+population. Um so now you got to think
+about like the the standards of th like
+
+ align:start position:0%
+about like the the standards of th like
+ 
+
+ align:start position:0%
+about like the the standards of th like
+the his every state has standards. The
+
+ align:start position:0%
+the his every state has standards. The
+ 
+
+ align:start position:0%
+the his every state has standards. The
+history standards of those four states
+
+ align:start position:0%
+history standards of those four states
+ 
+
+ align:start position:0%
+history standards of those four states
+are more important than the history
+
+ align:start position:0%
+are more important than the history
+ 
+
+ align:start position:0%
+are more important than the history
+standards of Maine and North Dakota. Um
+
+ align:start position:0%
+standards of Maine and North Dakota. Um
+ 
+
+ align:start position:0%
+standards of Maine and North Dakota. Um
+and as like political things come up
+
+ align:start position:0%
+and as like political things come up
+ 
+
+ align:start position:0%
+and as like political things come up
+around you know history is where this
+
+ align:start position:0%
+around you know history is where this
+ 
+
+ align:start position:0%
+around you know history is where this
+happens pretty frequently but it happens
+
+ align:start position:0%
+happens pretty frequently but it happens
+ 
+
+ align:start position:0%
+happens pretty frequently but it happens
+in math and reading and other things
+
+ align:start position:0%
+in math and reading and other things
+ 
+
+ align:start position:0%
+in math and reading and other things
+too. Um yeah actually I I used to do
+
+ align:start position:0%
+too. Um yeah actually I I used to do
+ 
+
+ align:start position:0%
+too. Um yeah actually I I used to do
+consulting for uh um uh history for
+
+ align:start position:0%
+consulting for uh um uh history for
+ 
+
+ align:start position:0%
+consulting for uh um uh history for
+publishers of history textbooks and once
+
+ align:start position:0%
+publishers of history textbooks and once
+ 
+
+ align:start position:0%
+publishers of history textbooks and once
+I saw the sort of matrix where it was
+
+ align:start position:0%
+I saw the sort of matrix where it was
+ 
+
+ align:start position:0%
+I saw the sort of matrix where it was
+like it was like all the possible topics
+
+ align:start position:0%
+like it was like all the possible topics
+ 
+
+ align:start position:0%
+like it was like all the possible topics
+along the the columns and all of the
+
+ align:start position:0%
+along the the columns and all of the
+ 
+
+ align:start position:0%
+along the the columns and all of the
+states along the rows and like x's of
+
+ align:start position:0%
+states along the rows and like x's of
+ 
+
+ align:start position:0%
+states along the rows and like x's of
+like where all the topics get t you know
+
+ align:start position:0%
+like where all the topics get t you know
+ 
+
+ align:start position:0%
+like where all the topics get t you know
+the I mean the other thing is for like
+
+ align:start position:0%
+the I mean the other thing is for like
+ 
+
+ align:start position:0%
+the I mean the other thing is for like
+there'll be a huge you know group of
+
+ align:start position:0%
+there'll be a huge you know group of
+ 
+
+ align:start position:0%
+there'll be a huge you know group of
+Polish immigrants that come to some
+
+ align:start position:0%
+Polish immigrants that come to some
+ 
+
+ align:start position:0%
+Polish immigrants that come to some
+state and like they won't see Polish
+
+ align:start position:0%
+state and like they won't see Polish
+ 
+
+ align:start position:0%
+state and like they won't see Polish
+people represented in their textbooks
+
+ align:start position:0%
+people represented in their textbooks
+ 
+
+ align:start position:0%
+people represented in their textbooks
+and so they'll be like we're, you know,
+
+ align:start position:0%
+and so they'll be like we're, you know,
+ 
+
+ align:start position:0%
+and so they'll be like we're, you know,
+we're only going to adopt books that
+
+ align:start position:0%
+we're only going to adopt books that
+ 
+
+ align:start position:0%
+we're only going to adopt books that
+like talk about the importance of Polish
+
+ align:start position:0%
+like talk about the importance of Polish
+ 
+
+ align:start position:0%
+like talk about the importance of Polish
+Americans in the history. You the
+
+ align:start position:0%
+Americans in the history. You the
+ 
+
+ align:start position:0%
+Americans in the history. You the
+publishing companies are like, "All
+
+ align:start position:0%
+publishing companies are like, "All
+ 
+
+ align:start position:0%
+publishing companies are like, "All
+right, add the Polish and then, you
+
+ align:start position:0%
+right, add the Polish and then, you
+ 
+
+ align:start position:0%
+right, add the Polish and then, you
+know, but then the Italians do it and
+
+ align:start position:0%
+know, but then the Italians do it and
+ 
+
+ align:start position:0%
+know, but then the Italians do it and
+the Cambodian do everybody else do it
+
+ align:start position:0%
+the Cambodian do everybody else do it
+ 
+
+ align:start position:0%
+the Cambodian do everybody else do it
+and the textbooks get, you know, that's
+
+ align:start position:0%
+and the textbooks get, you know, that's
+ 
+
+ align:start position:0%
+and the textbooks get, you know, that's
+why when you picked up your 800 pound um
+
+ align:start position:0%
+why when you picked up your 800 pound um
+ 
+
+ align:start position:0%
+why when you picked up your 800 pound um
+history textbook, it was full of like
+
+ align:start position:0%
+history textbook, it was full of like
+ 
+
+ align:start position:0%
+history textbook, it was full of like
+all these like weird little um bits and
+
+ align:start position:0%
+all these like weird little um bits and
+ 
+
+ align:start position:0%
+all these like weird little um bits and
+pieces and things like that. So yeah,
+
+ align:start position:0%
+pieces and things like that. So yeah,
+ 
+
+ align:start position:0%
+pieces and things like that. So yeah,
+these these state level I mean here's
+
+ align:start position:0%
+these these state level I mean here's
+ 
+
+ align:start position:0%
+these these state level I mean here's
+another like tiny feature of this but
+
+ align:start position:0%
+another like tiny feature of this but
+ 
+
+ align:start position:0%
+another like tiny feature of this but
+ends up being important. Um there are
+
+ align:start position:0%
+ends up being important. Um there are
+ 
+
+ align:start position:0%
+ends up being important. Um there are
+some states mostly in the south where
+
+ align:start position:0%
+some states mostly in the south where
+ 
+
+ align:start position:0%
+some states mostly in the south where
+material adoptions happen centrally or
+
+ align:start position:0%
+material adoptions happen centrally or
+ 
+
+ align:start position:0%
+material adoptions happen centrally or
+have some kind of centralized function.
+
+ align:start position:0%
+have some kind of centralized function.
+ 
+
+ align:start position:0%
+have some kind of centralized function.
+Um so Texas, Florida, they have state
+
+ align:start position:0%
+Um so Texas, Florida, they have state
+ 
+
+ align:start position:0%
+Um so Texas, Florida, they have state
+level boards that say you can only adopt
+
+ align:start position:0%
+level boards that say you can only adopt
+ 
+
+ align:start position:0%
+level boards that say you can only adopt
+books that pass these boards.
+
+ align:start position:0%
+books that pass these boards.
+ 
+
+ align:start position:0%
+books that pass these boards.
+Massachusetts is a huge local control
+
+ align:start position:0%
+Massachusetts is a huge local control
+ 
+
+ align:start position:0%
+Massachusetts is a huge local control
+state. Um the school districts in
+
+ align:start position:0%
+state. Um the school districts in
+ 
+
+ align:start position:0%
+state. Um the school districts in
+Massachusetts will go bonkers if the
+
+ align:start position:0%
+Massachusetts will go bonkers if the
+ 
+
+ align:start position:0%
+Massachusetts will go bonkers if the
+state tried to tell them which textbooks
+
+ align:start position:0%
+state tried to tell them which textbooks
+ 
+
+ align:start position:0%
+state tried to tell them which textbooks
+they could or could not use. You know,
+
+ align:start position:0%
+they could or could not use. You know,
+ 
+
+ align:start position:0%
+they could or could not use. You know,
+there'd be like another revolution. you
+
+ align:start position:0%
+there'd be like another revolution. you
+ 
+
+ align:start position:0%
+there'd be like another revolution. you
+know, one if buy land, two if buy um you
+
+ align:start position:0%
+know, one if buy land, two if buy um you
+ 
+
+ align:start position:0%
+know, one if buy land, two if buy um you
+know, C-class Mercedes or whatever it
+
+ align:start position:0%
+know, C-class Mercedes or whatever it
+ 
+
+ align:start position:0%
+know, C-class Mercedes or whatever it
+is. Um and uh they they just wouldn't
+
+ align:start position:0%
+is. Um and uh they they just wouldn't
+ 
+
+ align:start position:0%
+is. Um and uh they they just wouldn't
+allow it. But it means that those states
+
+ align:start position:0%
+allow it. But it means that those states
+ 
+
+ align:start position:0%
+allow it. But it means that those states
+that have this sort of centralized
+
+ align:start position:0%
+that have this sort of centralized
+ 
+
+ align:start position:0%
+that have this sort of centralized
+function actually end up having more
+
+ align:start position:0%
+function actually end up having more
+ 
+
+ align:start position:0%
+function actually end up having more
+influence over the publishers because
+
+ align:start position:0%
+influence over the publishers because
+ 
+
+ align:start position:0%
+influence over the publishers because
+they say, "Look, you want to sell a book
+
+ align:start position:0%
+they say, "Look, you want to sell a book
+ 
+
+ align:start position:0%
+they say, "Look, you want to sell a book
+here?" You know, and now it's not just a
+
+ align:start position:0%
+here?" You know, and now it's not just a
+ 
+
+ align:start position:0%
+here?" You know, and now it's not just a
+book, now it's a web program or things
+
+ align:start position:0%
+book, now it's a web program or things
+ 
+
+ align:start position:0%
+book, now it's a web program or things
+like that. Now, the thing that sort of
+
+ align:start position:0%
+like that. Now, the thing that sort of
+ 
+
+ align:start position:0%
+like that. Now, the thing that sort of
+like is breaking away some of that
+
+ align:start position:0%
+like is breaking away some of that
+ 
+
+ align:start position:0%
+like is breaking away some of that
+monopoly, although also causing kind of
+
+ align:start position:0%
+monopoly, although also causing kind of
+ 
+
+ align:start position:0%
+monopoly, although also causing kind of
+problems is, you know, states can say
+
+ align:start position:0%
+problems is, you know, states can say
+ 
+
+ align:start position:0%
+problems is, you know, states can say
+like, okay, we want to, you know, we're
+
+ align:start position:0%
+like, okay, we want to, you know, we're
+ 
+
+ align:start position:0%
+like, okay, we want to, you know, we're
+going to pass all these laws that b that
+
+ align:start position:0%
+going to pass all these laws that b that
+ 
+
+ align:start position:0%
+going to pass all these laws that b that
+have the effect of like way ramping down
+
+ align:start position:0%
+have the effect of like way ramping down
+ 
+
+ align:start position:0%
+have the effect of like way ramping down
+the teaching of black history. Um, and
+
+ align:start position:0%
+the teaching of black history. Um, and
+ 
+
+ align:start position:0%
+the teaching of black history. Um, and
+you know, publishers can be like, all
+
+ align:start position:0%
+you know, publishers can be like, all
+ 
+
+ align:start position:0%
+you know, publishers can be like, all
+right, well, your web version of that
+
+ align:start position:0%
+right, well, your web version of that
+ 
+
+ align:start position:0%
+right, well, your web version of that
+will delete this and this and this and
+
+ align:start position:0%
+will delete this and this and this and
+ 
+
+ align:start position:0%
+will delete this and this and this and
+this, but you know, over in New York or
+
+ align:start position:0%
+this, but you know, over in New York or
+ 
+
+ align:start position:0%
+this, but you know, over in New York or
+California and liberal states, you can
+
+ align:start position:0%
+California and liberal states, you can
+ 
+
+ align:start position:0%
+California and liberal states, you can
+have all that kind of stuff in there.
+
+ align:start position:0%
+have all that kind of stuff in there.
+ 
+
+ align:start position:0%
+have all that kind of stuff in there.
+Yeah. Khil. Yeah. And kind of like uh uh
+
+ align:start position:0%
+Yeah. Khil. Yeah. And kind of like uh uh
+ 
+
+ align:start position:0%
+Yeah. Khil. Yeah. And kind of like uh uh
+going off of that like the political
+
+ align:start position:0%
+going off of that like the political
+ 
+
+ align:start position:0%
+going off of that like the political
+platforms play a like a large role in
+
+ align:start position:0%
+platforms play a like a large role in
+ 
+
+ align:start position:0%
+platforms play a like a large role in
+most of these places in the US that's
+
+ align:start position:0%
+most of these places in the US that's
+ 
+
+ align:start position:0%
+most of these places in the US that's
+very like very much there but as an
+
+ align:start position:0%
+very like very much there but as an
+ 
+
+ align:start position:0%
+very like very much there but as an
+example from my own country like there
+
+ align:start position:0%
+example from my own country like there
+ 
+
+ align:start position:0%
+example from my own country like there
+at every public school they have like a
+
+ align:start position:0%
+at every public school they have like a
+ 
+
+ align:start position:0%
+at every public school they have like a
+speaker system like at the start of the
+
+ align:start position:0%
+speaker system like at the start of the
+ 
+
+ align:start position:0%
+speaker system like at the start of the
+school specifically because they want to
+
+ align:start position:0%
+school specifically because they want to
+ 
+
+ align:start position:0%
+school specifically because they want to
+play the national anthem. That's
+
+ align:start position:0%
+play the national anthem. That's
+ 
+
+ align:start position:0%
+play the national anthem. That's
+something they did really early. The
+
+ align:start position:0%
+something they did really early. The
+ 
+
+ align:start position:0%
+something they did really early. The
+kids have to uh to do it and to like oh
+
+ align:start position:0%
+kids have to uh to do it and to like oh
+ 
+
+ align:start position:0%
+kids have to uh to do it and to like oh
+there's so much like technology that
+
+ align:start position:0%
+there's so much like technology that
+ 
+
+ align:start position:0%
+there's so much like technology that
+just one thing why is this the only
+
+ align:start position:0%
+just one thing why is this the only
+ 
+
+ align:start position:0%
+just one thing why is this the only
+piece of there is like some kind of
+
+ align:start position:0%
+piece of there is like some kind of
+ 
+
+ align:start position:0%
+piece of there is like some kind of
+incentive they want to build with like
+
+ align:start position:0%
+incentive they want to build with like
+ 
+
+ align:start position:0%
+incentive they want to build with like
+you know kind of political motive. And
+
+ align:start position:0%
+you know kind of political motive. And
+ 
+
+ align:start position:0%
+you know kind of political motive. And
+then does does the does that broadcast
+
+ align:start position:0%
+then does does the does that broadcast
+ 
+
+ align:start position:0%
+then does does the does that broadcast
+system be used at other parts of the day
+
+ align:start position:0%
+system be used at other parts of the day
+ 
+
+ align:start position:0%
+system be used at other parts of the day
+as well or this only gets used at the
+
+ align:start position:0%
+as well or this only gets used at the
+ 
+
+ align:start position:0%
+as well or this only gets used at the
+start of the school where the national
+
+ align:start position:0%
+start of the school where the national
+ 
+
+ align:start position:0%
+start of the school where the national
+anthem have like some like some kids uh
+
+ align:start position:0%
+anthem have like some like some kids uh
+ 
+
+ align:start position:0%
+anthem have like some like some kids uh
+every like classroom does like a session
+
+ align:start position:0%
+every like classroom does like a session
+ 
+
+ align:start position:0%
+every like classroom does like a session
+where they just like do like some
+
+ align:start position:0%
+where they just like do like some
+ 
+
+ align:start position:0%
+where they just like do like some
+religious stuff uh some like Arabic
+
+ align:start position:0%
+religious stuff uh some like Arabic
+ 
+
+ align:start position:0%
+religious stuff uh some like Arabic
+poems some like fun facts and then just
+
+ align:start position:0%
+poems some like fun facts and then just
+ 
+
+ align:start position:0%
+poems some like fun facts and then just
+that but that's mostly just I I love
+
+ align:start position:0%
+that but that's mostly just I I love
+ 
+
+ align:start position:0%
+that but that's mostly just I I love
+that. I think that's a fabulous example.
+
+ align:start position:0%
+that. I think that's a fabulous example.
+ 
+
+ align:start position:0%
+that. I think that's a fabulous example.
+So, so the the whatever the state
+
+ align:start position:0%
+So, so the the whatever the state
+ 
+
+ align:start position:0%
+So, so the the whatever the state
+government is like the state is in the
+
+ align:start position:0%
+government is like the state is in the
+ 
+
+ align:start position:0%
+government is like the state is in the
+nation the nation state government um
+
+ align:start position:0%
+nation the nation state government um
+ 
+
+ align:start position:0%
+nation the nation state government um
+says every school must broadcast the
+
+ align:start position:0%
+says every school must broadcast the
+ 
+
+ align:start position:0%
+says every school must broadcast the
+national anthem every day. Um every
+
+ align:start position:0%
+national anthem every day. Um every
+ 
+
+ align:start position:0%
+national anthem every day. Um every
+single school in the country then has to
+
+ align:start position:0%
+single school in the country then has to
+ 
+
+ align:start position:0%
+single school in the country then has to
+build a technology infrastructure that
+
+ align:start position:0%
+build a technology infrastructure that
+ 
+
+ align:start position:0%
+build a technology infrastructure that
+allows that to happen and then once that
+
+ align:start position:0%
+allows that to happen and then once that
+ 
+
+ align:start position:0%
+allows that to happen and then once that
+technology infrastructure is there it
+
+ align:start position:0%
+technology infrastructure is there it
+ 
+
+ align:start position:0%
+technology infrastructure is there it
+can be used in other kinds of ways as
+
+ align:start position:0%
+can be used in other kinds of ways as
+ 
+
+ align:start position:0%
+can be used in other kinds of ways as
+well or not used or other kinds of
+
+ align:start position:0%
+well or not used or other kinds of
+ 
+
+ align:start position:0%
+well or not used or other kinds of
+things like that. Um you can find
+
+ align:start position:0%
+things like that. Um you can find
+ 
+
+ align:start position:0%
+things like that. Um you can find
+national examples of this in other kinds
+
+ align:start position:0%
+national examples of this in other kinds
+ 
+
+ align:start position:0%
+national examples of this in other kinds
+of ways. You know, one of the most
+
+ align:start position:0%
+of ways. You know, one of the most
+ 
+
+ align:start position:0%
+of ways. You know, one of the most
+interesting countries right now um for
+
+ align:start position:0%
+interesting countries right now um for
+ 
+
+ align:start position:0%
+interesting countries right now um for
+education policy makers to watch is
+
+ align:start position:0%
+education policy makers to watch is
+ 
+
+ align:start position:0%
+education policy makers to watch is
+Estonia. Um about every decade, like
+
+ align:start position:0%
+Estonia. Um about every decade, like
+ 
+
+ align:start position:0%
+Estonia. Um about every decade, like
+some country that people aren't really
+
+ align:start position:0%
+some country that people aren't really
+ 
+
+ align:start position:0%
+some country that people aren't really
+paying attention to um gets really good
+
+ align:start position:0%
+paying attention to um gets really good
+ 
+
+ align:start position:0%
+paying attention to um gets really good
+international test scores. Um so
+
+ align:start position:0%
+international test scores. Um so
+ 
+
+ align:start position:0%
+international test scores. Um so
+Singapore was it for a while, Finland
+
+ align:start position:0%
+Singapore was it for a while, Finland
+ 
+
+ align:start position:0%
+Singapore was it for a while, Finland
+was it for a while, people are obsessed
+
+ align:start position:0%
+was it for a while, people are obsessed
+ 
+
+ align:start position:0%
+was it for a while, people are obsessed
+with Finland for a while, and Estonia is
+
+ align:start position:0%
+with Finland for a while, and Estonia is
+ 
+
+ align:start position:0%
+with Finland for a while, and Estonia is
+kind of last like who are you people and
+
+ align:start position:0%
+kind of last like who are you people and
+ 
+
+ align:start position:0%
+kind of last like who are you people and
+why like why are you so good at reading?
+
+ align:start position:0%
+why like why are you so good at reading?
+ 
+
+ align:start position:0%
+why like why are you so good at reading?
+Um and uh Estonia is very famous for it
+
+ align:start position:0%
+Um and uh Estonia is very famous for it
+ 
+
+ align:start position:0%
+Um and uh Estonia is very famous for it
+sometimes it's called Estonia. um their
+
+ align:start position:0%
+sometimes it's called Estonia. um their
+ 
+
+ align:start position:0%
+sometimes it's called Estonia. um their
+government has really embraced the
+
+ align:start position:0%
+government has really embraced the
+ 
+
+ align:start position:0%
+government has really embraced the
+internet um in a very centralized kind
+
+ align:start position:0%
+internet um in a very centralized kind
+ 
+
+ align:start position:0%
+internet um in a very centralized kind
+of way. And so people are trying looking
+
+ align:start position:0%
+of way. And so people are trying looking
+ 
+
+ align:start position:0%
+of way. And so people are trying looking
+at and thinking about how education
+
+ align:start position:0%
+at and thinking about how education
+ 
+
+ align:start position:0%
+at and thinking about how education
+technologies are adopted in Estonia and
+
+ align:start position:0%
+technologies are adopted in Estonia and
+ 
+
+ align:start position:0%
+technologies are adopted in Estonia and
+other kinds of ways. But it but it
+
+ align:start position:0%
+other kinds of ways. But it but it
+ 
+
+ align:start position:0%
+other kinds of ways. But it but it
+wasn't a policy that was just for the
+
+ align:start position:0%
+wasn't a policy that was just for the
+ 
+
+ align:start position:0%
+wasn't a policy that was just for the
+schools. They were like we're going to
+
+ align:start position:0%
+schools. They were like we're going to
+ 
+
+ align:start position:0%
+schools. They were like we're going to
+put Estonia on the map by having really
+
+ align:start position:0%
+put Estonia on the map by having really
+ 
+
+ align:start position:0%
+put Estonia on the map by having really
+good digital government services. And
+
+ align:start position:0%
+good digital government services. And
+ 
+
+ align:start position:0%
+good digital government services. And
+that national policy decision ends up
+
+ align:start position:0%
+that national policy decision ends up
+ 
+
+ align:start position:0%
+that national policy decision ends up
+affecting the learning experiences of
+
+ align:start position:0%
+affecting the learning experiences of
+ 
+
+ align:start position:0%
+affecting the learning experiences of
+kids in schools in all kinds of places.
+
+ align:start position:0%
+kids in schools in all kinds of places.
+ 
+
+ align:start position:0%
+kids in schools in all kinds of places.
+Yeah, that's a great example.
+
+ align:start position:0%
+Yeah, that's a great example.
+ 
+
+ align:start position:0%
+Yeah, that's a great example.
+um students what are what are what are
+
+ align:start position:0%
+um students what are what are what are
+ 
+
+ align:start position:0%
+um students what are what are what are
+the interests and and and disincentives
+
+ align:start position:0%
+the interests and and and disincentives
+ 
+
+ align:start position:0%
+the interests and and and disincentives
+of students.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's cool. It's a new piece of
+
+ align:start position:0%
+It's cool. It's a new piece of
+ 
+
+ align:start position:0%
+It's cool. It's a new piece of
+technology. Okay. So, almost all of us
+
+ align:start position:0%
+technology. Okay. So, almost all of us
+ 
+
+ align:start position:0%
+technology. Okay. So, almost all of us
+like novelty. Um that is one of the
+
+ align:start position:0%
+like novelty. Um that is one of the
+ 
+
+ align:start position:0%
+like novelty. Um that is one of the
+advantages that technology has. One of
+
+ align:start position:0%
+advantages that technology has. One of
+ 
+
+ align:start position:0%
+advantages that technology has. One of
+the um uh although an amazing thing
+
+ align:start position:0%
+the um uh although an amazing thing
+ 
+
+ align:start position:0%
+the um uh although an amazing thing
+about novelty is how shockingly quickly
+
+ align:start position:0%
+about novelty is how shockingly quickly
+ 
+
+ align:start position:0%
+about novelty is how shockingly quickly
+it wears off. Um actually I was reading
+
+ align:start position:0%
+it wears off. Um actually I was reading
+ 
+
+ align:start position:0%
+it wears off. Um actually I was reading
+this on Reddit the other day. someone a
+
+ align:start position:0%
+this on Reddit the other day. someone a
+ 
+
+ align:start position:0%
+this on Reddit the other day. someone a
+teacher was being like like I don't like
+
+ align:start position:0%
+teacher was being like like I don't like
+ 
+
+ align:start position:0%
+teacher was being like like I don't like
+I brought a Nintendo Switch into class
+
+ align:start position:0%
+I brought a Nintendo Switch into class
+ 
+
+ align:start position:0%
+I brought a Nintendo Switch into class
+so we could play these mathematical
+
+ align:start position:0%
+so we could play these mathematical
+ 
+
+ align:start position:0%
+so we could play these mathematical
+logic games and my students were like oh
+
+ align:start position:0%
+logic games and my students were like oh
+ 
+
+ align:start position:0%
+logic games and my students were like oh
+please miss can we just do worksheets
+
+ align:start position:0%
+please miss can we just do worksheets
+ 
+
+ align:start position:0%
+please miss can we just do worksheets
+and I was like fine do worksheets then
+
+ align:start position:0%
+and I was like fine do worksheets then
+ 
+
+ align:start position:0%
+and I was like fine do worksheets then
+um but you know they're like oh man you
+
+ align:start position:0%
+um but you know they're like oh man you
+ 
+
+ align:start position:0%
+um but you know they're like oh man you
+want you play some online game I don't
+
+ align:start position:0%
+want you play some online game I don't
+ 
+
+ align:start position:0%
+want you play some online game I don't
+want to play you know now there would
+
+ align:start position:0%
+want to play you know now there would
+ 
+
+ align:start position:0%
+want to play you know now there would
+have been some moment that this class
+
+ align:start position:0%
+have been some moment that this class
+ 
+
+ align:start position:0%
+have been some moment that this class
+would be like what we could play a
+
+ align:start position:0%
+would be like what we could play a
+ 
+
+ align:start position:0%
+would be like what we could play a
+computer game in class this is amazing
+
+ align:start position:0%
+computer game in class this is amazing
+ 
+
+ align:start position:0%
+computer game in class this is amazing
+um but that is you know um it's a sort
+
+ align:start position:0%
+um but that is you know um it's a sort
+ 
+
+ align:start position:0%
+um but that is you know um it's a sort
+of it's a it's an interesting feature of
+
+ align:start position:0%
+of it's a it's an interesting feature of
+ 
+
+ align:start position:0%
+of it's a it's an interesting feature of
+education technology adoption that like
+
+ align:start position:0%
+education technology adoption that like
+ 
+
+ align:start position:0%
+education technology adoption that like
+novelty can be extremely compelling for
+
+ align:start position:0%
+novelty can be extremely compelling for
+ 
+
+ align:start position:0%
+novelty can be extremely compelling for
+a short period of time and then wear off
+
+ align:start position:0%
+a short period of time and then wear off
+ 
+
+ align:start position:0%
+a short period of time and then wear off
+pretty quickly. Do you have any comment
+
+ align:start position:0%
+pretty quickly. Do you have any comment
+ 
+
+ align:start position:0%
+pretty quickly. Do you have any comment
+on like why students default is now back
+
+ align:start position:0%
+on like why students default is now back
+ 
+
+ align:start position:0%
+on like why students default is now back
+to that pen and paper like the way like
+
+ align:start position:0%
+to that pen and paper like the way like
+ 
+
+ align:start position:0%
+to that pen and paper like the way like
+because I mean people are always like
+
+ align:start position:0%
+because I mean people are always like
+ 
+
+ align:start position:0%
+because I mean people are always like
+education has been the same for decades
+
+ align:start position:0%
+education has been the same for decades
+ 
+
+ align:start position:0%
+education has been the same for decades
+and why does it always look this way
+
+ align:start position:0%
+and why does it always look this way
+ 
+
+ align:start position:0%
+and why does it always look this way
+even after we've reformed it like why is
+
+ align:start position:0%
+even after we've reformed it like why is
+ 
+
+ align:start position:0%
+even after we've reformed it like why is
+the default that pen and paper? Good. So
+
+ align:start position:0%
+the default that pen and paper? Good. So
+ 
+
+ align:start position:0%
+the default that pen and paper? Good. So
+what well let's just highlight an
+
+ align:start position:0%
+what well let's just highlight an
+ 
+
+ align:start position:0%
+what well let's just highlight an
+important thing that you observed um
+
+ align:start position:0%
+important thing that you observed um
+ 
+
+ align:start position:0%
+important thing that you observed um
+which we we were talking about over here
+
+ align:start position:0%
+which we we were talking about over here
+ 
+
+ align:start position:0%
+which we we were talking about over here
+too which is just schools are incredibly
+
+ align:start position:0%
+too which is just schools are incredibly
+ 
+
+ align:start position:0%
+too which is just schools are incredibly
+conservative institutions. Um why why
+
+ align:start position:0%
+conservative institutions. Um why why
+ 
+
+ align:start position:0%
+conservative institutions. Um why why
+why would that cons small C conser not
+
+ align:start position:0%
+why would that cons small C conser not
+ 
+
+ align:start position:0%
+why would that cons small C conser not
+rightwing some of them are but um small
+
+ align:start position:0%
+rightwing some of them are but um small
+ 
+
+ align:start position:0%
+rightwing some of them are but um small
+C conservative they do things the same
+
+ align:start position:0%
+C conservative they do things the same
+ 
+
+ align:start position:0%
+C conservative they do things the same
+way over and over again. Um what are
+
+ align:start position:0%
+way over and over again. Um what are
+ 
+
+ align:start position:0%
+way over and over again. Um what are
+some possible reasons for that? One is
+
+ align:start position:0%
+some possible reasons for that? One is
+ 
+
+ align:start position:0%
+some possible reasons for that? One is
+if you went and interviewed parents and
+
+ align:start position:0%
+if you went and interviewed parents and
+ 
+
+ align:start position:0%
+if you went and interviewed parents and
+said who are another stakeholder that a
+
+ align:start position:0%
+said who are another stakeholder that a
+ 
+
+ align:start position:0%
+said who are another stakeholder that a
+bunch of people brought up um how much
+
+ align:start position:0%
+bunch of people brought up um how much
+ 
+
+ align:start position:0%
+bunch of people brought up um how much
+do you want us experimenting with your
+
+ align:start position:0%
+do you want us experimenting with your
+ 
+
+ align:start position:0%
+do you want us experimenting with your
+children? Um the answer to that is going
+
+ align:start position:0%
+children? Um the answer to that is going
+ 
+
+ align:start position:0%
+children? Um the answer to that is going
+to be pretty low. Like the enthusiasm
+
+ align:start position:0%
+to be pretty low. Like the enthusiasm
+ 
+
+ align:start position:0%
+to be pretty low. Like the enthusiasm
+that people have for experimenting on
+
+ align:start position:0%
+that people have for experimenting on
+ 
+
+ align:start position:0%
+that people have for experimenting on
+children is low. Um second um everyone
+
+ align:start position:0%
+children is low. Um second um everyone
+ 
+
+ align:start position:0%
+children is low. Um second um everyone
+in the educational system who's an adult
+
+ align:start position:0%
+in the educational system who's an adult
+ 
+
+ align:start position:0%
+in the educational system who's an adult
+has what's been sometimes called the
+
+ align:start position:0%
+has what's been sometimes called the
+ 
+
+ align:start position:0%
+has what's been sometimes called the
+apprenticeship of observation. Um you
+
+ align:start position:0%
+apprenticeship of observation. Um you
+ 
+
+ align:start position:0%
+apprenticeship of observation. Um you
+all have been in school somewhere
+
+ align:start position:0%
+all have been in school somewhere
+ 
+
+ align:start position:0%
+all have been in school somewhere
+between like 13 and 18 years. Um and
+
+ align:start position:0%
+between like 13 and 18 years. Um and
+ 
+
+ align:start position:0%
+between like 13 and 18 years. Um and
+that shapes your experience. And so
+
+ align:start position:0%
+that shapes your experience. And so
+ 
+
+ align:start position:0%
+that shapes your experience. And so
+people who have roughly the same
+
+ align:start position:0%
+people who have roughly the same
+ 
+
+ align:start position:0%
+people who have roughly the same
+education level as you go into schools
+
+ align:start position:0%
+education level as you go into schools
+ 
+
+ align:start position:0%
+education level as you go into schools
+and become teachers and they bring that
+
+ align:start position:0%
+and become teachers and they bring that
+ 
+
+ align:start position:0%
+and become teachers and they bring that
+13, 18, 20 years of educational
+
+ align:start position:0%
+13, 18, 20 years of educational
+ 
+
+ align:start position:0%
+13, 18, 20 years of educational
+experience with them. Um, and that
+
+ align:start position:0%
+experience with them. Um, and that
+ 
+
+ align:start position:0%
+experience with them. Um, and that
+shapes the way you think schools should
+
+ align:start position:0%
+shapes the way you think schools should
+ 
+
+ align:start position:0%
+shapes the way you think schools should
+unfold. Um, parents can bring those
+
+ align:start position:0%
+unfold. Um, parents can bring those
+ 
+
+ align:start position:0%
+unfold. Um, parents can bring those
+expectations in. I was I will never
+
+ align:start position:0%
+expectations in. I was I will never
+ 
+
+ align:start position:0%
+expectations in. I was I will never
+forget this. I was once working I was
+
+ align:start position:0%
+forget this. I was once working I was
+ 
+
+ align:start position:0%
+forget this. I was once working I was
+conversing with a school in Utah that
+
+ align:start position:0%
+conversing with a school in Utah that
+ 
+
+ align:start position:0%
+conversing with a school in Utah that
+was trying to switch to openly licensed
+
+ align:start position:0%
+was trying to switch to openly licensed
+ 
+
+ align:start position:0%
+was trying to switch to openly licensed
+materials. It was pretty I don't know 15
+
+ align:start position:0%
+materials. It was pretty I don't know 15
+ 
+
+ align:start position:0%
+materials. It was pretty I don't know 15
+years ago, 18 years ago or something
+
+ align:start position:0%
+years ago, 18 years ago or something
+ 
+
+ align:start position:0%
+years ago, 18 years ago or something
+like that. They were trying to get away
+
+ align:start position:0%
+like that. They were trying to get away
+ 
+
+ align:start position:0%
+like that. They were trying to get away
+from textbooks and to have people use
+
+ align:start position:0%
+from textbooks and to have people use
+ 
+
+ align:start position:0%
+from textbooks and to have people use
+digital materials, particularly digital
+
+ align:start position:0%
+digital materials, particularly digital
+ 
+
+ align:start position:0%
+digital materials, particularly digital
+materials that their teachers could edit
+
+ align:start position:0%
+materials that their teachers could edit
+ 
+
+ align:start position:0%
+materials that their teachers could edit
+um so that they could make them, you
+
+ align:start position:0%
+um so that they could make them, you
+ 
+
+ align:start position:0%
+um so that they could make them, you
+know, tailor to their students and
+
+ align:start position:0%
+know, tailor to their students and
+ 
+
+ align:start position:0%
+know, tailor to their students and
+things like that. And they said and they
+
+ align:start position:0%
+things like that. And they said and they
+ 
+
+ align:start position:0%
+things like that. And they said and they
+said, "But they still kept textbooks in
+
+ align:start position:0%
+said, "But they still kept textbooks in
+ 
+
+ align:start position:0%
+said, "But they still kept textbooks in
+classroom." And you know, I can't tell
+
+ align:start position:0%
+classroom." And you know, I can't tell
+ 
+
+ align:start position:0%
+classroom." And you know, I can't tell
+you whether or not that's true, but he
+
+ align:start position:0%
+you whether or not that's true, but he
+ 
+
+ align:start position:0%
+you whether or not that's true, but he
+says, "The reason why we keep textbooks
+
+ align:start position:0%
+says, "The reason why we keep textbooks
+ 
+
+ align:start position:0%
+says, "The reason why we keep textbooks
+in classrooms is if there aren't
+
+ align:start position:0%
+in classrooms is if there aren't
+ 
+
+ align:start position:0%
+in classrooms is if there aren't
+textbooks in classrooms, parents will be
+
+ align:start position:0%
+textbooks in classrooms, parents will be
+ 
+
+ align:start position:0%
+textbooks in classrooms, parents will be
+upset." Um that like parent like parents
+
+ align:start position:0%
+upset." Um that like parent like parents
+ 
+
+ align:start position:0%
+upset." Um that like parent like parents
+when they go into a classroom expect to
+
+ align:start position:0%
+when they go into a classroom expect to
+ 
+
+ align:start position:0%
+when they go into a classroom expect to
+see textbooks there. Basically, it was
+
+ align:start position:0%
+see textbooks there. Basically, it was
+ 
+
+ align:start position:0%
+see textbooks there. Basically, it was
+cheaper to keep buying enough textbooks
+
+ align:start position:0%
+cheaper to keep buying enough textbooks
+ 
+
+ align:start position:0%
+cheaper to keep buying enough textbooks
+to be in all of the classrooms than it
+
+ align:start position:0%
+to be in all of the classrooms than it
+ 
+
+ align:start position:0%
+to be in all of the classrooms than it
+was to like hire administrators to
+
+ align:start position:0%
+was to like hire administrators to
+ 
+
+ align:start position:0%
+was to like hire administrators to
+explain to parents why there weren't
+
+ align:start position:0%
+explain to parents why there weren't
+ 
+
+ align:start position:0%
+explain to parents why there weren't
+textbooks in the classroom anymore. Um
+
+ align:start position:0%
+textbooks in the classroom anymore. Um
+ 
+
+ align:start position:0%
+textbooks in the classroom anymore. Um
+so all of these different stakeholders
+
+ align:start position:0%
+so all of these different stakeholders
+ 
+
+ align:start position:0%
+so all of these different stakeholders
+um this sort of conservative vision of
+
+ align:start position:0%
+um this sort of conservative vision of
+ 
+
+ align:start position:0%
+um this sort of conservative vision of
+education is kind of part of that. Um
+
+ align:start position:0%
+education is kind of part of that. Um
+ 
+
+ align:start position:0%
+education is kind of part of that. Um
+one possibility is that that's really
+
+ align:start position:0%
+one possibility is that that's really
+ 
+
+ align:start position:0%
+one possibility is that that's really
+bad. Um that there actually like way
+
+ align:start position:0%
+bad. Um that there actually like way
+ 
+
+ align:start position:0%
+bad. Um that there actually like way
+better ways of doing things that are out
+
+ align:start position:0%
+better ways of doing things that are out
+ 
+
+ align:start position:0%
+better ways of doing things that are out
+there and it's a bummer that we're so
+
+ align:start position:0%
+there and it's a bummer that we're so
+ 
+
+ align:start position:0%
+there and it's a bummer that we're so
+conservative and that's really holding
+
+ align:start position:0%
+conservative and that's really holding
+ 
+
+ align:start position:0%
+conservative and that's really holding
+us back. Um, another possibility is that
+
+ align:start position:0%
+us back. Um, another possibility is that
+ 
+
+ align:start position:0%
+us back. Um, another possibility is that
+the practices that exist in schools have
+
+ align:start position:0%
+the practices that exist in schools have
+ 
+
+ align:start position:0%
+the practices that exist in schools have
+been refined over decades and centuries
+
+ align:start position:0%
+been refined over decades and centuries
+ 
+
+ align:start position:0%
+been refined over decades and centuries
+and they are the way they are because
+
+ align:start position:0%
+and they are the way they are because
+ 
+
+ align:start position:0%
+and they are the way they are because
+they're pretty darn good. Um, that they
+
+ align:start position:0%
+they're pretty darn good. Um, that they
+ 
+
+ align:start position:0%
+they're pretty darn good. Um, that they
+that that we keep doing certain kinds of
+
+ align:start position:0%
+that that we keep doing certain kinds of
+ 
+
+ align:start position:0%
+that that we keep doing certain kinds of
+things because they work. Um, so you'll
+
+ align:start position:0%
+things because they work. Um, so you'll
+ 
+
+ align:start position:0%
+things because they work. Um, so you'll
+have to figure out for yourself as you
+
+ align:start position:0%
+have to figure out for yourself as you
+ 
+
+ align:start position:0%
+have to figure out for yourself as you
+know if you hear examples of students
+
+ align:start position:0%
+know if you hear examples of students
+ 
+
+ align:start position:0%
+know if you hear examples of students
+kind of adopting old practices, are they
+
+ align:start position:0%
+kind of adopting old practices, are they
+ 
+
+ align:start position:0%
+kind of adopting old practices, are they
+adopting old practices because they work
+
+ align:start position:0%
+adopting old practices because they work
+ 
+
+ align:start position:0%
+adopting old practices because they work
+really well and because they like them,
+
+ align:start position:0%
+really well and because they like them,
+ 
+
+ align:start position:0%
+really well and because they like them,
+because they're comfortable and
+
+ align:start position:0%
+because they're comfortable and
+ 
+
+ align:start position:0%
+because they're comfortable and
+familiar? Um there's an argument that
+
+ align:start position:0%
+familiar? Um there's an argument that
+ 
+
+ align:start position:0%
+familiar? Um there's an argument that
+particularly in our age where students
+
+ align:start position:0%
+particularly in our age where students
+ 
+
+ align:start position:0%
+particularly in our age where students
+are sort of fixated on grades and
+
+ align:start position:0%
+are sort of fixated on grades and
+ 
+
+ align:start position:0%
+are sort of fixated on grades and
+performance in a way that they might
+
+ align:start position:0%
+performance in a way that they might
+ 
+
+ align:start position:0%
+performance in a way that they might
+have not been in decades past because
+
+ align:start position:0%
+have not been in decades past because
+ 
+
+ align:start position:0%
+have not been in decades past because
+you know not not because kids are like
+
+ align:start position:0%
+you know not not because kids are like
+ 
+
+ align:start position:0%
+you know not not because kids are like
+more materialistic or something. It's
+
+ align:start position:0%
+more materialistic or something. It's
+ 
+
+ align:start position:0%
+more materialistic or something. It's
+because of economic uncertainty. Um
+
+ align:start position:0%
+because of economic uncertainty. Um
+ 
+
+ align:start position:0%
+because of economic uncertainty. Um
+because as the gap between wealthy and
+
+ align:start position:0%
+because as the gap between wealthy and
+ 
+
+ align:start position:0%
+because as the gap between wealthy and
+poor people widens and the stakes of
+
+ align:start position:0%
+poor people widens and the stakes of
+ 
+
+ align:start position:0%
+poor people widens and the stakes of
+education become higher people become
+
+ align:start position:0%
+education become higher people become
+ 
+
+ align:start position:0%
+education become higher people become
+more fixated on it. Um and so those kids
+
+ align:start position:0%
+more fixated on it. Um and so those kids
+ 
+
+ align:start position:0%
+more fixated on it. Um and so those kids
+who are sort of adopting familiar
+
+ align:start position:0%
+who are sort of adopting familiar
+ 
+
+ align:start position:0%
+who are sort of adopting familiar
+matters like do they really like the
+
+ align:start position:0%
+matters like do they really like the
+ 
+
+ align:start position:0%
+matters like do they really like the
+familiarity or do they know how to do
+
+ align:start position:0%
+familiarity or do they know how to do
+ 
+
+ align:start position:0%
+familiarity or do they know how to do
+well in the familiarity and things like
+
+ align:start position:0%
+well in the familiarity and things like
+ 
+
+ align:start position:0%
+well in the familiarity and things like
+that. But again, like all the, you know,
+
+ align:start position:0%
+that. But again, like all the, you know,
+ 
+
+ align:start position:0%
+that. But again, like all the, you know,
+keep tying all the things we were
+
+ align:start position:0%
+keep tying all the things we were
+ 
+
+ align:start position:0%
+keep tying all the things we were
+talking about back to the decision of
+
+ align:start position:0%
+talking about back to the decision of
+ 
+
+ align:start position:0%
+talking about back to the decision of
+educators trying to implement new
+
+ align:start position:0%
+educators trying to implement new
+ 
+
+ align:start position:0%
+educators trying to implement new
+technologies.
+
+ align:start position:0%
+technologies.
+ 
+
+ align:start position:0%
+technologies.
+Um, everyone in your system is going to
+
+ align:start position:0%
+Um, everyone in your system is going to
+ 
+
+ align:start position:0%
+Um, everyone in your system is going to
+have some kind of conservative impulse
+
+ align:start position:0%
+have some kind of conservative impulse
+ 
+
+ align:start position:0%
+have some kind of conservative impulse
+all the way down to students. That
+
+ align:start position:0%
+all the way down to students. That
+ 
+
+ align:start position:0%
+all the way down to students. That
+conservative impulse might be balanced
+
+ align:start position:0%
+conservative impulse might be balanced
+ 
+
+ align:start position:0%
+conservative impulse might be balanced
+by the uh novelty effect that we're
+
+ align:start position:0%
+by the uh novelty effect that we're
+ 
+
+ align:start position:0%
+by the uh novelty effect that we're
+talking about, but it's in there. So if
+
+ align:start position:0%
+talking about, but it's in there. So if
+ 
+
+ align:start position:0%
+talking about, but it's in there. So if
+you want a new technology to really be
+
+ align:start position:0%
+you want a new technology to really be
+ 
+
+ align:start position:0%
+you want a new technology to really be
+adapted in some kind of meaningful way,
+
+ align:start position:0%
+adapted in some kind of meaningful way,
+ 
+
+ align:start position:0%
+adapted in some kind of meaningful way,
+one strategy you can have is to have it
+
+ align:start position:0%
+one strategy you can have is to have it
+ 
+
+ align:start position:0%
+one strategy you can have is to have it
+align with existing practices. You could
+
+ align:start position:0%
+align with existing practices. You could
+ 
+
+ align:start position:0%
+align with existing practices. You could
+say let's take technologies that do the
+
+ align:start position:0%
+say let's take technologies that do the
+ 
+
+ align:start position:0%
+say let's take technologies that do the
+kinds of things that are already
+
+ align:start position:0%
+kinds of things that are already
+ 
+
+ align:start position:0%
+kinds of things that are already
+happening in schools. Like that will be
+
+ align:start position:0%
+happening in schools. Like that will be
+ 
+
+ align:start position:0%
+happening in schools. Like that will be
+less upsetting. That'll require less
+
+ align:start position:0%
+less upsetting. That'll require less
+ 
+
+ align:start position:0%
+less upsetting. That'll require less
+training. That'll require less upset. It
+
+ align:start position:0%
+training. That'll require less upset. It
+ 
+
+ align:start position:0%
+training. That'll require less upset. It
+probably also won't help that much. Um I
+
+ align:start position:0%
+probably also won't help that much. Um I
+ 
+
+ align:start position:0%
+probably also won't help that much. Um I
+mean the people selling the technologies
+
+ align:start position:0%
+mean the people selling the technologies
+ 
+
+ align:start position:0%
+mean the people selling the technologies
+won't say that. But if you're just like
+
+ align:start position:0%
+won't say that. But if you're just like
+ 
+
+ align:start position:0%
+won't say that. But if you're just like
+digitizing existing practices, how how
+
+ align:start position:0%
+digitizing existing practices, how how
+ 
+
+ align:start position:0%
+digitizing existing practices, how how
+likely are you to have substantial gains
+
+ align:start position:0%
+likely are you to have substantial gains
+ 
+
+ align:start position:0%
+likely are you to have substantial gains
+from digitizing existing practices? Or
+
+ align:start position:0%
+from digitizing existing practices? Or
+ 
+
+ align:start position:0%
+from digitizing existing practices? Or
+maybe you're like a big ambitious
+
+ align:start position:0%
+maybe you're like a big ambitious
+ 
+
+ align:start position:0%
+maybe you're like a big ambitious
+reformer. You say, "No, no, no. We could
+
+ align:start position:0%
+reformer. You say, "No, no, no. We could
+ 
+
+ align:start position:0%
+reformer. You say, "No, no, no. We could
+be doing so much better. We could go
+
+ align:start position:0%
+be doing so much better. We could go
+ 
+
+ align:start position:0%
+be doing so much better. We could go
+from 2% to 100% efficiency in schools.
+
+ align:start position:0%
+from 2% to 100% efficiency in schools.
+ 
+
+ align:start position:0%
+from 2% to 100% efficiency in schools.
+We just have to make big changes in our
+
+ align:start position:0%
+We just have to make big changes in our
+ 
+
+ align:start position:0%
+We just have to make big changes in our
+practice." Well, making big changes in
+
+ align:start position:0%
+practice." Well, making big changes in
+ 
+
+ align:start position:0%
+practice." Well, making big changes in
+practice requires convincing people to
+
+ align:start position:0%
+practice requires convincing people to
+ 
+
+ align:start position:0%
+practice requires convincing people to
+change all of these things. Um there was
+
+ align:start position:0%
+change all of these things. Um there was
+ 
+
+ align:start position:0%
+change all of these things. Um there was
+a I you know, I've read this book a
+
+ align:start position:0%
+a I you know, I've read this book a
+ 
+
+ align:start position:0%
+a I you know, I've read this book a
+zillion times now, but I was just
+
+ align:start position:0%
+zillion times now, but I was just
+ 
+
+ align:start position:0%
+zillion times now, but I was just
+revisiting um a line in here that I
+
+ align:start position:0%
+revisiting um a line in here that I
+ 
+
+ align:start position:0%
+revisiting um a line in here that I
+loved. Um it was uh he says something
+
+ align:start position:0%
+loved. Um it was uh he says something
+ 
+
+ align:start position:0%
+loved. Um it was uh he says something
+towards the end that were like
+
+ align:start position:0%
+towards the end that were like
+ 
+
+ align:start position:0%
+towards the end that were like
+um settings have plans for their
+
+ align:start position:0%
+um settings have plans for their
+ 
+
+ align:start position:0%
+um settings have plans for their
+inhabitants. Anybody remember that? He
+
+ align:start position:0%
+inhabitants. Anybody remember that? He
+ 
+
+ align:start position:0%
+inhabitants. Anybody remember that? He
+was he was talking about the physical
+
+ align:start position:0%
+was he was talking about the physical
+ 
+
+ align:start position:0%
+was he was talking about the physical
+layout of a classroom but but he was
+
+ align:start position:0%
+layout of a classroom but but he was
+ 
+
+ align:start position:0%
+layout of a classroom but but he was
+using a broader sociological principle.
+
+ align:start position:0%
+using a broader sociological principle.
+ 
+
+ align:start position:0%
+using a broader sociological principle.
+Settings have plans for their
+
+ align:start position:0%
+Settings have plans for their
+ 
+
+ align:start position:0%
+Settings have plans for their
+inhabitants. Um people interact in a
+
+ align:start position:0%
+inhabitants. Um people interact in a
+ 
+
+ align:start position:0%
+inhabitants. Um people interact in a
+space in a certain way because the
+
+ align:start position:0%
+space in a certain way because the
+ 
+
+ align:start position:0%
+space in a certain way because the
+physical space is laid out and built in
+
+ align:start position:0%
+physical space is laid out and built in
+ 
+
+ align:start position:0%
+physical space is laid out and built in
+that way. So I was talking with these
+
+ align:start position:0%
+that way. So I was talking with these
+ 
+
+ align:start position:0%
+that way. So I was talking with these
+guys about one of the problems that film
+
+ align:start position:0%
+guys about one of the problems that film
+ 
+
+ align:start position:0%
+guys about one of the problems that film
+strips have. To have a film strip in
+
+ align:start position:0%
+strips have. To have a film strip in
+ 
+
+ align:start position:0%
+strips have. To have a film strip in
+your classroom, you have to take a giant
+
+ align:start position:0%
+your classroom, you have to take a giant
+ 
+
+ align:start position:0%
+your classroom, you have to take a giant
+projector on wheels and you have to roll
+
+ align:start position:0%
+projector on wheels and you have to roll
+ 
+
+ align:start position:0%
+projector on wheels and you have to roll
+it into the space. There would have been
+
+ align:start position:0%
+it into the space. There would have been
+ 
+
+ align:start position:0%
+it into the space. There would have been
+some classrooms, you know, filled with,
+
+ align:start position:0%
+some classrooms, you know, filled with,
+ 
+
+ align:start position:0%
+some classrooms, you know, filled with,
+you know, early 20th century, you know,
+
+ align:start position:0%
+you know, early 20th century, you know,
+ 
+
+ align:start position:0%
+you know, early 20th century, you know,
+urban schools with tons of immigrants
+
+ align:start position:0%
+urban schools with tons of immigrants
+ 
+
+ align:start position:0%
+urban schools with tons of immigrants
+who are pouring in on America's shores
+
+ align:start position:0%
+who are pouring in on America's shores
+ 
+
+ align:start position:0%
+who are pouring in on America's shores
+that don't have room in their classroom
+
+ align:start position:0%
+that don't have room in their classroom
+ 
+
+ align:start position:0%
+that don't have room in their classroom
+for a big thing. Um, the other thing
+
+ align:start position:0%
+for a big thing. Um, the other thing
+ 
+
+ align:start position:0%
+for a big thing. Um, the other thing
+that film strips had that was a huge
+
+ align:start position:0%
+that film strips had that was a huge
+ 
+
+ align:start position:0%
+that film strips had that was a huge
+pain is these giant film reels. You
+
+ align:start position:0%
+pain is these giant film reels. You
+ 
+
+ align:start position:0%
+pain is these giant film reels. You
+know, the early film reels were really,
+
+ align:start position:0%
+know, the early film reels were really,
+ 
+
+ align:start position:0%
+know, the early film reels were really,
+really big. Where are you going to put
+
+ align:start position:0%
+really big. Where are you going to put
+ 
+
+ align:start position:0%
+really big. Where are you going to put
+these things? You know, your town did
+
+ align:start position:0%
+these things? You know, your town did
+ 
+
+ align:start position:0%
+these things? You know, your town did
+not build a building um that that had
+
+ align:start position:0%
+not build a building um that that had
+ 
+
+ align:start position:0%
+not build a building um that that had
+like, you know, an archival film studio
+
+ align:start position:0%
+like, you know, an archival film studio
+ 
+
+ align:start position:0%
+like, you know, an archival film studio
+storage unit attached to it. Um let's
+
+ align:start position:0%
+storage unit attached to it. Um let's
+ 
+
+ align:start position:0%
+storage unit attached to it. Um let's
+say you have a big school and there are
+
+ align:start position:0%
+say you have a big school and there are
+ 
+
+ align:start position:0%
+say you have a big school and there are
+four first grade classes and you want to
+
+ align:start position:0%
+four first grade classes and you want to
+ 
+
+ align:start position:0%
+four first grade classes and you want to
+buy a film strip for all four of those
+
+ align:start position:0%
+buy a film strip for all four of those
+ 
+
+ align:start position:0%
+buy a film strip for all four of those
+first like are you going to build are
+
+ align:start position:0%
+first like are you going to build are
+ 
+
+ align:start position:0%
+first like are you going to build are
+you going to buy four copies of the same
+
+ align:start position:0%
+you going to buy four copies of the same
+ 
+
+ align:start position:0%
+you going to buy four copies of the same
+film strip? Like is each classroom going
+
+ align:start position:0%
+film strip? Like is each classroom going
+ 
+
+ align:start position:0%
+film strip? Like is each classroom going
+to have its own film library? If it has
+
+ align:start position:0%
+to have its own film library? If it has
+ 
+
+ align:start position:0%
+to have its own film library? If it has
+some centralized library, you have to
+
+ align:start position:0%
+some centralized library, you have to
+ 
+
+ align:start position:0%
+some centralized library, you have to
+have some way of like tagging,
+
+ align:start position:0%
+have some way of like tagging,
+ 
+
+ align:start position:0%
+have some way of like tagging,
+archiving, maintaining those things,
+
+ align:start position:0%
+archiving, maintaining those things,
+ 
+
+ align:start position:0%
+archiving, maintaining those things,
+bringing into classrooms. I mean, there
+
+ align:start position:0%
+bringing into classrooms. I mean, there
+ 
+
+ align:start position:0%
+bringing into classrooms. I mean, there
+are contemporary versions of all of
+
+ align:start position:0%
+are contemporary versions of all of
+ 
+
+ align:start position:0%
+are contemporary versions of all of
+these things. Um, oh, you want to give
+
+ align:start position:0%
+these things. Um, oh, you want to give
+ 
+
+ align:start position:0%
+these things. Um, oh, you want to give
+every kid a device? Um, how is that
+
+ align:start position:0%
+every kid a device? Um, how is that
+ 
+
+ align:start position:0%
+every kid a device? Um, how is that
+kid's device going to get on the
+
+ align:start position:0%
+kid's device going to get on the
+ 
+
+ align:start position:0%
+kid's device going to get on the
+network? How is they going to be able to
+
+ align:start position:0%
+network? How is they going to be able to
+ 
+
+ align:start position:0%
+network? How is they going to be able to
+log in? Who's going to deal when they
+
+ align:start position:0%
+log in? Who's going to deal when they
+ 
+
+ align:start position:0%
+log in? Who's going to deal when they
+lose their password? What's going to
+
+ align:start position:0%
+lose their password? What's going to
+ 
+
+ align:start position:0%
+lose their password? What's going to
+happen when their devices break? Are you
+
+ align:start position:0%
+happen when their devices break? Are you
+ 
+
+ align:start position:0%
+happen when their devices break? Are you
+going to make a Are you going to make
+
+ align:start position:0%
+going to make a Are you going to make
+ 
+
+ align:start position:0%
+going to make a Are you going to make
+families pay for the devices they break?
+
+ align:start position:0%
+families pay for the devices they break?
+ 
+
+ align:start position:0%
+families pay for the devices they break?
+Your kids are super poor. They can't
+
+ align:start position:0%
+Your kids are super poor. They can't
+ 
+
+ align:start position:0%
+Your kids are super poor. They can't
+afford that. So, you're going to
+
+ align:start position:0%
+afford that. So, you're going to
+ 
+
+ align:start position:0%
+afford that. So, you're going to
+contract with insurance company. who on
+
+ align:start position:0%
+contract with insurance company. who on
+ 
+
+ align:start position:0%
+contract with insurance company. who on
+your staff has experience contracting
+
+ align:start position:0%
+your staff has experience contracting
+ 
+
+ align:start position:0%
+your staff has experience contracting
+with insurance companies to ensure um uh
+
+ align:start position:0%
+with insurance companies to ensure um uh
+ 
+
+ align:start position:0%
+with insurance companies to ensure um uh
+you know uh uh computing devices like
+
+ align:start position:0%
+you know uh uh computing devices like
+ 
+
+ align:start position:0%
+you know uh uh computing devices like
+you didn't learn that at your I mean
+
+ align:start position:0%
+you didn't learn that at your I mean
+ 
+
+ align:start position:0%
+you didn't learn that at your I mean
+we'll talk with the education school
+
+ align:start position:0%
+we'll talk with the education school
+ 
+
+ align:start position:0%
+we'll talk with the education school
+deans on Wednesday but I'm pretty sure
+
+ align:start position:0%
+deans on Wednesday but I'm pretty sure
+ 
+
+ align:start position:0%
+deans on Wednesday but I'm pretty sure
+they're not teaching their um their
+
+ align:start position:0%
+they're not teaching their um their
+ 
+
+ align:start position:0%
+they're not teaching their um their
+their their students how to manage
+
+ align:start position:0%
+their their students how to manage
+ 
+
+ align:start position:0%
+their their students how to manage
+insurance contracts and things like
+
+ align:start position:0%
+insurance contracts and things like
+ 
+
+ align:start position:0%
+insurance contracts and things like
+that. Um all of those things become you
+
+ align:start position:0%
+that. Um all of those things become you
+ 
+
+ align:start position:0%
+that. Um all of those things become you
+know um if if well they you know they
+
+ align:start position:0%
+know um if if well they you know they
+ 
+
+ align:start position:0%
+know um if if well they you know they
+have a combination of incentives and
+
+ align:start position:0%
+have a combination of incentives and
+ 
+
+ align:start position:0%
+have a combination of incentives and
+disincentives that are associated with
+
+ align:start position:0%
+disincentives that are associated with
+ 
+
+ align:start position:0%
+disincentives that are associated with
+them. Um, good. Any any of these other
+
+ align:start position:0%
+them. Um, good. Any any of these other
+ 
+
+ align:start position:0%
+them. Um, good. Any any of these other
+people that it seems like is important
+
+ align:start position:0%
+people that it seems like is important
+ 
+
+ align:start position:0%
+people that it seems like is important
+for us to touch on before we um come to
+
+ align:start position:0%
+for us to touch on before we um come to
+ 
+
+ align:start position:0%
+for us to touch on before we um come to
+conclusion. We talked about parents. Um,
+
+ align:start position:0%
+conclusion. We talked about parents. Um,
+ 
+
+ align:start position:0%
+conclusion. We talked about parents. Um,
+you know, I I mean I don't know that how
+
+ align:start position:0%
+you know, I I mean I don't know that how
+ 
+
+ align:start position:0%
+you know, I I mean I don't know that how
+much we talked maybe here's one last
+
+ align:start position:0%
+much we talked maybe here's one last
+ 
+
+ align:start position:0%
+much we talked maybe here's one last
+thing that we could sort of talk about.
+
+ align:start position:0%
+thing that we could sort of talk about.
+ 
+
+ align:start position:0%
+thing that we could sort of talk about.
+We talked a little bit about school
+
+ align:start position:0%
+We talked a little bit about school
+ 
+
+ align:start position:0%
+We talked a little bit about school
+administrators. Um, but like a a thing
+
+ align:start position:0%
+administrators. Um, but like a a thing
+ 
+
+ align:start position:0%
+administrators. Um, but like a a thing
+to be particularly attentive to um in uh
+
+ align:start position:0%
+to be particularly attentive to um in uh
+ 
+
+ align:start position:0%
+to be particularly attentive to um in uh
+um in schools is just how many different
+
+ align:start position:0%
+um in schools is just how many different
+ 
+
+ align:start position:0%
+um in schools is just how many different
+kinds of adults with different roles
+
+ align:start position:0%
+kinds of adults with different roles
+ 
+
+ align:start position:0%
+kinds of adults with different roles
+there are. So, we talked about teachers.
+
+ align:start position:0%
+there are. So, we talked about teachers.
+ 
+
+ align:start position:0%
+there are. So, we talked about teachers.
+Um, there are people who are school
+
+ align:start position:0%
+Um, there are people who are school
+ 
+
+ align:start position:0%
+Um, there are people who are school
+principles. Like, if you're a school
+
+ align:start position:0%
+principles. Like, if you're a school
+ 
+
+ align:start position:0%
+principles. Like, if you're a school
+principal, what are what are the most
+
+ align:start position:0%
+principal, what are what are the most
+ 
+
+ align:start position:0%
+principal, what are what are the most
+urgent concerns that you have on any
+
+ align:start position:0%
+urgent concerns that you have on any
+ 
+
+ align:start position:0%
+urgent concerns that you have on any
+given day? Um, what what like what are
+
+ align:start position:0%
+given day? Um, what what like what are
+ 
+
+ align:start position:0%
+given day? Um, what what like what are
+what are the main incentives you have as
+
+ align:start position:0%
+what are the main incentives you have as
+ 
+
+ align:start position:0%
+what are the main incentives you have as
+a school principal? Your budget. Yep.
+
+ align:start position:0%
+a school principal? Your budget. Yep.
+ 
+
+ align:start position:0%
+a school principal? Your budget. Yep.
+You got to make sure you can pay for
+
+ align:start position:0%
+You got to make sure you can pay for
+ 
+
+ align:start position:0%
+You got to make sure you can pay for
+everything. A teacher's not worried
+
+ align:start position:0%
+everything. A teacher's not worried
+ 
+
+ align:start position:0%
+everything. A teacher's not worried
+about that. Teacher will buy as much,
+
+ align:start position:0%
+about that. Teacher will buy as much,
+ 
+
+ align:start position:0%
+about that. Teacher will buy as much,
+you know, if a school pay for it,
+
+ align:start position:0%
+you know, if a school pay for it,
+ 
+
+ align:start position:0%
+you know, if a school pay for it,
+they'll take as much technology as they
+
+ align:start position:0%
+they'll take as much technology as they
+ 
+
+ align:start position:0%
+they'll take as much technology as they
+want. you know, some of them, but
+
+ align:start position:0%
+want. you know, some of them, but
+ 
+
+ align:start position:0%
+want. you know, some of them, but
+principles have to balance a budget or
+
+ align:start position:0%
+principles have to balance a budget or
+ 
+
+ align:start position:0%
+principles have to balance a budget or
+or, you know, I mean, the weird thing is
+
+ align:start position:0%
+or, you know, I mean, the weird thing is
+ 
+
+ align:start position:0%
+or, you know, I mean, the weird thing is
+in the United States, it may not at all
+
+ align:start position:0%
+in the United States, it may not at all
+ 
+
+ align:start position:0%
+in the United States, it may not at all
+be a principal's role to balance a
+
+ align:start position:0%
+be a principal's role to balance a
+ 
+
+ align:start position:0%
+be a principal's role to balance a
+budget. It may be entirely a district
+
+ align:start position:0%
+budget. It may be entirely a district
+ 
+
+ align:start position:0%
+budget. It may be entirely a district
+role. So, there are some school
+
+ align:start position:0%
+role. So, there are some school
+ 
+
+ align:start position:0%
+role. So, there are some school
+districts where the district will make
+
+ align:start position:0%
+districts where the district will make
+ 
+
+ align:start position:0%
+districts where the district will make
+all the purchasing decisions. There are
+
+ align:start position:0%
+all the purchasing decisions. There are
+ 
+
+ align:start position:0%
+all the purchasing decisions. There are
+other districts where the districts will
+
+ align:start position:0%
+other districts where the districts will
+ 
+
+ align:start position:0%
+other districts where the districts will
+take big chunks of money, send it down
+
+ align:start position:0%
+take big chunks of money, send it down
+ 
+
+ align:start position:0%
+take big chunks of money, send it down
+to schools, and say, "Schools, make all
+
+ align:start position:0%
+to schools, and say, "Schools, make all
+ 
+
+ align:start position:0%
+to schools, and say, "Schools, make all
+the purchasing decisions."
+
+ align:start position:0%
+the purchasing decisions."
+ 
+
+ align:start position:0%
+the purchasing decisions."
+Um, what what else is super important
+
+ align:start position:0%
+Um, what what else is super important
+ 
+
+ align:start position:0%
+Um, what what else is super important
+for principles? I was going to say like
+
+ align:start position:0%
+for principles? I was going to say like
+ 
+
+ align:start position:0%
+for principles? I was going to say like
+just like maintaining the school
+
+ align:start position:0%
+just like maintaining the school
+ 
+
+ align:start position:0%
+just like maintaining the school
+building itself for like student safety.
+
+ align:start position:0%
+building itself for like student safety.
+ 
+
+ align:start position:0%
+building itself for like student safety.
+Yeah. Yep. student safety, maintaining
+
+ align:start position:0%
+Yeah. Yep. student safety, maintaining
+ 
+
+ align:start position:0%
+Yeah. Yep. student safety, maintaining
+the physical school building, making,
+
+ align:start position:0%
+the physical school building, making,
+ 
+
+ align:start position:0%
+the physical school building, making,
+you know, making sure things are running
+
+ align:start position:0%
+you know, making sure things are running
+ 
+
+ align:start position:0%
+you know, making sure things are running
+and operating and stuff like that. Are
+
+ align:start position:0%
+and operating and stuff like that. Are
+ 
+
+ align:start position:0%
+and operating and stuff like that. Are
+they also managing the relationships
+
+ align:start position:0%
+they also managing the relationships
+ 
+
+ align:start position:0%
+they also managing the relationships
+with like the district and also parents
+
+ align:start position:0%
+with like the district and also parents
+ 
+
+ align:start position:0%
+with like the district and also parents
+like all these outside? Yep. Yep. So,
+
+ align:start position:0%
+like all these outside? Yep. Yep. So,
+ 
+
+ align:start position:0%
+like all these outside? Yep. Yep. So,
+so, so, um, they and they are, you know,
+
+ align:start position:0%
+so, so, um, they and they are, you know,
+ 
+
+ align:start position:0%
+so, so, um, they and they are, you know,
+principles are sort of quintessential
+
+ align:start position:0%
+principles are sort of quintessential
+ 
+
+ align:start position:0%
+principles are sort of quintessential
+organizational behavior, middle
+
+ align:start position:0%
+organizational behavior, middle
+ 
+
+ align:start position:0%
+organizational behavior, middle
+managers. Um, they're like empowered to
+
+ align:start position:0%
+managers. Um, they're like empowered to
+ 
+
+ align:start position:0%
+managers. Um, they're like empowered to
+do some things but not others. They're
+
+ align:start position:0%
+do some things but not others. They're
+ 
+
+ align:start position:0%
+do some things but not others. They're
+accountable to lots of different kinds
+
+ align:start position:0%
+accountable to lots of different kinds
+ 
+
+ align:start position:0%
+accountable to lots of different kinds
+of stakeholders. There's all kind of
+
+ align:start position:0%
+of stakeholders. There's all kind of
+ 
+
+ align:start position:0%
+of stakeholders. There's all kind of
+complexity in what they're doing. Um uh
+
+ align:start position:0%
+complexity in what they're doing. Um uh
+ 
+
+ align:start position:0%
+complexity in what they're doing. Um uh
+a lot of them are pretty keyed evaluated
+
+ align:start position:0%
+a lot of them are pretty keyed evaluated
+ 
+
+ align:start position:0%
+a lot of them are pretty keyed evaluated
+based on test scores like especially in
+
+ align:start position:0%
+based on test scores like especially in
+ 
+
+ align:start position:0%
+based on test scores like especially in
+places where people are at where
+
+ align:start position:0%
+places where people are at where
+ 
+
+ align:start position:0%
+places where people are at where
+students are at risk of not passing
+
+ align:start position:0%
+students are at risk of not passing
+ 
+
+ align:start position:0%
+students are at risk of not passing
+tests. Um and depending upon the policy
+
+ align:start position:0%
+tests. Um and depending upon the policy
+ 
+
+ align:start position:0%
+tests. Um and depending upon the policy
+infrastructure test scores really matter
+
+ align:start position:0%
+infrastructure test scores really matter
+ 
+
+ align:start position:0%
+infrastructure test scores really matter
+to them. Um safety and the orderly
+
+ align:start position:0%
+to them. Um safety and the orderly
+ 
+
+ align:start position:0%
+to them. Um safety and the orderly
+operation of schools man like you know
+
+ align:start position:0%
+operation of schools man like you know
+ 
+
+ align:start position:0%
+operation of schools man like you know
+in in like every person in a building
+
+ align:start position:0%
+in in like every person in a building
+ 
+
+ align:start position:0%
+in in like every person in a building
+wants schools to be orderly but when
+
+ align:start position:0%
+wants schools to be orderly but when
+ 
+
+ align:start position:0%
+wants schools to be orderly but when
+schools are disorderly the person who
+
+ align:start position:0%
+schools are disorderly the person who
+ 
+
+ align:start position:0%
+schools are disorderly the person who
+has to deal with it the most is like an
+
+ align:start position:0%
+has to deal with it the most is like an
+ 
+
+ align:start position:0%
+has to deal with it the most is like an
+assistant principal or the principal.
+
+ align:start position:0%
+assistant principal or the principal.
+ 
+
+ align:start position:0%
+assistant principal or the principal.
+It's just more work for them. um you
+
+ align:start position:0%
+It's just more work for them. um you
+ 
+
+ align:start position:0%
+It's just more work for them. um you
+know you know um you like let all the
+
+ align:start position:0%
+know you know um you like let all the
+ 
+
+ align:start position:0%
+know you know um you like let all the
+kids have phones and you know fights
+
+ align:start position:0%
+kids have phones and you know fights
+ 
+
+ align:start position:0%
+kids have phones and you know fights
+break out and all kinds of things happen
+
+ align:start position:0%
+break out and all kinds of things happen
+ 
+
+ align:start position:0%
+break out and all kinds of things happen
+like it's the you know teachers have to
+
+ align:start position:0%
+like it's the you know teachers have to
+ 
+
+ align:start position:0%
+like it's the you know teachers have to
+deal with it but the principles really
+
+ align:start position:0%
+deal with it but the principles really
+ 
+
+ align:start position:0%
+deal with it but the principles really
+have to deal with it. I just like really
+
+ align:start position:0%
+have to deal with it. I just like really
+ 
+
+ align:start position:0%
+have to deal with it. I just like really
+short comment just when you asked us
+
+ align:start position:0%
+short comment just when you asked us
+ 
+
+ align:start position:0%
+short comment just when you asked us
+like what does a principal do? I've been
+
+ align:start position:0%
+like what does a principal do? I've been
+ 
+
+ align:start position:0%
+like what does a principal do? I've been
+around them my entire life and I was
+
+ align:start position:0%
+around them my entire life and I was
+ 
+
+ align:start position:0%
+around them my entire life and I was
+like I can only think of like two or
+
+ align:start position:0%
+like I can only think of like two or
+ 
+
+ align:start position:0%
+like I can only think of like two or
+three things that I know a principal
+
+ align:start position:0%
+three things that I know a principal
+ 
+
+ align:start position:0%
+three things that I know a principal
+actually does and I just think it's
+
+ align:start position:0%
+actually does and I just think it's
+ 
+
+ align:start position:0%
+actually does and I just think it's
+really strange that like most people
+
+ align:start position:0%
+really strange that like most people
+ 
+
+ align:start position:0%
+really strange that like most people
+aren't sitting you down being like this
+
+ align:start position:0%
+aren't sitting you down being like this
+ 
+
+ align:start position:0%
+aren't sitting you down being like this
+is the person you go to for x y and z
+
+ align:start position:0%
+is the person you go to for x y and z
+ 
+
+ align:start position:0%
+is the person you go to for x y and z
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+around these organizations good good so
+
+ align:start position:0%
+around these organizations good good so
+ 
+
+ align:start position:0%
+around these organizations good good so
+there there are I think there are a few
+
+ align:start position:0%
+there there are I think there are a few
+ 
+
+ align:start position:0%
+there there are I think there are a few
+things that you can grasp from that
+
+ align:start position:0%
+things that you can grasp from that
+ 
+
+ align:start position:0%
+things that you can grasp from that
+insight is first of all schools are just
+
+ align:start position:0%
+insight is first of all schools are just
+ 
+
+ align:start position:0%
+insight is first of all schools are just
+unbelievably complicated um I've spent
+
+ align:start position:0%
+unbelievably complicated um I've spent
+ 
+
+ align:start position:0%
+unbelievably complicated um I've spent
+the last 20 years basically doing
+
+ align:start position:0%
+the last 20 years basically doing
+ 
+
+ align:start position:0%
+the last 20 years basically doing
+nothing but thinking about schools and I
+
+ align:start position:0%
+nothing but thinking about schools and I
+ 
+
+ align:start position:0%
+nothing but thinking about schools and I
+still don't understand all the things
+
+ align:start position:0%
+still don't understand all the things
+ 
+
+ align:start position:0%
+still don't understand all the things
+that are going on in there. They are
+
+ align:start position:0%
+that are going on in there. They are
+ 
+
+ align:start position:0%
+that are going on in there. They are
+like if you want like just as an
+
+ align:start position:0%
+like if you want like just as an
+ 
+
+ align:start position:0%
+like if you want like just as an
+ecosystem, they're unbelievably complex
+
+ align:start position:0%
+ecosystem, they're unbelievably complex
+ 
+
+ align:start position:0%
+ecosystem, they're unbelievably complex
+and fascinating. Um the second is as you
+
+ align:start position:0%
+and fascinating. Um the second is as you
+ 
+
+ align:start position:0%
+and fascinating. Um the second is as you
+transition if you decide to work be
+
+ align:start position:0%
+transition if you decide to work be
+ 
+
+ align:start position:0%
+transition if you decide to work be
+involved in education, you sort you kind
+
+ align:start position:0%
+involved in education, you sort you kind
+ 
+
+ align:start position:0%
+involved in education, you sort you kind
+of have to like relearn all this stuff
+
+ align:start position:0%
+of have to like relearn all this stuff
+ 
+
+ align:start position:0%
+of have to like relearn all this stuff
+going from a student to being someone
+
+ align:start position:0%
+going from a student to being someone
+ 
+
+ align:start position:0%
+going from a student to being someone
+who's working in education. Like there's
+
+ align:start position:0%
+who's working in education. Like there's
+ 
+
+ align:start position:0%
+who's working in education. Like there's
+all kinds of things that were hidden
+
+ align:start position:0%
+all kinds of things that were hidden
+ 
+
+ align:start position:0%
+all kinds of things that were hidden
+from you, masked from you, or just sort
+
+ align:start position:0%
+from you, masked from you, or just sort
+ 
+
+ align:start position:0%
+from you, masked from you, or just sort
+of weren't important to you. You know,
+
+ align:start position:0%
+of weren't important to you. You know,
+ 
+
+ align:start position:0%
+of weren't important to you. You know,
+like the odds that any of you were like
+
+ align:start position:0%
+like the odds that any of you were like
+ 
+
+ align:start position:0%
+like the odds that any of you were like
+real troublemakers is pretty low given
+
+ align:start position:0%
+real troublemakers is pretty low given
+ 
+
+ align:start position:0%
+real troublemakers is pretty low given
+that you're at MIT. Um but you know
+
+ align:start position:0%
+that you're at MIT. Um but you know
+ 
+
+ align:start position:0%
+that you're at MIT. Um but you know
+there you know there's a classroom full
+
+ align:start position:0%
+there you know there's a classroom full
+ 
+
+ align:start position:0%
+there you know there's a classroom full
+of people sitting somewhere um that like
+
+ align:start position:0%
+of people sitting somewhere um that like
+ 
+
+ align:start position:0%
+of people sitting somewhere um that like
+knew principles pretty intimately
+
+ align:start position:0%
+knew principles pretty intimately
+ 
+
+ align:start position:0%
+knew principles pretty intimately
+because they spent a bunch of time in
+
+ align:start position:0%
+because they spent a bunch of time in
+ 
+
+ align:start position:0%
+because they spent a bunch of time in
+their office um because you know because
+
+ align:start position:0%
+their office um because you know because
+ 
+
+ align:start position:0%
+their office um because you know because
+of things that they did and so forth. So
+
+ align:start position:0%
+of things that they did and so forth. So
+ 
+
+ align:start position:0%
+of things that they did and so forth. So
+good. Yeah. If if if part of what
+
+ align:start position:0%
+good. Yeah. If if if part of what
+ 
+
+ align:start position:0%
+good. Yeah. If if if part of what
+happens to you in this class is uh a lot
+
+ align:start position:0%
+happens to you in this class is uh a lot
+ 
+
+ align:start position:0%
+happens to you in this class is uh a lot
+of times in social science we talk about
+
+ align:start position:0%
+of times in social science we talk about
+ 
+
+ align:start position:0%
+of times in social science we talk about
+making the familiar unfamiliar. Um a
+
+ align:start position:0%
+making the familiar unfamiliar. Um a
+ 
+
+ align:start position:0%
+making the familiar unfamiliar. Um a
+thing that you've looked at your whole
+
+ align:start position:0%
+thing that you've looked at your whole
+ 
+
+ align:start position:0%
+thing that you've looked at your whole
+life and being like whoa look at all
+
+ align:start position:0%
+life and being like whoa look at all
+ 
+
+ align:start position:0%
+life and being like whoa look at all
+these things there that I wasn't sort of
+
+ align:start position:0%
+these things there that I wasn't sort of
+ 
+
+ align:start position:0%
+these things there that I wasn't sort of
+paying attention to or you know wasn't
+
+ align:start position:0%
+paying attention to or you know wasn't
+ 
+
+ align:start position:0%
+paying attention to or you know wasn't
+made aware to me and those kinds of
+
+ align:start position:0%
+made aware to me and those kinds of
+ 
+
+ align:start position:0%
+made aware to me and those kinds of
+things. Um maybe here's here's one very
+
+ align:start position:0%
+things. Um maybe here's here's one very
+ 
+
+ align:start position:0%
+things. Um maybe here's here's one very
+concrete thing. Um uh let's think of
+
+ align:start position:0%
+concrete thing. Um uh let's think of
+ 
+
+ align:start position:0%
+concrete thing. Um uh let's think of
+something like uh um a student
+
+ align:start position:0%
+something like uh um a student
+ 
+
+ align:start position:0%
+something like uh um a student
+information system. Um or Canvas. Let's
+
+ align:start position:0%
+information system. Um or Canvas. Let's
+ 
+
+ align:start position:0%
+information system. Um or Canvas. Let's
+think of something like a learning
+
+ align:start position:0%
+think of something like a learning
+ 
+
+ align:start position:0%
+think of something like a learning
+management system. Who spends the most
+
+ align:start position:0%
+management system. Who spends the most
+ 
+
+ align:start position:0%
+management system. Who spends the most
+time using
+
+ align:start position:0%
+time using
+ 
+
+ align:start position:0%
+time using
+Canvas? Tell me about the people who use
+
+ align:start position:0%
+Canvas? Tell me about the people who use
+ 
+
+ align:start position:0%
+Canvas? Tell me about the people who use
+Canvas.
+
+ align:start position:0%
+Canvas.
+ 
+
+ align:start position:0%
+Canvas.
+Students. Students spend a lot of hours
+
+ align:start position:0%
+Students. Students spend a lot of hours
+ 
+
+ align:start position:0%
+Students. Students spend a lot of hours
+logged in looking at stuff on Canvas.
+
+ align:start position:0%
+logged in looking at stuff on Canvas.
+ 
+
+ align:start position:0%
+logged in looking at stuff on Canvas.
+Who else looks at Canvas? Teachers.
+
+ align:start position:0%
+Who else looks at Canvas? Teachers.
+ 
+
+ align:start position:0%
+Who else looks at Canvas? Teachers.
+Teachers. Who buys Canvas? this true not
+
+ align:start position:0%
+Teachers. Who buys Canvas? this true not
+ 
+
+ align:start position:0%
+Teachers. Who buys Canvas? this true not
+students and teachers in in in uh um in
+
+ align:start position:0%
+students and teachers in in in uh um in
+ 
+
+ align:start position:0%
+students and teachers in in in uh um in
+business school I think they would call
+
+ align:start position:0%
+business school I think they would call
+ 
+
+ align:start position:0%
+business school I think they would call
+this a third party payer problem. Um so
+
+ align:start position:0%
+this a third party payer problem. Um so
+ 
+
+ align:start position:0%
+this a third party payer problem. Um so
+if you are a company that's making a
+
+ align:start position:0%
+if you are a company that's making a
+ 
+
+ align:start position:0%
+if you are a company that's making a
+learning management
+
+ align:start position:0%
+learning management
+ 
+
+ align:start position:0%
+learning management
+system who's like of your
+
+ align:start position:0%
+system who's like of your
+ 
+
+ align:start position:0%
+system who's like of your
+stakeholders who has the most power to
+
+ align:start position:0%
+stakeholders who has the most power to
+ 
+
+ align:start position:0%
+stakeholders who has the most power to
+determine whether or not your thing gets
+
+ align:start position:0%
+determine whether or not your thing gets
+ 
+
+ align:start position:0%
+determine whether or not your thing gets
+purchased like some director of
+
+ align:start position:0%
+purchased like some director of
+ 
+
+ align:start position:0%
+purchased like some director of
+education technology or something like
+
+ align:start position:0%
+education technology or something like
+ 
+
+ align:start position:0%
+education technology or something like
+that some IT person. So, if you ever if
+
+ align:start position:0%
+that some IT person. So, if you ever if
+ 
+
+ align:start position:0%
+that some IT person. So, if you ever if
+you've ever wondered like why is this so
+
+ align:start position:0%
+you've ever wondered like why is this so
+ 
+
+ align:start position:0%
+you've ever wondered like why is this so
+terrible? Um, it wasn't built for you.
+
+ align:start position:0%
+terrible? Um, it wasn't built for you.
+ 
+
+ align:start position:0%
+terrible? Um, it wasn't built for you.
+Like in some in some important ways, it
+
+ align:start position:0%
+Like in some in some important ways, it
+ 
+
+ align:start position:0%
+Like in some in some important ways, it
+was literally not built for you. It was
+
+ align:start position:0%
+was literally not built for you. It was
+ 
+
+ align:start position:0%
+was literally not built for you. It was
+built to solve the problems of some
+
+ align:start position:0%
+built to solve the problems of some
+ 
+
+ align:start position:0%
+built to solve the problems of some
+middle level information technology
+
+ align:start position:0%
+middle level information technology
+ 
+
+ align:start position:0%
+middle level information technology
+manager. Who's going to buy one of those
+
+ align:start position:0%
+manager. Who's going to buy one of those
+ 
+
+ align:start position:0%
+manager. Who's going to buy one of those
+things? Um, so third-party payer
+
+ align:start position:0%
+things? Um, so third-party payer
+ 
+
+ align:start position:0%
+things? Um, so third-party payer
+problems are rife across. I mean, the
+
+ align:start position:0%
+problems are rife across. I mean, the
+ 
+
+ align:start position:0%
+problems are rife across. I mean, the
+problem with third-party payer problems
+
+ align:start position:0%
+problem with third-party payer problems
+ 
+
+ align:start position:0%
+problem with third-party payer problems
+from like a classical economics point of
+
+ align:start position:0%
+from like a classical economics point of
+ 
+
+ align:start position:0%
+from like a classical economics point of
+view is you just have misaligned
+
+ align:start position:0%
+view is you just have misaligned
+ 
+
+ align:start position:0%
+view is you just have misaligned
+incentives. um you know um in in some
+
+ align:start position:0%
+incentives. um you know um in in some
+ 
+
+ align:start position:0%
+incentives. um you know um in in some
+respects you could say that improving
+
+ align:start position:0%
+respects you could say that improving
+ 
+
+ align:start position:0%
+respects you could say that improving
+the teaching and learning experience on
+
+ align:start position:0%
+the teaching and learning experience on
+ 
+
+ align:start position:0%
+the teaching and learning experience on
+canvas is a cost um it's something that
+
+ align:start position:0%
+canvas is a cost um it's something that
+ 
+
+ align:start position:0%
+canvas is a cost um it's something that
+like reduces your pro profit obviously
+
+ align:start position:0%
+like reduces your pro profit obviously
+ 
+
+ align:start position:0%
+like reduces your pro profit obviously
+you have to make it good enough so that
+
+ align:start position:0%
+you have to make it good enough so that
+ 
+
+ align:start position:0%
+you have to make it good enough so that
+you know if like enough teachers and
+
+ align:start position:0%
+you know if like enough teachers and
+ 
+
+ align:start position:0%
+you know if like enough teachers and
+stuff are rolled I once anyone ever have
+
+ align:start position:0%
+stuff are rolled I once anyone ever have
+ 
+
+ align:start position:0%
+stuff are rolled I once anyone ever have
+to use blackboard
+
+ align:start position:0%
+to use blackboard
+ 
+
+ align:start position:0%
+to use blackboard
+okay good um I once met the I once met
+
+ align:start position:0%
+okay good um I once met the I once met
+ 
+
+ align:start position:0%
+okay good um I once met the I once met
+the guy who made blackboard and I was
+
+ align:start position:0%
+the guy who made blackboard and I was
+ 
+
+ align:start position:0%
+the guy who made blackboard and I was
+just standing there in line behind him
+
+ align:start position:0%
+just standing there in line behind him
+ 
+
+ align:start position:0%
+just standing there in line behind him
+or something like that being like what
+
+ align:start position:0%
+or something like that being like what
+ 
+
+ align:start position:0%
+or something like that being like what
+would it be like to have made a piece of
+
+ align:start position:0%
+would it be like to have made a piece of
+ 
+
+ align:start position:0%
+would it be like to have made a piece of
+software that millions of people hate
+
+ align:start position:0%
+software that millions of people hate
+ 
+
+ align:start position:0%
+software that millions of people hate
+like what like what would it have been
+
+ align:start position:0%
+like what like what would it have been
+ 
+
+ align:start position:0%
+like what like what would it have been
+like to like introduce so much
+
+ align:start position:0%
+like to like introduce so much
+ 
+
+ align:start position:0%
+like to like introduce so much
+unhappiness in the world with what
+
+ align:start position:0%
+unhappiness in the world with what
+ 
+
+ align:start position:0%
+unhappiness in the world with what
+you've built like and I it was it would
+
+ align:start position:0%
+you've built like and I it was it would
+ 
+
+ align:start position:0%
+you've built like and I it was it would
+have been rude I think in the buffet
+
+ align:start position:0%
+have been rude I think in the buffet
+ 
+
+ align:start position:0%
+have been rude I think in the buffet
+line to to to ask him to ask him that
+
+ align:start position:0%
+line to to to ask him to ask him that
+ 
+
+ align:start position:0%
+line to to to ask him to ask him that
+question. Um here's another thing that I
+
+ align:start position:0%
+question. Um here's another thing that I
+ 
+
+ align:start position:0%
+question. Um here's another thing that I
+want to say about who buys these things
+
+ align:start position:0%
+want to say about who buys these things
+ 
+
+ align:start position:0%
+want to say about who buys these things
+and this is really um important too
+
+ align:start position:0%
+and this is really um important too
+ 
+
+ align:start position:0%
+and this is really um important too
+especially to any of you who are
+
+ align:start position:0%
+especially to any of you who are
+ 
+
+ align:start position:0%
+especially to any of you who are
+interested in either an education like
+
+ align:start position:0%
+interested in either an education like
+ 
+
+ align:start position:0%
+interested in either an education like
+starting an education startup or other
+
+ align:start position:0%
+starting an education startup or other
+ 
+
+ align:start position:0%
+starting an education startup or other
+kinds of things. Um uh who in a school
+
+ align:start position:0%
+kinds of things. Um uh who in a school
+ 
+
+ align:start position:0%
+kinds of things. Um uh who in a school
+can buy technology? What are some
+
+ align:start position:0%
+can buy technology? What are some
+ 
+
+ align:start position:0%
+can buy technology? What are some
+possible titles of people who buy
+
+ align:start position:0%
+possible titles of people who buy
+ 
+
+ align:start position:0%
+possible titles of people who buy
+technology?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We've mentioned a few. Librarians, a
+
+ align:start position:0%
+We've mentioned a few. Librarians, a
+ 
+
+ align:start position:0%
+We've mentioned a few. Librarians, a
+librarian could buy technology.
+
+ align:start position:0%
+librarian could buy technology.
+ 
+
+ align:start position:0%
+librarian could buy technology.
+Department chair. A department chair
+
+ align:start position:0%
+Department chair. A department chair
+ 
+
+ align:start position:0%
+Department chair. A department chair
+could buy technology.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Teacher. A teacher. They're amongst the
+
+ align:start position:0%
+Teacher. A teacher. They're amongst the
+ 
+
+ align:start position:0%
+Teacher. A teacher. They're amongst the
+least likely. Actually, one of the
+
+ align:start position:0%
+least likely. Actually, one of the
+ 
+
+ align:start position:0%
+least likely. Actually, one of the
+sometimes people have made the argument
+
+ align:start position:0%
+sometimes people have made the argument
+ 
+
+ align:start position:0%
+sometimes people have made the argument
+that a that a problem in the education
+
+ align:start position:0%
+that a that a problem in the education
+ 
+
+ align:start position:0%
+that a that a problem in the education
+system is it's very it's very difficult
+
+ align:start position:0%
+system is it's very it's very difficult
+ 
+
+ align:start position:0%
+system is it's very it's very difficult
+to have a real sort of bottomup
+
+ align:start position:0%
+to have a real sort of bottomup
+ 
+
+ align:start position:0%
+to have a real sort of bottomup
+marketplace kind of effect. Um like
+
+ align:start position:0%
+marketplace kind of effect. Um like
+ 
+
+ align:start position:0%
+marketplace kind of effect. Um like
+teachers have in most places teachers
+
+ align:start position:0%
+teachers have in most places teachers
+ 
+
+ align:start position:0%
+teachers have in most places teachers
+have very few discretionary dollars um
+
+ align:start position:0%
+have very few discretionary dollars um
+ 
+
+ align:start position:0%
+have very few discretionary dollars um
+to the I mean that's why they're like
+
+ align:start position:0%
+to the I mean that's why they're like
+ 
+
+ align:start position:0%
+to the I mean that's why they're like
+holding big sales and asking like you
+
+ align:start position:0%
+holding big sales and asking like you
+ 
+
+ align:start position:0%
+holding big sales and asking like you
+know when you become parents like your
+
+ align:start position:0%
+know when you become parents like your
+ 
+
+ align:start position:0%
+know when you become parents like your
+teachers will ask you to bring in boxes
+
+ align:start position:0%
+teachers will ask you to bring in boxes
+ 
+
+ align:start position:0%
+teachers will ask you to bring in boxes
+of tissues and things like that and
+
+ align:start position:0%
+of tissues and things like that and
+ 
+
+ align:start position:0%
+of tissues and things like that and
+you'll be like what what broken failed
+
+ align:start position:0%
+you'll be like what what broken failed
+ 
+
+ align:start position:0%
+you'll be like what what broken failed
+country do we live in where you cannot
+
+ align:start position:0%
+country do we live in where you cannot
+ 
+
+ align:start position:0%
+country do we live in where you cannot
+simply buy all the tissues that you need
+
+ align:start position:0%
+simply buy all the tissues that you need
+ 
+
+ align:start position:0%
+simply buy all the tissues that you need
+for the children um or paper two reams
+
+ align:start position:0%
+for the children um or paper two reams
+ 
+
+ align:start position:0%
+for the children um or paper two reams
+two yeah two yeah two reams of paper a
+
+ align:start position:0%
+two yeah two yeah two reams of paper a
+ 
+
+ align:start position:0%
+two yeah two yeah two reams of paper a
+semester for all your students you know
+
+ align:start position:0%
+semester for all your students you know
+ 
+
+ align:start position:0%
+semester for all your students you know
+all right so the teachers don't have in
+
+ align:start position:0%
+all right so the teachers don't have in
+ 
+
+ align:start position:0%
+all right so the teachers don't have in
+some cases they do, but in a lot of
+
+ align:start position:0%
+some cases they do, but in a lot of
+ 
+
+ align:start position:0%
+some cases they do, but in a lot of
+cases you don't know what I mean.
+
+ align:start position:0%
+cases you don't know what I mean.
+ 
+
+ align:start position:0%
+cases you don't know what I mean.
+Principles can buy things, directors of
+
+ align:start position:0%
+Principles can buy things, directors of
+ 
+
+ align:start position:0%
+Principles can buy things, directors of
+instructional technology can buy things,
+
+ align:start position:0%
+instructional technology can buy things,
+ 
+
+ align:start position:0%
+instructional technology can buy things,
+assistant superintendents can buy
+
+ align:start position:0%
+assistant superintendents can buy
+ 
+
+ align:start position:0%
+assistant superintendents can buy
+things, superintendents can buy things,
+
+ align:start position:0%
+things, superintendents can buy things,
+ 
+
+ align:start position:0%
+things, superintendents can buy things,
+school boards in some places can
+
+ align:start position:0%
+school boards in some places can
+ 
+
+ align:start position:0%
+school boards in some places can
+directly authorize kinds of things,
+
+ align:start position:0%
+directly authorize kinds of things,
+ 
+
+ align:start position:0%
+directly authorize kinds of things,
+although that's probably more rare, but
+
+ align:start position:0%
+although that's probably more rare, but
+ 
+
+ align:start position:0%
+although that's probably more rare, but
+they can push for it. Um, but the point
+
+ align:start position:0%
+they can push for it. Um, but the point
+ 
+
+ align:start position:0%
+they can push for it. Um, but the point
+is across the 13,000 school districts
+
+ align:start position:0%
+is across the 13,000 school districts
+ 
+
+ align:start position:0%
+is across the 13,000 school districts
+and 130,000 schools in this country, the
+
+ align:start position:0%
+and 130,000 schools in this country, the
+ 
+
+ align:start position:0%
+and 130,000 schools in this country, the
+answer to the question, who can buy
+
+ align:start position:0%
+answer to the question, who can buy
+ 
+
+ align:start position:0%
+answer to the question, who can buy
+something is different in all of those
+
+ align:start position:0%
+something is different in all of those
+ 
+
+ align:start position:0%
+something is different in all of those
+contexts. Um, that makes starting an
+
+ align:start position:0%
+contexts. Um, that makes starting an
+ 
+
+ align:start position:0%
+contexts. Um, that makes starting an
+education technology company very very
+
+ align:start position:0%
+education technology company very very
+ 
+
+ align:start position:0%
+education technology company very very
+difficult.
+
+ align:start position:0%
+difficult.
+ 
+
+ align:start position:0%
+difficult.
+Um, when you go somewhere, you don't
+
+ align:start position:0%
+Um, when you go somewhere, you don't
+ 
+
+ align:start position:0%
+Um, when you go somewhere, you don't
+even know who can buy the thing. Um,
+
+ align:start position:0%
+even know who can buy the thing. Um,
+ 
+
+ align:start position:0%
+even know who can buy the thing. Um,
+like you don't even know who you're
+
+ align:start position:0%
+like you don't even know who you're
+ 
+
+ align:start position:0%
+like you don't even know who you're
+selling it to. Now, there are people who
+
+ align:start position:0%
+selling it to. Now, there are people who
+ 
+
+ align:start position:0%
+selling it to. Now, there are people who
+do know who buys all these things. The
+
+ align:start position:0%
+do know who buys all these things. The
+ 
+
+ align:start position:0%
+do know who buys all these things. The
+only people in the United States who
+
+ align:start position:0%
+only people in the United States who
+ 
+
+ align:start position:0%
+only people in the United States who
+know for every school in every district
+
+ align:start position:0%
+know for every school in every district
+ 
+
+ align:start position:0%
+know for every school in every district
+who has the power to buy stuff are giant
+
+ align:start position:0%
+who has the power to buy stuff are giant
+ 
+
+ align:start position:0%
+who has the power to buy stuff are giant
+publishers. Um, Pearson, Hotton,
+
+ align:start position:0%
+publishers. Um, Pearson, Hotton,
+ 
+
+ align:start position:0%
+publishers. Um, Pearson, Hotton,
+Mifflin, what was the company you work
+
+ align:start position:0%
+Mifflin, what was the company you work
+ 
+
+ align:start position:0%
+Mifflin, what was the company you work
+for? McGraill. McGraill. Perfect. They
+
+ align:start position:0%
+for? McGraill. McGraill. Perfect. They
+ 
+
+ align:start position:0%
+for? McGraill. McGraill. Perfect. They
+have an army of salespeople. this army
+
+ align:start position:0%
+have an army of salespeople. this army
+ 
+
+ align:start position:0%
+have an army of salespeople. this army
+of salespeople have fanned out across
+
+ align:start position:0%
+of salespeople have fanned out across
+ 
+
+ align:start position:0%
+of salespeople have fanned out across
+the 13,000 school districts and once a
+
+ align:start position:0%
+the 13,000 school districts and once a
+ 
+
+ align:start position:0%
+the 13,000 school districts and once a
+month, once a quarter, all the people
+
+ align:start position:0%
+month, once a quarter, all the people
+ 
+
+ align:start position:0%
+month, once a quarter, all the people
+who I just listed who can actually buy
+
+ align:start position:0%
+who I just listed who can actually buy
+ 
+
+ align:start position:0%
+who I just listed who can actually buy
+things, they take them out to lunch.
+
+ align:start position:0%
+things, they take them out to lunch.
+ 
+
+ align:start position:0%
+things, they take them out to lunch.
+They bring them free supplies. They do
+
+ align:start position:0%
+They bring them free supplies. They do
+ 
+
+ align:start position:0%
+They bring them free supplies. They do
+all that stuff. They, you know, like
+
+ align:start position:0%
+all that stuff. They, you know, like
+ 
+
+ align:start position:0%
+all that stuff. They, you know, like
+they probably don't have a master list
+
+ align:start position:0%
+they probably don't have a master list
+ 
+
+ align:start position:0%
+they probably don't have a master list
+somewhere. Instead, they have all these
+
+ align:start position:0%
+somewhere. Instead, they have all these
+ 
+
+ align:start position:0%
+somewhere. Instead, they have all these
+sales people who know the answers to
+
+ align:start position:0%
+sales people who know the answers to
+ 
+
+ align:start position:0%
+sales people who know the answers to
+these questions. Um, so if you're a
+
+ align:start position:0%
+these questions. Um, so if you're a
+ 
+
+ align:start position:0%
+these questions. Um, so if you're a
+Silicon Valley startup and you're like,
+
+ align:start position:0%
+Silicon Valley startup and you're like,
+ 
+
+ align:start position:0%
+Silicon Valley startup and you're like,
+"Oh, I know I've got this new like AI
+
+ align:start position:0%
+"Oh, I know I've got this new like AI
+ 
+
+ align:start position:0%
+"Oh, I know I've got this new like AI
+thing I'm building. It's super cool." Da
+
+ align:start position:0%
+thing I'm building. It's super cool." Da
+ 
+
+ align:start position:0%
+thing I'm building. It's super cool." Da
+da da. You don't have this massive
+
+ align:start position:0%
+da da. You don't have this massive
+ 
+
+ align:start position:0%
+da da. You don't have this massive
+network of sales connections to help you
+
+ align:start position:0%
+network of sales connections to help you
+ 
+
+ align:start position:0%
+network of sales connections to help you
+figure this out. Um, one my one of my
+
+ align:start position:0%
+figure this out. Um, one my one of my
+ 
+
+ align:start position:0%
+figure this out. Um, one my one of my
+favorite illustrations of this is at a
+
+ align:start position:0%
+favorite illustrations of this is at a
+ 
+
+ align:start position:0%
+favorite illustrations of this is at a
+bunch of education technology
+
+ align:start position:0%
+bunch of education technology
+ 
+
+ align:start position:0%
+bunch of education technology
+conferences. Um, how many of you ever
+
+ align:start position:0%
+conferences. Um, how many of you ever
+ 
+
+ align:start position:0%
+conferences. Um, how many of you ever
+have been to a conference where they
+
+ align:start position:0%
+have been to a conference where they
+ 
+
+ align:start position:0%
+have been to a conference where they
+have like you have you have a badge,
+
+ align:start position:0%
+have like you have you have a badge,
+ 
+
+ align:start position:0%
+have like you have you have a badge,
+right? And you can put stickers on your
+
+ align:start position:0%
+right? And you can put stickers on your
+ 
+
+ align:start position:0%
+right? And you can put stickers on your
+badges or other things like this.
+
+ align:start position:0%
+badges or other things like this.
+ 
+
+ align:start position:0%
+badges or other things like this.
+Basically, like one of the stickers you
+
+ align:start position:0%
+Basically, like one of the stickers you
+ 
+
+ align:start position:0%
+Basically, like one of the stickers you
+can put on your badge. You can put like
+
+ align:start position:0%
+can put on your badge. You can put like
+ 
+
+ align:start position:0%
+can put on your badge. You can put like
+your pronouns. You can put some other
+
+ align:start position:0%
+your pronouns. You can put some other
+ 
+
+ align:start position:0%
+your pronouns. You can put some other
+things like that. You can put um buyer.
+
+ align:start position:0%
+things like that. You can put um buyer.
+ 
+
+ align:start position:0%
+things like that. You can put um buyer.
+You can basically like signal to people
+
+ align:start position:0%
+You can basically like signal to people
+ 
+
+ align:start position:0%
+You can basically like signal to people
+like I actually have the power to
+
+ align:start position:0%
+like I actually have the power to
+ 
+
+ align:start position:0%
+like I actually have the power to
+purchase things. Um and then when you w
+
+ align:start position:0%
+purchase things. Um and then when you w
+ 
+
+ align:start position:0%
+purchase things. Um and then when you w
+you know um uh if you know when you walk
+
+ align:start position:0%
+you know um uh if you know when you walk
+ 
+
+ align:start position:0%
+you know um uh if you know when you walk
+through the exhibit hall they will pay
+
+ align:start position:0%
+through the exhibit hall they will pay
+ 
+
+ align:start position:0%
+through the exhibit hall they will pay
+more attention to the people who have
+
+ align:start position:0%
+more attention to the people who have
+ 
+
+ align:start position:0%
+more attention to the people who have
+the little buyer things on them than
+
+ align:start position:0%
+the little buyer things on them than
+ 
+
+ align:start position:0%
+the little buyer things on them than
+they will to like you know critical
+
+ align:start position:0%
+they will to like you know critical
+ 
+
+ align:start position:0%
+they will to like you know critical
+social science researcher badge um is
+
+ align:start position:0%
+social science researcher badge um is
+ 
+
+ align:start position:0%
+social science researcher badge um is
+put on your thing or something like
+
+ align:start position:0%
+put on your thing or something like
+ 
+
+ align:start position:0%
+put on your thing or something like
+that. So that is an incred so um here
+
+ align:start position:0%
+that. So that is an incred so um here
+ 
+
+ align:start position:0%
+that. So that is an incred so um here
+are some things that you should take
+
+ align:start position:0%
+are some things that you should take
+ 
+
+ align:start position:0%
+are some things that you should take
+away. These these systems are incredibly
+
+ align:start position:0%
+away. These these systems are incredibly
+ 
+
+ align:start position:0%
+away. These these systems are incredibly
+complicated. There are all kinds of
+
+ align:start position:0%
+complicated. There are all kinds of
+ 
+
+ align:start position:0%
+complicated. There are all kinds of
+stakeholders in them but they're they're
+
+ align:start position:0%
+stakeholders in them but they're they're
+ 
+
+ align:start position:0%
+stakeholders in them but they're they're
+not so infinite. they're not so complex
+
+ align:start position:0%
+not so infinite. they're not so complex
+ 
+
+ align:start position:0%
+not so infinite. they're not so complex
+that we can't like make a chart that
+
+ align:start position:0%
+that we can't like make a chart that
+ 
+
+ align:start position:0%
+that we can't like make a chart that
+sort of manages and starts to understand
+
+ align:start position:0%
+sort of manages and starts to understand
+ 
+
+ align:start position:0%
+sort of manages and starts to understand
+all these things. Um but as we move
+
+ align:start position:0%
+all these things. Um but as we move
+ 
+
+ align:start position:0%
+all these things. Um but as we move
+forward and as we um look at more sort
+
+ align:start position:0%
+forward and as we um look at more sort
+ 
+
+ align:start position:0%
+forward and as we um look at more sort
+of you know a thing that a thing that
+
+ align:start position:0%
+of you know a thing that a thing that
+ 
+
+ align:start position:0%
+of you know a thing that a thing that
+you can do in any kind of education
+
+ align:start position:0%
+you can do in any kind of education
+ 
+
+ align:start position:0%
+you can do in any kind of education
+technology problem any educational
+
+ align:start position:0%
+technology problem any educational
+ 
+
+ align:start position:0%
+technology problem any educational
+setting be like all right who are going
+
+ align:start position:0%
+setting be like all right who are going
+ 
+
+ align:start position:0%
+setting be like all right who are going
+to be the stakeholders for this problem
+
+ align:start position:0%
+to be the stakeholders for this problem
+ 
+
+ align:start position:0%
+to be the stakeholders for this problem
+this thing and what are going to be
+
+ align:start position:0%
+this thing and what are going to be
+ 
+
+ align:start position:0%
+this thing and what are going to be
+their interests. Um the more you know
+
+ align:start position:0%
+their interests. Um the more you know
+ 
+
+ align:start position:0%
+their interests. Um the more you know
+and not you know again not just like
+
+ align:start position:0%
+and not you know again not just like
+ 
+
+ align:start position:0%
+and not you know again not just like
+their official interest their official
+
+ align:start position:0%
+their official interest their official
+ 
+
+ align:start position:0%
+their official interest their official
+like state policy interest is to raise
+
+ align:start position:0%
+like state policy interest is to raise
+ 
+
+ align:start position:0%
+like state policy interest is to raise
+test scores or something like that. Um
+
+ align:start position:0%
+test scores or something like that. Um
+ 
+
+ align:start position:0%
+test scores or something like that. Um
+but one of my favorite examples um that
+
+ align:start position:0%
+but one of my favorite examples um that
+ 
+
+ align:start position:0%
+but one of my favorite examples um that
+we're talking about is uh televisions
+
+ align:start position:0%
+we're talking about is uh televisions
+ 
+
+ align:start position:0%
+we're talking about is uh televisions
+were more likely to be used at the end
+
+ align:start position:0%
+were more likely to be used at the end
+ 
+
+ align:start position:0%
+were more likely to be used at the end
+of the day because people were tired. Um
+
+ align:start position:0%
+of the day because people were tired. Um
+ 
+
+ align:start position:0%
+of the day because people were tired. Um
+like your body's circadian rhythm um
+
+ align:start position:0%
+like your body's circadian rhythm um
+ 
+
+ align:start position:0%
+like your body's circadian rhythm um
+indicates how technologies be used in
+
+ align:start position:0%
+indicates how technologies be used in
+ 
+
+ align:start position:0%
+indicates how technologies be used in
+classroom. And that is just as real is
+
+ align:start position:0%
+classroom. And that is just as real is
+ 
+
+ align:start position:0%
+classroom. And that is just as real is
+just as real as the policy mandate to
+
+ align:start position:0%
+just as real as the policy mandate to
+ 
+
+ align:start position:0%
+just as real as the policy mandate to
+raise test scores um or the school
+
+ align:start position:0%
+raise test scores um or the school
+ 
+
+ align:start position:0%
+raise test scores um or the school
+board's enthusiasm for technology or
+
+ align:start position:0%
+board's enthusiasm for technology or
+ 
+
+ align:start position:0%
+board's enthusiasm for technology or
+whatever it is. Um and so we we can in
+
+ align:start position:0%
+whatever it is. Um and so we we can in
+ 
+
+ align:start position:0%
+whatever it is. Um and so we we can in
+any kind of system we can figure out who
+
+ align:start position:0%
+any kind of system we can figure out who
+ 
+
+ align:start position:0%
+any kind of system we can figure out who
+are the stakeholders in the system. What
+
+ align:start position:0%
+are the stakeholders in the system. What
+ 
+
+ align:start position:0%
+are the stakeholders in the system. What
+are the interests of those things? What
+
+ align:start position:0%
+are the interests of those things? What
+ 
+
+ align:start position:0%
+are the interests of those things? What
+are the disinterests? A thing is more
+
+ align:start position:0%
+are the disinterests? A thing is more
+ 
+
+ align:start position:0%
+are the disinterests? A thing is more
+likely to work if it attends to those
+
+ align:start position:0%
+likely to work if it attends to those
+ 
+
+ align:start position:0%
+likely to work if it attends to those
+real meaningful felt interests and if it
+
+ align:start position:0%
+real meaningful felt interests and if it
+ 
+
+ align:start position:0%
+real meaningful felt interests and if it
+avoids those real meaningful felt
+
+ align:start position:0%
+avoids those real meaningful felt
+ 
+
+ align:start position:0%
+avoids those real meaningful felt
+disinterests. And of course we're doing
+
+ align:start position:0%
+disinterests. And of course we're doing
+ 
+
+ align:start position:0%
+disinterests. And of course we're doing
+this like in a very detailed way in
+
+ align:start position:0%
+this like in a very detailed way in
+ 
+
+ align:start position:0%
+this like in a very detailed way in
+education. But if you were to let leave
+
+ align:start position:0%
+education. But if you were to let leave
+ 
+
+ align:start position:0%
+education. But if you were to let leave
+education and you were to go into
+
+ align:start position:0%
+education and you were to go into
+ 
+
+ align:start position:0%
+education and you were to go into
+healthcare, if you were to go into legal
+
+ align:start position:0%
+healthcare, if you were to go into legal
+ 
+
+ align:start position:0%
+healthcare, if you were to go into legal
+technology, if you were going to retail,
+
+ align:start position:0%
+technology, if you were going to retail,
+ 
+
+ align:start position:0%
+technology, if you were going to retail,
+you can do the exact same exercise. um
+
+ align:start position:0%
+you can do the exact same exercise. um
+ 
+
+ align:start position:0%
+you can do the exact same exercise. um
+the technology that you're building for
+
+ align:start position:0%
+the technology that you're building for
+ 
+
+ align:start position:0%
+the technology that you're building for
+a hospital, like it has to work for a
+
+ align:start position:0%
+a hospital, like it has to work for a
+ 
+
+ align:start position:0%
+a hospital, like it has to work for a
+doctor, but it has to work for a nurse
+
+ align:start position:0%
+doctor, but it has to work for a nurse
+ 
+
+ align:start position:0%
+doctor, but it has to work for a nurse
+and an orderly and a patient and the
+
+ align:start position:0%
+and an orderly and a patient and the
+ 
+
+ align:start position:0%
+and an orderly and a patient and the
+patient's representative and the
+
+ align:start position:0%
+patient's representative and the
+ 
+
+ align:start position:0%
+patient's representative and the
+hospital's lawyers and all these
+
+ align:start position:0%
+hospital's lawyers and all these
+ 
+
+ align:start position:0%
+hospital's lawyers and all these
+different kinds of people. Um and so,
+
+ align:start position:0%
+different kinds of people. Um and so,
+ 
+
+ align:start position:0%
+different kinds of people. Um and so,
+you know, on the one hand, especially
+
+ align:start position:0%
+you know, on the one hand, especially
+ 
+
+ align:start position:0%
+you know, on the one hand, especially
+when people are designers of software,
+
+ align:start position:0%
+when people are designers of software,
+ 
+
+ align:start position:0%
+when people are designers of software,
+we can have this sense of like, oh, I'm
+
+ align:start position:0%
+we can have this sense of like, oh, I'm
+ 
+
+ align:start position:0%
+we can have this sense of like, oh, I'm
+building things for a user. I'm building
+
+ align:start position:0%
+building things for a user. I'm building
+ 
+
+ align:start position:0%
+building things for a user. I'm building
+things for like this individual user
+
+ align:start position:0%
+things for like this individual user
+ 
+
+ align:start position:0%
+things for like this individual user
+who's got their fingers on their
+
+ align:start position:0%
+who's got their fingers on their
+ 
+
+ align:start position:0%
+who's got their fingers on their
+keyboard or their thumb on the screen or
+
+ align:start position:0%
+keyboard or their thumb on the screen or
+ 
+
+ align:start position:0%
+keyboard or their thumb on the screen or
+something like that. Um, but I would
+
+ align:start position:0%
+something like that. Um, but I would
+ 
+
+ align:start position:0%
+something like that. Um, but I would
+encourage you as we're thinking through
+
+ align:start position:0%
+encourage you as we're thinking through
+ 
+
+ align:start position:0%
+encourage you as we're thinking through
+all these things to to think about these
+
+ align:start position:0%
+all these things to to think about these
+ 
+
+ align:start position:0%
+all these things to to think about these
+networks of interests and stakeholders
+
+ align:start position:0%
+networks of interests and stakeholders
+ 
+
+ align:start position:0%
+networks of interests and stakeholders
+much more broadly. Okay. Um, we'll talk
+
+ align:start position:0%
+much more broadly. Okay. Um, we'll talk
+ 
+
+ align:start position:0%
+much more broadly. Okay. Um, we'll talk
+to some education school deans on
+
+ align:start position:0%
+to some education school deans on
+ 
+
+ align:start position:0%
+to some education school deans on
+Wednesday. We'll learn a little bit
+
+ align:start position:0%
+Wednesday. We'll learn a little bit
+ 
+
+ align:start position:0%
+Wednesday. We'll learn a little bit
+about uh implementation, how you
+
+ align:start position:0%
+about uh implementation, how you
+ 
+
+ align:start position:0%
+about uh implementation, how you
+overcome some of these kinds of
+
+ align:start position:0%
+overcome some of these kinds of
+ 
+
+ align:start position:0%
+overcome some of these kinds of
+challenges from me. We'll hear a little
+
+ align:start position:0%
+challenges from me. We'll hear a little
+ 
+
+ align:start position:0%
+challenges from me. We'll hear a little
+bit about the National Education
+
+ align:start position:0%
+bit about the National Education
+ 
+
+ align:start position:0%
+bit about the National Education
+Technology Plan. Um, and I will pair you
+
+ align:start position:0%
+Technology Plan. Um, and I will pair you
+ 
+
+ align:start position:0%
+Technology Plan. Um, and I will pair you
+up with each other um to be able to do
+
+ align:start position:0%
+up with each other um to be able to do
+ 
+
+ align:start position:0%
+up with each other um to be able to do
+some peer editing of your essays and
+
+ align:start position:0%
+some peer editing of your essays and
+ 
+
+ align:start position:0%
+some peer editing of your essays and
+that will get us through the week. Sound
+
+ align:start position:0%
+that will get us through the week. Sound
+ 
+
+ align:start position:0%
+that will get us through the week. Sound
+good? Bueno, let me know if I can help
+
+ align:start position:0%
+good? Bueno, let me know if I can help
+ 
+
+ align:start position:0%
+good? Bueno, let me know if I can help
+you with anything. Otherwise, have a
+
+ align:start position:0%
+you with anything. Otherwise, have a
+ 
+
+ align:start position:0%
+you with anything. Otherwise, have a
+wonderful rest of your afternoon.
\ No newline at end of file
diff --git a/6XV3uLfKzog.txt b/6XV3uLfKzog.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f9f6d4b1195e102b5eb07ca8dd28b7c85d67c72f
--- /dev/null
+++ b/6XV3uLfKzog.txt
@@ -0,0 +1,527 @@
+The data path diagram isn't all that useful
+in diagramming the pipelined execution of
+
+an instruction sequence since we need a new
+copy of the diagram for each clock cycle.
+
+A more compact and easier-to-read diagram
+of pipelined execution is provided by the
+
+pipeline diagrams we met back in Part 1 of
+the course.
+
+There's one row in the diagram for each pipeline
+stage and one column for each cycle of execution.
+
+Entries in the table show which instruction
+is in each pipeline stage at each cycle.
+
+In normal operation, a particular instruction
+moves diagonally through the diagram as it
+
+proceeds through the five pipeline stages.
+
+To understand data hazards, let's first remind
+ourselves of when the register file is read
+
+and written for a particular instruction.
+
+Register reads happen when the instruction
+is in the RF stage, i.e., when we're reading
+
+the instruction's register operands.
+
+Register writes happen at the end of the cycle
+when the instruction is in the WB stage.
+
+For example, for the first LD instruction,
+we read R1 during cycle 2 and write R2 at
+
+the end of cycle 5.
+
+Or consider the register file operations in
+cycle 6:
+
+we're reading R12 and R13 for the MUL instruction
+in the RF stage, and writing R4 at the end
+
+of the cycle for the LD instruction in the
+WB stage.
+
+Okay, now let's see what happens when there
+are data hazards.
+
+In this instruction sequence, the ADDC instruction
+writes its result in R2, which is immediately
+
+read by the following SUBC instruction.
+
+Correct execution of the SUBC instruction
+clearly depends on the results of the ADDC
+
+instruction.
+
+This what we'd call a read-after-write dependency.
+
+This pipeline diagram shows the cycle-by-cycle
+execution where we've circled the cycles during
+
+which ADDC writes R2 and SUBC reads R2.
+
+Oops!
+
+ADDC doesn't write R2 until the end of cycle
+5, but SUBC is trying to read the R2 value
+
+in cycle 3.
+
+The value in R2 in the register file in cycle
+3 doesn't yet reflect the execution of the
+
+ADDC instruction.
+
+So as things stand the pipeline would *not*
+correctly execute this instruction sequence.
+
+This instruction sequence has triggered a
+data hazard.
+
+We want the pipelined CPU to generate the
+same program results as the unpipelined CPU,
+
+so we'll need to figure out a fix.
+
+There are three general strategies we can
+pursue to fix pipeline hazards.
+
+Any of the techniques will work, but as we'll
+see they have different tradeoffs for instruction
+
+throughput and circuit complexity.
+
+The first strategy is to stall instructions
+in the RF stage until the result they need
+
+has been written to the register file.
+
+"Stall" means that we don't reload the instruction
+register at the end of the cycle, so we'll
+
+try to execute the same instruction in the
+next cycle.
+
+If we stall one pipeline stage, all earlier
+stages must also be stalled since they are
+
+blocked by the stalled instruction.
+
+If an instruction is stalled in the RF stage,
+then the IF stage is also stalled.
+
+Stalling will always work, but has a negative
+impact on instruction throughput.
+
+Stall for too many cycles and you'll loose
+the performance advantages of pipelined execution!
+
+The second strategy is to route the needed
+value to earlier pipeline stages as soon as
+
+its computed.
+
+This called bypassing or forwarding.
+
+As it turns out, the value we need often exists
+somewhere in the pipelined data path, it just
+
+hasn't been written yet to the register file.
+
+If the value exists and can be forwarded to
+where it's needed, we won't need to stall.
+
+We'll be able to use this strategy to avoid
+stalling on most types of data hazards.
+
+The third strategy is called speculation.
+
+We'll make an intelligent guess for the needed
+value and continue execution.
+
+Once the actual value is determined, if we
+guessed correctly, we're all set.
+
+If we guessed incorrectly, we have to back
+up execution and restart with the correct
+
+value.
+
+Obviously speculation only makes sense if
+it's possible to make accurate guesses.
+
+We'll be able to use this strategy to avoid
+stalling on control hazards.
+
+Let's see how the first two strategies work
+when dealing with our data hazard.
+
+Applying the stall strategy to our data hazard,
+we need to stall the SUBC instruction in the
+
+RF stage until the ADDC instruction writes
+its result in R2.
+
+So in the pipeline diagram, SUBC is stalled
+three times in the RF stage until it can finally
+
+access the R2 value from the register file
+in cycle 6.
+
+Whenever the RF stage is stalled, the IF stage
+is also stalled.
+
+You can see that in the diagram too.
+
+But when RF is stalled, what should the ALU
+stage do in the next cycle?
+
+The RF stage hasn't finished its job and so
+can't pass along its instruction!
+
+The solution is for the RF stage to make-up
+an innocuous instruction for the ALU stage,
+
+what's called a NOP instruction, short for
+"no operation".
+
+A NOP instruction has no effect on the CPU
+state, i.e., it doesn't change the contents
+
+of the register file or main memory.
+
+For example any OP-class or OPC-class instruction
+that has R31 as its destination register is
+
+a NOP.
+
+The NOPs introduced into the pipeline by the
+stalled RF stage are shown in red.
+
+Since the SUBC is stalled in the RF stage
+for three cycles, three NOPs are introduced
+
+into the pipeline.
+
+We sometimes refer to these NOPs as "bubbles"
+in the pipeline.
+
+How does the pipeline know when to stall?
+
+It can compare the register numbers in the
+RA and RB fields of the instruction in the
+
+RF stage with the register numbers in the
+RC field of instructions in the ALU, MEM,
+
+and WB stage.
+
+If there's a match, there's a data hazard
+and the RF stage should be stalled.
+
+The stall will continue until there's no hazard
+detected.
+
+There are a few details to take care of:
+some instructions don't read both registers,
+
+the ST instruction doesn't use its RC field,
+and we don't want R31 to match since it's
+
+always okay to read R31 from the register
+file.
+
+Stalling will ensure correct pipelined execution,
+but it does increase the effective CPI.
+
+This will lead to longer execution times if
+the increase in CPI is larger than the decrease
+
+in cycle time afforded by pipelining.
+
+To implement stalling, we only need to make
+two simple changes to our pipelined data path.
+
+We generate a new control signal, STALL, which,
+when asserted, disables the loading of the
+
+three pipeline registers at the input of the
+IF and RF stages, which means they'll have
+
+the same value next cycle as they do this
+cycle.
+
+We also introduce a mux to choose the instruction
+to be sent along to the ALU stage.
+
+If STALL is 1, we choose a NOP instruction,
+e.g., an ADD with R31 as its destination.
+
+If STALL is 0, the RF stage is not stalled,
+so we pass its current instruction to the
+
+ALU.
+
+And here we see how to compute STALL as described
+in the previous slide.
+
+The additional logic needed to implement stalling
+is pretty modest, so the real design tradeoff
+
+is about increased CPI due to stalling vs.
+decreased cycle time due to pipelining.
+
+So we have a solution, although it carries
+some potential performance costs.
+
+Now let's consider our second strategy:
+bypassing, which is applicable if the data
+
+we need in the RF stage is somewhere in the
+pipelined data path.
+
+In our example, even though ADDC doesn't write
+R2 until the end of cycle 5, the value that
+
+will be written is computed during cycle 3
+when the ADDC is in the ALU stage.
+
+In cycle 3, the output of the ALU is the value
+needed by the SUBC that's in the RF stage
+
+in the same cycle.
+
+So, if we detect that the RA field of the
+instruction in the RF stage is the same as
+
+the RC field of the instruction in the ALU
+stage, we can use the output of the ALU in
+
+place of the (stale) RA value being read from
+the register file.
+
+No stalling necessary!
+
+In our example, in cycle 3 we want to route
+the output of the ALU to the RF stage to be
+
+used as the value for R2.
+
+We show this with a red "bypass arrow" showing
+data being routed from the ALU stage to the
+
+RF stage.
+
+To implement bypassing, we'll add a many-input
+multiplexer to the read ports of the register
+
+file so we can select the appropriate value
+from other pipeline stages.
+
+Here we show the combinational bypass paths
+from the ALU, MEM, and WB stages.
+
+For the bypassing example of the previous
+slides, we use the blue bypass path during
+
+cycle 3 to get the correct value for R2.
+
+The bypass muxes are controlled by logic that's
+matching the number of the source register
+
+to the number of the destination registers
+in the ALU, MEM, and WB stages, with the usual
+
+complications of dealing with R31.
+
+What if there are multiple matches, i.e.,
+if the RF stage is trying to read a register
+
+that's the destination for, say, the instructions
+in both the ALU and MEM stages?
+
+No problem!
+
+We want to select the result from the most
+recent instruction, so we'd chose the ALU
+
+match if there is one, then the MEM match,
+then the WB match, then, finally, the output
+
+of the register file.
+
+Here's diagram showing all the bypass paths
+we'll need.
+
+Note that branches and jumps write their PC+4
+value into the register file, so we'll need
+
+to bypass from the PC+4 values in the various
+stages as well as the ALU values.
+
+Note that the bypassing is happening at the
+end of the cycle, e.g., after the ALU has
+
+computed its answer.
+
+To accommodate the extra t_PD of the bypass
+mux, we'll have to extend the clock period
+
+by a small amount.
+
+So once again there's a design tradeoff - the
+increased CPI of stalling vs the slightly
+
+increased cycle time of bypassing.
+
+And, of course, in the case of bypassing there's
+the extra area needed for the necessary wiring
+
+and muxes.
+
+We can cut back on the costs by reducing the
+amount of bypassing, say, to only bypassing
+
+ALU results from the ALU stage and use stalling
+to deal with all the other data hazards.
+
+If we implement full bypassing, do we still
+need the STALL logic?
+
+As it turns out, we do!
+
+There's one data hazard that bypassing doesn't
+completely address.
+
+Consider trying to immediately the use the
+result of a LD instruction.
+
+In the example shown here, the SUBC is trying
+to use the value the immediately preceding
+
+LD is writing to R2.
+
+This is called a load-to-use hazard.
+
+Recalling that LD data isn't available in
+the data path until the cycle when LD reaches
+
+the WB stage, even with full bypassing we'll
+need to stall SUBC in the RF stage until cycle
+
+5, introducing two NOPs into the pipeline.
+
+Without bypassing from the WB stage, we need
+to stall until cycle 6.
+
+In summary, we have two strategies for dealing
+with data hazards.
+
+We can stall the IF and RF stages until the
+register values needed by the instruction
+
+in the RF stage are available in the register
+file.
+
+The required hardware is simple, but the NOPs
+introduced into the pipeline waste CPU cycles
+
+and result in an higher effective CPI.
+
+Or we can use bypass paths to route the required
+values to the RF stage assuming they exist
+
+somewhere in the pipelined data path.
+
+This approach requires more hardware than
+stalling, but doesn't reduce the effective
+
+CPI.
+
+Even if we implement bypassing, we'll still
+need stalls to deal with load-to-use hazards.
+
+Can we keep adding pipeline stages in the
+hopes of further reducing the clock period?
+
+More pipeline stages mean more instructions
+in the pipeline at the same time, which in
+
+turn increases the chance of a data hazard
+and the necessity of stalling, thus increasing
+
+CPI.
+
+Compilers can help reduce dependencies by
+reorganizing the assembly language code they
+
+produce.
+
+Here's the load-to-use hazard example we saw
+earlier.
+
+Even with full bypassing, we'd need to stall
+for 2 cycles.
+
+But if the compiler (or assembly language
+programmer!) notices that the MUL and XOR
+
+instructions are independent of the SUBC instruction
+and hence can be moved before the SUBC,
+
+the dependency is now such that the LD is
+naturally in the WB stage when the SUBC is
+
+in the RF stage, so no stalls are needed.
+
+This optimization only works when the compiler
+can find independent instructions to move
+
+around.
+
+Unfortunately there are plenty of programs
+where such instructions are hard to find.
+
+Then there's one final approach we could take
+-
+
+change the ISA so that data hazards are part
+of the ISA, i.e., just explain that writes
+
+to the destination register happen with a
+3-instruction delay!
+
+If NOPs are needed, make the programmer add
+them to the program.
+
+Simplify the hardware at the "small" cost
+of making the compilers work harder.
+
+You can imagine exactly how much the compiler
+writers will like this suggestion.
+
+Not to mention assembly language programmers!
+
+And you can change the ISA again when you
+add more pipeline stages!
+
+This is how a compiler writer views CPU architects
+who unilaterally change the ISA to save a
+
+few logic gates :)
+The bottom line is that successful ISAs have
+
+very long lifetimes and so shouldn't include
+tradeoffs driven by short-term implementation
+
+considerations.
+
+Best not to go there.
\ No newline at end of file
diff --git a/6gMgNriK1Nk.txt b/6gMgNriK1Nk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a47aba0981ac22019b367bc98ffbb19e5c5dac11
--- /dev/null
+++ b/6gMgNriK1Nk.txt
@@ -0,0 +1,3476 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: So last
+time we started
+
+talking about superfluid helium.
+
+And we said that the
+phase diagram of helium-4,
+
+the isotope that is a boson
+has the following interesting
+
+properties.
+
+First of all, helium
+stays a liquid
+
+all the way down
+to 0 temperature
+
+because of the combinations
+of its light mass and heat
+
+interactions.
+
+And secondly, that [INAUDIBLE]
+to cool down helium
+
+through this process
+of evaporated cooling,
+
+one immediately observes
+something interesting
+
+happening at temperatures
+below 2 degrees
+
+Kelvin, where it becomes
+this superfluid that
+
+has a number of
+interesting properties.
+
+And in particular as
+pertaining to viscosity,
+
+we made two observations.
+
+First of all, you can
+make these capillaries--
+
+and I'll show you been
+movie in more detail later
+
+on where it flows through
+capillaries as if there
+
+is no resistance
+and there is nothing
+
+that sticks to the walls
+of the capillaries.
+
+It flows without
+viscosity, whereas there
+
+was this experiment of
+Andronikashvili, in which you
+
+had something that
+was oscillating
+
+and you were calculating
+how much of the helium
+
+was stuck to the plates
+of the container.
+
+And the result was
+something like this,
+
+that is there was a decrease
+in the amount of fluid
+
+that is stuck to the plates.
+
+But it doesn't go
+immediately down to 0.
+
+It has a kind of
+form such as this
+
+that I will draw more
+clearly now and explain.
+
+So what we did last time was
+to note that people observed
+
+that there were
+some similarities
+
+between this
+superfluid transition
+
+and Bose-Einstein condensation.
+
+But what I would
+like to highlight
+
+in the beginning
+of this lecture is
+
+that there are also very
+important differences.
+
+So let's think about
+these distinctions
+
+between Bose-Einstein condensate
+add the superfluid helium.
+
+One set of things we would
+like to take from the picture
+
+that I have over there, which
+is diffraction of the fluid that
+
+is stuck to the plates
+and in some sense
+
+behaves like a normal fluid.
+
+Now let me make the analogy
+to Bose-Einstein condensation.
+
+You know that in the
+Bose-Einstein condensation
+
+there was also this phenomenon
+that there was a separation
+
+into two parts of
+the total density.
+
+And be regarded as a
+function of temperature
+
+some part of the density as
+belonging to the normal state.
+
+So when you are above
+Tc of n, everything
+
+is essentially normal.
+
+And then what happens is
+that when you hit Tc of n
+
+you can no longer put
+all of the particles
+
+that you have in
+the excited states.
+
+So the fraction that goes
+in the excited states
+
+goes down and eventually
+goes to 0 at 0 temperature.
+
+And essentially, this would
+be the reverse of the curve
+
+that we have in that
+figure over there.
+
+Basically, there's
+a portion that
+
+would be the normal part that
+would be looking like this.
+
+Now, the way that we
+obtained this result
+
+was that basically there
+was a fraction that
+
+was in the normal state.
+
+The part that was
+excited was described
+
+by this simple formula that was
+g over lambda cubed [INAUDIBLE]
+
+of 3/2.
+
+So it went to 0 as T to the 3/2.
+
+So basically, the
+proportionality
+
+here is T to the 3/2.
+
+And then basically,
+the curve would
+
+come down here and
+go to 0 linearly.
+
+Now what is shown
+in the experiment
+
+is that the curve
+actually goes to 0
+
+in a much more sharp fashion.
+
+And actually, when people try
+to fit a curve through this,
+
+the curve looks something like
+Tc minus T to the 2/3 over.
+
+But also it goes to 0 much
+more rapidly than the curve
+
+that we have for
+Bose-Einstein condensation.
+
+Indeed, it goes through
+0 proportionately to T
+
+to the fourth.
+
+And so that's something that we
+need to understand and explain.
+
+Now all of the properties of
+the Bose-Einstein condensate
+
+was very easy to
+describe once we realized
+
+that all of the things that
+correspond to excitation,
+
+such as the energy,
+heat capacity,
+
+pressure, come from
+this fraction that
+
+is in the excited state.
+
+And we can calculate,
+say, the contribution
+
+to energy heat
+capacity, et cetera.
+
+And in particular, if we look
+at the behavior of the heat
+
+capacity as a function
+of temperature,
+
+for this Bose-Einstein
+condensate, the behavior
+
+that we had was that again
+simply at low temperatures
+
+it was going proportionately
+to T to the 3/2,
+
+because this was the number
+of excitations that you had.
+
+So these two T to the
+3/2 are very much related
+
+to each other.
+
+And then this curve would
+basically go along its way
+
+until it hit Tc of
+n at some point.
+
+And we separately
+calculated the behavior
+
+coming from high temperatures.
+
+And the behavior from
+high temperatures
+
+would start with
+the classical result
+
+that the heat capacity
+is 3/2 per particle
+
+due to the kinetic energy that
+you can put in these things.
+
+And then it would rise, and it
+would then join this curve over
+
+here.
+
+Now when you look at the
+actual heat capacity,
+
+indeed the shape up
+the heat capacity
+
+is the thing that gives this
+transition the name of a lambda
+
+transition.
+
+It kind of looks like a lambda.
+
+And at Tc there are
+divergences approaching
+
+from the two sides that
+behave like the log.
+
+And again more
+importantly, what we
+
+find is that at
+0 temperature, it
+
+doesn't go through 0, the
+heat capacity as T to the 3/2,
+
+but rather as T to
+the third power.
+
+So the red curve
+corresponds to superfluid,
+
+the green curve corresponds
+to Bose-Einstein condensate.
+
+And so they're clearly
+different from each other.
+
+So that's what we would
+like you to understand.
+
+Well the thing that is easiest
+to understand and figure out
+
+is the difference between
+these heat capacities.
+
+And the reason for that
+is that we had already
+
+seen a form that was of
+the heat capacity that
+
+behaved like T cubed.
+
+That was when we were looking
+at phonons in a solid.
+
+So let's remind
+you why was it that
+
+for the Bose-Einstein
+condensate we
+
+were getting this T
+to the 3/2 behavior?
+
+The reason for that was that
+the various excitations,
+
+I could plot as a function
+of k, or p, which is h bar k.
+
+They're very much
+related to each other.
+
+And for the
+Bose-Einstein condensate,
+
+the form was simply
+a parabola, which
+
+is this p squared over
+2 mass of the helium.
+
+Let's say, assuming that
+what we are dealing with
+
+is non-interacting particles
+with mass of helium.
+
+And this parabolic
+curve essentially
+
+told us that various quantities
+behave as T to the 3/2.
+
+Roughly, the idea is that
+at some temperature that
+
+has energy of the order
+of kT, you figure out
+
+how far you have excited things.
+
+And since this
+form is a parabola,
+
+the typical p is going to
+scale like T to the 1/2.
+
+You have a volume in three
+dimensions in p space.
+
+If the radius goes
+like T to the 1/2,
+
+the volume goes
+like T to the 3/2.
+
+That's why you have all kinds
+of excitations such as this.
+
+And the reason for the
+Bose-Einstein condensation
+
+was that you would start to fill
+out all of these excitations.
+
+And when you were adding all
+of the mean occupation numbers,
+
+the answer was not
+coming up all the way
+
+to the total number
+of particles.
+
+So then you have to put
+an excess at p close
+
+to 0, which corresponds to the
+ground state of this system.
+
+Now of course when
+you look at helium,
+
+helium molecules, helium
+atoms have the interactions
+
+between them that we discussed.
+
+In particular, you can't really
+put them on top of each other.
+
+There is a hard exclusion
+when you bring things
+
+close to each other.
+
+So the ground
+state of the system
+
+must look very different
+from the ground state
+
+of the Bose-Einstein condensate
+in which the particles freely
+
+occupy the entire box.
+
+So there is a very
+difficult story
+
+associated with
+figuring out what
+
+the ground state of this
+combination of interacting
+
+particles that make
+up liquid helium is.
+
+What is the behavior?
+
+What's the many-body wave
+function at 0 temperature?
+
+Now as we see here, in order
+to understand the heat capacity
+
+we really don't
+need to know what
+
+is happening at
+the ground state.
+
+What we need to know in
+order to find heat capacity
+
+is how to put more energy in the
+system above the ground state.
+
+So we need to know
+something about excitations.
+
+And so that's the
+perspective that Landau took.
+
+Landau said, well, this is
+the spectrum of excitations
+
+if you had [? plain ?] particles
+without any interactions.
+
+Let's imagine what
+happens if we gradually
+
+tune in the interactions,
+the particles
+
+start to repel each
+other, et cetera.
+
+This non-interacting
+ground state
+
+that we had in which the
+particles were uniformly
+
+distributed across
+the system will
+
+evolve into some complicated
+ground state I don't know.
+
+And then, presumably
+there would be a spectrum
+
+of excitations around
+that ground state.
+
+Now the excitations around
+the non-interacting ground
+
+state we can label by
+this momentum peak.
+
+And it kind of
+makes sense that we
+
+should be able to have a
+singular label for excitations
+
+around the ground state of
+these interacting particles.
+
+And this is where
+you sort of needed
+
+a little bit of Landau's
+type of insight.
+
+He said, well,
+presumably what you
+
+do when you have
+excitations of momentum p
+
+is to distort the wave
+function in a manner that
+
+is consistent with having these
+kind of excitations of momentum
+
+p.
+
+And he said, well
+we typically know
+
+that if you have
+a fluid or a solid
+
+and we want to impart some
+momentum above the ground
+
+state, if will go in
+the form of phonons.
+
+These are distortions in
+which the density will
+
+vary in some sinusoidal or
+cosine way across the system.
+
+So he said that maybe
+what is happening
+
+is that for these
+excitations you
+
+have to take what ever this
+interacting ground state is--
+
+which we don't know and
+can't write that down--
+
+but hope that
+excitations around it
+
+correspond to these
+distortions in density.
+
+And that by analogy with
+what happens for fluids,
+
+that the spectrum of excitations
+will then become a linear.
+
+You would have something
+like a sound wave
+
+that you would have in
+a liquid or a solid.
+
+So if you do this, if you
+have a linear spectrum
+
+then we can see what happen.
+
+For a particular energy
+of the order of kT,
+
+we will go here,
+occupied momenta that
+
+would be of the order
+of kT over H bar.
+
+The number of excitations would
+be something like this cubed,
+
+and so you would
+imagine that you
+
+would get a heat capacity that
+is proportional to this times
+
+kB.
+
+And if you do things
+correctly, like really
+
+for the case of
+phonons or photons,
+
+you can even figure out what
+the numerical prefactor is here.
+
+And there's a velocity
+here because this curve
+
+goes like H bar vP.
+
+So then you can
+compare what you have
+
+over here with the coefficient
+of the T cubed over here,
+
+and you could even figure
+out what this velocity is.
+
+And it turns out to be of the
+order of 240 meters per second.
+
+A typical sound wave that
+you would have in a fluid.
+
+So that's kind of
+a reasonable thing.
+
+Now of course, when you go
+to higher and higher momenta,
+
+it corresponds to essentially
+shorter and shorter
+
+wavelengths.
+
+You expect that when
+you get wavelengths
+
+that is of the order of
+the interatomic spacing,
+
+then the interactions become
+less and less important.
+
+You have particles
+rattling in a cage
+
+that is set up by
+everybody else.
+
+And then you should regain
+this kind of spectrum
+
+at high values of momentum.
+
+And so what Landau
+did was he basically
+
+joined these things
+together and posed
+
+that there is a spectrum
+such as this that
+
+has what is called
+a phonon part, which
+
+is this linear part where
+energy goes like H bar,
+
+like the velocity
+times the momentum.
+
+And it has a part that in
+the vicinity of this point,
+
+you can expand parabolically.
+
+And it's called rotons.
+
+There is a gap
+delta, and then H bar
+
+squared over 2, some effective
+mass, k minus k0 squared.
+
+This k0 turns out to
+be roughly of the order
+
+of the inverse
+[INAUDIBLE], two Angstrom
+
+inverse, between particles.
+
+This mu is of the order
+of mass of [INAUDIBLE].
+
+So about 10 years
+or so after Landau,
+
+people are able to get to this
+whole spectrum of excitation
+
+through neutron scattering
+and other scattering
+
+types of experiments.
+
+And so this picture
+was confirmed.
+
+So, yes?
+
+AUDIENCE: What is a
+roton? [INAUDIBLE]
+
+PROFESSOR: Over here
+what you are seeing
+
+is essentially particles
+rattling in the cage.
+
+It is believed that
+what is happening here
+
+are collections of
+three or four atoms that
+
+are kind of rotating
+in a bigger cage.
+
+So something, the
+picture that people draw
+
+is three or four
+particles rotating around.
+
+Yes?
+
+AUDIENCE: Is there
+some [INAUDIBLE] curve
+
+where energy's
+decreasing [INAUDIBLE]?
+
+Does the transition between
+photon and roton [INAUDIBLE]?
+
+PROFESSOR: There is no
+thermodynamic or other rule
+
+that says that the energy should
+be one of [INAUDIBLE] momentum
+
+that I know.
+
+Yes?
+
+AUDIENCE: Is there an
+expression for that k0
+
+in terms of temperature and
+other properties of the system?
+
+PROFESSOR: This
+curve of excitations
+
+is supposed to be property
+of the ground state.
+
+That is, you take this
+system in its ground state,
+
+and then you create
+an excitation that
+
+has some particular
+momentum and calculate
+
+what the energy of that is.
+
+Actually, this whole
+curve is phenomenological,
+
+because in order to get
+the excitations you better
+
+have an expression for
+what the ground state is.
+
+And so writing a
+kind of wave function
+
+that describes the ground state
+of this interacting system
+
+is a very difficult task.
+
+I think Feynman has some
+variational type of wave
+
+function that we can start
+and work with, and then
+
+calculate things approximately
+in terms of that.
+
+Yes?
+
+AUDIENCE: What inspired
+Landau to propose
+
+that there was a [INAUDIBLE]?
+
+PROFESSOR: Actually,
+it was not so much
+
+I think looking at
+this curve, but which
+
+I think if you
+want to match that
+
+and that, you have to
+have something like this.
+
+But this was really that the
+whole experimental version
+
+of the heat capacity,
+it didn't seem
+
+like this expression
+was sufficient.
+
+And then there was some amount
+of excitation and energy
+
+at the temperatures that were
+experimentally accessible
+
+that heated at the presence
+of the rotons in the spectrum.
+
+Yes?
+
+AUDIENCE: So
+continuing [INAUDIBLE],
+
+if you raise the thermal energy
+kBT, [INAUDIBLE] level where
+
+you have multiple
+roots of this curve.
+
+PROFESSOR: Yes.
+
+AUDIENCE: So you will be
+able to excite some states
+
+and have some kind of gap, like
+a gap of momenta which are not.
+
+PROFESSOR: OK, so at any
+finite temperatures-- and I'll
+
+do the calculation for
+you shortly-- there
+
+is a finite probability for
+exciting all of these states.
+
+What you are saying
+is that when there
+
+is more occupation at this
+momentum compared to that,
+
+but much less compared to this.
+
+So that again does not
+violate any condition.
+
+So it is like, again, trying to
+shake this system of particles.
+
+Let's imagine that
+you have grains,
+
+and you are trying
+to shake them.
+
+And it may be that at
+some shaking frequencies,
+
+then there are things
+that are taking place
+
+at short distances in
+addition to some waves
+
+that you're generating.
+
+Yeah?
+
+AUDIENCE: I have a question
+about the methodology
+
+of getting this
+spectrum, because if we
+
+have a experimental result
+of the [INAUDIBLE] capacity,
+
+then if we assume
+there's a spectrum,
+
+there has to be
+this one, because it
+
+gives a one to one
+correspondence.
+
+So we can get the spectrum
+directly from the c.
+
+So--
+
+PROFESSOR: I'm not sure,
+because in reality this
+
+is going to be spectrum in
+three-dimensional space.
+
+And there is certainly
+an expression
+
+that relates the heat capacity
+to the excitation spectrum.
+
+What I'm not sure is
+whether mathematically
+
+that expression
+uniquely invertible.
+
+It is given an epsilon-- c,
+you have a unique epsilon of p.
+
+Certainly, given an epsilon
+of p, you have a unique c.
+
+Yes?
+
+AUDIENCE: But if the excitation
+spectrum only depends on,
+
+let's say, k squared, not on
+the three-dimensional components
+
+of k, then maybe
+it's much easier
+
+to draw a one to
+one correspondence?
+
+PROFESSOR: I don't
+know, because you
+
+have a function of
+temperature and you
+
+want to convert it to
+a function of momentum
+
+that after some
+integrations will give you
+
+that function of temperature.
+
+I don't know the difficulty
+of mathematically doing that.
+
+I know that I can't off my head
+think of an inversion formula.
+
+It's not like the function
+that you're inversing.
+
+So the Landau spectrum
+can explain this part.
+
+It turns out that the Landau
+spectrum cannot explain this
+
+logarithmic divergence.
+
+Yes?
+
+AUDIENCE: Sorry, one
+more question about this.
+
+The allowed values of
+k, do they get modified,
+
+or are they thought
+to be the same?
+
+PROFESSOR: No.
+
+So basically at some point,
+I have to change perspective
+
+from a sum over k to an integral
+over k or an integral over p.
+
+The density of
+states in momentum
+
+is something that is
+kind of invariant.
+
+It is a very slight
+function of shape.
+
+So the periodic
+boundary conditions
+
+and the open boundary
+conditions, et cetera,
+
+give you something slightly
+different over here.
+
+But by the time you
+go to the continuum,
+
+it's a property
+of dimension only.
+
+It doesn't really depend
+on the underlying shape.
+
+AUDIENCE: So we
+still change sums
+
+for integrals with
+the same rules?
+
+PROFESSOR: Yes.
+
+It's a sort of general
+density of state property.
+
+So there's some nice
+formula that tells you
+
+what the density of state
+is for an arbitrary shape,
+
+and the leading term is
+always proportional to volume
+
+or area [INAUDIBLE]
+the density of state
+
+that you have been calculating.
+
+And then there are
+some leading terms
+
+that are proportional to
+if it is volume to area,
+
+or number of edges, et cetera.
+
+But those are kind of subleading
+the thermodynamic sense.
+
+So I guess Feynman
+did a lot of work
+
+on formalizing these
+ideas of Landau getting
+
+some idea of what the ground
+state does, is, and excitations
+
+that you can have
+about the spectrum.
+
+And so he was very
+happy at being
+
+able to explain this,
+including the nature of rotons,
+
+et cetera.
+
+And he was worried
+that somehow he
+
+couldn't get this
+logarithmic divergence.
+
+And that bothered
+him a little bit,
+
+but Onsager told him
+that that's really
+
+a much more fundamental
+property that
+
+depends on critical phenomena,
+and for resolving that issue,
+
+you have to come to 8.334.
+
+So we will not discuss
+that, nor will we
+
+discuss why this is Tc minus
+T to the 2/3 power and not
+
+a linear dependence.
+
+It again is one of these
+critical properties.
+
+But we should be able to
+explain this T to the fourth.
+
+And clearly, this
+T to the fourth
+
+is not as simple as saying this
+exponent changed from 3/2 to 3,
+
+this 3/2 should
+also change the 3.
+
+No, it went to T to the fourth,
+so what's going on over here?
+
+So last time at the
+end of the lecture
+
+I wrote a statement that
+the BEC is not superfluid.
+
+And what that really
+means is that it
+
+has too many excitations,
+low energy excitations.
+
+So imagine the
+following, that maybe we
+
+have a container-- I don't
+know, maybe we have a tube--
+
+and we have our superfluid going
+through this with velocity v
+
+sub s.
+
+We want it to maintain that
+velocity without experiencing
+
+friction, which it
+seems to do in going
+
+through these capillaries.
+
+You don't have to push it, it
+seems to be going by itself.
+
+And so the question is,
+can any of these pictures
+
+that we drew for excitations
+be consistent with this?
+
+Now, why am I talking about
+excitations and consistency
+
+with superfluid?
+
+Because what can
+happen in principle
+
+is that within your system,
+you can spontaneously
+
+generate some excitation.
+
+This excitation will
+have some momentum p
+
+and some energy epsilon of p.
+
+And if you spontaneously can
+create these excitations that
+
+would take away energy from this
+kinetic energy of the flowing
+
+superfluid, gradually the
+superfluid will slow down.
+
+Its energy will be
+dissipated and the superfluid
+
+itself will heat up
+because you generated
+
+these excitations with it.
+
+So let's see what happens.
+
+If I were to create
+such an excitation,
+
+actually I have to worry
+about momentum conservation
+
+because I created something
+that carried momentum p.
+
+Now initially, let's say
+that this whole entity, all
+
+of the fluid that are
+superflowing with velocity Vs
+
+have mass M. So the initial
+momentum would be MVs.
+
+Now, I created some
+excitation that
+
+is carrying away
+some momentum p.
+
+So the only thing that
+can ensure this happens
+
+is that I have to
+slightly change
+
+the velocity of the fluid.
+
+Now this change in
+velocity is infinitesimal.
+
+It is Vs minus p
+divided by M. M is huge,
+
+so why bother
+thinking about this?
+
+Well, let's see what
+the change in energy is.
+
+Delta E. Let's say, well,
+you created this excitation
+
+so you have energy epsilon of p.
+
+But I say, in
+addition to that there
+
+is a change in the kinetic
+energy of the superfluid.
+
+I'm now moving at
+Vs prime squared,
+
+whereas initially when this
+excitation was not present,
+
+I was moving at Vs.
+
+And so what do you have here?
+
+We have epsilon of p, M
+over 2 Vs minus p over M,
+
+this infinitesimal change
+in velocity squared minus M
+
+over 2 Vs squared.
+
+We can see that the leading
+order of the kinetic energy
+
+goes away, but that there
+is a cross term here
+
+in which the M contribution--
+the contribution of the mass--
+
+goes away.
+
+And so the change in energy is
+actually something like this.
+
+So if I had a system that
+when stationary, the energy
+
+to create an excitation of
+momentum p was epsilon of p,
+
+when I put that in a frame that
+is moving with some velocity
+
+Vs, you have the
+ability to borrow
+
+some of that kinetic energy
+and the excitation energy
+
+goes down by this amount.
+
+So what happens if I take
+the Bose-Einstein type
+
+of excitation spectrum
+that is p squared over 2M
+
+and then subtract
+a v dot p from it?
+
+Essentially there is a
+linear subtraction going on,
+
+and I would get a
+curve such as this.
+
+So I probably exaggerated
+this by a lot.
+
+I shouldn't have
+subtracted so much.
+
+Let me actually not
+subject so much,
+
+because we don't want to go
+all the way in that range.
+
+But you can see that there
+is a range of momenta where
+
+you would spontaneously gain
+energy by creating excitations.
+
+If the spectrum was
+initially p squared over 2M,
+
+basically you just have too
+many low energy excitations.
+
+As soon as you
+start moving it, you
+
+will spontaneously
+excite these things.
+
+Even if you were initially
+at 0 temperature,
+
+these phonon excitations
+would be created spontaneously
+
+in your system.
+
+They would move
+all over the place.
+
+They would heat up your system.
+
+There is no way
+that you can pass
+
+the Bose-Einstein
+condensate-- actually,
+
+there's no way that you can even
+move it without losing energy.
+
+But you can see that
+this red curve does not
+
+have that difficulty.
+
+If I were to shift this curve
+by an amount that is linear,
+
+what do I get?
+
+I will get something like this.
+
+So the Landau spectrum
+is perfectly fine
+
+as far as excitations
+is concerned.
+
+At zero temperature, even if the
+whole fluid is moving then it
+
+cannot spontaneously
+create excitations,
+
+because you would increase
+energy of the system.
+
+So there's this difference.
+
+Ultimately, you would
+say that the first time
+
+you would get excitation is
+if you move it fast enough
+
+so that some portion of
+this curve goes to 0.
+
+And indeed, if you were
+to try to stir or move
+
+a superfluid fast
+enough, there's
+
+a velocity at which
+it breaks down,
+
+it stops being a superfluid.
+
+But it turns out that that
+velocity is much, much smaller
+
+than you would predict based on
+this roton spectrum going down.
+
+There are some other
+many body excitations
+
+that come before and cause
+the superfluid to lose energy
+
+and break down.
+
+But the genetic idea as
+to why a linear spectrum
+
+for k close to 0 is
+consist with superfluidity
+
+but the quadratic one
+is not remains correct.
+
+Now suppose I am
+in this situation.
+
+I have a moving super
+fluid, such as the one
+
+that I have described over here.
+
+The spectrum is going to
+be somewhat like this,
+
+but I'm not at 0 temperature.
+
+I want to try to describe
+this T to the fourth behavior,
+
+so I want to be at some
+finite temperature.
+
+So if I'm at some
+finite temperature,
+
+there is some probability to
+excite these different states,
+
+and the number that would
+correspond to some momentum p
+
+would be given by this
+general formula you have,
+
+1 over Z inverse e to the
+beta epsilon of p minus 1.
+
+Furthermore, if I think that
+I am in the regime where
+
+the number of excitations
+is not important because
+
+of the same reason that I had
+for Bose-Einstein condensate,
+
+I would have this formula
+except that I would use epsilon
+
+of p that is appropriate
+to this system.
+
+Actually, what is it
+appropriate to this system
+
+is that my epsilon of
+p was velocity times p.
+
+But then I started to move
+with this superfluid velocity.
+
+Actually, maybe I'll
+call this c so that I
+
+a distinction between c, which
+is the linear spectrum here,
+
+and the superfluid
+velocity dot p.
+
+No, this is actually
+a vectorial product.
+
+And because of that,
+I only drew one part
+
+of this curve that corresponds
+to positive momentum.
+
+If I had gone to
+negative momentum,
+
+actually, this curve
+would have continued
+
+and whereas one branch
+the energy is reduced,
+
+if I go to minus p,
+the energy goes up.
+
+So whereas if the
+superfluid was not moving,
+
+I can generate as many
+excitations with momentum p
+
+as momentum minus p.
+
+Once the superfluid is
+moving, there is a difference.
+
+One of them has a v dot p.
+
+The other has minus v dot p.
+
+So because of that,
+there is a net momentum
+
+that is carried by
+these excitations.
+
+This net momentum is
+obtained by summing
+
+over all of these
+things, multiplying
+
+with appropriate momentum.
+
+So I have beta is CP
+minus v dot p minus 1.
+
+This is the momentum
+of the excitation.
+
+This is the net momentum of
+the system for one excitation.
+
+But then I have to sum
+over all possible P's.
+
+Sum over P's, as
+we've discussed,
+
+I can replace with an integral.
+
+And sum over k be replaced with
+V. Integral over K, K and P
+
+are simply related
+by a factor of h bar.
+
+So whereas before for k I
+had 2 pi cubed for v cubed,
+
+I have 2 pi h bar cubed.
+
+So this is what I
+have to calculate.
+
+Now what happens for small v?
+
+I can make an expansion
+in vs. The 0 order term
+
+in the expansion
+is what we would
+
+have for non-moving fluid.
+
+Momenta in the two
+directions are the same,
+
+so that contribution goes away.
+
+The first contribution
+that I'm going to get
+
+is going to come from expanding
+this to lowest order in P.
+
+So there is a P that
+is sitting out front.
+
+When I make the
+expansion, I will
+
+get a vs dot P
+times the derivative
+
+of the exponential
+function gives me
+
+a factor of beta
+e to the beta CP.
+
+And down here I will have e to
+the beta CP minus 1 squared.
+
+Now, in the problem set you
+have to actually evaluate
+
+this integral.
+
+It's not that difficult.
+
+It's related to Zeta functions.
+
+But what I'm really
+only interested in what
+
+is the temperature dependence?
+
+You can see that I can rescale
+this combination, call it x.
+
+Essentially what it says is that
+whenever I see a factor of p,
+
+replace it by Kt over Cx.
+
+And how many P's do I have?
+
+I have three, four, five.
+
+So I have five factors of P. So
+I will have five factors of Kt.
+
+One of them gets
+killed by the beta,
+
+so this whole thing
+is proportional to T
+
+to the fourth power.
+
+So what have we found?
+
+We have found that as
+this fluid is moving
+
+at some finite
+temperature T, it will
+
+generate these excitations.
+
+And these excitations
+are preferably
+
+along the direction
+of the momentum.
+
+And they correspond to
+an additional momentum
+
+of the fluid that is
+proportional to the volume.
+
+It's proportional to temperature
+to the fourth and something.
+
+And of course, proportional
+to the velocity.
+
+Now, we are used to thinking of
+the proportionality of momentum
+
+and velocity to be
+some kind of a mass.
+
+If I divide that
+mass by the volume,
+
+I have a density of
+these excitations.
+
+And what we have established
+is that the density
+
+of those excitations
+is proportional to t
+
+to the fourth.
+
+And what is happening in this
+Andronikashvili experiment
+
+is that as these plates are
+moving, by this mechanism
+
+the superfluid
+that is in contact
+
+with them will
+create excitations.
+
+And the momentum of
+those excitations
+
+would correspond to some
+kind of a density that
+
+vanishes as T to
+the fourth, again
+
+in agreement with
+what we've seen here.
+
+OK?
+
+Yes?
+
+AUDIENCE: So in an
+integral expression
+
+you have vs as part
+of a dot product.
+
+PROFESSOR: Yes.
+
+AUDIENCE: And then in the
+next line [INAUDIBLE].
+
+So it's in that direction.
+
+PROFESSOR: So let's give these
+indices p in direction alpha.
+
+This is p in direction alpha.
+
+This is p in direction alpha.
+
+This is v in direction
+beta, p in direction
+
+beta, sum over beta.
+
+Now, I have to do an
+angular integration that
+
+is spherically symmetric.
+
+And then somewhere inside
+there it has a p alpha p beta.
+
+That angular
+integration will give me
+
+a p squared over three delta
+alpha beta, which then converts
+
+this v beta to a
+b alpha, which is
+
+in the direction
+of the momentum.
+
+Yes?
+
+AUDIENCE: Will
+you say once again
+
+what happened to the
+integral dimension?
+
+PROFESSOR: OK.
+
+So when we are in the
+Bose-Einstein condensate,
+
+as far as the
+excitations of concerned
+
+we have zero chemical potential.
+
+Whatever number of
+particle that we
+
+have in excess of what
+can be accommodated
+
+through the excitations we put
+together in the ground state.
+
+So if you like the ground
+state, the kp equals to 0
+
+or k equals to 0,
+is a reservoir.
+
+You can add as many
+particles there
+
+or bring as many particles
+out of it as you like.
+
+So effectively, you have
+no conservation number
+
+and no need for a [? z. ?]
+
+Of course, that we
+only know for the case
+
+of the true
+Bose-Einstein condensate.
+
+We are kind of
+jumping and giving
+
+that concept relevance for
+the interacting superfluid.
+
+OK?
+
+Any other questions?
+
+So this is actually
+the last item
+
+I wanted to cover for
+going on the board.
+
+The rest of the hour,
+we have this movie
+
+that I had promised you.
+
+I will let that movie run.
+
+I also have all the connection
+of problem sets, and exams,
+
+and test that you
+have not picked up.
+
+So while the movie runs, you
+are welcome to sit and enjoy it.
+
+It's very nice.
+
+Or you can go and take your
+stuff and go your own way
+
+or do whatever you like.
+
+So let's go back.
+
+[VIDEO PLAYBACK]
+
+PROFESSOR: There
+will be more action.
+
+-We just made a transfer
+from liquid helium
+
+out of the storage tank into
+our own experimental equipment.
+
+It is a remarkable [INAUDIBLE].
+
+It has two different and
+easily distinguishable
+
+liquid phases-- a
+warmer and a colder one.
+
+The warmer phase is called
+liquid helium I and the colder
+
+phase liquid helium II.
+
+The two stages are separated
+by a transition temperature,
+
+known as the lambda point.
+
+When liquid helium is pulled
+down through the lambda point,
+
+a transition from helium I to
+helium II is clearly visible.
+
+We will show it to you
+later in this film.
+
+The two liquids behave nothing
+like any other known liquid,
+
+although it could be said that
+helium I, the warmer phase,
+
+approximates the behavior
+of common liquids.
+
+But it is helium II,
+the colder phase,
+
+which is truly different.
+
+Because of this, it is
+called a superfluid.
+
+The temperatures involved when
+working with liquid helium
+
+are quite low.
+
+Helium boils at
+4.2 degrees Kelvin
+
+under conditions of
+atmospheric pressure.
+
+And the lambda point lies
+at roughly 2.2 degrees.
+
+Note that this
+corresponds to minus 269
+
+and minus 271
+degrees centigrade.
+
+The properties of liquid
+helium that I have just
+
+been telling you about
+are characteristic
+
+of the heavy isotope
+if helium, helium-4.
+
+The element occurs in the
+form of two stable isotopes.
+
+[INAUDIBLE] The second
+and lighter one,
+
+helium-3, is very rare.
+
+Its abundance is only
+about 1 part of 10 million.
+
+Pure liquid helium-3
+is the subject
+
+of intensive study
+at the present time,
+
+but so far no second
+superfluid liquid phase
+
+has been found to
+exist for helium-3.
+
+The low temperature at
+which we'll be working
+
+calls for well-insulated
+containers.
+
+The dewar meets
+our requirements.
+
+The word "dewar" is
+a scientific name
+
+given to a double-walled
+vessel with the space
+
+between the walls evacuated.
+
+When these dewars
+are made of glass,
+
+the surface of this
+inner space is usually
+
+filtered to cut down heat
+transfer by radiation.
+
+However, our dewars will
+have to be transparent
+
+so that we can look at
+what's going on inside.
+
+Now, liquid helium is commonly
+stored in double dewars.
+
+The design is quite
+simple, just put one
+
+inside the other like this.
+
+In the inner dewar, we
+put the liquid helium,
+
+and in the space between
+the inner and outer dewar,
+
+we maintain a supply
+of liquid air.
+
+Here is a double dewar
+exactly like the one
+
+we will be using in our
+demonstration experiment.
+
+The inner dewar is filled
+with liquid helium.
+
+The outer dewar
+contains liquid air.
+
+The normal boiling
+temperature of liquid air
+
+is about 80 degrees
+Kelvin, 75 or more degrees
+
+hotter than liquid helium.
+
+The purpose of the
+liquid air is twofold.
+
+First, we put the liquid air
+in the outer dewar well ahead
+
+of putting liquid helium
+in the inner dewar.
+
+In this way, the inner
+dewar is pre-cooled.
+
+Secondly, we maintain
+a supply of liquid air
+
+in the outer dewar
+because it provides
+
+an additional
+[INAUDIBLE] of insulation
+
+now that the liquid helium
+is in the inner dewar.
+
+The [INAUDIBLE] liquid
+air attests to the fact
+
+that it is absorbing
+some of the heat which
+
+enters the double dewar.
+
+Even with the boiling
+of the liquid air,
+
+the liquid helium
+is clearly visible.
+
+Later, we will use
+liquid air cooled
+
+below its boiling temperature
+to reduce or eliminate
+
+the air bubbles for
+better visibility.
+
+Now the liquid
+air is cooled down
+
+and we have eliminated boiling.
+
+The smaller bubbles of
+the boiling liquid helium
+
+are clearly visible.
+
+The cover over the inner dewar
+has a port, at present open.
+
+The liquid helium is at
+atmospheric pressure,
+
+so its temperature is
+4.2 degrees Kelvin.
+
+In other words, what
+we have in here now
+
+is liquid helium one, the
+warmer of the two phases.
+
+Before we cool it down to take
+a look at the superfluid phase,
+
+I want to dwell greatly on the
+properties of helium I. I've
+
+told you before
+that even helium I
+
+is different from
+the normal liquids.
+
+The distance between neighboring
+atoms and this liquid
+
+is quite large.
+
+The atoms are not
+as closely packed
+
+as in the classical liquids.
+
+The reason for this
+is quantum mechanics.
+
+The zero point energy is
+relatively more important
+
+here than in any other liquid.
+
+As a consequence,
+liquid helium has
+
+a very low mass density, only
+about 13% the density of water,
+
+and a very low optical density.
+
+The index of refraction
+is quite close to 1.
+
+This makes its surface hard
+to see with the naked eye
+
+under ordinary
+lighting conditions.
+
+You are no doubt
+familiar with the fact
+
+that the helium atom has
+closed shell atomic structure.
+
+This explains why helium is
+a chemically inert element.
+
+It also accounts for the fact
+that the force of attraction
+
+between neighboring helium
+atoms, the so-called van der
+
+Waals force, is small.
+
+It takes little energy to
+pull two helium atoms apart,
+
+as for example in evaporation.
+
+This gives liquid helium
+a better small latent
+
+heat of vaporization.
+
+Only five calories are
+needed to evaporate one gram.
+
+Compare this with water,
+where evaporation requires
+
+between 500 and 600
+calories per gram.
+
+The low van der Waals force
+combined with a large zero
+
+point energy also accounts for
+the fact that liquid helium
+
+does not freeze, cannot
+be solidified at ordinary
+
+pressure, no matter
+how far we cool it.
+
+However, liquid helium has been
+solidified at high pressure.
+
+The liquid helium in the
+dewar is at 4,2 degrees.
+
+We now want to cool it
+down to the lambda point
+
+and show you the transition
+to the [INAUDIBLE].
+
+Our method will be
+cooling by evaporation
+
+using a vacuum pump.
+
+Now, the lambda point lies at
+2.2 degrees, only 2 degrees
+
+colder than the [INAUDIBLE]
+temperature of the liquid.
+
+What's more, not
+very much heat has
+
+been removed from
+the liquid helium
+
+now in the dewar to bring
+it to the lambda point.
+
+It amounts to only
+about 250 calories.
+
+Nevertheless, don't get the
+idea that this cooling process
+
+is easy.
+
+On the contrary,
+it's quite difficult.
+
+More than 1/3 of the liquid
+helium now in the dewar
+
+has to be knocked
+away in vapor form
+
+before we can get what remains
+behind to the lambda point.
+
+That requires an
+awful lot of pumping
+
+and explains why we use this
+large and powerful vacuum
+
+pump over here.
+
+Even with this pump,
+the cooling process
+
+takes a considerable
+amount of time.
+
+Let me explain why
+it is so difficult
+
+to cool liquid helium
+to the lambda point.
+
+I have already mentioned
+that liquid helium has
+
+a remarkably small
+[INAUDIBLE] vaporization,
+
+only five calories per gram.
+
+At the same time, liquid
+helium at 4.2 degrees
+
+has a high specific heat,
+almost calorie per gram.
+
+Therefore, 1 gram of
+the vapor pumped away
+
+carries with it
+an amount of heat
+
+which can cool only 5 or 6 grams
+of liquid helium by 1 degree.
+
+That's not very much cooling.
+
+It is less by a
+factor of almost 100
+
+than when we cool
+water by evaporation.
+
+The situation gets even
+worse as cooling progresses
+
+below 4.2 degrees because the
+specific heat of liquid helium
+
+rises astonishingly.
+
+As we approach 2,17
+degrees, the lambda point.
+
+The heat of vaporization,
+on the other hand,
+
+remains roughly the same.
+
+So a given amount
+of vapor carried
+
+off produces less
+and less cooling
+
+as we approach 2.17 degrees,
+
+Our thermometer here
+is a low pressure gauge
+
+connected to the space
+above the liquid helium.
+
+The needle registers
+the pressure there.
+
+It is the saturated vapor
+pressure of liquid helium.
+
+The gauge is calibrated for
+the corresponding temperature.
+
+We call it a vapor
+pressure thermometer.
+
+As we approach 2.17
+degrees, boiling
+
+becomes increasingly violent.
+
+Suddenly it stops.
+
+This was the transition.
+
+The liquid you now
+see is helium II.
+
+Even though evaporation does
+continue, there is no boiling.
+
+The normal liquids, such
+as the water in this basin,
+
+boil because of their relatively
+low heat conductivity.
+
+Before heat,
+[INAUDIBLE] at one point
+
+can be carried away
+to a cooler place
+
+in the liquid bubbles
+of the vapor form.
+
+Helium I behaves like a
+normal liquid in this respect.
+
+The absence of
+boiling in helium II
+
+reveals that this
+phase acts as if it
+
+had a large heat conductivity.
+
+As a matter of fact, as
+the liquid helium passed
+
+through the lambda
+point transition
+
+you just saw, its
+heat conductivity
+
+increased by the fantastic
+factor of one million.
+
+The heat conductivity of
+helium II is many times
+
+greater than in the
+metals silver and copper,
+
+which are among the best
+solid heat conductors.
+
+And yet here we
+deal with a liquid.
+
+For this alone,
+helium II deserves
+
+the name of superfluid.
+
+Actually, the way in
+which helium II transports
+
+such large quantities
+of heat so rapidly
+
+is totally different from
+the classical concept
+
+for heat conduction.
+
+I'll come back to
+the subject later
+
+in connection with an
+experiment demonstrating
+
+the phenomenon of second
+sound in helium II.
+
+Remember that this great
+change in heat conductivity
+
+occurred at a single
+and fixed transition
+
+temperature, the lambda point.
+
+We do indeed deal with
+a change in phase,
+
+only here it is a change from
+one liquid to another liquid.
+
+As we told you before, the
+specific heat of liquid helium
+
+is very large as a lambda point.
+
+In fact, it behaves abnormally
+even below the lambda point
+
+and falls again very rapidly
+with the temperature.
+
+This discontinuity
+in specific heat
+
+is another reflection
+of the fact
+
+that we are dealing
+with a change
+
+in the phase of the substance.
+
+By the way, the curve resembles
+the Greek letter lambda.
+
+The transition
+temperature got its name
+
+from the shape of this curve.
+
+[INAUDIBLE]
+
+The next one has to do with
+the viscosity of liquid helium.
+
+When a normal liquid
+flows through a tube,
+
+it will resist the flow.
+
+In this experiment, we
+shall cause some glycerin
+
+to flow to a tube
+under its own weight.
+
+The top layer is
+colored glycerin.
+
+The liquid layer closest to
+the tube wall adheres to it.
+
+The layer next in from the one
+touching the wall flows by it
+
+and is retarded as it flows due
+to the interatomic, the van der
+
+Waals force of attraction.
+
+The second layer in
+turn drags on the third,
+
+and so on inward from the
+wall, producing fluid friction,
+
+or viscosity.
+
+The narrower the
+tube, the slower
+
+the liquid rate
+of flow through it
+
+under a given head of pressure.
+
+Here I have a beaker with
+an unglazed ceramic bottom
+
+of ultra-fine [INAUDIBLE].
+
+Many capillary channels run
+through this ceramic disk.
+
+The diameter is quite small,
+about one micron which is
+
+1/10,000 of a centimeter.
+
+There is liquid
+helium in the beaker.
+
+It is 4.2 degrees Kelvin,
+helium I, the normal phase.
+
+The capillaries in the
+disk are fine enough
+
+to prevent the liquid now in
+the beaker from flowing through
+
+under its on weight.
+
+Clearly, helium I is viscous.
+
+To be sure, its
+viscosity is very small.
+
+That's why we had to choose
+extremely fine capillaries
+
+to demonstrate it.
+
+Here you see the lambda
+point transition.
+
+The helium II all poured out.
+
+The rate of pouring would
+not be noticeably slower
+
+if the [INAUDIBLE]
+were made yet finer.
+
+We call this kind
+of flow a superflow.
+
+The temperature is
+now at 1.6 degrees.
+
+The superflow is even faster.
+
+The viscosity of helium
+II in this experiment
+
+is so small that it has
+not been possible to find
+
+a value for it.
+
+It is less than the experimental
+uncertainty incurred
+
+in attempts to measure it.
+
+We now believe that
+helium II, the superfluid,
+
+has zero viscosity, although
+we should be more precise here.
+
+We believe its viscosity is zero
+when observing capillary flow.
+
+Bear this statement
+in mind, for we
+
+will come up with a
+contradiction to it
+
+in the next experiment,
+where we will
+
+look for viscosity by
+a different method.
+
+There is a copper cylinder
+in the liquid helium,
+
+so mounted as we can turn
+it about a vertical axis.
+
+In order to turn it smoothly
+and with as little vibration as
+
+possible, we laid the
+cylinder into the [INAUDIBLE]
+
+of a simple induction
+motor energized
+
+from outside the dewar.
+
+The four horizontal
+coils you see
+
+provide the torque which
+turns the cylinder.
+
+The liquid helium is
+electrically non-conducting.
+
+The coil exerts no
+torque on it directly.
+
+Yet as we turn on our
+motor, the liquid layer
+
+bounding the cylinder is
+dragged along behind it.
+
+The boundary layer in turn
+drags on the next layer,
+
+and so on outward.
+
+Finally a circulation
+showing up in the helium
+
+due to its own viscosity and
+the wooden panels we [INAUDIBLE]
+
+is turned along.
+
+What we have just seen
+occurred in helium I,
+
+the normal phase at
+4.2 degrees Kelvin.
+
+That is to say,
+this demonstration
+
+is consistent with our results
+for helium I by capillary flow.
+
+Helium I is viscous.
+
+Here you see the liquid
+cooled down and passing
+
+into the superfluid
+phase, helium II.
+
+Let's turn on the motor.
+
+The paddle wheel starts again.
+
+What does this mean?
+
+First of all, let me
+emphasize that, like helium I,
+
+helium II is also non-conducting
+in the electrical sense.
+
+In other words, the
+circulation in the experiment
+
+can only have been caused
+through viscous drag.
+
+So we conclude from the
+rotating cylinder observations
+
+that helium II is viscous
+and from the method
+
+of capillary flow that
+it has zero viscosity.
+
+Our experimentation has
+come up with a paradox.
+
+No normal classical
+liquid is known
+
+to behave so inconsistently, in
+capillary flow on the one hand
+
+and in bulk flow on the other.
+
+This state of affairs
+forces us to think
+
+of helium II, the
+superfluid, not as a single,
+
+but as a dual liquid.
+
+It appeared as if helium
+II had two separate and yet
+
+interpenetrating
+component liquids.
+
+We shall call one
+component normal.
+
+It is this component
+which we call
+
+responsible for the
+appearance of viscosity
+
+below the lambda point in the
+rotating cylinder experiment.
+
+The normal component,
+as the name suggests,
+
+behaves like a normal liquid,
+and therefore as viscosity.
+
+It is the one which the cylinder
+drags along as its turned.
+
+But the normal components
+cannot flow through the narrow
+
+channels of the ceramic disc
+because of its viscosity.
+
+The second component
+has zero viscosity,
+
+and it's called the
+superfluid component.
+
+We think that it does
+not participate at all
+
+in the rotating cylinder
+experiment below the lambda
+
+point.
+
+It stays at rest.
+
+On the other hand, it can flow
+through channels of one micron
+
+diameter with the greatest
+of ease and countering
+
+no resistance whatever
+because it has no viscosity.
+
+As we'll see later, this
+flow is not repeated even
+
+when the capillary
+diameters are made
+
+far smaller than one micron.
+
+This [INAUDIBLE] construction
+is called the two fluid
+
+model for liquid helium II.
+
+Whether it is correct
+or not depends
+
+on further tests
+comparing the theory
+
+based on this model with
+experimental results.
+
+We now go on to another
+phenomenon, the fountain
+
+effect.
+
+What you see here
+is a tube which
+
+narrows down and then
+opens into a bulb.
+
+A small piece of cotton is
+stuffed into the [INAUDIBLE]
+
+section between the
+tube and the bulb.
+
+And the bulb has been tightly
+packed with one of the finest
+
+powders available, [INAUDIBLE].
+
+And second wad of cotton
+keeps the powder in the bulb.
+
+This powder presents extremely
+fine capillary channels.
+
+Their average diameter is a
+small fraction of 1 micron.
+
+This device has been
+placed in the dewar.
+
+The liquid helium is
+below the lambda point.
+
+We submerge the bulb, and then
+we'll send a beam of light
+
+from this lamp to a
+point near the top.
+
+You will see the light beam
+when the lamp is turned on.
+
+It focuses some heat in the
+form of infrared radiation
+
+on the point in question.
+
+The temperature will rise
+above the temperature
+
+of the rest of the apparatus.
+
+Let us turn it on.
+
+Liquid helium flows through the
+hole in the bottom of the bulb,
+
+through the fine
+powder, and rises
+
+above the level of
+liquid helium outside.
+
+The height to which
+it will go depends
+
+on the temperature
+increase produced
+
+bu the lamp focused on the bulb.
+
+We can very well ask, where
+does the mechanical energy
+
+come from that does the
+work necessary to pump
+
+the liquid above
+the ambient level?
+
+Before we attempt to
+discuss this question,
+
+there are two other facts
+that should be noted.
+
+The first is by now obvious.
+
+The upward flow through the bulb
+must clearly be a superfluid.
+
+Only the superfluid component
+of helium II could get through.
+
+The second fact is
+more significant.
+
+Let me explain it this way, the
+superfluid flows spontaneously
+
+from a to b,from a
+cooler to a warmer place.
+
+Point a is in the
+cold liquid, but b
+
+is being heated
+with infrared rays.
+
+The second law of thermodynamics
+positively says that heat
+
+cannot of itself flow from
+a point of lower to a point
+
+of higher temperature.
+
+What does this mean
+to us here, knowing
+
+as we do that the
+superfluid is flowing
+
+from a colder to a warmer spot?
+
+Simply this, it carries no
+heat, no thermal energy.
+
+Any internal energy
+[INAUDIBLE] is no longer
+
+thermally available.
+
+To say it precisely,
+it has zero entropy.
+
+We have discovered another
+remarkable property
+
+of helium II.
+
+Its superfluid component
+not only is friction free,
+
+it also contains no heat.
+
+The heat energy
+contained in helium II
+
+as a whole resides, all of
+it, in the normal component.
+
+We may, of course, add heat
+to the superfluid component,
+
+as we are doing when it passes
+the spot heated by the lamp.
+
+But in doing so, we
+are converting it
+
+into the normal component.
+
+Let me return briefly to
+a question posed earlier.
+
+Mechanical work is done
+in pumping the liquid
+
+above equilibrium level.
+
+Where does it come from?
+
+I cannot answer this
+question here in full,
+
+but it suffice to tell you that
+we are dealing here with a heat
+
+engine.
+
+The mechanical energy
+comes from the heat
+
+added at the light spot.
+
+An amusing demonstration
+of the same phenomenon
+
+again uses a bulb
+packed with rouge,
+
+but this one opens
+into a capillary.
+
+Light is beamed on a spot
+just below the capillary,
+
+and it produces a
+helium fountain.
+
+The phenomenon in this and
+the previous experiment
+
+has become known as
+the thermomechanical,
+
+or the fountain, effect.
+
+Below the lambda point,
+the superfluid component
+
+of liquid helium creeps
+up along the walls
+
+of its container in an
+extremely thin film.
+
+It is known as a Rollin film.
+
+This creeping film is
+a variety of superflow.
+
+It is difficult to make the film
+itself directly visible to you.
+
+To show it indirectly,
+we've put some liquid helium
+
+into a glass vessel.
+
+It is below the lambda point.
+
+There is no part porous
+bottom in this vessel.
+
+The film rises along
+the inside wall
+
+and comes down
+along the outside,
+
+collecting in drops
+at the bottom.
+
+The thickness of
+this creeping film
+
+is only a small fraction of
+1 micron and of the order
+
+of 200 to 300 angstrom.
+
+Its speed, while small just
+below the lambda point,
+
+may reach a value as
+high as 35 centimeters
+
+per second at
+lower temperatures.
+
+Our next experiment deals with
+the phenomenon of second sound.
+
+We are all familiar with wave
+motion in elastic materials,
+
+be they solids,
+liquids, or gases.
+
+Elastic energy of deformation,
+carried away from its source
+
+in the form of waves with
+a characteristic speed,
+
+the speed of sound.
+
+Liquid helium is an
+elastic substance
+
+both above and below
+the lambda point.
+
+Both helium one and two
+support sound waves.
+
+Now helium II, the
+superfluid phase,
+
+also conducts heat
+in the form of waves.
+
+This remarkable property is
+shared by no other substance.
+
+For better or for worse, it
+has been called second sound.
+
+Normal heat conduction
+is a diffusion process.
+
+The rate of flow of heat is
+proportional to the temperature
+
+differences.
+
+But in helium II it
+is a wave process.
+
+Heat flows through helium II
+with a characteristic speed,
+
+the speed of second sound.
+
+We shall send small heat pulses
+into helium II from a heater.
+
+They will spread away
+from the heater uniformly,
+
+carrying the heat
+energy with them.
+
+The speed of second
+sound is small just
+
+below the lambda point.
+
+In the neighborhood
+of 1.6 degrees Kelvin,
+
+it reaches a value of
+roughly 20 meters per second,
+
+and it is in this range that
+we will run our demonstration.
+
+The experimental
+procedure is as follows.
+
+There are two disks
+in the liquid helium.
+
+They are carbon resistors
+with the carbon applied
+
+in thin layers on one
+side of each disk.
+
+In this way, good
+thermal contact
+
+is established between the
+resistor and the liquid helium.
+
+The following resistor
+will be used as a heater.
+
+Electric currents will
+be sent through it
+
+in pulses from this pulse
+generator by means of the cable
+
+you see here.
+
+The [INAUDIBLE] of
+the generator is also
+
+connected via a second cable
+to a dual-trace oscilloscope,
+
+where it will be recorded
+on the bottom [? trip. ?]
+
+In other words, it will record
+the heat pulse as it enters
+
+the liquid helium.
+
+The pulses have been turned on.
+
+They themselves trigger
+the horizontal sweep
+
+of [INAUDIBLE], which
+records [INAUDIBLE].
+
+It is calibrated
+at 1 millisecond
+
+per unit on the scale.
+
+The pulses are 1
+millisecond long.
+
+The pulses leave the
+heater at the bottom
+
+in the form of
+second sound and move
+
+up to where they strike the
+carbon resistor at the top.
+
+Being heat pulses, they
+greatly raise is temperature.
+
+The carbon resistor is
+quite sensitive to changes
+
+in temperature.
+
+It acts as a thermometer.
+
+So the heat pulse
+of second sound
+
+creates a pulse-like
+change in the resistance
+
+of the [INAUDIBLE] up here.
+
+It isn't hard to
+convert this resistance
+
+pulse into a [INAUDIBLE].
+
+What we will do is to
+maintain a small DC
+
+current in the top resistor.
+
+It is supplied from a
+battery in this metal box.
+
+The box shields the
+circuits in order
+
+to reduce electronic noise.
+
+The voltage pulse is small.
+
+In this second box
+we have an amplifier.
+
+The amplified output is fed
+into the oscilloscope, where
+
+it will appear on
+the upper trace.
+
+The horizontal
+timescale on this trace
+
+is exactly the same as
+for the bottom trace.
+
+However, the upper trace
+records both exchanges
+
+as they occur in
+the top resistor,
+
+a detector of second sound.
+
+The temperature of the liquid
+is about 1.65 degrees Kelvin.
+
+The battery has been turned
+on, and now the amplifier.
+
+Among noise and other
+distortions in the upper trace,
+
+a clear-cut voltage pulse
+appears about 4 and 1/2 units
+
+to the right, 4 and
+1/2 milliseconds later
+
+than the pulse
+entering the heater.
+
+This pulse in the upper trace is
+also about 1 millisecond long.
+
+It is the second sound as it
+arrives at the upper resistor.
+
+The upper trace also shows
+a strong voltage pulse
+
+at the left, simultaneous
+to the heater pulse.
+
+That's due to pick-up
+by electromagnetic waves
+
+with the heater acting as
+transmitter and the detector
+
+as receiver.
+
+We're moving the detector
+toward the heater.
+
+The pulse moves
+with it to the left.
+
+Notice the echos of second sound
+which appear on the upper trace
+
+while the detector
+is near the heater.
+
+They're caused by multiple
+reflections between the two
+
+resistors.
+
+A total of three echos
+is clearly visible.
+
+[END VIDEO PLAYBACK]
+
+PROFESSOR: OK, you can watch
+the rest of it at home.
\ No newline at end of file
diff --git a/6swIAqXcvDQ.txt b/6swIAqXcvDQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5d15000cc828310e8ec0cf29ba045a32a2f60a06
--- /dev/null
+++ b/6swIAqXcvDQ.txt
@@ -0,0 +1,14619 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably the time has begun to begin
+
+ align:start position:0%
+probably the time has begun to begin
+ 
+
+ align:start position:0%
+probably the time has begun to begin
+welcome I've given a guest lecture in
+
+ align:start position:0%
+welcome I've given a guest lecture in
+ 
+
+ align:start position:0%
+welcome I've given a guest lecture in
+this class for a few years running now
+
+ align:start position:0%
+this class for a few years running now
+ 
+
+ align:start position:0%
+this class for a few years running now
+and so I'm always happy to return you're
+
+ align:start position:0%
+and so I'm always happy to return you're
+ 
+
+ align:start position:0%
+and so I'm always happy to return you're
+working on a good subject here I'm going
+
+ align:start position:0%
+working on a good subject here I'm going
+ 
+
+ align:start position:0%
+working on a good subject here I'm going
+to talk today about experimentation and
+
+ align:start position:0%
+to talk today about experimentation and
+ 
+
+ align:start position:0%
+to talk today about experimentation and
+robust design of engineering systems I
+
+ align:start position:0%
+robust design of engineering systems I
+ 
+
+ align:start position:0%
+robust design of engineering systems I
+think you've already had a few lectures
+
+ align:start position:0%
+think you've already had a few lectures
+ 
+
+ align:start position:0%
+think you've already had a few lectures
+on design of experiments formally so
+
+ align:start position:0%
+on design of experiments formally so
+ 
+
+ align:start position:0%
+on design of experiments formally so
+this will build on that the figure that
+
+ align:start position:0%
+this will build on that the figure that
+ 
+
+ align:start position:0%
+this will build on that the figure that
+I show on this first slide concerns on
+
+ align:start position:0%
+I show on this first slide concerns on
+ 
+
+ align:start position:0%
+I show on this first slide concerns on
+the right a method by which one can make
+
+ align:start position:0%
+the right a method by which one can make
+ 
+
+ align:start position:0%
+the right a method by which one can make
+improvements and robustness of a system
+
+ align:start position:0%
+improvements and robustness of a system
+ 
+
+ align:start position:0%
+improvements and robustness of a system
+by adaptively experimenting in the
+
+ align:start position:0%
+by adaptively experimenting in the
+ 
+
+ align:start position:0%
+by adaptively experimenting in the
+parameter space of that system and the
+
+ align:start position:0%
+parameter space of that system and the
+ 
+
+ align:start position:0%
+parameter space of that system and the
+figure on the left is meant to indicate
+
+ align:start position:0%
+figure on the left is meant to indicate
+ 
+
+ align:start position:0%
+figure on the left is meant to indicate
+why that approach has worked rather
+
+ align:start position:0%
+why that approach has worked rather
+ 
+
+ align:start position:0%
+why that approach has worked rather
+quite a lot better than people expected
+
+ align:start position:0%
+quite a lot better than people expected
+ 
+
+ align:start position:0%
+quite a lot better than people expected
+and I'll be going into that in some
+
+ align:start position:0%
+and I'll be going into that in some
+ 
+
+ align:start position:0%
+and I'll be going into that in some
+detail and I hope that as I go through
+
+ align:start position:0%
+detail and I hope that as I go through
+ 
+
+ align:start position:0%
+detail and I hope that as I go through
+all this you'll take time to ask
+
+ align:start position:0%
+all this you'll take time to ask
+ 
+
+ align:start position:0%
+all this you'll take time to ask
+questions because I think that's better
+
+ align:start position:0%
+questions because I think that's better
+ 
+
+ align:start position:0%
+questions because I think that's better
+for you and more interesting for me too
+
+ align:start position:0%
+for you and more interesting for me too
+ 
+
+ align:start position:0%
+for you and more interesting for me too
+so just to give you a little bit of
+
+ align:start position:0%
+so just to give you a little bit of
+ 
+
+ align:start position:0%
+so just to give you a little bit of
+context you know this this topic of a
+
+ align:start position:0%
+context you know this this topic of a
+ 
+
+ align:start position:0%
+context you know this this topic of a
+depth of experimentation and robust
+
+ align:start position:0%
+depth of experimentation and robust
+ 
+
+ align:start position:0%
+depth of experimentation and robust
+design is really central to my research
+
+ align:start position:0%
+design is really central to my research
+ 
+
+ align:start position:0%
+design is really central to my research
+it's I think the core of it but I'm
+
+ align:start position:0%
+it's I think the core of it but I'm
+ 
+
+ align:start position:0%
+it's I think the core of it but I'm
+interested in other things as well such
+
+ align:start position:0%
+interested in other things as well such
+ 
+
+ align:start position:0%
+interested in other things as well such
+as we do studies of systems generally
+
+ align:start position:0%
+as we do studies of systems generally
+ 
+
+ align:start position:0%
+as we do studies of systems generally
+and the regularities that exist in those
+
+ align:start position:0%
+and the regularities that exist in those
+ 
+
+ align:start position:0%
+and the regularities that exist in those
+engineered systems and that gives rise
+
+ align:start position:0%
+engineered systems and that gives rise
+ 
+
+ align:start position:0%
+engineered systems and that gives rise
+to data that we can use more generally
+
+ align:start position:0%
+to data that we can use more generally
+ 
+
+ align:start position:0%
+to data that we can use more generally
+in methodology validation so we can look
+
+ align:start position:0%
+in methodology validation so we can look
+ 
+
+ align:start position:0%
+in methodology validation so we can look
+at different ways that people will do
+
+ align:start position:0%
+at different ways that people will do
+ 
+
+ align:start position:0%
+at different ways that people will do
+engineering and try to assess its
+
+ align:start position:0%
+engineering and try to assess its
+ 
+
+ align:start position:0%
+engineering and try to assess its
+effectiveness and of course all this is
+
+ align:start position:0%
+effectiveness and of course all this is
+ 
+
+ align:start position:0%
+effectiveness and of course all this is
+linked in with the work on adaptive
+
+ align:start position:0%
+linked in with the work on adaptive
+ 
+
+ align:start position:0%
+linked in with the work on adaptive
+experimentation because we need a way to
+
+ align:start position:0%
+experimentation because we need a way to
+ 
+
+ align:start position:0%
+experimentation because we need a way to
+validate our work but the the main topic
+
+ align:start position:0%
+validate our work but the the main topic
+ 
+
+ align:start position:0%
+validate our work but the the main topic
+today will be what was in the middle of
+
+ align:start position:0%
+today will be what was in the middle of
+ 
+
+ align:start position:0%
+today will be what was in the middle of
+that slide that's adaptive
+
+ align:start position:0%
+that slide that's adaptive
+ 
+
+ align:start position:0%
+that slide that's adaptive
+experimentation I think I'll start with
+
+ align:start position:0%
+experimentation I think I'll start with
+ 
+
+ align:start position:0%
+experimentation I think I'll start with
+some history and use that to explain the
+
+ align:start position:0%
+some history and use that to explain the
+ 
+
+ align:start position:0%
+some history and use that to explain the
+motivation you know why is it that we're
+
+ align:start position:0%
+motivation you know why is it that we're
+ 
+
+ align:start position:0%
+motivation you know why is it that we're
+addressing this topic why are we
+
+ align:start position:0%
+addressing this topic why are we
+ 
+
+ align:start position:0%
+addressing this topic why are we
+addressing
+
+ align:start position:0%
+addressing
+ 
+
+ align:start position:0%
+addressing
+the way we're addressing it and then I'm
+
+ align:start position:0%
+the way we're addressing it and then I'm
+ 
+
+ align:start position:0%
+the way we're addressing it and then I'm
+going to show you the research itself on
+
+ align:start position:0%
+going to show you the research itself on
+ 
+
+ align:start position:0%
+going to show you the research itself on
+adaptive experimentation robust design
+
+ align:start position:0%
+adaptive experimentation robust design
+ 
+
+ align:start position:0%
+adaptive experimentation robust design
+so I start with this quote from Sir
+
+ align:start position:0%
+so I start with this quote from Sir
+ 
+
+ align:start position:0%
+so I start with this quote from Sir
+Edward John Russell now this fellow was
+
+ align:start position:0%
+Edward John Russell now this fellow was
+ 
+
+ align:start position:0%
+Edward John Russell now this fellow was
+prominent in his day you know he was
+
+ align:start position:0%
+prominent in his day you know he was
+ 
+
+ align:start position:0%
+prominent in his day you know he was
+knighted that's why it says Sir Edward
+
+ align:start position:0%
+knighted that's why it says Sir Edward
+ 
+
+ align:start position:0%
+knighted that's why it says Sir Edward
+John Russell there under his type under
+
+ align:start position:0%
+John Russell there under his type under
+ 
+
+ align:start position:0%
+John Russell there under his type under
+his picture and as late as 1926 he was
+
+ align:start position:0%
+his picture and as late as 1926 he was
+ 
+
+ align:start position:0%
+his picture and as late as 1926 he was
+still expressing a view about how to do
+
+ align:start position:0%
+still expressing a view about how to do
+ 
+
+ align:start position:0%
+still expressing a view about how to do
+experimentation he said that you should
+
+ align:start position:0%
+experimentation he said that you should
+ 
+
+ align:start position:0%
+experimentation he said that you should
+seek simplicity in the way that you
+
+ align:start position:0%
+seek simplicity in the way that you
+ 
+
+ align:start position:0%
+seek simplicity in the way that you
+conduct your experiments and maybe you
+
+ align:start position:0%
+conduct your experiments and maybe you
+ 
+
+ align:start position:0%
+conduct your experiments and maybe you
+should ask just a few questions at a
+
+ align:start position:0%
+should ask just a few questions at a
+ 
+
+ align:start position:0%
+should ask just a few questions at a
+time or maybe even just one question at
+
+ align:start position:0%
+time or maybe even just one question at
+ 
+
+ align:start position:0%
+time or maybe even just one question at
+a time as you're conducting your
+
+ align:start position:0%
+a time as you're conducting your
+ 
+
+ align:start position:0%
+a time as you're conducting your
+experiments and this was a prominent
+
+ align:start position:0%
+experiments and this was a prominent
+ 
+
+ align:start position:0%
+experiments and this was a prominent
+view in that day generally accepted and
+
+ align:start position:0%
+view in that day generally accepted and
+ 
+
+ align:start position:0%
+view in that day generally accepted and
+and you can trace it back at least as
+
+ align:start position:0%
+and you can trace it back at least as
+ 
+
+ align:start position:0%
+and you can trace it back at least as
+far as Francis Bacon and maybe farther
+
+ align:start position:0%
+far as Francis Bacon and maybe farther
+ 
+
+ align:start position:0%
+far as Francis Bacon and maybe farther
+and what's interesting about this is
+
+ align:start position:0%
+and what's interesting about this is
+ 
+
+ align:start position:0%
+and what's interesting about this is
+just at the time he's still expressing
+
+ align:start position:0%
+just at the time he's still expressing
+ 
+
+ align:start position:0%
+just at the time he's still expressing
+his views about how it is that they
+
+ align:start position:0%
+his views about how it is that they
+ 
+
+ align:start position:0%
+his views about how it is that they
+conducted experiments there at
+
+ align:start position:0%
+conducted experiments there at
+ 
+
+ align:start position:0%
+conducted experiments there at
+Rothamsted he hired another person our a
+
+ align:start position:0%
+Rothamsted he hired another person our a
+ 
+
+ align:start position:0%
+Rothamsted he hired another person our a
+fishery now I should say that this is an
+
+ align:start position:0%
+fishery now I should say that this is an
+ 
+
+ align:start position:0%
+fishery now I should say that this is an
+interesting confluence you have two men
+
+ align:start position:0%
+interesting confluence you have two men
+ 
+
+ align:start position:0%
+interesting confluence you have two men
+very prominent very successful coming
+
+ align:start position:0%
+very prominent very successful coming
+ 
+
+ align:start position:0%
+very prominent very successful coming
+together in the same place at the same
+
+ align:start position:0%
+together in the same place at the same
+ 
+
+ align:start position:0%
+together in the same place at the same
+time I think the reason for that was
+
+ align:start position:0%
+time I think the reason for that was
+ 
+
+ align:start position:0%
+time I think the reason for that was
+that this experimental station
+
+ align:start position:0%
+that this experimental station
+ 
+
+ align:start position:0%
+that this experimental station
+Rothamsted was addressing I think one of
+
+ align:start position:0%
+Rothamsted was addressing I think one of
+ 
+
+ align:start position:0%
+Rothamsted was addressing I think one of
+the great problems of their time which
+
+ align:start position:0%
+the great problems of their time which
+ 
+
+ align:start position:0%
+the great problems of their time which
+was consistency and efficiency of
+
+ align:start position:0%
+was consistency and efficiency of
+ 
+
+ align:start position:0%
+was consistency and efficiency of
+agricultural production if you think
+
+ align:start position:0%
+agricultural production if you think
+ 
+
+ align:start position:0%
+agricultural production if you think
+about the middle of the 19th century the
+
+ align:start position:0%
+about the middle of the 19th century the
+ 
+
+ align:start position:0%
+about the middle of the 19th century the
+UK and other parts of the world
+
+ align:start position:0%
+UK and other parts of the world
+ 
+
+ align:start position:0%
+UK and other parts of the world
+experienced a terrible famines and so
+
+ align:start position:0%
+experienced a terrible famines and so
+ 
+
+ align:start position:0%
+experienced a terrible famines and so
+trying to do much better in this area
+
+ align:start position:0%
+trying to do much better in this area
+ 
+
+ align:start position:0%
+trying to do much better in this area
+was a pressing problem probably
+
+ align:start position:0%
+was a pressing problem probably
+ 
+
+ align:start position:0%
+was a pressing problem probably
+equivalent today to the way we feel
+
+ align:start position:0%
+equivalent today to the way we feel
+ 
+
+ align:start position:0%
+equivalent today to the way we feel
+about energy supply or global warming
+
+ align:start position:0%
+about energy supply or global warming
+ 
+
+ align:start position:0%
+about energy supply or global warming
+and now in some ways we take for granted
+
+ align:start position:0%
+and now in some ways we take for granted
+ 
+
+ align:start position:0%
+and now in some ways we take for granted
+food supply at least in the developed
+
+ align:start position:0%
+food supply at least in the developed
+ 
+
+ align:start position:0%
+food supply at least in the developed
+world so here we have this confluence
+
+ align:start position:0%
+world so here we have this confluence
+ 
+
+ align:start position:0%
+world so here we have this confluence
+and are a Fisher comes into the lab and
+
+ align:start position:0%
+and are a Fisher comes into the lab and
+ 
+
+ align:start position:0%
+and are a Fisher comes into the lab and
+he has a very different view about how
+
+ align:start position:0%
+he has a very different view about how
+ 
+
+ align:start position:0%
+he has a very different view about how
+to do experimentation
+
+ align:start position:0%
+to do experimentation
+ 
+
+ align:start position:0%
+to do experimentation
+he analyzes this experiment in which we
+
+ align:start position:0%
+he analyzes this experiment in which we
+ 
+
+ align:start position:0%
+he analyzes this experiment in which we
+see the table three in the middle this
+
+ align:start position:0%
+see the table three in the middle this
+ 
+
+ align:start position:0%
+see the table three in the middle this
+is from RI Fisher's 1921 paper and what
+
+ align:start position:0%
+is from RI Fisher's 1921 paper and what
+ 
+
+ align:start position:0%
+is from RI Fisher's 1921 paper and what
+you see is a plot with different levels
+
+ align:start position:0%
+you see is a plot with different levels
+ 
+
+ align:start position:0%
+you see is a plot with different levels
+of ammonia being applied as fertilizer
+
+ align:start position:0%
+of ammonia being applied as fertilizer
+ 
+
+ align:start position:0%
+of ammonia being applied as fertilizer
+to the fields and you see the influence
+
+ align:start position:0%
+to the fields and you see the influence
+ 
+
+ align:start position:0%
+to the fields and you see the influence
+on the yield per acre of oats and the
+
+ align:start position:0%
+on the yield per acre of oats and the
+ 
+
+ align:start position:0%
+on the yield per acre of oats and the
+decrement in each year because when you
+
+ align:start position:0%
+decrement in each year because when you
+ 
+
+ align:start position:0%
+decrement in each year because when you
+apply the fertilizer to the same field
+
+ align:start position:0%
+apply the fertilizer to the same field
+ 
+
+ align:start position:0%
+apply the fertilizer to the same field
+year after year the its effects diminish
+
+ align:start position:0%
+year after year the its effects diminish
+ 
+
+ align:start position:0%
+year after year the its effects diminish
+over time and apparently Fischer was
+
+ align:start position:0%
+over time and apparently Fischer was
+ 
+
+ align:start position:0%
+over time and apparently Fischer was
+fairly discouraged by this experiment
+
+ align:start position:0%
+fairly discouraged by this experiment
+ 
+
+ align:start position:0%
+fairly discouraged by this experiment
+when you read the paper you you see the
+
+ align:start position:0%
+when you read the paper you you see the
+ 
+
+ align:start position:0%
+when you read the paper you you see the
+details and you see the difficulties
+
+ align:start position:0%
+details and you see the difficulties
+ 
+
+ align:start position:0%
+details and you see the difficulties
+they experienced in analyzing the data
+
+ align:start position:0%
+they experienced in analyzing the data
+ 
+
+ align:start position:0%
+they experienced in analyzing the data
+you know they had some pests intruding
+
+ align:start position:0%
+you know they had some pests intruding
+ 
+
+ align:start position:0%
+you know they had some pests intruding
+on parts of the land and this made it
+
+ align:start position:0%
+on parts of the land and this made it
+ 
+
+ align:start position:0%
+on parts of the land and this made it
+complex to draw inferences from the
+
+ align:start position:0%
+complex to draw inferences from the
+ 
+
+ align:start position:0%
+complex to draw inferences from the
+experiment and he was later quoted to
+
+ align:start position:0%
+experiment and he was later quoted to
+ 
+
+ align:start position:0%
+experiment and he was later quoted to
+say the following thing which expressed
+
+ align:start position:0%
+say the following thing which expressed
+ 
+
+ align:start position:0%
+say the following thing which expressed
+that frustration in a way you have a
+
+ align:start position:0%
+that frustration in a way you have a
+ 
+
+ align:start position:0%
+that frustration in a way you have a
+bunch of scientists plan an experiment
+
+ align:start position:0%
+bunch of scientists plan an experiment
+ 
+
+ align:start position:0%
+bunch of scientists plan an experiment
+based on their knowledge of what to do
+
+ align:start position:0%
+based on their knowledge of what to do
+ 
+
+ align:start position:0%
+based on their knowledge of what to do
+later in you call statisticians in to
+
+ align:start position:0%
+later in you call statisticians in to
+ 
+
+ align:start position:0%
+later in you call statisticians in to
+analyze the data and to get the most
+
+ align:start position:0%
+analyze the data and to get the most
+ 
+
+ align:start position:0%
+analyze the data and to get the most
+precise inferences you can and oppressor
+
+ align:start position:0%
+precise inferences you can and oppressor
+ 
+
+ align:start position:0%
+precise inferences you can and oppressor
+precise estimates and it's really too
+
+ align:start position:0%
+precise estimates and it's really too
+ 
+
+ align:start position:0%
+precise estimates and it's really too
+late the tylium for statistical thinking
+
+ align:start position:0%
+late the tylium for statistical thinking
+ 
+
+ align:start position:0%
+late the tylium for statistical thinking
+is before you actually run the
+
+ align:start position:0%
+is before you actually run the
+ 
+
+ align:start position:0%
+is before you actually run the
+experiment that's when you can get the
+
+ align:start position:0%
+experiment that's when you can get the
+ 
+
+ align:start position:0%
+experiment that's when you can get the
+greatest benefits and what he talked
+
+ align:start position:0%
+greatest benefits and what he talked
+ 
+
+ align:start position:0%
+greatest benefits and what he talked
+about is the idea that the most finesse
+
+ align:start position:0%
+about is the idea that the most finesse
+ 
+
+ align:start position:0%
+about is the idea that the most finesse
+you could apply might improve your
+
+ align:start position:0%
+you could apply might improve your
+ 
+
+ align:start position:0%
+you could apply might improve your
+analysis of the data by a few percent
+
+ align:start position:0%
+analysis of the data by a few percent
+ 
+
+ align:start position:0%
+analysis of the data by a few percent
+one way or other but if you brought in
+
+ align:start position:0%
+one way or other but if you brought in
+ 
+
+ align:start position:0%
+one way or other but if you brought in
+the experimenter earlier maybe you'd get
+
+ align:start position:0%
+the experimenter earlier maybe you'd get
+ 
+
+ align:start position:0%
+the experimenter earlier maybe you'd get
+a factor of two or five in efficiency
+
+ align:start position:0%
+a factor of two or five in efficiency
+ 
+
+ align:start position:0%
+a factor of two or five in efficiency
+and accuracy and you can see how
+
+ align:start position:0%
+and accuracy and you can see how
+ 
+
+ align:start position:0%
+and accuracy and you can see how
+thoughtful Fischer was you know you see
+
+ align:start position:0%
+thoughtful Fischer was you know you see
+ 
+
+ align:start position:0%
+thoughtful Fischer was you know you see
+he seems to be struggling a hard to
+
+ align:start position:0%
+he seems to be struggling a hard to
+ 
+
+ align:start position:0%
+he seems to be struggling a hard to
+think there and I think part of it is
+
+ align:start position:0%
+think there and I think part of it is
+ 
+
+ align:start position:0%
+think there and I think part of it is
+that machine that's in front of them
+
+ align:start position:0%
+that machine that's in front of them
+ 
+
+ align:start position:0%
+that machine that's in front of them
+which is I guess what you'd use for a
+
+ align:start position:0%
+which is I guess what you'd use for a
+ 
+
+ align:start position:0%
+which is I guess what you'd use for a
+computer in that day I guess it's some
+
+ align:start position:0%
+computer in that day I guess it's some
+ 
+
+ align:start position:0%
+computer in that day I guess it's some
+sort of mechanical adding device I think
+
+ align:start position:0%
+sort of mechanical adding device I think
+ 
+
+ align:start position:0%
+sort of mechanical adding device I think
+it's it's nice that we have
+
+ align:start position:0%
+it's it's nice that we have
+ 
+
+ align:start position:0%
+it's it's nice that we have
+much better machines now for this
+
+ align:start position:0%
+much better machines now for this
+ 
+
+ align:start position:0%
+much better machines now for this
+purpose in fact what we find is that you
+
+ align:start position:0%
+purpose in fact what we find is that you
+ 
+
+ align:start position:0%
+purpose in fact what we find is that you
+can do a lot with statistics these days
+
+ align:start position:0%
+can do a lot with statistics these days
+ 
+
+ align:start position:0%
+can do a lot with statistics these days
+by knowing how to work with computers
+
+ align:start position:0%
+by knowing how to work with computers
+ 
+
+ align:start position:0%
+by knowing how to work with computers
+right and in fact a lot of the research
+
+ align:start position:0%
+right and in fact a lot of the research
+ 
+
+ align:start position:0%
+right and in fact a lot of the research
+results I'll show you today we wouldn't
+
+ align:start position:0%
+results I'll show you today we wouldn't
+ 
+
+ align:start position:0%
+results I'll show you today we wouldn't
+be able to achieve them with without
+
+ align:start position:0%
+be able to achieve them with without
+ 
+
+ align:start position:0%
+be able to achieve them with without
+modern digital computers so Fisher
+
+ align:start position:0%
+modern digital computers so Fisher
+ 
+
+ align:start position:0%
+modern digital computers so Fisher
+begins to plant experiments in a
+
+ align:start position:0%
+begins to plant experiments in a
+ 
+
+ align:start position:0%
+begins to plant experiments in a
+different way and this is one of the
+
+ align:start position:0%
+different way and this is one of the
+ 
+
+ align:start position:0%
+different way and this is one of the
+first ones that in the literature this
+
+ align:start position:0%
+first ones that in the literature this
+ 
+
+ align:start position:0%
+first ones that in the literature this
+figure figure one from his 1926 paper on
+
+ align:start position:0%
+figure figure one from his 1926 paper on
+ 
+
+ align:start position:0%
+figure figure one from his 1926 paper on
+the arrangement of field experiments and
+
+ align:start position:0%
+the arrangement of field experiments and
+ 
+
+ align:start position:0%
+the arrangement of field experiments and
+if you've done some work already in this
+
+ align:start position:0%
+if you've done some work already in this
+ 
+
+ align:start position:0%
+if you've done some work already in this
+course on design of experiments you
+
+ align:start position:0%
+course on design of experiments you
+ 
+
+ align:start position:0%
+course on design of experiments you
+might recognize this
+
+ align:start position:0%
+might recognize this
+ 
+
+ align:start position:0%
+might recognize this
+you see somewhat indicated by darker
+
+ align:start position:0%
+you see somewhat indicated by darker
+ 
+
+ align:start position:0%
+you see somewhat indicated by darker
+lines that there are eight different
+
+ align:start position:0%
+lines that there are eight different
+ 
+
+ align:start position:0%
+lines that there are eight different
+subplots in this plot and if I focus my
+
+ align:start position:0%
+subplots in this plot and if I focus my
+ 
+
+ align:start position:0%
+subplots in this plot and if I focus my
+attention on just say the upper left
+
+ align:start position:0%
+attention on just say the upper left
+ 
+
+ align:start position:0%
+attention on just say the upper left
+what I see is and I think the people
+
+ align:start position:0%
+what I see is and I think the people
+ 
+
+ align:start position:0%
+what I see is and I think the people
+even remotely can see the arrow right
+
+ align:start position:0%
+even remotely can see the arrow right
+ 
+
+ align:start position:0%
+even remotely can see the arrow right
+you see the plot has three different
+
+ align:start position:0%
+you see the plot has three different
+ 
+
+ align:start position:0%
+you see the plot has three different
+indications in each plot in this case
+
+ align:start position:0%
+indications in each plot in this case
+ 
+
+ align:start position:0%
+indications in each plot in this case
+it's two and M and early and the next
+
+ align:start position:0%
+it's two and M and early and the next
+ 
+
+ align:start position:0%
+it's two and M and early and the next
+one it's two and s and late so the two
+
+ align:start position:0%
+one it's two and s and late so the two
+ 
+
+ align:start position:0%
+one it's two and s and late so the two
+and the one indicate an amount of a
+
+ align:start position:0%
+and the one indicate an amount of a
+ 
+
+ align:start position:0%
+and the one indicate an amount of a
+fertilizer that's been applied s and M
+
+ align:start position:0%
+fertilizer that's been applied s and M
+ 
+
+ align:start position:0%
+fertilizer that's been applied s and M
+indicate the type of the fertilizer and
+
+ align:start position:0%
+indicate the type of the fertilizer and
+ 
+
+ align:start position:0%
+indicate the type of the fertilizer and
+early in late describe the time in the
+
+ align:start position:0%
+early in late describe the time in the
+ 
+
+ align:start position:0%
+early in late describe the time in the
+season the planting season when it's
+
+ align:start position:0%
+season the planting season when it's
+ 
+
+ align:start position:0%
+season the planting season when it's
+applied and we see in this first block
+
+ align:start position:0%
+applied and we see in this first block
+ 
+
+ align:start position:0%
+applied and we see in this first block
+we have four of the twos and four of the
+
+ align:start position:0%
+we have four of the twos and four of the
+ 
+
+ align:start position:0%
+we have four of the twos and four of the
+ones and four of the Early's and four of
+
+ align:start position:0%
+ones and four of the Early's and four of
+ 
+
+ align:start position:0%
+ones and four of the Early's and four of
+the lates and so on and we even see that
+
+ align:start position:0%
+the lates and so on and we even see that
+ 
+
+ align:start position:0%
+the lates and so on and we even see that
+there is a balance in the sense that
+
+ align:start position:0%
+there is a balance in the sense that
+ 
+
+ align:start position:0%
+there is a balance in the sense that
+there are two of the two M's and two of
+
+ align:start position:0%
+there are two of the two M's and two of
+ 
+
+ align:start position:0%
+there are two of the two M's and two of
+the two S's so pairwise there's a
+
+ align:start position:0%
+the two S's so pairwise there's a
+ 
+
+ align:start position:0%
+the two S's so pairwise there's a
+balance and so on and you may recognize
+
+ align:start position:0%
+balance and so on and you may recognize
+ 
+
+ align:start position:0%
+balance and so on and you may recognize
+that if I just focus on two and M and
+
+ align:start position:0%
+that if I just focus on two and M and
+ 
+
+ align:start position:0%
+that if I just focus on two and M and
+early in late and there are eight of
+
+ align:start position:0%
+early in late and there are eight of
+ 
+
+ align:start position:0%
+early in late and there are eight of
+such blocks in here we have every
+
+ align:start position:0%
+such blocks in here we have every
+ 
+
+ align:start position:0%
+such blocks in here we have every
+permutation and combination of the
+
+ align:start position:0%
+permutation and combination of the
+ 
+
+ align:start position:0%
+permutation and combination of the
+factors in the level so I would say you
+
+ align:start position:0%
+factors in the level so I would say you
+ 
+
+ align:start position:0%
+factors in the level so I would say you
+could describe this as a
+
+ align:start position:0%
+could describe this as a
+ 
+
+ align:start position:0%
+could describe this as a
+two to three full factorial experiment
+
+ align:start position:0%
+two to three full factorial experiment
+ 
+
+ align:start position:0%
+two to three full factorial experiment
+within the block which is eight now you
+
+ align:start position:0%
+within the block which is eight now you
+ 
+
+ align:start position:0%
+within the block which is eight now you
+you might also say that it's a three
+
+ align:start position:0%
+you might also say that it's a three
+ 
+
+ align:start position:0%
+you might also say that it's a three
+raised to the one and and two raised to
+
+ align:start position:0%
+raised to the one and and two raised to
+ 
+
+ align:start position:0%
+raised to the one and and two raised to
+the two because there are also these
+
+ align:start position:0%
+the two because there are also these
+ 
+
+ align:start position:0%
+the two because there are also these
+four plots in which there are just X's
+
+ align:start position:0%
+four plots in which there are just X's
+ 
+
+ align:start position:0%
+four plots in which there are just X's
+and no fertilizers applied you could
+
+ align:start position:0%
+and no fertilizers applied you could
+ 
+
+ align:start position:0%
+and no fertilizers applied you could
+call that a control or you could say
+
+ align:start position:0%
+call that a control or you could say
+ 
+
+ align:start position:0%
+call that a control or you could say
+that this is actually a more complex
+
+ align:start position:0%
+that this is actually a more complex
+ 
+
+ align:start position:0%
+that this is actually a more complex
+factorial experiment where in one of the
+
+ align:start position:0%
+factorial experiment where in one of the
+ 
+
+ align:start position:0%
+factorial experiment where in one of the
+levels sort of obviates the other two
+
+ align:start position:0%
+levels sort of obviates the other two
+ 
+
+ align:start position:0%
+levels sort of obviates the other two
+and once you decide to apply no
+
+ align:start position:0%
+and once you decide to apply no
+ 
+
+ align:start position:0%
+and once you decide to apply no
+fertilizer it doesn't matter whether you
+
+ align:start position:0%
+fertilizer it doesn't matter whether you
+ 
+
+ align:start position:0%
+fertilizer it doesn't matter whether you
+apply type 1 or type 2 or quiet earlier
+
+ align:start position:0%
+apply type 1 or type 2 or quiet earlier
+ 
+
+ align:start position:0%
+apply type 1 or type 2 or quiet earlier
+late and then to further complicate the
+
+ align:start position:0%
+late and then to further complicate the
+ 
+
+ align:start position:0%
+late and then to further complicate the
+issue we have eight plots and within
+
+ align:start position:0%
+issue we have eight plots and within
+ 
+
+ align:start position:0%
+issue we have eight plots and within
+those blocks those subplots we have
+
+ align:start position:0%
+those blocks those subplots we have
+ 
+
+ align:start position:0%
+those blocks those subplots we have
+randomization in space of the different
+
+ align:start position:0%
+randomization in space of the different
+ 
+
+ align:start position:0%
+randomization in space of the different
+treatments and one of the things that
+
+ align:start position:0%
+treatments and one of the things that
+ 
+
+ align:start position:0%
+treatments and one of the things that
+Fischer talks about here is how poorly
+
+ align:start position:0%
+Fischer talks about here is how poorly
+ 
+
+ align:start position:0%
+Fischer talks about here is how poorly
+randomization actually works sometimes
+
+ align:start position:0%
+randomization actually works sometimes
+ 
+
+ align:start position:0%
+randomization actually works sometimes
+so if I look down on this plot it's on
+
+ align:start position:0%
+so if I look down on this plot it's on
+ 
+
+ align:start position:0%
+so if I look down on this plot it's on
+the lower right this this plot is
+
+ align:start position:0%
+the lower right this this plot is
+ 
+
+ align:start position:0%
+the lower right this this plot is
+randomized in spatial distribution of
+
+ align:start position:0%
+randomized in spatial distribution of
+ 
+
+ align:start position:0%
+randomized in spatial distribution of
+the treatments but you see that all of
+
+ align:start position:0%
+the treatments but you see that all of
+ 
+
+ align:start position:0%
+the treatments but you see that all of
+the left-hand plots are early and all of
+
+ align:start position:0%
+the left-hand plots are early and all of
+ 
+
+ align:start position:0%
+the left-hand plots are early and all of
+the right-hand plots are late so
+
+ align:start position:0%
+the right-hand plots are late so
+ 
+
+ align:start position:0%
+the right-hand plots are late so
+sometimes randomization gives you such
+
+ align:start position:0%
+sometimes randomization gives you such
+ 
+
+ align:start position:0%
+sometimes randomization gives you such
+such problems in fact these days often
+
+ align:start position:0%
+such problems in fact these days often
+ 
+
+ align:start position:0%
+such problems in fact these days often
+people will not use randomization and
+
+ align:start position:0%
+people will not use randomization and
+ 
+
+ align:start position:0%
+people will not use randomization and
+instead use something like a Latin
+
+ align:start position:0%
+instead use something like a Latin
+ 
+
+ align:start position:0%
+instead use something like a Latin
+hypercube design - rather than
+
+ align:start position:0%
+hypercube design - rather than
+ 
+
+ align:start position:0%
+hypercube design - rather than
+randomization but this was one of the
+
+ align:start position:0%
+randomization but this was one of the
+ 
+
+ align:start position:0%
+randomization but this was one of the
+early experiments that had been
+
+ align:start position:0%
+early experiments that had been
+ 
+
+ align:start position:0%
+early experiments that had been
+considered in a factorial design and I
+
+ align:start position:0%
+considered in a factorial design and I
+ 
+
+ align:start position:0%
+considered in a factorial design and I
+think it's interesting that Fischer
+
+ align:start position:0%
+think it's interesting that Fischer
+ 
+
+ align:start position:0%
+think it's interesting that Fischer
+decided to call it a complex experiment
+
+ align:start position:0%
+decided to call it a complex experiment
+ 
+
+ align:start position:0%
+decided to call it a complex experiment
+it's as if he was trying to emphasize as
+
+ align:start position:0%
+it's as if he was trying to emphasize as
+ 
+
+ align:start position:0%
+it's as if he was trying to emphasize as
+strongly as possible his difference of
+
+ align:start position:0%
+strongly as possible his difference of
+ 
+
+ align:start position:0%
+strongly as possible his difference of
+opinion with Russell his boss who had
+
+ align:start position:0%
+opinion with Russell his boss who had
+ 
+
+ align:start position:0%
+opinion with Russell his boss who had
+said that you should seek simplicity in
+
+ align:start position:0%
+said that you should seek simplicity in
+ 
+
+ align:start position:0%
+said that you should seek simplicity in
+your experiments
+
+ align:start position:0%
+your experiments
+ 
+
+ align:start position:0%
+your experiments
+and he was saying no I'm gonna do the
+
+ align:start position:0%
+and he was saying no I'm gonna do the
+ 
+
+ align:start position:0%
+and he was saying no I'm gonna do the
+exact opposite I'm gonna make my
+
+ align:start position:0%
+exact opposite I'm gonna make my
+ 
+
+ align:start position:0%
+exact opposite I'm gonna make my
+experiment as complex as I can and
+
+ align:start position:0%
+experiment as complex as I can and
+ 
+
+ align:start position:0%
+experiment as complex as I can and
+here's the motivation for doing that and
+
+ align:start position:0%
+here's the motivation for doing that and
+ 
+
+ align:start position:0%
+here's the motivation for doing that and
+this I think is one of the great results
+
+ align:start position:0%
+this I think is one of the great results
+ 
+
+ align:start position:0%
+this I think is one of the great results
+of Fischer is that he was able to
+
+ align:start position:0%
+of Fischer is that he was able to
+ 
+
+ align:start position:0%
+of Fischer is that he was able to
+demonstrate the specific value that you
+
+ align:start position:0%
+demonstrate the specific value that you
+ 
+
+ align:start position:0%
+demonstrate the specific value that you
+could you could attain by making the
+
+ align:start position:0%
+could you could attain by making the
+ 
+
+ align:start position:0%
+could you could attain by making the
+experiment complex and what we have here
+
+ align:start position:0%
+experiment complex and what we have here
+ 
+
+ align:start position:0%
+experiment complex and what we have here
+on the upper right of the slide is a
+
+ align:start position:0%
+on the upper right of the slide is a
+ 
+
+ align:start position:0%
+on the upper right of the slide is a
+cuboidal representation of the two to
+
+ align:start position:0%
+cuboidal representation of the two to
+ 
+
+ align:start position:0%
+cuboidal representation of the two to
+three factorial design this may not be
+
+ align:start position:0%
+three factorial design this may not be
+ 
+
+ align:start position:0%
+three factorial design this may not be
+the first time you've seen it in this
+
+ align:start position:0%
+the first time you've seen it in this
+ 
+
+ align:start position:0%
+the first time you've seen it in this
+course but you have the three different
+
+ align:start position:0%
+course but you have the three different
+ 
+
+ align:start position:0%
+course but you have the three different
+levels labeled as a B and C and the
+
+ align:start position:0%
+levels labeled as a B and C and the
+ 
+
+ align:start position:0%
+levels labeled as a B and C and the
+factors labeled as a B and seeing the
+
+ align:start position:0%
+factors labeled as a B and seeing the
+ 
+
+ align:start position:0%
+factors labeled as a B and seeing the
+levels indicate as pluses and minuses
+
+ align:start position:0%
+levels indicate as pluses and minuses
+ 
+
+ align:start position:0%
+levels indicate as pluses and minuses
+and the way that you would estimate the
+
+ align:start position:0%
+and the way that you would estimate the
+ 
+
+ align:start position:0%
+and the way that you would estimate the
+effect of a is by looking at the
+
+ align:start position:0%
+effect of a is by looking at the
+ 
+
+ align:start position:0%
+effect of a is by looking at the
+observations where a is at level plus
+
+ align:start position:0%
+observations where a is at level plus
+ 
+
+ align:start position:0%
+observations where a is at level plus
+taking the average of those four and
+
+ align:start position:0%
+taking the average of those four and
+ 
+
+ align:start position:0%
+taking the average of those four and
+then taking all of the observations
+
+ align:start position:0%
+then taking all of the observations
+ 
+
+ align:start position:0%
+then taking all of the observations
+where a is at minus and taking the
+
+ align:start position:0%
+where a is at minus and taking the
+ 
+
+ align:start position:0%
+where a is at minus and taking the
+average of those four and looking at
+
+ align:start position:0%
+average of those four and looking at
+ 
+
+ align:start position:0%
+average of those four and looking at
+that difference and that's the equation
+
+ align:start position:0%
+that difference and that's the equation
+ 
+
+ align:start position:0%
+that difference and that's the equation
+here the effect of a is defined as this
+
+ align:start position:0%
+here the effect of a is defined as this
+ 
+
+ align:start position:0%
+here the effect of a is defined as this
+equation which just implements what I
+
+ align:start position:0%
+equation which just implements what I
+ 
+
+ align:start position:0%
+equation which just implements what I
+just described in words and then what
+
+ align:start position:0%
+just described in words and then what
+ 
+
+ align:start position:0%
+just described in words and then what
+Fisher is able to show is that the
+
+ align:start position:0%
+Fisher is able to show is that the
+ 
+
+ align:start position:0%
+Fisher is able to show is that the
+standard deviation of the effect
+
+ align:start position:0%
+standard deviation of the effect
+ 
+
+ align:start position:0%
+standard deviation of the effect
+estimate has a the following form it is
+
+ align:start position:0%
+estimate has a the following form it is
+ 
+
+ align:start position:0%
+estimate has a the following form it is
+a function of the experimental error if
+
+ align:start position:0%
+a function of the experimental error if
+ 
+
+ align:start position:0%
+a function of the experimental error if
+I model the random variations in the
+
+ align:start position:0%
+I model the random variations in the
+ 
+
+ align:start position:0%
+I model the random variations in the
+observation do - let's say soil pH or
+
+ align:start position:0%
+observation do - let's say soil pH or
+ 
+
+ align:start position:0%
+observation do - let's say soil pH or
+the pests that I spoke of earlier or
+
+ align:start position:0%
+the pests that I spoke of earlier or
+ 
+
+ align:start position:0%
+the pests that I spoke of earlier or
+uneven distribution of water on the
+
+ align:start position:0%
+uneven distribution of water on the
+ 
+
+ align:start position:0%
+uneven distribution of water on the
+fields if all those nuisance factors
+
+ align:start position:0%
+fields if all those nuisance factors
+ 
+
+ align:start position:0%
+fields if all those nuisance factors
+that I didn't control influenced my
+
+ align:start position:0%
+that I didn't control influenced my
+ 
+
+ align:start position:0%
+that I didn't control influenced my
+yields at the various locations and
+
+ align:start position:0%
+yields at the various locations and
+ 
+
+ align:start position:0%
+yields at the various locations and
+those contribute to Sigma sub epsilon
+
+ align:start position:0%
+those contribute to Sigma sub epsilon
+ 
+
+ align:start position:0%
+those contribute to Sigma sub epsilon
+those will be reflected in Sigma sub a
+
+ align:start position:0%
+those will be reflected in Sigma sub a
+ 
+
+ align:start position:0%
+those will be reflected in Sigma sub a
+my estimate of the influence of say
+
+ align:start position:0%
+my estimate of the influence of say
+ 
+
+ align:start position:0%
+my estimate of the influence of say
+applying the fertilizer early or late
+
+ align:start position:0%
+applying the fertilizer early or late
+ 
+
+ align:start position:0%
+applying the fertilizer early or late
+but they are reflected in Sigma sub a
+
+ align:start position:0%
+but they are reflected in Sigma sub a
+ 
+
+ align:start position:0%
+but they are reflected in Sigma sub a
+substantially less if I use this
+
+ align:start position:0%
+substantially less if I use this
+ 
+
+ align:start position:0%
+substantially less if I use this
+factorial design rather than a single
+
+ align:start position:0%
+factorial design rather than a single
+ 
+
+ align:start position:0%
+factorial design rather than a single
+factor experiment and he could show that
+
+ align:start position:0%
+factor experiment and he could show that
+ 
+
+ align:start position:0%
+factor experiment and he could show that
+for the case of the two to the three
+
+ align:start position:0%
+for the case of the two to the three
+ 
+
+ align:start position:0%
+for the case of the two to the three
+full factorial the improvement in
+
+ align:start position:0%
+full factorial the improvement in
+ 
+
+ align:start position:0%
+full factorial the improvement in
+efficiency is a factor of two so it's a
+
+ align:start position:0%
+efficiency is a factor of two so it's a
+ 
+
+ align:start position:0%
+efficiency is a factor of two so it's a
+large benefit as compared to the
+
+ align:start position:0%
+large benefit as compared to the
+ 
+
+ align:start position:0%
+large benefit as compared to the
+benefits that you could derive by a
+
+ align:start position:0%
+benefits that you could derive by a
+ 
+
+ align:start position:0%
+benefits that you could derive by a
+different kind of analysis of the data
+
+ align:start position:0%
+different kind of analysis of the data
+ 
+
+ align:start position:0%
+different kind of analysis of the data
+the planning of the data made a huge
+
+ align:start position:0%
+the planning of the data made a huge
+ 
+
+ align:start position:0%
+the planning of the data made a huge
+difference but the problem is that if
+
+ align:start position:0%
+difference but the problem is that if
+ 
+
+ align:start position:0%
+difference but the problem is that if
+you're using a full factorial experiment
+
+ align:start position:0%
+you're using a full factorial experiment
+ 
+
+ align:start position:0%
+you're using a full factorial experiment
+you see 2 to 3 or 2 to the K the scaling
+
+ align:start position:0%
+you see 2 to 3 or 2 to the K the scaling
+ 
+
+ align:start position:0%
+you see 2 to 3 or 2 to the K the scaling
+with the number of factors is terrible
+
+ align:start position:0%
+with the number of factors is terrible
+ 
+
+ align:start position:0%
+with the number of factors is terrible
+right and so you find that you can't run
+
+ align:start position:0%
+right and so you find that you can't run
+ 
+
+ align:start position:0%
+right and so you find that you can't run
+such experiments with more than say 7
+
+ align:start position:0%
+such experiments with more than say 7
+ 
+
+ align:start position:0%
+such experiments with more than say 7
+factors that's about the largest that
+
+ align:start position:0%
+factors that's about the largest that
+ 
+
+ align:start position:0%
+factors that's about the largest that
+I've seen published in tables so that we
+
+ align:start position:0%
+I've seen published in tables so that we
+ 
+
+ align:start position:0%
+I've seen published in tables so that we
+can analyze them because then you have
+
+ align:start position:0%
+can analyze them because then you have
+ 
+
+ align:start position:0%
+can analyze them because then you have
+128 data elements to include in the
+
+ align:start position:0%
+128 data elements to include in the
+ 
+
+ align:start position:0%
+128 data elements to include in the
+appendix of your paper so they're rarely
+
+ align:start position:0%
+appendix of your paper so they're rarely
+ 
+
+ align:start position:0%
+appendix of your paper so they're rarely
+run with more than 7 factors and yet in
+
+ align:start position:0%
+run with more than 7 factors and yet in
+ 
+
+ align:start position:0%
+run with more than 7 factors and yet in
+an experimentation especially in
+
+ align:start position:0%
+an experimentation especially in
+ 
+
+ align:start position:0%
+an experimentation especially in
+engineering we often have many more than
+
+ align:start position:0%
+engineering we often have many more than
+ 
+
+ align:start position:0%
+engineering we often have many more than
+7 factors we're concerned with that's
+
+ align:start position:0%
+7 factors we're concerned with that's
+ 
+
+ align:start position:0%
+7 factors we're concerned with that's
+not at all uncommon and so almost
+
+ align:start position:0%
+not at all uncommon and so almost
+ 
+
+ align:start position:0%
+not at all uncommon and so almost
+immediately Fisher begins to consider
+
+ align:start position:0%
+immediately Fisher begins to consider
+ 
+
+ align:start position:0%
+immediately Fisher begins to consider
+the possibility of some means to reduce
+
+ align:start position:0%
+the possibility of some means to reduce
+ 
+
+ align:start position:0%
+the possibility of some means to reduce
+the size of the experiment even as the
+
+ align:start position:0%
+the size of the experiment even as the
+ 
+
+ align:start position:0%
+the size of the experiment even as the
+number of factors goes up and this is
+
+ align:start position:0%
+number of factors goes up and this is
+ 
+
+ align:start position:0%
+number of factors goes up and this is
+the way he describes thinking about that
+
+ align:start position:0%
+the way he describes thinking about that
+ 
+
+ align:start position:0%
+the way he describes thinking about that
+you you deliberately sacrifice
+
+ align:start position:0%
+you you deliberately sacrifice
+ 
+
+ align:start position:0%
+you you deliberately sacrifice
+possibility of obtaining information on
+
+ align:start position:0%
+possibility of obtaining information on
+ 
+
+ align:start position:0%
+possibility of obtaining information on
+some points so you decide there are
+
+ align:start position:0%
+some points so you decide there are
+ 
+
+ align:start position:0%
+some points so you decide there are
+certain things that you would be able to
+
+ align:start position:0%
+certain things that you would be able to
+ 
+
+ align:start position:0%
+certain things that you would be able to
+estimate in the full factorial but you
+
+ align:start position:0%
+estimate in the full factorial but you
+ 
+
+ align:start position:0%
+estimate in the full factorial but you
+just decide ahead of time that they're
+
+ align:start position:0%
+just decide ahead of time that they're
+ 
+
+ align:start position:0%
+just decide ahead of time that they're
+there they're not worth investigating
+
+ align:start position:0%
+there they're not worth investigating
+ 
+
+ align:start position:0%
+there they're not worth investigating
+that maybe they're unlikely a priori and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you design the experiment so that you
+
+ align:start position:0%
+so you design the experiment so that you
+ 
+
+ align:start position:0%
+so you design the experiment so that you
+can't possibly obtain information about
+
+ align:start position:0%
+can't possibly obtain information about
+ 
+
+ align:start position:0%
+can't possibly obtain information about
+them but actually it's a little worse
+
+ align:start position:0%
+them but actually it's a little worse
+ 
+
+ align:start position:0%
+them but actually it's a little worse
+than that I'm going to show you later
+
+ align:start position:0%
+than that I'm going to show you later
+ 
+
+ align:start position:0%
+than that I'm going to show you later
+not only do you not have a possibility
+
+ align:start position:0%
+not only do you not have a possibility
+ 
+
+ align:start position:0%
+not only do you not have a possibility
+of obtaining information about those
+
+ align:start position:0%
+of obtaining information about those
+ 
+
+ align:start position:0%
+of obtaining information about those
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+those specific points if they were to be
+
+ align:start position:0%
+those specific points if they were to be
+ 
+
+ align:start position:0%
+those specific points if they were to be
+consequential in the end would actually
+
+ align:start position:0%
+consequential in the end would actually
+ 
+
+ align:start position:0%
+consequential in the end would actually
+interfere considerably with your ability
+
+ align:start position:0%
+interfere considerably with your ability
+ 
+
+ align:start position:0%
+interfere considerably with your ability
+to make inferences and so this is the
+
+ align:start position:0%
+to make inferences and so this is the
+ 
+
+ align:start position:0%
+to make inferences and so this is the
+simplest fractional factorial I can show
+
+ align:start position:0%
+simplest fractional factorial I can show
+ 
+
+ align:start position:0%
+simplest fractional factorial I can show
+you again we have the cuboidal
+
+ align:start position:0%
+you again we have the cuboidal
+ 
+
+ align:start position:0%
+you again we have the cuboidal
+representation and what we do is just to
+
+ align:start position:0%
+representation and what we do is just to
+ 
+
+ align:start position:0%
+representation and what we do is just to
+make observations at half of the
+
+ align:start position:0%
+make observations at half of the
+ 
+
+ align:start position:0%
+make observations at half of the
+vertices so I indicate those by the
+
+ align:start position:0%
+vertices so I indicate those by the
+ 
+
+ align:start position:0%
+vertices so I indicate those by the
+black pluses and these four are selected
+
+ align:start position:0%
+black pluses and these four are selected
+ 
+
+ align:start position:0%
+black pluses and these four are selected
+and a specific arrangement to give us
+
+ align:start position:0%
+and a specific arrangement to give us
+ 
+
+ align:start position:0%
+and a specific arrangement to give us
+the two to the three minus 1/2 fraction
+
+ align:start position:0%
+the two to the three minus 1/2 fraction
+ 
+
+ align:start position:0%
+the two to the three minus 1/2 fraction
+with resolution three I'll describe what
+
+ align:start position:0%
+with resolution three I'll describe what
+ 
+
+ align:start position:0%
+with resolution three I'll describe what
+resolution three means and a second one
+
+ align:start position:0%
+resolution three means and a second one
+ 
+
+ align:start position:0%
+resolution three means and a second one
+of the things that's interesting about
+
+ align:start position:0%
+of the things that's interesting about
+ 
+
+ align:start position:0%
+of the things that's interesting about
+the experiment in my mind is its
+
+ align:start position:0%
+the experiment in my mind is its
+ 
+
+ align:start position:0%
+the experiment in my mind is its
+projective properties so we see that if
+
+ align:start position:0%
+projective properties so we see that if
+ 
+
+ align:start position:0%
+projective properties so we see that if
+we collapse factor a that is if we
+
+ align:start position:0%
+we collapse factor a that is if we
+ 
+
+ align:start position:0%
+we collapse factor a that is if we
+imagine that there is a flashlight or
+
+ align:start position:0%
+imagine that there is a flashlight or
+ 
+
+ align:start position:0%
+imagine that there is a flashlight or
+such a source of light off to the right
+
+ align:start position:0%
+such a source of light off to the right
+ 
+
+ align:start position:0%
+such a source of light off to the right
+and we get a projection of the matrix of
+
+ align:start position:0%
+and we get a projection of the matrix of
+ 
+
+ align:start position:0%
+and we get a projection of the matrix of
+the cube and now we just get a square we
+
+ align:start position:0%
+the cube and now we just get a square we
+ 
+
+ align:start position:0%
+the cube and now we just get a square we
+see that if factor a has collapsed we
+
+ align:start position:0%
+see that if factor a has collapsed we
+ 
+
+ align:start position:0%
+see that if factor a has collapsed we
+would have a full factorial experiment
+
+ align:start position:0%
+would have a full factorial experiment
+ 
+
+ align:start position:0%
+would have a full factorial experiment
+in B and C have you studied these
+
+ align:start position:0%
+in B and C have you studied these
+ 
+
+ align:start position:0%
+in B and C have you studied these
+projective properties and the other
+
+ align:start position:0%
+projective properties and the other
+ 
+
+ align:start position:0%
+projective properties and the other
+parts of the course okay and so it goes
+
+ align:start position:0%
+parts of the course okay and so it goes
+ 
+
+ align:start position:0%
+parts of the course okay and so it goes
+in the other dimensions as well and so
+
+ align:start position:0%
+in the other dimensions as well and so
+ 
+
+ align:start position:0%
+in the other dimensions as well and so
+in my mind what's interesting about this
+
+ align:start position:0%
+in my mind what's interesting about this
+ 
+
+ align:start position:0%
+in my mind what's interesting about this
+is that in a way the design of the
+
+ align:start position:0%
+is that in a way the design of the
+ 
+
+ align:start position:0%
+is that in a way the design of the
+experiment allows you to account for a
+
+ align:start position:0%
+experiment allows you to account for a
+ 
+
+ align:start position:0%
+experiment allows you to account for a
+particular kind of uncertainty if you
+
+ align:start position:0%
+particular kind of uncertainty if you
+ 
+
+ align:start position:0%
+particular kind of uncertainty if you
+have a long list of factors and you're
+
+ align:start position:0%
+have a long list of factors and you're
+ 
+
+ align:start position:0%
+have a long list of factors and you're
+not sure which ones are going to be the
+
+ align:start position:0%
+not sure which ones are going to be the
+ 
+
+ align:start position:0%
+not sure which ones are going to be the
+important ones you know that some few
+
+ align:start position:0%
+important ones you know that some few
+ 
+
+ align:start position:0%
+important ones you know that some few
+will turn out to be important but you're
+
+ align:start position:0%
+will turn out to be important but you're
+ 
+
+ align:start position:0%
+will turn out to be important but you're
+not sure which ones you can arrange it
+
+ align:start position:0%
+not sure which ones you can arrange it
+ 
+
+ align:start position:0%
+not sure which ones you can arrange it
+so that you will have done a full
+
+ align:start position:0%
+so that you will have done a full
+ 
+
+ align:start position:0%
+so that you will have done a full
+factorial in the few important factors
+
+ align:start position:0%
+factorial in the few important factors
+ 
+
+ align:start position:0%
+factorial in the few important factors
+without knowing exactly which ones you
+
+ align:start position:0%
+without knowing exactly which ones you
+ 
+
+ align:start position:0%
+without knowing exactly which ones you
+need to do a full factorial experiment
+
+ align:start position:0%
+need to do a full factorial experiment
+ 
+
+ align:start position:0%
+need to do a full factorial experiment
+in and that's what the projective
+
+ align:start position:0%
+in and that's what the projective
+ 
+
+ align:start position:0%
+in and that's what the projective
+properties allow you to do but all this
+
+ align:start position:0%
+properties allow you to do but all this
+ 
+
+ align:start position:0%
+properties allow you to do but all this
+comes at a cost and the cost is more
+
+ align:start position:0%
+comes at a cost and the cost is more
+ 
+
+ align:start position:0%
+comes at a cost and the cost is more
+easily described by looking at
+
+ align:start position:0%
+easily described by looking at
+ 
+
+ align:start position:0%
+easily described by looking at
+a larger fractional factorial experiment
+
+ align:start position:0%
+a larger fractional factorial experiment
+ 
+
+ align:start position:0%
+a larger fractional factorial experiment
+this is the to the 7-4 design and what
+
+ align:start position:0%
+this is the to the 7-4 design and what
+ 
+
+ align:start position:0%
+this is the to the 7-4 design and what
+we see here is that if we have seven
+
+ align:start position:0%
+we see here is that if we have seven
+ 
+
+ align:start position:0%
+we see here is that if we have seven
+factors and we want to stuff them into a
+
+ align:start position:0%
+factors and we want to stuff them into a
+ 
+
+ align:start position:0%
+factors and we want to stuff them into a
+small experiment with just say eight
+
+ align:start position:0%
+small experiment with just say eight
+ 
+
+ align:start position:0%
+small experiment with just say eight
+trials then what we can do is put them
+
+ align:start position:0%
+trials then what we can do is put them
+ 
+
+ align:start position:0%
+trials then what we can do is put them
+in this arrangement and the risk is that
+
+ align:start position:0%
+in this arrangement and the risk is that
+ 
+
+ align:start position:0%
+in this arrangement and the risk is that
+if for example there is a two factor
+
+ align:start position:0%
+if for example there is a two factor
+ 
+
+ align:start position:0%
+if for example there is a two factor
+interaction between F and G then that
+
+ align:start position:0%
+interaction between F and G then that
+ 
+
+ align:start position:0%
+interaction between F and G then that
+will emerge in this pattern that in the
+
+ align:start position:0%
+will emerge in this pattern that in the
+ 
+
+ align:start position:0%
+will emerge in this pattern that in the
+first four experiments F and G are all
+
+ align:start position:0%
+first four experiments F and G are all
+ 
+
+ align:start position:0%
+first four experiments F and G are all
+at the same level either plus and plus
+
+ align:start position:0%
+at the same level either plus and plus
+ 
+
+ align:start position:0%
+at the same level either plus and plus
+or minus and minus and in the last four
+
+ align:start position:0%
+or minus and minus and in the last four
+ 
+
+ align:start position:0%
+or minus and minus and in the last four
+experiments they're all at different
+
+ align:start position:0%
+experiments they're all at different
+ 
+
+ align:start position:0%
+experiments they're all at different
+levels such as minus and plus or plus
+
+ align:start position:0%
+levels such as minus and plus or plus
+ 
+
+ align:start position:0%
+levels such as minus and plus or plus
+and minus and so if the two are
+
+ align:start position:0%
+and minus and so if the two are
+ 
+
+ align:start position:0%
+and minus and so if the two are
+interacting in some important way the
+
+ align:start position:0%
+interacting in some important way the
+ 
+
+ align:start position:0%
+interacting in some important way the
+effect will emerge in such a way that it
+
+ align:start position:0%
+effect will emerge in such a way that it
+ 
+
+ align:start position:0%
+effect will emerge in such a way that it
+is coming into being exactly when a as
+
+ align:start position:0%
+is coming into being exactly when a as
+ 
+
+ align:start position:0%
+is coming into being exactly when a as
+at - or a as a plus and so you will
+
+ align:start position:0%
+at - or a as a plus and so you will
+ 
+
+ align:start position:0%
+at - or a as a plus and so you will
+confound the two in your analysis and if
+
+ align:start position:0%
+confound the two in your analysis and if
+ 
+
+ align:start position:0%
+confound the two in your analysis and if
+you think that an effect of a itself is
+
+ align:start position:0%
+you think that an effect of a itself is
+ 
+
+ align:start position:0%
+you think that an effect of a itself is
+more likely than a two factor
+
+ align:start position:0%
+more likely than a two factor
+ 
+
+ align:start position:0%
+more likely than a two factor
+interaction of F and G you're likely to
+
+ align:start position:0%
+interaction of F and G you're likely to
+ 
+
+ align:start position:0%
+interaction of F and G you're likely to
+make a mistake - to assign that effect
+
+ align:start position:0%
+make a mistake - to assign that effect
+ 
+
+ align:start position:0%
+make a mistake - to assign that effect
+to a whereas it actually occurred due to
+
+ align:start position:0%
+to a whereas it actually occurred due to
+ 
+
+ align:start position:0%
+to a whereas it actually occurred due to
+F and G that's the risk that you have to
+
+ align:start position:0%
+F and G that's the risk that you have to
+ 
+
+ align:start position:0%
+F and G that's the risk that you have to
+take to make a relatively small
+
+ align:start position:0%
+take to make a relatively small
+ 
+
+ align:start position:0%
+take to make a relatively small
+experiment that's investigating a lot of
+
+ align:start position:0%
+experiment that's investigating a lot of
+ 
+
+ align:start position:0%
+experiment that's investigating a lot of
+potential factors so these are the trade
+
+ align:start position:0%
+potential factors so these are the trade
+ 
+
+ align:start position:0%
+potential factors so these are the trade
+offs we we make an experimental design
+
+ align:start position:0%
+offs we we make an experimental design
+ 
+
+ align:start position:0%
+offs we we make an experimental design
+now one of the reasons that this whole
+
+ align:start position:0%
+now one of the reasons that this whole
+ 
+
+ align:start position:0%
+now one of the reasons that this whole
+topic is important to engineers is that
+
+ align:start position:0%
+topic is important to engineers is that
+ 
+
+ align:start position:0%
+topic is important to engineers is that
+we're concerned with robustness robust
+
+ align:start position:0%
+we're concerned with robustness robust
+ 
+
+ align:start position:0%
+we're concerned with robustness robust
+parameter design and what I'm showing
+
+ align:start position:0%
+parameter design and what I'm showing
+ 
+
+ align:start position:0%
+parameter design and what I'm showing
+here is the cover of one of the I think
+
+ align:start position:0%
+here is the cover of one of the I think
+ 
+
+ align:start position:0%
+here is the cover of one of the I think
+probably the best modern compilation of
+
+ align:start position:0%
+probably the best modern compilation of
+ 
+
+ align:start position:0%
+probably the best modern compilation of
+this topic on experimental design and
+
+ align:start position:0%
+this topic on experimental design and
+ 
+
+ align:start position:0%
+this topic on experimental design and
+its application to engineering systems
+
+ align:start position:0%
+its application to engineering systems
+ 
+
+ align:start position:0%
+its application to engineering systems
+in particular for the pursuit of
+
+ align:start position:0%
+in particular for the pursuit of
+ 
+
+ align:start position:0%
+in particular for the pursuit of
+robustness and he and Jeff flew and
+
+ align:start position:0%
+robustness and he and Jeff flew and
+ 
+
+ align:start position:0%
+robustness and he and Jeff flew and
+Michael Hamada defined robust parameter
+
+ align:start position:0%
+Michael Hamada defined robust parameter
+ 
+
+ align:start position:0%
+Michael Hamada defined robust parameter
+design here
+
+ align:start position:0%
+design here
+ 
+
+ align:start position:0%
+design here
+as a set of statistical and engineering
+
+ align:start position:0%
+as a set of statistical and engineering
+ 
+
+ align:start position:0%
+as a set of statistical and engineering
+methodology to reduce performance
+
+ align:start position:0%
+methodology to reduce performance
+ 
+
+ align:start position:0%
+methodology to reduce performance
+variation by choosing settings of
+
+ align:start position:0%
+variation by choosing settings of
+ 
+
+ align:start position:0%
+variation by choosing settings of
+control factors to make the system less
+
+ align:start position:0%
+control factors to make the system less
+ 
+
+ align:start position:0%
+control factors to make the system less
+sensitive so you're trying to find
+
+ align:start position:0%
+sensitive so you're trying to find
+ 
+
+ align:start position:0%
+sensitive so you're trying to find
+things that you can control in an
+
+ align:start position:0%
+things that you can control in an
+ 
+
+ align:start position:0%
+things that you can control in an
+experiment in a design and to use those
+
+ align:start position:0%
+experiment in a design and to use those
+ 
+
+ align:start position:0%
+experiment in a design and to use those
+to make performance less sensitive to
+
+ align:start position:0%
+to make performance less sensitive to
+ 
+
+ align:start position:0%
+to make performance less sensitive to
+things that you don't control can you
+
+ align:start position:0%
+things that you don't control can you
+ 
+
+ align:start position:0%
+things that you don't control can you
+think of examples relevant to your work
+
+ align:start position:0%
+think of examples relevant to your work
+ 
+
+ align:start position:0%
+think of examples relevant to your work
+of something you might make robust or
+
+ align:start position:0%
+of something you might make robust or
+ 
+
+ align:start position:0%
+of something you might make robust or
+even simpler just a of a noise factor
+
+ align:start position:0%
+even simpler just a of a noise factor
+ 
+
+ align:start position:0%
+even simpler just a of a noise factor
+you might be concerned with something
+
+ align:start position:0%
+you might be concerned with something
+ 
+
+ align:start position:0%
+you might be concerned with something
+that influences a system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we'll have more examples later and
+
+ align:start position:0%
+well we'll have more examples later and
+ 
+
+ align:start position:0%
+well we'll have more examples later and
+in fact I believe that in the past this
+
+ align:start position:0%
+in fact I believe that in the past this
+ 
+
+ align:start position:0%
+in fact I believe that in the past this
+course has had some projects associated
+
+ align:start position:0%
+course has had some projects associated
+ 
+
+ align:start position:0%
+course has had some projects associated
+with it
+
+ align:start position:0%
+with it
+ 
+
+ align:start position:0%
+with it
+and in some cases people want to do
+
+ align:start position:0%
+and in some cases people want to do
+ 
+
+ align:start position:0%
+and in some cases people want to do
+robust Prem resign and projects yes ok
+
+ align:start position:0%
+robust Prem resign and projects yes ok
+ 
+
+ align:start position:0%
+robust Prem resign and projects yes ok
+ok so you might be doing injection
+
+ align:start position:0%
+ok so you might be doing injection
+ 
+
+ align:start position:0%
+ok so you might be doing injection
+molding or a process like that and you
+
+ align:start position:0%
+molding or a process like that and you
+ 
+
+ align:start position:0%
+molding or a process like that and you
+kit you you could control temperature
+
+ align:start position:0%
+kit you you could control temperature
+ 
+
+ align:start position:0%
+kit you you could control temperature
+and humidity but at some great cost I
+
+ align:start position:0%
+and humidity but at some great cost I
+ 
+
+ align:start position:0%
+and humidity but at some great cost I
+guess so you might choose to allow those
+
+ align:start position:0%
+guess so you might choose to allow those
+ 
+
+ align:start position:0%
+guess so you might choose to allow those
+things to vary to some degree and if
+
+ align:start position:0%
+things to vary to some degree and if
+ 
+
+ align:start position:0%
+things to vary to some degree and if
+they influence say the geometry of your
+
+ align:start position:0%
+they influence say the geometry of your
+ 
+
+ align:start position:0%
+they influence say the geometry of your
+parts resulting parts too much you you
+
+ align:start position:0%
+parts resulting parts too much you you
+ 
+
+ align:start position:0%
+parts resulting parts too much you you
+would probably be producing less value
+
+ align:start position:0%
+would probably be producing less value
+ 
+
+ align:start position:0%
+would probably be producing less value
+to your customer probably the the
+
+ align:start position:0%
+to your customer probably the the
+ 
+
+ align:start position:0%
+to your customer probably the the
+function of your articles themselves
+
+ align:start position:0%
+function of your articles themselves
+ 
+
+ align:start position:0%
+function of your articles themselves
+might be degraded by that and so you
+
+ align:start position:0%
+might be degraded by that and so you
+ 
+
+ align:start position:0%
+might be degraded by that and so you
+might like to choose process parameters
+
+ align:start position:0%
+might like to choose process parameters
+ 
+
+ align:start position:0%
+might like to choose process parameters
+such as pressures and compositions of
+
+ align:start position:0%
+such as pressures and compositions of
+ 
+
+ align:start position:0%
+such as pressures and compositions of
+your plastic and so on so that that
+
+ align:start position:0%
+your plastic and so on so that that
+ 
+
+ align:start position:0%
+your plastic and so on so that that
+effect is minimized so you decide not to
+
+ align:start position:0%
+effect is minimized so you decide not to
+ 
+
+ align:start position:0%
+effect is minimized so you decide not to
+control the community but just to be
+
+ align:start position:0%
+control the community but just to be
+ 
+
+ align:start position:0%
+control the community but just to be
+insensitive to it they're good so on the
+
+ align:start position:0%
+insensitive to it they're good so on the
+ 
+
+ align:start position:0%
+insensitive to it they're good so on the
+cover of this textbook you see actually
+
+ align:start position:0%
+cover of this textbook you see actually
+ 
+
+ align:start position:0%
+cover of this textbook you see actually
+something called a crossed array it's
+
+ align:start position:0%
+something called a crossed array it's
+ 
+
+ align:start position:0%
+something called a crossed array it's
+hard to pick out unless you know you you
+
+ align:start position:0%
+hard to pick out unless you know you you
+ 
+
+ align:start position:0%
+hard to pick out unless you know you you
+go and zoom in on your own computer but
+
+ align:start position:0%
+go and zoom in on your own computer but
+ 
+
+ align:start position:0%
+go and zoom in on your own computer but
+you see capital A B and C over here and
+
+ align:start position:0%
+you see capital A B and C over here and
+ 
+
+ align:start position:0%
+you see capital A B and C over here and
+those represent control factors such as
+
+ align:start position:0%
+those represent control factors such as
+ 
+
+ align:start position:0%
+those represent control factors such as
+pressure and speed of the extruder and
+
+ align:start position:0%
+pressure and speed of the extruder and
+ 
+
+ align:start position:0%
+pressure and speed of the extruder and
+the composition of the plastic things
+
+ align:start position:0%
+the composition of the plastic things
+ 
+
+ align:start position:0%
+the composition of the plastic things
+that you might control nominally and
+
+ align:start position:0%
+that you might control nominally and
+ 
+
+ align:start position:0%
+that you might control nominally and
+then there's little a and B those are
+
+ align:start position:0%
+then there's little a and B those are
+ 
+
+ align:start position:0%
+then there's little a and B those are
+temperature and humidity and things you
+
+ align:start position:0%
+temperature and humidity and things you
+ 
+
+ align:start position:0%
+temperature and humidity and things you
+might decide you you're not going to
+
+ align:start position:0%
+might decide you you're not going to
+ 
+
+ align:start position:0%
+might decide you you're not going to
+control so much and you see that
+
+ align:start position:0%
+control so much and you see that
+ 
+
+ align:start position:0%
+control so much and you see that
+fractional factorial designs are or
+
+ align:start position:0%
+fractional factorial designs are or
+ 
+
+ align:start position:0%
+fractional factorial designs are or
+factorial designs are being used in each
+
+ align:start position:0%
+factorial designs are being used in each
+ 
+
+ align:start position:0%
+factorial designs are being used in each
+of these arrangements shown to the left
+
+ align:start position:0%
+of these arrangements shown to the left
+ 
+
+ align:start position:0%
+of these arrangements shown to the left
+and above and then the crossing the
+
+ align:start position:0%
+and above and then the crossing the
+ 
+
+ align:start position:0%
+and above and then the crossing the
+product of those two designs is
+
+ align:start position:0%
+product of those two designs is
+ 
+
+ align:start position:0%
+product of those two designs is
+indicated in the middle and here Wow
+
+ align:start position:0%
+indicated in the middle and here Wow
+ 
+
+ align:start position:0%
+indicated in the middle and here Wow
+actually begins to hint and foreshadow
+
+ align:start position:0%
+actually begins to hint and foreshadow
+ 
+
+ align:start position:0%
+actually begins to hint and foreshadow
+about the idea
+
+ align:start position:0%
+about the idea
+ 
+
+ align:start position:0%
+about the idea
+yeah what he calls a combiner experiment
+
+ align:start position:0%
+yeah what he calls a combiner experiment
+ 
+
+ align:start position:0%
+yeah what he calls a combiner experiment
+so he shows some of these being white
+
+ align:start position:0%
+so he shows some of these being white
+ 
+
+ align:start position:0%
+so he shows some of these being white
+and some being dark and he's suggesting
+
+ align:start position:0%
+and some being dark and he's suggesting
+ 
+
+ align:start position:0%
+and some being dark and he's suggesting
+that as a way to address the rather
+
+ align:start position:0%
+that as a way to address the rather
+ 
+
+ align:start position:0%
+that as a way to address the rather
+large size of this experiment so it
+
+ align:start position:0%
+large size of this experiment so it
+ 
+
+ align:start position:0%
+large size of this experiment so it
+turns out that the first person to
+
+ align:start position:0%
+turns out that the first person to
+ 
+
+ align:start position:0%
+turns out that the first person to
+pioneer this idea of bringing in
+
+ align:start position:0%
+pioneer this idea of bringing in
+ 
+
+ align:start position:0%
+pioneer this idea of bringing in
+fractional factorial designs into the
+
+ align:start position:0%
+fractional factorial designs into the
+ 
+
+ align:start position:0%
+fractional factorial designs into the
+plant and using them explicitly for the
+
+ align:start position:0%
+plant and using them explicitly for the
+ 
+
+ align:start position:0%
+plant and using them explicitly for the
+purpose of robustness improvements
+
+ align:start position:0%
+purpose of robustness improvements
+ 
+
+ align:start position:0%
+purpose of robustness improvements
+person who seems to most often get
+
+ align:start position:0%
+person who seems to most often get
+ 
+
+ align:start position:0%
+person who seems to most often get
+credit for this is Taguchi in Japan so
+
+ align:start position:0%
+credit for this is Taguchi in Japan so
+ 
+
+ align:start position:0%
+credit for this is Taguchi in Japan so
+he begins to do work in Japan after
+
+ align:start position:0%
+he begins to do work in Japan after
+ 
+
+ align:start position:0%
+he begins to do work in Japan after
+World War two when they're their
+
+ align:start position:0%
+World War two when they're their
+ 
+
+ align:start position:0%
+World War two when they're their
+manufacturing bases in disarray and
+
+ align:start position:0%
+manufacturing bases in disarray and
+ 
+
+ align:start position:0%
+manufacturing bases in disarray and
+their economy is in not good shape and
+
+ align:start position:0%
+their economy is in not good shape and
+ 
+
+ align:start position:0%
+their economy is in not good shape and
+their reputation for manufacturing is
+
+ align:start position:0%
+their reputation for manufacturing is
+ 
+
+ align:start position:0%
+their reputation for manufacturing is
+very poor at that time too so if you
+
+ align:start position:0%
+very poor at that time too so if you
+ 
+
+ align:start position:0%
+very poor at that time too so if you
+bought a product and said made in Japan
+
+ align:start position:0%
+bought a product and said made in Japan
+ 
+
+ align:start position:0%
+bought a product and said made in Japan
+on it people would actually imagine that
+
+ align:start position:0%
+on it people would actually imagine that
+ 
+
+ align:start position:0%
+on it people would actually imagine that
+that meant it was of rather poor quality
+
+ align:start position:0%
+that meant it was of rather poor quality
+ 
+
+ align:start position:0%
+that meant it was of rather poor quality
+and of course our impression is totally
+
+ align:start position:0%
+and of course our impression is totally
+ 
+
+ align:start position:0%
+and of course our impression is totally
+the opposite now and it's interesting to
+
+ align:start position:0%
+the opposite now and it's interesting to
+ 
+
+ align:start position:0%
+the opposite now and it's interesting to
+consider how that happened it was a lot
+
+ align:start position:0%
+consider how that happened it was a lot
+ 
+
+ align:start position:0%
+consider how that happened it was a lot
+of different things but maybe one of the
+
+ align:start position:0%
+of different things but maybe one of the
+ 
+
+ align:start position:0%
+of different things but maybe one of the
+things that brought that change about
+
+ align:start position:0%
+things that brought that change about
+ 
+
+ align:start position:0%
+things that brought that change about
+and our perception of Japanese
+
+ align:start position:0%
+and our perception of Japanese
+ 
+
+ align:start position:0%
+and our perception of Japanese
+manufacturer was some of this
+
+ align:start position:0%
+manufacturer was some of this
+ 
+
+ align:start position:0%
+manufacturer was some of this
+methodology and Taguchi correctly
+
+ align:start position:0%
+methodology and Taguchi correctly
+ 
+
+ align:start position:0%
+methodology and Taguchi correctly
+pointed out that robustness could be
+
+ align:start position:0%
+pointed out that robustness could be
+ 
+
+ align:start position:0%
+pointed out that robustness could be
+attained and it could be attained
+
+ align:start position:0%
+attained and it could be attained
+ 
+
+ align:start position:0%
+attained and it could be attained
+through experimentation and he suggested
+
+ align:start position:0%
+through experimentation and he suggested
+ 
+
+ align:start position:0%
+through experimentation and he suggested
+that you might for example run an
+
+ align:start position:0%
+that you might for example run an
+ 
+
+ align:start position:0%
+that you might for example run an
+experiment like this in our fog array or
+
+ align:start position:0%
+experiment like this in our fog array or
+ 
+
+ align:start position:0%
+experiment like this in our fog array or
+factorial design and control factors
+
+ align:start position:0%
+factorial design and control factors
+ 
+
+ align:start position:0%
+factorial design and control factors
+crossed with noise factors and in this
+
+ align:start position:0%
+crossed with noise factors and in this
+ 
+
+ align:start position:0%
+crossed with noise factors and in this
+case you take your eight run array of
+
+ align:start position:0%
+case you take your eight run array of
+ 
+
+ align:start position:0%
+case you take your eight run array of
+control factors cross it with your four
+
+ align:start position:0%
+control factors cross it with your four
+ 
+
+ align:start position:0%
+control factors cross it with your four
+run array of noise factors and you would
+
+ align:start position:0%
+run array of noise factors and you would
+ 
+
+ align:start position:0%
+run array of noise factors and you would
+have a thirty-two run cross array and so
+
+ align:start position:0%
+have a thirty-two run cross array and so
+ 
+
+ align:start position:0%
+have a thirty-two run cross array and so
+you see with this cross symbol the
+
+ align:start position:0%
+you see with this cross symbol the
+ 
+
+ align:start position:0%
+you see with this cross symbol the
+implication is that the size of the
+
+ align:start position:0%
+implication is that the size of the
+ 
+
+ align:start position:0%
+implication is that the size of the
+experiment scales at least like the
+
+ align:start position:0%
+experiment scales at least like the
+ 
+
+ align:start position:0%
+experiment scales at least like the
+product of the number of control factors
+
+ align:start position:0%
+product of the number of control factors
+ 
+
+ align:start position:0%
+product of the number of control factors
+plus one and the number of noise factors
+
+ align:start position:0%
+plus one and the number of noise factors
+ 
+
+ align:start position:0%
+plus one and the number of noise factors
+plus one which you know when you begin
+
+ align:start position:0%
+plus one which you know when you begin
+ 
+
+ align:start position:0%
+plus one which you know when you begin
+to consider lots of control of noise
+
+ align:start position:0%
+to consider lots of control of noise
+ 
+
+ align:start position:0%
+to consider lots of control of noise
+factors it gets awfully burdensome so
+
+ align:start position:0%
+factors it gets awfully burdensome so
+ 
+
+ align:start position:0%
+factors it gets awfully burdensome so
+people are looking for ways to do it
+
+ align:start position:0%
+people are looking for ways to do it
+ 
+
+ align:start position:0%
+people are looking for ways to do it
+more fish
+
+ align:start position:0%
+more fish
+ 
+
+ align:start position:0%
+more fish
+we and that leads to the cover of this
+
+ align:start position:0%
+we and that leads to the cover of this
+ 
+
+ align:start position:0%
+we and that leads to the cover of this
+this textbook the idea of just doing
+
+ align:start position:0%
+this textbook the idea of just doing
+ 
+
+ align:start position:0%
+this textbook the idea of just doing
+half of them so that you're actually not
+
+ align:start position:0%
+half of them so that you're actually not
+ 
+
+ align:start position:0%
+half of them so that you're actually not
+running exactly the same noise
+
+ align:start position:0%
+running exactly the same noise
+ 
+
+ align:start position:0%
+running exactly the same noise
+conditions at every setting of the
+
+ align:start position:0%
+conditions at every setting of the
+ 
+
+ align:start position:0%
+conditions at every setting of the
+control factors and what we've done in
+
+ align:start position:0%
+control factors and what we've done in
+ 
+
+ align:start position:0%
+control factors and what we've done in
+our methodology validation work actually
+
+ align:start position:0%
+our methodology validation work actually
+ 
+
+ align:start position:0%
+our methodology validation work actually
+is the show in a recent publication and
+
+ align:start position:0%
+is the show in a recent publication and
+ 
+
+ align:start position:0%
+is the show in a recent publication and
+journal quality technology that this
+
+ align:start position:0%
+journal quality technology that this
+ 
+
+ align:start position:0%
+journal quality technology that this
+procedure although theoretically looks
+
+ align:start position:0%
+procedure although theoretically looks
+ 
+
+ align:start position:0%
+procedure although theoretically looks
+promising
+
+ align:start position:0%
+promising
+ 
+
+ align:start position:0%
+promising
+in many specific cases it's failing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and yet you know if I if I look at
+
+ align:start position:0%
+and yet you know if I if I look at
+ 
+
+ align:start position:0%
+and yet you know if I if I look at
+industry practice today
+
+ align:start position:0%
+industry practice today
+ 
+
+ align:start position:0%
+industry practice today
+I think the methods of Taguchi and also
+
+ align:start position:0%
+I think the methods of Taguchi and also
+ 
+
+ align:start position:0%
+I think the methods of Taguchi and also
+the refinements proposed more recently
+
+ align:start position:0%
+the refinements proposed more recently
+ 
+
+ align:start position:0%
+the refinements proposed more recently
+on the basis of statistical theory are
+
+ align:start position:0%
+on the basis of statistical theory are
+ 
+
+ align:start position:0%
+on the basis of statistical theory are
+finding their way into industry practice
+
+ align:start position:0%
+finding their way into industry practice
+ 
+
+ align:start position:0%
+finding their way into industry practice
+and are really quite solidly entrenched
+
+ align:start position:0%
+and are really quite solidly entrenched
+ 
+
+ align:start position:0%
+and are really quite solidly entrenched
+so some of you may have had some
+
+ align:start position:0%
+so some of you may have had some
+ 
+
+ align:start position:0%
+so some of you may have had some
+experience with these Six Sigma programs
+
+ align:start position:0%
+experience with these Six Sigma programs
+ 
+
+ align:start position:0%
+experience with these Six Sigma programs
+by now maybe some of you are in General
+
+ align:start position:0%
+by now maybe some of you are in General
+ 
+
+ align:start position:0%
+by now maybe some of you are in General
+Electric maybe some in Motorola and I
+
+ align:start position:0%
+Electric maybe some in Motorola and I
+ 
+
+ align:start position:0%
+Electric maybe some in Motorola and I
+guess many other companies by now have
+
+ align:start position:0%
+guess many other companies by now have
+ 
+
+ align:start position:0%
+guess many other companies by now have
+such programs and a big part of such
+
+ align:start position:0%
+such programs and a big part of such
+ 
+
+ align:start position:0%
+such programs and a big part of such
+programs is that entering engineers will
+
+ align:start position:0%
+programs is that entering engineers will
+ 
+
+ align:start position:0%
+programs is that entering engineers will
+take some coursework even if they didn't
+
+ align:start position:0%
+take some coursework even if they didn't
+ 
+
+ align:start position:0%
+take some coursework even if they didn't
+get it in their undergraduate degrees
+
+ align:start position:0%
+get it in their undergraduate degrees
+ 
+
+ align:start position:0%
+get it in their undergraduate degrees
+they the company feels people broadly
+
+ align:start position:0%
+they the company feels people broadly
+ 
+
+ align:start position:0%
+they the company feels people broadly
+need this and so they get some
+
+ align:start position:0%
+need this and so they get some
+ 
+
+ align:start position:0%
+need this and so they get some
+coursework and then they do projects
+
+ align:start position:0%
+coursework and then they do projects
+ 
+
+ align:start position:0%
+coursework and then they do projects
+right and they demonstrate that they can
+
+ align:start position:0%
+right and they demonstrate that they can
+ 
+
+ align:start position:0%
+right and they demonstrate that they can
+do some of this kind of work for the
+
+ align:start position:0%
+do some of this kind of work for the
+ 
+
+ align:start position:0%
+do some of this kind of work for the
+company and afford at least the last
+
+ align:start position:0%
+company and afford at least the last
+ 
+
+ align:start position:0%
+company and afford at least the last
+time I checked their their design
+
+ align:start position:0%
+time I checked their their design
+ 
+
+ align:start position:0%
+time I checked their their design
+process and code it just this sort of
+
+ align:start position:0%
+process and code it just this sort of
+ 
+
+ align:start position:0%
+process and code it just this sort of
+thing and they have their multi-step
+
+ align:start position:0%
+thing and they have their multi-step
+ 
+
+ align:start position:0%
+thing and they have their multi-step
+process for attaining reliability and
+
+ align:start position:0%
+process for attaining reliability and
+ 
+
+ align:start position:0%
+process for attaining reliability and
+robustness and in step four I dig in and
+
+ align:start position:0%
+robustness and in step four I dig in and
+ 
+
+ align:start position:0%
+robustness and in step four I dig in and
+look at the details and the engineers
+
+ align:start position:0%
+look at the details and the engineers
+ 
+
+ align:start position:0%
+look at the details and the engineers
+are asked to select appropriate
+
+ align:start position:0%
+are asked to select appropriate
+ 
+
+ align:start position:0%
+are asked to select appropriate
+orthogonal arrays so the idea is that
+
+ align:start position:0%
+orthogonal arrays so the idea is that
+ 
+
+ align:start position:0%
+orthogonal arrays so the idea is that
+maybe they have some choices about what
+
+ align:start position:0%
+maybe they have some choices about what
+ 
+
+ align:start position:0%
+maybe they have some choices about what
+size are orthogonal array number of
+
+ align:start position:0%
+size are orthogonal array number of
+ 
+
+ align:start position:0%
+size are orthogonal array number of
+levels the crossed array versus the
+
+ align:start position:0%
+levels the crossed array versus the
+ 
+
+ align:start position:0%
+levels the crossed array versus the
+combined array such as Wu talked about
+
+ align:start position:0%
+combined array such as Wu talked about
+ 
+
+ align:start position:0%
+combined array such as Wu talked about
+but departure from North Ogden will
+
+ align:start position:0%
+but departure from North Ogden will
+ 
+
+ align:start position:0%
+but departure from North Ogden will
+raise itself is not really being
+
+ align:start position:0%
+raise itself is not really being
+ 
+
+ align:start position:0%
+raise itself is not really being
+considered anymore in industry and so
+
+ align:start position:0%
+considered anymore in industry and so
+ 
+
+ align:start position:0%
+considered anymore in industry and so
+this has become very much entrenched and
+
+ align:start position:0%
+this has become very much entrenched and
+ 
+
+ align:start position:0%
+this has become very much entrenched and
+in fact in some of the text books you
+
+ align:start position:0%
+in fact in some of the text books you
+ 
+
+ align:start position:0%
+in fact in some of the text books you
+see an even more extreme statement of
+
+ align:start position:0%
+see an even more extreme statement of
+ 
+
+ align:start position:0%
+see an even more extreme statement of
+the point in in this text they argue
+
+ align:start position:0%
+the point in in this text they argue
+ 
+
+ align:start position:0%
+the point in in this text they argue
+that the the idea that Edward John
+
+ align:start position:0%
+that the the idea that Edward John
+ 
+
+ align:start position:0%
+that the the idea that Edward John
+Russell expressed on that earlier slide
+
+ align:start position:0%
+Russell expressed on that earlier slide
+ 
+
+ align:start position:0%
+Russell expressed on that earlier slide
+that simplicity should be valued and
+
+ align:start position:0%
+that simplicity should be valued and
+ 
+
+ align:start position:0%
+that simplicity should be valued and
+that single factor experiments are often
+
+ align:start position:0%
+that single factor experiments are often
+ 
+
+ align:start position:0%
+that single factor experiments are often
+advisable that has seen its final demise
+
+ align:start position:0%
+advisable that has seen its final demise
+ 
+
+ align:start position:0%
+advisable that has seen its final demise
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+the opinion voiced in this particular
+
+ align:start position:0%
+the opinion voiced in this particular
+ 
+
+ align:start position:0%
+the opinion voiced in this particular
+textbook but we wanted to question this
+
+ align:start position:0%
+textbook but we wanted to question this
+ 
+
+ align:start position:0%
+textbook but we wanted to question this
+a little bit we wondered if sometimes
+
+ align:start position:0%
+a little bit we wondered if sometimes
+ 
+
+ align:start position:0%
+a little bit we wondered if sometimes
+there isn't a role for this the simpler
+
+ align:start position:0%
+there isn't a role for this the simpler
+ 
+
+ align:start position:0%
+there isn't a role for this the simpler
+experiment still and this decision to
+
+ align:start position:0%
+experiment still and this decision to
+ 
+
+ align:start position:0%
+experiment still and this decision to
+spend some time looking into this came
+
+ align:start position:0%
+spend some time looking into this came
+ 
+
+ align:start position:0%
+spend some time looking into this came
+out of some observations in industry and
+
+ align:start position:0%
+out of some observations in industry and
+ 
+
+ align:start position:0%
+out of some observations in industry and
+I thought it would in some ways now it
+
+ align:start position:0%
+I thought it would in some ways now it
+ 
+
+ align:start position:0%
+I thought it would in some ways now it
+it seems ironic to me that our initial
+
+ align:start position:0%
+it seems ironic to me that our initial
+ 
+
+ align:start position:0%
+it seems ironic to me that our initial
+thoughts along these lines came out of
+
+ align:start position:0%
+thoughts along these lines came out of
+ 
+
+ align:start position:0%
+thoughts along these lines came out of
+the farm again you know so that all
+
+ align:start position:0%
+the farm again you know so that all
+ 
+
+ align:start position:0%
+the farm again you know so that all
+these ideas of our thuggin arrays and so
+
+ align:start position:0%
+these ideas of our thuggin arrays and so
+ 
+
+ align:start position:0%
+these ideas of our thuggin arrays and so
+on came from agriculture in the first
+
+ align:start position:0%
+on came from agriculture in the first
+ 
+
+ align:start position:0%
+on came from agriculture in the first
+place and now our wanting to question
+
+ align:start position:0%
+place and now our wanting to question
+ 
+
+ align:start position:0%
+place and now our wanting to question
+them came off of the farm because we
+
+ align:start position:0%
+them came off of the farm because we
+ 
+
+ align:start position:0%
+them came off of the farm because we
+were working with a manufacturer of
+
+ align:start position:0%
+were working with a manufacturer of
+ 
+
+ align:start position:0%
+were working with a manufacturer of
+agricultural equipment and it seemed to
+
+ align:start position:0%
+agricultural equipment and it seemed to
+ 
+
+ align:start position:0%
+agricultural equipment and it seemed to
+me actually that farm equipment is one
+
+ align:start position:0%
+me actually that farm equipment is one
+ 
+
+ align:start position:0%
+me actually that farm equipment is one
+of the most significant robustness
+
+ align:start position:0%
+of the most significant robustness
+ 
+
+ align:start position:0%
+of the most significant robustness
+challenges in the world because what you
+
+ align:start position:0%
+challenges in the world because what you
+ 
+
+ align:start position:0%
+challenges in the world because what you
+have in a tractor or a windrow or a
+
+ align:start position:0%
+have in a tractor or a windrow or a
+ 
+
+ align:start position:0%
+have in a tractor or a windrow or a
+combine is really a factory I mean it
+
+ align:start position:0%
+combine is really a factory I mean it
+ 
+
+ align:start position:0%
+combine is really a factory I mean it
+needs to process something right
+
+ align:start position:0%
+needs to process something right
+ 
+
+ align:start position:0%
+needs to process something right
+sometimes they're not a very simple way
+
+ align:start position:0%
+sometimes they're not a very simple way
+ 
+
+ align:start position:0%
+sometimes they're not a very simple way
+you know sometimes it needs to take a
+
+ align:start position:0%
+you know sometimes it needs to take a
+ 
+
+ align:start position:0%
+you know sometimes it needs to take a
+piece of cotton off a plant and then
+
+ align:start position:0%
+piece of cotton off a plant and then
+ 
+
+ align:start position:0%
+piece of cotton off a plant and then
+strip away some part of it I mean it's
+
+ align:start position:0%
+strip away some part of it I mean it's
+ 
+
+ align:start position:0%
+strip away some part of it I mean it's
+not a simple thing and yet here it is
+
+ align:start position:0%
+not a simple thing and yet here it is
+ 
+
+ align:start position:0%
+not a simple thing and yet here it is
+and it's out in the weather it's out in
+
+ align:start position:0%
+and it's out in the weather it's out in
+ 
+
+ align:start position:0%
+and it's out in the weather it's out in
+a field whatever conditions prevail it
+
+ align:start position:0%
+a field whatever conditions prevail it
+ 
+
+ align:start position:0%
+a field whatever conditions prevail it
+has to deal with so it's a very
+
+ align:start position:0%
+has to deal with so it's a very
+ 
+
+ align:start position:0%
+has to deal with so it's a very
+difficult reliability challenge and this
+
+ align:start position:0%
+difficult reliability challenge and this
+ 
+
+ align:start position:0%
+difficult reliability challenge and this
+particular company had relatively
+
+ align:start position:0%
+particular company had relatively
+ 
+
+ align:start position:0%
+particular company had relatively
+recently brought in a lot of robust
+
+ align:start position:0%
+recently brought in a lot of robust
+ 
+
+ align:start position:0%
+recently brought in a lot of robust
+design methodology and they were looking
+
+ align:start position:0%
+design methodology and they were looking
+ 
+
+ align:start position:0%
+design methodology and they were looking
+forward to the benefits that would
+
+ align:start position:0%
+forward to the benefits that would
+ 
+
+ align:start position:0%
+forward to the benefits that would
+accrue and they got exactly the opposite
+
+ align:start position:0%
+accrue and they got exactly the opposite
+ 
+
+ align:start position:0%
+accrue and they got exactly the opposite
+that this most recent launch of a new
+
+ align:start position:0%
+that this most recent launch of a new
+ 
+
+ align:start position:0%
+that this most recent launch of a new
+tractor was one of the worst they'd ever
+
+ align:start position:0%
+tractor was one of the worst they'd ever
+ 
+
+ align:start position:0%
+tractor was one of the worst they'd ever
+had and was causing them real problems
+
+ align:start position:0%
+had and was causing them real problems
+ 
+
+ align:start position:0%
+had and was causing them real problems
+you know their customers were quite
+
+ align:start position:0%
+you know their customers were quite
+ 
+
+ align:start position:0%
+you know their customers were quite
+angry with them and so we wanted to look
+
+ align:start position:0%
+angry with them and so we wanted to look
+ 
+
+ align:start position:0%
+angry with them and so we wanted to look
+into that and we decided to in effect do
+
+ align:start position:0%
+into that and we decided to in effect do
+ 
+
+ align:start position:0%
+into that and we decided to in effect do
+an audit you know look at their design
+
+ align:start position:0%
+an audit you know look at their design
+ 
+
+ align:start position:0%
+an audit you know look at their design
+process for this tractor what had
+
+ align:start position:0%
+process for this tractor what had
+ 
+
+ align:start position:0%
+process for this tractor what had
+happened where there's some mistakes and
+
+ align:start position:0%
+happened where there's some mistakes and
+ 
+
+ align:start position:0%
+happened where there's some mistakes and
+choices of design or priority or
+
+ align:start position:0%
+choices of design or priority or
+ 
+
+ align:start position:0%
+choices of design or priority or
+management whatever so one of the things
+
+ align:start position:0%
+management whatever so one of the things
+ 
+
+ align:start position:0%
+management whatever so one of the things
+that we asked for is an accounting of
+
+ align:start position:0%
+that we asked for is an accounting of
+ 
+
+ align:start position:0%
+that we asked for is an accounting of
+all the different robust design
+
+ align:start position:0%
+all the different robust design
+ 
+
+ align:start position:0%
+all the different robust design
+experiments they had done and they gave
+
+ align:start position:0%
+experiments they had done and they gave
+ 
+
+ align:start position:0%
+experiments they had done and they gave
+us a list of experiments they planned it
+
+ align:start position:0%
+us a list of experiments they planned it
+ 
+
+ align:start position:0%
+us a list of experiments they planned it
+was a long list
+
+ align:start position:0%
+was a long list
+ 
+
+ align:start position:0%
+was a long list
+and then we said well yeah but we need
+
+ align:start position:0%
+and then we said well yeah but we need
+ 
+
+ align:start position:0%
+and then we said well yeah but we need
+more detail than this show us you know
+
+ align:start position:0%
+more detail than this show us you know
+ 
+
+ align:start position:0%
+more detail than this show us you know
+the written reports from all these
+
+ align:start position:0%
+the written reports from all these
+ 
+
+ align:start position:0%
+the written reports from all these
+experiments you know show us the data
+
+ align:start position:0%
+experiments you know show us the data
+ 
+
+ align:start position:0%
+experiments you know show us the data
+show a vision basis of the data and they
+
+ align:start position:0%
+show a vision basis of the data and they
+ 
+
+ align:start position:0%
+show a vision basis of the data and they
+gave us a much smaller list of reports
+
+ align:start position:0%
+gave us a much smaller list of reports
+ 
+
+ align:start position:0%
+gave us a much smaller list of reports
+and we said okay you had 30 and now we
+
+ align:start position:0%
+and we said okay you had 30 and now we
+ 
+
+ align:start position:0%
+and we said okay you had 30 and now we
+have five what about the other 25 and
+
+ align:start position:0%
+have five what about the other 25 and
+ 
+
+ align:start position:0%
+have five what about the other 25 and
+they said well those were never finished
+
+ align:start position:0%
+they said well those were never finished
+ 
+
+ align:start position:0%
+they said well those were never finished
+and that was interesting to us you know
+
+ align:start position:0%
+and that was interesting to us you know
+ 
+
+ align:start position:0%
+and that was interesting to us you know
+why is it that the majority weren't
+
+ align:start position:0%
+why is it that the majority weren't
+ 
+
+ align:start position:0%
+why is it that the majority weren't
+finished and we began to ask questions
+
+ align:start position:0%
+finished and we began to ask questions
+ 
+
+ align:start position:0%
+finished and we began to ask questions
+of the individuals involved and they
+
+ align:start position:0%
+of the individuals involved and they
+ 
+
+ align:start position:0%
+of the individuals involved and they
+always had pretty good reasons you know
+
+ align:start position:0%
+always had pretty good reasons you know
+ 
+
+ align:start position:0%
+always had pretty good reasons you know
+in some cases they would say that a
+
+ align:start position:0%
+in some cases they would say that a
+ 
+
+ align:start position:0%
+in some cases they would say that a
+piece of test equipment had broken down
+
+ align:start position:0%
+piece of test equipment had broken down
+ 
+
+ align:start position:0%
+piece of test equipment had broken down
+at some point along the way and was
+
+ align:start position:0%
+at some point along the way and was
+ 
+
+ align:start position:0%
+at some point along the way and was
+going to take a certain amount of time
+
+ align:start position:0%
+going to take a certain amount of time
+ 
+
+ align:start position:0%
+going to take a certain amount of time
+to repair so we had to move forward with
+
+ align:start position:0%
+to repair so we had to move forward with
+ 
+
+ align:start position:0%
+to repair so we had to move forward with
+the partial data set in fact a large
+
+ align:start position:0%
+the partial data set in fact a large
+ 
+
+ align:start position:0%
+the partial data set in fact a large
+fraction of the experiments aren't
+
+ align:start position:0%
+fraction of the experiments aren't
+ 
+
+ align:start position:0%
+fraction of the experiments aren't
+finished and this prompted us to wonder
+
+ align:start position:0%
+finished and this prompted us to wonder
+ 
+
+ align:start position:0%
+finished and this prompted us to wonder
+what would you do if you knew this from
+
+ align:start position:0%
+what would you do if you knew this from
+ 
+
+ align:start position:0%
+what would you do if you knew this from
+the outset let's say that you put a 60%
+
+ align:start position:0%
+the outset let's say that you put a 60%
+ 
+
+ align:start position:0%
+the outset let's say that you put a 60%
+probability on canceling any individual
+
+ align:start position:0%
+probability on canceling any individual
+ 
+
+ align:start position:0%
+probability on canceling any individual
+experiment you might run somewhere at a
+
+ align:start position:0%
+experiment you might run somewhere at a
+ 
+
+ align:start position:0%
+experiment you might run somewhere at a
+state of partial completion let's say
+
+ align:start position:0%
+state of partial completion let's say
+ 
+
+ align:start position:0%
+state of partial completion let's say
+that that were the case but you didn't
+
+ align:start position:0%
+that that were the case but you didn't
+ 
+
+ align:start position:0%
+that that were the case but you didn't
+know which 60 percent we're gonna be
+
+ align:start position:0%
+know which 60 percent we're gonna be
+ 
+
+ align:start position:0%
+know which 60 percent we're gonna be
+canceled because you probably don't know
+
+ align:start position:0%
+canceled because you probably don't know
+ 
+
+ align:start position:0%
+canceled because you probably don't know
+that what would you do well we thought
+
+ align:start position:0%
+that what would you do well we thought
+ 
+
+ align:start position:0%
+that what would you do well we thought
+perhaps you would do a one at a time
+
+ align:start position:0%
+perhaps you would do a one at a time
+ 
+
+ align:start position:0%
+perhaps you would do a one at a time
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+
+ align:start position:0%
+experiment because then at least no
+ 
+
+ align:start position:0%
+experiment because then at least no
+matter what you did you would have
+
+ align:start position:0%
+matter what you did you would have
+ 
+
+ align:start position:0%
+matter what you did you would have
+stopped and the data would be relatively
+
+ align:start position:0%
+stopped and the data would be relatively
+ 
+
+ align:start position:0%
+stopped and the data would be relatively
+simple to analyze you know such as what
+
+ align:start position:0%
+simple to analyze you know such as what
+ 
+
+ align:start position:0%
+simple to analyze you know such as what
+Russell talked about and we found that
+
+ align:start position:0%
+Russell talked about and we found that
+ 
+
+ align:start position:0%
+Russell talked about and we found that
+actually some of the most prominent
+
+ align:start position:0%
+actually some of the most prominent
+ 
+
+ align:start position:0%
+actually some of the most prominent
+statisticians of the past always felt
+
+ align:start position:0%
+statisticians of the past always felt
+ 
+
+ align:start position:0%
+statisticians of the past always felt
+that there was a a role for one factor
+
+ align:start position:0%
+that there was a a role for one factor
+ 
+
+ align:start position:0%
+that there was a a role for one factor
+at a time experiments so for example you
+
+ align:start position:0%
+at a time experiments so for example you
+ 
+
+ align:start position:0%
+at a time experiments so for example you
+may have heard of Milton Friedman in a
+
+ align:start position:0%
+may have heard of Milton Friedman in a
+ 
+
+ align:start position:0%
+may have heard of Milton Friedman in a
+different context what do you know him
+
+ align:start position:0%
+different context what do you know him
+ 
+
+ align:start position:0%
+different context what do you know him
+for yes
+
+ align:start position:0%
+for yes
+ 
+
+ align:start position:0%
+for yes
+yeah Nobel Prize in Economics for market
+
+ align:start position:0%
+yeah Nobel Prize in Economics for market
+ 
+
+ align:start position:0%
+yeah Nobel Prize in Economics for market
+view of economics and Leonard Savage who
+
+ align:start position:0%
+view of economics and Leonard Savage who
+ 
+
+ align:start position:0%
+view of economics and Leonard Savage who
+had written a excellent text on
+
+ align:start position:0%
+had written a excellent text on
+ 
+
+ align:start position:0%
+had written a excellent text on
+foundations of statistics they found
+
+ align:start position:0%
+foundations of statistics they found
+ 
+
+ align:start position:0%
+foundations of statistics they found
+that an efficient design for the present
+
+ align:start position:0%
+that an efficient design for the present
+ 
+
+ align:start position:0%
+that an efficient design for the present
+purposes so that was for maximization
+
+ align:start position:0%
+purposes so that was for maximization
+ 
+
+ align:start position:0%
+purposes so that was for maximization
+ought to adjust the experimental program
+
+ align:start position:0%
+ought to adjust the experimental program
+ 
+
+ align:start position:0%
+ought to adjust the experimental program
+on each stage in light of the prior
+
+ align:start position:0%
+on each stage in light of the prior
+ 
+
+ align:start position:0%
+on each stage in light of the prior
+stages and actually what they described
+
+ align:start position:0%
+stages and actually what they described
+ 
+
+ align:start position:0%
+stages and actually what they described
+was a one factor at a time experiment
+
+ align:start position:0%
+was a one factor at a time experiment
+ 
+
+ align:start position:0%
+was a one factor at a time experiment
+and then Cuthbert Daniel talked about a
+
+ align:start position:0%
+and then Cuthbert Daniel talked about a
+ 
+
+ align:start position:0%
+and then Cuthbert Daniel talked about a
+more sort of a social or psychological
+
+ align:start position:0%
+more sort of a social or psychological
+ 
+
+ align:start position:0%
+more sort of a social or psychological
+value of of simpler experiments you know
+
+ align:start position:0%
+value of of simpler experiments you know
+ 
+
+ align:start position:0%
+value of of simpler experiments you know
+just reimposing the points that Edward
+
+ align:start position:0%
+just reimposing the points that Edward
+ 
+
+ align:start position:0%
+just reimposing the points that Edward
+John Russell had made that somehow you
+
+ align:start position:0%
+John Russell had made that somehow you
+ 
+
+ align:start position:0%
+John Russell had made that somehow you
+feel that you can react to data more
+
+ align:start position:0%
+feel that you can react to data more
+ 
+
+ align:start position:0%
+feel that you can react to data more
+rapidly or learn something from each
+
+ align:start position:0%
+rapidly or learn something from each
+ 
+
+ align:start position:0%
+rapidly or learn something from each
+rung and he talked about some criteria
+
+ align:start position:0%
+rung and he talked about some criteria
+ 
+
+ align:start position:0%
+rung and he talked about some criteria
+by which you might make that choice that
+
+ align:start position:0%
+by which you might make that choice that
+ 
+
+ align:start position:0%
+by which you might make that choice that
+for example he had a demarcation maybe
+
+ align:start position:0%
+for example he had a demarcation maybe
+ 
+
+ align:start position:0%
+for example he had a demarcation maybe
+it's okay to do it as long as the
+
+ align:start position:0%
+it's okay to do it as long as the
+ 
+
+ align:start position:0%
+it's okay to do it as long as the
+effects are at least three or four times
+
+ align:start position:0%
+effects are at least three or four times
+ 
+
+ align:start position:0%
+effects are at least three or four times
+the average random error per trial so he
+
+ align:start position:0%
+the average random error per trial so he
+ 
+
+ align:start position:0%
+the average random error per trial so he
+had based on his experience come up with
+
+ align:start position:0%
+had based on his experience come up with
+ 
+
+ align:start position:0%
+had based on his experience come up with
+a demarcation effects three or four
+
+ align:start position:0%
+a demarcation effects three or four
+ 
+
+ align:start position:0%
+a demarcation effects three or four
+times random error and we wanted to
+
+ align:start position:0%
+times random error and we wanted to
+ 
+
+ align:start position:0%
+times random error and we wanted to
+understand whether that demarcation was
+
+ align:start position:0%
+understand whether that demarcation was
+ 
+
+ align:start position:0%
+understand whether that demarcation was
+about right so we began to study a sort
+
+ align:start position:0%
+about right so we began to study a sort
+ 
+
+ align:start position:0%
+about right so we began to study a sort
+of an adaptive variant of one factor at
+
+ align:start position:0%
+of an adaptive variant of one factor at
+ 
+
+ align:start position:0%
+of an adaptive variant of one factor at
+a time experiment ation and in the
+
+ align:start position:0%
+a time experiment ation and in the
+ 
+
+ align:start position:0%
+a time experiment ation and in the
+beginning we were we were interested
+
+ align:start position:0%
+beginning we were we were interested
+ 
+
+ align:start position:0%
+beginning we were we were interested
+primarily in knowing if you were to do
+
+ align:start position:0%
+primarily in knowing if you were to do
+ 
+
+ align:start position:0%
+primarily in knowing if you were to do
+this adaptive kind of experimentation
+
+ align:start position:0%
+this adaptive kind of experimentation
+ 
+
+ align:start position:0%
+this adaptive kind of experimentation
+how how what level of probability of
+
+ align:start position:0%
+how how what level of probability of
+ 
+
+ align:start position:0%
+how how what level of probability of
+canceling the experiments would make
+
+ align:start position:0%
+canceling the experiments would make
+ 
+
+ align:start position:0%
+canceling the experiments would make
+these expert this style look good and
+
+ align:start position:0%
+these expert this style look good and
+ 
+
+ align:start position:0%
+these expert this style look good and
+the funny thing about it is we started
+
+ align:start position:0%
+the funny thing about it is we started
+ 
+
+ align:start position:0%
+the funny thing about it is we started
+with some you know maybe 50% probability
+
+ align:start position:0%
+with some you know maybe 50% probability
+ 
+
+ align:start position:0%
+with some you know maybe 50% probability
+of canceling and we looked at the to
+
+ align:start position:0%
+of canceling and we looked at the to
+ 
+
+ align:start position:0%
+of canceling and we looked at the to
+experimentation styles adaptive and
+
+ align:start position:0%
+experimentation styles adaptive and
+ 
+
+ align:start position:0%
+experimentation styles adaptive and
+factorial and on the cases we were
+
+ align:start position:0%
+factorial and on the cases we were
+ 
+
+ align:start position:0%
+factorial and on the cases we were
+looking at adaptive looked better and so
+
+ align:start position:0%
+looking at adaptive looked better and so
+ 
+
+ align:start position:0%
+looking at adaptive looked better and so
+we dialed down the probability of
+
+ align:start position:0%
+we dialed down the probability of
+ 
+
+ align:start position:0%
+we dialed down the probability of
+canceling 10% and they still looked
+
+ align:start position:0%
+canceling 10% and they still looked
+ 
+
+ align:start position:0%
+canceling 10% and they still looked
+better and we dialed down to 0% and the
+
+ align:start position:0%
+better and we dialed down to 0% and the
+ 
+
+ align:start position:0%
+better and we dialed down to 0% and the
+adaptive experiments still looked better
+
+ align:start position:0%
+adaptive experiments still looked better
+ 
+
+ align:start position:0%
+adaptive experiments still looked better
+and we thought well now we know we've
+
+ align:start position:0%
+and we thought well now we know we've
+ 
+
+ align:start position:0%
+and we thought well now we know we've
+made a mistake because we saw it in the
+
+ align:start position:0%
+made a mistake because we saw it in the
+ 
+
+ align:start position:0%
+made a mistake because we saw it in the
+textbooks that this has this kind of
+
+ align:start position:0%
+textbooks that this has this kind of
+ 
+
+ align:start position:0%
+textbooks that this has this kind of
+experimentation has seen its final
+
+ align:start position:0%
+experimentation has seen its final
+ 
+
+ align:start position:0%
+experimentation has seen its final
+demise so either we made a mistake in
+
+ align:start position:0%
+demise so either we made a mistake in
+ 
+
+ align:start position:0%
+demise so either we made a mistake in
+the way we set up the study or we chose
+
+ align:start position:0%
+the way we set up the study or we chose
+ 
+
+ align:start position:0%
+the way we set up the study or we chose
+a strange case to start with we were
+
+ align:start position:0%
+a strange case to start with we were
+ 
+
+ align:start position:0%
+a strange case to start with we were
+perplexed so we did eventually a big
+
+ align:start position:0%
+perplexed so we did eventually a big
+ 
+
+ align:start position:0%
+perplexed so we did eventually a big
+empirical evaluation and we took 66
+
+ align:start position:0%
+empirical evaluation and we took 66
+ 
+
+ align:start position:0%
+empirical evaluation and we took 66
+different systems of a broad range of
+
+ align:start position:0%
+different systems of a broad range of
+ 
+
+ align:start position:0%
+different systems of a broad range of
+kinds you know chemical systems
+
+ align:start position:0%
+kinds you know chemical systems
+ 
+
+ align:start position:0%
+kinds you know chemical systems
+mechanicals
+
+ align:start position:0%
+mechanicals
+ 
+
+ align:start position:0%
+mechanicals
+electrical systems and we made our
+
+ align:start position:0%
+electrical systems and we made our
+ 
+
+ align:start position:0%
+electrical systems and we made our
+comparison in this case without
+
+ align:start position:0%
+comparison in this case without
+ 
+
+ align:start position:0%
+comparison in this case without
+canceling its now we were interested in
+
+ align:start position:0%
+canceling its now we were interested in
+ 
+
+ align:start position:0%
+canceling its now we were interested in
+that issue imagine that you're going to
+
+ align:start position:0%
+that issue imagine that you're going to
+ 
+
+ align:start position:0%
+that issue imagine that you're going to
+do it this adaptive one factor of time
+
+ align:start position:0%
+do it this adaptive one factor of time
+ 
+
+ align:start position:0%
+do it this adaptive one factor of time
+experimentation you're going to compare
+
+ align:start position:0%
+experimentation you're going to compare
+ 
+
+ align:start position:0%
+experimentation you're going to compare
+that with a fractional factorial
+
+ align:start position:0%
+that with a fractional factorial
+ 
+
+ align:start position:0%
+that with a fractional factorial
+experiment and see which one does better
+
+ align:start position:0%
+experiment and see which one does better
+ 
+
+ align:start position:0%
+experiment and see which one does better
+on average and this is what we found is
+
+ align:start position:0%
+on average and this is what we found is
+ 
+
+ align:start position:0%
+on average and this is what we found is
+that as long as experimental error was
+
+ align:start position:0%
+that as long as experimental error was
+ 
+
+ align:start position:0%
+that as long as experimental error was
+about 25 percent of combined factor
+
+ align:start position:0%
+about 25 percent of combined factor
+ 
+
+ align:start position:0%
+about 25 percent of combined factor
+effects or if interactions were large
+
+ align:start position:0%
+effects or if interactions were large
+ 
+
+ align:start position:0%
+effects or if interactions were large
+enough then you'd prefer the the
+
+ align:start position:0%
+enough then you'd prefer the the
+ 
+
+ align:start position:0%
+enough then you'd prefer the the
+adaptive experiments and so here is that
+
+ align:start position:0%
+adaptive experiments and so here is that
+ 
+
+ align:start position:0%
+adaptive experiments and so here is that
+same result shown in a tabular form so
+
+ align:start position:0%
+same result shown in a tabular form so
+ 
+
+ align:start position:0%
+same result shown in a tabular form so
+we have on the column headings the
+
+ align:start position:0%
+we have on the column headings the
+ 
+
+ align:start position:0%
+we have on the column headings the
+degree of experimental error expressed
+
+ align:start position:0%
+degree of experimental error expressed
+ 
+
+ align:start position:0%
+degree of experimental error expressed
+as a fraction of the factor effects and
+
+ align:start position:0%
+as a fraction of the factor effects and
+ 
+
+ align:start position:0%
+as a fraction of the factor effects and
+we have on the row headings the strength
+
+ align:start position:0%
+we have on the row headings the strength
+ 
+
+ align:start position:0%
+we have on the row headings the strength
+of interactions mild moderate strong
+
+ align:start position:0%
+of interactions mild moderate strong
+ 
+
+ align:start position:0%
+of interactions mild moderate strong
+dominant so strong by then strong
+
+ align:start position:0%
+dominant so strong by then strong
+ 
+
+ align:start position:0%
+dominant so strong by then strong
+interactions would indicate that the
+
+ align:start position:0%
+interactions would indicate that the
+ 
+
+ align:start position:0%
+interactions would indicate that the
+interactions are accounting for more
+
+ align:start position:0%
+interactions are accounting for more
+ 
+
+ align:start position:0%
+interactions are accounting for more
+than a quarter of you know effects in
+
+ align:start position:0%
+than a quarter of you know effects in
+ 
+
+ align:start position:0%
+than a quarter of you know effects in
+the system quite a big fraction and
+
+ align:start position:0%
+the system quite a big fraction and
+ 
+
+ align:start position:0%
+the system quite a big fraction and
+moderate is maybe you know 10 to 25
+
+ align:start position:0%
+moderate is maybe you know 10 to 25
+ 
+
+ align:start position:0%
+moderate is maybe you know 10 to 25
+percent and the gray boxes indicate that
+
+ align:start position:0%
+percent and the gray boxes indicate that
+ 
+
+ align:start position:0%
+percent and the gray boxes indicate that
+the adaptive one factor time experiments
+
+ align:start position:0%
+the adaptive one factor time experiments
+ 
+
+ align:start position:0%
+the adaptive one factor time experiments
+were giving at least as good or better
+
+ align:start position:0%
+were giving at least as good or better
+ 
+
+ align:start position:0%
+were giving at least as good or better
+results than the fractional factorial
+
+ align:start position:0%
+results than the fractional factorial
+ 
+
+ align:start position:0%
+results than the fractional factorial
+and so you might prefer them especially
+
+ align:start position:0%
+and so you might prefer them especially
+ 
+
+ align:start position:0%
+and so you might prefer them especially
+given their flexibility and so we were
+
+ align:start position:0%
+given their flexibility and so we were
+ 
+
+ align:start position:0%
+given their flexibility and so we were
+surprised that how much of that
+
+ align:start position:0%
+surprised that how much of that
+ 
+
+ align:start position:0%
+surprised that how much of that
+territory turns out to be gray and that
+
+ align:start position:0%
+territory turns out to be gray and that
+ 
+
+ align:start position:0%
+territory turns out to be gray and that
+was the main result we wanted to get
+
+ align:start position:0%
+was the main result we wanted to get
+ 
+
+ align:start position:0%
+was the main result we wanted to get
+across in this paper and we thought you
+
+ align:start position:0%
+across in this paper and we thought you
+ 
+
+ align:start position:0%
+across in this paper and we thought you
+know a strength of the experimental
+
+ align:start position:0%
+know a strength of the experimental
+ 
+
+ align:start position:0%
+know a strength of the experimental
+error as large as point four looks like
+
+ align:start position:0%
+error as large as point four looks like
+ 
+
+ align:start position:0%
+error as large as point four looks like
+a lot of experimental to error to us the
+
+ align:start position:0%
+a lot of experimental to error to us the
+ 
+
+ align:start position:0%
+a lot of experimental to error to us the
+engineers when you see a dependence such
+
+ align:start position:0%
+engineers when you see a dependence such
+ 
+
+ align:start position:0%
+engineers when you see a dependence such
+as this blue line here on the figure and
+
+ align:start position:0%
+as this blue line here on the figure and
+ 
+
+ align:start position:0%
+as this blue line here on the figure and
+and the scatter being indicated by the
+
+ align:start position:0%
+and the scatter being indicated by the
+ 
+
+ align:start position:0%
+and the scatter being indicated by the
+red that's about typical of the strength
+
+ align:start position:0%
+red that's about typical of the strength
+ 
+
+ align:start position:0%
+red that's about typical of the strength
+of experimental error at point four that
+
+ align:start position:0%
+of experimental error at point four that
+ 
+
+ align:start position:0%
+of experimental error at point four that
+we expressed and to us that looks like a
+
+ align:start position:0%
+we expressed and to us that looks like a
+ 
+
+ align:start position:0%
+we expressed and to us that looks like a
+pretty noisy experiment and so we
+
+ align:start position:0%
+pretty noisy experiment and so we
+ 
+
+ align:start position:0%
+pretty noisy experiment and so we
+thought it was interesting how much of
+
+ align:start position:0%
+thought it was interesting how much of
+ 
+
+ align:start position:0%
+thought it was interesting how much of
+the time you might recommend these
+
+ align:start position:0%
+the time you might recommend these
+ 
+
+ align:start position:0%
+the time you might recommend these
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+so we want to understand how this could
+
+ align:start position:0%
+so we want to understand how this could
+ 
+
+ align:start position:0%
+so we want to understand how this could
+be since it seemed so counterintuitive
+
+ align:start position:0%
+be since it seemed so counterintuitive
+ 
+
+ align:start position:0%
+be since it seemed so counterintuitive
+to us and so we delved into it a little
+
+ align:start position:0%
+to us and so we delved into it a little
+ 
+
+ align:start position:0%
+to us and so we delved into it a little
+more in terms of the mathematics and we
+
+ align:start position:0%
+more in terms of the mathematics and we
+ 
+
+ align:start position:0%
+more in terms of the mathematics and we
+tried to develop a theory that would
+
+ align:start position:0%
+tried to develop a theory that would
+ 
+
+ align:start position:0%
+tried to develop a theory that would
+account for this so we started to write
+
+ align:start position:0%
+account for this so we started to write
+ 
+
+ align:start position:0%
+account for this so we started to write
+a model of the procedure of adaptive one
+
+ align:start position:0%
+a model of the procedure of adaptive one
+ 
+
+ align:start position:0%
+a model of the procedure of adaptive one
+factor time experimentation and so
+
+ align:start position:0%
+factor time experimentation and so
+ 
+
+ align:start position:0%
+factor time experimentation and so
+there's just a little notation here you
+
+ align:start position:0%
+there's just a little notation here you
+ 
+
+ align:start position:0%
+there's just a little notation here you
+imagine that you you make an initial
+
+ align:start position:0%
+imagine that you you make an initial
+ 
+
+ align:start position:0%
+imagine that you you make an initial
+observation some of the symbols are
+
+ align:start position:0%
+observation some of the symbols are
+ 
+
+ align:start position:0%
+observation some of the symbols are
+coming up a little wrong this is a x
+
+ align:start position:0%
+coming up a little wrong this is a x
+ 
+
+ align:start position:0%
+coming up a little wrong this is a x
+with a tilde over it is an initial
+
+ align:start position:0%
+with a tilde over it is an initial
+ 
+
+ align:start position:0%
+with a tilde over it is an initial
+starting point level four for factor one
+
+ align:start position:0%
+starting point level four for factor one
+ 
+
+ align:start position:0%
+starting point level four for factor one
+and X two is the tilde is the same and
+
+ align:start position:0%
+and X two is the tilde is the same and
+ 
+
+ align:start position:0%
+and X two is the tilde is the same and
+that case should be an ellipsis three
+
+ align:start position:0%
+that case should be an ellipsis three
+ 
+
+ align:start position:0%
+that case should be an ellipsis three
+dots and then you you change one of the
+
+ align:start position:0%
+dots and then you you change one of the
+ 
+
+ align:start position:0%
+dots and then you you change one of the
+factors you toggle it change it to the
+
+ align:start position:0%
+factors you toggle it change it to the
+ 
+
+ align:start position:0%
+factors you toggle it change it to the
+opposite of the starting value and
+
+ align:start position:0%
+opposite of the starting value and
+ 
+
+ align:start position:0%
+opposite of the starting value and
+that's your first observation and then
+
+ align:start position:0%
+that's your first observation and then
+ 
+
+ align:start position:0%
+that's your first observation and then
+you make a decision about the level of
+
+ align:start position:0%
+you make a decision about the level of
+ 
+
+ align:start position:0%
+you make a decision about the level of
+the first factor based on the sign of
+
+ align:start position:0%
+the first factor based on the sign of
+ 
+
+ align:start position:0%
+the first factor based on the sign of
+the differences in the observations so
+
+ align:start position:0%
+the differences in the observations so
+ 
+
+ align:start position:0%
+the differences in the observations so
+if the improvement seems to obtain we
+
+ align:start position:0%
+if the improvement seems to obtain we
+ 
+
+ align:start position:0%
+if the improvement seems to obtain we
+change we adopt the change and then we
+
+ align:start position:0%
+change we adopt the change and then we
+ 
+
+ align:start position:0%
+change we adopt the change and then we
+go through that for every one of the
+
+ align:start position:0%
+go through that for every one of the
+ 
+
+ align:start position:0%
+go through that for every one of the
+different factors you know putting stars
+
+ align:start position:0%
+different factors you know putting stars
+ 
+
+ align:start position:0%
+different factors you know putting stars
+on our X's and we continue and we what
+
+ align:start position:0%
+on our X's and we continue and we what
+ 
+
+ align:start position:0%
+on our X's and we continue and we what
+we're interested in knowing is how does
+
+ align:start position:0%
+we're interested in knowing is how does
+ 
+
+ align:start position:0%
+we're interested in knowing is how does
+the expected value of improvement behave
+
+ align:start position:0%
+the expected value of improvement behave
+ 
+
+ align:start position:0%
+the expected value of improvement behave
+as a function of a number of parameters
+
+ align:start position:0%
+as a function of a number of parameters
+ 
+
+ align:start position:0%
+as a function of a number of parameters
+in a model and the parameters we put in
+
+ align:start position:0%
+in a model and the parameters we put in
+ 
+
+ align:start position:0%
+in a model and the parameters we put in
+our model are a few we talked about the
+
+ align:start position:0%
+our model are a few we talked about the
+ 
+
+ align:start position:0%
+our model are a few we talked about the
+size of main effects in general the size
+
+ align:start position:0%
+size of main effects in general the size
+ 
+
+ align:start position:0%
+size of main effects in general the size
+of interactions and the size of
+
+ align:start position:0%
+of interactions and the size of
+ 
+
+ align:start position:0%
+of interactions and the size of
+experimental error because our empirical
+
+ align:start position:0%
+experimental error because our empirical
+ 
+
+ align:start position:0%
+experimental error because our empirical
+investigation had shown that those were
+
+ align:start position:0%
+investigation had shown that those were
+ 
+
+ align:start position:0%
+investigation had shown that those were
+interesting to look at and here we show
+
+ align:start position:0%
+interesting to look at and here we show
+ 
+
+ align:start position:0%
+interesting to look at and here we show
+we wanted to normalize those with
+
+ align:start position:0%
+we wanted to normalize those with
+ 
+
+ align:start position:0%
+we wanted to normalize those with
+respect to the maximum the best that you
+
+ align:start position:0%
+respect to the maximum the best that you
+ 
+
+ align:start position:0%
+respect to the maximum the best that you
+could do so that our results could be
+
+ align:start position:0%
+could do so that our results could be
+ 
+
+ align:start position:0%
+could do so that our results could be
+easily interpreted and the another
+
+ align:start position:0%
+easily interpreted and the another
+ 
+
+ align:start position:0%
+easily interpreted and the another
+concept we introduced in this paper we
+
+ align:start position:0%
+concept we introduced in this paper we
+ 
+
+ align:start position:0%
+concept we introduced in this paper we
+we felt we needed to explain the results
+
+ align:start position:0%
+we felt we needed to explain the results
+ 
+
+ align:start position:0%
+we felt we needed to explain the results
+was the idea of exploiting an effect
+
+ align:start position:0%
+was the idea of exploiting an effect
+ 
+
+ align:start position:0%
+was the idea of exploiting an effect
+so we entered into introduced the idea
+
+ align:start position:0%
+so we entered into introduced the idea
+ 
+
+ align:start position:0%
+so we entered into introduced the idea
+that when you do an experiment if your
+
+ align:start position:0%
+that when you do an experiment if your
+ 
+
+ align:start position:0%
+that when you do an experiment if your
+system has a number of effects in it
+
+ align:start position:0%
+system has a number of effects in it
+ 
+
+ align:start position:0%
+system has a number of effects in it
+main effects and interactions they can
+
+ align:start position:0%
+main effects and interactions they can
+ 
+
+ align:start position:0%
+main effects and interactions they can
+either be exploited or not and we'll say
+
+ align:start position:0%
+either be exploited or not and we'll say
+ 
+
+ align:start position:0%
+either be exploited or not and we'll say
+that they're exploited just in case for
+
+ align:start position:0%
+that they're exploited just in case for
+ 
+
+ align:start position:0%
+that they're exploited just in case for
+example if you're trying to get a higher
+
+ align:start position:0%
+example if you're trying to get a higher
+ 
+
+ align:start position:0%
+example if you're trying to get a higher
+response out of the system let's say
+
+ align:start position:0%
+response out of the system let's say
+ 
+
+ align:start position:0%
+response out of the system let's say
+yield out of a field of oats or quality
+
+ align:start position:0%
+yield out of a field of oats or quality
+ 
+
+ align:start position:0%
+yield out of a field of oats or quality
+of a manufactured article then you
+
+ align:start position:0%
+of a manufactured article then you
+ 
+
+ align:start position:0%
+of a manufactured article then you
+exploit an effect if the coefficient in
+
+ align:start position:0%
+exploit an effect if the coefficient in
+ 
+
+ align:start position:0%
+exploit an effect if the coefficient in
+the model times the level of the factor
+
+ align:start position:0%
+the model times the level of the factor
+ 
+
+ align:start position:0%
+the model times the level of the factor
+is such that it's contributing
+
+ align:start position:0%
+is such that it's contributing
+ 
+
+ align:start position:0%
+is such that it's contributing
+positively to your outcome and you
+
+ align:start position:0%
+positively to your outcome and you
+ 
+
+ align:start position:0%
+positively to your outcome and you
+exploit an interaction in the system
+
+ align:start position:0%
+exploit an interaction in the system
+ 
+
+ align:start position:0%
+exploit an interaction in the system
+basically under the same condition that
+
+ align:start position:0%
+basically under the same condition that
+ 
+
+ align:start position:0%
+basically under the same condition that
+if the two factors involved are such
+
+ align:start position:0%
+if the two factors involved are such
+ 
+
+ align:start position:0%
+if the two factors involved are such
+that you're gaining benefit from the
+
+ align:start position:0%
+that you're gaining benefit from the
+ 
+
+ align:start position:0%
+that you're gaining benefit from the
+coefficient in the model either
+
+ align:start position:0%
+coefficient in the model either
+ 
+
+ align:start position:0%
+coefficient in the model either
+increasing or decreasing the response
+
+ align:start position:0%
+increasing or decreasing the response
+ 
+
+ align:start position:0%
+increasing or decreasing the response
+depending on what you prefer we call
+
+ align:start position:0%
+depending on what you prefer we call
+ 
+
+ align:start position:0%
+depending on what you prefer we call
+that one exploited so we wanted to
+
+ align:start position:0%
+that one exploited so we wanted to
+ 
+
+ align:start position:0%
+that one exploited so we wanted to
+understand the probabilities and
+
+ align:start position:0%
+understand the probabilities and
+ 
+
+ align:start position:0%
+understand the probabilities and
+conditional probabilities associated
+
+ align:start position:0%
+conditional probabilities associated
+ 
+
+ align:start position:0%
+conditional probabilities associated
+with this adaptive experiment so we
+
+ align:start position:0%
+with this adaptive experiment so we
+ 
+
+ align:start position:0%
+with this adaptive experiment so we
+begin to do the the theorem proving
+
+ align:start position:0%
+begin to do the the theorem proving
+ 
+
+ align:start position:0%
+begin to do the the theorem proving
+based on our model and we find first of
+
+ align:start position:0%
+based on our model and we find first of
+ 
+
+ align:start position:0%
+based on our model and we find first of
+all that if you change just the first
+
+ align:start position:0%
+all that if you change just the first
+ 
+
+ align:start position:0%
+all that if you change just the first
+factor and compute the expected value of
+
+ align:start position:0%
+factor and compute the expected value of
+ 
+
+ align:start position:0%
+factor and compute the expected value of
+improvement you have two different kinds
+
+ align:start position:0%
+improvement you have two different kinds
+ 
+
+ align:start position:0%
+improvement you have two different kinds
+of contributions one due to a main
+
+ align:start position:0%
+of contributions one due to a main
+ 
+
+ align:start position:0%
+of contributions one due to a main
+effect and n minus one due to
+
+ align:start position:0%
+effect and n minus one due to
+ 
+
+ align:start position:0%
+effect and n minus one due to
+interactions so you change factor one
+
+ align:start position:0%
+interactions so you change factor one
+ 
+
+ align:start position:0%
+interactions so you change factor one
+and this figure here is meant to
+
+ align:start position:0%
+and this figure here is meant to
+ 
+
+ align:start position:0%
+and this figure here is meant to
+indicate the condition with N equals
+
+ align:start position:0%
+indicate the condition with N equals
+ 
+
+ align:start position:0%
+indicate the condition with N equals
+seven you've got seven factors you're
+
+ align:start position:0%
+seven you've got seven factors you're
+ 
+
+ align:start position:0%
+seven you've got seven factors you're
+interested in and this stack of squares
+
+ align:start position:0%
+interested in and this stack of squares
+ 
+
+ align:start position:0%
+interested in and this stack of squares
+indicates the contribution of main
+
+ align:start position:0%
+indicates the contribution of main
+ 
+
+ align:start position:0%
+indicates the contribution of main
+effects and and none of these other
+
+ align:start position:0%
+effects and and none of these other
+ 
+
+ align:start position:0%
+effects and and none of these other
+factors are contributing anything but
+
+ align:start position:0%
+factors are contributing anything but
+ 
+
+ align:start position:0%
+factors are contributing anything but
+now the the main effect of the first
+
+ align:start position:0%
+now the the main effect of the first
+ 
+
+ align:start position:0%
+now the the main effect of the first
+factor is contributing quite a bit on
+
+ align:start position:0%
+factor is contributing quite a bit on
+ 
+
+ align:start position:0%
+factor is contributing quite a bit on
+average after you've done the adaptation
+
+ align:start position:0%
+average after you've done the adaptation
+ 
+
+ align:start position:0%
+average after you've done the adaptation
+and all of the six potential two-factor
+
+ align:start position:0%
+and all of the six potential two-factor
+ 
+
+ align:start position:0%
+and all of the six potential two-factor
+interactions are on average contributing
+
+ align:start position:0%
+interactions are on average contributing
+ 
+
+ align:start position:0%
+interactions are on average contributing
+a little to improvement because it may
+
+ align:start position:0%
+a little to improvement because it may
+ 
+
+ align:start position:0%
+a little to improvement because it may
+be that in some cases you'll there'll be
+
+ align:start position:0%
+be that in some cases you'll there'll be
+ 
+
+ align:start position:0%
+be that in some cases you'll there'll be
+a large two factor interaction and
+
+ align:start position:0%
+a large two factor interaction and
+ 
+
+ align:start position:0%
+a large two factor interaction and
+you'll see it when you toggle the
+
+ align:start position:0%
+you'll see it when you toggle the
+ 
+
+ align:start position:0%
+you'll see it when you toggle the
+factors and you'll go chase that and so
+
+ align:start position:0%
+factors and you'll go chase that and so
+ 
+
+ align:start position:0%
+factors and you'll go chase that and so
+on average it's contributing something
+
+ align:start position:0%
+on average it's contributing something
+ 
+
+ align:start position:0%
+on average it's contributing something
+and we could write
+
+ align:start position:0%
+and we could write
+ 
+
+ align:start position:0%
+and we could write
+closed-form expressions for the
+
+ align:start position:0%
+closed-form expressions for the
+ 
+
+ align:start position:0%
+closed-form expressions for the
+contribution and the contribution due to
+
+ align:start position:0%
+contribution and the contribution due to
+ 
+
+ align:start position:0%
+contribution and the contribution due to
+main effects is larger when the main
+
+ align:start position:0%
+main effects is larger when the main
+ 
+
+ align:start position:0%
+main effects is larger when the main
+effects are larger it is tends to be
+
+ align:start position:0%
+effects are larger it is tends to be
+ 
+
+ align:start position:0%
+effects are larger it is tends to be
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+when interactions are large and when
+
+ align:start position:0%
+when interactions are large and when
+ 
+
+ align:start position:0%
+when interactions are large and when
+error is large the contribution to the
+
+ align:start position:0%
+error is large the contribution to the
+ 
+
+ align:start position:0%
+error is large the contribution to the
+interactions are large when interactions
+
+ align:start position:0%
+interactions are large when interactions
+ 
+
+ align:start position:0%
+interactions are large when interactions
+are large in the model and interesting
+
+ align:start position:0%
+are large in the model and interesting
+ 
+
+ align:start position:0%
+are large in the model and interesting
+to us if you if you write out the
+
+ align:start position:0%
+to us if you if you write out the
+ 
+
+ align:start position:0%
+to us if you if you write out the
+expected value normalize it by the
+
+ align:start position:0%
+expected value normalize it by the
+ 
+
+ align:start position:0%
+expected value normalize it by the
+maximum so that the improvements are
+
+ align:start position:0%
+maximum so that the improvements are
+ 
+
+ align:start position:0%
+maximum so that the improvements are
+either x' you know on this scale either
+
+ align:start position:0%
+either x' you know on this scale either
+ 
+
+ align:start position:0%
+either x' you know on this scale either
+0 or 1
+
+ align:start position:0%
+0 or 1
+ 
+
+ align:start position:0%
+0 or 1
+you know or any or scaled in between the
+
+ align:start position:0%
+you know or any or scaled in between the
+ 
+
+ align:start position:0%
+you know or any or scaled in between the
+contribution you would get in in the
+
+ align:start position:0%
+contribution you would get in in the
+ 
+
+ align:start position:0%
+contribution you would get in in the
+case that experimental error is low so
+
+ align:start position:0%
+case that experimental error is low so
+ 
+
+ align:start position:0%
+case that experimental error is low so
+here I put experimental error at 10
+
+ align:start position:0%
+here I put experimental error at 10
+ 
+
+ align:start position:0%
+here I put experimental error at 10
+percent of a main effect the
+
+ align:start position:0%
+percent of a main effect the
+ 
+
+ align:start position:0%
+percent of a main effect the
+contribution you get after running 1 out
+
+ align:start position:0%
+contribution you get after running 1 out
+ 
+
+ align:start position:0%
+contribution you get after running 1 out
+of 7 factors is actually about 1/7 so
+
+ align:start position:0%
+of 7 factors is actually about 1/7 so
+ 
+
+ align:start position:0%
+of 7 factors is actually about 1/7 so
+you get 1/7 of the way toward the
+
+ align:start position:0%
+you get 1/7 of the way toward the
+ 
+
+ align:start position:0%
+you get 1/7 of the way toward the
+maximum by changing 1/7 of the factors
+
+ align:start position:0%
+maximum by changing 1/7 of the factors
+ 
+
+ align:start position:0%
+maximum by changing 1/7 of the factors
+that's a good start and the influence of
+
+ align:start position:0%
+that's a good start and the influence of
+ 
+
+ align:start position:0%
+that's a good start and the influence of
+error is I mean it's there you know as
+
+ align:start position:0%
+error is I mean it's there you know as
+ 
+
+ align:start position:0%
+error is I mean it's there you know as
+you go to error being as large as main
+
+ align:start position:0%
+you go to error being as large as main
+ 
+
+ align:start position:0%
+you go to error being as large as main
+effects it drops a little and of course
+
+ align:start position:0%
+effects it drops a little and of course
+ 
+
+ align:start position:0%
+effects it drops a little and of course
+if you if you make the error really huge
+
+ align:start position:0%
+if you if you make the error really huge
+ 
+
+ align:start position:0%
+if you if you make the error really huge
+it drops quite substantially but that
+
+ align:start position:0%
+it drops quite substantially but that
+ 
+
+ align:start position:0%
+it drops quite substantially but that
+that's you know a hard test to pass but
+
+ align:start position:0%
+that's you know a hard test to pass but
+ 
+
+ align:start position:0%
+that's you know a hard test to pass but
+we're just trying to understand what the
+
+ align:start position:0%
+we're just trying to understand what the
+ 
+
+ align:start position:0%
+we're just trying to understand what the
+influences are ok now let's talk about
+
+ align:start position:0%
+influences are ok now let's talk about
+ 
+
+ align:start position:0%
+influences are ok now let's talk about
+probably the explain the first main
+
+ align:start position:0%
+probably the explain the first main
+ 
+
+ align:start position:0%
+probably the explain the first main
+effect justing when when interactions
+
+ align:start position:0%
+effect justing when when interactions
+ 
+
+ align:start position:0%
+effect justing when when interactions
+are are small the probability of getting
+
+ align:start position:0%
+are are small the probability of getting
+ 
+
+ align:start position:0%
+are are small the probability of getting
+the benefit of the main effect is large
+
+ align:start position:0%
+the benefit of the main effect is large
+ 
+
+ align:start position:0%
+the benefit of the main effect is large
+and as interactions increase it's less
+
+ align:start position:0%
+and as interactions increase it's less
+ 
+
+ align:start position:0%
+and as interactions increase it's less
+likely that you'll get the benefit of
+
+ align:start position:0%
+likely that you'll get the benefit of
+ 
+
+ align:start position:0%
+likely that you'll get the benefit of
+the main effect now it becomes
+
+ align:start position:0%
+the main effect now it becomes
+ 
+
+ align:start position:0%
+the main effect now it becomes
+interesting at the second step now
+
+ align:start position:0%
+interesting at the second step now
+ 
+
+ align:start position:0%
+interesting at the second step now
+you've toggled two factors and then when
+
+ align:start position:0%
+you've toggled two factors and then when
+ 
+
+ align:start position:0%
+you've toggled two factors and then when
+we think about it is this now you've got
+
+ align:start position:0%
+we think about it is this now you've got
+ 
+
+ align:start position:0%
+we think about it is this now you've got
+the benefit of two main effects and you
+
+ align:start position:0%
+the benefit of two main effects and you
+ 
+
+ align:start position:0%
+the benefit of two main effects and you
+get first n minus 1 and then n minus 2
+
+ align:start position:0%
+get first n minus 1 and then n minus 2
+ 
+
+ align:start position:0%
+get first n minus 1 and then n minus 2
+interactions potentially contributing
+
+ align:start position:0%
+interactions potentially contributing
+ 
+
+ align:start position:0%
+interactions potentially contributing
+and at this point I hash it in because
+
+ align:start position:0%
+and at this point I hash it in because
+ 
+
+ align:start position:0%
+and at this point I hash it in because
+this is the first interaction which
+
+ align:start position:0%
+this is the first interaction which
+ 
+
+ align:start position:0%
+this is the first interaction which
+you've actually locked in in the sense
+
+ align:start position:0%
+you've actually locked in in the sense
+ 
+
+ align:start position:0%
+you've actually locked in in the sense
+that any further changes you make
+
+ align:start position:0%
+that any further changes you make
+ 
+
+ align:start position:0%
+that any further changes you make
+through the experiment
+
+ align:start position:0%
+through the experiment
+ 
+
+ align:start position:0%
+through the experiment
+process will not reverse whatever
+
+ align:start position:0%
+process will not reverse whatever
+ 
+
+ align:start position:0%
+process will not reverse whatever
+benefits you got because you've already
+
+ align:start position:0%
+benefits you got because you've already
+ 
+
+ align:start position:0%
+benefits you got because you've already
+changed one and changed two and you've
+
+ align:start position:0%
+changed one and changed two and you've
+ 
+
+ align:start position:0%
+changed one and changed two and you've
+made your decision about that and now we
+
+ align:start position:0%
+made your decision about that and now we
+ 
+
+ align:start position:0%
+made your decision about that and now we
+see that there's a contribution due to
+
+ align:start position:0%
+see that there's a contribution due to
+ 
+
+ align:start position:0%
+see that there's a contribution due to
+in the interaction and the interaction
+
+ align:start position:0%
+in the interaction and the interaction
+ 
+
+ align:start position:0%
+in the interaction and the interaction
+is the same functional form as I showed
+
+ align:start position:0%
+is the same functional form as I showed
+ 
+
+ align:start position:0%
+is the same functional form as I showed
+before that what the contribution is
+
+ align:start position:0%
+before that what the contribution is
+ 
+
+ align:start position:0%
+before that what the contribution is
+large when the interaction is large
+
+ align:start position:0%
+large when the interaction is large
+ 
+
+ align:start position:0%
+large when the interaction is large
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+we see that the the expected value is
+
+ align:start position:0%
+we see that the the expected value is
+ 
+
+ align:start position:0%
+we see that the the expected value is
+gone from about one seventh to about 2/7
+
+ align:start position:0%
+gone from about one seventh to about 2/7
+ 
+
+ align:start position:0%
+gone from about one seventh to about 2/7
+so we're continuing to step forward at a
+
+ align:start position:0%
+so we're continuing to step forward at a
+ 
+
+ align:start position:0%
+so we're continuing to step forward at a
+good rate and we want to understand why
+
+ align:start position:0%
+good rate and we want to understand why
+ 
+
+ align:start position:0%
+good rate and we want to understand why
+well okay we see the probability of
+
+ align:start position:0%
+well okay we see the probability of
+ 
+
+ align:start position:0%
+well okay we see the probability of
+exploiting the interaction we can write
+
+ align:start position:0%
+exploiting the interaction we can write
+ 
+
+ align:start position:0%
+exploiting the interaction we can write
+it's close form expression it's strictly
+
+ align:start position:0%
+it's close form expression it's strictly
+ 
+
+ align:start position:0%
+it's close form expression it's strictly
+better than 50/50 so it's in any case
+
+ align:start position:0%
+better than 50/50 so it's in any case
+ 
+
+ align:start position:0%
+better than 50/50 so it's in any case
+better than random and it goes up with
+
+ align:start position:0%
+better than random and it goes up with
+ 
+
+ align:start position:0%
+better than random and it goes up with
+interaction strength now the interesting
+
+ align:start position:0%
+interaction strength now the interesting
+ 
+
+ align:start position:0%
+interaction strength now the interesting
+thing about it it's never very high
+
+ align:start position:0%
+thing about it it's never very high
+ 
+
+ align:start position:0%
+thing about it it's never very high
+because actually that any particular
+
+ align:start position:0%
+because actually that any particular
+ 
+
+ align:start position:0%
+because actually that any particular
+interaction is competing with and choose
+
+ align:start position:0%
+interaction is competing with and choose
+ 
+
+ align:start position:0%
+interaction is competing with and choose
+two other interactions or n choose two
+
+ align:start position:0%
+two other interactions or n choose two
+ 
+
+ align:start position:0%
+two other interactions or n choose two
+minus one and so any particular one is
+
+ align:start position:0%
+minus one and so any particular one is
+ 
+
+ align:start position:0%
+minus one and so any particular one is
+unlikely to be exploited by this
+
+ align:start position:0%
+unlikely to be exploited by this
+ 
+
+ align:start position:0%
+unlikely to be exploited by this
+procedure and so maybe we get a 60%
+
+ align:start position:0%
+procedure and so maybe we get a 60%
+ 
+
+ align:start position:0%
+procedure and so maybe we get a 60%
+chance but if you condition that
+
+ align:start position:0%
+chance but if you condition that
+ 
+
+ align:start position:0%
+chance but if you condition that
+probability if you say well let's say
+
+ align:start position:0%
+probability if you say well let's say
+ 
+
+ align:start position:0%
+probability if you say well let's say
+that this particular interaction we just
+
+ align:start position:0%
+that this particular interaction we just
+ 
+
+ align:start position:0%
+that this particular interaction we just
+locked in it's somehow the largest one
+
+ align:start position:0%
+locked in it's somehow the largest one
+ 
+
+ align:start position:0%
+locked in it's somehow the largest one
+in the system let's say that that
+
+ align:start position:0%
+in the system let's say that that
+ 
+
+ align:start position:0%
+in the system let's say that that
+happened we condition the probability we
+
+ align:start position:0%
+happened we condition the probability we
+ 
+
+ align:start position:0%
+happened we condition the probability we
+get a new expression and the probability
+
+ align:start position:0%
+get a new expression and the probability
+ 
+
+ align:start position:0%
+get a new expression and the probability
+could be as high as eighty percent the
+
+ align:start position:0%
+could be as high as eighty percent the
+ 
+
+ align:start position:0%
+could be as high as eighty percent the
+reason that's interesting to us is that
+
+ align:start position:0%
+reason that's interesting to us is that
+ 
+
+ align:start position:0%
+reason that's interesting to us is that
+we know that the adaptive one factor
+
+ align:start position:0%
+we know that the adaptive one factor
+ 
+
+ align:start position:0%
+we know that the adaptive one factor
+experiments are just not capable of
+
+ align:start position:0%
+experiments are just not capable of
+ 
+
+ align:start position:0%
+experiments are just not capable of
+allowing you to estimate interactions
+
+ align:start position:0%
+allowing you to estimate interactions
+ 
+
+ align:start position:0%
+allowing you to estimate interactions
+you take a factor you change it you look
+
+ align:start position:0%
+you take a factor you change it you look
+ 
+
+ align:start position:0%
+you take a factor you change it you look
+at the influence and what you're seeing
+
+ align:start position:0%
+at the influence and what you're seeing
+ 
+
+ align:start position:0%
+at the influence and what you're seeing
+is a combination of the main effect of
+
+ align:start position:0%
+is a combination of the main effect of
+ 
+
+ align:start position:0%
+is a combination of the main effect of
+the factor and a bunch of conditional
+
+ align:start position:0%
+the factor and a bunch of conditional
+ 
+
+ align:start position:0%
+the factor and a bunch of conditional
+contributions due to a bunch of
+
+ align:start position:0%
+contributions due to a bunch of
+ 
+
+ align:start position:0%
+contributions due to a bunch of
+different interactions and so you can't
+
+ align:start position:0%
+different interactions and so you can't
+ 
+
+ align:start position:0%
+different interactions and so you can't
+sort out which one is which you would
+
+ align:start position:0%
+sort out which one is which you would
+ 
+
+ align:start position:0%
+sort out which one is which you would
+need more experiments to do that
+
+ align:start position:0%
+need more experiments to do that
+ 
+
+ align:start position:0%
+need more experiments to do that
+nevertheless if there's a big effect
+
+ align:start position:0%
+nevertheless if there's a big effect
+ 
+
+ align:start position:0%
+nevertheless if there's a big effect
+there there's a good chance you'll get
+
+ align:start position:0%
+there there's a good chance you'll get
+ 
+
+ align:start position:0%
+there there's a good chance you'll get
+benefit from it when you do this
+
+ align:start position:0%
+benefit from it when you do this
+ 
+
+ align:start position:0%
+benefit from it when you do this
+adaptive experiment
+
+ align:start position:0%
+adaptive experiment
+ 
+
+ align:start position:0%
+adaptive experiment
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the most important interaction anyway
+
+ align:start position:0%
+the most important interaction anyway
+ 
+
+ align:start position:0%
+the most important interaction anyway
+that would that mean that there's no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's an interesting question and
+
+ align:start position:0%
+yeah it's an interesting question and
+ 
+
+ align:start position:0%
+yeah it's an interesting question and
+this is something that we we were
+
+ align:start position:0%
+this is something that we we were
+ 
+
+ align:start position:0%
+this is something that we we were
+concerned with all the results I'm
+
+ align:start position:0%
+concerned with all the results I'm
+ 
+
+ align:start position:0%
+concerned with all the results I'm
+showing you today assume that you've
+
+ align:start position:0%
+showing you today assume that you've
+ 
+
+ align:start position:0%
+showing you today assume that you've
+randomized the ordering of the factors
+
+ align:start position:0%
+randomized the ordering of the factors
+ 
+
+ align:start position:0%
+randomized the ordering of the factors
+and that you've randomized the starting
+
+ align:start position:0%
+and that you've randomized the starting
+ 
+
+ align:start position:0%
+and that you've randomized the starting
+point and so far what our investigations
+
+ align:start position:0%
+point and so far what our investigations
+ 
+
+ align:start position:0%
+point and so far what our investigations
+show is that the ordering of the factors
+
+ align:start position:0%
+show is that the ordering of the factors
+ 
+
+ align:start position:0%
+show is that the ordering of the factors
+doesn't matter much but the starting
+
+ align:start position:0%
+doesn't matter much but the starting
+ 
+
+ align:start position:0%
+doesn't matter much but the starting
+points do so I would say whether or not
+
+ align:start position:0%
+points do so I would say whether or not
+ 
+
+ align:start position:0%
+points do so I would say whether or not
+you order the factors from next to the
+
+ align:start position:0%
+you order the factors from next to the
+ 
+
+ align:start position:0%
+you order the factors from next to the
+next it's a minor improvement not big
+
+ align:start position:0%
+next it's a minor improvement not big
+ 
+
+ align:start position:0%
+next it's a minor improvement not big
+but if you select a very promising
+
+ align:start position:0%
+but if you select a very promising
+ 
+
+ align:start position:0%
+but if you select a very promising
+starting point that is you know go with
+
+ align:start position:0%
+starting point that is you know go with
+ 
+
+ align:start position:0%
+starting point that is you know go with
+something that is likely to be very
+
+ align:start position:0%
+something that is likely to be very
+ 
+
+ align:start position:0%
+something that is likely to be very
+robust high performance that makes a big
+
+ align:start position:0%
+robust high performance that makes a big
+ 
+
+ align:start position:0%
+robust high performance that makes a big
+difference and it wasn't obvious to us
+
+ align:start position:0%
+difference and it wasn't obvious to us
+ 
+
+ align:start position:0%
+difference and it wasn't obvious to us
+start I thought probably what you said
+
+ align:start position:0%
+start I thought probably what you said
+ 
+
+ align:start position:0%
+start I thought probably what you said
+was was true it turned out to be the
+
+ align:start position:0%
+was was true it turned out to be the
+ 
+
+ align:start position:0%
+was was true it turned out to be the
+other way around so the dynamics of this
+
+ align:start position:0%
+other way around so the dynamics of this
+ 
+
+ align:start position:0%
+other way around so the dynamics of this
+process of experimentation are such that
+
+ align:start position:0%
+process of experimentation are such that
+ 
+
+ align:start position:0%
+process of experimentation are such that
+it turns out the the probability of
+
+ align:start position:0%
+it turns out the the probability of
+ 
+
+ align:start position:0%
+it turns out the the probability of
+exploiting interactions as you go gets
+
+ align:start position:0%
+exploiting interactions as you go gets
+ 
+
+ align:start position:0%
+exploiting interactions as you go gets
+higher and higher throughout the course
+
+ align:start position:0%
+higher and higher throughout the course
+ 
+
+ align:start position:0%
+higher and higher throughout the course
+of the experiment so it's true that if
+
+ align:start position:0%
+of the experiment so it's true that if
+ 
+
+ align:start position:0%
+of the experiment so it's true that if
+you knew where the interactions lie
+
+ align:start position:0%
+you knew where the interactions lie
+ 
+
+ align:start position:0%
+you knew where the interactions lie
+you'd like to toggle them for the last
+
+ align:start position:0%
+you'd like to toggle them for the last
+ 
+
+ align:start position:0%
+you'd like to toggle them for the last
+time as late as possible but I guess I I
+
+ align:start position:0%
+time as late as possible but I guess I I
+ 
+
+ align:start position:0%
+time as late as possible but I guess I I
+don't really believe that people would
+
+ align:start position:0%
+don't really believe that people would
+ 
+
+ align:start position:0%
+don't really believe that people would
+be able to identify which two
+
+ align:start position:0%
+be able to identify which two
+ 
+
+ align:start position:0%
+be able to identify which two
+interactions are going to participate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I ruled that out and didn't study it
+
+ align:start position:0%
+so I ruled that out and didn't study it
+ 
+
+ align:start position:0%
+so I ruled that out and didn't study it
+much but the point is that even if you
+
+ align:start position:0%
+much but the point is that even if you
+ 
+
+ align:start position:0%
+much but the point is that even if you
+didn't know where they lie the benefits
+
+ align:start position:0%
+didn't know where they lie the benefits
+ 
+
+ align:start position:0%
+didn't know where they lie the benefits
+continue to accrue almost linearly even
+
+ align:start position:0%
+continue to accrue almost linearly even
+ 
+
+ align:start position:0%
+continue to accrue almost linearly even
+though you're explaining fewer and fewer
+
+ align:start position:0%
+though you're explaining fewer and fewer
+ 
+
+ align:start position:0%
+though you're explaining fewer and fewer
+new interactions as you go you see the
+
+ align:start position:0%
+new interactions as you go you see the
+ 
+
+ align:start position:0%
+new interactions as you go you see the
+the white ones left to benefit are are
+
+ align:start position:0%
+the white ones left to benefit are are
+ 
+
+ align:start position:0%
+the white ones left to benefit are are
+diminishing over time but because their
+
+ align:start position:0%
+diminishing over time but because their
+ 
+
+ align:start position:0%
+diminishing over time but because their
+likelihood of coming in your favor is
+
+ align:start position:0%
+likelihood of coming in your favor is
+ 
+
+ align:start position:0%
+likelihood of coming in your favor is
+increasing you go up almost linearly and
+
+ align:start position:0%
+increasing you go up almost linearly and
+ 
+
+ align:start position:0%
+increasing you go up almost linearly and
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+almost to the end 80% you get almost to
+
+ align:start position:0%
+almost to the end 80% you get almost to
+ 
+
+ align:start position:0%
+almost to the end 80% you get almost to
+one well pretty close and what's
+
+ align:start position:0%
+one well pretty close and what's
+ 
+
+ align:start position:0%
+one well pretty close and what's
+interesting to us about this is take the
+
+ align:start position:0%
+interesting to us about this is take the
+ 
+
+ align:start position:0%
+interesting to us about this is take the
+case of seven factors you the adaptive
+
+ align:start position:0%
+case of seven factors you the adaptive
+ 
+
+ align:start position:0%
+case of seven factors you the adaptive
+one factor at a time assuming two levels
+
+ align:start position:0%
+one factor at a time assuming two levels
+ 
+
+ align:start position:0%
+one factor at a time assuming two levels
+that takes eight experiments the full
+
+ align:start position:0%
+that takes eight experiments the full
+ 
+
+ align:start position:0%
+that takes eight experiments the full
+factorial takes 128 so you've looked at
+
+ align:start position:0%
+factorial takes 128 so you've looked at
+ 
+
+ align:start position:0%
+factorial takes 128 so you've looked at
+a very small fraction of the overall
+
+ align:start position:0%
+a very small fraction of the overall
+ 
+
+ align:start position:0%
+a very small fraction of the overall
+space and you've gotten 80% of the way
+
+ align:start position:0%
+space and you've gotten 80% of the way
+ 
+
+ align:start position:0%
+space and you've gotten 80% of the way
+toward the best possible outcome in the
+
+ align:start position:0%
+toward the best possible outcome in the
+ 
+
+ align:start position:0%
+toward the best possible outcome in the
+space that sauce is interesting and then
+
+ align:start position:0%
+space that sauce is interesting and then
+ 
+
+ align:start position:0%
+space that sauce is interesting and then
+if I want to compare the the use of
+
+ align:start position:0%
+if I want to compare the the use of
+ 
+
+ align:start position:0%
+if I want to compare the the use of
+resolution three designs and adaptive
+
+ align:start position:0%
+resolution three designs and adaptive
+ 
+
+ align:start position:0%
+resolution three designs and adaptive
+designs we have expressions for each and
+
+ align:start position:0%
+designs we have expressions for each and
+ 
+
+ align:start position:0%
+designs we have expressions for each and
+then to make the comparison straight one
+
+ align:start position:0%
+then to make the comparison straight one
+ 
+
+ align:start position:0%
+then to make the comparison straight one
+against the other we do the following
+
+ align:start position:0%
+against the other we do the following
+ 
+
+ align:start position:0%
+against the other we do the following
+just hold them up against one another
+
+ align:start position:0%
+just hold them up against one another
+ 
+
+ align:start position:0%
+just hold them up against one another
+look at let's we see that experimental
+
+ align:start position:0%
+look at let's we see that experimental
+ 
+
+ align:start position:0%
+look at let's we see that experimental
+error is plotted parametrically so let's
+
+ align:start position:0%
+error is plotted parametrically so let's
+ 
+
+ align:start position:0%
+error is plotted parametrically so let's
+let's look at just the crossing point
+
+ align:start position:0%
+let's look at just the crossing point
+ 
+
+ align:start position:0%
+let's look at just the crossing point
+when experimental error is about the
+
+ align:start position:0%
+when experimental error is about the
+ 
+
+ align:start position:0%
+when experimental error is about the
+size of main effects they cross at the
+
+ align:start position:0%
+size of main effects they cross at the
+ 
+
+ align:start position:0%
+size of main effects they cross at the
+point where interactions are about a
+
+ align:start position:0%
+point where interactions are about a
+ 
+
+ align:start position:0%
+point where interactions are about a
+quarter of main effects the reason we
+
+ align:start position:0%
+quarter of main effects the reason we
+ 
+
+ align:start position:0%
+quarter of main effects the reason we
+think that one is interesting is that in
+
+ align:start position:0%
+think that one is interesting is that in
+ 
+
+ align:start position:0%
+think that one is interesting is that in
+our I alluded to earlier the idea that
+
+ align:start position:0%
+our I alluded to earlier the idea that
+ 
+
+ align:start position:0%
+our I alluded to earlier the idea that
+we are doing these studies big studies
+
+ align:start position:0%
+we are doing these studies big studies
+ 
+
+ align:start position:0%
+we are doing these studies big studies
+of complex systems and regularities and
+
+ align:start position:0%
+of complex systems and regularities and
+ 
+
+ align:start position:0%
+of complex systems and regularities and
+one of the things we found is that
+
+ align:start position:0%
+one of the things we found is that
+ 
+
+ align:start position:0%
+one of the things we found is that
+interactions being about a quarter the
+
+ align:start position:0%
+interactions being about a quarter the
+ 
+
+ align:start position:0%
+interactions being about a quarter the
+size of main effects that's pretty
+
+ align:start position:0%
+size of main effects that's pretty
+ 
+
+ align:start position:0%
+size of main effects that's pretty
+typical that's a typical amount so if
+
+ align:start position:0%
+typical that's a typical amount so if
+ 
+
+ align:start position:0%
+typical that's a typical amount so if
+you go into a factory and you get your
+
+ align:start position:0%
+you go into a factory and you get your
+ 
+
+ align:start position:0%
+you go into a factory and you get your
+engineers to list a number of factors
+
+ align:start position:0%
+engineers to list a number of factors
+ 
+
+ align:start position:0%
+engineers to list a number of factors
+they're interested in studying and then
+
+ align:start position:0%
+they're interested in studying and then
+ 
+
+ align:start position:0%
+they're interested in studying and then
+you run a big experiment and and study
+
+ align:start position:0%
+you run a big experiment and and study
+ 
+
+ align:start position:0%
+you run a big experiment and and study
+some of the interactions to you will
+
+ align:start position:0%
+some of the interactions to you will
+ 
+
+ align:start position:0%
+some of the interactions to you will
+generally find they're about a quarter
+
+ align:start position:0%
+generally find they're about a quarter
+ 
+
+ align:start position:0%
+generally find they're about a quarter
+of the size of the main effect it's just
+
+ align:start position:0%
+of the size of the main effect it's just
+ 
+
+ align:start position:0%
+of the size of the main effect it's just
+a reasonably reliable regularity and so
+
+ align:start position:0%
+a reasonably reliable regularity and so
+ 
+
+ align:start position:0%
+a reasonably reliable regularity and so
+we think that's typical and the way I
+
+ align:start position:0%
+we think that's typical and the way I
+ 
+
+ align:start position:0%
+we think that's typical and the way I
+would interpret the graph is that if
+
+ align:start position:0%
+would interpret the graph is that if
+ 
+
+ align:start position:0%
+would interpret the graph is that if
+your system is pretty typical in this
+
+ align:start position:0%
+your system is pretty typical in this
+ 
+
+ align:start position:0%
+your system is pretty typical in this
+regard strength of interactions you
+
+ align:start position:0%
+regard strength of interactions you
+ 
+
+ align:start position:0%
+regard strength of interactions you
+should be doing the adaptive experiments
+
+ align:start position:0%
+should be doing the adaptive experiments
+ 
+
+ align:start position:0%
+should be doing the adaptive experiments
+whatever error is less than main effects
+
+ align:start position:0%
+whatever error is less than main effects
+ 
+
+ align:start position:0%
+ 
+so Cuthbert Daniel's criterion for
+
+ align:start position:0%
+so Cuthbert Daniel's criterion for
+ 
+
+ align:start position:0%
+so Cuthbert Daniel's criterion for
+demarcation was err should be about a
+
+ align:start position:0%
+demarcation was err should be about a
+ 
+
+ align:start position:0%
+demarcation was err should be about a
+third or a quarter of main effects and
+
+ align:start position:0%
+third or a quarter of main effects and
+ 
+
+ align:start position:0%
+third or a quarter of main effects and
+we're saying now it's actually more like
+
+ align:start position:0%
+we're saying now it's actually more like
+ 
+
+ align:start position:0%
+we're saying now it's actually more like
+the size of Maine effects not a third or
+
+ align:start position:0%
+the size of Maine effects not a third or
+ 
+
+ align:start position:0%
+the size of Maine effects not a third or
+a quarter that's assuming importantly
+
+ align:start position:0%
+a quarter that's assuming importantly
+ 
+
+ align:start position:0%
+a quarter that's assuming importantly
+that your main goal is just getting
+
+ align:start position:0%
+that your main goal is just getting
+ 
+
+ align:start position:0%
+that your main goal is just getting
+improvement playing exactly where they
+
+ align:start position:0%
+improvement playing exactly where they
+ 
+
+ align:start position:0%
+improvement playing exactly where they
+came from or estimating effects
+
+ align:start position:0%
+came from or estimating effects
+ 
+
+ align:start position:0%
+came from or estimating effects
+accurately now our primary reason for
+
+ align:start position:0%
+accurately now our primary reason for
+ 
+
+ align:start position:0%
+accurately now our primary reason for
+going into all this in the first place
+
+ align:start position:0%
+going into all this in the first place
+ 
+
+ align:start position:0%
+going into all this in the first place
+was to deal with robust design in the
+
+ align:start position:0%
+was to deal with robust design in the
+ 
+
+ align:start position:0%
+was to deal with robust design in the
+end and so we we attempted lots of
+
+ align:start position:0%
+end and so we we attempted lots of
+ 
+
+ align:start position:0%
+end and so we we attempted lots of
+different ways of combining the noise
+
+ align:start position:0%
+different ways of combining the noise
+ 
+
+ align:start position:0%
+different ways of combining the noise
+factors with the control factors and so
+
+ align:start position:0%
+factors with the control factors and so
+ 
+
+ align:start position:0%
+factors with the control factors and so
+far the simplest thing turned out to be
+
+ align:start position:0%
+far the simplest thing turned out to be
+ 
+
+ align:start position:0%
+far the simplest thing turned out to be
+the best and that is what you see here
+
+ align:start position:0%
+the best and that is what you see here
+ 
+
+ align:start position:0%
+the best and that is what you see here
+in this cuboidal representation is our
+
+ align:start position:0%
+in this cuboidal representation is our
+ 
+
+ align:start position:0%
+in this cuboidal representation is our
+controllable factors a B and C when our
+
+ align:start position:0%
+controllable factors a B and C when our
+ 
+
+ align:start position:0%
+controllable factors a B and C when our
+noise factors little a B and C are being
+
+ align:start position:0%
+noise factors little a B and C are being
+ 
+
+ align:start position:0%
+noise factors little a B and C are being
+crossed in effect we take the adaptive
+
+ align:start position:0%
+crossed in effect we take the adaptive
+ 
+
+ align:start position:0%
+crossed in effect we take the adaptive
+procedure we run a factorial design in
+
+ align:start position:0%
+procedure we run a factorial design in
+ 
+
+ align:start position:0%
+procedure we run a factorial design in
+the noise then change one of the control
+
+ align:start position:0%
+the noise then change one of the control
+ 
+
+ align:start position:0%
+the noise then change one of the control
+factors just one and run again the exact
+
+ align:start position:0%
+factors just one and run again the exact
+ 
+
+ align:start position:0%
+factors just one and run again the exact
+same design and then what we do is we
+
+ align:start position:0%
+same design and then what we do is we
+ 
+
+ align:start position:0%
+same design and then what we do is we
+select our level in this case of a on
+
+ align:start position:0%
+select our level in this case of a on
+ 
+
+ align:start position:0%
+select our level in this case of a on
+the basis of our preference for this set
+
+ align:start position:0%
+the basis of our preference for this set
+ 
+
+ align:start position:0%
+the basis of our preference for this set
+of observations versus this set if we
+
+ align:start position:0%
+of observations versus this set if we
+ 
+
+ align:start position:0%
+of observations versus this set if we
+like this set because for example it has
+
+ align:start position:0%
+like this set because for example it has
+ 
+
+ align:start position:0%
+like this set because for example it has
+lower variation then we select it we
+
+ align:start position:0%
+lower variation then we select it we
+ 
+
+ align:start position:0%
+lower variation then we select it we
+select a is positive and then we just
+
+ align:start position:0%
+select a is positive and then we just
+ 
+
+ align:start position:0%
+select a is positive and then we just
+continue to wind our way through the
+
+ align:start position:0%
+continue to wind our way through the
+ 
+
+ align:start position:0%
+continue to wind our way through the
+space reversing changes that we don't
+
+ align:start position:0%
+space reversing changes that we don't
+ 
+
+ align:start position:0%
+space reversing changes that we don't
+like and adopting ones that we do and we
+
+ align:start position:0%
+like and adopting ones that we do and we
+ 
+
+ align:start position:0%
+like and adopting ones that we do and we
+we studied this this says except it
+
+ align:start position:0%
+we studied this this says except it
+ 
+
+ align:start position:0%
+we studied this this says except it
+actually appeared in a semi journal I've
+
+ align:start position:0%
+actually appeared in a semi journal I've
+ 
+
+ align:start position:0%
+actually appeared in a semi journal I've
+got to change that so we began to
+
+ align:start position:0%
+got to change that so we began to
+ 
+
+ align:start position:0%
+got to change that so we began to
+validate this approach by applying it
+
+ align:start position:0%
+validate this approach by applying it
+ 
+
+ align:start position:0%
+validate this approach by applying it
+through a number of different systems
+
+ align:start position:0%
+through a number of different systems
+ 
+
+ align:start position:0%
+through a number of different systems
+one that might be of interest to you is
+
+ align:start position:0%
+one that might be of interest to you is
+ 
+
+ align:start position:0%
+one that might be of interest to you is
+sheet metal spinning so in this process
+
+ align:start position:0%
+sheet metal spinning so in this process
+ 
+
+ align:start position:0%
+sheet metal spinning so in this process
+you go into your factory you take sheet
+
+ align:start position:0%
+you go into your factory you take sheet
+ 
+
+ align:start position:0%
+you go into your factory you take sheet
+metal articles and you turn them into
+
+ align:start position:0%
+metal articles and you turn them into
+ 
+
+ align:start position:0%
+metal articles and you turn them into
+manufactured goods surfaces of
+
+ align:start position:0%
+manufactured goods surfaces of
+ 
+
+ align:start position:0%
+manufactured goods surfaces of
+revolution cups and bells and whatever
+
+ align:start position:0%
+revolution cups and bells and whatever
+ 
+
+ align:start position:0%
+revolution cups and bells and whatever
+you need by taking the circular blank
+
+ align:start position:0%
+you need by taking the circular blank
+ 
+
+ align:start position:0%
+you need by taking the circular blank
+pressing it up again
+
+ align:start position:0%
+pressing it up again
+ 
+
+ align:start position:0%
+pressing it up again
+a mandrel repetitively until you get the
+
+ align:start position:0%
+a mandrel repetitively until you get the
+ 
+
+ align:start position:0%
+a mandrel repetitively until you get the
+deformation that you want and you might
+
+ align:start position:0%
+deformation that you want and you might
+ 
+
+ align:start position:0%
+deformation that you want and you might
+be interested for example in consistency
+
+ align:start position:0%
+be interested for example in consistency
+ 
+
+ align:start position:0%
+be interested for example in consistency
+of the geometry and you might be
+
+ align:start position:0%
+of the geometry and you might be
+ 
+
+ align:start position:0%
+of the geometry and you might be
+interested in how a number of different
+
+ align:start position:0%
+interested in how a number of different
+ 
+
+ align:start position:0%
+interested in how a number of different
+parameters affect that consistency of
+
+ align:start position:0%
+parameters affect that consistency of
+ 
+
+ align:start position:0%
+parameters affect that consistency of
+the geometry such as what material you
+
+ align:start position:0%
+the geometry such as what material you
+ 
+
+ align:start position:0%
+the geometry such as what material you
+chose the shape of the mandrel the shape
+
+ align:start position:0%
+chose the shape of the mandrel the shape
+ 
+
+ align:start position:0%
+chose the shape of the mandrel the shape
+of the the path which you which you use
+
+ align:start position:0%
+of the the path which you which you use
+ 
+
+ align:start position:0%
+of the the path which you which you use
+the number of times and with the force
+
+ align:start position:0%
+the number of times and with the force
+ 
+
+ align:start position:0%
+the number of times and with the force
+you apply and this was studied by a
+
+ align:start position:0%
+you apply and this was studied by a
+ 
+
+ align:start position:0%
+you apply and this was studied by a
+group in Germany and we used their
+
+ align:start position:0%
+group in Germany and we used their
+ 
+
+ align:start position:0%
+group in Germany and we used their
+results to simulate the process of
+
+ align:start position:0%
+results to simulate the process of
+ 
+
+ align:start position:0%
+results to simulate the process of
+running these adaptive experiments and
+
+ align:start position:0%
+running these adaptive experiments and
+ 
+
+ align:start position:0%
+running these adaptive experiments and
+running an alternative across their a
+
+ align:start position:0%
+running an alternative across their a
+ 
+
+ align:start position:0%
+running an alternative across their a
+design on these systems and we found
+
+ align:start position:0%
+design on these systems and we found
+ 
+
+ align:start position:0%
+design on these systems and we found
+that that the Taguchi style cross array
+
+ align:start position:0%
+that that the Taguchi style cross array
+ 
+
+ align:start position:0%
+that that the Taguchi style cross array
+made indeed improvements in signal noise
+
+ align:start position:0%
+made indeed improvements in signal noise
+ 
+
+ align:start position:0%
+made indeed improvements in signal noise
+ratio of the system but our adaptive
+
+ align:start position:0%
+ratio of the system but our adaptive
+ 
+
+ align:start position:0%
+ratio of the system but our adaptive
+procedures were doing a little better
+
+ align:start position:0%
+procedures were doing a little better
+ 
+
+ align:start position:0%
+procedures were doing a little better
+until you got to some crossing point
+
+ align:start position:0%
+until you got to some crossing point
+ 
+
+ align:start position:0%
+until you got to some crossing point
+experimental error up here of you know
+
+ align:start position:0%
+experimental error up here of you know
+ 
+
+ align:start position:0%
+experimental error up here of you know
+two millimeters squared of this quality
+
+ align:start position:0%
+two millimeters squared of this quality
+ 
+
+ align:start position:0%
+two millimeters squared of this quality
+measure and this is where we found
+
+ align:start position:0%
+measure and this is where we found
+ 
+
+ align:start position:0%
+measure and this is where we found
+another result the one that I alluded to
+
+ align:start position:0%
+another result the one that I alluded to
+ 
+
+ align:start position:0%
+another result the one that I alluded to
+earlier that if you gave the engineers
+
+ align:start position:0%
+earlier that if you gave the engineers
+ 
+
+ align:start position:0%
+earlier that if you gave the engineers
+the benefit of doubt and suggested that
+
+ align:start position:0%
+the benefit of doubt and suggested that
+ 
+
+ align:start position:0%
+the benefit of doubt and suggested that
+they didn't choose their starting points
+
+ align:start position:0%
+they didn't choose their starting points
+ 
+
+ align:start position:0%
+they didn't choose their starting points
+at random but instead choose inform
+
+ align:start position:0%
+at random but instead choose inform
+ 
+
+ align:start position:0%
+at random but instead choose inform
+starting points and let me define what I
+
+ align:start position:0%
+starting points and let me define what I
+ 
+
+ align:start position:0%
+starting points and let me define what I
+mean by that lets you give you have a
+
+ align:start position:0%
+mean by that lets you give you have a
+ 
+
+ align:start position:0%
+mean by that lets you give you have a
+number of factors there are two levels a
+
+ align:start position:0%
+number of factors there are two levels a
+ 
+
+ align:start position:0%
+number of factors there are two levels a
+random starting point is just flipping
+
+ align:start position:0%
+random starting point is just flipping
+ 
+
+ align:start position:0%
+random starting point is just flipping
+coins you choose each one but let's say
+
+ align:start position:0%
+coins you choose each one but let's say
+ 
+
+ align:start position:0%
+coins you choose each one but let's say
+that somehow the engineers are able to
+
+ align:start position:0%
+that somehow the engineers are able to
+ 
+
+ align:start position:0%
+that somehow the engineers are able to
+do better than 50 percent odds of
+
+ align:start position:0%
+do better than 50 percent odds of
+ 
+
+ align:start position:0%
+do better than 50 percent odds of
+getting the best setting for each factor
+
+ align:start position:0%
+getting the best setting for each factor
+ 
+
+ align:start position:0%
+getting the best setting for each factor
+but instead have 75 percent chance of
+
+ align:start position:0%
+but instead have 75 percent chance of
+ 
+
+ align:start position:0%
+but instead have 75 percent chance of
+defining the superior level of each
+
+ align:start position:0%
+defining the superior level of each
+ 
+
+ align:start position:0%
+defining the superior level of each
+factor in that case in the end they
+
+ align:start position:0%
+factor in that case in the end they
+ 
+
+ align:start position:0%
+factor in that case in the end they
+would get this result substantially
+
+ align:start position:0%
+would get this result substantially
+ 
+
+ align:start position:0%
+would get this result substantially
+higher than either of the other two
+
+ align:start position:0%
+higher than either of the other two
+ 
+
+ align:start position:0%
+higher than either of the other two
+alternatives and they'll never cross no
+
+ align:start position:0%
+alternatives and they'll never cross no
+ 
+
+ align:start position:0%
+alternatives and they'll never cross no
+matter how much error there is
+
+ align:start position:0%
+matter how much error there is
+ 
+
+ align:start position:0%
+matter how much error there is
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so smaller the better is the the
+
+ align:start position:0%
+yeah so smaller the better is the the
+ 
+
+ align:start position:0%
+yeah so smaller the better is the the
+parameter of interest was meant to be
+
+ align:start position:0%
+parameter of interest was meant to be
+ 
+
+ align:start position:0%
+parameter of interest was meant to be
+smaller is better but then when you
+
+ align:start position:0%
+smaller is better but then when you
+ 
+
+ align:start position:0%
+smaller is better but then when you
+compute a signal to noise ratio larger
+
+ align:start position:0%
+compute a signal to noise ratio larger
+ 
+
+ align:start position:0%
+compute a signal to noise ratio larger
+is better so the underlying parameter
+
+ align:start position:0%
+is better so the underlying parameter
+ 
+
+ align:start position:0%
+is better so the underlying parameter
+called a 20 in this case smaller was
+
+ align:start position:0%
+called a 20 in this case smaller was
+ 
+
+ align:start position:0%
+called a 20 in this case smaller was
+better but in taguchi's methodology you
+
+ align:start position:0%
+better but in taguchi's methodology you
+ 
+
+ align:start position:0%
+better but in taguchi's methodology you
+then take that parameter and it's
+
+ align:start position:0%
+then take that parameter and it's
+ 
+
+ align:start position:0%
+then take that parameter and it's
+variation and transform it to get a
+
+ align:start position:0%
+variation and transform it to get a
+ 
+
+ align:start position:0%
+variation and transform it to get a
+signal noise ratio and what signal noise
+
+ align:start position:0%
+signal noise ratio and what signal noise
+ 
+
+ align:start position:0%
+signal noise ratio and what signal noise
+ratio larger is always better
+
+ align:start position:0%
+ratio larger is always better
+ 
+
+ align:start position:0%
+ratio larger is always better
+so I appreciate why that's confusing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one I add I include it in the paper
+
+ align:start position:0%
+this one I add I include it in the paper
+ 
+
+ align:start position:0%
+this one I add I include it in the paper
+and I include it for you because in some
+
+ align:start position:0%
+and I include it for you because in some
+ 
+
+ align:start position:0%
+and I include it for you because in some
+cases you'll you'll feel skeptical about
+
+ align:start position:0%
+cases you'll you'll feel skeptical about
+ 
+
+ align:start position:0%
+cases you'll you'll feel skeptical about
+these results right because they still
+
+ align:start position:0%
+these results right because they still
+ 
+
+ align:start position:0%
+these results right because they still
+are pretty current to ative and you
+
+ align:start position:0%
+are pretty current to ative and you
+ 
+
+ align:start position:0%
+are pretty current to ative and you
+might need to demonstrate them to
+
+ align:start position:0%
+might need to demonstrate them to
+ 
+
+ align:start position:0%
+might need to demonstrate them to
+yourself and the paper airplane allows
+
+ align:start position:0%
+yourself and the paper airplane allows
+ 
+
+ align:start position:0%
+yourself and the paper airplane allows
+you to do that so Steve up and jerk came
+
+ align:start position:0%
+you to do that so Steve up and jerk came
+ 
+
+ align:start position:0%
+you to do that so Steve up and jerk came
+up with this template for demonstrating
+
+ align:start position:0%
+up with this template for demonstrating
+ 
+
+ align:start position:0%
+up with this template for demonstrating
+some of the methods here in robust
+
+ align:start position:0%
+some of the methods here in robust
+ 
+
+ align:start position:0%
+some of the methods here in robust
+design and design of experiments and the
+
+ align:start position:0%
+design and design of experiments and the
+ 
+
+ align:start position:0%
+design and design of experiments and the
+template allows you to fold a variety of
+
+ align:start position:0%
+template allows you to fold a variety of
+ 
+
+ align:start position:0%
+template allows you to fold a variety of
+different paper airplanes in this case
+
+ align:start position:0%
+different paper airplanes in this case
+ 
+
+ align:start position:0%
+different paper airplanes in this case
+it's 3 to the 4 or 81 different paper
+
+ align:start position:0%
+it's 3 to the 4 or 81 different paper
+ 
+
+ align:start position:0%
+it's 3 to the 4 or 81 different paper
+airplanes and we ran an experiment in
+
+ align:start position:0%
+airplanes and we ran an experiment in
+ 
+
+ align:start position:0%
+airplanes and we ran an experiment in
+which we had created different noise
+
+ align:start position:0%
+which we had created different noise
+ 
+
+ align:start position:0%
+which we had created different noise
+conditions for the flights and you could
+
+ align:start position:0%
+conditions for the flights and you could
+ 
+
+ align:start position:0%
+conditions for the flights and you could
+replicate our results actually throw
+
+ align:start position:0%
+replicate our results actually throw
+ 
+
+ align:start position:0%
+replicate our results actually throw
+these airplanes and do it adaptively one
+
+ align:start position:0%
+these airplanes and do it adaptively one
+ 
+
+ align:start position:0%
+these airplanes and do it adaptively one
+factor at a time and I think you'll find
+
+ align:start position:0%
+factor at a time and I think you'll find
+ 
+
+ align:start position:0%
+factor at a time and I think you'll find
+the same results as we did that if you
+
+ align:start position:0%
+the same results as we did that if you
+ 
+
+ align:start position:0%
+the same results as we did that if you
+do the l9 Taguchi array or else that's a
+
+ align:start position:0%
+do the l9 Taguchi array or else that's a
+ 
+
+ align:start position:0%
+do the l9 Taguchi array or else that's a
+placket Behrman design by another name
+
+ align:start position:0%
+placket Behrman design by another name
+ 
+
+ align:start position:0%
+placket Behrman design by another name
+cross it with a 2 or 3 minus 1 noise
+
+ align:start position:0%
+cross it with a 2 or 3 minus 1 noise
+ 
+
+ align:start position:0%
+cross it with a 2 or 3 minus 1 noise
+array you'd get these kind of
+
+ align:start position:0%
+array you'd get these kind of
+ 
+
+ align:start position:0%
+array you'd get these kind of
+improvements in signal noise ratio but
+
+ align:start position:0%
+improvements in signal noise ratio but
+ 
+
+ align:start position:0%
+improvements in signal noise ratio but
+if you run it adapted ly with random
+
+ align:start position:0%
+if you run it adapted ly with random
+ 
+
+ align:start position:0%
+if you run it adapted ly with random
+starting points you'll get better
+
+ align:start position:0%
+starting points you'll get better
+ 
+
+ align:start position:0%
+starting points you'll get better
+results and if you use an informed
+
+ align:start position:0%
+results and if you use an informed
+ 
+
+ align:start position:0%
+results and if you use an informed
+starting point such as you know looking
+
+ align:start position:0%
+starting point such as you know looking
+ 
+
+ align:start position:0%
+starting point such as you know looking
+at a plane that has about the right
+
+ align:start position:0%
+at a plane that has about the right
+ 
+
+ align:start position:0%
+at a plane that has about the right
+aspect ratio and and maybe you know
+
+ align:start position:0%
+aspect ratio and and maybe you know
+ 
+
+ align:start position:0%
+aspect ratio and and maybe you know
+right ahead that folding up the little
+
+ align:start position:0%
+right ahead that folding up the little
+ 
+
+ align:start position:0%
+right ahead that folding up the little
+winglets out here is probably better you
+
+ align:start position:0%
+winglets out here is probably better you
+ 
+
+ align:start position:0%
+winglets out here is probably better you
+know for lateral stability if you make
+
+ align:start position:0%
+know for lateral stability if you make
+ 
+
+ align:start position:0%
+know for lateral stability if you make
+such judgments you'll get even better
+
+ align:start position:0%
+such judgments you'll get even better
+ 
+
+ align:start position:0%
+such judgments you'll get even better
+results
+
+ align:start position:0%
+results
+ 
+
+ align:start position:0%
+results
+and so that's what the paper airplane
+
+ align:start position:0%
+and so that's what the paper airplane
+ 
+
+ align:start position:0%
+and so that's what the paper airplane
+studies tells us so we did for such
+
+ align:start position:0%
+studies tells us so we did for such
+ 
+
+ align:start position:0%
+studies tells us so we did for such
+studies and here's an here's a point
+
+ align:start position:0%
+studies and here's an here's a point
+ 
+
+ align:start position:0%
+studies and here's an here's a point
+that I find interesting okay first of
+
+ align:start position:0%
+that I find interesting okay first of
+ 
+
+ align:start position:0%
+that I find interesting okay first of
+all if you if you're at lower error
+
+ align:start position:0%
+all if you if you're at lower error
+ 
+
+ align:start position:0%
+all if you if you're at lower error
+states what you find is that on average
+
+ align:start position:0%
+states what you find is that on average
+ 
+
+ align:start position:0%
+states what you find is that on average
+the the random approach you know
+
+ align:start position:0%
+the the random approach you know
+ 
+
+ align:start position:0%
+the the random approach you know
+starting at random starting points works
+
+ align:start position:0%
+starting at random starting points works
+ 
+
+ align:start position:0%
+starting at random starting points works
+better than the fractional factorial in
+
+ align:start position:0%
+better than the fractional factorial in
+ 
+
+ align:start position:0%
+better than the fractional factorial in
+form starting points are better than
+
+ align:start position:0%
+form starting points are better than
+ 
+
+ align:start position:0%
+form starting points are better than
+that if you raise the error high enough
+
+ align:start position:0%
+that if you raise the error high enough
+ 
+
+ align:start position:0%
+that if you raise the error high enough
+things turn around and the factorial
+
+ align:start position:0%
+things turn around and the factorial
+ 
+
+ align:start position:0%
+things turn around and the factorial
+design is a little better than the
+
+ align:start position:0%
+design is a little better than the
+ 
+
+ align:start position:0%
+design is a little better than the
+adaptive approach unless you use the
+
+ align:start position:0%
+adaptive approach unless you use the
+ 
+
+ align:start position:0%
+adaptive approach unless you use the
+informed starting point but what I think
+
+ align:start position:0%
+informed starting point but what I think
+ 
+
+ align:start position:0%
+informed starting point but what I think
+is further interesting is that if you
+
+ align:start position:0%
+is further interesting is that if you
+ 
+
+ align:start position:0%
+is further interesting is that if you
+look at the inner quartile if you look
+
+ align:start position:0%
+look at the inner quartile if you look
+ 
+
+ align:start position:0%
+look at the inner quartile if you look
+at the range of results across cases the
+
+ align:start position:0%
+at the range of results across cases the
+ 
+
+ align:start position:0%
+at the range of results across cases the
+adaptive procedure even at high error to
+
+ align:start position:0%
+adaptive procedure even at high error to
+ 
+
+ align:start position:0%
+adaptive procedure even at high error to
+me that's a preferable range 51 to 87
+
+ align:start position:0%
+me that's a preferable range 51 to 87
+ 
+
+ align:start position:0%
+me that's a preferable range 51 to 87
+verses 36 to 88 I think you you actually
+
+ align:start position:0%
+verses 36 to 88 I think you you actually
+ 
+
+ align:start position:0%
+verses 36 to 88 I think you you actually
+take less risk from case to case with
+
+ align:start position:0%
+take less risk from case to case with
+ 
+
+ align:start position:0%
+take less risk from case to case with
+the adaptive method now so the the the
+
+ align:start position:0%
+the adaptive method now so the the the
+ 
+
+ align:start position:0%
+the adaptive method now so the the the
+the factorial design is optimally suited
+
+ align:start position:0%
+the factorial design is optimally suited
+ 
+
+ align:start position:0%
+the factorial design is optimally suited
+to minimize the influence of
+
+ align:start position:0%
+to minimize the influence of
+ 
+
+ align:start position:0%
+to minimize the influence of
+experimental error on your outcomes but
+
+ align:start position:0%
+experimental error on your outcomes but
+ 
+
+ align:start position:0%
+experimental error on your outcomes but
+some of the uncertainties you face an
+
+ align:start position:0%
+some of the uncertainties you face an
+ 
+
+ align:start position:0%
+some of the uncertainties you face an
+experimentation aren't that kind they're
+
+ align:start position:0%
+experimentation aren't that kind they're
+ 
+
+ align:start position:0%
+experimentation aren't that kind they're
+not experimental error they're actually
+
+ align:start position:0%
+not experimental error they're actually
+ 
+
+ align:start position:0%
+not experimental error they're actually
+uncertainties about where the
+
+ align:start position:0%
+uncertainties about where the
+ 
+
+ align:start position:0%
+uncertainties about where the
+interactions lie
+
+ align:start position:0%
+interactions lie
+ 
+
+ align:start position:0%
+interactions lie
+and in fact fractional factorial designs
+
+ align:start position:0%
+and in fact fractional factorial designs
+ 
+
+ align:start position:0%
+and in fact fractional factorial designs
+are among the most sensitive designs to
+
+ align:start position:0%
+are among the most sensitive designs to
+ 
+
+ align:start position:0%
+are among the most sensitive designs to
+that particular uncertainty because when
+
+ align:start position:0%
+that particular uncertainty because when
+ 
+
+ align:start position:0%
+that particular uncertainty because when
+you make this confounding between main
+
+ align:start position:0%
+you make this confounding between main
+ 
+
+ align:start position:0%
+you make this confounding between main
+effects and interactions it's actually
+
+ align:start position:0%
+effects and interactions it's actually
+ 
+
+ align:start position:0%
+effects and interactions it's actually
+very harmful to your outcomes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so those are the principal results that
+
+ align:start position:0%
+so those are the principal results that
+ 
+
+ align:start position:0%
+so those are the principal results that
+I meant to show you today there are a
+
+ align:start position:0%
+I meant to show you today there are a
+ 
+
+ align:start position:0%
+I meant to show you today there are a
+couple other things that have emerged
+
+ align:start position:0%
+couple other things that have emerged
+ 
+
+ align:start position:0%
+couple other things that have emerged
+more recently that I can talk about for
+
+ align:start position:0%
+more recently that I can talk about for
+ 
+
+ align:start position:0%
+more recently that I can talk about for
+example recently we've been interested
+
+ align:start position:0%
+example recently we've been interested
+ 
+
+ align:start position:0%
+example recently we've been interested
+in the idea producing ensembles now here
+
+ align:start position:0%
+in the idea producing ensembles now here
+ 
+
+ align:start position:0%
+in the idea producing ensembles now here
+the situation is that you might find
+
+ align:start position:0%
+the situation is that you might find
+ 
+
+ align:start position:0%
+the situation is that you might find
+that you have adequate budget to run a
+
+ align:start position:0%
+that you have adequate budget to run a
+ 
+
+ align:start position:0%
+that you have adequate budget to run a
+larger fractional factorial design let's
+
+ align:start position:0%
+larger fractional factorial design let's
+ 
+
+ align:start position:0%
+larger fractional factorial design let's
+say instead of a 2 to the 7 minus 4 you
+
+ align:start position:0%
+say instead of a 2 to the 7 minus 4 you
+ 
+
+ align:start position:0%
+say instead of a 2 to the 7 minus 4 you
+actually have a budget to run a much
+
+ align:start position:0%
+actually have a budget to run a much
+ 
+
+ align:start position:0%
+actually have a budget to run a much
+larger experiment 2 to 7 minus 2 so the
+
+ align:start position:0%
+larger experiment 2 to 7 minus 2 so the
+ 
+
+ align:start position:0%
+larger experiment 2 to 7 minus 2 so the
+counter-argument was from from some
+
+ align:start position:0%
+counter-argument was from from some
+ 
+
+ align:start position:0%
+counter-argument was from from some
+folks in industry was that they rarely
+
+ align:start position:0%
+folks in industry was that they rarely
+ 
+
+ align:start position:0%
+folks in industry was that they rarely
+ran resolution 3 designs they thought
+
+ align:start position:0%
+ran resolution 3 designs they thought
+ 
+
+ align:start position:0%
+ran resolution 3 designs they thought
+that that was too big a risk anyway they
+
+ align:start position:0%
+that that was too big a risk anyway they
+ 
+
+ align:start position:0%
+that that was too big a risk anyway they
+were tending to run larger experiments
+
+ align:start position:0%
+were tending to run larger experiments
+ 
+
+ align:start position:0%
+were tending to run larger experiments
+such as to the 7-2 higher resolution
+
+ align:start position:0%
+such as to the 7-2 higher resolution
+ 
+
+ align:start position:0%
+such as to the 7-2 higher resolution
+fractional factorial designs and they
+
+ align:start position:0%
+fractional factorial designs and they
+ 
+
+ align:start position:0%
+fractional factorial designs and they
+said so because of that I don't think we
+
+ align:start position:0%
+said so because of that I don't think we
+ 
+
+ align:start position:0%
+said so because of that I don't think we
+should do the adaptive effect and we
+
+ align:start position:0%
+should do the adaptive effect and we
+ 
+
+ align:start position:0%
+should do the adaptive effect and we
+were interested in that condition that
+
+ align:start position:0%
+were interested in that condition that
+ 
+
+ align:start position:0%
+were interested in that condition that
+issue it turns out that if you take the
+
+ align:start position:0%
+issue it turns out that if you take the
+ 
+
+ align:start position:0%
+issue it turns out that if you take the
+same budget that it takes to do to the 2
+
+ align:start position:0%
+same budget that it takes to do to the 2
+ 
+
+ align:start position:0%
+same budget that it takes to do to the 2
+to 7 minus 2 you would be able to run
+
+ align:start position:0%
+to 7 minus 2 you would be able to run
+ 
+
+ align:start position:0%
+to 7 minus 2 you would be able to run
+for ofat now if you do that if you
+
+ align:start position:0%
+for ofat now if you do that if you
+ 
+
+ align:start position:0%
+for ofat now if you do that if you
+choose 4 different starting points and 4
+
+ align:start position:0%
+choose 4 different starting points and 4
+ 
+
+ align:start position:0%
+choose 4 different starting points and 4
+different orderings of the factors and
+
+ align:start position:0%
+different orderings of the factors and
+ 
+
+ align:start position:0%
+different orderings of the factors and
+run for ofat and then take those results
+
+ align:start position:0%
+run for ofat and then take those results
+ 
+
+ align:start position:0%
+run for ofat and then take those results
+and make it ensemble of them and for
+
+ align:start position:0%
+and make it ensemble of them and for
+ 
+
+ align:start position:0%
+and make it ensemble of them and for
+example a simple thing you could do is
+
+ align:start position:0%
+example a simple thing you could do is
+ 
+
+ align:start position:0%
+example a simple thing you could do is
+just pick the best of the four again the
+
+ align:start position:0%
+just pick the best of the four again the
+ 
+
+ align:start position:0%
+just pick the best of the four again the
+ensemble would produce a better result
+
+ align:start position:0%
+ensemble would produce a better result
+ 
+
+ align:start position:0%
+ensemble would produce a better result
+than the fractional factorial design and
+
+ align:start position:0%
+than the fractional factorial design and
+ 
+
+ align:start position:0%
+than the fractional factorial design and
+then the interesting thing we find about
+
+ align:start position:0%
+then the interesting thing we find about
+ 
+
+ align:start position:0%
+then the interesting thing we find about
+it is remember before when you increase
+
+ align:start position:0%
+it is remember before when you increase
+ 
+
+ align:start position:0%
+it is remember before when you increase
+experimental error you expect the ofat
+
+ align:start position:0%
+experimental error you expect the ofat
+ 
+
+ align:start position:0%
+experimental error you expect the ofat
+to eventually degrade in performance and
+
+ align:start position:0%
+to eventually degrade in performance and
+ 
+
+ align:start position:0%
+to eventually degrade in performance and
+to cross with the fractional factorial
+
+ align:start position:0%
+to cross with the fractional factorial
+ 
+
+ align:start position:0%
+to cross with the fractional factorial
+so now the issue is how much
+
+ align:start position:0%
+so now the issue is how much
+ 
+
+ align:start position:0%
+so now the issue is how much
+experimental error can I endure before
+
+ align:start position:0%
+experimental error can I endure before
+ 
+
+ align:start position:0%
+experimental error can I endure before
+the adaptive experiment is no longer
+
+ align:start position:0%
+the adaptive experiment is no longer
+ 
+
+ align:start position:0%
+the adaptive experiment is no longer
+recommended with the ensemble method is
+
+ align:start position:0%
+recommended with the ensemble method is
+ 
+
+ align:start position:0%
+recommended with the ensemble method is
+actually the opposite way as you
+
+ align:start position:0%
+actually the opposite way as you
+ 
+
+ align:start position:0%
+actually the opposite way as you
+increase experimental error eventually
+
+ align:start position:0%
+increase experimental error eventually
+ 
+
+ align:start position:0%
+increase experimental error eventually
+the ensemble the distance between the
+
+ align:start position:0%
+the ensemble the distance between the
+ 
+
+ align:start position:0%
+the ensemble the distance between the
+ensemble and the fractional
+
+ align:start position:0%
+ensemble and the fractional
+ 
+
+ align:start position:0%
+ensemble and the fractional
+factorial increases so the ensemble
+
+ align:start position:0%
+factorial increases so the ensemble
+ 
+
+ align:start position:0%
+factorial increases so the ensemble
+method by itself is providing a kind of
+
+ align:start position:0%
+method by itself is providing a kind of
+ 
+
+ align:start position:0%
+method by itself is providing a kind of
+robustness to experimental error and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've been able to address another one
+
+ align:start position:0%
+we've been able to address another one
+ 
+
+ align:start position:0%
+we've been able to address another one
+of the counter points to the adaptive
+
+ align:start position:0%
+of the counter points to the adaptive
+ 
+
+ align:start position:0%
+of the counter points to the adaptive
+experimentation idea that in those cases
+
+ align:start position:0%
+experimentation idea that in those cases
+ 
+
+ align:start position:0%
+experimentation idea that in those cases
+where experimental budgets are higher
+
+ align:start position:0%
+where experimental budgets are higher
+ 
+
+ align:start position:0%
+where experimental budgets are higher
+you might still want to run these the
+
+ align:start position:0%
+you might still want to run these the
+ 
+
+ align:start position:0%
+you might still want to run these the
+other benefit of the ensembles that
+
+ align:start position:0%
+other benefit of the ensembles that
+ 
+
+ align:start position:0%
+other benefit of the ensembles that
+we've been able to show in another paper
+
+ align:start position:0%
+we've been able to show in another paper
+ 
+
+ align:start position:0%
+we've been able to show in another paper
+I didn't put some slides in but I want
+
+ align:start position:0%
+I didn't put some slides in but I want
+ 
+
+ align:start position:0%
+I didn't put some slides in but I want
+to tell you a little bit about it unless
+
+ align:start position:0%
+to tell you a little bit about it unless
+ 
+
+ align:start position:0%
+to tell you a little bit about it unless
+you have a question maybe I'll take your
+
+ align:start position:0%
+you have a question maybe I'll take your
+ 
+
+ align:start position:0%
+you have a question maybe I'll take your
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's right ya know so you make a
+
+ align:start position:0%
+yeah that's right ya know so you make a
+ 
+
+ align:start position:0%
+yeah that's right ya know so you make a
+good point for example we know in
+
+ align:start position:0%
+good point for example we know in
+ 
+
+ align:start position:0%
+good point for example we know in
+agriculture you want to run 64 different
+
+ align:start position:0%
+agriculture you want to run 64 different
+ 
+
+ align:start position:0%
+agriculture you want to run 64 different
+treatment conditions and it takes a
+
+ align:start position:0%
+treatment conditions and it takes a
+ 
+
+ align:start position:0%
+treatment conditions and it takes a
+season to get your results so you want
+
+ align:start position:0%
+season to get your results so you want
+ 
+
+ align:start position:0%
+season to get your results so you want
+to run them in parallel it's important
+
+ align:start position:0%
+to run them in parallel it's important
+ 
+
+ align:start position:0%
+to run them in parallel it's important
+to run experiments in parallel in
+
+ align:start position:0%
+to run experiments in parallel in
+ 
+
+ align:start position:0%
+to run experiments in parallel in
+agriculture and in agricultural
+
+ align:start position:0%
+agriculture and in agricultural
+ 
+
+ align:start position:0%
+agriculture and in agricultural
+equipment it's exactly the opposite so
+
+ align:start position:0%
+equipment it's exactly the opposite so
+ 
+
+ align:start position:0%
+equipment it's exactly the opposite so
+what happens is you're trying to develop
+
+ align:start position:0%
+what happens is you're trying to develop
+ 
+
+ align:start position:0%
+what happens is you're trying to develop
+the next generation of tractor and what
+
+ align:start position:0%
+the next generation of tractor and what
+ 
+
+ align:start position:0%
+the next generation of tractor and what
+they do is they take the last generation
+
+ align:start position:0%
+they do is they take the last generation
+ 
+
+ align:start position:0%
+they do is they take the last generation
+of tractor that they built and they use
+
+ align:start position:0%
+of tractor that they built and they use
+ 
+
+ align:start position:0%
+of tractor that they built and they use
+that as what they call a mule and the
+
+ align:start position:0%
+that as what they call a mule and the
+ 
+
+ align:start position:0%
+that as what they call a mule and the
+automotive industry uses the same term
+
+ align:start position:0%
+automotive industry uses the same term
+ 
+
+ align:start position:0%
+automotive industry uses the same term
+you know you're making the next Taurus
+
+ align:start position:0%
+you know you're making the next Taurus
+ 
+
+ align:start position:0%
+you know you're making the next Taurus
+you take the 2007 Taurus and you start
+
+ align:start position:0%
+you take the 2007 Taurus and you start
+ 
+
+ align:start position:0%
+you take the 2007 Taurus and you start
+using it
+
+ align:start position:0%
+using it
+ 
+
+ align:start position:0%
+using it
+putting additions on it new fuel
+
+ align:start position:0%
+putting additions on it new fuel
+ 
+
+ align:start position:0%
+putting additions on it new fuel
+injection new valve timing and so on you
+
+ align:start position:0%
+injection new valve timing and so on you
+ 
+
+ align:start position:0%
+injection new valve timing and so on you
+use that as a mule and when you're using
+
+ align:start position:0%
+use that as a mule and when you're using
+ 
+
+ align:start position:0%
+use that as a mule and when you're using
+articles like that in that style and you
+
+ align:start position:0%
+articles like that in that style and you
+ 
+
+ align:start position:0%
+articles like that in that style and you
+have a limited number of them actually
+
+ align:start position:0%
+have a limited number of them actually
+ 
+
+ align:start position:0%
+have a limited number of them actually
+your experiments are necessarily
+
+ align:start position:0%
+your experiments are necessarily
+ 
+
+ align:start position:0%
+your experiments are necessarily
+sequential whereas in agriculture
+
+ align:start position:0%
+sequential whereas in agriculture
+ 
+
+ align:start position:0%
+sequential whereas in agriculture
+they're necessarily parallel so I
+
+ align:start position:0%
+they're necessarily parallel so I
+ 
+
+ align:start position:0%
+they're necessarily parallel so I
+actually agree with you when you're in
+
+ align:start position:0%
+actually agree with you when you're in
+ 
+
+ align:start position:0%
+actually agree with you when you're in
+an engineering scenario and and your
+
+ align:start position:0%
+an engineering scenario and and your
+ 
+
+ align:start position:0%
+an engineering scenario and and your
+experiments are necessarily parallel it
+
+ align:start position:0%
+experiments are necessarily parallel it
+ 
+
+ align:start position:0%
+experiments are necessarily parallel it
+sometimes happens in say lithography you
+
+ align:start position:0%
+sometimes happens in say lithography you
+ 
+
+ align:start position:0%
+sometimes happens in say lithography you
+know you're gonna you're gonna you're
+
+ align:start position:0%
+know you're gonna you're gonna you're
+ 
+
+ align:start position:0%
+know you're gonna you're gonna you're
+gonna have to etch all these things all
+
+ align:start position:0%
+gonna have to etch all these things all
+ 
+
+ align:start position:0%
+gonna have to etch all these things all
+at the same time in a batch yeah that's
+
+ align:start position:0%
+at the same time in a batch yeah that's
+ 
+
+ align:start position:0%
+at the same time in a batch yeah that's
+that's a reason to do it the other way
+
+ align:start position:0%
+that's a reason to do it the other way
+ 
+
+ align:start position:0%
+that's a reason to do it the other way
+but I think more often than not we're
+
+ align:start position:0%
+but I think more often than not we're
+ 
+
+ align:start position:0%
+but I think more often than not we're
+doing our experiments necessarily
+
+ align:start position:0%
+doing our experiments necessarily
+ 
+
+ align:start position:0%
+doing our experiments necessarily
+sequentially or or maybe it's okay to do
+
+ align:start position:0%
+sequentially or or maybe it's okay to do
+ 
+
+ align:start position:0%
+sequentially or or maybe it's okay to do
+it sequentially another factor since you
+
+ align:start position:0%
+it sequentially another factor since you
+ 
+
+ align:start position:0%
+it sequentially another factor since you
+asked is the possibility of time trends
+
+ align:start position:0%
+asked is the possibility of time trends
+ 
+
+ align:start position:0%
+asked is the possibility of time trends
+and indeed when you do adaptive
+
+ align:start position:0%
+and indeed when you do adaptive
+ 
+
+ align:start position:0%
+and indeed when you do adaptive
+experimentation you are necessarily
+
+ align:start position:0%
+experimentation you are necessarily
+ 
+
+ align:start position:0%
+experimentation you are necessarily
+making restrictions on randomization
+
+ align:start position:0%
+making restrictions on randomization
+ 
+
+ align:start position:0%
+making restrictions on randomization
+right so let's say that you're your
+
+ align:start position:0%
+right so let's say that you're your
+ 
+
+ align:start position:0%
+right so let's say that you're your
+measuring apparatus is drifting over
+
+ align:start position:0%
+measuring apparatus is drifting over
+ 
+
+ align:start position:0%
+measuring apparatus is drifting over
+time let's say it's drifting
+
+ align:start position:0%
+time let's say it's drifting
+ 
+
+ align:start position:0%
+time let's say it's drifting
+toward making all your results look
+
+ align:start position:0%
+toward making all your results look
+ 
+
+ align:start position:0%
+toward making all your results look
+worse you know
+
+ align:start position:0%
+worse you know
+ 
+
+ align:start position:0%
+worse you know
+that would give you somewhat of a bias
+
+ align:start position:0%
+that would give you somewhat of a bias
+ 
+
+ align:start position:0%
+that would give you somewhat of a bias
+toward your starting points as a port as
+
+ align:start position:0%
+toward your starting points as a port as
+ 
+
+ align:start position:0%
+toward your starting points as a port as
+opposed to all the leader changes as
+
+ align:start position:0%
+opposed to all the leader changes as
+ 
+
+ align:start position:0%
+opposed to all the leader changes as
+best we can tell actually the the
+
+ align:start position:0%
+best we can tell actually the the
+ 
+
+ align:start position:0%
+best we can tell actually the the
+adaptive procedure is not so
+
+ align:start position:0%
+adaptive procedure is not so
+ 
+
+ align:start position:0%
+adaptive procedure is not so
+hypersensitive to those time trends they
+
+ align:start position:0%
+hypersensitive to those time trends they
+ 
+
+ align:start position:0%
+hypersensitive to those time trends they
+reflect themselves some degree as if
+
+ align:start position:0%
+reflect themselves some degree as if
+ 
+
+ align:start position:0%
+reflect themselves some degree as if
+they were additional experimental error
+
+ align:start position:0%
+they were additional experimental error
+ 
+
+ align:start position:0%
+they were additional experimental error
+but if you randomized the starting
+
+ align:start position:0%
+but if you randomized the starting
+ 
+
+ align:start position:0%
+but if you randomized the starting
+points anyway and the order of factors I
+
+ align:start position:0%
+points anyway and the order of factors I
+ 
+
+ align:start position:0%
+points anyway and the order of factors I
+don't think it's worse than experimental
+
+ align:start position:0%
+don't think it's worse than experimental
+ 
+
+ align:start position:0%
+don't think it's worse than experimental
+error because you're not interested in
+
+ align:start position:0%
+error because you're not interested in
+ 
+
+ align:start position:0%
+error because you're not interested in
+factor effects in the end anyway that
+
+ align:start position:0%
+factor effects in the end anyway that
+ 
+
+ align:start position:0%
+factor effects in the end anyway that
+this is this is the probably the biggest
+
+ align:start position:0%
+this is this is the probably the biggest
+ 
+
+ align:start position:0%
+this is this is the probably the biggest
+concern I think with the method as I'm
+
+ align:start position:0%
+concern I think with the method as I'm
+ 
+
+ align:start position:0%
+concern I think with the method as I'm
+describing it the biggest issue is
+
+ align:start position:0%
+describing it the biggest issue is
+ 
+
+ align:start position:0%
+describing it the biggest issue is
+you're making an explicit trade-off to
+
+ align:start position:0%
+you're making an explicit trade-off to
+ 
+
+ align:start position:0%
+you're making an explicit trade-off to
+say what I'm interested in doing in this
+
+ align:start position:0%
+say what I'm interested in doing in this
+ 
+
+ align:start position:0%
+say what I'm interested in doing in this
+case is getting some improvement and I'm
+
+ align:start position:0%
+case is getting some improvement and I'm
+ 
+
+ align:start position:0%
+case is getting some improvement and I'm
+willing to make a change in my
+
+ align:start position:0%
+willing to make a change in my
+ 
+
+ align:start position:0%
+willing to make a change in my
+experimental procedure that will give me
+
+ align:start position:0%
+experimental procedure that will give me
+ 
+
+ align:start position:0%
+experimental procedure that will give me
+somewhat less knowledge about why I got
+
+ align:start position:0%
+somewhat less knowledge about why I got
+ 
+
+ align:start position:0%
+somewhat less knowledge about why I got
+the improvement now if you are you know
+
+ align:start position:0%
+the improvement now if you are you know
+ 
+
+ align:start position:0%
+the improvement now if you are you know
+at Ford and you've got three months to
+
+ align:start position:0%
+at Ford and you've got three months to
+ 
+
+ align:start position:0%
+at Ford and you've got three months to
+product release and you you need to meet
+
+ align:start position:0%
+product release and you you need to meet
+ 
+
+ align:start position:0%
+product release and you you need to meet
+your emission standards and the goal is
+
+ align:start position:0%
+your emission standards and the goal is
+ 
+
+ align:start position:0%
+your emission standards and the goal is
+to reduce carbon monoxide in those three
+
+ align:start position:0%
+to reduce carbon monoxide in those three
+ 
+
+ align:start position:0%
+to reduce carbon monoxide in those three
+months and you think the learning that
+
+ align:start position:0%
+months and you think the learning that
+ 
+
+ align:start position:0%
+months and you think the learning that
+you're going to gain about this
+
+ align:start position:0%
+you're going to gain about this
+ 
+
+ align:start position:0%
+you're going to gain about this
+particular engine and its configuration
+
+ align:start position:0%
+particular engine and its configuration
+ 
+
+ align:start position:0%
+particular engine and its configuration
+is not likely to be reusable on the next
+
+ align:start position:0%
+is not likely to be reusable on the next
+ 
+
+ align:start position:0%
+is not likely to be reusable on the next
+one then in that case I think the
+
+ align:start position:0%
+one then in that case I think the
+ 
+
+ align:start position:0%
+one then in that case I think the
+adaptive method makes sense if instead
+
+ align:start position:0%
+adaptive method makes sense if instead
+ 
+
+ align:start position:0%
+adaptive method makes sense if instead
+you think the primary value of your
+
+ align:start position:0%
+you think the primary value of your
+ 
+
+ align:start position:0%
+you think the primary value of your
+experiment is archival right you're
+
+ align:start position:0%
+experiment is archival right you're
+ 
+
+ align:start position:0%
+experiment is archival right you're
+doing the experiment you're going to
+
+ align:start position:0%
+doing the experiment you're going to
+ 
+
+ align:start position:0%
+doing the experiment you're going to
+take the results you're going to make
+
+ align:start position:0%
+take the results you're going to make
+ 
+
+ align:start position:0%
+take the results you're going to make
+them available to all Ford engineers and
+
+ align:start position:0%
+them available to all Ford engineers and
+ 
+
+ align:start position:0%
+them available to all Ford engineers and
+you're going to benefit on the next
+
+ align:start position:0%
+you're going to benefit on the next
+ 
+
+ align:start position:0%
+you're going to benefit on the next
+model and the next model then yeah you
+
+ align:start position:0%
+model and the next model then yeah you
+ 
+
+ align:start position:0%
+model and the next model then yeah you
+probably ought to arrange the
+
+ align:start position:0%
+probably ought to arrange the
+ 
+
+ align:start position:0%
+probably ought to arrange the
+experiments so that you you get the
+
+ align:start position:0%
+experiments so that you you get the
+ 
+
+ align:start position:0%
+experiments so that you you get the
+highest precision of effect estimation
+
+ align:start position:0%
+highest precision of effect estimation
+ 
+
+ align:start position:0%
+highest precision of effect estimation
+the highest validity of inference that's
+
+ align:start position:0%
+the highest validity of inference that's
+ 
+
+ align:start position:0%
+the highest validity of inference that's
+design of experiments factorial design
+
+ align:start position:0%
+design of experiments factorial design
+ 
+
+ align:start position:0%
+design of experiments factorial design
+of experiments but we had an interesting
+
+ align:start position:0%
+of experiments but we had an interesting
+ 
+
+ align:start position:0%
+of experiments but we had an interesting
+learning along the way
+
+ align:start position:0%
+learning along the way
+ 
+
+ align:start position:0%
+learning along the way
+that is to do our big meta studies where
+
+ align:start position:0%
+that is to do our big meta studies where
+ 
+
+ align:start position:0%
+that is to do our big meta studies where
+we're trying to decide how bigger
+
+ align:start position:0%
+we're trying to decide how bigger
+ 
+
+ align:start position:0%
+we're trying to decide how bigger
+interactions when do they occur we went
+
+ align:start position:0%
+interactions when do they occur we went
+ 
+
+ align:start position:0%
+interactions when do they occur we went
+into Ford's databases they had run lots
+
+ align:start position:0%
+into Ford's databases they had run lots
+ 
+
+ align:start position:0%
+into Ford's databases they had run lots
+of experiments in the past and they had
+
+ align:start position:0%
+of experiments in the past and they had
+ 
+
+ align:start position:0%
+of experiments in the past and they had
+them in some kind of company database
+
+ align:start position:0%
+them in some kind of company database
+ 
+
+ align:start position:0%
+them in some kind of company database
+and we were drawing these datasets out
+
+ align:start position:0%
+and we were drawing these datasets out
+ 
+
+ align:start position:0%
+and we were drawing these datasets out
+to put them into one of our studies and
+
+ align:start position:0%
+to put them into one of our studies and
+ 
+
+ align:start position:0%
+to put them into one of our studies and
+very frequently we go through the table
+
+ align:start position:0%
+very frequently we go through the table
+ 
+
+ align:start position:0%
+very frequently we go through the table
+and there was some ambiguity in our
+
+ align:start position:0%
+and there was some ambiguity in our
+ 
+
+ align:start position:0%
+and there was some ambiguity in our
+minds some maybe you know there was a
+
+ align:start position:0%
+minds some maybe you know there was a
+ 
+
+ align:start position:0%
+minds some maybe you know there was a
+plus in in the experimental matrix where
+
+ align:start position:0%
+plus in in the experimental matrix where
+ 
+
+ align:start position:0%
+plus in in the experimental matrix where
+we thought there should have been a
+
+ align:start position:0%
+we thought there should have been a
+ 
+
+ align:start position:0%
+we thought there should have been a
+minus or there's some question and in
+
+ align:start position:0%
+minus or there's some question and in
+ 
+
+ align:start position:0%
+minus or there's some question and in
+those cases we would go track the person
+
+ align:start position:0%
+those cases we would go track the person
+ 
+
+ align:start position:0%
+those cases we would go track the person
+down and ask them what they meant and in
+
+ align:start position:0%
+down and ask them what they meant and in
+ 
+
+ align:start position:0%
+down and ask them what they meant and in
+almost every case that person would say
+
+ align:start position:0%
+almost every case that person would say
+ 
+
+ align:start position:0%
+almost every case that person would say
+huh you're the first person who ever
+
+ align:start position:0%
+huh you're the first person who ever
+ 
+
+ align:start position:0%
+huh you're the first person who ever
+called me about my experiment they'd put
+
+ align:start position:0%
+called me about my experiment they'd put
+ 
+
+ align:start position:0%
+called me about my experiment they'd put
+it in the database and no one was using
+
+ align:start position:0%
+it in the database and no one was using
+ 
+
+ align:start position:0%
+it in the database and no one was using
+it we were the first ones to just to go
+
+ align:start position:0%
+it we were the first ones to just to go
+ 
+
+ align:start position:0%
+it we were the first ones to just to go
+back in and use it so we are not so sang
+
+ align:start position:0%
+back in and use it so we are not so sang
+ 
+
+ align:start position:0%
+back in and use it so we are not so sang
+whine about the prospects of people
+
+ align:start position:0%
+whine about the prospects of people
+ 
+
+ align:start position:0%
+whine about the prospects of people
+reusing experimental data at least so
+
+ align:start position:0%
+reusing experimental data at least so
+ 
+
+ align:start position:0%
+reusing experimental data at least so
+far as you know industrial day-to-day
+
+ align:start position:0%
+far as you know industrial day-to-day
+ 
+
+ align:start position:0%
+far as you know industrial day-to-day
+experimentation is concerned most often
+
+ align:start position:0%
+experimentation is concerned most often
+ 
+
+ align:start position:0%
+experimentation is concerned most often
+those experiments serve their purposes
+
+ align:start position:0%
+those experiments serve their purposes
+ 
+
+ align:start position:0%
+those experiments serve their purposes
+at the time and then they're gone for
+
+ align:start position:0%
+at the time and then they're gone for
+ 
+
+ align:start position:0%
+at the time and then they're gone for
+practical purpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess it is yeah
+
+ align:start position:0%
+I guess it is yeah
+ 
+
+ align:start position:0%
+I guess it is yeah
+and in fact I I never formally tried to
+
+ align:start position:0%
+and in fact I I never formally tried to
+ 
+
+ align:start position:0%
+and in fact I I never formally tried to
+study this but if you if you back off a
+
+ align:start position:0%
+study this but if you if you back off a
+ 
+
+ align:start position:0%
+study this but if you if you back off a
+little bit from our structure and apply
+
+ align:start position:0%
+little bit from our structure and apply
+ 
+
+ align:start position:0%
+little bit from our structure and apply
+some different structure went one that
+
+ align:start position:0%
+some different structure went one that
+ 
+
+ align:start position:0%
+some different structure went one that
+suits your circumstances it's it's
+
+ align:start position:0%
+suits your circumstances it's it's
+ 
+
+ align:start position:0%
+suits your circumstances it's it's
+probably still pretty good it might even
+
+ align:start position:0%
+probably still pretty good it might even
+ 
+
+ align:start position:0%
+probably still pretty good it might even
+be better the the the the bigger point
+
+ align:start position:0%
+be better the the the the bigger point
+ 
+
+ align:start position:0%
+be better the the the the bigger point
+is that you're doing adaptation as you
+
+ align:start position:0%
+is that you're doing adaptation as you
+ 
+
+ align:start position:0%
+is that you're doing adaptation as you
+go and I have been asked the same
+
+ align:start position:0%
+go and I have been asked the same
+ 
+
+ align:start position:0%
+go and I have been asked the same
+question in fact Jeff who asked me at
+
+ align:start position:0%
+question in fact Jeff who asked me at
+ 
+
+ align:start position:0%
+question in fact Jeff who asked me at
+the last time I presented a conference
+
+ align:start position:0%
+the last time I presented a conference
+ 
+
+ align:start position:0%
+the last time I presented a conference
+heat he asked how much of this result is
+
+ align:start position:0%
+heat he asked how much of this result is
+ 
+
+ align:start position:0%
+heat he asked how much of this result is
+due to adaptation and how much is due to
+
+ align:start position:0%
+due to adaptation and how much is due to
+ 
+
+ align:start position:0%
+due to adaptation and how much is due to
+the one factor at a time part because
+
+ align:start position:0%
+the one factor at a time part because
+ 
+
+ align:start position:0%
+the one factor at a time part because
+this is both and it's a hard question to
+
+ align:start position:0%
+this is both and it's a hard question to
+ 
+
+ align:start position:0%
+this is both and it's a hard question to
+answer my sense is it's mostly
+
+ align:start position:0%
+answer my sense is it's mostly
+ 
+
+ align:start position:0%
+answer my sense is it's mostly
+adaptation on the other hand one factor
+
+ align:start position:0%
+adaptation on the other hand one factor
+ 
+
+ align:start position:0%
+adaptation on the other hand one factor
+at a time in some sense optimizes
+
+ align:start position:0%
+at a time in some sense optimizes
+ 
+
+ align:start position:0%
+at a time in some sense optimizes
+adaptation you can add you can be
+
+ align:start position:0%
+adaptation you can add you can be
+ 
+
+ align:start position:0%
+adaptation you can add you can be
+adaptive all the time with every new
+
+ align:start position:0%
+adaptive all the time with every new
+ 
+
+ align:start position:0%
+adaptive all the time with every new
+observation as much as possible so it's
+
+ align:start position:0%
+observation as much as possible so it's
+ 
+
+ align:start position:0%
+observation as much as possible so it's
+not it's not as if I can cleanly
+
+ align:start position:0%
+not it's not as if I can cleanly
+ 
+
+ align:start position:0%
+not it's not as if I can cleanly
+decompose the two contributions to the
+
+ align:start position:0%
+decompose the two contributions to the
+ 
+
+ align:start position:0%
+decompose the two contributions to the
+result but my sense is that it's mostly
+
+ align:start position:0%
+result but my sense is that it's mostly
+ 
+
+ align:start position:0%
+result but my sense is that it's mostly
+adaptation and if you're doing some
+
+ align:start position:0%
+adaptation and if you're doing some
+ 
+
+ align:start position:0%
+adaptation and if you're doing some
+other adaptive procedure especially if
+
+ align:start position:0%
+other adaptive procedure especially if
+ 
+
+ align:start position:0%
+other adaptive procedure especially if
+it's informed by some kind of prior
+
+ align:start position:0%
+it's informed by some kind of prior
+ 
+
+ align:start position:0%
+it's informed by some kind of prior
+knowledge or topical area knowledge it's
+
+ align:start position:0%
+knowledge or topical area knowledge it's
+ 
+
+ align:start position:0%
+knowledge or topical area knowledge it's
+probably a good approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'll just tell you about this one
+
+ align:start position:0%
+so I'll just tell you about this one
+ 
+
+ align:start position:0%
+so I'll just tell you about this one
+last thing okay we did an investigation
+
+ align:start position:0%
+last thing okay we did an investigation
+ 
+
+ align:start position:0%
+last thing okay we did an investigation
+about another kind of uncertainty in in
+
+ align:start position:0%
+about another kind of uncertainty in in
+ 
+
+ align:start position:0%
+about another kind of uncertainty in in
+large system so let's say that you're
+
+ align:start position:0%
+large system so let's say that you're
+ 
+
+ align:start position:0%
+large system so let's say that you're
+you're developing the next tractor or
+
+ align:start position:0%
+you're developing the next tractor or
+ 
+
+ align:start position:0%
+you're developing the next tractor or
+the next car and you think about
+
+ align:start position:0%
+the next car and you think about
+ 
+
+ align:start position:0%
+the next car and you think about
+applying some robust design to the
+
+ align:start position:0%
+applying some robust design to the
+ 
+
+ align:start position:0%
+applying some robust design to the
+system now for any reasonable scale
+
+ align:start position:0%
+system now for any reasonable scale
+ 
+
+ align:start position:0%
+system now for any reasonable scale
+product there are literally thousands of
+
+ align:start position:0%
+product there are literally thousands of
+ 
+
+ align:start position:0%
+product there are literally thousands of
+things which you could potentially apply
+
+ align:start position:0%
+things which you could potentially apply
+ 
+
+ align:start position:0%
+things which you could potentially apply
+a robust design experiment to you can
+
+ align:start position:0%
+a robust design experiment to you can
+ 
+
+ align:start position:0%
+a robust design experiment to you can
+run one on fuel injection you can run
+
+ align:start position:0%
+run one on fuel injection you can run
+ 
+
+ align:start position:0%
+run one on fuel injection you can run
+one on Carver on braking and one on
+
+ align:start position:0%
+one on Carver on braking and one on
+ 
+
+ align:start position:0%
+one on Carver on braking and one on
+environmental controls and one on
+
+ align:start position:0%
+environmental controls and one on
+ 
+
+ align:start position:0%
+environmental controls and one on
+electrical you know and just keep going
+
+ align:start position:0%
+electrical you know and just keep going
+ 
+
+ align:start position:0%
+electrical you know and just keep going
+and you're not going to do them all in
+
+ align:start position:0%
+and you're not going to do them all in
+ 
+
+ align:start position:0%
+and you're not going to do them all in
+fact I would say less than 5% of all
+
+ align:start position:0%
+fact I would say less than 5% of all
+ 
+
+ align:start position:0%
+fact I would say less than 5% of all
+opportunities to do robustness
+
+ align:start position:0%
+opportunities to do robustness
+ 
+
+ align:start position:0%
+opportunities to do robustness
+improvement work are actually executed
+
+ align:start position:0%
+improvement work are actually executed
+ 
+
+ align:start position:0%
+improvement work are actually executed
+and then the question I always ask
+
+ align:start position:0%
+and then the question I always ask
+ 
+
+ align:start position:0%
+and then the question I always ask
+myself is I wonder if let's say it's 5%
+
+ align:start position:0%
+myself is I wonder if let's say it's 5%
+ 
+
+ align:start position:0%
+myself is I wonder if let's say it's 5%
+I wonder if companies are doing the
+
+ align:start position:0%
+I wonder if companies are doing the
+ 
+
+ align:start position:0%
+I wonder if companies are doing the
+right 5% I wonder if they know where
+
+ align:start position:0%
+right 5% I wonder if they know where
+ 
+
+ align:start position:0%
+right 5% I wonder if they know where
+their biggest quality problems are now
+
+ align:start position:0%
+their biggest quality problems are now
+ 
+
+ align:start position:0%
+their biggest quality problems are now
+we know for a fact that if you look at
+
+ align:start position:0%
+we know for a fact that if you look at
+ 
+
+ align:start position:0%
+we know for a fact that if you look at
+retrospectively where there have been
+
+ align:start position:0%
+retrospectively where there have been
+ 
+
+ align:start position:0%
+retrospectively where there have been
+big quality problems if I look at Ford
+
+ align:start position:0%
+big quality problems if I look at Ford
+ 
+
+ align:start position:0%
+big quality problems if I look at Ford
+Explorer and the roll over and so on
+
+ align:start position:0%
+Explorer and the roll over and so on
+ 
+
+ align:start position:0%
+Explorer and the roll over and so on
+right I know they didn't do her a bus
+
+ align:start position:0%
+right I know they didn't do her a bus
+ 
+
+ align:start position:0%
+right I know they didn't do her a bus
+design study on tire inflation and it's
+
+ align:start position:0%
+design study on tire inflation and it's
+ 
+
+ align:start position:0%
+design study on tire inflation and it's
+delamination and rollover they didn't
+
+ align:start position:0%
+delamination and rollover they didn't
+ 
+
+ align:start position:0%
+delamination and rollover they didn't
+they didn't do it now why didn't they
+
+ align:start position:0%
+they didn't do it now why didn't they
+ 
+
+ align:start position:0%
+they didn't do it now why didn't they
+know that that was the one to do robust
+
+ align:start position:0%
+know that that was the one to do robust
+ 
+
+ align:start position:0%
+know that that was the one to do robust
+design on well they just didn't it was
+
+ align:start position:0%
+design on well they just didn't it was
+ 
+
+ align:start position:0%
+design on well they just didn't it was
+not so likely after all it wasn't
+
+ align:start position:0%
+not so likely after all it wasn't
+ 
+
+ align:start position:0%
+not so likely after all it wasn't
+happening to other SUVs so I asked
+
+ align:start position:0%
+happening to other SUVs so I asked
+ 
+
+ align:start position:0%
+happening to other SUVs so I asked
+myself if you could run a relatively
+
+ align:start position:0%
+myself if you could run a relatively
+ 
+
+ align:start position:0%
+myself if you could run a relatively
+expensive robust design study on 5%
+
+ align:start position:0%
+expensive robust design study on 5%
+ 
+
+ align:start position:0%
+expensive robust design study on 5%
+that's let's say that's the case you
+
+ align:start position:0%
+that's let's say that's the case you
+ 
+
+ align:start position:0%
+that's let's say that's the case you
+have the budget for that what if you did
+
+ align:start position:0%
+have the budget for that what if you did
+ 
+
+ align:start position:0%
+have the budget for that what if you did
+something a tenth as expensive and did
+
+ align:start position:0%
+something a tenth as expensive and did
+ 
+
+ align:start position:0%
+something a tenth as expensive and did
+on 50% of the system so we would call
+
+ align:start position:0%
+on 50% of the system so we would call
+ 
+
+ align:start position:0%
+on 50% of the system so we would call
+this idea of streamlining we know how to
+
+ align:start position:0%
+this idea of streamlining we know how to
+ 
+
+ align:start position:0%
+this idea of streamlining we know how to
+take any robust design experiment people
+
+ align:start position:0%
+take any robust design experiment people
+ 
+
+ align:start position:0%
+take any robust design experiment people
+are proposing and to do something
+
+ align:start position:0%
+are proposing and to do something
+ 
+
+ align:start position:0%
+are proposing and to do something
+little bit loose but to do it in a tenth
+
+ align:start position:0%
+little bit loose but to do it in a tenth
+ 
+
+ align:start position:0%
+little bit loose but to do it in a tenth
+of the cost and you'll get about 80% of
+
+ align:start position:0%
+of the cost and you'll get about 80% of
+ 
+
+ align:start position:0%
+of the cost and you'll get about 80% of
+the same benefit right the the trade-off
+
+ align:start position:0%
+the same benefit right the the trade-off
+ 
+
+ align:start position:0%
+the same benefit right the the trade-off
+works like it's it's a good old purrito
+
+ align:start position:0%
+works like it's it's a good old purrito
+ 
+
+ align:start position:0%
+works like it's it's a good old purrito
+80/20 sort of trade-off and we ask
+
+ align:start position:0%
+80/20 sort of trade-off and we ask
+ 
+
+ align:start position:0%
+80/20 sort of trade-off and we ask
+ourselves how that trade-off in doing
+
+ align:start position:0%
+ourselves how that trade-off in doing
+ 
+
+ align:start position:0%
+ourselves how that trade-off in doing
+relatively many relatively less perfect
+
+ align:start position:0%
+relatively many relatively less perfect
+ 
+
+ align:start position:0%
+relatively many relatively less perfect
+experiments compares to doing a few very
+
+ align:start position:0%
+experiments compares to doing a few very
+ 
+
+ align:start position:0%
+experiments compares to doing a few very
+good ones and we ask ourselves how this
+
+ align:start position:0%
+good ones and we ask ourselves how this
+ 
+
+ align:start position:0%
+good ones and we ask ourselves how this
+trade-off is affected by the likelihood
+
+ align:start position:0%
+trade-off is affected by the likelihood
+ 
+
+ align:start position:0%
+trade-off is affected by the likelihood
+of identifying the one or two biggest
+
+ align:start position:0%
+of identifying the one or two biggest
+ 
+
+ align:start position:0%
+of identifying the one or two biggest
+quality problems that you face because
+
+ align:start position:0%
+quality problems that you face because
+ 
+
+ align:start position:0%
+quality problems that you face because
+you know that rollover thing cost for it
+
+ align:start position:0%
+you know that rollover thing cost for it
+ 
+
+ align:start position:0%
+you know that rollover thing cost for it
+a lot you would pay a lot of money to
+
+ align:start position:0%
+a lot you would pay a lot of money to
+ 
+
+ align:start position:0%
+a lot you would pay a lot of money to
+avoid that one and so are the big
+
+ align:start position:0%
+avoid that one and so are the big
+ 
+
+ align:start position:0%
+avoid that one and so are the big
+conclusion of our study is you would
+
+ align:start position:0%
+conclusion of our study is you would
+ 
+
+ align:start position:0%
+conclusion of our study is you would
+have to have a pretty high probability
+
+ align:start position:0%
+have to have a pretty high probability
+ 
+
+ align:start position:0%
+have to have a pretty high probability
+of knowing exactly where your problems
+
+ align:start position:0%
+of knowing exactly where your problems
+ 
+
+ align:start position:0%
+of knowing exactly where your problems
+were in order to do it the way they do
+
+ align:start position:0%
+were in order to do it the way they do
+ 
+
+ align:start position:0%
+were in order to do it the way they do
+it now which is a relatively small
+
+ align:start position:0%
+it now which is a relatively small
+ 
+
+ align:start position:0%
+it now which is a relatively small
+number of expensive studies you'd have
+
+ align:start position:0%
+number of expensive studies you'd have
+ 
+
+ align:start position:0%
+number of expensive studies you'd have
+to know like 95% certainty where your
+
+ align:start position:0%
+to know like 95% certainty where your
+ 
+
+ align:start position:0%
+to know like 95% certainty where your
+biggest quality problem is if you are at
+
+ align:start position:0%
+biggest quality problem is if you are at
+ 
+
+ align:start position:0%
+biggest quality problem is if you are at
+least a little uncertain if you think
+
+ align:start position:0%
+least a little uncertain if you think
+ 
+
+ align:start position:0%
+least a little uncertain if you think
+you're only 70% sure where your problems
+
+ align:start position:0%
+you're only 70% sure where your problems
+ 
+
+ align:start position:0%
+you're only 70% sure where your problems
+lie scale them all back by a factor of
+
+ align:start position:0%
+lie scale them all back by a factor of
+ 
+
+ align:start position:0%
+lie scale them all back by a factor of
+10 and do 10 times as many you'll be
+
+ align:start position:0%
+10 and do 10 times as many you'll be
+ 
+
+ align:start position:0%
+10 and do 10 times as many you'll be
+much better off that's my view and we
+
+ align:start position:0%
+much better off that's my view and we
+ 
+
+ align:start position:0%
+much better off that's my view and we
+didn't have to make so many assumptions
+
+ align:start position:0%
+didn't have to make so many assumptions
+ 
+
+ align:start position:0%
+didn't have to make so many assumptions
+to come to this conclusion people's
+
+ align:start position:0%
+to come to this conclusion people's
+ 
+
+ align:start position:0%
+to come to this conclusion people's
+uncertainty about where their biggest
+
+ align:start position:0%
+uncertainty about where their biggest
+ 
+
+ align:start position:0%
+uncertainty about where their biggest
+issues lie are bigger than they think
+
+ align:start position:0%
+issues lie are bigger than they think
+ 
+
+ align:start position:0%
+issues lie are bigger than they think
+and therefore they need to get sort of
+
+ align:start position:0%
+and therefore they need to get sort of
+ 
+
+ align:start position:0%
+and therefore they need to get sort of
+democratized these kind of processes
+
+ align:start position:0%
+democratized these kind of processes
+ 
+
+ align:start position:0%
+democratized these kind of processes
+it's not that you have to do them very
+
+ align:start position:0%
+it's not that you have to do them very
+ 
+
+ align:start position:0%
+it's not that you have to do them very
+very well in a few cases what you need
+
+ align:start position:0%
+very well in a few cases what you need
+ 
+
+ align:start position:0%
+very well in a few cases what you need
+to do is make sure every engineer knows
+
+ align:start position:0%
+to do is make sure every engineer knows
+ 
+
+ align:start position:0%
+to do is make sure every engineer knows
+how to do this kind of thing and that
+
+ align:start position:0%
+how to do this kind of thing and that
+ 
+
+ align:start position:0%
+how to do this kind of thing and that
+they're doing it to almost everything at
+
+ align:start position:0%
+they're doing it to almost everything at
+ 
+
+ align:start position:0%
+they're doing it to almost everything at
+least almost everything that that for
+
+ align:start position:0%
+least almost everything that that for
+ 
+
+ align:start position:0%
+least almost everything that that for
+example is not proven in the field
+
+ align:start position:0%
+example is not proven in the field
+ 
+
+ align:start position:0%
+example is not proven in the field
+already I mean you don't need to do it
+
+ align:start position:0%
+already I mean you don't need to do it
+ 
+
+ align:start position:0%
+already I mean you don't need to do it
+on the alternator because you use that
+
+ align:start position:0%
+on the alternator because you use that
+ 
+
+ align:start position:0%
+on the alternator because you use that
+same alternator on the last three models
+
+ align:start position:0%
+same alternator on the last three models
+ 
+
+ align:start position:0%
+same alternator on the last three models
+and it's fine but for anything that's
+
+ align:start position:0%
+and it's fine but for anything that's
+ 
+
+ align:start position:0%
+and it's fine but for anything that's
+relatively new you need to be doing some
+
+ align:start position:0%
+relatively new you need to be doing some
+ 
+
+ align:start position:0%
+relatively new you need to be doing some
+of this robustness refinement
+
+ align:start position:0%
+of this robustness refinement
+ 
+
+ align:start position:0%
+of this robustness refinement
+and even if you do just a few
+
+ align:start position:0%
+and even if you do just a few
+ 
+
+ align:start position:0%
+and even if you do just a few
+experiments exposing your systems to up
+
+ align:start position:0%
+experiments exposing your systems to up
+ 
+
+ align:start position:0%
+experiments exposing your systems to up
+to harsh conditions making changes
+
+ align:start position:0%
+to harsh conditions making changes
+ 
+
+ align:start position:0%
+to harsh conditions making changes
+making improvements on the basis of what
+
+ align:start position:0%
+making improvements on the basis of what
+ 
+
+ align:start position:0%
+making improvements on the basis of what
+that reveals that's the key thing not so
+
+ align:start position:0%
+that reveals that's the key thing not so
+ 
+
+ align:start position:0%
+that reveals that's the key thing not so
+much the finesse you apply and anyway
+
+ align:start position:0%
+much the finesse you apply and anyway
+ 
+
+ align:start position:0%
+much the finesse you apply and anyway
+that's the conclusion we came to so far
+
+ align:start position:0%
+that's the conclusion we came to so far
+ 
+
+ align:start position:0%
+that's the conclusion we came to so far
+due to this research so our main
+
+ align:start position:0%
+due to this research so our main
+ 
+
+ align:start position:0%
+due to this research so our main
+conclusions are that we we can show
+
+ align:start position:0%
+conclusions are that we we can show
+ 
+
+ align:start position:0%
+conclusions are that we we can show
+through empirical work and through
+
+ align:start position:0%
+through empirical work and through
+ 
+
+ align:start position:0%
+through empirical work and through
+theorems that this adaptive procedure
+
+ align:start position:0%
+theorems that this adaptive procedure
+ 
+
+ align:start position:0%
+theorems that this adaptive procedure
+gives benefits you get a long way toward
+
+ align:start position:0%
+gives benefits you get a long way toward
+ 
+
+ align:start position:0%
+gives benefits you get a long way toward
+your results that are desired
+
+ align:start position:0%
+your results that are desired
+ 
+
+ align:start position:0%
+your results that are desired
+especially when interactions are not so
+
+ align:start position:0%
+especially when interactions are not so
+ 
+
+ align:start position:0%
+especially when interactions are not so
+small and that you can cross these
+
+ align:start position:0%
+small and that you can cross these
+ 
+
+ align:start position:0%
+small and that you can cross these
+adaptive experiments with fractional
+
+ align:start position:0%
+adaptive experiments with fractional
+ 
+
+ align:start position:0%
+adaptive experiments with fractional
+factorial designs to use them for
+
+ align:start position:0%
+factorial designs to use them for
+ 
+
+ align:start position:0%
+factorial designs to use them for
+robustness and it seems to work pretty
+
+ align:start position:0%
+robustness and it seems to work pretty
+ 
+
+ align:start position:0%
+robustness and it seems to work pretty
+well now I think I'm pretty much out of
+
+ align:start position:0%
+well now I think I'm pretty much out of
+ 
+
+ align:start position:0%
+well now I think I'm pretty much out of
+time now if you if you all have ideas
+
+ align:start position:0%
+time now if you if you all have ideas
+ 
+
+ align:start position:0%
+time now if you if you all have ideas
+for your case studies I'm always
+
+ align:start position:0%
+for your case studies I'm always
+ 
+
+ align:start position:0%
+for your case studies I'm always
+interested in head-to-head comparisons
+
+ align:start position:0%
+interested in head-to-head comparisons
+ 
+
+ align:start position:0%
+interested in head-to-head comparisons
+of experimental designs being done in
+
+ align:start position:0%
+of experimental designs being done in
+ 
+
+ align:start position:0%
+of experimental designs being done in
+companies and the adaptive procedures
+
+ align:start position:0%
+companies and the adaptive procedures
+ 
+
+ align:start position:0%
+companies and the adaptive procedures
+that I'm talking about now so I if
+
+ align:start position:0%
+that I'm talking about now so I if
+ 
+
+ align:start position:0%
+that I'm talking about now so I if
+you're interested in doing such things
+
+ align:start position:0%
+you're interested in doing such things
+ 
+
+ align:start position:0%
+you're interested in doing such things
+for your projects I'm interested in
+
+ align:start position:0%
+for your projects I'm interested in
+ 
+
+ align:start position:0%
+for your projects I'm interested in
+helping you to do that and you can see
+
+ align:start position:0%
+helping you to do that and you can see
+ 
+
+ align:start position:0%
+helping you to do that and you can see
+my email there in case you want to take
+
+ align:start position:0%
+my email there in case you want to take
+ 
+
+ align:start position:0%
+my email there in case you want to take
+me up on the offer okay all right all
+
+ align:start position:0%
+me up on the offer okay all right all
+ 
+
+ align:start position:0%
+me up on the offer okay all right all
+right good day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems that we run into quite often in
+
+ align:start position:0%
+problems that we run into quite often in
+ 
+
+ align:start position:0%
+problems that we run into quite often in
+microfabrication is that the metrology
+
+ align:start position:0%
+microfabrication is that the metrology
+ 
+
+ align:start position:0%
+microfabrication is that the metrology
+of the things that we've made takes up
+
+ align:start position:0%
+of the things that we've made takes up
+ 
+
+ align:start position:0%
+of the things that we've made takes up
+quite a lot of our time budgets and is
+
+ align:start position:0%
+quite a lot of our time budgets and is
+ 
+
+ align:start position:0%
+quite a lot of our time budgets and is
+quite easy to vary grammars and make
+
+ align:start position:0%
+quite easy to vary grammars and make
+ 
+
+ align:start position:0%
+quite easy to vary grammars and make
+many samples but choosing which ones to
+
+ align:start position:0%
+many samples but choosing which ones to
+ 
+
+ align:start position:0%
+many samples but choosing which ones to
+measure might be the biggest challenge
+
+ align:start position:0%
+measure might be the biggest challenge
+ 
+
+ align:start position:0%
+measure might be the biggest challenge
+and I wonder whether you've looked at
+
+ align:start position:0%
+and I wonder whether you've looked at
+ 
+
+ align:start position:0%
+and I wonder whether you've looked at
+situations whether where you know the
+
+ align:start position:0%
+situations whether where you know the
+ 
+
+ align:start position:0%
+situations whether where you know the
+the acquisition of the data lags the
+
+ align:start position:0%
+the acquisition of the data lags the
+ 
+
+ align:start position:0%
+the acquisition of the data lags the
+doing of the experiments but it's sort
+
+ align:start position:0%
+doing of the experiments but it's sort
+ 
+
+ align:start position:0%
+doing of the experiments but it's sort
+of concurrent but you can only measure a
+
+ align:start position:0%
+of concurrent but you can only measure a
+ 
+
+ align:start position:0%
+of concurrent but you can only measure a
+certain portion of the experiments you
+
+ align:start position:0%
+certain portion of the experiments you
+ 
+
+ align:start position:0%
+certain portion of the experiments you
+do you know are there more complicated
+
+ align:start position:0%
+do you know are there more complicated
+ 
+
+ align:start position:0%
+do you know are there more complicated
+situations like that where there's a
+
+ align:start position:0%
+situations like that where there's a
+ 
+
+ align:start position:0%
+situations like that where there's a
+there's a lag but it's not the case that
+
+ align:start position:0%
+there's a lag but it's not the case that
+ 
+
+ align:start position:0%
+there's a lag but it's not the case that
+you do all the experiments and then you
+
+ align:start position:0%
+you do all the experiments and then you
+ 
+
+ align:start position:0%
+you do all the experiments and then you
+do all the measurements it's an
+
+ align:start position:0%
+do all the measurements it's an
+ 
+
+ align:start position:0%
+do all the measurements it's an
+interesting question so you're saying
+
+ align:start position:0%
+interesting question so you're saying
+ 
+
+ align:start position:0%
+interesting question so you're saying
+that there you can do an experiment
+
+ align:start position:0%
+that there you can do an experiment
+ 
+
+ align:start position:0%
+that there you can do an experiment
+there's a time lag then you get an
+
+ align:start position:0%
+there's a time lag then you get an
+ 
+
+ align:start position:0%
+there's a time lag then you get an
+outcome and in some cases it's actually
+
+ align:start position:0%
+outcome and in some cases it's actually
+ 
+
+ align:start position:0%
+outcome and in some cases it's actually
+more complicated in that you get some
+
+ align:start position:0%
+more complicated in that you get some
+ 
+
+ align:start position:0%
+more complicated in that you get some
+indication right away but the more
+
+ align:start position:0%
+indication right away but the more
+ 
+
+ align:start position:0%
+indication right away but the more
+preferred measurement comes later so for
+
+ align:start position:0%
+preferred measurement comes later so for
+ 
+
+ align:start position:0%
+preferred measurement comes later so for
+example sometimes there's a categorical
+
+ align:start position:0%
+example sometimes there's a categorical
+ 
+
+ align:start position:0%
+example sometimes there's a categorical
+variable that comes immediately obvious
+
+ align:start position:0%
+variable that comes immediately obvious
+ 
+
+ align:start position:0%
+variable that comes immediately obvious
+either I heard cheddar or I didn't and
+
+ align:start position:0%
+either I heard cheddar or I didn't and
+ 
+
+ align:start position:0%
+either I heard cheddar or I didn't and
+then later I get a nice measurement of
+
+ align:start position:0%
+then later I get a nice measurement of
+ 
+
+ align:start position:0%
+then later I get a nice measurement of
+surface condition something like that
+
+ align:start position:0%
+surface condition something like that
+ 
+
+ align:start position:0%
+surface condition something like that
+well you know any of these delays tend
+
+ align:start position:0%
+well you know any of these delays tend
+ 
+
+ align:start position:0%
+well you know any of these delays tend
+away in favor of the factorial design is
+
+ align:start position:0%
+away in favor of the factorial design is
+ 
+
+ align:start position:0%
+away in favor of the factorial design is
+compared to the event you just admit
+
+ align:start position:0%
+compared to the event you just admit
+ 
+
+ align:start position:0%
+compared to the event you just admit
+that right away but then I'll say that
+
+ align:start position:0%
+that right away but then I'll say that
+ 
+
+ align:start position:0%
+that right away but then I'll say that
+you know sometimes the even with
+
+ align:start position:0%
+you know sometimes the even with
+ 
+
+ align:start position:0%
+you know sometimes the even with
+categorical variables immediately
+
+ align:start position:0%
+categorical variables immediately
+ 
+
+ align:start position:0%
+categorical variables immediately
+available perceptions you can get a lot
+
+ align:start position:0%
+available perceptions you can get a lot
+ 
+
+ align:start position:0%
+available perceptions you can get a lot
+of the benefit of adaptation from that
+
+ align:start position:0%
+of the benefit of adaptation from that
+ 
+
+ align:start position:0%
+of the benefit of adaptation from that
+yeah okay thank you very much
+
+ align:start position:0%
+yeah okay thank you very much
+ 
+
+ align:start position:0%
+yeah okay thank you very much
+anybody else so what we've arranged to
+
+ align:start position:0%
+anybody else so what we've arranged to
+ 
+
+ align:start position:0%
+anybody else so what we've arranged to
+have an extra half hour today where I
+
+ align:start position:0%
+have an extra half hour today where I
+ 
+
+ align:start position:0%
+have an extra half hour today where I
+can answer questions about problem sets
+
+ align:start position:0%
+can answer questions about problem sets
+ 
+
+ align:start position:0%
+can answer questions about problem sets
+and any questions that you might have in
+
+ align:start position:0%
+and any questions that you might have in
+ 
+
+ align:start position:0%
+and any questions that you might have in
+the run-up to the quiz so I think what
+
+ align:start position:0%
+the run-up to the quiz so I think what
+ 
+
+ align:start position:0%
+the run-up to the quiz so I think what
+we'll do is just go straight into that
+
+ align:start position:0%
+we'll do is just go straight into that
+ 
+
+ align:start position:0%
+we'll do is just go straight into that
+if people if people want to run off at
+
+ align:start position:0%
+if people if people want to run off at
+ 
+
+ align:start position:0%
+if people if people want to run off at
+this point then that's fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes so there's a few few
+
+ align:start position:0%
+yes yes so there's a few few
+ 
+
+ align:start position:0%
+yes yes so there's a few few
+housekeeping things first yes so problem
+
+ align:start position:0%
+housekeeping things first yes so problem
+ 
+
+ align:start position:0%
+housekeeping things first yes so problem
+sets I will I'll put the solutions 4 6 &
+
+ align:start position:0%
+sets I will I'll put the solutions 4 6 &
+ 
+
+ align:start position:0%
+sets I will I'll put the solutions 4 6 &
+7 up today at some point and I've I put
+
+ align:start position:0%
+7 up today at some point and I've I put
+ 
+
+ align:start position:0%
+7 up today at some point and I've I put
+the 2006 quiz 2 and solutions on the
+
+ align:start position:0%
+the 2006 quiz 2 and solutions on the
+ 
+
+ align:start position:0%
+the 2006 quiz 2 and solutions on the
+website I'm still trying to track down
+
+ align:start position:0%
+website I'm still trying to track down
+ 
+
+ align:start position:0%
+website I'm still trying to track down
+last year's quiz but hopefully that will
+
+ align:start position:0%
+last year's quiz but hopefully that will
+ 
+
+ align:start position:0%
+last year's quiz but hopefully that will
+be up today and yes for problem set 8 I
+
+ align:start position:0%
+be up today and yes for problem set 8 I
+ 
+
+ align:start position:0%
+be up today and yes for problem set 8 I
+know some people have been sending me
+
+ align:start position:0%
+know some people have been sending me
+ 
+
+ align:start position:0%
+know some people have been sending me
+questions which I'm happy to continue to
+
+ align:start position:0%
+questions which I'm happy to continue to
+ 
+
+ align:start position:0%
+questions which I'm happy to continue to
+answer by email I'll be around this
+
+ align:start position:0%
+answer by email I'll be around this
+ 
+
+ align:start position:0%
+answer by email I'll be around this
+afternoon if you want to come and speak
+
+ align:start position:0%
+afternoon if you want to come and speak
+ 
+
+ align:start position:0%
+afternoon if you want to come and speak
+to me in person and yes I lost last week
+
+ align:start position:0%
+to me in person and yes I lost last week
+ 
+
+ align:start position:0%
+to me in person and yes I lost last week
+a few people asked me for extensions I
+
+ align:start position:0%
+a few people asked me for extensions I
+ 
+
+ align:start position:0%
+a few people asked me for extensions I
+mean that's fine if you need an
+
+ align:start position:0%
+mean that's fine if you need an
+ 
+
+ align:start position:0%
+mean that's fine if you need an
+extension you can have an extension I'm
+
+ align:start position:0%
+extension you can have an extension I'm
+ 
+
+ align:start position:0%
+extension you can have an extension I'm
+not super strict about these things so
+
+ align:start position:0%
+not super strict about these things so
+ 
+
+ align:start position:0%
+not super strict about these things so
+okay so really I you know the floor is
+
+ align:start position:0%
+okay so really I you know the floor is
+ 
+
+ align:start position:0%
+okay so really I you know the floor is
+open for you to ask me things and and oh
+
+ align:start position:0%
+open for you to ask me things and and oh
+ 
+
+ align:start position:0%
+open for you to ask me things and and oh
+yes grades 6 & 7 will hopefully be done
+
+ align:start position:0%
+yes grades 6 & 7 will hopefully be done
+ 
+
+ align:start position:0%
+yes grades 6 & 7 will hopefully be done
+within the next day as well but yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I in question four on problem set eight
+
+ align:start position:0%
+I in question four on problem set eight
+ 
+
+ align:start position:0%
+I in question four on problem set eight
+we're talking about here yes yeah I I
+
+ align:start position:0%
+we're talking about here yes yeah I I
+ 
+
+ align:start position:0%
+we're talking about here yes yeah I I
+think that it's good - it's good to not
+
+ align:start position:0%
+think that it's good - it's good to not
+ 
+
+ align:start position:0%
+think that it's good - it's good to not
+include the quadratic terms in in that
+
+ align:start position:0%
+include the quadratic terms in in that
+ 
+
+ align:start position:0%
+include the quadratic terms in in that
+question although you might want to
+
+ align:start position:0%
+question although you might want to
+ 
+
+ align:start position:0%
+question although you might want to
+consider what would happen if you did an
+
+ align:start position:0%
+consider what would happen if you did an
+ 
+
+ align:start position:0%
+consider what would happen if you did an
+interaction yeah I think that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so I mean with it with this we're
+
+ align:start position:0%
+yeah so I mean with it with this we're
+ 
+
+ align:start position:0%
+yeah so I mean with it with this we're
+not really interested in quadratic
+
+ align:start position:0%
+not really interested in quadratic
+ 
+
+ align:start position:0%
+not really interested in quadratic
+factors just look at the the linear
+
+ align:start position:0%
+factors just look at the the linear
+ 
+
+ align:start position:0%
+factors just look at the the linear
+factors and the interactions okay more
+
+ align:start position:0%
+factors and the interactions okay more
+ 
+
+ align:start position:0%
+factors and the interactions okay more
+questions yeah everywhere yeah so I I
+
+ align:start position:0%
+questions yeah everywhere yeah so I I
+ 
+
+ align:start position:0%
+questions yeah everywhere yeah so I I
+wrote this question in an attempt to
+
+ align:start position:0%
+wrote this question in an attempt to
+ 
+
+ align:start position:0%
+wrote this question in an attempt to
+stretch everyone including myself so
+
+ align:start position:0%
+stretch everyone including myself so
+ 
+
+ align:start position:0%
+stretch everyone including myself so
+it's pretty it's pretty subtle I think
+
+ align:start position:0%
+it's pretty it's pretty subtle I think
+ 
+
+ align:start position:0%
+it's pretty it's pretty subtle I think
+but I would say the the right way to
+
+ align:start position:0%
+but I would say the the right way to
+ 
+
+ align:start position:0%
+but I would say the the right way to
+approach this is to is to re recast that
+
+ align:start position:0%
+approach this is to is to re recast that
+ 
+
+ align:start position:0%
+approach this is to is to re recast that
+model in terms of differences between
+
+ align:start position:0%
+model in terms of differences between
+ 
+
+ align:start position:0%
+model in terms of differences between
+the variables and the mean the mean
+
+ align:start position:0%
+the variables and the mean the mean
+ 
+
+ align:start position:0%
+the variables and the mean the mean
+input so if you have you know you have a
+
+ align:start position:0%
+input so if you have you know you have a
+ 
+
+ align:start position:0%
+input so if you have you know you have a
+set of data and those data have a a mean
+
+ align:start position:0%
+set of data and those data have a a mean
+ 
+
+ align:start position:0%
+set of data and those data have a a mean
+value for x1 and a mean value for X 2 so
+
+ align:start position:0%
+value for x1 and a mean value for X 2 so
+ 
+
+ align:start position:0%
+value for x1 and a mean value for X 2 so
+you might write some you know you might
+
+ align:start position:0%
+you might write some you know you might
+ 
+
+ align:start position:0%
+you might write some you know you might
+write it with some new coefficient a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X 2 minus X sorry X 1 bar X 2 bar and
+
+ align:start position:0%
+X 2 minus X sorry X 1 bar X 2 bar and
+ 
+
+ align:start position:0%
+X 2 minus X sorry X 1 bar X 2 bar and
+you know that that will be for some for
+
+ align:start position:0%
+you know that that will be for some for
+ 
+
+ align:start position:0%
+you know that that will be for some for
+some values of over the A's that have
+
+ align:start position:0%
+some values of over the A's that have
+ 
+
+ align:start position:0%
+some values of over the A's that have
+functions of the B's that will be that
+
+ align:start position:0%
+functions of the B's that will be that
+ 
+
+ align:start position:0%
+functions of the B's that will be that
+will be equivalent and then you know if
+
+ align:start position:0%
+will be equivalent and then you know if
+ 
+
+ align:start position:0%
+will be equivalent and then you know if
+it was just the first two terms that
+
+ align:start position:0%
+it was just the first two terms that
+ 
+
+ align:start position:0%
+it was just the first two terms that
+would be exactly the case that was that
+
+ align:start position:0%
+would be exactly the case that was that
+ 
+
+ align:start position:0%
+would be exactly the case that was that
+was derived in May in Spanos and then
+
+ align:start position:0%
+was derived in May in Spanos and then
+ 
+
+ align:start position:0%
+was derived in May in Spanos and then
+this term looks very much like this term
+
+ align:start position:0%
+this term looks very much like this term
+ 
+
+ align:start position:0%
+this term looks very much like this term
+except it's for a different variable so
+
+ align:start position:0%
+except it's for a different variable so
+ 
+
+ align:start position:0%
+except it's for a different variable so
+the standard error of that coefficient
+
+ align:start position:0%
+the standard error of that coefficient
+ 
+
+ align:start position:0%
+the standard error of that coefficient
+you can get up by the same way you got
+
+ align:start position:0%
+you can get up by the same way you got
+ 
+
+ align:start position:0%
+you can get up by the same way you got
+at this one and then if you look at this
+
+ align:start position:0%
+at this one and then if you look at this
+ 
+
+ align:start position:0%
+at this one and then if you look at this
+term well we have this coefficient here
+
+ align:start position:0%
+term well we have this coefficient here
+ 
+
+ align:start position:0%
+term well we have this coefficient here
+well if you're trying to evaluate the
+
+ align:start position:0%
+well if you're trying to evaluate the
+ 
+
+ align:start position:0%
+well if you're trying to evaluate the
+variance of Y hat you've got a product
+
+ align:start position:0%
+variance of Y hat you've got a product
+ 
+
+ align:start position:0%
+variance of Y hat you've got a product
+of two quantities you have an expression
+
+ align:start position:0%
+of two quantities you have an expression
+ 
+
+ align:start position:0%
+of two quantities you have an expression
+for the variance of a 1-1 which you're
+
+ align:start position:0%
+for the variance of a 1-1 which you're
+ 
+
+ align:start position:0%
+for the variance of a 1-1 which you're
+going to get at in a similar way to how
+
+ align:start position:0%
+going to get at in a similar way to how
+ 
+
+ align:start position:0%
+going to get at in a similar way to how
+you get at the expressions for these
+
+ align:start position:0%
+you get at the expressions for these
+ 
+
+ align:start position:0%
+you get at the expressions for these
+variances and you'll see that the
+
+ align:start position:0%
+variances and you'll see that the
+ 
+
+ align:start position:0%
+variances and you'll see that the
+expression for the standard error is a
+
+ align:start position:0%
+expression for the standard error is a
+ 
+
+ align:start position:0%
+expression for the standard error is a
+function of it's going to be a function
+
+ align:start position:0%
+function of it's going to be a function
+ 
+
+ align:start position:0%
+function of it's going to be a function
+of X 1 minus X 1 bar and and you know
+
+ align:start position:0%
+of X 1 minus X 1 bar and and you know
+ 
+
+ align:start position:0%
+of X 1 minus X 1 bar and and you know
+that when you're finding the variance of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some constant times something that you
+
+ align:start position:0%
+some constant times something that you
+ 
+
+ align:start position:0%
+some constant times something that you
+know the variance of u square that
+
+ align:start position:0%
+know the variance of u square that
+ 
+
+ align:start position:0%
+know the variance of u square that
+constant multiply it by the variance of
+
+ align:start position:0%
+constant multiply it by the variance of
+ 
+
+ align:start position:0%
+constant multiply it by the variance of
+the thing that that the constant is x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh sorry yes I mean yes these are
+
+ align:start position:0%
+oh sorry yes I mean yes these are
+ 
+
+ align:start position:0%
+oh sorry yes I mean yes these are
+exactly there you go
+
+ align:start position:0%
+exactly there you go
+ 
+
+ align:start position:0%
+exactly there you go
+so I mean this is yes you're trying to
+
+ align:start position:0%
+so I mean this is yes you're trying to
+ 
+
+ align:start position:0%
+so I mean this is yes you're trying to
+find a an expression for the for the
+
+ align:start position:0%
+find a an expression for the for the
+ 
+
+ align:start position:0%
+find a an expression for the for the
+confidence interval for you know as a
+
+ align:start position:0%
+confidence interval for you know as a
+ 
+
+ align:start position:0%
+confidence interval for you know as a
+function of X 1 star and X 2 star but at
+
+ align:start position:0%
+function of X 1 star and X 2 star but at
+ 
+
+ align:start position:0%
+function of X 1 star and X 2 star but at
+a given at a given combination of X 1
+
+ align:start position:0%
+a given at a given combination of X 1
+ 
+
+ align:start position:0%
+a given at a given combination of X 1
+star and X 2 star this is the thing that
+
+ align:start position:0%
+star and X 2 star this is the thing that
+ 
+
+ align:start position:0%
+star and X 2 star this is the thing that
+has variance and this for a fixed X 1
+
+ align:start position:0%
+has variance and this for a fixed X 1
+ 
+
+ align:start position:0%
+has variance and this for a fixed X 1
+star is a constant so you know it I
+
+ align:start position:0%
+star is a constant so you know it I
+ 
+
+ align:start position:0%
+star is a constant so you know it I
+don't wanna give too much away but sir I
+
+ align:start position:0%
+don't wanna give too much away but sir I
+ 
+
+ align:start position:0%
+don't wanna give too much away but sir I
+I think this is the right way there may
+
+ align:start position:0%
+I think this is the right way there may
+ 
+
+ align:start position:0%
+I think this is the right way there may
+be some subtleties that escape me so if
+
+ align:start position:0%
+be some subtleties that escape me so if
+ 
+
+ align:start position:0%
+be some subtleties that escape me so if
+you can think of any let me know I think
+
+ align:start position:0%
+you can think of any let me know I think
+ 
+
+ align:start position:0%
+you can think of any let me know I think
+because there aren't any interaction
+
+ align:start position:0%
+because there aren't any interaction
+ 
+
+ align:start position:0%
+because there aren't any interaction
+terms in our model I think that means
+
+ align:start position:0%
+terms in our model I think that means
+ 
+
+ align:start position:0%
+terms in our model I think that means
+that that covariance is don't need to
+
+ align:start position:0%
+that that covariance is don't need to
+ 
+
+ align:start position:0%
+that that covariance is don't need to
+concern you but if you think I'm wrong
+
+ align:start position:0%
+concern you but if you think I'm wrong
+ 
+
+ align:start position:0%
+concern you but if you think I'm wrong
+on that let me know ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah maybe maybe I'm wrong
+
+ align:start position:0%
+yeah yeah maybe maybe I'm wrong
+ 
+
+ align:start position:0%
+yeah yeah maybe maybe I'm wrong
+well if you want to you know if you can
+
+ align:start position:0%
+well if you want to you know if you can
+ 
+
+ align:start position:0%
+well if you want to you know if you can
+work out how to consider that then then
+
+ align:start position:0%
+work out how to consider that then then
+ 
+
+ align:start position:0%
+work out how to consider that then then
+tell me no I don't think so
+
+ align:start position:0%
+tell me no I don't think so
+ 
+
+ align:start position:0%
+tell me no I don't think so
+No
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone else have we run out of coffee
+
+ align:start position:0%
+anyone else have we run out of coffee
+ 
+
+ align:start position:0%
+anyone else have we run out of coffee
+yes I expect so let's see what it what
+
+ align:start position:0%
+yes I expect so let's see what it what
+ 
+
+ align:start position:0%
+yes I expect so let's see what it what
+are the things that people are most
+
+ align:start position:0%
+are the things that people are most
+ 
+
+ align:start position:0%
+are the things that people are most
+puzzled by in in the material since quiz
+
+ align:start position:0%
+puzzled by in in the material since quiz
+ 
+
+ align:start position:0%
+puzzled by in in the material since quiz
+1 I mean if someone if someone asked you
+
+ align:start position:0%
+1 I mean if someone if someone asked you
+ 
+
+ align:start position:0%
+1 I mean if someone if someone asked you
+to fit fit a model to a factorial
+
+ align:start position:0%
+to fit fit a model to a factorial
+ 
+
+ align:start position:0%
+to fit fit a model to a factorial
+experiments and you didn't have a mini
+
+ align:start position:0%
+experiments and you didn't have a mini
+ 
+
+ align:start position:0%
+experiments and you didn't have a mini
+attack would know what level of
+
+ align:start position:0%
+attack would know what level of
+ 
+
+ align:start position:0%
+attack would know what level of
+confidence could people have in doing
+
+ align:start position:0%
+confidence could people have in doing
+ 
+
+ align:start position:0%
+confidence could people have in doing
+that is it I mean is it really something
+
+ align:start position:0%
+that is it I mean is it really something
+ 
+
+ align:start position:0%
+that is it I mean is it really something
+where you rely on the structure that the
+
+ align:start position:0%
+where you rely on the structure that the
+ 
+
+ align:start position:0%
+where you rely on the structure that the
+software provides to know how to
+
+ align:start position:0%
+software provides to know how to
+ 
+
+ align:start position:0%
+software provides to know how to
+calculate some of the squares and so
+
+ align:start position:0%
+calculate some of the squares and so
+ 
+
+ align:start position:0%
+calculate some of the squares and so
+forth because I can I can foresee you
+
+ align:start position:0%
+forth because I can I can foresee you
+ 
+
+ align:start position:0%
+forth because I can I can foresee you
+know exam questions you know obviously
+
+ align:start position:0%
+know exam questions you know obviously
+ 
+
+ align:start position:0%
+know exam questions you know obviously
+not gonna have me attack we're going to
+
+ align:start position:0%
+not gonna have me attack we're going to
+ 
+
+ align:start position:0%
+not gonna have me attack we're going to
+be dealing with very small numbers of
+
+ align:start position:0%
+be dealing with very small numbers of
+ 
+
+ align:start position:0%
+be dealing with very small numbers of
+data and it's just going to be a case of
+
+ align:start position:0%
+data and it's just going to be a case of
+ 
+
+ align:start position:0%
+data and it's just going to be a case of
+knowing what to subtract from water or
+
+ align:start position:0%
+knowing what to subtract from water or
+ 
+
+ align:start position:0%
+knowing what to subtract from water or
+anything yeah absolutely yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes fair point
+
+ align:start position:0%
+yes fair point
+ 
+
+ align:start position:0%
+yes fair point
+yeah I need to I need to track it down
+
+ align:start position:0%
+yeah I need to I need to track it down
+ 
+
+ align:start position:0%
+yeah I need to I need to track it down
+because they didn't post it on stellar
+
+ align:start position:0%
+because they didn't post it on stellar
+ 
+
+ align:start position:0%
+because they didn't post it on stellar
+last year so I need to get it off day
+
+ align:start position:0%
+last year so I need to get it off day
+ 
+
+ align:start position:0%
+last year so I need to get it off day
+apart
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sure sure yeah this this questions
+
+ align:start position:0%
+yeah sure sure yeah this this questions
+ 
+
+ align:start position:0%
+yeah sure sure yeah this this questions
+a bit cryptic but really all it's asking
+
+ align:start position:0%
+a bit cryptic but really all it's asking
+ 
+
+ align:start position:0%
+a bit cryptic but really all it's asking
+you to do is is confirm your
+
+ align:start position:0%
+you to do is is confirm your
+ 
+
+ align:start position:0%
+you to do is is confirm your
+understanding of the last question on
+
+ align:start position:0%
+understanding of the last question on
+ 
+
+ align:start position:0%
+understanding of the last question on
+problem sets 7 you may recall recall
+
+ align:start position:0%
+problem sets 7 you may recall recall
+ 
+
+ align:start position:0%
+problem sets 7 you may recall recall
+from that from that question where you
+
+ align:start position:0%
+from that from that question where you
+ 
+
+ align:start position:0%
+from that from that question where you
+made that factor that factor Z that
+
+ align:start position:0%
+made that factor that factor Z that
+ 
+
+ align:start position:0%
+made that factor that factor Z that
+noise factor you were you were imagining
+
+ align:start position:0%
+noise factor you were you were imagining
+ 
+
+ align:start position:0%
+noise factor you were you were imagining
+that you could control it in that
+
+ align:start position:0%
+that you could control it in that
+ 
+
+ align:start position:0%
+that you could control it in that
+situation but then I I think you you
+
+ align:start position:0%
+situation but then I I think you you
+ 
+
+ align:start position:0%
+situation but then I I think you you
+will have written an expression for Y in
+
+ align:start position:0%
+will have written an expression for Y in
+ 
+
+ align:start position:0%
+will have written an expression for Y in
+terms of the two x's and that and the Z
+
+ align:start position:0%
+terms of the two x's and that and the Z
+ 
+
+ align:start position:0%
+terms of the two x's and that and the Z
+factor that showed that the sensitivity
+
+ align:start position:0%
+factor that showed that the sensitivity
+ 
+
+ align:start position:0%
+factor that showed that the sensitivity
+of the outputs to variations in Z were a
+
+ align:start position:0%
+of the outputs to variations in Z were a
+ 
+
+ align:start position:0%
+of the outputs to variations in Z were a
+function of X 1 and X 2 so you could you
+
+ align:start position:0%
+function of X 1 and X 2 so you could you
+ 
+
+ align:start position:0%
+function of X 1 and X 2 so you could you
+could choose a combination of the of the
+
+ align:start position:0%
+could choose a combination of the of the
+ 
+
+ align:start position:0%
+could choose a combination of the of the
+control parameters at X 1 and X 2 that
+
+ align:start position:0%
+control parameters at X 1 and X 2 that
+ 
+
+ align:start position:0%
+control parameters at X 1 and X 2 that
+would minimize the sensitivity to Z now
+
+ align:start position:0%
+would minimize the sensitivity to Z now
+ 
+
+ align:start position:0%
+would minimize the sensitivity to Z now
+really parts B and C of problem for are
+
+ align:start position:0%
+really parts B and C of problem for are
+ 
+
+ align:start position:0%
+really parts B and C of problem for are
+just to do checking but that that went
+
+ align:start position:0%
+just to do checking but that that went
+ 
+
+ align:start position:0%
+just to do checking but that that went
+in because if you can't control Z but
+
+ align:start position:0%
+in because if you can't control Z but
+ 
+
+ align:start position:0%
+in because if you can't control Z but
+you know that you know if you're not
+
+ align:start position:0%
+you know that you know if you're not
+ 
+
+ align:start position:0%
+you know that you know if you're not
+controlling it it's probably going to
+
+ align:start position:0%
+controlling it it's probably going to
+ 
+
+ align:start position:0%
+controlling it it's probably going to
+have a variance the input the noise
+
+ align:start position:0%
+have a variance the input the noise
+ 
+
+ align:start position:0%
+have a variance the input the noise
+input is probably going to have a
+
+ align:start position:0%
+input is probably going to have a
+ 
+
+ align:start position:0%
+input is probably going to have a
+variance that doesn't change with time
+
+ align:start position:0%
+variance that doesn't change with time
+ 
+
+ align:start position:0%
+variance that doesn't change with time
+so you can see how much of that noise
+
+ align:start position:0%
+so you can see how much of that noise
+ 
+
+ align:start position:0%
+so you can see how much of that noise
+propagates through to the outputs if the
+
+ align:start position:0%
+propagates through to the outputs if the
+ 
+
+ align:start position:0%
+propagates through to the outputs if the
+noise interacts with the control input
+
+ align:start position:0%
+noise interacts with the control input
+ 
+
+ align:start position:0%
+noise interacts with the control input
+variables in other words if there are
+
+ align:start position:0%
+variables in other words if there are
+ 
+
+ align:start position:0%
+variables in other words if there are
+these product terms of Z and X 1 you
+
+ align:start position:0%
+these product terms of Z and X 1 you
+ 
+
+ align:start position:0%
+these product terms of Z and X 1 you
+can't control Z you can't control X 1
+
+ align:start position:0%
+can't control Z you can't control X 1
+ 
+
+ align:start position:0%
+can't control Z you can't control X 1
+therefore you can control
+
+ align:start position:0%
+therefore you can control
+ 
+
+ align:start position:0%
+therefore you can control
+how much the noise propagates through to
+
+ align:start position:0%
+how much the noise propagates through to
+ 
+
+ align:start position:0%
+how much the noise propagates through to
+the output and and then B and C aren't
+
+ align:start position:0%
+the output and and then B and C aren't
+ 
+
+ align:start position:0%
+the output and and then B and C aren't
+asking you to write down very much it's
+
+ align:start position:0%
+asking you to write down very much it's
+ 
+
+ align:start position:0%
+asking you to write down very much it's
+just sort of checking that the concept
+
+ align:start position:0%
+just sort of checking that the concept
+ 
+
+ align:start position:0%
+just sort of checking that the concept
+is there really does that answer your
+
+ align:start position:0%
+is there really does that answer your
+ 
+
+ align:start position:0%
+is there really does that answer your
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay anyone else stay that's a very good
+
+ align:start position:0%
+okay anyone else stay that's a very good
+ 
+
+ align:start position:0%
+okay anyone else stay that's a very good
+idea yes yeah I'll try to come up with
+
+ align:start position:0%
+idea yes yeah I'll try to come up with
+ 
+
+ align:start position:0%
+idea yes yeah I'll try to come up with
+something yeah that's sort of manageable
+
+ align:start position:0%
+something yeah that's sort of manageable
+ 
+
+ align:start position:0%
+something yeah that's sort of manageable
+on a sheet of paper yes very very good
+
+ align:start position:0%
+on a sheet of paper yes very very good
+ 
+
+ align:start position:0%
+on a sheet of paper yes very very good
+thought we may I mean yeah we may be
+
+ align:start position:0%
+thought we may I mean yeah we may be
+ 
+
+ align:start position:0%
+thought we may I mean yeah we may be
+able to do it with some of the some of
+
+ align:start position:0%
+able to do it with some of the some of
+ 
+
+ align:start position:0%
+able to do it with some of the some of
+the datasets we used to look at and over
+
+ align:start position:0%
+the datasets we used to look at and over
+ 
+
+ align:start position:0%
+the datasets we used to look at and over
+but yeah fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+including okay fine fine so that was on
+
+ align:start position:0%
+including okay fine fine so that was on
+ 
+
+ align:start position:0%
+including okay fine fine so that was on
+problem set seven you were twelve one or
+
+ align:start position:0%
+problem set seven you were twelve one or
+ 
+
+ align:start position:0%
+problem set seven you were twelve one or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+yeah yeah right no that's that's a good
+
+ align:start position:0%
+yeah yeah right no that's that's a good
+ 
+
+ align:start position:0%
+yeah yeah right no that's that's a good
+point a lot of people had that I will
+
+ align:start position:0%
+point a lot of people had that I will
+ 
+
+ align:start position:0%
+point a lot of people had that I will
+look as well okay yeah I think I think
+
+ align:start position:0%
+look as well okay yeah I think I think
+ 
+
+ align:start position:0%
+look as well okay yeah I think I think
+there is a mistake in Montgomery I need
+
+ align:start position:0%
+there is a mistake in Montgomery I need
+ 
+
+ align:start position:0%
+there is a mistake in Montgomery I need
+to track it down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah yeah you're right
+
+ align:start position:0%
+okay yeah yeah you're right
+ 
+
+ align:start position:0%
+okay yeah yeah you're right
+eight-point yeah right well I sure I can
+
+ align:start position:0%
+eight-point yeah right well I sure I can
+ 
+
+ align:start position:0%
+eight-point yeah right well I sure I can
+I can try to find I complete derivation
+
+ align:start position:0%
+I can try to find I complete derivation
+ 
+
+ align:start position:0%
+I can try to find I complete derivation
+I think it's probably not worth spending
+
+ align:start position:0%
+I think it's probably not worth spending
+ 
+
+ align:start position:0%
+I think it's probably not worth spending
+a lot of time trying to understand that
+
+ align:start position:0%
+a lot of time trying to understand that
+ 
+
+ align:start position:0%
+a lot of time trying to understand that
+I would focus more on on the stuff
+
+ align:start position:0%
+I would focus more on on the stuff
+ 
+
+ align:start position:0%
+I would focus more on on the stuff
+that's been in the problem sets but sure
+
+ align:start position:0%
+that's been in the problem sets but sure
+ 
+
+ align:start position:0%
+that's been in the problem sets but sure
+I can I can try to find that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I'm sure you're right I'm sure
+
+ align:start position:0%
+yes I'm sure you're right I'm sure
+ 
+
+ align:start position:0%
+yes I'm sure you're right I'm sure
+you're right
\ No newline at end of file
diff --git a/71dUZmywpOM.txt b/71dUZmywpOM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..db415c848b87e68847ebfaf6af765dcd711cdba5
--- /dev/null
+++ b/71dUZmywpOM.txt
@@ -0,0 +1,1235 @@
+align:start position:0%
+ 
+so we've discussed
+
+ align:start position:0%
+so we've discussed
+ 
+
+ align:start position:0%
+so we've discussed
+the extent to which the size of a
+
+ align:start position:0%
+the extent to which the size of a
+ 
+
+ align:start position:0%
+the extent to which the size of a
+droplet can influence the infectivity or
+
+ align:start position:0%
+droplet can influence the infectivity or
+ 
+
+ align:start position:0%
+droplet can influence the infectivity or
+the ability of
+
+ align:start position:0%
+the ability of
+ 
+
+ align:start position:0%
+the ability of
+a virion to escape from that droplet and
+
+ align:start position:0%
+a virion to escape from that droplet and
+ 
+
+ align:start position:0%
+a virion to escape from that droplet and
+also to be transmitted to the deepest
+
+ align:start position:0%
+also to be transmitted to the deepest
+ 
+
+ align:start position:0%
+also to be transmitted to the deepest
+smallest passages in the lungs as a
+
+ align:start position:0%
+smallest passages in the lungs as a
+ 
+
+ align:start position:0%
+smallest passages in the lungs as a
+function of its size
+
+ align:start position:0%
+function of its size
+ 
+
+ align:start position:0%
+function of its size
+there's also a dependence on the
+
+ align:start position:0%
+there's also a dependence on the
+ 
+
+ align:start position:0%
+there's also a dependence on the
+relative humidity of the air
+
+ align:start position:0%
+relative humidity of the air
+ 
+
+ align:start position:0%
+relative humidity of the air
+which is related to size since as we've
+
+ align:start position:0%
+which is related to size since as we've
+ 
+
+ align:start position:0%
+which is related to size since as we've
+seen humidity does vary the size
+
+ align:start position:0%
+seen humidity does vary the size
+ 
+
+ align:start position:0%
+seen humidity does vary the size
+but there's believed to be also a more
+
+ align:start position:0%
+but there's believed to be also a more
+ 
+
+ align:start position:0%
+but there's believed to be also a more
+direct effect of humidity as i will now
+
+ align:start position:0%
+direct effect of humidity as i will now
+ 
+
+ align:start position:0%
+direct effect of humidity as i will now
+try to explain so i'm relying here on
+
+ align:start position:0%
+try to explain so i'm relying here on
+ 
+
+ align:start position:0%
+try to explain so i'm relying here on
+the recent work
+
+ align:start position:0%
+the recent work
+ 
+
+ align:start position:0%
+the recent work
+of the group of lindsey marr two two
+
+ align:start position:0%
+of the group of lindsey marr two two
+ 
+
+ align:start position:0%
+of the group of lindsey marr two two
+papers uh cited here
+
+ align:start position:0%
+papers uh cited here
+ 
+
+ align:start position:0%
+papers uh cited here
+so we can distinguish between two
+
+ align:start position:0%
+so we can distinguish between two
+ 
+
+ align:start position:0%
+so we can distinguish between two
+different types of pathogens the first
+
+ align:start position:0%
+different types of pathogens the first
+ 
+
+ align:start position:0%
+different types of pathogens the first
+or the bacteria
+
+ align:start position:0%
+or the bacteria
+ 
+
+ align:start position:0%
+or the bacteria
+and here there's a monotonic dependence
+
+ align:start position:0%
+and here there's a monotonic dependence
+ 
+
+ align:start position:0%
+and here there's a monotonic dependence
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+relative viability of the pathogen of
+
+ align:start position:0%
+relative viability of the pathogen of
+ 
+
+ align:start position:0%
+relative viability of the pathogen of
+the bacteria
+
+ align:start position:0%
+the bacteria
+ 
+
+ align:start position:0%
+the bacteria
+um after a certain time period let's say
+
+ align:start position:0%
+um after a certain time period let's say
+ 
+
+ align:start position:0%
+um after a certain time period let's say
+one hour
+
+ align:start position:0%
+one hour
+ 
+
+ align:start position:0%
+one hour
+and what is found is that above a
+
+ align:start position:0%
+and what is found is that above a
+ 
+
+ align:start position:0%
+and what is found is that above a
+certain threshold of humidity around 80
+
+ align:start position:0%
+certain threshold of humidity around 80
+ 
+
+ align:start position:0%
+certain threshold of humidity around 80
+percent
+
+ align:start position:0%
+percent
+ 
+
+ align:start position:0%
+percent
+relative humidity that there's
+
+ align:start position:0%
+relative humidity that there's
+ 
+
+ align:start position:0%
+relative humidity that there's
+essentially no change in the viability
+
+ align:start position:0%
+essentially no change in the viability
+ 
+
+ align:start position:0%
+essentially no change in the viability
+of the bacteria they're alive they're
+
+ align:start position:0%
+of the bacteria they're alive they're
+ 
+
+ align:start position:0%
+of the bacteria they're alive they're
+infectious
+
+ align:start position:0%
+infectious
+ 
+
+ align:start position:0%
+infectious
+uh but as the humidity relative humidity
+
+ align:start position:0%
+uh but as the humidity relative humidity
+ 
+
+ align:start position:0%
+uh but as the humidity relative humidity
+is reduced
+
+ align:start position:0%
+is reduced
+ 
+
+ align:start position:0%
+is reduced
+uh then there's significant drop off in
+
+ align:start position:0%
+uh then there's significant drop off in
+ 
+
+ align:start position:0%
+uh then there's significant drop off in
+viability which depends on the specific
+
+ align:start position:0%
+viability which depends on the specific
+ 
+
+ align:start position:0%
+viability which depends on the specific
+type of viru
+
+ align:start position:0%
+type of viru
+ 
+
+ align:start position:0%
+type of viru
+of bacteria but it's a fairly general
+
+ align:start position:0%
+of bacteria but it's a fairly general
+ 
+
+ align:start position:0%
+of bacteria but it's a fairly general
+trend that it comes down significantly
+
+ align:start position:0%
+trend that it comes down significantly
+ 
+
+ align:start position:0%
+trend that it comes down significantly
+as you approach more dry air
+
+ align:start position:0%
+as you approach more dry air
+ 
+
+ align:start position:0%
+as you approach more dry air
+now what's happening is the size of the
+
+ align:start position:0%
+now what's happening is the size of the
+ 
+
+ align:start position:0%
+now what's happening is the size of the
+droplets is shrinking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the case of the bacteria we can
+
+ align:start position:0%
+in the case of the bacteria we can
+ 
+
+ align:start position:0%
+in the case of the bacteria we can
+understand to some extent
+
+ align:start position:0%
+understand to some extent
+ 
+
+ align:start position:0%
+understand to some extent
+why this dependence might be here by
+
+ align:start position:0%
+why this dependence might be here by
+ 
+
+ align:start position:0%
+why this dependence might be here by
+thinking about
+
+ align:start position:0%
+thinking about
+ 
+
+ align:start position:0%
+thinking about
+solutes that are present especially
+
+ align:start position:0%
+solutes that are present especially
+ 
+
+ align:start position:0%
+solutes that are present especially
+salts in this in the system
+
+ align:start position:0%
+salts in this in the system
+ 
+
+ align:start position:0%
+salts in this in the system
+but also mucous mucosal proteins that
+
+ align:start position:0%
+but also mucous mucosal proteins that
+ 
+
+ align:start position:0%
+but also mucous mucosal proteins that
+we've also discussed
+
+ align:start position:0%
+we've also discussed
+ 
+
+ align:start position:0%
+we've also discussed
+and when the the particles become more
+
+ align:start position:0%
+and when the the particles become more
+ 
+
+ align:start position:0%
+and when the the particles become more
+dry
+
+ align:start position:0%
+dry
+ 
+
+ align:start position:0%
+dry
+then what happens is that the
+
+ align:start position:0%
+then what happens is that the
+ 
+
+ align:start position:0%
+then what happens is that the
+concentration goes up and there's an
+
+ align:start position:0%
+concentration goes up and there's an
+ 
+
+ align:start position:0%
+concentration goes up and there's an
+increase in the osmotic pressure
+
+ align:start position:0%
+increase in the osmotic pressure
+ 
+
+ align:start position:0%
+increase in the osmotic pressure
+of the fluid around the bacteria
+
+ align:start position:0%
+of the fluid around the bacteria
+ 
+
+ align:start position:0%
+of the fluid around the bacteria
+relative to the inside
+
+ align:start position:0%
+relative to the inside
+ 
+
+ align:start position:0%
+relative to the inside
+and as with many other kinds of cells
+
+ align:start position:0%
+and as with many other kinds of cells
+ 
+
+ align:start position:0%
+and as with many other kinds of cells
+when exposed to
+
+ align:start position:0%
+when exposed to
+ 
+
+ align:start position:0%
+when exposed to
+such high osmotic pressures that can
+
+ align:start position:0%
+such high osmotic pressures that can
+ 
+
+ align:start position:0%
+such high osmotic pressures that can
+cause
+
+ align:start position:0%
+cause
+ 
+
+ align:start position:0%
+cause
+stress on the cell and potentially even
+
+ align:start position:0%
+stress on the cell and potentially even
+ 
+
+ align:start position:0%
+stress on the cell and potentially even
+rupturing of membranes or other
+
+ align:start position:0%
+rupturing of membranes or other
+ 
+
+ align:start position:0%
+rupturing of membranes or other
+structures within the cell and
+
+ align:start position:0%
+structures within the cell and
+ 
+
+ align:start position:0%
+structures within the cell and
+obviously then is not good for the
+
+ align:start position:0%
+obviously then is not good for the
+ 
+
+ align:start position:0%
+obviously then is not good for the
+viability of that cell and leads to
+
+ align:start position:0%
+viability of that cell and leads to
+ 
+
+ align:start position:0%
+viability of that cell and leads to
+deactivation
+
+ align:start position:0%
+deactivation
+ 
+
+ align:start position:0%
+deactivation
+the case of viruses is a bit more
+
+ align:start position:0%
+the case of viruses is a bit more
+ 
+
+ align:start position:0%
+the case of viruses is a bit more
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+so some old data of harper from the
+
+ align:start position:0%
+so some old data of harper from the
+ 
+
+ align:start position:0%
+so some old data of harper from the
+1960s
+
+ align:start position:0%
+1960s
+ 
+
+ align:start position:0%
+1960s
+on the seasonal flu in particular human
+
+ align:start position:0%
+on the seasonal flu in particular human
+ 
+
+ align:start position:0%
+on the seasonal flu in particular human
+influenza virus
+
+ align:start position:0%
+influenza virus
+ 
+
+ align:start position:0%
+influenza virus
+a which was recently
+
+ align:start position:0%
+a which was recently
+ 
+
+ align:start position:0%
+a which was recently
+analyzed by mars group showed that there
+
+ align:start position:0%
+analyzed by mars group showed that there
+ 
+
+ align:start position:0%
+analyzed by mars group showed that there
+was a viral deactivation rate that
+
+ align:start position:0%
+was a viral deactivation rate that
+ 
+
+ align:start position:0%
+was a viral deactivation rate that
+essentially was scaling
+
+ align:start position:0%
+essentially was scaling
+ 
+
+ align:start position:0%
+essentially was scaling
+linearly with the relative humidity so
+
+ align:start position:0%
+linearly with the relative humidity so
+ 
+
+ align:start position:0%
+linearly with the relative humidity so
+it's uh there's a faster deactivation
+
+ align:start position:0%
+it's uh there's a faster deactivation
+ 
+
+ align:start position:0%
+it's uh there's a faster deactivation
+rate in more humid air
+
+ align:start position:0%
+rate in more humid air
+ 
+
+ align:start position:0%
+rate in more humid air
+less in dry air this is one way we can
+
+ align:start position:0%
+less in dry air this is one way we can
+ 
+
+ align:start position:0%
+less in dry air this is one way we can
+understand the seasonal nature of the
+
+ align:start position:0%
+understand the seasonal nature of the
+ 
+
+ align:start position:0%
+understand the seasonal nature of the
+flu
+
+ align:start position:0%
+flu
+ 
+
+ align:start position:0%
+flu
+in that in more dry wintry environments
+
+ align:start position:0%
+in that in more dry wintry environments
+ 
+
+ align:start position:0%
+in that in more dry wintry environments
+especially away from
+
+ align:start position:0%
+especially away from
+ 
+
+ align:start position:0%
+especially away from
+in sort of the northern or southern
+
+ align:start position:0%
+in sort of the northern or southern
+ 
+
+ align:start position:0%
+in sort of the northern or southern
+hemispheres
+
+ align:start position:0%
+hemispheres
+ 
+
+ align:start position:0%
+hemispheres
+we can expect that then the virus would
+
+ align:start position:0%
+we can expect that then the virus would
+ 
+
+ align:start position:0%
+we can expect that then the virus would
+be deactivating less
+
+ align:start position:0%
+be deactivating less
+ 
+
+ align:start position:0%
+be deactivating less
+but of course that's compounded by the
+
+ align:start position:0%
+but of course that's compounded by the
+ 
+
+ align:start position:0%
+but of course that's compounded by the
+effect that in the winter
+
+ align:start position:0%
+effect that in the winter
+ 
+
+ align:start position:0%
+effect that in the winter
+people spend more time indoors and so
+
+ align:start position:0%
+people spend more time indoors and so
+ 
+
+ align:start position:0%
+people spend more time indoors and so
+that's also leading to
+
+ align:start position:0%
+that's also leading to
+ 
+
+ align:start position:0%
+that's also leading to
+more seasonal transmission now if we
+
+ align:start position:0%
+more seasonal transmission now if we
+ 
+
+ align:start position:0%
+more seasonal transmission now if we
+convert the deactivation rate into a
+
+ align:start position:0%
+convert the deactivation rate into a
+ 
+
+ align:start position:0%
+convert the deactivation rate into a
+relative viability again
+
+ align:start position:0%
+relative viability again
+ 
+
+ align:start position:0%
+relative viability again
+then we see an interesting dependence in
+
+ align:start position:0%
+then we see an interesting dependence in
+ 
+
+ align:start position:0%
+then we see an interesting dependence in
+recent experiments which were done using
+
+ align:start position:0%
+recent experiments which were done using
+ 
+
+ align:start position:0%
+recent experiments which were done using
+bacteriophages which are models
+
+ align:start position:0%
+bacteriophages which are models
+ 
+
+ align:start position:0%
+bacteriophages which are models
+of different kinds of
+
+ align:start position:0%
+of different kinds of
+ 
+
+ align:start position:0%
+of different kinds of
+human pathogens including the seasonal
+
+ align:start position:0%
+human pathogens including the seasonal
+ 
+
+ align:start position:0%
+human pathogens including the seasonal
+flu
+
+ align:start position:0%
+flu
+ 
+
+ align:start position:0%
+flu
+and influenza viruses and in particular
+
+ align:start position:0%
+and influenza viruses and in particular
+ 
+
+ align:start position:0%
+and influenza viruses and in particular
+is a non-monotonic dependence where
+
+ align:start position:0%
+is a non-monotonic dependence where
+ 
+
+ align:start position:0%
+is a non-monotonic dependence where
+essentially there's a maximum rate of
+
+ align:start position:0%
+essentially there's a maximum rate of
+ 
+
+ align:start position:0%
+essentially there's a maximum rate of
+deactivation
+
+ align:start position:0%
+deactivation
+ 
+
+ align:start position:0%
+deactivation
+around the range of 70 or 80 percent
+
+ align:start position:0%
+around the range of 70 or 80 percent
+ 
+
+ align:start position:0%
+around the range of 70 or 80 percent
+humidity
+
+ align:start position:0%
+humidity
+ 
+
+ align:start position:0%
+humidity
+or 60 to 80 and similarly the viability
+
+ align:start position:0%
+or 60 to 80 and similarly the viability
+ 
+
+ align:start position:0%
+or 60 to 80 and similarly the viability
+was the lowest in that range and the way
+
+ align:start position:0%
+was the lowest in that range and the way
+ 
+
+ align:start position:0%
+was the lowest in that range and the way
+the authors proposed uh to explain that
+
+ align:start position:0%
+the authors proposed uh to explain that
+ 
+
+ align:start position:0%
+the authors proposed uh to explain that
+was a hypothesis
+
+ align:start position:0%
+was a hypothesis
+ 
+
+ align:start position:0%
+was a hypothesis
+that there are solutes that are present
+
+ align:start position:0%
+that there are solutes that are present
+ 
+
+ align:start position:0%
+that there are solutes that are present
+which may be for example
+
+ align:start position:0%
+which may be for example
+ 
+
+ align:start position:0%
+which may be for example
+sodium chloride or in particular
+
+ align:start position:0%
+sodium chloride or in particular
+ 
+
+ align:start position:0%
+sodium chloride or in particular
+chloride ions perhaps
+
+ align:start position:0%
+chloride ions perhaps
+ 
+
+ align:start position:0%
+chloride ions perhaps
+that when we reach the higher
+
+ align:start position:0%
+that when we reach the higher
+ 
+
+ align:start position:0%
+that when we reach the higher
+concentration in the shrunken droplets
+
+ align:start position:0%
+concentration in the shrunken droplets
+ 
+
+ align:start position:0%
+concentration in the shrunken droplets
+that there is again a stress on the
+
+ align:start position:0%
+that there is again a stress on the
+ 
+
+ align:start position:0%
+that there is again a stress on the
+virus but in this case
+
+ align:start position:0%
+virus but in this case
+ 
+
+ align:start position:0%
+virus but in this case
+uh regardless of the details of the uh
+
+ align:start position:0%
+uh regardless of the details of the uh
+ 
+
+ align:start position:0%
+uh regardless of the details of the uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the mechanism of deactivation for these
+
+ align:start position:0%
+the mechanism of deactivation for these
+ 
+
+ align:start position:0%
+the mechanism of deactivation for these
+encapsulated viruses
+
+ align:start position:0%
+encapsulated viruses
+ 
+
+ align:start position:0%
+encapsulated viruses
+the idea is that the cumulative dose or
+
+ align:start position:0%
+the idea is that the cumulative dose or
+ 
+
+ align:start position:0%
+the idea is that the cumulative dose or
+exposure to those solids is what's
+
+ align:start position:0%
+exposure to those solids is what's
+ 
+
+ align:start position:0%
+exposure to those solids is what's
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+so if the shrinking happens very fast
+
+ align:start position:0%
+so if the shrinking happens very fast
+ 
+
+ align:start position:0%
+so if the shrinking happens very fast
+and we end up with a droplet nucleus of
+
+ align:start position:0%
+and we end up with a droplet nucleus of
+ 
+
+ align:start position:0%
+and we end up with a droplet nucleus of
+mostly bound water
+
+ align:start position:0%
+mostly bound water
+ 
+
+ align:start position:0%
+mostly bound water
+and it happens over a short period of
+
+ align:start position:0%
+and it happens over a short period of
+ 
+
+ align:start position:0%
+and it happens over a short period of
+time the exposure to those solutes is
+
+ align:start position:0%
+time the exposure to those solutes is
+ 
+
+ align:start position:0%
+time the exposure to those solutes is
+limited and hence we
+
+ align:start position:0%
+limited and hence we
+ 
+
+ align:start position:0%
+limited and hence we
+end up with high viability low
+
+ align:start position:0%
+end up with high viability low
+ 
+
+ align:start position:0%
+end up with high viability low
+deactivation rate
+
+ align:start position:0%
+deactivation rate
+ 
+
+ align:start position:0%
+deactivation rate
+in dry conditions conversely in very
+
+ align:start position:0%
+in dry conditions conversely in very
+ 
+
+ align:start position:0%
+in dry conditions conversely in very
+humid conditions the droplets stay big
+
+ align:start position:0%
+humid conditions the droplets stay big
+ 
+
+ align:start position:0%
+humid conditions the droplets stay big
+in fact they may even grow
+
+ align:start position:0%
+in fact they may even grow
+ 
+
+ align:start position:0%
+in fact they may even grow
+because of the hydroscopic solutes and
+
+ align:start position:0%
+because of the hydroscopic solutes and
+ 
+
+ align:start position:0%
+because of the hydroscopic solutes and
+in that case
+
+ align:start position:0%
+in that case
+ 
+
+ align:start position:0%
+in that case
+there's plenty of solutes presence but
+
+ align:start position:0%
+there's plenty of solutes presence but
+ 
+
+ align:start position:0%
+there's plenty of solutes presence but
+they're very dilute and so again the
+
+ align:start position:0%
+they're very dilute and so again the
+ 
+
+ align:start position:0%
+they're very dilute and so again the
+effect on the virus is minimal
+
+ align:start position:0%
+effect on the virus is minimal
+ 
+
+ align:start position:0%
+effect on the virus is minimal
+and the greatest deactivation and also
+
+ align:start position:0%
+and the greatest deactivation and also
+ 
+
+ align:start position:0%
+and the greatest deactivation and also
+the maximum
+
+ align:start position:0%
+the maximum
+ 
+
+ align:start position:0%
+the maximum
+this or minimum viability is actually at
+
+ align:start position:0%
+this or minimum viability is actually at
+ 
+
+ align:start position:0%
+this or minimum viability is actually at
+an intermediate range of humidities
+
+ align:start position:0%
+an intermediate range of humidities
+ 
+
+ align:start position:0%
+an intermediate range of humidities
+so this tells you that maintaining a
+
+ align:start position:0%
+so this tells you that maintaining a
+ 
+
+ align:start position:0%
+so this tells you that maintaining a
+comfortable humidity in the range of 50
+
+ align:start position:0%
+comfortable humidity in the range of 50
+ 
+
+ align:start position:0%
+comfortable humidity in the range of 50
+to 80
+
+ align:start position:0%
+to 80
+ 
+
+ align:start position:0%
+to 80
+may actually be the best for minimizing
+
+ align:start position:0%
+may actually be the best for minimizing
+ 
+
+ align:start position:0%
+may actually be the best for minimizing
+the viability
+
+ align:start position:0%
+the viability
+ 
+
+ align:start position:0%
+the viability
+of viral pathogens
\ No newline at end of file
diff --git a/7MWXdi-e-DQ.txt b/7MWXdi-e-DQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3f04d84d47e37f67dd4834e3a1487e5256008b60
--- /dev/null
+++ b/7MWXdi-e-DQ.txt
@@ -0,0 +1,2528 @@
+align:start position:0%
+ 
+welcome to New lecture on the binomial
+
+ align:start position:0%
+welcome to New lecture on the binomial
+ 
+
+ align:start position:0%
+welcome to New lecture on the binomial
+theorem uh in this lecture we will look
+
+ align:start position:0%
+theorem uh in this lecture we will look
+ 
+
+ align:start position:0%
+theorem uh in this lecture we will look
+at certain divisibility results uh which
+
+ align:start position:0%
+at certain divisibility results uh which
+ 
+
+ align:start position:0%
+at certain divisibility results uh which
+can be derived based on the binomial
+
+ align:start position:0%
+can be derived based on the binomial
+ 
+
+ align:start position:0%
+can be derived based on the binomial
+theorem so once again recall the
+
+ align:start position:0%
+theorem so once again recall the
+ 
+
+ align:start position:0%
+theorem so once again recall the
+binomial theorem is given by x + y the
+
+ align:start position:0%
+binomial theorem is given by x + y the
+ 
+
+ align:start position:0%
+binomial theorem is given by x + y the
+whole power n equals summation R = 0 to
+
+ align:start position:0%
+whole power n equals summation R = 0 to
+ 
+
+ align:start position:0%
+whole power n equals summation R = 0 to
+n c r x^ n minus r y^ r where we use c r
+
+ align:start position:0%
+n c r x^ n minus r y^ r where we use c r
+ 
+
+ align:start position:0%
+n c r x^ n minus r y^ r where we use c r
+to denote
+
+ align:start position:0%
+to denote
+ 
+
+ align:start position:0%
+to denote
+NCR so to give you a flavor of the kind
+
+ align:start position:0%
+NCR so to give you a flavor of the kind
+ 
+
+ align:start position:0%
+NCR so to give you a flavor of the kind
+of results we'll be looking look at
+
+ align:start position:0%
+of results we'll be looking look at
+ 
+
+ align:start position:0%
+of results we'll be looking look at
+today uh let's look at the first example
+
+ align:start position:0%
+today uh let's look at the first example
+ 
+
+ align:start position:0%
+today uh let's look at the first example
+uh which asks you to show
+
+ align:start position:0%
+uh which asks you to show
+ 
+
+ align:start position:0%
+uh which asks you to show
+that 3 power 2 n +
+
+ align:start position:0%
+that 3 power 2 n +
+ 
+
+ align:start position:0%
+that 3 power 2 n +
+2 - 8 N -
+
+ align:start position:0%
+2 - 8 N -
+ 
+
+ align:start position:0%
+2 - 8 N -
+99 is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divisible by
+
+ align:start position:0%
+divisible by
+ 
+
+ align:start position:0%
+divisible by
+64 uh when N is a natural
+
+ align:start position:0%
+64 uh when N is a natural
+ 
+
+ align:start position:0%
+64 uh when N is a natural
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it asks you to show that this term is
+
+ align:start position:0%
+so it asks you to show that this term is
+ 
+
+ align:start position:0%
+so it asks you to show that this term is
+divisible by 64 for natural numbers
+
+ align:start position:0%
+divisible by 64 for natural numbers
+ 
+
+ align:start position:0%
+divisible by 64 for natural numbers
+n um so at First Sight there doesn't
+
+ align:start position:0%
+n um so at First Sight there doesn't
+ 
+
+ align:start position:0%
+n um so at First Sight there doesn't
+seem to be a binomial expansion you can
+
+ align:start position:0%
+seem to be a binomial expansion you can
+ 
+
+ align:start position:0%
+seem to be a binomial expansion you can
+apply uh to generate this result so we
+
+ align:start position:0%
+apply uh to generate this result so we
+ 
+
+ align:start position:0%
+apply uh to generate this result so we
+would like to create a binomial
+
+ align:start position:0%
+would like to create a binomial
+ 
+
+ align:start position:0%
+would like to create a binomial
+expansion to U derive this result and so
+
+ align:start position:0%
+expansion to U derive this result and so
+ 
+
+ align:start position:0%
+expansion to U derive this result and so
+notice that you have you have an
+
+ align:start position:0%
+notice that you have you have an
+ 
+
+ align:start position:0%
+notice that you have you have an
+exponent here but you also have some
+
+ align:start position:0%
+exponent here but you also have some
+ 
+
+ align:start position:0%
+exponent here but you also have some
+terms here and these terms are in
+
+ align:start position:0%
+terms here and these terms are in
+ 
+
+ align:start position:0%
+terms here and these terms are in
+general not divisible by 64 for n being
+
+ align:start position:0%
+general not divisible by 64 for n being
+ 
+
+ align:start position:0%
+general not divisible by 64 for n being
+natural numbers so you can plug in
+
+ align:start position:0%
+natural numbers so you can plug in
+ 
+
+ align:start position:0%
+natural numbers so you can plug in
+certain natural numbers and you can see
+
+ align:start position:0%
+certain natural numbers and you can see
+ 
+
+ align:start position:0%
+certain natural numbers and you can see
+that this uh this term which is being
+
+ align:start position:0%
+that this uh this term which is being
+ 
+
+ align:start position:0%
+that this uh this term which is being
+subtracted from 3^ 2 n + 2 is not going
+
+ align:start position:0%
+subtracted from 3^ 2 n + 2 is not going
+ 
+
+ align:start position:0%
+subtracted from 3^ 2 n + 2 is not going
+to be divisible by 64 and so we would
+
+ align:start position:0%
+to be divisible by 64 and so we would
+ 
+
+ align:start position:0%
+to be divisible by 64 and so we would
+like to somehow get rid of these terms
+
+ align:start position:0%
+like to somehow get rid of these terms
+ 
+
+ align:start position:0%
+like to somehow get rid of these terms
+and leave the remaining term to be
+
+ align:start position:0%
+and leave the remaining term to be
+ 
+
+ align:start position:0%
+and leave the remaining term to be
+divisible by 64 U so let's look at a way
+
+ align:start position:0%
+divisible by 64 U so let's look at a way
+ 
+
+ align:start position:0%
+divisible by 64 U so let's look at a way
+of reexpressing this term 3^ 2 n + 2 - 8
+
+ align:start position:0%
+of reexpressing this term 3^ 2 n + 2 - 8
+ 
+
+ align:start position:0%
+of reexpressing this term 3^ 2 n + 2 - 8
+N - 9 9 uh can be written
+
+ align:start position:0%
+N - 9 9 uh can be written
+ 
+
+ align:start position:0%
+N - 9 9 uh can be written
+as uh 9^ n + 1 where I've just taken a
+
+ align:start position:0%
+as uh 9^ n + 1 where I've just taken a
+ 
+
+ align:start position:0%
+as uh 9^ n + 1 where I've just taken a
+power of 2 into 3 and written 3 Square
+
+ align:start position:0%
+power of 2 into 3 and written 3 Square
+ 
+
+ align:start position:0%
+power of 2 into 3 and written 3 Square
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+9 and you still have minus 8 8 N -
+
+ align:start position:0%
+9 and you still have minus 8 8 N -
+ 
+
+ align:start position:0%
+9 and you still have minus 8 8 N -
+9 so now this looks a little more
+
+ align:start position:0%
+9 so now this looks a little more
+ 
+
+ align:start position:0%
+9 so now this looks a little more
+promising because you have 9^ n + 1 and
+
+ align:start position:0%
+promising because you have 9^ n + 1 and
+ 
+
+ align:start position:0%
+promising because you have 9^ n + 1 and
+you have a 9 and you have an 8 n so you
+
+ align:start position:0%
+you have a 9 and you have an 8 n so you
+ 
+
+ align:start position:0%
+you have a 9 and you have an 8 n so you
+can get rid of the 8 n potentially by
+
+ align:start position:0%
+can get rid of the 8 n potentially by
+ 
+
+ align:start position:0%
+can get rid of the 8 n potentially by
+writing 9 as uh 1 + 8 raise this power n
+
+ align:start position:0%
+writing 9 as uh 1 + 8 raise this power n
+ 
+
+ align:start position:0%
+writing 9 as uh 1 + 8 raise this power n
++ 1 and you have 8 n - 9 so this looks a
+
+ align:start position:0%
++ 1 and you have 8 n - 9 so this looks a
+ 
+
+ align:start position:0%
++ 1 and you have 8 n - 9 so this looks a
+little more promising and now you have a
+
+ align:start position:0%
+little more promising and now you have a
+ 
+
+ align:start position:0%
+little more promising and now you have a
+term which you can expand using the
+
+ align:start position:0%
+term which you can expand using the
+ 
+
+ align:start position:0%
+term which you can expand using the
+binomial theorem um so let's try and
+
+ align:start position:0%
+binomial theorem um so let's try and
+ 
+
+ align:start position:0%
+binomial theorem um so let's try and
+expand this term so this is nothing
+
+ align:start position:0%
+expand this term so this is nothing
+ 
+
+ align:start position:0%
+expand this term so this is nothing
+but n + 1
+
+ align:start position:0%
+but n + 1
+ 
+
+ align:start position:0%
+but n + 1
+c0 uh * 1^ n
+
+ align:start position:0%
+c0 uh * 1^ n
+ 
+
+ align:start position:0%
+c0 uh * 1^ n
++1 uh plus n + 1 C1
+
+ align:start position:0%
++1 uh plus n + 1 C1
+ 
+
+ align:start position:0%
++1 uh plus n + 1 C1
+* 1^ n * 8
+
+ align:start position:0%
+* 1^ n * 8
+ 
+
+ align:start position:0%
+* 1^ n * 8
++ n + 1
+
+ align:start position:0%
++ n + 1
+ 
+
+ align:start position:0%
++ n + 1
+c 2 1 power n minus 1 h² and so
+
+ align:start position:0%
+c 2 1 power n minus 1 h² and so
+ 
+
+ align:start position:0%
+c 2 1 power n minus 1 h² and so
+on so we'll we'll be concerned about the
+
+ align:start position:0%
+on so we'll we'll be concerned about the
+ 
+
+ align:start position:0%
+on so we'll we'll be concerned about the
+higher order terms later and we have we
+
+ align:start position:0%
+higher order terms later and we have we
+ 
+
+ align:start position:0%
+higher order terms later and we have we
+still subtracting eight and and N from
+
+ align:start position:0%
+still subtracting eight and and N from
+ 
+
+ align:start position:0%
+still subtracting eight and and N from
+this term so let's see how this
+
+ align:start position:0%
+this term so let's see how this
+ 
+
+ align:start position:0%
+this term so let's see how this
+simplifies to uh so this is nothing but
+
+ align:start position:0%
+simplifies to uh so this is nothing but
+ 
+
+ align:start position:0%
+simplifies to uh so this is nothing but
+the first term is one the second term is
+
+ align:start position:0%
+the first term is one the second term is
+ 
+
+ align:start position:0%
+the first term is one the second term is
+n + 1 uh * 1 * 8 and the remaining terms
+
+ align:start position:0%
+n + 1 uh * 1 * 8 and the remaining terms
+ 
+
+ align:start position:0%
+n + 1 uh * 1 * 8 and the remaining terms
+can be so simply written as summation R
+
+ align:start position:0%
+can be so simply written as summation R
+ 
+
+ align:start position:0%
+can be so simply written as summation R
+= 2 to n + 1 n + 1 c
+
+ align:start position:0%
+= 2 to n + 1 n + 1 c
+ 
+
+ align:start position:0%
+= 2 to n + 1 n + 1 c
+r 1^ n + 1 -
+
+ align:start position:0%
+r 1^ n + 1 -
+ 
+
+ align:start position:0%
+r 1^ n + 1 -
+R and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8^ R and you still have to subtract 8
+
+ align:start position:0%
+8^ R and you still have to subtract 8
+ 
+
+ align:start position:0%
+8^ R and you still have to subtract 8
+and and 9 from this expression so this
+
+ align:start position:0%
+and and 9 from this expression so this
+ 
+
+ align:start position:0%
+and and 9 from this expression so this
+looks a little more promising because
+
+ align:start position:0%
+looks a little more promising because
+ 
+
+ align:start position:0%
+looks a little more promising because
+you notice that these first two terms
+
+ align:start position:0%
+you notice that these first two terms
+ 
+
+ align:start position:0%
+you notice that these first two terms
+add up to exactly 8 n + 9 and so you can
+
+ align:start position:0%
+add up to exactly 8 n + 9 and so you can
+ 
+
+ align:start position:0%
+add up to exactly 8 n + 9 and so you can
+cancel these two terms and so you're
+
+ align:start position:0%
+cancel these two terms and so you're
+ 
+
+ align:start position:0%
+cancel these two terms and so you're
+just left with summation R = 2 to n + 1
+
+ align:start position:0%
+just left with summation R = 2 to n + 1
+ 
+
+ align:start position:0%
+just left with summation R = 2 to n + 1
+n + 1 c r uh 1 n + 1 - R is just 1 and
+
+ align:start position:0%
+n + 1 c r uh 1 n + 1 - R is just 1 and
+ 
+
+ align:start position:0%
+n + 1 c r uh 1 n + 1 - R is just 1 and
+you have 8 power
+
+ align:start position:0%
+you have 8 power
+ 
+
+ align:start position:0%
+you have 8 power
+R so this is what we're left with and we
+
+ align:start position:0%
+R so this is what we're left with and we
+ 
+
+ align:start position:0%
+R so this is what we're left with and we
+want to show that this is divisible by
+
+ align:start position:0%
+want to show that this is divisible by
+ 
+
+ align:start position:0%
+want to show that this is divisible by
+64 so notice that the summation runs
+
+ align:start position:0%
+64 so notice that the summation runs
+ 
+
+ align:start position:0%
+64 so notice that the summation runs
+from Ral to 2 so let's rewrite this
+
+ align:start position:0%
+from Ral to 2 so let's rewrite this
+ 
+
+ align:start position:0%
+from Ral to 2 so let's rewrite this
+as summation R = 0 to n -1 n +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 c r + + 2 8^ r + 2 so we' just used a
+
+ align:start position:0%
+1 c r + + 2 8^ r + 2 so we' just used a
+ 
+
+ align:start position:0%
+1 c r + + 2 8^ r + 2 so we' just used a
+change of indices to rewrite this
+
+ align:start position:0%
+change of indices to rewrite this
+ 
+
+ align:start position:0%
+change of indices to rewrite this
+summation and notice that there's an 8^
+
+ align:start position:0%
+summation and notice that there's an 8^
+ 
+
+ align:start position:0%
+summation and notice that there's an 8^
+two here you can pull that out this is
+
+ align:start position:0%
+two here you can pull that out this is
+ 
+
+ align:start position:0%
+two here you can pull that out this is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+64 * summation R = 0 to N -
+
+ align:start position:0%
+64 * summation R = 0 to N -
+ 
+
+ align:start position:0%
+64 * summation R = 0 to N -
+1 n + 1 c r + 2 8 power
+
+ align:start position:0%
+1 n + 1 c r + 2 8 power
+ 
+
+ align:start position:0%
+1 n + 1 c r + 2 8 power
+R so you have a 64 here and you wanted
+
+ align:start position:0%
+R so you have a 64 here and you wanted
+ 
+
+ align:start position:0%
+R so you have a 64 here and you wanted
+to show that this term is divisible by
+
+ align:start position:0%
+to show that this term is divisible by
+ 
+
+ align:start position:0%
+to show that this term is divisible by
+64 so that is good so what we have to
+
+ align:start position:0%
+64 so that is good so what we have to
+ 
+
+ align:start position:0%
+64 so that is good so what we have to
+show is that this term is an integer so
+
+ align:start position:0%
+show is that this term is an integer so
+ 
+
+ align:start position:0%
+show is that this term is an integer so
+that's all is um that remains so that
+
+ align:start position:0%
+that's all is um that remains so that
+ 
+
+ align:start position:0%
+that's all is um that remains so that
+term is clearly an integer because uh
+
+ align:start position:0%
+term is clearly an integer because uh
+ 
+
+ align:start position:0%
+term is clearly an integer because uh
+you have a summation of several terms
+
+ align:start position:0%
+you have a summation of several terms
+ 
+
+ align:start position:0%
+you have a summation of several terms
+where each term is uh made up of two
+
+ align:start position:0%
+where each term is uh made up of two
+ 
+
+ align:start position:0%
+where each term is uh made up of two
+integers themselves so 8 power R is an
+
+ align:start position:0%
+integers themselves so 8 power R is an
+ 
+
+ align:start position:0%
+integers themselves so 8 power R is an
+integer and n + 1 c r + 2 again is an
+
+ align:start position:0%
+integer and n + 1 c r + 2 again is an
+ 
+
+ align:start position:0%
+integer and n + 1 c r + 2 again is an
+integer so we have summation of integers
+
+ align:start position:0%
+integer so we have summation of integers
+ 
+
+ align:start position:0%
+integer so we have summation of integers
+and so this term is an integer so we
+
+ align:start position:0%
+and so this term is an integer so we
+ 
+
+ align:start position:0%
+and so this term is an integer so we
+have that this over overall term is
+
+ align:start position:0%
+have that this over overall term is
+ 
+
+ align:start position:0%
+have that this over overall term is
+divisible by 64 which is the desired
+
+ align:start position:0%
+divisible by 64 which is the desired
+ 
+
+ align:start position:0%
+divisible by 64 which is the desired
+result so we've
+
+ align:start position:0%
+result so we've
+ 
+
+ align:start position:0%
+result so we've
+seen U an application of the binomial
+
+ align:start position:0%
+seen U an application of the binomial
+ 
+
+ align:start position:0%
+seen U an application of the binomial
+theorem where we somehow reexpressed our
+
+ align:start position:0%
+theorem where we somehow reexpressed our
+ 
+
+ align:start position:0%
+theorem where we somehow reexpressed our
+given term uh in terms of uh in terms of
+
+ align:start position:0%
+given term uh in terms of uh in terms of
+ 
+
+ align:start position:0%
+given term uh in terms of uh in terms of
+an expression where from where we could
+
+ align:start position:0%
+an expression where from where we could
+ 
+
+ align:start position:0%
+an expression where from where we could
+use the binomial expansion and derive a
+
+ align:start position:0%
+use the binomial expansion and derive a
+ 
+
+ align:start position:0%
+use the binomial expansion and derive a
+divisibility result uh for the original
+
+ align:start position:0%
+divisibility result uh for the original
+ 
+
+ align:start position:0%
+divisibility result uh for the original
+term so let's look at a second
+
+ align:start position:0%
+term so let's look at a second
+ 
+
+ align:start position:0%
+term so let's look at a second
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+this example asks to show
+
+ align:start position:0%
+this example asks to show
+ 
+
+ align:start position:0%
+this example asks to show
+that 2^
+
+ align:start position:0%
+that 2^
+ 
+
+ align:start position:0%
+that 2^
+4n - 2^ n * 7 n +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divisible
+
+ align:start position:0%
+divisible
+ 
+
+ align:start position:0%
+divisible
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+196 whenever N is a natural
+
+ align:start position:0%
+196 whenever N is a natural
+ 
+
+ align:start position:0%
+196 whenever N is a natural
+number so this example is very similar
+
+ align:start position:0%
+number so this example is very similar
+ 
+
+ align:start position:0%
+number so this example is very similar
+to the previous one and once again we
+
+ align:start position:0%
+to the previous one and once again we
+ 
+
+ align:start position:0%
+to the previous one and once again we
+have to figure out how to rewrite this
+
+ align:start position:0%
+have to figure out how to rewrite this
+ 
+
+ align:start position:0%
+have to figure out how to rewrite this
+original term in a form which is
+
+ align:start position:0%
+original term in a form which is
+ 
+
+ align:start position:0%
+original term in a form which is
+amenable to the binomial expansion so
+
+ align:start position:0%
+amenable to the binomial expansion so
+ 
+
+ align:start position:0%
+amenable to the binomial expansion so
+notice now that we want to show that
+
+ align:start position:0%
+notice now that we want to show that
+ 
+
+ align:start position:0%
+notice now that we want to show that
+this term is diff by
+
+ align:start position:0%
+this term is diff by
+ 
+
+ align:start position:0%
+this term is diff by
+196 and 196 is nothing but 14 square and
+
+ align:start position:0%
+196 and 196 is nothing but 14 square and
+ 
+
+ align:start position:0%
+196 and 196 is nothing but 14 square and
+you have a 7 year and a 2 power n year
+
+ align:start position:0%
+you have a 7 year and a 2 power n year
+ 
+
+ align:start position:0%
+you have a 7 year and a 2 power n year
+so that looks
+
+ align:start position:0%
+so that looks
+ 
+
+ align:start position:0%
+so that looks
+promising so let's see what we can do so
+
+ align:start position:0%
+promising so let's see what we can do so
+ 
+
+ align:start position:0%
+promising so let's see what we can do so
+2 ^ 4 n - 2^ n * 7 n +
+
+ align:start position:0%
+2 ^ 4 n - 2^ n * 7 n +
+ 
+
+ align:start position:0%
+2 ^ 4 n - 2^ n * 7 n +
+1 can be uh Rewritten as 16 power N - 2^
+
+ align:start position:0%
+1 can be uh Rewritten as 16 power N - 2^
+ 
+
+ align:start position:0%
+1 can be uh Rewritten as 16 power N - 2^
+n * 7 n +
+
+ align:start position:0%
+n * 7 n +
+ 
+
+ align:start position:0%
+n * 7 n +
+1 where we just Rewritten 2^ 4 n as 16
+
+ align:start position:0%
+1 where we just Rewritten 2^ 4 n as 16
+ 
+
+ align:start position:0%
+1 where we just Rewritten 2^ 4 n as 16
+power n so now 16 can somehow uh be
+
+ align:start position:0%
+power n so now 16 can somehow uh be
+ 
+
+ align:start position:0%
+power n so now 16 can somehow uh be
+split into 14 and 2 um so we can rewrite
+
+ align:start position:0%
+split into 14 and 2 um so we can rewrite
+ 
+
+ align:start position:0%
+split into 14 and 2 um so we can rewrite
+this as 2 + 14^ n minus 2^ n * 7 n + 1
+
+ align:start position:0%
+this as 2 + 14^ n minus 2^ n * 7 n + 1
+ 
+
+ align:start position:0%
+this as 2 + 14^ n minus 2^ n * 7 n + 1
+so this looks promising because now we
+
+ align:start position:0%
+so this looks promising because now we
+ 
+
+ align:start position:0%
+so this looks promising because now we
+have a 14 appear um in a binomial term
+
+ align:start position:0%
+have a 14 appear um in a binomial term
+ 
+
+ align:start position:0%
+have a 14 appear um in a binomial term
+uh and we want to show that this whole
+
+ align:start position:0%
+uh and we want to show that this whole
+ 
+
+ align:start position:0%
+uh and we want to show that this whole
+term is divisible by
+
+ align:start position:0%
+term is divisible by
+ 
+
+ align:start position:0%
+term is divisible by
+196 which is 14
+
+ align:start position:0%
+196 which is 14
+ 
+
+ align:start position:0%
+196 which is 14
+squ so let's go through the uh motions
+
+ align:start position:0%
+squ so let's go through the uh motions
+ 
+
+ align:start position:0%
+squ so let's go through the uh motions
+again and use the binomial theorem to
+
+ align:start position:0%
+again and use the binomial theorem to
+ 
+
+ align:start position:0%
+again and use the binomial theorem to
+show that this is nothing but n c0 2^ n
+
+ align:start position:0%
+show that this is nothing but n c0 2^ n
+ 
+
+ align:start position:0%
+show that this is nothing but n c0 2^ n
+14^ 0 plus n
+
+ align:start position:0%
+14^ 0 plus n
+ 
+
+ align:start position:0%
+14^ 0 plus n
+C1 uh 2^ nus1 14^ 1
+
+ align:start position:0%
+C1 uh 2^ nus1 14^ 1
+ 
+
+ align:start position:0%
+C1 uh 2^ nus1 14^ 1
+1 plus let's rewrite the higher order
+
+ align:start position:0%
+1 plus let's rewrite the higher order
+ 
+
+ align:start position:0%
+1 plus let's rewrite the higher order
+terms the summation R = to 2 to
+
+ align:start position:0%
+terms the summation R = to 2 to
+ 
+
+ align:start position:0%
+terms the summation R = to 2 to
+n NC r 2^ n minus r 14^
+
+ align:start position:0%
+n NC r 2^ n minus r 14^
+ 
+
+ align:start position:0%
+n NC r 2^ n minus r 14^
+r and we subtract the
+
+ align:start position:0%
+r and we subtract the
+ 
+
+ align:start position:0%
+r and we subtract the
+original 2^ n * 7 n + 1 from this
+
+ align:start position:0%
+original 2^ n * 7 n + 1 from this
+ 
+
+ align:start position:0%
+original 2^ n * 7 n + 1 from this
+expansion so once again you can rewrite
+
+ align:start position:0%
+expansion so once again you can rewrite
+ 
+
+ align:start position:0%
+expansion so once again you can rewrite
+this as um 2^ n + n * 2^ N - 1 * 14 +
+
+ align:start position:0%
+this as um 2^ n + n * 2^ N - 1 * 14 +
+ 
+
+ align:start position:0%
+this as um 2^ n + n * 2^ N - 1 * 14 +
+summation R = 2 to
+
+ align:start position:0%
+summation R = 2 to
+ 
+
+ align:start position:0%
+summation R = 2 to
+n n c
+
+ align:start position:0%
+n n c
+ 
+
+ align:start position:0%
+n n c
+r 2^ nus r 14^
+
+ align:start position:0%
+r 2^ nus r 14^
+ 
+
+ align:start position:0%
+r 2^ nus r 14^
+r and u so we have to subtract 2^ n * 7
+
+ align:start position:0%
+r and u so we have to subtract 2^ n * 7
+ 
+
+ align:start position:0%
+r and u so we have to subtract 2^ n * 7
+n +
+
+ align:start position:0%
+n +
+ 
+
+ align:start position:0%
+n +
+1 so this is nothing but 2^
+
+ align:start position:0%
+1 so this is nothing but 2^
+ 
+
+ align:start position:0%
+1 so this is nothing but 2^
+n + n * 2^ n * 7 that I've factorized 14
+
+ align:start position:0%
+n + n * 2^ n * 7 that I've factorized 14
+ 
+
+ align:start position:0%
+n + n * 2^ n * 7 that I've factorized 14
+as 2 * 7 and you have a resulting
+
+ align:start position:0%
+as 2 * 7 and you have a resulting
+ 
+
+ align:start position:0%
+as 2 * 7 and you have a resulting
+summation R = to 2 to n n c r 2^ n minus
+
+ align:start position:0%
+summation R = to 2 to n n c r 2^ n minus
+ 
+
+ align:start position:0%
+summation R = to 2 to n n c r 2^ n minus
+r 14^
+
+ align:start position:0%
+r 14^
+ 
+
+ align:start position:0%
+r 14^
+r and you subtract 2^ n * 7 n and a 2
+
+ align:start position:0%
+r and you subtract 2^ n * 7 n and a 2
+ 
+
+ align:start position:0%
+r and you subtract 2^ n * 7 n and a 2
+power n where I just expanded this term
+
+ align:start position:0%
+power n where I just expanded this term
+ 
+
+ align:start position:0%
+power n where I just expanded this term
+so notice once again that you can cancel
+
+ align:start position:0%
+so notice once again that you can cancel
+ 
+
+ align:start position:0%
+so notice once again that you can cancel
+the first two terms with the terms being
+
+ align:start position:0%
+the first two terms with the terms being
+ 
+
+ align:start position:0%
+the first two terms with the terms being
+subtracted and you're still left with we
+
+ align:start position:0%
+subtracted and you're still left with we
+ 
+
+ align:start position:0%
+subtracted and you're still left with we
+are only left with this summation R = 2
+
+ align:start position:0%
+are only left with this summation R = 2
+ 
+
+ align:start position:0%
+are only left with this summation R = 2
+to n um n c r 2^ n minus r 14^ r now the
+
+ align:start position:0%
+to n um n c r 2^ n minus r 14^ r now the
+ 
+
+ align:start position:0%
+to n um n c r 2^ n minus r 14^ r now the
+arguments are uh quite similar to the
+
+ align:start position:0%
+arguments are uh quite similar to the
+ 
+
+ align:start position:0%
+arguments are uh quite similar to the
+previous one uh previous example we've
+
+ align:start position:0%
+previous one uh previous example we've
+ 
+
+ align:start position:0%
+previous one uh previous example we've
+seen so I won't go through this in
+
+ align:start position:0%
+seen so I won't go through this in
+ 
+
+ align:start position:0%
+seen so I won't go through this in
+detail you can just rewrite this as 14 s
+
+ align:start position:0%
+detail you can just rewrite this as 14 s
+ 
+
+ align:start position:0%
+detail you can just rewrite this as 14 s
+* summation R = 0
+
+ align:start position:0%
+* summation R = 0
+ 
+
+ align:start position:0%
+* summation R = 0
+to N -
+
+ align:start position:0%
+to N -
+ 
+
+ align:start position:0%
+to N -
+2 n c r +
+
+ align:start position:0%
+2 n c r +
+ 
+
+ align:start position:0%
+2 n c r +
+2 2 power
+
+ align:start position:0%
+2 2 power
+ 
+
+ align:start position:0%
+2 2 power
+nus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r -
+
+ align:start position:0%
+r -
+ 
+
+ align:start position:0%
+r -
+2 and 14
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power where here you started with 2^ n
+
+ align:start position:0%
+power where here you started with 2^ n
+ 
+
+ align:start position:0%
+power where here you started with 2^ n
+minus 2 and so you're starting with 2^ n
+
+ align:start position:0%
+minus 2 and so you're starting with 2^ n
+ 
+
+ align:start position:0%
+minus 2 and so you're starting with 2^ n
+minus 2 again and here you started with
+
+ align:start position:0%
+minus 2 again and here you started with
+ 
+
+ align:start position:0%
+minus 2 again and here you started with
+14 squ and here you start with 14 power
+
+ align:start position:0%
+14 squ and here you start with 14 power
+ 
+
+ align:start position:0%
+14 squ and here you start with 14 power
+0 since I pulled out a 14 Square here so
+
+ align:start position:0%
+0 since I pulled out a 14 Square here so
+ 
+
+ align:start position:0%
+0 since I pulled out a 14 Square here so
+so this is what we are left with and
+
+ align:start position:0%
+so this is what we are left with and
+ 
+
+ align:start position:0%
+so this is what we are left with and
+notice that this summation again is an
+
+ align:start position:0%
+notice that this summation again is an
+ 
+
+ align:start position:0%
+notice that this summation again is an
+integer and we have the summation being
+
+ align:start position:0%
+integer and we have the summation being
+ 
+
+ align:start position:0%
+integer and we have the summation being
+multiplied by 14 squ which is 196 which
+
+ align:start position:0%
+multiplied by 14 squ which is 196 which
+ 
+
+ align:start position:0%
+multiplied by 14 squ which is 196 which
+is again an integer and we wanted to
+
+ align:start position:0%
+is again an integer and we wanted to
+ 
+
+ align:start position:0%
+is again an integer and we wanted to
+show that this term is divisible by 196
+
+ align:start position:0%
+show that this term is divisible by 196
+ 
+
+ align:start position:0%
+show that this term is divisible by 196
+so that's exactly what we've shown since
+
+ align:start position:0%
+so that's exactly what we've shown since
+ 
+
+ align:start position:0%
+so that's exactly what we've shown since
+we've factorized it into a form where we
+
+ align:start position:0%
+we've factorized it into a form where we
+ 
+
+ align:start position:0%
+we've factorized it into a form where we
+have a leading um coefficient of 14
+
+ align:start position:0%
+have a leading um coefficient of 14
+ 
+
+ align:start position:0%
+have a leading um coefficient of 14
+Square um and so we've once again shown
+
+ align:start position:0%
+Square um and so we've once again shown
+ 
+
+ align:start position:0%
+Square um and so we've once again shown
+that the this term isible by 196
+
+ align:start position:0%
+that the this term isible by 196
+ 
+
+ align:start position:0%
+that the this term isible by 196
+whenever N is a natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number so let's look at a multiple
+
+ align:start position:0%
+number so let's look at a multiple
+ 
+
+ align:start position:0%
+number so let's look at a multiple
+choice question which is uh based on
+
+ align:start position:0%
+choice question which is uh based on
+ 
+
+ align:start position:0%
+choice question which is uh based on
+this flavor of problems so the question
+
+ align:start position:0%
+this flavor of problems so the question
+ 
+
+ align:start position:0%
+this flavor of problems so the question
+asks you to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+show asks you uh when 5 power 99 um is
+
+ align:start position:0%
+show asks you uh when 5 power 99 um is
+ 
+
+ align:start position:0%
+show asks you uh when 5 power 99 um is
+divided
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+13 uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remainder yes so it asks you to compute
+
+ align:start position:0%
+remainder yes so it asks you to compute
+ 
+
+ align:start position:0%
+remainder yes so it asks you to compute
+the remainder and 5^ 99 is divided by 13
+
+ align:start position:0%
+the remainder and 5^ 99 is divided by 13
+ 
+
+ align:start position:0%
+the remainder and 5^ 99 is divided by 13
+and the options are
+
+ align:start position:0%
+and the options are
+ 
+
+ align:start position:0%
+and the options are
+8 9
+
+ align:start position:0%
+8 9
+ 
+
+ align:start position:0%
+8 9
+10 and none of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+so this is a kind of problem where it's
+
+ align:start position:0%
+so this is a kind of problem where it's
+ 
+
+ align:start position:0%
+so this is a kind of problem where it's
+uh hard to eliminate the options without
+
+ align:start position:0%
+uh hard to eliminate the options without
+ 
+
+ align:start position:0%
+uh hard to eliminate the options without
+actually solving the problem uh because
+
+ align:start position:0%
+actually solving the problem uh because
+ 
+
+ align:start position:0%
+actually solving the problem uh because
+uh you have none of these uh where uh so
+
+ align:start position:0%
+uh you have none of these uh where uh so
+ 
+
+ align:start position:0%
+uh you have none of these uh where uh so
+even if you determine that this
+
+ align:start position:0%
+even if you determine that this
+ 
+
+ align:start position:0%
+even if you determine that this
+remainder is going to be even or odd uh
+
+ align:start position:0%
+remainder is going to be even or odd uh
+ 
+
+ align:start position:0%
+remainder is going to be even or odd uh
+you're not really sure whe which option
+
+ align:start position:0%
+you're not really sure whe which option
+ 
+
+ align:start position:0%
+you're not really sure whe which option
+it is since there's none of these and uh
+
+ align:start position:0%
+it is since there's none of these and uh
+ 
+
+ align:start position:0%
+it is since there's none of these and uh
+even if the remainder is odd you can't
+
+ align:start position:0%
+even if the remainder is odd you can't
+ 
+
+ align:start position:0%
+even if the remainder is odd you can't
+just conclude that the answer is nine uh
+
+ align:start position:0%
+just conclude that the answer is nine uh
+ 
+
+ align:start position:0%
+just conclude that the answer is nine uh
+so you would actually have to derive the
+
+ align:start position:0%
+so you would actually have to derive the
+ 
+
+ align:start position:0%
+so you would actually have to derive the
+result for this example so let's see how
+
+ align:start position:0%
+result for this example so let's see how
+ 
+
+ align:start position:0%
+result for this example so let's see how
+you can rewrite five 5 power 99 to
+
+ align:start position:0%
+you can rewrite five 5 power 99 to
+ 
+
+ align:start position:0%
+you can rewrite five 5 power 99 to
+obtain an amenable result so to to
+
+ align:start position:0%
+obtain an amenable result so to to
+ 
+
+ align:start position:0%
+obtain an amenable result so to to
+arrive at this the solution uh let's try
+
+ align:start position:0%
+arrive at this the solution uh let's try
+ 
+
+ align:start position:0%
+arrive at this the solution uh let's try
+Computing some powers of five uh to see
+
+ align:start position:0%
+Computing some powers of five uh to see
+ 
+
+ align:start position:0%
+Computing some powers of five uh to see
+where that gets us so 5 power 1 is
+
+ align:start position:0%
+where that gets us so 5 power 1 is
+ 
+
+ align:start position:0%
+where that gets us so 5 power 1 is
+5 uh which is quite far from 13 so
+
+ align:start position:0%
+5 uh which is quite far from 13 so
+ 
+
+ align:start position:0%
+5 uh which is quite far from 13 so
+there's not really much you can do about
+
+ align:start position:0%
+there's not really much you can do about
+ 
+
+ align:start position:0%
+there's not really much you can do about
+it uh 5 sare is 25 which is close to a
+
+ align:start position:0%
+it uh 5 sare is 25 which is close to a
+ 
+
+ align:start position:0%
+it uh 5 sare is 25 which is close to a
+multiple of 13 13 * 2 is 26 so this
+
+ align:start position:0%
+multiple of 13 13 * 2 is 26 so this
+ 
+
+ align:start position:0%
+multiple of 13 13 * 2 is 26 so this
+looks promising uh but 5 power 99 is not
+
+ align:start position:0%
+looks promising uh but 5 power 99 is not
+ 
+
+ align:start position:0%
+looks promising uh but 5 power 99 is not
+a direct power of not an integral power
+
+ align:start position:0%
+a direct power of not an integral power
+ 
+
+ align:start position:0%
+a direct power of not an integral power
+of 5 square and so let's try this
+
+ align:start position:0%
+of 5 square and so let's try this
+ 
+
+ align:start position:0%
+of 5 square and so let's try this
+approach let's write 5 power 99 as 5 * 5
+
+ align:start position:0%
+approach let's write 5 power 99 as 5 * 5
+ 
+
+ align:start position:0%
+approach let's write 5 power 99 as 5 * 5
+Power
+
+ align:start position:0%
+Power
+ 
+
+ align:start position:0%
+Power
+98 I've just factorized 5 99 into a more
+
+ align:start position:0%
+98 I've just factorized 5 99 into a more
+ 
+
+ align:start position:0%
+98 I've just factorized 5 99 into a more
+suitable form and now I can write this
+
+ align:start position:0%
+suitable form and now I can write this
+ 
+
+ align:start position:0%
+suitable form and now I can write this
+as 5 * 5 power 5 S power
+
+ align:start position:0%
+as 5 * 5 power 5 S power
+ 
+
+ align:start position:0%
+as 5 * 5 power 5 S power
+49 uh and since I know that 5 square is
+
+ align:start position:0%
+49 uh and since I know that 5 square is
+ 
+
+ align:start position:0%
+49 uh and since I know that 5 square is
+close to a multiple of 13 this is
+
+ align:start position:0%
+close to a multiple of 13 this is
+ 
+
+ align:start position:0%
+close to a multiple of 13 this is
+nothing but 5
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+* 26 -
+
+ align:start position:0%
+* 26 -
+ 
+
+ align:start position:0%
+* 26 -
+1^ 49 26 is a multiple of 13 so the
+
+ align:start position:0%
+1^ 49 26 is a multiple of 13 so the
+ 
+
+ align:start position:0%
+1^ 49 26 is a multiple of 13 so the
+divisibility results are going to be
+
+ align:start position:0%
+divisibility results are going to be
+ 
+
+ align:start position:0%
+divisibility results are going to be
+fairly easy to derive
+
+ align:start position:0%
+fairly easy to derive
+ 
+
+ align:start position:0%
+fairly easy to derive
+uh so this is nothing but five * and now
+
+ align:start position:0%
+uh so this is nothing but five * and now
+ 
+
+ align:start position:0%
+uh so this is nothing but five * and now
+you use the binomial expansion of 26 -
+
+ align:start position:0%
+you use the binomial expansion of 26 -
+ 
+
+ align:start position:0%
+you use the binomial expansion of 26 -
+1^ 49 uh so let's see how we can write
+
+ align:start position:0%
+1^ 49 uh so let's see how we can write
+ 
+
+ align:start position:0%
+1^ 49 uh so let's see how we can write
+this it's like
+
+ align:start position:0%
+this it's like
+ 
+
+ align:start position:0%
+this it's like
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+C 0 - 1 power
+
+ align:start position:0%
+C 0 - 1 power
+ 
+
+ align:start position:0%
+C 0 - 1 power
+49 26 power 0 so I'm starting off with
+
+ align:start position:0%
+49 26 power 0 so I'm starting off with
+ 
+
+ align:start position:0%
+49 26 power 0 so I'm starting off with
+-1 power 49 and 26 power 0 since we are
+
+ align:start position:0%
+-1 power 49 and 26 power 0 since we are
+ 
+
+ align:start position:0%
+-1 power 49 and 26 power 0 since we are
+only concerned with uh the power of 26
+
+ align:start position:0%
+only concerned with uh the power of 26
+ 
+
+ align:start position:0%
+only concerned with uh the power of 26
+which is zero since all other terms are
+
+ align:start position:0%
+which is zero since all other terms are
+ 
+
+ align:start position:0%
+which is zero since all other terms are
+going to be divisible by 13 so and you
+
+ align:start position:0%
+going to be divisible by 13 so and you
+ 
+
+ align:start position:0%
+going to be divisible by 13 so and you
+have 49 C1 - 1^
+
+ align:start position:0%
+have 49 C1 - 1^
+ 
+
+ align:start position:0%
+have 49 C1 - 1^
+48 26 power
+
+ align:start position:0%
+48 26 power
+ 
+
+ align:start position:0%
+48 26 power
+1 uh plus so
+
+ align:start position:0%
+1 uh plus so
+ 
+
+ align:start position:0%
+1 uh plus so
+on so this is going to be the expansion
+
+ align:start position:0%
+on so this is going to be the expansion
+ 
+
+ align:start position:0%
+on so this is going to be the expansion
+of 26 - 1 the^ 49 and you have a leading
+
+ align:start position:0%
+of 26 - 1 the^ 49 and you have a leading
+ 
+
+ align:start position:0%
+of 26 - 1 the^ 49 and you have a leading
+term which is five um in this expression
+
+ align:start position:0%
+term which is five um in this expression
+ 
+
+ align:start position:0%
+term which is five um in this expression
+so notice that all of these higher
+
+ align:start position:0%
+so notice that all of these higher
+ 
+
+ align:start position:0%
+so notice that all of these higher
+Powers as I mentioned are going to be
+
+ align:start position:0%
+Powers as I mentioned are going to be
+ 
+
+ align:start position:0%
+Powers as I mentioned are going to be
+divisible by 13 and so since we only
+
+ align:start position:0%
+divisible by 13 and so since we only
+ 
+
+ align:start position:0%
+divisible by 13 and so since we only
+care about remainder that this term
+
+ align:start position:0%
+care about remainder that this term
+ 
+
+ align:start position:0%
+care about remainder that this term
+leaves when divided by 13 we don't
+
+ align:start position:0%
+leaves when divided by 13 we don't
+ 
+
+ align:start position:0%
+leaves when divided by 13 we don't
+really care about these terms which are
+
+ align:start position:0%
+really care about these terms which are
+ 
+
+ align:start position:0%
+really care about these terms which are
+exactly divisible by 13 so this is the
+
+ align:start position:0%
+exactly divisible by 13 so this is the
+ 
+
+ align:start position:0%
+exactly divisible by 13 so this is the
+only remaining term is going to give us
+
+ align:start position:0%
+only remaining term is going to give us
+ 
+
+ align:start position:0%
+only remaining term is going to give us
+um the remainder when you divide 5 power
+
+ align:start position:0%
+um the remainder when you divide 5 power
+ 
+
+ align:start position:0%
+um the remainder when you divide 5 power
+99 by 13 so let's see what that gives us
+
+ align:start position:0%
+99 by 13 so let's see what that gives us
+ 
+
+ align:start position:0%
+99 by 13 so let's see what that gives us
+that's 5 * 49 C 0 is 1 uh * - 1^ 49 is
+
+ align:start position:0%
+that's 5 * 49 C 0 is 1 uh * - 1^ 49 is
+ 
+
+ align:start position:0%
+that's 5 * 49 C 0 is 1 uh * - 1^ 49 is
+-1 * 26 0 is 1 and so this gives us - 5
+
+ align:start position:0%
+-1 * 26 0 is 1 and so this gives us - 5
+ 
+
+ align:start position:0%
+-1 * 26 0 is 1 and so this gives us - 5
+so the remainder when 5^ 99 is divided
+
+ align:start position:0%
+so the remainder when 5^ 99 is divided
+ 
+
+ align:start position:0%
+so the remainder when 5^ 99 is divided
+by 13 is - 5 uh for those of you who
+
+ align:start position:0%
+by 13 is - 5 uh for those of you who
+ 
+
+ align:start position:0%
+by 13 is - 5 uh for those of you who
+aren't used to this kind of notation
+
+ align:start position:0%
+aren't used to this kind of notation
+ 
+
+ align:start position:0%
+aren't used to this kind of notation
+this might seem a little strange that
+
+ align:start position:0%
+this might seem a little strange that
+ 
+
+ align:start position:0%
+this might seem a little strange that
+you get a negative remainder but to just
+
+ align:start position:0%
+you get a negative remainder but to just
+ 
+
+ align:start position:0%
+you get a negative remainder but to just
+get a positive remainder you just add a
+
+ align:start position:0%
+get a positive remainder you just add a
+ 
+
+ align:start position:0%
+get a positive remainder you just add a
+multiple of 13 since we've ignored so
+
+ align:start position:0%
+multiple of 13 since we've ignored so
+ 
+
+ align:start position:0%
+multiple of 13 since we've ignored so
+many multiples of 13 you get a negative
+
+ align:start position:0%
+many multiples of 13 you get a negative
+ 
+
+ align:start position:0%
+many multiples of 13 you get a negative
+number but if you add a multiple of 13
+
+ align:start position:0%
+number but if you add a multiple of 13
+ 
+
+ align:start position:0%
+number but if you add a multiple of 13
+you get 8 so the remainder uh when 5
+
+ align:start position:0%
+you get 8 so the remainder uh when 5
+ 
+
+ align:start position:0%
+you get 8 so the remainder uh when 5
+power 99 is divided by 13 is 8
+
+ align:start position:0%
+power 99 is divided by 13 is 8
+ 
+
+ align:start position:0%
+power 99 is divided by 13 is 8
+for those of you who are familiar with
+
+ align:start position:0%
+for those of you who are familiar with
+ 
+
+ align:start position:0%
+for those of you who are familiar with
+modular arithmetic U you can notice that
+
+ align:start position:0%
+modular arithmetic U you can notice that
+ 
+
+ align:start position:0%
+modular arithmetic U you can notice that
+the approach we took is very similar to
+
+ align:start position:0%
+the approach we took is very similar to
+ 
+
+ align:start position:0%
+the approach we took is very similar to
+the approach you take uh when you use uh
+
+ align:start position:0%
+the approach you take uh when you use uh
+ 
+
+ align:start position:0%
+the approach you take uh when you use uh
+when you do such kinds of problems in
+
+ align:start position:0%
+when you do such kinds of problems in
+ 
+
+ align:start position:0%
+when you do such kinds of problems in
+number Theory where you try to get uh
+
+ align:start position:0%
+number Theory where you try to get uh
+ 
+
+ align:start position:0%
+number Theory where you try to get uh
+try to uh get at a power of five which
+
+ align:start position:0%
+try to uh get at a power of five which
+ 
+
+ align:start position:0%
+try to uh get at a power of five which
+is close to a multiple of 13 and you
+
+ align:start position:0%
+is close to a multiple of 13 and you
+ 
+
+ align:start position:0%
+is close to a multiple of 13 and you
+just used uh remainder arguments where
+
+ align:start position:0%
+just used uh remainder arguments where
+ 
+
+ align:start position:0%
+just used uh remainder arguments where
+you ignored uh terms which were
+
+ align:start position:0%
+you ignored uh terms which were
+ 
+
+ align:start position:0%
+you ignored uh terms which were
+multiples of 13 and So you you're only
+
+ align:start position:0%
+multiples of 13 and So you you're only
+ 
+
+ align:start position:0%
+multiples of 13 and So you you're only
+left with one term since only care about
+
+ align:start position:0%
+left with one term since only care about
+ 
+
+ align:start position:0%
+left with one term since only care about
+the remainder um so this is a sample of
+
+ align:start position:0%
+the remainder um so this is a sample of
+ 
+
+ align:start position:0%
+the remainder um so this is a sample of
+a problem which could appear in an exam
+
+ align:start position:0%
+a problem which could appear in an exam
+ 
+
+ align:start position:0%
+a problem which could appear in an exam
+type situation where you're asked to
+
+ align:start position:0%
+type situation where you're asked to
+ 
+
+ align:start position:0%
+type situation where you're asked to
+derive a result based on the
+
+ align:start position:0%
+derive a result based on the
+ 
+
+ align:start position:0%
+derive a result based on the
+divisibility U of A term U by a natural
+
+ align:start position:0%
+divisibility U of A term U by a natural
+ 
+
+ align:start position:0%
+divisibility U of A term U by a natural
+number uh using the binomial theorem so
+
+ align:start position:0%
+number uh using the binomial theorem so
+ 
+
+ align:start position:0%
+number uh using the binomial theorem so
+that's it for this lecture hope you
+
+ align:start position:0%
+that's it for this lecture hope you
+ 
+
+ align:start position:0%
+that's it for this lecture hope you
+enjoyed watching this lecture uh and in
+
+ align:start position:0%
+enjoyed watching this lecture uh and in
+ 
+
+ align:start position:0%
+enjoyed watching this lecture uh and in
+the next uh lectures we will look at
+
+ align:start position:0%
+the next uh lectures we will look at
+ 
+
+ align:start position:0%
+the next uh lectures we will look at
+some example problems based on the
+
+ align:start position:0%
+some example problems based on the
+ 
+
+ align:start position:0%
+some example problems based on the
+binomial theorem I thank you for your
+
+ align:start position:0%
+binomial theorem I thank you for your
+ 
+
+ align:start position:0%
+binomial theorem I thank you for your
+attention and hope you can join us next
+
+ align:start position:0%
+attention and hope you can join us next
+ 
+
+ align:start position:0%
+attention and hope you can join us next
+time
\ No newline at end of file
diff --git a/7QJyMB9qGQg.txt b/7QJyMB9qGQg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a257a0c6702c48071bb2898b3d6ed3a6067c059b
--- /dev/null
+++ b/7QJyMB9qGQg.txt
@@ -0,0 +1,499 @@
+align:start position:0%
+ 
+radiation therapy is one of the most
+
+ align:start position:0%
+radiation therapy is one of the most
+ 
+
+ align:start position:0%
+radiation therapy is one of the most
+well used applications of optimization
+
+ align:start position:0%
+well used applications of optimization
+ 
+
+ align:start position:0%
+well used applications of optimization
+in healthcare in practice radiation
+
+ align:start position:0%
+in healthcare in practice radiation
+ 
+
+ align:start position:0%
+in healthcare in practice radiation
+machines are connected to treatment
+
+ align:start position:0%
+machines are connected to treatment
+ 
+
+ align:start position:0%
+machines are connected to treatment
+planning software that implements and
+
+ align:start position:0%
+planning software that implements and
+ 
+
+ align:start position:0%
+planning software that implements and
+solves optimization models both linear
+
+ align:start position:0%
+solves optimization models both linear
+ 
+
+ align:start position:0%
+solves optimization models both linear
+optimization models like we saw here and
+
+ align:start position:0%
+optimization models like we saw here and
+ 
+
+ align:start position:0%
+optimization models like we saw here and
+other types of optimization models some
+
+ align:start position:0%
+other types of optimization models some
+ 
+
+ align:start position:0%
+other types of optimization models some
+examples of radiation machines that use
+
+ align:start position:0%
+examples of radiation machines that use
+ 
+
+ align:start position:0%
+examples of radiation machines that use
+optimization software are pinnacle by
+
+ align:start position:0%
+optimization software are pinnacle by
+ 
+
+ align:start position:0%
+optimization software are pinnacle by
+Philips ray station by research labs and
+
+ align:start position:0%
+Philips ray station by research labs and
+ 
+
+ align:start position:0%
+Philips ray station by research labs and
+Eclipse by Varian there are many
+
+ align:start position:0%
+Eclipse by Varian there are many
+ 
+
+ align:start position:0%
+Eclipse by Varian there are many
+extensions to the optimization model we
+
+ align:start position:0%
+extensions to the optimization model we
+ 
+
+ align:start position:0%
+extensions to the optimization model we
+described here one is the selection of
+
+ align:start position:0%
+described here one is the selection of
+ 
+
+ align:start position:0%
+described here one is the selection of
+beam angles the beam angles can be
+
+ align:start position:0%
+beam angles the beam angles can be
+ 
+
+ align:start position:0%
+beam angles the beam angles can be
+selected jointly with the intensity
+
+ align:start position:0%
+selected jointly with the intensity
+ 
+
+ align:start position:0%
+selected jointly with the intensity
+profiles by using integer optimization
+
+ align:start position:0%
+profiles by using integer optimization
+ 
+
+ align:start position:0%
+profiles by using integer optimization
+this allows the treatment to be further
+
+ align:start position:0%
+this allows the treatment to be further
+ 
+
+ align:start position:0%
+this allows the treatment to be further
+personalized to the specific tumor and
+
+ align:start position:0%
+personalized to the specific tumor and
+ 
+
+ align:start position:0%
+personalized to the specific tumor and
+person receiving the radiation integer
+
+ align:start position:0%
+person receiving the radiation integer
+ 
+
+ align:start position:0%
+person receiving the radiation integer
+optimization is another type of
+
+ align:start position:0%
+optimization is another type of
+ 
+
+ align:start position:0%
+optimization is another type of
+optimization model and will be the topic
+
+ align:start position:0%
+optimization model and will be the topic
+ 
+
+ align:start position:0%
+optimization model and will be the topic
+of next week another extension is
+
+ align:start position:0%
+of next week another extension is
+ 
+
+ align:start position:0%
+of next week another extension is
+accounting for uncertainty often the
+
+ align:start position:0%
+accounting for uncertainty often the
+ 
+
+ align:start position:0%
+accounting for uncertainty often the
+quality of imrt treatments is degraded
+
+ align:start position:0%
+quality of imrt treatments is degraded
+ 
+
+ align:start position:0%
+quality of imrt treatments is degraded
+due to uncertain organ motion for
+
+ align:start position:0%
+due to uncertain organ motion for
+ 
+
+ align:start position:0%
+due to uncertain organ motion for
+example in lung cancer the target area
+
+ align:start position:0%
+example in lung cancer the target area
+ 
+
+ align:start position:0%
+example in lung cancer the target area
+is around the lungs but since the
+
+ align:start position:0%
+is around the lungs but since the
+ 
+
+ align:start position:0%
+is around the lungs but since the
+patient is breathing throughout the
+
+ align:start position:0%
+patient is breathing throughout the
+ 
+
+ align:start position:0%
+patient is breathing throughout the
+treatment the target area is moving and
+
+ align:start position:0%
+treatment the target area is moving and
+ 
+
+ align:start position:0%
+treatment the target area is moving and
+the location is slightly uncertain we
+
+ align:start position:0%
+the location is slightly uncertain we
+ 
+
+ align:start position:0%
+the location is slightly uncertain we
+can manage this uncertainty using a
+
+ align:start position:0%
+can manage this uncertainty using a
+ 
+
+ align:start position:0%
+can manage this uncertainty using a
+method known as robust optimization
+
+ align:start position:0%
+method known as robust optimization
+ 
+
+ align:start position:0%
+method known as robust optimization
+there is a significant amount of
+
+ align:start position:0%
+there is a significant amount of
+ 
+
+ align:start position:0%
+there is a significant amount of
+literature on this method and its
+
+ align:start position:0%
+literature on this method and its
+ 
+
+ align:start position:0%
+literature on this method and its
+application to radiation therapy linear
+
+ align:start position:0%
+application to radiation therapy linear
+ 
+
+ align:start position:0%
+application to radiation therapy linear
+optimization significantly improves the
+
+ align:start position:0%
+optimization significantly improves the
+ 
+
+ align:start position:0%
+optimization significantly improves the
+efficiency of radiation therapy manually
+
+ align:start position:0%
+efficiency of radiation therapy manually
+ 
+
+ align:start position:0%
+efficiency of radiation therapy manually
+designing an IMRT treatment would be
+
+ align:start position:0%
+designing an IMRT treatment would be
+ 
+
+ align:start position:0%
+designing an IMRT treatment would be
+inefficient and impractical by using
+
+ align:start position:0%
+inefficient and impractical by using
+ 
+
+ align:start position:0%
+inefficient and impractical by using
+linear optimization
+
+ align:start position:0%
+linear optimization
+ 
+
+ align:start position:0%
+linear optimization
+I am RT can be designed in an efficient
+
+ align:start position:0%
+I am RT can be designed in an efficient
+ 
+
+ align:start position:0%
+I am RT can be designed in an efficient
+and systematic way as we saw in this
+
+ align:start position:0%
+and systematic way as we saw in this
+ 
+
+ align:start position:0%
+and systematic way as we saw in this
+lecture clinical criteria can be modeled
+
+ align:start position:0%
+lecture clinical criteria can be modeled
+ 
+
+ align:start position:0%
+lecture clinical criteria can be modeled
+using constraints and the treatment
+
+ align:start position:0%
+using constraints and the treatment
+ 
+
+ align:start position:0%
+using constraints and the treatment
+planner can explore trade-offs by change
+
+ align:start position:0%
+planner can explore trade-offs by change
+ 
+
+ align:start position:0%
+planner can explore trade-offs by change
+the model but ultimately I am RT in the
+
+ align:start position:0%
+the model but ultimately I am RT in the
+ 
+
+ align:start position:0%
+the model but ultimately I am RT in the
+use of optimization benefits the patient
+
+ align:start position:0%
+use of optimization benefits the patient
+ 
+
+ align:start position:0%
+use of optimization benefits the patient
+in head and neck cancers saliva glands
+
+ align:start position:0%
+in head and neck cancers saliva glands
+ 
+
+ align:start position:0%
+in head and neck cancers saliva glands
+were rarely spared prior to imrt but by
+
+ align:start position:0%
+were rarely spared prior to imrt but by
+ 
+
+ align:start position:0%
+were rarely spared prior to imrt but by
+using optimized
+
+ align:start position:0%
+using optimized
+ 
+
+ align:start position:0%
+using optimized
+imrt treatments saliva glands can now be
+
+ align:start position:0%
+imrt treatments saliva glands can now be
+ 
+
+ align:start position:0%
+imrt treatments saliva glands can now be
+spared in prostate cancer IMRT
+
+ align:start position:0%
+spared in prostate cancer IMRT
+ 
+
+ align:start position:0%
+spared in prostate cancer IMRT
+treatments reduce toxicities and allow
+
+ align:start position:0%
+treatments reduce toxicities and allow
+ 
+
+ align:start position:0%
+treatments reduce toxicities and allow
+for higher tumor doses to be delivered
+
+ align:start position:0%
+for higher tumor doses to be delivered
+ 
+
+ align:start position:0%
+for higher tumor doses to be delivered
+safely and in lung cancer
+
+ align:start position:0%
+safely and in lung cancer
+ 
+
+ align:start position:0%
+safely and in lung cancer
+optimized IMRT reduce the risk of
+
+ align:start position:0%
+optimized IMRT reduce the risk of
+ 
+
+ align:start position:0%
+optimized IMRT reduce the risk of
+radiation induced pneumonitis these are
+
+ align:start position:0%
+radiation induced pneumonitis these are
+ 
+
+ align:start position:0%
+radiation induced pneumonitis these are
+just three examples of the benefits of
+
+ align:start position:0%
+just three examples of the benefits of
+ 
+
+ align:start position:0%
+just three examples of the benefits of
+IMRT overall optimized IMRT allows
+
+ align:start position:0%
+IMRT overall optimized IMRT allows
+ 
+
+ align:start position:0%
+IMRT overall optimized IMRT allows
+clinicians to deliver treatment that was
+
+ align:start position:0%
+clinicians to deliver treatment that was
+ 
+
+ align:start position:0%
+clinicians to deliver treatment that was
+previously impossible and to improve the
+
+ align:start position:0%
+previously impossible and to improve the
+ 
+
+ align:start position:0%
+previously impossible and to improve the
+quality of life for patients
\ No newline at end of file
diff --git a/7UNiSHGyg1Q.txt b/7UNiSHGyg1Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b64dc99da45fc11c4d88a32aba86900643d86565
--- /dev/null
+++ b/7UNiSHGyg1Q.txt
@@ -0,0 +1,2515 @@
+align:start position:0%
+ 
+talks about a prospective lng plant that
+
+ align:start position:0%
+talks about a prospective lng plant that
+ 
+
+ align:start position:0%
+talks about a prospective lng plant that
+i worked on with these colleagues uh
+
+ align:start position:0%
+i worked on with these colleagues uh
+ 
+
+ align:start position:0%
+i worked on with these colleagues uh
+kardashian student uh kardash and he
+
+ align:start position:0%
+kardashian student uh kardash and he
+ 
+
+ align:start position:0%
+kardashian student uh kardash and he
+sees this student burani and others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+keppel offshore and marine corporation
+
+ align:start position:0%
+keppel offshore and marine corporation
+ 
+
+ align:start position:0%
+keppel offshore and marine corporation
+which is a big
+
+ align:start position:0%
+which is a big
+ 
+
+ align:start position:0%
+which is a big
+uh shipbuilding
+
+ align:start position:0%
+uh shipbuilding
+ 
+
+ align:start position:0%
+uh shipbuilding
+platform building metal bending uh
+
+ align:start position:0%
+platform building metal bending uh
+ 
+
+ align:start position:0%
+platform building metal bending uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+government company
+
+ align:start position:0%
+government company
+ 
+
+ align:start position:0%
+government company
+in singapore and they had this as a
+
+ align:start position:0%
+in singapore and they had this as a
+ 
+
+ align:start position:0%
+in singapore and they had this as a
+prospective case and
+
+ align:start position:0%
+prospective case and
+ 
+
+ align:start position:0%
+prospective case and
+as a they had a commission a design they
+
+ align:start position:0%
+as a they had a commission a design they
+ 
+
+ align:start position:0%
+as a they had a commission a design they
+were working on it for some oil company
+
+ align:start position:0%
+were working on it for some oil company
+ 
+
+ align:start position:0%
+were working on it for some oil company
+and we took this on as a way of thinking
+
+ align:start position:0%
+and we took this on as a way of thinking
+ 
+
+ align:start position:0%
+and we took this on as a way of thinking
+about can one do better as i think
+
+ align:start position:0%
+about can one do better as i think
+ 
+
+ align:start position:0%
+about can one do better as i think
+indeed we can and that's what this is
+
+ align:start position:0%
+indeed we can and that's what this is
+ 
+
+ align:start position:0%
+indeed we can and that's what this is
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it is first of all a parametric analysis
+
+ align:start position:0%
+it is first of all a parametric analysis
+ 
+
+ align:start position:0%
+it is first of all a parametric analysis
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+uh looks at a significant range of
+
+ align:start position:0%
+uh looks at a significant range of
+ 
+
+ align:start position:0%
+uh looks at a significant range of
+factors there's instead of saying this
+
+ align:start position:0%
+factors there's instead of saying this
+ 
+
+ align:start position:0%
+factors there's instead of saying this
+is the condition that says well what if
+
+ align:start position:0%
+is the condition that says well what if
+ 
+
+ align:start position:0%
+is the condition that says well what if
+the economy of the scale were longer
+
+ align:start position:0%
+the economy of the scale were longer
+ 
+
+ align:start position:0%
+the economy of the scale were longer
+what if the uncertainty was different
+
+ align:start position:0%
+what if the uncertainty was different
+ 
+
+ align:start position:0%
+what if the uncertainty was different
+what if
+
+ align:start position:0%
+what if
+ 
+
+ align:start position:0%
+what if
+learning was a different scale so that
+
+ align:start position:0%
+learning was a different scale so that
+ 
+
+ align:start position:0%
+learning was a different scale so that
+it's designed to illustrate a range of
+
+ align:start position:0%
+it's designed to illustrate a range of
+ 
+
+ align:start position:0%
+it's designed to illustrate a range of
+possible conditions of how you might do
+
+ align:start position:0%
+possible conditions of how you might do
+ 
+
+ align:start position:0%
+possible conditions of how you might do
+it rather than trying to specify a
+
+ align:start position:0%
+it rather than trying to specify a
+ 
+
+ align:start position:0%
+it rather than trying to specify a
+particular one so a design is a learning
+
+ align:start position:0%
+particular one so a design is a learning
+ 
+
+ align:start position:0%
+particular one so a design is a learning
+experience
+
+ align:start position:0%
+experience
+ 
+
+ align:start position:0%
+experience
+i hope you'll find it so
+
+ align:start position:0%
+i hope you'll find it so
+ 
+
+ align:start position:0%
+i hope you'll find it so
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+general idea is sort of to do mid-text
+
+ align:start position:0%
+general idea is sort of to do mid-text
+ 
+
+ align:start position:0%
+general idea is sort of to do mid-text
+if you want uh that homework in a much
+
+ align:start position:0%
+if you want uh that homework in a much
+ 
+
+ align:start position:0%
+if you want uh that homework in a much
+more detailed and
+
+ align:start position:0%
+more detailed and
+ 
+
+ align:start position:0%
+more detailed and
+complicated situation
+
+ align:start position:0%
+complicated situation
+ 
+
+ align:start position:0%
+complicated situation
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+to what conclusions can we talk about in
+
+ align:start position:0%
+to what conclusions can we talk about in
+ 
+
+ align:start position:0%
+to what conclusions can we talk about in
+terms of preferred strategies notice
+
+ align:start position:0%
+terms of preferred strategies notice
+ 
+
+ align:start position:0%
+terms of preferred strategies notice
+again that i've talked about preferred
+
+ align:start position:0%
+again that i've talked about preferred
+ 
+
+ align:start position:0%
+again that i've talked about preferred
+strategies because there's trade-offs
+
+ align:start position:0%
+strategies because there's trade-offs
+ 
+
+ align:start position:0%
+strategies because there's trade-offs
+about the cost and the and the risk
+
+ align:start position:0%
+about the cost and the and the risk
+ 
+
+ align:start position:0%
+about the cost and the and the risk
+their trade-offs about the political
+
+ align:start position:0%
+their trade-offs about the political
+ 
+
+ align:start position:0%
+their trade-offs about the political
+extent and there's a variety of other
+
+ align:start position:0%
+extent and there's a variety of other
+ 
+
+ align:start position:0%
+extent and there's a variety of other
+factors that are involved in it but um
+
+ align:start position:0%
+factors that are involved in it but um
+ 
+
+ align:start position:0%
+factors that are involved in it but um
+here are the focus on the economic
+
+ align:start position:0%
+here are the focus on the economic
+ 
+
+ align:start position:0%
+here are the focus on the economic
+aspects
+
+ align:start position:0%
+aspects
+ 
+
+ align:start position:0%
+aspects
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the key conclusion is a flexible can
+
+ align:start position:0%
+the key conclusion is a flexible can
+ 
+
+ align:start position:0%
+the key conclusion is a flexible can
+provide clear economic benefits i don't
+
+ align:start position:0%
+provide clear economic benefits i don't
+ 
+
+ align:start position:0%
+provide clear economic benefits i don't
+say it must
+
+ align:start position:0%
+say it must
+ 
+
+ align:start position:0%
+say it must
+but they
+
+ align:start position:0%
+but they
+ 
+
+ align:start position:0%
+but they
+it's pretty clear that they can provide
+
+ align:start position:0%
+it's pretty clear that they can provide
+ 
+
+ align:start position:0%
+it's pretty clear that they can provide
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+these are pushed
+
+ align:start position:0%
+these are pushed
+ 
+
+ align:start position:0%
+these are pushed
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+discount rate effects and learning
+
+ align:start position:0%
+discount rate effects and learning
+ 
+
+ align:start position:0%
+discount rate effects and learning
+effects discount rate because if you
+
+ align:start position:0%
+effects discount rate because if you
+ 
+
+ align:start position:0%
+effects discount rate because if you
+invest later on it costs less than terms
+
+ align:start position:0%
+invest later on it costs less than terms
+ 
+
+ align:start position:0%
+invest later on it costs less than terms
+of present value learning in fact is
+
+ align:start position:0%
+of present value learning in fact is
+ 
+
+ align:start position:0%
+of present value learning in fact is
+that if you build several modules the
+
+ align:start position:0%
+that if you build several modules the
+ 
+
+ align:start position:0%
+that if you build several modules the
+next time you do it you'll avoid
+
+ align:start position:0%
+next time you do it you'll avoid
+ 
+
+ align:start position:0%
+next time you do it you'll avoid
+mistakes or improve design and so forth
+
+ align:start position:0%
+mistakes or improve design and so forth
+ 
+
+ align:start position:0%
+mistakes or improve design and so forth
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+comes with building inject often but not
+
+ align:start position:0%
+comes with building inject often but not
+ 
+
+ align:start position:0%
+comes with building inject often but not
+necessarily on some kind of modularity
+
+ align:start position:0%
+necessarily on some kind of modularity
+ 
+
+ align:start position:0%
+necessarily on some kind of modularity
+of design
+
+ align:start position:0%
+of design
+ 
+
+ align:start position:0%
+of design
+and these factors discount rate learning
+
+ align:start position:0%
+and these factors discount rate learning
+ 
+
+ align:start position:0%
+and these factors discount rate learning
+effects module design work against the
+
+ align:start position:0%
+effects module design work against the
+ 
+
+ align:start position:0%
+effects module design work against the
+economies of scale which encourage
+
+ align:start position:0%
+economies of scale which encourage
+ 
+
+ align:start position:0%
+economies of scale which encourage
+people to
+
+ align:start position:0%
+people to
+ 
+
+ align:start position:0%
+people to
+uh build
+
+ align:start position:0%
+uh build
+ 
+
+ align:start position:0%
+uh build
+for all future capacity right up front
+
+ align:start position:0%
+for all future capacity right up front
+ 
+
+ align:start position:0%
+for all future capacity right up front
+which was
+
+ align:start position:0%
+which was
+ 
+
+ align:start position:0%
+which was
+part of the task of the mid-text example
+
+ align:start position:0%
+part of the task of the mid-text example
+ 
+
+ align:start position:0%
+part of the task of the mid-text example
+uh that you worked through was that many
+
+ align:start position:0%
+uh that you worked through was that many
+ 
+
+ align:start position:0%
+uh that you worked through was that many
+people had the
+
+ align:start position:0%
+people had the
+ 
+
+ align:start position:0%
+people had the
+normal reflex was oh yeah that's what we
+
+ align:start position:0%
+normal reflex was oh yeah that's what we
+ 
+
+ align:start position:0%
+normal reflex was oh yeah that's what we
+need we're going to build for it right
+
+ align:start position:0%
+need we're going to build for it right
+ 
+
+ align:start position:0%
+need we're going to build for it right
+at the beginning and not mess around
+
+ align:start position:0%
+at the beginning and not mess around
+ 
+
+ align:start position:0%
+at the beginning and not mess around
+with it but it turns out that that
+
+ align:start position:0%
+with it but it turns out that that
+ 
+
+ align:start position:0%
+with it but it turns out that that
+common reaction is often
+
+ align:start position:0%
+common reaction is often
+ 
+
+ align:start position:0%
+common reaction is often
+anti-economic
+
+ align:start position:0%
+anti-economic
+ 
+
+ align:start position:0%
+anti-economic
+so and also the actual expected value of
+
+ align:start position:0%
+so and also the actual expected value of
+ 
+
+ align:start position:0%
+so and also the actual expected value of
+the capex of the project under
+
+ align:start position:0%
+the capex of the project under
+ 
+
+ align:start position:0%
+the capex of the project under
+uncertainty is less than the
+
+ align:start position:0%
+uncertainty is less than the
+ 
+
+ align:start position:0%
+uncertainty is less than the
+deterministic estimation
+
+ align:start position:0%
+deterministic estimation
+ 
+
+ align:start position:0%
+deterministic estimation
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh that's where we're going
+
+ align:start position:0%
+uh that's where we're going
+ 
+
+ align:start position:0%
+uh that's where we're going
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i'm now giving you
+
+ align:start position:0%
+i'm now giving you
+ 
+
+ align:start position:0%
+i'm now giving you
+taking from it our presentation their
+
+ align:start position:0%
+taking from it our presentation their
+ 
+
+ align:start position:0%
+taking from it our presentation their
+presentation of the analysis has given
+
+ align:start position:0%
+presentation of the analysis has given
+ 
+
+ align:start position:0%
+presentation of the analysis has given
+for a
+
+ align:start position:0%
+for a
+ 
+
+ align:start position:0%
+for a
+a particular project uh a particular
+
+ align:start position:0%
+a particular project uh a particular
+ 
+
+ align:start position:0%
+a particular project uh a particular
+conference and so forth and
+
+ align:start position:0%
+conference and so forth and
+ 
+
+ align:start position:0%
+conference and so forth and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's go
+
+ align:start position:0%
+let's go
+ 
+
+ align:start position:0%
+let's go
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the motivation looking through design
+
+ align:start position:0%
+the motivation looking through design
+ 
+
+ align:start position:0%
+the motivation looking through design
+alternatives the methodology and the
+
+ align:start position:0%
+alternatives the methodology and the
+ 
+
+ align:start position:0%
+alternatives the methodology and the
+results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in location uh we're talking about
+
+ align:start position:0%
+so in location uh we're talking about
+ 
+
+ align:start position:0%
+so in location uh we're talking about
+the state of victoria which is this bit
+
+ align:start position:0%
+the state of victoria which is this bit
+ 
+
+ align:start position:0%
+the state of victoria which is this bit
+here of australia this is where sydney
+
+ align:start position:0%
+here of australia this is where sydney
+ 
+
+ align:start position:0%
+here of australia this is where sydney
+is new south wales this is where
+
+ align:start position:0%
+is new south wales this is where
+ 
+
+ align:start position:0%
+is new south wales this is where
+brisbane the gold coast is this is where
+
+ align:start position:0%
+brisbane the gold coast is this is where
+ 
+
+ align:start position:0%
+brisbane the gold coast is this is where
+the big mineral area is or some of the
+
+ align:start position:0%
+the big mineral area is or some of the
+ 
+
+ align:start position:0%
+the big mineral area is or some of the
+big mineral on the western australia and
+
+ align:start position:0%
+big mineral on the western australia and
+ 
+
+ align:start position:0%
+big mineral on the western australia and
+perth and this is the great
+
+ align:start position:0%
+perth and this is the great
+ 
+
+ align:start position:0%
+perth and this is the great
+nothing uh if i can put it that way um
+
+ align:start position:0%
+nothing uh if i can put it that way um
+ 
+
+ align:start position:0%
+nothing uh if i can put it that way um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and so we're i don't there's tasmania
+
+ align:start position:0%
+and so we're i don't there's tasmania
+ 
+
+ align:start position:0%
+and so we're i don't there's tasmania
+tassie down here
+
+ align:start position:0%
+tassie down here
+ 
+
+ align:start position:0%
+tassie down here
+here is um
+
+ align:start position:0%
+here is um
+ 
+
+ align:start position:0%
+here is um
+a melbourne and there are various sites
+
+ align:start position:0%
+a melbourne and there are various sites
+ 
+
+ align:start position:0%
+a melbourne and there are various sites
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+uh distribution so the plan was to be
+
+ align:start position:0%
+uh distribution so the plan was to be
+ 
+
+ align:start position:0%
+uh distribution so the plan was to be
+here and their sites for distribution of
+
+ align:start position:0%
+here and their sites for distribution of
+ 
+
+ align:start position:0%
+here and their sites for distribution of
+the product uh which i'll describe in a
+
+ align:start position:0%
+the product uh which i'll describe in a
+ 
+
+ align:start position:0%
+the product uh which i'll describe in a
+moment uh at these sites one through
+
+ align:start position:0%
+moment uh at these sites one through
+ 
+
+ align:start position:0%
+moment uh at these sites one through
+five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the whole idea is
+
+ align:start position:0%
+so the whole idea is
+ 
+
+ align:start position:0%
+so the whole idea is
+that you get uh
+
+ align:start position:0%
+that you get uh
+ 
+
+ align:start position:0%
+that you get uh
+lng liquid natural gas
+
+ align:start position:0%
+lng liquid natural gas
+ 
+
+ align:start position:0%
+lng liquid natural gas
+from the offshore used to do a certain
+
+ align:start position:0%
+from the offshore used to do a certain
+ 
+
+ align:start position:0%
+from the offshore used to do a certain
+amount of processing
+
+ align:start position:0%
+amount of processing
+ 
+
+ align:start position:0%
+amount of processing
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+separate out the good stuff get rid of
+
+ align:start position:0%
+separate out the good stuff get rid of
+ 
+
+ align:start position:0%
+separate out the good stuff get rid of
+the bad stuff
+
+ align:start position:0%
+the bad stuff
+ 
+
+ align:start position:0%
+the bad stuff
+you have somehow get it to land and then
+
+ align:start position:0%
+you have somehow get it to land and then
+ 
+
+ align:start position:0%
+you have somehow get it to land and then
+you liquefy it and it can be
+
+ align:start position:0%
+you liquefy it and it can be
+ 
+
+ align:start position:0%
+you liquefy it and it can be
+used for a variety of purposes
+
+ align:start position:0%
+used for a variety of purposes
+ 
+
+ align:start position:0%
+used for a variety of purposes
+but the idea here in australia was the
+
+ align:start position:0%
+but the idea here in australia was the
+ 
+
+ align:start position:0%
+but the idea here in australia was the
+project was to market it for the
+
+ align:start position:0%
+project was to market it for the
+ 
+
+ align:start position:0%
+project was to market it for the
+transportation sector that it would be
+
+ align:start position:0%
+transportation sector that it would be
+ 
+
+ align:start position:0%
+transportation sector that it would be
+uh cleaner um
+
+ align:start position:0%
+uh cleaner um
+ 
+
+ align:start position:0%
+uh cleaner um
+than diesel fuel and so forth and it'd
+
+ align:start position:0%
+than diesel fuel and so forth and it'd
+ 
+
+ align:start position:0%
+than diesel fuel and so forth and it'd
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+not only an environmental benefit but it
+
+ align:start position:0%
+not only an environmental benefit but it
+ 
+
+ align:start position:0%
+not only an environmental benefit but it
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+a good business for the oil companies
+
+ align:start position:0%
+a good business for the oil companies
+ 
+
+ align:start position:0%
+a good business for the oil companies
+which unfortunately in the past have
+
+ align:start position:0%
+which unfortunately in the past have
+ 
+
+ align:start position:0%
+which unfortunately in the past have
+often simply burned off the gas flared
+
+ align:start position:0%
+often simply burned off the gas flared
+ 
+
+ align:start position:0%
+often simply burned off the gas flared
+it which is neither profitable nor
+
+ align:start position:0%
+it which is neither profitable nor
+ 
+
+ align:start position:0%
+it which is neither profitable nor
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+environmentally desirable so it's viewed
+
+ align:start position:0%
+environmentally desirable so it's viewed
+ 
+
+ align:start position:0%
+environmentally desirable so it's viewed
+as a in this case as a transportation
+
+ align:start position:0%
+as a in this case as a transportation
+ 
+
+ align:start position:0%
+as a in this case as a transportation
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+uh in europe they use liquid national
+
+ align:start position:0%
+uh in europe they use liquid national
+ 
+
+ align:start position:0%
+uh in europe they use liquid national
+lng for
+
+ align:start position:0%
+lng for
+ 
+
+ align:start position:0%
+lng for
+home heating a lot and
+
+ align:start position:0%
+home heating a lot and
+ 
+
+ align:start position:0%
+home heating a lot and
+also for power plants but uh this is not
+
+ align:start position:0%
+also for power plants but uh this is not
+ 
+
+ align:start position:0%
+also for power plants but uh this is not
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+they don't particularly need heat in
+
+ align:start position:0%
+they don't particularly need heat in
+ 
+
+ align:start position:0%
+they don't particularly need heat in
+australia and south australia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+there are three uh versions of the
+
+ align:start position:0%
+there are three uh versions of the
+ 
+
+ align:start position:0%
+there are three uh versions of the
+system i want to sketch out for you
+
+ align:start position:0%
+system i want to sketch out for you
+ 
+
+ align:start position:0%
+system i want to sketch out for you
+that is the original design that uh
+
+ align:start position:0%
+that is the original design that uh
+ 
+
+ align:start position:0%
+that is the original design that uh
+keppel offshore and marine had developed
+
+ align:start position:0%
+keppel offshore and marine had developed
+ 
+
+ align:start position:0%
+keppel offshore and marine had developed
+was to have one big plant
+
+ align:start position:0%
+was to have one big plant
+ 
+
+ align:start position:0%
+was to have one big plant
+with the idea then that
+
+ align:start position:0%
+with the idea then that
+ 
+
+ align:start position:0%
+with the idea then that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+liquid product would be distributed to
+
+ align:start position:0%
+liquid product would be distributed to
+ 
+
+ align:start position:0%
+liquid product would be distributed to
+various sites the five sites i mentioned
+
+ align:start position:0%
+various sites the five sites i mentioned
+ 
+
+ align:start position:0%
+various sites the five sites i mentioned
+and from there they would you be used to
+
+ align:start position:0%
+and from there they would you be used to
+ 
+
+ align:start position:0%
+and from there they would you be used to
+fuel tanker oh
+
+ align:start position:0%
+fuel tanker oh
+ 
+
+ align:start position:0%
+fuel tanker oh
+trucks
+
+ align:start position:0%
+trucks
+ 
+
+ align:start position:0%
+trucks
+uh to uh
+
+ align:start position:0%
+uh to uh
+ 
+
+ align:start position:0%
+uh to uh
+deliver goods and whatever they were
+
+ align:start position:0%
+deliver goods and whatever they were
+ 
+
+ align:start position:0%
+deliver goods and whatever they were
+doing so one big plan economies of scale
+
+ align:start position:0%
+doing so one big plan economies of scale
+ 
+
+ align:start position:0%
+doing so one big plan economies of scale
+very much similar to the big plant
+
+ align:start position:0%
+very much similar to the big plant
+ 
+
+ align:start position:0%
+very much similar to the big plant
+and for the water except that it was not
+
+ align:start position:0%
+and for the water except that it was not
+ 
+
+ align:start position:0%
+and for the water except that it was not
+modular anyway it was one big thing
+
+ align:start position:0%
+modular anyway it was one big thing
+ 
+
+ align:start position:0%
+modular anyway it was one big thing
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+phase that we looked at kardan me and
+
+ align:start position:0%
+phase that we looked at kardan me and
+ 
+
+ align:start position:0%
+phase that we looked at kardan me and
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+was to have modular plants say all right
+
+ align:start position:0%
+was to have modular plants say all right
+ 
+
+ align:start position:0%
+was to have modular plants say all right
+where instead of having the whole size
+
+ align:start position:0%
+where instead of having the whole size
+ 
+
+ align:start position:0%
+where instead of having the whole size
+at once we're going to say what happened
+
+ align:start position:0%
+at once we're going to say what happened
+ 
+
+ align:start position:0%
+at once we're going to say what happened
+if we had modules of 25
+
+ align:start position:0%
+if we had modules of 25
+ 
+
+ align:start position:0%
+if we had modules of 25
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+tons there's 50 tons 75 100 tons so
+
+ align:start position:0%
+tons there's 50 tons 75 100 tons so
+ 
+
+ align:start position:0%
+tons there's 50 tons 75 100 tons so
+forth so
+
+ align:start position:0%
+forth so
+ 
+
+ align:start position:0%
+forth so
+we could
+
+ align:start position:0%
+we could
+ 
+
+ align:start position:0%
+we could
+what we could do about that was to phase
+
+ align:start position:0%
+what we could do about that was to phase
+ 
+
+ align:start position:0%
+what we could do about that was to phase
+it over time so we start off small
+
+ align:start position:0%
+it over time so we start off small
+ 
+
+ align:start position:0%
+it over time so we start off small
+because the demand was small and we'd
+
+ align:start position:0%
+because the demand was small and we'd
+ 
+
+ align:start position:0%
+because the demand was small and we'd
+add them very similar to the
+
+ align:start position:0%
+add them very similar to the
+ 
+
+ align:start position:0%
+add them very similar to the
+mid-text homework ii example is that all
+
+ align:start position:0%
+mid-text homework ii example is that all
+ 
+
+ align:start position:0%
+mid-text homework ii example is that all
+right what's the best way to to do this
+
+ align:start position:0%
+right what's the best way to to do this
+ 
+
+ align:start position:0%
+right what's the best way to to do this
+and we did this through a simulation
+
+ align:start position:0%
+and we did this through a simulation
+ 
+
+ align:start position:0%
+and we did this through a simulation
+analysis as i'll point out
+
+ align:start position:0%
+analysis as i'll point out
+ 
+
+ align:start position:0%
+analysis as i'll point out
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+there's we can play around with
+
+ align:start position:0%
+there's we can play around with
+ 
+
+ align:start position:0%
+there's we can play around with
+flexibility as to size one and also as
+
+ align:start position:0%
+flexibility as to size one and also as
+ 
+
+ align:start position:0%
+flexibility as to size one and also as
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+timing because of
+
+ align:start position:0%
+timing because of
+ 
+
+ align:start position:0%
+timing because of
+the size what is the right size and when
+
+ align:start position:0%
+the size what is the right size and when
+ 
+
+ align:start position:0%
+the size what is the right size and when
+do we time the additions
+
+ align:start position:0%
+do we time the additions
+ 
+
+ align:start position:0%
+do we time the additions
+but the third thing is we can also think
+
+ align:start position:0%
+but the third thing is we can also think
+ 
+
+ align:start position:0%
+but the third thing is we can also think
+about the um
+
+ align:start position:0%
+about the um
+ 
+
+ align:start position:0%
+about the um
+flexible design so that we can locate
+
+ align:start position:0%
+flexible design so that we can locate
+ 
+
+ align:start position:0%
+flexible design so that we can locate
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+plant elsewhere that
+
+ align:start position:0%
+plant elsewhere that
+ 
+
+ align:start position:0%
+plant elsewhere that
+as in many processes electric power for
+
+ align:start position:0%
+as in many processes electric power for
+ 
+
+ align:start position:0%
+as in many processes electric power for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+if you do everything in one large plant
+
+ align:start position:0%
+if you do everything in one large plant
+ 
+
+ align:start position:0%
+if you do everything in one large plant
+power for example you gotta transmit it
+
+ align:start position:0%
+power for example you gotta transmit it
+ 
+
+ align:start position:0%
+power for example you gotta transmit it
+a long ways to where it's actually being
+
+ align:start position:0%
+a long ways to where it's actually being
+ 
+
+ align:start position:0%
+a long ways to where it's actually being
+used right now in new england
+
+ align:start position:0%
+used right now in new england
+ 
+
+ align:start position:0%
+used right now in new england
+we are getting
+
+ align:start position:0%
+we are getting
+ 
+
+ align:start position:0%
+we are getting
+a fair amount of power from
+
+ align:start position:0%
+a fair amount of power from
+ 
+
+ align:start position:0%
+a fair amount of power from
+northern quebec which is transmitted
+
+ align:start position:0%
+northern quebec which is transmitted
+ 
+
+ align:start position:0%
+northern quebec which is transmitted
+through high voltage lines all the way
+
+ align:start position:0%
+through high voltage lines all the way
+ 
+
+ align:start position:0%
+through high voltage lines all the way
+down to boston or
+
+ align:start position:0%
+down to boston or
+ 
+
+ align:start position:0%
+down to boston or
+the boston area and
+
+ align:start position:0%
+the boston area and
+ 
+
+ align:start position:0%
+the boston area and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+uh maybe economical as
+
+ align:start position:0%
+uh maybe economical as
+ 
+
+ align:start position:0%
+uh maybe economical as
+as compared to building a plant but it
+
+ align:start position:0%
+as compared to building a plant but it
+ 
+
+ align:start position:0%
+as compared to building a plant but it
+costs a lot so if you can avoid
+
+ align:start position:0%
+costs a lot so if you can avoid
+ 
+
+ align:start position:0%
+costs a lot so if you can avoid
+the transportation costs and do it
+
+ align:start position:0%
+the transportation costs and do it
+ 
+
+ align:start position:0%
+the transportation costs and do it
+locally it might be better so
+
+ align:start position:0%
+locally it might be better so
+ 
+
+ align:start position:0%
+locally it might be better so
+having a thought that maybe will have a
+
+ align:start position:0%
+having a thought that maybe will have a
+ 
+
+ align:start position:0%
+having a thought that maybe will have a
+decentralized units of production
+
+ align:start position:0%
+decentralized units of production
+ 
+
+ align:start position:0%
+decentralized units of production
+a standard issue whether you're doing
+
+ align:start position:0%
+a standard issue whether you're doing
+ 
+
+ align:start position:0%
+a standard issue whether you're doing
+warehouses or electric power production
+
+ align:start position:0%
+warehouses or electric power production
+ 
+
+ align:start position:0%
+warehouses or electric power production
+or almost anything is not just how much
+
+ align:start position:0%
+or almost anything is not just how much
+ 
+
+ align:start position:0%
+or almost anything is not just how much
+capacity you have but where do you have
+
+ align:start position:0%
+capacity you have but where do you have
+ 
+
+ align:start position:0%
+capacity you have but where do you have
+it at what time so it's a
+
+ align:start position:0%
+it at what time so it's a
+ 
+
+ align:start position:0%
+it at what time so it's a
+generalizable
+
+ align:start position:0%
+generalizable
+ 
+
+ align:start position:0%
+generalizable
+uh example to applicable in thinking to
+
+ align:start position:0%
+uh example to applicable in thinking to
+ 
+
+ align:start position:0%
+uh example to applicable in thinking to
+many issues
+
+ align:start position:0%
+many issues
+ 
+
+ align:start position:0%
+many issues
+so here's a schema for
+
+ align:start position:0%
+so here's a schema for
+ 
+
+ align:start position:0%
+so here's a schema for
+the design and it's very similar to the
+
+ align:start position:0%
+the design and it's very similar to the
+ 
+
+ align:start position:0%
+the design and it's very similar to the
+the analysis this schema is very similar
+
+ align:start position:0%
+the analysis this schema is very similar
+ 
+
+ align:start position:0%
+the analysis this schema is very similar
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the garage case so the first step one
+
+ align:start position:0%
+the garage case so the first step one
+ 
+
+ align:start position:0%
+the garage case so the first step one
+was to say all right let's build the
+
+ align:start position:0%
+was to say all right let's build the
+ 
+
+ align:start position:0%
+was to say all right let's build the
+model of how this thing performs um
+
+ align:start position:0%
+model of how this thing performs um
+ 
+
+ align:start position:0%
+model of how this thing performs um
+uh as a one single large plant
+
+ align:start position:0%
+uh as a one single large plant
+ 
+
+ align:start position:0%
+uh as a one single large plant
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then because of the parametric one we
+
+ align:start position:0%
+then because of the parametric one we
+ 
+
+ align:start position:0%
+then because of the parametric one we
+say all right let's suppose we have a we
+
+ align:start position:0%
+say all right let's suppose we have a we
+ 
+
+ align:start position:0%
+say all right let's suppose we have a we
+know the demand is going to be we assume
+
+ align:start position:0%
+know the demand is going to be we assume
+ 
+
+ align:start position:0%
+know the demand is going to be we assume
+that do a deterministic analysis and
+
+ align:start position:0%
+that do a deterministic analysis and
+ 
+
+ align:start position:0%
+that do a deterministic analysis and
+think about what is the right size for
+
+ align:start position:0%
+think about what is the right size for
+ 
+
+ align:start position:0%
+think about what is the right size for
+the plant we ought to build
+
+ align:start position:0%
+the plant we ought to build
+ 
+
+ align:start position:0%
+the plant we ought to build
+that is that of course depends upon the
+
+ align:start position:0%
+that is that of course depends upon the
+ 
+
+ align:start position:0%
+that is that of course depends upon the
+economies of scale so that depending
+
+ align:start position:0%
+economies of scale so that depending
+ 
+
+ align:start position:0%
+economies of scale so that depending
+upon the economy the scale you build a
+
+ align:start position:0%
+upon the economy the scale you build a
+ 
+
+ align:start position:0%
+upon the economy the scale you build a
+smaller and then expand it or not this
+
+ align:start position:0%
+smaller and then expand it or not this
+ 
+
+ align:start position:0%
+smaller and then expand it or not this
+is the same kind of thing that man did
+
+ align:start position:0%
+is the same kind of thing that man did
+ 
+
+ align:start position:0%
+is the same kind of thing that man did
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in his very simple model that i showed
+
+ align:start position:0%
+in his very simple model that i showed
+ 
+
+ align:start position:0%
+in his very simple model that i showed
+you a couple of weeks ago
+
+ align:start position:0%
+you a couple of weeks ago
+ 
+
+ align:start position:0%
+you a couple of weeks ago
+so deterministic model first that's the
+
+ align:start position:0%
+so deterministic model first that's the
+ 
+
+ align:start position:0%
+so deterministic model first that's the
+base case
+
+ align:start position:0%
+base case
+ 
+
+ align:start position:0%
+base case
+secondly we said okay
+
+ align:start position:0%
+secondly we said okay
+ 
+
+ align:start position:0%
+secondly we said okay
+we recognize there's uncertainty so
+
+ align:start position:0%
+we recognize there's uncertainty so
+ 
+
+ align:start position:0%
+we recognize there's uncertainty so
+we're going to think about this and
+
+ align:start position:0%
+we're going to think about this and
+ 
+
+ align:start position:0%
+we're going to think about this and
+we're going to generate a lot of
+
+ align:start position:0%
+we're going to generate a lot of
+ 
+
+ align:start position:0%
+we're going to generate a lot of
+demand scenarios and see how the
+
+ align:start position:0%
+demand scenarios and see how the
+ 
+
+ align:start position:0%
+demand scenarios and see how the
+standard model performs under
+
+ align:start position:0%
+standard model performs under
+ 
+
+ align:start position:0%
+standard model performs under
+uncertainty are they the deterministic
+
+ align:start position:0%
+uncertainty are they the deterministic
+ 
+
+ align:start position:0%
+uncertainty are they the deterministic
+model performs under uncertainty
+
+ align:start position:0%
+model performs under uncertainty
+ 
+
+ align:start position:0%
+model performs under uncertainty
+and what you see is that once you
+
+ align:start position:0%
+and what you see is that once you
+ 
+
+ align:start position:0%
+and what you see is that once you
+recognize uncertainty the
+
+ align:start position:0%
+recognize uncertainty the
+ 
+
+ align:start position:0%
+recognize uncertainty the
+value of the project changes
+
+ align:start position:0%
+value of the project changes
+ 
+
+ align:start position:0%
+value of the project changes
+decreases because it's capacity limited
+
+ align:start position:0%
+decreases because it's capacity limited
+ 
+
+ align:start position:0%
+decreases because it's capacity limited
+in this case and secondly often the
+
+ align:start position:0%
+in this case and secondly often the
+ 
+
+ align:start position:0%
+in this case and secondly often the
+actual design changes so this is very
+
+ align:start position:0%
+actual design changes so this is very
+ 
+
+ align:start position:0%
+actual design changes so this is very
+much like the
+
+ align:start position:0%
+much like the
+ 
+
+ align:start position:0%
+much like the
+garage case except it's now applied into
+
+ align:start position:0%
+garage case except it's now applied into
+ 
+
+ align:start position:0%
+garage case except it's now applied into
+a much more complicated situation
+
+ align:start position:0%
+a much more complicated situation
+ 
+
+ align:start position:0%
+a much more complicated situation
+thirdly
+
+ align:start position:0%
+thirdly
+ 
+
+ align:start position:0%
+thirdly
+uh we said okay given that we have the
+
+ align:start position:0%
+uh we said okay given that we have the
+ 
+
+ align:start position:0%
+uh we said okay given that we have the
+demand scenarios let's think about
+
+ align:start position:0%
+demand scenarios let's think about
+ 
+
+ align:start position:0%
+demand scenarios let's think about
+having a flexible design that responded
+
+ align:start position:0%
+having a flexible design that responded
+ 
+
+ align:start position:0%
+having a flexible design that responded
+to the demand as it happened so if it
+
+ align:start position:0%
+to the demand as it happened so if it
+ 
+
+ align:start position:0%
+to the demand as it happened so if it
+was growing well uh transportation user
+
+ align:start position:0%
+was growing well uh transportation user
+ 
+
+ align:start position:0%
+was growing well uh transportation user
+uses were ballooning and going way up
+
+ align:start position:0%
+uses were ballooning and going way up
+ 
+
+ align:start position:0%
+uses were ballooning and going way up
+then we add more capacity if
+
+ align:start position:0%
+then we add more capacity if
+ 
+
+ align:start position:0%
+then we add more capacity if
+people weren't using it we would not do
+
+ align:start position:0%
+people weren't using it we would not do
+ 
+
+ align:start position:0%
+people weren't using it we would not do
+it and so we now had a design two
+
+ align:start position:0%
+it and so we now had a design two
+ 
+
+ align:start position:0%
+it and so we now had a design two
+designs one is thinking that we
+
+ align:start position:0%
+designs one is thinking that we
+ 
+
+ align:start position:0%
+designs one is thinking that we
+had flexible module designs but we are
+
+ align:start position:0%
+had flexible module designs but we are
+ 
+
+ align:start position:0%
+had flexible module designs but we are
+we're going to do all the plan in one
+
+ align:start position:0%
+we're going to do all the plan in one
+ 
+
+ align:start position:0%
+we're going to do all the plan in one
+place and the second one is say okay
+
+ align:start position:0%
+place and the second one is say okay
+ 
+
+ align:start position:0%
+place and the second one is say okay
+let's suppose it is possible and could
+
+ align:start position:0%
+let's suppose it is possible and could
+ 
+
+ align:start position:0%
+let's suppose it is possible and could
+be desirable to actually move some of
+
+ align:start position:0%
+be desirable to actually move some of
+ 
+
+ align:start position:0%
+be desirable to actually move some of
+the capacity to it so we had a more
+
+ align:start position:0%
+the capacity to it so we had a more
+ 
+
+ align:start position:0%
+the capacity to it so we had a more
+limited version of only about the timing
+
+ align:start position:0%
+limited version of only about the timing
+ 
+
+ align:start position:0%
+limited version of only about the timing
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a second version of the design with
+
+ align:start position:0%
+a second version of the design with
+ 
+
+ align:start position:0%
+a second version of the design with
+timing and locational choices
+
+ align:start position:0%
+timing and locational choices
+ 
+
+ align:start position:0%
+timing and locational choices
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then we were thinking about overall
+
+ align:start position:0%
+then we were thinking about overall
+ 
+
+ align:start position:0%
+then we were thinking about overall
+calculating the value of flexibility the
+
+ align:start position:0%
+calculating the value of flexibility the
+ 
+
+ align:start position:0%
+calculating the value of flexibility the
+kind of scale factor
+
+ align:start position:0%
+kind of scale factor
+ 
+
+ align:start position:0%
+kind of scale factor
+and the sensitivity analysis
\ No newline at end of file
diff --git a/7mcSMG0-3FU.txt b/7mcSMG0-3FU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2d53834ba4d59ff400dfae7da3b0353cf407ab66
--- /dev/null
+++ b/7mcSMG0-3FU.txt
@@ -0,0 +1,2470 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, let's
+get started.
+
+Why doesn't everyone go ahead
+and take 10 more seconds on
+
+this clicker question.
+
+It should look familiar.
+
+You were pretty split on this
+question on Friday, so we're
+
+hoping after learning a little
+bit more about delta g of
+
+formation, we have at
+least one direction
+
+that wins out here.
+
+OK, great.
+
+So now we're up to 85% of you,
+and hopefully in just a minute
+
+we'll be up to a 100%.
+
+But if delta g of formation here
+is less than zero, that
+
+means we're talking about a
+spontaneous reaction when we
+
+form the compound.
+
+So if it spontaneously forms the
+compound, that must mean
+
+that the compound is
+going to be stable
+
+relative to its elements.
+
+So that's kind of the last thing
+we went over in terms of
+
+topics on Friday, and we'll
+pick up right there today.
+
+All right.
+
+Here we have our notes for
+today, so reminder exam 2 is
+
+on Wednesday --
+
+I don't think I need to
+remind anyone of that.
+
+But just please, don't come to
+this room, make sure that you
+
+go to Walker to take the exam.
+
+And also if you have any
+questions or you feel like
+
+there's anything you don't
+understand, I have office
+
+hours today from 2 to
+4 in my office.
+
+Your TAs have also all moved
+their office hours so they
+
+fall before the exam.
+
+So make sure you get any of
+your questions addressed
+
+before you're trying to
+sit there and figure
+
+it out in exam time.
+
+All right, so today we're going
+to pick up where we left
+
+off on thermodynamics, so that
+was talking about free energy
+
+of formation.
+
+After that we're going to talk
+a little bit more about the
+
+effect of temperature
+on spontaneity.
+
+We touched upon this on Friday,
+but we're going to
+
+formalize exactly in which cases
+temperature can or can
+
+not affect whether a reaction
+is spontaneous or
+
+non-spontaneous.
+
+Then we're going to look a
+little bit into thermodynamics
+
+and biological systems.
+
+Two examples that I wanted to
+talk about were ATP coupled
+
+reactions -- those are very
+important in biology.
+
+And also, thinking about the
+idea of hydrogen bonding,
+
+we're going to combine our
+thoughts on bond enthalpies,
+
+and also our ideas of bonding
+that we had from thinking
+
+about covalent and
+ionic bonds.
+
+All right, so let's finish
+up first with
+
+free energy of formation.
+
+So as 85% of you just told me,
+when we have a case where
+
+delta g of formation is less
+than zero, what we're talking
+
+about here is a compound that
+is thermodynamically stable
+
+relative to its elements.
+
+So that means we know the
+inverse as well, which is when
+
+we're talking about a case where
+delta g is now greater
+
+than zero, the compound is going
+to be thermodynamically
+
+unstable relative
+to its elements.
+
+So any time you're looking at
+delta g of formation, just
+
+remember to think about this
+is just the delta g of a
+
+reaction where you're
+forming a compound.
+
+So it should make sense that if
+it's negative, it's going
+
+to be spontaneous and you're
+going to have a stable
+
+compound here.
+
+So we could look at any number
+of examples, really we could
+
+pick any compound to look at,
+but up on the screen here I'm
+
+just putting the compound, the
+formation of benzene, we've
+
+looked at benzene a lot.
+
+So benzene has a delta
+g of formation of 124
+
+kilojoules per mole.
+
+Is benzene stable or unstable
+compared to its elements?
+
+I can't really tell the
+difference between stable and
+
+unstable when you say it,
+so everyone start at
+
+the same time, go.
+
+STUDENT: Unstable.
+
+PROFESSOR: OK, excellent.
+
+Benzene is unstable compared
+to its elements.
+
+So that means the reverse
+reaction here is going to be
+
+stable -- or the reverse
+reaction is going to be
+
+spontaneous where we
+actually have the
+
+decomposition of benzene.
+
+So when we're seeing this, when
+we're seeing that the
+
+reverse reaction is spontaneous,
+a question that
+
+might immediately come to us is
+well, why did we just spend
+
+all the time talking about
+benzene because clearly
+
+benzene's just going to
+break down, right.
+
+Why do we form benzene and not
+have it immediately decompose
+
+into its elements.
+
+Thermodynamically that is what
+should happen and it is what
+
+does happen, but the reality
+is that this reaction, this
+
+decomposition of benzene is
+actually very, very slow.
+
+It's so slow that, you know we
+use benzene all the time in
+
+organic reactions, we don't see
+it break down even when we
+
+heat it up, is because
+even though this is
+
+thermodynamically a
+non-spontaneous reaction to
+
+form benzene, it's very slow for
+the actual decomposition
+
+of benzene to occur.
+
+So this is just another case,
+and I'll keep saying this, and
+
+when Professor Drennan starts
+talking about kinetics, she'll
+
+keep repeating this as well.
+
+What we want to keep in mind
+is that delta g tells us
+
+whether a reaction will happen
+or whether it won't happen.
+
+It tells us absolutely nothing
+about how long it takes for
+
+that reaction to happen.
+
+It tells us nothing about the
+rate of the reaction.
+
+We'll keep seeing examples of
+this, so hopefully no one will
+
+be confused by the time
+we do get to kinetics.
+
+So if we're talking about
+calculating delta g for any
+
+reaction, now we actually have
+several ways to do it.
+
+The first way is very analogous
+to thinking about
+
+delta h for the reaction.
+
+We can just look up a
+table where we have
+
+delta g as a formation.
+
+So we can take the sum of the
+delta g of formation of the
+
+products, and subtract from it
+the delta g of formation of
+
+the reactants.
+
+We also have another way if
+maybe we don't have that
+
+information available to us.
+
+We can also take a look at using
+this reaction or this
+
+equation right here, which is
+telling us that delta g of a
+
+reaction is equal to the
+change in enthalpy
+
+minus t delta s.
+
+So that tends to be very
+helpful, especially when we
+
+want to take into consideration
+temperature.
+
+So let's take into consideration
+temperature.
+
+We've done this a little bit so
+far, but let's really take
+
+a look at some reactions where
+temperature's going to make a
+
+big difference.
+
+So the reaction we're going
+to look at here is the
+
+decomposition of sodium
+bicarbonate, or sodium bicarb
+
+here, and it decomposes it into
+sodium carbonate, plus c
+
+o 2, carbon dioxide,
+and water.
+
+So we can think about
+calculating that delta g of
+
+this reaction.
+
+I'll tell you that the change in
+enthalpy, this is actually
+
+an endothermic reaction.
+
+It requires heat.
+
+It's plus 135 .
+
+6 kilojoules per mole.
+
+So let's go to a clicker
+question and I want you to
+
+pick out from several choices
+which of the changes in
+
+entropy seem reasonable
+to you here.
+
+So what would you predict
+the delta s for
+
+this reaction to be?
+
+All right, let's do 10
+more seconds on that.
+
+OK, so we've got the majority,
+but not everyone.
+
+So let's take a look at why this
+is the correct answer,
+
+that it should be plus 0.334 .
+
+If we're going from 2 moles of
+solid, to 1 mole of solid,
+
+plus 2 moles of gas, are
+we increasing or
+
+decreasing the disorder?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: We're increasing
+the disorder.
+
+If we're getting to a more
+disordered state, then we're
+
+going to have a positive
+change in entropy.
+
+We're going to increase
+the disorder.
+
+The only one with a positive
+delta s is this choice here.
+
+So if we switch back to our
+notes, we can see that, in
+
+fact, so what we see is that
+it's 0.334 kilojoules per k
+
+per mole is our delta s, so we
+can go ahead and calculate our
+
+delta g for the reaction,
+so we're just plugging
+
+in our delta h.
+
+So our delta h is 135 .
+
+6.
+
+And we're talking about to start
+with let's talk about
+
+room temperature.
+
+So 298 k times 0.334 .
+
+So what we end up having for the
+delta g of our reaction is
+
+that its 36 .
+
+1 kilojoules per mole.
+
+So this is at room
+temperature.
+
+So is our reaction spontaneous
+or non-spontaneous at room
+
+temperature?
+
+STUDENT: Non-spontaneous.
+
+PROFESSOR: Non-spontaneous.
+
+All right, but let's take
+a look at a different
+
+temperature.
+
+For example, let's look
+at baking temperature.
+
+So if we think about baking
+cookies, we maybe bake them at
+
+350 degrees fahrenheit, so that
+would be 450 kelvin --
+
+our ovens are usually set to
+fahrenheit and not kelvin.
+
+So if we think about this
+reaction that this
+
+temperature, first of all let
+me point out why we would be
+
+talking about baking
+cookies for this
+
+particular reaction here.
+
+Does anyone know what another
+name for sodium bicarb is?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Yeah, it's
+just baking soda.
+
+So this is the reaction that
+causes your cookies or your
+
+cakes to actually rise.
+
+So we're producing gas here, and
+when we're producing that
+
+gas when this sodium bicarb
+decomposes, we're forming
+
+these pockets of gas
+in our baked goods.
+
+So if we bake our cookies at
+room temperature, obviously,
+
+they don't bake and they also
+don't rise because the sodium
+
+bicarb, clearly it was
+non-spontaneous at room
+
+temperature, this reaction
+just doesn't happen.
+
+But if we take a look at baking
+temperature now, we're
+
+going to plug in this new
+temperature, which is 450 k,
+
+and plug this into our
+delta g reaction.
+
+What we find is now our delta
+g for the reaction
+
+is negative 14 .
+
+7 kilojoules per mole.
+
+So in this case, we are dealing
+with a spontaneous
+
+reaction, which is good, because
+this means that when
+
+we put our cookies in and we
+turn it to 350 fahrenheit or
+
+450 k, the baking soda will
+decompose and we'll got our
+
+cookies to rise a little bit.
+
+All right, so one thing that I
+want you to notice when we
+
+were talking about the case
+with the decomposition of
+
+sodium bicarb is that the delta
+h for that reaction and
+
+the delta s, they both
+had the same sign.
+
+And something that you can keep
+in mind in general is any
+
+time that both delta h and delta
+s have the same sign,
+
+it's actually possible to switch
+from spontaneous to
+
+non-spontaneous or vice versa
+just by changing the
+
+temperature of the reaction.
+
+And we can think about
+this graphically.
+
+If we assume that delta h and
+delta s are independent of
+
+temperature, which is a good
+assumption to a first
+
+approximation, in this case we
+find that the delta g of the
+
+reaction is the linear function
+of the temperature.
+
+So that means we can go ahead
+and graph what we saw for the
+
+case of baking soda.
+
+So our first point here was
+that we saw at room
+
+temperature, about 298 k, the
+delta g was positive, it was
+
+36 kilojoules per mole.
+
+We also saw that once we
+heated it up to baking
+
+temperature, we actually had the
+delta g now at negative 15
+
+kilojoules per mole.
+
+So since this is linear, we can
+actually draw a straight
+
+line right through here, and
+we can think about the fact
+
+that we have this temperature
+here where anything below this
+
+temperature has a positive delta
+g, and anything above
+
+this temperature is going to
+have a negative delta g.
+
+And let's actually think about
+the fact that this is a line
+
+and see what our slope and our
+y-intercept is going to mean.
+
+We can say that delta g is equal
+to negative delta s t
+
+plus delta h, if we want to put
+it in the formation of the
+
+equation for line.
+
+So what this tells us is that
+our slope is going to be
+
+negative delta s here, and
+if we think about our
+
+y-intercept, that's going to be
+the change in enthalpy for
+
+the reaction.
+
+So again, what I want to point
+out is that any time we're at
+
+a temperature that's lower
+than this change in
+
+temperature here, we're going
+to find that delta g is
+
+greater than zero, and we're
+going to be dealing with a
+
+non-spontaneous reaction.
+
+However, if we move our
+temperature up and up and up
+
+so we go across the graph this
+way, eventually we'll hit a
+
+point where if we're above that
+temperature, we'll find
+
+that delta g is less than
+zero, and now we have a
+
+spontaneous reaction.
+
+So we can actually think about
+what this temperature is.
+
+We can call this T star.
+
+This is the temperature at which
+our reaction switches,
+
+whether it's spontaneous
+or non-spontaneous.
+
+And if you're thinking about
+trying to get a reaction to
+
+go, it's very important to be
+able to calculate what this
+
+temperature is.
+
+A lot of times in organic
+chemistry laboratories, they
+
+need to heat up reactions --
+part of why they do that is
+
+kinetics, but the other part is
+sometimes they need to make
+
+a reaction go from being
+non-spontaneous to
+
+spontaneous.
+
+So let's think about how to
+calculate T star or this
+
+change in temperature.
+
+So we're talking about this
+threshold temperature, so
+
+we're talking about where delta
+g is going to be equal
+
+to zero, because if we set delta
+g equal to zero, we know
+
+that anything on one side of
+that temperature is going to
+
+be spontaneous, and the other
+side is going to be
+
+non-spontaneous.
+
+So if we do this, we can just
+rewrite our reaction, delta g
+
+equals delta h minus t delta s,
+and let's plug in our zero
+
+for delta g there, and now
+rearrange our reaction so that
+
+we're talking about this
+threshold temperature.
+
+So that T star is just going to
+be equal to the change in
+
+enthalpy divided by the
+change in entropy.
+
+So it's very easy for us to
+calculate, so let's go ahead
+
+and do this for the case
+with baking soda.
+
+And for baking soda what we saw
+was that delta h was 136
+
+kilojoules per mole, and the
+change in entropy was 0.334
+
+kilojoules per k mole.
+
+And that means if we do that
+simple division, then what we
+
+end up as our temperature
+star is 406 kelvin.
+
+So basically, what this tells us
+is if we tried to bake our
+
+cookies below 406 kelvin they
+would not rise, if we bake
+
+them above 406 kelvin they
+will rise because this
+
+reaction is now spontaneous.
+
+All right, so this was a case
+where we had seen that the
+
+delta h and the delta s both
+had a positive value.
+
+But let's take a look at what
+happens when now delta h and
+
+delta s are both negative.
+
+So we can think about this just
+by plotting it on our
+
+graph again -- we don't have
+actual values, but we can
+
+think about what the
+sign should be.
+
+So if we talk about our zero
+point where temperature is
+
+absolute zero, if we have a
+positive, or excuse me, if we
+
+have a negative delta h now
+and we're at temperature
+
+equals zero, what is delta
+g going to be?
+
+Negative or positive?
+
+Yeah, it's going
+to be negative.
+
+So if we have negative delta h
+and we're at temperature of
+
+zero, our s term completely
+falls out, so we're definitely
+
+going to start with a
+negative delta g.
+
+As we increase the temperature
+higher and higher, at some
+
+point that delta s term is going
+to become greater than
+
+our delta h term, so at some
+point we're going to flip to
+
+where the reaction has now
+a positive delta g.
+
+So you can draw this into your
+graphs in your notes where
+
+we're going to start, in this
+case if delta g is negative
+
+where delta g starts negative,
+and then when it hits that
+
+threshold temperature,
+anything above that
+
+temperature is going
+to be positive.
+
+So if we had actual numbers we
+could plug those into our
+
+graph, but we should be able to
+understand what the general
+
+trend is going to be even in a
+hypothetical case where we're
+
+just dealing with is it positive
+or is it negative.
+
+So what we see is that below
+this temperature, we have a
+
+spontaneous reaction, and above
+this temperature we have
+
+a non-spontaneous reaction.
+
+That was flipped from the case
+where we had delta h and delta
+
+s both be positive.
+
+All right, so let's actually
+summarize what all of our four
+
+different scenarios could be
+if we're dealing with delta
+
+h's and delta s's.
+
+So to start with, why don't you
+tell me what you think if
+
+we have a reaction where we have
+a negative delta h and we
+
+have a positive delta s, do you
+think that this will be a
+
+reaction that's never
+spontaneous, always
+
+spontaneous, or will this be one
+of these cases where the
+
+spontaneity depends
+on temperature?
+
+All right, let's take 10
+more seconds on this.
+
+OK, great.
+
+So most of you got it.
+
+So let's go back to the slides
+and think a little bit about
+
+why this is.
+
+So, this case is always
+spontaneous, because in this
+
+case we have a negative delta
+h, which contributes to a
+
+negative delta g, and a positive
+delta s, but since
+
+the equation says minus t delta
+s, that means a positive
+
+delta s is also going
+to contribute to a
+
+negative delta g.
+
+So regardless of what the
+temperature is, we're going to
+
+have a spontaneous reaction.
+
+So we say this is always
+spontaneous -- delta g is less
+
+than zero at all temperatures.
+
+All right.
+
+So let's look at the reverse
+case here where delta h is now
+
+greater than zero, and delta
+s is less than zero.
+
+Is this always, never, or
+sometimes spontaneous?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Nope.
+
+So, this is going to be never
+spontaneous in this case.
+
+So for the same reason, because
+delta h is greater
+
+than zero, that contributes to
+a positive delta g, and delta
+
+s being negative also
+contributes to a
+
+positive delta g.
+
+So we'll say again, that this
+delta g is greater than zero
+
+at all temperatures.
+
+All right, so now we have a case
+where delta h is greater
+
+than zero and delta s is greater
+than zero as well.
+
+Is this going to be always,
+never, or sometimes
+
+spontaneous?
+
+STUDENT: Sometimes.
+
+PROFESSOR: Sometimes, good.
+
+So, even before thinking, you
+can just remember if the signs
+
+are the same, we can
+have a dependence
+
+on temperature here.
+
+So what we find is that this
+is sometimes spontaneous.
+
+So we can think about
+when this happens.
+
+Would it be when the actual
+temperature is greater or less
+
+than that threshold
+temperature?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: All right, so I
+heard a lot of people say
+
+greater than.
+
+It's greater than, because when
+it's greater than that
+
+threshold temperature, that
+means that the delta s term is
+
+the one that's going to actually
+sort of take over,
+
+it's going to be at some point
+greater than the delta h term.
+
+The delta h is going to be
+making the delta g positive.
+
+That means it would make it
+non-spontaneous, but once
+
+delta s gets large enough,
+that's going to override, and
+
+now we're going to have a
+negative delta g only when the
+
+temperature is above that
+threshold temperature.
+
+So similarly, when we see that
+delta h is negative and delta
+
+s is negative, this is also
+going to be sometimes
+
+spontaneous, and specifically,
+it will be spontaneous or
+
+delta g will be less than 0 when
+the temperature is less
+
+than that threshold
+temperature.
+
+All right, so you should be able
+to look at any situation
+
+where you have or you figure
+out or you calculate the
+
+enthalpy and the enthropy change
+in the reaction, and
+
+you should right away, before
+doing any calculations, be
+
+able to know is this always
+spontaneous, is this never
+
+spontaneous, or is this
+something where I'm going to
+
+need to really take
+temperature into
+
+consideration.
+
+And if I do, you can actually
+calculate what that
+
+temperature is going to
+be where you flip from
+
+spontaneous to non-spontaneous
+or vice versa.
+
+All right, so shifting gears a
+little bit, let's take a look
+
+at a few examples where it's
+important to think about
+
+thermodynamics and biological
+systems.
+
+So there's two things I
+particularly want to focus on.
+
+So the first is the idea of
+ATP coupled reactions.
+
+So this is really important,
+because when we're talking
+
+about biological reactions, a
+lot of the reactions that take
+
+place in our body are actually
+non-spontaneous, so
+
+energetically we figure that the
+delta g for this reaction
+
+is actually positive.
+
+So I just show a schematic
+biological reaction here where
+
+we have some molecule that's
+broken up into
+
+two building blocks.
+
+So let's say, for example,
+this has a delta g that's
+
+greater than zero.
+
+We need to think about how it is
+that our body can actually
+
+make this reaction happen.
+
+And the way that it does this
+is that it takes the
+
+hydrolysis of ATP, and the
+hydrolysis of ATP is what's
+
+called that it's coupled to this
+non-spontaneous reaction.
+
+And when you have a spontaneous
+reaction coupled
+
+to a non-spontaneous reaction,
+you can potentially drive the
+
+reaction in the forward
+direction.
+
+Remember the hydrolysis of ATP
+is spontaneous, so what we're
+
+doing in this case is we're
+taking a spontaneous reaction
+
+where we give off energy, and
+we're coupling it to a
+
+non-spontaneous reaction
+that requires energy.
+
+So what we will hope is when
+we add up the total energy
+
+changes between these two
+reactions, if the sum of those
+
+two is a negative delta g total,
+now we can have this
+
+whole process move in the
+forward direction.
+
+So let's take a look at thinking
+about what we can do
+
+in terms of a coupled
+reaction.
+
+The first thing we need to do if
+we're thinking about using
+
+the hydrolysis of ATP is
+actually calculate what the
+
+delta g for the reaction of
+ATP hydrolysis is, and I
+
+picked 310 kelvin because
+that's the
+
+temperature of our bodies.
+
+So again, this reaction is
+taking adenosine triphosphate
+
+that has three phosphate groups
+and hydrolyzing it, so
+
+reacting it with water
+to form ADP plus
+
+phosphate plus acid here.
+
+So I'll tell you that the delta
+h of this reaction is
+
+negative 24 kilojoules
+per mole.
+
+This is what we actually
+calculated in class on Friday.
+
+And that the delta s is plus 22
+joules per k, per mole, so
+
+we can go ahead and calculate
+what this delta g is here.
+
+So the delta g of this overall
+reaction is just going to be,
+
+of course, delta h minus t delta
+s, and our delta h is
+
+minus 24 kilojoules per mole,
+and we'll subtract 310
+
+kelvin times 0 .
+
+022 kilojoules over k mole.
+
+So if we do this, what we end
+up getting is a delta g of
+
+negative 31 kilojoules
+per mole of ATP.
+
+All right, so again, this is
+good, we got a negative
+
+number, that's what
+we were expecting.
+
+So that means that we will have
+energy available to use
+
+if we hydrolyize ATP
+and couple it to
+
+another reaction here.
+
+So what we saw for our
+delta g, negative 31
+
+kilojoules per mole.
+
+All right, so let's talk about
+a reaction that is a ATP
+
+coupled reaction, and there's
+just tons of examples of this
+
+in our body.
+
+One I picked because it has to
+do with glucose, which we have
+
+talked so much about, is the
+conversion of glucose to
+
+glucose 6 p.
+
+So 6 p -- p just stands for a
+phosphate group here, so what
+
+we're doing is taking, if we
+numbered the glucose carbons,
+
+this would be carbon number
+six, and we're putting a
+
+phosphate group on carbon
+number six.
+
+So first of all, why would our
+body need to do this reaction?
+
+It turns out that glucose,
+we know that we
+
+use glucose for energy.
+
+Glucose is somewhat apolar, so
+it can actually move in and
+
+out of our cells, because
+our cell walls,
+
+those are very greasy.
+
+So what we're actually doing
+here is we're putting a
+
+charged molecule onto
+the glucose.
+
+There's two negative charges in
+a phosphate group, this is
+
+going to make sure that
+our glucose is now
+
+it's very polar molecule.
+
+And now that we have a very
+polar molecule, we're not
+
+going to be able to have
+the glucose move in
+
+and out of the cell.
+
+So we keep it in our cell
+by putting this
+
+phosphate group on it.
+
+That's why we want to do this
+reaction, but let's think
+
+about the energy of
+actually doing it.
+
+And it turns out that this
+requires energy.
+
+The delta g for this reaction
+is 17 kilojoules per mole.
+
+All right, so that could be a
+problem if our body had not
+
+come up with a way to solve it,
+which it has, and what it
+
+actually does is it couples this
+reaction here with the
+
+conversion of ATP into ADP.
+
+And we just calculated that that
+has a delta g of negative
+
+31 kilojoules per mole.
+
+So this means we can think about
+delta g total, and by
+
+total we mean of this overall
+process here.
+
+So that's just equal to 17,
+and we're adding it to the
+
+other delta g, which
+is negative 31.
+
+So we get an overall delta g for
+this process of negative
+
+14 kilojoules per mole.
+
+All right, so that's one really
+simple example just to
+
+illustrate to you how these ATP
+coupled reactions work.
+
+Some ATP coupled reactions
+require one molar equivalent
+
+of ATP, some require
+a lot more.
+
+But essentially, the
+idea is the same.
+
+We have this reaction that's
+energetically unfavorable that
+
+we couple with an
+
+energetically favorable reaction.
+
+So, quite literally, this is
+what we mean when we talk
+
+about ATP as being the energy
+currency for the cell.
+
+We spend some ATP in order to
+get these non-spontaneous
+
+reactions to go.
+
+All right, so I also want to
+talk to a little bit about
+
+hydrogen bonding.
+
+This also is a topic that deals
+with the thermodynamics,
+
+and it also is related to the
+ideas that we talked about
+
+before in terms of
+thinking about
+
+different types of bonds.
+
+So if we talk about a hydrogen
+bond, a hydrogen bond, first I
+
+just want to be really clear,
+is not a covalent bond.
+
+So this h x bond here is a
+covalent bond, this is not a
+
+hydrogen bond.
+
+But a hydrogen bond can form
+when you have a partial
+
+positive on a hydrogen, and
+you have what's called a
+
+hydrogen bond donor atom, which
+has a partial negative
+
+on it, and also has
+a lone pair.
+
+Typically this y atom will be
+on a separate molecule.
+
+And what happens is you have
+that Coulombic attraction
+
+between the partial positive
+on the hydrogen and the
+
+partial negative on this
+hydrogen bond donor atom.
+
+So what you form between them is
+a hydrogen bond, and you'll
+
+notice that I drew it
+as a dashed line.
+
+H bonds or hydrogen bonds are
+drawn either as dashed lines
+
+or as dotted lines, and
+they're done so to
+
+differentiate them from covalent
+bonds, which we draw
+
+with this straight line here.
+
+So let's think about what
+can form hydrogen bonds.
+
+First of all, there's a
+requirement for what this h x
+
+bond can be.
+
+It has to be a really
+electronegative atom in this x
+
+here, because we need to we
+need to form that partial
+
+positive on the hydrogen, which
+means that the atom that
+
+it's covalentally bonded to
+needs to be pulling away some
+
+of that electron density from
+the hydrogen, such that we
+
+have a delta positive
+on a hydrogen atom.
+
+Similarly, the same atoms are
+what can be the y here, so it
+
+can either be a nitrogen or
+an oxygen or a fluorine.
+
+So these are the only
+hydrogen bond donors
+
+that can form h bonds.
+
+And we can think about the
+reason for this and the reason
+
+is pretty straightforward.
+
+We need to have a small atom,
+but it also needs to be really
+
+electronegative.
+
+This should make sense because
+we need to have this partial
+
+negative charge here to have
+that Coulomb attraction.
+
+And the other requirement is
+that we definitely need to
+
+have that lone pair of electrons
+so it can actually
+
+interact in this hydrogen
+bond here.
+
+So let's take a look at an
+example of a hydrogen bond,
+
+and that's between two
+water molecules.
+
+So let's go ahead and re-draw
+our water molecules -- they're
+
+just kind of randomly
+oriented there.
+
+But let's re-draw them as if
+they were going to have a
+
+hydrogen bond between them.
+
+And one thing I want to point
+out about hydrogen bonds is
+
+that they're strongest when you
+actually have all three
+
+atoms in a straight line like
+this, because it keeps the
+
+dipoles the strongest, so the
+partial positive here and the
+
+partial negative here
+can interact.
+
+So let's re-draw our water
+molecules like that.
+
+So we have our first water
+molecule here, and let's say
+
+we're going to be talking about
+this hydrogen in terms
+
+of hydrogen bonding.
+
+Obviously, we have four
+hydrogens up there that can
+
+take place or take part in h
+bonding, but we're just going
+
+to focus on this one here.
+
+So that means we want our
+straight line to be something
+
+like this to our
+second oxygen.
+
+So let's draw the hydrogens on
+this water molecule as well.
+
+All right, so thinking about
+what the Lewis structure of
+
+water is, how many lone
+pairs do we have
+
+on this oxygen here?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Two lone
+pairs, great.
+
+So let's draw those in,
+and let's draw these
+
+lone pairs in as well.
+
+All right, and we're going to
+be talking about these two
+
+atoms in terms of our hydrogen
+bond, so does this have a
+
+delta plus or a delta
+negative on it?
+
+Delta plus.
+
+So this is a polar bond here,
+this o h bond, so we have a
+
+delta plus on our hydrogen, and
+we have a delta minus on
+
+our oxygen.
+
+So these also have delta
+plusses, of course, and this
+
+also has a delta minus.
+
+So because these two can
+interact and they're lined up
+
+to do so, what we can do is we
+can draw a hydrogen bond right
+
+in between this hydrogen and
+this oxygen atom here.
+
+So again, I pointed out that,
+in fact, hydrogen bonds are
+
+not as strong as
+covalent bonds.
+
+Since they're not as strong, if
+you remember thinking about
+
+the relationship between bond
+strength and bond length,
+
+would you expect a hydrogen bond
+to be longer or shorter
+
+than a covalent bond?
+
+STUDENT: Longer.
+
+PROFESSOR: Good, OK, it
+should be longer here.
+
+So this is our longer bond
+because it's our weaker bond.
+
+They're not held together
+as tightly.
+
+All right, so this is an example
+of an intermolecular
+
+hydrogen bond, it's between
+two different molecules.
+
+Hopefully, you can also see that
+if we're focusing on any
+
+single one water molecule, we
+could also form hydrogen bonds
+
+between other water molecules
+with either of these two
+
+hydrogens as well, and also with
+our other lone pair here.
+
+So any water molecule can
+actually form four different
+
+hydrogen bonds.
+
+All right, so let's talk a
+little bit about these
+
+hydrogen bonds in terms of their
+bond enthalpies here.
+
+I said that they were weaker
+than covalent bonds, so let's
+
+look at a few comparisons
+here.
+
+So we can look at an h o
+hydrogen bond versus an h o
+
+covalent bond.
+
+And what we find is that the
+bond enthalpies in kilojoules
+
+per mole, it's 20 kilojoules per
+mole for a hydrogen bond
+
+versus 463 kilojoules per mole
+for a covalent bond.
+
+So we're not talking about
+just a little bit weaker,
+
+we're talking about much,
+much weaker for the
+
+hydrogen bonds here.
+
+Similarly, if we look at
+nitrogen, for nitrogen
+
+hydrogen bonds, if we have an
+o h bound to a nitrogen,
+
+that's 29 kilojoules per mole.
+
+If it's an n h hydrogen bound
+to a nitrogen, that's 14
+
+kilojoules per mole, and if
+we're talking about an h n
+
+covalent bond, now we're
+talking about 388
+
+kilojoules per mole.
+
+All right, so again what we see
+in these cases is that the
+
+hydrogen bonds are much,
+much weaker.
+
+They tend to be as low as 5% of
+what the covalent bond is,
+
+so this is actually much weaker
+than any kinds of bonds
+
+we have within molecules, but
+it's also the strongest type
+
+of bond that we can
+have between
+
+two different molecules.
+
+And one thing that you find as
+in the case of water, is when
+
+you have lots of hydrogen bonds
+between molecules it
+
+changes the property of, for
+example, water here.
+
+It makes the boiling point much,
+much higher than you
+
+might expect if you looked at
+the other properties, because
+
+you have to actually break apart
+all of these individual
+
+hydrogen bonds, and even though
+it's not that much
+
+energy for one individual
+hydrogen bond, once you get a
+
+huge number of hydrogen bonds,
+you're talking about huge
+
+energies here.
+
+So let's look at some examples
+of where we see hydrogen bonds
+
+in biological processes.
+
+First thinking about proteins,
+they're absolutely hugely
+
+important in proteins.
+
+And in proteins, we're talking
+about a molecule that's so
+
+large that you don't just see
+h bonds in between two
+
+different molecules, what you
+actually see is what's called
+
+intramolecular hydrogen bonding,
+so hydrogen bonding
+
+within the protein
+molecule itself.
+
+And hydrogen bonding is
+incredibly important, it, in
+
+fact, is the shape of a protein,
+which I'm just
+
+showing an example here, histone
+deacetylase, and the
+
+histone deacetylase molecule
+actually has just countless
+
+hydrogen bonds in here, and
+the hydrogen bonds largely
+
+govern the shape of
+the molecule.
+
+So, if you're thinking about any
+protein that has a shape,
+
+so for example, we see these
+ribbon structures here,
+
+they're called alpha helices,
+you can see some arrows, which
+
+are just like a sheet structure
+or beta sheets, that
+
+actual shape is stabilized and
+formed in the first place by
+
+just many, many hydrogen bonds
+within the protein being in a
+
+correct orientation that allows
+for this particular
+
+shape to be stabilized.
+
+And we know that shape is so
+important when we're talking
+
+about proteins, and that's
+because the actual shape of
+
+the protein governs the
+interaction with other
+
+proteins or other
+small molecules.
+
+The shape of the protein is
+very important in terms of
+
+positioning the specific atoms
+that are involved in the
+
+chemistry that the enzyme
+carries out being in the
+
+correct position.
+
+So hydrogen bonds are very
+
+important in terms of proteins.
+
+We can also think of them
+in terms of sugars or
+
+polysaccharides.
+
+This is a nice dramatic example,
+thinking about the
+
+structure of a protein is a
+very microscopic way of
+
+thinking about hydrogen
+bonding.
+
+If we want to take it to the
+macroscopic level, we can talk
+
+about h bonding in trees.
+
+So if we're talking about trees,
+trees are made up -- a
+
+major part of a tree is the
+polysaccharide cellulose.
+
+So that's shown right here.
+
+Cellulose is a chain of glucose
+
+molecules linked together.
+
+It can be as many as 1,000 or
+more glucose molecules linked
+
+together covalentally.
+
+But what actually happens to
+those individual chains is
+
+that if you look at this picture
+here, all those dotted
+
+lines are actually
+hydrogen bonds.
+
+So the individual molecules are
+in a much larger chain of
+
+hydrogen bonded molecules and
+they're incredibly rigid.
+
+You have so many hydrogen bonds
+that now it takes a huge
+
+amount of energy to break
+all of these.
+
+So that accounts for
+why wood is such
+
+a hard, solid material.
+
+And also, I mean for any plant,
+and tree is the most
+
+dramatic, the structure of
+a tree, the macroscopic
+
+structure, can be explained
+by hydrogen bonding.
+
+It's hydrogen bonds that keep
+all of those molecules
+
+together in the forest
+and in trees.
+
+All right.
+
+So, that's proteins, that
+thinking about sugars.
+
+We can also talk about
+the importance of
+
+hydrogen bonding in DNA.
+
+So if you think about the
+characteristic DNA double
+
+helix, hydrogen bonds, we have
+in a double helix we have two
+
+strands of DNA that you can
+see are intertwined here.
+
+And those two strands are
+actually held together by
+
+hydrogen bonding.
+
+So specifically, it's hydrogen
+bonding between what are
+
+called complimentary bases
+within the DNA.
+
+So, for example, if we look at
+guanine and cytosine here, you
+
+can see that there's several
+places, when they're lined up
+
+like this, where we can
+have hydrogen bonds.
+
+So in terms of thinking about
+how these two molecules are
+
+lined up, how many h bonds
+would you expect
+
+between these two bases?
+
+Yeah, so it's lined up
+that there are three
+
+that can form here.
+
+So we have an o h hydrogen bond,
+an h n, and then an h o
+
+hydrogen bond that can form.
+
+So the other side of
+complimentary based pairs are
+
+AT base pairs, and if you look
+at the way these are lined up
+
+here, how many hydrogen
+bonds can form between
+
+A and T base pairs?
+
+Yup, so it it's two that
+we can form here.
+
+We have one between the h o, one
+between the n h, and you
+
+see that we've lost this
+nitrogen, this n h group here,
+
+and first of all this would be
+too far apart anyway for
+
+hydrogen bond, but we can't have
+a hydrogen bond form when
+
+we have a carbon h.
+
+Remember, it has to either be
+a nitrogen or an oxygen or a
+
+fluorine because those are the
+atoms that are going to pull
+
+away enough electron density
+from the hydrogen to give it a
+
+partial positive charge
+that it needs.
+
+So in terms of thinking about
+DNA, this is a really neat
+
+case to consider the actual
+thermodynamics or the bond
+
+enthalpies of the hydrogen
+bonds, because, of course,
+
+does not always stay in it's
+double helix -- when we're
+
+talking about transcription, we
+actually need to unzip or
+
+separate this helix into its
+two strands, so each
+
+individual strand
+can be copied.
+
+So it's really important that
+hydrogen bonds are strong
+
+enough to hold the DNA double
+strand together, but that
+
+they're not so strong that when
+you actually pull the
+
+hydrogen bonds apart to open up
+the double strand, that you
+
+actually, you don't want to
+break all of a covalent bonds
+
+in DNA as well.
+
+All right, so that's all we're
+going to say in terms of
+
+thinking about thermodynamics
+and biological systems.
+
+Hold on a sec, we have
+plenty of time left.
+
+I want to go over a few
+clicker questions.
+
+I didn't want to give you too
+long set of notes, because
+
+we're switching over to
+Professor Drennan's going to
+
+start lecturing on Friday, so
+I thought maybe I shouldn't
+
+have to have her finish
+up with my notes.
+
+So, Professor Drennan will
+continue talking about
+
+thermodynamics and thinking
+about equilibrium, and then
+
+she'll transition that into
+talking about kinetics.
+
+So that's actually what's going
+to start happening after
+
+the exam on Wednesday.
+
+But let's take a look, since we
+do you have a little bit of
+
+time left, at a few clicker
+questions just to make sure
+
+everyone has caught what
+we've gone over so far.
+
+And a few reviews for the exam,
+and I will have this
+
+clicker question or one of the
+ones following, be a clicker
+
+question quiz, so make sure you
+are still answering these
+
+questions here.
+
+So the first one covers what we
+went over today, so I want
+
+you to tell me and try to not
+look back in your notes for
+
+this, for a reaction where you
+have a positive enthalpy and a
+
+negative entropy change, would
+you expect this reaction to be
+
+never, always, or sometimes
+spontaneous?
+
+So let's take 10 seconds
+on that, that
+
+should be pretty fast.
+
+OK, excellent.
+
+90% is very good.
+
+So this should never be
+spontaneous, because we both
+
+have the entropy and the
+enthalpy term contributing to
+
+a positive delta g.
+
+All right, let's shift gears to
+a couple of questions that
+
+are review for the exam.
+
+So hopefully, these
+will all be very
+
+straightforward for you now.
+
+So I want you to think about
+bond lengths here, and tell me
+
+which molecule contains the
+shorter nitrogen oxygen bond.
+
+So, we're comparing n o minus
+1, and n o 2 minus 1.
+
+So if you wanted to get started
+on this problem,
+
+what's the first thing
+you should do?
+
+Yeah, draw some Lewis
+structures.
+
+So that might be a good
+place to start in
+
+thinking about this.
+
+So I'll do that up here as well,
+but don't look if you
+
+want to try it on your own.
+
+Remember, the quiz points
+come for answering, not
+
+for getting it right.
+
+So try doing it on
+your own here.
+
+All right, let's go ahead
+and take 10 more
+
+seconds on this one.
+
+OK, hold on.
+
+Don't show the correct answer.
+
+You know we're going to re-poll
+and give you a little
+
+bit more time to see if we
+come to a consensus here.
+
+So let's take another 30 seconds
+or so on this while I
+
+finish drawing these up here.
+
+OK, good.
+
+So we've got 81% have it correct
+that in the n o minus
+
+1 bond here, this is going
+to be a double bond.
+
+STUDENT: What if [INAUDIBLE].
+
+PROFESSOR: No.
+
+It would be a double
+bond here.
+
+So, if you follow just the Lewis
+structure rules, and you
+
+go ahead, you'll find that we
+end up having four bonding
+
+electrons available.
+
+So you can just go ahead and
+plug those in, and you end up
+
+with this many left.
+
+If we had a triple bond, then
+we would end up having more
+
+bonding -- or we would end up
+using more electrons than we
+
+have available for
+bonding here.
+
+All right, so we have a double
+bond in the case of n o.
+
+What is this bond that
+we have here?
+
+Yup, so it's actually a 1 .
+
+5 bond.
+
+What is this bond that
+we have here?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: All right,
+so we have two 1 .
+
+5 bonds in this case, how
+come these are 1.
+
+5 and not, for example,
+a double bond?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Great, so
+that's the key.
+
+Even though we have double
+bonds in each of these
+
+structures, in this case here,
+we have resonance, so it's
+
+turns out to be, in
+fact, two 1 .
+
+5 bonds.
+
+So since this is the double
+bond, it's going to be the
+
+stronger bond.
+
+Since it's the stronger bond,
+it's also going to be the
+
+shorter bond.
+
+So make sure you can make those
+relationships between
+
+bond strength and bond length
+and thinking about if you have
+
+resonance or you don't
+have resonance in
+
+a particular situation.
+
+All right, let's try one more
+clicker question here.
+
+We'll have this be the
+last one for you.
+
+So this is one that hopefully
+you'll all get right, because
+
+we've gone over this again and
+again both in class and
+
+recitation.
+
+So let's talk about the
+hybridization of the specific
+
+carbon and oxygen atoms in ATP,
+so I want you to go ahead
+
+and tell me what these
+hyrbridizations are
+
+for these two atoms.
+
+OK, let's take 10 more seconds
+here, get those
+
+final answers in.
+
+OK, good, so 83% of
+you got this.
+
+Let's take a look at why.
+
+So carbon a is bonded to three
+things, but it is bonded to no
+
+lone pairs, so we need to have
+it be three hybrid orbitals,
+
+so it's s p 2.
+
+And oxygen is bonded to two
+atoms plus two lone paris.
+
+So we need four hybrid
+orbitals or s p 3.
+
+All right, so this was your quiz
+question, so as long as
+
+you answered it, you got your
+quiz points for today.
+
+And you can get going a little
+bit early today and finish
+
+studying for this exam.
\ No newline at end of file
diff --git a/7w1qqEUwn2k.txt b/7w1qqEUwn2k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2c5dfde1df75f97637278cf59b58446c663f5036
--- /dev/null
+++ b/7w1qqEUwn2k.txt
@@ -0,0 +1,2616 @@
+align:start position:0%
+ 
+hi welcome back to recitation in lecture
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+ 
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+you've been learning about Stokes
+
+ align:start position:0%
+you've been learning about Stokes
+ 
+
+ align:start position:0%
+you've been learning about Stokes
+theorem and I have a nice exercise on
+
+ align:start position:0%
+theorem and I have a nice exercise on
+ 
+
+ align:start position:0%
+theorem and I have a nice exercise on
+Stokes theorem for you here so I'm going
+
+ align:start position:0%
+Stokes theorem for you here so I'm going
+ 
+
+ align:start position:0%
+Stokes theorem for you here so I'm going
+to let F be this field that I've written
+
+ align:start position:0%
+to let F be this field that I've written
+ 
+
+ align:start position:0%
+to let F be this field that I've written
+just above me so it's 2xz minus 2 y
+
+ align:start position:0%
+just above me so it's 2xz minus 2 y
+ 
+
+ align:start position:0%
+just above me so it's 2xz minus 2 y
+comma 2 YZ + 2x comma x^2 + y^2 + z^2
+
+ align:start position:0%
+comma 2 YZ + 2x comma x^2 + y^2 + z^2
+ 
+
+ align:start position:0%
+comma 2 YZ + 2x comma x^2 + y^2 + z^2
+and I've got C so C is this kind of
+
+ align:start position:0%
+and I've got C so C is this kind of
+ 
+
+ align:start position:0%
+and I've got C so C is this kind of
+complicated looking curve here so it
+
+ align:start position:0%
+complicated looking curve here so it
+ 
+
+ align:start position:0%
+complicated looking curve here so it
+sort of dips up and down and back around
+
+ align:start position:0%
+sort of dips up and down and back around
+ 
+
+ align:start position:0%
+sort of dips up and down and back around
+and it's but what you know about it the
+
+ align:start position:0%
+and it's but what you know about it the
+ 
+
+ align:start position:0%
+and it's but what you know about it the
+thing I'm really going to tell you about
+
+ align:start position:0%
+thing I'm really going to tell you about
+ 
+
+ align:start position:0%
+thing I'm really going to tell you about
+it is that it all lies on this on this
+
+ align:start position:0%
+it is that it all lies on this on this
+ 
+
+ align:start position:0%
+it is that it all lies on this on this
+cylinder of radius a uh sorry radius B
+
+ align:start position:0%
+cylinder of radius a uh sorry radius B
+ 
+
+ align:start position:0%
+cylinder of radius a uh sorry radius B
+so it's so C is this curve in the
+
+ align:start position:0%
+so it's so C is this curve in the
+ 
+
+ align:start position:0%
+so it's so C is this curve in the
+cylinder of radius B that wraps around
+
+ align:start position:0%
+cylinder of radius B that wraps around
+ 
+
+ align:start position:0%
+cylinder of radius B that wraps around
+it once but behaves kind of
+
+ align:start position:0%
+it once but behaves kind of
+ 
+
+ align:start position:0%
+it once but behaves kind of
+oddly while it's wrapping around so what
+
+ align:start position:0%
+oddly while it's wrapping around so what
+ 
+
+ align:start position:0%
+oddly while it's wrapping around so what
+I'd like you to do is I'd like you to
+
+ align:start position:0%
+I'd like you to do is I'd like you to
+ 
+
+ align:start position:0%
+I'd like you to do is I'd like you to
+use Stokes theorem to compute the
+
+ align:start position:0%
+use Stokes theorem to compute the
+ 
+
+ align:start position:0%
+use Stokes theorem to compute the
+integral around this curve of f.d now my
+
+ align:start position:0%
+integral around this curve of f.d now my
+ 
+
+ align:start position:0%
+integral around this curve of f.d now my
+hint to you is that for Stokes theorem
+
+ align:start position:0%
+hint to you is that for Stokes theorem
+ 
+
+ align:start position:0%
+hint to you is that for Stokes theorem
+you can use just like you have for
+
+ align:start position:0%
+you can use just like you have for
+ 
+
+ align:start position:0%
+you can use just like you have for
+greens theorem and for Divergence
+
+ align:start position:0%
+greens theorem and for Divergence
+ 
+
+ align:start position:0%
+greens theorem and for Divergence
+Theorem that we've that we've talked
+
+ align:start position:0%
+Theorem that we've that we've talked
+ 
+
+ align:start position:0%
+Theorem that we've that we've talked
+about before you have these extended
+
+ align:start position:0%
+about before you have these extended
+ 
+
+ align:start position:0%
+about before you have these extended
+versions that let you consider more than
+
+ align:start position:0%
+versions that let you consider more than
+ 
+
+ align:start position:0%
+versions that let you consider more than
+one boundary piece so the same thing
+
+ align:start position:0%
+one boundary piece so the same thing
+ 
+
+ align:start position:0%
+one boundary piece so the same thing
+works for Stokes theorem so there's so
+
+ align:start position:0%
+works for Stokes theorem so there's so
+ 
+
+ align:start position:0%
+works for Stokes theorem so there's so
+Stokes theorem works perfectly well when
+
+ align:start position:0%
+Stokes theorem works perfectly well when
+ 
+
+ align:start position:0%
+Stokes theorem works perfectly well when
+you have a when you have a piece of a
+
+ align:start position:0%
+you have a when you have a piece of a
+ 
+
+ align:start position:0%
+you have a when you have a piece of a
+surface with more than one boundary
+
+ align:start position:0%
+surface with more than one boundary
+ 
+
+ align:start position:0%
+surface with more than one boundary
+curve provided you Orient everything
+
+ align:start position:0%
+curve provided you Orient everything
+ 
+
+ align:start position:0%
+curve provided you Orient everything
+correctly so you might think about how
+
+ align:start position:0%
+correctly so you might think about how
+ 
+
+ align:start position:0%
+correctly so you might think about how
+you can use Stokes theorem to replace
+
+ align:start position:0%
+you can use Stokes theorem to replace
+ 
+
+ align:start position:0%
+you can use Stokes theorem to replace
+this complicated curve with a surface
+
+ align:start position:0%
+this complicated curve with a surface
+ 
+
+ align:start position:0%
+this complicated curve with a surface
+integral and an easier to understand
+
+ align:start position:0%
+integral and an easier to understand
+ 
+
+ align:start position:0%
+integral and an easier to understand
+curve and if you can do that then
+
+ align:start position:0%
+curve and if you can do that then
+ 
+
+ align:start position:0%
+curve and if you can do that then
+Computing the other two gives you the
+
+ align:start position:0%
+Computing the other two gives you the
+ 
+
+ align:start position:0%
+Computing the other two gives you the
+third one all right so that's my hint to
+
+ align:start position:0%
+third one all right so that's my hint to
+ 
+
+ align:start position:0%
+third one all right so that's my hint to
+you for for computing this
+
+ align:start position:0%
+you for for computing this
+ 
+
+ align:start position:0%
+you for for computing this
+integral um so why don't you pause the
+
+ align:start position:0%
+integral um so why don't you pause the
+ 
+
+ align:start position:0%
+integral um so why don't you pause the
+video have a go at that come back and we
+
+ align:start position:0%
+video have a go at that come back and we
+ 
+
+ align:start position:0%
+video have a go at that come back and we
+can work on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+hopefully you had some luck working on
+
+ align:start position:0%
+hopefully you had some luck working on
+ 
+
+ align:start position:0%
+hopefully you had some luck working on
+this problem let's let's talk about it
+
+ align:start position:0%
+this problem let's let's talk about it
+ 
+
+ align:start position:0%
+this problem let's let's talk about it
+so before I left I gave you this hint
+
+ align:start position:0%
+so before I left I gave you this hint
+ 
+
+ align:start position:0%
+so before I left I gave you this hint
+that maybe the thing to do here isn't to
+
+ align:start position:0%
+that maybe the thing to do here isn't to
+ 
+
+ align:start position:0%
+that maybe the thing to do here isn't to
+try and parameterize this curve directly
+
+ align:start position:0%
+try and parameterize this curve directly
+ 
+
+ align:start position:0%
+try and parameterize this curve directly
+and compute the line integral directly
+
+ align:start position:0%
+and compute the line integral directly
+ 
+
+ align:start position:0%
+and compute the line integral directly
+since it's a sort of complicated looking
+
+ align:start position:0%
+since it's a sort of complicated looking
+ 
+
+ align:start position:0%
+since it's a sort of complicated looking
+curve and also since I haven't really
+
+ align:start position:0%
+curve and also since I haven't really
+ 
+
+ align:start position:0%
+curve and also since I haven't really
+given you enough information to do that
+
+ align:start position:0%
+given you enough information to do that
+ 
+
+ align:start position:0%
+given you enough information to do that
+um and instead to think about applying
+
+ align:start position:0%
+um and instead to think about applying
+ 
+
+ align:start position:0%
+um and instead to think about applying
+Stokes theorem so to think about
+
+ align:start position:0%
+Stokes theorem so to think about
+ 
+
+ align:start position:0%
+Stokes theorem so to think about
+applying Stokes theorem what we'd like
+
+ align:start position:0%
+applying Stokes theorem what we'd like
+ 
+
+ align:start position:0%
+applying Stokes theorem what we'd like
+is a nice surface and and with this
+
+ align:start position:0%
+is a nice surface and and with this
+ 
+
+ align:start position:0%
+is a nice surface and and with this
+curve as part of its bounc
+
+ align:start position:0%
+curve as part of its bounc
+ 
+
+ align:start position:0%
+curve as part of its bounc
+um so well what is such a surface well
+
+ align:start position:0%
+um so well what is such a surface well
+ 
+
+ align:start position:0%
+um so well what is such a surface well
+this curve lies all on the cylinder of
+
+ align:start position:0%
+this curve lies all on the cylinder of
+ 
+
+ align:start position:0%
+this curve lies all on the cylinder of
+radius B so a natural choice for a
+
+ align:start position:0%
+radius B so a natural choice for a
+ 
+
+ align:start position:0%
+radius B so a natural choice for a
+surface is to use some piece of this
+
+ align:start position:0%
+surface is to use some piece of this
+ 
+
+ align:start position:0%
+surface is to use some piece of this
+cylinder so maybe we could use the piece
+
+ align:start position:0%
+cylinder so maybe we could use the piece
+ 
+
+ align:start position:0%
+cylinder so maybe we could use the piece
+of the cylinder with this as its upper
+
+ align:start position:0%
+of the cylinder with this as its upper
+ 
+
+ align:start position:0%
+of the cylinder with this as its upper
+boundary so then what might be a natural
+
+ align:start position:0%
+boundary so then what might be a natural
+ 
+
+ align:start position:0%
+boundary so then what might be a natural
+lower boundary to choose well we just
+
+ align:start position:0%
+lower boundary to choose well we just
+ 
+
+ align:start position:0%
+lower boundary to choose well we just
+want to choose something nice and simple
+
+ align:start position:0%
+want to choose something nice and simple
+ 
+
+ align:start position:0%
+want to choose something nice and simple
+right so what's nice and simple well
+
+ align:start position:0%
+right so what's nice and simple well
+ 
+
+ align:start position:0%
+right so what's nice and simple well
+maybe we can choose this this bottom
+
+ align:start position:0%
+maybe we can choose this this bottom
+ 
+
+ align:start position:0%
+maybe we can choose this this bottom
+curve this bottom Circle that's in the
+
+ align:start position:0%
+curve this bottom Circle that's in the
+ 
+
+ align:start position:0%
+curve this bottom Circle that's in the
+plane yal X all right so I'm going to
+
+ align:start position:0%
+plane yal X all right so I'm going to
+ 
+
+ align:start position:0%
+plane yal X all right so I'm going to
+call that that Circle C1 so that's the
+
+ align:start position:0%
+call that that Circle C1 so that's the
+ 
+
+ align:start position:0%
+call that that Circle C1 so that's the
+circle of radius B in the XY plane sorry
+
+ align:start position:0%
+circle of radius B in the XY plane sorry
+ 
+
+ align:start position:0%
+circle of radius B in the XY plane sorry
+not the plane Y equals X the XY plane
+
+ align:start position:0%
+not the plane Y equals X the XY plane
+ 
+
+ align:start position:0%
+not the plane Y equals X the XY plane
+the plane Z equals
+
+ align:start position:0%
+the plane Z equals
+ 
+
+ align:start position:0%
+the plane Z equals
+zero so we've got the the top curve C
+
+ align:start position:0%
+zero so we've got the the top curve C
+ 
+
+ align:start position:0%
+zero so we've got the the top curve C
+we've got this bottom curve C1 now the
+
+ align:start position:0%
+we've got this bottom curve C1 now the
+ 
+
+ align:start position:0%
+we've got this bottom curve C1 now the
+way I've oriented them I've oriented
+
+ align:start position:0%
+way I've oriented them I've oriented
+ 
+
+ align:start position:0%
+way I've oriented them I've oriented
+them both so that they're going
+
+ align:start position:0%
+them both so that they're going
+ 
+
+ align:start position:0%
+them both so that they're going
+counterclockwise as you look down from
+
+ align:start position:0%
+counterclockwise as you look down from
+ 
+
+ align:start position:0%
+counterclockwise as you look down from
+the z-axis so in in that case what does
+
+ align:start position:0%
+the z-axis so in in that case what does
+ 
+
+ align:start position:0%
+the z-axis so in in that case what does
+Stokes theorem say well Stokes theorem
+
+ align:start position:0%
+Stokes theorem say well Stokes theorem
+ 
+
+ align:start position:0%
+Stokes theorem say well Stokes theorem
+says that the integral over the piece of
+
+ align:start position:0%
+says that the integral over the piece of
+ 
+
+ align:start position:0%
+says that the integral over the piece of
+the surface between them let's call it s
+
+ align:start position:0%
+the surface between them let's call it s
+ 
+
+ align:start position:0%
+the surface between them let's call it s
+of curl
+
+ align:start position:0%
+of curl
+ 
+
+ align:start position:0%
+of curl
+F do n with respect to surface area is
+
+ align:start position:0%
+F do n with respect to surface area is
+ 
+
+ align:start position:0%
+F do n with respect to surface area is
+equal to okay so so let's say we can
+
+ align:start position:0%
+equal to okay so so let's say we can
+ 
+
+ align:start position:0%
+equal to okay so so let's say we can
+give it the outward pointing normal say
+
+ align:start position:0%
+give it the outward pointing normal say
+ 
+
+ align:start position:0%
+give it the outward pointing normal say
+in which case C1 will be positively
+
+ align:start position:0%
+in which case C1 will be positively
+ 
+
+ align:start position:0%
+in which case C1 will be positively
+oriented and c will be negatively
+
+ align:start position:0%
+oriented and c will be negatively
+ 
+
+ align:start position:0%
+oriented and c will be negatively
+oriented so this is equal to the line
+
+ align:start position:0%
+oriented so this is equal to the line
+ 
+
+ align:start position:0%
+oriented so this is equal to the line
+integral over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C1 of f dodr minus the line integral
+
+ align:start position:0%
+C1 of f dodr minus the line integral
+ 
+
+ align:start position:0%
+C1 of f dodr minus the line integral
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+C of f do Dr and so what's nice about
+
+ align:start position:0%
+C of f do Dr and so what's nice about
+ 
+
+ align:start position:0%
+C of f do Dr and so what's nice about
+this formula is that it replaces the
+
+ align:start position:0%
+this formula is that it replaces the
+ 
+
+ align:start position:0%
+this formula is that it replaces the
+thing that we Computing the thing that
+
+ align:start position:0%
+thing that we Computing the thing that
+ 
+
+ align:start position:0%
+thing that we Computing the thing that
+we want Computing the integral that we
+
+ align:start position:0%
+we want Computing the integral that we
+ 
+
+ align:start position:0%
+we want Computing the integral that we
+want instead of computing that we can
+
+ align:start position:0%
+want instead of computing that we can
+ 
+
+ align:start position:0%
+want instead of computing that we can
+try and compute this other line integral
+
+ align:start position:0%
+try and compute this other line integral
+ 
+
+ align:start position:0%
+try and compute this other line integral
+and the surface integral and if these
+
+ align:start position:0%
+and the surface integral and if these
+ 
+
+ align:start position:0%
+and the surface integral and if these
+are easier to compute well then the
+
+ align:start position:0%
+are easier to compute well then the
+ 
+
+ align:start position:0%
+are easier to compute well then the
+Computing the two of them gives us what
+
+ align:start position:0%
+Computing the two of them gives us what
+ 
+
+ align:start position:0%
+Computing the two of them gives us what
+the value of this is just by subtracting
+
+ align:start position:0%
+the value of this is just by subtracting
+ 
+
+ align:start position:0%
+the value of this is just by subtracting
+or adding and subtracting or whatever by
+
+ align:start position:0%
+or adding and subtracting or whatever by
+ 
+
+ align:start position:0%
+or adding and subtracting or whatever by
+arithmetic right so it so so if these
+
+ align:start position:0%
+arithmetic right so it so so if these
+ 
+
+ align:start position:0%
+arithmetic right so it so so if these
+integrals are easy to compute then that
+
+ align:start position:0%
+integrals are easy to compute then that
+ 
+
+ align:start position:0%
+integrals are easy to compute then that
+makes this one easy without actually
+
+ align:start position:0%
+makes this one easy without actually
+ 
+
+ align:start position:0%
+makes this one easy without actually
+having to parameterize and compute it so
+
+ align:start position:0%
+having to parameterize and compute it so
+ 
+
+ align:start position:0%
+having to parameterize and compute it so
+let's take a look at what these
+
+ align:start position:0%
+let's take a look at what these
+ 
+
+ align:start position:0%
+let's take a look at what these
+integrals are so we've got um let's
+
+ align:start position:0%
+integrals are so we've got um let's
+ 
+
+ align:start position:0%
+integrals are so we've got um let's
+let's do the surface integral first
+
+ align:start position:0%
+let's do the surface integral first
+ 
+
+ align:start position:0%
+let's do the surface integral first
+since it's on the left so in order to
+
+ align:start position:0%
+since it's on the left so in order to
+ 
+
+ align:start position:0%
+since it's on the left so in order to
+compute the surface integral we're going
+
+ align:start position:0%
+compute the surface integral we're going
+ 
+
+ align:start position:0%
+compute the surface integral we're going
+to need to compute the curl of f um so
+
+ align:start position:0%
+to need to compute the curl of f um so
+ 
+
+ align:start position:0%
+to need to compute the curl of f um so
+okay so f is this kind of messy looking
+
+ align:start position:0%
+okay so f is this kind of messy looking
+ 
+
+ align:start position:0%
+okay so f is this kind of messy looking
+thing here so curl of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f well okay so what have we got so it's
+
+ align:start position:0%
+f well okay so what have we got so it's
+ 
+
+ align:start position:0%
+f well okay so what have we got so it's
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+be big thing times I hat so it's going
+
+ align:start position:0%
+be big thing times I hat so it's going
+ 
+
+ align:start position:0%
+be big thing times I hat so it's going
+to be I hat times so you know it's this
+
+ align:start position:0%
+to be I hat times so you know it's this
+ 
+
+ align:start position:0%
+to be I hat times so you know it's this
+determinant right so let me let me write
+
+ align:start position:0%
+determinant right so let me let me write
+ 
+
+ align:start position:0%
+determinant right so let me let me write
+the determinant so we've got on top
+
+ align:start position:0%
+the determinant so we've got on top
+ 
+
+ align:start position:0%
+the determinant so we've got on top
+we've got I hat J hat K hat then we have
+
+ align:start position:0%
+we've got I hat J hat K hat then we have
+ 
+
+ align:start position:0%
+we've got I hat J hat K hat then we have
+the partial X partial y partial Z and
+
+ align:start position:0%
+the partial X partial y partial Z and
+ 
+
+ align:start position:0%
+the partial X partial y partial Z and
+then we have the components so these are
+
+ align:start position:0%
+then we have the components so these are
+ 
+
+ align:start position:0%
+then we have the components so these are
+2xz - 2 Y and 2 y z minus no +
+
+ align:start position:0%
+2xz - 2 Y and 2 y z minus no +
+ 
+
+ align:start position:0%
+2xz - 2 Y and 2 y z minus no +
+2x and x² + Y 2 + z s all right so
+
+ align:start position:0%
+2x and x² + Y 2 + z s all right so
+ 
+
+ align:start position:0%
+2x and x² + Y 2 + z s all right so
+that's I hat J hat K hat and we've
+
+ align:start position:0%
+that's I hat J hat K hat and we've
+ 
+
+ align:start position:0%
+that's I hat J hat K hat and we've
+got partial over partial X partial over
+
+ align:start position:0%
+got partial over partial X partial over
+ 
+
+ align:start position:0%
+got partial over partial X partial over
+partial Y and partial
+
+ align:start position:0%
+partial Y and partial
+ 
+
+ align:start position:0%
+partial Y and partial
+over partial Z so this is what the curl
+
+ align:start position:0%
+over partial Z so this is what the curl
+ 
+
+ align:start position:0%
+over partial Z so this is what the curl
+is and so now we have to expand this out
+
+ align:start position:0%
+is and so now we have to expand this out
+ 
+
+ align:start position:0%
+is and so now we have to expand this out
+so for I it's going to be partial y of
+
+ align:start position:0%
+so for I it's going to be partial y of
+ 
+
+ align:start position:0%
+so for I it's going to be partial y of
+X2 + y^2 + z^2 so that's 2
+
+ align:start position:0%
+X2 + y^2 + z^2 so that's 2
+ 
+
+ align:start position:0%
+X2 + y^2 + z^2 so that's 2
+y minus partial Z of 2 YZ + 2x so that's
+
+ align:start position:0%
+y minus partial Z of 2 YZ + 2x so that's
+ 
+
+ align:start position:0%
+y minus partial Z of 2 YZ + 2x so that's
+minus 2
+
+ align:start position:0%
+minus 2
+ 
+
+ align:start position:0%
+minus 2
+y i hat
+
+ align:start position:0%
+y i hat
+ 
+
+ align:start position:0%
+y i hat
+plus so for J hat it's going to be
+
+ align:start position:0%
+plus so for J hat it's going to be
+ 
+
+ align:start position:0%
+plus so for J hat it's going to be
+partial Z of
+
+ align:start position:0%
+partial Z of
+ 
+
+ align:start position:0%
+partial Z of
+2xz minus 2 y so that's
+
+ align:start position:0%
+2xz minus 2 y so that's
+ 
+
+ align:start position:0%
+2xz minus 2 y so that's
+2x minus partial X of x^2 + y^2 + z^2 so
+
+ align:start position:0%
+2x minus partial X of x^2 + y^2 + z^2 so
+ 
+
+ align:start position:0%
+2x minus partial X of x^2 + y^2 + z^2 so
+that's -
+
+ align:start position:0%
+that's -
+ 
+
+ align:start position:0%
+that's -
+2x J hat plus let's see for K hat we
+
+ align:start position:0%
+2x J hat plus let's see for K hat we
+ 
+
+ align:start position:0%
+2x J hat plus let's see for K hat we
+want partial X of 2 YZ + 2x so that's
+
+ align:start position:0%
+want partial X of 2 YZ + 2x so that's
+ 
+
+ align:start position:0%
+want partial X of 2 YZ + 2x so that's
+2 minus partial y of 2xz - 2 y y so
+
+ align:start position:0%
+2 minus partial y of 2xz - 2 y y so
+ 
+
+ align:start position:0%
+2 minus partial y of 2xz - 2 y y so
+that's Min - - 2 so that's + 2 K hat and
+
+ align:start position:0%
+that's Min - - 2 so that's + 2 K hat and
+ 
+
+ align:start position:0%
+that's Min - - 2 so that's + 2 K hat and
+oh all right so this okay so the I
+
+ align:start position:0%
+oh all right so this okay so the I
+ 
+
+ align:start position:0%
+oh all right so this okay so the I
+component is zero and the J component is
+
+ align:start position:0%
+component is zero and the J component is
+ 
+
+ align:start position:0%
+component is zero and the J component is
+zero so this is a nice simple one so the
+
+ align:start position:0%
+zero so this is a nice simple one so the
+ 
+
+ align:start position:0%
+zero so this is a nice simple one so the
+curl here the K component is just four
+
+ align:start position:0%
+curl here the K component is just four
+ 
+
+ align:start position:0%
+curl here the K component is just four
+so this is equal to
+
+ align:start position:0%
+so this is equal to
+ 
+
+ align:start position:0%
+so this is equal to
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+K okay so that's what the curl of f is
+
+ align:start position:0%
+K okay so that's what the curl of f is
+ 
+
+ align:start position:0%
+K okay so that's what the curl of f is
+now what do we need to compute we need
+
+ align:start position:0%
+now what do we need to compute we need
+ 
+
+ align:start position:0%
+now what do we need to compute we need
+to compute curl of f do the normal
+
+ align:start position:0%
+to compute curl of f do the normal
+ 
+
+ align:start position:0%
+to compute curl of f do the normal
+Vector with with respect to surface area
+
+ align:start position:0%
+Vector with with respect to surface area
+ 
+
+ align:start position:0%
+Vector with with respect to surface area
+now let's look at what our surface is
+
+ align:start position:0%
+now let's look at what our surface is
+ 
+
+ align:start position:0%
+now let's look at what our surface is
+our surface is right here and it's this
+
+ align:start position:0%
+our surface is right here and it's this
+ 
+
+ align:start position:0%
+our surface is right here and it's this
+cylinder it's this vertical cylinder
+
+ align:start position:0%
+cylinder it's this vertical cylinder
+ 
+
+ align:start position:0%
+cylinder it's this vertical cylinder
+well what is the normal Vector of a
+
+ align:start position:0%
+well what is the normal Vector of a
+ 
+
+ align:start position:0%
+well what is the normal Vector of a
+vertical cylinder well it's it's
+
+ align:start position:0%
+vertical cylinder well it's it's
+ 
+
+ align:start position:0%
+vertical cylinder well it's it's
+pointing straight away from the axis
+
+ align:start position:0%
+pointing straight away from the axis
+ 
+
+ align:start position:0%
+pointing straight away from the axis
+right it's it's perpendicular to the
+
+ align:start position:0%
+right it's it's perpendicular to the
+ 
+
+ align:start position:0%
+right it's it's perpendicular to the
+surface of the cylinder so it's parallel
+
+ align:start position:0%
+surface of the cylinder so it's parallel
+ 
+
+ align:start position:0%
+surface of the cylinder so it's parallel
+to the XY
+
+ align:start position:0%
+to the XY
+ 
+
+ align:start position:0%
+to the XY
+plane you know in whichever it rotates
+
+ align:start position:0%
+plane you know in whichever it rotates
+ 
+
+ align:start position:0%
+plane you know in whichever it rotates
+as you as you go around the cylinder but
+
+ align:start position:0%
+as you as you go around the cylinder but
+ 
+
+ align:start position:0%
+as you as you go around the cylinder but
+it's always in the XY plane so what is
+
+ align:start position:0%
+it's always in the XY plane so what is
+ 
+
+ align:start position:0%
+it's always in the XY plane so what is
+that mean well that means in particular
+
+ align:start position:0%
+that mean well that means in particular
+ 
+
+ align:start position:0%
+that mean well that means in particular
+it's perpendicular to to things in the Z
+
+ align:start position:0%
+it's perpendicular to to things in the Z
+ 
+
+ align:start position:0%
+it's perpendicular to to things in the Z
+direction right so if we look we see our
+
+ align:start position:0%
+direction right so if we look we see our
+ 
+
+ align:start position:0%
+direction right so if we look we see our
+curl here is just straight upward in the
+
+ align:start position:0%
+curl here is just straight upward in the
+ 
+
+ align:start position:0%
+curl here is just straight upward in the
+Z Direction and our normal Vector is has
+
+ align:start position:0%
+Z Direction and our normal Vector is has
+ 
+
+ align:start position:0%
+Z Direction and our normal Vector is has
+no Z component it's only in the in the
+
+ align:start position:0%
+no Z component it's only in the in the
+ 
+
+ align:start position:0%
+no Z component it's only in the in the
+XY plane so this this K hat is is
+
+ align:start position:0%
+XY plane so this this K hat is is
+ 
+
+ align:start position:0%
+XY plane so this this K hat is is
+orthogonal to n okay so the curl and N
+
+ align:start position:0%
+orthogonal to n okay so the curl and N
+ 
+
+ align:start position:0%
+orthogonal to n okay so the curl and N
+are orthogonal so their dot product is
+
+ align:start position:0%
+are orthogonal so their dot product is
+ 
+
+ align:start position:0%
+are orthogonal so their dot product is
+zero so this C surf integral is a
+
+ align:start position:0%
+zero so this C surf integral is a
+ 
+
+ align:start position:0%
+zero so this C surf integral is a
+Surface integral of zero so it just
+
+ align:start position:0%
+Surface integral of zero so it just
+ 
+
+ align:start position:0%
+Surface integral of zero so it just
+gives you zero okay so great so that's
+
+ align:start position:0%
+gives you zero okay so great so that's
+ 
+
+ align:start position:0%
+gives you zero okay so great so that's
+really nice that simplifies our life
+
+ align:start position:0%
+really nice that simplifies our life
+ 
+
+ align:start position:0%
+really nice that simplifies our life
+very much now our our line integral that
+
+ align:start position:0%
+very much now our our line integral that
+ 
+
+ align:start position:0%
+very much now our our line integral that
+we want we just have it in terms of just
+
+ align:start position:0%
+we want we just have it in terms of just
+ 
+
+ align:start position:0%
+we want we just have it in terms of just
+this one other line integral right so
+
+ align:start position:0%
+this one other line integral right so
+ 
+
+ align:start position:0%
+this one other line integral right so
+the surface integral is
+
+ align:start position:0%
+the surface integral is
+ 
+
+ align:start position:0%
+the surface integral is
+zero let me see where should I put this
+
+ align:start position:0%
+zero let me see where should I put this
+ 
+
+ align:start position:0%
+zero let me see where should I put this
+okay the curl is 4K
+
+ align:start position:0%
+okay the curl is 4K
+ 
+
+ align:start position:0%
+okay the curl is 4K
+so the surface
+
+ align:start position:0%
+so the surface
+ 
+
+ align:start position:0%
+so the surface
+integral curl f
+
+ align:start position:0%
+integral curl f
+ 
+
+ align:start position:0%
+integral curl f
+n DS is also equal to
+
+ align:start position:0%
+n DS is also equal to
+ 
+
+ align:start position:0%
+n DS is also equal to
+zero so having made that simplification
+
+ align:start position:0%
+zero so having made that simplification
+ 
+
+ align:start position:0%
+zero so having made that simplification
+now we just need now we just need this
+
+ align:start position:0%
+now we just need now we just need this
+ 
+
+ align:start position:0%
+now we just need now we just need this
+other uh integral we need this line
+
+ align:start position:0%
+other uh integral we need this line
+ 
+
+ align:start position:0%
+other uh integral we need this line
+integral over
+
+ align:start position:0%
+integral over
+ 
+
+ align:start position:0%
+integral over
+C1 and that'll give us what what we need
+
+ align:start position:0%
+C1 and that'll give us what what we need
+ 
+
+ align:start position:0%
+C1 and that'll give us what what we need
+so let's so let's have a go at that so
+
+ align:start position:0%
+so let's so let's have a go at that so
+ 
+
+ align:start position:0%
+so let's so let's have a go at that so
+C1 so C1 is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circle of
+
+ align:start position:0%
+circle of
+ 
+
+ align:start position:0%
+circle of
+radius B centered at the origin in the
+
+ align:start position:0%
+radius B centered at the origin in the
+ 
+
+ align:start position:0%
+radius B centered at the origin in the
+XY plane okay I'm not going to write
+
+ align:start position:0%
+XY plane okay I'm not going to write
+ 
+
+ align:start position:0%
+XY plane okay I'm not going to write
+that down I'm just going to say it's the
+
+ align:start position:0%
+that down I'm just going to say it's the
+ 
+
+ align:start position:0%
+that down I'm just going to say it's the
+circle of radius B centered at the
+
+ align:start position:0%
+circle of radius B centered at the
+ 
+
+ align:start position:0%
+circle of radius B centered at the
+origin in the XY plane so okay so it's
+
+ align:start position:0%
+origin in the XY plane so okay so it's
+ 
+
+ align:start position:0%
+origin in the XY plane so okay so it's
+not that hard to parameterize so we have
+
+ align:start position:0%
+not that hard to parameterize so we have
+ 
+
+ align:start position:0%
+not that hard to parameterize so we have
+that um so it's parameterized by xals B
+
+ align:start position:0%
+that um so it's parameterized by xals B
+ 
+
+ align:start position:0%
+that um so it's parameterized by xals B
+cosine Theta y
+
+ align:start position:0%
+cosine Theta y
+ 
+
+ align:start position:0%
+cosine Theta y
+= b sin Theta we should check we should
+
+ align:start position:0%
+= b sin Theta we should check we should
+ 
+
+ align:start position:0%
+= b sin Theta we should check we should
+double check that we're doing the right
+
+ align:start position:0%
+double check that we're doing the right
+ 
+
+ align:start position:0%
+double check that we're doing the right
+the right direction of parameterization
+
+ align:start position:0%
+the right direction of parameterization
+ 
+
+ align:start position:0%
+the right direction of parameterization
+let's go have a look let's
+
+ align:start position:0%
+let's go have a look let's
+ 
+
+ align:start position:0%
+let's go have a look let's
+see yes okay so we parameterized this
+
+ align:start position:0%
+see yes okay so we parameterized this
+ 
+
+ align:start position:0%
+see yes okay so we parameterized this
+circle going counterclockwise in the XY
+
+ align:start position:0%
+circle going counterclockwise in the XY
+ 
+
+ align:start position:0%
+circle going counterclockwise in the XY
+plane so good so this parameterization
+
+ align:start position:0%
+plane so good so this parameterization
+ 
+
+ align:start position:0%
+plane so good so this parameterization
+is going the right direction otherwise
+
+ align:start position:0%
+is going the right direction otherwise
+ 
+
+ align:start position:0%
+is going the right direction otherwise
+we'd have to you know change the sign of
+
+ align:start position:0%
+we'd have to you know change the sign of
+ 
+
+ align:start position:0%
+we'd have to you know change the sign of
+theta or something um so it's X is B
+
+ align:start position:0%
+theta or something um so it's X is B
+ 
+
+ align:start position:0%
+theta or something um so it's X is B
+cosine Theta Y is B sin Theta and we're
+
+ align:start position:0%
+cosine Theta Y is B sin Theta and we're
+ 
+
+ align:start position:0%
+cosine Theta Y is B sin Theta and we're
+going once around the circle so we want
+
+ align:start position:0%
+going once around the circle so we want
+ 
+
+ align:start position:0%
+going once around the circle so we want
+0 less than or equal to Theta less than
+
+ align:start position:0%
+0 less than or equal to Theta less than
+ 
+
+ align:start position:0%
+0 less than or equal to Theta less than
+or equal to 2 pi and so what do we have
+
+ align:start position:0%
+or equal to 2 pi and so what do we have
+ 
+
+ align:start position:0%
+or equal to 2 pi and so what do we have
+so now we want to look at we want to
+
+ align:start position:0%
+so now we want to look at we want to
+ 
+
+ align:start position:0%
+so now we want to look at we want to
+compute the integral over this circle
+
+ align:start position:0%
+compute the integral over this circle
+ 
+
+ align:start position:0%
+compute the integral over this circle
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+Dr so let's see what F looks like in
+
+ align:start position:0%
+Dr so let's see what F looks like in
+ 
+
+ align:start position:0%
+Dr so let's see what F looks like in
+this in this situation so let's go back
+
+ align:start position:0%
+this in this situation so let's go back
+ 
+
+ align:start position:0%
+this in this situation so let's go back
+and look at the expression for f over
+
+ align:start position:0%
+and look at the expression for f over
+ 
+
+ align:start position:0%
+and look at the expression for f over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um so in this plane we have Z is equal
+
+ align:start position:0%
+um so in this plane we have Z is equal
+ 
+
+ align:start position:0%
+um so in this plane we have Z is equal
+to zero so f is minus 2 y + 2x x^2 + y^
+
+ align:start position:0%
+to zero so f is minus 2 y + 2x x^2 + y^
+ 
+
+ align:start position:0%
+to zero so f is minus 2 y + 2x x^2 + y^
+2 okay so okay so let's come back then
+
+ align:start position:0%
+2 okay so okay so let's come back then
+ 
+
+ align:start position:0%
+2 okay so okay so let's come back then
+so f is that what I just said so this is
+
+ align:start position:0%
+so f is that what I just said so this is
+ 
+
+ align:start position:0%
+so f is that what I just said so this is
+equal to the integral of over C of - 2
+
+ align:start position:0%
+equal to the integral of over C of - 2
+ 
+
+ align:start position:0%
+equal to the integral of over C of - 2
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+DX +
+
+ align:start position:0%
+DX +
+ 
+
+ align:start position:0%
+DX +
+2x
+
+ align:start position:0%
+2x
+ 
+
+ align:start position:0%
+2x
+Dy plus okay X2 + y^2 DZ but we're in
+
+ align:start position:0%
+Dy plus okay X2 + y^2 DZ but we're in
+ 
+
+ align:start position:0%
+Dy plus okay X2 + y^2 DZ but we're in
+the plane Z equals z so DZ is always
+
+ align:start position:0%
+the plane Z equals z so DZ is always
+ 
+
+ align:start position:0%
+the plane Z equals z so DZ is always
+zero in that plane so we don't have a
+
+ align:start position:0%
+zero in that plane so we don't have a
+ 
+
+ align:start position:0%
+zero in that plane so we don't have a
+third term there great um so this is our
+
+ align:start position:0%
+third term there great um so this is our
+ 
+
+ align:start position:0%
+third term there great um so this is our
+our integral and now we can substitute
+
+ align:start position:0%
+our integral and now we can substitute
+ 
+
+ align:start position:0%
+our integral and now we can substitute
+from our parameterization here so this
+
+ align:start position:0%
+from our parameterization here so this
+ 
+
+ align:start position:0%
+from our parameterization here so this
+is equal to the integral from 0 to 2 pi
+
+ align:start position:0%
+is equal to the integral from 0 to 2 pi
+ 
+
+ align:start position:0%
+is equal to the integral from 0 to 2 pi
+let's see so 2 - 2 y DX so that's - 2b
+
+ align:start position:0%
+let's see so 2 - 2 y DX so that's - 2b
+ 
+
+ align:start position:0%
+let's see so 2 - 2 y DX so that's - 2b
+sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta times DX is minus
+
+ align:start position:0%
+Theta times DX is minus
+ 
+
+ align:start position:0%
+Theta times DX is minus
+B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sin
+
+ align:start position:0%
+sin
+ 
+
+ align:start position:0%
+sin
+Theta D
+
+ align:start position:0%
+Theta D
+ 
+
+ align:start position:0%
+Theta D
+theta plus 2X so that's 2 B cosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta time Dy which is B cosine Theta D
+
+ align:start position:0%
+Theta time Dy which is B cosine Theta D
+ 
+
+ align:start position:0%
+Theta time Dy which is B cosine Theta D
+Theta time B cosine Theta D Theta this
+
+ align:start position:0%
+Theta time B cosine Theta D Theta this
+ 
+
+ align:start position:0%
+Theta time B cosine Theta D Theta this
+is quite a long equation isn't it all
+
+ align:start position:0%
+is quite a long equation isn't it all
+ 
+
+ align:start position:0%
+is quite a long equation isn't it all
+right so or long expression I guess so
+
+ align:start position:0%
+right so or long expression I guess so
+ 
+
+ align:start position:0%
+right so or long expression I guess so
+we've got the so our our line integral
+
+ align:start position:0%
+we've got the so our our line integral
+ 
+
+ align:start position:0%
+we've got the so our our line integral
+on C around C of f dodr is equal to the
+
+ align:start position:0%
+on C around C of f dodr is equal to the
+ 
+
+ align:start position:0%
+on C around C of f dodr is equal to the
+integral from 0 to 2 pi of minus 2 B sin
+
+ align:start position:0%
+integral from 0 to 2 pi of minus 2 B sin
+ 
+
+ align:start position:0%
+integral from 0 to 2 pi of minus 2 B sin
+Theta * minus B sin Theta D Theta so
+
+ align:start position:0%
+Theta * minus B sin Theta D Theta so
+ 
+
+ align:start position:0%
+Theta * minus B sin Theta D Theta so
+this is 2 b^ 2 sin^2 Theta D Theta and
+
+ align:start position:0%
+this is 2 b^ 2 sin^2 Theta D Theta and
+ 
+
+ align:start position:0%
+this is 2 b^ 2 sin^2 Theta D Theta and
+this is 2 b^2 cosine 2 Theta D Theta so
+
+ align:start position:0%
+this is 2 b^2 cosine 2 Theta D Theta so
+ 
+
+ align:start position:0%
+this is 2 b^2 cosine 2 Theta D Theta so
+okay so we can that 2 b^2 that's a
+
+ align:start position:0%
+okay so we can that 2 b^2 that's a
+ 
+
+ align:start position:0%
+okay so we can that 2 b^2 that's a
+constant we can just Factor it out and
+
+ align:start position:0%
+constant we can just Factor it out and
+ 
+
+ align:start position:0%
+constant we can just Factor it out and
+we're left with sin squ theta plus
+
+ align:start position:0%
+we're left with sin squ theta plus
+ 
+
+ align:start position:0%
+we're left with sin squ theta plus
+cosine s Theta D Theta all right but
+
+ align:start position:0%
+cosine s Theta D Theta all right but
+ 
+
+ align:start position:0%
+cosine s Theta D Theta all right but
+that's okay that's you know that's great
+
+ align:start position:0%
+that's okay that's you know that's great
+ 
+
+ align:start position:0%
+that's okay that's you know that's great
+that I'm ha happy to have that right sin
+
+ align:start position:0%
+that I'm ha happy to have that right sin
+ 
+
+ align:start position:0%
+that I'm ha happy to have that right sin
+Square theta plus cosine Square Theta
+
+ align:start position:0%
+Square theta plus cosine Square Theta
+ 
+
+ align:start position:0%
+Square theta plus cosine Square Theta
+that's going to be one okay so let's so
+
+ align:start position:0%
+that's going to be one okay so let's so
+ 
+
+ align:start position:0%
+that's going to be one okay so let's so
+we can rewrite this I'm going to bring
+
+ align:start position:0%
+we can rewrite this I'm going to bring
+ 
+
+ align:start position:0%
+we can rewrite this I'm going to bring
+it back up here so that's equal to the
+
+ align:start position:0%
+it back up here so that's equal to the
+ 
+
+ align:start position:0%
+it back up here so that's equal to the
+integral from 0 to 2 pi of 2
+
+ align:start position:0%
+integral from 0 to 2 pi of 2
+ 
+
+ align:start position:0%
+integral from 0 to 2 pi of 2
+b^2 D Theta which is 4 pi b
+
+ align:start position:0%
+b^2 D Theta which is 4 pi b
+ 
+
+ align:start position:0%
+b^2 D Theta which is 4 pi b
+^2 great okay so that's our line
+
+ align:start position:0%
+^2 great okay so that's our line
+ 
+
+ align:start position:0%
+^2 great okay so that's our line
+integral around this bottom curve
+
+ align:start position:0%
+integral around this bottom curve
+ 
+
+ align:start position:0%
+integral around this bottom curve
+C oh dear I've been I've been writing C
+
+ align:start position:0%
+C oh dear I've been I've been writing C
+ 
+
+ align:start position:0%
+C oh dear I've been I've been writing C
+but this is our not our original curve C
+
+ align:start position:0%
+but this is our not our original curve C
+ 
+
+ align:start position:0%
+but this is our not our original curve C
+this is our new curve C1 like I wrote
+
+ align:start position:0%
+this is our new curve C1 like I wrote
+ 
+
+ align:start position:0%
+this is our new curve C1 like I wrote
+there sorry so everywhere I wrote the
+
+ align:start position:0%
+there sorry so everywhere I wrote the
+ 
+
+ align:start position:0%
+there sorry so everywhere I wrote the
+line integral over C both of these
+
+ align:start position:0%
+line integral over C both of these
+ 
+
+ align:start position:0%
+line integral over C both of these
+places it was supposed to be a line
+
+ align:start position:0%
+places it was supposed to be a line
+ 
+
+ align:start position:0%
+places it was supposed to be a line
+integral over C1 sorry about that so
+
+ align:start position:0%
+integral over C1 sorry about that so
+ 
+
+ align:start position:0%
+integral over C1 sorry about that so
+we've got this line integral over C1 and
+
+ align:start position:0%
+we've got this line integral over C1 and
+ 
+
+ align:start position:0%
+we've got this line integral over C1 and
+it worked out to 4 pi b ^2 just using
+
+ align:start position:0%
+it worked out to 4 pi b ^2 just using
+ 
+
+ align:start position:0%
+it worked out to 4 pi b ^2 just using
+our usual parameterize and and compute
+
+ align:start position:0%
+our usual parameterize and and compute
+ 
+
+ align:start position:0%
+our usual parameterize and and compute
+um technique for computing line
+
+ align:start position:0%
+um technique for computing line
+ 
+
+ align:start position:0%
+um technique for computing line
+integrals so okay so now let's see where
+
+ align:start position:0%
+integrals so okay so now let's see where
+ 
+
+ align:start position:0%
+integrals so okay so now let's see where
+we're at let's go back uh over here to
+
+ align:start position:0%
+we're at let's go back uh over here to
+ 
+
+ align:start position:0%
+we're at let's go back uh over here to
+to when we wrote down what the extended
+
+ align:start position:0%
+to when we wrote down what the extended
+ 
+
+ align:start position:0%
+to when we wrote down what the extended
+Stokes theorem says in our case so
+
+ align:start position:0%
+Stokes theorem says in our case so
+ 
+
+ align:start position:0%
+Stokes theorem says in our case so
+Stokes theor told us that the thing we
+
+ align:start position:0%
+Stokes theor told us that the thing we
+ 
+
+ align:start position:0%
+Stokes theor told us that the thing we
+were interested this is the the thing
+
+ align:start position:0%
+were interested this is the the thing
+ 
+
+ align:start position:0%
+were interested this is the the thing
+we're trying to compute right the
+
+ align:start position:0%
+we're trying to compute right the
+ 
+
+ align:start position:0%
+we're trying to compute right the
+problem asked us to compute the integral
+
+ align:start position:0%
+problem asked us to compute the integral
+ 
+
+ align:start position:0%
+problem asked us to compute the integral
+of the line integral over C of f.
+
+ align:start position:0%
+of the line integral over C of f.
+ 
+
+ align:start position:0%
+of the line integral over C of f.
+drr well extended Stokes theorem said in
+
+ align:start position:0%
+drr well extended Stokes theorem said in
+ 
+
+ align:start position:0%
+drr well extended Stokes theorem said in
+order to compute this this line integral
+
+ align:start position:0%
+order to compute this this line integral
+ 
+
+ align:start position:0%
+order to compute this this line integral
+what you can do is you can compute this
+
+ align:start position:0%
+what you can do is you can compute this
+ 
+
+ align:start position:0%
+what you can do is you can compute this
+surface integral over s and you can
+
+ align:start position:0%
+surface integral over s and you can
+ 
+
+ align:start position:0%
+surface integral over s and you can
+compute this line integral over this
+
+ align:start position:0%
+compute this line integral over this
+ 
+
+ align:start position:0%
+compute this line integral over this
+other curve C1 and then these three
+
+ align:start position:0%
+other curve C1 and then these three
+ 
+
+ align:start position:0%
+other curve C1 and then these three
+things have to satisfy this relationship
+
+ align:start position:0%
+things have to satisfy this relationship
+ 
+
+ align:start position:0%
+things have to satisfy this relationship
+that's what Stokes theorem says and now
+
+ align:start position:0%
+that's what Stokes theorem says and now
+ 
+
+ align:start position:0%
+that's what Stokes theorem says and now
+we've computed we've computed the
+
+ align:start position:0%
+we've computed we've computed the
+ 
+
+ align:start position:0%
+we've computed we've computed the
+service integral we found it was equal
+
+ align:start position:0%
+service integral we found it was equal
+ 
+
+ align:start position:0%
+service integral we found it was equal
+to zero by a simple geometric argument
+
+ align:start position:0%
+to zero by a simple geometric argument
+ 
+
+ align:start position:0%
+to zero by a simple geometric argument
+that didn't require us to actually
+
+ align:start position:0%
+that didn't require us to actually
+ 
+
+ align:start position:0%
+that didn't require us to actually
+compute a surface integral um and we
+
+ align:start position:0%
+compute a surface integral um and we
+ 
+
+ align:start position:0%
+compute a surface integral um and we
+computed this line integral just now uh
+
+ align:start position:0%
+computed this line integral just now uh
+ 
+
+ align:start position:0%
+computed this line integral just now uh
+by by parameterizing and comput again so
+
+ align:start position:0%
+by by parameterizing and comput again so
+ 
+
+ align:start position:0%
+by by parameterizing and comput again so
+okay so this was zero and this was 4 Pi
+
+ align:start position:0%
+okay so this was zero and this was 4 Pi
+ 
+
+ align:start position:0%
+okay so this was zero and this was 4 Pi
+b^2 so if we just add our integral in
+
+ align:start position:0%
+b^2 so if we just add our integral in
+ 
+
+ align:start position:0%
+b^2 so if we just add our integral in
+question to the other side what we find
+
+ align:start position:0%
+question to the other side what we find
+ 
+
+ align:start position:0%
+question to the other side what we find
+I'm going to go find some empty board
+
+ align:start position:0%
+I'm going to go find some empty board
+ 
+
+ align:start position:0%
+I'm going to go find some empty board
+space to write it down so our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral so our integral the integral
+
+ align:start position:0%
+integral so our integral the integral
+ 
+
+ align:start position:0%
+integral so our integral the integral
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+C of f dot Dr well it's equal to the
+
+ align:start position:0%
+C of f dot Dr well it's equal to the
+ 
+
+ align:start position:0%
+C of f dot Dr well it's equal to the
+surface integral sorry it's equal to the
+
+ align:start position:0%
+surface integral sorry it's equal to the
+ 
+
+ align:start position:0%
+surface integral sorry it's equal to the
+to our to this other line integral minus
+
+ align:start position:0%
+to our to this other line integral minus
+ 
+
+ align:start position:0%
+to our to this other line integral minus
+the surface integral so it's equal to 4
+
+ align:start position:0%
+the surface integral so it's equal to 4
+ 
+
+ align:start position:0%
+the surface integral so it's equal to 4
+piun B ^2 - 0 just rearranging that
+
+ align:start position:0%
+piun B ^2 - 0 just rearranging that
+ 
+
+ align:start position:0%
+piun B ^2 - 0 just rearranging that
+equation we were looking at a second ago
+
+ align:start position:0%
+equation we were looking at a second ago
+ 
+
+ align:start position:0%
+equation we were looking at a second ago
+from Stokes theorem so it's just 4 pi b
+
+ align:start position:0%
+from Stokes theorem so it's just 4 pi b
+ 
+
+ align:start position:0%
+from Stokes theorem so it's just 4 pi b
+^2 so that's the answer and I'll end
+
+ align:start position:0%
+^2 so that's the answer and I'll end
+ 
+
+ align:start position:0%
+^2 so that's the answer and I'll end
+there
\ No newline at end of file
diff --git a/8-HU6SwL9jo.txt b/8-HU6SwL9jo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..38d952566e7605377a2c39748dbeaa2c3ce94c5d
--- /dev/null
+++ b/8-HU6SwL9jo.txt
@@ -0,0 +1,1203 @@
+align:start position:0%
+ 
+all right so welcome back to 8701
+
+ align:start position:0%
+all right so welcome back to 8701
+ 
+
+ align:start position:0%
+all right so welcome back to 8701
+so we have all ingredients now to
+
+ align:start position:0%
+so we have all ingredients now to
+ 
+
+ align:start position:0%
+so we have all ingredients now to
+prepare
+
+ align:start position:0%
+prepare
+ 
+
+ align:start position:0%
+prepare
+fireman rules for qed so that's the
+
+ align:start position:0%
+fireman rules for qed so that's the
+ 
+
+ align:start position:0%
+fireman rules for qed so that's the
+toolkit we need in order to make
+
+ align:start position:0%
+toolkit we need in order to make
+ 
+
+ align:start position:0%
+toolkit we need in order to make
+calculations to calculate scattering
+
+ align:start position:0%
+calculations to calculate scattering
+ 
+
+ align:start position:0%
+calculations to calculate scattering
+processes
+
+ align:start position:0%
+processes
+ 
+
+ align:start position:0%
+processes
+in the case and we have already seen
+
+ align:start position:0%
+in the case and we have already seen
+ 
+
+ align:start position:0%
+in the case and we have already seen
+fileman rules for our toy theory
+
+ align:start position:0%
+fileman rules for our toy theory
+ 
+
+ align:start position:0%
+fileman rules for our toy theory
+again now the situation is a little bit
+
+ align:start position:0%
+again now the situation is a little bit
+ 
+
+ align:start position:0%
+again now the situation is a little bit
+more complicated because we can consider
+
+ align:start position:0%
+more complicated because we can consider
+ 
+
+ align:start position:0%
+more complicated because we can consider
+the spin of particles in addition
+
+ align:start position:0%
+the spin of particles in addition
+ 
+
+ align:start position:0%
+the spin of particles in addition
+to their energy and momenta the rules
+
+ align:start position:0%
+to their energy and momenta the rules
+ 
+
+ align:start position:0%
+to their energy and momenta the rules
+sequence of things are very much the
+
+ align:start position:0%
+sequence of things are very much the
+ 
+
+ align:start position:0%
+sequence of things are very much the
+same there is however a few caveats to
+
+ align:start position:0%
+same there is however a few caveats to
+ 
+
+ align:start position:0%
+same there is however a few caveats to
+keep in mind and i'll point out
+
+ align:start position:0%
+keep in mind and i'll point out
+ 
+
+ align:start position:0%
+keep in mind and i'll point out
+okay so the very first thing is to be
+
+ align:start position:0%
+okay so the very first thing is to be
+ 
+
+ align:start position:0%
+okay so the very first thing is to be
+very clear in
+
+ align:start position:0%
+very clear in
+ 
+
+ align:start position:0%
+very clear in
+our notation so this is an arbitrary
+
+ align:start position:0%
+our notation so this is an arbitrary
+ 
+
+ align:start position:0%
+our notation so this is an arbitrary
+or generic qed farming diagram we have
+
+ align:start position:0%
+or generic qed farming diagram we have
+ 
+
+ align:start position:0%
+or generic qed farming diagram we have
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+pointed out the incoming and the
+
+ align:start position:0%
+pointed out the incoming and the
+ 
+
+ align:start position:0%
+pointed out the incoming and the
+outgoing
+
+ align:start position:0%
+outgoing
+ 
+
+ align:start position:0%
+outgoing
+so there's internal lines which i didn't
+
+ align:start position:0%
+so there's internal lines which i didn't
+ 
+
+ align:start position:0%
+so there's internal lines which i didn't
+mention here
+
+ align:start position:0%
+mention here
+ 
+
+ align:start position:0%
+mention here
+important to note the momentum momentum
+
+ align:start position:0%
+important to note the momentum momentum
+ 
+
+ align:start position:0%
+important to note the momentum momentum
+and the directions the directions are
+
+ align:start position:0%
+and the directions the directions are
+ 
+
+ align:start position:0%
+and the directions the directions are
+arbitrary we just have to be clear on
+
+ align:start position:0%
+arbitrary we just have to be clear on
+ 
+
+ align:start position:0%
+arbitrary we just have to be clear on
+them and then
+
+ align:start position:0%
+them and then
+ 
+
+ align:start position:0%
+them and then
+treat them consistently right so this is
+
+ align:start position:0%
+treat them consistently right so this is
+ 
+
+ align:start position:0%
+treat them consistently right so this is
+not different in our previous discussion
+
+ align:start position:0%
+not different in our previous discussion
+ 
+
+ align:start position:0%
+not different in our previous discussion
+then here comes the difference um
+
+ align:start position:0%
+then here comes the difference um
+ 
+
+ align:start position:0%
+then here comes the difference um
+our external lines are either electron
+
+ align:start position:0%
+our external lines are either electron
+ 
+
+ align:start position:0%
+our external lines are either electron
+positrons or photons
+
+ align:start position:0%
+positrons or photons
+ 
+
+ align:start position:0%
+positrons or photons
+right you can fermions and photons
+
+ align:start position:0%
+right you can fermions and photons
+ 
+
+ align:start position:0%
+right you can fermions and photons
+charged fermions and photons so we
+
+ align:start position:0%
+charged fermions and photons so we
+ 
+
+ align:start position:0%
+charged fermions and photons so we
+discussed how the solutions look like
+
+ align:start position:0%
+discussed how the solutions look like
+ 
+
+ align:start position:0%
+discussed how the solutions look like
+our spinos u
+
+ align:start position:0%
+our spinos u
+ 
+
+ align:start position:0%
+our spinos u
+and v and for outgoing for outgoing
+
+ align:start position:0%
+and v and for outgoing for outgoing
+ 
+
+ align:start position:0%
+and v and for outgoing for outgoing
+electrons for outgoing particles we have
+
+ align:start position:0%
+electrons for outgoing particles we have
+ 
+
+ align:start position:0%
+electrons for outgoing particles we have
+this adjunct vector here which is given
+
+ align:start position:0%
+this adjunct vector here which is given
+ 
+
+ align:start position:0%
+this adjunct vector here which is given
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+u dagger gamma zero and similarly for
+
+ align:start position:0%
+u dagger gamma zero and similarly for
+ 
+
+ align:start position:0%
+u dagger gamma zero and similarly for
+the incoming anti-particle
+
+ align:start position:0%
+the incoming anti-particle
+ 
+
+ align:start position:0%
+the incoming anti-particle
+v dagger gamma zero for the photon we
+
+ align:start position:0%
+v dagger gamma zero for the photon we
+ 
+
+ align:start position:0%
+v dagger gamma zero for the photon we
+have the polarization vectors
+
+ align:start position:0%
+have the polarization vectors
+ 
+
+ align:start position:0%
+have the polarization vectors
+for incoming and outgoing photons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right then we have a vertex vector
+
+ align:start position:0%
+all right then we have a vertex vector
+ 
+
+ align:start position:0%
+all right then we have a vertex vector
+here now g
+
+ align:start position:0%
+here now g
+ 
+
+ align:start position:0%
+here now g
+zero or ge is a
+
+ align:start position:0%
+zero or ge is a
+ 
+
+ align:start position:0%
+zero or ge is a
+constant um and a dimensionless property
+
+ align:start position:0%
+constant um and a dimensionless property
+ 
+
+ align:start position:0%
+constant um and a dimensionless property
+but we do have to have a gamma gamma mu
+
+ align:start position:0%
+but we do have to have a gamma gamma mu
+ 
+
+ align:start position:0%
+but we do have to have a gamma gamma mu
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um as part of our vertex factor
+
+ align:start position:0%
+um as part of our vertex factor
+ 
+
+ align:start position:0%
+um as part of our vertex factor
+for the propagator or internal lines we
+
+ align:start position:0%
+for the propagator or internal lines we
+ 
+
+ align:start position:0%
+for the propagator or internal lines we
+have a difference between electrons
+
+ align:start position:0%
+have a difference between electrons
+ 
+
+ align:start position:0%
+have a difference between electrons
+positrons and photons and that comes
+
+ align:start position:0%
+positrons and photons and that comes
+ 
+
+ align:start position:0%
+positrons and photons and that comes
+from the fact
+
+ align:start position:0%
+from the fact
+ 
+
+ align:start position:0%
+from the fact
+that electrons impose it from the mass
+
+ align:start position:0%
+that electrons impose it from the mass
+ 
+
+ align:start position:0%
+that electrons impose it from the mass
+of particles
+
+ align:start position:0%
+of particles
+ 
+
+ align:start position:0%
+of particles
+so we have vertex vectors which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know have you know this one over q
+
+ align:start position:0%
+know have you know this one over q
+ 
+
+ align:start position:0%
+know have you know this one over q
+square behavior or one over excuse me
+
+ align:start position:0%
+square behavior or one over excuse me
+ 
+
+ align:start position:0%
+square behavior or one over excuse me
+minus m square behavior
+
+ align:start position:0%
+minus m square behavior
+ 
+
+ align:start position:0%
+minus m square behavior
+so here you can already see that there's
+
+ align:start position:0%
+so here you can already see that there's
+ 
+
+ align:start position:0%
+so here you can already see that there's
+going to be a complication later when we
+
+ align:start position:0%
+going to be a complication later when we
+ 
+
+ align:start position:0%
+going to be a complication later when we
+evaluate
+
+ align:start position:0%
+evaluate
+ 
+
+ align:start position:0%
+evaluate
+or integrate our momentum simply uh the
+
+ align:start position:0%
+or integrate our momentum simply uh the
+ 
+
+ align:start position:0%
+or integrate our momentum simply uh the
+same discussion had before and we
+
+ align:start position:0%
+same discussion had before and we
+ 
+
+ align:start position:0%
+same discussion had before and we
+already know how to solve this problem
+
+ align:start position:0%
+already know how to solve this problem
+ 
+
+ align:start position:0%
+already know how to solve this problem
+uh of infinities by renormalizing by
+
+ align:start position:0%
+uh of infinities by renormalizing by
+ 
+
+ align:start position:0%
+uh of infinities by renormalizing by
+having a cut off and we
+
+ align:start position:0%
+having a cut off and we
+ 
+
+ align:start position:0%
+having a cut off and we
+normalizing them excellent
+
+ align:start position:0%
+normalizing them excellent
+ 
+
+ align:start position:0%
+normalizing them excellent
+so the next steps end is very much the
+
+ align:start position:0%
+so the next steps end is very much the
+ 
+
+ align:start position:0%
+so the next steps end is very much the
+same uh there's no change
+
+ align:start position:0%
+same uh there's no change
+ 
+
+ align:start position:0%
+same uh there's no change
+we have to make sure that there's energy
+
+ align:start position:0%
+we have to make sure that there's energy
+ 
+
+ align:start position:0%
+we have to make sure that there's energy
+and momentum conservation and reinforces
+
+ align:start position:0%
+and momentum conservation and reinforces
+ 
+
+ align:start position:0%
+and momentum conservation and reinforces
+introducing delta functions uh we have
+
+ align:start position:0%
+introducing delta functions uh we have
+ 
+
+ align:start position:0%
+introducing delta functions uh we have
+to integrate over each and every
+
+ align:start position:0%
+to integrate over each and every
+ 
+
+ align:start position:0%
+to integrate over each and every
+internal momenta and each
+
+ align:start position:0%
+internal momenta and each
+ 
+
+ align:start position:0%
+internal momenta and each
+in each internal line
+
+ align:start position:0%
+in each internal line
+ 
+
+ align:start position:0%
+in each internal line
+gets one of those integration factors
+
+ align:start position:0%
+gets one of those integration factors
+ 
+
+ align:start position:0%
+gets one of those integration factors
+and then after we integrate we have to
+
+ align:start position:0%
+and then after we integrate we have to
+ 
+
+ align:start position:0%
+and then after we integrate we have to
+we are left with the delta function and
+
+ align:start position:0%
+we are left with the delta function and
+ 
+
+ align:start position:0%
+we are left with the delta function and
+we have to cancel that delta function
+
+ align:start position:0%
+we have to cancel that delta function
+ 
+
+ align:start position:0%
+we have to cancel that delta function
+all right in our toy experiment the
+
+ align:start position:0%
+all right in our toy experiment the
+ 
+
+ align:start position:0%
+all right in our toy experiment the
+order of things didn't matter
+
+ align:start position:0%
+order of things didn't matter
+ 
+
+ align:start position:0%
+order of things didn't matter
+everything we had in there was scala's
+
+ align:start position:0%
+everything we had in there was scala's
+ 
+
+ align:start position:0%
+everything we had in there was scala's
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+right here we do have a little bit more
+
+ align:start position:0%
+right here we do have a little bit more
+ 
+
+ align:start position:0%
+right here we do have a little bit more
+complicated problems so
+
+ align:start position:0%
+complicated problems so
+ 
+
+ align:start position:0%
+complicated problems so
+there's an importance in the order of
+
+ align:start position:0%
+there's an importance in the order of
+ 
+
+ align:start position:0%
+there's an importance in the order of
+which we execute things
+
+ align:start position:0%
+which we execute things
+ 
+
+ align:start position:0%
+which we execute things
+so what we're going to do is you know
+
+ align:start position:0%
+so what we're going to do is you know
+ 
+
+ align:start position:0%
+so what we're going to do is you know
+form firmware learn lines you just
+
+ align:start position:0%
+form firmware learn lines you just
+ 
+
+ align:start position:0%
+form firmware learn lines you just
+follow a fermion as we go from the left
+
+ align:start position:0%
+follow a fermion as we go from the left
+ 
+
+ align:start position:0%
+follow a fermion as we go from the left
+to the right
+
+ align:start position:0%
+to the right
+ 
+
+ align:start position:0%
+to the right
+and you will find things which are
+
+ align:start position:0%
+and you will find things which are
+ 
+
+ align:start position:0%
+and you will find things which are
+always of the form
+
+ align:start position:0%
+always of the form
+ 
+
+ align:start position:0%
+always of the form
+an adjoint spinner a four cross four
+
+ align:start position:0%
+an adjoint spinner a four cross four
+ 
+
+ align:start position:0%
+an adjoint spinner a four cross four
+times four matrix
+
+ align:start position:0%
+times four matrix
+ 
+
+ align:start position:0%
+times four matrix
+and a spino and the result of this is
+
+ align:start position:0%
+and a spino and the result of this is
+ 
+
+ align:start position:0%
+and a spino and the result of this is
+going to be a number
+
+ align:start position:0%
+going to be a number
+ 
+
+ align:start position:0%
+going to be a number
+all right great there is one additional
+
+ align:start position:0%
+all right great there is one additional
+ 
+
+ align:start position:0%
+all right great there is one additional
+complication
+
+ align:start position:0%
+complication
+ 
+
+ align:start position:0%
+complication
+is accounting for duplications and
+
+ align:start position:0%
+is accounting for duplications and
+ 
+
+ align:start position:0%
+is accounting for duplications and
+making sure that the sign is
+
+ align:start position:0%
+making sure that the sign is
+ 
+
+ align:start position:0%
+making sure that the sign is
+and i'm just mentioning this here this
+
+ align:start position:0%
+and i'm just mentioning this here this
+ 
+
+ align:start position:0%
+and i'm just mentioning this here this
+will become more clear
+
+ align:start position:0%
+will become more clear
+ 
+
+ align:start position:0%
+will become more clear
+as we walk through examples so there's
+
+ align:start position:0%
+as we walk through examples so there's
+ 
+
+ align:start position:0%
+as we walk through examples so there's
+an anti-semitration going on
+
+ align:start position:0%
+an anti-semitration going on
+ 
+
+ align:start position:0%
+an anti-semitration going on
+where we have to introduce a minus sign
+
+ align:start position:0%
+where we have to introduce a minus sign
+ 
+
+ align:start position:0%
+where we have to introduce a minus sign
+between the diagrams
+
+ align:start position:0%
+between the diagrams
+ 
+
+ align:start position:0%
+between the diagrams
+between different diagrams that differ
+
+ align:start position:0%
+between different diagrams that differ
+ 
+
+ align:start position:0%
+between different diagrams that differ
+only by the interchange or the exchange
+
+ align:start position:0%
+only by the interchange or the exchange
+ 
+
+ align:start position:0%
+only by the interchange or the exchange
+of two incoming
+
+ align:start position:0%
+of two incoming
+ 
+
+ align:start position:0%
+of two incoming
+or two outgoing electrons or positrons
+
+ align:start position:0%
+or two outgoing electrons or positrons
+ 
+
+ align:start position:0%
+or two outgoing electrons or positrons
+and or the incoming electron with an
+
+ align:start position:0%
+and or the incoming electron with an
+ 
+
+ align:start position:0%
+and or the incoming electron with an
+outgoing positron
+
+ align:start position:0%
+outgoing positron
+ 
+
+ align:start position:0%
+outgoing positron
+so you have a diagram which is exactly
+
+ align:start position:0%
+so you have a diagram which is exactly
+ 
+
+ align:start position:0%
+so you have a diagram which is exactly
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+but you know the two incoming electrons
+
+ align:start position:0%
+but you know the two incoming electrons
+ 
+
+ align:start position:0%
+but you know the two incoming electrons
+are interchanged you have to add those
+
+ align:start position:0%
+are interchanged you have to add those
+ 
+
+ align:start position:0%
+are interchanged you have to add those
+two diagrams
+
+ align:start position:0%
+two diagrams
+ 
+
+ align:start position:0%
+two diagrams
+you know you have to add all matrix
+
+ align:start position:0%
+you know you have to add all matrix
+ 
+
+ align:start position:0%
+you know you have to add all matrix
+elements together
+
+ align:start position:0%
+elements together
+ 
+
+ align:start position:0%
+elements together
+before we calculate an amplitude but you
+
+ align:start position:0%
+before we calculate an amplitude but you
+ 
+
+ align:start position:0%
+before we calculate an amplitude but you
+have to introduce a minus sign when you
+
+ align:start position:0%
+have to introduce a minus sign when you
+ 
+
+ align:start position:0%
+have to introduce a minus sign when you
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+those two particles so with that we have
+
+ align:start position:0%
+those two particles so with that we have
+ 
+
+ align:start position:0%
+those two particles so with that we have
+we can now
+
+ align:start position:0%
+we can now
+ 
+
+ align:start position:0%
+we can now
+just basically calculate whatever qd
+
+ align:start position:0%
+just basically calculate whatever qd
+ 
+
+ align:start position:0%
+just basically calculate whatever qd
+process we want
+
+ align:start position:0%
+process we want
+ 
+
+ align:start position:0%
+process we want
+all the tools are already here and what
+
+ align:start position:0%
+all the tools are already here and what
+ 
+
+ align:start position:0%
+all the tools are already here and what
+we want to do now next in the next video
+
+ align:start position:0%
+we want to do now next in the next video
+ 
+
+ align:start position:0%
+we want to do now next in the next video
+also in the in the recitation and
+
+ align:start position:0%
+also in the in the recitation and
+ 
+
+ align:start position:0%
+also in the in the recitation and
+homework
+
+ align:start position:0%
+homework
+ 
+
+ align:start position:0%
+homework
+is to go through a few examples to get a
+
+ align:start position:0%
+is to go through a few examples to get a
+ 
+
+ align:start position:0%
+is to go through a few examples to get a
+little practice with this
+
+ align:start position:0%
+little practice with this
+ 
+
+ align:start position:0%
+little practice with this
+there's a number of tricks um which will
+
+ align:start position:0%
+there's a number of tricks um which will
+ 
+
+ align:start position:0%
+there's a number of tricks um which will
+become handy and i explain those in a
+
+ align:start position:0%
+become handy and i explain those in a
+ 
+
+ align:start position:0%
+become handy and i explain those in a
+separate video
+
+ align:start position:0%
+separate video
+ 
+
+ align:start position:0%
+separate video
+they're just mathematical tricks which
+
+ align:start position:0%
+they're just mathematical tricks which
+ 
+
+ align:start position:0%
+they're just mathematical tricks which
+allow us to quickly evaluate
+
+ align:start position:0%
+allow us to quickly evaluate
+ 
+
+ align:start position:0%
+allow us to quickly evaluate
+the multiplication of spinos and matrix
+
+ align:start position:0%
+the multiplication of spinos and matrix
+ 
+
+ align:start position:0%
+the multiplication of spinos and matrix
+elements and so on
+
+ align:start position:0%
+elements and so on
+ 
+
+ align:start position:0%
+elements and so on
+all right that's it for this video
+
+ align:start position:0%
+all right that's it for this video
+ 
+
+ align:start position:0%
+all right that's it for this video
+um again there's going to be another two
+
+ align:start position:0%
+um again there's going to be another two
+ 
+
+ align:start position:0%
+um again there's going to be another two
+or three videos which deal with
+
+ align:start position:0%
+or three videos which deal with
+ 
+
+ align:start position:0%
+or three videos which deal with
+actually evaluating or calculating
+
+ align:start position:0%
+actually evaluating or calculating
+ 
+
+ align:start position:0%
+actually evaluating or calculating
+matrix elements
\ No newline at end of file
diff --git a/83lPKkTfGlY.txt b/83lPKkTfGlY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..266a55750913568d53d46451e2c0a4cfa60b2aee
--- /dev/null
+++ b/83lPKkTfGlY.txt
@@ -0,0 +1,2355 @@
+align:start position:0%
+ 
+so let's do a connection formula and use
+
+ align:start position:0%
+so let's do a connection formula and use
+ 
+
+ align:start position:0%
+so let's do a connection formula and use
+it to solve a problem the derivation of
+
+ align:start position:0%
+it to solve a problem the derivation of
+ 
+
+ align:start position:0%
+it to solve a problem the derivation of
+such connection formers we'll face it
+
+ align:start position:0%
+such connection formers we'll face it
+ 
+
+ align:start position:0%
+such connection formers we'll face it
+next time and we'll do further
+
+ align:start position:0%
+next time and we'll do further
+ 
+
+ align:start position:0%
+next time and we'll do further
+applications of the methods so yes right
+
+ align:start position:0%
+applications of the methods so yes right
+ 
+
+ align:start position:0%
+applications of the methods so yes right
+this is not a problem of the
+
+ align:start position:0%
+this is not a problem of the
+ 
+
+ align:start position:0%
+this is not a problem of the
+perturbation theory it's just our lack
+
+ align:start position:0%
+perturbation theory it's just our lack
+ 
+
+ align:start position:0%
+perturbation theory it's just our lack
+of ignore a lot of knowledge our
+
+ align:start position:0%
+of ignore a lot of knowledge our
+ 
+
+ align:start position:0%
+of ignore a lot of knowledge our
+ignorance of how the solution looks near
+
+ align:start position:0%
+ignorance of how the solution looks near
+ 
+
+ align:start position:0%
+ignorance of how the solution looks near
+there so there's nice wkb formulas for
+
+ align:start position:0%
+there so there's nice wkb formulas for
+ 
+
+ align:start position:0%
+there so there's nice wkb formulas for
+the solution away from the turning
+
+ align:start position:0%
+the solution away from the turning
+ 
+
+ align:start position:0%
+the solution away from the turning
+points those are this but the solutions
+
+ align:start position:0%
+points those are this but the solutions
+ 
+
+ align:start position:0%
+points those are this but the solutions
+near the turning points violate the
+
+ align:start position:0%
+near the turning points violate the
+ 
+
+ align:start position:0%
+near the turning points violate the
+semi-classical approximation therefore
+
+ align:start position:0%
+semi-classical approximation therefore
+ 
+
+ align:start position:0%
+semi-classical approximation therefore
+you have to find the solution near the
+
+ align:start position:0%
+you have to find the solution near the
+ 
+
+ align:start position:0%
+you have to find the solution near the
+turning points by any method you have
+
+ align:start position:0%
+turning points by any method you have
+ 
+
+ align:start position:0%
+turning points by any method you have
+there is not be gonna be the
+
+ align:start position:0%
+there is not be gonna be the
+ 
+
+ align:start position:0%
+there is not be gonna be the
+semi-classical method and then you will
+
+ align:start position:0%
+semi-classical method and then you will
+ 
+
+ align:start position:0%
+semi-classical method and then you will
+find the continuation now there's
+
+ align:start position:0%
+find the continuation now there's
+ 
+
+ align:start position:0%
+find the continuation now there's
+several ways people do this the most
+
+ align:start position:0%
+several ways people do this the most
+ 
+
+ align:start position:0%
+several ways people do this the most
+down-to-earth method would you say think
+
+ align:start position:0%
+down-to-earth method would you say think
+ 
+
+ align:start position:0%
+down-to-earth method would you say think
+the method we're going to use next time
+
+ align:start position:0%
+the method we're going to use next time
+ 
+
+ align:start position:0%
+the method we're going to use next time
+it's trying to solve the thing near
+
+ align:start position:0%
+it's trying to solve the thing near
+ 
+
+ align:start position:0%
+it's trying to solve the thing near
+there the solution people that are more
+
+ align:start position:0%
+there the solution people that are more
+ 
+
+ align:start position:0%
+there the solution people that are more
+sophisticated use complex variables
+
+ align:start position:0%
+sophisticated use complex variables
+ 
+
+ align:start position:0%
+sophisticated use complex variables
+methods in which they think of the
+
+ align:start position:0%
+methods in which they think of the
+ 
+
+ align:start position:0%
+methods in which they think of the
+solution in the complex plane the X
+
+ align:start position:0%
+solution in the complex plane the X
+ 
+
+ align:start position:0%
+solution in the complex plane the X
+plane becomes complex and they're coming
+
+ align:start position:0%
+plane becomes complex and they're coming
+ 
+
+ align:start position:0%
+plane becomes complex and they're coming
+to the turning point that they go off
+
+ align:start position:0%
+to the turning point that they go off
+ 
+
+ align:start position:0%
+to the turning point that they go off
+the imaginary axis to avoid it and come
+
+ align:start position:0%
+the imaginary axis to avoid it and come
+ 
+
+ align:start position:0%
+the imaginary axis to avoid it and come
+on the other side it's very elegant very
+
+ align:start position:0%
+on the other side it's very elegant very
+ 
+
+ align:start position:0%
+on the other side it's very elegant very
+nice harder to make read very precise
+
+ align:start position:0%
+nice harder to make read very precise
+ 
+
+ align:start position:0%
+nice harder to make read very precise
+and a little difficult to explain I
+
+ align:start position:0%
+and a little difficult to explain I
+ 
+
+ align:start position:0%
+and a little difficult to explain I
+don't know if I'll try to do
+
+ align:start position:0%
+don't know if I'll try to do
+ 
+
+ align:start position:0%
+don't know if I'll try to do
+but it's a it's a nice thing it's sort
+
+ align:start position:0%
+but it's a it's a nice thing it's sort
+ 
+
+ align:start position:0%
+but it's a it's a nice thing it's sort
+of avoiding the turning point by going
+
+ align:start position:0%
+of avoiding the turning point by going
+ 
+
+ align:start position:0%
+of avoiding the turning point by going
+off the axis it sounds crazy so here is
+
+ align:start position:0%
+off the axis it sounds crazy so here is
+ 
+
+ align:start position:0%
+off the axis it sounds crazy so here is
+a turning a connection formula here is x
+
+ align:start position:0%
+a turning a connection formula here is x
+ 
+
+ align:start position:0%
+a turning a connection formula here is x
+equals a here is V of X and here is a
+
+ align:start position:0%
+equals a here is V of X and here is a
+ 
+
+ align:start position:0%
+equals a here is V of X and here is a
+solution for X less than a little a I'll
+
+ align:start position:0%
+solution for X less than a little a I'll
+ 
+
+ align:start position:0%
+solution for X less than a little a I'll
+write it like that P of X cosine X to a
+
+ align:start position:0%
+write it like that P of X cosine X to a
+ 
+
+ align:start position:0%
+write it like that P of X cosine X to a
+Kappa K of X to the X prime minus PI
+
+ align:start position:0%
+Kappa K of X to the X prime minus PI
+ 
+
+ align:start position:0%
+Kappa K of X to the X prime minus PI
+over 4 minus B over square root of P of
+
+ align:start position:0%
+over 4 minus B over square root of P of
+ 
+
+ align:start position:0%
+over 4 minus B over square root of P of
+K of X K of X sine X to a K of X prime
+
+ align:start position:0%
+K of X K of X sine X to a K of X prime
+ 
+
+ align:start position:0%
+K of X K of X sine X to a K of X prime
+VX prime minus PI over 4 so look this is
+
+ align:start position:0%
+VX prime minus PI over 4 so look this is
+ 
+
+ align:start position:0%
+VX prime minus PI over 4 so look this is
+a general solution in allowed region no
+
+ align:start position:0%
+a general solution in allowed region no
+ 
+
+ align:start position:0%
+a general solution in allowed region no
+it doesn't look like what you wrote here
+
+ align:start position:0%
+it doesn't look like what you wrote here
+ 
+
+ align:start position:0%
+it doesn't look like what you wrote here
+but sines and cosines are linear
+
+ align:start position:0%
+but sines and cosines are linear
+ 
+
+ align:start position:0%
+but sines and cosines are linear
+combinations of these things and why do
+
+ align:start position:0%
+combinations of these things and why do
+ 
+
+ align:start position:0%
+combinations of these things and why do
+I put this silly minus PI over 4 because
+
+ align:start position:0%
+I put this silly minus PI over 4 because
+ 
+
+ align:start position:0%
+I put this silly minus PI over 4 because
+that's what nice solutions connect to
+
+ align:start position:0%
+that's what nice solutions connect to
+ 
+
+ align:start position:0%
+that's what nice solutions connect to
+solutions on the other side which is to
+
+ align:start position:0%
+solutions on the other side which is to
+ 
+
+ align:start position:0%
+solutions on the other side which is to
+say that the solution on the other side
+
+ align:start position:0%
+say that the solution on the other side
+ 
+
+ align:start position:0%
+say that the solution on the other side
+people that work this connection
+
+ align:start position:0%
+people that work this connection
+ 
+
+ align:start position:0%
+people that work this connection
+formulas discovered that takes this form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a 2x Kappa of X Prime the X prime plus B
+
+ align:start position:0%
+a 2x Kappa of X Prime the X prime plus B
+ 
+
+ align:start position:0%
+a 2x Kappa of X Prime the X prime plus B
+over square root of Kappa of X e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential a 2x top of X prime VX prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here it is those numbers a and B are
+
+ align:start position:0%
+so here it is those numbers a and B are
+ 
+
+ align:start position:0%
+so here it is those numbers a and B are
+things you have to keep track now they
+
+ align:start position:0%
+things you have to keep track now they
+ 
+
+ align:start position:0%
+things you have to keep track now they
+say if your solution for
+
+ align:start position:0%
+say if your solution for
+ 
+
+ align:start position:0%
+say if your solution for
+greater than a has this decaying
+
+ align:start position:0%
+greater than a has this decaying
+ 
+
+ align:start position:0%
+greater than a has this decaying
+explanation this grown exponential with
+
+ align:start position:0%
+explanation this grown exponential with
+ 
+
+ align:start position:0%
+explanation this grown exponential with
+B and a your solution far to the left
+
+ align:start position:0%
+B and a your solution far to the left
+ 
+
+ align:start position:0%
+B and a your solution far to the left
+will look like this it's a pretty
+
+ align:start position:0%
+will look like this it's a pretty
+ 
+
+ align:start position:0%
+will look like this it's a pretty
+strange statement sometimes you don't
+
+ align:start position:0%
+strange statement sometimes you don't
+ 
+
+ align:start position:0%
+strange statement sometimes you don't
+want B to be 0 sometimes you do let's do
+
+ align:start position:0%
+want B to be 0 sometimes you do let's do
+ 
+
+ align:start position:0%
+want B to be 0 sometimes you do let's do
+an example with this stuff so that you
+
+ align:start position:0%
+an example with this stuff so that you
+ 
+
+ align:start position:0%
+an example with this stuff so that you
+can appreciate what goes on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's your first look at the
+
+ align:start position:0%
+so that's your first look at the
+ 
+
+ align:start position:0%
+so that's your first look at the
+connection condition there's a little
+
+ align:start position:0%
+connection condition there's a little
+ 
+
+ align:start position:0%
+connection condition there's a little
+bit of subtleties and how to use them we
+
+ align:start position:0%
+bit of subtleties and how to use them we
+ 
+
+ align:start position:0%
+bit of subtleties and how to use them we
+will discuss those subtleties next time
+
+ align:start position:0%
+will discuss those subtleties next time
+ 
+
+ align:start position:0%
+will discuss those subtleties next time
+as well but let's use it in a case where
+
+ align:start position:0%
+as well but let's use it in a case where
+ 
+
+ align:start position:0%
+as well but let's use it in a case where
+we can make sense of this without too
+
+ align:start position:0%
+we can make sense of this without too
+ 
+
+ align:start position:0%
+we can make sense of this without too
+much trouble so here is the example and
+
+ align:start position:0%
+much trouble so here is the example and
+ 
+
+ align:start position:0%
+much trouble so here is the example and
+somebody what wants you to solve the
+
+ align:start position:0%
+somebody what wants you to solve the
+ 
+
+ align:start position:0%
+somebody what wants you to solve the
+following problem you have a some slowly
+
+ align:start position:0%
+following problem you have a some slowly
+ 
+
+ align:start position:0%
+following problem you have a some slowly
+varying potential that grows grows
+
+ align:start position:0%
+varying potential that grows grows
+ 
+
+ align:start position:0%
+varying potential that grows grows
+indefinitely the effect and you wish to
+
+ align:start position:0%
+indefinitely the effect and you wish to
+ 
+
+ align:start position:0%
+indefinitely the effect and you wish to
+find the energy eigenstates in
+
+ align:start position:0%
+find the energy eigenstates in
+ 
+
+ align:start position:0%
+find the energy eigenstates in
+particular you wish to find the energies
+
+ align:start position:0%
+particular you wish to find the energies
+ 
+
+ align:start position:0%
+particular you wish to find the energies
+what are the possible energies of this
+
+ align:start position:0%
+what are the possible energies of this
+ 
+
+ align:start position:0%
+what are the possible energies of this
+potential this potential will have a
+
+ align:start position:0%
+potential this potential will have a
+ 
+
+ align:start position:0%
+potential this potential will have a
+infinite wall here so potential is
+
+ align:start position:0%
+infinite wall here so potential is
+ 
+
+ align:start position:0%
+infinite wall here so potential is
+infinite here and it grows like that up
+
+ align:start position:0%
+infinite here and it grows like that up
+ 
+
+ align:start position:0%
+infinite here and it grows like that up
+on this side we're going to try to write
+
+ align:start position:0%
+on this side we're going to try to write
+ 
+
+ align:start position:0%
+on this side we're going to try to write
+the solution for this so we'll do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the wkb solution and let me do it
+
+ align:start position:0%
+with the wkb solution and let me do it
+ 
+
+ align:start position:0%
+with the wkb solution and let me do it
+in an efficient way so what do we have
+
+ align:start position:0%
+in an efficient way so what do we have
+ 
+
+ align:start position:0%
+in an efficient way so what do we have
+here this is the analog of our point x
+
+ align:start position:0%
+here this is the analog of our point x
+ 
+
+ align:start position:0%
+here this is the analog of our point x
+equals a is the write this is the point
+
+ align:start position:0%
+equals a is the write this is the point
+ 
+
+ align:start position:0%
+equals a is the write this is the point
+where the turning solution goes funny so
+
+ align:start position:0%
+where the turning solution goes funny so
+ 
+
+ align:start position:0%
+where the turning solution goes funny so
+we will call it for the same reason with
+
+ align:start position:0%
+we will call it for the same reason with
+ 
+
+ align:start position:0%
+we will call it for the same reason with
+it before this point a will make matters
+
+ align:start position:0%
+it before this point a will make matters
+ 
+
+ align:start position:0%
+it before this point a will make matters
+clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we truly don't know what that point is
+
+ align:start position:0%
+we truly don't know what that point is
+ 
+
+ align:start position:0%
+we truly don't know what that point is
+because we truly don't know what are
+
+ align:start position:0%
+because we truly don't know what are
+ 
+
+ align:start position:0%
+because we truly don't know what are
+they allow energies but so far we can
+
+ align:start position:0%
+they allow energies but so far we can
+ 
+
+ align:start position:0%
+they allow energies but so far we can
+write E is a variable that we don't know
+
+ align:start position:0%
+write E is a variable that we don't know
+ 
+
+ align:start position:0%
+write E is a variable that we don't know
+and a can be determined if you know E
+
+ align:start position:0%
+and a can be determined if you know E
+ 
+
+ align:start position:0%
+and a can be determined if you know E
+because you know the shape of the
+
+ align:start position:0%
+because you know the shape of the
+ 
+
+ align:start position:0%
+because you know the shape of the
+potential okay so let's think of the
+
+ align:start position:0%
+potential okay so let's think of the
+ 
+
+ align:start position:0%
+potential okay so let's think of the
+region X much greater than a we're here
+
+ align:start position:0%
+region X much greater than a we're here
+ 
+
+ align:start position:0%
+region X much greater than a we're here
+we're in a forbidden region and the
+
+ align:start position:0%
+we're in a forbidden region and the
+ 
+
+ align:start position:0%
+we're in a forbidden region and the
+potential is still slowly varying let's
+
+ align:start position:0%
+potential is still slowly varying let's
+ 
+
+ align:start position:0%
+potential is still slowly varying let's
+assume that slope is small so a solution
+
+ align:start position:0%
+assume that slope is small so a solution
+ 
+
+ align:start position:0%
+assume that slope is small so a solution
+of this type would make sense so we must
+
+ align:start position:0%
+of this type would make sense so we must
+ 
+
+ align:start position:0%
+of this type would make sense so we must
+have a wkb solution on this right-hand
+
+ align:start position:0%
+have a wkb solution on this right-hand
+ 
+
+ align:start position:0%
+have a wkb solution on this right-hand
+side to the right of a of x equals a and
+
+ align:start position:0%
+side to the right of a of x equals a and
+ 
+
+ align:start position:0%
+side to the right of a of x equals a and
+that's the most general solution will
+
+ align:start position:0%
+that's the most general solution will
+ 
+
+ align:start position:0%
+that's the most general solution will
+have on the other hand here there's two
+
+ align:start position:0%
+have on the other hand here there's two
+ 
+
+ align:start position:0%
+have on the other hand here there's two
+types of solutions a growing exponential
+
+ align:start position:0%
+types of solutions a growing exponential
+ 
+
+ align:start position:0%
+types of solutions a growing exponential
+and a decaying exponential and we must
+
+ align:start position:0%
+and a decaying exponential and we must
+ 
+
+ align:start position:0%
+and a decaying exponential and we must
+have only the decaying exponential
+
+ align:start position:0%
+have only the decaying exponential
+ 
+
+ align:start position:0%
+have only the decaying exponential
+because this potential never turns if
+
+ align:start position:0%
+because this potential never turns if
+ 
+
+ align:start position:0%
+because this potential never turns if
+this potential would grow here and then
+
+ align:start position:0%
+this potential would grow here and then
+ 
+
+ align:start position:0%
+this potential would grow here and then
+turn down you might have what is called
+
+ align:start position:0%
+turn down you might have what is called
+ 
+
+ align:start position:0%
+turn down you might have what is called
+the tunneling problem and this has to be
+
+ align:start position:0%
+the tunneling problem and this has to be
+ 
+
+ align:start position:0%
+the tunneling problem and this has to be
+rethought but this probably still a
+
+ align:start position:0%
+rethought but this probably still a
+ 
+
+ align:start position:0%
+rethought but this probably still a
+little easier we have just this
+
+ align:start position:0%
+little easier we have just this
+ 
+
+ align:start position:0%
+little easier we have just this
+potential growing forever and on the
+
+ align:start position:0%
+potential growing forever and on the
+ 
+
+ align:start position:0%
+potential growing forever and on the
+right we must have B equal to zero for X
+
+ align:start position:0%
+right we must have B equal to zero for X
+ 
+
+ align:start position:0%
+right we must have B equal to zero for X
+greater than a solution B is equal to 0
+
+ align:start position:0%
+greater than a solution B is equal to 0
+ 
+
+ align:start position:0%
+greater than a solution B is equal to 0
+the solution must have a different from
+
+ align:start position:0%
+the solution must have a different from
+ 
+
+ align:start position:0%
+the solution must have a different from
+0 but if the solution has a different
+
+ align:start position:0%
+0 but if the solution has a different
+ 
+
+ align:start position:0%
+0 but if the solution has a different
+from 0 we now know the solution on this
+
+ align:start position:0%
+from 0 we now know the solution on this
+ 
+
+ align:start position:0%
+from 0 we now know the solution on this
+region X less significantly less than a
+
+ align:start position:0%
+region X less significantly less than a
+ 
+
+ align:start position:0%
+region X less significantly less than a
+in this region we know the solution is
+
+ align:start position:0%
+in this region we know the solution is
+ 
+
+ align:start position:0%
+in this region we know the solution is
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+by that formula up there so our solution
+
+ align:start position:0%
+by that formula up there so our solution
+ 
+
+ align:start position:0%
+by that formula up there so our solution
+for X much less than a the solution must
+
+ align:start position:0%
+for X much less than a the solution must
+ 
+
+ align:start position:0%
+for X much less than a the solution must
+take the form whatever a is one two
+
+ align:start position:0%
+take the form whatever a is one two
+ 
+
+ align:start position:0%
+take the form whatever a is one two
+three I don't I kind of normalize these
+
+ align:start position:0%
+three I don't I kind of normalize these
+ 
+
+ align:start position:0%
+three I don't I kind of normalize these
+things yet
+
+ align:start position:0%
+things yet
+ 
+
+ align:start position:0%
+things yet
+so the solution I'll write its I effects
+
+ align:start position:0%
+so the solution I'll write its I effects
+ 
+
+ align:start position:0%
+so the solution I'll write its I effects
+will be of the form 1 over square root
+
+ align:start position:0%
+will be of the form 1 over square root
+ 
+
+ align:start position:0%
+will be of the form 1 over square root
+of K of X cosine of X to a K of X prime
+
+ align:start position:0%
+of K of X cosine of X to a K of X prime
+ 
+
+ align:start position:0%
+of K of X cosine of X to a K of X prime
+VX prime minus PI over 4 all right
+
+ align:start position:0%
+VX prime minus PI over 4 all right
+ 
+
+ align:start position:0%
+VX prime minus PI over 4 all right
+that's what wkb predicts because of the
+
+ align:start position:0%
+that's what wkb predicts because of the
+ 
+
+ align:start position:0%
+that's what wkb predicts because of the
+connection condition on the forbidden
+
+ align:start position:0%
+connection condition on the forbidden
+ 
+
+ align:start position:0%
+connection condition on the forbidden
+region you know which wave exists and
+
+ align:start position:0%
+region you know which wave exists and
+ 
+
+ align:start position:0%
+region you know which wave exists and
+therefore far to the left of the turning
+
+ align:start position:0%
+therefore far to the left of the turning
+ 
+
+ align:start position:0%
+therefore far to the left of the turning
+point you'd also know the wave function
+
+ align:start position:0%
+point you'd also know the wave function
+ 
+
+ align:start position:0%
+point you'd also know the wave function
+it's the term with an A so have we
+
+ align:start position:0%
+it's the term with an A so have we
+ 
+
+ align:start position:0%
+it's the term with an A so have we
+solved the problem well I don't think we
+
+ align:start position:0%
+solved the problem well I don't think we
+ 
+
+ align:start position:0%
+solved the problem well I don't think we
+have we still don't know the energy so
+
+ align:start position:0%
+have we still don't know the energy so
+ 
+
+ align:start position:0%
+have we still don't know the energy so
+we must have not solved it in fact it
+
+ align:start position:0%
+we must have not solved it in fact it
+ 
+
+ align:start position:0%
+we must have not solved it in fact it
+doesn't look like we've solved it at all
+
+ align:start position:0%
+doesn't look like we've solved it at all
+ 
+
+ align:start position:0%
+doesn't look like we've solved it at all
+because at x equals 0 this wave function
+
+ align:start position:0%
+because at x equals 0 this wave function
+ 
+
+ align:start position:0%
+because at x equals 0 this wave function
+should vanish because there's a hard
+
+ align:start position:0%
+should vanish because there's a hard
+ 
+
+ align:start position:0%
+should vanish because there's a hard
+wall and I don't see any reason why it
+
+ align:start position:0%
+wall and I don't see any reason why it
+ 
+
+ align:start position:0%
+wall and I don't see any reason why it
+would vanish so let's do a little work
+
+ align:start position:0%
+would vanish so let's do a little work
+ 
+
+ align:start position:0%
+would vanish so let's do a little work
+here orienting this expanding this and
+
+ align:start position:0%
+here orienting this expanding this and
+ 
+
+ align:start position:0%
+here orienting this expanding this and
+orienting it a little better so I want
+
+ align:start position:0%
+orienting it a little better so I want
+ 
+
+ align:start position:0%
+orienting it a little better so I want
+to write this integral from 0 X to a
+
+ align:start position:0%
+to write this integral from 0 X to a
+ 
+
+ align:start position:0%
+to write this integral from 0 X to a
+you're having an integral you have 0 X
+
+ align:start position:0%
+you're having an integral you have 0 X
+ 
+
+ align:start position:0%
+you're having an integral you have 0 X
+and a because we are in the X less than
+
+ align:start position:0%
+and a because we are in the X less than
+ 
+
+ align:start position:0%
+and a because we are in the X less than
+a region this integral is the one that
+
+ align:start position:0%
+a region this integral is the one that
+ 
+
+ align:start position:0%
+a region this integral is the one that
+we have here I'll write it as an
+
+ align:start position:0%
+we have here I'll write it as an
+ 
+
+ align:start position:0%
+we have here I'll write it as an
+integral from 0 to a minus an integral
+
+ align:start position:0%
+integral from 0 to a minus an integral
+ 
+
+ align:start position:0%
+integral from 0 to a minus an integral
+from 0 to
+
+ align:start position:0%
+from 0 to
+ 
+
+ align:start position:0%
+from 0 to
+so integral from X to a is equal to an
+
+ align:start position:0%
+so integral from X to a is equal to an
+ 
+
+ align:start position:0%
+so integral from X to a is equal to an
+integral from 0 to a - an integral from
+
+ align:start position:0%
+integral from 0 to a - an integral from
+ 
+
+ align:start position:0%
+integral from 0 to a - an integral from
+0 to X this will make things a little
+
+ align:start position:0%
+0 to X this will make things a little
+ 
+
+ align:start position:0%
+0 to X this will make things a little
+clearer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in fact we could do things still a
+
+ align:start position:0%
+so in fact we could do things still a
+ 
+
+ align:start position:0%
+so in fact we could do things still a
+little easier so what do we have here we
+
+ align:start position:0%
+little easier so what do we have here we
+ 
+
+ align:start position:0%
+little easier so what do we have here we
+have this exponential the wave function
+
+ align:start position:0%
+have this exponential the wave function
+ 
+
+ align:start position:0%
+have this exponential the wave function
+not an exponential trigonometric
+
+ align:start position:0%
+not an exponential trigonometric
+ 
+
+ align:start position:0%
+not an exponential trigonometric
+function 1 over square root of K of X
+
+ align:start position:0%
+function 1 over square root of K of X
+ 
+
+ align:start position:0%
+function 1 over square root of K of X
+cosine of minus the integral from 0 to X
+
+ align:start position:0%
+cosine of minus the integral from 0 to X
+ 
+
+ align:start position:0%
+cosine of minus the integral from 0 to X
+of K of X DX Prime that's this integral
+
+ align:start position:0%
+of K of X DX Prime that's this integral
+ 
+
+ align:start position:0%
+of K of X DX Prime that's this integral
+gives rise to two in the Wilson I wrote
+
+ align:start position:0%
+gives rise to two in the Wilson I wrote
+ 
+
+ align:start position:0%
+gives rise to two in the Wilson I wrote
+the first then I come with the other
+
+ align:start position:0%
+the first then I come with the other
+ 
+
+ align:start position:0%
+the first then I come with the other
+sign plus the integral from 0 to a of K
+
+ align:start position:0%
+sign plus the integral from 0 to a of K
+ 
+
+ align:start position:0%
+sign plus the integral from 0 to a of K
+prime of X DX prime minus PI over 4 and
+
+ align:start position:0%
+prime of X DX prime minus PI over 4 and
+ 
+
+ align:start position:0%
+prime of X DX prime minus PI over 4 and
+let's call this thing Delta ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's explore this wave function a
+
+ align:start position:0%
+so let's explore this wave function a
+ 
+
+ align:start position:0%
+so let's explore this wave function a
+little more so things have become kind
+
+ align:start position:0%
+little more so things have become kind
+ 
+
+ align:start position:0%
+little more so things have become kind
+of nice there's no X dependence here
+
+ align:start position:0%
+of nice there's no X dependence here
+ 
+
+ align:start position:0%
+of nice there's no X dependence here
+that's very nice about this part of the
+
+ align:start position:0%
+that's very nice about this part of the
+ 
+
+ align:start position:0%
+that's very nice about this part of the
+formula this is an angle no exponents
+
+ align:start position:0%
+formula this is an angle no exponents
+ 
+
+ align:start position:0%
+formula this is an angle no exponents
+and the X dependence is just here from
+
+ align:start position:0%
+and the X dependence is just here from
+ 
+
+ align:start position:0%
+and the X dependence is just here from
+this term and it's a nice X dependence
+
+ align:start position:0%
+this term and it's a nice X dependence
+ 
+
+ align:start position:0%
+this term and it's a nice X dependence
+because it's an interval
+
+ align:start position:0%
+because it's an interval
+ 
+
+ align:start position:0%
+because it's an interval
+from zero to X so it kind of nice the
+
+ align:start position:0%
+from zero to X so it kind of nice the
+ 
+
+ align:start position:0%
+from zero to X so it kind of nice the
+upper limit has the X it's all kind of
+
+ align:start position:0%
+upper limit has the X it's all kind of
+ 
+
+ align:start position:0%
+upper limit has the X it's all kind of
+elegant so trigonometric function of
+
+ align:start position:0%
+elegant so trigonometric function of
+ 
+
+ align:start position:0%
+elegant so trigonometric function of
+this cosine of a difference of things is
+
+ align:start position:0%
+this cosine of a difference of things is
+ 
+
+ align:start position:0%
+this cosine of a difference of things is
+equal to 2a muscle it's cosine of the
+
+ align:start position:0%
+equal to 2a muscle it's cosine of the
+ 
+
+ align:start position:0%
+equal to 2a muscle it's cosine of the
+first term 0 to X K of X prime DX prime
+
+ align:start position:0%
+first term 0 to X K of X prime DX prime
+ 
+
+ align:start position:0%
+first term 0 to X K of X prime DX prime
+cosine Delta plus sine of the first term
+
+ align:start position:0%
+cosine Delta plus sine of the first term
+ 
+
+ align:start position:0%
+cosine Delta plus sine of the first term
+0 to X K of X prime DX prime sine Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have this quantity and this Delta so
+
+ align:start position:0%
+you have this quantity and this Delta so
+ 
+
+ align:start position:0%
+you have this quantity and this Delta so
+I use this trigonometric sum
+
+ align:start position:0%
+I use this trigonometric sum
+ 
+
+ align:start position:0%
+I use this trigonometric sum
+okay but now you can see something nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what did we say about the wave function
+
+ align:start position:0%
+what did we say about the wave function
+ 
+
+ align:start position:0%
+what did we say about the wave function
+it had to vanish at the origin and let's
+
+ align:start position:0%
+it had to vanish at the origin and let's
+ 
+
+ align:start position:0%
+it had to vanish at the origin and let's
+look at these two functions which one
+
+ align:start position:0%
+look at these two functions which one
+ 
+
+ align:start position:0%
+look at these two functions which one
+vanishes at the origin you have cosine
+
+ align:start position:0%
+vanishes at the origin you have cosine
+ 
+
+ align:start position:0%
+vanishes at the origin you have cosine
+of the inter from 0 to X when X is equal
+
+ align:start position:0%
+of the inter from 0 to X when X is equal
+ 
+
+ align:start position:0%
+of the inter from 0 to X when X is equal
+to 0 at the origin this cosine of 0
+
+ align:start position:0%
+to 0 at the origin this cosine of 0
+ 
+
+ align:start position:0%
+to 0 at the origin this cosine of 0
+which is 1 on the other hand when X is
+
+ align:start position:0%
+which is 1 on the other hand when X is
+ 
+
+ align:start position:0%
+which is 1 on the other hand when X is
+smaller X goes to 0 you get 0 for the
+
+ align:start position:0%
+smaller X goes to 0 you get 0 for the
+ 
+
+ align:start position:0%
+smaller X goes to 0 you get 0 for the
+integral and the sine vanishes so this
+
+ align:start position:0%
+integral and the sine vanishes so this
+ 
+
+ align:start position:0%
+integral and the sine vanishes so this
+is the right term so this wave function
+
+ align:start position:0%
+is the right term so this wave function
+ 
+
+ align:start position:0%
+is the right term so this wave function
+would be correct if this term would be
+
+ align:start position:0%
+would be correct if this term would be
+ 
+
+ align:start position:0%
+would be correct if this term would be
+absent this is a term that you must make
+
+ align:start position:0%
+absent this is a term that you must make
+ 
+
+ align:start position:0%
+absent this is a term that you must make
+absent shy of X without that term would
+
+ align:start position:0%
+absent shy of X without that term would
+ 
+
+ align:start position:0%
+absent shy of X without that term would
+be a valid wave function it is the wave
+
+ align:start position:0%
+be a valid wave function it is the wave
+ 
+
+ align:start position:0%
+be a valid wave function it is the wave
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+therefore the right way function if we
+
+ align:start position:0%
+therefore the right way function if we
+ 
+
+ align:start position:0%
+therefore the right way function if we
+demand that cosine Delta be equal to
+
+ align:start position:0%
+demand that cosine Delta be equal to
+ 
+
+ align:start position:0%
+demand that cosine Delta be equal to
+zero so now we're imposing as something
+
+ align:start position:0%
+zero so now we're imposing as something
+ 
+
+ align:start position:0%
+zero so now we're imposing as something
+a very non trivial condition this wave
+
+ align:start position:0%
+a very non trivial condition this wave
+ 
+
+ align:start position:0%
+a very non trivial condition this wave
+over there this contribution to the
+
+ align:start position:0%
+over there this contribution to the
+ 
+
+ align:start position:0%
+over there this contribution to the
+argument to the angle here this Delta
+
+ align:start position:0%
+argument to the angle here this Delta
+ 
+
+ align:start position:0%
+argument to the angle here this Delta
+must be such that cosine Delta is 0 in
+
+ align:start position:0%
+must be such that cosine Delta is 0 in
+ 
+
+ align:start position:0%
+must be such that cosine Delta is 0 in
+which case this term would disappear and
+
+ align:start position:0%
+which case this term would disappear and
+ 
+
+ align:start position:0%
+which case this term would disappear and
+we would have a good wave function Phi
+
+ align:start position:0%
+we would have a good wave function Phi
+ 
+
+ align:start position:0%
+we would have a good wave function Phi
+of X if this is true is 1 over square
+
+ align:start position:0%
+of X if this is true is 1 over square
+ 
+
+ align:start position:0%
+of X if this is true is 1 over square
+root of K of X times sine times the sine
+
+ align:start position:0%
+root of K of X times sine times the sine
+ 
+
+ align:start position:0%
+root of K of X times sine times the sine
+Delta which is another number sine of 0
+
+ align:start position:0%
+Delta which is another number sine of 0
+ 
+
+ align:start position:0%
+Delta which is another number sine of 0
+to X K of X prime D X PRIZE so we need
+
+ align:start position:0%
+to X K of X prime D X PRIZE so we need
+ 
+
+ align:start position:0%
+to X K of X prime D X PRIZE so we need
+cosine Delta equal to 0
+
+ align:start position:0%
+cosine Delta equal to 0
+ 
+
+ align:start position:0%
+cosine Delta equal to 0
+you know this argument gives you this
+
+ align:start position:0%
+you know this argument gives you this
+ 
+
+ align:start position:0%
+you know this argument gives you this
+wave function in a nice way here written
+
+ align:start position:0%
+wave function in a nice way here written
+ 
+
+ align:start position:0%
+wave function in a nice way here written
+what it is but we would have been able
+
+ align:start position:0%
+what it is but we would have been able
+ 
+
+ align:start position:0%
+what it is but we would have been able
+to find this or even faster if you just
+
+ align:start position:0%
+to find this or even faster if you just
+ 
+
+ align:start position:0%
+to find this or even faster if you just
+beam and that sigh at x equals 0 is 0
+
+ align:start position:0%
+beam and that sigh at x equals 0 is 0
+ 
+
+ align:start position:0%
+beam and that sigh at x equals 0 is 0
+you must have that this thing the inter
+
+ align:start position:0%
+you must have that this thing the inter
+ 
+
+ align:start position:0%
+you must have that this thing the inter
+from 0 to a of this quantity minus PI
+
+ align:start position:0%
+from 0 to a of this quantity minus PI
+ 
+
+ align:start position:0%
+from 0 to a of this quantity minus PI
+over 4
+
+ align:start position:0%
+over 4
+ 
+
+ align:start position:0%
+over 4
+must have 0 cosine and that's the
+
+ align:start position:0%
+must have 0 cosine and that's the
+ 
+
+ align:start position:0%
+must have 0 cosine and that's the
+condition we did find the advantage of
+
+ align:start position:0%
+condition we did find the advantage of
+ 
+
+ align:start position:0%
+condition we did find the advantage of
+our rearrangement is that when that
+
+ align:start position:0%
+our rearrangement is that when that
+ 
+
+ align:start position:0%
+our rearrangement is that when that
+happens the whole wave function looks
+
+ align:start position:0%
+happens the whole wave function looks
+ 
+
+ align:start position:0%
+happens the whole wave function looks
+like that and that's kind of nice that
+
+ align:start position:0%
+like that and that's kind of nice that
+ 
+
+ align:start position:0%
+like that and that's kind of nice that
+gives you the picture of the wave
+
+ align:start position:0%
+gives you the picture of the wave
+ 
+
+ align:start position:0%
+gives you the picture of the wave
+function a fairly accurate picture of
+
+ align:start position:0%
+function a fairly accurate picture of
+ 
+
+ align:start position:0%
+function a fairly accurate picture of
+the wave function in this region not
+
+ align:start position:0%
+the wave function in this region not
+ 
+
+ align:start position:0%
+the wave function in this region not
+very near the turning point but you dot
+
+ align:start position:0%
+very near the turning point but you dot
+ 
+
+ align:start position:0%
+very near the turning point but you dot
+that so so what is this cosine Delta
+
+ align:start position:0%
+that so so what is this cosine Delta
+ 
+
+ align:start position:0%
+that so so what is this cosine Delta
+going to 0
+
+ align:start position:0%
+going to 0
+ 
+
+ align:start position:0%
+going to 0
+well then Delta must be 2 and plus 1
+
+ align:start position:0%
+well then Delta must be 2 and plus 1
+ 
+
+ align:start position:0%
+well then Delta must be 2 and plus 1
+times pi over 2 so the places where the
+
+ align:start position:0%
+times pi over 2 so the places where the
+ 
+
+ align:start position:0%
+times pi over 2 so the places where the
+cosine is 0 is PI over 2 that's for n
+
+ align:start position:0%
+cosine is 0 is PI over 2 that's for n
+ 
+
+ align:start position:0%
+cosine is 0 is PI over 2 that's for n
+equals 0 3 PI over 2 so for m equal 1
+
+ align:start position:0%
+equals 0 3 PI over 2 so for m equal 1
+ 
+
+ align:start position:0%
+equals 0 3 PI over 2 so for m equal 1
+and it just goes the vertical axis and
+
+ align:start position:0%
+and it just goes the vertical axis and
+ 
+
+ align:start position:0%
+and it just goes the vertical axis and
+the unit circle so this is for n equals
+
+ align:start position:0%
+the unit circle so this is for n equals
+ 
+
+ align:start position:0%
+the unit circle so this is for n equals
+0 1 2 3 goes on and on and this is a
+
+ align:start position:0%
+0 1 2 3 goes on and on and this is a
+ 
+
+ align:start position:0%
+0 1 2 3 goes on and on and this is a
+very wonderful condition this says that
+
+ align:start position:0%
+very wonderful condition this says that
+ 
+
+ align:start position:0%
+very wonderful condition this says that
+the integral from 0 to a of K of X prime
+
+ align:start position:0%
+the integral from 0 to a of K of X prime
+ 
+
+ align:start position:0%
+the integral from 0 to a of K of X prime
+DX prime minus PI over 4 so actually we
+
+ align:start position:0%
+DX prime minus PI over 4 so actually we
+ 
+
+ align:start position:0%
+DX prime minus PI over 4 so actually we
+have here you can multiply the two here
+
+ align:start position:0%
+have here you can multiply the two here
+ 
+
+ align:start position:0%
+have here you can multiply the two here
+you get an M and then you have PI over 2
+
+ align:start position:0%
+you get an M and then you have PI over 2
+ 
+
+ align:start position:0%
+you get an M and then you have PI over 2
+and the PI over 4 that comes from that
+
+ align:start position:0%
+and the PI over 4 that comes from that
+ 
+
+ align:start position:0%
+and the PI over 4 that comes from that
+term becomes n plus 3/4 pi it's a bar
+
+ align:start position:0%
+term becomes n plus 3/4 pi it's a bar
+ 
+
+ align:start position:0%
+term becomes n plus 3/4 pi it's a bar
+born Sommerfeld quantization condition
+
+ align:start position:0%
+born Sommerfeld quantization condition
+ 
+
+ align:start position:0%
+born Sommerfeld quantization condition
+look I box that equation because that
+
+ align:start position:0%
+look I box that equation because that
+ 
+
+ align:start position:0%
+look I box that equation because that
+really gives you the answer now why
+
+ align:start position:0%
+really gives you the answer now why
+ 
+
+ align:start position:0%
+really gives you the answer now why
+because you know what K is K P of X is
+
+ align:start position:0%
+because you know what K is K P of X is
+ 
+
+ align:start position:0%
+because you know what K is K P of X is
+equal to H Bar K a square root of 2m e
+
+ align:start position:0%
+equal to H Bar K a square root of 2m e
+ 
+
+ align:start position:0%
+equal to H Bar K a square root of 2m e
+minus V of X and if you know e you know
+
+ align:start position:0%
+minus V of X and if you know e you know
+ 
+
+ align:start position:0%
+minus V of X and if you know e you know
+a so you have now a name to grow and you
+
+ align:start position:0%
+a so you have now a name to grow and you
+ 
+
+ align:start position:0%
+a so you have now a name to grow and you
+take for example N equals 0 so you want
+
+ align:start position:0%
+take for example N equals 0 so you want
+ 
+
+ align:start position:0%
+take for example N equals 0 so you want
+the integral to be equal to 3/4 pi but
+
+ align:start position:0%
+the integral to be equal to 3/4 pi but
+ 
+
+ align:start position:0%
+the integral to be equal to 3/4 pi but
+you will have to start changing the
+
+ align:start position:0%
+you will have to start changing the
+ 
+
+ align:start position:0%
+you will have to start changing the
+value of the energy with your computer
+
+ align:start position:0%
+value of the energy with your computer
+ 
+
+ align:start position:0%
+value of the energy with your computer
+if you cannot do the integral
+
+ align:start position:0%
+if you cannot do the integral
+ 
+
+ align:start position:0%
+if you cannot do the integral
+analytically and find oops for this
+
+ align:start position:0%
+analytically and find oops for this
+ 
+
+ align:start position:0%
+analytically and find oops for this
+value of the energy the integral of what
+
+ align:start position:0%
+value of the energy the integral of what
+ 
+
+ align:start position:0%
+value of the energy the integral of what
+I know this is a known function gives me
+
+ align:start position:0%
+I know this is a known function gives me
+ 
+
+ align:start position:0%
+I know this is a known function gives me
+this value so this is a very practical
+
+ align:start position:0%
+this value so this is a very practical
+ 
+
+ align:start position:0%
+this value so this is a very practical
+way of finding the energy levels it does
+
+ align:start position:0%
+way of finding the energy levels it does
+ 
+
+ align:start position:0%
+way of finding the energy levels it does
+give you the energy of the approximate
+
+ align:start position:0%
+give you the energy of the approximate
+ 
+
+ align:start position:0%
+give you the energy of the approximate
+energy levels and it's remark
+
+ align:start position:0%
+energy levels and it's remark
+ 
+
+ align:start position:0%
+energy levels and it's remark
+accurate in many cases of it also has a
+
+ align:start position:0%
+accurate in many cases of it also has a
+ 
+
+ align:start position:0%
+accurate in many cases of it also has a
+little intuition this is for N equals
+
+ align:start position:0%
+little intuition this is for N equals
+ 
+
+ align:start position:0%
+little intuition this is for N equals
+zero would be like the ground state an
+
+ align:start position:0%
+zero would be like the ground state an
+ 
+
+ align:start position:0%
+zero would be like the ground state an
+equal one first set on excited States
+
+ align:start position:0%
+equal one first set on excited States
+ 
+
+ align:start position:0%
+equal one first set on excited States
+and indeed that makes sense because Z
+
+ align:start position:0%
+and indeed that makes sense because Z
+ 
+
+ align:start position:0%
+and indeed that makes sense because Z
+this integral from 0 to a of K is the
+
+ align:start position:0%
+this integral from 0 to a of K is the
+ 
+
+ align:start position:0%
+this integral from 0 to a of K is the
+total phase of the wave function as you
+
+ align:start position:0%
+total phase of the wave function as you
+ 
+
+ align:start position:0%
+total phase of the wave function as you
+move from zero to a and that wave is a
+
+ align:start position:0%
+move from zero to a and that wave is a
+ 
+
+ align:start position:0%
+move from zero to a and that wave is a
+number of factor n times pi plus a
+
+ align:start position:0%
+number of factor n times pi plus a
+ 
+
+ align:start position:0%
+number of factor n times pi plus a
+little bit so it has time for n zeros
+
+ align:start position:0%
+little bit so it has time for n zeros
+ 
+
+ align:start position:0%
+little bit so it has time for n zeros
+the face as you move from zero to a in
+
+ align:start position:0%
+the face as you move from zero to a in
+ 
+
+ align:start position:0%
+the face as you move from zero to a in
+the wave function will have the sine
+
+ align:start position:0%
+the wave function will have the sine
+ 
+
+ align:start position:0%
+the wave function will have the sine
+function will have n zeros if this
+
+ align:start position:0%
+function will have n zeros if this
+ 
+
+ align:start position:0%
+function will have n zeros if this
+condition is satisfied consistent with
+
+ align:start position:0%
+condition is satisfied consistent with
+ 
+
+ align:start position:0%
+condition is satisfied consistent with
+that solution so that's it we'll
+
+ align:start position:0%
+that solution so that's it we'll
+ 
+
+ align:start position:0%
+that solution so that's it we'll
+continue next time find the solution of
+
+ align:start position:0%
+continue next time find the solution of
+ 
+
+ align:start position:0%
+continue next time find the solution of
+wkb exactly all right
\ No newline at end of file
diff --git a/8Okyz-5hal0.txt b/8Okyz-5hal0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..27c2783a722f6757ae72551554d2cacf45054843
--- /dev/null
+++ b/8Okyz-5hal0.txt
@@ -0,0 +1,7715 @@
+align:start position:0%
+ 
+okay we talked about spinal reflexes
+
+ align:start position:0%
+okay we talked about spinal reflexes
+ 
+
+ align:start position:0%
+okay we talked about spinal reflexes
+last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is class 20. the second
+
+ align:start position:0%
+this is class 20. the second
+ 
+
+ align:start position:0%
+this is class 20. the second
+session on the motor system
+
+ align:start position:0%
+session on the motor system
+ 
+
+ align:start position:0%
+session on the motor system
+and we're going to continue talking
+
+ align:start position:0%
+and we're going to continue talking
+ 
+
+ align:start position:0%
+and we're going to continue talking
+about spinal reflexes
+
+ align:start position:0%
+about spinal reflexes
+ 
+
+ align:start position:0%
+about spinal reflexes
+last time
+
+ align:start position:0%
+last time
+ 
+
+ align:start position:0%
+last time
+the slide
+
+ align:start position:0%
+the slide
+ 
+
+ align:start position:0%
+the slide
+that i just mentioned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right here you can see i had crossed it
+
+ align:start position:0%
+right here you can see i had crossed it
+ 
+
+ align:start position:0%
+right here you can see i had crossed it
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+it says lateral horn
+
+ align:start position:0%
+it says lateral horn
+ 
+
+ align:start position:0%
+it says lateral horn
+it made sense to them that when the
+
+ align:start position:0%
+it made sense to them that when the
+ 
+
+ align:start position:0%
+it made sense to them that when the
+spinal cord looks like that that looks
+
+ align:start position:0%
+spinal cord looks like that that looks
+ 
+
+ align:start position:0%
+spinal cord looks like that that looks
+like it's the lateral horn but this is
+
+ align:start position:0%
+like it's the lateral horn but this is
+ 
+
+ align:start position:0%
+like it's the lateral horn but this is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+at an enlargement and this is all
+
+ align:start position:0%
+at an enlargement and this is all
+ 
+
+ align:start position:0%
+at an enlargement and this is all
+ventral horn
+
+ align:start position:0%
+ventral horn
+ 
+
+ align:start position:0%
+ventral horn
+the lateral horn is a tiny little
+
+ align:start position:0%
+the lateral horn is a tiny little
+ 
+
+ align:start position:0%
+the lateral horn is a tiny little
+protrusion in the gray matter right at
+
+ align:start position:0%
+protrusion in the gray matter right at
+ 
+
+ align:start position:0%
+protrusion in the gray matter right at
+that location where i'm putting the
+
+ align:start position:0%
+that location where i'm putting the
+ 
+
+ align:start position:0%
+that location where i'm putting the
+cursor
+
+ align:start position:0%
+cursor
+ 
+
+ align:start position:0%
+cursor
+or it would be there
+
+ align:start position:0%
+or it would be there
+ 
+
+ align:start position:0%
+or it would be there
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these were our
+
+ align:start position:0%
+so these were our
+ 
+
+ align:start position:0%
+so these were our
+slides from last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and today we're
+
+ align:start position:0%
+and today we're
+ 
+
+ align:start position:0%
+and today we're
+we'll talk about the stretch reflex and
+
+ align:start position:0%
+we'll talk about the stretch reflex and
+ 
+
+ align:start position:0%
+we'll talk about the stretch reflex and
+talk about its function
+
+ align:start position:0%
+talk about its function
+ 
+
+ align:start position:0%
+talk about its function
+then we'll say a little bit about
+
+ align:start position:0%
+then we'll say a little bit about
+ 
+
+ align:start position:0%
+then we'll say a little bit about
+intersegmental organization in the chord
+
+ align:start position:0%
+intersegmental organization in the chord
+ 
+
+ align:start position:0%
+intersegmental organization in the chord
+and then plasticity in the cord
+
+ align:start position:0%
+and then plasticity in the cord
+ 
+
+ align:start position:0%
+and then plasticity in the cord
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i don't know if we'll get to descending
+
+ align:start position:0%
+i don't know if we'll get to descending
+ 
+
+ align:start position:0%
+i don't know if we'll get to descending
+pathways but we need to cover that
+
+ align:start position:0%
+pathways but we need to cover that
+ 
+
+ align:start position:0%
+pathways but we need to cover that
+before we
+
+ align:start position:0%
+before we
+ 
+
+ align:start position:0%
+before we
+in order to introduce the film that
+
+ align:start position:0%
+in order to introduce the film that
+ 
+
+ align:start position:0%
+in order to introduce the film that
+we're going to see on friday
+
+ align:start position:0%
+we're going to see on friday
+ 
+
+ align:start position:0%
+we're going to see on friday
+okay on the function of descending
+
+ align:start position:0%
+okay on the function of descending
+ 
+
+ align:start position:0%
+okay on the function of descending
+pathways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the stretch reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is it
+
+ align:start position:0%
+what is it
+ 
+
+ align:start position:0%
+what is it
+it's the reflex they always test when
+
+ align:start position:0%
+it's the reflex they always test when
+ 
+
+ align:start position:0%
+it's the reflex they always test when
+the in the neurology clinic
+
+ align:start position:0%
+the in the neurology clinic
+ 
+
+ align:start position:0%
+the in the neurology clinic
+with a jerk of the knee
+
+ align:start position:0%
+with a jerk of the knee
+ 
+
+ align:start position:0%
+with a jerk of the knee
+the knee jerk reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now that's just an example of a stretch
+
+ align:start position:0%
+now that's just an example of a stretch
+ 
+
+ align:start position:0%
+now that's just an example of a stretch
+reflex
+
+ align:start position:0%
+reflex
+ 
+
+ align:start position:0%
+reflex
+all your striated muscles have stretch
+
+ align:start position:0%
+all your striated muscles have stretch
+ 
+
+ align:start position:0%
+all your striated muscles have stretch
+reflexes okay
+
+ align:start position:0%
+reflexes okay
+ 
+
+ align:start position:0%
+reflexes okay
+if you suddenly stretch any muscle
+
+ align:start position:0%
+if you suddenly stretch any muscle
+ 
+
+ align:start position:0%
+if you suddenly stretch any muscle
+you get a stretch reflex but ordinarily
+
+ align:start position:0%
+you get a stretch reflex but ordinarily
+ 
+
+ align:start position:0%
+you get a stretch reflex but ordinarily
+this reflex is operating
+
+ align:start position:0%
+this reflex is operating
+ 
+
+ align:start position:0%
+this reflex is operating
+not just the sudden stretches but to any
+
+ align:start position:0%
+not just the sudden stretches but to any
+ 
+
+ align:start position:0%
+not just the sudden stretches but to any
+stretch
+
+ align:start position:0%
+stretch
+ 
+
+ align:start position:0%
+stretch
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's talk about that
+
+ align:start position:0%
+and let's talk about that
+ 
+
+ align:start position:0%
+and let's talk about that
+the sensory organ is called the muscle
+
+ align:start position:0%
+the sensory organ is called the muscle
+ 
+
+ align:start position:0%
+the sensory organ is called the muscle
+spindle
+
+ align:start position:0%
+spindle
+ 
+
+ align:start position:0%
+spindle
+it's in the muscle in response to muscle
+
+ align:start position:0%
+it's in the muscle in response to muscle
+ 
+
+ align:start position:0%
+it's in the muscle in response to muscle
+stretch
+
+ align:start position:0%
+stretch
+ 
+
+ align:start position:0%
+stretch
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is your textbook picture
+
+ align:start position:0%
+so this is your textbook picture
+ 
+
+ align:start position:0%
+so this is your textbook picture
+it shows a little piece of the biceps
+
+ align:start position:0%
+it shows a little piece of the biceps
+ 
+
+ align:start position:0%
+it shows a little piece of the biceps
+muscle there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it shows two kinds of sensory
+
+ align:start position:0%
+and it shows two kinds of sensory
+ 
+
+ align:start position:0%
+and it shows two kinds of sensory
+innings there are endings in the tendons
+
+ align:start position:0%
+innings there are endings in the tendons
+ 
+
+ align:start position:0%
+innings there are endings in the tendons
+you see the enlargement here in the
+
+ align:start position:0%
+you see the enlargement here in the
+ 
+
+ align:start position:0%
+you see the enlargement here in the
+upper right
+
+ align:start position:0%
+upper right
+ 
+
+ align:start position:0%
+upper right
+the golgi tendon organ is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sensory axons that innervate the tendons
+
+ align:start position:0%
+sensory axons that innervate the tendons
+ 
+
+ align:start position:0%
+sensory axons that innervate the tendons
+and respond to tension
+
+ align:start position:0%
+and respond to tension
+ 
+
+ align:start position:0%
+and respond to tension
+in the tendon
+
+ align:start position:0%
+in the tendon
+ 
+
+ align:start position:0%
+in the tendon
+okay so the tighter the muscle
+
+ align:start position:0%
+okay so the tighter the muscle
+ 
+
+ align:start position:0%
+okay so the tighter the muscle
+whether the muscle is short or long
+
+ align:start position:0%
+whether the muscle is short or long
+ 
+
+ align:start position:0%
+whether the muscle is short or long
+doesn't matter if that
+
+ align:start position:0%
+doesn't matter if that
+ 
+
+ align:start position:0%
+doesn't matter if that
+tendon is tight those
+
+ align:start position:0%
+tendon is tight those
+ 
+
+ align:start position:0%
+tendon is tight those
+10 organs will fire and what's its
+
+ align:start position:0%
+10 organs will fire and what's its
+ 
+
+ align:start position:0%
+10 organs will fire and what's its
+function well if the muscle
+
+ align:start position:0%
+function well if the muscle
+ 
+
+ align:start position:0%
+function well if the muscle
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+tight
+
+ align:start position:0%
+tight
+ 
+
+ align:start position:0%
+tight
+that the muscle that the
+
+ align:start position:0%
+that the muscle that the
+ 
+
+ align:start position:0%
+that the muscle that the
+muscle is endangering itself or
+
+ align:start position:0%
+muscle is endangering itself or
+ 
+
+ align:start position:0%
+muscle is endangering itself or
+endangering the tendons or bones
+
+ align:start position:0%
+endangering the tendons or bones
+ 
+
+ align:start position:0%
+endangering the tendons or bones
+it will cause the muscle to suddenly
+
+ align:start position:0%
+it will cause the muscle to suddenly
+ 
+
+ align:start position:0%
+it will cause the muscle to suddenly
+relax
+
+ align:start position:0%
+relax
+ 
+
+ align:start position:0%
+relax
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's to protect
+
+ align:start position:0%
+that's to protect
+ 
+
+ align:start position:0%
+that's to protect
+your muscles and limbs
+
+ align:start position:0%
+your muscles and limbs
+ 
+
+ align:start position:0%
+your muscles and limbs
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but there's also in the muscle in
+
+ align:start position:0%
+but there's also in the muscle in
+ 
+
+ align:start position:0%
+but there's also in the muscle in
+parallel with the long muscle fibers
+
+ align:start position:0%
+parallel with the long muscle fibers
+ 
+
+ align:start position:0%
+parallel with the long muscle fibers
+there's little
+
+ align:start position:0%
+there's little
+ 
+
+ align:start position:0%
+there's little
+slender fibers
+
+ align:start position:0%
+slender fibers
+ 
+
+ align:start position:0%
+slender fibers
+called muscle spindles that contain not
+
+ align:start position:0%
+called muscle spindles that contain not
+ 
+
+ align:start position:0%
+called muscle spindles that contain not
+only muscle fibers
+
+ align:start position:0%
+only muscle fibers
+ 
+
+ align:start position:0%
+only muscle fibers
+much smaller muscle fibers than the
+
+ align:start position:0%
+much smaller muscle fibers than the
+ 
+
+ align:start position:0%
+much smaller muscle fibers than the
+striated muscle fibers that give power
+
+ align:start position:0%
+striated muscle fibers that give power
+ 
+
+ align:start position:0%
+striated muscle fibers that give power
+to the muscle
+
+ align:start position:0%
+to the muscle
+ 
+
+ align:start position:0%
+to the muscle
+but they contain sensory endings so for
+
+ align:start position:0%
+but they contain sensory endings so for
+ 
+
+ align:start position:0%
+but they contain sensory endings so for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+in blue here they show a large axon that
+
+ align:start position:0%
+in blue here they show a large axon that
+ 
+
+ align:start position:0%
+in blue here they show a large axon that
+comes down and then wraps itself around
+
+ align:start position:0%
+comes down and then wraps itself around
+ 
+
+ align:start position:0%
+comes down and then wraps itself around
+the spindle
+
+ align:start position:0%
+the spindle
+ 
+
+ align:start position:0%
+the spindle
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+designed to
+
+ align:start position:0%
+designed to
+ 
+
+ align:start position:0%
+designed to
+fire extra potentials when the muscle is
+
+ align:start position:0%
+fire extra potentials when the muscle is
+ 
+
+ align:start position:0%
+fire extra potentials when the muscle is
+stretched
+
+ align:start position:0%
+stretched
+ 
+
+ align:start position:0%
+stretched
+okay then there's a few other endings
+
+ align:start position:0%
+okay then there's a few other endings
+ 
+
+ align:start position:0%
+okay then there's a few other endings
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and then there's also motor axons the
+
+ align:start position:0%
+and then there's also motor axons the
+ 
+
+ align:start position:0%
+and then there's also motor axons the
+gamma motor fibers
+
+ align:start position:0%
+gamma motor fibers
+ 
+
+ align:start position:0%
+gamma motor fibers
+coming from gamma motor neurons in the
+
+ align:start position:0%
+coming from gamma motor neurons in the
+ 
+
+ align:start position:0%
+coming from gamma motor neurons in the
+ventral horn of the cord
+
+ align:start position:0%
+ventral horn of the cord
+ 
+
+ align:start position:0%
+ventral horn of the cord
+that innervate the muscle fiber
+
+ align:start position:0%
+that innervate the muscle fiber
+ 
+
+ align:start position:0%
+that innervate the muscle fiber
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+intrafusal muscle fiber
+
+ align:start position:0%
+intrafusal muscle fiber
+ 
+
+ align:start position:0%
+intrafusal muscle fiber
+fuse is for the shape
+
+ align:start position:0%
+fuse is for the shape
+ 
+
+ align:start position:0%
+fuse is for the shape
+so it's shaped like a spindle or a fuse
+
+ align:start position:0%
+so it's shaped like a spindle or a fuse
+ 
+
+ align:start position:0%
+so it's shaped like a spindle or a fuse
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we call it the intrafusal muscle
+
+ align:start position:0%
+so we call it the intrafusal muscle
+ 
+
+ align:start position:0%
+so we call it the intrafusal muscle
+fiber if it's that fiber that tightens
+
+ align:start position:0%
+fiber if it's that fiber that tightens
+ 
+
+ align:start position:0%
+fiber if it's that fiber that tightens
+up the spindle
+
+ align:start position:0%
+up the spindle
+ 
+
+ align:start position:0%
+up the spindle
+and okay
+
+ align:start position:0%
+and okay
+ 
+
+ align:start position:0%
+and okay
+so let's look at this picture now here
+
+ align:start position:0%
+so let's look at this picture now here
+ 
+
+ align:start position:0%
+so let's look at this picture now here
+they show
+
+ align:start position:0%
+they show
+ 
+
+ align:start position:0%
+they show
+a muscle fiber
+
+ align:start position:0%
+a muscle fiber
+ 
+
+ align:start position:0%
+a muscle fiber
+and a spindle organ which has smaller
+
+ align:start position:0%
+and a spindle organ which has smaller
+ 
+
+ align:start position:0%
+and a spindle organ which has smaller
+muscle fibers in it so this is the main
+
+ align:start position:0%
+muscle fibers in it so this is the main
+ 
+
+ align:start position:0%
+muscle fibers in it so this is the main
+striated muscle fiber
+
+ align:start position:0%
+striated muscle fiber
+ 
+
+ align:start position:0%
+striated muscle fiber
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and this just represents the attachments
+
+ align:start position:0%
+and this just represents the attachments
+ 
+
+ align:start position:0%
+and this just represents the attachments
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the bone on either side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if you stretch the muscle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens you stretch the spindle too
+
+ align:start position:0%
+what happens you stretch the spindle too
+ 
+
+ align:start position:0%
+what happens you stretch the spindle too
+okay what will happen is that the
+
+ align:start position:0%
+okay what will happen is that the
+ 
+
+ align:start position:0%
+okay what will happen is that the
+spindle afferent fibers
+
+ align:start position:0%
+spindle afferent fibers
+ 
+
+ align:start position:0%
+spindle afferent fibers
+will start firing so will the gold g10
+
+ align:start position:0%
+will start firing so will the gold g10
+ 
+
+ align:start position:0%
+will start firing so will the gold g10
+an organ
+
+ align:start position:0%
+an organ
+ 
+
+ align:start position:0%
+an organ
+the axons innervating the golgi tender
+
+ align:start position:0%
+the axons innervating the golgi tender
+ 
+
+ align:start position:0%
+the axons innervating the golgi tender
+organ when this just shows when the
+
+ align:start position:0%
+organ when this just shows when the
+ 
+
+ align:start position:0%
+organ when this just shows when the
+stretch occurs so as soon as it's
+
+ align:start position:0%
+stretch occurs so as soon as it's
+ 
+
+ align:start position:0%
+stretch occurs so as soon as it's
+stretched both of those afferents will
+
+ align:start position:0%
+stretched both of those afferents will
+ 
+
+ align:start position:0%
+stretched both of those afferents will
+fire
+
+ align:start position:0%
+fire
+ 
+
+ align:start position:0%
+fire
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you say well then why did you need two
+
+ align:start position:0%
+you say well then why did you need two
+ 
+
+ align:start position:0%
+you say well then why did you need two
+endings
+
+ align:start position:0%
+endings
+ 
+
+ align:start position:0%
+endings
+well you'll see
+
+ align:start position:0%
+well you'll see
+ 
+
+ align:start position:0%
+well you'll see
+here's a picture of
+
+ align:start position:0%
+here's a picture of
+ 
+
+ align:start position:0%
+here's a picture of
+when the muscle
+
+ align:start position:0%
+when the muscle
+ 
+
+ align:start position:0%
+when the muscle
+is contracted
+
+ align:start position:0%
+is contracted
+ 
+
+ align:start position:0%
+is contracted
+so the alpha motor neurons have fired
+
+ align:start position:0%
+so the alpha motor neurons have fired
+ 
+
+ align:start position:0%
+so the alpha motor neurons have fired
+caused this muscle to shorten okay
+
+ align:start position:0%
+caused this muscle to shorten okay
+ 
+
+ align:start position:0%
+caused this muscle to shorten okay
+when the muscle shortens the golgi
+
+ align:start position:0%
+when the muscle shortens the golgi
+ 
+
+ align:start position:0%
+when the muscle shortens the golgi
+tendon organ of course is going to fire
+
+ align:start position:0%
+tendon organ of course is going to fire
+ 
+
+ align:start position:0%
+tendon organ of course is going to fire
+because of the tension in the muscle but
+
+ align:start position:0%
+because of the tension in the muscle but
+ 
+
+ align:start position:0%
+because of the tension in the muscle but
+now the spindle
+
+ align:start position:0%
+now the spindle
+ 
+
+ align:start position:0%
+now the spindle
+has become relaxed
+
+ align:start position:0%
+has become relaxed
+ 
+
+ align:start position:0%
+has become relaxed
+if the muscle shortens
+
+ align:start position:0%
+if the muscle shortens
+ 
+
+ align:start position:0%
+if the muscle shortens
+the spindle is not stretched so it's
+
+ align:start position:0%
+the spindle is not stretched so it's
+ 
+
+ align:start position:0%
+the spindle is not stretched so it's
+gonna fire very little
+
+ align:start position:0%
+gonna fire very little
+ 
+
+ align:start position:0%
+gonna fire very little
+if at all
+
+ align:start position:0%
+if at all
+ 
+
+ align:start position:0%
+if at all
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that rarely happens except very
+
+ align:start position:0%
+that rarely happens except very
+ 
+
+ align:start position:0%
+that rarely happens except very
+transiently
+
+ align:start position:0%
+transiently
+ 
+
+ align:start position:0%
+transiently
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+because when this muscle contracts
+
+ align:start position:0%
+because when this muscle contracts
+ 
+
+ align:start position:0%
+because when this muscle contracts
+the gamma motor neurons also fire and
+
+ align:start position:0%
+the gamma motor neurons also fire and
+ 
+
+ align:start position:0%
+the gamma motor neurons also fire and
+shorten the spindle
+
+ align:start position:0%
+shorten the spindle
+ 
+
+ align:start position:0%
+shorten the spindle
+to keep it sensitive to stretch
+
+ align:start position:0%
+to keep it sensitive to stretch
+ 
+
+ align:start position:0%
+to keep it sensitive to stretch
+so its length is always being adjusted
+
+ align:start position:0%
+so its length is always being adjusted
+ 
+
+ align:start position:0%
+so its length is always being adjusted
+for the length of the muscle because we
+
+ align:start position:0%
+for the length of the muscle because we
+ 
+
+ align:start position:0%
+for the length of the muscle because we
+want it to be able to respond
+
+ align:start position:0%
+want it to be able to respond
+ 
+
+ align:start position:0%
+want it to be able to respond
+to a stretch
+
+ align:start position:0%
+to a stretch
+ 
+
+ align:start position:0%
+to a stretch
+that wasn't expected
+
+ align:start position:0%
+that wasn't expected
+ 
+
+ align:start position:0%
+that wasn't expected
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that system for controlling the
+
+ align:start position:0%
+and that system for controlling the
+ 
+
+ align:start position:0%
+and that system for controlling the
+length of the spindle we call the gamma
+
+ align:start position:0%
+length of the spindle we call the gamma
+ 
+
+ align:start position:0%
+length of the spindle we call the gamma
+efferent system
+
+ align:start position:0%
+efferent system
+ 
+
+ align:start position:0%
+efferent system
+coming from gamma motor neurons
+
+ align:start position:0%
+coming from gamma motor neurons
+ 
+
+ align:start position:0%
+coming from gamma motor neurons
+smaller motor neurons in the cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that shorten the spindle
+
+ align:start position:0%
+that shorten the spindle
+ 
+
+ align:start position:0%
+that shorten the spindle
+which would adjust its sensitivity keep
+
+ align:start position:0%
+which would adjust its sensitivity keep
+ 
+
+ align:start position:0%
+which would adjust its sensitivity keep
+it sensitive to southern stretch
+
+ align:start position:0%
+it sensitive to southern stretch
+ 
+
+ align:start position:0%
+it sensitive to southern stretch
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now why is that so essential
+
+ align:start position:0%
+now why is that so essential
+ 
+
+ align:start position:0%
+now why is that so essential
+why do we have to keep doing that
+
+ align:start position:0%
+why do we have to keep doing that
+ 
+
+ align:start position:0%
+why do we have to keep doing that
+if you look in any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nerve fiber innervating a muscle okay
+
+ align:start position:0%
+nerve fiber innervating a muscle okay
+ 
+
+ align:start position:0%
+nerve fiber innervating a muscle okay
+you're going to find like 30 percent of
+
+ align:start position:0%
+you're going to find like 30 percent of
+ 
+
+ align:start position:0%
+you're going to find like 30 percent of
+the accents or gamma
+
+ align:start position:0%
+the accents or gamma
+ 
+
+ align:start position:0%
+the accents or gamma
+accents accents from gamma motor neurons
+
+ align:start position:0%
+accents accents from gamma motor neurons
+ 
+
+ align:start position:0%
+accents accents from gamma motor neurons
+much smaller than the axons the alpha
+
+ align:start position:0%
+much smaller than the axons the alpha
+ 
+
+ align:start position:0%
+much smaller than the axons the alpha
+motor neurons okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well think about it if the spindles are
+
+ align:start position:0%
+well think about it if the spindles are
+ 
+
+ align:start position:0%
+well think about it if the spindles are
+a certain length and they stay that
+
+ align:start position:0%
+a certain length and they stay that
+ 
+
+ align:start position:0%
+a certain length and they stay that
+length then anytime the muscle
+
+ align:start position:0%
+length then anytime the muscle
+ 
+
+ align:start position:0%
+length then anytime the muscle
+stretches out
+
+ align:start position:0%
+stretches out
+ 
+
+ align:start position:0%
+stretches out
+let's say it's at a length so the
+
+ align:start position:0%
+let's say it's at a length so the
+ 
+
+ align:start position:0%
+let's say it's at a length so the
+spindles are
+
+ align:start position:0%
+spindles are
+ 
+
+ align:start position:0%
+spindles are
+firing very little when my arm is in
+
+ align:start position:0%
+firing very little when my arm is in
+ 
+
+ align:start position:0%
+firing very little when my arm is in
+this position and now i
+
+ align:start position:0%
+this position and now i
+ 
+
+ align:start position:0%
+this position and now i
+extend my arm
+
+ align:start position:0%
+extend my arm
+ 
+
+ align:start position:0%
+extend my arm
+i'm lengthening the biceps muscle
+
+ align:start position:0%
+i'm lengthening the biceps muscle
+ 
+
+ align:start position:0%
+i'm lengthening the biceps muscle
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the spindle won't fire at all but if
+
+ align:start position:0%
+so the spindle won't fire at all but if
+ 
+
+ align:start position:0%
+so the spindle won't fire at all but if
+i try to make it shorter
+
+ align:start position:0%
+i try to make it shorter
+ 
+
+ align:start position:0%
+i try to make it shorter
+sorry if i lengthen it i'm stretching it
+
+ align:start position:0%
+sorry if i lengthen it i'm stretching it
+ 
+
+ align:start position:0%
+sorry if i lengthen it i'm stretching it
+okay and what will happen the spindles
+
+ align:start position:0%
+okay and what will happen the spindles
+ 
+
+ align:start position:0%
+okay and what will happen the spindles
+organ will cause the afferents to fire
+
+ align:start position:0%
+organ will cause the afferents to fire
+ 
+
+ align:start position:0%
+organ will cause the afferents to fire
+and the muscle will tend to move back to
+
+ align:start position:0%
+and the muscle will tend to move back to
+ 
+
+ align:start position:0%
+and the muscle will tend to move back to
+its position
+
+ align:start position:0%
+its position
+ 
+
+ align:start position:0%
+its position
+tends to keep the muscles in that
+
+ align:start position:0%
+tends to keep the muscles in that
+ 
+
+ align:start position:0%
+tends to keep the muscles in that
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+okay if i shorten it they're not going
+
+ align:start position:0%
+okay if i shorten it they're not going
+ 
+
+ align:start position:0%
+okay if i shorten it they're not going
+to fire if those spindles now don't
+
+ align:start position:0%
+to fire if those spindles now don't
+ 
+
+ align:start position:0%
+to fire if those spindles now don't
+change but on the other hand there's
+
+ align:start position:0%
+change but on the other hand there's
+ 
+
+ align:start position:0%
+change but on the other hand there's
+spindles in the extensor muscle too
+
+ align:start position:0%
+spindles in the extensor muscle too
+ 
+
+ align:start position:0%
+spindles in the extensor muscle too
+so if the spindles are just set
+
+ align:start position:0%
+so if the spindles are just set
+ 
+
+ align:start position:0%
+so if the spindles are just set
+at a certain length the limb will stay
+
+ align:start position:0%
+at a certain length the limb will stay
+ 
+
+ align:start position:0%
+at a certain length the limb will stay
+in one position we'll try to anyway
+
+ align:start position:0%
+in one position we'll try to anyway
+ 
+
+ align:start position:0%
+in one position we'll try to anyway
+because of the muscle to muscle reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the afferent from
+
+ align:start position:0%
+the afferent from
+ 
+
+ align:start position:0%
+the afferent from
+the spindle organ
+
+ align:start position:0%
+the spindle organ
+ 
+
+ align:start position:0%
+the spindle organ
+comes in through the dorsal root by a
+
+ align:start position:0%
+comes in through the dorsal root by a
+ 
+
+ align:start position:0%
+comes in through the dorsal root by a
+very large fiber the largest fibers in
+
+ align:start position:0%
+very large fiber the largest fibers in
+ 
+
+ align:start position:0%
+very large fiber the largest fibers in
+the dorsal root the 1a afferents
+
+ align:start position:0%
+the dorsal root the 1a afferents
+ 
+
+ align:start position:0%
+the dorsal root the 1a afferents
+those axons go directly to motor neurons
+
+ align:start position:0%
+those axons go directly to motor neurons
+ 
+
+ align:start position:0%
+those axons go directly to motor neurons
+of the same muscle
+
+ align:start position:0%
+of the same muscle
+ 
+
+ align:start position:0%
+of the same muscle
+okay that's why we call it a muscle to
+
+ align:start position:0%
+okay that's why we call it a muscle to
+ 
+
+ align:start position:0%
+okay that's why we call it a muscle to
+muscle reflex okay
+
+ align:start position:0%
+muscle reflex okay
+ 
+
+ align:start position:0%
+muscle reflex okay
+that responds to muscle stretch so we
+
+ align:start position:0%
+that responds to muscle stretch so we
+ 
+
+ align:start position:0%
+that responds to muscle stretch so we
+also call it the stretch reflex
+
+ align:start position:0%
+also call it the stretch reflex
+ 
+
+ align:start position:0%
+also call it the stretch reflex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that is the monosynaptic reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have to every time we change
+
+ align:start position:0%
+and we have to every time we change
+ 
+
+ align:start position:0%
+and we have to every time we change
+position of the limb we have to change
+
+ align:start position:0%
+position of the limb we have to change
+ 
+
+ align:start position:0%
+position of the limb we have to change
+the length of the spindles
+
+ align:start position:0%
+the length of the spindles
+ 
+
+ align:start position:0%
+the length of the spindles
+in order to keep the spindle sensitive
+
+ align:start position:0%
+in order to keep the spindle sensitive
+ 
+
+ align:start position:0%
+in order to keep the spindle sensitive
+and to allow the muscle to assume any
+
+ align:start position:0%
+and to allow the muscle to assume any
+ 
+
+ align:start position:0%
+and to allow the muscle to assume any
+position that we command it to assume
+
+ align:start position:0%
+position that we command it to assume
+ 
+
+ align:start position:0%
+position that we command it to assume
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so alpha gamma co-activation is
+
+ align:start position:0%
+so alpha gamma co-activation is
+ 
+
+ align:start position:0%
+so alpha gamma co-activation is
+essential to the functioning of this
+
+ align:start position:0%
+essential to the functioning of this
+ 
+
+ align:start position:0%
+essential to the functioning of this
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i'm thinking about the function of
+
+ align:start position:0%
+now i'm thinking about the function of
+ 
+
+ align:start position:0%
+now i'm thinking about the function of
+the stretch reflex
+
+ align:start position:0%
+the stretch reflex
+ 
+
+ align:start position:0%
+the stretch reflex
+the obvious thing is well it restores
+
+ align:start position:0%
+the obvious thing is well it restores
+ 
+
+ align:start position:0%
+the obvious thing is well it restores
+muscle length
+
+ align:start position:0%
+muscle length
+ 
+
+ align:start position:0%
+muscle length
+let's say i'm i'm holding this and
+
+ align:start position:0%
+let's say i'm i'm holding this and
+ 
+
+ align:start position:0%
+let's say i'm i'm holding this and
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+nudges me and disturbs me
+
+ align:start position:0%
+nudges me and disturbs me
+ 
+
+ align:start position:0%
+nudges me and disturbs me
+right away
+
+ align:start position:0%
+right away
+ 
+
+ align:start position:0%
+right away
+if i'm trying to hold it in one position
+
+ align:start position:0%
+if i'm trying to hold it in one position
+ 
+
+ align:start position:0%
+if i'm trying to hold it in one position
+it'll rise up again because of the
+
+ align:start position:0%
+it'll rise up again because of the
+ 
+
+ align:start position:0%
+it'll rise up again because of the
+muscle muscle i don't even have to think
+
+ align:start position:0%
+muscle muscle i don't even have to think
+ 
+
+ align:start position:0%
+muscle muscle i don't even have to think
+about it okay it will tend to restore
+
+ align:start position:0%
+about it okay it will tend to restore
+ 
+
+ align:start position:0%
+about it okay it will tend to restore
+muscle length
+
+ align:start position:0%
+muscle length
+ 
+
+ align:start position:0%
+muscle length
+it was thought that that must be the
+
+ align:start position:0%
+it was thought that that must be the
+ 
+
+ align:start position:0%
+it was thought that that must be the
+function of the stretch reflex
+
+ align:start position:0%
+function of the stretch reflex
+ 
+
+ align:start position:0%
+function of the stretch reflex
+in fact it thought it was thought that
+
+ align:start position:0%
+in fact it thought it was thought that
+ 
+
+ align:start position:0%
+in fact it thought it was thought that
+well maybe we control our movements that
+
+ align:start position:0%
+well maybe we control our movements that
+ 
+
+ align:start position:0%
+well maybe we control our movements that
+way we just change the spindle settings
+
+ align:start position:0%
+way we just change the spindle settings
+ 
+
+ align:start position:0%
+way we just change the spindle settings
+and then the limb will try to go to the
+
+ align:start position:0%
+and then the limb will try to go to the
+ 
+
+ align:start position:0%
+and then the limb will try to go to the
+corresponding position
+
+ align:start position:0%
+corresponding position
+ 
+
+ align:start position:0%
+corresponding position
+seem like a very good way to
+
+ align:start position:0%
+seem like a very good way to
+ 
+
+ align:start position:0%
+seem like a very good way to
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+the limbs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even with varying amounts of
+
+ align:start position:0%
+even with varying amounts of
+ 
+
+ align:start position:0%
+even with varying amounts of
+resistance
+
+ align:start position:0%
+resistance
+ 
+
+ align:start position:0%
+resistance
+to the movement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it was found in studies that
+
+ align:start position:0%
+but it was found in studies that
+ 
+
+ align:start position:0%
+but it was found in studies that
+no more than about 30 percent of the
+
+ align:start position:0%
+no more than about 30 percent of the
+ 
+
+ align:start position:0%
+no more than about 30 percent of the
+compensation due to disturbance of the
+
+ align:start position:0%
+compensation due to disturbance of the
+ 
+
+ align:start position:0%
+compensation due to disturbance of the
+limb when it's trying to hold the
+
+ align:start position:0%
+limb when it's trying to hold the
+ 
+
+ align:start position:0%
+limb when it's trying to hold the
+position when you're trying to hold it
+
+ align:start position:0%
+position when you're trying to hold it
+ 
+
+ align:start position:0%
+position when you're trying to hold it
+in one position is due to the stretch
+
+ align:start position:0%
+in one position is due to the stretch
+ 
+
+ align:start position:0%
+in one position is due to the stretch
+reflexes
+
+ align:start position:0%
+reflexes
+ 
+
+ align:start position:0%
+reflexes
+most of it in fact
+
+ align:start position:0%
+most of it in fact
+ 
+
+ align:start position:0%
+most of it in fact
+is due to the spring-like properties of
+
+ align:start position:0%
+is due to the spring-like properties of
+ 
+
+ align:start position:0%
+is due to the spring-like properties of
+muscle you can think of the limb this
+
+ align:start position:0%
+muscle you can think of the limb this
+ 
+
+ align:start position:0%
+muscle you can think of the limb this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+okay with
+
+ align:start position:0%
+okay with
+ 
+
+ align:start position:0%
+okay with
+if this the green there represents my
+
+ align:start position:0%
+if this the green there represents my
+ 
+
+ align:start position:0%
+if this the green there represents my
+forearm
+
+ align:start position:0%
+forearm
+ 
+
+ align:start position:0%
+forearm
+you can think of the
+
+ align:start position:0%
+you can think of the
+ 
+
+ align:start position:0%
+you can think of the
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+the muscles holding the limb in this
+
+ align:start position:0%
+the muscles holding the limb in this
+ 
+
+ align:start position:0%
+the muscles holding the limb in this
+position like springs connected on
+
+ align:start position:0%
+position like springs connected on
+ 
+
+ align:start position:0%
+position like springs connected on
+either side okay and those springs are
+
+ align:start position:0%
+either side okay and those springs are
+ 
+
+ align:start position:0%
+either side okay and those springs are
+tense
+
+ align:start position:0%
+tense
+ 
+
+ align:start position:0%
+tense
+okay and so if the limb is disturbed
+
+ align:start position:0%
+okay and so if the limb is disturbed
+ 
+
+ align:start position:0%
+okay and so if the limb is disturbed
+okay what happens
+
+ align:start position:0%
+okay what happens
+ 
+
+ align:start position:0%
+okay what happens
+we push that down
+
+ align:start position:0%
+we push that down
+ 
+
+ align:start position:0%
+we push that down
+the spring gets tighter the upper spring
+
+ align:start position:0%
+the spring gets tighter the upper spring
+ 
+
+ align:start position:0%
+the spring gets tighter the upper spring
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+spring gets looser and it will spring
+
+ align:start position:0%
+spring gets looser and it will spring
+ 
+
+ align:start position:0%
+spring gets looser and it will spring
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+that's called the spring-like properties
+
+ align:start position:0%
+that's called the spring-like properties
+ 
+
+ align:start position:0%
+that's called the spring-like properties
+of muscle
+
+ align:start position:0%
+of muscle
+ 
+
+ align:start position:0%
+of muscle
+and a major person in
+
+ align:start position:0%
+and a major person in
+ 
+
+ align:start position:0%
+and a major person in
+specifying the spring-like properties of
+
+ align:start position:0%
+specifying the spring-like properties of
+ 
+
+ align:start position:0%
+specifying the spring-like properties of
+muscles was emilio beat see upstairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they worked out many of those details
+
+ align:start position:0%
+they worked out many of those details
+ 
+
+ align:start position:0%
+they worked out many of those details
+well the springs have to be have a
+
+ align:start position:0%
+well the springs have to be have a
+ 
+
+ align:start position:0%
+well the springs have to be have a
+certain amount of tension and the
+
+ align:start position:0%
+certain amount of tension and the
+ 
+
+ align:start position:0%
+certain amount of tension and the
+tension
+
+ align:start position:0%
+tension
+ 
+
+ align:start position:0%
+tension
+is what's set
+
+ align:start position:0%
+is what's set
+ 
+
+ align:start position:0%
+is what's set
+by the muscle to muscle reflex
+
+ align:start position:0%
+by the muscle to muscle reflex
+ 
+
+ align:start position:0%
+by the muscle to muscle reflex
+we call that tension muscle stiffness
+
+ align:start position:0%
+we call that tension muscle stiffness
+ 
+
+ align:start position:0%
+we call that tension muscle stiffness
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+muscle stiffness
+
+ align:start position:0%
+muscle stiffness
+ 
+
+ align:start position:0%
+muscle stiffness
+so muscle stiffness is simply how tight
+
+ align:start position:0%
+so muscle stiffness is simply how tight
+ 
+
+ align:start position:0%
+so muscle stiffness is simply how tight
+these springs are
+
+ align:start position:0%
+these springs are
+ 
+
+ align:start position:0%
+these springs are
+how tense the muscles what's the other
+
+ align:start position:0%
+how tense the muscles what's the other
+ 
+
+ align:start position:0%
+how tense the muscles what's the other
+term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we usually talk about muscle tone
+
+ align:start position:0%
+we usually talk about muscle tone
+ 
+
+ align:start position:0%
+we usually talk about muscle tone
+but resting tone is the
+
+ align:start position:0%
+but resting tone is the
+ 
+
+ align:start position:0%
+but resting tone is the
+how tight the muscles are when you're at
+
+ align:start position:0%
+how tight the muscles are when you're at
+ 
+
+ align:start position:0%
+how tight the muscles are when you're at
+rest okay
+
+ align:start position:0%
+rest okay
+ 
+
+ align:start position:0%
+rest okay
+so does that change
+
+ align:start position:0%
+so does that change
+ 
+
+ align:start position:0%
+so does that change
+try something put your arm your hand on
+
+ align:start position:0%
+try something put your arm your hand on
+ 
+
+ align:start position:0%
+try something put your arm your hand on
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+arm so you feel both the biceps and the
+
+ align:start position:0%
+arm so you feel both the biceps and the
+ 
+
+ align:start position:0%
+arm so you feel both the biceps and the
+extensor muscles the triceps on the
+
+ align:start position:0%
+extensor muscles the triceps on the
+ 
+
+ align:start position:0%
+extensor muscles the triceps on the
+other side okay and now you move it in a
+
+ align:start position:0%
+other side okay and now you move it in a
+ 
+
+ align:start position:0%
+other side okay and now you move it in a
+relaxed way
+
+ align:start position:0%
+relaxed way
+ 
+
+ align:start position:0%
+relaxed way
+okay you won't feel the muscles now and
+
+ align:start position:0%
+okay you won't feel the muscles now and
+ 
+
+ align:start position:0%
+okay you won't feel the muscles now and
+now do this speed up the movement and
+
+ align:start position:0%
+now do this speed up the movement and
+ 
+
+ align:start position:0%
+now do this speed up the movement and
+what happens they tighten up on both
+
+ align:start position:0%
+what happens they tighten up on both
+ 
+
+ align:start position:0%
+what happens they tighten up on both
+sides okay whenever you make faster
+
+ align:start position:0%
+sides okay whenever you make faster
+ 
+
+ align:start position:0%
+sides okay whenever you make faster
+movements you get tighter springs
+
+ align:start position:0%
+movements you get tighter springs
+ 
+
+ align:start position:0%
+movements you get tighter springs
+okay now what is that from
+
+ align:start position:0%
+okay now what is that from
+ 
+
+ align:start position:0%
+okay now what is that from
+it's because the gamma efferents are
+
+ align:start position:0%
+it's because the gamma efferents are
+ 
+
+ align:start position:0%
+it's because the gamma efferents are
+firing they tighten up
+
+ align:start position:0%
+firing they tighten up
+ 
+
+ align:start position:0%
+firing they tighten up
+that you get more action of the muscle
+
+ align:start position:0%
+that you get more action of the muscle
+ 
+
+ align:start position:0%
+that you get more action of the muscle
+to muscle reflex
+
+ align:start position:0%
+to muscle reflex
+ 
+
+ align:start position:0%
+to muscle reflex
+okay the muscle spindles are tighter
+
+ align:start position:0%
+okay the muscle spindles are tighter
+ 
+
+ align:start position:0%
+okay the muscle spindles are tighter
+okay getting increased
+
+ align:start position:0%
+okay getting increased
+ 
+
+ align:start position:0%
+okay getting increased
+muscle stiffness or muscle tone
+
+ align:start position:0%
+muscle stiffness or muscle tone
+ 
+
+ align:start position:0%
+muscle stiffness or muscle tone
+very important for fine control of
+
+ align:start position:0%
+very important for fine control of
+ 
+
+ align:start position:0%
+very important for fine control of
+movements
+
+ align:start position:0%
+movements
+ 
+
+ align:start position:0%
+movements
+they have those springs tight
+
+ align:start position:0%
+they have those springs tight
+ 
+
+ align:start position:0%
+they have those springs tight
+and in fact
+
+ align:start position:0%
+and in fact
+ 
+
+ align:start position:0%
+and in fact
+we have good evidence that they're
+
+ align:start position:0%
+we have good evidence that they're
+ 
+
+ align:start position:0%
+we have good evidence that they're
+important in
+
+ align:start position:0%
+important in
+ 
+
+ align:start position:0%
+important in
+fine movement control
+
+ align:start position:0%
+fine movement control
+ 
+
+ align:start position:0%
+fine movement control
+if we look at both phylogenetic
+
+ align:start position:0%
+if we look at both phylogenetic
+ 
+
+ align:start position:0%
+if we look at both phylogenetic
+differences in animals and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example we look at the iguana
+
+ align:start position:0%
+for example we look at the iguana
+ 
+
+ align:start position:0%
+for example we look at the iguana
+versus the frog i can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you take a picture here of the spinal
+
+ align:start position:0%
+if you take a picture here of the spinal
+ 
+
+ align:start position:0%
+if you take a picture here of the spinal
+cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let that be the gray matter on one side
+
+ align:start position:0%
+let that be the gray matter on one side
+ 
+
+ align:start position:0%
+let that be the gray matter on one side
+okay you find the large motor neurons in
+
+ align:start position:0%
+okay you find the large motor neurons in
+ 
+
+ align:start position:0%
+okay you find the large motor neurons in
+these animals that have dendrites that
+
+ align:start position:0%
+these animals that have dendrites that
+ 
+
+ align:start position:0%
+these animals that have dendrites that
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+go way up into the dorsal horn
+
+ align:start position:0%
+go way up into the dorsal horn
+ 
+
+ align:start position:0%
+go way up into the dorsal horn
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and if you're a
+
+ align:start position:0%
+and if you're a
+ 
+
+ align:start position:0%
+and if you're a
+if you're a frog
+
+ align:start position:0%
+if you're a frog
+ 
+
+ align:start position:0%
+if you're a frog
+these large afferent fibers coming in
+
+ align:start position:0%
+these large afferent fibers coming in
+ 
+
+ align:start position:0%
+these large afferent fibers coming in
+from the dorsal root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some of them will contact the very
+
+ align:start position:0%
+some of them will contact the very
+ 
+
+ align:start position:0%
+some of them will contact the very
+distal parts of those dendrites
+
+ align:start position:0%
+distal parts of those dendrites
+ 
+
+ align:start position:0%
+distal parts of those dendrites
+but if you're an iguana
+
+ align:start position:0%
+but if you're an iguana
+ 
+
+ align:start position:0%
+but if you're an iguana
+we'll make him purple here
+
+ align:start position:0%
+we'll make him purple here
+ 
+
+ align:start position:0%
+we'll make him purple here
+if you're an iguana these contacts are
+
+ align:start position:0%
+if you're an iguana these contacts are
+ 
+
+ align:start position:0%
+if you're an iguana these contacts are
+made much further down the dendrite
+
+ align:start position:0%
+made much further down the dendrite
+ 
+
+ align:start position:0%
+made much further down the dendrite
+getting much tighter
+
+ align:start position:0%
+getting much tighter
+ 
+
+ align:start position:0%
+getting much tighter
+control of the motor neurons by the
+
+ align:start position:0%
+control of the motor neurons by the
+ 
+
+ align:start position:0%
+control of the motor neurons by the
+muscle to muscle reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the other thing and perhaps the
+
+ align:start position:0%
+but the other thing and perhaps the
+ 
+
+ align:start position:0%
+but the other thing and perhaps the
+stronger evidence the iguana by the way
+
+ align:start position:0%
+stronger evidence the iguana by the way
+ 
+
+ align:start position:0%
+stronger evidence the iguana by the way
+is a more advanced lizard
+
+ align:start position:0%
+is a more advanced lizard
+ 
+
+ align:start position:0%
+is a more advanced lizard
+the frog is an amphibian
+
+ align:start position:0%
+the frog is an amphibian
+ 
+
+ align:start position:0%
+the frog is an amphibian
+the iguana has
+
+ align:start position:0%
+the iguana has
+ 
+
+ align:start position:0%
+the iguana has
+much more complex
+
+ align:start position:0%
+much more complex
+ 
+
+ align:start position:0%
+much more complex
+hands and control of his hands than the
+
+ align:start position:0%
+hands and control of his hands than the
+ 
+
+ align:start position:0%
+hands and control of his hands than the
+frog
+
+ align:start position:0%
+frog
+ 
+
+ align:start position:0%
+frog
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's just a correlation but if we
+
+ align:start position:0%
+so that's just a correlation but if we
+ 
+
+ align:start position:0%
+so that's just a correlation but if we
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+the density of muscle spindles okay
+
+ align:start position:0%
+the density of muscle spindles okay
+ 
+
+ align:start position:0%
+the density of muscle spindles okay
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+various muscles we see that it's much
+
+ align:start position:0%
+various muscles we see that it's much
+ 
+
+ align:start position:0%
+various muscles we see that it's much
+greater in muscles of fine control so
+
+ align:start position:0%
+greater in muscles of fine control so
+ 
+
+ align:start position:0%
+greater in muscles of fine control so
+you have many more spindles in the
+
+ align:start position:0%
+you have many more spindles in the
+ 
+
+ align:start position:0%
+you have many more spindles in the
+muscles of your fingers
+
+ align:start position:0%
+muscles of your fingers
+ 
+
+ align:start position:0%
+muscles of your fingers
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and your tongue
+
+ align:start position:0%
+and your tongue
+ 
+
+ align:start position:0%
+and your tongue
+than you have in
+
+ align:start position:0%
+than you have in
+ 
+
+ align:start position:0%
+than you have in
+the large muscles of your arm or
+
+ align:start position:0%
+the large muscles of your arm or
+ 
+
+ align:start position:0%
+the large muscles of your arm or
+certainly and you wouldn't have so many
+
+ align:start position:0%
+certainly and you wouldn't have so many
+ 
+
+ align:start position:0%
+certainly and you wouldn't have so many
+of the muscles in the back
+
+ align:start position:0%
+of the muscles in the back
+ 
+
+ align:start position:0%
+of the muscles in the back
+so it's mostly distal muscles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's talk a little bit about
+
+ align:start position:0%
+so let's talk a little bit about
+ 
+
+ align:start position:0%
+so let's talk a little bit about
+now spinal cord organization
+
+ align:start position:0%
+now spinal cord organization
+ 
+
+ align:start position:0%
+now spinal cord organization
+remember the name
+
+ align:start position:0%
+remember the name
+ 
+
+ align:start position:0%
+remember the name
+that we give
+
+ align:start position:0%
+that we give
+ 
+
+ align:start position:0%
+that we give
+connections that are formed
+
+ align:start position:0%
+connections that are formed
+ 
+
+ align:start position:0%
+connections that are formed
+within the chord
+
+ align:start position:0%
+within the chord
+ 
+
+ align:start position:0%
+within the chord
+from one part of the chord to another
+
+ align:start position:0%
+from one part of the chord to another
+ 
+
+ align:start position:0%
+from one part of the chord to another
+part of the chord so what we're talking
+
+ align:start position:0%
+part of the chord so what we're talking
+ 
+
+ align:start position:0%
+part of the chord so what we're talking
+about is the function of these
+
+ align:start position:0%
+about is the function of these
+ 
+
+ align:start position:0%
+about is the function of these
+appropriate spinal connections
+
+ align:start position:0%
+appropriate spinal connections
+ 
+
+ align:start position:0%
+appropriate spinal connections
+first of
+
+ align:start position:0%
+first of
+ 
+
+ align:start position:0%
+first of
+all we have action patterns that are
+
+ align:start position:0%
+all we have action patterns that are
+ 
+
+ align:start position:0%
+all we have action patterns that are
+inherited
+
+ align:start position:0%
+inherited
+ 
+
+ align:start position:0%
+inherited
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+formed by connections made all within
+
+ align:start position:0%
+formed by connections made all within
+ 
+
+ align:start position:0%
+formed by connections made all within
+the cord
+
+ align:start position:0%
+the cord
+ 
+
+ align:start position:0%
+the cord
+that when they mature we have these
+
+ align:start position:0%
+that when they mature we have these
+ 
+
+ align:start position:0%
+that when they mature we have these
+these abilities now what what kind of
+
+ align:start position:0%
+these abilities now what what kind of
+ 
+
+ align:start position:0%
+these abilities now what what kind of
+what kind of patterns am i talking about
+
+ align:start position:0%
+what kind of patterns am i talking about
+ 
+
+ align:start position:0%
+what kind of patterns am i talking about
+other than
+
+ align:start position:0%
+other than
+ 
+
+ align:start position:0%
+other than
+other than withdrawal and stretch
+
+ align:start position:0%
+other than withdrawal and stretch
+ 
+
+ align:start position:0%
+other than withdrawal and stretch
+reflexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+it's been studied by physiologists who
+
+ align:start position:0%
+it's been studied by physiologists who
+ 
+
+ align:start position:0%
+it's been studied by physiologists who
+separate the brain from the spinal cord
+
+ align:start position:0%
+separate the brain from the spinal cord
+ 
+
+ align:start position:0%
+separate the brain from the spinal cord
+and then they maintain it's usually done
+
+ align:start position:0%
+and then they maintain it's usually done
+ 
+
+ align:start position:0%
+and then they maintain it's usually done
+with cats and they maintain them in a
+
+ align:start position:0%
+with cats and they maintain them in a
+ 
+
+ align:start position:0%
+with cats and they maintain them in a
+respirator so they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they keep oxygenating the blood
+
+ align:start position:0%
+they keep oxygenating the blood
+ 
+
+ align:start position:0%
+they keep oxygenating the blood
+and they find that they have alternate
+
+ align:start position:0%
+and they find that they have alternate
+ 
+
+ align:start position:0%
+and they find that they have alternate
+movements of the limbs walking movements
+
+ align:start position:0%
+movements of the limbs walking movements
+ 
+
+ align:start position:0%
+movements of the limbs walking movements
+they find out that they have certain
+
+ align:start position:0%
+they find out that they have certain
+ 
+
+ align:start position:0%
+they find out that they have certain
+reef patterns they call them reflex
+
+ align:start position:0%
+reef patterns they call them reflex
+ 
+
+ align:start position:0%
+reef patterns they call them reflex
+patterns but if one leg hind leg is
+
+ align:start position:0%
+patterns but if one leg hind leg is
+ 
+
+ align:start position:0%
+patterns but if one leg hind leg is
+flexed and the other extended you will
+
+ align:start position:0%
+flexed and the other extended you will
+ 
+
+ align:start position:0%
+flexed and the other extended you will
+get this a similar pattern
+
+ align:start position:0%
+get this a similar pattern
+ 
+
+ align:start position:0%
+get this a similar pattern
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+as if they were walking in the upper
+
+ align:start position:0%
+as if they were walking in the upper
+ 
+
+ align:start position:0%
+as if they were walking in the upper
+limbs okay
+
+ align:start position:0%
+limbs okay
+ 
+
+ align:start position:0%
+limbs okay
+all the basic movements of walking are
+
+ align:start position:0%
+all the basic movements of walking are
+ 
+
+ align:start position:0%
+all the basic movements of walking are
+there and if you
+
+ align:start position:0%
+there and if you
+ 
+
+ align:start position:0%
+there and if you
+put the cap
+
+ align:start position:0%
+put the cap
+ 
+
+ align:start position:0%
+put the cap
+put his hind lips on a treadmill
+
+ align:start position:0%
+put his hind lips on a treadmill
+ 
+
+ align:start position:0%
+put his hind lips on a treadmill
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and you activate the cord a little bit
+
+ align:start position:0%
+and you activate the cord a little bit
+ 
+
+ align:start position:0%
+and you activate the cord a little bit
+by stimulating the animal
+
+ align:start position:0%
+by stimulating the animal
+ 
+
+ align:start position:0%
+by stimulating the animal
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that might be by a descending
+
+ align:start position:0%
+and that might be by a descending
+ 
+
+ align:start position:0%
+and that might be by a descending
+connection that you've spared but there
+
+ align:start position:0%
+connection that you've spared but there
+ 
+
+ align:start position:0%
+connection that you've spared but there
+are other ways to provide input you can
+
+ align:start position:0%
+are other ways to provide input you can
+ 
+
+ align:start position:0%
+are other ways to provide input you can
+stimulate the animal around the anus for
+
+ align:start position:0%
+stimulate the animal around the anus for
+ 
+
+ align:start position:0%
+stimulate the animal around the anus for
+example and it will activate the cord
+
+ align:start position:0%
+example and it will activate the cord
+ 
+
+ align:start position:0%
+example and it will activate the cord
+enough that he will start stepping
+
+ align:start position:0%
+enough that he will start stepping
+ 
+
+ align:start position:0%
+enough that he will start stepping
+and he will walk on the treadmill even
+
+ align:start position:0%
+and he will walk on the treadmill even
+ 
+
+ align:start position:0%
+and he will walk on the treadmill even
+though he's got no connection with the
+
+ align:start position:0%
+though he's got no connection with the
+ 
+
+ align:start position:0%
+though he's got no connection with the
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+so it's got to be spinal the whole thing
+
+ align:start position:0%
+so it's got to be spinal the whole thing
+ 
+
+ align:start position:0%
+so it's got to be spinal the whole thing
+has to be organized in the spinal cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the scratch reflex is another spinal
+
+ align:start position:0%
+the scratch reflex is another spinal
+ 
+
+ align:start position:0%
+the scratch reflex is another spinal
+reflex we call it that is actually a
+
+ align:start position:0%
+reflex we call it that is actually a
+ 
+
+ align:start position:0%
+reflex we call it that is actually a
+fixed action pattern if we put a
+
+ align:start position:0%
+fixed action pattern if we put a
+ 
+
+ align:start position:0%
+fixed action pattern if we put a
+stimulus say on the back of the cat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he will raise a hind limb in order to
+
+ align:start position:0%
+he will raise a hind limb in order to
+ 
+
+ align:start position:0%
+he will raise a hind limb in order to
+scratch it
+
+ align:start position:0%
+scratch it
+ 
+
+ align:start position:0%
+scratch it
+he will actually scratch and he will
+
+ align:start position:0%
+he will actually scratch and he will
+ 
+
+ align:start position:0%
+he will actually scratch and he will
+show the rhythmic movements of the
+
+ align:start position:0%
+show the rhythmic movements of the
+ 
+
+ align:start position:0%
+show the rhythmic movements of the
+scratching those rhythmic movements and
+
+ align:start position:0%
+scratching those rhythmic movements and
+ 
+
+ align:start position:0%
+scratching those rhythmic movements and
+the positioning of the limb are all
+
+ align:start position:0%
+the positioning of the limb are all
+ 
+
+ align:start position:0%
+the positioning of the limb are all
+controlled by
+
+ align:start position:0%
+controlled by
+ 
+
+ align:start position:0%
+controlled by
+spinal mechanisms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's talk about
+
+ align:start position:0%
+now let's talk about
+ 
+
+ align:start position:0%
+now let's talk about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+spinal modulus of limb movement control
+
+ align:start position:0%
+spinal modulus of limb movement control
+ 
+
+ align:start position:0%
+spinal modulus of limb movement control
+this has to do with how the descending
+
+ align:start position:0%
+this has to do with how the descending
+ 
+
+ align:start position:0%
+this has to do with how the descending
+connections
+
+ align:start position:0%
+connections
+ 
+
+ align:start position:0%
+connections
+control the position of limbs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the bc lab a few years ago
+
+ align:start position:0%
+in the bc lab a few years ago
+ 
+
+ align:start position:0%
+in the bc lab a few years ago
+they used
+
+ align:start position:0%
+they used
+ 
+
+ align:start position:0%
+they used
+at that time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frogs
+
+ align:start position:0%
+frogs
+ 
+
+ align:start position:0%
+frogs
+all the initial work was done with frogs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they wanted an animal who had a large
+
+ align:start position:0%
+they wanted an animal who had a large
+ 
+
+ align:start position:0%
+they wanted an animal who had a large
+enough cord but also made very simple
+
+ align:start position:0%
+enough cord but also made very simple
+ 
+
+ align:start position:0%
+enough cord but also made very simple
+movements the limbs
+
+ align:start position:0%
+movements the limbs
+ 
+
+ align:start position:0%
+movements the limbs
+it was easy to work with in the
+
+ align:start position:0%
+it was easy to work with in the
+ 
+
+ align:start position:0%
+it was easy to work with in the
+laboratory so they used large bullfrogs
+
+ align:start position:0%
+laboratory so they used large bullfrogs
+ 
+
+ align:start position:0%
+laboratory so they used large bullfrogs
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and later they verified the work with
+
+ align:start position:0%
+and later they verified the work with
+ 
+
+ align:start position:0%
+and later they verified the work with
+rats large ads
+
+ align:start position:0%
+rats large ads
+ 
+
+ align:start position:0%
+rats large ads
+and i asked you to read a paper on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically what they found
+
+ align:start position:0%
+basically what they found
+ 
+
+ align:start position:0%
+basically what they found
+they used this kind of setup okay
+
+ align:start position:0%
+they used this kind of setup okay
+ 
+
+ align:start position:0%
+they used this kind of setup okay
+they had a frog that they had
+
+ align:start position:0%
+they had a frog that they had
+ 
+
+ align:start position:0%
+they had a frog that they had
+clamped in position
+
+ align:start position:0%
+clamped in position
+ 
+
+ align:start position:0%
+clamped in position
+and they put
+
+ align:start position:0%
+and they put
+ 
+
+ align:start position:0%
+and they put
+very tiny electrodes into the spinal
+
+ align:start position:0%
+very tiny electrodes into the spinal
+ 
+
+ align:start position:0%
+very tiny electrodes into the spinal
+cord
+
+ align:start position:0%
+cord
+ 
+
+ align:start position:0%
+cord
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they had one limb hooked up to a force
+
+ align:start position:0%
+they had one limb hooked up to a force
+ 
+
+ align:start position:0%
+they had one limb hooked up to a force
+transducer and they could also measure
+
+ align:start position:0%
+transducer and they could also measure
+ 
+
+ align:start position:0%
+transducer and they could also measure
+tension in the muscles with
+
+ align:start position:0%
+tension in the muscles with
+ 
+
+ align:start position:0%
+tension in the muscles with
+electromyograms
+
+ align:start position:0%
+electromyograms
+ 
+
+ align:start position:0%
+electromyograms
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you see the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the limb
+
+ align:start position:0%
+the limb
+ 
+
+ align:start position:0%
+the limb
+in one position
+
+ align:start position:0%
+in one position
+ 
+
+ align:start position:0%
+in one position
+and then they apply
+
+ align:start position:0%
+and then they apply
+ 
+
+ align:start position:0%
+and then they apply
+the spinal cord
+
+ align:start position:0%
+the spinal cord
+ 
+
+ align:start position:0%
+the spinal cord
+and what they found was when they
+
+ align:start position:0%
+and what they found was when they
+ 
+
+ align:start position:0%
+and what they found was when they
+stimulate certain part of the spinal
+
+ align:start position:0%
+stimulate certain part of the spinal
+ 
+
+ align:start position:0%
+stimulate certain part of the spinal
+cord with this tiny electrode the limb
+
+ align:start position:0%
+cord with this tiny electrode the limb
+ 
+
+ align:start position:0%
+cord with this tiny electrode the limb
+will try to move okay
+
+ align:start position:0%
+will try to move okay
+ 
+
+ align:start position:0%
+will try to move okay
+and what they're depicting in this kind
+
+ align:start position:0%
+and what they're depicting in this kind
+ 
+
+ align:start position:0%
+and what they're depicting in this kind
+of picture
+
+ align:start position:0%
+of picture
+ 
+
+ align:start position:0%
+of picture
+is that if they move
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the end of the limb here the
+
+ align:start position:0%
+the end of the limb here the
+ 
+
+ align:start position:0%
+the end of the limb here the
+foot
+
+ align:start position:0%
+foot
+ 
+
+ align:start position:0%
+foot
+into various starting positions and keep
+
+ align:start position:0%
+into various starting positions and keep
+ 
+
+ align:start position:0%
+into various starting positions and keep
+stimulating that same place
+
+ align:start position:0%
+stimulating that same place
+ 
+
+ align:start position:0%
+stimulating that same place
+the limb seems to always move towards
+
+ align:start position:0%
+the limb seems to always move towards
+ 
+
+ align:start position:0%
+the limb seems to always move towards
+a certain position we call that the
+
+ align:start position:0%
+a certain position we call that the
+ 
+
+ align:start position:0%
+a certain position we call that the
+equilibrium point and so if the limb
+
+ align:start position:0%
+equilibrium point and so if the limb
+ 
+
+ align:start position:0%
+equilibrium point and so if the limb
+starts out on that equilibrium point and
+
+ align:start position:0%
+starts out on that equilibrium point and
+ 
+
+ align:start position:0%
+starts out on that equilibrium point and
+you stimulate the cord it will stay
+
+ align:start position:0%
+you stimulate the cord it will stay
+ 
+
+ align:start position:0%
+you stimulate the cord it will stay
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it seems to move the limb towards one
+
+ align:start position:0%
+so it seems to move the limb towards one
+ 
+
+ align:start position:0%
+so it seems to move the limb towards one
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+and so they
+
+ align:start position:0%
+and so they
+ 
+
+ align:start position:0%
+and so they
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+created these kinds of pictures vector
+
+ align:start position:0%
+created these kinds of pictures vector
+ 
+
+ align:start position:0%
+created these kinds of pictures vector
+pictures
+
+ align:start position:0%
+pictures
+ 
+
+ align:start position:0%
+pictures
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+various points of stimulation within the
+
+ align:start position:0%
+various points of stimulation within the
+ 
+
+ align:start position:0%
+various points of stimulation within the
+chord and the interesting finding was
+
+ align:start position:0%
+chord and the interesting finding was
+ 
+
+ align:start position:0%
+chord and the interesting finding was
+that even though they stimulated many
+
+ align:start position:0%
+that even though they stimulated many
+ 
+
+ align:start position:0%
+that even though they stimulated many
+many different parts of the gray matter
+
+ align:start position:0%
+many different parts of the gray matter
+ 
+
+ align:start position:0%
+many different parts of the gray matter
+they found only a very limited number of
+
+ align:start position:0%
+they found only a very limited number of
+ 
+
+ align:start position:0%
+they found only a very limited number of
+positions
+
+ align:start position:0%
+positions
+ 
+
+ align:start position:0%
+positions
+in other words many neurons
+
+ align:start position:0%
+in other words many neurons
+ 
+
+ align:start position:0%
+in other words many neurons
+seem to all do the same thing and they
+
+ align:start position:0%
+seem to all do the same thing and they
+ 
+
+ align:start position:0%
+seem to all do the same thing and they
+found that these neurons were
+
+ align:start position:0%
+found that these neurons were
+ 
+
+ align:start position:0%
+found that these neurons were
+distributed in longitudinal columns
+
+ align:start position:0%
+distributed in longitudinal columns
+ 
+
+ align:start position:0%
+distributed in longitudinal columns
+within the core and there were a limited
+
+ align:start position:0%
+within the core and there were a limited
+ 
+
+ align:start position:0%
+within the core and there were a limited
+number of those columns representing
+
+ align:start position:0%
+number of those columns representing
+ 
+
+ align:start position:0%
+number of those columns representing
+a limb
+
+ align:start position:0%
+a limb
+ 
+
+ align:start position:0%
+a limb
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the conclusion was that it sort of
+
+ align:start position:0%
+the conclusion was that it sort of
+ 
+
+ align:start position:0%
+the conclusion was that it sort of
+constitutes a very elementary alphabet
+
+ align:start position:0%
+constitutes a very elementary alphabet
+ 
+
+ align:start position:0%
+constitutes a very elementary alphabet
+for producing complex movements now how
+
+ align:start position:0%
+for producing complex movements now how
+ 
+
+ align:start position:0%
+for producing complex movements now how
+would that be
+
+ align:start position:0%
+would that be
+ 
+
+ align:start position:0%
+would that be
+well they found that if you stimulate
+
+ align:start position:0%
+well they found that if you stimulate
+ 
+
+ align:start position:0%
+well they found that if you stimulate
+more than one
+
+ align:start position:0%
+more than one
+ 
+
+ align:start position:0%
+more than one
+of those columns you sort of get a
+
+ align:start position:0%
+of those columns you sort of get a
+ 
+
+ align:start position:0%
+of those columns you sort of get a
+vector sum
+
+ align:start position:0%
+vector sum
+ 
+
+ align:start position:0%
+vector sum
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the result of the stimulations done
+
+ align:start position:0%
+the result of the stimulations done
+ 
+
+ align:start position:0%
+the result of the stimulations done
+separately so with the limited number of
+
+ align:start position:0%
+separately so with the limited number of
+ 
+
+ align:start position:0%
+separately so with the limited number of
+columns like that you could get
+
+ align:start position:0%
+columns like that you could get
+ 
+
+ align:start position:0%
+columns like that you could get
+many different kinds of movement
+
+ align:start position:0%
+many different kinds of movement
+ 
+
+ align:start position:0%
+many different kinds of movement
+and move the limb into various positions
+
+ align:start position:0%
+and move the limb into various positions
+ 
+
+ align:start position:0%
+and move the limb into various positions
+now they don't know just they know
+
+ align:start position:0%
+now they don't know just they know
+ 
+
+ align:start position:0%
+now they don't know just they know
+there's not very many
+
+ align:start position:0%
+there's not very many
+ 
+
+ align:start position:0%
+there's not very many
+there's probably more in the rat
+
+ align:start position:0%
+there's probably more in the rat
+ 
+
+ align:start position:0%
+there's probably more in the rat
+and of course they were dealing with
+
+ align:start position:0%
+and of course they were dealing with
+ 
+
+ align:start position:0%
+and of course they were dealing with
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+only one plane of movement so they've
+
+ align:start position:0%
+only one plane of movement so they've
+ 
+
+ align:start position:0%
+only one plane of movement so they've
+simplified the situation quite a bit
+
+ align:start position:0%
+simplified the situation quite a bit
+ 
+
+ align:start position:0%
+simplified the situation quite a bit
+but it's a very basic discovery on how
+
+ align:start position:0%
+but it's a very basic discovery on how
+ 
+
+ align:start position:0%
+but it's a very basic discovery on how
+about spinal organization that
+
+ align:start position:0%
+about spinal organization that
+ 
+
+ align:start position:0%
+about spinal organization that
+simplified the problem of how
+
+ align:start position:0%
+simplified the problem of how
+ 
+
+ align:start position:0%
+simplified the problem of how
+descending connections are controlling
+
+ align:start position:0%
+descending connections are controlling
+ 
+
+ align:start position:0%
+descending connections are controlling
+movement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's just
+
+ align:start position:0%
+now let's just
+ 
+
+ align:start position:0%
+now let's just
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+a little bit above the
+
+ align:start position:0%
+a little bit above the
+ 
+
+ align:start position:0%
+a little bit above the
+spinal cord the rostral extension of the
+
+ align:start position:0%
+spinal cord the rostral extension of the
+ 
+
+ align:start position:0%
+spinal cord the rostral extension of the
+cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in latin
+
+ align:start position:0%
+in latin
+ 
+
+ align:start position:0%
+in latin
+the spinal cord is the medulla
+
+ align:start position:0%
+the spinal cord is the medulla
+ 
+
+ align:start position:0%
+the spinal cord is the medulla
+spinalis
+
+ align:start position:0%
+spinalis
+ 
+
+ align:start position:0%
+spinalis
+the spinal marrow
+
+ align:start position:0%
+the spinal marrow
+ 
+
+ align:start position:0%
+the spinal marrow
+the marrow of the spine okay
+
+ align:start position:0%
+the marrow of the spine okay
+ 
+
+ align:start position:0%
+the marrow of the spine okay
+and the oblongation the ex forward
+
+ align:start position:0%
+and the oblongation the ex forward
+ 
+
+ align:start position:0%
+and the oblongation the ex forward
+extension of that is the medulla
+
+ align:start position:0%
+extension of that is the medulla
+ 
+
+ align:start position:0%
+extension of that is the medulla
+oblongata okay so that's the
+
+ align:start position:0%
+oblongata okay so that's the
+ 
+
+ align:start position:0%
+oblongata okay so that's the
+caudal part of the hindbrain
+
+ align:start position:0%
+caudal part of the hindbrain
+ 
+
+ align:start position:0%
+caudal part of the hindbrain
+and when reflexes involve the
+
+ align:start position:0%
+and when reflexes involve the
+ 
+
+ align:start position:0%
+and when reflexes involve the
+medulla oblongata we call them
+
+ align:start position:0%
+medulla oblongata we call them
+ 
+
+ align:start position:0%
+medulla oblongata we call them
+suprasegmental because they're above the
+
+ align:start position:0%
+suprasegmental because they're above the
+ 
+
+ align:start position:0%
+suprasegmental because they're above the
+segment so that they involve connections
+
+ align:start position:0%
+segment so that they involve connections
+ 
+
+ align:start position:0%
+segment so that they involve connections
+above the segments of the cord
+
+ align:start position:0%
+above the segments of the cord
+ 
+
+ align:start position:0%
+above the segments of the cord
+where we have various
+
+ align:start position:0%
+where we have various
+ 
+
+ align:start position:0%
+where we have various
+reflexes controlled autonomic system
+
+ align:start position:0%
+reflexes controlled autonomic system
+ 
+
+ align:start position:0%
+reflexes controlled autonomic system
+reflexes for example controlling blood
+
+ align:start position:0%
+reflexes for example controlling blood
+ 
+
+ align:start position:0%
+reflexes for example controlling blood
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+you say well what reflex controls blood
+
+ align:start position:0%
+you say well what reflex controls blood
+ 
+
+ align:start position:0%
+you say well what reflex controls blood
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+well you have sensory
+
+ align:start position:0%
+well you have sensory
+ 
+
+ align:start position:0%
+well you have sensory
+axons innervating
+
+ align:start position:0%
+axons innervating
+ 
+
+ align:start position:0%
+axons innervating
+special little organs
+
+ align:start position:0%
+special little organs
+ 
+
+ align:start position:0%
+special little organs
+around the branches of the aorta that
+
+ align:start position:0%
+around the branches of the aorta that
+ 
+
+ align:start position:0%
+around the branches of the aorta that
+detect carbon dioxide concentration in
+
+ align:start position:0%
+detect carbon dioxide concentration in
+ 
+
+ align:start position:0%
+detect carbon dioxide concentration in
+the blood so if carbon dioxide goes up
+
+ align:start position:0%
+the blood so if carbon dioxide goes up
+ 
+
+ align:start position:0%
+the blood so if carbon dioxide goes up
+you want to increase hard action
+
+ align:start position:0%
+you want to increase hard action
+ 
+
+ align:start position:0%
+you want to increase hard action
+to get more oxygen
+
+ align:start position:0%
+to get more oxygen
+ 
+
+ align:start position:0%
+to get more oxygen
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's the glomerus reflex and that's
+
+ align:start position:0%
+that's the glomerus reflex and that's
+ 
+
+ align:start position:0%
+that's the glomerus reflex and that's
+behind brain reflex
+
+ align:start position:0%
+behind brain reflex
+ 
+
+ align:start position:0%
+behind brain reflex
+and other factor other types of reflexes
+
+ align:start position:0%
+and other factor other types of reflexes
+ 
+
+ align:start position:0%
+and other factor other types of reflexes
+that regulate heartbeat okay
+
+ align:start position:0%
+that regulate heartbeat okay
+ 
+
+ align:start position:0%
+that regulate heartbeat okay
+the heart will beat on its own without
+
+ align:start position:0%
+the heart will beat on its own without
+ 
+
+ align:start position:0%
+the heart will beat on its own without
+that but these hind brain reflexes are
+
+ align:start position:0%
+that but these hind brain reflexes are
+ 
+
+ align:start position:0%
+that but these hind brain reflexes are
+modulating it speeding it up or slowing
+
+ align:start position:0%
+modulating it speeding it up or slowing
+ 
+
+ align:start position:0%
+modulating it speeding it up or slowing
+it down and then we have various
+
+ align:start position:0%
+it down and then we have various
+ 
+
+ align:start position:0%
+it down and then we have various
+protective reflexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the gag reflex well that's
+
+ align:start position:0%
+the gag reflex well that's
+ 
+
+ align:start position:0%
+the gag reflex well that's
+has to do with swallowing right
+
+ align:start position:0%
+has to do with swallowing right
+ 
+
+ align:start position:0%
+has to do with swallowing right
+i think we triggered that once a few of
+
+ align:start position:0%
+i think we triggered that once a few of
+ 
+
+ align:start position:0%
+i think we triggered that once a few of
+you brave souls did you stuck your hand
+
+ align:start position:0%
+you brave souls did you stuck your hand
+ 
+
+ align:start position:0%
+you brave souls did you stuck your hand
+beyond the circumvent papillion rear of
+
+ align:start position:0%
+beyond the circumvent papillion rear of
+ 
+
+ align:start position:0%
+beyond the circumvent papillion rear of
+your tongue to trigger that reflex gag
+
+ align:start position:0%
+your tongue to trigger that reflex gag
+ 
+
+ align:start position:0%
+your tongue to trigger that reflex gag
+reflex
+
+ align:start position:0%
+reflex
+ 
+
+ align:start position:0%
+reflex
+vomiting is another reflex what normally
+
+ align:start position:0%
+vomiting is another reflex what normally
+ 
+
+ align:start position:0%
+vomiting is another reflex what normally
+triggers vomiting
+
+ align:start position:0%
+triggers vomiting
+ 
+
+ align:start position:0%
+triggers vomiting
+why is it why is it a reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+certain toxins
+
+ align:start position:0%
+certain toxins
+ 
+
+ align:start position:0%
+certain toxins
+bad things get into your blood
+
+ align:start position:0%
+bad things get into your blood
+ 
+
+ align:start position:0%
+bad things get into your blood
+from something you've eaten
+
+ align:start position:0%
+from something you've eaten
+ 
+
+ align:start position:0%
+from something you've eaten
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and it gets into the hindbrain
+
+ align:start position:0%
+and it gets into the hindbrain
+ 
+
+ align:start position:0%
+and it gets into the hindbrain
+to a place in the hindbrain where unlike
+
+ align:start position:0%
+to a place in the hindbrain where unlike
+ 
+
+ align:start position:0%
+to a place in the hindbrain where unlike
+most areas in the brain things from the
+
+ align:start position:0%
+most areas in the brain things from the
+ 
+
+ align:start position:0%
+most areas in the brain things from the
+blood can get in
+
+ align:start position:0%
+blood can get in
+ 
+
+ align:start position:0%
+blood can get in
+right around the area pustrima
+
+ align:start position:0%
+right around the area pustrima
+ 
+
+ align:start position:0%
+right around the area pustrima
+near the obex okay
+
+ align:start position:0%
+near the obex okay
+ 
+
+ align:start position:0%
+near the obex okay
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+caudal end of the
+
+ align:start position:0%
+caudal end of the
+ 
+
+ align:start position:0%
+caudal end of the
+fourth ventricle
+
+ align:start position:0%
+fourth ventricle
+ 
+
+ align:start position:0%
+fourth ventricle
+and you trigger
+
+ align:start position:0%
+and you trigger
+ 
+
+ align:start position:0%
+and you trigger
+that response the vomiting very
+
+ align:start position:0%
+that response the vomiting very
+ 
+
+ align:start position:0%
+that response the vomiting very
+important for
+
+ align:start position:0%
+important for
+ 
+
+ align:start position:0%
+important for
+keeping us alive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reflexes and other mechanisms
+
+ align:start position:0%
+reflexes and other mechanisms
+ 
+
+ align:start position:0%
+reflexes and other mechanisms
+controlling breathing
+
+ align:start position:0%
+controlling breathing
+ 
+
+ align:start position:0%
+controlling breathing
+are also mainly hind brain though they
+
+ align:start position:0%
+are also mainly hind brain though they
+ 
+
+ align:start position:0%
+are also mainly hind brain though they
+involve the caudal midbrain also
+
+ align:start position:0%
+involve the caudal midbrain also
+ 
+
+ align:start position:0%
+involve the caudal midbrain also
+okay and i will talk a little bit about
+
+ align:start position:0%
+okay and i will talk a little bit about
+ 
+
+ align:start position:0%
+okay and i will talk a little bit about
+breathing control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+after just after the midterm when we
+
+ align:start position:0%
+after just after the midterm when we
+ 
+
+ align:start position:0%
+after just after the midterm when we
+talk about rhythmic movements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you have other senses coming into
+
+ align:start position:0%
+now you have other senses coming into
+ 
+
+ align:start position:0%
+now you have other senses coming into
+the time brain too like vestibular sense
+
+ align:start position:0%
+the time brain too like vestibular sense
+ 
+
+ align:start position:0%
+the time brain too like vestibular sense
+auditory sense
+
+ align:start position:0%
+auditory sense
+ 
+
+ align:start position:0%
+auditory sense
+an example of reflexes controlled by
+
+ align:start position:0%
+an example of reflexes controlled by
+ 
+
+ align:start position:0%
+an example of reflexes controlled by
+vestibular sense would be
+
+ align:start position:0%
+vestibular sense would be
+ 
+
+ align:start position:0%
+vestibular sense would be
+the writing reflex
+
+ align:start position:0%
+the writing reflex
+ 
+
+ align:start position:0%
+the writing reflex
+which gets more than just is triggered
+
+ align:start position:0%
+which gets more than just is triggered
+ 
+
+ align:start position:0%
+which gets more than just is triggered
+not only by vestibular input but
+
+ align:start position:0%
+not only by vestibular input but
+ 
+
+ align:start position:0%
+not only by vestibular input but
+semi-sensory input as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that's the reflex where if we get
+
+ align:start position:0%
+but that's the reflex where if we get
+ 
+
+ align:start position:0%
+but that's the reflex where if we get
+knocked over we
+
+ align:start position:0%
+knocked over we
+ 
+
+ align:start position:0%
+knocked over we
+tend to ride ourselves it's
+
+ align:start position:0%
+tend to ride ourselves it's
+ 
+
+ align:start position:0%
+tend to ride ourselves it's
+very obvious in an animal like a cat
+
+ align:start position:0%
+very obvious in an animal like a cat
+ 
+
+ align:start position:0%
+very obvious in an animal like a cat
+which will tend to ride itself even in
+
+ align:start position:0%
+which will tend to ride itself even in
+ 
+
+ align:start position:0%
+which will tend to ride itself even in
+the air okay
+
+ align:start position:0%
+the air okay
+ 
+
+ align:start position:0%
+the air okay
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you any animal if you knock him over
+
+ align:start position:0%
+if you any animal if you knock him over
+ 
+
+ align:start position:0%
+if you any animal if you knock him over
+will tend to write himself with a
+
+ align:start position:0%
+will tend to write himself with a
+ 
+
+ align:start position:0%
+will tend to write himself with a
+combination of vestibular and some
+
+ align:start position:0%
+combination of vestibular and some
+ 
+
+ align:start position:0%
+combination of vestibular and some
+sensory reflexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then finally
+
+ align:start position:0%
+and then finally
+ 
+
+ align:start position:0%
+and then finally
+subject of your paper many fixed action
+
+ align:start position:0%
+subject of your paper many fixed action
+ 
+
+ align:start position:0%
+subject of your paper many fixed action
+patterns
+
+ align:start position:0%
+patterns
+ 
+
+ align:start position:0%
+patterns
+controlled by hindbrain
+
+ align:start position:0%
+controlled by hindbrain
+ 
+
+ align:start position:0%
+controlled by hindbrain
+at the very simplest level the eye blink
+
+ align:start position:0%
+at the very simplest level the eye blink
+ 
+
+ align:start position:0%
+at the very simplest level the eye blink
+which is more than just a reflex because
+
+ align:start position:0%
+which is more than just a reflex because
+ 
+
+ align:start position:0%
+which is more than just a reflex because
+there's a drive that builds up makes us
+
+ align:start position:0%
+there's a drive that builds up makes us
+ 
+
+ align:start position:0%
+there's a drive that builds up makes us
+want to blink
+
+ align:start position:0%
+want to blink
+ 
+
+ align:start position:0%
+want to blink
+but it's very simple in its connections
+
+ align:start position:0%
+but it's very simple in its connections
+ 
+
+ align:start position:0%
+but it's very simple in its connections
+the swallowing reflex is also really a
+
+ align:start position:0%
+the swallowing reflex is also really a
+ 
+
+ align:start position:0%
+the swallowing reflex is also really a
+fixed action pattern which also has a
+
+ align:start position:0%
+fixed action pattern which also has a
+ 
+
+ align:start position:0%
+fixed action pattern which also has a
+motivational component which builds up
+
+ align:start position:0%
+motivational component which builds up
+ 
+
+ align:start position:0%
+motivational component which builds up
+and involves
+
+ align:start position:0%
+and involves
+ 
+
+ align:start position:0%
+and involves
+over 20 different muscles
+
+ align:start position:0%
+over 20 different muscles
+ 
+
+ align:start position:0%
+over 20 different muscles
+mostly controlled by
+
+ align:start position:0%
+mostly controlled by
+ 
+
+ align:start position:0%
+mostly controlled by
+various levels behind brain and upper
+
+ align:start position:0%
+various levels behind brain and upper
+ 
+
+ align:start position:0%
+various levels behind brain and upper
+even the upper spinal cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+finally we have many fixed action
+
+ align:start position:0%
+finally we have many fixed action
+ 
+
+ align:start position:0%
+finally we have many fixed action
+patterns involving
+
+ align:start position:0%
+patterns involving
+ 
+
+ align:start position:0%
+patterns involving
+resulting in facial expression
+
+ align:start position:0%
+resulting in facial expression
+ 
+
+ align:start position:0%
+resulting in facial expression
+which also involve control of the tongue
+
+ align:start position:0%
+which also involve control of the tongue
+ 
+
+ align:start position:0%
+which also involve control of the tongue
+as well as
+
+ align:start position:0%
+as well as
+ 
+
+ align:start position:0%
+as well as
+the muscles of the around the lips and
+
+ align:start position:0%
+the muscles of the around the lips and
+ 
+
+ align:start position:0%
+the muscles of the around the lips and
+the whole face
+
+ align:start position:0%
+the whole face
+ 
+
+ align:start position:0%
+the whole face
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+controlled mesial mainly by the facial
+
+ align:start position:0%
+controlled mesial mainly by the facial
+ 
+
+ align:start position:0%
+controlled mesial mainly by the facial
+motor nucleus
+
+ align:start position:0%
+motor nucleus
+ 
+
+ align:start position:0%
+motor nucleus
+and nerve 7.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're not talking about the input side
+
+ align:start position:0%
+we're not talking about the input side
+ 
+
+ align:start position:0%
+we're not talking about the input side
+since many inputs from the limbic
+
+ align:start position:0%
+since many inputs from the limbic
+ 
+
+ align:start position:0%
+since many inputs from the limbic
+forebrain and visual system control
+
+ align:start position:0%
+forebrain and visual system control
+ 
+
+ align:start position:0%
+forebrain and visual system control
+facial expressions as well we're just
+
+ align:start position:0%
+facial expressions as well we're just
+ 
+
+ align:start position:0%
+facial expressions as well we're just
+talking about the fixed action pattern
+
+ align:start position:0%
+talking about the fixed action pattern
+ 
+
+ align:start position:0%
+talking about the fixed action pattern
+the output side
+
+ align:start position:0%
+the output side
+ 
+
+ align:start position:0%
+the output side
+which is through the hind brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's talk a little bit about
+
+ align:start position:0%
+okay let's talk a little bit about
+ 
+
+ align:start position:0%
+okay let's talk a little bit about
+plasticity and reflex connections
+
+ align:start position:0%
+plasticity and reflex connections
+ 
+
+ align:start position:0%
+plasticity and reflex connections
+first let me define
+
+ align:start position:0%
+first let me define
+ 
+
+ align:start position:0%
+first let me define
+post titanic potentiation we talked
+
+ align:start position:0%
+post titanic potentiation we talked
+ 
+
+ align:start position:0%
+post titanic potentiation we talked
+about monosynaptic reflexes
+
+ align:start position:0%
+about monosynaptic reflexes
+ 
+
+ align:start position:0%
+about monosynaptic reflexes
+you can enhance
+
+ align:start position:0%
+you can enhance
+ 
+
+ align:start position:0%
+you can enhance
+a monosynaptic reflex in the following
+
+ align:start position:0%
+a monosynaptic reflex in the following
+ 
+
+ align:start position:0%
+a monosynaptic reflex in the following
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+say you first
+
+ align:start position:0%
+say you first
+ 
+
+ align:start position:0%
+say you first
+give a test pulse
+
+ align:start position:0%
+give a test pulse
+ 
+
+ align:start position:0%
+give a test pulse
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the sensory fibers coming from a muscle
+
+ align:start position:0%
+the sensory fibers coming from a muscle
+ 
+
+ align:start position:0%
+the sensory fibers coming from a muscle
+okay and you will get a twitch of the
+
+ align:start position:0%
+okay and you will get a twitch of the
+ 
+
+ align:start position:0%
+okay and you will get a twitch of the
+muscle
+
+ align:start position:0%
+muscle
+ 
+
+ align:start position:0%
+muscle
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+through the monosynaptic reflex art
+
+ align:start position:0%
+through the monosynaptic reflex art
+ 
+
+ align:start position:0%
+through the monosynaptic reflex art
+we're stimulating input fibers okay so
+
+ align:start position:0%
+we're stimulating input fibers okay so
+ 
+
+ align:start position:0%
+we're stimulating input fibers okay so
+we give a pulse and we'll get a
+
+ align:start position:0%
+we give a pulse and we'll get a
+ 
+
+ align:start position:0%
+we give a pulse and we'll get a
+contraction the muscle okay now we
+
+ align:start position:0%
+contraction the muscle okay now we
+ 
+
+ align:start position:0%
+contraction the muscle okay now we
+stimulate with a tetanus a tetanus means
+
+ align:start position:0%
+stimulate with a tetanus a tetanus means
+ 
+
+ align:start position:0%
+stimulate with a tetanus a tetanus means
+rapid fire
+
+ align:start position:0%
+rapid fire
+ 
+
+ align:start position:0%
+rapid fire
+stimulation
+
+ align:start position:0%
+stimulation
+ 
+
+ align:start position:0%
+stimulation
+you know not just
+
+ align:start position:0%
+you know not just
+ 
+
+ align:start position:0%
+you know not just
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+dot but
+
+ align:start position:0%
+dot but
+ 
+
+ align:start position:0%
+dot but
+okay you stimulate rapidly that's a
+
+ align:start position:0%
+okay you stimulate rapidly that's a
+ 
+
+ align:start position:0%
+okay you stimulate rapidly that's a
+deadness again if you do that for a
+
+ align:start position:0%
+deadness again if you do that for a
+ 
+
+ align:start position:0%
+deadness again if you do that for a
+little while and now give another single
+
+ align:start position:0%
+little while and now give another single
+ 
+
+ align:start position:0%
+little while and now give another single
+pulse you'll find that you get a greater
+
+ align:start position:0%
+pulse you'll find that you get a greater
+ 
+
+ align:start position:0%
+pulse you'll find that you get a greater
+response than you did before because you
+
+ align:start position:0%
+response than you did before because you
+ 
+
+ align:start position:0%
+response than you did before because you
+have potentiated the monosynaptic reflex
+
+ align:start position:0%
+have potentiated the monosynaptic reflex
+ 
+
+ align:start position:0%
+have potentiated the monosynaptic reflex
+that's post titanic
+
+ align:start position:0%
+that's post titanic
+ 
+
+ align:start position:0%
+that's post titanic
+potentiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the much studied long-term
+
+ align:start position:0%
+and the much studied long-term
+ 
+
+ align:start position:0%
+and the much studied long-term
+potentiation here
+
+ align:start position:0%
+potentiation here
+ 
+
+ align:start position:0%
+potentiation here
+of neurons in the central nervous system
+
+ align:start position:0%
+of neurons in the central nervous system
+ 
+
+ align:start position:0%
+of neurons in the central nervous system
+are really a very similar thing
+
+ align:start position:0%
+are really a very similar thing
+ 
+
+ align:start position:0%
+are really a very similar thing
+but not in usually involving such rapid
+
+ align:start position:0%
+but not in usually involving such rapid
+ 
+
+ align:start position:0%
+but not in usually involving such rapid
+stimulation but a potentiation of a
+
+ align:start position:0%
+stimulation but a potentiation of a
+ 
+
+ align:start position:0%
+stimulation but a potentiation of a
+synaptic connection
+
+ align:start position:0%
+synaptic connection
+ 
+
+ align:start position:0%
+synaptic connection
+that lasts a long time is called
+
+ align:start position:0%
+that lasts a long time is called
+ 
+
+ align:start position:0%
+that lasts a long time is called
+long-term potentiation
+
+ align:start position:0%
+long-term potentiation
+ 
+
+ align:start position:0%
+long-term potentiation
+okay now you don't always get
+
+ align:start position:0%
+okay now you don't always get
+ 
+
+ align:start position:0%
+okay now you don't always get
+potentiation by stimulation
+
+ align:start position:0%
+potentiation by stimulation
+ 
+
+ align:start position:0%
+potentiation by stimulation
+okay it happens of course in
+
+ align:start position:0%
+okay it happens of course in
+ 
+
+ align:start position:0%
+okay it happens of course in
+conditioning procedures it happens in
+
+ align:start position:0%
+conditioning procedures it happens in
+ 
+
+ align:start position:0%
+conditioning procedures it happens in
+certain many pathways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you stimulate at the right rate
+
+ align:start position:0%
+if you stimulate at the right rate
+ 
+
+ align:start position:0%
+if you stimulate at the right rate
+you'll get potentiation but you often if
+
+ align:start position:0%
+you'll get potentiation but you often if
+ 
+
+ align:start position:0%
+you'll get potentiation but you often if
+you get repeated stimulation
+
+ align:start position:0%
+you get repeated stimulation
+ 
+
+ align:start position:0%
+you get repeated stimulation
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+less and less sensitive connections you
+
+ align:start position:0%
+less and less sensitive connections you
+ 
+
+ align:start position:0%
+less and less sensitive connections you
+get habituation
+
+ align:start position:0%
+get habituation
+ 
+
+ align:start position:0%
+get habituation
+so for example
+
+ align:start position:0%
+so for example
+ 
+
+ align:start position:0%
+so for example
+if we have a novel stimulus
+
+ align:start position:0%
+if we have a novel stimulus
+ 
+
+ align:start position:0%
+if we have a novel stimulus
+that causes you to turn your head okay
+
+ align:start position:0%
+that causes you to turn your head okay
+ 
+
+ align:start position:0%
+that causes you to turn your head okay
+you hear a sound that you weren't used
+
+ align:start position:0%
+you hear a sound that you weren't used
+ 
+
+ align:start position:0%
+you hear a sound that you weren't used
+to and you all turned to see what is
+
+ align:start position:0%
+to and you all turned to see what is
+ 
+
+ align:start position:0%
+to and you all turned to see what is
+that you know so you figured out what it
+
+ align:start position:0%
+that you know so you figured out what it
+ 
+
+ align:start position:0%
+that you know so you figured out what it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+and it elicited a response but what
+
+ align:start position:0%
+and it elicited a response but what
+ 
+
+ align:start position:0%
+and it elicited a response but what
+happens if it keeps up you habituate to
+
+ align:start position:0%
+happens if it keeps up you habituate to
+ 
+
+ align:start position:0%
+happens if it keeps up you habituate to
+it and pretty soon you're totally
+
+ align:start position:0%
+it and pretty soon you're totally
+ 
+
+ align:start position:0%
+it and pretty soon you're totally
+ignoring it you might not even even hear
+
+ align:start position:0%
+ignoring it you might not even even hear
+ 
+
+ align:start position:0%
+ignoring it you might not even even hear
+it anymore if it's an auditory stimulus
+
+ align:start position:0%
+it anymore if it's an auditory stimulus
+ 
+
+ align:start position:0%
+it anymore if it's an auditory stimulus
+and obviously we habituate to the
+
+ align:start position:0%
+and obviously we habituate to the
+ 
+
+ align:start position:0%
+and obviously we habituate to the
+clothes we're wearing we habituate too
+
+ align:start position:0%
+clothes we're wearing we habituate too
+ 
+
+ align:start position:0%
+clothes we're wearing we habituate too
+many stimuli that we just don't pay
+
+ align:start position:0%
+many stimuli that we just don't pay
+ 
+
+ align:start position:0%
+many stimuli that we just don't pay
+attention to anymore
+
+ align:start position:0%
+attention to anymore
+ 
+
+ align:start position:0%
+attention to anymore
+that's a decreased sensitivity well in
+
+ align:start position:0%
+that's a decreased sensitivity well in
+ 
+
+ align:start position:0%
+that's a decreased sensitivity well in
+physiology
+
+ align:start position:0%
+physiology
+ 
+
+ align:start position:0%
+physiology
+they discovered that some of those same
+
+ align:start position:0%
+they discovered that some of those same
+ 
+
+ align:start position:0%
+they discovered that some of those same
+connections that if stimulated at one
+
+ align:start position:0%
+connections that if stimulated at one
+ 
+
+ align:start position:0%
+connections that if stimulated at one
+rate you get potentiation you get
+
+ align:start position:0%
+rate you get potentiation you get
+ 
+
+ align:start position:0%
+rate you get potentiation you get
+long-term potentiation if you stimulate
+
+ align:start position:0%
+long-term potentiation if you stimulate
+ 
+
+ align:start position:0%
+long-term potentiation if you stimulate
+at a much slower rate
+
+ align:start position:0%
+at a much slower rate
+ 
+
+ align:start position:0%
+at a much slower rate
+you'll get reduced sensitivity so they
+
+ align:start position:0%
+you'll get reduced sensitivity so they
+ 
+
+ align:start position:0%
+you'll get reduced sensitivity so they
+call that
+
+ align:start position:0%
+call that
+ 
+
+ align:start position:0%
+call that
+low frequency depression
+
+ align:start position:0%
+low frequency depression
+ 
+
+ align:start position:0%
+low frequency depression
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+these are the physiological phenomena
+
+ align:start position:0%
+these are the physiological phenomena
+ 
+
+ align:start position:0%
+these are the physiological phenomena
+that correspond
+
+ align:start position:0%
+that correspond
+ 
+
+ align:start position:0%
+that correspond
+to the behavioral phenomenon of
+
+ align:start position:0%
+to the behavioral phenomenon of
+ 
+
+ align:start position:0%
+to the behavioral phenomenon of
+habituation or sensitization of reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if we just deal with a spinal cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can it learn anything
+
+ align:start position:0%
+can it learn anything
+ 
+
+ align:start position:0%
+can it learn anything
+can you get anything besides this post
+
+ align:start position:0%
+can you get anything besides this post
+ 
+
+ align:start position:0%
+can you get anything besides this post
+satanic potentiation
+
+ align:start position:0%
+satanic potentiation
+ 
+
+ align:start position:0%
+satanic potentiation
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me describe an experiment that
+
+ align:start position:0%
+so let me describe an experiment that
+ 
+
+ align:start position:0%
+so let me describe an experiment that
+was done that showed that the spinal
+
+ align:start position:0%
+was done that showed that the spinal
+ 
+
+ align:start position:0%
+was done that showed that the spinal
+cord is capable of some learning it was
+
+ align:start position:0%
+cord is capable of some learning it was
+ 
+
+ align:start position:0%
+cord is capable of some learning it was
+based
+
+ align:start position:0%
+based
+ 
+
+ align:start position:0%
+based
+on a simple experiment
+
+ align:start position:0%
+on a simple experiment
+ 
+
+ align:start position:0%
+on a simple experiment
+where they
+
+ align:start position:0%
+where they
+ 
+
+ align:start position:0%
+where they
+took a cockroach
+
+ align:start position:0%
+took a cockroach
+ 
+
+ align:start position:0%
+took a cockroach
+left him attached to the a ganglion
+
+ align:start position:0%
+left him attached to the a ganglion
+ 
+
+ align:start position:0%
+left him attached to the a ganglion
+that's the cockroach's leg and here's a
+
+ align:start position:0%
+that's the cockroach's leg and here's a
+ 
+
+ align:start position:0%
+that's the cockroach's leg and here's a
+beaker of water okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's the water
+
+ align:start position:0%
+and here's the water
+ 
+
+ align:start position:0%
+and here's the water
+and it's conductive we put some salt in
+
+ align:start position:0%
+and it's conductive we put some salt in
+ 
+
+ align:start position:0%
+and it's conductive we put some salt in
+it and it's conductive
+
+ align:start position:0%
+it and it's conductive
+ 
+
+ align:start position:0%
+it and it's conductive
+okay now we we hook that up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we hook it up to a stimulator here okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we put one probe there
+
+ align:start position:0%
+we put one probe there
+ 
+
+ align:start position:0%
+we put one probe there
+and the other probe will attach to the
+
+ align:start position:0%
+and the other probe will attach to the
+ 
+
+ align:start position:0%
+and the other probe will attach to the
+leg
+
+ align:start position:0%
+leg
+ 
+
+ align:start position:0%
+leg
+okay so what happens we've we've
+
+ align:start position:0%
+okay so what happens we've we've
+ 
+
+ align:start position:0%
+okay so what happens we've we've
+suspended the cockroach leg that way
+
+ align:start position:0%
+suspended the cockroach leg that way
+ 
+
+ align:start position:0%
+suspended the cockroach leg that way
+and you don't even need the cockroach
+
+ align:start position:0%
+and you don't even need the cockroach
+ 
+
+ align:start position:0%
+and you don't even need the cockroach
+there but you do need the ganglion that
+
+ align:start position:0%
+there but you do need the ganglion that
+ 
+
+ align:start position:0%
+there but you do need the ganglion that
+controls it
+
+ align:start position:0%
+controls it
+ 
+
+ align:start position:0%
+controls it
+so you can have part of the cockroach
+
+ align:start position:0%
+so you can have part of the cockroach
+ 
+
+ align:start position:0%
+so you can have part of the cockroach
+the leg in the ganglion okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what happens well the leg will extend
+
+ align:start position:0%
+so what happens well the leg will extend
+ 
+
+ align:start position:0%
+so what happens well the leg will extend
+it's not going to stay flexed all the
+
+ align:start position:0%
+it's not going to stay flexed all the
+ 
+
+ align:start position:0%
+it's not going to stay flexed all the
+time it will extend down into the water
+
+ align:start position:0%
+time it will extend down into the water
+ 
+
+ align:start position:0%
+time it will extend down into the water
+and as soon as it touches the water it
+
+ align:start position:0%
+and as soon as it touches the water it
+ 
+
+ align:start position:0%
+and as soon as it touches the water it
+gets a shock
+
+ align:start position:0%
+gets a shock
+ 
+
+ align:start position:0%
+gets a shock
+okay we have it hooked up to a
+
+ align:start position:0%
+okay we have it hooked up to a
+ 
+
+ align:start position:0%
+okay we have it hooked up to a
+stimulator
+
+ align:start position:0%
+stimulator
+ 
+
+ align:start position:0%
+stimulator
+okay so it closes the circuit
+
+ align:start position:0%
+okay so it closes the circuit
+ 
+
+ align:start position:0%
+okay so it closes the circuit
+shocks the leg and you get a withdrawal
+
+ align:start position:0%
+shocks the leg and you get a withdrawal
+ 
+
+ align:start position:0%
+shocks the leg and you get a withdrawal
+reflex
+
+ align:start position:0%
+reflex
+ 
+
+ align:start position:0%
+reflex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then the leg will extend again it
+
+ align:start position:0%
+and then the leg will extend again it
+ 
+
+ align:start position:0%
+and then the leg will extend again it
+will touch the water
+
+ align:start position:0%
+will touch the water
+ 
+
+ align:start position:0%
+will touch the water
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what will happen is that eventually
+
+ align:start position:0%
+well what will happen is that eventually
+ 
+
+ align:start position:0%
+well what will happen is that eventually
+the leg stays up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if you have another leg and you hook
+
+ align:start position:0%
+now if you have another leg and you hook
+ 
+
+ align:start position:0%
+now if you have another leg and you hook
+it up in series
+
+ align:start position:0%
+it up in series
+ 
+
+ align:start position:0%
+it up in series
+in that circuit
+
+ align:start position:0%
+in that circuit
+ 
+
+ align:start position:0%
+in that circuit
+but it's it's stimulated
+
+ align:start position:0%
+but it's it's stimulated
+ 
+
+ align:start position:0%
+but it's it's stimulated
+in a way that's uncorrelated with the
+
+ align:start position:0%
+in a way that's uncorrelated with the
+ 
+
+ align:start position:0%
+in a way that's uncorrelated with the
+position of the leg
+
+ align:start position:0%
+position of the leg
+ 
+
+ align:start position:0%
+position of the leg
+that leg doesn't learn to stay up
+
+ align:start position:0%
+that leg doesn't learn to stay up
+ 
+
+ align:start position:0%
+that leg doesn't learn to stay up
+it's only where you have this
+
+ align:start position:0%
+it's only where you have this
+ 
+
+ align:start position:0%
+it's only where you have this
+the position of the limb is related to
+
+ align:start position:0%
+the position of the limb is related to
+ 
+
+ align:start position:0%
+the position of the limb is related to
+when the stimulus occurs
+
+ align:start position:0%
+when the stimulus occurs
+ 
+
+ align:start position:0%
+when the stimulus occurs
+that you'll condition it so
+
+ align:start position:0%
+that you'll condition it so
+ 
+
+ align:start position:0%
+that you'll condition it so
+dr charlie gross former mit professor
+
+ align:start position:0%
+dr charlie gross former mit professor
+ 
+
+ align:start position:0%
+dr charlie gross former mit professor
+now it's been for many years now a
+
+ align:start position:0%
+now it's been for many years now a
+ 
+
+ align:start position:0%
+now it's been for many years now a
+professor in the department of
+
+ align:start position:0%
+professor in the department of
+ 
+
+ align:start position:0%
+professor in the department of
+psychology at princeton university
+
+ align:start position:0%
+psychology at princeton university
+ 
+
+ align:start position:0%
+psychology at princeton university
+with his students did
+
+ align:start position:0%
+with his students did
+ 
+
+ align:start position:0%
+with his students did
+a similar experiment on the rat
+
+ align:start position:0%
+a similar experiment on the rat
+ 
+
+ align:start position:0%
+a similar experiment on the rat
+now here they had the whole rat but they
+
+ align:start position:0%
+now here they had the whole rat but they
+ 
+
+ align:start position:0%
+now here they had the whole rat but they
+made him a spinal rat or at least for
+
+ align:start position:0%
+made him a spinal rat or at least for
+ 
+
+ align:start position:0%
+made him a spinal rat or at least for
+the hind limb by doing a mid-thoracic
+
+ align:start position:0%
+the hind limb by doing a mid-thoracic
+ 
+
+ align:start position:0%
+the hind limb by doing a mid-thoracic
+section of the cord okay
+
+ align:start position:0%
+section of the cord okay
+ 
+
+ align:start position:0%
+section of the cord okay
+so now instead of just the cockroach
+
+ align:start position:0%
+so now instead of just the cockroach
+ 
+
+ align:start position:0%
+so now instead of just the cockroach
+they had that was a rat leg
+
+ align:start position:0%
+they had that was a rat leg
+ 
+
+ align:start position:0%
+they had that was a rat leg
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but they hooked him up the same way they
+
+ align:start position:0%
+but they hooked him up the same way they
+ 
+
+ align:start position:0%
+but they hooked him up the same way they
+were inspired by the cockroach work
+
+ align:start position:0%
+were inspired by the cockroach work
+ 
+
+ align:start position:0%
+were inspired by the cockroach work
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and again they put another rat in series
+
+ align:start position:0%
+and again they put another rat in series
+ 
+
+ align:start position:0%
+and again they put another rat in series
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can imagine how they would do
+
+ align:start position:0%
+so you can imagine how they would do
+ 
+
+ align:start position:0%
+so you can imagine how they would do
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they put the other this this hook to
+
+ align:start position:0%
+they put the other this this hook to
+ 
+
+ align:start position:0%
+they put the other this this hook to
+another rad over here okay
+
+ align:start position:0%
+another rad over here okay
+ 
+
+ align:start position:0%
+another rad over here okay
+and there's the rat foot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now when the if this is the first rod
+
+ align:start position:0%
+so now when the if this is the first rod
+ 
+
+ align:start position:0%
+so now when the if this is the first rod
+over here whenever that rat extends its
+
+ align:start position:0%
+over here whenever that rat extends its
+ 
+
+ align:start position:0%
+over here whenever that rat extends its
+leg
+
+ align:start position:0%
+leg
+ 
+
+ align:start position:0%
+leg
+into the fluid okay both legs get
+
+ align:start position:0%
+into the fluid okay both legs get
+ 
+
+ align:start position:0%
+into the fluid okay both legs get
+stimulated
+
+ align:start position:0%
+stimulated
+ 
+
+ align:start position:0%
+stimulated
+but the leg on the left is only being
+
+ align:start position:0%
+but the leg on the left is only being
+ 
+
+ align:start position:0%
+but the leg on the left is only being
+stimulated when the leg is extending
+
+ align:start position:0%
+stimulated when the leg is extending
+ 
+
+ align:start position:0%
+stimulated when the leg is extending
+into the water the leg on the right is
+
+ align:start position:0%
+into the water the leg on the right is
+ 
+
+ align:start position:0%
+into the water the leg on the right is
+being stimulated at random
+
+ align:start position:0%
+being stimulated at random
+ 
+
+ align:start position:0%
+being stimulated at random
+because it's it's not moving and
+
+ align:start position:0%
+because it's it's not moving and
+ 
+
+ align:start position:0%
+because it's it's not moving and
+synchrony with the other rat it's a
+
+ align:start position:0%
+synchrony with the other rat it's a
+ 
+
+ align:start position:0%
+synchrony with the other rat it's a
+separate rat okay
+
+ align:start position:0%
+separate rat okay
+ 
+
+ align:start position:0%
+separate rat okay
+and what they discovered was the rat
+
+ align:start position:0%
+and what they discovered was the rat
+ 
+
+ align:start position:0%
+and what they discovered was the rat
+with the correlated stimulation gets
+
+ align:start position:0%
+with the correlated stimulation gets
+ 
+
+ align:start position:0%
+with the correlated stimulation gets
+conditioned
+
+ align:start position:0%
+conditioned
+ 
+
+ align:start position:0%
+conditioned
+and the other leg doesn't
+
+ align:start position:0%
+and the other leg doesn't
+ 
+
+ align:start position:0%
+and the other leg doesn't
+you might affect the responses a little
+
+ align:start position:0%
+you might affect the responses a little
+ 
+
+ align:start position:0%
+you might affect the responses a little
+bit of the one on the on the right there
+
+ align:start position:0%
+bit of the one on the on the right there
+ 
+
+ align:start position:0%
+bit of the one on the on the right there
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but you don't get the conditioning that
+
+ align:start position:0%
+but you don't get the conditioning that
+ 
+
+ align:start position:0%
+but you don't get the conditioning that
+you do on the left so they got they got
+
+ align:start position:0%
+you do on the left so they got they got
+ 
+
+ align:start position:0%
+you do on the left so they got they got
+some spinal conditioning retention
+
+ align:start position:0%
+some spinal conditioning retention
+ 
+
+ align:start position:0%
+some spinal conditioning retention
+of that learning was not for very long
+
+ align:start position:0%
+of that learning was not for very long
+ 
+
+ align:start position:0%
+of that learning was not for very long
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it was for many hours okay
+
+ align:start position:0%
+it was for many hours okay
+ 
+
+ align:start position:0%
+it was for many hours okay
+so they did get conditioning in the
+
+ align:start position:0%
+so they did get conditioning in the
+ 
+
+ align:start position:0%
+so they did get conditioning in the
+spinal cord so we know there's some
+
+ align:start position:0%
+spinal cord so we know there's some
+ 
+
+ align:start position:0%
+spinal cord so we know there's some
+simple learning even within the spinal
+
+ align:start position:0%
+simple learning even within the spinal
+ 
+
+ align:start position:0%
+simple learning even within the spinal
+cord
+
+ align:start position:0%
+cord
+ 
+
+ align:start position:0%
+cord
+there's been other experiments on
+
+ align:start position:0%
+there's been other experiments on
+ 
+
+ align:start position:0%
+there's been other experiments on
+spinal control and one favorite one that
+
+ align:start position:0%
+spinal control and one favorite one that
+ 
+
+ align:start position:0%
+spinal control and one favorite one that
+i like was done with crossing of nerves
+
+ align:start position:0%
+i like was done with crossing of nerves
+ 
+
+ align:start position:0%
+i like was done with crossing of nerves
+they took
+
+ align:start position:0%
+they took
+ 
+
+ align:start position:0%
+they took
+this is the last thing we'll talk about
+
+ align:start position:0%
+this is the last thing we'll talk about
+ 
+
+ align:start position:0%
+this is the last thing we'll talk about
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you take
+
+ align:start position:0%
+if you take
+ 
+
+ align:start position:0%
+if you take
+the nerves to the
+
+ align:start position:0%
+the nerves to the
+ 
+
+ align:start position:0%
+the nerves to the
+foot
+
+ align:start position:0%
+foot
+ 
+
+ align:start position:0%
+foot
+and you
+
+ align:start position:0%
+and you
+ 
+
+ align:start position:0%
+and you
+sever the extensors and the flexors
+
+ align:start position:0%
+sever the extensors and the flexors
+ 
+
+ align:start position:0%
+sever the extensors and the flexors
+cross them over and get them to
+
+ align:start position:0%
+cross them over and get them to
+ 
+
+ align:start position:0%
+cross them over and get them to
+regenerate to the wrong muscles so now
+
+ align:start position:0%
+regenerate to the wrong muscles so now
+ 
+
+ align:start position:0%
+regenerate to the wrong muscles so now
+the the nerve that would innervate
+
+ align:start position:0%
+the the nerve that would innervate
+ 
+
+ align:start position:0%
+the the nerve that would innervate
+flexors is now stimulating the extensors
+
+ align:start position:0%
+flexors is now stimulating the extensors
+ 
+
+ align:start position:0%
+flexors is now stimulating the extensors
+it regenerates into the extensor muscles
+
+ align:start position:0%
+it regenerates into the extensor muscles
+ 
+
+ align:start position:0%
+it regenerates into the extensor muscles
+okay so now when that when they
+
+ align:start position:0%
+okay so now when that when they
+ 
+
+ align:start position:0%
+okay so now when that when they
+regenerate if you've done that to a rat
+
+ align:start position:0%
+regenerate if you've done that to a rat
+ 
+
+ align:start position:0%
+regenerate if you've done that to a rat
+every time the rat wants to raise his
+
+ align:start position:0%
+every time the rat wants to raise his
+ 
+
+ align:start position:0%
+every time the rat wants to raise his
+foot he lowers it and when he wants to
+
+ align:start position:0%
+foot he lowers it and when he wants to
+ 
+
+ align:start position:0%
+foot he lowers it and when he wants to
+lower it he raises it
+
+ align:start position:0%
+lower it he raises it
+ 
+
+ align:start position:0%
+lower it he raises it
+and they've done that with monkeys and
+
+ align:start position:0%
+and they've done that with monkeys and
+ 
+
+ align:start position:0%
+and they've done that with monkeys and
+cats and rats
+
+ align:start position:0%
+cats and rats
+ 
+
+ align:start position:0%
+cats and rats
+now what happens
+
+ align:start position:0%
+now what happens
+ 
+
+ align:start position:0%
+now what happens
+over time of course all the feedback is
+
+ align:start position:0%
+over time of course all the feedback is
+ 
+
+ align:start position:0%
+over time of course all the feedback is
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+so do they learn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rats learn almost nothing
+
+ align:start position:0%
+rats learn almost nothing
+ 
+
+ align:start position:0%
+rats learn almost nothing
+they keep they maintain their
+
+ align:start position:0%
+they keep they maintain their
+ 
+
+ align:start position:0%
+they keep they maintain their
+uncoordinated movements because the
+
+ align:start position:0%
+uncoordinated movements because the
+ 
+
+ align:start position:0%
+uncoordinated movements because the
+spinal cord is not adapting to the
+
+ align:start position:0%
+spinal cord is not adapting to the
+ 
+
+ align:start position:0%
+spinal cord is not adapting to the
+abnormal feedback
+
+ align:start position:0%
+abnormal feedback
+ 
+
+ align:start position:0%
+abnormal feedback
+it's not learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in the monkey they found that over
+
+ align:start position:0%
+but in the monkey they found that over
+ 
+
+ align:start position:0%
+but in the monkey they found that over
+time the monkey learns to coordinate
+
+ align:start position:0%
+time the monkey learns to coordinate
+ 
+
+ align:start position:0%
+time the monkey learns to coordinate
+islam again
+
+ align:start position:0%
+islam again
+ 
+
+ align:start position:0%
+islam again
+okay does that mean the monkey spinal
+
+ align:start position:0%
+okay does that mean the monkey spinal
+ 
+
+ align:start position:0%
+okay does that mean the monkey spinal
+cord is more plastic than the rat spinal
+
+ align:start position:0%
+cord is more plastic than the rat spinal
+ 
+
+ align:start position:0%
+cord is more plastic than the rat spinal
+cord well not necessarily because these
+
+ align:start position:0%
+cord well not necessarily because these
+ 
+
+ align:start position:0%
+cord well not necessarily because these
+are not spinal animals
+
+ align:start position:0%
+are not spinal animals
+ 
+
+ align:start position:0%
+are not spinal animals
+so they tried then severing descending
+
+ align:start position:0%
+so they tried then severing descending
+ 
+
+ align:start position:0%
+so they tried then severing descending
+connections
+
+ align:start position:0%
+connections
+ 
+
+ align:start position:0%
+connections
+in those monkeys and they found that as
+
+ align:start position:0%
+in those monkeys and they found that as
+ 
+
+ align:start position:0%
+in those monkeys and they found that as
+soon as the descending connections were
+
+ align:start position:0%
+soon as the descending connections were
+ 
+
+ align:start position:0%
+soon as the descending connections were
+severed the monkey becomes like the rat
+
+ align:start position:0%
+severed the monkey becomes like the rat
+ 
+
+ align:start position:0%
+severed the monkey becomes like the rat
+he shows the reverse all the adaptation
+
+ align:start position:0%
+he shows the reverse all the adaptation
+ 
+
+ align:start position:0%
+he shows the reverse all the adaptation
+all the learning had taken place above
+
+ align:start position:0%
+all the learning had taken place above
+ 
+
+ align:start position:0%
+all the learning had taken place above
+the level of the spinal cord okay so the
+
+ align:start position:0%
+the level of the spinal cord okay so the
+ 
+
+ align:start position:0%
+the level of the spinal cord okay so the
+even though we can get some simple
+
+ align:start position:0%
+even though we can get some simple
+ 
+
+ align:start position:0%
+even though we can get some simple
+conditioning at the level of spinal cord
+
+ align:start position:0%
+conditioning at the level of spinal cord
+ 
+
+ align:start position:0%
+conditioning at the level of spinal cord
+it doesn't extend to this kind of
+
+ align:start position:0%
+it doesn't extend to this kind of
+ 
+
+ align:start position:0%
+it doesn't extend to this kind of
+adaptation an adaptation to such a
+
+ align:start position:0%
+adaptation an adaptation to such a
+ 
+
+ align:start position:0%
+adaptation an adaptation to such a
+mis-wiring of the connections okay
+
+ align:start position:0%
+mis-wiring of the connections okay
+ 
+
+ align:start position:0%
+mis-wiring of the connections okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+next time we were going to talk about
+
+ align:start position:0%
+next time we were going to talk about
+ 
+
+ align:start position:0%
+next time we were going to talk about
+the higher systems the role of
+
+ align:start position:0%
+the higher systems the role of
+ 
+
+ align:start position:0%
+the higher systems the role of
+descending pathways we'll describe the
+
+ align:start position:0%
+descending pathways we'll describe the
+ 
+
+ align:start position:0%
+descending pathways we'll describe the
+anatomy and then we'll see a film of a
+
+ align:start position:0%
+anatomy and then we'll see a film of a
+ 
+
+ align:start position:0%
+anatomy and then we'll see a film of a
+famous experiment on monkeys
\ No newline at end of file
diff --git a/945Cm4obJ5o.txt b/945Cm4obJ5o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8db202e08de24bdb4162f53f31bae3f5addfae01
--- /dev/null
+++ b/945Cm4obJ5o.txt
@@ -0,0 +1,8435 @@
+align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we've discussed motor system at
+
+ align:start position:0%
+now we've discussed motor system at
+ 
+
+ align:start position:0%
+now we've discussed motor system at
+spinal level a few basic things
+
+ align:start position:0%
+spinal level a few basic things
+ 
+
+ align:start position:0%
+spinal level a few basic things
+dealing with spinal reflexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applies also to hindbrain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a first wash at the motor looking at
+
+ align:start position:0%
+a first wash at the motor looking at
+ 
+
+ align:start position:0%
+a first wash at the motor looking at
+higher control is just to continue
+
+ align:start position:0%
+higher control is just to continue
+ 
+
+ align:start position:0%
+higher control is just to continue
+using the reflex model
+
+ align:start position:0%
+using the reflex model
+ 
+
+ align:start position:0%
+using the reflex model
+and speak of motor control in terms of a
+
+ align:start position:0%
+and speak of motor control in terms of a
+ 
+
+ align:start position:0%
+and speak of motor control in terms of a
+hierarchy of reflexes
+
+ align:start position:0%
+hierarchy of reflexes
+ 
+
+ align:start position:0%
+hierarchy of reflexes
+in other words you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have reflexes involving various
+
+ align:start position:0%
+you have reflexes involving various
+ 
+
+ align:start position:0%
+you have reflexes involving various
+length of password pathways reaching
+
+ align:start position:0%
+length of password pathways reaching
+ 
+
+ align:start position:0%
+length of password pathways reaching
+finally the neocortex
+
+ align:start position:0%
+finally the neocortex
+ 
+
+ align:start position:0%
+finally the neocortex
+the idea is that
+
+ align:start position:0%
+the idea is that
+ 
+
+ align:start position:0%
+the idea is that
+information from this one of the somatic
+
+ align:start position:0%
+information from this one of the somatic
+ 
+
+ align:start position:0%
+information from this one of the somatic
+systems
+
+ align:start position:0%
+systems
+ 
+
+ align:start position:0%
+systems
+reaches a primary sensory area of
+
+ align:start position:0%
+reaches a primary sensory area of
+ 
+
+ align:start position:0%
+reaches a primary sensory area of
+neocortex
+
+ align:start position:0%
+neocortex
+ 
+
+ align:start position:0%
+neocortex
+and from there it goes to association
+
+ align:start position:0%
+and from there it goes to association
+ 
+
+ align:start position:0%
+and from there it goes to association
+areas and from there it finally will
+
+ align:start position:0%
+areas and from there it finally will
+ 
+
+ align:start position:0%
+areas and from there it finally will
+reach
+
+ align:start position:0%
+reach
+ 
+
+ align:start position:0%
+reach
+motor cortex
+
+ align:start position:0%
+motor cortex
+ 
+
+ align:start position:0%
+motor cortex
+and that way influence movement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+first of all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+information does follow such pathways
+
+ align:start position:0%
+information does follow such pathways
+ 
+
+ align:start position:0%
+information does follow such pathways
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+anatomical studies and physiological
+
+ align:start position:0%
+anatomical studies and physiological
+ 
+
+ align:start position:0%
+anatomical studies and physiological
+studies that demonstrate that
+
+ align:start position:0%
+studies that demonstrate that
+ 
+
+ align:start position:0%
+studies that demonstrate that
+there are such pathways
+
+ align:start position:0%
+there are such pathways
+ 
+
+ align:start position:0%
+there are such pathways
+so isn't that been
+
+ align:start position:0%
+so isn't that been
+ 
+
+ align:start position:0%
+so isn't that been
+the adequate way to think about it
+
+ align:start position:0%
+the adequate way to think about it
+ 
+
+ align:start position:0%
+the adequate way to think about it
+and you'll see it written that about it
+
+ align:start position:0%
+and you'll see it written that about it
+ 
+
+ align:start position:0%
+and you'll see it written that about it
+this way in textbooks and so forth
+
+ align:start position:0%
+this way in textbooks and so forth
+ 
+
+ align:start position:0%
+this way in textbooks and so forth
+but there's a number of problems with it
+
+ align:start position:0%
+but there's a number of problems with it
+ 
+
+ align:start position:0%
+but there's a number of problems with it
+one is that is an adequate theory
+
+ align:start position:0%
+one is that is an adequate theory
+ 
+
+ align:start position:0%
+one is that is an adequate theory
+because one is that neocortical areas
+
+ align:start position:0%
+because one is that neocortical areas
+ 
+
+ align:start position:0%
+because one is that neocortical areas
+have many outputs other than these
+
+ align:start position:0%
+have many outputs other than these
+ 
+
+ align:start position:0%
+have many outputs other than these
+transcortical pathways that reach the
+
+ align:start position:0%
+transcortical pathways that reach the
+ 
+
+ align:start position:0%
+transcortical pathways that reach the
+motor cortex
+
+ align:start position:0%
+motor cortex
+ 
+
+ align:start position:0%
+motor cortex
+they can control movements
+
+ align:start position:0%
+they can control movements
+ 
+
+ align:start position:0%
+they can control movements
+without any motor cortex
+
+ align:start position:0%
+without any motor cortex
+ 
+
+ align:start position:0%
+without any motor cortex
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example visual cortex
+
+ align:start position:0%
+for example visual cortex
+ 
+
+ align:start position:0%
+for example visual cortex
+doesn't just project
+
+ align:start position:0%
+doesn't just project
+ 
+
+ align:start position:0%
+doesn't just project
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+areas adjacent to it and then
+
+ align:start position:0%
+areas adjacent to it and then
+ 
+
+ align:start position:0%
+areas adjacent to it and then
+and there are some very nice
+
+ align:start position:0%
+and there are some very nice
+ 
+
+ align:start position:0%
+and there are some very nice
+transcriptable pathways and they are
+
+ align:start position:0%
+transcriptable pathways and they are
+ 
+
+ align:start position:0%
+transcriptable pathways and they are
+made of major importance in our vision
+
+ align:start position:0%
+made of major importance in our vision
+ 
+
+ align:start position:0%
+made of major importance in our vision
+but it also projects directly to
+
+ align:start position:0%
+but it also projects directly to
+ 
+
+ align:start position:0%
+but it also projects directly to
+subcortical systems it projects to the
+
+ align:start position:0%
+subcortical systems it projects to the
+ 
+
+ align:start position:0%
+subcortical systems it projects to the
+tectum for example as do other visual
+
+ align:start position:0%
+tectum for example as do other visual
+ 
+
+ align:start position:0%
+tectum for example as do other visual
+areas okay
+
+ align:start position:0%
+areas okay
+ 
+
+ align:start position:0%
+areas okay
+and they can affect movement directly
+
+ align:start position:0%
+and they can affect movement directly
+ 
+
+ align:start position:0%
+and they can affect movement directly
+through their pathway to the midbrain
+
+ align:start position:0%
+through their pathway to the midbrain
+ 
+
+ align:start position:0%
+through their pathway to the midbrain
+without going to motor cortex
+
+ align:start position:0%
+without going to motor cortex
+ 
+
+ align:start position:0%
+without going to motor cortex
+and also we have this
+
+ align:start position:0%
+and also we have this
+ 
+
+ align:start position:0%
+and also we have this
+issue of endogenous control you can have
+
+ align:start position:0%
+issue of endogenous control you can have
+ 
+
+ align:start position:0%
+issue of endogenous control you can have
+movement that originates from activity
+
+ align:start position:0%
+movement that originates from activity
+ 
+
+ align:start position:0%
+movement that originates from activity
+generated within the nervous system not
+
+ align:start position:0%
+generated within the nervous system not
+ 
+
+ align:start position:0%
+generated within the nervous system not
+involving specific inputs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in clinical neurology
+
+ align:start position:0%
+now in clinical neurology
+ 
+
+ align:start position:0%
+now in clinical neurology
+frequently
+
+ align:start position:0%
+frequently
+ 
+
+ align:start position:0%
+frequently
+a chapter on the motor system
+
+ align:start position:0%
+a chapter on the motor system
+ 
+
+ align:start position:0%
+a chapter on the motor system
+will begin by defining the pyramidal
+
+ align:start position:0%
+will begin by defining the pyramidal
+ 
+
+ align:start position:0%
+will begin by defining the pyramidal
+system and extra grammar systems
+
+ align:start position:0%
+system and extra grammar systems
+ 
+
+ align:start position:0%
+system and extra grammar systems
+and in fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a view that you will still still
+
+ align:start position:0%
+a view that you will still still
+ 
+
+ align:start position:0%
+a view that you will still still
+sometimes see
+
+ align:start position:0%
+sometimes see
+ 
+
+ align:start position:0%
+sometimes see
+taught is that the pyramidal system is
+
+ align:start position:0%
+taught is that the pyramidal system is
+ 
+
+ align:start position:0%
+taught is that the pyramidal system is
+our system for voluntary motor control
+
+ align:start position:0%
+our system for voluntary motor control
+ 
+
+ align:start position:0%
+our system for voluntary motor control
+extra parameter system for involuntary
+
+ align:start position:0%
+extra parameter system for involuntary
+ 
+
+ align:start position:0%
+extra parameter system for involuntary
+movement
+
+ align:start position:0%
+movement
+ 
+
+ align:start position:0%
+movement
+you will see in the film that that is
+
+ align:start position:0%
+you will see in the film that that is
+ 
+
+ align:start position:0%
+you will see in the film that that is
+very very unlikely but you don't have
+
+ align:start position:0%
+very very unlikely but you don't have
+ 
+
+ align:start position:0%
+very very unlikely but you don't have
+this if the film is about monkey work
+
+ align:start position:0%
+this if the film is about monkey work
+ 
+
+ align:start position:0%
+this if the film is about monkey work
+even with human work you can have people
+
+ align:start position:0%
+even with human work you can have people
+ 
+
+ align:start position:0%
+even with human work you can have people
+that have had sections of pyramidal
+
+ align:start position:0%
+that have had sections of pyramidal
+ 
+
+ align:start position:0%
+that have had sections of pyramidal
+track
+
+ align:start position:0%
+track
+ 
+
+ align:start position:0%
+track
+they lack the pramble system for motor
+
+ align:start position:0%
+they lack the pramble system for motor
+ 
+
+ align:start position:0%
+they lack the pramble system for motor
+control and yet
+
+ align:start position:0%
+control and yet
+ 
+
+ align:start position:0%
+control and yet
+they certainly have voluntary movement
+
+ align:start position:0%
+they certainly have voluntary movement
+ 
+
+ align:start position:0%
+they certainly have voluntary movement
+it may not be completely normal
+
+ align:start position:0%
+it may not be completely normal
+ 
+
+ align:start position:0%
+it may not be completely normal
+they have motor defects
+
+ align:start position:0%
+they have motor defects
+ 
+
+ align:start position:0%
+they have motor defects
+and we'll see that for the monkeys in
+
+ align:start position:0%
+and we'll see that for the monkeys in
+ 
+
+ align:start position:0%
+and we'll see that for the monkeys in
+the film
+
+ align:start position:0%
+the film
+ 
+
+ align:start position:0%
+the film
+okay but it's this initial consideration
+
+ align:start position:0%
+okay but it's this initial consideration
+ 
+
+ align:start position:0%
+okay but it's this initial consideration
+that it has to do with
+
+ align:start position:0%
+that it has to do with
+ 
+
+ align:start position:0%
+that it has to do with
+voluntary and involuntary is certainly
+
+ align:start position:0%
+voluntary and involuntary is certainly
+ 
+
+ align:start position:0%
+voluntary and involuntary is certainly
+not the case
+
+ align:start position:0%
+not the case
+ 
+
+ align:start position:0%
+not the case
+but their anatomical considerations that
+
+ align:start position:0%
+but their anatomical considerations that
+ 
+
+ align:start position:0%
+but their anatomical considerations that
+also show that this is unlikely
+
+ align:start position:0%
+also show that this is unlikely
+ 
+
+ align:start position:0%
+also show that this is unlikely
+at least some of the major
+
+ align:start position:0%
+at least some of the major
+ 
+
+ align:start position:0%
+at least some of the major
+extrapyramidal systems the two major
+
+ align:start position:0%
+extrapyramidal systems the two major
+ 
+
+ align:start position:0%
+extrapyramidal systems the two major
+ones usually discussed in medical school
+
+ align:start position:0%
+ones usually discussed in medical school
+ 
+
+ align:start position:0%
+ones usually discussed in medical school
+textbooks are the cerebellar system and
+
+ align:start position:0%
+textbooks are the cerebellar system and
+ 
+
+ align:start position:0%
+textbooks are the cerebellar system and
+corpus
+
+ align:start position:0%
+corpus
+ 
+
+ align:start position:0%
+corpus
+triada in fact their major outputs in
+
+ align:start position:0%
+triada in fact their major outputs in
+ 
+
+ align:start position:0%
+triada in fact their major outputs in
+higher mammals
+
+ align:start position:0%
+higher mammals
+ 
+
+ align:start position:0%
+higher mammals
+is to the pyramidal system
+
+ align:start position:0%
+is to the pyramidal system
+ 
+
+ align:start position:0%
+is to the pyramidal system
+and i pointed out here how that works
+
+ align:start position:0%
+and i pointed out here how that works
+ 
+
+ align:start position:0%
+and i pointed out here how that works
+cerebellum projects to these more
+
+ align:start position:0%
+cerebellum projects to these more
+ 
+
+ align:start position:0%
+cerebellum projects to these more
+anterior parts of the ventral nucleus of
+
+ align:start position:0%
+anterior parts of the ventral nucleus of
+ 
+
+ align:start position:0%
+anterior parts of the ventral nucleus of
+the thalamus the vl in the va
+
+ align:start position:0%
+the thalamus the vl in the va
+ 
+
+ align:start position:0%
+the thalamus the vl in the va
+cerebellum goes
+
+ align:start position:0%
+cerebellum goes
+ 
+
+ align:start position:0%
+cerebellum goes
+mainly to vl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which then projects to motor cortex
+
+ align:start position:0%
+which then projects to motor cortex
+ 
+
+ align:start position:0%
+which then projects to motor cortex
+sorry did i
+
+ align:start position:0%
+sorry did i
+ 
+
+ align:start position:0%
+sorry did i
+not reading what i'm writing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cerebellum goes mainly to vl copies
+
+ align:start position:0%
+cerebellum goes mainly to vl copies
+ 
+
+ align:start position:0%
+cerebellum goes mainly to vl copies
+triadon to va okay but they both project
+
+ align:start position:0%
+triadon to va okay but they both project
+ 
+
+ align:start position:0%
+triadon to va okay but they both project
+to both those areas and they go to the
+
+ align:start position:0%
+to both those areas and they go to the
+ 
+
+ align:start position:0%
+to both those areas and they go to the
+motor cortex okay
+
+ align:start position:0%
+motor cortex okay
+ 
+
+ align:start position:0%
+motor cortex okay
+and which then is the major contributor
+
+ align:start position:0%
+and which then is the major contributor
+ 
+
+ align:start position:0%
+and which then is the major contributor
+at least forty percent of the pyramidal
+
+ align:start position:0%
+at least forty percent of the pyramidal
+ 
+
+ align:start position:0%
+at least forty percent of the pyramidal
+track comes from the motor cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these neocortical areas even the
+
+ align:start position:0%
+and these neocortical areas even the
+ 
+
+ align:start position:0%
+and these neocortical areas even the
+motor cortex have many other projections
+
+ align:start position:0%
+motor cortex have many other projections
+ 
+
+ align:start position:0%
+motor cortex have many other projections
+other than to the pyramidal tract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+almost the entire neocortex projects to
+
+ align:start position:0%
+almost the entire neocortex projects to
+ 
+
+ align:start position:0%
+almost the entire neocortex projects to
+the corpus triatum which has outputs
+
+ align:start position:0%
+the corpus triatum which has outputs
+ 
+
+ align:start position:0%
+the corpus triatum which has outputs
+separate
+
+ align:start position:0%
+separate
+ 
+
+ align:start position:0%
+separate
+from those that go back to the thalamus
+
+ align:start position:0%
+from those that go back to the thalamus
+ 
+
+ align:start position:0%
+from those that go back to the thalamus
+and motor cortex so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way we're going to do this is we're
+
+ align:start position:0%
+the way we're going to do this is we're
+ 
+
+ align:start position:0%
+the way we're going to do this is we're
+going to follow lawrence and kuipers and
+
+ align:start position:0%
+going to follow lawrence and kuipers and
+ 
+
+ align:start position:0%
+going to follow lawrence and kuipers and
+their classic work which was began with
+
+ align:start position:0%
+their classic work which was began with
+ 
+
+ align:start position:0%
+their classic work which was began with
+neuroanatomical studies of descending
+
+ align:start position:0%
+neuroanatomical studies of descending
+ 
+
+ align:start position:0%
+neuroanatomical studies of descending
+pathways
+
+ align:start position:0%
+pathways
+ 
+
+ align:start position:0%
+pathways
+and the organization of spinal cord
+
+ align:start position:0%
+and the organization of spinal cord
+ 
+
+ align:start position:0%
+and the organization of spinal cord
+motor neurons
+
+ align:start position:0%
+motor neurons
+ 
+
+ align:start position:0%
+motor neurons
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll look at the spinal cord at one
+
+ align:start position:0%
+so we'll look at the spinal cord at one
+ 
+
+ align:start position:0%
+so we'll look at the spinal cord at one
+of the enlargements
+
+ align:start position:0%
+of the enlargements
+ 
+
+ align:start position:0%
+of the enlargements
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the organization of motor neurons and
+
+ align:start position:0%
+the organization of motor neurons and
+ 
+
+ align:start position:0%
+the organization of motor neurons and
+then we'll talk about how the higher
+
+ align:start position:0%
+then we'll talk about how the higher
+ 
+
+ align:start position:0%
+then we'll talk about how the higher
+systems project to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are their two pictures
+
+ align:start position:0%
+so these are their two pictures
+ 
+
+ align:start position:0%
+so these are their two pictures
+i have an enlargement of this one okay
+
+ align:start position:0%
+i have an enlargement of this one okay
+ 
+
+ align:start position:0%
+i have an enlargement of this one okay
+so i want you to understand what this is
+
+ align:start position:0%
+so i want you to understand what this is
+ 
+
+ align:start position:0%
+so i want you to understand what this is
+showing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the top there you have these are all
+
+ align:start position:0%
+at the top there you have these are all
+ 
+
+ align:start position:0%
+at the top there you have these are all
+cross sections of the spinal cord at the
+
+ align:start position:0%
+cross sections of the spinal cord at the
+ 
+
+ align:start position:0%
+cross sections of the spinal cord at the
+lumbar enlargement okay controlling the
+
+ align:start position:0%
+lumbar enlargement okay controlling the
+ 
+
+ align:start position:0%
+lumbar enlargement okay controlling the
+lower limb muscles okay
+
+ align:start position:0%
+lower limb muscles okay
+ 
+
+ align:start position:0%
+lower limb muscles okay
+so first look at the bottom here
+
+ align:start position:0%
+so first look at the bottom here
+ 
+
+ align:start position:0%
+so first look at the bottom here
+they're showing motor neurons
+
+ align:start position:0%
+they're showing motor neurons
+ 
+
+ align:start position:0%
+they're showing motor neurons
+they're located
+
+ align:start position:0%
+they're located
+ 
+
+ align:start position:0%
+they're located
+all across from medial
+
+ align:start position:0%
+all across from medial
+ 
+
+ align:start position:0%
+all across from medial
+to lateral here
+
+ align:start position:0%
+to lateral here
+ 
+
+ align:start position:0%
+to lateral here
+we'll call this dorsolateral here we'll
+
+ align:start position:0%
+we'll call this dorsolateral here we'll
+ 
+
+ align:start position:0%
+we'll call this dorsolateral here we'll
+just call it lateral
+
+ align:start position:0%
+just call it lateral
+ 
+
+ align:start position:0%
+just call it lateral
+this is ventromedial we'll call it
+
+ align:start position:0%
+this is ventromedial we'll call it
+ 
+
+ align:start position:0%
+this is ventromedial we'll call it
+medial okay
+
+ align:start position:0%
+medial okay
+ 
+
+ align:start position:0%
+medial okay
+now those motor neurons are arranged
+
+ align:start position:0%
+now those motor neurons are arranged
+ 
+
+ align:start position:0%
+now those motor neurons are arranged
+in an orderly way so that the most
+
+ align:start position:0%
+in an orderly way so that the most
+ 
+
+ align:start position:0%
+in an orderly way so that the most
+distal muscles are represented laterally
+
+ align:start position:0%
+distal muscles are represented laterally
+ 
+
+ align:start position:0%
+distal muscles are represented laterally
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you wanted to find a neuron
+
+ align:start position:0%
+so if you wanted to find a neuron
+ 
+
+ align:start position:0%
+so if you wanted to find a neuron
+controlling the toe
+
+ align:start position:0%
+controlling the toe
+ 
+
+ align:start position:0%
+controlling the toe
+you would look way out here
+
+ align:start position:0%
+you would look way out here
+ 
+
+ align:start position:0%
+you would look way out here
+if you wanted to find a motor neuron
+
+ align:start position:0%
+if you wanted to find a motor neuron
+ 
+
+ align:start position:0%
+if you wanted to find a motor neuron
+controlling
+
+ align:start position:0%
+controlling
+ 
+
+ align:start position:0%
+controlling
+say the muscles along the back
+
+ align:start position:0%
+say the muscles along the back
+ 
+
+ align:start position:0%
+say the muscles along the back
+you would look
+
+ align:start position:0%
+you would look
+ 
+
+ align:start position:0%
+you would look
+in the most medial area okay here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in between you would find motor
+
+ align:start position:0%
+and in between you would find motor
+ 
+
+ align:start position:0%
+and in between you would find motor
+neurons controlling the hip
+
+ align:start position:0%
+neurons controlling the hip
+ 
+
+ align:start position:0%
+neurons controlling the hip
+okay similarly now for the
+
+ align:start position:0%
+okay similarly now for the
+ 
+
+ align:start position:0%
+okay similarly now for the
+cervical enlargement
+
+ align:start position:0%
+cervical enlargement
+ 
+
+ align:start position:0%
+cervical enlargement
+the lateral motor neurons would be
+
+ align:start position:0%
+the lateral motor neurons would be
+ 
+
+ align:start position:0%
+the lateral motor neurons would be
+controlling our fingers
+
+ align:start position:0%
+controlling our fingers
+ 
+
+ align:start position:0%
+controlling our fingers
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+the arms as you move medially
+
+ align:start position:0%
+the arms as you move medially
+ 
+
+ align:start position:0%
+the arms as you move medially
+and then the girdle muscles the shoulder
+
+ align:start position:0%
+and then the girdle muscles the shoulder
+ 
+
+ align:start position:0%
+and then the girdle muscles the shoulder
+and then most immediately the axial
+
+ align:start position:0%
+and then most immediately the axial
+ 
+
+ align:start position:0%
+and then most immediately the axial
+muscle
+
+ align:start position:0%
+muscle
+ 
+
+ align:start position:0%
+muscle
+keeping us upright controlling our
+
+ align:start position:0%
+keeping us upright controlling our
+ 
+
+ align:start position:0%
+keeping us upright controlling our
+balance and posture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what connects to those well first of
+
+ align:start position:0%
+so what connects to those well first of
+ 
+
+ align:start position:0%
+so what connects to those well first of
+all the interneuronal pool
+
+ align:start position:0%
+all the interneuronal pool
+ 
+
+ align:start position:0%
+all the interneuronal pool
+of neurons that are not motor neurons
+
+ align:start position:0%
+of neurons that are not motor neurons
+ 
+
+ align:start position:0%
+of neurons that are not motor neurons
+but they connect to motor neurons they
+
+ align:start position:0%
+but they connect to motor neurons they
+ 
+
+ align:start position:0%
+but they connect to motor neurons they
+also connect in an orderly way so the
+
+ align:start position:0%
+also connect in an orderly way so the
+ 
+
+ align:start position:0%
+also connect in an orderly way so the
+lateral or dorsolateral part here
+
+ align:start position:0%
+lateral or dorsolateral part here
+ 
+
+ align:start position:0%
+lateral or dorsolateral part here
+connect the lateral motor neurons the
+
+ align:start position:0%
+connect the lateral motor neurons the
+ 
+
+ align:start position:0%
+connect the lateral motor neurons the
+medial ones connect the medial there's
+
+ align:start position:0%
+medial ones connect the medial there's
+ 
+
+ align:start position:0%
+medial ones connect the medial there's
+one other point about that the medial
+
+ align:start position:0%
+one other point about that the medial
+ 
+
+ align:start position:0%
+one other point about that the medial
+interneurons tend to have axons that go
+
+ align:start position:0%
+interneurons tend to have axons that go
+ 
+
+ align:start position:0%
+interneurons tend to have axons that go
+to both sides
+
+ align:start position:0%
+to both sides
+ 
+
+ align:start position:0%
+to both sides
+but not the lateral ones okay
+
+ align:start position:0%
+but not the lateral ones okay
+ 
+
+ align:start position:0%
+but not the lateral ones okay
+and that will see
+
+ align:start position:0%
+and that will see
+ 
+
+ align:start position:0%
+and that will see
+a consistent pattern here that those
+
+ align:start position:0%
+a consistent pattern here that those
+ 
+
+ align:start position:0%
+a consistent pattern here that those
+medial ones tend to be more bilateral in
+
+ align:start position:0%
+medial ones tend to be more bilateral in
+ 
+
+ align:start position:0%
+medial ones tend to be more bilateral in
+their connections
+
+ align:start position:0%
+their connections
+ 
+
+ align:start position:0%
+their connections
+and we'll see that's because they're
+
+ align:start position:0%
+and we'll see that's because they're
+ 
+
+ align:start position:0%
+and we'll see that's because they're
+controlling whole body movements
+
+ align:start position:0%
+controlling whole body movements
+ 
+
+ align:start position:0%
+controlling whole body movements
+movements of large part of the body
+
+ align:start position:0%
+movements of large part of the body
+ 
+
+ align:start position:0%
+movements of large part of the body
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so then the next step for lawrence and
+
+ align:start position:0%
+so then the next step for lawrence and
+ 
+
+ align:start position:0%
+so then the next step for lawrence and
+kuipers was to say okay what projects to
+
+ align:start position:0%
+kuipers was to say okay what projects to
+ 
+
+ align:start position:0%
+kuipers was to say okay what projects to
+those interneurons
+
+ align:start position:0%
+those interneurons
+ 
+
+ align:start position:0%
+those interneurons
+they knew that major contributors were
+
+ align:start position:0%
+they knew that major contributors were
+ 
+
+ align:start position:0%
+they knew that major contributors were
+coming from the brain so they looked at
+
+ align:start position:0%
+coming from the brain so they looked at
+ 
+
+ align:start position:0%
+coming from the brain so they looked at
+the corticospinal tract and they saw
+
+ align:start position:0%
+the corticospinal tract and they saw
+ 
+
+ align:start position:0%
+the corticospinal tract and they saw
+these were degeneration studies they're
+
+ align:start position:0%
+these were degeneration studies they're
+ 
+
+ align:start position:0%
+these were degeneration studies they're
+looking at the pattern of projections
+
+ align:start position:0%
+looking at the pattern of projections
+ 
+
+ align:start position:0%
+looking at the pattern of projections
+shown by degenerating axons after legion
+
+ align:start position:0%
+shown by degenerating axons after legion
+ 
+
+ align:start position:0%
+shown by degenerating axons after legion
+of motor cortex or a section of the
+
+ align:start position:0%
+of motor cortex or a section of the
+ 
+
+ align:start position:0%
+of motor cortex or a section of the
+parameter and they see that it goes to
+
+ align:start position:0%
+parameter and they see that it goes to
+ 
+
+ align:start position:0%
+parameter and they see that it goes to
+the whole thing here
+
+ align:start position:0%
+the whole thing here
+ 
+
+ align:start position:0%
+the whole thing here
+it goes laterally it goes medially and a
+
+ align:start position:0%
+it goes laterally it goes medially and a
+ 
+
+ align:start position:0%
+it goes laterally it goes medially and a
+little bit to the other side but when it
+
+ align:start position:0%
+little bit to the other side but when it
+ 
+
+ align:start position:0%
+little bit to the other side but when it
+goes to the other side it goes only to
+
+ align:start position:0%
+goes to the other side it goes only to
+ 
+
+ align:start position:0%
+goes to the other side it goes only to
+that ventral medial area almost entirely
+
+ align:start position:0%
+that ventral medial area almost entirely
+ 
+
+ align:start position:0%
+that ventral medial area almost entirely
+okay so now
+
+ align:start position:0%
+okay so now
+ 
+
+ align:start position:0%
+okay so now
+other than the pyramidal tract
+
+ align:start position:0%
+other than the pyramidal tract
+ 
+
+ align:start position:0%
+other than the pyramidal tract
+where the other descending connections
+
+ align:start position:0%
+where the other descending connections
+ 
+
+ align:start position:0%
+where the other descending connections
+that come from the brainstem go
+
+ align:start position:0%
+that come from the brainstem go
+ 
+
+ align:start position:0%
+that come from the brainstem go
+they saw that they were nicely divided
+
+ align:start position:0%
+they saw that they were nicely divided
+ 
+
+ align:start position:0%
+they saw that they were nicely divided
+into two types of connections
+
+ align:start position:0%
+into two types of connections
+ 
+
+ align:start position:0%
+into two types of connections
+the red nucleus the rubric spinal tract
+
+ align:start position:0%
+the red nucleus the rubric spinal tract
+ 
+
+ align:start position:0%
+the red nucleus the rubric spinal tract
+connects to the more lateral internal
+
+ align:start position:0%
+connects to the more lateral internal
+ 
+
+ align:start position:0%
+connects to the more lateral internal
+pool
+
+ align:start position:0%
+pool
+ 
+
+ align:start position:0%
+pool
+connecting then to the left which then
+
+ align:start position:0%
+connecting then to the left which then
+ 
+
+ align:start position:0%
+connecting then to the left which then
+would be influencing the lateral motor
+
+ align:start position:0%
+would be influencing the lateral motor
+ 
+
+ align:start position:0%
+would be influencing the lateral motor
+neurons so and that fits functional
+
+ align:start position:0%
+neurons so and that fits functional
+ 
+
+ align:start position:0%
+neurons so and that fits functional
+studies that show that the red nucleus
+
+ align:start position:0%
+studies that show that the red nucleus
+ 
+
+ align:start position:0%
+studies that show that the red nucleus
+is particularly important in limb
+
+ align:start position:0%
+is particularly important in limb
+ 
+
+ align:start position:0%
+is particularly important in limb
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+limb and hand control okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whereas the pathways that follow
+
+ align:start position:0%
+whereas the pathways that follow
+ 
+
+ align:start position:0%
+whereas the pathways that follow
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+that come from the ventromedial hind
+
+ align:start position:0%
+that come from the ventromedial hind
+ 
+
+ align:start position:0%
+that come from the ventromedial hind
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+and they tend to travel
+
+ align:start position:0%
+and they tend to travel
+ 
+
+ align:start position:0%
+and they tend to travel
+in the ventral and these ventral columns
+
+ align:start position:0%
+in the ventral and these ventral columns
+ 
+
+ align:start position:0%
+in the ventral and these ventral columns
+of the core the ventral
+
+ align:start position:0%
+of the core the ventral
+ 
+
+ align:start position:0%
+of the core the ventral
+funiculus okay
+
+ align:start position:0%
+funiculus okay
+ 
+
+ align:start position:0%
+funiculus okay
+they project to that ventral medial area
+
+ align:start position:0%
+they project to that ventral medial area
+ 
+
+ align:start position:0%
+they project to that ventral medial area
+controlling axial muscles
+
+ align:start position:0%
+controlling axial muscles
+ 
+
+ align:start position:0%
+controlling axial muscles
+and again axons coming here down the
+
+ align:start position:0%
+and again axons coming here down the
+ 
+
+ align:start position:0%
+and again axons coming here down the
+left side will also tend to cross over
+
+ align:start position:0%
+left side will also tend to cross over
+ 
+
+ align:start position:0%
+left side will also tend to cross over
+and go to the other side
+
+ align:start position:0%
+and go to the other side
+ 
+
+ align:start position:0%
+and go to the other side
+now what are those pathways
+
+ align:start position:0%
+now what are those pathways
+ 
+
+ align:start position:0%
+now what are those pathways
+vestibulospinal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tactile spinal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cerebellospinal the vestigial spinal
+
+ align:start position:0%
+cerebellospinal the vestigial spinal
+ 
+
+ align:start position:0%
+cerebellospinal the vestigial spinal
+sometimes we call it because it comes
+
+ align:start position:0%
+sometimes we call it because it comes
+ 
+
+ align:start position:0%
+sometimes we call it because it comes
+from the this digital nucleus the most
+
+ align:start position:0%
+from the this digital nucleus the most
+ 
+
+ align:start position:0%
+from the this digital nucleus the most
+medial nucleus in the cerebellum okay
+
+ align:start position:0%
+medial nucleus in the cerebellum okay
+ 
+
+ align:start position:0%
+medial nucleus in the cerebellum okay
+and also from the medial reticular
+
+ align:start position:0%
+and also from the medial reticular
+ 
+
+ align:start position:0%
+and also from the medial reticular
+formation large neurons in the reticular
+
+ align:start position:0%
+formation large neurons in the reticular
+ 
+
+ align:start position:0%
+formation large neurons in the reticular
+formation which we know are concerned
+
+ align:start position:0%
+formation which we know are concerned
+ 
+
+ align:start position:0%
+formation which we know are concerned
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+various fixed action patterns and so
+
+ align:start position:0%
+various fixed action patterns and so
+ 
+
+ align:start position:0%
+various fixed action patterns and so
+forth controlled often often concerned
+
+ align:start position:0%
+forth controlled often often concerned
+ 
+
+ align:start position:0%
+forth controlled often often concerned
+with whole body movements
+
+ align:start position:0%
+with whole body movements
+ 
+
+ align:start position:0%
+with whole body movements
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i just list them there for you
+
+ align:start position:0%
+i just list them there for you
+ 
+
+ align:start position:0%
+i just list them there for you
+so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this just shows the same pathways
+
+ align:start position:0%
+this just shows the same pathways
+ 
+
+ align:start position:0%
+this just shows the same pathways
+instead of on a cross section here i put
+
+ align:start position:0%
+instead of on a cross section here i put
+ 
+
+ align:start position:0%
+instead of on a cross section here i put
+them on a picture of the monkey brain
+
+ align:start position:0%
+them on a picture of the monkey brain
+ 
+
+ align:start position:0%
+them on a picture of the monkey brain
+and i show here the motor cortex
+
+ align:start position:0%
+and i show here the motor cortex
+ 
+
+ align:start position:0%
+and i show here the motor cortex
+with the areas representing the distal
+
+ align:start position:0%
+with the areas representing the distal
+ 
+
+ align:start position:0%
+with the areas representing the distal
+muscles
+
+ align:start position:0%
+muscles
+ 
+
+ align:start position:0%
+muscles
+in the dark lines and then i also show
+
+ align:start position:0%
+in the dark lines and then i also show
+ 
+
+ align:start position:0%
+in the dark lines and then i also show
+the the other they i show that both
+
+ align:start position:0%
+the the other they i show that both
+ 
+
+ align:start position:0%
+the the other they i show that both
+systems are going throughout the cord
+
+ align:start position:0%
+systems are going throughout the cord
+ 
+
+ align:start position:0%
+systems are going throughout the cord
+if you're just looking at motor neurons
+
+ align:start position:0%
+if you're just looking at motor neurons
+ 
+
+ align:start position:0%
+if you're just looking at motor neurons
+representing hands they would go to the
+
+ align:start position:0%
+representing hands they would go to the
+ 
+
+ align:start position:0%
+representing hands they would go to the
+upper enlargement the feet the lower
+
+ align:start position:0%
+upper enlargement the feet the lower
+ 
+
+ align:start position:0%
+upper enlargement the feet the lower
+enlargement
+
+ align:start position:0%
+enlargement
+ 
+
+ align:start position:0%
+enlargement
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+basically the neocortex goes to all
+
+ align:start position:0%
+basically the neocortex goes to all
+ 
+
+ align:start position:0%
+basically the neocortex goes to all
+levels and all parts
+
+ align:start position:0%
+levels and all parts
+ 
+
+ align:start position:0%
+levels and all parts
+of that system medial and lateral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if we go
+
+ align:start position:0%
+now if we go
+ 
+
+ align:start position:0%
+now if we go
+here's the red nucleus and i show its
+
+ align:start position:0%
+here's the red nucleus and i show its
+ 
+
+ align:start position:0%
+here's the red nucleus and i show its
+cross projection here you see where it
+
+ align:start position:0%
+cross projection here you see where it
+ 
+
+ align:start position:0%
+cross projection here you see where it
+travels laterally in the hindbrain and
+
+ align:start position:0%
+travels laterally in the hindbrain and
+ 
+
+ align:start position:0%
+travels laterally in the hindbrain and
+here it's on the longitudinal view it's
+
+ align:start position:0%
+here it's on the longitudinal view it's
+ 
+
+ align:start position:0%
+here it's on the longitudinal view it's
+crossing over it projects to the lateral
+
+ align:start position:0%
+crossing over it projects to the lateral
+ 
+
+ align:start position:0%
+crossing over it projects to the lateral
+hind brain and then it projects mainly
+
+ align:start position:0%
+hind brain and then it projects mainly
+ 
+
+ align:start position:0%
+hind brain and then it projects mainly
+laterally in the core of the
+
+ align:start position:0%
+laterally in the core of the
+ 
+
+ align:start position:0%
+laterally in the core of the
+enlargements
+
+ align:start position:0%
+enlargements
+ 
+
+ align:start position:0%
+enlargements
+the medial pathways
+
+ align:start position:0%
+the medial pathways
+ 
+
+ align:start position:0%
+the medial pathways
+travel medially in the cord and they
+
+ align:start position:0%
+travel medially in the cord and they
+ 
+
+ align:start position:0%
+travel medially in the cord and they
+tend to distribute bilaterally here they
+
+ align:start position:0%
+tend to distribute bilaterally here they
+ 
+
+ align:start position:0%
+tend to distribute bilaterally here they
+are going through the hindbrain
+
+ align:start position:0%
+are going through the hindbrain
+ 
+
+ align:start position:0%
+are going through the hindbrain
+here's the origin of the tectospinal
+
+ align:start position:0%
+here's the origin of the tectospinal
+ 
+
+ align:start position:0%
+here's the origin of the tectospinal
+tract
+
+ align:start position:0%
+tract
+ 
+
+ align:start position:0%
+tract
+here i'm showing the way that the
+
+ align:start position:0%
+here i'm showing the way that the
+ 
+
+ align:start position:0%
+here i'm showing the way that the
+stimulospinal tract originates okay
+
+ align:start position:0%
+stimulospinal tract originates okay
+ 
+
+ align:start position:0%
+stimulospinal tract originates okay
+descends
+
+ align:start position:0%
+descends
+ 
+
+ align:start position:0%
+descends
+to all levels of the chord now not just
+
+ align:start position:0%
+to all levels of the chord now not just
+ 
+
+ align:start position:0%
+to all levels of the chord now not just
+the enlargements but all levels okay and
+
+ align:start position:0%
+the enlargements but all levels okay and
+ 
+
+ align:start position:0%
+the enlargements but all levels okay and
+tends to terminate in that medial part
+
+ align:start position:0%
+tends to terminate in that medial part
+ 
+
+ align:start position:0%
+tends to terminate in that medial part
+of the chord
+
+ align:start position:0%
+of the chord
+ 
+
+ align:start position:0%
+of the chord
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is just to show you that my
+
+ align:start position:0%
+this is just to show you that my
+ 
+
+ align:start position:0%
+this is just to show you that my
+pictures are a lot better than appears
+
+ align:start position:0%
+pictures are a lot better than appears
+ 
+
+ align:start position:0%
+pictures are a lot better than appears
+in the textbooks
+
+ align:start position:0%
+in the textbooks
+ 
+
+ align:start position:0%
+in the textbooks
+i these are very difficult to understand
+
+ align:start position:0%
+i these are very difficult to understand
+ 
+
+ align:start position:0%
+i these are very difficult to understand
+if you study it for a while you might be
+
+ align:start position:0%
+if you study it for a while you might be
+ 
+
+ align:start position:0%
+if you study it for a while you might be
+able to make it out and relate it to
+
+ align:start position:0%
+able to make it out and relate it to
+ 
+
+ align:start position:0%
+able to make it out and relate it to
+what i've shown you
+
+ align:start position:0%
+what i've shown you
+ 
+
+ align:start position:0%
+what i've shown you
+showing here the corticospinal tract
+
+ align:start position:0%
+showing here the corticospinal tract
+ 
+
+ align:start position:0%
+showing here the corticospinal tract
+traveling laterally here
+
+ align:start position:0%
+traveling laterally here
+ 
+
+ align:start position:0%
+traveling laterally here
+the lateral funiculus of the cord and
+
+ align:start position:0%
+the lateral funiculus of the cord and
+ 
+
+ align:start position:0%
+the lateral funiculus of the cord and
+trying to depict various levels
+
+ align:start position:0%
+trying to depict various levels
+ 
+
+ align:start position:0%
+trying to depict various levels
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let's we're going to look at this
+
+ align:start position:0%
+so now let's we're going to look at this
+ 
+
+ align:start position:0%
+so now let's we're going to look at this
+film and this is what we're going to see
+
+ align:start position:0%
+film and this is what we're going to see
+ 
+
+ align:start position:0%
+film and this is what we're going to see
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+they did paramedotomies they section the
+
+ align:start position:0%
+they did paramedotomies they section the
+ 
+
+ align:start position:0%
+they did paramedotomies they section the
+pyramidal track
+
+ align:start position:0%
+pyramidal track
+ 
+
+ align:start position:0%
+pyramidal track
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the first lesion on that
+
+ align:start position:0%
+here's the first lesion on that
+ 
+
+ align:start position:0%
+here's the first lesion on that
+anatomical diagram they cut the primal
+
+ align:start position:0%
+anatomical diagram they cut the primal
+ 
+
+ align:start position:0%
+anatomical diagram they cut the primal
+tract here in the hindbrain so here in
+
+ align:start position:0%
+tract here in the hindbrain so here in
+ 
+
+ align:start position:0%
+tract here in the hindbrain so here in
+this picture that's where they cut it
+
+ align:start position:0%
+this picture that's where they cut it
+ 
+
+ align:start position:0%
+this picture that's where they cut it
+they cut it bilaterally
+
+ align:start position:0%
+they cut it bilaterally
+ 
+
+ align:start position:0%
+they cut it bilaterally
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we'll see a monkey then with no
+
+ align:start position:0%
+so we'll see a monkey then with no
+ 
+
+ align:start position:0%
+so we'll see a monkey then with no
+paranormal track and we'll see he has a
+
+ align:start position:0%
+paranormal track and we'll see he has a
+ 
+
+ align:start position:0%
+paranormal track and we'll see he has a
+lot of voluntary movement we'll see what
+
+ align:start position:0%
+lot of voluntary movement we'll see what
+ 
+
+ align:start position:0%
+lot of voluntary movement we'll see what
+he lacks he doesn't have single digit
+
+ align:start position:0%
+he lacks he doesn't have single digit
+ 
+
+ align:start position:0%
+he lacks he doesn't have single digit
+control he loses some
+
+ align:start position:0%
+control he loses some
+ 
+
+ align:start position:0%
+control he loses some
+he loses some manual dexterity also
+
+ align:start position:0%
+he loses some manual dexterity also
+ 
+
+ align:start position:0%
+he loses some manual dexterity also
+loses speed
+
+ align:start position:0%
+loses speed
+ 
+
+ align:start position:0%
+loses speed
+okay then lesion two
+
+ align:start position:0%
+okay then lesion two
+ 
+
+ align:start position:0%
+okay then lesion two
+they made a bilateral cut
+
+ align:start position:0%
+they made a bilateral cut
+ 
+
+ align:start position:0%
+they made a bilateral cut
+in the hind brain sectioning all those
+
+ align:start position:0%
+in the hind brain sectioning all those
+ 
+
+ align:start position:0%
+in the hind brain sectioning all those
+medial pathways they're going right
+
+ align:start position:0%
+medial pathways they're going right
+ 
+
+ align:start position:0%
+medial pathways they're going right
+there through the primal track but
+
+ align:start position:0%
+there through the primal track but
+ 
+
+ align:start position:0%
+there through the primal track but
+that's already degenerating and we'll
+
+ align:start position:0%
+that's already degenerating and we'll
+ 
+
+ align:start position:0%
+that's already degenerating and we'll
+see the histological sections
+
+ align:start position:0%
+see the histological sections
+ 
+
+ align:start position:0%
+see the histological sections
+demonstrating that okay
+
+ align:start position:0%
+demonstrating that okay
+ 
+
+ align:start position:0%
+demonstrating that okay
+and i'll explain that when we see it so
+
+ align:start position:0%
+and i'll explain that when we see it so
+ 
+
+ align:start position:0%
+and i'll explain that when we see it so
+here on this view there's where they're
+
+ align:start position:0%
+here on this view there's where they're
+ 
+
+ align:start position:0%
+here on this view there's where they're
+cutting it
+
+ align:start position:0%
+cutting it
+ 
+
+ align:start position:0%
+cutting it
+they if they do that lesion you know i
+
+ align:start position:0%
+they if they do that lesion you know i
+ 
+
+ align:start position:0%
+they if they do that lesion you know i
+believe they didn't get much effect but
+
+ align:start position:0%
+believe they didn't get much effect but
+ 
+
+ align:start position:0%
+believe they didn't get much effect but
+remember that system tends to be
+
+ align:start position:0%
+remember that system tends to be
+ 
+
+ align:start position:0%
+remember that system tends to be
+bilateral in its connections so you
+
+ align:start position:0%
+bilateral in its connections so you
+ 
+
+ align:start position:0%
+bilateral in its connections so you
+really have to cut it on both sides the
+
+ align:start position:0%
+really have to cut it on both sides the
+ 
+
+ align:start position:0%
+really have to cut it on both sides the
+most impaired monkey you'll see in the
+
+ align:start position:0%
+most impaired monkey you'll see in the
+ 
+
+ align:start position:0%
+most impaired monkey you'll see in the
+film is one with that
+
+ align:start position:0%
+film is one with that
+ 
+
+ align:start position:0%
+film is one with that
+the pyramidal track lesion first and
+
+ align:start position:0%
+the pyramidal track lesion first and
+ 
+
+ align:start position:0%
+the pyramidal track lesion first and
+then this
+
+ align:start position:0%
+then this
+ 
+
+ align:start position:0%
+then this
+the medial hindbrain
+
+ align:start position:0%
+the medial hindbrain
+ 
+
+ align:start position:0%
+the medial hindbrain
+pathways section
+
+ align:start position:0%
+pathways section
+ 
+
+ align:start position:0%
+pathways section
+because he can't write himself not for
+
+ align:start position:0%
+because he can't write himself not for
+ 
+
+ align:start position:0%
+because he can't write himself not for
+40 days anyway he finally
+
+ align:start position:0%
+40 days anyway he finally
+ 
+
+ align:start position:0%
+40 days anyway he finally
+recovers enough that the sensory control
+
+ align:start position:0%
+recovers enough that the sensory control
+ 
+
+ align:start position:0%
+recovers enough that the sensory control
+of writing
+
+ align:start position:0%
+of writing
+ 
+
+ align:start position:0%
+of writing
+that he can write himself again he lacks
+
+ align:start position:0%
+that he can write himself again he lacks
+ 
+
+ align:start position:0%
+that he can write himself again he lacks
+those vestibular pathways okay
+
+ align:start position:0%
+those vestibular pathways okay
+ 
+
+ align:start position:0%
+those vestibular pathways okay
+and then finally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in some of the parameterized monkeys
+
+ align:start position:0%
+in some of the parameterized monkeys
+ 
+
+ align:start position:0%
+in some of the parameterized monkeys
+they tried just doing the lateral
+
+ align:start position:0%
+they tried just doing the lateral
+ 
+
+ align:start position:0%
+they tried just doing the lateral
+pathways but only on one side and then
+
+ align:start position:0%
+pathways but only on one side and then
+ 
+
+ align:start position:0%
+pathways but only on one side and then
+we'll compare the two hands
+
+ align:start position:0%
+we'll compare the two hands
+ 
+
+ align:start position:0%
+we'll compare the two hands
+okay and you'll see
+
+ align:start position:0%
+okay and you'll see
+ 
+
+ align:start position:0%
+okay and you'll see
+how they affect the limp the hand
+
+ align:start position:0%
+how they affect the limp the hand
+ 
+
+ align:start position:0%
+how they affect the limp the hand
+movements now are mainly under control
+
+ align:start position:0%
+movements now are mainly under control
+ 
+
+ align:start position:0%
+movements now are mainly under control
+of that system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+could you hit that button and see if we
+
+ align:start position:0%
+could you hit that button and see if we
+ 
+
+ align:start position:0%
+could you hit that button and see if we
+can get the video
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh good
+
+ align:start position:0%
+oh good
+ 
+
+ align:start position:0%
+oh good
+okay so first just a normal animal and
+
+ align:start position:0%
+okay so first just a normal animal and
+ 
+
+ align:start position:0%
+okay so first just a normal animal and
+you'll see how they're testing him
+
+ align:start position:0%
+you'll see how they're testing him
+ 
+
+ align:start position:0%
+you'll see how they're testing him
+they have him strapped to the chair so
+
+ align:start position:0%
+they have him strapped to the chair so
+ 
+
+ align:start position:0%
+they have him strapped to the chair so
+he can't run around and they're
+
+ align:start position:0%
+he can't run around and they're
+ 
+
+ align:start position:0%
+he can't run around and they're
+presenting little pieces of apple here
+
+ align:start position:0%
+presenting little pieces of apple here
+ 
+
+ align:start position:0%
+presenting little pieces of apple here
+you see the normal animal
+
+ align:start position:0%
+you see the normal animal
+ 
+
+ align:start position:0%
+you see the normal animal
+very dexterous moves very fast
+
+ align:start position:0%
+very dexterous moves very fast
+ 
+
+ align:start position:0%
+very dexterous moves very fast
+can grab
+
+ align:start position:0%
+can grab
+ 
+
+ align:start position:0%
+can grab
+just about as well as we could
+
+ align:start position:0%
+just about as well as we could
+ 
+
+ align:start position:0%
+just about as well as we could
+the pieces of apple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and on this little board they make the
+
+ align:start position:0%
+and on this little board they make the
+ 
+
+ align:start position:0%
+and on this little board they make the
+holes smaller and smaller so he has to
+
+ align:start position:0%
+holes smaller and smaller so he has to
+ 
+
+ align:start position:0%
+holes smaller and smaller so he has to
+be more dexterous to get the
+
+ align:start position:0%
+be more dexterous to get the
+ 
+
+ align:start position:0%
+be more dexterous to get the
+apple out of the tiny holes and when he
+
+ align:start position:0%
+apple out of the tiny holes and when he
+ 
+
+ align:start position:0%
+apple out of the tiny holes and when he
+gets so excited he has a little problem
+
+ align:start position:0%
+gets so excited he has a little problem
+ 
+
+ align:start position:0%
+gets so excited he has a little problem
+but he can do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monkeys have hands similar to ours
+
+ align:start position:0%
+monkeys have hands similar to ours
+ 
+
+ align:start position:0%
+monkeys have hands similar to ours
+they're very dexterous okay they also
+
+ align:start position:0%
+they're very dexterous okay they also
+ 
+
+ align:start position:0%
+they're very dexterous okay they also
+have the opposing thumb
+
+ align:start position:0%
+have the opposing thumb
+ 
+
+ align:start position:0%
+have the opposing thumb
+although not nearly as good as ours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order to prevent the animal from
+
+ align:start position:0%
+in order to prevent the animal from
+ 
+
+ align:start position:0%
+in order to prevent the animal from
+using both hands they often have to hold
+
+ align:start position:0%
+using both hands they often have to hold
+ 
+
+ align:start position:0%
+using both hands they often have to hold
+or hold one hand down
+
+ align:start position:0%
+or hold one hand down
+ 
+
+ align:start position:0%
+or hold one hand down
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+monkeys that just get their dry food
+
+ align:start position:0%
+monkeys that just get their dry food
+ 
+
+ align:start position:0%
+monkeys that just get their dry food
+will always want this fruit
+
+ align:start position:0%
+will always want this fruit
+ 
+
+ align:start position:0%
+will always want this fruit
+okay so you don't have to deprive them
+
+ align:start position:0%
+okay so you don't have to deprive them
+ 
+
+ align:start position:0%
+okay so you don't have to deprive them
+much to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like hamsters with
+
+ align:start position:0%
+like hamsters with
+ 
+
+ align:start position:0%
+like hamsters with
+hamsters with sunflower seeds okay
+
+ align:start position:0%
+hamsters with sunflower seeds okay
+ 
+
+ align:start position:0%
+hamsters with sunflower seeds okay
+so now in these little holes he can't
+
+ align:start position:0%
+so now in these little holes he can't
+ 
+
+ align:start position:0%
+so now in these little holes he can't
+get it out unless he can use one digit
+
+ align:start position:0%
+get it out unless he can use one digit
+ 
+
+ align:start position:0%
+get it out unless he can use one digit
+he has to have some independent control
+
+ align:start position:0%
+he has to have some independent control
+ 
+
+ align:start position:0%
+he has to have some independent control
+of the one digit that's what they're
+
+ align:start position:0%
+of the one digit that's what they're
+ 
+
+ align:start position:0%
+of the one digit that's what they're
+showing here
+
+ align:start position:0%
+showing here
+ 
+
+ align:start position:0%
+showing here
+just like a person
+
+ align:start position:0%
+just like a person
+ 
+
+ align:start position:0%
+just like a person
+just like a person they're pretty good
+
+ align:start position:0%
+just like a person they're pretty good
+ 
+
+ align:start position:0%
+just like a person they're pretty good
+at that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now they do the pyramidal tract
+
+ align:start position:0%
+okay so now they do the pyramidal tract
+ 
+
+ align:start position:0%
+okay so now they do the pyramidal tract
+lesion and we're going to see him this
+
+ align:start position:0%
+lesion and we're going to see him this
+ 
+
+ align:start position:0%
+lesion and we're going to see him this
+first monkey five months later
+
+ align:start position:0%
+first monkey five months later
+ 
+
+ align:start position:0%
+first monkey five months later
+after that bilateral section at behind
+
+ align:start position:0%
+after that bilateral section at behind
+ 
+
+ align:start position:0%
+after that bilateral section at behind
+brain level of the pyramidal tract
+
+ align:start position:0%
+brain level of the pyramidal tract
+ 
+
+ align:start position:0%
+brain level of the pyramidal tract
+and on these histological sections
+
+ align:start position:0%
+and on these histological sections
+ 
+
+ align:start position:0%
+and on these histological sections
+if they're standing for myelin see the
+
+ align:start position:0%
+if they're standing for myelin see the
+ 
+
+ align:start position:0%
+if they're standing for myelin see the
+one at the bottom it's white at the
+
+ align:start position:0%
+one at the bottom it's white at the
+ 
+
+ align:start position:0%
+one at the bottom it's white at the
+bottom because the paranal tract it's
+
+ align:start position:0%
+bottom because the paranal tract it's
+ 
+
+ align:start position:0%
+bottom because the paranal tract it's
+lost it smile and this section this
+
+ align:start position:0%
+lost it smile and this section this
+ 
+
+ align:start position:0%
+lost it smile and this section this
+section
+
+ align:start position:0%
+section
+ 
+
+ align:start position:0%
+section
+there you see some torn tissue but you
+
+ align:start position:0%
+there you see some torn tissue but you
+ 
+
+ align:start position:0%
+there you see some torn tissue but you
+also see these dark areas
+
+ align:start position:0%
+also see these dark areas
+ 
+
+ align:start position:0%
+also see these dark areas
+that's an accumulation of glial cells
+
+ align:start position:0%
+that's an accumulation of glial cells
+ 
+
+ align:start position:0%
+that's an accumulation of glial cells
+it's called gliosis that happens with
+
+ align:start position:0%
+it's called gliosis that happens with
+ 
+
+ align:start position:0%
+it's called gliosis that happens with
+lesions okay
+
+ align:start position:0%
+lesions okay
+ 
+
+ align:start position:0%
+lesions okay
+the the glial cells are phagocytic they
+
+ align:start position:0%
+the the glial cells are phagocytic they
+ 
+
+ align:start position:0%
+the the glial cells are phagocytic they
+eat up the dead tissue and they
+
+ align:start position:0%
+eat up the dead tissue and they
+ 
+
+ align:start position:0%
+eat up the dead tissue and they
+accumulate and remain in these these
+
+ align:start position:0%
+accumulate and remain in these these
+ 
+
+ align:start position:0%
+accumulate and remain in these these
+lesions at least some of them remain
+
+ align:start position:0%
+lesions at least some of them remain
+ 
+
+ align:start position:0%
+lesions at least some of them remain
+okay so now this is five months he's
+
+ align:start position:0%
+okay so now this is five months he's
+ 
+
+ align:start position:0%
+okay so now this is five months he's
+recovered pretty well and pay attention
+
+ align:start position:0%
+recovered pretty well and pay attention
+ 
+
+ align:start position:0%
+recovered pretty well and pay attention
+to how he's using the hands he's not
+
+ align:start position:0%
+to how he's using the hands he's not
+ 
+
+ align:start position:0%
+to how he's using the hands he's not
+quite as fast but you will see that he
+
+ align:start position:0%
+quite as fast but you will see that he
+ 
+
+ align:start position:0%
+quite as fast but you will see that he
+moves the into all his fingers together
+
+ align:start position:0%
+moves the into all his fingers together
+ 
+
+ align:start position:0%
+moves the into all his fingers together
+like a baby grasping something
+
+ align:start position:0%
+like a baby grasping something
+ 
+
+ align:start position:0%
+like a baby grasping something
+okay a baby a newer human in the first
+
+ align:start position:0%
+okay a baby a newer human in the first
+ 
+
+ align:start position:0%
+okay a baby a newer human in the first
+few months of life doesn't have
+
+ align:start position:0%
+few months of life doesn't have
+ 
+
+ align:start position:0%
+few months of life doesn't have
+pyramidal track connections yet so he
+
+ align:start position:0%
+pyramidal track connections yet so he
+ 
+
+ align:start position:0%
+pyramidal track connections yet so he
+moves his hand like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or she's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you'll see that's pretty consistent
+
+ align:start position:0%
+and you'll see that's pretty consistent
+ 
+
+ align:start position:0%
+and you'll see that's pretty consistent
+here they use the whole hand together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they have pretty good control
+
+ align:start position:0%
+they have pretty good control
+ 
+
+ align:start position:0%
+they have pretty good control
+they tend to flex a little more than
+
+ align:start position:0%
+they tend to flex a little more than
+ 
+
+ align:start position:0%
+they tend to flex a little more than
+usual they have a flexor bias so they
+
+ align:start position:0%
+usual they have a flexor bias so they
+ 
+
+ align:start position:0%
+usual they have a flexor bias so they
+have to move the board a little closer
+
+ align:start position:0%
+have to move the board a little closer
+ 
+
+ align:start position:0%
+have to move the board a little closer
+but he can definitely
+
+ align:start position:0%
+but he can definitely
+ 
+
+ align:start position:0%
+but he can definitely
+do it
+
+ align:start position:0%
+do it
+ 
+
+ align:start position:0%
+do it
+now if you look
+
+ align:start position:0%
+now if you look
+ 
+
+ align:start position:0%
+now if you look
+sooner after the lesion you'll see a
+
+ align:start position:0%
+sooner after the lesion you'll see a
+ 
+
+ align:start position:0%
+sooner after the lesion you'll see a
+greater impairment because of the
+
+ align:start position:0%
+greater impairment because of the
+ 
+
+ align:start position:0%
+greater impairment because of the
+diasthesis effects
+
+ align:start position:0%
+diasthesis effects
+ 
+
+ align:start position:0%
+diasthesis effects
+of the removal of all those axons to the
+
+ align:start position:0%
+of the removal of all those axons to the
+ 
+
+ align:start position:0%
+of the removal of all those axons to the
+cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and later when they did the histology
+
+ align:start position:0%
+and later when they did the histology
+ 
+
+ align:start position:0%
+and later when they did the histology
+you saw the demyelinization of the
+
+ align:start position:0%
+you saw the demyelinization of the
+ 
+
+ align:start position:0%
+you saw the demyelinization of the
+primal tract it appeared to be a
+
+ align:start position:0%
+primal tract it appeared to be a
+ 
+
+ align:start position:0%
+primal tract it appeared to be a
+complete lesion
+
+ align:start position:0%
+complete lesion
+ 
+
+ align:start position:0%
+complete lesion
+and here you see the gliosis in the
+
+ align:start position:0%
+and here you see the gliosis in the
+ 
+
+ align:start position:0%
+and here you see the gliosis in the
+primal tract here you see the torn
+
+ align:start position:0%
+primal tract here you see the torn
+ 
+
+ align:start position:0%
+primal tract here you see the torn
+picture so with enough sections you can
+
+ align:start position:0%
+picture so with enough sections you can
+ 
+
+ align:start position:0%
+picture so with enough sections you can
+reconstruct the pathway of the knife
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difficult surgery to do because if you
+
+ align:start position:0%
+difficult surgery to do because if you
+ 
+
+ align:start position:0%
+difficult surgery to do because if you
+don't do it right in this part of the
+
+ align:start position:0%
+don't do it right in this part of the
+ 
+
+ align:start position:0%
+don't do it right in this part of the
+brain the animal will lose
+
+ align:start position:0%
+brain the animal will lose
+ 
+
+ align:start position:0%
+brain the animal will lose
+vital functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all you see that he's actually
+
+ align:start position:0%
+first of all you see that he's actually
+ 
+
+ align:start position:0%
+first of all you see that he's actually
+able to climb
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+his reflexes are slowed a bit
+
+ align:start position:0%
+his reflexes are slowed a bit
+ 
+
+ align:start position:0%
+his reflexes are slowed a bit
+but he's able to climb grasp his cage
+
+ align:start position:0%
+but he's able to climb grasp his cage
+ 
+
+ align:start position:0%
+but he's able to climb grasp his cage
+bars and so forth
+
+ align:start position:0%
+bars and so forth
+ 
+
+ align:start position:0%
+bars and so forth
+shows a lot of voluntary movement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the slow placing reflexes
+
+ align:start position:0%
+here's the slow placing reflexes
+ 
+
+ align:start position:0%
+here's the slow placing reflexes
+when you touch his chin this should be
+
+ align:start position:0%
+when you touch his chin this should be
+ 
+
+ align:start position:0%
+when you touch his chin this should be
+the most this is the greatest impairment
+
+ align:start position:0%
+the most this is the greatest impairment
+ 
+
+ align:start position:0%
+the most this is the greatest impairment
+you'll see just after parameter
+
+ align:start position:0%
+you'll see just after parameter
+ 
+
+ align:start position:0%
+you'll see just after parameter
+pyramidal track section now just
+
+ align:start position:0%
+pyramidal track section now just
+ 
+
+ align:start position:0%
+pyramidal track section now just
+corticospinal tract axons
+
+ align:start position:0%
+corticospinal tract axons
+ 
+
+ align:start position:0%
+corticospinal tract axons
+their lesions were pretty good
+
+ align:start position:0%
+their lesions were pretty good
+ 
+
+ align:start position:0%
+their lesions were pretty good
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+this animal died earlier but you do see
+
+ align:start position:0%
+this animal died earlier but you do see
+ 
+
+ align:start position:0%
+this animal died earlier but you do see
+the course of the knife here it has not
+
+ align:start position:0%
+the course of the knife here it has not
+ 
+
+ align:start position:0%
+the course of the knife here it has not
+had time to accumulate too many of the
+
+ align:start position:0%
+had time to accumulate too many of the
+ 
+
+ align:start position:0%
+had time to accumulate too many of the
+glia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if they spare some of the primal
+
+ align:start position:0%
+now if they spare some of the primal
+ 
+
+ align:start position:0%
+now if they spare some of the primal
+tract you will get
+
+ align:start position:0%
+tract you will get
+ 
+
+ align:start position:0%
+tract you will get
+you will get some sparing of the
+
+ align:start position:0%
+you will get some sparing of the
+ 
+
+ align:start position:0%
+you will get some sparing of the
+individual digit control
+
+ align:start position:0%
+individual digit control
+ 
+
+ align:start position:0%
+individual digit control
+many pathways in the brain in order to
+
+ align:start position:0%
+many pathways in the brain in order to
+ 
+
+ align:start position:0%
+many pathways in the brain in order to
+get a complete deficit you pretty much
+
+ align:start position:0%
+get a complete deficit you pretty much
+ 
+
+ align:start position:0%
+get a complete deficit you pretty much
+have to get the entire thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so neurologists who have not seen this
+
+ align:start position:0%
+so neurologists who have not seen this
+ 
+
+ align:start position:0%
+so neurologists who have not seen this
+study and
+
+ align:start position:0%
+study and
+ 
+
+ align:start position:0%
+study and
+have not seen humans of course very rare
+
+ align:start position:0%
+have not seen humans of course very rare
+ 
+
+ align:start position:0%
+have not seen humans of course very rare
+will have a parallel track section like
+
+ align:start position:0%
+will have a parallel track section like
+ 
+
+ align:start position:0%
+will have a parallel track section like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+they might be surprised that their
+
+ align:start position:0%
+they might be surprised that their
+ 
+
+ align:start position:0%
+they might be surprised that their
+textbooks
+
+ align:start position:0%
+textbooks
+ 
+
+ align:start position:0%
+textbooks
+are not correct about voluntary movement
+
+ align:start position:0%
+are not correct about voluntary movement
+ 
+
+ align:start position:0%
+are not correct about voluntary movement
+but notice here how he can climb
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+oh yes they can climb once they
+
+ align:start position:0%
+oh yes they can climb once they
+ 
+
+ align:start position:0%
+oh yes they can climb once they
+pretty much spinal mechanisms but they
+
+ align:start position:0%
+pretty much spinal mechanisms but they
+ 
+
+ align:start position:0%
+pretty much spinal mechanisms but they
+do learn of course
+
+ align:start position:0%
+do learn of course
+ 
+
+ align:start position:0%
+do learn of course
+details of
+
+ align:start position:0%
+details of
+ 
+
+ align:start position:0%
+details of
+cages
+
+ align:start position:0%
+cages
+ 
+
+ align:start position:0%
+cages
+compared with trees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think this animal when they feed him
+
+ align:start position:0%
+i think this animal when they feed him
+ 
+
+ align:start position:0%
+i think this animal when they feed him
+because he has difficulty reaching well
+
+ align:start position:0%
+because he has difficulty reaching well
+ 
+
+ align:start position:0%
+because he has difficulty reaching well
+he tries to get the food with like a dog
+
+ align:start position:0%
+he tries to get the food with like a dog
+ 
+
+ align:start position:0%
+he tries to get the food with like a dog
+just directly with his mouth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're just doing this to demonstrate
+
+ align:start position:0%
+they're just doing this to demonstrate
+ 
+
+ align:start position:0%
+they're just doing this to demonstrate
+that he has a lot of movement control
+
+ align:start position:0%
+that he has a lot of movement control
+ 
+
+ align:start position:0%
+that he has a lot of movement control
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+and here you see him he's a little
+
+ align:start position:0%
+and here you see him he's a little
+ 
+
+ align:start position:0%
+and here you see him he's a little
+reluctant to reach he wants to just
+
+ align:start position:0%
+reluctant to reach he wants to just
+ 
+
+ align:start position:0%
+reluctant to reach he wants to just
+reach out with his mouth and grab it
+
+ align:start position:0%
+reach out with his mouth and grab it
+ 
+
+ align:start position:0%
+reach out with his mouth and grab it
+because after just such a short time
+
+ align:start position:0%
+because after just such a short time
+ 
+
+ align:start position:0%
+because after just such a short time
+after the lesion he doesn't have good
+
+ align:start position:0%
+after the lesion he doesn't have good
+ 
+
+ align:start position:0%
+after the lesion he doesn't have good
+control of his hands
+
+ align:start position:0%
+control of his hands
+ 
+
+ align:start position:0%
+control of his hands
+okay but we know that not
+
+ align:start position:0%
+okay but we know that not
+ 
+
+ align:start position:0%
+okay but we know that not
+just give him a little time and that
+
+ align:start position:0%
+just give him a little time and that
+ 
+
+ align:start position:0%
+just give him a little time and that
+will come back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now before this study was done i should
+
+ align:start position:0%
+now before this study was done i should
+ 
+
+ align:start position:0%
+now before this study was done i should
+point out that
+
+ align:start position:0%
+point out that
+ 
+
+ align:start position:0%
+point out that
+clinical
+
+ align:start position:0%
+clinical
+ 
+
+ align:start position:0%
+clinical
+neurologist you know we're
+
+ align:start position:0%
+neurologist you know we're
+ 
+
+ align:start position:0%
+neurologist you know we're
+a little bit in the dark about
+
+ align:start position:0%
+a little bit in the dark about
+ 
+
+ align:start position:0%
+a little bit in the dark about
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+these lesions would do and so it was a
+
+ align:start position:0%
+these lesions would do and so it was a
+ 
+
+ align:start position:0%
+these lesions would do and so it was a
+very important study for human clinic
+
+ align:start position:0%
+very important study for human clinic
+ 
+
+ align:start position:0%
+very important study for human clinic
+okay so now remember these animals now
+
+ align:start position:0%
+okay so now remember these animals now
+ 
+
+ align:start position:0%
+okay so now remember these animals now
+you'll see all had the pyramid atomy
+
+ align:start position:0%
+you'll see all had the pyramid atomy
+ 
+
+ align:start position:0%
+you'll see all had the pyramid atomy
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+okay and there's the
+
+ align:start position:0%
+okay and there's the
+ 
+
+ align:start position:0%
+okay and there's the
+demolition of the pyramidal track the
+
+ align:start position:0%
+demolition of the pyramidal track the
+ 
+
+ align:start position:0%
+demolition of the pyramidal track the
+gliosis the pyramidal track but here
+
+ align:start position:0%
+gliosis the pyramidal track but here
+ 
+
+ align:start position:0%
+gliosis the pyramidal track but here
+they've shown you with they've drawn
+
+ align:start position:0%
+they've shown you with they've drawn
+ 
+
+ align:start position:0%
+they've shown you with they've drawn
+onto the section here the reconstructed
+
+ align:start position:0%
+onto the section here the reconstructed
+ 
+
+ align:start position:0%
+onto the section here the reconstructed
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+of the knife
+
+ align:start position:0%
+of the knife
+ 
+
+ align:start position:0%
+of the knife
+that so that in addition to the primal
+
+ align:start position:0%
+that so that in addition to the primal
+ 
+
+ align:start position:0%
+that so that in addition to the primal
+track section now they move the knife
+
+ align:start position:0%
+track section now they move the knife
+ 
+
+ align:start position:0%
+track section now they move the knife
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+through the brain stem so it cut all the
+
+ align:start position:0%
+through the brain stem so it cut all the
+ 
+
+ align:start position:0%
+through the brain stem so it cut all the
+pathways that travel medially in the
+
+ align:start position:0%
+pathways that travel medially in the
+ 
+
+ align:start position:0%
+pathways that travel medially in the
+hind brain all right
+
+ align:start position:0%
+hind brain all right
+ 
+
+ align:start position:0%
+hind brain all right
+so this will be the most impaired animal
+
+ align:start position:0%
+so this will be the most impaired animal
+ 
+
+ align:start position:0%
+so this will be the most impaired animal
+you'll see
+
+ align:start position:0%
+you'll see
+ 
+
+ align:start position:0%
+you'll see
+i know it's a little disturbing to some
+
+ align:start position:0%
+i know it's a little disturbing to some
+ 
+
+ align:start position:0%
+i know it's a little disturbing to some
+of you to see the animal that can't get
+
+ align:start position:0%
+of you to see the animal that can't get
+ 
+
+ align:start position:0%
+of you to see the animal that can't get
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+but it didn't last forever
+
+ align:start position:0%
+but it didn't last forever
+ 
+
+ align:start position:0%
+but it didn't last forever
+but he's
+
+ align:start position:0%
+but he's
+ 
+
+ align:start position:0%
+but he's
+now with no pyramidal tract and without
+
+ align:start position:0%
+now with no pyramidal tract and without
+ 
+
+ align:start position:0%
+now with no pyramidal tract and without
+the medial pathways he's
+
+ align:start position:0%
+the medial pathways he's
+ 
+
+ align:start position:0%
+the medial pathways he's
+he doesn't have good axial control
+
+ align:start position:0%
+he doesn't have good axial control
+ 
+
+ align:start position:0%
+he doesn't have good axial control
+okay so he doesn't have his writing
+
+ align:start position:0%
+okay so he doesn't have his writing
+ 
+
+ align:start position:0%
+okay so he doesn't have his writing
+responses it was only with recovery from
+
+ align:start position:0%
+responses it was only with recovery from
+ 
+
+ align:start position:0%
+responses it was only with recovery from
+diasthesis that he was able then to
+
+ align:start position:0%
+diasthesis that he was able then to
+ 
+
+ align:start position:0%
+diasthesis that he was able then to
+recover some sensory control final
+
+ align:start position:0%
+recover some sensory control final
+ 
+
+ align:start position:0%
+recover some sensory control final
+control of writing and he was able to
+
+ align:start position:0%
+control of writing and he was able to
+ 
+
+ align:start position:0%
+control of writing and he was able to
+get up after 40 days
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you'll see in a minute here that
+
+ align:start position:0%
+and you'll see in a minute here that
+ 
+
+ align:start position:0%
+and you'll see in a minute here that
+these animals that can be so entirely
+
+ align:start position:0%
+these animals that can be so entirely
+ 
+
+ align:start position:0%
+these animals that can be so entirely
+almost helpless in these situations
+
+ align:start position:0%
+almost helpless in these situations
+ 
+
+ align:start position:0%
+almost helpless in these situations
+actually have quite a bit of control for
+
+ align:start position:0%
+actually have quite a bit of control for
+ 
+
+ align:start position:0%
+actually have quite a bit of control for
+one thing they have good head control
+
+ align:start position:0%
+one thing they have good head control
+ 
+
+ align:start position:0%
+one thing they have good head control
+this is now
+
+ align:start position:0%
+this is now
+ 
+
+ align:start position:0%
+this is now
+a little later
+
+ align:start position:0%
+a little later
+ 
+
+ align:start position:0%
+a little later
+five months after param diatomy one
+
+ align:start position:0%
+five months after param diatomy one
+ 
+
+ align:start position:0%
+five months after param diatomy one
+month after the medial reticular
+
+ align:start position:0%
+month after the medial reticular
+ 
+
+ align:start position:0%
+month after the medial reticular
+formation lesion
+
+ align:start position:0%
+formation lesion
+ 
+
+ align:start position:0%
+formation lesion
+it's a different animal they're showing
+
+ align:start position:0%
+it's a different animal they're showing
+ 
+
+ align:start position:0%
+it's a different animal they're showing
+the lesion here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+showing the gliosis in the pyramidal
+
+ align:start position:0%
+showing the gliosis in the pyramidal
+ 
+
+ align:start position:0%
+showing the gliosis in the pyramidal
+tract and there you can see
+
+ align:start position:0%
+tract and there you can see
+ 
+
+ align:start position:0%
+tract and there you can see
+where the knife passed the medial lesion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're not showing the midbrain so we
+
+ align:start position:0%
+they're not showing the midbrain so we
+ 
+
+ align:start position:0%
+they're not showing the midbrain so we
+can't see the red nucleus but they did
+
+ align:start position:0%
+can't see the red nucleus but they did
+ 
+
+ align:start position:0%
+can't see the red nucleus but they did
+look at that and they know they spared
+
+ align:start position:0%
+look at that and they know they spared
+ 
+
+ align:start position:0%
+look at that and they know they spared
+the lateral brainstem pathways that come
+
+ align:start position:0%
+the lateral brainstem pathways that come
+ 
+
+ align:start position:0%
+the lateral brainstem pathways that come
+from the red nucleus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they'll show those sections when they in
+
+ align:start position:0%
+they'll show those sections when they in
+ 
+
+ align:start position:0%
+they'll show those sections when they in
+the cases where they did that lesion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they cut off a lot of the section the
+
+ align:start position:0%
+they cut off a lot of the section the
+ 
+
+ align:start position:0%
+they cut off a lot of the section the
+cerebellum would be
+
+ align:start position:0%
+cerebellum would be
+ 
+
+ align:start position:0%
+cerebellum would be
+huge here in the monkey
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these are at
+
+ align:start position:0%
+and these are at
+ 
+
+ align:start position:0%
+and these are at
+this one is at the cerebellar level
+
+ align:start position:0%
+this one is at the cerebellar level
+ 
+
+ align:start position:0%
+this one is at the cerebellar level
+and there you see a little bit of
+
+ align:start position:0%
+and there you see a little bit of
+ 
+
+ align:start position:0%
+and there you see a little bit of
+cerebellum at the top there that's
+
+ align:start position:0%
+cerebellum at the top there that's
+ 
+
+ align:start position:0%
+cerebellum at the top there that's
+cerebellar granule cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now they're starting out with
+
+ align:start position:0%
+okay now they're starting out with
+ 
+
+ align:start position:0%
+okay now they're starting out with
+showing the animal in the reaching
+
+ align:start position:0%
+showing the animal in the reaching
+ 
+
+ align:start position:0%
+showing the animal in the reaching
+situation now he's strapped to the chair
+
+ align:start position:0%
+situation now he's strapped to the chair
+ 
+
+ align:start position:0%
+situation now he's strapped to the chair
+they have to strap into the chair
+
+ align:start position:0%
+they have to strap into the chair
+ 
+
+ align:start position:0%
+they have to strap into the chair
+because he doesn't have good balance so
+
+ align:start position:0%
+because he doesn't have good balance so
+ 
+
+ align:start position:0%
+because he doesn't have good balance so
+they they hold him like
+
+ align:start position:0%
+they they hold him like
+ 
+
+ align:start position:0%
+they they hold him like
+that and now he's holding his arms and
+
+ align:start position:0%
+that and now he's holding his arms and
+ 
+
+ align:start position:0%
+that and now he's holding his arms and
+usually flex but in fact he can grasp
+
+ align:start position:0%
+usually flex but in fact he can grasp
+ 
+
+ align:start position:0%
+usually flex but in fact he can grasp
+the food
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as long as they allow him to
+
+ align:start position:0%
+as long as they allow him to
+ 
+
+ align:start position:0%
+as long as they allow him to
+be a little bit hyper flexed he can
+
+ align:start position:0%
+be a little bit hyper flexed he can
+ 
+
+ align:start position:0%
+be a little bit hyper flexed he can
+grasp the food he does it with whole
+
+ align:start position:0%
+grasp the food he does it with whole
+ 
+
+ align:start position:0%
+grasp the food he does it with whole
+hand movements he's still pretty slow
+
+ align:start position:0%
+hand movements he's still pretty slow
+ 
+
+ align:start position:0%
+hand movements he's still pretty slow
+because he hasn't recovered enough from
+
+ align:start position:0%
+because he hasn't recovered enough from
+ 
+
+ align:start position:0%
+because he hasn't recovered enough from
+the lesion yet so this is just a month
+
+ align:start position:0%
+the lesion yet so this is just a month
+ 
+
+ align:start position:0%
+the lesion yet so this is just a month
+later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you see he's recovered a little bit
+
+ align:start position:0%
+and you see he's recovered a little bit
+ 
+
+ align:start position:0%
+and you see he's recovered a little bit
+he's now better at grasping the apple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll see later that that movement
+
+ align:start position:0%
+and we'll see later that that movement
+ 
+
+ align:start position:0%
+and we'll see later that that movement
+is more dependent on that pathway from
+
+ align:start position:0%
+is more dependent on that pathway from
+ 
+
+ align:start position:0%
+is more dependent on that pathway from
+the midbrain from the red nucleus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again they're holding one hand down so
+
+ align:start position:0%
+again they're holding one hand down so
+ 
+
+ align:start position:0%
+again they're holding one hand down so
+you can just use one at a time
+
+ align:start position:0%
+you can just use one at a time
+ 
+
+ align:start position:0%
+you can just use one at a time
+they test the two hands separately
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when they offer him
+
+ align:start position:0%
+when they offer him
+ 
+
+ align:start position:0%
+when they offer him
+when he has to use one digit to get the
+
+ align:start position:0%
+when he has to use one digit to get the
+ 
+
+ align:start position:0%
+when he has to use one digit to get the
+apple out of the small holes he can't do
+
+ align:start position:0%
+apple out of the small holes he can't do
+ 
+
+ align:start position:0%
+apple out of the small holes he can't do
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it shows that he's got pretty vigorous
+
+ align:start position:0%
+it shows that he's got pretty vigorous
+ 
+
+ align:start position:0%
+it shows that he's got pretty vigorous
+responses of his limbs in the tests of
+
+ align:start position:0%
+responses of his limbs in the tests of
+ 
+
+ align:start position:0%
+responses of his limbs in the tests of
+placing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know this is a different monkey
+
+ align:start position:0%
+you know this is a different monkey
+ 
+
+ align:start position:0%
+you know this is a different monkey
+again with the pyramidal tract lesion
+
+ align:start position:0%
+again with the pyramidal tract lesion
+ 
+
+ align:start position:0%
+again with the pyramidal tract lesion
+and then two months after the medial
+
+ align:start position:0%
+and then two months after the medial
+ 
+
+ align:start position:0%
+and then two months after the medial
+hind brain reticular formation so this
+
+ align:start position:0%
+hind brain reticular formation so this
+ 
+
+ align:start position:0%
+hind brain reticular formation so this
+is just a replication
+
+ align:start position:0%
+is just a replication
+ 
+
+ align:start position:0%
+is just a replication
+of that experiment
+
+ align:start position:0%
+of that experiment
+ 
+
+ align:start position:0%
+of that experiment
+you see the
+
+ align:start position:0%
+you see the
+ 
+
+ align:start position:0%
+you see the
+demyelinization and the gliosis and the
+
+ align:start position:0%
+demyelinization and the gliosis and the
+ 
+
+ align:start position:0%
+demyelinization and the gliosis and the
+primal tract
+
+ align:start position:0%
+primal tract
+ 
+
+ align:start position:0%
+primal tract
+and then the reconstruction of the you
+
+ align:start position:0%
+and then the reconstruction of the you
+ 
+
+ align:start position:0%
+and then the reconstruction of the you
+see a little bit of the lesion here
+
+ align:start position:0%
+see a little bit of the lesion here
+ 
+
+ align:start position:0%
+see a little bit of the lesion here
+nucleotic areas
+
+ align:start position:0%
+nucleotic areas
+ 
+
+ align:start position:0%
+nucleotic areas
+you need to see all the sections
+
+ align:start position:0%
+you need to see all the sections
+ 
+
+ align:start position:0%
+you need to see all the sections
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this animal when he walks
+
+ align:start position:0%
+so this animal when he walks
+ 
+
+ align:start position:0%
+so this animal when he walks
+in very good poor control of his
+
+ align:start position:0%
+in very good poor control of his
+ 
+
+ align:start position:0%
+in very good poor control of his
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're just making him and there he
+
+ align:start position:0%
+they're just making him and there he
+ 
+
+ align:start position:0%
+they're just making him and there he
+falls over
+
+ align:start position:0%
+falls over
+ 
+
+ align:start position:0%
+falls over
+and you see he wasn't able to write
+
+ align:start position:0%
+and you see he wasn't able to write
+ 
+
+ align:start position:0%
+and you see he wasn't able to write
+himself very rapidly his medicine
+
+ align:start position:0%
+himself very rapidly his medicine
+ 
+
+ align:start position:0%
+himself very rapidly his medicine
+writing responses haven't
+
+ align:start position:0%
+writing responses haven't
+ 
+
+ align:start position:0%
+writing responses haven't
+come back much
+
+ align:start position:0%
+come back much
+ 
+
+ align:start position:0%
+come back much
+of course now if this were a normal
+
+ align:start position:0%
+of course now if this were a normal
+ 
+
+ align:start position:0%
+of course now if this were a normal
+monkey he would just pick it up
+
+ align:start position:0%
+monkey he would just pick it up
+ 
+
+ align:start position:0%
+monkey he would just pick it up
+but without the primal trackies a little
+
+ align:start position:0%
+but without the primal trackies a little
+ 
+
+ align:start position:0%
+but without the primal trackies a little
+more like a dog
+
+ align:start position:0%
+more like a dog
+ 
+
+ align:start position:0%
+more like a dog
+in the way he responds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very unsteady with the lack of
+
+ align:start position:0%
+very unsteady with the lack of
+ 
+
+ align:start position:0%
+very unsteady with the lack of
+vestibular spinal
+
+ align:start position:0%
+vestibular spinal
+ 
+
+ align:start position:0%
+vestibular spinal
+and without the tactile spinal he's also
+
+ align:start position:0%
+and without the tactile spinal he's also
+ 
+
+ align:start position:0%
+and without the tactile spinal he's also
+not very good at orienting his head and
+
+ align:start position:0%
+not very good at orienting his head and
+ 
+
+ align:start position:0%
+not very good at orienting his head and
+eyes
+
+ align:start position:0%
+eyes
+ 
+
+ align:start position:0%
+eyes
+his eye movements by the way are
+
+ align:start position:0%
+his eye movements by the way are
+ 
+
+ align:start position:0%
+his eye movements by the way are
+actually pretty normal if you
+
+ align:start position:0%
+actually pretty normal if you
+ 
+
+ align:start position:0%
+actually pretty normal if you
+see him in the chair and study them and
+
+ align:start position:0%
+see him in the chair and study them and
+ 
+
+ align:start position:0%
+see him in the chair and study them and
+that's because he has the connections to
+
+ align:start position:0%
+that's because he has the connections to
+ 
+
+ align:start position:0%
+that's because he has the connections to
+the ocular motor nuclei intact
+
+ align:start position:0%
+the ocular motor nuclei intact
+ 
+
+ align:start position:0%
+the ocular motor nuclei intact
+they've cut those pathways further down
+
+ align:start position:0%
+they've cut those pathways further down
+ 
+
+ align:start position:0%
+they've cut those pathways further down
+behind brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now this will be the first of
+
+ align:start position:0%
+okay so now this will be the first of
+ 
+
+ align:start position:0%
+okay so now this will be the first of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+third type of animal where they have
+
+ align:start position:0%
+third type of animal where they have
+ 
+
+ align:start position:0%
+third type of animal where they have
+paramidotomy first and then
+
+ align:start position:0%
+paramidotomy first and then
+ 
+
+ align:start position:0%
+paramidotomy first and then
+this is just a short a few days five
+
+ align:start position:0%
+this is just a short a few days five
+ 
+
+ align:start position:0%
+this is just a short a few days five
+days after the lesion of the lateral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behind brain you see it right here
+
+ align:start position:0%
+behind brain you see it right here
+ 
+
+ align:start position:0%
+behind brain you see it right here
+he's missing the primal tract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is working less and less okay there
+
+ align:start position:0%
+this is working less and less okay there
+ 
+
+ align:start position:0%
+this is working less and less okay there
+you see it
+
+ align:start position:0%
+you see it
+ 
+
+ align:start position:0%
+you see it
+see the gliosis
+
+ align:start position:0%
+see the gliosis
+ 
+
+ align:start position:0%
+see the gliosis
+and the question is now did they cut the
+
+ align:start position:0%
+and the question is now did they cut the
+ 
+
+ align:start position:0%
+and the question is now did they cut the
+ribospinal tract if you look up here
+
+ align:start position:0%
+ribospinal tract if you look up here
+ 
+
+ align:start position:0%
+ribospinal tract if you look up here
+there's some big neurons in the red
+
+ align:start position:0%
+there's some big neurons in the red
+ 
+
+ align:start position:0%
+there's some big neurons in the red
+nucleus there and we can't see any there
+
+ align:start position:0%
+nucleus there and we can't see any there
+ 
+
+ align:start position:0%
+nucleus there and we can't see any there
+in the red nucleus in the midbrain this
+
+ align:start position:0%
+in the red nucleus in the midbrain this
+ 
+
+ align:start position:0%
+in the red nucleus in the midbrain this
+is midbrain level that's the
+
+ align:start position:0%
+is midbrain level that's the
+ 
+
+ align:start position:0%
+is midbrain level that's the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+cerebral peduncle down there
+
+ align:start position:0%
+cerebral peduncle down there
+ 
+
+ align:start position:0%
+cerebral peduncle down there
+okay so it looks like a good lesion even
+
+ align:start position:0%
+okay so it looks like a good lesion even
+ 
+
+ align:start position:0%
+okay so it looks like a good lesion even
+though it was small it seemed to have
+
+ align:start position:0%
+though it was small it seemed to have
+ 
+
+ align:start position:0%
+though it was small it seemed to have
+severed the ribospinal tract in the
+
+ align:start position:0%
+severed the ribospinal tract in the
+ 
+
+ align:start position:0%
+severed the ribospinal tract in the
+hindbrain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now they're going to test the two hands
+
+ align:start position:0%
+now they're going to test the two hands
+ 
+
+ align:start position:0%
+now they're going to test the two hands
+separately
+
+ align:start position:0%
+separately
+ 
+
+ align:start position:0%
+separately
+you see the left hand
+
+ align:start position:0%
+you see the left hand
+ 
+
+ align:start position:0%
+you see the left hand
+is pretty good and he can reach he's got
+
+ align:start position:0%
+is pretty good and he can reach he's got
+ 
+
+ align:start position:0%
+is pretty good and he can reach he's got
+some control of his shoulders
+
+ align:start position:0%
+some control of his shoulders
+ 
+
+ align:start position:0%
+some control of his shoulders
+but very very poor control almost no
+
+ align:start position:0%
+but very very poor control almost no
+ 
+
+ align:start position:0%
+but very very poor control almost no
+control now left of his
+
+ align:start position:0%
+control now left of his
+ 
+
+ align:start position:0%
+control now left of his
+most distal muscles there with the left
+
+ align:start position:0%
+most distal muscles there with the left
+ 
+
+ align:start position:0%
+most distal muscles there with the left
+hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if he can he learns later to sort of
+
+ align:start position:0%
+if he can he learns later to sort of
+ 
+
+ align:start position:0%
+if he can he learns later to sort of
+engage his whole body in doing it and
+
+ align:start position:0%
+engage his whole body in doing it and
+ 
+
+ align:start position:0%
+engage his whole body in doing it and
+then sometimes he can get the spinal
+
+ align:start position:0%
+then sometimes he can get the spinal
+ 
+
+ align:start position:0%
+then sometimes he can get the spinal
+mechanisms of whole body control
+
+ align:start position:0%
+mechanisms of whole body control
+ 
+
+ align:start position:0%
+mechanisms of whole body control
+activated and he gets a little bit
+
+ align:start position:0%
+activated and he gets a little bit
+ 
+
+ align:start position:0%
+activated and he gets a little bit
+better control of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we'll see him one and then two
+
+ align:start position:0%
+okay so we'll see him one and then two
+ 
+
+ align:start position:0%
+okay so we'll see him one and then two
+months after the right
+
+ align:start position:0%
+months after the right
+ 
+
+ align:start position:0%
+months after the right
+lateral pontine lesion so the same
+
+ align:start position:0%
+lateral pontine lesion so the same
+ 
+
+ align:start position:0%
+lateral pontine lesion so the same
+simulation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the hand that's not affected
+
+ align:start position:0%
+the hand that's not affected
+ 
+
+ align:start position:0%
+the hand that's not affected
+by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+section of the descending lateral
+
+ align:start position:0%
+section of the descending lateral
+ 
+
+ align:start position:0%
+section of the descending lateral
+pathway
+
+ align:start position:0%
+pathway
+ 
+
+ align:start position:0%
+pathway
+and here's the side that is affected
+
+ align:start position:0%
+and here's the side that is affected
+ 
+
+ align:start position:0%
+and here's the side that is affected
+and again if they let him engage his
+
+ align:start position:0%
+and again if they let him engage his
+ 
+
+ align:start position:0%
+and again if they let him engage his
+whole arm
+
+ align:start position:0%
+whole arm
+ 
+
+ align:start position:0%
+whole arm
+he can sometimes do it he's learned a
+
+ align:start position:0%
+he can sometimes do it he's learned a
+ 
+
+ align:start position:0%
+he can sometimes do it he's learned a
+little bit about that but
+
+ align:start position:0%
+little bit about that but
+ 
+
+ align:start position:0%
+little bit about that but
+if he doesn't get his whole body
+
+ align:start position:0%
+if he doesn't get his whole body
+ 
+
+ align:start position:0%
+if he doesn't get his whole body
+and doing it
+
+ align:start position:0%
+and doing it
+ 
+
+ align:start position:0%
+and doing it
+he can't
+
+ align:start position:0%
+he can't
+ 
+
+ align:start position:0%
+he can't
+he doesn't have good individual control
+
+ align:start position:0%
+he doesn't have good individual control
+ 
+
+ align:start position:0%
+he doesn't have good individual control
+of the hand at all
+
+ align:start position:0%
+of the hand at all
+ 
+
+ align:start position:0%
+of the hand at all
+so much worse than just the medial
+
+ align:start position:0%
+so much worse than just the medial
+ 
+
+ align:start position:0%
+so much worse than just the medial
+pathway
+
+ align:start position:0%
+pathway
+ 
+
+ align:start position:0%
+pathway
+sorry just the pyramidal tract
+
+ align:start position:0%
+sorry just the pyramidal tract
+ 
+
+ align:start position:0%
+sorry just the pyramidal tract
+it's it's added a considerable amount of
+
+ align:start position:0%
+it's it's added a considerable amount of
+ 
+
+ align:start position:0%
+it's it's added a considerable amount of
+deficiency to the
+
+ align:start position:0%
+deficiency to the
+ 
+
+ align:start position:0%
+deficiency to the
+control of the hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you'll see that something quite
+
+ align:start position:0%
+and then you'll see that something quite
+ 
+
+ align:start position:0%
+and then you'll see that something quite
+remarkable here in a minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+poor individual control when they're
+
+ align:start position:0%
+poor individual control when they're
+ 
+
+ align:start position:0%
+poor individual control when they're
+getting to use that limb by itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here they're just showing that it
+
+ align:start position:0%
+here they're just showing that it
+ 
+
+ align:start position:0%
+here they're just showing that it
+doesn't depend on
+
+ align:start position:0%
+doesn't depend on
+ 
+
+ align:start position:0%
+doesn't depend on
+his posture some there are some
+
+ align:start position:0%
+his posture some there are some
+ 
+
+ align:start position:0%
+his posture some there are some
+neurological deficits where you change
+
+ align:start position:0%
+neurological deficits where you change
+ 
+
+ align:start position:0%
+neurological deficits where you change
+the posture they might do a lot better
+
+ align:start position:0%
+the posture they might do a lot better
+ 
+
+ align:start position:0%
+the posture they might do a lot better
+but you'll see is about the same
+
+ align:start position:0%
+but you'll see is about the same
+ 
+
+ align:start position:0%
+but you'll see is about the same
+in this posture
+
+ align:start position:0%
+in this posture
+ 
+
+ align:start position:0%
+in this posture
+i can control the arm a little bit from
+
+ align:start position:0%
+i can control the arm a little bit from
+ 
+
+ align:start position:0%
+i can control the arm a little bit from
+the shoulder but that's about it
+
+ align:start position:0%
+the shoulder but that's about it
+ 
+
+ align:start position:0%
+the shoulder but that's about it
+unless he can make his scooping movement
+
+ align:start position:0%
+unless he can make his scooping movement
+ 
+
+ align:start position:0%
+unless he can make his scooping movement
+with his whole body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they tried very hard to get them to
+
+ align:start position:0%
+and they tried very hard to get them to
+ 
+
+ align:start position:0%
+and they tried very hard to get them to
+recover and they they did get a little
+
+ align:start position:0%
+recover and they they did get a little
+ 
+
+ align:start position:0%
+recover and they they did get a little
+bit it was important for the human
+
+ align:start position:0%
+bit it was important for the human
+ 
+
+ align:start position:0%
+bit it was important for the human
+studies to know just how far can the
+
+ align:start position:0%
+studies to know just how far can the
+ 
+
+ align:start position:0%
+studies to know just how far can the
+recovery go
+
+ align:start position:0%
+recovery go
+ 
+
+ align:start position:0%
+recovery go
+you know and there's anything they could
+
+ align:start position:0%
+you know and there's anything they could
+ 
+
+ align:start position:0%
+you know and there's anything they could
+do to promote it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now you'll see some other responses
+
+ align:start position:0%
+and now you'll see some other responses
+ 
+
+ align:start position:0%
+and now you'll see some other responses
+where he's now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+able to use whole body movements more
+
+ align:start position:0%
+able to use whole body movements more
+ 
+
+ align:start position:0%
+able to use whole body movements more
+and you'll see it's much harder now to
+
+ align:start position:0%
+and you'll see it's much harder now to
+ 
+
+ align:start position:0%
+and you'll see it's much harder now to
+tell which is the limb affected by the
+
+ align:start position:0%
+tell which is the limb affected by the
+ 
+
+ align:start position:0%
+tell which is the limb affected by the
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+lesion
+
+ align:start position:0%
+lesion
+ 
+
+ align:start position:0%
+lesion
+especially here he's using both hands
+
+ align:start position:0%
+especially here he's using both hands
+ 
+
+ align:start position:0%
+especially here he's using both hands
+he's grasping the cage
+
+ align:start position:0%
+he's grasping the cage
+ 
+
+ align:start position:0%
+he's grasping the cage
+the same hand that could not grasp the
+
+ align:start position:0%
+the same hand that could not grasp the
+ 
+
+ align:start position:0%
+the same hand that could not grasp the
+apple pieces is grasping the cage why
+
+ align:start position:0%
+apple pieces is grasping the cage why
+ 
+
+ align:start position:0%
+apple pieces is grasping the cage why
+because when we think of the word
+
+ align:start position:0%
+because when we think of the word
+ 
+
+ align:start position:0%
+because when we think of the word
+paralysis
+
+ align:start position:0%
+paralysis
+ 
+
+ align:start position:0%
+paralysis
+it's sometimes very specific to the type
+
+ align:start position:0%
+it's sometimes very specific to the type
+ 
+
+ align:start position:0%
+it's sometimes very specific to the type
+of movement
+
+ align:start position:0%
+of movement
+ 
+
+ align:start position:0%
+of movement
+okay he cannot use the hand in one
+
+ align:start position:0%
+okay he cannot use the hand in one
+ 
+
+ align:start position:0%
+okay he cannot use the hand in one
+situation
+
+ align:start position:0%
+situation
+ 
+
+ align:start position:0%
+situation
+but in climbing
+
+ align:start position:0%
+but in climbing
+ 
+
+ align:start position:0%
+but in climbing
+fixed action patterns governed by a
+
+ align:start position:0%
+fixed action patterns governed by a
+ 
+
+ align:start position:0%
+fixed action patterns governed by a
+hindbrain and spinal cord he can do
+
+ align:start position:0%
+hindbrain and spinal cord he can do
+ 
+
+ align:start position:0%
+hindbrain and spinal cord he can do
+quite well
+
+ align:start position:0%
+quite well
+ 
+
+ align:start position:0%
+quite well
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's an important point
+
+ align:start position:0%
+that's an important point
+ 
+
+ align:start position:0%
+that's an important point
+this is the very same animal
+
+ align:start position:0%
+this is the very same animal
+ 
+
+ align:start position:0%
+this is the very same animal
+very hard to tell which is the defective
+
+ align:start position:0%
+very hard to tell which is the defective
+ 
+
+ align:start position:0%
+very hard to tell which is the defective
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+so this is now
+
+ align:start position:0%
+so this is now
+ 
+
+ align:start position:0%
+so this is now
+a similar
+
+ align:start position:0%
+a similar
+ 
+
+ align:start position:0%
+a similar
+replication of that experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case though
+
+ align:start position:0%
+in this case though
+ 
+
+ align:start position:0%
+in this case though
+the lesion of the hindbrain it looks
+
+ align:start position:0%
+the lesion of the hindbrain it looks
+ 
+
+ align:start position:0%
+the lesion of the hindbrain it looks
+larger here but in fact they missed some
+
+ align:start position:0%
+larger here but in fact they missed some
+ 
+
+ align:start position:0%
+larger here but in fact they missed some
+of the rubospinal tract because you see
+
+ align:start position:0%
+of the rubospinal tract because you see
+ 
+
+ align:start position:0%
+of the rubospinal tract because you see
+some large neurons here in the red
+
+ align:start position:0%
+some large neurons here in the red
+ 
+
+ align:start position:0%
+some large neurons here in the red
+nucleus soy if i'm right i think this
+
+ align:start position:0%
+nucleus soy if i'm right i think this
+ 
+
+ align:start position:0%
+nucleus soy if i'm right i think this
+animal shows more sparing
+
+ align:start position:0%
+animal shows more sparing
+ 
+
+ align:start position:0%
+animal shows more sparing
+that was why it's always important when
+
+ align:start position:0%
+that was why it's always important when
+ 
+
+ align:start position:0%
+that was why it's always important when
+you do such studies to do careful
+
+ align:start position:0%
+you do such studies to do careful
+ 
+
+ align:start position:0%
+you do such studies to do careful
+histology and do your best to
+
+ align:start position:0%
+histology and do your best to
+ 
+
+ align:start position:0%
+histology and do your best to
+reconstruct exactly what you did in the
+
+ align:start position:0%
+reconstruct exactly what you did in the
+ 
+
+ align:start position:0%
+reconstruct exactly what you did in the
+surgery
+
+ align:start position:0%
+surgery
+ 
+
+ align:start position:0%
+surgery
+it's not always possible to control it
+
+ align:start position:0%
+it's not always possible to control it
+ 
+
+ align:start position:0%
+it's not always possible to control it
+perfectly and also there's a little bit
+
+ align:start position:0%
+perfectly and also there's a little bit
+ 
+
+ align:start position:0%
+perfectly and also there's a little bit
+of variation
+
+ align:start position:0%
+of variation
+ 
+
+ align:start position:0%
+of variation
+from animal to animal and exactly how
+
+ align:start position:0%
+from animal to animal and exactly how
+ 
+
+ align:start position:0%
+from animal to animal and exactly how
+those pathways travel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see the central gray there
+
+ align:start position:0%
+see the central gray there
+ 
+
+ align:start position:0%
+see the central gray there
+several pineapples down here
+
+ align:start position:0%
+several pineapples down here
+ 
+
+ align:start position:0%
+several pineapples down here
+this would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+certainly deficient but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more control than the other animals
+
+ align:start position:0%
+more control than the other animals
+ 
+
+ align:start position:0%
+more control than the other animals
+just with the sparing of a
+
+ align:start position:0%
+just with the sparing of a
+ 
+
+ align:start position:0%
+just with the sparing of a
+small part
+
+ align:start position:0%
+small part
+ 
+
+ align:start position:0%
+small part
+of that pathway
+
+ align:start position:0%
+of that pathway
+ 
+
+ align:start position:0%
+of that pathway
+and that's why in human cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a tumor or something that's gradually
+
+ align:start position:0%
+a tumor or something that's gradually
+ 
+
+ align:start position:0%
+a tumor or something that's gradually
+destroying more and more of a pathway
+
+ align:start position:0%
+destroying more and more of a pathway
+ 
+
+ align:start position:0%
+destroying more and more of a pathway
+sometimes you will not see the defect
+
+ align:start position:0%
+sometimes you will not see the defect
+ 
+
+ align:start position:0%
+sometimes you will not see the defect
+until it's almost completely destroyed a
+
+ align:start position:0%
+until it's almost completely destroyed a
+ 
+
+ align:start position:0%
+until it's almost completely destroyed a
+pathway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now here they're making the lesion
+
+ align:start position:0%
+okay now here they're making the lesion
+ 
+
+ align:start position:0%
+okay now here they're making the lesion
+further down so now they're getting the
+
+ align:start position:0%
+further down so now they're getting the
+ 
+
+ align:start position:0%
+further down so now they're getting the
+lateral pathway
+
+ align:start position:0%
+lateral pathway
+ 
+
+ align:start position:0%
+lateral pathway
+in the medullary region
+
+ align:start position:0%
+in the medullary region
+ 
+
+ align:start position:0%
+in the medullary region
+it's a little easier to get all of it
+
+ align:start position:0%
+it's a little easier to get all of it
+ 
+
+ align:start position:0%
+it's a little easier to get all of it
+here you see in the this is medulla
+
+ align:start position:0%
+here you see in the this is medulla
+ 
+
+ align:start position:0%
+here you see in the this is medulla
+oblongata the coral part of the
+
+ align:start position:0%
+oblongata the coral part of the
+ 
+
+ align:start position:0%
+oblongata the coral part of the
+hindbrain and you see the lesion there
+
+ align:start position:0%
+hindbrain and you see the lesion there
+ 
+
+ align:start position:0%
+hindbrain and you see the lesion there
+an animal had already had the primal
+
+ align:start position:0%
+an animal had already had the primal
+ 
+
+ align:start position:0%
+an animal had already had the primal
+tract and here's the red nucleus with
+
+ align:start position:0%
+tract and here's the red nucleus with
+ 
+
+ align:start position:0%
+tract and here's the red nucleus with
+neurons on this side and not on this
+
+ align:start position:0%
+neurons on this side and not on this
+ 
+
+ align:start position:0%
+neurons on this side and not on this
+side these are akira motor nuclei here
+
+ align:start position:0%
+side these are akira motor nuclei here
+ 
+
+ align:start position:0%
+side these are akira motor nuclei here
+there's the central gray there's the
+
+ align:start position:0%
+there's the central gray there's the
+ 
+
+ align:start position:0%
+there's the central gray there's the
+aqueduct of silvius going through the
+
+ align:start position:0%
+aqueduct of silvius going through the
+ 
+
+ align:start position:0%
+aqueduct of silvius going through the
+midbrain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the larger ventricle and the
+
+ align:start position:0%
+here's the larger ventricle and the
+ 
+
+ align:start position:0%
+here's the larger ventricle and the
+fourth ventricle the hindbrain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the cola hindbrain is looking more like
+
+ align:start position:0%
+the cola hindbrain is looking more like
+ 
+
+ align:start position:0%
+the cola hindbrain is looking more like
+spinal cord but you can still see the
+
+ align:start position:0%
+spinal cord but you can still see the
+ 
+
+ align:start position:0%
+spinal cord but you can still see the
+widened ventricle there
+
+ align:start position:0%
+widened ventricle there
+ 
+
+ align:start position:0%
+widened ventricle there
+here you're almost at the beginning of
+
+ align:start position:0%
+here you're almost at the beginning of
+ 
+
+ align:start position:0%
+here you're almost at the beginning of
+the spinal cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think we'll look at this one and then
+
+ align:start position:0%
+i think we'll look at this one and then
+ 
+
+ align:start position:0%
+i think we'll look at this one and then
+we won't look at any more because at the
+
+ align:start position:0%
+we won't look at any more because at the
+ 
+
+ align:start position:0%
+we won't look at any more because at the
+time they do some control experiments
+
+ align:start position:0%
+time they do some control experiments
+ 
+
+ align:start position:0%
+time they do some control experiments
+where they
+
+ align:start position:0%
+where they
+ 
+
+ align:start position:0%
+where they
+they look to just make sure they're not
+
+ align:start position:0%
+they look to just make sure they're not
+ 
+
+ align:start position:0%
+they look to just make sure they're not
+getting to some of these effects because
+
+ align:start position:0%
+getting to some of these effects because
+ 
+
+ align:start position:0%
+getting to some of these effects because
+of some other sensory effects they could
+
+ align:start position:0%
+of some other sensory effects they could
+ 
+
+ align:start position:0%
+of some other sensory effects they could
+be it was important to figure that out
+
+ align:start position:0%
+be it was important to figure that out
+ 
+
+ align:start position:0%
+be it was important to figure that out
+these were really motor control
+
+ align:start position:0%
+these were really motor control
+ 
+
+ align:start position:0%
+these were really motor control
+effects and not due to sensation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again with a pretty complete lesion
+
+ align:start position:0%
+so again with a pretty complete lesion
+ 
+
+ align:start position:0%
+so again with a pretty complete lesion
+of the rubber spinal tract he's almost
+
+ align:start position:0%
+of the rubber spinal tract he's almost
+ 
+
+ align:start position:0%
+of the rubber spinal tract he's almost
+completely unable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to move his limbs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we'll have to try to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see if we can get that working again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's still on video hit that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there we are
+
+ align:start position:0%
+there we are
+ 
+
+ align:start position:0%
+there we are
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the result
+
+ align:start position:0%
+so the result
+ 
+
+ align:start position:0%
+so the result
+is that we have they were able to
+
+ align:start position:0%
+is that we have they were able to
+ 
+
+ align:start position:0%
+is that we have they were able to
+separate two systems one for control of
+
+ align:start position:0%
+separate two systems one for control of
+ 
+
+ align:start position:0%
+separate two systems one for control of
+axial muscles and whole body movements
+
+ align:start position:0%
+axial muscles and whole body movements
+ 
+
+ align:start position:0%
+axial muscles and whole body movements
+the other for control of distal muscles
+
+ align:start position:0%
+the other for control of distal muscles
+ 
+
+ align:start position:0%
+the other for control of distal muscles
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+fractionated movements not just control
+
+ align:start position:0%
+fractionated movements not just control
+ 
+
+ align:start position:0%
+fractionated movements not just control
+the distal muscles but the ability to
+
+ align:start position:0%
+the distal muscles but the ability to
+ 
+
+ align:start position:0%
+the distal muscles but the ability to
+move individual digits
+
+ align:start position:0%
+move individual digits
+ 
+
+ align:start position:0%
+move individual digits
+something that
+
+ align:start position:0%
+something that
+ 
+
+ align:start position:0%
+something that
+we don't see in humans until they've
+
+ align:start position:0%
+we don't see in humans until they've
+ 
+
+ align:start position:0%
+we don't see in humans until they've
+developed
+
+ align:start position:0%
+developed
+ 
+
+ align:start position:0%
+developed
+in the salmon monkeys until there's a
+
+ align:start position:0%
+in the salmon monkeys until there's a
+ 
+
+ align:start position:0%
+in the salmon monkeys until there's a
+maturation
+
+ align:start position:0%
+maturation
+ 
+
+ align:start position:0%
+maturation
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+connections between neocortex and motor
+
+ align:start position:0%
+connections between neocortex and motor
+ 
+
+ align:start position:0%
+connections between neocortex and motor
+neurons in the spinal enlargements
+
+ align:start position:0%
+neurons in the spinal enlargements
+ 
+
+ align:start position:0%
+neurons in the spinal enlargements
+okay and this just summarizes for you
+
+ align:start position:0%
+okay and this just summarizes for you
+ 
+
+ align:start position:0%
+okay and this just summarizes for you
+what you saw
+
+ align:start position:0%
+what you saw
+ 
+
+ align:start position:0%
+what you saw
+in the film okay the effects of
+
+ align:start position:0%
+in the film okay the effects of
+ 
+
+ align:start position:0%
+in the film okay the effects of
+paramidotomy
+
+ align:start position:0%
+paramidotomy
+ 
+
+ align:start position:0%
+paramidotomy
+the medial pathway lesion
+
+ align:start position:0%
+the medial pathway lesion
+ 
+
+ align:start position:0%
+the medial pathway lesion
+and the lateral hind brain
+
+ align:start position:0%
+and the lateral hind brain
+ 
+
+ align:start position:0%
+and the lateral hind brain
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now just a few more things on motor
+
+ align:start position:0%
+now just a few more things on motor
+ 
+
+ align:start position:0%
+now just a few more things on motor
+control if you look at a human
+
+ align:start position:0%
+control if you look at a human
+ 
+
+ align:start position:0%
+control if you look at a human
+who's lost
+
+ align:start position:0%
+who's lost
+ 
+
+ align:start position:0%
+who's lost
+control of his movements because of
+
+ align:start position:0%
+control of his movements because of
+ 
+
+ align:start position:0%
+control of his movements because of
+severance of descending pathways
+
+ align:start position:0%
+severance of descending pathways
+ 
+
+ align:start position:0%
+severance of descending pathways
+you might have spinal reflexes
+
+ align:start position:0%
+you might have spinal reflexes
+ 
+
+ align:start position:0%
+you might have spinal reflexes
+in fact the brain areas
+
+ align:start position:0%
+in fact the brain areas
+ 
+
+ align:start position:0%
+in fact the brain areas
+in the motor cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will still be active if he's
+
+ align:start position:0%
+will still be active if he's
+ 
+
+ align:start position:0%
+will still be active if he's
+wanting to move
+
+ align:start position:0%
+wanting to move
+ 
+
+ align:start position:0%
+wanting to move
+so if you ask him try to move your hand
+
+ align:start position:0%
+so if you ask him try to move your hand
+ 
+
+ align:start position:0%
+so if you ask him try to move your hand
+nothing his hand doesn't move but in the
+
+ align:start position:0%
+nothing his hand doesn't move but in the
+ 
+
+ align:start position:0%
+nothing his hand doesn't move but in the
+imaging you'll see
+
+ align:start position:0%
+imaging you'll see
+ 
+
+ align:start position:0%
+imaging you'll see
+a hand area become active
+
+ align:start position:0%
+a hand area become active
+ 
+
+ align:start position:0%
+a hand area become active
+and these are functional imaging studies
+
+ align:start position:0%
+and these are functional imaging studies
+ 
+
+ align:start position:0%
+and these are functional imaging studies
+showing that
+
+ align:start position:0%
+showing that
+ 
+
+ align:start position:0%
+showing that
+this was a study just a couple years ago
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now does this help us understand other
+
+ align:start position:0%
+now does this help us understand other
+ 
+
+ align:start position:0%
+now does this help us understand other
+systems well if you look at the
+
+ align:start position:0%
+systems well if you look at the
+ 
+
+ align:start position:0%
+systems well if you look at the
+cerebellum you do see a related
+
+ align:start position:0%
+cerebellum you do see a related
+ 
+
+ align:start position:0%
+cerebellum you do see a related
+organization
+
+ align:start position:0%
+organization
+ 
+
+ align:start position:0%
+organization
+there's many aspects of cerebellum here
+
+ align:start position:0%
+there's many aspects of cerebellum here
+ 
+
+ align:start position:0%
+there's many aspects of cerebellum here
+we're not talking about
+
+ align:start position:0%
+we're not talking about
+ 
+
+ align:start position:0%
+we're not talking about
+but they're definitely medial and
+
+ align:start position:0%
+but they're definitely medial and
+ 
+
+ align:start position:0%
+but they're definitely medial and
+lateral systems and the lat the
+
+ align:start position:0%
+lateral systems and the lat the
+ 
+
+ align:start position:0%
+lateral systems and the lat the
+hemispheres which are huge in humans
+
+ align:start position:0%
+hemispheres which are huge in humans
+ 
+
+ align:start position:0%
+hemispheres which are huge in humans
+uh are definitely more concerned with
+
+ align:start position:0%
+uh are definitely more concerned with
+ 
+
+ align:start position:0%
+uh are definitely more concerned with
+distal muscle control they're concerned
+
+ align:start position:0%
+distal muscle control they're concerned
+ 
+
+ align:start position:0%
+distal muscle control they're concerned
+with other things too but
+
+ align:start position:0%
+with other things too but
+ 
+
+ align:start position:0%
+with other things too but
+it's only the most medial part of the
+
+ align:start position:0%
+it's only the most medial part of the
+ 
+
+ align:start position:0%
+it's only the most medial part of the
+cerebellum which is also the most
+
+ align:start position:0%
+cerebellum which is also the most
+ 
+
+ align:start position:0%
+cerebellum which is also the most
+ancient part remember the cerebellum
+
+ align:start position:0%
+ancient part remember the cerebellum
+ 
+
+ align:start position:0%
+ancient part remember the cerebellum
+develop seems to have evolved out of the
+
+ align:start position:0%
+develop seems to have evolved out of the
+ 
+
+ align:start position:0%
+develop seems to have evolved out of the
+vestibular system okay
+
+ align:start position:0%
+vestibular system okay
+ 
+
+ align:start position:0%
+vestibular system okay
+and the part
+
+ align:start position:0%
+and the part
+ 
+
+ align:start position:0%
+and the part
+the medial
+
+ align:start position:0%
+the medial
+ 
+
+ align:start position:0%
+the medial
+and caudal cerebellum that's connected
+
+ align:start position:0%
+and caudal cerebellum that's connected
+ 
+
+ align:start position:0%
+and caudal cerebellum that's connected
+to the vestibular system it affects
+
+ align:start position:0%
+to the vestibular system it affects
+ 
+
+ align:start position:0%
+to the vestibular system it affects
+spinal cord through the vestibular
+
+ align:start position:0%
+spinal cord through the vestibular
+ 
+
+ align:start position:0%
+spinal cord through the vestibular
+spinal tract and also connections to the
+
+ align:start position:0%
+spinal tract and also connections to the
+ 
+
+ align:start position:0%
+spinal tract and also connections to the
+reticular formation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it
+
+ align:start position:0%
+and it
+ 
+
+ align:start position:0%
+and it
+correspondingly
+
+ align:start position:0%
+correspondingly
+ 
+
+ align:start position:0%
+correspondingly
+to what we just saw
+
+ align:start position:0%
+to what we just saw
+ 
+
+ align:start position:0%
+to what we just saw
+its coordinates axial muscles whole body
+
+ align:start position:0%
+its coordinates axial muscles whole body
+ 
+
+ align:start position:0%
+its coordinates axial muscles whole body
+movements the lateral cerebellum
+
+ align:start position:0%
+movements the lateral cerebellum
+ 
+
+ align:start position:0%
+movements the lateral cerebellum
+and i mentioned here
+
+ align:start position:0%
+and i mentioned here
+ 
+
+ align:start position:0%
+and i mentioned here
+its outputs it has a
+
+ align:start position:0%
+its outputs it has a
+ 
+
+ align:start position:0%
+its outputs it has a
+name i don't require you to learn it
+
+ align:start position:0%
+name i don't require you to learn it
+ 
+
+ align:start position:0%
+name i don't require you to learn it
+here but it projects forward to the
+
+ align:start position:0%
+here but it projects forward to the
+ 
+
+ align:start position:0%
+here but it projects forward to the
+opposite hemisphere and also that
+
+ align:start position:0%
+opposite hemisphere and also that
+ 
+
+ align:start position:0%
+opposite hemisphere and also that
+pathway connects to the red nucleus then
+
+ align:start position:0%
+pathway connects to the red nucleus then
+ 
+
+ align:start position:0%
+pathway connects to the red nucleus then
+it goes to the primarily the vl of the
+
+ align:start position:0%
+it goes to the primarily the vl of the
+ 
+
+ align:start position:0%
+it goes to the primarily the vl of the
+thalamus
+
+ align:start position:0%
+thalamus
+ 
+
+ align:start position:0%
+thalamus
+goes to the which projects the motor
+
+ align:start position:0%
+goes to the which projects the motor
+ 
+
+ align:start position:0%
+goes to the which projects the motor
+cortex and very important for
+
+ align:start position:0%
+cortex and very important for
+ 
+
+ align:start position:0%
+cortex and very important for
+coordinating the timing of neocortical
+
+ align:start position:0%
+coordinating the timing of neocortical
+ 
+
+ align:start position:0%
+coordinating the timing of neocortical
+control movements
+
+ align:start position:0%
+control movements
+ 
+
+ align:start position:0%
+control movements
+if we get a lesion
+
+ align:start position:0%
+if we get a lesion
+ 
+
+ align:start position:0%
+if we get a lesion
+we can affect those things for example a
+
+ align:start position:0%
+we can affect those things for example a
+ 
+
+ align:start position:0%
+we can affect those things for example a
+lesion of the hemispheres that affect
+
+ align:start position:0%
+lesion of the hemispheres that affect
+ 
+
+ align:start position:0%
+lesion of the hemispheres that affect
+hand control
+
+ align:start position:0%
+hand control
+ 
+
+ align:start position:0%
+hand control
+when a hand in arm control if a person
+
+ align:start position:0%
+when a hand in arm control if a person
+ 
+
+ align:start position:0%
+when a hand in arm control if a person
+has a cerebellar lesion when he tries to
+
+ align:start position:0%
+has a cerebellar lesion when he tries to
+ 
+
+ align:start position:0%
+has a cerebellar lesion when he tries to
+reach you know he'll say he reaches out
+
+ align:start position:0%
+reach you know he'll say he reaches out
+ 
+
+ align:start position:0%
+reach you know he'll say he reaches out
+here for the stylist as he nears the
+
+ align:start position:0%
+here for the stylist as he nears the
+ 
+
+ align:start position:0%
+here for the stylist as he nears the
+stylus he starts he gets a bad dreamer
+
+ align:start position:0%
+stylus he starts he gets a bad dreamer
+ 
+
+ align:start position:0%
+stylus he starts he gets a bad dreamer
+it's called intention dreamer it happens
+
+ align:start position:0%
+it's called intention dreamer it happens
+ 
+
+ align:start position:0%
+it's called intention dreamer it happens
+when he's trying to do something he's
+
+ align:start position:0%
+when he's trying to do something he's
+ 
+
+ align:start position:0%
+when he's trying to do something he's
+trying to make a movement and he will
+
+ align:start position:0%
+trying to make a movement and he will
+ 
+
+ align:start position:0%
+trying to make a movement and he will
+shake okay he has poor control timing
+
+ align:start position:0%
+shake okay he has poor control timing
+ 
+
+ align:start position:0%
+shake okay he has poor control timing
+timing and
+
+ align:start position:0%
+timing and
+ 
+
+ align:start position:0%
+timing and
+gain now you do get recovery from
+
+ align:start position:0%
+gain now you do get recovery from
+ 
+
+ align:start position:0%
+gain now you do get recovery from
+cerebellar lesions but they take a long
+
+ align:start position:0%
+cerebellar lesions but they take a long
+ 
+
+ align:start position:0%
+cerebellar lesions but they take a long
+time and they coordinate it's not a
+
+ align:start position:0%
+time and they coordinate it's not a
+ 
+
+ align:start position:0%
+time and they coordinate it's not a
+complete recovery
+
+ align:start position:0%
+complete recovery
+ 
+
+ align:start position:0%
+complete recovery
+okay because other parts of the brain
+
+ align:start position:0%
+okay because other parts of the brain
+ 
+
+ align:start position:0%
+okay because other parts of the brain
+particularly parietal cortex
+
+ align:start position:0%
+particularly parietal cortex
+ 
+
+ align:start position:0%
+particularly parietal cortex
+can take over some of those functions
+
+ align:start position:0%
+can take over some of those functions
+ 
+
+ align:start position:0%
+can take over some of those functions
+now what about corpus triadum this has
+
+ align:start position:0%
+now what about corpus triadum this has
+ 
+
+ align:start position:0%
+now what about corpus triadum this has
+been much more complex and difficult to
+
+ align:start position:0%
+been much more complex and difficult to
+ 
+
+ align:start position:0%
+been much more complex and difficult to
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+but the main
+
+ align:start position:0%
+but the main
+ 
+
+ align:start position:0%
+but the main
+evidence we have of its important
+
+ align:start position:0%
+evidence we have of its important
+ 
+
+ align:start position:0%
+evidence we have of its important
+movement importance in movement control
+
+ align:start position:0%
+movement importance in movement control
+ 
+
+ align:start position:0%
+movement importance in movement control
+where the
+
+ align:start position:0%
+where the
+ 
+
+ align:start position:0%
+where the
+the dyskinesis of
+
+ align:start position:0%
+the dyskinesis of
+ 
+
+ align:start position:0%
+the dyskinesis of
+of basal ganglia
+
+ align:start position:0%
+of basal ganglia
+ 
+
+ align:start position:0%
+of basal ganglia
+pathologies so for example in
+
+ align:start position:0%
+pathologies so for example in
+ 
+
+ align:start position:0%
+pathologies so for example in
+huntington's disease
+
+ align:start position:0%
+huntington's disease
+ 
+
+ align:start position:0%
+huntington's disease
+the patient makes as the as the disease
+
+ align:start position:0%
+the patient makes as the as the disease
+ 
+
+ align:start position:0%
+the patient makes as the as the disease
+gets worse he makes involuntary writhing
+
+ align:start position:0%
+gets worse he makes involuntary writhing
+ 
+
+ align:start position:0%
+gets worse he makes involuntary writhing
+movements that sometimes are called
+
+ align:start position:0%
+movements that sometimes are called
+ 
+
+ align:start position:0%
+movements that sometimes are called
+choreoform because they look like
+
+ align:start position:0%
+choreoform because they look like
+ 
+
+ align:start position:0%
+choreoform because they look like
+they're dance movements
+
+ align:start position:0%
+they're dance movements
+ 
+
+ align:start position:0%
+they're dance movements
+korea means dancing
+
+ align:start position:0%
+korea means dancing
+ 
+
+ align:start position:0%
+korea means dancing
+okay and another pathology of the output
+
+ align:start position:0%
+okay and another pathology of the output
+ 
+
+ align:start position:0%
+okay and another pathology of the output
+circuitry of the corpus tree atom
+
+ align:start position:0%
+circuitry of the corpus tree atom
+ 
+
+ align:start position:0%
+circuitry of the corpus tree atom
+when part of that degenerates you can
+
+ align:start position:0%
+when part of that degenerates you can
+ 
+
+ align:start position:0%
+when part of that degenerates you can
+get people that when they try to move
+
+ align:start position:0%
+get people that when they try to move
+ 
+
+ align:start position:0%
+get people that when they try to move
+their arm move it in a ballistic way so
+
+ align:start position:0%
+their arm move it in a ballistic way so
+ 
+
+ align:start position:0%
+their arm move it in a ballistic way so
+they're flinging movements of the arm
+
+ align:start position:0%
+they're flinging movements of the arm
+ 
+
+ align:start position:0%
+they're flinging movements of the arm
+instead of smooth coordinated movements
+
+ align:start position:0%
+instead of smooth coordinated movements
+ 
+
+ align:start position:0%
+instead of smooth coordinated movements
+that's called ballisticus and hemi
+
+ align:start position:0%
+that's called ballisticus and hemi
+ 
+
+ align:start position:0%
+that's called ballisticus and hemi
+ballism is a if they have the problem
+
+ align:start position:0%
+ballism is a if they have the problem
+ 
+
+ align:start position:0%
+ballism is a if they have the problem
+the degeneration on one side of the
+
+ align:start position:0%
+the degeneration on one side of the
+ 
+
+ align:start position:0%
+the degeneration on one side of the
+output pathways in corpus triad and
+
+ align:start position:0%
+output pathways in corpus triad and
+ 
+
+ align:start position:0%
+output pathways in corpus triad and
+they'll develop that problem on only one
+
+ align:start position:0%
+they'll develop that problem on only one
+ 
+
+ align:start position:0%
+they'll develop that problem on only one
+side of the body
+
+ align:start position:0%
+side of the body
+ 
+
+ align:start position:0%
+side of the body
+the best known
+
+ align:start position:0%
+the best known
+ 
+
+ align:start position:0%
+the best known
+basal ganglia disease is parkinson's
+
+ align:start position:0%
+basal ganglia disease is parkinson's
+ 
+
+ align:start position:0%
+basal ganglia disease is parkinson's
+disease
+
+ align:start position:0%
+disease
+ 
+
+ align:start position:0%
+disease
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+they have a different kind of tremor
+
+ align:start position:0%
+they have a different kind of tremor
+ 
+
+ align:start position:0%
+they have a different kind of tremor
+when they're just sitting at rest they
+
+ align:start position:0%
+when they're just sitting at rest they
+ 
+
+ align:start position:0%
+when they're just sitting at rest they
+will shake many of you seen this many
+
+ align:start position:0%
+will shake many of you seen this many
+ 
+
+ align:start position:0%
+will shake many of you seen this many
+older people get
+
+ align:start position:0%
+older people get
+ 
+
+ align:start position:0%
+older people get
+at least some of this
+
+ align:start position:0%
+at least some of this
+ 
+
+ align:start position:0%
+at least some of this
+but it's a specific disease and when it
+
+ align:start position:0%
+but it's a specific disease and when it
+ 
+
+ align:start position:0%
+but it's a specific disease and when it
+strikes younger people it's particularly
+
+ align:start position:0%
+strikes younger people it's particularly
+ 
+
+ align:start position:0%
+strikes younger people it's particularly
+tragic
+
+ align:start position:0%
+tragic
+ 
+
+ align:start position:0%
+tragic
+they develop the resting creamer they
+
+ align:start position:0%
+they develop the resting creamer they
+ 
+
+ align:start position:0%
+they develop the resting creamer they
+become increasingly rigid their
+
+ align:start position:0%
+become increasingly rigid their
+ 
+
+ align:start position:0%
+become increasingly rigid their
+movements slow down
+
+ align:start position:0%
+movements slow down
+ 
+
+ align:start position:0%
+movements slow down
+and then they get a loss of emotional
+
+ align:start position:0%
+and then they get a loss of emotional
+ 
+
+ align:start position:0%
+and then they get a loss of emotional
+displays it begins to affect these
+
+ align:start position:0%
+displays it begins to affect these
+ 
+
+ align:start position:0%
+displays it begins to affect these
+control of these higher functions
+
+ align:start position:0%
+control of these higher functions
+ 
+
+ align:start position:0%
+control of these higher functions
+and it's correlated with loss of neurons
+
+ align:start position:0%
+and it's correlated with loss of neurons
+ 
+
+ align:start position:0%
+and it's correlated with loss of neurons
+in the substantia which is part of
+
+ align:start position:0%
+in the substantia which is part of
+ 
+
+ align:start position:0%
+in the substantia which is part of
+the midbrain
+
+ align:start position:0%
+the midbrain
+ 
+
+ align:start position:0%
+the midbrain
+that contain dopamine and they project
+
+ align:start position:0%
+that contain dopamine and they project
+ 
+
+ align:start position:0%
+that contain dopamine and they project
+forward to the corpus tree atom and as
+
+ align:start position:0%
+forward to the corpus tree atom and as
+ 
+
+ align:start position:0%
+forward to the corpus tree atom and as
+dopamine becomes depleted you begin to
+
+ align:start position:0%
+dopamine becomes depleted you begin to
+ 
+
+ align:start position:0%
+dopamine becomes depleted you begin to
+get these symptoms
+
+ align:start position:0%
+get these symptoms
+ 
+
+ align:start position:0%
+get these symptoms
+okay and this is what it shows
+
+ align:start position:0%
+okay and this is what it shows
+ 
+
+ align:start position:0%
+okay and this is what it shows
+in here
+
+ align:start position:0%
+in here
+ 
+
+ align:start position:0%
+in here
+in dopamine receptors increase with the
+
+ align:start position:0%
+in dopamine receptors increase with the
+ 
+
+ align:start position:0%
+in dopamine receptors increase with the
+loss of axons to come in compensate
+
+ align:start position:0%
+loss of axons to come in compensate
+ 
+
+ align:start position:0%
+loss of axons to come in compensate
+compensation for the loss
+
+ align:start position:0%
+compensation for the loss
+ 
+
+ align:start position:0%
+compensation for the loss
+but then with more and more neurons lost
+
+ align:start position:0%
+but then with more and more neurons lost
+ 
+
+ align:start position:0%
+but then with more and more neurons lost
+and here you see the loss of pigmented
+
+ align:start position:0%
+and here you see the loss of pigmented
+ 
+
+ align:start position:0%
+and here you see the loss of pigmented
+neurons in the
+
+ align:start position:0%
+neurons in the
+ 
+
+ align:start position:0%
+neurons in the
+finally the receptors go down too and
+
+ align:start position:0%
+finally the receptors go down too and
+ 
+
+ align:start position:0%
+finally the receptors go down too and
+the parkinson's symptoms
+
+ align:start position:0%
+the parkinson's symptoms
+ 
+
+ align:start position:0%
+the parkinson's symptoms
+appear late after there's been a lot of
+
+ align:start position:0%
+appear late after there's been a lot of
+ 
+
+ align:start position:0%
+appear late after there's been a lot of
+loss as i mentioned before you these
+
+ align:start position:0%
+loss as i mentioned before you these
+ 
+
+ align:start position:0%
+loss as i mentioned before you these
+slow
+
+ align:start position:0%
+slow
+ 
+
+ align:start position:0%
+slow
+pathologies slower slowly at developing
+
+ align:start position:0%
+pathologies slower slowly at developing
+ 
+
+ align:start position:0%
+pathologies slower slowly at developing
+lesions
+
+ align:start position:0%
+lesions
+ 
+
+ align:start position:0%
+lesions
+often the the
+
+ align:start position:0%
+often the the
+ 
+
+ align:start position:0%
+often the the
+behavioral change is seen late okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they've developed ways of trying to
+
+ align:start position:0%
+and they've developed ways of trying to
+ 
+
+ align:start position:0%
+and they've developed ways of trying to
+replace the dopamine in the striatum
+
+ align:start position:0%
+replace the dopamine in the striatum
+ 
+
+ align:start position:0%
+replace the dopamine in the striatum
+and then i've mentioned that implicit
+
+ align:start position:0%
+and then i've mentioned that implicit
+ 
+
+ align:start position:0%
+and then i've mentioned that implicit
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+especially the word at work and graybill
+
+ align:start position:0%
+especially the word at work and graybill
+ 
+
+ align:start position:0%
+especially the word at work and graybill
+and other people working on this they
+
+ align:start position:0%
+and other people working on this they
+ 
+
+ align:start position:0%
+and other people working on this they
+find that somehow there's an interaction
+
+ align:start position:0%
+find that somehow there's an interaction
+ 
+
+ align:start position:0%
+find that somehow there's an interaction
+in the corpus triadum
+
+ align:start position:0%
+in the corpus triadum
+ 
+
+ align:start position:0%
+in the corpus triadum
+when we learn habits
+
+ align:start position:0%
+when we learn habits
+ 
+
+ align:start position:0%
+when we learn habits
+reward and reinforcement for movements
+
+ align:start position:0%
+reward and reinforcement for movements
+ 
+
+ align:start position:0%
+reward and reinforcement for movements
+seems to act in the corpus triad and
+
+ align:start position:0%
+seems to act in the corpus triad and
+ 
+
+ align:start position:0%
+seems to act in the corpus triad and
+alter the connections
+
+ align:start position:0%
+alter the connections
+ 
+
+ align:start position:0%
+alter the connections
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and we know of course that over time
+
+ align:start position:0%
+and we know of course that over time
+ 
+
+ align:start position:0%
+and we know of course that over time
+things movements that were initially
+
+ align:start position:0%
+things movements that were initially
+ 
+
+ align:start position:0%
+things movements that were initially
+voluntary become habitual
+
+ align:start position:0%
+voluntary become habitual
+ 
+
+ align:start position:0%
+voluntary become habitual
+and that always seems to involve the
+
+ align:start position:0%
+and that always seems to involve the
+ 
+
+ align:start position:0%
+and that always seems to involve the
+corpus triadum and that's all we have
+
+ align:start position:0%
+corpus triadum and that's all we have
+ 
+
+ align:start position:0%
+corpus triadum and that's all we have
+time for i will
\ No newline at end of file
diff --git a/9RZa3zBruVA.txt b/9RZa3zBruVA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9bdc97a22f2c3a34f1c4a923d5f10aa0bdf432bc
--- /dev/null
+++ b/9RZa3zBruVA.txt
@@ -0,0 +1,1691 @@
+align:start position:0%
+ 
+so my philosophy of teaching Chinese uh
+
+ align:start position:0%
+so my philosophy of teaching Chinese uh
+ 
+
+ align:start position:0%
+so my philosophy of teaching Chinese uh
+well it's very interesting uh process
+
+ align:start position:0%
+well it's very interesting uh process
+ 
+
+ align:start position:0%
+well it's very interesting uh process
+because when I started I knew one method
+
+ align:start position:0%
+because when I started I knew one method
+ 
+
+ align:start position:0%
+because when I started I knew one method
+and I thought that was the best in the
+
+ align:start position:0%
+and I thought that was the best in the
+ 
+
+ align:start position:0%
+and I thought that was the best in the
+world uh to do drill instruct you know
+
+ align:start position:0%
+world uh to do drill instruct you know
+ 
+
+ align:start position:0%
+world uh to do drill instruct you know
+like drill the students all the time
+
+ align:start position:0%
+like drill the students all the time
+ 
+
+ align:start position:0%
+like drill the students all the time
+make them repeat but throughout the
+
+ align:start position:0%
+make them repeat but throughout the
+ 
+
+ align:start position:0%
+make them repeat but throughout the
+years I realized uh they can say certain
+
+ align:start position:0%
+years I realized uh they can say certain
+ 
+
+ align:start position:0%
+years I realized uh they can say certain
+things but they could not have a
+
+ align:start position:0%
+things but they could not have a
+ 
+
+ align:start position:0%
+things but they could not have a
+conversation so they're they can do well
+
+ align:start position:0%
+conversation so they're they can do well
+ 
+
+ align:start position:0%
+conversation so they're they can do well
+and test that doesn't mean they can go
+
+ align:start position:0%
+and test that doesn't mean they can go
+ 
+
+ align:start position:0%
+and test that doesn't mean they can go
+out have a conversation so I think I've
+
+ align:start position:0%
+out have a conversation so I think I've
+ 
+
+ align:start position:0%
+out have a conversation so I think I've
+evolved and I right now I think the main
+
+ align:start position:0%
+evolved and I right now I think the main
+ 
+
+ align:start position:0%
+evolved and I right now I think the main
+uh Philosophy for me is to have a
+
+ align:start position:0%
+uh Philosophy for me is to have a
+ 
+
+ align:start position:0%
+uh Philosophy for me is to have a
+welcoming
+
+ align:start position:0%
+welcoming
+ 
+
+ align:start position:0%
+welcoming
+environment to help student to speak the
+
+ align:start position:0%
+environment to help student to speak the
+ 
+
+ align:start position:0%
+environment to help student to speak the
+language not to talk about the
+
+ align:start position:0%
+language not to talk about the
+ 
+
+ align:start position:0%
+language not to talk about the
+language um so that's my current f
+
+ align:start position:0%
+language um so that's my current f
+ 
+
+ align:start position:0%
+language um so that's my current f
+philosophical idea so everything I do is
+
+ align:start position:0%
+philosophical idea so everything I do is
+ 
+
+ align:start position:0%
+philosophical idea so everything I do is
+to uh carry this out and create
+
+ align:start position:0%
+to uh carry this out and create
+ 
+
+ align:start position:0%
+to uh carry this out and create
+environment for this
+
+ align:start position:0%
+environment for this
+ 
+
+ align:start position:0%
+environment for this
+philosophy so um so I did a lot um right
+
+ align:start position:0%
+philosophy so um so I did a lot um right
+ 
+
+ align:start position:0%
+philosophy so um so I did a lot um right
+for the past few years I start started
+
+ align:start position:0%
+for the past few years I start started
+ 
+
+ align:start position:0%
+for the past few years I start started
+changing and I did a lot um they said a
+
+ align:start position:0%
+changing and I did a lot um they said a
+ 
+
+ align:start position:0%
+changing and I did a lot um they said a
+scaold scaffolding uh instructions and
+
+ align:start position:0%
+scaold scaffolding uh instructions and
+ 
+
+ align:start position:0%
+scaold scaffolding uh instructions and
+very student centered instruction I used
+
+ align:start position:0%
+very student centered instruction I used
+ 
+
+ align:start position:0%
+very student centered instruction I used
+used to be very teacher center it's very
+
+ align:start position:0%
+used to be very teacher center it's very
+ 
+
+ align:start position:0%
+used to be very teacher center it's very
+efficient don't get me wrong it's very
+
+ align:start position:0%
+efficient don't get me wrong it's very
+ 
+
+ align:start position:0%
+efficient don't get me wrong it's very
+effective too you keep the uh you kept
+
+ align:start position:0%
+effective too you keep the uh you kept
+ 
+
+ align:start position:0%
+effective too you keep the uh you kept
+the students on their toes they have to
+
+ align:start position:0%
+the students on their toes they have to
+ 
+
+ align:start position:0%
+the students on their toes they have to
+you know gge back right away but really
+
+ align:start position:0%
+you know gge back right away but really
+ 
+
+ align:start position:0%
+you know gge back right away but really
+and I got this evaluation one year they
+
+ align:start position:0%
+and I got this evaluation one year they
+ 
+
+ align:start position:0%
+and I got this evaluation one year they
+say oh the teacher is incredible she's
+
+ align:start position:0%
+say oh the teacher is incredible she's
+ 
+
+ align:start position:0%
+say oh the teacher is incredible she's
+so good but I wish I can learn how to
+
+ align:start position:0%
+so good but I wish I can learn how to
+ 
+
+ align:start position:0%
+so good but I wish I can learn how to
+speak I was like what does that mean and
+
+ align:start position:0%
+speak I was like what does that mean and
+ 
+
+ align:start position:0%
+speak I was like what does that mean and
+you you spoke well and I realized he was
+
+ align:start position:0%
+you you spoke well and I realized he was
+ 
+
+ align:start position:0%
+you you spoke well and I realized he was
+doing the drill pattern he can say so
+
+ align:start position:0%
+doing the drill pattern he can say so
+ 
+
+ align:start position:0%
+doing the drill pattern he can say so
+certain sentence when I asked him to say
+
+ align:start position:0%
+certain sentence when I asked him to say
+ 
+
+ align:start position:0%
+certain sentence when I asked him to say
+it and repeat after me but have him to
+
+ align:start position:0%
+it and repeat after me but have him to
+ 
+
+ align:start position:0%
+it and repeat after me but have him to
+have a natural conversation was really
+
+ align:start position:0%
+have a natural conversation was really
+ 
+
+ align:start position:0%
+have a natural conversation was really
+difficult so that dawned on me I start
+
+ align:start position:0%
+difficult so that dawned on me I start
+ 
+
+ align:start position:0%
+difficult so that dawned on me I start
+changing and I try to uh attend
+
+ align:start position:0%
+changing and I try to uh attend
+ 
+
+ align:start position:0%
+changing and I try to uh attend
+conference and workshop not related to
+
+ align:start position:0%
+conference and workshop not related to
+ 
+
+ align:start position:0%
+conference and workshop not related to
+just teaching Chinese more like um how
+
+ align:start position:0%
+just teaching Chinese more like um how
+ 
+
+ align:start position:0%
+just teaching Chinese more like um how
+to educate people more education and how
+
+ align:start position:0%
+to educate people more education and how
+ 
+
+ align:start position:0%
+to educate people more education and how
+to uh create environment for all student
+
+ align:start position:0%
+to uh create environment for all student
+ 
+
+ align:start position:0%
+to uh create environment for all student
+feel safe so I adapt those philosophy in
+
+ align:start position:0%
+feel safe so I adapt those philosophy in
+ 
+
+ align:start position:0%
+feel safe so I adapt those philosophy in
+my course to so my My Philosophy is a
+
+ align:start position:0%
+my course to so my My Philosophy is a
+ 
+
+ align:start position:0%
+my course to so my My Philosophy is a
+weling welcoming environment that means
+
+ align:start position:0%
+weling welcoming environment that means
+ 
+
+ align:start position:0%
+weling welcoming environment that means
+um building a community for student feel
+
+ align:start position:0%
+um building a community for student feel
+ 
+
+ align:start position:0%
+um building a community for student feel
+very safe to speak the language in this
+
+ align:start position:0%
+very safe to speak the language in this
+ 
+
+ align:start position:0%
+very safe to speak the language in this
+community they're not afraid to make
+
+ align:start position:0%
+community they're not afraid to make
+ 
+
+ align:start position:0%
+community they're not afraid to make
+mistakes and they're they always
+
+ align:start position:0%
+mistakes and they're they always
+ 
+
+ align:start position:0%
+mistakes and they're they always
+volunteer uh their opinions that's my
+
+ align:start position:0%
+volunteer uh their opinions that's my
+ 
+
+ align:start position:0%
+volunteer uh their opinions that's my
+goal the first
+
+ align:start position:0%
+goal the first
+ 
+
+ align:start position:0%
+goal the first
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+uh as I said My Philosophy is to create
+
+ align:start position:0%
+uh as I said My Philosophy is to create
+ 
+
+ align:start position:0%
+uh as I said My Philosophy is to create
+a welcoming environment to build a
+
+ align:start position:0%
+a welcoming environment to build a
+ 
+
+ align:start position:0%
+a welcoming environment to build a
+community so for example I umum recently
+
+ align:start position:0%
+community so for example I umum recently
+ 
+
+ align:start position:0%
+community so for example I umum recently
+uh two years ago I went to a workshop
+
+ align:start position:0%
+uh two years ago I went to a workshop
+ 
+
+ align:start position:0%
+uh two years ago I went to a workshop
+called responsive classroom uh
+
+ align:start position:0%
+called responsive classroom uh
+ 
+
+ align:start position:0%
+called responsive classroom uh
+responsive uh responsive classrooms
+
+ align:start position:0%
+responsive uh responsive classrooms
+ 
+
+ align:start position:0%
+responsive uh responsive classrooms
+geared to a k212 is talking about it's
+
+ align:start position:0%
+geared to a k212 is talking about it's
+ 
+
+ align:start position:0%
+geared to a k212 is talking about it's
+more it's more treating the younger kids
+
+ align:start position:0%
+more it's more treating the younger kids
+ 
+
+ align:start position:0%
+more it's more treating the younger kids
+try to get rid of the behavior issue I
+
+ align:start position:0%
+try to get rid of the behavior issue I
+ 
+
+ align:start position:0%
+try to get rid of the behavior issue I
+don't need to do it in my classroom but
+
+ align:start position:0%
+don't need to do it in my classroom but
+ 
+
+ align:start position:0%
+don't need to do it in my classroom but
+I think strategy there is actually works
+
+ align:start position:0%
+I think strategy there is actually works
+ 
+
+ align:start position:0%
+I think strategy there is actually works
+first thing they do is building
+
+ align:start position:0%
+first thing they do is building
+ 
+
+ align:start position:0%
+first thing they do is building
+community so for example I do the first
+
+ align:start position:0%
+community so for example I do the first
+ 
+
+ align:start position:0%
+community so for example I do the first
+week of my course and these are harage
+
+ align:start position:0%
+week of my course and these are harage
+ 
+
+ align:start position:0%
+week of my course and these are harage
+to learn they already know how to speak
+
+ align:start position:0%
+to learn they already know how to speak
+ 
+
+ align:start position:0%
+to learn they already know how to speak
+but they are so embarrassed with them
+
+ align:start position:0%
+but they are so embarrassed with them
+ 
+
+ align:start position:0%
+but they are so embarrassed with them
+because they will tell me my
+
+ align:start position:0%
+because they will tell me my
+ 
+
+ align:start position:0%
+because they will tell me my
+pronunciation is bad I don't speak to
+
+ align:start position:0%
+pronunciation is bad I don't speak to
+ 
+
+ align:start position:0%
+pronunciation is bad I don't speak to
+anybody else only to my parents I don't
+
+ align:start position:0%
+anybody else only to my parents I don't
+ 
+
+ align:start position:0%
+anybody else only to my parents I don't
+want to speak in the classroom so
+
+ align:start position:0%
+want to speak in the classroom so
+ 
+
+ align:start position:0%
+want to speak in the classroom so
+basically I do the greeting the very
+
+ align:start position:0%
+basically I do the greeting the very
+ 
+
+ align:start position:0%
+basically I do the greeting the very
+easy things they're comfortable with for
+
+ align:start position:0%
+easy things they're comfortable with for
+ 
+
+ align:start position:0%
+easy things they're comfortable with for
+instance they talk about their name name
+
+ align:start position:0%
+instance they talk about their name name
+ 
+
+ align:start position:0%
+instance they talk about their name name
+whe they're major they can all speak
+
+ align:start position:0%
+whe they're major they can all speak
+ 
+
+ align:start position:0%
+whe they're major they can all speak
+these you know in Chinese so what I do
+
+ align:start position:0%
+these you know in Chinese so what I do
+ 
+
+ align:start position:0%
+these you know in Chinese so what I do
+is the first day like that and then
+
+ align:start position:0%
+is the first day like that and then
+ 
+
+ align:start position:0%
+is the first day like that and then
+started I build into a routine so every
+
+ align:start position:0%
+started I build into a routine so every
+ 
+
+ align:start position:0%
+started I build into a routine so every
+class I spend five to 10 minutes every
+
+ align:start position:0%
+class I spend five to 10 minutes every
+ 
+
+ align:start position:0%
+class I spend five to 10 minutes every
+day we call G every class not every day
+
+ align:start position:0%
+day we call G every class not every day
+ 
+
+ align:start position:0%
+day we call G every class not every day
+we don't have a everyday class called
+
+ align:start position:0%
+we don't have a everyday class called
+ 
+
+ align:start position:0%
+we don't have a everyday class called
+greeting basically you I ask everybody
+
+ align:start position:0%
+greeting basically you I ask everybody
+ 
+
+ align:start position:0%
+greeting basically you I ask everybody
+to write their name on a car so I
+
+ align:start position:0%
+to write their name on a car so I
+ 
+
+ align:start position:0%
+to write their name on a car so I
+collect the car I put a car in the
+
+ align:start position:0%
+collect the car I put a car in the
+ 
+
+ align:start position:0%
+collect the car I put a car in the
+middle of the classroom so one student I
+
+ align:start position:0%
+middle of the classroom so one student I
+ 
+
+ align:start position:0%
+middle of the classroom so one student I
+will start because I need to to model
+
+ align:start position:0%
+will start because I need to to model
+ 
+
+ align:start position:0%
+will start because I need to to model
+what it means so I will pick up a
+
+ align:start position:0%
+what it means so I will pick up a
+ 
+
+ align:start position:0%
+what it means so I will pick up a
+students's c for instance I say oh Sarah
+
+ align:start position:0%
+students's c for instance I say oh Sarah
+ 
+
+ align:start position:0%
+students's c for instance I say oh Sarah
+Leen okay and I call her in her Chinese
+
+ align:start position:0%
+Leen okay and I call her in her Chinese
+ 
+
+ align:start position:0%
+Leen okay and I call her in her Chinese
+name and I would start saying how are
+
+ align:start position:0%
+name and I would start saying how are
+ 
+
+ align:start position:0%
+name and I would start saying how are
+you today you know what did you do last
+
+ align:start position:0%
+you today you know what did you do last
+ 
+
+ align:start position:0%
+you today you know what did you do last
+night stuff like that daily life things
+
+ align:start position:0%
+night stuff like that daily life things
+ 
+
+ align:start position:0%
+night stuff like that daily life things
+and then I asked the student did you see
+
+ align:start position:0%
+and then I asked the student did you see
+ 
+
+ align:start position:0%
+and then I asked the student did you see
+what I did so follow my model and come
+
+ align:start position:0%
+what I did so follow my model and come
+ 
+
+ align:start position:0%
+what I did so follow my model and come
+here pick up car greet your classmates
+
+ align:start position:0%
+here pick up car greet your classmates
+ 
+
+ align:start position:0%
+here pick up car greet your classmates
+so every day I do this uh I think after
+
+ align:start position:0%
+so every day I do this uh I think after
+ 
+
+ align:start position:0%
+so every day I do this uh I think after
+two weeks everybody knows everybody's
+
+ align:start position:0%
+two weeks everybody knows everybody's
+ 
+
+ align:start position:0%
+two weeks everybody knows everybody's
+name
+
+ align:start position:0%
+name
+ 
+
+ align:start position:0%
+name
+and while greeting this is not just
+
+ align:start position:0%
+and while greeting this is not just
+ 
+
+ align:start position:0%
+and while greeting this is not just
+simple greeting because you have a
+
+ align:start position:0%
+simple greeting because you have a
+ 
+
+ align:start position:0%
+simple greeting because you have a
+natural conversation when you say oh I
+
+ align:start position:0%
+natural conversation when you say oh I
+ 
+
+ align:start position:0%
+natural conversation when you say oh I
+went to bed really late last night and
+
+ align:start position:0%
+went to bed really late last night and
+ 
+
+ align:start position:0%
+went to bed really late last night and
+people were say why you know that so so
+
+ align:start position:0%
+people were say why you know that so so
+ 
+
+ align:start position:0%
+people were say why you know that so so
+I started very structure for instance
+
+ align:start position:0%
+I started very structure for instance
+ 
+
+ align:start position:0%
+I started very structure for instance
+just everybody's just say very limited
+
+ align:start position:0%
+just everybody's just say very limited
+ 
+
+ align:start position:0%
+just everybody's just say very limited
+things and then I will say okay so Sarah
+
+ align:start position:0%
+things and then I will say okay so Sarah
+ 
+
+ align:start position:0%
+things and then I will say okay so Sarah
+say she went to bed really late last
+
+ align:start position:0%
+say she went to bed really late last
+ 
+
+ align:start position:0%
+say she went to bed really late last
+night do you guys want to know why you
+
+ align:start position:0%
+night do you guys want to know why you
+ 
+
+ align:start position:0%
+night do you guys want to know why you
+know all in Chinese so they will start
+
+ align:start position:0%
+know all in Chinese so they will start
+ 
+
+ align:start position:0%
+know all in Chinese so they will start
+asking so I buil on that difficulty so
+
+ align:start position:0%
+asking so I buil on that difficulty so
+ 
+
+ align:start position:0%
+asking so I buil on that difficulty so
+um the weekend the Monday class is
+
+ align:start position:0%
+um the weekend the Monday class is
+ 
+
+ align:start position:0%
+um the weekend the Monday class is
+really fun they love it because you can
+
+ align:start position:0%
+really fun they love it because you can
+ 
+
+ align:start position:0%
+really fun they love it because you can
+talk about your weekend so kids here
+
+ align:start position:0%
+talk about your weekend so kids here
+ 
+
+ align:start position:0%
+talk about your weekend so kids here
+they did all kinds of activity during
+
+ align:start position:0%
+they did all kinds of activity during
+ 
+
+ align:start position:0%
+they did all kinds of activity during
+the weekend so they're so interested in
+
+ align:start position:0%
+the weekend so they're so interested in
+ 
+
+ align:start position:0%
+the weekend so they're so interested in
+finding out what their classmate did
+
+ align:start position:0%
+finding out what their classmate did
+ 
+
+ align:start position:0%
+finding out what their classmate did
+because they might not know each other
+
+ align:start position:0%
+because they might not know each other
+ 
+
+ align:start position:0%
+because they might not know each other
+or some took classes together so they
+
+ align:start position:0%
+or some took classes together so they
+ 
+
+ align:start position:0%
+or some took classes together so they
+were complain same course together in
+
+ align:start position:0%
+were complain same course together in
+ 
+
+ align:start position:0%
+were complain same course together in
+the classroom many teachers probably
+
+ align:start position:0%
+the classroom many teachers probably
+ 
+
+ align:start position:0%
+the classroom many teachers probably
+think it's a waste of time it's you know
+
+ align:start position:0%
+think it's a waste of time it's you know
+ 
+
+ align:start position:0%
+think it's a waste of time it's you know
+really you know why are you talking
+
+ align:start position:0%
+really you know why are you talking
+ 
+
+ align:start position:0%
+really you know why are you talking
+about that but I think it's is through
+
+ align:start position:0%
+about that but I think it's is through
+ 
+
+ align:start position:0%
+about that but I think it's is through
+this you build a community so the moment
+
+ align:start position:0%
+this you build a community so the moment
+ 
+
+ align:start position:0%
+this you build a community so the moment
+they walk into the classroom after one
+
+ align:start position:0%
+they walk into the classroom after one
+ 
+
+ align:start position:0%
+they walk into the classroom after one
+month they're this the the you know they
+
+ align:start position:0%
+month they're this the the you know they
+ 
+
+ align:start position:0%
+month they're this the the you know they
+could have a test before the Chinese
+
+ align:start position:0%
+could have a test before the Chinese
+ 
+
+ align:start position:0%
+could have a test before the Chinese
+class the moment they walk into because
+
+ align:start position:0%
+class the moment they walk into because
+ 
+
+ align:start position:0%
+class the moment they walk into because
+of this greeting rituals they have to
+
+ align:start position:0%
+of this greeting rituals they have to
+ 
+
+ align:start position:0%
+of this greeting rituals they have to
+switch their gear into speaking Chinese
+
+ align:start position:0%
+switch their gear into speaking Chinese
+ 
+
+ align:start position:0%
+switch their gear into speaking Chinese
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+away and they because you're you're
+
+ align:start position:0%
+away and they because you're you're
+ 
+
+ align:start position:0%
+away and they because you're you're
+having a conversation so you really need
+
+ align:start position:0%
+having a conversation so you really need
+ 
+
+ align:start position:0%
+having a conversation so you really need
+to engage your classmates so that what I
+
+ align:start position:0%
+to engage your classmates so that what I
+ 
+
+ align:start position:0%
+to engage your classmates so that what I
+mean building a community they feel so
+
+ align:start position:0%
+mean building a community they feel so
+ 
+
+ align:start position:0%
+mean building a community they feel so
+freely can talk about anything they
+
+ align:start position:0%
+freely can talk about anything they
+ 
+
+ align:start position:0%
+freely can talk about anything they
+could and they don't know the words they
+
+ align:start position:0%
+could and they don't know the words they
+ 
+
+ align:start position:0%
+could and they don't know the words they
+will ask me how do you say this you know
+
+ align:start position:0%
+will ask me how do you say this you know
+ 
+
+ align:start position:0%
+will ask me how do you say this you know
+this is what I'm doing right now it's
+
+ align:start position:0%
+this is what I'm doing right now it's
+ 
+
+ align:start position:0%
+this is what I'm doing right now it's
+really blah blah blah so and people
+
+ align:start position:0%
+really blah blah blah so and people
+ 
+
+ align:start position:0%
+really blah blah blah so and people
+really want to find out and I add
+
+ align:start position:0%
+really want to find out and I add
+ 
+
+ align:start position:0%
+really want to find out and I add
+another component after a few weeks um
+
+ align:start position:0%
+another component after a few weeks um
+ 
+
+ align:start position:0%
+another component after a few weeks um
+is to by the time now they already know
+
+ align:start position:0%
+is to by the time now they already know
+ 
+
+ align:start position:0%
+is to by the time now they already know
+each other's name so I like to every
+
+ align:start position:0%
+each other's name so I like to every
+ 
+
+ align:start position:0%
+each other's name so I like to every
+lesson I ask them to write an essay I
+
+ align:start position:0%
+lesson I ask them to write an essay I
+ 
+
+ align:start position:0%
+lesson I ask them to write an essay I
+give them a topic to write an essay so I
+
+ align:start position:0%
+give them a topic to write an essay so I
+ 
+
+ align:start position:0%
+give them a topic to write an essay so I
+will ask them for instance I'll say um
+
+ align:start position:0%
+will ask them for instance I'll say um
+ 
+
+ align:start position:0%
+will ask them for instance I'll say um
+we talk about uh family so our topic is
+
+ align:start position:0%
+we talk about uh family so our topic is
+ 
+
+ align:start position:0%
+we talk about uh family so our topic is
+Chinese family so I want them to go home
+
+ align:start position:0%
+Chinese family so I want them to go home
+ 
+
+ align:start position:0%
+Chinese family so I want them to go home
+to write about uh maybe a Italian family
+
+ align:start position:0%
+to write about uh maybe a Italian family
+ 
+
+ align:start position:0%
+to write about uh maybe a Italian family
+or Spanish family so the structure model
+
+ align:start position:0%
+or Spanish family so the structure model
+ 
+
+ align:start position:0%
+or Spanish family so the structure model
+on the textbook so nobody knows what
+
+ align:start position:0%
+on the textbook so nobody knows what
+ 
+
+ align:start position:0%
+on the textbook so nobody knows what
+other students were writing about right
+
+ align:start position:0%
+other students were writing about right
+ 
+
+ align:start position:0%
+other students were writing about right
+so this time we call sharing so this
+
+ align:start position:0%
+so this time we call sharing so this
+ 
+
+ align:start position:0%
+so this time we call sharing so this
+sharing part is talk about your what did
+
+ align:start position:0%
+sharing part is talk about your what did
+ 
+
+ align:start position:0%
+sharing part is talk about your what did
+you write right so some students oh I I
+
+ align:start position:0%
+you write right so some students oh I I
+ 
+
+ align:start position:0%
+you write right so some students oh I I
+wrote about Spanish family and I said
+
+ align:start position:0%
+wrote about Spanish family and I said
+ 
+
+ align:start position:0%
+wrote about Spanish family and I said
+what was that tell us not just the title
+
+ align:start position:0%
+what was that tell us not just the title
+ 
+
+ align:start position:0%
+what was that tell us not just the title
+what's the content about so they talk
+
+ align:start position:0%
+what's the content about so they talk
+ 
+
+ align:start position:0%
+what's the content about so they talk
+about everybody has a chance to talk
+
+ align:start position:0%
+about everybody has a chance to talk
+ 
+
+ align:start position:0%
+about everybody has a chance to talk
+about quickly and then I said oh this is
+
+ align:start position:0%
+about quickly and then I said oh this is
+ 
+
+ align:start position:0%
+about quickly and then I said oh this is
+very interesting so so student will you
+
+ align:start position:0%
+very interesting so so student will you
+ 
+
+ align:start position:0%
+very interesting so so student will you
+know automat automatically naturally
+
+ align:start position:0%
+know automat automatically naturally
+ 
+
+ align:start position:0%
+know automat automatically naturally
+just has why do you pick this topic it's
+
+ align:start position:0%
+just has why do you pick this topic it's
+ 
+
+ align:start position:0%
+just has why do you pick this topic it's
+so did you know any Spanish people you
+
+ align:start position:0%
+so did you know any Spanish people you
+ 
+
+ align:start position:0%
+so did you know any Spanish people you
+know so the natural conversation just
+
+ align:start position:0%
+know so the natural conversation just
+ 
+
+ align:start position:0%
+know so the natural conversation just
+flow so it get into a routine so every
+
+ align:start position:0%
+flow so it get into a routine so every
+ 
+
+ align:start position:0%
+flow so it get into a routine so every
+time they come to my classroom they know
+
+ align:start position:0%
+time they come to my classroom they know
+ 
+
+ align:start position:0%
+time they come to my classroom they know
+there should speak chines and they
+
+ align:start position:0%
+there should speak chines and they
+ 
+
+ align:start position:0%
+there should speak chines and they
+should talk about their life and that's
+
+ align:start position:0%
+should talk about their life and that's
+ 
+
+ align:start position:0%
+should talk about their life and that's
+what they're good at they cannot talk
+
+ align:start position:0%
+what they're good at they cannot talk
+ 
+
+ align:start position:0%
+what they're good at they cannot talk
+about politics they cannot talk about uh
+
+ align:start position:0%
+about politics they cannot talk about uh
+ 
+
+ align:start position:0%
+about politics they cannot talk about uh
+history but they can talk about
+
+ align:start position:0%
+history but they can talk about
+ 
+
+ align:start position:0%
+history but they can talk about
+themselves and so to make them um the
+
+ align:start position:0%
+themselves and so to make them um the
+ 
+
+ align:start position:0%
+themselves and so to make them um the
+Ora proficiency higher and they can
+
+ align:start position:0%
+Ora proficiency higher and they can
+ 
+
+ align:start position:0%
+Ora proficiency higher and they can
+speak uh much better as remember there's
+
+ align:start position:0%
+speak uh much better as remember there's
+ 
+
+ align:start position:0%
+speak uh much better as remember there's
+one student after the
+
+ align:start position:0%
+one student after the
+ 
+
+ align:start position:0%
+one student after the
+Thanksgiving she came back she was so
+
+ align:start position:0%
+Thanksgiving she came back she was so
+ 
+
+ align:start position:0%
+Thanksgiving she came back she was so
+excited she
+
+ align:start position:0%
+excited she
+ 
+
+ align:start position:0%
+excited she
+said oh um L that's how they address me
+
+ align:start position:0%
+said oh um L that's how they address me
+ 
+
+ align:start position:0%
+said oh um L that's how they address me
+as teacher and he said you know I um I
+
+ align:start position:0%
+as teacher and he said you know I um I
+ 
+
+ align:start position:0%
+as teacher and he said you know I um I
+my father had this uh friend and I
+
+ align:start position:0%
+my father had this uh friend and I
+ 
+
+ align:start position:0%
+my father had this uh friend and I
+always call him Uncle he's from China he
+
+ align:start position:0%
+always call him Uncle he's from China he
+ 
+
+ align:start position:0%
+always call him Uncle he's from China he
+doesn't speak any English so I met him
+
+ align:start position:0%
+doesn't speak any English so I met him
+ 
+
+ align:start position:0%
+doesn't speak any English so I met him
+in New York and when it was September I
+
+ align:start position:0%
+in New York and when it was September I
+ 
+
+ align:start position:0%
+in New York and when it was September I
+cannot communicate with him at all so
+
+ align:start position:0%
+cannot communicate with him at all so
+ 
+
+ align:start position:0%
+cannot communicate with him at all so
+during the Thanksgiving my home is so
+
+ align:start position:0%
+during the Thanksgiving my home is so
+ 
+
+ align:start position:0%
+during the Thanksgiving my home is so
+far away so I went to my uncle's place
+
+ align:start position:0%
+far away so I went to my uncle's place
+ 
+
+ align:start position:0%
+far away so I went to my uncle's place
+and I can talk to him and he kept saying
+
+ align:start position:0%
+and I can talk to him and he kept saying
+ 
+
+ align:start position:0%
+and I can talk to him and he kept saying
+that my Chinese improve and he said oh
+
+ align:start position:0%
+that my Chinese improve and he said oh
+ 
+
+ align:start position:0%
+that my Chinese improve and he said oh
+my God it's only two months I can't
+
+ align:start position:0%
+my God it's only two months I can't
+ 
+
+ align:start position:0%
+my God it's only two months I can't
+believe I can speak the most Chinese
+
+ align:start position:0%
+believe I can speak the most Chinese
+ 
+
+ align:start position:0%
+believe I can speak the most Chinese
+even though I speak Chinese with my
+
+ align:start position:0%
+even though I speak Chinese with my
+ 
+
+ align:start position:0%
+even though I speak Chinese with my
+parents I can never speak to anybody and
+
+ align:start position:0%
+parents I can never speak to anybody and
+ 
+
+ align:start position:0%
+parents I can never speak to anybody and
+she just came by so excit you know so
+
+ align:start position:0%
+she just came by so excit you know so
+ 
+
+ align:start position:0%
+she just came by so excit you know so
+excited and I so I feel great so I know
+
+ align:start position:0%
+excited and I so I feel great so I know
+ 
+
+ align:start position:0%
+excited and I so I feel great so I know
+it worked yeah because to her talking
+
+ align:start position:0%
+it worked yeah because to her talking
+ 
+
+ align:start position:0%
+it worked yeah because to her talking
+speaking in Chinese doesn't have to be
+
+ align:start position:0%
+speaking in Chinese doesn't have to be
+ 
+
+ align:start position:0%
+speaking in Chinese doesn't have to be
+something she to think about you know
+
+ align:start position:0%
+something she to think about you know
+ 
+
+ align:start position:0%
+something she to think about you know
+how do I come up with the first sentence
+
+ align:start position:0%
+how do I come up with the first sentence
+ 
+
+ align:start position:0%
+how do I come up with the first sentence
+anymore because she does that in her in
+
+ align:start position:0%
+anymore because she does that in her in
+ 
+
+ align:start position:0%
+anymore because she does that in her in
+our class every time so it's very
+
+ align:start position:0%
+our class every time so it's very
+ 
+
+ align:start position:0%
+our class every time so it's very
+natural for her and plus she's you know
+
+ align:start position:0%
+natural for her and plus she's you know
+ 
+
+ align:start position:0%
+natural for her and plus she's you know
+she actually knows Chinese because her
+
+ align:start position:0%
+she actually knows Chinese because her
+ 
+
+ align:start position:0%
+she actually knows Chinese because her
+background so she crossed the barrier be
+
+ align:start position:0%
+background so she crossed the barrier be
+ 
+
+ align:start position:0%
+background so she crossed the barrier be
+able to speak to other people which is
+
+ align:start position:0%
+able to speak to other people which is
+ 
+
+ align:start position:0%
+able to speak to other people which is
+fantastic
\ No newline at end of file
diff --git a/9yfcqI-lEj0.txt b/9yfcqI-lEj0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..301f5d07f00258b227a4bf0c9fbac83bc4e02d36
--- /dev/null
+++ b/9yfcqI-lEj0.txt
@@ -0,0 +1,10845 @@
+align:start position:0%
+ 
+means you had the states switched yes
+
+ align:start position:0%
+means you had the states switched yes
+ 
+
+ align:start position:0%
+means you had the states switched yes
+that cut you you meant the composition
+
+ align:start position:0%
+that cut you you meant the composition
+ 
+
+ align:start position:0%
+that cut you you meant the composition
+of states does that mean the the basis
+
+ align:start position:0%
+of states does that mean the the basis
+ 
+
+ align:start position:0%
+of states does that mean the the basis
+states that go to form the the the the
+
+ align:start position:0%
+states that go to form the the the the
+ 
+
+ align:start position:0%
+states that go to form the the the the
+states that make up those curves switch
+
+ align:start position:0%
+states that make up those curves switch
+ 
+
+ align:start position:0%
+states that make up those curves switch
+is that what you're saying yeah um I
+
+ align:start position:0%
+is that what you're saying yeah um I
+ 
+
+ align:start position:0%
+is that what you're saying yeah um I
+mean you can so
+
+ align:start position:0%
+mean you can so
+ 
+
+ align:start position:0%
+mean you can so
+let's uh when you have a weekly avoided
+
+ align:start position:0%
+let's uh when you have a weekly avoided
+ 
+
+ align:start position:0%
+let's uh when you have a weekly avoided
+Crossing you get this kind of a a
+
+ align:start position:0%
+Crossing you get this kind of a a
+ 
+
+ align:start position:0%
+Crossing you get this kind of a a
+behavior and so up in here
+
+ align:start position:0%
+behavior and so up in here
+ 
+
+ align:start position:0%
+behavior and so up in here
+this would be a uh an electronic state
+
+ align:start position:0%
+this would be a uh an electronic state
+ 
+
+ align:start position:0%
+this would be a uh an electronic state
+has an electronic
+
+ align:start position:0%
+has an electronic
+ 
+
+ align:start position:0%
+has an electronic
+configuration which is the same as the
+
+ align:start position:0%
+configuration which is the same as the
+ 
+
+ align:start position:0%
+configuration which is the same as the
+or similar to the electronic
+
+ align:start position:0%
+or similar to the electronic
+ 
+
+ align:start position:0%
+or similar to the electronic
+configuration down here okay and so uh
+
+ align:start position:0%
+configuration down here okay and so uh
+ 
+
+ align:start position:0%
+configuration down here okay and so uh
+what happens is you have a mixture you
+
+ align:start position:0%
+what happens is you have a mixture you
+ 
+
+ align:start position:0%
+what happens is you have a mixture you
+have say configuration number one
+
+ align:start position:0%
+have say configuration number one
+ 
+
+ align:start position:0%
+have say configuration number one
+configuration number two and near here
+
+ align:start position:0%
+configuration number two and near here
+ 
+
+ align:start position:0%
+configuration number two and near here
+all of a sudden uh you go from almost
+
+ align:start position:0%
+all of a sudden uh you go from almost
+ 
+
+ align:start position:0%
+all of a sudden uh you go from almost
+pure configuration 2 to almost pure
+
+ align:start position:0%
+pure configuration 2 to almost pure
+ 
+
+ align:start position:0%
+pure configuration 2 to almost pure
+configuration one and right here you
+
+ align:start position:0%
+configuration one and right here you
+ 
+
+ align:start position:0%
+configuration one and right here you
+have a 50/50
+
+ align:start position:0%
+have a 50/50
+ 
+
+ align:start position:0%
+have a 50/50
+mixture and so the electronic character
+
+ align:start position:0%
+mixture and so the electronic character
+ 
+
+ align:start position:0%
+mixture and so the electronic character
+is hardly changing at all until right
+
+ align:start position:0%
+is hardly changing at all until right
+ 
+
+ align:start position:0%
+is hardly changing at all until right
+here where it changes very fast and that
+
+ align:start position:0%
+here where it changes very fast and that
+ 
+
+ align:start position:0%
+here where it changes very fast and that
+that leads to gross violations of the
+
+ align:start position:0%
+that leads to gross violations of the
+ 
+
+ align:start position:0%
+that leads to gross violations of the
+Assumption uh that the wave function is
+
+ align:start position:0%
+Assumption uh that the wave function is
+ 
+
+ align:start position:0%
+Assumption uh that the wave function is
+independent or approximately independent
+
+ align:start position:0%
+independent or approximately independent
+ 
+
+ align:start position:0%
+independent or approximately independent
+of internuclear distance and as a result
+
+ align:start position:0%
+of internuclear distance and as a result
+ 
+
+ align:start position:0%
+of internuclear distance and as a result
+there are large coupling
+
+ align:start position:0%
+there are large coupling
+ 
+
+ align:start position:0%
+there are large coupling
+that uh um are outside the zero order
+
+ align:start position:0%
+that uh um are outside the zero order
+ 
+
+ align:start position:0%
+that uh um are outside the zero order
+model and you have to put them in in
+
+ align:start position:0%
+model and you have to put them in in
+ 
+
+ align:start position:0%
+model and you have to put them in in
+order to get the
+
+ align:start position:0%
+order to get the
+ 
+
+ align:start position:0%
+order to get the
+truth and so when you have really really
+
+ align:start position:0%
+truth and so when you have really really
+ 
+
+ align:start position:0%
+truth and so when you have really really
+weak uh configuration interactions
+
+ align:start position:0%
+weak uh configuration interactions
+ 
+
+ align:start position:0%
+weak uh configuration interactions
+really really weak electrostatic
+
+ align:start position:0%
+really really weak electrostatic
+ 
+
+ align:start position:0%
+really really weak electrostatic
+perturbation then you get this cusp if
+
+ align:start position:0%
+perturbation then you get this cusp if
+ 
+
+ align:start position:0%
+perturbation then you get this cusp if
+it's really strong you get a kind of
+
+ align:start position:0%
+it's really strong you get a kind of
+ 
+
+ align:start position:0%
+it's really strong you get a kind of
+behavior sort of like this and uh you
+
+ align:start position:0%
+behavior sort of like this and uh you
+ 
+
+ align:start position:0%
+behavior sort of like this and uh you
+hardly know that there was of an avoided
+
+ align:start position:0%
+hardly know that there was of an avoided
+ 
+
+ align:start position:0%
+hardly know that there was of an avoided
+Crossing because the two halves of the
+
+ align:start position:0%
+Crossing because the two halves of the
+ 
+
+ align:start position:0%
+Crossing because the two halves of the
+avoided Crossing are so far apart and
+
+ align:start position:0%
+avoided Crossing are so far apart and
+ 
+
+ align:start position:0%
+avoided Crossing are so far apart and
+because uh there is so little anomalous
+
+ align:start position:0%
+because uh there is so little anomalous
+ 
+
+ align:start position:0%
+because uh there is so little anomalous
+curvature you don't really know that
+
+ align:start position:0%
+curvature you don't really know that
+ 
+
+ align:start position:0%
+curvature you don't really know that
+that this is different from a simple
+
+ align:start position:0%
+that this is different from a simple
+ 
+
+ align:start position:0%
+that this is different from a simple
+picture of what you expect to go
+
+ align:start position:0%
+picture of what you expect to go
+ 
+
+ align:start position:0%
+picture of what you expect to go
+on okay and so and that also tells you
+
+ align:start position:0%
+on okay and so and that also tells you
+ 
+
+ align:start position:0%
+on okay and so and that also tells you
+that probably the ADBA curves are the
+
+ align:start position:0%
+that probably the ADBA curves are the
+ 
+
+ align:start position:0%
+that probably the ADBA curves are the
+good way to think about the
+
+ align:start position:0%
+good way to think about the
+ 
+
+ align:start position:0%
+good way to think about the
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+and another way of knowing that is if
+
+ align:start position:0%
+and another way of knowing that is if
+ 
+
+ align:start position:0%
+and another way of knowing that is if
+you have something like this half the
+
+ align:start position:0%
+you have something like this half the
+ 
+
+ align:start position:0%
+you have something like this half the
+distance of closest approach is the
+
+ align:start position:0%
+distance of closest approach is the
+ 
+
+ align:start position:0%
+distance of closest approach is the
+electrostatic Matrix element which is
+
+ align:start position:0%
+electrostatic Matrix element which is
+ 
+
+ align:start position:0%
+electrostatic Matrix element which is
+enormous and you don't want to have
+
+ align:start position:0%
+enormous and you don't want to have
+ 
+
+ align:start position:0%
+enormous and you don't want to have
+something enormous off diagonal in your
+
+ align:start position:0%
+something enormous off diagonal in your
+ 
+
+ align:start position:0%
+something enormous off diagonal in your
+model it'll still work but the model
+
+ align:start position:0%
+model it'll still work but the model
+ 
+
+ align:start position:0%
+model it'll still work but the model
+won't look like or what's on the
+
+ align:start position:0%
+won't look like or what's on the
+ 
+
+ align:start position:0%
+won't look like or what's on the
+diagonal of the model won't look like
+
+ align:start position:0%
+diagonal of the model won't look like
+ 
+
+ align:start position:0%
+diagonal of the model won't look like
+what you've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observe so this is I mean it's really
+
+ align:start position:0%
+observe so this is I mean it's really
+ 
+
+ align:start position:0%
+observe so this is I mean it's really
+important to distinguish between the
+
+ align:start position:0%
+important to distinguish between the
+ 
+
+ align:start position:0%
+important to distinguish between the
+model which puts and in fact this is
+
+ align:start position:0%
+model which puts and in fact this is
+ 
+
+ align:start position:0%
+model which puts and in fact this is
+what I left off I didn't uh have a
+
+ align:start position:0%
+what I left off I didn't uh have a
+ 
+
+ align:start position:0%
+what I left off I didn't uh have a
+chance to finish properly at the end of
+
+ align:start position:0%
+chance to finish properly at the end of
+ 
+
+ align:start position:0%
+chance to finish properly at the end of
+last lecture and uh uh so we have a
+
+ align:start position:0%
+last lecture and uh uh so we have a
+ 
+
+ align:start position:0%
+last lecture and uh uh so we have a
+model where the Hiltonia might consist
+
+ align:start position:0%
+model where the Hiltonia might consist
+ 
+
+ align:start position:0%
+model where the Hiltonia might consist
+of three terms we'll call them A and C
+
+ align:start position:0%
+of three terms we'll call them A and C
+ 
+
+ align:start position:0%
+of three terms we'll call them A and C
+but one might be electrostatic one might
+
+ align:start position:0%
+but one might be electrostatic one might
+ 
+
+ align:start position:0%
+but one might be electrostatic one might
+be spin orbit one might be root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh you have a choice of what you put
+
+ align:start position:0%
+and uh you have a choice of what you put
+ 
+
+ align:start position:0%
+and uh you have a choice of what you put
+into the zero order picture you could
+
+ align:start position:0%
+into the zero order picture you could
+ 
+
+ align:start position:0%
+into the zero order picture you could
+say for one case you have a + b is a
+
+ align:start position:0%
+say for one case you have a + b is a
+ 
+
+ align:start position:0%
+say for one case you have a + b is a
+zero order picture and in another case
+
+ align:start position:0%
+zero order picture and in another case
+ 
+
+ align:start position:0%
+zero order picture and in another case
+you might have a +
+
+ align:start position:0%
+you might have a +
+ 
+
+ align:start position:0%
+you might have a +
+C it implies that B and
+
+ align:start position:0%
+C it implies that B and
+ 
+
+ align:start position:0%
+C it implies that B and
+C are incompatible
+
+ align:start position:0%
+C are incompatible
+ 
+
+ align:start position:0%
+C are incompatible
+and so in your zero order
+
+ align:start position:0%
+and so in your zero order
+ 
+
+ align:start position:0%
+and so in your zero order
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+um you're out of luck you
+
+ align:start position:0%
+um you're out of luck you
+ 
+
+ align:start position:0%
+um you're out of luck you
+don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay uh so uh we'll make the copy and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we but what I'm talking about right now
+
+ align:start position:0%
+we but what I'm talking about right now
+ 
+
+ align:start position:0%
+we but what I'm talking about right now
+isn't in anybody's lecture
+
+ align:start position:0%
+isn't in anybody's lecture
+ 
+
+ align:start position:0%
+isn't in anybody's lecture
+Nots
+
+ align:start position:0%
+Nots
+ 
+
+ align:start position:0%
+Nots
+um what why don't I but before we go on
+
+ align:start position:0%
+um what why don't I but before we go on
+ 
+
+ align:start position:0%
+um what why don't I but before we go on
+why don't I circulate this uh list if
+
+ align:start position:0%
+why don't I circulate this uh list if
+ 
+
+ align:start position:0%
+why don't I circulate this uh list if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+want a PDF copy of the typed lecture
+
+ align:start position:0%
+want a PDF copy of the typed lecture
+ 
+
+ align:start position:0%
+want a PDF copy of the typed lecture
+notes after they're proof read and so on
+
+ align:start position:0%
+notes after they're proof read and so on
+ 
+
+ align:start position:0%
+notes after they're proof read and so on
+put your name and email address here and
+
+ align:start position:0%
+put your name and email address here and
+ 
+
+ align:start position:0%
+put your name and email address here and
+Peter will send them out so the first
+
+ align:start position:0%
+Peter will send them out so the first
+ 
+
+ align:start position:0%
+Peter will send them out so the first
+lecture notes are nearly ready and the
+
+ align:start position:0%
+lecture notes are nearly ready and the
+ 
+
+ align:start position:0%
+lecture notes are nearly ready and the
+SE one second ones will probably be
+
+ align:start position:0%
+SE one second ones will probably be
+ 
+
+ align:start position:0%
+SE one second ones will probably be
+ready
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tomorrow okay
+
+ align:start position:0%
+tomorrow okay
+ 
+
+ align:start position:0%
+tomorrow okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+B and C are operators which are
+
+ align:start position:0%
+B and C are operators which are
+ 
+
+ align:start position:0%
+B and C are operators which are
+incompatible in other words you can't
+
+ align:start position:0%
+incompatible in other words you can't
+ 
+
+ align:start position:0%
+incompatible in other words you can't
+have states which are I States or of
+
+ align:start position:0%
+have states which are I States or of
+ 
+
+ align:start position:0%
+have states which are I States or of
+both B and C or you can't find a
+
+ align:start position:0%
+both B and C or you can't find a
+ 
+
+ align:start position:0%
+both B and C or you can't find a
+representation in which B and C are both
+
+ align:start position:0%
+representation in which B and C are both
+ 
+
+ align:start position:0%
+representation in which B and C are both
+diagonal you can
+
+ align:start position:0%
+diagonal you can
+ 
+
+ align:start position:0%
+diagonal you can
+diagonalize a and b simultaneously and A
+
+ align:start position:0%
+diagonalize a and b simultaneously and A
+ 
+
+ align:start position:0%
+diagonalize a and b simultaneously and A
+and C
+
+ align:start position:0%
+and C
+ 
+
+ align:start position:0%
+and C
+simultaneously but not B and C these are
+
+ align:start position:0%
+simultaneously but not B and C these are
+ 
+
+ align:start position:0%
+simultaneously but not B and C these are
+two mutually incompatible terms in your
+
+ align:start position:0%
+two mutually incompatible terms in your
+ 
+
+ align:start position:0%
+two mutually incompatible terms in your
+picture and you always make a choice
+
+ align:start position:0%
+picture and you always make a choice
+ 
+
+ align:start position:0%
+picture and you always make a choice
+there are always going to be mutually
+
+ align:start position:0%
+there are always going to be mutually
+ 
+
+ align:start position:0%
+there are always going to be mutually
+incompatible terms in your model for
+
+ align:start position:0%
+incompatible terms in your model for
+ 
+
+ align:start position:0%
+incompatible terms in your model for
+what's going on and you have to choose
+
+ align:start position:0%
+what's going on and you have to choose
+ 
+
+ align:start position:0%
+what's going on and you have to choose
+which one is the one that is better to
+
+ align:start position:0%
+which one is the one that is better to
+ 
+
+ align:start position:0%
+which one is the one that is better to
+put into the zero order picture so
+
+ align:start position:0%
+put into the zero order picture so
+ 
+
+ align:start position:0%
+put into the zero order picture so
+you'll capture most of the important
+
+ align:start position:0%
+you'll capture most of the important
+ 
+
+ align:start position:0%
+you'll capture most of the important
+structure that you're going to see in
+
+ align:start position:0%
+structure that you're going to see in
+ 
+
+ align:start position:0%
+structure that you're going to see in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+experiment and then you put the other
+
+ align:start position:0%
+experiment and then you put the other
+ 
+
+ align:start position:0%
+experiment and then you put the other
+one in as a
+
+ align:start position:0%
+one in as a
+ 
+
+ align:start position:0%
+one in as a
+perturbation
+
+ align:start position:0%
+perturbation
+ 
+
+ align:start position:0%
+perturbation
+and you then uh use the I states of the
+
+ align:start position:0%
+and you then uh use the I states of the
+ 
+
+ align:start position:0%
+and you then uh use the I states of the
+part of the problem you've chosen to
+
+ align:start position:0%
+part of the problem you've chosen to
+ 
+
+ align:start position:0%
+part of the problem you've chosen to
+make H
+
+ align:start position:0%
+make H
+ 
+
+ align:start position:0%
+make H
+zero to evaluate the effects of the
+
+ align:start position:0%
+zero to evaluate the effects of the
+ 
+
+ align:start position:0%
+zero to evaluate the effects of the
+missing
+
+ align:start position:0%
+missing
+ 
+
+ align:start position:0%
+missing
+part and this
+
+ align:start position:0%
+part and this
+ 
+
+ align:start position:0%
+part and this
+is basically that's all spectroscopy is
+
+ align:start position:0%
+is basically that's all spectroscopy is
+ 
+
+ align:start position:0%
+is basically that's all spectroscopy is
+in fact I would imagine that's pretty
+
+ align:start position:0%
+in fact I would imagine that's pretty
+ 
+
+ align:start position:0%
+in fact I would imagine that's pretty
+much all uh any representation of a
+
+ align:start position:0%
+much all uh any representation of a
+ 
+
+ align:start position:0%
+much all uh any representation of a
+complex situation is that you you say
+
+ align:start position:0%
+complex situation is that you you say
+ 
+
+ align:start position:0%
+complex situation is that you you say
+this is the part that that is uh that
+
+ align:start position:0%
+this is the part that that is uh that
+ 
+
+ align:start position:0%
+this is the part that that is uh that
+captures most of the problem and that I
+
+ align:start position:0%
+captures most of the problem and that I
+ 
+
+ align:start position:0%
+captures most of the problem and that I
+can describe
+
+ align:start position:0%
+can describe
+ 
+
+ align:start position:0%
+can describe
+it in a
+
+ align:start position:0%
+it in a
+ 
+
+ align:start position:0%
+it in a
+convenient way and then I put in the
+
+ align:start position:0%
+convenient way and then I put in the
+ 
+
+ align:start position:0%
+convenient way and then I put in the
+other part as uh some kind of a
+
+ align:start position:0%
+other part as uh some kind of a
+ 
+
+ align:start position:0%
+other part as uh some kind of a
+perturbation term which I also treat
+
+ align:start position:0%
+perturbation term which I also treat
+ 
+
+ align:start position:0%
+perturbation term which I also treat
+accurately and honestly and completely
+
+ align:start position:0%
+accurately and honestly and completely
+ 
+
+ align:start position:0%
+accurately and honestly and completely
+but only as a modification of what is
+
+ align:start position:0%
+but only as a modification of what is
+ 
+
+ align:start position:0%
+but only as a modification of what is
+the fundamental Simplicity of this
+
+ align:start position:0%
+the fundamental Simplicity of this
+ 
+
+ align:start position:0%
+the fundamental Simplicity of this
+particular particular situation and let
+
+ align:start position:0%
+particular particular situation and let
+ 
+
+ align:start position:0%
+particular particular situation and let
+me uh uh be a little more
+
+ align:start position:0%
+me uh uh be a little more
+ 
+
+ align:start position:0%
+me uh uh be a little more
+specific in the hamiltonian for a
+
+ align:start position:0%
+specific in the hamiltonian for a
+ 
+
+ align:start position:0%
+specific in the hamiltonian for a
+diatomic molecule we have a contribution
+
+ align:start position:0%
+diatomic molecule we have a contribution
+ 
+
+ align:start position:0%
+diatomic molecule we have a contribution
+from the spin orbit
+
+ align:start position:0%
+from the spin orbit
+ 
+
+ align:start position:0%
+from the spin orbit
+operator the spin orbit constant times
+
+ align:start position:0%
+operator the spin orbit constant times
+ 
+
+ align:start position:0%
+operator the spin orbit constant times
+lzs this gives rise to the spin orbit
+
+ align:start position:0%
+lzs this gives rise to the spin orbit
+ 
+
+ align:start position:0%
+lzs this gives rise to the spin orbit
+splitting of a multipet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state and we also have a term from the
+
+ align:start position:0%
+state and we also have a term from the
+ 
+
+ align:start position:0%
+state and we also have a term from the
+rotational hamiltonian the rotational
+
+ align:start position:0%
+rotational hamiltonian the rotational
+ 
+
+ align:start position:0%
+rotational hamiltonian the rotational
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+times uh J +
+
+ align:start position:0%
+times uh J +
+ 
+
+ align:start position:0%
+times uh J +
+s- say minus
+
+ align:start position:0%
+s- say minus
+ 
+
+ align:start position:0%
+s- say minus
+s+ where this is called the spin
+
+ align:start position:0%
+s+ where this is called the spin
+ 
+
+ align:start position:0%
+s+ where this is called the spin
+uncoupling
+
+ align:start position:0%
+uncoupling
+ 
+
+ align:start position:0%
+uncoupling
+term this is off diagonal between states
+
+ align:start position:0%
+term this is off diagonal between states
+ 
+
+ align:start position:0%
+term this is off diagonal between states
+of different values of the projection
+
+ align:start position:0%
+of different values of the projection
+ 
+
+ align:start position:0%
+of different values of the projection
+quantum number
+
+ align:start position:0%
+quantum number
+ 
+
+ align:start position:0%
+quantum number
+JZ and the projection quantum number for
+
+ align:start position:0%
+JZ and the projection quantum number for
+ 
+
+ align:start position:0%
+JZ and the projection quantum number for
+SZ this is called Omega and this is
+
+ align:start position:0%
+SZ this is called Omega and this is
+ 
+
+ align:start position:0%
+SZ this is called Omega and this is
+called Sigma so we could choose a basis
+
+ align:start position:0%
+called Sigma so we could choose a basis
+ 
+
+ align:start position:0%
+called Sigma so we could choose a basis
+set where this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonal and as a result this goes into
+
+ align:start position:0%
+diagonal and as a result this goes into
+ 
+
+ align:start position:0%
+diagonal and as a result this goes into
+h0 and this is not diagonal and this
+
+ align:start position:0%
+h0 and this is not diagonal and this
+ 
+
+ align:start position:0%
+h0 and this is not diagonal and this
+term we we call the perturbation term
+
+ align:start position:0%
+term we we call the perturbation term
+ 
+
+ align:start position:0%
+term we we call the perturbation term
+and it leads to
+
+ align:start position:0%
+and it leads to
+ 
+
+ align:start position:0%
+and it leads to
+small modifications of a characteristic
+
+ align:start position:0%
+small modifications of a characteristic
+ 
+
+ align:start position:0%
+small modifications of a characteristic
+pattern which is easy to
+
+ align:start position:0%
+pattern which is easy to
+ 
+
+ align:start position:0%
+pattern which is easy to
+recognize and that called hun case
+
+ align:start position:0%
+recognize and that called hun case
+ 
+
+ align:start position:0%
+recognize and that called hun case
+a or we can put this
+
+ align:start position:0%
+a or we can put this
+ 
+
+ align:start position:0%
+a or we can put this
+in and this forces us to a situation
+
+ align:start position:0%
+in and this forces us to a situation
+ 
+
+ align:start position:0%
+in and this forces us to a situation
+where the good quantum number is n which
+
+ align:start position:0%
+where the good quantum number is n which
+ 
+
+ align:start position:0%
+where the good quantum number is n which
+is J -
+
+ align:start position:0%
+is J -
+ 
+
+ align:start position:0%
+is J -
+s and then the rotational levels go as B
+
+ align:start position:0%
+s and then the rotational levels go as B
+ 
+
+ align:start position:0%
+s and then the rotational levels go as B
+* NN + 1 and there's nothing from the
+
+ align:start position:0%
+* NN + 1 and there's nothing from the
+ 
+
+ align:start position:0%
+* NN + 1 and there's nothing from the
+rotational hamiltonian that's off
+
+ align:start position:0%
+rotational hamiltonian that's off
+ 
+
+ align:start position:0%
+rotational hamiltonian that's off
+diagonal but this is off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diag and that's called H's case b now
+
+ align:start position:0%
+diag and that's called H's case b now
+ 
+
+ align:start position:0%
+diag and that's called H's case b now
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+also take something from the last page
+
+ align:start position:0%
+also take something from the last page
+ 
+
+ align:start position:0%
+also take something from the last page
+of the notes from last time that we
+
+ align:start position:0%
+of the notes from last time that we
+ 
+
+ align:start position:0%
+of the notes from last time that we
+didn't get to so let's say we have two
+
+ align:start position:0%
+didn't get to so let's say we have two
+ 
+
+ align:start position:0%
+didn't get to so let's say we have two
+hamiltonians hamiltonian number
+
+ align:start position:0%
+hamiltonians hamiltonian number
+ 
+
+ align:start position:0%
+hamiltonians hamiltonian number
+one which has the form Delta 2 0 0us
+
+ align:start position:0%
+one which has the form Delta 2 0 0us
+ 
+
+ align:start position:0%
+one which has the form Delta 2 0 0us
+Delta 2 in other words splitting of the
+
+ align:start position:0%
+Delta 2 in other words splitting of the
+ 
+
+ align:start position:0%
+Delta 2 in other words splitting of the
+states on the diagonal of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta so there's some term in the
+
+ align:start position:0%
+Delta so there's some term in the
+ 
+
+ align:start position:0%
+Delta so there's some term in the
+hamiltonian that lifts a
+
+ align:start position:0%
+hamiltonian that lifts a
+ 
+
+ align:start position:0%
+hamiltonian that lifts a
+degeneracy that creates a
+
+ align:start position:0%
+degeneracy that creates a
+ 
+
+ align:start position:0%
+degeneracy that creates a
+pattern and there's going to be another
+
+ align:start position:0%
+pattern and there's going to be another
+ 
+
+ align:start position:0%
+pattern and there's going to be another
+term in the hamiltonian that tries to
+
+ align:start position:0%
+term in the hamiltonian that tries to
+ 
+
+ align:start position:0%
+term in the hamiltonian that tries to
+destroy that pattern now for a 2X two
+
+ align:start position:0%
+destroy that pattern now for a 2X two
+ 
+
+ align:start position:0%
+destroy that pattern now for a 2X two
+it's easy to do all the algebra but
+
+ align:start position:0%
+it's easy to do all the algebra but
+ 
+
+ align:start position:0%
+it's easy to do all the algebra but
+generally the the problems we deal with
+
+ align:start position:0%
+generally the the problems we deal with
+ 
+
+ align:start position:0%
+generally the the problems we deal with
+are a little bit bigger than 2x two but
+
+ align:start position:0%
+are a little bit bigger than 2x two but
+ 
+
+ align:start position:0%
+are a little bit bigger than 2x two but
+not much bigger but the pattern is much
+
+ align:start position:0%
+not much bigger but the pattern is much
+ 
+
+ align:start position:0%
+not much bigger but the pattern is much
+harder to see and the amount of crank
+
+ align:start position:0%
+harder to see and the amount of crank
+ 
+
+ align:start position:0%
+harder to see and the amount of crank
+turning to to do the algebra is much
+
+ align:start position:0%
+turning to to do the algebra is much
+ 
+
+ align:start position:0%
+turning to to do the algebra is much
+more severe so this the other
+
+ align:start position:0%
+more severe so this the other
+ 
+
+ align:start position:0%
+more severe so this the other
+hilon uh is 0 0
+
+ align:start position:0%
+hilon uh is 0 0
+ 
+
+ align:start position:0%
+hilon uh is 0 0
+BB this is an off diagonal hamiltonian
+
+ align:start position:0%
+BB this is an off diagonal hamiltonian
+ 
+
+ align:start position:0%
+BB this is an off diagonal hamiltonian
+with no difference in energy on the
+
+ align:start position:0%
+with no difference in energy on the
+ 
+
+ align:start position:0%
+with no difference in energy on the
+diagonal so our full hamiltonian is the
+
+ align:start position:0%
+diagonal so our full hamiltonian is the
+ 
+
+ align:start position:0%
+diagonal so our full hamiltonian is the
+sum of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+now we can use a basis set where this
+
+ align:start position:0%
+now we can use a basis set where this
+ 
+
+ align:start position:0%
+now we can use a basis set where this
+hamiltonian stays
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonal but then there's going to be
+
+ align:start position:0%
+diagonal but then there's going to be
+ 
+
+ align:start position:0%
+diagonal but then there's going to be
+this thing here and we either do
+
+ align:start position:0%
+this thing here and we either do
+ 
+
+ align:start position:0%
+this thing here and we either do
+corrections by second order perturbation
+
+ align:start position:0%
+corrections by second order perturbation
+ 
+
+ align:start position:0%
+corrections by second order perturbation
+Theory which would be correct the
+
+ align:start position:0%
+Theory which would be correct the
+ 
+
+ align:start position:0%
+Theory which would be correct the
+energies by v^2 over Delta provided V
+
+ align:start position:0%
+energies by v^2 over Delta provided V
+ 
+
+ align:start position:0%
+energies by v^2 over Delta provided V
+over Delta absolute value is less than
+
+ align:start position:0%
+over Delta absolute value is less than
+ 
+
+ align:start position:0%
+over Delta absolute value is less than
+one that's the the uh convergence
+
+ align:start position:0%
+one that's the the uh convergence
+ 
+
+ align:start position:0%
+one that's the the uh convergence
+Criterion for ation
+
+ align:start position:0%
+Criterion for ation
+ 
+
+ align:start position:0%
+Criterion for ation
+Theory when V over Delta is not less
+
+ align:start position:0%
+Theory when V over Delta is not less
+ 
+
+ align:start position:0%
+Theory when V over Delta is not less
+than one then we actually have to
+
+ align:start position:0%
+than one then we actually have to
+ 
+
+ align:start position:0%
+than one then we actually have to
+diagonalize this
+
+ align:start position:0%
+diagonalize this
+ 
+
+ align:start position:0%
+diagonalize this
+Matrix now this is an easy Matrix to
+
+ align:start position:0%
+Matrix now this is an easy Matrix to
+ 
+
+ align:start position:0%
+Matrix now this is an easy Matrix to
+diagonalize because the off diagonal the
+
+ align:start position:0%
+diagonalize because the off diagonal the
+ 
+
+ align:start position:0%
+diagonalize because the off diagonal the
+diagonal elements have the same energy I
+
+ align:start position:0%
+diagonal elements have the same energy I
+ 
+
+ align:start position:0%
+diagonal elements have the same energy I
+can write down the transformation to
+
+ align:start position:0%
+can write down the transformation to
+ 
+
+ align:start position:0%
+can write down the transformation to
+diagonalize that without
+
+ align:start position:0%
+diagonalize that without
+ 
+
+ align:start position:0%
+diagonalize that without
+thinking so what I'm going to do is go
+
+ align:start position:0%
+thinking so what I'm going to do is go
+ 
+
+ align:start position:0%
+thinking so what I'm going to do is go
+to the basis
+
+ align:start position:0%
+to the basis
+ 
+
+ align:start position:0%
+to the basis
+set or go to the igen vectors of
+
+ align:start position:0%
+set or go to the igen vectors of
+ 
+
+ align:start position:0%
+set or go to the igen vectors of
+this okay and those are 1 > 2 * 1 + or -
+
+ align:start position:0%
+this okay and those are 1 > 2 * 1 + or -
+ 
+
+ align:start position:0%
+this okay and those are 1 > 2 * 1 + or -
+2 where these are the I vectors of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay is for the people who only had
+
+ align:start position:0%
+this okay is for the people who only had
+ 
+
+ align:start position:0%
+this okay is for the people who only had
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+or who haven't had 561 this is a reach
+
+ align:start position:0%
+or who haven't had 561 this is a reach
+ 
+
+ align:start position:0%
+or who haven't had 561 this is a reach
+but I want you to get this for my
+
+ align:start position:0%
+but I want you to get this for my
+ 
+
+ align:start position:0%
+but I want you to get this for my
+students this is not a reach but this is
+
+ align:start position:0%
+students this is not a reach but this is
+ 
+
+ align:start position:0%
+students this is not a reach but this is
+really a crucial
+
+ align:start position:0%
+really a crucial
+ 
+
+ align:start position:0%
+really a crucial
+Point okay
+
+ align:start position:0%
+Point okay
+ 
+
+ align:start position:0%
+Point okay
+so this will diagonalize this
+
+ align:start position:0%
+so this will diagonalize this
+ 
+
+ align:start position:0%
+so this will diagonalize this
+honia and how do we know that well let's
+
+ align:start position:0%
+honia and how do we know that well let's
+ 
+
+ align:start position:0%
+honia and how do we know that well let's
+calculate the Matrix elements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the symbol let's take
+
+ align:start position:0%
+okay so this is the symbol let's take
+ 
+
+ align:start position:0%
+okay so this is the symbol let's take
+the Diagon the the plus with the Plus or
+
+ align:start position:0%
+the Diagon the the plus with the Plus or
+ 
+
+ align:start position:0%
+the Diagon the the plus with the Plus or
+the minus with the minus so these are
+
+ align:start position:0%
+the minus with the minus so these are
+ 
+
+ align:start position:0%
+the minus with the minus so these are
+actually two elements at once and this
+
+ align:start position:0%
+actually two elements at once and this
+ 
+
+ align:start position:0%
+actually two elements at once and this
+is plus with the minus or minus with the
+
+ align:start position:0%
+is plus with the minus or minus with the
+ 
+
+ align:start position:0%
+is plus with the minus or minus with the
+plus and uh so we're going to have to
+
+ align:start position:0%
+plus and uh so we're going to have to
+ 
+
+ align:start position:0%
+plus and uh so we're going to have to
+wave function twice so we'll get 1 2 SAR
+
+ align:start position:0%
+wave function twice so we'll get 1 2 SAR
+ 
+
+ align:start position:0%
+wave function twice so we'll get 1 2 SAR
+so we'll get a half
+
+ align:start position:0%
+so we'll get a half
+ 
+
+ align:start position:0%
+so we'll get a half
+and then uh we'll have
+
+ align:start position:0%
+and then uh we'll have
+ 
+
+ align:start position:0%
+and then uh we'll have
+h211 plus H2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+22 plus or minus
+
+ align:start position:0%
+22 plus or minus
+ 
+
+ align:start position:0%
+22 plus or minus
+h212 plus orus H2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+21 okay so in H2 these two things are
+
+ align:start position:0%
+21 okay so in H2 these two things are
+ 
+
+ align:start position:0%
+21 okay so in H2 these two things are
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+and these two things are both V and so
+
+ align:start position:0%
+and these two things are both V and so
+ 
+
+ align:start position:0%
+and these two things are both V and so
+we get plus or minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V and when we go through so we're just
+
+ align:start position:0%
+V and when we go through so we're just
+ 
+
+ align:start position:0%
+V and when we go through so we're just
+putting this in and calculating the
+
+ align:start position:0%
+putting this in and calculating the
+ 
+
+ align:start position:0%
+putting this in and calculating the
+Matrix elements of these things now I
+
+ align:start position:0%
+Matrix elements of these things now I
+ 
+
+ align:start position:0%
+Matrix elements of these things now I
+can do this sort of almost in my head
+
+ align:start position:0%
+can do this sort of almost in my head
+ 
+
+ align:start position:0%
+can do this sort of almost in my head
+but this is going to require a little
+
+ align:start position:0%
+but this is going to require a little
+ 
+
+ align:start position:0%
+but this is going to require a little
+bit of study from people who haven't
+
+ align:start position:0%
+bit of study from people who haven't
+ 
+
+ align:start position:0%
+bit of study from people who haven't
+done it before okay but I want to write
+
+ align:start position:0%
+done it before okay but I want to write
+ 
+
+ align:start position:0%
+done it before okay but I want to write
+it out so that you can convince yourself
+
+ align:start position:0%
+it out so that you can convince yourself
+ 
+
+ align:start position:0%
+it out so that you can convince yourself
+that you can derive
+
+ align:start position:0%
+that you can derive
+ 
+
+ align:start position:0%
+that you can derive
+that it would have been easier if I just
+
+ align:start position:0%
+that it would have been easier if I just
+ 
+
+ align:start position:0%
+that it would have been easier if I just
+wrote an extra
+
+ align:start position:0%
+wrote an extra
+ 
+
+ align:start position:0%
+wrote an extra
+line on the black
+
+ align:start position:0%
+line on the black
+ 
+
+ align:start position:0%
+line on the black
+board okay uh for the second one we have
+
+ align:start position:0%
+board okay uh for the second one we have
+ 
+
+ align:start position:0%
+board okay uh for the second one we have
+a half time
+
+ align:start position:0%
+a half time
+ 
+
+ align:start position:0%
+a half time
+h11 uh for Hamilton number two- H2
+
+ align:start position:0%
+h11 uh for Hamilton number two- H2
+ 
+
+ align:start position:0%
+h11 uh for Hamilton number two- H2
+2 2 minus or plus
+
+ align:start position:0%
+2 2 minus or plus
+ 
+
+ align:start position:0%
+2 2 minus or plus
+H1 2 plus or
+
+ align:start position:0%
+H1 2 plus or
+ 
+
+ align:start position:0%
+H1 2 plus or
+minus 2
+
+ align:start position:0%
+minus 2
+ 
+
+ align:start position:0%
+minus 2
+one and these These are zero but this is
+
+ align:start position:0%
+one and these These are zero but this is
+ 
+
+ align:start position:0%
+one and these These are zero but this is
+V and this is V and so whichever choice
+
+ align:start position:0%
+V and this is V and so whichever choice
+ 
+
+ align:start position:0%
+V and this is V and so whichever choice
+of sign we choose we get zero and so H2
+
+ align:start position:0%
+of sign we choose we get zero and so H2
+ 
+
+ align:start position:0%
+of sign we choose we get zero and so H2
+transform give it that little symbol
+
+ align:start position:0%
+transform give it that little symbol
+ 
+
+ align:start position:0%
+transform give it that little symbol
+looks like this V 0 0 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V we go through the same thing for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H1 and I'm just going to write that
+
+ align:start position:0%
+H1 and I'm just going to write that
+ 
+
+ align:start position:0%
+H1 and I'm just going to write that
+down uh for H1 when we transform
+
+ align:start position:0%
+down uh for H1 when we transform
+ 
+
+ align:start position:0%
+down uh for H1 when we transform
+H1 we
+
+ align:start position:0%
+H1 we
+ 
+
+ align:start position:0%
+H1 we
+get 0 Delta 2 Delta
+
+ align:start position:0%
+get 0 Delta 2 Delta
+ 
+
+ align:start position:0%
+get 0 Delta 2 Delta
+zero doesn't it look interesting this
+
+ align:start position:0%
+zero doesn't it look interesting this
+ 
+
+ align:start position:0%
+zero doesn't it look interesting this
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+almost like the
+
+ align:start position:0%
+almost like the
+ 
+
+ align:start position:0%
+almost like the
+old
+
+ align:start position:0%
+old
+ 
+
+ align:start position:0%
+old
+H2 we have the same number off diagonal
+
+ align:start position:0%
+H2 we have the same number off diagonal
+ 
+
+ align:start position:0%
+H2 we have the same number off diagonal
+nothing on
+
+ align:start position:0%
+nothing on
+ 
+
+ align:start position:0%
+nothing on
+diagonal and this looks like the old
+
+ align:start position:0%
+diagonal and this looks like the old
+ 
+
+ align:start position:0%
+diagonal and this looks like the old
+H1 we have the same number but with
+
+ align:start position:0%
+H1 we have the same number but with
+ 
+
+ align:start position:0%
+H1 we have the same number but with
+opposite sign of the
+
+ align:start position:0%
+opposite sign of the
+ 
+
+ align:start position:0%
+opposite sign of the
+diagonal so if we choose to choose one
+
+ align:start position:0%
+diagonal so if we choose to choose one
+ 
+
+ align:start position:0%
+diagonal so if we choose to choose one
+basis set we have one term on the
+
+ align:start position:0%
+basis set we have one term on the
+ 
+
+ align:start position:0%
+basis set we have one term on the
+diagonal creating a difference in energy
+
+ align:start position:0%
+diagonal creating a difference in energy
+ 
+
+ align:start position:0%
+diagonal creating a difference in energy
+between the
+
+ align:start position:0%
+between the
+ 
+
+ align:start position:0%
+between the
+states and the other term off the
+
+ align:start position:0%
+states and the other term off the
+ 
+
+ align:start position:0%
+states and the other term off the
+ago trying to spoil that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture if we choose the opposite
+
+ align:start position:0%
+picture if we choose the opposite
+ 
+
+ align:start position:0%
+picture if we choose the opposite
+basis the roles of the two terms the
+
+ align:start position:0%
+basis the roles of the two terms the
+ 
+
+ align:start position:0%
+basis the roles of the two terms the
+good term and the bad term switch and
+
+ align:start position:0%
+good term and the bad term switch and
+ 
+
+ align:start position:0%
+good term and the bad term switch and
+good becomes bad and bad becomes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good and this is everywhere what is
+
+ align:start position:0%
+good and this is everywhere what is
+ 
+
+ align:start position:0%
+good and this is everywhere what is
+happening and
+
+ align:start position:0%
+happening and
+ 
+
+ align:start position:0%
+happening and
+sometimes uh in order to understand the
+
+ align:start position:0%
+sometimes uh in order to understand the
+ 
+
+ align:start position:0%
+sometimes uh in order to understand the
+mechanism of what's going on it's
+
+ align:start position:0%
+mechanism of what's going on it's
+ 
+
+ align:start position:0%
+mechanism of what's going on it's
+necessary to make one of these
+
+ align:start position:0%
+necessary to make one of these
+ 
+
+ align:start position:0%
+necessary to make one of these
+Transformations and the reason for some
+
+ align:start position:0%
+Transformations and the reason for some
+ 
+
+ align:start position:0%
+Transformations and the reason for some
+off diagonal interaction between states
+
+ align:start position:0%
+off diagonal interaction between states
+ 
+
+ align:start position:0%
+off diagonal interaction between states
+that leads to some Dynamics or some
+
+ align:start position:0%
+that leads to some Dynamics or some
+ 
+
+ align:start position:0%
+that leads to some Dynamics or some
+complexity in the Spectrum is much
+
+ align:start position:0%
+complexity in the Spectrum is much
+ 
+
+ align:start position:0%
+complexity in the Spectrum is much
+clearer in one representation as opposed
+
+ align:start position:0%
+clearer in one representation as opposed
+ 
+
+ align:start position:0%
+clearer in one representation as opposed
+to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other and
+
+ align:start position:0%
+other and
+ 
+
+ align:start position:0%
+other and
+uh one example of that which we might
+
+ align:start position:0%
+uh one example of that which we might
+ 
+
+ align:start position:0%
+uh one example of that which we might
+get to today and might not get to it all
+
+ align:start position:0%
+get to today and might not get to it all
+ 
+
+ align:start position:0%
+get to today and might not get to it all
+is rotational Auto
+
+ align:start position:0%
+is rotational Auto
+ 
+
+ align:start position:0%
+is rotational Auto
+ionization I'll get to that I'll talk
+
+ align:start position:0%
+ionization I'll get to that I'll talk
+ 
+
+ align:start position:0%
+ionization I'll get to that I'll talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+perturbations now okay
+
+ align:start position:0%
+perturbations now okay
+ 
+
+ align:start position:0%
+perturbations now okay
+so this is what was left from the last
+
+ align:start position:0%
+so this is what was left from the last
+ 
+
+ align:start position:0%
+so this is what was left from the last
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+and it's probably the most important
+
+ align:start position:0%
+and it's probably the most important
+ 
+
+ align:start position:0%
+and it's probably the most important
+point from the last lecture we have
+
+ align:start position:0%
+point from the last lecture we have
+ 
+
+ align:start position:0%
+point from the last lecture we have
+always mutually incompatible terms in
+
+ align:start position:0%
+always mutually incompatible terms in
+ 
+
+ align:start position:0%
+always mutually incompatible terms in
+the hamiltonian and we choose one to go
+
+ align:start position:0%
+the hamiltonian and we choose one to go
+ 
+
+ align:start position:0%
+the hamiltonian and we choose one to go
+into h0 and the rest to put uh off
+
+ align:start position:0%
+into h0 and the rest to put uh off
+ 
+
+ align:start position:0%
+into h0 and the rest to put uh off
+diagonal and treat as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perturbations every choice when you do
+
+ align:start position:0%
+perturbations every choice when you do
+ 
+
+ align:start position:0%
+perturbations every choice when you do
+the problem completely including all the
+
+ align:start position:0%
+the problem completely including all the
+ 
+
+ align:start position:0%
+the problem completely including all the
+off elements gives an equally good
+
+ align:start position:0%
+off elements gives an equally good
+ 
+
+ align:start position:0%
+off elements gives an equally good
+representation of reality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the different approaches when you
+
+ align:start position:0%
+but the different approaches when you
+ 
+
+ align:start position:0%
+but the different approaches when you
+ignore the
+
+ align:start position:0%
+ignore the
+ 
+
+ align:start position:0%
+ignore the
+alagon give very different
+
+ align:start position:0%
+alagon give very different
+ 
+
+ align:start position:0%
+alagon give very different
+correspondence to
+
+ align:start position:0%
+correspondence to
+ 
+
+ align:start position:0%
+correspondence to
+reality an appropriate representation
+
+ align:start position:0%
+reality an appropriate representation
+ 
+
+ align:start position:0%
+reality an appropriate representation
+gives a
+
+ align:start position:0%
+gives a
+ 
+
+ align:start position:0%
+gives a
+recognizable uh description of reality
+
+ align:start position:0%
+recognizable uh description of reality
+ 
+
+ align:start position:0%
+recognizable uh description of reality
+where there are small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deviations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The crucial actor in our treatment of
+
+ align:start position:0%
+The crucial actor in our treatment of
+ 
+
+ align:start position:0%
+The crucial actor in our treatment of
+molecules was the Bor Oppenheimer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation so I keep dividing up the
+
+ align:start position:0%
+approximation so I keep dividing up the
+ 
+
+ align:start position:0%
+approximation so I keep dividing up the
+Hamilton slightly different we have the
+
+ align:start position:0%
+Hamilton slightly different we have the
+ 
+
+ align:start position:0%
+Hamilton slightly different we have the
+electronic plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibrational we have spin
+
+ align:start position:0%
+vibrational we have spin
+ 
+
+ align:start position:0%
+vibrational we have spin
+orb and
+
+ align:start position:0%
+orb and
+ 
+
+ align:start position:0%
+orb and
+rotation the reason I put these together
+
+ align:start position:0%
+rotation the reason I put these together
+ 
+
+ align:start position:0%
+rotation the reason I put these together
+is that when we do the born Oppenheimer
+
+ align:start position:0%
+is that when we do the born Oppenheimer
+ 
+
+ align:start position:0%
+is that when we do the born Oppenheimer
+approximation we generate the potential
+
+ align:start position:0%
+approximation we generate the potential
+ 
+
+ align:start position:0%
+approximation we generate the potential
+curves and once we have the potential
+
+ align:start position:0%
+curves and once we have the potential
+ 
+
+ align:start position:0%
+curves and once we have the potential
+curves we solve the vibrational
+
+ align:start position:0%
+curves we solve the vibrational
+ 
+
+ align:start position:0%
+curves we solve the vibrational
+problem and uh whether we make a
+
+ align:start position:0%
+problem and uh whether we make a
+ 
+
+ align:start position:0%
+problem and uh whether we make a
+diabetic or adiabetic choice we get
+
+ align:start position:0%
+diabetic or adiabetic choice we get
+ 
+
+ align:start position:0%
+diabetic or adiabetic choice we get
+different potential curves so the
+
+ align:start position:0%
+different potential curves so the
+ 
+
+ align:start position:0%
+different potential curves so the
+vibrational problem is different but
+
+ align:start position:0%
+vibrational problem is different but
+ 
+
+ align:start position:0%
+vibrational problem is different but
+it's the same crank you turn you have a
+
+ align:start position:0%
+it's the same crank you turn you have a
+ 
+
+ align:start position:0%
+it's the same crank you turn you have a
+potential energy curve
+
+ align:start position:0%
+potential energy curve
+ 
+
+ align:start position:0%
+potential energy curve
+and you have the nuclear kinetic energy
+
+ align:start position:0%
+and you have the nuclear kinetic energy
+ 
+
+ align:start position:0%
+and you have the nuclear kinetic energy
+you solve the nuclear shorting equation
+
+ align:start position:0%
+you solve the nuclear shorting equation
+ 
+
+ align:start position:0%
+you solve the nuclear shorting equation
+you get IG functions and I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Val
+
+ align:start position:0%
+Val
+ 
+
+ align:start position:0%
+Val
+okay the most for diatomic molecules the
+
+ align:start position:0%
+okay the most for diatomic molecules the
+ 
+
+ align:start position:0%
+okay the most for diatomic molecules the
+most convenient from the point of view
+
+ align:start position:0%
+most convenient from the point of view
+ 
+
+ align:start position:0%
+most convenient from the point of view
+of writing down Matrix elements and
+
+ align:start position:0%
+of writing down Matrix elements and
+ 
+
+ align:start position:0%
+of writing down Matrix elements and
+representing the problem the most
+
+ align:start position:0%
+representing the problem the most
+ 
+
+ align:start position:0%
+representing the problem the most
+convenient basis set is generally the
+
+ align:start position:0%
+convenient basis set is generally the
+ 
+
+ align:start position:0%
+convenient basis set is generally the
+Huns case a basis set and so case
+
+ align:start position:0%
+Huns case a basis set and so case
+ 
+
+ align:start position:0%
+Huns case a basis set and so case
+a basis functions look like this we have
+
+ align:start position:0%
+a basis functions look like this we have
+ 
+
+ align:start position:0%
+a basis functions look like this we have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+electronic uh a symbol that says which
+
+ align:start position:0%
+electronic uh a symbol that says which
+ 
+
+ align:start position:0%
+electronic uh a symbol that says which
+electronic statement come with an i and
+
+ align:start position:0%
+electronic statement come with an i and
+ 
+
+ align:start position:0%
+electronic statement come with an i and
+then we have L which is never really
+
+ align:start position:0%
+then we have L which is never really
+ 
+
+ align:start position:0%
+then we have L which is never really
+good but we often include it as a uh
+
+ align:start position:0%
+good but we often include it as a uh
+ 
+
+ align:start position:0%
+good but we often include it as a uh
+label Lambda s
+
+ align:start position:0%
+label Lambda s
+ 
+
+ align:start position:0%
+label Lambda s
+Sigma and then Omega k m
+
+ align:start position:0%
+Sigma and then Omega k m
+ 
+
+ align:start position:0%
+Sigma and then Omega k m
+so these are the quantum numbers and
+
+ align:start position:0%
+so these are the quantum numbers and
+ 
+
+ align:start position:0%
+so these are the quantum numbers and
+these are our basis
+
+ align:start position:0%
+these are our basis
+ 
+
+ align:start position:0%
+these are our basis
+functions and in order to make any
+
+ align:start position:0%
+functions and in order to make any
+ 
+
+ align:start position:0%
+functions and in order to make any
+progress with diatomic molecules we need
+
+ align:start position:0%
+progress with diatomic molecules we need
+ 
+
+ align:start position:0%
+progress with diatomic molecules we need
+to know how to evaluate Matrix elements
+
+ align:start position:0%
+to know how to evaluate Matrix elements
+ 
+
+ align:start position:0%
+to know how to evaluate Matrix elements
+of all operators in the hamiltonian in
+
+ align:start position:0%
+of all operators in the hamiltonian in
+ 
+
+ align:start position:0%
+of all operators in the hamiltonian in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+so for
+
+ align:start position:0%
+so for
+ 
+
+ align:start position:0%
+so for
+angular
+
+ align:start position:0%
+angular
+ 
+
+ align:start position:0%
+angular
+momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elements you want to look at
+
+ align:start position:0%
+elements you want to look at
+ 
+
+ align:start position:0%
+elements you want to look at
+Pages 72 to 81 for my book which I
+
+ align:start position:0%
+Pages 72 to 81 for my book which I
+ 
+
+ align:start position:0%
+Pages 72 to 81 for my book which I
+handed out until I ran out of
+
+ align:start position:0%
+handed out until I ran out of
+ 
+
+ align:start position:0%
+handed out until I ran out of
+copies uh some of you haven't it's it's
+
+ align:start position:0%
+copies uh some of you haven't it's it's
+ 
+
+ align:start position:0%
+copies uh some of you haven't it's it's
+in that
+
+ align:start position:0%
+in that
+ 
+
+ align:start position:0%
+in that
+handout
+
+ align:start position:0%
+handout
+ 
+
+ align:start position:0%
+handout
+uh there's three pages that are with
+
+ align:start position:0%
+uh there's three pages that are with
+ 
+
+ align:start position:0%
+uh there's three pages that are with
+nice pictures which I'll get to and then
+
+ align:start position:0%
+nice pictures which I'll get to and then
+ 
+
+ align:start position:0%
+nice pictures which I'll get to and then
+there is the Machinery okay so let us
+
+ align:start position:0%
+there is the Machinery okay so let us
+ 
+
+ align:start position:0%
+there is the Machinery okay so let us
+say that a is an angular momentum and
+
+ align:start position:0%
+say that a is an angular momentum and
+ 
+
+ align:start position:0%
+say that a is an angular momentum and
+some operator some angular momentum and
+
+ align:start position:0%
+some operator some angular momentum and
+ 
+
+ align:start position:0%
+some operator some angular momentum and
+the nice thing about angular momenta is
+
+ align:start position:0%
+the nice thing about angular momenta is
+ 
+
+ align:start position:0%
+the nice thing about angular momenta is
+that once you know what the Matrix
+
+ align:start position:0%
+that once you know what the Matrix
+ 
+
+ align:start position:0%
+that once you know what the Matrix
+elements for one angular momentum are
+
+ align:start position:0%
+elements for one angular momentum are
+ 
+
+ align:start position:0%
+elements for one angular momentum are
+you know them all and
+
+ align:start position:0%
+you know them all and
+ 
+
+ align:start position:0%
+you know them all and
+so we have the angular momentum Square
+
+ align:start position:0%
+so we have the angular momentum Square
+ 
+
+ align:start position:0%
+so we have the angular momentum Square
+operating on
+
+ align:start position:0%
+operating on
+ 
+
+ align:start position:0%
+operating on
+a basis function which is expressed with
+
+ align:start position:0%
+a basis function which is expressed with
+ 
+
+ align:start position:0%
+a basis function which is expressed with
+two quantum numbers the quantum number
+
+ align:start position:0%
+two quantum numbers the quantum number
+ 
+
+ align:start position:0%
+two quantum numbers the quantum number
+associated with the total angular
+
+ align:start position:0%
+associated with the total angular
+ 
+
+ align:start position:0%
+associated with the total angular
+momentum and with a projection of that
+
+ align:start position:0%
+momentum and with a projection of that
+ 
+
+ align:start position:0%
+momentum and with a projection of that
+angular
+
+ align:start position:0%
+angular
+ 
+
+ align:start position:0%
+angular
+momentum projection on what we call the
+
+ align:start position:0%
+momentum projection on what we call the
+ 
+
+ align:start position:0%
+momentum projection on what we call the
+the Symmetry Axis or the
+
+ align:start position:0%
+the Symmetry Axis or the
+ 
+
+ align:start position:0%
+the Symmetry Axis or the
+z-axis okay we're two free to choose but
+
+ align:start position:0%
+z-axis okay we're two free to choose but
+ 
+
+ align:start position:0%
+z-axis okay we're two free to choose but
+in diatomic molecules you would be kind
+
+ align:start position:0%
+in diatomic molecules you would be kind
+ 
+
+ align:start position:0%
+in diatomic molecules you would be kind
+of stupid to choose anything but the
+
+ align:start position:0%
+of stupid to choose anything but the
+ 
+
+ align:start position:0%
+of stupid to choose anything but the
+internuclear axis of Z because that's an
+
+ align:start position:0%
+internuclear axis of Z because that's an
+ 
+
+ align:start position:0%
+internuclear axis of Z because that's an
+axis of cylindri iCal symmetry but it
+
+ align:start position:0%
+axis of cylindri iCal symmetry but it
+ 
+
+ align:start position:0%
+axis of cylindri iCal symmetry but it
+turns out that for ridberg States
+
+ align:start position:0%
+turns out that for ridberg States
+ 
+
+ align:start position:0%
+turns out that for ridberg States
+sometimes the quantization axis is not
+
+ align:start position:0%
+sometimes the quantization axis is not
+ 
+
+ align:start position:0%
+sometimes the quantization axis is not
+the internuclear axis but it's the axis
+
+ align:start position:0%
+the internuclear axis but it's the axis
+ 
+
+ align:start position:0%
+the internuclear axis but it's the axis
+about which the molecule
+
+ align:start position:0%
+about which the molecule
+ 
+
+ align:start position:0%
+about which the molecule
+rotates and that leads to some
+
+ align:start position:0%
+rotates and that leads to some
+ 
+
+ align:start position:0%
+rotates and that leads to some
+Strang but so you have a magnitude and a
+
+ align:start position:0%
+Strang but so you have a magnitude and a
+ 
+
+ align:start position:0%
+Strang but so you have a magnitude and a
+projection and so you get a a
+
+ align:start position:0%
+projection and so you get a a
+ 
+
+ align:start position:0%
+projection and so you get a a
++1 a
+
+ align:start position:0%
++1 a
+ 
+
+ align:start position:0%
++1 a
+Al
+
+ align:start position:0%
+Al
+ 
+
+ align:start position:0%
+Al
+we have the space fixed the the
+
+ align:start position:0%
+we have the space fixed the the
+ 
+
+ align:start position:0%
+we have the space fixed the the
+laborator sorry the body fixed
+
+ align:start position:0%
+laborator sorry the body fixed
+ 
+
+ align:start position:0%
+laborator sorry the body fixed
+zis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projection and that's Alpha a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Al then we have the raising and lowering
+
+ align:start position:0%
+Al then we have the raising and lowering
+ 
+
+ align:start position:0%
+Al then we have the raising and lowering
+operators which are a X plus orus I a y
+
+ align:start position:0%
+operators which are a X plus orus I a y
+ 
+
+ align:start position:0%
+operators which are a X plus orus I a y
+and a +us on a alpha gives a a +
+
+ align:start position:0%
+and a +us on a alpha gives a a +
+ 
+
+ align:start position:0%
+and a +us on a alpha gives a a +
+1us alpha alpha Plus or - 1
+
+ align:start position:0%
+1us alpha alpha Plus or - 1
+ 
+
+ align:start position:0%
+1us alpha alpha Plus or - 1
+square a plus-
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and that's all that's all you
+
+ align:start position:0%
+1 and that's all that's all you
+ 
+
+ align:start position:0%
+1 and that's all that's all you
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+this is a you know a small amount to
+
+ align:start position:0%
+this is a you know a small amount to
+ 
+
+ align:start position:0%
+this is a you know a small amount to
+learn in order to be able to address
+
+ align:start position:0%
+learn in order to be able to address
+ 
+
+ align:start position:0%
+learn in order to be able to address
+practically any problem in diatomic
+
+ align:start position:0%
+practically any problem in diatomic
+ 
+
+ align:start position:0%
+practically any problem in diatomic
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+spectroscopy and the reason case a is
+
+ align:start position:0%
+spectroscopy and the reason case a is
+ 
+
+ align:start position:0%
+spectroscopy and the reason case a is
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+is you have three important angular
+
+ align:start position:0%
+is you have three important angular
+ 
+
+ align:start position:0%
+is you have three important angular
+momentum and each of them have their
+
+ align:start position:0%
+momentum and each of them have their
+ 
+
+ align:start position:0%
+momentum and each of them have their
+projection
+
+ align:start position:0%
+projection
+ 
+
+ align:start position:0%
+projection
+specified so so that means it is
+
+ align:start position:0%
+specified so so that means it is
+ 
+
+ align:start position:0%
+specified so so that means it is
+completely transparent to write Matrix
+
+ align:start position:0%
+completely transparent to write Matrix
+ 
+
+ align:start position:0%
+completely transparent to write Matrix
+elements of a s a z and A+ minus there
+
+ align:start position:0%
+elements of a s a z and A+ minus there
+ 
+
+ align:start position:0%
+elements of a s a z and A+ minus there
+isn't anything
+
+ align:start position:0%
+isn't anything
+ 
+
+ align:start position:0%
+isn't anything
+else so you don't have to use CL Cordon
+
+ align:start position:0%
+else so you don't have to use CL Cordon
+ 
+
+ align:start position:0%
+else so you don't have to use CL Cordon
+coefficients or 3j
+
+ align:start position:0%
+coefficients or 3j
+ 
+
+ align:start position:0%
+coefficients or 3j
+coefficients if you're in case
+
+ align:start position:0%
+coefficients if you're in case
+ 
+
+ align:start position:0%
+coefficients if you're in case
+a so even for situations where case a is
+
+ align:start position:0%
+a so even for situations where case a is
+ 
+
+ align:start position:0%
+a so even for situations where case a is
+inappropriate many people prefer to use
+
+ align:start position:0%
+inappropriate many people prefer to use
+ 
+
+ align:start position:0%
+inappropriate many people prefer to use
+Cas a because there it's easy for them
+
+ align:start position:0%
+Cas a because there it's easy for them
+ 
+
+ align:start position:0%
+Cas a because there it's easy for them
+to set up the machine that represents
+
+ align:start position:0%
+to set up the machine that represents
+ 
+
+ align:start position:0%
+to set up the machine that represents
+their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spect now there's no big deal using 3j
+
+ align:start position:0%
+spect now there's no big deal using 3j
+ 
+
+ align:start position:0%
+spect now there's no big deal using 3j
+coefficients to deal with angular
+
+ align:start position:0%
+coefficients to deal with angular
+ 
+
+ align:start position:0%
+coefficients to deal with angular
+momenta coupling and uncoupling and if
+
+ align:start position:0%
+momenta coupling and uncoupling and if
+ 
+
+ align:start position:0%
+momenta coupling and uncoupling and if
+you're going to be a professional you
+
+ align:start position:0%
+you're going to be a professional you
+ 
+
+ align:start position:0%
+you're going to be a professional you
+want to be able to work in different
+
+ align:start position:0%
+want to be able to work in different
+ 
+
+ align:start position:0%
+want to be able to work in different
+basis sets and to transform between them
+
+ align:start position:0%
+basis sets and to transform between them
+ 
+
+ align:start position:0%
+basis sets and to transform between them
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh the vector coupling or 3j
+
+ align:start position:0%
+uh the vector coupling or 3j
+ 
+
+ align:start position:0%
+uh the vector coupling or 3j
+coefficients um and you can get a
+
+ align:start position:0%
+coefficients um and you can get a
+ 
+
+ align:start position:0%
+coefficients um and you can get a
+computer routine that will calculate any
+
+ align:start position:0%
+computer routine that will calculate any
+ 
+
+ align:start position:0%
+computer routine that will calculate any
+of those you ever need and so the only
+
+ align:start position:0%
+of those you ever need and so the only
+ 
+
+ align:start position:0%
+of those you ever need and so the only
+difficulty is that 3j coefficients are
+
+ align:start position:0%
+difficulty is that 3j coefficients are
+ 
+
+ align:start position:0%
+difficulty is that 3j coefficients are
+expressed angular momentum
+
+ align:start position:0%
+expressed angular momentum
+ 
+
+ align:start position:0%
+expressed angular momentum
+transformation coefficients are
+
+ align:start position:0%
+transformation coefficients are
+ 
+
+ align:start position:0%
+transformation coefficients are
+expressed or are labeled with six
+
+ align:start position:0%
+expressed or are labeled with six
+ 
+
+ align:start position:0%
+expressed or are labeled with six
+quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers and so somehow you have to think
+
+ align:start position:0%
+numbers and so somehow you have to think
+ 
+
+ align:start position:0%
+numbers and so somehow you have to think
+about six quantum
+
+ align:start position:0%
+about six quantum
+ 
+
+ align:start position:0%
+about six quantum
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+and after a while it
+
+ align:start position:0%
+and after a while it
+ 
+
+ align:start position:0%
+and after a while it
+becomes not so hard
+
+ align:start position:0%
+becomes not so hard
+ 
+
+ align:start position:0%
+becomes not so hard
+but this this is a more linear approach
+
+ align:start position:0%
+but this this is a more linear approach
+ 
+
+ align:start position:0%
+but this this is a more linear approach
+in some sense okay so I said enough
+
+ align:start position:0%
+in some sense okay so I said enough
+ 
+
+ align:start position:0%
+in some sense okay so I said enough
+about that uh if you're going to start
+
+ align:start position:0%
+about that uh if you're going to start
+ 
+
+ align:start position:0%
+about that uh if you're going to start
+out doing uh datomic molecules I
+
+ align:start position:0%
+out doing uh datomic molecules I
+ 
+
+ align:start position:0%
+out doing uh datomic molecules I
+strongly recommend case
+
+ align:start position:0%
+strongly recommend case
+ 
+
+ align:start position:0%
+strongly recommend case
+a yes you remind us I can't remember is
+
+ align:start position:0%
+a yes you remind us I can't remember is
+ 
+
+ align:start position:0%
+a yes you remind us I can't remember is
+there any obvious way to to look at a
+
+ align:start position:0%
+there any obvious way to to look at a
+ 
+
+ align:start position:0%
+there any obvious way to to look at a
+datomic molecule and guess whether it's
+
+ align:start position:0%
+datomic molecule and guess whether it's
+ 
+
+ align:start position:0%
+datomic molecule and guess whether it's
+going to be case A or B is it has
+
+ align:start position:0%
+going to be case A or B is it has
+ 
+
+ align:start position:0%
+going to be case A or B is it has
+something to do with the size type of
+
+ align:start position:0%
+something to do with the size type of
+ 
+
+ align:start position:0%
+something to do with the size type of
+you have to look at
+
+ align:start position:0%
+you have to look at
+ 
+
+ align:start position:0%
+you have to look at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+versus
+
+ align:start position:0%
+versus
+ 
+
+ align:start position:0%
+versus
+B uh
+
+ align:start position:0%
+B uh
+ 
+
+ align:start position:0%
+B uh
+J okay so all you have to know is this
+
+ align:start position:0%
+J okay so all you have to know is this
+ 
+
+ align:start position:0%
+J okay so all you have to know is this
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+orbit the rotational Conant that's right
+
+ align:start position:0%
+orbit the rotational Conant that's right
+ 
+
+ align:start position:0%
+orbit the rotational Conant that's right
+and so a is small for the beginning of
+
+ align:start position:0%
+and so a is small for the beginning of
+ 
+
+ align:start position:0%
+and so a is small for the beginning of
+the periodic table it gets larger and
+
+ align:start position:0%
+the periodic table it gets larger and
+ 
+
+ align:start position:0%
+the periodic table it gets larger and
+larger and uh B uh is uh large for
+
+ align:start position:0%
+larger and uh B uh is uh large for
+ 
+
+ align:start position:0%
+larger and uh B uh is uh large for
+hydrogen and large for molecules that
+
+ align:start position:0%
+hydrogen and large for molecules that
+ 
+
+ align:start position:0%
+hydrogen and large for molecules that
+have one
+
+ align:start position:0%
+have one
+ 
+
+ align:start position:0%
+have one
+hydrogen and sort of intermediate for
+
+ align:start position:0%
+hydrogen and sort of intermediate for
+ 
+
+ align:start position:0%
+hydrogen and sort of intermediate for
+molecules that have two second row atoms
+
+ align:start position:0%
+molecules that have two second row atoms
+ 
+
+ align:start position:0%
+molecules that have two second row atoms
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+Co and uh for heavier atoms B is very
+
+ align:start position:0%
+Co and uh for heavier atoms B is very
+ 
+
+ align:start position:0%
+Co and uh for heavier atoms B is very
+small and so as you go down the periodic
+
+ align:start position:0%
+small and so as you go down the periodic
+ 
+
+ align:start position:0%
+small and so as you go down the periodic
+table a heavier heavier molecule
+
+ align:start position:0%
+table a heavier heavier molecule
+ 
+
+ align:start position:0%
+table a heavier heavier molecule
+you tend to go towards case
+
+ align:start position:0%
+you tend to go towards case
+ 
+
+ align:start position:0%
+you tend to go towards case
+a but if Lambda is zero in other words
+
+ align:start position:0%
+a but if Lambda is zero in other words
+ 
+
+ align:start position:0%
+a but if Lambda is zero in other words
+Sigma States you're always in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KP but it's not a big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deal okay now I said it was easy but
+
+ align:start position:0%
+deal okay now I said it was easy but
+ 
+
+ align:start position:0%
+deal okay now I said it was easy but
+there's one little patch if you want to
+
+ align:start position:0%
+there's one little patch if you want to
+ 
+
+ align:start position:0%
+there's one little patch if you want to
+do this without thinking you have to say
+
+ align:start position:0%
+do this without thinking you have to say
+ 
+
+ align:start position:0%
+do this without thinking you have to say
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+uh Bob told me that if we have an
+
+ align:start position:0%
+uh Bob told me that if we have an
+ 
+
+ align:start position:0%
+uh Bob told me that if we have an
+angular momentum that controls the RO
+
+ align:start position:0%
+angular momentum that controls the RO
+ 
+
+ align:start position:0%
+angular momentum that controls the RO
+the rotation of the body fixed
+
+ align:start position:0%
+the rotation of the body fixed
+ 
+
+ align:start position:0%
+the rotation of the body fixed
+coordinate system relative to the
+
+ align:start position:0%
+coordinate system relative to the
+ 
+
+ align:start position:0%
+coordinate system relative to the
+laboratory coordinate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system then I have to make a small patch
+
+ align:start position:0%
+system then I have to make a small patch
+ 
+
+ align:start position:0%
+system then I have to make a small patch
+and it turns out that
+
+ align:start position:0%
+and it turns out that
+ 
+
+ align:start position:0%
+and it turns out that
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+n and R J is the total angular momentum
+
+ align:start position:0%
+n and R J is the total angular momentum
+ 
+
+ align:start position:0%
+n and R J is the total angular momentum
+n is J minus s the total angular
+
+ align:start position:0%
+n is J minus s the total angular
+ 
+
+ align:start position:0%
+n is J minus s the total angular
+momentum exclusive of Spin and R is the
+
+ align:start position:0%
+momentum exclusive of Spin and R is the
+ 
+
+ align:start position:0%
+momentum exclusive of Spin and R is the
+nuclear
+
+ align:start position:0%
+nuclear
+ 
+
+ align:start position:0%
+nuclear
+rotation then J plus
+
+ align:start position:0%
+rotation then J plus
+ 
+
+ align:start position:0%
+rotation then J plus
+lowers Omega instead of raising
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it n plus lowers r+ well r+ can't really
+
+ align:start position:0%
+it n plus lowers r+ well r+ can't really
+ 
+
+ align:start position:0%
+it n plus lowers r+ well r+ can't really
+do anything because there is no
+
+ align:start position:0%
+do anything because there is no
+ 
+
+ align:start position:0%
+do anything because there is no
+projection of r on the inter nuclear
+
+ align:start position:0%
+projection of r on the inter nuclear
+ 
+
+ align:start position:0%
+projection of r on the inter nuclear
+axis because R is we have Atomic
+
+ align:start position:0%
+axis because R is we have Atomic
+ 
+
+ align:start position:0%
+axis because R is we have Atomic
+molecule and R by definition is
+
+ align:start position:0%
+molecule and R by definition is
+ 
+
+ align:start position:0%
+molecule and R by definition is
+perpendicular so but these angular
+
+ align:start position:0%
+perpendicular so but these angular
+ 
+
+ align:start position:0%
+perpendicular so but these angular
+moment have some special
+
+ align:start position:0%
+moment have some special
+ 
+
+ align:start position:0%
+moment have some special
+property and you can you can understand
+
+ align:start position:0%
+property and you can you can understand
+ 
+
+ align:start position:0%
+property and you can you can understand
+that when you look carefully at the
+
+ align:start position:0%
+that when you look carefully at the
+ 
+
+ align:start position:0%
+that when you look carefully at the
+transformation that takes you from body
+
+ align:start position:0%
+transformation that takes you from body
+ 
+
+ align:start position:0%
+transformation that takes you from body
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+laboratory Direction cosign and when you
+
+ align:start position:0%
+laboratory Direction cosign and when you
+ 
+
+ align:start position:0%
+laboratory Direction cosign and when you
+work when you develop more facility with
+
+ align:start position:0%
+work when you develop more facility with
+ 
+
+ align:start position:0%
+work when you develop more facility with
+the the true classical mechanics and one
+
+ align:start position:0%
+the the true classical mechanics and one
+ 
+
+ align:start position:0%
+the the true classical mechanics and one
+mechanics of the system okay but right
+
+ align:start position:0%
+mechanics of the system okay but right
+ 
+
+ align:start position:0%
+mechanics of the system okay but right
+now I just say this is a
+
+ align:start position:0%
+now I just say this is a
+ 
+
+ align:start position:0%
+now I just say this is a
+patch and basically you are now
+
+ align:start position:0%
+patch and basically you are now
+ 
+
+ align:start position:0%
+patch and basically you are now
+empowered to do all calculations on
+
+ align:start position:0%
+empowered to do all calculations on
+ 
+
+ align:start position:0%
+empowered to do all calculations on
+datomic
+
+ align:start position:0%
+datomic
+ 
+
+ align:start position:0%
+datomic
+molecules at least as far as the angular
+
+ align:start position:0%
+molecules at least as far as the angular
+ 
+
+ align:start position:0%
+molecules at least as far as the angular
+meor are
+
+ align:start position:0%
+meor are
+ 
+
+ align:start position:0%
+meor are
+concerned okay now if you want to deal
+
+ align:start position:0%
+concerned okay now if you want to deal
+ 
+
+ align:start position:0%
+concerned okay now if you want to deal
+with the nuclear
+
+ align:start position:0%
+with the nuclear
+ 
+
+ align:start position:0%
+with the nuclear
+motion that's another topic which I will
+
+ align:start position:0%
+motion that's another topic which I will
+ 
+
+ align:start position:0%
+motion that's another topic which I will
+address okay so now I make a little
+
+ align:start position:0%
+address okay so now I make a little
+ 
+
+ align:start position:0%
+address okay so now I make a little
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+table of all the angular momenta you're
+
+ align:start position:0%
+table of all the angular momenta you're
+ 
+
+ align:start position:0%
+table of all the angular momenta you're
+likely to
+
+ align:start position:0%
+likely to
+ 
+
+ align:start position:0%
+likely to
+encounter well a lot of them many is so
+
+ align:start position:0%
+encounter well a lot of them many is so
+ 
+
+ align:start position:0%
+encounter well a lot of them many is so
+we have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator the quantum
+
+ align:start position:0%
+operator the quantum
+ 
+
+ align:start position:0%
+operator the quantum
+number and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+selction so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+s j z J
+
+ align:start position:0%
+s j z J
+ 
+
+ align:start position:0%
+s j z J
+plusus I'm not going to be able to do
+
+ align:start position:0%
+plusus I'm not going to be able to do
+ 
+
+ align:start position:0%
+plusus I'm not going to be able to do
+this all on one board but you'll get the
+
+ align:start position:0%
+this all on one board but you'll get the
+ 
+
+ align:start position:0%
+this all on one board but you'll get the
+idea so operators are generally
+
+ align:start position:0%
+idea so operators are generally
+ 
+
+ align:start position:0%
+idea so operators are generally
+represented as a bold face oops
+
+ align:start position:0%
+represented as a bold face oops
+ 
+
+ align:start position:0%
+represented as a bold face oops
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+um J has two projection quantum numbers
+
+ align:start position:0%
+um J has two projection quantum numbers
+ 
+
+ align:start position:0%
+um J has two projection quantum numbers
+one in the laboratory and one in the
+
+ align:start position:0%
+one in the laboratory and one in the
+ 
+
+ align:start position:0%
+one in the laboratory and one in the
+body and so I've chosen to use the Su
+
+ align:start position:0%
+body and so I've chosen to use the Su
+ 
+
+ align:start position:0%
+body and so I've chosen to use the Su
+superscript for body and subscript for
+
+ align:start position:0%
+superscript for body and subscript for
+ 
+
+ align:start position:0%
+superscript for body and subscript for
+laboratory you encounter that less often
+
+ align:start position:0%
+laboratory you encounter that less often
+ 
+
+ align:start position:0%
+laboratory you encounter that less often
+uh and so I'm not even going to talk
+
+ align:start position:0%
+uh and so I'm not even going to talk
+ 
+
+ align:start position:0%
+uh and so I'm not even going to talk
+about it so we have the quantum number
+
+ align:start position:0%
+about it so we have the quantum number
+ 
+
+ align:start position:0%
+about it so we have the quantum number
+is J and for JJ for J squ you get JJ +
+
+ align:start position:0%
+is J and for JJ for J squ you get JJ +
+ 
+
+ align:start position:0%
+is J and for JJ for J squ you get JJ +
+one and quantum number are generally
+
+ align:start position:0%
+one and quantum number are generally
+ 
+
+ align:start position:0%
+one and quantum number are generally
+written as I tell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it the selection rule for j s is Delta =
+
+ align:start position:0%
+it the selection rule for j s is Delta =
+ 
+
+ align:start position:0%
+it the selection rule for j s is Delta =
+0 Delta Omega = 0 the quantum number for
+
+ align:start position:0%
+0 Delta Omega = 0 the quantum number for
+ 
+
+ align:start position:0%
+0 Delta Omega = 0 the quantum number for
+JZ is
+
+ align:start position:0%
+JZ is
+ 
+
+ align:start position:0%
+JZ is
+Omega Delta J
+
+ align:start position:0%
+Omega Delta J
+ 
+
+ align:start position:0%
+Omega Delta J
+=
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delega there's no quantum number for
+
+ align:start position:0%
+delega there's no quantum number for
+ 
+
+ align:start position:0%
+delega there's no quantum number for
+this operator because it's an off
+
+ align:start position:0%
+this operator because it's an off
+ 
+
+ align:start position:0%
+this operator because it's an off
+diagonal
+
+ align:start position:0%
+diagonal
+ 
+
+ align:start position:0%
+diagonal
+operator and the selection R is Delta j
+
+ align:start position:0%
+operator and the selection R is Delta j
+ 
+
+ align:start position:0%
+operator and the selection R is Delta j
+= 0 Delta
+
+ align:start position:0%
+= 0 Delta
+ 
+
+ align:start position:0%
+= 0 Delta
+Omega = minus or +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one similarly for s² s z and S
+
+ align:start position:0%
+one similarly for s² s z and S
+ 
+
+ align:start position:0%
+one similarly for s² s z and S
++ s s
+
+ align:start position:0%
++ s s
+ 
+
+ align:start position:0%
++ s s
++1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sigma Delta S = 0 Delta Sigma = 0 Delta
+
+ align:start position:0%
+Sigma Delta S = 0 Delta Sigma = 0 Delta
+ 
+
+ align:start position:0%
+Sigma Delta S = 0 Delta Sigma = 0 Delta
+Sigma S = 0 Delta Sigma = 0 Delta S = 0
+
+ align:start position:0%
+Sigma S = 0 Delta Sigma = 0 Delta S = 0
+ 
+
+ align:start position:0%
+Sigma S = 0 Delta Sigma = 0 Delta S = 0
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+Sigma
+
+ align:start position:0%
+Sigma
+ 
+
+ align:start position:0%
+Sigma
+and we can go on for a long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time now we come to
+
+ align:start position:0%
+time now we come to
+ 
+
+ align:start position:0%
+time now we come to
+l or l squ because a molecule isn't
+
+ align:start position:0%
+l or l squ because a molecule isn't
+ 
+
+ align:start position:0%
+l or l squ because a molecule isn't
+spherical L is usually not
+
+ align:start position:0%
+spherical L is usually not
+ 
+
+ align:start position:0%
+spherical L is usually not
+defined but we can still Define out Z
+
+ align:start position:0%
+defined but we can still Define out Z
+ 
+
+ align:start position:0%
+defined but we can still Define out Z
+and we can still use l+
+
+ align:start position:0%
+and we can still use l+
+ 
+
+ align:start position:0%
+and we can still use l+
+minus so we don't have a quantum number
+
+ align:start position:0%
+minus so we don't have a quantum number
+ 
+
+ align:start position:0%
+minus so we don't have a quantum number
+here although we'd like to write LL +
+
+ align:start position:0%
+here although we'd like to write LL +
+ 
+
+ align:start position:0%
+here although we'd like to write LL +
+one and we we don't have a a qualum
+
+ align:start position:0%
+one and we we don't have a a qualum
+ 
+
+ align:start position:0%
+one and we we don't have a a qualum
+number for a selection rule for L
+
+ align:start position:0%
+number for a selection rule for L
+ 
+
+ align:start position:0%
+number for a selection rule for L
+because we don't know what L is but we
+
+ align:start position:0%
+because we don't know what L is but we
+ 
+
+ align:start position:0%
+because we don't know what L is but we
+still have Delta Lambda equals z and
+
+ align:start position:0%
+still have Delta Lambda equals z and
+ 
+
+ align:start position:0%
+still have Delta Lambda equals z and
+here we still have Delta Lambda equal Z
+
+ align:start position:0%
+here we still have Delta Lambda equal Z
+ 
+
+ align:start position:0%
+here we still have Delta Lambda equal Z
+and here we have Delta
+
+ align:start position:0%
+and here we have Delta
+ 
+
+ align:start position:0%
+and here we have Delta
+Lambda plus orus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one there are other quantum numbers like
+
+ align:start position:0%
+one there are other quantum numbers like
+ 
+
+ align:start position:0%
+one there are other quantum numbers like
+or operators like n which is J -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+and it turns out that n
+
+ align:start position:0%
+and it turns out that n
+ 
+
+ align:start position:0%
+and it turns out that n
+z has the quantum number
+
+ align:start position:0%
+z has the quantum number
+ 
+
+ align:start position:0%
+z has the quantum number
+Lambda because NZ is identical to
+
+ align:start position:0%
+Lambda because NZ is identical to
+ 
+
+ align:start position:0%
+Lambda because NZ is identical to
+LZ as far as the part that can have uh a
+
+ align:start position:0%
+LZ as far as the part that can have uh a
+ 
+
+ align:start position:0%
+LZ as far as the part that can have uh a
+projection because
+
+ align:start position:0%
+projection because
+ 
+
+ align:start position:0%
+projection because
+NZ uh
+
+ align:start position:0%
+NZ uh
+ 
+
+ align:start position:0%
+NZ uh
+um we I mean JZ is LZ plus SZ plus RZ RZ
+
+ align:start position:0%
+um we I mean JZ is LZ plus SZ plus RZ RZ
+ 
+
+ align:start position:0%
+um we I mean JZ is LZ plus SZ plus RZ RZ
+the projection of the nuclear rotation
+
+ align:start position:0%
+the projection of the nuclear rotation
+ 
+
+ align:start position:0%
+the projection of the nuclear rotation
+on the inter nuclear axis is has to be
+
+ align:start position:0%
+on the inter nuclear axis is has to be
+ 
+
+ align:start position:0%
+on the inter nuclear axis is has to be
+zero and so uh JZ minus uh JZ minus SZ
+
+ align:start position:0%
+zero and so uh JZ minus uh JZ minus SZ
+ 
+
+ align:start position:0%
+zero and so uh JZ minus uh JZ minus SZ
+is LZ
+
+ align:start position:0%
+is LZ
+ 
+
+ align:start position:0%
+is LZ
+so LZ is
+
+ align:start position:0%
+so LZ is
+ 
+
+ align:start position:0%
+so LZ is
+NZ uh okay now we get to more esoteric
+
+ align:start position:0%
+NZ uh okay now we get to more esoteric
+ 
+
+ align:start position:0%
+NZ uh okay now we get to more esoteric
+situations uh but I want to talk about
+
+ align:start position:0%
+situations uh but I want to talk about
+ 
+
+ align:start position:0%
+situations uh but I want to talk about
+them suppose you have a
+
+ align:start position:0%
+them suppose you have a
+ 
+
+ align:start position:0%
+them suppose you have a
+molecule uh which has sort of a a a
+
+ align:start position:0%
+molecule uh which has sort of a a a
+ 
+
+ align:start position:0%
+molecule uh which has sort of a a a
+closed shell or nearly close shell core
+
+ align:start position:0%
+closed shell or nearly close shell core
+ 
+
+ align:start position:0%
+closed shell or nearly close shell core
+an electron far away from it and so this
+
+ align:start position:0%
+an electron far away from it and so this
+ 
+
+ align:start position:0%
+an electron far away from it and so this
+is an ion
+
+ align:start position:0%
+is an ion
+ 
+
+ align:start position:0%
+is an ion
+and this is called a redberg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state when the electron is far away from
+
+ align:start position:0%
+state when the electron is far away from
+ 
+
+ align:start position:0%
+state when the electron is far away from
+the ion it thinks it's on an atom and we
+
+ align:start position:0%
+the ion it thinks it's on an atom and we
+ 
+
+ align:start position:0%
+the ion it thinks it's on an atom and we
+get L back so but we get not Big L but
+
+ align:start position:0%
+get L back so but we get not Big L but
+ 
+
+ align:start position:0%
+get L back so but we get not Big L but
+little L the L for this rer
+
+ align:start position:0%
+little L the L for this rer
+ 
+
+ align:start position:0%
+little L the L for this rer
+electron and so we start having more
+
+ align:start position:0%
+electron and so we start having more
+ 
+
+ align:start position:0%
+electron and so we start having more
+quantum numbers we have the quantum
+
+ align:start position:0%
+quantum numbers we have the quantum
+ 
+
+ align:start position:0%
+quantum numbers we have the quantum
+numbers associated with all of the
+
+ align:start position:0%
+numbers associated with all of the
+ 
+
+ align:start position:0%
+numbers associated with all of the
+angular momentum of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ion and you have the quantum numbers
+
+ align:start position:0%
+ion and you have the quantum numbers
+ 
+
+ align:start position:0%
+ion and you have the quantum numbers
+associated with the
+
+ align:start position:0%
+associated with the
+ 
+
+ align:start position:0%
+associated with the
+rber so instead of
+
+ align:start position:0%
+rber so instead of
+ 
+
+ align:start position:0%
+rber so instead of
+having uh just
+
+ align:start position:0%
+having uh just
+ 
+
+ align:start position:0%
+having uh just
+some uh L S and J as our quantum numbers
+
+ align:start position:0%
+some uh L S and J as our quantum numbers
+ 
+
+ align:start position:0%
+some uh L S and J as our quantum numbers
+we start having six quantum numbers we
+
+ align:start position:0%
+we start having six quantum numbers we
+ 
+
+ align:start position:0%
+we start having six quantum numbers we
+have L plus S Plus and j+ and little L
+
+ align:start position:0%
+have L plus S Plus and j+ and little L
+ 
+
+ align:start position:0%
+have L plus S Plus and j+ and little L
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+s uh and Little J or something like that
+
+ align:start position:0%
+s uh and Little J or something like that
+ 
+
+ align:start position:0%
+s uh and Little J or something like that
+so we still can couple them together we
+
+ align:start position:0%
+so we still can couple them together we
+ 
+
+ align:start position:0%
+so we still can couple them together we
+can still use case a
+
+ align:start position:0%
+can still use case a
+ 
+
+ align:start position:0%
+can still use case a
+methods uh and so we we can have
+
+ align:start position:0%
+methods uh and so we we can have
+ 
+
+ align:start position:0%
+methods uh and so we we can have
+j+ now this is not the raising or
+
+ align:start position:0%
+j+ now this is not the raising or
+ 
+
+ align:start position:0%
+j+ now this is not the raising or
+lowering operator this is J for the ion
+
+ align:start position:0%
+lowering operator this is J for the ion
+ 
+
+ align:start position:0%
+lowering operator this is J for the ion
+we use plus and you can tell the
+
+ align:start position:0%
+we use plus and you can tell the
+ 
+
+ align:start position:0%
+we use plus and you can tell the
+difference because when you have a bold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator a bold symbol it's an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator and when you have an italic
+
+ align:start position:0%
+operator and when you have an italic
+ 
+
+ align:start position:0%
+operator and when you have an italic
+symbol uh it's a quantum number and so
+
+ align:start position:0%
+symbol uh it's a quantum number and so
+ 
+
+ align:start position:0%
+symbol uh it's a quantum number and so
+uh and when there's a problem uh when
+
+ align:start position:0%
+uh and when there's a problem uh when
+ 
+
+ align:start position:0%
+uh and when there's a problem uh when
+you have an operator and you want raing
+
+ align:start position:0%
+you have an operator and you want raing
+ 
+
+ align:start position:0%
+you have an operator and you want raing
+and lowering operators a bit and you
+
+ align:start position:0%
+and lowering operators a bit and you
+ 
+
+ align:start position:0%
+and lowering operators a bit and you
+put okay and so uh we would uh we would
+
+ align:start position:0%
+put okay and so uh we would uh we would
+ 
+
+ align:start position:0%
+put okay and so uh we would uh we would
+the the quantum numbers associated with
+
+ align:start position:0%
+the the quantum numbers associated with
+ 
+
+ align:start position:0%
+the the quantum numbers associated with
+uh the projection
+
+ align:start position:0%
+uh the projection
+ 
+
+ align:start position:0%
+uh the projection
+okay so suppose we have the J +
+
+ align:start position:0%
+okay so suppose we have the J +
+ 
+
+ align:start position:0%
+okay so suppose we have the J +
+z that would be called Omega plus the
+
+ align:start position:0%
+z that would be called Omega plus the
+ 
+
+ align:start position:0%
+z that would be called Omega plus the
+quantum number okay this is more
+
+ align:start position:0%
+quantum number okay this is more
+ 
+
+ align:start position:0%
+quantum number okay this is more
+detailed than you
+
+ align:start position:0%
+detailed than you
+ 
+
+ align:start position:0%
+detailed than you
+need okay so we have we just put a Plus
+
+ align:start position:0%
+need okay so we have we just put a Plus
+ 
+
+ align:start position:0%
+need okay so we have we just put a Plus
+on the quantum numbers for the ion and
+
+ align:start position:0%
+on the quantum numbers for the ion and
+ 
+
+ align:start position:0%
+on the quantum numbers for the ion and
+since this is a one electron quantity we
+
+ align:start position:0%
+since this is a one electron quantity we
+ 
+
+ align:start position:0%
+since this is a one electron quantity we
+use lowercase letters Little J little L
+
+ align:start position:0%
+use lowercase letters Little J little L
+ 
+
+ align:start position:0%
+use lowercase letters Little J little L
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+s little little Omega lowercase Omega
+
+ align:start position:0%
+s little little Omega lowercase Omega
+ 
+
+ align:start position:0%
+s little little Omega lowercase Omega
+lowercase Lambda lowercase Sigma for the
+
+ align:start position:0%
+lowercase Lambda lowercase Sigma for the
+ 
+
+ align:start position:0%
+lowercase Lambda lowercase Sigma for the
+quantum numbers of the
+
+ align:start position:0%
+quantum numbers of the
+ 
+
+ align:start position:0%
+quantum numbers of the
+electron so there isn't any ambiguity
+
+ align:start position:0%
+electron so there isn't any ambiguity
+ 
+
+ align:start position:0%
+electron so there isn't any ambiguity
+there's lots of angular momenta and
+
+ align:start position:0%
+there's lots of angular momenta and
+ 
+
+ align:start position:0%
+there's lots of angular momenta and
+there's lots of coupling cases remember
+
+ align:start position:0%
+there's lots of coupling cases remember
+ 
+
+ align:start position:0%
+there's lots of coupling cases remember
+when we talked about the coupling cases
+
+ align:start position:0%
+when we talked about the coupling cases
+ 
+
+ align:start position:0%
+when we talked about the coupling cases
+last time I said we had three turns
+
+ align:start position:0%
+last time I said we had three turns
+ 
+
+ align:start position:0%
+last time I said we had three turns
+electronic spit orbit and rotation and
+
+ align:start position:0%
+electronic spit orbit and rotation and
+ 
+
+ align:start position:0%
+electronic spit orbit and rotation and
+we can arras them in
+
+ align:start position:0%
+we can arras them in
+ 
+
+ align:start position:0%
+we can arras them in
+six orders of relative size and that
+
+ align:start position:0%
+six orders of relative size and that
+ 
+
+ align:start position:0%
+six orders of relative size and that
+leads to the five known Hood coupling
+
+ align:start position:0%
+leads to the five known Hood coupling
+ 
+
+ align:start position:0%
+leads to the five known Hood coupling
+cases and one other but now if we have
+
+ align:start position:0%
+cases and one other but now if we have
+ 
+
+ align:start position:0%
+cases and one other but now if we have
+more quantum
+
+ align:start position:0%
+more quantum
+ 
+
+ align:start position:0%
+more quantum
+numbers you can imagine how many
+
+ align:start position:0%
+numbers you can imagine how many
+ 
+
+ align:start position:0%
+numbers you can imagine how many
+coupling cases there
+
+ align:start position:0%
+coupling cases there
+ 
+
+ align:start position:0%
+coupling cases there
+are but it's no big deal because the
+
+ align:start position:0%
+are but it's no big deal because the
+ 
+
+ align:start position:0%
+are but it's no big deal because the
+same techniques you use to evaluate the
+
+ align:start position:0%
+same techniques you use to evaluate the
+ 
+
+ align:start position:0%
+same techniques you use to evaluate the
+Matrix elements and rearrange terms of
+
+ align:start position:0%
+Matrix elements and rearrange terms of
+ 
+
+ align:start position:0%
+Matrix elements and rearrange terms of
+the Hiltonia there's nothing different
+
+ align:start position:0%
+the Hiltonia there's nothing different
+ 
+
+ align:start position:0%
+the Hiltonia there's nothing different
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you are empowered to deal with
+
+ align:start position:0%
+so you are empowered to deal with
+ 
+
+ align:start position:0%
+so you are empowered to deal with
+angular and diatomic molecules even if
+
+ align:start position:0%
+angular and diatomic molecules even if
+ 
+
+ align:start position:0%
+angular and diatomic molecules even if
+we have six rather than three important
+
+ align:start position:0%
+we have six rather than three important
+ 
+
+ align:start position:0%
+we have six rather than three important
+angular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment so what's what's left well
+
+ align:start position:0%
+moment so what's what's left well
+ 
+
+ align:start position:0%
+moment so what's what's left well
+there's the vibrational
+
+ align:start position:0%
+there's the vibrational
+ 
+
+ align:start position:0%
+there's the vibrational
+equ and let's talk about them and I'm
+
+ align:start position:0%
+equ and let's talk about them and I'm
+ 
+
+ align:start position:0%
+equ and let's talk about them and I'm
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+to present a very very important
+
+ align:start position:0%
+to present a very very important
+ 
+
+ align:start position:0%
+to present a very very important
+approximation that enables us to uh
+
+ align:start position:0%
+approximation that enables us to uh
+ 
+
+ align:start position:0%
+approximation that enables us to uh
+simplify our work dealing with
+
+ align:start position:0%
+simplify our work dealing with
+ 
+
+ align:start position:0%
+simplify our work dealing with
+vibrational
+
+ align:start position:0%
+vibrational
+ 
+
+ align:start position:0%
+vibrational
+matrixes okay so the vibrational wave
+
+ align:start position:0%
+matrixes okay so the vibrational wave
+ 
+
+ align:start position:0%
+matrixes okay so the vibrational wave
+function we have that should be a Kai we
+
+ align:start position:0%
+function we have that should be a Kai we
+ 
+
+ align:start position:0%
+function we have that should be a Kai we
+have a vibrational wave function for the
+
+ align:start position:0%
+have a vibrational wave function for the
+ 
+
+ align:start position:0%
+have a vibrational wave function for the
+I electronic State and then it's got a
+
+ align:start position:0%
+I electronic State and then it's got a
+ 
+
+ align:start position:0%
+I electronic State and then it's got a
+vibrational qu is the function of
+
+ align:start position:0%
+vibrational qu is the function of
+ 
+
+ align:start position:0%
+vibrational qu is the function of
+r in direct notation that object is the
+
+ align:start position:0%
+r in direct notation that object is the
+ 
+
+ align:start position:0%
+r in direct notation that object is the
+same thing as
+
+ align:start position:0%
+same thing as
+ 
+
+ align:start position:0%
+same thing as
+this okay uh we tend to like to think of
+
+ align:start position:0%
+this okay uh we tend to like to think of
+ 
+
+ align:start position:0%
+this okay uh we tend to like to think of
+vibrational wave functions as functions
+
+ align:start position:0%
+vibrational wave functions as functions
+ 
+
+ align:start position:0%
+vibrational wave functions as functions
+and angular momentum wave functions is
+
+ align:start position:0%
+and angular momentum wave functions is
+ 
+
+ align:start position:0%
+and angular momentum wave functions is
+vectors because we don't what I
+
+ align:start position:0%
+vectors because we don't what I
+ 
+
+ align:start position:0%
+vectors because we don't what I
+mean this is a simple one-dimensional
+
+ align:start position:0%
+mean this is a simple one-dimensional
+ 
+
+ align:start position:0%
+mean this is a simple one-dimensional
+function and we're going to be
+
+ align:start position:0%
+function and we're going to be
+ 
+
+ align:start position:0%
+function and we're going to be
+calculating integrals over it there
+
+ align:start position:0%
+calculating integrals over it there
+ 
+
+ align:start position:0%
+calculating integrals over it there
+aren't nice uh angular momentum like
+
+ align:start position:0%
+aren't nice uh angular momentum like
+ 
+
+ align:start position:0%
+aren't nice uh angular momentum like
+algebra for vibrational weight
+
+ align:start position:0%
+algebra for vibrational weight
+ 
+
+ align:start position:0%
+algebra for vibrational weight
+functions whereas angular momentum wave
+
+ align:start position:0%
+functions whereas angular momentum wave
+ 
+
+ align:start position:0%
+functions whereas angular momentum wave
+functions are treated by an algebra
+
+ align:start position:0%
+functions are treated by an algebra
+ 
+
+ align:start position:0%
+functions are treated by an algebra
+where basically all the Matrix elements
+
+ align:start position:0%
+where basically all the Matrix elements
+ 
+
+ align:start position:0%
+where basically all the Matrix elements
+are directly evaluated and you never
+
+ align:start position:0%
+are directly evaluated and you never
+ 
+
+ align:start position:0%
+are directly evaluated and you never
+look at the differential operators that
+
+ align:start position:0%
+look at the differential operators that
+ 
+
+ align:start position:0%
+look at the differential operators that
+correspond to the angular momentum nor
+
+ align:start position:0%
+correspond to the angular momentum nor
+ 
+
+ align:start position:0%
+correspond to the angular momentum nor
+the forms of the wave
+
+ align:start position:0%
+the forms of the wave
+ 
+
+ align:start position:0%
+the forms of the wave
+functions so it
+
+ align:start position:0%
+functions so it
+ 
+
+ align:start position:0%
+functions so it
+is tempting to look at these sorts of
+
+ align:start position:0%
+is tempting to look at these sorts of
+ 
+
+ align:start position:0%
+is tempting to look at these sorts of
+things rather than this kind of a symbol
+
+ align:start position:0%
+things rather than this kind of a symbol
+ 
+
+ align:start position:0%
+things rather than this kind of a symbol
+for vibration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we have a wave function which is a
+
+ align:start position:0%
+now we have a wave function which is a
+ 
+
+ align:start position:0%
+now we have a wave function which is a
+product of an electronic vibrational and
+
+ align:start position:0%
+product of an electronic vibrational and
+ 
+
+ align:start position:0%
+product of an electronic vibrational and
+a rotational part so in order to
+
+ align:start position:0%
+a rotational part so in order to
+ 
+
+ align:start position:0%
+a rotational part so in order to
+calculate Matrix elements we're always
+
+ align:start position:0%
+calculate Matrix elements we're always
+ 
+
+ align:start position:0%
+calculate Matrix elements we're always
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+evaluating uh a product of three factors
+
+ align:start position:0%
+evaluating uh a product of three factors
+ 
+
+ align:start position:0%
+evaluating uh a product of three factors
+a rotational Matrix element a
+
+ align:start position:0%
+a rotational Matrix element a
+ 
+
+ align:start position:0%
+a rotational Matrix element a
+vibrational Matrix element and
+
+ align:start position:0%
+vibrational Matrix element and
+ 
+
+ align:start position:0%
+vibrational Matrix element and
+electronic Matrix
+
+ align:start position:0%
+electronic Matrix
+ 
+
+ align:start position:0%
+electronic Matrix
+element so the electronic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part we deal with first
+
+ align:start position:0%
+part we deal with first
+ 
+
+ align:start position:0%
+part we deal with first
+because uh we get rid of it almost
+
+ align:start position:0%
+because uh we get rid of it almost
+ 
+
+ align:start position:0%
+because uh we get rid of it almost
+immediately so we have some electronic
+
+ align:start position:0%
+immediately so we have some electronic
+ 
+
+ align:start position:0%
+immediately so we have some electronic
+operator and we have two different
+
+ align:start position:0%
+operator and we have two different
+ 
+
+ align:start position:0%
+operator and we have two different
+electronic
+
+ align:start position:0%
+electronic
+ 
+
+ align:start position:0%
+electronic
+States and according to the Bourn
+
+ align:start position:0%
+States and according to the Bourn
+ 
+
+ align:start position:0%
+States and according to the Bourn
+Oppenheimer
+
+ align:start position:0%
+Oppenheimer
+ 
+
+ align:start position:0%
+Oppenheimer
+approximation these functions are
+
+ align:start position:0%
+approximation these functions are
+ 
+
+ align:start position:0%
+approximation these functions are
+parametric functions of internuclear
+
+ align:start position:0%
+parametric functions of internuclear
+ 
+
+ align:start position:0%
+parametric functions of internuclear
+distance so that means that we're going
+
+ align:start position:0%
+distance so that means that we're going
+ 
+
+ align:start position:0%
+distance so that means that we're going
+to have this Matrix element is going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be a function an implicit function of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inter so the borop says well we do the
+
+ align:start position:0%
+inter so the borop says well we do the
+ 
+
+ align:start position:0%
+inter so the borop says well we do the
+electronic integral it will be a number
+
+ align:start position:0%
+electronic integral it will be a number
+ 
+
+ align:start position:0%
+electronic integral it will be a number
+but this number will probably weakly
+
+ align:start position:0%
+but this number will probably weakly
+ 
+
+ align:start position:0%
+but this number will probably weakly
+depend on
+
+ align:start position:0%
+depend on
+ 
+
+ align:start position:0%
+depend on
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+now if this operator has an explicit
+
+ align:start position:0%
+now if this operator has an explicit
+ 
+
+ align:start position:0%
+now if this operator has an explicit
+dependence on r that also appear here
+
+ align:start position:0%
+dependence on r that also appear here
+ 
+
+ align:start position:0%
+dependence on r that also appear here
+now one operator that has an explicit
+
+ align:start position:0%
+now one operator that has an explicit
+ 
+
+ align:start position:0%
+now one operator that has an explicit
+dependence on R is the rotational
+
+ align:start position:0%
+dependence on R is the rotational
+ 
+
+ align:start position:0%
+dependence on R is the rotational
+constant HR S 2 u r
+
+ align:start position:0%
+constant HR S 2 u r
+ 
+
+ align:start position:0%
+constant HR S 2 u r
+s now that's not an electronic
+
+ align:start position:0%
+s now that's not an electronic
+ 
+
+ align:start position:0%
+s now that's not an electronic
+operator but so we're often going to
+
+ align:start position:0%
+operator but so we're often going to
+ 
+
+ align:start position:0%
+operator but so we're often going to
+have things that either implicitly or
+
+ align:start position:0%
+have things that either implicitly or
+ 
+
+ align:start position:0%
+have things that either implicitly or
+explicitly depend on intern includ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance this is a problem
+
+ align:start position:0%
+distance this is a problem
+ 
+
+ align:start position:0%
+distance this is a problem
+because when we have an electronic
+
+ align:start position:0%
+because when we have an electronic
+ 
+
+ align:start position:0%
+because when we have an electronic
+property that depends on our and we want
+
+ align:start position:0%
+property that depends on our and we want
+ 
+
+ align:start position:0%
+property that depends on our and we want
+to evaluate Matrix elements now I am uh
+
+ align:start position:0%
+to evaluate Matrix elements now I am uh
+ 
+
+ align:start position:0%
+to evaluate Matrix elements now I am uh
+writing the vibrational wave functions
+
+ align:start position:0%
+writing the vibrational wave functions
+ 
+
+ align:start position:0%
+writing the vibrational wave functions
+as as bro and KS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so this is a vibrational Matrix
+
+ align:start position:0%
+here so this is a vibrational Matrix
+ 
+
+ align:start position:0%
+here so this is a vibrational Matrix
+once we've done the electronic integral
+
+ align:start position:0%
+once we've done the electronic integral
+ 
+
+ align:start position:0%
+once we've done the electronic integral
+now we have to do the vibration
+
+ align:start position:0%
+now we have to do the vibration
+ 
+
+ align:start position:0%
+now we have to do the vibration
+interval if this is a function of our we
+
+ align:start position:0%
+interval if this is a function of our we
+ 
+
+ align:start position:0%
+interval if this is a function of our we
+got B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems we like to ignore the
+
+ align:start position:0%
+problems we like to ignore the
+ 
+
+ align:start position:0%
+problems we like to ignore the
+dependence on
+
+ align:start position:0%
+dependence on
+ 
+
+ align:start position:0%
+dependence on
+R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how bad is this how bad a problem is
+
+ align:start position:0%
+so how bad is this how bad a problem is
+ 
+
+ align:start position:0%
+so how bad is this how bad a problem is
+this well one can always expand this as
+
+ align:start position:0%
+this well one can always expand this as
+ 
+
+ align:start position:0%
+this well one can always expand this as
+a power Series in
+
+ align:start position:0%
+a power Series in
+ 
+
+ align:start position:0%
+a power Series in
+R and then evaluate all the necessary
+
+ align:start position:0%
+R and then evaluate all the necessary
+ 
+
+ align:start position:0%
+R and then evaluate all the necessary
+integrals so that would mean we have
+
+ align:start position:0%
+integrals so that would mean we have
+ 
+
+ align:start position:0%
+integrals so that would mean we have
+have uh things like just the vibrational
+
+ align:start position:0%
+have uh things like just the vibrational
+ 
+
+ align:start position:0%
+have uh things like just the vibrational
+overlap we'd have v r
+
+ align:start position:0%
+overlap we'd have v r
+ 
+
+ align:start position:0%
+overlap we'd have v r
+VJ we'd have VI R 2
+
+ align:start position:0%
+VJ we'd have VI R 2
+ 
+
+ align:start position:0%
+VJ we'd have VI R 2
+VJ we'd have to calculate lots and
+
+ align:start position:0%
+VJ we'd have to calculate lots and
+ 
+
+ align:start position:0%
+VJ we'd have to calculate lots and
+lots of
+
+ align:start position:0%
+lots of
+ 
+
+ align:start position:0%
+lots of
+vibrational Matrix
+
+ align:start position:0%
+vibrational Matrix
+ 
+
+ align:start position:0%
+vibrational Matrix
+elements and this would be inconvenient
+
+ align:start position:0%
+elements and this would be inconvenient
+ 
+
+ align:start position:0%
+elements and this would be inconvenient
+and it would also be costly in terms of
+
+ align:start position:0%
+and it would also be costly in terms of
+ 
+
+ align:start position:0%
+and it would also be costly in terms of
+our understanding of the problem
+
+ align:start position:0%
+our understanding of the problem
+ 
+
+ align:start position:0%
+our understanding of the problem
+and so we'd like to make that go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away so it turns
+
+ align:start position:0%
+away so it turns
+ 
+
+ align:start position:0%
+away so it turns
+out that we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always or almost always replace this
+
+ align:start position:0%
+always or almost always replace this
+ 
+
+ align:start position:0%
+always or almost always replace this
+kind of an integral with VI VJ a simple
+
+ align:start position:0%
+kind of an integral with VI VJ a simple
+ 
+
+ align:start position:0%
+kind of an integral with VI VJ a simple
+vibrational
+
+ align:start position:0%
+vibrational
+ 
+
+ align:start position:0%
+vibrational
+overlap times o i j of r v i VJ r
+
+ align:start position:0%
+overlap times o i j of r v i VJ r
+ 
+
+ align:start position:0%
+overlap times o i j of r v i VJ r
+that's called the r
+
+ align:start position:0%
+that's called the r
+ 
+
+ align:start position:0%
+that's called the r
+centroid the r
+
+ align:start position:0%
+centroid the r
+ 
+
+ align:start position:0%
+centroid the r
+centroid is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as it's this quantity The Matrix element
+
+ align:start position:0%
+as it's this quantity The Matrix element
+ 
+
+ align:start position:0%
+as it's this quantity The Matrix element
+of r divided by the overlapping
+
+ align:start position:0%
+of r divided by the overlapping
+ 
+
+ align:start position:0%
+of r divided by the overlapping
+that's perfectly reasonable it it is the
+
+ align:start position:0%
+that's perfectly reasonable it it is the
+ 
+
+ align:start position:0%
+that's perfectly reasonable it it is the
+way you would Define the average value
+
+ align:start position:0%
+way you would Define the average value
+ 
+
+ align:start position:0%
+way you would Define the average value
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R so the r centroid this is the r
+
+ align:start position:0%
+R so the r centroid this is the r
+ 
+
+ align:start position:0%
+R so the r centroid this is the r
+centroid the r centroid approximation
+
+ align:start position:0%
+centroid the r centroid approximation
+ 
+
+ align:start position:0%
+centroid the r centroid approximation
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+replace this integral of the function of
+
+ align:start position:0%
+replace this integral of the function of
+ 
+
+ align:start position:0%
+replace this integral of the function of
+r by the overlap integral the only
+
+ align:start position:0%
+r by the overlap integral the only
+ 
+
+ align:start position:0%
+r by the overlap integral the only
+vibrational integral you're going to
+
+ align:start position:0%
+vibrational integral you're going to
+ 
+
+ align:start position:0%
+vibrational integral you're going to
+have to calculate
+
+ align:start position:0%
+have to calculate
+ 
+
+ align:start position:0%
+have to calculate
+we not the only one times the r centroid
+
+ align:start position:0%
+we not the only one times the r centroid
+ 
+
+ align:start position:0%
+we not the only one times the r centroid
+this o of the r centroid instead of O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R that's an approximation it's a very
+
+ align:start position:0%
+R that's an approximation it's a very
+ 
+
+ align:start position:0%
+R that's an approximation it's a very
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+approximation and it's based on the
+
+ align:start position:0%
+approximation and it's based on the
+ 
+
+ align:start position:0%
+approximation and it's based on the
+assumption that r r v i VJ is equal to r
+
+ align:start position:0%
+assumption that r r v i VJ is equal to r
+ 
+
+ align:start position:0%
+assumption that r r v i VJ is equal to r
+n r e
+
+ align:start position:0%
+n r e
+ 
+
+ align:start position:0%
+n r e
+DJ over r nus1 e
+
+ align:start position:0%
+DJ over r nus1 e
+ 
+
+ align:start position:0%
+DJ over r nus1 e
+DJ this is the r centroid
+
+ align:start position:0%
+DJ this is the r centroid
+ 
+
+ align:start position:0%
+DJ this is the r centroid
+approximation the r centroid is this is
+
+ align:start position:0%
+approximation the r centroid is this is
+ 
+
+ align:start position:0%
+approximation the r centroid is this is
+given by any value of any power of n
+
+ align:start position:0%
+given by any value of any power of n
+ 
+
+ align:start position:0%
+given by any value of any power of n
+this ratio n n minus
+
+ align:start position:0%
+this ratio n n minus
+ 
+
+ align:start position:0%
+this ratio n n minus
+one now why should that be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+it's astonishingly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true how can we
+
+ align:start position:0%
+true how can we
+ 
+
+ align:start position:0%
+true how can we
+expect vibrational integrals involving
+
+ align:start position:0%
+expect vibrational integrals involving
+ 
+
+ align:start position:0%
+expect vibrational integrals involving
+different powers of R to have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property this gives us a hint of
+
+ align:start position:0%
+property this gives us a hint of
+ 
+
+ align:start position:0%
+property this gives us a hint of
+something that's going to be really
+
+ align:start position:0%
+something that's going to be really
+ 
+
+ align:start position:0%
+something that's going to be really
+important the
+
+ align:start position:0%
+important the
+ 
+
+ align:start position:0%
+important the
+integrals
+
+ align:start position:0%
+integrals
+ 
+
+ align:start position:0%
+integrals
+accumulate all always in a very narrow
+
+ align:start position:0%
+accumulate all always in a very narrow
+ 
+
+ align:start position:0%
+accumulate all always in a very narrow
+range of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+art that's called the stationary phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation and we'll get to that but
+
+ align:start position:0%
+approximation and we'll get to that but
+ 
+
+ align:start position:0%
+approximation and we'll get to that but
+that leads to really important
+
+ align:start position:0%
+that leads to really important
+ 
+
+ align:start position:0%
+that leads to really important
+simplifications because
+
+ align:start position:0%
+simplifications because
+ 
+
+ align:start position:0%
+simplifications because
+often one can
+
+ align:start position:0%
+often one can
+ 
+
+ align:start position:0%
+often one can
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+explicitly what region narrow region of
+
+ align:start position:0%
+explicitly what region narrow region of
+ 
+
+ align:start position:0%
+explicitly what region narrow region of
+internuclear a distance the integral
+
+ align:start position:0%
+internuclear a distance the integral
+ 
+
+ align:start position:0%
+internuclear a distance the integral
+will accumulate
+
+ align:start position:0%
+will accumulate
+ 
+
+ align:start position:0%
+will accumulate
+it for example if we have a problem like
+
+ align:start position:0%
+it for example if we have a problem like
+ 
+
+ align:start position:0%
+it for example if we have a problem like
+this where we have two potential
+
+ align:start position:0%
+this where we have two potential
+ 
+
+ align:start position:0%
+this where we have two potential
+curves and they cross and we want to
+
+ align:start position:0%
+curves and they cross and we want to
+ 
+
+ align:start position:0%
+curves and they cross and we want to
+calculate the vibration overlap between
+
+ align:start position:0%
+calculate the vibration overlap between
+ 
+
+ align:start position:0%
+calculate the vibration overlap between
+these two levels at about the same
+
+ align:start position:0%
+these two levels at about the same
+ 
+
+ align:start position:0%
+these two levels at about the same
+energy they integral the vibrational
+
+ align:start position:0%
+energy they integral the vibrational
+ 
+
+ align:start position:0%
+energy they integral the vibrational
+overlap and any integral involving any
+
+ align:start position:0%
+overlap and any integral involving any
+ 
+
+ align:start position:0%
+overlap and any integral involving any
+power of R will accumulate in a narrow
+
+ align:start position:0%
+power of R will accumulate in a narrow
+ 
+
+ align:start position:0%
+power of R will accumulate in a narrow
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+at the internuclear distance where the
+
+ align:start position:0%
+at the internuclear distance where the
+ 
+
+ align:start position:0%
+at the internuclear distance where the
+two curves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross and so for all vibrational Matrix
+
+ align:start position:0%
+cross and so for all vibrational Matrix
+ 
+
+ align:start position:0%
+cross and so for all vibrational Matrix
+elements there is hiding in here this
+
+ align:start position:0%
+elements there is hiding in here this
+ 
+
+ align:start position:0%
+elements there is hiding in here this
+stationary phase
+
+ align:start position:0%
+stationary phase
+ 
+
+ align:start position:0%
+stationary phase
+situation this just means that when the
+
+ align:start position:0%
+situation this just means that when the
+ 
+
+ align:start position:0%
+situation this just means that when the
+two wave functions have the
+
+ align:start position:0%
+two wave functions have the
+ 
+
+ align:start position:0%
+two wave functions have the
+same nuclear kinetic
+
+ align:start position:0%
+same nuclear kinetic
+ 
+
+ align:start position:0%
+same nuclear kinetic
+energy they're oscillating at the same
+
+ align:start position:0%
+energy they're oscillating at the same
+ 
+
+ align:start position:0%
+energy they're oscillating at the same
+spatial
+
+ align:start position:0%
+spatial
+ 
+
+ align:start position:0%
+spatial
+frequency they have the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum and the momentum gives you the
+
+ align:start position:0%
+momentum and the momentum gives you the
+ 
+
+ align:start position:0%
+momentum and the momentum gives you the
+de Bry
+
+ align:start position:0%
+de Bry
+ 
+
+ align:start position:0%
+de Bry
+wavelength to the BR wavelength Lambda
+
+ align:start position:0%
+wavelength to the BR wavelength Lambda
+ 
+
+ align:start position:0%
+wavelength to the BR wavelength Lambda
+is uh H over
+
+ align:start position:0%
+is uh H over
+ 
+
+ align:start position:0%
+is uh H over
+e and so if they have the same kinetic
+
+ align:start position:0%
+e and so if they have the same kinetic
+ 
+
+ align:start position:0%
+e and so if they have the same kinetic
+energy they have the same
+
+ align:start position:0%
+energy they have the same
+ 
+
+ align:start position:0%
+energy they have the same
+momentum they have the same wavelength
+
+ align:start position:0%
+momentum they have the same wavelength
+ 
+
+ align:start position:0%
+momentum they have the same wavelength
+that means that at this point they're
+
+ align:start position:0%
+that means that at this point they're
+ 
+
+ align:start position:0%
+that means that at this point they're
+oscillating at the same
+
+ align:start position:0%
+oscillating at the same
+ 
+
+ align:start position:0%
+oscillating at the same
+frequency and so the
+
+ align:start position:0%
+frequency and so the
+ 
+
+ align:start position:0%
+frequency and so the
+integrant uh which uh is the product of
+
+ align:start position:0%
+integrant uh which uh is the product of
+ 
+
+ align:start position:0%
+integrant uh which uh is the product of
+two wave functions that integrant
+
+ align:start position:0%
+two wave functions that integrant
+ 
+
+ align:start position:0%
+two wave functions that integrant
+oscillates very fast except near this
+
+ align:start position:0%
+oscillates very fast except near this
+ 
+
+ align:start position:0%
+oscillates very fast except near this
+point and that's why the r centr
+
+ align:start position:0%
+point and that's why the r centr
+ 
+
+ align:start position:0%
+point and that's why the r centr
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+works and we'll return to this when we
+
+ align:start position:0%
+works and we'll return to this when we
+ 
+
+ align:start position:0%
+works and we'll return to this when we
+talk about the semic classical approach
+
+ align:start position:0%
+talk about the semic classical approach
+ 
+
+ align:start position:0%
+talk about the semic classical approach
+to uh everything
+
+ align:start position:0%
+to uh everything
+ 
+
+ align:start position:0%
+to uh everything
+okay but the rcent approximation is very
+
+ align:start position:0%
+okay but the rcent approximation is very
+ 
+
+ align:start position:0%
+okay but the rcent approximation is very
+convenient because in order to deal
+
+ align:start position:0%
+convenient because in order to deal
+ 
+
+ align:start position:0%
+convenient because in order to deal
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+um these kinds of Matrix elements one
+
+ align:start position:0%
+um these kinds of Matrix elements one
+ 
+
+ align:start position:0%
+um these kinds of Matrix elements one
+has to calculate only two integrals this
+
+ align:start position:0%
+has to calculate only two integrals this
+ 
+
+ align:start position:0%
+has to calculate only two integrals this
+one and the integral involving R the r
+
+ align:start position:0%
+one and the integral involving R the r
+ 
+
+ align:start position:0%
+one and the integral involving R the r
+centroid is this over
+
+ align:start position:0%
+centroid is this over
+ 
+
+ align:start position:0%
+centroid is this over
+that uh is the uh yes so there's only
+
+ align:start position:0%
+that uh is the uh yes so there's only
+ 
+
+ align:start position:0%
+that uh is the uh yes so there's only
+for every pair of VI and VJ instead of
+
+ align:start position:0%
+for every pair of VI and VJ instead of
+ 
+
+ align:start position:0%
+for every pair of VI and VJ instead of
+having to calculate Matrix elements of
+
+ align:start position:0%
+having to calculate Matrix elements of
+ 
+
+ align:start position:0%
+having to calculate Matrix elements of
+all powers of R when just calculates the
+
+ align:start position:0%
+all powers of R when just calculates the
+ 
+
+ align:start position:0%
+all powers of R when just calculates the
+overlap and the Matrix element of R to
+
+ align:start position:0%
+overlap and the Matrix element of R to
+ 
+
+ align:start position:0%
+overlap and the Matrix element of R to
+the one
+
+ align:start position:0%
+the one
+ 
+
+ align:start position:0%
+the one
+power and that leads to tremendous
+
+ align:start position:0%
+power and that leads to tremendous
+ 
+
+ align:start position:0%
+power and that leads to tremendous
+simplification of effort and it also
+
+ align:start position:0%
+simplification of effort and it also
+ 
+
+ align:start position:0%
+simplification of effort and it also
+allows us to describe things in a way
+
+ align:start position:0%
+allows us to describe things in a way
+ 
+
+ align:start position:0%
+allows us to describe things in a way
+that's much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simpler
+
+ align:start position:0%
+simpler
+ 
+
+ align:start position:0%
+simpler
+the observables s
+
+ align:start position:0%
+the observables s
+ 
+
+ align:start position:0%
+the observables s
+the AR
+
+ align:start position:0%
+the AR
+ 
+
+ align:start position:0%
+the AR
+dependence of electronic quantities only
+
+ align:start position:0%
+dependence of electronic quantities only
+ 
+
+ align:start position:0%
+dependence of electronic quantities only
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+vicinity of some special point which you
+
+ align:start position:0%
+vicinity of some special point which you
+ 
+
+ align:start position:0%
+vicinity of some special point which you
+know and so they're not terribly
+
+ align:start position:0%
+know and so they're not terribly
+ 
+
+ align:start position:0%
+know and so they're not terribly
+sensitive to curvature to strange
+
+ align:start position:0%
+sensitive to curvature to strange
+ 
+
+ align:start position:0%
+sensitive to curvature to strange
+variations and so one can ignore the r
+
+ align:start position:0%
+variations and so one can ignore the r
+ 
+
+ align:start position:0%
+variations and so one can ignore the r
+dependence of electronic
+
+ align:start position:0%
+dependence of electronic
+ 
+
+ align:start position:0%
+dependence of electronic
+quantities for most
+
+ align:start position:0%
+quantities for most
+ 
+
+ align:start position:0%
+quantities for most
+calculations this is very
+
+ align:start position:0%
+calculations this is very
+ 
+
+ align:start position:0%
+calculations this is very
+helpful and it would not be
+
+ align:start position:0%
+helpful and it would not be
+ 
+
+ align:start position:0%
+helpful and it would not be
+clear if you were simply doing numerical
+
+ align:start position:0%
+clear if you were simply doing numerical
+ 
+
+ align:start position:0%
+clear if you were simply doing numerical
+calculations because you would always do
+
+ align:start position:0%
+calculations because you would always do
+ 
+
+ align:start position:0%
+calculations because you would always do
+the numerical calculation correctly and
+
+ align:start position:0%
+the numerical calculation correctly and
+ 
+
+ align:start position:0%
+the numerical calculation correctly and
+you'd be doing you know you turn the
+
+ align:start position:0%
+you'd be doing you know you turn the
+ 
+
+ align:start position:0%
+you'd be doing you know you turn the
+crank and youd get something but you
+
+ align:start position:0%
+crank and youd get something but you
+ 
+
+ align:start position:0%
+crank and youd get something but you
+wouldn't know
+
+ align:start position:0%
+wouldn't know
+ 
+
+ align:start position:0%
+wouldn't know
+that everything interesting is happening
+
+ align:start position:0%
+that everything interesting is happening
+ 
+
+ align:start position:0%
+that everything interesting is happening
+in a particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place and the nature of your wave
+
+ align:start position:0%
+place and the nature of your wave
+ 
+
+ align:start position:0%
+place and the nature of your wave
+function at that internuclear distance
+
+ align:start position:0%
+function at that internuclear distance
+ 
+
+ align:start position:0%
+function at that internuclear distance
+is what determines what happens in the
+
+ align:start position:0%
+is what determines what happens in the
+ 
+
+ align:start position:0%
+is what determines what happens in the
+experiment and a different experiment
+
+ align:start position:0%
+experiment and a different experiment
+ 
+
+ align:start position:0%
+experiment and a different experiment
+might have curve cross at a different R
+
+ align:start position:0%
+might have curve cross at a different R
+ 
+
+ align:start position:0%
+might have curve cross at a different R
+and it might sample the away from a
+
+ align:start position:0%
+and it might sample the away from a
+ 
+
+ align:start position:0%
+and it might sample the away from a
+different place and give you something
+
+ align:start position:0%
+different place and give you something
+ 
+
+ align:start position:0%
+different place and give you something
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+okay yes so where would this would break
+
+ align:start position:0%
+okay yes so where would this would break
+ 
+
+ align:start position:0%
+okay yes so where would this would break
+down if you had say uh two peaks if your
+
+ align:start position:0%
+down if you had say uh two peaks if your
+ 
+
+ align:start position:0%
+down if you had say uh two peaks if your
+wave function had two maximum and they
+
+ align:start position:0%
+wave function had two maximum and they
+ 
+
+ align:start position:0%
+wave function had two maximum and they
+would that be a case of where it breaks
+
+ align:start position:0%
+would that be a case of where it breaks
+ 
+
+ align:start position:0%
+would that be a case of where it breaks
+down no it'll break down when you have
+
+ align:start position:0%
+down no it'll break down when you have
+ 
+
+ align:start position:0%
+down no it'll break down when you have
+something like this where there's no
+
+ align:start position:0%
+something like this where there's no
+ 
+
+ align:start position:0%
+something like this where there's no
+spatial
+
+ align:start position:0%
+spatial
+ 
+
+ align:start position:0%
+spatial
+overlap between the two vibrational WS
+
+ align:start position:0%
+overlap between the two vibrational WS
+ 
+
+ align:start position:0%
+overlap between the two vibrational WS
+an R will be in the middle it we'll try
+
+ align:start position:0%
+an R will be in the middle it we'll try
+ 
+
+ align:start position:0%
+an R will be in the middle it we'll try
+to be somewhere here and the the so it's
+
+ align:start position:0%
+to be somewhere here and the the so it's
+ 
+
+ align:start position:0%
+to be somewhere here and the the so it's
+in the Tails of the wave functions and
+
+ align:start position:0%
+in the Tails of the wave functions and
+ 
+
+ align:start position:0%
+in the Tails of the wave functions and
+so there's just no get a weird value for
+
+ align:start position:0%
+so there's just no get a weird value for
+ 
+
+ align:start position:0%
+so there's just no get a weird value for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+elect that's going to be really high
+
+ align:start position:0%
+elect that's going to be really high
+ 
+
+ align:start position:0%
+elect that's going to be really high
+because it's really high on those curves
+
+ align:start position:0%
+because it's really high on those curves
+ 
+
+ align:start position:0%
+because it's really high on those curves
+and the wave functions aren't even there
+
+ align:start position:0%
+and the wave functions aren't even there
+ 
+
+ align:start position:0%
+and the wave functions aren't even there
+that's right so when you have when
+
+ align:start position:0%
+that's right so when you have when
+ 
+
+ align:start position:0%
+that's right so when you have when
+you're dividing by zero you don't expect
+
+ align:start position:0%
+you're dividing by zero you don't expect
+ 
+
+ align:start position:0%
+you're dividing by zero you don't expect
+to have very much of a purchase on
+
+ align:start position:0%
+to have very much of a purchase on
+ 
+
+ align:start position:0%
+to have very much of a purchase on
+whatever it is you're King so then the
+
+ align:start position:0%
+whatever it is you're King so then the
+ 
+
+ align:start position:0%
+whatever it is you're King so then the
+overlap integral is really small for a
+
+ align:start position:0%
+overlap integral is really small for a
+ 
+
+ align:start position:0%
+overlap integral is really small for a
+good reason right as opposed to because
+
+ align:start position:0%
+good reason right as opposed to because
+ 
+
+ align:start position:0%
+good reason right as opposed to because
+of an accidental
+
+ align:start position:0%
+of an accidental
+ 
+
+ align:start position:0%
+of an accidental
+cancellation then the r centroid
+
+ align:start position:0%
+cancellation then the r centroid
+ 
+
+ align:start position:0%
+cancellation then the r centroid
+approximation really fails I was just
+
+ align:start position:0%
+approximation really fails I was just
+ 
+
+ align:start position:0%
+approximation really fails I was just
+wondering if you had if the wave
+
+ align:start position:0%
+wondering if you had if the wave
+ 
+
+ align:start position:0%
+wondering if you had if the wave
+functions happen to have two Maxima and
+
+ align:start position:0%
+functions happen to have two Maxima and
+ 
+
+ align:start position:0%
+functions happen to have two Maxima and
+those happen to be if if they had two
+
+ align:start position:0%
+those happen to be if if they had two
+ 
+
+ align:start position:0%
+those happen to be if if they had two
+maximum basically essentially what
+
+ align:start position:0%
+maximum basically essentially what
+ 
+
+ align:start position:0%
+maximum basically essentially what
+you're calculating is the average value
+
+ align:start position:0%
+you're calculating is the average value
+ 
+
+ align:start position:0%
+you're calculating is the average value
+of r
+
+ align:start position:0%
+of r
+ 
+
+ align:start position:0%
+of r
+with the the that first with the r
+
+ align:start position:0%
+with the the that first with the r
+ 
+
+ align:start position:0%
+with the the that first with the r
+centroid right and so if you had two
+
+ align:start position:0%
+centroid right and so if you had two
+ 
+
+ align:start position:0%
+centroid right and so if you had two
+Maxima of the wave function the average
+
+ align:start position:0%
+Maxima of the wave function the average
+ 
+
+ align:start position:0%
+Maxima of the wave function the average
+value of R might turn out to be in
+
+ align:start position:0%
+value of R might turn out to be in
+ 
+
+ align:start position:0%
+value of R might turn out to be in
+between them that's okay because the
+
+ align:start position:0%
+between them that's okay because the
+ 
+
+ align:start position:0%
+between them that's okay because the
+wave function isn't zero except at
+
+ align:start position:0%
+wave function isn't zero except at
+ 
+
+ align:start position:0%
+wave function isn't zero except at
+nodes right and so uh what you're
+
+ align:start position:0%
+nodes right and so uh what you're
+ 
+
+ align:start position:0%
+nodes right and so uh what you're
+basically doing is you're measuring at
+
+ align:start position:0%
+basically doing is you're measuring at
+ 
+
+ align:start position:0%
+basically doing is you're measuring at
+this special Point what is the classical
+
+ align:start position:0%
+this special Point what is the classical
+ 
+
+ align:start position:0%
+this special Point what is the classical
+probability which is related to the
+
+ align:start position:0%
+probability which is related to the
+ 
+
+ align:start position:0%
+probability which is related to the
+classical velocity
+
+ align:start position:0%
+classical velocity
+ 
+
+ align:start position:0%
+classical velocity
+or one over the classical velocity which
+
+ align:start position:0%
+or one over the classical velocity which
+ 
+
+ align:start position:0%
+or one over the classical velocity which
+is related to the classical moment
+
+ align:start position:0%
+is related to the classical moment
+ 
+
+ align:start position:0%
+is related to the classical moment
+momentum so you can uh you can still
+
+ align:start position:0%
+momentum so you can uh you can still
+ 
+
+ align:start position:0%
+momentum so you can uh you can still
+have small vibrational
+
+ align:start position:0%
+have small vibrational
+ 
+
+ align:start position:0%
+have small vibrational
+overlaps and still have the AR centroid
+
+ align:start position:0%
+overlaps and still have the AR centroid
+ 
+
+ align:start position:0%
+overlaps and still have the AR centroid
+approximation work because it's
+
+ align:start position:0%
+approximation work because it's
+ 
+
+ align:start position:0%
+approximation work because it's
+basically telling you that it's at this
+
+ align:start position:0%
+basically telling you that it's at this
+ 
+
+ align:start position:0%
+basically telling you that it's at this
+place and the the two uh the two
+
+ align:start position:0%
+place and the the two uh the two
+ 
+
+ align:start position:0%
+place and the the two uh the two
+vibrational levels correspond to the
+
+ align:start position:0%
+vibrational levels correspond to the
+ 
+
+ align:start position:0%
+vibrational levels correspond to the
+particle moving really fast in that
+
+ align:start position:0%
+particle moving really fast in that
+ 
+
+ align:start position:0%
+particle moving really fast in that
+region but there's it's still classical
+
+ align:start position:0%
+region but there's it's still classical
+ 
+
+ align:start position:0%
+region but there's it's still classical
+you still get the results by using
+
+ align:start position:0%
+you still get the results by using
+ 
+
+ align:start position:0%
+you still get the results by using
+classical mechanics in account in
+
+ align:start position:0%
+classical mechanics in account in
+ 
+
+ align:start position:0%
+classical mechanics in account in
+a semiquantum mechanical
+
+ align:start position:0%
+a semiquantum mechanical
+ 
+
+ align:start position:0%
+a semiquantum mechanical
+way it's almost always true that you can
+
+ align:start position:0%
+way it's almost always true that you can
+ 
+
+ align:start position:0%
+way it's almost always true that you can
+use classical
+
+ align:start position:0%
+use classical
+ 
+
+ align:start position:0%
+use classical
+mechanics embedded in a quantum
+
+ align:start position:0%
+mechanics embedded in a quantum
+ 
+
+ align:start position:0%
+mechanics embedded in a quantum
+mechanical
+
+ align:start position:0%
+mechanical
+ 
+
+ align:start position:0%
+mechanical
+framework and get the
+
+ align:start position:0%
+framework and get the
+ 
+
+ align:start position:0%
+framework and get the
+answer and when you do that you get what
+
+ align:start position:0%
+answer and when you do that you get what
+ 
+
+ align:start position:0%
+answer and when you do that you get what
+you're told you're not supposed to be
+
+ align:start position:0%
+you're told you're not supposed to be
+ 
+
+ align:start position:0%
+you're told you're not supposed to be
+able to get from quantum
+
+ align:start position:0%
+able to get from quantum
+ 
+
+ align:start position:0%
+able to get from quantum
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+is uh where does something
+
+ align:start position:0%
+is uh where does something
+ 
+
+ align:start position:0%
+is uh where does something
+happen in quantum mechanics it says this
+
+ align:start position:0%
+happen in quantum mechanics it says this
+ 
+
+ align:start position:0%
+happen in quantum mechanics it says this
+is the probability of something
+
+ align:start position:0%
+is the probability of something
+ 
+
+ align:start position:0%
+is the probability of something
+happening but in classical mechanics
+
+ align:start position:0%
+happening but in classical mechanics
+ 
+
+ align:start position:0%
+happening but in classical mechanics
+you're watching X and P as a function of
+
+ align:start position:0%
+you're watching X and P as a function of
+ 
+
+ align:start position:0%
+you're watching X and P as a function of
+time and you can say something happened
+
+ align:start position:0%
+time and you can say something happened
+ 
+
+ align:start position:0%
+time and you can say something happened
+at this position and at this time and
+
+ align:start position:0%
+at this position and at this time and
+ 
+
+ align:start position:0%
+at this position and at this time and
+the particle was going this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fast and so you know what the forces
+
+ align:start position:0%
+fast and so you know what the forces
+ 
+
+ align:start position:0%
+fast and so you know what the forces
+were and you know you know so everything
+
+ align:start position:0%
+were and you know you know so everything
+ 
+
+ align:start position:0%
+were and you know you know so everything
+starts to have interpretation when you
+
+ align:start position:0%
+starts to have interpretation when you
+ 
+
+ align:start position:0%
+starts to have interpretation when you
+can embed classical mechanics in quantum
+
+ align:start position:0%
+can embed classical mechanics in quantum
+ 
+
+ align:start position:0%
+can embed classical mechanics in quantum
+mechanics so quantum mechanics says
+
+ align:start position:0%
+mechanics so quantum mechanics says
+ 
+
+ align:start position:0%
+mechanics so quantum mechanics says
+you're not supposed to know this stuff
+
+ align:start position:0%
+you're not supposed to know this stuff
+ 
+
+ align:start position:0%
+you're not supposed to know this stuff
+but usually you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can and whenever you have an
+
+ align:start position:0%
+can and whenever you have an
+ 
+
+ align:start position:0%
+can and whenever you have an
+approximation like this saying you know
+
+ align:start position:0%
+approximation like this saying you know
+ 
+
+ align:start position:0%
+approximation like this saying you know
+everything accumulates I mean the only
+
+ align:start position:0%
+everything accumulates I mean the only
+ 
+
+ align:start position:0%
+everything accumulates I mean the only
+way you can have the r centroid
+
+ align:start position:0%
+way you can have the r centroid
+ 
+
+ align:start position:0%
+way you can have the r centroid
+approximation work is if things
+
+ align:start position:0%
+approximation work is if things
+ 
+
+ align:start position:0%
+approximation work is if things
+accumulated at a specific r
+
+ align:start position:0%
+accumulated at a specific r
+ 
+
+ align:start position:0%
+accumulated at a specific r
+I think this is what I mean Dave's
+
+ align:start position:0%
+I think this is what I mean Dave's
+ 
+
+ align:start position:0%
+I think this is what I mean Dave's
+question kind of recap is if you have
+
+ align:start position:0%
+question kind of recap is if you have
+ 
+
+ align:start position:0%
+question kind of recap is if you have
+two different potentials yes and they
+
+ align:start position:0%
+two different potentials yes and they
+ 
+
+ align:start position:0%
+two different potentials yes and they
+both have all their you know you're high
+
+ align:start position:0%
+both have all their you know you're high
+ 
+
+ align:start position:0%
+both have all their you know you're high
+vibrational State all the probability of
+
+ align:start position:0%
+vibrational State all the probability of
+ 
+
+ align:start position:0%
+vibrational State all the probability of
+two sides of both yes you're calculating
+
+ align:start position:0%
+two sides of both yes you're calculating
+ 
+
+ align:start position:0%
+two sides of both yes you're calculating
+an over electronic integral between
+
+ align:start position:0%
+an over electronic integral between
+ 
+
+ align:start position:0%
+an over electronic integral between
+those two yes you're going to say the
+
+ align:start position:0%
+those two yes you're going to say the
+ 
+
+ align:start position:0%
+those two yes you're going to say the
+are centroids in the middle and there's
+
+ align:start position:0%
+are centroids in the middle and there's
+ 
+
+ align:start position:0%
+are centroids in the middle and there's
+nothing there because all the action
+
+ align:start position:0%
+nothing there because all the action
+ 
+
+ align:start position:0%
+nothing there because all the action
+happens at the sides of both but
+
+ align:start position:0%
+happens at the sides of both but
+ 
+
+ align:start position:0%
+happens at the sides of both but
+classically uh you know how much you you
+
+ align:start position:0%
+classically uh you know how much you you
+ 
+
+ align:start position:0%
+classically uh you know how much you you
+know what I mean there is nothing there
+
+ align:start position:0%
+know what I mean there is nothing there
+ 
+
+ align:start position:0%
+know what I mean there is nothing there
+there's a little bit
+
+ align:start position:0%
+there's a little bit
+ 
+
+ align:start position:0%
+there's a little bit
+there and you know exactly how to
+
+ align:start position:0%
+there and you know exactly how to
+ 
+
+ align:start position:0%
+there and you know exactly how to
+calculate that because in the middle
+
+ align:start position:0%
+calculate that because in the middle
+ 
+
+ align:start position:0%
+calculate that because in the middle
+region where things are going really
+
+ align:start position:0%
+region where things are going really
+ 
+
+ align:start position:0%
+region where things are going really
+fast it's a lot of
+
+ align:start position:0%
+fast it's a lot of
+ 
+
+ align:start position:0%
+fast it's a lot of
+oscillations and uh so there's not going
+
+ align:start position:0%
+oscillations and uh so there's not going
+ 
+
+ align:start position:0%
+oscillations and uh so there's not going
+to be but then you're saying that the
+
+ align:start position:0%
+to be but then you're saying that the
+ 
+
+ align:start position:0%
+to be but then you're saying that the
+electronic whatever electronic integral
+
+ align:start position:0%
+electronic whatever electronic integral
+ 
+
+ align:start position:0%
+electronic whatever electronic integral
+you're calculating is determined by that
+
+ align:start position:0%
+you're calculating is determined by that
+ 
+
+ align:start position:0%
+you're calculating is determined by that
+point when you think would be determined
+
+ align:start position:0%
+point when you think would be determined
+ 
+
+ align:start position:0%
+point when you think would be determined
+where by where all the vibrational
+
+ align:start position:0%
+where by where all the vibrational
+ 
+
+ align:start position:0%
+where by where all the vibrational
+amplitude is the turning points but you
+
+ align:start position:0%
+amplitude is the turning points but you
+ 
+
+ align:start position:0%
+amplitude is the turning points but you
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+it's determined where the stationary
+
+ align:start position:0%
+it's determined where the stationary
+ 
+
+ align:start position:0%
+it's determined where the stationary
+phase is and it's determined by how much
+
+ align:start position:0%
+phase is and it's determined by how much
+ 
+
+ align:start position:0%
+phase is and it's determined by how much
+time the particle spends in the
+
+ align:start position:0%
+time the particle spends in the
+ 
+
+ align:start position:0%
+time the particle spends in the
+stationary phase region what does that
+
+ align:start position:0%
+stationary phase region what does that
+ 
+
+ align:start position:0%
+stationary phase region what does that
+mean well we know a
+
+ align:start position:0%
+mean well we know a
+ 
+
+ align:start position:0%
+mean well we know a
+velocity and we ask well what is the
+
+ align:start position:0%
+velocity and we ask well what is the
+ 
+
+ align:start position:0%
+velocity and we ask well what is the
+stationary phase how far can it go
+
+ align:start position:0%
+stationary phase how far can it go
+ 
+
+ align:start position:0%
+stationary phase how far can it go
+before the two wave functions get pile
+
+ align:start position:0%
+before the two wave functions get pile
+ 
+
+ align:start position:0%
+before the two wave functions get pile
+out of phase or accumulate a pi phase
+
+ align:start position:0%
+out of phase or accumulate a pi phase
+ 
+
+ align:start position:0%
+out of phase or accumulate a pi phase
+error so the
+
+ align:start position:0%
+error so the
+ 
+
+ align:start position:0%
+error so the
+integrand the integral will accumulate
+
+ align:start position:0%
+integrand the integral will accumulate
+ 
+
+ align:start position:0%
+integrand the integral will accumulate
+about the stationary face Point overall
+
+ align:start position:0%
+about the stationary face Point overall
+ 
+
+ align:start position:0%
+about the stationary face Point overall
+length which is determined by how far
+
+ align:start position:0%
+length which is determined by how far
+ 
+
+ align:start position:0%
+length which is determined by how far
+you can go before the two-way function
+
+ align:start position:0%
+you can go before the two-way function
+ 
+
+ align:start position:0%
+you can go before the two-way function
+Pi phase
+
+ align:start position:0%
+Pi phase
+ 
+
+ align:start position:0%
+Pi phase
+difference and that's related to the
+
+ align:start position:0%
+difference and that's related to the
+ 
+
+ align:start position:0%
+difference and that's related to the
+difference in slopes of the
+
+ align:start position:0%
+difference in slopes of the
+ 
+
+ align:start position:0%
+difference in slopes of the
+potentials and the the value that
+
+ align:start position:0%
+potentials and the the value that
+ 
+
+ align:start position:0%
+potentials and the the value that
+accumulates is the classical
+
+ align:start position:0%
+accumulates is the classical
+ 
+
+ align:start position:0%
+accumulates is the classical
+envelope which is one over the velocity
+
+ align:start position:0%
+envelope which is one over the velocity
+ 
+
+ align:start position:0%
+envelope which is one over the velocity
+and so you can basically evaluate this
+
+ align:start position:0%
+and so you can basically evaluate this
+ 
+
+ align:start position:0%
+and so you can basically evaluate this
+integral not by numerical integration
+
+ align:start position:0%
+integral not by numerical integration
+ 
+
+ align:start position:0%
+integral not by numerical integration
+but by classical
+
+ align:start position:0%
+but by classical
+ 
+
+ align:start position:0%
+but by classical
+mechanics you need to know the period of
+
+ align:start position:0%
+mechanics you need to know the period of
+ 
+
+ align:start position:0%
+mechanics you need to know the period of
+oscillation the
+
+ align:start position:0%
+oscillation the
+ 
+
+ align:start position:0%
+oscillation the
+velocity and the stationary phase point
+
+ align:start position:0%
+velocity and the stationary phase point
+ 
+
+ align:start position:0%
+velocity and the stationary phase point
+and how long is the stationary phase
+
+ align:start position:0%
+and how long is the stationary phase
+ 
+
+ align:start position:0%
+and how long is the stationary phase
+region and all of those you can get
+
+ align:start position:0%
+region and all of those you can get
+ 
+
+ align:start position:0%
+region and all of those you can get
+simply by looking at the uh um potential
+
+ align:start position:0%
+simply by looking at the uh um potential
+ 
+
+ align:start position:0%
+simply by looking at the uh um potential
+burs and the fact that the wave
+
+ align:start position:0%
+burs and the fact that the wave
+ 
+
+ align:start position:0%
+burs and the fact that the wave
+functions have big loes that don't
+
+ align:start position:0%
+functions have big loes that don't
+ 
+
+ align:start position:0%
+functions have big loes that don't
+overlap with each other it means that
+
+ align:start position:0%
+overlap with each other it means that
+ 
+
+ align:start position:0%
+overlap with each other it means that
+the the integral is going to be small
+
+ align:start position:0%
+the the integral is going to be small
+ 
+
+ align:start position:0%
+the the integral is going to be small
+but the value of that integral you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculate and you can use very simple
+
+ align:start position:0%
+calculate and you can use very simple
+ 
+
+ align:start position:0%
+calculate and you can use very simple
+ideas to get these integrals to factor
+
+ align:start position:0%
+ideas to get these integrals to factor
+ 
+
+ align:start position:0%
+ideas to get these integrals to factor
+to accuracy or you can use a functions
+
+ align:start position:0%
+to accuracy or you can use a functions
+ 
+
+ align:start position:0%
+to accuracy or you can use a functions
+to get the integrals to whatever
+
+ align:start position:0%
+to get the integrals to whatever
+ 
+
+ align:start position:0%
+to get the integrals to whatever
+accuracy you want and to have all of the
+
+ align:start position:0%
+accuracy you want and to have all of the
+ 
+
+ align:start position:0%
+accuracy you want and to have all of the
+you know the dependence on energy and
+
+ align:start position:0%
+you know the dependence on energy and
+ 
+
+ align:start position:0%
+you know the dependence on energy and
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+stuff are you I still
+
+ align:start position:0%
+stuff are you I still
+ 
+
+ align:start position:0%
+stuff are you I still
+what if what if you have two stationary
+
+ align:start position:0%
+what if what if you have two stationary
+ 
+
+ align:start position:0%
+what if what if you have two stationary
+phases if you have two if you have two
+
+ align:start position:0%
+phases if you have two if you have two
+ 
+
+ align:start position:0%
+phases if you have two if you have two
+stationary pH points you're screw I'm
+
+ align:start position:0%
+stationary pH points you're screw I'm
+ 
+
+ align:start position:0%
+stationary pH points you're screw I'm
+not yeah I'm not saying that you have
+
+ align:start position:0%
+not yeah I'm not saying that you have
+ 
+
+ align:start position:0%
+not yeah I'm not saying that you have
+each weight function separately has a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lob two stationary well then and then
+
+ align:start position:0%
+lob two stationary well then and then
+ 
+
+ align:start position:0%
+lob two stationary well then and then
+you end up with an average in the middle
+
+ align:start position:0%
+you end up with an average in the middle
+ 
+
+ align:start position:0%
+you end up with an average in the middle
+that's that's right that's exactly
+
+ align:start position:0%
+that's that's right that's exactly
+ 
+
+ align:start position:0%
+that's that's right that's exactly
+that's if you have two stationary face
+
+ align:start position:0%
+that's if you have two stationary face
+ 
+
+ align:start position:0%
+that's if you have two stationary face
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+then semi classical arguments will not
+
+ align:start position:0%
+then semi classical arguments will not
+ 
+
+ align:start position:0%
+then semi classical arguments will not
+help you because each one is going to
+
+ align:start position:0%
+help you because each one is going to
+ 
+
+ align:start position:0%
+help you because each one is going to
+generate a large
+
+ align:start position:0%
+generate a large
+ 
+
+ align:start position:0%
+generate a large
+contribution to the integral right and
+
+ align:start position:0%
+contribution to the integral right and
+ 
+
+ align:start position:0%
+contribution to the integral right and
+you don't know their relative phas and
+
+ align:start position:0%
+you don't know their relative phas and
+ 
+
+ align:start position:0%
+you don't know their relative phas and
+you end up I mean it seems like our
+
+ align:start position:0%
+you end up I mean it seems like our
+ 
+
+ align:start position:0%
+you end up I mean it seems like our
+average is in the middle even occurring
+
+ align:start position:0%
+average is in the middle even occurring
+ 
+
+ align:start position:0%
+average is in the middle even occurring
+both at the Ed when there are two
+
+ align:start position:0%
+both at the Ed when there are two
+ 
+
+ align:start position:0%
+both at the Ed when there are two
+stationary phase points if you calculate
+
+ align:start position:0%
+stationary phase points if you calculate
+ 
+
+ align:start position:0%
+stationary phase points if you calculate
+the r centroid for uh several different
+
+ align:start position:0%
+the r centroid for uh several different
+ 
+
+ align:start position:0%
+the r centroid for uh several different
+uh uh successive vibration it'll jump
+
+ align:start position:0%
+uh uh successive vibration it'll jump
+ 
+
+ align:start position:0%
+uh uh successive vibration it'll jump
+all over the place okay so there will be
+
+ align:start position:0%
+all over the place okay so there will be
+ 
+
+ align:start position:0%
+all over the place okay so there will be
+warnings okay so that's your warning is
+
+ align:start position:0%
+warnings okay so that's your warning is
+ 
+
+ align:start position:0%
+warnings okay so that's your warning is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+you're so and you can tell you you have
+
+ align:start position:0%
+you're so and you can tell you you have
+ 
+
+ align:start position:0%
+you're so and you can tell you you have
+two potential
+
+ align:start position:0%
+two potential
+ 
+
+ align:start position:0%
+two potential
+curves um and you subtract the
+
+ align:start position:0%
+curves um and you subtract the
+ 
+
+ align:start position:0%
+curves um and you subtract the
+two and you look at the difference
+
+ align:start position:0%
+two and you look at the difference
+ 
+
+ align:start position:0%
+two and you look at the difference
+potential as a function R the stationary
+
+ align:start position:0%
+potential as a function R the stationary
+ 
+
+ align:start position:0%
+potential as a function R the stationary
+face point is where the difference
+
+ align:start position:0%
+face point is where the difference
+ 
+
+ align:start position:0%
+face point is where the difference
+potential has zero
+
+ align:start position:0%
+potential has zero
+ 
+
+ align:start position:0%
+potential has zero
+derivative and if there's two or three
+
+ align:start position:0%
+derivative and if there's two or three
+ 
+
+ align:start position:0%
+derivative and if there's two or three
+places where it has zero derivative
+
+ align:start position:0%
+places where it has zero derivative
+ 
+
+ align:start position:0%
+places where it has zero derivative
+you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+warned and sometimes you can get away
+
+ align:start position:0%
+warned and sometimes you can get away
+ 
+
+ align:start position:0%
+warned and sometimes you can get away
+with it because there's only large
+
+ align:start position:0%
+with it because there's only large
+ 
+
+ align:start position:0%
+with it because there's only large
+amplitude at one of those uh if there's
+
+ align:start position:0%
+amplitude at one of those uh if there's
+ 
+
+ align:start position:0%
+amplitude at one of those uh if there's
+large amplitude at Several of them or
+
+ align:start position:0%
+large amplitude at Several of them or
+ 
+
+ align:start position:0%
+large amplitude at Several of them or
+small amplitude at all of them then
+
+ align:start position:0%
+small amplitude at all of them then
+ 
+
+ align:start position:0%
+small amplitude at all of them then
+you're going to have to worry about the
+
+ align:start position:0%
+you're going to have to worry about the
+ 
+
+ align:start position:0%
+you're going to have to worry about the
+relative phases and that's where quantum
+
+ align:start position:0%
+relative phases and that's where quantum
+ 
+
+ align:start position:0%
+relative phases and that's where quantum
+mechanics does stuff that classical
+
+ align:start position:0%
+mechanics does stuff that classical
+ 
+
+ align:start position:0%
+mechanics does stuff that classical
+mechanics can't
+
+ align:start position:0%
+mechanics can't
+ 
+
+ align:start position:0%
+mechanics can't
+touch I mean there isn't interference in
+
+ align:start position:0%
+touch I mean there isn't interference in
+ 
+
+ align:start position:0%
+touch I mean there isn't interference in
+classical
+
+ align:start position:0%
+classical
+ 
+
+ align:start position:0%
+classical
+mechanics you can still use classical
+
+ align:start position:0%
+mechanics you can still use classical
+ 
+
+ align:start position:0%
+mechanics you can still use classical
+mechanics to guide you to the one thing
+
+ align:start position:0%
+mechanics to guide you to the one thing
+ 
+
+ align:start position:0%
+mechanics to guide you to the one thing
+you have to get from the
+
+ align:start position:0%
+you have to get from the
+ 
+
+ align:start position:0%
+you have to get from the
+clchs but often there's no point once
+
+ align:start position:0%
+clchs but often there's no point once
+ 
+
+ align:start position:0%
+clchs but often there's no point once
+you go that part you might as well use
+
+ align:start position:0%
+you go that part you might as well use
+ 
+
+ align:start position:0%
+you go that part you might as well use
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qu okay uh we still have a few
+
+ align:start position:0%
+qu okay uh we still have a few
+ 
+
+ align:start position:0%
+qu okay uh we still have a few
+minutes okay now we're on page five of
+
+ align:start position:0%
+minutes okay now we're on page five of
+ 
+
+ align:start position:0%
+minutes okay now we're on page five of
+my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notes
+
+ align:start position:0%
+notes
+ 
+
+ align:start position:0%
+notes
+so the born up and armor approximation
+
+ align:start position:0%
+so the born up and armor approximation
+ 
+
+ align:start position:0%
+so the born up and armor approximation
+tells us how to
+
+ align:start position:0%
+tells us how to
+ 
+
+ align:start position:0%
+tells us how to
+begin and uh usually life is a lot
+
+ align:start position:0%
+begin and uh usually life is a lot
+ 
+
+ align:start position:0%
+begin and uh usually life is a lot
+simpler than you have any reason to
+
+ align:start position:0%
+simpler than you have any reason to
+ 
+
+ align:start position:0%
+simpler than you have any reason to
+expect that the Spectra are really
+
+ align:start position:0%
+expect that the Spectra are really
+ 
+
+ align:start position:0%
+expect that the Spectra are really
+regular that there are nice simple
+
+ align:start position:0%
+regular that there are nice simple
+ 
+
+ align:start position:0%
+regular that there are nice simple
+patterns and uh uh that there is no hint
+
+ align:start position:0%
+patterns and uh uh that there is no hint
+ 
+
+ align:start position:0%
+patterns and uh uh that there is no hint
+that bad things are happening or could
+
+ align:start position:0%
+that bad things are happening or could
+ 
+
+ align:start position:0%
+that bad things are happening or could
+happen and so there's two limits one is
+
+ align:start position:0%
+happen and so there's two limits one is
+ 
+
+ align:start position:0%
+happen and so there's two limits one is
+the limit where H I J the op diagonal
+
+ align:start position:0%
+the limit where H I J the op diagonal
+ 
+
+ align:start position:0%
+the limit where H I J the op diagonal
+matrix element between two states that
+
+ align:start position:0%
+matrix element between two states that
+ 
+
+ align:start position:0%
+matrix element between two states that
+might be near each other two zero order
+
+ align:start position:0%
+might be near each other two zero order
+ 
+
+ align:start position:0%
+might be near each other two zero order
+born alimer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States or case a diabetic States or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever so the Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+element over the energy difference is
+
+ align:start position:0%
+element over the energy difference is
+ 
+
+ align:start position:0%
+element over the energy difference is
+small so this is the situation that
+
+ align:start position:0%
+small so this is the situation that
+ 
+
+ align:start position:0%
+small so this is the situation that
+leads to unexpected Simplicity
+
+ align:start position:0%
+leads to unexpected Simplicity
+ 
+
+ align:start position:0%
+leads to unexpected Simplicity
+undeserved
+
+ align:start position:0%
+undeserved
+ 
+
+ align:start position:0%
+undeserved
+Simplicity there are all sorts of off
+
+ align:start position:0%
+Simplicity there are all sorts of off
+ 
+
+ align:start position:0%
+Simplicity there are all sorts of off
+diagonal matrix
+
+ align:start position:0%
+diagonal matrix
+ 
+
+ align:start position:0%
+diagonal matrix
+lurking but none of them lead to
+
+ align:start position:0%
+lurking but none of them lead to
+ 
+
+ align:start position:0%
+lurking but none of them lead to
+observable
+
+ align:start position:0%
+observable
+ 
+
+ align:start position:0%
+observable
+effects or very important effects when
+
+ align:start position:0%
+effects or very important effects when
+ 
+
+ align:start position:0%
+effects or very important effects when
+this is true one can always correct uh
+
+ align:start position:0%
+this is true one can always correct uh
+ 
+
+ align:start position:0%
+this is true one can always correct uh
+the energies by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idation so this is Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e um so the energies are corrected by
+
+ align:start position:0%
+e um so the energies are corrected by
+ 
+
+ align:start position:0%
+e um so the energies are corrected by
+this this is small it usually varies
+
+ align:start position:0%
+this this is small it usually varies
+ 
+
+ align:start position:0%
+this this is small it usually varies
+with uh State smoothly and so you don't
+
+ align:start position:0%
+with uh State smoothly and so you don't
+ 
+
+ align:start position:0%
+with uh State smoothly and so you don't
+really see anything
+
+ align:start position:0%
+really see anything
+ 
+
+ align:start position:0%
+really see anything
+weird but then there's the other limit
+
+ align:start position:0%
+weird but then there's the other limit
+ 
+
+ align:start position:0%
+weird but then there's the other limit
+where this quantity is much much larger
+
+ align:start position:0%
+where this quantity is much much larger
+ 
+
+ align:start position:0%
+where this quantity is much much larger
+than one and that's usually because of
+
+ align:start position:0%
+than one and that's usually because of
+ 
+
+ align:start position:0%
+than one and that's usually because of
+an accidental
+
+ align:start position:0%
+an accidental
+ 
+
+ align:start position:0%
+an accidental
+degeneracy so there's nothing really in
+
+ align:start position:0%
+degeneracy so there's nothing really in
+ 
+
+ align:start position:0%
+degeneracy so there's nothing really in
+the hamiltonian that says this is going
+
+ align:start position:0%
+the hamiltonian that says this is going
+ 
+
+ align:start position:0%
+the hamiltonian that says this is going
+to happen it's just the levels which
+
+ align:start position:0%
+to happen it's just the levels which
+ 
+
+ align:start position:0%
+to happen it's just the levels which
+you've normally been ignoring
+
+ align:start position:0%
+you've normally been ignoring
+ 
+
+ align:start position:0%
+you've normally been ignoring
+interactions between accidentally fall
+
+ align:start position:0%
+interactions between accidentally fall
+ 
+
+ align:start position:0%
+interactions between accidentally fall
+near each
+
+ align:start position:0%
+near each
+ 
+
+ align:start position:0%
+near each
+other and whenever that happens you
+
+ align:start position:0%
+other and whenever that happens you
+ 
+
+ align:start position:0%
+other and whenever that happens you
+can't use Ordinary second order
+
+ align:start position:0%
+can't use Ordinary second order
+ 
+
+ align:start position:0%
+can't use Ordinary second order
+perturbation Theory you get local
+
+ align:start position:0%
+perturbation Theory you get local
+ 
+
+ align:start position:0%
+perturbation Theory you get local
+effects and these are called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perations the this regular thing is
+
+ align:start position:0%
+perations the this regular thing is
+ 
+
+ align:start position:0%
+perations the this regular thing is
+messed up there is something that looks
+
+ align:start position:0%
+messed up there is something that looks
+ 
+
+ align:start position:0%
+messed up there is something that looks
+wrong except there's nothing wrong about
+
+ align:start position:0%
+wrong except there's nothing wrong about
+ 
+
+ align:start position:0%
+wrong except there's nothing wrong about
+it U and but it requires a special
+
+ align:start position:0%
+it U and but it requires a special
+ 
+
+ align:start position:0%
+it U and but it requires a special
+treatment because of
+
+ align:start position:0%
+treatment because of
+ 
+
+ align:start position:0%
+treatment because of
+this unusual energy denominator that
+
+ align:start position:0%
+this unusual energy denominator that
+ 
+
+ align:start position:0%
+this unusual energy denominator that
+brings these zero order States close
+
+ align:start position:0%
+brings these zero order States close
+ 
+
+ align:start position:0%
+brings these zero order States close
+together and forces you to deal with the
+
+ align:start position:0%
+together and forces you to deal with the
+ 
+
+ align:start position:0%
+together and forces you to deal with the
+true evil of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nature
+
+ align:start position:0%
+nature
+ 
+
+ align:start position:0%
+nature
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there's there's many types of
+
+ align:start position:0%
+there's there's many types of
+ 
+
+ align:start position:0%
+there's there's many types of
+perturbations one is we have a bound
+
+ align:start position:0%
+perturbations one is we have a bound
+ 
+
+ align:start position:0%
+perturbations one is we have a bound
+potential curve and another bound
+
+ align:start position:0%
+potential curve and another bound
+ 
+
+ align:start position:0%
+potential curve and another bound
+potential curve and we have vibrational
+
+ align:start position:0%
+potential curve and we have vibrational
+ 
+
+ align:start position:0%
+potential curve and we have vibrational
+levels of this and vibrational levels of
+
+ align:start position:0%
+levels of this and vibrational levels of
+ 
+
+ align:start position:0%
+levels of this and vibrational levels of
+this and they're near each other and
+
+ align:start position:0%
+this and they're near each other and
+ 
+
+ align:start position:0%
+this and they're near each other and
+then if we look at the
+
+ align:start position:0%
+then if we look at the
+ 
+
+ align:start position:0%
+then if we look at the
+energy versus J * J +
+
+ align:start position:0%
+energy versus J * J +
+ 
+
+ align:start position:0%
+energy versus J * J +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+we get something like that remember uh
+
+ align:start position:0%
+we get something like that remember uh
+ 
+
+ align:start position:0%
+we get something like that remember uh
+the energies versus J J + 1 will appear
+
+ align:start position:0%
+the energies versus J J + 1 will appear
+ 
+
+ align:start position:0%
+the energies versus J J + 1 will appear
+as straight lines with slope of B and if
+
+ align:start position:0%
+as straight lines with slope of B and if
+ 
+
+ align:start position:0%
+as straight lines with slope of B and if
+you have different rotational constants
+
+ align:start position:0%
+you have different rotational constants
+ 
+
+ align:start position:0%
+you have different rotational constants
+these curves will
+
+ align:start position:0%
+these curves will
+ 
+
+ align:start position:0%
+these curves will
+cross so at this place where we have
+
+ align:start position:0%
+cross so at this place where we have
+ 
+
+ align:start position:0%
+cross so at this place where we have
+states of the same J that are degenerate
+
+ align:start position:0%
+states of the same J that are degenerate
+ 
+
+ align:start position:0%
+states of the same J that are degenerate
+something bad is going to happen and now
+
+ align:start position:0%
+something bad is going to happen and now
+ 
+
+ align:start position:0%
+something bad is going to happen and now
+suppose Nature has said well I can to
+
+ align:start position:0%
+suppose Nature has said well I can to
+ 
+
+ align:start position:0%
+suppose Nature has said well I can to
+this level because like we have a
+
+ align:start position:0%
+this level because like we have a
+ 
+
+ align:start position:0%
+this level because like we have a
+singlet ground state this is a singlet
+
+ align:start position:0%
+singlet ground state this is a singlet
+ 
+
+ align:start position:0%
+singlet ground state this is a singlet
+state but this is a triplet State I
+
+ align:start position:0%
+state but this is a triplet State I
+ 
+
+ align:start position:0%
+state but this is a triplet State I
+can't exite to that this is called a
+
+ align:start position:0%
+can't exite to that this is called a
+ 
+
+ align:start position:0%
+can't exite to that this is called a
+Bright State this is called a dark
+
+ align:start position:0%
+Bright State this is called a dark
+ 
+
+ align:start position:0%
+Bright State this is called a dark
+State and so uh uh if I um well now
+
+ align:start position:0%
+State and so uh uh if I um well now
+ 
+
+ align:start position:0%
+State and so uh uh if I um well now
+there's some pictures that I handed out
+
+ align:start position:0%
+there's some pictures that I handed out
+ 
+
+ align:start position:0%
+there's some pictures that I handed out
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this uh what is a peration here is a
+
+ align:start position:0%
+this uh what is a peration here is a
+ 
+
+ align:start position:0%
+this uh what is a peration here is a
+spectrum recorded on a photographic
+
+ align:start position:0%
+spectrum recorded on a photographic
+ 
+
+ align:start position:0%
+spectrum recorded on a photographic
+plate which nobody ever does it but it
+
+ align:start position:0%
+plate which nobody ever does it but it
+ 
+
+ align:start position:0%
+plate which nobody ever does it but it
+it uh makes it so clear you see this
+
+ align:start position:0%
+it uh makes it so clear you see this
+ 
+
+ align:start position:0%
+it uh makes it so clear you see this
+regular spacing of
+
+ align:start position:0%
+regular spacing of
+ 
+
+ align:start position:0%
+regular spacing of
+lines that's an unperturbed Spectrum
+
+ align:start position:0%
+lines that's an unperturbed Spectrum
+ 
+
+ align:start position:0%
+lines that's an unperturbed Spectrum
+that's a textbook Spectrum there's no
+
+ align:start position:0%
+that's a textbook Spectrum there's no
+ 
+
+ align:start position:0%
+that's a textbook Spectrum there's no
+Dynamics in it nothing
+
+ align:start position:0%
+Dynamics in it nothing
+ 
+
+ align:start position:0%
+Dynamics in it nothing
+interesting and that's what most people
+
+ align:start position:0%
+interesting and that's what most people
+ 
+
+ align:start position:0%
+interesting and that's what most people
+would like to see because they're risk
+
+ align:start position:0%
+would like to see because they're risk
+ 
+
+ align:start position:0%
+would like to see because they're risk
+ofers and then this is just the next
+
+ align:start position:0%
+ofers and then this is just the next
+ 
+
+ align:start position:0%
+ofers and then this is just the next
+vibrational level higher in that same
+
+ align:start position:0%
+vibrational level higher in that same
+ 
+
+ align:start position:0%
+vibrational level higher in that same
+electronic State and you can see there's
+
+ align:start position:0%
+electronic State and you can see there's
+ 
+
+ align:start position:0%
+electronic State and you can see there's
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+wrong it's not there's no regular
+
+ align:start position:0%
+wrong it's not there's no regular
+ 
+
+ align:start position:0%
+wrong it's not there's no regular
+spacing of
+
+ align:start position:0%
+spacing of
+ 
+
+ align:start position:0%
+spacing of
+lines there are lines that have been
+
+ align:start position:0%
+lines there are lines that have been
+ 
+
+ align:start position:0%
+lines there are lines that have been
+shifted around and there's extra lines
+
+ align:start position:0%
+shifted around and there's extra lines
+ 
+
+ align:start position:0%
+shifted around and there's extra lines
+there's more lines in here you see how
+
+ align:start position:0%
+there's more lines in here you see how
+ 
+
+ align:start position:0%
+there's more lines in here you see how
+many lines in this lower you see they
+
+ align:start position:0%
+many lines in this lower you see they
+ 
+
+ align:start position:0%
+many lines in this lower you see they
+they're not just there's many closely
+
+ align:start position:0%
+they're not just there's many closely
+ 
+
+ align:start position:0%
+they're not just there's many closely
+spaced
+
+ align:start position:0%
+spaced
+ 
+
+ align:start position:0%
+spaced
+things and that the reason for that is
+
+ align:start position:0%
+things and that the reason for that is
+ 
+
+ align:start position:0%
+things and that the reason for that is
+because uh you're not just seeing the
+
+ align:start position:0%
+because uh you're not just seeing the
+ 
+
+ align:start position:0%
+because uh you're not just seeing the
+bright state but you're seeing the dark
+
+ align:start position:0%
+bright state but you're seeing the dark
+ 
+
+ align:start position:0%
+bright state but you're seeing the dark
+St that because of this accidental
+
+ align:start position:0%
+St that because of this accidental
+ 
+
+ align:start position:0%
+St that because of this accidental
+degeneracy there are Level
+
+ align:start position:0%
+degeneracy there are Level
+ 
+
+ align:start position:0%
+degeneracy there are Level
+shifts and intensity borro you open a
+
+ align:start position:0%
+shifts and intensity borro you open a
+ 
+
+ align:start position:0%
+shifts and intensity borro you open a
+window onto what you're not supposed to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see and some of us still get a thrill
+
+ align:start position:0%
+see and some of us still get a thrill
+ 
+
+ align:start position:0%
+see and some of us still get a thrill
+when we can look through a window we're
+
+ align:start position:0%
+when we can look through a window we're
+ 
+
+ align:start position:0%
+when we can look through a window we're
+not supposed to see
+
+ align:start position:0%
+not supposed to see
+ 
+
+ align:start position:0%
+not supposed to see
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+uh all right
+
+ align:start position:0%
+uh all right
+ 
+
+ align:start position:0%
+uh all right
+so uh we learn about other states
+
+ align:start position:0%
+so uh we learn about other states
+ 
+
+ align:start position:0%
+so uh we learn about other states
+uh we learned about the coupling Matrix
+
+ align:start position:0%
+uh we learned about the coupling Matrix
+ 
+
+ align:start position:0%
+uh we learned about the coupling Matrix
+element we learned about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dynamics okay so I'd like to say more
+
+ align:start position:0%
+Dynamics okay so I'd like to say more
+ 
+
+ align:start position:0%
+Dynamics okay so I'd like to say more
+about peration
+
+ align:start position:0%
+about peration
+ 
+
+ align:start position:0%
+about peration
+but there's another kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perturbation so we might have a bound
+
+ align:start position:0%
+perturbation so we might have a bound
+ 
+
+ align:start position:0%
+perturbation so we might have a bound
+State crossed by a repulsive
+
+ align:start position:0%
+State crossed by a repulsive
+ 
+
+ align:start position:0%
+State crossed by a repulsive
+state so this leads to a b going to A+
+
+ align:start position:0%
+state so this leads to a b going to A+
+ 
+
+ align:start position:0%
+state so this leads to a b going to A+
+B this leads to a Breaking of the
+
+ align:start position:0%
+B this leads to a Breaking of the
+ 
+
+ align:start position:0%
+B this leads to a Breaking of the
+bond pre dissociation so we have a
+
+ align:start position:0%
+bond pre dissociation so we have a
+ 
+
+ align:start position:0%
+bond pre dissociation so we have a
+vibrational level here and a Contin
+
+ align:start position:0%
+vibrational level here and a Contin
+ 
+
+ align:start position:0%
+vibrational level here and a Contin
+vibrational Continuum here and because
+
+ align:start position:0%
+vibrational Continuum here and because
+ 
+
+ align:start position:0%
+vibrational Continuum here and because
+there are coupling Matrix elements
+
+ align:start position:0%
+there are coupling Matrix elements
+ 
+
+ align:start position:0%
+there are coupling Matrix elements
+between the bound State and the
+
+ align:start position:0%
+between the bound State and the
+ 
+
+ align:start position:0%
+between the bound State and the
+Continuum what happens is if we look
+
+ align:start position:0%
+Continuum what happens is if we look
+ 
+
+ align:start position:0%
+Continuum what happens is if we look
+very carefully the bound state gets
+
+ align:start position:0%
+very carefully the bound state gets
+ 
+
+ align:start position:0%
+very carefully the bound state gets
+broadened might get shifted and since
+
+ align:start position:0%
+broadened might get shifted and since
+ 
+
+ align:start position:0%
+broadened might get shifted and since
+there's Continuum above it and below
+
+ align:start position:0%
+there's Continuum above it and below
+ 
+
+ align:start position:0%
+there's Continuum above it and below
+it it is not likely to get pushed one
+
+ align:start position:0%
+it it is not likely to get pushed one
+ 
+
+ align:start position:0%
+it it is not likely to get pushed one
+way or the other by more density of
+
+ align:start position:0%
+way or the other by more density of
+ 
+
+ align:start position:0%
+way or the other by more density of
+States above or below so that level
+
+ align:start position:0%
+States above or below so that level
+ 
+
+ align:start position:0%
+States above or below so that level
+shifts are not important but level
+
+ align:start position:0%
+shifts are not important but level
+ 
+
+ align:start position:0%
+shifts are not important but level
+broadening occurs and again on these
+
+ align:start position:0%
+broadening occurs and again on these
+ 
+
+ align:start position:0%
+broadening occurs and again on these
+pictures that I gave you it
+
+ align:start position:0%
+pictures that I gave you it
+ 
+
+ align:start position:0%
+pictures that I gave you it
+shows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the second picture is still another
+
+ align:start position:0%
+um the second picture is still another
+ 
+
+ align:start position:0%
+um the second picture is still another
+perturbation but it's a small one but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this third picture um
+
+ align:start position:0%
+this third picture um
+ 
+
+ align:start position:0%
+this third picture um
+shows Something Happening Here is the
+
+ align:start position:0%
+shows Something Happening Here is the
+ 
+
+ align:start position:0%
+shows Something Happening Here is the
+absorption spectrum and here is the
+
+ align:start position:0%
+absorption spectrum and here is the
+ 
+
+ align:start position:0%
+absorption spectrum and here is the
+emission spectrum same band in the
+
+ align:start position:0%
+emission spectrum same band in the
+ 
+
+ align:start position:0%
+emission spectrum same band in the
+absorption it doesn't care if the
+
+ align:start position:0%
+absorption it doesn't care if the
+ 
+
+ align:start position:0%
+absorption it doesn't care if the
+excited state can't live to emit a
+
+ align:start position:0%
+excited state can't live to emit a
+ 
+
+ align:start position:0%
+excited state can't live to emit a
+photon but in the emission spectrum if
+
+ align:start position:0%
+photon but in the emission spectrum if
+ 
+
+ align:start position:0%
+photon but in the emission spectrum if
+the dissociation rate becomes large
+
+ align:start position:0%
+the dissociation rate becomes large
+ 
+
+ align:start position:0%
+the dissociation rate becomes large
+compared to the spontaneous emission
+
+ align:start position:0%
+compared to the spontaneous emission
+ 
+
+ align:start position:0%
+compared to the spontaneous emission
+rate you get no
+
+ align:start position:0%
+rate you get no
+ 
+
+ align:start position:0%
+rate you get no
+fluoresence so this is a
+
+ align:start position:0%
+fluoresence so this is a
+ 
+
+ align:start position:0%
+fluoresence so this is a
+predissociation and it's interesting if
+
+ align:start position:0%
+predissociation and it's interesting if
+ 
+
+ align:start position:0%
+predissociation and it's interesting if
+you look closely that there's a sudden
+
+ align:start position:0%
+you look closely that there's a sudden
+ 
+
+ align:start position:0%
+you look closely that there's a sudden
+drop in intensity and then it picks up
+
+ align:start position:0%
+drop in intensity and then it picks up
+ 
+
+ align:start position:0%
+drop in intensity and then it picks up
+again that the uh the dissociation rate
+
+ align:start position:0%
+again that the uh the dissociation rate
+ 
+
+ align:start position:0%
+again that the uh the dissociation rate
+is uh slowing down as you go away from
+
+ align:start position:0%
+is uh slowing down as you go away from
+ 
+
+ align:start position:0%
+is uh slowing down as you go away from
+the the first J that is hit and so you
+
+ align:start position:0%
+the the first J that is hit and so you
+ 
+
+ align:start position:0%
+the the first J that is hit and so you
+you get uh a large variation in these
+
+ align:start position:0%
+you get uh a large variation in these
+ 
+
+ align:start position:0%
+you get uh a large variation in these
+mixings
+
+ align:start position:0%
+mixings
+ 
+
+ align:start position:0%
+mixings
+so we can still describe Creed
+
+ align:start position:0%
+so we can still describe Creed
+ 
+
+ align:start position:0%
+so we can still describe Creed
+Association by
+
+ align:start position:0%
+Association by
+ 
+
+ align:start position:0%
+Association by
+calculating the electronic Matrix
+
+ align:start position:0%
+calculating the electronic Matrix
+ 
+
+ align:start position:0%
+calculating the electronic Matrix
+element times the rotational Matrix
+
+ align:start position:0%
+element times the rotational Matrix
+ 
+
+ align:start position:0%
+element times the rotational Matrix
+element times the vibrational Matrix
+
+ align:start position:0%
+element times the vibrational Matrix
+ 
+
+ align:start position:0%
+element times the vibrational Matrix
+element and the Complicated new thing is
+
+ align:start position:0%
+element and the Complicated new thing is
+ 
+
+ align:start position:0%
+element and the Complicated new thing is
+we have a bound vibrational State
+
+ align:start position:0%
+we have a bound vibrational State
+ 
+
+ align:start position:0%
+we have a bound vibrational State
+interacting with a Continuum vibrational
+
+ align:start position:0%
+interacting with a Continuum vibrational
+ 
+
+ align:start position:0%
+interacting with a Continuum vibrational
+state but there's still a stationary
+
+ align:start position:0%
+state but there's still a stationary
+ 
+
+ align:start position:0%
+state but there's still a stationary
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+region and that's determining
+
+ align:start position:0%
+region and that's determining
+ 
+
+ align:start position:0%
+region and that's determining
+everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and there is another kind of
+
+ align:start position:0%
+um and there is another kind of
+ 
+
+ align:start position:0%
+um and there is another kind of
+perturbation that leads
+
+ align:start position:0%
+perturbation that leads
+ 
+
+ align:start position:0%
+perturbation that leads
+to what we call automization so we have
+
+ align:start position:0%
+to what we call automization so we have
+ 
+
+ align:start position:0%
+to what we call automization so we have
+a process a going to
+
+ align:start position:0%
+a process a going to
+ 
+
+ align:start position:0%
+a process a going to
+a plus plus an
+
+ align:start position:0%
+a plus plus an
+ 
+
+ align:start position:0%
+a plus plus an
+electr this is harder to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+draw basically what happens is
+
+ align:start position:0%
+draw basically what happens is
+ 
+
+ align:start position:0%
+draw basically what happens is
+we have an
+
+ align:start position:0%
+we have an
+ 
+
+ align:start position:0%
+we have an
+electron bound to an
+
+ align:start position:0%
+electron bound to an
+ 
+
+ align:start position:0%
+electron bound to an
+ion and the ion can have electronic
+
+ align:start position:0%
+ion and the ion can have electronic
+ 
+
+ align:start position:0%
+ion and the ion can have electronic
+exitation spin
+
+ align:start position:0%
+exitation spin
+ 
+
+ align:start position:0%
+exitation spin
+orbit vibrational exitation rotational
+
+ align:start position:0%
+orbit vibrational exitation rotational
+ 
+
+ align:start position:0%
+orbit vibrational exitation rotational
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+somehow the
+
+ align:start position:0%
+somehow the
+ 
+
+ align:start position:0%
+somehow the
+energy in the ion Finds Its a way to get
+
+ align:start position:0%
+energy in the ion Finds Its a way to get
+ 
+
+ align:start position:0%
+energy in the ion Finds Its a way to get
+into the electron to transfer to the
+
+ align:start position:0%
+into the electron to transfer to the
+ 
+
+ align:start position:0%
+into the electron to transfer to the
+electron and when when it does that the
+
+ align:start position:0%
+electron and when when it does that the
+ 
+
+ align:start position:0%
+electron and when when it does that the
+electron is too much kinetic energy to
+
+ align:start position:0%
+electron is too much kinetic energy to
+ 
+
+ align:start position:0%
+electron is too much kinetic energy to
+remain bound to the ion it falls
+
+ align:start position:0%
+remain bound to the ion it falls
+ 
+
+ align:start position:0%
+remain bound to the ion it falls
+off and there are
+
+ align:start position:0%
+off and there are
+ 
+
+ align:start position:0%
+off and there are
+beautiful mechanisms that describe how
+
+ align:start position:0%
+beautiful mechanisms that describe how
+ 
+
+ align:start position:0%
+beautiful mechanisms that describe how
+this Auto ionization
+
+ align:start position:0%
+this Auto ionization
+ 
+
+ align:start position:0%
+this Auto ionization
+occurs and each of the
+
+ align:start position:0%
+occurs and each of the
+ 
+
+ align:start position:0%
+occurs and each of the
+processes uh electronic spin orbit
+
+ align:start position:0%
+processes uh electronic spin orbit
+ 
+
+ align:start position:0%
+processes uh electronic spin orbit
+vibrational rotational Auto ionization
+
+ align:start position:0%
+vibrational rotational Auto ionization
+ 
+
+ align:start position:0%
+vibrational rotational Auto ionization
+has a nice
+
+ align:start position:0%
+has a nice
+ 
+
+ align:start position:0%
+has a nice
+mechanism
\ No newline at end of file
diff --git a/Ajar_6MAOLw.txt b/Ajar_6MAOLw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1075b6dbb13d58b8a49463c7beef74dae0eb974f
--- /dev/null
+++ b/Ajar_6MAOLw.txt
@@ -0,0 +1,1291 @@
+align:start position:0%
+ 
+we will now take a step towards
+
+ align:start position:0%
+we will now take a step towards
+ 
+
+ align:start position:0%
+we will now take a step towards
+abstraction and discuss the issue of
+
+ align:start position:0%
+abstraction and discuss the issue of
+ 
+
+ align:start position:0%
+abstraction and discuss the issue of
+convergence of random variables let us
+
+ align:start position:0%
+convergence of random variables let us
+ 
+
+ align:start position:0%
+convergence of random variables let us
+look at the weak law of large numbers it
+
+ align:start position:0%
+look at the weak law of large numbers it
+ 
+
+ align:start position:0%
+look at the weak law of large numbers it
+tells us that with high probability the
+
+ align:start position:0%
+tells us that with high probability the
+ 
+
+ align:start position:0%
+tells us that with high probability the
+sample mean falls close to the true mean
+
+ align:start position:0%
+sample mean falls close to the true mean
+ 
+
+ align:start position:0%
+sample mean falls close to the true mean
+as n goes to infinity we would like to
+
+ align:start position:0%
+as n goes to infinity we would like to
+ 
+
+ align:start position:0%
+as n goes to infinity we would like to
+interpret the statement by saying that
+
+ align:start position:0%
+interpret the statement by saying that
+ 
+
+ align:start position:0%
+interpret the statement by saying that
+the sample mean converges to the true
+
+ align:start position:0%
+the sample mean converges to the true
+ 
+
+ align:start position:0%
+the sample mean converges to the true
+mean however before we can make such a
+
+ align:start position:0%
+mean however before we can make such a
+ 
+
+ align:start position:0%
+mean however before we can make such a
+statement we should first define
+
+ align:start position:0%
+statement we should first define
+ 
+
+ align:start position:0%
+statement we should first define
+carefully the word converges and we need
+
+ align:start position:0%
+carefully the word converges and we need
+ 
+
+ align:start position:0%
+carefully the word converges and we need
+a notion of convergence that refers to
+
+ align:start position:0%
+a notion of convergence that refers to
+ 
+
+ align:start position:0%
+a notion of convergence that refers to
+convergence of random variables here is
+
+ align:start position:0%
+convergence of random variables here is
+ 
+
+ align:start position:0%
+convergence of random variables here is
+the definition suppose that we have a
+
+ align:start position:0%
+the definition suppose that we have a
+ 
+
+ align:start position:0%
+the definition suppose that we have a
+sequence of random variables that are
+
+ align:start position:0%
+sequence of random variables that are
+ 
+
+ align:start position:0%
+sequence of random variables that are
+not necessarily independent we say that
+
+ align:start position:0%
+not necessarily independent we say that
+ 
+
+ align:start position:0%
+not necessarily independent we say that
+this sequence of random variables
+
+ align:start position:0%
+this sequence of random variables
+ 
+
+ align:start position:0%
+this sequence of random variables
+converges in probability that's the
+
+ align:start position:0%
+converges in probability that's the
+ 
+
+ align:start position:0%
+converges in probability that's the
+particular notion of convergence we're
+
+ align:start position:0%
+particular notion of convergence we're
+ 
+
+ align:start position:0%
+particular notion of convergence we're
+defining it converges to a certain
+
+ align:start position:0%
+defining it converges to a certain
+ 
+
+ align:start position:0%
+defining it converges to a certain
+number if the following is true no
+
+ align:start position:0%
+number if the following is true no
+ 
+
+ align:start position:0%
+number if the following is true no
+matter what epsilon is as long as it is
+
+ align:start position:0%
+matter what epsilon is as long as it is
+ 
+
+ align:start position:0%
+matter what epsilon is as long as it is
+a positive number the probability that
+
+ align:start position:0%
+a positive number the probability that
+ 
+
+ align:start position:0%
+a positive number the probability that
+the random variable falls far from this
+
+ align:start position:0%
+the random variable falls far from this
+ 
+
+ align:start position:0%
+the random variable falls far from this
+number that is epsilon or further away
+
+ align:start position:0%
+number that is epsilon or further away
+ 
+
+ align:start position:0%
+number that is epsilon or further away
+from that number that probability
+
+ align:start position:0%
+from that number that probability
+ 
+
+ align:start position:0%
+from that number that probability
+converges to 0 as n increases that is as
+
+ align:start position:0%
+converges to 0 as n increases that is as
+ 
+
+ align:start position:0%
+converges to 0 as n increases that is as
+n increases there is higher and higher
+
+ align:start position:0%
+n increases there is higher and higher
+ 
+
+ align:start position:0%
+n increases there is higher and higher
+probability that Y n will be close to
+
+ align:start position:0%
+probability that Y n will be close to
+ 
+
+ align:start position:0%
+probability that Y n will be close to
+this particular number a this is the
+
+ align:start position:0%
+this particular number a this is the
+ 
+
+ align:start position:0%
+this particular number a this is the
+notion of convergence that we have
+
+ align:start position:0%
+notion of convergence that we have
+ 
+
+ align:start position:0%
+notion of convergence that we have
+defined and notice that this notion of
+
+ align:start position:0%
+defined and notice that this notion of
+ 
+
+ align:start position:0%
+defined and notice that this notion of
+convergence corresponds exactly to what
+
+ align:start position:0%
+convergence corresponds exactly to what
+ 
+
+ align:start position:0%
+convergence corresponds exactly to what
+is happening in the weak law of large
+
+ align:start position:0%
+is happening in the weak law of large
+ 
+
+ align:start position:0%
+is happening in the weak law of large
+numbers and so in particular we can
+
+ align:start position:0%
+numbers and so in particular we can
+ 
+
+ align:start position:0%
+numbers and so in particular we can
+describe the weak law of large numbers
+
+ align:start position:0%
+describe the weak law of large numbers
+ 
+
+ align:start position:0%
+describe the weak law of large numbers
+as saying that m and the sample mean
+
+ align:start position:0%
+as saying that m and the sample mean
+ 
+
+ align:start position:0%
+as saying that m and the sample mean
+converges to MU as n goes to infinity
+
+ align:start position:0%
+converges to MU as n goes to infinity
+ 
+
+ align:start position:0%
+converges to MU as n goes to infinity
+but in a particular sense in the sense
+
+ align:start position:0%
+but in a particular sense in the sense
+ 
+
+ align:start position:0%
+but in a particular sense in the sense
+of convergence in probability let us now
+
+ align:start position:0%
+of convergence in probability let us now
+ 
+
+ align:start position:0%
+of convergence in probability let us now
+try to understand a little better what
+
+ align:start position:0%
+try to understand a little better what
+ 
+
+ align:start position:0%
+try to understand a little better what
+convergence in probability really
+
+ align:start position:0%
+convergence in probability really
+ 
+
+ align:start position:0%
+convergence in probability really
+amounts to and we will do that by making
+
+ align:start position:0%
+amounts to and we will do that by making
+ 
+
+ align:start position:0%
+amounts to and we will do that by making
+a comparison with the ordinary notion of
+
+ align:start position:0%
+a comparison with the ordinary notion of
+ 
+
+ align:start position:0%
+a comparison with the ordinary notion of
+convergence of real numbers
+
+ align:start position:0%
+convergence of real numbers
+ 
+
+ align:start position:0%
+convergence of real numbers
+when we're dealing with convergence of
+
+ align:start position:0%
+when we're dealing with convergence of
+ 
+
+ align:start position:0%
+when we're dealing with convergence of
+numbers we start with a sequence of
+
+ align:start position:0%
+numbers we start with a sequence of
+ 
+
+ align:start position:0%
+numbers we start with a sequence of
+numbers and we are interested in the
+
+ align:start position:0%
+numbers and we are interested in the
+ 
+
+ align:start position:0%
+numbers and we are interested in the
+statement that this sequence converges
+
+ align:start position:0%
+statement that this sequence converges
+ 
+
+ align:start position:0%
+statement that this sequence converges
+to a certain limit what does that mean
+
+ align:start position:0%
+to a certain limit what does that mean
+ 
+
+ align:start position:0%
+to a certain limit what does that mean
+what we mean is that the elements of the
+
+ align:start position:0%
+what we mean is that the elements of the
+ 
+
+ align:start position:0%
+what we mean is that the elements of the
+sequence eventually that is when n is
+
+ align:start position:0%
+sequence eventually that is when n is
+ 
+
+ align:start position:0%
+sequence eventually that is when n is
+large enough we'll get and stay
+
+ align:start position:0%
+large enough we'll get and stay
+ 
+
+ align:start position:0%
+large enough we'll get and stay
+arbitrarily close to this particular
+
+ align:start position:0%
+arbitrarily close to this particular
+ 
+
+ align:start position:0%
+arbitrarily close to this particular
+number a which is the limit in terms of
+
+ align:start position:0%
+number a which is the limit in terms of
+ 
+
+ align:start position:0%
+number a which is the limit in terms of
+a picture here is a the limit here is n
+
+ align:start position:0%
+a picture here is a the limit here is n
+ 
+
+ align:start position:0%
+a picture here is a the limit here is n
+we take a small band around this number
+
+ align:start position:0%
+we take a small band around this number
+ 
+
+ align:start position:0%
+we take a small band around this number
+a and what we require is that the
+
+ align:start position:0%
+a and what we require is that the
+ 
+
+ align:start position:0%
+a and what we require is that the
+elements of the sequence eventually get
+
+ align:start position:0%
+elements of the sequence eventually get
+ 
+
+ align:start position:0%
+elements of the sequence eventually get
+within this band around the number a
+
+ align:start position:0%
+within this band around the number a
+ 
+
+ align:start position:0%
+within this band around the number a
+they might get outside the band get
+
+ align:start position:0%
+they might get outside the band get
+ 
+
+ align:start position:0%
+they might get outside the band get
+inside again but eventually that is
+
+ align:start position:0%
+inside again but eventually that is
+ 
+
+ align:start position:0%
+inside again but eventually that is
+after some time the elements of the
+
+ align:start position:0%
+after some time the elements of the
+ 
+
+ align:start position:0%
+after some time the elements of the
+sequence will only stay inside this band
+
+ align:start position:0%
+sequence will only stay inside this band
+ 
+
+ align:start position:0%
+sequence will only stay inside this band
+now to translate this into a more formal
+
+ align:start position:0%
+now to translate this into a more formal
+ 
+
+ align:start position:0%
+now to translate this into a more formal
+mathematical statement which is the
+
+ align:start position:0%
+mathematical statement which is the
+ 
+
+ align:start position:0%
+mathematical statement which is the
+mathematical definition of the notion of
+
+ align:start position:0%
+mathematical definition of the notion of
+ 
+
+ align:start position:0%
+mathematical definition of the notion of
+convergence we have the following if I
+
+ align:start position:0%
+convergence we have the following if I
+ 
+
+ align:start position:0%
+convergence we have the following if I
+give you some epsilon epsilon could be a
+
+ align:start position:0%
+give you some epsilon epsilon could be a
+ 
+
+ align:start position:0%
+give you some epsilon epsilon could be a
+very small number I form a band around a
+
+ align:start position:0%
+very small number I form a band around a
+ 
+
+ align:start position:0%
+very small number I form a band around a
+that goes from a minus epsilon to a plus
+
+ align:start position:0%
+that goes from a minus epsilon to a plus
+ 
+
+ align:start position:0%
+that goes from a minus epsilon to a plus
+Epsilon what I want is that there exists
+
+ align:start position:0%
+Epsilon what I want is that there exists
+ 
+
+ align:start position:0%
+Epsilon what I want is that there exists
+a certain time and zero in this picture
+
+ align:start position:0%
+a certain time and zero in this picture
+ 
+
+ align:start position:0%
+a certain time and zero in this picture
+and zero would be here such that for all
+
+ align:start position:0%
+and zero would be here such that for all
+ 
+
+ align:start position:0%
+and zero would be here such that for all
+times after n zero our sequence stays
+
+ align:start position:0%
+times after n zero our sequence stays
+ 
+
+ align:start position:0%
+times after n zero our sequence stays
+within Epsilon from a that is our
+
+ align:start position:0%
+within Epsilon from a that is our
+ 
+
+ align:start position:0%
+within Epsilon from a that is our
+sequence stays inside this band now let
+
+ align:start position:0%
+sequence stays inside this band now let
+ 
+
+ align:start position:0%
+sequence stays inside this band now let
+us move to the case of random variables
+
+ align:start position:0%
+us move to the case of random variables
+ 
+
+ align:start position:0%
+us move to the case of random variables
+and see what convergence in probability
+
+ align:start position:0%
+and see what convergence in probability
+ 
+
+ align:start position:0%
+and see what convergence in probability
+is talking about here instead of a
+
+ align:start position:0%
+is talking about here instead of a
+ 
+
+ align:start position:0%
+is talking about here instead of a
+sequence of numbers we have a sequence
+
+ align:start position:0%
+sequence of numbers we have a sequence
+ 
+
+ align:start position:0%
+sequence of numbers we have a sequence
+of random variables and we're interested
+
+ align:start position:0%
+of random variables and we're interested
+ 
+
+ align:start position:0%
+of random variables and we're interested
+in the meaning of the convergence of the
+
+ align:start position:0%
+in the meaning of the convergence of the
+ 
+
+ align:start position:0%
+in the meaning of the convergence of the
+sequence of run
+
+ align:start position:0%
+sequence of run
+ 
+
+ align:start position:0%
+sequence of run
+variables to a particular number in
+
+ align:start position:0%
+variables to a particular number in
+ 
+
+ align:start position:0%
+variables to a particular number in
+words what this means is that if I fix a
+
+ align:start position:0%
+words what this means is that if I fix a
+ 
+
+ align:start position:0%
+words what this means is that if I fix a
+certain epsilon as in this picture then
+
+ align:start position:0%
+certain epsilon as in this picture then
+ 
+
+ align:start position:0%
+certain epsilon as in this picture then
+the probability that the random variable
+
+ align:start position:0%
+the probability that the random variable
+ 
+
+ align:start position:0%
+the probability that the random variable
+falls outside this band converges to
+
+ align:start position:0%
+falls outside this band converges to
+ 
+
+ align:start position:0%
+falls outside this band converges to
+zero so the picture would be as follows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have again or limit we fix some
+
+ align:start position:0%
+we have again or limit we fix some
+ 
+
+ align:start position:0%
+we have again or limit we fix some
+epsilon which could be an arbitrarily
+
+ align:start position:0%
+epsilon which could be an arbitrarily
+ 
+
+ align:start position:0%
+epsilon which could be an arbitrarily
+small number for any fixed choice of
+
+ align:start position:0%
+small number for any fixed choice of
+ 
+
+ align:start position:0%
+small number for any fixed choice of
+epsilon we take this band and for any
+
+ align:start position:0%
+epsilon we take this band and for any
+ 
+
+ align:start position:0%
+epsilon we take this band and for any
+given n we look into the probability
+
+ align:start position:0%
+given n we look into the probability
+ 
+
+ align:start position:0%
+given n we look into the probability
+that a random variable falls inside that
+
+ align:start position:0%
+that a random variable falls inside that
+ 
+
+ align:start position:0%
+that a random variable falls inside that
+band so if I am to draw the distribution
+
+ align:start position:0%
+band so if I am to draw the distribution
+ 
+
+ align:start position:0%
+band so if I am to draw the distribution
+of our random variable the distribution
+
+ align:start position:0%
+of our random variable the distribution
+ 
+
+ align:start position:0%
+of our random variable the distribution
+might be something like this so there is
+
+ align:start position:0%
+might be something like this so there is
+ 
+
+ align:start position:0%
+might be something like this so there is
+a certain probability that it falls
+
+ align:start position:0%
+a certain probability that it falls
+ 
+
+ align:start position:0%
+a certain probability that it falls
+outside this band but when n becomes
+
+ align:start position:0%
+outside this band but when n becomes
+ 
+
+ align:start position:0%
+outside this band but when n becomes
+large this probability of falling
+
+ align:start position:0%
+large this probability of falling
+ 
+
+ align:start position:0%
+large this probability of falling
+outside this band becomes very small so
+
+ align:start position:0%
+outside this band becomes very small so
+ 
+
+ align:start position:0%
+outside this band becomes very small so
+the probability of falling outside the
+
+ align:start position:0%
+the probability of falling outside the
+ 
+
+ align:start position:0%
+the probability of falling outside the
+band becomes tiny so the bulk of the
+
+ align:start position:0%
+band becomes tiny so the bulk of the
+ 
+
+ align:start position:0%
+band becomes tiny so the bulk of the
+distribution that is most of the
+
+ align:start position:0%
+distribution that is most of the
+ 
+
+ align:start position:0%
+distribution that is most of the
+probability is concentrated inside this
+
+ align:start position:0%
+probability is concentrated inside this
+ 
+
+ align:start position:0%
+probability is concentrated inside this
+band and this is true no matter how
+
+ align:start position:0%
+band and this is true no matter how
+ 
+
+ align:start position:0%
+band and this is true no matter how
+small epsilon is if I take a much
+
+ align:start position:0%
+small epsilon is if I take a much
+ 
+
+ align:start position:0%
+small epsilon is if I take a much
+narrower band around a I still want all
+
+ align:start position:0%
+narrower band around a I still want all
+ 
+
+ align:start position:0%
+narrower band around a I still want all
+the probability to be eventually
+
+ align:start position:0%
+the probability to be eventually
+ 
+
+ align:start position:0%
+the probability to be eventually
+concentrated inside that band of course
+
+ align:start position:0%
+concentrated inside that band of course
+ 
+
+ align:start position:0%
+concentrated inside that band of course
+it might take longer it might take a
+
+ align:start position:0%
+it might take longer it might take a
+ 
+
+ align:start position:0%
+it might take longer it might take a
+larger value of n but I want that when n
+
+ align:start position:0%
+larger value of n but I want that when n
+ 
+
+ align:start position:0%
+larger value of n but I want that when n
+is very large the bulk of the
+
+ align:start position:0%
+is very large the bulk of the
+ 
+
+ align:start position:0%
+is very large the bulk of the
+distribution is again concentrated
+
+ align:start position:0%
+distribution is again concentrated
+ 
+
+ align:start position:0%
+distribution is again concentrated
+inside this narrow band so inwards
+
+ align:start position:0%
+inside this narrow band so inwards
+ 
+
+ align:start position:0%
+inside this narrow band so inwards
+convergence in probability means that
+
+ align:start position:0%
+convergence in probability means that
+ 
+
+ align:start position:0%
+convergence in probability means that
+almost all of the probability mass of
+
+ align:start position:0%
+almost all of the probability mass of
+ 
+
+ align:start position:0%
+almost all of the probability mass of
+the random variable Y n when n is large
+
+ align:start position:0%
+the random variable Y n when n is large
+ 
+
+ align:start position:0%
+the random variable Y n when n is large
+that probability mass gets concentrated
+
+ align:start position:0%
+that probability mass gets concentrated
+ 
+
+ align:start position:0%
+that probability mass gets concentrated
+within a narrow band around the limit of
+
+ align:start position:0%
+within a narrow band around the limit of
+ 
+
+ align:start position:0%
+within a narrow band around the limit of
+the random variable
+
+ align:start position:0%
+the random variable
+ 
+
+ align:start position:0%
+the random variable
+we finally point out a few useful
+
+ align:start position:0%
+we finally point out a few useful
+ 
+
+ align:start position:0%
+we finally point out a few useful
+properties of convergence in probability
+
+ align:start position:0%
+properties of convergence in probability
+ 
+
+ align:start position:0%
+properties of convergence in probability
+that parallel well-known properties of
+
+ align:start position:0%
+that parallel well-known properties of
+ 
+
+ align:start position:0%
+that parallel well-known properties of
+convergence of sequences suppose that we
+
+ align:start position:0%
+convergence of sequences suppose that we
+ 
+
+ align:start position:0%
+convergence of sequences suppose that we
+have a sequence of random variables that
+
+ align:start position:0%
+have a sequence of random variables that
+ 
+
+ align:start position:0%
+have a sequence of random variables that
+converges in probability to a certain
+
+ align:start position:0%
+converges in probability to a certain
+ 
+
+ align:start position:0%
+converges in probability to a certain
+number a and another sequence that
+
+ align:start position:0%
+number a and another sequence that
+ 
+
+ align:start position:0%
+number a and another sequence that
+converges in probability to some other
+
+ align:start position:0%
+converges in probability to some other
+ 
+
+ align:start position:0%
+converges in probability to some other
+number B we do not make any assumptions
+
+ align:start position:0%
+number B we do not make any assumptions
+ 
+
+ align:start position:0%
+number B we do not make any assumptions
+about independence we do not assume that
+
+ align:start position:0%
+about independence we do not assume that
+ 
+
+ align:start position:0%
+about independence we do not assume that
+the accents are independent of each
+
+ align:start position:0%
+the accents are independent of each
+ 
+
+ align:start position:0%
+the accents are independent of each
+other we do not assume that the sequence
+
+ align:start position:0%
+other we do not assume that the sequence
+ 
+
+ align:start position:0%
+other we do not assume that the sequence
+of accents is independent of Y n we then
+
+ align:start position:0%
+of accents is independent of Y n we then
+ 
+
+ align:start position:0%
+of accents is independent of Y n we then
+have the following properties if G is a
+
+ align:start position:0%
+have the following properties if G is a
+ 
+
+ align:start position:0%
+have the following properties if G is a
+continuous function then the function of
+
+ align:start position:0%
+continuous function then the function of
+ 
+
+ align:start position:0%
+continuous function then the function of
+the random variables converges to the
+
+ align:start position:0%
+the random variables converges to the
+ 
+
+ align:start position:0%
+the random variables converges to the
+function of the number so for example
+
+ align:start position:0%
+function of the number so for example
+ 
+
+ align:start position:0%
+function of the number so for example
+the sequence of random variables xn
+
+ align:start position:0%
+the sequence of random variables xn
+ 
+
+ align:start position:0%
+the sequence of random variables xn
+squared is going to converge to a
+
+ align:start position:0%
+squared is going to converge to a
+ 
+
+ align:start position:0%
+squared is going to converge to a
+squared another fact is that the sum of
+
+ align:start position:0%
+squared another fact is that the sum of
+ 
+
+ align:start position:0%
+squared another fact is that the sum of
+these two random variables converges to
+
+ align:start position:0%
+these two random variables converges to
+ 
+
+ align:start position:0%
+these two random variables converges to
+the sum of their limits both of these
+
+ align:start position:0%
+the sum of their limits both of these
+ 
+
+ align:start position:0%
+the sum of their limits both of these
+properties are analogous to what happens
+
+ align:start position:0%
+properties are analogous to what happens
+ 
+
+ align:start position:0%
+properties are analogous to what happens
+with ordinary convergence of numbers and
+
+ align:start position:0%
+with ordinary convergence of numbers and
+ 
+
+ align:start position:0%
+with ordinary convergence of numbers and
+they tell us that in some sense
+
+ align:start position:0%
+they tell us that in some sense
+ 
+
+ align:start position:0%
+they tell us that in some sense
+convergence in probability is not a very
+
+ align:start position:0%
+convergence in probability is not a very
+ 
+
+ align:start position:0%
+convergence in probability is not a very
+different notion we will not prove those
+
+ align:start position:0%
+different notion we will not prove those
+ 
+
+ align:start position:0%
+different notion we will not prove those
+properties at this point but they're
+
+ align:start position:0%
+properties at this point but they're
+ 
+
+ align:start position:0%
+properties at this point but they're
+useful to know however there's an
+
+ align:start position:0%
+useful to know however there's an
+ 
+
+ align:start position:0%
+useful to know however there's an
+important caveat xn might converge to a
+
+ align:start position:0%
+important caveat xn might converge to a
+ 
+
+ align:start position:0%
+important caveat xn might converge to a
+certain number in probability
+
+ align:start position:0%
+certain number in probability
+ 
+
+ align:start position:0%
+certain number in probability
+however the expected value of xn does
+
+ align:start position:0%
+however the expected value of xn does
+ 
+
+ align:start position:0%
+however the expected value of xn does
+not necessarily converge to that same
+
+ align:start position:0%
+not necessarily converge to that same
+ 
+
+ align:start position:0%
+not necessarily converge to that same
+limit so convergence of random variables
+
+ align:start position:0%
+limit so convergence of random variables
+ 
+
+ align:start position:0%
+limit so convergence of random variables
+does not imply convergence of
+
+ align:start position:0%
+does not imply convergence of
+ 
+
+ align:start position:0%
+does not imply convergence of
+expectations and we will be seeing an
+
+ align:start position:0%
+expectations and we will be seeing an
+ 
+
+ align:start position:0%
+expectations and we will be seeing an
+example where this convergence does not
+
+ align:start position:0%
+example where this convergence does not
+ 
+
+ align:start position:0%
+example where this convergence does not
+take place
\ No newline at end of file
diff --git a/BGL8we3QUxI.txt b/BGL8we3QUxI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..36a9595b0f5f67d2c059d0322c0d1dabf3e98b5e
--- /dev/null
+++ b/BGL8we3QUxI.txt
@@ -0,0 +1,4425 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: So welcome back.
+
+Today, we're going to look
+at the modular synthesizer.
+
+And our area of focus
+right now is still
+
+looking at musical interfaces.
+
+A lot of people present
+the modular synthesizer
+
+in the context of basic
+synthesis techniques
+
+and the development of
+musical instruments.
+
+I think it's very
+useful for us to think
+
+of the modular synthesizer as
+a type of musical interface,
+
+and particularly the
+interface available
+
+through the creative patching
+and combination of modules.
+
+So what we're going
+to do is we're
+
+going to look at a little bit of
+the history of the development
+
+of modular synthesizers,
+starting with the giant RCA
+
+synth, and then
+moving on to the Moog.
+
+We're going to spend a little
+time with the basic Moog design
+
+and look at some of the
+basic synthesis techniques.
+
+We're going to do
+that by looking
+
+at the emulation of
+virtual Moog that we
+
+have available through
+Arturia's very nice virtual Moog
+
+instrument plug-in, which
+is going to give us a way
+
+to hear some of the sounds
+and see some of the approaches
+
+to patching this instrument.
+
+And then next time we meet in
+workshop mode next Tuesday,
+
+we're going to build some
+similar designs in PD
+
+using the Martingale
+Library and explore
+
+some of these
+approaches, as well.
+
+We're going to listen to some
+music and then if we get to it,
+
+talk about some
+semi-modular synths.
+
+And see the design go from
+fully modular synthesizers
+
+to semi-modular and
+non-modular synthesizers, which
+
+is a valuable trajectory to see.
+
+So coming up on the horizon, we
+have a brief quiz on Thursday.
+
+Keep that in mind.
+
+Your music technology
+case studies--
+
+the draft is due on Tuesday.
+
+If you have any questions about
+this as you approach this,
+
+feel free to drop me
+an email or the like.
+
+And that's it for now.
+
+Any questions?
+
+OK.
+
+So now with the
+modular synthesizer,
+
+we see numerous things
+start to come together.
+
+We saw in the early studios
+used by Varese, by Stockhausen,
+
+and others, this cobbling
+together of various components
+
+and interconnecting them
+into sound-producing devices.
+
+We see with the
+modular synthesizer
+
+these components
+start to solidify
+
+into a single common
+collection of entities.
+
+With these semi-modular
+designs, we
+
+see this solidification
+happen even more.
+
+And the designs solidify
+into a single common thing.
+
+There wasn't anything shockingly
+new about the technologies used
+
+in the modular synthesizer.
+
+Again, they were
+technologies that
+
+had been around
+for 10 or 20 years.
+
+But really, the
+interface, and the design,
+
+and the integration of these
+components, in my view,
+
+was the really important thing.
+
+Voltage control-- the ability
+to interconnect and control
+
+these devices with
+voltages-- was really
+
+the key technology that made
+this synthesizer more flexible,
+
+more powerful, and more
+creative for the operator.
+
+Now we start with the RCA
+synthesizer, which isn't really
+
+a modular synthesizer.
+
+To my knowledge, this device
+had a fairly fixed signal path.
+
+So it wasn't really modular.
+
+It had components.
+
+But you couldn't
+interconnect the components
+
+with patch cords.
+
+You couldn't radically
+change the type of sounds
+
+that it made.
+
+Now this synthesizer came
+in two different forms.
+
+There was the first one, which
+later became known as the Mark
+
+I and then the Mark II,
+the later version of this.
+
+This synthesizer was the result
+of quite a bit of research
+
+by Olson and Belar,
+who were working
+
+at RCA for a number of years.
+
+The Holmes text nicely
+describes their early research
+
+with music synthesis
+technologies.
+
+Does anybody recall
+what they were
+
+trying to do in the
+beginning-- Olson and Belar.
+
+Their first attempt
+at synthesis was
+
+directed towards this
+certain activity.
+
+Anybody recall?
+
+They were trying to synthesize
+Steven Walter pop tunes-- pop
+
+melodies-- basic melodies,
+using essentially Markov chains.
+
+And they were trying to
+create a machine that
+
+could compose simple melodies
+by analyzing basic tunes
+
+and then re-synthesizing them.
+
+In that process, they
+developed some technologies
+
+for creating
+oscillators and filters.
+
+And that led to their
+first RCA synthesizer.
+
+So this device used essentially
+tuning-fork-based oscillators.
+
+So their basic oscillator
+was a tuning fork
+
+that was set in motion and
+picked up electromagnetically.
+
+And that signal was then divided
+to shift into different octaves
+
+and transformed into a square
+wave to create a rich tone.
+
+And then they filtered
+that tone to create
+
+the variety of timbres that
+the instrument could make.
+
+The device featured
+a number of filters,
+
+as well-- high- and low-pass
+filters and this really kind
+
+of bizarre resonator
+chain, which
+
+is an interesting
+selective filter.
+
+This image here is from
+their first publication
+
+on the synthesizer from 1955.
+
+And it's also reproduced
+in the Holmes book.
+
+We can see the basic way
+that the synthesizer worked.
+
+Information was encoded on
+something kind of like a piano
+
+roll, but just storing
+control information
+
+in a binary representation.
+
+Here, rather than
+using a vacuum,
+
+brushes are used to pick up
+when an opening in the hole
+
+was to trigger a circuit.
+
+The frequency source
+here is those oscillators
+
+controlled by tuning forks.
+
+And that signal is then
+split by the octiver.
+
+And then it has the
+frequency glider,
+
+which allows the transition
+between pitches, the growth,
+
+and decay, which is a fancy
+name for an envelope generator.
+
+Or not fancy, I guess--
+historic-- various high-pass,
+
+low-pass filters,
+volume control,
+
+low-frequency
+modulator, probably
+
+for adding vibrato or other
+slow changes to the sound.
+
+Resonator change--
+that's that unique filter
+
+I was talking about--
+timbre control, probably
+
+additional filters.
+
+Or I'm not exactly sure what
+that last component did.
+
+But that's something to look at.
+
+And then finally, all going
+to a nice record cutter,
+
+which allowed you
+to record the sound.
+
+So there were two
+nearly identical voices
+
+that could be used and
+controlled by this paper roll.
+
+So partly out of Olson and
+Belar's earlier research
+
+in synthesizing pop tunes,
+they approached a synthesizer
+
+as a device that needed to be
+controlled, not by a keyboard,
+
+not by some other
+type of interface,
+
+but by a type of notation.
+
+And their notation was this
+punched-hole paper record,
+
+which again, is kind of like
+a piano roll but different.
+
+Because rather than a one-to-one
+relationship with parameters
+
+and their values,
+these are essentially
+
+three- and four-bit codes that
+determine frequency, octave,
+
+timbre, the envelope growth
+and decay, and volume.
+
+So frequency is determined by
+these four on-and-off switches,
+
+which give us 16
+possible values.
+
+But they only used 12.
+
+Octave could be selected.
+
+Similarly here, timbre, the
+envelope, volume, et cetera.
+
+This roll right there shows
+us the necessary information
+
+to encode these six pitches.
+
+So you can imagine working
+with this device would
+
+be a little tedious.
+
+But it offered explicit,
+complete control.
+
+This nice diagram, also
+from that original article,
+
+shows us a massive
+simplification of the device,
+
+going from reading the
+roll, to the two synthesizer
+
+channels, mixer, amplifier, and
+then a direct-to-disk cutting
+
+lathe.
+
+Some notable thing
+about this-- it
+
+was really the first
+attempt to parameterize
+
+musical information in a very
+rigorous and complete way.
+
+We saw with the player
+piano an earlier attempt
+
+at parameterization.
+
+But here, we're starting
+to parameterize timbre,
+
+amplitude envelopes, and
+volume and level controls
+
+at a greater degree than we
+had with the player piano.
+
+Also important about
+this instrument
+
+is it was not designed
+for performance.
+
+It was really designed
+as a machine where
+
+you composed in
+advance and played back
+
+what you had notated.
+
+That was the Mark
+I. The Mark II was
+
+housed at Princeton University.
+
+And that started a relationship
+with Columbia and Princeton
+
+University, which led to
+Columbia and Princeton
+
+getting a grant from the
+Rockefeller Foundation
+
+to buy the second version of
+this synth-- the RCA Mark II.
+
+This synth was very
+similar to the Mark I,
+
+except for it added a
+white-noise generator, which
+
+was useful for creating a
+variety of noisier percussive
+
+sounds.
+
+It had four voices
+instead of two.
+
+It had a microphone input.
+
+And it had some variable
+frequency oscillators.
+
+Similar to the RCA Mark I, it
+was a room-sized giant beast
+
+of a synthesizer.
+
+In this picture, we can
+see the disk cutters here.
+
+We can see, also, some tape.
+
+Eventually, they did
+add tape machines.
+
+And we can see the
+paper readers there.
+
+Notice that we don't see,
+really, a patch bay or patch
+
+cords.
+
+This was a modular synthesizer
+in that had modules.
+
+But it wasn't freely
+interconnectable in the way
+
+that we later find with our
+Moog and Buchla synthesizers.
+
+Now I sent you guys the link
+to this demo recording, which
+
+has this great narrator
+helping us along the way.
+
+This demo record
+was made in 1955.
+
+I believe it was a
+recording of the Mark II.
+
+The reason why is because
+in this demonstration,
+
+they use a filtered white noise.
+
+And I think this is a
+very nice example where
+
+they tried to synthesize the
+sound of a complete dance band.
+
+So they had four voices.
+
+So they used some of the
+voices for bass, percussion,
+
+and melody.
+
+Let's listen to
+a little of this.
+
+[HIGH-PITCHED SYNTHESIZER BEEPS]
+
+PROFESSOR: That's
+the high-hat sound.
+
+[LOW-PITCHED SYNTHESIZER BEEPS]
+
+PROFESSOR: And that's the bass.
+
+[SYNTHESIZER]
+
+PROFESSOR: And here's
+everything altogether.
+
+[VIDEO PLAYBACK]
+
+-We can also
+synthesize a part where
+
+each tone has a rapid growth
+and slow decay, like this.
+
+[END VIDEO PLAYBACK]
+
+PROFESSOR: Let's go
+back to that dance band.
+
+[LOW-PITCHED SYNTHESIZER BEEPS]
+
+PROFESSOR: Come on.
+
+[SYNTHESIZED MUSIC]
+
+PROFESSOR: There we go.
+
+Notice the white noise being
+used for the snare-like sound
+
+there.
+
+So as this demo record shows,
+and as the history of Olson
+
+and Belar's work
+shows, they were
+
+very interested in
+using the synthesizer
+
+to generate pop music,
+which is interesting.
+
+Because what it became used
+for was not popular music,
+
+but music of composers
+like Milton Babbitt, Mario
+
+Davidovsky, and other
+composers working
+
+at the Columbia-Princeton
+studios.
+
+One of our listenings for today
+was "Philomel," Babbitt's 1964
+
+composition that used
+the RCA synthesizer.
+
+Let's listen to a
+little bit of this
+
+to remind you guys
+what this sounds like.
+
+[MUSIC -- MILTON BABBITT,
+ "PHILOMEL"]
+
+PROFESSOR: So
+there's three sources
+
+of sound in this composition.
+
+What are they-- three
+sources of sound?
+
+AUDIENCE: There's the voice.
+
+PROFESSOR: Right,
+the live voice.
+
+AUDIENCE: There's
+the synthesizer.
+
+Not sure what the third was.
+
+PROFESSOR: Anybody
+notice or recall?
+
+There's also pre-recorded voice.
+
+So there's some tape-recorded
+and processed voice sounds
+
+in here, which are used to
+create some very nice distance
+
+echo and some
+depth to the voice.
+
+And actually in my view, one
+of the most interesting things
+
+about this piece is
+how the tape part
+
+blends with the synthesis
+and acts as an intermediary.
+
+Thoughts about this piece?
+
+AUDIENCE: It's very sporadic.
+
+PROFESSOR: Sporadic-- what
+do you mean, sporadic?
+
+AUDIENCE: Very jagged.
+
+I don't know.
+
+It's not really-- they
+follow a certain pattern.
+
+But there's not a ton of tune.
+
+PROFESSOR: Yeah, there's this
+jagged, jerky, gestural shape
+
+to a lot of the musical parts.
+
+And that's clear in the voice
+and also in the synthesizer
+
+parts.
+
+AUDIENCE: As the piece
+goes on, the voice
+
+smooths out a
+little bit, though,
+
+if I remember correctly.
+
+And then the synthesizer's still
+doing the jagged [INAUDIBLE].
+
+So it has the background
+interjections, I guess.
+
+It seems like longer stretches.
+
+AUDIENCE: Yeah.
+
+PROFESSOR: Yeah, let's
+jump to the end in here.
+
+[MUSIC -- MILTON BABBITT,
+ "PHILOMEL"]
+
+PROFESSOR: Now Babbitt was
+using a method of organization
+
+that we have talked
+about previously.
+
+What was that method
+of organization?
+
+AUDIENCE: Serialism.
+
+PROFESSOR: Serialism, or
+the 12-tone technique.
+
+Did the RCA synthesizer
+provide facilities
+
+for 12-tone composers?
+
+Was it well suited for that?
+
+I mean, Olson and Belar wanted
+to use it to do popular music.
+
+AUDIENCE: You had absolute
+control over everything, right?
+
+So it was perfect.
+
+PROFESSOR: Right.
+
+All your parameters
+were fixed on the roll.
+
+So you could compose very
+carefully crafted lines
+
+in a very organized way.
+
+And that's very much
+what we hear here.
+
+It's kind of, I think, ironic
+in that Olson and Belar imagined
+
+this instrument
+originally to create
+
+an endless variety
+of pop tunes to sell
+
+in the commercial market.
+
+And of course, it
+ended up being used
+
+to create some very esoteric,
+non-commercial music
+
+in the end.
+
+And that's one of
+our many examples
+
+of unintended consequences
+of certain technologies.
+
+Other comments or
+reflections on this piece?
+
+AUDIENCE: I thought
+it was really
+
+cool to use the
+operatic voice with it,
+
+as opposed to other
+singing styles.
+
+Because in conjunction
+with the synthesizer,
+
+the strange timbre
+of operatic singing
+
+became this thing that
+was more like a thing
+
+to listen to than typically
+what operatic singing is about.
+
+PROFESSOR: Yeah,
+that's interesting.
+
+For me, the really striking
+thing is the vibrato.
+
+Because the vibrato
+is really, really
+
+wide-- contrast between that
+wide vibrato and the more flat
+
+tones we're getting
+out of the synthesizer.
+
+Are you hearing
+something else, as well?
+
+AUDIENCE: No, that's
+the sort of thing.
+
+But then also in the
+tape-modulated parts.
+
+Because he speeds her
+up and slows her down.
+
+And so this thing happens
+with the vibrato right
+
+where they like.
+
+It was very tight, or
+even looser and lower.
+
+And there's this
+really, I think,
+
+great interplay between that
+and the synthesized sounds.
+
+PROFESSOR: Yeah, I agree.
+
+Yep.
+
+AUDIENCE: Yeah,
+the sound I heard
+
+reminded me a lot
+of science fiction.
+
+PROFESSOR: Uh-huh. [LAUGHS]
+
+AUDIENCE: There seems
+to be a common thread
+
+about that recording.
+
+PROFESSOR: Yeah.
+
+Well, a lot of the early
+sounds of early synthesizers
+
+were used in science fiction and
+film, since Forbidden Planet,
+
+and even before that
+with the theremin.
+
+The connection has been
+there for some time.
+
+We don't hear a lot of
+variety of timbres and colors
+
+with the synthesizer.
+
+A lot of it is sinusoidal
+or filtered waveforms.
+
+So there's not a huge variety
+of sounds out of the synth.
+
+But it didn't provide a
+tremendous amount of control,
+
+as we can tell by looking
+at the control information
+
+available on the tape.
+
+AUDIENCE: Do you know
+anything about how
+
+it was serialed, whether he
+used all of his parameters
+
+in the serial way?
+
+I was trying to parse it
+out, and I had no idea.
+
+PROFESSOR: Yeah.
+
+I mean, it's worth
+looking at further.
+
+I suspect, given
+Babbitt's inclinations,
+
+that both pitch and the other
+parameters were serialized.
+
+So it's very likely
+he had the opportunity
+
+to serialize envelopes
+and serialize
+
+the timbre controls
+of the synth.
+
+So I think it's very
+likely that he probably
+
+did, which is similar to an
+approach taken by Stockhausen,
+
+who was rigorously exploring
+some of these things.
+
+But with the RCA synthesizer,
+this became very notatable
+
+in a way that wasn't
+possible before.
+
+Do you have another comment?
+
+OK.
+
+So two innovators followed
+the RCA synthesizer
+
+with devices that were
+more flexible than the RCA
+
+synthesizer.
+
+They were more flexible in
+that they allowed the operator
+
+to reconnect the
+modules in various ways.
+
+Rather than that fixed sequence
+of oscillator, filter, et
+
+cetera, these devices
+allowed the operator
+
+to interconnect them in a
+variety of different ways
+
+and also allowed the
+operator to control them
+
+in a variety of different
+ways, not with punched paper
+
+but with various types
+of input devices.
+
+Buchla generally gets credit
+for coming a little bit
+
+before Moog.
+
+His devices were very diverse
+and often custom-designed
+
+for particular people,
+particular studios.
+
+His interest as a
+composer himself
+
+was in creating diverse
+and unique instruments,
+
+not really in creating
+a commercial market
+
+for the synthesizer.
+
+So he not only explored a wide
+variety of different modules
+
+that use noise and
+randomness in different ways,
+
+but also various
+types of input devices
+
+other than the keyboard.
+
+And our readings for today
+emphasize the point about how
+
+Buchla initially didn't want
+a keyboard control for his
+
+instrument, and
+Moog embraced that,
+
+which is an issue we'll talk
+about when we talk about
+
+the [? Pinchen-Trocho ?]
+reading.
+
+In 1965, he releases
+the Buchla Box
+
+without a keyboard-- a
+very popular instrument.
+
+1970, he has this 200
+series Electric Music Box,
+
+which you can see there.
+
+Also doesn't have a
+keyboard, but has a variety
+
+of sliders, knobs, and
+other interface components.
+
+In the '70s, he released
+some portable devices.
+
+This one, although apparently I
+think Holmes says that only 200
+
+of these were made-- wouldn't
+you like one of these?
+
+He did use a keyboard at times.
+
+But notice that this is a
+touch-sensitive keyboard
+
+and probably does some
+things we wouldn't expect.
+
+A small, portable
+modular synthesizer--
+
+if you can find one
+of these, get it.
+
+[LAUGHS]
+
+Buchla is still
+making synthesizers.
+
+They're very expensive.
+
+But they really offer
+some unique designs.
+
+Looking at his designs--
+you can go to his website--
+
+are really fascinating, creative
+approaches to the synthesizer.
+
+Buchla is a separate
+thread from that of Moog.
+
+Because Moog's instruments
+were dedicated to meeting the
+
+needs-- the demands--
+of musicians.
+
+Our readings make
+that very clear.
+
+He worked with musicians
+in a variety of ways.
+
+He invited musicians
+to come to his factory
+
+and explore his instruments.
+
+He adapted his instruments
+to the demands of musicians
+
+in order to meet their needs,
+and really, through that,
+
+made a very successful
+commercial instrument.
+
+Now we've already
+talked about how
+
+Moog got started with
+the theremin as a kid,
+
+creating theremin
+kits in his garage.
+
+In 1954, he published this
+article in Radio and Television
+
+News about his design for
+a tube-based theremin.
+
+This article's great.
+
+You can check it out online.
+
+It also has the whole schematic
+diagram for the circuit.
+
+At this time in
+the '40s and '50s,
+
+there was this whole
+kit-bit building culture,
+
+and a lot of interest
+in building theremin.
+
+So his design
+became very popular
+
+and attracted a
+lot of attention.
+
+He published another
+article in 1961
+
+using a transistor-based
+theremin that was actually
+
+featured on the cover
+of this magazine
+
+and also got him a
+lot of attention.
+
+He, by then, had a business.
+
+He and his dad were selling
+theremins out of their garage--
+
+theremin kits.
+
+By the '60s, he meets a
+composer by the name of Deutsch,
+
+who knew Moog because
+of the theremin--
+
+his theremin kits-- and
+wanted to know about, well,
+
+if he can do some other types
+of synthesizing devices--
+
+some other types of
+devices that allowed
+
+you to take basic oscillators,
+interconnect them, and put them
+
+under flexible control.
+
+Moog develops his first
+synthesizer, the 900 Series,
+
+in 1965.
+
+This device wasn't
+distributed broadly.
+
+It was used mostly by
+composers and some studios.
+
+In 1966, he patents
+his low-pass filter,
+
+which becomes a very important
+part of his synthesizer.
+
+Because it allowed to take
+a rich, wide bandwidth
+
+sound and control its timbre
+and give it a very crisp tone.
+
+We'll hear some of that
+sound very shortly.
+
+People say that this was the
+only thing that Moog patented.
+
+But there are some other patents
+associated with the Moog name.
+
+It was definitely the first
+device that he patented.
+
+And the low-pass filter
+was novel in that it
+
+had a particularly
+steep roll-off curve.
+
+So it was able to really focus
+the sound underneath the cutoff
+
+frequency.
+
+And it had an
+adjustable resonance,
+
+which provided a nice peak
+at that cutoff frequency.
+
+Now it's in 1967
+that he releases
+
+his first real commercial
+product, the series Systems 1,
+
+2, and 3.
+
+This is an earlier device.
+
+We can see with this
+one, the keyboard.
+
+We can see some of
+the basic modules.
+
+And we can see, also, a ribbon
+controller, another type
+
+of input device
+that he explored.
+
+This got later
+refined into devices
+
+of this sort, which
+is very often what
+
+we see when we imagine
+the Moog synthesizer.
+
+Here we have a number of
+oscillators, filters, up here.
+
+And this over here
+is a sequencer,
+
+which we're actually going
+to talk about sequencing
+
+next time we meet-- also,
+the keyboard and the ribbon
+
+controller, as well.
+
+So with the Systems
+1, 2, and 3 in 1967,
+
+there was some standard
+packages you could buy.
+
+But you could still
+buy individual modules
+
+for your own synthesizer.
+
+And this nice
+price list shows us
+
+some of the prices
+of these devices.
+
+We could get a
+voltage-controlled amplifier
+
+for $150-- fair price.
+
+That voltage-controlled
+low-pass, high-pass filter,
+
+$475 for one filter in 1968.
+
+That's pretty expensive.
+
+These synthesizers were
+extremely expensive.
+
+But they started to be
+sold and commercialized.
+
+And people started to buy them.
+
+But one thing in particular led
+to the explosion of the Moog
+
+industry, and that was Wendy
+Carlos's Switched-on Bach
+
+recording, recorded in
+1968, released in '69,
+
+and garnered a huge
+amount of attention
+
+to the Moog synthesizer.
+
+We'll talk about Wendy
+Carlos and her recording
+
+in a little bit.
+
+But let's review
+some of the concepts
+
+of the modular synthesizer.
+
+So we have two basic components.
+
+We have things that
+generate sound,
+
+like our oscillators
+and other devices.
+
+And we have components
+that modify those sounds.
+
+So we have these
+two different types
+
+of modules that can be
+interconnected and modified.
+
+The input four module
+is either the knobs
+
+on the front panel
+or another voltage.
+
+And some devices
+allow you to switch
+
+between using the knob
+or a voltage as an input,
+
+or using both-- using the
+knob to set a basic level
+
+and then the input voltage
+to adjust it further.
+
+The output of these
+modules is another voltage,
+
+which can be interconnected to
+modules further down the line.
+
+Within the modular synthesizer,
+we have two types of signals.
+
+We have control signals
+and audio signals.
+
+Both of these,
+depending on the design,
+
+can be interconnected
+in various ways.
+
+Audio signals are
+the things that we're
+
+used to-- sounds represented
+as a bipolar voltage.
+
+Voltage ranges would generally
+between negative 3 and 3 volts.
+
+Sometimes higher or wider
+ranges were possible.
+
+Control signals were also
+voltages but generally unipolar
+
+voltages between maybe
+0 and plus 5 volts.
+
+These were often
+more slowly moving
+
+signals that could
+be used to control
+
+the parameters of
+another module.
+
+Control signals were used,
+obviously, to shape envelopes.
+
+And these envelopes
+could be applied
+
+to parameters other than
+the amplitude of the sound,
+
+such as a cutoff
+frequency or the like.
+
+Now a key concept of
+the modular synthesizer
+
+was the ability to
+reuse the modules.
+
+We could use an oscillator
+to produce a tone
+
+and hear that tone
+of the oscillator.
+
+We could also use an
+oscillator to shape
+
+the amplitude of a sound
+and produce a tremolo,
+
+or to modulate the frequency
+of another oscillator
+
+and produce a vibrato, or use
+the output of an oscillator
+
+to modulate the cutoff
+frequency to create
+
+a variable timbre to a sound.
+
+I'm going to demonstrate
+all of those in a second.
+
+This ability to reuse these
+modules-- to mix audio signals
+
+and control signals and
+transform one to the other--
+
+was really the key feature
+of the modular synthesizer,
+
+combined with voltage
+control, and gave it
+
+a great degree of flexibility.
+
+Now in this golden age of
+the modular synthesizer,
+
+when you sat down
+to this instrument,
+
+you got nothing for free.
+
+You sat down.
+
+It didn't make any sound.
+
+In order to make a sound, you
+had to design an instrument.
+
+So the interface, in order to
+make a sound, became patching.
+
+You had to patch
+to make a sound.
+
+No sounds were given to you.
+
+And this promoted a huge degree
+of freedom and creativity
+
+in the design of sounds.
+
+We see, over the
+history of synthesizers,
+
+this start to decrease.
+
+And so in the late '60s is
+when we have the most freedom.
+
+And as the '70s move
+on, we see synthesizers
+
+that reduce the
+ability of patching
+
+and make it easier to get
+a sound more automatically.
+
+And then by the early
+'80s, we have synthesizers
+
+that are programmable but
+have very little in terms
+
+of a customizable interface.
+
+Some of the basic components
+of the synthesizer-- these
+
+are screenshots
+of virtual synths,
+
+which is kind of amusing.
+
+But they allow us
+to see more clearly
+
+some of the designs
+of these synthesizers.
+
+So our basic oscillators, or
+voltage-control oscillators,
+
+generally provided a
+control for frequency.
+
+Often, the range of
+the frequency knob
+
+would be variable in steps.
+
+So we have a dedicated
+low-frequency switch
+
+for low-frequency oscillators.
+
+And then we have
+various higher ranges,
+
+which use the terminology
+derived from organs--
+
+32 foot, 16 foot, 8
+foot, and the like.
+
+We had the ability to
+get different waveforms
+
+from the same
+oscillator, which is
+
+a nice convenience
+of such devices.
+
+We have various noise sources,
+and we'll hear example of those
+
+as well.
+
+And we have a sample on
+hold generators, which
+
+allow us to take an input signal
+and sample it periodically
+
+to create a stepped shape.
+
+I'll demonstrate that in
+a little bit, as well.
+
+Now our modular
+synthesizers usually
+
+had some sort of mixing
+control-- some ability
+
+to combine signals.
+
+And this sometimes was under
+control of another voltage.
+
+So we have voltage-control
+amplifiers, or VCAs.
+
+Sometimes we have
+mixers that use
+
+various toggles or
+on-off switches.
+
+This is from the design
+of the Minimoog, where
+
+the various oscillators had
+a level control and then
+
+a toggle switch.
+
+And some devices
+had various types
+
+of matrix-mixing and
+patching controls,
+
+which are very, very cool.
+
+This EMS synthesizer--
+the Synthi,
+
+Synth-I-- allowed you to control
+the routing of signals, rather
+
+than through patch
+cords through a matrix.
+
+This was a template
+used to help you
+
+remember your patch
+with this synth.
+
+These synths are very cool.
+
+If you can find one, grab it.
+
+Notice the convenient handle.
+
+You can take it with you.
+
+All of our synthesizers have
+various types of filters.
+
+A VCF, or
+voltage-control filter,
+
+allows you to adjust
+the parameters
+
+with a voltage, the low-pass
+filter and high-pass filter
+
+being the most common,
+a band-pass filter
+
+and other varieties also found.
+
+In our modular synthesizer,
+we have various types
+
+of envelope generators.
+
+The envelope is
+a unipolar signal
+
+that we can apply to the
+amplitude of a sound.
+
+But we can also
+apply the envelope
+
+to other musical parameters.
+
+The key thing about an
+envelope is its control signal
+
+that's designed to be triggered.
+
+It's a control signal
+that's designed
+
+to start at a certain
+time and end, as opposed
+
+to something like a
+low-frequency oscillator that
+
+is continuous and ongoing.
+
+The ADSR is probably
+the most common type
+
+of envelope control on these
+early modular synthesizers,
+
+although there were
+other varieties, as well.
+
+There was AR filters and
+attack-decay-sustain filters--
+
+various simplifications
+of the ADSR model.
+
+The key approach to using
+the modular synthesizer
+
+at this time is often called
+subtractive synthesis.
+
+The idea of
+subtractive synthesis
+
+is we start with a
+rich, complex tone,
+
+and we use our filters to
+take away from that tone
+
+and get the sound
+that we're looking at.
+
+This is part of the reason
+why Moog's low-pass filter was
+
+so important.
+
+Because we could start with
+a complex tone and then
+
+use the low-pass filter to
+shape out the frequencies
+
+that we did not want.
+
+So our basic approach of
+working in subtractive synthesis
+
+would be to start with
+a rich complex tone,
+
+to cut out some of
+those frequencies,
+
+apply amplitude
+envelopes to vary
+
+the amplitude shape
+of that sound,
+
+and then use modulation
+to vary the parameters.
+
+And this starts to
+become really interesting
+
+when we modulate the modulators.
+
+And we'll listen to what
+that sounds like in a second.
+
+Questions, comments, ideas?
+
+OK.
+
+So let's hear what
+this sounds like.
+
+Now probably the most
+basic approach on one
+
+of the most common approaches
+to creating a complex sound
+
+would be combining
+multiple oscillators.
+
+And this design is embodied
+in some of the early Moog
+
+synthesizers, where we
+have three oscillators--
+
+like these three oscillators
+right here-- all under one
+
+driver to control the
+three oscillators.
+
+The idea embodied
+in the interface
+
+here is that we're
+going to create
+
+a rich tone by
+combining oscillators.
+
+We can tune each of
+these oscillators
+
+to different octaves and
+slight tuning differences.
+
+But they're all going to
+be under a single control.
+
+Let's listen to what
+this sounds like.
+
+So our first example-- if we
+start off with just a single
+
+oscillator--
+
+[LOW-PITCH SYNTHESIZER TONES]
+
+So here, we're hearing
+a sawtooth waveform.
+
+And I'm taking it
+from this oscillator
+
+here and just dropping it
+over into my big ADSR envelope
+
+there.
+
+If we want to hear a sign
+tone, we can just replace that.
+
+[SYNTHESIZER]
+
+That's it.
+
+A strong sign tone.
+
+And we have our
+triangle waveform here.
+
+[SYNTHESIZER BEATS]
+
+Our triangle waveform
+sounds dead at that range.
+
+[SYNTHESIZER BEATS AND TONE]
+
+That's unexpected.
+
+Let's go back to this.
+
+I wonder if I--
+
+[SYNTHESIZER]
+
+There's our saw.
+
+And then we have our
+square wave, which also--
+
+[FAINT SYNTHESIZER TONES]
+
+--is not performing
+well, strangely.
+
+OK.
+
+So that's our basic oscillators.
+
+Now we can combine these
+to create a rich tone.
+
+So here, what I've
+done is combine
+
+the sound of three oscillators.
+
+And let me tune them
+all the same first.
+
+[SYNTHESIZER]
+
+So we're actually hearing
+three oscillators.
+
+And if you think about what you
+think of a Moog sounding like,
+
+this thick sound is very
+much what we think about.
+
+We're hearing sawtooth
+and square waves here
+
+at different octaves.
+
+Let me vary the octaves
+of this a little bit.
+
+[SYNTHESIZER]
+
+Hear that square wave at
+the higher octave there?
+
+[SYNTHESIZER]
+
+Or if I move up one of
+the sawtooth waves--
+
+[SYNTHESIZER]
+
+Or if I set them all
+to low registers.
+
+[LOW-PITCHED SYNTHESIZER TONES]
+
+Now we can tune each of
+these oscillators separately.
+
+And a very common
+practice would be
+
+to make the oscillators
+slightly out of tune
+
+to create an even thicker sound.
+
+So if I tune each
+of these oscillators
+
+out a little bit
+from the center--
+
+[SYNTHESIZER]
+
+Let me go even further.
+
+[DISCORDANT SYNTHESIZER TONES]
+
+Now right there, it sounds
+like out-of-tune oscillators.
+
+But if I bring this
+closer together--
+
+[WAVERING SYNTHESIZER TONES]
+
+--we get a thick sound, rather
+than an out-of-tune sound.
+
+Let me shift this one
+up an octave or two.
+
+[SYNTHESIZER]
+
+And let me set this to be a
+little bit more out of tune.
+
+[WAVERING SYNTHESIZER TONES]
+
+You don't hear it as
+out-of-tune oscillators.
+
+You hear it as a
+single complex tone.
+
+Now we can see already that most
+of these early modular designs
+
+were designed to be monophonic,
+so produce one sound at a time.
+
+Early on, it was
+figured out that it'd
+
+be pretty nice to
+be able to control
+
+the transition between
+these monophonic voices.
+
+And so we have the use
+of a portamento control.
+
+This was available in the
+RCA synthesizer, as well.
+
+And this would
+often set the amount
+
+of glide between
+adjacent pitches.
+
+So--
+
+[SYNTHESIZER]
+
+Right here, we're hearing
+one note at a time.
+
+If I set the glide--
+
+[GLIDING SYNTHESIZER TONES]
+
+That's a little long there.
+
+Let me make it a little shorter.
+
+[CHOPPY SYNTHESIZER TONES]
+
+A little longer--
+
+[GLIDING SYNTHESIZER TONES]
+
+--which was used very
+prominently by musicians--
+
+[SYNTHESIZER]
+
+--to create transitions
+between notes,
+
+and is really one of
+the most common sounds
+
+from these early
+monophonic synthesizers.
+
+Questions?
+
+AUDIENCE: [INAUDIBLE]
+the glide of it?
+
+Because it seems like
+a weird parameter
+
+to become such a
+central thing, or even
+
+to decide that you need it right
+there next to the keyboard.
+
+It's the thing that you need.
+
+So was there a reason?
+
+Obviously there was
+a reason for that.
+
+But was it prominent in music
+in a way that [INAUDIBLE]?
+
+PROFESSOR: Well, I mean, if
+a normal musician can control
+
+this-- for instance, on a guitar
+or other string instrument,
+
+even a lot of wind
+instruments, as well.
+
+And I think the idea was
+some musical passages
+
+you would want to be staccato,
+and short, and broken.
+
+And other cases,
+depending on the context,
+
+you would want to have
+that glide control.
+
+If you want to make it
+sound like a theremin,
+
+you can set it all
+the way up, and then
+
+get continuous pitch variations.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, exactly.
+
+AUDIENCE: [LAUGHTER]
+
+PROFESSOR: OK.
+
+So our first step in
+subtractive synthesis
+
+is creating a complex tone.
+
+And we've done that by combining
+and de-tuning oscillators.
+
+We can use a variety of
+different wave shapes
+
+with those oscillators.
+
+And we can de-tune them.
+
+And we can add three or-- I
+don't know, should we go crazy?
+
+[SYNTHESIZER]
+
+If we want to add some
+more, let's-- I don't know.
+
+What does six sound like?
+
+Let's see.
+
+Let's throw in a sign tone.
+
+[SYNTHESIZER]
+
+That's kind of nice.
+
+And let's throw in
+another sawtooth.
+
+[SYNTHESIZER]
+
+[LAUGHS] OK.
+
+You get the idea.
+
+So we've produced
+our complex tone.
+
+The next basic step of
+subtractive synthesis
+
+is to apply a filter.
+
+And this is where Moog's
+patented low-pass filter comes
+
+into play and why his steep
+roll-off curve was so valuable.
+
+We take our complex
+tone generated
+
+by three or more oscillators.
+
+And we filter it.
+
+And let's start off
+with just the filtered--
+
+[SYNTHESIZER]
+
+OK.
+
+[SYNTHESIZER]
+
+We're a little bit ahead
+of where we want to be.
+
+Let's start first
+with our complex tone.
+
+[SYNTHESIZER]
+
+There's our complex tone.
+
+And our filter provides
+cutoff frequency
+
+to shape the timbre of that
+sound and a resonance control
+
+to set the amount of amplitude
+on the peak of the cutoff
+
+frequency.
+
+[HIGH-PITCHED SYNTHESIZER TONES]
+
+One of the design features
+of Moog's low-pass filter
+
+was that it could self-resonate.
+
+So if the resonance
+was set loud enough--
+
+[SYNTHESIZER]
+
+--we could actually produce
+a very clear sinusoidal sound
+
+at the cutoff frequency.
+
+[SYNTHESIZER]
+
+Yeah, you get the idea.
+
+[SYNTHESIZER]
+
+So there's our low-pass
+filter-- taking our thick tone,
+
+put it through a
+low-pass filter.
+
+One of the most common
+things we want to do
+
+and one of the easy advantages
+of using a modular synthesizer
+
+is we can take a sign tone,
+or some other wave shape,
+
+and use it to modulate
+the cutoff frequency.
+
+[STATICKY SYNTHESIZER TONES]
+
+There it's a little fast.
+
+Let me slow it down.
+
+[PULSING SYNTHESIZER TONES]
+
+So now we're modulating
+the cutoff frequency
+
+by a sign tone, whose
+frequency I can control--
+
+[SLOW WARPED SYNTHESIZER TONES]
+
+--and whose depth
+I can control here.
+
+We would have to scale it.
+
+This is much harder to
+do with a real synth.
+
+But this makes it nice and easy.
+
+[SYNTHESIZER]
+
+So a very common sound,
+using a low-frequency
+
+oscillator to control
+the cutoff frequency.
+
+Yeah.
+
+AUDIENCE: Is there a
+noticeable difference
+
+if we modulate the cutoff
+of the square or a sawtooth?
+
+PROFESSOR: Yeah, let's hear it.
+
+[SYNTHESIZER]
+
+So yeah, you can
+definitely notice it.
+
+Because here, we're hearing
+the smooth transition.
+
+So let's try a square wave.
+
+[SYNTHESIZER]
+
+Right, so we hear
+the step pattern.
+
+If we speed this up, this
+is actually pretty cool.
+
+[SYNTHESIZER TONES WITH BEEPS]
+
+We get a nice switching.
+
+And then if we do the-- let's
+try a triangle waveform.
+
+It's not as smooth as a sign.
+
+We'll get a--
+
+[SYNTHESIZER]
+
+[WARPED SYNTHESIZER TONES]
+
+There we go.
+
+So we get a different sound.
+
+Yeah?
+
+AUDIENCE: Oh, I just
+wanted to clarify
+
+that all the audio outputs are
+also used as control outputs,
+
+right?
+
+There's no separation between--
+
+PROFESSOR: Different synths
+had different designs
+
+in terms of that.
+
+AUDIENCE: With the Moog, though.
+
+PROFESSOR: With
+the Moog, well, I
+
+believe except for the
+voltage ranges, sometimes
+
+you would need to
+scale an audio input.
+
+Some devices, you would need
+to transform your voltage
+
+before you could use it.
+
+But you could take
+an audio oscillator
+
+and use it as a control
+voltage if it could perform
+
+at a slow enough rate as a
+low-frequency oscillator.
+
+Some designs, you would need
+a dedicated low-frequency
+
+oscillator.
+
+Because it couldn't perform
+slowly in a reliable way.
+
+That would be an issue
+why sometimes there
+
+would be a dedicated
+low-frequency oscillator.
+
+But with computers, doing
+low-frequency oscillation
+
+is easy.
+
+So it's more interoperable.
+
+AUDIENCE: Is there
+some responsiveness
+
+issue with that, where it seems
+like you [? couldn't ?] do
+
+really cool things if you
+took audio signal that
+
+was not synthesized but
+recorded, and amplified,
+
+and made to control things,
+like a [INAUDIBLE], kind of.
+
+PROFESSOR: Absolutely.
+
+AUDIENCE: Is there a
+responsiveness issue?
+
+Because what you were saying
+before about control-voltage
+
+versus audio signals is
+that the control tends
+
+to be at a slow--
+like obviously,
+
+audio is at a higher rate,
+not [INAUDIBLE] not digital.
+
+PROFESSOR: Right.
+
+AUDIENCE: With
+that kind of thing,
+
+is that a problem if you want
+to modulate, say, the filter
+
+with your voice?
+
+PROFESSOR: Exactly.
+
+Yeah, I mentioned in passing
+that the RCA synthesizer had
+
+a microphone input.
+
+And Moog's synthesizers
+had-- this one
+
+doesn't show us a
+good example of that--
+
+but had microphone inputs.
+
+We could take an analog
+signal, use a low-pass filter
+
+to smooth out the edges,
+and use that to drive
+
+some other parameters.
+
+So it was possible
+to take other inputs,
+
+use them to control
+your musical parameters.
+
+That general
+technique is something
+
+we call envelope following.
+
+And sometimes there would be
+dedicated envelope followers
+
+in these early synths to
+make that even easier.
+
+AUDIENCE: So like optimize
+it for that, kind of?
+
+PROFESSOR: Yeah.
+
+OK.
+
+So what we just did was
+have our dense combination
+
+of oscillators.
+
+And we use an LFO to shape
+the sound in a periodic way.
+
+A very common--
+probably the most common
+
+approach to
+subtractive synthesis--
+
+so common that it was embodied
+in the design of the Minimoog
+
+a few years later from the
+time of this synthesizer--
+
+was using an envelope to
+control the cutoff frequency.
+
+Why would you use an envelope
+to control the cutoff frequency?
+
+So with the LFO, we get
+that continuous change
+
+in the timbre, no matter
+when we trigger the note.
+
+Why would we want to use an
+envelope, which we generally
+
+use to control the
+amplitude, to control
+
+the cutoff frequency
+of a filter?
+
+Any ideas?
+
+AUDIENCE: More like a
+real instrument then,
+
+if it's linked to when you
+play, as opposed to continuous.
+
+PROFESSOR: That's right.
+
+Many real instruments
+have different timbres
+
+over the course
+of their envelope.
+
+Many instruments are often
+brighter at the initial onset--
+
+the articulation-- and then
+darken as the tone sustains.
+
+So a very common approach is to
+use a-- pull it up-- envelope.
+
+And here, I'm using
+an ADSR set to trigger
+
+when I press a note
+to control the cutoff
+
+frequency of the filter.
+
+And I'll start off with the
+modulation of this being small.
+
+[SYNTHESIZER]
+
+Here on the onset-- the initial
+little bump in the frequency--
+
+let me make this broader.
+
+[SYNTHESIZER]
+
+And even broader.
+
+And I'll start off with
+the lower start point.
+
+[SYNTHESIZER TONE BURSTS]
+
+So that's an extreme setting.
+
+We're using the ADSR to
+control the cutoff frequency.
+
+[SYNTHESIZER]
+
+And I can adjust the attack.
+
+So if the attack is quick,
+we'll get a bright sound
+
+at the very beginning
+and then it'll get dark.
+
+[SYNTHESIZER]
+
+Ever hear a synthesizer sound
+like that before, maybe?
+
+Probably the most
+common approach--
+
+subtractive synthesis.
+
+Use an envelope to
+control the cutoff
+
+frequency of a rich tone.
+
+If I set the attack
+to be longer--
+
+[SYNTHESIZER]
+
+--even longer still--
+
+[LONG SYNTHESIZER TONE]
+
+--we get a very slow increase
+in the cutoff frequency.
+
+And then that was so long, it
+didn't even come back down.
+
+There we go.
+
+[SYNTHESIZER]
+
+Good.
+
+Questions?
+
+So again, that
+approach was so common,
+
+it was embodied in nearly
+almost every synthesizer that
+
+came after the Moog,
+this idea of applying
+
+a filter to the
+cutoff frequencies.
+
+Some designs, like the Minimoog,
+even had a dedicated envelope
+
+just to control the
+cutoff frequency.
+
+So what else could we do
+with the modular synthesizer?
+
+Well, we could do amplitude
+modulation and ring modulation,
+
+where we modulate the
+amplitude of the sound,
+
+either with a sinusoidal
+shape or some other shape.
+
+And we can use this to
+create tremolo effects when
+
+we use a low-frequency
+oscillator
+
+or amplitude-modulation
+or ring-modulation effects
+
+as we speed up the modulation.
+
+So in the first
+example here, we're
+
+taking the output of our
+three oscillators here,
+
+and we're putting them
+into what is essentially
+
+a voltage-controlled amplifier.
+
+And we're modulating the
+voltage of the amplifier
+
+by another oscillator.
+
+So--
+
+[SHORT SYNTHESIZER TONE]
+
+That was intentional.
+
+[SYNTHESIZER TONES]
+
+So this is an
+oscillator controlling
+
+the amplitude of our rich tone.
+
+As we speed this up--
+
+[SYNTHESIZER PULSE TONES]
+
+--we get a sort
+of tremolo sound.
+
+And as we take this oscillator
+into the audio range--
+
+this is a great example
+of being able to use
+
+our modules for both audio and
+control-rate signals-- we start
+
+to get some amplitude-modulated
+
+[SYNTHESIZER]
+
+--sounds.
+
+And if I increase
+the modulation--
+
+[DISTORTED SYNTHESIZER TONES]
+
+--and again, low frequency.
+
+[RAPID PULSING SYNTHESIZER
+ TONES]
+
+And as before, we can
+change the wave shape
+
+of the amplitude modulation
+between our other wave shapes.
+
+So here, I'm using a sinusoid.
+
+We could use squares,
+or triangles,
+
+or other shapes, as well.
+
+Now of course, the next thing to
+do is modulate the modulators.
+
+So if I vary the modulation
+of the modulator--
+
+[LAUGHS] so here, I'm using
+one oscillator to control
+
+the frequency of another
+oscillator that's being used
+
+to control the amplitude
+of our rich tone,
+
+controlled by
+three oscillators--
+
+[PULSING SYNTHESIZER TONES]
+
+--we get a gradual
+shift from tremolo
+
+to amplitude modulation
+as I speed this up.
+
+[SYNTHESIZER]
+
+Let's see.
+
+And let's try
+something even faster
+
+and see what that sounds like.
+
+[PULSING SYNTHESIZER TONES]
+
+Yeah, we're not hearing
+the transition there.
+
+[SYNTHESIZER]
+
+And let's try one
+more thing and see.
+
+[SYNTHESIZER]
+
+So there, we're doing
+variable-rate amplitude
+
+modulation, where the
+variance and the rate--
+
+[SYNTHESIZER]
+
+--is determined by
+this other oscillator.
+
+Let's try one more at
+this super high speed.
+
+[RAPID SYNTHESIZER PULSE TONES]
+
+All right.
+
+You get the idea.
+
+Questions?
+
+So that's amplitude modulation.
+
+Ring modulation--
+closely related
+
+to amplitude modulation.
+
+Sometimes there would
+be dedicated devices
+
+for doing ring modulation.
+
+On the Moog, there was a
+dedicated ring modulator
+
+that used a special circuit
+that was quite popular later.
+
+Let's just hear a
+little bit about how
+
+that ring motivation
+sounds like.
+
+[WARPED SYNTHESIZER TONES]
+
+Now here, I'm using an
+envelope to modulate
+
+the frequency of ring
+modulation so that we
+
+get a dynamic contour over
+the length of the event--
+
+[WARPED SYNTHESIZER TONES]
+
+--which is kind of fun.
+
+Good.
+
+So that's amplitude modulation.
+
+We can use our oscillators
+to control frequency
+
+and the-- oh yeah, sure.
+
+AUDIENCE: When you use an
+envelope to control the cutoff
+
+frequency of your
+low-pass filter,
+
+is that still the same
+envelope of the output?
+
+PROFESSOR: I'm using a
+different envelope generator.
+
+So it's like I'm using a
+different envelope generator.
+
+I'm triggering them
+at the same time.
+
+But I'm using a different
+ADSR to control that cutoff
+
+frequency.
+
+AUDIENCE: OK.
+
+PROFESSOR: So I'm using
+one ADSR to control
+
+the output envelope
+and another ADSR
+
+to control the cutoff frequency.
+
+AUDIENCE: OK.
+
+PROFESSOR: Yeah?
+
+AUDIENCE: Do key
+presses on the keyboard
+
+trigger all of the whole thing?
+
+PROFESSOR: It depends on the
+design of the synthesizer
+
+and what's going on.
+
+For this emulation,
+there's an easy way for us
+
+to set the trigger
+for envelopes.
+
+And you see this
+little red light right
+
+there allows me to
+set-- that envelope
+
+is triggered when
+a key press is set.
+
+There's other ways to
+trigger envelopes, as well.
+
+So vibrato-- our very
+basic approach to vibrato
+
+is done by simply using
+one of our oscillators.
+
+This, of course, is why we
+need so many oscillators.
+
+Because we can use them
+for so many things.
+
+We're using one
+of our oscillators
+
+to modulate the frequency
+of our complex tone.
+
+[WARPED SYNTHESIZER TONES]
+
+OK.
+
+Well maybe that doesn't sound
+much like a normal vibrato.
+
+[WARPED SYNTHESIZER TONES]
+
+So if we reduce the
+degree of modulation--
+
+[SLOWING WARPED SYNTHESIZER
+ TONES]
+
+Let's make it a little slower.
+
+[SLOWING SYNTHESIZER TONES]
+
+OK.
+
+Well, why don't we just
+make it really wide?
+
+[SYNTHESIZER TONES]
+
+So we can go from something
+like a normal vibrato
+
+to very wide frequency sweeps.
+
+We still don't
+have something that
+
+sounds like a more
+human vibrato.
+
+Does anybody know why
+we don't have something
+
+that sounds like
+a human vibrato?
+
+Anybody want to speculate?
+
+It's constant, right?
+
+The vibrato is constant
+the whole time.
+
+And often, musicians maybe
+start off with a straight tone,
+
+and then lean into the vibrato,
+and then stop the vibrato.
+
+AUDIENCE: And in that
+case, you could just
+
+modulate that modulator to
+create that human [INAUDIBLE].
+
+PROFESSOR: That's right.
+
+So we can--
+
+AUDIENCE: Envelope on the--
+
+AUDIENCE: Right.
+
+AUDIENCE: Yeah.
+
+PROFESSOR: That's right.
+
+We use an envelope to
+scale the amplitude
+
+of the low-frequency
+oscillator that's
+
+driving the
+frequency modulation.
+
+Again, what we do is we
+take an ADSR envelope that's
+
+being triggered when
+the note starts.
+
+And we're putting
+that into one of
+
+our voltage-controlled
+amplifiers.
+
+We're taking the output
+of one of our oscillators,
+
+and scaling the
+output by that ADSR,
+
+and taking the output of
+that now modified control
+
+signal to modulate the frequency
+of our rich tone produced
+
+by three oscillators,
+which gives us--
+
+[SYNTHESIZER]
+
+--a vibrato that nicely
+fades in and then fades out.
+
+What determines
+the fade-in time?
+
+Well, it's the attack
+of this envelope.
+
+So if we want it to
+come in right away--
+
+[SYNTHESIZER]
+
+--if we want it to
+take a long time--
+
+[SYNTHESIZER]
+
+--the depth is set by our
+voltage-control amplifier.
+
+[SYNTHESIZER KNOCKING TONES]
+
+[LAUGHTER]
+
+PROFESSOR: OK, maybe I went
+a little too far there.
+
+[WARPED SYNTHESIZER TONES]
+
+[LAUGHS] OK.
+
+[LONG SYNTHESIZER TONES AND
+ TRILLS]
+
+You get the idea.
+
+So that's a great example
+of using our modules
+
+for a lot of different things.
+
+We're using an oscillator to
+create variation in frequency.
+
+We're using one of our envelopes
+to scale that variation
+
+before applying it
+to other oscillators.
+
+Now as we started
+to hear there, we
+
+can push this frequency
+modulation even further
+
+and start to create
+new harmonics.
+
+Frequency modulation,
+or FM modulation,
+
+is when we modulate the
+frequency at, or near,
+
+or beyond the audio
+rate, producing
+
+even more frequencies and
+then even more complex timbre.
+
+Frequency modulation is often
+done with assigned tones.
+
+But we already have a rich tone.
+
+So what if we just modulate
+the frequency of our rich tone
+
+at the audio rate?
+
+I'll start with a slow--
+
+[SYNTHESIZER]
+
+You can hear it's already--
+here's low frequency.
+
+Let me speed it up.
+
+[SYNTHESIZER]
+
+And as I increase the
+amount of modulation--
+
+[VARYING SYNTHESIZER TONES]
+
+--we get all sorts of
+new spectral components
+
+due to the frequency modulation.
+
+And of course, we could scale
+that frequency modulation.
+
+We could modulate the modulator.
+
+So we could control the
+parameters of the modulation
+
+with another oscillator
+or another envelope.
+
+And the process goes on and on.
+
+Now a very common technique
+available as early as the RCA
+
+synthesizer-- we heard
+a little taste of this--
+
+was the use of filtered noise.
+
+We can use our noise sources
+through either a low-pass or
+
+band-pass filter to
+create some novel timbres.
+
+This was used in that
+example we listened
+
+to before to create
+a drum sound.
+
+And it can be used for a
+lot of interesting sounds.
+
+Oh, sorry.
+
+[SYNTHESIZER]
+
+That was modulating
+the modulator of FM.
+
+Here's our
+filtered-noise example.
+
+[STATICKY SYNTHESIZER TONES]
+
+So here I'm using a white-noise
+source into a band-pass filter.
+
+And I'm controlling
+the cutoff frequency
+
+of that band-pass
+filter by the keyboard.
+
+[STATICKY SYNTHESIZER TONES]
+
+So we can create
+something somewhat
+
+in between a pitched
+and unpitched sound.
+
+[STATICKY AND WARPED SYNTHESIZER
+ TONES]
+
+If we try with a
+low-pass filter--
+
+[SYNTHESIZER TAPS]
+
+Let's see what this sounds like.
+
+[VARYING SYNTHESIZER TAPS AND
+ BEEPS]
+
+So that's simply noise through
+a low-pass filter where
+
+the cutoff frequency is
+controlled by the keyboard,
+
+which gives us the
+ability to create--
+
+[SYNTHESIZER BEEPS]
+
+--some novel sounds.
+
+Yeah.
+
+AUDIENCE: What happens
+when you modulate
+
+the modulator with
+the audio output?
+
+[INAUDIBLE]
+
+Can you even do
+that on the Moog?
+
+PROFESSOR: Yeah.
+
+On the Moog?
+
+I'm not sure I
+can do it on this.
+
+But with a computer, we need
+to insert a little bit of delay
+
+in there.
+
+We'll do that with PD.
+
+When we work this with
+PD, we'll feed that back
+
+and see what happens.
+
+You could use
+feedback on the Moog,
+
+particularly with delay,
+which is something
+
+that sometimes people would use.
+
+Because we still had
+the old tape technique.
+
+So some people would
+integrate tape delay
+
+with the synthesizer,
+send a signal out,
+
+put it through tape
+delay, bring it back in,
+
+which allowed you to do some
+pretty interesting things.
+
+I believe we heard that in the
+Oliveros tune, "Alien Bog."
+
+She used a lot of tape delay.
+
+The last example I
+have for you guys
+
+is one of the most common sounds
+from the modular synthesizer,
+
+or one of the many
+common sounds.
+
+And this is using
+the sample and hold
+
+generator applied to noise.
+
+So here, what I'm doing
+is taking white noise,
+
+bringing it into the
+sample-and-hold generator.
+
+The sample and hold takes
+that noise and samples
+
+values from it in
+a periodic fashion.
+
+Here, I'm using the internal
+trigger to sample the noise.
+
+And I'm applying the output
+of that to an oscillator
+
+to do frequency modulation
+of the oscillator.
+
+So in short--
+
+[SYNTHESIZER BEEPS]
+
+--we get this.
+
+Sound familiar?
+
+[SYNTHESIZER BEEPS]
+
+So what we're
+doing, again, we're
+
+taking noise and using it
+as a source of randomness.
+
+But the noise is coming
+out at the audio rate.
+
+So basically, what we need
+to do is slow it down.
+
+And the sample and hold gives
+us a way to slow down a signal
+
+and make it into
+a stepped pattern.
+
+[SYNTHESIZER]
+
+Here, it's really slow.
+
+I can speed it up.
+
+[FASTER SYNTHESIZER TONES]
+
+And even faster.
+
+[RAPID SYNTHESIZER TONES]
+
+And this sample and hold has
+a nice glide parameter here,
+
+which will smooth out the
+transition between each step.
+
+[SYNTHESIZER]
+
+We spend all our time
+gliding, and we don't even
+
+get to the points.
+
+[SYNTHESIZER]
+
+Sample and holds
+are a lot of fun.
+
+Taking noise, putting
+it through a sample
+
+and hold-- a very powerful
+way to get random parameters.
+
+Here, we're hearing
+those random parameters
+
+scaled in a very
+wide frequency range.
+
+We can use it in a much
+more narrow range--
+
+[SYNTHESIZER]
+
+--to create more subtle effects.
+
+Let's see if we can
+hear a random vibrato.
+
+[SYNTHESIZER]
+
+Oh, I need to scale
+this even more.
+
+[SYNTHESIZER]
+
+Sort of a random vibrato--
+a very unhuman approach
+
+and one very idiomatic
+to the synthesizer.
+
+Questions?
+
+AUDIENCE: The [INAUDIBLE]
+is very digital, right?
+
+PROFESSOR: Well, in a way.
+
+I mean, the way that
+analog-to-digital conversion
+
+works is essentially through a
+process of sampling and holding
+
+the value.
+
+But sample and hold processors
+were available for a long time.
+
+AUDIENCE: Yeah.
+
+But it seems like
+an in-between step,
+
+between this idea of sampling
+these individual values out
+
+and then putting them out.
+
+It's very digital, kind of.
+
+PROFESSOR: Yeah, absolutely.
+
+But then with this
+glide control,
+
+we get right back into
+the smooth analog domain.
+
+So that's--
+
+AUDIENCE: It's just like a
+A-B-C, B-A-C built together.
+
+PROFESSOR: Yeah, that's true.
+
+So--
+
+AUDIENCE: I have a question.
+
+PROFESSOR: Yeah.
+
+AUDIENCE: So you showed us the
+matrix, like the plug-in one.
+
+Do they have virtual
+versions of the matrix?
+
+Or is it just a bad interface?
+
+PROFESSOR: Oh, I think
+it's a great interface.
+
+But I don't know of
+a virtualized version
+
+of those EMS synths yet.
+
+EMS really explore that.
+
+And there is another
+synthesizer-- look
+
+at this, ARP 2500--
+that use matrices
+
+for the entire patching system.
+
+I would love to see a
+virtualization of that.
+
+But I don't know of one yet.
+
+AUDIENCE: It's sort
+of like [INAUDIBLE]
+
+matrix-based
+controls [INAUDIBLE].
+
+Does it do--
+
+PROFESSOR: Max has a
+matrix GUI control.
+
+Yeah.
+
+AUDIENCE: So you can [INAUDIBLE]
+things and [INAUDIBLE] similar,
+
+but not--
+
+PROFESSOR: Of course,
+with this design,
+
+depending on how
+it's implemented,
+
+you can do one-to-one
+connections,
+
+like with a patch bay.
+
+But you can also do one-to-many
+connections, as long
+
+as that doesn't weaken
+your signal too much.
+
+Right.
+
+So we listened to a
+number of different pieces
+
+using the modular
+synthesizer-- various sorts.
+
+Probably some of the
+most important in terms
+
+of the history of
+music technology
+
+were those that were released
+on the Switched-on Bach album.
+
+This was released in
+1968 by Wendy Carlos
+
+and featured this very
+unhappy looking guy, well,
+
+I guess he-- I don't know.
+
+It's supposed to be Bach.
+
+He's got headphones.
+
+And he's sitting in front
+of the Moog synthesizer.
+
+This really solidifies
+some of the issues
+
+in music and technology that
+we've seen again and again.
+
+In order for new instruments
+to be successful,
+
+they often need to be tied
+to historical practice.
+
+And if you want to
+legitimize an instrument,
+
+well, play Bach on it.
+
+And if you can play Bach on it,
+then it's got to be legitimate.
+
+Quotes of Moog and others
+talk about the importance
+
+of this album in showing people
+what this thing was-- what
+
+the synthesizer was,
+that it could be used
+
+as a musical
+instrument and really,
+
+inspired a whole generation
+or generations of musicians
+
+to become interested
+in the Moog.
+
+They say that sales
+of the Moog exploded
+
+after the release of this album,
+at least for a couple of years,
+
+even though the Moog
+was so expensive.
+
+So I had you guys
+listen to two-- refresh
+
+our memory of these.
+
+First, "Cantata 147."
+
+[MUSIC -- JS BACH, "CANTATA
+ 147"]
+
+Notice there.
+
+This is one of my favorite
+timbres in this whole album.
+
+That's a filtered noise
+sound you can hear there.
+
+But it's got a little bit of
+modulation on the frequency.
+
+So it's kind of like there's
+a little vibrato on it.
+
+[MUSIC -- JS BACH, "CANTATA
+ 147"]
+
+So there's that, and then
+"Well-Tempered Clavier, Book 1,
+
+Prelude and Fugue in C Minor."
+
+[MUSIC -- JS BACH, "THE
+WELL-TEMPERED CLAVIER, BOOK 1,
+
+PRELUDE AND FUGUE IN C MINOR"]
+
+Nice, huh?
+
+What do you guys think?
+
+AUDIENCE: I said this
+earlier, but that
+
+was my favorite part
+of all the listenings.
+
+PROFESSOR: Yeah.
+
+AUDIENCE: They
+were very pleasant.
+
+PROFESSOR: They
+were very pleasant.
+
+I mean, at the time, I
+imagine for some people
+
+they were probably
+pretty jarring.
+
+Some of the timbres in that
+are pretty strident timbres.
+
+But it's still Bach.
+
+And it relates to
+organ sounds that you
+
+might associate some
+of these sounds with.
+
+Other observations about this?
+
+AUDIENCE: There was
+some volume modulation.
+
+Was that done independently?
+
+PROFESSOR: In that right there?
+
+AUDIENCE: The last one, yeah.
+
+PROFESSOR: Yeah, you here
+it as stepped dynamics.
+
+And that's because dynamics
+was a weak point of the Moog.
+
+You had a volume control,
+but the keyboards
+
+weren't velocity sensitive.
+
+So adjusting volume
+was difficult.
+
+So this album was recorded
+through multi-track recording.
+
+So they could do it
+in the mixing process
+
+of recording different
+layers or adjusting--
+
+AUDIENCE: Yeah, it
+seemed a little--
+
+PROFESSOR: --the knobs.
+
+It seems a little
+artificial, yeah.
+
+You hear the step
+dynamics there.
+
+AUDIENCE: So did that
+[INAUDIBLE] portable
+
+synthesizers, the red one with
+the keyboard that we looked
+
+at earlier, have touch-sensitive
+keys so the performer could
+
+actually express dynamics
+without having to--
+
+PROFESSOR: I'm not sure if
+they were just on-off switches
+
+or if they had some sort of
+the more contact the louder,
+
+or something of the sort.
+
+That would be
+something to look at.
+
+AUDIENCE: [INAUDIBLE]
+ribbon-style controller
+
+up and down, like they're
+higher on key or lower on key.
+
+I'd notice that.
+
+But I don't know if
+it knows how loud.
+
+PROFESSOR: Right.
+
+Yeah.
+
+We have many devices--
+even Moog explored
+
+in ribbons-- that would use
+a lateral movement for pitch.
+
+But I'm not sure when we got
+a really flexible amplitude
+
+control into our synths.
+
+AUDIENCE: Was any
+of that sequenced?
+
+PROFESSOR: It wasn't sequenced.
+
+It was all performed live.
+
+But it's a mistake
+to think of this
+
+as just a demonstration
+of the Moog synth.
+
+This composition
+was a demonstration
+
+of the Moog synth and some very
+excellent multi-track recording
+
+and audio production.
+
+Because this was all
+composed and performed
+
+one part at a time,
+recorded to tape,
+
+and layered one part at a time.
+
+Remember, the Moog
+synth is essentially
+
+a monophonic instrument
+at this time.
+
+And so she had to play one
+part at a time, and layer,
+
+and re-record, and every
+time, adjusting the timbre.
+
+In many ways, this album--
+I really recommend you guys
+
+listen to the whole album,
+because it's fantastic.
+
+It's a catalog of sounds you can
+make with the Moog synthesizer
+
+and served as a catalog for
+many others afterwards, going,
+
+what was that sound?
+
+What was that sound?
+
+Trying to get the sounds from
+that album-- really a resource
+
+for many other
+musicians, I think.
+
+Other comments about this?
+
+AUDIENCE: There was a
+bit in the reading that
+
+says that Carlos
+commissioned Moog
+
+to build touch-sensitive
+keyboards that
+
+had velocity control.
+
+PROFESSOR: Oh, that's great.
+
+Was it before or after this?
+
+AUDIENCE: It must've been after.
+
+PROFESSOR: OK.
+
+AUDIENCE: I can't
+imagine why you'd
+
+want to [INAUDIBLE]
+the volume control.
+
+PROFESSOR: That's
+interesting, yeah.
+
+She worked with
+Moog quite a bit.
+
+She worked with Moog to
+create that Moog demo
+
+LP, which I sent you
+guys the link to.
+
+She worked with Moog, I think,
+to improve the sequencer
+
+design.
+
+And that's an interesting issue
+about the touch-sensitive,
+
+volume-sensitive keyboard.
+
+It'd be interesting to
+see when that came in
+
+and how that was applied.
+
+So that was a key
+point in our history
+
+of music and technology,
+the legitimization
+
+of the instrument through Bach.
+
+Now something totally
+different comes to us
+
+from the Netherlands.
+
+And this is a composition
+by Gottfried Michael Koenig,
+
+a German composer who had
+been living and working
+
+in the Netherlands.
+
+And he was the artistic
+director of a place called
+
+the Institute of Sonology,
+first in Utrecht and now
+
+in the Hague, where
+they had over a period
+
+of a number of years, developed
+their own modular synthesizer
+
+from scratch.
+
+So while Moog led to the
+first commercial packaged
+
+synthesizer, many
+people were developing
+
+custom-built synthesizers
+that looked something
+
+like this, where you have
+numerous individual components
+
+often custom designed,
+scattered around the room,
+
+and a giant patch bay to
+connect them all together.
+
+This synthesizer is
+still in existence.
+
+In fact, I took this
+photo five years ago.
+
+This isn't historical.
+
+It looks like that still.
+
+And it sounds fantastic.
+
+It's an amazing-sounding
+synthesizer.
+
+His composition that we
+listened to-- "Gray Function,"
+
+is how it translates-- is part
+of a series of function pieces
+
+that explored automating
+some of the parameters
+
+of the modular synthesizer
+using a single control
+
+voltage as a pattern
+that was applied
+
+to numerous different parameters
+of a synthesis system.
+
+We can hear a little bit of
+this piece to remind you.
+
+[MUSIC -- GOTTFRIED MICHAEL
+ KOENIG, "GRAY FUNCTION"]
+
+Now this piece was
+composed for four channels.
+
+And the four channels were
+composed independently.
+
+So you can hear that in
+this two-channel mix.
+
+You can hear the four
+sources independently moving.
+
+Thoughts about this piece?
+
+Is it still going? [LAUGHS]
+That was interesting. [LAUGHS]
+
+What do you think?
+
+AUDIENCE: I like
+the Carlos better.
+
+But it's interesting.
+
+PROFESSOR: It's a
+little more melodic.
+
+AUDIENCE: It's
+interesting in terms
+
+of the technical aspect
+of how it was created.
+
+PROFESSOR: Yeah, I think
+of this piece providing
+
+a landscape of noise
+textures that we can make.
+
+Often, we hear these
+oscillators combined and used
+
+for pitch sounds.
+
+This composition really
+gives us a sampling
+
+of the variety of noise
+timbres that could be produced.
+
+The Institute of
+Sonology synthesizer also
+
+features a number
+of modules not found
+
+on the Moog-- for instance,
+voltage-controlled envelope
+
+generators, so where the
+attack, decay, sustain,
+
+release parameters
+could be controlled
+
+by voltages, which is
+pretty interesting.
+
+So if you think
+about that, you could
+
+set the attack and the
+release of a series of sounds
+
+to be controlled by a
+low-frequency oscillator
+
+or something else,
+which allows you
+
+to create series of
+dynamic envelopes.
+
+So moving on-- Subotnick,
+"Silver Apples of the Moon."
+
+This piece was composed
+with a Buchla synthesizer.
+
+It's not exactly clear how
+much multi-track layering
+
+was going on in the
+production of this.
+
+It's not clear if
+this was one set up,
+
+or if it was multiple
+takes of layer.
+
+That's something to look at
+in the production of this.
+
+This composition
+was noted for being
+
+one of the first recordings
+made for commercial distribution
+
+with a synthesizer.
+
+It actually predates
+Switched-on Bach by a few years
+
+but didn't have quite
+the commercial success
+
+of Switched-on Bach.
+
+Let's listen to a
+little bit of this.
+
+[MUSIC -- MORTON SUBOTNICK,
+ "SILVER APPLES OF THE MOON"]
+
+Notice the filtered
+noise timbres
+
+coming out of the
+speaker right there.
+
+Notice, also, the--
+say you had a Buchla
+
+and you wanted to create
+that flute-like sound,
+
+how might you do that?
+
+Any ideas?
+
+It sounds to me like an
+oscillator with a glide time,
+
+with its pitch being controlled
+by a sample and hold.
+
+Although we're only getting
+a few couple pitches,
+
+that might be a way that
+some of the frequencies
+
+are chosen in this
+composition, using a sample
+
+and hold adjusted and shifted
+to control the frequencies.
+
+What sort of musical
+roles are we hearing?
+
+Are we hearing
+musical roles or parts
+
+that sound like
+acoustic instruments,
+
+or musical roles
+or parts that sound
+
+like something
+totally different?
+
+I think that's a
+useful way for us
+
+to approach some
+of these pieces.
+
+With the Carlos,
+we hear synthesizer
+
+being used to emulate
+parts that were
+
+done by acoustic instruments.
+
+In the Koenig
+composition, we heard
+
+sounds that sound nothing
+like acoustic instruments.
+
+With this, we have
+a nice mixture
+
+of sounds that are
+somewhat acoustic-sounding
+
+in their roles and
+somewhat electronic.
+
+Let's listen to a little bit
+and think about which is which.
+
+[MUSIC -- MORTON SUBOTNICK,
+ "SILVER APPLES OF THE MOON"]
+
+Well, that was a good
+point to do that.
+
+Because our initial
+flute-like sound
+
+transformed into a something
+that a flute player
+
+couldn't normally do.
+
+Now in Part B of this, we
+get a very surprising change.
+
+[MUSIC -- MORTON SUBOTNICK,
+ "SILVER APPLES OF THE MOON"]
+
+We get this rhythmic section
+building up at the end here.
+
+[MUSIC -- MORTON SUBOTNICK,
+ "SILVER APPLES OF THE MOON"]
+
+Now Buchla's early
+synthesizers were often notable
+
+for the use of both
+randomness and sequencers.
+
+So we had various types
+of random controllers
+
+that were pretty novel.
+
+Your book mentions
+that one of them
+
+was called a Source
+of Uncertainty, which
+
+is a very evocative name
+for a random generator,
+
+and also had
+dedicated sequencers.
+
+We're going to talk about
+sequencers next time we meet.
+
+But we hear there some
+use of the sequencer
+
+to create patterns
+of voltages that
+
+are applied to pitch or
+other musical parameters.
+
+Reflections on this piece?
+
+Did you like it?
+
+AUDIENCE: It is long.
+
+PROFESSOR: It is long.
+
+AUDIENCE: The first
+part, in Part A,
+
+the noise, I guess, sort of
+sounds like the [INAUDIBLE].
+
+I think it had like the
+[INAUDIBLE] in there.
+
+PROFESSOR: Right.
+
+Did you hear accelerating and
+de-accelerating articulations?
+
+AUDIENCE: Sort of.
+
+Like for real.
+
+Just the timbre really
+matched the usual [INAUDIBLE].
+
+[INAUDIBLE] start out
+with that one [INAUDIBLE],
+
+but that timbre's faster.
+
+PROFESSOR: Yeah,
+that's interesting.
+
+Although that was--
+you sampled here,
+
+these are all synthesized.
+
+But yeah, that's
+a good connection.
+
+Anything else?
+
+I think the depth
+of this composition
+
+is pretty remarkable.
+
+There's just so much
+going on in terms
+
+of background and
+foreground that
+
+makes it such a
+thick composition.
+
+There had to be
+multi-track layering
+
+going on in this
+composition, I think.
+
+Either that, or they hooked up
+numerous synths all together
+
+in some massive piece.
+
+All right.
+
+We had the Oliveros as
+well, which is probably
+
+the one of the most novel
+compositions in that it
+
+doesn't sound at all
+like Western instruments
+
+but really takes advantage
+of the synthesizer
+
+in some unique ways.
+
+Next time we meet, we're going
+to talk about the sequencer
+
+and continue our trajectory
+up to drum machines.
+
+I'll see you then.
+
+See you guys.
\ No newline at end of file
diff --git a/Bv9kVDcj7yo.txt b/Bv9kVDcj7yo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4f2f5b8aa286db98dfec4ba98058c990130f7a4e
--- /dev/null
+++ b/Bv9kVDcj7yo.txt
@@ -0,0 +1,6843 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu well um because our subject
+
+ align:start position:0%
+ocw.mit.edu well um because our subject
+ 
+
+ align:start position:0%
+ocw.mit.edu well um because our subject
+today is uh trig integrals and
+
+ align:start position:0%
+today is uh trig integrals and
+ 
+
+ align:start position:0%
+today is uh trig integrals and
+substitutions Professor jarrison called
+
+ align:start position:0%
+substitutions Professor jarrison called
+ 
+
+ align:start position:0%
+substitutions Professor jarrison called
+in his substitute teacher for today
+
+ align:start position:0%
+in his substitute teacher for today
+ 
+
+ align:start position:0%
+in his substitute teacher for today
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me Professor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Miller and I'm going to try to tell you
+
+ align:start position:0%
+Miller and I'm going to try to tell you
+ 
+
+ align:start position:0%
+Miller and I'm going to try to tell you
+about trig trig substitutions and trig
+
+ align:start position:0%
+about trig trig substitutions and trig
+ 
+
+ align:start position:0%
+about trig trig substitutions and trig
+integrals and I'll be here tomorrow to
+
+ align:start position:0%
+integrals and I'll be here tomorrow to
+ 
+
+ align:start position:0%
+integrals and I'll be here tomorrow to
+do more of the same as
+
+ align:start position:0%
+do more of the same as
+ 
+
+ align:start position:0%
+do more of the same as
+well so this is about trigonometry and
+
+ align:start position:0%
+well so this is about trigonometry and
+ 
+
+ align:start position:0%
+well so this is about trigonometry and
+maybe the first thing I'll do is remind
+
+ align:start position:0%
+maybe the first thing I'll do is remind
+ 
+
+ align:start position:0%
+maybe the first thing I'll do is remind
+you of some basic things about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trigonometry so if I have a circle all
+
+ align:start position:0%
+trigonometry so if I have a circle all
+ 
+
+ align:start position:0%
+trigonometry so if I have a circle all
+trigonometry is all based on this circle
+
+ align:start position:0%
+trigonometry is all based on this circle
+ 
+
+ align:start position:0%
+trigonometry is all based on this circle
+of radius one and and centered at the
+
+ align:start position:0%
+of radius one and and centered at the
+ 
+
+ align:start position:0%
+of radius one and and centered at the
+origin and so if this is an angle of
+
+ align:start position:0%
+origin and so if this is an angle of
+ 
+
+ align:start position:0%
+origin and so if this is an angle of
+theta up from the x-axis then the
+
+ align:start position:0%
+theta up from the x-axis then the
+ 
+
+ align:start position:0%
+theta up from the x-axis then the
+coordinates of this point are cosine
+
+ align:start position:0%
+coordinates of this point are cosine
+ 
+
+ align:start position:0%
+coordinates of this point are cosine
+Theta and S
+
+ align:start position:0%
+Theta and S
+ 
+
+ align:start position:0%
+Theta and S
+Theta and so that leads right away to
+
+ align:start position:0%
+Theta and so that leads right away to
+ 
+
+ align:start position:0%
+Theta and so that leads right away to
+some trig identities which you know very
+
+ align:start position:0%
+some trig identities which you know very
+ 
+
+ align:start position:0%
+some trig identities which you know very
+well but I'm going to put them up here U
+
+ align:start position:0%
+well but I'm going to put them up here U
+ 
+
+ align:start position:0%
+well but I'm going to put them up here U
+because we'll use them over and over
+
+ align:start position:0%
+because we'll use them over and over
+ 
+
+ align:start position:0%
+because we'll use them over and over
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today remember the convention sin squ of
+
+ align:start position:0%
+today remember the convention sin squ of
+ 
+
+ align:start position:0%
+today remember the convention sin squ of
+theta secretly means s of theta quantity
+
+ align:start position:0%
+theta secretly means s of theta quantity
+ 
+
+ align:start position:0%
+theta secretly means s of theta quantity
+squared it would be more sensible to
+
+ align:start position:0%
+squared it would be more sensible to
+ 
+
+ align:start position:0%
+squared it would be more sensible to
+write a parth is around the sign of
+
+ align:start position:0%
+write a parth is around the sign of
+ 
+
+ align:start position:0%
+write a parth is around the sign of
+theta and then say you square that but
+
+ align:start position:0%
+theta and then say you square that but
+ 
+
+ align:start position:0%
+theta and then say you square that but
+everybody in the world puts the two up
+
+ align:start position:0%
+everybody in the world puts the two up
+ 
+
+ align:start position:0%
+everybody in the world puts the two up
+there over the sign and so I'll do that
+
+ align:start position:0%
+there over the sign and so I'll do that
+ 
+
+ align:start position:0%
+there over the sign and so I'll do that
+too so that follows just because the
+
+ align:start position:0%
+too so that follows just because the
+ 
+
+ align:start position:0%
+too so that follows just because the
+circle has radius one but then there are
+
+ align:start position:0%
+circle has radius one but then there are
+ 
+
+ align:start position:0%
+circle has radius one but then there are
+some other identities too which I think
+
+ align:start position:0%
+some other identities too which I think
+ 
+
+ align:start position:0%
+some other identities too which I think
+you remember I'll write them down here
+
+ align:start position:0%
+you remember I'll write them down here
+ 
+
+ align:start position:0%
+you remember I'll write them down here
+cosine of 2 Theta there's this double
+
+ align:start position:0%
+cosine of 2 Theta there's this double
+ 
+
+ align:start position:0%
+cosine of 2 Theta there's this double
+angle formula that says cosine of 2
+
+ align:start position:0%
+angle formula that says cosine of 2
+ 
+
+ align:start position:0%
+angle formula that says cosine of 2
+Theta is cosine s of
+
+ align:start position:0%
+Theta is cosine s of
+ 
+
+ align:start position:0%
+Theta is cosine s of
+theta minus the sin squ of
+
+ align:start position:0%
+theta minus the sin squ of
+ 
+
+ align:start position:0%
+theta minus the sin squ of
+thet and there's also the double angle
+
+ align:start position:0%
+thet and there's also the double angle
+ 
+
+ align:start position:0%
+thet and there's also the double angle
+formula for the S of 2 Theta uh remember
+
+ align:start position:0%
+formula for the S of 2 Theta uh remember
+ 
+
+ align:start position:0%
+formula for the S of 2 Theta uh remember
+what that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+says 2 sin Theta cosine
+
+ align:start position:0%
+says 2 sin Theta cosine
+ 
+
+ align:start position:0%
+says 2 sin Theta cosine
+Theta now um I'm going to use these trig
+
+ align:start position:0%
+Theta now um I'm going to use these trig
+ 
+
+ align:start position:0%
+Theta now um I'm going to use these trig
+identities and I'm going to use them in
+
+ align:start position:0%
+identities and I'm going to use them in
+ 
+
+ align:start position:0%
+identities and I'm going to use them in
+a slightly different way and so I'd like
+
+ align:start position:0%
+a slightly different way and so I'd like
+ 
+
+ align:start position:0%
+a slightly different way and so I'd like
+to pay a little more attention to this
+
+ align:start position:0%
+to pay a little more attention to this
+ 
+
+ align:start position:0%
+to pay a little more attention to this
+one and get some more get a different
+
+ align:start position:0%
+one and get some more get a different
+ 
+
+ align:start position:0%
+one and get some more get a different
+way of writing this one out so this is
+
+ align:start position:0%
+way of writing this one out so this is
+ 
+
+ align:start position:0%
+way of writing this one out so this is
+the actually the half angle formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that says uh I'm I'm going to try to
+
+ align:start position:0%
+and that says uh I'm I'm going to try to
+ 
+
+ align:start position:0%
+and that says uh I'm I'm going to try to
+express
+
+ align:start position:0%
+express
+ 
+
+ align:start position:0%
+express
+um the cosine of theta in terms of the
+
+ align:start position:0%
+um the cosine of theta in terms of the
+ 
+
+ align:start position:0%
+um the cosine of theta in terms of the
+cosine of 2 Theta so if I know the
+
+ align:start position:0%
+cosine of 2 Theta so if I know the
+ 
+
+ align:start position:0%
+cosine of 2 Theta so if I know the
+cosine of 2 Theta I want to try to
+
+ align:start position:0%
+cosine of 2 Theta I want to try to
+ 
+
+ align:start position:0%
+cosine of 2 Theta I want to try to
+express the cosine of theta in terms of
+
+ align:start position:0%
+express the cosine of theta in terms of
+ 
+
+ align:start position:0%
+express the cosine of theta in terms of
+it yeah well I'll start with a cosine of
+
+ align:start position:0%
+it yeah well I'll start with a cosine of
+ 
+
+ align:start position:0%
+it yeah well I'll start with a cosine of
+2 Theta and play with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+okay well we know what this is It's
+
+ align:start position:0%
+okay well we know what this is It's
+ 
+
+ align:start position:0%
+okay well we know what this is It's
+cosine
+
+ align:start position:0%
+cosine
+ 
+
+ align:start position:0%
+cosine
+2 thet minus the sin s of theta but we
+
+ align:start position:0%
+2 thet minus the sin s of theta but we
+ 
+
+ align:start position:0%
+2 thet minus the sin s of theta but we
+also know what the sin squ of theta is
+
+ align:start position:0%
+also know what the sin squ of theta is
+ 
+
+ align:start position:0%
+also know what the sin squ of theta is
+in terms of the cosine so I can
+
+ align:start position:0%
+in terms of the cosine so I can
+ 
+
+ align:start position:0%
+in terms of the cosine so I can
+eliminate the sin squar from this
+
+ align:start position:0%
+eliminate the sin squar from this
+ 
+
+ align:start position:0%
+eliminate the sin squar from this
+picture so this is equal to the cosine s
+
+ align:start position:0%
+picture so this is equal to the cosine s
+ 
+
+ align:start position:0%
+picture so this is equal to the cosine s
+of theta minus the quantity 1us cosine s
+
+ align:start position:0%
+of theta minus the quantity 1us cosine s
+ 
+
+ align:start position:0%
+of theta minus the quantity 1us cosine s
+of thet I put in what sin squ is in
+
+ align:start position:0%
+of thet I put in what sin squ is in
+ 
+
+ align:start position:0%
+of thet I put in what sin squ is in
+terms of cosine
+
+ align:start position:0%
+terms of cosine
+ 
+
+ align:start position:0%
+terms of cosine
+squ and so that's twice the cosine s of
+
+ align:start position:0%
+squ and so that's twice the cosine s of
+ 
+
+ align:start position:0%
+squ and so that's twice the cosine s of
+theta minus 1 there's this cosine
+
+ align:start position:0%
+theta minus 1 there's this cosine
+ 
+
+ align:start position:0%
+theta minus 1 there's this cosine
+squared which gets a plus sign because
+
+ align:start position:0%
+squared which gets a plus sign because
+ 
+
+ align:start position:0%
+squared which gets a plus sign because
+of these two minus signs and there's the
+
+ align:start position:0%
+of these two minus signs and there's the
+ 
+
+ align:start position:0%
+of these two minus signs and there's the
+one that was there before so altogether
+
+ align:start position:0%
+one that was there before so altogether
+ 
+
+ align:start position:0%
+one that was there before so altogether
+there are two of
+
+ align:start position:0%
+there are two of
+ 
+
+ align:start position:0%
+there are two of
+them I want to isolate what cosine is or
+
+ align:start position:0%
+them I want to isolate what cosine is or
+ 
+
+ align:start position:0%
+them I want to isolate what cosine is or
+rather what cosine squar
+
+ align:start position:0%
+rather what cosine squar
+ 
+
+ align:start position:0%
+rather what cosine squar
+is so let's solve for that so I'll put
+
+ align:start position:0%
+is so let's solve for that so I'll put
+ 
+
+ align:start position:0%
+is so let's solve for that so I'll put
+the one on the other side and I get 1 +
+
+ align:start position:0%
+the one on the other side and I get 1 +
+ 
+
+ align:start position:0%
+the one on the other side and I get 1 +
+cosine of 2
+
+ align:start position:0%
+cosine of 2
+ 
+
+ align:start position:0%
+cosine of 2
+thet and then I want to divide by this
+
+ align:start position:0%
+thet and then I want to divide by this
+ 
+
+ align:start position:0%
+thet and then I want to divide by this
+two and so that puts a two in this
+
+ align:start position:0%
+two and so that puts a two in this
+ 
+
+ align:start position:0%
+two and so that puts a two in this
+denominator here
+
+ align:start position:0%
+denominator here
+ 
+
+ align:start position:0%
+denominator here
+so some people call that the half angle
+
+ align:start position:0%
+so some people call that the half angle
+ 
+
+ align:start position:0%
+so some people call that the half angle
+formula it's a way of what it really is
+
+ align:start position:0%
+formula it's a way of what it really is
+ 
+
+ align:start position:0%
+formula it's a way of what it really is
+for us is it's a way of eliminating
+
+ align:start position:0%
+for us is it's a way of eliminating
+ 
+
+ align:start position:0%
+for us is it's a way of eliminating
+powers from signs and cosin I've gotten
+
+ align:start position:0%
+powers from signs and cosin I've gotten
+ 
+
+ align:start position:0%
+powers from signs and cosin I've gotten
+rid of this square at the expense of
+
+ align:start position:0%
+rid of this square at the expense of
+ 
+
+ align:start position:0%
+rid of this square at the expense of
+putting in a 2 Theta here we'll use that
+
+ align:start position:0%
+putting in a 2 Theta here we'll use that
+ 
+
+ align:start position:0%
+putting in a 2 Theta here we'll use that
+and similarly same calculation shows
+
+ align:start position:0%
+and similarly same calculation shows
+ 
+
+ align:start position:0%
+and similarly same calculation shows
+that the sin squ of theta is 1 minus
+
+ align:start position:0%
+that the sin squ of theta is 1 minus
+ 
+
+ align:start position:0%
+that the sin squ of theta is 1 minus
+cosine of 2 th / two same
+
+ align:start position:0%
+cosine of 2 th / two same
+ 
+
+ align:start position:0%
+cosine of 2 th / two same
+cosine in that formula also but it has a
+
+ align:start position:0%
+cosine in that formula also but it has a
+ 
+
+ align:start position:0%
+cosine in that formula also but it has a
+minus sign for the sin
+
+ align:start position:0%
+minus sign for the sin
+ 
+
+ align:start position:0%
+minus sign for the sin
+squ okay so that's my little review of
+
+ align:start position:0%
+squ okay so that's my little review of
+ 
+
+ align:start position:0%
+squ okay so that's my little review of
+trig identities that we'll make use of
+
+ align:start position:0%
+trig identities that we'll make use of
+ 
+
+ align:start position:0%
+trig identities that we'll make use of
+uh as this this lecture goes
+
+ align:start position:0%
+uh as this this lecture goes
+ 
+
+ align:start position:0%
+uh as this this lecture goes
+on I want to talk about trig identity
+
+ align:start position:0%
+on I want to talk about trig identity
+ 
+
+ align:start position:0%
+on I want to talk about trig identity
+trig integrals and you know some trig
+
+ align:start position:0%
+trig integrals and you know some trig
+ 
+
+ align:start position:0%
+trig integrals and you know some trig
+integrals I'm sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already uh like well let me write the
+
+ align:start position:0%
+already uh like well let me write the
+ 
+
+ align:start position:0%
+already uh like well let me write the
+differential form first you know that D
+
+ align:start position:0%
+differential form first you know that D
+ 
+
+ align:start position:0%
+differential form first you know that D
+sin Theta or maybe I'll say d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sinx is let's see that's the derivative
+
+ align:start position:0%
+sinx is let's see that's the derivative
+ 
+
+ align:start position:0%
+sinx is let's see that's the derivative
+of sinx * DX right the derivative of
+
+ align:start position:0%
+of sinx * DX right the derivative of
+ 
+
+ align:start position:0%
+of sinx * DX right the derivative of
+sinx is cosine
+
+ align:start position:0%
+sinx is cosine
+ 
+
+ align:start position:0%
+sinx is cosine
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+DX and so if I integrate both sides here
+
+ align:start position:0%
+DX and so if I integrate both sides here
+ 
+
+ align:start position:0%
+DX and so if I integrate both sides here
+the integral form of this is the
+
+ align:start position:0%
+the integral form of this is the
+ 
+
+ align:start position:0%
+the integral form of this is the
+integral of the cosine of x
+
+ align:start position:0%
+integral of the cosine of x
+ 
+
+ align:start position:0%
+integral of the cosine of x
+DX is the S of X plus a constant
+
+ align:start position:0%
+DX is the S of X plus a constant
+ 
+
+ align:start position:0%
+DX is the S of X plus a constant
+and the same way D cosine of x is minus
+
+ align:start position:0%
+and the same way D cosine of x is minus
+ 
+
+ align:start position:0%
+and the same way D cosine of x is minus
+the sin of X DX right the derivative of
+
+ align:start position:0%
+the sin of X DX right the derivative of
+ 
+
+ align:start position:0%
+the sin of X DX right the derivative of
+the cosine is minus the sign and when I
+
+ align:start position:0%
+the cosine is minus the sign and when I
+ 
+
+ align:start position:0%
+the cosine is minus the sign and when I
+integrate that I find the integral of
+
+ align:start position:0%
+integrate that I find the integral of
+ 
+
+ align:start position:0%
+integrate that I find the integral of
+the S of X DX is minus the cosine of x
+
+ align:start position:0%
+the S of X DX is minus the cosine of x
+ 
+
+ align:start position:0%
+the S of X DX is minus the cosine of x
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+C so that's our starting point and the
+
+ align:start position:0%
+C so that's our starting point and the
+ 
+
+ align:start position:0%
+C so that's our starting point and the
+game today uh for the first half of the
+
+ align:start position:0%
+game today uh for the first half of the
+ 
+
+ align:start position:0%
+game today uh for the first half of the
+lecture um is to use uh that base basic
+
+ align:start position:0%
+lecture um is to use uh that base basic
+ 
+
+ align:start position:0%
+lecture um is to use uh that base basic
+those just those basic um integration
+
+ align:start position:0%
+those just those basic um integration
+ 
+
+ align:start position:0%
+those just those basic um integration
+formulas together with clever use of
+
+ align:start position:0%
+formulas together with clever use of
+ 
+
+ align:start position:0%
+formulas together with clever use of
+trig identities in order to compute more
+
+ align:start position:0%
+trig identities in order to compute more
+ 
+
+ align:start position:0%
+trig identities in order to compute more
+complicated formulas involving trig
+
+ align:start position:0%
+complicated formulas involving trig
+ 
+
+ align:start position:0%
+complicated formulas involving trig
+functions so the first
+
+ align:start position:0%
+functions so the first
+ 
+
+ align:start position:0%
+functions so the first
+thing the first uh topic is to think
+
+ align:start position:0%
+thing the first uh topic is to think
+ 
+
+ align:start position:0%
+thing the first uh topic is to think
+about integrals of the form s to the nth
+
+ align:start position:0%
+about integrals of the form s to the nth
+ 
+
+ align:start position:0%
+about integrals of the form s to the nth
+power of x cosine to the nth power of
+
+ align:start position:0%
+power of x cosine to the nth power of
+ 
+
+ align:start position:0%
+power of x cosine to the nth power of
+X DX where here I have in mind m and n
+
+ align:start position:0%
+X DX where here I have in mind m and n
+ 
+
+ align:start position:0%
+X DX where here I have in mind m and n
+are uh posit non- negative
+
+ align:start position:0%
+are uh posit non- negative
+ 
+
+ align:start position:0%
+are uh posit non- negative
+integers so let's try to integrate these
+
+ align:start position:0%
+integers so let's try to integrate these
+ 
+
+ align:start position:0%
+integers so let's try to integrate these
+I'll show you some applications of these
+
+ align:start position:0%
+I'll show you some applications of these
+ 
+
+ align:start position:0%
+I'll show you some applications of these
+pretty soon uh looking down the road a
+
+ align:start position:0%
+pretty soon uh looking down the road a
+ 
+
+ align:start position:0%
+pretty soon uh looking down the road a
+little bit integrals like this show up
+
+ align:start position:0%
+little bit integrals like this show up
+ 
+
+ align:start position:0%
+little bit integrals like this show up
+in fora series and many other uh
+
+ align:start position:0%
+in fora series and many other uh
+ 
+
+ align:start position:0%
+in fora series and many other uh
+subjects in mathematics it turns out
+
+ align:start position:0%
+subjects in mathematics it turns out
+ 
+
+ align:start position:0%
+subjects in mathematics it turns out
+they're quite important to uh be able to
+
+ align:start position:0%
+they're quite important to uh be able to
+ 
+
+ align:start position:0%
+they're quite important to uh be able to
+do so that's why we're doing them
+
+ align:start position:0%
+do so that's why we're doing them
+ 
+
+ align:start position:0%
+do so that's why we're doing them
+now well so um there are two two cases
+
+ align:start position:0%
+now well so um there are two two cases
+ 
+
+ align:start position:0%
+now well so um there are two two cases
+to think about here when you're
+
+ align:start position:0%
+to think about here when you're
+ 
+
+ align:start position:0%
+to think about here when you're
+integrating things like this there's the
+
+ align:start position:0%
+integrating things like this there's the
+ 
+
+ align:start position:0%
+integrating things like this there's the
+easy case and let's do that one first
+
+ align:start position:0%
+easy case and let's do that one first
+ 
+
+ align:start position:0%
+easy case and let's do that one first
+the easy case is
+
+ align:start position:0%
+the easy case is
+ 
+
+ align:start position:0%
+the easy case is
+when at
+
+ align:start position:0%
+when at
+ 
+
+ align:start position:0%
+when at
+least one exponent is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+odd that's the easy case so for example
+
+ align:start position:0%
+odd that's the easy case so for example
+ 
+
+ align:start position:0%
+odd that's the easy case so for example
+suppose that I wanted to
+
+ align:start position:0%
+suppose that I wanted to
+ 
+
+ align:start position:0%
+suppose that I wanted to
+integrate uh well let's take the case m
+
+ align:start position:0%
+integrate uh well let's take the case m
+ 
+
+ align:start position:0%
+integrate uh well let's take the case m
+equals 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm integrating sin to the N power of
+
+ align:start position:0%
+so I'm integrating sin to the N power of
+ 
+
+ align:start position:0%
+so I'm integrating sin to the N power of
+x * the cosine of x DX I'm taking uh
+
+ align:start position:0%
+x * the cosine of x DX I'm taking uh
+ 
+
+ align:start position:0%
+x * the cosine of x DX I'm taking uh
+oh uh um I could do that one let's see
+
+ align:start position:0%
+oh uh um I could do that one let's see
+ 
+
+ align:start position:0%
+oh uh um I could do that one let's see
+if that's what I want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the my confusion is that I meant to
+
+ align:start position:0%
+yeah the my confusion is that I meant to
+ 
+
+ align:start position:0%
+yeah the my confusion is that I meant to
+have this a different Power you were
+
+ align:start position:0%
+have this a different Power you were
+ 
+
+ align:start position:0%
+have this a different Power you were
+thinking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so let's do this case when m is one
+
+ align:start position:0%
+that so let's do this case when m is one
+ 
+
+ align:start position:0%
+that so let's do this case when m is one
+so the integral I'm trying to do is any
+
+ align:start position:0%
+so the integral I'm trying to do is any
+ 
+
+ align:start position:0%
+so the integral I'm trying to do is any
+power of the sign times the
+
+ align:start position:0%
+power of the sign times the
+ 
+
+ align:start position:0%
+power of the sign times the
+cosine well um here's the trick uh
+
+ align:start position:0%
+cosine well um here's the trick uh
+ 
+
+ align:start position:0%
+cosine well um here's the trick uh
+recognize use uh this formula up at the
+
+ align:start position:0%
+recognize use uh this formula up at the
+ 
+
+ align:start position:0%
+recognize use uh this formula up at the
+top there to to see cosine of x DX as
+
+ align:start position:0%
+top there to to see cosine of x DX as
+ 
+
+ align:start position:0%
+top there to to see cosine of x DX as
+something that we already have on the
+
+ align:start position:0%
+something that we already have on the
+ 
+
+ align:start position:0%
+something that we already have on the
+Blackboard so the way to to to exploit
+
+ align:start position:0%
+Blackboard so the way to to to exploit
+ 
+
+ align:start position:0%
+Blackboard so the way to to to exploit
+that is to make a substitute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tion and the substitution is going to be
+
+ align:start position:0%
+tion and the substitution is going to be
+ 
+
+ align:start position:0%
+tion and the substitution is going to be
+U is the S of X and here's why then this
+
+ align:start position:0%
+U is the S of X and here's why then this
+ 
+
+ align:start position:0%
+U is the S of X and here's why then this
+integral that I'm trying to do is the
+
+ align:start position:0%
+integral that I'm trying to do is the
+ 
+
+ align:start position:0%
+integral that I'm trying to do is the
+integral of U to the N that's that's
+
+ align:start position:0%
+integral of U to the N that's that's
+ 
+
+ align:start position:0%
+integral of U to the N that's that's
+already a
+
+ align:start position:0%
+already a
+ 
+
+ align:start position:0%
+already a
+simplification and then there's that
+
+ align:start position:0%
+simplification and then there's that
+ 
+
+ align:start position:0%
+simplification and then there's that
+cosine of x * DX when you make a
+
+ align:start position:0%
+cosine of x * DX when you make a
+ 
+
+ align:start position:0%
+cosine of x * DX when you make a
+substitution you've got to go all the
+
+ align:start position:0%
+substitution you've got to go all the
+ 
+
+ align:start position:0%
+substitution you've got to go all the
+way and replace everything in the
+
+ align:start position:0%
+way and replace everything in the
+ 
+
+ align:start position:0%
+way and replace everything in the
+expression by things involved involving
+
+ align:start position:0%
+expression by things involved involving
+ 
+
+ align:start position:0%
+expression by things involved involving
+this new variable that I've introduced
+
+ align:start position:0%
+this new variable that I've introduced
+ 
+
+ align:start position:0%
+this new variable that I've introduced
+so i' better get rid of the cosine of x
+
+ align:start position:0%
+so i' better get rid of the cosine of x
+ 
+
+ align:start position:0%
+so i' better get rid of the cosine of x
+DX and rewrite it in terms of du or in
+
+ align:start position:0%
+DX and rewrite it in terms of du or in
+ 
+
+ align:start position:0%
+DX and rewrite it in terms of du or in
+terms of U and I can do that because
+
+ align:start position:0%
+terms of U and I can do that because
+ 
+
+ align:start position:0%
+terms of U and I can do that because
+du according to that formula is the
+
+ align:start position:0%
+du according to that formula is the
+ 
+
+ align:start position:0%
+du according to that formula is the
+cosine of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+DX let me put a box around that that's
+
+ align:start position:0%
+DX let me put a box around that that's
+ 
+
+ align:start position:0%
+DX let me put a box around that that's
+our substitution when you make a
+
+ align:start position:0%
+our substitution when you make a
+ 
+
+ align:start position:0%
+our substitution when you make a
+substitution you also want to compute
+
+ align:start position:0%
+substitution you also want to compute
+ 
+
+ align:start position:0%
+substitution you also want to compute
+the differential
+
+ align:start position:0%
+the differential
+ 
+
+ align:start position:0%
+the differential
+of the variable that you substitute in
+
+ align:start position:0%
+of the variable that you substitute in
+ 
+
+ align:start position:0%
+of the variable that you substitute in
+so the so the cosine of x DX that
+
+ align:start position:0%
+so the so the cosine of x DX that
+ 
+
+ align:start position:0%
+so the so the cosine of x DX that
+appears here is just exactly du and I've
+
+ align:start position:0%
+appears here is just exactly du and I've
+ 
+
+ align:start position:0%
+appears here is just exactly du and I've
+replaced this trig integral with
+
+ align:start position:0%
+replaced this trig integral with
+ 
+
+ align:start position:0%
+replaced this trig integral with
+something that doesn't involve trig
+
+ align:start position:0%
+something that doesn't involve trig
+ 
+
+ align:start position:0%
+something that doesn't involve trig
+functions at all this is a lot easier we
+
+ align:start position:0%
+functions at all this is a lot easier we
+ 
+
+ align:start position:0%
+functions at all this is a lot easier we
+can just plug into what we know here
+
+ align:start position:0%
+can just plug into what we know here
+ 
+
+ align:start position:0%
+can just plug into what we know here
+this is U to the N +1 Over N
+
+ align:start position:0%
+this is U to the N +1 Over N
+ 
+
+ align:start position:0%
+this is U to the N +1 Over N
++1 plus a constant and I've done the
+
+ align:start position:0%
++1 plus a constant and I've done the
+ 
+
+ align:start position:0%
++1 plus a constant and I've done the
+integral but I'm not quite done with the
+
+ align:start position:0%
+integral but I'm not quite done with the
+ 
+
+ align:start position:0%
+integral but I'm not quite done with the
+problem yet because to be nice to your
+
+ align:start position:0%
+problem yet because to be nice to your
+ 
+
+ align:start position:0%
+problem yet because to be nice to your
+reader and to yourself you should go
+
+ align:start position:0%
+reader and to yourself you should go
+ 
+
+ align:start position:0%
+reader and to yourself you should go
+back at this point probably go back and
+
+ align:start position:0%
+back at this point probably go back and
+ 
+
+ align:start position:0%
+back at this point probably go back and
+get rid of this new variable that you
+
+ align:start position:0%
+get rid of this new variable that you
+ 
+
+ align:start position:0%
+get rid of this new variable that you
+introduced you're the one who introduced
+
+ align:start position:0%
+introduced you're the one who introduced
+ 
+
+ align:start position:0%
+introduced you're the one who introduced
+this variable youu nobody except you
+
+ align:start position:0%
+this variable youu nobody except you
+ 
+
+ align:start position:0%
+this variable youu nobody except you
+really knows what it is right but the
+
+ align:start position:0%
+really knows what it is right but the
+ 
+
+ align:start position:0%
+really knows what it is right but the
+rest of the world knows what they asked
+
+ align:start position:0%
+rest of the world knows what they asked
+ 
+
+ align:start position:0%
+rest of the world knows what they asked
+for in the first place that involved X
+
+ align:start position:0%
+for in the first place that involved X
+ 
+
+ align:start position:0%
+for in the first place that involved X
+so I have to go back and get rid of this
+
+ align:start position:0%
+so I have to go back and get rid of this
+ 
+
+ align:start position:0%
+so I have to go back and get rid of this
+and that's not hard to do in this case
+
+ align:start position:0%
+and that's not hard to do in this case
+ 
+
+ align:start position:0%
+and that's not hard to do in this case
+because U is the sign of X and so I make
+
+ align:start position:0%
+because U is the sign of X and so I make
+ 
+
+ align:start position:0%
+because U is the sign of X and so I make
+this back sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtitution and that's what you get so
+
+ align:start position:0%
+subtitution and that's what you get so
+ 
+
+ align:start position:0%
+subtitution and that's what you get so
+there's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer okay so the game was I used this
+
+ align:start position:0%
+answer okay so the game was I used this
+ 
+
+ align:start position:0%
+answer okay so the game was I used this
+odd power of of the cosine here and I
+
+ align:start position:0%
+odd power of of the cosine here and I
+ 
+
+ align:start position:0%
+odd power of of the cosine here and I
+could see it appearing as the
+
+ align:start position:0%
+could see it appearing as the
+ 
+
+ align:start position:0%
+could see it appearing as the
+differential of the sign so that's what
+
+ align:start position:0%
+differential of the sign so that's what
+ 
+
+ align:start position:0%
+differential of the sign so that's what
+made this substitution work let's do
+
+ align:start position:0%
+made this substitution work let's do
+ 
+
+ align:start position:0%
+made this substitution work let's do
+another example to see how that works
+
+ align:start position:0%
+another example to see how that works
+ 
+
+ align:start position:0%
+another example to see how that works
+out in a slightly different case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example okay now I do have an odd power
+
+ align:start position:0%
+example okay now I do have an odd power
+ 
+
+ align:start position:0%
+example okay now I do have an odd power
+one of the exponents is odd so I'm in
+
+ align:start position:0%
+one of the exponents is odd so I'm in
+ 
+
+ align:start position:0%
+one of the exponents is odd so I'm in
+the e e easy case but it's not one okay
+
+ align:start position:0%
+the e e easy case but it's not one okay
+ 
+
+ align:start position:0%
+the e e easy case but it's not one okay
+the game now is to use uh
+
+ align:start position:0%
+the game now is to use uh
+ 
+
+ align:start position:0%
+the game now is to use uh
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+use uh this this trig
+
+ align:start position:0%
+use uh this this trig
+ 
+
+ align:start position:0%
+use uh this this trig
+identity to get rid of the largest even
+
+ align:start position:0%
+identity to get rid of the largest even
+ 
+
+ align:start position:0%
+identity to get rid of the largest even
+power uh that you can from this odd
+
+ align:start position:0%
+power uh that you can from this odd
+ 
+
+ align:start position:0%
+power uh that you can from this odd
+power here so use uh sin s x is 1us the
+
+ align:start position:0%
+power here so use uh sin s x is 1us the
+ 
+
+ align:start position:0%
+power here so use uh sin s x is 1us the
+cosine s of x to eliminate a lot of
+
+ align:start position:0%
+cosine s of x to eliminate a lot of
+ 
+
+ align:start position:0%
+cosine s of x to eliminate a lot of
+powers from that odd power Watch What
+
+ align:start position:0%
+powers from that odd power Watch What
+ 
+
+ align:start position:0%
+powers from that odd power Watch What
+Happens so this is not
+
+ align:start position:0%
+Happens so this is not
+ 
+
+ align:start position:0%
+Happens so this is not
+really a substitution or anything this
+
+ align:start position:0%
+really a substitution or anything this
+ 
+
+ align:start position:0%
+really a substitution or anything this
+is just a trig
+
+ align:start position:0%
+is just a trig
+ 
+
+ align:start position:0%
+is just a trig
+identity uh this sin cubed is sin squar
+
+ align:start position:0%
+identity uh this sin cubed is sin squar
+ 
+
+ align:start position:0%
+identity uh this sin cubed is sin squar
+time the S and sin squ is 1us the cosine
+
+ align:start position:0%
+time the S and sin squ is 1us the cosine
+ 
+
+ align:start position:0%
+time the S and sin squ is 1us the cosine
+squ of x and then I have the remaining s
+
+ align:start position:0%
+squ of x and then I have the remaining s
+ 
+
+ align:start position:0%
+squ of x and then I have the remaining s
+of X and then I have cosine squ of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX so let me rewrite that a little bit
+
+ align:start position:0%
+DX so let me rewrite that a little bit
+ 
+
+ align:start position:0%
+DX so let me rewrite that a little bit
+to see how this works out this is the
+
+ align:start position:0%
+to see how this works out this is the
+ 
+
+ align:start position:0%
+to see how this works out this is the
+integral of uh cosine 2 of x minus
+
+ align:start position:0%
+integral of uh cosine 2 of x minus
+ 
+
+ align:start position:0%
+integral of uh cosine 2 of x minus
+and then there's the product of these
+
+ align:start position:0%
+and then there's the product of these
+ 
+
+ align:start position:0%
+and then there's the product of these
+two that's cosine 4 of X time the S of
+
+ align:start position:0%
+two that's cosine 4 of X time the S of
+ 
+
+ align:start position:0%
+two that's cosine 4 of X time the S of
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+DX so now I'm really exactly in the
+
+ align:start position:0%
+DX so now I'm really exactly in the
+ 
+
+ align:start position:0%
+DX so now I'm really exactly in the
+situation that I was in over here I've
+
+ align:start position:0%
+situation that I was in over here I've
+ 
+
+ align:start position:0%
+situation that I was in over here I've
+got a single power of a of a s or cosine
+
+ align:start position:0%
+got a single power of a of a s or cosine
+ 
+
+ align:start position:0%
+got a single power of a of a s or cosine
+it happens that it's a sign here uh but
+
+ align:start position:0%
+it happens that it's a sign here uh but
+ 
+
+ align:start position:0%
+it happens that it's a sign here uh but
+that's not going to cause any trouble we
+
+ align:start position:0%
+that's not going to cause any trouble we
+ 
+
+ align:start position:0%
+that's not going to cause any trouble we
+can go ahead and play the same same game
+
+ align:start position:0%
+can go ahead and play the same same game
+ 
+
+ align:start position:0%
+can go ahead and play the same same game
+that I did there so so far I've just
+
+ align:start position:0%
+that I did there so so far I've just
+ 
+
+ align:start position:0%
+that I did there so so far I've just
+been using trig identities but now now
+
+ align:start position:0%
+been using trig identities but now now
+ 
+
+ align:start position:0%
+been using trig identities but now now
+I'll use a trigged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substitution and I think I want to write
+
+ align:start position:0%
+substitution and I think I want to write
+ 
+
+ align:start position:0%
+substitution and I think I want to write
+these as powers of a variable and then
+
+ align:start position:0%
+these as powers of a variable and then
+ 
+
+ align:start position:0%
+these as powers of a variable and then
+this is going to be the differential of
+
+ align:start position:0%
+this is going to be the differential of
+ 
+
+ align:start position:0%
+this is going to be the differential of
+that variable so I'll take U to be
+
+ align:start position:0%
+that variable so I'll take U to be
+ 
+
+ align:start position:0%
+that variable so I'll take U to be
+cosine of x and that means that du is
+
+ align:start position:0%
+cosine of x and that means that du is
+ 
+
+ align:start position:0%
+cosine of x and that means that du is
+minus the S of
+
+ align:start position:0%
+minus the S of
+ 
+
+ align:start position:0%
+minus the S of
+X DX there's the substitution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so when I make that
+
+ align:start position:0%
+and so when I make that
+ 
+
+ align:start position:0%
+and so when I make that
+substitution uh what do we get cosine
+
+ align:start position:0%
+substitution uh what do we get cosine
+ 
+
+ align:start position:0%
+substitution uh what do we get cosine
+squar becomes u^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 cosine to 4th becomes U
+
+ align:start position:0%
+2 cosine to 4th becomes U
+ 
+
+ align:start position:0%
+2 cosine to 4th becomes U
+4th and sin of X DX becomes not quite du
+
+ align:start position:0%
+4th and sin of X DX becomes not quite du
+ 
+
+ align:start position:0%
+4th and sin of X DX becomes not quite du
+watch for the Signum watch for this
+
+ align:start position:0%
+watch for the Signum watch for this
+ 
+
+ align:start position:0%
+watch for the Signum watch for this
+minus sign here it becomes minus du
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that's okay the minus sign comes
+
+ align:start position:0%
+but that's okay the minus sign comes
+ 
+
+ align:start position:0%
+but that's okay the minus sign comes
+outside and I can integrate both of
+
+ align:start position:0%
+outside and I can integrate both of
+ 
+
+ align:start position:0%
+outside and I can integrate both of
+these Powers so I get
+
+ align:start position:0%
+these Powers so I get
+ 
+
+ align:start position:0%
+these Powers so I get
+minus U minus U cubed over
+
+ align:start position:0%
+minus U minus U cubed over
+ 
+
+ align:start position:0%
+minus U minus U cubed over
+3 and then this fourth power gives me a
+
+ align:start position:0%
+3 and then this fourth power gives me a
+ 
+
+ align:start position:0%
+3 and then this fourth power gives me a
+fifth power when I
+
+ align:start position:0%
+fifth power when I
+ 
+
+ align:start position:0%
+fifth power when I
+integrate and don't forget the
+
+ align:start position:0%
+integrate and don't forget the
+ 
+
+ align:start position:0%
+integrate and don't forget the
+constant am I done not quite done I have
+
+ align:start position:0%
+constant am I done not quite done I have
+ 
+
+ align:start position:0%
+constant am I done not quite done I have
+to back substitute and get rid of my
+
+ align:start position:0%
+to back substitute and get rid of my
+ 
+
+ align:start position:0%
+to back substitute and get rid of my
+choice of Vari variable U and replace it
+
+ align:start position:0%
+choice of Vari variable U and replace it
+ 
+
+ align:start position:0%
+choice of Vari variable U and replace it
+with yours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions there should indeed I forgot
+
+ align:start position:0%
+questions there should indeed I forgot
+ 
+
+ align:start position:0%
+questions there should indeed I forgot
+this minus sign when I came down here so
+
+ align:start position:0%
+this minus sign when I came down here so
+ 
+
+ align:start position:0%
+this minus sign when I came down here so
+these two gang up to give me a plus is
+
+ align:start position:0%
+these two gang up to give me a plus is
+ 
+
+ align:start position:0%
+these two gang up to give me a plus is
+that what the other question was about
+
+ align:start position:0%
+that what the other question was about
+ 
+
+ align:start position:0%
+that what the other question was about
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+thanks so let's back substitute and I'm
+
+ align:start position:0%
+thanks so let's back substitute and I'm
+ 
+
+ align:start position:0%
+thanks so let's back substitute and I'm
+going to put that over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and the result is well I just
+
+ align:start position:0%
+here and the result is well I just
+ 
+
+ align:start position:0%
+here and the result is well I just
+replace the U by cosine of x so this is
+
+ align:start position:0%
+replace the U by cosine of x so this is
+ 
+
+ align:start position:0%
+replace the U by cosine of x so this is
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+cine uh cubed of X over 3 plus thank you
+
+ align:start position:0%
+cine uh cubed of X over 3 plus thank you
+ 
+
+ align:start position:0%
+cine uh cubed of X over 3 plus thank you
+cosine to 5th of X over 5 plus a
+
+ align:start position:0%
+cosine to 5th of X over 5 plus a
+ 
+
+ align:start position:0%
+cosine to 5th of X over 5 plus a
+constant there's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer by the way you can remember one
+
+ align:start position:0%
+answer by the way you can remember one
+ 
+
+ align:start position:0%
+answer by the way you can remember one
+of the nice things about doing an
+
+ align:start position:0%
+of the nice things about doing an
+ 
+
+ align:start position:0%
+of the nice things about doing an
+integral is it's fairly easy to check
+
+ align:start position:0%
+integral is it's fairly easy to check
+ 
+
+ align:start position:0%
+integral is it's fairly easy to check
+your answer you can always differentiate
+
+ align:start position:0%
+your answer you can always differentiate
+ 
+
+ align:start position:0%
+your answer you can always differentiate
+the thing you get and see whether it you
+
+ align:start position:0%
+the thing you get and see whether it you
+ 
+
+ align:start position:0%
+the thing you get and see whether it you
+get the right thing when you go back
+
+ align:start position:0%
+get the right thing when you go back
+ 
+
+ align:start position:0%
+get the right thing when you go back
+it's not too hard to use the power rules
+
+ align:start position:0%
+it's not too hard to use the power rules
+ 
+
+ align:start position:0%
+it's not too hard to use the power rules
+and the uh differentiation rule for the
+
+ align:start position:0%
+and the uh differentiation rule for the
+ 
+
+ align:start position:0%
+and the uh differentiation rule for the
+cosine to uh get back to this if you if
+
+ align:start position:0%
+cosine to uh get back to this if you if
+ 
+
+ align:start position:0%
+cosine to uh get back to this if you if
+you want to check the
+
+ align:start position:0%
+you want to check the
+ 
+
+ align:start position:0%
+you want to check the
+work let's do one more example just to
+
+ align:start position:0%
+work let's do one more example just to
+ 
+
+ align:start position:0%
+work let's do one more example just to
+uh take handle a case an example of this
+
+ align:start position:0%
+uh take handle a case an example of this
+ 
+
+ align:start position:0%
+uh take handle a case an example of this
+easy case which you might not have
+
+ align:start position:0%
+easy case which you might not have
+ 
+
+ align:start position:0%
+easy case which you might not have
+thought of at for at first suppose I
+
+ align:start position:0%
+thought of at for at first suppose I
+ 
+
+ align:start position:0%
+thought of at for at first suppose I
+just want to integrate a cube s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubed of x
+
+ align:start position:0%
+cubed of x
+ 
+
+ align:start position:0%
+cubed of x
+no cosine in
+
+ align:start position:0%
+no cosine in
+ 
+
+ align:start position:0%
+no cosine in
+sight but I do have an odd power of a of
+
+ align:start position:0%
+sight but I do have an odd power of a of
+ 
+
+ align:start position:0%
+sight but I do have an odd power of a of
+a uh trig function of a sign or cosine
+
+ align:start position:0%
+a uh trig function of a sign or cosine
+ 
+
+ align:start position:0%
+a uh trig function of a sign or cosine
+so I'm in the easy case and the um the
+
+ align:start position:0%
+so I'm in the easy case and the um the
+ 
+
+ align:start position:0%
+so I'm in the easy case and the um the
+the procedure that I was suggesting says
+
+ align:start position:0%
+the procedure that I was suggesting says
+ 
+
+ align:start position:0%
+the procedure that I was suggesting says
+I want to take out the largest even
+
+ align:start position:0%
+I want to take out the largest even
+ 
+
+ align:start position:0%
+I want to take out the largest even
+power that I can from the S cubed so
+
+ align:start position:0%
+power that I can from the S cubed so
+ 
+
+ align:start position:0%
+power that I can from the S cubed so
+I'll take that out that's a s squared
+
+ align:start position:0%
+I'll take that out that's a s squared
+ 
+
+ align:start position:0%
+I'll take that out that's a s squared
+and write it as 1 minus cosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squ well now I'm very happy because it's
+
+ align:start position:0%
+squ well now I'm very happy because it's
+ 
+
+ align:start position:0%
+squ well now I'm very happy because it's
+just like the situation we had
+
+ align:start position:0%
+just like the situation we had
+ 
+
+ align:start position:0%
+just like the situation we had
+um uh somewhere on the board here it's
+
+ align:start position:0%
+um uh somewhere on the board here it's
+ 
+
+ align:start position:0%
+um uh somewhere on the board here it's
+just like the situation we had up here
+
+ align:start position:0%
+just like the situation we had up here
+ 
+
+ align:start position:0%
+just like the situation we had up here
+I've got a power of a cosine time sin of
+
+ align:start position:0%
+I've got a power of a cosine time sin of
+ 
+
+ align:start position:0%
+I've got a power of a cosine time sin of
+X DX so exactly the same substitution
+
+ align:start position:0%
+X DX so exactly the same substitution
+ 
+
+ align:start position:0%
+X DX so exactly the same substitution
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+in you get and and maybe you can see uh
+
+ align:start position:0%
+in you get and and maybe you can see uh
+ 
+
+ align:start position:0%
+in you get and and maybe you can see uh
+what happens without doing doing the
+
+ align:start position:0%
+what happens without doing doing the
+ 
+
+ align:start position:0%
+what happens without doing doing the
+work shall I do the work here I'll make
+
+ align:start position:0%
+work shall I do the work here I'll make
+ 
+
+ align:start position:0%
+work shall I do the work here I'll make
+the same substitution and so this is 1
+
+ align:start position:0%
+the same substitution and so this is 1
+ 
+
+ align:start position:0%
+the same substitution and so this is 1
+minus uh u^2 * minus
+
+ align:start position:0%
+minus uh u^2 * minus
+ 
+
+ align:start position:0%
+minus uh u^2 * minus
+du which
+
+ align:start position:0%
+du which
+ 
+
+ align:start position:0%
+du which
+is U minus U Cub over 3 but then I want
+
+ align:start position:0%
+is U minus U Cub over 3 but then I want
+ 
+
+ align:start position:0%
+is U minus U Cub over 3 but then I want
+to put this minus sign in place and so
+
+ align:start position:0%
+to put this minus sign in place and so
+ 
+
+ align:start position:0%
+to put this minus sign in place and so
+that gives me minus U plus u Cub over3
+
+ align:start position:0%
+that gives me minus U plus u Cub over3
+ 
+
+ align:start position:0%
+that gives me minus U plus u Cub over3
+plus a
+
+ align:start position:0%
+plus a
+ 
+
+ align:start position:0%
+plus a
+constant and then I back substitute and
+
+ align:start position:0%
+constant and then I back substitute and
+ 
+
+ align:start position:0%
+constant and then I back substitute and
+get cosine of x plus cosine Cub of X
+
+ align:start position:0%
+get cosine of x plus cosine Cub of X
+ 
+
+ align:start position:0%
+get cosine of x plus cosine Cub of X
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 so this easy case if you have some odd
+
+ align:start position:0%
+3 so this easy case if you have some odd
+ 
+
+ align:start position:0%
+3 so this easy case if you have some odd
+power to play with then you can make use
+
+ align:start position:0%
+power to play with then you can make use
+ 
+
+ align:start position:0%
+power to play with then you can make use
+of it and uh it's pretty
+
+ align:start position:0%
+of it and uh it's pretty
+ 
+
+ align:start position:0%
+of it and uh it's pretty
+straightforward okay the harder case is
+
+ align:start position:0%
+straightforward okay the harder case is
+ 
+
+ align:start position:0%
+straightforward okay the harder case is
+when you don't have an odd power so
+
+ align:start position:0%
+when you don't have an odd power so
+ 
+
+ align:start position:0%
+when you don't have an odd power so
+what's the program I'm going to do the
+
+ align:start position:0%
+what's the program I'm going to do the
+ 
+
+ align:start position:0%
+what's the program I'm going to do the
+harder case and then I'm going to show
+
+ align:start position:0%
+harder case and then I'm going to show
+ 
+
+ align:start position:0%
+harder case and then I'm going to show
+you an example of how to uh integrate uh
+
+ align:start position:0%
+you an example of how to uh integrate uh
+ 
+
+ align:start position:0%
+you an example of how to uh integrate uh
+square roots uh and do an application
+
+ align:start position:0%
+square roots uh and do an application
+ 
+
+ align:start position:0%
+square roots uh and do an application
+using these ideas from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trigonometry so I want to keep this
+
+ align:start position:0%
+trigonometry so I want to keep this
+ 
+
+ align:start position:0%
+trigonometry so I want to keep this
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+maybe I'll come back and start here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again so the harder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case is when there are only even
+
+ align:start position:0%
+case is when there are only even
+ 
+
+ align:start position:0%
+case is when there are only even
+exponents I'm still trying to integrate
+
+ align:start position:0%
+exponents I'm still trying to integrate
+ 
+
+ align:start position:0%
+exponents I'm still trying to integrate
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+form but now all the exponents are even
+
+ align:start position:0%
+form but now all the exponents are even
+ 
+
+ align:start position:0%
+form but now all the exponents are even
+so we have to do some
+
+ align:start position:0%
+so we have to do some
+ 
+
+ align:start position:0%
+so we have to do some
+game and here the game is use the half
+
+ align:start position:0%
+game and here the game is use the half
+ 
+
+ align:start position:0%
+game and here the game is use the half
+angle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula which I've just erased very
+
+ align:start position:0%
+formula which I've just erased very
+ 
+
+ align:start position:0%
+formula which I've just erased very
+sadly on the board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here maybe I'll rewrite them over here
+
+ align:start position:0%
+here maybe I'll rewrite them over here
+ 
+
+ align:start position:0%
+here maybe I'll rewrite them over here
+so we have them on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board I think I remember what they were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the game is I'm going to use
+
+ align:start position:0%
+okay so the game is I'm going to use
+ 
+
+ align:start position:0%
+okay so the game is I'm going to use
+that half angle formula to start getting
+
+ align:start position:0%
+that half angle formula to start getting
+ 
+
+ align:start position:0%
+that half angle formula to start getting
+rid of those even
+
+ align:start position:0%
+rid of those even
+ 
+
+ align:start position:0%
+rid of those even
+Powers half angle formula written like
+
+ align:start position:0%
+Powers half angle formula written like
+ 
+
+ align:start position:0%
+Powers half angle formula written like
+this exactly is going to talks about it
+
+ align:start position:0%
+this exactly is going to talks about it
+ 
+
+ align:start position:0%
+this exactly is going to talks about it
+rewrites even powers of ss and cosines
+
+ align:start position:0%
+rewrites even powers of ss and cosines
+ 
+
+ align:start position:0%
+rewrites even powers of ss and cosines
+so let's see how that works out in an
+
+ align:start position:0%
+so let's see how that works out in an
+ 
+
+ align:start position:0%
+so let's see how that works out in an
+example how about just the cosine squar
+
+ align:start position:0%
+example how about just the cosine squar
+ 
+
+ align:start position:0%
+example how about just the cosine squar
+for for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start what to do I can't pull pull
+
+ align:start position:0%
+start what to do I can't pull pull
+ 
+
+ align:start position:0%
+start what to do I can't pull pull
+anything out uh I could rewrite this as
+
+ align:start position:0%
+anything out uh I could rewrite this as
+ 
+
+ align:start position:0%
+anything out uh I could rewrite this as
+one minus Co sin squar but then I'd be
+
+ align:start position:0%
+one minus Co sin squar but then I'd be
+ 
+
+ align:start position:0%
+one minus Co sin squar but then I'd be
+faced with integrating the S squar which
+
+ align:start position:0%
+faced with integrating the S squar which
+ 
+
+ align:start position:0%
+faced with integrating the S squar which
+is exactly as hard so instead let's use
+
+ align:start position:0%
+is exactly as hard so instead let's use
+ 
+
+ align:start position:0%
+is exactly as hard so instead let's use
+this formula here this is really the
+
+ align:start position:0%
+this formula here this is really the
+ 
+
+ align:start position:0%
+this formula here this is really the
+same as 1 plus the cosine of 2 Theta / 2
+
+ align:start position:0%
+same as 1 plus the cosine of 2 Theta / 2
+ 
+
+ align:start position:0%
+same as 1 plus the cosine of 2 Theta / 2
+and now um this is
+
+ align:start position:0%
+and now um this is
+ 
+
+ align:start position:0%
+and now um this is
+easy uh it's got two parts to it
+
+ align:start position:0%
+easy uh it's got two parts to it
+ 
+
+ align:start position:0%
+easy uh it's got two parts to it
+integrating 1/2 gives me Theta over
+
+ align:start position:0%
+integrating 1/2 gives me Theta over
+ 
+
+ align:start position:0%
+integrating 1/2 gives me Theta over
+oh miraculously the X turned into a
+
+ align:start position:0%
+oh miraculously the X turned into a
+ 
+
+ align:start position:0%
+oh miraculously the X turned into a
+Theta let's put it back as X I get X
+
+ align:start position:0%
+Theta let's put it back as X I get X
+ 
+
+ align:start position:0%
+Theta let's put it back as X I get X
+over2 by integrating a half so notice
+
+ align:start position:0%
+over2 by integrating a half so notice
+ 
+
+ align:start position:0%
+over2 by integrating a half so notice
+that something non-t trigonometric
+
+ align:start position:0%
+that something non-t trigonometric
+ 
+
+ align:start position:0%
+that something non-t trigonometric
+occurs here when I do these even
+
+ align:start position:0%
+occurs here when I do these even
+ 
+
+ align:start position:0%
+occurs here when I do these even
+integrals X over two
+
+ align:start position:0%
+integrals X over two
+ 
+
+ align:start position:0%
+integrals X over two
+appears and then the other one okay so
+
+ align:start position:0%
+appears and then the other one okay so
+ 
+
+ align:start position:0%
+appears and then the other one okay so
+this takes a little thought the integral
+
+ align:start position:0%
+this takes a little thought the integral
+ 
+
+ align:start position:0%
+this takes a little thought the integral
+of the the cosine is the
+
+ align:start position:0%
+of the the cosine is the
+ 
+
+ align:start position:0%
+of the the cosine is the
+sign or is it minus the sign negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+okay should we take a vote I think it's
+
+ align:start position:0%
+okay should we take a vote I think it's
+ 
+
+ align:start position:0%
+okay should we take a vote I think it's
+positive so you get the sign of 2x but
+
+ align:start position:0%
+positive so you get the sign of 2x but
+ 
+
+ align:start position:0%
+positive so you get the sign of 2x but
+is that right over two if I
+
+ align:start position:0%
+is that right over two if I
+ 
+
+ align:start position:0%
+is that right over two if I
+differentiate the S of 2x this two comes
+
+ align:start position:0%
+differentiate the S of 2x this two comes
+ 
+
+ align:start position:0%
+differentiate the S of 2x this two comes
+out and would give me an extra two here
+
+ align:start position:0%
+out and would give me an extra two here
+ 
+
+ align:start position:0%
+out and would give me an extra two here
+so it's there's an extra two that I have
+
+ align:start position:0%
+so it's there's an extra two that I have
+ 
+
+ align:start position:0%
+so it's there's an extra two that I have
+to put in here when I integrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and there's the
+
+ align:start position:0%
+it and there's the
+ 
+
+ align:start position:0%
+it and there's the
+answer this is not a substitution I just
+
+ align:start position:0%
+answer this is not a substitution I just
+ 
+
+ align:start position:0%
+answer this is not a substitution I just
+played with trig identities here and
+
+ align:start position:0%
+played with trig identities here and
+ 
+
+ align:start position:0%
+played with trig identities here and
+then did a simple uh trig integral
+
+ align:start position:0%
+then did a simple uh trig integral
+ 
+
+ align:start position:0%
+then did a simple uh trig integral
+getting your help to get the sign right
+
+ align:start position:0%
+getting your help to get the sign right
+ 
+
+ align:start position:0%
+getting your help to get the sign right
+and thinking about what this two is
+
+ align:start position:0%
+and thinking about what this two is
+ 
+
+ align:start position:0%
+and thinking about what this two is
+going to do it produces a two in the
+
+ align:start position:0%
+going to do it produces a two in the
+ 
+
+ align:start position:0%
+going to do it produces a two in the
+denominator but it's not applying any
+
+ align:start position:0%
+denominator but it's not applying any
+ 
+
+ align:start position:0%
+denominator but it's not applying any
+um any complicated thing
+
+ align:start position:0%
+um any complicated thing
+ 
+
+ align:start position:0%
+um any complicated thing
+it's just using this
+
+ align:start position:0%
+it's just using this
+ 
+
+ align:start position:0%
+it's just using this
+identity all right let's do another
+
+ align:start position:0%
+identity all right let's do another
+ 
+
+ align:start position:0%
+identity all right let's do another
+example uh that's a little bit harder
+
+ align:start position:0%
+example uh that's a little bit harder
+ 
+
+ align:start position:0%
+example uh that's a little bit harder
+this time s squ time cosine squ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again no odd Powers I've got to work a
+
+ align:start position:0%
+again no odd Powers I've got to work a
+ 
+
+ align:start position:0%
+again no odd Powers I've got to work a
+little bit harder and what I'm going to
+
+ align:start position:0%
+little bit harder and what I'm going to
+ 
+
+ align:start position:0%
+little bit harder and what I'm going to
+do is apply those identities up there
+
+ align:start position:0%
+do is apply those identities up there
+ 
+
+ align:start position:0%
+do is apply those identities up there
+now what I recommend doing in this
+
+ align:start position:0%
+now what I recommend doing in this
+ 
+
+ align:start position:0%
+now what I recommend doing in this
+situation is going over uh to the side
+
+ align:start position:0%
+situation is going over uh to the side
+ 
+
+ align:start position:0%
+situation is going over uh to the side
+somewhere and do some side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work because it's all just playing with
+
+ align:start position:0%
+work because it's all just playing with
+ 
+
+ align:start position:0%
+work because it's all just playing with
+trig function it's not um actually doing
+
+ align:start position:0%
+trig function it's not um actually doing
+ 
+
+ align:start position:0%
+trig function it's not um actually doing
+any integrals for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while so I guess one way to get rid of
+
+ align:start position:0%
+while so I guess one way to get rid of
+ 
+
+ align:start position:0%
+while so I guess one way to get rid of
+the S squared and the cosine squar is to
+
+ align:start position:0%
+the S squared and the cosine squar is to
+ 
+
+ align:start position:0%
+the S squared and the cosine squar is to
+use those identities and so let's do
+
+ align:start position:0%
+use those identities and so let's do
+ 
+
+ align:start position:0%
+use those identities and so let's do
+that so the S is 1 minus the cosine of
+
+ align:start position:0%
+that so the S is 1 minus the cosine of
+ 
+
+ align:start position:0%
+that so the S is 1 minus the cosine of
+2x over 2 and the cosine is 1 plus the
+
+ align:start position:0%
+2x over 2 and the cosine is 1 plus the
+ 
+
+ align:start position:0%
+2x over 2 and the cosine is 1 plus the
+cosine of 2x over
+
+ align:start position:0%
+cosine of 2x over
+ 
+
+ align:start position:0%
+cosine of 2x over
+2 so I just substitute them in and now I
+
+ align:start position:0%
+2 so I just substitute them in and now I
+ 
+
+ align:start position:0%
+2 so I just substitute them in and now I
+can multiply that out and it's not what
+
+ align:start position:0%
+can multiply that out and it's not what
+ 
+
+ align:start position:0%
+can multiply that out and it's not what
+I have is a a difference times a product
+
+ align:start position:0%
+I have is a a difference times a product
+ 
+
+ align:start position:0%
+I have is a a difference times a product
+sorry difference times a sum so you know
+
+ align:start position:0%
+sorry difference times a sum so you know
+ 
+
+ align:start position:0%
+sorry difference times a sum so you know
+a formula for that um getting taking the
+
+ align:start position:0%
+a formula for that um getting taking the
+ 
+
+ align:start position:0%
+a formula for that um getting taking the
+product of these two things well
+
+ align:start position:0%
+product of these two things well
+ 
+
+ align:start position:0%
+product of these two things well
+there'll be a four in the denominator
+
+ align:start position:0%
+there'll be a four in the denominator
+ 
+
+ align:start position:0%
+there'll be a four in the denominator
+and then in the numerator get I get the
+
+ align:start position:0%
+and then in the numerator get I get the
+ 
+
+ align:start position:0%
+and then in the numerator get I get the
+square of this minus the square of this
+
+ align:start position:0%
+square of this minus the square of this
+ 
+
+ align:start position:0%
+square of this minus the square of this
+right A minus B * a plus b is a^ 2 minus
+
+ align:start position:0%
+right A minus B * a plus b is a^ 2 minus
+ 
+
+ align:start position:0%
+right A minus B * a plus b is a^ 2 minus
+b^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so I get that
+
+ align:start position:0%
+2 so I get that
+ 
+
+ align:start position:0%
+2 so I get that
+well I'm a little bit happier because at
+
+ align:start position:0%
+well I'm a little bit happier because at
+ 
+
+ align:start position:0%
+well I'm a little bit happier because at
+least I don't have four I don't have two
+
+ align:start position:0%
+least I don't have four I don't have two
+ 
+
+ align:start position:0%
+least I don't have four I don't have two
+uh different squares um I still have a
+
+ align:start position:0%
+uh different squares um I still have a
+ 
+
+ align:start position:0%
+uh different squares um I still have a
+square I want to integrate this I'm
+
+ align:start position:0%
+square I want to integrate this I'm
+ 
+
+ align:start position:0%
+square I want to integrate this I'm
+still not in the easy case I got myself
+
+ align:start position:0%
+still not in the easy case I got myself
+ 
+
+ align:start position:0%
+still not in the easy case I got myself
+back to an easier hard
+
+ align:start position:0%
+back to an easier hard
+ 
+
+ align:start position:0%
+back to an easier hard
+case okay but we do know what to do
+
+ align:start position:0%
+case okay but we do know what to do
+ 
+
+ align:start position:0%
+case okay but we do know what to do
+about this because I just did it up
+
+ align:start position:0%
+about this because I just did it up
+ 
+
+ align:start position:0%
+about this because I just did it up
+there um and I could play into this
+
+ align:start position:0%
+there um and I could play into this
+ 
+
+ align:start position:0%
+there um and I could play into this
+formula that we got but I think it's
+
+ align:start position:0%
+formula that we got but I think it's
+ 
+
+ align:start position:0%
+formula that we got but I think it's
+just as easy to start to to continue to
+
+ align:start position:0%
+just as easy to start to to continue to
+ 
+
+ align:start position:0%
+just as easy to start to to continue to
+calculate here use the half angle
+
+ align:start position:0%
+calculate here use the half angle
+ 
+
+ align:start position:0%
+calculate here use the half angle
+formula again for this and continue on
+
+ align:start position:0%
+formula again for this and continue on
+ 
+
+ align:start position:0%
+formula again for this and continue on
+your way so I get a quarter from this
+
+ align:start position:0%
+your way so I get a quarter from this
+ 
+
+ align:start position:0%
+your way so I get a quarter from this
+bit and then minus a
+
+ align:start position:0%
+bit and then minus a
+ 
+
+ align:start position:0%
+bit and then minus a
+quarter of the cosine SAR of 2x okay now
+
+ align:start position:0%
+quarter of the cosine SAR of 2x okay now
+ 
+
+ align:start position:0%
+quarter of the cosine SAR of 2x okay now
+when I plug in 2x in for Theta there in
+
+ align:start position:0%
+when I plug in 2x in for Theta there in
+ 
+
+ align:start position:0%
+when I plug in 2x in for Theta there in
+the top
+
+ align:start position:0%
+the top
+ 
+
+ align:start position:0%
+the top
+board I'm going to get a
+
+ align:start position:0%
+board I'm going to get a
+ 
+
+ align:start position:0%
+board I'm going to get a
+4X on the right hand side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it comes out like
+
+ align:start position:0%
+so it comes out like
+ 
+
+ align:start position:0%
+so it comes out like
+that and I guess I could simplify that a
+
+ align:start position:0%
+that and I guess I could simplify that a
+ 
+
+ align:start position:0%
+that and I guess I could simplify that a
+little bit more this is a quarter oh but
+
+ align:start position:0%
+little bit more this is a quarter oh but
+ 
+
+ align:start position:0%
+little bit more this is a quarter oh but
+then there's a two here it's half
+
+ align:start position:0%
+then there's a two here it's half
+ 
+
+ align:start position:0%
+then there's a two here it's half
+that so then I can simplify a little
+
+ align:start position:0%
+that so then I can simplify a little
+ 
+
+ align:start position:0%
+that so then I can simplify a little
+more it's a quarter minus an e which is
+
+ align:start position:0%
+more it's a quarter minus an e which is
+ 
+
+ align:start position:0%
+more it's a quarter minus an e which is
+an eighth and then I have uh an eighth
+
+ align:start position:0%
+an eighth and then I have uh an eighth
+ 
+
+ align:start position:0%
+an eighth and then I have uh an eighth
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+cosine of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4X okay that's my side work I just did
+
+ align:start position:0%
+4X okay that's my side work I just did
+ 
+
+ align:start position:0%
+4X okay that's my side work I just did
+some trig identities over here and
+
+ align:start position:0%
+some trig identities over here and
+ 
+
+ align:start position:0%
+some trig identities over here and
+rewrote sin s time cosine squ as
+
+ align:start position:0%
+rewrote sin s time cosine squ as
+ 
+
+ align:start position:0%
+rewrote sin s time cosine squ as
+something which involves just no powers
+
+ align:start position:0%
+something which involves just no powers
+ 
+
+ align:start position:0%
+something which involves just no powers
+of trig just cosine by itself and a and
+
+ align:start position:0%
+of trig just cosine by itself and a and
+ 
+
+ align:start position:0%
+of trig just cosine by itself and a and
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+constant so I can take that and
+
+ align:start position:0%
+constant so I can take that and
+ 
+
+ align:start position:0%
+constant so I can take that and
+substitute it in here and now the
+
+ align:start position:0%
+substitute it in here and now the
+ 
+
+ align:start position:0%
+substitute it in here and now the
+integration is pretty
+
+ align:start position:0%
+integration is pretty
+ 
+
+ align:start position:0%
+integration is pretty
+easy
+
+ align:start position:0%
+easy
+ 
+
+ align:start position:0%
+easy
+1/8 cosine of 4X over
+
+ align:start position:0%
+1/8 cosine of 4X over
+ 
+
+ align:start position:0%
+1/8 cosine of 4X over
+8 DX which is okay the 18 is going to
+
+ align:start position:0%
+8 DX which is okay the 18 is going to
+ 
+
+ align:start position:0%
+8 DX which is okay the 18 is going to
+give me x
+
+ align:start position:0%
+give me x
+ 
+
+ align:start position:0%
+give me x
+8 the integral of cosine is plus or
+
+ align:start position:0%
+8 the integral of cosine is plus or
+ 
+
+ align:start position:0%
+8 the integral of cosine is plus or
+minus the
+
+ align:start position:0%
+minus the
+ 
+
+ align:start position:0%
+minus the
+sign the derivative of the sign is plus
+
+ align:start position:0%
+sign the derivative of the sign is plus
+ 
+
+ align:start position:0%
+sign the derivative of the sign is plus
+the cosine so it's going to be plus the
+
+ align:start position:0%
+the cosine so it's going to be plus the
+ 
+
+ align:start position:0%
+the cosine so it's going to be plus the
+only there's a minus here so it's going
+
+ align:start position:0%
+only there's a minus here so it's going
+ 
+
+ align:start position:0%
+only there's a minus here so it's going
+to be the sign minus the S of 4X divided
+
+ align:start position:0%
+to be the sign minus the S of 4X divided
+ 
+
+ align:start position:0%
+to be the sign minus the S of 4X divided
+by this8 but then I have an additional
+
+ align:start position:0%
+by this8 but then I have an additional
+ 
+
+ align:start position:0%
+by this8 but then I have an additional
+factor in the denominator and what's it
+
+ align:start position:0%
+factor in the denominator and what's it
+ 
+
+ align:start position:0%
+factor in the denominator and what's it
+going to be I have to put a four there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've done that calculation
+
+ align:start position:0%
+so we've done that calculation
+ 
+
+ align:start position:0%
+so we've done that calculation
+too so um any of these if you if you
+
+ align:start position:0%
+too so um any of these if you if you
+ 
+
+ align:start position:0%
+too so um any of these if you if you
+keep doing this uh kind of process these
+
+ align:start position:0%
+keep doing this uh kind of process these
+ 
+
+ align:start position:0%
+keep doing this uh kind of process these
+these two kinds of procedures uh any uh
+
+ align:start position:0%
+these two kinds of procedures uh any uh
+ 
+
+ align:start position:0%
+these two kinds of procedures uh any uh
+any you can you you can now integrate
+
+ align:start position:0%
+any you can you you can now integrate
+ 
+
+ align:start position:0%
+any you can you you can now integrate
+any um expression that has a power of a
+
+ align:start position:0%
+any um expression that has a power of a
+ 
+
+ align:start position:0%
+any um expression that has a power of a
+sign times a power of a cosine in it by
+
+ align:start position:0%
+sign times a power of a cosine in it by
+ 
+
+ align:start position:0%
+sign times a power of a cosine in it by
+using these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas now let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh Leah let me give you an alternate
+
+ align:start position:0%
+oh Leah let me give you an alternate
+ 
+
+ align:start position:0%
+oh Leah let me give you an alternate
+method for for this last one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I know what I'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do let me give an alternate method for
+
+ align:start position:0%
+do let me give an alternate method for
+ 
+
+ align:start position:0%
+do let me give an alternate method for
+doing uh really doing the side work over
+
+ align:start position:0%
+doing uh really doing the side work over
+ 
+
+ align:start position:0%
+doing uh really doing the side work over
+there I'm TR trying to deal with sin s
+
+ align:start position:0%
+there I'm TR trying to deal with sin s
+ 
+
+ align:start position:0%
+there I'm TR trying to deal with sin s
+time cosine squ well that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+square that's the square of the S of X
+
+ align:start position:0%
+square that's the square of the S of X
+ 
+
+ align:start position:0%
+square that's the square of the S of X
+time the cosine of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x and the S of X time the cosine of x
+
+ align:start position:0%
+x and the S of X time the cosine of x
+ 
+
+ align:start position:0%
+x and the S of X time the cosine of x
+shows up right here in another trig
+
+ align:start position:0%
+shows up right here in another trig
+ 
+
+ align:start position:0%
+shows up right here in another trig
+identity so we can make use of that too
+
+ align:start position:0%
+identity so we can make use of that too
+ 
+
+ align:start position:0%
+identity so we can make use of that too
+um that reduces the number of factors of
+
+ align:start position:0%
+um that reduces the number of factors of
+ 
+
+ align:start position:0%
+um that reduces the number of factors of
+ss and cosiness by one so it's going in
+
+ align:start position:0%
+ss and cosiness by one so it's going in
+ 
+
+ align:start position:0%
+ss and cosiness by one so it's going in
+the right direction this is equal to 12
+
+ align:start position:0%
+the right direction this is equal to 12
+ 
+
+ align:start position:0%
+the right direction this is equal to 12
+s of
+
+ align:start position:0%
+s of
+ 
+
+ align:start position:0%
+s of
+2x squared right s time cosine is a half
+
+ align:start position:0%
+2x squared right s time cosine is a half
+ 
+
+ align:start position:0%
+2x squared right s time cosine is a half
+uh say this
+
+ align:start position:0%
+uh say this
+ 
+
+ align:start position:0%
+uh say this
+right it's s of 2x over two and then I
+
+ align:start position:0%
+right it's s of 2x over two and then I
+ 
+
+ align:start position:0%
+right it's s of 2x over two and then I
+want to square that so what I get is the
+
+ align:start position:0%
+want to square that so what I get is the
+ 
+
+ align:start position:0%
+want to square that so what I get is the
+s^ SAR of
+
+ align:start position:0%
+s^ SAR of
+ 
+
+ align:start position:0%
+s^ SAR of
+2x over 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is well I'm not too happy yet
+
+ align:start position:0%
+which is well I'm not too happy yet
+ 
+
+ align:start position:0%
+which is well I'm not too happy yet
+because I still have an even power
+
+ align:start position:0%
+because I still have an even power
+ 
+
+ align:start position:0%
+because I still have an even power
+remember I'm trying to integrate this
+
+ align:start position:0%
+remember I'm trying to integrate this
+ 
+
+ align:start position:0%
+remember I'm trying to integrate this
+thing in the end even powers are bad I
+
+ align:start position:0%
+thing in the end even powers are bad I
+ 
+
+ align:start position:0%
+thing in the end even powers are bad I
+try to get rid of them by using that um
+
+ align:start position:0%
+try to get rid of them by using that um
+ 
+
+ align:start position:0%
+try to get rid of them by using that um
+formula for the the half angle formula
+
+ align:start position:0%
+formula for the the half angle formula
+ 
+
+ align:start position:0%
+formula for the the half angle formula
+so I can apply that to the S of X here
+
+ align:start position:0%
+so I can apply that to the S of X here
+ 
+
+ align:start position:0%
+so I can apply that to the S of X here
+again I get one quarter of um 1us the
+
+ align:start position:0%
+again I get one quarter of um 1us the
+ 
+
+ align:start position:0%
+again I get one quarter of um 1us the
+cosine of 4X / 2 that's what the half
+
+ align:start position:0%
+cosine of 4X / 2 that's what the half
+ 
+
+ align:start position:0%
+cosine of 4X / 2 that's what the half
+angle formula says for the sin squar of
+
+ align:start position:0%
+angle formula says for the sin squar of
+ 
+
+ align:start position:0%
+angle formula says for the sin squar of
+2x and that's exactly the same as the
+
+ align:start position:0%
+2x and that's exactly the same as the
+ 
+
+ align:start position:0%
+2x and that's exactly the same as the
+expression that I got up here as
+
+ align:start position:0%
+expression that I got up here as
+ 
+
+ align:start position:0%
+expression that I got up here as
+well it's the same expression that I
+
+ align:start position:0%
+well it's the same expression that I
+ 
+
+ align:start position:0%
+well it's the same expression that I
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+there so um it's the same expression as
+
+ align:start position:0%
+there so um it's the same expression as
+ 
+
+ align:start position:0%
+there so um it's the same expression as
+I have here so this is just an alternate
+
+ align:start position:0%
+I have here so this is just an alternate
+ 
+
+ align:start position:0%
+I have here so this is just an alternate
+way to play this game of using the half
+
+ align:start position:0%
+way to play this game of using the half
+ 
+
+ align:start position:0%
+way to play this game of using the half
+angle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula okay let's do a little
+
+ align:start position:0%
+formula okay let's do a little
+ 
+
+ align:start position:0%
+formula okay let's do a little
+application of these things and uh
+
+ align:start position:0%
+application of these things and uh
+ 
+
+ align:start position:0%
+application of these things and uh
+change the change the topic a little
+
+ align:start position:0%
+change the change the topic a little
+ 
+
+ align:start position:0%
+change the change the topic a little
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit so here's the problem so this is an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+application and
+
+ align:start position:0%
+application and
+ 
+
+ align:start position:0%
+application and
+example of a real tra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substitution so here's the problem I
+
+ align:start position:0%
+substitution so here's the problem I
+ 
+
+ align:start position:0%
+substitution so here's the problem I
+want to look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at okay so I have a circle whose radius
+
+ align:start position:0%
+at okay so I have a circle whose radius
+ 
+
+ align:start position:0%
+at okay so I have a circle whose radius
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+a and I cut out from it um a sort of tab
+
+ align:start position:0%
+a and I cut out from it um a sort of tab
+ 
+
+ align:start position:0%
+a and I cut out from it um a sort of tab
+here this tab
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and the height of this thing is B
+
+ align:start position:0%
+here and the height of this thing is B
+ 
+
+ align:start position:0%
+here and the height of this thing is B
+so this this length is a number B and
+
+ align:start position:0%
+so this this length is a number B and
+ 
+
+ align:start position:0%
+so this this length is a number B and
+what I want to do is compute the area of
+
+ align:start position:0%
+what I want to do is compute the area of
+ 
+
+ align:start position:0%
+what I want to do is compute the area of
+that little
+
+ align:start position:0%
+that little
+ 
+
+ align:start position:0%
+that little
+tab that's the problem so there's an arc
+
+ align:start position:0%
+tab that's the problem so there's an arc
+ 
+
+ align:start position:0%
+tab that's the problem so there's an arc
+over here and that's what I want I want
+
+ align:start position:0%
+over here and that's what I want I want
+ 
+
+ align:start position:0%
+over here and that's what I want I want
+to find the area of this for for A and B
+
+ align:start position:0%
+to find the area of this for for A and B
+ 
+
+ align:start position:0%
+to find the area of this for for A and B
+in terms of of A and B so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area well um I guess one way to compute
+
+ align:start position:0%
+area well um I guess one way to compute
+ 
+
+ align:start position:0%
+area well um I guess one way to compute
+the area would be to take the integral
+
+ align:start position:0%
+the area would be to take the integral
+ 
+
+ align:start position:0%
+the area would be to take the integral
+of Y
+
+ align:start position:0%
+of Y
+ 
+
+ align:start position:0%
+of Y
+DX I think you've you've seen the idea
+
+ align:start position:0%
+DX I think you've you've seen the idea
+ 
+
+ align:start position:0%
+DX I think you've you've seen the idea
+of splitting this uh up into vertical
+
+ align:start position:0%
+of splitting this uh up into vertical
+ 
+
+ align:start position:0%
+of splitting this uh up into vertical
+strips um whose height is given by a
+
+ align:start position:0%
+strips um whose height is given by a
+ 
+
+ align:start position:0%
+strips um whose height is given by a
+function y of X and then you integrate
+
+ align:start position:0%
+function y of X and then you integrate
+ 
+
+ align:start position:0%
+function y of X and then you integrate
+that that's an interpretation for the
+
+ align:start position:0%
+that that's an interpretation for the
+ 
+
+ align:start position:0%
+that that's an interpretation for the
+integral the area is given by y
+
+ align:start position:0%
+integral the area is given by y
+ 
+
+ align:start position:0%
+integral the area is given by y
+DX but that's a little bit bit awkward
+
+ align:start position:0%
+DX but that's a little bit bit awkward
+ 
+
+ align:start position:0%
+DX but that's a little bit bit awkward
+because my formula for y is going to be
+
+ align:start position:0%
+because my formula for y is going to be
+ 
+
+ align:start position:0%
+because my formula for y is going to be
+a little strange it's constant value of
+
+ align:start position:0%
+a little strange it's constant value of
+ 
+
+ align:start position:0%
+a little strange it's constant value of
+b along here and then at this point it
+
+ align:start position:0%
+b along here and then at this point it
+ 
+
+ align:start position:0%
+b along here and then at this point it
+becomes this Arc of the
+
+ align:start position:0%
+becomes this Arc of the
+ 
+
+ align:start position:0%
+becomes this Arc of the
+circle so working this out I could do it
+
+ align:start position:0%
+circle so working this out I could do it
+ 
+
+ align:start position:0%
+circle so working this out I could do it
+but it's a little awkward because
+
+ align:start position:0%
+but it's a little awkward because
+ 
+
+ align:start position:0%
+but it's a little awkward because
+expressing y as a function of X the top
+
+ align:start position:0%
+expressing y as a function of X the top
+ 
+
+ align:start position:0%
+expressing y as a function of X the top
+edge of this shape it's a little awkward
+
+ align:start position:0%
+edge of this shape it's a little awkward
+ 
+
+ align:start position:0%
+edge of this shape it's a little awkward
+and it takes two different regions to
+
+ align:start position:0%
+and it takes two different regions to
+ 
+
+ align:start position:0%
+and it takes two different regions to
+express so a different way to say it is
+
+ align:start position:0%
+express so a different way to say it is
+ 
+
+ align:start position:0%
+express so a different way to say it is
+to say x Dy
+
+ align:start position:0%
+to say x Dy
+ 
+
+ align:start position:0%
+to say x Dy
+maybe that'll work a little bit better
+
+ align:start position:0%
+maybe that'll work a little bit better
+ 
+
+ align:start position:0%
+maybe that'll work a little bit better
+or maybe it won't but it's worth trying
+
+ align:start position:0%
+or maybe it won't but it's worth trying
+ 
+
+ align:start position:0%
+or maybe it won't but it's worth trying
+I could just as well split this region
+
+ align:start position:0%
+I could just as well split this region
+ 
+
+ align:start position:0%
+I could just as well split this region
+up into horizontal
+
+ align:start position:0%
+up into horizontal
+ 
+
+ align:start position:0%
+up into horizontal
+strips whose width is dy and whose
+
+ align:start position:0%
+strips whose width is dy and whose
+ 
+
+ align:start position:0%
+strips whose width is dy and whose
+length is X now I'm thinking of this as
+
+ align:start position:0%
+length is X now I'm thinking of this as
+ 
+
+ align:start position:0%
+length is X now I'm thinking of this as
+a function of Y this is the graph of a
+
+ align:start position:0%
+a function of Y this is the graph of a
+ 
+
+ align:start position:0%
+a function of Y this is the graph of a
+function of
+
+ align:start position:0%
+function of
+ 
+
+ align:start position:0%
+function of
+Y and that's much better because the
+
+ align:start position:0%
+Y and that's much better because the
+ 
+
+ align:start position:0%
+Y and that's much better because the
+function of Y is well it's the square
+
+ align:start position:0%
+function of Y is well it's the square
+ 
+
+ align:start position:0%
+function of Y is well it's the square
+root of a^2 - y^2 isn't it that's a^2
+
+ align:start position:0%
+root of a^2 - y^2 isn't it that's a^2
+ 
+
+ align:start position:0%
+root of a^2 - y^2 isn't it that's a^2
+plus x^2 + y^2 =
+
+ align:start position:0%
+plus x^2 + y^2 =
+ 
+
+ align:start position:0%
+plus x^2 + y^2 =
+A2 so that's what x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is and that's when I'm asked to
+
+ align:start position:0%
+is and that's when I'm asked to
+ 
+
+ align:start position:0%
+is and that's when I'm asked to
+integrate then the square root of a^2 -
+
+ align:start position:0%
+integrate then the square root of a^2 -
+ 
+
+ align:start position:0%
+integrate then the square root of a^2 -
+y s Dy and I can even put in limits of
+
+ align:start position:0%
+y s Dy and I can even put in limits of
+ 
+
+ align:start position:0%
+y s Dy and I can even put in limits of
+integration maybe I should do that
+
+ align:start position:0%
+integration maybe I should do that
+ 
+
+ align:start position:0%
+integration maybe I should do that
+because this is supposed to be an actual
+
+ align:start position:0%
+because this is supposed to be an actual
+ 
+
+ align:start position:0%
+because this is supposed to be an actual
+number I guess I'm integrating it from
+
+ align:start position:0%
+number I guess I'm integrating it from
+ 
+
+ align:start position:0%
+number I guess I'm integrating it from
+yal Z that's here to yal B Dy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what I want to find this is a
+
+ align:start position:0%
+so this is what I want to find this is a
+ 
+
+ align:start position:0%
+so this is what I want to find this is a
+Formula an integral formula for the area
+
+ align:start position:0%
+Formula an integral formula for the area
+ 
+
+ align:start position:0%
+Formula an integral formula for the area
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+region and this is a new form I don't
+
+ align:start position:0%
+region and this is a new form I don't
+ 
+
+ align:start position:0%
+region and this is a new form I don't
+think that uh that
+
+ align:start position:0%
+think that uh that
+ 
+
+ align:start position:0%
+think that uh that
+you've thought
+
+ align:start position:0%
+you've thought
+ 
+
+ align:start position:0%
+you've thought
+about integrating uh expressions like
+
+ align:start position:0%
+about integrating uh expressions like
+ 
+
+ align:start position:0%
+about integrating uh expressions like
+this uh in this class before so it's a
+
+ align:start position:0%
+this uh in this class before so it's a
+ 
+
+ align:start position:0%
+this uh in this class before so it's a
+new form and I want to show you how to
+
+ align:start position:0%
+new form and I want to show you how to
+ 
+
+ align:start position:0%
+new form and I want to show you how to
+do it how it's related to trigonometry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it's it's related to trigonometry
+
+ align:start position:0%
+well it's it's related to trigonometry
+ 
+
+ align:start position:0%
+well it's it's related to trigonometry
+through that exact picture that we have
+
+ align:start position:0%
+through that exact picture that we have
+ 
+
+ align:start position:0%
+through that exact picture that we have
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+Blackboard after all this a^2 minus y^2
+
+ align:start position:0%
+Blackboard after all this a^2 minus y^2
+ 
+
+ align:start position:0%
+Blackboard after all this a^2 minus y^2
+is the the formula for this Arc and so
+
+ align:start position:0%
+is the the formula for this Arc and so
+ 
+
+ align:start position:0%
+is the the formula for this Arc and so
+um what I propose is that we try to try
+
+ align:start position:0%
+um what I propose is that we try to try
+ 
+
+ align:start position:0%
+um what I propose is that we try to try
+to exploit the connection with the
+
+ align:start position:0%
+to exploit the connection with the
+ 
+
+ align:start position:0%
+to exploit the connection with the
+circle and introduce polar
+
+ align:start position:0%
+circle and introduce polar
+ 
+
+ align:start position:0%
+circle and introduce polar
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+so here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if I take and measure this
+
+ align:start position:0%
+uh if I take and measure this
+ 
+
+ align:start position:0%
+uh if I take and measure this
+angle then there are various things you
+
+ align:start position:0%
+angle then there are various things you
+ 
+
+ align:start position:0%
+angle then there are various things you
+can say like the coordinates of this
+
+ align:start position:0%
+can say like the coordinates of this
+ 
+
+ align:start position:0%
+can say like the coordinates of this
+point here are a cosine Theta a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I'm sorry it's
+
+ align:start position:0%
+well I'm sorry it's
+ 
+
+ align:start position:0%
+well I'm sorry it's
+not that's an angle but I want to call
+
+ align:start position:0%
+not that's an angle but I want to call
+ 
+
+ align:start position:0%
+not that's an angle but I want to call
+it Theta zero and in general you know
+
+ align:start position:0%
+it Theta zero and in general you know
+ 
+
+ align:start position:0%
+it Theta zero and in general you know
+that the coordinates of this point are a
+
+ align:start position:0%
+that the coordinates of this point are a
+ 
+
+ align:start position:0%
+that the coordinates of this point are a
+cosine Theta a
+
+ align:start position:0%
+cosine Theta a
+ 
+
+ align:start position:0%
+cosine Theta a
+sin Theta if the Ang if the radius is is
+
+ align:start position:0%
+sin Theta if the Ang if the radius is is
+ 
+
+ align:start position:0%
+sin Theta if the Ang if the radius is is
+a and the angle here is
+
+ align:start position:0%
+a and the angle here is
+ 
+
+ align:start position:0%
+a and the angle here is
+Theta so X is cosine of is a cosine
+
+ align:start position:0%
+Theta so X is cosine of is a cosine
+ 
+
+ align:start position:0%
+Theta so X is cosine of is a cosine
+Theta and Y is a sin Theta and just from
+
+ align:start position:0%
+Theta and Y is a sin Theta and just from
+ 
+
+ align:start position:0%
+Theta and Y is a sin Theta and just from
+looking at the geometry of the
+
+ align:start position:0%
+looking at the geometry of the
+ 
+
+ align:start position:0%
+looking at the geometry of the
+circle so let's make that substitution y
+
+ align:start position:0%
+circle so let's make that substitution y
+ 
+
+ align:start position:0%
+circle so let's make that substitution y
+equal a sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta I'm using the the picture to
+
+ align:start position:0%
+Theta I'm using the the picture to
+ 
+
+ align:start position:0%
+Theta I'm using the the picture to
+suggest that maybe making this
+
+ align:start position:0%
+suggest that maybe making this
+ 
+
+ align:start position:0%
+suggest that maybe making this
+substitution is a good thing to do let's
+
+ align:start position:0%
+substitution is a good thing to do let's
+ 
+
+ align:start position:0%
+substitution is a good thing to do let's
+follow along and see what
+
+ align:start position:0%
+follow along and see what
+ 
+
+ align:start position:0%
+follow along and see what
+happens if that's true what we're
+
+ align:start position:0%
+happens if that's true what we're
+ 
+
+ align:start position:0%
+happens if that's true what we're
+interested in is integrating a^2 minus
+
+ align:start position:0%
+interested in is integrating a^2 minus
+ 
+
+ align:start position:0%
+interested in is integrating a^2 minus
+y^2 which is a
+
+ align:start position:0%
+y^2 which is a
+ 
+
+ align:start position:0%
+y^2 which is a
+2 you're interested in integrating the
+
+ align:start position:0%
+2 you're interested in integrating the
+ 
+
+ align:start position:0%
+2 you're interested in integrating the
+square root of a^2 minus y^2 which is
+
+ align:start position:0%
+square root of a^2 minus y^2 which is
+ 
+
+ align:start position:0%
+square root of a^2 minus y^2 which is
+the square root of a^2 minus this a^ 2
+
+ align:start position:0%
+the square root of a^2 minus this a^ 2
+ 
+
+ align:start position:0%
+the square root of a^2 minus this a^ 2
+sin^2 Theta and well that's the square
+
+ align:start position:0%
+sin^2 Theta and well that's the square
+ 
+
+ align:start position:0%
+sin^2 Theta and well that's the square
+root that's equal
+
+ align:start position:0%
+root that's equal
+ 
+
+ align:start position:0%
+root that's equal
+to a * the cosine of theta right that's
+
+ align:start position:0%
+to a * the cosine of theta right that's
+ 
+
+ align:start position:0%
+to a * the cosine of theta right that's
+just a that's just sin s plus cosine squ
+
+ align:start position:0%
+just a that's just sin s plus cosine squ
+ 
+
+ align:start position:0%
+just a that's just sin s plus cosine squ
+equal 1 all over again it's also X this
+
+ align:start position:0%
+equal 1 all over again it's also X this
+ 
+
+ align:start position:0%
+equal 1 all over again it's also X this
+is X and this was X so there a lot of
+
+ align:start position:0%
+is X and this was X so there a lot of
+ 
+
+ align:start position:0%
+is X and this was X so there a lot of
+different ways to think of this but no
+
+ align:start position:0%
+different ways to think of this but no
+ 
+
+ align:start position:0%
+different ways to think of this but no
+matter how you say it the thing we're
+
+ align:start position:0%
+matter how you say it the thing we're
+ 
+
+ align:start position:0%
+matter how you say it the thing we're
+trying to integrate a^2 minus y^2 is in
+
+ align:start position:0%
+trying to integrate a^2 minus y^2 is in
+ 
+
+ align:start position:0%
+trying to integrate a^2 minus y^2 is in
+under this substitution it is a cosine
+
+ align:start position:0%
+under this substitution it is a cosine
+ 
+
+ align:start position:0%
+under this substitution it is a cosine
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+theta so I'm interested in integrating
+
+ align:start position:0%
+theta so I'm interested in integrating
+ 
+
+ align:start position:0%
+theta so I'm interested in integrating
+the square root of a squ - y^2
+
+ align:start position:0%
+the square root of a squ - y^2
+ 
+
+ align:start position:0%
+the square root of a squ - y^2
+Dy and I'm going to make this
+
+ align:start position:0%
+Dy and I'm going to make this
+ 
+
+ align:start position:0%
+Dy and I'm going to make this
+substitution Y is
+
+ align:start position:0%
+substitution Y is
+ 
+
+ align:start position:0%
+substitution Y is
+a Time the S of
+
+ align:start position:0%
+a Time the S of
+ 
+
+ align:start position:0%
+a Time the S of
+theta and so under that
+
+ align:start position:0%
+theta and so under that
+ 
+
+ align:start position:0%
+theta and so under that
+substitution I've decided that theare
+
+ align:start position:0%
+substitution I've decided that theare
+ 
+
+ align:start position:0%
+substitution I've decided that theare
+root of a^ 2us y^2 is a cosine Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+this what about the Dy well I better
+
+ align:start position:0%
+this what about the Dy well I better
+ 
+
+ align:start position:0%
+this what about the Dy well I better
+compute the
+
+ align:start position:0%
+compute the
+ 
+
+ align:start position:0%
+compute the
+Dy so Dy just differentiating this
+
+ align:start position:0%
+Dy so Dy just differentiating this
+ 
+
+ align:start position:0%
+Dy so Dy just differentiating this
+expression is a cosine
+
+ align:start position:0%
+expression is a cosine
+ 
+
+ align:start position:0%
+expression is a cosine
+Theta D
+
+ align:start position:0%
+Theta D
+ 
+
+ align:start position:0%
+Theta D
+Theta so let's put that in Dy is a
+
+ align:start position:0%
+Theta so let's put that in Dy is a
+ 
+
+ align:start position:0%
+Theta so let's put that in Dy is a
+cosine Theta D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta okay
+
+ align:start position:0%
+Theta okay
+ 
+
+ align:start position:0%
+Theta okay
+making that trig substitution y equal a
+
+ align:start position:0%
+making that trig substitution y equal a
+ 
+
+ align:start position:0%
+making that trig substitution y equal a
+sin Theta has replaced this integral
+
+ align:start position:0%
+sin Theta has replaced this integral
+ 
+
+ align:start position:0%
+sin Theta has replaced this integral
+that has a square root in it and no trig
+
+ align:start position:0%
+that has a square root in it and no trig
+ 
+
+ align:start position:0%
+that has a square root in it and no trig
+functions with an integral that involves
+
+ align:start position:0%
+functions with an integral that involves
+ 
+
+ align:start position:0%
+functions with an integral that involves
+no square roots and only trig
+
+ align:start position:0%
+no square roots and only trig
+ 
+
+ align:start position:0%
+no square roots and only trig
+functions uh in fact it's not too hard
+
+ align:start position:0%
+functions uh in fact it's not too hard
+ 
+
+ align:start position:0%
+functions uh in fact it's not too hard
+to integrate this now because of the
+
+ align:start position:0%
+to integrate this now because of the
+ 
+
+ align:start position:0%
+to integrate this now because of the
+work that we've done the a squ comes out
+
+ align:start position:0%
+work that we've done the a squ comes out
+ 
+
+ align:start position:0%
+work that we've done the a squ comes out
+this is cine 2
+
+ align:start position:0%
+this is cine 2
+ 
+
+ align:start position:0%
+this is cine 2
+Theta D Theta and maybe we've done that
+
+ align:start position:0%
+Theta D Theta and maybe we've done that
+ 
+
+ align:start position:0%
+Theta D Theta and maybe we've done that
+example already today I think we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have uh maybe we can think it through
+
+ align:start position:0%
+have uh maybe we can think it through
+ 
+
+ align:start position:0%
+have uh maybe we can think it through
+but maybe the easiest thing is to look
+
+ align:start position:0%
+but maybe the easiest thing is to look
+ 
+
+ align:start position:0%
+but maybe the easiest thing is to look
+back at notes and see what we got
+
+ align:start position:0%
+back at notes and see what we got
+ 
+
+ align:start position:0%
+back at notes and see what we got
+before that was the first example in the
+
+ align:start position:0%
+before that was the first example in the
+ 
+
+ align:start position:0%
+before that was the first example in the
+hard case that I did and what it came
+
+ align:start position:0%
+hard case that I did and what it came
+ 
+
+ align:start position:0%
+hard case that I did and what it came
+out to I used X instead of theta at the
+
+ align:start position:0%
+out to I used X instead of theta at the
+ 
+
+ align:start position:0%
+out to I used X instead of theta at the
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so we've this is a good step
+
+ align:start position:0%
+Okay so we've this is a good step
+ 
+
+ align:start position:0%
+Okay so we've this is a good step
+forward I started with this integral
+
+ align:start position:0%
+forward I started with this integral
+ 
+
+ align:start position:0%
+forward I started with this integral
+that um I really didn't know how to do
+
+ align:start position:0%
+that um I really didn't know how to do
+ 
+
+ align:start position:0%
+that um I really didn't know how to do
+by any uh means that we've had so far
+
+ align:start position:0%
+by any uh means that we've had so far
+ 
+
+ align:start position:0%
+by any uh means that we've had so far
+and I've replaced it by an a trig
+
+ align:start position:0%
+and I've replaced it by an a trig
+ 
+
+ align:start position:0%
+and I've replaced it by an a trig
+integral that we do know how to do and
+
+ align:start position:0%
+integral that we do know how to do and
+ 
+
+ align:start position:0%
+integral that we do know how to do and
+now I've done that trig
+
+ align:start position:0%
+now I've done that trig
+ 
+
+ align:start position:0%
+now I've done that trig
+integral but we're still not quite done
+
+ align:start position:0%
+integral but we're still not quite done
+ 
+
+ align:start position:0%
+integral but we're still not quite done
+because of the problem of back
+
+ align:start position:0%
+because of the problem of back
+ 
+
+ align:start position:0%
+because of the problem of back
+substituting I'd like to go back and
+
+ align:start position:0%
+substituting I'd like to go back and
+ 
+
+ align:start position:0%
+substituting I'd like to go back and
+rewrite this uh in term terms of um of
+
+ align:start position:0%
+rewrite this uh in term terms of um of
+ 
+
+ align:start position:0%
+rewrite this uh in term terms of um of
+the original variable y or I'd like to
+
+ align:start position:0%
+the original variable y or I'd like to
+ 
+
+ align:start position:0%
+the original variable y or I'd like to
+go back and rewrite it in terms of the
+
+ align:start position:0%
+go back and rewrite it in terms of the
+ 
+
+ align:start position:0%
+go back and rewrite it in terms of the
+original limits of integration that we
+
+ align:start position:0%
+original limits of integration that we
+ 
+
+ align:start position:0%
+original limits of integration that we
+had in the original
+
+ align:start position:0%
+had in the original
+ 
+
+ align:start position:0%
+had in the original
+problem in doing that it's going to be
+
+ align:start position:0%
+problem in doing that it's going to be
+ 
+
+ align:start position:0%
+problem in doing that it's going to be
+useful to rewrite this
+
+ align:start position:0%
+useful to rewrite this
+ 
+
+ align:start position:0%
+useful to rewrite this
+expression uh and get rid of the S of 2
+
+ align:start position:0%
+expression uh and get rid of the S of 2
+ 
+
+ align:start position:0%
+expression uh and get rid of the S of 2
+Theta a after all um the original y was
+
+ align:start position:0%
+Theta a after all um the original y was
+ 
+
+ align:start position:0%
+Theta a after all um the original y was
+expressed in terms of the S of theta not
+
+ align:start position:0%
+expressed in terms of the S of theta not
+ 
+
+ align:start position:0%
+expressed in terms of the S of theta not
+the S of 2 Theta so let me just do that
+
+ align:start position:0%
+the S of 2 Theta so let me just do that
+ 
+
+ align:start position:0%
+the S of 2 Theta so let me just do that
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and say that this in turn is equal to
+
+ align:start position:0%
+um and say that this in turn is equal to
+ 
+
+ align:start position:0%
+um and say that this in turn is equal to
+a^ 2 th/ 2 plus well the S of 2 Theta is
+
+ align:start position:0%
+a^ 2 th/ 2 plus well the S of 2 Theta is
+ 
+
+ align:start position:0%
+a^ 2 th/ 2 plus well the S of 2 Theta is
+um twice the S of theta times the cosine
+
+ align:start position:0%
+um twice the S of theta times the cosine
+ 
+
+ align:start position:0%
+um twice the S of theta times the cosine
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+theta and so when there's a four in the
+
+ align:start position:0%
+theta and so when there's a four in the
+ 
+
+ align:start position:0%
+theta and so when there's a four in the
+denominator what I'll get
+
+ align:start position:0%
+denominator what I'll get
+ 
+
+ align:start position:0%
+denominator what I'll get
+is s of theta cosine of theta over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I did that because I because I'm getting
+
+ align:start position:0%
+I did that because I because I'm getting
+ 
+
+ align:start position:0%
+I did that because I because I'm getting
+closer to the original terms that the
+
+ align:start position:0%
+closer to the original terms that the
+ 
+
+ align:start position:0%
+closer to the original terms that the
+problem uh started with which was s of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me write down the the the
+
+ align:start position:0%
+so let me write down the the the
+ 
+
+ align:start position:0%
+so let me write down the the the
+integral that we have now the square otk
+
+ align:start position:0%
+integral that we have now the square otk
+ 
+
+ align:start position:0%
+integral that we have now the square otk
+of a^ 2us y^2 Dy is uh so far what we
+
+ align:start position:0%
+of a^ 2us y^2 Dy is uh so far what we
+ 
+
+ align:start position:0%
+of a^ 2us y^2 Dy is uh so far what we
+know is a^2 Theta / 2
+
+ align:start position:0%
+know is a^2 Theta / 2
+ 
+
+ align:start position:0%
+know is a^2 Theta / 2
+plus sin Theta cosine Theta over
+
+ align:start position:0%
+plus sin Theta cosine Theta over
+ 
+
+ align:start position:0%
+plus sin Theta cosine Theta over
+two plus
+
+ align:start position:0%
+two plus
+ 
+
+ align:start position:0%
+two plus
+C but I want to go back and rewrite this
+
+ align:start position:0%
+C but I want to go back and rewrite this
+ 
+
+ align:start position:0%
+C but I want to go back and rewrite this
+in terms of the original value the
+
+ align:start position:0%
+in terms of the original value the
+ 
+
+ align:start position:0%
+in terms of the original value the
+original variable y well what is Theta
+
+ align:start position:0%
+original variable y well what is Theta
+ 
+
+ align:start position:0%
+original variable y well what is Theta
+in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y let's see Y in terms of theta was
+
+ align:start position:0%
+Y let's see Y in terms of theta was
+ 
+
+ align:start position:0%
+Y let's see Y in terms of theta was
+given like this so what is Theta in
+
+ align:start position:0%
+given like this so what is Theta in
+ 
+
+ align:start position:0%
+given like this so what is Theta in
+terms of Y ah so here the Fearsome arc
+
+ align:start position:0%
+terms of Y ah so here the Fearsome arc
+ 
+
+ align:start position:0%
+terms of Y ah so here the Fearsome arc
+sign rears its head right Theta is the
+
+ align:start position:0%
+sign rears its head right Theta is the
+ 
+
+ align:start position:0%
+sign rears its head right Theta is the
+angle so that y equals a sin of theta so
+
+ align:start position:0%
+angle so that y equals a sin of theta so
+ 
+
+ align:start position:0%
+angle so that y equals a sin of theta so
+that means that Theta is the arc sign or
+
+ align:start position:0%
+that means that Theta is the arc sign or
+ 
+
+ align:start position:0%
+that means that Theta is the arc sign or
+sign inverse of well y /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so that's what that's the
+
+ align:start position:0%
+a so that's what that's the
+ 
+
+ align:start position:0%
+a so that's what that's the
+first thing that shows up here Ark
+
+ align:start position:0%
+first thing that shows up here Ark
+ 
+
+ align:start position:0%
+first thing that shows up here Ark
+sign of Y over a all over two that's
+
+ align:start position:0%
+sign of Y over a all over two that's
+ 
+
+ align:start position:0%
+sign of Y over a all over two that's
+this term Theta is the ark sign of Y
+
+ align:start position:0%
+this term Theta is the ark sign of Y
+ 
+
+ align:start position:0%
+this term Theta is the ark sign of Y
+over a divided by
+
+ align:start position:0%
+over a divided by
+ 
+
+ align:start position:0%
+over a divided by
+two what about the other side here well
+
+ align:start position:0%
+two what about the other side here well
+ 
+
+ align:start position:0%
+two what about the other side here well
+s and cosine we knew what they were in
+
+ align:start position:0%
+s and cosine we knew what they were in
+ 
+
+ align:start position:0%
+s and cosine we knew what they were in
+terms of Y and in terms of x if you like
+
+ align:start position:0%
+terms of Y and in terms of x if you like
+ 
+
+ align:start position:0%
+terms of Y and in terms of x if you like
+uh s is a
+
+ align:start position:0%
+uh s is a
+ 
+
+ align:start position:0%
+uh s is a
+is actually um maybe I'll put the a squ
+
+ align:start position:0%
+is actually um maybe I'll put the a squ
+ 
+
+ align:start position:0%
+is actually um maybe I'll put the a squ
+inside here that makes a little bit
+
+ align:start position:0%
+inside here that makes a little bit
+ 
+
+ align:start position:0%
+inside here that makes a little bit
+nicer
+
+ align:start position:0%
+nicer
+ 
+
+ align:start position:0%
+nicer
+plus and then the other term is a^ 2 sin
+
+ align:start position:0%
+plus and then the other term is a^ 2 sin
+ 
+
+ align:start position:0%
+plus and then the other term is a^ 2 sin
+of theta cosine of theta so the a * s of
+
+ align:start position:0%
+of theta cosine of theta so the a * s of
+ 
+
+ align:start position:0%
+of theta cosine of theta so the a * s of
+theta is just y maybe I'll write this a
+
+ align:start position:0%
+theta is just y maybe I'll write this a
+ 
+
+ align:start position:0%
+theta is just y maybe I'll write this a
+s of theta a cosine of theta over two
+
+ align:start position:0%
+s of theta a cosine of theta over two
+ 
+
+ align:start position:0%
+s of theta a cosine of theta over two
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+C and so I get the same thing and now
+
+ align:start position:0%
+C and so I get the same thing and now
+ 
+
+ align:start position:0%
+C and so I get the same thing and now
+here a s of theta that's Y and what's
+
+ align:start position:0%
+here a s of theta that's Y and what's
+ 
+
+ align:start position:0%
+here a s of theta that's Y and what's
+the a Time the cosine of
+
+ align:start position:0%
+the a Time the cosine of
+ 
+
+ align:start position:0%
+the a Time the cosine of
+theta it's X or if you like it's the
+
+ align:start position:0%
+theta it's X or if you like it's the
+ 
+
+ align:start position:0%
+theta it's X or if you like it's the
+square root of a a^2 minus y^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 and so there I've Rewritten everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back in terms of the original variable Y
+
+ align:start position:0%
+back in terms of the original variable Y
+ 
+
+ align:start position:0%
+back in terms of the original variable Y
+and there's an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer so I've done this indefinite
+
+ align:start position:0%
+answer so I've done this indefinite
+ 
+
+ align:start position:0%
+answer so I've done this indefinite
+integration of a of a form in of of this
+
+ align:start position:0%
+integration of a of a form in of of this
+ 
+
+ align:start position:0%
+integration of a of a form in of of this
+quadratic this this uh square root of
+
+ align:start position:0%
+quadratic this this uh square root of
+ 
+
+ align:start position:0%
+quadratic this this uh square root of
+something which is a constant minus y^2
+
+ align:start position:0%
+something which is a constant minus y^2
+ 
+
+ align:start position:0%
+something which is a constant minus y^2
+whenever you see that the thing to think
+
+ align:start position:0%
+whenever you see that the thing to think
+ 
+
+ align:start position:0%
+whenever you see that the thing to think
+of is trigonometry that's going to play
+
+ align:start position:0%
+of is trigonometry that's going to play
+ 
+
+ align:start position:0%
+of is trigonometry that's going to play
+into the sin^2 plus cosine squ identity
+
+ align:start position:0%
+into the sin^2 plus cosine squ identity
+ 
+
+ align:start position:0%
+into the sin^2 plus cosine squ identity
+and the way to exploit it is to make the
+
+ align:start position:0%
+and the way to exploit it is to make the
+ 
+
+ align:start position:0%
+and the way to exploit it is to make the
+substitution y y = a sin of
+
+ align:start position:0%
+substitution y y = a sin of
+ 
+
+ align:start position:0%
+substitution y y = a sin of
+theta you could also make a substitution
+
+ align:start position:0%
+theta you could also make a substitution
+ 
+
+ align:start position:0%
+theta you could also make a substitution
+yal a cosine of theta if you wanted to
+
+ align:start position:0%
+yal a cosine of theta if you wanted to
+ 
+
+ align:start position:0%
+yal a cosine of theta if you wanted to
+and the result would come out to be
+
+ align:start position:0%
+and the result would come out to be
+ 
+
+ align:start position:0%
+and the result would come out to be
+exactly the same in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+end I'm still not quite done with the
+
+ align:start position:0%
+end I'm still not quite done with the
+ 
+
+ align:start position:0%
+end I'm still not quite done with the
+original problem that I
+
+ align:start position:0%
+original problem that I
+ 
+
+ align:start position:0%
+original problem that I
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um because the original problem asked
+
+ align:start position:0%
+um because the original problem asked
+ 
+
+ align:start position:0%
+um because the original problem asked
+for a definite integral so let's just go
+
+ align:start position:0%
+for a definite integral so let's just go
+ 
+
+ align:start position:0%
+for a definite integral so let's just go
+back and finish that as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area was the integral from 0 to B of
+
+ align:start position:0%
+area was the integral from 0 to B of
+ 
+
+ align:start position:0%
+area was the integral from 0 to B of
+this square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+root so I just want to evaluate the
+
+ align:start position:0%
+root so I just want to evaluate the
+ 
+
+ align:start position:0%
+root so I just want to evaluate the
+right hand side here the answer that we
+
+ align:start position:0%
+right hand side here the answer that we
+ 
+
+ align:start position:0%
+right hand side here the answer that we
+came up with this indefinite integral I
+
+ align:start position:0%
+came up with this indefinite integral I
+ 
+
+ align:start position:0%
+came up with this indefinite integral I
+want to evaluate it at zero and at B
+
+ align:start position:0%
+want to evaluate it at zero and at B
+ 
+
+ align:start position:0%
+want to evaluate it at zero and at B
+well let's see when I evaluate it at B I
+
+ align:start position:0%
+well let's see when I evaluate it at B I
+ 
+
+ align:start position:0%
+well let's see when I evaluate it at B I
+get a^2 times the ark
+
+ align:start position:0%
+get a^2 times the ark
+ 
+
+ align:start position:0%
+get a^2 times the ark
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+of of B over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a over
+
+ align:start position:0%
+a over
+ 
+
+ align:start position:0%
+a over
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+plus uh Y which is
+
+ align:start position:0%
+plus uh Y which is
+ 
+
+ align:start position:0%
+plus uh Y which is
+btimes the sare < TK of a^ 2 minus b^2
+
+ align:start position:0%
+btimes the sare < TK of a^ 2 minus b^2
+ 
+
+ align:start position:0%
+btimes the sare < TK of a^ 2 minus b^2
+putting y equal to B divided by
+
+ align:start position:0%
+putting y equal to B divided by
+ 
+
+ align:start position:0%
+putting y equal to B divided by
+two so I've plugged in yals B into that
+
+ align:start position:0%
+two so I've plugged in yals B into that
+ 
+
+ align:start position:0%
+two so I've plugged in yals B into that
+formula this is what I get then when I
+
+ align:start position:0%
+formula this is what I get then when I
+ 
+
+ align:start position:0%
+formula this is what I get then when I
+plug in y equals 0 well the sign of 0 is
+
+ align:start position:0%
+plug in y equals 0 well the sign of 0 is
+ 
+
+ align:start position:0%
+plug in y equals 0 well the sign of 0 is
+0 so the arc sign of 0 is 0o so this
+
+ align:start position:0%
+0 so the arc sign of 0 is 0o so this
+ 
+
+ align:start position:0%
+0 so the arc sign of 0 is 0o so this
+term goes away and when Y is equal to
+
+ align:start position:0%
+term goes away and when Y is equal to
+ 
+
+ align:start position:0%
+term goes away and when Y is equal to
+zero this term is zero also and so I
+
+ align:start position:0%
+zero this term is zero also and so I
+ 
+
+ align:start position:0%
+zero this term is zero also and so I
+don't get any subtracted terms at all so
+
+ align:start position:0%
+don't get any subtracted terms at all so
+ 
+
+ align:start position:0%
+don't get any subtracted terms at all so
+there's an expression for this notice
+
+ align:start position:0%
+there's an expression for this notice
+ 
+
+ align:start position:0%
+there's an expression for this notice
+that this Ark sign of B over
+
+ align:start position:0%
+that this Ark sign of B over
+ 
+
+ align:start position:0%
+that this Ark sign of B over
+a that's exactly this angle the ark sign
+
+ align:start position:0%
+a that's exactly this angle the ark sign
+ 
+
+ align:start position:0%
+a that's exactly this angle the ark sign
+of B over a uh it's the angle that that
+
+ align:start position:0%
+of B over a uh it's the angle that that
+ 
+
+ align:start position:0%
+of B over a uh it's the angle that that
+you get when y equals B so this Theta is
+
+ align:start position:0%
+you get when y equals B so this Theta is
+ 
+
+ align:start position:0%
+you get when y equals B so this Theta is
+the AR
+
+ align:start position:0%
+the AR
+ 
+
+ align:start position:0%
+the AR
+sign of B over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a put this over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here that is Theta 0 that is the angle
+
+ align:start position:0%
+here that is Theta 0 that is the angle
+ 
+
+ align:start position:0%
+here that is Theta 0 that is the angle
+that the corner
+
+ align:start position:0%
+that the corner
+ 
+
+ align:start position:0%
+that the corner
+makes so I could rewrite this as a^ 2
+
+ align:start position:0%
+makes so I could rewrite this as a^ 2
+ 
+
+ align:start position:0%
+makes so I could rewrite this as a^ 2
+Theta 0 / 2 + B * the < TK of a^ 2 - b^
+
+ align:start position:0%
+Theta 0 / 2 + B * the < TK of a^ 2 - b^
+ 
+
+ align:start position:0%
+Theta 0 / 2 + B * the < TK of a^ 2 - b^
+2 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 let's just think about this for a
+
+ align:start position:0%
+2 let's just think about this for a
+ 
+
+ align:start position:0%
+2 let's just think about this for a
+minute I have these two terms in the sum
+
+ align:start position:0%
+minute I have these two terms in the sum
+ 
+
+ align:start position:0%
+minute I have these two terms in the sum
+is that reasonable the first term is a s
+
+ align:start position:0%
+is that reasonable the first term is a s
+ 
+
+ align:start position:0%
+is that reasonable the first term is a s
+that's the radius squar times this angle
+
+ align:start position:0%
+that's the radius squar times this angle
+ 
+
+ align:start position:0%
+that's the radius squar times this angle
+times a
+
+ align:start position:0%
+times a
+ 
+
+ align:start position:0%
+times a
+half well I think that is exactly the
+
+ align:start position:0%
+half well I think that is exactly the
+ 
+
+ align:start position:0%
+half well I think that is exactly the
+area of this sector a^2 thet / 2 is the
+
+ align:start position:0%
+area of this sector a^2 thet / 2 is the
+ 
+
+ align:start position:0%
+area of this sector a^2 thet / 2 is the
+formula for the area of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sector and this one this is the vertical
+
+ align:start position:0%
+sector and this one this is the vertical
+ 
+
+ align:start position:0%
+sector and this one this is the vertical
+elevation this is the horizontal B a^2
+
+ align:start position:0%
+elevation this is the horizontal B a^2
+ 
+
+ align:start position:0%
+elevation this is the horizontal B a^2
+minus b^2 is this
+
+ align:start position:0%
+minus b^2 is this
+ 
+
+ align:start position:0%
+minus b^2 is this
+distance square root of a^ 2us b^ 2 so
+
+ align:start position:0%
+distance square root of a^ 2us b^ 2 so
+ 
+
+ align:start position:0%
+distance square root of a^ 2us b^ 2 so
+the right hand term is B time theun of
+
+ align:start position:0%
+the right hand term is B time theun of
+ 
+
+ align:start position:0%
+the right hand term is B time theun of
+a^ 2us b s divided two that's the area
+
+ align:start position:0%
+a^ 2us b s divided two that's the area
+ 
+
+ align:start position:0%
+a^ 2us b s divided two that's the area
+of that triangle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so using a little bit of geometry gives
+
+ align:start position:0%
+so using a little bit of geometry gives
+ 
+
+ align:start position:0%
+so using a little bit of geometry gives
+you the same answer as all of this
+
+ align:start position:0%
+you the same answer as all of this
+ 
+
+ align:start position:0%
+you the same answer as all of this
+elaborate calculus uh uh maybe that's
+
+ align:start position:0%
+elaborate calculus uh uh maybe that's
+ 
+
+ align:start position:0%
+elaborate calculus uh uh maybe that's
+enough cause for celebration for us to
+
+ align:start position:0%
+enough cause for celebration for us to
+ 
+
+ align:start position:0%
+enough cause for celebration for us to
+quit for today
\ No newline at end of file
diff --git a/CD_HqiEdNOw.txt b/CD_HqiEdNOw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1f4de5fa2bf8d97431dd444b457bed22939be849
--- /dev/null
+++ b/CD_HqiEdNOw.txt
@@ -0,0 +1,8947 @@
+align:start position:0%
+ 
+so today we are going to move on to a
+
+ align:start position:0%
+so today we are going to move on to a
+ 
+
+ align:start position:0%
+so today we are going to move on to a
+new topic once again to remind you where
+
+ align:start position:0%
+new topic once again to remind you where
+ 
+
+ align:start position:0%
+new topic once again to remind you where
+of of the path of how we got here in
+
+ align:start position:0%
+of of the path of how we got here in
+ 
+
+ align:start position:0%
+of of the path of how we got here in
+within producer Theory we said that it's
+
+ align:start position:0%
+within producer Theory we said that it's
+ 
+
+ align:start position:0%
+within producer Theory we said that it's
+harder than consumer Theory because you
+
+ align:start position:0%
+harder than consumer Theory because you
+ 
+
+ align:start position:0%
+harder than consumer Theory because you
+don't only do the standard optimization
+
+ align:start position:0%
+don't only do the standard optimization
+ 
+
+ align:start position:0%
+don't only do the standard optimization
+the consumer Theory but you need a third
+
+ align:start position:0%
+the consumer Theory but you need a third
+ 
+
+ align:start position:0%
+the consumer Theory but you need a third
+condition you need a market structure
+
+ align:start position:0%
+condition you need a market structure
+ 
+
+ align:start position:0%
+condition you need a market structure
+condition to pin down the equilibrium
+
+ align:start position:0%
+condition to pin down the equilibrium
+ 
+
+ align:start position:0%
+condition to pin down the equilibrium
+for the last few lectures we relied on a
+
+ align:start position:0%
+for the last few lectures we relied on a
+ 
+
+ align:start position:0%
+for the last few lectures we relied on a
+particular Market structure which was
+
+ align:start position:0%
+particular Market structure which was
+ 
+
+ align:start position:0%
+particular Market structure which was
+perfect competition that allowed us to
+
+ align:start position:0%
+perfect competition that allowed us to
+ 
+
+ align:start position:0%
+perfect competition that allowed us to
+show that a perfect competition price
+
+ align:start position:0%
+show that a perfect competition price
+ 
+
+ align:start position:0%
+show that a perfect competition price
+equals marginal cost and that allowed us
+
+ align:start position:0%
+equals marginal cost and that allowed us
+ 
+
+ align:start position:0%
+equals marginal cost and that allowed us
+to solve the system for how firms choose
+
+ align:start position:0%
+to solve the system for how firms choose
+ 
+
+ align:start position:0%
+to solve the system for how firms choose
+their quantity and prices in perfect
+
+ align:start position:0%
+their quantity and prices in perfect
+ 
+
+ align:start position:0%
+their quantity and prices in perfect
+competition but as we discussed that's
+
+ align:start position:0%
+competition but as we discussed that's
+ 
+
+ align:start position:0%
+competition but as we discussed that's
+an incredibly extreme assumption and
+
+ align:start position:0%
+an incredibly extreme assumption and
+ 
+
+ align:start position:0%
+an incredibly extreme assumption and
+pretty much unrealistic for almost any
+
+ align:start position:0%
+pretty much unrealistic for almost any
+ 
+
+ align:start position:0%
+pretty much unrealistic for almost any
+Market there are some markets that more
+
+ align:start position:0%
+Market there are some markets that more
+ 
+
+ align:start position:0%
+Market there are some markets that more
+competitive than others but there's
+
+ align:start position:0%
+competitive than others but there's
+ 
+
+ align:start position:0%
+competitive than others but there's
+really no such thing as a perfectly
+
+ align:start position:0%
+really no such thing as a perfectly
+ 
+
+ align:start position:0%
+really no such thing as a perfectly
+competitive market so what we're going
+
+ align:start position:0%
+competitive market so what we're going
+ 
+
+ align:start position:0%
+competitive market so what we're going
+to do now is move on in the next few
+
+ align:start position:0%
+to do now is move on in the next few
+ 
+
+ align:start position:0%
+to do now is move on in the next few
+lectures and talk about Alternative
+
+ align:start position:0%
+lectures and talk about Alternative
+ 
+
+ align:start position:0%
+lectures and talk about Alternative
+Market structures and how they change
+
+ align:start position:0%
+Market structures and how they change
+ 
+
+ align:start position:0%
+Market structures and how they change
+the conclusions we draw this is going to
+
+ align:start position:0%
+the conclusions we draw this is going to
+ 
+
+ align:start position:0%
+the conclusions we draw this is going to
+be important for two reasons first of
+
+ align:start position:0%
+be important for two reasons first of
+ 
+
+ align:start position:0%
+be important for two reasons first of
+all it's going to be important because
+
+ align:start position:0%
+all it's going to be important because
+ 
+
+ align:start position:0%
+all it's going to be important because
+it's more
+
+ align:start position:0%
+it's more
+ 
+
+ align:start position:0%
+it's more
+realistic second of all is going be
+
+ align:start position:0%
+realistic second of all is going be
+ 
+
+ align:start position:0%
+realistic second of all is going be
+important because having established the
+
+ align:start position:0%
+important because having established the
+ 
+
+ align:start position:0%
+important because having established the
+first fundamental theorem of welfare
+
+ align:start position:0%
+first fundamental theorem of welfare
+ 
+
+ align:start position:0%
+first fundamental theorem of welfare
+economics which is the perfectly
+
+ align:start position:0%
+economics which is the perfectly
+ 
+
+ align:start position:0%
+economics which is the perfectly
+competitive outcome is the best outcome
+
+ align:start position:0%
+competitive outcome is the best outcome
+ 
+
+ align:start position:0%
+competitive outcome is the best outcome
+we're not going to talk you about why
+
+ align:start position:0%
+we're not going to talk you about why
+ 
+
+ align:start position:0%
+we're not going to talk you about why
+that doesn't work in reality and why in
+
+ align:start position:0%
+that doesn't work in reality and why in
+ 
+
+ align:start position:0%
+that doesn't work in reality and why in
+fact governments aren't just agents of
+
+ align:start position:0%
+fact governments aren't just agents of
+ 
+
+ align:start position:0%
+fact governments aren't just agents of
+chaos but can actually do good things in
+
+ align:start position:0%
+chaos but can actually do good things in
+ 
+
+ align:start position:0%
+chaos but can actually do good things in
+improving potential market failures so
+
+ align:start position:0%
+improving potential market failures so
+ 
+
+ align:start position:0%
+improving potential market failures so
+by introducing these Alternative Market
+
+ align:start position:0%
+by introducing these Alternative Market
+ 
+
+ align:start position:0%
+by introducing these Alternative Market
+structures will also juuce the concept
+
+ align:start position:0%
+structures will also juuce the concept
+ 
+
+ align:start position:0%
+structures will also juuce the concept
+of a market failure which is markets not
+
+ align:start position:0%
+of a market failure which is markets not
+ 
+
+ align:start position:0%
+of a market failure which is markets not
+working to deliver the efficient
+
+ align:start position:0%
+working to deliver the efficient
+ 
+
+ align:start position:0%
+working to deliver the efficient
+outcome so we're going to start today by
+
+ align:start position:0%
+outcome so we're going to start today by
+ 
+
+ align:start position:0%
+outcome so we're going to start today by
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+Monopoly so we're going to go from one
+
+ align:start position:0%
+Monopoly so we're going to go from one
+ 
+
+ align:start position:0%
+Monopoly so we're going to go from one
+extreme to another the one extreme we
+
+ align:start position:0%
+extreme to another the one extreme we
+ 
+
+ align:start position:0%
+extreme to another the one extreme we
+started with was a perfectly competitive
+
+ align:start position:0%
+started with was a perfectly competitive
+ 
+
+ align:start position:0%
+started with was a perfectly competitive
+market with a large number firms
+
+ align:start position:0%
+market with a large number firms
+ 
+
+ align:start position:0%
+market with a large number firms
+competing to deliver identical products
+
+ align:start position:0%
+competing to deliver identical products
+ 
+
+ align:start position:0%
+competing to deliver identical products
+we're going to move all the way to the
+
+ align:start position:0%
+we're going to move all the way to the
+ 
+
+ align:start position:0%
+we're going to move all the way to the
+Other Extreme which is Monopoly which is
+
+ align:start position:0%
+Other Extreme which is Monopoly which is
+ 
+
+ align:start position:0%
+Other Extreme which is Monopoly which is
+not the game but rather the name for a
+
+ align:start position:0%
+not the game but rather the name for a
+ 
+
+ align:start position:0%
+not the game but rather the name for a
+market with one
+
+ align:start position:0%
+market with one
+ 
+
+ align:start position:0%
+market with one
+firm that delivers all that delivers the
+
+ align:start position:0%
+firm that delivers all that delivers the
+ 
+
+ align:start position:0%
+firm that delivers all that delivers the
+goods for the entire Market s from uh
+
+ align:start position:0%
+goods for the entire Market s from uh
+ 
+
+ align:start position:0%
+goods for the entire Market s from uh
+many firms competing to one firm
+
+ align:start position:0%
+many firms competing to one firm
+ 
+
+ align:start position:0%
+many firms competing to one firm
+dominating the market and the key thing
+
+ align:start position:0%
+dominating the market and the key thing
+ 
+
+ align:start position:0%
+dominating the market and the key thing
+about Monopoly the key thing that's
+
+ align:start position:0%
+about Monopoly the key thing that's
+ 
+
+ align:start position:0%
+about Monopoly the key thing that's
+going to change is that firms are going
+
+ align:start position:0%
+going to change is that firms are going
+ 
+
+ align:start position:0%
+going to change is that firms are going
+to be price makers not just price acers
+
+ align:start position:0%
+to be price makers not just price acers
+ 
+
+ align:start position:0%
+to be price makers not just price acers
+remember in perfect competition the
+
+ align:start position:0%
+remember in perfect competition the
+ 
+
+ align:start position:0%
+remember in perfect competition the
+price was just sort of given to you from
+
+ align:start position:0%
+price was just sort of given to you from
+ 
+
+ align:start position:0%
+price was just sort of given to you from
+God it came from some market equilibrium
+
+ align:start position:0%
+God it came from some market equilibrium
+ 
+
+ align:start position:0%
+God it came from some market equilibrium
+you don't know where it came from you
+
+ align:start position:0%
+you don't know where it came from you
+ 
+
+ align:start position:0%
+you don't know where it came from you
+just knows the price and you couldn't
+
+ align:start position:0%
+just knows the price and you couldn't
+ 
+
+ align:start position:0%
+just knows the price and you couldn't
+affect it well that's kind of silly
+
+ align:start position:0%
+affect it well that's kind of silly
+ 
+
+ align:start position:0%
+affect it well that's kind of silly
+firms can obviously choose the prices
+
+ align:start position:0%
+firms can obviously choose the prices
+ 
+
+ align:start position:0%
+firms can obviously choose the prices
+they set so now we move to Monopoly
+
+ align:start position:0%
+they set so now we move to Monopoly
+ 
+
+ align:start position:0%
+they set so now we move to Monopoly
+we'll actually let firms be price price
+
+ align:start position:0%
+we'll actually let firms be price price
+ 
+
+ align:start position:0%
+we'll actually let firms be price price
+makers as well as price
+
+ align:start position:0%
+makers as well as price
+ 
+
+ align:start position:0%
+makers as well as price
+takers okay now in fact once again
+
+ align:start position:0%
+takers okay now in fact once again
+ 
+
+ align:start position:0%
+takers okay now in fact once again
+Monopoly is very extreme it's not
+
+ align:start position:0%
+Monopoly is very extreme it's not
+ 
+
+ align:start position:0%
+Monopoly is very extreme it's not
+extreme perfect competition monopolies
+
+ align:start position:0%
+extreme perfect competition monopolies
+ 
+
+ align:start position:0%
+extreme perfect competition monopolies
+do exist even if perfectly competitive
+
+ align:start position:0%
+do exist even if perfectly competitive
+ 
+
+ align:start position:0%
+do exist even if perfectly competitive
+markets don't but but it's still a
+
+ align:start position:0%
+markets don't but but it's still a
+ 
+
+ align:start position:0%
+markets don't but but it's still a
+relatively small share of reality after
+
+ align:start position:0%
+relatively small share of reality after
+ 
+
+ align:start position:0%
+relatively small share of reality after
+a couple lectures of Monopoly we'll then
+
+ align:start position:0%
+a couple lectures of Monopoly we'll then
+ 
+
+ align:start position:0%
+a couple lectures of Monopoly we'll then
+turn to the more realistic case in my
+
+ align:start position:0%
+turn to the more realistic case in my
+ 
+
+ align:start position:0%
+turn to the more realistic case in my
+favorite word in economics
+
+ align:start position:0%
+favorite word in economics
+ 
+
+ align:start position:0%
+favorite word in economics
+oligopoly which is the case of several
+
+ align:start position:0%
+oligopoly which is the case of several
+ 
+
+ align:start position:0%
+oligopoly which is the case of several
+firms competing where this competition
+
+ align:start position:0%
+firms competing where this competition
+ 
+
+ align:start position:0%
+firms competing where this competition
+but it's less than perfect competition
+
+ align:start position:0%
+but it's less than perfect competition
+ 
+
+ align:start position:0%
+but it's less than perfect competition
+and we'll come back to that but for the
+
+ align:start position:0%
+and we'll come back to that but for the
+ 
+
+ align:start position:0%
+and we'll come back to that but for the
+next two lectures we're going to move to
+
+ align:start position:0%
+next two lectures we're going to move to
+ 
+
+ align:start position:0%
+next two lectures we're going to move to
+the Other Extreme which is Monopoly okay
+
+ align:start position:0%
+the Other Extreme which is Monopoly okay
+ 
+
+ align:start position:0%
+the Other Extreme which is Monopoly okay
+and we're talk today about how
+
+ align:start position:0%
+and we're talk today about how
+ 
+
+ align:start position:0%
+and we're talk today about how
+monopolists maximize profits how to
+
+ align:start position:0%
+monopolists maximize profits how to
+ 
+
+ align:start position:0%
+monopolists maximize profits how to
+monopolis maximize
+
+ align:start position:0%
+monopolis maximize
+ 
+
+ align:start position:0%
+monopolis maximize
+profits okay well to do that we're going
+
+ align:start position:0%
+profits okay well to do that we're going
+ 
+
+ align:start position:0%
+profits okay well to do that we're going
+to turn to a
+
+ align:start position:0%
+to turn to a
+ 
+
+ align:start position:0%
+to turn to a
+concept that we've already talked about
+
+ align:start position:0%
+concept that we've already talked about
+ 
+
+ align:start position:0%
+concept that we've already talked about
+but it's been sort of meaningless so far
+
+ align:start position:0%
+but it's been sort of meaningless so far
+ 
+
+ align:start position:0%
+but it's been sort of meaningless so far
+which is the concept of marginal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+revenue the marginal revenue is the
+
+ align:start position:0%
+revenue the marginal revenue is the
+ 
+
+ align:start position:0%
+revenue the marginal revenue is the
+revenue you earn on the next unit you
+
+ align:start position:0%
+revenue you earn on the next unit you
+ 
+
+ align:start position:0%
+revenue you earn on the next unit you
+sell which in perfect competition wasn't
+
+ align:start position:0%
+sell which in perfect competition wasn't
+ 
+
+ align:start position:0%
+sell which in perfect competition wasn't
+interesting it was just the
+
+ align:start position:0%
+interesting it was just the
+ 
+
+ align:start position:0%
+interesting it was just the
+price but it's going to get more
+
+ align:start position:0%
+price but it's going to get more
+ 
+
+ align:start position:0%
+price but it's going to get more
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+today okay so we're going to talk about
+
+ align:start position:0%
+today okay so we're going to talk about
+ 
+
+ align:start position:0%
+today okay so we're going to talk about
+what happen so let's go back
+
+ align:start position:0%
+what happen so let's go back
+ 
+
+ align:start position:0%
+what happen so let's go back
+and think about a perfectly competitive
+
+ align:start position:0%
+and think about a perfectly competitive
+ 
+
+ align:start position:0%
+and think about a perfectly competitive
+firm and think about what their marginal
+
+ align:start position:0%
+firm and think about what their marginal
+ 
+
+ align:start position:0%
+firm and think about what their marginal
+revenues so in figure
+
+ align:start position:0%
+revenues so in figure
+ 
+
+ align:start position:0%
+revenues so in figure
+111 you have a perfectly competitive
+
+ align:start position:0%
+111 you have a perfectly competitive
+ 
+
+ align:start position:0%
+111 you have a perfectly competitive
+firm they The Firm M faces a perfectly
+
+ align:start position:0%
+firm they The Firm M faces a perfectly
+ 
+
+ align:start position:0%
+firm they The Firm M faces a perfectly
+elastic demand curve a perfectly
+
+ align:start position:0%
+elastic demand curve a perfectly
+ 
+
+ align:start position:0%
+elastic demand curve a perfectly
+competitive firm this doesn't mean the
+
+ align:start position:0%
+competitive firm this doesn't mean the
+ 
+
+ align:start position:0%
+competitive firm this doesn't mean the
+market demand's elastic but each firm in
+
+ align:start position:0%
+market demand's elastic but each firm in
+ 
+
+ align:start position:0%
+market demand's elastic but each firm in
+perfect competition faces a perfectly
+
+ align:start position:0%
+perfect competition faces a perfectly
+ 
+
+ align:start position:0%
+perfect competition faces a perfectly
+elastic demand curve so if they sell
+
+ align:start position:0%
+elastic demand curve so if they sell
+ 
+
+ align:start position:0%
+elastic demand curve so if they sell
+little Q units they make Revenue
+
+ align:start position:0%
+little Q units they make Revenue
+ 
+
+ align:start position:0%
+little Q units they make Revenue
+a if they sell Q plus1 units they make
+
+ align:start position:0%
+a if they sell Q plus1 units they make
+ 
+
+ align:start position:0%
+a if they sell Q plus1 units they make
+Revenue a plus b they add B well we know
+
+ align:start position:0%
+Revenue a plus b they add B well we know
+ 
+
+ align:start position:0%
+Revenue a plus b they add B well we know
+what B is the width is one and the
+
+ align:start position:0%
+what B is the width is one and the
+ 
+
+ align:start position:0%
+what B is the width is one and the
+height is the price so the marginal
+
+ align:start position:0%
+height is the price so the marginal
+ 
+
+ align:start position:0%
+height is the price so the marginal
+revenue from selling the Q plus plus one
+
+ align:start position:0%
+revenue from selling the Q plus plus one
+ 
+
+ align:start position:0%
+revenue from selling the Q plus plus one
+unit plus one
+
+ align:start position:0%
+unit plus one
+ 
+
+ align:start position:0%
+unit plus one
+unit is the price okay it's just an
+
+ align:start position:0%
+unit is the price okay it's just an
+ 
+
+ align:start position:0%
+unit is the price okay it's just an
+illustration what we learned before
+
+ align:start position:0%
+illustration what we learned before
+ 
+
+ align:start position:0%
+illustration what we learned before
+Monopoly is going to be different and in
+
+ align:start position:0%
+Monopoly is going to be different and in
+ 
+
+ align:start position:0%
+Monopoly is going to be different and in
+particular monopo is going to be
+
+ align:start position:0%
+particular monopo is going to be
+ 
+
+ align:start position:0%
+particular monopo is going to be
+different because we're going to make a
+
+ align:start position:0%
+different because we're going to make a
+ 
+
+ align:start position:0%
+different because we're going to make a
+critical
+
+ align:start position:0%
+critical
+ 
+
+ align:start position:0%
+critical
+assumption for how monopolis behave we
+
+ align:start position:0%
+assumption for how monopolis behave we
+ 
+
+ align:start position:0%
+assumption for how monopolis behave we
+are going to assume
+
+ align:start position:0%
+are going to assume
+ 
+
+ align:start position:0%
+are going to assume
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+monopolis that um we're assume that
+
+ align:start position:0%
+monopolis that um we're assume that
+ 
+
+ align:start position:0%
+monopolis that um we're assume that
+monopolis uh cannot price
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discriminate that is when a monopolis
+
+ align:start position:0%
+discriminate that is when a monopolis
+ 
+
+ align:start position:0%
+discriminate that is when a monopolis
+sets a
+
+ align:start position:0%
+sets a
+ 
+
+ align:start position:0%
+sets a
+price they set that price for All units
+
+ align:start position:0%
+price they set that price for All units
+ 
+
+ align:start position:0%
+price they set that price for All units
+they sell so monopolis sets the price
+
+ align:start position:0%
+they sell so monopolis sets the price
+ 
+
+ align:start position:0%
+they sell so monopolis sets the price
+they're price maker but it's not quite
+
+ align:start position:0%
+they're price maker but it's not quite
+ 
+
+ align:start position:0%
+they're price maker but it's not quite
+free Price setting because we're not
+
+ align:start position:0%
+free Price setting because we're not
+ 
+
+ align:start position:0%
+free Price setting because we're not
+going to let them set a different price
+
+ align:start position:0%
+going to let them set a different price
+ 
+
+ align:start position:0%
+going to let them set a different price
+to me and you when they set price they
+
+ align:start position:0%
+to me and you when they set price they
+ 
+
+ align:start position:0%
+to me and you when they set price they
+set the price for everyone so we're
+
+ align:start position:0%
+set the price for everyone so we're
+ 
+
+ align:start position:0%
+set the price for everyone so we're
+going to assume no price discrimination
+
+ align:start position:0%
+going to assume no price discrimination
+ 
+
+ align:start position:0%
+going to assume no price discrimination
+we'll come back to that but for now
+
+ align:start position:0%
+we'll come back to that but for now
+ 
+
+ align:start position:0%
+we'll come back to that but for now
+we're going to say that when I'm we're
+
+ align:start position:0%
+we're going to say that when I'm we're
+ 
+
+ align:start position:0%
+we're going to say that when I'm we're
+going to let the monopolis set his price
+
+ align:start position:0%
+going to let the monopolis set his price
+ 
+
+ align:start position:0%
+going to let the monopolis set his price
+but critically it's one price for
+
+ align:start position:0%
+but critically it's one price for
+ 
+
+ align:start position:0%
+but critically it's one price for
+everyone and you'll see in a minute why
+
+ align:start position:0%
+everyone and you'll see in a minute why
+ 
+
+ align:start position:0%
+everyone and you'll see in a minute why
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+important okay so to understand that
+
+ align:start position:0%
+important okay so to understand that
+ 
+
+ align:start position:0%
+important okay so to understand that
+let's go to figure
+
+ align:start position:0%
+let's go to figure
+ 
+
+ align:start position:0%
+let's go to figure
+112 112 is for Monopoly Market all
+
+ align:start position:0%
+112 112 is for Monopoly Market all
+ 
+
+ align:start position:0%
+112 112 is for Monopoly Market all
+that's changed
+
+ align:start position:0%
+that's changed
+ 
+
+ align:start position:0%
+that's changed
+here is that now firm demand is market
+
+ align:start position:0%
+here is that now firm demand is market
+ 
+
+ align:start position:0%
+here is that now firm demand is market
+demand
+
+ align:start position:0%
+demand
+ 
+
+ align:start position:0%
+demand
+okay with perfect competition firm
+
+ align:start position:0%
+okay with perfect competition firm
+ 
+
+ align:start position:0%
+okay with perfect competition firm
+demand was perfectly elastic because
+
+ align:start position:0%
+demand was perfectly elastic because
+ 
+
+ align:start position:0%
+demand was perfectly elastic because
+there are many firms but now firm
+
+ align:start position:0%
+there are many firms but now firm
+ 
+
+ align:start position:0%
+there are many firms but now firm
+demand's market demand and unless the
+
+ align:start position:0%
+demand's market demand and unless the
+ 
+
+ align:start position:0%
+demand's market demand and unless the
+market itself features perfectly elastic
+
+ align:start position:0%
+market itself features perfectly elastic
+ 
+
+ align:start position:0%
+market itself features perfectly elastic
+demand The Firm will now face a downward
+
+ align:start position:0%
+demand The Firm will now face a downward
+ 
+
+ align:start position:0%
+demand The Firm will now face a downward
+sloping demand curve so now little Q is
+
+ align:start position:0%
+sloping demand curve so now little Q is
+ 
+
+ align:start position:0%
+sloping demand curve so now little Q is
+Big Q you notice on the x- axis I moved
+
+ align:start position:0%
+Big Q you notice on the x- axis I moved
+ 
+
+ align:start position:0%
+Big Q you notice on the x- axis I moved
+to Big Q which we used to refer to the
+
+ align:start position:0%
+to Big Q which we used to refer to the
+ 
+
+ align:start position:0%
+to Big Q which we used to refer to the
+market well with Monopoly markets little
+
+ align:start position:0%
+market well with Monopoly markets little
+ 
+
+ align:start position:0%
+market well with Monopoly markets little
+Q is Big Q there's one firm so the firm
+
+ align:start position:0%
+Q is Big Q there's one firm so the firm
+ 
+
+ align:start position:0%
+Q is Big Q there's one firm so the firm
+is the market and that firm faces a
+
+ align:start position:0%
+is the market and that firm faces a
+ 
+
+ align:start position:0%
+is the market and that firm faces a
+downward sloping demand curve so let's
+
+ align:start position:0%
+downward sloping demand curve so let's
+ 
+
+ align:start position:0%
+downward sloping demand curve so let's
+say that firm initially wants to sell Q
+
+ align:start position:0%
+say that firm initially wants to sell Q
+ 
+
+ align:start position:0%
+say that firm initially wants to sell Q
+q1 I'm sorry want sell Q if it wants to
+
+ align:start position:0%
+q1 I'm sorry want sell Q if it wants to
+ 
+
+ align:start position:0%
+q1 I'm sorry want sell Q if it wants to
+sell
+
+ align:start position:0%
+sell
+ 
+
+ align:start position:0%
+sell
+Q it has to respect demand so if it
+
+ align:start position:0%
+Q it has to respect demand so if it
+ 
+
+ align:start position:0%
+Q it has to respect demand so if it
+wants to sell Q it's going to set the
+
+ align:start position:0%
+wants to sell Q it's going to set the
+ 
+
+ align:start position:0%
+wants to sell Q it's going to set the
+price at
+
+ align:start position:0%
+price at
+ 
+
+ align:start position:0%
+price at
+P1 a price of P1 allows them to sell Q
+
+ align:start position:0%
+P1 a price of P1 allows them to sell Q
+ 
+
+ align:start position:0%
+P1 a price of P1 allows them to sell Q
+units remember they get set the price
+
+ align:start position:0%
+units remember they get set the price
+ 
+
+ align:start position:0%
+units remember they get set the price
+now so price of P1 allows to sell Q
+
+ align:start position:0%
+now so price of P1 allows to sell Q
+ 
+
+ align:start position:0%
+now so price of P1 allows to sell Q
+units now imagine they want to sell one
+
+ align:start position:0%
+units now imagine they want to sell one
+ 
+
+ align:start position:0%
+units now imagine they want to sell one
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+unit what happens well two things happen
+
+ align:start position:0%
+unit what happens well two things happen
+ 
+
+ align:start position:0%
+unit what happens well two things happen
+okay and in particular if they want to
+
+ align:start position:0%
+okay and in particular if they want to
+ 
+
+ align:start position:0%
+okay and in particular if they want to
+sell one more
+
+ align:start position:0%
+sell one more
+ 
+
+ align:start position:0%
+sell one more
+unit okay they have to lower the
+
+ align:start position:0%
+unit okay they have to lower the
+ 
+
+ align:start position:0%
+unit okay they have to lower the
+price why because demand is downward
+
+ align:start position:0%
+price why because demand is downward
+ 
+
+ align:start position:0%
+price why because demand is downward
+sloping and there's just one price so if
+
+ align:start position:0%
+sloping and there's just one price so if
+ 
+
+ align:start position:0%
+sloping and there's just one price so if
+the monopolis wants to move from selling
+
+ align:start position:0%
+the monopolis wants to move from selling
+ 
+
+ align:start position:0%
+the monopolis wants to move from selling
+Q to selling q+ one it has to lower the
+
+ align:start position:0%
+Q to selling q+ one it has to lower the
+ 
+
+ align:start position:0%
+Q to selling q+ one it has to lower the
+price from P1 to P2 there's no choice it
+
+ align:start position:0%
+price from P1 to P2 there's no choice it
+ 
+
+ align:start position:0%
+price from P1 to P2 there's no choice it
+has to be on the demand
+
+ align:start position:0%
+has to be on the demand
+ 
+
+ align:start position:0%
+has to be on the demand
+curve so when the anopolis wants to
+
+ align:start position:0%
+curve so when the anopolis wants to
+ 
+
+ align:start position:0%
+curve so when the anopolis wants to
+sell two more two
+
+ align:start position:0%
+sell two more two
+ 
+
+ align:start position:0%
+sell two more two
+units okay the marginal revenue they get
+
+ align:start position:0%
+units okay the marginal revenue they get
+ 
+
+ align:start position:0%
+units okay the marginal revenue they get
+want sell one more unit they get the
+
+ align:start position:0%
+want sell one more unit they get the
+ 
+
+ align:start position:0%
+want sell one more unit they get the
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+B which they sell one more unit at the
+
+ align:start position:0%
+B which they sell one more unit at the
+ 
+
+ align:start position:0%
+B which they sell one more unit at the
+price P2 but they lose the amount
+
+ align:start position:0%
+price P2 but they lose the amount
+ 
+
+ align:start position:0%
+price P2 but they lose the amount
+C they get the amount B but they lose
+
+ align:start position:0%
+C they get the amount B but they lose
+ 
+
+ align:start position:0%
+C they get the amount B but they lose
+the amount C or in other words what do
+
+ align:start position:0%
+the amount C or in other words what do
+ 
+
+ align:start position:0%
+the amount C or in other words what do
+they what does a monopolis get from
+
+ align:start position:0%
+they what does a monopolis get from
+ 
+
+ align:start position:0%
+they what does a monopolis get from
+selling one more unit monopis say sells
+
+ align:start position:0%
+selling one more unit monopis say sells
+ 
+
+ align:start position:0%
+selling one more unit monopis say sells
+one more unit the monopolis gets P2
+
+ align:start position:0%
+one more unit the monopolis gets P2
+ 
+
+ align:start position:0%
+one more unit the monopolis gets P2
+minus P1
+
+ align:start position:0%
+minus P1
+ 
+
+ align:start position:0%
+minus P1
+times um I'm sorry P2
+
+ align:start position:0%
+times um I'm sorry P2
+ 
+
+ align:start position:0%
+times um I'm sorry P2
+minus P2 minus P1 minus P2 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+q1 okay the monopolist gets some money
+
+ align:start position:0%
+q1 okay the monopolist gets some money
+ 
+
+ align:start position:0%
+q1 okay the monopolist gets some money
+from selling additional unit but loses
+
+ align:start position:0%
+from selling additional unit but loses
+ 
+
+ align:start position:0%
+from selling additional unit but loses
+some money because it had to lower the
+
+ align:start position:0%
+some money because it had to lower the
+ 
+
+ align:start position:0%
+some money because it had to lower the
+price on all its previous units you
+
+ align:start position:0%
+price on all its previous units you
+ 
+
+ align:start position:0%
+price on all its previous units you
+might say that once again stop and think
+
+ align:start position:0%
+might say that once again stop and think
+ 
+
+ align:start position:0%
+might say that once again stop and think
+for me for a second it doesn't make
+
+ align:start position:0%
+for me for a second it doesn't make
+ 
+
+ align:start position:0%
+for me for a second it doesn't make
+sense why does it have to well it has to
+
+ align:start position:0%
+sense why does it have to well it has to
+ 
+
+ align:start position:0%
+sense why does it have to well it has to
+because it can only set one
+
+ align:start position:0%
+because it can only set one
+ 
+
+ align:start position:0%
+because it can only set one
+price so if it wants to set sell more
+
+ align:start position:0%
+price so if it wants to set sell more
+ 
+
+ align:start position:0%
+price so if it wants to set sell more
+it's got to set a lower price which
+
+ align:start position:0%
+it's got to set a lower price which
+ 
+
+ align:start position:0%
+it's got to set a lower price which
+means it's going to make less than all
+
+ align:start position:0%
+means it's going to make less than all
+ 
+
+ align:start position:0%
+means it's going to make less than all
+its previous
+
+ align:start position:0%
+its previous
+ 
+
+ align:start position:0%
+its previous
+units okay so basically when the
+
+ align:start position:0%
+units okay so basically when the
+ 
+
+ align:start position:0%
+units okay so basically when the
+monopolis sets the price there's now a
+
+ align:start position:0%
+monopolis sets the price there's now a
+ 
+
+ align:start position:0%
+monopolis sets the price there's now a
+tradeoff the tradeoff is if he wants to
+
+ align:start position:0%
+tradeoff the tradeoff is if he wants to
+ 
+
+ align:start position:0%
+tradeoff the tradeoff is if he wants to
+sell more he has to lower the price but
+
+ align:start position:0%
+sell more he has to lower the price but
+ 
+
+ align:start position:0%
+sell more he has to lower the price but
+in doing so the monopolis makes less
+
+ align:start position:0%
+in doing so the monopolis makes less
+ 
+
+ align:start position:0%
+in doing so the monopolis makes less
+money on the previous units they
+
+ align:start position:0%
+money on the previous units they
+ 
+
+ align:start position:0%
+money on the previous units they
+sold okay and that's because they set
+
+ align:start position:0%
+sold okay and that's because they set
+ 
+
+ align:start position:0%
+sold okay and that's because they set
+the same price price for All consumers
+
+ align:start position:0%
+the same price price for All consumers
+ 
+
+ align:start position:0%
+the same price price for All consumers
+this is the key intuition that drives
+
+ align:start position:0%
+this is the key intuition that drives
+ 
+
+ align:start position:0%
+this is the key intuition that drives
+our analysis of
+
+ align:start position:0%
+our analysis of
+ 
+
+ align:start position:0%
+our analysis of
+Monopoly okay I like to refer to
+
+ align:start position:0%
+Monopoly okay I like to refer to
+ 
+
+ align:start position:0%
+Monopoly okay I like to refer to
+this as what I call the poisoning
+
+ align:start position:0%
+this as what I call the poisoning
+ 
+
+ align:start position:0%
+this as what I call the poisoning
+effect I call it the poisoning effect
+
+ align:start position:0%
+effect I call it the poisoning effect
+ 
+
+ align:start position:0%
+effect I call it the poisoning effect
+it's just the term I like to use because
+
+ align:start position:0%
+it's just the term I like to use because
+ 
+
+ align:start position:0%
+it's just the term I like to use because
+the idea is if I want to sell one more
+
+ align:start position:0%
+the idea is if I want to sell one more
+ 
+
+ align:start position:0%
+the idea is if I want to sell one more
+unit I have to poison all my previous
+
+ align:start position:0%
+unit I have to poison all my previous
+ 
+
+ align:start position:0%
+unit I have to poison all my previous
+sales by lowering their
+
+ align:start position:0%
+sales by lowering their
+ 
+
+ align:start position:0%
+sales by lowering their
+price because I can't sell another unit
+
+ align:start position:0%
+price because I can't sell another unit
+ 
+
+ align:start position:0%
+price because I can't sell another unit
+without a lower price and if I lower
+
+ align:start position:0%
+without a lower price and if I lower
+ 
+
+ align:start position:0%
+without a lower price and if I lower
+price I make less money on my previous
+
+ align:start position:0%
+price I make less money on my previous
+ 
+
+ align:start position:0%
+price I make less money on my previous
+sales okay don't think it's a changing
+
+ align:start position:0%
+sales okay don't think it's a changing
+ 
+
+ align:start position:0%
+sales okay don't think it's a changing
+your price day by day think of this I
+
+ align:start position:0%
+your price day by day think of this I
+ 
+
+ align:start position:0%
+your price day by day think of this I
+have to set one price
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes this is the marginal this is
+
+ align:start position:0%
+yeah yes this is the marginal this is
+ 
+
+ align:start position:0%
+yeah yes this is the marginal this is
+the marginal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+revenue yeah P P1 minus P2 * q1 it's in
+
+ align:start position:0%
+revenue yeah P P1 minus P2 * q1 it's in
+ 
+
+ align:start position:0%
+revenue yeah P P1 minus P2 * q1 it's in
+parenthesis okay so basically the
+
+ align:start position:0%
+parenthesis okay so basically the
+ 
+
+ align:start position:0%
+parenthesis okay so basically the
+marginal revenue is if I if I want to
+
+ align:start position:0%
+marginal revenue is if I if I want to
+ 
+
+ align:start position:0%
+marginal revenue is if I if I want to
+sell one more unit I get P2 for that
+
+ align:start position:0%
+sell one more unit I get P2 for that
+ 
+
+ align:start position:0%
+sell one more unit I get P2 for that
+unit that's what I get for that unit but
+
+ align:start position:0%
+unit that's what I get for that unit but
+ 
+
+ align:start position:0%
+unit that's what I get for that unit but
+I give up what I was making on all the
+
+ align:start position:0%
+I give up what I was making on all the
+ 
+
+ align:start position:0%
+I give up what I was making on all the
+old units the difference in the price
+
+ align:start position:0%
+old units the difference in the price
+ 
+
+ align:start position:0%
+old units the difference in the price
+that I was making on all the old
+
+ align:start position:0%
+that I was making on all the old
+ 
+
+ align:start position:0%
+that I was making on all the old
+units okay and that is basically the
+
+ align:start position:0%
+units okay and that is basically the
+ 
+
+ align:start position:0%
+units okay and that is basically the
+definition of marginal revenue in the
+
+ align:start position:0%
+definition of marginal revenue in the
+ 
+
+ align:start position:0%
+definition of marginal revenue in the
+monopolis case so in other words more
+
+ align:start position:0%
+monopolis case so in other words more
+ 
+
+ align:start position:0%
+monopolis case so in other words more
+generally if you write Revenue as P * Q
+
+ align:start position:0%
+generally if you write Revenue as P * Q
+ 
+
+ align:start position:0%
+generally if you write Revenue as P * Q
+then marginal revenue you can write if
+
+ align:start position:0%
+then marginal revenue you can write if
+ 
+
+ align:start position:0%
+then marginal revenue you can write if
+you write P * Q the marginal revenue is
+
+ align:start position:0%
+you write P * Q the marginal revenue is
+ 
+
+ align:start position:0%
+you write P * Q the marginal revenue is
+uh Dr DQ okay if you take margin with
+
+ align:start position:0%
+uh Dr DQ okay if you take margin with
+ 
+
+ align:start position:0%
+uh Dr DQ okay if you take margin with
+respect to Q is
+
+ align:start position:0%
+respect to Q is
+ 
+
+ align:start position:0%
+respect to Q is
+Dr
+
+ align:start position:0%
+Dr
+ 
+
+ align:start position:0%
+Dr
+DQ well that equals P plus
+
+ align:start position:0%
+DQ well that equals P plus
+ 
+
+ align:start position:0%
+DQ well that equals P plus
+d p DQ time
+
+ align:start position:0%
+d p DQ time
+ 
+
+ align:start position:0%
+d p DQ time
+Q so when you want to sell one more unit
+
+ align:start position:0%
+Q so when you want to sell one more unit
+ 
+
+ align:start position:0%
+Q so when you want to sell one more unit
+if I the marginal revenue there's a
+
+ align:start position:0%
+if I the marginal revenue there's a
+ 
+
+ align:start position:0%
+if I the marginal revenue there's a
+positive term which I sell one more unit
+
+ align:start position:0%
+positive term which I sell one more unit
+ 
+
+ align:start position:0%
+positive term which I sell one more unit
+but there's a negative term which is I
+
+ align:start position:0%
+but there's a negative term which is I
+ 
+
+ align:start position:0%
+but there's a negative term which is I
+had to lower my price to sell that
+
+ align:start position:0%
+had to lower my price to sell that
+ 
+
+ align:start position:0%
+had to lower my price to sell that
+unit so when I'm setting my price I have
+
+ align:start position:0%
+unit so when I'm setting my price I have
+ 
+
+ align:start position:0%
+unit so when I'm setting my price I have
+to trade these things
+
+ align:start position:0%
+to trade these things
+ 
+
+ align:start position:0%
+to trade these things
+off okay I have to trade these things
+
+ align:start position:0%
+off okay I have to trade these things
+ 
+
+ align:start position:0%
+off okay I have to trade these things
+off which is basically that I have to
+
+ align:start position:0%
+off which is basically that I have to
+ 
+
+ align:start position:0%
+off which is basically that I have to
+trade off the fact that I'm make I'm
+
+ align:start position:0%
+trade off the fact that I'm make I'm
+ 
+
+ align:start position:0%
+trade off the fact that I'm make I'm
+going to sell more units but I'm going
+
+ align:start position:0%
+going to sell more units but I'm going
+ 
+
+ align:start position:0%
+going to sell more units but I'm going
+to make um make less money to each unit
+
+ align:start position:0%
+to make um make less money to each unit
+ 
+
+ align:start position:0%
+to make um make less money to each unit
+Why didn't the competitive firm face
+
+ align:start position:0%
+Why didn't the competitive firm face
+ 
+
+ align:start position:0%
+Why didn't the competitive firm face
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+tradeoff why why was this trade-off not
+
+ align:start position:0%
+tradeoff why why was this trade-off not
+ 
+
+ align:start position:0%
+tradeoff why why was this trade-off not
+an issue for the competitive firm
+
+ align:start position:0%
+an issue for the competitive firm
+ 
+
+ align:start position:0%
+an issue for the competitive firm
+mathematically what's different from the
+
+ align:start position:0%
+mathematically what's different from the
+ 
+
+ align:start position:0%
+mathematically what's different from the
+competitive
+
+ align:start position:0%
+competitive
+ 
+
+ align:start position:0%
+competitive
+firm yeah
+
+ align:start position:0%
+firm yeah
+ 
+
+ align:start position:0%
+firm yeah
+dpq is zero for the competitive firm
+
+ align:start position:0%
+dpq is zero for the competitive firm
+ 
+
+ align:start position:0%
+dpq is zero for the competitive firm
+because it's a price taker it can sell
+
+ align:start position:0%
+because it's a price taker it can sell
+ 
+
+ align:start position:0%
+because it's a price taker it can sell
+as much as it wants at the market
+
+ align:start position:0%
+as much as it wants at the market
+ 
+
+ align:start position:0%
+as much as it wants at the market
+price so for the competitive firm March
+
+ align:start position:0%
+price so for the competitive firm March
+ 
+
+ align:start position:0%
+price so for the competitive firm March
+revenue is just
+
+ align:start position:0%
+revenue is just
+ 
+
+ align:start position:0%
+revenue is just
+price but for the monopis that's not
+
+ align:start position:0%
+price but for the monopis that's not
+ 
+
+ align:start position:0%
+price but for the monopis that's not
+true by to sell more it has to lower the
+
+ align:start position:0%
+true by to sell more it has to lower the
+ 
+
+ align:start position:0%
+true by to sell more it has to lower the
+price okay so we can graph a monopolis
+
+ align:start position:0%
+price okay so we can graph a monopolis
+ 
+
+ align:start position:0%
+price okay so we can graph a monopolis
+marginal revenue curve and we'll do that
+
+ align:start position:0%
+marginal revenue curve and we'll do that
+ 
+
+ align:start position:0%
+marginal revenue curve and we'll do that
+in figure 113 so let's go through the
+
+ align:start position:0%
+in figure 113 so let's go through the
+ 
+
+ align:start position:0%
+in figure 113 so let's go through the
+math here let's do an
+
+ align:start position:0%
+math here let's do an
+ 
+
+ align:start position:0%
+math here let's do an
+example imagine we have an example where
+
+ align:start position:0%
+example imagine we have an example where
+ 
+
+ align:start position:0%
+example imagine we have an example where
+demand is described by the equation Q =
+
+ align:start position:0%
+demand is described by the equation Q =
+ 
+
+ align:start position:0%
+demand is described by the equation Q =
+24 minus P just a standard well- behaved
+
+ align:start position:0%
+24 minus P just a standard well- behaved
+ 
+
+ align:start position:0%
+24 minus P just a standard well- behaved
+demand equation you know how to derive
+
+ align:start position:0%
+demand equation you know how to derive
+ 
+
+ align:start position:0%
+demand equation you know how to derive
+that from utility okay imagine that's
+
+ align:start position:0%
+that from utility okay imagine that's
+ 
+
+ align:start position:0%
+that from utility okay imagine that's
+the demand
+
+ align:start position:0%
+the demand
+ 
+
+ align:start position:0%
+the demand
+equation well the first step to solve a
+
+ align:start position:0%
+equation well the first step to solve a
+ 
+
+ align:start position:0%
+equation well the first step to solve a
+monopoly problem is let's rewrite this
+
+ align:start position:0%
+monopoly problem is let's rewrite this
+ 
+
+ align:start position:0%
+monopoly problem is let's rewrite this
+as P equal 24 minus Q makes the math a
+
+ align:start position:0%
+as P equal 24 minus Q makes the math a
+ 
+
+ align:start position:0%
+as P equal 24 minus Q makes the math a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+easier and now let's multiply both sides
+
+ align:start position:0%
+easier and now let's multiply both sides
+ 
+
+ align:start position:0%
+easier and now let's multiply both sides
+by Q to make it a revenue equation so
+
+ align:start position:0%
+by Q to make it a revenue equation so
+ 
+
+ align:start position:0%
+by Q to make it a revenue equation so
+Revenue which is p * Q = 24 Q - Q ^2
+
+ align:start position:0%
+Revenue which is p * Q = 24 Q - Q ^2
+ 
+
+ align:start position:0%
+Revenue which is p * Q = 24 Q - Q ^2
+that's the revenue that the firm earns
+
+ align:start position:0%
+that's the revenue that the firm earns
+ 
+
+ align:start position:0%
+that's the revenue that the firm earns
+it's p which comes from demand times the
+
+ align:start position:0%
+it's p which comes from demand times the
+ 
+
+ align:start position:0%
+it's p which comes from demand times the
+amount of units sold differentiating
+
+ align:start position:0%
+amount of units sold differentiating
+ 
+
+ align:start position:0%
+amount of units sold differentiating
+this marginal revenue is 24 minus 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q that's the marginal revenue curve for
+
+ align:start position:0%
+Q that's the marginal revenue curve for
+ 
+
+ align:start position:0%
+Q that's the marginal revenue curve for
+that firm and you can see this in figure
+
+ align:start position:0%
+that firm and you can see this in figure
+ 
+
+ align:start position:0%
+that firm and you can see this in figure
+113 here we graph the demain curve
+
+ align:start position:0%
+113 here we graph the demain curve
+ 
+
+ align:start position:0%
+113 here we graph the demain curve
+that's the Blue Line the demand curve is
+
+ align:start position:0%
+that's the Blue Line the demand curve is
+ 
+
+ align:start position:0%
+that's the Blue Line the demand curve is
+just a standard demand curve where you
+
+ align:start position:0%
+just a standard demand curve where you
+ 
+
+ align:start position:0%
+just a standard demand curve where you
+can have 24 units per day at a price of
+
+ align:start position:0%
+can have 24 units per day at a price of
+ 
+
+ align:start position:0%
+can have 24 units per day at a price of
+zero and you want zero units per day at
+
+ align:start position:0%
+zero and you want zero units per day at
+ 
+
+ align:start position:0%
+zero and you want zero units per day at
+a price of
+
+ align:start position:0%
+a price of
+ 
+
+ align:start position:0%
+a price of
+24 okay and then the the marginal
+
+ align:start position:0%
+24 okay and then the the marginal
+ 
+
+ align:start position:0%
+24 okay and then the the marginal
+revenue curve is everywhere below the
+
+ align:start position:0%
+revenue curve is everywhere below the
+ 
+
+ align:start position:0%
+revenue curve is everywhere below the
+demand curve it has the same
+
+ align:start position:0%
+demand curve it has the same
+ 
+
+ align:start position:0%
+demand curve it has the same
+intersection on the y- axis but it's
+
+ align:start position:0%
+intersection on the y- axis but it's
+ 
+
+ align:start position:0%
+intersection on the y- axis but it's
+everywhere below the demand curve is the
+
+ align:start position:0%
+everywhere below the demand curve is the
+ 
+
+ align:start position:0%
+everywhere below the demand curve is the
+marginal revenue curve now um the fact
+
+ align:start position:0%
+marginal revenue curve now um the fact
+ 
+
+ align:start position:0%
+marginal revenue curve now um the fact
+that the margin Ry curve starts at the
+
+ align:start position:0%
+that the margin Ry curve starts at the
+ 
+
+ align:start position:0%
+that the margin Ry curve starts at the
+same Y intercept is not General it's
+
+ align:start position:0%
+same Y intercept is not General it's
+ 
+
+ align:start position:0%
+same Y intercept is not General it's
+only because this is linear in a
+
+ align:start position:0%
+only because this is linear in a
+ 
+
+ align:start position:0%
+only because this is linear in a
+nonlinear case the margin Ry curve can
+
+ align:start position:0%
+nonlinear case the margin Ry curve can
+ 
+
+ align:start position:0%
+nonlinear case the margin Ry curve can
+start at a different Y intercept but the
+
+ align:start position:0%
+start at a different Y intercept but the
+ 
+
+ align:start position:0%
+start at a different Y intercept but the
+fact that margin revenue is everywhere
+
+ align:start position:0%
+fact that margin revenue is everywhere
+ 
+
+ align:start position:0%
+fact that margin revenue is everywhere
+below demand is
+
+ align:start position:0%
+below demand is
+ 
+
+ align:start position:0%
+below demand is
+General margin revenue is always below
+
+ align:start position:0%
+General margin revenue is always below
+ 
+
+ align:start position:0%
+General margin revenue is always below
+demand okay because of this poisoning
+
+ align:start position:0%
+demand okay because of this poisoning
+ 
+
+ align:start position:0%
+demand okay because of this poisoning
+effect Marg revenue is always below uh
+
+ align:start position:0%
+effect Marg revenue is always below uh
+ 
+
+ align:start position:0%
+effect Marg revenue is always below uh
+demand okay questions about that this is
+
+ align:start position:0%
+demand okay questions about that this is
+ 
+
+ align:start position:0%
+demand okay questions about that this is
+not a simple intuition so questions
+
+ align:start position:0%
+not a simple intuition so questions
+ 
+
+ align:start position:0%
+not a simple intuition so questions
+about how this works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well arm with that let's talk about
+
+ align:start position:0%
+okay well arm with that let's talk about
+ 
+
+ align:start position:0%
+okay well arm with that let's talk about
+how monopolis maximize profits let's go
+
+ align:start position:0%
+how monopolis maximize profits let's go
+ 
+
+ align:start position:0%
+how monopolis maximize profits let's go
+to figure 114 figure
+
+ align:start position:0%
+to figure 114 figure
+ 
+
+ align:start position:0%
+to figure 114 figure
+114 I'm going to now add a cost function
+
+ align:start position:0%
+114 I'm going to now add a cost function
+ 
+
+ align:start position:0%
+114 I'm going to now add a cost function
+let me say that
+
+ align:start position:0%
+let me say that
+ 
+
+ align:start position:0%
+let me say that
+C equals I'm just going to assume C
+
+ align:start position:0%
+C equals I'm just going to assume C
+ 
+
+ align:start position:0%
+C equals I'm just going to assume C
+equals 12 plus
+
+ align:start position:0%
+equals 12 plus
+ 
+
+ align:start position:0%
+equals 12 plus
+q^2 I'm just making just once again you
+
+ align:start position:0%
+q^2 I'm just making just once again you
+ 
+
+ align:start position:0%
+q^2 I'm just making just once again you
+know how to derive that if I gave you
+
+ align:start position:0%
+know how to derive that if I gave you
+ 
+
+ align:start position:0%
+know how to derive that if I gave you
+production function input prices you
+
+ align:start position:0%
+production function input prices you
+ 
+
+ align:start position:0%
+production function input prices you
+could derive that okay but I'm just
+
+ align:start position:0%
+could derive that okay but I'm just
+ 
+
+ align:start position:0%
+could derive that okay but I'm just
+going to assume Cal 12+ q^2 so in that
+
+ align:start position:0%
+going to assume Cal 12+ q^2 so in that
+ 
+
+ align:start position:0%
+going to assume Cal 12+ q^2 so in that
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+what do we know we can draft we can
+
+ align:start position:0%
+what do we know we can draft we can
+ 
+
+ align:start position:0%
+what do we know we can draft we can
+graph the marginal cost marginal cost is
+
+ align:start position:0%
+graph the marginal cost marginal cost is
+ 
+
+ align:start position:0%
+graph the marginal cost marginal cost is
+just 2 Q right that's the marginal cost
+
+ align:start position:0%
+just 2 Q right that's the marginal cost
+ 
+
+ align:start position:0%
+just 2 Q right that's the marginal cost
+line in figure 114 marginal cost is 2 Q
+
+ align:start position:0%
+line in figure 114 marginal cost is 2 Q
+ 
+
+ align:start position:0%
+line in figure 114 marginal cost is 2 Q
+we can graph average total cost average
+
+ align:start position:0%
+we can graph average total cost average
+ 
+
+ align:start position:0%
+we can graph average total cost average
+variable cost and average fixed cost
+
+ align:start position:0%
+variable cost and average fixed cost
+ 
+
+ align:start position:0%
+variable cost and average fixed cost
+those are all things we learned to graph
+
+ align:start position:0%
+those are all things we learned to graph
+ 
+
+ align:start position:0%
+those are all things we learned to graph
+before we can put those all in the
+
+ align:start position:0%
+before we can put those all in the
+ 
+
+ align:start position:0%
+before we can put those all in the
+graph okay now we can solve for the
+
+ align:start position:0%
+graph okay now we can solve for the
+ 
+
+ align:start position:0%
+graph okay now we can solve for the
+Monopoly profit maximizing decision
+
+ align:start position:0%
+Monopoly profit maximizing decision
+ 
+
+ align:start position:0%
+Monopoly profit maximizing decision
+remember profit maximization always
+
+ align:start position:0%
+remember profit maximization always
+ 
+
+ align:start position:0%
+remember profit maximization always
+happens regardless of Market
+
+ align:start position:0%
+happens regardless of Market
+ 
+
+ align:start position:0%
+happens regardless of Market
+structure profit maximization happens
+
+ align:start position:0%
+structure profit maximization happens
+ 
+
+ align:start position:0%
+structure profit maximization happens
+when marginal revenue equals marginal
+
+ align:start position:0%
+when marginal revenue equals marginal
+ 
+
+ align:start position:0%
+when marginal revenue equals marginal
+cost right remember just to remind you
+
+ align:start position:0%
+cost right remember just to remind you
+ 
+
+ align:start position:0%
+cost right remember just to remind you
+profits equals Revenue Minus cost so to
+
+ align:start position:0%
+profits equals Revenue Minus cost so to
+ 
+
+ align:start position:0%
+profits equals Revenue Minus cost so to
+maximize this we say marginal revenue uh
+
+ align:start position:0%
+maximize this we say marginal revenue uh
+ 
+
+ align:start position:0%
+maximize this we say marginal revenue uh
+minus marginal cost equals zero that's
+
+ align:start position:0%
+minus marginal cost equals zero that's
+ 
+
+ align:start position:0%
+minus marginal cost equals zero that's
+how we maximize profits right so if
+
+ align:start position:0%
+how we maximize profits right so if
+ 
+
+ align:start position:0%
+how we maximize profits right so if
+profits is revenue Minus cost and
+
+ align:start position:0%
+profits is revenue Minus cost and
+ 
+
+ align:start position:0%
+profits is revenue Minus cost and
+profits are maximized or marginal rumiz
+
+ align:start position:0%
+profits are maximized or marginal rumiz
+ 
+
+ align:start position:0%
+profits are maximized or marginal rumiz
+marginal cost equals zero so the profit
+
+ align:start position:0%
+marginal cost equals zero so the profit
+ 
+
+ align:start position:0%
+marginal cost equals zero so the profit
+maximizing condition is marginal revenue
+
+ align:start position:0%
+maximizing condition is marginal revenue
+ 
+
+ align:start position:0%
+maximizing condition is marginal revenue
+equals marginal
+
+ align:start position:0%
+equals marginal
+ 
+
+ align:start position:0%
+equals marginal
+cost okay that's true with any Market
+
+ align:start position:0%
+cost okay that's true with any Market
+ 
+
+ align:start position:0%
+cost okay that's true with any Market
+structure margin re that's always profit
+
+ align:start position:0%
+structure margin re that's always profit
+ 
+
+ align:start position:0%
+structure margin re that's always profit
+maximizing well what's marginal marginal
+
+ align:start position:0%
+maximizing well what's marginal marginal
+ 
+
+ align:start position:0%
+maximizing well what's marginal marginal
+revenue here is 24 minus 2
+
+ align:start position:0%
+revenue here is 24 minus 2
+ 
+
+ align:start position:0%
+revenue here is 24 minus 2
+Q marginal cost is 2 Q oh I should have
+
+ align:start position:0%
+Q marginal cost is 2 Q oh I should have
+ 
+
+ align:start position:0%
+Q marginal cost is 2 Q oh I should have
+made this a big Q well it doesn't matter
+
+ align:start position:0%
+made this a big Q well it doesn't matter
+ 
+
+ align:start position:0%
+made this a big Q well it doesn't matter
+right because little Q is Big q but to
+
+ align:start position:0%
+right because little Q is Big q but to
+ 
+
+ align:start position:0%
+right because little Q is Big q but to
+make life easier let's make that a big
+
+ align:start position:0%
+make life easier let's make that a big
+ 
+
+ align:start position:0%
+make life easier let's make that a big
+Q so what this says is that
+
+ align:start position:0%
+Q so what this says is that
+ 
+
+ align:start position:0%
+Q so what this says is that
+qar equal
+
+ align:start position:0%
+qar equal
+ 
+
+ align:start position:0%
+qar equal
+six that the optimal Monopoly quantity
+
+ align:start position:0%
+six that the optimal Monopoly quantity
+ 
+
+ align:start position:0%
+six that the optimal Monopoly quantity
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+six and how did I do this once again not
+
+ align:start position:0%
+six and how did I do this once again not
+ 
+
+ align:start position:0%
+six and how did I do this once again not
+too hard from the perspective of your
+
+ align:start position:0%
+too hard from the perspective of your
+ 
+
+ align:start position:0%
+too hard from the perspective of your
+aome math skills I simply took the
+
+ align:start position:0%
+aome math skills I simply took the
+ 
+
+ align:start position:0%
+aome math skills I simply took the
+demand curve created a revenue
+
+ align:start position:0%
+demand curve created a revenue
+ 
+
+ align:start position:0%
+demand curve created a revenue
+equation differentiated that to get
+
+ align:start position:0%
+equation differentiated that to get
+ 
+
+ align:start position:0%
+equation differentiated that to get
+marginal revenue have a cost equation
+
+ align:start position:0%
+marginal revenue have a cost equation
+ 
+
+ align:start position:0%
+marginal revenue have a cost equation
+differentiate that to get marginal cost
+
+ align:start position:0%
+differentiate that to get marginal cost
+ 
+
+ align:start position:0%
+differentiate that to get marginal cost
+set them equal and you get
+
+ align:start position:0%
+set them equal and you get
+ 
+
+ align:start position:0%
+set them equal and you get
+qar that's all you got to do
+
+ align:start position:0%
+qar that's all you got to do
+ 
+
+ align:start position:0%
+qar that's all you got to do
+okay now what is the
+
+ align:start position:0%
+okay now what is the
+ 
+
+ align:start position:0%
+okay now what is the
+price I solve for Q but it's not obvious
+
+ align:start position:0%
+price I solve for Q but it's not obvious
+ 
+
+ align:start position:0%
+price I solve for Q but it's not obvious
+here how you get back how do you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price so what's what's what's what price
+
+ align:start position:0%
+price so what's what's what's what price
+ 
+
+ align:start position:0%
+price so what's what's what's what price
+does the monopolis set
+
+ align:start position:0%
+does the monopolis set
+ 
+
+ align:start position:0%
+does the monopolis set
+yeah why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+18 exactly so you skip the usual thing
+
+ align:start position:0%
+18 exactly so you skip the usual thing
+ 
+
+ align:start position:0%
+18 exactly so you skip the usual thing
+where someone gives the wrong answer
+
+ align:start position:0%
+where someone gives the wrong answer
+ 
+
+ align:start position:0%
+where someone gives the wrong answer
+okay people often say well look Mar cost
+
+ align:start position:0%
+okay people often say well look Mar cost
+ 
+
+ align:start position:0%
+okay people often say well look Mar cost
+equals marginal revenue the quantity six
+
+ align:start position:0%
+equals marginal revenue the quantity six
+ 
+
+ align:start position:0%
+equals marginal revenue the quantity six
+and the price is
+
+ align:start position:0%
+and the price is
+ 
+
+ align:start position:0%
+and the price is
+12 that's the typical answer you say
+
+ align:start position:0%
+12 that's the typical answer you say
+ 
+
+ align:start position:0%
+12 that's the typical answer you say
+well look if marginal cost equals
+
+ align:start position:0%
+well look if marginal cost equals
+ 
+
+ align:start position:0%
+well look if marginal cost equals
+marginal revenue it's six then you go
+
+ align:start position:0%
+marginal revenue it's six then you go
+ 
+
+ align:start position:0%
+marginal revenue it's six then you go
+over to the y- axis and it's 12 and why
+
+ align:start position:0%
+over to the y- axis and it's 12 and why
+ 
+
+ align:start position:0%
+over to the y- axis and it's 12 and why
+is that wrong that's wrong because the
+
+ align:start position:0%
+is that wrong that's wrong because the
+ 
+
+ align:start position:0%
+is that wrong that's wrong because the
+monopolis still has to respect the
+
+ align:start position:0%
+monopolis still has to respect the
+ 
+
+ align:start position:0%
+monopolis still has to respect the
+demand curve anopolis cannot charge a
+
+ align:start position:0%
+demand curve anopolis cannot charge a
+ 
+
+ align:start position:0%
+demand curve anopolis cannot charge a
+price that people aren't willing to
+
+ align:start position:0%
+price that people aren't willing to
+ 
+
+ align:start position:0%
+price that people aren't willing to
+pay okay at a price of 12 that on on the
+
+ align:start position:0%
+pay okay at a price of 12 that on on the
+ 
+
+ align:start position:0%
+pay okay at a price of 12 that on on the
+demand curve people want way more at a
+
+ align:start position:0%
+demand curve people want way more at a
+ 
+
+ align:start position:0%
+demand curve people want way more at a
+price of 12 to be on the demand could to
+
+ align:start position:0%
+price of 12 to be on the demand could to
+ 
+
+ align:start position:0%
+price of 12 to be on the demand could to
+get to price we go back to the demand
+
+ align:start position:0%
+get to price we go back to the demand
+ 
+
+ align:start position:0%
+get to price we go back to the demand
+equation Q = 20 P = 24 minus Q well I
+
+ align:start position:0%
+equation Q = 20 P = 24 minus Q well I
+ 
+
+ align:start position:0%
+equation Q = 20 P = 24 minus Q well I
+just solved for qar so P
+
+ align:start position:0%
+just solved for qar so P
+ 
+
+ align:start position:0%
+just solved for qar so P
+staral 24 minus
+
+ align:start position:0%
+staral 24 minus
+ 
+
+ align:start position:0%
+staral 24 minus
+qar equals
+
+ align:start position:0%
+qar equals
+ 
+
+ align:start position:0%
+qar equals
+18 and this is where people get screwed
+
+ align:start position:0%
+18 and this is where people get screwed
+ 
+
+ align:start position:0%
+18 and this is where people get screwed
+up in the math here okay remember the
+
+ align:start position:0%
+up in the math here okay remember the
+ 
+
+ align:start position:0%
+up in the math here okay remember the
+monopolis has to respect the demand
+
+ align:start position:0%
+monopolis has to respect the demand
+ 
+
+ align:start position:0%
+monopolis has to respect the demand
+curve they're a price taker price maker
+
+ align:start position:0%
+curve they're a price taker price maker
+ 
+
+ align:start position:0%
+curve they're a price taker price maker
+I'm sorry but a price maker within the
+
+ align:start position:0%
+I'm sorry but a price maker within the
+ 
+
+ align:start position:0%
+I'm sorry but a price maker within the
+constraints the market gives them and
+
+ align:start position:0%
+constraints the market gives them and
+ 
+
+ align:start position:0%
+constraints the market gives them and
+the constraint the market gives them is
+
+ align:start position:0%
+the constraint the market gives them is
+ 
+
+ align:start position:0%
+the constraint the market gives them is
+the demain
+
+ align:start position:0%
+the demain
+ 
+
+ align:start position:0%
+the demain
+curve so basic so the the the um profit
+
+ align:start position:0%
+curve so basic so the the the um profit
+ 
+
+ align:start position:0%
+curve so basic so the the the um profit
+maximizing point is a price of 18 and
+
+ align:start position:0%
+maximizing point is a price of 18 and
+ 
+
+ align:start position:0%
+maximizing point is a price of 18 and
+selling six units and you could see at
+
+ align:start position:0%
+selling six units and you could see at
+ 
+
+ align:start position:0%
+selling six units and you could see at
+that point what are their profits well
+
+ align:start position:0%
+that point what are their profits well
+ 
+
+ align:start position:0%
+that point what are their profits well
+the profits are price minus average cost
+
+ align:start position:0%
+the profits are price minus average cost
+ 
+
+ align:start position:0%
+the profits are price minus average cost
+well at six units average cost is
+
+ align:start position:0%
+well at six units average cost is
+ 
+
+ align:start position:0%
+well at six units average cost is
+eight so they are making 10 per
+
+ align:start position:0%
+eight so they are making 10 per
+ 
+
+ align:start position:0%
+eight so they are making 10 per
+unit times six units is 60 and that's
+
+ align:start position:0%
+unit times six units is 60 and that's
+ 
+
+ align:start position:0%
+unit times six units is 60 and that's
+their profits
+
+ align:start position:0%
+their profits
+ 
+
+ align:start position:0%
+their profits
+now you might say
+
+ align:start position:0%
+now you might say
+ 
+
+ align:start position:0%
+now you might say
+gee consumers are willing to buy a lot
+
+ align:start position:0%
+gee consumers are willing to buy a lot
+ 
+
+ align:start position:0%
+gee consumers are willing to buy a lot
+more units think about think about the
+
+ align:start position:0%
+more units think about think about the
+ 
+
+ align:start position:0%
+more units think about think about the
+seventh
+
+ align:start position:0%
+seventh
+ 
+
+ align:start position:0%
+seventh
+unit say the seventh unit well this is
+
+ align:start position:0%
+unit say the seventh unit well this is
+ 
+
+ align:start position:0%
+unit say the seventh unit well this is
+what's weird to me if you look at the
+
+ align:start position:0%
+what's weird to me if you look at the
+ 
+
+ align:start position:0%
+what's weird to me if you look at the
+seventh unit demand is above
+
+ align:start position:0%
+seventh unit demand is above
+ 
+
+ align:start position:0%
+seventh unit demand is above
+cost consumer's willingness to
+
+ align:start position:0%
+cost consumer's willingness to
+ 
+
+ align:start position:0%
+cost consumer's willingness to
+pay at the seventh unit is seven I'm
+
+ align:start position:0%
+pay at the seventh unit is seven I'm
+ 
+
+ align:start position:0%
+pay at the seventh unit is seven I'm
+sorry 17 right if you had a price if you
+
+ align:start position:0%
+sorry 17 right if you had a price if you
+ 
+
+ align:start position:0%
+sorry 17 right if you had a price if you
+had a price of seven
+
+ align:start position:0%
+had a price of seven
+ 
+
+ align:start position:0%
+had a price of seven
+uh I'm sorry if you want to sell seven
+
+ align:start position:0%
+uh I'm sorry if you want to sell seven
+ 
+
+ align:start position:0%
+uh I'm sorry if you want to sell seven
+units consumer willing to pay
+
+ align:start position:0%
+units consumer willing to pay
+ 
+
+ align:start position:0%
+units consumer willing to pay
+17 and what's the marginal cost at seven
+
+ align:start position:0%
+17 and what's the marginal cost at seven
+ 
+
+ align:start position:0%
+17 and what's the marginal cost at seven
+units well it's
+
+ align:start position:0%
+units well it's
+ 
+
+ align:start position:0%
+units well it's
+14 so this is weird marginal revenue I'm
+
+ align:start position:0%
+14 so this is weird marginal revenue I'm
+ 
+
+ align:start position:0%
+14 so this is weird marginal revenue I'm
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+price exceeds marginal cost so why don't
+
+ align:start position:0%
+price exceeds marginal cost so why don't
+ 
+
+ align:start position:0%
+price exceeds marginal cost so why don't
+they produce that seventh unit because
+
+ align:start position:0%
+they produce that seventh unit because
+ 
+
+ align:start position:0%
+they produce that seventh unit because
+of the poisoning
+
+ align:start position:0%
+of the poisoning
+ 
+
+ align:start position:0%
+of the poisoning
+effect to produce that seventh unit
+
+ align:start position:0%
+effect to produce that seventh unit
+ 
+
+ align:start position:0%
+effect to produce that seventh unit
+they'd have to lower the price to 17 to
+
+ align:start position:0%
+they'd have to lower the price to 17 to
+ 
+
+ align:start position:0%
+they'd have to lower the price to 17 to
+sell it not to to produce it to sell it
+
+ align:start position:0%
+sell it not to to produce it to sell it
+ 
+
+ align:start position:0%
+sell it not to to produce it to sell it
+lower price 17 they lower price 17 they
+
+ align:start position:0%
+lower price 17 they lower price 17 they
+ 
+
+ align:start position:0%
+lower price 17 they lower price 17 they
+make less money on the first six
+
+ align:start position:0%
+make less money on the first six
+ 
+
+ align:start position:0%
+make less money on the first six
+units indeed what are their profits if
+
+ align:start position:0%
+units indeed what are their profits if
+ 
+
+ align:start position:0%
+units indeed what are their profits if
+they sell seven well if they sell seven
+
+ align:start position:0%
+they sell seven well if they sell seven
+ 
+
+ align:start position:0%
+they sell seven well if they sell seven
+units what are their profits well they
+
+ align:start position:0%
+units what are their profits well they
+ 
+
+ align:start position:0%
+units what are their profits well they
+sell seven units profits equal seven
+
+ align:start position:0%
+sell seven units profits equal seven
+ 
+
+ align:start position:0%
+sell seven units profits equal seven
+units at a price of 17 minus costs what
+
+ align:start position:0%
+units at a price of 17 minus costs what
+ 
+
+ align:start position:0%
+units at a price of 17 minus costs what
+are their costs if they're producing
+
+ align:start position:0%
+are their costs if they're producing
+ 
+
+ align:start position:0%
+are their costs if they're producing
+seventh units well it's 12 + 7 squared
+
+ align:start position:0%
+seventh units well it's 12 + 7 squared
+ 
+
+ align:start position:0%
+seventh units well it's 12 + 7 squared
+so it's 12 + 7 squared uh so that's uh
+
+ align:start position:0%
+so it's 12 + 7 squared uh so that's uh
+ 
+
+ align:start position:0%
+so it's 12 + 7 squared uh so that's uh
+12 +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+49 and if you do the math you get
+
+ align:start position:0%
+49 and if you do the math you get
+ 
+
+ align:start position:0%
+49 and if you do the math you get
+profits are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+58 they get lower profits selling seven
+
+ align:start position:0%
+58 they get lower profits selling seven
+ 
+
+ align:start position:0%
+58 they get lower profits selling seven
+units this is crazy think about this we
+
+ align:start position:0%
+units this is crazy think about this we
+ 
+
+ align:start position:0%
+units this is crazy think about this we
+have units where people are willing to
+
+ align:start position:0%
+have units where people are willing to
+ 
+
+ align:start position:0%
+have units where people are willing to
+pay more than it costs to produce and
+
+ align:start position:0%
+pay more than it costs to produce and
+ 
+
+ align:start position:0%
+pay more than it costs to produce and
+yet to sell them monopolis will actually
+
+ align:start position:0%
+yet to sell them monopolis will actually
+ 
+
+ align:start position:0%
+yet to sell them monopolis will actually
+lower their
+
+ align:start position:0%
+lower their
+ 
+
+ align:start position:0%
+lower their
+profits That's The Power of this
+
+ align:start position:0%
+profits That's The Power of this
+ 
+
+ align:start position:0%
+profits That's The Power of this
+poisoning effect effect the reason lower
+
+ align:start position:0%
+poisoning effect effect the reason lower
+ 
+
+ align:start position:0%
+poisoning effect effect the reason lower
+their profits because they they can make
+
+ align:start position:0%
+their profits because they they can make
+ 
+
+ align:start position:0%
+their profits because they they can make
+more money by selling less at a higher
+
+ align:start position:0%
+more money by selling less at a higher
+ 
+
+ align:start position:0%
+more money by selling less at a higher
+price
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what I said they can't do that I
+
+ align:start position:0%
+yeah what I said they can't do that I
+ 
+
+ align:start position:0%
+yeah what I said they can't do that I
+just ruled that out we're going to come
+
+ align:start position:0%
+just ruled that out we're going to come
+ 
+
+ align:start position:0%
+just ruled that out we're going to come
+back to that but that's the key is don't
+
+ align:start position:0%
+back to that but that's the key is don't
+ 
+
+ align:start position:0%
+back to that but that's the key is don't
+the way I describe it is the way you
+
+ align:start position:0%
+the way I describe it is the way you
+ 
+
+ align:start position:0%
+the way I describe it is the way you
+think of the decision- making don't
+
+ align:start position:0%
+think of the decision- making don't
+ 
+
+ align:start position:0%
+think of the decision- making don't
+think of them saying I'm gon to set this
+
+ align:start position:0%
+think of them saying I'm gon to set this
+ 
+
+ align:start position:0%
+think of them saying I'm gon to set this
+for this just think I want to sell X
+
+ align:start position:0%
+for this just think I want to sell X
+ 
+
+ align:start position:0%
+for this just think I want to sell X
+units what do I have to charge so
+
+ align:start position:0%
+units what do I have to charge so
+ 
+
+ align:start position:0%
+units what do I have to charge so
+they're sitting back saying how many
+
+ align:start position:0%
+they're sitting back saying how many
+ 
+
+ align:start position:0%
+they're sitting back saying how many
+units should I produce well if I produce
+
+ align:start position:0%
+units should I produce well if I produce
+ 
+
+ align:start position:0%
+units should I produce well if I produce
+six I can sell for 18 I make 60 if I
+
+ align:start position:0%
+six I can sell for 18 I make 60 if I
+ 
+
+ align:start position:0%
+six I can sell for 18 I make 60 if I
+produce seven I sell for 17 I make 58
+
+ align:start position:0%
+produce seven I sell for 17 I make 58
+ 
+
+ align:start position:0%
+produce seven I sell for 17 I make 58
+I'm going to produce six that's the way
+
+ align:start position:0%
+I'm going to produce six that's the way
+ 
+
+ align:start position:0%
+I'm going to produce six that's the way
+they think about it okay so that is the
+
+ align:start position:0%
+they think about it okay so that is the
+ 
+
+ align:start position:0%
+they think about it okay so that is the
+power here now what does this
+
+ align:start position:0%
+power here now what does this
+ 
+
+ align:start position:0%
+power here now what does this
+mean this means that monopolists because
+
+ align:start position:0%
+mean this means that monopolists because
+ 
+
+ align:start position:0%
+mean this means that monopolists because
+they can set price have something we
+
+ align:start position:0%
+they can set price have something we
+ 
+
+ align:start position:0%
+they can set price have something we
+call Market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power monopolists have Market power what
+
+ align:start position:0%
+power monopolists have Market power what
+ 
+
+ align:start position:0%
+power monopolists have Market power what
+do I mean by
+
+ align:start position:0%
+do I mean by
+ 
+
+ align:start position:0%
+do I mean by
+that market power means that basically
+
+ align:start position:0%
+that market power means that basically
+ 
+
+ align:start position:0%
+that market power means that basically
+monopolists can make money even in the
+
+ align:start position:0%
+monopolists can make money even in the
+ 
+
+ align:start position:0%
+monopolists can make money even in the
+long run to see this let's think about
+
+ align:start position:0%
+long run to see this let's think about
+ 
+
+ align:start position:0%
+long run to see this let's think about
+um the marginal revenue expression so
+
+ align:start position:0%
+um the marginal revenue expression so
+ 
+
+ align:start position:0%
+um the marginal revenue expression so
+marginal
+
+ align:start position:0%
+marginal
+ 
+
+ align:start position:0%
+marginal
+revenue okay marginal
+
+ align:start position:0%
+revenue okay marginal
+ 
+
+ align:start position:0%
+revenue okay marginal
+revenue equals
+
+ align:start position:0%
+revenue equals
+ 
+
+ align:start position:0%
+revenue equals
+p+ DP DQ * Q
+
+ align:start position:0%
+p+ DP DQ * Q
+ 
+
+ align:start position:0%
+p+ DP DQ * Q
+now take that
+
+ align:start position:0%
+now take that
+ 
+
+ align:start position:0%
+now take that
+equation and multip and take the uh
+
+ align:start position:0%
+equation and multip and take the uh
+ 
+
+ align:start position:0%
+equation and multip and take the uh
+second term and multiply and divide by
+
+ align:start position:0%
+second term and multiply and divide by
+ 
+
+ align:start position:0%
+second term and multiply and divide by
+price so I want to take the second term
+
+ align:start position:0%
+price so I want to take the second term
+ 
+
+ align:start position:0%
+price so I want to take the second term
+I want to rewrite as P
+
+ align:start position:0%
+I want to rewrite as P
+ 
+
+ align:start position:0%
+I want to rewrite as P
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+DP
+
+ align:start position:0%
+DP
+ 
+
+ align:start position:0%
+DP
+DQ time Q over P * p i just multiply and
+
+ align:start position:0%
+DQ time Q over P * p i just multiply and
+ 
+
+ align:start position:0%
+DQ time Q over P * p i just multiply and
+divide it by
+
+ align:start position:0%
+divide it by
+ 
+
+ align:start position:0%
+divide it by
+price it's all I
+
+ align:start position:0%
+price it's all I
+ 
+
+ align:start position:0%
+price it's all I
+did can anyone tell
+
+ align:start position:0%
+did can anyone tell
+ 
+
+ align:start position:0%
+did can anyone tell
+me what this term looks
+
+ align:start position:0%
+me what this term looks
+ 
+
+ align:start position:0%
+me what this term looks
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+yeah the elasticity of demand but
+
+ align:start position:0%
+yeah the elasticity of demand but
+ 
+
+ align:start position:0%
+yeah the elasticity of demand but
+inverted this is the inverse of price
+
+ align:start position:0%
+inverted this is the inverse of price
+ 
+
+ align:start position:0%
+inverted this is the inverse of price
+elicity demand so I can rewrite marginal
+
+ align:start position:0%
+elicity demand so I can rewrite marginal
+ 
+
+ align:start position:0%
+elicity demand so I can rewrite marginal
+revenue I can rewrite marginal
+
+ align:start position:0%
+revenue I can rewrite marginal
+ 
+
+ align:start position:0%
+revenue I can rewrite marginal
+revenue as P * 1 + one over the
+
+ align:start position:0%
+revenue as P * 1 + one over the
+ 
+
+ align:start position:0%
+revenue as P * 1 + one over the
+elasticity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demand okay all I did no trick here I
+
+ align:start position:0%
+demand okay all I did no trick here I
+ 
+
+ align:start position:0%
+demand okay all I did no trick here I
+just well there's a little math trick
+
+ align:start position:0%
+just well there's a little math trick
+ 
+
+ align:start position:0%
+just well there's a little math trick
+rote margin Revenue multiply and divide
+
+ align:start position:0%
+rote margin Revenue multiply and divide
+ 
+
+ align:start position:0%
+rote margin Revenue multiply and divide
+the second term by P kept the first
+
+ align:start position:0%
+the second term by P kept the first
+ 
+
+ align:start position:0%
+the second term by P kept the first
+term then realize this is the inverse
+
+ align:start position:0%
+term then realize this is the inverse
+ 
+
+ align:start position:0%
+term then realize this is the inverse
+the elasticity of demand so I can write
+
+ align:start position:0%
+the elasticity of demand so I can write
+ 
+
+ align:start position:0%
+the elasticity of demand so I can write
+margin Revenue as P * 1 plus the inverse
+
+ align:start position:0%
+margin Revenue as P * 1 plus the inverse
+ 
+
+ align:start position:0%
+margin Revenue as P * 1 plus the inverse
+the elasticity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demand okay why is this
+
+ align:start position:0%
+demand okay why is this
+ 
+
+ align:start position:0%
+demand okay why is this
+important because what this says is the
+
+ align:start position:0%
+important because what this says is the
+ 
+
+ align:start position:0%
+important because what this says is the
+amount the ability of monopolis to make
+
+ align:start position:0%
+amount the ability of monopolis to make
+ 
+
+ align:start position:0%
+amount the ability of monopolis to make
+money depends on how elastic is the
+
+ align:start position:0%
+money depends on how elastic is the
+ 
+
+ align:start position:0%
+money depends on how elastic is the
+demand they
+
+ align:start position:0%
+demand they
+ 
+
+ align:start position:0%
+demand they
+face okay so what would happen here if
+
+ align:start position:0%
+face okay so what would happen here if
+ 
+
+ align:start position:0%
+face okay so what would happen here if
+the elasticity demand was negative
+
+ align:start position:0%
+the elasticity demand was negative
+ 
+
+ align:start position:0%
+the elasticity demand was negative
+Infinity what would marginal revenue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be if the is negative Infinity what
+
+ align:start position:0%
+be if the is negative Infinity what
+ 
+
+ align:start position:0%
+be if the is negative Infinity what
+marginal revenue
+
+ align:start position:0%
+marginal revenue
+ 
+
+ align:start position:0%
+marginal revenue
+be come on you guys your MIT students
+
+ align:start position:0%
+be come on you guys your MIT students
+ 
+
+ align:start position:0%
+be come on you guys your MIT students
+don't be shy raise your
+
+ align:start position:0%
+don't be shy raise your
+ 
+
+ align:start position:0%
+don't be shy raise your
+hand yeah P what does that sound like
+
+ align:start position:0%
+hand yeah P what does that sound like
+ 
+
+ align:start position:0%
+hand yeah P what does that sound like
+margin REM equals P we've heard that
+
+ align:start position:0%
+margin REM equals P we've heard that
+ 
+
+ align:start position:0%
+margin REM equals P we've heard that
+before that's the perfectly competitive
+
+ align:start position:0%
+before that's the perfectly competitive
+ 
+
+ align:start position:0%
+before that's the perfectly competitive
+case well perfectly competitive case
+
+ align:start position:0%
+case well perfectly competitive case
+ 
+
+ align:start position:0%
+case well perfectly competitive case
+firms face perfectly elastic demand so
+
+ align:start position:0%
+firms face perfectly elastic demand so
+ 
+
+ align:start position:0%
+firms face perfectly elastic demand so
+if demand in the market was perfectly
+
+ align:start position:0%
+if demand in the market was perfectly
+ 
+
+ align:start position:0%
+if demand in the market was perfectly
+elastic monopolis would behave just like
+
+ align:start position:0%
+elastic monopolis would behave just like
+ 
+
+ align:start position:0%
+elastic monopolis would behave just like
+perfectly competitive
+
+ align:start position:0%
+perfectly competitive
+ 
+
+ align:start position:0%
+perfectly competitive
+firms okay on the other hand as the
+
+ align:start position:0%
+firms okay on the other hand as the
+ 
+
+ align:start position:0%
+firms okay on the other hand as the
+elasticity Falls or Rises or Falls at
+
+ align:start position:0%
+elasticity Falls or Rises or Falls at
+ 
+
+ align:start position:0%
+elasticity Falls or Rises or Falls at
+absolute value but rises from Nega 50
+
+ align:start position:0%
+absolute value but rises from Nega 50
+ 
+
+ align:start position:0%
+absolute value but rises from Nega 50
+towards zero monopolists start to be
+
+ align:start position:0%
+towards zero monopolists start to be
+ 
+
+ align:start position:0%
+towards zero monopolists start to be
+able to charge more than monopolis start
+
+ align:start position:0%
+able to charge more than monopolis start
+ 
+
+ align:start position:0%
+able to charge more than monopolis start
+tab marginal revenue above the
+
+ align:start position:0%
+tab marginal revenue above the
+ 
+
+ align:start position:0%
+tab marginal revenue above the
+price okay monopolis start tab marginal
+
+ align:start position:0%
+price okay monopolis start tab marginal
+ 
+
+ align:start position:0%
+price okay monopolis start tab marginal
+revenue above the price okay so we can
+
+ align:start position:0%
+revenue above the price okay so we can
+ 
+
+ align:start position:0%
+revenue above the price okay so we can
+rewrite this let's rewrite the condition
+
+ align:start position:0%
+rewrite this let's rewrite the condition
+ 
+
+ align:start position:0%
+rewrite this let's rewrite the condition
+for profit maximization profit
+
+ align:start position:0%
+for profit maximization profit
+ 
+
+ align:start position:0%
+for profit maximization profit
+maximization is that marginal revenue
+
+ align:start position:0%
+maximization is that marginal revenue
+ 
+
+ align:start position:0%
+maximization is that marginal revenue
+which equals P * 1 + 1 over the Allis
+
+ align:start position:0%
+which equals P * 1 + 1 over the Allis
+ 
+
+ align:start position:0%
+which equals P * 1 + 1 over the Allis
+demand equals marginal
+
+ align:start position:0%
+demand equals marginal
+ 
+
+ align:start position:0%
+demand equals marginal
+cost okay that's our profit maximizing
+
+ align:start position:0%
+cost okay that's our profit maximizing
+ 
+
+ align:start position:0%
+cost okay that's our profit maximizing
+condition okay so in other words we can
+
+ align:start position:0%
+condition okay so in other words we can
+ 
+
+ align:start position:0%
+condition okay so in other words we can
+write that marginal cost over price
+
+ align:start position:0%
+write that marginal cost over price
+ 
+
+ align:start position:0%
+write that marginal cost over price
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+1 + 1
+
+ align:start position:0%
+1 + 1
+ 
+
+ align:start position:0%
+1 + 1
+Epsilon marginal cost over price equals
+
+ align:start position:0%
+Epsilon marginal cost over price equals
+ 
+
+ align:start position:0%
+Epsilon marginal cost over price equals
+1 plus uh 1 plus 1 over Epsilon now
+
+ align:start position:0%
+1 plus uh 1 plus 1 over Epsilon now
+ 
+
+ align:start position:0%
+1 plus uh 1 plus 1 over Epsilon now
+let's define something I'm going to call
+
+ align:start position:0%
+let's define something I'm going to call
+ 
+
+ align:start position:0%
+let's define something I'm going to call
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+markup the markup is how much more
+
+ align:start position:0%
+markup the markup is how much more
+ 
+
+ align:start position:0%
+markup the markup is how much more
+monopolis can charge in perfectly
+
+ align:start position:0%
+monopolis can charge in perfectly
+ 
+
+ align:start position:0%
+monopolis can charge in perfectly
+competitive firms I'm going to find the
+
+ align:start position:0%
+competitive firms I'm going to find the
+ 
+
+ align:start position:0%
+competitive firms I'm going to find the
+markup as P minus MC over P that's what
+
+ align:start position:0%
+markup as P minus MC over P that's what
+ 
+
+ align:start position:0%
+markup as P minus MC over P that's what
+we call the
+
+ align:start position:0%
+we call the
+ 
+
+ align:start position:0%
+we call the
+markup that is how much more can
+
+ align:start position:0%
+markup that is how much more can
+ 
+
+ align:start position:0%
+markup that is how much more can
+monopolis charge than competitive firms
+
+ align:start position:0%
+monopolis charge than competitive firms
+ 
+
+ align:start position:0%
+monopolis charge than competitive firms
+it's the markup well the answer is equal
+
+ align:start position:0%
+it's the markup well the answer is equal
+ 
+
+ align:start position:0%
+it's the markup well the answer is equal
+to if we do the math the answer is equal
+
+ align:start position:0%
+to if we do the math the answer is equal
+ 
+
+ align:start position:0%
+to if we do the math the answer is equal
+to minus one over the elasticity of
+
+ align:start position:0%
+to minus one over the elasticity of
+ 
+
+ align:start position:0%
+to minus one over the elasticity of
+demand if you do the math the markup is
+
+ align:start position:0%
+demand if you do the math the markup is
+ 
+
+ align:start position:0%
+demand if you do the math the markup is
+minus one over thees demand in other
+
+ align:start position:0%
+minus one over thees demand in other
+ 
+
+ align:start position:0%
+minus one over thees demand in other
+words the profits monopolis can make are
+
+ align:start position:0%
+words the profits monopolis can make are
+ 
+
+ align:start position:0%
+words the profits monopolis can make are
+inversely proportional to the elasticity
+
+ align:start position:0%
+inversely proportional to the elasticity
+ 
+
+ align:start position:0%
+inversely proportional to the elasticity
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+demand why does that make
+
+ align:start position:0%
+demand why does that make
+ 
+
+ align:start position:0%
+demand why does that make
+sense why does it makes sense that the
+
+ align:start position:0%
+sense why does it makes sense that the
+ 
+
+ align:start position:0%
+sense why does it makes sense that the
+elastic demand as markets get more in
+
+ align:start position:0%
+elastic demand as markets get more in
+ 
+
+ align:start position:0%
+elastic demand as markets get more in
+elastic monopolis make more money as
+
+ align:start position:0%
+elastic monopolis make more money as
+ 
+
+ align:start position:0%
+elastic monopolis make more money as
+markets get more elastic monopolis make
+
+ align:start position:0%
+markets get more elastic monopolis make
+ 
+
+ align:start position:0%
+markets get more elastic monopolis make
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+money why does that make
+
+ align:start position:0%
+money why does that make
+ 
+
+ align:start position:0%
+money why does that make
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah insulin the perfectly in
+
+ align:start position:0%
+yeah yeah insulin the perfectly in
+ 
+
+ align:start position:0%
+yeah yeah insulin the perfectly in
+elastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good exactly you have to buy it so given
+
+ align:start position:0%
+good exactly you have to buy it so given
+ 
+
+ align:start position:0%
+good exactly you have to buy it so given
+that they can charge ever the hell they
+
+ align:start position:0%
+that they can charge ever the hell they
+ 
+
+ align:start position:0%
+that they can charge ever the hell they
+want this is the answer to the question
+
+ align:start position:0%
+want this is the answer to the question
+ 
+
+ align:start position:0%
+want this is the answer to the question
+you might have first thought or some
+
+ align:start position:0%
+you might have first thought or some
+ 
+
+ align:start position:0%
+you might have first thought or some
+might think is well gee if a firm's a
+
+ align:start position:0%
+might think is well gee if a firm's a
+ 
+
+ align:start position:0%
+might think is well gee if a firm's a
+monopoly why don't they just charge
+
+ align:start position:0%
+monopoly why don't they just charge
+ 
+
+ align:start position:0%
+monopoly why don't they just charge
+whatever they want why do monopolists
+
+ align:start position:0%
+whatever they want why do monopolists
+ 
+
+ align:start position:0%
+whatever they want why do monopolists
+have to with they're price makers
+
+ align:start position:0%
+have to with they're price makers
+ 
+
+ align:start position:0%
+have to with they're price makers
+they're the only game in town why don't
+
+ align:start position:0%
+they're the only game in town why don't
+ 
+
+ align:start position:0%
+they're the only game in town why don't
+they just charge whatever the hell they
+
+ align:start position:0%
+they just charge whatever the hell they
+ 
+
+ align:start position:0%
+they just charge whatever the hell they
+want and the answer is because while
+
+ align:start position:0%
+want and the answer is because while
+ 
+
+ align:start position:0%
+want and the answer is because while
+people can't substitute to other firms
+
+ align:start position:0%
+people can't substitute to other firms
+ 
+
+ align:start position:0%
+people can't substitute to other firms
+they can substitute to other
+
+ align:start position:0%
+they can substitute to other
+ 
+
+ align:start position:0%
+they can substitute to other
+Goods so if it's a good if you're
+
+ align:start position:0%
+Goods so if it's a good if you're
+ 
+
+ align:start position:0%
+Goods so if it's a good if you're
+monopolizing a good with there's very
+
+ align:start position:0%
+monopolizing a good with there's very
+ 
+
+ align:start position:0%
+monopolizing a good with there's very
+good substitutes and you try to charge a
+
+ align:start position:0%
+good substitutes and you try to charge a
+ 
+
+ align:start position:0%
+good substitutes and you try to charge a
+very high price they'll just switch to
+
+ align:start position:0%
+very high price they'll just switch to
+ 
+
+ align:start position:0%
+very high price they'll just switch to
+the The
+
+ align:start position:0%
+the The
+ 
+
+ align:start position:0%
+the The
+Substitute so if the elastic demand is
+
+ align:start position:0%
+Substitute so if the elastic demand is
+ 
+
+ align:start position:0%
+Substitute so if the elastic demand is
+very large a large negative number they
+
+ align:start position:0%
+very large a large negative number they
+ 
+
+ align:start position:0%
+very large a large negative number they
+can't make much profit sure they're the
+
+ align:start position:0%
+can't make much profit sure they're the
+ 
+
+ align:start position:0%
+can't make much profit sure they're the
+only firm but if they're the only firm
+
+ align:start position:0%
+only firm but if they're the only firm
+ 
+
+ align:start position:0%
+only firm but if they're the only firm
+making spearmint gum and people are
+
+ align:start position:0%
+making spearmint gum and people are
+ 
+
+ align:start position:0%
+making spearmint gum and people are
+pretty different between spearmint gum
+
+ align:start position:0%
+pretty different between spearmint gum
+ 
+
+ align:start position:0%
+pretty different between spearmint gum
+and peppermint gum they can't charge
+
+ align:start position:0%
+and peppermint gum they can't charge
+ 
+
+ align:start position:0%
+and peppermint gum they can't charge
+outrageously high prices because people
+
+ align:start position:0%
+outrageously high prices because people
+ 
+
+ align:start position:0%
+outrageously high prices because people
+just switch to peppermint gum but if
+
+ align:start position:0%
+just switch to peppermint gum but if
+ 
+
+ align:start position:0%
+just switch to peppermint gum but if
+they're the only firm making insulin
+
+ align:start position:0%
+they're the only firm making insulin
+ 
+
+ align:start position:0%
+they're the only firm making insulin
+then they can charge an outrageously
+
+ align:start position:0%
+then they can charge an outrageously
+ 
+
+ align:start position:0%
+then they can charge an outrageously
+high price because there's nowhere to
+
+ align:start position:0%
+high price because there's nowhere to
+ 
+
+ align:start position:0%
+high price because there's nowhere to
+go so the money monopolis make monopolis
+
+ align:start position:0%
+go so the money monopolis make monopolis
+ 
+
+ align:start position:0%
+go so the money monopolis make monopolis
+in a perfect competitive market firms
+
+ align:start position:0%
+in a perfect competitive market firms
+ 
+
+ align:start position:0%
+in a perfect competitive market firms
+are disciplined by competition from
+
+ align:start position:0%
+are disciplined by competition from
+ 
+
+ align:start position:0%
+are disciplined by competition from
+other firms in a monopoly Market firms
+
+ align:start position:0%
+other firms in a monopoly Market firms
+ 
+
+ align:start position:0%
+other firms in a monopoly Market firms
+are disciplined only by the elasticity
+
+ align:start position:0%
+are disciplined only by the elasticity
+ 
+
+ align:start position:0%
+are disciplined only by the elasticity
+of demand that's the only disciplining
+
+ align:start position:0%
+of demand that's the only disciplining
+ 
+
+ align:start position:0%
+of demand that's the only disciplining
+effect on the
+
+ align:start position:0%
+effect on the
+ 
+
+ align:start position:0%
+effect on the
+firm okay so let's do a simple example
+
+ align:start position:0%
+firm okay so let's do a simple example
+ 
+
+ align:start position:0%
+firm okay so let's do a simple example
+two books you guys probably had to read
+
+ align:start position:0%
+two books you guys probably had to read
+ 
+
+ align:start position:0%
+two books you guys probably had to read
+in high school Huckleberry thin and
+
+ align:start position:0%
+in high school Huckleberry thin and
+ 
+
+ align:start position:0%
+in high school Huckleberry thin and
+Fahrenheit
+
+ align:start position:0%
+Fahrenheit
+ 
+
+ align:start position:0%
+Fahrenheit
+451 if you go on Amazon right now you
+
+ align:start position:0%
+451 if you go on Amazon right now you
+ 
+
+ align:start position:0%
+451 if you go on Amazon right now you
+can get Huckleberry fin for about four
+
+ align:start position:0%
+can get Huckleberry fin for about four
+ 
+
+ align:start position:0%
+can get Huckleberry fin for about four
+bucks in paperback or zero on
+
+ align:start position:0%
+bucks in paperback or zero on
+ 
+
+ align:start position:0%
+bucks in paperback or zero on
+Kindle uh fahren 451 is about n bucks
+
+ align:start position:0%
+Kindle uh fahren 451 is about n bucks
+ 
+
+ align:start position:0%
+Kindle uh fahren 451 is about n bucks
+and about the same on
+
+ align:start position:0%
+and about the same on
+ 
+
+ align:start position:0%
+and about the same on
+Kindle why they're both twoo old books
+
+ align:start position:0%
+Kindle why they're both twoo old books
+ 
+
+ align:start position:0%
+Kindle why they're both twoo old books
+people have to basically read them about
+
+ align:start position:0%
+people have to basically read them about
+ 
+
+ align:start position:0%
+people have to basically read them about
+the same they're all high school
+
+ align:start position:0%
+the same they're all high school
+ 
+
+ align:start position:0%
+the same they're all high school
+required books the marginal cost of
+
+ align:start position:0%
+required books the marginal cost of
+ 
+
+ align:start position:0%
+required books the marginal cost of
+production can't be that
+
+ align:start position:0%
+production can't be that
+ 
+
+ align:start position:0%
+production can't be that
+different of producing Fahrenheit for
+
+ align:start position:0%
+different of producing Fahrenheit for
+ 
+
+ align:start position:0%
+different of producing Fahrenheit for
+they're they're slightly different
+
+ align:start position:0%
+they're they're slightly different
+ 
+
+ align:start position:0%
+they're they're slightly different
+lengths but not that different certainly
+
+ align:start position:0%
+lengths but not that different certainly
+ 
+
+ align:start position:0%
+lengths but not that different certainly
+un Kindle the marginal cost of
+
+ align:start position:0%
+un Kindle the marginal cost of
+ 
+
+ align:start position:0%
+un Kindle the marginal cost of
+Productions comparable so why why is
+
+ align:start position:0%
+Productions comparable so why why is
+ 
+
+ align:start position:0%
+Productions comparable so why why is
+Fahrenheit 451 so much more expensive
+
+ align:start position:0%
+Fahrenheit 451 so much more expensive
+ 
+
+ align:start position:0%
+Fahrenheit 451 so much more expensive
+than Huckleberry Finn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do anyone
+
+ align:start position:0%
+do anyone
+ 
+
+ align:start position:0%
+do anyone
+know go ahead you have an idea any
+
+ align:start position:0%
+know go ahead you have an idea any
+ 
+
+ align:start position:0%
+know go ahead you have an idea any
+thoughts okay well the reason is because
+
+ align:start position:0%
+thoughts okay well the reason is because
+ 
+
+ align:start position:0%
+thoughts okay well the reason is because
+in the US oh yeah go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead exactly in the US we have
+
+ align:start position:0%
+ahead exactly in the US we have
+ 
+
+ align:start position:0%
+ahead exactly in the US we have
+something called copyright laws which
+
+ align:start position:0%
+something called copyright laws which
+ 
+
+ align:start position:0%
+something called copyright laws which
+say that for 75 years after the author's
+
+ align:start position:0%
+say that for 75 years after the author's
+ 
+
+ align:start position:0%
+say that for 75 years after the author's
+death only the author or his estate or
+
+ align:start position:0%
+death only the author or his estate or
+ 
+
+ align:start position:0%
+death only the author or his estate or
+her estate can approve production of the
+
+ align:start position:0%
+her estate can approve production of the
+ 
+
+ align:start position:0%
+her estate can approve production of the
+book which gives them a monopoly Mark
+
+ align:start position:0%
+book which gives them a monopoly Mark
+ 
+
+ align:start position:0%
+book which gives them a monopoly Mark
+Twain died more than 75 years ago Ray
+
+ align:start position:0%
+Twain died more than 75 years ago Ray
+ 
+
+ align:start position:0%
+Twain died more than 75 years ago Ray
+Bradberry did not so as a result there's
+
+ align:start position:0%
+Bradberry did not so as a result there's
+ 
+
+ align:start position:0%
+Bradberry did not so as a result there's
+no more Monopoly anybody with a printing
+
+ align:start position:0%
+no more Monopoly anybody with a printing
+ 
+
+ align:start position:0%
+no more Monopoly anybody with a printing
+press or whatever it is to make an ebook
+
+ align:start position:0%
+press or whatever it is to make an ebook
+ 
+
+ align:start position:0%
+press or whatever it is to make an ebook
+I don't know how you do that can make a
+
+ align:start position:0%
+I don't know how you do that can make a
+ 
+
+ align:start position:0%
+I don't know how you do that can make a
+copy Huckleberry
+
+ align:start position:0%
+copy Huckleberry
+ 
+
+ align:start position:0%
+copy Huckleberry
+Finn so it's perfectly
+
+ align:start position:0%
+Finn so it's perfectly
+ 
+
+ align:start position:0%
+Finn so it's perfectly
+competitive okay and so profits get
+
+ align:start position:0%
+competitive okay and so profits get
+ 
+
+ align:start position:0%
+competitive okay and so profits get
+driven to zero but fite 451 they still
+
+ align:start position:0%
+driven to zero but fite 451 they still
+ 
+
+ align:start position:0%
+driven to zero but fite 451 they still
+have a monopoly right so they're making
+
+ align:start position:0%
+have a monopoly right so they're making
+ 
+
+ align:start position:0%
+have a monopoly right so they're making
+profits now why is 451 everyone has to
+
+ align:start position:0%
+profits now why is 451 everyone has to
+ 
+
+ align:start position:0%
+profits now why is 451 everyone has to
+read Fahrenheit 451 why don't they
+
+ align:start position:0%
+read Fahrenheit 451 why don't they
+ 
+
+ align:start position:0%
+read Fahrenheit 451 why don't they
+charge a 100 bucks because then high
+
+ align:start position:0%
+charge a 100 bucks because then high
+ 
+
+ align:start position:0%
+charge a 100 bucks because then high
+schools say you know what Fahrenheit 451
+
+ align:start position:0%
+schools say you know what Fahrenheit 451
+ 
+
+ align:start position:0%
+schools say you know what Fahrenheit 451
+is fine but you know there's other ones
+
+ align:start position:0%
+is fine but you know there's other ones
+ 
+
+ align:start position:0%
+is fine but you know there's other ones
+that are okay
+
+ align:start position:0%
+that are okay
+ 
+
+ align:start position:0%
+that are okay
+too so there's some eless this demand
+
+ align:start position:0%
+too so there's some eless this demand
+ 
+
+ align:start position:0%
+too so there's some eless this demand
+disciplining the market for Fahrenheit
+
+ align:start position:0%
+disciplining the market for Fahrenheit
+ 
+
+ align:start position:0%
+disciplining the market for Fahrenheit
+451 but it's not as much as disciplin
+
+ align:start position:0%
+451 but it's not as much as disciplin
+ 
+
+ align:start position:0%
+451 but it's not as much as disciplin
+the market for Huckleberry fin okay
+
+ align:start position:0%
+the market for Huckleberry fin okay
+ 
+
+ align:start position:0%
+the market for Huckleberry fin okay
+questions about
+
+ align:start position:0%
+questions about
+ 
+
+ align:start position:0%
+questions about
+that okay let's go on then and talk
+
+ align:start position:0%
+that okay let's go on then and talk
+ 
+
+ align:start position:0%
+that okay let's go on then and talk
+about the welfare effects of Monopoly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because now we have the tools in this
+
+ align:start position:0%
+because now we have the tools in this
+ 
+
+ align:start position:0%
+because now we have the tools in this
+class to move Beyond positive economics
+
+ align:start position:0%
+class to move Beyond positive economics
+ 
+
+ align:start position:0%
+class to move Beyond positive economics
+talk about normative
+
+ align:start position:0%
+talk about normative
+ 
+
+ align:start position:0%
+talk about normative
+economics and we have the tools to show
+
+ align:start position:0%
+economics and we have the tools to show
+ 
+
+ align:start position:0%
+economics and we have the tools to show
+you that Monopoly causes our first
+
+ align:start position:0%
+you that Monopoly causes our first
+ 
+
+ align:start position:0%
+you that Monopoly causes our first
+example what we call a market
+
+ align:start position:0%
+example what we call a market
+ 
+
+ align:start position:0%
+example what we call a market
+failure let's look at figure
+
+ align:start position:0%
+failure let's look at figure
+ 
+
+ align:start position:0%
+failure let's look at figure
+115 back to the example we used the
+
+ align:start position:0%
+115 back to the example we used the
+ 
+
+ align:start position:0%
+115 back to the example we used the
+domain curve is 24 minus Q the marginal
+
+ align:start position:0%
+domain curve is 24 minus Q the marginal
+ 
+
+ align:start position:0%
+domain curve is 24 minus Q the marginal
+cost is 2 Q same example we were just
+
+ align:start position:0%
+cost is 2 Q same example we were just
+ 
+
+ align:start position:0%
+cost is 2 Q same example we were just
+using the monopolis sells six units at a
+
+ align:start position:0%
+using the monopolis sells six units at a
+ 
+
+ align:start position:0%
+using the monopolis sells six units at a
+price of
+
+ align:start position:0%
+price of
+ 
+
+ align:start position:0%
+price of
+18 okay the competitive
+
+ align:start position:0%
+18 okay the competitive
+ 
+
+ align:start position:0%
+18 okay the competitive
+equilibrium would be eight units at a
+
+ align:start position:0%
+equilibrium would be eight units at a
+ 
+
+ align:start position:0%
+equilibrium would be eight units at a
+price of
+
+ align:start position:0%
+price of
+ 
+
+ align:start position:0%
+price of
+16 how do we know this well we just said
+
+ align:start position:0%
+16 how do we know this well we just said
+ 
+
+ align:start position:0%
+16 how do we know this well we just said
+price equal the marginal cost marginal
+
+ align:start position:0%
+price equal the marginal cost marginal
+ 
+
+ align:start position:0%
+price equal the marginal cost marginal
+cost equals 2 Q so that would be true at
+
+ align:start position:0%
+cost equals 2 Q so that would be true at
+ 
+
+ align:start position:0%
+cost equals 2 Q so that would be true at
+qal 8 p equal 16 we all could see it
+
+ align:start position:0%
+qal 8 p equal 16 we all could see it
+ 
+
+ align:start position:0%
+qal 8 p equal 16 we all could see it
+from the intersection the demand Supply
+
+ align:start position:0%
+from the intersection the demand Supply
+ 
+
+ align:start position:0%
+from the intersection the demand Supply
+curves so the competitive case they sell
+
+ align:start position:0%
+curves so the competitive case they sell
+ 
+
+ align:start position:0%
+curves so the competitive case they sell
+eight units at a price of 16 the
+
+ align:start position:0%
+eight units at a price of 16 the
+ 
+
+ align:start position:0%
+eight units at a price of 16 the
+Monopoly case they sell six units at a
+
+ align:start position:0%
+Monopoly case they sell six units at a
+ 
+
+ align:start position:0%
+Monopoly case they sell six units at a
+price of
+
+ align:start position:0%
+price of
+ 
+
+ align:start position:0%
+price of
+18 what is the consumer surplus in the
+
+ align:start position:0%
+18 what is the consumer surplus in the
+ 
+
+ align:start position:0%
+18 what is the consumer surplus in the
+competitive case what letters represent
+
+ align:start position:0%
+competitive case what letters represent
+ 
+
+ align:start position:0%
+competitive case what letters represent
+the consumer surplus in the competitive
+
+ align:start position:0%
+the consumer surplus in the competitive
+ 
+
+ align:start position:0%
+the consumer surplus in the competitive
+case at Point
+
+ align:start position:0%
+case at Point
+ 
+
+ align:start position:0%
+case at Point
+EC don't raise their hand and tell
+
+ align:start position:0%
+EC don't raise their hand and tell
+ 
+
+ align:start position:0%
+EC don't raise their hand and tell
+me come on guys help me out here yeah
+
+ align:start position:0%
+me come on guys help me out here yeah
+ 
+
+ align:start position:0%
+me come on guys help me out here yeah
+loud
+
+ align:start position:0%
+loud
+ 
+
+ align:start position:0%
+loud
+loud a plus b plus
+
+ align:start position:0%
+loud a plus b plus
+ 
+
+ align:start position:0%
+loud a plus b plus
+C same person what's the producer
+
+ align:start position:0%
+C same person what's the producer
+ 
+
+ align:start position:0%
+C same person what's the producer
+Surplus in competitive
+
+ align:start position:0%
+Surplus in competitive
+ 
+
+ align:start position:0%
+Surplus in competitive
+case D plus e now now in the Monopoly
+
+ align:start position:0%
+case D plus e now now in the Monopoly
+ 
+
+ align:start position:0%
+case D plus e now now in the Monopoly
+case what has happened to consumer
+
+ align:start position:0%
+case what has happened to consumer
+ 
+
+ align:start position:0%
+case what has happened to consumer
+surplus it has fallen from a plus b plus
+
+ align:start position:0%
+surplus it has fallen from a plus b plus
+ 
+
+ align:start position:0%
+surplus it has fallen from a plus b plus
+C to just a so consumer
+
+ align:start position:0%
+C to just a so consumer
+ 
+
+ align:start position:0%
+C to just a so consumer
+surplus from the competitive case to
+
+ align:start position:0%
+surplus from the competitive case to
+ 
+
+ align:start position:0%
+surplus from the competitive case to
+Monopoly case has gone from a plus b
+
+ align:start position:0%
+Monopoly case has gone from a plus b
+ 
+
+ align:start position:0%
+Monopoly case has gone from a plus b
+plus C to just
+
+ align:start position:0%
+plus C to just
+ 
+
+ align:start position:0%
+plus C to just
+a what about producer Surplus producer
+
+ align:start position:0%
+a what about producer Surplus producer
+ 
+
+ align:start position:0%
+a what about producer Surplus producer
+Surplus in the competitive
+
+ align:start position:0%
+Surplus in the competitive
+ 
+
+ align:start position:0%
+Surplus in the competitive
+case was just D plus e well now what is
+
+ align:start position:0%
+case was just D plus e well now what is
+ 
+
+ align:start position:0%
+case was just D plus e well now what is
+it well they lose
+
+ align:start position:0%
+it well they lose
+ 
+
+ align:start position:0%
+it well they lose
+e but they gain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B so what's happened is two things we
+
+ align:start position:0%
+B so what's happened is two things we
+ 
+
+ align:start position:0%
+B so what's happened is two things we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+transferred area B from consumers to
+
+ align:start position:0%
+transferred area B from consumers to
+ 
+
+ align:start position:0%
+transferred area B from consumers to
+producers remember that's sort of we
+
+ align:start position:0%
+producers remember that's sort of we
+ 
+
+ align:start position:0%
+producers remember that's sort of we
+don't care from that in the total social
+
+ align:start position:0%
+don't care from that in the total social
+ 
+
+ align:start position:0%
+don't care from that in the total social
+welfare framework we just care about the
+
+ align:start position:0%
+welfare framework we just care about the
+ 
+
+ align:start position:0%
+welfare framework we just care about the
+sum producer consumer surplus we don't
+
+ align:start position:0%
+sum producer consumer surplus we don't
+ 
+
+ align:start position:0%
+sum producer consumer surplus we don't
+care who has it so that transfer is not
+
+ align:start position:0%
+care who has it so that transfer is not
+ 
+
+ align:start position:0%
+care who has it so that transfer is not
+important not consequential what's
+
+ align:start position:0%
+important not consequential what's
+ 
+
+ align:start position:0%
+important not consequential what's
+consequential is we've created a dead
+
+ align:start position:0%
+consequential is we've created a dead
+ 
+
+ align:start position:0%
+consequential is we've created a dead
+weight
+
+ align:start position:0%
+weight
+ 
+
+ align:start position:0%
+weight
+loss of of
+
+ align:start position:0%
+loss of of
+ 
+
+ align:start position:0%
+loss of of
+c+e we've created a dead weight loss of
+
+ align:start position:0%
+c+e we've created a dead weight loss of
+ 
+
+ align:start position:0%
+c+e we've created a dead weight loss of
+c+e there's an inefficiency why because
+
+ align:start position:0%
+c+e there's an inefficiency why because
+ 
+
+ align:start position:0%
+c+e there's an inefficiency why because
+there are trades that would make Society
+
+ align:start position:0%
+there are trades that would make Society
+ 
+
+ align:start position:0%
+there are trades that would make Society
+better off that are not happening
+
+ align:start position:0%
+better off that are not happening
+ 
+
+ align:start position:0%
+better off that are not happening
+remember if we went if we sold that
+
+ align:start position:0%
+remember if we went if we sold that
+ 
+
+ align:start position:0%
+remember if we went if we sold that
+seventh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unit could the benefit of that unit to
+
+ align:start position:0%
+unit could the benefit of that unit to
+ 
+
+ align:start position:0%
+unit could the benefit of that unit to
+Consumers exceeds the cost of producing
+
+ align:start position:0%
+Consumers exceeds the cost of producing
+ 
+
+ align:start position:0%
+Consumers exceeds the cost of producing
+it therefore society's better off if
+
+ align:start position:0%
+it therefore society's better off if
+ 
+
+ align:start position:0%
+it therefore society's better off if
+it's sold but it's not being sold
+
+ align:start position:0%
+it's sold but it's not being sold
+ 
+
+ align:start position:0%
+it's sold but it's not being sold
+because this poisoning effect so
+
+ align:start position:0%
+because this poisoning effect so
+ 
+
+ align:start position:0%
+because this poisoning effect so
+Monopoly has created a dead weight loss
+
+ align:start position:0%
+Monopoly has created a dead weight loss
+ 
+
+ align:start position:0%
+Monopoly has created a dead weight loss
+and the first example the dead weight
+
+ align:start position:0%
+and the first example the dead weight
+ 
+
+ align:start position:0%
+and the first example the dead weight
+loss and
+
+ align:start position:0%
+loss and
+ 
+
+ align:start position:0%
+loss and
+Monopoly is the first example of what we
+
+ align:start position:0%
+Monopoly is the first example of what we
+ 
+
+ align:start position:0%
+Monopoly is the first example of what we
+call in this class a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+failure when I did welfare the last
+
+ align:start position:0%
+failure when I did welfare the last
+ 
+
+ align:start position:0%
+failure when I did welfare the last
+couple lectures the only thing that
+
+ align:start position:0%
+couple lectures the only thing that
+ 
+
+ align:start position:0%
+couple lectures the only thing that
+caused de loss was the government
+
+ align:start position:0%
+caused de loss was the government
+ 
+
+ align:start position:0%
+caused de loss was the government
+screwing things up as long as you left
+
+ align:start position:0%
+screwing things up as long as you left
+ 
+
+ align:start position:0%
+screwing things up as long as you left
+the market rip you got the perfectly
+
+ align:start position:0%
+the market rip you got the perfectly
+ 
+
+ align:start position:0%
+the market rip you got the perfectly
+efficient outcome well here we're
+
+ align:start position:0%
+efficient outcome well here we're
+ 
+
+ align:start position:0%
+efficient outcome well here we're
+letting the market rip and not getting
+
+ align:start position:0%
+letting the market rip and not getting
+ 
+
+ align:start position:0%
+letting the market rip and not getting
+the perfectly efficient outcome now I'll
+
+ align:start position:0%
+the perfectly efficient outcome now I'll
+ 
+
+ align:start position:0%
+the perfectly efficient outcome now I'll
+stop right there this does not imply
+
+ align:start position:0%
+stop right there this does not imply
+ 
+
+ align:start position:0%
+stop right there this does not imply
+government can make things better we'll
+
+ align:start position:0%
+government can make things better we'll
+ 
+
+ align:start position:0%
+government can make things better we'll
+talk about that next time all I'm saying
+
+ align:start position:0%
+talk about that next time all I'm saying
+ 
+
+ align:start position:0%
+talk about that next time all I'm saying
+here is a simpler statement which is
+
+ align:start position:0%
+here is a simpler statement which is
+ 
+
+ align:start position:0%
+here is a simpler statement which is
+unlike the perfectly competitive case if
+
+ align:start position:0%
+unlike the perfectly competitive case if
+ 
+
+ align:start position:0%
+unlike the perfectly competitive case if
+you let the market rip you get an
+
+ align:start position:0%
+you let the market rip you get an
+ 
+
+ align:start position:0%
+you let the market rip you get an
+inefficient
+
+ align:start position:0%
+inefficient
+ 
+
+ align:start position:0%
+inefficient
+outcome that's a fundamental change
+
+ align:start position:0%
+outcome that's a fundamental change
+ 
+
+ align:start position:0%
+outcome that's a fundamental change
+that's a fundamental challenge to
+
+ align:start position:0%
+that's a fundamental challenge to
+ 
+
+ align:start position:0%
+that's a fundamental challenge to
+everything we've learned so far it
+
+ align:start position:0%
+everything we've learned so far it
+ 
+
+ align:start position:0%
+everything we've learned so far it
+doesn't come from any magic or any
+
+ align:start position:0%
+doesn't come from any magic or any
+ 
+
+ align:start position:0%
+doesn't come from any magic or any
+government intervention it's just the
+
+ align:start position:0%
+government intervention it's just the
+ 
+
+ align:start position:0%
+government intervention it's just the
+way monopolis make
+
+ align:start position:0%
+way monopolis make
+ 
+
+ align:start position:0%
+way monopolis make
+decisions okay so because monopolis
+
+ align:start position:0%
+decisions okay so because monopolis
+ 
+
+ align:start position:0%
+decisions okay so because monopolis
+don't want to lower the price because
+
+ align:start position:0%
+don't want to lower the price because
+ 
+
+ align:start position:0%
+don't want to lower the price because
+that's not profit maximizing we end up
+
+ align:start position:0%
+that's not profit maximizing we end up
+ 
+
+ align:start position:0%
+that's not profit maximizing we end up
+not selling units that and that would
+
+ align:start position:0%
+not selling units that and that would
+ 
+
+ align:start position:0%
+not selling units that and that would
+make Society better off so the private
+
+ align:start position:0%
+make Society better off so the private
+ 
+
+ align:start position:0%
+make Society better off so the private
+incentives put another way the positive
+
+ align:start position:0%
+incentives put another way the positive
+ 
+
+ align:start position:0%
+incentives put another way the positive
+and normative outcomes don't don't align
+
+ align:start position:0%
+and normative outcomes don't don't align
+ 
+
+ align:start position:0%
+and normative outcomes don't don't align
+with the competitive market the positive
+
+ align:start position:0%
+with the competitive market the positive
+ 
+
+ align:start position:0%
+with the competitive market the positive
+outcome was no profits that was also the
+
+ align:start position:0%
+outcome was no profits that was also the
+ 
+
+ align:start position:0%
+outcome was no profits that was also the
+welfare maximizing outcome in a monopoly
+
+ align:start position:0%
+welfare maximizing outcome in a monopoly
+ 
+
+ align:start position:0%
+welfare maximizing outcome in a monopoly
+case the private
+
+ align:start position:0%
+case the private
+ 
+
+ align:start position:0%
+case the private
+outcome is different than the social
+
+ align:start position:0%
+outcome is different than the social
+ 
+
+ align:start position:0%
+outcome is different than the social
+welfare maximizing outcome and that lead
+
+ align:start position:0%
+welfare maximizing outcome and that lead
+ 
+
+ align:start position:0%
+welfare maximizing outcome and that lead
+leads to a market failure questions
+
+ align:start position:0%
+leads to a market failure questions
+ 
+
+ align:start position:0%
+leads to a market failure questions
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that okay
+
+ align:start position:0%
+that okay
+ 
+
+ align:start position:0%
+that okay
+now this raises the natural question
+
+ align:start position:0%
+now this raises the natural question
+ 
+
+ align:start position:0%
+now this raises the natural question
+which was raised here and which has been
+
+ align:start position:0%
+which was raised here and which has been
+ 
+
+ align:start position:0%
+which was raised here and which has been
+on your mind the whole time which is why
+
+ align:start position:0%
+on your mind the whole time which is why
+ 
+
+ align:start position:0%
+on your mind the whole time which is why
+do monopolis have to charge just one
+
+ align:start position:0%
+do monopolis have to charge just one
+ 
+
+ align:start position:0%
+do monopolis have to charge just one
+price what loss is that no firm charge
+
+ align:start position:0%
+price what loss is that no firm charge
+ 
+
+ align:start position:0%
+price what loss is that no firm charge
+is just one price firms charge different
+
+ align:start position:0%
+is just one price firms charge different
+ 
+
+ align:start position:0%
+is just one price firms charge different
+prices for different sorts of things you
+
+ align:start position:0%
+prices for different sorts of things you
+ 
+
+ align:start position:0%
+prices for different sorts of things you
+know for different and we'll come to
+
+ align:start position:0%
+know for different and we'll come to
+ 
+
+ align:start position:0%
+know for different and we'll come to
+some examples so what if we move to the
+
+ align:start position:0%
+some examples so what if we move to the
+ 
+
+ align:start position:0%
+some examples so what if we move to the
+more realistic case where monopolist can
+
+ align:start position:0%
+more realistic case where monopolist can
+ 
+
+ align:start position:0%
+more realistic case where monopolist can
+price
+
+ align:start position:0%
+price
+ 
+
+ align:start position:0%
+price
+discriminate what if monopolis could
+
+ align:start position:0%
+discriminate what if monopolis could
+ 
+
+ align:start position:0%
+discriminate what if monopolis could
+charge different prices for different
+
+ align:start position:0%
+charge different prices for different
+ 
+
+ align:start position:0%
+charge different prices for different
+quantities well in fact what would
+
+ align:start position:0%
+quantities well in fact what would
+ 
+
+ align:start position:0%
+quantities well in fact what would
+happen let's go to the extreme of
+
+ align:start position:0%
+happen let's go to the extreme of
+ 
+
+ align:start position:0%
+happen let's go to the extreme of
+perfect price
+
+ align:start position:0%
+perfect price
+ 
+
+ align:start position:0%
+perfect price
+discrimination Perfect Right
+
+ align:start position:0%
+discrimination Perfect Right
+ 
+
+ align:start position:0%
+discrimination Perfect Right
+discrimination is a magag monopolist
+
+ align:start position:0%
+discrimination is a magag monopolist
+ 
+
+ align:start position:0%
+discrimination is a magag monopolist
+could go to Every
+
+ align:start position:0%
+could go to Every
+ 
+
+ align:start position:0%
+could go to Every
+individual figure out what their
+
+ align:start position:0%
+individual figure out what their
+ 
+
+ align:start position:0%
+individual figure out what their
+willingness to pay was and charge them
+
+ align:start position:0%
+willingness to pay was and charge them
+ 
+
+ align:start position:0%
+willingness to pay was and charge them
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+amount that'd be perfectly price
+
+ align:start position:0%
+amount that'd be perfectly price
+ 
+
+ align:start position:0%
+amount that'd be perfectly price
+discriminating monopolis they would
+
+ align:start position:0%
+discriminating monopolis they would
+ 
+
+ align:start position:0%
+discriminating monopolis they would
+charge every person their own individual
+
+ align:start position:0%
+charge every person their own individual
+ 
+
+ align:start position:0%
+charge every person their own individual
+price and that price will correspond to
+
+ align:start position:0%
+price and that price will correspond to
+ 
+
+ align:start position:0%
+price and that price will correspond to
+their willingness to
+
+ align:start position:0%
+their willingness to
+ 
+
+ align:start position:0%
+their willingness to
+pay what would that lead to that would
+
+ align:start position:0%
+pay what would that lead to that would
+ 
+
+ align:start position:0%
+pay what would that lead to that would
+lead to figure
+
+ align:start position:0%
+lead to figure
+ 
+
+ align:start position:0%
+lead to figure
+116 the first person person
+
+ align:start position:0%
+116 the first person person
+ 
+
+ align:start position:0%
+116 the first person person
+one they are willing to pay that entire
+
+ align:start position:0%
+one they are willing to pay that entire
+ 
+
+ align:start position:0%
+one they are willing to pay that entire
+um uh trapezoid that'll be to the left
+
+ align:start position:0%
+um uh trapezoid that'll be to the left
+ 
+
+ align:start position:0%
+um uh trapezoid that'll be to the left
+of unit one they only pay a lot so you
+
+ align:start position:0%
+of unit one they only pay a lot so you
+ 
+
+ align:start position:0%
+of unit one they only pay a lot so you
+charge them a lot all the way down to
+
+ align:start position:0%
+charge them a lot all the way down to
+ 
+
+ align:start position:0%
+charge them a lot all the way down to
+the eighth person you charge them what
+
+ align:start position:0%
+the eighth person you charge them what
+ 
+
+ align:start position:0%
+the eighth person you charge them what
+they're willing to pay which is 16
+
+ align:start position:0%
+they're willing to pay which is 16
+ 
+
+ align:start position:0%
+they're willing to pay which is 16
+charge the eighth person 16 the seventh
+
+ align:start position:0%
+charge the eighth person 16 the seventh
+ 
+
+ align:start position:0%
+charge the eighth person 16 the seventh
+person 17 the sixth person 18 and so on
+
+ align:start position:0%
+person 17 the sixth person 18 and so on
+ 
+
+ align:start position:0%
+person 17 the sixth person 18 and so on
+why would you want to do
+
+ align:start position:0%
+why would you want to do
+ 
+
+ align:start position:0%
+why would you want to do
+that well now what has happened to
+
+ align:start position:0%
+that well now what has happened to
+ 
+
+ align:start position:0%
+that well now what has happened to
+consumer surplus someone raise their
+
+ align:start position:0%
+consumer surplus someone raise their
+ 
+
+ align:start position:0%
+consumer surplus someone raise their
+hand and tell me yeah zero why is
+
+ align:start position:0%
+hand and tell me yeah zero why is
+ 
+
+ align:start position:0%
+hand and tell me yeah zero why is
+consumer surplus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero exactly consumer surplus is the
+
+ align:start position:0%
+zero exactly consumer surplus is the
+ 
+
+ align:start position:0%
+zero exactly consumer surplus is the
+benefit you get from valuing something
+
+ align:start position:0%
+benefit you get from valuing something
+ 
+
+ align:start position:0%
+benefit you get from valuing something
+above its price that's gone they're
+
+ align:start position:0%
+above its price that's gone they're
+ 
+
+ align:start position:0%
+above its price that's gone they're
+charging you what you're willing to pay
+
+ align:start position:0%
+charging you what you're willing to pay
+ 
+
+ align:start position:0%
+charging you what you're willing to pay
+so by definition there's no consumer
+
+ align:start position:0%
+so by definition there's no consumer
+ 
+
+ align:start position:0%
+so by definition there's no consumer
+surplus so all the rest is producer
+
+ align:start position:0%
+surplus so all the rest is producer
+ 
+
+ align:start position:0%
+surplus so all the rest is producer
+Surplus so the firm has converted the
+
+ align:start position:0%
+Surplus so the firm has converted the
+ 
+
+ align:start position:0%
+Surplus so the firm has converted the
+entire Surplus to producer Surplus by
+
+ align:start position:0%
+entire Surplus to producer Surplus by
+ 
+
+ align:start position:0%
+entire Surplus to producer Surplus by
+Perfect price
+
+ align:start position:0%
+Perfect price
+ 
+
+ align:start position:0%
+Perfect price
+discrimination what else is notable in
+
+ align:start position:0%
+discrimination what else is notable in
+ 
+
+ align:start position:0%
+discrimination what else is notable in
+this case with per price discrimination
+
+ align:start position:0%
+this case with per price discrimination
+ 
+
+ align:start position:0%
+this case with per price discrimination
+firms will sell eight units so what else
+
+ align:start position:0%
+firms will sell eight units so what else
+ 
+
+ align:start position:0%
+firms will sell eight units so what else
+is notable no dead weight
+
+ align:start position:0%
+is notable no dead weight
+ 
+
+ align:start position:0%
+is notable no dead weight
+loss a perfectly priced discriminating
+
+ align:start position:0%
+loss a perfectly priced discriminating
+ 
+
+ align:start position:0%
+loss a perfectly priced discriminating
+firm creates no dead weight loss why
+
+ align:start position:0%
+firm creates no dead weight loss why
+ 
+
+ align:start position:0%
+firm creates no dead weight loss why
+because there's no poisoning effect the
+
+ align:start position:0%
+because there's no poisoning effect the
+ 
+
+ align:start position:0%
+because there's no poisoning effect the
+poisoning effect comes from the fact
+
+ align:start position:0%
+poisoning effect comes from the fact
+ 
+
+ align:start position:0%
+poisoning effect comes from the fact
+that if I want to sell more units I got
+
+ align:start position:0%
+that if I want to sell more units I got
+ 
+
+ align:start position:0%
+that if I want to sell more units I got
+to lower my price well here I don't have
+
+ align:start position:0%
+to lower my price well here I don't have
+ 
+
+ align:start position:0%
+to lower my price well here I don't have
+to lower my price to sell more units
+
+ align:start position:0%
+to lower my price to sell more units
+ 
+
+ align:start position:0%
+to lower my price to sell more units
+given that I might as well sell as many
+
+ align:start position:0%
+given that I might as well sell as many
+ 
+
+ align:start position:0%
+given that I might as well sell as many
+units as people are willing to pay for
+
+ align:start position:0%
+units as people are willing to pay for
+ 
+
+ align:start position:0%
+units as people are willing to pay for
+that are above my cost so I might as
+
+ align:start position:0%
+that are above my cost so I might as
+ 
+
+ align:start position:0%
+that are above my cost so I might as
+well do the welfare maximizing thing
+
+ align:start position:0%
+well do the welfare maximizing thing
+ 
+
+ align:start position:0%
+well do the welfare maximizing thing
+which is sell 8
+
+ align:start position:0%
+which is sell 8
+ 
+
+ align:start position:0%
+which is sell 8
+units this is the first inclination that
+
+ align:start position:0%
+units this is the first inclination that
+ 
+
+ align:start position:0%
+units this is the first inclination that
+we have to car care about fairness in
+
+ align:start position:0%
+we have to car care about fairness in
+ 
+
+ align:start position:0%
+we have to car care about fairness in
+economics because what this says what
+
+ align:start position:0%
+economics because what this says what
+ 
+
+ align:start position:0%
+economics because what this says what
+the existing course would teach you so
+
+ align:start position:0%
+the existing course would teach you so
+ 
+
+ align:start position:0%
+the existing course would teach you so
+far is I'm completely
+
+ align:start position:0%
+far is I'm completely
+ 
+
+ align:start position:0%
+far is I'm completely
+indifferent between the perfectly
+
+ align:start position:0%
+indifferent between the perfectly
+ 
+
+ align:start position:0%
+indifferent between the perfectly
+competitive case as illustrated by EC
+
+ align:start position:0%
+competitive case as illustrated by EC
+ 
+
+ align:start position:0%
+competitive case as illustrated by EC
+above where consumers get a plus b plus
+
+ align:start position:0%
+above where consumers get a plus b plus
+ 
+
+ align:start position:0%
+above where consumers get a plus b plus
+C I'm indifferent between that case and
+
+ align:start position:0%
+C I'm indifferent between that case and
+ 
+
+ align:start position:0%
+C I'm indifferent between that case and
+the perfect price discrimination case
+
+ align:start position:0%
+the perfect price discrimination case
+ 
+
+ align:start position:0%
+the perfect price discrimination case
+that is I'm indifferent between whether
+
+ align:start position:0%
+that is I'm indifferent between whether
+ 
+
+ align:start position:0%
+that is I'm indifferent between whether
+consumer's
+
+ align:start position:0%
+consumer's
+ 
+
+ align:start position:0%
+consumer's
+gift okay I'm completely indifferent all
+
+ align:start position:0%
+gift okay I'm completely indifferent all
+ 
+
+ align:start position:0%
+gift okay I'm completely indifferent all
+I care about is the total right it's the
+
+ align:start position:0%
+I care about is the total right it's the
+ 
+
+ align:start position:0%
+I care about is the total right it's the
+sum that can't make sense right it can't
+
+ align:start position:0%
+sum that can't make sense right it can't
+ 
+
+ align:start position:0%
+sum that can't make sense right it can't
+make sense that I'm completely different
+
+ align:start position:0%
+make sense that I'm completely different
+ 
+
+ align:start position:0%
+make sense that I'm completely different
+in a world where producers have
+
+ align:start position:0%
+in a world where producers have
+ 
+
+ align:start position:0%
+in a world where producers have
+everything and where consumers have some
+
+ align:start position:0%
+everything and where consumers have some
+ 
+
+ align:start position:0%
+everything and where consumers have some
+producers have some there's no way that
+
+ align:start position:0%
+producers have some there's no way that
+ 
+
+ align:start position:0%
+producers have some there's no way that
+anyone would be truly indifferent in
+
+ align:start position:0%
+anyone would be truly indifferent in
+ 
+
+ align:start position:0%
+anyone would be truly indifferent in
+those worlds and that's the first hint
+
+ align:start position:0%
+those worlds and that's the first hint
+ 
+
+ align:start position:0%
+those worlds and that's the first hint
+that in economics we have to care about
+
+ align:start position:0%
+that in economics we have to care about
+ 
+
+ align:start position:0%
+that in economics we have to care about
+fairness we have to not just care about
+
+ align:start position:0%
+fairness we have to not just care about
+ 
+
+ align:start position:0%
+fairness we have to not just care about
+the total sum of social surplus but who
+
+ align:start position:0%
+the total sum of social surplus but who
+ 
+
+ align:start position:0%
+the total sum of social surplus but who
+gets
+
+ align:start position:0%
+gets
+ 
+
+ align:start position:0%
+gets
+what okay and we're going to come back
+
+ align:start position:0%
+what okay and we're going to come back
+ 
+
+ align:start position:0%
+what okay and we're going to come back
+to that later for now we'll stick with
+
+ align:start position:0%
+to that later for now we'll stick with
+ 
+
+ align:start position:0%
+to that later for now we'll stick with
+our definition we're just care about the
+
+ align:start position:0%
+our definition we're just care about the
+ 
+
+ align:start position:0%
+our definition we're just care about the
+total but this is sort of the hint of
+
+ align:start position:0%
+total but this is sort of the hint of
+ 
+
+ align:start position:0%
+total but this is sort of the hint of
+why we need to come back to
+
+ align:start position:0%
+why we need to come back to
+ 
+
+ align:start position:0%
+why we need to come back to
+that okay so that is what would happen
+
+ align:start position:0%
+that okay so that is what would happen
+ 
+
+ align:start position:0%
+that okay so that is what would happen
+with perfect price discrimination now in
+
+ align:start position:0%
+with perfect price discrimination now in
+ 
+
+ align:start position:0%
+with perfect price discrimination now in
+fact okay um firms can't perfectly price
+
+ align:start position:0%
+fact okay um firms can't perfectly price
+ 
+
+ align:start position:0%
+fact okay um firms can't perfectly price
+discriminate in fact firms can't go and
+
+ align:start position:0%
+discriminate in fact firms can't go and
+ 
+
+ align:start position:0%
+discriminate in fact firms can't go and
+get your willingness to pay so in
+
+ align:start position:0%
+get your willingness to pay so in
+ 
+
+ align:start position:0%
+get your willingness to pay so in
+reality what do firms do well they price
+
+ align:start position:0%
+reality what do firms do well they price
+ 
+
+ align:start position:0%
+reality what do firms do well they price
+discriminate by trying to guess who is
+
+ align:start position:0%
+discriminate by trying to guess who is
+ 
+
+ align:start position:0%
+discriminate by trying to guess who is
+more price
+
+ align:start position:0%
+more price
+ 
+
+ align:start position:0%
+more price
+sensitive firms engage in price
+
+ align:start position:0%
+sensitive firms engage in price
+ 
+
+ align:start position:0%
+sensitive firms engage in price
+discrimination and the way they do it is
+
+ align:start position:0%
+discrimination and the way they do it is
+ 
+
+ align:start position:0%
+discrimination and the way they do it is
+they look for correlates of
+
+ align:start position:0%
+they look for correlates of
+ 
+
+ align:start position:0%
+they look for correlates of
+Epsilon you you basically if you're a
+
+ align:start position:0%
+Epsilon you you basically if you're a
+ 
+
+ align:start position:0%
+Epsilon you you basically if you're a
+monopolist you want to charge a higher
+
+ align:start position:0%
+monopolist you want to charge a higher
+ 
+
+ align:start position:0%
+monopolist you want to charge a higher
+price to a low Epsilon guy and a low
+
+ align:start position:0%
+price to a low Epsilon guy and a low
+ 
+
+ align:start position:0%
+price to a low Epsilon guy and a low
+remember guys gender neutral term and a
+
+ align:start position:0%
+remember guys gender neutral term and a
+ 
+
+ align:start position:0%
+remember guys gender neutral term and a
+lower price to a high Epsilon guy so
+
+ align:start position:0%
+lower price to a high Epsilon guy so
+ 
+
+ align:start position:0%
+lower price to a high Epsilon guy so
+basically if I knew everyone's Epsilon
+
+ align:start position:0%
+basically if I knew everyone's Epsilon
+ 
+
+ align:start position:0%
+basically if I knew everyone's Epsilon
+I'd be done but I don't so what I do is
+
+ align:start position:0%
+I'd be done but I don't so what I do is
+ 
+
+ align:start position:0%
+I'd be done but I don't so what I do is
+I look for signals that are correlated
+
+ align:start position:0%
+I look for signals that are correlated
+ 
+
+ align:start position:0%
+I look for signals that are correlated
+with your
+
+ align:start position:0%
+with your
+ 
+
+ align:start position:0%
+with your
+Epsilon so for
+
+ align:start position:0%
+Epsilon so for
+ 
+
+ align:start position:0%
+Epsilon so for
+example airlines charge more if you buy
+
+ align:start position:0%
+example airlines charge more if you buy
+ 
+
+ align:start position:0%
+example airlines charge more if you buy
+at the last minute
+
+ align:start position:0%
+at the last minute
+ 
+
+ align:start position:0%
+at the last minute
+that if you buy four months in
+
+ align:start position:0%
+that if you buy four months in
+ 
+
+ align:start position:0%
+that if you buy four months in
+advance why it's the same seat same
+
+ align:start position:0%
+advance why it's the same seat same
+ 
+
+ align:start position:0%
+advance why it's the same seat same
+produ same marginal cost to flying on
+
+ align:start position:0%
+produ same marginal cost to flying on
+ 
+
+ align:start position:0%
+produ same marginal cost to flying on
+the plane
+
+ align:start position:0%
+the plane
+ 
+
+ align:start position:0%
+the plane
+yeah yeah if you buy the last you
+
+ align:start position:0%
+yeah yeah if you buy the last you
+ 
+
+ align:start position:0%
+yeah yeah if you buy the last you
+clearly got to go okay you're a business
+
+ align:start position:0%
+clearly got to go okay you're a business
+ 
+
+ align:start position:0%
+clearly got to go okay you're a business
+person's got a last minute meeting
+
+ align:start position:0%
+person's got a last minute meeting
+ 
+
+ align:start position:0%
+person's got a last minute meeting
+you've gotta you've got to love one
+
+ align:start position:0%
+you've gotta you've got to love one
+ 
+
+ align:start position:0%
+you've gotta you've got to love one
+who's sick who's got you got to go see
+
+ align:start position:0%
+who's sick who's got you got to go see
+ 
+
+ align:start position:0%
+who's sick who's got you got to go see
+Etc if you buy four months in advance
+
+ align:start position:0%
+Etc if you buy four months in advance
+ 
+
+ align:start position:0%
+Etc if you buy four months in advance
+you're clearly shopping you have lots of
+
+ align:start position:0%
+you're clearly shopping you have lots of
+ 
+
+ align:start position:0%
+you're clearly shopping you have lots of
+options but if you're buying the last
+
+ align:start position:0%
+options but if you're buying the last
+ 
+
+ align:start position:0%
+options but if you're buying the last
+minute you don't have a lot of options
+
+ align:start position:0%
+minute you don't have a lot of options
+ 
+
+ align:start position:0%
+minute you don't have a lot of options
+now I can't charge you infinity because
+
+ align:start position:0%
+now I can't charge you infinity because
+ 
+
+ align:start position:0%
+now I can't charge you infinity because
+as other airlines you could fly but
+
+ align:start position:0%
+as other airlines you could fly but
+ 
+
+ align:start position:0%
+as other airlines you could fly but
+clearly you are less price sensitive if
+
+ align:start position:0%
+clearly you are less price sensitive if
+ 
+
+ align:start position:0%
+clearly you are less price sensitive if
+you're buying at the last minute than if
+
+ align:start position:0%
+you're buying at the last minute than if
+ 
+
+ align:start position:0%
+you're buying at the last minute than if
+you're buying four months in
+
+ align:start position:0%
+you're buying four months in
+ 
+
+ align:start position:0%
+you're buying four months in
+advance that's one example okay why do
+
+ align:start position:0%
+advance that's one example okay why do
+ 
+
+ align:start position:0%
+advance that's one example okay why do
+movie theaters charge less for Maes than
+
+ align:start position:0%
+movie theaters charge less for Maes than
+ 
+
+ align:start position:0%
+movie theaters charge less for Maes than
+movies at night why do movie theaters
+
+ align:start position:0%
+movies at night why do movie theaters
+ 
+
+ align:start position:0%
+movies at night why do movie theaters
+charge less when you go during the day
+
+ align:start position:0%
+charge less when you go during the day
+ 
+
+ align:start position:0%
+charge less when you go during the day
+it's the same marginal cost again same
+
+ align:start position:0%
+it's the same marginal cost again same
+ 
+
+ align:start position:0%
+it's the same marginal cost again same
+popcorn cost same projector costs why do
+
+ align:start position:0%
+popcorn cost same projector costs why do
+ 
+
+ align:start position:0%
+popcorn cost same projector costs why do
+movie theaters charge less when you go
+
+ align:start position:0%
+movie theaters charge less when you go
+ 
+
+ align:start position:0%
+movie theaters charge less when you go
+during the day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well lower Demand by itself is not
+
+ align:start position:0%
+yeah well lower Demand by itself is not
+ 
+
+ align:start position:0%
+yeah well lower Demand by itself is not
+necessarily the answer it's really about
+
+ align:start position:0%
+necessarily the answer it's really about
+ 
+
+ align:start position:0%
+necessarily the answer it's really about
+elasticity of demand why are people less
+
+ align:start position:0%
+elasticity of demand why are people less
+ 
+
+ align:start position:0%
+elasticity of demand why are people less
+price sensitive during the why are
+
+ align:start position:0%
+price sensitive during the why are
+ 
+
+ align:start position:0%
+price sensitive during the why are
+people more price sensitive during the
+
+ align:start position:0%
+people more price sensitive during the
+ 
+
+ align:start position:0%
+people more price sensitive during the
+day than at
+
+ align:start position:0%
+day than at
+ 
+
+ align:start position:0%
+day than at
+night think about who goes to the movies
+
+ align:start position:0%
+night think about who goes to the movies
+ 
+
+ align:start position:0%
+night think about who goes to the movies
+during the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+day yeah mean people are like retirees
+
+ align:start position:0%
+day yeah mean people are like retirees
+ 
+
+ align:start position:0%
+day yeah mean people are like retirees
+and things which have plenty of time in
+
+ align:start position:0%
+and things which have plenty of time in
+ 
+
+ align:start position:0%
+and things which have plenty of time in
+their hands if you go to the movie at
+
+ align:start position:0%
+their hands if you go to the movie at
+ 
+
+ align:start position:0%
+their hands if you go to the movie at
+night it's like you're done with work
+
+ align:start position:0%
+night it's like you're done with work
+ 
+
+ align:start position:0%
+night it's like you're done with work
+you got to go at night you can't you
+
+ align:start position:0%
+you got to go at night you can't you
+ 
+
+ align:start position:0%
+you got to go at night you can't you
+know maybe you decide between the 7
+
+ align:start position:0%
+know maybe you decide between the 7
+ 
+
+ align:start position:0%
+know maybe you decide between the 7
+o'clock showing the 11:00 showing but
+
+ align:start position:0%
+o'clock showing the 11:00 showing but
+ 
+
+ align:start position:0%
+o'clock showing the 11:00 showing but
+the bottom line is there's one time you
+
+ align:start position:0%
+the bottom line is there's one time you
+ 
+
+ align:start position:0%
+the bottom line is there's one time you
+can go if you're going during the day
+
+ align:start position:0%
+can go if you're going during the day
+ 
+
+ align:start position:0%
+can go if you're going during the day
+you've shown you have lots of time to go
+
+ align:start position:0%
+you've shown you have lots of time to go
+ 
+
+ align:start position:0%
+you've shown you have lots of time to go
+see movies you can go at night you can
+
+ align:start position:0%
+see movies you can go at night you can
+ 
+
+ align:start position:0%
+see movies you can go at night you can
+go during the day so anybody who goes to
+
+ align:start position:0%
+go during the day so anybody who goes to
+ 
+
+ align:start position:0%
+go during the day so anybody who goes to
+movie during the day unless they work a
+
+ align:start position:0%
+movie during the day unless they work a
+ 
+
+ align:start position:0%
+movie during the day unless they work a
+weird shift okay has basically shown
+
+ align:start position:0%
+weird shift okay has basically shown
+ 
+
+ align:start position:0%
+weird shift okay has basically shown
+that they have more flexibility on when
+
+ align:start position:0%
+that they have more flexibility on when
+ 
+
+ align:start position:0%
+that they have more flexibility on when
+they go to the
+
+ align:start position:0%
+they go to the
+ 
+
+ align:start position:0%
+they go to the
+movie as a result you charge them a
+
+ align:start position:0%
+movie as a result you charge them a
+ 
+
+ align:start position:0%
+movie as a result you charge them a
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+price this is everywhere you look all of
+
+ align:start position:0%
+price this is everywhere you look all of
+ 
+
+ align:start position:0%
+price this is everywhere you look all of
+a sudden I've opened up to you a world
+
+ align:start position:0%
+a sudden I've opened up to you a world
+ 
+
+ align:start position:0%
+a sudden I've opened up to you a world
+of understanding why price are
+
+ align:start position:0%
+of understanding why price are
+ 
+
+ align:start position:0%
+of understanding why price are
+differentiated okay remember we
+
+ align:start position:0%
+differentiated okay remember we
+ 
+
+ align:start position:0%
+differentiated okay remember we
+discussed this a long time ago we talked
+
+ align:start position:0%
+discussed this a long time ago we talked
+ 
+
+ align:start position:0%
+discussed this a long time ago we talked
+about why the incremental large
+
+ align:start position:0%
+about why the incremental large
+ 
+
+ align:start position:0%
+about why the incremental large
+drink at McDonald's the incremental cost
+
+ align:start position:0%
+drink at McDonald's the incremental cost
+ 
+
+ align:start position:0%
+drink at McDonald's the incremental cost
+of a large drink is Tri is very small
+
+ align:start position:0%
+of a large drink is Tri is very small
+ 
+
+ align:start position:0%
+of a large drink is Tri is very small
+compared to the cost of a small drink
+
+ align:start position:0%
+compared to the cost of a small drink
+ 
+
+ align:start position:0%
+compared to the cost of a small drink
+because there's different elas demand
+
+ align:start position:0%
+because there's different elas demand
+ 
+
+ align:start position:0%
+because there's different elas demand
+for the small drink and and the
+
+ align:start position:0%
+for the small drink and and the
+ 
+
+ align:start position:0%
+for the small drink and and the
+incremental to the large drink so
+
+ align:start position:0%
+incremental to the large drink so
+ 
+
+ align:start position:0%
+incremental to the large drink so
+everywhere you look when you go out in
+
+ align:start position:0%
+everywhere you look when you go out in
+ 
+
+ align:start position:0%
+everywhere you look when you go out in
+the real world now look at prices you'll
+
+ align:start position:0%
+the real world now look at prices you'll
+ 
+
+ align:start position:0%
+the real world now look at prices you'll
+see this firms pricing to try to Target
+
+ align:start position:0%
+see this firms pricing to try to Target
+ 
+
+ align:start position:0%
+see this firms pricing to try to Target
+the lower prices to the most elastic
+
+ align:start position:0%
+the lower prices to the most elastic
+ 
+
+ align:start position:0%
+the lower prices to the most elastic
+consumers
+
+ align:start position:0%
+consumers
+ 
+
+ align:start position:0%
+consumers
+okay now perhaps the best example of
+
+ align:start position:0%
+okay now perhaps the best example of
+ 
+
+ align:start position:0%
+okay now perhaps the best example of
+this was a example a few years ago with
+
+ align:start position:0%
+this was a example a few years ago with
+ 
+
+ align:start position:0%
+this was a example a few years ago with
+Tesla Tesla sells electric cars you know
+
+ align:start position:0%
+Tesla Tesla sells electric cars you know
+ 
+
+ align:start position:0%
+Tesla Tesla sells electric cars you know
+and the original model S could go for
+
+ align:start position:0%
+and the original model S could go for
+ 
+
+ align:start position:0%
+and the original model S could go for
+250 miles on a battery charge what they
+
+ align:start position:0%
+250 miles on a battery charge what they
+ 
+
+ align:start position:0%
+250 miles on a battery charge what they
+said is we are going to offer a cheaper
+
+ align:start position:0%
+said is we are going to offer a cheaper
+ 
+
+ align:start position:0%
+said is we are going to offer a cheaper
+Model S that can only go about half as
+
+ align:start position:0%
+Model S that can only go about half as
+ 
+
+ align:start position:0%
+Model S that can only go about half as
+far about 125 150 miles per per battery
+
+ align:start position:0%
+far about 125 150 miles per per battery
+ 
+
+ align:start position:0%
+far about 125 150 miles per per battery
+charge so you can buy the more expensive
+
+ align:start position:0%
+charge so you can buy the more expensive
+ 
+
+ align:start position:0%
+charge so you can buy the more expensive
+one because it's got this fancier
+
+ align:start position:0%
+one because it's got this fancier
+ 
+
+ align:start position:0%
+one because it's got this fancier
+battery 250 miles you can go it cost
+
+ align:start position:0%
+battery 250 miles you can go it cost
+ 
+
+ align:start position:0%
+battery 250 miles you can go it cost
+more money or the less expensive one
+
+ align:start position:0%
+more money or the less expensive one
+ 
+
+ align:start position:0%
+more money or the less expensive one
+with a less expens less fancy battery it
+
+ align:start position:0%
+with a less expens less fancy battery it
+ 
+
+ align:start position:0%
+with a less expens less fancy battery it
+only go 150
+
+ align:start position:0%
+only go 150
+ 
+
+ align:start position:0%
+only go 150
+mil well um in September 2017 there was
+
+ align:start position:0%
+mil well um in September 2017 there was
+ 
+
+ align:start position:0%
+mil well um in September 2017 there was
+a huge hurricane in Florida and people
+
+ align:start position:0%
+a huge hurricane in Florida and people
+ 
+
+ align:start position:0%
+a huge hurricane in Florida and people
+had to evacuate and Tesla understood
+
+ align:start position:0%
+had to evacuate and Tesla understood
+ 
+
+ align:start position:0%
+had to evacuate and Tesla understood
+that the limits on how far you could
+
+ align:start position:0%
+that the limits on how far you could
+ 
+
+ align:start position:0%
+that the limits on how far you could
+drive Florida's a big state could get in
+
+ align:start position:0%
+drive Florida's a big state could get in
+ 
+
+ align:start position:0%
+drive Florida's a big state could get in
+the way of people
+
+ align:start position:0%
+the way of people
+ 
+
+ align:start position:0%
+the way of people
+evacuating so Tesla said you know what
+
+ align:start position:0%
+evacuating so Tesla said you know what
+ 
+
+ align:start position:0%
+evacuating so Tesla said you know what
+all cars can now go 250 miles on their
+
+ align:start position:0%
+all cars can now go 250 miles on their
+ 
+
+ align:start position:0%
+all cars can now go 250 miles on their
+battery people like what the what do you
+
+ align:start position:0%
+battery people like what the what do you
+ 
+
+ align:start position:0%
+battery people like what the what do you
+mean we can go 250 miles in the battery
+
+ align:start position:0%
+mean we can go 250 miles in the battery
+ 
+
+ align:start position:0%
+mean we can go 250 miles in the battery
+well turn out it's the same battery they
+
+ align:start position:0%
+well turn out it's the same battery they
+ 
+
+ align:start position:0%
+well turn out it's the same battery they
+just had a piece of code that limited
+
+ align:start position:0%
+just had a piece of code that limited
+ 
+
+ align:start position:0%
+just had a piece of code that limited
+how far you could go in the cheaper car
+
+ align:start position:0%
+how far you could go in the cheaper car
+ 
+
+ align:start position:0%
+how far you could go in the cheaper car
+why would they do that why would they
+
+ align:start position:0%
+why would they do that why would they
+ 
+
+ align:start position:0%
+why would they do that why would they
+literally have the same battery and
+
+ align:start position:0%
+literally have the same battery and
+ 
+
+ align:start position:0%
+literally have the same battery and
+literally add money to add code to limit
+
+ align:start position:0%
+literally add money to add code to limit
+ 
+
+ align:start position:0%
+literally add money to add code to limit
+how far you could go why' they do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly there's two types of people
+
+ align:start position:0%
+exactly there's two types of people
+ 
+
+ align:start position:0%
+exactly there's two types of people
+people who have a lot of money and are
+
+ align:start position:0%
+people who have a lot of money and are
+ 
+
+ align:start position:0%
+people who have a lot of money and are
+willing to pay for a better car people
+
+ align:start position:0%
+willing to pay for a better car people
+ 
+
+ align:start position:0%
+willing to pay for a better car people
+don't a lot of money not willing to pay
+
+ align:start position:0%
+don't a lot of money not willing to pay
+ 
+
+ align:start position:0%
+don't a lot of money not willing to pay
+for a better car if they just simply
+
+ align:start position:0%
+for a better car if they just simply
+ 
+
+ align:start position:0%
+for a better car if they just simply
+said we're going to sell Modelo 250
+
+ align:start position:0%
+said we're going to sell Modelo 250
+ 
+
+ align:start position:0%
+said we're going to sell Modelo 250
+miles a bunch of lower income people
+
+ align:start position:0%
+miles a bunch of lower income people
+ 
+
+ align:start position:0%
+miles a bunch of lower income people
+wouldn't have bought it if they said
+
+ align:start position:0%
+wouldn't have bought it if they said
+ 
+
+ align:start position:0%
+wouldn't have bought it if they said
+we're going to let everyone go 250 miles
+
+ align:start position:0%
+we're going to let everyone go 250 miles
+ 
+
+ align:start position:0%
+we're going to let everyone go 250 miles
+on a cheaper price then they wouldn't
+
+ align:start position:0%
+on a cheaper price then they wouldn't
+ 
+
+ align:start position:0%
+on a cheaper price then they wouldn't
+have made as much money so they said a
+
+ align:start position:0%
+have made as much money so they said a
+ 
+
+ align:start position:0%
+have made as much money so they said a
+high price for a premium product to grab
+
+ align:start position:0%
+high price for a premium product to grab
+ 
+
+ align:start position:0%
+high price for a premium product to grab
+all the low elasticity consumers and a
+
+ align:start position:0%
+all the low elasticity consumers and a
+ 
+
+ align:start position:0%
+all the low elasticity consumers and a
+lower price for a less premium product
+
+ align:start position:0%
+lower price for a less premium product
+ 
+
+ align:start position:0%
+lower price for a less premium product
+to grab the high elasticity consumers
+
+ align:start position:0%
+to grab the high elasticity consumers
+ 
+
+ align:start position:0%
+to grab the high elasticity consumers
+even though the products were the same
+
+ align:start position:0%
+even though the products were the same
+ 
+
+ align:start position:0%
+even though the products were the same
+this actually uh Tesla is not Al loness
+
+ align:start position:0%
+this actually uh Tesla is not Al loness
+ 
+
+ align:start position:0%
+this actually uh Tesla is not Al loness
+when IBM first created the the uh uh
+
+ align:start position:0%
+when IBM first created the the uh uh
+ 
+
+ align:start position:0%
+when IBM first created the the uh uh
+digital
+
+ align:start position:0%
+digital
+ 
+
+ align:start position:0%
+digital
+printer uh it uh said had a home version
+
+ align:start position:0%
+printer uh it uh said had a home version
+ 
+
+ align:start position:0%
+printer uh it uh said had a home version
+which was much less efficient than the
+
+ align:start position:0%
+which was much less efficient than the
+ 
+
+ align:start position:0%
+which was much less efficient than the
+office version and it turned out someone
+
+ align:start position:0%
+office version and it turned out someone
+ 
+
+ align:start position:0%
+office version and it turned out someone
+took them apart and it was the same
+
+ align:start position:0%
+took them apart and it was the same
+ 
+
+ align:start position:0%
+took them apart and it was the same
+printer there's added crap to the motor
+
+ align:start position:0%
+printer there's added crap to the motor
+ 
+
+ align:start position:0%
+printer there's added crap to the motor
+on the home version to make it go
+
+ align:start position:0%
+on the home version to make it go
+ 
+
+ align:start position:0%
+on the home version to make it go
+slower okay because they want to take
+
+ align:start position:0%
+slower okay because they want to take
+ 
+
+ align:start position:0%
+slower okay because they want to take
+that same Advantage they want to be able
+
+ align:start position:0%
+that same Advantage they want to be able
+ 
+
+ align:start position:0%
+that same Advantage they want to be able
+to charge a lot for the office one
+
+ align:start position:0%
+to charge a lot for the office one
+ 
+
+ align:start position:0%
+to charge a lot for the office one
+because people are less price elastic in
+
+ align:start position:0%
+because people are less price elastic in
+ 
+
+ align:start position:0%
+because people are less price elastic in
+the office okay turns out you could take
+
+ align:start position:0%
+the office okay turns out you could take
+ 
+
+ align:start position:0%
+the office okay turns out you could take
+this too far Amazon tried to go further
+
+ align:start position:0%
+this too far Amazon tried to go further
+ 
+
+ align:start position:0%
+this too far Amazon tried to go further
+with this Amazon actually tried to set
+
+ align:start position:0%
+with this Amazon actually tried to set
+ 
+
+ align:start position:0%
+with this Amazon actually tried to set
+prices by IP
+
+ align:start position:0%
+prices by IP
+ 
+
+ align:start position:0%
+prices by IP
+address so Amazon literally an exercise
+
+ align:start position:0%
+address so Amazon literally an exercise
+ 
+
+ align:start position:0%
+address so Amazon literally an exercise
+where literally they would differentiate
+
+ align:start position:0%
+where literally they would differentiate
+ 
+
+ align:start position:0%
+where literally they would differentiate
+the price you'd see online by your IP
+
+ align:start position:0%
+the price you'd see online by your IP
+ 
+
+ align:start position:0%
+the price you'd see online by your IP
+address why would they do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that why would they be once again
+
+ align:start position:0%
+that why would they be once again
+ 
+
+ align:start position:0%
+that why would they be once again
+regardless of your feelings about Jeff
+
+ align:start position:0%
+regardless of your feelings about Jeff
+ 
+
+ align:start position:0%
+regardless of your feelings about Jeff
+Bezos why would they do that why would
+
+ align:start position:0%
+Bezos why would they do that why would
+ 
+
+ align:start position:0%
+Bezos why would they do that why would
+they differentiate the price
+
+ align:start position:0%
+they differentiate the price
+ 
+
+ align:start position:0%
+they differentiate the price
+yeah yeah but how would they know by
+
+ align:start position:0%
+yeah yeah but how would they know by
+ 
+
+ align:start position:0%
+yeah yeah but how would they know by
+your IP
+
+ align:start position:0%
+your IP
+ 
+
+ align:start position:0%
+your IP
+address what's
+
+ align:start position:0%
+address what's
+ 
+
+ align:start position:0%
+address what's
+that P sales is one reason what else
+
+ align:start position:0%
+that P sales is one reason what else
+ 
+
+ align:start position:0%
+that P sales is one reason what else
+yeah your ZIP code that's another
+
+ align:start position:0%
+yeah your ZIP code that's another
+ 
+
+ align:start position:0%
+yeah your ZIP code that's another
+reason what else who's willing to pay a
+
+ align:start position:0%
+reason what else who's willing to pay a
+ 
+
+ align:start position:0%
+reason what else who's willing to pay a
+lot yeah what's that yeah basically if
+
+ align:start position:0%
+lot yeah what's that yeah basically if
+ 
+
+ align:start position:0%
+lot yeah what's that yeah basically if
+you're ordering from Goldman Sachs IP
+
+ align:start position:0%
+you're ordering from Goldman Sachs IP
+ 
+
+ align:start position:0%
+you're ordering from Goldman Sachs IP
+address they're like you're rich we're
+
+ align:start position:0%
+address they're like you're rich we're
+ 
+
+ align:start position:0%
+address they're like you're rich we're
+going to charge you a lot if you're
+
+ align:start position:0%
+going to charge you a lot if you're
+ 
+
+ align:start position:0%
+going to charge you a lot if you're
+ordering from some you know homeless
+
+ align:start position:0%
+ordering from some you know homeless
+ 
+
+ align:start position:0%
+ordering from some you know homeless
+shelter or some place people don't have
+
+ align:start position:0%
+shelter or some place people don't have
+ 
+
+ align:start position:0%
+shelter or some place people don't have
+any money they'll charge you less so
+
+ align:start position:0%
+any money they'll charge you less so
+ 
+
+ align:start position:0%
+any money they'll charge you less so
+basically they said we've got a great IP
+
+ align:start position:0%
+basically they said we've got a great IP
+ 
+
+ align:start position:0%
+basically they said we've got a great IP
+address is a great signal of willingness
+
+ align:start position:0%
+address is a great signal of willingness
+ 
+
+ align:start position:0%
+address is a great signal of willingness
+to pay will suck up all that consumer
+
+ align:start position:0%
+to pay will suck up all that consumer
+ 
+
+ align:start position:0%
+to pay will suck up all that consumer
+surplus by varying the price by
+
+ align:start position:0%
+surplus by varying the price by
+ 
+
+ align:start position:0%
+surplus by varying the price by
+willingness to pay they got busted and
+
+ align:start position:0%
+willingness to pay they got busted and
+ 
+
+ align:start position:0%
+willingness to pay they got busted and
+couldn't do it
+
+ align:start position:0%
+couldn't do it
+ 
+
+ align:start position:0%
+couldn't do it
+anymore uh they were told they couldn't
+
+ align:start position:0%
+anymore uh they were told they couldn't
+ 
+
+ align:start position:0%
+anymore uh they were told they couldn't
+do that now it's not clear why not uh in
+
+ align:start position:0%
+do that now it's not clear why not uh in
+ 
+
+ align:start position:0%
+do that now it's not clear why not uh in
+fact the reason why not you might say
+
+ align:start position:0%
+fact the reason why not you might say
+ 
+
+ align:start position:0%
+fact the reason why not you might say
+well look why shouldn't they do that
+
+ align:start position:0%
+well look why shouldn't they do that
+ 
+
+ align:start position:0%
+well look why shouldn't they do that
+they're increasing efficiency if they
+
+ align:start position:0%
+they're increasing efficiency if they
+ 
+
+ align:start position:0%
+they're increasing efficiency if they
+don't do that we're losing C plus e by
+
+ align:start position:0%
+don't do that we're losing C plus e by
+ 
+
+ align:start position:0%
+don't do that we're losing C plus e by
+doing that we're gaining efficiency
+
+ align:start position:0%
+doing that we're gaining efficiency
+ 
+
+ align:start position:0%
+doing that we're gaining efficiency
+they're selling more units they wouldn't
+
+ align:start position:0%
+they're selling more units they wouldn't
+ 
+
+ align:start position:0%
+they're selling more units they wouldn't
+have sold those low-income consumers
+
+ align:start position:0%
+have sold those low-income consumers
+ 
+
+ align:start position:0%
+have sold those low-income consumers
+Tesla wouldn't have sold those cheaper
+
+ align:start position:0%
+Tesla wouldn't have sold those cheaper
+ 
+
+ align:start position:0%
+Tesla wouldn't have sold those cheaper
+model X's or whatever they were so
+
+ align:start position:0%
+model X's or whatever they were so
+ 
+
+ align:start position:0%
+model X's or whatever they were so
+what's wrong with that and the answer is
+
+ align:start position:0%
+what's wrong with that and the answer is
+ 
+
+ align:start position:0%
+what's wrong with that and the answer is
+in a tral economics world nothing TR
+
+ align:start position:0%
+in a tral economics world nothing TR
+ 
+
+ align:start position:0%
+in a tral economics world nothing TR
+economics world we should have let Tesla
+
+ align:start position:0%
+economics world we should have let Tesla
+ 
+
+ align:start position:0%
+economics world we should have let Tesla
+do that we should have let IBM make the
+
+ align:start position:0%
+do that we should have let IBM make the
+ 
+
+ align:start position:0%
+do that we should have let IBM make the
+crappy home printer we should have let
+
+ align:start position:0%
+crappy home printer we should have let
+ 
+
+ align:start position:0%
+crappy home printer we should have let
+Amazon differentiate by IP address the
+
+ align:start position:0%
+Amazon differentiate by IP address the
+ 
+
+ align:start position:0%
+Amazon differentiate by IP address the
+reason we didn't speaks the fact that
+
+ align:start position:0%
+reason we didn't speaks the fact that
+ 
+
+ align:start position:0%
+reason we didn't speaks the fact that
+people don't think consumer producer
+
+ align:start position:0%
+people don't think consumer producer
+ 
+
+ align:start position:0%
+people don't think consumer producer
+Surplus are really valed equally that we
+
+ align:start position:0%
+Surplus are really valed equally that we
+ 
+
+ align:start position:0%
+Surplus are really valed equally that we
+care about both separately and that's
+
+ align:start position:0%
+care about both separately and that's
+ 
+
+ align:start position:0%
+care about both separately and that's
+what we'll start talking about more in a
+
+ align:start position:0%
+what we'll start talking about more in a
+ 
+
+ align:start position:0%
+what we'll start talking about more in a
+few lectures okay questions about that
+
+ align:start position:0%
+few lectures okay questions about that
+ 
+
+ align:start position:0%
+few lectures okay questions about that
+all right uh we'll come back on
+
+ align:start position:0%
+all right uh we'll come back on
+ 
+
+ align:start position:0%
+all right uh we'll come back on
+Wednesday do a second Monopoly lecture
+
+ align:start position:0%
+Wednesday do a second Monopoly lecture
+ 
+
+ align:start position:0%
+Wednesday do a second Monopoly lecture
+you're responsible for the lectures this
+
+ align:start position:0%
+you're responsible for the lectures this
+ 
+
+ align:start position:0%
+you're responsible for the lectures this
+week on the midterm Monday's lecture
+
+ align:start position:0%
+week on the midterm Monday's lecture
+ 
+
+ align:start position:0%
+week on the midterm Monday's lecture
+will go on a new topic which is not in
+
+ align:start position:0%
+will go on a new topic which is not in
+ 
+
+ align:start position:0%
+will go on a new topic which is not in
+the midterm but it's on the final so you
+
+ align:start position:0%
+the midterm but it's on the final so you
+ 
+
+ align:start position:0%
+the midterm but it's on the final so you
+don't want to miss it plus it involves
+
+ align:start position:0%
+don't want to miss it plus it involves
+ 
+
+ align:start position:0%
+don't want to miss it plus it involves
+allop which is fun
\ No newline at end of file
diff --git a/CSkcBXUIJh4.txt b/CSkcBXUIJh4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a7ec1bdd7ddaa933916d9a45c7a75cd936cd4e37
--- /dev/null
+++ b/CSkcBXUIJh4.txt
@@ -0,0 +1,529 @@
+Hey guys.
+
+Welcome back.
+
+Today we're going to do a fun
+problem that will test your
+
+knowledge of the law
+of total variance.
+
+And in the process, we'll also
+get more practice dealing with
+
+joint PDFs and computing
+conditional expectations and
+
+conditional variances.
+
+So in this problem, we are given
+a joint PDF for x and y.
+
+So we're told that x and y can
+take on the following values
+
+in the shape of this
+
+parallelogram, which I've drawn.
+
+And moreover, that x and y are
+uniformly distributed.
+
+So the joint PDF is just flat
+over this parallelogram.
+
+And because the parallelogram
+has an area of 1, the height
+
+of the PDF must also be 1 so
+that the PDF integrates to 1.
+
+OK.
+
+And then we are asked
+to compute the
+
+variance of x plus y.
+
+So you can think of x plus y as
+a new random variable whose
+
+variance we want to compute.
+
+And moreover, we're told we
+should compute this variance
+
+by using something called the
+law of total variance.
+
+So from lecture, you should
+remember or you should recall
+
+that the law of total variance
+can be written
+
+in these two ways.
+
+And the reason why there's two
+different forms for this case
+
+is because the formula
+always has you
+
+conditioning on something.
+
+Here we condition on x, here
+we condition on y.
+
+And for this problem, the
+logical choice you have for
+
+what to condition
+on is x or y.
+
+So again, we have this option.
+
+And my claim is that we
+should condition on x.
+
+And the reason has to do with
+the geometry of this diagram.
+
+So notice that if you freeze an
+x and then you sort of vary
+
+x, the width of this
+parallelogram stays constant.
+
+However, if you condition on y
+and look at the width this
+
+way, you see that the width
+of the slices you get by
+
+conditioning vary with y.
+
+So to make our lives easier,
+we're going to condition on x.
+
+And I'm going to erase this
+bottom one, because
+
+we're not using it.
+
+So this really can seem quite
+intimidating, because we have
+
+nested variances and
+expectations going on, but
+
+we'll just take it slowly
+step by step.
+
+So first, I want to focus
+on this term--
+
+the conditional expectation of
+x plus y conditioned on x.
+
+So coming back over to this
+picture, if you fix an
+
+arbitrary x in the interval,
+0 to 1, we're restricting
+
+ourselves to this universe.
+
+So y can only vary between this
+point and this point.
+
+Now, I've already written down
+here that the formula for this
+
+line is given by y
+is equal to x.
+
+And the formula for this
+line is given by y is
+
+equal to x plus 1.
+
+So in particular, when we
+condition on x, we know that y
+
+varies between x and x plus 1.
+
+But we actually know
+more than that.
+
+We know that in the
+unconditional universe, x and
+
+y were uniformly distributed.
+
+So it follows that in the
+conditional universe, y should
+
+also be uniformly distributed,
+because conditioning doesn't
+
+change the relative frequency
+of outcomes.
+
+So that reasoning means that
+we can draw the conditional
+
+PDF of y conditioned
+on x as this.
+
+We said it varies between
+x and x plus 1.
+
+And we also said that it's
+uniform, which means that it
+
+must have a height of 1.
+
+So this is py given
+x, y given x.
+
+Now, you might be concerned,
+because, well, we're trying to
+
+compute the expectation of
+x plus y and this is the
+
+conditional PDF of y, not of the
+random variable, x plus y.
+
+But I claim that we're OK, this
+is still useful, because
+
+if we're conditioning
+on x, this x
+
+just acts as a constant.
+
+It's not really going to change
+anything except shift
+
+the expectation of y
+by an amount of x.
+
+So what I'm saying in math terms
+is that this is actually
+
+just x plus the expectation
+of y given x.
+
+And now our conditional
+PDF comes into play.
+
+Conditioned on x, this
+is the PDF of y.
+
+And because it's uniformly
+distributed and because
+
+expectation acts like center
+of mass, we know that the
+
+expectation should be
+the midpoint, right?
+
+And so to compute this point, we
+simply take the average of
+
+the endpoints, x plus 1 plus
+x over 2, which gives us
+
+2x plus 1 over 2.
+
+So plugging this back up here,
+we get 2x/2 plus 2x plus 1
+
+over 2, which is 4x plus 1
+over 2, or 2x plus 1/2.
+
+OK.
+
+So now I want to look at the
+next term, the next inner
+
+term, which is this guy.
+
+So this computation is
+going to be very
+
+similar in nature, actually.
+
+So we already discussed
+that the joint--
+
+sorry, not the joint, the
+conditional PDF of y given x
+
+is this guy.
+
+So the variance of x plus y
+conditioned on x, we sort of
+
+have a similar phenomenon
+occurring.
+
+x now in this conditional
+world just acts like a
+
+constant that shifts the PDF but
+doesn't change the width
+
+of the distribution at all.
+
+So this is actually just equal
+to the variance of y given x,
+
+because constants don't
+affect the variance.
+
+And now we can look at this
+conditional PDF to figure out
+
+what this is.
+
+So we're going to take a quick
+tangent over here, and I'm
+
+just going to remind you guys
+that we have a formula for
+
+computing the variance of a
+random variable when it's
+
+uniformly distributed between
+two endpoints.
+
+So say we have a random variable
+whose PDF looks
+
+something like this.
+
+Let's call it, let's say, w.
+
+This is pww.
+
+We have a formula that says
+variance of w is equal to b
+
+minus a squared over 12.
+
+So we can apply that
+formula over here.
+
+b is x plus 1, a is x.
+
+So b minus a squared over
+12 is just 1/12.
+
+So we get 1/12.
+
+So we're making good progress,
+because we have this inner
+
+quantity and this
+inner quantity.
+
+So now all we need to do is take
+the outer variance and
+
+the outer expectation.
+
+So writing this all down, we
+get variance of x plus y is
+
+equal to variance of this guy,
+2x plus 1/2 plus the
+
+expectation of 1/12.
+
+ 
+
+So this term is quite simple.
+
+We know that the expectation of
+a constant or of a scalar
+
+is simply that scalar.
+
+So this evaluates to 1/12.
+
+And this one is not
+bad either.
+
+So similar to our discussion up
+here, we know constants do
+
+not affect variance.
+
+You know they shift your
+distribution, they don't
+
+change the variance.
+
+So we can ignore the 1/2.
+
+This scaling factor
+of 2, however,
+
+will change the variance.
+
+But we know how to handle
+this already
+
+from previous lectures.
+
+We know that you can just take
+out this scalar scaling factor
+
+as long as we square it.
+
+So this becomes 2 squared,
+or 4 times the
+
+variance of x plus 1/12.
+
+And now to compute the variance
+of x, we're going to
+
+use that formula again,
+and we're
+
+going to use this picture.
+
+So here we have the joint PDF of
+x and y, but really we want
+
+now the PDF of x, so we
+can figure out what
+
+the variance is.
+
+So hopefully you remember a
+trick we taught you called
+
+marginalization.
+
+To get the PDF of x given
+a joint PDF, you simply
+
+marginalize over the
+values of y.
+
+So if you freeze x is equal to
+0, you get the probability
+
+density line over x by
+integrating over this
+
+interval, over y.
+
+So if you integrate over
+this strip, you get 1.
+
+If you move x over a little
+bit and you integrate over
+
+this strip, you get 1.
+
+This is the argument I was
+making earlier that the width
+
+of this interval stays the same,
+and hence, the variance
+
+stays the same.
+
+So based on that argument, which
+was slightly hand wavy,
+
+let's come over here
+and draw it.
+
+ 
+
+We're claiming that the PDF of
+x, px of x, looks like this.
+
+It's just uniformly distributed
+between 0 and 1.
+
+And if you buy that, then we're
+done, we're home free,
+
+because we can apply this
+formula, b minus a squared
+
+over 12, gives us
+the variance.
+
+So b is 1, a is 0, which
+gives variance of
+
+x is equal to 1/12.
+
+So coming back over here, we
+get 4 times 1/12 plus 1/12,
+
+which is 5/12.
+
+And that is our answer.
+
+So this problem was
+straightforward in the sense
+
+that our task was very clear.
+
+We had to compute this, and we
+had to do so by using the law
+
+of total variance.
+
+But we sort of reviewed a lot
+of concepts along the way.
+
+We saw how, given a joint
+PDF, you marginalize to
+
+get the PDF of x.
+
+We saw how constants don't
+change variance.
+
+We got a lot of practice
+finding conditional
+
+distributions and computing
+conditional
+
+expectations and variances.
+
+And we also saw this trick.
+
+And it might seem like cheating
+to memorize formulas,
+
+but there's a few important
+ones you should know.
+
+And it will help you sort of
+become faster at doing
+
+computations.
+
+And that's important,
+especially if you
+
+guys take the exams.
+
+So that's it.
+
+See you next time.
\ No newline at end of file
diff --git a/DF9fniCnL10.txt b/DF9fniCnL10.txt
new file mode 100644
index 0000000000000000000000000000000000000000..20ff87161a344dc88ada679e01510bbb8a78e623
--- /dev/null
+++ b/DF9fniCnL10.txt
@@ -0,0 +1,8331 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah so the publisher can demand you
+
+ align:start position:0%
+so yeah so the publisher can demand you
+ 
+
+ align:start position:0%
+so yeah so the publisher can demand you
+know I want to see this feature EA
+
+ align:start position:0%
+know I want to see this feature EA
+ 
+
+ align:start position:0%
+know I want to see this feature EA
+demands that this game work with origin
+
+ align:start position:0%
+demands that this game work with origin
+ 
+
+ align:start position:0%
+demands that this game work with origin
+ubisoft demands that you do play with
+
+ align:start position:0%
+ubisoft demands that you do play with
+ 
+
+ align:start position:0%
+ubisoft demands that you do play with
+that was that their Universal sign up
+
+ align:start position:0%
+that was that their Universal sign up
+ 
+
+ align:start position:0%
+that was that their Universal sign up
+system gets added odd things like that
+
+ align:start position:0%
+system gets added odd things like that
+ 
+
+ align:start position:0%
+system gets added odd things like that
+right that happens all the time other
+
+ align:start position:0%
+right that happens all the time other
+ 
+
+ align:start position:0%
+right that happens all the time other
+stuff that's maybe money related or
+
+ align:start position:0%
+stuff that's maybe money related or
+ 
+
+ align:start position:0%
+stuff that's maybe money related or
+market related plus light expectations
+
+ align:start position:0%
+market related plus light expectations
+ 
+
+ align:start position:0%
+market related plus light expectations
+just yeah that usually is similar to the
+
+ align:start position:0%
+just yeah that usually is similar to the
+ 
+
+ align:start position:0%
+just yeah that usually is similar to the
+publisher thing someone's got to push
+
+ align:start position:0%
+publisher thing someone's got to push
+ 
+
+ align:start position:0%
+publisher thing someone's got to push
+that but somebody could come internally
+
+ align:start position:0%
+that but somebody could come internally
+ 
+
+ align:start position:0%
+that but somebody could come internally
+from it from your developer from the
+
+ align:start position:0%
+from it from your developer from the
+ 
+
+ align:start position:0%
+from it from your developer from the
+development team right they look at
+
+ align:start position:0%
+development team right they look at
+ 
+
+ align:start position:0%
+development team right they look at
+competing products and says hey this
+
+ align:start position:0%
+competing products and says hey this
+ 
+
+ align:start position:0%
+competing products and says hey this
+thing seems to be doing well
+
+ align:start position:0%
+thing seems to be doing well
+ 
+
+ align:start position:0%
+thing seems to be doing well
+and I'll let that hats because hats seem
+
+ align:start position:0%
+and I'll let that hats because hats seem
+ 
+
+ align:start position:0%
+and I'll let that hats because hats seem
+to be doing well for some games so you
+
+ align:start position:0%
+to be doing well for some games so you
+ 
+
+ align:start position:0%
+to be doing well for some games so you
+know we can add hands to our game it's
+
+ align:start position:0%
+know we can add hands to our game it's
+ 
+
+ align:start position:0%
+know we can add hands to our game it's
+not going to necessarily change the way
+
+ align:start position:0%
+not going to necessarily change the way
+ 
+
+ align:start position:0%
+not going to necessarily change the way
+how to give functions better so a new
+
+ align:start position:0%
+how to give functions better so a new
+ 
+
+ align:start position:0%
+how to give functions better so a new
+feature is still a new you still got to
+
+ align:start position:0%
+feature is still a new you still got to
+ 
+
+ align:start position:0%
+feature is still a new you still got to
+come up with mechanics to unlock new
+
+ align:start position:0%
+come up with mechanics to unlock new
+ 
+
+ align:start position:0%
+come up with mechanics to unlock new
+hats and equipped new hats and make sure
+
+ align:start position:0%
+hats and equipped new hats and make sure
+ 
+
+ align:start position:0%
+hats and equipped new hats and make sure
+the enemy correctly and things like that
+
+ align:start position:0%
+the enemy correctly and things like that
+ 
+
+ align:start position:0%
+the enemy correctly and things like that
+even if necessarily the gameplay
+
+ align:start position:0%
+even if necessarily the gameplay
+ 
+
+ align:start position:0%
+even if necessarily the gameplay
+decision making you're making the game
+
+ align:start position:0%
+decision making you're making the game
+ 
+
+ align:start position:0%
+decision making you're making the game
+doesn't change of course hat certainly
+
+ align:start position:0%
+doesn't change of course hat certainly
+ 
+
+ align:start position:0%
+doesn't change of course hat certainly
+do change the way how some games work
+
+ align:start position:0%
+do change the way how some games work
+ 
+
+ align:start position:0%
+do change the way how some games work
+the changes in marketplace in general
+
+ align:start position:0%
+the changes in marketplace in general
+ 
+
+ align:start position:0%
+the changes in marketplace in general
+and sometimes are making a sequel to a
+
+ align:start position:0%
+and sometimes are making a sequel to a
+ 
+
+ align:start position:0%
+and sometimes are making a sequel to a
+game right sometimes you you you've got
+
+ align:start position:0%
+game right sometimes you you you've got
+ 
+
+ align:start position:0%
+game right sometimes you you you've got
+your adding number two or number three
+
+ align:start position:0%
+your adding number two or number three
+ 
+
+ align:start position:0%
+your adding number two or number three
+at the end of the title and your players
+
+ align:start position:0%
+at the end of the title and your players
+ 
+
+ align:start position:0%
+at the end of the title and your players
+are gonna expect something new and so
+
+ align:start position:0%
+are gonna expect something new and so
+ 
+
+ align:start position:0%
+are gonna expect something new and so
+there's some pressure for you to sort of
+
+ align:start position:0%
+there's some pressure for you to sort of
+ 
+
+ align:start position:0%
+there's some pressure for you to sort of
+add new mechanics instead of simply say
+
+ align:start position:0%
+add new mechanics instead of simply say
+ 
+
+ align:start position:0%
+add new mechanics instead of simply say
+iterating on the old ones why would you
+
+ align:start position:0%
+iterating on the old ones why would you
+ 
+
+ align:start position:0%
+iterating on the old ones why would you
+cut cut mechanics not necessarily
+
+ align:start position:0%
+cut cut mechanics not necessarily
+ 
+
+ align:start position:0%
+cut cut mechanics not necessarily
+cutting features but cutting mechanics
+
+ align:start position:0%
+cutting features but cutting mechanics
+ 
+
+ align:start position:0%
+cutting features but cutting mechanics
+game mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's one that's one good reason I've
+
+ align:start position:0%
+that's one that's one good reason I've
+ 
+
+ align:start position:0%
+that's one that's one good reason I've
+been drilling into you all semester long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreasing Curtis I know this separate
+
+ align:start position:0%
+decreasing Curtis I know this separate
+ 
+
+ align:start position:0%
+decreasing Curtis I know this separate
+from simple if I gave they both both
+
+ align:start position:0%
+from simple if I gave they both both
+ 
+
+ align:start position:0%
+from simple if I gave they both both
+good points right there all the
+
+ align:start position:0%
+good points right there all the
+ 
+
+ align:start position:0%
+good points right there all the
+decreasing learned learning curve is
+
+ align:start position:0%
+decreasing learned learning curve is
+ 
+
+ align:start position:0%
+decreasing learned learning curve is
+like testers just don't get how this
+
+ align:start position:0%
+like testers just don't get how this
+ 
+
+ align:start position:0%
+like testers just don't get how this
+game functions because too much stuff
+
+ align:start position:0%
+game functions because too much stuff
+ 
+
+ align:start position:0%
+game functions because too much stuff
+going on simultaneously
+
+ align:start position:0%
+going on simultaneously
+ 
+
+ align:start position:0%
+going on simultaneously
+you could try to tune those mechanics to
+
+ align:start position:0%
+you could try to tune those mechanics to
+ 
+
+ align:start position:0%
+you could try to tune those mechanics to
+make it a little bit more legible if you
+
+ align:start position:0%
+make it a little bit more legible if you
+ 
+
+ align:start position:0%
+make it a little bit more legible if you
+just try taking mechanics completely out
+
+ align:start position:0%
+just try taking mechanics completely out
+ 
+
+ align:start position:0%
+just try taking mechanics completely out
+so that people can achieve it simplify
+
+ align:start position:0%
+so that people can achieve it simplify
+ 
+
+ align:start position:0%
+so that people can achieve it simplify
+any game could could be that but it also
+
+ align:start position:0%
+any game could could be that but it also
+ 
+
+ align:start position:0%
+any game could could be that but it also
+could be just trying to make what score
+
+ align:start position:0%
+could be just trying to make what score
+ 
+
+ align:start position:0%
+could be just trying to make what score
+about the game more obvious you know
+
+ align:start position:0%
+about the game more obvious you know
+ 
+
+ align:start position:0%
+about the game more obvious you know
+this game is really about generations
+
+ align:start position:0%
+this game is really about generations
+ 
+
+ align:start position:0%
+this game is really about generations
+and generations of heroes you know that
+
+ align:start position:0%
+and generations of heroes you know that
+ 
+
+ align:start position:0%
+and generations of heroes you know that
+there's a game by hero generators yeah
+
+ align:start position:0%
+there's a game by hero generators yeah
+ 
+
+ align:start position:0%
+there's a game by hero generators yeah
+and and you want you know and you've got
+
+ align:start position:0%
+and and you want you know and you've got
+ 
+
+ align:start position:0%
+and and you want you know and you've got
+say some sort of very elaborate weapons
+
+ align:start position:0%
+say some sort of very elaborate weapons
+ 
+
+ align:start position:0%
+say some sort of very elaborate weapons
+crafting mechanic or something like in
+
+ align:start position:0%
+crafting mechanic or something like in
+ 
+
+ align:start position:0%
+crafting mechanic or something like in
+there well the weapons crafty mechanic
+
+ align:start position:0%
+there well the weapons crafty mechanic
+ 
+
+ align:start position:0%
+there well the weapons crafty mechanic
+may not be really what your games about
+
+ align:start position:0%
+may not be really what your games about
+ 
+
+ align:start position:0%
+may not be really what your games about
+so you might want to take that out
+
+ align:start position:0%
+so you might want to take that out
+ 
+
+ align:start position:0%
+so you might want to take that out
+because people saw forget about what the
+
+ align:start position:0%
+because people saw forget about what the
+ 
+
+ align:start position:0%
+because people saw forget about what the
+core experience of the game is supposed
+
+ align:start position:0%
+core experience of the game is supposed
+ 
+
+ align:start position:0%
+core experience of the game is supposed
+to be so focusing back on the core of
+
+ align:start position:0%
+to be so focusing back on the core of
+ 
+
+ align:start position:0%
+to be so focusing back on the core of
+the game what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say okay well all new new technologies
+
+ align:start position:0%
+say okay well all new new technologies
+ 
+
+ align:start position:0%
+say okay well all new new technologies
+come out like what physics you know
+
+ align:start position:0%
+come out like what physics you know
+ 
+
+ align:start position:0%
+come out like what physics you know
+maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+well that's true right I tried to think
+
+ align:start position:0%
+well that's true right I tried to think
+ 
+
+ align:start position:0%
+well that's true right I tried to think
+of a game what that's a really obvious
+
+ align:start position:0%
+of a game what that's a really obvious
+ 
+
+ align:start position:0%
+of a game what that's a really obvious
+example can I want to think of a game
+
+ align:start position:0%
+example can I want to think of a game
+ 
+
+ align:start position:0%
+example can I want to think of a game
+mechanic that substantially changed when
+
+ align:start position:0%
+mechanic that substantially changed when
+ 
+
+ align:start position:0%
+mechanic that substantially changed when
+it went from 2d to 3d I'm thinking Mario
+
+ align:start position:0%
+it went from 2d to 3d I'm thinking Mario
+ 
+
+ align:start position:0%
+it went from 2d to 3d I'm thinking Mario
+but just just played on movement
+
+ align:start position:0%
+but just just played on movement
+ 
+
+ align:start position:0%
+but just just played on movement
+well the way how the camera responds to
+
+ align:start position:0%
+well the way how the camera responds to
+ 
+
+ align:start position:0%
+well the way how the camera responds to
+movement as well that that's that's a
+
+ align:start position:0%
+movement as well that that's that's a
+ 
+
+ align:start position:0%
+movement as well that that's that's a
+big one right in a 2d game say a
+
+ align:start position:0%
+big one right in a 2d game say a
+ 
+
+ align:start position:0%
+big one right in a 2d game say a
+side-scrolling game like Metroid or
+
+ align:start position:0%
+side-scrolling game like Metroid or
+ 
+
+ align:start position:0%
+side-scrolling game like Metroid or
+something like that
+
+ align:start position:0%
+something like that
+ 
+
+ align:start position:0%
+something like that
+you don't have this situation where the
+
+ align:start position:0%
+you don't have this situation where the
+ 
+
+ align:start position:0%
+you don't have this situation where the
+place where you are trying to go to is
+
+ align:start position:0%
+place where you are trying to go to is
+ 
+
+ align:start position:0%
+place where you are trying to go to is
+obscured unless it's actually physically
+
+ align:start position:0%
+obscured unless it's actually physically
+ 
+
+ align:start position:0%
+obscured unless it's actually physically
+blocked by something now you have to
+
+ align:start position:0%
+blocked by something now you have to
+ 
+
+ align:start position:0%
+blocked by something now you have to
+destroy or open up or something and in a
+
+ align:start position:0%
+destroy or open up or something and in a
+ 
+
+ align:start position:0%
+destroy or open up or something and in a
+3d space you that happens all the time
+
+ align:start position:0%
+3d space you that happens all the time
+ 
+
+ align:start position:0%
+3d space you that happens all the time
+you know you've just got bits of
+
+ align:start position:0%
+you know you've just got bits of
+ 
+
+ align:start position:0%
+you know you've just got bits of
+background scenery getting in a way off
+
+ align:start position:0%
+background scenery getting in a way off
+ 
+
+ align:start position:0%
+background scenery getting in a way off
+the camera Mario just changed the way
+
+ align:start position:0%
+the camera Mario just changed the way
+ 
+
+ align:start position:0%
+the camera Mario just changed the way
+how jumps work entirely when he went
+
+ align:start position:0%
+how jumps work entirely when he went
+ 
+
+ align:start position:0%
+how jumps work entirely when he went
+from the 2d Mario's to the Super Mario
+
+ align:start position:0%
+from the 2d Mario's to the Super Mario
+ 
+
+ align:start position:0%
+from the 2d Mario's to the Super Mario
+64 and they added and every iteration on
+
+ align:start position:0%
+64 and they added and every iteration on
+ 
+
+ align:start position:0%
+64 and they added and every iteration on
+top of that has added new ways to jump
+
+ align:start position:0%
+top of that has added new ways to jump
+ 
+
+ align:start position:0%
+top of that has added new ways to jump
+double jump struggle jumps jumping off
+
+ align:start position:0%
+double jump struggle jumps jumping off
+ 
+
+ align:start position:0%
+double jump struggle jumps jumping off
+the wall and stuff at it now now the
+
+ align:start position:0%
+the wall and stuff at it now now the
+ 
+
+ align:start position:0%
+the wall and stuff at it now now the
+latest Mario gives expect that you know
+
+ align:start position:0%
+latest Mario gives expect that you know
+ 
+
+ align:start position:0%
+latest Mario gives expect that you know
+all of that which is why I can't play
+
+ align:start position:0%
+all of that which is why I can't play
+ 
+
+ align:start position:0%
+all of that which is why I can't play
+Mario anymore because I didn't go
+
+ align:start position:0%
+Mario anymore because I didn't go
+ 
+
+ align:start position:0%
+Mario anymore because I didn't go
+through that process although the games
+
+ align:start position:0%
+through that process although the games
+ 
+
+ align:start position:0%
+through that process although the games
+are not at least the first couple of
+
+ align:start position:0%
+are not at least the first couple of
+ 
+
+ align:start position:0%
+are not at least the first couple of
+levels are not that harsh let's see what
+
+ align:start position:0%
+levels are not that harsh let's see what
+ 
+
+ align:start position:0%
+levels are not that harsh let's see what
+else this one I've been always
+
+ align:start position:0%
+else this one I've been always
+ 
+
+ align:start position:0%
+else this one I've been always
+mentioning there's an entire semester
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just to try something yeah oh yeah yeah
+
+ align:start position:0%
+just to try something yeah oh yeah yeah
+ 
+
+ align:start position:0%
+just to try something yeah oh yeah yeah
+justjust just to see how he's gonna
+
+ align:start position:0%
+justjust just to see how he's gonna
+ 
+
+ align:start position:0%
+justjust just to see how he's gonna
+change how the gameplay works right you
+
+ align:start position:0%
+change how the gameplay works right you
+ 
+
+ align:start position:0%
+change how the gameplay works right you
+know it is let's take something out and
+
+ align:start position:0%
+know it is let's take something out and
+ 
+
+ align:start position:0%
+know it is let's take something out and
+see whether that was actually essential
+
+ align:start position:0%
+see whether that was actually essential
+ 
+
+ align:start position:0%
+see whether that was actually essential
+to the experience or maybe I was getting
+
+ align:start position:0%
+to the experience or maybe I was getting
+ 
+
+ align:start position:0%
+to the experience or maybe I was getting
+in way of the experience you don't know
+
+ align:start position:0%
+in way of the experience you don't know
+ 
+
+ align:start position:0%
+in way of the experience you don't know
+you know like the emergent results of
+
+ align:start position:0%
+you know like the emergent results of
+ 
+
+ align:start position:0%
+you know like the emergent results of
+taking out a mechanic might actually end
+
+ align:start position:0%
+taking out a mechanic might actually end
+ 
+
+ align:start position:0%
+taking out a mechanic might actually end
+up as more like more interesting
+
+ align:start position:0%
+up as more like more interesting
+ 
+
+ align:start position:0%
+up as more like more interesting
+experience one of one thing that a book
+
+ align:start position:0%
+experience one of one thing that a book
+ 
+
+ align:start position:0%
+experience one of one thing that a book
+does mentioned is to take stuff out that
+
+ align:start position:0%
+does mentioned is to take stuff out that
+ 
+
+ align:start position:0%
+does mentioned is to take stuff out that
+might actually change to the ESRB rating
+
+ align:start position:0%
+might actually change to the ESRB rating
+ 
+
+ align:start position:0%
+might actually change to the ESRB rating
+of your game or the PEGI rating
+
+ align:start position:0%
+of your game or the PEGI rating
+ 
+
+ align:start position:0%
+of your game or the PEGI rating
+understanding something in the UK or in
+
+ align:start position:0%
+understanding something in the UK or in
+ 
+
+ align:start position:0%
+understanding something in the UK or in
+Europe so for instance if your game if
+
+ align:start position:0%
+Europe so for instance if your game if
+ 
+
+ align:start position:0%
+Europe so for instance if your game if
+you had if you're building the top of
+
+ align:start position:0%
+you had if you're building the top of
+ 
+
+ align:start position:0%
+you had if you're building the top of
+the game engine like unreal or something
+
+ align:start position:0%
+the game engine like unreal or something
+ 
+
+ align:start position:0%
+the game engine like unreal or something
+like that which has body body location
+
+ align:start position:0%
+like that which has body body location
+ 
+
+ align:start position:0%
+like that which has body body location
+damage if you shoot a head you know the
+
+ align:start position:0%
+damage if you shoot a head you know the
+ 
+
+ align:start position:0%
+damage if you shoot a head you know the
+game knows that it that you shot the
+
+ align:start position:0%
+game knows that it that you shot the
+ 
+
+ align:start position:0%
+game knows that it that you shot the
+head but maybe you don't want your game
+
+ align:start position:0%
+head but maybe you don't want your game
+ 
+
+ align:start position:0%
+head but maybe you don't want your game
+to be that specific
+
+ align:start position:0%
+to be that specific
+ 
+
+ align:start position:0%
+to be that specific
+maybe you're designing a game for kids
+
+ align:start position:0%
+maybe you're designing a game for kids
+ 
+
+ align:start position:0%
+maybe you're designing a game for kids
+or something like that and it's like oh
+
+ align:start position:0%
+or something like that and it's like oh
+ 
+
+ align:start position:0%
+or something like that and it's like oh
+you wanting kids for a hitch for
+
+ align:start position:0%
+you wanting kids for a hitch for
+ 
+
+ align:start position:0%
+you wanting kids for a hitch for
+successfully head-chopping each other is
+
+ align:start position:0%
+successfully head-chopping each other is
+ 
+
+ align:start position:0%
+successfully head-chopping each other is
+maybe not lit feel that we want to go
+
+ align:start position:0%
+maybe not lit feel that we want to go
+ 
+
+ align:start position:0%
+maybe not lit feel that we want to go
+for I initially put sense push us into
+
+ align:start position:0%
+for I initially put sense push us into
+ 
+
+ align:start position:0%
+for I initially put sense push us into
+out of the E for Everyone and into
+
+ align:start position:0%
+out of the E for Everyone and into
+ 
+
+ align:start position:0%
+out of the E for Everyone and into
+what's what's what's the next way mt t
+
+ align:start position:0%
+what's what's what's the next way mt t
+ 
+
+ align:start position:0%
+what's what's what's the next way mt t
+yeah ye 10 rating is that used to be
+
+ align:start position:0%
+yeah ye 10 rating is that used to be
+ 
+
+ align:start position:0%
+yeah ye 10 rating is that used to be
+okay and sometimes you just gotta cut
+
+ align:start position:0%
+okay and sometimes you just gotta cut
+ 
+
+ align:start position:0%
+okay and sometimes you just gotta cut
+mechanics because you don't have time to
+
+ align:start position:0%
+mechanics because you don't have time to
+ 
+
+ align:start position:0%
+mechanics because you don't have time to
+do them they're great ideas they both
+
+ align:start position:0%
+do them they're great ideas they both
+ 
+
+ align:start position:0%
+do them they're great ideas they both
+actually make your game better if you
+
+ align:start position:0%
+actually make your game better if you
+ 
+
+ align:start position:0%
+actually make your game better if you
+had time to be able to polish them and
+
+ align:start position:0%
+had time to be able to polish them and
+ 
+
+ align:start position:0%
+had time to be able to polish them and
+make them understandable and smooth and
+
+ align:start position:0%
+make them understandable and smooth and
+ 
+
+ align:start position:0%
+make them understandable and smooth and
+everything they just find out all times
+
+ align:start position:0%
+everything they just find out all times
+ 
+
+ align:start position:0%
+everything they just find out all times
+and you just want to be able to ship so
+
+ align:start position:0%
+and you just want to be able to ship so
+ 
+
+ align:start position:0%
+and you just want to be able to ship so
+that's a perfectly legitimate
+
+ align:start position:0%
+that's a perfectly legitimate
+ 
+
+ align:start position:0%
+that's a perfectly legitimate
+consideration oh so so that that's this
+
+ align:start position:0%
+consideration oh so so that that's this
+ 
+
+ align:start position:0%
+consideration oh so so that that's this
+process of like generating ideas so you
+
+ align:start position:0%
+process of like generating ideas so you
+ 
+
+ align:start position:0%
+process of like generating ideas so you
+say say this is like an axis of my the
+
+ align:start position:0%
+say say this is like an axis of my the
+ 
+
+ align:start position:0%
+say say this is like an axis of my the
+number of ideas that you've got in your
+
+ align:start position:0%
+number of ideas that you've got in your
+ 
+
+ align:start position:0%
+number of ideas that you've got in your
+game and mechanics in terms of either
+
+ align:start position:0%
+game and mechanics in terms of either
+ 
+
+ align:start position:0%
+game and mechanics in terms of either
+rules in a computer game of the code in
+
+ align:start position:0%
+rules in a computer game of the code in
+ 
+
+ align:start position:0%
+rules in a computer game of the code in
+these games let's just say it's rules as
+
+ align:start position:0%
+these games let's just say it's rules as
+ 
+
+ align:start position:0%
+these games let's just say it's rules as
+pieces for everything we have to make
+
+ align:start position:0%
+pieces for everything we have to make
+ 
+
+ align:start position:0%
+pieces for everything we have to make
+your game work and you kind of go
+
+ align:start position:0%
+your game work and you kind of go
+ 
+
+ align:start position:0%
+your game work and you kind of go
+through this brainstorming phase where
+
+ align:start position:0%
+through this brainstorming phase where
+ 
+
+ align:start position:0%
+through this brainstorming phase where
+you get like a ton of ideas right
+
+ align:start position:0%
+you get like a ton of ideas right
+ 
+
+ align:start position:0%
+you get like a ton of ideas right
+because some good ones up here cuz some
+
+ align:start position:0%
+because some good ones up here cuz some
+ 
+
+ align:start position:0%
+because some good ones up here cuz some
+crappy ones down there it's probably
+
+ align:start position:0%
+crappy ones down there it's probably
+ 
+
+ align:start position:0%
+crappy ones down there it's probably
+more like like a whole bunch of crappy
+
+ align:start position:0%
+more like like a whole bunch of crappy
+ 
+
+ align:start position:0%
+more like like a whole bunch of crappy
+ideas a couple of good ideas but you get
+
+ align:start position:0%
+ideas a couple of good ideas but you get
+ 
+
+ align:start position:0%
+ideas a couple of good ideas but you get
+this big explosion of ideas where where
+
+ align:start position:0%
+this big explosion of ideas where where
+ 
+
+ align:start position:0%
+this big explosion of ideas where where
+I use turning to experiments somebody my
+
+ align:start position:0%
+I use turning to experiments somebody my
+ 
+
+ align:start position:0%
+I use turning to experiments somebody my
+phone experiments they're thinking you
+
+ align:start position:0%
+phone experiments they're thinking you
+ 
+
+ align:start position:0%
+phone experiments they're thinking you
+know just just discussing them among
+
+ align:start position:0%
+know just just discussing them among
+ 
+
+ align:start position:0%
+know just just discussing them among
+your team what if we did this what if we
+
+ align:start position:0%
+your team what if we did this what if we
+ 
+
+ align:start position:0%
+your team what if we did this what if we
+did how we solve that problem we really
+
+ align:start position:0%
+did how we solve that problem we really
+ 
+
+ align:start position:0%
+did how we solve that problem we really
+be real interests of all experiments
+
+ align:start position:0%
+be real interests of all experiments
+ 
+
+ align:start position:0%
+be real interests of all experiments
+where you're something that you can play
+
+ align:start position:0%
+where you're something that you can play
+ 
+
+ align:start position:0%
+where you're something that you can play
+you know something that you whip up
+
+ align:start position:0%
+you know something that you whip up
+ 
+
+ align:start position:0%
+you know something that you whip up
+within an hour or half an hour and you
+
+ align:start position:0%
+within an hour or half an hour and you
+ 
+
+ align:start position:0%
+within an hour or half an hour and you
+actually put it in front we've been
+
+ align:start position:0%
+actually put it in front we've been
+ 
+
+ align:start position:0%
+actually put it in front we've been
+doing that all all semester some of the
+
+ align:start position:0%
+doing that all all semester some of the
+ 
+
+ align:start position:0%
+doing that all all semester some of the
+ideas we just come up off you know
+
+ align:start position:0%
+ideas we just come up off you know
+ 
+
+ align:start position:0%
+ideas we just come up off you know
+different ideas interacting and says
+
+ align:start position:0%
+different ideas interacting and says
+ 
+
+ align:start position:0%
+different ideas interacting and says
+what if we had you know dogs in our game
+
+ align:start position:0%
+what if we had you know dogs in our game
+ 
+
+ align:start position:0%
+what if we had you know dogs in our game
+what if we had solar power and game what
+
+ align:start position:0%
+what if we had solar power and game what
+ 
+
+ align:start position:0%
+what if we had solar power and game what
+every day has solar powered talks about
+
+ align:start position:0%
+every day has solar powered talks about
+ 
+
+ align:start position:0%
+every day has solar powered talks about
+game it things like that you know and
+
+ align:start position:0%
+game it things like that you know and
+ 
+
+ align:start position:0%
+game it things like that you know and
+then I guess just happened um however
+
+ align:start position:0%
+then I guess just happened um however
+ 
+
+ align:start position:0%
+then I guess just happened um however
+it's important that's so fun sort of in
+
+ align:start position:0%
+it's important that's so fun sort of in
+ 
+
+ align:start position:0%
+it's important that's so fun sort of in
+describing the brainstorming process
+
+ align:start position:0%
+describing the brainstorming process
+ 
+
+ align:start position:0%
+describing the brainstorming process
+that you can all been through already
+
+ align:start position:0%
+that you can all been through already
+ 
+
+ align:start position:0%
+that you can all been through already
+but one thing that we haven't
+
+ align:start position:0%
+but one thing that we haven't
+ 
+
+ align:start position:0%
+but one thing that we haven't
+necessarily asked you to do nearly as
+
+ align:start position:0%
+necessarily asked you to do nearly as
+ 
+
+ align:start position:0%
+necessarily asked you to do nearly as
+much is to come up with heart with with
+
+ align:start position:0%
+much is to come up with heart with with
+ 
+
+ align:start position:0%
+much is to come up with heart with with
+actual discrete experiments and I was
+
+ align:start position:0%
+actual discrete experiments and I was
+ 
+
+ align:start position:0%
+actual discrete experiments and I was
+like here's an idea actually come up
+
+ align:start position:0%
+like here's an idea actually come up
+ 
+
+ align:start position:0%
+like here's an idea actually come up
+with a criteria of success that you're
+
+ align:start position:0%
+with a criteria of success that you're
+ 
+
+ align:start position:0%
+with a criteria of success that you're
+looking for how do we know whether this
+
+ align:start position:0%
+looking for how do we know whether this
+ 
+
+ align:start position:0%
+looking for how do we know whether this
+particular idea this particular
+
+ align:start position:0%
+particular idea this particular
+ 
+
+ align:start position:0%
+particular idea this particular
+experiment version of the idea is
+
+ align:start position:0%
+experiment version of the idea is
+ 
+
+ align:start position:0%
+experiment version of the idea is
+succeeding or not and you're going to
+
+ align:start position:0%
+succeeding or not and you're going to
+ 
+
+ align:start position:0%
+succeeding or not and you're going to
+need that because you're going to need
+
+ align:start position:0%
+need that because you're going to need
+ 
+
+ align:start position:0%
+need that because you're going to need
+to call yeah you're gonna need to like
+
+ align:start position:0%
+to call yeah you're gonna need to like
+ 
+
+ align:start position:0%
+to call yeah you're gonna need to like
+reduce this back down try to keep this
+
+ align:start position:0%
+reduce this back down try to keep this
+ 
+
+ align:start position:0%
+reduce this back down try to keep this
+or maybe even build this up a little bit
+
+ align:start position:0%
+or maybe even build this up a little bit
+ 
+
+ align:start position:0%
+or maybe even build this up a little bit
+actually springing ball like you're
+
+ align:start position:0%
+actually springing ball like you're
+ 
+
+ align:start position:0%
+actually springing ball like you're
+going to come
+
+ align:start position:0%
+going to come
+ 
+
+ align:start position:0%
+going to come
+then you wonder brace yourself up again
+
+ align:start position:0%
+then you wonder brace yourself up again
+ 
+
+ align:start position:0%
+then you wonder brace yourself up again
+and each time each time discuss you have
+
+ align:start position:0%
+and each time each time discuss you have
+ 
+
+ align:start position:0%
+and each time each time discuss you have
+kind of an increase of bad idea you'll
+
+ align:start position:0%
+kind of an increase of bad idea you'll
+ 
+
+ align:start position:0%
+kind of an increase of bad idea you'll
+have increase and bad ideas but decrease
+
+ align:start position:0%
+have increase and bad ideas but decrease
+ 
+
+ align:start position:0%
+have increase and bad ideas but decrease
+of bad ideas but your total number of
+
+ align:start position:0%
+of bad ideas but your total number of
+ 
+
+ align:start position:0%
+of bad ideas but your total number of
+good ideas just keep going on right am i
+
+ align:start position:0%
+good ideas just keep going on right am i
+ 
+
+ align:start position:0%
+good ideas just keep going on right am i
+good I'm using a very big term it could
+
+ align:start position:0%
+good I'm using a very big term it could
+ 
+
+ align:start position:0%
+good I'm using a very big term it could
+be it could be polished it could mean
+
+ align:start position:0%
+be it could be polished it could mean
+ 
+
+ align:start position:0%
+be it could be polished it could mean
+actually good for gameplay it could mean
+
+ align:start position:0%
+actually good for gameplay it could mean
+ 
+
+ align:start position:0%
+actually good for gameplay it could mean
+you know something that's been proven in
+
+ align:start position:0%
+you know something that's been proven in
+ 
+
+ align:start position:0%
+you know something that's been proven in
+the marketplace something desirable that
+
+ align:start position:0%
+the marketplace something desirable that
+ 
+
+ align:start position:0%
+the marketplace something desirable that
+you want to keep in a game things it
+
+ align:start position:0%
+you want to keep in a game things it
+ 
+
+ align:start position:0%
+you want to keep in a game things it
+could be like it should be good for the
+
+ align:start position:0%
+could be like it should be good for the
+ 
+
+ align:start position:0%
+could be like it should be good for the
+core experience one of the problems
+
+ align:start position:0%
+core experience one of the problems
+ 
+
+ align:start position:0%
+core experience one of the problems
+could be they are just they're good
+
+ align:start position:0%
+could be they are just they're good
+ 
+
+ align:start position:0%
+could be they are just they're good
+working mechanics let's see that dark up
+
+ align:start position:0%
+working mechanics let's see that dark up
+ 
+
+ align:start position:0%
+working mechanics let's see that dark up
+there are a couple of agents even in
+
+ align:start position:0%
+there are a couple of agents even in
+ 
+
+ align:start position:0%
+there are a couple of agents even in
+this early brainstorming process so I'm
+
+ align:start position:0%
+this early brainstorming process so I'm
+ 
+
+ align:start position:0%
+this early brainstorming process so I'm
+just looking at this just this yeah Oh
+
+ align:start position:0%
+just looking at this just this yeah Oh
+ 
+
+ align:start position:0%
+just looking at this just this yeah Oh
+what is that you pretty much already
+
+ align:start position:0%
+what is that you pretty much already
+ 
+
+ align:start position:0%
+what is that you pretty much already
+think you already know what game I'm
+
+ align:start position:0%
+think you already know what game I'm
+ 
+
+ align:start position:0%
+think you already know what game I'm
+gonna make you call a single solution
+
+ align:start position:0%
+gonna make you call a single solution
+ 
+
+ align:start position:0%
+gonna make you call a single solution
+you know say say you're taking the
+
+ align:start position:0%
+you know say say you're taking the
+ 
+
+ align:start position:0%
+you know say say you're taking the
+computer game version of this class and
+
+ align:start position:0%
+computer game version of this class and
+ 
+
+ align:start position:0%
+computer game version of this class and
+you decide that you're going to make an
+
+ align:start position:0%
+you decide that you're going to make an
+ 
+
+ align:start position:0%
+you decide that you're going to make an
+RPG and your model is Final Fantasy 6 ok
+
+ align:start position:0%
+RPG and your model is Final Fantasy 6 ok
+ 
+
+ align:start position:0%
+RPG and your model is Final Fantasy 6 ok
+so everything is going to basically
+
+ align:start position:0%
+so everything is going to basically
+ 
+
+ align:start position:0%
+so everything is going to basically
+follow the Final Fantasy 6 template so
+
+ align:start position:0%
+follow the Final Fantasy 6 template so
+ 
+
+ align:start position:0%
+follow the Final Fantasy 6 template so
+you're basically pursuing one single
+
+ align:start position:0%
+you're basically pursuing one single
+ 
+
+ align:start position:0%
+you're basically pursuing one single
+solution and the problem with that is
+
+ align:start position:0%
+solution and the problem with that is
+ 
+
+ align:start position:0%
+solution and the problem with that is
+that your implementation ability of
+
+ align:start position:0%
+that your implementation ability of
+ 
+
+ align:start position:0%
+that your implementation ability of
+actually making all of those things fit
+
+ align:start position:0%
+actually making all of those things fit
+ 
+
+ align:start position:0%
+actually making all of those things fit
+that template is already not you are not
+
+ align:start position:0%
+that template is already not you are not
+ 
+
+ align:start position:0%
+that template is already not you are not
+square right you you you don't have all
+
+ align:start position:0%
+square right you you you don't have all
+ 
+
+ align:start position:0%
+square right you you you don't have all
+the resources that Square had even back
+
+ align:start position:0%
+the resources that Square had even back
+ 
+
+ align:start position:0%
+the resources that Square had even back
+in Final Fantasy 6 schema how old is
+
+ align:start position:0%
+in Final Fantasy 6 schema how old is
+ 
+
+ align:start position:0%
+in Final Fantasy 6 schema how old is
+Final Fantasy 6 1994 2
+
+ align:start position:0%
+Final Fantasy 6 1994 2
+ 
+
+ align:start position:0%
+Final Fantasy 6 1994 2
+something like that I mean even then
+
+ align:start position:0%
+something like that I mean even then
+ 
+
+ align:start position:0%
+something like that I mean even then
+they were a large team with many years
+
+ align:start position:0%
+they were a large team with many years
+ 
+
+ align:start position:0%
+they were a large team with many years
+to work on on at least many at least a
+
+ align:start position:0%
+to work on on at least many at least a
+ 
+
+ align:start position:0%
+to work on on at least many at least a
+year to work on the game I don't know
+
+ align:start position:0%
+year to work on the game I don't know
+ 
+
+ align:start position:0%
+year to work on the game I don't know
+how long they actually worked on that
+
+ align:start position:0%
+how long they actually worked on that
+ 
+
+ align:start position:0%
+how long they actually worked on that
+game it's very very good chance that
+
+ align:start position:0%
+game it's very very good chance that
+ 
+
+ align:start position:0%
+game it's very very good chance that
+your that your ability to actually even
+
+ align:start position:0%
+your that your ability to actually even
+ 
+
+ align:start position:0%
+your that your ability to actually even
+implement something that you know how it
+
+ align:start position:0%
+implement something that you know how it
+ 
+
+ align:start position:0%
+implement something that you know how it
+already works may not be able to meet
+
+ align:start position:0%
+already works may not be able to meet
+ 
+
+ align:start position:0%
+already works may not be able to meet
+that so you will have a failed
+
+ align:start position:0%
+that so you will have a failed
+ 
+
+ align:start position:0%
+that so you will have a failed
+experiment and then you're kind of stuck
+
+ align:start position:0%
+experiment and then you're kind of stuck
+ 
+
+ align:start position:0%
+experiment and then you're kind of stuck
+you don't know what to do so you're
+
+ align:start position:0%
+you don't know what to do so you're
+ 
+
+ align:start position:0%
+you don't know what to do so you're
+gonna have to do lots and lots of
+
+ align:start position:0%
+gonna have to do lots and lots of
+ 
+
+ align:start position:0%
+gonna have to do lots and lots of
+experiments um
+
+ align:start position:0%
+experiments um
+ 
+
+ align:start position:0%
+experiments um
+but experiments are expensive everything
+
+ align:start position:0%
+but experiments are expensive everything
+ 
+
+ align:start position:0%
+but experiments are expensive everything
+takes time and everything is going to
+
+ align:start position:0%
+takes time and everything is going to
+ 
+
+ align:start position:0%
+takes time and everything is going to
+need culling
+
+ align:start position:0%
+need culling
+ 
+
+ align:start position:0%
+need culling
+at some point of time and which needs a
+
+ align:start position:0%
+at some point of time and which needs a
+ 
+
+ align:start position:0%
+at some point of time and which needs a
+certain amount of time that isn't going
+
+ align:start position:0%
+certain amount of time that isn't going
+ 
+
+ align:start position:0%
+certain amount of time that isn't going
+to end up going into making this this
+
+ align:start position:0%
+to end up going into making this this
+ 
+
+ align:start position:0%
+to end up going into making this this
+chunk actually went into discharge which
+
+ align:start position:0%
+chunk actually went into discharge which
+ 
+
+ align:start position:0%
+chunk actually went into discharge which
+is why we've been trying to teach you
+
+ align:start position:0%
+is why we've been trying to teach you
+ 
+
+ align:start position:0%
+is why we've been trying to teach you
+how to prototype really really quickly
+
+ align:start position:0%
+how to prototype really really quickly
+ 
+
+ align:start position:0%
+how to prototype really really quickly
+it's a little bit of a recap because we
+
+ align:start position:0%
+it's a little bit of a recap because we
+ 
+
+ align:start position:0%
+it's a little bit of a recap because we
+want you to try to be able to get out to
+
+ align:start position:0%
+want you to try to be able to get out to
+ 
+
+ align:start position:0%
+want you to try to be able to get out to
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+come to a conclusion about whether that
+
+ align:start position:0%
+come to a conclusion about whether that
+ 
+
+ align:start position:0%
+come to a conclusion about whether that
+idea was good or not as fast as possible
+
+ align:start position:0%
+idea was good or not as fast as possible
+ 
+
+ align:start position:0%
+idea was good or not as fast as possible
+so that you kind of reduce the cost of
+
+ align:start position:0%
+so that you kind of reduce the cost of
+ 
+
+ align:start position:0%
+so that you kind of reduce the cost of
+doing a single experiment and yeah it's
+
+ align:start position:0%
+doing a single experiment and yeah it's
+ 
+
+ align:start position:0%
+doing a single experiment and yeah it's
+true that you're not going to be able to
+
+ align:start position:0%
+true that you're not going to be able to
+ 
+
+ align:start position:0%
+true that you're not going to be able to
+conduct an experiment on every single
+
+ align:start position:0%
+conduct an experiment on every single
+ 
+
+ align:start position:0%
+conduct an experiment on every single
+idea that you've got so you have to kind
+
+ align:start position:0%
+idea that you've got so you have to kind
+ 
+
+ align:start position:0%
+idea that you've got so you have to kind
+of pick and choose a select number of of
+
+ align:start position:0%
+of pick and choose a select number of of
+ 
+
+ align:start position:0%
+of pick and choose a select number of of
+ideas to be able to take to experimental
+
+ align:start position:0%
+ideas to be able to take to experimental
+ 
+
+ align:start position:0%
+ideas to be able to take to experimental
+experimental stage now there are a
+
+ align:start position:0%
+experimental stage now there are a
+ 
+
+ align:start position:0%
+experimental stage now there are a
+couple of things that you can look out
+
+ align:start position:0%
+couple of things that you can look out
+ 
+
+ align:start position:0%
+couple of things that you can look out
+for to say maybe we don't want to
+
+ align:start position:0%
+for to say maybe we don't want to
+ 
+
+ align:start position:0%
+for to say maybe we don't want to
+conduct an experiment or something one
+
+ align:start position:0%
+conduct an experiment or something one
+ 
+
+ align:start position:0%
+conduct an experiment or something one
+is a brittle idea and a better idea is
+
+ align:start position:0%
+is a brittle idea and a better idea is
+ 
+
+ align:start position:0%
+is a brittle idea and a better idea is
+that you kind of have to kind of twist
+
+ align:start position:0%
+that you kind of have to kind of twist
+ 
+
+ align:start position:0%
+that you kind of have to kind of twist
+it really really really hard to be able
+
+ align:start position:0%
+it really really really hard to be able
+ 
+
+ align:start position:0%
+it really really really hard to be able
+to make it fit with any idea that you've
+
+ align:start position:0%
+to make it fit with any idea that you've
+ 
+
+ align:start position:0%
+to make it fit with any idea that you've
+already got you know you I'm assuming
+
+ align:start position:0%
+already got you know you I'm assuming
+ 
+
+ align:start position:0%
+already got you know you I'm assuming
+that you've already got as a concept
+
+ align:start position:0%
+that you've already got as a concept
+ 
+
+ align:start position:0%
+that you've already got as a concept
+that your team was kind of build around
+
+ align:start position:0%
+that your team was kind of build around
+ 
+
+ align:start position:0%
+that your team was kind of build around
+this concept somebody comes up with an
+
+ align:start position:0%
+this concept somebody comes up with an
+ 
+
+ align:start position:0%
+this concept somebody comes up with an
+idea and there's a huge amount of
+
+ align:start position:0%
+idea and there's a huge amount of
+ 
+
+ align:start position:0%
+idea and there's a huge amount of
+twisting and turning to be able to even
+
+ align:start position:0%
+twisting and turning to be able to even
+ 
+
+ align:start position:0%
+twisting and turning to be able to even
+make it fit close even though you think
+
+ align:start position:0%
+make it fit close even though you think
+ 
+
+ align:start position:0%
+make it fit close even though you think
+that on its own this idea is a really
+
+ align:start position:0%
+that on its own this idea is a really
+ 
+
+ align:start position:0%
+that on its own this idea is a really
+good idea you might actually want to see
+
+ align:start position:0%
+good idea you might actually want to see
+ 
+
+ align:start position:0%
+good idea you might actually want to see
+how many different ways could this
+
+ align:start position:0%
+how many different ways could this
+ 
+
+ align:start position:0%
+how many different ways could this
+particular idea be executed before you
+
+ align:start position:0%
+particular idea be executed before you
+ 
+
+ align:start position:0%
+particular idea be executed before you
+actually decide on a weight or on an
+
+ align:start position:0%
+actually decide on a weight or on an
+ 
+
+ align:start position:0%
+actually decide on a weight or on an
+experiment to conduct on that idea two
+
+ align:start position:0%
+experiment to conduct on that idea two
+ 
+
+ align:start position:0%
+experiment to conduct on that idea two
+ways that you can do that one is
+
+ align:start position:0%
+ways that you can do that one is
+ 
+
+ align:start position:0%
+ways that you can do that one is
+you just specify you just spent
+
+ align:start position:0%
+you just specify you just spent
+ 
+
+ align:start position:0%
+you just specify you just spent
+specifying what is the goal of this
+
+ align:start position:0%
+specifying what is the goal of this
+ 
+
+ align:start position:0%
+specifying what is the goal of this
+possibly pretty right here right it
+
+ align:start position:0%
+possibly pretty right here right it
+ 
+
+ align:start position:0%
+possibly pretty right here right it
+takes a lot of testing why do we need
+
+ align:start position:0%
+takes a lot of testing why do we need
+ 
+
+ align:start position:0%
+takes a lot of testing why do we need
+this idea in the first place is it
+
+ align:start position:0%
+this idea in the first place is it
+ 
+
+ align:start position:0%
+this idea in the first place is it
+because the challenge in the game is too
+
+ align:start position:0%
+because the challenge in the game is too
+ 
+
+ align:start position:0%
+because the challenge in the game is too
+low
+
+ align:start position:0%
+low
+ 
+
+ align:start position:0%
+low
+is it because the players have too much
+
+ align:start position:0%
+is it because the players have too much
+ 
+
+ align:start position:0%
+is it because the players have too much
+information or not enough information
+
+ align:start position:0%
+information or not enough information
+ 
+
+ align:start position:0%
+information or not enough information
+about what they're supposed to do is it
+
+ align:start position:0%
+about what they're supposed to do is it
+ 
+
+ align:start position:0%
+about what they're supposed to do is it
+because you want to introduce a little
+
+ align:start position:0%
+because you want to introduce a little
+ 
+
+ align:start position:0%
+because you want to introduce a little
+element of chance or low or maybe setup
+
+ align:start position:0%
+element of chance or low or maybe setup
+ 
+
+ align:start position:0%
+element of chance or low or maybe setup
+give some sort of strategic
+
+ align:start position:0%
+give some sort of strategic
+ 
+
+ align:start position:0%
+give some sort of strategic
+decision-making try to identify what is
+
+ align:start position:0%
+decision-making try to identify what is
+ 
+
+ align:start position:0%
+decision-making try to identify what is
+this problem that you're trying to solve
+
+ align:start position:0%
+this problem that you're trying to solve
+ 
+
+ align:start position:0%
+this problem that you're trying to solve
+in the first place with this kind of
+
+ align:start position:0%
+in the first place with this kind of
+ 
+
+ align:start position:0%
+in the first place with this kind of
+unwieldy idea all right and once you'd
+
+ align:start position:0%
+unwieldy idea all right and once you'd
+ 
+
+ align:start position:0%
+unwieldy idea all right and once you'd
+be able to identify that then you come
+
+ align:start position:0%
+be able to identify that then you come
+ 
+
+ align:start position:0%
+be able to identify that then you come
+up with all right what are all the
+
+ align:start position:0%
+up with all right what are all the
+ 
+
+ align:start position:0%
+up with all right what are all the
+different ways that we could address
+
+ align:start position:0%
+different ways that we could address
+ 
+
+ align:start position:0%
+different ways that we could address
+that problem as opposed to here's this
+
+ align:start position:0%
+that problem as opposed to here's this
+ 
+
+ align:start position:0%
+that problem as opposed to here's this
+one solution is kind of unwieldy that
+
+ align:start position:0%
+one solution is kind of unwieldy that
+ 
+
+ align:start position:0%
+one solution is kind of unwieldy that
+words that might very well solve that
+
+ align:start position:0%
+words that might very well solve that
+ 
+
+ align:start position:0%
+words that might very well solve that
+problem but maybe there are alternatives
+
+ align:start position:0%
+problem but maybe there are alternatives
+ 
+
+ align:start position:0%
+problem but maybe there are alternatives
+has anyone encountered this in your own
+
+ align:start position:0%
+has anyone encountered this in your own
+ 
+
+ align:start position:0%
+has anyone encountered this in your own
+prototyping maybe this assignment maybe
+
+ align:start position:0%
+prototyping maybe this assignment maybe
+ 
+
+ align:start position:0%
+prototyping maybe this assignment maybe
+in a previous assignment like somebody
+
+ align:start position:0%
+in a previous assignment like somebody
+ 
+
+ align:start position:0%
+in a previous assignment like somebody
+had an idea that was just kind of hard
+
+ align:start position:0%
+had an idea that was just kind of hard
+ 
+
+ align:start position:0%
+had an idea that was just kind of hard
+to use but then twenty idea was tried to
+
+ align:start position:0%
+to use but then twenty idea was tried to
+ 
+
+ align:start position:0%
+to use but then twenty idea was tried to
+solve was actually a good problem to
+
+ align:start position:0%
+solve was actually a good problem to
+ 
+
+ align:start position:0%
+solve was actually a good problem to
+solve no not yet I thought it's awesome
+
+ align:start position:0%
+solve no not yet I thought it's awesome
+ 
+
+ align:start position:0%
+solve no not yet I thought it's awesome
+nuts if you've encountered it I'd love
+
+ align:start position:0%
+nuts if you've encountered it I'd love
+ 
+
+ align:start position:0%
+nuts if you've encountered it I'd love
+to get an example from one of you I can
+
+ align:start position:0%
+to get an example from one of you I can
+ 
+
+ align:start position:0%
+to get an example from one of you I can
+throw in it I can throw out examples but
+
+ align:start position:0%
+throw in it I can throw out examples but
+ 
+
+ align:start position:0%
+throw in it I can throw out examples but
+I'd love to be able to hear examples
+
+ align:start position:0%
+I'd love to be able to hear examples
+ 
+
+ align:start position:0%
+I'd love to be able to hear examples
+from one of you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+against our skin we noticed a couple
+
+ align:start position:0%
+against our skin we noticed a couple
+ 
+
+ align:start position:0%
+against our skin we noticed a couple
+problems with the game so he came up
+
+ align:start position:0%
+problems with the game so he came up
+ 
+
+ align:start position:0%
+problems with the game so he came up
+with various ways of trying to resolve
+
+ align:start position:0%
+with various ways of trying to resolve
+ 
+
+ align:start position:0%
+with various ways of trying to resolve
+it mmm that generally work for the game
+
+ align:start position:0%
+it mmm that generally work for the game
+ 
+
+ align:start position:0%
+it mmm that generally work for the game
+itself but solved the smaller problem
+
+ align:start position:0%
+itself but solved the smaller problem
+ 
+
+ align:start position:0%
+itself but solved the smaller problem
+okay be more specific about what the
+
+ align:start position:0%
+okay be more specific about what the
+ 
+
+ align:start position:0%
+okay be more specific about what the
+problem yes was that the way our game
+
+ align:start position:0%
+problem yes was that the way our game
+ 
+
+ align:start position:0%
+problem yes was that the way our game
+was with you know the Seneca tic-tac-toe
+
+ align:start position:0%
+was with you know the Seneca tic-tac-toe
+ 
+
+ align:start position:0%
+was with you know the Seneca tic-tac-toe
+it was really hard to see what what sets
+
+ align:start position:0%
+it was really hard to see what what sets
+ 
+
+ align:start position:0%
+it was really hard to see what what sets
+were available on the board right this
+
+ align:start position:0%
+were available on the board right this
+ 
+
+ align:start position:0%
+were available on the board right this
+was a set this up in the game sure yeah
+
+ align:start position:0%
+was a set this up in the game sure yeah
+ 
+
+ align:start position:0%
+was a set this up in the game sure yeah
+yeah and so one of these we tried to do
+
+ align:start position:0%
+yeah and so one of these we tried to do
+ 
+
+ align:start position:0%
+yeah and so one of these we tried to do
+was removing the center tile all
+
+ align:start position:0%
+was removing the center tile all
+ 
+
+ align:start position:0%
+was removing the center tile all
+together mmm so that you could only play
+
+ align:start position:0%
+together mmm so that you could only play
+ 
+
+ align:start position:0%
+together mmm so that you could only play
+around the edges which did solve the
+
+ align:start position:0%
+around the edges which did solve the
+ 
+
+ align:start position:0%
+around the edges which did solve the
+problem of now you can really see what
+
+ align:start position:0%
+problem of now you can really see what
+ 
+
+ align:start position:0%
+problem of now you can really see what
+everything was there's a lot easier in
+
+ align:start position:0%
+everything was there's a lot easier in
+ 
+
+ align:start position:0%
+everything was there's a lot easier in
+that sense except there's just a lot
+
+ align:start position:0%
+that sense except there's just a lot
+ 
+
+ align:start position:0%
+that sense except there's just a lot
+less interesting the game because
+
+ align:start position:0%
+less interesting the game because
+ 
+
+ align:start position:0%
+less interesting the game because
+there's a lot less strategy to it so you
+
+ align:start position:0%
+there's a lot less strategy to it so you
+ 
+
+ align:start position:0%
+there's a lot less strategy to it so you
+had a version of the game where all the
+
+ align:start position:0%
+had a version of the game where all the
+ 
+
+ align:start position:0%
+had a version of the game where all the
+squares were in play including the
+
+ align:start position:0%
+squares were in play including the
+ 
+
+ align:start position:0%
+squares were in play including the
+center tile and it just made it
+
+ align:start position:0%
+center tile and it just made it
+ 
+
+ align:start position:0%
+center tile and it just made it
+confusing for your players and you have
+
+ align:start position:0%
+confusing for your players and you have
+ 
+
+ align:start position:0%
+confusing for your players and you have
+a version of the game what is just like
+
+ align:start position:0%
+a version of the game what is just like
+ 
+
+ align:start position:0%
+a version of the game what is just like
+with this one possible solution to this
+
+ align:start position:0%
+with this one possible solution to this
+ 
+
+ align:start position:0%
+with this one possible solution to this
+problem is just take the center tile out
+
+ align:start position:0%
+problem is just take the center tile out
+ 
+
+ align:start position:0%
+problem is just take the center tile out
+yeah but that made it trivial oh yeah
+
+ align:start position:0%
+yeah but that made it trivial oh yeah
+ 
+
+ align:start position:0%
+yeah but that made it trivial oh yeah
+so we trying to find a middle ground and
+
+ align:start position:0%
+so we trying to find a middle ground and
+ 
+
+ align:start position:0%
+so we trying to find a middle ground and
+that's how we ended up with the idea
+
+ align:start position:0%
+that's how we ended up with the idea
+ 
+
+ align:start position:0%
+that's how we ended up with the idea
+where we had one single card in the
+
+ align:start position:0%
+where we had one single card in the
+ 
+
+ align:start position:0%
+where we had one single card in the
+middle because you can still use it we
+
+ align:start position:0%
+middle because you can still use it we
+ 
+
+ align:start position:0%
+middle because you can still use it we
+didn't have to worry about like the
+
+ align:start position:0%
+didn't have to worry about like the
+ 
+
+ align:start position:0%
+didn't have to worry about like the
+lines of play going through the middle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so actually sounds like instead of
+
+ align:start position:0%
+okay so actually sounds like instead of
+ 
+
+ align:start position:0%
+okay so actually sounds like instead of
+a brittle idea you actually had a good
+
+ align:start position:0%
+a brittle idea you actually had a good
+ 
+
+ align:start position:0%
+a brittle idea you actually had a good
+robust idea which is that Center square
+
+ align:start position:0%
+robust idea which is that Center square
+ 
+
+ align:start position:0%
+robust idea which is that Center square
+is really problematic it's it has hope
+
+ align:start position:0%
+is really problematic it's it has hope
+ 
+
+ align:start position:0%
+is really problematic it's it has hope
+it has possibilities it has really
+
+ align:start position:0%
+it has possibilities it has really
+ 
+
+ align:start position:0%
+it has possibilities it has really
+interesting gameplay possibilities but
+
+ align:start position:0%
+interesting gameplay possibilities but
+ 
+
+ align:start position:0%
+interesting gameplay possibilities but
+for learning the game and stopping up
+
+ align:start position:0%
+for learning the game and stopping up
+ 
+
+ align:start position:0%
+for learning the game and stopping up
+the game it's problematic
+
+ align:start position:0%
+the game it's problematic
+ 
+
+ align:start position:0%
+the game it's problematic
+and so you'll found a way to say all
+
+ align:start position:0%
+and so you'll found a way to say all
+ 
+
+ align:start position:0%
+and so you'll found a way to say all
+right how do we deal with this center
+
+ align:start position:0%
+right how do we deal with this center
+ 
+
+ align:start position:0%
+right how do we deal with this center
+square instead of the solution of just
+
+ align:start position:0%
+square instead of the solution of just
+ 
+
+ align:start position:0%
+square instead of the solution of just
+delete the center square you know let's
+
+ align:start position:0%
+delete the center square you know let's
+ 
+
+ align:start position:0%
+delete the center square you know let's
+let's find a different way to work in
+
+ align:start position:0%
+let's find a different way to work in
+ 
+
+ align:start position:0%
+let's find a different way to work in
+into the game and and your and your
+
+ align:start position:0%
+into the game and and your and your
+ 
+
+ align:start position:0%
+into the game and and your and your
+final game as she does that something
+
+ align:start position:0%
+final game as she does that something
+ 
+
+ align:start position:0%
+final game as she does that something
+else that you can do is you know you if
+
+ align:start position:0%
+else that you can do is you know you if
+ 
+
+ align:start position:0%
+else that you can do is you know you if
+you've got an idea for your game it's
+
+ align:start position:0%
+you've got an idea for your game it's
+ 
+
+ align:start position:0%
+you've got an idea for your game it's
+kind of an wildy not quite sure what to
+
+ align:start position:0%
+kind of an wildy not quite sure what to
+ 
+
+ align:start position:0%
+kind of an wildy not quite sure what to
+do about it discuss it among your team
+
+ align:start position:0%
+do about it discuss it among your team
+ 
+
+ align:start position:0%
+do about it discuss it among your team
+but don't contact an experiment on it
+
+ align:start position:0%
+but don't contact an experiment on it
+ 
+
+ align:start position:0%
+but don't contact an experiment on it
+don't work in your rules don't try to
+
+ align:start position:0%
+don't work in your rules don't try to
+ 
+
+ align:start position:0%
+don't work in your rules don't try to
+implement it
+
+ align:start position:0%
+implement it
+ 
+
+ align:start position:0%
+implement it
+just get into everybody's heads because
+
+ align:start position:0%
+just get into everybody's heads because
+ 
+
+ align:start position:0%
+just get into everybody's heads because
+that idea may come bubbling up later and
+
+ align:start position:0%
+that idea may come bubbling up later and
+ 
+
+ align:start position:0%
+that idea may come bubbling up later and
+the bits of it might be applicable and
+
+ align:start position:0%
+the bits of it might be applicable and
+ 
+
+ align:start position:0%
+the bits of it might be applicable and
+slightly easier to implement way as you
+
+ align:start position:0%
+slightly easier to implement way as you
+ 
+
+ align:start position:0%
+slightly easier to implement way as you
+make progress in your game so none of us
+
+ align:start position:0%
+make progress in your game so none of us
+ 
+
+ align:start position:0%
+make progress in your game so none of us
+put it on a back burner but make sure
+
+ align:start position:0%
+put it on a back burner but make sure
+ 
+
+ align:start position:0%
+put it on a back burner but make sure
+you have actually had a chance to
+
+ align:start position:0%
+you have actually had a chance to
+ 
+
+ align:start position:0%
+you have actually had a chance to
+discuss it so that everyone's and all
+
+ align:start position:0%
+discuss it so that everyone's and all
+ 
+
+ align:start position:0%
+discuss it so that everyone's and all
+kind of thinking about it even if it's
+
+ align:start position:0%
+kind of thinking about it even if it's
+ 
+
+ align:start position:0%
+kind of thinking about it even if it's
+not something that you've decided that
+
+ align:start position:0%
+not something that you've decided that
+ 
+
+ align:start position:0%
+not something that you've decided that
+you why should we want to do right away
+
+ align:start position:0%
+you why should we want to do right away
+ 
+
+ align:start position:0%
+you why should we want to do right away
+might be a lot faster to just have a
+
+ align:start position:0%
+might be a lot faster to just have a
+ 
+
+ align:start position:0%
+might be a lot faster to just have a
+quick discussion to actually extend
+
+ align:start position:0%
+quick discussion to actually extend
+ 
+
+ align:start position:0%
+quick discussion to actually extend
+contact the experiment um yep so so
+
+ align:start position:0%
+contact the experiment um yep so so
+ 
+
+ align:start position:0%
+contact the experiment um yep so so
+those are a couple of strategies on it's
+
+ align:start position:0%
+those are a couple of strategies on it's
+ 
+
+ align:start position:0%
+those are a couple of strategies on it's
+like how do you sort of focus your
+
+ align:start position:0%
+like how do you sort of focus your
+ 
+
+ align:start position:0%
+like how do you sort of focus your
+experimenting time and this is probably
+
+ align:start position:0%
+experimenting time and this is probably
+ 
+
+ align:start position:0%
+experimenting time and this is probably
+not going to be very useful for Simon to
+
+ align:start position:0%
+not going to be very useful for Simon to
+ 
+
+ align:start position:0%
+not going to be very useful for Simon to
+but it is going to be useful for
+
+ align:start position:0%
+but it is going to be useful for
+ 
+
+ align:start position:0%
+but it is going to be useful for
+assignment three because it in Simon -
+
+ align:start position:0%
+assignment three because it in Simon -
+ 
+
+ align:start position:0%
+assignment three because it in Simon -
+yeah well pass hopefully you're well
+
+ align:start position:0%
+yeah well pass hopefully you're well
+ 
+
+ align:start position:0%
+yeah well pass hopefully you're well
+past the creating and adding new
+
+ align:start position:0%
+past the creating and adding new
+ 
+
+ align:start position:0%
+past the creating and adding new
+features the part and now you're just
+
+ align:start position:0%
+features the part and now you're just
+ 
+
+ align:start position:0%
+features the part and now you're just
+trying to get this out of the door for
+
+ align:start position:0%
+trying to get this out of the door for
+ 
+
+ align:start position:0%
+trying to get this out of the door for
+Wednesday so so let's talk about this
+
+ align:start position:0%
+Wednesday so so let's talk about this
+ 
+
+ align:start position:0%
+Wednesday so so let's talk about this
+this days now the well yeah in fact I'm
+
+ align:start position:0%
+this days now the well yeah in fact I'm
+ 
+
+ align:start position:0%
+this days now the well yeah in fact I'm
+gonna focus on this one isn't it sort of
+
+ align:start position:0%
+gonna focus on this one isn't it sort of
+ 
+
+ align:start position:0%
+gonna focus on this one isn't it sort of
+like cutting case where you're both
+
+ align:start position:0%
+like cutting case where you're both
+ 
+
+ align:start position:0%
+like cutting case where you're both
+cutting good stuff and bad stuff while
+
+ align:start position:0%
+cutting good stuff and bad stuff while
+ 
+
+ align:start position:0%
+cutting good stuff and bad stuff while
+you're cutting stuff in general because
+
+ align:start position:0%
+you're cutting stuff in general because
+ 
+
+ align:start position:0%
+you're cutting stuff in general because
+you have to be maybe because you're
+
+ align:start position:0%
+you have to be maybe because you're
+ 
+
+ align:start position:0%
+you have to be maybe because you're
+running out of time maybe because you
+
+ align:start position:0%
+running out of time maybe because you
+ 
+
+ align:start position:0%
+running out of time maybe because you
+are trying to get rid of the bad stuff
+
+ align:start position:0%
+are trying to get rid of the bad stuff
+ 
+
+ align:start position:0%
+are trying to get rid of the bad stuff
+so things that you need to do and this
+
+ align:start position:0%
+so things that you need to do and this
+ 
+
+ align:start position:0%
+so things that you need to do and this
+is something that I would like you to do
+
+ align:start position:0%
+is something that I would like you to do
+ 
+
+ align:start position:0%
+is something that I would like you to do
+today when you meet up in your teams is
+
+ align:start position:0%
+today when you meet up in your teams is
+ 
+
+ align:start position:0%
+today when you meet up in your teams is
+to determine what is the criteria which
+
+ align:start position:0%
+to determine what is the criteria which
+ 
+
+ align:start position:0%
+to determine what is the criteria which
+are going to cut a feature for instance
+
+ align:start position:0%
+are going to cut a feature for instance
+ 
+
+ align:start position:0%
+are going to cut a feature for instance
+come up with a quick description about
+
+ align:start position:0%
+come up with a quick description about
+ 
+
+ align:start position:0%
+come up with a quick description about
+what your games supposed to be all about
+
+ align:start position:0%
+what your games supposed to be all about
+ 
+
+ align:start position:0%
+what your games supposed to be all about
+you may already have written this in
+
+ align:start position:0%
+you may already have written this in
+ 
+
+ align:start position:0%
+you may already have written this in
+your rule so it might be in the very
+
+ align:start position:0%
+your rule so it might be in the very
+ 
+
+ align:start position:0%
+your rule so it might be in the very
+first paragraph all of your rules saying
+
+ align:start position:0%
+first paragraph all of your rules saying
+ 
+
+ align:start position:0%
+first paragraph all of your rules saying
+that our game is about getting entangled
+
+ align:start position:0%
+that our game is about getting entangled
+ 
+
+ align:start position:0%
+that our game is about getting entangled
+with other people you know yeah or all
+
+ align:start position:0%
+with other people you know yeah or all
+ 
+
+ align:start position:0%
+with other people you know yeah or all
+pushing them over for instance I I know
+
+ align:start position:0%
+pushing them over for instance I I know
+ 
+
+ align:start position:0%
+pushing them over for instance I I know
+that which is it you know and being I
+
+ align:start position:0%
+that which is it you know and being I
+ 
+
+ align:start position:0%
+that which is it you know and being I
+being able to identify and then when you
+
+ align:start position:0%
+being able to identify and then when you
+ 
+
+ align:start position:0%
+being able to identify and then when you
+look at all the rules in your game you
+
+ align:start position:0%
+look at all the rules in your game you
+ 
+
+ align:start position:0%
+look at all the rules in your game you
+can actually determine okay which chunks
+
+ align:start position:0%
+can actually determine okay which chunks
+ 
+
+ align:start position:0%
+can actually determine okay which chunks
+of our mechanics actually serve that
+
+ align:start position:0%
+of our mechanics actually serve that
+ 
+
+ align:start position:0%
+of our mechanics actually serve that
+goal
+
+ align:start position:0%
+goal
+ 
+
+ align:start position:0%
+goal
+everyone's don't you know there are
+
+ align:start position:0%
+everyone's don't you know there are
+ 
+
+ align:start position:0%
+everyone's don't you know there are
+things that this that just to keep your
+
+ align:start position:0%
+things that this that just to keep your
+ 
+
+ align:start position:0%
+things that this that just to keep your
+game going those may be fine to keep but
+
+ align:start position:0%
+game going those may be fine to keep but
+ 
+
+ align:start position:0%
+game going those may be fine to keep but
+are directly contributing to how good
+
+ align:start position:0%
+are directly contributing to how good
+ 
+
+ align:start position:0%
+are directly contributing to how good
+your game is those are just basically
+
+ align:start position:0%
+your game is those are just basically
+ 
+
+ align:start position:0%
+your game is those are just basically
+there to keep the thing working and
+
+ align:start position:0%
+there to keep the thing working and
+ 
+
+ align:start position:0%
+there to keep the thing working and
+maybe they can take a little bit about
+
+ align:start position:0%
+maybe they can take a little bit about
+ 
+
+ align:start position:0%
+maybe they can take a little bit about
+you that kind of suspect and then
+
+ align:start position:0%
+you that kind of suspect and then
+ 
+
+ align:start position:0%
+you that kind of suspect and then
+there's things that directly contribute
+
+ align:start position:0%
+there's things that directly contribute
+ 
+
+ align:start position:0%
+there's things that directly contribute
+to your whole gameplay that you're
+
+ align:start position:0%
+to your whole gameplay that you're
+ 
+
+ align:start position:0%
+to your whole gameplay that you're
+trying to achieve with your game and
+
+ align:start position:0%
+trying to achieve with your game and
+ 
+
+ align:start position:0%
+trying to achieve with your game and
+those are probably things that you want
+
+ align:start position:0%
+those are probably things that you want
+ 
+
+ align:start position:0%
+those are probably things that you want
+to spend a lot more time making sure
+
+ align:start position:0%
+to spend a lot more time making sure
+ 
+
+ align:start position:0%
+to spend a lot more time making sure
+that the rules are absolutely clear your
+
+ align:start position:0%
+that the rules are absolutely clear your
+ 
+
+ align:start position:0%
+that the rules are absolutely clear your
+players understand what they mean that
+
+ align:start position:0%
+players understand what they mean that
+ 
+
+ align:start position:0%
+players understand what they mean that
+you know if there's any other mechanics
+
+ align:start position:0%
+you know if there's any other mechanics
+ 
+
+ align:start position:0%
+you know if there's any other mechanics
+in your game they're supporting that you
+
+ align:start position:0%
+in your game they're supporting that you
+ 
+
+ align:start position:0%
+in your game they're supporting that you
+know that's that that you're the best
+
+ align:start position:0%
+know that's that that you're the best
+ 
+
+ align:start position:0%
+know that's that that you're the best
+meet your criteria for for what should
+
+ align:start position:0%
+meet your criteria for for what should
+ 
+
+ align:start position:0%
+meet your criteria for for what should
+stay in your game and then because once
+
+ align:start position:0%
+stay in your game and then because once
+ 
+
+ align:start position:0%
+stay in your game and then because once
+you know what your criteria is becomes a
+
+ align:start position:0%
+you know what your criteria is becomes a
+ 
+
+ align:start position:0%
+you know what your criteria is becomes a
+lot easier to be able to just look at
+
+ align:start position:0%
+lot easier to be able to just look at
+ 
+
+ align:start position:0%
+lot easier to be able to just look at
+everything that you've got deciding what
+
+ align:start position:0%
+everything that you've got deciding what
+ 
+
+ align:start position:0%
+everything that you've got deciding what
+to keep an invest more time in and what
+
+ align:start position:0%
+to keep an invest more time in and what
+ 
+
+ align:start position:0%
+to keep an invest more time in and what
+occurred there's couple of problems that
+
+ align:start position:0%
+occurred there's couple of problems that
+ 
+
+ align:start position:0%
+occurred there's couple of problems that
+people typically run into when it comes
+
+ align:start position:0%
+people typically run into when it comes
+ 
+
+ align:start position:0%
+people typically run into when it comes
+to cutting stuff out a couple of game
+
+ align:start position:0%
+to cutting stuff out a couple of game
+ 
+
+ align:start position:0%
+to cutting stuff out a couple of game
+developers refer to this as culling
+
+ align:start position:0%
+developers refer to this as culling
+ 
+
+ align:start position:0%
+developers refer to this as culling
+if you come from 3d graphics culling is
+
+ align:start position:0%
+if you come from 3d graphics culling is
+ 
+
+ align:start position:0%
+if you come from 3d graphics culling is
+a very common word is just to be able to
+
+ align:start position:0%
+a very common word is just to be able to
+ 
+
+ align:start position:0%
+a very common word is just to be able to
+just cut all the stuff out that you
+
+ align:start position:0%
+just cut all the stuff out that you
+ 
+
+ align:start position:0%
+just cut all the stuff out that you
+don't need um so for instance if you
+
+ align:start position:0%
+don't need um so for instance if you
+ 
+
+ align:start position:0%
+don't need um so for instance if you
+don't have an explicit culling criteria
+
+ align:start position:0%
+don't have an explicit culling criteria
+ 
+
+ align:start position:0%
+don't have an explicit culling criteria
+then you don't actually know you don't
+
+ align:start position:0%
+then you don't actually know you don't
+ 
+
+ align:start position:0%
+then you don't actually know you don't
+actually know why why a certain mechanic
+
+ align:start position:0%
+actually know why why a certain mechanic
+ 
+
+ align:start position:0%
+actually know why why a certain mechanic
+exists and you don't actually know
+
+ align:start position:0%
+exists and you don't actually know
+ 
+
+ align:start position:0%
+exists and you don't actually know
+whether you should keep it or not
+
+ align:start position:0%
+whether you should keep it or not
+ 
+
+ align:start position:0%
+whether you should keep it or not
+so that discussion should be something
+
+ align:start position:0%
+so that discussion should be something
+ 
+
+ align:start position:0%
+so that discussion should be something
+that you happen today you know
+
+ align:start position:0%
+that you happen today you know
+ 
+
+ align:start position:0%
+that you happen today you know
+everything in the end what is your game
+
+ align:start position:0%
+everything in the end what is your game
+ 
+
+ align:start position:0%
+everything in the end what is your game
+about and that's your game might really
+
+ align:start position:0%
+about and that's your game might really
+ 
+
+ align:start position:0%
+about and that's your game might really
+need that the other cut you can't have
+
+ align:start position:0%
+need that the other cut you can't have
+ 
+
+ align:start position:0%
+need that the other cut you can't have
+other coloring criteria that aren't that
+
+ align:start position:0%
+other coloring criteria that aren't that
+ 
+
+ align:start position:0%
+other coloring criteria that aren't that
+there are that this game run in five
+
+ align:start position:0%
+there are that this game run in five
+ 
+
+ align:start position:0%
+there are that this game run in five
+minutes I was a limit for this one ten
+
+ align:start position:0%
+minutes I was a limit for this one ten
+ 
+
+ align:start position:0%
+minutes I was a limit for this one ten
+minutes I believe was twenty minutes
+
+ align:start position:0%
+minutes I believe was twenty minutes
+ 
+
+ align:start position:0%
+minutes I believe was twenty minutes
+okay so the game doesn't run you know if
+
+ align:start position:0%
+okay so the game doesn't run you know if
+ 
+
+ align:start position:0%
+okay so the game doesn't run you know if
+the game needs to run in twenty minutes
+
+ align:start position:0%
+the game needs to run in twenty minutes
+ 
+
+ align:start position:0%
+the game needs to run in twenty minutes
+because we as instructors gave you that
+
+ align:start position:0%
+because we as instructors gave you that
+ 
+
+ align:start position:0%
+because we as instructors gave you that
+limitation then that's probably a
+
+ align:start position:0%
+limitation then that's probably a
+ 
+
+ align:start position:0%
+limitation then that's probably a
+perfectly reasonable calling criteria
+
+ align:start position:0%
+perfectly reasonable calling criteria
+ 
+
+ align:start position:0%
+perfectly reasonable calling criteria
+for you to use what in our game is sort
+
+ align:start position:0%
+for you to use what in our game is sort
+ 
+
+ align:start position:0%
+for you to use what in our game is sort
+of contributing to towards this and
+
+ align:start position:0%
+of contributing to towards this and
+ 
+
+ align:start position:0%
+of contributing to towards this and
+what's actually getting in our way of
+
+ align:start position:0%
+what's actually getting in our way of
+ 
+
+ align:start position:0%
+what's actually getting in our way of
+hitting that target
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see something else that comes in
+
+ align:start position:0%
+let's see something else that comes in
+ 
+
+ align:start position:0%
+let's see something else that comes in
+that affects culling that affects this
+
+ align:start position:0%
+that affects culling that affects this
+ 
+
+ align:start position:0%
+that affects culling that affects this
+phase is when you conduct experiments
+
+ align:start position:0%
+phase is when you conduct experiments
+ 
+
+ align:start position:0%
+phase is when you conduct experiments
+here but your experiments are not very
+
+ align:start position:0%
+here but your experiments are not very
+ 
+
+ align:start position:0%
+here but your experiments are not very
+tangible the kind of floaty and wavy
+
+ align:start position:0%
+tangible the kind of floaty and wavy
+ 
+
+ align:start position:0%
+tangible the kind of floaty and wavy
+this usually happens in teams that like
+
+ align:start position:0%
+this usually happens in teams that like
+ 
+
+ align:start position:0%
+this usually happens in teams that like
+to talk out all of their ideas but I
+
+ align:start position:0%
+to talk out all of their ideas but I
+ 
+
+ align:start position:0%
+to talk out all of their ideas but I
+don't actually like to do a lot of like
+
+ align:start position:0%
+don't actually like to do a lot of like
+ 
+
+ align:start position:0%
+don't actually like to do a lot of like
+hardcore prototyping and play testing I
+
+ align:start position:0%
+hardcore prototyping and play testing I
+ 
+
+ align:start position:0%
+hardcore prototyping and play testing I
+hope that's not so much of a problem for
+
+ align:start position:0%
+hope that's not so much of a problem for
+ 
+
+ align:start position:0%
+hope that's not so much of a problem for
+anyone in this class by now you've got
+
+ align:start position:0%
+anyone in this class by now you've got
+ 
+
+ align:start position:0%
+anyone in this class by now you've got
+in a lot of practice in that but you may
+
+ align:start position:0%
+in a lot of practice in that but you may
+ 
+
+ align:start position:0%
+in a lot of practice in that but you may
+have a couple of rules our mechanics
+
+ align:start position:0%
+have a couple of rules our mechanics
+ 
+
+ align:start position:0%
+have a couple of rules our mechanics
+that have ended up in your game that you
+
+ align:start position:0%
+that have ended up in your game that you
+ 
+
+ align:start position:0%
+that have ended up in your game that you
+never actually prototype that you've
+
+ align:start position:0%
+never actually prototype that you've
+ 
+
+ align:start position:0%
+never actually prototype that you've
+never actually tested out where real
+
+ align:start position:0%
+never actually tested out where real
+ 
+
+ align:start position:0%
+never actually tested out where real
+people make sure that whatever actually
+
+ align:start position:0%
+people make sure that whatever actually
+ 
+
+ align:start position:0%
+people make sure that whatever actually
+ends up in the version that you hand
+
+ align:start position:0%
+ends up in the version that you hand
+ 
+
+ align:start position:0%
+ends up in the version that you hand
+them on Wednesday is something that
+
+ align:start position:0%
+them on Wednesday is something that
+ 
+
+ align:start position:0%
+them on Wednesday is something that
+you've actually tested it's something
+
+ align:start position:0%
+you've actually tested it's something
+ 
+
+ align:start position:0%
+you've actually tested it's something
+that you've actually gotten some real
+
+ align:start position:0%
+that you've actually gotten some real
+ 
+
+ align:start position:0%
+that you've actually gotten some real
+data about whether is working or not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one this one happens with every
+
+ align:start position:0%
+this one this one happens with every
+ 
+
+ align:start position:0%
+this one this one happens with every
+student project but the students general
+
+ align:start position:0%
+student project but the students general
+ 
+
+ align:start position:0%
+student project but the students general
+game developers in general always
+
+ align:start position:0%
+game developers in general always
+ 
+
+ align:start position:0%
+game developers in general always
+assumed that adding more stuff is better
+
+ align:start position:0%
+assumed that adding more stuff is better
+ 
+
+ align:start position:0%
+assumed that adding more stuff is better
+takes a very very very seasoned game
+
+ align:start position:0%
+takes a very very very seasoned game
+ 
+
+ align:start position:0%
+takes a very very very seasoned game
+designer to sort of realize that
+
+ align:start position:0%
+designer to sort of realize that
+ 
+
+ align:start position:0%
+designer to sort of realize that
+sometimes simplicity is good and again I
+
+ align:start position:0%
+sometimes simplicity is good and again I
+ 
+
+ align:start position:0%
+sometimes simplicity is good and again I
+hope this is not the terribly new
+
+ align:start position:0%
+hope this is not the terribly new
+ 
+
+ align:start position:0%
+hope this is not the terribly new
+revelation to the people in this class
+
+ align:start position:0%
+revelation to the people in this class
+ 
+
+ align:start position:0%
+revelation to the people in this class
+but I see in the student projects all
+
+ align:start position:0%
+but I see in the student projects all
+ 
+
+ align:start position:0%
+but I see in the student projects all
+time I see in certain projects where
+
+ align:start position:0%
+time I see in certain projects where
+ 
+
+ align:start position:0%
+time I see in certain projects where
+they assume that more features and more
+
+ align:start position:0%
+they assume that more features and more
+ 
+
+ align:start position:0%
+they assume that more features and more
+complexity is going to be better in fact
+
+ align:start position:0%
+complexity is going to be better in fact
+ 
+
+ align:start position:0%
+complexity is going to be better in fact
+I saw some of them in assignment one and
+
+ align:start position:0%
+I saw some of them in assignment one and
+ 
+
+ align:start position:0%
+I saw some of them in assignment one and
+we're going to be talking a little bit
+
+ align:start position:0%
+we're going to be talking a little bit
+ 
+
+ align:start position:0%
+we're going to be talking a little bit
+about that more complexity doesn't
+
+ align:start position:0%
+about that more complexity doesn't
+ 
+
+ align:start position:0%
+about that more complexity doesn't
+necessarily always make for a better
+
+ align:start position:0%
+necessarily always make for a better
+ 
+
+ align:start position:0%
+necessarily always make for a better
+game maybe making a more interesting
+
+ align:start position:0%
+game maybe making a more interesting
+ 
+
+ align:start position:0%
+game maybe making a more interesting
+intellectual problem there's not
+
+ align:start position:0%
+intellectual problem there's not
+ 
+
+ align:start position:0%
+intellectual problem there's not
+necessarily always making into a more
+
+ align:start position:0%
+necessarily always making into a more
+ 
+
+ align:start position:0%
+necessarily always making into a more
+entertaining game let's see one thing
+
+ align:start position:0%
+entertaining game let's see one thing
+ 
+
+ align:start position:0%
+entertaining game let's see one thing
+about culling is that cutting features
+
+ align:start position:0%
+about culling is that cutting features
+ 
+
+ align:start position:0%
+about culling is that cutting features
+and cutting stuff out kind of takes
+
+ align:start position:0%
+and cutting stuff out kind of takes
+ 
+
+ align:start position:0%
+and cutting stuff out kind of takes
+practice you've got to do it fairly
+
+ align:start position:0%
+practice you've got to do it fairly
+ 
+
+ align:start position:0%
+practice you've got to do it fairly
+regularly for the a for assignment three
+
+ align:start position:0%
+regularly for the a for assignment three
+ 
+
+ align:start position:0%
+regularly for the a for assignment three
+which is going to be starting on
+
+ align:start position:0%
+which is going to be starting on
+ 
+
+ align:start position:0%
+which is going to be starting on
+Wednesday we actually started on
+
+ align:start position:0%
+Wednesday we actually started on
+ 
+
+ align:start position:0%
+Wednesday we actually started on
+Wednesday what I'm going to ask you to
+
+ align:start position:0%
+Wednesday what I'm going to ask you to
+ 
+
+ align:start position:0%
+Wednesday what I'm going to ask you to
+do is try cutting a feature every week
+
+ align:start position:0%
+do is try cutting a feature every week
+ 
+
+ align:start position:0%
+do is try cutting a feature every week
+you know like just say all right what's
+
+ align:start position:0%
+you know like just say all right what's
+ 
+
+ align:start position:0%
+you know like just say all right what's
+on a chopping block this week you know
+
+ align:start position:0%
+on a chopping block this week you know
+ 
+
+ align:start position:0%
+on a chopping block this week you know
+every every Monday oh you know
+
+ align:start position:0%
+every every Monday oh you know
+ 
+
+ align:start position:0%
+every every Monday oh you know
+Wednesday or if you have regular meeting
+
+ align:start position:0%
+Wednesday or if you have regular meeting
+ 
+
+ align:start position:0%
+Wednesday or if you have regular meeting
+time on Saturday or something like that
+
+ align:start position:0%
+time on Saturday or something like that
+ 
+
+ align:start position:0%
+time on Saturday or something like that
+just like what's on the chopping about
+
+ align:start position:0%
+just like what's on the chopping about
+ 
+
+ align:start position:0%
+just like what's on the chopping about
+what what is the least useful thing that
+
+ align:start position:0%
+what what is the least useful thing that
+ 
+
+ align:start position:0%
+what what is the least useful thing that
+we've got in our game right now and just
+
+ align:start position:0%
+we've got in our game right now and just
+ 
+
+ align:start position:0%
+we've got in our game right now and just
+try that because you can always add
+
+ align:start position:0%
+try that because you can always add
+ 
+
+ align:start position:0%
+try that because you can always add
+stuff in later you can always remember
+
+ align:start position:0%
+stuff in later you can always remember
+ 
+
+ align:start position:0%
+stuff in later you can always remember
+that this is a cyclical this is a
+
+ align:start position:0%
+that this is a cyclical this is a
+ 
+
+ align:start position:0%
+that this is a cyclical this is a
+cyclical thing they're going to be
+
+ align:start position:0%
+cyclical thing they're going to be
+ 
+
+ align:start position:0%
+cyclical thing they're going to be
+adding they're cutting adding and
+
+ align:start position:0%
+adding they're cutting adding and
+ 
+
+ align:start position:0%
+adding they're cutting adding and
+cutting adding a lot of practice or the
+
+ align:start position:0%
+cutting adding a lot of practice or the
+ 
+
+ align:start position:0%
+cutting adding a lot of practice or the
+adding part but how but but you've got
+
+ align:start position:0%
+adding part but how but but you've got
+ 
+
+ align:start position:0%
+adding part but how but but you've got
+to practice a little bit more on the
+
+ align:start position:0%
+to practice a little bit more on the
+ 
+
+ align:start position:0%
+to practice a little bit more on the
+cutting part now and you've got time to
+
+ align:start position:0%
+cutting part now and you've got time to
+ 
+
+ align:start position:0%
+cutting part now and you've got time to
+be able to do this for assignment read a
+
+ align:start position:0%
+be able to do this for assignment read a
+ 
+
+ align:start position:0%
+be able to do this for assignment read a
+little bit more time on assignment
+
+ align:start position:0%
+little bit more time on assignment
+ 
+
+ align:start position:0%
+little bit more time on assignment
+through that that you had on assignment
+
+ align:start position:0%
+through that that you had on assignment
+ 
+
+ align:start position:0%
+through that that you had on assignment
+- so start setting yourself like a
+
+ align:start position:0%
+- so start setting yourself like a
+ 
+
+ align:start position:0%
+- so start setting yourself like a
+schedule
+
+ align:start position:0%
+schedule
+ 
+
+ align:start position:0%
+schedule
+all right maybe definitely going to cut
+
+ align:start position:0%
+all right maybe definitely going to cut
+ 
+
+ align:start position:0%
+all right maybe definitely going to cut
+something I don't know what it is but
+
+ align:start position:0%
+something I don't know what it is but
+ 
+
+ align:start position:0%
+something I don't know what it is but
+we're going to meet up as a team and
+
+ align:start position:0%
+we're going to meet up as a team and
+ 
+
+ align:start position:0%
+we're going to meet up as a team and
+we're going to decide that and if it
+
+ align:start position:0%
+we're going to decide that and if it
+ 
+
+ align:start position:0%
+we're going to decide that and if it
+turns out that was the wrong thing to
+
+ align:start position:0%
+turns out that was the wrong thing to
+ 
+
+ align:start position:0%
+turns out that was the wrong thing to
+cut you can add it back later but that
+
+ align:start position:0%
+cut you can add it back later but that
+ 
+
+ align:start position:0%
+cut you can add it back later but that
+allows you to focus your efforts on the
+
+ align:start position:0%
+allows you to focus your efforts on the
+ 
+
+ align:start position:0%
+allows you to focus your efforts on the
+things that you've said that you deem is
+
+ align:start position:0%
+things that you've said that you deem is
+ 
+
+ align:start position:0%
+things that you've said that you deem is
+more important for a short amount of
+
+ align:start position:0%
+more important for a short amount of
+ 
+
+ align:start position:0%
+more important for a short amount of
+time it can be hard to be objective
+
+ align:start position:0%
+time it can be hard to be objective
+ 
+
+ align:start position:0%
+time it can be hard to be objective
+about this process something that we've
+
+ align:start position:0%
+about this process something that we've
+ 
+
+ align:start position:0%
+about this process something that we've
+done in mostly our video game
+
+ align:start position:0%
+done in mostly our video game
+ 
+
+ align:start position:0%
+done in mostly our video game
+development but you can do this in paper
+
+ align:start position:0%
+development but you can do this in paper
+ 
+
+ align:start position:0%
+development but you can do this in paper
+prototypes so have it so had people very
+
+ align:start position:0%
+prototypes so have it so had people very
+ 
+
+ align:start position:0%
+prototypes so have it so had people very
+very simple survey forms that basically
+
+ align:start position:0%
+very simple survey forms that basically
+ 
+
+ align:start position:0%
+very simple survey forms that basically
+say how fun did you find this how fun
+
+ align:start position:0%
+say how fun did you find this how fun
+ 
+
+ align:start position:0%
+say how fun did you find this how fun
+did you find that you know say your game
+
+ align:start position:0%
+did you find that you know say your game
+ 
+
+ align:start position:0%
+did you find that you know say your game
+has different roles you know you have a
+
+ align:start position:0%
+has different roles you know you have a
+ 
+
+ align:start position:0%
+has different roles you know you have a
+tinker tailor soldier spy these are your
+
+ align:start position:0%
+tinker tailor soldier spy these are your
+ 
+
+ align:start position:0%
+tinker tailor soldier spy these are your
+four roles in your game you know and you
+
+ align:start position:0%
+four roles in your game you know and you
+ 
+
+ align:start position:0%
+four roles in your game you know and you
+just hand out the survey form the how
+
+ align:start position:0%
+just hand out the survey form the how
+ 
+
+ align:start position:0%
+just hand out the survey form the how
+fun did you find being a tinker how
+
+ align:start position:0%
+fun did you find being a tinker how
+ 
+
+ align:start position:0%
+fun did you find being a tinker how
+often do you find being a tailor it is
+
+ align:start position:0%
+often do you find being a tailor it is
+ 
+
+ align:start position:0%
+often do you find being a tailor it is
+one to five you know and that that isn't
+
+ align:start position:0%
+one to five you know and that that isn't
+ 
+
+ align:start position:0%
+one to five you know and that that isn't
+terribly much information but it gives
+
+ align:start position:0%
+terribly much information but it gives
+ 
+
+ align:start position:0%
+terribly much information but it gives
+you just enough information to to help
+
+ align:start position:0%
+you just enough information to to help
+ 
+
+ align:start position:0%
+you just enough information to to help
+you concentrate your efforts on what's
+
+ align:start position:0%
+you concentrate your efforts on what's
+ 
+
+ align:start position:0%
+you concentrate your efforts on what's
+the most problematic thing in our game
+
+ align:start position:0%
+the most problematic thing in our game
+ 
+
+ align:start position:0%
+the most problematic thing in our game
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+you know you can't go into greater
+
+ align:start position:0%
+you know you can't go into greater
+ 
+
+ align:start position:0%
+you know you can't go into greater
+detail later you think that the game was
+
+ align:start position:0%
+detail later you think that the game was
+ 
+
+ align:start position:0%
+detail later you think that the game was
+too long too short you you know you too
+
+ align:start position:0%
+too long too short you you know you too
+ 
+
+ align:start position:0%
+too long too short you you know you too
+too challenging
+
+ align:start position:0%
+too challenging
+ 
+
+ align:start position:0%
+too challenging
+too easy to lock based you know require
+
+ align:start position:0%
+too easy to lock based you know require
+ 
+
+ align:start position:0%
+too easy to lock based you know require
+too much thought you can put these
+
+ align:start position:0%
+too much thought you can put these
+ 
+
+ align:start position:0%
+too much thought you can put these
+things on these like five-point scales
+
+ align:start position:0%
+things on these like five-point scales
+ 
+
+ align:start position:0%
+things on these like five-point scales
+and to be able to give you a little bit
+
+ align:start position:0%
+and to be able to give you a little bit
+ 
+
+ align:start position:0%
+and to be able to give you a little bit
+of feedback doesn't necessarily tell you
+
+ align:start position:0%
+of feedback doesn't necessarily tell you
+ 
+
+ align:start position:0%
+of feedback doesn't necessarily tell you
+what the problem is
+
+ align:start position:0%
+what the problem is
+ 
+
+ align:start position:0%
+what the problem is
+but it tells you where the problem might
+
+ align:start position:0%
+but it tells you where the problem might
+ 
+
+ align:start position:0%
+but it tells you where the problem might
+lie and that will help focus your
+
+ align:start position:0%
+lie and that will help focus your
+ 
+
+ align:start position:0%
+lie and that will help focus your
+discussion than your efforts a little
+
+ align:start position:0%
+discussion than your efforts a little
+ 
+
+ align:start position:0%
+discussion than your efforts a little
+bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and finally the most important
+
+ align:start position:0%
+yeah and finally the most important
+ 
+
+ align:start position:0%
+yeah and finally the most important
+thing is that you've got to keep doing
+
+ align:start position:0%
+thing is that you've got to keep doing
+ 
+
+ align:start position:0%
+thing is that you've got to keep doing
+this over and over and over again if you
+
+ align:start position:0%
+this over and over and over again if you
+ 
+
+ align:start position:0%
+this over and over and over again if you
+just do this once you you you kind of
+
+ align:start position:0%
+just do this once you you you kind of
+ 
+
+ align:start position:0%
+just do this once you you you kind of
+end up in this situation where you've
+
+ align:start position:0%
+end up in this situation where you've
+ 
+
+ align:start position:0%
+end up in this situation where you've
+got a bunch of good ideas but the bad
+
+ align:start position:0%
+got a bunch of good ideas but the bad
+ 
+
+ align:start position:0%
+got a bunch of good ideas but the bad
+ideas are still there what you
+
+ align:start position:0%
+ideas are still there what you
+ 
+
+ align:start position:0%
+ideas are still there what you
+eventually want to get to I'm gonna
+
+ align:start position:0%
+eventually want to get to I'm gonna
+ 
+
+ align:start position:0%
+eventually want to get to I'm gonna
+extend this greater this what you
+
+ align:start position:0%
+extend this greater this what you
+ 
+
+ align:start position:0%
+extend this greater this what you
+eventually want to get to is a situation
+
+ align:start position:0%
+eventually want to get to is a situation
+ 
+
+ align:start position:0%
+eventually want to get to is a situation
+where the only stuff that's left in your
+
+ align:start position:0%
+where the only stuff that's left in your
+ 
+
+ align:start position:0%
+where the only stuff that's left in your
+game is the stuff that you that is worth
+
+ align:start position:0%
+game is the stuff that you that is worth
+ 
+
+ align:start position:0%
+game is the stuff that you that is worth
+keeping and that works well and all the
+
+ align:start position:0%
+keeping and that works well and all the
+ 
+
+ align:start position:0%
+keeping and that works well and all the
+stuff that's that and all the stuff that
+
+ align:start position:0%
+stuff that's that and all the stuff that
+ 
+
+ align:start position:0%
+stuff that's that and all the stuff that
+was bad you find a completely cut it out
+
+ align:start position:0%
+was bad you find a completely cut it out
+ 
+
+ align:start position:0%
+was bad you find a completely cut it out
+you know all you've improved it to the
+
+ align:start position:0%
+you know all you've improved it to the
+ 
+
+ align:start position:0%
+you know all you've improved it to the
+point where it is actually a desirable
+
+ align:start position:0%
+point where it is actually a desirable
+ 
+
+ align:start position:0%
+point where it is actually a desirable
+feature and you're only going to be able
+
+ align:start position:0%
+feature and you're only going to be able
+ 
+
+ align:start position:0%
+feature and you're only going to be able
+to get through at through multiple
+
+ align:start position:0%
+to get through at through multiple
+ 
+
+ align:start position:0%
+to get through at through multiple
+iterations are not going to get through
+
+ align:start position:0%
+iterations are not going to get through
+ 
+
+ align:start position:0%
+iterations are not going to get through
+that just by introducing something at
+
+ align:start position:0%
+that just by introducing something at
+ 
+
+ align:start position:0%
+that just by introducing something at
+the last minute and hoping that it works
+
+ align:start position:0%
+the last minute and hoping that it works
+ 
+
+ align:start position:0%
+the last minute and hoping that it works
+because you haven't had time to actually
+
+ align:start position:0%
+because you haven't had time to actually
+ 
+
+ align:start position:0%
+because you haven't had time to actually
+improve it and polish it yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now some something that's less of a
+
+ align:start position:0%
+now some something that's less of a
+ 
+
+ align:start position:0%
+now some something that's less of a
+problem for this class but maybe a
+
+ align:start position:0%
+problem for this class but maybe a
+ 
+
+ align:start position:0%
+problem for this class but maybe a
+problem in your other game design
+
+ align:start position:0%
+problem in your other game design
+ 
+
+ align:start position:0%
+problem in your other game design
+experiments outside of class is that you
+
+ align:start position:0%
+experiments outside of class is that you
+ 
+
+ align:start position:0%
+experiments outside of class is that you
+may not know when to where to call it a
+
+ align:start position:0%
+may not know when to where to call it a
+ 
+
+ align:start position:0%
+may not know when to where to call it a
+day right like you can repeat this
+
+ align:start position:0%
+day right like you can repeat this
+ 
+
+ align:start position:0%
+day right like you can repeat this
+process forever
+
+ align:start position:0%
+process forever
+ 
+
+ align:start position:0%
+process forever
+and you've heard about games that have
+
+ align:start position:0%
+and you've heard about games that have
+ 
+
+ align:start position:0%
+and you've heard about games that have
+been going on for four or five years how
+
+ align:start position:0%
+been going on for four or five years how
+ 
+
+ align:start position:0%
+been going on for four or five years how
+long you can forever in production for
+
+ align:start position:0%
+long you can forever in production for
+ 
+
+ align:start position:0%
+long you can forever in production for
+fifteen at least ten and that was
+
+ align:start position:0%
+fifteen at least ten and that was
+ 
+
+ align:start position:0%
+fifteen at least ten and that was
+actually a pro one one example of where
+
+ align:start position:0%
+actually a pro one one example of where
+ 
+
+ align:start position:0%
+actually a pro one one example of where
+new technology just ended up changing
+
+ align:start position:0%
+new technology just ended up changing
+ 
+
+ align:start position:0%
+new technology just ended up changing
+the teaching the foundation of which
+
+ align:start position:0%
+the teaching the foundation of which
+ 
+
+ align:start position:0%
+the teaching the foundation of which
+that game was built on over and over and
+
+ align:start position:0%
+that game was built on over and over and
+ 
+
+ align:start position:0%
+that game was built on over and over and
+over again they just kept resetting the
+
+ align:start position:0%
+over again they just kept resetting the
+ 
+
+ align:start position:0%
+over again they just kept resetting the
+game engine development and just up
+
+ align:start position:0%
+game engine development and just up
+ 
+
+ align:start position:0%
+game engine development and just up
+forever one of the one thing that that
+
+ align:start position:0%
+forever one of the one thing that that
+ 
+
+ align:start position:0%
+forever one of the one thing that that
+that game could probably have used is
+
+ align:start position:0%
+that game could probably have used is
+ 
+
+ align:start position:0%
+that game could probably have used is
+just some sort of like standard criteria
+
+ align:start position:0%
+just some sort of like standard criteria
+ 
+
+ align:start position:0%
+just some sort of like standard criteria
+of saying like once we hit this criteria
+
+ align:start position:0%
+of saying like once we hit this criteria
+ 
+
+ align:start position:0%
+of saying like once we hit this criteria
+we're shipping this game right it could
+
+ align:start position:0%
+we're shipping this game right it could
+ 
+
+ align:start position:0%
+we're shipping this game right it could
+be once we spent X amount of money that
+
+ align:start position:0%
+be once we spent X amount of money that
+ 
+
+ align:start position:0%
+be once we spent X amount of money that
+probably should have made a case for
+
+ align:start position:0%
+probably should have made a case for
+ 
+
+ align:start position:0%
+probably should have made a case for
+that particular game but but it could
+
+ align:start position:0%
+that particular game but but it could
+ 
+
+ align:start position:0%
+that particular game but but it could
+have been once
+
+ align:start position:0%
+have been once
+ 
+
+ align:start position:0%
+have been once
+our informal internal surveys hit a
+
+ align:start position:0%
+our informal internal surveys hit a
+ 
+
+ align:start position:0%
+our informal internal surveys hit a
+rating of 4 out of 5 right you know that
+
+ align:start position:0%
+rating of 4 out of 5 right you know that
+ 
+
+ align:start position:0%
+rating of 4 out of 5 right you know that
+might have been good enough some
+
+ align:start position:0%
+might have been good enough some
+ 
+
+ align:start position:0%
+might have been good enough some
+companies don't settle for that there
+
+ align:start position:0%
+companies don't settle for that there
+ 
+
+ align:start position:0%
+companies don't settle for that there
+are a couple
+
+ align:start position:0%
+are a couple
+ 
+
+ align:start position:0%
+are a couple
+like we're only going to release the
+
+ align:start position:0%
+like we're only going to release the
+ 
+
+ align:start position:0%
+like we're only going to release the
+absolute best game that we absolutely
+
+ align:start position:0%
+absolute best game that we absolutely
+ 
+
+ align:start position:0%
+absolute best game that we absolutely
+can but don't get yourself internally
+
+ align:start position:0%
+can but don't get yourself internally
+ 
+
+ align:start position:0%
+can but don't get yourself internally
+they do have criteria and when these
+
+ align:start position:0%
+they do have criteria and when these
+ 
+
+ align:start position:0%
+they do have criteria and when these
+games have Bishop even in ten daughters
+
+ align:start position:0%
+games have Bishop even in ten daughters
+ 
+
+ align:start position:0%
+games have Bishop even in ten daughters
+and in ten dozen notorious from shipping
+
+ align:start position:0%
+and in ten dozen notorious from shipping
+ 
+
+ align:start position:0%
+and in ten dozen notorious from shipping
+make games because they have this mantra
+
+ align:start position:0%
+make games because they have this mantra
+ 
+
+ align:start position:0%
+make games because they have this mantra
+that a game is late for a short while
+
+ align:start position:0%
+that a game is late for a short while
+ 
+
+ align:start position:0%
+that a game is late for a short while
+and a bad game is bad forever so so
+
+ align:start position:0%
+and a bad game is bad forever so so
+ 
+
+ align:start position:0%
+and a bad game is bad forever so so
+that's that's that's why they say to the
+
+ align:start position:0%
+that's that's that's why they say to the
+ 
+
+ align:start position:0%
+that's that's that's why they say to the
+public internally they ship by Christmas
+
+ align:start position:0%
+public internally they ship by Christmas
+ 
+
+ align:start position:0%
+public internally they ship by Christmas
+they get those games help to the market
+
+ align:start position:0%
+they get those games help to the market
+ 
+
+ align:start position:0%
+they get those games help to the market
+because they have a time box that's the
+
+ align:start position:0%
+because they have a time box that's the
+ 
+
+ align:start position:0%
+because they have a time box that's the
+other way to do it and it says like well
+
+ align:start position:0%
+other way to do it and it says like well
+ 
+
+ align:start position:0%
+other way to do it and it says like well
+we have to be able to get into the
+
+ align:start position:0%
+we have to be able to get into the
+ 
+
+ align:start position:0%
+we have to be able to get into the
+manufacturing process to print those
+
+ align:start position:0%
+manufacturing process to print those
+ 
+
+ align:start position:0%
+manufacturing process to print those
+discs less of an issue nowadays but
+
+ align:start position:0%
+discs less of an issue nowadays but
+ 
+
+ align:start position:0%
+discs less of an issue nowadays but
+Nintendo still operates in in this
+
+ align:start position:0%
+Nintendo still operates in in this
+ 
+
+ align:start position:0%
+Nintendo still operates in in this
+fashion because they grew up as
+
+ align:start position:0%
+fashion because they grew up as
+ 
+
+ align:start position:0%
+fashion because they grew up as
+cartridge manufacturers so they actually
+
+ align:start position:0%
+cartridge manufacturers so they actually
+ 
+
+ align:start position:0%
+cartridge manufacturers so they actually
+had to print it now when it comes to
+
+ align:start position:0%
+had to print it now when it comes to
+ 
+
+ align:start position:0%
+had to print it now when it comes to
+publishing paper King no that's that
+
+ align:start position:0%
+publishing paper King no that's that
+ 
+
+ align:start position:0%
+publishing paper King no that's that
+timeline can be even longer right
+
+ align:start position:0%
+timeline can be even longer right
+ 
+
+ align:start position:0%
+timeline can be even longer right
+because you have to put stuff on you
+
+ align:start position:0%
+because you have to put stuff on you
+ 
+
+ align:start position:0%
+because you have to put stuff on you
+have to put ink on paper you have to
+
+ align:start position:0%
+have to put ink on paper you have to
+ 
+
+ align:start position:0%
+have to put ink on paper you have to
+have it folded you have to get all the
+
+ align:start position:0%
+have it folded you have to get all the
+ 
+
+ align:start position:0%
+have it folded you have to get all the
+plastic and stuff put in plastic bags
+
+ align:start position:0%
+plastic and stuff put in plastic bags
+ 
+
+ align:start position:0%
+plastic and stuff put in plastic bags
+and then put into the box and then put
+
+ align:start position:0%
+and then put into the box and then put
+ 
+
+ align:start position:0%
+and then put into the box and then put
+into pallets and then shipped from China
+
+ align:start position:0%
+into pallets and then shipped from China
+ 
+
+ align:start position:0%
+into pallets and then shipped from China
+usually over to stars all over the
+
+ align:start position:0%
+usually over to stars all over the
+ 
+
+ align:start position:0%
+usually over to stars all over the
+United States so that they're in stores
+
+ align:start position:0%
+United States so that they're in stores
+ 
+
+ align:start position:0%
+United States so that they're in stores
+in time for Christmas and that's like a
+
+ align:start position:0%
+in time for Christmas and that's like a
+ 
+
+ align:start position:0%
+in time for Christmas and that's like a
+huge time like so that's so that became
+
+ align:start position:0%
+huge time like so that's so that became
+ 
+
+ align:start position:0%
+huge time like so that's so that became
+the time limit you sometimes you just
+
+ align:start position:0%
+the time limit you sometimes you just
+ 
+
+ align:start position:0%
+the time limit you sometimes you just
+set a time limit because you have to be
+
+ align:start position:0%
+set a time limit because you have to be
+ 
+
+ align:start position:0%
+set a time limit because you have to be
+able to meet ship dates um it's not that
+
+ align:start position:0%
+able to meet ship dates um it's not that
+ 
+
+ align:start position:0%
+able to meet ship dates um it's not that
+very complicated now you're working your
+
+ align:start position:0%
+very complicated now you're working your
+ 
+
+ align:start position:0%
+very complicated now you're working your
+own internal Kickstarter project or
+
+ align:start position:0%
+own internal Kickstarter project or
+ 
+
+ align:start position:0%
+own internal Kickstarter project or
+something with where you are well you
+
+ align:start position:0%
+something with where you are well you
+ 
+
+ align:start position:0%
+something with where you are well you
+already know who's going to buy your
+
+ align:start position:0%
+already know who's going to buy your
+ 
+
+ align:start position:0%
+already know who's going to buy your
+game because they pay for it upfront
+
+ align:start position:0%
+game because they pay for it upfront
+ 
+
+ align:start position:0%
+game because they pay for it upfront
+before you even started manufacturing um
+
+ align:start position:0%
+before you even started manufacturing um
+ 
+
+ align:start position:0%
+before you even started manufacturing um
+I think we'll hear about more about that
+
+ align:start position:0%
+I think we'll hear about more about that
+ 
+
+ align:start position:0%
+I think we'll hear about more about that
+maybe in about two weeks
+
+ align:start position:0%
+maybe in about two weeks
+ 
+
+ align:start position:0%
+maybe in about two weeks
+about one week April 9th yeah we'll have
+
+ align:start position:0%
+about one week April 9th yeah we'll have
+ 
+
+ align:start position:0%
+about one week April 9th yeah we'll have
+a couple of folks who actually work in
+
+ align:start position:0%
+a couple of folks who actually work in
+ 
+
+ align:start position:0%
+a couple of folks who actually work in
+the the board game publishing industry
+
+ align:start position:0%
+the the board game publishing industry
+ 
+
+ align:start position:0%
+the the board game publishing industry
+to talk a little bit about how they set
+
+ align:start position:0%
+to talk a little bit about how they set
+ 
+
+ align:start position:0%
+to talk a little bit about how they set
+goal goal posts and time and deadlines
+
+ align:start position:0%
+goal goal posts and time and deadlines
+ 
+
+ align:start position:0%
+goal goal posts and time and deadlines
+for themselves one of the considerations
+
+ align:start position:0%
+for themselves one of the considerations
+ 
+
+ align:start position:0%
+for themselves one of the considerations
+or that but in the end is just they had
+
+ align:start position:0%
+or that but in the end is just they had
+ 
+
+ align:start position:0%
+or that but in the end is just they had
+to set a goal somehow either is a
+
+ align:start position:0%
+to set a goal somehow either is a
+ 
+
+ align:start position:0%
+to set a goal somehow either is a
+quality goal or is a time goal and once
+
+ align:start position:0%
+quality goal or is a time goal and once
+ 
+
+ align:start position:0%
+quality goal or is a time goal and once
+you hit that you have to ship because
+
+ align:start position:0%
+you hit that you have to ship because
+ 
+
+ align:start position:0%
+you hit that you have to ship because
+you can always do
+
+ align:start position:0%
+you can always do
+ 
+
+ align:start position:0%
+you can always do
+if you saw the quality goal you can
+
+ align:start position:0%
+if you saw the quality goal you can
+ 
+
+ align:start position:0%
+if you saw the quality goal you can
+always do better than that the more time
+
+ align:start position:0%
+always do better than that the more time
+ 
+
+ align:start position:0%
+always do better than that the more time
+that you spend the more you know the
+
+ align:start position:0%
+that you spend the more you know the
+ 
+
+ align:start position:0%
+that you spend the more you know the
+higher goal but theoretically you are
+
+ align:start position:0%
+higher goal but theoretically you are
+ 
+
+ align:start position:0%
+higher goal but theoretically you are
+sticking to this the higher quality your
+
+ align:start position:0%
+sticking to this the higher quality your
+ 
+
+ align:start position:0%
+sticking to this the higher quality your
+game is going to get but any don't ship
+
+ align:start position:0%
+game is going to get but any don't ship
+ 
+
+ align:start position:0%
+game is going to get but any don't ship
+you just have to manage angry returns so
+
+ align:start position:0%
+you just have to manage angry returns so
+ 
+
+ align:start position:0%
+you just have to manage angry returns so
+never be able to move on to your next
+
+ align:start position:0%
+never be able to move on to your next
+ 
+
+ align:start position:0%
+never be able to move on to your next
+project and I'm going to get revenue
+
+ align:start position:0%
+project and I'm going to get revenue
+ 
+
+ align:start position:0%
+project and I'm going to get revenue
+from the from from the project that you
+
+ align:start position:0%
+from the from from the project that you
+ 
+
+ align:start position:0%
+from the from from the project that you
+started and your game may not be
+
+ align:start position:0%
+started and your game may not be
+ 
+
+ align:start position:0%
+started and your game may not be
+improved by that much more just by
+
+ align:start position:0%
+improved by that much more just by
+ 
+
+ align:start position:0%
+improved by that much more just by
+spending extra time on it um okay so
+
+ align:start position:0%
+spending extra time on it um okay so
+ 
+
+ align:start position:0%
+spending extra time on it um okay so
+again we're going to talk a little bit
+
+ align:start position:0%
+again we're going to talk a little bit
+ 
+
+ align:start position:0%
+again we're going to talk a little bit
+about things that are relevant to to
+
+ align:start position:0%
+about things that are relevant to to
+ 
+
+ align:start position:0%
+about things that are relevant to to
+start from what we've observed from
+
+ align:start position:0%
+start from what we've observed from
+ 
+
+ align:start position:0%
+start from what we've observed from
+assignment 1 and then for us for for
+
+ align:start position:0%
+assignment 1 and then for us for for
+ 
+
+ align:start position:0%
+assignment 1 and then for us for for
+your team time to today start talking
+
+ align:start position:0%
+your team time to today start talking
+ 
+
+ align:start position:0%
+your team time to today start talking
+about what is your calling criteria what
+
+ align:start position:0%
+about what is your calling criteria what
+ 
+
+ align:start position:0%
+about what is your calling criteria what
+are you trying to achieve with what
+
+ align:start position:0%
+are you trying to achieve with what
+ 
+
+ align:start position:0%
+are you trying to achieve with what
+what's the simplest thing that you're
+
+ align:start position:0%
+what's the simplest thing that you're
+ 
+
+ align:start position:0%
+what's the simplest thing that you're
+trying to achieve with this game
+
+ align:start position:0%
+trying to achieve with this game
+ 
+
+ align:start position:0%
+trying to achieve with this game
+simplest and the simplest way to
+
+ align:start position:0%
+simplest and the simplest way to
+ 
+
+ align:start position:0%
+simplest and the simplest way to
+describe it and then look at all the
+
+ align:start position:0%
+describe it and then look at all the
+ 
+
+ align:start position:0%
+describe it and then look at all the
+things in your game based on that
+
+ align:start position:0%
+things in your game based on that
+ 
+
+ align:start position:0%
+things in your game based on that
+criteria and whatever doesn't meet that
+
+ align:start position:0%
+criteria and whatever doesn't meet that
+ 
+
+ align:start position:0%
+criteria and whatever doesn't meet that
+might be something that you want to cut
+
+ align:start position:0%
+might be something that you want to cut
+ 
+
+ align:start position:0%
+might be something that you want to cut
+out especially if it's already causing
+
+ align:start position:0%
+out especially if it's already causing
+ 
+
+ align:start position:0%
+out especially if it's already causing
+you problems you know and maybe you're
+
+ align:start position:0%
+you problems you know and maybe you're
+ 
+
+ align:start position:0%
+you problems you know and maybe you're
+just say cute I'm free up a little bit
+
+ align:start position:0%
+just say cute I'm free up a little bit
+ 
+
+ align:start position:0%
+just say cute I'm free up a little bit
+more time to work on the stuff that's
+
+ align:start position:0%
+more time to work on the stuff that's
+ 
+
+ align:start position:0%
+more time to work on the stuff that's
+already working you can polish up a
+
+ align:start position:0%
+already working you can polish up a
+ 
+
+ align:start position:0%
+already working you can polish up a
+little bit more so any questions about
+
+ align:start position:0%
+little bit more so any questions about
+ 
+
+ align:start position:0%
+little bit more so any questions about
+adding and cutting teachers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so related taking all this relating
+
+ align:start position:0%
+okay so related taking all this relating
+ 
+
+ align:start position:0%
+okay so related taking all this relating
+it to this kind of wine and then going
+
+ align:start position:0%
+it to this kind of wine and then going
+ 
+
+ align:start position:0%
+it to this kind of wine and then going
+into assignment two and also starting to
+
+ align:start position:0%
+into assignment two and also starting to
+ 
+
+ align:start position:0%
+into assignment two and also starting to
+cut inside of one so when it comes to
+
+ align:start position:0%
+cut inside of one so when it comes to
+ 
+
+ align:start position:0%
+cut inside of one so when it comes to
+advanced rules and basic rules if you're
+
+ align:start position:0%
+advanced rules and basic rules if you're
+ 
+
+ align:start position:0%
+advanced rules and basic rules if you're
+gonna have if you're going to do an
+
+ align:start position:0%
+gonna have if you're going to do an
+ 
+
+ align:start position:0%
+gonna have if you're going to do an
+advanced rule set and a basic rule set
+
+ align:start position:0%
+advanced rule set and a basic rule set
+ 
+
+ align:start position:0%
+advanced rule set and a basic rule set
+make sure your basic rule set matches
+
+ align:start position:0%
+make sure your basic rule set matches
+ 
+
+ align:start position:0%
+make sure your basic rule set matches
+the core experience you're trying to
+
+ align:start position:0%
+the core experience you're trying to
+ 
+
+ align:start position:0%
+the core experience you're trying to
+make with the game it's really really
+
+ align:start position:0%
+make with the game it's really really
+ 
+
+ align:start position:0%
+make with the game it's really really
+important for assignment two for this
+
+ align:start position:0%
+important for assignment two for this
+ 
+
+ align:start position:0%
+important for assignment two for this
+furnace month because that's what we
+
+ align:start position:0%
+furnace month because that's what we
+ 
+
+ align:start position:0%
+furnace month because that's what we
+said we set out right as we said come up
+
+ align:start position:0%
+said we set out right as we said come up
+ 
+
+ align:start position:0%
+said we set out right as we said come up
+with something that's going to have a
+
+ align:start position:0%
+with something that's going to have a
+ 
+
+ align:start position:0%
+with something that's going to have a
+very particular experience if you want
+
+ align:start position:0%
+very particular experience if you want
+ 
+
+ align:start position:0%
+very particular experience if you want
+the players to have at the end so if
+
+ align:start position:0%
+the players to have at the end so if
+ 
+
+ align:start position:0%
+the players to have at the end so if
+you're gonna do advanced rules and basic
+
+ align:start position:0%
+you're gonna do advanced rules and basic
+ 
+
+ align:start position:0%
+you're gonna do advanced rules and basic
+rules that criteria should be part of
+
+ align:start position:0%
+rules that criteria should be part of
+ 
+
+ align:start position:0%
+rules that criteria should be part of
+what your basic rules are the advanced
+
+ align:start position:0%
+what your basic rules are the advanced
+ 
+
+ align:start position:0%
+what your basic rules are the advanced
+rules as as Phil mentioned yes they for
+
+ align:start position:0%
+rules as as Phil mentioned yes they for
+ 
+
+ align:start position:0%
+rules as as Phil mentioned yes they for
+sometimes for some of them it could be
+
+ align:start position:0%
+sometimes for some of them it could be
+ 
+
+ align:start position:0%
+sometimes for some of them it could be
+it could add more interest it could be
+
+ align:start position:0%
+it could add more interest it could be
+ 
+
+ align:start position:0%
+it could add more interest it could be
+more see common intellectually
+
+ align:start position:0%
+more see common intellectually
+ 
+
+ align:start position:0%
+more see common intellectually
+stimulating but really the basic rules
+
+ align:start position:0%
+stimulating but really the basic rules
+ 
+
+ align:start position:0%
+stimulating but really the basic rules
+shouldn't support everything the game
+
+ align:start position:0%
+shouldn't support everything the game
+ 
+
+ align:start position:0%
+shouldn't support everything the game
+has that the advanced rules are just
+
+ align:start position:0%
+has that the advanced rules are just
+ 
+
+ align:start position:0%
+has that the advanced rules are just
+patents and actually if you don't want
+
+ align:start position:0%
+patents and actually if you don't want
+ 
+
+ align:start position:0%
+patents and actually if you don't want
+to send us in the ass rules don't just
+
+ align:start position:0%
+to send us in the ass rules don't just
+ 
+
+ align:start position:0%
+to send us in the ass rules don't just
+cut it cut it completely say we're not
+
+ align:start position:0%
+cut it cut it completely say we're not
+ 
+
+ align:start position:0%
+cut it cut it completely say we're not
+gonna we're not going to use the rules
+
+ align:start position:0%
+gonna we're not going to use the rules
+ 
+
+ align:start position:0%
+gonna we're not going to use the rules
+are in advanced rules because we just
+
+ align:start position:0%
+are in advanced rules because we just
+ 
+
+ align:start position:0%
+are in advanced rules because we just
+could not get them to work in time
+
+ align:start position:0%
+could not get them to work in time
+ 
+
+ align:start position:0%
+could not get them to work in time
+that's absolutely perfectly fine so long
+
+ align:start position:0%
+that's absolutely perfectly fine so long
+ 
+
+ align:start position:0%
+that's absolutely perfectly fine so long
+as this basically will still match the
+
+ align:start position:0%
+as this basically will still match the
+ 
+
+ align:start position:0%
+as this basically will still match the
+core experience you're trying to get
+
+ align:start position:0%
+core experience you're trying to get
+ 
+
+ align:start position:0%
+core experience you're trying to get
+across I think one thing I do want to
+
+ align:start position:0%
+across I think one thing I do want to
+ 
+
+ align:start position:0%
+across I think one thing I do want to
+add to that that for the most part basic
+
+ align:start position:0%
+add to that that for the most part basic
+ 
+
+ align:start position:0%
+add to that that for the most part basic
+rules are tricky time good yeah much
+
+ align:start position:0%
+rules are tricky time good yeah much
+ 
+
+ align:start position:0%
+rules are tricky time good yeah much
+better than a lot of the adventurers
+
+ align:start position:0%
+better than a lot of the adventurers
+ 
+
+ align:start position:0%
+better than a lot of the adventurers
+maybe because the the wording and the
+
+ align:start position:0%
+maybe because the the wording and the
+ 
+
+ align:start position:0%
+maybe because the the wording and the
+basic rules had a little bit more care
+
+ align:start position:0%
+basic rules had a little bit more care
+ 
+
+ align:start position:0%
+basic rules had a little bit more care
+maybe you tested if we found increasing
+
+ align:start position:0%
+maybe you tested if we found increasing
+ 
+
+ align:start position:0%
+maybe you tested if we found increasing
+games very playable and pretty enjoyable
+
+ align:start position:0%
+games very playable and pretty enjoyable
+ 
+
+ align:start position:0%
+games very playable and pretty enjoyable
+I was probably just fighting for
+
+ align:start position:0%
+I was probably just fighting for
+ 
+
+ align:start position:0%
+I was probably just fighting for
+so a lot of these something you had the
+
+ align:start position:0%
+so a lot of these something you had the
+ 
+
+ align:start position:0%
+so a lot of these something you had the
+adventurous
+
+ align:start position:0%
+adventurous
+ 
+
+ align:start position:0%
+adventurous
+I do realize some of those were things
+
+ align:start position:0%
+I do realize some of those were things
+ 
+
+ align:start position:0%
+I do realize some of those were things
+that came up in a testing process that
+
+ align:start position:0%
+that came up in a testing process that
+ 
+
+ align:start position:0%
+that came up in a testing process that
+you thought you know this is the game
+
+ align:start position:0%
+you thought you know this is the game
+ 
+
+ align:start position:0%
+you thought you know this is the game
+that our game has evolved into but once
+
+ align:start position:0%
+that our game has evolved into but once
+ 
+
+ align:start position:0%
+that our game has evolved into but once
+you do once it realize that there is a
+
+ align:start position:0%
+you do once it realize that there is a
+ 
+
+ align:start position:0%
+you do once it realize that there is a
+core game core basic game that works and
+
+ align:start position:0%
+core game core basic game that works and
+ 
+
+ align:start position:0%
+core game core basic game that works and
+then that this sort of like slightly
+
+ align:start position:0%
+then that this sort of like slightly
+ 
+
+ align:start position:0%
+then that this sort of like slightly
+more complicated version of the game
+
+ align:start position:0%
+more complicated version of the game
+ 
+
+ align:start position:0%
+more complicated version of the game
+that's slightly more complicated stuff
+
+ align:start position:0%
+that's slightly more complicated stuff
+ 
+
+ align:start position:0%
+that's slightly more complicated stuff
+is all candidates for cutting because
+
+ align:start position:0%
+is all candidates for cutting because
+ 
+
+ align:start position:0%
+is all candidates for cutting because
+you've already identified what the
+
+ align:start position:0%
+you've already identified what the
+ 
+
+ align:start position:0%
+you've already identified what the
+important one inside and they're only
+
+ align:start position:0%
+important one inside and they're only
+ 
+
+ align:start position:0%
+important one inside and they're only
+there basically when it comes to time
+
+ align:start position:0%
+there basically when it comes to time
+ 
+
+ align:start position:0%
+there basically when it comes to time
+any deadlines of course adopt a common
+
+ align:start position:0%
+any deadlines of course adopt a common
+ 
+
+ align:start position:0%
+any deadlines of course adopt a common
+lingo adopt a common language
+
+ align:start position:0%
+lingo adopt a common language
+ 
+
+ align:start position:0%
+lingo adopt a common language
+stick with it proofread your rules I
+
+ align:start position:0%
+stick with it proofread your rules I
+ 
+
+ align:start position:0%
+stick with it proofread your rules I
+think I have it written down the very
+
+ align:start position:0%
+think I have it written down the very
+ 
+
+ align:start position:0%
+think I have it written down the very
+bottom proofread cool so I'll say that a
+
+ align:start position:0%
+bottom proofread cool so I'll say that a
+ 
+
+ align:start position:0%
+bottom proofread cool so I'll say that a
+third time the airline and that means
+
+ align:start position:0%
+third time the airline and that means
+ 
+
+ align:start position:0%
+third time the airline and that means
+like naming conventions for the pieces
+
+ align:start position:0%
+like naming conventions for the pieces
+ 
+
+ align:start position:0%
+like naming conventions for the pieces
+for what you've chosen to call things in
+
+ align:start position:0%
+for what you've chosen to call things in
+ 
+
+ align:start position:0%
+for what you've chosen to call things in
+your game that could be naming
+
+ align:start position:0%
+your game that could be naming
+ 
+
+ align:start position:0%
+your game that could be naming
+conventions based on the rules but also
+
+ align:start position:0%
+conventions based on the rules but also
+ 
+
+ align:start position:0%
+conventions based on the rules but also
+proofreading your cards to making sure
+
+ align:start position:0%
+proofreading your cards to making sure
+ 
+
+ align:start position:0%
+proofreading your cards to making sure
+all your pieces are using the same
+
+ align:start position:0%
+all your pieces are using the same
+ 
+
+ align:start position:0%
+all your pieces are using the same
+language when it comes to talking about
+
+ align:start position:0%
+language when it comes to talking about
+ 
+
+ align:start position:0%
+language when it comes to talking about
+what the player does we did notice some
+
+ align:start position:0%
+what the player does we did notice some
+ 
+
+ align:start position:0%
+what the player does we did notice some
+some should versus may vs. must kind of
+
+ align:start position:0%
+some should versus may vs. must kind of
+ 
+
+ align:start position:0%
+some should versus may vs. must kind of
+getting mixed up so when we're playing
+
+ align:start position:0%
+getting mixed up so when we're playing
+ 
+
+ align:start position:0%
+getting mixed up so when we're playing
+the game I'm not quite sure
+
+ align:start position:0%
+the game I'm not quite sure
+ 
+
+ align:start position:0%
+the game I'm not quite sure
+well if I should do this if I may do
+
+ align:start position:0%
+well if I should do this if I may do
+ 
+
+ align:start position:0%
+well if I should do this if I may do
+this why is it if it's made here is a
+
+ align:start position:0%
+this why is it if it's made here is a
+ 
+
+ align:start position:0%
+this why is it if it's made here is a
+massive bang over here was it over
+
+ align:start position:0%
+massive bang over here was it over
+ 
+
+ align:start position:0%
+massive bang over here was it over
+here this wasn't quite quite sure wasn't
+
+ align:start position:0%
+here this wasn't quite quite sure wasn't
+ 
+
+ align:start position:0%
+here this wasn't quite quite sure wasn't
+what was it quite clear so I definitely
+
+ align:start position:0%
+what was it quite clear so I definitely
+ 
+
+ align:start position:0%
+what was it quite clear so I definitely
+recommend spending today working in a
+
+ align:start position:0%
+recommend spending today working in a
+ 
+
+ align:start position:0%
+recommend spending today working in a
+rule spend today having us play your
+
+ align:start position:0%
+rule spend today having us play your
+ 
+
+ align:start position:0%
+rule spend today having us play your
+game using your current rules and then
+
+ align:start position:0%
+game using your current rules and then
+ 
+
+ align:start position:0%
+game using your current rules and then
+taking our feedback and then and then
+
+ align:start position:0%
+taking our feedback and then and then
+ 
+
+ align:start position:0%
+taking our feedback and then and then
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+for trailing one thing and again when it
+
+ align:start position:0%
+for trailing one thing and again when it
+ 
+
+ align:start position:0%
+for trailing one thing and again when it
+comes to cutting things when you are
+
+ align:start position:0%
+comes to cutting things when you are
+ 
+
+ align:start position:0%
+comes to cutting things when you are
+cutting making sure that you are filling
+
+ align:start position:0%
+cutting making sure that you are filling
+ 
+
+ align:start position:0%
+cutting making sure that you are filling
+in the gaps so if you cut something out
+
+ align:start position:0%
+in the gaps so if you cut something out
+ 
+
+ align:start position:0%
+in the gaps so if you cut something out
+there might be a system there might be a
+
+ align:start position:0%
+there might be a system there might be a
+ 
+
+ align:start position:0%
+there might be a system there might be a
+rule in this case it's generally was
+
+ align:start position:0%
+rule in this case it's generally was
+ 
+
+ align:start position:0%
+rule in this case it's generally was
+polish issues so if something was
+
+ align:start position:0%
+polish issues so if something was
+ 
+
+ align:start position:0%
+polish issues so if something was
+removed from from from one of the rule
+
+ align:start position:0%
+removed from from from one of the rule
+ 
+
+ align:start position:0%
+removed from from from one of the rule
+sets we saw a little bit of remnants of
+
+ align:start position:0%
+sets we saw a little bit of remnants of
+ 
+
+ align:start position:0%
+sets we saw a little bit of remnants of
+it like spread spread in the rules so
+
+ align:start position:0%
+it like spread spread in the rules so
+ 
+
+ align:start position:0%
+it like spread spread in the rules so
+for instance if you're it's say you're
+
+ align:start position:0%
+for instance if you're it's say you're
+ 
+
+ align:start position:0%
+for instance if you're it's say you're
+one of those groups that had basic rules
+
+ align:start position:0%
+one of those groups that had basic rules
+ 
+
+ align:start position:0%
+one of those groups that had basic rules
+and advanced rules and use and you took
+
+ align:start position:0%
+and advanced rules and use and you took
+ 
+
+ align:start position:0%
+and advanced rules and use and you took
+the chunk of the game it moved into
+
+ align:start position:0%
+the chunk of the game it moved into
+ 
+
+ align:start position:0%
+the chunk of the game it moved into
+advanced rules because you rise the core
+
+ align:start position:0%
+advanced rules because you rise the core
+ 
+
+ align:start position:0%
+advanced rules because you rise the core
+base game was playable without that when
+
+ align:start position:0%
+base game was playable without that when
+ 
+
+ align:start position:0%
+base game was playable without that when
+your basic rules still refer to bits of
+
+ align:start position:0%
+your basic rules still refer to bits of
+ 
+
+ align:start position:0%
+your basic rules still refer to bits of
+the advanced rules and I guess really
+
+ align:start position:0%
+the advanced rules and I guess really
+ 
+
+ align:start position:0%
+the advanced rules and I guess really
+confusing because adventures are
+
+ align:start position:0%
+confusing because adventures are
+ 
+
+ align:start position:0%
+confusing because adventures are
+complete from the different section of
+
+ align:start position:0%
+complete from the different section of
+ 
+
+ align:start position:0%
+complete from the different section of
+their rules that we have for setup so if
+
+ align:start position:0%
+their rules that we have for setup so if
+ 
+
+ align:start position:0%
+their rules that we have for setup so if
+you're gonna have a setup section before
+
+ align:start position:0%
+you're gonna have a setup section before
+ 
+
+ align:start position:0%
+you're gonna have a setup section before
+your rules it's actually highly
+
+ align:start position:0%
+your rules it's actually highly
+ 
+
+ align:start position:0%
+your rules it's actually highly
+recommended having set up section that
+
+ align:start position:0%
+recommended having set up section that
+ 
+
+ align:start position:0%
+recommended having set up section that
+is split out that is different from your
+
+ align:start position:0%
+is split out that is different from your
+ 
+
+ align:start position:0%
+is split out that is different from your
+rule section so we know exactly how to
+
+ align:start position:0%
+rule section so we know exactly how to
+ 
+
+ align:start position:0%
+rule section so we know exactly how to
+setup the game include diagrams and
+
+ align:start position:0%
+setup the game include diagrams and
+ 
+
+ align:start position:0%
+setup the game include diagrams and
+photos where are you where two player
+
+ align:start position:0%
+photos where are you where two player
+ 
+
+ align:start position:0%
+photos where are you where two player
+sits what is the orientation of cards
+
+ align:start position:0%
+sits what is the orientation of cards
+ 
+
+ align:start position:0%
+sits what is the orientation of cards
+what art is what is if you have a card
+
+ align:start position:0%
+what art is what is if you have a card
+ 
+
+ align:start position:0%
+what art is what is if you have a card
+that has all this information on it what
+
+ align:start position:0%
+that has all this information on it what
+ 
+
+ align:start position:0%
+that has all this information on it what
+is that common information across all
+
+ align:start position:0%
+is that common information across all
+ 
+
+ align:start position:0%
+is that common information across all
+cards if you think about a Magic the
+
+ align:start position:0%
+cards if you think about a Magic the
+ 
+
+ align:start position:0%
+cards if you think about a Magic the
+Gathering cards and all the different
+
+ align:start position:0%
+Gathering cards and all the different
+ 
+
+ align:start position:0%
+Gathering cards and all the different
+icons hopefully yours cards aren't as
+
+ align:start position:0%
+icons hopefully yours cards aren't as
+ 
+
+ align:start position:0%
+icons hopefully yours cards aren't as
+complex but you'll have the same thing
+
+ align:start position:0%
+complex but you'll have the same thing
+ 
+
+ align:start position:0%
+complex but you'll have the same thing
+in the same place of all the cards and
+
+ align:start position:0%
+in the same place of all the cards and
+ 
+
+ align:start position:0%
+in the same place of all the cards and
+so you can then tell us what that thing
+
+ align:start position:0%
+so you can then tell us what that thing
+ 
+
+ align:start position:0%
+so you can then tell us what that thing
+is and why it's useful and how to use it
+
+ align:start position:0%
+is and why it's useful and how to use it
+ 
+
+ align:start position:0%
+is and why it's useful and how to use it
+hasn't played the game and in particular
+
+ align:start position:0%
+hasn't played the game and in particular
+ 
+
+ align:start position:0%
+hasn't played the game and in particular
+let your game tell us teach us the game
+
+ align:start position:0%
+let your game tell us teach us the game
+ 
+
+ align:start position:0%
+let your game tell us teach us the game
+how to play is possible if you've got
+
+ align:start position:0%
+how to play is possible if you've got
+ 
+
+ align:start position:0%
+how to play is possible if you've got
+time if not it should still be in the
+
+ align:start position:0%
+time if not it should still be in the
+ 
+
+ align:start position:0%
+time if not it should still be in the
+rules well you mean do I let your game
+
+ align:start position:0%
+rules well you mean do I let your game
+ 
+
+ align:start position:0%
+rules well you mean do I let your game
+teach us is the if you're gonna have a
+
+ align:start position:0%
+teach us is the if you're gonna have a
+ 
+
+ align:start position:0%
+teach us is the if you're gonna have a
+board the board has a lot of empty space
+
+ align:start position:0%
+board the board has a lot of empty space
+ 
+
+ align:start position:0%
+board the board has a lot of empty space
+on it you can put some of your rules
+
+ align:start position:0%
+on it you can put some of your rules
+ 
+
+ align:start position:0%
+on it you can put some of your rules
+into the board you can put some of the
+
+ align:start position:0%
+into the board you can put some of the
+ 
+
+ align:start position:0%
+into the board you can put some of the
+setup features into the board
+
+ align:start position:0%
+setup features into the board
+ 
+
+ align:start position:0%
+setup features into the board
+got time right now for free drools and
+
+ align:start position:0%
+got time right now for free drools and
+ 
+
+ align:start position:0%
+got time right now for free drools and
+turn in as many copies of your rules if
+
+ align:start position:0%
+turn in as many copies of your rules if
+ 
+
+ align:start position:0%
+turn in as many copies of your rules if
+you have players in your game so the
+
+ align:start position:0%
+you have players in your game so the
+ 
+
+ align:start position:0%
+you have players in your game so the
+assignment did say it's a set number of
+
+ align:start position:0%
+assignment did say it's a set number of
+ 
+
+ align:start position:0%
+assignment did say it's a set number of
+two three or four players for your game
+
+ align:start position:0%
+two three or four players for your game
+ 
+
+ align:start position:0%
+two three or four players for your game
+if it's a four player game give us four
+
+ align:start position:0%
+if it's a four player game give us four
+ 
+
+ align:start position:0%
+if it's a four player game give us four
+copies for your rules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's all the basic stuff yeah and then
+
+ align:start position:0%
+that's all the basic stuff yeah and then
+ 
+
+ align:start position:0%
+that's all the basic stuff yeah and then
+we'll have we'll be getting your
+
+ align:start position:0%
+we'll have we'll be getting your
+ 
+
+ align:start position:0%
+we'll have we'll be getting your
+feedback specifically about for each
+
+ align:start position:0%
+feedback specifically about for each
+ 
+
+ align:start position:0%
+feedback specifically about for each
+individual game tomorrow yeah we'll give
+
+ align:start position:0%
+individual game tomorrow yeah we'll give
+ 
+
+ align:start position:0%
+individual game tomorrow yeah we'll give
+you that before turning in I just want
+
+ align:start position:0%
+you that before turning in I just want
+ 
+
+ align:start position:0%
+you that before turning in I just want
+to clarify one thing what should be best
+
+ align:start position:0%
+to clarify one thing what should be best
+ 
+
+ align:start position:0%
+to clarify one thing what should be best
+I'm not sure because I'm trying to think
+
+ align:start position:0%
+I'm not sure because I'm trying to think
+ 
+
+ align:start position:0%
+I'm not sure because I'm trying to think
+of a more concrete example so it's like
+
+ align:start position:0%
+of a more concrete example so it's like
+ 
+
+ align:start position:0%
+of a more concrete example so it's like
+within your rules you say the player
+
+ align:start position:0%
+within your rules you say the player
+ 
+
+ align:start position:0%
+within your rules you say the player
+should move their piece his or her piece
+
+ align:start position:0%
+should move their piece his or her piece
+ 
+
+ align:start position:0%
+should move their piece his or her piece
+you know from from one square to another
+
+ align:start position:0%
+you know from from one square to another
+ 
+
+ align:start position:0%
+you know from from one square to another
+we're not quite sure whether you are
+
+ align:start position:0%
+we're not quite sure whether you are
+ 
+
+ align:start position:0%
+we're not quite sure whether you are
+describing this as a good strategy as
+
+ align:start position:0%
+describing this as a good strategy as
+ 
+
+ align:start position:0%
+describing this as a good strategy as
+something that the player you know will
+
+ align:start position:0%
+something that the player you know will
+ 
+
+ align:start position:0%
+something that the player you know will
+should generally be doing because it's
+
+ align:start position:0%
+should generally be doing because it's
+ 
+
+ align:start position:0%
+should generally be doing because it's
+going to put the player head on
+
+ align:start position:0%
+going to put the player head on
+ 
+
+ align:start position:0%
+going to put the player head on
+something that a player must be doing
+
+ align:start position:0%
+something that a player must be doing
+ 
+
+ align:start position:0%
+something that a player must be doing
+because the rules require the player to
+
+ align:start position:0%
+because the rules require the player to
+ 
+
+ align:start position:0%
+because the rules require the player to
+do this other thing
+
+ align:start position:0%
+do this other thing
+ 
+
+ align:start position:0%
+do this other thing
+shoulders are very very difficult work
+
+ align:start position:0%
+shoulders are very very difficult work
+ 
+
+ align:start position:0%
+shoulders are very very difficult work
+to figure out for us if you're going to
+
+ align:start position:0%
+to figure out for us if you're going to
+ 
+
+ align:start position:0%
+to figure out for us if you're going to
+be if possible tell me sometimes context
+
+ align:start position:0%
+be if possible tell me sometimes context
+ 
+
+ align:start position:0%
+be if possible tell me sometimes context
+explains it for you but it does
+
+ align:start position:0%
+explains it for you but it does
+ 
+
+ align:start position:0%
+explains it for you but it does
+buddy things more often than it helps I
+
+ align:start position:0%
+buddy things more often than it helps I
+ 
+
+ align:start position:0%
+buddy things more often than it helps I
+find short makes perfect sense and
+
+ align:start position:0%
+find short makes perfect sense and
+ 
+
+ align:start position:0%
+find short makes perfect sense and
+you're going to give an example you're
+
+ align:start position:0%
+you're going to give an example you're
+ 
+
+ align:start position:0%
+you're going to give an example you're
+going to give an example make it
+
+ align:start position:0%
+going to give an example make it
+ 
+
+ align:start position:0%
+going to give an example make it
+italicize make it obvious or even like
+
+ align:start position:0%
+italicize make it obvious or even like
+ 
+
+ align:start position:0%
+italicize make it obvious or even like
+immigrant debts
+
+ align:start position:0%
+immigrant debts
+ 
+
+ align:start position:0%
+immigrant debts
+yeah intense on a sidebar or something
+
+ align:start position:0%
+yeah intense on a sidebar or something
+ 
+
+ align:start position:0%
+yeah intense on a sidebar or something
+to make it clear that this is not
+
+ align:start position:0%
+to make it clear that this is not
+ 
+
+ align:start position:0%
+to make it clear that this is not
+actually part of the rules this is an
+
+ align:start position:0%
+actually part of the rules this is an
+ 
+
+ align:start position:0%
+actually part of the rules this is an
+example of how this set of the rules
+
+ align:start position:0%
+example of how this set of the rules
+ 
+
+ align:start position:0%
+example of how this set of the rules
+plays out I think it use words like
+
+ align:start position:0%
+plays out I think it use words like
+ 
+
+ align:start position:0%
+plays out I think it use words like
+short right you know player one should
+
+ align:start position:0%
+short right you know player one should
+ 
+
+ align:start position:0%
+short right you know player one should
+do this because you're describing a
+
+ align:start position:0%
+do this because you're describing a
+ 
+
+ align:start position:0%
+do this because you're describing a
+strategy you're not saying that the
+
+ align:start position:0%
+strategy you're not saying that the
+ 
+
+ align:start position:0%
+strategy you're not saying that the
+rules require this to happen
+
+ align:start position:0%
+rules require this to happen
+ 
+
+ align:start position:0%
+rules require this to happen
+must say must when it's must and if a
+
+ align:start position:0%
+must say must when it's must and if a
+ 
+
+ align:start position:0%
+must say must when it's must and if a
+player must do something
+
+ align:start position:0%
+player must do something
+ 
+
+ align:start position:0%
+player must do something
+something and when you say a play of me
+
+ align:start position:0%
+something and when you say a play of me
+ 
+
+ align:start position:0%
+something and when you say a play of me
+be very very clear of what else the play
+
+ align:start position:0%
+be very very clear of what else the play
+ 
+
+ align:start position:0%
+be very very clear of what else the play
+of being do say for instance it's one
+
+ align:start position:0%
+of being do say for instance it's one
+ 
+
+ align:start position:0%
+of being do say for instance it's one
+out of five different options you said
+
+ align:start position:0%
+out of five different options you said
+ 
+
+ align:start position:0%
+out of five different options you said
+yeah the player may do one of these five
+
+ align:start position:0%
+yeah the player may do one of these five
+ 
+
+ align:start position:0%
+yeah the player may do one of these five
+four five options for the point but the
+
+ align:start position:0%
+four five options for the point but the
+ 
+
+ align:start position:0%
+four five options for the point but the
+point of the point for the point for the
+
+ align:start position:0%
+point of the point for the point for the
+ 
+
+ align:start position:0%
+point of the point for the point for the
+point yeah the last bullet tuck point is
+
+ align:start position:0%
+point yeah the last bullet tuck point is
+ 
+
+ align:start position:0%
+point yeah the last bullet tuck point is
+probably like do nothing you know it's
+
+ align:start position:0%
+probably like do nothing you know it's
+ 
+
+ align:start position:0%
+probably like do nothing you know it's
+like if a game with us or there's
+
+ align:start position:0%
+like if a game with us or there's
+ 
+
+ align:start position:0%
+like if a game with us or there's
+something bullet points are really
+
+ align:start position:0%
+something bullet points are really
+ 
+
+ align:start position:0%
+something bullet points are really
+really useful if there's any kind of
+
+ align:start position:0%
+really useful if there's any kind of
+ 
+
+ align:start position:0%
+really useful if there's any kind of
+option either even if it's just like
+
+ align:start position:0%
+option either even if it's just like
+ 
+
+ align:start position:0%
+option either even if it's just like
+player may do this or this break out the
+
+ align:start position:0%
+player may do this or this break out the
+ 
+
+ align:start position:0%
+player may do this or this break out the
+or and its own line give it bold put a
+
+ align:start position:0%
+or and its own line give it bold put a
+ 
+
+ align:start position:0%
+or and its own line give it bold put a
+couple lines around it put the next
+
+ align:start position:0%
+couple lines around it put the next
+ 
+
+ align:start position:0%
+couple lines around it put the next
+thing that they can do the other thing
+
+ align:start position:0%
+thing that they can do the other thing
+ 
+
+ align:start position:0%
+thing that they can do the other thing
+they can do after it make it really
+
+ align:start position:0%
+they can do after it make it really
+ 
+
+ align:start position:0%
+they can do after it make it really
+really clear it's one or the other not
+
+ align:start position:0%
+really clear it's one or the other not
+ 
+
+ align:start position:0%
+really clear it's one or the other not
+both yeah yeah yeah that goes the same
+
+ align:start position:0%
+both yeah yeah yeah that goes the same
+ 
+
+ align:start position:0%
+both yeah yeah yeah that goes the same
+for not just the appeal you're pretty
+
+ align:start position:0%
+for not just the appeal you're pretty
+ 
+
+ align:start position:0%
+for not just the appeal you're pretty
+rulesheet proposal cards stuff on the
+
+ align:start position:0%
+rulesheet proposal cards stuff on the
+ 
+
+ align:start position:0%
+rulesheet proposal cards stuff on the
+board you know because sometimes there
+
+ align:start position:0%
+board you know because sometimes there
+ 
+
+ align:start position:0%
+board you know because sometimes there
+are games where you have options on the
+
+ align:start position:0%
+are games where you have options on the
+ 
+
+ align:start position:0%
+are games where you have options on the
+card right and you made us do this or
+
+ align:start position:0%
+card right and you made us do this or
+ 
+
+ align:start position:0%
+card right and you made us do this or
+you may do that it's not entirely
+
+ align:start position:0%
+you may do that it's not entirely
+ 
+
+ align:start position:0%
+you may do that it's not entirely
+obvious if say the card does both of
+
+ align:start position:0%
+obvious if say the card does both of
+ 
+
+ align:start position:0%
+obvious if say the card does both of
+those things or you've got to choose one
+
+ align:start position:0%
+those things or you've got to choose one
+ 
+
+ align:start position:0%
+those things or you've got to choose one
+of those things and who gets to choose
+
+ align:start position:0%
+of those things and who gets to choose
+ 
+
+ align:start position:0%
+of those things and who gets to choose
+one of those two things so that's
+
+ align:start position:0%
+one of those two things so that's
+ 
+
+ align:start position:0%
+one of those two things so that's
+something to keep in mind you only use
+
+ align:start position:0%
+something to keep in mind you only use
+ 
+
+ align:start position:0%
+something to keep in mind you only use
+numbered bullet points whatever one two
+
+ align:start position:0%
+numbered bullet points whatever one two
+ 
+
+ align:start position:0%
+numbered bullet points whatever one two
+three four
+
+ align:start position:0%
+three four
+ 
+
+ align:start position:0%
+three four
+if something is going to be sequential
+
+ align:start position:0%
+if something is going to be sequential
+ 
+
+ align:start position:0%
+if something is going to be sequential
+no it's good for things like here are
+
+ align:start position:0%
+no it's good for things like here are
+ 
+
+ align:start position:0%
+no it's good for things like here are
+the steps of a round of game play you
+
+ align:start position:0%
+the steps of a round of game play you
+ 
+
+ align:start position:0%
+the steps of a round of game play you
+know first you do this then you do this
+
+ align:start position:0%
+know first you do this then you do this
+ 
+
+ align:start position:0%
+know first you do this then you do this
+then you do this
+
+ align:start position:0%
+then you do this
+ 
+
+ align:start position:0%
+then you do this
+don't talk don't say the player may do
+
+ align:start position:0%
+don't talk don't say the player may do
+ 
+
+ align:start position:0%
+don't talk don't say the player may do
+one of the following 1.2.3 doctors like
+
+ align:start position:0%
+one of the following 1.2.3 doctors like
+ 
+
+ align:start position:0%
+one of the following 1.2.3 doctors like
+now in operation okay yeah then yeah
+
+ align:start position:0%
+now in operation okay yeah then yeah
+ 
+
+ align:start position:0%
+now in operation okay yeah then yeah
+then actually this part of rounds stages
+
+ align:start position:0%
+then actually this part of rounds stages
+ 
+
+ align:start position:0%
+then actually this part of rounds stages
+phases oh that's that's decibel Cabul
+
+ align:start position:0%
+phases oh that's that's decibel Cabul
+ 
+
+ align:start position:0%
+phases oh that's that's decibel Cabul
+area that yeah and yes
+
+ align:start position:0%
+area that yeah and yes
+ 
+
+ align:start position:0%
+area that yeah and yes
+choose one stick with it um proofread it
+
+ align:start position:0%
+choose one stick with it um proofread it
+ 
+
+ align:start position:0%
+choose one stick with it um proofread it
+and make sure you chose it make sure it
+
+ align:start position:0%
+and make sure you chose it make sure it
+ 
+
+ align:start position:0%
+and make sure you chose it make sure it
+works especially if you're gonna make
+
+ align:start position:0%
+works especially if you're gonna make
+ 
+
+ align:start position:0%
+works especially if you're gonna make
+any changes today and you're turning it
+
+ align:start position:0%
+any changes today and you're turning it
+ 
+
+ align:start position:0%
+any changes today and you're turning it
+in two days have somebody who is not you
+
+ align:start position:0%
+in two days have somebody who is not you
+ 
+
+ align:start position:0%
+in two days have somebody who is not you
+proofread it and make sure
+
+ align:start position:0%
+proofread it and make sure
+ 
+
+ align:start position:0%
+proofread it and make sure
+you're using the same language
+
+ align:start position:0%
+you're using the same language
+ 
+
+ align:start position:0%
+you're using the same language
+throughout rounds usually involves
+
+ align:start position:0%
+throughout rounds usually involves
+ 
+
+ align:start position:0%
+throughout rounds usually involves
+everybody around the table doing one
+
+ align:start position:0%
+everybody around the table doing one
+ 
+
+ align:start position:0%
+everybody around the table doing one
+thing in sequence the same sort of thing
+
+ align:start position:0%
+thing in sequence the same sort of thing
+ 
+
+ align:start position:0%
+thing in sequence the same sort of thing
+in sequence steps are really big you
+
+ align:start position:0%
+in sequence steps are really big you
+ 
+
+ align:start position:0%
+in sequence steps are really big you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+phases so usually like describing large
+
+ align:start position:0%
+phases so usually like describing large
+ 
+
+ align:start position:0%
+phases so usually like describing large
+chunks of game but you know things like
+
+ align:start position:0%
+chunks of game but you know things like
+ 
+
+ align:start position:0%
+chunks of game but you know things like
+Oh opening candids bit gain and
+
+ align:start position:0%
+Oh opening candids bit gain and
+ 
+
+ align:start position:0%
+Oh opening candids bit gain and
+gain:feed Jesus and usually not using
+
+ align:start position:0%
+gain:feed Jesus and usually not using
+ 
+
+ align:start position:0%
+gain:feed Jesus and usually not using
+rules but I know that some game vixx
+
+ align:start position:0%
+rules but I know that some game vixx
+ 
+
+ align:start position:0%
+rules but I know that some game vixx
+game yeah 18 XS I know that's as
+
+ align:start position:0%
+game yeah 18 XS I know that's as
+ 
+
+ align:start position:0%
+game yeah 18 XS I know that's as
+business-wise maddening sweet but we
+
+ align:start position:0%
+business-wise maddening sweet but we
+ 
+
+ align:start position:0%
+business-wise maddening sweet but we
+continue to work on context steps
+
+ align:start position:0%
+continue to work on context steps
+ 
+
+ align:start position:0%
+continue to work on context steps
+especially it is a sequential sequence
+
+ align:start position:0%
+especially it is a sequential sequence
+ 
+
+ align:start position:0%
+especially it is a sequential sequence
+of things like this look this is my turn
+
+ align:start position:0%
+of things like this look this is my turn
+ 
+
+ align:start position:0%
+of things like this look this is my turn
+in or out and here are the three steps I
+
+ align:start position:0%
+in or out and here are the three steps I
+ 
+
+ align:start position:0%
+in or out and here are the three steps I
+get to do you know I draw step one draw
+
+ align:start position:0%
+get to do you know I draw step one draw
+ 
+
+ align:start position:0%
+get to do you know I draw step one draw
+a card step two choose a car cut my
+
+ align:start position:0%
+a card step two choose a car cut my
+ 
+
+ align:start position:0%
+a card step two choose a car cut my
+hands that three players right now
+
+ align:start position:0%
+hands that three players right now
+ 
+
+ align:start position:0%
+hands that three players right now
+things like that that that sort of us
+
+ align:start position:0%
+things like that that that sort of us
+ 
+
+ align:start position:0%
+things like that that that sort of us
+faces I've also included described in
+
+ align:start position:0%
+faces I've also included described in
+ 
+
+ align:start position:0%
+faces I've also included described in
+things like there is round round one is
+
+ align:start position:0%
+things like there is round round one is
+ 
+
+ align:start position:0%
+things like there is round round one is
+one kind of action and round twos it's
+
+ align:start position:0%
+one kind of action and round twos it's
+ 
+
+ align:start position:0%
+one kind of action and round twos it's
+like a completely different kind of
+
+ align:start position:0%
+like a completely different kind of
+ 
+
+ align:start position:0%
+like a completely different kind of
+action around three is gonna be demanded
+
+ align:start position:0%
+action around three is gonna be demanded
+ 
+
+ align:start position:0%
+action around three is gonna be demanded
+like faces and it's like oh my god
+
+ align:start position:0%
+like faces and it's like oh my god
+ 
+
+ align:start position:0%
+like faces and it's like oh my god
+that's that Palgrave does that actually
+
+ align:start position:0%
+that's that Palgrave does that actually
+ 
+
+ align:start position:0%
+that's that Palgrave does that actually
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are turns and yes yes this is why
+
+ align:start position:0%
+there are turns and yes yes this is why
+ 
+
+ align:start position:0%
+there are turns and yes yes this is why
+the game is thank you so much harder to
+
+ align:start position:0%
+the game is thank you so much harder to
+ 
+
+ align:start position:0%
+the game is thank you so much harder to
+learn that in a safety play to play let
+
+ align:start position:0%
+learn that in a safety play to play let
+ 
+
+ align:start position:0%
+learn that in a safety play to play let
+me not at hurt but when Davis case yeah
+
+ align:start position:0%
+me not at hurt but when Davis case yeah
+ 
+
+ align:start position:0%
+me not at hurt but when Davis case yeah
+so so that's why faces complete called
+
+ align:start position:0%
+so so that's why faces complete called
+ 
+
+ align:start position:0%
+so so that's why faces complete called
+complicate things sometimes the
+
+ align:start position:0%
+complicate things sometimes the
+ 
+
+ align:start position:0%
+complicate things sometimes the
+disinfect the right word but it's just
+
+ align:start position:0%
+disinfect the right word but it's just
+ 
+
+ align:start position:0%
+disinfect the right word but it's just
+hard to be able to convince to expect at
+
+ align:start position:0%
+hard to be able to convince to expect at
+ 
+
+ align:start position:0%
+hard to be able to convince to expect at
+every single player the code you put
+
+ align:start position:0%
+every single player the code you put
+ 
+
+ align:start position:0%
+every single player the code you put
+that word the same way okay so you can
+
+ align:start position:0%
+that word the same way okay so you can
+ 
+
+ align:start position:0%
+that word the same way okay so you can
+break up new teams keep working on your
+
+ align:start position:0%
+break up new teams keep working on your
+ 
+
+ align:start position:0%
+break up new teams keep working on your
+games
+
+ align:start position:0%
+games
+ 
+
+ align:start position:0%
+games
+this is play test its time so in
+
+ align:start position:0%
+this is play test its time so in
+ 
+
+ align:start position:0%
+this is play test its time so in
+particular play test your rules if you
+
+ align:start position:0%
+particular play test your rules if you
+ 
+
+ align:start position:0%
+particular play test your rules if you
+want us to play your play your rules and
+
+ align:start position:0%
+want us to play your play your rules and
+ 
+
+ align:start position:0%
+want us to play your play your rules and
+give you feedback before you turn in
+
+ align:start position:0%
+give you feedback before you turn in
+ 
+
+ align:start position:0%
+give you feedback before you turn in
+today's the day to do it cheats right
+
+ align:start position:0%
+today's the day to do it cheats right
+ 
+
+ align:start position:0%
+today's the day to do it cheats right
+there she's over there
\ No newline at end of file
diff --git a/DdY98Zaff5I.txt b/DdY98Zaff5I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0cd96bedff97f2b12823897326ff9b351ea2681e
--- /dev/null
+++ b/DdY98Zaff5I.txt
@@ -0,0 +1,15515 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license
+
+ align:start position:0%
+a creative commons license
+ 
+
+ align:start position:0%
+a creative commons license
+your support will help mit
+
+ align:start position:0%
+your support will help mit
+ 
+
+ align:start position:0%
+your support will help mit
+opencourseware continue to offer high
+
+ align:start position:0%
+opencourseware continue to offer high
+ 
+
+ align:start position:0%
+opencourseware continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit open courseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+let me remind you
+
+ align:start position:0%
+let me remind you
+ 
+
+ align:start position:0%
+let me remind you
+where we were before spring break
+
+ align:start position:0%
+where we were before spring break
+ 
+
+ align:start position:0%
+where we were before spring break
+so first of all
+
+ align:start position:0%
+so first of all
+ 
+
+ align:start position:0%
+so first of all
+there's a posting with the projects list
+
+ align:start position:0%
+there's a posting with the projects list
+ 
+
+ align:start position:0%
+there's a posting with the projects list
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+feel free to pick a project as soon as
+
+ align:start position:0%
+feel free to pick a project as soon as
+ 
+
+ align:start position:0%
+feel free to pick a project as soon as
+you're ready
+
+ align:start position:0%
+you're ready
+ 
+
+ align:start position:0%
+you're ready
+send me your choice
+
+ align:start position:0%
+send me your choice
+ 
+
+ align:start position:0%
+send me your choice
+problem set number three do today
+
+ align:start position:0%
+problem set number three do today
+ 
+
+ align:start position:0%
+problem set number three do today
+problem set number four is posted this
+
+ align:start position:0%
+problem set number four is posted this
+ 
+
+ align:start position:0%
+problem set number four is posted this
+morning
+
+ align:start position:0%
+morning
+ 
+
+ align:start position:0%
+morning
+it will be due
+
+ align:start position:0%
+it will be due
+ 
+
+ align:start position:0%
+it will be due
+in two weeks plus two days so two weeks
+
+ align:start position:0%
+in two weeks plus two days so two weeks
+ 
+
+ align:start position:0%
+in two weeks plus two days so two weeks
+from now there's actually a holiday so
+
+ align:start position:0%
+from now there's actually a holiday so
+ 
+
+ align:start position:0%
+from now there's actually a holiday so
+we'll be doing that thursday
+
+ align:start position:0%
+we'll be doing that thursday
+ 
+
+ align:start position:0%
+we'll be doing that thursday
+last time we were talking about two
+
+ align:start position:0%
+last time we were talking about two
+ 
+
+ align:start position:0%
+last time we were talking about two
+nucleon effective field theory
+
+ align:start position:0%
+nucleon effective field theory
+ 
+
+ align:start position:0%
+nucleon effective field theory
+so this was a non-relativistic field
+
+ align:start position:0%
+so this was a non-relativistic field
+ 
+
+ align:start position:0%
+so this was a non-relativistic field
+theory both of these terms here in the
+
+ align:start position:0%
+theory both of these terms here in the
+ 
+
+ align:start position:0%
+theory both of these terms here in the
+action were the same size they were the
+
+ align:start position:0%
+action were the same size they were the
+ 
+
+ align:start position:0%
+action were the same size they were the
+same relevance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we talked about that last time
+
+ align:start position:0%
+and we talked about that last time
+ 
+
+ align:start position:0%
+and we talked about that last time
+so in hqt it would just be the first
+
+ align:start position:0%
+so in hqt it would just be the first
+ 
+
+ align:start position:0%
+so in hqt it would just be the first
+term but in this case of two nucleons we
+
+ align:start position:0%
+term but in this case of two nucleons we
+ 
+
+ align:start position:0%
+term but in this case of two nucleons we
+actually need the kinetic term as well
+
+ align:start position:0%
+actually need the kinetic term as well
+ 
+
+ align:start position:0%
+actually need the kinetic term as well
+and both of these terms are equally
+
+ align:start position:0%
+and both of these terms are equally
+ 
+
+ align:start position:0%
+and both of these terms are equally
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+and that basically means that in this
+
+ align:start position:0%
+and that basically means that in this
+ 
+
+ align:start position:0%
+and that basically means that in this
+type of system the time derivatives and
+
+ align:start position:0%
+type of system the time derivatives and
+ 
+
+ align:start position:0%
+type of system the time derivatives and
+spatial derivatives are counted
+
+ align:start position:0%
+spatial derivatives are counted
+ 
+
+ align:start position:0%
+spatial derivatives are counted
+differently but you can organize the
+
+ align:start position:0%
+differently but you can organize the
+ 
+
+ align:start position:0%
+differently but you can organize the
+field there using equations of motion so
+
+ align:start position:0%
+field there using equations of motion so
+ 
+
+ align:start position:0%
+field there using equations of motion so
+that these are just local operators with
+
+ align:start position:0%
+that these are just local operators with
+ 
+
+ align:start position:0%
+that these are just local operators with
+spatial derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you basically deal with the time
+
+ align:start position:0%
+you basically deal with the time
+ 
+
+ align:start position:0%
+you basically deal with the time
+derivatives once and for all and you
+
+ align:start position:0%
+derivatives once and for all and you
+ 
+
+ align:start position:0%
+derivatives once and for all and you
+could always use equations of motion to
+
+ align:start position:0%
+could always use equations of motion to
+ 
+
+ align:start position:0%
+could always use equations of motion to
+eliminate them there
+
+ align:start position:0%
+eliminate them there
+ 
+
+ align:start position:0%
+eliminate them there
+and so you just have really this one
+
+ align:start position:0%
+and so you just have really this one
+ 
+
+ align:start position:0%
+and so you just have really this one
+time derivative
+
+ align:start position:0%
+time derivative
+ 
+
+ align:start position:0%
+time derivative
+this theory is particularly simple if we
+
+ align:start position:0%
+this theory is particularly simple if we
+ 
+
+ align:start position:0%
+this theory is particularly simple if we
+neglect the relativistic corrections
+
+ align:start position:0%
+neglect the relativistic corrections
+ 
+
+ align:start position:0%
+neglect the relativistic corrections
+and that's because it's not because it's
+
+ align:start position:0%
+and that's because it's not because it's
+ 
+
+ align:start position:0%
+and that's because it's not because it's
+a non-relativistic field theory the
+
+ align:start position:0%
+a non-relativistic field theory the
+ 
+
+ align:start position:0%
+a non-relativistic field theory the
+bubble we just have these bubble
+
+ align:start position:0%
+bubble we just have these bubble
+ 
+
+ align:start position:0%
+bubble we just have these bubble
+diagrams
+
+ align:start position:0%
+diagrams
+ 
+
+ align:start position:0%
+diagrams
+and they're just contact interactions so
+
+ align:start position:0%
+and they're just contact interactions so
+ 
+
+ align:start position:0%
+and they're just contact interactions so
+they all decouple from each other so at
+
+ align:start position:0%
+they all decouple from each other so at
+ 
+
+ align:start position:0%
+they all decouple from each other so at
+n loop order we can just write down what
+
+ align:start position:0%
+n loop order we can just write down what
+ 
+
+ align:start position:0%
+n loop order we can just write down what
+the loops are
+
+ align:start position:0%
+the loops are
+ 
+
+ align:start position:0%
+the loops are
+we talked about the fact that
+
+ align:start position:0%
+we talked about the fact that
+ 
+
+ align:start position:0%
+we talked about the fact that
+in terms of power counting things were
+
+ align:start position:0%
+in terms of power counting things were
+ 
+
+ align:start position:0%
+in terms of power counting things were
+could be a little subtle
+
+ align:start position:0%
+could be a little subtle
+ 
+
+ align:start position:0%
+could be a little subtle
+and that was related also to a power
+
+ align:start position:0%
+and that was related also to a power
+ 
+
+ align:start position:0%
+and that was related also to a power
+divergence that occurs in this diagram
+
+ align:start position:0%
+divergence that occurs in this diagram
+ 
+
+ align:start position:0%
+divergence that occurs in this diagram
+and we could track that power divergence
+
+ align:start position:0%
+and we could track that power divergence
+ 
+
+ align:start position:0%
+and we could track that power divergence
+by using particular schemes that gave
+
+ align:start position:0%
+by using particular schemes that gave
+ 
+
+ align:start position:0%
+by using particular schemes that gave
+this extra mu r term and i won't repeat
+
+ align:start position:0%
+this extra mu r term and i won't repeat
+ 
+
+ align:start position:0%
+this extra mu r term and i won't repeat
+all that story but
+
+ align:start position:0%
+all that story but
+ 
+
+ align:start position:0%
+all that story but
+that led us to adding a finite counter
+
+ align:start position:0%
+that led us to adding a finite counter
+ 
+
+ align:start position:0%
+that led us to adding a finite counter
+term to this bubble diagram to track the
+
+ align:start position:0%
+term to this bubble diagram to track the
+ 
+
+ align:start position:0%
+term to this bubble diagram to track the
+power law divergent term
+
+ align:start position:0%
+power law divergent term
+ 
+
+ align:start position:0%
+power law divergent term
+and that allowed us to come up with a
+
+ align:start position:0%
+and that allowed us to come up with a
+ 
+
+ align:start position:0%
+and that allowed us to come up with a
+counting power counting that would take
+
+ align:start position:0%
+counting power counting that would take
+ 
+
+ align:start position:0%
+counting power counting that would take
+into account systems where the
+
+ align:start position:0%
+into account systems where the
+ 
+
+ align:start position:0%
+into account systems where the
+scattering length is large or in
+
+ align:start position:0%
+scattering length is large or in
+ 
+
+ align:start position:0%
+scattering length is large or in
+particular the scattering length times
+
+ align:start position:0%
+particular the scattering length times
+ 
+
+ align:start position:0%
+particular the scattering length times
+the momentum is greater than one and in
+
+ align:start position:0%
+the momentum is greater than one and in
+ 
+
+ align:start position:0%
+the momentum is greater than one and in
+these two nucleon systems that's exactly
+
+ align:start position:0%
+these two nucleon systems that's exactly
+ 
+
+ align:start position:0%
+these two nucleon systems that's exactly
+the scenario that we're in
+
+ align:start position:0%
+the scenario that we're in
+ 
+
+ align:start position:0%
+the scenario that we're in
+so what we then had was a power counting
+
+ align:start position:0%
+so what we then had was a power counting
+ 
+
+ align:start position:0%
+so what we then had was a power counting
+that assigned the very first operator
+
+ align:start position:0%
+that assigned the very first operator
+ 
+
+ align:start position:0%
+that assigned the very first operator
+to scale like one over a power of
+
+ align:start position:0%
+to scale like one over a power of
+ 
+
+ align:start position:0%
+to scale like one over a power of
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+so not like a one over a power of a
+
+ align:start position:0%
+so not like a one over a power of a
+ 
+
+ align:start position:0%
+so not like a one over a power of a
+large scale but actually one over a
+
+ align:start position:0%
+large scale but actually one over a
+ 
+
+ align:start position:0%
+large scale but actually one over a
+power of something small the momentum
+
+ align:start position:0%
+power of something small the momentum
+ 
+
+ align:start position:0%
+power of something small the momentum
+that we're interested in studying so
+
+ align:start position:0%
+that we're interested in studying so
+ 
+
+ align:start position:0%
+that we're interested in studying so
+it's enhanced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the power counting that we wanted to
+
+ align:start position:0%
+in the power counting that we wanted to
+ 
+
+ align:start position:0%
+in the power counting that we wanted to
+adopt and that meant basically that you
+
+ align:start position:0%
+adopt and that meant basically that you
+ 
+
+ align:start position:0%
+adopt and that meant basically that you
+had to treat this one coupling c0
+
+ align:start position:0%
+had to treat this one coupling c0
+ 
+
+ align:start position:0%
+had to treat this one coupling c0
+non-perturbatively
+
+ align:start position:0%
+non-perturbatively
+ 
+
+ align:start position:0%
+non-perturbatively
+you summed it up to all orders so the
+
+ align:start position:0%
+you summed it up to all orders so the
+ 
+
+ align:start position:0%
+you summed it up to all orders so the
+term here
+
+ align:start position:0%
+term here
+ 
+
+ align:start position:0%
+term here
+comes from adding up all the diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with any number of bubbles
+
+ align:start position:0%
+with any number of bubbles
+ 
+
+ align:start position:0%
+with any number of bubbles
+and that all give this first term
+
+ align:start position:0%
+and that all give this first term
+ 
+
+ align:start position:0%
+and that all give this first term
+and then the rest of the couplings are
+
+ align:start position:0%
+and then the rest of the couplings are
+ 
+
+ align:start position:0%
+and then the rest of the couplings are
+treated perturbatively the higher
+
+ align:start position:0%
+treated perturbatively the higher
+ 
+
+ align:start position:0%
+treated perturbatively the higher
+derivative term so a term c2 which comes
+
+ align:start position:0%
+derivative term so a term c2 which comes
+ 
+
+ align:start position:0%
+derivative term so a term c2 which comes
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+a grad squared and that gives us extra p
+
+ align:start position:0%
+a grad squared and that gives us extra p
+ 
+
+ align:start position:0%
+a grad squared and that gives us extra p
+squared and the numerator here gets
+
+ align:start position:0%
+squared and the numerator here gets
+ 
+
+ align:start position:0%
+squared and the numerator here gets
+treated uh perturbatively and there's
+
+ align:start position:0%
+treated uh perturbatively and there's
+ 
+
+ align:start position:0%
+treated uh perturbatively and there's
+this term and then there's higher terms
+
+ align:start position:0%
+this term and then there's higher terms
+ 
+
+ align:start position:0%
+this term and then there's higher terms
+and that's how we could organize this
+
+ align:start position:0%
+and that's how we could organize this
+ 
+
+ align:start position:0%
+and that's how we could organize this
+theory and this sums up all these powers
+
+ align:start position:0%
+theory and this sums up all these powers
+ 
+
+ align:start position:0%
+theory and this sums up all these powers
+of a times p
+
+ align:start position:0%
+of a times p
+ 
+
+ align:start position:0%
+of a times p
+these denominators that i'm showing you
+
+ align:start position:0%
+these denominators that i'm showing you
+ 
+
+ align:start position:0%
+these denominators that i'm showing you
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+so what i want to do for the first part
+
+ align:start position:0%
+so what i want to do for the first part
+ 
+
+ align:start position:0%
+so what i want to do for the first part
+of today is just really continue with
+
+ align:start position:0%
+of today is just really continue with
+ 
+
+ align:start position:0%
+of today is just really continue with
+this this effective field theory
+
+ align:start position:0%
+this this effective field theory
+ 
+
+ align:start position:0%
+this this effective field theory
+and talk about a few more of its
+
+ align:start position:0%
+and talk about a few more of its
+ 
+
+ align:start position:0%
+and talk about a few more of its
+features
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first i want to talk start with
+
+ align:start position:0%
+first i want to talk start with
+ 
+
+ align:start position:0%
+first i want to talk start with
+symmetries and then we'll talk about
+
+ align:start position:0%
+symmetries and then we'll talk about
+ 
+
+ align:start position:0%
+symmetries and then we'll talk about
+something called the deuteron
+
+ align:start position:0%
+something called the deuteron
+ 
+
+ align:start position:0%
+something called the deuteron
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+there's a question about the
+
+ align:start position:0%
+there's a question about the
+ 
+
+ align:start position:0%
+there's a question about the
+relevance of the kinetic term yeah so
+
+ align:start position:0%
+relevance of the kinetic term yeah so
+ 
+
+ align:start position:0%
+relevance of the kinetic term yeah so
+other than getting a pinching on your
+
+ align:start position:0%
+other than getting a pinching on your
+ 
+
+ align:start position:0%
+other than getting a pinching on your
+integrals is there
+
+ align:start position:0%
+integrals is there
+ 
+
+ align:start position:0%
+integrals is there
+i don't know a more power counting
+
+ align:start position:0%
+i don't know a more power counting
+ 
+
+ align:start position:0%
+i don't know a more power counting
+friendly kind of argument yeah so you
+
+ align:start position:0%
+friendly kind of argument yeah so you
+ 
+
+ align:start position:0%
+friendly kind of argument yeah so you
+can think about it like really what
+
+ align:start position:0%
+can think about it like really what
+ 
+
+ align:start position:0%
+can think about it like really what
+we're doing here is non-relativistic
+
+ align:start position:0%
+we're doing here is non-relativistic
+ 
+
+ align:start position:0%
+we're doing here is non-relativistic
+quantum mechanics
+
+ align:start position:0%
+quantum mechanics
+ 
+
+ align:start position:0%
+quantum mechanics
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh if you think about non-relativistic
+
+ align:start position:0%
+uh if you think about non-relativistic
+ 
+
+ align:start position:0%
+uh if you think about non-relativistic
+quantum connects you think about like
+
+ align:start position:0%
+quantum connects you think about like
+ 
+
+ align:start position:0%
+quantum connects you think about like
+the viral theorem you're used to
+
+ align:start position:0%
+the viral theorem you're used to
+ 
+
+ align:start position:0%
+the viral theorem you're used to
+thinking about the fact that kinetic
+
+ align:start position:0%
+thinking about the fact that kinetic
+ 
+
+ align:start position:0%
+thinking about the fact that kinetic
+energy and potential energy are equally
+
+ align:start position:0%
+energy and potential energy are equally
+ 
+
+ align:start position:0%
+energy and potential energy are equally
+relevant
+
+ align:start position:0%
+relevant
+ 
+
+ align:start position:0%
+relevant
+right so from a physics standpoint if i
+
+ align:start position:0%
+right so from a physics standpoint if i
+ 
+
+ align:start position:0%
+right so from a physics standpoint if i
+didn't want to
+
+ align:start position:0%
+didn't want to
+ 
+
+ align:start position:0%
+didn't want to
+talk about diagrams or
+
+ align:start position:0%
+talk about diagrams or
+ 
+
+ align:start position:0%
+talk about diagrams or
+i just wanted to make a physics argument
+
+ align:start position:0%
+i just wanted to make a physics argument
+ 
+
+ align:start position:0%
+i just wanted to make a physics argument
+for why that would be the right thing to
+
+ align:start position:0%
+for why that would be the right thing to
+ 
+
+ align:start position:0%
+for why that would be the right thing to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+i could simply tell you
+
+ align:start position:0%
+i could simply tell you
+ 
+
+ align:start position:0%
+i could simply tell you
+i want non-relativistic quantum
+
+ align:start position:0%
+i want non-relativistic quantum
+ 
+
+ align:start position:0%
+i want non-relativistic quantum
+mechanics at lowest order this is a
+
+ align:start position:0%
+mechanics at lowest order this is a
+ 
+
+ align:start position:0%
+mechanics at lowest order this is a
+system with two heavy particles and
+
+ align:start position:0%
+system with two heavy particles and
+ 
+
+ align:start position:0%
+system with two heavy particles and
+that's what the physics should be
+
+ align:start position:0%
+that's what the physics should be
+ 
+
+ align:start position:0%
+that's what the physics should be
+if you start with the wrong theory then
+
+ align:start position:0%
+if you start with the wrong theory then
+ 
+
+ align:start position:0%
+if you start with the wrong theory then
+you run into problems and that's kind of
+
+ align:start position:0%
+you run into problems and that's kind of
+ 
+
+ align:start position:0%
+you run into problems and that's kind of
+what we saw if we started with an hqt
+
+ align:start position:0%
+what we saw if we started with an hqt
+ 
+
+ align:start position:0%
+what we saw if we started with an hqt
+like reasoning
+
+ align:start position:0%
+like reasoning
+ 
+
+ align:start position:0%
+like reasoning
+and we see this pinch singularity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is resolved by the kinetic term
+
+ align:start position:0%
+which is resolved by the kinetic term
+ 
+
+ align:start position:0%
+which is resolved by the kinetic term
+okay why is it that non-ultimate quantum
+
+ align:start position:0%
+okay why is it that non-ultimate quantum
+ 
+
+ align:start position:0%
+okay why is it that non-ultimate quantum
+mechanics has the form that does that
+
+ align:start position:0%
+mechanics has the form that does that
+ 
+
+ align:start position:0%
+mechanics has the form that does that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+why does non-relativistic quantum
+
+ align:start position:0%
+why does non-relativistic quantum
+ 
+
+ align:start position:0%
+why does non-relativistic quantum
+mechanics have the form that it does
+
+ align:start position:0%
+mechanics have the form that it does
+ 
+
+ align:start position:0%
+mechanics have the form that it does
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+think about think about it from the
+
+ align:start position:0%
+think about think about it from the
+ 
+
+ align:start position:0%
+think about think about it from the
+following point of view so when when we
+
+ align:start position:0%
+following point of view so when when we
+ 
+
+ align:start position:0%
+following point of view so when when we
+just had this term
+
+ align:start position:0%
+just had this term
+ 
+
+ align:start position:0%
+just had this term
+what was the new what was the particle
+
+ align:start position:0%
+what was the new what was the particle
+ 
+
+ align:start position:0%
+what was the new what was the particle
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+when we just had the partial t term we
+
+ align:start position:0%
+when we just had the partial t term we
+ 
+
+ align:start position:0%
+when we just had the partial t term we
+it's like a source we had a single
+
+ align:start position:0%
+it's like a source we had a single
+ 
+
+ align:start position:0%
+it's like a source we had a single
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+sitting there and we were interacting
+
+ align:start position:0%
+sitting there and we were interacting
+ 
+
+ align:start position:0%
+sitting there and we were interacting
+with it with some white stuff that was
+
+ align:start position:0%
+with it with some white stuff that was
+ 
+
+ align:start position:0%
+with it with some white stuff that was
+hqet
+
+ align:start position:0%
+hqet
+ 
+
+ align:start position:0%
+hqet
+here we have two sources
+
+ align:start position:0%
+here we have two sources
+ 
+
+ align:start position:0%
+here we have two sources
+and they have to interact with each
+
+ align:start position:0%
+and they have to interact with each
+ 
+
+ align:start position:0%
+and they have to interact with each
+other and the problem is that two
+
+ align:start position:0%
+other and the problem is that two
+ 
+
+ align:start position:0%
+other and the problem is that two
+sources interacting with each other
+
+ align:start position:0%
+sources interacting with each other
+ 
+
+ align:start position:0%
+sources interacting with each other
+really the kinetic energy is becomes a
+
+ align:start position:0%
+really the kinetic energy is becomes a
+ 
+
+ align:start position:0%
+really the kinetic energy is becomes a
+relevant
+
+ align:start position:0%
+relevant
+ 
+
+ align:start position:0%
+relevant
+thing it's not
+
+ align:start position:0%
+thing it's not
+ 
+
+ align:start position:0%
+thing it's not
+i mean it's actually a little more
+
+ align:start position:0%
+i mean it's actually a little more
+ 
+
+ align:start position:0%
+i mean it's actually a little more
+subtle than that
+
+ align:start position:0%
+subtle than that
+ 
+
+ align:start position:0%
+subtle than that
+if you really want to go into it in a
+
+ align:start position:0%
+if you really want to go into it in a
+ 
+
+ align:start position:0%
+if you really want to go into it in a
+gauge theory there's sort of situations
+
+ align:start position:0%
+gauge theory there's sort of situations
+ 
+
+ align:start position:0%
+gauge theory there's sort of situations
+where these two heavy sources act like
+
+ align:start position:0%
+where these two heavy sources act like
+ 
+
+ align:start position:0%
+where these two heavy sources act like
+two heavy sources like hqet and there's
+
+ align:start position:0%
+two heavy sources like hqet and there's
+ 
+
+ align:start position:0%
+two heavy sources like hqet and there's
+situations where they wiggle
+
+ align:start position:0%
+situations where they wiggle
+ 
+
+ align:start position:0%
+situations where they wiggle
+and the situations where they wiggle are
+
+ align:start position:0%
+and the situations where they wiggle are
+ 
+
+ align:start position:0%
+and the situations where they wiggle are
+exactly the things that the schrodinger
+
+ align:start position:0%
+exactly the things that the schrodinger
+ 
+
+ align:start position:0%
+exactly the things that the schrodinger
+equation is giving you
+
+ align:start position:0%
+equation is giving you
+ 
+
+ align:start position:0%
+equation is giving you
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if you like
+
+ align:start position:0%
+if you like
+ 
+
+ align:start position:0%
+if you like
+yeah so that to say it precisely
+
+ align:start position:0%
+yeah so that to say it precisely
+ 
+
+ align:start position:0%
+yeah so that to say it precisely
+the potential that between the two heavy
+
+ align:start position:0%
+the potential that between the two heavy
+ 
+
+ align:start position:0%
+the potential that between the two heavy
+particles for the purposes of figuring
+
+ align:start position:0%
+particles for the purposes of figuring
+ 
+
+ align:start position:0%
+particles for the purposes of figuring
+out that potential you can treat them as
+
+ align:start position:0%
+out that potential you can treat them as
+ 
+
+ align:start position:0%
+out that potential you can treat them as
+static and fixed
+
+ align:start position:0%
+static and fixed
+ 
+
+ align:start position:0%
+static and fixed
+but then once you have that potential
+
+ align:start position:0%
+but then once you have that potential
+ 
+
+ align:start position:0%
+but then once you have that potential
+these bubble diagrams are kind of the
+
+ align:start position:0%
+these bubble diagrams are kind of the
+ 
+
+ align:start position:0%
+these bubble diagrams are kind of the
+way in which
+
+ align:start position:0%
+way in which
+ 
+
+ align:start position:0%
+way in which
+that potential gets iterated into the
+
+ align:start position:0%
+that potential gets iterated into the
+ 
+
+ align:start position:0%
+that potential gets iterated into the
+thing that you would get from solving
+
+ align:start position:0%
+thing that you would get from solving
+ 
+
+ align:start position:0%
+thing that you would get from solving
+the schrodinger equation so solving the
+
+ align:start position:0%
+the schrodinger equation so solving the
+ 
+
+ align:start position:0%
+the schrodinger equation so solving the
+shorter equation you're effectively
+
+ align:start position:0%
+shorter equation you're effectively
+ 
+
+ align:start position:0%
+shorter equation you're effectively
+treating the potential to all orders in
+
+ align:start position:0%
+treating the potential to all orders in
+ 
+
+ align:start position:0%
+treating the potential to all orders in
+this series exactly this bubble series
+
+ align:start position:0%
+this series exactly this bubble series
+ 
+
+ align:start position:0%
+this series exactly this bubble series
+and when you solve that you need to
+
+ align:start position:0%
+and when you solve that you need to
+ 
+
+ align:start position:0%
+and when you solve that you need to
+include the kinetic this grad squared
+
+ align:start position:0%
+include the kinetic this grad squared
+ 
+
+ align:start position:0%
+include the kinetic this grad squared
+over 2m for the same reason that it's a
+
+ align:start position:0%
+over 2m for the same reason that it's a
+ 
+
+ align:start position:0%
+over 2m for the same reason that it's a
+relevant thing to include in
+
+ align:start position:0%
+relevant thing to include in
+ 
+
+ align:start position:0%
+relevant thing to include in
+quantum mechanics
+
+ align:start position:0%
+quantum mechanics
+ 
+
+ align:start position:0%
+quantum mechanics
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good good project choice
+
+ align:start position:0%
+good good project choice
+ 
+
+ align:start position:0%
+good good project choice
+i urge you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's talk about some of the
+
+ align:start position:0%
+okay so let's talk about some of the
+ 
+
+ align:start position:0%
+okay so let's talk about some of the
+symmetries of this theory which are kind
+
+ align:start position:0%
+symmetries of this theory which are kind
+ 
+
+ align:start position:0%
+symmetries of this theory which are kind
+of interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first one is that this syria
+
+ align:start position:0%
+so the first one is that this syria
+ 
+
+ align:start position:0%
+so the first one is that this syria
+actually has a
+
+ align:start position:0%
+actually has a
+ 
+
+ align:start position:0%
+actually has a
+non-relativistic conformal invariance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is a non-relativistic conformal
+
+ align:start position:0%
+so what is a non-relativistic conformal
+ 
+
+ align:start position:0%
+so what is a non-relativistic conformal
+invariant so this is
+
+ align:start position:0%
+invariant so this is
+ 
+
+ align:start position:0%
+invariant so this is
+an extension of the galilean group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rather than the poincare group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have the usual translations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have rotations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we don't have lorenz boost but we do
+
+ align:start position:0%
+we don't have lorenz boost but we do
+ 
+
+ align:start position:0%
+we don't have lorenz boost but we do
+have galilean boost for a
+
+ align:start position:0%
+have galilean boost for a
+ 
+
+ align:start position:0%
+have galilean boost for a
+non-relativistic
+
+ align:start position:0%
+non-relativistic
+ 
+
+ align:start position:0%
+non-relativistic
+system like this
+
+ align:start position:0%
+system like this
+ 
+
+ align:start position:0%
+system like this
+so what would those be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so under a galilean boost time is not
+
+ align:start position:0%
+so under a galilean boost time is not
+ 
+
+ align:start position:0%
+so under a galilean boost time is not
+changed and the spatial coordinates are
+
+ align:start position:0%
+changed and the spatial coordinates are
+ 
+
+ align:start position:0%
+changed and the spatial coordinates are
+changed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's additional generators
+
+ align:start position:0%
+and then there's additional generators
+ 
+
+ align:start position:0%
+and then there's additional generators
+that you have in this conformal for a
+
+ align:start position:0%
+that you have in this conformal for a
+ 
+
+ align:start position:0%
+that you have in this conformal for a
+conformal invariants
+
+ align:start position:0%
+conformal invariants
+ 
+
+ align:start position:0%
+conformal invariants
+one is a scale transformation
+
+ align:start position:0%
+one is a scale transformation
+ 
+
+ align:start position:0%
+one is a scale transformation
+one generator
+
+ align:start position:0%
+one generator
+ 
+
+ align:start position:0%
+one generator
+and the way that the scale
+
+ align:start position:0%
+and the way that the scale
+ 
+
+ align:start position:0%
+and the way that the scale
+transformation works is as follows
+
+ align:start position:0%
+transformation works is as follows
+ 
+
+ align:start position:0%
+transformation works is as follows
+you rescale the coordinates by some
+
+ align:start position:0%
+you rescale the coordinates by some
+ 
+
+ align:start position:0%
+you rescale the coordinates by some
+let's call it e to the s
+
+ align:start position:0%
+let's call it e to the s
+ 
+
+ align:start position:0%
+let's call it e to the s
+but you have to rescale time differently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by e to the 2s
+
+ align:start position:0%
+by e to the 2s
+ 
+
+ align:start position:0%
+by e to the 2s
+and the reason that you have to do that
+
+ align:start position:0%
+and the reason that you have to do that
+ 
+
+ align:start position:0%
+and the reason that you have to do that
+is exactly because
+
+ align:start position:0%
+is exactly because
+ 
+
+ align:start position:0%
+is exactly because
+these two terms should be treated the
+
+ align:start position:0%
+these two terms should be treated the
+ 
+
+ align:start position:0%
+these two terms should be treated the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+so you have to rescale time
+
+ align:start position:0%
+so you have to rescale time
+ 
+
+ align:start position:0%
+so you have to rescale time
+twice as much as you rescale the spatial
+
+ align:start position:0%
+twice as much as you rescale the spatial
+ 
+
+ align:start position:0%
+twice as much as you rescale the spatial
+derivatives if you like
+
+ align:start position:0%
+derivatives if you like
+ 
+
+ align:start position:0%
+derivatives if you like
+so that's what gives rise to the two
+
+ align:start position:0%
+so that's what gives rise to the two
+ 
+
+ align:start position:0%
+so that's what gives rise to the two
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and that just goes to the heart of sort
+
+ align:start position:0%
+and that just goes to the heart of sort
+ 
+
+ align:start position:0%
+and that just goes to the heart of sort
+of counting time and
+
+ align:start position:0%
+of counting time and
+ 
+
+ align:start position:0%
+of counting time and
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+differently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then finally there's there isn't a
+
+ align:start position:0%
+and then finally there's there isn't a
+ 
+
+ align:start position:0%
+and then finally there's there isn't a
+conformal generator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's actually only one generator
+
+ align:start position:0%
+and there's actually only one generator
+ 
+
+ align:start position:0%
+and there's actually only one generator
+in this non-relativistic case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and basically what this generator
+
+ align:start position:0%
+and basically what this generator
+ 
+
+ align:start position:0%
+and basically what this generator
+corresponds to is it
+
+ align:start position:0%
+corresponds to is it
+ 
+
+ align:start position:0%
+corresponds to is it
+a shift of inverse time
+
+ align:start position:0%
+a shift of inverse time
+ 
+
+ align:start position:0%
+a shift of inverse time
+and then a corresponding change to the
+
+ align:start position:0%
+and then a corresponding change to the
+ 
+
+ align:start position:0%
+and then a corresponding change to the
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+and if you take all these things
+
+ align:start position:0%
+and if you take all these things
+ 
+
+ align:start position:0%
+and if you take all these things
+together it's actually something called
+
+ align:start position:0%
+together it's actually something called
+ 
+
+ align:start position:0%
+together it's actually something called
+the schrodinger group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the theory we've been talking about
+
+ align:start position:0%
+and the theory we've been talking about
+ 
+
+ align:start position:0%
+and the theory we've been talking about
+actually has this non-relativistic
+
+ align:start position:0%
+actually has this non-relativistic
+ 
+
+ align:start position:0%
+actually has this non-relativistic
+conformal symmetry
+
+ align:start position:0%
+conformal symmetry
+ 
+
+ align:start position:0%
+conformal symmetry
+if a goes to infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm not going to spend a lot of time
+
+ align:start position:0%
+so i'm not going to spend a lot of time
+ 
+
+ align:start position:0%
+so i'm not going to spend a lot of time
+talking about this
+
+ align:start position:0%
+talking about this
+ 
+
+ align:start position:0%
+talking about this
+but just to give you some of the ideas
+
+ align:start position:0%
+but just to give you some of the ideas
+ 
+
+ align:start position:0%
+but just to give you some of the ideas
+of what is going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you look back last time at our
+
+ align:start position:0%
+if you look back last time at our
+ 
+
+ align:start position:0%
+if you look back last time at our
+solutions for this coupling constant and
+
+ align:start position:0%
+solutions for this coupling constant and
+ 
+
+ align:start position:0%
+solutions for this coupling constant and
+you take a goes to infinity
+
+ align:start position:0%
+you take a goes to infinity
+ 
+
+ align:start position:0%
+you take a goes to infinity
+that's a perfectly smooth limit you can
+
+ align:start position:0%
+that's a perfectly smooth limit you can
+ 
+
+ align:start position:0%
+that's a perfectly smooth limit you can
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+and then the coupling c 0 of mu has no
+
+ align:start position:0%
+and then the coupling c 0 of mu has no
+ 
+
+ align:start position:0%
+and then the coupling c 0 of mu has no
+free parameters it's just given by 4 pi
+
+ align:start position:0%
+free parameters it's just given by 4 pi
+ 
+
+ align:start position:0%
+free parameters it's just given by 4 pi
+over mu
+
+ align:start position:0%
+over mu
+ 
+
+ align:start position:0%
+over mu
+and that's corresponds to sitting at
+
+ align:start position:0%
+and that's corresponds to sitting at
+ 
+
+ align:start position:0%
+and that's corresponds to sitting at
+this what i call what we last time saw
+
+ align:start position:0%
+this what i call what we last time saw
+ 
+
+ align:start position:0%
+this what i call what we last time saw
+was a fixed point of the beta function
+
+ align:start position:0%
+was a fixed point of the beta function
+ 
+
+ align:start position:0%
+was a fixed point of the beta function
+and at that fixed point there's enhanced
+
+ align:start position:0%
+and at that fixed point there's enhanced
+ 
+
+ align:start position:0%
+and at that fixed point there's enhanced
+symmetry which is this conformal
+
+ align:start position:0%
+symmetry which is this conformal
+ 
+
+ align:start position:0%
+symmetry which is this conformal
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and basically what you can show is that
+
+ align:start position:0%
+and basically what you can show is that
+ 
+
+ align:start position:0%
+and basically what you can show is that
+if you scale here mu
+
+ align:start position:0%
+if you scale here mu
+ 
+
+ align:start position:0%
+if you scale here mu
+just like it was a momentum
+
+ align:start position:0%
+just like it was a momentum
+ 
+
+ align:start position:0%
+just like it was a momentum
+so mu goes to e to the s mu
+
+ align:start position:0%
+so mu goes to e to the s mu
+ 
+
+ align:start position:0%
+so mu goes to e to the s mu
+then the lagrangian is scalar variant
+
+ align:start position:0%
+then the lagrangian is scalar variant
+ 
+
+ align:start position:0%
+then the lagrangian is scalar variant
+maybe in my notation up there would be
+
+ align:start position:0%
+maybe in my notation up there would be
+ 
+
+ align:start position:0%
+maybe in my notation up there would be
+minus s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that is basically kind of the
+
+ align:start position:0%
+okay and that is basically kind of the
+ 
+
+ align:start position:0%
+okay and that is basically kind of the
+same thing as making it into a relevant
+
+ align:start position:0%
+same thing as making it into a relevant
+ 
+
+ align:start position:0%
+same thing as making it into a relevant
+coupling once it's got no free
+
+ align:start position:0%
+coupling once it's got no free
+ 
+
+ align:start position:0%
+coupling once it's got no free
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+you can sort of see that
+
+ align:start position:0%
+you can sort of see that
+ 
+
+ align:start position:0%
+you can sort of see that
+if i have a certain scaling that makes
+
+ align:start position:0%
+if i have a certain scaling that makes
+ 
+
+ align:start position:0%
+if i have a certain scaling that makes
+the free theory
+
+ align:start position:0%
+the free theory
+ 
+
+ align:start position:0%
+the free theory
+schroedinger invariant which is so the
+
+ align:start position:0%
+schroedinger invariant which is so the
+ 
+
+ align:start position:0%
+schroedinger invariant which is so the
+schrodinger group is the is the symmetry
+
+ align:start position:0%
+schrodinger group is the is the symmetry
+ 
+
+ align:start position:0%
+schrodinger group is the is the symmetry
+group of the free schrodinger equation
+
+ align:start position:0%
+group of the free schrodinger equation
+ 
+
+ align:start position:0%
+group of the free schrodinger equation
+so just this term in this term then the
+
+ align:start position:0%
+so just this term in this term then the
+ 
+
+ align:start position:0%
+so just this term in this term then the
+question is what interactions can you
+
+ align:start position:0%
+question is what interactions can you
+ 
+
+ align:start position:0%
+question is what interactions can you
+add that would preserve that symmetry
+
+ align:start position:0%
+add that would preserve that symmetry
+ 
+
+ align:start position:0%
+add that would preserve that symmetry
+and i'm just telling you that in terms
+
+ align:start position:0%
+and i'm just telling you that in terms
+ 
+
+ align:start position:0%
+and i'm just telling you that in terms
+of just the scale transformation
+
+ align:start position:0%
+of just the scale transformation
+ 
+
+ align:start position:0%
+of just the scale transformation
+you could if you're able to scale the
+
+ align:start position:0%
+you could if you're able to scale the
+ 
+
+ align:start position:0%
+you could if you're able to scale the
+coupling in some way in particular to
+
+ align:start position:0%
+coupling in some way in particular to
+ 
+
+ align:start position:0%
+coupling in some way in particular to
+make it a relevant interaction then that
+
+ align:start position:0%
+make it a relevant interaction then that
+ 
+
+ align:start position:0%
+make it a relevant interaction then that
+will make it a scale invariant theory
+
+ align:start position:0%
+will make it a scale invariant theory
+ 
+
+ align:start position:0%
+will make it a scale invariant theory
+and so the ability to scale this
+
+ align:start position:0%
+and so the ability to scale this
+ 
+
+ align:start position:0%
+and so the ability to scale this
+coupling because you scale this mu
+
+ align:start position:0%
+coupling because you scale this mu
+ 
+
+ align:start position:0%
+coupling because you scale this mu
+allows it to be a scale invariant theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a little harder to see that it's
+
+ align:start position:0%
+it's a little harder to see that it's
+ 
+
+ align:start position:0%
+it's a little harder to see that it's
+conformal but you can work that out too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conform scale and variant theories tend
+
+ align:start position:0%
+conform scale and variant theories tend
+ 
+
+ align:start position:0%
+conform scale and variant theories tend
+to be conformally invariant and the same
+
+ align:start position:0%
+to be conformally invariant and the same
+ 
+
+ align:start position:0%
+to be conformally invariant and the same
+is true of this
+
+ align:start position:0%
+is true of this
+ 
+
+ align:start position:0%
+is true of this
+non-relativistic conformal invariance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you sort of add up the bubbles
+
+ align:start position:0%
+so if you sort of add up the bubbles
+ 
+
+ align:start position:0%
+so if you sort of add up the bubbles
+that we were talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you find
+
+ align:start position:0%
+then you find
+ 
+
+ align:start position:0%
+then you find
+in general an amplitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is this thing that has a square
+
+ align:start position:0%
+which is this thing that has a square
+ 
+
+ align:start position:0%
+which is this thing that has a square
+root
+
+ align:start position:0%
+root
+ 
+
+ align:start position:0%
+root
+but if i'm not particular to what frame
+
+ align:start position:0%
+but if i'm not particular to what frame
+ 
+
+ align:start position:0%
+but if i'm not particular to what frame
+i'm in now if i just write it for a
+
+ align:start position:0%
+i'm in now if i just write it for a
+ 
+
+ align:start position:0%
+i'm in now if i just write it for a
+general frame
+
+ align:start position:0%
+general frame
+ 
+
+ align:start position:0%
+general frame
+before we write it for the center of
+
+ align:start position:0%
+before we write it for the center of
+ 
+
+ align:start position:0%
+before we write it for the center of
+mass frame now let me write it for a
+
+ align:start position:0%
+mass frame now let me write it for a
+ 
+
+ align:start position:0%
+mass frame now let me write it for a
+general frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then it would look like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that thing
+
+ align:start position:0%
+and that thing
+ 
+
+ align:start position:0%
+and that thing
+goes like one over p so it has and again
+
+ align:start position:0%
+goes like one over p so it has and again
+ 
+
+ align:start position:0%
+goes like one over p so it has and again
+e scale differently than ps
+
+ align:start position:0%
+e scale differently than ps
+ 
+
+ align:start position:0%
+e scale differently than ps
+so this thing has the right
+
+ align:start position:0%
+so this thing has the right
+ 
+
+ align:start position:0%
+so this thing has the right
+scaling for a scale invariant amplitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it turns out if you do
+
+ align:start position:0%
+and it turns out if you do
+ 
+
+ align:start position:0%
+and it turns out if you do
+work out the conformal transformation
+
+ align:start position:0%
+work out the conformal transformation
+ 
+
+ align:start position:0%
+work out the conformal transformation
+it's also conformal invariant
+
+ align:start position:0%
+it's also conformal invariant
+ 
+
+ align:start position:0%
+it's also conformal invariant
+and i'm not going to go through that but
+
+ align:start position:0%
+and i'm not going to go through that but
+ 
+
+ align:start position:0%
+and i'm not going to go through that but
+i've posted a reference to show you how
+
+ align:start position:0%
+i've posted a reference to show you how
+ 
+
+ align:start position:0%
+i've posted a reference to show you how
+it works
+
+ align:start position:0%
+it works
+ 
+
+ align:start position:0%
+it works
+and basically what this leads to is a
+
+ align:start position:0%
+and basically what this leads to is a
+ 
+
+ align:start position:0%
+and basically what this leads to is a
+cross section
+
+ align:start position:0%
+cross section
+ 
+
+ align:start position:0%
+cross section
+which is four pi over p squared
+
+ align:start position:0%
+which is four pi over p squared
+ 
+
+ align:start position:0%
+which is four pi over p squared
+which is the scale and variant version
+
+ align:start position:0%
+which is the scale and variant version
+ 
+
+ align:start position:0%
+which is the scale and variant version
+of a cross section where the
+
+ align:start position:0%
+of a cross section where the
+ 
+
+ align:start position:0%
+of a cross section where the
+cross section units are just set by p so
+
+ align:start position:0%
+cross section units are just set by p so
+ 
+
+ align:start position:0%
+cross section units are just set by p so
+there's no other scale in the problem
+
+ align:start position:0%
+there's no other scale in the problem
+ 
+
+ align:start position:0%
+there's no other scale in the problem
+okay so that's kind of interesting and
+
+ align:start position:0%
+okay so that's kind of interesting and
+ 
+
+ align:start position:0%
+okay so that's kind of interesting and
+one can make some predictions with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is actually something that's
+
+ align:start position:0%
+this is actually something that's
+ 
+
+ align:start position:0%
+this is actually something that's
+also you know investigated these days
+
+ align:start position:0%
+also you know investigated these days
+ 
+
+ align:start position:0%
+also you know investigated these days
+both from a string theory point of view
+
+ align:start position:0%
+both from a string theory point of view
+ 
+
+ align:start position:0%
+both from a string theory point of view
+as well as in cold atoms so the
+
+ align:start position:0%
+as well as in cold atoms so the
+ 
+
+ align:start position:0%
+as well as in cold atoms so the
+informal symmetries
+
+ align:start position:0%
+informal symmetries
+ 
+
+ align:start position:0%
+informal symmetries
+are always fun to play with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's also another set of symmetries
+
+ align:start position:0%
+there's also another set of symmetries
+ 
+
+ align:start position:0%
+there's also another set of symmetries
+that this theory has in this limit which
+
+ align:start position:0%
+that this theory has in this limit which
+ 
+
+ align:start position:0%
+that this theory has in this limit which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+also interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is like hqet there's an
+
+ align:start position:0%
+and that is like hqet there's an
+ 
+
+ align:start position:0%
+and that is like hqet there's an
+enhanced spin symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this this time the enhanced spin
+
+ align:start position:0%
+this this time the enhanced spin
+ 
+
+ align:start position:0%
+this this time the enhanced spin
+symmetry comes about by combining spin
+
+ align:start position:0%
+symmetry comes about by combining spin
+ 
+
+ align:start position:0%
+symmetry comes about by combining spin
+and isospin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a symmetry that's
+
+ align:start position:0%
+and this is a symmetry that's
+ 
+
+ align:start position:0%
+and this is a symmetry that's
+known as wigner's
+
+ align:start position:0%
+known as wigner's
+ 
+
+ align:start position:0%
+known as wigner's
+su4 symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so vigner
+
+ align:start position:0%
+so vigner
+ 
+
+ align:start position:0%
+so vigner
+i don't know how many years ago
+
+ align:start position:0%
+i don't know how many years ago
+ 
+
+ align:start position:0%
+i don't know how many years ago
+noticed long long ago vigner noticed
+
+ align:start position:0%
+noticed long long ago vigner noticed
+ 
+
+ align:start position:0%
+noticed long long ago vigner noticed
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+nuclei tend to have a symmetry which is
+
+ align:start position:0%
+nuclei tend to have a symmetry which is
+ 
+
+ align:start position:0%
+nuclei tend to have a symmetry which is
+a combination of spin and isospin into a
+
+ align:start position:0%
+a combination of spin and isospin into a
+ 
+
+ align:start position:0%
+a combination of spin and isospin into a
+full su4
+
+ align:start position:0%
+full su4
+ 
+
+ align:start position:0%
+full su4
+and we can understand actually partly
+
+ align:start position:0%
+and we can understand actually partly
+ 
+
+ align:start position:0%
+and we can understand actually partly
+where that comes from from this
+
+ align:start position:0%
+where that comes from from this
+ 
+
+ align:start position:0%
+where that comes from from this
+effective field theory
+
+ align:start position:0%
+effective field theory
+ 
+
+ align:start position:0%
+effective field theory
+so what is this su 4
+
+ align:start position:0%
+so what is this su 4
+ 
+
+ align:start position:0%
+so what is this su 4
+think of it as just transforming the
+
+ align:start position:0%
+think of it as just transforming the
+ 
+
+ align:start position:0%
+think of it as just transforming the
+nucleon field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+under a way where you could mix up the
+
+ align:start position:0%
+under a way where you could mix up the
+ 
+
+ align:start position:0%
+under a way where you could mix up the
+spin in the isospin so if sigma is for
+
+ align:start position:0%
+spin in the isospin so if sigma is for
+ 
+
+ align:start position:0%
+spin in the isospin so if sigma is for
+the spin tau is for the isospin
+
+ align:start position:0%
+the spin tau is for the isospin
+ 
+
+ align:start position:0%
+the spin tau is for the isospin
+then some combined transformation where
+
+ align:start position:0%
+then some combined transformation where
+ 
+
+ align:start position:0%
+then some combined transformation where
+i can mix up the mu and news we just
+
+ align:start position:0%
+i can mix up the mu and news we just
+ 
+
+ align:start position:0%
+i can mix up the mu and news we just
+have some set of generators where i
+
+ align:start position:0%
+have some set of generators where i
+ 
+
+ align:start position:0%
+have some set of generators where i
+label them by mu and nu
+
+ align:start position:0%
+label them by mu and nu
+ 
+
+ align:start position:0%
+label them by mu and nu
+sigma mu here is one comma sigma vector
+
+ align:start position:0%
+sigma mu here is one comma sigma vector
+ 
+
+ align:start position:0%
+sigma mu here is one comma sigma vector
+tau nu
+
+ align:start position:0%
+tau nu
+ 
+
+ align:start position:0%
+tau nu
+one comma tau vector for the isospin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you just take the one from both of
+
+ align:start position:0%
+if you just take the one from both of
+ 
+
+ align:start position:0%
+if you just take the one from both of
+them that's baryon number and that is
+
+ align:start position:0%
+them that's baryon number and that is
+ 
+
+ align:start position:0%
+them that's baryon number and that is
+you know what return the se4 into a u
+
+ align:start position:0%
+you know what return the se4 into a u
+ 
+
+ align:start position:0%
+you know what return the se4 into a u
+floor so
+
+ align:start position:0%
+floor so
+ 
+
+ align:start position:0%
+floor so
+you can remove that generator if you
+
+ align:start position:0%
+you can remove that generator if you
+ 
+
+ align:start position:0%
+you can remove that generator if you
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+so there's a u1 as well but the
+
+ align:start position:0%
+so there's a u1 as well but the
+ 
+
+ align:start position:0%
+so there's a u1 as well but the
+non-trivial part where you take either
+
+ align:start position:0%
+non-trivial part where you take either
+ 
+
+ align:start position:0%
+non-trivial part where you take either
+this or that or both is an su4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can think about this symmetry with
+
+ align:start position:0%
+so we can think about this symmetry with
+ 
+
+ align:start position:0%
+so we can think about this symmetry with
+our theory if we write it as follows so
+
+ align:start position:0%
+our theory if we write it as follows so
+ 
+
+ align:start position:0%
+our theory if we write it as follows so
+take the interaction terms that we've
+
+ align:start position:0%
+take the interaction terms that we've
+ 
+
+ align:start position:0%
+take the interaction terms that we've
+been talking about
+
+ align:start position:0%
+been talking about
+ 
+
+ align:start position:0%
+been talking about
+and write them in a slightly different
+
+ align:start position:0%
+and write them in a slightly different
+ 
+
+ align:start position:0%
+and write them in a slightly different
+basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just take these
+
+ align:start position:0%
+just take these
+ 
+
+ align:start position:0%
+just take these
+two to two scattering
+
+ align:start position:0%
+two to two scattering
+ 
+
+ align:start position:0%
+two to two scattering
+terms which note with had no no
+
+ align:start position:0%
+terms which note with had no no
+ 
+
+ align:start position:0%
+terms which note with had no no
+derivatives
+
+ align:start position:0%
+derivatives
+ 
+
+ align:start position:0%
+derivatives
+and i'll write them in a slightly
+
+ align:start position:0%
+and i'll write them in a slightly
+ 
+
+ align:start position:0%
+and i'll write them in a slightly
+different basis
+
+ align:start position:0%
+different basis
+ 
+
+ align:start position:0%
+different basis
+before we wrote them in sort of the
+
+ align:start position:0%
+before we wrote them in sort of the
+ 
+
+ align:start position:0%
+before we wrote them in sort of the
+physical basis where we had 3s1 and 1s0
+
+ align:start position:0%
+physical basis where we had 3s1 and 1s0
+ 
+
+ align:start position:0%
+physical basis where we had 3s1 and 1s0
+that's what we did last time
+
+ align:start position:0%
+that's what we did last time
+ 
+
+ align:start position:0%
+that's what we did last time
+but there's other possible bases and i
+
+ align:start position:0%
+but there's other possible bases and i
+ 
+
+ align:start position:0%
+but there's other possible bases and i
+can write them in this basis
+
+ align:start position:0%
+can write them in this basis
+ 
+
+ align:start position:0%
+can write them in this basis
+triplet basis
+
+ align:start position:0%
+triplet basis
+ 
+
+ align:start position:0%
+triplet basis
+and the advantage of this basis is this
+
+ align:start position:0%
+and the advantage of this basis is this
+ 
+
+ align:start position:0%
+and the advantage of this basis is this
+thing here is just super symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you want to write down the
+
+ align:start position:0%
+and if you want to write down the
+ 
+
+ align:start position:0%
+and if you want to write down the
+relation to the previous basis
+
+ align:start position:0%
+relation to the previous basis
+ 
+
+ align:start position:0%
+relation to the previous basis
+you can work that out
+
+ align:start position:0%
+you can work that out
+ 
+
+ align:start position:0%
+you can work that out
+and just tell you what it would be
+
+ align:start position:0%
+and just tell you what it would be
+ 
+
+ align:start position:0%
+and just tell you what it would be
+by writing down what the coefficients
+
+ align:start position:0%
+by writing down what the coefficients
+ 
+
+ align:start position:0%
+by writing down what the coefficients
+here are in terms of the ones we had
+
+ align:start position:0%
+here are in terms of the ones we had
+ 
+
+ align:start position:0%
+here are in terms of the ones we had
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we go back to the basis where we
+
+ align:start position:0%
+so if we go back to the basis where we
+ 
+
+ align:start position:0%
+so if we go back to the basis where we
+had coefficients for the 3s1 channel on
+
+ align:start position:0%
+had coefficients for the 3s1 channel on
+ 
+
+ align:start position:0%
+had coefficients for the 3s1 channel on
+the 1s0 channel
+
+ align:start position:0%
+the 1s0 channel
+ 
+
+ align:start position:0%
+the 1s0 channel
+then this c0s becomes this combination
+
+ align:start position:0%
+then this c0s becomes this combination
+ 
+
+ align:start position:0%
+then this c0s becomes this combination
+and c0t is this combination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in nature
+
+ align:start position:0%
+now in nature
+ 
+
+ align:start position:0%
+now in nature
+so one way you could have su4 symmetry
+
+ align:start position:0%
+so one way you could have su4 symmetry
+ 
+
+ align:start position:0%
+so one way you could have su4 symmetry
+would just be for the scattering lengths
+
+ align:start position:0%
+would just be for the scattering lengths
+ 
+
+ align:start position:0%
+would just be for the scattering lengths
+the physical parameters c01s
+
+ align:start position:0%
+the physical parameters c01s
+ 
+
+ align:start position:0%
+the physical parameters c01s
+0 and c03s1 to be equal
+
+ align:start position:0%
+0 and c03s1 to be equal
+ 
+
+ align:start position:0%
+0 and c03s1 to be equal
+but in nature they're not equal at all
+
+ align:start position:0%
+but in nature they're not equal at all
+ 
+
+ align:start position:0%
+but in nature they're not equal at all
+they in fact the scattering links have
+
+ align:start position:0%
+they in fact the scattering links have
+ 
+
+ align:start position:0%
+they in fact the scattering links have
+different signs there's no
+
+ align:start position:0%
+different signs there's no
+ 
+
+ align:start position:0%
+different signs there's no
+sense in which they're equal
+
+ align:start position:0%
+sense in which they're equal
+ 
+
+ align:start position:0%
+sense in which they're equal
+so what is the sense in which we have
+
+ align:start position:0%
+so what is the sense in which we have
+ 
+
+ align:start position:0%
+so what is the sense in which we have
+this symmetry
+
+ align:start position:0%
+this symmetry
+ 
+
+ align:start position:0%
+this symmetry
+the sense in which we have this symmetry
+
+ align:start position:0%
+the sense in which we have this symmetry
+ 
+
+ align:start position:0%
+the sense in which we have this symmetry
+is the fact that if
+
+ align:start position:0%
+is the fact that if
+ 
+
+ align:start position:0%
+is the fact that if
+the scattering lengths are both infinity
+
+ align:start position:0%
+the scattering lengths are both infinity
+ 
+
+ align:start position:0%
+the scattering lengths are both infinity
+then both couplings are just this
+
+ align:start position:0%
+then both couplings are just this
+ 
+
+ align:start position:0%
+then both couplings are just this
+so the fact that the scattering lengths
+
+ align:start position:0%
+so the fact that the scattering lengths
+ 
+
+ align:start position:0%
+so the fact that the scattering lengths
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+have different signs but are both large
+
+ align:start position:0%
+have different signs but are both large
+ 
+
+ align:start position:0%
+have different signs but are both large
+makes them close to this fixed point
+
+ align:start position:0%
+makes them close to this fixed point
+ 
+
+ align:start position:0%
+makes them close to this fixed point
+which then gives us symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so because of what i just said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a goes to infinity
+
+ align:start position:0%
+for a goes to infinity
+ 
+
+ align:start position:0%
+for a goes to infinity
+c0s which is sort of equal
+
+ align:start position:0%
+c0s which is sort of equal
+ 
+
+ align:start position:0%
+c0s which is sort of equal
+some symmetric combination of these two
+
+ align:start position:0%
+some symmetric combination of these two
+ 
+
+ align:start position:0%
+some symmetric combination of these two
+that become equal
+
+ align:start position:0%
+that become equal
+ 
+
+ align:start position:0%
+that become equal
+would just become
+
+ align:start position:0%
+would just become
+ 
+
+ align:start position:0%
+would just become
+4 pi over mu
+
+ align:start position:0%
+4 pi over mu
+ 
+
+ align:start position:0%
+4 pi over mu
+and this is for a1 s0 and a 3 s 1
+
+ align:start position:0%
+and this is for a1 s0 and a 3 s 1
+ 
+
+ align:start position:0%
+and this is for a1 s0 and a 3 s 1
+both going to infinity this one's minus
+
+ align:start position:0%
+both going to infinity this one's minus
+ 
+
+ align:start position:0%
+both going to infinity this one's minus
+infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the triplet 1 if we just work
+
+ align:start position:0%
+and then the triplet 1 if we just work
+ 
+
+ align:start position:0%
+and then the triplet 1 if we just work
+out what it is from our formulas for
+
+ align:start position:0%
+out what it is from our formulas for
+ 
+
+ align:start position:0%
+out what it is from our formulas for
+those other couplings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just
+
+ align:start position:0%
+and just
+ 
+
+ align:start position:0%
+and just
+work out the combination from formulas
+
+ align:start position:0%
+work out the combination from formulas
+ 
+
+ align:start position:0%
+work out the combination from formulas
+we had last time
+
+ align:start position:0%
+we had last time
+ 
+
+ align:start position:0%
+we had last time
+and we see that as the a's go to
+
+ align:start position:0%
+and we see that as the a's go to
+ 
+
+ align:start position:0%
+and we see that as the a's go to
+infinity this coupling vanishes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+when we're in the limit where both of
+
+ align:start position:0%
+when we're in the limit where both of
+ 
+
+ align:start position:0%
+when we're in the limit where both of
+the couplings become equal or if we use
+
+ align:start position:0%
+the couplings become equal or if we use
+ 
+
+ align:start position:0%
+the couplings become equal or if we use
+this basis where this coupling becomes
+
+ align:start position:0%
+this basis where this coupling becomes
+ 
+
+ align:start position:0%
+this basis where this coupling becomes
+zero we just have this
+
+ align:start position:0%
+zero we just have this
+ 
+
+ align:start position:0%
+zero we just have this
+n dagger n squared operator then we have
+
+ align:start position:0%
+n dagger n squared operator then we have
+ 
+
+ align:start position:0%
+n dagger n squared operator then we have
+this su4 symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on your on one of the problems on this
+
+ align:start position:0%
+on your on one of the problems on this
+ 
+
+ align:start position:0%
+on your on one of the problems on this
+new problem set is to think about what
+
+ align:start position:0%
+new problem set is to think about what
+ 
+
+ align:start position:0%
+new problem set is to think about what
+how much to what degree you still have
+
+ align:start position:0%
+how much to what degree you still have
+ 
+
+ align:start position:0%
+how much to what degree you still have
+that symmetry when you think about
+
+ align:start position:0%
+that symmetry when you think about
+ 
+
+ align:start position:0%
+that symmetry when you think about
+higher body operators three body and
+
+ align:start position:0%
+higher body operators three body and
+ 
+
+ align:start position:0%
+higher body operators three body and
+forebody
+
+ align:start position:0%
+forebody
+ 
+
+ align:start position:0%
+forebody
+and there's actually some very nice
+
+ align:start position:0%
+and there's actually some very nice
+ 
+
+ align:start position:0%
+and there's actually some very nice
+little group theory arguments where you
+
+ align:start position:0%
+little group theory arguments where you
+ 
+
+ align:start position:0%
+little group theory arguments where you
+can basically figure out how what to
+
+ align:start position:0%
+can basically figure out how what to
+ 
+
+ align:start position:0%
+can basically figure out how what to
+what degree you have that symmetry
+
+ align:start position:0%
+what degree you have that symmetry
+ 
+
+ align:start position:0%
+what degree you have that symmetry
+in the higher body operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it turns out that it's also present
+
+ align:start position:0%
+it turns out that it's also present
+ 
+
+ align:start position:0%
+it turns out that it's also present
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+is one way of thinking about why
+
+ align:start position:0%
+is one way of thinking about why
+ 
+
+ align:start position:0%
+is one way of thinking about why
+vigner's symmetries exist in nature it's
+
+ align:start position:0%
+vigner's symmetries exist in nature it's
+ 
+
+ align:start position:0%
+vigner's symmetries exist in nature it's
+not that we're
+
+ align:start position:0%
+not that we're
+ 
+
+ align:start position:0%
+not that we're
+in any sense having scattering lengths
+
+ align:start position:0%
+in any sense having scattering lengths
+ 
+
+ align:start position:0%
+in any sense having scattering lengths
+that are similar in this these two
+
+ align:start position:0%
+that are similar in this these two
+ 
+
+ align:start position:0%
+that are similar in this these two
+channels but since they're both large
+
+ align:start position:0%
+channels but since they're both large
+ 
+
+ align:start position:0%
+channels but since they're both large
+we're close to the same we're close to
+
+ align:start position:0%
+we're close to the same we're close to
+ 
+
+ align:start position:0%
+we're close to the same we're close to
+these fixed points
+
+ align:start position:0%
+these fixed points
+ 
+
+ align:start position:0%
+these fixed points
+which have this symmetry
+
+ align:start position:0%
+which have this symmetry
+ 
+
+ align:start position:0%
+which have this symmetry
+okay so it's like hqet in a sense where
+
+ align:start position:0%
+okay so it's like hqet in a sense where
+ 
+
+ align:start position:0%
+okay so it's like hqet in a sense where
+we didn't have heavy cork spin symmetry
+
+ align:start position:0%
+we didn't have heavy cork spin symmetry
+ 
+
+ align:start position:0%
+we didn't have heavy cork spin symmetry
+when the masses are finite but if the
+
+ align:start position:0%
+when the masses are finite but if the
+ 
+
+ align:start position:0%
+when the masses are finite but if the
+charm mass and the b mass are both
+
+ align:start position:0%
+charm mass and the b mass are both
+ 
+
+ align:start position:0%
+charm mass and the b mass are both
+infinite then there's this new symmetry
+
+ align:start position:0%
+infinite then there's this new symmetry
+ 
+
+ align:start position:0%
+infinite then there's this new symmetry
+that pops up
+
+ align:start position:0%
+that pops up
+ 
+
+ align:start position:0%
+that pops up
+it's kind of like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so rather than talk about the
+
+ align:start position:0%
+all right so rather than talk about the
+ 
+
+ align:start position:0%
+all right so rather than talk about the
+symmetries in any more detail than that
+
+ align:start position:0%
+symmetries in any more detail than that
+ 
+
+ align:start position:0%
+symmetries in any more detail than that
+what i wanted to do is actually do
+
+ align:start position:0%
+what i wanted to do is actually do
+ 
+
+ align:start position:0%
+what i wanted to do is actually do
+something a little different with this
+
+ align:start position:0%
+something a little different with this
+ 
+
+ align:start position:0%
+something a little different with this
+theory so there's lots of things we
+
+ align:start position:0%
+theory so there's lots of things we
+ 
+
+ align:start position:0%
+theory so there's lots of things we
+could discuss here
+
+ align:start position:0%
+could discuss here
+ 
+
+ align:start position:0%
+could discuss here
+but the thing i want to discuss is
+
+ align:start position:0%
+but the thing i want to discuss is
+ 
+
+ align:start position:0%
+but the thing i want to discuss is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+treating a bound state
+
+ align:start position:0%
+treating a bound state
+ 
+
+ align:start position:0%
+treating a bound state
+in the in a field theory
+
+ align:start position:0%
+in the in a field theory
+ 
+
+ align:start position:0%
+in the in a field theory
+this field theory has
+
+ align:start position:0%
+this field theory has
+ 
+
+ align:start position:0%
+this field theory has
+a very nice property that we can
+
+ align:start position:0%
+a very nice property that we can
+ 
+
+ align:start position:0%
+a very nice property that we can
+calculate everything
+
+ align:start position:0%
+calculate everything
+ 
+
+ align:start position:0%
+calculate everything
+so we can actually see how you're
+
+ align:start position:0%
+so we can actually see how you're
+ 
+
+ align:start position:0%
+so we can actually see how you're
+supposed to treat bound states
+
+ align:start position:0%
+supposed to treat bound states
+ 
+
+ align:start position:0%
+supposed to treat bound states
+exactly because we can actually just
+
+ align:start position:0%
+exactly because we can actually just
+ 
+
+ align:start position:0%
+exactly because we can actually just
+look for the pole that corresponds to
+
+ align:start position:0%
+look for the pole that corresponds to
+ 
+
+ align:start position:0%
+look for the pole that corresponds to
+that bounce state in this theory that's
+
+ align:start position:0%
+that bounce state in this theory that's
+ 
+
+ align:start position:0%
+that bounce state in this theory that's
+what we're going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so usually if you have a bound state
+
+ align:start position:0%
+so usually if you have a bound state
+ 
+
+ align:start position:0%
+so usually if you have a bound state
+it's either
+
+ align:start position:0%
+it's either
+ 
+
+ align:start position:0%
+it's either
+something that's non non-perturbative
+
+ align:start position:0%
+something that's non non-perturbative
+ 
+
+ align:start position:0%
+something that's non non-perturbative
+that you have trouble dealing with
+
+ align:start position:0%
+that you have trouble dealing with
+ 
+
+ align:start position:0%
+that you have trouble dealing with
+analytically like in qcd
+
+ align:start position:0%
+analytically like in qcd
+ 
+
+ align:start position:0%
+analytically like in qcd
+or coulombic even then the calculations
+
+ align:start position:0%
+or coulombic even then the calculations
+ 
+
+ align:start position:0%
+or coulombic even then the calculations
+get kind of hairy although you can deal
+
+ align:start position:0%
+get kind of hairy although you can deal
+ 
+
+ align:start position:0%
+get kind of hairy although you can deal
+with it there
+
+ align:start position:0%
+with it there
+ 
+
+ align:start position:0%
+with it there
+but here the calculations are very
+
+ align:start position:0%
+but here the calculations are very
+ 
+
+ align:start position:0%
+but here the calculations are very
+simple so we can really follow all the
+
+ align:start position:0%
+simple so we can really follow all the
+ 
+
+ align:start position:0%
+simple so we can really follow all the
+steps of properly dealing with the bound
+
+ align:start position:0%
+steps of properly dealing with the bound
+ 
+
+ align:start position:0%
+steps of properly dealing with the bound
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the bound state has something to do
+
+ align:start position:0%
+and the bound state has something to do
+ 
+
+ align:start position:0%
+and the bound state has something to do
+with nature it's a stated nature called
+
+ align:start position:0%
+with nature it's a stated nature called
+ 
+
+ align:start position:0%
+with nature it's a stated nature called
+the deuteron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the deuteron is a balanced need of a
+
+ align:start position:0%
+so the deuteron is a balanced need of a
+ 
+
+ align:start position:0%
+so the deuteron is a balanced need of a
+neutron and a proton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it has isospin zero
+
+ align:start position:0%
+it has isospin zero
+ 
+
+ align:start position:0%
+it has isospin zero
+spin one
+
+ align:start position:0%
+spin one
+ 
+
+ align:start position:0%
+spin one
+so it's in this 3s1 state that we talked
+
+ align:start position:0%
+so it's in this 3s1 state that we talked
+ 
+
+ align:start position:0%
+so it's in this 3s1 state that we talked
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when you want to look for a bounce
+
+ align:start position:0%
+and when you want to look for a bounce
+ 
+
+ align:start position:0%
+and when you want to look for a bounce
+state in field theory what you do
+
+ align:start position:0%
+state in field theory what you do
+ 
+
+ align:start position:0%
+state in field theory what you do
+if you you may have heard of this from
+
+ align:start position:0%
+if you you may have heard of this from
+ 
+
+ align:start position:0%
+if you you may have heard of this from
+the lattice point of view what you do is
+
+ align:start position:0%
+the lattice point of view what you do is
+ 
+
+ align:start position:0%
+the lattice point of view what you do is
+you write down some interpolating field
+
+ align:start position:0%
+you write down some interpolating field
+ 
+
+ align:start position:0%
+you write down some interpolating field
+that has overlap
+
+ align:start position:0%
+that has overlap
+ 
+
+ align:start position:0%
+that has overlap
+with that state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what would that be for us
+
+ align:start position:0%
+so what would that be for us
+ 
+
+ align:start position:0%
+so what would that be for us
+that would be
+
+ align:start position:0%
+that would be
+ 
+
+ align:start position:0%
+that would be
+this operator that we called
+
+ align:start position:0%
+this operator that we called
+ 
+
+ align:start position:0%
+this operator that we called
+pi3s1 which had the quantum numbers for
+
+ align:start position:0%
+pi3s1 which had the quantum numbers for
+ 
+
+ align:start position:0%
+pi3s1 which had the quantum numbers for
+i equals 0 and s equals 1.
+
+ align:start position:0%
+i equals 0 and s equals 1.
+ 
+
+ align:start position:0%
+i equals 0 and s equals 1.
+and we can build an interpolating field
+
+ align:start position:0%
+and we can build an interpolating field
+ 
+
+ align:start position:0%
+and we can build an interpolating field
+out of our n transpose n and actually
+
+ align:start position:0%
+out of our n transpose n and actually
+ 
+
+ align:start position:0%
+out of our n transpose n and actually
+any interpolating field that we write
+
+ align:start position:0%
+any interpolating field that we write
+ 
+
+ align:start position:0%
+any interpolating field that we write
+down here is equally good
+
+ align:start position:0%
+down here is equally good
+ 
+
+ align:start position:0%
+down here is equally good
+a lot of qcd people like to tune what
+
+ align:start position:0%
+a lot of qcd people like to tune what
+ 
+
+ align:start position:0%
+a lot of qcd people like to tune what
+they write down
+
+ align:start position:0%
+they write down
+ 
+
+ align:start position:0%
+they write down
+in order to improve the overlap with the
+
+ align:start position:0%
+in order to improve the overlap with the
+ 
+
+ align:start position:0%
+in order to improve the overlap with the
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+but for our purposes the simplest
+
+ align:start position:0%
+but for our purposes the simplest
+ 
+
+ align:start position:0%
+but for our purposes the simplest
+possible thing will be enough
+
+ align:start position:0%
+possible thing will be enough
+ 
+
+ align:start position:0%
+possible thing will be enough
+and then you can ask the question is the
+
+ align:start position:0%
+and then you can ask the question is the
+ 
+
+ align:start position:0%
+and then you can ask the question is the
+deuteron in the theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and to answer that question you can just
+
+ align:start position:0%
+and to answer that question you can just
+ 
+
+ align:start position:0%
+and to answer that question you can just
+look for the poll that would correspond
+
+ align:start position:0%
+look for the poll that would correspond
+ 
+
+ align:start position:0%
+look for the poll that would correspond
+to that state
+
+ align:start position:0%
+to that state
+ 
+
+ align:start position:0%
+to that state
+and the advantage of this theory is that
+
+ align:start position:0%
+and the advantage of this theory is that
+ 
+
+ align:start position:0%
+and the advantage of this theory is that
+we can just look for that poll
+
+ align:start position:0%
+we can just look for that poll
+ 
+
+ align:start position:0%
+we can just look for that poll
+analytically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'll write down a greens function
+
+ align:start position:0%
+so i'll write down a greens function
+ 
+
+ align:start position:0%
+so i'll write down a greens function
+for the two particle state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is just the time order product of
+
+ align:start position:0%
+which is just the time order product of
+ 
+
+ align:start position:0%
+which is just the time order product of
+two of these interplaying fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then ask the question if i look at
+
+ align:start position:0%
+and then ask the question if i look at
+ 
+
+ align:start position:0%
+and then ask the question if i look at
+that thai water product is there a pole
+
+ align:start position:0%
+that thai water product is there a pole
+ 
+
+ align:start position:0%
+that thai water product is there a pole
+that would correspond to this state
+
+ align:start position:0%
+that would correspond to this state
+ 
+
+ align:start position:0%
+that would correspond to this state
+i somewhere is there a pole
+
+ align:start position:0%
+i somewhere is there a pole
+ 
+
+ align:start position:0%
+i somewhere is there a pole
+which would behave as follows
+
+ align:start position:0%
+which would behave as follows
+ 
+
+ align:start position:0%
+which would behave as follows
+some kind of z
+
+ align:start position:0%
+some kind of z
+ 
+
+ align:start position:0%
+some kind of z
+factor and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case because of our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because of the way we've scaled energies
+
+ align:start position:0%
+because of the way we've scaled energies
+ 
+
+ align:start position:0%
+because of the way we've scaled energies
+we would just be looking for a pole
+
+ align:start position:0%
+we would just be looking for a pole
+ 
+
+ align:start position:0%
+we would just be looking for a pole
+that's linear in the energy at some
+
+ align:start position:0%
+that's linear in the energy at some
+ 
+
+ align:start position:0%
+that's linear in the energy at some
+negative energy corresponding to the
+
+ align:start position:0%
+negative energy corresponding to the
+ 
+
+ align:start position:0%
+negative energy corresponding to the
+binding energy of that state
+
+ align:start position:0%
+binding energy of that state
+ 
+
+ align:start position:0%
+binding energy of that state
+so remember that we pulled out the mass
+
+ align:start position:0%
+so remember that we pulled out the mass
+ 
+
+ align:start position:0%
+so remember that we pulled out the mass
+of the nucleon that wasn't in our
+
+ align:start position:0%
+of the nucleon that wasn't in our
+ 
+
+ align:start position:0%
+of the nucleon that wasn't in our
+lagrangian so
+
+ align:start position:0%
+lagrangian so
+ 
+
+ align:start position:0%
+lagrangian so
+really the the if you think about what
+
+ align:start position:0%
+really the the if you think about what
+ 
+
+ align:start position:0%
+really the the if you think about what
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the mass the sort of energy of this
+
+ align:start position:0%
+the mass the sort of energy of this
+ 
+
+ align:start position:0%
+the mass the sort of energy of this
+state is it's two nucleons so it's got
+
+ align:start position:0%
+state is it's two nucleons so it's got
+ 
+
+ align:start position:0%
+state is it's two nucleons so it's got
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+energy of those two nucleons but then
+
+ align:start position:0%
+energy of those two nucleons but then
+ 
+
+ align:start position:0%
+energy of those two nucleons but then
+there's a little bit less because it's a
+
+ align:start position:0%
+there's a little bit less because it's a
+ 
+
+ align:start position:0%
+there's a little bit less because it's a
+bound state
+
+ align:start position:0%
+bound state
+ 
+
+ align:start position:0%
+bound state
+and this is the amount by
+
+ align:start position:0%
+and this is the amount by
+ 
+
+ align:start position:0%
+and this is the amount by
+how much less
+
+ align:start position:0%
+how much less
+ 
+
+ align:start position:0%
+how much less
+and so the energy for the pole is
+
+ align:start position:0%
+and so the energy for the pole is
+ 
+
+ align:start position:0%
+and so the energy for the pole is
+negative e bar is less than zero because
+
+ align:start position:0%
+negative e bar is less than zero because
+ 
+
+ align:start position:0%
+negative e bar is less than zero because
+it's how much less than the two nucleon
+
+ align:start position:0%
+it's how much less than the two nucleon
+ 
+
+ align:start position:0%
+it's how much less than the two nucleon
+mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this e bar is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two nucleon center of mass energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+in the conventions we were using last
+
+ align:start position:0%
+in the conventions we were using last
+ 
+
+ align:start position:0%
+in the conventions we were using last
+time is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we had e
+
+ align:start position:0%
+we had e
+ 
+
+ align:start position:0%
+we had e
+energy e over 2 for each of the nucleons
+
+ align:start position:0%
+energy e over 2 for each of the nucleons
+ 
+
+ align:start position:0%
+energy e over 2 for each of the nucleons
+so the sum would be e
+
+ align:start position:0%
+so the sum would be e
+ 
+
+ align:start position:0%
+so the sum would be e
+there's some kinetic term as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what are the diagrams that we would
+
+ align:start position:0%
+so what are the diagrams that we would
+ 
+
+ align:start position:0%
+so what are the diagrams that we would
+consider to do this
+
+ align:start position:0%
+consider to do this
+ 
+
+ align:start position:0%
+consider to do this
+well at lowest order it's just our
+
+ align:start position:0%
+well at lowest order it's just our
+ 
+
+ align:start position:0%
+well at lowest order it's just our
+friends the bubble sum
+
+ align:start position:0%
+friends the bubble sum
+ 
+
+ align:start position:0%
+friends the bubble sum
+and in fact when you go to higher orders
+
+ align:start position:0%
+and in fact when you go to higher orders
+ 
+
+ align:start position:0%
+and in fact when you go to higher orders
+there's also we also had bubbles there
+
+ align:start position:0%
+there's also we also had bubbles there
+ 
+
+ align:start position:0%
+there's also we also had bubbles there
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+to add to this question we insert the
+
+ align:start position:0%
+to add to this question we insert the
+ 
+
+ align:start position:0%
+to add to this question we insert the
+field we create two nucleons and then
+
+ align:start position:0%
+field we create two nucleons and then
+ 
+
+ align:start position:0%
+field we create two nucleons and then
+they can interact with c zeros
+
+ align:start position:0%
+they can interact with c zeros
+ 
+
+ align:start position:0%
+they can interact with c zeros
+and then we annihilate them with our
+
+ align:start position:0%
+and then we annihilate them with our
+ 
+
+ align:start position:0%
+and then we annihilate them with our
+interplaying field
+
+ align:start position:0%
+interplaying field
+ 
+
+ align:start position:0%
+interplaying field
+so these are just our c0 bubbles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and those are very easy to compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just the geometric series that we
+
+ align:start position:0%
+it's just the geometric series that we
+ 
+
+ align:start position:0%
+it's just the geometric series that we
+already computed
+
+ align:start position:0%
+already computed
+ 
+
+ align:start position:0%
+already computed
+and instead of having two nucleons in
+
+ align:start position:0%
+and instead of having two nucleons in
+ 
+
+ align:start position:0%
+and instead of having two nucleons in
+two nucleons out we just have this
+
+ align:start position:0%
+two nucleons out we just have this
+ 
+
+ align:start position:0%
+two nucleons out we just have this
+deuteron state in deuteronomy state out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the greens function
+
+ align:start position:0%
+okay so the greens function
+ 
+
+ align:start position:0%
+okay so the greens function
+starts with one of these
+
+ align:start position:0%
+starts with one of these
+ 
+
+ align:start position:0%
+starts with one of these
+and then just
+
+ align:start position:0%
+and then just
+ 
+
+ align:start position:0%
+and then just
+iterates into a
+
+ align:start position:0%
+iterates into a
+ 
+
+ align:start position:0%
+iterates into a
+iterates into a geometric series
+
+ align:start position:0%
+iterates into a geometric series
+ 
+
+ align:start position:0%
+iterates into a geometric series
+where sigma i could define as
+
+ align:start position:0%
+where sigma i could define as
+ 
+
+ align:start position:0%
+where sigma i could define as
+two particle irreducible c0 graphs so
+
+ align:start position:0%
+two particle irreducible c0 graphs so
+ 
+
+ align:start position:0%
+two particle irreducible c0 graphs so
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+taking out the c0 iterations
+
+ align:start position:0%
+taking out the c0 iterations
+ 
+
+ align:start position:0%
+taking out the c0 iterations
+so the sigma 1 that i'm talking about
+
+ align:start position:0%
+so the sigma 1 that i'm talking about
+ 
+
+ align:start position:0%
+so the sigma 1 that i'm talking about
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is just this bubble all by itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's something that we computed
+
+ align:start position:0%
+and that's something that we computed
+ 
+
+ align:start position:0%
+and that's something that we computed
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then these
+
+ align:start position:0%
+and then these
+ 
+
+ align:start position:0%
+and then these
+normalization schemes that we like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just comes out to be this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's an m out front and nucleon
+
+ align:start position:0%
+so there's an m out front and nucleon
+ 
+
+ align:start position:0%
+so there's an m out front and nucleon
+it's not an it's an m not a mu
+
+ align:start position:0%
+it's not an it's an m not a mu
+ 
+
+ align:start position:0%
+it's not an it's an m not a mu
+and then in terms of this e bar it just
+
+ align:start position:0%
+and then in terms of this e bar it just
+ 
+
+ align:start position:0%
+and then in terms of this e bar it just
+comes out through that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you could think of making a positive
+
+ align:start position:0%
+so you could think of making a positive
+ 
+
+ align:start position:0%
+so you could think of making a positive
+energy by taking e bar to be minus e
+
+ align:start position:0%
+energy by taking e bar to be minus e
+ 
+
+ align:start position:0%
+energy by taking e bar to be minus e
+bound
+
+ align:start position:0%
+bound
+ 
+
+ align:start position:0%
+bound
+which is less than zero
+
+ align:start position:0%
+which is less than zero
+ 
+
+ align:start position:0%
+which is less than zero
+and then the square root would be square
+
+ align:start position:0%
+and then the square root would be square
+ 
+
+ align:start position:0%
+and then the square root would be square
+root of m
+
+ align:start position:0%
+root of m
+ 
+
+ align:start position:0%
+root of m
+e b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's convenient to define that to be
+
+ align:start position:0%
+and it's convenient to define that to be
+ 
+
+ align:start position:0%
+and it's convenient to define that to be
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+so i'll call it gamma b
+
+ align:start position:0%
+so i'll call it gamma b
+ 
+
+ align:start position:0%
+so i'll call it gamma b
+so that's some quantity greater than
+
+ align:start position:0%
+so that's some quantity greater than
+ 
+
+ align:start position:0%
+so that's some quantity greater than
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+and with this little notation this
+
+ align:start position:0%
+and with this little notation this
+ 
+
+ align:start position:0%
+and with this little notation this
+square root
+
+ align:start position:0%
+square root
+ 
+
+ align:start position:0%
+square root
+of minus m e bar
+
+ align:start position:0%
+of minus m e bar
+ 
+
+ align:start position:0%
+of minus m e bar
+minus i0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to minus ip
+
+ align:start position:0%
+is equal to minus ip
+ 
+
+ align:start position:0%
+is equal to minus ip
+and we're looking for whether that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would be sort of
+
+ align:start position:0%
+would be sort of
+ 
+
+ align:start position:0%
+would be sort of
+going over to this gamma b
+
+ align:start position:0%
+going over to this gamma b
+ 
+
+ align:start position:0%
+going over to this gamma b
+sorry so this is equal to gamma b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so gamma b is just like a momentum
+
+ align:start position:0%
+so gamma b is just like a momentum
+ 
+
+ align:start position:0%
+so gamma b is just like a momentum
+version of the bound state energy
+
+ align:start position:0%
+version of the bound state energy
+ 
+
+ align:start position:0%
+version of the bound state energy
+absorbing the extra eye
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is what it would have been
+
+ align:start position:0%
+okay this is what it would have been
+ 
+
+ align:start position:0%
+okay this is what it would have been
+previously but now it's gamma b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we know what g was we already
+
+ align:start position:0%
+so we know what g was we already
+ 
+
+ align:start position:0%
+so we know what g was we already
+computed it earlier g
+
+ align:start position:0%
+computed it earlier g
+ 
+
+ align:start position:0%
+computed it earlier g
+was just proportional to 1 over a
+
+ align:start position:0%
+was just proportional to 1 over a
+ 
+
+ align:start position:0%
+was just proportional to 1 over a
+plus i p
+
+ align:start position:0%
+plus i p
+ 
+
+ align:start position:0%
+plus i p
+and now if i just make that replacement
+
+ align:start position:0%
+and now if i just make that replacement
+ 
+
+ align:start position:0%
+and now if i just make that replacement
+which is why i wanted to derive that
+
+ align:start position:0%
+which is why i wanted to derive that
+ 
+
+ align:start position:0%
+which is why i wanted to derive that
+because i wanted to just see how i would
+
+ align:start position:0%
+because i wanted to just see how i would
+ 
+
+ align:start position:0%
+because i wanted to just see how i would
+replace the ip
+
+ align:start position:0%
+replace the ip
+ 
+
+ align:start position:0%
+replace the ip
+becomes 1 over a minus gamma b so gamma
+
+ align:start position:0%
+becomes 1 over a minus gamma b so gamma
+ 
+
+ align:start position:0%
+becomes 1 over a minus gamma b so gamma
+b is a kinematic variable it's like a
+
+ align:start position:0%
+b is a kinematic variable it's like a
+ 
+
+ align:start position:0%
+b is a kinematic variable it's like a
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+but it's the right kinematic variable to
+
+ align:start position:0%
+but it's the right kinematic variable to
+ 
+
+ align:start position:0%
+but it's the right kinematic variable to
+be talking about for the bound state
+
+ align:start position:0%
+be talking about for the bound state
+ 
+
+ align:start position:0%
+be talking about for the bound state
+it's a positive thing
+
+ align:start position:0%
+it's a positive thing
+ 
+
+ align:start position:0%
+it's a positive thing
+and you can see there's a pole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's the pole corresponding
+
+ align:start position:0%
+okay so there's the pole corresponding
+ 
+
+ align:start position:0%
+okay so there's the pole corresponding
+to the deer around state it just
+
+ align:start position:0%
+to the deer around state it just
+ 
+
+ align:start position:0%
+to the deer around state it just
+corresponds to gamma equals 1 over
+
+ align:start position:0%
+corresponds to gamma equals 1 over
+ 
+
+ align:start position:0%
+corresponds to gamma equals 1 over
+a of the 3s1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which in nature is like
+
+ align:start position:0%
+which in nature is like
+ 
+
+ align:start position:0%
+which in nature is like
+36 mev
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greater than zero if you looked at the
+
+ align:start position:0%
+greater than zero if you looked at the
+ 
+
+ align:start position:0%
+greater than zero if you looked at the
+other channel the 1s 0 channel then the
+
+ align:start position:0%
+other channel the 1s 0 channel then the
+ 
+
+ align:start position:0%
+other channel the 1s 0 channel then the
+scatting length was negative
+
+ align:start position:0%
+scatting length was negative
+ 
+
+ align:start position:0%
+scatting length was negative
+so then both terms would be negative and
+
+ align:start position:0%
+so then both terms would be negative and
+ 
+
+ align:start position:0%
+so then both terms would be negative and
+there's no pull
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for the 3s1 channel we have a
+
+ align:start position:0%
+okay so for the 3s1 channel we have a
+ 
+
+ align:start position:0%
+okay so for the 3s1 channel we have a
+pole that's the physical deuteron state
+
+ align:start position:0%
+pole that's the physical deuteron state
+ 
+
+ align:start position:0%
+pole that's the physical deuteron state
+for the other channel there is no pull
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the binding energy that you would
+
+ align:start position:0%
+and the binding energy that you would
+ 
+
+ align:start position:0%
+and the binding energy that you would
+get from this is gamma b squared
+
+ align:start position:0%
+get from this is gamma b squared
+ 
+
+ align:start position:0%
+get from this is gamma b squared
+over m with our conventions
+
+ align:start position:0%
+over m with our conventions
+ 
+
+ align:start position:0%
+over m with our conventions
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+if you calculate it is 1.4 mev
+
+ align:start position:0%
+if you calculate it is 1.4 mev
+ 
+
+ align:start position:0%
+if you calculate it is 1.4 mev
+and that's not ridiculously different
+
+ align:start position:0%
+and that's not ridiculously different
+ 
+
+ align:start position:0%
+and that's not ridiculously different
+than the real binding energy of the
+
+ align:start position:0%
+than the real binding energy of the
+ 
+
+ align:start position:0%
+than the real binding energy of the
+deuteron
+
+ align:start position:0%
+deuteron
+ 
+
+ align:start position:0%
+deuteron
+which is 2.2 mev
+
+ align:start position:0%
+which is 2.2 mev
+ 
+
+ align:start position:0%
+which is 2.2 mev
+okay it's not
+
+ align:start position:0%
+okay it's not
+ 
+
+ align:start position:0%
+okay it's not
+it's the right order of magnitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that's the deuteron it
+
+ align:start position:0%
+all right so that's the deuteron it
+ 
+
+ align:start position:0%
+all right so that's the deuteron it
+exists in this theory and we can
+
+ align:start position:0%
+exists in this theory and we can
+ 
+
+ align:start position:0%
+exists in this theory and we can
+perturbatively correct towards this
+
+ align:start position:0%
+perturbatively correct towards this
+ 
+
+ align:start position:0%
+perturbatively correct towards this
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+mining energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this deuteron really exists in
+
+ align:start position:0%
+okay so this deuteron really exists in
+ 
+
+ align:start position:0%
+okay so this deuteron really exists in
+the field theory and that means we can
+
+ align:start position:0%
+the field theory and that means we can
+ 
+
+ align:start position:0%
+the field theory and that means we can
+calculate properties of the deuteron
+
+ align:start position:0%
+calculate properties of the deuteron
+ 
+
+ align:start position:0%
+calculate properties of the deuteron
+with this field theory
+
+ align:start position:0%
+with this field theory
+ 
+
+ align:start position:0%
+with this field theory
+we can calculate scattering processes
+
+ align:start position:0%
+we can calculate scattering processes
+ 
+
+ align:start position:0%
+we can calculate scattering processes
+that involve this bound state and it's
+
+ align:start position:0%
+that involve this bound state and it's
+ 
+
+ align:start position:0%
+that involve this bound state and it's
+no more difficult than
+
+ align:start position:0%
+no more difficult than
+ 
+
+ align:start position:0%
+no more difficult than
+doing calculations that we would
+
+ align:start position:0%
+doing calculations that we would
+ 
+
+ align:start position:0%
+doing calculations that we would
+normally do with free fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we just have to if we want to do
+
+ align:start position:0%
+and we just have to if we want to do
+ 
+
+ align:start position:0%
+and we just have to if we want to do
+something with the deuteron we have to
+
+ align:start position:0%
+something with the deuteron we have to
+ 
+
+ align:start position:0%
+something with the deuteron we have to
+go to the right pole
+
+ align:start position:0%
+go to the right pole
+ 
+
+ align:start position:0%
+go to the right pole
+that's basically what it boils down to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in order to show you really how to do
+
+ align:start position:0%
+so in order to show you really how to do
+ 
+
+ align:start position:0%
+so in order to show you really how to do
+that i'm going to give one example
+
+ align:start position:0%
+that i'm going to give one example
+ 
+
+ align:start position:0%
+that i'm going to give one example
+calculating something non-trivial that
+
+ align:start position:0%
+calculating something non-trivial that
+ 
+
+ align:start position:0%
+calculating something non-trivial that
+involves a deuteron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll calculate
+
+ align:start position:0%
+so we'll calculate
+ 
+
+ align:start position:0%
+so we'll calculate
+a form factor for the deuteron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a nice example if you like
+
+ align:start position:0%
+so this is a nice example if you like
+ 
+
+ align:start position:0%
+so this is a nice example if you like
+of really showing you how to use the lsc
+
+ align:start position:0%
+of really showing you how to use the lsc
+ 
+
+ align:start position:0%
+of really showing you how to use the lsc
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+which you learned about in a very sort
+
+ align:start position:0%
+which you learned about in a very sort
+ 
+
+ align:start position:0%
+which you learned about in a very sort
+of abstract way at some point
+
+ align:start position:0%
+of abstract way at some point
+ 
+
+ align:start position:0%
+of abstract way at some point
+how to use it for bound states
+
+ align:start position:0%
+how to use it for bound states
+ 
+
+ align:start position:0%
+how to use it for bound states
+because here we have a bound state
+
+ align:start position:0%
+because here we have a bound state
+ 
+
+ align:start position:0%
+because here we have a bound state
+exists in the theory
+
+ align:start position:0%
+exists in the theory
+ 
+
+ align:start position:0%
+exists in the theory
+and if we want to
+
+ align:start position:0%
+and if we want to
+ 
+
+ align:start position:0%
+and if we want to
+derive properties of that bound state we
+
+ align:start position:0%
+derive properties of that bound state we
+ 
+
+ align:start position:0%
+derive properties of that bound state we
+better properly use the lsd formula for
+
+ align:start position:0%
+better properly use the lsd formula for
+ 
+
+ align:start position:0%
+better properly use the lsd formula for
+that bound state
+
+ align:start position:0%
+that bound state
+ 
+
+ align:start position:0%
+that bound state
+let's see how that works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what we'd like to do
+
+ align:start position:0%
+okay so what we'd like to do
+ 
+
+ align:start position:0%
+okay so what we'd like to do
+is we'd like to have we have some
+
+ align:start position:0%
+is we'd like to have we have some
+ 
+
+ align:start position:0%
+is we'd like to have we have some
+deuteron state and we'd like to take the
+
+ align:start position:0%
+deuteron state and we'd like to take the
+ 
+
+ align:start position:0%
+deuteron state and we'd like to take the
+matrix element with the electromagnetic
+
+ align:start position:0%
+matrix element with the electromagnetic
+ 
+
+ align:start position:0%
+matrix element with the electromagnetic
+current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you work out what possible form
+
+ align:start position:0%
+and if you work out what possible form
+ 
+
+ align:start position:0%
+and if you work out what possible form
+factors you can have for this matrix
+
+ align:start position:0%
+factors you can have for this matrix
+ 
+
+ align:start position:0%
+factors you can have for this matrix
+element there's actually three
+
+ align:start position:0%
+element there's actually three
+ 
+
+ align:start position:0%
+element there's actually three
+and i'm not going to spend much time
+
+ align:start position:0%
+and i'm not going to spend much time
+ 
+
+ align:start position:0%
+and i'm not going to spend much time
+talking about the
+
+ align:start position:0%
+talking about the
+ 
+
+ align:start position:0%
+talking about the
+the sort of different couplings with
+
+ align:start position:0%
+the sort of different couplings with
+ 
+
+ align:start position:0%
+the sort of different couplings with
+spin and stuff that correspond to these
+
+ align:start position:0%
+spin and stuff that correspond to these
+ 
+
+ align:start position:0%
+spin and stuff that correspond to these
+different cases but i'll list them for
+
+ align:start position:0%
+different cases but i'll list them for
+ 
+
+ align:start position:0%
+different cases but i'll list them for
+you at least
+
+ align:start position:0%
+you at least
+ 
+
+ align:start position:0%
+you at least
+provide you some additional references
+
+ align:start position:0%
+provide you some additional references
+ 
+
+ align:start position:0%
+provide you some additional references
+if you want to dig deeper into this
+
+ align:start position:0%
+if you want to dig deeper into this
+ 
+
+ align:start position:0%
+if you want to dig deeper into this
+so there's a magnetic electric and
+
+ align:start position:0%
+so there's a magnetic electric and
+ 
+
+ align:start position:0%
+so there's a magnetic electric and
+quadrupole form factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the charge of the deuteron
+
+ align:start position:0%
+the charge of the deuteron
+ 
+
+ align:start position:0%
+the charge of the deuteron
+tells us that this
+
+ align:start position:0%
+tells us that this
+ 
+
+ align:start position:0%
+tells us that this
+electric form factor at q squared equals
+
+ align:start position:0%
+electric form factor at q squared equals
+ 
+
+ align:start position:0%
+electric form factor at q squared equals
+zero should be one
+
+ align:start position:0%
+zero should be one
+ 
+
+ align:start position:0%
+zero should be one
+the magnetic form factor is like the
+
+ align:start position:0%
+the magnetic form factor is like the
+ 
+
+ align:start position:0%
+the magnetic form factor is like the
+magnetic form factor for electron
+
+ align:start position:0%
+magnetic form factor for electron
+ 
+
+ align:start position:0%
+magnetic form factor for electron
+in the sense that if you go to q squared
+
+ align:start position:0%
+in the sense that if you go to q squared
+ 
+
+ align:start position:0%
+in the sense that if you go to q squared
+equals zero then that's giving you the
+
+ align:start position:0%
+equals zero then that's giving you the
+ 
+
+ align:start position:0%
+equals zero then that's giving you the
+magnetic moment but here it's the
+
+ align:start position:0%
+magnetic moment but here it's the
+ 
+
+ align:start position:0%
+magnetic moment but here it's the
+magnetic moment of the deuteron not the
+
+ align:start position:0%
+magnetic moment of the deuteron not the
+ 
+
+ align:start position:0%
+magnetic moment of the deuteron not the
+magnetic moment of the electron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a non-trivial number
+
+ align:start position:0%
+it's a non-trivial number
+ 
+
+ align:start position:0%
+it's a non-trivial number
+in this case whereas here
+
+ align:start position:0%
+in this case whereas here
+ 
+
+ align:start position:0%
+in this case whereas here
+it's just one because charge is
+
+ align:start position:0%
+it's just one because charge is
+ 
+
+ align:start position:0%
+it's just one because charge is
+conserved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we wanted to
+
+ align:start position:0%
+and if we wanted to
+ 
+
+ align:start position:0%
+and if we wanted to
+think about putting electromagnetism
+
+ align:start position:0%
+think about putting electromagnetism
+ 
+
+ align:start position:0%
+think about putting electromagnetism
+into the nucleon theory which we haven't
+
+ align:start position:0%
+into the nucleon theory which we haven't
+ 
+
+ align:start position:0%
+into the nucleon theory which we haven't
+so far
+
+ align:start position:0%
+so far
+ 
+
+ align:start position:0%
+so far
+then we would turn our derivatives into
+
+ align:start position:0%
+then we would turn our derivatives into
+ 
+
+ align:start position:0%
+then we would turn our derivatives into
+covariant derivatives so
+
+ align:start position:0%
+covariant derivatives so
+ 
+
+ align:start position:0%
+covariant derivatives so
+d mu nucleon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have to write down
+
+ align:start position:0%
+we have to write down
+ 
+
+ align:start position:0%
+we have to write down
+a charge matrix that couples that takes
+
+ align:start position:0%
+a charge matrix that couples that takes
+ 
+
+ align:start position:0%
+a charge matrix that couples that takes
+into account the proton has charge but
+
+ align:start position:0%
+into account the proton has charge but
+ 
+
+ align:start position:0%
+into account the proton has charge but
+the neutron doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+that charge matrix
+
+ align:start position:0%
+that charge matrix
+ 
+
+ align:start position:0%
+that charge matrix
+for electromagnetism
+
+ align:start position:0%
+for electromagnetism
+ 
+
+ align:start position:0%
+for electromagnetism
+okay so it's not
+
+ align:start position:0%
+okay so it's not
+ 
+
+ align:start position:0%
+okay so it's not
+difficult so that's easy enough just
+
+ align:start position:0%
+difficult so that's easy enough just
+ 
+
+ align:start position:0%
+difficult so that's easy enough just
+change your derivatives into covariant
+
+ align:start position:0%
+change your derivatives into covariant
+ 
+
+ align:start position:0%
+change your derivatives into covariant
+derivatives
+
+ align:start position:0%
+derivatives
+ 
+
+ align:start position:0%
+derivatives
+for both d 0 and d partial and d
+
+ align:start position:0%
+for both d 0 and d partial and d
+ 
+
+ align:start position:0%
+for both d 0 and d partial and d
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+there's also some additional operators
+
+ align:start position:0%
+there's also some additional operators
+ 
+
+ align:start position:0%
+there's also some additional operators
+that you have to write down
+
+ align:start position:0%
+that you have to write down
+ 
+
+ align:start position:0%
+that you have to write down
+so there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators for example that are just
+
+ align:start position:0%
+operators for example that are just
+ 
+
+ align:start position:0%
+operators for example that are just
+contact interactions with the magnetic
+
+ align:start position:0%
+contact interactions with the magnetic
+ 
+
+ align:start position:0%
+contact interactions with the magnetic
+with the electric magnetic fields in
+
+ align:start position:0%
+with the electric magnetic fields in
+ 
+
+ align:start position:0%
+with the electric magnetic fields in
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+and the first such one
+
+ align:start position:0%
+and the first such one
+ 
+
+ align:start position:0%
+and the first such one
+that shows up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just by way of sort of telling you
+
+ align:start position:0%
+just by way of sort of telling you
+ 
+
+ align:start position:0%
+just by way of sort of telling you
+a range of possibilities would be
+
+ align:start position:0%
+a range of possibilities would be
+ 
+
+ align:start position:0%
+a range of possibilities would be
+something like this where you just have
+
+ align:start position:0%
+something like this where you just have
+ 
+
+ align:start position:0%
+something like this where you just have
+a sigma.b magnetic field insertion
+
+ align:start position:0%
+a sigma.b magnetic field insertion
+ 
+
+ align:start position:0%
+a sigma.b magnetic field insertion
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+magnetic field
+
+ align:start position:0%
+magnetic field
+ 
+
+ align:start position:0%
+magnetic field
+for electromagnetism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so if you want to think about the
+
+ align:start position:0%
+and so if you want to think about the
+ 
+
+ align:start position:0%
+and so if you want to think about the
+type of finemen diagram you'd draw for
+
+ align:start position:0%
+type of finemen diagram you'd draw for
+ 
+
+ align:start position:0%
+type of finemen diagram you'd draw for
+this you'd have four nucleons and then
+
+ align:start position:0%
+this you'd have four nucleons and then
+ 
+
+ align:start position:0%
+this you'd have four nucleons and then
+you just have a photon
+
+ align:start position:0%
+you just have a photon
+ 
+
+ align:start position:0%
+you just have a photon
+coming out right
+
+ align:start position:0%
+coming out right
+ 
+
+ align:start position:0%
+coming out right
+if you want to think about where that
+
+ align:start position:0%
+if you want to think about where that
+ 
+
+ align:start position:0%
+if you want to think about where that
+could possibly come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's one really easy thing to think
+
+ align:start position:0%
+there's one really easy thing to think
+ 
+
+ align:start position:0%
+there's one really easy thing to think
+about would just be to have a pioneer
+
+ align:start position:0%
+about would just be to have a pioneer
+ 
+
+ align:start position:0%
+about would just be to have a pioneer
+exchange
+
+ align:start position:0%
+exchange
+ 
+
+ align:start position:0%
+exchange
+and maybe it's a pi minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+photon couples to a pi minus because
+
+ align:start position:0%
+photon couples to a pi minus because
+ 
+
+ align:start position:0%
+photon couples to a pi minus because
+it's got electric charge
+
+ align:start position:0%
+it's got electric charge
+ 
+
+ align:start position:0%
+it's got electric charge
+and when i integrate out the pion then i
+
+ align:start position:0%
+and when i integrate out the pion then i
+ 
+
+ align:start position:0%
+and when i integrate out the pion then i
+just get something that looks like this
+
+ align:start position:0%
+just get something that looks like this
+ 
+
+ align:start position:0%
+just get something that looks like this
+could be any exchange it could be a real
+
+ align:start position:0%
+could be any exchange it could be a real
+ 
+
+ align:start position:0%
+could be any exchange it could be a real
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+anything would give an operator it looks
+
+ align:start position:0%
+anything would give an operator it looks
+ 
+
+ align:start position:0%
+anything would give an operator it looks
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+okay so there's additional contact
+
+ align:start position:0%
+okay so there's additional contact
+ 
+
+ align:start position:0%
+okay so there's additional contact
+interactions involving electromagnetism
+
+ align:start position:0%
+interactions involving electromagnetism
+ 
+
+ align:start position:0%
+interactions involving electromagnetism
+then you gauge the gauge the derivatives
+
+ align:start position:0%
+then you gauge the gauge the derivatives
+ 
+
+ align:start position:0%
+then you gauge the gauge the derivatives
+then you can put electromagnetism into
+
+ align:start position:0%
+then you can put electromagnetism into
+ 
+
+ align:start position:0%
+then you can put electromagnetism into
+the theory
+
+ align:start position:0%
+the theory
+ 
+
+ align:start position:0%
+the theory
+it's a little more non-trivial then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's what we need to do if we want
+
+ align:start position:0%
+and that's what we need to do if we want
+ 
+
+ align:start position:0%
+and that's what we need to do if we want
+to talk about electromagnetism coupling
+
+ align:start position:0%
+to talk about electromagnetism coupling
+ 
+
+ align:start position:0%
+to talk about electromagnetism coupling
+for the deuteron
+
+ align:start position:0%
+for the deuteron
+ 
+
+ align:start position:0%
+for the deuteron
+but i'm mostly interested here in how
+
+ align:start position:0%
+but i'm mostly interested here in how
+ 
+
+ align:start position:0%
+but i'm mostly interested here in how
+the llc works
+
+ align:start position:0%
+the llc works
+ 
+
+ align:start position:0%
+the llc works
+so what does lz say
+
+ align:start position:0%
+so what does lz say
+ 
+
+ align:start position:0%
+so what does lz say
+so lsc says that if i have this state p
+
+ align:start position:0%
+so lsc says that if i have this state p
+ 
+
+ align:start position:0%
+so lsc says that if i have this state p
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+j out
+
+ align:start position:0%
+j out
+ 
+
+ align:start position:0%
+j out
+jmu electromagnetism
+
+ align:start position:0%
+jmu electromagnetism
+ 
+
+ align:start position:0%
+jmu electromagnetism
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+i n
+
+ align:start position:0%
+i n
+ 
+
+ align:start position:0%
+i n
+i is like a spin index because we have a
+
+ align:start position:0%
+i is like a spin index because we have a
+ 
+
+ align:start position:0%
+i is like a spin index because we have a
+triplet under spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this is how you should calculate it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+q is like the
+
+ align:start position:0%
+q is like the
+ 
+
+ align:start position:0%
+q is like the
+well i guess i'm in momentum space all
+
+ align:start position:0%
+well i guess i'm in momentum space all
+ 
+
+ align:start position:0%
+well i guess i'm in momentum space all
+of a sudden
+
+ align:start position:0%
+of a sudden
+ 
+
+ align:start position:0%
+of a sudden
+well no q is just a p p minus p prime
+
+ align:start position:0%
+well no q is just a p p minus p prime
+ 
+
+ align:start position:0%
+well no q is just a p p minus p prime
+e and e bar are related to the p and the
+
+ align:start position:0%
+e and e bar are related to the p and the
+ 
+
+ align:start position:0%
+e and e bar are related to the p and the
+p prime also
+
+ align:start position:0%
+p prime also
+ 
+
+ align:start position:0%
+p prime also
+and what i do is i have some z factor
+
+ align:start position:0%
+and what i do is i have some z factor
+ 
+
+ align:start position:0%
+and what i do is i have some z factor
+out front which is the bound state z
+
+ align:start position:0%
+out front which is the bound state z
+ 
+
+ align:start position:0%
+out front which is the bound state z
+factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lsd tells me to be careful about that c
+
+ align:start position:0%
+lsd tells me to be careful about that c
+ 
+
+ align:start position:0%
+lsd tells me to be careful about that c
+factor
+
+ align:start position:0%
+factor
+ 
+
+ align:start position:0%
+factor
+these guys here are just two point
+
+ align:start position:0%
+these guys here are just two point
+ 
+
+ align:start position:0%
+these guys here are just two point
+functions and that's because i have to
+
+ align:start position:0%
+functions and that's because i have to
+ 
+
+ align:start position:0%
+functions and that's because i have to
+truncate
+
+ align:start position:0%
+truncate
+ 
+
+ align:start position:0%
+truncate
+the lines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is truncation by two point
+
+ align:start position:0%
+this is truncation by two point
+ 
+
+ align:start position:0%
+this is truncation by two point
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+but they're two point functions for the
+
+ align:start position:0%
+but they're two point functions for the
+ 
+
+ align:start position:0%
+but they're two point functions for the
+bound states of two lines
+
+ align:start position:0%
+bound states of two lines
+ 
+
+ align:start position:0%
+bound states of two lines
+and then this is the three point
+
+ align:start position:0%
+and then this is the three point
+ 
+
+ align:start position:0%
+and then this is the three point
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for the three point functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would the time order product be for
+
+ align:start position:0%
+what would the time order product be for
+ 
+
+ align:start position:0%
+what would the time order product be for
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a time warner product of three
+
+ align:start position:0%
+it's a time warner product of three
+ 
+
+ align:start position:0%
+it's a time warner product of three
+things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the two point function we already
+
+ align:start position:0%
+so the two point function we already
+ 
+
+ align:start position:0%
+so the two point function we already
+defined it was just a time order product
+
+ align:start position:0%
+defined it was just a time order product
+ 
+
+ align:start position:0%
+defined it was just a time order product
+of the two deuteron fields
+
+ align:start position:0%
+of the two deuteron fields
+ 
+
+ align:start position:0%
+of the two deuteron fields
+and the three-point function has an
+
+ align:start position:0%
+and the three-point function has an
+ 
+
+ align:start position:0%
+and the three-point function has an
+additional
+
+ align:start position:0%
+additional
+ 
+
+ align:start position:0%
+additional
+electromagnetic current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we would formulate you know all
+
+ align:start position:0%
+which we would formulate you know all
+ 
+
+ align:start position:0%
+which we would formulate you know all
+the couplings here this way that i was
+
+ align:start position:0%
+the couplings here this way that i was
+ 
+
+ align:start position:0%
+the couplings here this way that i was
+talking about over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in terms of diagrams which are easier
+
+ align:start position:0%
+so in terms of diagrams which are easier
+ 
+
+ align:start position:0%
+so in terms of diagrams which are easier
+to think about in
+
+ align:start position:0%
+to think about in
+ 
+
+ align:start position:0%
+to think about in
+some ways than time order products
+
+ align:start position:0%
+some ways than time order products
+ 
+
+ align:start position:0%
+some ways than time order products
+we have the two point function
+
+ align:start position:0%
+we have the two point function
+ 
+
+ align:start position:0%
+we have the two point function
+which if i just define all possible two
+
+ align:start position:0%
+which if i just define all possible two
+ 
+
+ align:start position:0%
+which if i just define all possible two
+functions as g
+
+ align:start position:0%
+functions as g
+ 
+
+ align:start position:0%
+functions as g
+and this is the thing that
+
+ align:start position:0%
+and this is the thing that
+ 
+
+ align:start position:0%
+and this is the thing that
+was our two particle was our irreducible
+
+ align:start position:0%
+was our two particle was our irreducible
+ 
+
+ align:start position:0%
+was our two particle was our irreducible
+c zero contributions plus iterations of
+
+ align:start position:0%
+c zero contributions plus iterations of
+ 
+
+ align:start position:0%
+c zero contributions plus iterations of
+c zeros
+
+ align:start position:0%
+c zeros
+ 
+
+ align:start position:0%
+c zeros
+all right since the c zero is a
+
+ align:start position:0%
+all right since the c zero is a
+ 
+
+ align:start position:0%
+all right since the c zero is a
+non-perturbative coupling we have to
+
+ align:start position:0%
+non-perturbative coupling we have to
+ 
+
+ align:start position:0%
+non-perturbative coupling we have to
+iterate
+
+ align:start position:0%
+iterate
+ 
+
+ align:start position:0%
+iterate
+and this is what we already
+
+ align:start position:0%
+and this is what we already
+ 
+
+ align:start position:0%
+and this is what we already
+said you could define as
+
+ align:start position:0%
+said you could define as
+ 
+
+ align:start position:0%
+said you could define as
+summing up that geometric series and
+
+ align:start position:0%
+summing up that geometric series and
+ 
+
+ align:start position:0%
+summing up that geometric series and
+then just define it as something which
+
+ align:start position:0%
+then just define it as something which
+ 
+
+ align:start position:0%
+then just define it as something which
+is the full greens function in terms of
+
+ align:start position:0%
+is the full greens function in terms of
+ 
+
+ align:start position:0%
+is the full greens function in terms of
+this irreducible piece in the usual sort
+
+ align:start position:0%
+this irreducible piece in the usual sort
+ 
+
+ align:start position:0%
+this irreducible piece in the usual sort
+of way
+
+ align:start position:0%
+of way
+ 
+
+ align:start position:0%
+of way
+and then for this other g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll draw a blob which i'll also call g
+
+ align:start position:0%
+i'll draw a blob which i'll also call g
+ 
+
+ align:start position:0%
+i'll draw a blob which i'll also call g
+but with an additional photon hanging
+
+ align:start position:0%
+but with an additional photon hanging
+ 
+
+ align:start position:0%
+but with an additional photon hanging
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+those are all three point functions
+
+ align:start position:0%
+those are all three point functions
+ 
+
+ align:start position:0%
+those are all three point functions
+and in a kind of similar notation
+
+ align:start position:0%
+and in a kind of similar notation
+ 
+
+ align:start position:0%
+and in a kind of similar notation
+i can have kind of an irreducible
+
+ align:start position:0%
+i can have kind of an irreducible
+ 
+
+ align:start position:0%
+i can have kind of an irreducible
+piece
+
+ align:start position:0%
+piece
+ 
+
+ align:start position:0%
+piece
+and then i can have iterations
+
+ align:start position:0%
+and then i can have iterations
+ 
+
+ align:start position:0%
+and then i can have iterations
+with c zeros
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+etc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if i sum up those irreducible
+
+ align:start position:0%
+and if i sum up those irreducible
+ 
+
+ align:start position:0%
+and if i sum up those irreducible
+diagrams i can write the full greens
+
+ align:start position:0%
+diagrams i can write the full greens
+ 
+
+ align:start position:0%
+diagrams i can write the full greens
+function in terms of the irreducible
+
+ align:start position:0%
+function in terms of the irreducible
+ 
+
+ align:start position:0%
+function in terms of the irreducible
+pieces again in a similar sort of
+
+ align:start position:0%
+pieces again in a similar sort of
+ 
+
+ align:start position:0%
+pieces again in a similar sort of
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+it's just gamma which carries the
+
+ align:start position:0%
+it's just gamma which carries the
+ 
+
+ align:start position:0%
+it's just gamma which carries the
+indices
+
+ align:start position:0%
+indices
+ 
+
+ align:start position:0%
+indices
+and then there's just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a couple of now there's geometric series
+
+ align:start position:0%
+a couple of now there's geometric series
+ 
+
+ align:start position:0%
+a couple of now there's geometric series
+on both sides so when i sum them up i
+
+ align:start position:0%
+on both sides so when i sum them up i
+ 
+
+ align:start position:0%
+on both sides so when i sum them up i
+get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is giving you the
+
+ align:start position:0%
+okay so this is giving you the
+ 
+
+ align:start position:0%
+okay so this is giving you the
+ingredients that we need to plug into
+
+ align:start position:0%
+ingredients that we need to plug into
+ 
+
+ align:start position:0%
+ingredients that we need to plug into
+this formula we need g inverse this is g
+
+ align:start position:0%
+this formula we need g inverse this is g
+ 
+
+ align:start position:0%
+this formula we need g inverse this is g
+the two point
+
+ align:start position:0%
+the two point
+ 
+
+ align:start position:0%
+the two point
+we need the g mu i j which we can write
+
+ align:start position:0%
+we need the g mu i j which we can write
+ 
+
+ align:start position:0%
+we need the g mu i j which we can write
+in terms of the irreducible guy like
+
+ align:start position:0%
+in terms of the irreducible guy like
+ 
+
+ align:start position:0%
+in terms of the irreducible guy like
+that and then the last thing we need is
+
+ align:start position:0%
+that and then the last thing we need is
+ 
+
+ align:start position:0%
+that and then the last thing we need is
+this bound state z factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah what i really i'm kind of using a
+
+ align:start position:0%
+yeah what i really i'm kind of using a
+ 
+
+ align:start position:0%
+yeah what i really i'm kind of using a
+shorthand here with this t product for
+
+ align:start position:0%
+shorthand here with this t product for
+ 
+
+ align:start position:0%
+shorthand here with this t product for
+all the diagrams that come from what i
+
+ align:start position:0%
+all the diagrams that come from what i
+ 
+
+ align:start position:0%
+all the diagrams that come from what i
+was talking about over there
+
+ align:start position:0%
+was talking about over there
+ 
+
+ align:start position:0%
+was talking about over there
+yeah i kind of wrote it as an
+
+ align:start position:0%
+yeah i kind of wrote it as an
+ 
+
+ align:start position:0%
+yeah i kind of wrote it as an
+electromagnetic current but really what
+
+ align:start position:0%
+electromagnetic current but really what
+ 
+
+ align:start position:0%
+electromagnetic current but really what
+i mean by it is sort of all the ways
+
+ align:start position:0%
+i mean by it is sort of all the ways
+ 
+
+ align:start position:0%
+i mean by it is sort of all the ways
+that electromagnetism can appear in the
+
+ align:start position:0%
+that electromagnetism can appear in the
+ 
+
+ align:start position:0%
+that electromagnetism can appear in the
+effective theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can think of formulating a
+
+ align:start position:0%
+so you can think of formulating a
+ 
+
+ align:start position:0%
+so you can think of formulating a
+current in the effective theory
+
+ align:start position:0%
+current in the effective theory
+ 
+
+ align:start position:0%
+current in the effective theory
+by just sort of take looking for one
+
+ align:start position:0%
+by just sort of take looking for one
+ 
+
+ align:start position:0%
+by just sort of take looking for one
+photon lopping it off and then writing
+
+ align:start position:0%
+photon lopping it off and then writing
+ 
+
+ align:start position:0%
+photon lopping it off and then writing
+down that operator all the operators and
+
+ align:start position:0%
+down that operator all the operators and
+ 
+
+ align:start position:0%
+down that operator all the operators and
+that's what really what i mean by this
+
+ align:start position:0%
+that's what really what i mean by this
+ 
+
+ align:start position:0%
+that's what really what i mean by this
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what's the final thing we need
+
+ align:start position:0%
+okay so what's the final thing we need
+ 
+
+ align:start position:0%
+okay so what's the final thing we need
+which is the bound state z factor
+
+ align:start position:0%
+which is the bound state z factor
+ 
+
+ align:start position:0%
+which is the bound state z factor
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+when we look back at this kind of form
+
+ align:start position:0%
+when we look back at this kind of form
+ 
+
+ align:start position:0%
+when we look back at this kind of form
+that we had for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for g we said it's i z but now let's
+
+ align:start position:0%
+for g we said it's i z but now let's
+ 
+
+ align:start position:0%
+for g we said it's i z but now let's
+denote the fact that z is really a
+
+ align:start position:0%
+denote the fact that z is really a
+ 
+
+ align:start position:0%
+denote the fact that z is really a
+principle a function of e bar
+
+ align:start position:0%
+principle a function of e bar
+ 
+
+ align:start position:0%
+principle a function of e bar
+and it's really the residue of the pole
+
+ align:start position:0%
+and it's really the residue of the pole
+ 
+
+ align:start position:0%
+and it's really the residue of the pole
+and what z
+
+ align:start position:0%
+and what z
+ 
+
+ align:start position:0%
+and what z
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+z that appears in the formula over there
+
+ align:start position:0%
+z that appears in the formula over there
+ 
+
+ align:start position:0%
+z that appears in the formula over there
+it's z at the pole
+
+ align:start position:0%
+it's z at the pole
+ 
+
+ align:start position:0%
+it's z at the pole
+so that's where i set
+
+ align:start position:0%
+so that's where i set
+ 
+
+ align:start position:0%
+so that's where i set
+e bar equal to minus bd in the numerator
+
+ align:start position:0%
+e bar equal to minus bd in the numerator
+ 
+
+ align:start position:0%
+e bar equal to minus bd in the numerator
+so this is the residue of the pole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and with a little bit of manipulation we
+
+ align:start position:0%
+and with a little bit of manipulation we
+ 
+
+ align:start position:0%
+and with a little bit of manipulation we
+can write that as the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can relate it to a derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the pole
+
+ align:start position:0%
+at the pole
+ 
+
+ align:start position:0%
+at the pole
+okay so take the inverse
+
+ align:start position:0%
+okay so take the inverse
+ 
+
+ align:start position:0%
+okay so take the inverse
+take a derivative to sort of get just
+
+ align:start position:0%
+take a derivative to sort of get just
+ 
+
+ align:start position:0%
+take a derivative to sort of get just
+this factor take an inverse again we can
+
+ align:start position:0%
+this factor take an inverse again we can
+ 
+
+ align:start position:0%
+this factor take an inverse again we can
+extract off that residue
+
+ align:start position:0%
+extract off that residue
+ 
+
+ align:start position:0%
+extract off that residue
+killing off some other pieces by going
+
+ align:start position:0%
+killing off some other pieces by going
+ 
+
+ align:start position:0%
+killing off some other pieces by going
+to the pole
+
+ align:start position:0%
+to the pole
+ 
+
+ align:start position:0%
+to the pole
+okay so i won't go through the
+
+ align:start position:0%
+okay so i won't go through the
+ 
+
+ align:start position:0%
+okay so i won't go through the
+derivation of that little manipulation
+
+ align:start position:0%
+derivation of that little manipulation
+ 
+
+ align:start position:0%
+derivation of that little manipulation
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it's a straightforward consequence
+
+ align:start position:0%
+it's a straightforward consequence
+ 
+
+ align:start position:0%
+it's a straightforward consequence
+and if you put in
+
+ align:start position:0%
+and if you put in
+ 
+
+ align:start position:0%
+and if you put in
+kind of the formula that we had over
+
+ align:start position:0%
+kind of the formula that we had over
+ 
+
+ align:start position:0%
+kind of the formula that we had over
+here for g
+
+ align:start position:0%
+here for g
+ 
+
+ align:start position:0%
+here for g
+and you do that then you can write a
+
+ align:start position:0%
+and you do that then you can write a
+ 
+
+ align:start position:0%
+and you do that then you can write a
+formula in terms of sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and after that kind of manipulation it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again just some algebra to show that
+
+ align:start position:0%
+again just some algebra to show that
+ 
+
+ align:start position:0%
+again just some algebra to show that
+this is true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can put all the pieces
+
+ align:start position:0%
+so now we can put all the pieces
+ 
+
+ align:start position:0%
+so now we can put all the pieces
+together we have this formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get this formula
+
+ align:start position:0%
+get this formula
+ 
+
+ align:start position:0%
+get this formula
+this formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put them into the formula up there
+
+ align:start position:0%
+put them into the formula up there
+ 
+
+ align:start position:0%
+put them into the formula up there
+and what we find
+
+ align:start position:0%
+and what we find
+ 
+
+ align:start position:0%
+and what we find
+is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can write the kind of result of it
+
+ align:start position:0%
+we can write the kind of result of it
+ 
+
+ align:start position:0%
+we can write the kind of result of it
+using lsd in a kind of very compact way
+
+ align:start position:0%
+using lsd in a kind of very compact way
+ 
+
+ align:start position:0%
+using lsd in a kind of very compact way
+just in terms of irreducible things
+
+ align:start position:0%
+just in terms of irreducible things
+ 
+
+ align:start position:0%
+just in terms of irreducible things
+c0 irreducible things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it's not just the irreducible
+
+ align:start position:0%
+it's not just the irreducible
+ 
+
+ align:start position:0%
+it's not just the irreducible
+three-point functions there is a
+
+ align:start position:0%
+three-point functions there is a
+ 
+
+ align:start position:0%
+three-point functions there is a
+contribution from the two-point function
+
+ align:start position:0%
+contribution from the two-point function
+ 
+
+ align:start position:0%
+contribution from the two-point function
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+in this case d sigma-d bar
+
+ align:start position:0%
+in this case d sigma-d bar
+ 
+
+ align:start position:0%
+in this case d sigma-d bar
+where you take
+
+ align:start position:0%
+where you take
+ 
+
+ align:start position:0%
+where you take
+e-bar and e-bar prime incoming and
+
+ align:start position:0%
+e-bar and e-bar prime incoming and
+ 
+
+ align:start position:0%
+e-bar and e-bar prime incoming and
+outgoing energies to be
+
+ align:start position:0%
+outgoing energies to be
+ 
+
+ align:start position:0%
+outgoing energies to be
+the right energies for the bound states
+
+ align:start position:0%
+the right energies for the bound states
+ 
+
+ align:start position:0%
+the right energies for the bound states
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+minus the binding energy
+
+ align:start position:0%
+minus the binding energy
+ 
+
+ align:start position:0%
+minus the binding energy
+okay so the
+
+ align:start position:0%
+okay so the
+ 
+
+ align:start position:0%
+okay so the
+this factor came from here
+
+ align:start position:0%
+this factor came from here
+ 
+
+ align:start position:0%
+this factor came from here
+there's a sigma squared in the numerator
+
+ align:start position:0%
+there's a sigma squared in the numerator
+ 
+
+ align:start position:0%
+there's a sigma squared in the numerator
+but when i take the inverse of two of
+
+ align:start position:0%
+but when i take the inverse of two of
+ 
+
+ align:start position:0%
+but when i take the inverse of two of
+these guys there's a sigma squared in
+
+ align:start position:0%
+these guys there's a sigma squared in
+ 
+
+ align:start position:0%
+these guys there's a sigma squared in
+the denominator and those cancelled
+
+ align:start position:0%
+the denominator and those cancelled
+ 
+
+ align:start position:0%
+the denominator and those cancelled
+the inverse of these guys also had
+
+ align:start position:0%
+the inverse of these guys also had
+ 
+
+ align:start position:0%
+the inverse of these guys also had
+factors of one plus i c zero sigma in
+
+ align:start position:0%
+factors of one plus i c zero sigma in
+ 
+
+ align:start position:0%
+factors of one plus i c zero sigma in
+the numerator and that canceled these
+
+ align:start position:0%
+the numerator and that canceled these
+ 
+
+ align:start position:0%
+the numerator and that canceled these
+factors here
+
+ align:start position:0%
+factors here
+ 
+
+ align:start position:0%
+factors here
+so the only thing left is the gamma
+
+ align:start position:0%
+so the only thing left is the gamma
+ 
+
+ align:start position:0%
+so the only thing left is the gamma
+and the d sigma d e bar
+
+ align:start position:0%
+and the d sigma d e bar
+ 
+
+ align:start position:0%
+and the d sigma d e bar
+okay so that's what lsc says
+
+ align:start position:0%
+okay so that's what lsc says
+ 
+
+ align:start position:0%
+okay so that's what lsc says
+in this situation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's actually important to take this
+
+ align:start position:0%
+and it's actually important to take this
+ 
+
+ align:start position:0%
+and it's actually important to take this
+factor into account if you didn't take
+
+ align:start position:0%
+factor into account if you didn't take
+ 
+
+ align:start position:0%
+factor into account if you didn't take
+this factor into account you wouldn't
+
+ align:start position:0%
+this factor into account you wouldn't
+ 
+
+ align:start position:0%
+this factor into account you wouldn't
+even preserve for example that the
+
+ align:start position:0%
+even preserve for example that the
+ 
+
+ align:start position:0%
+even preserve for example that the
+charge of the deuteron is one
+
+ align:start position:0%
+charge of the deuteron is one
+ 
+
+ align:start position:0%
+charge of the deuteron is one
+i mean it's quite important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you look at this at lowest order
+
+ align:start position:0%
+if you look at this at lowest order
+ 
+
+ align:start position:0%
+if you look at this at lowest order
+and you just look at the electromagnetic
+
+ align:start position:0%
+and you just look at the electromagnetic
+ 
+
+ align:start position:0%
+and you just look at the electromagnetic
+current for the electric case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can do that with j0
+
+ align:start position:0%
+and you can do that with j0
+ 
+
+ align:start position:0%
+and you can do that with j0
+looking at the d0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we can
+
+ align:start position:0%
+and we can
+ 
+
+ align:start position:0%
+and we can
+use our previous calculations
+
+ align:start position:0%
+use our previous calculations
+ 
+
+ align:start position:0%
+use our previous calculations
+to figure out what
+
+ align:start position:0%
+to figure out what
+ 
+
+ align:start position:0%
+to figure out what
+the two point function is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+when i go to the poll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this factor where gamma b would be set
+
+ align:start position:0%
+this factor where gamma b would be set
+ 
+
+ align:start position:0%
+this factor where gamma b would be set
+equal to exactly the
+
+ align:start position:0%
+equal to exactly the
+ 
+
+ align:start position:0%
+equal to exactly the
+binding energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's just from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the trivial
+
+ align:start position:0%
+the trivial
+ 
+
+ align:start position:0%
+the trivial
+diagram
+
+ align:start position:0%
+diagram
+ 
+
+ align:start position:0%
+diagram
+and then the first contribution that
+
+ align:start position:0%
+and then the first contribution that
+ 
+
+ align:start position:0%
+and then the first contribution that
+comes into the
+
+ align:start position:0%
+comes into the
+ 
+
+ align:start position:0%
+comes into the
+three-point function
+
+ align:start position:0%
+three-point function
+ 
+
+ align:start position:0%
+three-point function
+can be calculated it's pretty
+
+ align:start position:0%
+can be calculated it's pretty
+ 
+
+ align:start position:0%
+can be calculated it's pretty
+straightforward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it gives a tan inverse actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that just comes from
+
+ align:start position:0%
+and that just comes from
+ 
+
+ align:start position:0%
+and that just comes from
+coupling
+
+ align:start position:0%
+coupling
+ 
+
+ align:start position:0%
+coupling
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+electromagnetic proton that's inside the
+
+ align:start position:0%
+electromagnetic proton that's inside the
+ 
+
+ align:start position:0%
+electromagnetic proton that's inside the
+deuteron so this is the proton
+
+ align:start position:0%
+deuteron so this is the proton
+ 
+
+ align:start position:0%
+deuteron so this is the proton
+which has an electromagnetic coupling
+
+ align:start position:0%
+which has an electromagnetic coupling
+ 
+
+ align:start position:0%
+which has an electromagnetic coupling
+this is the neutron
+
+ align:start position:0%
+this is the neutron
+ 
+
+ align:start position:0%
+this is the neutron
+okay and that gives this formula take
+
+ align:start position:0%
+okay and that gives this formula take
+ 
+
+ align:start position:0%
+okay and that gives this formula take
+the ratio you get the lowest order form
+
+ align:start position:0%
+the ratio you get the lowest order form
+ 
+
+ align:start position:0%
+the ratio you get the lowest order form
+factor
+
+ align:start position:0%
+factor
+ 
+
+ align:start position:0%
+factor
+this is a systematically improvable
+
+ align:start position:0%
+this is a systematically improvable
+ 
+
+ align:start position:0%
+this is a systematically improvable
+thing so you can do nlo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can do an nlo et cetera
+
+ align:start position:0%
+you can do an nlo et cetera
+ 
+
+ align:start position:0%
+you can do an nlo et cetera
+okay so we can really calculate
+
+ align:start position:0%
+okay so we can really calculate
+ 
+
+ align:start position:0%
+okay so we can really calculate
+properties of the deuteron
+
+ align:start position:0%
+properties of the deuteron
+ 
+
+ align:start position:0%
+properties of the deuteron
+and check whether they work
+
+ align:start position:0%
+and check whether they work
+ 
+
+ align:start position:0%
+and check whether they work
+experimentally and this works extremely
+
+ align:start position:0%
+experimentally and this works extremely
+ 
+
+ align:start position:0%
+experimentally and this works extremely
+well experimentally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you actually don't see the
+
+ align:start position:0%
+you actually don't see the
+ 
+
+ align:start position:0%
+you actually don't see the
+violation of charge conjugation
+
+ align:start position:0%
+violation of charge conjugation
+ 
+
+ align:start position:0%
+violation of charge conjugation
+conservation in the form factor until
+
+ align:start position:0%
+conservation in the form factor until
+ 
+
+ align:start position:0%
+conservation in the form factor until
+you do nlo then you really see that you
+
+ align:start position:0%
+you do nlo then you really see that you
+ 
+
+ align:start position:0%
+you do nlo then you really see that you
+need this
+
+ align:start position:0%
+need this
+ 
+
+ align:start position:0%
+need this
+guy in order to make sure that the
+
+ align:start position:0%
+guy in order to make sure that the
+ 
+
+ align:start position:0%
+guy in order to make sure that the
+charge is conserved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there would be some pieces that would
+
+ align:start position:0%
+there would be some pieces that would
+ 
+
+ align:start position:0%
+there would be some pieces that would
+show up that would seem like they were
+
+ align:start position:0%
+show up that would seem like they were
+ 
+
+ align:start position:0%
+show up that would seem like they were
+correcting the charge violating
+
+ align:start position:0%
+correcting the charge violating
+ 
+
+ align:start position:0%
+correcting the charge violating
+electromagnetism
+
+ align:start position:0%
+electromagnetism
+ 
+
+ align:start position:0%
+electromagnetism
+magnetic gauging variance until you but
+
+ align:start position:0%
+magnetic gauging variance until you but
+ 
+
+ align:start position:0%
+magnetic gauging variance until you but
+then when you put the z factor in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the z factor contribution and everything
+
+ align:start position:0%
+the z factor contribution and everything
+ 
+
+ align:start position:0%
+the z factor contribution and everything
+is nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this theory has actually been used
+
+ align:start position:0%
+and this theory has actually been used
+ 
+
+ align:start position:0%
+and this theory has actually been used
+to do phenomenology
+
+ align:start position:0%
+to do phenomenology
+ 
+
+ align:start position:0%
+to do phenomenology
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just to give you some examples of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can do a process like
+
+ align:start position:0%
+so you can do a process like
+ 
+
+ align:start position:0%
+so you can do a process like
+neutron on proton
+
+ align:start position:0%
+neutron on proton
+ 
+
+ align:start position:0%
+neutron on proton
+produces a deuteron and a photon which
+
+ align:start position:0%
+produces a deuteron and a photon which
+ 
+
+ align:start position:0%
+produces a deuteron and a photon which
+is something that shows up in big bang
+
+ align:start position:0%
+is something that shows up in big bang
+ 
+
+ align:start position:0%
+is something that shows up in big bang
+nuclear synthesis
+
+ align:start position:0%
+nuclear synthesis
+ 
+
+ align:start position:0%
+nuclear synthesis
+and it's been calculated to n4lo
+
+ align:start position:0%
+and it's been calculated to n4lo
+ 
+
+ align:start position:0%
+and it's been calculated to n4lo
+in this effective field theory
+
+ align:start position:0%
+in this effective field theory
+ 
+
+ align:start position:0%
+in this effective field theory
+okay and it provides the most accurate
+
+ align:start position:0%
+okay and it provides the most accurate
+ 
+
+ align:start position:0%
+okay and it provides the most accurate
+way of determining
+
+ align:start position:0%
+way of determining
+ 
+
+ align:start position:0%
+way of determining
+the process for big bang blue synthesis
+
+ align:start position:0%
+the process for big bang blue synthesis
+ 
+
+ align:start position:0%
+the process for big bang blue synthesis
+you can reverse it
+
+ align:start position:0%
+you can reverse it
+ 
+
+ align:start position:0%
+you can reverse it
+talk about deuteron breakup
+
+ align:start position:0%
+talk about deuteron breakup
+ 
+
+ align:start position:0%
+talk about deuteron breakup
+you could do processes with neutrinos on
+
+ align:start position:0%
+you could do processes with neutrinos on
+ 
+
+ align:start position:0%
+you could do processes with neutrinos on
+deuterons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you could have neutrinos deuteron
+
+ align:start position:0%
+so you could have neutrinos deuteron
+ 
+
+ align:start position:0%
+so you could have neutrinos deuteron
+scattering to proton proton e minus
+
+ align:start position:0%
+scattering to proton proton e minus
+ 
+
+ align:start position:0%
+scattering to proton proton e minus
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+the charge current process at snow
+
+ align:start position:0%
+the charge current process at snow
+ 
+
+ align:start position:0%
+the charge current process at snow
+or the neutral current process of snow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all these things are within the realm of
+
+ align:start position:0%
+all these things are within the realm of
+ 
+
+ align:start position:0%
+all these things are within the realm of
+things that you can talk about in this
+
+ align:start position:0%
+things that you can talk about in this
+ 
+
+ align:start position:0%
+things that you can talk about in this
+effective field theory
+
+ align:start position:0%
+effective field theory
+ 
+
+ align:start position:0%
+effective field theory
+okay so it has some uses
+
+ align:start position:0%
+okay so it has some uses
+ 
+
+ align:start position:0%
+okay so it has some uses
+let me do one more
+
+ align:start position:0%
+let me do one more
+ 
+
+ align:start position:0%
+let me do one more
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you could look at neutron nucleon
+
+ align:start position:0%
+so you could look at neutron nucleon
+ 
+
+ align:start position:0%
+so you could look at neutron nucleon
+nucleon
+
+ align:start position:0%
+nucleon
+ 
+
+ align:start position:0%
+nucleon
+to nucleon nucleon plus an axon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's sort of a
+
+ align:start position:0%
+and there's sort of a
+ 
+
+ align:start position:0%
+and there's sort of a
+lesson here
+
+ align:start position:0%
+lesson here
+ 
+
+ align:start position:0%
+lesson here
+so if you look at how the axion couples
+
+ align:start position:0%
+so if you look at how the axion couples
+ 
+
+ align:start position:0%
+so if you look at how the axion couples
+to the nucleon
+
+ align:start position:0%
+to the nucleon
+ 
+
+ align:start position:0%
+to the nucleon
+it's derivatively coupled
+
+ align:start position:0%
+it's derivatively coupled
+ 
+
+ align:start position:0%
+it's derivatively coupled
+so you have
+
+ align:start position:0%
+so you have
+ 
+
+ align:start position:0%
+so you have
+a gradient of the axion field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's two possible couplings that
+
+ align:start position:0%
+and there's two possible couplings that
+ 
+
+ align:start position:0%
+and there's two possible couplings that
+you can write down just consider the
+
+ align:start position:0%
+you can write down just consider the
+ 
+
+ align:start position:0%
+you can write down just consider the
+sort of lowest dimension
+
+ align:start position:0%
+sort of lowest dimension
+ 
+
+ align:start position:0%
+sort of lowest dimension
+in our power counting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a process that actually is
+
+ align:start position:0%
+and this is a process that actually is
+ 
+
+ align:start position:0%
+and this is a process that actually is
+important for bounding axion physics
+
+ align:start position:0%
+important for bounding axion physics
+ 
+
+ align:start position:0%
+important for bounding axion physics
+for example axions in the sun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worry about how they couple to nucleons
+
+ align:start position:0%
+worry about how they couple to nucleons
+ 
+
+ align:start position:0%
+worry about how they couple to nucleons
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the thing that's actually important is
+
+ align:start position:0%
+the thing that's actually important is
+ 
+
+ align:start position:0%
+the thing that's actually important is
+if you're thinking about this kind of
+
+ align:start position:0%
+if you're thinking about this kind of
+ 
+
+ align:start position:0%
+if you're thinking about this kind of
+process you have to decide kinematically
+
+ align:start position:0%
+process you have to decide kinematically
+ 
+
+ align:start position:0%
+process you have to decide kinematically
+what region are you looking at if you're
+
+ align:start position:0%
+what region are you looking at if you're
+ 
+
+ align:start position:0%
+what region are you looking at if you're
+interested in bounds from the sun
+
+ align:start position:0%
+interested in bounds from the sun
+ 
+
+ align:start position:0%
+interested in bounds from the sun
+you're interested in a situation where
+
+ align:start position:0%
+you're interested in a situation where
+ 
+
+ align:start position:0%
+you're interested in a situation where
+the energy of the axion is of order of
+
+ align:start position:0%
+the energy of the axion is of order of
+ 
+
+ align:start position:0%
+the energy of the axion is of order of
+the energy of the nucleons
+
+ align:start position:0%
+the energy of the nucleons
+ 
+
+ align:start position:0%
+the energy of the nucleons
+but the momentum of the axiom is much
+
+ align:start position:0%
+but the momentum of the axiom is much
+ 
+
+ align:start position:0%
+but the momentum of the axiom is much
+less so
+
+ align:start position:0%
+less so
+ 
+
+ align:start position:0%
+less so
+i'll call that k axion
+
+ align:start position:0%
+i'll call that k axion
+ 
+
+ align:start position:0%
+i'll call that k axion
+is much less than
+
+ align:start position:0%
+is much less than
+ 
+
+ align:start position:0%
+is much less than
+p nucleon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so from a power counting perspective the
+
+ align:start position:0%
+so from a power counting perspective the
+ 
+
+ align:start position:0%
+so from a power counting perspective the
+energies are the same size but the
+
+ align:start position:0%
+energies are the same size but the
+ 
+
+ align:start position:0%
+energies are the same size but the
+momentum of the axion which is a
+
+ align:start position:0%
+momentum of the axion which is a
+ 
+
+ align:start position:0%
+momentum of the axion which is a
+relativistic particle and is complical
+
+ align:start position:0%
+relativistic particle and is complical
+ 
+
+ align:start position:0%
+relativistic particle and is complical
+to the energy
+
+ align:start position:0%
+to the energy
+ 
+
+ align:start position:0%
+to the energy
+is much less since the nucleon momentum
+
+ align:start position:0%
+is much less since the nucleon momentum
+ 
+
+ align:start position:0%
+is much less since the nucleon momentum
+is much bigger than its energy remember
+
+ align:start position:0%
+is much bigger than its energy remember
+ 
+
+ align:start position:0%
+is much bigger than its energy remember
+that the energy goes like p squared over
+
+ align:start position:0%
+that the energy goes like p squared over
+ 
+
+ align:start position:0%
+that the energy goes like p squared over
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+so the momentum are bigger
+
+ align:start position:0%
+so the momentum are bigger
+ 
+
+ align:start position:0%
+so the momentum are bigger
+and if that's the situation that you're
+
+ align:start position:0%
+and if that's the situation that you're
+ 
+
+ align:start position:0%
+and if that's the situation that you're
+in then when you're doing a lagrangian
+
+ align:start position:0%
+in then when you're doing a lagrangian
+ 
+
+ align:start position:0%
+in then when you're doing a lagrangian
+like this you have to be careful about
+
+ align:start position:0%
+like this you have to be careful about
+ 
+
+ align:start position:0%
+like this you have to be careful about
+implementing something like that
+
+ align:start position:0%
+implementing something like that
+ 
+
+ align:start position:0%
+implementing something like that
+and the way that it gets implemented is
+
+ align:start position:0%
+and the way that it gets implemented is
+ 
+
+ align:start position:0%
+and the way that it gets implemented is
+by a multiple expansion which we'll have
+
+ align:start position:0%
+by a multiple expansion which we'll have
+ 
+
+ align:start position:0%
+by a multiple expansion which we'll have
+opportunity to talk more about
+
+ align:start position:0%
+opportunity to talk more about
+ 
+
+ align:start position:0%
+opportunity to talk more about
+the near
+
+ align:start position:0%
+the near
+ 
+
+ align:start position:0%
+the near
+future but basically what it corresponds
+
+ align:start position:0%
+future but basically what it corresponds
+ 
+
+ align:start position:0%
+future but basically what it corresponds
+to is that you've got to make sure that
+
+ align:start position:0%
+to is that you've got to make sure that
+ 
+
+ align:start position:0%
+to is that you've got to make sure that
+you're not
+
+ align:start position:0%
+you're not
+ 
+
+ align:start position:0%
+you're not
+that you're sort of exchanging energy
+
+ align:start position:0%
+that you're sort of exchanging energy
+ 
+
+ align:start position:0%
+that you're sort of exchanging energy
+between these operators but not momenta
+
+ align:start position:0%
+between these operators but not momenta
+ 
+
+ align:start position:0%
+between these operators but not momenta
+that's what happens at lowest order so
+
+ align:start position:0%
+that's what happens at lowest order so
+ 
+
+ align:start position:0%
+that's what happens at lowest order so
+if you make this expansion in the
+
+ align:start position:0%
+if you make this expansion in the
+ 
+
+ align:start position:0%
+if you make this expansion in the
+lagrangian
+
+ align:start position:0%
+lagrangian
+ 
+
+ align:start position:0%
+lagrangian
+it corresponds to setting the spatial
+
+ align:start position:0%
+it corresponds to setting the spatial
+ 
+
+ align:start position:0%
+it corresponds to setting the spatial
+components of the axon field
+
+ align:start position:0%
+components of the axon field
+ 
+
+ align:start position:0%
+components of the axon field
+to zero
+
+ align:start position:0%
+to zero
+ 
+
+ align:start position:0%
+to zero
+okay so this is like doing a derivative
+
+ align:start position:0%
+okay so this is like doing a derivative
+ 
+
+ align:start position:0%
+okay so this is like doing a derivative
+doing an expansion around x vector
+
+ align:start position:0%
+doing an expansion around x vector
+ 
+
+ align:start position:0%
+doing an expansion around x vector
+equals zero and that
+
+ align:start position:0%
+equals zero and that
+ 
+
+ align:start position:0%
+equals zero and that
+the same thing in position space is this
+
+ align:start position:0%
+the same thing in position space is this
+ 
+
+ align:start position:0%
+the same thing in position space is this
+expansion here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implements
+
+ align:start position:0%
+implements
+ 
+
+ align:start position:0%
+implements
+the k much less than p
+
+ align:start position:0%
+the k much less than p
+ 
+
+ align:start position:0%
+the k much less than p
+expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that would actually be the
+
+ align:start position:0%
+okay so that would actually be the
+ 
+
+ align:start position:0%
+okay so that would actually be the
+operator that you would use to do a
+
+ align:start position:0%
+operator that you would use to do a
+ 
+
+ align:start position:0%
+operator that you would use to do a
+couple axons to nucleon
+
+ align:start position:0%
+couple axons to nucleon
+ 
+
+ align:start position:0%
+couple axons to nucleon
+now the interesting thing about this
+
+ align:start position:0%
+now the interesting thing about this
+ 
+
+ align:start position:0%
+now the interesting thing about this
+operator which ties into what we started
+
+ align:start position:0%
+operator which ties into what we started
+ 
+
+ align:start position:0%
+operator which ties into what we started
+talking about today
+
+ align:start position:0%
+talking about today
+ 
+
+ align:start position:0%
+talking about today
+is that once you take x equals zero the
+
+ align:start position:0%
+is that once you take x equals zero the
+ 
+
+ align:start position:0%
+is that once you take x equals zero the
+things that you're left with here
+
+ align:start position:0%
+things that you're left with here
+ 
+
+ align:start position:0%
+things that you're left with here
+are related to conserved charges of the
+
+ align:start position:0%
+are related to conserved charges of the
+ 
+
+ align:start position:0%
+are related to conserved charges of the
+su-4 symmetry
+
+ align:start position:0%
+su-4 symmetry
+ 
+
+ align:start position:0%
+su-4 symmetry
+so q-mu nu
+
+ align:start position:0%
+so q-mu nu
+ 
+
+ align:start position:0%
+so q-mu nu
+which is an integral overall space
+
+ align:start position:0%
+which is an integral overall space
+ 
+
+ align:start position:0%
+which is an integral overall space
+of n dagger
+
+ align:start position:0%
+of n dagger
+ 
+
+ align:start position:0%
+of n dagger
+sigma mu tau nu
+
+ align:start position:0%
+sigma mu tau nu
+ 
+
+ align:start position:0%
+sigma mu tau nu
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that's the charge of su4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason that it's that it's
+
+ align:start position:0%
+and the reason that it's that it's
+ 
+
+ align:start position:0%
+and the reason that it's that it's
+related to that is because once i take x
+
+ align:start position:0%
+related to that is because once i take x
+ 
+
+ align:start position:0%
+related to that is because once i take x
+equals zero here once i do the integral
+
+ align:start position:0%
+equals zero here once i do the integral
+ 
+
+ align:start position:0%
+equals zero here once i do the integral
+d4 x of the lagrangian the time this
+
+ align:start position:0%
+d4 x of the lagrangian the time this
+ 
+
+ align:start position:0%
+d4 x of the lagrangian the time this
+still depends on time but it doesn't
+
+ align:start position:0%
+still depends on time but it doesn't
+ 
+
+ align:start position:0%
+still depends on time but it doesn't
+depend on space so i can move the d3x
+
+ align:start position:0%
+depend on space so i can move the d3x
+ 
+
+ align:start position:0%
+depend on space so i can move the d3x
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+just let it act on this
+
+ align:start position:0%
+just let it act on this
+ 
+
+ align:start position:0%
+just let it act on this
+just let it act on that
+
+ align:start position:0%
+just let it act on that
+ 
+
+ align:start position:0%
+just let it act on that
+and then i get cumulu
+
+ align:start position:0%
+and then i get cumulu
+ 
+
+ align:start position:0%
+and then i get cumulu
+q0 j and q
+
+ align:start position:0%
+q0 j and q
+ 
+
+ align:start position:0%
+q0 j and q
+our q j 0 and q j 3.
+
+ align:start position:0%
+our q j 0 and q j 3.
+ 
+
+ align:start position:0%
+our q j 0 and q j 3.
+so this guy here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+color
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+qj3
+
+ align:start position:0%
+qj3
+ 
+
+ align:start position:0%
+qj3
+qj0
+
+ align:start position:0%
+qj0
+ 
+
+ align:start position:0%
+qj0
+let's go here
+
+ align:start position:0%
+let's go here
+ 
+
+ align:start position:0%
+let's go here
+j3
+
+ align:start position:0%
+j3
+ 
+
+ align:start position:0%
+j3
+and that actually has non-trivial
+
+ align:start position:0%
+and that actually has non-trivial
+ 
+
+ align:start position:0%
+and that actually has non-trivial
+consequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because charges if they're charges of
+
+ align:start position:0%
+because charges if they're charges of
+ 
+
+ align:start position:0%
+because charges if they're charges of
+asymmetry
+
+ align:start position:0%
+asymmetry
+ 
+
+ align:start position:0%
+asymmetry
+are time independent
+
+ align:start position:0%
+are time independent
+ 
+
+ align:start position:0%
+are time independent
+so even though in principle
+
+ align:start position:0%
+so even though in principle
+ 
+
+ align:start position:0%
+so even though in principle
+i didn't make any assumptions
+
+ align:start position:0%
+i didn't make any assumptions
+ 
+
+ align:start position:0%
+i didn't make any assumptions
+about the time dependence here
+
+ align:start position:0%
+about the time dependence here
+ 
+
+ align:start position:0%
+about the time dependence here
+and these operators could exchange
+
+ align:start position:0%
+and these operators could exchange
+ 
+
+ align:start position:0%
+and these operators could exchange
+energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i know that they're related to
+
+ align:start position:0%
+if i know that they're related to
+ 
+
+ align:start position:0%
+if i know that they're related to
+charges of the effect of the effective
+
+ align:start position:0%
+charges of the effect of the effective
+ 
+
+ align:start position:0%
+charges of the effect of the effective
+field theory then charges are conserved
+
+ align:start position:0%
+field theory then charges are conserved
+ 
+
+ align:start position:0%
+field theory then charges are conserved
+there's no time dependence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so charges of the field theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are time independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what that means then is that this
+
+ align:start position:0%
+and what that means then is that this
+ 
+
+ align:start position:0%
+and what that means then is that this
+is time independent and there's actually
+
+ align:start position:0%
+is time independent and there's actually
+ 
+
+ align:start position:0%
+is time independent and there's actually
+no energy exchange
+
+ align:start position:0%
+no energy exchange
+ 
+
+ align:start position:0%
+no energy exchange
+so the axion can only sort of exchange
+
+ align:start position:0%
+so the axion can only sort of exchange
+ 
+
+ align:start position:0%
+so the axion can only sort of exchange
+energy the only way the axon can couple
+
+ align:start position:0%
+energy the only way the axon can couple
+ 
+
+ align:start position:0%
+energy the only way the axon can couple
+is with zero energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since it's derivatively coupled it
+
+ align:start position:0%
+and since it's derivatively coupled it
+ 
+
+ align:start position:0%
+and since it's derivatively coupled it
+has zero energy it has zero momentum and
+
+ align:start position:0%
+has zero energy it has zero momentum and
+ 
+
+ align:start position:0%
+has zero energy it has zero momentum and
+there's no coupling
+
+ align:start position:0%
+there's no coupling
+ 
+
+ align:start position:0%
+there's no coupling
+so in this limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we talked about is a symmetry limit
+
+ align:start position:0%
+that we talked about is a symmetry limit
+ 
+
+ align:start position:0%
+that we talked about is a symmetry limit
+the axon just doesn't couple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there we're predicting something
+
+ align:start position:0%
+okay so there we're predicting something
+ 
+
+ align:start position:0%
+okay so there we're predicting something
+falling through kind of the consequences
+
+ align:start position:0%
+falling through kind of the consequences
+ 
+
+ align:start position:0%
+falling through kind of the consequences
+of symmetry
+
+ align:start position:0%
+of symmetry
+ 
+
+ align:start position:0%
+of symmetry
+on this effective field there predicting
+
+ align:start position:0%
+on this effective field there predicting
+ 
+
+ align:start position:0%
+on this effective field there predicting
+something about how axions coupled to
+
+ align:start position:0%
+something about how axions coupled to
+ 
+
+ align:start position:0%
+something about how axions coupled to
+the nucleons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if you look sort of through the possible
+
+ align:start position:0%
+if you look sort of through the possible
+ 
+
+ align:start position:0%
+if you look sort of through the possible
+processes
+
+ align:start position:0%
+processes
+ 
+
+ align:start position:0%
+processes
+that you could have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could have two nucleons in a 3s1
+
+ align:start position:0%
+you could have two nucleons in a 3s1
+ 
+
+ align:start position:0%
+you could have two nucleons in a 3s1
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+try to produce an axion
+
+ align:start position:0%
+try to produce an axion
+ 
+
+ align:start position:0%
+try to produce an axion
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that actually vanishes irrespective of
+
+ align:start position:0%
+that actually vanishes irrespective of
+ 
+
+ align:start position:0%
+that actually vanishes irrespective of
+the scattering lengths
+
+ align:start position:0%
+the scattering lengths
+ 
+
+ align:start position:0%
+the scattering lengths
+because you're coupling here to spin
+
+ align:start position:0%
+because you're coupling here to spin
+ 
+
+ align:start position:0%
+because you're coupling here to spin
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+is always a good charge of the
+
+ align:start position:0%
+is always a good charge of the
+ 
+
+ align:start position:0%
+is always a good charge of the
+non-relativistic theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there is a way that you could have
+
+ align:start position:0%
+but there is a way that you could have
+ 
+
+ align:start position:0%
+but there is a way that you could have
+the process go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where you switch from a 1s0 state to a
+
+ align:start position:0%
+where you switch from a 1s0 state to a
+ 
+
+ align:start position:0%
+where you switch from a 1s0 state to a
+3s1 state
+
+ align:start position:0%
+3s1 state
+ 
+
+ align:start position:0%
+3s1 state
+and this guy vanishes if the scouting
+
+ align:start position:0%
+and this guy vanishes if the scouting
+ 
+
+ align:start position:0%
+and this guy vanishes if the scouting
+lengths go to infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you ignored what i just said and
+
+ align:start position:0%
+so if you ignored what i just said and
+ 
+
+ align:start position:0%
+so if you ignored what i just said and
+you ignored this
+
+ align:start position:0%
+you ignored this
+ 
+
+ align:start position:0%
+you ignored this
+here and you just went ahead and
+
+ align:start position:0%
+here and you just went ahead and
+ 
+
+ align:start position:0%
+here and you just went ahead and
+calculated the finemen diagrams
+
+ align:start position:0%
+calculated the finemen diagrams
+ 
+
+ align:start position:0%
+calculated the finemen diagrams
+we would just find that the amplitude to
+
+ align:start position:0%
+we would just find that the amplitude to
+ 
+
+ align:start position:0%
+we would just find that the amplitude to
+this thing
+
+ align:start position:0%
+this thing
+ 
+
+ align:start position:0%
+this thing
+is proportional to this kind of factor
+
+ align:start position:0%
+is proportional to this kind of factor
+ 
+
+ align:start position:0%
+is proportional to this kind of factor
+that we saw before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since the scattering lengths are
+
+ align:start position:0%
+and since the scattering lengths are
+ 
+
+ align:start position:0%
+and since the scattering lengths are
+large it's vanishing if the scattering
+
+ align:start position:0%
+large it's vanishing if the scattering
+ 
+
+ align:start position:0%
+large it's vanishing if the scattering
+lines go to infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so at lowest order the effective theory
+
+ align:start position:0%
+so at lowest order the effective theory
+ 
+
+ align:start position:0%
+so at lowest order the effective theory
+is suppressed this process and that has
+
+ align:start position:0%
+is suppressed this process and that has
+ 
+
+ align:start position:0%
+is suppressed this process and that has
+implications for of course the
+
+ align:start position:0%
+implications for of course the
+ 
+
+ align:start position:0%
+implications for of course the
+phenomenology you could also put in
+
+ align:start position:0%
+phenomenology you could also put in
+ 
+
+ align:start position:0%
+phenomenology you could also put in
+higher dimension operators like the c2s
+
+ align:start position:0%
+higher dimension operators like the c2s
+ 
+
+ align:start position:0%
+higher dimension operators like the c2s
+then of course you can get a
+
+ align:start position:0%
+then of course you can get a
+ 
+
+ align:start position:0%
+then of course you can get a
+contribution but that's higher order in
+
+ align:start position:0%
+contribution but that's higher order in
+ 
+
+ align:start position:0%
+contribution but that's higher order in
+the power counting and that affects how
+
+ align:start position:0%
+the power counting and that affects how
+ 
+
+ align:start position:0%
+the power counting and that affects how
+the axiom can be constrained in the sun
+
+ align:start position:0%
+the axiom can be constrained in the sun
+ 
+
+ align:start position:0%
+the axiom can be constrained in the sun
+okay so that gives you a little bit of
+
+ align:start position:0%
+okay so that gives you a little bit of
+ 
+
+ align:start position:0%
+okay so that gives you a little bit of
+feeling for what you can do with this
+
+ align:start position:0%
+feeling for what you can do with this
+ 
+
+ align:start position:0%
+feeling for what you can do with this
+effective field theory and how you can
+
+ align:start position:0%
+effective field theory and how you can
+ 
+
+ align:start position:0%
+effective field theory and how you can
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+exploit symmetry as well as the
+
+ align:start position:0%
+exploit symmetry as well as the
+ 
+
+ align:start position:0%
+exploit symmetry as well as the
+calculability of the effective theory to
+
+ align:start position:0%
+calculability of the effective theory to
+ 
+
+ align:start position:0%
+calculability of the effective theory to
+make lots of interesting predictions
+
+ align:start position:0%
+make lots of interesting predictions
+ 
+
+ align:start position:0%
+make lots of interesting predictions
+okay so any questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh that's all i have to say about that
+
+ align:start position:0%
+uh that's all i have to say about that
+ 
+
+ align:start position:0%
+uh that's all i have to say about that
+effective theory so we're now going to
+
+ align:start position:0%
+effective theory so we're now going to
+ 
+
+ align:start position:0%
+effective theory so we're now going to
+move on to our final effective field
+
+ align:start position:0%
+move on to our final effective field
+ 
+
+ align:start position:0%
+move on to our final effective field
+theory which is soft linear effective
+
+ align:start position:0%
+theory which is soft linear effective
+ 
+
+ align:start position:0%
+theory which is soft linear effective
+theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what i intend to do with this part of
+
+ align:start position:0%
+so what i intend to do with this part of
+ 
+
+ align:start position:0%
+so what i intend to do with this part of
+the course which will take us through
+
+ align:start position:0%
+the course which will take us through
+ 
+
+ align:start position:0%
+the course which will take us through
+the rest of the year is i'm going to
+
+ align:start position:0%
+the rest of the year is i'm going to
+ 
+
+ align:start position:0%
+the rest of the year is i'm going to
+hand out lecture notes for you to read
+
+ align:start position:0%
+hand out lecture notes for you to read
+ 
+
+ align:start position:0%
+hand out lecture notes for you to read
+which i'm going to write
+
+ align:start position:0%
+which i'm going to write
+ 
+
+ align:start position:0%
+which i'm going to write
+so i haven't done that yet i'm going to
+
+ align:start position:0%
+so i haven't done that yet i'm going to
+ 
+
+ align:start position:0%
+so i haven't done that yet i'm going to
+continue to post
+
+ align:start position:0%
+continue to post
+ 
+
+ align:start position:0%
+continue to post
+i mean i have some rough copy of them
+
+ align:start position:0%
+i mean i have some rough copy of them
+ 
+
+ align:start position:0%
+i mean i have some rough copy of them
+but i'm going to make it pretty and
+
+ align:start position:0%
+but i'm going to make it pretty and
+ 
+
+ align:start position:0%
+but i'm going to make it pretty and
+beautiful for you or more beautiful than
+
+ align:start position:0%
+beautiful for you or more beautiful than
+ 
+
+ align:start position:0%
+beautiful for you or more beautiful than
+it currently is
+
+ align:start position:0%
+it currently is
+ 
+
+ align:start position:0%
+it currently is
+i'm also going to continue to post the
+
+ align:start position:0%
+i'm also going to continue to post the
+ 
+
+ align:start position:0%
+i'm also going to continue to post the
+lecture notes that i of what i present
+
+ align:start position:0%
+lecture notes that i of what i present
+ 
+
+ align:start position:0%
+lecture notes that i of what i present
+in lectures so you'll have sort of two
+
+ align:start position:0%
+in lectures so you'll have sort of two
+ 
+
+ align:start position:0%
+in lectures so you'll have sort of two
+versions of that you can read either the
+
+ align:start position:0%
+versions of that you can read either the
+ 
+
+ align:start position:0%
+versions of that you can read either the
+latex version or the handwritten version
+
+ align:start position:0%
+latex version or the handwritten version
+ 
+
+ align:start position:0%
+latex version or the handwritten version
+and depending on your taste you can
+
+ align:start position:0%
+and depending on your taste you can
+ 
+
+ align:start position:0%
+and depending on your taste you can
+look at one or the other
+
+ align:start position:0%
+look at one or the other
+ 
+
+ align:start position:0%
+look at one or the other
+so what we'll do today is we'll just
+
+ align:start position:0%
+so what we'll do today is we'll just
+ 
+
+ align:start position:0%
+so what we'll do today is we'll just
+sort of briefly introduce ourselves to
+
+ align:start position:0%
+sort of briefly introduce ourselves to
+ 
+
+ align:start position:0%
+sort of briefly introduce ourselves to
+this effective theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by way of introduction to any
+
+ align:start position:0%
+and by way of introduction to any
+ 
+
+ align:start position:0%
+and by way of introduction to any
+effective theory the kind of things that
+
+ align:start position:0%
+effective theory the kind of things that
+ 
+
+ align:start position:0%
+effective theory the kind of things that
+we should talk about are y
+
+ align:start position:0%
+we should talk about are y
+ 
+
+ align:start position:0%
+we should talk about are y
+so we'll talk about why
+
+ align:start position:0%
+so we'll talk about why
+ 
+
+ align:start position:0%
+so we'll talk about why
+then we should talk about what the
+
+ align:start position:0%
+then we should talk about what the
+ 
+
+ align:start position:0%
+then we should talk about what the
+degrees of freedom are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in this case we'll also talk about
+
+ align:start position:0%
+and in this case we'll also talk about
+ 
+
+ align:start position:0%
+and in this case we'll also talk about
+kind of what are convenient coordinates
+
+ align:start position:0%
+kind of what are convenient coordinates
+ 
+
+ align:start position:0%
+kind of what are convenient coordinates
+to be using for this effective theory
+
+ align:start position:0%
+to be using for this effective theory
+ 
+
+ align:start position:0%
+to be using for this effective theory
+so that's where we'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we'll start covering today
+
+ align:start position:0%
+but we'll start covering today
+ 
+
+ align:start position:0%
+but we'll start covering today
+so what is sct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's an effective field theory that
+
+ align:start position:0%
+so it's an effective field theory that
+ 
+
+ align:start position:0%
+so it's an effective field theory that
+you can use for multiple things
+
+ align:start position:0%
+you can use for multiple things
+ 
+
+ align:start position:0%
+you can use for multiple things
+one is for
+
+ align:start position:0%
+one is for
+ 
+
+ align:start position:0%
+one is for
+energetic hadrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the energy of the hadron should be
+
+ align:start position:0%
+so the energy of the hadron should be
+ 
+
+ align:start position:0%
+so the energy of the hadron should be
+something that's a large scale which
+
+ align:start position:0%
+something that's a large scale which
+ 
+
+ align:start position:0%
+something that's a large scale which
+i'll call q
+
+ align:start position:0%
+i'll call q
+ 
+
+ align:start position:0%
+i'll call q
+conventional notation
+
+ align:start position:0%
+conventional notation
+ 
+
+ align:start position:0%
+conventional notation
+and by energetic it means much more
+
+ align:start position:0%
+and by energetic it means much more
+ 
+
+ align:start position:0%
+and by energetic it means much more
+energetic than the mass of the hadrons
+
+ align:start position:0%
+energetic than the mass of the hadrons
+ 
+
+ align:start position:0%
+energetic than the mass of the hadrons
+which is the water
+
+ align:start position:0%
+which is the water
+ 
+
+ align:start position:0%
+which is the water
+lambda qcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's also an effective theory for
+
+ align:start position:0%
+it's also an effective theory for
+ 
+
+ align:start position:0%
+it's also an effective theory for
+energetic jets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the situation is in some ways
+
+ align:start position:0%
+and the situation is in some ways
+ 
+
+ align:start position:0%
+and the situation is in some ways
+similar to the hadrons
+
+ align:start position:0%
+similar to the hadrons
+ 
+
+ align:start position:0%
+similar to the hadrons
+you have a jet energy that's large of
+
+ align:start position:0%
+you have a jet energy that's large of
+ 
+
+ align:start position:0%
+you have a jet energy that's large of
+order some q and that's much bigger than
+
+ align:start position:0%
+order some q and that's much bigger than
+ 
+
+ align:start position:0%
+order some q and that's much bigger than
+the jet mass which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a root squared of some form momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by the name you should also imagine
+
+ align:start position:0%
+and by the name you should also imagine
+ 
+
+ align:start position:0%
+and by the name you should also imagine
+that really what it is is something to
+
+ align:start position:0%
+that really what it is is something to
+ 
+
+ align:start position:0%
+that really what it is is something to
+do with qcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well maybe not not by the name but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is something to do with qcd
+
+ align:start position:0%
+it is something to do with qcd
+ 
+
+ align:start position:0%
+it is something to do with qcd
+and it's kind of what you get if you
+
+ align:start position:0%
+and it's kind of what you get if you
+ 
+
+ align:start position:0%
+and it's kind of what you get if you
+start with qcd and you focus your
+
+ align:start position:0%
+start with qcd and you focus your
+ 
+
+ align:start position:0%
+start with qcd and you focus your
+attention
+
+ align:start position:0%
+attention
+ 
+
+ align:start position:0%
+attention
+on a certain set of interactions
+
+ align:start position:0%
+on a certain set of interactions
+ 
+
+ align:start position:0%
+on a certain set of interactions
+which are collinear and soft
+
+ align:start position:0%
+which are collinear and soft
+ 
+
+ align:start position:0%
+which are collinear and soft
+interactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've met several different examples
+
+ align:start position:0%
+so we've met several different examples
+ 
+
+ align:start position:0%
+so we've met several different examples
+of effective field theories so far in
+
+ align:start position:0%
+of effective field theories so far in
+ 
+
+ align:start position:0%
+of effective field theories so far in
+the course some of them were bottom-up
+
+ align:start position:0%
+the course some of them were bottom-up
+ 
+
+ align:start position:0%
+the course some of them were bottom-up
+some of them were top down this is going
+
+ align:start position:0%
+some of them were top down this is going
+ 
+
+ align:start position:0%
+some of them were top down this is going
+to be a top-down effective field theory
+
+ align:start position:0%
+to be a top-down effective field theory
+ 
+
+ align:start position:0%
+to be a top-down effective field theory
+just like hqet was a top-down effective
+
+ align:start position:0%
+just like hqet was a top-down effective
+ 
+
+ align:start position:0%
+just like hqet was a top-down effective
+field theory
+
+ align:start position:0%
+field theory
+ 
+
+ align:start position:0%
+field theory
+so we'll be able to start with the qcd
+
+ align:start position:0%
+so we'll be able to start with the qcd
+ 
+
+ align:start position:0%
+so we'll be able to start with the qcd
+lagrangian and derive this theory by
+
+ align:start position:0%
+lagrangian and derive this theory by
+ 
+
+ align:start position:0%
+lagrangian and derive this theory by
+taking certain limits and that's what
+
+ align:start position:0%
+taking certain limits and that's what
+ 
+
+ align:start position:0%
+taking certain limits and that's what
+we'll do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so why why study this i will come to
+
+ align:start position:0%
+so why why study this i will come to
+ 
+
+ align:start position:0%
+so why why study this i will come to
+that in a bit but
+
+ align:start position:0%
+that in a bit but
+ 
+
+ align:start position:0%
+that in a bit but
+what are the kind of features of this
+
+ align:start position:0%
+what are the kind of features of this
+ 
+
+ align:start position:0%
+what are the kind of features of this
+from an effective field theory point of
+
+ align:start position:0%
+from an effective field theory point of
+ 
+
+ align:start position:0%
+from an effective field theory point of
+view that make it interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll talk about the answer to both
+
+ align:start position:0%
+we'll talk about the answer to both
+ 
+
+ align:start position:0%
+we'll talk about the answer to both
+those questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first
+
+ align:start position:0%
+so first
+ 
+
+ align:start position:0%
+so first
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+study this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's this effective theory good for
+
+ align:start position:0%
+what's this effective theory good for
+ 
+
+ align:start position:0%
+what's this effective theory good for
+so one thing it's good for is
+
+ align:start position:0%
+so one thing it's good for is
+ 
+
+ align:start position:0%
+so one thing it's good for is
+understanding factorization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you think about what we're doing
+
+ align:start position:0%
+and if you think about what we're doing
+ 
+
+ align:start position:0%
+and if you think about what we're doing
+when we probe for short distance physics
+
+ align:start position:0%
+when we probe for short distance physics
+ 
+
+ align:start position:0%
+when we probe for short distance physics
+say at the lhc
+
+ align:start position:0%
+say at the lhc
+ 
+
+ align:start position:0%
+say at the lhc
+we're probing for short distance physics
+
+ align:start position:0%
+we're probing for short distance physics
+ 
+
+ align:start position:0%
+we're probing for short distance physics
+by colliding things at high energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're carrying out hard collisions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energetic collisions of particles
+
+ align:start position:0%
+energetic collisions of particles
+ 
+
+ align:start position:0%
+energetic collisions of particles
+so the fact that this effective field
+
+ align:start position:0%
+so the fact that this effective field
+ 
+
+ align:start position:0%
+so the fact that this effective field
+theory deals with energetic particles
+
+ align:start position:0%
+theory deals with energetic particles
+ 
+
+ align:start position:0%
+theory deals with energetic particles
+may
+
+ align:start position:0%
+may
+ 
+
+ align:start position:0%
+may
+ring a bell as being something useful
+
+ align:start position:0%
+ring a bell as being something useful
+ 
+
+ align:start position:0%
+ring a bell as being something useful
+for understanding short distance physics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so what this effective theory allows
+
+ align:start position:0%
+and so what this effective theory allows
+ 
+
+ align:start position:0%
+and so what this effective theory allows
+you to do is disentangle the short
+
+ align:start position:0%
+you to do is disentangle the short
+ 
+
+ align:start position:0%
+you to do is disentangle the short
+distance physics that you're interested
+
+ align:start position:0%
+distance physics that you're interested
+ 
+
+ align:start position:0%
+distance physics that you're interested
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+from the longer distance physics that's
+
+ align:start position:0%
+from the longer distance physics that's
+ 
+
+ align:start position:0%
+from the longer distance physics that's
+associated to winding together into
+
+ align:start position:0%
+associated to winding together into
+ 
+
+ align:start position:0%
+associated to winding together into
+hadrons or producing these energetic
+
+ align:start position:0%
+hadrons or producing these energetic
+ 
+
+ align:start position:0%
+hadrons or producing these energetic
+dots
+
+ align:start position:0%
+dots
+ 
+
+ align:start position:0%
+dots
+so it's really disentangling the long
+
+ align:start position:0%
+so it's really disentangling the long
+ 
+
+ align:start position:0%
+so it's really disentangling the long
+and short distance physics
+
+ align:start position:0%
+and short distance physics
+ 
+
+ align:start position:0%
+and short distance physics
+in the standard model or the standard
+
+ align:start position:0%
+in the standard model or the standard
+ 
+
+ align:start position:0%
+in the standard model or the standard
+model plus new physics
+
+ align:start position:0%
+model plus new physics
+ 
+
+ align:start position:0%
+model plus new physics
+and basically what that amounts to is
+
+ align:start position:0%
+and basically what that amounts to is
+ 
+
+ align:start position:0%
+and basically what that amounts to is
+disentangling long and short distance
+
+ align:start position:0%
+disentangling long and short distance
+ 
+
+ align:start position:0%
+disentangling long and short distance
+physics in qcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me write it this way
+
+ align:start position:0%
+so let me write it this way
+ 
+
+ align:start position:0%
+so let me write it this way
+disentangling the physics of qcd with
+
+ align:start position:0%
+disentangling the physics of qcd with
+ 
+
+ align:start position:0%
+disentangling the physics of qcd with
+addition electroweak or bsm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics requires a separation of scales
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have to decide what's short distance
+
+ align:start position:0%
+we have to decide what's short distance
+ 
+
+ align:start position:0%
+we have to decide what's short distance
+what's long distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we're interested in a process like
+
+ align:start position:0%
+if we're interested in a process like
+ 
+
+ align:start position:0%
+if we're interested in a process like
+the lhc where we're colliding together
+
+ align:start position:0%
+the lhc where we're colliding together
+ 
+
+ align:start position:0%
+the lhc where we're colliding together
+hadrons then that's of course
+
+ align:start position:0%
+hadrons then that's of course
+ 
+
+ align:start position:0%
+hadrons then that's of course
+absolutely necessary
+
+ align:start position:0%
+absolutely necessary
+ 
+
+ align:start position:0%
+absolutely necessary
+because the hadrons are long distance
+
+ align:start position:0%
+because the hadrons are long distance
+ 
+
+ align:start position:0%
+because the hadrons are long distance
+things and we're interested in short
+
+ align:start position:0%
+things and we're interested in short
+ 
+
+ align:start position:0%
+things and we're interested in short
+distance physics
+
+ align:start position:0%
+distance physics
+ 
+
+ align:start position:0%
+distance physics
+and we can do that with sct
+
+ align:start position:0%
+and we can do that with sct
+ 
+
+ align:start position:0%
+and we can do that with sct
+that's perhaps the biggest motivation
+
+ align:start position:0%
+that's perhaps the biggest motivation
+ 
+
+ align:start position:0%
+that's perhaps the biggest motivation
+for us today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we make hard collisions these jets
+
+ align:start position:0%
+when we make hard collisions these jets
+ 
+
+ align:start position:0%
+when we make hard collisions these jets
+and energetic hadrons are very common
+
+ align:start position:0%
+and energetic hadrons are very common
+ 
+
+ align:start position:0%
+and energetic hadrons are very common
+they're the most common things that are
+
+ align:start position:0%
+they're the most common things that are
+ 
+
+ align:start position:0%
+they're the most common things that are
+produced
+
+ align:start position:0%
+produced
+ 
+
+ align:start position:0%
+produced
+and from a physics point of view that
+
+ align:start position:0%
+and from a physics point of view that
+ 
+
+ align:start position:0%
+and from a physics point of view that
+means that there's many many different
+
+ align:start position:0%
+means that there's many many different
+ 
+
+ align:start position:0%
+means that there's many many different
+processes that you can actually use this
+
+ align:start position:0%
+processes that you can actually use this
+ 
+
+ align:start position:0%
+processes that you can actually use this
+effective field theory for and that's
+
+ align:start position:0%
+effective field theory for and that's
+ 
+
+ align:start position:0%
+effective field theory for and that's
+one of the reasons it's popular
+
+ align:start position:0%
+one of the reasons it's popular
+ 
+
+ align:start position:0%
+one of the reasons it's popular
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me give you some examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could do deep inelastic scattering
+
+ align:start position:0%
+you could do deep inelastic scattering
+ 
+
+ align:start position:0%
+you could do deep inelastic scattering
+with this effective theory deep in
+
+ align:start position:0%
+with this effective theory deep in
+ 
+
+ align:start position:0%
+with this effective theory deep in
+elastic scattering involves a hard
+
+ align:start position:0%
+elastic scattering involves a hard
+ 
+
+ align:start position:0%
+elastic scattering involves a hard
+collision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and even class classic textbook deep
+
+ align:start position:0%
+and even class classic textbook deep
+ 
+
+ align:start position:0%
+and even class classic textbook deep
+inelastic scattering is made very much
+
+ align:start position:0%
+inelastic scattering is made very much
+ 
+
+ align:start position:0%
+inelastic scattering is made very much
+simpler by this effective field theory
+
+ align:start position:0%
+simpler by this effective field theory
+ 
+
+ align:start position:0%
+simpler by this effective field theory
+and we'll
+
+ align:start position:0%
+and we'll
+ 
+
+ align:start position:0%
+and we'll
+show you that example is one of our
+
+ align:start position:0%
+show you that example is one of our
+ 
+
+ align:start position:0%
+show you that example is one of our
+examples later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on you could do dualian with
+
+ align:start position:0%
+on you could do dualian with
+ 
+
+ align:start position:0%
+on you could do dualian with
+either protons and antiprotons or
+
+ align:start position:0%
+either protons and antiprotons or
+ 
+
+ align:start position:0%
+either protons and antiprotons or
+protons and protons
+
+ align:start position:0%
+protons and protons
+ 
+
+ align:start position:0%
+protons and protons
+you could do
+
+ align:start position:0%
+you could do
+ 
+
+ align:start position:0%
+you could do
+higgs production
+
+ align:start position:0%
+higgs production
+ 
+
+ align:start position:0%
+higgs production
+and people use this effective field
+
+ align:start position:0%
+and people use this effective field
+ 
+
+ align:start position:0%
+and people use this effective field
+theory to study higgs production
+
+ align:start position:0%
+theory to study higgs production
+ 
+
+ align:start position:0%
+theory to study higgs production
+at the lhc
+
+ align:start position:0%
+at the lhc
+ 
+
+ align:start position:0%
+at the lhc
+you could do it by way of trying to make
+
+ align:start position:0%
+you could do it by way of trying to make
+ 
+
+ align:start position:0%
+you could do it by way of trying to make
+the examples more varied
+
+ align:start position:0%
+the examples more varied
+ 
+
+ align:start position:0%
+the examples more varied
+e plus e minus two jets this is another
+
+ align:start position:0%
+e plus e minus two jets this is another
+ 
+
+ align:start position:0%
+e plus e minus two jets this is another
+thing that the effective theory is used
+
+ align:start position:0%
+thing that the effective theory is used
+ 
+
+ align:start position:0%
+thing that the effective theory is used
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+you could do quarkonia physics e plus
+
+ align:start position:0%
+you could do quarkonia physics e plus
+ 
+
+ align:start position:0%
+you could do quarkonia physics e plus
+and minus producing a j psi and an x
+
+ align:start position:0%
+and minus producing a j psi and an x
+ 
+
+ align:start position:0%
+and minus producing a j psi and an x
+uh here you need a combination if the
+
+ align:start position:0%
+uh here you need a combination if the
+ 
+
+ align:start position:0%
+uh here you need a combination if the
+json is produced at large energy of kind
+
+ align:start position:0%
+json is produced at large energy of kind
+ 
+
+ align:start position:0%
+json is produced at large energy of kind
+of a non-relativistic qcd for this cc
+
+ align:start position:0%
+of a non-relativistic qcd for this cc
+ 
+
+ align:start position:0%
+of a non-relativistic qcd for this cc
+bar bound state
+
+ align:start position:0%
+bar bound state
+ 
+
+ align:start position:0%
+bar bound state
+as well as an sct for the fact that it's
+
+ align:start position:0%
+as well as an sct for the fact that it's
+ 
+
+ align:start position:0%
+as well as an sct for the fact that it's
+a energetic state
+
+ align:start position:0%
+a energetic state
+ 
+
+ align:start position:0%
+a energetic state
+so this would be actually a combination
+
+ align:start position:0%
+so this would be actually a combination
+ 
+
+ align:start position:0%
+so this would be actually a combination
+of two different effective field
+
+ align:start position:0%
+of two different effective field
+ 
+
+ align:start position:0%
+of two different effective field
+theories
+
+ align:start position:0%
+theories
+ 
+
+ align:start position:0%
+theories
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+use it for thinking about jet
+
+ align:start position:0%
+use it for thinking about jet
+ 
+
+ align:start position:0%
+use it for thinking about jet
+substructure
+
+ align:start position:0%
+substructure
+ 
+
+ align:start position:0%
+substructure
+so all sorts of things that you might be
+
+ align:start position:0%
+so all sorts of things that you might be
+ 
+
+ align:start position:0%
+so all sorts of things that you might be
+interested in and thinking about having
+
+ align:start position:0%
+interested in and thinking about having
+ 
+
+ align:start position:0%
+interested in and thinking about having
+to do with hard scattering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's also another way that you could
+
+ align:start position:0%
+there's also another way that you could
+ 
+
+ align:start position:0%
+there's also another way that you could
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+energetic particles even if you don't
+
+ align:start position:0%
+energetic particles even if you don't
+ 
+
+ align:start position:0%
+energetic particles even if you don't
+force them to be energetic and that is
+
+ align:start position:0%
+force them to be energetic and that is
+ 
+
+ align:start position:0%
+force them to be energetic and that is
+if you had a very heavy particle
+
+ align:start position:0%
+if you had a very heavy particle
+ 
+
+ align:start position:0%
+if you had a very heavy particle
+decaying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you had a beam as on decaying and
+
+ align:start position:0%
+so if you had a beam as on decaying and
+ 
+
+ align:start position:0%
+so if you had a beam as on decaying and
+it decayed to light stuff
+
+ align:start position:0%
+it decayed to light stuff
+ 
+
+ align:start position:0%
+it decayed to light stuff
+this would also be the right effective
+
+ align:start position:0%
+this would also be the right effective
+ 
+
+ align:start position:0%
+this would also be the right effective
+theory for that
+
+ align:start position:0%
+theory for that
+ 
+
+ align:start position:0%
+theory for that
+so for example in the process bds gamma
+
+ align:start position:0%
+so for example in the process bds gamma
+ 
+
+ align:start position:0%
+so for example in the process bds gamma
+this effective theory plays a role
+
+ align:start position:0%
+this effective theory plays a role
+ 
+
+ align:start position:0%
+this effective theory plays a role
+in the process b to d pi where the pion
+
+ align:start position:0%
+in the process b to d pi where the pion
+ 
+
+ align:start position:0%
+in the process b to d pi where the pion
+comes out very energetic
+
+ align:start position:0%
+comes out very energetic
+ 
+
+ align:start position:0%
+comes out very energetic
+or b to pi pi which is something very
+
+ align:start position:0%
+or b to pi pi which is something very
+ 
+
+ align:start position:0%
+or b to pi pi which is something very
+interesting for studying cp violation
+
+ align:start position:0%
+interesting for studying cp violation
+ 
+
+ align:start position:0%
+interesting for studying cp violation
+you can use this effective theory to
+
+ align:start position:0%
+you can use this effective theory to
+ 
+
+ align:start position:0%
+you can use this effective theory to
+understand the short and long distance
+
+ align:start position:0%
+understand the short and long distance
+ 
+
+ align:start position:0%
+understand the short and long distance
+physics in those processes as well
+
+ align:start position:0%
+physics in those processes as well
+ 
+
+ align:start position:0%
+physics in those processes as well
+okay and this is coming about because
+
+ align:start position:0%
+okay and this is coming about because
+ 
+
+ align:start position:0%
+okay and this is coming about because
+this b meson is heavy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a sort of range of
+
+ align:start position:0%
+so that's a sort of range of
+ 
+
+ align:start position:0%
+so that's a sort of range of
+examples and it's really not really
+
+ align:start position:0%
+examples and it's really not really
+ 
+
+ align:start position:0%
+examples and it's really not really
+complete in any sense there's just lots
+
+ align:start position:0%
+complete in any sense there's just lots
+ 
+
+ align:start position:0%
+complete in any sense there's just lots
+of different things you can
+
+ align:start position:0%
+of different things you can
+ 
+
+ align:start position:0%
+of different things you can
+study with this theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this i already said let me write it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i sort of alluded to separating
+
+ align:start position:0%
+i sort of alluded to separating
+ 
+
+ align:start position:0%
+i sort of alluded to separating
+perturbative physics
+
+ align:start position:0%
+perturbative physics
+ 
+
+ align:start position:0%
+perturbative physics
+at short distances
+
+ align:start position:0%
+at short distances
+ 
+
+ align:start position:0%
+at short distances
+from the non-perturbative physics
+
+ align:start position:0%
+from the non-perturbative physics
+ 
+
+ align:start position:0%
+from the non-perturbative physics
+at long distances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the non-protective physics if you're
+
+ align:start position:0%
+and the non-protective physics if you're
+ 
+
+ align:start position:0%
+and the non-protective physics if you're
+lucky maybe only encoded in part-time
+
+ align:start position:0%
+lucky maybe only encoded in part-time
+ 
+
+ align:start position:0%
+lucky maybe only encoded in part-time
+distribution functions or something if
+
+ align:start position:0%
+distribution functions or something if
+ 
+
+ align:start position:0%
+distribution functions or something if
+you're doing a pp collision
+
+ align:start position:0%
+you're doing a pp collision
+ 
+
+ align:start position:0%
+you're doing a pp collision
+and you'd like to separate that from
+
+ align:start position:0%
+and you'd like to separate that from
+ 
+
+ align:start position:0%
+and you'd like to separate that from
+shorter distance physics that you can
+
+ align:start position:0%
+shorter distance physics that you can
+ 
+
+ align:start position:0%
+shorter distance physics that you can
+calculate perturbatively and this is a
+
+ align:start position:0%
+calculate perturbatively and this is a
+ 
+
+ align:start position:0%
+calculate perturbatively and this is a
+way of doing that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+there's our normalization group in this
+
+ align:start position:0%
+there's our normalization group in this
+ 
+
+ align:start position:0%
+there's our normalization group in this
+effective theory
+
+ align:start position:0%
+effective theory
+ 
+
+ align:start position:0%
+effective theory
+and that normalization group actually
+
+ align:start position:0%
+and that normalization group actually
+ 
+
+ align:start position:0%
+and that normalization group actually
+allows you to do something cool too
+
+ align:start position:0%
+allows you to do something cool too
+ 
+
+ align:start position:0%
+allows you to do something cool too
+and that is that you can sum up
+
+ align:start position:0%
+and that is that you can sum up
+ 
+
+ align:start position:0%
+and that is that you can sum up
+something called
+
+ align:start position:0%
+something called
+ 
+
+ align:start position:0%
+something called
+sudikov logarithms which are logarithms
+
+ align:start position:0%
+sudikov logarithms which are logarithms
+ 
+
+ align:start position:0%
+sudikov logarithms which are logarithms
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+are appearing in our canonical way as
+
+ align:start position:0%
+are appearing in our canonical way as
+ 
+
+ align:start position:0%
+are appearing in our canonical way as
+alpha s times a logarithm
+
+ align:start position:0%
+alpha s times a logarithm
+ 
+
+ align:start position:0%
+alpha s times a logarithm
+but instead of one logarithm you
+
+ align:start position:0%
+but instead of one logarithm you
+ 
+
+ align:start position:0%
+but instead of one logarithm you
+actually get two
+
+ align:start position:0%
+actually get two
+ 
+
+ align:start position:0%
+actually get two
+and so the normalization group in this
+
+ align:start position:0%
+and so the normalization group in this
+ 
+
+ align:start position:0%
+and so the normalization group in this
+effective theory will allow you to
+
+ align:start position:0%
+effective theory will allow you to
+ 
+
+ align:start position:0%
+effective theory will allow you to
+handle those pseudocop logarithms
+
+ align:start position:0%
+handle those pseudocop logarithms
+ 
+
+ align:start position:0%
+handle those pseudocop logarithms
+okay so that's some set of things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are we going to have to do that we
+
+ align:start position:0%
+what are we going to have to do that we
+ 
+
+ align:start position:0%
+what are we going to have to do that we
+haven't done before what are the kind of
+
+ align:start position:0%
+haven't done before what are the kind of
+ 
+
+ align:start position:0%
+haven't done before what are the kind of
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+ingredients that we're going to run into
+
+ align:start position:0%
+ingredients that we're going to run into
+ 
+
+ align:start position:0%
+ingredients that we're going to run into
+so sort of a prelude to things to come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or another way of saying what makes sct
+
+ align:start position:0%
+or another way of saying what makes sct
+ 
+
+ align:start position:0%
+or another way of saying what makes sct
+different from the effective theories
+
+ align:start position:0%
+different from the effective theories
+ 
+
+ align:start position:0%
+different from the effective theories
+we've seen so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's have a little list for that as
+
+ align:start position:0%
+let's have a little list for that as
+ 
+
+ align:start position:0%
+let's have a little list for that as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+so perhaps the most uh interesting one
+
+ align:start position:0%
+so perhaps the most uh interesting one
+ 
+
+ align:start position:0%
+so perhaps the most uh interesting one
+is that we are going to have
+
+ align:start position:0%
+is that we are going to have
+ 
+
+ align:start position:0%
+is that we are going to have
+more than one field
+
+ align:start position:0%
+more than one field
+ 
+
+ align:start position:0%
+more than one field
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+each degree of freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to have more than one
+
+ align:start position:0%
+so we're going to have more than one
+ 
+
+ align:start position:0%
+so we're going to have more than one
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+that's not quite the right way of saying
+
+ align:start position:0%
+that's not quite the right way of saying
+ 
+
+ align:start position:0%
+that's not quite the right way of saying
+it we're going to have more than one
+
+ align:start position:0%
+it we're going to have more than one
+ 
+
+ align:start position:0%
+it we're going to have more than one
+field for the same particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a slightly different statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to have a field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we'll talk about
+
+ align:start position:0%
+which we'll talk about
+ 
+
+ align:start position:0%
+which we'll talk about
+that i'll call c sub n which is a linear
+
+ align:start position:0%
+that i'll call c sub n which is a linear
+ 
+
+ align:start position:0%
+that i'll call c sub n which is a linear
+cork field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for some quark say an up quark
+
+ align:start position:0%
+for some quark say an up quark
+ 
+
+ align:start position:0%
+for some quark say an up quark
+and there's also going to be another
+
+ align:start position:0%
+and there's also going to be another
+ 
+
+ align:start position:0%
+and there's also going to be another
+field q sub s
+
+ align:start position:0%
+field q sub s
+ 
+
+ align:start position:0%
+field q sub s
+which is a soft cork field for the same
+
+ align:start position:0%
+which is a soft cork field for the same
+ 
+
+ align:start position:0%
+which is a soft cork field for the same
+up quark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say for the up quark say just
+
+ align:start position:0%
+so let's say for the up quark say just
+ 
+
+ align:start position:0%
+so let's say for the up quark say just
+to make it definite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason that we're going to have
+
+ align:start position:0%
+and the reason that we're going to have
+ 
+
+ align:start position:0%
+and the reason that we're going to have
+these two different fields is because
+
+ align:start position:0%
+these two different fields is because
+ 
+
+ align:start position:0%
+these two different fields is because
+they're going to describe the same
+
+ align:start position:0%
+they're going to describe the same
+ 
+
+ align:start position:0%
+they're going to describe the same
+particle but in different regions of
+
+ align:start position:0%
+particle but in different regions of
+ 
+
+ align:start position:0%
+particle but in different regions of
+momentum space
+
+ align:start position:0%
+momentum space
+ 
+
+ align:start position:0%
+momentum space
+so if you're like they're describing
+
+ align:start position:0%
+so if you're like they're describing
+ 
+
+ align:start position:0%
+so if you're like they're describing
+different degrees of freedom of the same
+
+ align:start position:0%
+different degrees of freedom of the same
+ 
+
+ align:start position:0%
+different degrees of freedom of the same
+particle because they're in different
+
+ align:start position:0%
+particle because they're in different
+ 
+
+ align:start position:0%
+particle because they're in different
+regions of momentum space but it still
+
+ align:start position:0%
+regions of momentum space but it still
+ 
+
+ align:start position:0%
+regions of momentum space but it still
+is the same particle and that's not
+
+ align:start position:0%
+is the same particle and that's not
+ 
+
+ align:start position:0%
+is the same particle and that's not
+something we've had to deal with
+
+ align:start position:0%
+something we've had to deal with
+ 
+
+ align:start position:0%
+something we've had to deal with
+in any of our examples so far we always
+
+ align:start position:0%
+in any of our examples so far we always
+ 
+
+ align:start position:0%
+in any of our examples so far we always
+had one field for each particle now
+
+ align:start position:0%
+had one field for each particle now
+ 
+
+ align:start position:0%
+had one field for each particle now
+we're going to have more than one
+
+ align:start position:0%
+we're going to have more than one
+ 
+
+ align:start position:0%
+we're going to have more than one
+so that's one complication
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this second one we have actually
+
+ align:start position:0%
+this second one we have actually
+ 
+
+ align:start position:0%
+this second one we have actually
+encountered before
+
+ align:start position:0%
+encountered before
+ 
+
+ align:start position:0%
+encountered before
+and that is that we're going to
+
+ align:start position:0%
+and that is that we're going to
+ 
+
+ align:start position:0%
+and that is that we're going to
+integrate out
+
+ align:start position:0%
+integrate out
+ 
+
+ align:start position:0%
+integrate out
+off shell modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a field
+
+ align:start position:0%
+of a field
+ 
+
+ align:start position:0%
+of a field
+but not the entire
+
+ align:start position:0%
+but not the entire
+ 
+
+ align:start position:0%
+but not the entire
+not the entire
+
+ align:start position:0%
+not the entire
+ 
+
+ align:start position:0%
+not the entire
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not the entire degree of freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we encountered that when we talked
+
+ align:start position:0%
+and we encountered that when we talked
+ 
+
+ align:start position:0%
+and we encountered that when we talked
+about hqt
+
+ align:start position:0%
+about hqt
+ 
+
+ align:start position:0%
+about hqt
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the situation here will be a little more
+
+ align:start position:0%
+the situation here will be a little more
+ 
+
+ align:start position:0%
+the situation here will be a little more
+complicated than hqet but
+
+ align:start position:0%
+complicated than hqet but
+ 
+
+ align:start position:0%
+complicated than hqet but
+this second point is like hqet and we'll
+
+ align:start position:0%
+this second point is like hqet and we'll
+ 
+
+ align:start position:0%
+this second point is like hqet and we'll
+use some of our experience that
+
+ align:start position:0%
+use some of our experience that
+ 
+
+ align:start position:0%
+use some of our experience that
+we gained from studying hqt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which one it never can be
+
+ align:start position:0%
+which one it never can be
+ 
+
+ align:start position:0%
+which one it never can be
+right both
+
+ align:start position:0%
+right both
+ 
+
+ align:start position:0%
+right both
+it will have to decide whether it's one
+
+ align:start position:0%
+it will have to decide whether it's one
+ 
+
+ align:start position:0%
+it will have to decide whether it's one
+or the other
+
+ align:start position:0%
+or the other
+ 
+
+ align:start position:0%
+or the other
+so an important thing
+
+ align:start position:0%
+so an important thing
+ 
+
+ align:start position:0%
+so an important thing
+exactly this issue of which which is it
+
+ align:start position:0%
+exactly this issue of which which is it
+ 
+
+ align:start position:0%
+exactly this issue of which which is it
+is an important thing because you you're
+
+ align:start position:0%
+is an important thing because you you're
+ 
+
+ align:start position:0%
+is an important thing because you you're
+going to be describing with these fields
+
+ align:start position:0%
+going to be describing with these fields
+ 
+
+ align:start position:0%
+going to be describing with these fields
+certain fluctuations and you don't want
+
+ align:start position:0%
+certain fluctuations and you don't want
+ 
+
+ align:start position:0%
+certain fluctuations and you don't want
+overlap
+
+ align:start position:0%
+overlap
+ 
+
+ align:start position:0%
+overlap
+so you're going to have to if you point
+
+ align:start position:0%
+so you're going to have to if you point
+ 
+
+ align:start position:0%
+so you're going to have to if you point
+your finger somewhere in momentum space
+
+ align:start position:0%
+your finger somewhere in momentum space
+ 
+
+ align:start position:0%
+your finger somewhere in momentum space
+we'll have to decide is it in this
+
+ align:start position:0%
+we'll have to decide is it in this
+ 
+
+ align:start position:0%
+we'll have to decide is it in this
+category this category it can't be in
+
+ align:start position:0%
+category this category it can't be in
+ 
+
+ align:start position:0%
+category this category it can't be in
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+but that will be important that that
+
+ align:start position:0%
+but that will be important that that
+ 
+
+ align:start position:0%
+but that will be important that that
+will come back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two regions
+
+ align:start position:0%
+two regions
+ 
+
+ align:start position:0%
+two regions
+and no overlap
+
+ align:start position:0%
+and no overlap
+ 
+
+ align:start position:0%
+and no overlap
+but we'll have to work a little bit to
+
+ align:start position:0%
+but we'll have to work a little bit to
+ 
+
+ align:start position:0%
+but we'll have to work a little bit to
+make sure that's true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah we don't want to make sure to not
+
+ align:start position:0%
+yeah we don't want to make sure to not
+ 
+
+ align:start position:0%
+yeah we don't want to make sure to not
+have double counting in the effective
+
+ align:start position:0%
+have double counting in the effective
+ 
+
+ align:start position:0%
+have double counting in the effective
+theory where you know we could write
+
+ align:start position:0%
+theory where you know we could write
+ 
+
+ align:start position:0%
+theory where you know we could write
+down something
+
+ align:start position:0%
+down something
+ 
+
+ align:start position:0%
+down something
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+looks like it could be described by
+
+ align:start position:0%
+looks like it could be described by
+ 
+
+ align:start position:0%
+looks like it could be described by
+either one and if that was true then we
+
+ align:start position:0%
+either one and if that was true then we
+ 
+
+ align:start position:0%
+either one and if that was true then we
+would be have a problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so another thing that makes sct
+
+ align:start position:0%
+so another thing that makes sct
+ 
+
+ align:start position:0%
+so another thing that makes sct
+interesting from a
+
+ align:start position:0%
+interesting from a
+ 
+
+ align:start position:0%
+interesting from a
+eft point of view is that we have
+
+ align:start position:0%
+eft point of view is that we have
+ 
+
+ align:start position:0%
+eft point of view is that we have
+convolutions
+
+ align:start position:0%
+convolutions
+ 
+
+ align:start position:0%
+convolutions
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+usually in an effective theory you think
+
+ align:start position:0%
+usually in an effective theory you think
+ 
+
+ align:start position:0%
+usually in an effective theory you think
+about having multiple operators that
+
+ align:start position:0%
+about having multiple operators that
+ 
+
+ align:start position:0%
+about having multiple operators that
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+same quantum numbers we sum over those
+
+ align:start position:0%
+same quantum numbers we sum over those
+ 
+
+ align:start position:0%
+same quantum numbers we sum over those
+operators say some order in the power
+
+ align:start position:0%
+operators say some order in the power
+ 
+
+ align:start position:0%
+operators say some order in the power
+counting
+
+ align:start position:0%
+counting
+ 
+
+ align:start position:0%
+counting
+some over i of wilson coefficients times
+
+ align:start position:0%
+some over i of wilson coefficients times
+ 
+
+ align:start position:0%
+some over i of wilson coefficients times
+operators
+
+ align:start position:0%
+operators
+ 
+
+ align:start position:0%
+operators
+and this sum becomes a continuous
+
+ align:start position:0%
+and this sum becomes a continuous
+ 
+
+ align:start position:0%
+and this sum becomes a continuous
+integral in the
+
+ align:start position:0%
+integral in the
+ 
+
+ align:start position:0%
+integral in the
+in sct
+
+ align:start position:0%
+in sct
+ 
+
+ align:start position:0%
+in sct
+we'll see how that works
+
+ align:start position:0%
+we'll see how that works
+ 
+
+ align:start position:0%
+we'll see how that works
+and that actually leads to convolutions
+
+ align:start position:0%
+and that actually leads to convolutions
+ 
+
+ align:start position:0%
+and that actually leads to convolutions
+in fact exactly this little manipulation
+
+ align:start position:0%
+in fact exactly this little manipulation
+ 
+
+ align:start position:0%
+in fact exactly this little manipulation
+here is what leads to the convolution of
+
+ align:start position:0%
+here is what leads to the convolution of
+ 
+
+ align:start position:0%
+here is what leads to the convolution of
+the part-time distribution function
+
+ align:start position:0%
+the part-time distribution function
+ 
+
+ align:start position:0%
+the part-time distribution function
+with heart scattering if you think about
+
+ align:start position:0%
+with heart scattering if you think about
+ 
+
+ align:start position:0%
+with heart scattering if you think about
+this operator as describing
+
+ align:start position:0%
+this operator as describing
+ 
+
+ align:start position:0%
+this operator as describing
+the matrix elements of this operator as
+
+ align:start position:0%
+the matrix elements of this operator as
+ 
+
+ align:start position:0%
+the matrix elements of this operator as
+describing a part-time distribution
+
+ align:start position:0%
+describing a part-time distribution
+ 
+
+ align:start position:0%
+describing a part-time distribution
+function the wilson's coefficients is
+
+ align:start position:0%
+function the wilson's coefficients is
+ 
+
+ align:start position:0%
+function the wilson's coefficients is
+describing the hard scattering exactly
+
+ align:start position:0%
+describing the hard scattering exactly
+ 
+
+ align:start position:0%
+describing the hard scattering exactly
+this integral is what leads to the
+
+ align:start position:0%
+this integral is what leads to the
+ 
+
+ align:start position:0%
+this integral is what leads to the
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+that convolutes together part-time
+
+ align:start position:0%
+that convolutes together part-time
+ 
+
+ align:start position:0%
+that convolutes together part-time
+distribution functions
+
+ align:start position:0%
+distribution functions
+ 
+
+ align:start position:0%
+distribution functions
+and hard scattering matrix almonds
+
+ align:start position:0%
+and hard scattering matrix almonds
+ 
+
+ align:start position:0%
+and hard scattering matrix almonds
+come back to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's going to be a power counting
+
+ align:start position:0%
+so there's going to be a power counting
+ 
+
+ align:start position:0%
+so there's going to be a power counting
+for this effective theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to call the power
+
+ align:start position:0%
+and we're going to call the power
+ 
+
+ align:start position:0%
+and we're going to call the power
+counting parameter lambda
+
+ align:start position:0%
+counting parameter lambda
+ 
+
+ align:start position:0%
+counting parameter lambda
+and it's not going to be related to the
+
+ align:start position:0%
+and it's not going to be related to the
+ 
+
+ align:start position:0%
+and it's not going to be related to the
+mass dimension of fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll have to figure out
+
+ align:start position:0%
+we'll have to figure out
+ 
+
+ align:start position:0%
+we'll have to figure out
+how to do the power counting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's going to be something called the
+
+ align:start position:0%
+there's going to be something called the
+ 
+
+ align:start position:0%
+there's going to be something called the
+wilson line
+
+ align:start position:0%
+wilson line
+ 
+
+ align:start position:0%
+wilson line
+which show up all over the place in this
+
+ align:start position:0%
+which show up all over the place in this
+ 
+
+ align:start position:0%
+which show up all over the place in this
+effective theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are lines in space that are
+
+ align:start position:0%
+so these are lines in space that are
+ 
+
+ align:start position:0%
+so these are lines in space that are
+coupled to the gauge field a
+
+ align:start position:0%
+coupled to the gauge field a
+ 
+
+ align:start position:0%
+coupled to the gauge field a
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we'll see why they're showing up but
+
+ align:start position:0%
+we'll see why they're showing up but
+ 
+
+ align:start position:0%
+we'll see why they're showing up but
+it's related actually to the fact that
+
+ align:start position:0%
+it's related actually to the fact that
+ 
+
+ align:start position:0%
+it's related actually to the fact that
+this effective theory has a very
+
+ align:start position:0%
+this effective theory has a very
+ 
+
+ align:start position:0%
+this effective theory has a very
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+and perhaps subtle
+
+ align:start position:0%
+and perhaps subtle
+ 
+
+ align:start position:0%
+and perhaps subtle
+gauge symmetry structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one way of actually already seeing why
+
+ align:start position:0%
+one way of actually already seeing why
+ 
+
+ align:start position:0%
+one way of actually already seeing why
+that is true is because i told you over
+
+ align:start position:0%
+that is true is because i told you over
+ 
+
+ align:start position:0%
+that is true is because i told you over
+here that we have two types of quarks
+
+ align:start position:0%
+here that we have two types of quarks
+ 
+
+ align:start position:0%
+here that we have two types of quarks
+everything i say about quarks is also
+
+ align:start position:0%
+everything i say about quarks is also
+ 
+
+ align:start position:0%
+everything i say about quarks is also
+true of gluon so there's going to be two
+
+ align:start position:0%
+true of gluon so there's going to be two
+ 
+
+ align:start position:0%
+true of gluon so there's going to be two
+types of gluons an a n gluon and a s
+
+ align:start position:0%
+types of gluons an a n gluon and a s
+ 
+
+ align:start position:0%
+types of gluons an a n gluon and a s
+gluon
+
+ align:start position:0%
+gluon
+ 
+
+ align:start position:0%
+gluon
+and once there's two types of gluons you
+
+ align:start position:0%
+and once there's two types of gluons you
+ 
+
+ align:start position:0%
+and once there's two types of gluons you
+should say well what's the gauge group
+
+ align:start position:0%
+should say well what's the gauge group
+ 
+
+ align:start position:0%
+should say well what's the gauge group
+of this gluon and what's the gauge group
+
+ align:start position:0%
+of this gluon and what's the gauge group
+ 
+
+ align:start position:0%
+of this gluon and what's the gauge group
+of that glue well they're both the same
+
+ align:start position:0%
+of that glue well they're both the same
+ 
+
+ align:start position:0%
+of that glue well they're both the same
+gauge group it's qcd
+
+ align:start position:0%
+gauge group it's qcd
+ 
+
+ align:start position:0%
+gauge group it's qcd
+so we've partitioned qcd in some
+
+ align:start position:0%
+so we've partitioned qcd in some
+ 
+
+ align:start position:0%
+so we've partitioned qcd in some
+kind of weird way where we have two
+
+ align:start position:0%
+kind of weird way where we have two
+ 
+
+ align:start position:0%
+kind of weird way where we have two
+fields for the gage group rather than
+
+ align:start position:0%
+fields for the gage group rather than
+ 
+
+ align:start position:0%
+fields for the gage group rather than
+just one
+
+ align:start position:0%
+just one
+ 
+
+ align:start position:0%
+just one
+part of that story is going to be
+
+ align:start position:0%
+part of that story is going to be
+ 
+
+ align:start position:0%
+part of that story is going to be
+related to these wilson lines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally one final kind of
+
+ align:start position:0%
+and finally one final kind of
+ 
+
+ align:start position:0%
+and finally one final kind of
+interesting thing that's going to happen
+
+ align:start position:0%
+interesting thing that's going to happen
+ 
+
+ align:start position:0%
+interesting thing that's going to happen
+is we're going to see when we do one
+
+ align:start position:0%
+is we're going to see when we do one
+ 
+
+ align:start position:0%
+is we're going to see when we do one
+loop calculations in this theory
+
+ align:start position:0%
+loop calculations in this theory
+ 
+
+ align:start position:0%
+loop calculations in this theory
+that we find one over epsilon squared
+
+ align:start position:0%
+that we find one over epsilon squared
+ 
+
+ align:start position:0%
+that we find one over epsilon squared
+divergences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so usually when you do an effective
+
+ align:start position:0%
+so usually when you do an effective
+ 
+
+ align:start position:0%
+so usually when you do an effective
+field theory calculation at one loop you
+
+ align:start position:0%
+field theory calculation at one loop you
+ 
+
+ align:start position:0%
+field theory calculation at one loop you
+find a one over epsilon
+
+ align:start position:0%
+find a one over epsilon
+ 
+
+ align:start position:0%
+find a one over epsilon
+pull not a one over epsilon squared
+
+ align:start position:0%
+pull not a one over epsilon squared
+ 
+
+ align:start position:0%
+pull not a one over epsilon squared
+and i don't
+
+ align:start position:0%
+and i don't
+ 
+
+ align:start position:0%
+and i don't
+denote it by epsilon u v because both
+
+ align:start position:0%
+denote it by epsilon u v because both
+ 
+
+ align:start position:0%
+denote it by epsilon u v because both
+poles here require
+
+ align:start position:0%
+poles here require
+ 
+
+ align:start position:0%
+poles here require
+u v or normalization
+
+ align:start position:0%
+u v or normalization
+ 
+
+ align:start position:0%
+u v or normalization
+we need to add a counter term to cancel
+
+ align:start position:0%
+we need to add a counter term to cancel
+ 
+
+ align:start position:0%
+we need to add a counter term to cancel
+this double pole
+
+ align:start position:0%
+this double pole
+ 
+
+ align:start position:0%
+this double pole
+and exactly the presence of that double
+
+ align:start position:0%
+and exactly the presence of that double
+ 
+
+ align:start position:0%
+and exactly the presence of that double
+pole is what leads to these
+
+ align:start position:0%
+pole is what leads to these
+ 
+
+ align:start position:0%
+pole is what leads to these
+pseudocoph logs that i was mentioning
+
+ align:start position:0%
+pseudocoph logs that i was mentioning
+ 
+
+ align:start position:0%
+pseudocoph logs that i was mentioning
+the fact that we have these double logs
+
+ align:start position:0%
+the fact that we have these double logs
+ 
+
+ align:start position:0%
+the fact that we have these double logs
+going along with each alpha s
+
+ align:start position:0%
+going along with each alpha s
+ 
+
+ align:start position:0%
+going along with each alpha s
+so we'll see that the taking care of
+
+ align:start position:0%
+so we'll see that the taking care of
+ 
+
+ align:start position:0%
+so we'll see that the taking care of
+this for normalization which is a little
+
+ align:start position:0%
+this for normalization which is a little
+ 
+
+ align:start position:0%
+this for normalization which is a little
+different than the normalization you're
+
+ align:start position:0%
+different than the normalization you're
+ 
+
+ align:start position:0%
+different than the normalization you're
+used to
+
+ align:start position:0%
+used to
+ 
+
+ align:start position:0%
+used to
+will allow us to sum up those pseudocoph
+
+ align:start position:0%
+will allow us to sum up those pseudocoph
+ 
+
+ align:start position:0%
+will allow us to sum up those pseudocoph
+logarithms
+
+ align:start position:0%
+logarithms
+ 
+
+ align:start position:0%
+logarithms
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's a kind of
+
+ align:start position:0%
+so that's a kind of
+ 
+
+ align:start position:0%
+so that's a kind of
+hint of the things that we will be
+
+ align:start position:0%
+hint of the things that we will be
+ 
+
+ align:start position:0%
+hint of the things that we will be
+studying
+
+ align:start position:0%
+studying
+ 
+
+ align:start position:0%
+studying
+not supposed to understand any of them
+
+ align:start position:0%
+not supposed to understand any of them
+ 
+
+ align:start position:0%
+not supposed to understand any of them
+yet unless you studied sct but we will
+
+ align:start position:0%
+yet unless you studied sct but we will
+ 
+
+ align:start position:0%
+yet unless you studied sct but we will
+understand all of these by the end of
+
+ align:start position:0%
+understand all of these by the end of
+ 
+
+ align:start position:0%
+understand all of these by the end of
+the course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+any question anything i missed on my
+
+ align:start position:0%
+any question anything i missed on my
+ 
+
+ align:start position:0%
+any question anything i missed on my
+list
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's spend some time talking about
+
+ align:start position:0%
+so let's spend some time talking about
+ 
+
+ align:start position:0%
+so let's spend some time talking about
+degrees of freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way i like to think about degrees of
+
+ align:start position:0%
+the way i like to think about degrees of
+ 
+
+ align:start position:0%
+the way i like to think about degrees of
+freedom for any effective field theory
+
+ align:start position:0%
+freedom for any effective field theory
+ 
+
+ align:start position:0%
+freedom for any effective field theory
+is this is where you have to think about
+
+ align:start position:0%
+is this is where you have to think about
+ 
+
+ align:start position:0%
+is this is where you have to think about
+the physics of what you're doing
+
+ align:start position:0%
+the physics of what you're doing
+ 
+
+ align:start position:0%
+the physics of what you're doing
+okay so let's think about some physical
+
+ align:start position:0%
+okay so let's think about some physical
+ 
+
+ align:start position:0%
+okay so let's think about some physical
+process i'm going to consider two
+
+ align:start position:0%
+process i'm going to consider two
+ 
+
+ align:start position:0%
+process i'm going to consider two
+different physical processes
+
+ align:start position:0%
+different physical processes
+ 
+
+ align:start position:0%
+different physical processes
+actually today i'll only start talking
+
+ align:start position:0%
+actually today i'll only start talking
+ 
+
+ align:start position:0%
+actually today i'll only start talking
+about one of them and then we'll talk
+
+ align:start position:0%
+about one of them and then we'll talk
+ 
+
+ align:start position:0%
+about one of them and then we'll talk
+about the other one next time
+
+ align:start position:0%
+about the other one next time
+ 
+
+ align:start position:0%
+about the other one next time
+think about some physical process and
+
+ align:start position:0%
+think about some physical process and
+ 
+
+ align:start position:0%
+think about some physical process and
+try to identify what the right degrees
+
+ align:start position:0%
+try to identify what the right degrees
+ 
+
+ align:start position:0%
+try to identify what the right degrees
+of freedom are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you could look at the process of a
+
+ align:start position:0%
+so you could look at the process of a
+ 
+
+ align:start position:0%
+so you could look at the process of a
+beam azon changing into a d meson and a
+
+ align:start position:0%
+beam azon changing into a d meson and a
+ 
+
+ align:start position:0%
+beam azon changing into a d meson and a
+pion
+
+ align:start position:0%
+pion
+ 
+
+ align:start position:0%
+pion
+the advantage of starting with this one
+
+ align:start position:0%
+the advantage of starting with this one
+ 
+
+ align:start position:0%
+the advantage of starting with this one
+is that we've already talked about hqet
+
+ align:start position:0%
+is that we've already talked about hqet
+ 
+
+ align:start position:0%
+is that we've already talked about hqet
+so we understand how to do b mesons and
+
+ align:start position:0%
+so we understand how to do b mesons and
+ 
+
+ align:start position:0%
+so we understand how to do b mesons and
+d masons we just have to understand how
+
+ align:start position:0%
+d masons we just have to understand how
+ 
+
+ align:start position:0%
+d masons we just have to understand how
+to do the pion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have a b mouse on let's think
+
+ align:start position:0%
+so we have a b mouse on let's think
+ 
+
+ align:start position:0%
+so we have a b mouse on let's think
+about it in the rest frame
+
+ align:start position:0%
+about it in the rest frame
+ 
+
+ align:start position:0%
+about it in the rest frame
+the case to a very heavy demelzon and a
+
+ align:start position:0%
+the case to a very heavy demelzon and a
+ 
+
+ align:start position:0%
+the case to a very heavy demelzon and a
+very light pion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the demelzon we can treat with hqet
+
+ align:start position:0%
+so the demelzon we can treat with hqet
+ 
+
+ align:start position:0%
+so the demelzon we can treat with hqet
+the bmilson we can trade with each hqet
+
+ align:start position:0%
+the bmilson we can trade with each hqet
+ 
+
+ align:start position:0%
+the bmilson we can trade with each hqet
+the problem is this pion because it's
+
+ align:start position:0%
+the problem is this pion because it's
+ 
+
+ align:start position:0%
+the problem is this pion because it's
+very energetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you look at the
+
+ align:start position:0%
+if you look at the
+ 
+
+ align:start position:0%
+if you look at the
+momentum of that pion and the way i've
+
+ align:start position:0%
+momentum of that pion and the way i've
+ 
+
+ align:start position:0%
+momentum of that pion and the way i've
+drawn it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you put in some numbers just to
+
+ align:start position:0%
+and you put in some numbers just to
+ 
+
+ align:start position:0%
+and you put in some numbers just to
+get a sense of what we're talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then it's got an energy which is
+
+ align:start position:0%
+then it's got an energy which is
+ 
+
+ align:start position:0%
+then it's got an energy which is
+slightly bigger than the momentum and
+
+ align:start position:0%
+slightly bigger than the momentum and
+ 
+
+ align:start position:0%
+slightly bigger than the momentum and
+that's because it has a mass but it's a
+
+ align:start position:0%
+that's because it has a mass but it's a
+ 
+
+ align:start position:0%
+that's because it has a mass but it's a
+pretty small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass squared minus p squared is 135
+
+ align:start position:0%
+mass squared minus p squared is 135
+ 
+
+ align:start position:0%
+mass squared minus p squared is 135
+mmv
+
+ align:start position:0%
+mmv
+ 
+
+ align:start position:0%
+mmv
+squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so if you look at that
+
+ align:start position:0%
+and so if you look at that
+ 
+
+ align:start position:0%
+and so if you look at that
+you see
+
+ align:start position:0%
+you see
+ 
+
+ align:start position:0%
+you see
+that this momentum of the pion is very
+
+ align:start position:0%
+that this momentum of the pion is very
+ 
+
+ align:start position:0%
+that this momentum of the pion is very
+close to the light cone the light cone
+
+ align:start position:0%
+close to the light cone the light cone
+ 
+
+ align:start position:0%
+close to the light cone the light cone
+would be if these two are equal
+
+ align:start position:0%
+would be if these two are equal
+ 
+
+ align:start position:0%
+would be if these two are equal
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+what a massless particle would do
+
+ align:start position:0%
+what a massless particle would do
+ 
+
+ align:start position:0%
+what a massless particle would do
+ion is pretty light
+
+ align:start position:0%
+ion is pretty light
+ 
+
+ align:start position:0%
+ion is pretty light
+and it's moving relativistically
+
+ align:start position:0%
+and it's moving relativistically
+ 
+
+ align:start position:0%
+and it's moving relativistically
+and there's no sense in which we can
+
+ align:start position:0%
+and there's no sense in which we can
+ 
+
+ align:start position:0%
+and there's no sense in which we can
+think about 2.3 gv is a small scale
+
+ align:start position:0%
+think about 2.3 gv is a small scale
+ 
+
+ align:start position:0%
+think about 2.3 gv is a small scale
+we're not going to expand in 2.3 gb over
+
+ align:start position:0%
+we're not going to expand in 2.3 gb over
+ 
+
+ align:start position:0%
+we're not going to expand in 2.3 gb over
+mb because that's a pretty lousy
+
+ align:start position:0%
+mb because that's a pretty lousy
+ 
+
+ align:start position:0%
+mb because that's a pretty lousy
+expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so p pi mu here
+
+ align:start position:0%
+so p pi mu here
+ 
+
+ align:start position:0%
+so p pi mu here
+is basically some scale times a light
+
+ align:start position:0%
+is basically some scale times a light
+ 
+
+ align:start position:0%
+is basically some scale times a light
+like vector
+
+ align:start position:0%
+like vector
+ 
+
+ align:start position:0%
+like vector
+where n mu
+
+ align:start position:0%
+where n mu
+ 
+
+ align:start position:0%
+where n mu
+is one
+
+ align:start position:0%
+is one
+ 
+
+ align:start position:0%
+is one
+zero zero minus one
+
+ align:start position:0%
+zero zero minus one
+ 
+
+ align:start position:0%
+zero zero minus one
+and that's to a good approximation
+
+ align:start position:0%
+and that's to a good approximation
+ 
+
+ align:start position:0%
+and that's to a good approximation
+you can see how good over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to use light like vectors
+
+ align:start position:0%
+so we're going to use light like vectors
+ 
+
+ align:start position:0%
+so we're going to use light like vectors
+to talk about particles like a pion
+
+ align:start position:0%
+to talk about particles like a pion
+ 
+
+ align:start position:0%
+to talk about particles like a pion
+so n mu is a light like vector
+
+ align:start position:0%
+so n mu is a light like vector
+ 
+
+ align:start position:0%
+so n mu is a light like vector
+n squared is zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what we're going to be expanding in
+
+ align:start position:0%
+and what we're going to be expanding in
+ 
+
+ align:start position:0%
+and what we're going to be expanding in
+instead of expanding in q over mb
+
+ align:start position:0%
+instead of expanding in q over mb
+ 
+
+ align:start position:0%
+instead of expanding in q over mb
+q of the pion we're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think about the dynamics with this q
+
+ align:start position:0%
+think about the dynamics with this q
+ 
+
+ align:start position:0%
+think about the dynamics with this q
+scale 2.3 gv as being much bigger than
+
+ align:start position:0%
+scale 2.3 gv as being much bigger than
+ 
+
+ align:start position:0%
+scale 2.3 gv as being much bigger than
+lambda qcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to use for particles like
+
+ align:start position:0%
+so we're going to use for particles like
+ 
+
+ align:start position:0%
+so we're going to use for particles like
+this pion that are very energetic light
+
+ align:start position:0%
+this pion that are very energetic light
+ 
+
+ align:start position:0%
+this pion that are very energetic light
+cone coordinates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+when you have a light cone vector like n
+
+ align:start position:0%
+when you have a light cone vector like n
+ 
+
+ align:start position:0%
+when you have a light cone vector like n
+and you want to decompose any vector in
+
+ align:start position:0%
+and you want to decompose any vector in
+ 
+
+ align:start position:0%
+and you want to decompose any vector in
+terms of it
+
+ align:start position:0%
+terms of it
+ 
+
+ align:start position:0%
+terms of it
+you need another auxiliary vector which
+
+ align:start position:0%
+you need another auxiliary vector which
+ 
+
+ align:start position:0%
+you need another auxiliary vector which
+i'm going to call in bar
+
+ align:start position:0%
+i'm going to call in bar
+ 
+
+ align:start position:0%
+i'm going to call in bar
+so these are two light-like vectors
+
+ align:start position:0%
+so these are two light-like vectors
+ 
+
+ align:start position:0%
+so these are two light-like vectors
+they both square to zero
+
+ align:start position:0%
+they both square to zero
+ 
+
+ align:start position:0%
+they both square to zero
+and the reason i need two of them is
+
+ align:start position:0%
+and the reason i need two of them is
+ 
+
+ align:start position:0%
+and the reason i need two of them is
+because i need some notion of
+
+ align:start position:0%
+because i need some notion of
+ 
+
+ align:start position:0%
+because i need some notion of
+orthogonality so you should think of
+
+ align:start position:0%
+orthogonality so you should think of
+ 
+
+ align:start position:0%
+orthogonality so you should think of
+nvar as like the complementary vector
+
+ align:start position:0%
+nvar as like the complementary vector
+ 
+
+ align:start position:0%
+nvar as like the complementary vector
+to n
+
+ align:start position:0%
+to n
+ 
+
+ align:start position:0%
+to n
+the dual vector in the orthogonal
+
+ align:start position:0%
+the dual vector in the orthogonal
+ 
+
+ align:start position:0%
+the dual vector in the orthogonal
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so with those two vectors you can
+
+ align:start position:0%
+so with those two vectors you can
+ 
+
+ align:start position:0%
+so with those two vectors you can
+decompose any vector in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use them as a basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is how it works
+
+ align:start position:0%
+this is how it works
+ 
+
+ align:start position:0%
+this is how it works
+my conventions
+
+ align:start position:0%
+my conventions
+ 
+
+ align:start position:0%
+my conventions
+so you have
+
+ align:start position:0%
+so you have
+ 
+
+ align:start position:0%
+so you have
+two components that you can decompose
+
+ align:start position:0%
+two components that you can decompose
+ 
+
+ align:start position:0%
+two components that you can decompose
+along n and n bar
+
+ align:start position:0%
+along n and n bar
+ 
+
+ align:start position:0%
+along n and n bar
+and the value of the the momentum along
+
+ align:start position:0%
+and the value of the the momentum along
+ 
+
+ align:start position:0%
+and the value of the the momentum along
+that direction is the complementary
+
+ align:start position:0%
+that direction is the complementary
+ 
+
+ align:start position:0%
+that direction is the complementary
+vector dotted into p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we usually with this notation we
+
+ align:start position:0%
+and so we usually with this notation we
+ 
+
+ align:start position:0%
+and so we usually with this notation we
+call n bar dot p p minus
+
+ align:start position:0%
+call n bar dot p p minus
+ 
+
+ align:start position:0%
+call n bar dot p p minus
+so that's just a shorthand
+
+ align:start position:0%
+so that's just a shorthand
+ 
+
+ align:start position:0%
+so that's just a shorthand
+and n dot p is p plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it's going to be useful to
+
+ align:start position:0%
+okay so it's going to be useful to
+ 
+
+ align:start position:0%
+okay so it's going to be useful to
+decompose things along these directions
+
+ align:start position:0%
+decompose things along these directions
+ 
+
+ align:start position:0%
+decompose things along these directions
+for the same reason that you kind of saw
+
+ align:start position:0%
+for the same reason that you kind of saw
+ 
+
+ align:start position:0%
+for the same reason that you kind of saw
+here that the pion was naturally
+
+ align:start position:0%
+here that the pion was naturally
+ 
+
+ align:start position:0%
+here that the pion was naturally
+decomposing itself along a particular
+
+ align:start position:0%
+decomposing itself along a particular
+ 
+
+ align:start position:0%
+decomposing itself along a particular
+light-like direction
+
+ align:start position:0%
+light-like direction
+ 
+
+ align:start position:0%
+light-like direction
+so we're going to want to do that more
+
+ align:start position:0%
+so we're going to want to do that more
+ 
+
+ align:start position:0%
+so we're going to want to do that more
+generally and that's how we'll do it for
+
+ align:start position:0%
+generally and that's how we'll do it for
+ 
+
+ align:start position:0%
+generally and that's how we'll do it for
+momenta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we talk about p squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i just square the components here
+
+ align:start position:0%
+and i just square the components here
+ 
+
+ align:start position:0%
+and i just square the components here
+n dotted into perp is zero
+
+ align:start position:0%
+n dotted into perp is zero
+ 
+
+ align:start position:0%
+n dotted into perp is zero
+and bar dotted into purpose zero there's
+
+ align:start position:0%
+and bar dotted into purpose zero there's
+ 
+
+ align:start position:0%
+and bar dotted into purpose zero there's
+a non-trivial crop this squared is zero
+
+ align:start position:0%
+a non-trivial crop this squared is zero
+ 
+
+ align:start position:0%
+a non-trivial crop this squared is zero
+that's square root of zero there's a
+
+ align:start position:0%
+that's square root of zero there's a
+ 
+
+ align:start position:0%
+that's square root of zero there's a
+non-trivial cross term between those two
+
+ align:start position:0%
+non-trivial cross term between those two
+ 
+
+ align:start position:0%
+non-trivial cross term between those two
+which is this
+
+ align:start position:0%
+which is this
+ 
+
+ align:start position:0%
+which is this
+this guy can be squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we use our shorthand then it's
+
+ align:start position:0%
+if we use our shorthand then it's
+ 
+
+ align:start position:0%
+if we use our shorthand then it's
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and if we want to use euclidean
+
+ align:start position:0%
+and if we want to use euclidean
+ 
+
+ align:start position:0%
+and if we want to use euclidean
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+then i can
+
+ align:start position:0%
+then i can
+ 
+
+ align:start position:0%
+then i can
+i'll switch and i'll
+
+ align:start position:0%
+i'll switch and i'll
+ 
+
+ align:start position:0%
+i'll switch and i'll
+say that p perp squared which is a
+
+ align:start position:0%
+say that p perp squared which is a
+ 
+
+ align:start position:0%
+say that p perp squared which is a
+minkowski negative quantity is minus p
+
+ align:start position:0%
+minkowski negative quantity is minus p
+ 
+
+ align:start position:0%
+minkowski negative quantity is minus p
+vector perp squared
+
+ align:start position:0%
+vector perp squared
+ 
+
+ align:start position:0%
+vector perp squared
+where p vector perp squared is euclidean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so sometimes i'll have
+
+ align:start position:0%
+so sometimes i'll have
+ 
+
+ align:start position:0%
+so sometimes i'll have
+used for both of those notations
+
+ align:start position:0%
+used for both of those notations
+ 
+
+ align:start position:0%
+used for both of those notations
+all right so i think we're out of time
+
+ align:start position:0%
+all right so i think we're out of time
+ 
+
+ align:start position:0%
+all right so i think we're out of time
+for today we'll continue with this
+
+ align:start position:0%
+for today we'll continue with this
+ 
+
+ align:start position:0%
+for today we'll continue with this
+discussion of degrees of freedom next
+
+ align:start position:0%
+discussion of degrees of freedom next
+ 
+
+ align:start position:0%
+discussion of degrees of freedom next
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+talk a little bit more about coordinates
+
+ align:start position:0%
+talk a little bit more about coordinates
+ 
+
+ align:start position:0%
+talk a little bit more about coordinates
+as well
\ No newline at end of file
diff --git a/DjMaDN3EtWc.txt b/DjMaDN3EtWc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e0581e2ab349f9d20a52563d31f6acfd25e2fc20
--- /dev/null
+++ b/DjMaDN3EtWc.txt
@@ -0,0 +1,476 @@
+Servomotors are widely used electro-mechanical
+components. For example, they are used in
+
+steering systems for scale model helicopters
+and other radio controlled cars, robots, and
+
+aircraft, including military "drones".
+
+A servomotor includes an electric motor, circuitry
+to control its speed and direction, and gearing
+
+to attain the high torques needed to apply
+moderately large forces over relatively short
+
+linear displacements. The gearing inside this
+servo is a compound gear train with four stages.
+
+In this video, we will understand how linear
+algebra can help us to predict the losses
+
+and understand the design trade-offs when
+converting high speeds and low torques into
+
+low speeds and high torques using a gear train.
+
+This video is part of the Linearity Video
+Series. Many complex systems are modeled or
+
+approximated linearly because of the mathematical
+advantages.
+
+Hi, my name is Dan Frey, and I am a professor
+of Mechanical Engineering and Engineering
+
+Systems at MIT.
+
+Before watching this video, you should be
+able to identify and describe the forces and
+
+torques that act on a system.
+
+After watching this video and some practice,
+you will be able to:
+
+Model the forces and torques in a gear train
+as a system of linear equations.
+
+Combine these linear equations into a matrix
+equation.
+
+First, let's get a quick overview of the design.
+Here's a servomotor with the case opened.
+
+Inside the case is a DC motor with a small
+pinion gear on it. The pinion has 10 teeth
+
+and is mated to a gear with 72 teeth. So the
+first pair provides a speed reduction of 7.2:1.
+
+This large, 72 tooth gear is part of a single
+molding with a 10 tooth gear.
+
+The 10 tooth gear on top of the 72 tooth gear
+is mated to a plastic gear with 48 teeth as
+
+you see here. So that stage provides a speed
+reduction of 4.8:1. The 48 tooth gear is molded
+
+to another 10 tooth gear.
+
+The 11-tooth gear is mated to a black 36-tooth
+gear. This 36-tooth gear is molded to a 16-tooth
+
+gear. The 16-tooth gear is mated to this black
+42 tooth gear, which is splined onto the output
+
+shaft.
+
+The overall sequence of gear pairs is: 10
+teeth mated to 72 teeth, 10 mated to 48, 11
+
+mated to 36 and finally 16 mated to 42 teeth
+on the splined output shaft.
+
+The overall gear ratio is the product of all
+the gear ratios of the gear pairs in the train.
+
+Therefore about 326 to 1 as shown by this
+formula.
+
+Based on the motor's output and some measurement
+and calculation, we would expect an output
+
+torque of 6.8 Newton meters in an idealized
+gear train.
+
+But there are frictional losses at every stage
+of the power transmission process, so we guess
+
+the output shaft will provide substantially
+less torque than that. So let's start by measuring
+
+the maximum force at the output shaft, and
+convert that to an output torque.
+
+We attach weights to a servo horn that has
+been connected with the output shaft on the
+
+servomotor. An electrical power source (in
+this case, a battery) is connected through
+
+a radio controller.
+
+Here you see the servomotor lifting 1 kg.
+Here it is lifting about 2kg. And here it
+
+lifts even 3kg! This lightweight (100 gram)
+servomotor produces large amounts of torque,
+
+which can apparently lift more than 30 times
+its own weight.
+
+In this set-up, the servomotor will lift a
+4.42kg weight starting from a 90 degree angle.
+
+As the motor lifts the weight, the readout
+on the scale should change.
+
+Here you see the initial weight, with slack
+in the string, is 9.75 lbs. This is about
+
+4.42kg. With the motor pulling at maximum
+capacity, the scale reads 3.70 lbs, which
+
+is 1.68 kg.
+
+A calculation tells us that the maximum torque
+available at the output shaft according to
+
+our tests is 1.47 Newton meters.
+
+We can use linear algebra to work out a better
+estimate. The force transmission and frictional
+
+losses in each step of the train can be modeled
+by a set of linear equations, (summing forces
+
+and summing torques on the rigid body). For
+the three rigid bodies that are comprised
+
+of two gears molded together, we will need
+three equations (sums of separate x and y
+
+forces and sums of torques).
+
+The pinion gear and last gear in the train
+are simpler, because there is only one gear
+
+in the body, so we can combine each of those
+into a single equation.
+
+The equations modeling the entire train can
+be assembled by linking together the five
+
+sets of equations with four additional equations
+to link each mating pair, so the overall system
+
+will have 15 equations--- 3 sets of 3 each
+(9 total) plus 1 each for the input and output
+
+gears plus 4 equations that model the connections
+between the mating gears. The solution to
+
+that set of equations helps us to estimate
+performance of the machine and also gives
+
+us insight into its design.
+
+Let's make the model of just one gear body
+now, say the 10 tooth and 48 tooth molded
+
+gear seen here. One way to model the system
+is to posit that there are three unknown forces
+
+acting on this single body of two gears molded
+together.
+
+We can name these forces F-TL2, F-TS2 , F-ShaftX2,
+and F-ShaftY2. The force F-TL2 is a force
+
+tangent to the gear pitch circle on the larger
+of the two gears. The T is for Tangent, the
+
+L is for Large, and the 2 indicates that this
+is the second compound gear in the train.
+
+The force F-TS2 is a force tangent to the
+gear pitch circle on the smaller of the two
+
+gears. Again the T means tangent, and the
+S here means small.
+
+Recall that these tangential forces really
+come from forces normal to the gear teeth.
+
+These gears are designed so that all of the
+gears in this servomotor have a pressure angle
+
+of 20 degrees. So there is a X component to
+this force, the separation force between the
+
+mating gears, which has magnitude given by
+FTL2 and FTS2 times tan 0.35, where 0.35 is
+
+20 degrees expressed in radians.
+
+The forces F-ShaftX2 and F-ShaftY2 are the
+X and Y components of the normal force to
+
+the shaft, which is applied to the gear it
+supports.
+
+There are also frictional forces associated
+with the normal force supporting the shaft,
+
+but they are not separate unknowns, they link
+the X and Y components normal forces by the
+
+friction coefficient, mu2.
+
+This completes the description of the unknown
+forces in our model. Those four forces appear
+
+in three different linear equations as represented
+by this matrix:
+
+Take a moment to verify that these equations
+balance the forces and torques.
+
+The 
+first row in the matrix represents a sum of
+the forces on the gear in the X direction.
+
+The second row represents a sum of the forces
+on the gear in the Y direction. The third
+
+row represents a sum of the torques or moments
+on the gear in the direction parallel to the
+
+gear shaft.
+
+Now let's work on the model of the next gear
+in the train -- the one with 16 teeth and
+
+36 teeth molded together. Again, we model
+the system by positing that there are four
+
+unknown forces acting on this single body
+having two gears molded together and we can
+
+name these forces FTL3, FTS3 , FShaftX3, and
+FShaftY3. And we obtain this matrix.
+
+How can we link these two matrices together
+to get a model of the second and third gears
+
+combined? We see that the smaller gear on
+body 2 is in contact with the larger gear
+
+on body 3. According to Newton's third law,
+the reaction force on body 2 should be equal
+
+and opposite to that on body 3.
+
+In fact, the situation is more complex. As
+the gears enter mating they slide into engagement.
+
+As the gears depart contact, they slide back
+out. There are losses at the interface that
+
+are complex to model, and we will represent
+them simply using the efficiency in the average
+
+transmitted force.
+
+Now we can join the model of the second gear
+and the third gear into a single system of
+
+linear equations represented by this matrix:
+
+The row in the middle is like "glue" holding
+the two models together. The force on the
+
+large gear on body 3 is equal to the force
+on the large gear on body 2 except a penalty
+
+is applied for inefficiencies. The principal
+mechanism for loss of power and torque is
+
+sliding friction -- in this case, shearing
+the lubricant on the gear faces.
+
+Before going on to assemble more of the model,
+it is worth inspecting our work so far for
+
+patterns. Note that the top right and bottom
+left of our matrices are filled with 3x4 matrices
+
+of zeros. That is a clue that our matrix is
+shaping up to be banded in structure. Although
+
+every variable affects every other variable,
+the influences propagate locally (in some
+
+sense). For example, the frictional losses
+on shaft 2 do influence the frictional losses
+
+on shaft 3, but only indirectly through their
+effect on the force between the two bodies.
+
+Because we arranged the variables in our vectors
+in a way that respects this structure, our
+
+matrix has a band in the middle from the top
+left corner to the bottom right. We will try
+
+to keep this up as we continue building the
+model. It will clarify interpretation of the
+
+model and also aid in efficiency and stability
+of the computations needed to solve it.
+
+Now it's your turn, take a moment to write
+a matrix that models the force and torque
+
+balance on the first rigid body gear in the
+gear train.
+
+This matrix is completely analogous to the
+matrices we obtained in for the 2nd and 3rd
+
+gear bodies.
+
+When we add the pinion gear and fourth gear
+into the model, we need to take additional
+
+care. These will have slightly different structure.
+The gear connected to the pinion on the motor
+
+has an applied torque due to the motor. The
+reaction at the output shaft is an externally
+
+applied torque, due entirely to the large
+fourth gear. It is possible to combine these
+
+into a single equation for each gear.
+
+Pause the video and try to write out the full
+system of linear equations for the overall
+
+4 gear train system.
+
+Placing these into the model as the first
+and last rows, the overall system of linear
+
+equations is:
+
+Note that the matrix has 15 rows and 15 columns.
+This should be expected as the system should
+
+be neither overdetermined nor underdetermined.
+Given a particular torque input at the motor,
+
+there should be a single value of output torque
+consistent with our gear train model and its
+
+deterministically defined parameters.
+
+By solving this system, we find unique values
+for all the unknowns. When we assembled the
+
+equations, we guessed the direction of each
+force in the free body diagram. So, it's useful
+
+to inspect the solution for negative values.
+For the parameter values we chose, the reaction
+
+force at the shaft of the third body in the
+x direction turns out to be negative.
+
+We should ask ourselves, did we guess wrong
+about the direction of the force, or is there
+
+something wrong with our matrix? Looking at
+the forces computed it seems that the friction
+
+in the x direction due to support of the large
+y reaction on this gear was more dominant
+
+that we expected.
+
+It's sensible to run some sanity checks in
+a case like this. If the friction on that
+
+gear were very low, would the sign be positive
+as expected? We ran that scenario, and the
+
+sign did become positive. So our guess about
+the direction of the reaction force was wrong.
+
+Our assumptions for the magnitude of the friction
+were too low. But it seems the model is behaving
+
+in reasonable ways.
+
+Now that we have a reasonable level of confidence
+in the model, we can begin to use it to explore
+
+the design decisions that the engineers made.
+If we put in reasonable values for the gear
+
+mating efficiency, such as 96%, and reasonable
+values for the friction coefficients at the
+
+bushings, such as 0.3, we find an overall
+efficiency of the gear train is about 52%.
+
+This is in reasonable agreement with our simple
+measurements. We found that the maximum torque
+
+available at the output shaft is 1.47 Newton
+meters, which would imply an efficiency closer
+
+to 25%.
+
+But our measurement used an overhanging load,
+which caused the shaft to bend. Our simple
+
+model makes a large and optimistic assumption
+of loading the servomotor with torques only.
+
+It's not surprising that the answers differ
+substantially. It suggests installing the
+
+servo so that bending loads are supported
+elsewhere, not in the servo itself.
+
+The gears in automotive transmissions with
+similar ratios are much more efficient, perhaps
+
+90% to 95% efficient. But for a compact and
+inexpensive gear train, this design performs
+
+well, especially since the plastic the gears
+are molded from adds a great deal of rolling
+
+friction.
+
+To summarize, we built an engineering model
+of a servomotor gear train using systems of
+
+linear equations. The matrix representations
+helped us to explore the interactions among
+
+variables in the system like separation forces
+between gears and friction at the shafts.
+
+Since the 15 by 15 system of equations is
+so fast and easy to solve on a modern computer,
+
+we could run a large number of "what if" scenarios.
+
+We hope this video helped you see how linear
+algebra can be used to make and understand
+
+engineering design decisions.
\ No newline at end of file
diff --git a/DpNZ70Uam0M.txt b/DpNZ70Uam0M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..007e5e9decee69838341bfea41a139fd5ea303ee
--- /dev/null
+++ b/DpNZ70Uam0M.txt
@@ -0,0 +1,6323 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm really I'm really sick today and I
+
+ align:start position:0%
+I'm really I'm really sick today and I
+ 
+
+ align:start position:0%
+I'm really I'm really sick today and I
+hope I can make it through this lecture
+
+ align:start position:0%
+hope I can make it through this lecture
+ 
+
+ align:start position:0%
+hope I can make it through this lecture
+without disgracing myself but this is a
+
+ align:start position:0%
+without disgracing myself but this is a
+ 
+
+ align:start position:0%
+without disgracing myself but this is a
+favorite topic of mine too so maybe
+
+ align:start position:0%
+favorite topic of mine too so maybe
+ 
+
+ align:start position:0%
+favorite topic of mine too so maybe
+we'll be okay so we're going to talk
+
+ align:start position:0%
+we'll be okay so we're going to talk
+ 
+
+ align:start position:0%
+we'll be okay so we're going to talk
+about the helium atom which is really an
+
+ align:start position:0%
+about the helium atom which is really an
+ 
+
+ align:start position:0%
+about the helium atom which is really an
+amazing thing because hydrogen is
+
+ align:start position:0%
+amazing thing because hydrogen is
+ 
+
+ align:start position:0%
+amazing thing because hydrogen is
+possible to solve it exactly all sorts
+
+ align:start position:0%
+possible to solve it exactly all sorts
+ 
+
+ align:start position:0%
+possible to solve it exactly all sorts
+of fantastic things happened and it
+
+ align:start position:0%
+of fantastic things happened and it
+ 
+
+ align:start position:0%
+of fantastic things happened and it
+seemed like just a small step from
+
+ align:start position:0%
+seemed like just a small step from
+ 
+
+ align:start position:0%
+seemed like just a small step from
+hydrogen to helium and nobody can take
+
+ align:start position:0%
+hydrogen to helium and nobody can take
+ 
+
+ align:start position:0%
+hydrogen to helium and nobody can take
+that step it's entirely approximate and
+
+ align:start position:0%
+that step it's entirely approximate and
+ 
+
+ align:start position:0%
+that step it's entirely approximate and
+you can do better and better on the
+
+ align:start position:0%
+you can do better and better on the
+ 
+
+ align:start position:0%
+you can do better and better on the
+approximations but we'd like to have
+
+ align:start position:0%
+approximations but we'd like to have
+ 
+
+ align:start position:0%
+approximations but we'd like to have
+some some physical sense of what's going
+
+ align:start position:0%
+some some physical sense of what's going
+ 
+
+ align:start position:0%
+some some physical sense of what's going
+on and what are the important terms and
+
+ align:start position:0%
+on and what are the important terms and
+ 
+
+ align:start position:0%
+on and what are the important terms and
+can we steal things from hydrogen and
+
+ align:start position:0%
+can we steal things from hydrogen and
+ 
+
+ align:start position:0%
+can we steal things from hydrogen and
+the answer is yeah we can and that was
+
+ align:start position:0%
+the answer is yeah we can and that was
+ 
+
+ align:start position:0%
+the answer is yeah we can and that was
+what last lecture was mostly about the
+
+ align:start position:0%
+what last lecture was mostly about the
+ 
+
+ align:start position:0%
+what last lecture was mostly about the
+energies for hydrogen are minus Z
+
+ align:start position:0%
+energies for hydrogen are minus Z
+ 
+
+ align:start position:0%
+energies for hydrogen are minus Z
+squared H C time to rid burg over N
+
+ align:start position:0%
+squared H C time to rid burg over N
+ 
+
+ align:start position:0%
+squared H C time to rid burg over N
+squared and we have the ionization
+
+ align:start position:0%
+squared and we have the ionization
+ 
+
+ align:start position:0%
+squared and we have the ionization
+energy from the nth level and so this
+
+ align:start position:0%
+energy from the nth level and so this
+ 
+
+ align:start position:0%
+energy from the nth level and so this
+actually is the way we make a link to
+
+ align:start position:0%
+actually is the way we make a link to
+ 
+
+ align:start position:0%
+actually is the way we make a link to
+this concept of electronegativity
+
+ align:start position:0%
+this concept of electronegativity
+ 
+
+ align:start position:0%
+this concept of electronegativity
+because the dominant thing in
+
+ align:start position:0%
+because the dominant thing in
+ 
+
+ align:start position:0%
+because the dominant thing in
+electronegativity is the ionization
+
+ align:start position:0%
+electronegativity is the ionization
+ 
+
+ align:start position:0%
+electronegativity is the ionization
+energy and this is the ionization energy
+
+ align:start position:0%
+energy and this is the ionization energy
+ 
+
+ align:start position:0%
+energy and this is the ionization energy
+and when you put them together and solve
+
+ align:start position:0%
+and when you put them together and solve
+ 
+
+ align:start position:0%
+and when you put them together and solve
+for n you get this arrangement hcz
+
+ align:start position:0%
+for n you get this arrangement hcz
+ 
+
+ align:start position:0%
+for n you get this arrangement hcz
+squared times the red burg over the
+
+ align:start position:0%
+squared times the red burg over the
+ 
+
+ align:start position:0%
+squared times the red burg over the
+ionization energy square root that's N
+
+ align:start position:0%
+ionization energy square root that's N
+ 
+
+ align:start position:0%
+ionization energy square root that's N
+or the effective principal quantum
+
+ align:start position:0%
+or the effective principal quantum
+ 
+
+ align:start position:0%
+or the effective principal quantum
+number and then we have all of these
+
+ align:start position:0%
+number and then we have all of these
+ 
+
+ align:start position:0%
+number and then we have all of these
+formulas that can be derived from
+
+ align:start position:0%
+formulas that can be derived from
+ 
+
+ align:start position:0%
+formulas that can be derived from
+hydrogenic wave functions both for
+
+ align:start position:0%
+hydrogenic wave functions both for
+ 
+
+ align:start position:0%
+hydrogenic wave functions both for
+diagonal make spectate invaluable
+
+ align:start position:0%
+diagonal make spectate invaluable
+ 
+
+ align:start position:0%
+diagonal make spectate invaluable
+matrix elements they're all close form
+
+ align:start position:0%
+matrix elements they're all close form
+ 
+
+ align:start position:0%
+matrix elements they're all close form
+and this is wonderful because it then
+
+ align:start position:0%
+and this is wonderful because it then
+ 
+
+ align:start position:0%
+and this is wonderful because it then
+enables you to use the formulas that are
+
+ align:start position:0%
+enables you to use the formulas that are
+ 
+
+ align:start position:0%
+enables you to use the formulas that are
+obtained exactly for hydrogenic wave
+
+ align:start position:0%
+obtained exactly for hydrogenic wave
+ 
+
+ align:start position:0%
+obtained exactly for hydrogenic wave
+functions and so if we know the
+
+ align:start position:0%
+functions and so if we know the
+ 
+
+ align:start position:0%
+functions and so if we know the
+dependence of an electronic property on
+
+ align:start position:0%
+dependence of an electronic property on
+ 
+
+ align:start position:0%
+dependence of an electronic property on
+N and Al now L is well n is
+
+ align:start position:0%
+N and Al now L is well n is
+ 
+
+ align:start position:0%
+N and Al now L is well n is
+experimentally determined the distance
+
+ align:start position:0%
+experimentally determined the distance
+ 
+
+ align:start position:0%
+experimentally determined the distance
+from ionization L is determined from or
+
+ align:start position:0%
+from ionization L is determined from or
+ 
+
+ align:start position:0%
+from ionization L is determined from or
+angular momentum then we can determine
+
+ align:start position:0%
+angular momentum then we can determine
+ 
+
+ align:start position:0%
+angular momentum then we can determine
+the expected scaling of everything on
+
+ align:start position:0%
+the expected scaling of everything on
+ 
+
+ align:start position:0%
+the expected scaling of everything on
+the quantum numbers and even if that's
+
+ align:start position:0%
+the quantum numbers and even if that's
+ 
+
+ align:start position:0%
+the quantum numbers and even if that's
+wrong it tells you the the qualitative
+
+ align:start position:0%
+wrong it tells you the the qualitative
+ 
+
+ align:start position:0%
+wrong it tells you the the qualitative
+effects when you get to more complicated
+
+ align:start position:0%
+effects when you get to more complicated
+ 
+
+ align:start position:0%
+effects when you get to more complicated
+systems than one electron atoms and this
+
+ align:start position:0%
+systems than one electron atoms and this
+ 
+
+ align:start position:0%
+systems than one electron atoms and this
+is really what I meant by structure
+
+ align:start position:0%
+is really what I meant by structure
+ 
+
+ align:start position:0%
+is really what I meant by structure
+where everything is related to basically
+
+ align:start position:0%
+where everything is related to basically
+ 
+
+ align:start position:0%
+where everything is related to basically
+one observation there's one other thing
+
+ align:start position:0%
+one observation there's one other thing
+ 
+
+ align:start position:0%
+one observation there's one other thing
+that I haven't been stress and it's
+
+ align:start position:0%
+that I haven't been stress and it's
+ 
+
+ align:start position:0%
+that I haven't been stress and it's
+another concept from 511 to and that
+
+ align:start position:0%
+another concept from 511 to and that
+ 
+
+ align:start position:0%
+another concept from 511 to and that
+shielding so suppose we have a sodium
+
+ align:start position:0%
+shielding so suppose we have a sodium
+ 
+
+ align:start position:0%
+shielding so suppose we have a sodium
+atom most of the electrons are in a
+
+ align:start position:0%
+atom most of the electrons are in a
+ 
+
+ align:start position:0%
+atom most of the electrons are in a
+compact core the outer electron sees a
+
+ align:start position:0%
+compact core the outer electron sees a
+ 
+
+ align:start position:0%
+compact core the outer electron sees a
+charge of one even though the charge on
+
+ align:start position:0%
+charge of one even though the charge on
+ 
+
+ align:start position:0%
+charge of one even though the charge on
+the nucleus is larger than one and
+
+ align:start position:0%
+the nucleus is larger than one and
+ 
+
+ align:start position:0%
+the nucleus is larger than one and
+there's if you ask well suppose we look
+
+ align:start position:0%
+there's if you ask well suppose we look
+ 
+
+ align:start position:0%
+there's if you ask well suppose we look
+at this inner region and we have an
+
+ align:start position:0%
+at this inner region and we have an
+ 
+
+ align:start position:0%
+at this inner region and we have an
+electron inside of it the charge that
+
+ align:start position:0%
+electron inside of it the charge that
+ 
+
+ align:start position:0%
+electron inside of it the charge that
+that electron sees is the amount of
+
+ align:start position:0%
+that electron sees is the amount of
+ 
+
+ align:start position:0%
+that electron sees is the amount of
+electrons inside the sphere defined by
+
+ align:start position:0%
+electrons inside the sphere defined by
+ 
+
+ align:start position:0%
+electrons inside the sphere defined by
+this radius and and so the Z we can call
+
+ align:start position:0%
+this radius and and so the Z we can call
+ 
+
+ align:start position:0%
+this radius and and so the Z we can call
+it the Z effective is a function of R
+
+ align:start position:0%
+it the Z effective is a function of R
+ 
+
+ align:start position:0%
+it the Z effective is a function of R
+and you have a different function for a
+
+ align:start position:0%
+and you have a different function for a
+ 
+
+ align:start position:0%
+and you have a different function for a
+real and so it's a way of putting in
+
+ align:start position:0%
+real and so it's a way of putting in
+ 
+
+ align:start position:0%
+real and so it's a way of putting in
+more insight and I I've made a lot of
+
+ align:start position:0%
+more insight and I I've made a lot of
+ 
+
+ align:start position:0%
+more insight and I I've made a lot of
+mileage in my career on these sorts of
+
+ align:start position:0%
+mileage in my career on these sorts of
+ 
+
+ align:start position:0%
+mileage in my career on these sorts of
+scaling arguments
+
+ align:start position:0%
+scaling arguments
+ 
+
+ align:start position:0%
+scaling arguments
+okay so helium the notes are beautiful
+
+ align:start position:0%
+okay so helium the notes are beautiful
+ 
+
+ align:start position:0%
+okay so helium the notes are beautiful
+they're written by Troy and they're very
+
+ align:start position:0%
+they're written by Troy and they're very
+ 
+
+ align:start position:0%
+they're written by Troy and they're very
+long and they're very correct and
+
+ align:start position:0%
+long and they're very correct and
+ 
+
+ align:start position:0%
+long and they're very correct and
+incisive and even if I weren't sick I
+
+ align:start position:0%
+incisive and even if I weren't sick I
+ 
+
+ align:start position:0%
+incisive and even if I weren't sick I
+couldn't cover all those notes so I'm
+
+ align:start position:0%
+couldn't cover all those notes so I'm
+ 
+
+ align:start position:0%
+couldn't cover all those notes so I'm
+going to make a rather Express trip
+
+ align:start position:0%
+going to make a rather Express trip
+ 
+
+ align:start position:0%
+going to make a rather Express trip
+through the notes and the critical thing
+
+ align:start position:0%
+through the notes and the critical thing
+ 
+
+ align:start position:0%
+through the notes and the critical thing
+is we have two electrons and so we can't
+
+ align:start position:0%
+is we have two electrons and so we can't
+ 
+
+ align:start position:0%
+is we have two electrons and so we can't
+simply solve the the problem by using
+
+ align:start position:0%
+simply solve the the problem by using
+ 
+
+ align:start position:0%
+simply solve the the problem by using
+hydrogenic functions although we would
+
+ align:start position:0%
+hydrogenic functions although we would
+ 
+
+ align:start position:0%
+hydrogenic functions although we would
+like to and the crucial thing that is
+
+ align:start position:0%
+like to and the crucial thing that is
+ 
+
+ align:start position:0%
+like to and the crucial thing that is
+missing is you know if if we could
+
+ align:start position:0%
+missing is you know if if we could
+ 
+
+ align:start position:0%
+missing is you know if if we could
+ignore the interactions between the two
+
+ align:start position:0%
+ignore the interactions between the two
+ 
+
+ align:start position:0%
+ignore the interactions between the two
+electrons which are enormous then we
+
+ align:start position:0%
+electrons which are enormous then we
+ 
+
+ align:start position:0%
+electrons which are enormous then we
+would be using hydrogen actions and
+
+ align:start position:0%
+would be using hydrogen actions and
+ 
+
+ align:start position:0%
+would be using hydrogen actions and
+everything would be fine so we can't and
+
+ align:start position:0%
+everything would be fine so we can't and
+ 
+
+ align:start position:0%
+everything would be fine so we can't and
+we use the what's what's called the
+
+ align:start position:0%
+we use the what's what's called the
+ 
+
+ align:start position:0%
+we use the what's what's called the
+independent electron approximation where
+
+ align:start position:0%
+independent electron approximation where
+ 
+
+ align:start position:0%
+independent electron approximation where
+we're still using hydrogenic orbitals
+
+ align:start position:0%
+we're still using hydrogenic orbitals
+ 
+
+ align:start position:0%
+we're still using hydrogenic orbitals
+and energies but we're using those to
+
+ align:start position:0%
+and energies but we're using those to
+ 
+
+ align:start position:0%
+and energies but we're using those to
+include the first order perturbation
+
+ align:start position:0%
+include the first order perturbation
+ 
+
+ align:start position:0%
+include the first order perturbation
+correction to the energies so there's a
+
+ align:start position:0%
+correction to the energies so there's a
+ 
+
+ align:start position:0%
+correction to the energies so there's a
+term the inter inter electron repulsion
+
+ align:start position:0%
+term the inter inter electron repulsion
+ 
+
+ align:start position:0%
+term the inter inter electron repulsion
+that leads to this extra correction
+
+ align:start position:0%
+that leads to this extra correction
+ 
+
+ align:start position:0%
+that leads to this extra correction
+energy and that's most of the difference
+
+ align:start position:0%
+energy and that's most of the difference
+ 
+
+ align:start position:0%
+energy and that's most of the difference
+but then we have identical particles and
+
+ align:start position:0%
+but then we have identical particles and
+ 
+
+ align:start position:0%
+but then we have identical particles and
+when we have identical particles the
+
+ align:start position:0%
+when we have identical particles the
+ 
+
+ align:start position:0%
+when we have identical particles the
+permutation of those two particles has
+
+ align:start position:0%
+permutation of those two particles has
+ 
+
+ align:start position:0%
+permutation of those two particles has
+to commute with the Hamiltonian because
+
+ align:start position:0%
+to commute with the Hamiltonian because
+ 
+
+ align:start position:0%
+to commute with the Hamiltonian because
+the hamiltonian only knows that we're
+
+ align:start position:0%
+the hamiltonian only knows that we're
+ 
+
+ align:start position:0%
+the hamiltonian only knows that we're
+dealing with all the electrons it
+
+ align:start position:0%
+dealing with all the electrons it
+ 
+
+ align:start position:0%
+dealing with all the electrons it
+doesn't put names on the individual
+
+ align:start position:0%
+doesn't put names on the individual
+ 
+
+ align:start position:0%
+doesn't put names on the individual
+electrons and so there's a permutation
+
+ align:start position:0%
+electrons and so there's a permutation
+ 
+
+ align:start position:0%
+electrons and so there's a permutation
+symmetry that has to be imposed and this
+
+ align:start position:0%
+symmetry that has to be imposed and this
+ 
+
+ align:start position:0%
+symmetry that has to be imposed and this
+is very subtle because the permutation
+
+ align:start position:0%
+is very subtle because the permutation
+ 
+
+ align:start position:0%
+is very subtle because the permutation
+symmetry has nothing to do with the
+
+ align:start position:0%
+symmetry has nothing to do with the
+ 
+
+ align:start position:0%
+symmetry has nothing to do with the
+energy but it has to do with the energy
+
+ align:start position:0%
+energy but it has to do with the energy
+ 
+
+ align:start position:0%
+energy but it has to do with the energy
+states and and so we'll explore that now
+
+ align:start position:0%
+states and and so we'll explore that now
+ 
+
+ align:start position:0%
+states and and so we'll explore that now
+since we're going to be dealing with
+
+ align:start position:0%
+since we're going to be dealing with
+ 
+
+ align:start position:0%
+since we're going to be dealing with
+more than one electron there's a lot of
+
+ align:start position:0%
+more than one electron there's a lot of
+ 
+
+ align:start position:0%
+more than one electron there's a lot of
+symbols that we're going to be carrying
+
+ align:start position:0%
+symbols that we're going to be carrying
+ 
+
+ align:start position:0%
+symbols that we're going to be carrying
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+and so there's a useful thing called the
+
+ align:start position:0%
+and so there's a useful thing called the
+ 
+
+ align:start position:0%
+and so there's a useful thing called the
+the atomic units which sets most of the
+
+ align:start position:0%
+the atomic units which sets most of the
+ 
+
+ align:start position:0%
+the atomic units which sets most of the
+physical constants to one and that means
+
+ align:start position:0%
+physical constants to one and that means
+ 
+
+ align:start position:0%
+physical constants to one and that means
+all of the rubble that you have to carry
+
+ align:start position:0%
+all of the rubble that you have to carry
+ 
+
+ align:start position:0%
+all of the rubble that you have to carry
+around goes away and it's not a big deal
+
+ align:start position:0%
+around goes away and it's not a big deal
+ 
+
+ align:start position:0%
+around goes away and it's not a big deal
+because if you use all of the things in
+
+ align:start position:0%
+because if you use all of the things in
+ 
+
+ align:start position:0%
+because if you use all of the things in
+your calculation in atomic units namely
+
+ align:start position:0%
+your calculation in atomic units namely
+ 
+
+ align:start position:0%
+your calculation in atomic units namely
+value 1 or something like 1 then at the
+
+ align:start position:0%
+value 1 or something like 1 then at the
+ 
+
+ align:start position:0%
+value 1 or something like 1 then at the
+end you're going to get the energy in
+
+ align:start position:0%
+end you're going to get the energy in
+ 
+
+ align:start position:0%
+end you're going to get the energy in
+atomic units and we know what that is in
+
+ align:start position:0%
+atomic units and we know what that is in
+ 
+
+ align:start position:0%
+atomic units and we know what that is in
+conventional units so it it it's a risky
+
+ align:start position:0%
+conventional units so it it it's a risky
+ 
+
+ align:start position:0%
+conventional units so it it it's a risky
+thing because you don't really know what
+
+ align:start position:0%
+thing because you don't really know what
+ 
+
+ align:start position:0%
+thing because you don't really know what
+you're doing but at the end you can
+
+ align:start position:0%
+you're doing but at the end you can
+ 
+
+ align:start position:0%
+you're doing but at the end you can
+probably convert your number which is a
+
+ align:start position:0%
+probably convert your number which is a
+ 
+
+ align:start position:0%
+probably convert your number which is a
+pure number into an actual energy ok so
+
+ align:start position:0%
+pure number into an actual energy ok so
+ 
+
+ align:start position:0%
+pure number into an actual energy ok so
+let me start with the good news well
+
+ align:start position:0%
+let me start with the good news well
+ 
+
+ align:start position:0%
+let me start with the good news well
+maybe I should leave this the good news
+
+ align:start position:0%
+maybe I should leave this the good news
+ 
+
+ align:start position:0%
+maybe I should leave this the good news
+is we have two particles for helium the
+
+ align:start position:0%
+is we have two particles for helium the
+ 
+
+ align:start position:0%
+is we have two particles for helium the
+vector R momentum momentum the vector
+
+ align:start position:0%
+vector R momentum momentum the vector
+ 
+
+ align:start position:0%
+vector R momentum momentum the vector
+for particle 1 vector momentum ok so
+
+ align:start position:0%
+for particle 1 vector momentum ok so
+ 
+
+ align:start position:0%
+for particle 1 vector momentum ok so
+these are the actors and when do we have
+
+ align:start position:0%
+these are the actors and when do we have
+ 
+
+ align:start position:0%
+these are the actors and when do we have
+to worry about commutation or non
+
+ align:start position:0%
+to worry about commutation or non
+ 
+
+ align:start position:0%
+to worry about commutation or non
+commutation well the answer is the
+
+ align:start position:0%
+commutation well the answer is the
+ 
+
+ align:start position:0%
+commutation well the answer is the
+coordinates associated with different
+
+ align:start position:0%
+coordinates associated with different
+ 
+
+ align:start position:0%
+coordinates associated with different
+particles they don't haven't they
+
+ align:start position:0%
+particles they don't haven't they
+ 
+
+ align:start position:0%
+particles they don't haven't they
+contribute to the energy but there's no
+
+ align:start position:0%
+contribute to the energy but there's no
+ 
+
+ align:start position:0%
+contribute to the energy but there's no
+problem of commutation the momenta don't
+
+ align:start position:0%
+problem of commutation the momenta don't
+ 
+
+ align:start position:0%
+problem of commutation the momenta don't
+also compute commute the coordinates for
+
+ align:start position:0%
+also compute commute the coordinates for
+ 
+
+ align:start position:0%
+also compute commute the coordinates for
+particle 1 and the momentum for particle
+
+ align:start position:0%
+particle 1 and the momentum for particle
+ 
+
+ align:start position:0%
+particle 1 and the momentum for particle
+2 they commute the only things that
+
+ align:start position:0%
+2 they commute the only things that
+ 
+
+ align:start position:0%
+2 they commute the only things that
+doesn't commute is R 1 X P 1 X those
+
+ align:start position:0%
+doesn't commute is R 1 X P 1 X those
+ 
+
+ align:start position:0%
+doesn't commute is R 1 X P 1 X those
+kinds of things and those are their
+
+ align:start position:0%
+kinds of things and those are their
+ 
+
+ align:start position:0%
+kinds of things and those are their
+commutator is IH bar and that means
+
+ align:start position:0%
+commutator is IH bar and that means
+ 
+
+ align:start position:0%
+commutator is IH bar and that means
+there's some problems so most of the
+
+ align:start position:0%
+there's some problems so most of the
+ 
+
+ align:start position:0%
+there's some problems so most of the
+variables are coming
+
+ align:start position:0%
+variables are coming
+ 
+
+ align:start position:0%
+variables are coming
+variables but some are not and you have
+
+ align:start position:0%
+variables but some are not and you have
+ 
+
+ align:start position:0%
+variables but some are not and you have
+to deal with that okay we know that if
+
+ align:start position:0%
+to deal with that okay we know that if
+ 
+
+ align:start position:0%
+to deal with that okay we know that if
+we have as for example in a three
+
+ align:start position:0%
+we have as for example in a three
+ 
+
+ align:start position:0%
+we have as for example in a three
+dimensional harmonic oscillator if we
+
+ align:start position:0%
+dimensional harmonic oscillator if we
+ 
+
+ align:start position:0%
+dimensional harmonic oscillator if we
+have a Hamiltonian that doesn't commute
+
+ align:start position:0%
+have a Hamiltonian that doesn't commute
+ 
+
+ align:start position:0%
+have a Hamiltonian that doesn't commute
+if we can divide the system up in two
+
+ align:start position:0%
+if we can divide the system up in two
+ 
+
+ align:start position:0%
+if we can divide the system up in two
+parts and the Hamiltonian for each part
+
+ align:start position:0%
+parts and the Hamiltonian for each part
+ 
+
+ align:start position:0%
+parts and the Hamiltonian for each part
+commutes with the Hamiltonian for the
+
+ align:start position:0%
+commutes with the Hamiltonian for the
+ 
+
+ align:start position:0%
+commutes with the Hamiltonian for the
+other part which is part of this then
+
+ align:start position:0%
+other part which is part of this then
+ 
+
+ align:start position:0%
+other part which is part of this then
+the you can write the Hamiltonian as a
+
+ align:start position:0%
+the you can write the Hamiltonian as a
+ 
+
+ align:start position:0%
+the you can write the Hamiltonian as a
+sum of individual system hamiltonians
+
+ align:start position:0%
+sum of individual system hamiltonians
+ 
+
+ align:start position:0%
+sum of individual system hamiltonians
+that could be with each other the
+
+ align:start position:0%
+that could be with each other the
+ 
+
+ align:start position:0%
+that could be with each other the
+energies as the sum and the wave
+
+ align:start position:0%
+energies as the sum and the wave
+ 
+
+ align:start position:0%
+energies as the sum and the wave
+functions is the product and so we like
+
+ align:start position:0%
+functions is the product and so we like
+ 
+
+ align:start position:0%
+functions is the product and so we like
+that and we'd like to be able to build a
+
+ align:start position:0%
+that and we'd like to be able to build a
+ 
+
+ align:start position:0%
+that and we'd like to be able to build a
+picture for helium that is like that and
+
+ align:start position:0%
+picture for helium that is like that and
+ 
+
+ align:start position:0%
+picture for helium that is like that and
+so if we write the Hamiltonian for
+
+ align:start position:0%
+so if we write the Hamiltonian for
+ 
+
+ align:start position:0%
+so if we write the Hamiltonian for
+helium we have P squared for particle 1
+
+ align:start position:0%
+helium we have P squared for particle 1
+ 
+
+ align:start position:0%
+helium we have P squared for particle 1
+over 2m e of B squared I don't know let
+
+ align:start position:0%
+over 2m e of B squared I don't know let
+ 
+
+ align:start position:0%
+over 2m e of B squared I don't know let
+me let me organize better minus Z Z
+
+ align:start position:0%
+me let me organize better minus Z Z
+ 
+
+ align:start position:0%
+me let me organize better minus Z Z
+squared over 4 PI epsilon zero R one and
+
+ align:start position:0%
+squared over 4 PI epsilon zero R one and
+ 
+
+ align:start position:0%
+squared over 4 PI epsilon zero R one and
+then we have another term like this for
+
+ align:start position:0%
+then we have another term like this for
+ 
+
+ align:start position:0%
+then we have another term like this for
+particle two and we can call this
+
+ align:start position:0%
+particle two and we can call this
+ 
+
+ align:start position:0%
+particle two and we can call this
+Hamiltonian one I Hamiltonian one in
+
+ align:start position:0%
+Hamiltonian one I Hamiltonian one in
+ 
+
+ align:start position:0%
+Hamiltonian one I Hamiltonian one in
+this Hamiltonian - and these are
+
+ align:start position:0%
+this Hamiltonian - and these are
+ 
+
+ align:start position:0%
+this Hamiltonian - and these are
+hydrogen atom hamiltonians and we know
+
+ align:start position:0%
+hydrogen atom hamiltonians and we know
+ 
+
+ align:start position:0%
+hydrogen atom hamiltonians and we know
+everything about them so it's a
+
+ align:start position:0%
+everything about them so it's a
+ 
+
+ align:start position:0%
+everything about them so it's a
+fantastic way to build up a basis set
+
+ align:start position:0%
+fantastic way to build up a basis set
+ 
+
+ align:start position:0%
+fantastic way to build up a basis set
+consisting of energy zero order energies
+
+ align:start position:0%
+consisting of energy zero order energies
+ 
+
+ align:start position:0%
+consisting of energy zero order energies
+and zero order wave functions with which
+
+ align:start position:0%
+and zero order wave functions with which
+ 
+
+ align:start position:0%
+and zero order wave functions with which
+we can calculate anything and so then we
+
+ align:start position:0%
+we can calculate anything and so then we
+ 
+
+ align:start position:0%
+we can calculate anything and so then we
+have this one other term which - no plus
+
+ align:start position:0%
+have this one other term which - no plus
+ 
+
+ align:start position:0%
+have this one other term which - no plus
+x squared
+
+ align:start position:0%
+x squared
+ 
+
+ align:start position:0%
+x squared
+over 4pi epsilon 0 / 1 - r are vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the bad news this says we have a
+
+ align:start position:0%
+that's the bad news this says we have a
+ 
+
+ align:start position:0%
+that's the bad news this says we have a
+Hamiltonian which where we can't use the
+
+ align:start position:0%
+Hamiltonian which where we can't use the
+ 
+
+ align:start position:0%
+Hamiltonian which where we can't use the
+eigenvalues and eigen functions of the
+
+ align:start position:0%
+eigenvalues and eigen functions of the
+ 
+
+ align:start position:0%
+eigenvalues and eigen functions of the
+hydrogenic things unless we do so we can
+
+ align:start position:0%
+hydrogenic things unless we do so we can
+ 
+
+ align:start position:0%
+hydrogenic things unless we do so we can
+say well these give the first-order
+
+ align:start position:0%
+say well these give the first-order
+ 
+
+ align:start position:0%
+say well these give the first-order
+energies for whatever state we want but
+
+ align:start position:0%
+energies for whatever state we want but
+ 
+
+ align:start position:0%
+energies for whatever state we want but
+we can calculate matrix elements of this
+
+ align:start position:0%
+we can calculate matrix elements of this
+ 
+
+ align:start position:0%
+we can calculate matrix elements of this
+term in the basis set associated with
+
+ align:start position:0%
+term in the basis set associated with
+ 
+
+ align:start position:0%
+term in the basis set associated with
+hydrogen and that's fine that's
+
+ align:start position:0%
+hydrogen and that's fine that's
+ 
+
+ align:start position:0%
+hydrogen and that's fine that's
+perfectly good way to calculate the
+
+ align:start position:0%
+perfectly good way to calculate the
+ 
+
+ align:start position:0%
+perfectly good way to calculate the
+first order correction to the energy but
+
+ align:start position:0%
+first order correction to the energy but
+ 
+
+ align:start position:0%
+first order correction to the energy but
+what about this when we do perturbation
+
+ align:start position:0%
+what about this when we do perturbation
+ 
+
+ align:start position:0%
+what about this when we do perturbation
+theory and calculate the second order
+
+ align:start position:0%
+theory and calculate the second order
+ 
+
+ align:start position:0%
+theory and calculate the second order
+corrections to the energy what is that
+
+ align:start position:0%
+corrections to the energy what is that
+ 
+
+ align:start position:0%
+corrections to the energy what is that
+usually made
+
+ align:start position:0%
+usually made
+ 
+
+ align:start position:0%
+usually made
+that's the question clearly enough well
+
+ align:start position:0%
+that's the question clearly enough well
+ 
+
+ align:start position:0%
+that's the question clearly enough well
+you have to do to get these second-order
+
+ align:start position:0%
+you have to do to get these second-order
+ 
+
+ align:start position:0%
+you have to do to get these second-order
+energies in an infinite dimension
+
+ align:start position:0%
+energies in an infinite dimension
+ 
+
+ align:start position:0%
+energies in an infinite dimension
+problem I just gave it away somebody has
+
+ align:start position:0%
+problem I just gave it away somebody has
+ 
+
+ align:start position:0%
+problem I just gave it away somebody has
+to have the courage to to say something
+
+ align:start position:0%
+to have the courage to to say something
+ 
+
+ align:start position:0%
+to have the courage to to say something
+here remember we have a sum and not
+
+ align:start position:0%
+here remember we have a sum and not
+ 
+
+ align:start position:0%
+here remember we have a sum and not
+equal to n from 0 to infinity yeah
+
+ align:start position:0%
+equal to n from 0 to infinity yeah
+ 
+
+ align:start position:0%
+equal to n from 0 to infinity yeah
+that's it you okay I encouraged you so
+
+ align:start position:0%
+that's it you okay I encouraged you so
+ 
+
+ align:start position:0%
+that's it you okay I encouraged you so
+the the way we could use this basis set
+
+ align:start position:0%
+the the way we could use this basis set
+ 
+
+ align:start position:0%
+the the way we could use this basis set
+would be in a perturbation Theory format
+
+ align:start position:0%
+would be in a perturbation Theory format
+ 
+
+ align:start position:0%
+would be in a perturbation Theory format
+is to calculate an infinite number of
+
+ align:start position:0%
+is to calculate an infinite number of
+ 
+
+ align:start position:0%
+is to calculate an infinite number of
+off diagonal matrix elements of the
+
+ align:start position:0%
+off diagonal matrix elements of the
+ 
+
+ align:start position:0%
+off diagonal matrix elements of the
+hydrogenic wave functions and that could
+
+ align:start position:0%
+hydrogenic wave functions and that could
+ 
+
+ align:start position:0%
+hydrogenic wave functions and that could
+yield the results but it's not the way
+
+ align:start position:0%
+yield the results but it's not the way
+ 
+
+ align:start position:0%
+yield the results but it's not the way
+it's done usually there's a variational
+
+ align:start position:0%
+it's done usually there's a variational
+ 
+
+ align:start position:0%
+it's done usually there's a variational
+calculation that you use to get the
+
+ align:start position:0%
+calculation that you use to get the
+ 
+
+ align:start position:0%
+calculation that you use to get the
+better wave functions but we're not
+
+ align:start position:0%
+better wave functions but we're not
+ 
+
+ align:start position:0%
+better wave functions but we're not
+going to do that here we're going to go
+
+ align:start position:0%
+going to do that here we're going to go
+ 
+
+ align:start position:0%
+going to do that here we're going to go
+as far as we can without actually
+
+ align:start position:0%
+as far as we can without actually
+ 
+
+ align:start position:0%
+as far as we can without actually
+addressing what's wrong if we stop here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this guy is h1 the source of all
+
+ align:start position:0%
+okay so this guy is h1 the source of all
+ 
+
+ align:start position:0%
+okay so this guy is h1 the source of all
+trouble and how we deal with it is there
+
+ align:start position:0%
+trouble and how we deal with it is there
+ 
+
+ align:start position:0%
+trouble and how we deal with it is there
+are two steps three steps one is ignore
+
+ align:start position:0%
+are two steps three steps one is ignore
+ 
+
+ align:start position:0%
+are two steps three steps one is ignore
+it the other is use it to calculate use
+
+ align:start position:0%
+it the other is use it to calculate use
+ 
+
+ align:start position:0%
+it the other is use it to calculate use
+our hydrogen ions to calculate matrix
+
+ align:start position:0%
+our hydrogen ions to calculate matrix
+ 
+
+ align:start position:0%
+our hydrogen ions to calculate matrix
+elements of this and and get an h1
+
+ align:start position:0%
+elements of this and and get an h1
+ 
+
+ align:start position:0%
+elements of this and and get an h1
+anyone and the third step would be to
+
+ align:start position:0%
+anyone and the third step would be to
+ 
+
+ align:start position:0%
+anyone and the third step would be to
+get the exact answer by doing an
+
+ align:start position:0%
+get the exact answer by doing an
+ 
+
+ align:start position:0%
+get the exact answer by doing an
+infinitely difficult calculation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is going to be a notational
+
+ align:start position:0%
+so this is going to be a notational
+ 
+
+ align:start position:0%
+so this is going to be a notational
+voyage which is horrible because there's
+
+ align:start position:0%
+voyage which is horrible because there's
+ 
+
+ align:start position:0%
+voyage which is horrible because there's
+so because we have many particles and
+
+ align:start position:0%
+so because we have many particles and
+ 
+
+ align:start position:0%
+so because we have many particles and
+particles have coordinates and spins
+
+ align:start position:0%
+particles have coordinates and spins
+ 
+
+ align:start position:0%
+particles have coordinates and spins
+we're going to have an explosion of
+
+ align:start position:0%
+we're going to have an explosion of
+ 
+
+ align:start position:0%
+we're going to have an explosion of
+stuff even if we get rid of the
+
+ align:start position:0%
+stuff even if we get rid of the
+ 
+
+ align:start position:0%
+stuff even if we get rid of the
+extraneous units but let's get rid of
+
+ align:start position:0%
+extraneous units but let's get rid of
+ 
+
+ align:start position:0%
+extraneous units but let's get rid of
+the extraneous units and so atomic units
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can choose any internally consistent
+
+ align:start position:0%
+we can choose any internally consistent
+ 
+
+ align:start position:0%
+we can choose any internally consistent
+set of units we want and in atomic units
+
+ align:start position:0%
+set of units we want and in atomic units
+ 
+
+ align:start position:0%
+set of units we want and in atomic units
+we said say that the mass of the
+
+ align:start position:0%
+we said say that the mass of the
+ 
+
+ align:start position:0%
+we said say that the mass of the
+electron is 1 the charge of the electron
+
+ align:start position:0%
+electron is 1 the charge of the electron
+ 
+
+ align:start position:0%
+electron is 1 the charge of the electron
+is 1 the h-bar is 1 4 PI epsilon 0 is 1
+
+ align:start position:0%
+is 1 the h-bar is 1 4 PI epsilon 0 is 1
+ 
+
+ align:start position:0%
+is 1 the h-bar is 1 4 PI epsilon 0 is 1
+that's good
+
+ align:start position:0%
+that's good
+ 
+
+ align:start position:0%
+that's good
+a lot of stuff just gone away ok and the
+
+ align:start position:0%
+a lot of stuff just gone away ok and the
+ 
+
+ align:start position:0%
+a lot of stuff just gone away ok and the
+energy in atomic units is not 1 the
+
+ align:start position:0%
+energy in atomic units is not 1 the
+ 
+
+ align:start position:0%
+energy in atomic units is not 1 the
+energy in atomic units is minus 2 times
+
+ align:start position:0%
+energy in atomic units is minus 2 times
+ 
+
+ align:start position:0%
+energy in atomic units is minus 2 times
+the energy of the hydrogen ik 1s orbital
+
+ align:start position:0%
+the energy of the hydrogen ik 1s orbital
+ 
+
+ align:start position:0%
+the energy of the hydrogen ik 1s orbital
+and that comes out to be 27 point 2 1
+
+ align:start position:0%
+and that comes out to be 27 point 2 1
+ 
+
+ align:start position:0%
+and that comes out to be 27 point 2 1
+electron volts in more convenient units
+
+ align:start position:0%
+electron volts in more convenient units
+ 
+
+ align:start position:0%
+electron volts in more convenient units
+so so you calculate a number and then
+
+ align:start position:0%
+so so you calculate a number and then
+ 
+
+ align:start position:0%
+so so you calculate a number and then
+you multiply it by this to get the real
+
+ align:start position:0%
+you multiply it by this to get the real
+ 
+
+ align:start position:0%
+you multiply it by this to get the real
+energy ok and the unit of length is a0
+
+ align:start position:0%
+energy ok and the unit of length is a0
+ 
+
+ align:start position:0%
+energy ok and the unit of length is a0
+which is the radius of the N equals 1
+
+ align:start position:0%
+which is the radius of the N equals 1
+ 
+
+ align:start position:0%
+which is the radius of the N equals 1
+hydrogenic Bohr orbital or before orbit
+
+ align:start position:0%
+hydrogenic Bohr orbital or before orbit
+ 
+
+ align:start position:0%
+hydrogenic Bohr orbital or before orbit
+and that's 0.5 to 9 angstroms with a lot
+
+ align:start position:0%
+and that's 0.5 to 9 angstroms with a lot
+ 
+
+ align:start position:0%
+and that's 0.5 to 9 angstroms with a lot
+more digits if you need them
+
+ align:start position:0%
+more digits if you need them
+ 
+
+ align:start position:0%
+more digits if you need them
+ok and the speed of light is 137 in
+
+ align:start position:0%
+ok and the speed of light is 137 in
+ 
+
+ align:start position:0%
+ok and the speed of light is 137 in
+atomic units so this you know everything
+
+ align:start position:0%
+atomic units so this you know everything
+ 
+
+ align:start position:0%
+atomic units so this you know everything
+that you're going to need is either 1 or
+
+ align:start position:0%
+that you're going to need is either 1 or
+ 
+
+ align:start position:0%
+that you're going to need is either 1 or
+something that is related to two ok so
+
+ align:start position:0%
+something that is related to two ok so
+ 
+
+ align:start position:0%
+something that is related to two ok so
+you can you can do this and I don't like
+
+ align:start position:0%
+you can you can do this and I don't like
+ 
+
+ align:start position:0%
+you can you can do this and I don't like
+it because it's so easy in a big
+
+ align:start position:0%
+it because it's so easy in a big
+ 
+
+ align:start position:0%
+it because it's so easy in a big
+calculation to get to get your units
+
+ align:start position:0%
+calculation to get to get your units
+ 
+
+ align:start position:0%
+calculation to get to get your units
+screwed up
+
+ align:start position:0%
+screwed up
+ 
+
+ align:start position:0%
+screwed up
+but it's certainly great for lecturing
+
+ align:start position:0%
+but it's certainly great for lecturing
+ 
+
+ align:start position:0%
+but it's certainly great for lecturing
+and perhaps for writing computer
+
+ align:start position:0%
+and perhaps for writing computer
+ 
+
+ align:start position:0%
+and perhaps for writing computer
+programs okay so let's start with a non
+
+ align:start position:0%
+programs okay so let's start with a non
+ 
+
+ align:start position:0%
+programs okay so let's start with a non
+interacting electron or proximation and
+
+ align:start position:0%
+interacting electron or proximation and
+ 
+
+ align:start position:0%
+interacting electron or proximation and
+in the notes it's represented by these
+
+ align:start position:0%
+in the notes it's represented by these
+ 
+
+ align:start position:0%
+in the notes it's represented by these
+letters I don't know whether there's a
+
+ align:start position:0%
+letters I don't know whether there's a
+ 
+
+ align:start position:0%
+letters I don't know whether there's a
+the this is Troy notation or widely
+
+ align:start position:0%
+the this is Troy notation or widely
+ 
+
+ align:start position:0%
+the this is Troy notation or widely
+adopted in quantum chemical circular
+
+ align:start position:0%
+adopted in quantum chemical circular
+ 
+
+ align:start position:0%
+adopted in quantum chemical circular
+circles but so but it's easier to write
+
+ align:start position:0%
+circles but so but it's easier to write
+ 
+
+ align:start position:0%
+circles but so but it's easier to write
+this than that and that just means we're
+
+ align:start position:0%
+this than that and that just means we're
+ 
+
+ align:start position:0%
+this than that and that just means we're
+going to ignore this we just forget
+
+ align:start position:0%
+going to ignore this we just forget
+ 
+
+ align:start position:0%
+going to ignore this we just forget
+about it now we know that's stupid
+
+ align:start position:0%
+about it now we know that's stupid
+ 
+
+ align:start position:0%
+about it now we know that's stupid
+because the electrons have charge of one
+
+ align:start position:0%
+because the electrons have charge of one
+ 
+
+ align:start position:0%
+because the electrons have charge of one
+and they repel each other and the
+
+ align:start position:0%
+and they repel each other and the
+ 
+
+ align:start position:0%
+and they repel each other and the
+nucleus has charge of two in the case of
+
+ align:start position:0%
+nucleus has charge of two in the case of
+ 
+
+ align:start position:0%
+nucleus has charge of two in the case of
+helium and and so we know that the this
+
+ align:start position:0%
+helium and and so we know that the this
+ 
+
+ align:start position:0%
+helium and and so we know that the this
+term is rather similar to H zero and we
+
+ align:start position:0%
+term is rather similar to H zero and we
+ 
+
+ align:start position:0%
+term is rather similar to H zero and we
+can't expect to get very far completely
+
+ align:start position:0%
+can't expect to get very far completely
+ 
+
+ align:start position:0%
+can't expect to get very far completely
+ignoring it but we can do it we can do a
+
+ align:start position:0%
+ignoring it but we can do it we can do a
+ 
+
+ align:start position:0%
+ignoring it but we can do it we can do a
+calculation and we can find out how well
+
+ align:start position:0%
+calculation and we can find out how well
+ 
+
+ align:start position:0%
+calculation and we can find out how well
+it works so and I'm just first of all
+
+ align:start position:0%
+it works so and I'm just first of all
+ 
+
+ align:start position:0%
+it works so and I'm just first of all
+it's clear in the notes and I'm just
+
+ align:start position:0%
+it's clear in the notes and I'm just
+ 
+
+ align:start position:0%
+it's clear in the notes and I'm just
+going to skip to the answer so the
+
+ align:start position:0%
+going to skip to the answer so the
+ 
+
+ align:start position:0%
+going to skip to the answer so the
+energy for helium in the 1s 1s orbital
+
+ align:start position:0%
+energy for helium in the 1s 1s orbital
+ 
+
+ align:start position:0%
+energy for helium in the 1s 1s orbital
+or 1x1 s configuration when we're going
+
+ align:start position:0%
+or 1x1 s configuration when we're going
+ 
+
+ align:start position:0%
+or 1x1 s configuration when we're going
+to use this word configuration what that
+
+ align:start position:0%
+to use this word configuration what that
+ 
+
+ align:start position:0%
+to use this word configuration what that
+means is the list of orbitals that are
+
+ align:start position:0%
+means is the list of orbitals that are
+ 
+
+ align:start position:0%
+means is the list of orbitals that are
+occupied now we're listening principal
+
+ align:start position:0%
+occupied now we're listening principal
+ 
+
+ align:start position:0%
+occupied now we're listening principal
+quantum number and orbital angular
+
+ align:start position:0%
+quantum number and orbital angular
+ 
+
+ align:start position:0%
+quantum number and orbital angular
+momentum there's more stuff which
+
+ align:start position:0%
+momentum there's more stuff which
+ 
+
+ align:start position:0%
+momentum there's more stuff which
+doesn't get listed and that leads to
+
+ align:start position:0%
+doesn't get listed and that leads to
+ 
+
+ align:start position:0%
+doesn't get listed and that leads to
+very interesting stuff but if we have a
+
+ align:start position:0%
+very interesting stuff but if we have a
+ 
+
+ align:start position:0%
+very interesting stuff but if we have a
+list of the orbitals that are occupied
+
+ align:start position:0%
+list of the orbitals that are occupied
+ 
+
+ align:start position:0%
+list of the orbitals that are occupied
+that's called the electronic
+
+ align:start position:0%
+that's called the electronic
+ 
+
+ align:start position:0%
+that's called the electronic
+configuration and I'm an electronic
+
+ align:start position:0%
+configuration and I'm an electronic
+ 
+
+ align:start position:0%
+configuration and I'm an electronic
+spectroscopy so you can be sure the
+
+ align:start position:0%
+spectroscopy so you can be sure the
+ 
+
+ align:start position:0%
+spectroscopy so you can be sure the
+is something I care a lot about so so we
+
+ align:start position:0%
+is something I care a lot about so so we
+ 
+
+ align:start position:0%
+is something I care a lot about so so we
+can calculate this in the hydrogen
+
+ align:start position:0%
+can calculate this in the hydrogen
+ 
+
+ align:start position:0%
+can calculate this in the hydrogen
+acacia sand what you end up getting is
+
+ align:start position:0%
+acacia sand what you end up getting is
+ 
+
+ align:start position:0%
+acacia sand what you end up getting is
+where is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm sorry this is the experimental value
+
+ align:start position:0%
+I'm sorry this is the experimental value
+ 
+
+ align:start position:0%
+I'm sorry this is the experimental value
+Vig the calculated value is C I'm trying
+
+ align:start position:0%
+Vig the calculated value is C I'm trying
+ 
+
+ align:start position:0%
+Vig the calculated value is C I'm trying
+to improve on my notes and in my present
+
+ align:start position:0%
+to improve on my notes and in my present
+ 
+
+ align:start position:0%
+to improve on my notes and in my present
+state I don't make a lot of mistakes so
+
+ align:start position:0%
+state I don't make a lot of mistakes so
+ 
+
+ align:start position:0%
+state I don't make a lot of mistakes so
+that is 108 point 8 electron volts so
+
+ align:start position:0%
+that is 108 point 8 electron volts so
+ 
+
+ align:start position:0%
+that is 108 point 8 electron volts so
+this is the energy of the 1s 1s state
+
+ align:start position:0%
+this is the energy of the 1s 1s state
+ 
+
+ align:start position:0%
+this is the energy of the 1s 1s state
+below the ionization limit so that's
+
+ align:start position:0%
+below the ionization limit so that's
+ 
+
+ align:start position:0%
+below the ionization limit so that's
+what we predict except this is not the
+
+ align:start position:0%
+what we predict except this is not the
+ 
+
+ align:start position:0%
+what we predict except this is not the
+ionization limit this is helium 2 plus
+
+ align:start position:0%
+ionization limit this is helium 2 plus
+ 
+
+ align:start position:0%
+ionization limit this is helium 2 plus
+plus 2 electrons because we use the
+
+ align:start position:0%
+plus 2 electrons because we use the
+ 
+
+ align:start position:0%
+plus 2 electrons because we use the
+energy to ionize both hydrogen atoms and
+
+ align:start position:0%
+energy to ionize both hydrogen atoms and
+ 
+
+ align:start position:0%
+energy to ionize both hydrogen atoms and
+so that so this is 108 point 8 now you
+
+ align:start position:0%
+so that so this is 108 point 8 now you
+ 
+
+ align:start position:0%
+so that so this is 108 point 8 now you
+can measure this experimentally you can
+
+ align:start position:0%
+can measure this experimentally you can
+ 
+
+ align:start position:0%
+can measure this experimentally you can
+do helium helium plus plus electron and
+
+ align:start position:0%
+do helium helium plus plus electron and
+ 
+
+ align:start position:0%
+do helium helium plus plus electron and
+then he then plus going to helium 2 plus
+
+ align:start position:0%
+then he then plus going to helium 2 plus
+ 
+
+ align:start position:0%
+then he then plus going to helium 2 plus
+plus an electron and the observed value
+
+ align:start position:0%
+plus an electron and the observed value
+ 
+
+ align:start position:0%
+plus an electron and the observed value
+is what I wrote before observed is equal
+
+ align:start position:0%
+is what I wrote before observed is equal
+ 
+
+ align:start position:0%
+is what I wrote before observed is equal
+to minus 70 9.0 electron volt well you
+
+ align:start position:0%
+to minus 70 9.0 electron volt well you
+ 
+
+ align:start position:0%
+to minus 70 9.0 electron volt well you
+might say well that's pretty good it's
+
+ align:start position:0%
+might say well that's pretty good it's
+ 
+
+ align:start position:0%
+might say well that's pretty good it's
+the same order of magnitude it's not
+
+ align:start position:0%
+the same order of magnitude it's not
+ 
+
+ align:start position:0%
+the same order of magnitude it's not
+even off by a factor 2 but
+
+ align:start position:0%
+even off by a factor 2 but
+ 
+
+ align:start position:0%
+even off by a factor 2 but
+almost everybody in this room is a
+
+ align:start position:0%
+almost everybody in this room is a
+ 
+
+ align:start position:0%
+almost everybody in this room is a
+chemist and this distance difference
+
+ align:start position:0%
+chemist and this distance difference
+ 
+
+ align:start position:0%
+chemist and this distance difference
+between the the calculated value and the
+
+ align:start position:0%
+between the the calculated value and the
+ 
+
+ align:start position:0%
+between the the calculated value and the
+observed value is 30 electron volts a
+
+ align:start position:0%
+observed value is 30 electron volts a
+ 
+
+ align:start position:0%
+observed value is 30 electron volts a
+chemical bond is typically 5 electron
+
+ align:start position:0%
+chemical bond is typically 5 electron
+ 
+
+ align:start position:0%
+chemical bond is typically 5 electron
+volts so this is totally ridiculous for
+
+ align:start position:0%
+volts so this is totally ridiculous for
+ 
+
+ align:start position:0%
+volts so this is totally ridiculous for
+chemistry we can't use it it we don't
+
+ align:start position:0%
+chemistry we can't use it it we don't
+ 
+
+ align:start position:0%
+chemistry we can't use it it we don't
+even want to think about it because it's
+
+ align:start position:0%
+even want to think about it because it's
+ 
+
+ align:start position:0%
+even want to think about it because it's
+you know it's an order of magnitude away
+
+ align:start position:0%
+you know it's an order of magnitude away
+ 
+
+ align:start position:0%
+you know it's an order of magnitude away
+from what we need so we improve on it by
+
+ align:start position:0%
+from what we need so we improve on it by
+ 
+
+ align:start position:0%
+from what we need so we improve on it by
+including II 1 which is related to H 1
+
+ align:start position:0%
+including II 1 which is related to H 1
+ 
+
+ align:start position:0%
+including II 1 which is related to H 1
+which is that simple looking thing over
+
+ align:start position:0%
+which is that simple looking thing over
+ 
+
+ align:start position:0%
+which is that simple looking thing over
+there so the inner electron repulsions
+
+ align:start position:0%
+there so the inner electron repulsions
+ 
+
+ align:start position:0%
+there so the inner electron repulsions
+can be dealt with not exactly
+
+ align:start position:0%
+can be dealt with not exactly
+ 
+
+ align:start position:0%
+can be dealt with not exactly
+but by calculating diagonal matrix
+
+ align:start position:0%
+but by calculating diagonal matrix
+ 
+
+ align:start position:0%
+but by calculating diagonal matrix
+elements of the inner electronic
+
+ align:start position:0%
+elements of the inner electronic
+ 
+
+ align:start position:0%
+elements of the inner electronic
+electron repulsion and that's what the
+
+ align:start position:0%
+electron repulsion and that's what the
+ 
+
+ align:start position:0%
+electron repulsion and that's what the
+the independent electron approximation
+
+ align:start position:0%
+the independent electron approximation
+ 
+
+ align:start position:0%
+the independent electron approximation
+is so that's all there is but now we
+
+ align:start position:0%
+is so that's all there is but now we
+ 
+
+ align:start position:0%
+is so that's all there is but now we
+bring in something that we hadn't
+
+ align:start position:0%
+bring in something that we hadn't
+ 
+
+ align:start position:0%
+bring in something that we hadn't
+expected would be a problem so we have
+
+ align:start position:0%
+expected would be a problem so we have
+ 
+
+ align:start position:0%
+expected would be a problem so we have
+this mystical or mythical or whatever
+
+ align:start position:0%
+this mystical or mythical or whatever
+ 
+
+ align:start position:0%
+this mystical or mythical or whatever
+operator p1 to operate on some function
+
+ align:start position:0%
+operator p1 to operate on some function
+ 
+
+ align:start position:0%
+operator p1 to operate on some function
+of r1 and r2 and what it does is it
+
+ align:start position:0%
+of r1 and r2 and what it does is it
+ 
+
+ align:start position:0%
+of r1 and r2 and what it does is it
+permutes the electrons we know that if
+
+ align:start position:0%
+permutes the electrons we know that if
+ 
+
+ align:start position:0%
+permutes the electrons we know that if
+something is operating on the names of
+
+ align:start position:0%
+something is operating on the names of
+ 
+
+ align:start position:0%
+something is operating on the names of
+the electrons it has to commute with the
+
+ align:start position:0%
+the electrons it has to commute with the
+ 
+
+ align:start position:0%
+the electrons it has to commute with the
+Hamiltonian so that means that this
+
+ align:start position:0%
+Hamiltonian so that means that this
+ 
+
+ align:start position:0%
+Hamiltonian so that means that this
+operator has to have eigenvalues if if
+
+ align:start position:0%
+operator has to have eigenvalues if if
+ 
+
+ align:start position:0%
+operator has to have eigenvalues if if
+these states are eigenfunctions
+
+ align:start position:0%
+these states are eigenfunctions
+ 
+
+ align:start position:0%
+these states are eigenfunctions
+tonin and there are two possible
+
+ align:start position:0%
+tonin and there are two possible
+ 
+
+ align:start position:0%
+tonin and there are two possible
+eigenvalues because we know P 1 2
+
+ align:start position:0%
+eigenvalues because we know P 1 2
+ 
+
+ align:start position:0%
+eigenvalues because we know P 1 2
+squared on sy is equal to plus so the
+
+ align:start position:0%
+squared on sy is equal to plus so the
+ 
+
+ align:start position:0%
+squared on sy is equal to plus so the
+only way you can do that is having the
+
+ align:start position:0%
+only way you can do that is having the
+ 
+
+ align:start position:0%
+only way you can do that is having the
+eigen value of the permutation operator
+
+ align:start position:0%
+eigen value of the permutation operator
+ 
+
+ align:start position:0%
+eigen value of the permutation operator
+be either plus 1 or minus 1 and this is
+
+ align:start position:0%
+be either plus 1 or minus 1 and this is
+ 
+
+ align:start position:0%
+be either plus 1 or minus 1 and this is
+a fundamental symmetry and it I can't
+
+ align:start position:0%
+a fundamental symmetry and it I can't
+ 
+
+ align:start position:0%
+a fundamental symmetry and it I can't
+possibly tell you where it comes from or
+
+ align:start position:0%
+possibly tell you where it comes from or
+ 
+
+ align:start position:0%
+possibly tell you where it comes from or
+where what I'm about to write on the
+
+ align:start position:0%
+where what I'm about to write on the
+ 
+
+ align:start position:0%
+where what I'm about to write on the
+board comes from but so Oh half f
+
+ align:start position:0%
+board comes from but so Oh half f
+ 
+
+ align:start position:0%
+board comes from but so Oh half f
+integer spins correspond to anti
+
+ align:start position:0%
+integer spins correspond to anti
+ 
+
+ align:start position:0%
+integer spins correspond to anti
+symmetry or belong to the eigenvalue
+
+ align:start position:0%
+symmetry or belong to the eigenvalue
+ 
+
+ align:start position:0%
+symmetry or belong to the eigenvalue
+minus 1 and they're called fermions and
+
+ align:start position:0%
+minus 1 and they're called fermions and
+ 
+
+ align:start position:0%
+minus 1 and they're called fermions and
+integer spins are symmetric with
+
+ align:start position:0%
+integer spins are symmetric with
+ 
+
+ align:start position:0%
+integer spins are symmetric with
+permutation and so integer are symmetric
+
+ align:start position:0%
+permutation and so integer are symmetric
+ 
+
+ align:start position:0%
+permutation and so integer are symmetric
+and they're bosons so we have to write
+
+ align:start position:0%
+and they're bosons so we have to write
+ 
+
+ align:start position:0%
+and they're bosons so we have to write
+wave functions which are wave functions
+
+ align:start position:0%
+wave functions which are wave functions
+ 
+
+ align:start position:0%
+wave functions which are wave functions
+of the electrons which are anti
+
+ align:start position:0%
+of the electrons which are anti
+ 
+
+ align:start position:0%
+of the electrons which are anti
+symmetric with respect to the
+
+ align:start position:0%
+symmetric with respect to the
+ 
+
+ align:start position:0%
+symmetric with respect to the
+permutation of every pair of electrons
+
+ align:start position:0%
+permutation of every pair of electrons
+ 
+
+ align:start position:0%
+permutation of every pair of electrons
+so helium we only have two electrons
+
+ align:start position:0%
+so helium we only have two electrons
+ 
+
+ align:start position:0%
+so helium we only have two electrons
+it's not so bad but any when you when
+
+ align:start position:0%
+it's not so bad but any when you when
+ 
+
+ align:start position:0%
+it's not so bad but any when you when
+you think about something like carbon
+
+ align:start position:0%
+you think about something like carbon
+ 
+
+ align:start position:0%
+you think about something like carbon
+monoxide which I always think about or
+
+ align:start position:0%
+monoxide which I always think about or
+ 
+
+ align:start position:0%
+monoxide which I always think about or
+some other molecule where there's more
+
+ align:start position:0%
+some other molecule where there's more
+ 
+
+ align:start position:0%
+some other molecule where there's more
+than two electrons there's a god-awful
+
+ align:start position:0%
+than two electrons there's a god-awful
+ 
+
+ align:start position:0%
+than two electrons there's a god-awful
+number of permutations and you have to
+
+ align:start position:0%
+number of permutations and you have to
+ 
+
+ align:start position:0%
+number of permutations and you have to
+build them all into the wave function
+
+ align:start position:0%
+build them all into the wave function
+ 
+
+ align:start position:0%
+build them all into the wave function
+and the normal feeling when you hear
+
+ align:start position:0%
+and the normal feeling when you hear
+ 
+
+ align:start position:0%
+and the normal feeling when you hear
+that is oh no I can't possibly imagine
+
+ align:start position:0%
+that is oh no I can't possibly imagine
+ 
+
+ align:start position:0%
+that is oh no I can't possibly imagine
+how to do that and if I could there
+
+ align:start position:0%
+how to do that and if I could there
+ 
+
+ align:start position:0%
+how to do that and if I could there
+would be a ridiculous number of
+
+ align:start position:0%
+would be a ridiculous number of
+ 
+
+ align:start position:0%
+would be a ridiculous number of
+integrals that I would have
+
+ align:start position:0%
+integrals that I would have
+ 
+
+ align:start position:0%
+integrals that I would have
+evaluate and it's true there are a
+
+ align:start position:0%
+evaluate and it's true there are a
+ 
+
+ align:start position:0%
+evaluate and it's true there are a
+ridiculous number of integrals but there
+
+ align:start position:0%
+ridiculous number of integrals but there
+ 
+
+ align:start position:0%
+ridiculous number of integrals but there
+is a simple algebra that enables you how
+
+ align:start position:0%
+is a simple algebra that enables you how
+ 
+
+ align:start position:0%
+is a simple algebra that enables you how
+to deal with them and it involves
+
+ align:start position:0%
+to deal with them and it involves
+ 
+
+ align:start position:0%
+to deal with them and it involves
+creating using what is called Slater
+
+ align:start position:0%
+creating using what is called Slater
+ 
+
+ align:start position:0%
+creating using what is called Slater
+determinant wave functions and I'll talk
+
+ align:start position:0%
+determinant wave functions and I'll talk
+ 
+
+ align:start position:0%
+determinant wave functions and I'll talk
+about that Slater was an MIT professor
+
+ align:start position:0%
+about that Slater was an MIT professor
+ 
+
+ align:start position:0%
+about that Slater was an MIT professor
+he wrote a lot of books and but his
+
+ align:start position:0%
+he wrote a lot of books and but his
+ 
+
+ align:start position:0%
+he wrote a lot of books and but his
+mother thing integer
+
+ align:start position:0%
+mother thing integer
+ 
+
+ align:start position:0%
+mother thing integer
+Oh there's sort of a the-- the the most
+
+ align:start position:0%
+Oh there's sort of a the-- the the most
+ 
+
+ align:start position:0%
+Oh there's sort of a the-- the the most
+important thing he did was to develop
+
+ align:start position:0%
+important thing he did was to develop
+ 
+
+ align:start position:0%
+important thing he did was to develop
+this way of dealing with anti-symmetric
+
+ align:start position:0%
+this way of dealing with anti-symmetric
+ 
+
+ align:start position:0%
+this way of dealing with anti-symmetric
+electronic wave functions so the next
+
+ align:start position:0%
+electronic wave functions so the next
+ 
+
+ align:start position:0%
+electronic wave functions so the next
+thing we have to do is discover how do
+
+ align:start position:0%
+thing we have to do is discover how do
+ 
+
+ align:start position:0%
+thing we have to do is discover how do
+we build symmetric wave functions for
+
+ align:start position:0%
+we build symmetric wave functions for
+ 
+
+ align:start position:0%
+we build symmetric wave functions for
+the simplest possible case where there's
+
+ align:start position:0%
+the simplest possible case where there's
+ 
+
+ align:start position:0%
+the simplest possible case where there's
+two electrons and already we discover
+
+ align:start position:0%
+two electrons and already we discover
+ 
+
+ align:start position:0%
+two electrons and already we discover
+some surprising consequences for this
+
+ align:start position:0%
+some surprising consequences for this
+ 
+
+ align:start position:0%
+some surprising consequences for this
+and so I'm going to go through this but
+
+ align:start position:0%
+and so I'm going to go through this but
+ 
+
+ align:start position:0%
+and so I'm going to go through this but
+I'm going to skip a lot of steps because
+
+ align:start position:0%
+I'm going to skip a lot of steps because
+ 
+
+ align:start position:0%
+I'm going to skip a lot of steps because
+it's so clearly written in the notes and
+
+ align:start position:0%
+it's so clearly written in the notes and
+ 
+
+ align:start position:0%
+it's so clearly written in the notes and
+because we don't really have time to
+
+ align:start position:0%
+because we don't really have time to
+ 
+
+ align:start position:0%
+because we don't really have time to
+deal with fifteen pages of single spaced
+
+ align:start position:0%
+deal with fifteen pages of single spaced
+ 
+
+ align:start position:0%
+deal with fifteen pages of single spaced
+notes and I'm not sufficiently at my
+
+ align:start position:0%
+notes and I'm not sufficiently at my
+ 
+
+ align:start position:0%
+notes and I'm not sufficiently at my
+best to get through maybe twelve and you
+
+ align:start position:0%
+best to get through maybe twelve and you
+ 
+
+ align:start position:0%
+best to get through maybe twelve and you
+don't want that anyway okay so let us
+
+ align:start position:0%
+don't want that anyway okay so let us
+ 
+
+ align:start position:0%
+don't want that anyway okay so let us
+see what what has what happens here and
+
+ align:start position:0%
+see what what has what happens here and
+ 
+
+ align:start position:0%
+see what what has what happens here and
+so let's get to work suppose we have an
+
+ align:start position:0%
+so let's get to work suppose we have an
+ 
+
+ align:start position:0%
+so let's get to work suppose we have an
+electronic state 1s alpha spins we know
+
+ align:start position:0%
+electronic state 1s alpha spins we know
+ 
+
+ align:start position:0%
+electronic state 1s alpha spins we know
+alphas MS equals plus 1/2 and beta is
+
+ align:start position:0%
+alphas MS equals plus 1/2 and beta is
+ 
+
+ align:start position:0%
+alphas MS equals plus 1/2 and beta is
+m/s equals minus 1/2 so this is the
+
+ align:start position:0%
+m/s equals minus 1/2 so this is the
+ 
+
+ align:start position:0%
+m/s equals minus 1/2 so this is the
+spatial coordinate this is the spin
+
+ align:start position:0%
+spatial coordinate this is the spin
+ 
+
+ align:start position:0%
+spatial coordinate this is the spin
+coordinate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here is a simple product of two
+
+ align:start position:0%
+okay so here is a simple product of two
+ 
+
+ align:start position:0%
+okay so here is a simple product of two
+wave functions and we know what they are
+
+ align:start position:0%
+wave functions and we know what they are
+ 
+
+ align:start position:0%
+wave functions and we know what they are
+and so if we apply p1 to this we get
+
+ align:start position:0%
+and so if we apply p1 to this we get
+ 
+
+ align:start position:0%
+and so if we apply p1 to this we get
+side 1s alpha are 2 Sigma 2 s beta R 1
+
+ align:start position:0%
+side 1s alpha are 2 Sigma 2 s beta R 1
+ 
+
+ align:start position:0%
+side 1s alpha are 2 Sigma 2 s beta R 1
+Sigma 1 we don't even know what this is
+
+ align:start position:0%
+Sigma 1 we don't even know what this is
+ 
+
+ align:start position:0%
+Sigma 1 we don't even know what this is
+relative to that so symbolically these
+
+ align:start position:0%
+relative to that so symbolically these
+ 
+
+ align:start position:0%
+relative to that so symbolically these
+are two unrelated quantities so we're
+
+ align:start position:0%
+are two unrelated quantities so we're
+ 
+
+ align:start position:0%
+are two unrelated quantities so we're
+but they are eigenfunctions of the zero
+
+ align:start position:0%
+but they are eigenfunctions of the zero
+ 
+
+ align:start position:0%
+but they are eigenfunctions of the zero
+order Hamiltonian so we can take a
+
+ align:start position:0%
+order Hamiltonian so we can take a
+ 
+
+ align:start position:0%
+order Hamiltonian so we can take a
+linear combination of eigenfunctions
+
+ align:start position:0%
+linear combination of eigenfunctions
+ 
+
+ align:start position:0%
+linear combination of eigenfunctions
+that belong to the same eigenvalue and
+
+ align:start position:0%
+that belong to the same eigenvalue and
+ 
+
+ align:start position:0%
+that belong to the same eigenvalue and
+it's still the same energy so we do that
+
+ align:start position:0%
+it's still the same energy so we do that
+ 
+
+ align:start position:0%
+it's still the same energy so we do that
+and so what we can do is is write a
+
+ align:start position:0%
+and so what we can do is is write a
+ 
+
+ align:start position:0%
+and so what we can do is is write a
+combination of this function and that
+
+ align:start position:0%
+combination of this function and that
+ 
+
+ align:start position:0%
+combination of this function and that
+function and if we do that so now we can
+
+ align:start position:0%
+function and if we do that so now we can
+ 
+
+ align:start position:0%
+function and if we do that so now we can
+have side 1s 2s and what we get is 1 or
+
+ align:start position:0%
+have side 1s 2s and what we get is 1 or
+ 
+
+ align:start position:0%
+have side 1s 2s and what we get is 1 or
+a square root of 2 for normalization and
+
+ align:start position:0%
+a square root of 2 for normalization and
+ 
+
+ align:start position:0%
+a square root of 2 for normalization and
+we have side 1s alpha R 1 Sigma 1 minus
+
+ align:start position:0%
+we have side 1s alpha R 1 Sigma 1 minus
+ 
+
+ align:start position:0%
+we have side 1s alpha R 1 Sigma 1 minus
+sy 1 s beta R 1 R 2 Sigma 2 and this in
+
+ align:start position:0%
+sy 1 s beta R 1 R 2 Sigma 2 and this in
+ 
+
+ align:start position:0%
+sy 1 s beta R 1 R 2 Sigma 2 and this in
+fact is anti-symmetric if you apply the
+
+ align:start position:0%
+fact is anti-symmetric if you apply the
+ 
+
+ align:start position:0%
+fact is anti-symmetric if you apply the
+permutation operator to this it is an
+
+ align:start position:0%
+permutation operator to this it is an
+ 
+
+ align:start position:0%
+permutation operator to this it is an
+anti-symmetric function so this does the
+
+ align:start position:0%
+anti-symmetric function so this does the
+ 
+
+ align:start position:0%
+anti-symmetric function so this does the
+job
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now since the hamiltonian doesn't depend
+
+ align:start position:0%
+now since the hamiltonian doesn't depend
+ 
+
+ align:start position:0%
+now since the hamiltonian doesn't depend
+on spin the energy of this state and the
+
+ align:start position:0%
+on spin the energy of this state and the
+ 
+
+ align:start position:0%
+on spin the energy of this state and the
+energy of that state are the same there
+
+ align:start position:0%
+energy of that state are the same there
+ 
+
+ align:start position:0%
+energy of that state are the same there
+hydrogenic and so using this wave
+
+ align:start position:0%
+hydrogenic and so using this wave
+ 
+
+ align:start position:0%
+hydrogenic and so using this wave
+function rather than the individual non
+
+ align:start position:0%
+function rather than the individual non
+ 
+
+ align:start position:0%
+function rather than the individual non
+symmetrized functions doesn't change the
+
+ align:start position:0%
+symmetrized functions doesn't change the
+ 
+
+ align:start position:0%
+symmetrized functions doesn't change the
+energy so are we wasting our time I'm
+
+ align:start position:0%
+energy so are we wasting our time I'm
+ 
+
+ align:start position:0%
+energy so are we wasting our time I'm
+sorry I just want to see what I what I
+
+ align:start position:0%
+sorry I just want to see what I what I
+ 
+
+ align:start position:0%
+sorry I just want to see what I what I
+wrote here so yeah what I wrote is wrong
+
+ align:start position:0%
+wrote here so yeah what I wrote is wrong
+ 
+
+ align:start position:0%
+wrote here so yeah what I wrote is wrong
+1s alpha and we'll just put one in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 s beta 2 minus 1s alpha 2 1 s beta 1
+
+ align:start position:0%
+1 s beta 2 minus 1s alpha 2 1 s beta 1
+ 
+
+ align:start position:0%
+1 s beta 2 minus 1s alpha 2 1 s beta 1
+ok this is what I should have written
+
+ align:start position:0%
+ok this is what I should have written
+ 
+
+ align:start position:0%
+ok this is what I should have written
+and this is in fact anti-symmetric thank
+
+ align:start position:0%
+and this is in fact anti-symmetric thank
+ 
+
+ align:start position:0%
+and this is in fact anti-symmetric thank
+you I wrote what's in my notes which is
+
+ align:start position:0%
+you I wrote what's in my notes which is
+ 
+
+ align:start position:0%
+you I wrote what's in my notes which is
+wrong and that's and I didn't realize I
+
+ align:start position:0%
+wrong and that's and I didn't realize I
+ 
+
+ align:start position:0%
+wrong and that's and I didn't realize I
+had done that because I knew the answer
+
+ align:start position:0%
+had done that because I knew the answer
+ 
+
+ align:start position:0%
+had done that because I knew the answer
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+ok so we can use this kind of function
+
+ align:start position:0%
+ok so we can use this kind of function
+ 
+
+ align:start position:0%
+ok so we can use this kind of function
+it's legal because it's an eigenfunction
+
+ align:start position:0%
+it's legal because it's an eigenfunction
+ 
+
+ align:start position:0%
+it's legal because it's an eigenfunction
+of the permutation operator with
+
+ align:start position:0%
+of the permutation operator with
+ 
+
+ align:start position:0%
+of the permutation operator with
+negative symmetry which we're told
+
+ align:start position:0%
+negative symmetry which we're told
+ 
+
+ align:start position:0%
+negative symmetry which we're told
+that's what we have to use for electrons
+
+ align:start position:0%
+that's what we have to use for electrons
+ 
+
+ align:start position:0%
+that's what we have to use for electrons
+I can't tell you where it comes from
+
+ align:start position:0%
+I can't tell you where it comes from
+ 
+
+ align:start position:0%
+I can't tell you where it comes from
+although it came from Pauli and the
+
+ align:start position:0%
+although it came from Pauli and the
+ 
+
+ align:start position:0%
+although it came from Pauli and the
+exclusion principle really is this
+
+ align:start position:0%
+exclusion principle really is this
+ 
+
+ align:start position:0%
+exclusion principle really is this
+rather than what you've memorized its
+
+ align:start position:0%
+rather than what you've memorized its
+ 
+
+ align:start position:0%
+rather than what you've memorized its
+consequence is that you can only put one
+
+ align:start position:0%
+consequence is that you can only put one
+ 
+
+ align:start position:0%
+consequence is that you can only put one
+elect
+
+ align:start position:0%
+elect
+ 
+
+ align:start position:0%
+elect
+on orbital but this is the exclusion
+
+ align:start position:0%
+on orbital but this is the exclusion
+ 
+
+ align:start position:0%
+on orbital but this is the exclusion
+principle and it is poly okay so now we
+
+ align:start position:0%
+principle and it is poly okay so now we
+ 
+
+ align:start position:0%
+principle and it is poly okay so now we
+know what to do and we can calculate the
+
+ align:start position:0%
+know what to do and we can calculate the
+ 
+
+ align:start position:0%
+know what to do and we can calculate the
+matrix elements so i1 s alpha colon 1 s
+
+ align:start position:0%
+matrix elements so i1 s alpha colon 1 s
+ 
+
+ align:start position:0%
+matrix elements so i1 s alpha colon 1 s
+beta this is a product of 2 the anti
+
+ align:start position:0%
+beta this is a product of 2 the anti
+ 
+
+ align:start position:0%
+beta this is a product of 2 the anti
+symmetries product of 2 electrons matrix
+
+ align:start position:0%
+symmetries product of 2 electrons matrix
+ 
+
+ align:start position:0%
+symmetries product of 2 electrons matrix
+element 1 for Hamiltonian 1 plus 1 over
+
+ align:start position:0%
+element 1 for Hamiltonian 1 plus 1 over
+ 
+
+ align:start position:0%
+element 1 for Hamiltonian 1 plus 1 over
+R 1 minus R 2 alpha know this is a
+
+ align:start position:0%
+R 1 minus R 2 alpha know this is a
+ 
+
+ align:start position:0%
+R 1 minus R 2 alpha know this is a
+perfectly legitimate thing to calculate
+
+ align:start position:0%
+perfectly legitimate thing to calculate
+ 
+
+ align:start position:0%
+perfectly legitimate thing to calculate
+we know how to do it or McQuarrie knows
+
+ align:start position:0%
+we know how to do it or McQuarrie knows
+ 
+
+ align:start position:0%
+we know how to do it or McQuarrie knows
+how to do it and you don't really need
+
+ align:start position:0%
+how to do it and you don't really need
+ 
+
+ align:start position:0%
+how to do it and you don't really need
+to worry about doing these integrals
+
+ align:start position:0%
+to worry about doing these integrals
+ 
+
+ align:start position:0%
+to worry about doing these integrals
+because what this is at such a low level
+
+ align:start position:0%
+because what this is at such a low level
+ 
+
+ align:start position:0%
+because what this is at such a low level
+of approximation it does nothing for you
+
+ align:start position:0%
+of approximation it does nothing for you
+ 
+
+ align:start position:0%
+of approximation it does nothing for you
+except teach you how to approach these
+
+ align:start position:0%
+except teach you how to approach these
+ 
+
+ align:start position:0%
+except teach you how to approach these
+problems but we can still do these
+
+ align:start position:0%
+problems but we can still do these
+ 
+
+ align:start position:0%
+problems but we can still do these
+integrals and it's useful so what do you
+
+ align:start position:0%
+integrals and it's useful so what do you
+ 
+
+ align:start position:0%
+integrals and it's useful so what do you
+get when you get minus 4 why because
+
+ align:start position:0%
+get when you get minus 4 why because
+ 
+
+ align:start position:0%
+get when you get minus 4 why because
+these are hydrogenic with a nucleus of
+
+ align:start position:0%
+these are hydrogenic with a nucleus of
+ 
+
+ align:start position:0%
+these are hydrogenic with a nucleus of
+plus 2 and in the atomic units the
+
+ align:start position:0%
+plus 2 and in the atomic units the
+ 
+
+ align:start position:0%
+plus 2 and in the atomic units the
+energy of hydrogen atom to a charge of 1
+
+ align:start position:0%
+energy of hydrogen atom to a charge of 1
+ 
+
+ align:start position:0%
+energy of hydrogen atom to a charge of 1
+is 1/2 not 1 and so and these go as Z
+
+ align:start position:0%
+is 1/2 not 1 and so and these go as Z
+ 
+
+ align:start position:0%
+is 1/2 not 1 and so and these go as Z
+squared so we get 4 over 2 plus 4 over 2
+
+ align:start position:0%
+squared so we get 4 over 2 plus 4 over 2
+ 
+
+ align:start position:0%
+squared so we get 4 over 2 plus 4 over 2
+so we get this minus 4 oh you get - yes
+
+ align:start position:0%
+so we get this minus 4 oh you get - yes
+ 
+
+ align:start position:0%
+so we get this minus 4 oh you get - yes
+and then we get something else and
+
+ align:start position:0%
+and then we get something else and
+ 
+
+ align:start position:0%
+and then we get something else and
+that's this this integral that we look
+
+ align:start position:0%
+that's this this integral that we look
+ 
+
+ align:start position:0%
+that's this this integral that we look
+like which is integral of 1 s alpha beta
+
+ align:start position:0%
+like which is integral of 1 s alpha beta
+ 
+
+ align:start position:0%
+like which is integral of 1 s alpha beta
+squared over R 1 minus R 2
+
+ align:start position:0%
+squared over R 1 minus R 2
+ 
+
+ align:start position:0%
+squared over R 1 minus R 2
+our one the two so we can do this
+
+ align:start position:0%
+our one the two so we can do this
+ 
+
+ align:start position:0%
+our one the two so we can do this
+integral or mr. Macquarie and many of
+
+ align:start position:0%
+integral or mr. Macquarie and many of
+ 
+
+ align:start position:0%
+integral or mr. Macquarie and many of
+his predecessors can do that integral
+
+ align:start position:0%
+his predecessors can do that integral
+ 
+
+ align:start position:0%
+his predecessors can do that integral
+and you get a result and this integral
+
+ align:start position:0%
+and you get a result and this integral
+ 
+
+ align:start position:0%
+and you get a result and this integral
+turns out to be 5z over eight and
+
+ align:start position:0%
+turns out to be 5z over eight and
+ 
+
+ align:start position:0%
+turns out to be 5z over eight and
+converting that into units that we are
+
+ align:start position:0%
+converting that into units that we are
+ 
+
+ align:start position:0%
+converting that into units that we are
+and that's 5/4 au and that's why that
+
+ align:start position:0%
+and that's 5/4 au and that's why that
+ 
+
+ align:start position:0%
+and that's 5/4 au and that's why that
+doesn't seem right
+
+ align:start position:0%
+doesn't seem right
+ 
+
+ align:start position:0%
+doesn't seem right
+anyway it's 34 electron volts or minus
+
+ align:start position:0%
+anyway it's 34 electron volts or minus
+ 
+
+ align:start position:0%
+anyway it's 34 electron volts or minus
+34 electron plus plus 34 electron volts
+
+ align:start position:0%
+34 electron plus plus 34 electron volts
+ 
+
+ align:start position:0%
+34 electron plus plus 34 electron volts
+so the inter electronic repulsion for
+
+ align:start position:0%
+so the inter electronic repulsion for
+ 
+
+ align:start position:0%
+so the inter electronic repulsion for
+hydrogenic orbitals on the same nucleus
+
+ align:start position:0%
+hydrogenic orbitals on the same nucleus
+ 
+
+ align:start position:0%
+hydrogenic orbitals on the same nucleus
+is 34 electoral votes it's a big number
+
+ align:start position:0%
+is 34 electoral votes it's a big number
+ 
+
+ align:start position:0%
+is 34 electoral votes it's a big number
+and so we can correct our observed the
+
+ align:start position:0%
+and so we can correct our observed the
+ 
+
+ align:start position:0%
+and so we can correct our observed the
+calculated vs. observed energy and
+
+ align:start position:0%
+calculated vs. observed energy and
+ 
+
+ align:start position:0%
+calculated vs. observed energy and
+instead of having well the experimental
+
+ align:start position:0%
+instead of having well the experimental
+ 
+
+ align:start position:0%
+instead of having well the experimental
+value is 79 and now the calculated value
+
+ align:start position:0%
+value is 79 and now the calculated value
+ 
+
+ align:start position:0%
+value is 79 and now the calculated value
+is minus seventy four point eight
+
+ align:start position:0%
+is minus seventy four point eight
+ 
+
+ align:start position:0%
+is minus seventy four point eight
+electron volts so this is marginally
+
+ align:start position:0%
+electron volts so this is marginally
+ 
+
+ align:start position:0%
+electron volts so this is marginally
+relevant to chemistry because the error
+
+ align:start position:0%
+relevant to chemistry because the error
+ 
+
+ align:start position:0%
+relevant to chemistry because the error
+is about one of the typical binds bond
+
+ align:start position:0%
+is about one of the typical binds bond
+ 
+
+ align:start position:0%
+is about one of the typical binds bond
+energy and so we can we can do stuff
+
+ align:start position:0%
+energy and so we can we can do stuff
+ 
+
+ align:start position:0%
+energy and so we can we can do stuff
+with this we know that it's not accurate
+
+ align:start position:0%
+with this we know that it's not accurate
+ 
+
+ align:start position:0%
+with this we know that it's not accurate
+enough to do anything quantitative but
+
+ align:start position:0%
+enough to do anything quantitative but
+ 
+
+ align:start position:0%
+enough to do anything quantitative but
+you can use it for qualitative arguments
+
+ align:start position:0%
+you can use it for qualitative arguments
+ 
+
+ align:start position:0%
+you can use it for qualitative arguments
+and we can do much better than this
+
+ align:start position:0%
+and we can do much better than this
+ 
+
+ align:start position:0%
+and we can do much better than this
+using what's going to be called the
+
+ align:start position:0%
+using what's going to be called the
+ 
+
+ align:start position:0%
+using what's going to be called the
+variational principle which is coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we're going to be dealing
+
+ align:start position:0%
+okay so now we're going to be dealing
+ 
+
+ align:start position:0%
+okay so now we're going to be dealing
+with a problem that has lots of symbols
+
+ align:start position:0%
+with a problem that has lots of symbols
+ 
+
+ align:start position:0%
+with a problem that has lots of symbols
+and equations and it's best to start
+
+ align:start position:0%
+and equations and it's best to start
+ 
+
+ align:start position:0%
+and equations and it's best to start
+using notation called stick diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it's completely transparent what
+
+ align:start position:0%
+because it's completely transparent what
+ 
+
+ align:start position:0%
+because it's completely transparent what
+they mean and so it's a shortcut for
+
+ align:start position:0%
+they mean and so it's a shortcut for
+ 
+
+ align:start position:0%
+they mean and so it's a shortcut for
+writing the correct equations so we we
+
+ align:start position:0%
+writing the correct equations so we we
+ 
+
+ align:start position:0%
+writing the correct equations so we we
+have for the ground state of hydrogen
+
+ align:start position:0%
+have for the ground state of hydrogen
+ 
+
+ align:start position:0%
+have for the ground state of hydrogen
+I'm sorry we want to talk about excited
+
+ align:start position:0%
+I'm sorry we want to talk about excited
+ 
+
+ align:start position:0%
+I'm sorry we want to talk about excited
+States because 1s with 1s doesn't have
+
+ align:start position:0%
+States because 1s with 1s doesn't have
+ 
+
+ align:start position:0%
+States because 1s with 1s doesn't have
+enough complexity to attract our
+
+ align:start position:0%
+enough complexity to attract our
+ 
+
+ align:start position:0%
+enough complexity to attract our
+attention and it when we do deal with
+
+ align:start position:0%
+attention and it when we do deal with
+ 
+
+ align:start position:0%
+attention and it when we do deal with
+excited States 1s and 2s we discover
+
+ align:start position:0%
+excited States 1s and 2s we discover
+ 
+
+ align:start position:0%
+excited States 1s and 2s we discover
+something important that's new and it's
+
+ align:start position:0%
+something important that's new and it's
+ 
+
+ align:start position:0%
+something important that's new and it's
+the last thing we really need in order
+
+ align:start position:0%
+the last thing we really need in order
+ 
+
+ align:start position:0%
+the last thing we really need in order
+to understand electronic structure or
+
+ align:start position:0%
+to understand electronic structure or
+ 
+
+ align:start position:0%
+to understand electronic structure or
+how the electronic states that arise
+
+ align:start position:0%
+how the electronic states that arise
+ 
+
+ align:start position:0%
+how the electronic states that arise
+from a configuration are distinguished
+
+ align:start position:0%
+from a configuration are distinguished
+ 
+
+ align:start position:0%
+from a configuration are distinguished
+and so we have for the 1s 2s
+
+ align:start position:0%
+and so we have for the 1s 2s
+ 
+
+ align:start position:0%
+and so we have for the 1s 2s
+configuration there are 4 ways of
+
+ align:start position:0%
+configuration there are 4 ways of
+ 
+
+ align:start position:0%
+configuration there are 4 ways of
+writing this in stick diagrams so we
+
+ align:start position:0%
+writing this in stick diagrams so we
+ 
+
+ align:start position:0%
+writing this in stick diagrams so we
+have 1s 2s and we can have spins up
+
+ align:start position:0%
+have 1s 2s and we can have spins up
+ 
+
+ align:start position:0%
+have 1s 2s and we can have spins up
+alpha alpha and we can have us - we can
+
+ align:start position:0%
+alpha alpha and we can have us - we can
+ 
+
+ align:start position:0%
+alpha alpha and we can have us - we can
+have spins up and down us - it spins
+
+ align:start position:0%
+have spins up and down us - it spins
+ 
+
+ align:start position:0%
+have spins up and down us - it spins
+down and up and 2's what else spins down
+
+ align:start position:0%
+down and up and 2's what else spins down
+ 
+
+ align:start position:0%
+down and up and 2's what else spins down
+so it's much easier to write these
+
+ align:start position:0%
+so it's much easier to write these
+ 
+
+ align:start position:0%
+so it's much easier to write these
+things because they have a
+
+ align:start position:0%
+things because they have a
+ 
+
+ align:start position:0%
+things because they have a
+an equation associated with them and you
+
+ align:start position:0%
+an equation associated with them and you
+ 
+
+ align:start position:0%
+an equation associated with them and you
+can you can play with these symbols so
+
+ align:start position:0%
+can you can play with these symbols so
+ 
+
+ align:start position:0%
+can you can play with these symbols so
+the first thing you notice is this
+
+ align:start position:0%
+the first thing you notice is this
+ 
+
+ align:start position:0%
+the first thing you notice is this
+symbol can be written as an anti
+
+ align:start position:0%
+symbol can be written as an anti
+ 
+
+ align:start position:0%
+symbol can be written as an anti
+symmetrized product and so this symbol
+
+ align:start position:0%
+symmetrized product and so this symbol
+ 
+
+ align:start position:0%
+symmetrized product and so this symbol
+you know we just take the alpha alpha
+
+ align:start position:0%
+you know we just take the alpha alpha
+ 
+
+ align:start position:0%
+you know we just take the alpha alpha
+and so let me just write it out 1 over
+
+ align:start position:0%
+and so let me just write it out 1 over
+ 
+
+ align:start position:0%
+and so let me just write it out 1 over
+square root of 2 times 1 s r1 to s r2
+
+ align:start position:0%
+square root of 2 times 1 s r1 to s r2
+ 
+
+ align:start position:0%
+square root of 2 times 1 s r1 to s r2
+minus so I 1s are - sigh - s r1 and then
+
+ align:start position:0%
+minus so I 1s are - sigh - s r1 and then
+ 
+
+ align:start position:0%
+minus so I 1s are - sigh - s r1 and then
+times a spin part alpha we can just
+
+ align:start position:0%
+times a spin part alpha we can just
+ 
+
+ align:start position:0%
+times a spin part alpha we can just
+abbreviate to 1 and alpha ok so we have
+
+ align:start position:0%
+abbreviate to 1 and alpha ok so we have
+ 
+
+ align:start position:0%
+abbreviate to 1 and alpha ok so we have
+factored the wave function to a spatial
+
+ align:start position:0%
+factored the wave function to a spatial
+ 
+
+ align:start position:0%
+factored the wave function to a spatial
+part and a spin part now I'll make an
+
+ align:start position:0%
+part and a spin part now I'll make an
+ 
+
+ align:start position:0%
+part and a spin part now I'll make an
+outrageous statement doesn't matter how
+
+ align:start position:0%
+outrageous statement doesn't matter how
+ 
+
+ align:start position:0%
+outrageous statement doesn't matter how
+many electrons you'll always be able to
+
+ align:start position:0%
+many electrons you'll always be able to
+ 
+
+ align:start position:0%
+many electrons you'll always be able to
+factor it into a special part and a spin
+
+ align:start position:0%
+factor it into a special part and a spin
+ 
+
+ align:start position:0%
+factor it into a special part and a spin
+part now what is necessary is always
+
+ align:start position:0%
+part now what is necessary is always
+ 
+
+ align:start position:0%
+part now what is necessary is always
+this function that has to be anti
+
+ align:start position:0%
+this function that has to be anti
+ 
+
+ align:start position:0%
+this function that has to be anti
+symmetric and in this case it's the
+
+ align:start position:0%
+symmetric and in this case it's the
+ 
+
+ align:start position:0%
+symmetric and in this case it's the
+spatial part that's anti symmetric and
+
+ align:start position:0%
+spatial part that's anti symmetric and
+ 
+
+ align:start position:0%
+spatial part that's anti symmetric and
+the spin part that's symmetric now when
+
+ align:start position:0%
+the spin part that's symmetric now when
+ 
+
+ align:start position:0%
+the spin part that's symmetric now when
+we try to do these to stick diagrams we
+
+ align:start position:0%
+we try to do these to stick diagrams we
+ 
+
+ align:start position:0%
+we try to do these to stick diagrams we
+cannot write any correct equation for
+
+ align:start position:0%
+cannot write any correct equation for
+ 
+
+ align:start position:0%
+cannot write any correct equation for
+this guy we have to do both of them we
+
+ align:start position:0%
+this guy we have to do both of them we
+ 
+
+ align:start position:0%
+this guy we have to do both of them we
+have to combine the two and that will
+
+ align:start position:0%
+have to combine the two and that will
+ 
+
+ align:start position:0%
+have to combine the two and that will
+give us a separated spin part in spatial
+
+ align:start position:0%
+give us a separated spin part in spatial
+ 
+
+ align:start position:0%
+give us a separated spin part in spatial
+part and it's anti-symmetric you can't
+
+ align:start position:0%
+part and it's anti-symmetric you can't
+ 
+
+ align:start position:0%
+part and it's anti-symmetric you can't
+make an antisymmetric function of this
+
+ align:start position:0%
+make an antisymmetric function of this
+ 
+
+ align:start position:0%
+make an antisymmetric function of this
+just switching the coordinates so
+
+ align:start position:0%
+just switching the coordinates so
+ 
+
+ align:start position:0%
+just switching the coordinates so
+and what you find when you do this is
+
+ align:start position:0%
+and what you find when you do this is
+ 
+
+ align:start position:0%
+and what you find when you do this is
+going to be that we get functions which
+
+ align:start position:0%
+going to be that we get functions which
+ 
+
+ align:start position:0%
+going to be that we get functions which
+look like alpha beta plus or minus beta
+
+ align:start position:0%
+look like alpha beta plus or minus beta
+ 
+
+ align:start position:0%
+look like alpha beta plus or minus beta
+alpha okay so spin one alpha spin to
+
+ align:start position:0%
+alpha okay so spin one alpha spin to
+ 
+
+ align:start position:0%
+alpha okay so spin one alpha spin to
+beta plus or minus spin one beta spin to
+
+ align:start position:0%
+beta plus or minus spin one beta spin to
+ 
+
+ align:start position:0%
+beta plus or minus spin one beta spin to
+alpha and it turns out that there are
+
+ align:start position:0%
+alpha and it turns out that there are
+ 
+
+ align:start position:0%
+alpha and it turns out that there are
+three functions three spin functions
+
+ align:start position:0%
+three functions three spin functions
+ 
+
+ align:start position:0%
+three functions three spin functions
+that we get which are symmetric and all
+
+ align:start position:0%
+that we get which are symmetric and all
+ 
+
+ align:start position:0%
+that we get which are symmetric and all
+three of these are associated with this
+
+ align:start position:0%
+three of these are associated with this
+ 
+
+ align:start position:0%
+three of these are associated with this
+anti-symmetric spatial function they
+
+ align:start position:0%
+anti-symmetric spatial function they
+ 
+
+ align:start position:0%
+anti-symmetric spatial function they
+have the same energy and since there are
+
+ align:start position:0%
+have the same energy and since there are
+ 
+
+ align:start position:0%
+have the same energy and since there are
+three of them we call them a triplet and
+
+ align:start position:0%
+three of them we call them a triplet and
+ 
+
+ align:start position:0%
+three of them we call them a triplet and
+since we're talking about spins this
+
+ align:start position:0%
+since we're talking about spins this
+ 
+
+ align:start position:0%
+since we're talking about spins this
+triplet corresponds to s equals one and
+
+ align:start position:0%
+triplet corresponds to s equals one and
+ 
+
+ align:start position:0%
+triplet corresponds to s equals one and
+you can use s equals one and creation
+
+ align:start position:0%
+you can use s equals one and creation
+ 
+
+ align:start position:0%
+you can use s equals one and creation
+and annihilation operators or raising
+
+ align:start position:0%
+and annihilation operators or raising
+ 
+
+ align:start position:0%
+and annihilation operators or raising
+and lowering operators to show that
+
+ align:start position:0%
+and lowering operators to show that
+ 
+
+ align:start position:0%
+and lowering operators to show that
+these are in fact the three eigenstates
+
+ align:start position:0%
+these are in fact the three eigenstates
+ 
+
+ align:start position:0%
+these are in fact the three eigenstates
+of S sub Z so we call it a triplet
+
+ align:start position:0%
+of S sub Z so we call it a triplet
+ 
+
+ align:start position:0%
+of S sub Z so we call it a triplet
+because they're three of them and it
+
+ align:start position:0%
+because they're three of them and it
+ 
+
+ align:start position:0%
+because they're three of them and it
+also corresponds to s equals one and
+
+ align:start position:0%
+also corresponds to s equals one and
+ 
+
+ align:start position:0%
+also corresponds to s equals one and
+there's one alpha beta minus beta alpha
+
+ align:start position:0%
+there's one alpha beta minus beta alpha
+ 
+
+ align:start position:0%
+there's one alpha beta minus beta alpha
+which is antisymmetric and is associated
+
+ align:start position:0%
+which is antisymmetric and is associated
+ 
+
+ align:start position:0%
+which is antisymmetric and is associated
+with a different spatial function which
+
+ align:start position:0%
+with a different spatial function which
+ 
+
+ align:start position:0%
+with a different spatial function which
+is symmetric and it has to have a
+
+ align:start position:0%
+is symmetric and it has to have a
+ 
+
+ align:start position:0%
+is symmetric and it has to have a
+different energy because the hamiltonian
+
+ align:start position:0%
+different energy because the hamiltonian
+ 
+
+ align:start position:0%
+different energy because the hamiltonian
+operates on the spatial part and not on
+
+ align:start position:0%
+operates on the spatial part and not on
+ 
+
+ align:start position:0%
+operates on the spatial part and not on
+the spin part so anti symmetry has
+
+ align:start position:0%
+the spin part so anti symmetry has
+ 
+
+ align:start position:0%
+the spin part so anti symmetry has
+forced you to have two different spatial
+
+ align:start position:0%
+forced you to have two different spatial
+ 
+
+ align:start position:0%
+forced you to have two different spatial
+wave functions and that guarantees that
+
+ align:start position:0%
+wave functions and that guarantees that
+ 
+
+ align:start position:0%
+wave functions and that guarantees that
+these guys will have different energies
+
+ align:start position:0%
+these guys will have different energies
+ 
+
+ align:start position:0%
+these guys will have different energies
+and since there's only one of them we
+
+ align:start position:0%
+and since there's only one of them we
+ 
+
+ align:start position:0%
+and since there's only one of them we
+call it a singlet and it corresponds to
+
+ align:start position:0%
+call it a singlet and it corresponds to
+ 
+
+ align:start position:0%
+call it a singlet and it corresponds to
+s equals zero so now we want to know
+
+ align:start position:0%
+s equals zero so now we want to know
+ 
+
+ align:start position:0%
+s equals zero so now we want to know
+which is higher in energy the singlet or
+
+ align:start position:0%
+which is higher in energy the singlet or
+ 
+
+ align:start position:0%
+which is higher in energy the singlet or
+the triplet and how much higher
+
+ align:start position:0%
+the triplet and how much higher
+ 
+
+ align:start position:0%
+the triplet and how much higher
+and so again we take the wave functions
+
+ align:start position:0%
+and so again we take the wave functions
+ 
+
+ align:start position:0%
+and so again we take the wave functions
+that are correct as far as permutation
+
+ align:start position:0%
+that are correct as far as permutation
+ 
+
+ align:start position:0%
+that are correct as far as permutation
+is concerned but only approximate as far
+
+ align:start position:0%
+is concerned but only approximate as far
+ 
+
+ align:start position:0%
+is concerned but only approximate as far
+as using hydrogenic functions and we
+
+ align:start position:0%
+as using hydrogenic functions and we
+ 
+
+ align:start position:0%
+as using hydrogenic functions and we
+evaluate the relevant terms in the
+
+ align:start position:0%
+evaluate the relevant terms in the
+ 
+
+ align:start position:0%
+evaluate the relevant terms in the
+Hamiltonian okay so we can forget about
+
+ align:start position:0%
+Hamiltonian okay so we can forget about
+ 
+
+ align:start position:0%
+Hamiltonian okay so we can forget about
+the spin parts now we know we're going
+
+ align:start position:0%
+the spin parts now we know we're going
+ 
+
+ align:start position:0%
+the spin parts now we know we're going
+to have two different spatial wave
+
+ align:start position:0%
+to have two different spatial wave
+ 
+
+ align:start position:0%
+to have two different spatial wave
+functions and we're going to calculate
+
+ align:start position:0%
+functions and we're going to calculate
+ 
+
+ align:start position:0%
+functions and we're going to calculate
+yes that should be I can't here I
+
+ align:start position:0%
+yes that should be I can't here I
+ 
+
+ align:start position:0%
+yes that should be I can't here I
+understand the last word no both spins
+
+ align:start position:0%
+understand the last word no both spins
+ 
+
+ align:start position:0%
+understand the last word no both spins
+up the the vector sum of 1/2 and 1/2 is
+
+ align:start position:0%
+up the the vector sum of 1/2 and 1/2 is
+ 
+
+ align:start position:0%
+up the the vector sum of 1/2 and 1/2 is
+1 and so the total spin is going to be 1
+
+ align:start position:0%
+1 and so the total spin is going to be 1
+ 
+
+ align:start position:0%
+1 and so the total spin is going to be 1
+and it'll and so we have three I mean if
+
+ align:start position:0%
+and it'll and so we have three I mean if
+ 
+
+ align:start position:0%
+and it'll and so we have three I mean if
+we're applying s - stop suppose we start
+
+ align:start position:0%
+we're applying s - stop suppose we start
+ 
+
+ align:start position:0%
+we're applying s - stop suppose we start
+with sorry
+
+ align:start position:0%
+with sorry
+ 
+
+ align:start position:0%
+with sorry
+I I can't hear properly yes it has s
+
+ align:start position:0%
+I I can't hear properly yes it has s
+ 
+
+ align:start position:0%
+I I can't hear properly yes it has s
+equals one okay and now I don't want to
+
+ align:start position:0%
+equals one okay and now I don't want to
+ 
+
+ align:start position:0%
+equals one okay and now I don't want to
+go into the the angular momentum a trick
+
+ align:start position:0%
+go into the the angular momentum a trick
+ 
+
+ align:start position:0%
+go into the the angular momentum a trick
+settlement that would be the last thing
+
+ align:start position:0%
+settlement that would be the last thing
+ 
+
+ align:start position:0%
+settlement that would be the last thing
+in this lecture so yes the projection
+
+ align:start position:0%
+in this lecture so yes the projection
+ 
+
+ align:start position:0%
+in this lecture so yes the projection
+quantum numbers are not uniquely
+
+ align:start position:0%
+quantum numbers are not uniquely
+ 
+
+ align:start position:0%
+quantum numbers are not uniquely
+associated with the total spin but if
+
+ align:start position:0%
+associated with the total spin but if
+ 
+
+ align:start position:0%
+associated with the total spin but if
+you have alpha alpha you can show that
+
+ align:start position:0%
+you have alpha alpha you can show that
+ 
+
+ align:start position:0%
+you have alpha alpha you can show that
+it's s equals one and alpha beta plus
+
+ align:start position:0%
+it's s equals one and alpha beta plus
+ 
+
+ align:start position:0%
+it's s equals one and alpha beta plus
+beta alpha is 1 and beta beta is one but
+
+ align:start position:0%
+beta alpha is 1 and beta beta is one but
+ 
+
+ align:start position:0%
+beta alpha is 1 and beta beta is one but
+alpha beta minus beta alpha is spin zero
+
+ align:start position:0%
+alpha beta minus beta alpha is spin zero
+ 
+
+ align:start position:0%
+alpha beta minus beta alpha is spin zero
+you can do that using creation
+
+ align:start position:0%
+you can do that using creation
+ 
+
+ align:start position:0%
+you can do that using creation
+annihilation operators it's clear okay
+
+ align:start position:0%
+annihilation operators it's clear okay
+ 
+
+ align:start position:0%
+annihilation operators it's clear okay
+so you can't have to take it on faith
+
+ align:start position:0%
+so you can't have to take it on faith
+ 
+
+ align:start position:0%
+so you can't have to take it on faith
+until you prove but I've just said and
+
+ align:start position:0%
+until you prove but I've just said and
+ 
+
+ align:start position:0%
+until you prove but I've just said and
+it takes about two minutes okay so we
+
+ align:start position:0%
+it takes about two minutes okay so we
+ 
+
+ align:start position:0%
+it takes about two minutes okay so we
+can evaluate the integrals and something
+
+ align:start position:0%
+can evaluate the integrals and something
+ 
+
+ align:start position:0%
+can evaluate the integrals and something
+very beautiful occurs and it's done very
+
+ align:start position:0%
+very beautiful occurs and it's done very
+ 
+
+ align:start position:0%
+very beautiful occurs and it's done very
+very clearly in the notes and it would
+
+ align:start position:0%
+very clearly in the notes and it would
+ 
+
+ align:start position:0%
+very clearly in the notes and it would
+take me more time do we have left to do
+
+ align:start position:0%
+take me more time do we have left to do
+ 
+
+ align:start position:0%
+take me more time do we have left to do
+it and I didn't plan on do it anyway so
+
+ align:start position:0%
+it and I didn't plan on do it anyway so
+ 
+
+ align:start position:0%
+it and I didn't plan on do it anyway so
+we get the energies for the singlet and
+
+ align:start position:0%
+we get the energies for the singlet and
+ 
+
+ align:start position:0%
+we get the energies for the singlet and
+triplet states which are B 1 s plus e 2
+
+ align:start position:0%
+triplet states which are B 1 s plus e 2
+ 
+
+ align:start position:0%
+triplet states which are B 1 s plus e 2
+s now remember these are for a 1s
+
+ align:start position:0%
+s now remember these are for a 1s
+ 
+
+ align:start position:0%
+s now remember these are for a 1s
+orbital on helium so it's going to be
+
+ align:start position:0%
+orbital on helium so it's going to be
+ 
+
+ align:start position:0%
+orbital on helium so it's going to be
+four times the energy of the 1s orbital
+
+ align:start position:0%
+four times the energy of the 1s orbital
+ 
+
+ align:start position:0%
+four times the energy of the 1s orbital
+of hydrogen but we know what they are
+
+ align:start position:0%
+of hydrogen but we know what they are
+ 
+
+ align:start position:0%
+of hydrogen but we know what they are
+plus what we call J 1s 2s plus or minus
+
+ align:start position:0%
+plus what we call J 1s 2s plus or minus
+ 
+
+ align:start position:0%
+plus what we call J 1s 2s plus or minus
+K 1s
+
+ align:start position:0%
+K 1s
+ 
+
+ align:start position:0%
+K 1s
+yes so this is clear and the integral
+
+ align:start position:0%
+yes so this is clear and the integral
+ 
+
+ align:start position:0%
+yes so this is clear and the integral
+associated with this is taking the
+
+ align:start position:0%
+associated with this is taking the
+ 
+
+ align:start position:0%
+associated with this is taking the
+square of the wave function and
+
+ align:start position:0%
+square of the wave function and
+ 
+
+ align:start position:0%
+square of the wave function and
+basically we're evaluating the
+
+ align:start position:0%
+basically we're evaluating the
+ 
+
+ align:start position:0%
+basically we're evaluating the
+interaction between an electron 1 in the
+
+ align:start position:0%
+interaction between an electron 1 in the
+ 
+
+ align:start position:0%
+interaction between an electron 1 in the
+1s orbital
+
+ align:start position:0%
+1s orbital
+ 
+
+ align:start position:0%
+1s orbital
+an electron to in the 2's orbital so
+
+ align:start position:0%
+an electron to in the 2's orbital so
+ 
+
+ align:start position:0%
+an electron to in the 2's orbital so
+that's a perfectly doable thing it's a
+
+ align:start position:0%
+that's a perfectly doable thing it's a
+ 
+
+ align:start position:0%
+that's a perfectly doable thing it's a
+classical quantity we have to charge
+
+ align:start position:0%
+classical quantity we have to charge
+ 
+
+ align:start position:0%
+classical quantity we have to charge
+distributions and we're calculating the
+
+ align:start position:0%
+distributions and we're calculating the
+ 
+
+ align:start position:0%
+distributions and we're calculating the
+energy interaction between two electrons
+
+ align:start position:0%
+energy interaction between two electrons
+ 
+
+ align:start position:0%
+energy interaction between two electrons
+in these two charge distributions so
+
+ align:start position:0%
+in these two charge distributions so
+ 
+
+ align:start position:0%
+in these two charge distributions so
+this is called the Coulomb integral and
+
+ align:start position:0%
+this is called the Coulomb integral and
+ 
+
+ align:start position:0%
+this is called the Coulomb integral and
+that is an entirely classical quantity
+
+ align:start position:0%
+that is an entirely classical quantity
+ 
+
+ align:start position:0%
+that is an entirely classical quantity
+and this is called the exchange integral
+
+ align:start position:0%
+and this is called the exchange integral
+ 
+
+ align:start position:0%
+and this is called the exchange integral
+and the reason we call it an exchange
+
+ align:start position:0%
+and the reason we call it an exchange
+ 
+
+ align:start position:0%
+and the reason we call it an exchange
+integral is basically we're switching
+
+ align:start position:0%
+integral is basically we're switching
+ 
+
+ align:start position:0%
+integral is basically we're switching
+the electrons between these two orbitals
+
+ align:start position:0%
+the electrons between these two orbitals
+ 
+
+ align:start position:0%
+the electrons between these two orbitals
+and this is something which is entirely
+
+ align:start position:0%
+and this is something which is entirely
+ 
+
+ align:start position:0%
+and this is something which is entirely
+quantum mechanical it comes about
+
+ align:start position:0%
+quantum mechanical it comes about
+ 
+
+ align:start position:0%
+quantum mechanical it comes about
+because of the permutation symmetry
+
+ align:start position:0%
+because of the permutation symmetry
+ 
+
+ align:start position:0%
+because of the permutation symmetry
+that's required for fermions
+
+ align:start position:0%
+that's required for fermions
+ 
+
+ align:start position:0%
+that's required for fermions
+and so this is the surprise and it's
+
+ align:start position:0%
+and so this is the surprise and it's
+ 
+
+ align:start position:0%
+and so this is the surprise and it's
+also depends on the size whether you
+
+ align:start position:0%
+also depends on the size whether you
+ 
+
+ align:start position:0%
+also depends on the size whether you
+have a symmetric or an anti-symmetric or
+
+ align:start position:0%
+have a symmetric or an anti-symmetric or
+ 
+
+ align:start position:0%
+have a symmetric or an anti-symmetric or
+a singlet or a triplet and so you end up
+
+ align:start position:0%
+a singlet or a triplet and so you end up
+ 
+
+ align:start position:0%
+a singlet or a triplet and so you end up
+getting an energy level diagram for the
+
+ align:start position:0%
+getting an energy level diagram for the
+ 
+
+ align:start position:0%
+getting an energy level diagram for the
+snakes of a configuration which looks
+
+ align:start position:0%
+snakes of a configuration which looks
+ 
+
+ align:start position:0%
+snakes of a configuration which looks
+like this so we start out with a 0 1s 2s
+
+ align:start position:0%
+like this so we start out with a 0 1s 2s
+ 
+
+ align:start position:0%
+like this so we start out with a 0 1s 2s
+and then we allow the charge
+
+ align:start position:0%
+and then we allow the charge
+ 
+
+ align:start position:0%
+and then we allow the charge
+distributions to interact and the
+
+ align:start position:0%
+distributions to interact and the
+ 
+
+ align:start position:0%
+distributions to interact and the
+electrons are going to repel each other
+
+ align:start position:0%
+electrons are going to repel each other
+ 
+
+ align:start position:0%
+electrons are going to repel each other
+it's a positive energy and so this is e0
+
+ align:start position:0%
+it's a positive energy and so this is e0
+ 
+
+ align:start position:0%
+it's a positive energy and so this is e0
+plus J and then we include the exchange
+
+ align:start position:0%
+plus J and then we include the exchange
+ 
+
+ align:start position:0%
+plus J and then we include the exchange
+interaction and so this is the
+
+ align:start position:0%
+interaction and so this is the
+ 
+
+ align:start position:0%
+interaction and so this is the
+difference 2 K and this is e 0 plus J
+
+ align:start position:0%
+difference 2 K and this is e 0 plus J
+ 
+
+ align:start position:0%
+difference 2 K and this is e 0 plus J
+plus K and this is e 0 plus J minus K
+
+ align:start position:0%
+plus K and this is e 0 plus J minus K
+ 
+
+ align:start position:0%
+plus K and this is e 0 plus J minus K
+and this is the singlet state as a
+
+ align:start position:0%
+and this is the singlet state as a
+ 
+
+ align:start position:0%
+and this is the singlet state as a
+triplet state and this is a singlet and
+
+ align:start position:0%
+triplet state and this is a singlet and
+ 
+
+ align:start position:0%
+triplet state and this is a singlet and
+for helium we called the singlet state
+
+ align:start position:0%
+for helium we called the singlet state
+ 
+
+ align:start position:0%
+for helium we called the singlet state
+singlet s because total angular momentum
+
+ align:start position:0%
+singlet s because total angular momentum
+ 
+
+ align:start position:0%
+singlet s because total angular momentum
+is 0 and spin has zero and the triplet
+
+ align:start position:0%
+is 0 and spin has zero and the triplet
+ 
+
+ align:start position:0%
+is 0 and spin has zero and the triplet
+we call it triplet us now if
+
+ align:start position:0%
+we call it triplet us now if
+ 
+
+ align:start position:0%
+we call it triplet us now if
+we did one s2p we would get singlet and
+
+ align:start position:0%
+we did one s2p we would get singlet and
+ 
+
+ align:start position:0%
+we did one s2p we would get singlet and
+triplet P states but the important thing
+
+ align:start position:0%
+triplet P states but the important thing
+ 
+
+ align:start position:0%
+triplet P states but the important thing
+is how big is K and remember K is an
+
+ align:start position:0%
+is how big is K and remember K is an
+ 
+
+ align:start position:0%
+is how big is K and remember K is an
+approximation it's it's a real quantity
+
+ align:start position:0%
+approximation it's it's a real quantity
+ 
+
+ align:start position:0%
+approximation it's it's a real quantity
+but for hydrogenic orbitals is going to
+
+ align:start position:0%
+but for hydrogenic orbitals is going to
+ 
+
+ align:start position:0%
+but for hydrogenic orbitals is going to
+be incorrect and so two k12 is 2.4
+
+ align:start position:0%
+be incorrect and so two k12 is 2.4
+ 
+
+ align:start position:0%
+be incorrect and so two k12 is 2.4
+electron volts and that's a perfectly
+
+ align:start position:0%
+electron volts and that's a perfectly
+ 
+
+ align:start position:0%
+electron volts and that's a perfectly
+doable calculation because you're
+
+ align:start position:0%
+doable calculation because you're
+ 
+
+ align:start position:0%
+doable calculation because you're
+dealing with simple functions and you
+
+ align:start position:0%
+dealing with simple functions and you
+ 
+
+ align:start position:0%
+dealing with simple functions and you
+can do this integral and you can
+
+ align:start position:0%
+can do this integral and you can
+ 
+
+ align:start position:0%
+can do this integral and you can
+actually do it in closed form but it's
+
+ align:start position:0%
+actually do it in closed form but it's
+ 
+
+ align:start position:0%
+actually do it in closed form but it's
+2.4 electron volts and experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's 0.8 and this tells you something
+
+ align:start position:0%
+it's 0.8 and this tells you something
+ 
+
+ align:start position:0%
+it's 0.8 and this tells you something
+really important the repulsion between
+
+ align:start position:0%
+really important the repulsion between
+ 
+
+ align:start position:0%
+really important the repulsion between
+two electrons when you have the correct
+
+ align:start position:0%
+two electrons when you have the correct
+ 
+
+ align:start position:0%
+two electrons when you have the correct
+wave function is less than it would be
+
+ align:start position:0%
+wave function is less than it would be
+ 
+
+ align:start position:0%
+wave function is less than it would be
+if you're using the wrong wave functions
+
+ align:start position:0%
+if you're using the wrong wave functions
+ 
+
+ align:start position:0%
+if you're using the wrong wave functions
+and basically whenever you do anything
+
+ align:start position:0%
+and basically whenever you do anything
+ 
+
+ align:start position:0%
+and basically whenever you do anything
+using the wrong wave functions your
+
+ align:start position:0%
+using the wrong wave functions your
+ 
+
+ align:start position:0%
+using the wrong wave functions your
+energy levels are too large or the
+
+ align:start position:0%
+energy levels are too large or the
+ 
+
+ align:start position:0%
+energy levels are too large or the
+energy differences are too large and in
+
+ align:start position:0%
+energy differences are too large and in
+ 
+
+ align:start position:0%
+energy differences are too large and in
+this case the electrons and when you
+
+ align:start position:0%
+this case the electrons and when you
+ 
+
+ align:start position:0%
+this case the electrons and when you
+solve the exact Schrodinger equation the
+
+ align:start position:0%
+solve the exact Schrodinger equation the
+ 
+
+ align:start position:0%
+solve the exact Schrodinger equation the
+electrons know about how to absorb and
+
+ align:start position:0%
+electrons know about how to absorb and
+ 
+
+ align:start position:0%
+electrons know about how to absorb and
+to avoid each other
+
+ align:start position:0%
+to avoid each other
+ 
+
+ align:start position:0%
+to avoid each other
+it's called correlation energy and this
+
+ align:start position:0%
+it's called correlation energy and this
+ 
+
+ align:start position:0%
+it's called correlation energy and this
+is what makes all the calculations hard
+
+ align:start position:0%
+is what makes all the calculations hard
+ 
+
+ align:start position:0%
+is what makes all the calculations hard
+because there is no closed form analytic
+
+ align:start position:0%
+because there is no closed form analytic
+ 
+
+ align:start position:0%
+because there is no closed form analytic
+expression for the correlation energy
+
+ align:start position:0%
+expression for the correlation energy
+ 
+
+ align:start position:0%
+expression for the correlation energy
+and the way you minimize the correlation
+
+ align:start position:0%
+and the way you minimize the correlation
+ 
+
+ align:start position:0%
+and the way you minimize the correlation
+correlation that are you optimize the
+
+ align:start position:0%
+correlation that are you optimize the
+ 
+
+ align:start position:0%
+correlation that are you optimize the
+correlation energy is throwing a huge
+
+ align:start position:0%
+correlation energy is throwing a huge
+ 
+
+ align:start position:0%
+correlation energy is throwing a huge
+basis set at the problem and this is why
+
+ align:start position:0%
+basis set at the problem and this is why
+ 
+
+ align:start position:0%
+basis set at the problem and this is why
+it takes so long and you never know that
+
+ align:start position:0%
+it takes so long and you never know that
+ 
+
+ align:start position:0%
+it takes so long and you never know that
+you've converged until you've thrown
+
+ align:start position:0%
+you've converged until you've thrown
+ 
+
+ align:start position:0%
+you've converged until you've thrown
+another million functions ok but so
+
+ align:start position:0%
+another million functions ok but so
+ 
+
+ align:start position:0%
+another million functions ok but so
+there's several lessons and that is
+
+ align:start position:0%
+there's several lessons and that is
+ 
+
+ align:start position:0%
+there's several lessons and that is
+we have something that's completely
+
+ align:start position:0%
+we have something that's completely
+ 
+
+ align:start position:0%
+we have something that's completely
+classical and we understand what it is
+
+ align:start position:0%
+classical and we understand what it is
+ 
+
+ align:start position:0%
+classical and we understand what it is
+and then we have this extra thing that
+
+ align:start position:0%
+and then we have this extra thing that
+ 
+
+ align:start position:0%
+and then we have this extra thing that
+is a consequence of the permutation
+
+ align:start position:0%
+is a consequence of the permutation
+ 
+
+ align:start position:0%
+is a consequence of the permutation
+symmetry and so this extra thing is we
+
+ align:start position:0%
+symmetry and so this extra thing is we
+ 
+
+ align:start position:0%
+symmetry and so this extra thing is we
+calculate it too big but it sells says
+
+ align:start position:0%
+calculate it too big but it sells says
+ 
+
+ align:start position:0%
+calculate it too big but it sells says
+that if we have states that belong to
+
+ align:start position:0%
+that if we have states that belong to
+ 
+
+ align:start position:0%
+that if we have states that belong to
+the same electronic configuration in
+
+ align:start position:0%
+the same electronic configuration in
+ 
+
+ align:start position:0%
+the same electronic configuration in
+other words if we specify the orbitals
+
+ align:start position:0%
+other words if we specify the orbitals
+ 
+
+ align:start position:0%
+other words if we specify the orbitals
+that are occupied there's going to be
+
+ align:start position:0%
+that are occupied there's going to be
+ 
+
+ align:start position:0%
+that are occupied there's going to be
+more than one electronic state and so
+
+ align:start position:0%
+more than one electronic state and so
+ 
+
+ align:start position:0%
+more than one electronic state and so
+configuration split into many different
+
+ align:start position:0%
+configuration split into many different
+ 
+
+ align:start position:0%
+configuration split into many different
+electronic states and we know the
+
+ align:start position:0%
+electronic states and we know the
+ 
+
+ align:start position:0%
+electronic states and we know the
+machinery that enables us to calculate
+
+ align:start position:0%
+machinery that enables us to calculate
+ 
+
+ align:start position:0%
+machinery that enables us to calculate
+their relative energies and some of it
+
+ align:start position:0%
+their relative energies and some of it
+ 
+
+ align:start position:0%
+their relative energies and some of it
+is simple Coulomb's law and some of it
+
+ align:start position:0%
+is simple Coulomb's law and some of it
+ 
+
+ align:start position:0%
+is simple Coulomb's law and some of it
+is something that's caused by the
+
+ align:start position:0%
+is something that's caused by the
+ 
+
+ align:start position:0%
+is something that's caused by the
+required permutation symmetry so I'm I'm
+
+ align:start position:0%
+required permutation symmetry so I'm I'm
+ 
+
+ align:start position:0%
+required permutation symmetry so I'm I'm
+over time but this is I really I can't
+
+ align:start position:0%
+over time but this is I really I can't
+ 
+
+ align:start position:0%
+over time but this is I really I can't
+believe that I got to this point because
+
+ align:start position:0%
+believe that I got to this point because
+ 
+
+ align:start position:0%
+believe that I got to this point because
+that I delivered everything that was
+
+ align:start position:0%
+that I delivered everything that was
+ 
+
+ align:start position:0%
+that I delivered everything that was
+really important when we have more than
+
+ align:start position:0%
+really important when we have more than
+ 
+
+ align:start position:0%
+really important when we have more than
+two electrons everything I've said is
+
+ align:start position:0%
+two electrons everything I've said is
+ 
+
+ align:start position:0%
+two electrons everything I've said is
+true it's just more complicated and we
+
+ align:start position:0%
+true it's just more complicated and we
+ 
+
+ align:start position:0%
+true it's just more complicated and we
+have to evaluate matrix elements between
+
+ align:start position:0%
+have to evaluate matrix elements between
+ 
+
+ align:start position:0%
+have to evaluate matrix elements between
+determinantal wave functions which looks
+
+ align:start position:0%
+determinantal wave functions which looks
+ 
+
+ align:start position:0%
+determinantal wave functions which looks
+like you know if you have n electrons
+
+ align:start position:0%
+like you know if you have n electrons
+ 
+
+ align:start position:0%
+like you know if you have n electrons
+there's n factorial terms in a
+
+ align:start position:0%
+there's n factorial terms in a
+ 
+
+ align:start position:0%
+there's n factorial terms in a
+determinant and we have n factorial
+
+ align:start position:0%
+determinant and we have n factorial
+ 
+
+ align:start position:0%
+determinant and we have n factorial
+squared matrix elements and you don't
+
+ align:start position:0%
+squared matrix elements and you don't
+ 
+
+ align:start position:0%
+squared matrix elements and you don't
+want to do that but there turns out to
+
+ align:start position:0%
+want to do that but there turns out to
+ 
+
+ align:start position:0%
+want to do that but there turns out to
+be a simple algebra that makes it all
+
+ align:start position:0%
+be a simple algebra that makes it all
+ 
+
+ align:start position:0%
+be a simple algebra that makes it all
+pop out almost with the same level of
+
+ align:start position:0%
+pop out almost with the same level of
+ 
+
+ align:start position:0%
+pop out almost with the same level of
+effort as this and so we'll talk about
+
+ align:start position:0%
+effort as this and so we'll talk about
+ 
+
+ align:start position:0%
+effort as this and so we'll talk about
+many electron atoms and then we'll go on
+
+ align:start position:0%
+many electron atoms and then we'll go on
+ 
+
+ align:start position:0%
+many electron atoms and then we'll go on
+to molecules after the many electron
+
+ align:start position:0%
+to molecules after the many electron
+ 
+
+ align:start position:0%
+to molecules after the many electron
+atoms lecture ok
\ No newline at end of file
diff --git a/Du9eDHwGeAw.txt b/Du9eDHwGeAw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..60e3fda372cc87416a8280047756c52dee195c03
--- /dev/null
+++ b/Du9eDHwGeAw.txt
@@ -0,0 +1,2984 @@
+align:start position:0%
+ 
+it's time for step two what don't we
+
+ align:start position:0%
+it's time for step two what don't we
+ 
+
+ align:start position:0%
+it's time for step two what don't we
+know here well we don't know anything
+
+ align:start position:0%
+know here well we don't know anything
+ 
+
+ align:start position:0%
+know here well we don't know anything
+about the state correction so and one
+
+ align:start position:0%
+about the state correction so and one
+ 
+
+ align:start position:0%
+about the state correction so and one
+what is in one so step two is find the
+
+ align:start position:0%
+what is in one so step two is find the
+ 
+
+ align:start position:0%
+what is in one so step two is find the
+piece of n1k the piece that is in the
+
+ align:start position:0%
+piece of n1k the piece that is in the
+ 
+
+ align:start position:0%
+piece of n1k the piece that is in the
+space be hot so I will use this notation
+
+ align:start position:0%
+space be hot so I will use this notation
+ 
+
+ align:start position:0%
+space be hot so I will use this notation
+a bar here saying of this vector the
+
+ align:start position:0%
+a bar here saying of this vector the
+ 
+
+ align:start position:0%
+a bar here saying of this vector the
+piece in that subspace then we of course
+
+ align:start position:0%
+piece in that subspace then we of course
+ 
+
+ align:start position:0%
+piece in that subspace then we of course
+need to find the piece in the degenerate
+
+ align:start position:0%
+need to find the piece in the degenerate
+ 
+
+ align:start position:0%
+need to find the piece in the degenerate
+subspace remember the corrections are
+
+ align:start position:0%
+subspace remember the corrections are
+ 
+
+ align:start position:0%
+subspace remember the corrections are
+orthogonal to the original state but the
+
+ align:start position:0%
+orthogonal to the original state but the
+ 
+
+ align:start position:0%
+orthogonal to the original state but the
+corrections have can have a piece on VM
+
+ align:start position:0%
+corrections have can have a piece on VM
+ 
+
+ align:start position:0%
+corrections have can have a piece on VM
+the VM has more state so it can't have a
+
+ align:start position:0%
+the VM has more state so it can't have a
+ 
+
+ align:start position:0%
+the VM has more state so it can't have a
+piece in Vienna and that's typically the
+
+ align:start position:0%
+piece in Vienna and that's typically the
+ 
+
+ align:start position:0%
+piece in Vienna and that's typically the
+part that is a little hard to do so what
+
+ align:start position:0%
+part that is a little hard to do so what
+ 
+
+ align:start position:0%
+part that is a little hard to do so what
+do we do here we take the order one
+
+ align:start position:0%
+do we do here we take the order one
+ 
+
+ align:start position:0%
+do we do here we take the order one
+equation lambda equal one and we hit it
+
+ align:start position:0%
+equation lambda equal one and we hit it
+ 
+
+ align:start position:0%
+equation lambda equal one and we hit it
+with peanut so we'll hit with peanut on
+
+ align:start position:0%
+with peanut so we'll hit with peanut on
+ 
+
+ align:start position:0%
+with peanut so we'll hit with peanut on
+the order lambda equation okay so think
+
+ align:start position:0%
+the order lambda equation okay so think
+ 
+
+ align:start position:0%
+the order lambda equation okay so think
+of the peanut vector
+
+ align:start position:0%
+of the peanut vector
+ 
+
+ align:start position:0%
+of the peanut vector
+bra appearing here we know the energy of
+
+ align:start position:0%
+bra appearing here we know the energy of
+ 
+
+ align:start position:0%
+bra appearing here we know the energy of
+it so this will become a number so we
+
+ align:start position:0%
+it so this will become a number so we
+ 
+
+ align:start position:0%
+it so this will become a number so we
+get EP 0 minus e n 0 P naught and 1k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and indeed when you see here you say oh
+
+ align:start position:0%
+and indeed when you see here you say oh
+ 
+
+ align:start position:0%
+and indeed when you see here you say oh
+this is my unknown I don't know the
+
+ align:start position:0%
+this is my unknown I don't know the
+ 
+
+ align:start position:0%
+this is my unknown I don't know the
+first order correction and I'm getting
+
+ align:start position:0%
+first order correction and I'm getting
+ 
+
+ align:start position:0%
+first order correction and I'm getting
+the components of this unknown
+
+ align:start position:0%
+the components of this unknown
+ 
+
+ align:start position:0%
+the components of this unknown
+correction along with V hat space that's
+
+ align:start position:0%
+correction along with V hat space that's
+ 
+
+ align:start position:0%
+correction along with V hat space that's
+why this calculation can only give me
+
+ align:start position:0%
+why this calculation can only give me
+ 
+
+ align:start position:0%
+why this calculation can only give me
+the piece of n1 k along the hat and then
+
+ align:start position:0%
+the piece of n1 k along the hat and then
+ 
+
+ align:start position:0%
+the piece of n1 k along the hat and then
+what do we have here we have P naught e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NK 1 minus Delta H and 0 K it's just
+
+ align:start position:0%
+NK 1 minus Delta H and 0 K it's just
+ 
+
+ align:start position:0%
+NK 1 minus Delta H and 0 K it's just
+that order one equation calculated here
+
+ align:start position:0%
+that order one equation calculated here
+ 
+
+ align:start position:0%
+that order one equation calculated here
+so what is you know you recognize the
+
+ align:start position:0%
+so what is you know you recognize the
+ 
+
+ align:start position:0%
+so what is you know you recognize the
+challenge here is always sort of trying
+
+ align:start position:0%
+challenge here is always sort of trying
+ 
+
+ align:start position:0%
+challenge here is always sort of trying
+to remember what the symbols mean and
+
+ align:start position:0%
+to remember what the symbols mean and
+ 
+
+ align:start position:0%
+to remember what the symbols mean and
+simplify things so for example here this
+
+ align:start position:0%
+simplify things so for example here this
+ 
+
+ align:start position:0%
+simplify things so for example here this
+is a number so what you must ask is
+
+ align:start position:0%
+is a number so what you must ask is
+ 
+
+ align:start position:0%
+is a number so what you must ask is
+whether this vector is orthogonal to
+
+ align:start position:0%
+whether this vector is orthogonal to
+ 
+
+ align:start position:0%
+whether this vector is orthogonal to
+this one because you're gonna get an
+
+ align:start position:0%
+this one because you're gonna get an
+ 
+
+ align:start position:0%
+this one because you're gonna get an
+inner product and this is a vector in V
+
+ align:start position:0%
+inner product and this is a vector in V
+ 
+
+ align:start position:0%
+inner product and this is a vector in V
+hat and this is a vector in V capital n
+
+ align:start position:0%
+hat and this is a vector in V capital n
+ 
+
+ align:start position:0%
+hat and this is a vector in V capital n
+so therefore they are orthogonal so this
+
+ align:start position:0%
+so therefore they are orthogonal so this
+ 
+
+ align:start position:0%
+so therefore they are orthogonal so this
+term vanishes by orthogonal ax T of
+
+ align:start position:0%
+term vanishes by orthogonal ax T of
+ 
+
+ align:start position:0%
+term vanishes by orthogonal ax T of
+these two on the other hand we are left
+
+ align:start position:0%
+these two on the other hand we are left
+ 
+
+ align:start position:0%
+these two on the other hand we are left
+with this part here now that's a matrix
+
+ align:start position:0%
+with this part here now that's a matrix
+ 
+
+ align:start position:0%
+with this part here now that's a matrix
+element of Delta H between the generate
+
+ align:start position:0%
+element of Delta H between the generate
+ 
+
+ align:start position:0%
+element of Delta H between the generate
+state and then the rest of the state so
+
+ align:start position:0%
+state and then the rest of the state so
+ 
+
+ align:start position:0%
+state and then the rest of the state so
+that's something you have to calculate
+
+ align:start position:0%
+that's something you have to calculate
+ 
+
+ align:start position:0%
+that's something you have to calculate
+there's no way around it so we use our
+
+ align:start position:0%
+there's no way around it so we use our
+ 
+
+ align:start position:0%
+there's no way around it so we use our
+notation and in our notation this would
+
+ align:start position:0%
+notation and in our notation this would
+ 
+
+ align:start position:0%
+notation and in our notation this would
+be Delta H P and K all right so this
+
+ align:start position:0%
+be Delta H P and K all right so this
+ 
+
+ align:start position:0%
+be Delta H P and K all right so this
+gives us we're done with this equation
+
+ align:start position:0%
+gives us we're done with this equation
+ 
+
+ align:start position:0%
+gives us we're done with this equation
+it was simple no no big sweat we now
+
+ align:start position:0%
+it was simple no no big sweat we now
+ 
+
+ align:start position:0%
+it was simple no no big sweat we now
+have these coefficients because these
+
+ align:start position:0%
+have these coefficients because these
+ 
+
+ align:start position:0%
+have these coefficients because these
+are numbers and we can just divide over
+
+ align:start position:0%
+are numbers and we can just divide over
+ 
+
+ align:start position:0%
+are numbers and we can just divide over
+here and
+
+ align:start position:0%
+here and
+ 
+
+ align:start position:0%
+here and
+and this factor is nonzero because all
+
+ align:start position:0%
+and this factor is nonzero because all
+ 
+
+ align:start position:0%
+and this factor is nonzero because all
+the peace states that are in we have
+
+ align:start position:0%
+the peace states that are in we have
+ 
+
+ align:start position:0%
+the peace states that are in we have
+have different energy from our
+
+ align:start position:0%
+have different energy from our
+ 
+
+ align:start position:0%
+have different energy from our
+degenerate ones so there are the
+
+ align:start position:0%
+degenerate ones so there are the
+ 
+
+ align:start position:0%
+degenerate ones so there are the
+components of this so we have p 0 and 1
+
+ align:start position:0%
+components of this so we have p 0 and 1
+ 
+
+ align:start position:0%
+components of this so we have p 0 and 1
+k is equal to minus delta h p NK divided
+
+ align:start position:0%
+k is equal to minus delta h p NK divided
+ 
+
+ align:start position:0%
+k is equal to minus delta h p NK divided
+by this quantity p 0 minus e m 0 and
+
+ align:start position:0%
+by this quantity p 0 minus e m 0 and
+ 
+
+ align:start position:0%
+by this quantity p 0 minus e m 0 and
+therefore we can write n 1 k if you have
+
+ align:start position:0%
+therefore we can write n 1 k if you have
+ 
+
+ align:start position:0%
+therefore we can write n 1 k if you have
+the inner products of a state with p
+
+ align:start position:0%
+the inner products of a state with p
+ 
+
+ align:start position:0%
+the inner products of a state with p
+arbitrary the state is the sum of over
+
+ align:start position:0%
+arbitrary the state is the sum of over
+ 
+
+ align:start position:0%
+arbitrary the state is the sum of over
+piece times that inner product so i'll
+
+ align:start position:0%
+piece times that inner product so i'll
+ 
+
+ align:start position:0%
+piece times that inner product so i'll
+write it as minus because of that minus
+
+ align:start position:0%
+write it as minus because of that minus
+ 
+
+ align:start position:0%
+write it as minus because of that minus
+here the sum over P of Delta H P and K
+
+ align:start position:0%
+here the sum over P of Delta H P and K
+ 
+
+ align:start position:0%
+here the sum over P of Delta H P and K
+over EP 0 minus a 0 T 0 written like
+
+ align:start position:0%
+over EP 0 minus a 0 T 0 written like
+ 
+
+ align:start position:0%
+over EP 0 minus a 0 T 0 written like
+that this is something you know maybe it
+
+ align:start position:0%
+that this is something you know maybe it
+ 
+
+ align:start position:0%
+that this is something you know maybe it
+sounds a little fast but if you have a
+
+ align:start position:0%
+sounds a little fast but if you have a
+ 
+
+ align:start position:0%
+sounds a little fast but if you have a
+basis vector alpha I with sy being the
+
+ align:start position:0%
+basis vector alpha I with sy being the
+ 
+
+ align:start position:0%
+basis vector alpha I with sy being the
+number beta I the states I is equal to
+
+ align:start position:0%
+number beta I the states I is equal to
+ 
+
+ align:start position:0%
+number beta I the states I is equal to
+the sum of beta eyes alpha eyes once you
+
+ align:start position:0%
+the sum of beta eyes alpha eyes once you
+ 
+
+ align:start position:0%
+the sum of beta eyes alpha eyes once you
+have the components the vector can be
+
+ align:start position:0%
+have the components the vector can be
+ 
+
+ align:start position:0%
+have the components the vector can be
+reconstructed as the components times
+
+ align:start position:0%
+reconstructed as the components times
+ 
+
+ align:start position:0%
+reconstructed as the components times
+the basis vectors so that's what we did
+
+ align:start position:0%
+the basis vectors so that's what we did
+ 
+
+ align:start position:0%
+the basis vectors so that's what we did
+here we have the components here and
+
+ align:start position:0%
+here we have the components here and
+ 
+
+ align:start position:0%
+here we have the components here and
+therefore the vector is the components
+
+ align:start position:0%
+therefore the vector is the components
+ 
+
+ align:start position:0%
+therefore the vector is the components
+times the basis vectors you can check
+
+ align:start position:0%
+times the basis vectors you can check
+ 
+
+ align:start position:0%
+times the basis vectors you can check
+that if if that makes you a little and
+
+ align:start position:0%
+that if if that makes you a little and
+ 
+
+ align:start position:0%
+that if if that makes you a little and
+you see just put a p 0 here and reach
+
+ align:start position:0%
+you see just put a p 0 here and reach
+ 
+
+ align:start position:0%
+you see just put a p 0 here and reach
+calculate that and you will get that
+
+ align:start position:0%
+calculate that and you will get that
+ 
+
+ align:start position:0%
+calculate that and you will get that
+answer now as written it there it's
+
+ align:start position:0%
+answer now as written it there it's
+ 
+
+ align:start position:0%
+answer now as written it there it's
+really not precise you're making
+
+ align:start position:0%
+really not precise you're making
+ 
+
+ align:start position:0%
+really not precise you're making
+technically a mistake this is equation
+
+ align:start position:0%
+technically a mistake this is equation
+ 
+
+ align:start position:0%
+technically a mistake this is equation
+is technically wrong because that's not
+
+ align:start position:0%
+is technically wrong because that's not
+ 
+
+ align:start position:0%
+is technically wrong because that's not
+n1k that is only the components of n1 k
+
+ align:start position:0%
+n1k that is only the components of n1 k
+ 
+
+ align:start position:0%
+n1k that is only the components of n1 k
+along we had so this will is be hard if
+
+ align:start position:0%
+along we had so this will is be hard if
+ 
+
+ align:start position:0%
+along we had so this will is be hard if
+n1 K has something along the degenerate
+
+ align:start position:0%
+n1 K has something along the degenerate
+ 
+
+ align:start position:0%
+n1 K has something along the degenerate
+subspace we haven't found it but this
+
+ align:start position:0%
+subspace we haven't found it but this
+ 
+
+ align:start position:0%
+subspace we haven't found it but this
+much we found we found part of the
+
+ align:start position:0%
+much we found we found part of the
+ 
+
+ align:start position:0%
+much we found we found part of the
+correction so the generous is always a
+
+ align:start position:0%
+correction so the generous is always a
+ 
+
+ align:start position:0%
+correction so the generous is always a
+complicated thing so we're gonna try to
+
+ align:start position:0%
+complicated thing so we're gonna try to
+ 
+
+ align:start position:0%
+complicated thing so we're gonna try to
+find we're gonna find in fact now the
+
+ align:start position:0%
+find we're gonna find in fact now the
+ 
+
+ align:start position:0%
+find we're gonna find in fact now the
+component of the correction around the
+
+ align:start position:0%
+component of the correction around the
+ 
+
+ align:start position:0%
+component of the correction around the
+degenerate space now in non degenerate
+
+ align:start position:0%
+degenerate space now in non degenerate
+ 
+
+ align:start position:0%
+degenerate space now in non degenerate
+perturbation theory we managed to use
+
+ align:start position:0%
+perturbation theory we managed to use
+ 
+
+ align:start position:0%
+perturbation theory we managed to use
+this equation to calculate fully the
+
+ align:start position:0%
+this equation to calculate fully the
+ 
+
+ align:start position:0%
+this equation to calculate fully the
+state but now we've used this equation
+
+ align:start position:0%
+state but now we've used this equation
+ 
+
+ align:start position:0%
+state but now we've used this equation
+all the way we put states in the
+
+ align:start position:0%
+all the way we put states in the
+ 
+
+ align:start position:0%
+all the way we put states in the
+degenerate subspace and we found the
+
+ align:start position:0%
+degenerate subspace and we found the
+ 
+
+ align:start position:0%
+degenerate subspace and we found the
+energies we put in the other part of the
+
+ align:start position:0%
+energies we put in the other part of the
+ 
+
+ align:start position:0%
+energies we put in the other part of the
+space V hat and we found the part of n1
+
+ align:start position:0%
+space V hat and we found the part of n1
+ 
+
+ align:start position:0%
+space V hat and we found the part of n1
+in in along V hat and we ran out of
+
+ align:start position:0%
+in in along V hat and we ran out of
+ 
+
+ align:start position:0%
+in in along V hat and we ran out of
+things from that order one equation has
+
+ align:start position:0%
+things from that order one equation has
+ 
+
+ align:start position:0%
+things from that order one equation has
+no more information so somehow it must
+
+ align:start position:0%
+no more information so somehow it must
+ 
+
+ align:start position:0%
+no more information so somehow it must
+be that the next equation that we
+
+ align:start position:0%
+be that the next equation that we
+ 
+
+ align:start position:0%
+be that the next equation that we
+usually need to go to second order in
+
+ align:start position:0%
+usually need to go to second order in
+ 
+
+ align:start position:0%
+usually need to go to second order in
+energy will tell us something about the
+
+ align:start position:0%
+energy will tell us something about the
+ 
+
+ align:start position:0%
+energy will tell us something about the
+missing part of n1 so that's the
+
+ align:start position:0%
+missing part of n1 so that's the
+ 
+
+ align:start position:0%
+missing part of n1 so that's the
+surprising thing you have to go to order
+
+ align:start position:0%
+surprising thing you have to go to order
+ 
+
+ align:start position:0%
+surprising thing you have to go to order
+lambda square to find the first order
+
+ align:start position:0%
+lambda square to find the first order
+ 
+
+ align:start position:0%
+lambda square to find the first order
+correction to the degenerate part of the
+
+ align:start position:0%
+correction to the degenerate part of the
+ 
+
+ align:start position:0%
+correction to the degenerate part of the
+state that's why the general
+
+ align:start position:0%
+state that's why the general
+ 
+
+ align:start position:0%
+state that's why the general
+perturbation theory has a is famous for
+
+ align:start position:0%
+perturbation theory has a is famous for
+ 
+
+ align:start position:0%
+perturbation theory has a is famous for
+its complication if you really need to
+
+ align:start position:0%
+its complication if you really need to
+ 
+
+ align:start position:0%
+its complication if you really need to
+go pretty high to find the things so
+
+ align:start position:0%
+go pretty high to find the things so
+ 
+
+ align:start position:0%
+go pretty high to find the things so
+let's do it so this is step three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you hit the order lambda squared
+
+ align:start position:0%
+you hit the order lambda squared
+ 
+
+ align:start position:0%
+you hit the order lambda squared
+equation with M 0 L and therefore the
+
+ align:start position:0%
+equation with M 0 L and therefore the
+ 
+
+ align:start position:0%
+equation with M 0 L and therefore the
+left hand side is going to be 0 because
+
+ align:start position:0%
+left hand side is going to be 0 because
+ 
+
+ align:start position:0%
+left hand side is going to be 0 because
+that operator on the left hand side
+
+ align:start position:0%
+that operator on the left hand side
+ 
+
+ align:start position:0%
+that operator on the left hand side
+always kills those states now you could
+
+ align:start position:0%
+always kills those states now you could
+ 
+
+ align:start position:0%
+always kills those states now you could
+have been a little sloppy here I was
+
+ align:start position:0%
+have been a little sloppy here I was
+ 
+
+ align:start position:0%
+have been a little sloppy here I was
+sloppy when I first solve those
+
+ align:start position:0%
+sloppy when I first solve those
+ 
+
+ align:start position:0%
+sloppy when I first solve those
+equations that I didn't say okay this is
+
+ align:start position:0%
+equations that I didn't say okay this is
+ 
+
+ align:start position:0%
+equations that I didn't say okay this is
+we had I said that's the answer that's
+
+ align:start position:0%
+we had I said that's the answer that's
+ 
+
+ align:start position:0%
+we had I said that's the answer that's
+the whole state
+
+ align:start position:0%
+the whole state
+ 
+
+ align:start position:0%
+the whole state
+there's nothing along the degenerate
+
+ align:start position:0%
+there's nothing along the degenerate
+ 
+
+ align:start position:0%
+there's nothing along the degenerate
+subspace but then if you stop there you
+
+ align:start position:0%
+subspace but then if you stop there you
+ 
+
+ align:start position:0%
+subspace but then if you stop there you
+can live happily the rest of your life
+
+ align:start position:0%
+can live happily the rest of your life
+ 
+
+ align:start position:0%
+can live happily the rest of your life
+but if you go to the next equation you
+
+ align:start position:0%
+but if you go to the next equation you
+ 
+
+ align:start position:0%
+but if you go to the next equation you
+find that it's wrong there was a piece
+
+ align:start position:0%
+find that it's wrong there was a piece
+ 
+
+ align:start position:0%
+find that it's wrong there was a piece
+along the degenerate subspace so let's
+
+ align:start position:0%
+along the degenerate subspace so let's
+ 
+
+ align:start position:0%
+along the degenerate subspace so let's
+see that so we'll also write as we've
+
+ align:start position:0%
+see that so we'll also write as we've
+ 
+
+ align:start position:0%
+see that so we'll also write as we've
+started to do and 1k being equal to n 1k
+
+ align:start position:0%
+started to do and 1k being equal to n 1k
+ 
+
+ align:start position:0%
+started to do and 1k being equal to n 1k
+along V hat plus the piece of n 1k along
+
+ align:start position:0%
+along V hat plus the piece of n 1k along
+ 
+
+ align:start position:0%
+along V hat plus the piece of n 1k along
+the end and this one we got and this one
+
+ align:start position:0%
+the end and this one we got and this one
+ 
+
+ align:start position:0%
+the end and this one we got and this one
+well is it there do we need it does the
+
+ align:start position:0%
+well is it there do we need it does the
+ 
+
+ align:start position:0%
+well is it there do we need it does the
+state receive a correction in that space
+
+ align:start position:0%
+state receive a correction in that space
+ 
+
+ align:start position:0%
+state receive a correction in that space
+or not well let's do the work let's hit
+
+ align:start position:0%
+or not well let's do the work let's hit
+ 
+
+ align:start position:0%
+or not well let's do the work let's hit
+this with those states so what happens
+
+ align:start position:0%
+this with those states so what happens
+ 
+
+ align:start position:0%
+this with those states so what happens
+we have n 0 L e and K 1 minus Delta H
+
+ align:start position:0%
+we have n 0 L e and K 1 minus Delta H
+ 
+
+ align:start position:0%
+we have n 0 L e and K 1 minus Delta H
+and 1k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's our term there actually I will
+
+ align:start position:0%
+that's our term there actually I will
+ 
+
+ align:start position:0%
+that's our term there actually I will
+write it off twice so I'll copy it again
+
+ align:start position:0%
+write it off twice so I'll copy it again
+ 
+
+ align:start position:0%
+write it off twice so I'll copy it again
+and 0 KL e NK 1 minus Delta H and 1 K
+
+ align:start position:0%
+and 0 KL e NK 1 minus Delta H and 1 K
+ 
+
+ align:start position:0%
+and 0 KL e NK 1 minus Delta H and 1 K
+why do I copied again because I will
+
+ align:start position:0%
+why do I copied again because I will
+ 
+
+ align:start position:0%
+why do I copied again because I will
+just put here on V hat and on V n so it
+
+ align:start position:0%
+just put here on V hat and on V n so it
+ 
+
+ align:start position:0%
+just put here on V hat and on V n so it
+was one term with an N 1 K but you know
+
+ align:start position:0%
+was one term with an N 1 K but you know
+ 
+
+ align:start position:0%
+was one term with an N 1 K but you know
+the N 1 K vector has components along
+
+ align:start position:0%
+the N 1 K vector has components along
+ 
+
+ align:start position:0%
+the N 1 K vector has components along
+two subspaces and therefore we might as
+
+ align:start position:0%
+two subspaces and therefore we might as
+ 
+
+ align:start position:0%
+two subspaces and therefore we might as
+well put each one separately so we can
+
+ align:start position:0%
+well put each one separately so we can
+ 
+
+ align:start position:0%
+well put each one separately so we can
+think about them in a clearer way then
+
+ align:start position:0%
+think about them in a clearer way then
+ 
+
+ align:start position:0%
+think about them in a clearer way then
+what else there's one more term the e n
+
+ align:start position:0%
+what else there's one more term the e n
+ 
+
+ align:start position:0%
+what else there's one more term the e n
+2 K and that is relatively simple
+
+ align:start position:0%
+2 K and that is relatively simple
+ 
+
+ align:start position:0%
+2 K and that is relatively simple
+because that's e and k 2 and then we
+
+ align:start position:0%
+because that's e and k 2 and then we
+ 
+
+ align:start position:0%
+because that's e and k 2 and then we
+have the overlap of at n 0 L with an N 0
+
+ align:start position:0%
+have the overlap of at n 0 L with an N 0
+ 
+
+ align:start position:0%
+have the overlap of at n 0 L with an N 0
+K which is a Delta L K so this whole
+
+ align:start position:0%
+K which is a Delta L K so this whole
+ 
+
+ align:start position:0%
+K which is a Delta L K so this whole
+thing must be 0 that was the right hand
+
+ align:start position:0%
+thing must be 0 that was the right hand
+ 
+
+ align:start position:0%
+thing must be 0 that was the right hand
+side of the equation but the left hand
+
+ align:start position:0%
+side of the equation but the left hand
+ 
+
+ align:start position:0%
+side of the equation but the left hand
+side of the equation was 0 so that's 0
+
+ align:start position:0%
+side of the equation was 0 so that's 0
+ 
+
+ align:start position:0%
+side of the equation was 0 so that's 0
+ok so now we have to think about this
+
+ align:start position:0%
+ok so now we have to think about this
+ 
+
+ align:start position:0%
+ok so now we have to think about this
+this terms what do we know what is 0 to
+
+ align:start position:0%
+this terms what do we know what is 0 to
+ 
+
+ align:start position:0%
+this terms what do we know what is 0 to
+begin with what is not 0 this term in
+
+ align:start position:0%
+begin with what is not 0 this term in
+ 
+
+ align:start position:0%
+begin with what is not 0 this term in
+here we know in 1 K already we found it
+
+ align:start position:0%
+here we know in 1 K already we found it
+ 
+
+ align:start position:0%
+here we know in 1 K already we found it
+there so that's nice we know n 1 K we
+
+ align:start position:0%
+there so that's nice we know n 1 K we
+ 
+
+ align:start position:0%
+there so that's nice we know n 1 K we
+know these Corrections but this is
+
+ align:start position:0%
+know these Corrections but this is
+ 
+
+ align:start position:0%
+know these Corrections but this is
+simpler because n 0 L is in the
+
+ align:start position:0%
+simpler because n 0 L is in the
+ 
+
+ align:start position:0%
+simpler because n 0 L is in the
+degenerate subspace this is a number and
+
+ align:start position:0%
+degenerate subspace this is a number and
+ 
+
+ align:start position:0%
+degenerate subspace this is a number and
+this is in big hat so that's 0 again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's a simplification here we
+
+ align:start position:0%
+okay so that's a simplification here we
+ 
+
+ align:start position:0%
+okay so that's a simplification here we
+have a very interesting situation I will
+
+ align:start position:0%
+have a very interesting situation I will
+ 
+
+ align:start position:0%
+have a very interesting situation I will
+have the Delta H and we have this basis
+
+ align:start position:0%
+have the Delta H and we have this basis
+ 
+
+ align:start position:0%
+have the Delta H and we have this basis
+state of the degenerate subspace we know
+
+ align:start position:0%
+state of the degenerate subspace we know
+ 
+
+ align:start position:0%
+state of the degenerate subspace we know
+that Delta H is diagonal in the
+
+ align:start position:0%
+that Delta H is diagonal in the
+ 
+
+ align:start position:0%
+that Delta H is diagonal in the
+degenerate subspace but is this n0l an
+
+ align:start position:0%
+degenerate subspace but is this n0l an
+ 
+
+ align:start position:0%
+degenerate subspace but is this n0l an
+eigenvalue of Delta H not quite because
+
+ align:start position:0%
+eigenvalue of Delta H not quite because
+ 
+
+ align:start position:0%
+eigenvalue of Delta H not quite because
+being diagonal these basis vectors are
+
+ align:start position:0%
+being diagonal these basis vectors are
+ 
+
+ align:start position:0%
+being diagonal these basis vectors are
+provide make Delta H diagonal so Delta H
+
+ align:start position:0%
+provide make Delta H diagonal so Delta H
+ 
+
+ align:start position:0%
+provide make Delta H diagonal so Delta H
+is diagonal in this subspace but doesn't
+
+ align:start position:0%
+is diagonal in this subspace but doesn't
+ 
+
+ align:start position:0%
+is diagonal in this subspace but doesn't
+mean this thing is an eigenvector
+
+ align:start position:0%
+mean this thing is an eigenvector
+ 
+
+ align:start position:0%
+mean this thing is an eigenvector
+because it can give you something
+
+ align:start position:0%
+because it can give you something
+ 
+
+ align:start position:0%
+because it can give you something
+outside the degenerate subspace so we
+
+ align:start position:0%
+outside the degenerate subspace so we
+ 
+
+ align:start position:0%
+outside the degenerate subspace so we
+cannot quite just say that this the
+
+ align:start position:0%
+cannot quite just say that this the
+ 
+
+ align:start position:0%
+cannot quite just say that this the
+eigenvalue of this is the first energy
+
+ align:start position:0%
+eigenvalue of this is the first energy
+ 
+
+ align:start position:0%
+eigenvalue of this is the first energy
+correction but actually we can let me
+
+ align:start position:0%
+correction but actually we can let me
+ 
+
+ align:start position:0%
+correction but actually we can let me
+explain that so let's look at this term
+
+ align:start position:0%
+explain that so let's look at this term
+ 
+
+ align:start position:0%
+explain that so let's look at this term
+alone with this term alone now this time
+
+ align:start position:0%
+alone with this term alone now this time
+ 
+
+ align:start position:0%
+alone with this term alone now this time
+I cannot kill this this constant because
+
+ align:start position:0%
+I cannot kill this this constant because
+ 
+
+ align:start position:0%
+I cannot kill this this constant because
+this is in the degenerate subspace and
+
+ align:start position:0%
+this is in the degenerate subspace and
+ 
+
+ align:start position:0%
+this is in the degenerate subspace and
+this is in the degenerate subspace so we
+
+ align:start position:0%
+this is in the degenerate subspace so we
+ 
+
+ align:start position:0%
+this is in the degenerate subspace so we
+will have to deal with that so let's
+
+ align:start position:0%
+will have to deal with that so let's
+ 
+
+ align:start position:0%
+will have to deal with that so let's
+let's do this okay so I'll put here M 0
+
+ align:start position:0%
+let's do this okay so I'll put here M 0
+ 
+
+ align:start position:0%
+let's do this okay so I'll put here M 0
+L Delta H and 1k we're going to try to
+
+ align:start position:0%
+L Delta H and 1k we're going to try to
+ 
+
+ align:start position:0%
+L Delta H and 1k we're going to try to
+simplify this and the way to do it this
+
+ align:start position:0%
+simplify this and the way to do it this
+ 
+
+ align:start position:0%
+simplify this and the way to do it this
+is n 1k very important in VN is to
+
+ align:start position:0%
+is n 1k very important in VN is to
+ 
+
+ align:start position:0%
+is n 1k very important in VN is to
+insert a resolution of the identity here
+
+ align:start position:0%
+insert a resolution of the identity here
+ 
+
+ align:start position:0%
+insert a resolution of the identity here
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I'll do it we'll put n0 L Delta H and
+
+ align:start position:0%
+I'll do it we'll put n0 L Delta H and
+ 
+
+ align:start position:0%
+I'll do it we'll put n0 L Delta H and
+now we'll put the whole resolution of
+
+ align:start position:0%
+now we'll put the whole resolution of
+ 
+
+ align:start position:0%
+now we'll put the whole resolution of
+the identity so we'll put the sum over Q
+
+ align:start position:0%
+the identity so we'll put the sum over Q
+ 
+
+ align:start position:0%
+the identity so we'll put the sum over Q
+and 0 Q and 0 Q plus a sum over P p 0 p
+
+ align:start position:0%
+and 0 Q and 0 Q plus a sum over P p 0 p
+ 
+
+ align:start position:0%
+and 0 Q and 0 Q plus a sum over P p 0 p
+0 all acting on em 1k of VN I actually
+
+ align:start position:0%
+0 all acting on em 1k of VN I actually
+ 
+
+ align:start position:0%
+0 all acting on em 1k of VN I actually
+want to remark that all what I'm doing
+
+ align:start position:0%
+want to remark that all what I'm doing
+ 
+
+ align:start position:0%
+want to remark that all what I'm doing
+in this line so let's break this this
+
+ align:start position:0%
+in this line so let's break this this
+ 
+
+ align:start position:0%
+in this line so let's break this this
+the equation was up to here and we
+
+ align:start position:0%
+the equation was up to here and we
+ 
+
+ align:start position:0%
+the equation was up to here and we
+decided to try to understand this term
+
+ align:start position:0%
+decided to try to understand this term
+ 
+
+ align:start position:0%
+decided to try to understand this term
+so we're trying to understand this term
+
+ align:start position:0%
+so we're trying to understand this term
+ 
+
+ align:start position:0%
+so we're trying to understand this term
+just that term now Delta H here is
+
+ align:start position:0%
+just that term now Delta H here is
+ 
+
+ align:start position:0%
+just that term now Delta H here is
+acting between and the generates
+
+ align:start position:0%
+acting between and the generates
+ 
+
+ align:start position:0%
+acting between and the generates
+eigenstate here and here some arbitrary
+
+ align:start position:0%
+eigenstate here and here some arbitrary
+ 
+
+ align:start position:0%
+eigenstate here and here some arbitrary
+state in the degenerate subspace so we
+
+ align:start position:0%
+state in the degenerate subspace so we
+ 
+
+ align:start position:0%
+state in the degenerate subspace so we
+go here and we say ok since this is in
+
+ align:start position:0%
+go here and we say ok since this is in
+ 
+
+ align:start position:0%
+go here and we say ok since this is in
+the degenerate subspace that's inner
+
+ align:start position:0%
+the degenerate subspace that's inner
+ 
+
+ align:start position:0%
+the degenerate subspace that's inner
+product with vector in v hat with this
+
+ align:start position:0%
+product with vector in v hat with this
+ 
+
+ align:start position:0%
+product with vector in v hat with this
+is 0 so that part of the resolution of
+
+ align:start position:0%
+is 0 so that part of the resolution of
+ 
+
+ align:start position:0%
+is 0 so that part of the resolution of
+the identity is not relevant
+
+ align:start position:0%
+the identity is not relevant
+ 
+
+ align:start position:0%
+the identity is not relevant
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if that part of the resolution of the
+
+ align:start position:0%
+if that part of the resolution of the
+ 
+
+ align:start position:0%
+if that part of the resolution of the
+identity is not relevant we are left
+
+ align:start position:0%
+identity is not relevant we are left
+ 
+
+ align:start position:0%
+identity is not relevant we are left
+with and sum over Q and zero L Delta H
+
+ align:start position:0%
+with and sum over Q and zero L Delta H
+ 
+
+ align:start position:0%
+with and sum over Q and zero L Delta H
+and 0 q n0 q times n 1 k vm and now you
+
+ align:start position:0%
+and 0 q n0 q times n 1 k vm and now you
+ 
+
+ align:start position:0%
+and 0 q n0 q times n 1 k vm and now you
+can use that this matrix is indeed
+
+ align:start position:0%
+can use that this matrix is indeed
+ 
+
+ align:start position:0%
+can use that this matrix is indeed
+diagonal in the degenerate subspace and
+
+ align:start position:0%
+diagonal in the degenerate subspace and
+ 
+
+ align:start position:0%
+diagonal in the degenerate subspace and
+therefore this matrix element is the
+
+ align:start position:0%
+therefore this matrix element is the
+ 
+
+ align:start position:0%
+therefore this matrix element is the
+energy E and L 1 the first order
+
+ align:start position:0%
+energy E and L 1 the first order
+ 
+
+ align:start position:0%
+energy E and L 1 the first order
+correction times a delta L Q and then we
+
+ align:start position:0%
+correction times a delta L Q and then we
+ 
+
+ align:start position:0%
+correction times a delta L Q and then we
+can do the sum over Q because there is a
+
+ align:start position:0%
+can do the sum over Q because there is a
+ 
+
+ align:start position:0%
+can do the sum over Q because there is a
+delta function here and this becomes e
+
+ align:start position:0%
+delta function here and this becomes e
+ 
+
+ align:start position:0%
+delta function here and this becomes e
+and L 1 and 0 L and 1 k VN so this is
+
+ align:start position:0%
+and L 1 and 0 L and 1 k VN so this is
+ 
+
+ align:start position:0%
+and L 1 and 0 L and 1 k VN so this is
+very nice it took us a little bit of
+
+ align:start position:0%
+very nice it took us a little bit of
+ 
+
+ align:start position:0%
+very nice it took us a little bit of
+work but look what has happened this
+
+ align:start position:0%
+work but look what has happened this
+ 
+
+ align:start position:0%
+work but look what has happened this
+Delta H term is going to become the same
+
+ align:start position:0%
+Delta H term is going to become the same
+ 
+
+ align:start position:0%
+Delta H term is going to become the same
+structure and 0 L and 1k overlap so it's
+
+ align:start position:0%
+structure and 0 L and 1k overlap so it's
+ 
+
+ align:start position:0%
+structure and 0 L and 1k overlap so it's
+great progress so what does our equation
+
+ align:start position:0%
+great progress so what does our equation
+ 
+
+ align:start position:0%
+great progress so what does our equation
+become well the from the first term this
+
+ align:start position:0%
+become well the from the first term this
+ 
+
+ align:start position:0%
+become well the from the first term this
+is the rest of the end of the aside from
+
+ align:start position:0%
+is the rest of the end of the aside from
+ 
+
+ align:start position:0%
+is the rest of the end of the aside from
+the first term we have minus and 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta H and 1k envy hat that's all that
+
+ align:start position:0%
+Delta H and 1k envy hat that's all that
+ 
+
+ align:start position:0%
+Delta H and 1k envy hat that's all that
+was left from that first term and this
+
+ align:start position:0%
+was left from that first term and this
+ 
+
+ align:start position:0%
+was left from that first term and this
+term is known because N 1 is known along
+
+ align:start position:0%
+term is known because N 1 is known along
+ 
+
+ align:start position:0%
+term is known because N 1 is known along
+the rest of the hilbert space the second
+
+ align:start position:0%
+the rest of the hilbert space the second
+ 
+
+ align:start position:0%
+the rest of the hilbert space the second
+term over there that was giving us
+
+ align:start position:0%
+term over there that was giving us
+ 
+
+ align:start position:0%
+term over there that was giving us
+trouble has become something very simple
+
+ align:start position:0%
+trouble has become something very simple
+ 
+
+ align:start position:0%
+trouble has become something very simple
+it has become e NK minus e n L both 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplied by n 0 L + 1 K I could put
+
+ align:start position:0%
+multiplied by n 0 L + 1 K I could put
+ 
+
+ align:start position:0%
+multiplied by n 0 L + 1 K I could put
+this VM or now I may not put it either
+
+ align:start position:0%
+this VM or now I may not put it either
+ 
+
+ align:start position:0%
+this VM or now I may not put it either
+because I'm already projecting to a
+
+ align:start position:0%
+because I'm already projecting to a
+ 
+
+ align:start position:0%
+because I'm already projecting to a
+state in the degenerate subspace so I'm
+
+ align:start position:0%
+state in the degenerate subspace so I'm
+ 
+
+ align:start position:0%
+state in the degenerate subspace so I'm
+finding the component along the
+
+ align:start position:0%
+finding the component along the
+ 
+
+ align:start position:0%
+finding the component along the
+degenerate subspace so even if n1 k had
+
+ align:start position:0%
+degenerate subspace so even if n1 k had
+ 
+
+ align:start position:0%
+degenerate subspace so even if n1 k had
+a piece along we had it would drop out
+
+ align:start position:0%
+a piece along we had it would drop out
+ 
+
+ align:start position:0%
+a piece along we had it would drop out
+here so it's completely legal and it's
+
+ align:start position:0%
+here so it's completely legal and it's
+ 
+
+ align:start position:0%
+here so it's completely legal and it's
+simpler to erase the VN k and then the
+
+ align:start position:0%
+simpler to erase the VN k and then the
+ 
+
+ align:start position:0%
+simpler to erase the VN k and then the
+last term is still there + e + k2 Delta
+
+ align:start position:0%
+last term is still there + e + k2 Delta
+ 
+
+ align:start position:0%
+last term is still there + e + k2 Delta
+L K equals 0 ok this is our master
+
+ align:start position:0%
+L K equals 0 ok this is our master
+ 
+
+ align:start position:0%
+L K equals 0 ok this is our master
+equation after thinking of this equation
+
+ align:start position:0%
+equation after thinking of this equation
+ 
+
+ align:start position:0%
+equation after thinking of this equation
+for a while and using our properties we
+
+ align:start position:0%
+for a while and using our properties we
+ 
+
+ align:start position:0%
+for a while and using our properties we
+got this far it's a very nice equation
+
+ align:start position:0%
+got this far it's a very nice equation
+ 
+
+ align:start position:0%
+got this far it's a very nice equation
+it does give you the second-order
+
+ align:start position:0%
+it does give you the second-order
+ 
+
+ align:start position:0%
+it does give you the second-order
+energies we were looking for the part of
+
+ align:start position:0%
+energies we were looking for the part of
+ 
+
+ align:start position:0%
+energies we were looking for the part of
+the state along the degenerate subspace
+
+ align:start position:0%
+the state along the degenerate subspace
+ 
+
+ align:start position:0%
+the state along the degenerate subspace
+this was our main unknown and but still
+
+ align:start position:0%
+this was our main unknown and but still
+ 
+
+ align:start position:0%
+this was our main unknown and but still
+we can get the energies why because we
+
+ align:start position:0%
+we can get the energies why because we
+ 
+
+ align:start position:0%
+we can get the energies why because we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+take L equals 2k in which case the term
+
+ align:start position:0%
+take L equals 2k in which case the term
+ 
+
+ align:start position:0%
+take L equals 2k in which case the term
+that we know now drops out because n L
+
+ align:start position:0%
+that we know now drops out because n L
+ 
+
+ align:start position:0%
+that we know now drops out because n L
+equals 2k this thing's cancelled so when
+
+ align:start position:0%
+equals 2k this thing's cancelled so when
+ 
+
+ align:start position:0%
+equals 2k this thing's cancelled so when
+L is equal to K we get that e MK to the
+
+ align:start position:0%
+L is equal to K we get that e MK to the
+ 
+
+ align:start position:0%
+L is equal to K we get that e MK to the
+second order correction to the energy is
+
+ align:start position:0%
+second order correction to the energy is
+ 
+
+ align:start position:0%
+second order correction to the energy is
+M 0 K Delta H and 1 K V hat that's it
+
+ align:start position:0%
+M 0 K Delta H and 1 K V hat that's it
+ 
+
+ align:start position:0%
+M 0 K Delta H and 1 K V hat that's it
+that's your second correction to the
+
+ align:start position:0%
+that's your second correction to the
+ 
+
+ align:start position:0%
+that's your second correction to the
+energy and that's very nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why do we say that's it because we
+
+ align:start position:0%
+why do we say that's it because we
+ 
+
+ align:start position:0%
+why do we say that's it because we
+actually have the answer for N 1 so we
+
+ align:start position:0%
+actually have the answer for N 1 so we
+ 
+
+ align:start position:0%
+actually have the answer for N 1 so we
+can find a complete formula for this
+
+ align:start position:0%
+can find a complete formula for this
+ 
+
+ align:start position:0%
+can find a complete formula for this
+I'll write it here after a couple of
+
+ align:start position:0%
+I'll write it here after a couple of
+ 
+
+ align:start position:0%
+I'll write it here after a couple of
+steps of algebra this gives minus the
+
+ align:start position:0%
+steps of algebra this gives minus the
+ 
+
+ align:start position:0%
+steps of algebra this gives minus the
+sum over P Delta H MK p over p 0 minus e
+
+ align:start position:0%
+sum over P Delta H MK p over p 0 minus e
+ 
+
+ align:start position:0%
+sum over P Delta H MK p over p 0 minus e
+m 0 squared look at that formula it has
+
+ align:start position:0%
+m 0 squared look at that formula it has
+ 
+
+ align:start position:0%
+m 0 squared look at that formula it has
+the same form as the second order
+
+ align:start position:0%
+the same form as the second order
+ 
+
+ align:start position:0%
+the same form as the second order
+correction to non degenerate states same
+
+ align:start position:0%
+correction to non degenerate states same
+ 
+
+ align:start position:0%
+correction to non degenerate states same
+look except that you only sum over the
+
+ align:start position:0%
+look except that you only sum over the
+ 
+
+ align:start position:0%
+look except that you only sum over the
+states that are outside the degenerate
+
+ align:start position:0%
+states that are outside the degenerate
+ 
+
+ align:start position:0%
+states that are outside the degenerate
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+it was exactly of this form the second
+
+ align:start position:0%
+it was exactly of this form the second
+ 
+
+ align:start position:0%
+it was exactly of this form the second
+order energy correction so it's kind of
+
+ align:start position:0%
+order energy correction so it's kind of
+ 
+
+ align:start position:0%
+order energy correction so it's kind of
+nice and simple but let's look at this
+
+ align:start position:0%
+nice and simple but let's look at this
+ 
+
+ align:start position:0%
+nice and simple but let's look at this
+equation again and here is a the thing
+
+ align:start position:0%
+equation again and here is a the thing
+ 
+
+ align:start position:0%
+equation again and here is a the thing
+that would have been shocking if we
+
+ align:start position:0%
+that would have been shocking if we
+ 
+
+ align:start position:0%
+that would have been shocking if we
+didn't do this right if we had set L
+
+ align:start position:0%
+didn't do this right if we had set L
+ 
+
+ align:start position:0%
+didn't do this right if we had set L
+different from K here if L is different
+
+ align:start position:0%
+different from K here if L is different
+ 
+
+ align:start position:0%
+different from K here if L is different
+from K then this term is zero if we
+
+ align:start position:0%
+from K then this term is zero if we
+ 
+
+ align:start position:0%
+from K then this term is zero if we
+didn't think if we hadn't suspected that
+
+ align:start position:0%
+didn't think if we hadn't suspected that
+ 
+
+ align:start position:0%
+didn't think if we hadn't suspected that
+the state n1 k had a piece along the
+
+ align:start position:0%
+the state n1 k had a piece along the
+ 
+
+ align:start position:0%
+the state n1 k had a piece along the
+degenerate subspace we would have not
+
+ align:start position:0%
+degenerate subspace we would have not
+ 
+
+ align:start position:0%
+degenerate subspace we would have not
+introduced it and we would have had not
+
+ align:start position:0%
+introduced it and we would have had not
+ 
+
+ align:start position:0%
+introduced it and we would have had not
+this term and the equation would have
+
+ align:start position:0%
+this term and the equation would have
+ 
+
+ align:start position:0%
+this term and the equation would have
+become this equal to zero which is not
+
+ align:start position:0%
+become this equal to zero which is not
+ 
+
+ align:start position:0%
+become this equal to zero which is not
+you have there n1 of K and you can look
+
+ align:start position:0%
+you have there n1 of K and you can look
+ 
+
+ align:start position:0%
+you have there n1 of K and you can look
+at it and look at it for hours and it's
+
+ align:start position:0%
+at it and look at it for hours and it's
+ 
+
+ align:start position:0%
+at it and look at it for hours and it's
+just not zero so unless we have this
+
+ align:start position:0%
+just not zero so unless we have this
+ 
+
+ align:start position:0%
+just not zero so unless we have this
+piece the equation doesn't make sense so
+
+ align:start position:0%
+piece the equation doesn't make sense so
+ 
+
+ align:start position:0%
+piece the equation doesn't make sense so
+this proves that the state must develop
+
+ align:start position:0%
+this proves that the state must develop
+ 
+
+ align:start position:0%
+this proves that the state must develop
+a component along the degenerate
+
+ align:start position:0%
+a component along the degenerate
+ 
+
+ align:start position:0%
+a component along the degenerate
+subspace and let's now finally get it
+
+ align:start position:0%
+subspace and let's now finally get it
+ 
+
+ align:start position:0%
+subspace and let's now finally get it
+it's just one line at this point we
+
+ align:start position:0%
+it's just one line at this point we
+ 
+
+ align:start position:0%
+it's just one line at this point we
+don't have to do much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so when L is different from K L
+
+ align:start position:0%
+so when L is different from K L
+ 
+
+ align:start position:0%
+so when L is different from K L
+different from K so what do we get for
+
+ align:start position:0%
+different from K so what do we get for
+ 
+
+ align:start position:0%
+different from K so what do we get for
+the equation look at it there we can
+
+ align:start position:0%
+the equation look at it there we can
+ 
+
+ align:start position:0%
+the equation look at it there we can
+solve directly for the piece and 0 L and
+
+ align:start position:0%
+solve directly for the piece and 0 L and
+ 
+
+ align:start position:0%
+solve directly for the piece and 0 L and
+1 K is equal to solve for the second
+
+ align:start position:0%
+1 K is equal to solve for the second
+ 
+
+ align:start position:0%
+1 K is equal to solve for the second
+term this other term goes on the
+
+ align:start position:0%
+term this other term goes on the
+ 
+
+ align:start position:0%
+term this other term goes on the
+right-hand side so and 0 L Delta H and 1
+
+ align:start position:0%
+right-hand side so and 0 L Delta H and 1
+ 
+
+ align:start position:0%
+right-hand side so and 0 L Delta H and 1
+K over E and K 1 minus e and L 1 and
+
+ align:start position:0%
+K over E and K 1 minus e and L 1 and
+ 
+
+ align:start position:0%
+K over E and K 1 minus e and L 1 and
+here is another thing that ended up
+
+ align:start position:0%
+here is another thing that ended up
+ 
+
+ align:start position:0%
+here is another thing that ended up
+working well if the degeneracy had not
+
+ align:start position:0%
+working well if the degeneracy had not
+ 
+
+ align:start position:0%
+working well if the degeneracy had not
+been broken we're doing L different from
+
+ align:start position:0%
+been broken we're doing L different from
+ 
+
+ align:start position:0%
+been broken we're doing L different from
+K if some of these would have been 0
+
+ align:start position:0%
+K if some of these would have been 0
+ 
+
+ align:start position:0%
+K if some of these would have been 0
+this would give you 0 in the denominator
+
+ align:start position:0%
+this would give you 0 in the denominator
+ 
+
+ align:start position:0%
+this would give you 0 in the denominator
+this wouldn't work out so it was urgent
+
+ align:start position:0%
+this wouldn't work out so it was urgent
+ 
+
+ align:start position:0%
+this wouldn't work out so it was urgent
+here that all the degeneracy had been
+
+ align:start position:0%
+here that all the degeneracy had been
+ 
+
+ align:start position:0%
+here that all the degeneracy had been
+broken the first order otherwise you
+
+ align:start position:0%
+broken the first order otherwise you
+ 
+
+ align:start position:0%
+broken the first order otherwise you
+couldn't have computed this state this
+
+ align:start position:0%
+couldn't have computed this state this
+ 
+
+ align:start position:0%
+couldn't have computed this state this
+way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this means that n 1k to wrap it up here
+
+ align:start position:0%
+this means that n 1k to wrap it up here
+ 
+
+ align:start position:0%
+this means that n 1k to wrap it up here
+is when this in the subspace V n is the
+
+ align:start position:0%
+is when this in the subspace V n is the
+ 
+
+ align:start position:0%
+is when this in the subspace V n is the
+sum over L different from K because this
+
+ align:start position:0%
+sum over L different from K because this
+ 
+
+ align:start position:0%
+sum over L different from K because this
+inner product only makes sense for L
+
+ align:start position:0%
+inner product only makes sense for L
+ 
+
+ align:start position:0%
+inner product only makes sense for L
+different from K of n 0 L times this
+
+ align:start position:0%
+different from K of n 0 L times this
+ 
+
+ align:start position:0%
+different from K of n 0 L times this
+coefficient 1 over e MK 1 minus e and L
+
+ align:start position:0%
+coefficient 1 over e MK 1 minus e and L
+ 
+
+ align:start position:0%
+coefficient 1 over e MK 1 minus e and L
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and 0l delta h and 1k it's a lot of work
+
+ align:start position:0%
+and 0l delta h and 1k it's a lot of work
+ 
+
+ align:start position:0%
+and 0l delta h and 1k it's a lot of work
+to get here but actually it's good that
+
+ align:start position:0%
+to get here but actually it's good that
+ 
+
+ align:start position:0%
+to get here but actually it's good that
+we could get there if you even want to
+
+ align:start position:0%
+we could get there if you even want to
+ 
+
+ align:start position:0%
+we could get there if you even want to
+write it more explicitly you substitute
+
+ align:start position:0%
+write it more explicitly you substitute
+ 
+
+ align:start position:0%
+write it more explicitly you substitute
+what n1 k is and it goes there
+
+ align:start position:0%
+what n1 k is and it goes there
+ 
+
+ align:start position:0%
+what n1 k is and it goes there
+now there's something a little strange
+
+ align:start position:0%
+now there's something a little strange
+ 
+
+ align:start position:0%
+now there's something a little strange
+at first sight if you look at it you say
+
+ align:start position:0%
+at first sight if you look at it you say
+ 
+
+ align:start position:0%
+at first sight if you look at it you say
+okay let's see this is first-order in
+
+ align:start position:0%
+okay let's see this is first-order in
+ 
+
+ align:start position:0%
+okay let's see this is first-order in
+perturbation theory we have to go to the
+
+ align:start position:0%
+perturbation theory we have to go to the
+ 
+
+ align:start position:0%
+perturbation theory we have to go to the
+second order equation and that's why we
+
+ align:start position:0%
+second order equation and that's why we
+ 
+
+ align:start position:0%
+second order equation and that's why we
+seem to be counting orders wrong because
+
+ align:start position:0%
+seem to be counting orders wrong because
+ 
+
+ align:start position:0%
+seem to be counting orders wrong because
+this is first order in perturbation this
+
+ align:start position:0%
+this is first order in perturbation this
+ 
+
+ align:start position:0%
+this is first order in perturbation this
+is another order in perturbation that's
+
+ align:start position:0%
+is another order in perturbation that's
+ 
+
+ align:start position:0%
+is another order in perturbation that's
+second order in perturbation that's
+
+ align:start position:0%
+second order in perturbation that's
+ 
+
+ align:start position:0%
+second order in perturbation that's
+indeed Delta H and one is second order
+
+ align:start position:0%
+indeed Delta H and one is second order
+ 
+
+ align:start position:0%
+indeed Delta H and one is second order
+Delta H and one appeared to second order
+
+ align:start position:0%
+Delta H and one appeared to second order
+ 
+
+ align:start position:0%
+Delta H and one appeared to second order
+so how come we'll get a first order term
+
+ align:start position:0%
+so how come we'll get a first order term
+ 
+
+ align:start position:0%
+so how come we'll get a first order term
+that seems to depend on second order
+
+ align:start position:0%
+that seems to depend on second order
+ 
+
+ align:start position:0%
+that seems to depend on second order
+stuff maybe it's wrong what we did and
+
+ align:start position:0%
+stuff maybe it's wrong what we did and
+ 
+
+ align:start position:0%
+stuff maybe it's wrong what we did and
+we we thought we were gonna get the
+
+ align:start position:0%
+we we thought we were gonna get the
+ 
+
+ align:start position:0%
+we we thought we were gonna get the
+degenerate first order piece from the
+
+ align:start position:0%
+degenerate first order piece from the
+ 
+
+ align:start position:0%
+degenerate first order piece from the
+second equation but here this is hitting
+
+ align:start position:0%
+second equation but here this is hitting
+ 
+
+ align:start position:0%
+second equation but here this is hitting
+us back yes
+
+ align:start position:0%
+us back yes
+ 
+
+ align:start position:0%
+us back yes
+the denominator is also first-order so
+
+ align:start position:0%
+the denominator is also first-order so
+ 
+
+ align:start position:0%
+the denominator is also first-order so
+this is second order this is first order
+
+ align:start position:0%
+this is second order this is first order
+ 
+
+ align:start position:0%
+this is second order this is first order
+the ratio is first order all is good
+
+ align:start position:0%
+the ratio is first order all is good
+ 
+
+ align:start position:0%
+the ratio is first order all is good
+here this is a good formula this is a
+
+ align:start position:0%
+here this is a good formula this is a
+ 
+
+ align:start position:0%
+here this is a good formula this is a
+real result so this completes our
+
+ align:start position:0%
+real result so this completes our
+ 
+
+ align:start position:0%
+real result so this completes our
+analysis of the general perturbation
+
+ align:start position:0%
+analysis of the general perturbation
+ 
+
+ align:start position:0%
+analysis of the general perturbation
+theory when the perturbation the first
+
+ align:start position:0%
+theory when the perturbation the first
+ 
+
+ align:start position:0%
+theory when the perturbation the first
+order perturbation splits all the levels
+
+ align:start position:0%
+order perturbation splits all the levels
+ 
+
+ align:start position:0%
+order perturbation splits all the levels
+what we're going to do now is set the
+
+ align:start position:0%
+what we're going to do now is set the
+ 
+
+ align:start position:0%
+what we're going to do now is set the
+general perturbation theory when the
+
+ align:start position:0%
+general perturbation theory when the
+ 
+
+ align:start position:0%
+general perturbation theory when the
+first order correction doesn't split any
+
+ align:start position:0%
+first order correction doesn't split any
+ 
+
+ align:start position:0%
+first order correction doesn't split any
+of the levels doesn't split them at all
+
+ align:start position:0%
+of the levels doesn't split them at all
+ 
+
+ align:start position:0%
+of the levels doesn't split them at all
+what happens what can we do
\ No newline at end of file
diff --git a/EBdgFFf54U0.txt b/EBdgFFf54U0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..940c73a627313ca7d0b57711135afd8a2411852e
--- /dev/null
+++ b/EBdgFFf54U0.txt
@@ -0,0 +1,12680 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we introduced pre-hilbert spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as Specter spaces uh that come equipped
+
+ align:start position:0%
+as Specter spaces uh that come equipped
+ 
+
+ align:start position:0%
+as Specter spaces uh that come equipped
+with a hermitian inner product our
+
+ align:start position:0%
+with a hermitian inner product our
+ 
+
+ align:start position:0%
+with a hermitian inner product our
+mission inner product is linear is uh so
+
+ align:start position:0%
+mission inner product is linear is uh so
+ 
+
+ align:start position:0%
+mission inner product is linear is uh so
+it's a pairing between two elements that
+
+ align:start position:0%
+it's a pairing between two elements that
+ 
+
+ align:start position:0%
+it's a pairing between two elements that
+gives you a complex number that's linear
+
+ align:start position:0%
+gives you a complex number that's linear
+ 
+
+ align:start position:0%
+gives you a complex number that's linear
+in the first entry
+
+ align:start position:0%
+in the first entry
+ 
+
+ align:start position:0%
+in the first entry
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and if you switch the entries that's
+
+ align:start position:0%
+and if you switch the entries that's
+ 
+
+ align:start position:0%
+and if you switch the entries that's
+equal to the pairing of the original two
+
+ align:start position:0%
+equal to the pairing of the original two
+ 
+
+ align:start position:0%
+equal to the pairing of the original two
+entries uh
+
+ align:start position:0%
+entries uh
+ 
+
+ align:start position:0%
+entries uh
+taking the complex conjugate of that and
+
+ align:start position:0%
+taking the complex conjugate of that and
+ 
+
+ align:start position:0%
+taking the complex conjugate of that and
+it's positive definite meaning if I take
+
+ align:start position:0%
+it's positive definite meaning if I take
+ 
+
+ align:start position:0%
+it's positive definite meaning if I take
+the inner product of a vector with
+
+ align:start position:0%
+the inner product of a vector with
+ 
+
+ align:start position:0%
+the inner product of a vector with
+itself it's not negative and zero if and
+
+ align:start position:0%
+itself it's not negative and zero if and
+ 
+
+ align:start position:0%
+itself it's not negative and zero if and
+only if
+
+ align:start position:0%
+only if
+ 
+
+ align:start position:0%
+only if
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the element is zero and we proved the
+
+ align:start position:0%
+the element is zero and we proved the
+ 
+
+ align:start position:0%
+the element is zero and we proved the
+koshy Schwartz inequality so let me
+
+ align:start position:0%
+koshy Schwartz inequality so let me
+ 
+
+ align:start position:0%
+koshy Schwartz inequality so let me
+actually just recall that we defined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for if H is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pre-hubert space
+
+ align:start position:0%
+pre-hubert space
+ 
+
+ align:start position:0%
+pre-hubert space
+we defined
+
+ align:start position:0%
+we defined
+ 
+
+ align:start position:0%
+we defined
+what we called uh or using this Norm
+
+ align:start position:0%
+what we called uh or using this Norm
+ 
+
+ align:start position:0%
+what we called uh or using this Norm
+notation although I haven't proved it to
+
+ align:start position:0%
+notation although I haven't proved it to
+ 
+
+ align:start position:0%
+notation although I haven't proved it to
+Norm yet
+
+ align:start position:0%
+Norm yet
+ 
+
+ align:start position:0%
+Norm yet
+to be the inner product of V with itself
+
+ align:start position:0%
+to be the inner product of V with itself
+ 
+
+ align:start position:0%
+to be the inner product of V with itself
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+raised to the one-half power
+
+ align:start position:0%
+raised to the one-half power
+ 
+
+ align:start position:0%
+raised to the one-half power
+and this is a non-negative real number
+
+ align:start position:0%
+and this is a non-negative real number
+ 
+
+ align:start position:0%
+and this is a non-negative real number
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this is a non-negative number so
+
+ align:start position:0%
+this is a non-negative number so
+ 
+
+ align:start position:0%
+this is a non-negative number so
+taking the one-half power is Meaningful
+
+ align:start position:0%
+taking the one-half power is Meaningful
+ 
+
+ align:start position:0%
+taking the one-half power is Meaningful
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and we proved at the end of last time
+
+ align:start position:0%
+and we proved at the end of last time
+ 
+
+ align:start position:0%
+and we proved at the end of last time
+the koshy Schwartz inequality
+
+ align:start position:0%
+the koshy Schwartz inequality
+ 
+
+ align:start position:0%
+the koshy Schwartz inequality
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+for all you
+
+ align:start position:0%
+for all you
+ 
+
+ align:start position:0%
+for all you
+and B and H
+
+ align:start position:0%
+and B and H
+ 
+
+ align:start position:0%
+and B and H
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+I take the inner product of u and v take
+
+ align:start position:0%
+I take the inner product of u and v take
+ 
+
+ align:start position:0%
+I take the inner product of u and v take
+its absolute value this is less than or
+
+ align:start position:0%
+its absolute value this is less than or
+ 
+
+ align:start position:0%
+its absolute value this is less than or
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+normal View
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the norm of V
+
+ align:start position:0%
+times the norm of V
+ 
+
+ align:start position:0%
+times the norm of V
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let's uh use this to actually
+
+ align:start position:0%
+so now let's uh use this to actually
+ 
+
+ align:start position:0%
+so now let's uh use this to actually
+prove or to prove that this thing that
+
+ align:start position:0%
+prove or to prove that this thing that
+ 
+
+ align:start position:0%
+prove or to prove that this thing that
+I've been
+
+ align:start position:0%
+I've been
+ 
+
+ align:start position:0%
+I've been
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+denoting what this Norm notation is in
+
+ align:start position:0%
+denoting what this Norm notation is in
+ 
+
+ align:start position:0%
+denoting what this Norm notation is in
+fact a norm on a pre-hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so theorem
+
+ align:start position:0%
+so theorem
+ 
+
+ align:start position:0%
+so theorem
+with h
+
+ align:start position:0%
+with h
+ 
+
+ align:start position:0%
+with h
+is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this uh thing here defined in this way
+
+ align:start position:0%
+this uh thing here defined in this way
+ 
+
+ align:start position:0%
+this uh thing here defined in this way
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a norm on H okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember we have to prove to or we
+
+ align:start position:0%
+so remember we have to prove to or we
+ 
+
+ align:start position:0%
+so remember we have to prove to or we
+have to prove three things for for
+
+ align:start position:0%
+have to prove three things for for
+ 
+
+ align:start position:0%
+have to prove three things for for
+something to be a norm we have to prove
+
+ align:start position:0%
+something to be a norm we have to prove
+ 
+
+ align:start position:0%
+something to be a norm we have to prove
+it's positive definite and then we also
+
+ align:start position:0%
+it's positive definite and then we also
+ 
+
+ align:start position:0%
+it's positive definite and then we also
+have to prove homogeneity and the
+
+ align:start position:0%
+have to prove homogeneity and the
+ 
+
+ align:start position:0%
+have to prove homogeneity and the
+triangle inequality so
+
+ align:start position:0%
+triangle inequality so
+ 
+
+ align:start position:0%
+triangle inequality so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this quantity here equals zero
+
+ align:start position:0%
+this quantity here equals zero
+ 
+
+ align:start position:0%
+this quantity here equals zero
+if and only if
+
+ align:start position:0%
+if and only if
+ 
+
+ align:start position:0%
+if and only if
+the inner product of V with itself is
+
+ align:start position:0%
+the inner product of V with itself is
+ 
+
+ align:start position:0%
+the inner product of V with itself is
+zero which
+
+ align:start position:0%
+zero which
+ 
+
+ align:start position:0%
+zero which
+by the positive definite quantity of a
+
+ align:start position:0%
+by the positive definite quantity of a
+ 
+
+ align:start position:0%
+by the positive definite quantity of a
+hermitian inner product implies that V
+
+ align:start position:0%
+hermitian inner product implies that V
+ 
+
+ align:start position:0%
+hermitian inner product implies that V
+equals zero so that proves that this
+
+ align:start position:0%
+equals zero so that proves that this
+ 
+
+ align:start position:0%
+equals zero so that proves that this
+function here on H is in fact positive
+
+ align:start position:0%
+function here on H is in fact positive
+ 
+
+ align:start position:0%
+function here on H is in fact positive
+definite
+
+ align:start position:0%
+definite
+ 
+
+ align:start position:0%
+definite
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now if Lambda is a complex number
+
+ align:start position:0%
+now if Lambda is a complex number
+ 
+
+ align:start position:0%
+now if Lambda is a complex number
+V is in h if I take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we kind of saw this at the uh and the
+
+ align:start position:0%
+so we kind of saw this at the uh and the
+ 
+
+ align:start position:0%
+so we kind of saw this at the uh and the
+proof of the koshy Schwartz inequality
+
+ align:start position:0%
+proof of the koshy Schwartz inequality
+ 
+
+ align:start position:0%
+proof of the koshy Schwartz inequality
+but if I take Lambda times V an inner
+
+ align:start position:0%
+but if I take Lambda times V an inner
+ 
+
+ align:start position:0%
+but if I take Lambda times V an inner
+product Lambda times V this is equal to
+
+ align:start position:0%
+product Lambda times V this is equal to
+ 
+
+ align:start position:0%
+product Lambda times V this is equal to
+Lambda times Lambda bar
+
+ align:start position:0%
+Lambda times Lambda bar
+ 
+
+ align:start position:0%
+Lambda times Lambda bar
+a scalar pulls out of the first entry
+
+ align:start position:0%
+a scalar pulls out of the first entry
+ 
+
+ align:start position:0%
+a scalar pulls out of the first entry
+unphased the second if a scalar is in
+
+ align:start position:0%
+unphased the second if a scalar is in
+ 
+
+ align:start position:0%
+unphased the second if a scalar is in
+the second entry it comes out with a
+
+ align:start position:0%
+the second entry it comes out with a
+ 
+
+ align:start position:0%
+the second entry it comes out with a
+complex conjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then of course for a complex number
+
+ align:start position:0%
+and then of course for a complex number
+ 
+
+ align:start position:0%
+and then of course for a complex number
+times this complex conjugate I get uh
+
+ align:start position:0%
+times this complex conjugate I get uh
+ 
+
+ align:start position:0%
+times this complex conjugate I get uh
+the norm of that or the length of that
+
+ align:start position:0%
+the norm of that or the length of that
+ 
+
+ align:start position:0%
+the norm of that or the length of that
+the absolute value of that complex
+
+ align:start position:0%
+the absolute value of that complex
+ 
+
+ align:start position:0%
+the absolute value of that complex
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+squared so taking the square root of
+
+ align:start position:0%
+squared so taking the square root of
+ 
+
+ align:start position:0%
+squared so taking the square root of
+both sides of this which is equal to
+
+ align:start position:0%
+both sides of this which is equal to
+ 
+
+ align:start position:0%
+both sides of this which is equal to
+this I get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ABS the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this quantity here is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the absolute value of Lambda times this
+
+ align:start position:0%
+the absolute value of Lambda times this
+ 
+
+ align:start position:0%
+the absolute value of Lambda times this
+Norm of V
+
+ align:start position:0%
+Norm of V
+ 
+
+ align:start position:0%
+Norm of V
+which proves
+
+ align:start position:0%
+which proves
+ 
+
+ align:start position:0%
+which proves
+homogeneity of
+
+ align:start position:0%
+homogeneity of
+ 
+
+ align:start position:0%
+homogeneity of
+dysfunction on H okay so that all All
+
+ align:start position:0%
+dysfunction on H okay so that all All
+ 
+
+ align:start position:0%
+dysfunction on H okay so that all All
+That Remains to prove that this is an
+
+ align:start position:0%
+That Remains to prove that this is an
+ 
+
+ align:start position:0%
+That Remains to prove that this is an
+actual Norm so I don't have to keep
+
+ align:start position:0%
+actual Norm so I don't have to keep
+ 
+
+ align:start position:0%
+actual Norm so I don't have to keep
+being uh or at least trying to be
+
+ align:start position:0%
+being uh or at least trying to be
+ 
+
+ align:start position:0%
+being uh or at least trying to be
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+careful with what words I'm using
+
+ align:start position:0%
+careful with what words I'm using
+ 
+
+ align:start position:0%
+careful with what words I'm using
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will prove that this is a norm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay so now we need to prove the
+
+ align:start position:0%
+uh okay so now we need to prove the
+ 
+
+ align:start position:0%
+uh okay so now we need to prove the
+triangle inequality
+
+ align:start position:0%
+triangle inequality
+ 
+
+ align:start position:0%
+triangle inequality
+yeah you let UV be an H
+
+ align:start position:0%
+yeah you let UV be an H
+ 
+
+ align:start position:0%
+yeah you let UV be an H
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I compute U plus v squared this is equal
+
+ align:start position:0%
+I compute U plus v squared this is equal
+ 
+
+ align:start position:0%
+I compute U plus v squared this is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+U plus v u plus v
+
+ align:start position:0%
+U plus v u plus v
+ 
+
+ align:start position:0%
+U plus v u plus v
+which is equal to
+
+ align:start position:0%
+which is equal to
+ 
+
+ align:start position:0%
+which is equal to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+just how we computed it for uh
+
+ align:start position:0%
+just how we computed it for uh
+ 
+
+ align:start position:0%
+just how we computed it for uh
+you know when we had a t here and a t
+
+ align:start position:0%
+you know when we had a t here and a t
+ 
+
+ align:start position:0%
+you know when we had a t here and a t
+here when we did the proof of the koshy
+
+ align:start position:0%
+here when we did the proof of the koshy
+ 
+
+ align:start position:0%
+here when we did the proof of the koshy
+Schwartz inequality and we'll use this
+
+ align:start position:0%
+Schwartz inequality and we'll use this
+ 
+
+ align:start position:0%
+Schwartz inequality and we'll use this
+identity quite often that the norm of U
+
+ align:start position:0%
+identity quite often that the norm of U
+ 
+
+ align:start position:0%
+identity quite often that the norm of U
+plus v squared is Norm U squared plus
+
+ align:start position:0%
+plus v squared is Norm U squared plus
+ 
+
+ align:start position:0%
+plus v squared is Norm U squared plus
+Norm
+
+ align:start position:0%
+Norm
+ 
+
+ align:start position:0%
+Norm
+B squared plus two times
+
+ align:start position:0%
+B squared plus two times
+ 
+
+ align:start position:0%
+B squared plus two times
+the real part
+
+ align:start position:0%
+the real part
+ 
+
+ align:start position:0%
+the real part
+of u and v the real part of the inner
+
+ align:start position:0%
+of u and v the real part of the inner
+ 
+
+ align:start position:0%
+of u and v the real part of the inner
+product of u and v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now this is less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RM squared plus v squared
+
+ align:start position:0%
+RM squared plus v squared
+ 
+
+ align:start position:0%
+RM squared plus v squared
+plus the absolute value of the real part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the absolute value of the real part
+
+ align:start position:0%
+now the absolute value of the real part
+ 
+
+ align:start position:0%
+now the absolute value of the real part
+of a complex number is less than or
+
+ align:start position:0%
+of a complex number is less than or
+ 
+
+ align:start position:0%
+of a complex number is less than or
+equal to the absolute value of that
+
+ align:start position:0%
+equal to the absolute value of that
+ 
+
+ align:start position:0%
+equal to the absolute value of that
+complex number so this is less than or
+
+ align:start position:0%
+complex number so this is less than or
+ 
+
+ align:start position:0%
+complex number so this is less than or
+equal to the absolute value of the inner
+
+ align:start position:0%
+equal to the absolute value of the inner
+ 
+
+ align:start position:0%
+equal to the absolute value of the inner
+product of u and v
+
+ align:start position:0%
+product of u and v
+ 
+
+ align:start position:0%
+product of u and v
+and by koshy Schwartz that let that is
+
+ align:start position:0%
+and by koshy Schwartz that let that is
+ 
+
+ align:start position:0%
+and by koshy Schwartz that let that is
+less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so still what I have before plus 2
+
+ align:start position:0%
+so still what I have before plus 2
+ 
+
+ align:start position:0%
+so still what I have before plus 2
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the inner product of u and v and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I guess let me go to the next four
+
+ align:start position:0%
+I guess let me go to the next four
+ 
+
+ align:start position:0%
+I guess let me go to the next four
+oh the proof is essentially done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I had before is
+
+ align:start position:0%
+what I had before is
+ 
+
+ align:start position:0%
+what I had before is
+equal to normal View
+
+ align:start position:0%
+equal to normal View
+ 
+
+ align:start position:0%
+equal to normal View
+plus normal V
+
+ align:start position:0%
+plus normal V
+ 
+
+ align:start position:0%
+plus normal V
+squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I.E so I had started off with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the norm of U plus v squared and I had
+
+ align:start position:0%
+the norm of U plus v squared and I had
+ 
+
+ align:start position:0%
+the norm of U plus v squared and I had
+proved that's less than or equal to this
+
+ align:start position:0%
+proved that's less than or equal to this
+ 
+
+ align:start position:0%
+proved that's less than or equal to this
+thing here
+
+ align:start position:0%
+thing here
+ 
+
+ align:start position:0%
+thing here
+squared so taking the square root of
+
+ align:start position:0%
+squared so taking the square root of
+ 
+
+ align:start position:0%
+squared so taking the square root of
+both sides I get
+
+ align:start position:0%
+both sides I get
+ 
+
+ align:start position:0%
+both sides I get
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the norm of U plus v is less than or
+
+ align:start position:0%
+the norm of U plus v is less than or
+ 
+
+ align:start position:0%
+the norm of U plus v is less than or
+equal to the normal view plus the normal
+
+ align:start position:0%
+equal to the normal view plus the normal
+ 
+
+ align:start position:0%
+equal to the normal view plus the normal
+V okay so this thing that I defined
+
+ align:start position:0%
+V okay so this thing that I defined
+ 
+
+ align:start position:0%
+V okay so this thing that I defined
+before is in fact a norm
+
+ align:start position:0%
+before is in fact a norm
+ 
+
+ align:start position:0%
+before is in fact a norm
+and I'm not just using a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that notation to denote an imposter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using the koshy Schwartz inequality we
+
+ align:start position:0%
+using the koshy Schwartz inequality we
+ 
+
+ align:start position:0%
+using the koshy Schwartz inequality we
+can also prove that taking the inner
+
+ align:start position:0%
+can also prove that taking the inner
+ 
+
+ align:start position:0%
+can also prove that taking the inner
+product is
+
+ align:start position:0%
+product is
+ 
+
+ align:start position:0%
+product is
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know it's a function on H cross h
+
+ align:start position:0%
+you know it's a function on H cross h
+ 
+
+ align:start position:0%
+you know it's a function on H cross h
+that's continuous Okay so
+
+ align:start position:0%
+that's continuous Okay so
+ 
+
+ align:start position:0%
+that's continuous Okay so
+let me label this as
+
+ align:start position:0%
+let me label this as
+ 
+
+ align:start position:0%
+let me label this as
+continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the inner product
+
+ align:start position:0%
+the inner product
+ 
+
+ align:start position:0%
+the inner product
+so let me state it as the following if
+
+ align:start position:0%
+so let me state it as the following if
+ 
+
+ align:start position:0%
+so let me state it as the following if
+we're in a pre-hilbert space and un
+
+ align:start position:0%
+we're in a pre-hilbert space and un
+ 
+
+ align:start position:0%
+we're in a pre-hilbert space and un
+converges to U
+
+ align:start position:0%
+converges to U
+ 
+
+ align:start position:0%
+converges to U
+and VN converges to B
+
+ align:start position:0%
+and VN converges to B
+ 
+
+ align:start position:0%
+and VN converges to B
+in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pre-hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with Norm
+
+ align:start position:0%
+with Norm
+ 
+
+ align:start position:0%
+with Norm
+as defined uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as before
+
+ align:start position:0%
+as before
+ 
+
+ align:start position:0%
+as before
+right so now we have a norm on a
+
+ align:start position:0%
+right so now we have a norm on a
+ 
+
+ align:start position:0%
+right so now we have a norm on a
+pre-hilward space and so we can Define
+
+ align:start position:0%
+pre-hilward space and so we can Define
+ 
+
+ align:start position:0%
+pre-hilward space and so we can Define
+convergence uh since it's a norm space
+
+ align:start position:0%
+convergence uh since it's a norm space
+ 
+
+ align:start position:0%
+convergence uh since it's a norm space
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free Hilbert space H would Norm this
+
+ align:start position:0%
+free Hilbert space H would Norm this
+ 
+
+ align:start position:0%
+free Hilbert space H would Norm this
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you and inner product VN
+
+ align:start position:0%
+you and inner product VN
+ 
+
+ align:start position:0%
+you and inner product VN
+converges to
+
+ align:start position:0%
+converges to
+ 
+
+ align:start position:0%
+converges to
+you and our product fee
+
+ align:start position:0%
+you and our product fee
+ 
+
+ align:start position:0%
+you and our product fee
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+why is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so last time
+
+ align:start position:0%
+so last time
+ 
+
+ align:start position:0%
+so last time
+and the previous proof I mean you know
+
+ align:start position:0%
+and the previous proof I mean you know
+ 
+
+ align:start position:0%
+and the previous proof I mean you know
+we really didn't use the full strength
+
+ align:start position:0%
+we really didn't use the full strength
+ 
+
+ align:start position:0%
+we really didn't use the full strength
+of the coachy Schwartz inequality we
+
+ align:start position:0%
+of the coachy Schwartz inequality we
+ 
+
+ align:start position:0%
+of the coachy Schwartz inequality we
+could have just gotten by with the real
+
+ align:start position:0%
+could have just gotten by with the real
+ 
+
+ align:start position:0%
+could have just gotten by with the real
+part uh having just proven that the real
+
+ align:start position:0%
+part uh having just proven that the real
+ 
+
+ align:start position:0%
+part uh having just proven that the real
+part of the inner product
+
+ align:start position:0%
+part of the inner product
+ 
+
+ align:start position:0%
+part of the inner product
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is an absolute value less than or equal
+
+ align:start position:0%
+is an absolute value less than or equal
+ 
+
+ align:start position:0%
+is an absolute value less than or equal
+to the inner product of or the product
+
+ align:start position:0%
+to the inner product of or the product
+ 
+
+ align:start position:0%
+to the inner product of or the product
+of the Norms of u and v here we'll
+
+ align:start position:0%
+of the Norms of u and v here we'll
+ 
+
+ align:start position:0%
+of the Norms of u and v here we'll
+actually use the full koshy Schwartz
+
+ align:start position:0%
+actually use the full koshy Schwartz
+ 
+
+ align:start position:0%
+actually use the full koshy Schwartz
+inequality so the proof is quite simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If U N converges to U
+
+ align:start position:0%
+If U N converges to U
+ 
+
+ align:start position:0%
+If U N converges to U
+and VN converges to B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I.E let me just
+
+ align:start position:0%
+I.E let me just
+ 
+
+ align:start position:0%
+I.E let me just
+spell this out for you
+
+ align:start position:0%
+spell this out for you
+ 
+
+ align:start position:0%
+spell this out for you
+u n minus U converges to zero
+
+ align:start position:0%
+u n minus U converges to zero
+ 
+
+ align:start position:0%
+u n minus U converges to zero
+and Norm of
+
+ align:start position:0%
+and Norm of
+ 
+
+ align:start position:0%
+and Norm of
+VN minus B converges to zero
+
+ align:start position:0%
+VN minus B converges to zero
+ 
+
+ align:start position:0%
+VN minus B converges to zero
+as n converges to as n goes to Infinity
+
+ align:start position:0%
+as n converges to as n goes to Infinity
+ 
+
+ align:start position:0%
+as n converges to as n goes to Infinity
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll use the squeeze theorem
+
+ align:start position:0%
+we'll use the squeeze theorem
+ 
+
+ align:start position:0%
+we'll use the squeeze theorem
+to show that this quantity converges to
+
+ align:start position:0%
+to show that this quantity converges to
+ 
+
+ align:start position:0%
+to show that this quantity converges to
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+in a product with UV so I have to show
+
+ align:start position:0%
+in a product with UV so I have to show
+ 
+
+ align:start position:0%
+in a product with UV so I have to show
+that this quantity here let me not put
+
+ align:start position:0%
+that this quantity here let me not put
+ 
+
+ align:start position:0%
+that this quantity here let me not put
+that we're not in 18 100.
+
+ align:start position:0%
+that we're not in 18 100.
+ 
+
+ align:start position:0%
+that we're not in 18 100.
+typically in 18100 when
+
+ align:start position:0%
+typically in 18100 when
+ 
+
+ align:start position:0%
+typically in 18100 when
+I first started teaching the squeeze
+
+ align:start position:0%
+I first started teaching the squeeze
+ 
+
+ align:start position:0%
+I first started teaching the squeeze
+theorem I always include the lower bound
+
+ align:start position:0%
+theorem I always include the lower bound
+ 
+
+ align:start position:0%
+theorem I always include the lower bound
+but it should be clear that this is
+
+ align:start position:0%
+but it should be clear that this is
+ 
+
+ align:start position:0%
+but it should be clear that this is
+always less than always bigger than or
+
+ align:start position:0%
+always less than always bigger than or
+ 
+
+ align:start position:0%
+always less than always bigger than or
+equal to zero since it's absolute value
+
+ align:start position:0%
+equal to zero since it's absolute value
+ 
+
+ align:start position:0%
+equal to zero since it's absolute value
+or of a complex number
+
+ align:start position:0%
+or of a complex number
+ 
+
+ align:start position:0%
+or of a complex number
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so this is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u n minus u v n plus
+
+ align:start position:0%
+u n minus u v n plus
+ 
+
+ align:start position:0%
+u n minus u v n plus
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U and a product v n minus V
+
+ align:start position:0%
+U and a product v n minus V
+ 
+
+ align:start position:0%
+U and a product v n minus V
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the triangle inequality now just for the
+
+ align:start position:0%
+the triangle inequality now just for the
+ 
+
+ align:start position:0%
+the triangle inequality now just for the
+you know modulus or absolute value of
+
+ align:start position:0%
+you know modulus or absolute value of
+ 
+
+ align:start position:0%
+you know modulus or absolute value of
+complex numbers that's less than or
+
+ align:start position:0%
+complex numbers that's less than or
+ 
+
+ align:start position:0%
+complex numbers that's less than or
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+u n minus U
+
+ align:start position:0%
+u n minus U
+ 
+
+ align:start position:0%
+u n minus U
+being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolute value of U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v n minus V
+
+ align:start position:0%
+v n minus V
+ 
+
+ align:start position:0%
+v n minus V
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is less than or equal to by the
+
+ align:start position:0%
+and this is less than or equal to by the
+ 
+
+ align:start position:0%
+and this is less than or equal to by the
+koshy Schwartz inequality
+
+ align:start position:0%
+koshy Schwartz inequality
+ 
+
+ align:start position:0%
+koshy Schwartz inequality
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Norm of u n minus U times the norm of VN
+
+ align:start position:0%
+Norm of u n minus U times the norm of VN
+ 
+
+ align:start position:0%
+Norm of u n minus U times the norm of VN
+plus Norm of U
+
+ align:start position:0%
+plus Norm of U
+ 
+
+ align:start position:0%
+plus Norm of U
+is Norm of VN minus
+
+ align:start position:0%
+is Norm of VN minus
+ 
+
+ align:start position:0%
+is Norm of VN minus
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the VNS are so the VNS are converging to
+
+ align:start position:0%
+the VNS are so the VNS are converging to
+ 
+
+ align:start position:0%
+the VNS are so the VNS are converging to
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+and therefore the Norms of the VNS are
+
+ align:start position:0%
+and therefore the Norms of the VNS are
+ 
+
+ align:start position:0%
+and therefore the Norms of the VNS are
+converging to the norm of B right so
+
+ align:start position:0%
+converging to the norm of B right so
+ 
+
+ align:start position:0%
+converging to the norm of B right so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recall that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+active VN converges to V
+
+ align:start position:0%
+active VN converges to V
+ 
+
+ align:start position:0%
+active VN converges to V
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+form of VN converges to
+
+ align:start position:0%
+form of VN converges to
+ 
+
+ align:start position:0%
+form of VN converges to
+Norma B okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um and again so let me add
+
+ align:start position:0%
+um and again so let me add
+ 
+
+ align:start position:0%
+um and again so let me add
+since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one can prove as you do in
+
+ align:start position:0%
+one can prove as you do in
+ 
+
+ align:start position:0%
+one can prove as you do in
+real analysis the following reverse
+
+ align:start position:0%
+real analysis the following reverse
+ 
+
+ align:start position:0%
+real analysis the following reverse
+triangle inequality since if I have two
+
+ align:start position:0%
+triangle inequality since if I have two
+ 
+
+ align:start position:0%
+triangle inequality since if I have two
+vectors A and B in in H
+
+ align:start position:0%
+vectors A and B in in H
+ 
+
+ align:start position:0%
+vectors A and B in in H
+so this just works in any button space
+
+ align:start position:0%
+so this just works in any button space
+ 
+
+ align:start position:0%
+so this just works in any button space
+not necessarily A pre-operate spaced the
+
+ align:start position:0%
+not necessarily A pre-operate spaced the
+ 
+
+ align:start position:0%
+not necessarily A pre-operate spaced the
+absolute value of the difference in
+
+ align:start position:0%
+absolute value of the difference in
+ 
+
+ align:start position:0%
+absolute value of the difference in
+Norms is less than or equal to the norm
+
+ align:start position:0%
+Norms is less than or equal to the norm
+ 
+
+ align:start position:0%
+Norms is less than or equal to the norm
+of the difference
+
+ align:start position:0%
+of the difference
+ 
+
+ align:start position:0%
+of the difference
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is a convergent uh uh sequence
+
+ align:start position:0%
+so this is a convergent uh uh sequence
+ 
+
+ align:start position:0%
+so this is a convergent uh uh sequence
+of real numbers so it must be bounded so
+
+ align:start position:0%
+of real numbers so it must be bounded so
+ 
+
+ align:start position:0%
+of real numbers so it must be bounded so
+I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say that's less than or equal to times
+
+ align:start position:0%
+say that's less than or equal to times
+ 
+
+ align:start position:0%
+say that's less than or equal to times
+soup of n
+
+ align:start position:0%
+soup of n
+ 
+
+ align:start position:0%
+soup of n
+or let's use a different letter k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form of v n minus V times
+
+ align:start position:0%
+form of v n minus V times
+ 
+
+ align:start position:0%
+form of v n minus V times
+Norm of U now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a
+
+ align:start position:0%
+this is a
+ 
+
+ align:start position:0%
+this is a
+this is something converging to zero
+
+ align:start position:0%
+this is something converging to zero
+ 
+
+ align:start position:0%
+this is something converging to zero
+times a fixed number this is something
+
+ align:start position:0%
+times a fixed number this is something
+ 
+
+ align:start position:0%
+times a fixed number this is something
+converging to zero times a fixed number
+
+ align:start position:0%
+converging to zero times a fixed number
+ 
+
+ align:start position:0%
+converging to zero times a fixed number
+and therefore this goes to zero as n
+
+ align:start position:0%
+and therefore this goes to zero as n
+ 
+
+ align:start position:0%
+and therefore this goes to zero as n
+goes to infinity and therefore uh the
+
+ align:start position:0%
+goes to infinity and therefore uh the
+ 
+
+ align:start position:0%
+goes to infinity and therefore uh the
+thing which we started with so this
+
+ align:start position:0%
+thing which we started with so this
+ 
+
+ align:start position:0%
+thing which we started with so this
+quantity here an absolute value is less
+
+ align:start position:0%
+quantity here an absolute value is less
+ 
+
+ align:start position:0%
+quantity here an absolute value is less
+than or equal to something converging to
+
+ align:start position:0%
+than or equal to something converging to
+ 
+
+ align:start position:0%
+than or equal to something converging to
+zero and it's also not negative so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore I get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is by The Squeeze theorem
+
+ align:start position:0%
+so this is by The Squeeze theorem
+ 
+
+ align:start position:0%
+so this is by The Squeeze theorem
+I.E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so on uh pre-hilbert space we can define
+
+ align:start position:0%
+so on uh pre-hilbert space we can define
+ 
+
+ align:start position:0%
+so on uh pre-hilbert space we can define
+a norm
+
+ align:start position:0%
+a norm
+ 
+
+ align:start position:0%
+a norm
+using the inner product
+
+ align:start position:0%
+using the inner product
+ 
+
+ align:start position:0%
+using the inner product
+and this inner product is continuous
+
+ align:start position:0%
+and this inner product is continuous
+ 
+
+ align:start position:0%
+and this inner product is continuous
+with respect to this Norm okay because
+
+ align:start position:0%
+with respect to this Norm okay because
+ 
+
+ align:start position:0%
+with respect to this Norm okay because
+once we have a norm we have convergence
+
+ align:start position:0%
+once we have a norm we have convergence
+ 
+
+ align:start position:0%
+once we have a norm we have convergence
+so we can talk about uh once we have a
+
+ align:start position:0%
+so we can talk about uh once we have a
+ 
+
+ align:start position:0%
+so we can talk about uh once we have a
+norm we have a notion of distance so we
+
+ align:start position:0%
+norm we have a notion of distance so we
+ 
+
+ align:start position:0%
+norm we have a notion of distance so we
+can talk about
+
+ align:start position:0%
+can talk about
+ 
+
+ align:start position:0%
+can talk about
+convergence of sequences and you know
+
+ align:start position:0%
+convergence of sequences and you know
+ 
+
+ align:start position:0%
+convergence of sequences and you know
+uh things like that
+
+ align:start position:0%
+uh things like that
+ 
+
+ align:start position:0%
+uh things like that
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a pre-hilbert space is what is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hilbert space
+
+ align:start position:0%
+Hilbert space
+ 
+
+ align:start position:0%
+Hilbert space
+this is simply a pre-hilbert space which
+
+ align:start position:0%
+this is simply a pre-hilbert space which
+ 
+
+ align:start position:0%
+this is simply a pre-hilbert space which
+is complete with respect to this Norm
+
+ align:start position:0%
+is complete with respect to this Norm
+ 
+
+ align:start position:0%
+is complete with respect to this Norm
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a Hilbert space h
+
+ align:start position:0%
+a Hilbert space h
+ 
+
+ align:start position:0%
+a Hilbert space h
+is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pre-hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the norm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+with respect to this Norm which again I
+
+ align:start position:0%
+with respect to this Norm which again I
+ 
+
+ align:start position:0%
+with respect to this Norm which again I
+remember was defined as
+
+ align:start position:0%
+remember was defined as
+ 
+
+ align:start position:0%
+remember was defined as
+I stick a vector
+
+ align:start position:0%
+I stick a vector
+ 
+
+ align:start position:0%
+I stick a vector
+the norm of a vector here is equal to
+
+ align:start position:0%
+the norm of a vector here is equal to
+ 
+
+ align:start position:0%
+the norm of a vector here is equal to
+the inner product of the vector with
+
+ align:start position:0%
+the inner product of the vector with
+ 
+
+ align:start position:0%
+the inner product of the vector with
+itself raised to the one-half power
+
+ align:start position:0%
+itself raised to the one-half power
+ 
+
+ align:start position:0%
+itself raised to the one-half power
+all right so this is the new terminology
+
+ align:start position:0%
+all right so this is the new terminology
+ 
+
+ align:start position:0%
+all right so this is the new terminology
+and as we'll see
+
+ align:start position:0%
+and as we'll see
+ 
+
+ align:start position:0%
+and as we'll see
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+or at least we'll
+
+ align:start position:0%
+or at least we'll
+ 
+
+ align:start position:0%
+or at least we'll
+explicitly spell out in the in a form of
+
+ align:start position:0%
+explicitly spell out in the in a form of
+ 
+
+ align:start position:0%
+explicitly spell out in the in a form of
+a theorem but we will see
+
+ align:start position:0%
+a theorem but we will see
+ 
+
+ align:start position:0%
+a theorem but we will see
+probably by the end of this lecture
+
+ align:start position:0%
+probably by the end of this lecture
+ 
+
+ align:start position:0%
+probably by the end of this lecture
+that really there's for
+
+ align:start position:0%
+that really there's for
+ 
+
+ align:start position:0%
+that really there's for
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a reasonable Hilbert space you're either
+
+ align:start position:0%
+a reasonable Hilbert space you're either
+ 
+
+ align:start position:0%
+a reasonable Hilbert space you're either
+one of two
+
+ align:start position:0%
+one of two
+ 
+
+ align:start position:0%
+one of two
+things so let me first give the examples
+
+ align:start position:0%
+things so let me first give the examples
+ 
+
+ align:start position:0%
+things so let me first give the examples
+the basic examples of
+
+ align:start position:0%
+the basic examples of
+ 
+
+ align:start position:0%
+the basic examples of
+Hilbert space
+
+ align:start position:0%
+Hilbert space
+ 
+
+ align:start position:0%
+Hilbert space
+so for example c n
+
+ align:start position:0%
+so for example c n
+ 
+
+ align:start position:0%
+so for example c n
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+a set of n-tuples how do I denote this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the inner product of two
+
+ align:start position:0%
+where the inner product of two
+ 
+
+ align:start position:0%
+where the inner product of two
+uh vectors
+
+ align:start position:0%
+uh vectors
+ 
+
+ align:start position:0%
+uh vectors
+Z and W is equal to some
+
+ align:start position:0%
+Z and W is equal to some
+ 
+
+ align:start position:0%
+Z and W is equal to some
+J equals 1 to n
+
+ align:start position:0%
+J equals 1 to n
+ 
+
+ align:start position:0%
+J equals 1 to n
+g z J
+
+ align:start position:0%
+g z J
+ 
+
+ align:start position:0%
+g z J
+W J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this is an example
+
+ align:start position:0%
+so this is an example
+ 
+
+ align:start position:0%
+so this is an example
+of a Hilbert space finite dimensional
+
+ align:start position:0%
+of a Hilbert space finite dimensional
+ 
+
+ align:start position:0%
+of a Hilbert space finite dimensional
+one meaning it's a bionics it's a vector
+
+ align:start position:0%
+one meaning it's a bionics it's a vector
+ 
+
+ align:start position:0%
+one meaning it's a bionics it's a vector
+space of finite Dimension
+
+ align:start position:0%
+space of finite Dimension
+ 
+
+ align:start position:0%
+space of finite Dimension
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the other example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the space middle L2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this was the space of sequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+each of these is a complex number
+
+ align:start position:0%
+each of these is a complex number
+ 
+
+ align:start position:0%
+each of these is a complex number
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this uh series is convergent is finite
+
+ align:start position:0%
+this uh series is convergent is finite
+ 
+
+ align:start position:0%
+this uh series is convergent is finite
+um some of the absolute value of the AK
+
+ align:start position:0%
+um some of the absolute value of the AK
+ 
+
+ align:start position:0%
+um some of the absolute value of the AK
+squares this is a Hilbert's face as well
+
+ align:start position:0%
+squares this is a Hilbert's face as well
+ 
+
+ align:start position:0%
+squares this is a Hilbert's face as well
+with what's the inner product of two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+elements of little L2 this is the sum
+
+ align:start position:0%
+elements of little L2 this is the sum
+ 
+
+ align:start position:0%
+elements of little L2 this is the sum
+from k equals one to Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+8K BK
+
+ align:start position:0%
+8K BK
+ 
+
+ align:start position:0%
+8K BK
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and note so
+
+ align:start position:0%
+and note so
+ 
+
+ align:start position:0%
+and note so
+you know this is uh pretty clear but
+
+ align:start position:0%
+you know this is uh pretty clear but
+ 
+
+ align:start position:0%
+you know this is uh pretty clear but
+note that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the norm I get uh by
+
+ align:start position:0%
+the norm I get uh by
+ 
+
+ align:start position:0%
+the norm I get uh by
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know from this inner product this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was a little L2 Norm right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um you know these are two basic examples
+
+ align:start position:0%
+um you know these are two basic examples
+ 
+
+ align:start position:0%
+um you know these are two basic examples
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know a Hilbert space
+
+ align:start position:0%
+you know a Hilbert space
+ 
+
+ align:start position:0%
+you know a Hilbert space
+uh we will in fact show that
+
+ align:start position:0%
+uh we will in fact show that
+ 
+
+ align:start position:0%
+uh we will in fact show that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+every separable Hilbert space
+
+ align:start position:0%
+every separable Hilbert space
+ 
+
+ align:start position:0%
+every separable Hilbert space
+can be in a inner product and and
+
+ align:start position:0%
+can be in a inner product and and
+ 
+
+ align:start position:0%
+can be in a inner product and and
+therefore a link preserving way
+
+ align:start position:0%
+therefore a link preserving way
+ 
+
+ align:start position:0%
+therefore a link preserving way
+be mapped so that's usually called a
+
+ align:start position:0%
+be mapped so that's usually called a
+ 
+
+ align:start position:0%
+be mapped so that's usually called a
+an isometric isomorphism can be mapped
+
+ align:start position:0%
+an isometric isomorphism can be mapped
+ 
+
+ align:start position:0%
+an isometric isomorphism can be mapped
+isometrically
+
+ align:start position:0%
+isometrically
+ 
+
+ align:start position:0%
+isometrically
+to either see in or little L2 okay so
+
+ align:start position:0%
+to either see in or little L2 okay so
+ 
+
+ align:start position:0%
+to either see in or little L2 okay so
+these two kind of if one wants to go
+
+ align:start position:0%
+these two kind of if one wants to go
+ 
+
+ align:start position:0%
+these two kind of if one wants to go
+about uh you know
+
+ align:start position:0%
+about uh you know
+ 
+
+ align:start position:0%
+about uh you know
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+categorizing all of the possible Hilbert
+
+ align:start position:0%
+categorizing all of the possible Hilbert
+ 
+
+ align:start position:0%
+categorizing all of the possible Hilbert
+spaces as far as separable Hilbert
+
+ align:start position:0%
+spaces as far as separable Hilbert
+ 
+
+ align:start position:0%
+spaces as far as separable Hilbert
+spaces which are kind of the
+
+ align:start position:0%
+spaces which are kind of the
+ 
+
+ align:start position:0%
+spaces which are kind of the
+only reasonable ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of course come you know one can come up
+
+ align:start position:0%
+of course come you know one can come up
+ 
+
+ align:start position:0%
+of course come you know one can come up
+with wild examples of
+
+ align:start position:0%
+with wild examples of
+ 
+
+ align:start position:0%
+with wild examples of
+Hilbert's faces which are not then these
+
+ align:start position:0%
+Hilbert's faces which are not then these
+ 
+
+ align:start position:0%
+Hilbert's faces which are not then these
+are the only two I shouldn't say two
+
+ align:start position:0%
+are the only two I shouldn't say two
+ 
+
+ align:start position:0%
+are the only two I shouldn't say two
+because you know this one's indexed by
+
+ align:start position:0%
+because you know this one's indexed by
+ 
+
+ align:start position:0%
+because you know this one's indexed by
+its Dimension but these are the only two
+
+ align:start position:0%
+its Dimension but these are the only two
+ 
+
+ align:start position:0%
+its Dimension but these are the only two
+types that you come up with either a
+
+ align:start position:0%
+types that you come up with either a
+ 
+
+ align:start position:0%
+types that you come up with either a
+finite dimensional uh CN or it's
+
+ align:start position:0%
+finite dimensional uh CN or it's
+ 
+
+ align:start position:0%
+finite dimensional uh CN or it's
+isometric to little L2 okay
+
+ align:start position:0%
+isometric to little L2 okay
+ 
+
+ align:start position:0%
+isometric to little L2 okay
+but um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but I will still you know write down
+
+ align:start position:0%
+so but I will still you know write down
+ 
+
+ align:start position:0%
+so but I will still you know write down
+another example for
+
+ align:start position:0%
+another example for
+ 
+
+ align:start position:0%
+another example for
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since we went to all that work
+
+ align:start position:0%
+since we went to all that work
+ 
+
+ align:start position:0%
+since we went to all that work
+if e is a measurable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 of e the big L2 of e which
+
+ align:start position:0%
+2 of e the big L2 of e which
+ 
+
+ align:start position:0%
+2 of e the big L2 of e which
+remember this was a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space of measurable functions F from E
+
+ align:start position:0%
+space of measurable functions F from E
+ 
+
+ align:start position:0%
+space of measurable functions F from E
+to C such that
+
+ align:start position:0%
+to C such that
+ 
+
+ align:start position:0%
+to C such that
+F squared e is finite
+
+ align:start position:0%
+F squared e is finite
+ 
+
+ align:start position:0%
+F squared e is finite
+this is also
+
+ align:start position:0%
+this is also
+ 
+
+ align:start position:0%
+this is also
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a Hilbert space what's the inner
+
+ align:start position:0%
+this is a Hilbert space what's the inner
+ 
+
+ align:start position:0%
+this is a Hilbert space what's the inner
+product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the the inner product of
+
+ align:start position:0%
+with the the inner product of
+ 
+
+ align:start position:0%
+with the the inner product of
+two elements in L2 defined to be
+
+ align:start position:0%
+two elements in L2 defined to be
+ 
+
+ align:start position:0%
+two elements in L2 defined to be
+kind of just the analog of little L2
+
+ align:start position:0%
+kind of just the analog of little L2
+ 
+
+ align:start position:0%
+kind of just the analog of little L2
+where we replace the sum with an
+
+ align:start position:0%
+where we replace the sum with an
+ 
+
+ align:start position:0%
+where we replace the sum with an
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+times G
+
+ align:start position:0%
+times G
+ 
+
+ align:start position:0%
+times G
+okay the label integral of f times
+
+ align:start position:0%
+okay the label integral of f times
+ 
+
+ align:start position:0%
+okay the label integral of f times
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the complex conjugate of G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now um
+
+ align:start position:0%
+now um
+ 
+
+ align:start position:0%
+now um
+you know I wrote down Capital L2 I wrote
+
+ align:start position:0%
+you know I wrote down Capital L2 I wrote
+ 
+
+ align:start position:0%
+you know I wrote down Capital L2 I wrote
+down little L2
+
+ align:start position:0%
+down little L2
+ 
+
+ align:start position:0%
+down little L2
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but what about the other little LP and
+
+ align:start position:0%
+but what about the other little LP and
+ 
+
+ align:start position:0%
+but what about the other little LP and
+and big LP spaces or any of those
+
+ align:start position:0%
+and big LP spaces or any of those
+ 
+
+ align:start position:0%
+and big LP spaces or any of those
+Hilbert spaces
+
+ align:start position:0%
+Hilbert spaces
+ 
+
+ align:start position:0%
+Hilbert spaces
+um you know so
+
+ align:start position:0%
+um you know so
+ 
+
+ align:start position:0%
+um you know so
+of course if I Define the inner product
+
+ align:start position:0%
+of course if I Define the inner product
+ 
+
+ align:start position:0%
+of course if I Define the inner product
+in this way
+
+ align:start position:0%
+in this way
+ 
+
+ align:start position:0%
+in this way
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+as I did before then that only induces
+
+ align:start position:0%
+as I did before then that only induces
+ 
+
+ align:start position:0%
+as I did before then that only induces
+you know the little L2 and the big L2
+
+ align:start position:0%
+you know the little L2 and the big L2
+ 
+
+ align:start position:0%
+you know the little L2 and the big L2
+Norm right but is there
+
+ align:start position:0%
+Norm right but is there
+ 
+
+ align:start position:0%
+Norm right but is there
+perhaps some other kind of magic inner
+
+ align:start position:0%
+perhaps some other kind of magic inner
+ 
+
+ align:start position:0%
+perhaps some other kind of magic inner
+product out there that I can put on
+
+ align:start position:0%
+product out there that I can put on
+ 
+
+ align:start position:0%
+product out there that I can put on
+little LP or big LP
+
+ align:start position:0%
+little LP or big LP
+ 
+
+ align:start position:0%
+little LP or big LP
+so that I would get out
+
+ align:start position:0%
+so that I would get out
+ 
+
+ align:start position:0%
+so that I would get out
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the little LP or big LP Norm when I
+
+ align:start position:0%
+the little LP or big LP Norm when I
+ 
+
+ align:start position:0%
+the little LP or big LP Norm when I
+Define the norm according to you know
+
+ align:start position:0%
+Define the norm according to you know
+ 
+
+ align:start position:0%
+Define the norm according to you know
+how I've been doing it
+
+ align:start position:0%
+how I've been doing it
+ 
+
+ align:start position:0%
+how I've been doing it
+um so the question
+
+ align:start position:0%
+um so the question
+ 
+
+ align:start position:0%
+um so the question
+you know on hand is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other little LP or big LP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also Hilbert spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so again it's clear that if I were
+
+ align:start position:0%
+right so again it's clear that if I were
+ 
+
+ align:start position:0%
+right so again it's clear that if I were
+to define the inner product in in the
+
+ align:start position:0%
+to define the inner product in in the
+ 
+
+ align:start position:0%
+to define the inner product in in the
+way I did in the two examples then that
+
+ align:start position:0%
+way I did in the two examples then that
+ 
+
+ align:start position:0%
+way I did in the two examples then that
+only is going to give the the L2 Norm
+
+ align:start position:0%
+only is going to give the the L2 Norm
+ 
+
+ align:start position:0%
+only is going to give the the L2 Norm
+I'm asking now is there some magical
+
+ align:start position:0%
+I'm asking now is there some magical
+ 
+
+ align:start position:0%
+I'm asking now is there some magical
+inner product I can Define on these
+
+ align:start position:0%
+inner product I can Define on these
+ 
+
+ align:start position:0%
+inner product I can Define on these
+spaces
+
+ align:start position:0%
+spaces
+ 
+
+ align:start position:0%
+spaces
+that spits out the little LP or big LP
+
+ align:start position:0%
+that spits out the little LP or big LP
+ 
+
+ align:start position:0%
+that spits out the little LP or big LP
+Norm right
+
+ align:start position:0%
+Norm right
+ 
+
+ align:start position:0%
+Norm right
+um so the answer is no and there's in
+
+ align:start position:0%
+um so the answer is no and there's in
+ 
+
+ align:start position:0%
+um so the answer is no and there's in
+fact
+
+ align:start position:0%
+fact
+ 
+
+ align:start position:0%
+fact
+you know a way
+
+ align:start position:0%
+you know a way
+ 
+
+ align:start position:0%
+you know a way
+to determine whether or not
+
+ align:start position:0%
+to determine whether or not
+ 
+
+ align:start position:0%
+to determine whether or not
+a space is a Hilbert space because if
+
+ align:start position:0%
+a space is a Hilbert space because if
+ 
+
+ align:start position:0%
+a space is a Hilbert space because if
+you think about it the way you know
+
+ align:start position:0%
+you think about it the way you know
+ 
+
+ align:start position:0%
+you think about it the way you know
+we've come about
+
+ align:start position:0%
+we've come about
+ 
+
+ align:start position:0%
+we've come about
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know introducing uh what a
+
+ align:start position:0%
+you know introducing uh what a
+ 
+
+ align:start position:0%
+you know introducing uh what a
+pre-opered space is and the Hilbert
+
+ align:start position:0%
+pre-opered space is and the Hilbert
+ 
+
+ align:start position:0%
+pre-opered space is and the Hilbert
+space is we first had a norm in our hand
+
+ align:start position:0%
+space is we first had a norm in our hand
+ 
+
+ align:start position:0%
+space is we first had a norm in our hand
+and then we defined an inner product
+
+ align:start position:0%
+and then we defined an inner product
+ 
+
+ align:start position:0%
+and then we defined an inner product
+well if that's the way you're building
+
+ align:start position:0%
+well if that's the way you're building
+ 
+
+ align:start position:0%
+well if that's the way you're building
+your space and you know automatically
+
+ align:start position:0%
+your space and you know automatically
+ 
+
+ align:start position:0%
+your space and you know automatically
+that it's a Hilbert space because you
+
+ align:start position:0%
+that it's a Hilbert space because you
+ 
+
+ align:start position:0%
+that it's a Hilbert space because you
+had an inner product first and then you
+
+ align:start position:0%
+had an inner product first and then you
+ 
+
+ align:start position:0%
+had an inner product first and then you
+defined the norm second let's suppose
+
+ align:start position:0%
+defined the norm second let's suppose
+ 
+
+ align:start position:0%
+defined the norm second let's suppose
+you're only given the data you're given
+
+ align:start position:0%
+you're only given the data you're given
+ 
+
+ align:start position:0%
+you're only given the data you're given
+is some Norm on the space
+
+ align:start position:0%
+is some Norm on the space
+ 
+
+ align:start position:0%
+is some Norm on the space
+when can you determine if that Norm
+
+ align:start position:0%
+when can you determine if that Norm
+ 
+
+ align:start position:0%
+when can you determine if that Norm
+comes from an inner product right that's
+
+ align:start position:0%
+comes from an inner product right that's
+ 
+
+ align:start position:0%
+comes from an inner product right that's
+the question that uh you know is
+
+ align:start position:0%
+the question that uh you know is
+ 
+
+ align:start position:0%
+the question that uh you know is
+underlying this question I wrote on the
+
+ align:start position:0%
+underlying this question I wrote on the
+ 
+
+ align:start position:0%
+underlying this question I wrote on the
+board if I have a norm space
+
+ align:start position:0%
+board if I have a norm space
+ 
+
+ align:start position:0%
+board if I have a norm space
+right so all my initial data is the norm
+
+ align:start position:0%
+right so all my initial data is the norm
+ 
+
+ align:start position:0%
+right so all my initial data is the norm
+when can I tell that that Norm comes
+
+ align:start position:0%
+when can I tell that that Norm comes
+ 
+
+ align:start position:0%
+when can I tell that that Norm comes
+from an inner product
+
+ align:start position:0%
+from an inner product
+ 
+
+ align:start position:0%
+from an inner product
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+it so you'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prove this basically by direct
+
+ align:start position:0%
+prove this basically by direct
+ 
+
+ align:start position:0%
+prove this basically by direct
+calculation but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the following parallelogram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law which is the following if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pre-hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+all u v and H
+
+ align:start position:0%
+all u v and H
+ 
+
+ align:start position:0%
+all u v and H
+if I take
+
+ align:start position:0%
+if I take
+ 
+
+ align:start position:0%
+if I take
+the norm of U plus v squared
+
+ align:start position:0%
+the norm of U plus v squared
+ 
+
+ align:start position:0%
+the norm of U plus v squared
+and I add the norm of U minus V squared
+
+ align:start position:0%
+and I add the norm of U minus V squared
+ 
+
+ align:start position:0%
+and I add the norm of U minus V squared
+this is equal to twice
+
+ align:start position:0%
+this is equal to twice
+ 
+
+ align:start position:0%
+this is equal to twice
+the norm of U squared plus the norm
+
+ align:start position:0%
+the norm of U squared plus the norm
+ 
+
+ align:start position:0%
+the norm of U squared plus the norm
+of V squared right so this is a
+
+ align:start position:0%
+of V squared right so this is a
+ 
+
+ align:start position:0%
+of V squared right so this is a
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that is stated purely in terms of the
+
+ align:start position:0%
+that is stated purely in terms of the
+ 
+
+ align:start position:0%
+that is stated purely in terms of the
+norm right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moreover uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+H is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Norm space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfying star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then H is a
+
+ align:start position:0%
+then H is a
+ 
+
+ align:start position:0%
+then H is a
+pre-hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in other words uh
+
+ align:start position:0%
+okay in other words uh
+ 
+
+ align:start position:0%
+okay in other words uh
+although it seems like you know we
+
+ align:start position:0%
+although it seems like you know we
+ 
+
+ align:start position:0%
+although it seems like you know we
+defined Hilbert spaces or pre-hilbert
+
+ align:start position:0%
+defined Hilbert spaces or pre-hilbert
+ 
+
+ align:start position:0%
+defined Hilbert spaces or pre-hilbert
+spaces initially in terms of an inner
+
+ align:start position:0%
+spaces initially in terms of an inner
+ 
+
+ align:start position:0%
+spaces initially in terms of an inner
+product in fact you can say a norm space
+
+ align:start position:0%
+product in fact you can say a norm space
+ 
+
+ align:start position:0%
+product in fact you can say a norm space
+is a pre-hubert space if and only if it
+
+ align:start position:0%
+is a pre-hubert space if and only if it
+ 
+
+ align:start position:0%
+is a pre-hubert space if and only if it
+satisfies this parallelogram law
+
+ align:start position:0%
+satisfies this parallelogram law
+ 
+
+ align:start position:0%
+satisfies this parallelogram law
+okay so if you have on your hands just
+
+ align:start position:0%
+okay so if you have on your hands just
+ 
+
+ align:start position:0%
+okay so if you have on your hands just
+the norm
+
+ align:start position:0%
+the norm
+ 
+
+ align:start position:0%
+the norm
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+as long as that Norm satisfies this
+
+ align:start position:0%
+as long as that Norm satisfies this
+ 
+
+ align:start position:0%
+as long as that Norm satisfies this
+identity that Norm can be derived from
+
+ align:start position:0%
+identity that Norm can be derived from
+ 
+
+ align:start position:0%
+identity that Norm can be derived from
+an inner product
+
+ align:start position:0%
+an inner product
+ 
+
+ align:start position:0%
+an inner product
+so using this theorem you can check that
+
+ align:start position:0%
+so using this theorem you can check that
+ 
+
+ align:start position:0%
+so using this theorem you can check that
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the answer is only for
+
+ align:start position:0%
+the answer is only for
+ 
+
+ align:start position:0%
+the answer is only for
+P equals 2.
+
+ align:start position:0%
+P equals 2.
+ 
+
+ align:start position:0%
+P equals 2.
+okay so in other words if you you can
+
+ align:start position:0%
+okay so in other words if you you can
+ 
+
+ align:start position:0%
+okay so in other words if you you can
+come up with u and v
+
+ align:start position:0%
+come up with u and v
+ 
+
+ align:start position:0%
+come up with u and v
+that so that this inequality is not
+
+ align:start position:0%
+that so that this inequality is not
+ 
+
+ align:start position:0%
+that so that this inequality is not
+satisfied when p is not equal to two
+
+ align:start position:0%
+satisfied when p is not equal to two
+ 
+
+ align:start position:0%
+satisfied when p is not equal to two
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this
+
+ align:start position:0%
+okay so this
+ 
+
+ align:start position:0%
+okay so this
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have the notion of a Hilbert
+
+ align:start position:0%
+so now we have the notion of a Hilbert
+ 
+
+ align:start position:0%
+so now we have the notion of a Hilbert
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+where this Norm uh given in terms of an
+
+ align:start position:0%
+where this Norm uh given in terms of an
+ 
+
+ align:start position:0%
+where this Norm uh given in terms of an
+inner product
+
+ align:start position:0%
+inner product
+ 
+
+ align:start position:0%
+inner product
+the space is complete
+
+ align:start position:0%
+the space is complete
+ 
+
+ align:start position:0%
+the space is complete
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+we have an inner product so
+
+ align:start position:0%
+we have an inner product so
+ 
+
+ align:start position:0%
+we have an inner product so
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+vectors being orthogonal to other
+
+ align:start position:0%
+vectors being orthogonal to other
+ 
+
+ align:start position:0%
+vectors being orthogonal to other
+vectors or
+
+ align:start position:0%
+vectors or
+ 
+
+ align:start position:0%
+vectors or
+or the normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets
+
+ align:start position:0%
+sets
+ 
+
+ align:start position:0%
+sets
+um which you know when I first started
+
+ align:start position:0%
+um which you know when I first started
+ 
+
+ align:start position:0%
+um which you know when I first started
+lecturing about this stuff I started I
+
+ align:start position:0%
+lecturing about this stuff I started I
+ 
+
+ align:start position:0%
+lecturing about this stuff I started I
+was already using the terminology this
+
+ align:start position:0%
+was already using the terminology this
+ 
+
+ align:start position:0%
+was already using the terminology this
+thing being orthogonal to this thing or
+
+ align:start position:0%
+thing being orthogonal to this thing or
+ 
+
+ align:start position:0%
+thing being orthogonal to this thing or
+something like that
+
+ align:start position:0%
+something like that
+ 
+
+ align:start position:0%
+something like that
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+of course if you don't remember what
+
+ align:start position:0%
+of course if you don't remember what
+ 
+
+ align:start position:0%
+of course if you don't remember what
+those words mean
+
+ align:start position:0%
+those words mean
+ 
+
+ align:start position:0%
+those words mean
+um from
+
+ align:start position:0%
+um from
+ 
+
+ align:start position:0%
+um from
+linear algebra I'll brief I'll quickly
+
+ align:start position:0%
+linear algebra I'll brief I'll quickly
+ 
+
+ align:start position:0%
+linear algebra I'll brief I'll quickly
+remind you
+
+ align:start position:0%
+remind you
+ 
+
+ align:start position:0%
+remind you
+so suppose we're in a hill pre-hilbert
+
+ align:start position:0%
+so suppose we're in a hill pre-hilbert
+ 
+
+ align:start position:0%
+so suppose we're in a hill pre-hilbert
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we say that two elements u and v are
+
+ align:start position:0%
+we say that two elements u and v are
+ 
+
+ align:start position:0%
+we say that two elements u and v are
+orthogonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if their inner product is zero
+
+ align:start position:0%
+if their inner product is zero
+ 
+
+ align:start position:0%
+if their inner product is zero
+right and we
+
+ align:start position:0%
+right and we
+ 
+
+ align:start position:0%
+right and we
+if uh instead of saying orthogonal I
+
+ align:start position:0%
+if uh instead of saying orthogonal I
+ 
+
+ align:start position:0%
+if uh instead of saying orthogonal I
+want to write this in words I'll write
+
+ align:start position:0%
+want to write this in words I'll write
+ 
+
+ align:start position:0%
+want to write this in words I'll write
+you Purp
+
+ align:start position:0%
+you Purp
+ 
+
+ align:start position:0%
+you Purp
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+throughout H is going to be uh
+
+ align:start position:0%
+throughout H is going to be uh
+ 
+
+ align:start position:0%
+throughout H is going to be uh
+pre-hubert's face if I don't actually
+
+ align:start position:0%
+pre-hubert's face if I don't actually
+ 
+
+ align:start position:0%
+pre-hubert's face if I don't actually
+write it if H is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pre-hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which I'll denote by Eden Lambda Lambda
+
+ align:start position:0%
+which I'll denote by Eden Lambda Lambda
+ 
+
+ align:start position:0%
+which I'll denote by Eden Lambda Lambda
+and Capital Lambda so just some subset
+
+ align:start position:0%
+and Capital Lambda so just some subset
+ 
+
+ align:start position:0%
+and Capital Lambda so just some subset
+indexed by some indexing set Capital
+
+ align:start position:0%
+indexed by some indexing set Capital
+ 
+
+ align:start position:0%
+indexed by some indexing set Capital
+Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we say this set is orthonormal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+we're all Lambda each one of these
+
+ align:start position:0%
+we're all Lambda each one of these
+ 
+
+ align:start position:0%
+we're all Lambda each one of these
+vectors and the subset has unit length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+I need to
+
+ align:start position:0%
+I need to
+ 
+
+ align:start position:0%
+I need to
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different indexed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elements implies that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they are orthogonal
+
+ align:start position:0%
+they are orthogonal
+ 
+
+ align:start position:0%
+they are orthogonal
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um maybe this notation scares you
+
+ align:start position:0%
+um maybe this notation scares you
+ 
+
+ align:start position:0%
+um maybe this notation scares you
+because what's this indexing set
+
+ align:start position:0%
+because what's this indexing set
+ 
+
+ align:start position:0%
+because what's this indexing set
+typically we just use the natural number
+
+ align:start position:0%
+typically we just use the natural number
+ 
+
+ align:start position:0%
+typically we just use the natural number
+so let me just make that remark although
+
+ align:start position:0%
+so let me just make that remark although
+ 
+
+ align:start position:0%
+so let me just make that remark although
+I'll make a few remarks in general about
+
+ align:start position:0%
+I'll make a few remarks in general about
+ 
+
+ align:start position:0%
+I'll make a few remarks in general about
+what the normal sets that are not
+
+ align:start position:0%
+what the normal sets that are not
+ 
+
+ align:start position:0%
+what the normal sets that are not
+necessarily indexed by the natural
+
+ align:start position:0%
+necessarily indexed by the natural
+ 
+
+ align:start position:0%
+necessarily indexed by the natural
+numbers will mainly be interested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know a finite
+
+ align:start position:0%
+and you know a finite
+ 
+
+ align:start position:0%
+and you know a finite
+set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or accountably infinite set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so mainly so although uh an
+
+ align:start position:0%
+okay so mainly so although uh an
+ 
+
+ align:start position:0%
+okay so mainly so although uh an
+orthonormal uh subset of H is
+
+ align:start position:0%
+orthonormal uh subset of H is
+ 
+
+ align:start position:0%
+orthonormal uh subset of H is
+you know could be a very crazy type of
+
+ align:start position:0%
+you know could be a very crazy type of
+ 
+
+ align:start position:0%
+you know could be a very crazy type of
+uh subset mainly we're going to be
+
+ align:start position:0%
+uh subset mainly we're going to be
+ 
+
+ align:start position:0%
+uh subset mainly we're going to be
+interested only in
+
+ align:start position:0%
+interested only in
+ 
+
+ align:start position:0%
+interested only in
+finite or countable
+
+ align:start position:0%
+finite or countable
+ 
+
+ align:start position:0%
+finite or countable
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+accountably infinite uh orthonormal sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's uh
+
+ align:start position:0%
+so what's uh
+ 
+
+ align:start position:0%
+so what's uh
+what are some examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um simplest examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah if
+
+ align:start position:0%
+ah if
+ 
+
+ align:start position:0%
+ah if
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an example of a set of orthonormal or an
+
+ align:start position:0%
+an example of a set of orthonormal or an
+ 
+
+ align:start position:0%
+an example of a set of orthonormal or an
+orthonormal subset of C2 or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is also an example of an
+
+ align:start position:0%
+this is also an example of an
+ 
+
+ align:start position:0%
+this is also an example of an
+orthonormal subset of C3
+
+ align:start position:0%
+orthonormal subset of C3
+ 
+
+ align:start position:0%
+orthonormal subset of C3
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's say
+
+ align:start position:0%
+let's say
+ 
+
+ align:start position:0%
+let's say
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+using notation from before if I denote
+
+ align:start position:0%
+using notation from before if I denote
+ 
+
+ align:start position:0%
+using notation from before if I denote
+by E sub n this is uh the sequence
+
+ align:start position:0%
+by E sub n this is uh the sequence
+ 
+
+ align:start position:0%
+by E sub n this is uh the sequence
+consisting of zeros up until I hit the
+
+ align:start position:0%
+consisting of zeros up until I hit the
+ 
+
+ align:start position:0%
+consisting of zeros up until I hit the
+end spot
+
+ align:start position:0%
+end spot
+ 
+
+ align:start position:0%
+end spot
+and then 0 afterwards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and entry
+
+ align:start position:0%
+and entry
+ 
+
+ align:start position:0%
+and entry
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+which is an element of little L2
+
+ align:start position:0%
+which is an element of little L2
+ 
+
+ align:start position:0%
+which is an element of little L2
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is an orthonormal subset of L2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one other
+
+ align:start position:0%
+one other
+ 
+
+ align:start position:0%
+one other
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+let's look at the functions one over
+
+ align:start position:0%
+let's look at the functions one over
+ 
+
+ align:start position:0%
+let's look at the functions one over
+square root of 2 pi times e to the I and
+
+ align:start position:0%
+square root of 2 pi times e to the I and
+ 
+
+ align:start position:0%
+square root of 2 pi times e to the I and
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+and let's think of these as elements of
+
+ align:start position:0%
+and let's think of these as elements of
+ 
+
+ align:start position:0%
+and let's think of these as elements of
+L2 and minus pi to Pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is an orthonormal subset of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my right o-n instead of orthonorm
+
+ align:start position:0%
+my right o-n instead of orthonorm
+ 
+
+ align:start position:0%
+my right o-n instead of orthonorm
+instead of writing out uh orthonormal
+
+ align:start position:0%
+instead of writing out uh orthonormal
+ 
+
+ align:start position:0%
+instead of writing out uh orthonormal
+but this is an orthonormal subset of L2
+
+ align:start position:0%
+but this is an orthonormal subset of L2
+ 
+
+ align:start position:0%
+but this is an orthonormal subset of L2
+right since uh if I take the inner
+
+ align:start position:0%
+right since uh if I take the inner
+ 
+
+ align:start position:0%
+right since uh if I take the inner
+product of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two of these guys I get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say I just look at uh two
+
+ align:start position:0%
+let's say I just look at uh two
+ 
+
+ align:start position:0%
+let's say I just look at uh two
+different ones
+
+ align:start position:0%
+different ones
+ 
+
+ align:start position:0%
+different ones
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M does not equal n so then I take the
+
+ align:start position:0%
+M does not equal n so then I take the
+ 
+
+ align:start position:0%
+M does not equal n so then I take the
+inner product of i m x
+
+ align:start position:0%
+inner product of i m x
+ 
+
+ align:start position:0%
+inner product of i m x
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+inner product of
+
+ align:start position:0%
+inner product of
+ 
+
+ align:start position:0%
+inner product of
+i n x complex conjugate
+
+ align:start position:0%
+i n x complex conjugate
+ 
+
+ align:start position:0%
+i n x complex conjugate
+so that's the inner product on big L2
+
+ align:start position:0%
+so that's the inner product on big L2
+ 
+
+ align:start position:0%
+so that's the inner product on big L2
+and this is equal to
+
+ align:start position:0%
+and this is equal to
+ 
+
+ align:start position:0%
+and this is equal to
+1 over
+
+ align:start position:0%
+1 over
+ 
+
+ align:start position:0%
+1 over
+2 pi times minus pi to Pi of now if m
+
+ align:start position:0%
+2 pi times minus pi to Pi of now if m
+ 
+
+ align:start position:0%
+2 pi times minus pi to Pi of now if m
+equals n then this I just get the length
+
+ align:start position:0%
+equals n then this I just get the length
+ 
+
+ align:start position:0%
+equals n then this I just get the length
+of e to the i m in n x squared the
+
+ align:start position:0%
+of e to the i m in n x squared the
+ 
+
+ align:start position:0%
+of e to the i m in n x squared the
+length of e to the i m x is 1 and
+
+ align:start position:0%
+length of e to the i m x is 1 and
+ 
+
+ align:start position:0%
+length of e to the i m x is 1 and
+therefore I would just get one here DX
+
+ align:start position:0%
+therefore I would just get one here DX
+ 
+
+ align:start position:0%
+therefore I would just get one here DX
+over 2 pi which gives me 1. but now
+
+ align:start position:0%
+over 2 pi which gives me 1. but now
+ 
+
+ align:start position:0%
+over 2 pi which gives me 1. but now
+they're eight they're not equal so I get
+
+ align:start position:0%
+they're eight they're not equal so I get
+ 
+
+ align:start position:0%
+they're eight they're not equal so I get
+e to the I
+
+ align:start position:0%
+e to the I
+ 
+
+ align:start position:0%
+e to the I
+M minus n x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the integral of this creature so
+
+ align:start position:0%
+now the integral of this creature so
+ 
+
+ align:start position:0%
+now the integral of this creature so
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+e to the I let's say
+
+ align:start position:0%
+e to the I let's say
+ 
+
+ align:start position:0%
+e to the I let's say
+I'm going to come up with some e to the
+
+ align:start position:0%
+I'm going to come up with some e to the
+ 
+
+ align:start position:0%
+I'm going to come up with some e to the
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y when Y is a real number this is by
+
+ align:start position:0%
+y when Y is a real number this is by
+ 
+
+ align:start position:0%
+y when Y is a real number this is by
+definition cosine of y plus I sine y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you can check that fundamental
+
+ align:start position:0%
+now you can check that fundamental
+ 
+
+ align:start position:0%
+now you can check that fundamental
+theorem of calculus still holds for uh e
+
+ align:start position:0%
+theorem of calculus still holds for uh e
+ 
+
+ align:start position:0%
+theorem of calculus still holds for uh e
+to the i m minus n over X and this
+
+ align:start position:0%
+to the i m minus n over X and this
+ 
+
+ align:start position:0%
+to the i m minus n over X and this
+equals e to the i m minus n
+
+ align:start position:0%
+equals e to the i m minus n
+ 
+
+ align:start position:0%
+equals e to the i m minus n
+X over I times M minus n
+
+ align:start position:0%
+X over I times M minus n
+ 
+
+ align:start position:0%
+X over I times M minus n
+and uh e to the i m minus n times x is 2
+
+ align:start position:0%
+and uh e to the i m minus n times x is 2
+ 
+
+ align:start position:0%
+and uh e to the i m minus n times x is 2
+pi periodic so when I
+
+ align:start position:0%
+pi periodic so when I
+ 
+
+ align:start position:0%
+pi periodic so when I
+evaluated at minus Pi I get the same
+
+ align:start position:0%
+evaluated at minus Pi I get the same
+ 
+
+ align:start position:0%
+evaluated at minus Pi I get the same
+value if I evaluate it at Pi so this
+
+ align:start position:0%
+value if I evaluate it at Pi so this
+ 
+
+ align:start position:0%
+value if I evaluate it at Pi so this
+equals 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a
+
+ align:start position:0%
+so that's a
+ 
+
+ align:start position:0%
+so that's a
+or it's the normal subset of big L2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know this collection of vectors
+
+ align:start position:0%
+so you know this collection of vectors
+ 
+
+ align:start position:0%
+so you know this collection of vectors
+and and I'm calling them vectors but
+
+ align:start position:0%
+and and I'm calling them vectors but
+ 
+
+ align:start position:0%
+and and I'm calling them vectors but
+this collection of elements in big L2
+
+ align:start position:0%
+this collection of elements in big L2
+ 
+
+ align:start position:0%
+this collection of elements in big L2
+you know is still countable even though
+
+ align:start position:0%
+you know is still countable even though
+ 
+
+ align:start position:0%
+you know is still countable even though
+I'm indexing it by the integers rather
+
+ align:start position:0%
+I'm indexing it by the integers rather
+ 
+
+ align:start position:0%
+I'm indexing it by the integers rather
+than the natural numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+okay so we have the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+now you know most of what I'm going to
+
+ align:start position:0%
+now you know most of what I'm going to
+ 
+
+ align:start position:0%
+now you know most of what I'm going to
+say with regards to
+
+ align:start position:0%
+say with regards to
+ 
+
+ align:start position:0%
+say with regards to
+um accountable subsets of
+
+ align:start position:0%
+um accountable subsets of
+ 
+
+ align:start position:0%
+um accountable subsets of
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so accountable orthonormal sets
+
+ align:start position:0%
+so accountable orthonormal sets
+ 
+
+ align:start position:0%
+so accountable orthonormal sets
+still carries through to possibly
+
+ align:start position:0%
+still carries through to possibly
+ 
+
+ align:start position:0%
+still carries through to possibly
+uncountable orthonormal sets where now
+
+ align:start position:0%
+uncountable orthonormal sets where now
+ 
+
+ align:start position:0%
+uncountable orthonormal sets where now
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+a infinite sum over an uncountable
+
+ align:start position:0%
+a infinite sum over an uncountable
+ 
+
+ align:start position:0%
+a infinite sum over an uncountable
+number of elements has to be defined in
+
+ align:start position:0%
+number of elements has to be defined in
+ 
+
+ align:start position:0%
+number of elements has to be defined in
+a precise way but um
+
+ align:start position:0%
+a precise way but um
+ 
+
+ align:start position:0%
+a precise way but um
+I will really just stick mostly to the
+
+ align:start position:0%
+I will really just stick mostly to the
+ 
+
+ align:start position:0%
+I will really just stick mostly to the
+accountable case and if you're
+
+ align:start position:0%
+accountable case and if you're
+ 
+
+ align:start position:0%
+accountable case and if you're
+interested you can always look that
+
+ align:start position:0%
+interested you can always look that
+ 
+
+ align:start position:0%
+interested you can always look that
+stuff up
+
+ align:start position:0%
+stuff up
+ 
+
+ align:start position:0%
+stuff up
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so I should say you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I haven't said is that
+
+ align:start position:0%
+what I haven't said is that
+ 
+
+ align:start position:0%
+what I haven't said is that
+whether or not the lp spaces let's say
+
+ align:start position:0%
+whether or not the lp spaces let's say
+ 
+
+ align:start position:0%
+whether or not the lp spaces let's say
+over an interval a b or over R are
+
+ align:start position:0%
+over an interval a b or over R are
+ 
+
+ align:start position:0%
+over an interval a b or over R are
+separable
+
+ align:start position:0%
+separable
+ 
+
+ align:start position:0%
+separable
+or not or even over a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or even over a yeah so let's stick to
+
+ align:start position:0%
+or even over a yeah so let's stick to
+ 
+
+ align:start position:0%
+or even over a yeah so let's stick to
+either close and bounded interval over
+
+ align:start position:0%
+either close and bounded interval over
+ 
+
+ align:start position:0%
+either close and bounded interval over
+or r
+
+ align:start position:0%
+or r
+ 
+
+ align:start position:0%
+or r
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+why are these spaces separable and
+
+ align:start position:0%
+why are these spaces separable and
+ 
+
+ align:start position:0%
+why are these spaces separable and
+meaning they have accountably dense uh
+
+ align:start position:0%
+meaning they have accountably dense uh
+ 
+
+ align:start position:0%
+meaning they have accountably dense uh
+subset
+
+ align:start position:0%
+subset
+ 
+
+ align:start position:0%
+subset
+so including big L2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the reason is the following so what you
+
+ align:start position:0%
+the reason is the following so what you
+ 
+
+ align:start position:0%
+the reason is the following so what you
+proved
+
+ align:start position:0%
+proved
+ 
+
+ align:start position:0%
+proved
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in the assignment
+
+ align:start position:0%
+in the assignment
+ 
+
+ align:start position:0%
+in the assignment
+is that the continuous functions are
+
+ align:start position:0%
+is that the continuous functions are
+ 
+
+ align:start position:0%
+is that the continuous functions are
+dense and little and big LP for p
+
+ align:start position:0%
+dense and little and big LP for p
+ 
+
+ align:start position:0%
+dense and little and big LP for p
+between P equals uh
+
+ align:start position:0%
+between P equals uh
+ 
+
+ align:start position:0%
+between P equals uh
+1 to Infinity strictly less than
+
+ align:start position:0%
+1 to Infinity strictly less than
+ 
+
+ align:start position:0%
+1 to Infinity strictly less than
+infinity okay they're not dense in L
+
+ align:start position:0%
+infinity okay they're not dense in L
+ 
+
+ align:start position:0%
+infinity okay they're not dense in L
+Infinity so as long as you stay away
+
+ align:start position:0%
+Infinity so as long as you stay away
+ 
+
+ align:start position:0%
+Infinity so as long as you stay away
+from that they're dense okay
+
+ align:start position:0%
+from that they're dense okay
+ 
+
+ align:start position:0%
+from that they're dense okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so continuous functions are dense in LP
+
+ align:start position:0%
+so continuous functions are dense in LP
+ 
+
+ align:start position:0%
+so continuous functions are dense in LP
+now what's one way to approximate a
+
+ align:start position:0%
+now what's one way to approximate a
+ 
+
+ align:start position:0%
+now what's one way to approximate a
+continuous function
+
+ align:start position:0%
+continuous function
+ 
+
+ align:start position:0%
+continuous function
+you can going back to your introductory
+
+ align:start position:0%
+you can going back to your introductory
+ 
+
+ align:start position:0%
+you can going back to your introductory
+analysis class hopefully you covered
+
+ align:start position:0%
+analysis class hopefully you covered
+ 
+
+ align:start position:0%
+analysis class hopefully you covered
+What's called the virus drops
+
+ align:start position:0%
+What's called the virus drops
+ 
+
+ align:start position:0%
+What's called the virus drops
+approximation theorem which says that
+
+ align:start position:0%
+approximation theorem which says that
+ 
+
+ align:start position:0%
+approximation theorem which says that
+for every continuous function you can
+
+ align:start position:0%
+for every continuous function you can
+ 
+
+ align:start position:0%
+for every continuous function you can
+approximate it uniformly on the interval
+
+ align:start position:0%
+approximate it uniformly on the interval
+ 
+
+ align:start position:0%
+approximate it uniformly on the interval
+by a polynomial
+
+ align:start position:0%
+by a polynomial
+ 
+
+ align:start position:0%
+by a polynomial
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that shows that polynomials are dense
+
+ align:start position:0%
+so that shows that polynomials are dense
+ 
+
+ align:start position:0%
+so that shows that polynomials are dense
+and all the lp spaces of course not L
+
+ align:start position:0%
+and all the lp spaces of course not L
+ 
+
+ align:start position:0%
+and all the lp spaces of course not L
+Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+how do you go from the set of
+
+ align:start position:0%
+how do you go from the set of
+ 
+
+ align:start position:0%
+how do you go from the set of
+polynomials which is uncountable to a
+
+ align:start position:0%
+polynomials which is uncountable to a
+ 
+
+ align:start position:0%
+polynomials which is uncountable to a
+count of which is dense in LP but is
+
+ align:start position:0%
+count of which is dense in LP but is
+ 
+
+ align:start position:0%
+count of which is dense in LP but is
+uncountable to a countable dense subset
+
+ align:start position:0%
+uncountable to a countable dense subset
+ 
+
+ align:start position:0%
+uncountable to a countable dense subset
+which is density no p
+
+ align:start position:0%
+which is density no p
+ 
+
+ align:start position:0%
+which is density no p
+make everything rational okay the set of
+
+ align:start position:0%
+make everything rational okay the set of
+ 
+
+ align:start position:0%
+make everything rational okay the set of
+polynomials with rational coefficients
+
+ align:start position:0%
+polynomials with rational coefficients
+ 
+
+ align:start position:0%
+polynomials with rational coefficients
+is in fact countable
+
+ align:start position:0%
+is in fact countable
+ 
+
+ align:start position:0%
+is in fact countable
+okay and so
+
+ align:start position:0%
+okay and so
+ 
+
+ align:start position:0%
+okay and so
+and you can approximate every polynomial
+
+ align:start position:0%
+and you can approximate every polynomial
+ 
+
+ align:start position:0%
+and you can approximate every polynomial
+with real coefficients by on a closed
+
+ align:start position:0%
+with real coefficients by on a closed
+ 
+
+ align:start position:0%
+with real coefficients by on a closed
+and bounded uh interval by
+
+ align:start position:0%
+and bounded uh interval by
+ 
+
+ align:start position:0%
+and bounded uh interval by
+a polynomial with rational coefficients
+
+ align:start position:0%
+a polynomial with rational coefficients
+ 
+
+ align:start position:0%
+a polynomial with rational coefficients
+is not too difficult to to believe
+
+ align:start position:0%
+is not too difficult to to believe
+ 
+
+ align:start position:0%
+is not too difficult to to believe
+and therefore the polynomials with
+
+ align:start position:0%
+and therefore the polynomials with
+ 
+
+ align:start position:0%
+and therefore the polynomials with
+rational coefficients
+
+ align:start position:0%
+rational coefficients
+ 
+
+ align:start position:0%
+rational coefficients
+okay are dense and the lp spaces as long
+
+ align:start position:0%
+okay are dense and the lp spaces as long
+ 
+
+ align:start position:0%
+okay are dense and the lp spaces as long
+as I'm not in L Infinity
+
+ align:start position:0%
+as I'm not in L Infinity
+ 
+
+ align:start position:0%
+as I'm not in L Infinity
+um and therefore all the lp spaces are
+
+ align:start position:0%
+um and therefore all the lp spaces are
+ 
+
+ align:start position:0%
+um and therefore all the lp spaces are
+separable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the little LP spaces are also separable
+
+ align:start position:0%
+the little LP spaces are also separable
+ 
+
+ align:start position:0%
+the little LP spaces are also separable
+because except for L Infinity also which
+
+ align:start position:0%
+because except for L Infinity also which
+ 
+
+ align:start position:0%
+because except for L Infinity also which
+is not separable
+
+ align:start position:0%
+is not separable
+ 
+
+ align:start position:0%
+is not separable
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+because first off
+
+ align:start position:0%
+because first off
+ 
+
+ align:start position:0%
+because first off
+a dense
+
+ align:start position:0%
+a dense
+ 
+
+ align:start position:0%
+a dense
+subset of the let's say little O2 let's
+
+ align:start position:0%
+subset of the let's say little O2 let's
+ 
+
+ align:start position:0%
+subset of the let's say little O2 let's
+make things definite
+
+ align:start position:0%
+make things definite
+ 
+
+ align:start position:0%
+make things definite
+is the Subspace consisting of all
+
+ align:start position:0%
+is the Subspace consisting of all
+ 
+
+ align:start position:0%
+is the Subspace consisting of all
+sequences which terminate after
+
+ align:start position:0%
+sequences which terminate after
+ 
+
+ align:start position:0%
+sequences which terminate after
+some entry in other words it's zero
+
+ align:start position:0%
+some entry in other words it's zero
+ 
+
+ align:start position:0%
+some entry in other words it's zero
+after that okay
+
+ align:start position:0%
+after that okay
+ 
+
+ align:start position:0%
+after that okay
+you know convince yourself that this
+
+ align:start position:0%
+you know convince yourself that this
+ 
+
+ align:start position:0%
+you know convince yourself that this
+Subspace of all finitely terminating
+
+ align:start position:0%
+Subspace of all finitely terminating
+ 
+
+ align:start position:0%
+Subspace of all finitely terminating
+sequences this is dense and little LP
+
+ align:start position:0%
+sequences this is dense and little LP
+ 
+
+ align:start position:0%
+sequences this is dense and little LP
+for every uh for p between one and
+
+ align:start position:0%
+for every uh for p between one and
+ 
+
+ align:start position:0%
+for every uh for p between one and
+infinity not equal to Infinity
+
+ align:start position:0%
+infinity not equal to Infinity
+ 
+
+ align:start position:0%
+infinity not equal to Infinity
+okay so finitely terminating sequences
+
+ align:start position:0%
+okay so finitely terminating sequences
+ 
+
+ align:start position:0%
+okay so finitely terminating sequences
+are dense and little LP
+
+ align:start position:0%
+are dense and little LP
+ 
+
+ align:start position:0%
+are dense and little LP
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+unfortunately that's again an
+
+ align:start position:0%
+unfortunately that's again an
+ 
+
+ align:start position:0%
+unfortunately that's again an
+uncountable uh
+
+ align:start position:0%
+uncountable uh
+ 
+
+ align:start position:0%
+uncountable uh
+I mean it's a it's a Subspace so it's
+
+ align:start position:0%
+I mean it's a it's a Subspace so it's
+ 
+
+ align:start position:0%
+I mean it's a it's a Subspace so it's
+going to be uncountable
+
+ align:start position:0%
+going to be uncountable
+ 
+
+ align:start position:0%
+going to be uncountable
+so how do I get now accountable thing
+
+ align:start position:0%
+so how do I get now accountable thing
+ 
+
+ align:start position:0%
+so how do I get now accountable thing
+again I replace everything by rational
+
+ align:start position:0%
+again I replace everything by rational
+ 
+
+ align:start position:0%
+again I replace everything by rational
+numbers so if I uh I can approximate
+
+ align:start position:0%
+numbers so if I uh I can approximate
+ 
+
+ align:start position:0%
+numbers so if I uh I can approximate
+every sequence which terminates after a
+
+ align:start position:0%
+every sequence which terminates after a
+ 
+
+ align:start position:0%
+every sequence which terminates after a
+certain point
+
+ align:start position:0%
+certain point
+ 
+
+ align:start position:0%
+certain point
+consisting of real numbers by a sequence
+
+ align:start position:0%
+consisting of real numbers by a sequence
+ 
+
+ align:start position:0%
+consisting of real numbers by a sequence
+full of just rationals terminating after
+
+ align:start position:0%
+full of just rationals terminating after
+ 
+
+ align:start position:0%
+full of just rationals terminating after
+a certain point
+
+ align:start position:0%
+a certain point
+ 
+
+ align:start position:0%
+a certain point
+by just choosing the rationals very
+
+ align:start position:0%
+by just choosing the rationals very
+ 
+
+ align:start position:0%
+by just choosing the rationals very
+close to those real numbers right we're
+
+ align:start position:0%
+close to those real numbers right we're
+ 
+
+ align:start position:0%
+close to those real numbers right we're
+using here and I said didn't say this
+
+ align:start position:0%
+using here and I said didn't say this
+ 
+
+ align:start position:0%
+using here and I said didn't say this
+explicitly a minute ago that you know we
+
+ align:start position:0%
+explicitly a minute ago that you know we
+ 
+
+ align:start position:0%
+explicitly a minute ago that you know we
+still have we have the density of the
+
+ align:start position:0%
+still have we have the density of the
+ 
+
+ align:start position:0%
+still have we have the density of the
+rationals and the reels for every reel I
+
+ align:start position:0%
+rationals and the reels for every reel I
+ 
+
+ align:start position:0%
+rationals and the reels for every reel I
+can find a rational very close to it
+
+ align:start position:0%
+can find a rational very close to it
+ 
+
+ align:start position:0%
+can find a rational very close to it
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know this is kind of thinking that
+
+ align:start position:0%
+you know this is kind of thinking that
+ 
+
+ align:start position:0%
+you know this is kind of thinking that
+goes in goes on so but now the set of
+
+ align:start position:0%
+goes in goes on so but now the set of
+ 
+
+ align:start position:0%
+goes in goes on so but now the set of
+all finitely terminating sequences with
+
+ align:start position:0%
+all finitely terminating sequences with
+ 
+
+ align:start position:0%
+all finitely terminating sequences with
+rational coefficients this is a
+
+ align:start position:0%
+rational coefficients this is a
+ 
+
+ align:start position:0%
+rational coefficients this is a
+countable set
+
+ align:start position:0%
+countable set
+ 
+
+ align:start position:0%
+countable set
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that countable set is dense and
+
+ align:start position:0%
+and that countable set is dense and
+ 
+
+ align:start position:0%
+and that countable set is dense and
+little LP and therefore little LP is
+
+ align:start position:0%
+little LP and therefore little LP is
+ 
+
+ align:start position:0%
+little LP and therefore little LP is
+separable as long as p is between one
+
+ align:start position:0%
+separable as long as p is between one
+ 
+
+ align:start position:0%
+separable as long as p is between one
+and Infinity uh excluding Infinity okay
+
+ align:start position:0%
+and Infinity uh excluding Infinity okay
+ 
+
+ align:start position:0%
+and Infinity uh excluding Infinity okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know I said at the beginning that
+
+ align:start position:0%
+you know I said at the beginning that
+ 
+
+ align:start position:0%
+you know I said at the beginning that
+we're going to be mainly interested in
+
+ align:start position:0%
+we're going to be mainly interested in
+ 
+
+ align:start position:0%
+we're going to be mainly interested in
+in separable spaces without actually
+
+ align:start position:0%
+in separable spaces without actually
+ 
+
+ align:start position:0%
+in separable spaces without actually
+saying why little LP or little L2 and
+
+ align:start position:0%
+saying why little LP or little L2 and
+ 
+
+ align:start position:0%
+saying why little LP or little L2 and
+big L2 are separable
+
+ align:start position:0%
+big L2 are separable
+ 
+
+ align:start position:0%
+big L2 are separable
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but uh so I just gave you the argument
+
+ align:start position:0%
+but uh so I just gave you the argument
+ 
+
+ align:start position:0%
+but uh so I just gave you the argument
+by word
+
+ align:start position:0%
+by word
+ 
+
+ align:start position:0%
+by word
+of mouth now instead of actually writing
+
+ align:start position:0%
+of mouth now instead of actually writing
+ 
+
+ align:start position:0%
+of mouth now instead of actually writing
+it down Okay so
+
+ align:start position:0%
+it down Okay so
+ 
+
+ align:start position:0%
+it down Okay so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have the following vessels inequality
+
+ align:start position:0%
+we have the following vessels inequality
+ 
+
+ align:start position:0%
+we have the following vessels inequality
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal accountable orthonormal
+
+ align:start position:0%
+orthonormal accountable orthonormal
+ 
+
+ align:start position:0%
+orthonormal accountable orthonormal
+subsets so
+
+ align:start position:0%
+subsets so
+ 
+
+ align:start position:0%
+subsets so
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+the n
+
+ align:start position:0%
+the n
+ 
+
+ align:start position:0%
+the n
+is well let me just put n here if this
+
+ align:start position:0%
+is well let me just put n here if this
+ 
+
+ align:start position:0%
+is well let me just put n here if this
+is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+countable
+
+ align:start position:0%
+countable
+ 
+
+ align:start position:0%
+countable
+meaning it's either finite or it's
+
+ align:start position:0%
+meaning it's either finite or it's
+ 
+
+ align:start position:0%
+meaning it's either finite or it's
+countably infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's countable
+
+ align:start position:0%
+but it's countable
+ 
+
+ align:start position:0%
+but it's countable
+uh orthonormal subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a pre-hilbert's face
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for all U and H
+
+ align:start position:0%
+and for all U and H
+ 
+
+ align:start position:0%
+and for all U and H
+if I look at the sum of squares U and a
+
+ align:start position:0%
+if I look at the sum of squares U and a
+ 
+
+ align:start position:0%
+if I look at the sum of squares U and a
+product e sub n
+
+ align:start position:0%
+product e sub n
+ 
+
+ align:start position:0%
+product e sub n
+this is less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the norm of U squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so our discussion here of orthonormal
+
+ align:start position:0%
+so our discussion here of orthonormal
+ 
+
+ align:start position:0%
+so our discussion here of orthonormal
+subsets is taking place within a
+
+ align:start position:0%
+subsets is taking place within a
+ 
+
+ align:start position:0%
+subsets is taking place within a
+pre-hilbert space
+
+ align:start position:0%
+pre-hilbert space
+ 
+
+ align:start position:0%
+pre-hilbert space
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+don't need Hilbert spaces to talk about
+
+ align:start position:0%
+don't need Hilbert spaces to talk about
+ 
+
+ align:start position:0%
+don't need Hilbert spaces to talk about
+these Concepts uh yeah but when we're in
+
+ align:start position:0%
+these Concepts uh yeah but when we're in
+ 
+
+ align:start position:0%
+these Concepts uh yeah but when we're in
+a Hilbert space and we have a certain
+
+ align:start position:0%
+a Hilbert space and we have a certain
+ 
+
+ align:start position:0%
+a Hilbert space and we have a certain
+orthonormal subset that will be
+
+ align:start position:0%
+orthonormal subset that will be
+ 
+
+ align:start position:0%
+orthonormal subset that will be
+important that that we're in the Hilbert
+
+ align:start position:0%
+important that that we're in the Hilbert
+ 
+
+ align:start position:0%
+important that that we're in the Hilbert
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+okay so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the proof is
+
+ align:start position:0%
+the proof is
+ 
+
+ align:start position:0%
+the proof is
+uh let's do the finite case first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose I have
+
+ align:start position:0%
+suppose I have
+ 
+
+ align:start position:0%
+suppose I have
+finite collection of orthonormal or
+
+ align:start position:0%
+finite collection of orthonormal or
+ 
+
+ align:start position:0%
+finite collection of orthonormal or
+finite orthonormal subset of H or a fine
+
+ align:start position:0%
+finite orthonormal subset of H or a fine
+ 
+
+ align:start position:0%
+finite orthonormal subset of H or a fine
+or I'll often say finite collection of
+
+ align:start position:0%
+or I'll often say finite collection of
+ 
+
+ align:start position:0%
+or I'll often say finite collection of
+orthonormal vectors in H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no end subset of H
+
+ align:start position:0%
+no end subset of H
+ 
+
+ align:start position:0%
+no end subset of H
+again o n
+
+ align:start position:0%
+again o n
+ 
+
+ align:start position:0%
+again o n
+standing in for orthonormal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then let me just record a few identities
+
+ align:start position:0%
+then let me just record a few identities
+ 
+
+ align:start position:0%
+then let me just record a few identities
+which are pretty easy to verify
+
+ align:start position:0%
+which are pretty easy to verify
+ 
+
+ align:start position:0%
+which are pretty easy to verify
+some from n equals 1 to n of U inner
+
+ align:start position:0%
+some from n equals 1 to n of U inner
+ 
+
+ align:start position:0%
+some from n equals 1 to n of U inner
+product e n e n
+
+ align:start position:0%
+product e n e n
+ 
+
+ align:start position:0%
+product e n e n
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if I take the norm of this thing squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's compute this out this is the inner
+
+ align:start position:0%
+let's compute this out this is the inner
+ 
+
+ align:start position:0%
+let's compute this out this is the inner
+product of
+
+ align:start position:0%
+product of
+ 
+
+ align:start position:0%
+product of
+with the understanding that n is going
+
+ align:start position:0%
+with the understanding that n is going
+ 
+
+ align:start position:0%
+with the understanding that n is going
+from one to capital n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's use a different index here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is equal to n m
+
+ align:start position:0%
+and this is equal to n m
+ 
+
+ align:start position:0%
+and this is equal to n m
+u e n
+
+ align:start position:0%
+u e n
+ 
+
+ align:start position:0%
+u e n
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+now I have this sum here of
+
+ align:start position:0%
+now I have this sum here of
+ 
+
+ align:start position:0%
+now I have this sum here of
+I should leaving out e in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of u b m
+
+ align:start position:0%
+of u b m
+ 
+
+ align:start position:0%
+of u b m
+complex conjugate times the inner
+
+ align:start position:0%
+complex conjugate times the inner
+ 
+
+ align:start position:0%
+complex conjugate times the inner
+product of e n with e m that's the two
+
+ align:start position:0%
+product of e n with e m that's the two
+ 
+
+ align:start position:0%
+product of e n with e m that's the two
+vectors that are taking the complex
+
+ align:start position:0%
+vectors that are taking the complex
+ 
+
+ align:start position:0%
+vectors that are taking the complex
+complex conjugate of this is a number
+
+ align:start position:0%
+complex conjugate of this is a number
+ 
+
+ align:start position:0%
+complex conjugate of this is a number
+here it just comes out this number here
+
+ align:start position:0%
+here it just comes out this number here
+ 
+
+ align:start position:0%
+here it just comes out this number here
+gets hit with a complex conjugate when
+
+ align:start position:0%
+gets hit with a complex conjugate when
+ 
+
+ align:start position:0%
+gets hit with a complex conjugate when
+it comes out now the inner product of En
+
+ align:start position:0%
+it comes out now the inner product of En
+ 
+
+ align:start position:0%
+it comes out now the inner product of En
+with em is 0 when n does not equal m and
+
+ align:start position:0%
+with em is 0 when n does not equal m and
+ 
+
+ align:start position:0%
+with em is 0 when n does not equal m and
+is equal to one because it's equal to
+
+ align:start position:0%
+is equal to one because it's equal to
+ 
+
+ align:start position:0%
+is equal to one because it's equal to
+the norm of E N squared when n equals m
+
+ align:start position:0%
+the norm of E N squared when n equals m
+ 
+
+ align:start position:0%
+the norm of E N squared when n equals m
+so all I pick up from this double sum
+
+ align:start position:0%
+so all I pick up from this double sum
+ 
+
+ align:start position:0%
+so all I pick up from this double sum
+which is just a finite double sum is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when n equals m
+
+ align:start position:0%
+when n equals m
+ 
+
+ align:start position:0%
+when n equals m
+and N going from one to n
+
+ align:start position:0%
+and N going from one to n
+ 
+
+ align:start position:0%
+and N going from one to n
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore this is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u e n
+
+ align:start position:0%
+u e n
+ 
+
+ align:start position:0%
+u e n
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula I want to have another one is
+
+ align:start position:0%
+formula I want to have another one is
+ 
+
+ align:start position:0%
+formula I want to have another one is
+that if I take the inner product of U
+
+ align:start position:0%
+that if I take the inner product of U
+ 
+
+ align:start position:0%
+that if I take the inner product of U
+with n equals 1 to n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the sum and you know maybe you recognize
+
+ align:start position:0%
+the sum and you know maybe you recognize
+ 
+
+ align:start position:0%
+the sum and you know maybe you recognize
+what this uh sum here actually is I'll
+
+ align:start position:0%
+what this uh sum here actually is I'll
+ 
+
+ align:start position:0%
+what this uh sum here actually is I'll
+say so in a minute so this is equal to
+
+ align:start position:0%
+say so in a minute so this is equal to
+ 
+
+ align:start position:0%
+say so in a minute so this is equal to
+sum from n equals one
+
+ align:start position:0%
+sum from n equals one
+ 
+
+ align:start position:0%
+sum from n equals one
+to n of so
+
+ align:start position:0%
+to n of so
+ 
+
+ align:start position:0%
+to n of so
+U and a product e sub n times this
+
+ align:start position:0%
+U and a product e sub n times this
+ 
+
+ align:start position:0%
+U and a product e sub n times this
+number this number comes out and gives
+
+ align:start position:0%
+number this number comes out and gives
+ 
+
+ align:start position:0%
+number this number comes out and gives
+me a complex conjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero which is bigger than or equal to
+
+ align:start position:0%
+zero which is bigger than or equal to
+ 
+
+ align:start position:0%
+zero which is bigger than or equal to
+the norm of U minus
+
+ align:start position:0%
+the norm of U minus
+ 
+
+ align:start position:0%
+the norm of U minus
+n equals 1 to n of
+
+ align:start position:0%
+n equals 1 to n of
+ 
+
+ align:start position:0%
+n equals 1 to n of
+u e n e n
+
+ align:start position:0%
+u e n e n
+ 
+
+ align:start position:0%
+u e n e n
+now if you remember back from linear
+
+ align:start position:0%
+now if you remember back from linear
+ 
+
+ align:start position:0%
+now if you remember back from linear
+algebra from calculus that if I have
+
+ align:start position:0%
+algebra from calculus that if I have
+ 
+
+ align:start position:0%
+algebra from calculus that if I have
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+orthonormal vectors and I have a vector
+
+ align:start position:0%
+orthonormal vectors and I have a vector
+ 
+
+ align:start position:0%
+orthonormal vectors and I have a vector
+U this quantity is nothing but the
+
+ align:start position:0%
+U this quantity is nothing but the
+ 
+
+ align:start position:0%
+U this quantity is nothing but the
+projection of U onto the span of those
+
+ align:start position:0%
+projection of U onto the span of those
+ 
+
+ align:start position:0%
+projection of U onto the span of those
+orthonormal vectors okay
+
+ align:start position:0%
+orthonormal vectors okay
+ 
+
+ align:start position:0%
+orthonormal vectors okay
+so what I'm looking at here is
+
+ align:start position:0%
+so what I'm looking at here is
+ 
+
+ align:start position:0%
+so what I'm looking at here is
+if you like
+
+ align:start position:0%
+if you like
+ 
+
+ align:start position:0%
+if you like
+the norm of the part of you that's
+
+ align:start position:0%
+the norm of the part of you that's
+ 
+
+ align:start position:0%
+the norm of the part of you that's
+orthogonal to these finitely many
+
+ align:start position:0%
+orthogonal to these finitely many
+ 
+
+ align:start position:0%
+orthogonal to these finitely many
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this thing's bigger than or
+
+ align:start position:0%
+okay so this thing's bigger than or
+ 
+
+ align:start position:0%
+okay so this thing's bigger than or
+equal to zero we use that formula of how
+
+ align:start position:0%
+equal to zero we use that formula of how
+ 
+
+ align:start position:0%
+equal to zero we use that formula of how
+to compute the norm of something plus
+
+ align:start position:0%
+to compute the norm of something plus
+ 
+
+ align:start position:0%
+to compute the norm of something plus
+something and this is equal to Norm of U
+
+ align:start position:0%
+something and this is equal to Norm of U
+ 
+
+ align:start position:0%
+something and this is equal to Norm of U
+squared plus Norm
+
+ align:start position:0%
+squared plus Norm
+ 
+
+ align:start position:0%
+squared plus Norm
+equals one to n u e n e n
+
+ align:start position:0%
+equals one to n u e n e n
+ 
+
+ align:start position:0%
+equals one to n u e n e n
+squared minus 2 times the real part of U
+
+ align:start position:0%
+squared minus 2 times the real part of U
+ 
+
+ align:start position:0%
+squared minus 2 times the real part of U
+inner product
+
+ align:start position:0%
+inner product
+ 
+
+ align:start position:0%
+inner product
+sum from n equals 1 to n of U
+
+ align:start position:0%
+sum from n equals 1 to n of U
+ 
+
+ align:start position:0%
+sum from n equals 1 to n of U
+e n a n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and now we know what all of these
+
+ align:start position:0%
+okay and now we know what all of these
+ 
+
+ align:start position:0%
+okay and now we know what all of these
+things are this is equal to uh I'm not
+
+ align:start position:0%
+things are this is equal to uh I'm not
+ 
+
+ align:start position:0%
+things are this is equal to uh I'm not
+even going to go over this is equal to
+
+ align:start position:0%
+even going to go over this is equal to
+ 
+
+ align:start position:0%
+even going to go over this is equal to
+this no this quantity here as is this
+
+ align:start position:0%
+this no this quantity here as is this
+ 
+
+ align:start position:0%
+this no this quantity here as is this
+inner product it's also equal to this
+
+ align:start position:0%
+inner product it's also equal to this
+ 
+
+ align:start position:0%
+inner product it's also equal to this
+thing here so the real part is equal to
+
+ align:start position:0%
+thing here so the real part is equal to
+ 
+
+ align:start position:0%
+thing here so the real part is equal to
+this thing here because this is a real
+
+ align:start position:0%
+this thing here because this is a real
+ 
+
+ align:start position:0%
+this thing here because this is a real
+number and I get since this comes with a
+
+ align:start position:0%
+number and I get since this comes with a
+ 
+
+ align:start position:0%
+number and I get since this comes with a
+2 I cancel one of those so I get normal
+
+ align:start position:0%
+2 I cancel one of those so I get normal
+ 
+
+ align:start position:0%
+2 I cancel one of those so I get normal
+View
+
+ align:start position:0%
+View
+ 
+
+ align:start position:0%
+View
+squared minus sum from n equals 1 to n
+
+ align:start position:0%
+squared minus sum from n equals 1 to n
+ 
+
+ align:start position:0%
+squared minus sum from n equals 1 to n
+of U
+
+ align:start position:0%
+of U
+ 
+
+ align:start position:0%
+of U
+e n
+
+ align:start position:0%
+e n
+ 
+
+ align:start position:0%
+e n
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+okay which is exactly what I wanted to
+
+ align:start position:0%
+okay which is exactly what I wanted to
+ 
+
+ align:start position:0%
+okay which is exactly what I wanted to
+prove for the finite case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the infinite case then follows from
+
+ align:start position:0%
+but the infinite case then follows from
+ 
+
+ align:start position:0%
+but the infinite case then follows from
+the finite case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and by letting capital N Go to Infinity
+
+ align:start position:0%
+and by letting capital N Go to Infinity
+ 
+
+ align:start position:0%
+and by letting capital N Go to Infinity
+so infinite case
+
+ align:start position:0%
+so infinite case
+ 
+
+ align:start position:0%
+so infinite case
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+e n
+
+ align:start position:0%
+e n
+ 
+
+ align:start position:0%
+e n
+equals 1 to Infinity is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+then we know that for all n capital n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have that
+
+ align:start position:0%
+we have that
+ 
+
+ align:start position:0%
+we have that
+sum Over N equals 1 to n of u e n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is less than or equal to
+
+ align:start position:0%
+this is less than or equal to
+ 
+
+ align:start position:0%
+this is less than or equal to
+the norm of U squared so I can just send
+
+ align:start position:0%
+the norm of U squared so I can just send
+ 
+
+ align:start position:0%
+the norm of U squared so I can just send
+capital n
+
+ align:start position:0%
+capital n
+ 
+
+ align:start position:0%
+capital n
+to Infinity to get that the sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals 1 to Infinity of Norm of U
+
+ align:start position:0%
+equals 1 to Infinity of Norm of U
+ 
+
+ align:start position:0%
+equals 1 to Infinity of Norm of U
+E N squared is less than or equal to
+
+ align:start position:0%
+E N squared is less than or equal to
+ 
+
+ align:start position:0%
+E N squared is less than or equal to
+U squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+orthonormal subsets
+
+ align:start position:0%
+orthonormal subsets
+ 
+
+ align:start position:0%
+orthonormal subsets
+we can Define
+
+ align:start position:0%
+we can Define
+ 
+
+ align:start position:0%
+we can Define
+as you know a collection of vectors that
+
+ align:start position:0%
+as you know a collection of vectors that
+ 
+
+ align:start position:0%
+as you know a collection of vectors that
+have unit length and are mutually
+
+ align:start position:0%
+have unit length and are mutually
+ 
+
+ align:start position:0%
+have unit length and are mutually
+orthogonal
+
+ align:start position:0%
+orthogonal
+ 
+
+ align:start position:0%
+orthogonal
+to each other
+
+ align:start position:0%
+to each other
+ 
+
+ align:start position:0%
+to each other
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now just orthonormal subsets
+
+ align:start position:0%
+now just orthonormal subsets
+ 
+
+ align:start position:0%
+now just orthonormal subsets
+list any old orthonormal subset is not
+
+ align:start position:0%
+list any old orthonormal subset is not
+ 
+
+ align:start position:0%
+list any old orthonormal subset is not
+really the most
+
+ align:start position:0%
+really the most
+ 
+
+ align:start position:0%
+really the most
+useful thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we're trying to study the entire
+
+ align:start position:0%
+if we're trying to study the entire
+ 
+
+ align:start position:0%
+if we're trying to study the entire
+Hilbert's or pre-hubble pre-hilbert
+
+ align:start position:0%
+Hilbert's or pre-hubble pre-hilbert
+ 
+
+ align:start position:0%
+Hilbert's or pre-hubble pre-hilbert
+space h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we may miss something if we
+
+ align:start position:0%
+because we may miss something if we
+ 
+
+ align:start position:0%
+because we may miss something if we
+leave out certain
+
+ align:start position:0%
+leave out certain
+ 
+
+ align:start position:0%
+leave out certain
+orthonormal vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+but a more useful
+
+ align:start position:0%
+but a more useful
+ 
+
+ align:start position:0%
+but a more useful
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+type of orthonormal
+
+ align:start position:0%
+type of orthonormal
+ 
+
+ align:start position:0%
+type of orthonormal
+effect is a maximal orthonormal set or
+
+ align:start position:0%
+effect is a maximal orthonormal set or
+ 
+
+ align:start position:0%
+effect is a maximal orthonormal set or
+which is defined as follows
+
+ align:start position:0%
+which is defined as follows
+ 
+
+ align:start position:0%
+which is defined as follows
+an orthonormal subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e Lambda
+
+ align:start position:0%
+e Lambda
+ 
+
+ align:start position:0%
+e Lambda
+Lambda and capital Lambda of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a pre-hilbert space h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximal
+
+ align:start position:0%
+maximal
+ 
+
+ align:start position:0%
+maximal
+so again if you know having a possibly
+
+ align:start position:0%
+so again if you know having a possibly
+ 
+
+ align:start position:0%
+so again if you know having a possibly
+uncountable collection of what the
+
+ align:start position:0%
+uncountable collection of what the
+ 
+
+ align:start position:0%
+uncountable collection of what the
+normal subsets indexed by some
+
+ align:start position:0%
+normal subsets indexed by some
+ 
+
+ align:start position:0%
+normal subsets indexed by some
+indexing set makes you uncomfortable
+
+ align:start position:0%
+indexing set makes you uncomfortable
+ 
+
+ align:start position:0%
+indexing set makes you uncomfortable
+replace this with you know in where n is
+
+ align:start position:0%
+replace this with you know in where n is
+ 
+
+ align:start position:0%
+replace this with you know in where n is
+going from one to capital N or n is
+
+ align:start position:0%
+going from one to capital N or n is
+ 
+
+ align:start position:0%
+going from one to capital N or n is
+going from one to infinity and so
+
+ align:start position:0%
+going from one to infinity and so
+ 
+
+ align:start position:0%
+going from one to infinity and so
+accountable collection if you like but
+
+ align:start position:0%
+accountable collection if you like but
+ 
+
+ align:start position:0%
+accountable collection if you like but
+I'm stating this so that
+
+ align:start position:0%
+I'm stating this so that
+ 
+
+ align:start position:0%
+I'm stating this so that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know that uh more something more
+
+ align:start position:0%
+you know that uh more something more
+ 
+
+ align:start position:0%
+you know that uh more something more
+General is true so this is maximal if
+
+ align:start position:0%
+General is true so this is maximal if
+ 
+
+ align:start position:0%
+General is true so this is maximal if
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+um The Following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+holds If U is an H
+
+ align:start position:0%
+holds If U is an H
+ 
+
+ align:start position:0%
+holds If U is an H
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um U is orthogonal
+
+ align:start position:0%
+um U is orthogonal
+ 
+
+ align:start position:0%
+um U is orthogonal
+to everything in this orthonormal subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies that U is zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an example of course is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can check that this collection here
+
+ align:start position:0%
+you can check that this collection here
+ 
+
+ align:start position:0%
+you can check that this collection here
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a maximal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal subset of C2
+
+ align:start position:0%
+orthonormal subset of C2
+ 
+
+ align:start position:0%
+orthonormal subset of C2
+a non-example right
+
+ align:start position:0%
+a non-example right
+ 
+
+ align:start position:0%
+a non-example right
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+kind of maybe see this coming
+
+ align:start position:0%
+kind of maybe see this coming
+ 
+
+ align:start position:0%
+kind of maybe see this coming
+the one we had a minute ago
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is not maximal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since there's a vector that has inner
+
+ align:start position:0%
+since there's a vector that has inner
+ 
+
+ align:start position:0%
+since there's a vector that has inner
+product zero with both of these but is
+
+ align:start position:0%
+product zero with both of these but is
+ 
+
+ align:start position:0%
+product zero with both of these but is
+non-zero right since
+
+ align:start position:0%
+non-zero right since
+ 
+
+ align:start position:0%
+non-zero right since
+this should be C3
+
+ align:start position:0%
+this should be C3
+ 
+
+ align:start position:0%
+this should be C3
+since
+
+ align:start position:0%
+since
+ 
+
+ align:start position:0%
+since
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just write it kind of loosely
+
+ align:start position:0%
+let me just write it kind of loosely
+ 
+
+ align:start position:0%
+let me just write it kind of loosely
+this way since this Vector is 0 1 0 is
+
+ align:start position:0%
+this way since this Vector is 0 1 0 is
+ 
+
+ align:start position:0%
+this way since this Vector is 0 1 0 is
+orthogonal to both of these but it's
+
+ align:start position:0%
+orthogonal to both of these but it's
+ 
+
+ align:start position:0%
+orthogonal to both of these but it's
+non-zero right maximal means if you're
+
+ align:start position:0%
+non-zero right maximal means if you're
+ 
+
+ align:start position:0%
+non-zero right maximal means if you're
+orthogonal to everything in your
+
+ align:start position:0%
+orthogonal to everything in your
+ 
+
+ align:start position:0%
+orthogonal to everything in your
+collection then it has to be zero but
+
+ align:start position:0%
+collection then it has to be zero but
+ 
+
+ align:start position:0%
+collection then it has to be zero but
+this is non-zero and it's orthogonal too
+
+ align:start position:0%
+this is non-zero and it's orthogonal too
+ 
+
+ align:start position:0%
+this is non-zero and it's orthogonal too
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh everything to these two vectors there
+
+ align:start position:0%
+uh everything to these two vectors there
+ 
+
+ align:start position:0%
+uh everything to these two vectors there
+another example is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know again
+
+ align:start position:0%
+you know again
+ 
+
+ align:start position:0%
+you know again
+with the notation from before this is
+
+ align:start position:0%
+with the notation from before this is
+ 
+
+ align:start position:0%
+with the notation from before this is
+where this is the sequence that is zero
+
+ align:start position:0%
+where this is the sequence that is zero
+ 
+
+ align:start position:0%
+where this is the sequence that is zero
+except for the end spot where it is one
+
+ align:start position:0%
+except for the end spot where it is one
+ 
+
+ align:start position:0%
+except for the end spot where it is one
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+maximal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal subset of little L2
+
+ align:start position:0%
+orthonormal subset of little L2
+ 
+
+ align:start position:0%
+orthonormal subset of little L2
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what we're going to see very shortly
+
+ align:start position:0%
+now what we're going to see very shortly
+ 
+
+ align:start position:0%
+now what we're going to see very shortly
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if we have a countably infinite maximal
+
+ align:start position:0%
+if we have a countably infinite maximal
+ 
+
+ align:start position:0%
+if we have a countably infinite maximal
+subset of a Hilbert space then that set
+
+ align:start position:0%
+subset of a Hilbert space then that set
+ 
+
+ align:start position:0%
+subset of a Hilbert space then that set
+serves kind of the same purpose as a
+
+ align:start position:0%
+serves kind of the same purpose as a
+ 
+
+ align:start position:0%
+serves kind of the same purpose as a
+basis as a orthonormal basis does in
+
+ align:start position:0%
+basis as a orthonormal basis does in
+ 
+
+ align:start position:0%
+basis as a orthonormal basis does in
+linear algebra right I mean if you look
+
+ align:start position:0%
+linear algebra right I mean if you look
+ 
+
+ align:start position:0%
+linear algebra right I mean if you look
+at here already you know this
+
+ align:start position:0%
+at here already you know this
+ 
+
+ align:start position:0%
+at here already you know this
+orthonormal set is maximal and it also
+
+ align:start position:0%
+orthonormal set is maximal and it also
+ 
+
+ align:start position:0%
+orthonormal set is maximal and it also
+forms a basis for C2 right this was not
+
+ align:start position:0%
+forms a basis for C2 right this was not
+ 
+
+ align:start position:0%
+forms a basis for C2 right this was not
+maximal and you see it doesn't form a
+
+ align:start position:0%
+maximal and you see it doesn't form a
+ 
+
+ align:start position:0%
+maximal and you see it doesn't form a
+basis for C3
+
+ align:start position:0%
+basis for C3
+ 
+
+ align:start position:0%
+basis for C3
+right so maximal is gonna
+
+ align:start position:0%
+right so maximal is gonna
+ 
+
+ align:start position:0%
+right so maximal is gonna
+kind of give us a
+
+ align:start position:0%
+kind of give us a
+ 
+
+ align:start position:0%
+kind of give us a
+a condition which is is
+
+ align:start position:0%
+a condition which is is
+ 
+
+ align:start position:0%
+a condition which is is
+kind of equally useful as being a basis
+
+ align:start position:0%
+kind of equally useful as being a basis
+ 
+
+ align:start position:0%
+kind of equally useful as being a basis
+but it won't be a Hammel based these
+
+ align:start position:0%
+but it won't be a Hammel based these
+ 
+
+ align:start position:0%
+but it won't be a Hammel based these
+subsets won't be a Hammel basis in the
+
+ align:start position:0%
+subsets won't be a Hammel basis in the
+ 
+
+ align:start position:0%
+subsets won't be a Hammel basis in the
+sense that every Vector can be written
+
+ align:start position:0%
+sense that every Vector can be written
+ 
+
+ align:start position:0%
+sense that every Vector can be written
+as a finite linear combination of the
+
+ align:start position:0%
+as a finite linear combination of the
+ 
+
+ align:start position:0%
+as a finite linear combination of the
+elements of a maximal orthonormal subset
+
+ align:start position:0%
+elements of a maximal orthonormal subset
+ 
+
+ align:start position:0%
+elements of a maximal orthonormal subset
+but what is true is that we can write it
+
+ align:start position:0%
+but what is true is that we can write it
+ 
+
+ align:start position:0%
+but what is true is that we can write it
+as possibly an infinite sum involving uh
+
+ align:start position:0%
+as possibly an infinite sum involving uh
+ 
+
+ align:start position:0%
+as possibly an infinite sum involving uh
+uh the or the maximal or the normal
+
+ align:start position:0%
+uh the or the maximal or the normal
+ 
+
+ align:start position:0%
+uh the or the maximal or the normal
+subset you know which is
+
+ align:start position:0%
+subset you know which is
+ 
+
+ align:start position:0%
+subset you know which is
+in most cases just as uh good if you
+
+ align:start position:0%
+in most cases just as uh good if you
+ 
+
+ align:start position:0%
+in most cases just as uh good if you
+want to use that all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um first off when
+
+ align:start position:0%
+okay so um first off when
+ 
+
+ align:start position:0%
+okay so um first off when
+does every uh pre-hilbert space have a
+
+ align:start position:0%
+does every uh pre-hilbert space have a
+ 
+
+ align:start position:0%
+does every uh pre-hilbert space have a
+maximal uh
+
+ align:start position:0%
+maximal uh
+ 
+
+ align:start position:0%
+maximal uh
+uh subset
+
+ align:start position:0%
+uh subset
+ 
+
+ align:start position:0%
+uh subset
+so let me State this as a theorem in
+
+ align:start position:0%
+so let me State this as a theorem in
+ 
+
+ align:start position:0%
+so let me State this as a theorem in
+fact it'll state two theorems the first
+
+ align:start position:0%
+fact it'll state two theorems the first
+ 
+
+ align:start position:0%
+fact it'll state two theorems the first
+is uh
+
+ align:start position:0%
+is uh
+ 
+
+ align:start position:0%
+is uh
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-trivial
+
+ align:start position:0%
+non-trivial
+ 
+
+ align:start position:0%
+non-trivial
+because we could have the Hilbert space
+
+ align:start position:0%
+because we could have the Hilbert space
+ 
+
+ align:start position:0%
+because we could have the Hilbert space
+the speed the zero Vector Hilbert's
+
+ align:start position:0%
+the speed the zero Vector Hilbert's
+ 
+
+ align:start position:0%
+the speed the zero Vector Hilbert's
+pre-hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximal
+
+ align:start position:0%
+maximal
+ 
+
+ align:start position:0%
+maximal
+or the normal
+
+ align:start position:0%
+or the normal
+ 
+
+ align:start position:0%
+or the normal
+subset whether it's separable or not it
+
+ align:start position:0%
+subset whether it's separable or not it
+ 
+
+ align:start position:0%
+subset whether it's separable or not it
+has a maximal orthonormal subset and the
+
+ align:start position:0%
+has a maximal orthonormal subset and the
+ 
+
+ align:start position:0%
+has a maximal orthonormal subset and the
+way you prove this is using so I'm not
+
+ align:start position:0%
+way you prove this is using so I'm not
+ 
+
+ align:start position:0%
+way you prove this is using so I'm not
+going to give her proof of this I'm
+
+ align:start position:0%
+going to give her proof of this I'm
+ 
+
+ align:start position:0%
+going to give her proof of this I'm
+going to give you a proof of something a
+
+ align:start position:0%
+going to give you a proof of something a
+ 
+
+ align:start position:0%
+going to give you a proof of something a
+little less strong but about as useful
+
+ align:start position:0%
+little less strong but about as useful
+ 
+
+ align:start position:0%
+little less strong but about as useful
+as as we'll need
+
+ align:start position:0%
+as as we'll need
+ 
+
+ align:start position:0%
+as as we'll need
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+one proves this by uh
+
+ align:start position:0%
+one proves this by uh
+ 
+
+ align:start position:0%
+one proves this by uh
+the by using Zorn's Lemma
+
+ align:start position:0%
+the by using Zorn's Lemma
+ 
+
+ align:start position:0%
+the by using Zorn's Lemma
+by you know taking a set your set that
+
+ align:start position:0%
+by you know taking a set your set that
+ 
+
+ align:start position:0%
+by you know taking a set your set that
+you're going to put a partial order on
+
+ align:start position:0%
+you're going to put a partial order on
+ 
+
+ align:start position:0%
+you're going to put a partial order on
+to be the collections of orthonormal
+
+ align:start position:0%
+to be the collections of orthonormal
+ 
+
+ align:start position:0%
+to be the collections of orthonormal
+bases are not orthonormal bases a Max of
+
+ align:start position:0%
+bases are not orthonormal bases a Max of
+ 
+
+ align:start position:0%
+bases are not orthonormal bases a Max of
+orthonormal subsets and then ordered by
+
+ align:start position:0%
+orthonormal subsets and then ordered by
+ 
+
+ align:start position:0%
+orthonormal subsets and then ordered by
+inclusion and then one can do a Zorn's
+
+ align:start position:0%
+inclusion and then one can do a Zorn's
+ 
+
+ align:start position:0%
+inclusion and then one can do a Zorn's
+Lemma argument and apply Zorn's Lemma to
+
+ align:start position:0%
+Lemma argument and apply Zorn's Lemma to
+ 
+
+ align:start position:0%
+Lemma argument and apply Zorn's Lemma to
+to obtain a maximal
+
+ align:start position:0%
+to obtain a maximal
+ 
+
+ align:start position:0%
+to obtain a maximal
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+orthonormal subset but that's kind of
+
+ align:start position:0%
+orthonormal subset but that's kind of
+ 
+
+ align:start position:0%
+orthonormal subset but that's kind of
+hands off and maybe that scares you a
+
+ align:start position:0%
+hands off and maybe that scares you a
+ 
+
+ align:start position:0%
+hands off and maybe that scares you a
+little bit because uh Zorn's Lemma is a
+
+ align:start position:0%
+little bit because uh Zorn's Lemma is a
+ 
+
+ align:start position:0%
+little bit because uh Zorn's Lemma is a
+equivalent to the Axiom of choice so
+
+ align:start position:0%
+equivalent to the Axiom of choice so
+ 
+
+ align:start position:0%
+equivalent to the Axiom of choice so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+if you don't like using the Axiom of
+
+ align:start position:0%
+if you don't like using the Axiom of
+ 
+
+ align:start position:0%
+if you don't like using the Axiom of
+choice maybe you have a problem with
+
+ align:start position:0%
+choice maybe you have a problem with
+ 
+
+ align:start position:0%
+choice maybe you have a problem with
+using it to construct a maximal
+
+ align:start position:0%
+using it to construct a maximal
+ 
+
+ align:start position:0%
+using it to construct a maximal
+orthonormal subset of a
+
+ align:start position:0%
+orthonormal subset of a
+ 
+
+ align:start position:0%
+orthonormal subset of a
+pre-hilbert space but
+
+ align:start position:0%
+pre-hilbert space but
+ 
+
+ align:start position:0%
+pre-hilbert space but
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+we can actually do this by hand if the
+
+ align:start position:0%
+we can actually do this by hand if the
+ 
+
+ align:start position:0%
+we can actually do this by hand if the
+Hilbert space is separable so this is
+
+ align:start position:0%
+Hilbert space is separable so this is
+ 
+
+ align:start position:0%
+Hilbert space is separable so this is
+the theorem will actually prove every uh
+
+ align:start position:0%
+the theorem will actually prove every uh
+ 
+
+ align:start position:0%
+the theorem will actually prove every uh
+non-trivial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separable meaning it had meaning the
+
+ align:start position:0%
+separable meaning it had meaning the
+ 
+
+ align:start position:0%
+separable meaning it had meaning the
+pre-hubert space has a countably dense
+
+ align:start position:0%
+pre-hubert space has a countably dense
+ 
+
+ align:start position:0%
+pre-hubert space has a countably dense
+subset every non-trivial separable
+
+ align:start position:0%
+subset every non-trivial separable
+ 
+
+ align:start position:0%
+subset every non-trivial separable
+pre-hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accountable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximal
+
+ align:start position:0%
+maximal
+ 
+
+ align:start position:0%
+maximal
+orthonormal subset
+
+ align:start position:0%
+orthonormal subset
+ 
+
+ align:start position:0%
+orthonormal subset
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+which as I said this is kind of the main
+
+ align:start position:0%
+which as I said this is kind of the main
+ 
+
+ align:start position:0%
+which as I said this is kind of the main
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+types of orthonormal subsets we'll be
+
+ align:start position:0%
+types of orthonormal subsets we'll be
+ 
+
+ align:start position:0%
+types of orthonormal subsets we'll be
+interested in just because you know
+
+ align:start position:0%
+interested in just because you know
+ 
+
+ align:start position:0%
+interested in just because you know
+defining infinite sums is easier to do
+
+ align:start position:0%
+defining infinite sums is easier to do
+ 
+
+ align:start position:0%
+defining infinite sums is easier to do
+over a countable uh index than it is an
+
+ align:start position:0%
+over a countable uh index than it is an
+ 
+
+ align:start position:0%
+over a countable uh index than it is an
+uncountable index but uh anyways so
+
+ align:start position:0%
+uncountable index but uh anyways so
+ 
+
+ align:start position:0%
+uncountable index but uh anyways so
+we're going to prove and actually
+
+ align:start position:0%
+we're going to prove and actually
+ 
+
+ align:start position:0%
+we're going to prove and actually
+construct this essentially by hand
+
+ align:start position:0%
+construct this essentially by hand
+ 
+
+ align:start position:0%
+construct this essentially by hand
+um using
+
+ align:start position:0%
+um using
+ 
+
+ align:start position:0%
+um using
+uh the process that's the name of this
+
+ align:start position:0%
+uh the process that's the name of this
+ 
+
+ align:start position:0%
+uh the process that's the name of this
+little section the Graham Schmidt
+
+ align:start position:0%
+little section the Graham Schmidt
+ 
+
+ align:start position:0%
+little section the Graham Schmidt
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you from remember from linear
+
+ align:start position:0%
+so if you from remember from linear
+ 
+
+ align:start position:0%
+so if you from remember from linear
+algebra if you have a collection of
+
+ align:start position:0%
+algebra if you have a collection of
+ 
+
+ align:start position:0%
+algebra if you have a collection of
+um vectors you can always find and
+
+ align:start position:0%
+um vectors you can always find and
+ 
+
+ align:start position:0%
+um vectors you can always find and
+orthonormal collection of vectors that
+
+ align:start position:0%
+orthonormal collection of vectors that
+ 
+
+ align:start position:0%
+orthonormal collection of vectors that
+span uh the Vector space that is spanned
+
+ align:start position:0%
+span uh the Vector space that is spanned
+ 
+
+ align:start position:0%
+span uh the Vector space that is spanned
+by the original set of vectors okay
+
+ align:start position:0%
+by the original set of vectors okay
+ 
+
+ align:start position:0%
+by the original set of vectors okay
+and that's what we'll do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since H is separable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let be a
+
+ align:start position:0%
+let be a
+ 
+
+ align:start position:0%
+let be a
+countable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset of
+
+ align:start position:0%
+subset of
+ 
+
+ align:start position:0%
+subset of
+H and it's uh this is a non-trivial
+
+ align:start position:0%
+H and it's uh this is a non-trivial
+ 
+
+ align:start position:0%
+H and it's uh this is a non-trivial
+pre-hubert space so
+
+ align:start position:0%
+pre-hubert space so
+ 
+
+ align:start position:0%
+pre-hubert space so
+we can always make sure that
+
+ align:start position:0%
+we can always make sure that
+ 
+
+ align:start position:0%
+we can always make sure that
+the first one is a non-zero Vector okay
+
+ align:start position:0%
+the first one is a non-zero Vector okay
+ 
+
+ align:start position:0%
+the first one is a non-zero Vector okay
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+you know accountable means dense
+
+ align:start position:0%
+you know accountable means dense
+ 
+
+ align:start position:0%
+you know accountable means dense
+remember means that for any element in h
+
+ align:start position:0%
+remember means that for any element in h
+ 
+
+ align:start position:0%
+remember means that for any element in h
+there exists an element from this
+
+ align:start position:0%
+there exists an element from this
+ 
+
+ align:start position:0%
+there exists an element from this
+sequence uh
+
+ align:start position:0%
+sequence uh
+ 
+
+ align:start position:0%
+sequence uh
+or from this collection that's within
+
+ align:start position:0%
+or from this collection that's within
+ 
+
+ align:start position:0%
+or from this collection that's within
+Epsilon of uh that Vector from h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I'm going to make the following
+
+ align:start position:0%
+so now I'm going to make the following
+ 
+
+ align:start position:0%
+so now I'm going to make the following
+claim this is essentially a
+
+ align:start position:0%
+claim this is essentially a
+ 
+
+ align:start position:0%
+claim this is essentially a
+the gram
+
+ align:start position:0%
+the gram
+ 
+
+ align:start position:0%
+the gram
+Schmidt process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which will improve which will approve by
+
+ align:start position:0%
+which will improve which will approve by
+ 
+
+ align:start position:0%
+which will improve which will approve by
+induction
+
+ align:start position:0%
+induction
+ 
+
+ align:start position:0%
+induction
+we're all in
+
+ align:start position:0%
+we're all in
+ 
+
+ align:start position:0%
+we're all in
+natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another integer a natural number M of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and orthonormal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset
+
+ align:start position:0%
+subset
+ 
+
+ align:start position:0%
+subset
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+up to em
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+the following is true
+
+ align:start position:0%
+the following is true
+ 
+
+ align:start position:0%
+the following is true
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+first is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the span of E1
+
+ align:start position:0%
+the span of E1
+ 
+
+ align:start position:0%
+the span of E1
+up to e m of n
+
+ align:start position:0%
+up to e m of n
+ 
+
+ align:start position:0%
+up to e m of n
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+the span of B1 up to VN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you see
+
+ align:start position:0%
+and so you see
+ 
+
+ align:start position:0%
+and so you see
+you know n is changing so maybe for each
+
+ align:start position:0%
+you know n is changing so maybe for each
+ 
+
+ align:start position:0%
+you know n is changing so maybe for each
+time I change N I get a different
+
+ align:start position:0%
+time I change N I get a different
+ 
+
+ align:start position:0%
+time I change N I get a different
+orthonormal subset
+
+ align:start position:0%
+orthonormal subset
+ 
+
+ align:start position:0%
+orthonormal subset
+or a wildly different orthonormal subset
+
+ align:start position:0%
+or a wildly different orthonormal subset
+ 
+
+ align:start position:0%
+or a wildly different orthonormal subset
+from uh
+
+ align:start position:0%
+from uh
+ 
+
+ align:start position:0%
+from uh
+the integer before it but
+
+ align:start position:0%
+the integer before it but
+ 
+
+ align:start position:0%
+the integer before it but
+um so the property of these subsets are
+
+ align:start position:0%
+um so the property of these subsets are
+ 
+
+ align:start position:0%
+um so the property of these subsets are
+that I'm just simply adding a
+
+ align:start position:0%
+that I'm just simply adding a
+ 
+
+ align:start position:0%
+that I'm just simply adding a
+a vector or not so and
+
+ align:start position:0%
+a vector or not so and
+ 
+
+ align:start position:0%
+a vector or not so and
+E1
+
+ align:start position:0%
+E1
+ 
+
+ align:start position:0%
+E1
+to e m of n so this collection is equal
+
+ align:start position:0%
+to e m of n so this collection is equal
+ 
+
+ align:start position:0%
+to e m of n so this collection is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the previous collection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Union either the empty set
+
+ align:start position:0%
+Union either the empty set
+ 
+
+ align:start position:0%
+Union either the empty set
+if VN
+
+ align:start position:0%
+if VN
+ 
+
+ align:start position:0%
+if VN
+is in the span of
+
+ align:start position:0%
+is in the span of
+ 
+
+ align:start position:0%
+is in the span of
+the one up to B n minus 1
+
+ align:start position:0%
+the one up to B n minus 1
+ 
+
+ align:start position:0%
+the one up to B n minus 1
+and some new Vector e of M sub n
+
+ align:start position:0%
+and some new Vector e of M sub n
+ 
+
+ align:start position:0%
+and some new Vector e of M sub n
+and I'll tell you what e of M sub n is
+
+ align:start position:0%
+and I'll tell you what e of M sub n is
+ 
+
+ align:start position:0%
+and I'll tell you what e of M sub n is
+it otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what I'm saying here is that I
+
+ align:start position:0%
+okay so what I'm saying here is that I
+ 
+
+ align:start position:0%
+okay so what I'm saying here is that I
+have this countably infinite list of B's
+
+ align:start position:0%
+have this countably infinite list of B's
+ 
+
+ align:start position:0%
+have this countably infinite list of B's
+and for each N I can come up with a
+
+ align:start position:0%
+and for each N I can come up with a
+ 
+
+ align:start position:0%
+and for each N I can come up with a
+finite orthonormal subset
+
+ align:start position:0%
+finite orthonormal subset
+ 
+
+ align:start position:0%
+finite orthonormal subset
+that spans the same span as V1 up to V
+
+ align:start position:0%
+that spans the same span as V1 up to V
+ 
+
+ align:start position:0%
+that spans the same span as V1 up to V
+in and at each stage all I do is add a
+
+ align:start position:0%
+in and at each stage all I do is add a
+ 
+
+ align:start position:0%
+in and at each stage all I do is add a
+vector or not depending on if the next V
+
+ align:start position:0%
+vector or not depending on if the next V
+ 
+
+ align:start position:0%
+vector or not depending on if the next V
+is in the span of the previous or not
+
+ align:start position:0%
+is in the span of the previous or not
+ 
+
+ align:start position:0%
+is in the span of the previous or not
+okay so I hope that's clear
+
+ align:start position:0%
+okay so I hope that's clear
+ 
+
+ align:start position:0%
+okay so I hope that's clear
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+to prove this by induction so proof of
+
+ align:start position:0%
+to prove this by induction so proof of
+ 
+
+ align:start position:0%
+to prove this by induction so proof of
+claim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is by induction
+
+ align:start position:0%
+this is by induction
+ 
+
+ align:start position:0%
+this is by induction
+so let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the base case n equals one uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take we take E1 to B
+
+ align:start position:0%
+let's take we take E1 to B
+ 
+
+ align:start position:0%
+let's take we take E1 to B
+B1 over
+
+ align:start position:0%
+B1 over
+ 
+
+ align:start position:0%
+B1 over
+length of V
+
+ align:start position:0%
+length of V
+ 
+
+ align:start position:0%
+length of V
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so now we're started
+
+ align:start position:0%
+so now we're started
+ 
+
+ align:start position:0%
+so now we're started
+now we've got our first
+
+ align:start position:0%
+now we've got our first
+ 
+
+ align:start position:0%
+now we've got our first
+Vector in this list that we're building
+
+ align:start position:0%
+Vector in this list that we're building
+ 
+
+ align:start position:0%
+Vector in this list that we're building
+up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inductive step
+
+ align:start position:0%
+inductive step
+ 
+
+ align:start position:0%
+inductive step
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call this what I want to prove
+
+ align:start position:0%
+let's call this what I want to prove
+ 
+
+ align:start position:0%
+let's call this what I want to prove
+star so suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the star holds
+
+ align:start position:0%
+the star holds
+ 
+
+ align:start position:0%
+the star holds
+for uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this whole claim here I shouldn't say
+
+ align:start position:0%
+so this whole claim here I shouldn't say
+ 
+
+ align:start position:0%
+so this whole claim here I shouldn't say
+Just A and B but the whole claim holds
+
+ align:start position:0%
+Just A and B but the whole claim holds
+ 
+
+ align:start position:0%
+Just A and B but the whole claim holds
+for n equals K and now I want to prove
+
+ align:start position:0%
+for n equals K and now I want to prove
+ 
+
+ align:start position:0%
+for n equals K and now I want to prove
+it holds for n equals K plus one so I
+
+ align:start position:0%
+it holds for n equals K plus one so I
+ 
+
+ align:start position:0%
+it holds for n equals K plus one so I
+wanna
+
+ align:start position:0%
+wanna
+ 
+
+ align:start position:0%
+wanna
+what kind of vector do I need to add to
+
+ align:start position:0%
+what kind of vector do I need to add to
+ 
+
+ align:start position:0%
+what kind of vector do I need to add to
+the previous uh collection of vectors to
+
+ align:start position:0%
+the previous uh collection of vectors to
+ 
+
+ align:start position:0%
+the previous uh collection of vectors to
+now span V1 up to V K plus 1.
+
+ align:start position:0%
+now span V1 up to V K plus 1.
+ 
+
+ align:start position:0%
+now span V1 up to V K plus 1.
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh if B K plus 1 is in
+
+ align:start position:0%
+so uh if B K plus 1 is in
+ 
+
+ align:start position:0%
+so uh if B K plus 1 is in
+span of B1 up to V K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+E1 up to e m of K
+
+ align:start position:0%
+E1 up to e m of K
+ 
+
+ align:start position:0%
+E1 up to e m of K
+I should say the span of these vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+span of V1 up to V
+
+ align:start position:0%
+span of V1 up to V
+ 
+
+ align:start position:0%
+span of V1 up to V
+k equals
+
+ align:start position:0%
+k equals
+ 
+
+ align:start position:0%
+k equals
+because V K plus 1 is in this span this
+
+ align:start position:0%
+because V K plus 1 is in this span this
+ 
+
+ align:start position:0%
+because V K plus 1 is in this span this
+span is also equal to
+
+ align:start position:0%
+span is also equal to
+ 
+
+ align:start position:0%
+span is also equal to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+K plus 1.
+
+ align:start position:0%
+K plus 1.
+ 
+
+ align:start position:0%
+K plus 1.
+and therefore uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this case is handled and we're in this
+
+ align:start position:0%
+this case is handled and we're in this
+ 
+
+ align:start position:0%
+this case is handled and we're in this
+spot where we don't add anything to the
+
+ align:start position:0%
+spot where we don't add anything to the
+ 
+
+ align:start position:0%
+spot where we don't add anything to the
+previous uh collection okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this proves uh what we wanted to for n
+
+ align:start position:0%
+this proves uh what we wanted to for n
+ 
+
+ align:start position:0%
+this proves uh what we wanted to for n
+equals K plus one
+
+ align:start position:0%
+equals K plus one
+ 
+
+ align:start position:0%
+equals K plus one
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+by not adding anything so this was in
+
+ align:start position:0%
+by not adding anything so this was in
+ 
+
+ align:start position:0%
+by not adding anything so this was in
+the case that VK plus one is in the span
+
+ align:start position:0%
+the case that VK plus one is in the span
+ 
+
+ align:start position:0%
+the case that VK plus one is in the span
+of V1 up to VK so now let's do the more
+
+ align:start position:0%
+of V1 up to VK so now let's do the more
+ 
+
+ align:start position:0%
+of V1 up to VK so now let's do the more
+interesting case of V1 not equal or not
+
+ align:start position:0%
+interesting case of V1 not equal or not
+ 
+
+ align:start position:0%
+interesting case of V1 not equal or not
+in the span of V1 up to VK
+
+ align:start position:0%
+in the span of V1 up to VK
+ 
+
+ align:start position:0%
+in the span of V1 up to VK
+so now suppose
+
+ align:start position:0%
+so now suppose
+ 
+
+ align:start position:0%
+so now suppose
+be K plus one
+
+ align:start position:0%
+be K plus one
+ 
+
+ align:start position:0%
+be K plus one
+is not in
+
+ align:start position:0%
+is not in
+ 
+
+ align:start position:0%
+is not in
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+span of V1 to VK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I Define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+w k Plus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be V A plus 1 minus its projection
+
+ align:start position:0%
+to be V A plus 1 minus its projection
+ 
+
+ align:start position:0%
+to be V A plus 1 minus its projection
+onto the previous uh list of orthonormal
+
+ align:start position:0%
+onto the previous uh list of orthonormal
+ 
+
+ align:start position:0%
+onto the previous uh list of orthonormal
+vectors so some from J equals one
+
+ align:start position:0%
+vectors so some from J equals one
+ 
+
+ align:start position:0%
+vectors so some from J equals one
+M of K
+
+ align:start position:0%
+M of K
+ 
+
+ align:start position:0%
+M of K
+B K plus 1.
+
+ align:start position:0%
+B K plus 1.
+ 
+
+ align:start position:0%
+B K plus 1.
+e j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+first note that
+
+ align:start position:0%
+first note that
+ 
+
+ align:start position:0%
+first note that
+this Vector cannot be so w k plus 1 this
+
+ align:start position:0%
+this Vector cannot be so w k plus 1 this
+ 
+
+ align:start position:0%
+this Vector cannot be so w k plus 1 this
+this Vector cannot be zero right
+
+ align:start position:0%
+this Vector cannot be zero right
+ 
+
+ align:start position:0%
+this Vector cannot be zero right
+otherwise this would imply that V K plus
+
+ align:start position:0%
+otherwise this would imply that V K plus
+ 
+
+ align:start position:0%
+otherwise this would imply that V K plus
+1 is equal to this quantity here and
+
+ align:start position:0%
+1 is equal to this quantity here and
+ 
+
+ align:start position:0%
+1 is equal to this quantity here and
+therefore since uh and therefore V K
+
+ align:start position:0%
+therefore since uh and therefore V K
+ 
+
+ align:start position:0%
+therefore since uh and therefore V K
+plus 1 is in the span of the ejs for J
+
+ align:start position:0%
+plus 1 is in the span of the ejs for J
+ 
+
+ align:start position:0%
+plus 1 is in the span of the ejs for J
+between one of between 1 and M sub K
+
+ align:start position:0%
+between one of between 1 and M sub K
+ 
+
+ align:start position:0%
+between one of between 1 and M sub K
+which is equal to the span of the V J is
+
+ align:start position:0%
+which is equal to the span of the V J is
+ 
+
+ align:start position:0%
+which is equal to the span of the V J is
+for one up to K so but we're assuming
+
+ align:start position:0%
+for one up to K so but we're assuming
+ 
+
+ align:start position:0%
+for one up to K so but we're assuming
+this is not in the span
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+should say this is equal to the span of
+
+ align:start position:0%
+should say this is equal to the span of
+ 
+
+ align:start position:0%
+should say this is equal to the span of
+E1 up to a m sub K right that's what
+
+ align:start position:0%
+E1 up to a m sub K right that's what
+ 
+
+ align:start position:0%
+E1 up to a m sub K right that's what
+we're assuming that's the inductive
+
+ align:start position:0%
+we're assuming that's the inductive
+ 
+
+ align:start position:0%
+we're assuming that's the inductive
+hypothesis right
+
+ align:start position:0%
+hypothesis right
+ 
+
+ align:start position:0%
+hypothesis right
+so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this uh
+
+ align:start position:0%
+this uh
+ 
+
+ align:start position:0%
+this uh
+Vector does not equal zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Define e
+
+ align:start position:0%
+and Define e
+ 
+
+ align:start position:0%
+and Define e
+M sub K plus 1 or M to be the vector
+
+ align:start position:0%
+M sub K plus 1 or M to be the vector
+ 
+
+ align:start position:0%
+M sub K plus 1 or M to be the vector
+WK over its length for plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is a unit vector
+
+ align:start position:0%
+now this is a unit vector
+ 
+
+ align:start position:0%
+now this is a unit vector
+um and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what and
+
+ align:start position:0%
+and what and
+ 
+
+ align:start position:0%
+and what and
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if I take so now I claim this is
+
+ align:start position:0%
+and if I take so now I claim this is
+ 
+
+ align:start position:0%
+and if I take so now I claim this is
+orthogonal to E1 up to e of M sub k
+
+ align:start position:0%
+orthogonal to E1 up to e of M sub k
+ 
+
+ align:start position:0%
+orthogonal to E1 up to e of M sub k
+if I take e
+
+ align:start position:0%
+if I take e
+ 
+
+ align:start position:0%
+if I take e
+M K plus 1 and a product e sub N Sub J
+
+ align:start position:0%
+M K plus 1 and a product e sub N Sub J
+ 
+
+ align:start position:0%
+M K plus 1 and a product e sub N Sub J
+so let's take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equal to Simply by definition 1
+
+ align:start position:0%
+this is equal to Simply by definition 1
+ 
+
+ align:start position:0%
+this is equal to Simply by definition 1
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+length of M K plus 1 times the inner
+
+ align:start position:0%
+length of M K plus 1 times the inner
+ 
+
+ align:start position:0%
+length of M K plus 1 times the inner
+product of V K plus one minus
+
+ align:start position:0%
+product of V K plus one minus
+ 
+
+ align:start position:0%
+product of V K plus one minus
+sum from J equals one to M sub K so
+
+ align:start position:0%
+sum from J equals one to M sub K so
+ 
+
+ align:start position:0%
+sum from J equals one to M sub K so
+remember this this is supposed to be the
+
+ align:start position:0%
+remember this this is supposed to be the
+ 
+
+ align:start position:0%
+remember this this is supposed to be the
+projection onto the E1 up to e m sub K
+
+ align:start position:0%
+projection onto the E1 up to e m sub K
+ 
+
+ align:start position:0%
+projection onto the E1 up to e m sub K
+and V K plus 1 minus that is supposed to
+
+ align:start position:0%
+and V K plus 1 minus that is supposed to
+ 
+
+ align:start position:0%
+and V K plus 1 minus that is supposed to
+be orthogonal to those guys so we'll see
+
+ align:start position:0%
+be orthogonal to those guys so we'll see
+ 
+
+ align:start position:0%
+be orthogonal to those guys so we'll see
+that this ends up being zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me
+
+ align:start position:0%
+and let me
+ 
+
+ align:start position:0%
+and let me
+change this J to an L since I am
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I get
+
+ align:start position:0%
+and I get
+ 
+
+ align:start position:0%
+and I get
+one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the sum uh
+
+ align:start position:0%
+times the sum uh
+ 
+
+ align:start position:0%
+times the sum uh
+or times
+
+ align:start position:0%
+or times
+ 
+
+ align:start position:0%
+or times
+V A plus one
+
+ align:start position:0%
+V A plus one
+ 
+
+ align:start position:0%
+V A plus one
+Isabel
+
+ align:start position:0%
+Isabel
+ 
+
+ align:start position:0%
+Isabel
+minus now Isabel inner product with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sum right now this is the sum from J
+
+ align:start position:0%
+the sum right now this is the sum from J
+ 
+
+ align:start position:0%
+the sum right now this is the sum from J
+equals 1 to M sub K of this number here
+
+ align:start position:0%
+equals 1 to M sub K of this number here
+ 
+
+ align:start position:0%
+equals 1 to M sub K of this number here
+times the inner product of e sub J inner
+
+ align:start position:0%
+times the inner product of e sub J inner
+ 
+
+ align:start position:0%
+times the inner product of e sub J inner
+product e sub l
+
+ align:start position:0%
+product e sub l
+ 
+
+ align:start position:0%
+product e sub l
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um now the inner product of e sub J and
+
+ align:start position:0%
+um now the inner product of e sub J and
+ 
+
+ align:start position:0%
+um now the inner product of e sub J and
+E sub L is zero unless J equals L and
+
+ align:start position:0%
+E sub L is zero unless J equals L and
+ 
+
+ align:start position:0%
+E sub L is zero unless J equals L and
+one other and one if J equals l and so I
+
+ align:start position:0%
+one other and one if J equals l and so I
+ 
+
+ align:start position:0%
+one other and one if J equals l and so I
+only pick up
+
+ align:start position:0%
+only pick up
+ 
+
+ align:start position:0%
+only pick up
+uh the J equals L part of this sum when
+
+ align:start position:0%
+uh the J equals L part of this sum when
+ 
+
+ align:start position:0%
+uh the J equals L part of this sum when
+this inner product hits e sub l
+
+ align:start position:0%
+this inner product hits e sub l
+ 
+
+ align:start position:0%
+this inner product hits e sub l
+uh in particular I only pick up the
+
+ align:start position:0%
+uh in particular I only pick up the
+ 
+
+ align:start position:0%
+uh in particular I only pick up the
+coefficient in front since these have
+
+ align:start position:0%
+coefficient in front since these have
+ 
+
+ align:start position:0%
+coefficient in front since these have
+unit length so I get V sub
+
+ align:start position:0%
+unit length so I get V sub
+ 
+
+ align:start position:0%
+unit length so I get V sub
+Plus One V sub l
+
+ align:start position:0%
+Plus One V sub l
+ 
+
+ align:start position:0%
+Plus One V sub l
+equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+now does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the job so I would write a little bit
+
+ align:start position:0%
+in the job so I would write a little bit
+ 
+
+ align:start position:0%
+in the job so I would write a little bit
+more but I'm running short on time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so we've proved the claim
+
+ align:start position:0%
+um so we've proved the claim
+ 
+
+ align:start position:0%
+um so we've proved the claim
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's use this to conclude
+
+ align:start position:0%
+now let's use this to conclude
+ 
+
+ align:start position:0%
+now let's use this to conclude
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this collection of all of these Els
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um are maximal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s to be
+
+ align:start position:0%
+s to be
+ 
+
+ align:start position:0%
+s to be
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V sub n
+
+ align:start position:0%
+V sub n
+ 
+
+ align:start position:0%
+V sub n
+which equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and s is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an orthonormal subset of h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So eventually so you know I may not be
+
+ align:start position:0%
+So eventually so you know I may not be
+ 
+
+ align:start position:0%
+So eventually so you know I may not be
+adding any more vectors after a certain
+
+ align:start position:0%
+adding any more vectors after a certain
+ 
+
+ align:start position:0%
+adding any more vectors after a certain
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+and therefore just have a finite
+
+ align:start position:0%
+and therefore just have a finite
+ 
+
+ align:start position:0%
+and therefore just have a finite
+collection that's also
+
+ align:start position:0%
+collection that's also
+ 
+
+ align:start position:0%
+collection that's also
+possible but I may also have a
+
+ align:start position:0%
+possible but I may also have a
+ 
+
+ align:start position:0%
+possible but I may also have a
+accountably infinite collection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a orthonormal set by
+
+ align:start position:0%
+so this is a orthonormal set by
+ 
+
+ align:start position:0%
+so this is a orthonormal set by
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+we now show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is maximum
+
+ align:start position:0%
+X is maximum
+ 
+
+ align:start position:0%
+X is maximum
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right here is where so we haven't
+
+ align:start position:0%
+all right here is where so we haven't
+ 
+
+ align:start position:0%
+all right here is where so we haven't
+used anything about the nature of this
+
+ align:start position:0%
+used anything about the nature of this
+ 
+
+ align:start position:0%
+used anything about the nature of this
+subset of H all we've used is that you
+
+ align:start position:0%
+subset of H all we've used is that you
+ 
+
+ align:start position:0%
+subset of H all we've used is that you
+know it's accountable so we could do
+
+ align:start position:0%
+know it's accountable so we could do
+ 
+
+ align:start position:0%
+know it's accountable so we could do
+this step by step where we construct
+
+ align:start position:0%
+this step by step where we construct
+ 
+
+ align:start position:0%
+this step by step where we construct
+these orthonormal vectors that span each
+
+ align:start position:0%
+these orthonormal vectors that span each
+ 
+
+ align:start position:0%
+these orthonormal vectors that span each
+finite uh
+
+ align:start position:0%
+finite uh
+ 
+
+ align:start position:0%
+finite uh
+equal to the span of each finite
+
+ align:start position:0%
+equal to the span of each finite
+ 
+
+ align:start position:0%
+equal to the span of each finite
+collection of vectors now to show its
+
+ align:start position:0%
+collection of vectors now to show its
+ 
+
+ align:start position:0%
+collection of vectors now to show its
+maximal this is where we use the fact
+
+ align:start position:0%
+maximal this is where we use the fact
+ 
+
+ align:start position:0%
+maximal this is where we use the fact
+that this collection of these were dense
+
+ align:start position:0%
+that this collection of these were dense
+ 
+
+ align:start position:0%
+that this collection of these were dense
+there are dense in h so
+
+ align:start position:0%
+there are dense in h so
+ 
+
+ align:start position:0%
+there are dense in h so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose U is an H
+
+ align:start position:0%
+suppose U is an H
+ 
+
+ align:start position:0%
+suppose U is an H
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+for all l
+
+ align:start position:0%
+for all l
+ 
+
+ align:start position:0%
+for all l
+U of e sub l
+
+ align:start position:0%
+U of e sub l
+ 
+
+ align:start position:0%
+U of e sub l
+equals zero so this is either a finite
+
+ align:start position:0%
+equals zero so this is either a finite
+ 
+
+ align:start position:0%
+equals zero so this is either a finite
+set so L is between 1 and N or it's a
+
+ align:start position:0%
+set so L is between 1 and N or it's a
+ 
+
+ align:start position:0%
+set so L is between 1 and N or it's a
+countable set and L is going from 1 to
+
+ align:start position:0%
+countable set and L is going from 1 to
+ 
+
+ align:start position:0%
+countable set and L is going from 1 to
+Infinity so this equals it
+
+ align:start position:0%
+Infinity so this equals it
+ 
+
+ align:start position:0%
+Infinity so this equals it
+either this is equal to E
+
+ align:start position:0%
+either this is equal to E
+ 
+
+ align:start position:0%
+either this is equal to E
+1 up to E
+
+ align:start position:0%
+1 up to E
+ 
+
+ align:start position:0%
+1 up to E
+M sub n for some n or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B1
+
+ align:start position:0%
+B1
+ 
+
+ align:start position:0%
+B1
+is countably infinite okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v j
+
+ align:start position:0%
+v j
+ 
+
+ align:start position:0%
+v j
+this is a dense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset of H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can find a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of elements from this collection so V of
+
+ align:start position:0%
+of elements from this collection so V of
+ 
+
+ align:start position:0%
+of elements from this collection so V of
+J sub k
+
+ align:start position:0%
+J sub k
+ 
+
+ align:start position:0%
+J sub k
+equals 1 to Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+v j of K converges to U
+
+ align:start position:0%
+v j of K converges to U
+ 
+
+ align:start position:0%
+v j of K converges to U
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+K goes to Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by property a
+
+ align:start position:0%
+by property a
+ 
+
+ align:start position:0%
+by property a
+the fact that this span is equal to that
+
+ align:start position:0%
+the fact that this span is equal to that
+ 
+
+ align:start position:0%
+the fact that this span is equal to that
+span
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V of J sub K is in
+
+ align:start position:0%
+V of J sub K is in
+ 
+
+ align:start position:0%
+V of J sub K is in
+span of E1 up to E
+
+ align:start position:0%
+span of E1 up to E
+ 
+
+ align:start position:0%
+span of E1 up to E
+M of
+
+ align:start position:0%
+M of
+ 
+
+ align:start position:0%
+M of
+J sub k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+my vessels inequality
+
+ align:start position:0%
+my vessels inequality
+ 
+
+ align:start position:0%
+my vessels inequality
+and the fact that U is orthogonal to all
+
+ align:start position:0%
+and the fact that U is orthogonal to all
+ 
+
+ align:start position:0%
+and the fact that U is orthogonal to all
+of these uh uh orthonormal vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I get that
+
+ align:start position:0%
+I get that
+ 
+
+ align:start position:0%
+I get that
+V of
+
+ align:start position:0%
+V of
+ 
+
+ align:start position:0%
+V of
+J
+
+ align:start position:0%
+J
+ 
+
+ align:start position:0%
+J
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+now V of J sub of J of K this is in this
+
+ align:start position:0%
+now V of J sub of J of K this is in this
+ 
+
+ align:start position:0%
+now V of J sub of J of K this is in this
+span so you can show that in fact
+
+ align:start position:0%
+span so you can show that in fact
+ 
+
+ align:start position:0%
+span so you can show that in fact
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Norm is in fact equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the sum of the coefficients that I
+
+ align:start position:0%
+to the sum of the coefficients that I
+ 
+
+ align:start position:0%
+to the sum of the coefficients that I
+get from taking the inner product of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if I have a vector in the span of a
+
+ align:start position:0%
+okay if I have a vector in the span of a
+ 
+
+ align:start position:0%
+okay if I have a vector in the span of a
+collection of orthonormal vectors a
+
+ align:start position:0%
+collection of orthonormal vectors a
+ 
+
+ align:start position:0%
+collection of orthonormal vectors a
+finite collection of orthonormal vectors
+
+ align:start position:0%
+finite collection of orthonormal vectors
+ 
+
+ align:start position:0%
+finite collection of orthonormal vectors
+then the norm squared is equal to the
+
+ align:start position:0%
+then the norm squared is equal to the
+ 
+
+ align:start position:0%
+then the norm squared is equal to the
+sum of the coefficients just like an RN
+
+ align:start position:0%
+sum of the coefficients just like an RN
+ 
+
+ align:start position:0%
+sum of the coefficients just like an RN
+and Since U is orthogonal to each of
+
+ align:start position:0%
+and Since U is orthogonal to each of
+ 
+
+ align:start position:0%
+and Since U is orthogonal to each of
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this I can write as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by vessels inequality this is less
+
+ align:start position:0%
+and by vessels inequality this is less
+ 
+
+ align:start position:0%
+and by vessels inequality this is less
+than or equal to
+
+ align:start position:0%
+than or equal to
+ 
+
+ align:start position:0%
+than or equal to
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sum of these things squared is less
+
+ align:start position:0%
+the sum of these things squared is less
+ 
+
+ align:start position:0%
+the sum of these things squared is less
+than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared and this goes to zero
+
+ align:start position:0%
+squared and this goes to zero
+ 
+
+ align:start position:0%
+squared and this goes to zero
+because K goes to Infinity since the V
+
+ align:start position:0%
+because K goes to Infinity since the V
+ 
+
+ align:start position:0%
+because K goes to Infinity since the V
+of J sub K is converge to U but we
+
+ align:start position:0%
+of J sub K is converge to U but we
+ 
+
+ align:start position:0%
+of J sub K is converge to U but we
+started off with the norm of V of J sub
+
+ align:start position:0%
+started off with the norm of V of J sub
+ 
+
+ align:start position:0%
+started off with the norm of V of J sub
+K which implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 and therefore
+
+ align:start position:0%
+0 and therefore
+ 
+
+ align:start position:0%
+0 and therefore
+U which is the limit of these must be
+
+ align:start position:0%
+U which is the limit of these must be
+ 
+
+ align:start position:0%
+U which is the limit of these must be
+zero proving that this is a maximum
+
+ align:start position:0%
+zero proving that this is a maximum
+ 
+
+ align:start position:0%
+zero proving that this is a maximum
+subset
+
+ align:start position:0%
+subset
+ 
+
+ align:start position:0%
+subset
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+all right so next time we'll prove that
+
+ align:start position:0%
+all right so next time we'll prove that
+ 
+
+ align:start position:0%
+all right so next time we'll prove that
+these maximal orthonormal countable
+
+ align:start position:0%
+these maximal orthonormal countable
+ 
+
+ align:start position:0%
+these maximal orthonormal countable
+count of these
+
+ align:start position:0%
+count of these
+ 
+
+ align:start position:0%
+count of these
+maximal countable orthonormal subsets in
+
+ align:start position:0%
+maximal countable orthonormal subsets in
+ 
+
+ align:start position:0%
+maximal countable orthonormal subsets in
+fact form a pretty good analog of uh
+
+ align:start position:0%
+fact form a pretty good analog of uh
+ 
+
+ align:start position:0%
+fact form a pretty good analog of uh
+bases that you find in finite
+
+ align:start position:0%
+bases that you find in finite
+ 
+
+ align:start position:0%
+bases that you find in finite
+dimensional linear algebra
+
+ align:start position:0%
+dimensional linear algebra
+ 
+
+ align:start position:0%
+dimensional linear algebra
+we'll stop there
\ No newline at end of file
diff --git a/EmeWBxXlzKA.txt b/EmeWBxXlzKA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2175d83b8f58d2dd17ce53df1109b3da44d4bfed
--- /dev/null
+++ b/EmeWBxXlzKA.txt
@@ -0,0 +1,1219 @@
+align:start position:0%
+ 
+let's talk about the more circle an
+
+ align:start position:0%
+let's talk about the more circle an
+ 
+
+ align:start position:0%
+let's talk about the more circle an
+important tool in material science and
+
+ align:start position:0%
+important tool in material science and
+ 
+
+ align:start position:0%
+important tool in material science and
+mechanical engineering
+
+ align:start position:0%
+mechanical engineering
+ 
+
+ align:start position:0%
+mechanical engineering
+what is more circle and what does it do
+
+ align:start position:0%
+what is more circle and what does it do
+ 
+
+ align:start position:0%
+what is more circle and what does it do
+assume we have a rod and you want to
+
+ align:start position:0%
+assume we have a rod and you want to
+ 
+
+ align:start position:0%
+assume we have a rod and you want to
+break it with your hands what can you do
+
+ align:start position:0%
+break it with your hands what can you do
+ 
+
+ align:start position:0%
+break it with your hands what can you do
+about it you can pull it compress it or
+
+ align:start position:0%
+about it you can pull it compress it or
+ 
+
+ align:start position:0%
+about it you can pull it compress it or
+twist it each of these will induce a
+
+ align:start position:0%
+twist it each of these will induce a
+ 
+
+ align:start position:0%
+twist it each of these will induce a
+stress in the rod in a different way and
+
+ align:start position:0%
+stress in the rod in a different way and
+ 
+
+ align:start position:0%
+stress in the rod in a different way and
+the Mohr circle helps you analyze this
+
+ align:start position:0%
+the Mohr circle helps you analyze this
+ 
+
+ align:start position:0%
+the Mohr circle helps you analyze this
+Mohr circle is a graphical tool a visual
+
+ align:start position:0%
+Mohr circle is a graphical tool a visual
+ 
+
+ align:start position:0%
+Mohr circle is a graphical tool a visual
+way to see how to go from one state of
+
+ align:start position:0%
+way to see how to go from one state of
+ 
+
+ align:start position:0%
+way to see how to go from one state of
+stress to another usually you're given a
+
+ align:start position:0%
+stress to another usually you're given a
+ 
+
+ align:start position:0%
+stress to another usually you're given a
+state of stress that you calculated from
+
+ align:start position:0%
+state of stress that you calculated from
+ 
+
+ align:start position:0%
+state of stress that you calculated from
+using stress equations then you want to
+
+ align:start position:0%
+using stress equations then you want to
+ 
+
+ align:start position:0%
+using stress equations then you want to
+find a state of stress at a new angle of
+
+ align:start position:0%
+find a state of stress at a new angle of
+ 
+
+ align:start position:0%
+find a state of stress at a new angle of
+orientation or principal stresses at
+
+ align:start position:0%
+orientation or principal stresses at
+ 
+
+ align:start position:0%
+orientation or principal stresses at
+that orientation or the maximum in plane
+
+ align:start position:0%
+that orientation or the maximum in plane
+ 
+
+ align:start position:0%
+that orientation or the maximum in plane
+shear stresses and Mohr circle allows
+
+ align:start position:0%
+shear stresses and Mohr circle allows
+ 
+
+ align:start position:0%
+shear stresses and Mohr circle allows
+you to draw this representative element
+
+ align:start position:0%
+you to draw this representative element
+ 
+
+ align:start position:0%
+you to draw this representative element
+to visualize the calculations for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's derive the Mohr circle so now
+
+ align:start position:0%
+now let's derive the Mohr circle so now
+ 
+
+ align:start position:0%
+now let's derive the Mohr circle so now
+we take a look at the piece of material
+
+ align:start position:0%
+we take a look at the piece of material
+ 
+
+ align:start position:0%
+we take a look at the piece of material
+that we cut from the rod that we're
+
+ align:start position:0%
+that we cut from the rod that we're
+ 
+
+ align:start position:0%
+that we cut from the rod that we're
+trying to break and originally we had
+
+ align:start position:0%
+trying to break and originally we had
+ 
+
+ align:start position:0%
+trying to break and originally we had
+this coordinate system and we have some
+
+ align:start position:0%
+this coordinate system and we have some
+ 
+
+ align:start position:0%
+this coordinate system and we have some
+stresses where the Sigma is represented
+
+ align:start position:0%
+stresses where the Sigma is represented
+ 
+
+ align:start position:0%
+stresses where the Sigma is represented
+normal stress and the towels represent
+
+ align:start position:0%
+normal stress and the towels represent
+ 
+
+ align:start position:0%
+normal stress and the towels represent
+the shear stress so we draw this
+
+ align:start position:0%
+the shear stress so we draw this
+ 
+
+ align:start position:0%
+the shear stress so we draw this
+representative pair of stresses for
+
+ align:start position:0%
+representative pair of stresses for
+ 
+
+ align:start position:0%
+representative pair of stresses for
+convenience
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we want to analyze those
+
+ align:start position:0%
+and then we want to analyze those
+ 
+
+ align:start position:0%
+and then we want to analyze those
+stresses on this cross-section area so
+
+ align:start position:0%
+stresses on this cross-section area so
+ 
+
+ align:start position:0%
+stresses on this cross-section area so
+we do is we need to rotate the
+
+ align:start position:0%
+we do is we need to rotate the
+ 
+
+ align:start position:0%
+we do is we need to rotate the
+coordinate system so that the x-axis
+
+ align:start position:0%
+coordinate system so that the x-axis
+ 
+
+ align:start position:0%
+coordinate system so that the x-axis
+would line up with the unit normal
+
+ align:start position:0%
+would line up with the unit normal
+ 
+
+ align:start position:0%
+would line up with the unit normal
+vector to this cross sectional area and
+
+ align:start position:0%
+vector to this cross sectional area and
+ 
+
+ align:start position:0%
+vector to this cross sectional area and
+then the y axis would be rotated to this
+
+ align:start position:0%
+then the y axis would be rotated to this
+ 
+
+ align:start position:0%
+then the y axis would be rotated to this
+direction and would be lined up with and
+
+ align:start position:0%
+direction and would be lined up with and
+ 
+
+ align:start position:0%
+direction and would be lined up with and
+primed unit vector is shown here so this
+
+ align:start position:0%
+primed unit vector is shown here so this
+ 
+
+ align:start position:0%
+primed unit vector is shown here so this
+is done by rotating this coordinate
+
+ align:start position:0%
+is done by rotating this coordinate
+ 
+
+ align:start position:0%
+is done by rotating this coordinate
+system by an angle theta
+
+ align:start position:0%
+system by an angle theta
+ 
+
+ align:start position:0%
+system by an angle theta
+counterclockwise then we can obtain the
+
+ align:start position:0%
+counterclockwise then we can obtain the
+ 
+
+ align:start position:0%
+counterclockwise then we can obtain the
+unit normal vector in matrix form and
+
+ align:start position:0%
+unit normal vector in matrix form and
+ 
+
+ align:start position:0%
+unit normal vector in matrix form and
+that is just cosine theta and sine theta
+
+ align:start position:0%
+that is just cosine theta and sine theta
+ 
+
+ align:start position:0%
+that is just cosine theta and sine theta
+and similarly the N prime vector that's
+
+ align:start position:0%
+and similarly the N prime vector that's
+ 
+
+ align:start position:0%
+and similarly the N prime vector that's
+just negative sine theta and cosine
+
+ align:start position:0%
+just negative sine theta and cosine
+ 
+
+ align:start position:0%
+just negative sine theta and cosine
+theta so we can now get the stress
+
+ align:start position:0%
+theta so we can now get the stress
+ 
+
+ align:start position:0%
+theta so we can now get the stress
+tensor by taking the dot product of the
+
+ align:start position:0%
+tensor by taking the dot product of the
+ 
+
+ align:start position:0%
+tensor by taking the dot product of the
+stresses in the x-direction with the
+
+ align:start position:0%
+stresses in the x-direction with the
+ 
+
+ align:start position:0%
+stresses in the x-direction with the
+unit normal vector and the dot
+
+ align:start position:0%
+unit normal vector and the dot
+ 
+
+ align:start position:0%
+unit normal vector and the dot
+properties stresses in the y-direction
+
+ align:start position:0%
+properties stresses in the y-direction
+ 
+
+ align:start position:0%
+properties stresses in the y-direction
+with the unit normal vector so now we
+
+ align:start position:0%
+with the unit normal vector so now we
+ 
+
+ align:start position:0%
+with the unit normal vector so now we
+can write out the normal stress in the
+
+ align:start position:0%
+can write out the normal stress in the
+ 
+
+ align:start position:0%
+can write out the normal stress in the
+new coordinate system by just taking the
+
+ align:start position:0%
+new coordinate system by just taking the
+ 
+
+ align:start position:0%
+new coordinate system by just taking the
+dot product of the stress tensor with
+
+ align:start position:0%
+dot product of the stress tensor with
+ 
+
+ align:start position:0%
+dot product of the stress tensor with
+the unit normal vector and similarly we
+
+ align:start position:0%
+the unit normal vector and similarly we
+ 
+
+ align:start position:0%
+the unit normal vector and similarly we
+can find the shear stress in the new
+
+ align:start position:0%
+can find the shear stress in the new
+ 
+
+ align:start position:0%
+can find the shear stress in the new
+coordinate system by taking the dot
+
+ align:start position:0%
+coordinate system by taking the dot
+ 
+
+ align:start position:0%
+coordinate system by taking the dot
+product of the stress tensor with the M
+
+ align:start position:0%
+product of the stress tensor with the M
+ 
+
+ align:start position:0%
+product of the stress tensor with the M
+Prime and we can do these complicated
+
+ align:start position:0%
+Prime and we can do these complicated
+ 
+
+ align:start position:0%
+Prime and we can do these complicated
+calculations on Mathematica which I will
+
+ align:start position:0%
+calculations on Mathematica which I will
+ 
+
+ align:start position:0%
+calculations on Mathematica which I will
+show you right now so I've already typed
+
+ align:start position:0%
+show you right now so I've already typed
+ 
+
+ align:start position:0%
+show you right now so I've already typed
+in these vectors into Mathematica and n
+
+ align:start position:0%
+in these vectors into Mathematica and n
+ 
+
+ align:start position:0%
+in these vectors into Mathematica and n
+represents the unit normal vector and NP
+
+ align:start position:0%
+represents the unit normal vector and NP
+ 
+
+ align:start position:0%
+represents the unit normal vector and NP
+is just n prime and T is the stress
+
+ align:start position:0%
+is just n prime and T is the stress
+ 
+
+ align:start position:0%
+is just n prime and T is the stress
+tensor
+
+ align:start position:0%
+tensor
+ 
+
+ align:start position:0%
+tensor
+so we want to find the normal stress in
+
+ align:start position:0%
+so we want to find the normal stress in
+ 
+
+ align:start position:0%
+so we want to find the normal stress in
+the new coordinate system Sigma prime
+
+ align:start position:0%
+the new coordinate system Sigma prime
+ 
+
+ align:start position:0%
+the new coordinate system Sigma prime
+and that is just dotting T with N and we
+
+ align:start position:0%
+and that is just dotting T with N and we
+ 
+
+ align:start position:0%
+and that is just dotting T with N and we
+get this simplified version that so
+
+ align:start position:0%
+get this simplified version that so
+ 
+
+ align:start position:0%
+get this simplified version that so
+that's our signal Prime then we want to
+
+ align:start position:0%
+that's our signal Prime then we want to
+ 
+
+ align:start position:0%
+that's our signal Prime then we want to
+find our tau prime and that is just T
+
+ align:start position:0%
+find our tau prime and that is just T
+ 
+
+ align:start position:0%
+find our tau prime and that is just T
+dotted with NP again we want to find a
+
+ align:start position:0%
+dotted with NP again we want to find a
+ 
+
+ align:start position:0%
+dotted with NP again we want to find a
+simplified version so that's that and
+
+ align:start position:0%
+simplified version so that's that and
+ 
+
+ align:start position:0%
+simplified version so that's that and
+don't worry about this theta Xin to
+
+ align:start position:0%
+don't worry about this theta Xin to
+ 
+
+ align:start position:0%
+don't worry about this theta Xin to
+Thetas we'll use trig identities to
+
+ align:start position:0%
+Thetas we'll use trig identities to
+ 
+
+ align:start position:0%
+Thetas we'll use trig identities to
+change them so here's our trig
+
+ align:start position:0%
+change them so here's our trig
+ 
+
+ align:start position:0%
+change them so here's our trig
+identities and we just plug them back in
+
+ align:start position:0%
+identities and we just plug them back in
+ 
+
+ align:start position:0%
+identities and we just plug them back in
+and we obtain these two equations for
+
+ align:start position:0%
+and we obtain these two equations for
+ 
+
+ align:start position:0%
+and we obtain these two equations for
+our new stresses then we move all the
+
+ align:start position:0%
+our new stresses then we move all the
+ 
+
+ align:start position:0%
+our new stresses then we move all the
+terms containing two theta to the right
+
+ align:start position:0%
+terms containing two theta to the right
+ 
+
+ align:start position:0%
+terms containing two theta to the right
+side of the equations and all the rest
+
+ align:start position:0%
+side of the equations and all the rest
+ 
+
+ align:start position:0%
+side of the equations and all the rest
+of the terms the left side of equations
+
+ align:start position:0%
+of the terms the left side of equations
+ 
+
+ align:start position:0%
+of the terms the left side of equations
+and we square both sides of the
+
+ align:start position:0%
+and we square both sides of the
+ 
+
+ align:start position:0%
+and we square both sides of the
+equations to get equation one and
+
+ align:start position:0%
+equations to get equation one and
+ 
+
+ align:start position:0%
+equations to get equation one and
+equation two as shown here we add
+
+ align:start position:0%
+equation two as shown here we add
+ 
+
+ align:start position:0%
+equation two as shown here we add
+equation one and equation two and some
+
+ align:start position:0%
+equation one and equation two and some
+ 
+
+ align:start position:0%
+equation one and equation two and some
+terms cancel finally we get this really
+
+ align:start position:0%
+terms cancel finally we get this really
+ 
+
+ align:start position:0%
+terms cancel finally we get this really
+creamy equation shown here now look
+
+ align:start position:0%
+creamy equation shown here now look
+ 
+
+ align:start position:0%
+creamy equation shown here now look
+closely to this equation what form of
+
+ align:start position:0%
+closely to this equation what form of
+ 
+
+ align:start position:0%
+closely to this equation what form of
+equation does it look like
+
+ align:start position:0%
+equation does it look like
+ 
+
+ align:start position:0%
+equation does it look like
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you might have guessed that it looks
+
+ align:start position:0%
+you might have guessed that it looks
+ 
+
+ align:start position:0%
+you might have guessed that it looks
+like the equation of a circle and you're
+
+ align:start position:0%
+like the equation of a circle and you're
+ 
+
+ align:start position:0%
+like the equation of a circle and you're
+absolutely right this is exactly how
+
+ align:start position:0%
+absolutely right this is exactly how
+ 
+
+ align:start position:0%
+absolutely right this is exactly how
+more circle is derived we can compare
+
+ align:start position:0%
+more circle is derived we can compare
+ 
+
+ align:start position:0%
+more circle is derived we can compare
+the equation with the equation of a
+
+ align:start position:0%
+the equation with the equation of a
+ 
+
+ align:start position:0%
+the equation with the equation of a
+circle and we see that more circle is
+
+ align:start position:0%
+circle and we see that more circle is
+ 
+
+ align:start position:0%
+circle and we see that more circle is
+centered at the coordinates Sigma X plus
+
+ align:start position:0%
+centered at the coordinates Sigma X plus
+ 
+
+ align:start position:0%
+centered at the coordinates Sigma X plus
+Sigma Y over to 0 and Sigma X plus Sigma
+
+ align:start position:0%
+Sigma Y over to 0 and Sigma X plus Sigma
+ 
+
+ align:start position:0%
+Sigma Y over to 0 and Sigma X plus Sigma
+Y over 2 is the average normal stress in
+
+ align:start position:0%
+Y over 2 is the average normal stress in
+ 
+
+ align:start position:0%
+Y over 2 is the average normal stress in
+the old coordinate system we can also
+
+ align:start position:0%
+the old coordinate system we can also
+ 
+
+ align:start position:0%
+the old coordinate system we can also
+obtain the radius of more circle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let me draw this more circle for you
+
+ align:start position:0%
+now let me draw this more circle for you
+ 
+
+ align:start position:0%
+now let me draw this more circle for you
+so we go back to our old coordinate
+
+ align:start position:0%
+so we go back to our old coordinate
+ 
+
+ align:start position:0%
+so we go back to our old coordinate
+system with some calculated stresses and
+
+ align:start position:0%
+system with some calculated stresses and
+ 
+
+ align:start position:0%
+system with some calculated stresses and
+then we need to construct this new
+
+ align:start position:0%
+then we need to construct this new
+ 
+
+ align:start position:0%
+then we need to construct this new
+coordinate system to draw this Mohr
+
+ align:start position:0%
+coordinate system to draw this Mohr
+ 
+
+ align:start position:0%
+coordinate system to draw this Mohr
+circle on I take the positive
+
+ align:start position:0%
+circle on I take the positive
+ 
+
+ align:start position:0%
+circle on I take the positive
+x-direction that's the plus sigma and
+
+ align:start position:0%
+x-direction that's the plus sigma and
+ 
+
+ align:start position:0%
+x-direction that's the plus sigma and
+the negative y-direction is plus tau
+
+ align:start position:0%
+the negative y-direction is plus tau
+ 
+
+ align:start position:0%
+the negative y-direction is plus tau
+just by convention then in order to draw
+
+ align:start position:0%
+just by convention then in order to draw
+ 
+
+ align:start position:0%
+just by convention then in order to draw
+the circle we take a pair of normal
+
+ align:start position:0%
+the circle we take a pair of normal
+ 
+
+ align:start position:0%
+the circle we take a pair of normal
+stress and shear stress and we plot
+
+ align:start position:0%
+stress and shear stress and we plot
+ 
+
+ align:start position:0%
+stress and shear stress and we plot
+their values as the coordinates in our
+
+ align:start position:0%
+their values as the coordinates in our
+ 
+
+ align:start position:0%
+their values as the coordinates in our
+coordinate system so we find a dot and
+
+ align:start position:0%
+coordinate system so we find a dot and
+ 
+
+ align:start position:0%
+coordinate system so we find a dot and
+is represented by Sigma X and tau XY
+
+ align:start position:0%
+is represented by Sigma X and tau XY
+ 
+
+ align:start position:0%
+is represented by Sigma X and tau XY
+then by our previous equations that we
+
+ align:start position:0%
+then by our previous equations that we
+ 
+
+ align:start position:0%
+then by our previous equations that we
+derived we can find the center of the
+
+ align:start position:0%
+derived we can find the center of the
+ 
+
+ align:start position:0%
+derived we can find the center of the
+circle which is located at Sigma average
+
+ align:start position:0%
+circle which is located at Sigma average
+ 
+
+ align:start position:0%
+circle which is located at Sigma average
+and 0 and Sigma average is just Sigma X
+
+ align:start position:0%
+and 0 and Sigma average is just Sigma X
+ 
+
+ align:start position:0%
+and 0 and Sigma average is just Sigma X
+plus Sigma Y over 2 then we find these
+
+ align:start position:0%
+plus Sigma Y over 2 then we find these
+ 
+
+ align:start position:0%
+plus Sigma Y over 2 then we find these
+values and we plot that on our Sigma
+
+ align:start position:0%
+values and we plot that on our Sigma
+ 
+
+ align:start position:0%
+values and we plot that on our Sigma
+axis
+
+ align:start position:0%
+axis
+ 
+
+ align:start position:0%
+axis
+that's just our center of the circle
+
+ align:start position:0%
+that's just our center of the circle
+ 
+
+ align:start position:0%
+that's just our center of the circle
+then we connect these two dots that we
+
+ align:start position:0%
+then we connect these two dots that we
+ 
+
+ align:start position:0%
+then we connect these two dots that we
+drew and that's just the radius of the
+
+ align:start position:0%
+drew and that's just the radius of the
+ 
+
+ align:start position:0%
+drew and that's just the radius of the
+circle now we can draw this circle since
+
+ align:start position:0%
+circle now we can draw this circle since
+ 
+
+ align:start position:0%
+circle now we can draw this circle since
+we know it's Center and a dot on its
+
+ align:start position:0%
+we know it's Center and a dot on its
+ 
+
+ align:start position:0%
+we know it's Center and a dot on its
+circumference we can now confirm the
+
+ align:start position:0%
+circumference we can now confirm the
+ 
+
+ align:start position:0%
+circumference we can now confirm the
+equation for the radius of the circle by
+
+ align:start position:0%
+equation for the radius of the circle by
+ 
+
+ align:start position:0%
+equation for the radius of the circle by
+doing some geometry here so this length
+
+ align:start position:0%
+doing some geometry here so this length
+ 
+
+ align:start position:0%
+doing some geometry here so this length
+is just Sigma average and then we have
+
+ align:start position:0%
+is just Sigma average and then we have
+ 
+
+ align:start position:0%
+is just Sigma average and then we have
+another length that's just Sigma X and
+
+ align:start position:0%
+another length that's just Sigma X and
+ 
+
+ align:start position:0%
+another length that's just Sigma X and
+the difference between these lengths is
+
+ align:start position:0%
+the difference between these lengths is
+ 
+
+ align:start position:0%
+the difference between these lengths is
+just Sigma X minus Sigma average then
+
+ align:start position:0%
+just Sigma X minus Sigma average then
+ 
+
+ align:start position:0%
+just Sigma X minus Sigma average then
+this length right here is simply tau XY
+
+ align:start position:0%
+this length right here is simply tau XY
+ 
+
+ align:start position:0%
+this length right here is simply tau XY
+and by looking at this right triangle
+
+ align:start position:0%
+and by looking at this right triangle
+ 
+
+ align:start position:0%
+and by looking at this right triangle
+and using pythagoras theorem we can
+
+ align:start position:0%
+and using pythagoras theorem we can
+ 
+
+ align:start position:0%
+and using pythagoras theorem we can
+obtain the radius of the circle which is
+
+ align:start position:0%
+obtain the radius of the circle which is
+ 
+
+ align:start position:0%
+obtain the radius of the circle which is
+written here under the square root it
+
+ align:start position:0%
+written here under the square root it
+ 
+
+ align:start position:0%
+written here under the square root it
+actually it confirms our original
+
+ align:start position:0%
+actually it confirms our original
+ 
+
+ align:start position:0%
+actually it confirms our original
+equation for obtaining the radius R of
+
+ align:start position:0%
+equation for obtaining the radius R of
+ 
+
+ align:start position:0%
+equation for obtaining the radius R of
+our circle so Mohr circle is very useful
+
+ align:start position:0%
+our circle so Mohr circle is very useful
+ 
+
+ align:start position:0%
+our circle so Mohr circle is very useful
+for visualizing the stresses on the
+
+ align:start position:0%
+for visualizing the stresses on the
+ 
+
+ align:start position:0%
+for visualizing the stresses on the
+material so we can just by doing simple
+
+ align:start position:0%
+material so we can just by doing simple
+ 
+
+ align:start position:0%
+material so we can just by doing simple
+geometry find the values for its
+
+ align:start position:0%
+geometry find the values for its
+ 
+
+ align:start position:0%
+geometry find the values for its
+principal stresses so in green you can
+
+ align:start position:0%
+principal stresses so in green you can
+ 
+
+ align:start position:0%
+principal stresses so in green you can
+see on the circle there's the maximum
+
+ align:start position:0%
+see on the circle there's the maximum
+ 
+
+ align:start position:0%
+see on the circle there's the maximum
+normal stress and minimum normal stress
+
+ align:start position:0%
+normal stress and minimum normal stress
+ 
+
+ align:start position:0%
+normal stress and minimum normal stress
+and now in red I'm labeling the minimum
+
+ align:start position:0%
+and now in red I'm labeling the minimum
+ 
+
+ align:start position:0%
+and now in red I'm labeling the minimum
+and maximum shear stresses
\ No newline at end of file
diff --git a/F7H6Ko0KL0Y.txt b/F7H6Ko0KL0Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..260f1e11946d6923b3af679110929c84625ce001
--- /dev/null
+++ b/F7H6Ko0KL0Y.txt
@@ -0,0 +1,1832 @@
+align:start position:0%
+ 
+hi
+
+ align:start position:0%
+hi
+ 
+
+ align:start position:0%
+hi
+everyone okay so for the first H part of
+
+ align:start position:0%
+everyone okay so for the first H part of
+ 
+
+ align:start position:0%
+everyone okay so for the first H part of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+course we've learned basically the ins
+
+ align:start position:0%
+course we've learned basically the ins
+ 
+
+ align:start position:0%
+course we've learned basically the ins
+and outs of of solving linear systems of
+
+ align:start position:0%
+and outs of of solving linear systems of
+ 
+
+ align:start position:0%
+and outs of of solving linear systems of
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+um today we're going to do a little
+
+ align:start position:0%
+um today we're going to do a little
+ 
+
+ align:start position:0%
+um today we're going to do a little
+review of of the basic concepts um hope
+
+ align:start position:0%
+review of of the basic concepts um hope
+ 
+
+ align:start position:0%
+review of of the basic concepts um hope
+hopefully we'll we'll see um a few of
+
+ align:start position:0%
+hopefully we'll we'll see um a few of
+ 
+
+ align:start position:0%
+hopefully we'll we'll see um a few of
+them in the in the following problem
+
+ align:start position:0%
+them in the in the following problem
+ 
+
+ align:start position:0%
+them in the in the following problem
+we're given a square Matrix a a 3X3
+
+ align:start position:0%
+we're given a square Matrix a a 3X3
+ 
+
+ align:start position:0%
+we're given a square Matrix a a 3X3
+Square Matrix a where the last entry is
+
+ align:start position:0%
+Square Matrix a where the last entry is
+ 
+
+ align:start position:0%
+Square Matrix a where the last entry is
+a parameter
+
+ align:start position:0%
+a parameter
+ 
+
+ align:start position:0%
+a parameter
+K and this parameter will vary and we'll
+
+ align:start position:0%
+K and this parameter will vary and we'll
+ 
+
+ align:start position:0%
+K and this parameter will vary and we'll
+see how the system um whe what happens
+
+ align:start position:0%
+see how the system um whe what happens
+ 
+
+ align:start position:0%
+see how the system um whe what happens
+to the system of equations ax equal to
+
+ align:start position:0%
+to the system of equations ax equal to
+ 
+
+ align:start position:0%
+to the system of equations ax equal to
+237 whether for which K has a unique
+
+ align:start position:0%
+237 whether for which K has a unique
+ 
+
+ align:start position:0%
+237 whether for which K has a unique
+solution for which Kate has infinitely
+
+ align:start position:0%
+solution for which Kate has infinitely
+ 
+
+ align:start position:0%
+solution for which Kate has infinitely
+many solutions then we'll find the lud
+
+ align:start position:0%
+many solutions then we'll find the lud
+ 
+
+ align:start position:0%
+many solutions then we'll find the lud
+DEC composition and finally we'll write
+
+ align:start position:0%
+DEC composition and finally we'll write
+ 
+
+ align:start position:0%
+DEC composition and finally we'll write
+down the complete solution to the system
+
+ align:start position:0%
+down the complete solution to the system
+ 
+
+ align:start position:0%
+down the complete solution to the system
+so I'll give you a few minutes to work
+
+ align:start position:0%
+so I'll give you a few minutes to work
+ 
+
+ align:start position:0%
+so I'll give you a few minutes to work
+this um problem on your own and then
+
+ align:start position:0%
+this um problem on your own and then
+ 
+
+ align:start position:0%
+this um problem on your own and then
+please come back and see how I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it all right welcome
+
+ align:start position:0%
+it all right welcome
+ 
+
+ align:start position:0%
+it all right welcome
+back so let's start with part a for
+
+ align:start position:0%
+back so let's start with part a for
+ 
+
+ align:start position:0%
+back so let's start with part a for
+which K does this system axal 237 have a
+
+ align:start position:0%
+which K does this system axal 237 have a
+ 
+
+ align:start position:0%
+which K does this system axal 237 have a
+unique
+
+ align:start position:0%
+unique
+ 
+
+ align:start position:0%
+unique
+solution so what do we know about um
+
+ align:start position:0%
+solution so what do we know about um
+ 
+
+ align:start position:0%
+solution so what do we know about um
+Square systems
+
+ align:start position:0%
+Square systems
+ 
+
+ align:start position:0%
+Square systems
+of square systems of linear
+
+ align:start position:0%
+of square systems of linear
+ 
+
+ align:start position:0%
+of square systems of linear
+equations um they have a unique solution
+
+ align:start position:0%
+equations um they have a unique solution
+ 
+
+ align:start position:0%
+equations um they have a unique solution
+when the Matrix a is invertible okay so
+
+ align:start position:0%
+when the Matrix a is invertible okay so
+ 
+
+ align:start position:0%
+when the Matrix a is invertible okay so
+now when is a invertible it is
+
+ align:start position:0%
+now when is a invertible it is
+ 
+
+ align:start position:0%
+now when is a invertible it is
+invertible when it is a full Rank and
+
+ align:start position:0%
+invertible when it is a full Rank and
+ 
+
+ align:start position:0%
+invertible when it is a full Rank and
+how do we figure this this out we do it
+
+ align:start position:0%
+how do we figure this this out we do it
+ 
+
+ align:start position:0%
+how do we figure this this out we do it
+by performing um row operations we do it
+
+ align:start position:0%
+by performing um row operations we do it
+ 
+
+ align:start position:0%
+by performing um row operations we do it
+by doing eliminations on The
+
+ align:start position:0%
+by doing eliminations on The
+ 
+
+ align:start position:0%
+by doing eliminations on The
+Matrix okay um but since we want to
+
+ align:start position:0%
+Matrix okay um but since we want to
+ 
+
+ align:start position:0%
+Matrix okay um but since we want to
+simulate an exam setting uh it always
+
+ align:start position:0%
+simulate an exam setting uh it always
+ 
+
+ align:start position:0%
+simulate an exam setting uh it always
+pays off to see what um tasks lie ahead
+
+ align:start position:0%
+pays off to see what um tasks lie ahead
+ 
+
+ align:start position:0%
+pays off to see what um tasks lie ahead
+of us so in in part C we'll um we're
+
+ align:start position:0%
+of us so in in part C we'll um we're
+ 
+
+ align:start position:0%
+of us so in in part C we'll um we're
+asked to find the lud composition this
+
+ align:start position:0%
+asked to find the lud composition this
+ 
+
+ align:start position:0%
+asked to find the lud composition this
+means that when we do um row operations
+
+ align:start position:0%
+means that when we do um row operations
+ 
+
+ align:start position:0%
+means that when we do um row operations
+we better keep track
+
+ align:start position:0%
+we better keep track
+ 
+
+ align:start position:0%
+we better keep track
+what row operations we're doing
+
+ align:start position:0%
+what row operations we're doing
+ 
+
+ align:start position:0%
+what row operations we're doing
+exactly um in particular we'll write
+
+ align:start position:0%
+exactly um in particular we'll write
+ 
+
+ align:start position:0%
+exactly um in particular we'll write
+them down as Elementary
+
+ align:start position:0%
+them down as Elementary
+ 
+
+ align:start position:0%
+them down as Elementary
+matrices and in part D we will be asked
+
+ align:start position:0%
+matrices and in part D we will be asked
+ 
+
+ align:start position:0%
+matrices and in part D we will be asked
+to compute the complete solution and
+
+ align:start position:0%
+to compute the complete solution and
+ 
+
+ align:start position:0%
+to compute the complete solution and
+therefore um it's good to do row
+
+ align:start position:0%
+therefore um it's good to do row
+ 
+
+ align:start position:0%
+therefore um it's good to do row
+operations on the augmented Matrix a
+
+ align:start position:0%
+operations on the augmented Matrix a
+ 
+
+ align:start position:0%
+operations on the augmented Matrix a
+okay so let's do
+
+ align:start position:0%
+okay so let's do
+ 
+
+ align:start position:0%
+okay so let's do
+this um I'm going to write this well the
+
+ align:start position:0%
+this um I'm going to write this well the
+ 
+
+ align:start position:0%
+this um I'm going to write this well the
+augmented
+
+ align:start position:0%
+augmented
+ 
+
+ align:start position:0%
+augmented
+Matrix e is the following
+
+ align:start position:0%
+Matrix e is the following
+ 
+
+ align:start position:0%
+Matrix e is the following
+Beast one one
+
+ align:start position:0%
+Beast one one
+ 
+
+ align:start position:0%
+Beast one one
+one one 2
+
+ align:start position:0%
+one one 2
+ 
+
+ align:start position:0%
+one one 2
+3 3 4
+
+ align:start position:0%
+3 3 4
+ 
+
+ align:start position:0%
+3 3 4
+K and then 2 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+7 okay so first thing we we subtract row
+
+ align:start position:0%
+7 okay so first thing we we subtract row
+ 
+
+ align:start position:0%
+7 okay so first thing we we subtract row
+multiple of Row one from row two and
+
+ align:start position:0%
+multiple of Row one from row two and
+ 
+
+ align:start position:0%
+multiple of Row one from row two and
+it's exactly um -1 times the uh first
+
+ align:start position:0%
+it's exactly um -1 times the uh first
+ 
+
+ align:start position:0%
+it's exactly um -1 times the uh first
+row plus the second right so uh let me
+
+ align:start position:0%
+row plus the second right so uh let me
+ 
+
+ align:start position:0%
+row plus the second right so uh let me
+write down the corresponding elementary
+
+ align:start position:0%
+write down the corresponding elementary
+ 
+
+ align:start position:0%
+write down the corresponding elementary
+elementary Matrix that does this it's e
+
+ align:start position:0%
+elementary Matrix that does this it's e
+ 
+
+ align:start position:0%
+elementary Matrix that does this it's e
+um 2 one and it's lower diagonal with
+
+ align:start position:0%
+um 2 one and it's lower diagonal with
+ 
+
+ align:start position:0%
+um 2 one and it's lower diagonal with
+ones on the diagonal and it's going to
+
+ align:start position:0%
+ones on the diagonal and it's going to
+ 
+
+ align:start position:0%
+ones on the diagonal and it's going to
+be exactly minus1 in in the first entry
+
+ align:start position:0%
+be exactly minus1 in in the first entry
+ 
+
+ align:start position:0%
+be exactly minus1 in in the first entry
+of the second row
+
+ align:start position:0%
+of the second row
+ 
+
+ align:start position:0%
+of the second row
+okay so we get one one one
+
+ align:start position:0%
+okay so we get one one one
+ 
+
+ align:start position:0%
+okay so we get one one one
+2 0 1 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and we copy down the third row
+
+ align:start position:0%
+1 and we copy down the third row
+ 
+
+ align:start position:0%
+1 and we copy down the third row
+okay now we subtract a multiple of the
+
+ align:start position:0%
+okay now we subtract a multiple of the
+ 
+
+ align:start position:0%
+okay now we subtract a multiple of the
+first row from the third
+
+ align:start position:0%
+first row from the third
+ 
+
+ align:start position:0%
+first row from the third
+one and
+
+ align:start position:0%
+one and
+ 
+
+ align:start position:0%
+one and
+write this
+
+ align:start position:0%
+write this
+ 
+
+ align:start position:0%
+write this
+here it's precisely we'll multi yeah
+
+ align:start position:0%
+here it's precisely we'll multi yeah
+ 
+
+ align:start position:0%
+here it's precisely we'll multi yeah
+we'll multiply the F first row by -3 and
+
+ align:start position:0%
+we'll multiply the F first row by -3 and
+ 
+
+ align:start position:0%
+we'll multiply the F first row by -3 and
+add it to the third one this is
+
+ align:start position:0%
+add it to the third one this is
+ 
+
+ align:start position:0%
+add it to the third one this is
+accomplished by the elementary Matrix
+
+ align:start position:0%
+accomplished by the elementary Matrix
+ 
+
+ align:start position:0%
+accomplished by the elementary Matrix
+E31 which is 1 1 1 -3 and then 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 okay one one one two uh zero 1 2 one
+
+ align:start position:0%
+0 okay one one one two uh zero 1 2 one
+ 
+
+ align:start position:0%
+0 okay one one one two uh zero 1 2 one
+we copy the first two rows and then the
+
+ align:start position:0%
+we copy the first two rows and then the
+ 
+
+ align:start position:0%
+we copy the first two rows and then the
+third one will be zero
+
+ align:start position:0%
+third one will be zero
+ 
+
+ align:start position:0%
+third one will be zero
+1 um K -
+
+ align:start position:0%
+1 um K -
+ 
+
+ align:start position:0%
+1 um K -
+3 and 7 - 3 * 2 7 - 6
+
+ align:start position:0%
+3 and 7 - 3 * 2 7 - 6
+ 
+
+ align:start position:0%
+3 and 7 - 3 * 2 7 - 6
+1 okay we have essentially well one last
+
+ align:start position:0%
+1 okay we have essentially well one last
+ 
+
+ align:start position:0%
+1 okay we have essentially well one last
+row operation to to perform let me do it
+
+ align:start position:0%
+row operation to to perform let me do it
+ 
+
+ align:start position:0%
+row operation to to perform let me do it
+here so we'll subtract the second Row
+
+ align:start position:0%
+here so we'll subtract the second Row
+ 
+
+ align:start position:0%
+here so we'll subtract the second Row
+from the third one and we get one one
+
+ align:start position:0%
+from the third one and we get one one
+ 
+
+ align:start position:0%
+from the third one and we get one one
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+2 0 1 2 1
+
+ align:start position:0%
+2 0 1 2 1
+ 
+
+ align:start position:0%
+2 0 1 2 1
+0 0 K minus
+
+ align:start position:0%
+0 0 K minus
+ 
+
+ align:start position:0%
+0 0 K minus
+5 and then
+
+ align:start position:0%
+5 and then
+ 
+
+ align:start position:0%
+5 and then
+zero and this was achieved
+
+ align:start position:0%
+zero and this was achieved
+ 
+
+ align:start position:0%
+zero and this was achieved
+by the elementary Matrix e32 which was
+
+ align:start position:0%
+by the elementary Matrix e32 which was
+ 
+
+ align:start position:0%
+by the elementary Matrix e32 which was
+one one one and then uh negative
+
+ align:start position:0%
+one one one and then uh negative
+ 
+
+ align:start position:0%
+one one one and then uh negative
+one okay because yeah we multiplied the
+
+ align:start position:0%
+one okay because yeah we multiplied the
+ 
+
+ align:start position:0%
+one okay because yeah we multiplied the
+second row by negative one and added it
+
+ align:start position:0%
+second row by negative one and added it
+ 
+
+ align:start position:0%
+second row by negative one and added it
+to the third
+
+ align:start position:0%
+to the third
+ 
+
+ align:start position:0%
+to the third
+one okay so we have the um we have we we
+
+ align:start position:0%
+one okay so we have the um we have we we
+ 
+
+ align:start position:0%
+one okay so we have the um we have we we
+got to uh Matrix which was which is
+
+ align:start position:0%
+got to uh Matrix which was which is
+ 
+
+ align:start position:0%
+got to uh Matrix which was which is
+upper
+
+ align:start position:0%
+upper
+ 
+
+ align:start position:0%
+upper
+triangular and we want to yeah we want
+
+ align:start position:0%
+triangular and we want to yeah we want
+ 
+
+ align:start position:0%
+triangular and we want to yeah we want
+to figure out for which value of the
+
+ align:start position:0%
+to figure out for which value of the
+ 
+
+ align:start position:0%
+to figure out for which value of the
+parameter K is this Matrix uh Matrix of
+
+ align:start position:0%
+parameter K is this Matrix uh Matrix of
+ 
+
+ align:start position:0%
+parameter K is this Matrix uh Matrix of
+full full rank well this pivot is this
+
+ align:start position:0%
+full full rank well this pivot is this
+ 
+
+ align:start position:0%
+full full rank well this pivot is this
+is a pivot this is a pivot and we want
+
+ align:start position:0%
+is a pivot this is a pivot and we want
+ 
+
+ align:start position:0%
+is a pivot this is a pivot and we want
+this one to be a pivot as well and that
+
+ align:start position:0%
+this one to be a pivot as well and that
+ 
+
+ align:start position:0%
+this one to be a pivot as well and that
+happens when uh K minus 5 is not zero
+
+ align:start position:0%
+happens when uh K minus 5 is not zero
+ 
+
+ align:start position:0%
+happens when uh K minus 5 is not zero
+okay so when K is different from
+
+ align:start position:0%
+okay so when K is different from
+ 
+
+ align:start position:0%
+okay so when K is different from
+five The Matrix a is a full Rank and
+
+ align:start position:0%
+five The Matrix a is a full Rank and
+ 
+
+ align:start position:0%
+five The Matrix a is a full Rank and
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+um the system ax equals to 237 has a
+
+ align:start position:0%
+um the system ax equals to 237 has a
+ 
+
+ align:start position:0%
+um the system ax equals to 237 has a
+unique
+
+ align:start position:0%
+unique
+ 
+
+ align:start position:0%
+unique
+solution now Part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B for which K do we have infinitely many
+
+ align:start position:0%
+B for which K do we have infinitely many
+ 
+
+ align:start position:0%
+B for which K do we have infinitely many
+solutions so when when when when are we
+
+ align:start position:0%
+solutions so when when when when are we
+ 
+
+ align:start position:0%
+solutions so when when when when are we
+in such a
+
+ align:start position:0%
+in such a
+ 
+
+ align:start position:0%
+in such a
+situation we are in such a situation
+
+ align:start position:0%
+situation we are in such a situation
+ 
+
+ align:start position:0%
+situation we are in such a situation
+when the null space of the Matrix a is
+
+ align:start position:0%
+when the null space of the Matrix a is
+ 
+
+ align:start position:0%
+when the null space of the Matrix a is
+non-trivial um so the no space will be
+
+ align:start position:0%
+non-trivial um so the no space will be
+ 
+
+ align:start position:0%
+non-trivial um so the no space will be
+non non-trivial when this K minus
+
+ align:start position:0%
+non non-trivial when this K minus
+ 
+
+ align:start position:0%
+non non-trivial when this K minus
+5 uh number here which is was the pivot
+
+ align:start position:0%
+5 uh number here which is was the pivot
+ 
+
+ align:start position:0%
+5 uh number here which is was the pivot
+in the first case is zero
+
+ align:start position:0%
+in the first case is zero
+ 
+
+ align:start position:0%
+in the first case is zero
+so K minus 5 equals to
+
+ align:start position:0%
+so K minus 5 equals to
+ 
+
+ align:start position:0%
+so K minus 5 equals to
+zero you see yeah there's a little
+
+ align:start position:0%
+zero you see yeah there's a little
+ 
+
+ align:start position:0%
+zero you see yeah there's a little
+caveat here um when yeah K is equal to
+
+ align:start position:0%
+caveat here um when yeah K is equal to
+ 
+
+ align:start position:0%
+caveat here um when yeah K is equal to
+five we get the third row of the
+
+ align:start position:0%
+five we get the third row of the
+ 
+
+ align:start position:0%
+five we get the third row of the
+augmented Matrix 0 0 0 equal to Z this
+
+ align:start position:0%
+augmented Matrix 0 0 0 equal to Z this
+ 
+
+ align:start position:0%
+augmented Matrix 0 0 0 equal to Z this
+means that the Matrix is actually
+
+ align:start position:0%
+means that the Matrix is actually
+ 
+
+ align:start position:0%
+means that the Matrix is actually
+consistent and we indeed have a solution
+
+ align:start position:0%
+consistent and we indeed have a solution
+ 
+
+ align:start position:0%
+consistent and we indeed have a solution
+but if this entry were non zero then we
+
+ align:start position:0%
+but if this entry were non zero then we
+ 
+
+ align:start position:0%
+but if this entry were non zero then we
+would get no Solutions
+
+ align:start position:0%
+would get no Solutions
+ 
+
+ align:start position:0%
+would get no Solutions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now off to part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C we want to compute the lud de
+
+ align:start position:0%
+C we want to compute the lud de
+ 
+
+ align:start position:0%
+C we want to compute the lud de
+composition well we already got what the
+
+ align:start position:0%
+composition well we already got what the
+ 
+
+ align:start position:0%
+composition well we already got what the
+uh matx U is through yeah performing
+
+ align:start position:0%
+uh matx U is through yeah performing
+ 
+
+ align:start position:0%
+uh matx U is through yeah performing
+grow operations it's is this guy here
+
+ align:start position:0%
+grow operations it's is this guy here
+ 
+
+ align:start position:0%
+grow operations it's is this guy here
+let me write it
+
+ align:start position:0%
+let me write it
+ 
+
+ align:start position:0%
+let me write it
+down 1 one one 0 1 2 0 0 K -
+
+ align:start position:0%
+down 1 one one 0 1 2 0 0 K -
+ 
+
+ align:start position:0%
+down 1 one one 0 1 2 0 0 K -
+5 and when K is equal to 4 this entry is
+
+ align:start position:0%
+5 and when K is equal to 4 this entry is
+ 
+
+ align:start position:0%
+5 and when K is equal to 4 this entry is
+NE
+
+ align:start position:0%
+NE
+ 
+
+ align:start position:0%
+NE
+-1 okay and now what about the Matrix L
+
+ align:start position:0%
+-1 okay and now what about the Matrix L
+ 
+
+ align:start position:0%
+-1 okay and now what about the Matrix L
+well well how did we get to this U we
+
+ align:start position:0%
+well well how did we get to this U we
+ 
+
+ align:start position:0%
+well well how did we get to this U we
+had the Matrix a we got the Matrix U and
+
+ align:start position:0%
+had the Matrix a we got the Matrix U and
+ 
+
+ align:start position:0%
+had the Matrix a we got the Matrix U and
+what we did was first we applied
+
+ align:start position:0%
+what we did was first we applied
+ 
+
+ align:start position:0%
+what we did was first we applied
+a21 then we applied a31 E31 and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e32
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a a is we get a by inverting this
+
+ align:start position:0%
+so a a is we get a by inverting this
+ 
+
+ align:start position:0%
+so a a is we get a by inverting this
+equation so it's going to be e 21
+
+ align:start position:0%
+equation so it's going to be e 21
+ 
+
+ align:start position:0%
+equation so it's going to be e 21
+inverse E31 inverse
+
+ align:start position:0%
+inverse E31 inverse
+ 
+
+ align:start position:0%
+inverse E31 inverse
+e32 inverse * U and this is
+
+ align:start position:0%
+e32 inverse * U and this is
+ 
+
+ align:start position:0%
+e32 inverse * U and this is
+our Matrix
+
+ align:start position:0%
+our Matrix
+ 
+
+ align:start position:0%
+our Matrix
+L and we know it's fairly easy to invert
+
+ align:start position:0%
+L and we know it's fairly easy to invert
+ 
+
+ align:start position:0%
+L and we know it's fairly easy to invert
+these Elementary matrices e we just yeah
+
+ align:start position:0%
+these Elementary matrices e we just yeah
+ 
+
+ align:start position:0%
+these Elementary matrices e we just yeah
+we flip the signs of the of diagonal
+
+ align:start position:0%
+we flip the signs of the of diagonal
+ 
+
+ align:start position:0%
+we flip the signs of the of diagonal
+entries Okay so
+
+ align:start position:0%
+entries Okay so
+ 
+
+ align:start position:0%
+entries Okay so
+um I'm not going to write down the the
+
+ align:start position:0%
+um I'm not going to write down the the
+ 
+
+ align:start position:0%
+um I'm not going to write down the the
+again the inverses of of these guys um
+
+ align:start position:0%
+again the inverses of of these guys um
+ 
+
+ align:start position:0%
+again the inverses of of these guys um
+I'm yeah I'm just going to write the
+
+ align:start position:0%
+I'm yeah I'm just going to write the
+ 
+
+ align:start position:0%
+I'm yeah I'm just going to write the
+product of the inverses and that's also
+
+ align:start position:0%
+product of the inverses and that's also
+ 
+
+ align:start position:0%
+product of the inverses and that's also
+very easy um to to compute because when
+
+ align:start position:0%
+very easy um to to compute because when
+ 
+
+ align:start position:0%
+very easy um to to compute because when
+we invert the signs we just um send the
+
+ align:start position:0%
+we invert the signs we just um send the
+ 
+
+ align:start position:0%
+we invert the signs we just um send the
+numbers in
+
+ align:start position:0%
+numbers in
+ 
+
+ align:start position:0%
+numbers in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+their corresponding entry available I
+
+ align:start position:0%
+their corresponding entry available I
+ 
+
+ align:start position:0%
+their corresponding entry available I
+mean the following thing so minus one
+
+ align:start position:0%
+mean the following thing so minus one
+ 
+
+ align:start position:0%
+mean the following thing so minus one
+becomes a one
+
+ align:start position:0%
+becomes a one
+ 
+
+ align:start position:0%
+becomes a one
+and uh it comes here in its respective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entry for E yeah for E
+
+ align:start position:0%
+entry for E yeah for E
+ 
+
+ align:start position:0%
+entry for E yeah for E
+31 this becomes we flip the sign first
+
+ align:start position:0%
+31 this becomes we flip the sign first
+ 
+
+ align:start position:0%
+31 this becomes we flip the sign first
+three and we plug it in
+
+ align:start position:0%
+three and we plug it in
+ 
+
+ align:start position:0%
+three and we plug it in
+here and for e32 we we flip the sign of
+
+ align:start position:0%
+here and for e32 we we flip the sign of
+ 
+
+ align:start position:0%
+here and for e32 we we flip the sign of
+this guy becomes one and we plug it in
+
+ align:start position:0%
+this guy becomes one and we plug it in
+ 
+
+ align:start position:0%
+this guy becomes one and we plug it in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so give me a few moments to erase
+
+ align:start position:0%
+okay so give me a few moments to erase
+ 
+
+ align:start position:0%
+okay so give me a few moments to erase
+the board and then I I'll do part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four okay we're back and we're going to
+
+ align:start position:0%
+four okay we're back and we're going to
+ 
+
+ align:start position:0%
+four okay we're back and we're going to
+do Part D now
+
+ align:start position:0%
+do Part D now
+ 
+
+ align:start position:0%
+do Part D now
+um okay so we need to find the complete
+
+ align:start position:0%
+um okay so we need to find the complete
+ 
+
+ align:start position:0%
+um okay so we need to find the complete
+solution of the system for all K and we
+
+ align:start position:0%
+solution of the system for all K and we
+ 
+
+ align:start position:0%
+solution of the system for all K and we
+saw that for k equal to 5 the system um
+
+ align:start position:0%
+saw that for k equal to 5 the system um
+ 
+
+ align:start position:0%
+saw that for k equal to 5 the system um
+had many many solutions and for K not
+
+ align:start position:0%
+had many many solutions and for K not
+ 
+
+ align:start position:0%
+had many many solutions and for K not
+equal to 5 it had only one okay so first
+
+ align:start position:0%
+equal to 5 it had only one okay so first
+ 
+
+ align:start position:0%
+equal to 5 it had only one okay so first
+let's uh look at the case k not equal to
+
+ align:start position:0%
+let's uh look at the case k not equal to
+ 
+
+ align:start position:0%
+let's uh look at the case k not equal to
+5 when the Matrix a was was
+
+ align:start position:0%
+5 when the Matrix a was was
+ 
+
+ align:start position:0%
+5 when the Matrix a was was
+invertible um the well we can it's it's
+
+ align:start position:0%
+invertible um the well we can it's it's
+ 
+
+ align:start position:0%
+invertible um the well we can it's it's
+not hard to see what the solution of the
+
+ align:start position:0%
+not hard to see what the solution of the
+ 
+
+ align:start position:0%
+not hard to see what the solution of the
+system then is um it's going to be let
+
+ align:start position:0%
+system then is um it's going to be let
+ 
+
+ align:start position:0%
+system then is um it's going to be let
+me just write it down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when K is not equal to
+
+ align:start position:0%
+so when K is not equal to
+ 
+
+ align:start position:0%
+so when K is not equal to
+5 this was non zero therefore um X3
+
+ align:start position:0%
+5 this was non zero therefore um X3
+ 
+
+ align:start position:0%
+5 this was non zero therefore um X3
+needs to be zero
+
+ align:start position:0%
+needs to be zero
+ 
+
+ align:start position:0%
+needs to be zero
+right when X3 is zero we have X2 + 2 *
+
+ align:start position:0%
+right when X3 is zero we have X2 + 2 *
+ 
+
+ align:start position:0%
+right when X3 is zero we have X2 + 2 *
+X3 so X2 + 0 = 1 therefore X2 is
+
+ align:start position:0%
+X3 so X2 + 0 = 1 therefore X2 is
+ 
+
+ align:start position:0%
+X3 so X2 + 0 = 1 therefore X2 is
+1 and then we go back to the first row
+
+ align:start position:0%
+1 and then we go back to the first row
+ 
+
+ align:start position:0%
+1 and then we go back to the first row
+we have X1 + X2 + X3 = 2 so X1 + 1 + 0 =
+
+ align:start position:0%
+we have X1 + X2 + X3 = 2 so X1 + 1 + 0 =
+ 
+
+ align:start position:0%
+we have X1 + X2 + X3 = 2 so X1 + 1 + 0 =
+2 so X1 + 1 = 2 and therefore X1 is
+
+ align:start position:0%
+2 so X1 + 1 = 2 and therefore X1 is
+ 
+
+ align:start position:0%
+2 so X1 + 1 = 2 and therefore X1 is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+good now what
+
+ align:start position:0%
+good now what
+ 
+
+ align:start position:0%
+good now what
+about k equal to
+
+ align:start position:0%
+about k equal to
+ 
+
+ align:start position:0%
+about k equal to
+5 then we see that X3 is a free variable
+
+ align:start position:0%
+5 then we see that X3 is a free variable
+ 
+
+ align:start position:0%
+5 then we see that X3 is a free variable
+Okay so the solution will be X1 X2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X3 three can be X3 can be
+
+ align:start position:0%
+X3 three can be X3 can be
+ 
+
+ align:start position:0%
+X3 three can be X3 can be
+any number
+
+ align:start position:0%
+any number
+ 
+
+ align:start position:0%
+any number
+c from the second row we'll get the
+
+ align:start position:0%
+c from the second row we'll get the
+ 
+
+ align:start position:0%
+c from the second row we'll get the
+value of X2 it's 1 - 2 * X3 so 1 - 2 *
+
+ align:start position:0%
+value of X2 it's 1 - 2 * X3 so 1 - 2 *
+ 
+
+ align:start position:0%
+value of X2 it's 1 - 2 * X3 so 1 - 2 *
+C and uh X1 is 2 minus X it's 2 2 - X1 -
+
+ align:start position:0%
+C and uh X1 is 2 minus X it's 2 2 - X1 -
+ 
+
+ align:start position:0%
+C and uh X1 is 2 minus X it's 2 2 - X1 -
+x sorry 2 * 2 - X2 - X3 so let me
+
+ align:start position:0%
+x sorry 2 * 2 - X2 - X3 so let me
+ 
+
+ align:start position:0%
+x sorry 2 * 2 - X2 - X3 so let me
+rewrite this as 2 minus X2 is 1
+
+ align:start position:0%
+rewrite this as 2 minus X2 is 1
+ 
+
+ align:start position:0%
+rewrite this as 2 minus X2 is 1
+minus chalk 2 C minus c 1 - 2 c
+
+ align:start position:0%
+minus chalk 2 C minus c 1 - 2 c
+ 
+
+ align:start position:0%
+minus chalk 2 C minus c 1 - 2 c
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+okay so we'll decompose this Vector here
+
+ align:start position:0%
+okay so we'll decompose this Vector here
+ 
+
+ align:start position:0%
+okay so we'll decompose this Vector here
+into a component which is independent of
+
+ align:start position:0%
+into a component which is independent of
+ 
+
+ align:start position:0%
+into a component which is independent of
+c and a component which is a multiple of
+
+ align:start position:0%
+c and a component which is a multiple of
+ 
+
+ align:start position:0%
+c and a component which is a multiple of
+C okay so this is um 2 - 1 should be 1 1
+
+ align:start position:0%
+C okay so this is um 2 - 1 should be 1 1
+ 
+
+ align:start position:0%
+C okay so this is um 2 - 1 should be 1 1
+Z plus C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+* we'll have 2 C minus c c so C *
+
+ align:start position:0%
+* we'll have 2 C minus c c so C *
+ 
+
+ align:start position:0%
+* we'll have 2 C minus c c so C *
+1 uh here we'll have minus 2 C so -2 and
+
+ align:start position:0%
+1 uh here we'll have minus 2 C so -2 and
+ 
+
+ align:start position:0%
+1 uh here we'll have minus 2 C so -2 and
+here we'll have
+
+ align:start position:0%
+here we'll have
+ 
+
+ align:start position:0%
+here we'll have
+one and thus we get the particular
+
+ align:start position:0%
+one and thus we get the particular
+ 
+
+ align:start position:0%
+one and thus we get the particular
+solution for the system and the special
+
+ align:start position:0%
+solution for the system and the special
+ 
+
+ align:start position:0%
+solution for the system and the special
+solution for the
+
+ align:start position:0%
+solution for the
+ 
+
+ align:start position:0%
+solution for the
+system okay we're kind of done here uh
+
+ align:start position:0%
+system okay we're kind of done here uh
+ 
+
+ align:start position:0%
+system okay we're kind of done here uh
+if you're at an exam you should
+
+ align:start position:0%
+if you're at an exam you should
+ 
+
+ align:start position:0%
+if you're at an exam you should
+immediately start the next problem good
+
+ align:start position:0%
+immediately start the next problem good
+ 
+
+ align:start position:0%
+immediately start the next problem good
+luck and I'll see you later
\ No newline at end of file
diff --git a/FBpe3xFvPrQ.txt b/FBpe3xFvPrQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ba940bfc04f48a483e06ba15802c5c9ea746767e
--- /dev/null
+++ b/FBpe3xFvPrQ.txt
@@ -0,0 +1,1776 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Good morning,
+everybody.
+
+Let's go back to
+where we were.
+
+We were talking about abstract
+data types and the notion of
+
+object oriented programming.
+
+And in particular, the role
+of classes in all of that.
+
+A lot of people think this
+notion of object oriented
+
+programming is a new notion.
+
+In fact, it's not.
+
+It's been around for probably
+at least 35
+
+years, maybe even longer.
+
+But it's only been widely
+practiced for maybe 15 years.
+
+Even that to most of you will
+seem like a long time.
+
+It started in the mid 1970s
+when people began to write
+
+articles explaining this
+advantage of the approach to
+
+programming.
+
+And at about the same time,
+the language Smalltalk was
+
+developed at Xerox Park and
+CLU developed at MIT.
+
+And they were the first
+languages that, in an elegant
+
+way, provided linguistic support
+for this style of
+
+programming.
+
+But it didn't really take off
+in the public until the
+
+introduction of Java,
+considerably later.
+
+And Java was the first popular
+language to support object
+
+oriented programming.
+
+After that there was C++, which
+supports it in not a
+
+very elegant but a usable way.
+
+And today probably Python is the
+fastest growing language
+
+supporting object oriented
+programming.
+
+It's used widely, and
+that's one of the
+
+reasons we teach it here.
+
+As I said, at the bottom of it
+all, the most fundamental
+
+notion is that of an
+abstract data type.
+
+And the idea is that we can
+extend our programming
+
+language by adding user
+defined types.
+
+And we'll shortly see why that's
+such a useful thing.
+
+And that these types can be used
+just as easily as any of
+
+the built in types.
+
+Why do we call them abstract
+data types rather than just
+
+data types?
+
+We do that because we are
+essentially going to define
+
+for each type an interface.
+
+And essentially, what the
+interface does is it explains
+
+what the methods do.
+
+What do I mean by
+what they do?
+
+What they do at the level of the
+user, not how they do it.
+
+That, of course, is the way
+the built in types work.
+
+It wasn't until Tuesday that you
+understood how Python made
+
+dicts do what they do.
+
+Before then, I just explained,
+that you could put in a key
+
+and a value, and you could
+look it up and do an
+
+associative retrieval.
+
+It was maybe not magic, but it
+was wonderful that you could
+
+do this and not have to bother
+your heads with how it was
+
+made to work.
+
+And that was because we
+provided, or the designers of
+
+Python provided, an interface
+that lets you use it.
+
+We'll do the same thing with
+the abstract data types.
+
+The key idea here is one we've
+talked about before and that's
+
+a specification.
+
+It is the specification of a
+type, or of a function, or of
+
+a method, that tells us
+what that thing does.
+
+And we'll now until the end of
+the term try and maintain a
+
+very clear distinction between
+specifications and
+
+implementations.
+
+Let's look at an example.
+
+So the example should
+be familiar to you.
+
+You will remember that on
+Tuesday at the start of the
+
+lecture, we looked at how we
+could use hashing to implement
+
+a set of integers.
+
+And I explained to you that I
+wasn't very happy with the
+
+implementation because
+of the way it
+
+used this global variable.
+
+Now we're going to see a much
+more elegant approach.
+
+So I'm going to define a new
+abstract type called intSet.
+
+I do that by writing the word,
+class, followed by
+
+the name of the class.
+
+And then there's this funny
+thing saying that it is a
+
+subclass of objects.
+
+Ignore that for now.
+
+And I'm going to come
+back to it later.
+
+But fundamentally what it's
+saying is that every instance
+
+of intSet is an object.
+
+That's not very interesting
+because everything in Python
+
+is an object.
+
+So from an information theoretic
+point of view,
+
+there's no information here.
+
+Later we'll see that we can use
+this mechanism in a more
+
+interesting way.
+
+Now let's look at the methods.
+
+So first I tell you a comment,
+it's a set of integers.
+
+Then I've got this funny
+method called underbar
+
+underbar init.
+
+Whenever you see something with
+an underbar underbar in
+
+its name, it has a special
+status in Python that lets us
+
+do elegant things
+with the syntax.
+
+What will happen every time I
+create a new object of type
+
+intSet, the underbar underbar
+init method, or function, of
+
+the class will be executed
+on that object.
+
+What it will do, in this case,
+is introduce two attributes of
+
+the object.
+
+The attributes are numBuckets
+which is now replacing the
+
+global variable we looked
+at last time.
+
+And I've arbitrarily
+chosen 47.
+
+And Vals.
+
+This will be the hash table
+itself containing the values.
+
+And then, exactly as we did
+on Tuesday, I'm going to
+
+initialize the values so that
+each element of this list is
+
+now an empty list.
+
+Now what's going on with this
+funny notion of self.
+
+Let's look at an example here.
+
+I'm going to say s equals
+intSet open close.
+
+This will create a new intSet
+object, execute the underbar
+
+underbar init.
+
+So if, for example, I print
+self.numBuckets--
+
+whoops, can't do that because
+self is not defined in this
+
+environment.
+
+Self was a local variable to
+underbar underbar init.
+
+In fact, the formal parameter.
+
+But I can write s.numBuckets,
+and I'll see it's 47.
+
+NumBuckets and Val are
+now attributes of s.
+
+Attributes of the instance
+s of the class intSet.
+
+And I [[UNINTELLIGIBLE]
+
+what we would expect.
+
+Yes?
+
+AUDIENCE: You didn't put any
+object in between the
+
+parentheses.
+
+PROFESSOR: Yes.
+
+So that--
+
+the question is well, it looks
+like underbar underbar intSet
+
+or underbar underbar init
+has a formal parameter.
+
+And I've given it no
+
+corresponding actual parameter.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yes.
+
+Let me finish.
+
+So that's what it looks like.
+
+And that's the magic
+of this syntax.
+
+It automatically passes
+an implicit object,
+
+or it creates one.
+
+It's a very special role for
+underbar underbar init.
+
+Self is used to refer to the
+object being created.
+
+I'm going to come back in a
+minute to discuss more fully
+
+the concept of self and
+how it's used here.
+
+So just give me a minute
+to get there.
+
+The next thing we
+see is hashE.
+
+This is something we looked
+at again on Tuesday.
+
+It's a private function in this
+case that I don't intend
+
+to be used outside the class.
+
+So if we think of the
+specifications here, the
+
+interface of the class, it
+does not include hashE.
+
+That's what private
+means here.
+
+This is a convention.
+
+It's not enforced
+by the language.
+
+And unfortunately, as we'll see,
+a lot of useful things
+
+are not enforced by
+the language.
+
+But nevertheless, good
+programmers follow the
+
+conventions.
+
+And we expect you guys to do so
+as well because, of course,
+
+you're good programmers.
+
+So this doesn't do anything
+very exciting.
+
+It's just what we saw.
+
+Insert is more interesting.
+
+Let's look at what that does.
+
+It apparently takes two
+arguments, the formals named
+
+self and E and inserts
+E into self.vals.
+
+However, if we go look at the
+code that uses it in say
+
+testone what you'll note is I'm
+saying for i in range 40--
+
+this is just like the testone
+we looked at Tuesday.
+
+I'm going to say
+s.insert of i.
+
+It looks like I'm calling insert
+with only one argument,
+
+but as we discussed last time,
+this s before the dot is
+
+actually the first argument
+to the method insert.
+
+And so it's getting two
+arguments really.
+
+And by convention, that implicit
+first argument is
+
+always called self in Python.
+
+It's not enforced.
+
+You could call it George if you
+preferred, or Alice, or
+
+whatever you like.
+
+But if you do, you will confuse
+the heck out of
+
+anybody who ever reads your
+code, including any
+
+TA you ask for help.
+
+So please do use self.
+
+It's just a name.
+
+It has nothing to do with
+what a philosopher, or a
+
+psychologist, or an ethicist
+might think as the concept of
+
+self, this wonderful
+elevated concept.
+
+It's none of those.
+
+It's just a name.
+
+But stick to using that name.
+
+So if we go back, I can insert
+a bunch of things.
+
+I'm going to then print s.
+
+That's kind of interesting.
+
+UnderBar underbar STR, underbar
+underbar is one of
+
+those special names as well.
+
+The code is pretty simple.
+
+All it is is returning a string
+
+representation of the set.
+
+And it could be anything
+you want.
+
+I chose sort of a conventional
+way of denoting sets.
+
+What's interesting
+is that it gets
+
+automatically called by print.
+
+So when I write the command,
+print s, in test one, the
+
+Python interpreter is smart
+enough to know oh, I better
+
+take s, convert it to a string,
+and then print it.
+
+How does it know to convert
+it to a string?
+
+It automatically invokes the
+underbar underbar STR method.
+
+And then the other operation
+is member, which again is
+
+exactly what we looked
+at before.
+
+But you'll notice in this code
+that uses intSets, I make no
+
+reference to the data attributes
+of the class
+
+directly, or I shouldn't.
+
+You'll notice that I wrote
+evil next to s.vals.
+
+Python will let me do
+it, but I shouldn't.
+
+Why shouldn't I do it?
+
+Why am I saying this is evil?
+
+Well, would you be happy if you
+got a message saying IDLE
+
+was changed.
+
+Please download a new version
+and the new version happened
+
+to have a different
+
+implementation of lists or dicts.
+
+And it caused all of your
+programs to stop working.
+
+You would be pretty unhappy.
+
+Now why won't that happen?
+
+Because your programs don't
+depend, in any way, on the way
+
+in which people chose to
+implement those built in types
+
+because you programmed to the
+specification of the types,
+
+not to the implementation.
+
+The specification of intSet
+did not mention Vals or
+
+numBuckets.
+
+Therefore, as the implementer of
+that class, I'm entitled to
+
+go back and change it.
+
+So I'm not going to use
+a hash table at all.
+
+I'm going to do something
+else.
+
+I'm going to use a red, black
+tree, or some other fancy
+
+implementation.
+
+I'm allowed to do that.
+
+And if I make that change, and
+Vals disappears and numBuckets
+
+disappears, your program should
+continue to work so
+
+long as I still meet
+the specification.
+
+The minute you go in and
+directly access the variables
+
+of the class, those attributes,
+you have used
+
+things that do not appear
+in this specification.
+
+And if I change the
+implementation, your program
+
+might break.
+
+So you shouldn't do that.
+
+Does that make sense
+to everybody?
+
+It's a very important concept.
+
+The concept is known
+as data hiding.
+
+It is really the most important
+development that
+
+makes abstract data
+types useful.
+
+It gives them the same status
+as the built in types.
+
+The minute you choose to
+ignore this, you do
+
+so at your own peril.
+
+Some programming languages, like
+Java, provide a mechanism
+
+to enforce data hiding.
+
+The designers of Python, for
+reasons I do not understand,
+
+chose not to.
+
+I think it is a flaw
+in the language.
+
+The things we're hiding are
+the instance variable.
+
+Those are the variables
+associated with each instance
+
+of the class.
+
+We should also hide
+class variables.
+
+We haven't seen those yet,
+and we'll see them later.
+
+The instance variables, we get
+a new copy of each time we
+
+created a new instance
+of the class, a new
+
+intSet in this case.
+
+The class variables
+are associated
+
+with the class itself.
+
+And you get only one
+copy of them.
+
+Later on, we'll see an
+example where class
+
+variables are useful.
+
+All right.
+
+So let's run this just to
+make sure it works.
+
+It does what we would expect.
+
+True/False.
+
+And then you'll see
+this nice string
+
+representation of the set.
+
+And then just to show you what
+happens when you do the evil
+
+thing, I printed as we did
+last time the actual
+
+list that came out.
+
+Let's now look at a more
+interesting example.
+
+And the idea I want to convey
+here is how we use classes and
+
+abstract data types to
+design programs.
+
+So imagine that you're writing a
+program to keep track of all
+
+the students, faculty, and
+maybe staff at MIT.
+
+It's certainly possible to write
+that program without
+
+using any classes.
+
+For each student, you might
+give them a family name, a
+
+given name, a home address,
+years, grades, et cetera.
+
+And you could do this with some
+complicated combination
+
+of lists and dictionaries.
+
+But it wouldn't be
+very elegant.
+
+So what I want to do before
+writing that program--
+
+and I won't actually
+write that program.
+
+I'll just write some of the
+classes we can use--
+
+I want to pull back and
+think about what
+
+abstractions would be useful.
+
+So this style of programming
+in which you organize your
+
+programs around abstract data
+types says before we write the
+
+code in detail, we think about
+these types that would make it
+
+easy to write the code.
+
+So for example, if you were
+a finance student, and you
+
+wanted to write some code
+dealing with markets, you
+
+might want to have an
+abstraction of a government
+
+bond, and another abstraction
+of an equity, and an
+
+extraction of a call option.
+
+Whatever you want it.
+
+But you'd say I want to think at
+that level of abstraction.
+
+I don't want to think about
+lists, and dicts, and floats.
+
+I just want to think about
+options, which have a strike
+
+price, a date, and
+things like that.
+
+Similarly, as I'm working on
+this database for MIT, I want
+
+to think about abstractions
+of students, and
+
+faculty, and staff.
+
+I'm also going to use what's
+called inheritance to set up a
+
+hierarchy of these.
+
+And the reason I'm going to do
+that is I want to be able to
+
+share a code.
+
+I know that there will be
+certain similarities between
+
+students and faculty.
+
+Some differences too.
+
+But I want to begin by saying
+what's not different?
+
+What's similar?
+
+What's the same?
+
+So that I only have to
+implement it once and
+
+get to reuse it.
+
+So if I pull back and say is
+there an abstraction that
+
+covers the shared attributes of
+students, and faculty, and
+
+staff, I might say
+it's a person.
+
+They're all people.
+
+And it's arguable whether every
+faculty member is a
+
+human being, but for
+now let's pretend.
+
+And so I'm going to start with
+this abstraction person.
+
+I'm going to import something
+called DateTime.
+
+I'll show you what we're doing
+when we get there.
+
+But it's like we've imported
+math before.
+
+This is a class somebody else
+wrote that deals with dates
+
+and time in a fairly
+reasonable way.
+
+So I'm going to import that
+here into person.
+
+Probably didn't need
+to import it twice.
+
+Maybe I'll just simplify it by
+getting rid of this one.
+
+UnderBar underbar init
+here will create a
+
+person with name 'Name'.
+
+And you'll notice what I'm doing
+here is introducing an
+
+extra attribute lastName
+-- self.lastName.
+
+And that's because I just want
+to make life easy for myself.
+
+I figure I'll want to find
+the last name frequently.
+
+Let's once and for all get it
+and put it in something.
+
+And I'm going to initialize
+birthday to none.
+
+The next attribute, or the next
+method, is get lastName.
+
+I have that here because I
+don't want users of this
+
+abstraction to even know that
+I have an attribute
+
+self.lastname.
+
+That's part of the
+implementation.
+
+And so I have this method
+that fetches it.
+
+And you'll see as you build
+classes that you often have
+
+things called get.
+
+And those are typically methods
+that return some
+
+information about an instance
+of the class.
+
+You'll also frequently have set
+methods, for example, set
+
+birthday that gives values to
+instances of the class.
+
+More interestingly,
+I have get age.
+
+And that's using some of the
+built in operations on
+
+DateTime conveniently.
+
+It allows me to subtract one
+date from another and get a
+
+number of days.
+
+So this will allow me to return
+somebody's age in days.
+
+Then I've got another underbar
+underbar method we
+
+haven't seen yet.
+
+lt stands for less than.
+
+Not a big surprise.
+
+And I'm going to use this to
+order names, or order people.
+
+Why am I using a special
+operator rather than just
+
+putting in the method
+L-E-S-S-T-H. A-N?
+
+E-N?
+
+I'm doing that because I want
+to be able to write things
+
+like p1 less than
+p2 in my code.
+
+And Python will take that and
+turn it into the underbar
+
+underbar LT.
+
+Better yet, if I have a list say
+of person's, I can use the
+
+built in sort operator on that
+list, and it will be smart
+
+enough to know when it's
+comparing two people to do the
+
+sort to use the underbar
+underbar LT.
+
+Very convenient kind of thing.
+
+Let's look at an example.
+
+Let's look at some code.
+
+So I'm going to set me to John
+Guttag, and him to Barack
+
+Hussein Obama, her to Madonna.
+
+And we'll print some things.
+
+So I printed him, and I printed
+him.getlastName.
+
+I can now set some birthdays.
+
+Let's look at this line.
+
+How do you feel about
+him.birthday equals 8/4/61?
+
+We'll come back to it.
+
+But I want you to
+think about it.
+
+And we see that Obama is--
+
+well, we see their ages here.
+
+Actually, we see that
+Madonna is older.
+
+She looks really old when you
+look at that number of days,
+
+doesn't it.
+
+Maybe she is.
+
+Now what's going
+to happen here?
+
+I messed up.
+
+And I messed up because I went
+in and directly accessed the
+
+instance variable and assigned
+it what I thought was a
+
+reasonable representation
+of a birthdate.
+
+But I shouldn't have because
+that's not even the
+
+appropriate type.
+
+It's a string rather than
+something from DateTime.
+
+So again, we see the impact of
+my having done this evil thing
+
+of violating the abstraction
+boundary and stuck in there
+
+try to directly access
+an instance variable.
+
+We can do some comparisons.
+
+And what we see is that I'm
+not less than Madonna.
+
+I guess that's OK.
+
+You with me so far?
+
+I can make a list of these
+things and print the list.
+
+So it does a fairly nice job
+calling the underbar underbar
+
+STR operator.
+
+And you'll note I had no trouble
+throwing objects of
+
+type person into the list.
+
+No different than putting
+ints, or floats,
+
+or any of the built-ins.
+
+So it all works nicely.
+
+And then I can sort
+it and print that.
+
+And now the lists come out in a
+different order because it's
+
+using the underbar underbar LT
+operator to sort the elements.
+
+All of this is just by way of
+showing you how convenient it
+
+is to write code that uses
+a data abstraction.
+
+If we go back and look at the
+code, we'll see that once
+
+again person was a subclass
+of object.
+
+That's why we can do all
+these things we've
+
+been doing with it.
+
+But now I'm going to start
+using the hierarchy.
+
+MIT people are special.
+
+I hate to say that because
+I know we have non-MIT
+
+people in the room.
+
+But MIT people are special.
+
+Well here's at least
+one of the special
+
+attributes of MIT people.
+
+They all have an ID.
+
+So I'm now going to say
+an MIT person is a
+
+special subclass of person.
+
+So it has all of the properties
+of a person.
+
+And the way we describe that is
+it inherits the properties
+
+of the super class.
+
+And it adds a property.
+
+We can now assign
+an ID number.
+
+And now we're going to see the
+thing I promised to show you,
+
+which is a class variable.
+
+Next ID num is not associated
+with an instance of MIT
+
+person, but it's associated
+with the class itself.
+
+It's a class variable.
+
+I can do that because classes
+are themselves objects.
+
+And the advantage of this is
+every time I get a new
+
+instance of this class, I
+can assign a unique ID.
+
+Similar to the way we were using
+global variables earlier
+
+in the term, typically once we
+have classes, we'd stop using
+
+global variables because we have
+these class variables,
+
+which can serve very much the
+same purpose in many cases.
+
+And so now every time I get a
+new MIT person, I give them an
+
+ID and then increment the ID
+number so that the next person
+
+will get a different one.
+
+So I added a property, this ID
+number property, which I find
+
+by get ID num.
+
+I've also overwritten an
+existing property.
+
+You'll note that I've changed
+the definition of underbar
+
+underbar LT.
+
+So it's now saying we're going
+to compare two people not on
+
+the basis of their
+names but on the
+
+basis of their ID numbers.
+
+So let's look at some
+code that uses this.
+
+Get rid of the other
+code so it doesn't
+
+clutter up the screen.
+
+So we'll look at some
+things here.
+
+We'll get some MIT people
+called p1, p2, and p3.
+
+And we'll print their ID nums
+by calling get ID num.
+
+And you can see that Barbara
+Beaver gets 0, and the first
+
+Sue Wong gets 1, and the second
+Sue Wong has ID 2.
+
+I can create even a
+third such person.
+
+And now let's think about
+what happens here.
+
+I'm going to print whether or
+not p1 is less than p2 and
+
+whether or not p3
+is less than p2.
+
+What should we get
+when we do this?
+
+Somebody?
+
+Pardon?
+
+AUDIENCE: True and false.
+
+PROFESSOR: I heard
+a true false.
+
+And indeed that's right because
+it's comparing IDs.
+
+Now, suppose I want
+to compare names.
+
+I could if I chose do this.
+
+I could call person underbar
+underbar LT.
+
+And what this says
+is don't use the
+
+less than of the subclass.
+
+Go up and use the super class
+one to do the comparison.
+
+So it's going up
+and doing that.
+
+I can do other things.
+
+I can compare things
+for equality.
+
+Let me just rip through all of
+these and see what we get.
+
+Whoops.
+
+Surprise!
+
+Well, before we get
+to that surprise--
+
+and it's not actually
+a surprise.
+
+I shouldn't have
+uncommented it.
+
+Let's look at the other ones.
+
+We can say is p1 equal to p4?
+
+And we discover it's not.
+
+That's good.
+
+And we can say is
+p4 less than p3?
+
+That all works.
+
+It's not.
+
+But I can't say p3
+less than p4.
+
+And why can't I do that?
+
+Why did I get an error message
+when I did that?
+
+Yes?
+
+Someone wanted to answer that?
+
+AUDIENCE: That's because you
+mix [UNINTELLIGIBLE]?
+
+PROFESSOR: Can you say
+that more loudly?
+
+AUDIENCE: She's a person,
+not an MIT person.
+
+So you didn't assign
+her an ID number.
+
+PROFESSOR: Exactly right.
+
+The answer--
+
+I hit somebody right
+on the head.
+
+Now there's going to be a
+traumatic brain injury.
+
+I'm going to get sued.
+
+It's going to be messy.
+
+Time to leave the country.
+
+All right.
+
+Because it looks at p3 less than
+p4, looks at the first
+
+argument, which is p3, and says
+OK, what's the underbar
+
+underbar LT associated
+with p3?
+
+It's the one associated
+with an MIT person.
+
+Let's go execute that.
+
+And then it tries to retrieve
+the ID number of p4, which is
+
+not an MIT person, and it
+gets an error message.
+
+All right.
+
+Nothing subtle.
+
+It's the same kind of thing
+we've seen all along when we
+
+use type errors.
+
+In this case it's called an
+attribute error because we've
+
+attempted to access an attribute
+of an instance that
+
+doesn't exist.
+
+And so we could catch it.
+
+It's raised an exception.
+
+We could catch it as we looked
+at Tuesday, but we're not
+
+going to do that because it's
+really a programming bug when
+
+that happens.
+
+OK, let's continue.
+
+We were interested
+in students.
+
+So we're going to continue
+our hierarchy here.
+
+And now I'm going to introduce
+a subclass of an MIT person
+
+called an UG, short
+for undergraduate.
+
+Underbar underbar init is
+going to call MIT person
+
+underbar underbar init, which
+will give the UG an ID number
+
+and a name.
+
+And it's going to introduce
+yet another instance
+
+attribute, or field,
+called the year.
+
+And so the year, initially,
+is none.
+
+Then I can set the year.
+
+Though if I try and set it as
+something greater than 5, I'm
+
+going to raise an overflow
+error called too many.
+
+No undergraduate should be
+a year greater than 5.
+
+And I can get the year.
+
+Let's look at what happens
+when we do that.
+
+So I'll have two UG's.
+
+Both happen to be
+named Jane Doe.
+
+And then the same MIT
+person as before.
+
+Let's run this code and see--
+well, what's going to happen?
+
+What's going to happen
+when I say print UG1?
+
+The first thing it's going to do
+is going to say is there an
+
+underbar underbar STR
+associated with UGs?
+
+And the answer is no.
+
+That's OK because I know an
+UG is also an MIT person.
+
+If I don't find it at the
+lowest level class, I'll
+
+bounce up and say all right, is
+there an underbar underbar
+
+STR associated with
+an MIT person?
+
+No.
+
+That's OK.
+
+I'll go up another level and
+say, well, I know an MIT
+
+person happens to be a person.
+
+And then they'll say oh, good
+there is an underbar underbar
+
+STR associated with person.
+
+So I'll use that one.
+
+So it looks at the class.
+
+If it doesn't find it, it
+goes to the super class.
+
+If it doesn't find it, it
+goes to the super class.
+
+And it does that all the way
+up until the end, where at
+
+worst, it will use the built-in
+thing for printing
+
+objects because remember
+everything is
+
+a subclass of objects.
+
+You don't want to do that.
+
+You want to have something more
+elegant than object at
+
+location xe345, or whatever
+if would have printed.
+
+Then we'll do some
+comparisons.
+
+It will first look for the most
+local and then work its
+
+way up as needed.
+
+OK?
+
+Let's keep going.
+
+We're going to introduce another
+kind of person called
+
+a graduate student.
+
+And I'm going to write pass.
+
+What that means is a G is an
+MIT person with no special
+
+properties, all the usual
+properties of an MIT person.
+
+Does not have a year because
+graduate students could be
+
+here more or less forever,
+which goes like
+
+this when I say that.
+
+Why did I introduce the type
+in the first place?
+
+Because it lets me
+do type checking.
+
+I can now check whether or not a
+person is a graduate student
+
+because an instance of G will
+have all of the properties of
+
+an MIT person, but it will
+have a different type.
+
+It will be type G.
+
+And so I can now ask the
+question is the type of this
+
+object a G. Or is it
+an MIT person and
+
+get a different answer.
+
+So I can do this.
+
+And if I go type of G1--
+
+well, that's interesting.
+
+It says classmain.G.
+
+It's going to upset its class.
+
+And the class is defined at the
+outermost level, which is
+
+called main.
+
+And the classes name is G,
+which is what we expect.
+
+And so I could write something
+like that.
+
+Type of G1 equals equals
+G. And I get True.
+
+Ok.
+
+So it's a handy thing
+to be able to do.
+
+And in fact, I'm now going to
+bounce back to MIT person and
+
+add another method to it.
+
+And this happens all the time
+when I'm programming that I go
+
+define a class, think I'm done,
+and then some time later
+
+decide that it would be
+convenient to add something
+
+new, another method.
+
+In this case, I'm now adding the
+method is student, which
+
+returns type of self equal equal
+UG or type of self equal
+
+equals G.
+
+So this will let me distinguish
+a student from
+
+another kind of MIT person.
+
+So for example, if I want
+to have a course list--
+
+another class, this is
+a subclass of object.
+
+You'll note I have an add
+student method, which takes
+
+self and who, maybe
+it should be whom.
+
+And it says, if not
+who.isstudent raise type error
+
+not a student.
+
+So I'm getting some leverage
+now out of this.
+
+Now I wouldn't need to
+necessarily do this.
+
+I could have said if not type
+of who equals G, or type of
+
+who equals UG.
+
+But I chose not to.
+
+The reason I chose not to is
+looking ahead, I might want to
+
+add some other students.
+
+I might want to add special
+student, for example.
+
+Or I might want to add cross
+registering student as
+
+separate types.
+
+Now, the nice thing is I don't
+have to make a lot of changes.
+
+I know there's exactly one place
+in my code that defines
+
+what it means to be
+an MIT student.
+
+I go back and I change
+that method.
+
+And even if I asked whether
+somebody's a student in a 100
+
+different places, I only
+have to make one
+
+change to fix my code.
+
+So I'm getting some modularity
+by associating the method with
+
+the class MIT person rather
+than every time
+
+I need to use it.
\ No newline at end of file
diff --git a/FscOJbr_bvs.txt b/FscOJbr_bvs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f1354921ad543beb1b7e74842476b3163c67fb69
--- /dev/null
+++ b/FscOJbr_bvs.txt
@@ -0,0 +1,1115 @@
+align:start position:0%
+ 
+welcome back to age 20. in this section
+
+ align:start position:0%
+welcome back to age 20. in this section
+ 
+
+ align:start position:0%
+welcome back to age 20. in this section
+we want to talk about
+
+ align:start position:0%
+we want to talk about
+ 
+
+ align:start position:0%
+we want to talk about
+cause and effect and causality
+
+ align:start position:0%
+cause and effect and causality
+ 
+
+ align:start position:0%
+cause and effect and causality
+and we do this with an example which
+
+ align:start position:0%
+and we do this with an example which
+ 
+
+ align:start position:0%
+and we do this with an example which
+talks about the good guys and the bad
+
+ align:start position:0%
+talks about the good guys and the bad
+ 
+
+ align:start position:0%
+talks about the good guys and the bad
+guys there's always good guys and bad
+
+ align:start position:0%
+guys there's always good guys and bad
+ 
+
+ align:start position:0%
+guys there's always good guys and bad
+guys in the universe in this example
+
+ align:start position:0%
+guys in the universe in this example
+ 
+
+ align:start position:0%
+guys in the universe in this example
+those two groups they were fighting a
+
+ align:start position:0%
+those two groups they were fighting a
+ 
+
+ align:start position:0%
+those two groups they were fighting a
+war and after some very long and cooling
+
+ align:start position:0%
+war and after some very long and cooling
+ 
+
+ align:start position:0%
+war and after some very long and cooling
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+they were able to sign a peace treaty so
+
+ align:start position:0%
+they were able to sign a peace treaty so
+ 
+
+ align:start position:0%
+they were able to sign a peace treaty so
+this happens in this story at year
+
+ align:start position:0%
+this happens in this story at year
+ 
+
+ align:start position:0%
+this happens in this story at year
+number zero so in year zero a peace
+
+ align:start position:0%
+number zero so in year zero a peace
+ 
+
+ align:start position:0%
+number zero so in year zero a peace
+treaty is signed and the good guys they
+
+ align:start position:0%
+treaty is signed and the good guys they
+ 
+
+ align:start position:0%
+treaty is signed and the good guys they
+go back to their families they go back
+
+ align:start position:0%
+go back to their families they go back
+ 
+
+ align:start position:0%
+go back to their families they go back
+home to their planet is a spacecraft
+
+ align:start position:0%
+home to their planet is a spacecraft
+ 
+
+ align:start position:0%
+home to their planet is a spacecraft
+which is able to go with a velocity of
+
+ align:start position:0%
+which is able to go with a velocity of
+ 
+
+ align:start position:0%
+which is able to go with a velocity of
+0.6 times the speed of light
+
+ align:start position:0%
+0.6 times the speed of light
+ 
+
+ align:start position:0%
+0.6 times the speed of light
+the bad guys
+
+ align:start position:0%
+the bad guys
+ 
+
+ align:start position:0%
+the bad guys
+are still bad guys and so they develop a
+
+ align:start position:0%
+are still bad guys and so they develop a
+ 
+
+ align:start position:0%
+are still bad guys and so they develop a
+faster than the speed of light
+
+ align:start position:0%
+faster than the speed of light
+ 
+
+ align:start position:0%
+faster than the speed of light
+spacecraft follow the good guys
+
+ align:start position:0%
+spacecraft follow the good guys
+ 
+
+ align:start position:0%
+spacecraft follow the good guys
+and they succeed with the development of
+
+ align:start position:0%
+and they succeed with the development of
+ 
+
+ align:start position:0%
+and they succeed with the development of
+the spacecraft after four years
+
+ align:start position:0%
+the spacecraft after four years
+ 
+
+ align:start position:0%
+the spacecraft after four years
+so they do they follow the good guys
+
+ align:start position:0%
+so they do they follow the good guys
+ 
+
+ align:start position:0%
+so they do they follow the good guys
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in year number five the bad guys attack
+
+ align:start position:0%
+in year number five the bad guys attack
+ 
+
+ align:start position:0%
+in year number five the bad guys attack
+and destroy the good
+
+ align:start position:0%
+and destroy the good
+ 
+
+ align:start position:0%
+and destroy the good
+guys so the challenge for you now is to
+
+ align:start position:0%
+guys so the challenge for you now is to
+ 
+
+ align:start position:0%
+guys so the challenge for you now is to
+explain the story and answer the
+
+ align:start position:0%
+explain the story and answer the
+ 
+
+ align:start position:0%
+explain the story and answer the
+following question
+
+ align:start position:0%
+following question
+ 
+
+ align:start position:0%
+following question
+when and where does the attack happen
+
+ align:start position:0%
+when and where does the attack happen
+ 
+
+ align:start position:0%
+when and where does the attack happen
+from the good guys perspective
+
+ align:start position:0%
+from the good guys perspective
+ 
+
+ align:start position:0%
+from the good guys perspective
+and when did the bad guys invent the
+
+ align:start position:0%
+and when did the bad guys invent the
+ 
+
+ align:start position:0%
+and when did the bad guys invent the
+spacecraft from the good guys
+
+ align:start position:0%
+spacecraft from the good guys
+ 
+
+ align:start position:0%
+spacecraft from the good guys
+perspective and you will see
+
+ align:start position:0%
+perspective and you will see
+ 
+
+ align:start position:0%
+perspective and you will see
+some surprising results in this another
+
+ align:start position:0%
+some surprising results in this another
+ 
+
+ align:start position:0%
+some surprising results in this another
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so please stop the video and try to work
+
+ align:start position:0%
+so please stop the video and try to work
+ 
+
+ align:start position:0%
+so please stop the video and try to work
+this out i recommend drawing a space
+
+ align:start position:0%
+this out i recommend drawing a space
+ 
+
+ align:start position:0%
+this out i recommend drawing a space
+time diagram
+
+ align:start position:0%
+time diagram
+ 
+
+ align:start position:0%
+time diagram
+in order to get to a good picture of
+
+ align:start position:0%
+in order to get to a good picture of
+ 
+
+ align:start position:0%
+in order to get to a good picture of
+what is actually happening here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we do this you find this base time
+
+ align:start position:0%
+so if we do this you find this base time
+ 
+
+ align:start position:0%
+so if we do this you find this base time
+diagram here for the bad guys so again
+
+ align:start position:0%
+diagram here for the bad guys so again
+ 
+
+ align:start position:0%
+diagram here for the bad guys so again
+there's a number of important event
+
+ align:start position:0%
+there's a number of important event
+ 
+
+ align:start position:0%
+there's a number of important event
+in year number zero
+
+ align:start position:0%
+in year number zero
+ 
+
+ align:start position:0%
+in year number zero
+the speed the the peace treaty is is
+
+ align:start position:0%
+the speed the the peace treaty is is
+ 
+
+ align:start position:0%
+the speed the the peace treaty is is
+signed and then
+
+ align:start position:0%
+signed and then
+ 
+
+ align:start position:0%
+signed and then
+the good guys they start traveling away
+
+ align:start position:0%
+the good guys they start traveling away
+ 
+
+ align:start position:0%
+the good guys they start traveling away
+with 0.6 times the speed of light so
+
+ align:start position:0%
+with 0.6 times the speed of light so
+ 
+
+ align:start position:0%
+with 0.6 times the speed of light so
+what you see here is the word line of
+
+ align:start position:0%
+what you see here is the word line of
+ 
+
+ align:start position:0%
+what you see here is the word line of
+the good
+
+ align:start position:0%
+the good
+ 
+
+ align:start position:0%
+the good
+guys in year number four
+
+ align:start position:0%
+guys in year number four
+ 
+
+ align:start position:0%
+guys in year number four
+in the reference frame of the bad guys
+
+ align:start position:0%
+in the reference frame of the bad guys
+ 
+
+ align:start position:0%
+in the reference frame of the bad guys
+they developed their spacecraft and they
+
+ align:start position:0%
+they developed their spacecraft and they
+ 
+
+ align:start position:0%
+they developed their spacecraft and they
+keep following
+
+ align:start position:0%
+keep following
+ 
+
+ align:start position:0%
+keep following
+the good guys
+
+ align:start position:0%
+the good guys
+ 
+
+ align:start position:0%
+the good guys
+and here in here number five
+
+ align:start position:0%
+and here in here number five
+ 
+
+ align:start position:0%
+and here in here number five
+the attack actually happens
+
+ align:start position:0%
+the attack actually happens
+ 
+
+ align:start position:0%
+the attack actually happens
+so if we analyze this for the good guys
+
+ align:start position:0%
+so if we analyze this for the good guys
+ 
+
+ align:start position:0%
+so if we analyze this for the good guys
+we find that the
+
+ align:start position:0%
+we find that the
+ 
+
+ align:start position:0%
+we find that the
+x position the position of the attack
+
+ align:start position:0%
+x position the position of the attack
+ 
+
+ align:start position:0%
+x position the position of the attack
+is in their spacecraft so let's figure
+
+ align:start position:0%
+is in their spacecraft so let's figure
+ 
+
+ align:start position:0%
+is in their spacecraft so let's figure
+out whether or not this is correct
+
+ align:start position:0%
+out whether or not this is correct
+ 
+
+ align:start position:0%
+out whether or not this is correct
+we find gamma times xb
+
+ align:start position:0%
+we find gamma times xb
+ 
+
+ align:start position:0%
+we find gamma times xb
+minus v
+
+ align:start position:0%
+minus v
+ 
+
+ align:start position:0%
+minus v
+times tb
+
+ align:start position:0%
+times tb
+ 
+
+ align:start position:0%
+times tb
+if you put in the numbers you find
+
+ align:start position:0%
+if you put in the numbers you find
+ 
+
+ align:start position:0%
+if you put in the numbers you find
+luckily
+
+ align:start position:0%
+luckily
+ 
+
+ align:start position:0%
+luckily
+the x position is equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at what time did this event happen
+
+ align:start position:0%
+at what time did this event happen
+ 
+
+ align:start position:0%
+at what time did this event happen
+um here for the good guys you find gamma
+
+ align:start position:0%
+um here for the good guys you find gamma
+ 
+
+ align:start position:0%
+um here for the good guys you find gamma
+times t b minus v over c x b
+
+ align:start position:0%
+times t b minus v over c x b
+ 
+
+ align:start position:0%
+times t b minus v over c x b
+and again if you put the numbers in the
+
+ align:start position:0%
+and again if you put the numbers in the
+ 
+
+ align:start position:0%
+and again if you put the numbers in the
+attack for the good guys happens in year
+
+ align:start position:0%
+attack for the good guys happens in year
+ 
+
+ align:start position:0%
+attack for the good guys happens in year
+number four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then the question is
+
+ align:start position:0%
+but then the question is
+ 
+
+ align:start position:0%
+but then the question is
+when did the bad guys invent
+
+ align:start position:0%
+when did the bad guys invent
+ 
+
+ align:start position:0%
+when did the bad guys invent
+the spacecraft in the reference frame of
+
+ align:start position:0%
+the spacecraft in the reference frame of
+ 
+
+ align:start position:0%
+the spacecraft in the reference frame of
+the good guys and if you put in the
+
+ align:start position:0%
+the good guys and if you put in the
+ 
+
+ align:start position:0%
+the good guys and if you put in the
+numbers you find the invention actually
+
+ align:start position:0%
+numbers you find the invention actually
+ 
+
+ align:start position:0%
+numbers you find the invention actually
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+in year number five
+
+ align:start position:0%
+in year number five
+ 
+
+ align:start position:0%
+in year number five
+so the attack happens before the
+
+ align:start position:0%
+so the attack happens before the
+ 
+
+ align:start position:0%
+so the attack happens before the
+spacecraft is invented in the reference
+
+ align:start position:0%
+spacecraft is invented in the reference
+ 
+
+ align:start position:0%
+spacecraft is invented in the reference
+frame of the good guys
+
+ align:start position:0%
+frame of the good guys
+ 
+
+ align:start position:0%
+frame of the good guys
+and this clearly
+
+ align:start position:0%
+and this clearly
+ 
+
+ align:start position:0%
+and this clearly
+violates
+
+ align:start position:0%
+violates
+ 
+
+ align:start position:0%
+violates
+you cannot use the device which is not
+
+ align:start position:0%
+you cannot use the device which is not
+ 
+
+ align:start position:0%
+you cannot use the device which is not
+even invented yet unless you
+
+ align:start position:0%
+even invented yet unless you
+ 
+
+ align:start position:0%
+even invented yet unless you
+travel faster than the speed of light
+
+ align:start position:0%
+travel faster than the speed of light
+ 
+
+ align:start position:0%
+travel faster than the speed of light
+you travel in time
+
+ align:start position:0%
+you travel in time
+ 
+
+ align:start position:0%
+you travel in time
+all right i find this a really funny and
+
+ align:start position:0%
+all right i find this a really funny and
+ 
+
+ align:start position:0%
+all right i find this a really funny and
+geeky example and the reason why this
+
+ align:start position:0%
+geeky example and the reason why this
+ 
+
+ align:start position:0%
+geeky example and the reason why this
+doesn't work out why it's geeky is that
+
+ align:start position:0%
+doesn't work out why it's geeky is that
+ 
+
+ align:start position:0%
+doesn't work out why it's geeky is that
+they travel faster than the speed of
+
+ align:start position:0%
+they travel faster than the speed of
+ 
+
+ align:start position:0%
+they travel faster than the speed of
+light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+let me conclude this this part of this
+
+ align:start position:0%
+let me conclude this this part of this
+ 
+
+ align:start position:0%
+let me conclude this this part of this
+section here with a concept question
+
+ align:start position:0%
+section here with a concept question
+ 
+
+ align:start position:0%
+section here with a concept question
+we have an event a and ask ourselves can
+
+ align:start position:0%
+we have an event a and ask ourselves can
+ 
+
+ align:start position:0%
+we have an event a and ask ourselves can
+event a cause other events so event a
+
+ align:start position:0%
+event a cause other events so event a
+ 
+
+ align:start position:0%
+event a cause other events so event a
+might be the invention of a spacecraft
+
+ align:start position:0%
+might be the invention of a spacecraft
+ 
+
+ align:start position:0%
+might be the invention of a spacecraft
+can event a cause event c
+
+ align:start position:0%
+can event a cause event c
+ 
+
+ align:start position:0%
+can event a cause event c
+event d
+
+ align:start position:0%
+event d
+ 
+
+ align:start position:0%
+event d
+or more than one event like b and c or b
+
+ align:start position:0%
+or more than one event like b and c or b
+ 
+
+ align:start position:0%
+or more than one event like b and c or b
+and d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so note that the time axis here has
+
+ align:start position:0%
+so note that the time axis here has
+ 
+
+ align:start position:0%
+so note that the time axis here has
+units years and the x-axis has units
+
+ align:start position:0%
+units years and the x-axis has units
+ 
+
+ align:start position:0%
+units years and the x-axis has units
+light years
+
+ align:start position:0%
+light years
+ 
+
+ align:start position:0%
+light years
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+you know stop your video here think
+
+ align:start position:0%
+you know stop your video here think
+ 
+
+ align:start position:0%
+you know stop your video here think
+about the answer maybe you draw in the
+
+ align:start position:0%
+about the answer maybe you draw in the
+ 
+
+ align:start position:0%
+about the answer maybe you draw in the
+space-time diagram in order to find the
+
+ align:start position:0%
+space-time diagram in order to find the
+ 
+
+ align:start position:0%
+space-time diagram in order to find the
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+and the answer is the correct answer is
+
+ align:start position:0%
+and the answer is the correct answer is
+ 
+
+ align:start position:0%
+and the answer is the correct answer is
+c only when c can be caused because only
+
+ align:start position:0%
+c only when c can be caused because only
+ 
+
+ align:start position:0%
+c only when c can be caused because only
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+lies within what we call the light cone
+
+ align:start position:0%
+lies within what we call the light cone
+ 
+
+ align:start position:0%
+lies within what we call the light cone
+of event a
+
+ align:start position:0%
+of event a
+ 
+
+ align:start position:0%
+of event a
+in order to impact in order to cause an
+
+ align:start position:0%
+in order to impact in order to cause an
+ 
+
+ align:start position:0%
+in order to impact in order to cause an
+effect on any other event
+
+ align:start position:0%
+effect on any other event
+ 
+
+ align:start position:0%
+effect on any other event
+the message needs to be traveling
+
+ align:start position:0%
+the message needs to be traveling
+ 
+
+ align:start position:0%
+the message needs to be traveling
+with speed
+
+ align:start position:0%
+with speed
+ 
+
+ align:start position:0%
+with speed
+smaller than the speed of light
+
+ align:start position:0%
+smaller than the speed of light
+ 
+
+ align:start position:0%
+smaller than the speed of light
+so that means that in order for to reach
+
+ align:start position:0%
+so that means that in order for to reach
+ 
+
+ align:start position:0%
+so that means that in order for to reach
+event
+
+ align:start position:0%
+event
+ 
+
+ align:start position:0%
+event
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+we can you know design a spacecraft or
+
+ align:start position:0%
+we can you know design a spacecraft or
+ 
+
+ align:start position:0%
+we can you know design a spacecraft or
+we can send a light beam
+
+ align:start position:0%
+we can send a light beam
+ 
+
+ align:start position:0%
+we can send a light beam
+to this event
+
+ align:start position:0%
+to this event
+ 
+
+ align:start position:0%
+to this event
+or to this in this direction and then
+
+ align:start position:0%
+or to this in this direction and then
+ 
+
+ align:start position:0%
+or to this in this direction and then
+just wait a little bit
+
+ align:start position:0%
+just wait a little bit
+ 
+
+ align:start position:0%
+just wait a little bit
+in order to make any sort of impact on
+
+ align:start position:0%
+in order to make any sort of impact on
+ 
+
+ align:start position:0%
+in order to make any sort of impact on
+event c we cannot travel faster than the
+
+ align:start position:0%
+event c we cannot travel faster than the
+ 
+
+ align:start position:0%
+event c we cannot travel faster than the
+speed of light which would be necessary
+
+ align:start position:0%
+speed of light which would be necessary
+ 
+
+ align:start position:0%
+speed of light which would be necessary
+in order to reach when d
+
+ align:start position:0%
+in order to reach when d
+ 
+
+ align:start position:0%
+in order to reach when d
+and we can also not go backwards in time
+
+ align:start position:0%
+and we can also not go backwards in time
+ 
+
+ align:start position:0%
+and we can also not go backwards in time
+with messages in order to reach event b
\ No newline at end of file
diff --git a/G8B_Wzmeo_8.txt b/G8B_Wzmeo_8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..55d20705eb7eced741da60346493529c7a76c939
--- /dev/null
+++ b/G8B_Wzmeo_8.txt
@@ -0,0 +1,307 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+T that came in that little bit of time
+
+ align:start position:0%
+T that came in that little bit of time
+ 
+
+ align:start position:0%
+T that came in that little bit of time
+see how it's kind of red why do you
+
+ align:start position:0%
+see how it's kind of red why do you
+ 
+
+ align:start position:0%
+see how it's kind of red why do you
+think it's a little red it's all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iron and this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here there we
+
+ align:start position:0%
+here there we
+ 
+
+ align:start position:0%
+here there we
+go there's another one now if we did
+
+ align:start position:0%
+go there's another one now if we did
+ 
+
+ align:start position:0%
+go there's another one now if we did
+phosphate measurements on these I would
+
+ align:start position:0%
+phosphate measurements on these I would
+ 
+
+ align:start position:0%
+phosphate measurements on these I would
+guess it would be
+
+ align:start position:0%
+guess it would be
+ 
+
+ align:start position:0%
+guess it would be
+zero I know it would be zero cuz we
+
+ align:start position:0%
+zero I know it would be zero cuz we
+ 
+
+ align:start position:0%
+zero I know it would be zero cuz we
+tried it last week okay so that's uh and
+
+ align:start position:0%
+tried it last week okay so that's uh and
+ 
+
+ align:start position:0%
+tried it last week okay so that's uh and
+then you can take this you can measure
+
+ align:start position:0%
+then you can take this you can measure
+ 
+
+ align:start position:0%
+then you can take this you can measure
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+flow um measure the you know volume time
+
+ align:start position:0%
+flow um measure the you know volume time
+ 
+
+ align:start position:0%
+flow um measure the you know volume time
+you left it on surface area and you can
+
+ align:start position:0%
+you left it on surface area and you can
+ 
+
+ align:start position:0%
+you left it on surface area and you can
+get a number of liters per square you
+
+ align:start position:0%
+get a number of liters per square you
+ 
+
+ align:start position:0%
+get a number of liters per square you
+know for for a square foot or per square
+
+ align:start position:0%
+know for for a square foot or per square
+ 
+
+ align:start position:0%
+know for for a square foot or per square
+meter and then you can begin to do this
+
+ align:start position:0%
+meter and then you can begin to do this
+ 
+
+ align:start position:0%
+meter and then you can begin to do this
+in a number of spots and actually
+
+ align:start position:0%
+in a number of spots and actually
+ 
+
+ align:start position:0%
+in a number of spots and actually
+integrate it and come up with a total
+
+ align:start position:0%
+integrate it and come up with a total
+ 
+
+ align:start position:0%
+integrate it and come up with a total
+flux make sense and you're going to see
+
+ align:start position:0%
+flux make sense and you're going to see
+ 
+
+ align:start position:0%
+flux make sense and you're going to see
+I think Charlie is doing that at Lacoy
+
+ align:start position:0%
+I think Charlie is doing that at Lacoy
+ 
+
+ align:start position:0%
+I think Charlie is doing that at Lacoy
+Bay extensively so there you go
+
+ align:start position:0%
+Bay extensively so there you go
+ 
+
+ align:start position:0%
+Bay extensively so there you go
+if somebody would be so willing is to
+
+ align:start position:0%
+if somebody would be so willing is to
+ 
+
+ align:start position:0%
+if somebody would be so willing is to
+hold on to those and let those drain out
+
+ align:start position:0%
+hold on to those and let those drain out
+ 
+
+ align:start position:0%
+hold on to those and let those drain out
+that would be
+
+ align:start position:0%
+that would be
+ 
+
+ align:start position:0%
+that would be
+great I'm going to pop these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lids there's one
+
+ align:start position:0%
+Lids there's one
+ 
+
+ align:start position:0%
+Lids there's one
+lid take that back up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know what's really cool about these
+
+ align:start position:0%
+you know what's really cool about these
+ 
+
+ align:start position:0%
+you know what's really cool about these
+CES meters is um we have a a study going
+
+ align:start position:0%
+CES meters is um we have a a study going
+ 
+
+ align:start position:0%
+CES meters is um we have a a study going
+on right now looking at uh nutrient
+
+ align:start position:0%
+on right now looking at uh nutrient
+ 
+
+ align:start position:0%
+on right now looking at uh nutrient
+outflow from the lake and you can go to
+
+ align:start position:0%
+outflow from the lake and you can go to
+ 
+
+ align:start position:0%
+outflow from the lake and you can go to
+a site like we have on the downstream
+
+ align:start position:0%
+a site like we have on the downstream
+ 
+
+ align:start position:0%
+a site like we have on the downstream
+side of the lake and you fill the bag
+
+ align:start position:0%
+side of the lake and you fill the bag
+ 
+
+ align:start position:0%
+side of the lake and you fill the bag
+with water to start and you watch it
+
+ align:start position:0%
+with water to start and you watch it
+ 
+
+ align:start position:0%
+with water to start and you watch it
+drain away it's really cool just the B
+
+ align:start position:0%
+drain away it's really cool just the B
+ 
+
+ align:start position:0%
+drain away it's really cool just the B
+water is sucked out of the
+
+ align:start position:0%
+water is sucked out of the
+ 
+
+ align:start position:0%
+water is sucked out of the
+bag that's it
\ No newline at end of file
diff --git a/GBL28_Tw6UQ.txt b/GBL28_Tw6UQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..73466832e8e46c2438907532c5826d10d3055b2f
--- /dev/null
+++ b/GBL28_Tw6UQ.txt
@@ -0,0 +1,257 @@
+SRAMs are organized as an array of memory
+locations, where a memory access is either
+
+reading or writing all the bits in a single
+location.
+
+Here we see the component layout for a 8-location
+SRAM array where each location hold 6 bits
+
+of data.
+
+You can see that the individual bit cells
+are organized as 8 rows (one row per location)
+
+by 6 columns (one column per bit in each memory
+word).
+
+The circuitry around the periphery is used
+to decode addresses and support read and write
+
+operations.
+
+To access the SRAM, we need provide enough
+address bits to uniquely specify the location.
+
+In this case we need 3 address bits to select
+one of the 8 memory locations.
+
+The address decoder logic sets one of the
+8 wordlines (the horizontal wires in the array)
+
+high to enable a particular row (location)
+for the upcoming access.
+
+The remaining wordlines are set low, disabling
+the cells they control.
+
+The active wordline enables each of the SRAM
+bit cells on the selected row, connecting
+
+each cell to a pair of bit lines (the vertical
+wires in the array).
+
+During read operations the bit lines carry
+the analog signals from the enabled bit cells
+
+to the sense amplifiers, which convert the
+analog signals to digital data.
+
+During write operations incoming data is driven
+onto the bit lines to be stored into the enabled
+
+bit cells.
+
+Larger SRAMs will have a more complex organization
+in order to minimize the length, and hence
+
+the capacitance, of the bit lines.
+
+The heart of the SRAM are the bit cells.
+
+The typical cell has two CMOS inverters wired
+in a positive feedback loop to create a bistable
+
+storage element.
+
+The diagram on the right shows the two stable
+configurations.
+
+In the top configuration, the cell is storing
+a "1" bit.
+
+In the bottom configuration, it's storing
+a 0 bit.
+
+The cell provides stable storage in the sense
+that as long as there's power, the noise immunity
+
+of the inverters will ensure that the logic
+values will be maintained even if there's
+
+electrical noise on either inverter input.
+
+Both sides of the feedback loop are connected
+via access FETs to the two vertical bit lines.
+
+When the wordline connected to the gates of
+the access FETs is high, the FETs are "on",
+
+i.e., they will make an electrical connection
+between the cell's internal circuity and the
+
+bitlines.
+
+When the wordline is low, the access FETs
+are "off" and the bistable feedback loop is
+
+isolated from the bitlines and will happily
+maintain the stored value as long as there's
+
+power.
+
+During a read operation, the drivers first
+recharge all the bitlines to Vdd (i.e., a
+
+logical "1" value) and then disconnect, leaving
+the bitlines floating at 1.
+
+Then the address decoder sets one of the wordlines
+high, connecting a row of bit cells to their
+
+bitlines.
+
+Each cell in the selected row then pulls one
+of its two bitlines to GND.
+
+In this example, it's the right bitline that's
+pulled low.
+
+Transitions on the bitlines are slow since
+the bitline has a large total capacitance
+
+and the MOSFETs in the two inverters are small
+to keep the cell has small as possible.
+
+The large capacitance comes partly from the
+bitline's length and partly from the diffusion
+
+capacitance of the access FETs in other cells
+in the same column.
+
+Rather than wait for the bitline to reach
+a valid logic level, sense amplifiers are
+
+used to quickly detect the small voltage difference
+developing between the two bitlines and generate
+
+the appropriate digital output.
+
+Since detecting small changes in a voltage
+is very sensitive to electrical noise, the
+
+SRAM uses a pair of bitlines for each bit
+and a differential sense amplifier to provide
+
+greater noise immunity.
+
+As you can see, designing a low-latency SRAM
+involves a lot of expertise with the analog
+
+behavior of MOSFETs and some cleverness to
+ensure electrical noise will not interfere
+
+with the correct operation of the circuitry.
+
+Write operations start by driving the bitlines
+to the appropriate values.
+
+In the example shown here, we want to write
+a 0-bit into the cell, so the left bitline
+
+is set to GND and the right bitline is set
+to VDD.
+
+As before, the address decoder then sets one
+of the wordlines high, selecting all the cells
+
+in a particular row for the write operation.
+
+The drivers have much larger MOSFETs than
+those in the cell's inverters, so the internal
+
+signals in the enabled cells are forced to
+the values on the bitlines and the bistable
+
+circuits "flip" into the new stable configuration.
+
+We're basically shorting together the outputs
+of the driver and the internal inverter, so
+
+this is another analog operation!
+
+This would be a no-no in a strictly digital
+circuit.
+
+Since n-fets usually carry much higher source-drain
+currents than p-fets of the same width and
+
+given the threshold-drop of the n-fet access
+transistor,
+
+almost all the work of the write is performed
+by the large n-fet pulldown transistor connected
+
+to the bitline with the 0 value, which easily
+overpowers the small p-fet pullup of the inverters
+
+in the cell.
+
+Again, SRAM designers need a lot of expertise
+to correctly balance the sizes of MOSFETs
+
+to ensure fast and reliable write operations.
+
+It's not hard to augment the SRAM to support
+multiple read/write ports, a handy addition
+
+for register file circuits.
+
+We'll do this by adding additional sets of
+wordlines, bitlines, drivers, and sense amps.
+
+This will give us multiple paths to independently
+access the bistable storage elements in the
+
+various rows of the memory array.
+
+With an N-port SRAM, for each bit we'll need
+N wordlines, 2N bitlines and 2N access FETs.
+
+The additional wordlines increase the effective
+height of the cell and the additional bitlines
+
+increase the effective width of the cell and
+so the area required by all these wires quickly
+
+dominates the size of the SRAM.
+
+Since both the height and width of a cell
+increase when adding ports, the overall area
+
+grows as the square of the number of read/write
+ports.
+
+So one has to take care not to gratuitously
+add ports lest the cost of the SRAM get out
+
+of hand.
+
+In summary, the circuitry for the SRAM is
+organized as an array of bit cells, with one
+
+row for each memory location and one column
+for each bit in a location.
+
+Each bit is stored by two inverters connected
+to form a bistable storage element.
+
+Reads and writes are essentially analog operations
+performed via the bitlines and access FETs.
+
+The SRAM uses 6 MOSFETs for each bit cell.
+
+Can we do better?
+
+What's the minimum number of MOSFETs needed
+to store a single bit of information?
\ No newline at end of file
diff --git a/GOgA8JGUiwI.txt b/GOgA8JGUiwI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e2bf9bb9aabf9b534ea7221c3aee9312dd0f3940
--- /dev/null
+++ b/GOgA8JGUiwI.txt
@@ -0,0 +1,13523 @@
+align:start position:0%
+ 
+All right, let's get started. Uh,
+
+ align:start position:0%
+All right, let's get started. Uh,
+ 
+
+ align:start position:0%
+All right, let's get started. Uh,
+welcome back to 61200. I am the second
+
+ align:start position:0%
+welcome back to 61200. I am the second
+ 
+
+ align:start position:0%
+welcome back to 61200. I am the second
+of the three lecturers in this class.
+
+ align:start position:0%
+of the three lecturers in this class.
+ 
+
+ align:start position:0%
+of the three lecturers in this class.
+Uh, you can call me Eric. Um, and
+
+ align:start position:0%
+Uh, you can call me Eric. Um, and
+ 
+
+ align:start position:0%
+Uh, you can call me Eric. Um, and
+Binmore will be on next week. Uh so
+
+ align:start position:0%
+Binmore will be on next week. Uh so
+ 
+
+ align:start position:0%
+Binmore will be on next week. Uh so
+today we are going to uh continue our
+
+ align:start position:0%
+today we are going to uh continue our
+ 
+
+ align:start position:0%
+today we are going to uh continue our
+theme of induction and prove some even
+
+ align:start position:0%
+theme of induction and prove some even
+ 
+
+ align:start position:0%
+theme of induction and prove some even
+cooler and stronger forms of induction.
+
+ align:start position:0%
+cooler and stronger forms of induction.
+ 
+
+ align:start position:0%
+cooler and stronger forms of induction.
+Just a recap of where we were last time.
+
+ align:start position:0%
+Just a recap of where we were last time.
+ 
+
+ align:start position:0%
+Just a recap of where we were last time.
+As we've seen, we're we're growing our
+
+ align:start position:0%
+As we've seen, we're we're growing our
+ 
+
+ align:start position:0%
+As we've seen, we're we're growing our
+catalog of different proof techniques of
+
+ align:start position:0%
+catalog of different proof techniques of
+ 
+
+ align:start position:0%
+catalog of different proof techniques of
+how to prove uh different types of
+
+ align:start position:0%
+how to prove uh different types of
+ 
+
+ align:start position:0%
+how to prove uh different types of
+theorems almost by like a cookbook. If
+
+ align:start position:0%
+theorems almost by like a cookbook. If
+ 
+
+ align:start position:0%
+theorems almost by like a cookbook. If
+you want to cook this, here's how you
+
+ align:start position:0%
+you want to cook this, here's how you
+ 
+
+ align:start position:0%
+you want to cook this, here's how you
+get started. And so here's a a brief
+
+ align:start position:0%
+get started. And so here's a a brief
+ 
+
+ align:start position:0%
+get started. And so here's a a brief
+summary of this. uh if the theorem you
+
+ align:start position:0%
+summary of this. uh if the theorem you
+ 
+
+ align:start position:0%
+summary of this. uh if the theorem you
+want to prove starts with there exists
+
+ align:start position:0%
+want to prove starts with there exists
+ 
+
+ align:start position:0%
+want to prove starts with there exists
+something then a natural way to prove
+
+ align:start position:0%
+something then a natural way to prove
+ 
+
+ align:start position:0%
+something then a natural way to prove
+that is by example or by construction
+
+ align:start position:0%
+that is by example or by construction
+ 
+
+ align:start position:0%
+that is by example or by construction
+you construct a particular x star and
+
+ align:start position:0%
+you construct a particular x star and
+ 
+
+ align:start position:0%
+you construct a particular x star and
+prove that p of xstar is true and if you
+
+ align:start position:0%
+prove that p of xstar is true and if you
+ 
+
+ align:start position:0%
+prove that p of xstar is true and if you
+can do that uh then you've proved that
+
+ align:start position:0%
+can do that uh then you've proved that
+ 
+
+ align:start position:0%
+can do that uh then you've proved that
+there exists an x where p of x is true
+
+ align:start position:0%
+there exists an x where p of x is true
+ 
+
+ align:start position:0%
+there exists an x where p of x is true
+it's kind of straightforward but it lets
+
+ align:start position:0%
+it's kind of straightforward but it lets
+ 
+
+ align:start position:0%
+it's kind of straightforward but it lets
+you unwrap if I give you an expression
+
+ align:start position:0%
+you unwrap if I give you an expression
+ 
+
+ align:start position:0%
+you unwrap if I give you an expression
+starts with exist then you know your
+
+ align:start position:0%
+starts with exist then you know your
+ 
+
+ align:start position:0%
+starts with exist then you know your
+first step is try to figure out an x
+
+ align:start position:0%
+first step is try to figure out an x
+ 
+
+ align:start position:0%
+first step is try to figure out an x
+where this is true um and of course to
+
+ align:start position:0%
+where this is true um and of course to
+ 
+
+ align:start position:0%
+where this is true um and of course to
+prove p of xar you probably recur
+
+ align:start position:0%
+prove p of xar you probably recur
+ 
+
+ align:start position:0%
+prove p of xar you probably recur
+cursively use this cookbook. If you want
+
+ align:start position:0%
+cursively use this cookbook. If you want
+ 
+
+ align:start position:0%
+cursively use this cookbook. If you want
+to prove a universal uh one common way
+
+ align:start position:0%
+to prove a universal uh one common way
+ 
+
+ align:start position:0%
+to prove a universal uh one common way
+if you want to prove for all x p of x is
+
+ align:start position:0%
+if you want to prove for all x p of x is
+ 
+
+ align:start position:0%
+if you want to prove for all x p of x is
+true uh typically your first line is
+
+ align:start position:0%
+true uh typically your first line is
+ 
+
+ align:start position:0%
+true uh typically your first line is
+take an arbitrary x just give it a name
+
+ align:start position:0%
+take an arbitrary x just give it a name
+ 
+
+ align:start position:0%
+take an arbitrary x just give it a name
+x and then prove that p of x is true no
+
+ align:start position:0%
+x and then prove that p of x is true no
+ 
+
+ align:start position:0%
+x and then prove that p of x is true no
+matter what x you started with therefore
+
+ align:start position:0%
+matter what x you started with therefore
+ 
+
+ align:start position:0%
+matter what x you started with therefore
+it's true for all of them. Uh come back
+
+ align:start position:0%
+it's true for all of them. Uh come back
+ 
+
+ align:start position:0%
+it's true for all of them. Uh come back
+to induction in a second. If you're if
+
+ align:start position:0%
+to induction in a second. If you're if
+ 
+
+ align:start position:0%
+to induction in a second. If you're if
+the main thing you want to prove is an
+
+ align:start position:0%
+the main thing you want to prove is an
+ 
+
+ align:start position:0%
+the main thing you want to prove is an
+implication, P implies Q. This is if P
+
+ align:start position:0%
+implication, P implies Q. This is if P
+ 
+
+ align:start position:0%
+implication, P implies Q. This is if P
+then Q. And I want to remind you that um
+
+ align:start position:0%
+then Q. And I want to remind you that um
+ 
+
+ align:start position:0%
+then Q. And I want to remind you that um
+P implies Q is the same thing as not P
+
+ align:start position:0%
+P implies Q is the same thing as not P
+ 
+
+ align:start position:0%
+P implies Q is the same thing as not P
+or Q. We'll use this a bunch uh today.
+
+ align:start position:0%
+or Q. We'll use this a bunch uh today.
+ 
+
+ align:start position:0%
+or Q. We'll use this a bunch uh today.
+Um then uh the direct way to prove this
+
+ align:start position:0%
+Um then uh the direct way to prove this
+ 
+
+ align:start position:0%
+Um then uh the direct way to prove this
+what we call a direct argument is assume
+
+ align:start position:0%
+what we call a direct argument is assume
+ 
+
+ align:start position:0%
+what we call a direct argument is assume
+P is true and then prove Q is true.
+
+ align:start position:0%
+P is true and then prove Q is true.
+ 
+
+ align:start position:0%
+P is true and then prove Q is true.
+Because this implication we only need to
+
+ align:start position:0%
+Because this implication we only need to
+ 
+
+ align:start position:0%
+Because this implication we only need to
+prove that Q is true when P is true. If
+
+ align:start position:0%
+prove that Q is true when P is true. If
+ 
+
+ align:start position:0%
+prove that Q is true when P is true. If
+P then Q. Uh or another way to prove
+
+ align:start position:0%
+P then Q. Uh or another way to prove
+ 
+
+ align:start position:0%
+P then Q. Uh or another way to prove
+that same statement P implies Q is
+
+ align:start position:0%
+that same statement P implies Q is
+ 
+
+ align:start position:0%
+that same statement P implies Q is
+what's called the contraositive. It
+
+ align:start position:0%
+what's called the contraositive. It
+ 
+
+ align:start position:0%
+what's called the contraositive. It
+turns out P implies Q is the same
+
+ align:start position:0%
+turns out P implies Q is the same
+ 
+
+ align:start position:0%
+turns out P implies Q is the same
+statement. It's equivalent to not Q
+
+ align:start position:0%
+statement. It's equivalent to not Q
+ 
+
+ align:start position:0%
+statement. It's equivalent to not Q
+implies not P. Remember this uh symbol
+
+ align:start position:0%
+implies not P. Remember this uh symbol
+ 
+
+ align:start position:0%
+implies not P. Remember this uh symbol
+is a negation
+
+ align:start position:0%
+is a negation
+ 
+
+ align:start position:0%
+is a negation
+um flip true and false. So to do that
+
+ align:start position:0%
+um flip true and false. So to do that
+ 
+
+ align:start position:0%
+um flip true and false. So to do that
+with a direct argument we would prove
+
+ align:start position:0%
+with a direct argument we would prove
+ 
+
+ align:start position:0%
+with a direct argument we would prove
+that uh if not Q is true then not P is
+
+ align:start position:0%
+that uh if not Q is true then not P is
+ 
+
+ align:start position:0%
+that uh if not Q is true then not P is
+true. In other words, assume not Q and
+
+ align:start position:0%
+true. In other words, assume not Q and
+ 
+
+ align:start position:0%
+true. In other words, assume not Q and
+then prove not P.
+
+ align:start position:0%
+then prove not P.
+ 
+
+ align:start position:0%
+then prove not P.
+This may seem kind of magical. Why is P
+
+ align:start position:0%
+This may seem kind of magical. Why is P
+ 
+
+ align:start position:0%
+This may seem kind of magical. Why is P
+implies Q the same as not Q implies not
+
+ align:start position:0%
+implies Q the same as not Q implies not
+ 
+
+ align:start position:0%
+implies Q the same as not Q implies not
+P? But it actually follows directly from
+
+ align:start position:0%
+P? But it actually follows directly from
+ 
+
+ align:start position:0%
+P? But it actually follows directly from
+this equivalence. If you look at not Q
+
+ align:start position:0%
+this equivalence. If you look at not Q
+ 
+
+ align:start position:0%
+this equivalence. If you look at not Q
+implies not P. Uh this is the same thing
+
+ align:start position:0%
+implies not P. Uh this is the same thing
+ 
+
+ align:start position:0%
+implies not P. Uh this is the same thing
+as let me go over here. Not not Q or not
+
+ align:start position:0%
+as let me go over here. Not not Q or not
+ 
+
+ align:start position:0%
+as let me go over here. Not not Q or not
+P,
+
+ align:start position:0%
+P,
+ 
+
+ align:start position:0%
+P,
+right? because it implies is the same
+
+ align:start position:0%
+right? because it implies is the same
+ 
+
+ align:start position:0%
+right? because it implies is the same
+thing as taking an or if you negate the
+
+ align:start position:0%
+thing as taking an or if you negate the
+ 
+
+ align:start position:0%
+thing as taking an or if you negate the
+first the part on the left and not not Q
+
+ align:start position:0%
+first the part on the left and not not Q
+ 
+
+ align:start position:0%
+first the part on the left and not not Q
+is the same as Q.
+
+ align:start position:0%
+is the same as Q.
+ 
+
+ align:start position:0%
+is the same as Q.
+Okay, so this was uh not Q implies not P
+
+ align:start position:0%
+Okay, so this was uh not Q implies not P
+ 
+
+ align:start position:0%
+Okay, so this was uh not Q implies not P
+is the same thing as this is the same
+
+ align:start position:0%
+is the same thing as this is the same
+ 
+
+ align:start position:0%
+is the same thing as this is the same
+thing as this and that is exactly this
+
+ align:start position:0%
+thing as this and that is exactly this
+ 
+
+ align:start position:0%
+thing as this and that is exactly this
+uh just by switching the order of the
+
+ align:start position:0%
+uh just by switching the order of the
+ 
+
+ align:start position:0%
+uh just by switching the order of the
+ors and so P implies Q is the same thing
+
+ align:start position:0%
+ors and so P implies Q is the same thing
+ 
+
+ align:start position:0%
+ors and so P implies Q is the same thing
+as not Q implies not P uh more uh so
+
+ align:start position:0%
+as not Q implies not P uh more uh so
+ 
+
+ align:start position:0%
+as not Q implies not P uh more uh so
+that was contraositive there's a related
+
+ align:start position:0%
+that was contraositive there's a related
+ 
+
+ align:start position:0%
+that was contraositive there's a related
+notion of contradiction where if you
+
+ align:start position:0%
+notion of contradiction where if you
+ 
+
+ align:start position:0%
+notion of contradiction where if you
+want to prove any statement P um you
+
+ align:start position:0%
+want to prove any statement P um you
+ 
+
+ align:start position:0%
+want to prove any statement P um you
+assume that not P is true and then find
+
+ align:start position:0%
+assume that not P is true and then find
+ 
+
+ align:start position:0%
+assume that not P is true and then find
+a contradiction prove that in fact false
+
+ align:start position:0%
+a contradiction prove that in fact false
+ 
+
+ align:start position:0%
+a contradiction prove that in fact false
+is true or something is both true and
+
+ align:start position:0%
+is true or something is both true and
+ 
+
+ align:start position:0%
+is true or something is both true and
+false. All these things are very very
+
+ align:start position:0%
+false. All these things are very very
+ 
+
+ align:start position:0%
+false. All these things are very very
+bad because we assume that our axioms
+
+ align:start position:0%
+bad because we assume that our axioms
+ 
+
+ align:start position:0%
+bad because we assume that our axioms
+are consistent. And so if you can prove
+
+ align:start position:0%
+are consistent. And so if you can prove
+ 
+
+ align:start position:0%
+are consistent. And so if you can prove
+false that means that what you assumed
+
+ align:start position:0%
+false that means that what you assumed
+ 
+
+ align:start position:0%
+false that means that what you assumed
+must also be false.
+
+ align:start position:0%
+must also be false.
+ 
+
+ align:start position:0%
+must also be false.
+Uh and if so if not P is false that's
+
+ align:start position:0%
+Uh and if so if not P is false that's
+ 
+
+ align:start position:0%
+Uh and if so if not P is false that's
+the same thing as saying P is true.
+
+ align:start position:0%
+the same thing as saying P is true.
+ 
+
+ align:start position:0%
+the same thing as saying P is true.
+Feels very backwards. Lots of double
+
+ align:start position:0%
+Feels very backwards. Lots of double
+ 
+
+ align:start position:0%
+Feels very backwards. Lots of double
+negatives in there but that's the nature
+
+ align:start position:0%
+negatives in there but that's the nature
+ 
+
+ align:start position:0%
+negatives in there but that's the nature
+of contradiction. We try to avoid them
+
+ align:start position:0%
+of contradiction. We try to avoid them
+ 
+
+ align:start position:0%
+of contradiction. We try to avoid them
+when we can but sometimes it's really
+
+ align:start position:0%
+when we can but sometimes it's really
+ 
+
+ align:start position:0%
+when we can but sometimes it's really
+the right way to prove something. And
+
+ align:start position:0%
+the right way to prove something. And
+ 
+
+ align:start position:0%
+the right way to prove something. And
+the last technique we saw was induction.
+
+ align:start position:0%
+the last technique we saw was induction.
+ 
+
+ align:start position:0%
+the last technique we saw was induction.
+uh where if we have a universal
+
+ align:start position:0%
+uh where if we have a universal
+ 
+
+ align:start position:0%
+uh where if we have a universal
+quantifier over the natural numbers, we
+
+ align:start position:0%
+quantifier over the natural numbers, we
+ 
+
+ align:start position:0%
+quantifier over the natural numbers, we
+want to prove P of N is true for all
+
+ align:start position:0%
+want to prove P of N is true for all
+ 
+
+ align:start position:0%
+want to prove P of N is true for all
+natural numbers 0 1 2 3 and so on. Uh
+
+ align:start position:0%
+natural numbers 0 1 2 3 and so on. Uh
+ 
+
+ align:start position:0%
+natural numbers 0 1 2 3 and so on. Uh
+then we only need to prove it for some
+
+ align:start position:0%
+then we only need to prove it for some
+ 
+
+ align:start position:0%
+then we only need to prove it for some
+base case P of 0 and then we need to
+
+ align:start position:0%
+base case P of 0 and then we need to
+ 
+
+ align:start position:0%
+base case P of 0 and then we need to
+prove that P of N implies P of N plus
+
+ align:start position:0%
+prove that P of N implies P of N plus
+ 
+
+ align:start position:0%
+prove that P of N implies P of N plus
+one for all N. So we'll talk more about
+
+ align:start position:0%
+one for all N. So we'll talk more about
+ 
+
+ align:start position:0%
+one for all N. So we'll talk more about
+induction in a little bit. Uh
+
+ align:start position:0%
+induction in a little bit. Uh
+ 
+
+ align:start position:0%
+induction in a little bit. Uh
+today we're going to add to this list
+
+ align:start position:0%
+today we're going to add to this list
+ 
+
+ align:start position:0%
+today we're going to add to this list
+two more proof techniques. One is proof
+
+ align:start position:0%
+two more proof techniques. One is proof
+ 
+
+ align:start position:0%
+two more proof techniques. One is proof
+by cases and the other is strong
+
+ align:start position:0%
+by cases and the other is strong
+ 
+
+ align:start position:0%
+by cases and the other is strong
+induction. So proof by cases is just a
+
+ align:start position:0%
+induction. So proof by cases is just a
+ 
+
+ align:start position:0%
+induction. So proof by cases is just a
+nice general technique to be aware of.
+
+ align:start position:0%
+nice general technique to be aware of.
+ 
+
+ align:start position:0%
+nice general technique to be aware of.
+Uh it's can be very powerful. Strong
+
+ align:start position:0%
+Uh it's can be very powerful. Strong
+ 
+
+ align:start position:0%
+Uh it's can be very powerful. Strong
+induction is going to be an even cooler
+
+ align:start position:0%
+induction is going to be an even cooler
+ 
+
+ align:start position:0%
+induction is going to be an even cooler
+form of induction.
+
+ align:start position:0%
+form of induction.
+ 
+
+ align:start position:0%
+form of induction.
+All right. But we'll start today with
+
+ align:start position:0%
+All right. But we'll start today with
+ 
+
+ align:start position:0%
+All right. But we'll start today with
+proof by cases. And we'll start with
+
+ align:start position:0%
+proof by cases. And we'll start with
+ 
+
+ align:start position:0%
+proof by cases. And we'll start with
+proof by two cases.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we'll generalize to more than
+
+ align:start position:0%
+and then we'll generalize to more than
+ 
+
+ align:start position:0%
+and then we'll generalize to more than
+two cases.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, uh the idea is take any proposition
+
+ align:start position:0%
+So, uh the idea is take any proposition
+ 
+
+ align:start position:0%
+So, uh the idea is take any proposition
+C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and observe that C or not C is a
+
+ align:start position:0%
+and observe that C or not C is a
+ 
+
+ align:start position:0%
+and observe that C or not C is a
+tautology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaning uh always true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, if C is true, then this whole
+
+ align:start position:0%
+Okay, if C is true, then this whole
+ 
+
+ align:start position:0%
+Okay, if C is true, then this whole
+thing is true because C is true. If C is
+
+ align:start position:0%
+thing is true because C is true. If C is
+ 
+
+ align:start position:0%
+thing is true because C is true. If C is
+false, then not C is true. And so this
+
+ align:start position:0%
+false, then not C is true. And so this
+ 
+
+ align:start position:0%
+false, then not C is true. And so this
+whole thing is true. I'm going to remind
+
+ align:start position:0%
+whole thing is true. I'm going to remind
+ 
+
+ align:start position:0%
+whole thing is true. I'm going to remind
+you uh this uh so V symbol is an or.
+
+ align:start position:0%
+you uh this uh so V symbol is an or.
+ 
+
+ align:start position:0%
+you uh this uh so V symbol is an or.
+Uh whereas the opposite symbol is an
+
+ align:start position:0%
+Uh whereas the opposite symbol is an
+ 
+
+ align:start position:0%
+Uh whereas the opposite symbol is an
+and.
+
+ align:start position:0%
+and.
+ 
+
+ align:start position:0%
+and.
+I think the pneumonic here is this looks
+
+ align:start position:0%
+I think the pneumonic here is this looks
+ 
+
+ align:start position:0%
+I think the pneumonic here is this looks
+like a letter A. This looks like a
+
+ align:start position:0%
+like a letter A. This looks like a
+ 
+
+ align:start position:0%
+like a letter A. This looks like a
+letter O. I've heard some people say
+
+ align:start position:0%
+letter O. I've heard some people say
+ 
+
+ align:start position:0%
+letter O. I've heard some people say
+this looks like a lowercase R for or. Um
+
+ align:start position:0%
+this looks like a lowercase R for or. Um
+ 
+
+ align:start position:0%
+this looks like a lowercase R for or. Um
+anyway, you just remember these things.
+
+ align:start position:0%
+anyway, you just remember these things.
+ 
+
+ align:start position:0%
+anyway, you just remember these things.
+This is or this is and uh so C or not C
+
+ align:start position:0%
+This is or this is and uh so C or not C
+ 
+
+ align:start position:0%
+This is or this is and uh so C or not C
+is the question no is always true. Uh so
+
+ align:start position:0%
+is the question no is always true. Uh so
+ 
+
+ align:start position:0%
+is the question no is always true. Uh so
+we call it a tautology fancy word for
+
+ align:start position:0%
+we call it a tautology fancy word for
+ 
+
+ align:start position:0%
+we call it a tautology fancy word for
+being always true. And so uh
+
+ align:start position:0%
+being always true. And so uh
+ 
+
+ align:start position:0%
+being always true. And so uh
+what this tells us is that our
+
+ align:start position:0%
+what this tells us is that our
+ 
+
+ align:start position:0%
+what this tells us is that our
+proposition P let's say we want to prove
+
+ align:start position:0%
+proposition P let's say we want to prove
+ 
+
+ align:start position:0%
+proposition P let's say we want to prove
+P is equivalent to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh C or not C
+
+ align:start position:0%
+uh C or not C
+ 
+
+ align:start position:0%
+uh C or not C
+implies P.
+
+ align:start position:0%
+implies P.
+ 
+
+ align:start position:0%
+implies P.
+So this is saying if C or not C then P
+
+ align:start position:0%
+So this is saying if C or not C then P
+ 
+
+ align:start position:0%
+So this is saying if C or not C then P
+is true. C or not C is just always true.
+
+ align:start position:0%
+is true. C or not C is just always true.
+ 
+
+ align:start position:0%
+is true. C or not C is just always true.
+So this is saying if true in other words
+
+ align:start position:0%
+So this is saying if true in other words
+ 
+
+ align:start position:0%
+So this is saying if true in other words
+always P better be true. So P and this
+
+ align:start position:0%
+always P better be true. So P and this
+ 
+
+ align:start position:0%
+always P better be true. So P and this
+implication are equivalent. Another way
+
+ align:start position:0%
+implication are equivalent. Another way
+ 
+
+ align:start position:0%
+implication are equivalent. Another way
+to see that is to rewrite this
+
+ align:start position:0%
+to see that is to rewrite this
+ 
+
+ align:start position:0%
+to see that is to rewrite this
+implication as uh a negation I guess. So
+
+ align:start position:0%
+implication as uh a negation I guess. So
+ 
+
+ align:start position:0%
+implication as uh a negation I guess. So
+this is like saying not uh true
+
+ align:start position:0%
+this is like saying not uh true
+ 
+
+ align:start position:0%
+this is like saying not uh true
+or P and so that's just the same thing
+
+ align:start position:0%
+or P and so that's just the same thing
+ 
+
+ align:start position:0%
+or P and so that's just the same thing
+as P
+
+ align:start position:0%
+as P
+ 
+
+ align:start position:0%
+as P
+because this is true.
+
+ align:start position:0%
+because this is true.
+ 
+
+ align:start position:0%
+because this is true.
+Okay, cool. Uh so I want to rewrite this
+
+ align:start position:0%
+Okay, cool. Uh so I want to rewrite this
+ 
+
+ align:start position:0%
+Okay, cool. Uh so I want to rewrite this
+a little bit and say this thing is
+
+ align:start position:0%
+a little bit and say this thing is
+ 
+
+ align:start position:0%
+a little bit and say this thing is
+equivalent to C implies P and not C
+
+ align:start position:0%
+equivalent to C implies P and not C
+ 
+
+ align:start position:0%
+equivalent to C implies P and not C
+implies P.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh why is this true? Uh it's like a
+
+ align:start position:0%
+Uh why is this true? Uh it's like a
+ 
+
+ align:start position:0%
+Uh why is this true? Uh it's like a
+distributive law. This is saying I want
+
+ align:start position:0%
+distributive law. This is saying I want
+ 
+
+ align:start position:0%
+distributive law. This is saying I want
+to prove that C implies P and I want to
+
+ align:start position:0%
+to prove that C implies P and I want to
+ 
+
+ align:start position:0%
+to prove that C implies P and I want to
+prove that not C implies P. That's what
+
+ align:start position:0%
+prove that not C implies P. That's what
+ 
+
+ align:start position:0%
+prove that not C implies P. That's what
+I wrote over there. Uh that implies that
+
+ align:start position:0%
+I wrote over there. Uh that implies that
+ 
+
+ align:start position:0%
+I wrote over there. Uh that implies that
+the combination of C and not C implies
+
+ align:start position:0%
+the combination of C and not C implies
+ 
+
+ align:start position:0%
+the combination of C and not C implies
+P.
+
+ align:start position:0%
+P.
+ 
+
+ align:start position:0%
+P.
+Okay. So I claim these are equivalent.
+
+ align:start position:0%
+Okay. So I claim these are equivalent.
+ 
+
+ align:start position:0%
+Okay. So I claim these are equivalent.
+You could one way to verify it is with
+
+ align:start position:0%
+You could one way to verify it is with
+ 
+
+ align:start position:0%
+You could one way to verify it is with
+the truth table or you can do it with
+
+ align:start position:0%
+the truth table or you can do it with
+ 
+
+ align:start position:0%
+the truth table or you can do it with
+some manipulation.
+
+ align:start position:0%
+some manipulation.
+ 
+
+ align:start position:0%
+some manipulation.
+All right. So uh we have
+
+ align:start position:0%
+All right. So uh we have
+ 
+
+ align:start position:0%
+All right. So uh we have
+uh what this is saying is in order to
+
+ align:start position:0%
+uh what this is saying is in order to
+ 
+
+ align:start position:0%
+uh what this is saying is in order to
+prove P we need to prove that P is true
+
+ align:start position:0%
+prove P we need to prove that P is true
+ 
+
+ align:start position:0%
+prove P we need to prove that P is true
+assuming C and prove that P is true
+
+ align:start position:0%
+assuming C and prove that P is true
+ 
+
+ align:start position:0%
+assuming C and prove that P is true
+assuming not C. And these are the two
+
+ align:start position:0%
+assuming not C. And these are the two
+ 
+
+ align:start position:0%
+assuming not C. And these are the two
+cases and proof by cases. Let me write
+
+ align:start position:0%
+cases and proof by cases. Let me write
+ 
+
+ align:start position:0%
+cases and proof by cases. Let me write
+out a little template for you.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's suppose the theorem we want to
+
+ align:start position:0%
+Let's suppose the theorem we want to
+ 
+
+ align:start position:0%
+Let's suppose the theorem we want to
+prove
+
+ align:start position:0%
+prove
+ 
+
+ align:start position:0%
+prove
+is P.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theorem means something that's true and
+
+ align:start position:0%
+Theorem means something that's true and
+ 
+
+ align:start position:0%
+Theorem means something that's true and
+that we're about to prove.
+
+ align:start position:0%
+that we're about to prove.
+ 
+
+ align:start position:0%
+that we're about to prove.
+Uh and so we'd usually say proof by
+
+ align:start position:0%
+Uh and so we'd usually say proof by
+ 
+
+ align:start position:0%
+Uh and so we'd usually say proof by
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+on the truth value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of C. So this is uh for any
+
+ align:start position:0%
+of C. So this is uh for any
+ 
+
+ align:start position:0%
+of C. So this is uh for any
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement seek
+
+ align:start position:0%
+statement seek
+ 
+
+ align:start position:0%
+statement seek
+proposition is what the word I was
+
+ align:start position:0%
+proposition is what the word I was
+ 
+
+ align:start position:0%
+proposition is what the word I was
+looking for. Any proposition C, it's
+
+ align:start position:0%
+looking for. Any proposition C, it's
+ 
+
+ align:start position:0%
+looking for. Any proposition C, it's
+either true or false.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh and so we're going to do proof by
+
+ align:start position:0%
+Uh and so we're going to do proof by
+ 
+
+ align:start position:0%
+Uh and so we're going to do proof by
+cases on the truth value of C. Case one
+
+ align:start position:0%
+cases on the truth value of C. Case one
+ 
+
+ align:start position:0%
+cases on the truth value of C. Case one
+is that C is true
+
+ align:start position:0%
+is that C is true
+ 
+
+ align:start position:0%
+is that C is true
+and case two is that C is false.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so what do we do in each case? Uh
+
+ align:start position:0%
+And so what do we do in each case? Uh
+ 
+
+ align:start position:0%
+And so what do we do in each case? Uh
+well in the case that C is true this
+
+ align:start position:0%
+well in the case that C is true this
+ 
+
+ align:start position:0%
+well in the case that C is true this
+means that we get to assume that C is
+
+ align:start position:0%
+means that we get to assume that C is
+ 
+
+ align:start position:0%
+means that we get to assume that C is
+true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and then use that to prove that P is
+
+ align:start position:0%
+uh and then use that to prove that P is
+ 
+
+ align:start position:0%
+uh and then use that to prove that P is
+true. And so the the missing step in
+
+ align:start position:0%
+true. And so the the missing step in
+ 
+
+ align:start position:0%
+true. And so the the missing step in
+this uh proof outline or this template
+
+ align:start position:0%
+this uh proof outline or this template
+ 
+
+ align:start position:0%
+this uh proof outline or this template
+uh is we need to say P is true because
+
+ align:start position:0%
+uh is we need to say P is true because
+ 
+
+ align:start position:0%
+uh is we need to say P is true because
+some reasons which we need to fill in.
+
+ align:start position:0%
+some reasons which we need to fill in.
+ 
+
+ align:start position:0%
+some reasons which we need to fill in.
+uh and similarly in the else in the C is
+
+ align:start position:0%
+uh and similarly in the else in the C is
+ 
+
+ align:start position:0%
+uh and similarly in the else in the C is
+false case we need to prove P is true
+
+ align:start position:0%
+false case we need to prove P is true
+ 
+
+ align:start position:0%
+false case we need to prove P is true
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+for some reasons. Okay, so we need twice
+
+ align:start position:0%
+for some reasons. Okay, so we need twice
+ 
+
+ align:start position:0%
+for some reasons. Okay, so we need twice
+as many reasons but the idea is that
+
+ align:start position:0%
+as many reasons but the idea is that
+ 
+
+ align:start position:0%
+as many reasons but the idea is that
+maybe assuming C is true makes it easier
+
+ align:start position:0%
+maybe assuming C is true makes it easier
+ 
+
+ align:start position:0%
+maybe assuming C is true makes it easier
+to prove P is true. Maybe also proving
+
+ align:start position:0%
+to prove P is true. Maybe also proving
+ 
+
+ align:start position:0%
+to prove P is true. Maybe also proving
+assuming C is false makes it easier to
+
+ align:start position:0%
+assuming C is false makes it easier to
+ 
+
+ align:start position:0%
+assuming C is false makes it easier to
+to prove that P is true. So in these
+
+ align:start position:0%
+to prove that P is true. So in these
+ 
+
+ align:start position:0%
+to prove that P is true. So in these
+boxes here we get to use C and in here
+
+ align:start position:0%
+boxes here we get to use C and in here
+ 
+
+ align:start position:0%
+boxes here we get to use C and in here
+we get to use not C. And often this
+
+ align:start position:0%
+we get to use not C. And often this
+ 
+
+ align:start position:0%
+we get to use not C. And often this
+makes proofs easier. But the challenging
+
+ align:start position:0%
+makes proofs easier. But the challenging
+ 
+
+ align:start position:0%
+makes proofs easier. But the challenging
+part is to pick the correct C. What's
+
+ align:start position:0%
+part is to pick the correct C. What's
+ 
+
+ align:start position:0%
+part is to pick the correct C. What's
+the right choice of C for this to be
+
+ align:start position:0%
+the right choice of C for this to be
+ 
+
+ align:start position:0%
+the right choice of C for this to be
+true. Um, and maybe one more line I want
+
+ align:start position:0%
+true. Um, and maybe one more line I want
+ 
+
+ align:start position:0%
+true. Um, and maybe one more line I want
+to add to this template, which is pretty
+
+ align:start position:0%
+to add to this template, which is pretty
+ 
+
+ align:start position:0%
+to add to this template, which is pretty
+obvious in this setting, but gets much
+
+ align:start position:0%
+obvious in this setting, but gets much
+ 
+
+ align:start position:0%
+obvious in this setting, but gets much
+less obvious when you think about more
+
+ align:start position:0%
+less obvious when you think about more
+ 
+
+ align:start position:0%
+less obvious when you think about more
+than two cases. So a final step in this
+
+ align:start position:0%
+than two cases. So a final step in this
+ 
+
+ align:start position:0%
+than two cases. So a final step in this
+proof would be to say uh C is either
+
+ align:start position:0%
+proof would be to say uh C is either
+ 
+
+ align:start position:0%
+proof would be to say uh C is either
+true or false because all propositions
+
+ align:start position:0%
+true or false because all propositions
+ 
+
+ align:start position:0%
+true or false because all propositions
+are either true or false.
+
+ align:start position:0%
+are either true or false.
+ 
+
+ align:start position:0%
+are either true or false.
+And so uh the cases are exhaustive.
+
+ align:start position:0%
+And so uh the cases are exhaustive.
+ 
+
+ align:start position:0%
+And so uh the cases are exhaustive.
+So this is also called a proof by
+
+ align:start position:0%
+So this is also called a proof by
+ 
+
+ align:start position:0%
+So this is also called a proof by
+exhaustion. Not because we're really
+
+ align:start position:0%
+exhaustion. Not because we're really
+ 
+
+ align:start position:0%
+exhaustion. Not because we're really
+tired, maybe we are also. But the idea
+
+ align:start position:0%
+tired, maybe we are also. But the idea
+ 
+
+ align:start position:0%
+tired, maybe we are also. But the idea
+is we want to exhaust all possible
+
+ align:start position:0%
+is we want to exhaust all possible
+ 
+
+ align:start position:0%
+is we want to exhaust all possible
+cases. And if we prove that we we
+
+ align:start position:0%
+cases. And if we prove that we we
+ 
+
+ align:start position:0%
+cases. And if we prove that we we
+captured every possible situation and
+
+ align:start position:0%
+captured every possible situation and
+ 
+
+ align:start position:0%
+captured every possible situation and
+all of them P is true then we're done.
+
+ align:start position:0%
+all of them P is true then we're done.
+ 
+
+ align:start position:0%
+all of them P is true then we're done.
+Okay. So that's what we'd like to do.
+
+ align:start position:0%
+Okay. So that's what we'd like to do.
+ 
+
+ align:start position:0%
+Okay. So that's what we'd like to do.
+I'm going to give you two examples.
+
+ align:start position:0%
+I'm going to give you two examples.
+ 
+
+ align:start position:0%
+I'm going to give you two examples.
+First one is very simple. The second one
+
+ align:start position:0%
+First one is very simple. The second one
+ 
+
+ align:start position:0%
+First one is very simple. The second one
+is more interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions. All right. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the claim is this is a general fact
+
+ align:start position:0%
+so the claim is this is a general fact
+ 
+
+ align:start position:0%
+so the claim is this is a general fact
+that a implies b or b implies c is a
+
+ align:start position:0%
+that a implies b or b implies c is a
+ 
+
+ align:start position:0%
+that a implies b or b implies c is a
+tautology. So this means it's always
+
+ align:start position:0%
+tautology. So this means it's always
+ 
+
+ align:start position:0%
+tautology. So this means it's always
+true again. So you can rewrite this as
+
+ align:start position:0%
+true again. So you can rewrite this as
+ 
+
+ align:start position:0%
+true again. So you can rewrite this as
+for all a, b and c uh which are either
+
+ align:start position:0%
+for all a, b and c uh which are either
+ 
+
+ align:start position:0%
+for all a, b and c uh which are either
+true or false
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we have that a implies b or b implies
+
+ align:start position:0%
+uh we have that a implies b or b implies
+ 
+
+ align:start position:0%
+uh we have that a implies b or b implies
+c is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, fun fun fact. Um let's prove it.
+
+ align:start position:0%
+Okay, fun fun fact. Um let's prove it.
+ 
+
+ align:start position:0%
+Okay, fun fun fact. Um let's prove it.
+And the proof technique we're going to
+
+ align:start position:0%
+And the proof technique we're going to
+ 
+
+ align:start position:0%
+And the proof technique we're going to
+use by cases by two cases namely uh on B
+
+ align:start position:0%
+use by cases by two cases namely uh on B
+ 
+
+ align:start position:0%
+use by cases by two cases namely uh on B
+B is either true or false.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We could try to do a case analysis in
+
+ align:start position:0%
+We could try to do a case analysis in
+ 
+
+ align:start position:0%
+We could try to do a case analysis in
+terms of A or in terms of C. Turns out B
+
+ align:start position:0%
+terms of A or in terms of C. Turns out B
+ 
+
+ align:start position:0%
+terms of A or in terms of C. Turns out B
+is sort of the right answer here. It
+
+ align:start position:0%
+is sort of the right answer here. It
+ 
+
+ align:start position:0%
+is sort of the right answer here. It
+will lead to the fewest cases. We'll
+
+ align:start position:0%
+will lead to the fewest cases. We'll
+ 
+
+ align:start position:0%
+will lead to the fewest cases. We'll
+only need two uh intuitively because B
+
+ align:start position:0%
+only need two uh intuitively because B
+ 
+
+ align:start position:0%
+only need two uh intuitively because B
+is in both of these expressions. So it
+
+ align:start position:0%
+is in both of these expressions. So it
+ 
+
+ align:start position:0%
+is in both of these expressions. So it
+seems good to split on B because it will
+
+ align:start position:0%
+seems good to split on B because it will
+ 
+
+ align:start position:0%
+seems good to split on B because it will
+impact this one and this one.
+
+ align:start position:0%
+impact this one and this one.
+ 
+
+ align:start position:0%
+impact this one and this one.
+Okay. Uh so
+
+ align:start position:0%
+Okay. Uh so
+ 
+
+ align:start position:0%
+Okay. Uh so
+case one
+
+ align:start position:0%
+case one
+ 
+
+ align:start position:0%
+case one
+is that B is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+uh if B is true, I claim that A implies
+
+ align:start position:0%
+uh if B is true, I claim that A implies
+ 
+
+ align:start position:0%
+uh if B is true, I claim that A implies
+B is true,
+
+ align:start position:0%
+B is true,
+ 
+
+ align:start position:0%
+B is true,
+which is this first half.
+
+ align:start position:0%
+which is this first half.
+ 
+
+ align:start position:0%
+which is this first half.
+Why?
+
+ align:start position:0%
+Why?
+ 
+
+ align:start position:0%
+Why?
+Uh in other words, I I claim that A
+
+ align:start position:0%
+Uh in other words, I I claim that A
+ 
+
+ align:start position:0%
+Uh in other words, I I claim that A
+implies true is a tautology.
+
+ align:start position:0%
+implies true is a tautology.
+ 
+
+ align:start position:0%
+implies true is a tautology.
+I think another again an easy way to see
+
+ align:start position:0%
+I think another again an easy way to see
+ 
+
+ align:start position:0%
+I think another again an easy way to see
+this is to rewrite uh rewrite this
+
+ align:start position:0%
+this is to rewrite uh rewrite this
+ 
+
+ align:start position:0%
+this is to rewrite uh rewrite this
+implication as not the left hand side or
+
+ align:start position:0%
+implication as not the left hand side or
+ 
+
+ align:start position:0%
+implication as not the left hand side or
+the right hand side.
+
+ align:start position:0%
+the right hand side.
+ 
+
+ align:start position:0%
+the right hand side.
+Right? Not a or true. Well, that's just
+
+ align:start position:0%
+Right? Not a or true. Well, that's just
+ 
+
+ align:start position:0%
+Right? Not a or true. Well, that's just
+true. True or anything is true. Okay?
+
+ align:start position:0%
+true. True or anything is true. Okay?
+ 
+
+ align:start position:0%
+true. True or anything is true. Okay?
+So, in particular over here, uh not a or
+
+ align:start position:0%
+So, in particular over here, uh not a or
+ 
+
+ align:start position:0%
+So, in particular over here, uh not a or
+b is true because we just assume that b
+
+ align:start position:0%
+b is true because we just assume that b
+ 
+
+ align:start position:0%
+b is true because we just assume that b
+is true.
+
+ align:start position:0%
+is true.
+ 
+
+ align:start position:0%
+is true.
+Okay. So, this tells us that uh a
+
+ align:start position:0%
+Okay. So, this tells us that uh a
+ 
+
+ align:start position:0%
+Okay. So, this tells us that uh a
+implies b or anything in particular b or
+
+ align:start position:0%
+implies b or anything in particular b or
+ 
+
+ align:start position:0%
+implies b or anything in particular b or
+c is also true.
+
+ align:start position:0%
+c is also true.
+ 
+
+ align:start position:0%
+c is also true.
+Okay. So, kind of trivial, right? Right?
+
+ align:start position:0%
+Okay. So, kind of trivial, right? Right?
+ 
+
+ align:start position:0%
+Okay. So, kind of trivial, right? Right?
+If you assume B is true, then of course
+
+ align:start position:0%
+If you assume B is true, then of course
+ 
+
+ align:start position:0%
+If you assume B is true, then of course
+this is true and so of course the whole
+
+ align:start position:0%
+this is true and so of course the whole
+ 
+
+ align:start position:0%
+this is true and so of course the whole
+thing is true.
+
+ align:start position:0%
+thing is true.
+ 
+
+ align:start position:0%
+thing is true.
+So easy when you have the correct case.
+
+ align:start position:0%
+So easy when you have the correct case.
+ 
+
+ align:start position:0%
+So easy when you have the correct case.
+Uh let's think about the other case.
+
+ align:start position:0%
+Uh let's think about the other case.
+ 
+
+ align:start position:0%
+Uh let's think about the other case.
+It's not enough to just have one half of
+
+ align:start position:0%
+It's not enough to just have one half of
+ 
+
+ align:start position:0%
+It's not enough to just have one half of
+the cases. We also need to think about
+
+ align:start position:0%
+the cases. We also need to think about
+ 
+
+ align:start position:0%
+the cases. We also need to think about
+when B is false.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+When B is false, I claim that the other
+
+ align:start position:0%
+When B is false, I claim that the other
+ 
+
+ align:start position:0%
+When B is false, I claim that the other
+term is true. I claim that B implies C
+
+ align:start position:0%
+term is true. I claim that B implies C
+ 
+
+ align:start position:0%
+term is true. I claim that B implies C
+is true.
+
+ align:start position:0%
+is true.
+ 
+
+ align:start position:0%
+is true.
+Uh this is maybe a little less
+
+ align:start position:0%
+Uh this is maybe a little less
+ 
+
+ align:start position:0%
+Uh this is maybe a little less
+intuitive. This is saying that false
+
+ align:start position:0%
+intuitive. This is saying that false
+ 
+
+ align:start position:0%
+intuitive. This is saying that false
+implies C is a tautology like for any C
+
+ align:start position:0%
+implies C is a tautology like for any C
+ 
+
+ align:start position:0%
+implies C is a tautology like for any C
+false implies it. Um and this should
+
+ align:start position:0%
+false implies it. Um and this should
+ 
+
+ align:start position:0%
+false implies it. Um and this should
+eventually become intuitive for you when
+
+ align:start position:0%
+eventually become intuitive for you when
+ 
+
+ align:start position:0%
+eventually become intuitive for you when
+you get used to implies and if then this
+
+ align:start position:0%
+you get used to implies and if then this
+ 
+
+ align:start position:0%
+you get used to implies and if then this
+is saying if false which means never uh
+
+ align:start position:0%
+is saying if false which means never uh
+ 
+
+ align:start position:0%
+is saying if false which means never uh
+I need C to be true. But if I if this
+
+ align:start position:0%
+I need C to be true. But if I if this
+ 
+
+ align:start position:0%
+I need C to be true. But if I if this
+condition is never true then I don't
+
+ align:start position:0%
+condition is never true then I don't
+ 
+
+ align:start position:0%
+condition is never true then I don't
+care about the right hand side. If it's
+
+ align:start position:0%
+care about the right hand side. If it's
+ 
+
+ align:start position:0%
+care about the right hand side. If it's
+if you know if uh pigs fly then I don't
+
+ align:start position:0%
+if you know if uh pigs fly then I don't
+ 
+
+ align:start position:0%
+if you know if uh pigs fly then I don't
+know apples are orange or something. Um
+
+ align:start position:0%
+know apples are orange or something. Um
+ 
+
+ align:start position:0%
+know apples are orange or something. Um
+it that's a true statement because it
+
+ align:start position:0%
+it that's a true statement because it
+ 
+
+ align:start position:0%
+it that's a true statement because it
+will never be the case that pigs fly at
+
+ align:start position:0%
+will never be the case that pigs fly at
+ 
+
+ align:start position:0%
+will never be the case that pigs fly at
+least in the present time. So uh another
+
+ align:start position:0%
+least in the present time. So uh another
+ 
+
+ align:start position:0%
+least in the present time. So uh another
+way to see that is to think about again
+
+ align:start position:0%
+way to see that is to think about again
+ 
+
+ align:start position:0%
+way to see that is to think about again
+not B or C.
+
+ align:start position:0%
+not B or C.
+ 
+
+ align:start position:0%
+not B or C.
+B is false so not B is true and so of
+
+ align:start position:0%
+B is false so not B is true and so of
+ 
+
+ align:start position:0%
+B is false so not B is true and so of
+course true or C is also true.
+
+ align:start position:0%
+course true or C is also true.
+ 
+
+ align:start position:0%
+course true or C is also true.
+Okay. And so that tells us that anything
+
+ align:start position:0%
+Okay. And so that tells us that anything
+ 
+
+ align:start position:0%
+Okay. And so that tells us that anything
+or B implies C is also true.
+
+ align:start position:0%
+or B implies C is also true.
+ 
+
+ align:start position:0%
+or B implies C is also true.
+So in other words, this statement
+
+ align:start position:0%
+So in other words, this statement
+ 
+
+ align:start position:0%
+So in other words, this statement
+maybe I'll call P, I'll say in either
+
+ align:start position:0%
+maybe I'll call P, I'll say in either
+ 
+
+ align:start position:0%
+maybe I'll call P, I'll say in either
+case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P is true. And so I write my little end
+
+ align:start position:0%
+P is true. And so I write my little end
+ 
+
+ align:start position:0%
+P is true. And so I write my little end
+of crew symbol. This is QED from last
+
+ align:start position:0%
+of crew symbol. This is QED from last
+ 
+
+ align:start position:0%
+of crew symbol. This is QED from last
+time. Uh this means that I have
+
+ align:start position:0%
+time. Uh this means that I have
+ 
+
+ align:start position:0%
+time. Uh this means that I have
+demonstrated the theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. So in one case this part was
+
+ align:start position:0%
+Cool. So in one case this part was
+ 
+
+ align:start position:0%
+Cool. So in one case this part was
+trivial. In the other case this part was
+
+ align:start position:0%
+trivial. In the other case this part was
+ 
+
+ align:start position:0%
+trivial. In the other case this part was
+trivial because it's an or. We're happy
+
+ align:start position:0%
+trivial because it's an or. We're happy
+ 
+
+ align:start position:0%
+trivial because it's an or. We're happy
+in either case. And we've done our proof
+
+ align:start position:0%
+in either case. And we've done our proof
+ 
+
+ align:start position:0%
+in either case. And we've done our proof
+first proof by cases. Pretty
+
+ align:start position:0%
+first proof by cases. Pretty
+ 
+
+ align:start position:0%
+first proof by cases. Pretty
+straightforward.
+
+ align:start position:0%
+straightforward.
+ 
+
+ align:start position:0%
+straightforward.
+Let's do a more surprising result
+
+ align:start position:0%
+Let's do a more surprising result
+ 
+
+ align:start position:0%
+Let's do a more surprising result
+using proof by cases called
+
+ align:start position:0%
+using proof by cases called
+ 
+
+ align:start position:0%
+using proof by cases called
+mutual
+
+ align:start position:0%
+mutual
+ 
+
+ align:start position:0%
+mutual
+friends and strangers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is actually a famous mathematical
+
+ align:start position:0%
+This is actually a famous mathematical
+ 
+
+ align:start position:0%
+This is actually a famous mathematical
+problem we're going to solve today a
+
+ align:start position:0%
+problem we're going to solve today a
+ 
+
+ align:start position:0%
+problem we're going to solve today a
+particular case of it
+
+ align:start position:0%
+particular case of it
+ 
+
+ align:start position:0%
+particular case of it
+which is suppose you have six people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and every two of them are either
+
+ align:start position:0%
+um and every two of them are either
+ 
+
+ align:start position:0%
+um and every two of them are either
+friends or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and this is an exclusive or so. So
+
+ align:start position:0%
+uh and this is an exclusive or so. So
+ 
+
+ align:start position:0%
+uh and this is an exclusive or so. So
+I'm going to write exor. You're allowed
+
+ align:start position:0%
+I'm going to write exor. You're allowed
+ 
+
+ align:start position:0%
+I'm going to write exor. You're allowed
+to be friends or or not friends, not
+
+ align:start position:0%
+to be friends or or not friends, not
+ 
+
+ align:start position:0%
+to be friends or or not friends, not
+both and not neither. And in the not
+
+ align:start position:0%
+both and not neither. And in the not
+ 
+
+ align:start position:0%
+both and not neither. And in the not
+friends case, I'm also going to call
+
+ align:start position:0%
+friends case, I'm also going to call
+ 
+
+ align:start position:0%
+friends case, I'm also going to call
+them uh strangers.
+
+ align:start position:0%
+them uh strangers.
+ 
+
+ align:start position:0%
+them uh strangers.
+So this is like extreme friendship.
+
+ align:start position:0%
+So this is like extreme friendship.
+ 
+
+ align:start position:0%
+So this is like extreme friendship.
+Either you declare yourself as friends
+
+ align:start position:0%
+Either you declare yourself as friends
+ 
+
+ align:start position:0%
+Either you declare yourself as friends
+or as knowing each other or you don't
+
+ align:start position:0%
+or as knowing each other or you don't
+ 
+
+ align:start position:0%
+or as knowing each other or you don't
+know each other. In that case, you're
+
+ align:start position:0%
+know each other. In that case, you're
+ 
+
+ align:start position:0%
+know each other. In that case, you're
+strangers. You're just never both. It's
+
+ align:start position:0%
+strangers. You're just never both. It's
+ 
+
+ align:start position:0%
+strangers. You're just never both. It's
+always one or the other. Okay? So, you
+
+ align:start position:0%
+always one or the other. Okay? So, you
+ 
+
+ align:start position:0%
+always one or the other. Okay? So, you
+can think of this as I can draw a little
+
+ align:start position:0%
+can think of this as I can draw a little
+ 
+
+ align:start position:0%
+can think of this as I can draw a little
+picture of their six people represent by
+
+ align:start position:0%
+picture of their six people represent by
+ 
+
+ align:start position:0%
+picture of their six people represent by
+circles. You can put smiley faces in
+
+ align:start position:0%
+circles. You can put smiley faces in
+ 
+
+ align:start position:0%
+circles. You can put smiley faces in
+them if you want. And maybe I connect
+
+ align:start position:0%
+them if you want. And maybe I connect
+ 
+
+ align:start position:0%
+them if you want. And maybe I connect
+them via a white line if they are
+
+ align:start position:0%
+them via a white line if they are
+ 
+
+ align:start position:0%
+them via a white line if they are
+friends and a dotted line if they're
+
+ align:start position:0%
+friends and a dotted line if they're
+ 
+
+ align:start position:0%
+friends and a dotted line if they're
+strangers. So let's And every two of
+
+ align:start position:0%
+strangers. So let's And every two of
+ 
+
+ align:start position:0%
+strangers. So let's And every two of
+them have one of these two pictures.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Probably missing some
+
+ align:start position:0%
+Probably missing some
+ 
+
+ align:start position:0%
+Probably missing some
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+That's them all. Uh then
+
+ align:start position:0%
+That's them all. Uh then
+ 
+
+ align:start position:0%
+That's them all. Uh then
+I claim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no matter how what the situation is,
+
+ align:start position:0%
+no matter how what the situation is,
+ 
+
+ align:start position:0%
+no matter how what the situation is,
+which ones are friends, which ones are
+
+ align:start position:0%
+which ones are friends, which ones are
+ 
+
+ align:start position:0%
+which ones are friends, which ones are
+strangers, there's always
+
+ align:start position:0%
+strangers, there's always
+ 
+
+ align:start position:0%
+strangers, there's always
+uh either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three mutual friends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+three mutual strangers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, in this example,
+
+ align:start position:0%
+Okay, in this example,
+ 
+
+ align:start position:0%
+Okay, in this example,
+hopefully I drew enough. Yeah. Uh, these
+
+ align:start position:0%
+hopefully I drew enough. Yeah. Uh, these
+ 
+
+ align:start position:0%
+hopefully I drew enough. Yeah. Uh, these
+three people are mutual strangers.
+
+ align:start position:0%
+three people are mutual strangers.
+ 
+
+ align:start position:0%
+three people are mutual strangers.
+They're connected by a a triangle of
+
+ align:start position:0%
+They're connected by a a triangle of
+ 
+
+ align:start position:0%
+They're connected by a a triangle of
+dashed lines. Okay. If I drew some other
+
+ align:start position:0%
+dashed lines. Okay. If I drew some other
+ 
+
+ align:start position:0%
+dashed lines. Okay. If I drew some other
+pattern, like if they were all solid
+
+ align:start position:0%
+pattern, like if they were all solid
+ 
+
+ align:start position:0%
+pattern, like if they were all solid
+lines, then uh I might get the other
+
+ align:start position:0%
+lines, then uh I might get the other
+ 
+
+ align:start position:0%
+lines, then uh I might get the other
+situation, at least three mutual
+
+ align:start position:0%
+situation, at least three mutual
+ 
+
+ align:start position:0%
+situation, at least three mutual
+friends. But it turns out if you have
+
+ align:start position:0%
+friends. But it turns out if you have
+ 
+
+ align:start position:0%
+friends. But it turns out if you have
+six people, they're always at least
+
+ align:start position:0%
+six people, they're always at least
+ 
+
+ align:start position:0%
+six people, they're always at least
+three mutual friends or three mutual
+
+ align:start position:0%
+three mutual friends or three mutual
+ 
+
+ align:start position:0%
+three mutual friends or three mutual
+strangers. Let's prove this by cases.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Whenever we apply a proof by cases, we
+
+ align:start position:0%
+Whenever we apply a proof by cases, we
+ 
+
+ align:start position:0%
+Whenever we apply a proof by cases, we
+need to come up with some proposition C
+
+ align:start position:0%
+need to come up with some proposition C
+ 
+
+ align:start position:0%
+need to come up with some proposition C
+that's either true or false. Well, for a
+
+ align:start position:0%
+that's either true or false. Well, for a
+ 
+
+ align:start position:0%
+that's either true or false. Well, for a
+proof by two cases, which this will be
+
+ align:start position:0%
+proof by two cases, which this will be
+ 
+
+ align:start position:0%
+proof by two cases, which this will be
+uh and it's a little work in this case
+
+ align:start position:0%
+uh and it's a little work in this case
+ 
+
+ align:start position:0%
+uh and it's a little work in this case
+to to do it. It turns out a useful first
+
+ align:start position:0%
+to to do it. It turns out a useful first
+ 
+
+ align:start position:0%
+to to do it. It turns out a useful first
+step is to pick any person P.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So just take the first person or the
+
+ align:start position:0%
+So just take the first person or the
+ 
+
+ align:start position:0%
+So just take the first person or the
+seventh or the the fifth person ahead of
+
+ align:start position:0%
+seventh or the the fifth person ahead of
+ 
+
+ align:start position:0%
+seventh or the the fifth person ahead of
+six doesn't matter which one but label
+
+ align:start position:0%
+six doesn't matter which one but label
+ 
+
+ align:start position:0%
+six doesn't matter which one but label
+it P. So now we have a person to talk
+
+ align:start position:0%
+it P. So now we have a person to talk
+ 
+
+ align:start position:0%
+it P. So now we have a person to talk
+about. This is sort of like the proof by
+
+ align:start position:0%
+about. This is sort of like the proof by
+ 
+
+ align:start position:0%
+about. This is sort of like the proof by
+example or by construction right we want
+
+ align:start position:0%
+example or by construction right we want
+ 
+
+ align:start position:0%
+example or by construction right we want
+to overall there we want to prove an
+
+ align:start position:0%
+to overall there we want to prove an
+ 
+
+ align:start position:0%
+to overall there we want to prove an
+existence we want to prove existence of
+
+ align:start position:0%
+existence we want to prove existence of
+ 
+
+ align:start position:0%
+existence we want to prove existence of
+three mutual friends or existence of
+
+ align:start position:0%
+three mutual friends or existence of
+ 
+
+ align:start position:0%
+three mutual friends or existence of
+three mutual strangers. So it's a useful
+
+ align:start position:0%
+three mutual strangers. So it's a useful
+ 
+
+ align:start position:0%
+three mutual strangers. So it's a useful
+step to either construct one or in this
+
+ align:start position:0%
+step to either construct one or in this
+ 
+
+ align:start position:0%
+step to either construct one or in this
+case we're actually not doing much of a
+
+ align:start position:0%
+case we're actually not doing much of a
+ 
+
+ align:start position:0%
+case we're actually not doing much of a
+construction. We're just taking an
+
+ align:start position:0%
+construction. We're just taking an
+ 
+
+ align:start position:0%
+construction. We're just taking an
+arbitrary X, but that will be enough for
+
+ align:start position:0%
+arbitrary X, but that will be enough for
+ 
+
+ align:start position:0%
+arbitrary X, but that will be enough for
+this for this problem. Okay, so let me
+
+ align:start position:0%
+this for this problem. Okay, so let me
+ 
+
+ align:start position:0%
+this for this problem. Okay, so let me
+draw a little circle for P.
+
+ align:start position:0%
+draw a little circle for P.
+ 
+
+ align:start position:0%
+draw a little circle for P.
+Uh, and it might have some friends and
+
+ align:start position:0%
+Uh, and it might have some friends and
+ 
+
+ align:start position:0%
+Uh, and it might have some friends and
+it might have some strangers. Okay, how
+
+ align:start position:0%
+it might have some strangers. Okay, how
+ 
+
+ align:start position:0%
+it might have some strangers. Okay, how
+many of these lines coming out of P are
+
+ align:start position:0%
+many of these lines coming out of P are
+ 
+
+ align:start position:0%
+many of these lines coming out of P are
+there? Five. Exactly. Because there's
+
+ align:start position:0%
+there? Five. Exactly. Because there's
+ 
+
+ align:start position:0%
+there? Five. Exactly. Because there's
+six people total. P is one of them. So
+
+ align:start position:0%
+six people total. P is one of them. So
+ 
+
+ align:start position:0%
+six people total. P is one of them. So
+there are five people over here.
+
+ align:start position:0%
+there are five people over here.
+ 
+
+ align:start position:0%
+there are five people over here.
+Okay, so turns out useful case strategy
+
+ align:start position:0%
+Okay, so turns out useful case strategy
+ 
+
+ align:start position:0%
+Okay, so turns out useful case strategy
+is to uh say either P has at least three
+
+ align:start position:0%
+is to uh say either P has at least three
+ 
+
+ align:start position:0%
+is to uh say either P has at least three
+friends
+
+ align:start position:0%
+friends
+ 
+
+ align:start position:0%
+friends
+or it has less than three friends,
+
+ align:start position:0%
+or it has less than three friends,
+ 
+
+ align:start position:0%
+or it has less than three friends,
+right? Either there are three solid
+
+ align:start position:0%
+right? Either there are three solid
+ 
+
+ align:start position:0%
+right? Either there are three solid
+lines like I've drawn here or there at
+
+ align:start position:0%
+lines like I've drawn here or there at
+ 
+
+ align:start position:0%
+lines like I've drawn here or there at
+least three or they're at most two solid
+
+ align:start position:0%
+least three or they're at most two solid
+ 
+
+ align:start position:0%
+least three or they're at most two solid
+lines. Okay, let's think about this
+
+ align:start position:0%
+lines. Okay, let's think about this
+ 
+
+ align:start position:0%
+lines. Okay, let's think about this
+first case. P has at least three
+
+ align:start position:0%
+first case. P has at least three
+ 
+
+ align:start position:0%
+first case. P has at least three
+friends. Let's uh give them a name
+
+ align:start position:0%
+friends. Let's uh give them a name
+ 
+
+ align:start position:0%
+friends. Let's uh give them a name
+uh Q, R, and S.
+
+ align:start position:0%
+uh Q, R, and S.
+ 
+
+ align:start position:0%
+uh Q, R, and S.
+So uh that's sort of a general picture.
+
+ align:start position:0%
+So uh that's sort of a general picture.
+ 
+
+ align:start position:0%
+So uh that's sort of a general picture.
+Now we're assuming P has three solid
+
+ align:start position:0%
+Now we're assuming P has three solid
+ 
+
+ align:start position:0%
+Now we're assuming P has three solid
+lines to three people Q, R, and S.
+
+ align:start position:0%
+lines to three people Q, R, and S.
+ 
+
+ align:start position:0%
+lines to three people Q, R, and S.
+Okay, this is not yet a triangle. We
+
+ align:start position:0%
+Okay, this is not yet a triangle. We
+ 
+
+ align:start position:0%
+Okay, this is not yet a triangle. We
+haven't solved the problem yet, but uh
+
+ align:start position:0%
+haven't solved the problem yet, but uh
+ 
+
+ align:start position:0%
+haven't solved the problem yet, but uh
+if we break into more cases, we'll be
+
+ align:start position:0%
+if we break into more cases, we'll be
+ 
+
+ align:start position:0%
+if we break into more cases, we'll be
+able to. Okay. So, uh case
+
+ align:start position:0%
+able to. Okay. So, uh case
+ 
+
+ align:start position:0%
+able to. Okay. So, uh case
+1 A is going to be
+
+ align:start position:0%
+1 A is going to be
+ 
+
+ align:start position:0%
+1 A is going to be
+uh sum two
+
+ align:start position:0%
+uh sum two
+ 
+
+ align:start position:0%
+uh sum two
+of Q, R and S are friends.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Suppose
+
+ align:start position:0%
+Okay. Suppose
+ 
+
+ align:start position:0%
+Okay. Suppose
+uh for example Q and S are friends. Have
+
+ align:start position:0%
+uh for example Q and S are friends. Have
+ 
+
+ align:start position:0%
+uh for example Q and S are friends. Have
+I found a triangle? Yes. P Q and S are
+
+ align:start position:0%
+I found a triangle? Yes. P Q and S are
+ 
+
+ align:start position:0%
+I found a triangle? Yes. P Q and S are
+mutual friends. If this edge is here or
+
+ align:start position:0%
+mutual friends. If this edge is here or
+ 
+
+ align:start position:0%
+mutual friends. If this edge is here or
+if this edge is here then these three
+
+ align:start position:0%
+if this edge is here then these three
+ 
+
+ align:start position:0%
+if this edge is here then these three
+people are three mutual friends or if
+
+ align:start position:0%
+people are three mutual friends or if
+ 
+
+ align:start position:0%
+people are three mutual friends or if
+this edge is here these three people are
+
+ align:start position:0%
+this edge is here these three people are
+ 
+
+ align:start position:0%
+this edge is here these three people are
+mutual friends. If there's any edge in
+
+ align:start position:0%
+mutual friends. If there's any edge in
+ 
+
+ align:start position:0%
+mutual friends. If there's any edge in
+here that I can draw any uh solid line
+
+ align:start position:0%
+here that I can draw any uh solid line
+ 
+
+ align:start position:0%
+here that I can draw any uh solid line
+between QR and S then those two people
+
+ align:start position:0%
+between QR and S then those two people
+ 
+
+ align:start position:0%
+between QR and S then those two people
+plus P form three mutual friends.
+
+ align:start position:0%
+plus P form three mutual friends.
+ 
+
+ align:start position:0%
+plus P form three mutual friends.
+Okay. So that case is actually easy.
+
+ align:start position:0%
+Okay. So that case is actually easy.
+ 
+
+ align:start position:0%
+Okay. So that case is actually easy.
+Great.
+
+ align:start position:0%
+Great.
+ 
+
+ align:start position:0%
+Great.
+Then uh P plus those two people
+
+ align:start position:0%
+Then uh P plus those two people
+ 
+
+ align:start position:0%
+Then uh P plus those two people
+are three mutual friends.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, which uh was situation one up
+
+ align:start position:0%
+Okay, which uh was situation one up
+ 
+
+ align:start position:0%
+Okay, which uh was situation one up
+here. There's always either three mutual
+
+ align:start position:0%
+here. There's always either three mutual
+ 
+
+ align:start position:0%
+here. There's always either three mutual
+friends or three mutual strangers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, uh so now we need to think about
+
+ align:start position:0%
+Okay, uh so now we need to think about
+ 
+
+ align:start position:0%
+Okay, uh so now we need to think about
+the other cases. Let's go over here.
+
+ align:start position:0%
+the other cases. Let's go over here.
+ 
+
+ align:start position:0%
+the other cases. Let's go over here.
+We found one case that was easy, but uh
+
+ align:start position:0%
+We found one case that was easy, but uh
+ 
+
+ align:start position:0%
+We found one case that was easy, but uh
+there's case 1B, which is maybe there
+
+ align:start position:0%
+there's case 1B, which is maybe there
+ 
+
+ align:start position:0%
+there's case 1B, which is maybe there
+aren't two mutual friends, and there's
+
+ align:start position:0%
+aren't two mutual friends, and there's
+ 
+
+ align:start position:0%
+aren't two mutual friends, and there's
+case two where P does not have at least
+
+ align:start position:0%
+case two where P does not have at least
+ 
+
+ align:start position:0%
+case two where P does not have at least
+three friends. Okay, but it turns out
+
+ align:start position:0%
+three friends. Okay, but it turns out
+ 
+
+ align:start position:0%
+three friends. Okay, but it turns out
+all of these cases will be easy. So,
+
+ align:start position:0%
+all of these cases will be easy. So,
+ 
+
+ align:start position:0%
+all of these cases will be easy. So,
+let's do uh case 1 B.
+
+ align:start position:0%
+let's do uh case 1 B.
+ 
+
+ align:start position:0%
+let's do uh case 1 B.
+Now, I get to sort of freely choose what
+
+ align:start position:0%
+Now, I get to sort of freely choose what
+ 
+
+ align:start position:0%
+Now, I get to sort of freely choose what
+case one was, and I get to freely choose
+
+ align:start position:0%
+case one was, and I get to freely choose
+ 
+
+ align:start position:0%
+case one was, and I get to freely choose
+what case 1 A was because whenever I
+
+ align:start position:0%
+what case 1 A was because whenever I
+ 
+
+ align:start position:0%
+what case 1 A was because whenever I
+split into cases, I get to choose my
+
+ align:start position:0%
+split into cases, I get to choose my
+ 
+
+ align:start position:0%
+split into cases, I get to choose my
+proposition C to be anything I want. So
+
+ align:start position:0%
+proposition C to be anything I want. So
+ 
+
+ align:start position:0%
+proposition C to be anything I want. So
+this was C in the first case. This was C
+
+ align:start position:0%
+this was C in the first case. This was C
+ 
+
+ align:start position:0%
+this was C in the first case. This was C
+in the second case. But generally if
+
+ align:start position:0%
+in the second case. But generally if
+ 
+
+ align:start position:0%
+in the second case. But generally if
+you're doing proof by two cases, you
+
+ align:start position:0%
+you're doing proof by two cases, you
+ 
+
+ align:start position:0%
+you're doing proof by two cases, you
+have no choice at this point. So case 1
+
+ align:start position:0%
+have no choice at this point. So case 1
+ 
+
+ align:start position:0%
+have no choice at this point. So case 1
+A was whatever. Case 1 B has to be the
+
+ align:start position:0%
+A was whatever. Case 1 B has to be the
+ 
+
+ align:start position:0%
+A was whatever. Case 1 B has to be the
+negation of this.
+
+ align:start position:0%
+negation of this.
+ 
+
+ align:start position:0%
+negation of this.
+Okay. So case 1B literally is uh not sum
+
+ align:start position:0%
+Okay. So case 1B literally is uh not sum
+ 
+
+ align:start position:0%
+Okay. So case 1B literally is uh not sum
+to uh of QRS are friends. Uh but if you
+
+ align:start position:0%
+to uh of QRS are friends. Uh but if you
+ 
+
+ align:start position:0%
+to uh of QRS are friends. Uh but if you
+think about that for a little bit, this
+
+ align:start position:0%
+think about that for a little bit, this
+ 
+
+ align:start position:0%
+think about that for a little bit, this
+is saying um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q R and S uh let me let me write this uh
+
+ align:start position:0%
+Q R and S uh let me let me write this uh
+ 
+
+ align:start position:0%
+Q R and S uh let me let me write this uh
+in a couple of steps. No two of Q R and
+
+ align:start position:0%
+in a couple of steps. No two of Q R and
+ 
+
+ align:start position:0%
+in a couple of steps. No two of Q R and
+S are friends.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But that's the same thing as saying QR
+
+ align:start position:0%
+But that's the same thing as saying QR
+ 
+
+ align:start position:0%
+But that's the same thing as saying QR
+and S are mutual strangers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we're using this fact or this
+
+ align:start position:0%
+Okay, we're using this fact or this
+ 
+
+ align:start position:0%
+Okay, we're using this fact or this
+assumption that every two people are
+
+ align:start position:0%
+assumption that every two people are
+ 
+
+ align:start position:0%
+assumption that every two people are
+either friends or strangers.
+
+ align:start position:0%
+either friends or strangers.
+ 
+
+ align:start position:0%
+either friends or strangers.
+Always one or the other. So if there's
+
+ align:start position:0%
+Always one or the other. So if there's
+ 
+
+ align:start position:0%
+Always one or the other. So if there's
+no solid line over here, then all of
+
+ align:start position:0%
+no solid line over here, then all of
+ 
+
+ align:start position:0%
+no solid line over here, then all of
+these are dash lines. So all three of
+
+ align:start position:0%
+these are dash lines. So all three of
+ 
+
+ align:start position:0%
+these are dash lines. So all three of
+these are mutual strangers. And there we
+
+ align:start position:0%
+these are mutual strangers. And there we
+ 
+
+ align:start position:0%
+these are mutual strangers. And there we
+found our triangle of strangers.
+
+ align:start position:0%
+found our triangle of strangers.
+ 
+
+ align:start position:0%
+found our triangle of strangers.
+Okay. So it turns out case 1 A and case
+
+ align:start position:0%
+Okay. So it turns out case 1 A and case
+ 
+
+ align:start position:0%
+Okay. So it turns out case 1 A and case
+1 B are actually just as easy, just sort
+
+ align:start position:0%
+1 B are actually just as easy, just sort
+ 
+
+ align:start position:0%
+1 B are actually just as easy, just sort
+of reversed. Uh so this was situation
+
+ align:start position:0%
+of reversed. Uh so this was situation
+ 
+
+ align:start position:0%
+of reversed. Uh so this was situation
+two.
+
+ align:start position:0%
+two.
+ 
+
+ align:start position:0%
+two.
+So either we got three mutual friends or
+
+ align:start position:0%
+So either we got three mutual friends or
+ 
+
+ align:start position:0%
+So either we got three mutual friends or
+we got three mutual strangers, but we're
+
+ align:start position:0%
+we got three mutual strangers, but we're
+ 
+
+ align:start position:0%
+we got three mutual strangers, but we're
+still inside case one. We just finished
+
+ align:start position:0%
+still inside case one. We just finished
+ 
+
+ align:start position:0%
+still inside case one. We just finished
+case one. Now we need to think about
+
+ align:start position:0%
+case one. Now we need to think about
+ 
+
+ align:start position:0%
+case one. Now we need to think about
+case two. So I'm going to unindent here
+
+ align:start position:0%
+case two. So I'm going to unindent here
+ 
+
+ align:start position:0%
+case two. So I'm going to unindent here
+and go to case two.
+
+ align:start position:0%
+and go to case two.
+ 
+
+ align:start position:0%
+and go to case two.
+Case two again has to be exactly the
+
+ align:start position:0%
+Case two again has to be exactly the
+ 
+
+ align:start position:0%
+Case two again has to be exactly the
+opposite of this. So P does not have at
+
+ align:start position:0%
+opposite of this. So P does not have at
+ 
+
+ align:start position:0%
+opposite of this. So P does not have at
+least three friends.
+
+ align:start position:0%
+least three friends.
+ 
+
+ align:start position:0%
+least three friends.
+Uh by
+
+ align:start position:0%
+Uh by
+ 
+
+ align:start position:0%
+Uh by
+number of people being an integer. This
+
+ align:start position:0%
+number of people being an integer. This
+ 
+
+ align:start position:0%
+number of people being an integer. This
+is saying P has at most two friends.
+
+ align:start position:0%
+is saying P has at most two friends.
+ 
+
+ align:start position:0%
+is saying P has at most two friends.
+Okay. If it doesn't have at least three,
+
+ align:start position:0%
+Okay. If it doesn't have at least three,
+ 
+
+ align:start position:0%
+Okay. If it doesn't have at least three,
+it's at most two because number of
+
+ align:start position:0%
+it's at most two because number of
+ 
+
+ align:start position:0%
+it's at most two because number of
+friends is always an integer.
+
+ align:start position:0%
+friends is always an integer.
+ 
+
+ align:start position:0%
+friends is always an integer.
+Okay, great. So that case two is a
+
+ align:start position:0%
+Okay, great. So that case two is a
+ 
+
+ align:start position:0%
+Okay, great. So that case two is a
+negation of case one. Um, and it turns
+
+ align:start position:0%
+negation of case one. Um, and it turns
+ 
+
+ align:start position:0%
+negation of case one. Um, and it turns
+out that is also kind of easy for a
+
+ align:start position:0%
+out that is also kind of easy for a
+ 
+
+ align:start position:0%
+out that is also kind of easy for a
+symmetric reason. Uh, remember there are
+
+ align:start position:0%
+symmetric reason. Uh, remember there are
+ 
+
+ align:start position:0%
+symmetric reason. Uh, remember there are
+six people total. So there's P and five
+
+ align:start position:0%
+six people total. So there's P and five
+ 
+
+ align:start position:0%
+six people total. So there's P and five
+others.
+
+ align:start position:0%
+others.
+ 
+
+ align:start position:0%
+others.
+So uh, how many strangers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is P with or how many people is P a
+
+ align:start position:0%
+is P with or how many people is P a
+ 
+
+ align:start position:0%
+is P with or how many people is P a
+stranger to?
+
+ align:start position:0%
+stranger to?
+ 
+
+ align:start position:0%
+stranger to?
+Uh, well, it's at least uh, all the
+
+ align:start position:0%
+Uh, well, it's at least uh, all the
+ 
+
+ align:start position:0%
+Uh, well, it's at least uh, all the
+others. 5 minus 2 is at most two of them
+
+ align:start position:0%
+others. 5 minus 2 is at most two of them
+ 
+
+ align:start position:0%
+others. 5 minus 2 is at most two of them
+are friends. The remainder have to be
+
+ align:start position:0%
+are friends. The remainder have to be
+ 
+
+ align:start position:0%
+are friends. The remainder have to be
+strangers. And so this is three.
+
+ align:start position:0%
+strangers. And so this is three.
+ 
+
+ align:start position:0%
+strangers. And so this is three.
+So P having at most two friends is the
+
+ align:start position:0%
+So P having at most two friends is the
+ 
+
+ align:start position:0%
+So P having at most two friends is the
+same thing as P having at least three
+
+ align:start position:0%
+same thing as P having at least three
+ 
+
+ align:start position:0%
+same thing as P having at least three
+strangers because there are five other
+
+ align:start position:0%
+strangers because there are five other
+ 
+
+ align:start position:0%
+strangers because there are five other
+people total. 2 + 3 is 5. Uh so P case
+
+ align:start position:0%
+people total. 2 + 3 is 5. Uh so P case
+ 
+
+ align:start position:0%
+people total. 2 + 3 is 5. Uh so P case
+two is P has at least three strangers.
+
+ align:start position:0%
+two is P has at least three strangers.
+ 
+
+ align:start position:0%
+two is P has at least three strangers.
+Case one was P has at least three
+
+ align:start position:0%
+Case one was P has at least three
+ 
+
+ align:start position:0%
+Case one was P has at least three
+friends. These are almost the same. I
+
+ align:start position:0%
+friends. These are almost the same. I
+ 
+
+ align:start position:0%
+friends. These are almost the same. I
+just have to flip friends versus
+
+ align:start position:0%
+just have to flip friends versus
+ 
+
+ align:start position:0%
+just have to flip friends versus
+strangers.
+
+ align:start position:0%
+strangers.
+ 
+
+ align:start position:0%
+strangers.
+So the way I would write this in a proof
+
+ align:start position:0%
+So the way I would write this in a proof
+ 
+
+ align:start position:0%
+So the way I would write this in a proof
+is uh this is symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to case one
+
+ align:start position:0%
+to case one
+ 
+
+ align:start position:0%
+to case one
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+swapping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+friends uh versus strangers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And of course uh case one or situation
+
+ align:start position:0%
+And of course uh case one or situation
+ 
+
+ align:start position:0%
+And of course uh case one or situation
+one with situation two.
+
+ align:start position:0%
+one with situation two.
+ 
+
+ align:start position:0%
+one with situation two.
+Okay. So case two would be P has at
+
+ align:start position:0%
+Okay. So case two would be P has at
+ 
+
+ align:start position:0%
+Okay. So case two would be P has at
+least three strangers QR and S. Case 1 A
+
+ align:start position:0%
+least three strangers QR and S. Case 1 A
+ 
+
+ align:start position:0%
+least three strangers QR and S. Case 1 A
+is that sum two of QR and S are
+
+ align:start position:0%
+is that sum two of QR and S are
+ 
+
+ align:start position:0%
+is that sum two of QR and S are
+strangers. Then we conclude that P plus
+
+ align:start position:0%
+strangers. Then we conclude that P plus
+ 
+
+ align:start position:0%
+strangers. Then we conclude that P plus
+those two are three mutual strangers
+
+ align:start position:0%
+those two are three mutual strangers
+ 
+
+ align:start position:0%
+those two are three mutual strangers
+which is situation two. Or case 2B would
+
+ align:start position:0%
+which is situation two. Or case 2B would
+ 
+
+ align:start position:0%
+which is situation two. Or case 2B would
+be no two of QRS are strangers. In other
+
+ align:start position:0%
+be no two of QRS are strangers. In other
+ 
+
+ align:start position:0%
+be no two of QRS are strangers. In other
+words, QRS are mutual friends. And then
+
+ align:start position:0%
+words, QRS are mutual friends. And then
+ 
+
+ align:start position:0%
+words, QRS are mutual friends. And then
+we're in situation one. So case two
+
+ align:start position:0%
+we're in situation one. So case two
+ 
+
+ align:start position:0%
+we're in situation one. So case two
+works just like case one just swapping
+
+ align:start position:0%
+works just like case one just swapping
+ 
+
+ align:start position:0%
+works just like case one just swapping
+the words friends and strangers because
+
+ align:start position:0%
+the words friends and strangers because
+ 
+
+ align:start position:0%
+the words friends and strangers because
+they didn't really have any meaning.
+
+ align:start position:0%
+they didn't really have any meaning.
+ 
+
+ align:start position:0%
+they didn't really have any meaning.
+They were just words.
+
+ align:start position:0%
+They were just words.
+ 
+
+ align:start position:0%
+They were just words.
+Cool. So in all cases
+
+ align:start position:0%
+Cool. So in all cases
+ 
+
+ align:start position:0%
+Cool. So in all cases
+uh we prove the desired result either
+
+ align:start position:0%
+uh we prove the desired result either
+ 
+
+ align:start position:0%
+uh we prove the desired result either
+situation one or situation two happens.
+
+ align:start position:0%
+situation one or situation two happens.
+ 
+
+ align:start position:0%
+situation one or situation two happens.
+Um this is a particular case of
+
+ align:start position:0%
+Um this is a particular case of
+ 
+
+ align:start position:0%
+Um this is a particular case of
+something called Ramsey theory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What we've just found is that something
+
+ align:start position:0%
+What we've just found is that something
+ 
+
+ align:start position:0%
+What we've just found is that something
+called r of 33 is uh at most six uh in
+
+ align:start position:0%
+called r of 33 is uh at most six uh in
+ 
+
+ align:start position:0%
+called r of 33 is uh at most six uh in
+general r of f comma s is the number of
+
+ align:start position:0%
+general r of f comma s is the number of
+ 
+
+ align:start position:0%
+general r of f comma s is the number of
+people you need uh in order to guarantee
+
+ align:start position:0%
+people you need uh in order to guarantee
+ 
+
+ align:start position:0%
+people you need uh in order to guarantee
+that there's at least f friends or at
+
+ align:start position:0%
+that there's at least f friends or at
+ 
+
+ align:start position:0%
+that there's at least f friends or at
+least s strangers. So we just did at
+
+ align:start position:0%
+least s strangers. So we just did at
+ 
+
+ align:start position:0%
+least s strangers. So we just did at
+least three friends or at least three
+
+ align:start position:0%
+least three friends or at least three
+ 
+
+ align:start position:0%
+least three friends or at least three
+strangers. We showed that six people was
+
+ align:start position:0%
+strangers. We showed that six people was
+ 
+
+ align:start position:0%
+strangers. We showed that six people was
+enough. It turns out uh six people is
+
+ align:start position:0%
+enough. It turns out uh six people is
+ 
+
+ align:start position:0%
+enough. It turns out uh six people is
+exactly the right number. You need six
+
+ align:start position:0%
+exactly the right number. You need six
+ 
+
+ align:start position:0%
+exactly the right number. You need six
+people in order to guarantee at least
+
+ align:start position:0%
+people in order to guarantee at least
+ 
+
+ align:start position:0%
+people in order to guarantee at least
+three friends or three strangers. If you
+
+ align:start position:0%
+three friends or three strangers. If you
+ 
+
+ align:start position:0%
+three friends or three strangers. If you
+wanted to guarantee four friends or four
+
+ align:start position:0%
+wanted to guarantee four friends or four
+ 
+
+ align:start position:0%
+wanted to guarantee four friends or four
+strangers, turns out you need 18 people.
+
+ align:start position:0%
+strangers, turns out you need 18 people.
+ 
+
+ align:start position:0%
+strangers, turns out you need 18 people.
+Uh if you want to guarantee five friends
+
+ align:start position:0%
+Uh if you want to guarantee five friends
+ 
+
+ align:start position:0%
+Uh if you want to guarantee five friends
+or five strangers, turns out you need uh
+
+ align:start position:0%
+or five strangers, turns out you need uh
+ 
+
+ align:start position:0%
+or five strangers, turns out you need uh
+somewhere between 43 and 48 people. But
+
+ align:start position:0%
+somewhere between 43 and 48 people. But
+ 
+
+ align:start position:0%
+somewhere between 43 and 48 people. But
+we don't know how many. So while this
+
+ align:start position:0%
+we don't know how many. So while this
+ 
+
+ align:start position:0%
+we don't know how many. So while this
+problem was relatively easy, three
+
+ align:start position:0%
+problem was relatively easy, three
+ 
+
+ align:start position:0%
+problem was relatively easy, three
+friends or three strangers, five friends
+
+ align:start position:0%
+friends or three strangers, five friends
+ 
+
+ align:start position:0%
+friends or three strangers, five friends
+and five strangers already is an
+
+ align:start position:0%
+and five strangers already is an
+ 
+
+ align:start position:0%
+and five strangers already is an
+unsolved mathematical problem. So that's
+
+ align:start position:0%
+unsolved mathematical problem. So that's
+ 
+
+ align:start position:0%
+unsolved mathematical problem. So that's
+kind of cool and crazy how easily you
+
+ align:start position:0%
+kind of cool and crazy how easily you
+ 
+
+ align:start position:0%
+kind of cool and crazy how easily you
+get to very difficult problems. Of
+
+ align:start position:0%
+get to very difficult problems. Of
+ 
+
+ align:start position:0%
+get to very difficult problems. Of
+course, people try to compute larger
+
+ align:start position:0%
+course, people try to compute larger
+ 
+
+ align:start position:0%
+course, people try to compute larger
+numbers too, but we don't have tight
+
+ align:start position:0%
+numbers too, but we don't have tight
+ 
+
+ align:start position:0%
+numbers too, but we don't have tight
+bounds generally.
+
+ align:start position:0%
+bounds generally.
+ 
+
+ align:start position:0%
+bounds generally.
+Okay, I want to say one more thing about
+
+ align:start position:0%
+Okay, I want to say one more thing about
+ 
+
+ align:start position:0%
+Okay, I want to say one more thing about
+proof by cases, which is what if we want
+
+ align:start position:0%
+proof by cases, which is what if we want
+ 
+
+ align:start position:0%
+proof by cases, which is what if we want
+more than two cases?
+
+ align:start position:0%
+more than two cases?
+ 
+
+ align:start position:0%
+more than two cases?
+Uh so
+
+ align:start position:0%
+Uh so
+ 
+
+ align:start position:0%
+Uh so
+more generally proof by K cases.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So instead of just C or not C, let's
+
+ align:start position:0%
+So instead of just C or not C, let's
+ 
+
+ align:start position:0%
+So instead of just C or not C, let's
+suppose we have a bunch of propositions
+
+ align:start position:0%
+suppose we have a bunch of propositions
+ 
+
+ align:start position:0%
+suppose we have a bunch of propositions
+C1 through CK. And let's suppose that
+
+ align:start position:0%
+C1 through CK. And let's suppose that
+ 
+
+ align:start position:0%
+C1 through CK. And let's suppose that
+this is a tautology.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+favorite word for the day. So suppose
+
+ align:start position:0%
+favorite word for the day. So suppose
+ 
+
+ align:start position:0%
+favorite word for the day. So suppose
+that it's always the case C1 or C2 or
+
+ align:start position:0%
+that it's always the case C1 or C2 or
+ 
+
+ align:start position:0%
+that it's always the case C1 or C2 or
+dot dot dot or CK one of these things is
+
+ align:start position:0%
+dot dot dot or CK one of these things is
+ 
+
+ align:start position:0%
+dot dot dot or CK one of these things is
+always true.
+
+ align:start position:0%
+always true.
+ 
+
+ align:start position:0%
+always true.
+Then uh we can follow this template
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is uh suppose we want to prove a
+
+ align:start position:0%
+which is uh suppose we want to prove a
+ 
+
+ align:start position:0%
+which is uh suppose we want to prove a
+theorem that some proposition P is true
+
+ align:start position:0%
+theorem that some proposition P is true
+ 
+
+ align:start position:0%
+theorem that some proposition P is true
+then we'll say proof
+
+ align:start position:0%
+then we'll say proof
+ 
+
+ align:start position:0%
+then we'll say proof
+uh by cases
+
+ align:start position:0%
+uh by cases
+ 
+
+ align:start position:0%
+uh by cases
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's K of them so I'm just going to
+
+ align:start position:0%
+there's K of them so I'm just going to
+ 
+
+ align:start position:0%
+there's K of them so I'm just going to
+write it generically in case I
+
+ align:start position:0%
+write it generically in case I
+ 
+
+ align:start position:0%
+write it generically in case I
+is that CI is true. In other words, we
+
+ align:start position:0%
+is that CI is true. In other words, we
+ 
+
+ align:start position:0%
+is that CI is true. In other words, we
+get to assume CI is true.
+
+ align:start position:0%
+get to assume CI is true.
+ 
+
+ align:start position:0%
+get to assume CI is true.
+And then what we need to do is prove
+
+ align:start position:0%
+And then what we need to do is prove
+ 
+
+ align:start position:0%
+And then what we need to do is prove
+that P is true in that scenario. And P
+
+ align:start position:0%
+that P is true in that scenario. And P
+ 
+
+ align:start position:0%
+that P is true in that scenario. And P
+is true
+
+ align:start position:0%
+is true
+ 
+
+ align:start position:0%
+is true
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+reasons.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh and then here it's especially
+
+ align:start position:0%
+Uh and then here it's especially
+ 
+
+ align:start position:0%
+Uh and then here it's especially
+important to say that the cases
+
+ align:start position:0%
+important to say that the cases
+ 
+
+ align:start position:0%
+important to say that the cases
+are exhaustive.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+reasons and exhaustive here just means
+
+ align:start position:0%
+reasons and exhaustive here just means
+ 
+
+ align:start position:0%
+reasons and exhaustive here just means
+that uh C1 or C2 or up to CK is a
+
+ align:start position:0%
+that uh C1 or C2 or up to CK is a
+ 
+
+ align:start position:0%
+that uh C1 or C2 or up to CK is a
+tautology.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so you need to prove that C1 or or
+
+ align:start position:0%
+Okay, so you need to prove that C1 or or
+ 
+
+ align:start position:0%
+Okay, so you need to prove that C1 or or
+up dot dot dot or CK is is always true.
+
+ align:start position:0%
+up dot dot dot or CK is is always true.
+ 
+
+ align:start position:0%
+up dot dot dot or CK is is always true.
+That's the meaning of the cases being
+
+ align:start position:0%
+That's the meaning of the cases being
+ 
+
+ align:start position:0%
+That's the meaning of the cases being
+exhaustive. So there's sort of two
+
+ align:start position:0%
+exhaustive. So there's sort of two
+ 
+
+ align:start position:0%
+exhaustive. So there's sort of two
+parts. So one is to prove that each case
+
+ align:start position:0%
+parts. So one is to prove that each case
+ 
+
+ align:start position:0%
+parts. So one is to prove that each case
+is okay. The other is to prove that
+
+ align:start position:0%
+is okay. The other is to prove that
+ 
+
+ align:start position:0%
+is okay. The other is to prove that
+those cases cover everything.
+
+ align:start position:0%
+those cases cover everything.
+ 
+
+ align:start position:0%
+those cases cover everything.
+Okay. So um I won't show an example of K
+
+ align:start position:0%
+Okay. So um I won't show an example of K
+ 
+
+ align:start position:0%
+Okay. So um I won't show an example of K
+cases here. We'll see that I'm in
+
+ align:start position:0%
+cases here. We'll see that I'm in
+ 
+
+ align:start position:0%
+cases here. We'll see that I'm in
+restitation and so on. Uh but I will
+
+ align:start position:0%
+restitation and so on. Uh but I will
+ 
+
+ align:start position:0%
+restitation and so on. Uh but I will
+tell you a story about one uh famous
+
+ align:start position:0%
+tell you a story about one uh famous
+ 
+
+ align:start position:0%
+tell you a story about one uh famous
+proof by cases which is the fourcolor
+
+ align:start position:0%
+proof by cases which is the fourcolor
+ 
+
+ align:start position:0%
+proof by cases which is the fourcolor
+theorem.
+
+ align:start position:0%
+theorem.
+ 
+
+ align:start position:0%
+theorem.
+Uh I'll illustrate the four color
+
+ align:start position:0%
+Uh I'll illustrate the four color
+ 
+
+ align:start position:0%
+Uh I'll illustrate the four color
+theorem with an example. So here's a map
+
+ align:start position:0%
+theorem with an example. So here's a map
+ 
+
+ align:start position:0%
+theorem with an example. So here's a map
+of United States. uh and I've colored
+
+ align:start position:0%
+of United States. uh and I've colored
+ 
+
+ align:start position:0%
+of United States. uh and I've colored
+all the states, all the regions of this
+
+ align:start position:0%
+all the states, all the regions of this
+ 
+
+ align:start position:0%
+all the states, all the regions of this
+map with four different colors red,
+
+ align:start position:0%
+map with four different colors red,
+ 
+
+ align:start position:0%
+map with four different colors red,
+green, blue, yellow in such a way that
+
+ align:start position:0%
+green, blue, yellow in such a way that
+ 
+
+ align:start position:0%
+green, blue, yellow in such a way that
+if you have two regions that share a
+
+ align:start position:0%
+if you have two regions that share a
+ 
+
+ align:start position:0%
+if you have two regions that share a
+positive length boundary, then this
+
+ align:start position:0%
+positive length boundary, then this
+ 
+
+ align:start position:0%
+positive length boundary, then this
+color A is different from this color B.
+
+ align:start position:0%
+color A is different from this color B.
+ 
+
+ align:start position:0%
+color A is different from this color B.
+Okay, it has to be not equal. Otherwise,
+
+ align:start position:0%
+Okay, it has to be not equal. Otherwise,
+ 
+
+ align:start position:0%
+Okay, it has to be not equal. Otherwise,
+if you had two red regions next to each
+
+ align:start position:0%
+if you had two red regions next to each
+ 
+
+ align:start position:0%
+if you had two red regions next to each
+other, it' be hard to see the boundary.
+
+ align:start position:0%
+other, it' be hard to see the boundary.
+ 
+
+ align:start position:0%
+other, it' be hard to see the boundary.
+So the colors illustrate the boundaries
+
+ align:start position:0%
+So the colors illustrate the boundaries
+ 
+
+ align:start position:0%
+So the colors illustrate the boundaries
+between all the regions. Four colors
+
+ align:start position:0%
+between all the regions. Four colors
+ 
+
+ align:start position:0%
+between all the regions. Four colors
+seems to be enough for this map. Uh it's
+
+ align:start position:0%
+seems to be enough for this map. Uh it's
+ 
+
+ align:start position:0%
+seems to be enough for this map. Uh it's
+also enough for this map of all the
+
+ align:start position:0%
+also enough for this map of all the
+ 
+
+ align:start position:0%
+also enough for this map of all the
+countries.
+
+ align:start position:0%
+countries.
+ 
+
+ align:start position:0%
+countries.
+Is it true for all the maps? Turns out
+
+ align:start position:0%
+Is it true for all the maps? Turns out
+ 
+
+ align:start position:0%
+Is it true for all the maps? Turns out
+yes. This is called for a long time
+
+ align:start position:0%
+yes. This is called for a long time
+ 
+
+ align:start position:0%
+yes. This is called for a long time
+called the fourcolor conjecture and then
+
+ align:start position:0%
+called the fourcolor conjecture and then
+ 
+
+ align:start position:0%
+called the fourcolor conjecture and then
+it became the fourcolor theorem at some
+
+ align:start position:0%
+it became the fourcolor theorem at some
+ 
+
+ align:start position:0%
+it became the fourcolor theorem at some
+date. Uh so fourcolor theorem says you
+
+ align:start position:0%
+date. Uh so fourcolor theorem says you
+ 
+
+ align:start position:0%
+date. Uh so fourcolor theorem says you
+can color the regions of any planer map
+
+ align:start position:0%
+can color the regions of any planer map
+ 
+
+ align:start position:0%
+can color the regions of any planer map
+with four colors so the neighboring
+
+ align:start position:0%
+with four colors so the neighboring
+ 
+
+ align:start position:0%
+with four colors so the neighboring
+regions get different colors. This was
+
+ align:start position:0%
+regions get different colors. This was
+ 
+
+ align:start position:0%
+regions get different colors. This was
+first observed and sort of conjectured
+
+ align:start position:0%
+first observed and sort of conjectured
+ 
+
+ align:start position:0%
+first observed and sort of conjectured
+uh in 1852 by a guy named Guthrie who
+
+ align:start position:0%
+uh in 1852 by a guy named Guthrie who
+ 
+
+ align:start position:0%
+uh in 1852 by a guy named Guthrie who
+was a student of deorggan. De Morgan I
+
+ align:start position:0%
+was a student of deorggan. De Morgan I
+ 
+
+ align:start position:0%
+was a student of deorggan. De Morgan I
+think his name will come up in a moment
+
+ align:start position:0%
+think his name will come up in a moment
+ 
+
+ align:start position:0%
+think his name will come up in a moment
+famous logician. He actually invented
+
+ align:start position:0%
+famous logician. He actually invented
+ 
+
+ align:start position:0%
+famous logician. He actually invented
+induction as we
+
+ align:start position:0%
+induction as we
+ 
+
+ align:start position:0%
+induction as we
+one of the first people to he invented
+
+ align:start position:0%
+one of the first people to he invented
+ 
+
+ align:start position:0%
+one of the first people to he invented
+the term mathematical induction at the
+
+ align:start position:0%
+the term mathematical induction at the
+ 
+
+ align:start position:0%
+the term mathematical induction at the
+very least and really uh sort of made it
+
+ align:start position:0%
+very least and really uh sort of made it
+ 
+
+ align:start position:0%
+very least and really uh sort of made it
+more formal.
+
+ align:start position:0%
+more formal.
+ 
+
+ align:start position:0%
+more formal.
+Uh so a student of him Guthrie said hey
+
+ align:start position:0%
+Uh so a student of him Guthrie said hey
+ 
+
+ align:start position:0%
+Uh so a student of him Guthrie said hey
+I took all the counties of England and
+
+ align:start position:0%
+I took all the counties of England and
+ 
+
+ align:start position:0%
+I took all the counties of England and
+it turned out I only needed four colors
+
+ align:start position:0%
+it turned out I only needed four colors
+ 
+
+ align:start position:0%
+it turned out I only needed four colors
+is this a theorem and he asked uh
+
+ align:start position:0%
+is this a theorem and he asked uh
+ 
+
+ align:start position:0%
+is this a theorem and he asked uh
+indirectly de Morgan uh and Morgan said
+
+ align:start position:0%
+indirectly de Morgan uh and Morgan said
+ 
+
+ align:start position:0%
+indirectly de Morgan uh and Morgan said
+hey seems cool I don't know maybe then
+
+ align:start position:0%
+hey seems cool I don't know maybe then
+ 
+
+ align:start position:0%
+hey seems cool I don't know maybe then
+the following year 1853
+
+ align:start position:0%
+the following year 1853
+ 
+
+ align:start position:0%
+the following year 1853
+uh another mathematician named Kemp
+
+ align:start position:0%
+uh another mathematician named Kemp
+ 
+
+ align:start position:0%
+uh another mathematician named Kemp
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proved the theorem
+
+ align:start position:0%
+proved the theorem
+ 
+
+ align:start position:0%
+proved the theorem
+but uh proved should be in quotes
+
+ align:start position:0%
+but uh proved should be in quotes
+ 
+
+ align:start position:0%
+but uh proved should be in quotes
+because uh 11 years later 1864 before
+
+ align:start position:0%
+because uh 11 years later 1864 before
+ 
+
+ align:start position:0%
+because uh 11 years later 1864 before
+Haywood found a bug in that proof. Turns
+
+ align:start position:0%
+Haywood found a bug in that proof. Turns
+ 
+
+ align:start position:0%
+Haywood found a bug in that proof. Turns
+out there were a lot of cases in this
+
+ align:start position:0%
+out there were a lot of cases in this
+ 
+
+ align:start position:0%
+out there were a lot of cases in this
+proof and the cases were not exhaustive.
+
+ align:start position:0%
+proof and the cases were not exhaustive.
+ 
+
+ align:start position:0%
+proof and the cases were not exhaustive.
+So it wasn't done. Then uh 15 years
+
+ align:start position:0%
+So it wasn't done. Then uh 15 years
+ 
+
+ align:start position:0%
+So it wasn't done. Then uh 15 years
+later, 1880, Tate proved the theorem.
+
+ align:start position:0%
+later, 1880, Tate proved the theorem.
+ 
+
+ align:start position:0%
+later, 1880, Tate proved the theorem.
+Then 11 years later, Peterson found a
+
+ align:start position:0%
+Then 11 years later, Peterson found a
+ 
+
+ align:start position:0%
+Then 11 years later, Peterson found a
+bug in that proof. Again, not all the
+
+ align:start position:0%
+bug in that proof. Again, not all the
+ 
+
+ align:start position:0%
+bug in that proof. Again, not all the
+cases were exhaustive. Then uh 85 years
+
+ align:start position:0%
+cases were exhaustive. Then uh 85 years
+ 
+
+ align:start position:0%
+cases were exhaustive. Then uh 85 years
+later, 1976
+
+ align:start position:0%
+later, 1976
+ 
+
+ align:start position:0%
+later, 1976
+uh Apple and Haken or maybe it's a PEL,
+
+ align:start position:0%
+uh Apple and Haken or maybe it's a PEL,
+ 
+
+ align:start position:0%
+uh Apple and Haken or maybe it's a PEL,
+I'm not sure, uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proved the theorem and I think most
+
+ align:start position:0%
+proved the theorem and I think most
+ 
+
+ align:start position:0%
+proved the theorem and I think most
+people consider this an actual proof. Uh
+
+ align:start position:0%
+people consider this an actual proof. Uh
+ 
+
+ align:start position:0%
+people consider this an actual proof. Uh
+but it's a little tricky. Uh just to
+
+ align:start position:0%
+but it's a little tricky. Uh just to
+ 
+
+ align:start position:0%
+but it's a little tricky. Uh just to
+give you a sense, this this is where
+
+ align:start position:0%
+give you a sense, this this is where
+ 
+
+ align:start position:0%
+give you a sense, this this is where
+sort of my started I started hearing
+
+ align:start position:0%
+sort of my started I started hearing
+ 
+
+ align:start position:0%
+sort of my started I started hearing
+about the problem. I wasn't alive in
+
+ align:start position:0%
+about the problem. I wasn't alive in
+ 
+
+ align:start position:0%
+about the problem. I wasn't alive in
+1976, but I heard about it later on. Um
+
+ align:start position:0%
+1976, but I heard about it later on. Um
+ 
+
+ align:start position:0%
+1976, but I heard about it later on. Um
+there are 1,834
+
+ align:start position:0%
+there are 1,834
+ 
+
+ align:start position:0%
+there are 1,834
+cases in this proof. They occupy about a
+
+ align:start position:0%
+cases in this proof. They occupy about a
+ 
+
+ align:start position:0%
+cases in this proof. They occupy about a
+400page printout from a computer
+
+ align:start position:0%
+400page printout from a computer
+ 
+
+ align:start position:0%
+400page printout from a computer
+program. And so th this is one of the
+
+ align:start position:0%
+program. And so th this is one of the
+ 
+
+ align:start position:0%
+program. And so th this is one of the
+first mathematical proofs that used a
+
+ align:start position:0%
+first mathematical proofs that used a
+ 
+
+ align:start position:0%
+first mathematical proofs that used a
+computer to assist in checking all the
+
+ align:start position:0%
+computer to assist in checking all the
+ 
+
+ align:start position:0%
+computer to assist in checking all the
+cases because there's so many 8 1,834.
+
+ align:start position:0%
+cases because there's so many 8 1,834.
+ 
+
+ align:start position:0%
+cases because there's so many 8 1,834.
+It's hard to do that by hand and be sure
+
+ align:start position:0%
+It's hard to do that by hand and be sure
+ 
+
+ align:start position:0%
+It's hard to do that by hand and be sure
+that you didn't make a mistake. So the
+
+ align:start position:0%
+that you didn't make a mistake. So the
+ 
+
+ align:start position:0%
+that you didn't make a mistake. So the
+computer proof to me is a little bit
+
+ align:start position:0%
+computer proof to me is a little bit
+ 
+
+ align:start position:0%
+computer proof to me is a little bit
+more sound. uh also apparently checked
+
+ align:start position:0%
+more sound. uh also apparently checked
+ 
+
+ align:start position:0%
+more sound. uh also apparently checked
+by hand uh by Haken's daughter. Um then
+
+ align:start position:0%
+by hand uh by Haken's daughter. Um then
+ 
+
+ align:start position:0%
+by hand uh by Haken's daughter. Um then
+five years later uh Schmidt found what
+
+ align:start position:0%
+five years later uh Schmidt found what
+ 
+
+ align:start position:0%
+five years later uh Schmidt found what
+you could interpret as a bug in this
+
+ align:start position:0%
+you could interpret as a bug in this
+ 
+
+ align:start position:0%
+you could interpret as a bug in this
+proof. Let's say an emission or
+
+ align:start position:0%
+proof. Let's say an emission or
+ 
+
+ align:start position:0%
+proof. Let's say an emission or
+something uh but a missing situation. Uh
+
+ align:start position:0%
+something uh but a missing situation. Uh
+ 
+
+ align:start position:0%
+something uh but a missing situation. Uh
+and then over the next eight years Apple
+
+ align:start position:0%
+and then over the next eight years Apple
+ 
+
+ align:start position:0%
+and then over the next eight years Apple
+and Haken fixed all the bugs they could
+
+ align:start position:0%
+and Haken fixed all the bugs they could
+ 
+
+ align:start position:0%
+and Haken fixed all the bugs they could
+find that one and some other sort of
+
+ align:start position:0%
+find that one and some other sort of
+ 
+
+ align:start position:0%
+find that one and some other sort of
+wording issues and so on and they
+
+ align:start position:0%
+wording issues and so on and they
+ 
+
+ align:start position:0%
+wording issues and so on and they
+proofed they published it in a book but
+
+ align:start position:0%
+proofed they published it in a book but
+ 
+
+ align:start position:0%
+proofed they published it in a book but
+book isn't refereed. So I don't know how
+
+ align:start position:0%
+book isn't refereed. So I don't know how
+ 
+
+ align:start position:0%
+book isn't refereed. So I don't know how
+many people have read that book. Um,
+
+ align:start position:0%
+many people have read that book. Um,
+ 
+
+ align:start position:0%
+many people have read that book. Um,
+seems like this proof is maybe correct.
+
+ align:start position:0%
+seems like this proof is maybe correct.
+ 
+
+ align:start position:0%
+seems like this proof is maybe correct.
+It's been many years and no one has
+
+ align:start position:0%
+It's been many years and no one has
+ 
+
+ align:start position:0%
+It's been many years and no one has
+found a bug. Uh, a little bit later
+
+ align:start position:0%
+found a bug. Uh, a little bit later
+ 
+
+ align:start position:0%
+found a bug. Uh, a little bit later
+though, 1996, Robertson, Sanders,
+
+ align:start position:0%
+though, 1996, Robertson, Sanders,
+ 
+
+ align:start position:0%
+though, 1996, Robertson, Sanders,
+Seymour, and Thomas, some of the top
+
+ align:start position:0%
+Seymour, and Thomas, some of the top
+ 
+
+ align:start position:0%
+Seymour, and Thomas, some of the top
+graph theorists in the world, uh, found
+
+ align:start position:0%
+graph theorists in the world, uh, found
+ 
+
+ align:start position:0%
+graph theorists in the world, uh, found
+a simpler proof. That proof only has 633
+
+ align:start position:0%
+a simpler proof. That proof only has 633
+ 
+
+ align:start position:0%
+a simpler proof. That proof only has 633
+cases. So that's a lot less, maybe three
+
+ align:start position:0%
+cases. So that's a lot less, maybe three
+ 
+
+ align:start position:0%
+cases. So that's a lot less, maybe three
+times fewer cases. And also the length
+
+ align:start position:0%
+times fewer cases. And also the length
+ 
+
+ align:start position:0%
+times fewer cases. And also the length
+of the paper is shorter, maybe 10 times
+
+ align:start position:0%
+of the paper is shorter, maybe 10 times
+ 
+
+ align:start position:0%
+of the paper is shorter, maybe 10 times
+shorter. Uh so that's progress but you
+
+ align:start position:0%
+shorter. Uh so that's progress but you
+ 
+
+ align:start position:0%
+shorter. Uh so that's progress but you
+know is that proof true it also used a
+
+ align:start position:0%
+know is that proof true it also used a
+ 
+
+ align:start position:0%
+know is that proof true it also used a
+computer to check the cases. Uh finally
+
+ align:start position:0%
+computer to check the cases. Uh finally
+ 
+
+ align:start position:0%
+computer to check the cases. Uh finally
+in 2005
+
+ align:start position:0%
+in 2005
+ 
+
+ align:start position:0%
+in 2005
+uh Verer and Gonier uh developed a fully
+
+ align:start position:0%
+uh Verer and Gonier uh developed a fully
+ 
+
+ align:start position:0%
+uh Verer and Gonier uh developed a fully
+computer checkable proof using uh a
+
+ align:start position:0%
+computer checkable proof using uh a
+ 
+
+ align:start position:0%
+computer checkable proof using uh a
+system called coaul where you write down
+
+ align:start position:0%
+system called coaul where you write down
+ 
+
+ align:start position:0%
+system called coaul where you write down
+uh every step in the proof and then the
+
+ align:start position:0%
+uh every step in the proof and then the
+ 
+
+ align:start position:0%
+uh every step in the proof and then the
+computer just has to check that every u
+
+ align:start position:0%
+computer just has to check that every u
+ 
+
+ align:start position:0%
+computer just has to check that every u
+mathematical derivation like all the
+
+ align:start position:0%
+mathematical derivation like all the
+ 
+
+ align:start position:0%
+mathematical derivation like all the
+derivations we saw last class modus
+
+ align:start position:0%
+derivations we saw last class modus
+ 
+
+ align:start position:0%
+derivations we saw last class modus
+ponus and all those things are correct.
+
+ align:start position:0%
+ponus and all those things are correct.
+ 
+
+ align:start position:0%
+ponus and all those things are correct.
+this this program has been has withstood
+
+ align:start position:0%
+this this program has been has withstood
+ 
+
+ align:start position:0%
+this this program has been has withstood
+many many years of scrutiny. So we all
+
+ align:start position:0%
+many many years of scrutiny. So we all
+ 
+
+ align:start position:0%
+many many years of scrutiny. So we all
+believe that it's correct and so the
+
+ align:start position:0%
+believe that it's correct and so the
+ 
+
+ align:start position:0%
+believe that it's correct and so the
+fact that you can write the entire proof
+
+ align:start position:0%
+fact that you can write the entire proof
+ 
+
+ align:start position:0%
+fact that you can write the entire proof
+in this proof language suggests that
+
+ align:start position:0%
+in this proof language suggests that
+ 
+
+ align:start position:0%
+in this proof language suggests that
+this really is a true theorem. Now
+
+ align:start position:0%
+this really is a true theorem. Now
+ 
+
+ align:start position:0%
+this really is a true theorem. Now
+thankfully there won't be more missing
+
+ align:start position:0%
+thankfully there won't be more missing
+ 
+
+ align:start position:0%
+thankfully there won't be more missing
+cases. I believe that is just an
+
+ align:start position:0%
+cases. I believe that is just an
+ 
+
+ align:start position:0%
+cases. I believe that is just an
+implementation of the Robertson proof.
+
+ align:start position:0%
+implementation of the Robertson proof.
+ 
+
+ align:start position:0%
+implementation of the Robertson proof.
+So uh that one withtood scrutiny but
+
+ align:start position:0%
+So uh that one withtood scrutiny but
+ 
+
+ align:start position:0%
+So uh that one withtood scrutiny but
+it's very tedious to write these proofs
+
+ align:start position:0%
+it's very tedious to write these proofs
+ 
+
+ align:start position:0%
+it's very tedious to write these proofs
+and so uh for the fourcolor theorem it's
+
+ align:start position:0%
+and so uh for the fourcolor theorem it's
+ 
+
+ align:start position:0%
+and so uh for the fourcolor theorem it's
+uh worth it I would say all right so
+
+ align:start position:0%
+uh worth it I would say all right so
+ 
+
+ align:start position:0%
+uh worth it I would say all right so
+that's just an example of in general
+
+ align:start position:0%
+that's just an example of in general
+ 
+
+ align:start position:0%
+that's just an example of in general
+proofs by cases can involve a zillion
+
+ align:start position:0%
+proofs by cases can involve a zillion
+ 
+
+ align:start position:0%
+proofs by cases can involve a zillion
+cases it's very annoying but sometimes
+
+ align:start position:0%
+cases it's very annoying but sometimes
+ 
+
+ align:start position:0%
+cases it's very annoying but sometimes
+that's the best thing we know how to do
+
+ align:start position:0%
+that's the best thing we know how to do
+ 
+
+ align:start position:0%
+that's the best thing we know how to do
+maybe we'll come up with a simpler
+
+ align:start position:0%
+maybe we'll come up with a simpler
+ 
+
+ align:start position:0%
+maybe we'll come up with a simpler
+fourcolor theorem proof at some point
+
+ align:start position:0%
+fourcolor theorem proof at some point
+ 
+
+ align:start position:0%
+fourcolor theorem proof at some point
+but best we know so far has hundreds of
+
+ align:start position:0%
+but best we know so far has hundreds of
+ 
+
+ align:start position:0%
+but best we know so far has hundreds of
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+all right let's go back to induction
+
+ align:start position:0%
+all right let's go back to induction
+ 
+
+ align:start position:0%
+all right let's go back to induction
+Uh first I want to review induction a
+
+ align:start position:0%
+Uh first I want to review induction a
+ 
+
+ align:start position:0%
+Uh first I want to review induction a
+little bit and then we will get a
+
+ align:start position:0%
+little bit and then we will get a
+ 
+
+ align:start position:0%
+little bit and then we will get a
+stronger form of it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So uh I'm going to call this the
+
+ align:start position:0%
+So uh I'm going to call this the
+ 
+
+ align:start position:0%
+So uh I'm going to call this the
+induction axiom. This is what we talked
+
+ align:start position:0%
+induction axiom. This is what we talked
+ 
+
+ align:start position:0%
+induction axiom. This is what we talked
+about last class. Uh we didn't call it
+
+ align:start position:0%
+about last class. Uh we didn't call it
+ 
+
+ align:start position:0%
+about last class. Uh we didn't call it
+an axiom and in some setups it is an
+
+ align:start position:0%
+an axiom and in some setups it is an
+ 
+
+ align:start position:0%
+an axiom and in some setups it is an
+axiom. We're going to take it as one.
+
+ align:start position:0%
+axiom. We're going to take it as one.
+ 
+
+ align:start position:0%
+axiom. We're going to take it as one.
+something that we just assume is true.
+
+ align:start position:0%
+something that we just assume is true.
+ 
+
+ align:start position:0%
+something that we just assume is true.
+Uh although as Zach mentioned in modern
+
+ align:start position:0%
+Uh although as Zach mentioned in modern
+ 
+
+ align:start position:0%
+Uh although as Zach mentioned in modern
+times you usually prove this using other
+
+ align:start position:0%
+times you usually prove this using other
+ 
+
+ align:start position:0%
+times you usually prove this using other
+using the definition of the natural
+
+ align:start position:0%
+using the definition of the natural
+ 
+
+ align:start position:0%
+using the definition of the natural
+numbers.
+
+ align:start position:0%
+numbers.
+ 
+
+ align:start position:0%
+numbers.
+Uh but I'll just take it as something is
+
+ align:start position:0%
+Uh but I'll just take it as something is
+ 
+
+ align:start position:0%
+Uh but I'll just take it as something is
+true. So for any predicate p of n over
+
+ align:start position:0%
+true. So for any predicate p of n over
+ 
+
+ align:start position:0%
+true. So for any predicate p of n over
+the natural numbers if on the one hand p
+
+ align:start position:0%
+the natural numbers if on the one hand p
+ 
+
+ align:start position:0%
+the natural numbers if on the one hand p
+of zero is true
+
+ align:start position:0%
+of zero is true
+ 
+
+ align:start position:0%
+of zero is true
+and on the other hand
+
+ align:start position:0%
+and on the other hand
+ 
+
+ align:start position:0%
+and on the other hand
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+p of n implies p of n + one
+
+ align:start position:0%
+p of n implies p of n + one
+ 
+
+ align:start position:0%
+p of n implies p of n + one
+uh for all natural numbers n
+
+ align:start position:0%
+uh for all natural numbers n
+ 
+
+ align:start position:0%
+uh for all natural numbers n
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh p of n is true uh for all natural
+
+ align:start position:0%
+uh p of n is true uh for all natural
+ 
+
+ align:start position:0%
+uh p of n is true uh for all natural
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+Okay, this is the magic of induction.
+
+ align:start position:0%
+Okay, this is the magic of induction.
+ 
+
+ align:start position:0%
+Okay, this is the magic of induction.
+You should use this probably in every
+
+ align:start position:0%
+You should use this probably in every
+ 
+
+ align:start position:0%
+You should use this probably in every
+problem you solve. Not every problem,
+
+ align:start position:0%
+problem you solve. Not every problem,
+ 
+
+ align:start position:0%
+problem you solve. Not every problem,
+but uh extremely powerful tool. We're
+
+ align:start position:0%
+but uh extremely powerful tool. We're
+ 
+
+ align:start position:0%
+but uh extremely powerful tool. We're
+going to use it all the time throughout
+
+ align:start position:0%
+going to use it all the time throughout
+ 
+
+ align:start position:0%
+going to use it all the time throughout
+this class. I want to give you a visual
+
+ align:start position:0%
+this class. I want to give you a visual
+ 
+
+ align:start position:0%
+this class. I want to give you a visual
+way of thinking about what's going on
+
+ align:start position:0%
+way of thinking about what's going on
+ 
+
+ align:start position:0%
+way of thinking about what's going on
+with induction, which I call block
+
+ align:start position:0%
+with induction, which I call block
+ 
+
+ align:start position:0%
+with induction, which I call block
+diagrams.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh so um I'm going to think of
+
+ align:start position:0%
+Uh so um I'm going to think of
+ 
+
+ align:start position:0%
+Uh so um I'm going to think of
+a block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like a little box here that takes as
+
+ align:start position:0%
+like a little box here that takes as
+ 
+
+ align:start position:0%
+like a little box here that takes as
+input. Think of it as a procedure. You
+
+ align:start position:0%
+input. Think of it as a procedure. You
+ 
+
+ align:start position:0%
+input. Think of it as a procedure. You
+give it some true uh propositions on the
+
+ align:start position:0%
+give it some true uh propositions on the
+ 
+
+ align:start position:0%
+give it some true uh propositions on the
+left and it produces a true proposition
+
+ align:start position:0%
+left and it produces a true proposition
+ 
+
+ align:start position:0%
+left and it produces a true proposition
+on the right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay? Or you could think of it as if I
+
+ align:start position:0%
+Okay? Or you could think of it as if I
+ 
+
+ align:start position:0%
+Okay? Or you could think of it as if I
+give you some proofs of these
+
+ align:start position:0%
+give you some proofs of these
+ 
+
+ align:start position:0%
+give you some proofs of these
+propositions, then this block will give
+
+ align:start position:0%
+propositions, then this block will give
+ 
+
+ align:start position:0%
+propositions, then this block will give
+you uh a proof of a proposition on the
+
+ align:start position:0%
+you uh a proof of a proposition on the
+ 
+
+ align:start position:0%
+you uh a proof of a proposition on the
+right. Okay? So, uh what's going on with
+
+ align:start position:0%
+right. Okay? So, uh what's going on with
+ 
+
+ align:start position:0%
+right. Okay? So, uh what's going on with
+induction is we're given two of these
+
+ align:start position:0%
+induction is we're given two of these
+ 
+
+ align:start position:0%
+induction is we're given two of these
+blocks, these two. So, you can think of
+
+ align:start position:0%
+blocks, these two. So, you can think of
+ 
+
+ align:start position:0%
+blocks, these two. So, you can think of
+part one P of 0 is true as a block that
+
+ align:start position:0%
+part one P of 0 is true as a block that
+ 
+
+ align:start position:0%
+part one P of 0 is true as a block that
+has no input. So, this is what we
+
+ align:start position:0%
+has no input. So, this is what we
+ 
+
+ align:start position:0%
+has no input. So, this is what we
+normally call the base case. So it
+
+ align:start position:0%
+normally call the base case. So it
+ 
+
+ align:start position:0%
+normally call the base case. So it
+doesn't need to assume anything and it
+
+ align:start position:0%
+doesn't need to assume anything and it
+ 
+
+ align:start position:0%
+doesn't need to assume anything and it
+just produces for you a proof that P of
+
+ align:start position:0%
+just produces for you a proof that P of
+ 
+
+ align:start position:0%
+just produces for you a proof that P of
+0 is true.
+
+ align:start position:0%
+0 is true.
+ 
+
+ align:start position:0%
+0 is true.
+Okay. And the second part here, the
+
+ align:start position:0%
+Okay. And the second part here, the
+ 
+
+ align:start position:0%
+Okay. And the second part here, the
+induction step
+
+ align:start position:0%
+induction step
+ 
+
+ align:start position:0%
+induction step
+says that if you can prove P of N is
+
+ align:start position:0%
+says that if you can prove P of N is
+ 
+
+ align:start position:0%
+says that if you can prove P of N is
+true and you plug it into the induction
+
+ align:start position:0%
+true and you plug it into the induction
+ 
+
+ align:start position:0%
+true and you plug it into the induction
+step, then it will give you a proof that
+
+ align:start position:0%
+step, then it will give you a proof that
+ 
+
+ align:start position:0%
+step, then it will give you a proof that
+P of N plus one is true. Saw a bunch of
+
+ align:start position:0%
+P of N plus one is true. Saw a bunch of
+ 
+
+ align:start position:0%
+P of N plus one is true. Saw a bunch of
+examples of this last time. We assume P
+
+ align:start position:0%
+examples of this last time. We assume P
+ 
+
+ align:start position:0%
+examples of this last time. We assume P
+of N and we use that to prove P of N
+
+ align:start position:0%
+of N and we use that to prove P of N
+ 
+
+ align:start position:0%
+of N and we use that to prove P of N
+plus one. Okay. Now the cool thing about
+
+ align:start position:0%
+plus one. Okay. Now the cool thing about
+ 
+
+ align:start position:0%
+plus one. Okay. Now the cool thing about
+blocks is you can just uh chain them
+
+ align:start position:0%
+blocks is you can just uh chain them
+ 
+
+ align:start position:0%
+blocks is you can just uh chain them
+together.
+
+ align:start position:0%
+together.
+ 
+
+ align:start position:0%
+together.
+So if we chain
+
+ align:start position:0%
+So if we chain
+ 
+
+ align:start position:0%
+So if we chain
+uh the only block we can place first is
+
+ align:start position:0%
+uh the only block we can place first is
+ 
+
+ align:start position:0%
+uh the only block we can place first is
+uh this base case because it doesn't
+
+ align:start position:0%
+uh this base case because it doesn't
+ 
+
+ align:start position:0%
+uh this base case because it doesn't
+need anything to get started. So we
+
+ align:start position:0%
+need anything to get started. So we
+ 
+
+ align:start position:0%
+need anything to get started. So we
+start with the base case argument that
+
+ align:start position:0%
+start with the base case argument that
+ 
+
+ align:start position:0%
+start with the base case argument that
+produces P of zero. Now we plug this
+
+ align:start position:0%
+produces P of zero. Now we plug this
+ 
+
+ align:start position:0%
+produces P of zero. Now we plug this
+into the step. This step has to work for
+
+ align:start position:0%
+into the step. This step has to work for
+ 
+
+ align:start position:0%
+into the step. This step has to work for
+all n.
+
+ align:start position:0%
+all n.
+ 
+
+ align:start position:0%
+all n.
+So in particular it works for n equals
+
+ align:start position:0%
+So in particular it works for n equals
+ 
+
+ align:start position:0%
+So in particular it works for n equals
+z. And so we plug that into the step and
+
+ align:start position:0%
+z. And so we plug that into the step and
+ 
+
+ align:start position:0%
+z. And so we plug that into the step and
+we get uh p of 1. We plug p of 1 into
+
+ align:start position:0%
+we get uh p of 1. We plug p of 1 into
+ 
+
+ align:start position:0%
+we get uh p of 1. We plug p of 1 into
+the step. So n equals 1.
+
+ align:start position:0%
+the step. So n equals 1.
+ 
+
+ align:start position:0%
+the step. So n equals 1.
+Then we get p of n plus one namely p of
+
+ align:start position:0%
+Then we get p of n plus one namely p of
+ 
+
+ align:start position:0%
+Then we get p of n plus one namely p of
+two. And we plug that into the step and
+
+ align:start position:0%
+two. And we plug that into the step and
+ 
+
+ align:start position:0%
+two. And we plug that into the step and
+we get p of three and so on.
+
+ align:start position:0%
+we get p of three and so on.
+ 
+
+ align:start position:0%
+we get p of three and so on.
+Okay. Okay, so this just gives you some
+
+ align:start position:0%
+Okay. Okay, so this just gives you some
+ 
+
+ align:start position:0%
+Okay. Okay, so this just gives you some
+intuition for if I can build an argument
+
+ align:start position:0%
+intuition for if I can build an argument
+ 
+
+ align:start position:0%
+intuition for if I can build an argument
+for why P of 0 is true and I can build
+
+ align:start position:0%
+for why P of 0 is true and I can build
+ 
+
+ align:start position:0%
+for why P of 0 is true and I can build
+an argument for why if P of N is true
+
+ align:start position:0%
+an argument for why if P of N is true
+ 
+
+ align:start position:0%
+an argument for why if P of N is true
+then P of N plus one is also true then I
+
+ align:start position:0%
+then P of N plus one is also true then I
+ 
+
+ align:start position:0%
+then P of N plus one is also true then I
+can just repeat that argument over and
+
+ align:start position:0%
+can just repeat that argument over and
+ 
+
+ align:start position:0%
+can just repeat that argument over and
+over with different n increasing N by
+
+ align:start position:0%
+over with different n increasing N by
+ 
+
+ align:start position:0%
+over with different n increasing N by
+one each time and I can use that to
+
+ align:start position:0%
+one each time and I can use that to
+ 
+
+ align:start position:0%
+one each time and I can use that to
+prove that all the P of N's are true.
+
+ align:start position:0%
+prove that all the P of N's are true.
+ 
+
+ align:start position:0%
+prove that all the P of N's are true.
+Okay, this is like visual intuition for
+
+ align:start position:0%
+Okay, this is like visual intuition for
+ 
+
+ align:start position:0%
+Okay, this is like visual intuition for
+why why this works. Um, of course, we're
+
+ align:start position:0%
+why why this works. Um, of course, we're
+ 
+
+ align:start position:0%
+why why this works. Um, of course, we're
+not going to actually prove P of N is
+
+ align:start position:0%
+not going to actually prove P of N is
+ 
+
+ align:start position:0%
+not going to actually prove P of N is
+true for all N, but uh should be pretty
+
+ align:start position:0%
+true for all N, but uh should be pretty
+ 
+
+ align:start position:0%
+true for all N, but uh should be pretty
+straight pretty intuitive from that.
+
+ align:start position:0%
+straight pretty intuitive from that.
+ 
+
+ align:start position:0%
+straight pretty intuitive from that.
+Uh or more abstractly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can actually think of induction
+
+ align:start position:0%
+you can actually think of induction
+ 
+
+ align:start position:0%
+you can actually think of induction
+itself as one of these blocks. Uh let me
+
+ align:start position:0%
+itself as one of these blocks. Uh let me
+ 
+
+ align:start position:0%
+itself as one of these blocks. Uh let me
+use another color.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we have on the one hand uh a block
+
+ align:start position:0%
+So we have on the one hand uh a block
+ 
+
+ align:start position:0%
+So we have on the one hand uh a block
+base which produces P of zero and we
+
+ align:start position:0%
+base which produces P of zero and we
+ 
+
+ align:start position:0%
+base which produces P of zero and we
+have uh an induction step which given P
+
+ align:start position:0%
+have uh an induction step which given P
+ 
+
+ align:start position:0%
+have uh an induction step which given P
+of N produces
+
+ align:start position:0%
+of N produces
+ 
+
+ align:start position:0%
+of N produces
+uh P of N plus one.
+
+ align:start position:0%
+uh P of N plus one.
+ 
+
+ align:start position:0%
+uh P of N plus one.
+So I'm going to think of this as a thing
+
+ align:start position:0%
+So I'm going to think of this as a thing
+ 
+
+ align:start position:0%
+So I'm going to think of this as a thing
+that's true and this as a thing that's
+
+ align:start position:0%
+that's true and this as a thing that's
+ 
+
+ align:start position:0%
+that's true and this as a thing that's
+true. And then what induction gives me?
+
+ align:start position:0%
+true. And then what induction gives me?
+ 
+
+ align:start position:0%
+true. And then what induction gives me?
+Induction is a block that given these
+
+ align:start position:0%
+Induction is a block that given these
+ 
+
+ align:start position:0%
+Induction is a block that given these
+two facts, if you can prove each of
+
+ align:start position:0%
+two facts, if you can prove each of
+ 
+
+ align:start position:0%
+two facts, if you can prove each of
+these things, then it gives me a new
+
+ align:start position:0%
+these things, then it gives me a new
+ 
+
+ align:start position:0%
+these things, then it gives me a new
+fact which is uh for all natural numbers
+
+ align:start position:0%
+fact which is uh for all natural numbers
+ 
+
+ align:start position:0%
+fact which is uh for all natural numbers
+n uh p of n is true.
+
+ align:start position:0%
+n uh p of n is true.
+ 
+
+ align:start position:0%
+n uh p of n is true.
+Okay, so that's sort of the instead of
+
+ align:start position:0%
+Okay, so that's sort of the instead of
+ 
+
+ align:start position:0%
+Okay, so that's sort of the instead of
+having to draw out this infinite length
+
+ align:start position:0%
+having to draw out this infinite length
+ 
+
+ align:start position:0%
+having to draw out this infinite length
+path, induction just does it all at
+
+ align:start position:0%
+path, induction just does it all at
+ 
+
+ align:start position:0%
+path, induction just does it all at
+once. It says, "Oh, I know I can chain
+
+ align:start position:0%
+once. It says, "Oh, I know I can chain
+ 
+
+ align:start position:0%
+once. It says, "Oh, I know I can chain
+these all together forever. Therefore, P
+
+ align:start position:0%
+these all together forever. Therefore, P
+ 
+
+ align:start position:0%
+these all together forever. Therefore, P
+of N is true for all N." Okay, I don't
+
+ align:start position:0%
+of N is true for all N." Okay, I don't
+ 
+
+ align:start position:0%
+of N is true for all N." Okay, I don't
+know if that helps, but
+
+ align:start position:0%
+know if that helps, but
+ 
+
+ align:start position:0%
+know if that helps, but
+it's another visual way of thinking
+
+ align:start position:0%
+it's another visual way of thinking
+ 
+
+ align:start position:0%
+it's another visual way of thinking
+about induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Let me tell you another uh equivalent
+
+ align:start position:0%
+Let me tell you another uh equivalent
+ 
+
+ align:start position:0%
+Let me tell you another uh equivalent
+formulation of induction which I prefer.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+starts out starts out the same. Suppose
+
+ align:start position:0%
+starts out starts out the same. Suppose
+ 
+
+ align:start position:0%
+starts out starts out the same. Suppose
+P of 0 is true. Uh the second the
+
+ align:start position:0%
+P of 0 is true. Uh the second the
+ 
+
+ align:start position:0%
+P of 0 is true. Uh the second the
+induction step I'm going to phrase
+
+ align:start position:0%
+induction step I'm going to phrase
+ 
+
+ align:start position:0%
+induction step I'm going to phrase
+slightly differently almost the same.
+
+ align:start position:0%
+slightly differently almost the same.
+ 
+
+ align:start position:0%
+slightly differently almost the same.
+For all n at least one
+
+ align:start position:0%
+For all n at least one
+ 
+
+ align:start position:0%
+For all n at least one
+uh p of n minus one implies p of n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then
+
+ align:start position:0%
+Then
+ 
+
+ align:start position:0%
+Then
+uh for all natural numbers
+
+ align:start position:0%
+uh for all natural numbers
+ 
+
+ align:start position:0%
+uh for all natural numbers
+uh p of n.
+
+ align:start position:0%
+uh p of n.
+ 
+
+ align:start position:0%
+uh p of n.
+So uh the first and last lines are the
+
+ align:start position:0%
+So uh the first and last lines are the
+ 
+
+ align:start position:0%
+So uh the first and last lines are the
+same. We're assume P of 0 is true. We're
+
+ align:start position:0%
+same. We're assume P of 0 is true. We're
+ 
+
+ align:start position:0%
+same. We're assume P of 0 is true. We're
+going to conclude P of N is true for all
+
+ align:start position:0%
+going to conclude P of N is true for all
+ 
+
+ align:start position:0%
+going to conclude P of N is true for all
+natural numbers. Here we started at zero
+
+ align:start position:0%
+natural numbers. Here we started at zero
+ 
+
+ align:start position:0%
+natural numbers. Here we started at zero
+and we wanted to show that P of N
+
+ align:start position:0%
+and we wanted to show that P of N
+ 
+
+ align:start position:0%
+and we wanted to show that P of N
+implies P of N plus one. Over here we're
+
+ align:start position:0%
+implies P of N plus one. Over here we're
+ 
+
+ align:start position:0%
+implies P of N plus one. Over here we're
+starting at one and we're proving that P
+
+ align:start position:0%
+starting at one and we're proving that P
+ 
+
+ align:start position:0%
+starting at one and we're proving that P
+of N minus one implies P of N. These are
+
+ align:start position:0%
+of N minus one implies P of N. These are
+ 
+
+ align:start position:0%
+of N minus one implies P of N. These are
+exactly the same things. I've just
+
+ align:start position:0%
+exactly the same things. I've just
+ 
+
+ align:start position:0%
+exactly the same things. I've just
+shifted the indices by one. So these are
+
+ align:start position:0%
+shifted the indices by one. So these are
+ 
+
+ align:start position:0%
+shifted the indices by one. So these are
+identical statements or equivalent
+
+ align:start position:0%
+identical statements or equivalent
+ 
+
+ align:start position:0%
+identical statements or equivalent
+statements. Um I like this version in
+
+ align:start position:0%
+statements. Um I like this version in
+ 
+
+ align:start position:0%
+statements. Um I like this version in
+particular. it will lead into strong
+
+ align:start position:0%
+particular. it will lead into strong
+ 
+
+ align:start position:0%
+particular. it will lead into strong
+induction. But I like this version as a
+
+ align:start position:0%
+induction. But I like this version as a
+ 
+
+ align:start position:0%
+induction. But I like this version as a
+computer scientist because I always want
+
+ align:start position:0%
+computer scientist because I always want
+ 
+
+ align:start position:0%
+computer scientist because I always want
+to think about well I want to prove P of
+
+ align:start position:0%
+to think about well I want to prove P of
+ 
+
+ align:start position:0%
+to think about well I want to prove P of
+N not P of N plus one. It's confusing to
+
+ align:start position:0%
+N not P of N plus one. It's confusing to
+ 
+
+ align:start position:0%
+N not P of N plus one. It's confusing to
+think about proving P of N plus one. I
+
+ align:start position:0%
+think about proving P of N plus one. I
+ 
+
+ align:start position:0%
+think about proving P of N plus one. I
+always want to prove P of N when N
+
+ align:start position:0%
+always want to prove P of N when N
+ 
+
+ align:start position:0%
+always want to prove P of N when N
+equals zero. Okay, that's my base case.
+
+ align:start position:0%
+equals zero. Okay, that's my base case.
+ 
+
+ align:start position:0%
+equals zero. Okay, that's my base case.
+I prove that specially when N is at
+
+ align:start position:0%
+I prove that specially when N is at
+ 
+
+ align:start position:0%
+I prove that specially when N is at
+least one. I'm not in the base case and
+
+ align:start position:0%
+least one. I'm not in the base case and
+ 
+
+ align:start position:0%
+least one. I'm not in the base case and
+I get to assume that P of N minus one is
+
+ align:start position:0%
+I get to assume that P of N minus one is
+ 
+
+ align:start position:0%
+I get to assume that P of N minus one is
+true. You can think of this like a
+
+ align:start position:0%
+true. You can think of this like a
+ 
+
+ align:start position:0%
+true. You can think of this like a
+computer program. Think of a proving p
+
+ align:start position:0%
+computer program. Think of a proving p
+ 
+
+ align:start position:0%
+computer program. Think of a proving p
+of n is like running a computation f of
+
+ align:start position:0%
+of n is like running a computation f of
+ 
+
+ align:start position:0%
+of n is like running a computation f of
+n or p of n and I get to recursively
+
+ align:start position:0%
+n or p of n and I get to recursively
+ 
+
+ align:start position:0%
+n or p of n and I get to recursively
+call p of n minus one in order to
+
+ align:start position:0%
+call p of n minus one in order to
+ 
+
+ align:start position:0%
+call p of n minus one in order to
+compute p of n. n is given to me. This
+
+ align:start position:0%
+compute p of n. n is given to me. This
+ 
+
+ align:start position:0%
+compute p of n. n is given to me. This
+is the one I want to solve. If n is zero
+
+ align:start position:0%
+is the one I want to solve. If n is zero
+ 
+
+ align:start position:0%
+is the one I want to solve. If n is zero
+then I solve it one way. If n is bigger
+
+ align:start position:0%
+then I solve it one way. If n is bigger
+ 
+
+ align:start position:0%
+then I solve it one way. If n is bigger
+than zero or at least one then I
+
+ align:start position:0%
+than zero or at least one then I
+ 
+
+ align:start position:0%
+than zero or at least one then I
+recursively call p of n minus one or
+
+ align:start position:0%
+recursively call p of n minus one or
+ 
+
+ align:start position:0%
+recursively call p of n minus one or
+depend on that proof and use it to prove
+
+ align:start position:0%
+depend on that proof and use it to prove
+ 
+
+ align:start position:0%
+depend on that proof and use it to prove
+p of n. Okay. But you can use either one
+
+ align:start position:0%
+p of n. Okay. But you can use either one
+ 
+
+ align:start position:0%
+p of n. Okay. But you can use either one
+whichever is more comfortable to you.
+
+ align:start position:0%
+whichever is more comfortable to you.
+ 
+
+ align:start position:0%
+whichever is more comfortable to you.
+uh but really you should use neither and
+
+ align:start position:0%
+uh but really you should use neither and
+ 
+
+ align:start position:0%
+uh but really you should use neither and
+you should use this stronger form uh
+
+ align:start position:0%
+you should use this stronger form uh
+ 
+
+ align:start position:0%
+you should use this stronger form uh
+called strong induction. So let's let's
+
+ align:start position:0%
+called strong induction. So let's let's
+ 
+
+ align:start position:0%
+called strong induction. So let's let's
+do that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Strong induction just gives you more to
+
+ align:start position:0%
+Strong induction just gives you more to
+ 
+
+ align:start position:0%
+Strong induction just gives you more to
+work with.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it's in some sense more powerful
+
+ align:start position:0%
+So it's in some sense more powerful
+ 
+
+ align:start position:0%
+So it's in some sense more powerful
+logically it's identical to induction.
+
+ align:start position:0%
+logically it's identical to induction.
+ 
+
+ align:start position:0%
+logically it's identical to induction.
+You can actually prove it using
+
+ align:start position:0%
+You can actually prove it using
+ 
+
+ align:start position:0%
+You can actually prove it using
+induction and we'll do that. Uh let me
+
+ align:start position:0%
+induction and we'll do that. Uh let me
+ 
+
+ align:start position:0%
+induction and we'll do that. Uh let me
+first state the theorem. So if
+
+ align:start position:0%
+first state the theorem. So if
+ 
+
+ align:start position:0%
+first state the theorem. So if
+any natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is true
+
+ align:start position:0%
+this is true
+ 
+
+ align:start position:0%
+this is true
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh any natural number p of n is true.
+
+ align:start position:0%
+uh any natural number p of n is true.
+ 
+
+ align:start position:0%
+uh any natural number p of n is true.
+Okay. Uh let me bring this one down to
+
+ align:start position:0%
+Okay. Uh let me bring this one down to
+ 
+
+ align:start position:0%
+Okay. Uh let me bring this one down to
+compare.
+
+ align:start position:0%
+compare.
+ 
+
+ align:start position:0%
+compare.
+Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh first thing maybe to notice is
+
+ align:start position:0%
+so uh first thing maybe to notice is
+ 
+
+ align:start position:0%
+so uh first thing maybe to notice is
+there doesn't seem to be a base case
+
+ align:start position:0%
+there doesn't seem to be a base case
+ 
+
+ align:start position:0%
+there doesn't seem to be a base case
+here. uh which is a little weird. It's
+
+ align:start position:0%
+here. uh which is a little weird. It's
+ 
+
+ align:start position:0%
+here. uh which is a little weird. It's
+just one condition then this let's
+
+ align:start position:0%
+just one condition then this let's
+ 
+
+ align:start position:0%
+just one condition then this let's
+compare the steps first of all um so or
+
+ align:start position:0%
+compare the steps first of all um so or
+ 
+
+ align:start position:0%
+compare the steps first of all um so or
+I guess let's let's think about the case
+
+ align:start position:0%
+I guess let's let's think about the case
+ 
+
+ align:start position:0%
+I guess let's let's think about the case
+this has to be true for all n if we
+
+ align:start position:0%
+this has to be true for all n if we
+ 
+
+ align:start position:0%
+this has to be true for all n if we
+think about when n equals 0 that's the
+
+ align:start position:0%
+think about when n equals 0 that's the
+ 
+
+ align:start position:0%
+think about when n equals 0 that's the
+missing base case what this is actually
+
+ align:start position:0%
+missing base case what this is actually
+ 
+
+ align:start position:0%
+missing base case what this is actually
+saying is p 0 up to p minus one implies
+
+ align:start position:0%
+saying is p 0 up to p minus one implies
+ 
+
+ align:start position:0%
+saying is p 0 up to p minus one implies
+p of zero okay so this is kind of weird
+
+ align:start position:0%
+p of zero okay so this is kind of weird
+ 
+
+ align:start position:0%
+p of zero okay so this is kind of weird
+notation I'm I'm abusing the dot dot dot
+
+ align:start position:0%
+notation I'm I'm abusing the dot dot dot
+ 
+
+ align:start position:0%
+notation I'm I'm abusing the dot dot dot
+a little bit here and uh for when n
+
+ align:start position:0%
+a little bit here and uh for when n
+ 
+
+ align:start position:0%
+a little bit here and uh for when n
+equals one this is p of 0 when n equals
+
+ align:start position:0%
+equals one this is p of 0 when n equals
+ 
+
+ align:start position:0%
+equals one this is p of 0 when n equals
+2 this is p of 0 and p of 1 when n
+
+ align:start position:0%
+2 this is p of 0 and p of 1 when n
+ 
+
+ align:start position:0%
+2 this is p of 0 and p of 1 when n
+equals 3 I mean for a larger n it's very
+
+ align:start position:0%
+equals 3 I mean for a larger n it's very
+ 
+
+ align:start position:0%
+equals 3 I mean for a larger n it's very
+clear what this dot dot dot means but
+
+ align:start position:0%
+clear what this dot dot dot means but
+ 
+
+ align:start position:0%
+clear what this dot dot dot means but
+when n equals 0 it's confusing so I need
+
+ align:start position:0%
+when n equals 0 it's confusing so I need
+ 
+
+ align:start position:0%
+when n equals 0 it's confusing so I need
+to specify uh this is defined to be true
+
+ align:start position:0%
+to specify uh this is defined to be true
+ 
+
+ align:start position:0%
+to specify uh this is defined to be true
+uh for n equals 0
+
+ align:start position:0%
+uh for n equals 0
+ 
+
+ align:start position:0%
+uh for n equals 0
+okay so for n equals 0 what you have to
+
+ align:start position:0%
+okay so for n equals 0 what you have to
+ 
+
+ align:start position:0%
+okay so for n equals 0 what you have to
+do is prove that true implies p of zero
+
+ align:start position:0%
+do is prove that true implies p of zero
+ 
+
+ align:start position:0%
+do is prove that true implies p of zero
+in other words p of zero must be true in
+
+ align:start position:0%
+in other words p of zero must be true in
+ 
+
+ align:start position:0%
+in other words p of zero must be true in
+all cases okay so there's Um, but then
+
+ align:start position:0%
+all cases okay so there's Um, but then
+ 
+
+ align:start position:0%
+all cases okay so there's Um, but then
+for larger n, what this is saying is not
+
+ align:start position:0%
+for larger n, what this is saying is not
+ 
+
+ align:start position:0%
+for larger n, what this is saying is not
+only do I get to assume p of n minus
+
+ align:start position:0%
+only do I get to assume p of n minus
+ 
+
+ align:start position:0%
+only do I get to assume p of n minus
+one, but I get to assume all the p of
+
+ align:start position:0%
+one, but I get to assume all the p of
+ 
+
+ align:start position:0%
+one, but I get to assume all the p of
+i's before p of n. So I would I would
+
+ align:start position:0%
+i's before p of n. So I would I would
+ 
+
+ align:start position:0%
+i's before p of n. So I would I would
+normally say uh p of i is true for all i
+
+ align:start position:0%
+normally say uh p of i is true for all i
+ 
+
+ align:start position:0%
+normally say uh p of i is true for all i
+less than n. This is what I get to
+
+ align:start position:0%
+less than n. This is what I get to
+ 
+
+ align:start position:0%
+less than n. This is what I get to
+assume.
+
+ align:start position:0%
+assume.
+ 
+
+ align:start position:0%
+assume.
+That's probably actually a better way to
+
+ align:start position:0%
+That's probably actually a better way to
+ 
+
+ align:start position:0%
+That's probably actually a better way to
+state this this thing.
+
+ align:start position:0%
+state this this thing.
+ 
+
+ align:start position:0%
+state this this thing.
+So with regular induction here, I got to
+
+ align:start position:0%
+So with regular induction here, I got to
+ 
+
+ align:start position:0%
+So with regular induction here, I got to
+assume that the previous P of N minus
+
+ align:start position:0%
+assume that the previous P of N minus
+ 
+
+ align:start position:0%
+assume that the previous P of N minus
+one was true and I needed to use that to
+
+ align:start position:0%
+one was true and I needed to use that to
+ 
+
+ align:start position:0%
+one was true and I needed to use that to
+pro prove that P of N is true. But
+
+ align:start position:0%
+pro prove that P of N is true. But
+ 
+
+ align:start position:0%
+pro prove that P of N is true. But
+actually if you look at this chain like
+
+ align:start position:0%
+actually if you look at this chain like
+ 
+
+ align:start position:0%
+actually if you look at this chain like
+by the time I'm proving P of three, I've
+
+ align:start position:0%
+by the time I'm proving P of three, I've
+ 
+
+ align:start position:0%
+by the time I'm proving P of three, I've
+already proved all the smaller PIs.
+
+ align:start position:0%
+already proved all the smaller PIs.
+ 
+
+ align:start position:0%
+already proved all the smaller PIs.
+So why not and assume that with strong
+
+ align:start position:0%
+So why not and assume that with strong
+ 
+
+ align:start position:0%
+So why not and assume that with strong
+induction I get to assume that in order
+
+ align:start position:0%
+induction I get to assume that in order
+ 
+
+ align:start position:0%
+induction I get to assume that in order
+to prove P of N I get to assume all the
+
+ align:start position:0%
+to prove P of N I get to assume all the
+ 
+
+ align:start position:0%
+to prove P of N I get to assume all the
+PI's where I is less than M. Okay. Now
+
+ align:start position:0%
+PI's where I is less than M. Okay. Now
+ 
+
+ align:start position:0%
+PI's where I is less than M. Okay. Now
+when N equals Z, I don't get to assume
+
+ align:start position:0%
+when N equals Z, I don't get to assume
+ 
+
+ align:start position:0%
+when N equals Z, I don't get to assume
+anything because there are no smaller
+
+ align:start position:0%
+anything because there are no smaller
+ 
+
+ align:start position:0%
+anything because there are no smaller
+I's. Uh but when I get to P of five, I
+
+ align:start position:0%
+I's. Uh but when I get to P of five, I
+ 
+
+ align:start position:0%
+I's. Uh but when I get to P of five, I
+get to assume P 0, P4, P 0, P1, P2, P3,
+
+ align:start position:0%
+get to assume P 0, P4, P 0, P1, P2, P3,
+ 
+
+ align:start position:0%
+get to assume P 0, P4, P 0, P1, P2, P3,
+P4. Uh so I get to assume more. So this
+
+ align:start position:0%
+P4. Uh so I get to assume more. So this
+ 
+
+ align:start position:0%
+P4. Uh so I get to assume more. So this
+only makes my proof easier.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um to be clear, uh this is usually
+
+ align:start position:0%
+Okay. Um to be clear, uh this is usually
+ 
+
+ align:start position:0%
+Okay. Um to be clear, uh this is usually
+proved in cases normally you need to uh
+
+ align:start position:0%
+proved in cases normally you need to uh
+ 
+
+ align:start position:0%
+proved in cases normally you need to uh
+check zero specially. That might be a
+
+ align:start position:0%
+check zero specially. That might be a
+ 
+
+ align:start position:0%
+check zero specially. That might be a
+base case. Maybe you have to check one
+
+ align:start position:0%
+base case. Maybe you have to check one
+ 
+
+ align:start position:0%
+base case. Maybe you have to check one
+specially. It depends on your
+
+ align:start position:0%
+specially. It depends on your
+ 
+
+ align:start position:0%
+specially. It depends on your
+implication argument. this uh often this
+
+ align:start position:0%
+implication argument. this uh often this
+ 
+
+ align:start position:0%
+implication argument. this uh often this
+implication
+
+ align:start position:0%
+implication
+ 
+
+ align:start position:0%
+implication
+assumes that n is at least something and
+
+ align:start position:0%
+assumes that n is at least something and
+ 
+
+ align:start position:0%
+assumes that n is at least something and
+then you have to prove all the smaller
+
+ align:start position:0%
+then you have to prove all the smaller
+ 
+
+ align:start position:0%
+then you have to prove all the smaller
+ns to be true specially but we'll we'll
+
+ align:start position:0%
+ns to be true specially but we'll we'll
+ 
+
+ align:start position:0%
+ns to be true specially but we'll we'll
+get to examples in a moment. What I'd
+
+ align:start position:0%
+get to examples in a moment. What I'd
+ 
+
+ align:start position:0%
+get to examples in a moment. What I'd
+like to do first is actually prove that
+
+ align:start position:0%
+like to do first is actually prove that
+ 
+
+ align:start position:0%
+like to do first is actually prove that
+strong induction is true.
+
+ align:start position:0%
+strong induction is true.
+ 
+
+ align:start position:0%
+strong induction is true.
+This is not something you would repeat
+
+ align:start position:0%
+This is not something you would repeat
+ 
+
+ align:start position:0%
+This is not something you would repeat
+in your homework. You should just assume
+
+ align:start position:0%
+in your homework. You should just assume
+ 
+
+ align:start position:0%
+in your homework. You should just assume
+strong induction is true. But I think
+
+ align:start position:0%
+strong induction is true. But I think
+ 
+
+ align:start position:0%
+strong induction is true. But I think
+it's instructive to see why it's true
+
+ align:start position:0%
+it's instructive to see why it's true
+ 
+
+ align:start position:0%
+it's instructive to see why it's true
+as yet another example of induction.
+
+ align:start position:0%
+as yet another example of induction.
+ 
+
+ align:start position:0%
+as yet another example of induction.
+Okay, so we're going to use regular
+
+ align:start position:0%
+Okay, so we're going to use regular
+ 
+
+ align:start position:0%
+Okay, so we're going to use regular
+induction this version or actually I
+
+ align:start position:0%
+induction this version or actually I
+ 
+
+ align:start position:0%
+induction this version or actually I
+think this version the induction axiom
+
+ align:start position:0%
+think this version the induction axiom
+ 
+
+ align:start position:0%
+think this version the induction axiom
+uh to prove strong induction.
+
+ align:start position:0%
+uh to prove strong induction.
+ 
+
+ align:start position:0%
+uh to prove strong induction.
+Okay. Now, this is a situation where we
+
+ align:start position:0%
+Okay. Now, this is a situation where we
+ 
+
+ align:start position:0%
+Okay. Now, this is a situation where we
+need to define a particular induction
+
+ align:start position:0%
+need to define a particular induction
+ 
+
+ align:start position:0%
+need to define a particular induction
+hypothesis. This not the obvious one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is not at all obvious, but I'm
+
+ align:start position:0%
+and this is not at all obvious, but I'm
+ 
+
+ align:start position:0%
+and this is not at all obvious, but I'm
+going to define uh IH of N to be uh this
+
+ align:start position:0%
+going to define uh IH of N to be uh this
+ 
+
+ align:start position:0%
+going to define uh IH of N to be uh this
+P of 0 and P of N minus one. In other
+
+ align:start position:0%
+P of 0 and P of N minus one. In other
+ 
+
+ align:start position:0%
+P of 0 and P of N minus one. In other
+words, uh for all I less than N, P of I.
+
+ align:start position:0%
+words, uh for all I less than N, P of I.
+ 
+
+ align:start position:0%
+words, uh for all I less than N, P of I.
+I like that better because it works even
+
+ align:start position:0%
+I like that better because it works even
+ 
+
+ align:start position:0%
+I like that better because it works even
+when n is zero because there are no i's
+
+ align:start position:0%
+when n is zero because there are no i's
+ 
+
+ align:start position:0%
+when n is zero because there are no i's
+less than zero. So that's just true when
+
+ align:start position:0%
+less than zero. So that's just true when
+ 
+
+ align:start position:0%
+less than zero. So that's just true when
+I when n is zero. Okay, so this is the
+
+ align:start position:0%
+I when n is zero. Okay, so this is the
+ 
+
+ align:start position:0%
+I when n is zero. Okay, so this is the
+thing I want to prove for all n.
+
+ align:start position:0%
+thing I want to prove for all n.
+ 
+
+ align:start position:0%
+thing I want to prove for all n.
+And how do we do it? Well, uh as usual
+
+ align:start position:0%
+And how do we do it? Well, uh as usual
+ 
+
+ align:start position:0%
+And how do we do it? Well, uh as usual
+with an induction, we have a base case.
+
+ align:start position:0%
+with an induction, we have a base case.
+ 
+
+ align:start position:0%
+with an induction, we have a base case.
+Base case is ih of zero.
+
+ align:start position:0%
+Base case is ih of zero.
+ 
+
+ align:start position:0%
+Base case is ih of zero.
+So uh ih of zero is actually literally
+
+ align:start position:0%
+So uh ih of zero is actually literally
+ 
+
+ align:start position:0%
+So uh ih of zero is actually literally
+just true.
+
+ align:start position:0%
+just true.
+ 
+
+ align:start position:0%
+just true.
+uh because we defined it to be that way.
+
+ align:start position:0%
+uh because we defined it to be that way.
+ 
+
+ align:start position:0%
+uh because we defined it to be that way.
+We said when n equals 0 this dot dot dot
+
+ align:start position:0%
+We said when n equals 0 this dot dot dot
+ 
+
+ align:start position:0%
+We said when n equals 0 this dot dot dot
+is true or you could say uh this is
+
+ align:start position:0%
+is true or you could say uh this is
+ 
+
+ align:start position:0%
+is true or you could say uh this is
+saying for all i less than zero where i
+
+ align:start position:0%
+saying for all i less than zero where i
+ 
+
+ align:start position:0%
+saying for all i less than zero where i
+is a natural number but there are no
+
+ align:start position:0%
+is a natural number but there are no
+ 
+
+ align:start position:0%
+is a natural number but there are no
+natural numbers less than zero. So this
+
+ align:start position:0%
+natural numbers less than zero. So this
+ 
+
+ align:start position:0%
+natural numbers less than zero. So this
+is like saying if false then something
+
+ align:start position:0%
+is like saying if false then something
+ 
+
+ align:start position:0%
+is like saying if false then something
+and that's just always true. So this is
+
+ align:start position:0%
+and that's just always true. So this is
+ 
+
+ align:start position:0%
+and that's just always true. So this is
+by definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh ih of z is true. Great easy base case
+
+ align:start position:0%
+uh ih of z is true. Great easy base case
+ 
+
+ align:start position:0%
+uh ih of z is true. Great easy base case
+as usual. Uh what's the induction step
+
+ align:start position:0%
+as usual. Uh what's the induction step
+ 
+
+ align:start position:0%
+as usual. Uh what's the induction step
+look like? I'm going to I get to choose.
+
+ align:start position:0%
+look like? I'm going to I get to choose.
+ 
+
+ align:start position:0%
+look like? I'm going to I get to choose.
+I could either assume I of N minus one
+
+ align:start position:0%
+I could either assume I of N minus one
+ 
+
+ align:start position:0%
+I could either assume I of N minus one
+and prove IH of N or I'm going to assume
+
+ align:start position:0%
+and prove IH of N or I'm going to assume
+ 
+
+ align:start position:0%
+and prove IH of N or I'm going to assume
+I of N and uh prove uh IH of N + one. So
+
+ align:start position:0%
+I of N and uh prove uh IH of N + one. So
+ 
+
+ align:start position:0%
+I of N and uh prove uh IH of N + one. So
+we want to show if N plus1 assuming IH
+
+ align:start position:0%
+we want to show if N plus1 assuming IH
+ 
+
+ align:start position:0%
+we want to show if N plus1 assuming IH
+of N. Uh
+
+ align:start position:0%
+of N. Uh
+ 
+
+ align:start position:0%
+of N. Uh
+cool. So the key thing is we get to
+
+ align:start position:0%
+cool. So the key thing is we get to
+ 
+
+ align:start position:0%
+cool. So the key thing is we get to
+assume this is true. The strong
+
+ align:start position:0%
+assume this is true. The strong
+ 
+
+ align:start position:0%
+assume this is true. The strong
+induction says if this then this. So
+
+ align:start position:0%
+induction says if this then this. So
+ 
+
+ align:start position:0%
+induction says if this then this. So
+we're assuming the if part we're
+
+ align:start position:0%
+we're assuming the if part we're
+ 
+
+ align:start position:0%
+we're assuming the if part we're
+assuming that if uh this implication
+
+ align:start position:0%
+assuming that if uh this implication
+ 
+
+ align:start position:0%
+assuming that if uh this implication
+and this thing here is exactly IH of N,
+
+ align:start position:0%
+and this thing here is exactly IH of N,
+ 
+
+ align:start position:0%
+and this thing here is exactly IH of N,
+right? So this says IH of N implies P of
+
+ align:start position:0%
+right? So this says IH of N implies P of
+ 
+
+ align:start position:0%
+right? So this says IH of N implies P of
+N. So we know
+
+ align:start position:0%
+N. So we know
+ 
+
+ align:start position:0%
+N. So we know
+IH ofN implies P of N. That's uh what
+
+ align:start position:0%
+IH ofN implies P of N. That's uh what
+ 
+
+ align:start position:0%
+IH ofN implies P of N. That's uh what
+we're get to assume in our theorem
+
+ align:start position:0%
+we're get to assume in our theorem
+ 
+
+ align:start position:0%
+we're get to assume in our theorem
+statement here. and we just assumed that
+
+ align:start position:0%
+statement here. and we just assumed that
+ 
+
+ align:start position:0%
+statement here. and we just assumed that
+IH of N is true. Therefore, P of N is
+
+ align:start position:0%
+IH of N is true. Therefore, P of N is
+ 
+
+ align:start position:0%
+IH of N is true. Therefore, P of N is
+true.
+
+ align:start position:0%
+true.
+ 
+
+ align:start position:0%
+true.
+Okay, but P of N was not what we wanted
+
+ align:start position:0%
+Okay, but P of N was not what we wanted
+ 
+
+ align:start position:0%
+Okay, but P of N was not what we wanted
+to prove. We wanted to prove IH of N
+
+ align:start position:0%
+to prove. We wanted to prove IH of N
+ 
+
+ align:start position:0%
+to prove. We wanted to prove IH of N
+plus1. So, what is IH of N plus1?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh let's just expand out this definition
+
+ align:start position:0%
+Uh let's just expand out this definition
+ 
+
+ align:start position:0%
+Uh let's just expand out this definition
+here. It is P of zero or dot dot dot or
+
+ align:start position:0%
+here. It is P of zero or dot dot dot or
+ 
+
+ align:start position:0%
+here. It is P of zero or dot dot dot or
+P of N minus one or P of N because I've
+
+ align:start position:0%
+P of N minus one or P of N because I've
+ 
+
+ align:start position:0%
+P of N minus one or P of N because I've
+incremented N by one. This no longer
+
+ align:start position:0%
+incremented N by one. This no longer
+ 
+
+ align:start position:0%
+incremented N by one. This no longer
+ends at P of N minus one. It now ends at
+
+ align:start position:0%
+ends at P of N minus one. It now ends at
+ 
+
+ align:start position:0%
+ends at P of N minus one. It now ends at
+P of N. Okay, but this is almost what we
+
+ align:start position:0%
+P of N. Okay, but this is almost what we
+ 
+
+ align:start position:0%
+P of N. Okay, but this is almost what we
+had before. This is the induction
+
+ align:start position:0%
+had before. This is the induction
+ 
+
+ align:start position:0%
+had before. This is the induction
+hypothesis of N. That's this part
+
+ align:start position:0%
+hypothesis of N. That's this part
+ 
+
+ align:start position:0%
+hypothesis of N. That's this part
+or P of N,
+
+ align:start position:0%
+or P of N,
+ 
+
+ align:start position:0%
+or P of N,
+right? That's just formula manipulation.
+
+ align:start position:0%
+right? That's just formula manipulation.
+ 
+
+ align:start position:0%
+right? That's just formula manipulation.
+And this we assumed is true. IH of N is
+
+ align:start position:0%
+And this we assumed is true. IH of N is
+ 
+
+ align:start position:0%
+And this we assumed is true. IH of N is
+true. And P ofN we just proved is true.
+
+ align:start position:0%
+true. And P ofN we just proved is true.
+ 
+
+ align:start position:0%
+true. And P ofN we just proved is true.
+Sorry. Uh I wrote or here but I meant
+
+ align:start position:0%
+Sorry. Uh I wrote or here but I meant
+ 
+
+ align:start position:0%
+Sorry. Uh I wrote or here but I meant
+and everywhere. This is and
+
+ align:start position:0%
+and everywhere. This is and
+ 
+
+ align:start position:0%
+and everywhere. This is and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+see even professors get the V's and
+
+ align:start position:0%
+see even professors get the V's and
+ 
+
+ align:start position:0%
+see even professors get the V's and
+wedges upside down. So I wrote it
+
+ align:start position:0%
+wedges upside down. So I wrote it
+ 
+
+ align:start position:0%
+wedges upside down. So I wrote it
+correctly here. It's the and of P 0 up
+
+ align:start position:0%
+correctly here. It's the and of P 0 up
+ 
+
+ align:start position:0%
+correctly here. It's the and of P 0 up
+to PN minus one. Here we have the end of
+
+ align:start position:0%
+to PN minus one. Here we have the end of
+ 
+
+ align:start position:0%
+to PN minus one. Here we have the end of
+P 0 up to PN. And so this is IH of N
+
+ align:start position:0%
+P 0 up to PN. And so this is IH of N
+ 
+
+ align:start position:0%
+P 0 up to PN. And so this is IH of N
+which we assumed was true by induction.
+
+ align:start position:0%
+which we assumed was true by induction.
+ 
+
+ align:start position:0%
+which we assumed was true by induction.
+and P ofn which we just proved using one
+
+ align:start position:0%
+and P ofn which we just proved using one
+ 
+
+ align:start position:0%
+and P ofn which we just proved using one
+induction step. Therefore, the and is
+
+ align:start position:0%
+induction step. Therefore, the and is
+ 
+
+ align:start position:0%
+induction step. Therefore, the and is
+also true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I believe that's the end of the
+
+ align:start position:0%
+And I believe that's the end of the
+ 
+
+ align:start position:0%
+And I believe that's the end of the
+proof,
+
+ align:start position:0%
+proof,
+ 
+
+ align:start position:0%
+proof,
+right? I did a base case, I did a step.
+
+ align:start position:0%
+right? I did a base case, I did a step.
+ 
+
+ align:start position:0%
+right? I did a base case, I did a step.
+Oh, no. Quite not quite the answer.
+
+ align:start position:0%
+Oh, no. Quite not quite the answer.
+ 
+
+ align:start position:0%
+Oh, no. Quite not quite the answer.
+Sorry, there's one more step here
+
+ align:start position:0%
+Sorry, there's one more step here
+ 
+
+ align:start position:0%
+Sorry, there's one more step here
+uh which I will put over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's a good illustration and not
+
+ align:start position:0%
+It's a good illustration and not
+ 
+
+ align:start position:0%
+It's a good illustration and not
+skipping steps. Uh what did we actually
+
+ align:start position:0%
+skipping steps. Uh what did we actually
+ 
+
+ align:start position:0%
+skipping steps. Uh what did we actually
+prove by induction? We proved induction
+
+ align:start position:0%
+prove by induction? We proved induction
+ 
+
+ align:start position:0%
+prove by induction? We proved induction
+hypothesis of n is true for all n. So by
+
+ align:start position:0%
+hypothesis of n is true for all n. So by
+ 
+
+ align:start position:0%
+hypothesis of n is true for all n. So by
+induction
+
+ align:start position:0%
+induction
+ 
+
+ align:start position:0%
+induction
+like the regular old induction axiom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh for all natural numbers n uh
+
+ align:start position:0%
+uh for all natural numbers n uh
+ 
+
+ align:start position:0%
+uh for all natural numbers n uh
+induction hypothesis of n is true
+
+ align:start position:0%
+induction hypothesis of n is true
+ 
+
+ align:start position:0%
+induction hypothesis of n is true
+induction hypothesis of n is this thing
+
+ align:start position:0%
+induction hypothesis of n is this thing
+ 
+
+ align:start position:0%
+induction hypothesis of n is this thing
+but that's not what we wanted to prove.
+
+ align:start position:0%
+but that's not what we wanted to prove.
+ 
+
+ align:start position:0%
+but that's not what we wanted to prove.
+We wanted to prove p of n is true for
+
+ align:start position:0%
+We wanted to prove p of n is true for
+ 
+
+ align:start position:0%
+We wanted to prove p of n is true for
+all all n. uh but I can do some
+
+ align:start position:0%
+all all n. uh but I can do some
+ 
+
+ align:start position:0%
+all all n. uh but I can do some
+manipulation to make that what I want.
+
+ align:start position:0%
+manipulation to make that what I want.
+ 
+
+ align:start position:0%
+manipulation to make that what I want.
+So this is like saying for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+let's see actually probably this is
+
+ align:start position:0%
+let's see actually probably this is
+ 
+
+ align:start position:0%
+let's see actually probably this is
+nicer for all natural numbers
+
+ align:start position:0%
+nicer for all natural numbers
+ 
+
+ align:start position:0%
+nicer for all natural numbers
+uh ih of n plus one is true okay this is
+
+ align:start position:0%
+uh ih of n plus one is true okay this is
+ 
+
+ align:start position:0%
+uh ih of n plus one is true okay this is
+a shift it's actually a weaker shift
+
+ align:start position:0%
+a shift it's actually a weaker shift
+ 
+
+ align:start position:0%
+a shift it's actually a weaker shift
+this includes ih of zero this
+
+ align:start position:0%
+this includes ih of zero this
+ 
+
+ align:start position:0%
+this includes ih of zero this
+should not be greater than equal to this
+
+ align:start position:0%
+should not be greater than equal to this
+ 
+
+ align:start position:0%
+should not be greater than equal to this
+should be an element of uh this includes
+
+ align:start position:0%
+should be an element of uh this includes
+ 
+
+ align:start position:0%
+should be an element of uh this includes
+zero this doesn't this starts at one and
+
+ align:start position:0%
+zero this doesn't this starts at one and
+ 
+
+ align:start position:0%
+zero this doesn't this starts at one and
+it goes upwards But this is nice. Uh
+
+ align:start position:0%
+it goes upwards But this is nice. Uh
+ 
+
+ align:start position:0%
+it goes upwards But this is nice. Uh
+this so this implies this, right? Uh
+
+ align:start position:0%
+this so this implies this, right? Uh
+ 
+
+ align:start position:0%
+this so this implies this, right? Uh
+this is what we've shown. This is a
+
+ align:start position:0%
+this is what we've shown. This is a
+ 
+
+ align:start position:0%
+this is what we've shown. This is a
+weaker statement because I just threw
+
+ align:start position:0%
+weaker statement because I just threw
+ 
+
+ align:start position:0%
+weaker statement because I just threw
+away I of zero. I of zero wasn't
+
+ align:start position:0%
+away I of zero. I of zero wasn't
+ 
+
+ align:start position:0%
+away I of zero. I of zero wasn't
+interesting anyway.
+
+ align:start position:0%
+interesting anyway.
+ 
+
+ align:start position:0%
+interesting anyway.
+I of one uh includes inside of it. So
+
+ align:start position:0%
+I of one uh includes inside of it. So
+ 
+
+ align:start position:0%
+I of one uh includes inside of it. So
+it's an and of a bunch of things. But
+
+ align:start position:0%
+it's an and of a bunch of things. But
+ 
+
+ align:start position:0%
+it's an and of a bunch of things. But
+then the last term is P of N.
+
+ align:start position:0%
+then the last term is P of N.
+ 
+
+ align:start position:0%
+then the last term is P of N.
+Right? That's if I take Ih of N + one,
+
+ align:start position:0%
+Right? That's if I take Ih of N + one,
+ 
+
+ align:start position:0%
+Right? That's if I take Ih of N + one,
+the last term in is P of N. So it's also
+
+ align:start position:0%
+the last term in is P of N. So it's also
+ 
+
+ align:start position:0%
+the last term in is P of N. So it's also
+anded but uh if the and is true then
+
+ align:start position:0%
+anded but uh if the and is true then
+ 
+
+ align:start position:0%
+anded but uh if the and is true then
+every term is true and so therefore p of
+
+ align:start position:0%
+every term is true and so therefore p of
+ 
+
+ align:start position:0%
+every term is true and so therefore p of
+n is true for all n. Okay, so this was a
+
+ align:start position:0%
+n is true for all n. Okay, so this was a
+ 
+
+ align:start position:0%
+n is true for all n. Okay, so this was a
+final clean up after we did induction.
+
+ align:start position:0%
+final clean up after we did induction.
+ 
+
+ align:start position:0%
+final clean up after we did induction.
+We didn't quite get the statement we
+
+ align:start position:0%
+We didn't quite get the statement we
+ 
+
+ align:start position:0%
+We didn't quite get the statement we
+wanted because we used a more gen a
+
+ align:start position:0%
+wanted because we used a more gen a
+ 
+
+ align:start position:0%
+wanted because we used a more gen a
+different induction hypothesis than just
+
+ align:start position:0%
+different induction hypothesis than just
+ 
+
+ align:start position:0%
+different induction hypothesis than just
+p. Uh and then we needed to show that
+
+ align:start position:0%
+p. Uh and then we needed to show that
+ 
+
+ align:start position:0%
+p. Uh and then we needed to show that
+that implied p of n for all n. Okay, but
+
+ align:start position:0%
+that implied p of n for all n. Okay, but
+ 
+
+ align:start position:0%
+that implied p of n for all n. Okay, but
+it works.
+
+ align:start position:0%
+it works.
+ 
+
+ align:start position:0%
+it works.
+Cool. So now uh there should be no
+
+ align:start position:0%
+Cool. So now uh there should be no
+ 
+
+ align:start position:0%
+Cool. So now uh there should be no
+question about why strong induction is
+
+ align:start position:0%
+question about why strong induction is
+ 
+
+ align:start position:0%
+question about why strong induction is
+true assuming you believe this proof. Um
+
+ align:start position:0%
+true assuming you believe this proof. Um
+ 
+
+ align:start position:0%
+true assuming you believe this proof. Um
+you can draw a diagram. Uh it's a little
+
+ align:start position:0%
+you can draw a diagram. Uh it's a little
+ 
+
+ align:start position:0%
+you can draw a diagram. Uh it's a little
+trickier to do. Maybe I will show you uh
+
+ align:start position:0%
+trickier to do. Maybe I will show you uh
+ 
+
+ align:start position:0%
+trickier to do. Maybe I will show you uh
+in my handwritten notes
+
+ align:start position:0%
+in my handwritten notes
+ 
+
+ align:start position:0%
+in my handwritten notes
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Here is a block diagram for strong
+
+ align:start position:0%
+Here is a block diagram for strong
+ 
+
+ align:start position:0%
+Here is a block diagram for strong
+induction.
+
+ align:start position:0%
+induction.
+ 
+
+ align:start position:0%
+induction.
+uh it's harder to draw because you
+
+ align:start position:0%
+uh it's harder to draw because you
+ 
+
+ align:start position:0%
+uh it's harder to draw because you
+depend on so many things when I apply
+
+ align:start position:0%
+depend on so many things when I apply
+ 
+
+ align:start position:0%
+depend on so many things when I apply
+the fourth step here when I want to
+
+ align:start position:0%
+the fourth step here when I want to
+ 
+
+ align:start position:0%
+the fourth step here when I want to
+conclude P of four I assume all the
+
+ align:start position:0%
+conclude P of four I assume all the
+ 
+
+ align:start position:0%
+conclude P of four I assume all the
+previous PS so P 0 P1 P2 P3 they all
+
+ align:start position:0%
+previous PS so P 0 P1 P2 P3 they all
+ 
+
+ align:start position:0%
+previous PS so P 0 P1 P2 P3 they all
+feed into this box in the beginning it's
+
+ align:start position:0%
+feed into this box in the beginning it's
+ 
+
+ align:start position:0%
+feed into this box in the beginning it's
+very similar I apply a step I get P of 0
+
+ align:start position:0%
+very similar I apply a step I get P of 0
+ 
+
+ align:start position:0%
+very similar I apply a step I get P of 0
+then I apply that P of 0 to a step I get
+
+ align:start position:0%
+then I apply that P of 0 to a step I get
+ 
+
+ align:start position:0%
+then I apply that P of 0 to a step I get
+P of one uh but then as I proceed I'm
+
+ align:start position:0%
+P of one uh but then as I proceed I'm
+ 
+
+ align:start position:0%
+P of one uh but then as I proceed I'm
+feeding more and more PI's into the step
+
+ align:start position:0%
+feeding more and more PI's into the step
+ 
+
+ align:start position:0%
+feeding more and more PI's into the step
+and it gives me one more pi. Okay, so
+
+ align:start position:0%
+and it gives me one more pi. Okay, so
+ 
+
+ align:start position:0%
+and it gives me one more pi. Okay, so
+it's a much more complicated diagram
+
+ align:start position:0%
+it's a much more complicated diagram
+ 
+
+ align:start position:0%
+it's a much more complicated diagram
+what's going on under the hood. But from
+
+ align:start position:0%
+what's going on under the hood. But from
+ 
+
+ align:start position:0%
+what's going on under the hood. But from
+a usage standpoint, it's it only helps
+
+ align:start position:0%
+a usage standpoint, it's it only helps
+ 
+
+ align:start position:0%
+a usage standpoint, it's it only helps
+you when you're trying to prove P of N.
+
+ align:start position:0%
+you when you're trying to prove P of N.
+ 
+
+ align:start position:0%
+you when you're trying to prove P of N.
+You don't just get to assume P of N
+
+ align:start position:0%
+You don't just get to assume P of N
+ 
+
+ align:start position:0%
+You don't just get to assume P of N
+minus one. You get to assume all the
+
+ align:start position:0%
+minus one. You get to assume all the
+ 
+
+ align:start position:0%
+minus one. You get to assume all the
+PI's uh where I is less than N.
+
+ align:start position:0%
+PI's uh where I is less than N.
+ 
+
+ align:start position:0%
+PI's uh where I is less than N.
+I forgot one part of the fourcolor
+
+ align:start position:0%
+I forgot one part of the fourcolor
+ 
+
+ align:start position:0%
+I forgot one part of the fourcolor
+theorem story which was when I was
+
+ align:start position:0%
+theorem story which was when I was
+ 
+
+ align:start position:0%
+theorem story which was when I was
+growing up I read a reprint of this
+
+ align:start position:0%
+growing up I read a reprint of this
+ 
+
+ align:start position:0%
+growing up I read a reprint of this
+article by Martin Gardner which turned
+
+ align:start position:0%
+article by Martin Gardner which turned
+ 
+
+ align:start position:0%
+article by Martin Gardner which turned
+out to be published on April fools but I
+
+ align:start position:0%
+out to be published on April fools but I
+ 
+
+ align:start position:0%
+out to be published on April fools but I
+didn't know it at the time uh and in at
+
+ align:start position:0%
+didn't know it at the time uh and in at
+ 
+
+ align:start position:0%
+didn't know it at the time uh and in at
+that in 1975 there was no proof of the
+
+ align:start position:0%
+that in 1975 there was no proof of the
+ 
+
+ align:start position:0%
+that in 1975 there was no proof of the
+fourcolor theorem Haken was I think one
+
+ align:start position:0%
+fourcolor theorem Haken was I think one
+ 
+
+ align:start position:0%
+fourcolor theorem Haken was I think one
+year later uh so at this point he
+
+ align:start position:0%
+year later uh so at this point he
+ 
+
+ align:start position:0%
+year later uh so at this point he
+published a joke saying in fact McGregor
+
+ align:start position:0%
+published a joke saying in fact McGregor
+ 
+
+ align:start position:0%
+published a joke saying in fact McGregor
+found this map which requires five
+
+ align:start position:0%
+found this map which requires five
+ 
+
+ align:start position:0%
+found this map which requires five
+colors I remember sitting trying to
+
+ align:start position:0%
+colors I remember sitting trying to
+ 
+
+ align:start position:0%
+colors I remember sitting trying to
+color it with with four colors and
+
+ align:start position:0%
+color it with with four colors and
+ 
+
+ align:start position:0%
+color it with with four colors and
+always failing. It's like, oh my gosh,
+
+ align:start position:0%
+always failing. It's like, oh my gosh,
+ 
+
+ align:start position:0%
+always failing. It's like, oh my gosh,
+fourcolor theorem isn't true. This is or
+
+ align:start position:0%
+fourcolor theorem isn't true. This is or
+ 
+
+ align:start position:0%
+fourcolor theorem isn't true. This is or
+fourcolor conjecture as it was called
+
+ align:start position:0%
+fourcolor conjecture as it was called
+ 
+
+ align:start position:0%
+fourcolor conjecture as it was called
+then isn't true. Isn't that amazing? But
+
+ align:start position:0%
+then isn't true. Isn't that amazing? But
+ 
+
+ align:start position:0%
+then isn't true. Isn't that amazing? But
+it was all a lie. In fact, you can
+
+ align:start position:0%
+it was all a lie. In fact, you can
+ 
+
+ align:start position:0%
+it was all a lie. In fact, you can
+fourcolor that map. Uh but it's is a
+
+ align:start position:0%
+fourcolor that map. Uh but it's is a
+ 
+
+ align:start position:0%
+fourcolor that map. Uh but it's is a
+very funny article. If you want to read
+
+ align:start position:0%
+very funny article. If you want to read
+ 
+
+ align:start position:0%
+very funny article. If you want to read
+it, it's in in the lecture notes or part
+
+ align:start position:0%
+it, it's in in the lecture notes or part
+ 
+
+ align:start position:0%
+it, it's in in the lecture notes or part
+of it is there all sorts of crazy things
+
+ align:start position:0%
+of it is there all sorts of crazy things
+ 
+
+ align:start position:0%
+of it is there all sorts of crazy things
+like oh it turns out if you take uh e
+
+ align:start position:0%
+like oh it turns out if you take uh e
+ 
+
+ align:start position:0%
+like oh it turns out if you take uh e
+and you raise it to pi time<unk> of 163,
+
+ align:start position:0%
+and you raise it to pi time<unk> of 163,
+ 
+
+ align:start position:0%
+and you raise it to pi time<unk> of 163,
+the result is an integer.
+
+ align:start position:0%
+the result is an integer.
+ 
+
+ align:start position:0%
+the result is an integer.
+It's not true. But, uh, all sorts of
+
+ align:start position:0%
+It's not true. But, uh, all sorts of
+ 
+
+ align:start position:0%
+It's not true. But, uh, all sorts of
+crazy things. Also, uh, chess has a
+
+ align:start position:0%
+crazy things. Also, uh, chess has a
+ 
+
+ align:start position:0%
+crazy things. Also, uh, chess has a
+crazy winning move. And anyway,
+
+ align:start position:0%
+crazy winning move. And anyway,
+ 
+
+ align:start position:0%
+crazy winning move. And anyway,
+uh, to relive the youth. All right. Um,
+
+ align:start position:0%
+uh, to relive the youth. All right. Um,
+ 
+
+ align:start position:0%
+uh, to relive the youth. All right. Um,
+I think I'd like to, uh, yeah, show you
+
+ align:start position:0%
+I think I'd like to, uh, yeah, show you
+ 
+
+ align:start position:0%
+I think I'd like to, uh, yeah, show you
+some examples of strong induction, but
+
+ align:start position:0%
+some examples of strong induction, but
+ 
+
+ align:start position:0%
+some examples of strong induction, but
+maybe first I should show you a template
+
+ align:start position:0%
+maybe first I should show you a template
+ 
+
+ align:start position:0%
+maybe first I should show you a template
+for applying induction. Strong
+
+ align:start position:0%
+for applying induction. Strong
+ 
+
+ align:start position:0%
+for applying induction. Strong
+induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we'll repeat some of the things that
+
+ align:start position:0%
+uh we'll repeat some of the things that
+ 
+
+ align:start position:0%
+uh we'll repeat some of the things that
+I've said but I think it's good to have
+
+ align:start position:0%
+I've said but I think it's good to have
+ 
+
+ align:start position:0%
+I've said but I think it's good to have
+it concrete.
+
+ align:start position:0%
+it concrete.
+ 
+
+ align:start position:0%
+it concrete.
+So here is a template.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Suppose you want to prove
+
+ align:start position:0%
+Suppose you want to prove
+ 
+
+ align:start position:0%
+Suppose you want to prove
+uh something is true for all natural
+
+ align:start position:0%
+uh something is true for all natural
+ 
+
+ align:start position:0%
+uh something is true for all natural
+numbers. So for all natural numbers n uh
+
+ align:start position:0%
+numbers. So for all natural numbers n uh
+ 
+
+ align:start position:0%
+numbers. So for all natural numbers n uh
+p of n is true. Then here's what the
+
+ align:start position:0%
+p of n is true. Then here's what the
+ 
+
+ align:start position:0%
+p of n is true. Then here's what the
+proof will look like.
+
+ align:start position:0%
+proof will look like.
+ 
+
+ align:start position:0%
+proof will look like.
+uh by proof by strong induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+so generally we're assuming p of k uh
+
+ align:start position:0%
+so generally we're assuming p of k uh
+ 
+
+ align:start position:0%
+so generally we're assuming p of k uh
+for all k less than n
+
+ align:start position:0%
+for all k less than n
+ 
+
+ align:start position:0%
+for all k less than n
+and then we want to show p of n.
+
+ align:start position:0%
+and then we want to show p of n.
+ 
+
+ align:start position:0%
+and then we want to show p of n.
+Okay? Or you could shift the numbers by
+
+ align:start position:0%
+Okay? Or you could shift the numbers by
+ 
+
+ align:start position:0%
+Okay? Or you could shift the numbers by
+one but this is my preferred way of
+
+ align:start position:0%
+one but this is my preferred way of
+ 
+
+ align:start position:0%
+one but this is my preferred way of
+thinking about it. uh usually we prove
+
+ align:start position:0%
+thinking about it. uh usually we prove
+ 
+
+ align:start position:0%
+thinking about it. uh usually we prove
+this by cases
+
+ align:start position:0%
+this by cases
+ 
+
+ align:start position:0%
+this by cases
+which is the method we just saw. This is
+
+ align:start position:0%
+which is the method we just saw. This is
+ 
+
+ align:start position:0%
+which is the method we just saw. This is
+why we're pairing proof by cases with
+
+ align:start position:0%
+why we're pairing proof by cases with
+ 
+
+ align:start position:0%
+why we're pairing proof by cases with
+strong induction. How do we prove p of
+
+ align:start position:0%
+strong induction. How do we prove p of
+ 
+
+ align:start position:0%
+strong induction. How do we prove p of
+n? Well, it might depend. Often we have
+
+ align:start position:0%
+n? Well, it might depend. Often we have
+ 
+
+ align:start position:0%
+n? Well, it might depend. Often we have
+some base cases
+
+ align:start position:0%
+some base cases
+ 
+
+ align:start position:0%
+some base cases
+where n is small.
+
+ align:start position:0%
+where n is small.
+ 
+
+ align:start position:0%
+where n is small.
+So uh maybe we have to prove p of zero,
+
+ align:start position:0%
+So uh maybe we have to prove p of zero,
+ 
+
+ align:start position:0%
+So uh maybe we have to prove p of zero,
+maybe we have to prove p of one. Uh who
+
+ align:start position:0%
+maybe we have to prove p of one. Uh who
+ 
+
+ align:start position:0%
+maybe we have to prove p of one. Uh who
+knows? Let's say up to P of little B are
+
+ align:start position:0%
+knows? Let's say up to P of little B are
+ 
+
+ align:start position:0%
+knows? Let's say up to P of little B are
+the base cases. Maybe you have to prove
+
+ align:start position:0%
+the base cases. Maybe you have to prove
+ 
+
+ align:start position:0%
+the base cases. Maybe you have to prove
+those specially for some reason.
+
+ align:start position:0%
+those specially for some reason.
+ 
+
+ align:start position:0%
+those specially for some reason.
+Okay. Then we do an induction step.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I'll say by cases here.
+
+ align:start position:0%
+So I'll say by cases here.
+ 
+
+ align:start position:0%
+So I'll say by cases here.
+Uh induction step. We get to assume
+
+ align:start position:0%
+Uh induction step. We get to assume
+ 
+
+ align:start position:0%
+Uh induction step. We get to assume
+n is bigger than b because we just prove
+
+ align:start position:0%
+n is bigger than b because we just prove
+ 
+
+ align:start position:0%
+n is bigger than b because we just prove
+zero up to b manually.
+
+ align:start position:0%
+zero up to b manually.
+ 
+
+ align:start position:0%
+zero up to b manually.
+uh and then we need to prove in those
+
+ align:start position:0%
+uh and then we need to prove in those
+ 
+
+ align:start position:0%
+uh and then we need to prove in those
+scenarios p of n is true because
+
+ align:start position:0%
+scenarios p of n is true because
+ 
+
+ align:start position:0%
+scenarios p of n is true because
+uh reasons.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. But the the big thing here is we
+
+ align:start position:0%
+Okay. But the the big thing here is we
+ 
+
+ align:start position:0%
+Okay. But the the big thing here is we
+get to assume in in these reasons uh we
+
+ align:start position:0%
+get to assume in in these reasons uh we
+ 
+
+ align:start position:0%
+get to assume in in these reasons uh we
+get to use
+
+ align:start position:0%
+get to use
+ 
+
+ align:start position:0%
+get to use
+uh p 0 p1
+
+ align:start position:0%
+uh p 0 p1
+ 
+
+ align:start position:0%
+uh p 0 p1
+up to p n minus one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So uh that's the big win. And in
+
+ align:start position:0%
+Okay. So uh that's the big win. And in
+ 
+
+ align:start position:0%
+Okay. So uh that's the big win. And in
+the base cases you don't I mean you also
+
+ align:start position:0%
+the base cases you don't I mean you also
+ 
+
+ align:start position:0%
+the base cases you don't I mean you also
+get to assume this but for example when
+
+ align:start position:0%
+get to assume this but for example when
+ 
+
+ align:start position:0%
+get to assume this but for example when
+you're proving P 0 you don't really get
+
+ align:start position:0%
+you're proving P 0 you don't really get
+ 
+
+ align:start position:0%
+you're proving P 0 you don't really get
+to assume anything because there are no
+
+ align:start position:0%
+to assume anything because there are no
+ 
+
+ align:start position:0%
+to assume anything because there are no
+smaller pis. Uh so often you have to do
+
+ align:start position:0%
+smaller pis. Uh so often you have to do
+ 
+
+ align:start position:0%
+smaller pis. Uh so often you have to do
+these specially because the induction
+
+ align:start position:0%
+these specially because the induction
+ 
+
+ align:start position:0%
+these specially because the induction
+step assumes somehow that n is bigger
+
+ align:start position:0%
+step assumes somehow that n is bigger
+ 
+
+ align:start position:0%
+step assumes somehow that n is bigger
+than zero.
+
+ align:start position:0%
+than zero.
+ 
+
+ align:start position:0%
+than zero.
+Sometimes you get lucky you just need
+
+ align:start position:0%
+Sometimes you get lucky you just need
+ 
+
+ align:start position:0%
+Sometimes you get lucky you just need
+the induction step but usually you need
+
+ align:start position:0%
+the induction step but usually you need
+ 
+
+ align:start position:0%
+the induction step but usually you need
+base cases. Let's see some examples and
+
+ align:start position:0%
+base cases. Let's see some examples and
+ 
+
+ align:start position:0%
+base cases. Let's see some examples and
+this will become much clearer.
+
+ align:start position:0%
+this will become much clearer.
+ 
+
+ align:start position:0%
+this will become much clearer.
+So let's play a game.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called item stacking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or it's really unstacking.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unstacking game.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we're going to start with
+
+ align:start position:0%
+So, we're going to start with
+ 
+
+ align:start position:0%
+So, we're going to start with
+one stack
+
+ align:start position:0%
+one stack
+ 
+
+ align:start position:0%
+one stack
+of n
+
+ align:start position:0%
+of n
+ 
+
+ align:start position:0%
+of n
+and then a move
+
+ align:start position:0%
+and then a move
+ 
+
+ align:start position:0%
+and then a move
+uh splits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+stack
+
+ align:start position:0%
+stack
+ 
+
+ align:start position:0%
+stack
+of s bigger than one items.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+two stacks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with A items in one and B items in the
+
+ align:start position:0%
+with A items in one and B items in the
+ 
+
+ align:start position:0%
+with A items in one and B items in the
+other.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And you get to choose these numbers A
+
+ align:start position:0%
+And you get to choose these numbers A
+ 
+
+ align:start position:0%
+And you get to choose these numbers A
+and B, but you need conservation. So A
+
+ align:start position:0%
+and B, but you need conservation. So A
+ 
+
+ align:start position:0%
+and B, but you need conservation. So A
+plus B has to equal S.
+
+ align:start position:0%
+plus B has to equal S.
+ 
+
+ align:start position:0%
+plus B has to equal S.
+And uh we also don't want zero height
+
+ align:start position:0%
+And uh we also don't want zero height
+ 
+
+ align:start position:0%
+And uh we also don't want zero height
+stack. So we need A at least one and B
+
+ align:start position:0%
+stack. So we need A at least one and B
+ 
+
+ align:start position:0%
+stack. So we need A at least one and B
+at least one. Okay. So you get to choose
+
+ align:start position:0%
+at least one. Okay. So you get to choose
+ 
+
+ align:start position:0%
+at least one. Okay. So you get to choose
+A and B however you want so long as
+
+ align:start position:0%
+A and B however you want so long as
+ 
+
+ align:start position:0%
+A and B however you want so long as
+there's at least one item in each stack.
+
+ align:start position:0%
+there's at least one item in each stack.
+ 
+
+ align:start position:0%
+there's at least one item in each stack.
+So let's take a physical example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and got lots of blocks here, but I have
+
+ align:start position:0%
+and got lots of blocks here, but I have
+ 
+
+ align:start position:0%
+and got lots of blocks here, but I have
+no audience, so we're just going to demo
+
+ align:start position:0%
+no audience, so we're just going to demo
+ 
+
+ align:start position:0%
+no audience, so we're just going to demo
+this myself in in real life. Uh this is
+
+ align:start position:0%
+this myself in in real life. Uh this is
+ 
+
+ align:start position:0%
+this myself in in real life. Uh this is
+actually this was a snow day at MIT and
+
+ align:start position:0%
+actually this was a snow day at MIT and
+ 
+
+ align:start position:0%
+actually this was a snow day at MIT and
+so we're recording after the fact. So
+
+ align:start position:0%
+so we're recording after the fact. So
+ 
+
+ align:start position:0%
+so we're recording after the fact. So
+all the students MIT students have seen
+
+ align:start position:0%
+all the students MIT students have seen
+ 
+
+ align:start position:0%
+all the students MIT students have seen
+it. This is specially for you at OCW.
+
+ align:start position:0%
+it. This is specially for you at OCW.
+ 
+
+ align:start position:0%
+it. This is specially for you at OCW.
+Uh so when we do a move uh from S. So
+
+ align:start position:0%
+Uh so when we do a move uh from S. So
+ 
+
+ align:start position:0%
+Uh so when we do a move uh from S. So
+this is we have a stack of size S and we
+
+ align:start position:0%
+this is we have a stack of size S and we
+ 
+
+ align:start position:0%
+this is we have a stack of size S and we
+convert it into a stack of size A and a
+
+ align:start position:0%
+convert it into a stack of size A and a
+ 
+
+ align:start position:0%
+convert it into a stack of size A and a
+stack of size B. We get A time B points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's just the definition of the game.
+
+ align:start position:0%
+That's just the definition of the game.
+ 
+
+ align:start position:0%
+That's just the definition of the game.
+A* B points. When you split into a stack
+
+ align:start position:0%
+A* B points. When you split into a stack
+ 
+
+ align:start position:0%
+A* B points. When you split into a stack
+of size A and a stack of size B. Uh so
+
+ align:start position:0%
+of size A and a stack of size B. Uh so
+ 
+
+ align:start position:0%
+of size A and a stack of size B. Uh so
+how should I maximize my score in this
+
+ align:start position:0%
+how should I maximize my score in this
+ 
+
+ align:start position:0%
+how should I maximize my score in this
+game? What's the best strategy? Uh the
+
+ align:start position:0%
+game? What's the best strategy? Uh the
+ 
+
+ align:start position:0%
+game? What's the best strategy? Uh the
+game ends when all your stacks have size
+
+ align:start position:0%
+game ends when all your stacks have size
+ 
+
+ align:start position:0%
+game ends when all your stacks have size
+one because you can't make a move on a
+
+ align:start position:0%
+one because you can't make a move on a
+ 
+
+ align:start position:0%
+one because you can't make a move on a
+stack of one item. It has to be greater
+
+ align:start position:0%
+stack of one item. It has to be greater
+ 
+
+ align:start position:0%
+stack of one item. It has to be greater
+than one items. So let's try here. I
+
+ align:start position:0%
+than one items. So let's try here. I
+ 
+
+ align:start position:0%
+than one items. So let's try here. I
+have a stack of five blocks.
+
+ align:start position:0%
+have a stack of five blocks.
+ 
+
+ align:start position:0%
+have a stack of five blocks.
+And uh one thing maybe I'll try to split
+
+ align:start position:0%
+And uh one thing maybe I'll try to split
+ 
+
+ align:start position:0%
+And uh one thing maybe I'll try to split
+it roughly in the middle. So now here
+
+ align:start position:0%
+it roughly in the middle. So now here
+ 
+
+ align:start position:0%
+it roughly in the middle. So now here
+I'll rotate this so you can see the
+
+ align:start position:0%
+I'll rotate this so you can see the
+ 
+
+ align:start position:0%
+I'll rotate this so you can see the
+blocks a little bigger. Uh these are
+
+ align:start position:0%
+blocks a little bigger. Uh these are
+ 
+
+ align:start position:0%
+blocks a little bigger. Uh these are
+five blocks. uh I split like this. So
+
+ align:start position:0%
+five blocks. uh I split like this. So
+ 
+
+ align:start position:0%
+five blocks. uh I split like this. So
+that's a I group of two and a group of
+
+ align:start position:0%
+that's a I group of two and a group of
+ 
+
+ align:start position:0%
+that's a I group of two and a group of
+three. Product of two * three is six. I
+
+ align:start position:0%
+three. Product of two * three is six. I
+ 
+
+ align:start position:0%
+three. Product of two * three is six. I
+can do this level of arithmetic. So six
+
+ align:start position:0%
+can do this level of arithmetic. So six
+ 
+
+ align:start position:0%
+can do this level of arithmetic. So six
+is our total so far. When I split this
+
+ align:start position:0%
+is our total so far. When I split this
+ 
+
+ align:start position:0%
+is our total so far. When I split this
+one, I get one more point. That's seven.
+
+ align:start position:0%
+one, I get one more point. That's seven.
+ 
+
+ align:start position:0%
+one, I get one more point. That's seven.
+When I split this one, doesn't matter
+
+ align:start position:0%
+When I split this one, doesn't matter
+ 
+
+ align:start position:0%
+When I split this one, doesn't matter
+how I do it, I get uh 2 * 1. So that's
+
+ align:start position:0%
+how I do it, I get uh 2 * 1. So that's
+ 
+
+ align:start position:0%
+how I do it, I get uh 2 * 1. So that's
+two more points. That's nine. And when I
+
+ align:start position:0%
+two more points. That's nine. And when I
+ 
+
+ align:start position:0%
+two more points. That's nine. And when I
+split this group, I get one more point.
+
+ align:start position:0%
+split this group, I get one more point.
+ 
+
+ align:start position:0%
+split this group, I get one more point.
+That's 10. Okay. So one approach gives
+
+ align:start position:0%
+That's 10. Okay. So one approach gives
+ 
+
+ align:start position:0%
+That's 10. Okay. So one approach gives
+me 10 points. What if another natural
+
+ align:start position:0%
+me 10 points. What if another natural
+ 
+
+ align:start position:0%
+me 10 points. What if another natural
+strategy that was like splitting in the
+
+ align:start position:0%
+strategy that was like splitting in the
+ 
+
+ align:start position:0%
+strategy that was like splitting in the
+middle? Another natural strategy is I
+
+ align:start position:0%
+middle? Another natural strategy is I
+ 
+
+ align:start position:0%
+middle? Another natural strategy is I
+just take one off each time. So if I
+
+ align:start position:0%
+just take one off each time. So if I
+ 
+
+ align:start position:0%
+just take one off each time. So if I
+take one off here, I get four points. Uh
+
+ align:start position:0%
+take one off here, I get four points. Uh
+ 
+
+ align:start position:0%
+take one off here, I get four points. Uh
+if I take one more off, I get three more
+
+ align:start position:0%
+if I take one more off, I get three more
+ 
+
+ align:start position:0%
+if I take one more off, I get three more
+points. That's seven. 4 + 3 is seven. I
+
+ align:start position:0%
+points. That's seven. 4 + 3 is seven. I
+ 
+
+ align:start position:0%
+points. That's seven. 4 + 3 is seven. I
+take one more off, I get two points,
+
+ align:start position:0%
+take one more off, I get two points,
+ 
+
+ align:start position:0%
+take one more off, I get two points,
+that's nine. I take one more off, that's
+
+ align:start position:0%
+that's nine. I take one more off, that's
+ 
+
+ align:start position:0%
+that's nine. I take one more off, that's
+one point, that's 10. Huh? 10 points
+
+ align:start position:0%
+one point, that's 10. Huh? 10 points
+ 
+
+ align:start position:0%
+one point, that's 10. Huh? 10 points
+that way, 10 points the other way as
+
+ align:start position:0%
+that way, 10 points the other way as
+ 
+
+ align:start position:0%
+that way, 10 points the other way as
+well. Maybe there's a theorem here.
+
+ align:start position:0%
+well. Maybe there's a theorem here.
+ 
+
+ align:start position:0%
+well. Maybe there's a theorem here.
+Maybe no matter what I do, I get 10
+
+ align:start position:0%
+Maybe no matter what I do, I get 10
+ 
+
+ align:start position:0%
+Maybe no matter what I do, I get 10
+points. Well, that won't be true. But
+
+ align:start position:0%
+points. Well, that won't be true. But
+ 
+
+ align:start position:0%
+points. Well, that won't be true. But
+for five blocks, I will always get 10
+
+ align:start position:0%
+for five blocks, I will always get 10
+ 
+
+ align:start position:0%
+for five blocks, I will always get 10
+points. For six blocks, I will always
+
+ align:start position:0%
+points. For six blocks, I will always
+ 
+
+ align:start position:0%
+points. For six blocks, I will always
+get, I don't know, 15, some more points.
+
+ align:start position:0%
+get, I don't know, 15, some more points.
+ 
+
+ align:start position:0%
+get, I don't know, 15, some more points.
+Uh, it turns out it doesn't matter what
+
+ align:start position:0%
+Uh, it turns out it doesn't matter what
+ 
+
+ align:start position:0%
+Uh, it turns out it doesn't matter what
+strategy you follow, you always get the
+
+ align:start position:0%
+strategy you follow, you always get the
+ 
+
+ align:start position:0%
+strategy you follow, you always get the
+same number of points for a given
+
+ align:start position:0%
+same number of points for a given
+ 
+
+ align:start position:0%
+same number of points for a given
+initial stack of size n.
+
+ align:start position:0%
+initial stack of size n.
+ 
+
+ align:start position:0%
+initial stack of size n.
+Let's prove that with strong induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So theorem is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all natural numbers
+
+ align:start position:0%
+for all natural numbers
+ 
+
+ align:start position:0%
+for all natural numbers
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+every strategy
+
+ align:start position:0%
+every strategy
+ 
+
+ align:start position:0%
+every strategy
+for this game.
+
+ align:start position:0%
+for this game.
+ 
+
+ align:start position:0%
+for this game.
+Uh starting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh with the stack one stack of n items
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scores
+
+ align:start position:0%
+scores
+ 
+
+ align:start position:0%
+scores
+magic formula is n * n minus one over 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's the theorem and we're going to
+
+ align:start position:0%
+So that's the theorem and we're going to
+ 
+
+ align:start position:0%
+So that's the theorem and we're going to
+prove it by strong induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in sort of the straightforward way. So
+
+ align:start position:0%
+in sort of the straightforward way. So
+ 
+
+ align:start position:0%
+in sort of the straightforward way. So
+our induction hypothesis is going to be
+
+ align:start position:0%
+our induction hypothesis is going to be
+ 
+
+ align:start position:0%
+our induction hypothesis is going to be
+exactly the theorem statement uh for a
+
+ align:start position:0%
+exactly the theorem statement uh for a
+ 
+
+ align:start position:0%
+exactly the theorem statement uh for a
+particular n. So I'm going to highlight
+
+ align:start position:0%
+particular n. So I'm going to highlight
+ 
+
+ align:start position:0%
+particular n. So I'm going to highlight
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+statement everything except the
+
+ align:start position:0%
+statement everything except the
+ 
+
+ align:start position:0%
+statement everything except the
+quantifier and I'll call that p of n. So
+
+ align:start position:0%
+quantifier and I'll call that p of n. So
+ 
+
+ align:start position:0%
+quantifier and I'll call that p of n. So
+what I want to prove is for all natural
+
+ align:start position:0%
+what I want to prove is for all natural
+ 
+
+ align:start position:0%
+what I want to prove is for all natural
+numbers n P of N is true. And so that's
+
+ align:start position:0%
+numbers n P of N is true. And so that's
+ 
+
+ align:start position:0%
+numbers n P of N is true. And so that's
+that's just going to be our induction
+
+ align:start position:0%
+that's just going to be our induction
+ 
+
+ align:start position:0%
+that's just going to be our induction
+hypothesis. We're going to plug that
+
+ align:start position:0%
+hypothesis. We're going to plug that
+ 
+
+ align:start position:0%
+hypothesis. We're going to plug that
+into this template here. Assume that P
+
+ align:start position:0%
+into this template here. Assume that P
+ 
+
+ align:start position:0%
+into this template here. Assume that P
+of K is true for all K less than N and
+
+ align:start position:0%
+of K is true for all K less than N and
+ 
+
+ align:start position:0%
+of K is true for all K less than N and
+then prove P of N is true. So let's just
+
+ align:start position:0%
+then prove P of N is true. So let's just
+ 
+
+ align:start position:0%
+then prove P of N is true. So let's just
+try to do that.
+
+ align:start position:0%
+try to do that.
+ 
+
+ align:start position:0%
+try to do that.
+So what I would normally write here is
+
+ align:start position:0%
+So what I would normally write here is
+ 
+
+ align:start position:0%
+So what I would normally write here is
+assume
+
+ align:start position:0%
+assume
+ 
+
+ align:start position:0%
+assume
+true assume that my theorem is true.
+
+ align:start position:0%
+true assume that my theorem is true.
+ 
+
+ align:start position:0%
+true assume that my theorem is true.
+Assume P of N is true. uh sorry p of k
+
+ align:start position:0%
+Assume P of N is true. uh sorry p of k
+ 
+
+ align:start position:0%
+Assume P of N is true. uh sorry p of k
+is true for all k less than n. I would
+
+ align:start position:0%
+is true for all k less than n. I would
+ 
+
+ align:start position:0%
+is true for all k less than n. I would
+say assume true for all smaller n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, let's uh we need to do something
+
+ align:start position:0%
+Okay, let's uh we need to do something
+ 
+
+ align:start position:0%
+Okay, let's uh we need to do something
+with the game. We start with a pile of
+
+ align:start position:0%
+with the game. We start with a pile of
+ 
+
+ align:start position:0%
+with the game. We start with a pile of
+size n. Let's just think about the first
+
+ align:start position:0%
+size n. Let's just think about the first
+ 
+
+ align:start position:0%
+size n. Let's just think about the first
+move.
+
+ align:start position:0%
+move.
+ 
+
+ align:start position:0%
+move.
+First move is something. It's takes our
+
+ align:start position:0%
+First move is something. It's takes our
+ 
+
+ align:start position:0%
+First move is something. It's takes our
+pile of size n and it splits it into
+
+ align:start position:0%
+pile of size n and it splits it into
+ 
+
+ align:start position:0%
+pile of size n and it splits it into
+some piles a and b.
+
+ align:start position:0%
+some piles a and b.
+ 
+
+ align:start position:0%
+some piles a and b.
+So uh we don't know what it is. We don't
+
+ align:start position:0%
+So uh we don't know what it is. We don't
+ 
+
+ align:start position:0%
+So uh we don't know what it is. We don't
+know what a and b are. But we can give
+
+ align:start position:0%
+know what a and b are. But we can give
+ 
+
+ align:start position:0%
+know what a and b are. But we can give
+them a name. Like this has to work no
+
+ align:start position:0%
+them a name. Like this has to work no
+ 
+
+ align:start position:0%
+them a name. Like this has to work no
+matter what a and b are. But let's say
+
+ align:start position:0%
+matter what a and b are. But let's say
+ 
+
+ align:start position:0%
+matter what a and b are. But let's say
+consider first move which we know we
+
+ align:start position:0%
+consider first move which we know we
+ 
+
+ align:start position:0%
+consider first move which we know we
+start with a pile of size n. And we
+
+ align:start position:0%
+start with a pile of size n. And we
+ 
+
+ align:start position:0%
+start with a pile of size n. And we
+produce piles of size a and b. And again
+
+ align:start position:0%
+produce piles of size a and b. And again
+ 
+
+ align:start position:0%
+produce piles of size a and b. And again
+uh a + b equals n and a and b are at
+
+ align:start position:0%
+uh a + b equals n and a and b are at
+ 
+
+ align:start position:0%
+uh a + b equals n and a and b are at
+least one. But otherwise we don't know
+
+ align:start position:0%
+least one. But otherwise we don't know
+ 
+
+ align:start position:0%
+least one. But otherwise we don't know
+what a and b are.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so we go down to here. Um,
+
+ align:start position:0%
+so we go down to here. Um,
+ 
+
+ align:start position:0%
+so we go down to here. Um,
+so we now have a pile of size A and we
+
+ align:start position:0%
+so we now have a pile of size A and we
+ 
+
+ align:start position:0%
+so we now have a pile of size A and we
+have a pile of size B. Again, we don't
+
+ align:start position:0%
+have a pile of size B. Again, we don't
+ 
+
+ align:start position:0%
+have a pile of size B. Again, we don't
+know how big they are, but they are
+
+ align:start position:0%
+know how big they are, but they are
+ 
+
+ align:start position:0%
+know how big they are, but they are
+smaller than B. So I want to claim we
+
+ align:start position:0%
+smaller than B. So I want to claim we
+ 
+
+ align:start position:0%
+smaller than B. So I want to claim we
+are uh left
+
+ align:start position:0%
+are uh left
+ 
+
+ align:start position:0%
+are uh left
+with two piles or we can really think of
+
+ align:start position:0%
+with two piles or we can really think of
+ 
+
+ align:start position:0%
+with two piles or we can really think of
+those as two completely separate games
+
+ align:start position:0%
+those as two completely separate games
+ 
+
+ align:start position:0%
+those as two completely separate games
+A and B. We're going to get some points
+
+ align:start position:0%
+A and B. We're going to get some points
+ 
+
+ align:start position:0%
+A and B. We're going to get some points
+from splitting up A. We're going to get
+
+ align:start position:0%
+from splitting up A. We're going to get
+ 
+
+ align:start position:0%
+from splitting up A. We're going to get
+some points from splitting up B. They
+
+ align:start position:0%
+some points from splitting up B. They
+ 
+
+ align:start position:0%
+some points from splitting up B. They
+sum together, but the these piles don't
+
+ align:start position:0%
+sum together, but the these piles don't
+ 
+
+ align:start position:0%
+sum together, but the these piles don't
+really interact from here on. We got uh
+
+ align:start position:0%
+really interact from here on. We got uh
+ 
+
+ align:start position:0%
+really interact from here on. We got uh
+we got A* B points from this first step.
+
+ align:start position:0%
+we got A* B points from this first step.
+ 
+
+ align:start position:0%
+we got A* B points from this first step.
+We're going to get some points from the
+
+ align:start position:0%
+We're going to get some points from the
+ 
+
+ align:start position:0%
+We're going to get some points from the
+pile of size A. We're going to get some
+
+ align:start position:0%
+pile of size A. We're going to get some
+ 
+
+ align:start position:0%
+pile of size A. We're going to get some
+points to the pile of size B. How many
+
+ align:start position:0%
+points to the pile of size B. How many
+ 
+
+ align:start position:0%
+points to the pile of size B. How many
+points do we get? Uh well, in fact, our
+
+ align:start position:0%
+points do we get? Uh well, in fact, our
+ 
+
+ align:start position:0%
+points do we get? Uh well, in fact, our
+induction hypothesis will tell us
+
+ align:start position:0%
+induction hypothesis will tell us
+ 
+
+ align:start position:0%
+induction hypothesis will tell us
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh A and B are strictly less than N.
+
+ align:start position:0%
+uh A and B are strictly less than N.
+ 
+
+ align:start position:0%
+uh A and B are strictly less than N.
+Why? Because
+
+ align:start position:0%
+Why? Because
+ 
+
+ align:start position:0%
+Why? Because
+uh a + b= n and a and b are at least
+
+ align:start position:0%
+uh a + b= n and a and b are at least
+ 
+
+ align:start position:0%
+uh a + b= n and a and b are at least
+one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there's at least one in each of a and
+
+ align:start position:0%
+So there's at least one in each of a and
+ 
+
+ align:start position:0%
+So there's at least one in each of a and
+b. And so the remainder must be strictly
+
+ align:start position:0%
+b. And so the remainder must be strictly
+ 
+
+ align:start position:0%
+b. And so the remainder must be strictly
+less than n. If there's one in a, then
+
+ align:start position:0%
+less than n. If there's one in a, then
+ 
+
+ align:start position:0%
+less than n. If there's one in a, then
+there'll be n minus one in b. If there's
+
+ align:start position:0%
+there'll be n minus one in b. If there's
+ 
+
+ align:start position:0%
+there'll be n minus one in b. If there's
+two in a, there'll be n minus two in b.
+
+ align:start position:0%
+two in a, there'll be n minus two in b.
+ 
+
+ align:start position:0%
+two in a, there'll be n minus two in b.
+In all cases, less than n. Okay? Because
+
+ align:start position:0%
+In all cases, less than n. Okay? Because
+ 
+
+ align:start position:0%
+In all cases, less than n. Okay? Because
+a and b are less than n, they're not
+
+ align:start position:0%
+a and b are less than n, they're not
+ 
+
+ align:start position:0%
+a and b are less than n, they're not
+just they're not necessarily n minus
+
+ align:start position:0%
+just they're not necessarily n minus
+ 
+
+ align:start position:0%
+just they're not necessarily n minus
+one. So we couldn't just use regular
+
+ align:start position:0%
+one. So we couldn't just use regular
+ 
+
+ align:start position:0%
+one. So we couldn't just use regular
+induction. But we have they're less than
+
+ align:start position:0%
+induction. But we have they're less than
+ 
+
+ align:start position:0%
+induction. But we have they're less than
+n. And so by strong induction
+
+ align:start position:0%
+n. And so by strong induction
+ 
+
+ align:start position:0%
+n. And so by strong induction
+uh by strong induction
+
+ align:start position:0%
+uh by strong induction
+ 
+
+ align:start position:0%
+uh by strong induction
+we know that P of A is true and P of B
+
+ align:start position:0%
+we know that P of A is true and P of B
+ 
+
+ align:start position:0%
+we know that P of A is true and P of B
+is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we wrote that up here. So P of K
+
+ align:start position:0%
+Okay, we wrote that up here. So P of K
+ 
+
+ align:start position:0%
+Okay, we wrote that up here. So P of K
+for all K less than N. So A and B are
+
+ align:start position:0%
+for all K less than N. So A and B are
+ 
+
+ align:start position:0%
+for all K less than N. So A and B are
+less than N. So P of A is true and P of
+
+ align:start position:0%
+less than N. So P of A is true and P of
+ 
+
+ align:start position:0%
+less than N. So P of A is true and P of
+B are is true. So that means from the
+
+ align:start position:0%
+B are is true. So that means from the
+ 
+
+ align:start position:0%
+B are is true. So that means from the
+pile of size a
+
+ align:start position:0%
+pile of size a
+ 
+
+ align:start position:0%
+pile of size a
+we get uh a * a minus1 / 2 points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the a pile. We get b * b minus one
+
+ align:start position:0%
+from the a pile. We get b * b minus one
+ 
+
+ align:start position:0%
+from the a pile. We get b * b minus one
+over two points from the b pile.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then of course we got a time b move
+
+ align:start position:0%
+And then of course we got a time b move
+ 
+
+ align:start position:0%
+And then of course we got a time b move
+points uh from the first move.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now we just need to do some
+
+ align:start position:0%
+And so now we just need to do some
+ 
+
+ align:start position:0%
+And so now we just need to do some
+algebra and add up all these points.
+
+ align:start position:0%
+algebra and add up all these points.
+ 
+
+ align:start position:0%
+algebra and add up all these points.
+So the total number of points that we
+
+ align:start position:0%
+So the total number of points that we
+ 
+
+ align:start position:0%
+So the total number of points that we
+get is a * b + a * a -1 / 2 plus b * b -
+
+ align:start position:0%
+get is a * b + a * a -1 / 2 plus b * b -
+ 
+
+ align:start position:0%
+get is a * b + a * a -1 / 2 plus b * b -
+1 / 2
+
+ align:start position:0%
+1 / 2
+ 
+
+ align:start position:0%
+1 / 2
+These two were by induction. This was
+
+ align:start position:0%
+These two were by induction. This was
+ 
+
+ align:start position:0%
+These two were by induction. This was
+the first move. Uh, and now let's just
+
+ align:start position:0%
+the first move. Uh, and now let's just
+ 
+
+ align:start position:0%
+the first move. Uh, and now let's just
+put everything over two. So this is 2 *
+
+ align:start position:0%
+put everything over two. So this is 2 *
+ 
+
+ align:start position:0%
+put everything over two. So this is 2 *
+a * b plus I don't know a^ 2 - a + b ^ 2
+
+ align:start position:0%
+a * b plus I don't know a^ 2 - a + b ^ 2
+ 
+
+ align:start position:0%
+a * b plus I don't know a^ 2 - a + b ^ 2
+- b all over two.
+
+ align:start position:0%
+- b all over two.
+ 
+
+ align:start position:0%
+- b all over two.
+Okay. And now what do I want to get to?
+
+ align:start position:0%
+Okay. And now what do I want to get to?
+ 
+
+ align:start position:0%
+Okay. And now what do I want to get to?
+This is supposed to equal n * n minus
+
+ align:start position:0%
+This is supposed to equal n * n minus
+ 
+
+ align:start position:0%
+This is supposed to equal n * n minus
+one over two. And what was n? n was a
+
+ align:start position:0%
+one over two. And what was n? n was a
+ 
+
+ align:start position:0%
+one over two. And what was n? n was a
+plus b.
+
+ align:start position:0%
+plus b.
+ 
+
+ align:start position:0%
+plus b.
+So, what I'd really like to show here is
+
+ align:start position:0%
+So, what I'd really like to show here is
+ 
+
+ align:start position:0%
+So, what I'd really like to show here is
+uh a + b * a + b minus one over two.
+
+ align:start position:0%
+uh a + b * a + b minus one over two.
+ 
+
+ align:start position:0%
+uh a + b * a + b minus one over two.
+That's my goal. And what I need to do is
+
+ align:start position:0%
+That's my goal. And what I need to do is
+ 
+
+ align:start position:0%
+That's my goal. And what I need to do is
+fill in the in between.
+
+ align:start position:0%
+fill in the in between.
+ 
+
+ align:start position:0%
+fill in the in between.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+but this is not too hard because let's
+
+ align:start position:0%
+but this is not too hard because let's
+ 
+
+ align:start position:0%
+but this is not too hard because let's
+see. Uh I see a time b here and a * b
+
+ align:start position:0%
+see. Uh I see a time b here and a * b
+ 
+
+ align:start position:0%
+see. Uh I see a time b here and a * b
+here. I mean in fact you can just expand
+
+ align:start position:0%
+here. I mean in fact you can just expand
+ 
+
+ align:start position:0%
+here. I mean in fact you can just expand
+this out and you'll get exactly the same
+
+ align:start position:0%
+this out and you'll get exactly the same
+ 
+
+ align:start position:0%
+this out and you'll get exactly the same
+thing here. uh I think slightly more
+
+ align:start position:0%
+thing here. uh I think slightly more
+ 
+
+ align:start position:0%
+thing here. uh I think slightly more
+intuitive is to see oh look at this term
+
+ align:start position:0%
+intuitive is to see oh look at this term
+ 
+
+ align:start position:0%
+intuitive is to see oh look at this term
+this term and this term that is
+
+ align:start position:0%
+this term and this term that is
+ 
+
+ align:start position:0%
+this term and this term that is
+uh a^2 + 2 a b + b^ 2 that is a + b^ 2
+
+ align:start position:0%
+uh a^2 + 2 a b + b^ 2 that is a + b^ 2
+ 
+
+ align:start position:0%
+uh a^2 + 2 a b + b^ 2 that is a + b^ 2
+and then we have a minus a minus b over
+
+ align:start position:0%
+and then we have a minus a minus b over
+ 
+
+ align:start position:0%
+and then we have a minus a minus b over
+2 but interject a rule in between we
+
+ align:start position:0%
+2 but interject a rule in between we
+ 
+
+ align:start position:0%
+2 but interject a rule in between we
+have a + b^ 2 minus a + b over 2
+
+ align:start position:0%
+have a + b^ 2 minus a + b over 2
+ 
+
+ align:start position:0%
+have a + b^ 2 minus a + b over 2
+uh and then these two are the same
+
+ align:start position:0%
+uh and then these two are the same
+ 
+
+ align:start position:0%
+uh and then these two are the same
+thing. I think that's pretty clear. So
+
+ align:start position:0%
+thing. I think that's pretty clear. So
+ 
+
+ align:start position:0%
+thing. I think that's pretty clear. So
+cool. We did some algebra and the we
+
+ align:start position:0%
+cool. We did some algebra and the we
+ 
+
+ align:start position:0%
+cool. We did some algebra and the we
+just computed what we get out of
+
+ align:start position:0%
+just computed what we get out of
+ 
+
+ align:start position:0%
+just computed what we get out of
+induction and then boom, we get the
+
+ align:start position:0%
+induction and then boom, we get the
+ 
+
+ align:start position:0%
+induction and then boom, we get the
+answer n * n minus one over two and it
+
+ align:start position:0%
+answer n * n minus one over two and it
+ 
+
+ align:start position:0%
+answer n * n minus one over two and it
+works. How did we know this is the right
+
+ align:start position:0%
+works. How did we know this is the right
+ 
+
+ align:start position:0%
+works. How did we know this is the right
+answer? I mean, we were just told that
+
+ align:start position:0%
+answer? I mean, we were just told that
+ 
+
+ align:start position:0%
+answer? I mean, we were just told that
+by the theorem. Uh probably you would
+
+ align:start position:0%
+by the theorem. Uh probably you would
+ 
+
+ align:start position:0%
+by the theorem. Uh probably you would
+try this for very small n and make a
+
+ align:start position:0%
+try this for very small n and make a
+ 
+
+ align:start position:0%
+try this for very small n and make a
+conjecture. Oh, it seems like it's n * n
+
+ align:start position:0%
+conjecture. Oh, it seems like it's n * n
+ 
+
+ align:start position:0%
+conjecture. Oh, it seems like it's n * n
+minus one over two. Let's try to prove
+
+ align:start position:0%
+minus one over two. Let's try to prove
+ 
+
+ align:start position:0%
+minus one over two. Let's try to prove
+it. And when you assume the right thing,
+
+ align:start position:0%
+it. And when you assume the right thing,
+ 
+
+ align:start position:0%
+it. And when you assume the right thing,
+the proof just works. And it's kind of
+
+ align:start position:0%
+the proof just works. And it's kind of
+ 
+
+ align:start position:0%
+the proof just works. And it's kind of
+magical. And that's strong induction.
+
+ align:start position:0%
+magical. And that's strong induction.
+ 
+
+ align:start position:0%
+magical. And that's strong induction.
+Again, we needed strong induction here
+
+ align:start position:0%
+Again, we needed strong induction here
+ 
+
+ align:start position:0%
+Again, we needed strong induction here
+because we needed to assume uh what we
+
+ align:start position:0%
+because we needed to assume uh what we
+ 
+
+ align:start position:0%
+because we needed to assume uh what we
+wanted for all smaller n because we
+
+ align:start position:0%
+wanted for all smaller n because we
+ 
+
+ align:start position:0%
+wanted for all smaller n because we
+don't know what a and b are. This has to
+
+ align:start position:0%
+don't know what a and b are. This has to
+ 
+
+ align:start position:0%
+don't know what a and b are. This has to
+work for all a and b less than n. Um
+
+ align:start position:0%
+work for all a and b less than n. Um
+ 
+
+ align:start position:0%
+work for all a and b less than n. Um
+so luckily strong induction gives us
+
+ align:start position:0%
+so luckily strong induction gives us
+ 
+
+ align:start position:0%
+so luckily strong induction gives us
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+All right, I have one more example to
+
+ align:start position:0%
+All right, I have one more example to
+ 
+
+ align:start position:0%
+All right, I have one more example to
+tell you about. Uh,
+
+ align:start position:0%
+tell you about. Uh,
+ 
+
+ align:start position:0%
+tell you about. Uh,
+a slightly more complicated version of
+
+ align:start position:0%
+a slightly more complicated version of
+ 
+
+ align:start position:0%
+a slightly more complicated version of
+the same thing. We're going to use
+
+ align:start position:0%
+the same thing. We're going to use
+ 
+
+ align:start position:0%
+the same thing. We're going to use
+strong induction. Don't need any of
+
+ align:start position:0%
+strong induction. Don't need any of
+ 
+
+ align:start position:0%
+strong induction. Don't need any of
+these.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, let's
+
+ align:start position:0%
+So, let's
+ 
+
+ align:start position:0%
+So, let's
+go.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's a problem called beat ordering.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess somewhat relevant today because
+
+ align:start position:0%
+I guess somewhat relevant today because
+ 
+
+ align:start position:0%
+I guess somewhat relevant today because
+uh there's a Super Bowl, but this is
+
+ align:start position:0%
+uh there's a Super Bowl, but this is
+ 
+
+ align:start position:0%
+uh there's a Super Bowl, but this is
+just about
+
+ align:start position:0%
+just about
+ 
+
+ align:start position:0%
+just about
+any teams of games. Sorry, end teams in
+
+ align:start position:0%
+any teams of games. Sorry, end teams in
+ 
+
+ align:start position:0%
+any teams of games. Sorry, end teams in
+some game. And setup is that every two
+
+ align:start position:0%
+some game. And setup is that every two
+ 
+
+ align:start position:0%
+some game. And setup is that every two
+teams play a game
+
+ align:start position:0%
+teams play a game
+ 
+
+ align:start position:0%
+teams play a game
+and there are no ties.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One team wins
+
+ align:start position:0%
+One team wins
+ 
+
+ align:start position:0%
+One team wins
+and the other loses.
+
+ align:start position:0%
+and the other loses.
+ 
+
+ align:start position:0%
+and the other loses.
+Okay, this is sort of like stranger
+
+ align:start position:0%
+Okay, this is sort of like stranger
+ 
+
+ align:start position:0%
+Okay, this is sort of like stranger
+friends and strangers uh where it's
+
+ align:start position:0%
+friends and strangers uh where it's
+ 
+
+ align:start position:0%
+friends and strangers uh where it's
+either one or the other. But in this
+
+ align:start position:0%
+either one or the other. But in this
+ 
+
+ align:start position:0%
+either one or the other. But in this
+case, it's asymmetric. It's not they're
+
+ align:start position:0%
+case, it's asymmetric. It's not they're
+ 
+
+ align:start position:0%
+case, it's asymmetric. It's not they're
+not both happy or both sad. One's happy
+
+ align:start position:0%
+not both happy or both sad. One's happy
+ 
+
+ align:start position:0%
+not both happy or both sad. One's happy
+and one is sad.
+
+ align:start position:0%
+and one is sad.
+ 
+
+ align:start position:0%
+and one is sad.
+Okay, this is what's called a roundroin
+
+ align:start position:0%
+Okay, this is what's called a roundroin
+ 
+
+ align:start position:0%
+Okay, this is what's called a roundroin
+tournament. Most sports are not played
+
+ align:start position:0%
+tournament. Most sports are not played
+ 
+
+ align:start position:0%
+tournament. Most sports are not played
+this way unless it's small number of
+
+ align:start position:0%
+this way unless it's small number of
+ 
+
+ align:start position:0%
+this way unless it's small number of
+teams because it's a lot of different
+
+ align:start position:0%
+teams because it's a lot of different
+ 
+
+ align:start position:0%
+teams because it's a lot of different
+teams. It's actually n * n + one over
+
+ align:start position:0%
+teams. It's actually n * n + one over
+ 
+
+ align:start position:0%
+teams. It's actually n * n + one over
+two teams uh games which is a lot. All
+
+ align:start position:0%
+two teams uh games which is a lot. All
+ 
+
+ align:start position:0%
+two teams uh games which is a lot. All
+right. So what we would like
+
+ align:start position:0%
+right. So what we would like
+ 
+
+ align:start position:0%
+right. So what we would like
+is what's called a beat ordering.
+
+ align:start position:0%
+is what's called a beat ordering.
+ 
+
+ align:start position:0%
+is what's called a beat ordering.
+Uh this is
+
+ align:start position:0%
+Uh this is
+ 
+
+ align:start position:0%
+Uh this is
+um an ordering of the teams
+
+ align:start position:0%
+um an ordering of the teams
+ 
+
+ align:start position:0%
+um an ordering of the teams
+t1 t2 up to tn
+
+ align:start position:0%
+t1 t2 up to tn
+ 
+
+ align:start position:0%
+t1 t2 up to tn
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b1 beat
+
+ align:start position:0%
+b1 beat
+ 
+
+ align:start position:0%
+b1 beat
+uh sorry t1 t for teams t1 beats t2 t2
+
+ align:start position:0%
+uh sorry t1 t for teams t1 beats t2 t2
+ 
+
+ align:start position:0%
+uh sorry t1 t for teams t1 beats t2 t2
+beat t3 and so on
+
+ align:start position:0%
+beat t3 and so on
+ 
+
+ align:start position:0%
+beat t3 and so on
+and a TN minus one beats TN.
+
+ align:start position:0%
+and a TN minus one beats TN.
+ 
+
+ align:start position:0%
+and a TN minus one beats TN.
+Okay, let's draw a little example. Uh
+
+ align:start position:0%
+Okay, let's draw a little example. Uh
+ 
+
+ align:start position:0%
+Okay, let's draw a little example. Uh
+there's team rock,
+
+ align:start position:0%
+there's team rock,
+ 
+
+ align:start position:0%
+there's team rock,
+team scissors,
+
+ align:start position:0%
+team scissors,
+ 
+
+ align:start position:0%
+team scissors,
+and team paper.
+
+ align:start position:0%
+and team paper.
+ 
+
+ align:start position:0%
+and team paper.
+Okay, paper beats rock, rock beats
+
+ align:start position:0%
+Okay, paper beats rock, rock beats
+ 
+
+ align:start position:0%
+Okay, paper beats rock, rock beats
+scissors, scissors beats paper. Okay,
+
+ align:start position:0%
+scissors, scissors beats paper. Okay,
+ 
+
+ align:start position:0%
+scissors, scissors beats paper. Okay,
+this is a possible outcome in a three
+
+ align:start position:0%
+this is a possible outcome in a three
+ 
+
+ align:start position:0%
+this is a possible outcome in a three
+team tournament. There's there's not
+
+ align:start position:0%
+team tournament. There's there's not
+ 
+
+ align:start position:0%
+team tournament. There's there's not
+necessarily one best team here. There is
+
+ align:start position:0%
+necessarily one best team here. There is
+ 
+
+ align:start position:0%
+necessarily one best team here. There is
+no best team. But maybe paper and rock
+
+ align:start position:0%
+no best team. But maybe paper and rock
+ 
+
+ align:start position:0%
+no best team. But maybe paper and rock
+play a game and it happens that paper
+
+ align:start position:0%
+play a game and it happens that paper
+ 
+
+ align:start position:0%
+play a game and it happens that paper
+won. Maybe rock plays against scissors
+
+ align:start position:0%
+won. Maybe rock plays against scissors
+ 
+
+ align:start position:0%
+won. Maybe rock plays against scissors
+and it happens rock one and scissors
+
+ align:start position:0%
+and it happens rock one and scissors
+ 
+
+ align:start position:0%
+and it happens rock one and scissors
+played against paper. It happens
+
+ align:start position:0%
+played against paper. It happens
+ 
+
+ align:start position:0%
+played against paper. It happens
+scissors one. Okay, you can tell why I
+
+ align:start position:0%
+scissors one. Okay, you can tell why I
+ 
+
+ align:start position:0%
+scissors one. Okay, you can tell why I
+named the teams this way. Uh then one
+
+ align:start position:0%
+named the teams this way. Uh then one
+ 
+
+ align:start position:0%
+named the teams this way. Uh then one
+way I could order these teams is paper,
+
+ align:start position:0%
+way I could order these teams is paper,
+ 
+
+ align:start position:0%
+way I could order these teams is paper,
+rock,
+
+ align:start position:0%
+rock,
+ 
+
+ align:start position:0%
+rock,
+scissors
+
+ align:start position:0%
+scissors
+ 
+
+ align:start position:0%
+scissors
+because paper beats rock, rock beats
+
+ align:start position:0%
+because paper beats rock, rock beats
+ 
+
+ align:start position:0%
+because paper beats rock, rock beats
+scissors. Okay, so this is sort of the
+
+ align:start position:0%
+scissors. Okay, so this is sort of the
+ 
+
+ align:start position:0%
+scissors. Okay, so this is sort of the
+input and this is my goal
+
+ align:start position:0%
+input and this is my goal
+ 
+
+ align:start position:0%
+input and this is my goal
+is to produce an ordering like this. But
+
+ align:start position:0%
+is to produce an ordering like this. But
+ 
+
+ align:start position:0%
+is to produce an ordering like this. But
+I need to do it for n teams not just for
+
+ align:start position:0%
+I need to do it for n teams not just for
+ 
+
+ align:start position:0%
+I need to do it for n teams not just for
+three.
+
+ align:start position:0%
+three.
+ 
+
+ align:start position:0%
+three.
+Okay. So let's uh do let's do strong
+
+ align:start position:0%
+Okay. So let's uh do let's do strong
+ 
+
+ align:start position:0%
+Okay. So let's uh do let's do strong
+induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to prove that uh the theorem is a bead
+
+ align:start position:0%
+to prove that uh the theorem is a bead
+ 
+
+ align:start position:0%
+to prove that uh the theorem is a bead
+ordering always exists.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And when I say this always exists, what
+
+ align:start position:0%
+And when I say this always exists, what
+ 
+
+ align:start position:0%
+And when I say this always exists, what
+I really mean is uh for all n
+
+ align:start position:0%
+I really mean is uh for all n
+ 
+
+ align:start position:0%
+I really mean is uh for all n
+and then for all tournaments
+
+ align:start position:0%
+and then for all tournaments
+ 
+
+ align:start position:0%
+and then for all tournaments
+of size n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there exists a beat order.
+
+ align:start position:0%
+uh there exists a beat order.
+ 
+
+ align:start position:0%
+uh there exists a beat order.
+Okay, there exists an ordering of the
+
+ align:start position:0%
+Okay, there exists an ordering of the
+ 
+
+ align:start position:0%
+Okay, there exists an ordering of the
+end team such the first one beat the
+
+ align:start position:0%
+end team such the first one beat the
+ 
+
+ align:start position:0%
+end team such the first one beat the
+second one, second one beat the third
+
+ align:start position:0%
+second one, second one beat the third
+ 
+
+ align:start position:0%
+second one, second one beat the third
+one and so on. I should say uh for all I
+
+ align:start position:0%
+one and so on. I should say uh for all I
+ 
+
+ align:start position:0%
+one and so on. I should say uh for all I
+uh t i beat t i + one.
+
+ align:start position:0%
+uh t i beat t i + one.
+ 
+
+ align:start position:0%
+uh t i beat t i + one.
+Okay, so we claim this is true.
+
+ align:start position:0%
+Okay, so we claim this is true.
+ 
+
+ align:start position:0%
+Okay, so we claim this is true.
+Proof by strong induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we're going to assume that this
+
+ align:start position:0%
+So we're going to assume that this
+ 
+
+ align:start position:0%
+So we're going to assume that this
+statement is true. namely this statement
+
+ align:start position:0%
+statement is true. namely this statement
+ 
+
+ align:start position:0%
+statement is true. namely this statement
+uh is true for smaller n and then we're
+
+ align:start position:0%
+uh is true for smaller n and then we're
+ 
+
+ align:start position:0%
+uh is true for smaller n and then we're
+going to prove it for n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Uh let's
+
+ align:start position:0%
+Okay. Uh let's
+ 
+
+ align:start position:0%
+Okay. Uh let's
+pick a team
+
+ align:start position:0%
+pick a team
+ 
+
+ align:start position:0%
+pick a team
+any team
+
+ align:start position:0%
+any team
+ 
+
+ align:start position:0%
+any team
+call it t.
+
+ align:start position:0%
+call it t.
+ 
+
+ align:start position:0%
+call it t.
+Then I'm going to split everything with
+
+ align:start position:0%
+Then I'm going to split everything with
+ 
+
+ align:start position:0%
+Then I'm going to split everything with
+respect to t. So I'm going to define uh
+
+ align:start position:0%
+respect to t. So I'm going to define uh
+ 
+
+ align:start position:0%
+respect to t. So I'm going to define uh
+W to be the set of teams that win
+
+ align:start position:0%
+W to be the set of teams that win
+ 
+
+ align:start position:0%
+W to be the set of teams that win
+against T. So this is going to be a set
+
+ align:start position:0%
+against T. So this is going to be a set
+ 
+
+ align:start position:0%
+against T. So this is going to be a set
+of all teams S where S beat T.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is one versus T. These teams win
+
+ align:start position:0%
+So this is one versus T. These teams win
+ 
+
+ align:start position:0%
+So this is one versus T. These teams win
+versus T or one versus T. And L is going
+
+ align:start position:0%
+versus T or one versus T. And L is going
+ 
+
+ align:start position:0%
+versus T or one versus T. And L is going
+to be the set of teams that lose against
+
+ align:start position:0%
+to be the set of teams that lose against
+ 
+
+ align:start position:0%
+to be the set of teams that lose against
+T. So this is the set of teams S where
+
+ align:start position:0%
+T. So this is the set of teams S where
+ 
+
+ align:start position:0%
+T. So this is the set of teams S where
+TBS.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is a loss versus T. Then
+
+ align:start position:0%
+So this is a loss versus T. Then
+ 
+
+ align:start position:0%
+So this is a loss versus T. Then
+intuitively what we'd like to do is put
+
+ align:start position:0%
+intuitively what we'd like to do is put
+ 
+
+ align:start position:0%
+intuitively what we'd like to do is put
+the winners first, then put T, then put
+
+ align:start position:0%
+the winners first, then put T, then put
+ 
+
+ align:start position:0%
+the winners first, then put T, then put
+the losers.
+
+ align:start position:0%
+the losers.
+ 
+
+ align:start position:0%
+the losers.
+I claim that works. Okay. But how do I
+
+ align:start position:0%
+I claim that works. Okay. But how do I
+ 
+
+ align:start position:0%
+I claim that works. Okay. But how do I
+order the winners? How do I order the
+
+ align:start position:0%
+order the winners? How do I order the
+ 
+
+ align:start position:0%
+order the winners? How do I order the
+losers? Well, by induction.
+
+ align:start position:0%
+losers? Well, by induction.
+ 
+
+ align:start position:0%
+losers? Well, by induction.
+I claim uh the size of w this vertical
+
+ align:start position:0%
+I claim uh the size of w this vertical
+ 
+
+ align:start position:0%
+I claim uh the size of w this vertical
+bar means the size of the set is less
+
+ align:start position:0%
+bar means the size of the set is less
+ 
+
+ align:start position:0%
+bar means the size of the set is less
+than n and the size of l is less than n
+
+ align:start position:0%
+than n and the size of l is less than n
+ 
+
+ align:start position:0%
+than n and the size of l is less than n
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh the size of the winners plus the size
+
+ align:start position:0%
+uh the size of the winners plus the size
+ 
+
+ align:start position:0%
+uh the size of the winners plus the size
+of the losers plus one equals n. This is
+
+ align:start position:0%
+of the losers plus one equals n. This is
+ 
+
+ align:start position:0%
+of the losers plus one equals n. This is
+a one. Why? because every team is either
+
+ align:start position:0%
+a one. Why? because every team is either
+ 
+
+ align:start position:0%
+a one. Why? because every team is either
+T or they won against T or they lost
+
+ align:start position:0%
+T or they won against T or they lost
+ 
+
+ align:start position:0%
+T or they won against T or they lost
+against T. So this is counting all of
+
+ align:start position:0%
+against T. So this is counting all of
+ 
+
+ align:start position:0%
+against T. So this is counting all of
+the teams. There's T itself, the ones
+
+ align:start position:0%
+the teams. There's T itself, the ones
+ 
+
+ align:start position:0%
+the teams. There's T itself, the ones
+that win against T, the ones that lose
+
+ align:start position:0%
+that win against T, the ones that lose
+ 
+
+ align:start position:0%
+that win against T, the ones that lose
+against T. Together that ex is exactly
+
+ align:start position:0%
+against T. Together that ex is exactly
+ 
+
+ align:start position:0%
+against T. Together that ex is exactly
+N. Every team is exactly one of these
+
+ align:start position:0%
+N. Every team is exactly one of these
+ 
+
+ align:start position:0%
+N. Every team is exactly one of these
+categories. Uh and there's a plus one
+
+ align:start position:0%
+categories. Uh and there's a plus one
+ 
+
+ align:start position:0%
+categories. Uh and there's a plus one
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+And all of these are non- negative.
+
+ align:start position:0%
+And all of these are non- negative.
+ 
+
+ align:start position:0%
+And all of these are non- negative.
+These here W and L might be zero, but
+
+ align:start position:0%
+These here W and L might be zero, but
+ 
+
+ align:start position:0%
+These here W and L might be zero, but
+there's this plus one. That means both W
+
+ align:start position:0%
+there's this plus one. That means both W
+ 
+
+ align:start position:0%
+there's this plus one. That means both W
+and L are strictly less than M. So the
+
+ align:start position:0%
+and L are strictly less than M. So the
+ 
+
+ align:start position:0%
+and L are strictly less than M. So the
+induction applies to them.
+
+ align:start position:0%
+induction applies to them.
+ 
+
+ align:start position:0%
+induction applies to them.
+So by induction
+
+ align:start position:0%
+So by induction
+ 
+
+ align:start position:0%
+So by induction
+uh this thing is true for any tournament
+
+ align:start position:0%
+uh this thing is true for any tournament
+ 
+
+ align:start position:0%
+uh this thing is true for any tournament
+of size W there exists a beat ordering
+
+ align:start position:0%
+of size W there exists a beat ordering
+ 
+
+ align:start position:0%
+of size W there exists a beat ordering
+of W. For every tournament of size L
+
+ align:start position:0%
+of W. For every tournament of size L
+ 
+
+ align:start position:0%
+of W. For every tournament of size L
+there exists a beat uh ordering of L. So
+
+ align:start position:0%
+there exists a beat uh ordering of L. So
+ 
+
+ align:start position:0%
+there exists a beat uh ordering of L. So
+we get a beat ordering
+
+ align:start position:0%
+we get a beat ordering
+ 
+
+ align:start position:0%
+we get a beat ordering
+let's we get two of them really. Uh
+
+ align:start position:0%
+let's we get two of them really. Uh
+ 
+
+ align:start position:0%
+let's we get two of them really. Uh
+let's call it W1
+
+ align:start position:0%
+let's call it W1
+ 
+
+ align:start position:0%
+let's call it W1
+W2 dot dot dot W size of W. This is for
+
+ align:start position:0%
+W2 dot dot dot W size of W. This is for
+ 
+
+ align:start position:0%
+W2 dot dot dot W size of W. This is for
+this is an ordering of capital W. And we
+
+ align:start position:0%
+this is an ordering of capital W. And we
+ 
+
+ align:start position:0%
+this is an ordering of capital W. And we
+get L1 L2 dot dot dot L size of L
+
+ align:start position:0%
+get L1 L2 dot dot dot L size of L
+ 
+
+ align:start position:0%
+get L1 L2 dot dot dot L size of L
+as a beat ordering of capital L
+
+ align:start position:0%
+as a beat ordering of capital L
+ 
+
+ align:start position:0%
+as a beat ordering of capital L
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+uh we concatenate.
+
+ align:start position:0%
+uh we concatenate.
+ 
+
+ align:start position:0%
+uh we concatenate.
+So we claim uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W1
+
+ align:start position:0%
+W1
+ 
+
+ align:start position:0%
+W1
+dot dot dot W size of W
+
+ align:start position:0%
+dot dot dot W size of W
+ 
+
+ align:start position:0%
+dot dot dot W size of W
+then T then L1
+
+ align:start position:0%
+then T then L1
+ 
+
+ align:start position:0%
+then T then L1
+dot dot dot L size of L
+
+ align:start position:0%
+dot dot dot L size of L
+ 
+
+ align:start position:0%
+dot dot dot L size of L
+is a beat ordering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of all N teams.
+
+ align:start position:0%
+of all N teams.
+ 
+
+ align:start position:0%
+of all N teams.
+Again, this is all the teams. All the
+
+ align:start position:0%
+Again, this is all the teams. All the
+ 
+
+ align:start position:0%
+Again, this is all the teams. All the
+teams either won against T or they are T
+
+ align:start position:0%
+teams either won against T or they are T
+ 
+
+ align:start position:0%
+teams either won against T or they are T
+or they lost against T. And the idea is
+
+ align:start position:0%
+or they lost against T. And the idea is
+ 
+
+ align:start position:0%
+or they lost against T. And the idea is
+this part is beat. W1 beats W2. W2 beats
+
+ align:start position:0%
+this part is beat. W1 beats W2. W2 beats
+ 
+
+ align:start position:0%
+this part is beat. W1 beats W2. W2 beats
+W3 and so on by induction because this
+
+ align:start position:0%
+W3 and so on by induction because this
+ 
+
+ align:start position:0%
+W3 and so on by induction because this
+is a beat ordering of capital W. Over
+
+ align:start position:0%
+is a beat ordering of capital W. Over
+ 
+
+ align:start position:0%
+is a beat ordering of capital W. Over
+here, this is a beat ordering of of
+
+ align:start position:0%
+here, this is a beat ordering of of
+ 
+
+ align:start position:0%
+here, this is a beat ordering of of
+capital L. And so by induction, uh all
+
+ align:start position:0%
+capital L. And so by induction, uh all
+ 
+
+ align:start position:0%
+capital L. And so by induction, uh all
+these are are okay. L1 beat L2, L2 beat
+
+ align:start position:0%
+these are are okay. L1 beat L2, L2 beat
+ 
+
+ align:start position:0%
+these are are okay. L1 beat L2, L2 beat
+so on, dot dot dot beat L size of L. The
+
+ align:start position:0%
+so on, dot dot dot beat L size of L. The
+ 
+
+ align:start position:0%
+so on, dot dot dot beat L size of L. The
+only things we need to check are these
+
+ align:start position:0%
+only things we need to check are these
+ 
+
+ align:start position:0%
+only things we need to check are these
+two commas. We need to check that W sub
+
+ align:start position:0%
+two commas. We need to check that W sub
+ 
+
+ align:start position:0%
+two commas. We need to check that W sub
+big W, W subsize of W beats T and T beat
+
+ align:start position:0%
+big W, W subsize of W beats T and T beat
+ 
+
+ align:start position:0%
+big W, W subsize of W beats T and T beat
+L1. Why are those true? By our
+
+ align:start position:0%
+L1. Why are those true? By our
+ 
+
+ align:start position:0%
+L1. Why are those true? By our
+definition of W and L. Everything in W
+
+ align:start position:0%
+definition of W and L. Everything in W
+ 
+
+ align:start position:0%
+definition of W and L. Everything in W
+beat T. So this is by by the definition
+
+ align:start position:0%
+beat T. So this is by by the definition
+ 
+
+ align:start position:0%
+beat T. So this is by by the definition
+of W. We know that all of these beat T.
+
+ align:start position:0%
+of W. We know that all of these beat T.
+ 
+
+ align:start position:0%
+of W. We know that all of these beat T.
+So in particular, this one beat T. And
+
+ align:start position:0%
+So in particular, this one beat T. And
+ 
+
+ align:start position:0%
+So in particular, this one beat T. And
+we know by the definition
+
+ align:start position:0%
+we know by the definition
+ 
+
+ align:start position:0%
+we know by the definition
+of L,
+
+ align:start position:0%
+of L,
+ 
+
+ align:start position:0%
+of L,
+uh, all of these teams lost against T.
+
+ align:start position:0%
+uh, all of these teams lost against T.
+ 
+
+ align:start position:0%
+uh, all of these teams lost against T.
+In other words, T beats all of these
+
+ align:start position:0%
+In other words, T beats all of these
+ 
+
+ align:start position:0%
+In other words, T beats all of these
+teams. In particular, T beat L1. And so
+
+ align:start position:0%
+teams. In particular, T beat L1. And so
+ 
+
+ align:start position:0%
+teams. In particular, T beat L1. And so
+by combining all these beat statements
+
+ align:start position:0%
+by combining all these beat statements
+ 
+
+ align:start position:0%
+by combining all these beat statements
+together, we know that this entire thing
+
+ align:start position:0%
+together, we know that this entire thing
+ 
+
+ align:start position:0%
+together, we know that this entire thing
+is a beat ordering. each item beats the
+
+ align:start position:0%
+is a beat ordering. each item beats the
+ 
+
+ align:start position:0%
+is a beat ordering. each item beats the
+one right after it. So it's a little
+
+ align:start position:0%
+one right after it. So it's a little
+ 
+
+ align:start position:0%
+one right after it. So it's a little
+more complicated, but again, we're just
+
+ align:start position:0%
+more complicated, but again, we're just
+ 
+
+ align:start position:0%
+more complicated, but again, we're just
+quite often with strong induction
+
+ align:start position:0%
+quite often with strong induction
+ 
+
+ align:start position:0%
+quite often with strong induction
+proofs, you apply induction twice. You
+
+ align:start position:0%
+proofs, you apply induction twice. You
+ 
+
+ align:start position:0%
+proofs, you apply induction twice. You
+you have some problem of size n, you
+
+ align:start position:0%
+you have some problem of size n, you
+ 
+
+ align:start position:0%
+you have some problem of size n, you
+split it into two parts. In general, you
+
+ align:start position:0%
+split it into two parts. In general, you
+ 
+
+ align:start position:0%
+split it into two parts. In general, you
+might split it into many parts. Then you
+
+ align:start position:0%
+might split it into many parts. Then you
+ 
+
+ align:start position:0%
+might split it into many parts. Then you
+recursively solve the two parts or the
+
+ align:start position:0%
+recursively solve the two parts or the
+ 
+
+ align:start position:0%
+recursively solve the two parts or the
+many parts. As long as they're strictly
+
+ align:start position:0%
+many parts. As long as they're strictly
+ 
+
+ align:start position:0%
+many parts. As long as they're strictly
+smaller than n. By induction, we know
+
+ align:start position:0%
+smaller than n. By induction, we know
+ 
+
+ align:start position:0%
+smaller than n. By induction, we know
+they work out. By strong induction, we
+
+ align:start position:0%
+they work out. By strong induction, we
+ 
+
+ align:start position:0%
+they work out. By strong induction, we
+know they work out. You take those
+
+ align:start position:0%
+know they work out. You take those
+ 
+
+ align:start position:0%
+know they work out. You take those
+solutions and you combine them in some
+
+ align:start position:0%
+solutions and you combine them in some
+ 
+
+ align:start position:0%
+solutions and you combine them in some
+way. Here we concatenated with t in the
+
+ align:start position:0%
+way. Here we concatenated with t in the
+ 
+
+ align:start position:0%
+way. Here we concatenated with t in the
+middle. Um over here we summed them up.
+
+ align:start position:0%
+middle. Um over here we summed them up.
+ 
+
+ align:start position:0%
+middle. Um over here we summed them up.
+We summed up the number of points we got
+
+ align:start position:0%
+We summed up the number of points we got
+ 
+
+ align:start position:0%
+We summed up the number of points we got
+in each one plus the number of points we
+
+ align:start position:0%
+in each one plus the number of points we
+ 
+
+ align:start position:0%
+in each one plus the number of points we
+got in the first step. Uh and in general
+
+ align:start position:0%
+got in the first step. Uh and in general
+ 
+
+ align:start position:0%
+got in the first step. Uh and in general
+you combine them in some way and you
+
+ align:start position:0%
+you combine them in some way and you
+ 
+
+ align:start position:0%
+you combine them in some way and you
+prove that it's still that you're uh the
+
+ align:start position:0%
+prove that it's still that you're uh the
+ 
+
+ align:start position:0%
+prove that it's still that you're uh the
+thing you want to prove holds for size n
+
+ align:start position:0%
+thing you want to prove holds for size n
+ 
+
+ align:start position:0%
+thing you want to prove holds for size n
+and then you get your theorem. So that
+
+ align:start position:0%
+and then you get your theorem. So that
+ 
+
+ align:start position:0%
+and then you get your theorem. So that
+is the power of strong induction.
+
+ align:start position:0%
+is the power of strong induction.
+ 
+
+ align:start position:0%
+is the power of strong induction.
+Thanks.
\ No newline at end of file
diff --git a/GbVdTqIvIPw.txt b/GbVdTqIvIPw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..47b752b84c71c02aa8c4320cd459b2e9c531a64e
--- /dev/null
+++ b/GbVdTqIvIPw.txt
@@ -0,0 +1,6851 @@
+align:start position:0%
+ 
+great so where were we last time last
+
+ align:start position:0%
+great so where were we last time last
+ 
+
+ align:start position:0%
+great so where were we last time last
+time we had discovered that radiation
+
+ align:start position:0%
+time we had discovered that radiation
+ 
+
+ align:start position:0%
+time we had discovered that radiation
+and we're going back to lecture four
+
+ align:start position:0%
+and we're going back to lecture four
+ 
+
+ align:start position:0%
+and we're going back to lecture four
+notes because I think I have a little
+
+ align:start position:0%
+notes because I think I have a little
+ 
+
+ align:start position:0%
+notes because I think I have a little
+bit uh left on lecture four
+
+ align:start position:0%
+bit uh left on lecture four
+ 
+
+ align:start position:0%
+bit uh left on lecture four
+notes we discovered that radiation also
+
+ align:start position:0%
+notes we discovered that radiation also
+ 
+
+ align:start position:0%
+notes we discovered that radiation also
+behaves like a uh a
+
+ align:start position:0%
+behaves like a uh a
+ 
+
+ align:start position:0%
+behaves like a uh a
+particle and behaves like a particle as
+
+ align:start position:0%
+particle and behaves like a particle as
+ 
+
+ align:start position:0%
+particle and behaves like a particle as
+exhibited in this photoelectric effect
+
+ align:start position:0%
+exhibited in this photoelectric effect
+ 
+
+ align:start position:0%
+exhibited in this photoelectric effect
+that is in order to get an electron out
+
+ align:start position:0%
+that is in order to get an electron out
+ 
+
+ align:start position:0%
+that is in order to get an electron out
+what we needed to do was to put in a
+
+ align:start position:0%
+what we needed to do was to put in a
+ 
+
+ align:start position:0%
+what we needed to do was to put in a
+particle of energy we needed to put in a
+
+ align:start position:0%
+particle of energy we needed to put in a
+ 
+
+ align:start position:0%
+particle of energy we needed to put in a
+packet of energy we needed to put in a
+
+ align:start position:0%
+packet of energy we needed to put in a
+ 
+
+ align:start position:0%
+packet of energy we needed to put in a
+Quantum of
+
+ align:start position:0%
+Quantum of
+ 
+
+ align:start position:0%
+Quantum of
+energy and as long as that Quantum of
+
+ align:start position:0%
+energy and as long as that Quantum of
+ 
+
+ align:start position:0%
+energy and as long as that Quantum of
+energy that packet of energy that
+
+ align:start position:0%
+energy that packet of energy that
+ 
+
+ align:start position:0%
+energy that packet of energy that
+particle of energy was larger than the
+
+ align:start position:0%
+particle of energy was larger than the
+ 
+
+ align:start position:0%
+particle of energy was larger than the
+work function we would get one electron
+
+ align:start position:0%
+work function we would get one electron
+ 
+
+ align:start position:0%
+work function we would get one electron
+out for every packet we put in all
+
+ align:start position:0%
+out for every packet we put in all
+ 
+
+ align:start position:0%
+out for every packet we put in all
+right so that's an example of the
+
+ align:start position:0%
+right so that's an example of the
+ 
+
+ align:start position:0%
+right so that's an example of the
+particle like nature to radiation this
+
+ align:start position:0%
+particle like nature to radiation this
+ 
+
+ align:start position:0%
+particle like nature to radiation this
+photoelectric
+
+ align:start position:0%
+photoelectric
+ 
+
+ align:start position:0%
+photoelectric
+effect all right but um Einstein
+
+ align:start position:0%
+effect all right but um Einstein
+ 
+
+ align:start position:0%
+effect all right but um Einstein
+also went on to show an even more
+
+ align:start position:0%
+also went on to show an even more
+ 
+
+ align:start position:0%
+also went on to show an even more
+convincing property of the particle like
+
+ align:start position:0%
+convincing property of the particle like
+ 
+
+ align:start position:0%
+convincing property of the particle like
+nature of radiation or a
+
+ align:start position:0%
+nature of radiation or a
+ 
+
+ align:start position:0%
+nature of radiation or a
+photon and that is that he showed that a
+
+ align:start position:0%
+photon and that is that he showed that a
+ 
+
+ align:start position:0%
+photon and that is that he showed that a
+photon has
+
+ align:start position:0%
+photon has
+ 
+
+ align:start position:0%
+photon has
+momentum even though a photon does not
+
+ align:start position:0%
+momentum even though a photon does not
+ 
+
+ align:start position:0%
+momentum even though a photon does not
+have mass or essentially No Rest Mass
+
+ align:start position:0%
+have mass or essentially No Rest Mass
+ 
+
+ align:start position:0%
+have mass or essentially No Rest Mass
+okay and of course momentum is a very
+
+ align:start position:0%
+okay and of course momentum is a very
+ 
+
+ align:start position:0%
+okay and of course momentum is a very
+particle like property right momentum
+
+ align:start position:0%
+particle like property right momentum
+ 
+
+ align:start position:0%
+particle like property right momentum
+hey P for momentum is equal to the mass
+
+ align:start position:0%
+hey P for momentum is equal to the mass
+ 
+
+ align:start position:0%
+hey P for momentum is equal to the mass
+times velocity
+
+ align:start position:0%
+times velocity
+ 
+
+ align:start position:0%
+times velocity
+right so if a particle or if a if a
+
+ align:start position:0%
+right so if a particle or if a if a
+ 
+
+ align:start position:0%
+right so if a particle or if a if a
+photon if
+
+ align:start position:0%
+photon if
+ 
+
+ align:start position:0%
+photon if
+um if radiation has momentum well gee
+
+ align:start position:0%
+um if radiation has momentum well gee
+ 
+
+ align:start position:0%
+um if radiation has momentum well gee
+it's acting very much like a particle
+
+ align:start position:0%
+it's acting very much like a particle
+ 
+
+ align:start position:0%
+it's acting very much like a particle
+right all right how did he do this
+
+ align:start position:0%
+right all right how did he do this
+ 
+
+ align:start position:0%
+right all right how did he do this
+well Einstein took the relativistic
+
+ align:start position:0%
+well Einstein took the relativistic
+ 
+
+ align:start position:0%
+well Einstein took the relativistic
+equations of motion which he himself
+
+ align:start position:0%
+equations of motion which he himself
+ 
+
+ align:start position:0%
+equations of motion which he himself
+wrote
+
+ align:start position:0%
+wrote
+ 
+
+ align:start position:0%
+wrote
+down and what he showed from that is
+
+ align:start position:0%
+down and what he showed from that is
+ 
+
+ align:start position:0%
+down and what he showed from that is
+that a photon
+
+ align:start position:0%
+that a photon
+ 
+
+ align:start position:0%
+that a photon
+had momentum P
+
+ align:start position:0%
+had momentum P
+ 
+
+ align:start position:0%
+had momentum P
+here and the momentum of the photon was
+
+ align:start position:0%
+here and the momentum of the photon was
+ 
+
+ align:start position:0%
+here and the momentum of the photon was
+defined by the frequency of the
+
+ align:start position:0%
+defined by the frequency of the
+ 
+
+ align:start position:0%
+defined by the frequency of the
+radiation that is that momentum was
+
+ align:start position:0%
+radiation that is that momentum was
+ 
+
+ align:start position:0%
+radiation that is that momentum was
+given by H again Plank's constant there
+
+ align:start position:0%
+given by H again Plank's constant there
+ 
+
+ align:start position:0%
+given by H again Plank's constant there
+that quantization constant times the
+
+ align:start position:0%
+that quantization constant times the
+ 
+
+ align:start position:0%
+that quantization constant times the
+frequency over the speed of
+
+ align:start position:0%
+frequency over the speed of
+ 
+
+ align:start position:0%
+frequency over the speed of
+light and since of course we know the
+
+ align:start position:0%
+light and since of course we know the
+ 
+
+ align:start position:0%
+light and since of course we know the
+relationship between the frequency in
+
+ align:start position:0%
+relationship between the frequency in
+ 
+
+ align:start position:0%
+relationship between the frequency in
+the wavelength we can write the momentum
+
+ align:start position:0%
+the wavelength we can write the momentum
+ 
+
+ align:start position:0%
+the wavelength we can write the momentum
+of a photon as H over Lambda right so if
+
+ align:start position:0%
+of a photon as H over Lambda right so if
+ 
+
+ align:start position:0%
+of a photon as H over Lambda right so if
+you have radiation of some wavelength
+
+ align:start position:0%
+you have radiation of some wavelength
+ 
+
+ align:start position:0%
+you have radiation of some wavelength
+Lambda that
+
+ align:start position:0%
+Lambda that
+ 
+
+ align:start position:0%
+Lambda that
+radiation those photons have this
+
+ align:start position:0%
+radiation those photons have this
+ 
+
+ align:start position:0%
+radiation those photons have this
+momentum H over Lambda this Photon
+
+ align:start position:0%
+momentum H over Lambda this Photon
+ 
+
+ align:start position:0%
+momentum H over Lambda this Photon
+momentum even though photons don't have
+
+ align:start position:0%
+momentum even though photons don't have
+ 
+
+ align:start position:0%
+momentum even though photons don't have
+mass okay
+
+ align:start position:0%
+mass okay
+ 
+
+ align:start position:0%
+mass okay
+and the actual demonstration of this
+
+ align:start position:0%
+and the actual demonstration of this
+ 
+
+ align:start position:0%
+and the actual demonstration of this
+took a few more years experimentally
+
+ align:start position:0%
+took a few more years experimentally
+ 
+
+ align:start position:0%
+took a few more years experimentally
+took a few more years and it was
+
+ align:start position:0%
+took a few more years and it was
+ 
+
+ align:start position:0%
+took a few more years and it was
+demonstrated first in something called
+
+ align:start position:0%
+demonstrated first in something called
+ 
+
+ align:start position:0%
+demonstrated first in something called
+the Compton effect which was the
+
+ align:start position:0%
+the Compton effect which was the
+ 
+
+ align:start position:0%
+the Compton effect which was the
+interaction of an x-ray photon with some
+
+ align:start position:0%
+interaction of an x-ray photon with some
+ 
+
+ align:start position:0%
+interaction of an x-ray photon with some
+matter and you could see it transfer
+
+ align:start position:0%
+matter and you could see it transfer
+ 
+
+ align:start position:0%
+matter and you could see it transfer
+momentum and um I got to show you here a
+
+ align:start position:0%
+momentum and um I got to show you here a
+ 
+
+ align:start position:0%
+momentum and um I got to show you here a
+this uh website from the University of
+
+ align:start position:0%
+this uh website from the University of
+ 
+
+ align:start position:0%
+this uh website from the University of
+Colorado
+
+ align:start position:0%
+Colorado
+ 
+
+ align:start position:0%
+Colorado
+again and uh
+
+ align:start position:0%
+again and uh
+ 
+
+ align:start position:0%
+again and uh
+here this is a just a a uh a video of um
+
+ align:start position:0%
+here this is a just a a uh a video of um
+ 
+
+ align:start position:0%
+here this is a just a a uh a video of um
+you know a photon gun here shooting
+
+ align:start position:0%
+you know a photon gun here shooting
+ 
+
+ align:start position:0%
+you know a photon gun here shooting
+photons and here's this enemy atom
+
+ align:start position:0%
+photons and here's this enemy atom
+ 
+
+ align:start position:0%
+photons and here's this enemy atom
+coming at you and you're shooting these
+
+ align:start position:0%
+coming at you and you're shooting these
+ 
+
+ align:start position:0%
+coming at you and you're shooting these
+photons and sure enough you can uh repel
+
+ align:start position:0%
+photons and sure enough you can uh repel
+ 
+
+ align:start position:0%
+photons and sure enough you can uh repel
+that atom make it go the other direction
+
+ align:start position:0%
+that atom make it go the other direction
+ 
+
+ align:start position:0%
+that atom make it go the other direction
+because of the photon of the moment
+
+ align:start position:0%
+because of the photon of the moment
+ 
+
+ align:start position:0%
+because of the photon of the moment
+because of the momentum of the photon
+
+ align:start position:0%
+because of the momentum of the photon
+ 
+
+ align:start position:0%
+because of the momentum of the photon
+but of course if you lower the power and
+
+ align:start position:0%
+but of course if you lower the power and
+ 
+
+ align:start position:0%
+but of course if you lower the power and
+you're not really good with your fingers
+
+ align:start position:0%
+you're not really good with your fingers
+ 
+
+ align:start position:0%
+you're not really good with your fingers
+here you can get clobbered right right
+
+ align:start position:0%
+here you can get clobbered right right
+ 
+
+ align:start position:0%
+here you can get clobbered right right
+so so here now I'm going to try this
+
+ align:start position:0%
+so so here now I'm going to try this
+ 
+
+ align:start position:0%
+so so here now I'm going to try this
+again this is though almost too
+
+ align:start position:0%
+again this is though almost too
+ 
+
+ align:start position:0%
+again this is though almost too
+easy okay so now I lower the power so
+
+ align:start position:0%
+easy okay so now I lower the power so
+ 
+
+ align:start position:0%
+easy okay so now I lower the power so
+that the rate of the photons are coming
+
+ align:start position:0%
+that the rate of the photons are coming
+ 
+
+ align:start position:0%
+that the rate of the photons are coming
+are much slower and I'm going to be able
+
+ align:start position:0%
+are much slower and I'm going to be able
+ 
+
+ align:start position:0%
+are much slower and I'm going to be able
+to turn this guy around no problem there
+
+ align:start position:0%
+to turn this guy around no problem there
+ 
+
+ align:start position:0%
+to turn this guy around no problem there
+we go repel it right off okay so it it
+
+ align:start position:0%
+we go repel it right off okay so it it
+ 
+
+ align:start position:0%
+we go repel it right off okay so it it
+really is the case that uh let me see if
+
+ align:start position:0%
+really is the case that uh let me see if
+ 
+
+ align:start position:0%
+really is the case that uh let me see if
+I can get this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I got cled okay okay well you'll be
+
+ align:start position:0%
+here I got cled okay okay well you'll be
+ 
+
+ align:start position:0%
+here I got cled okay okay well you'll be
+better at that game than I
+
+ align:start position:0%
+better at that game than I
+ 
+
+ align:start position:0%
+better at that game than I
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+am but um it was it it's just that
+
+ align:start position:0%
+am but um it was it it's just that
+ 
+
+ align:start position:0%
+am but um it was it it's just that
+phenomena what I'm showing you here that
+
+ align:start position:0%
+phenomena what I'm showing you here that
+ 
+
+ align:start position:0%
+phenomena what I'm showing you here that
+led to the experimental feat of Adam
+
+ align:start position:0%
+led to the experimental feat of Adam
+ 
+
+ align:start position:0%
+led to the experimental feat of Adam
+trapping you know trapping an atom in
+
+ align:start position:0%
+trapping you know trapping an atom in
+ 
+
+ align:start position:0%
+trapping you know trapping an atom in
+space and how did they do that well what
+
+ align:start position:0%
+space and how did they do that well what
+ 
+
+ align:start position:0%
+space and how did they do that well what
+they did is they took some unsuspecting
+
+ align:start position:0%
+they did is they took some unsuspecting
+ 
+
+ align:start position:0%
+they did is they took some unsuspecting
+adom and they came in with some photons
+
+ align:start position:0%
+adom and they came in with some photons
+ 
+
+ align:start position:0%
+adom and they came in with some photons
+laser beam high power laser beam
+
+ align:start position:0%
+laser beam high power laser beam
+ 
+
+ align:start position:0%
+laser beam high power laser beam
+directed in this way and of course that
+
+ align:start position:0%
+directed in this way and of course that
+ 
+
+ align:start position:0%
+directed in this way and of course that
+that push the atoms that push this atom
+
+ align:start position:0%
+that push the atoms that push this atom
+ 
+
+ align:start position:0%
+that push the atoms that push this atom
+down but now if you come in with a laser
+
+ align:start position:0%
+down but now if you come in with a laser
+ 
+
+ align:start position:0%
+down but now if you come in with a laser
+beam in that direction well the photon
+
+ align:start position:0%
+beam in that direction well the photon
+ 
+
+ align:start position:0%
+beam in that direction well the photon
+momentum is going to push the atom up so
+
+ align:start position:0%
+momentum is going to push the atom up so
+ 
+
+ align:start position:0%
+momentum is going to push the atom up so
+now you've constrained it in this
+
+ align:start position:0%
+now you've constrained it in this
+ 
+
+ align:start position:0%
+now you've constrained it in this
+Dimension and you do it you've send
+
+ align:start position:0%
+Dimension and you do it you've send
+ 
+
+ align:start position:0%
+Dimension and you do it you've send
+another laser beam this way and another
+
+ align:start position:0%
+another laser beam this way and another
+ 
+
+ align:start position:0%
+another laser beam this way and another
+one this way and now you've constrained
+
+ align:start position:0%
+one this way and now you've constrained
+ 
+
+ align:start position:0%
+one this way and now you've constrained
+it in this Dimension then you send a
+
+ align:start position:0%
+it in this Dimension then you send a
+ 
+
+ align:start position:0%
+it in this Dimension then you send a
+laser beam in this way and a laser beam
+
+ align:start position:0%
+laser beam in this way and a laser beam
+ 
+
+ align:start position:0%
+laser beam in this way and a laser beam
+in that way constrained it in the third
+
+ align:start position:0%
+in that way constrained it in the third
+ 
+
+ align:start position:0%
+in that way constrained it in the third
+dimension hey you've trapped an atom in
+
+ align:start position:0%
+dimension hey you've trapped an atom in
+ 
+
+ align:start position:0%
+dimension hey you've trapped an atom in
+space all right via Photon momentum and
+
+ align:start position:0%
+space all right via Photon momentum and
+ 
+
+ align:start position:0%
+space all right via Photon momentum and
+this is what Steve 2 and and Stanford
+
+ align:start position:0%
+this is what Steve 2 and and Stanford
+ 
+
+ align:start position:0%
+this is what Steve 2 and and Stanford
+and Bill Phillips at nist uh did uh in
+
+ align:start position:0%
+and Bill Phillips at nist uh did uh in
+ 
+
+ align:start position:0%
+and Bill Phillips at nist uh did uh in
+the middle 1990s and received a Nobel
+
+ align:start position:0%
+the middle 1990s and received a Nobel
+ 
+
+ align:start position:0%
+the middle 1990s and received a Nobel
+Prize for this Adam trapping here in uh
+
+ align:start position:0%
+Prize for this Adam trapping here in uh
+ 
+
+ align:start position:0%
+Prize for this Adam trapping here in uh
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1977 no 1997 sorry okay Photon has
+
+ align:start position:0%
+1977 no 1997 sorry okay Photon has
+ 
+
+ align:start position:0%
+1977 no 1997 sorry okay Photon has
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+and the reason this is so important or
+
+ align:start position:0%
+and the reason this is so important or
+ 
+
+ align:start position:0%
+and the reason this is so important or
+the reason this experiment was also so
+
+ align:start position:0%
+the reason this experiment was also so
+ 
+
+ align:start position:0%
+the reason this experiment was also so
+important is because it is the first
+
+ align:start position:0%
+important is because it is the first
+ 
+
+ align:start position:0%
+important is because it is the first
+step in producing a Bose Einstein
+
+ align:start position:0%
+step in producing a Bose Einstein
+ 
+
+ align:start position:0%
+step in producing a Bose Einstein
+condensate a Bose Einstein
+
+ align:start position:0%
+condensate a Bose Einstein
+ 
+
+ align:start position:0%
+condensate a Bose Einstein
+condensate is um where you take an atom
+
+ align:start position:0%
+condensate is um where you take an atom
+ 
+
+ align:start position:0%
+condensate is um where you take an atom
+which has which is a bon actually and
+
+ align:start position:0%
+which has which is a bon actually and
+ 
+
+ align:start position:0%
+which has which is a bon actually and
+you cool it down to such low
+
+ align:start position:0%
+you cool it down to such low
+ 
+
+ align:start position:0%
+you cool it down to such low
+temperatures that they condense that
+
+ align:start position:0%
+temperatures that they condense that
+ 
+
+ align:start position:0%
+temperatures that they condense that
+these atoms condense so you've got to
+
+ align:start position:0%
+these atoms condense so you've got to
+ 
+
+ align:start position:0%
+these atoms condense so you've got to
+cool it down very much so you have to
+
+ align:start position:0%
+cool it down very much so you have to
+ 
+
+ align:start position:0%
+cool it down very much so you have to
+get to the micr Kelvin
+
+ align:start position:0%
+get to the micr Kelvin
+ 
+
+ align:start position:0%
+get to the micr Kelvin
+range and the first step in cooling an
+
+ align:start position:0%
+range and the first step in cooling an
+ 
+
+ align:start position:0%
+range and the first step in cooling an
+atom down is this atom trapping this
+
+ align:start position:0%
+atom down is this atom trapping this
+ 
+
+ align:start position:0%
+atom down is this atom trapping this
+laser atom trapping okay and this will
+
+ align:start position:0%
+laser atom trapping okay and this will
+ 
+
+ align:start position:0%
+laser atom trapping okay and this will
+get you down to Kelvin or a little bit
+
+ align:start position:0%
+get you down to Kelvin or a little bit
+ 
+
+ align:start position:0%
+get you down to Kelvin or a little bit
+lower or so and of course what I mean by
+
+ align:start position:0%
+lower or so and of course what I mean by
+ 
+
+ align:start position:0%
+lower or so and of course what I mean by
+lowering the temperature is that you
+
+ align:start position:0%
+lowering the temperature is that you
+ 
+
+ align:start position:0%
+lowering the temperature is that you
+know I load this atom down right the
+
+ align:start position:0%
+know I load this atom down right the
+ 
+
+ align:start position:0%
+know I load this atom down right the
+temperature of of the gas is related to
+
+ align:start position:0%
+temperature of of the gas is related to
+ 
+
+ align:start position:0%
+temperature of of the gas is related to
+how fast those atoms moving if I slow it
+
+ align:start position:0%
+how fast those atoms moving if I slow it
+ 
+
+ align:start position:0%
+how fast those atoms moving if I slow it
+down I'm cooling the gas right so this
+
+ align:start position:0%
+down I'm cooling the gas right so this
+ 
+
+ align:start position:0%
+down I'm cooling the gas right so this
+here is that first step in getting the
+
+ align:start position:0%
+here is that first step in getting the
+ 
+
+ align:start position:0%
+here is that first step in getting the
+atoms to condense it's the first step in
+
+ align:start position:0%
+atoms to condense it's the first step in
+ 
+
+ align:start position:0%
+atoms to condense it's the first step in
+cooling the gas down then there are many
+
+ align:start position:0%
+cooling the gas down then there are many
+ 
+
+ align:start position:0%
+cooling the gas down then there are many
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+steps and actually the Bine condensate
+
+ align:start position:0%
+steps and actually the Bine condensate
+ 
+
+ align:start position:0%
+steps and actually the Bine condensate
+one of the individuals who
+
+ align:start position:0%
+one of the individuals who
+ 
+
+ align:start position:0%
+one of the individuals who
+accomplish that feat is right here in
+
+ align:start position:0%
+accomplish that feat is right here in
+ 
+
+ align:start position:0%
+accomplish that feat is right here in
+the physics department one of my
+
+ align:start position:0%
+the physics department one of my
+ 
+
+ align:start position:0%
+the physics department one of my
+colleagues wolf Gan K kly many of you
+
+ align:start position:0%
+colleagues wolf Gan K kly many of you
+ 
+
+ align:start position:0%
+colleagues wolf Gan K kly many of you
+will get to meet Wolf Gang kly in fact
+
+ align:start position:0%
+will get to meet Wolf Gang kly in fact
+ 
+
+ align:start position:0%
+will get to meet Wolf Gang kly in fact
+he might even be teaching a section of
+
+ align:start position:0%
+he might even be teaching a section of
+ 
+
+ align:start position:0%
+he might even be teaching a section of
+801 is that right pardon recitation okay
+
+ align:start position:0%
+801 is that right pardon recitation okay
+ 
+
+ align:start position:0%
+801 is that right pardon recitation okay
+all right great maybe he'll tell you
+
+ align:start position:0%
+all right great maybe he'll tell you
+ 
+
+ align:start position:0%
+all right great maybe he'll tell you
+some more about it if he hasn't already
+
+ align:start position:0%
+some more about it if he hasn't already
+ 
+
+ align:start position:0%
+some more about it if he hasn't already
+okay all right so photons have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum so now what have we seen
+
+ align:start position:0%
+momentum so now what have we seen
+ 
+
+ align:start position:0%
+momentum so now what have we seen
+well what we've seen is that radiation
+
+ align:start position:0%
+well what we've seen is that radiation
+ 
+
+ align:start position:0%
+well what we've seen is that radiation
+exhibits both the wav like behavior and
+
+ align:start position:0%
+exhibits both the wav like behavior and
+ 
+
+ align:start position:0%
+exhibits both the wav like behavior and
+this particle like behavior and just in
+
+ align:start position:0%
+this particle like behavior and just in
+ 
+
+ align:start position:0%
+this particle like behavior and just in
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+experiments where the radiation produces
+
+ align:start position:0%
+experiments where the radiation produces
+ 
+
+ align:start position:0%
+experiments where the radiation produces
+a change in matter like the
+
+ align:start position:0%
+a change in matter like the
+ 
+
+ align:start position:0%
+a change in matter like the
+photoelectric effect that's a change in
+
+ align:start position:0%
+photoelectric effect that's a change in
+ 
+
+ align:start position:0%
+photoelectric effect that's a change in
+matter right an electron gets ripped off
+
+ align:start position:0%
+matter right an electron gets ripped off
+ 
+
+ align:start position:0%
+matter right an electron gets ripped off
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+material experiments in which a change
+
+ align:start position:0%
+material experiments in which a change
+ 
+
+ align:start position:0%
+material experiments in which a change
+in the matter uh is affected in that
+
+ align:start position:0%
+in the matter uh is affected in that
+ 
+
+ align:start position:0%
+in the matter uh is affected in that
+case usually the radiation exhibits
+
+ align:start position:0%
+case usually the radiation exhibits
+ 
+
+ align:start position:0%
+case usually the radiation exhibits
+particle like
+
+ align:start position:0%
+particle like
+ 
+
+ align:start position:0%
+particle like
+Behavior experiments in which the
+
+ align:start position:0%
+Behavior experiments in which the
+ 
+
+ align:start position:0%
+Behavior experiments in which the
+radiation interaction results in a
+
+ align:start position:0%
+radiation interaction results in a
+ 
+
+ align:start position:0%
+radiation interaction results in a
+change in the spatial distribution of
+
+ align:start position:0%
+change in the spatial distribution of
+ 
+
+ align:start position:0%
+change in the spatial distribution of
+the radiation well in that case then
+
+ align:start position:0%
+the radiation well in that case then
+ 
+
+ align:start position:0%
+the radiation well in that case then
+radiation exhibits its wavelike uh
+
+ align:start position:0%
+radiation exhibits its wavelike uh
+ 
+
+ align:start position:0%
+radiation exhibits its wavelike uh
+behavior and so you know it's not really
+
+ align:start position:0%
+behavior and so you know it's not really
+ 
+
+ align:start position:0%
+behavior and so you know it's not really
+a proper question or an appropriate
+
+ align:start position:0%
+a proper question or an appropriate
+ 
+
+ align:start position:0%
+a proper question or an appropriate
+question to ask whether light is a
+
+ align:start position:0%
+question to ask whether light is a
+ 
+
+ align:start position:0%
+question to ask whether light is a
+particle or is it a
+
+ align:start position:0%
+particle or is it a
+ 
+
+ align:start position:0%
+particle or is it a
+wave the appropriate question is is to
+
+ align:start position:0%
+wave the appropriate question is is to
+ 
+
+ align:start position:0%
+wave the appropriate question is is to
+ask whether light behaves like a
+
+ align:start position:0%
+ask whether light behaves like a
+ 
+
+ align:start position:0%
+ask whether light behaves like a
+particle or behaves like a wave
+
+ align:start position:0%
+particle or behaves like a wave
+ 
+
+ align:start position:0%
+particle or behaves like a wave
+depending on the particular experimental
+
+ align:start position:0%
+depending on the particular experimental
+ 
+
+ align:start position:0%
+depending on the particular experimental
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+conditions now this kind of wave
+
+ align:start position:0%
+conditions now this kind of wave
+ 
+
+ align:start position:0%
+conditions now this kind of wave
+particle duality or the ability of it to
+
+ align:start position:0%
+particle duality or the ability of it to
+ 
+
+ align:start position:0%
+particle duality or the ability of it to
+behave like a wave or a particle is not
+
+ align:start position:0%
+behave like a wave or a particle is not
+ 
+
+ align:start position:0%
+behave like a wave or a particle is not
+a contradiction it's just the
+
+ align:start position:0%
+a contradiction it's just the
+ 
+
+ align:start position:0%
+a contradiction it's just the
+fundamental nature of light it might
+
+ align:start position:0%
+fundamental nature of light it might
+ 
+
+ align:start position:0%
+fundamental nature of light it might
+seem like a contradiction to you because
+
+ align:start position:0%
+seem like a contradiction to you because
+ 
+
+ align:start position:0%
+seem like a contradiction to you because
+your everyday
+
+ align:start position:0%
+your everyday
+ 
+
+ align:start position:0%
+your everyday
+experience doesn't allow you to see that
+
+ align:start position:0%
+experience doesn't allow you to see that
+ 
+
+ align:start position:0%
+experience doesn't allow you to see that
+both properties can be there your
+
+ align:start position:0%
+both properties can be there your
+ 
+
+ align:start position:0%
+both properties can be there your
+everyday experience says it's a particle
+
+ align:start position:0%
+everyday experience says it's a particle
+ 
+
+ align:start position:0%
+everyday experience says it's a particle
+or it's a wave right but this is a part
+
+ align:start position:0%
+or it's a wave right but this is a part
+ 
+
+ align:start position:0%
+or it's a wave right but this is a part
+of the of nature of our world that you
+
+ align:start position:0%
+of the of nature of our world that you
+ 
+
+ align:start position:0%
+of the of nature of our world that you
+don't have the experience with every
+
+ align:start position:0%
+don't have the experience with every
+ 
+
+ align:start position:0%
+don't have the experience with every
+single day so it seems strange strange
+
+ align:start position:0%
+single day so it seems strange strange
+ 
+
+ align:start position:0%
+single day so it seems strange strange
+but it is the way light works right it's
+
+ align:start position:0%
+but it is the way light works right it's
+ 
+
+ align:start position:0%
+but it is the way light works right it's
+like someone asked me what is the form
+
+ align:start position:0%
+like someone asked me what is the form
+ 
+
+ align:start position:0%
+like someone asked me what is the form
+of a photon and when you ask that
+
+ align:start position:0%
+of a photon and when you ask that
+ 
+
+ align:start position:0%
+of a photon and when you ask that
+question that's fine but you have to
+
+ align:start position:0%
+question that's fine but you have to
+ 
+
+ align:start position:0%
+question that's fine but you have to
+realize what you want for an answer is
+
+ align:start position:0%
+realize what you want for an answer is
+ 
+
+ align:start position:0%
+realize what you want for an answer is
+to draw an analogy between that Photon
+
+ align:start position:0%
+to draw an analogy between that Photon
+ 
+
+ align:start position:0%
+to draw an analogy between that Photon
+and something that you can experience
+
+ align:start position:0%
+and something that you can experience
+ 
+
+ align:start position:0%
+and something that you can experience
+every day and the bottom line is you
+
+ align:start position:0%
+every day and the bottom line is you
+ 
+
+ align:start position:0%
+every day and the bottom line is you
+can't draw that analogy correctly
+
+ align:start position:0%
+can't draw that analogy correctly
+ 
+
+ align:start position:0%
+can't draw that analogy correctly
+because that photon is not not something
+
+ align:start position:0%
+because that photon is not not something
+ 
+
+ align:start position:0%
+because that photon is not not something
+that you can relate correctly to your
+
+ align:start position:0%
+that you can relate correctly to your
+ 
+
+ align:start position:0%
+that you can relate correctly to your
+everyday experience it's a different
+
+ align:start position:0%
+everyday experience it's a different
+ 
+
+ align:start position:0%
+everyday experience it's a different
+part of nature it's just one that you
+
+ align:start position:0%
+part of nature it's just one that you
+ 
+
+ align:start position:0%
+part of nature it's just one that you
+don't see every day so it seems strange
+
+ align:start position:0%
+don't see every day so it seems strange
+ 
+
+ align:start position:0%
+don't see every day so it seems strange
+right so you have to be uh you have to
+
+ align:start position:0%
+right so you have to be uh you have to
+ 
+
+ align:start position:0%
+right so you have to be uh you have to
+be willing to accept kind of new rules
+
+ align:start position:0%
+be willing to accept kind of new rules
+ 
+
+ align:start position:0%
+be willing to accept kind of new rules
+new phenomena that are just outside of
+
+ align:start position:0%
+new phenomena that are just outside of
+ 
+
+ align:start position:0%
+new phenomena that are just outside of
+your everyday experience they're out
+
+ align:start position:0%
+your everyday experience they're out
+ 
+
+ align:start position:0%
+your everyday experience they're out
+there as you delve into nature more more
+
+ align:start position:0%
+there as you delve into nature more more
+ 
+
+ align:start position:0%
+there as you delve into nature more more
+deeply you'll see that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay Okay so we've taken care of
+
+ align:start position:0%
+Okay Okay so we've taken care of
+ 
+
+ align:start position:0%
+Okay Okay so we've taken care of
+radiation the wave particle duality of
+
+ align:start position:0%
+radiation the wave particle duality of
+ 
+
+ align:start position:0%
+radiation the wave particle duality of
+light and matter and now what we've got
+
+ align:start position:0%
+light and matter and now what we've got
+ 
+
+ align:start position:0%
+light and matter and now what we've got
+to do is we got to talk about matter and
+
+ align:start position:0%
+to do is we got to talk about matter and
+ 
+
+ align:start position:0%
+to do is we got to talk about matter and
+we got to talk about its uh wav like
+
+ align:start position:0%
+we got to talk about its uh wav like
+ 
+
+ align:start position:0%
+we got to talk about its uh wav like
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+and also its particle like
+
+ align:start position:0%
+and also its particle like
+ 
+
+ align:start position:0%
+and also its particle like
+properties well its particle like
+
+ align:start position:0%
+properties well its particle like
+ 
+
+ align:start position:0%
+properties well its particle like
+properties um are certainly something
+
+ align:start position:0%
+properties um are certainly something
+ 
+
+ align:start position:0%
+properties um are certainly something
+that is within your everyday experience
+
+ align:start position:0%
+that is within your everyday experience
+ 
+
+ align:start position:0%
+that is within your everyday experience
+right you can understand matter as a
+
+ align:start position:0%
+right you can understand matter as a
+ 
+
+ align:start position:0%
+right you can understand matter as a
+particle what's more difficult to
+
+ align:start position:0%
+particle what's more difficult to
+ 
+
+ align:start position:0%
+particle what's more difficult to
+understand is
+
+ align:start position:0%
+understand is
+ 
+
+ align:start position:0%
+understand is
+matter behaving like a
+
+ align:start position:0%
+matter behaving like a
+ 
+
+ align:start position:0%
+matter behaving like a
+wave so for
+
+ align:start position:0%
+wave so for
+ 
+
+ align:start position:0%
+wave so for
+example if you had uh the situation
+
+ align:start position:0%
+example if you had uh the situation
+ 
+
+ align:start position:0%
+example if you had uh the situation
+where you have a the surface of a nickel
+
+ align:start position:0%
+where you have a the surface of a nickel
+ 
+
+ align:start position:0%
+where you have a the surface of a nickel
+Crystal and what I'm showing you right
+
+ align:start position:0%
+Crystal and what I'm showing you right
+ 
+
+ align:start position:0%
+Crystal and what I'm showing you right
+up here are two nickel atoms just two
+
+ align:start position:0%
+up here are two nickel atoms just two
+ 
+
+ align:start position:0%
+up here are two nickel atoms just two
+nickel atoms of this surface
+
+ align:start position:0%
+nickel atoms of this surface
+ 
+
+ align:start position:0%
+nickel atoms of this surface
+here right and the two nickel atoms are
+
+ align:start position:0%
+here right and the two nickel atoms are
+ 
+
+ align:start position:0%
+here right and the two nickel atoms are
+spaced about 2 * 10us 10 m from each
+
+ align:start position:0%
+spaced about 2 * 10us 10 m from each
+ 
+
+ align:start position:0%
+spaced about 2 * 10us 10 m from each
+other given the lattice spacing of a
+
+ align:start position:0%
+other given the lattice spacing of a
+ 
+
+ align:start position:0%
+other given the lattice spacing of a
+nickel
+
+ align:start position:0%
+nickel
+ 
+
+ align:start position:0%
+nickel
+Crystal and now if I went and I sent
+
+ align:start position:0%
+Crystal and now if I went and I sent
+ 
+
+ align:start position:0%
+Crystal and now if I went and I sent
+electrons into this nickel surface and
+
+ align:start position:0%
+electrons into this nickel surface and
+ 
+
+ align:start position:0%
+electrons into this nickel surface and
+again I'm just showing you two of the
+
+ align:start position:0%
+again I'm just showing you two of the
+ 
+
+ align:start position:0%
+again I'm just showing you two of the
+atoms if I came in with electrons
+
+ align:start position:0%
+atoms if I came in with electrons
+ 
+
+ align:start position:0%
+atoms if I came in with electrons
+electrons are particles you know JJ
+
+ align:start position:0%
+electrons are particles you know JJ
+ 
+
+ align:start position:0%
+electrons are particles you know JJ
+Thompson showed us that and um uh
+
+ align:start position:0%
+Thompson showed us that and um uh
+ 
+
+ align:start position:0%
+Thompson showed us that and um uh
+eventually the mass of those electrons
+
+ align:start position:0%
+eventually the mass of those electrons
+ 
+
+ align:start position:0%
+eventually the mass of those electrons
+was determined but what you might expect
+
+ align:start position:0%
+was determined but what you might expect
+ 
+
+ align:start position:0%
+was determined but what you might expect
+is that those electrons would come in
+
+ align:start position:0%
+is that those electrons would come in
+ 
+
+ align:start position:0%
+is that those electrons would come in
+and then back scatter from these surface
+
+ align:start position:0%
+and then back scatter from these surface
+ 
+
+ align:start position:0%
+and then back scatter from these surface
+atoms and do so in all
+
+ align:start position:0%
+atoms and do so in all
+ 
+
+ align:start position:0%
+atoms and do so in all
+directions so that out here where we
+
+ align:start position:0%
+directions so that out here where we
+ 
+
+ align:start position:0%
+directions so that out here where we
+have a phosphor screen and now that
+
+ align:start position:0%
+have a phosphor screen and now that
+ 
+
+ align:start position:0%
+have a phosphor screen and now that
+screen happens to be curved just so
+
+ align:start position:0%
+screen happens to be curved just so
+ 
+
+ align:start position:0%
+screen happens to be curved just so
+it'll be easier for us to talk about the
+
+ align:start position:0%
+it'll be easier for us to talk about the
+ 
+
+ align:start position:0%
+it'll be easier for us to talk about the
+geometry of this problem here you would
+
+ align:start position:0%
+geometry of this problem here you would
+ 
+
+ align:start position:0%
+geometry of this problem here you would
+you might expect naively that the these
+
+ align:start position:0%
+you might expect naively that the these
+ 
+
+ align:start position:0%
+you might expect naively that the these
+electrons scatter in all Direction and
+
+ align:start position:0%
+electrons scatter in all Direction and
+ 
+
+ align:start position:0%
+electrons scatter in all Direction and
+everywhere where they hit the screen hey
+
+ align:start position:0%
+everywhere where they hit the screen hey
+ 
+
+ align:start position:0%
+everywhere where they hit the screen hey
+the screen lights up
+
+ align:start position:0%
+the screen lights up
+ 
+
+ align:start position:0%
+the screen lights up
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well this is just the experiment that
+
+ align:start position:0%
+well this is just the experiment that
+ 
+
+ align:start position:0%
+well this is just the experiment that
+Davidson and germer did in 1927 along
+
+ align:start position:0%
+Davidson and germer did in 1927 along
+ 
+
+ align:start position:0%
+Davidson and germer did in 1927 along
+with G Thompson George Thompson the son
+
+ align:start position:0%
+with G Thompson George Thompson the son
+ 
+
+ align:start position:0%
+with G Thompson George Thompson the son
+of JJ Thompson actually G Thompson did
+
+ align:start position:0%
+of JJ Thompson actually G Thompson did
+ 
+
+ align:start position:0%
+of JJ Thompson actually G Thompson did
+the experiment in a little different way
+
+ align:start position:0%
+the experiment in a little different way
+ 
+
+ align:start position:0%
+the experiment in a little different way
+than Davidson and gmer but I'm going to
+
+ align:start position:0%
+than Davidson and gmer but I'm going to
+ 
+
+ align:start position:0%
+than Davidson and gmer but I'm going to
+explain the DAV and germer experiment
+
+ align:start position:0%
+explain the DAV and germer experiment
+ 
+
+ align:start position:0%
+explain the DAV and germer experiment
+Here and Now what I've done is I've
+
+ align:start position:0%
+Here and Now what I've done is I've
+ 
+
+ align:start position:0%
+Here and Now what I've done is I've
+taken my nickel atoms and just made them
+
+ align:start position:0%
+taken my nickel atoms and just made them
+ 
+
+ align:start position:0%
+taken my nickel atoms and just made them
+smaller and I did so because I need to
+
+ align:start position:0%
+smaller and I did so because I need to
+ 
+
+ align:start position:0%
+smaller and I did so because I need to
+clean up this uh diagram a little bit
+
+ align:start position:0%
+clean up this uh diagram a little bit
+ 
+
+ align:start position:0%
+clean up this uh diagram a little bit
+for the geometry that we're going to do
+
+ align:start position:0%
+for the geometry that we're going to do
+ 
+
+ align:start position:0%
+for the geometry that we're going to do
+but I've left the lattice spacing
+
+ align:start position:0%
+but I've left the lattice spacing
+ 
+
+ align:start position:0%
+but I've left the lattice spacing
+accurate
+
+ align:start position:0%
+accurate
+ 
+
+ align:start position:0%
+accurate
+here and what Davidson and germer did is
+
+ align:start position:0%
+here and what Davidson and germer did is
+ 
+
+ align:start position:0%
+here and what Davidson and germer did is
+to bring in an electron Beam at 54
+
+ align:start position:0%
+to bring in an electron Beam at 54
+ 
+
+ align:start position:0%
+to bring in an electron Beam at 54
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+bolts and they look to see
+
+ align:start position:0%
+bolts and they look to see
+ 
+
+ align:start position:0%
+bolts and they look to see
+how these electrons scattered back from
+
+ align:start position:0%
+how these electrons scattered back from
+ 
+
+ align:start position:0%
+how these electrons scattered back from
+that surface right onto that screen and
+
+ align:start position:0%
+that surface right onto that screen and
+ 
+
+ align:start position:0%
+that surface right onto that screen and
+lo and behold what they found is that
+
+ align:start position:0%
+lo and behold what they found is that
+ 
+
+ align:start position:0%
+lo and behold what they found is that
+those electrons did not scatter
+
+ align:start position:0%
+those electrons did not scatter
+ 
+
+ align:start position:0%
+those electrons did not scatter
+isotropically they did not go in all
+
+ align:start position:0%
+isotropically they did not go in all
+ 
+
+ align:start position:0%
+isotropically they did not go in all
+directions but there seemed to be a
+
+ align:start position:0%
+directions but there seemed to be a
+ 
+
+ align:start position:0%
+directions but there seemed to be a
+preferred scattering angle
+
+ align:start position:0%
+preferred scattering angle
+ 
+
+ align:start position:0%
+preferred scattering angle
+here and one of those scattering angles
+
+ align:start position:0%
+here and one of those scattering angles
+ 
+
+ align:start position:0%
+here and one of those scattering angles
+right here is um 50 7° so this angle
+
+ align:start position:0%
+right here is um 50 7° so this angle
+ 
+
+ align:start position:0%
+right here is um 50 7° so this angle
+right in here that's the angle from the
+
+ align:start position:0%
+right in here that's the angle from the
+ 
+
+ align:start position:0%
+right in here that's the angle from the
+surface normal to the direction in which
+
+ align:start position:0%
+surface normal to the direction in which
+ 
+
+ align:start position:0%
+surface normal to the direction in which
+this electron scatters right so they
+
+ align:start position:0%
+this electron scatters right so they
+ 
+
+ align:start position:0%
+this electron scatters right so they
+observed some scattered intensity lots
+
+ align:start position:0%
+observed some scattered intensity lots
+ 
+
+ align:start position:0%
+observed some scattered intensity lots
+of electron flux at this angle here
+
+ align:start position:0%
+of electron flux at this angle here
+ 
+
+ align:start position:0%
+of electron flux at this angle here
+about 50.7
+
+ align:start position:0%
+about 50.7
+ 
+
+ align:start position:0%
+about 50.7
+degrees and they observed a lot of
+
+ align:start position:0%
+degrees and they observed a lot of
+ 
+
+ align:start position:0%
+degrees and they observed a lot of
+intensity right at the normal angle
+
+ align:start position:0%
+intensity right at the normal angle
+ 
+
+ align:start position:0%
+intensity right at the normal angle
+right here so the electron comes in and
+
+ align:start position:0%
+right here so the electron comes in and
+ 
+
+ align:start position:0%
+right here so the electron comes in and
+scatters right
+
+ align:start position:0%
+scatters right
+ 
+
+ align:start position:0%
+scatters right
+back and and depending on the uh
+
+ align:start position:0%
+back and and depending on the uh
+ 
+
+ align:start position:0%
+back and and depending on the uh
+experimental conditions they observe
+
+ align:start position:0%
+experimental conditions they observe
+ 
+
+ align:start position:0%
+experimental conditions they observe
+some intensity at a very large
+
+ align:start position:0%
+some intensity at a very large
+ 
+
+ align:start position:0%
+some intensity at a very large
+scattering angle here all right what
+
+ align:start position:0%
+scattering angle here all right what
+ 
+
+ align:start position:0%
+scattering angle here all right what
+does this look like hey it looks like
+
+ align:start position:0%
+does this look like hey it looks like
+ 
+
+ align:start position:0%
+does this look like hey it looks like
+interference phenomena right looks like
+
+ align:start position:0%
+interference phenomena right looks like
+ 
+
+ align:start position:0%
+interference phenomena right looks like
+the results of the two slit experiment
+
+ align:start position:0%
+the results of the two slit experiment
+ 
+
+ align:start position:0%
+the results of the two slit experiment
+that we did there's a very bright
+
+ align:start position:0%
+that we did there's a very bright
+ 
+
+ align:start position:0%
+that we did there's a very bright
+spot most very intense spot right in the
+
+ align:start position:0%
+spot most very intense spot right in the
+ 
+
+ align:start position:0%
+spot most very intense spot right in the
+center then there's a dark spot then
+
+ align:start position:0%
+center then there's a dark spot then
+ 
+
+ align:start position:0%
+center then there's a dark spot then
+there's a very intense spot then there's
+
+ align:start position:0%
+there's a very intense spot then there's
+ 
+
+ align:start position:0%
+there's a very intense spot then there's
+a dark spot then another intense spot
+
+ align:start position:0%
+a dark spot then another intense spot
+ 
+
+ align:start position:0%
+a dark spot then another intense spot
+hey looks like interference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phenomena well let's see if we can
+
+ align:start position:0%
+phenomena well let's see if we can
+ 
+
+ align:start position:0%
+phenomena well let's see if we can
+understand that interference
+
+ align:start position:0%
+understand that interference
+ 
+
+ align:start position:0%
+understand that interference
+phenomena so here's that same diagram I
+
+ align:start position:0%
+phenomena so here's that same diagram I
+ 
+
+ align:start position:0%
+phenomena so here's that same diagram I
+just uh cleaned it up a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit and um so what we're doing in the
+
+ align:start position:0%
+bit and um so what we're doing in the
+ 
+
+ align:start position:0%
+bit and um so what we're doing in the
+experiment is we're bringing in a
+
+ align:start position:0%
+experiment is we're bringing in a
+ 
+
+ align:start position:0%
+experiment is we're bringing in a
+continuous stream of electrons and
+
+ align:start position:0%
+continuous stream of electrons and
+ 
+
+ align:start position:0%
+continuous stream of electrons and
+here's my continuous stream of elect
+
+ align:start position:0%
+here's my continuous stream of elect
+ 
+
+ align:start position:0%
+here's my continuous stream of elect
+Rons and I'm only showing you two
+
+ align:start position:0%
+Rons and I'm only showing you two
+ 
+
+ align:start position:0%
+Rons and I'm only showing you two
+atoms but the same thing's happening on
+
+ align:start position:0%
+atoms but the same thing's happening on
+ 
+
+ align:start position:0%
+atoms but the same thing's happening on
+a lot of
+
+ align:start position:0%
+a lot of
+ 
+
+ align:start position:0%
+a lot of
+atoms all right so what it looks like is
+
+ align:start position:0%
+atoms all right so what it looks like is
+ 
+
+ align:start position:0%
+atoms all right so what it looks like is
+that these electrons are coming in and
+
+ align:start position:0%
+that these electrons are coming in and
+ 
+
+ align:start position:0%
+that these electrons are coming in and
+then each one of these atoms are kind of
+
+ align:start position:0%
+then each one of these atoms are kind of
+ 
+
+ align:start position:0%
+then each one of these atoms are kind of
+acting like a point
+
+ align:start position:0%
+acting like a point
+ 
+
+ align:start position:0%
+acting like a point
+source reflecting the electrons
+
+ align:start position:0%
+source reflecting the electrons
+ 
+
+ align:start position:0%
+source reflecting the electrons
+isotropically as a wave right that is
+
+ align:start position:0%
+isotropically as a wave right that is
+ 
+
+ align:start position:0%
+isotropically as a wave right that is
+that there's a wave that's emanating out
+
+ align:start position:0%
+that there's a wave that's emanating out
+ 
+
+ align:start position:0%
+that there's a wave that's emanating out
+from each one of these atoms all right
+
+ align:start position:0%
+from each one of these atoms all right
+ 
+
+ align:start position:0%
+from each one of these atoms all right
+and of course as time goes on that
+
+ align:start position:0%
+and of course as time goes on that
+ 
+
+ align:start position:0%
+and of course as time goes on that
+propagates out and then another
+
+ align:start position:0%
+propagates out and then another
+ 
+
+ align:start position:0%
+propagates out and then another
+wavefront another maximum emanates out
+
+ align:start position:0%
+wavefront another maximum emanates out
+ 
+
+ align:start position:0%
+wavefront another maximum emanates out
+and of course the distance between these
+
+ align:start position:0%
+and of course the distance between these
+ 
+
+ align:start position:0%
+and of course the distance between these
+two Maxima is the
+
+ align:start position:0%
+two Maxima is the
+ 
+
+ align:start position:0%
+two Maxima is the
+wavelength right because this is the
+
+ align:start position:0%
+wavelength right because this is the
+ 
+
+ align:start position:0%
+wavelength right because this is the
+maximum wavefront here's another one
+
+ align:start position:0%
+maximum wavefront here's another one
+ 
+
+ align:start position:0%
+maximum wavefront here's another one
+with time it can continues to emanate
+
+ align:start position:0%
+with time it can continues to emanate
+ 
+
+ align:start position:0%
+with time it can continues to emanate
+out with time it continues to emanate
+
+ align:start position:0%
+out with time it continues to emanate
+ 
+
+ align:start position:0%
+out with time it continues to emanate
+out as long as we are uh throwing
+
+ align:start position:0%
+out as long as we are uh throwing
+ 
+
+ align:start position:0%
+out as long as we are uh throwing
+electrons at that nickel Crystal and it
+
+ align:start position:0%
+electrons at that nickel Crystal and it
+ 
+
+ align:start position:0%
+electrons at that nickel Crystal and it
+continues to eminate out until it gets
+
+ align:start position:0%
+continues to eminate out until it gets
+ 
+
+ align:start position:0%
+continues to eminate out until it gets
+to the screen and then we see some
+
+ align:start position:0%
+to the screen and then we see some
+ 
+
+ align:start position:0%
+to the screen and then we see some
+bright dark bright dark bright spots
+
+ align:start position:0%
+bright dark bright dark bright spots
+ 
+
+ align:start position:0%
+bright dark bright dark bright spots
+okay hey looks just like the two slit
+
+ align:start position:0%
+okay hey looks just like the two slit
+ 
+
+ align:start position:0%
+okay hey looks just like the two slit
+experiment and now if we go to analyze
+
+ align:start position:0%
+experiment and now if we go to analyze
+ 
+
+ align:start position:0%
+experiment and now if we go to analyze
+this and again this is the same drawing
+
+ align:start position:0%
+this and again this is the same drawing
+ 
+
+ align:start position:0%
+this and again this is the same drawing
+I just cleaned it up a little a little
+
+ align:start position:0%
+I just cleaned it up a little a little
+ 
+
+ align:start position:0%
+I just cleaned it up a little a little
+bit if you look at this point right here
+
+ align:start position:0%
+bit if you look at this point right here
+ 
+
+ align:start position:0%
+bit if you look at this point right here
+what do you see well you see the maximum
+
+ align:start position:0%
+what do you see well you see the maximum
+ 
+
+ align:start position:0%
+what do you see well you see the maximum
+of a wave scattered from atom one at the
+
+ align:start position:0%
+of a wave scattered from atom one at the
+ 
+
+ align:start position:0%
+of a wave scattered from atom one at the
+same point in space as the maximum of
+
+ align:start position:0%
+same point in space as the maximum of
+ 
+
+ align:start position:0%
+same point in space as the maximum of
+the wave scattered from atom
+
+ align:start position:0%
+the wave scattered from atom
+ 
+
+ align:start position:0%
+the wave scattered from atom
+two hey constructive
+
+ align:start position:0%
+two hey constructive
+ 
+
+ align:start position:0%
+two hey constructive
+interference next Point here again two
+
+ align:start position:0%
+interference next Point here again two
+ 
+
+ align:start position:0%
+interference next Point here again two
+Maxima the same point in space
+
+ align:start position:0%
+Maxima the same point in space
+ 
+
+ align:start position:0%
+Maxima the same point in space
+constructive interference here two
+
+ align:start position:0%
+constructive interference here two
+ 
+
+ align:start position:0%
+constructive interference here two
+maximum same point in space constructive
+
+ align:start position:0%
+maximum same point in space constructive
+ 
+
+ align:start position:0%
+maximum same point in space constructive
+interference everywhere along that line
+
+ align:start position:0%
+interference everywhere along that line
+ 
+
+ align:start position:0%
+interference everywhere along that line
+we have constructive interference and so
+
+ align:start position:0%
+we have constructive interference and so
+ 
+
+ align:start position:0%
+we have constructive interference and so
+if you project out to the screen you're
+
+ align:start position:0%
+if you project out to the screen you're
+ 
+
+ align:start position:0%
+if you project out to the screen you're
+going to have a bright spot there you're
+
+ align:start position:0%
+going to have a bright spot there you're
+ 
+
+ align:start position:0%
+going to have a bright spot there you're
+going to have electrons being scattered
+
+ align:start position:0%
+going to have electrons being scattered
+ 
+
+ align:start position:0%
+going to have electrons being scattered
+right in that angle
+
+ align:start position:0%
+right in that angle
+ 
+
+ align:start position:0%
+right in that angle
+okay and now we know we talked about
+
+ align:start position:0%
+okay and now we know we talked about
+ 
+
+ align:start position:0%
+okay and now we know we talked about
+last time what the condition was from
+
+ align:start position:0%
+last time what the condition was from
+ 
+
+ align:start position:0%
+last time what the condition was from
+for constructive
+
+ align:start position:0%
+for constructive
+ 
+
+ align:start position:0%
+for constructive
+interference and the condition is that
+
+ align:start position:0%
+interference and the condition is that
+ 
+
+ align:start position:0%
+interference and the condition is that
+the difference in the distance travel by
+
+ align:start position:0%
+the difference in the distance travel by
+ 
+
+ align:start position:0%
+the difference in the distance travel by
+the two waves that are constructively
+
+ align:start position:0%
+the two waves that are constructively
+ 
+
+ align:start position:0%
+the two waves that are constructively
+interfering and now I use the letters d
+
+ align:start position:0%
+interfering and now I use the letters d
+ 
+
+ align:start position:0%
+interfering and now I use the letters d
+instead of R okay but the difference in
+
+ align:start position:0%
+instead of R okay but the difference in
+ 
+
+ align:start position:0%
+instead of R okay but the difference in
+the distance has to be equal to an
+
+ align:start position:0%
+the distance has to be equal to an
+ 
+
+ align:start position:0%
+the distance has to be equal to an
+integral multiple of the
+
+ align:start position:0%
+integral multiple of the
+ 
+
+ align:start position:0%
+integral multiple of the
+wavelength and if you analyzed this line
+
+ align:start position:0%
+wavelength and if you analyzed this line
+ 
+
+ align:start position:0%
+wavelength and if you analyzed this line
+here of constructive interference you'd
+
+ align:start position:0%
+here of constructive interference you'd
+ 
+
+ align:start position:0%
+here of constructive interference you'd
+find it was n equal one the difference
+
+ align:start position:0%
+find it was n equal one the difference
+ 
+
+ align:start position:0%
+find it was n equal one the difference
+in the distance traveled was one Lambda
+
+ align:start position:0%
+in the distance traveled was one Lambda
+ 
+
+ align:start position:0%
+in the distance traveled was one Lambda
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right and over here you can see a a row
+
+ align:start position:0%
+right and over here you can see a a row
+ 
+
+ align:start position:0%
+right and over here you can see a a row
+of constructive
+
+ align:start position:0%
+of constructive
+ 
+
+ align:start position:0%
+of constructive
+interference and if you Analyze This
+
+ align:start position:0%
+interference and if you Analyze This
+ 
+
+ align:start position:0%
+interference and if you Analyze This
+constructive interference you would find
+
+ align:start position:0%
+constructive interference you would find
+ 
+
+ align:start position:0%
+constructive interference you would find
+the difference in the distance traveled
+
+ align:start position:0%
+the difference in the distance traveled
+ 
+
+ align:start position:0%
+the difference in the distance traveled
+was 2 Lambda this is our second order
+
+ align:start position:0%
+was 2 Lambda this is our second order
+ 
+
+ align:start position:0%
+was 2 Lambda this is our second order
+defraction spot or second or order
+
+ align:start position:0%
+defraction spot or second or order
+ 
+
+ align:start position:0%
+defraction spot or second or order
+interference feature and then of course
+
+ align:start position:0%
+interference feature and then of course
+ 
+
+ align:start position:0%
+interference feature and then of course
+we have the zero order interference
+
+ align:start position:0%
+we have the zero order interference
+ 
+
+ align:start position:0%
+we have the zero order interference
+feature hey these electrons are behaving
+
+ align:start position:0%
+feature hey these electrons are behaving
+ 
+
+ align:start position:0%
+feature hey these electrons are behaving
+like waves right it's constructive and
+
+ align:start position:0%
+like waves right it's constructive and
+ 
+
+ align:start position:0%
+like waves right it's constructive and
+destructive
+
+ align:start position:0%
+destructive
+ 
+
+ align:start position:0%
+destructive
+interference now what we're going to
+
+ align:start position:0%
+interference now what we're going to
+ 
+
+ align:start position:0%
+interference now what we're going to
+do is that we're going to analyze the
+
+ align:start position:0%
+do is that we're going to analyze the
+ 
+
+ align:start position:0%
+do is that we're going to analyze the
+geometry of this setup a little bit more
+
+ align:start position:0%
+geometry of this setup a little bit more
+ 
+
+ align:start position:0%
+geometry of this setup a little bit more
+we didn't do this for the two slit
+
+ align:start position:0%
+we didn't do this for the two slit
+ 
+
+ align:start position:0%
+we didn't do this for the two slit
+experiment with light we could have but
+
+ align:start position:0%
+experiment with light we could have but
+ 
+
+ align:start position:0%
+experiment with light we could have but
+we didn't we're going to do it here for
+
+ align:start position:0%
+we didn't we're going to do it here for
+ 
+
+ align:start position:0%
+we didn't we're going to do it here for
+the electron scattering it's really the
+
+ align:start position:0%
+the electron scattering it's really the
+ 
+
+ align:start position:0%
+the electron scattering it's really the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+thing and um we're going to do it just
+
+ align:start position:0%
+thing and um we're going to do it just
+ 
+
+ align:start position:0%
+thing and um we're going to do it just
+like Davidson and germer did it because
+
+ align:start position:0%
+like Davidson and germer did it because
+ 
+
+ align:start position:0%
+like Davidson and germer did it because
+from this
+
+ align:start position:0%
+from this
+ 
+
+ align:start position:0%
+from this
+analysis in particular from knowing what
+
+ align:start position:0%
+analysis in particular from knowing what
+ 
+
+ align:start position:0%
+analysis in particular from knowing what
+the scattering angle is this is the
+
+ align:start position:0%
+the scattering angle is this is the
+ 
+
+ align:start position:0%
+the scattering angle is this is the
+quantity that Davidson and germer wanted
+
+ align:start position:0%
+quantity that Davidson and germer wanted
+ 
+
+ align:start position:0%
+quantity that Davidson and germer wanted
+to measure right or we're really
+
+ align:start position:0%
+to measure right or we're really
+ 
+
+ align:start position:0%
+to measure right or we're really
+interested in this scattering angle
+
+ align:start position:0%
+interested in this scattering angle
+ 
+
+ align:start position:0%
+interested in this scattering angle
+which turns out to be 50.7 degrees for
+
+ align:start position:0%
+which turns out to be 50.7 degrees for
+ 
+
+ align:start position:0%
+which turns out to be 50.7 degrees for
+this first order defraction
+
+ align:start position:0%
+this first order defraction
+ 
+
+ align:start position:0%
+this first order defraction
+beam we're going to use
+
+ align:start position:0%
+beam we're going to use
+ 
+
+ align:start position:0%
+beam we're going to use
+that knowledge to calculate the
+
+ align:start position:0%
+that knowledge to calculate the
+ 
+
+ align:start position:0%
+that knowledge to calculate the
+wavelength of the electrons that's what
+
+ align:start position:0%
+wavelength of the electrons that's what
+ 
+
+ align:start position:0%
+wavelength of the electrons that's what
+we're we're aiming for
+
+ align:start position:0%
+we're we're aiming for
+ 
+
+ align:start position:0%
+we're we're aiming for
+here and we're going to do that because
+
+ align:start position:0%
+here and we're going to do that because
+ 
+
+ align:start position:0%
+here and we're going to do that because
+of this known condition right for
+
+ align:start position:0%
+of this known condition right for
+ 
+
+ align:start position:0%
+of this known condition right for
+constructive interference that the
+
+ align:start position:0%
+constructive interference that the
+ 
+
+ align:start position:0%
+constructive interference that the
+difference in the distance traveled by
+
+ align:start position:0%
+difference in the distance traveled by
+ 
+
+ align:start position:0%
+difference in the distance traveled by
+the two waves that gives the
+
+ align:start position:0%
+the two waves that gives the
+ 
+
+ align:start position:0%
+the two waves that gives the
+constructive interference has to be an
+
+ align:start position:0%
+constructive interference has to be an
+ 
+
+ align:start position:0%
+constructive interference has to be an
+integral multiple of the
+
+ align:start position:0%
+integral multiple of the
+ 
+
+ align:start position:0%
+integral multiple of the
+wavelength all right that's where we're
+
+ align:start position:0%
+wavelength all right that's where we're
+ 
+
+ align:start position:0%
+wavelength all right that's where we're
+headed so now see this line from atom
+
+ align:start position:0%
+headed so now see this line from atom
+ 
+
+ align:start position:0%
+headed so now see this line from atom
+number two to the screen I called it D2
+
+ align:start position:0%
+number two to the screen I called it D2
+ 
+
+ align:start position:0%
+number two to the screen I called it D2
+D2 is the length of that line it's the
+
+ align:start position:0%
+D2 is the length of that line it's the
+ 
+
+ align:start position:0%
+D2 is the length of that line it's the
+distance that the wave has traveled from
+
+ align:start position:0%
+distance that the wave has traveled from
+ 
+
+ align:start position:0%
+distance that the wave has traveled from
+atom two to the
+
+ align:start position:0%
+atom two to the
+ 
+
+ align:start position:0%
+atom two to the
+screen D1 is the distance that the wav
+
+ align:start position:0%
+screen D1 is the distance that the wav
+ 
+
+ align:start position:0%
+screen D1 is the distance that the wav
+scattered from atom one has traveled to
+
+ align:start position:0%
+scattered from atom one has traveled to
+ 
+
+ align:start position:0%
+scattered from atom one has traveled to
+the screen all
+
+ align:start position:0%
+the screen all
+ 
+
+ align:start position:0%
+the screen all
+right now I'm going to draw a
+
+ align:start position:0%
+right now I'm going to draw a
+ 
+
+ align:start position:0%
+right now I'm going to draw a
+perpendicular right here all right I'm
+
+ align:start position:0%
+perpendicular right here all right I'm
+ 
+
+ align:start position:0%
+perpendicular right here all right I'm
+going to draw a perpendicular from atom
+
+ align:start position:0%
+going to draw a perpendicular from atom
+ 
+
+ align:start position:0%
+going to draw a perpendicular from atom
+one to this line 2 here's the right
+
+ align:start position:0%
+one to this line 2 here's the right
+ 
+
+ align:start position:0%
+one to this line 2 here's the right
+angle that's really nice because look at
+
+ align:start position:0%
+angle that's really nice because look at
+ 
+
+ align:start position:0%
+angle that's really nice because look at
+what this leg of the triangle is then
+
+ align:start position:0%
+what this leg of the triangle is then
+ 
+
+ align:start position:0%
+what this leg of the triangle is then
+it's D2 minus D1 hey that's a quantity
+
+ align:start position:0%
+it's D2 minus D1 hey that's a quantity
+ 
+
+ align:start position:0%
+it's D2 minus D1 hey that's a quantity
+that's going to be interesting to us
+
+ align:start position:0%
+that's going to be interesting to us
+ 
+
+ align:start position:0%
+that's going to be interesting to us
+okay all right now what you have to do
+
+ align:start position:0%
+okay all right now what you have to do
+ 
+
+ align:start position:0%
+okay all right now what you have to do
+is you have to convince yourself that
+
+ align:start position:0%
+is you have to convince yourself that
+ 
+
+ align:start position:0%
+is you have to convince yourself that
+this angle right in here in this
+
+ align:start position:0%
+this angle right in here in this
+ 
+
+ align:start position:0%
+this angle right in here in this
+triangle is equal to this scattering
+
+ align:start position:0%
+triangle is equal to this scattering
+ 
+
+ align:start position:0%
+triangle is equal to this scattering
+angle Theta all right if you're good at
+
+ align:start position:0%
+angle Theta all right if you're good at
+ 
+
+ align:start position:0%
+angle Theta all right if you're good at
+geometry you can see that
+
+ align:start position:0%
+geometry you can see that
+ 
+
+ align:start position:0%
+geometry you can see that
+immediately or you might have to think
+
+ align:start position:0%
+immediately or you might have to think
+ 
+
+ align:start position:0%
+immediately or you might have to think
+about it a little bit but it is equal to
+
+ align:start position:0%
+about it a little bit but it is equal to
+ 
+
+ align:start position:0%
+about it a little bit but it is equal to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay well that's good because now I got
+
+ align:start position:0%
+okay well that's good because now I got
+ 
+
+ align:start position:0%
+okay well that's good because now I got
+a triangle right here and I know the
+
+ align:start position:0%
+a triangle right here and I know the
+ 
+
+ align:start position:0%
+a triangle right here and I know the
+length of one side that's the distance
+
+ align:start position:0%
+length of one side that's the distance
+ 
+
+ align:start position:0%
+length of one side that's the distance
+the spacing between the two nickel atoms
+
+ align:start position:0%
+the spacing between the two nickel atoms
+ 
+
+ align:start position:0%
+the spacing between the two nickel atoms
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+Crystal and um I know what Theta is
+
+ align:start position:0%
+Crystal and um I know what Theta is
+ 
+
+ align:start position:0%
+Crystal and um I know what Theta is
+because that's what Davidson and germer
+
+ align:start position:0%
+because that's what Davidson and germer
+ 
+
+ align:start position:0%
+because that's what Davidson and germer
+measure it's pretty good I can use that
+
+ align:start position:0%
+measure it's pretty good I can use that
+ 
+
+ align:start position:0%
+measure it's pretty good I can use that
+uh I can use this geometry to say that
+
+ align:start position:0%
+uh I can use this geometry to say that
+ 
+
+ align:start position:0%
+uh I can use this geometry to say that
+sin Theta is equal to the opposite the
+
+ align:start position:0%
+sin Theta is equal to the opposite the
+ 
+
+ align:start position:0%
+sin Theta is equal to the opposite the
+length of the opposite side D2 minus D1
+
+ align:start position:0%
+length of the opposite side D2 minus D1
+ 
+
+ align:start position:0%
+length of the opposite side D2 minus D1
+over the hypotenuse
+
+ align:start position:0%
+over the hypotenuse
+ 
+
+ align:start position:0%
+over the hypotenuse
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+okay and now if this is the condition
+
+ align:start position:0%
+okay and now if this is the condition
+ 
+
+ align:start position:0%
+okay and now if this is the condition
+that has to obtain to have constructive
+
+ align:start position:0%
+that has to obtain to have constructive
+ 
+
+ align:start position:0%
+that has to obtain to have constructive
+interference and then this
+
+ align:start position:0%
+interference and then this
+ 
+
+ align:start position:0%
+interference and then this
+expression is comes from the geometry of
+
+ align:start position:0%
+expression is comes from the geometry of
+ 
+
+ align:start position:0%
+expression is comes from the geometry of
+the problem that I'm solving so this is
+
+ align:start position:0%
+the problem that I'm solving so this is
+ 
+
+ align:start position:0%
+the problem that I'm solving so this is
+the theory this is the geometry of the
+
+ align:start position:0%
+the theory this is the geometry of the
+ 
+
+ align:start position:0%
+the theory this is the geometry of the
+problem I'm solving well then n Lambda
+
+ align:start position:0%
+problem I'm solving well then n Lambda
+ 
+
+ align:start position:0%
+problem I'm solving well then n Lambda
+has to be equal to a sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta and therefore I can rearrange that
+
+ align:start position:0%
+Theta and therefore I can rearrange that
+ 
+
+ align:start position:0%
+Theta and therefore I can rearrange that
+to get Lambda Lambda is equal to a sin
+
+ align:start position:0%
+to get Lambda Lambda is equal to a sin
+ 
+
+ align:start position:0%
+to get Lambda Lambda is equal to a sin
+Theta /
+
+ align:start position:0%
+Theta /
+ 
+
+ align:start position:0%
+Theta /
+n and now I can use this information
+
+ align:start position:0%
+n and now I can use this information
+ 
+
+ align:start position:0%
+n and now I can use this information
+here to calculate what Lambda is all
+
+ align:start position:0%
+here to calculate what Lambda is all
+ 
+
+ align:start position:0%
+here to calculate what Lambda is all
+right I know that the scattering angle
+
+ align:start position:0%
+right I know that the scattering angle
+ 
+
+ align:start position:0%
+right I know that the scattering angle
+is 50.7
+
+ align:start position:0%
+is 50.7
+ 
+
+ align:start position:0%
+is 50.7
+De I know what n is it's the first order
+
+ align:start position:0%
+De I know what n is it's the first order
+ 
+
+ align:start position:0%
+De I know what n is it's the first order
+defraction feature because it is the
+
+ align:start position:0%
+defraction feature because it is the
+ 
+
+ align:start position:0%
+defraction feature because it is the
+most intense spot that's closest to the
+
+ align:start position:0%
+most intense spot that's closest to the
+ 
+
+ align:start position:0%
+most intense spot that's closest to the
+zero order the zero order is always
+
+ align:start position:0%
+zero order the zero order is always
+ 
+
+ align:start position:0%
+zero order the zero order is always
+going to be normal to your sample normal
+
+ align:start position:0%
+going to be normal to your sample normal
+ 
+
+ align:start position:0%
+going to be normal to your sample normal
+to the crystal all right so therefore I
+
+ align:start position:0%
+to the crystal all right so therefore I
+ 
+
+ align:start position:0%
+to the crystal all right so therefore I
+can plug some numbers in there and I get
+
+ align:start position:0%
+can plug some numbers in there and I get
+ 
+
+ align:start position:0%
+can plug some numbers in there and I get
+for the wavelength 1.66 * 10us 10
+
+ align:start position:0%
+for the wavelength 1.66 * 10us 10
+ 
+
+ align:start position:0%
+for the wavelength 1.66 * 10us 10
+m all right so this experiment says that
+
+ align:start position:0%
+m all right so this experiment says that
+ 
+
+ align:start position:0%
+m all right so this experiment says that
+if you have electrons that are 54 EV in
+
+ align:start position:0%
+if you have electrons that are 54 EV in
+ 
+
+ align:start position:0%
+if you have electrons that are 54 EV in
+energy the wavelength of those electrons
+
+ align:start position:0%
+energy the wavelength of those electrons
+ 
+
+ align:start position:0%
+energy the wavelength of those electrons
+is 1.66 * 10 - 10
+
+ align:start position:0%
+is 1.66 * 10 - 10
+ 
+
+ align:start position:0%
+is 1.66 * 10 - 10
+m okay so Davidson germer and Thompson
+
+ align:start position:0%
+m okay so Davidson germer and Thompson
+ 
+
+ align:start position:0%
+m okay so Davidson germer and Thompson
+hey not only did they demonstrate the
+
+ align:start position:0%
+hey not only did they demonstrate the
+ 
+
+ align:start position:0%
+hey not only did they demonstrate the
+interference phenomena of
+
+ align:start position:0%
+interference phenomena of
+ 
+
+ align:start position:0%
+interference phenomena of
+particles right particles that had Mass
+
+ align:start position:0%
+particles right particles that had Mass
+ 
+
+ align:start position:0%
+particles right particles that had Mass
+but but they were able to calculate from
+
+ align:start position:0%
+but but they were able to calculate from
+ 
+
+ align:start position:0%
+but but they were able to calculate from
+that experiment the wavelength the
+
+ align:start position:0%
+that experiment the wavelength the
+ 
+
+ align:start position:0%
+that experiment the wavelength the
+corresponding
+
+ align:start position:0%
+corresponding
+ 
+
+ align:start position:0%
+corresponding
+wavelength all right but now I just want
+
+ align:start position:0%
+wavelength all right but now I just want
+ 
+
+ align:start position:0%
+wavelength all right but now I just want
+to take a moment as an
+
+ align:start position:0%
+to take a moment as an
+ 
+
+ align:start position:0%
+to take a moment as an
+aside to tell you that this geometry
+
+ align:start position:0%
+aside to tell you that this geometry
+ 
+
+ align:start position:0%
+aside to tell you that this geometry
+that I Illustrated right here is the
+
+ align:start position:0%
+that I Illustrated right here is the
+ 
+
+ align:start position:0%
+that I Illustrated right here is the
+identical
+
+ align:start position:0%
+identical
+ 
+
+ align:start position:0%
+identical
+geometry that uh is used in x-ray
+
+ align:start position:0%
+geometry that uh is used in x-ray
+ 
+
+ align:start position:0%
+geometry that uh is used in x-ray
+defraction x-ray defraction is the
+
+ align:start position:0%
+defraction x-ray defraction is the
+ 
+
+ align:start position:0%
+defraction x-ray defraction is the
+interference or the defraction of x-rays
+
+ align:start position:0%
+interference or the defraction of x-rays
+ 
+
+ align:start position:0%
+interference or the defraction of x-rays
+photon
+
+ align:start position:0%
+photon
+ 
+
+ align:start position:0%
+photon
+right this is electron
+
+ align:start position:0%
+right this is electron
+ 
+
+ align:start position:0%
+right this is electron
+defraction but the geometries are the
+
+ align:start position:0%
+defraction but the geometries are the
+ 
+
+ align:start position:0%
+defraction but the geometries are the
+same the concepts are the same but the
+
+ align:start position:0%
+same the concepts are the same but the
+ 
+
+ align:start position:0%
+same the concepts are the same but the
+reason I bring up x-ray defraction is
+
+ align:start position:0%
+reason I bring up x-ray defraction is
+ 
+
+ align:start position:0%
+reason I bring up x-ray defraction is
+because it's a very important technique
+
+ align:start position:0%
+because it's a very important technique
+ 
+
+ align:start position:0%
+because it's a very important technique
+for you in your future whether you're
+
+ align:start position:0%
+for you in your future whether you're
+ 
+
+ align:start position:0%
+for you in your future whether you're
+going to be looking at materials to get
+
+ align:start position:0%
+going to be looking at materials to get
+ 
+
+ align:start position:0%
+going to be looking at materials to get
+the structure
+
+ align:start position:0%
+the structure
+ 
+
+ align:start position:0%
+the structure
+materials or whether you're going to be
+
+ align:start position:0%
+materials or whether you're going to be
+ 
+
+ align:start position:0%
+materials or whether you're going to be
+doing some kind of biological chemistry
+
+ align:start position:0%
+doing some kind of biological chemistry
+ 
+
+ align:start position:0%
+doing some kind of biological chemistry
+because x-ray
+
+ align:start position:0%
+because x-ray
+ 
+
+ align:start position:0%
+because x-ray
+defraction is used to get structures
+
+ align:start position:0%
+defraction is used to get structures
+ 
+
+ align:start position:0%
+defraction is used to get structures
+Crystal structures particularly of
+
+ align:start position:0%
+Crystal structures particularly of
+ 
+
+ align:start position:0%
+Crystal structures particularly of
+proteins and the reason why you want to
+
+ align:start position:0%
+proteins and the reason why you want to
+ 
+
+ align:start position:0%
+proteins and the reason why you want to
+know the structure of a protein is
+
+ align:start position:0%
+know the structure of a protein is
+ 
+
+ align:start position:0%
+know the structure of a protein is
+because that structure does give you
+
+ align:start position:0%
+because that structure does give you
+ 
+
+ align:start position:0%
+because that structure does give you
+some hints as to what the function of
+
+ align:start position:0%
+some hints as to what the function of
+ 
+
+ align:start position:0%
+some hints as to what the function of
+the protein is
+
+ align:start position:0%
+the protein is
+ 
+
+ align:start position:0%
+the protein is
+right and actually Professor drenan
+
+ align:start position:0%
+right and actually Professor drenan
+ 
+
+ align:start position:0%
+right and actually Professor drenan
+who's going to lecture the second half
+
+ align:start position:0%
+who's going to lecture the second half
+ 
+
+ align:start position:0%
+who's going to lecture the second half
+of the course that's her specialty is
+
+ align:start position:0%
+of the course that's her specialty is
+ 
+
+ align:start position:0%
+of the course that's her specialty is
+x-ray defraction of uh Pro uh Crystal
+
+ align:start position:0%
+x-ray defraction of uh Pro uh Crystal
+ 
+
+ align:start position:0%
+x-ray defraction of uh Pro uh Crystal
+proteins okay and I'm sure she'll tell
+
+ align:start position:0%
+proteins okay and I'm sure she'll tell
+ 
+
+ align:start position:0%
+proteins okay and I'm sure she'll tell
+you much more about
+
+ align:start position:0%
+you much more about
+ 
+
+ align:start position:0%
+you much more about
+that all right but in xrate Def
+
+ align:start position:0%
+that all right but in xrate Def
+ 
+
+ align:start position:0%
+that all right but in xrate Def
+fraction what they do is they use those
+
+ align:start position:0%
+fraction what they do is they use those
+ 
+
+ align:start position:0%
+fraction what they do is they use those
+results not to get the
+
+ align:start position:0%
+results not to get the
+ 
+
+ align:start position:0%
+results not to get the
+wavelength but they use those results to
+
+ align:start position:0%
+wavelength but they use those results to
+ 
+
+ align:start position:0%
+wavelength but they use those results to
+get this distance here a the distance
+
+ align:start position:0%
+get this distance here a the distance
+ 
+
+ align:start position:0%
+get this distance here a the distance
+between the atoms that's what I mean by
+
+ align:start position:0%
+between the atoms that's what I mean by
+ 
+
+ align:start position:0%
+between the atoms that's what I mean by
+getting out the
+
+ align:start position:0%
+getting out the
+ 
+
+ align:start position:0%
+getting out the
+structure in x-ray defraction they
+
+ align:start position:0%
+structure in x-ray defraction they
+ 
+
+ align:start position:0%
+structure in x-ray defraction they
+coming in with an x-ray beam and they
+
+ align:start position:0%
+coming in with an x-ray beam and they
+ 
+
+ align:start position:0%
+coming in with an x-ray beam and they
+know what the wavelength is of their
+
+ align:start position:0%
+know what the wavelength is of their
+ 
+
+ align:start position:0%
+know what the wavelength is of their
+x-ray beam so they know what Lambda is
+
+ align:start position:0%
+x-ray beam so they know what Lambda is
+ 
+
+ align:start position:0%
+x-ray beam so they know what Lambda is
+and then they go and measure what Theta
+
+ align:start position:0%
+and then they go and measure what Theta
+ 
+
+ align:start position:0%
+and then they go and measure what Theta
+is the scattering angle okay and from
+
+ align:start position:0%
+is the scattering angle okay and from
+ 
+
+ align:start position:0%
+is the scattering angle okay and from
+those two quantities Lambda and Theta
+
+ align:start position:0%
+those two quantities Lambda and Theta
+ 
+
+ align:start position:0%
+those two quantities Lambda and Theta
+they figure out what a is the distance
+
+ align:start position:0%
+they figure out what a is the distance
+ 
+
+ align:start position:0%
+they figure out what a is the distance
+between the atoms and therefore work out
+
+ align:start position:0%
+between the atoms and therefore work out
+ 
+
+ align:start position:0%
+between the atoms and therefore work out
+the structure of the protein okay so
+
+ align:start position:0%
+the structure of the protein okay so
+ 
+
+ align:start position:0%
+the structure of the protein okay so
+that's how x-ray fraction is actually
+
+ align:start position:0%
+that's how x-ray fraction is actually
+ 
+
+ align:start position:0%
+that's how x-ray fraction is actually
+used all
+
+ align:start position:0%
+used all
+ 
+
+ align:start position:0%
+used all
+right well um now I'm going to need the
+
+ align:start position:0%
+right well um now I'm going to need the
+ 
+
+ align:start position:0%
+right well um now I'm going to need the
+I can I think I can turn these back
+
+ align:start position:0%
+I can I think I can turn these back
+ 
+
+ align:start position:0%
+I can I think I can turn these back
+on just get this up a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit I'm not going to get the screen all
+
+ align:start position:0%
+bit I'm not going to get the screen all
+ 
+
+ align:start position:0%
+bit I'm not going to get the screen all
+the way up because I still want that
+
+ align:start position:0%
+the way up because I still want that
+ 
+
+ align:start position:0%
+the way up because I still want that
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so not only did Davidson and germer and
+
+ align:start position:0%
+so not only did Davidson and germer and
+ 
+
+ align:start position:0%
+so not only did Davidson and germer and
+Thompson demonstrate the interference
+
+ align:start position:0%
+Thompson demonstrate the interference
+ 
+
+ align:start position:0%
+Thompson demonstrate the interference
+phenomena but they also um got out of
+
+ align:start position:0%
+phenomena but they also um got out of
+ 
+
+ align:start position:0%
+phenomena but they also um got out of
+all of that they got a value for the um
+
+ align:start position:0%
+all of that they got a value for the um
+ 
+
+ align:start position:0%
+all of that they got a value for the um
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+wavelength and that was very
+
+ align:start position:0%
+wavelength and that was very
+ 
+
+ align:start position:0%
+wavelength and that was very
+important and the reason why it was so
+
+ align:start position:0%
+important and the reason why it was so
+ 
+
+ align:start position:0%
+important and the reason why it was so
+important is because um a few years
+
+ align:start position:0%
+important is because um a few years
+ 
+
+ align:start position:0%
+important is because um a few years
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+1924 there was a prediction ition for
+
+ align:start position:0%
+1924 there was a prediction ition for
+ 
+
+ align:start position:0%
+1924 there was a prediction ition for
+what the wavelength of particles ought
+
+ align:start position:0%
+what the wavelength of particles ought
+ 
+
+ align:start position:0%
+what the wavelength of particles ought
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+be and that prediction was made by this
+
+ align:start position:0%
+be and that prediction was made by this
+ 
+
+ align:start position:0%
+be and that prediction was made by this
+gentleman de Bo de
+
+ align:start position:0%
+gentleman de Bo de
+ 
+
+ align:start position:0%
+gentleman de Bo de
+bryley de
+
+ align:start position:0%
+bryley de
+ 
+
+ align:start position:0%
+bryley de
+bryley in his PhD thesis no
+
+ align:start position:0%
+bryley in his PhD thesis no
+ 
+
+ align:start position:0%
+bryley in his PhD thesis no
+less he made a prediction for what the
+
+ align:start position:0%
+less he made a prediction for what the
+ 
+
+ align:start position:0%
+less he made a prediction for what the
+wavelength of particles ought to
+
+ align:start position:0%
+wavelength of particles ought to
+ 
+
+ align:start position:0%
+wavelength of particles ought to
+be what he did is he took the
+
+ align:start position:0%
+be what he did is he took the
+ 
+
+ align:start position:0%
+be what he did is he took the
+relativistic equations of motion of
+
+ align:start position:0%
+relativistic equations of motion of
+ 
+
+ align:start position:0%
+relativistic equations of motion of
+Einstein the same identical equations he
+
+ align:start position:0%
+Einstein the same identical equations he
+ 
+
+ align:start position:0%
+Einstein the same identical equations he
+knew of Einstein's work PhD thesis right
+
+ align:start position:0%
+knew of Einstein's work PhD thesis right
+ 
+
+ align:start position:0%
+knew of Einstein's work PhD thesis right
+and he
+
+ align:start position:0%
+and he
+ 
+
+ align:start position:0%
+and he
+realized that those relativistic
+
+ align:start position:0%
+realized that those relativistic
+ 
+
+ align:start position:0%
+realized that those relativistic
+equations of
+
+ align:start position:0%
+equations of
+ 
+
+ align:start position:0%
+equations of
+motion applied to matter as well as to
+
+ align:start position:0%
+motion applied to matter as well as to
+ 
+
+ align:start position:0%
+motion applied to matter as well as to
+photons to
+
+ align:start position:0%
+photons to
+ 
+
+ align:start position:0%
+photons to
+radiation and so he said that if you if
+
+ align:start position:0%
+radiation and so he said that if you if
+ 
+
+ align:start position:0%
+radiation and so he said that if you if
+you have of course then a
+
+ align:start position:0%
+you have of course then a
+ 
+
+ align:start position:0%
+you have of course then a
+photon which has a wavelength Lambda of
+
+ align:start position:0%
+photon which has a wavelength Lambda of
+ 
+
+ align:start position:0%
+photon which has a wavelength Lambda of
+course then that momentum of that photon
+
+ align:start position:0%
+course then that momentum of that photon
+ 
+
+ align:start position:0%
+course then that momentum of that photon
+is p but since those equations also
+
+ align:start position:0%
+is p but since those equations also
+ 
+
+ align:start position:0%
+is p but since those equations also
+applied to matter he then said well if
+
+ align:start position:0%
+applied to matter he then said well if
+ 
+
+ align:start position:0%
+applied to matter he then said well if
+you have a particle with momentum P hey
+
+ align:start position:0%
+you have a particle with momentum P hey
+ 
+
+ align:start position:0%
+you have a particle with momentum P hey
+that particle ought to have a wavelength
+
+ align:start position:0%
+that particle ought to have a wavelength
+ 
+
+ align:start position:0%
+that particle ought to have a wavelength
+Lambda he turned Einstein's relativistic
+
+ align:start position:0%
+Lambda he turned Einstein's relativistic
+ 
+
+ align:start position:0%
+Lambda he turned Einstein's relativistic
+equations relativistic equations of
+
+ align:start position:0%
+equations relativistic equations of
+ 
+
+ align:start position:0%
+equations relativistic equations of
+motion around right he said well you
+
+ align:start position:0%
+motion around right he said well you
+ 
+
+ align:start position:0%
+motion around right he said well you
+know if radiation has a wavelength
+
+ align:start position:0%
+know if radiation has a wavelength
+ 
+
+ align:start position:0%
+know if radiation has a wavelength
+Lambda it ought to have momentum P this
+
+ align:start position:0%
+Lambda it ought to have momentum P this
+ 
+
+ align:start position:0%
+Lambda it ought to have momentum P this
+is what Einstein said de bryley said
+
+ align:start position:0%
+is what Einstein said de bryley said
+ 
+
+ align:start position:0%
+is what Einstein said de bryley said
+well then matter with a momentum P
+
+ align:start position:0%
+well then matter with a momentum P
+ 
+
+ align:start position:0%
+well then matter with a momentum P
+better have a wavelength
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda okay that's de bry's
+
+ align:start position:0%
+Lambda okay that's de bry's
+ 
+
+ align:start position:0%
+Lambda okay that's de bry's
+wavelength isn't that amazing I think
+
+ align:start position:0%
+wavelength isn't that amazing I think
+ 
+
+ align:start position:0%
+wavelength isn't that amazing I think
+that's amazing why didn't Einstein
+
+ align:start position:0%
+that's amazing why didn't Einstein
+ 
+
+ align:start position:0%
+that's amazing why didn't Einstein
+realize this or did Einstein realize
+
+ align:start position:0%
+realize this or did Einstein realize
+ 
+
+ align:start position:0%
+realize this or did Einstein realize
+that I don't
+
+ align:start position:0%
+that I don't
+ 
+
+ align:start position:0%
+that I don't
+know but now let's see about this
+
+ align:start position:0%
+know but now let's see about this
+ 
+
+ align:start position:0%
+know but now let's see about this
+prediction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here what we know is that in the deyle
+
+ align:start position:0%
+here what we know is that in the deyle
+ 
+
+ align:start position:0%
+here what we know is that in the deyle
+experiment that we had electrons of 54
+
+ align:start position:0%
+experiment that we had electrons of 54
+ 
+
+ align:start position:0%
+experiment that we had electrons of 54
+EV that means that's the kinetic energy
+
+ align:start position:0%
+EV that means that's the kinetic energy
+ 
+
+ align:start position:0%
+EV that means that's the kinetic energy
+that's 12 M * V ^ 2
+
+ align:start position:0%
+that's 12 M * V ^ 2
+ 
+
+ align:start position:0%
+that's 12 M * V ^ 2
+you can write kinetic energy as p^2 over
+
+ align:start position:0%
+you can write kinetic energy as p^2 over
+ 
+
+ align:start position:0%
+you can write kinetic energy as p^2 over
+2m you can convince yourself of this and
+
+ align:start position:0%
+2m you can convince yourself of this and
+ 
+
+ align:start position:0%
+2m you can convince yourself of this and
+this is useful to know for these kinds
+
+ align:start position:0%
+this is useful to know for these kinds
+ 
+
+ align:start position:0%
+this is useful to know for these kinds
+of problems all right p^2 over 2 m is
+
+ align:start position:0%
+of problems all right p^2 over 2 m is
+ 
+
+ align:start position:0%
+of problems all right p^2 over 2 m is
+the kinetic
+
+ align:start position:0%
+the kinetic
+ 
+
+ align:start position:0%
+the kinetic
+energy and
+
+ align:start position:0%
+energy and
+ 
+
+ align:start position:0%
+energy and
+therefore if this is the energy you can
+
+ align:start position:0%
+therefore if this is the energy you can
+ 
+
+ align:start position:0%
+therefore if this is the energy you can
+calculate the momentum of those 54 EV
+
+ align:start position:0%
+calculate the momentum of those 54 EV
+ 
+
+ align:start position:0%
+calculate the momentum of those 54 EV
+electrons so the
+
+ align:start position:0%
+electrons so the
+ 
+
+ align:start position:0%
+electrons so the
+momentum is 4.0 * 10 the- 24 kg m/
+
+ align:start position:0%
+momentum is 4.0 * 10 the- 24 kg m/
+ 
+
+ align:start position:0%
+momentum is 4.0 * 10 the- 24 kg m/
+second and now we can use de bry's
+
+ align:start position:0%
+second and now we can use de bry's
+ 
+
+ align:start position:0%
+second and now we can use de bry's
+wavelength here that expression that he
+
+ align:start position:0%
+wavelength here that expression that he
+ 
+
+ align:start position:0%
+wavelength here that expression that he
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+uh gotten out of Einstein's relativistic
+
+ align:start position:0%
+uh gotten out of Einstein's relativistic
+ 
+
+ align:start position:0%
+uh gotten out of Einstein's relativistic
+equations of motion to solve for Lambda
+
+ align:start position:0%
+equations of motion to solve for Lambda
+ 
+
+ align:start position:0%
+equations of motion to solve for Lambda
+so that's H 6.6 26 * 10- 20 34 Jew
+
+ align:start position:0%
+so that's H 6.6 26 * 10- 20 34 Jew
+ 
+
+ align:start position:0%
+so that's H 6.6 26 * 10- 20 34 Jew
+seconds over over the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum and that gives us 17 * 10us 10
+
+ align:start position:0%
+momentum and that gives us 17 * 10us 10
+ 
+
+ align:start position:0%
+momentum and that gives us 17 * 10us 10
+m hey same as the
+
+ align:start position:0%
+m hey same as the
+ 
+
+ align:start position:0%
+m hey same as the
+experiment it predicted exactly what the
+
+ align:start position:0%
+experiment it predicted exactly what the
+ 
+
+ align:start position:0%
+experiment it predicted exactly what the
+experimentalist measured for the
+
+ align:start position:0%
+experimentalist measured for the
+ 
+
+ align:start position:0%
+experimentalist measured for the
+wavelength of the electron all right
+
+ align:start position:0%
+wavelength of the electron all right
+ 
+
+ align:start position:0%
+wavelength of the electron all right
+this was a real coup here for de bryley
+
+ align:start position:0%
+this was a real coup here for de bryley
+ 
+
+ align:start position:0%
+this was a real coup here for de bryley
+and for
+
+ align:start position:0%
+and for
+ 
+
+ align:start position:0%
+and for
+science so
+
+ align:start position:0%
+science so
+ 
+
+ align:start position:0%
+science so
+what do we have we have Davidson and
+
+ align:start position:0%
+what do we have we have Davidson and
+ 
+
+ align:start position:0%
+what do we have we have Davidson and
+germer and George
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thompson who have demonstrated and in
+
+ align:start position:0%
+Thompson who have demonstrated and in
+ 
+
+ align:start position:0%
+Thompson who have demonstrated and in
+particular George Thompson who has
+
+ align:start position:0%
+particular George Thompson who has
+ 
+
+ align:start position:0%
+particular George Thompson who has
+demonstrated that uh an
+
+ align:start position:0%
+demonstrated that uh an
+ 
+
+ align:start position:0%
+demonstrated that uh an
+electron has wavelike
+
+ align:start position:0%
+electron has wavelike
+ 
+
+ align:start position:0%
+electron has wavelike
+behavior in contrast here's George
+
+ align:start position:0%
+behavior in contrast here's George
+ 
+
+ align:start position:0%
+behavior in contrast here's George
+Thompson's father JJ Thompson who has
+
+ align:start position:0%
+Thompson's father JJ Thompson who has
+ 
+
+ align:start position:0%
+Thompson's father JJ Thompson who has
+demonstrated that an electron is a
+
+ align:start position:0%
+demonstrated that an electron is a
+ 
+
+ align:start position:0%
+demonstrated that an electron is a
+particle has mass right
+
+ align:start position:0%
+particle has mass right
+ 
+
+ align:start position:0%
+particle has mass right
+and both the Son and the father are
+
+ align:start position:0%
+and both the Son and the father are
+ 
+
+ align:start position:0%
+and both the Son and the father are
+correct how often does that happen right
+
+ align:start position:0%
+correct how often does that happen right
+ 
+
+ align:start position:0%
+correct how often does that happen right
+it's really amazing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+story
+
+ align:start position:0%
+story
+ 
+
+ align:start position:0%
+story
+okay all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now now I'm going to have to put the
+
+ align:start position:0%
+now now I'm going to have to put the
+ 
+
+ align:start position:0%
+now now I'm going to have to put the
+lights off here I'm getting my lights
+
+ align:start position:0%
+lights off here I'm getting my lights
+ 
+
+ align:start position:0%
+lights off here I'm getting my lights
+confused all right so now now we're at
+
+ align:start position:0%
+confused all right so now now we're at
+ 
+
+ align:start position:0%
+confused all right so now now we're at
+the point where
+
+ align:start position:0%
+the point where
+ 
+
+ align:start position:0%
+the point where
+um we can begin to understand the
+
+ align:start position:0%
+um we can begin to understand the
+ 
+
+ align:start position:0%
+um we can begin to understand the
+structure of the atam
+
+ align:start position:0%
+structure of the atam
+ 
+
+ align:start position:0%
+structure of the atam
+right because it was this
+
+ align:start position:0%
+right because it was this
+ 
+
+ align:start position:0%
+right because it was this
+realization that an electron had wav
+
+ align:start position:0%
+realization that an electron had wav
+ 
+
+ align:start position:0%
+realization that an electron had wav
+likee properties it was that
+
+ align:start position:0%
+likee properties it was that
+ 
+
+ align:start position:0%
+likee properties it was that
+realization of those wave likee
+
+ align:start position:0%
+realization of those wave likee
+ 
+
+ align:start position:0%
+realization of those wave likee
+properties that led uh this gentleman
+
+ align:start position:0%
+properties that led uh this gentleman
+ 
+
+ align:start position:0%
+properties that led uh this gentleman
+right here right to uh realized that
+
+ align:start position:0%
+right here right to uh realized that
+ 
+
+ align:start position:0%
+right here right to uh realized that
+maybe he had to treat the electrons as a
+
+ align:start position:0%
+maybe he had to treat the electrons as a
+ 
+
+ align:start position:0%
+maybe he had to treat the electrons as a
+wave Mr
+
+ align:start position:0%
+wave Mr
+ 
+
+ align:start position:0%
+wave Mr
+Schrodinger it was that realization that
+
+ align:start position:0%
+Schrodinger it was that realization that
+ 
+
+ align:start position:0%
+Schrodinger it was that realization that
+led Mr Schrodinger to write down the
+
+ align:start position:0%
+led Mr Schrodinger to write down the
+ 
+
+ align:start position:0%
+led Mr Schrodinger to write down the
+Schrodinger equation the wave
+
+ align:start position:0%
+Schrodinger equation the wave
+ 
+
+ align:start position:0%
+Schrodinger equation the wave
+equation the wave the equation of motion
+
+ align:start position:0%
+equation the wave the equation of motion
+ 
+
+ align:start position:0%
+equation the wave the equation of motion
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+particles like an
+
+ align:start position:0%
+particles like an
+ 
+
+ align:start position:0%
+particles like an
+electron that um actually have a
+
+ align:start position:0%
+electron that um actually have a
+ 
+
+ align:start position:0%
+electron that um actually have a
+wavelength on the order of their
+
+ align:start position:0%
+wavelength on the order of their
+ 
+
+ align:start position:0%
+wavelength on the order of their
+environment okay and actually I just
+
+ align:start position:0%
+environment okay and actually I just
+ 
+
+ align:start position:0%
+environment okay and actually I just
+realize that I skipped something in your
+
+ align:start position:0%
+realize that I skipped something in your
+ 
+
+ align:start position:0%
+realize that I skipped something in your
+notes that I wanted to talk
+
+ align:start position:0%
+notes that I wanted to talk
+ 
+
+ align:start position:0%
+notes that I wanted to talk
+about and I apologize for
+
+ align:start position:0%
+about and I apologize for
+ 
+
+ align:start position:0%
+about and I apologize for
+that we're going to get to the wave
+
+ align:start position:0%
+that we're going to get to the wave
+ 
+
+ align:start position:0%
+that we're going to get to the wave
+equation in a
+
+ align:start position:0%
+equation in a
+ 
+
+ align:start position:0%
+equation in a
+moment it's very
+
+ align:start position:0%
+moment it's very
+ 
+
+ align:start position:0%
+moment it's very
+important but I did want to just uh talk
+
+ align:start position:0%
+important but I did want to just uh talk
+ 
+
+ align:start position:0%
+important but I did want to just uh talk
+about for a moment
+
+ align:start position:0%
+about for a moment
+ 
+
+ align:start position:0%
+about for a moment
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+uh if
+
+ align:start position:0%
+uh if
+ 
+
+ align:start position:0%
+uh if
+particles have waves or have wavelike
+
+ align:start position:0%
+particles have waves or have wavelike
+ 
+
+ align:start position:0%
+particles have waves or have wavelike
+phenomena then why hadn't uh why hadn't
+
+ align:start position:0%
+phenomena then why hadn't uh why hadn't
+ 
+
+ align:start position:0%
+phenomena then why hadn't uh why hadn't
+this wavelike phenomena been seen
+
+ align:start position:0%
+this wavelike phenomena been seen
+ 
+
+ align:start position:0%
+this wavelike phenomena been seen
+before so what this also should mean
+
+ align:start position:0%
+before so what this also should mean
+ 
+
+ align:start position:0%
+before so what this also should mean
+with de bryley is that you and I have a
+
+ align:start position:0%
+with de bryley is that you and I have a
+ 
+
+ align:start position:0%
+with de bryley is that you and I have a
+wavelength because we got momentum we
+
+ align:start position:0%
+wavelength because we got momentum we
+ 
+
+ align:start position:0%
+wavelength because we got momentum we
+got mass times velocity we also ought to
+
+ align:start position:0%
+got mass times velocity we also ought to
+ 
+
+ align:start position:0%
+got mass times velocity we also ought to
+have a a wave
+
+ align:start position:0%
+have a a wave
+ 
+
+ align:start position:0%
+have a a wave
+l so
+
+ align:start position:0%
+l so
+ 
+
+ align:start position:0%
+l so
+um pardon they take a while to to go up
+
+ align:start position:0%
+um pardon they take a while to to go up
+ 
+
+ align:start position:0%
+um pardon they take a while to to go up
+yeah all right so let's uh consider the
+
+ align:start position:0%
+yeah all right so let's uh consider the
+ 
+
+ align:start position:0%
+yeah all right so let's uh consider the
+problem with our wavelength
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here well let's talk about the
+
+ align:start position:0%
+here well let's talk about the
+ 
+
+ align:start position:0%
+here well let's talk about the
+wavelength of a
+
+ align:start position:0%
+wavelength of a
+ 
+
+ align:start position:0%
+wavelength of a
+baseball so we have a 5 O baseball right
+
+ align:start position:0%
+baseball so we have a 5 O baseball right
+ 
+
+ align:start position:0%
+baseball so we have a 5 O baseball right
+being pck Ed by Kurt chilling at 90 M an
+
+ align:start position:0%
+being pck Ed by Kurt chilling at 90 M an
+ 
+
+ align:start position:0%
+being pck Ed by Kurt chilling at 90 M an
+hour all
+
+ align:start position:0%
+hour all
+ 
+
+ align:start position:0%
+hour all
+right and it's being pitched at a very
+
+ align:start position:0%
+right and it's being pitched at a very
+ 
+
+ align:start position:0%
+right and it's being pitched at a very
+large nickel Crystal so let's think of
+
+ align:start position:0%
+large nickel Crystal so let's think of
+ 
+
+ align:start position:0%
+large nickel Crystal so let's think of
+an experiment of
+
+ align:start position:0%
+an experiment of
+ 
+
+ align:start position:0%
+an experiment of
+defraction of baseballs from a large
+
+ align:start position:0%
+defraction of baseballs from a large
+ 
+
+ align:start position:0%
+defraction of baseballs from a large
+Crystal just like the defraction of the
+
+ align:start position:0%
+Crystal just like the defraction of the
+ 
+
+ align:start position:0%
+Crystal just like the defraction of the
+electrons uh from that nickel Crystal
+
+ align:start position:0%
+electrons uh from that nickel Crystal
+ 
+
+ align:start position:0%
+electrons uh from that nickel Crystal
+well let's calculate the momentum of
+
+ align:start position:0%
+well let's calculate the momentum of
+ 
+
+ align:start position:0%
+well let's calculate the momentum of
+that baseball
+
+ align:start position:0%
+that baseball
+ 
+
+ align:start position:0%
+that baseball
+that momentum is M time
+
+ align:start position:0%
+that momentum is M time
+ 
+
+ align:start position:0%
+that momentum is M time
+V and 5 ounces 90 miles per hour get all
+
+ align:start position:0%
+V and 5 ounces 90 miles per hour get all
+ 
+
+ align:start position:0%
+V and 5 ounces 90 miles per hour get all
+your units right it's
+
+ align:start position:0%
+your units right it's
+ 
+
+ align:start position:0%
+your units right it's
+5.6 kilogram meter per second all
+
+ align:start position:0%
+5.6 kilogram meter per second all
+ 
+
+ align:start position:0%
+5.6 kilogram meter per second all
+right then we're going to use de bry's
+
+ align:start position:0%
+right then we're going to use de bry's
+ 
+
+ align:start position:0%
+right then we're going to use de bry's
+relationship right here to calculate
+
+ align:start position:0%
+relationship right here to calculate
+ 
+
+ align:start position:0%
+relationship right here to calculate
+what the wavelength is of that pitched
+
+ align:start position:0%
+what the wavelength is of that pitched
+ 
+
+ align:start position:0%
+what the wavelength is of that pitched
+baseball and when we do that H is equal
+
+ align:start position:0%
+baseball and when we do that H is equal
+ 
+
+ align:start position:0%
+baseball and when we do that H is equal
+uh Lambda is equal H over P if you put
+
+ align:start position:0%
+uh Lambda is equal H over P if you put
+ 
+
+ align:start position:0%
+uh Lambda is equal H over P if you put
+in this m or you put in this P put in h
+
+ align:start position:0%
+in this m or you put in this P put in h
+ 
+
+ align:start position:0%
+in this m or you put in this P put in h
+hey that comes out to be 1.2 * 10- 34
+
+ align:start position:0%
+hey that comes out to be 1.2 * 10- 34
+ 
+
+ align:start position:0%
+hey that comes out to be 1.2 * 10- 34
+M okay pretty
+
+ align:start position:0%
+M okay pretty
+ 
+
+ align:start position:0%
+M okay pretty
+small all right
+
+ align:start position:0%
+small all right
+ 
+
+ align:start position:0%
+small all right
+but what do we know well we know the
+
+ align:start position:0%
+but what do we know well we know the
+ 
+
+ align:start position:0%
+but what do we know well we know the
+condition for constructive interference
+
+ align:start position:0%
+condition for constructive interference
+ 
+
+ align:start position:0%
+condition for constructive interference
+D2 minus D1 has to be equal to n *
+
+ align:start position:0%
+D2 minus D1 has to be equal to n *
+ 
+
+ align:start position:0%
+D2 minus D1 has to be equal to n *
+Lambda has to be equal to a
+
+ align:start position:0%
+Lambda has to be equal to a
+ 
+
+ align:start position:0%
+Lambda has to be equal to a
+sin
+
+ align:start position:0%
+sin
+ 
+
+ align:start position:0%
+sin
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+right so now let's
+
+ align:start position:0%
+right so now let's
+ 
+
+ align:start position:0%
+right so now let's
+calculate what the angle Theta ought to
+
+ align:start position:0%
+calculate what the angle Theta ought to
+ 
+
+ align:start position:0%
+calculate what the angle Theta ought to
+be for the first or first order
+
+ align:start position:0%
+be for the first or first order
+ 
+
+ align:start position:0%
+be for the first or first order
+defraction feature of baseballs from a
+
+ align:start position:0%
+defraction feature of baseballs from a
+ 
+
+ align:start position:0%
+defraction feature of baseballs from a
+nickel Crystal so you have Kurt chilling
+
+ align:start position:0%
+nickel Crystal so you have Kurt chilling
+ 
+
+ align:start position:0%
+nickel Crystal so you have Kurt chilling
+throwing these baseballs one or another
+
+ align:start position:0%
+throwing these baseballs one or another
+ 
+
+ align:start position:0%
+throwing these baseballs one or another
+right at this nickel Crystal and you're
+
+ align:start position:0%
+right at this nickel Crystal and you're
+ 
+
+ align:start position:0%
+right at this nickel Crystal and you're
+trying to see at what angle you're going
+
+ align:start position:0%
+trying to see at what angle you're going
+ 
+
+ align:start position:0%
+trying to see at what angle you're going
+to see that first order defraction
+
+ align:start position:0%
+to see that first order defraction
+ 
+
+ align:start position:0%
+to see that first order defraction
+feature well we can set this up so that
+
+ align:start position:0%
+feature well we can set this up so that
+ 
+
+ align:start position:0%
+feature well we can set this up so that
+s Theta here is going to be equal to n
+
+ align:start position:0%
+s Theta here is going to be equal to n
+ 
+
+ align:start position:0%
+s Theta here is going to be equal to n
+Lambda over a so n is 1 Lambda is 1.2 *
+
+ align:start position:0%
+Lambda over a so n is 1 Lambda is 1.2 *
+ 
+
+ align:start position:0%
+Lambda over a so n is 1 Lambda is 1.2 *
+10- 34
+
+ align:start position:0%
+10- 34
+ 
+
+ align:start position:0%
+10- 34
+M and then a is 2.15 * 10us 10 m hey if
+
+ align:start position:0%
+M and then a is 2.15 * 10us 10 m hey if
+ 
+
+ align:start position:0%
+M and then a is 2.15 * 10us 10 m hey if
+you go and evaluate what Theta ought to
+
+ align:start position:0%
+you go and evaluate what Theta ought to
+ 
+
+ align:start position:0%
+you go and evaluate what Theta ought to
+be it's 3 * 10 the-
+
+ align:start position:0%
+be it's 3 * 10 the-
+ 
+
+ align:start position:0%
+be it's 3 * 10 the-
+23° all right so that means I have my
+
+ align:start position:0%
+23° all right so that means I have my
+ 
+
+ align:start position:0%
+23° all right so that means I have my
+nickel huge nickel Crystal here and
+
+ align:start position:0%
+nickel huge nickel Crystal here and
+ 
+
+ align:start position:0%
+nickel huge nickel Crystal here and
+here's the normal to the sample well
+
+ align:start position:0%
+here's the normal to the sample well
+ 
+
+ align:start position:0%
+here's the normal to the sample well
+then that first order defraction feature
+
+ align:start position:0%
+then that first order defraction feature
+ 
+
+ align:start position:0%
+then that first order defraction feature
+here is at about 10us
+
+ align:start position:0%
+here is at about 10us
+ 
+
+ align:start position:0%
+here is at about 10us
+23° from the normal are you going to be
+
+ align:start position:0%
+23° from the normal are you going to be
+ 
+
+ align:start position:0%
+23° from the normal are you going to be
+able to resolve
+
+ align:start position:0%
+able to resolve
+ 
+
+ align:start position:0%
+able to resolve
+that no right you're not going to be
+
+ align:start position:0%
+that no right you're not going to be
+ 
+
+ align:start position:0%
+that no right you're not going to be
+able to see the the normal noral
+
+ align:start position:0%
+able to see the the normal noral
+ 
+
+ align:start position:0%
+able to see the the normal noral
+reflection and then no base balls and
+
+ align:start position:0%
+reflection and then no base balls and
+ 
+
+ align:start position:0%
+reflection and then no base balls and
+then a very
+
+ align:start position:0%
+then a very
+ 
+
+ align:start position:0%
+then a very
+intense uh very intense beam of
+
+ align:start position:0%
+intense uh very intense beam of
+ 
+
+ align:start position:0%
+intense uh very intense beam of
+baseballs you're not going to be able to
+
+ align:start position:0%
+baseballs you're not going to be able to
+ 
+
+ align:start position:0%
+baseballs you're not going to be able to
+resolve 10 the minus 20 23
+
+ align:start position:0%
+resolve 10 the minus 20 23
+ 
+
+ align:start position:0%
+resolve 10 the minus 20 23
+degrees so you say well okay uh if
+
+ align:start position:0%
+degrees so you say well okay uh if
+ 
+
+ align:start position:0%
+degrees so you say well okay uh if
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+problem then maybe I can help myself
+
+ align:start position:0%
+problem then maybe I can help myself
+ 
+
+ align:start position:0%
+problem then maybe I can help myself
+out by
+
+ align:start position:0%
+out by
+ 
+
+ align:start position:0%
+out by
+changing this a here right by changing
+
+ align:start position:0%
+changing this a here right by changing
+ 
+
+ align:start position:0%
+changing this a here right by changing
+the distance of my uh particles that are
+
+ align:start position:0%
+the distance of my uh particles that are
+ 
+
+ align:start position:0%
+the distance of my uh particles that are
+doing the diffracting my two nickel
+
+ align:start position:0%
+doing the diffracting my two nickel
+ 
+
+ align:start position:0%
+doing the diffracting my two nickel
+atoms hey let's change that distance
+
+ align:start position:0%
+atoms hey let's change that distance
+ 
+
+ align:start position:0%
+atoms hey let's change that distance
+let's find some other Crystal such that
+
+ align:start position:0%
+let's find some other Crystal such that
+ 
+
+ align:start position:0%
+let's find some other Crystal such that
+I change that distance to oh let's see
+
+ align:start position:0%
+I change that distance to oh let's see
+ 
+
+ align:start position:0%
+I change that distance to oh let's see
+how about uh 7 * 10- 33 M all
+
+ align:start position:0%
+how about uh 7 * 10- 33 M all
+ 
+
+ align:start position:0%
+how about uh 7 * 10- 33 M all
+right when I do that and I go and
+
+ align:start position:0%
+right when I do that and I go and
+ 
+
+ align:start position:0%
+right when I do that and I go and
+calculate what Theta ought to be that
+
+ align:start position:0%
+calculate what Theta ought to be that
+ 
+
+ align:start position:0%
+calculate what Theta ought to be that
+first defraction feature well that comes
+
+ align:start position:0%
+first defraction feature well that comes
+ 
+
+ align:start position:0%
+first defraction feature well that comes
+out to about one
+
+ align:start position:0%
+out to about one
+ 
+
+ align:start position:0%
+out to about one
+degree
+
+ align:start position:0%
+degree
+ 
+
+ align:start position:0%
+degree
+so if I were pitching baseballs at the
+
+ align:start position:0%
+so if I were pitching baseballs at the
+ 
+
+ align:start position:0%
+so if I were pitching baseballs at the
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+angle and I was looking to see if I had
+
+ align:start position:0%
+angle and I was looking to see if I had
+ 
+
+ align:start position:0%
+angle and I was looking to see if I had
+a maximum of
+
+ align:start position:0%
+a maximum of
+ 
+
+ align:start position:0%
+a maximum of
+baseballs one degree from that normal
+
+ align:start position:0%
+baseballs one degree from that normal
+ 
+
+ align:start position:0%
+baseballs one degree from that normal
+angle one degree could I resolve that ah
+
+ align:start position:0%
+angle one degree could I resolve that ah
+ 
+
+ align:start position:0%
+angle one degree could I resolve that ah
+maybe maybe you could get an experiment
+
+ align:start position:0%
+maybe maybe you could get an experiment
+ 
+
+ align:start position:0%
+maybe maybe you could get an experiment
+like that since it up maybe but the
+
+ align:start position:0%
+like that since it up maybe but the
+ 
+
+ align:start position:0%
+like that since it up maybe but the
+problem is Right
+
+ align:start position:0%
+problem is Right
+ 
+
+ align:start position:0%
+problem is Right
+Here Right the problem is in this a the
+
+ align:start position:0%
+Here Right the problem is in this a the
+ 
+
+ align:start position:0%
+Here Right the problem is in this a the
+distance between the atoms that are um
+
+ align:start position:0%
+distance between the atoms that are um
+ 
+
+ align:start position:0%
+distance between the atoms that are um
+the distance between the atoms and the
+
+ align:start position:0%
+the distance between the atoms and the
+ 
+
+ align:start position:0%
+the distance between the atoms and the
+nickel Crystal that are going to reflect
+
+ align:start position:0%
+nickel Crystal that are going to reflect
+ 
+
+ align:start position:0%
+nickel Crystal that are going to reflect
+these base balls this distance is 7 *
+
+ align:start position:0%
+these base balls this distance is 7 *
+ 
+
+ align:start position:0%
+these base balls this distance is 7 *
+10us 33
+
+ align:start position:0%
+10us 33
+ 
+
+ align:start position:0%
+10us 33
+M how big was the diameter of a nucleus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+-10 how about another
+
+ align:start position:0%
+-10 how about another
+ 
+
+ align:start position:0%
+-10 how about another
+number1 how about another
+
+ align:start position:0%
+number1 how about another
+ 
+
+ align:start position:0%
+number1 how about another
+number 14 10 Theus 14 MERS that's a good
+
+ align:start position:0%
+number 14 10 Theus 14 MERS that's a good
+ 
+
+ align:start position:0%
+number 14 10 Theus 14 MERS that's a good
+number to
+
+ align:start position:0%
+number to
+ 
+
+ align:start position:0%
+number to
+know what am I looking at here I'm
+
+ align:start position:0%
+know what am I looking at here I'm
+ 
+
+ align:start position:0%
+know what am I looking at here I'm
+looking at a distance between the atoms
+
+ align:start position:0%
+looking at a distance between the atoms
+ 
+
+ align:start position:0%
+looking at a distance between the atoms
+of 10us 33 MERS here hey we're 20 orders
+
+ align:start position:0%
+of 10us 33 MERS here hey we're 20 orders
+ 
+
+ align:start position:0%
+of 10us 33 MERS here hey we're 20 orders
+of magnitude smaller than the size of
+
+ align:start position:0%
+of magnitude smaller than the size of
+ 
+
+ align:start position:0%
+of magnitude smaller than the size of
+the nucleus do we have a crystal to
+
+ align:start position:0%
+the nucleus do we have a crystal to
+ 
+
+ align:start position:0%
+the nucleus do we have a crystal to
+defract baseballs off of where the atoms
+
+ align:start position:0%
+defract baseballs off of where the atoms
+ 
+
+ align:start position:0%
+defract baseballs off of where the atoms
+are 10us 33 meters
+
+ align:start position:0%
+are 10us 33 meters
+ 
+
+ align:start position:0%
+are 10us 33 meters
+apart
+
+ align:start position:0%
+apart
+ 
+
+ align:start position:0%
+apart
+uhuh okay we
+
+ align:start position:0%
+uhuh okay we
+ 
+
+ align:start position:0%
+uhuh okay we
+don't and that's why wav likee
+
+ align:start position:0%
+don't and that's why wav likee
+ 
+
+ align:start position:0%
+don't and that's why wav likee
+phenomena on macroscopic particles has
+
+ align:start position:0%
+phenomena on macroscopic particles has
+ 
+
+ align:start position:0%
+phenomena on macroscopic particles has
+not been
+
+ align:start position:0%
+not been
+ 
+
+ align:start position:0%
+not been
+observed because our wavelengths your
+
+ align:start position:0%
+observed because our wavelengths your
+ 
+
+ align:start position:0%
+observed because our wavelengths your
+wavelength my wavelength baseball
+
+ align:start position:0%
+wavelength my wavelength baseball
+ 
+
+ align:start position:0%
+wavelength my wavelength baseball
+wavelengths these wavelengths are way
+
+ align:start position:0%
+wavelengths these wavelengths are way
+ 
+
+ align:start position:0%
+wavelengths these wavelengths are way
+too small they're they're way too small
+
+ align:start position:0%
+too small they're they're way too small
+ 
+
+ align:start position:0%
+too small they're they're way too small
+because the mass is way too
+
+ align:start position:0%
+because the mass is way too
+ 
+
+ align:start position:0%
+because the mass is way too
+large and so there is no way in the
+
+ align:start position:0%
+large and so there is no way in the
+ 
+
+ align:start position:0%
+large and so there is no way in the
+macroscopic world that we're going to
+
+ align:start position:0%
+macroscopic world that we're going to
+ 
+
+ align:start position:0%
+macroscopic world that we're going to
+see any effects any wav likee behavior
+
+ align:start position:0%
+see any effects any wav likee behavior
+ 
+
+ align:start position:0%
+see any effects any wav likee behavior
+for macroscopic objects our wavelengths
+
+ align:start position:0%
+for macroscopic objects our wavelengths
+ 
+
+ align:start position:0%
+for macroscopic objects our wavelengths
+are too small we've no way to see that
+
+ align:start position:0%
+are too small we've no way to see that
+ 
+
+ align:start position:0%
+are too small we've no way to see that
+wav likee Behavior you're going to need
+
+ align:start position:0%
+wav likee Behavior you're going to need
+ 
+
+ align:start position:0%
+wav likee Behavior you're going to need
+slits or you're going to need
+
+ align:start position:0%
+slits or you're going to need
+ 
+
+ align:start position:0%
+slits or you're going to need
+atoms that are about 10 of the - 33 M
+
+ align:start position:0%
+atoms that are about 10 of the - 33 M
+ 
+
+ align:start position:0%
+atoms that are about 10 of the - 33 M
+from each other and that's just not
+
+ align:start position:0%
+from each other and that's just not
+ 
+
+ align:start position:0%
+from each other and that's just not
+practical okay so for macroscopic
+
+ align:start position:0%
+practical okay so for macroscopic
+ 
+
+ align:start position:0%
+practical okay so for macroscopic
+objects for you and me hey our
+
+ align:start position:0%
+objects for you and me hey our
+ 
+
+ align:start position:0%
+objects for you and me hey our
+wavelengths don't mean anything they are
+
+ align:start position:0%
+wavelengths don't mean anything they are
+ 
+
+ align:start position:0%
+wavelengths don't mean anything they are
+of no consequence in the observation of
+
+ align:start position:0%
+of no consequence in the observation of
+ 
+
+ align:start position:0%
+of no consequence in the observation of
+what we see around us right however they
+
+ align:start position:0%
+what we see around us right however they
+ 
+
+ align:start position:0%
+what we see around us right however they
+have lots of
+
+ align:start position:0%
+have lots of
+ 
+
+ align:start position:0%
+have lots of
+consequences for particles such as an
+
+ align:start position:0%
+consequences for particles such as an
+ 
+
+ align:start position:0%
+consequences for particles such as an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+whose environment is on the scale of the
+
+ align:start position:0%
+whose environment is on the scale of the
+ 
+
+ align:start position:0%
+whose environment is on the scale of the
+their wavelength so I'm saying here in
+
+ align:start position:0%
+their wavelength so I'm saying here in
+ 
+
+ align:start position:0%
+their wavelength so I'm saying here in
+this in this case for the electron where
+
+ align:start position:0%
+this in this case for the electron where
+ 
+
+ align:start position:0%
+this in this case for the electron where
+the wavelength is 10us 10 m hey that is
+
+ align:start position:0%
+the wavelength is 10us 10 m hey that is
+ 
+
+ align:start position:0%
+the wavelength is 10us 10 m hey that is
+a wavelength that's on the order of the
+
+ align:start position:0%
+a wavelength that's on the order of the
+ 
+
+ align:start position:0%
+a wavelength that's on the order of the
+size of the electron's environment in an
+
+ align:start position:0%
+size of the electron's environment in an
+ 
+
+ align:start position:0%
+size of the electron's environment in an
+atom that's 10 Theus 10
+
+ align:start position:0%
+atom that's 10 Theus 10
+ 
+
+ align:start position:0%
+atom that's 10 Theus 10
+m in those cases when that wavelength is
+
+ align:start position:0%
+m in those cases when that wavelength is
+ 
+
+ align:start position:0%
+m in those cases when that wavelength is
+is about the size of the environment
+
+ align:start position:0%
+is about the size of the environment
+ 
+
+ align:start position:0%
+is about the size of the environment
+then the wavelike properties
+
+ align:start position:0%
+then the wavelike properties
+ 
+
+ align:start position:0%
+then the wavelike properties
+matter they matter you see the
+
+ align:start position:0%
+matter they matter you see the
+ 
+
+ align:start position:0%
+matter they matter you see the
+interference phenomena you see those
+
+ align:start position:0%
+interference phenomena you see those
+ 
+
+ align:start position:0%
+interference phenomena you see those
+effects of those wavelike
+
+ align:start position:0%
+effects of those wavelike
+ 
+
+ align:start position:0%
+effects of those wavelike
+properties and it is just that
+
+ align:start position:0%
+properties and it is just that
+ 
+
+ align:start position:0%
+properties and it is just that
+realization that led schinger here who's
+
+ align:start position:0%
+realization that led schinger here who's
+ 
+
+ align:start position:0%
+realization that led schinger here who's
+now washed out right to write down the
+
+ align:start position:0%
+now washed out right to write down the
+ 
+
+ align:start position:0%
+now washed out right to write down the
+wave equation of
+
+ align:start position:0%
+wave equation of
+ 
+
+ align:start position:0%
+wave equation of
+motion and that's an equation of motion
+
+ align:start position:0%
+motion and that's an equation of motion
+ 
+
+ align:start position:0%
+motion and that's an equation of motion
+for particles whose wavelength is on the
+
+ align:start position:0%
+for particles whose wavelength is on the
+ 
+
+ align:start position:0%
+for particles whose wavelength is on the
+order of the size of their environment
+
+ align:start position:0%
+order of the size of their environment
+ 
+
+ align:start position:0%
+order of the size of their environment
+and you have to use that equation of
+
+ align:start position:0%
+and you have to use that equation of
+ 
+
+ align:start position:0%
+and you have to use that equation of
+motion to understand how that electron
+
+ align:start position:0%
+motion to understand how that electron
+ 
+
+ align:start position:0%
+motion to understand how that electron
+so to speak moves you can't use f equal
+
+ align:start position:0%
+so to speak moves you can't use f equal
+ 
+
+ align:start position:0%
+so to speak moves you can't use f equal
+Ma and that's where we will pick up next
+
+ align:start position:0%
+Ma and that's where we will pick up next
+ 
+
+ align:start position:0%
+Ma and that's where we will pick up next
+Wednesday
\ No newline at end of file
diff --git a/GwOklYjwHDI.txt b/GwOklYjwHDI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ebe4f825701dcd7ec2c795479efe0b24e4140844
--- /dev/null
+++ b/GwOklYjwHDI.txt
@@ -0,0 +1,347 @@
+align:start position:0%
+ 
+in this segment we go through a quick
+
+ align:start position:0%
+in this segment we go through a quick
+ 
+
+ align:start position:0%
+in this segment we go through a quick
+review of a few properties of the
+
+ align:start position:0%
+review of a few properties of the
+ 
+
+ align:start position:0%
+review of a few properties of the
+Bernoulli process that we already know
+
+ align:start position:0%
+Bernoulli process that we already know
+ 
+
+ align:start position:0%
+Bernoulli process that we already know
+we start by thinking about the number of
+
+ align:start position:0%
+we start by thinking about the number of
+ 
+
+ align:start position:0%
+we start by thinking about the number of
+successes or arrivals in the first n
+
+ align:start position:0%
+successes or arrivals in the first n
+ 
+
+ align:start position:0%
+successes or arrivals in the first n
+time slots this is the following
+
+ align:start position:0%
+time slots this is the following
+ 
+
+ align:start position:0%
+time slots this is the following
+quantity at each time we add a 0 or a 1
+
+ align:start position:0%
+quantity at each time we add a 0 or a 1
+ 
+
+ align:start position:0%
+quantity at each time we add a 0 or a 1
+depending on whether we've had a success
+
+ align:start position:0%
+depending on whether we've had a success
+ 
+
+ align:start position:0%
+depending on whether we've had a success
+or not and by adding those numbers we
+
+ align:start position:0%
+or not and by adding those numbers we
+ 
+
+ align:start position:0%
+or not and by adding those numbers we
+get the total number of successes now we
+
+ align:start position:0%
+get the total number of successes now we
+ 
+
+ align:start position:0%
+get the total number of successes now we
+already know that the number of
+
+ align:start position:0%
+already know that the number of
+ 
+
+ align:start position:0%
+already know that the number of
+successes in n trials obeys a binomial
+
+ align:start position:0%
+successes in n trials obeys a binomial
+ 
+
+ align:start position:0%
+successes in n trials obeys a binomial
+distribution so the probability of
+
+ align:start position:0%
+distribution so the probability of
+ 
+
+ align:start position:0%
+distribution so the probability of
+having K successes is given by the
+
+ align:start position:0%
+having K successes is given by the
+ 
+
+ align:start position:0%
+having K successes is given by the
+binomial probabilities and this is a
+
+ align:start position:0%
+binomial probabilities and this is a
+ 
+
+ align:start position:0%
+binomial probabilities and this is a
+formula that holds for k equal to 0 up
+
+ align:start position:0%
+formula that holds for k equal to 0 up
+ 
+
+ align:start position:0%
+formula that holds for k equal to 0 up
+to n which are the possible numbers for
+
+ align:start position:0%
+to n which are the possible numbers for
+ 
+
+ align:start position:0%
+to n which are the possible numbers for
+the random variable s for this random
+
+ align:start position:0%
+the random variable s for this random
+ 
+
+ align:start position:0%
+the random variable s for this random
+variable we know the expected value it's
+
+ align:start position:0%
+variable we know the expected value it's
+ 
+
+ align:start position:0%
+variable we know the expected value it's
+n times P and we also know it's variance
+
+ align:start position:0%
+n times P and we also know it's variance
+ 
+
+ align:start position:0%
+n times P and we also know it's variance
+which is n times P times 1 minus P
+
+ align:start position:0%
+which is n times P times 1 minus P
+ 
+
+ align:start position:0%
+which is n times P times 1 minus P
+another random variable of interest is
+
+ align:start position:0%
+another random variable of interest is
+ 
+
+ align:start position:0%
+another random variable of interest is
+the time until the first success or
+
+ align:start position:0%
+the time until the first success or
+ 
+
+ align:start position:0%
+the time until the first success or
+arrival so this is defined to be the
+
+ align:start position:0%
+arrival so this is defined to be the
+ 
+
+ align:start position:0%
+arrival so this is defined to be the
+smallest I for which the random variable
+
+ align:start position:0%
+smallest I for which the random variable
+ 
+
+ align:start position:0%
+smallest I for which the random variable
+X I is equal to 1 we have done this
+
+ align:start position:0%
+X I is equal to 1 we have done this
+ 
+
+ align:start position:0%
+X I is equal to 1 we have done this
+calculation in the past the probability
+
+ align:start position:0%
+calculation in the past the probability
+ 
+
+ align:start position:0%
+calculation in the past the probability
+that the first success appears at time k
+
+ align:start position:0%
+that the first success appears at time k
+ 
+
+ align:start position:0%
+that the first success appears at time k
+is the same as the probability that the
+
+ align:start position:0%
+is the same as the probability that the
+ 
+
+ align:start position:0%
+is the same as the probability that the
+first K minus 1 trials resulted in zeros
+
+ align:start position:0%
+first K minus 1 trials resulted in zeros
+ 
+
+ align:start position:0%
+first K minus 1 trials resulted in zeros
+and then the case trial resulted in a 1
+
+ align:start position:0%
+and then the case trial resulted in a 1
+ 
+
+ align:start position:0%
+and then the case trial resulted in a 1
+and so the probability of this is 1
+
+ align:start position:0%
+and so the probability of this is 1
+ 
+
+ align:start position:0%
+and so the probability of this is 1
+minus P the probability of 0 and we have
+
+ align:start position:0%
+minus P the probability of 0 and we have
+ 
+
+ align:start position:0%
+minus P the probability of 0 and we have
+K minus 1 of them times P the
+
+ align:start position:0%
+K minus 1 of them times P the
+ 
+
+ align:start position:0%
+K minus 1 of them times P the
+probability that the next trial gives us
+
+ align:start position:0%
+probability that the next trial gives us
+ 
+
+ align:start position:0%
+probability that the next trial gives us
+a success and this formula is valid for
+
+ align:start position:0%
+a success and this formula is valid for
+ 
+
+ align:start position:0%
+a success and this formula is valid for
+K being 1 2 and so on which is the range
+
+ align:start position:0%
+K being 1 2 and so on which is the range
+ 
+
+ align:start position:0%
+K being 1 2 and so on which is the range
+of possible values of this random
+
+ align:start position:0%
+of possible values of this random
+ 
+
+ align:start position:0%
+of possible values of this random
+variable T 1 this is the familiar
+
+ align:start position:0%
+variable T 1 this is the familiar
+ 
+
+ align:start position:0%
+variable T 1 this is the familiar
+geometric distribution that we have
+
+ align:start position:0%
+geometric distribution that we have
+ 
+
+ align:start position:0%
+geometric distribution that we have
+dealt with in several locations and
+
+ align:start position:0%
+dealt with in several locations and
+ 
+
+ align:start position:0%
+dealt with in several locations and
+particularly we know the expected value
+
+ align:start position:0%
+particularly we know the expected value
+ 
+
+ align:start position:0%
+particularly we know the expected value
+and the variance of a geometric random
+
+ align:start position:0%
+and the variance of a geometric random
+ 
+
+ align:start position:0%
+and the variance of a geometric random
+variable
\ No newline at end of file
diff --git a/H0MFJwQH2fo.txt b/H0MFJwQH2fo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..54c99588f1a307d8ab690fe854796d28b32ef4d9
--- /dev/null
+++ b/H0MFJwQH2fo.txt
@@ -0,0 +1,6475 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+some content in this audio lecture is
+
+ align:start position:0%
+some content in this audio lecture is
+ 
+
+ align:start position:0%
+some content in this audio lecture is
+not covered under our Creative Commons
+
+ align:start position:0%
+not covered under our Creative Commons
+ 
+
+ align:start position:0%
+not covered under our Creative Commons
+license please listen to the end credits
+
+ align:start position:0%
+license please listen to the end credits
+ 
+
+ align:start position:0%
+license please listen to the end credits
+for more information ok alright so
+
+ align:start position:0%
+for more information ok alright so
+ 
+
+ align:start position:0%
+for more information ok alright so
+today's reading was the MDA paper by
+
+ align:start position:0%
+today's reading was the MDA paper by
+ 
+
+ align:start position:0%
+today's reading was the MDA paper by
+Robin Hood ek Robins Abeka matt LeBlanc
+
+ align:start position:0%
+Robin Hood ek Robins Abeka matt LeBlanc
+ 
+
+ align:start position:0%
+Robin Hood ek Robins Abeka matt LeBlanc
+and it's pretty III hope you found it
+
+ align:start position:0%
+and it's pretty III hope you found it
+ 
+
+ align:start position:0%
+and it's pretty III hope you found it
+pretty light reading because it was
+
+ align:start position:0%
+pretty light reading because it was
+ 
+
+ align:start position:0%
+pretty light reading because it was
+intended to be pretty light and the
+
+ align:start position:0%
+intended to be pretty light and the
+ 
+
+ align:start position:0%
+intended to be pretty light and the
+whole point of it was that we will be
+
+ align:start position:0%
+whole point of it was that we will be
+ 
+
+ align:start position:0%
+whole point of it was that we will be
+getting through this pretty quickly
+
+ align:start position:0%
+getting through this pretty quickly
+ 
+
+ align:start position:0%
+getting through this pretty quickly
+today so then you have time to sit with
+
+ align:start position:0%
+today so then you have time to sit with
+ 
+
+ align:start position:0%
+today so then you have time to sit with
+your teams talk about your project work
+
+ align:start position:0%
+your teams talk about your project work
+ 
+
+ align:start position:0%
+your teams talk about your project work
+on it a little bit all the prototyping
+
+ align:start position:0%
+on it a little bit all the prototyping
+ 
+
+ align:start position:0%
+on it a little bit all the prototyping
+but materials in the front I'm going to
+
+ align:start position:0%
+but materials in the front I'm going to
+ 
+
+ align:start position:0%
+but materials in the front I'm going to
+people put in the table the boxes all on
+
+ align:start position:0%
+people put in the table the boxes all on
+ 
+
+ align:start position:0%
+people put in the table the boxes all on
+the tables are you more or less see done
+
+ align:start position:0%
+the tables are you more or less see done
+ 
+
+ align:start position:0%
+the tables are you more or less see done
+with your tees right now more or less ok
+
+ align:start position:0%
+with your tees right now more or less ok
+ 
+
+ align:start position:0%
+with your tees right now more or less ok
+every team represented let's see you are
+
+ align:start position:0%
+every team represented let's see you are
+ 
+
+ align:start position:0%
+every team represented let's see you are
+the building team you guys are done
+
+ align:start position:0%
+the building team you guys are done
+ 
+
+ align:start position:0%
+the building team you guys are done
+which the different building team right
+
+ align:start position:0%
+which the different building team right
+ 
+
+ align:start position:0%
+which the different building team right
+the LEGO building team ok team is that
+
+ align:start position:0%
+the LEGO building team ok team is that
+ 
+
+ align:start position:0%
+the LEGO building team ok team is that
+the what the hidden information team the
+
+ align:start position:0%
+the what the hidden information team the
+ 
+
+ align:start position:0%
+the what the hidden information team the
+thievery stealing stuff oh and the pack
+
+ align:start position:0%
+thievery stealing stuff oh and the pack
+ 
+
+ align:start position:0%
+thievery stealing stuff oh and the pack
+tonic ok all right so all right cool
+
+ align:start position:0%
+tonic ok all right so all right cool
+ 
+
+ align:start position:0%
+tonic ok all right so all right cool
+Piper here great well hopefully you're
+
+ align:start position:0%
+Piper here great well hopefully you're
+ 
+
+ align:start position:0%
+Piper here great well hopefully you're
+able to like make a little bit of
+
+ align:start position:0%
+able to like make a little bit of
+ 
+
+ align:start position:0%
+able to like make a little bit of
+progress on your teams all your projects
+
+ align:start position:0%
+progress on your teams all your projects
+ 
+
+ align:start position:0%
+progress on your teams all your projects
+so who managed to like play a little bit
+
+ align:start position:0%
+so who managed to like play a little bit
+ 
+
+ align:start position:0%
+so who managed to like play a little bit
+more of the games whether it was the
+
+ align:start position:0%
+more of the games whether it was the
+ 
+
+ align:start position:0%
+more of the games whether it was the
+prototype that you played on Wednesday
+
+ align:start position:0%
+prototype that you played on Wednesday
+ 
+
+ align:start position:0%
+prototype that you played on Wednesday
+or whether it was something else that
+
+ align:start position:0%
+or whether it was something else that
+ 
+
+ align:start position:0%
+or whether it was something else that
+you deposit along the way who made sure
+
+ align:start position:0%
+you deposit along the way who made sure
+ 
+
+ align:start position:0%
+you deposit along the way who made sure
+she gets get some play cut okay a few
+
+ align:start position:0%
+she gets get some play cut okay a few
+ 
+
+ align:start position:0%
+she gets get some play cut okay a few
+people who do you play it with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're back to the drawing board and redo
+
+ align:start position:0%
+we're back to the drawing board and redo
+ 
+
+ align:start position:0%
+we're back to the drawing board and redo
+you games okay welcome yourselves okay
+
+ align:start position:0%
+you games okay welcome yourselves okay
+ 
+
+ align:start position:0%
+you games okay welcome yourselves okay
+and would you play with okay dog door
+
+ align:start position:0%
+and would you play with okay dog door
+ 
+
+ align:start position:0%
+and would you play with okay dog door
+pay its basic here hey what else what
+
+ align:start position:0%
+pay its basic here hey what else what
+ 
+
+ align:start position:0%
+pay its basic here hey what else what
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+yep just with the jet team yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what did you the video play iteration
+
+ align:start position:0%
+what did you the video play iteration
+ 
+
+ align:start position:0%
+what did you the video play iteration
+that you didn't develop yourself anyone
+
+ align:start position:0%
+that you didn't develop yourself anyone
+ 
+
+ align:start position:0%
+that you didn't develop yourself anyone
+it's like if you play with that your
+
+ align:start position:0%
+it's like if you play with that your
+ 
+
+ align:start position:0%
+it's like if you play with that your
+team obviously you know you you okay so
+
+ align:start position:0%
+team obviously you know you you okay so
+ 
+
+ align:start position:0%
+team obviously you know you you okay so
+so if you played a version that you
+
+ align:start position:0%
+so if you played a version that you
+ 
+
+ align:start position:0%
+so if you played a version that you
+hadn't about yourself or if you played
+
+ align:start position:0%
+hadn't about yourself or if you played
+ 
+
+ align:start position:0%
+hadn't about yourself or if you played
+it with other people who weren't
+
+ align:start position:0%
+it with other people who weren't
+ 
+
+ align:start position:0%
+it with other people who weren't
+developing the game with you how do you
+
+ align:start position:0%
+developing the game with you how do you
+ 
+
+ align:start position:0%
+developing the game with you how do you
+what was some of the things that you
+
+ align:start position:0%
+what was some of the things that you
+ 
+
+ align:start position:0%
+what was some of the things that you
+felt that you felt about the game or
+
+ align:start position:0%
+felt that you felt about the game or
+ 
+
+ align:start position:0%
+felt that you felt about the game or
+what what do people say about your game
+
+ align:start position:0%
+what what do people say about your game
+ 
+
+ align:start position:0%
+what what do people say about your game
+once the game was done but what what do
+
+ align:start position:0%
+once the game was done but what what do
+ 
+
+ align:start position:0%
+once the game was done but what what do
+people seem to like or not like about it
+
+ align:start position:0%
+people seem to like or not like about it
+ 
+
+ align:start position:0%
+people seem to like or not like about it
+what what's up of like they got things
+
+ align:start position:0%
+what what's up of like they got things
+ 
+
+ align:start position:0%
+what what's up of like they got things
+that it was saying it did it end okay
+
+ align:start position:0%
+that it was saying it did it end okay
+ 
+
+ align:start position:0%
+that it was saying it did it end okay
+alright what else do you think it could
+
+ align:start position:0%
+alright what else do you think it could
+ 
+
+ align:start position:0%
+alright what else do you think it could
+have been negative feedback it could it
+
+ align:start position:0%
+have been negative feedback it could it
+ 
+
+ align:start position:0%
+have been negative feedback it could it
+could have been wow this is terrible
+
+ align:start position:0%
+could have been wow this is terrible
+ 
+
+ align:start position:0%
+could have been wow this is terrible
+because black what was the bad or it
+
+ align:start position:0%
+because black what was the bad or it
+ 
+
+ align:start position:0%
+because black what was the bad or it
+could have been wow that was kind of
+
+ align:start position:0%
+could have been wow that was kind of
+ 
+
+ align:start position:0%
+could have been wow that was kind of
+cool because of black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nothing don't we give you any feedback
+
+ align:start position:0%
+nothing don't we give you any feedback
+ 
+
+ align:start position:0%
+nothing don't we give you any feedback
+they just kind of sat there passively
+
+ align:start position:0%
+they just kind of sat there passively
+ 
+
+ align:start position:0%
+they just kind of sat there passively
+why are you making us play this okay
+
+ align:start position:0%
+why are you making us play this okay
+ 
+
+ align:start position:0%
+why are you making us play this okay
+well I also week that that was for segue
+
+ align:start position:0%
+well I also week that that was for segue
+ 
+
+ align:start position:0%
+well I also week that that was for segue
+into a little bit it will talk about
+
+ align:start position:0%
+into a little bit it will talk about
+ 
+
+ align:start position:0%
+into a little bit it will talk about
+aesthetics actually uh maybe what I'll
+
+ align:start position:0%
+aesthetics actually uh maybe what I'll
+ 
+
+ align:start position:0%
+aesthetics actually uh maybe what I'll
+do that is I could make you play a game
+
+ align:start position:0%
+do that is I could make you play a game
+ 
+
+ align:start position:0%
+do that is I could make you play a game
+a short game that the game that you were
+
+ align:start position:0%
+a short game that the game that you were
+ 
+
+ align:start position:0%
+a short game that the game that you were
+seeing who's played it before yeah Oh a
+
+ align:start position:0%
+seeing who's played it before yeah Oh a
+ 
+
+ align:start position:0%
+seeing who's played it before yeah Oh a
+cysts also known as defense of which is
+
+ align:start position:0%
+cysts also known as defense of which is
+ 
+
+ align:start position:0%
+cysts also known as defense of which is
+easily confused Dora but it's not gonna
+
+ align:start position:0%
+easily confused Dora but it's not gonna
+ 
+
+ align:start position:0%
+easily confused Dora but it's not gonna
+all right if somebody would like to
+
+ align:start position:0%
+all right if somebody would like to
+ 
+
+ align:start position:0%
+all right if somebody would like to
+volunteer to play through early easy
+
+ align:start position:0%
+volunteer to play through early easy
+ 
+
+ align:start position:0%
+volunteer to play through early easy
+level level wow that's a lot of it you
+
+ align:start position:0%
+level level wow that's a lot of it you
+ 
+
+ align:start position:0%
+level level wow that's a lot of it you
+know what well but you are gonna charge
+
+ align:start position:0%
+know what well but you are gonna charge
+ 
+
+ align:start position:0%
+know what well but you are gonna charge
+the place in one round because each
+
+ align:start position:0%
+the place in one round because each
+ 
+
+ align:start position:0%
+the place in one round because each
+round is pretty fast
+
+ align:start position:0%
+round is pretty fast
+ 
+
+ align:start position:0%
+round is pretty fast
+so what stop with with you and then
+
+ align:start position:0%
+so what stop with with you and then
+ 
+
+ align:start position:0%
+so what stop with with you and then
+we'll go on okay and then everybody else
+
+ align:start position:0%
+we'll go on okay and then everybody else
+ 
+
+ align:start position:0%
+we'll go on okay and then everybody else
+pay attention because I guess he's
+
+ align:start position:0%
+pay attention because I guess he's
+ 
+
+ align:start position:0%
+pay attention because I guess he's
+pretty much played to the janitorial
+
+ align:start position:0%
+pretty much played to the janitorial
+ 
+
+ align:start position:0%
+pretty much played to the janitorial
+level so it's all it was all juried the
+
+ align:start position:0%
+level so it's all it was all juried the
+ 
+
+ align:start position:0%
+level so it's all it was all juried the
+design for the PC and was actually one
+
+ align:start position:0%
+design for the PC and was actually one
+ 
+
+ align:start position:0%
+design for the PC and was actually one
+of the it came out roughly you can't
+
+ align:start position:0%
+of the it came out roughly you can't
+ 
+
+ align:start position:0%
+of the it came out roughly you can't
+just go ahead and play it came out
+
+ align:start position:0%
+just go ahead and play it came out
+ 
+
+ align:start position:0%
+just go ahead and play it came out
+roughly about the same time as casual
+
+ align:start position:0%
+roughly about the same time as casual
+ 
+
+ align:start position:0%
+roughly about the same time as casual
+games downloadable casual games started
+
+ align:start position:0%
+games downloadable casual games started
+ 
+
+ align:start position:0%
+games downloadable casual games started
+picking up on on the pocket this was I
+
+ align:start position:0%
+picking up on on the pocket this was I
+ 
+
+ align:start position:0%
+picking up on on the pocket this was I
+don't think that was ever sold as a
+
+ align:start position:0%
+don't think that was ever sold as a
+ 
+
+ align:start position:0%
+don't think that was ever sold as a
+cross product or if it was that really
+
+ align:start position:0%
+cross product or if it was that really
+ 
+
+ align:start position:0%
+cross product or if it was that really
+was at the point of its business model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you you click around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that already searched
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hello not gonna get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you should use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so though though resort rates are going
+
+ align:start position:0%
+so though though resort rates are going
+ 
+
+ align:start position:0%
+so though though resort rates are going
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they like music darling okay big shiny
+
+ align:start position:0%
+they like music darling okay big shiny
+ 
+
+ align:start position:0%
+they like music darling okay big shiny
+thing how do we increase population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yay look what this guy is down there so
+
+ align:start position:0%
+yay look what this guy is down there so
+ 
+
+ align:start position:0%
+yay look what this guy is down there so
+this this actually turns out not to be
+
+ align:start position:0%
+this this actually turns out not to be
+ 
+
+ align:start position:0%
+this this actually turns out not to be
+the tutorial level this just a thought
+
+ align:start position:0%
+the tutorial level this just a thought
+ 
+
+ align:start position:0%
+the tutorial level this just a thought
+to be the first level that's true
+
+ align:start position:0%
+to be the first level that's true
+ 
+
+ align:start position:0%
+to be the first level that's true
+people don't like late tutorials is true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have 22 times about to - barbarian
+
+ align:start position:0%
+you have 22 times about to - barbarian
+ 
+
+ align:start position:0%
+you have 22 times about to - barbarian
+hordes arriving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+oh I did something clever okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't know I do have a smoke here
+
+ align:start position:0%
+I don't know I do have a smoke here
+ 
+
+ align:start position:0%
+I don't know I do have a smoke here
+March things go bad
+
+ align:start position:0%
+March things go bad
+ 
+
+ align:start position:0%
+March things go bad
+my parents are coming to a city to move
+
+ align:start position:0%
+my parents are coming to a city to move
+ 
+
+ align:start position:0%
+my parents are coming to a city to move
+troops they're here yeah you're learning
+
+ align:start position:0%
+troops they're here yeah you're learning
+ 
+
+ align:start position:0%
+troops they're here yeah you're learning
+feel the learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think I want what did they do
+
+ align:start position:0%
+I think I want what did they do
+ 
+
+ align:start position:0%
+I think I want what did they do
+oh I saw it okay so you did in fact
+
+ align:start position:0%
+oh I saw it okay so you did in fact
+ 
+
+ align:start position:0%
+oh I saw it okay so you did in fact
+complete the level but yeah probably
+
+ align:start position:0%
+complete the level but yeah probably
+ 
+
+ align:start position:0%
+complete the level but yeah probably
+what happened here touching squares
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+search okay that's okay
+
+ align:start position:0%
+search okay that's okay
+ 
+
+ align:start position:0%
+search okay that's okay
+steps that's what you figured out what
+
+ align:start position:0%
+steps that's what you figured out what
+ 
+
+ align:start position:0%
+steps that's what you figured out what
+about the rules but how do you
+
+ align:start position:0%
+about the rules but how do you
+ 
+
+ align:start position:0%
+about the rules but how do you
+personally feel about this game I mean
+
+ align:start position:0%
+personally feel about this game I mean
+ 
+
+ align:start position:0%
+personally feel about this game I mean
+glad that you already pick one one one
+
+ align:start position:0%
+glad that you already pick one one one
+ 
+
+ align:start position:0%
+glad that you already pick one one one
+level and clearly the game goes on okay
+
+ align:start position:0%
+level and clearly the game goes on okay
+ 
+
+ align:start position:0%
+level and clearly the game goes on okay
+alright so if you psychics out of your
+
+ align:start position:0%
+alright so if you psychics out of your
+ 
+
+ align:start position:0%
+alright so if you psychics out of your
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+yeah okay so so so back up lack of
+
+ align:start position:0%
+yeah okay so so so back up lack of
+ 
+
+ align:start position:0%
+yeah okay so so so back up lack of
+influence influence or possibly lack of
+
+ align:start position:0%
+influence influence or possibly lack of
+ 
+
+ align:start position:0%
+influence influence or possibly lack of
+control something of that all right so
+
+ align:start position:0%
+control something of that all right so
+ 
+
+ align:start position:0%
+control something of that all right so
+the next person providing themselves so
+
+ align:start position:0%
+the next person providing themselves so
+ 
+
+ align:start position:0%
+the next person providing themselves so
+young makes you're gonna play that level
+
+ align:start position:0%
+young makes you're gonna play that level
+ 
+
+ align:start position:0%
+young makes you're gonna play that level
+two taking it everything that you've
+
+ align:start position:0%
+two taking it everything that you've
+ 
+
+ align:start position:0%
+two taking it everything that you've
+seen so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm purple area of course anyone has any
+
+ align:start position:0%
+I'm purple area of course anyone has any
+ 
+
+ align:start position:0%
+I'm purple area of course anyone has any
+ideas about what he should be doing go
+
+ align:start position:0%
+ideas about what he should be doing go
+ 
+
+ align:start position:0%
+ideas about what he should be doing go
+ahead and say so he's other types of
+
+ align:start position:0%
+ahead and say so he's other types of
+ 
+
+ align:start position:0%
+ahead and say so he's other types of
+plate as I'm doing this yeah that's
+
+ align:start position:0%
+plate as I'm doing this yeah that's
+ 
+
+ align:start position:0%
+plate as I'm doing this yeah that's
+right but then I'm going to put up
+
+ align:start position:0%
+right but then I'm going to put up
+ 
+
+ align:start position:0%
+right but then I'm going to put up
+myself
+
+ align:start position:0%
+myself
+ 
+
+ align:start position:0%
+myself
+oh no do it in one turn straight you'd
+
+ align:start position:0%
+oh no do it in one turn straight you'd
+ 
+
+ align:start position:0%
+oh no do it in one turn straight you'd
+you go one purple square at a time yeah
+
+ align:start position:0%
+you go one purple square at a time yeah
+ 
+
+ align:start position:0%
+you go one purple square at a time yeah
+but I'm saying I want to control the
+
+ align:start position:0%
+but I'm saying I want to control the
+ 
+
+ align:start position:0%
+but I'm saying I want to control the
+squares up underneath that mountain does
+
+ align:start position:0%
+squares up underneath that mountain does
+ 
+
+ align:start position:0%
+squares up underneath that mountain does
+something okay what you people saying
+
+ align:start position:0%
+something okay what you people saying
+ 
+
+ align:start position:0%
+something okay what you people saying
+that there's wave when he put 20 people
+
+ align:start position:0%
+that there's wave when he put 20 people
+ 
+
+ align:start position:0%
+that there's wave when he put 20 people
+when when when you click on the mine
+
+ align:start position:0%
+when when when you click on the mine
+ 
+
+ align:start position:0%
+when when when you click on the mine
+what what do you think have it okay go
+
+ align:start position:0%
+what what do you think have it okay go
+ 
+
+ align:start position:0%
+what what do you think have it okay go
+go ahead hit do whatever you people I
+
+ align:start position:0%
+go ahead hit do whatever you people I
+ 
+
+ align:start position:0%
+go ahead hit do whatever you people I
+don't know I waste turns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+still one turn but does follow yeah yeah
+
+ align:start position:0%
+still one turn but does follow yeah yeah
+ 
+
+ align:start position:0%
+still one turn but does follow yeah yeah
+ooh but I got something I got archery
+
+ align:start position:0%
+ooh but I got something I got archery
+ 
+
+ align:start position:0%
+ooh but I got something I got archery
+I like archery bows increase your chance
+
+ align:start position:0%
+I like archery bows increase your chance
+ 
+
+ align:start position:0%
+I like archery bows increase your chance
+of 13 damage and the barbarians good
+
+ align:start position:0%
+of 13 damage and the barbarians good
+ 
+
+ align:start position:0%
+of 13 damage and the barbarians good
+keep doing that stuff I'm huge city city
+
+ align:start position:0%
+keep doing that stuff I'm huge city city
+ 
+
+ align:start position:0%
+keep doing that stuff I'm huge city city
+and get over look at that I don't know
+
+ align:start position:0%
+and get over look at that I don't know
+ 
+
+ align:start position:0%
+and get over look at that I don't know
+what that means but you found another
+
+ align:start position:0%
+what that means but you found another
+ 
+
+ align:start position:0%
+what that means but you found another
+technology it looks like I have no idea
+
+ align:start position:0%
+technology it looks like I have no idea
+ 
+
+ align:start position:0%
+technology it looks like I have no idea
+what the hell this Oh another city
+
+ align:start position:0%
+what the hell this Oh another city
+ 
+
+ align:start position:0%
+what the hell this Oh another city
+greetings at least two cities five I'll
+
+ align:start position:0%
+greetings at least two cities five I'll
+ 
+
+ align:start position:0%
+greetings at least two cities five I'll
+join your cause okay you can tell the
+
+ align:start position:0%
+join your cause okay you can tell the
+ 
+
+ align:start position:0%
+join your cause okay you can tell the
+doctors damn it oh good another city I
+
+ align:start position:0%
+doctors damn it oh good another city I
+ 
+
+ align:start position:0%
+doctors damn it oh good another city I
+should have certain look you got no
+
+ align:start position:0%
+should have certain look you got no
+ 
+
+ align:start position:0%
+should have certain look you got no
+technology than I did very nice very
+
+ align:start position:0%
+technology than I did very nice very
+ 
+
+ align:start position:0%
+technology than I did very nice very
+soon recess city projections the city to
+
+ align:start position:0%
+soon recess city projections the city to
+ 
+
+ align:start position:0%
+soon recess city projections the city to
+might survive cause he's defending a
+
+ align:start position:0%
+might survive cause he's defending a
+ 
+
+ align:start position:0%
+might survive cause he's defending a
+second city
+
+ align:start position:0%
+second city
+ 
+
+ align:start position:0%
+second city
+I think I think I think you mean before
+
+ align:start position:0%
+I think I think I think you mean before
+ 
+
+ align:start position:0%
+I think I think I think you mean before
+class started yeah okay so you feel
+
+ align:start position:0%
+class started yeah okay so you feel
+ 
+
+ align:start position:0%
+class started yeah okay so you feel
+awesome but you still don't know what I
+
+ align:start position:0%
+awesome but you still don't know what I
+ 
+
+ align:start position:0%
+awesome but you still don't know what I
+do know explore he's very good okay so
+
+ align:start position:0%
+do know explore he's very good okay so
+ 
+
+ align:start position:0%
+do know explore he's very good okay so
+here that one out so that's some sort of
+
+ align:start position:0%
+here that one out so that's some sort of
+ 
+
+ align:start position:0%
+here that one out so that's some sort of
+like exploring all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay figure out how to build a road
+
+ align:start position:0%
+okay figure out how to build a road
+ 
+
+ align:start position:0%
+okay figure out how to build a road
+he'll talk dirty with that dot for
+
+ align:start position:0%
+he'll talk dirty with that dot for
+ 
+
+ align:start position:0%
+he'll talk dirty with that dot for
+something yeah we don't know oh okay
+
+ align:start position:0%
+something yeah we don't know oh okay
+ 
+
+ align:start position:0%
+something yeah we don't know oh okay
+plus 20 starting villagers that's huge
+
+ align:start position:0%
+plus 20 starting villagers that's huge
+ 
+
+ align:start position:0%
+plus 20 starting villagers that's huge
+and mother set the fuse bomb
+
+ align:start position:0%
+and mother set the fuse bomb
+ 
+
+ align:start position:0%
+and mother set the fuse bomb
+hey perfect click it again always
+
+ align:start position:0%
+hey perfect click it again always
+ 
+
+ align:start position:0%
+hey perfect click it again always
+temples have a city that did nothing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are those two temple mount's do you
+
+ align:start position:0%
+what are those two temple mount's do you
+ 
+
+ align:start position:0%
+what are those two temple mount's do you
+wanna check that out
+
+ align:start position:0%
+wanna check that out
+ 
+
+ align:start position:0%
+wanna check that out
+oh okay so I think I figured out the
+
+ align:start position:0%
+oh okay so I think I figured out the
+ 
+
+ align:start position:0%
+oh okay so I think I figured out the
+money's at the bottom that's like oh
+
+ align:start position:0%
+money's at the bottom that's like oh
+ 
+
+ align:start position:0%
+money's at the bottom that's like oh
+yeah oh so you want to increase mines so
+
+ align:start position:0%
+yeah oh so you want to increase mines so
+ 
+
+ align:start position:0%
+yeah oh so you want to increase mines so
+you put more bad would buy that it's a
+
+ align:start position:0%
+you put more bad would buy that it's a
+ 
+
+ align:start position:0%
+you put more bad would buy that it's a
+multiplier yeah did you build a road
+
+ align:start position:0%
+multiplier yeah did you build a road
+ 
+
+ align:start position:0%
+multiplier yeah did you build a road
+how'd you do that how do build a road
+
+ align:start position:0%
+how'd you do that how do build a road
+ 
+
+ align:start position:0%
+how'd you do that how do build a road
+just like on the five hours I only need
+
+ align:start position:0%
+just like on the five hours I only need
+ 
+
+ align:start position:0%
+just like on the five hours I only need
+followers to kasi followers to do so
+
+ align:start position:0%
+followers to kasi followers to do so
+ 
+
+ align:start position:0%
+followers to kasi followers to do so
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+get more followers and Bill Gross later
+
+ align:start position:0%
+get more followers and Bill Gross later
+ 
+
+ align:start position:0%
+get more followers and Bill Gross later
+what follows can you say bro you also
+
+ align:start position:0%
+what follows can you say bro you also
+ 
+
+ align:start position:0%
+what follows can you say bro you also
+put them inside the mines how does he
+
+ align:start position:0%
+put them inside the mines how does he
+ 
+
+ align:start position:0%
+put them inside the mines how does he
+have multiple options that you can do
+
+ align:start position:0%
+have multiple options that you can do
+ 
+
+ align:start position:0%
+have multiple options that you can do
+with your followers did you ever
+
+ align:start position:0%
+with your followers did you ever
+ 
+
+ align:start position:0%
+with your followers did you ever
+searched your upper city where you have
+
+ align:start position:0%
+searched your upper city where you have
+ 
+
+ align:start position:0%
+searched your upper city where you have
+46 people now the populations only
+
+ align:start position:0%
+46 people now the populations only
+ 
+
+ align:start position:0%
+46 people now the populations only
+points on the first level finding the
+
+ align:start position:0%
+points on the first level finding the
+ 
+
+ align:start position:0%
+points on the first level finding the
+whole river good including the police
+
+ align:start position:0%
+whole river good including the police
+ 
+
+ align:start position:0%
+whole river good including the police
+yeah the point may take you a letter oh
+
+ align:start position:0%
+yeah the point may take you a letter oh
+ 
+
+ align:start position:0%
+yeah the point may take you a letter oh
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hey look at that
+
+ align:start position:0%
+Hey look at that
+ 
+
+ align:start position:0%
+Hey look at that
+now you never that's it it's like
+
+ align:start position:0%
+now you never that's it it's like
+ 
+
+ align:start position:0%
+now you never that's it it's like
+pitbull oh yeah more cities by the way
+
+ align:start position:0%
+pitbull oh yeah more cities by the way
+ 
+
+ align:start position:0%
+pitbull oh yeah more cities by the way
+that looks like a pathway through Oh
+
+ align:start position:0%
+that looks like a pathway through Oh
+ 
+
+ align:start position:0%
+that looks like a pathway through Oh
+perfect give a new mind you a new
+
+ align:start position:0%
+perfect give a new mind you a new
+ 
+
+ align:start position:0%
+perfect give a new mind you a new
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+you've now rope going downward help
+
+ align:start position:0%
+you've now rope going downward help
+ 
+
+ align:start position:0%
+you've now rope going downward help
+don't forget to put men just that mind
+
+ align:start position:0%
+don't forget to put men just that mind
+ 
+
+ align:start position:0%
+don't forget to put men just that mind
+you're 20 turns valium to insurance 251
+
+ align:start position:0%
+you're 20 turns valium to insurance 251
+ 
+
+ align:start position:0%
+you're 20 turns valium to insurance 251
+City increasing all right you're just
+
+ align:start position:0%
+City increasing all right you're just
+ 
+
+ align:start position:0%
+City increasing all right you're just
+made it nice
+
+ align:start position:0%
+made it nice
+ 
+
+ align:start position:0%
+made it nice
+did you search that I do to followers in
+
+ align:start position:0%
+did you search that I do to followers in
+ 
+
+ align:start position:0%
+did you search that I do to followers in
+the mind that pop I don't do too much
+
+ align:start position:0%
+the mind that pop I don't do too much
+ 
+
+ align:start position:0%
+the mind that pop I don't do too much
+he's yet to find oh good you found one
+
+ align:start position:0%
+he's yet to find oh good you found one
+ 
+
+ align:start position:0%
+he's yet to find oh good you found one
+of the upper symbols yeah we don't know
+
+ align:start position:0%
+of the upper symbols yeah we don't know
+ 
+
+ align:start position:0%
+of the upper symbols yeah we don't know
+another Corgi I'm looking for Emily and
+
+ align:start position:0%
+another Corgi I'm looking for Emily and
+ 
+
+ align:start position:0%
+another Corgi I'm looking for Emily and
+in the bottom right to the top left the
+
+ align:start position:0%
+in the bottom right to the top left the
+ 
+
+ align:start position:0%
+in the bottom right to the top left the
+only ones up here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh all three now can you connect roads
+
+ align:start position:0%
+oh all three now can you connect roads
+ 
+
+ align:start position:0%
+oh all three now can you connect roads
+in time you two turns no house for the
+
+ align:start position:0%
+in time you two turns no house for the
+ 
+
+ align:start position:0%
+in time you two turns no house for the
+last two trips put your followers in
+
+ align:start position:0%
+last two trips put your followers in
+ 
+
+ align:start position:0%
+last two trips put your followers in
+your mind there's a last technology
+
+ align:start position:0%
+your mind there's a last technology
+ 
+
+ align:start position:0%
+your mind there's a last technology
+Minotauro in sir it's fine I don't think
+
+ align:start position:0%
+Minotauro in sir it's fine I don't think
+ 
+
+ align:start position:0%
+Minotauro in sir it's fine I don't think
+I'll have enough to do that I'm okay but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+firstly the British disease is possible
+
+ align:start position:0%
+firstly the British disease is possible
+ 
+
+ align:start position:0%
+firstly the British disease is possible
+you need more technology also this like
+
+ align:start position:0%
+you need more technology also this like
+ 
+
+ align:start position:0%
+you need more technology also this like
+how ok so if you if you like like like
+
+ align:start position:0%
+how ok so if you if you like like like
+ 
+
+ align:start position:0%
+how ok so if you if you like like like
+you like you salvation
+
+ align:start position:0%
+you like you salvation
+ 
+
+ align:start position:0%
+you like you salvation
+what's that volunteer I thought I saw
+
+ align:start position:0%
+what's that volunteer I thought I saw
+ 
+
+ align:start position:0%
+what's that volunteer I thought I saw
+four hands
+
+ align:start position:0%
+four hands
+ 
+
+ align:start position:0%
+four hands
+try it one more time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put everyone online
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's do we search the US
+
+ align:start position:0%
+that's do we search the US
+ 
+
+ align:start position:0%
+that's do we search the US
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it valuable to build rows in between
+
+ align:start position:0%
+is it valuable to build rows in between
+ 
+
+ align:start position:0%
+is it valuable to build rows in between
+lines and cities
+
+ align:start position:0%
+lines and cities
+ 
+
+ align:start position:0%
+lines and cities
+don't think
+
+ align:start position:0%
+don't think
+ 
+
+ align:start position:0%
+don't think
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right now you go through that
+
+ align:start position:0%
+all right now you go through that
+ 
+
+ align:start position:0%
+all right now you go through that
+passage I see the arc yeah they don't
+
+ align:start position:0%
+passage I see the arc yeah they don't
+ 
+
+ align:start position:0%
+passage I see the arc yeah they don't
+get to searches see what you got oh look
+
+ align:start position:0%
+get to searches see what you got oh look
+ 
+
+ align:start position:0%
+get to searches see what you got oh look
+at that very nice tiny population
+
+ align:start position:0%
+at that very nice tiny population
+ 
+
+ align:start position:0%
+at that very nice tiny population
+increase probably want to get see cities
+
+ align:start position:0%
+increase probably want to get see cities
+ 
+
+ align:start position:0%
+increase probably want to get see cities
+first into the Oasis last night you
+
+ align:start position:0%
+first into the Oasis last night you
+ 
+
+ align:start position:0%
+first into the Oasis last night you
+better be Oh keep going up there was
+
+ align:start position:0%
+better be Oh keep going up there was
+ 
+
+ align:start position:0%
+better be Oh keep going up there was
+something there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right he searched the city bus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're just jumping all over the place
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seas gaily to offers
+
+ align:start position:0%
+seas gaily to offers
+ 
+
+ align:start position:0%
+seas gaily to offers
+oh I'm waiting on your cities
+
+ align:start position:0%
+oh I'm waiting on your cities
+ 
+
+ align:start position:0%
+oh I'm waiting on your cities
+no you just never know sitting there
+
+ align:start position:0%
+no you just never know sitting there
+ 
+
+ align:start position:0%
+no you just never know sitting there
+make a city dump all your juicy operator
+
+ align:start position:0%
+make a city dump all your juicy operator
+ 
+
+ align:start position:0%
+make a city dump all your juicy operator
+bottom left just 220 units that's very
+
+ align:start position:0%
+bottom left just 220 units that's very
+ 
+
+ align:start position:0%
+bottom left just 220 units that's very
+nice nice you got at least three
+
+ align:start position:0%
+nice nice you got at least three
+ 
+
+ align:start position:0%
+nice nice you got at least three
+technology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah
+
+ align:start position:0%
+oh yeah
+ 
+
+ align:start position:0%
+oh yeah
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so so you feel that there
+
+ align:start position:0%
+okay all right so so you feel that there
+ 
+
+ align:start position:0%
+okay all right so so you feel that there
+are some there's some redundancy going
+
+ align:start position:0%
+are some there's some redundancy going
+ 
+
+ align:start position:0%
+are some there's some redundancy going
+though yeah okay all right all right
+
+ align:start position:0%
+though yeah okay all right all right
+ 
+
+ align:start position:0%
+though yeah okay all right all right
+cool thank you thank you thank you very
+
+ align:start position:0%
+cool thank you thank you thank you very
+ 
+
+ align:start position:0%
+cool thank you thank you thank you very
+much so these are kinds of the things
+
+ align:start position:0%
+much so these are kinds of the things
+ 
+
+ align:start position:0%
+much so these are kinds of the things
+that ask players you know the sensations
+
+ align:start position:0%
+that ask players you know the sensations
+ 
+
+ align:start position:0%
+that ask players you know the sensations
+that you get right you know you get kind
+
+ align:start position:0%
+that you get right you know you get kind
+ 
+
+ align:start position:0%
+that you get right you know you get kind
+of like a joy of exploring you know
+
+ align:start position:0%
+of like a joy of exploring you know
+ 
+
+ align:start position:0%
+of like a joy of exploring you know
+finding out new things pushing back to
+
+ align:start position:0%
+finding out new things pushing back to
+ 
+
+ align:start position:0%
+finding out new things pushing back to
+funk at the beginning of learning a game
+
+ align:start position:0%
+funk at the beginning of learning a game
+ 
+
+ align:start position:0%
+funk at the beginning of learning a game
+you know this confusion that's before
+
+ align:start position:0%
+you know this confusion that's before
+ 
+
+ align:start position:0%
+you know this confusion that's before
+the ones you don't actually know how
+
+ align:start position:0%
+the ones you don't actually know how
+ 
+
+ align:start position:0%
+the ones you don't actually know how
+your actions are you know changing
+
+ align:start position:0%
+your actions are you know changing
+ 
+
+ align:start position:0%
+your actions are you know changing
+things but if you play a lot of games
+
+ align:start position:0%
+things but if you play a lot of games
+ 
+
+ align:start position:0%
+things but if you play a lot of games
+you usually sort of primed to sort of
+
+ align:start position:0%
+you usually sort of primed to sort of
+ 
+
+ align:start position:0%
+you usually sort of primed to sort of
+accept a little bit of that and
+
+ align:start position:0%
+accept a little bit of that and
+ 
+
+ align:start position:0%
+accept a little bit of that and
+sometimes it's it's balanced well enough
+
+ align:start position:0%
+sometimes it's it's balanced well enough
+ 
+
+ align:start position:0%
+sometimes it's it's balanced well enough
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+
+ align:start position:0%
+that it's sort of it feeds you rather
+ 
+
+ align:start position:0%
+that it's sort of it feeds you rather
+than you know puts you off but sometimes
+
+ align:start position:0%
+than you know puts you off but sometimes
+ 
+
+ align:start position:0%
+than you know puts you off but sometimes
+it just puts you off somewhat said that
+
+ align:start position:0%
+it just puts you off somewhat said that
+ 
+
+ align:start position:0%
+it just puts you off somewhat said that
+was a it felt good to save people you
+
+ align:start position:0%
+was a it felt good to save people you
+ 
+
+ align:start position:0%
+was a it felt good to save people you
+know best there's that you described it
+
+ align:start position:0%
+know best there's that you described it
+ 
+
+ align:start position:0%
+know best there's that you described it
+as feeling kind of fun and in the paper
+
+ align:start position:0%
+as feeling kind of fun and in the paper
+ 
+
+ align:start position:0%
+as feeling kind of fun and in the paper
+some different ways how we can some
+
+ align:start position:0%
+some different ways how we can some
+ 
+
+ align:start position:0%
+some different ways how we can some
+describe fun you know the the it's just
+
+ align:start position:0%
+describe fun you know the the it's just
+ 
+
+ align:start position:0%
+describe fun you know the the it's just
+eight different types but even in a
+
+ align:start position:0%
+eight different types but even in a
+ 
+
+ align:start position:0%
+eight different types but even in a
+paper it states it isn't meant to be a
+
+ align:start position:0%
+paper it states it isn't meant to be a
+ 
+
+ align:start position:0%
+paper it states it isn't meant to be a
+comprehensive place is it where to be a
+
+ align:start position:0%
+comprehensive place is it where to be a
+ 
+
+ align:start position:0%
+comprehensive place is it where to be a
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+
+ align:start position:0%
+list that's just exhausting every single
+ 
+
+ align:start position:0%
+list that's just exhausting every single
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+
+ align:start position:0%
+op a kind of fun out there it's just
+ 
+
+ align:start position:0%
+op a kind of fun out there it's just
+there to show that there's a lot of
+
+ align:start position:0%
+there to show that there's a lot of
+ 
+
+ align:start position:0%
+there to show that there's a lot of
+different kinds of fun when you when you
+
+ align:start position:0%
+different kinds of fun when you when you
+ 
+
+ align:start position:0%
+different kinds of fun when you when you
+play a game like exploring things well
+
+ align:start position:0%
+play a game like exploring things well
+ 
+
+ align:start position:0%
+play a game like exploring things well
+you know inhabiting a role or overcoming
+
+ align:start position:0%
+you know inhabiting a role or overcoming
+ 
+
+ align:start position:0%
+you know inhabiting a role or overcoming
+a challenge or just you know passing
+
+ align:start position:0%
+a challenge or just you know passing
+ 
+
+ align:start position:0%
+a challenge or just you know passing
+time in a you know in
+
+ align:start position:0%
+time in a you know in
+ 
+
+ align:start position:0%
+time in a you know in
+in a way to alleviate boredom sorry I
+
+ align:start position:0%
+in a way to alleviate boredom sorry I
+ 
+
+ align:start position:0%
+in a way to alleviate boredom sorry I
+have a bit of cold so my my speeches a
+
+ align:start position:0%
+have a bit of cold so my my speeches a
+ 
+
+ align:start position:0%
+have a bit of cold so my my speeches a
+little bit under today there is there
+
+ align:start position:0%
+little bit under today there is there
+ 
+
+ align:start position:0%
+little bit under today there is there
+are a number of game mechanics in here
+
+ align:start position:0%
+are a number of game mechanics in here
+ 
+
+ align:start position:0%
+are a number of game mechanics in here
+that generate some of these sensations
+
+ align:start position:0%
+that generate some of these sensations
+ 
+
+ align:start position:0%
+that generate some of these sensations
+I'm going to put aside stuff about
+
+ align:start position:0%
+I'm going to put aside stuff about
+ 
+
+ align:start position:0%
+I'm going to put aside stuff about
+confusion and lack of all influence
+
+ align:start position:0%
+confusion and lack of all influence
+ 
+
+ align:start position:0%
+confusion and lack of all influence
+right now because some of that addressed
+
+ align:start position:0%
+right now because some of that addressed
+ 
+
+ align:start position:0%
+right now because some of that addressed
+in a tutorial is like if you if if you
+
+ align:start position:0%
+in a tutorial is like if you if if you
+ 
+
+ align:start position:0%
+in a tutorial is like if you if if you
+went through the tutorial and explain to
+
+ align:start position:0%
+went through the tutorial and explain to
+ 
+
+ align:start position:0%
+went through the tutorial and explain to
+you what all the actions were you
+
+ align:start position:0%
+you what all the actions were you
+ 
+
+ align:start position:0%
+you what all the actions were you
+probably wouldn't feel quite so confused
+
+ align:start position:0%
+probably wouldn't feel quite so confused
+ 
+
+ align:start position:0%
+probably wouldn't feel quite so confused
+about what you could do however I think
+
+ align:start position:0%
+about what you could do however I think
+ 
+
+ align:start position:0%
+about what you could do however I think
+it's reasonable to sort of address the
+
+ align:start position:0%
+it's reasonable to sort of address the
+ 
+
+ align:start position:0%
+it's reasonable to sort of address the
+lack of control that you might feel even
+
+ align:start position:0%
+lack of control that you might feel even
+ 
+
+ align:start position:0%
+lack of control that you might feel even
+after knowing what you could do right so
+
+ align:start position:0%
+after knowing what you could do right so
+ 
+
+ align:start position:0%
+after knowing what you could do right so
+let's talk about but that's right these
+
+ align:start position:0%
+let's talk about but that's right these
+ 
+
+ align:start position:0%
+let's talk about but that's right these
+are the things that the people will
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+are the things that the people will
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+
+ align:start position:0%
+are the things that the people will
+describe as aesthetics the thing that
+
+ align:start position:0%
+describe as aesthetics the thing that
+ 
+
+ align:start position:0%
+describe as aesthetics the thing that
+the player feels whether the the paper
+
+ align:start position:0%
+the player feels whether the the paper
+ 
+
+ align:start position:0%
+the player feels whether the the paper
+describes them as desirable experiences
+
+ align:start position:0%
+describes them as desirable experiences
+ 
+
+ align:start position:0%
+describes them as desirable experiences
+that's not necessarily always the case
+
+ align:start position:0%
+that's not necessarily always the case
+ 
+
+ align:start position:0%
+that's not necessarily always the case
+it's not always desirable I mean I'm
+
+ align:start position:0%
+it's not always desirable I mean I'm
+ 
+
+ align:start position:0%
+it's not always desirable I mean I'm
+pretty sure
+
+ align:start position:0%
+pretty sure
+ 
+
+ align:start position:0%
+pretty sure
+confusion was not a desire what was was
+
+ align:start position:0%
+confusion was not a desire what was was
+ 
+
+ align:start position:0%
+confusion was not a desire what was was
+not a desire experience that the
+
+ align:start position:0%
+not a desire experience that the
+ 
+
+ align:start position:0%
+not a desire experience that the
+designer of this game wanted you to have
+
+ align:start position:0%
+designer of this game wanted you to have
+ 
+
+ align:start position:0%
+designer of this game wanted you to have
+by the way one of the designers of that
+
+ align:start position:0%
+by the way one of the designers of that
+ 
+
+ align:start position:0%
+by the way one of the designers of that
+game is actually also one of the writers
+
+ align:start position:0%
+game is actually also one of the writers
+ 
+
+ align:start position:0%
+game is actually also one of the writers
+of this paper which is why we're playing
+
+ align:start position:0%
+of this paper which is why we're playing
+ 
+
+ align:start position:0%
+of this paper which is why we're playing
+this game in particular so these are
+
+ align:start position:0%
+this game in particular so these are
+ 
+
+ align:start position:0%
+this game in particular so these are
+aesthetics let's talk about some of the
+
+ align:start position:0%
+aesthetics let's talk about some of the
+ 
+
+ align:start position:0%
+aesthetics let's talk about some of the
+mechanics of the game execution of the
+
+ align:start position:0%
+mechanics of the game execution of the
+ 
+
+ align:start position:0%
+mechanics of the game execution of the
+screen uh trigger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's talk about some other mechanics
+
+ align:start position:0%
+so let's talk about some other mechanics
+ 
+
+ align:start position:0%
+so let's talk about some other mechanics
+in this game well someone described it
+
+ align:start position:0%
+in this game well someone described it
+ 
+
+ align:start position:0%
+in this game well someone described it
+this right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay alright so so it's turn-based until
+
+ align:start position:0%
+okay alright so so it's turn-based until
+ 
+
+ align:start position:0%
+okay alright so so it's turn-based until
+use this until you've made your final
+
+ align:start position:0%
+use this until you've made your final
+ 
+
+ align:start position:0%
+use this until you've made your final
+move right and then that's ten seconds
+
+ align:start position:0%
+move right and then that's ten seconds
+ 
+
+ align:start position:0%
+move right and then that's ten seconds
+when it counts down as you see things
+
+ align:start position:0%
+when it counts down as you see things
+ 
+
+ align:start position:0%
+when it counts down as you see things
+continue to happen
+
+ align:start position:0%
+continue to happen
+ 
+
+ align:start position:0%
+continue to happen
+okay all right there is called badness
+
+ align:start position:0%
+okay all right there is called badness
+ 
+
+ align:start position:0%
+okay all right there is called badness
+of mechanicus that's some sort of a I
+
+ align:start position:0%
+of mechanicus that's some sort of a I
+ 
+
+ align:start position:0%
+of mechanicus that's some sort of a I
+call back right
+
+ align:start position:0%
+call back right
+ 
+
+ align:start position:0%
+call back right
+you don't actually directly tell tell
+
+ align:start position:0%
+you don't actually directly tell tell
+ 
+
+ align:start position:0%
+you don't actually directly tell tell
+your troops to attack you to face that
+
+ align:start position:0%
+your troops to attack you to face that
+ 
+
+ align:start position:0%
+your troops to attack you to face that
+ahead of time and then they just wail at
+
+ align:start position:0%
+ahead of time and then they just wail at
+ 
+
+ align:start position:0%
+ahead of time and then they just wail at
+each other using some sort of algorithm
+
+ align:start position:0%
+each other using some sort of algorithm
+ 
+
+ align:start position:0%
+each other using some sort of algorithm
+some sort of computation of who are on
+
+ align:start position:0%
+some sort of computation of who are on
+ 
+
+ align:start position:0%
+some sort of computation of who are on
+how the numbers of how the magician
+
+ align:start position:0%
+how the numbers of how the magician
+ 
+
+ align:start position:0%
+how the numbers of how the magician
+works what else is in the game
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+declaration so go ahead make that say
+
+ align:start position:0%
+declaration so go ahead make that say
+ 
+
+ align:start position:0%
+declaration so go ahead make that say
+you're like okay so so how do you find
+
+ align:start position:0%
+you're like okay so so how do you find
+ 
+
+ align:start position:0%
+you're like okay so so how do you find
+cities how do you find city okay so so
+
+ align:start position:0%
+cities how do you find city okay so so
+ 
+
+ align:start position:0%
+cities how do you find city okay so so
+you you you click on the purple squares
+
+ align:start position:0%
+you you you click on the purple squares
+ 
+
+ align:start position:0%
+you you you click on the purple squares
+right and then that shows you what's
+
+ align:start position:0%
+right and then that shows you what's
+ 
+
+ align:start position:0%
+right and then that shows you what's
+underneath the purple square basically
+
+ align:start position:0%
+underneath the purple square basically
+ 
+
+ align:start position:0%
+underneath the purple square basically
+the fog so so that's they've got a sort
+
+ align:start position:0%
+the fog so so that's they've got a sort
+ 
+
+ align:start position:0%
+the fog so so that's they've got a sort
+of it's not full of war exactly but you
+
+ align:start position:0%
+of it's not full of war exactly but you
+ 
+
+ align:start position:0%
+of it's not full of war exactly but you
+know they've got a sort of uh unexplored
+
+ align:start position:0%
+know they've got a sort of uh unexplored
+ 
+
+ align:start position:0%
+know they've got a sort of uh unexplored
+fog right which you tap to to disappear
+
+ align:start position:0%
+fog right which you tap to to disappear
+ 
+
+ align:start position:0%
+fog right which you tap to to disappear
+is that the only clue about how to find
+
+ align:start position:0%
+is that the only clue about how to find
+ 
+
+ align:start position:0%
+is that the only clue about how to find
+a city sometimes you can be deposited
+
+ align:start position:0%
+a city sometimes you can be deposited
+ 
+
+ align:start position:0%
+a city sometimes you can be deposited
+right there's something there yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on speed but on the iPad defines all
+
+ align:start position:0%
+on speed but on the iPad defines all
+ 
+
+ align:start position:0%
+on speed but on the iPad defines all
+these cities so if you step on something
+
+ align:start position:0%
+these cities so if you step on something
+ 
+
+ align:start position:0%
+these cities so if you step on something
+greed in the city somewhere nearby
+
+ align:start position:0%
+greed in the city somewhere nearby
+ 
+
+ align:start position:0%
+greed in the city somewhere nearby
+instead of mine sweepers to doesn't what
+
+ align:start position:0%
+instead of mine sweepers to doesn't what
+ 
+
+ align:start position:0%
+instead of mine sweepers to doesn't what
+else deal with okay so what what about
+
+ align:start position:0%
+else deal with okay so what what about
+ 
+
+ align:start position:0%
+else deal with okay so what what about
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+looking for it and as soon as you hit
+
+ align:start position:0%
+looking for it and as soon as you hit
+ 
+
+ align:start position:0%
+looking for it and as soon as you hit
+one of the squares of those you be more
+
+ align:start position:0%
+one of the squares of those you be more
+ 
+
+ align:start position:0%
+one of the squares of those you be more
+or less like figure out where the other
+
+ align:start position:0%
+or less like figure out where the other
+ 
+
+ align:start position:0%
+or less like figure out where the other
+ones are okay because it seems to always
+
+ align:start position:0%
+ones are okay because it seems to always
+ 
+
+ align:start position:0%
+ones are okay because it seems to always
+be in the same 3 by 4 yeah so so the
+
+ align:start position:0%
+be in the same 3 by 4 yeah so so the
+ 
+
+ align:start position:0%
+be in the same 3 by 4 yeah so so the
+Oasis creativity right like you feel
+
+ align:start position:0%
+Oasis creativity right like you feel
+ 
+
+ align:start position:0%
+Oasis creativity right like you feel
+like yeah well the Oasis is always a
+
+ align:start position:0%
+like yeah well the Oasis is always a
+ 
+
+ align:start position:0%
+like yeah well the Oasis is always a
+rectangle
+
+ align:start position:0%
+rectangle
+ 
+
+ align:start position:0%
+rectangle
+I'm sorry sorry so you find Carter yeah
+
+ align:start position:0%
+I'm sorry sorry so you find Carter yeah
+ 
+
+ align:start position:0%
+I'm sorry sorry so you find Carter yeah
+you know you know that if you follow
+
+ align:start position:0%
+you know you know that if you follow
+ 
+
+ align:start position:0%
+you know you know that if you follow
+what those things do you can see the tip
+
+ align:start position:0%
+what those things do you can see the tip
+ 
+
+ align:start position:0%
+what those things do you can see the tip
+as well like United plate
+
+ align:start position:0%
+as well like United plate
+ 
+
+ align:start position:0%
+as well like United plate
+it's either grass on this side water on
+
+ align:start position:0%
+it's either grass on this side water on
+ 
+
+ align:start position:0%
+it's either grass on this side water on
+this side right so so so if the grid was
+
+ align:start position:0%
+this side right so so so if the grid was
+ 
+
+ align:start position:0%
+this side right so so so if the grid was
+like that you know once the what would
+
+ align:start position:0%
+like that you know once the what would
+ 
+
+ align:start position:0%
+like that you know once the what would
+you find one corner you know which way
+
+ align:start position:0%
+you find one corner you know which way
+ 
+
+ align:start position:0%
+you find one corner you know which way
+to explore off the river so analysis
+
+ align:start position:0%
+to explore off the river so analysis
+ 
+
+ align:start position:0%
+to explore off the river so analysis
+gives you clues the title of the always
+
+ align:start position:0%
+gives you clues the title of the always
+ 
+
+ align:start position:0%
+gives you clues the title of the always
+does alone to give you clues in the same
+
+ align:start position:0%
+does alone to give you clues in the same
+ 
+
+ align:start position:0%
+does alone to give you clues in the same
+way that the farm to keep include upon
+
+ align:start position:0%
+way that the farm to keep include upon
+ 
+
+ align:start position:0%
+way that the farm to keep include upon
+decisions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or bill groves or cities - how do you
+
+ align:start position:0%
+or bill groves or cities - how do you
+ 
+
+ align:start position:0%
+or bill groves or cities - how do you
+allocate resources in this game you just
+
+ align:start position:0%
+allocate resources in this game you just
+ 
+
+ align:start position:0%
+allocate resources in this game you just
+type it and what happens when you tap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you you have a limited number of
+
+ align:start position:0%
+so you you have a limited number of
+ 
+
+ align:start position:0%
+so you you have a limited number of
+followers and tapping assigns them to
+
+ align:start position:0%
+followers and tapping assigns them to
+ 
+
+ align:start position:0%
+followers and tapping assigns them to
+spend them basically to get to for
+
+ align:start position:0%
+spend them basically to get to for
+ 
+
+ align:start position:0%
+spend them basically to get to for
+follow some sort of some task so so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+followers for science science the
+
+ align:start position:0%
+followers for science science the
+ 
+
+ align:start position:0%
+followers for science science the
+followers okay other ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's this work
+
+ align:start position:0%
+there's this work
+ 
+
+ align:start position:0%
+there's this work
+it's courting again which is different
+
+ align:start position:0%
+it's courting again which is different
+ 
+
+ align:start position:0%
+it's courting again which is different
+you know from what actually like when
+
+ align:start position:0%
+you know from what actually like when
+ 
+
+ align:start position:0%
+you know from what actually like when
+you add your level
+
+ align:start position:0%
+you add your level
+ 
+
+ align:start position:0%
+you add your level
+well there did your well and then
+
+ align:start position:0%
+well there did your well and then
+ 
+
+ align:start position:0%
+well there did your well and then
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+didn't always respond during this war
+
+ align:start position:0%
+didn't always respond during this war
+ 
+
+ align:start position:0%
+didn't always respond during this war
+right the score isn't necessary so the
+
+ align:start position:0%
+right the score isn't necessary so the
+ 
+
+ align:start position:0%
+right the score isn't necessary so the
+score is that the score has is kind of
+
+ align:start position:0%
+score is that the score has is kind of
+ 
+
+ align:start position:0%
+score is that the score has is kind of
+different from what you from from from
+
+ align:start position:0%
+different from what you from from from
+ 
+
+ align:start position:0%
+different from what you from from from
+from what engage immediately giving you
+
+ align:start position:0%
+from what engage immediately giving you
+ 
+
+ align:start position:0%
+from what engage immediately giving you
+feedback on this score is kind of like a
+
+ align:start position:0%
+feedback on this score is kind of like a
+ 
+
+ align:start position:0%
+feedback on this score is kind of like a
+completely different kind of feedback
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size was very confused when like we won
+
+ align:start position:0%
+size was very confused when like we won
+ 
+
+ align:start position:0%
+size was very confused when like we won
+first low because everyone died but we
+
+ align:start position:0%
+first low because everyone died but we
+ 
+
+ align:start position:0%
+first low because everyone died but we
+got four zero which kind of made sense
+
+ align:start position:0%
+got four zero which kind of made sense
+ 
+
+ align:start position:0%
+got four zero which kind of made sense
+then and like when I went above people
+
+ align:start position:0%
+then and like when I went above people
+ 
+
+ align:start position:0%
+then and like when I went above people
+died like so much level like that made
+
+ align:start position:0%
+died like so much level like that made
+ 
+
+ align:start position:0%
+died like so much level like that made
+sense bad two cities left I still got
+
+ align:start position:0%
+sense bad two cities left I still got
+ 
+
+ align:start position:0%
+sense bad two cities left I still got
+score zero because I lost tons of people
+
+ align:start position:0%
+score zero because I lost tons of people
+ 
+
+ align:start position:0%
+score zero because I lost tons of people
+then when we made it so we didn't lose a
+
+ align:start position:0%
+then when we made it so we didn't lose a
+ 
+
+ align:start position:0%
+then when we made it so we didn't lose a
+single City we got the exported house or
+
+ align:start position:0%
+single City we got the exported house or
+ 
+
+ align:start position:0%
+single City we got the exported house or
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I know the score makes sense
+
+ align:start position:0%
+I know the score makes sense
+ 
+
+ align:start position:0%
+I know the score makes sense
+maybe the level progression in person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes we love I said you've added you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there you go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patience and a score for foreground to
+
+ align:start position:0%
+patience and a score for foreground to
+ 
+
+ align:start position:0%
+patience and a score for foreground to
+be equivalent standards and that's a
+
+ align:start position:0%
+be equivalent standards and that's a
+ 
+
+ align:start position:0%
+be equivalent standards and that's a
+perfectly find another truck
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I understand there was another mechanic
+
+ align:start position:0%
+I understand there was another mechanic
+ 
+
+ align:start position:0%
+I understand there was another mechanic
+we didn't really get to discover it but
+
+ align:start position:0%
+we didn't really get to discover it but
+ 
+
+ align:start position:0%
+we didn't really get to discover it but
+those of the link blowing Oh a right
+
+ align:start position:0%
+those of the link blowing Oh a right
+ 
+
+ align:start position:0%
+those of the link blowing Oh a right
+right right right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clearly leading to something we haven't
+
+ align:start position:0%
+clearly leading to something we haven't
+ 
+
+ align:start position:0%
+clearly leading to something we haven't
+figured out yet okay there is no special
+
+ align:start position:0%
+figured out yet okay there is no special
+ 
+
+ align:start position:0%
+figured out yet okay there is no special
+power that we got that's okay yeah I
+
+ align:start position:0%
+power that we got that's okay yeah I
+ 
+
+ align:start position:0%
+power that we got that's okay yeah I
+think they called experts advice was
+
+ align:start position:0%
+think they called experts advice was
+ 
+
+ align:start position:0%
+think they called experts advice was
+that followers part of this because you
+
+ align:start position:0%
+that followers part of this because you
+ 
+
+ align:start position:0%
+that followers part of this because you
+know exactly how do with this yeah I got
+
+ align:start position:0%
+know exactly how do with this yeah I got
+ 
+
+ align:start position:0%
+know exactly how do with this yeah I got
+transported artwork right
+
+ align:start position:0%
+transported artwork right
+ 
+
+ align:start position:0%
+transported artwork right
+okay so when where did this go up to
+
+ align:start position:0%
+okay so when where did this go up to
+ 
+
+ align:start position:0%
+okay so when where did this go up to
+appeared anyone know this you're
+
+ align:start position:0%
+appeared anyone know this you're
+ 
+
+ align:start position:0%
+appeared anyone know this you're
+uncovering the tiles but when you
+
+ align:start position:0%
+uncovering the tiles but when you
+ 
+
+ align:start position:0%
+uncovering the tiles but when you
+searched if you didn't get when you pick
+
+ align:start position:0%
+searched if you didn't get when you pick
+ 
+
+ align:start position:0%
+searched if you didn't get when you pick
+up the always when you walk over the
+
+ align:start position:0%
+up the always when you walk over the
+ 
+
+ align:start position:0%
+up the always when you walk over the
+Oasis you get the worms so you always
+
+ align:start position:0%
+Oasis you get the worms so you always
+ 
+
+ align:start position:0%
+Oasis you get the worms so you always
+this also gives you just like the bluest
+
+ align:start position:0%
+this also gives you just like the bluest
+ 
+
+ align:start position:0%
+this also gives you just like the bluest
+thing on the screen we do click on it
+
+ align:start position:0%
+thing on the screen we do click on it
+ 
+
+ align:start position:0%
+thing on the screen we do click on it
+blue things move so there's some sort of
+
+ align:start position:0%
+blue things move so there's some sort of
+ 
+
+ align:start position:0%
+blue things move so there's some sort of
+like color coordination oh yes yes one
+
+ align:start position:0%
+like color coordination oh yes yes one
+ 
+
+ align:start position:0%
+like color coordination oh yes yes one
+time we got to be wait somethin happened
+
+ align:start position:0%
+time we got to be wait somethin happened
+ 
+
+ align:start position:0%
+time we got to be wait somethin happened
+everyone so so either the barbarians are
+
+ align:start position:0%
+everyone so so either the barbarians are
+ 
+
+ align:start position:0%
+everyone so so either the barbarians are
+taking away your blue or you're using
+
+ align:start position:0%
+taking away your blue or you're using
+ 
+
+ align:start position:0%
+taking away your blue or you're using
+your blue to smite the barbarians either
+
+ align:start position:0%
+your blue to smite the barbarians either
+ 
+
+ align:start position:0%
+your blue to smite the barbarians either
+way you end up with no barbarians and
+
+ align:start position:0%
+way you end up with no barbarians and
+ 
+
+ align:start position:0%
+way you end up with no barbarians and
+less blue right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you will never for out like a 15 like
+
+ align:start position:0%
+you will never for out like a 15 like
+ 
+
+ align:start position:0%
+you will never for out like a 15 like
+yeah I can tell you one one of the
+
+ align:start position:0%
+yeah I can tell you one one of the
+ 
+
+ align:start position:0%
+yeah I can tell you one one of the
+things that this particular game
+
+ align:start position:0%
+things that this particular game
+ 
+
+ align:start position:0%
+things that this particular game
+designer has told me is that he doesn't
+
+ align:start position:0%
+designer has told me is that he doesn't
+ 
+
+ align:start position:0%
+designer has told me is that he doesn't
+believe in game balance he just believes
+
+ align:start position:0%
+believe in game balance he just believes
+ 
+
+ align:start position:0%
+believe in game balance he just believes
+in making a game starts so ridiculously
+
+ align:start position:0%
+in making a game starts so ridiculously
+ 
+
+ align:start position:0%
+in making a game starts so ridiculously
+easy and end and almost an impossible
+
+ align:start position:0%
+easy and end and almost an impossible
+ 
+
+ align:start position:0%
+easy and end and almost an impossible
+level so somewhere along the way you
+
+ align:start position:0%
+level so somewhere along the way you
+ 
+
+ align:start position:0%
+level so somewhere along the way you
+meet the level that you're good at and
+
+ align:start position:0%
+meet the level that you're good at and
+ 
+
+ align:start position:0%
+meet the level that you're good at and
+that's a balanced game that's that's one
+
+ align:start position:0%
+that's a balanced game that's that's one
+ 
+
+ align:start position:0%
+that's a balanced game that's that's one
+way of looking at it so so maybe fine
+
+ align:start position:0%
+way of looking at it so so maybe fine
+ 
+
+ align:start position:0%
+way of looking at it so so maybe fine
+okay fine a bunch of game mechanics we
+
+ align:start position:0%
+okay fine a bunch of game mechanics we
+ 
+
+ align:start position:0%
+okay fine a bunch of game mechanics we
+didn't go into things like roads and
+
+ align:start position:0%
+didn't go into things like roads and
+ 
+
+ align:start position:0%
+didn't go into things like roads and
+technologies and find this of it and
+
+ align:start position:0%
+technologies and find this of it and
+ 
+
+ align:start position:0%
+technologies and find this of it and
+there's a ton of game mechanics in here
+
+ align:start position:0%
+there's a ton of game mechanics in here
+ 
+
+ align:start position:0%
+there's a ton of game mechanics in here
+these are the kinds of things that a
+
+ align:start position:0%
+these are the kinds of things that a
+ 
+
+ align:start position:0%
+these are the kinds of things that a
+game designer can design right these are
+
+ align:start position:0%
+game designer can design right these are
+ 
+
+ align:start position:0%
+game designer can design right these are
+rules you know things as simple as you
+
+ align:start position:0%
+rules you know things as simple as you
+ 
+
+ align:start position:0%
+rules you know things as simple as you
+always say this always in a rectangle
+
+ align:start position:0%
+always say this always in a rectangle
+ 
+
+ align:start position:0%
+always say this always in a rectangle
+that's no reason for that it could have
+
+ align:start position:0%
+that's no reason for that it could have
+ 
+
+ align:start position:0%
+that's no reason for that it could have
+been a river but yeah but you're right
+
+ align:start position:0%
+been a river but yeah but you're right
+ 
+
+ align:start position:0%
+been a river but yeah but you're right
+that is actually a rule it every time
+
+ align:start position:0%
+that is actually a rule it every time
+ 
+
+ align:start position:0%
+that is actually a rule it every time
+you find always it's always going to be
+
+ align:start position:0%
+you find always it's always going to be
+ 
+
+ align:start position:0%
+you find always it's always going to be
+a rectangular shape these are the things
+
+ align:start position:0%
+a rectangular shape these are the things
+ 
+
+ align:start position:0%
+a rectangular shape these are the things
+that that the designer decides and you
+
+ align:start position:0%
+that that the designer decides and you
+ 
+
+ align:start position:0%
+that that the designer decides and you
+get dynamics well out of a bunch of
+
+ align:start position:0%
+get dynamics well out of a bunch of
+ 
+
+ align:start position:0%
+get dynamics well out of a bunch of
+these mechanics interacting with each
+
+ align:start position:0%
+these mechanics interacting with each
+ 
+
+ align:start position:0%
+these mechanics interacting with each
+other so I'm gonna give one example of a
+
+ align:start position:0%
+other so I'm gonna give one example of a
+ 
+
+ align:start position:0%
+other so I'm gonna give one example of a
+Titanic one of the dynamics is that as
+
+ align:start position:0%
+Titanic one of the dynamics is that as
+ 
+
+ align:start position:0%
+Titanic one of the dynamics is that as
+you revealed information about the stuff
+
+ align:start position:0%
+you revealed information about the stuff
+ 
+
+ align:start position:0%
+you revealed information about the stuff
+that's underneath the foam you start
+
+ align:start position:0%
+that's underneath the foam you start
+ 
+
+ align:start position:0%
+that's underneath the foam you start
+having more decisions to make well what
+
+ align:start position:0%
+having more decisions to make well what
+ 
+
+ align:start position:0%
+having more decisions to make well what
+you know mix that going to be because
+
+ align:start position:0%
+you know mix that going to be because
+ 
+
+ align:start position:0%
+you know mix that going to be because
+you could click on the thing that you
+
+ align:start position:0%
+you could click on the thing that you
+ 
+
+ align:start position:0%
+you could click on the thing that you
+just discovered like if you find us
+
+ align:start position:0%
+just discovered like if you find us
+ 
+
+ align:start position:0%
+just discovered like if you find us
+sending one of the things that that
+
+ align:start position:0%
+sending one of the things that that
+ 
+
+ align:start position:0%
+sending one of the things that that
+people which are my surgeon right now
+
+ align:start position:0%
+people which are my surgeon right now
+ 
+
+ align:start position:0%
+people which are my surgeon right now
+right but then you can also find you
+
+ align:start position:0%
+right but then you can also find you
+ 
+
+ align:start position:0%
+right but then you can also find you
+know a mind and you can assign followers
+
+ align:start position:0%
+know a mind and you can assign followers
+ 
+
+ align:start position:0%
+know a mind and you can assign followers
+into it you could build a road and some
+
+ align:start position:0%
+into it you could build a road and some
+ 
+
+ align:start position:0%
+into it you could build a road and some
+people I think might have noticed what
+
+ align:start position:0%
+people I think might have noticed what
+ 
+
+ align:start position:0%
+people I think might have noticed what
+what roles did
+
+ align:start position:0%
+what roles did
+ 
+
+ align:start position:0%
+what roles did
+thing but yeah your city start actually
+
+ align:start position:0%
+thing but yeah your city start actually
+ 
+
+ align:start position:0%
+thing but yeah your city start actually
+growing a number once you connect them
+
+ align:start position:0%
+growing a number once you connect them
+ 
+
+ align:start position:0%
+growing a number once you connect them
+up a gross error plus that helps with
+
+ align:start position:0%
+up a gross error plus that helps with
+ 
+
+ align:start position:0%
+up a gross error plus that helps with
+defense so so what are the what are the
+
+ align:start position:0%
+defense so so what are the what are the
+ 
+
+ align:start position:0%
+defense so so what are the what are the
+dynamics in this game is that the
+
+ align:start position:0%
+dynamics in this game is that the
+ 
+
+ align:start position:0%
+dynamics in this game is that the
+further that you play in a level the
+
+ align:start position:0%
+further that you play in a level the
+ 
+
+ align:start position:0%
+further that you play in a level the
+board is system all kinds of decisions
+
+ align:start position:0%
+board is system all kinds of decisions
+ 
+
+ align:start position:0%
+board is system all kinds of decisions
+you can make at the beginning of the
+
+ align:start position:0%
+you can make at the beginning of the
+ 
+
+ align:start position:0%
+you can make at the beginning of the
+game you have to make no decisions
+
+ align:start position:0%
+game you have to make no decisions
+ 
+
+ align:start position:0%
+game you have to make no decisions
+decides which one of these things two
+
+ align:start position:0%
+decides which one of these things two
+ 
+
+ align:start position:0%
+decides which one of these things two
+squares am I going to start searching
+
+ align:start position:0%
+squares am I going to start searching
+ 
+
+ align:start position:0%
+squares am I going to start searching
+right up on left you know I think you
+
+ align:start position:0%
+right up on left you know I think you
+ 
+
+ align:start position:0%
+right up on left you know I think you
+always start in one of the corners so
+
+ align:start position:0%
+always start in one of the corners so
+ 
+
+ align:start position:0%
+always start in one of the corners so
+there's only two directions that you
+
+ align:start position:0%
+there's only two directions that you
+ 
+
+ align:start position:0%
+there's only two directions that you
+possibly search what are the dynamics
+
+ align:start position:0%
+possibly search what are the dynamics
+ 
+
+ align:start position:0%
+possibly search what are the dynamics
+are there these are things that arise on
+
+ align:start position:0%
+are there these are things that arise on
+ 
+
+ align:start position:0%
+are there these are things that arise on
+combination of these mechanics okay so
+
+ align:start position:0%
+combination of these mechanics okay so
+ 
+
+ align:start position:0%
+combination of these mechanics okay so
+what are the things is you you set up
+
+ align:start position:0%
+what are the things is you you set up
+ 
+
+ align:start position:0%
+what are the things is you you set up
+initial conditions for hopefully these
+
+ align:start position:0%
+initial conditions for hopefully these
+ 
+
+ align:start position:0%
+initial conditions for hopefully these
+things to work out the circle there's
+
+ align:start position:0%
+things to work out the circle there's
+ 
+
+ align:start position:0%
+things to work out the circle there's
+the system to emerge it in the behavior
+
+ align:start position:0%
+the system to emerge it in the behavior
+ 
+
+ align:start position:0%
+the system to emerge it in the behavior
+right okay what else that's then the
+
+ align:start position:0%
+right okay what else that's then the
+ 
+
+ align:start position:0%
+right okay what else that's then the
+stuff that you set up even before all
+
+ align:start position:0%
+stuff that you set up even before all
+ 
+
+ align:start position:0%
+stuff that you set up even before all
+your trips are over like if you set them
+
+ align:start position:0%
+your trips are over like if you set them
+ 
+
+ align:start position:0%
+your trips are over like if you set them
+people in a bind the - just keep taking
+
+ align:start position:0%
+people in a bind the - just keep taking
+ 
+
+ align:start position:0%
+people in a bind the - just keep taking
+each turn you know it's like you don't
+
+ align:start position:0%
+each turn you know it's like you don't
+ 
+
+ align:start position:0%
+each turn you know it's like you don't
+have to babysit them they'll do they'll
+
+ align:start position:0%
+have to babysit them they'll do they'll
+ 
+
+ align:start position:0%
+have to babysit them they'll do they'll
+keep digging it'll find stuff you know
+
+ align:start position:0%
+keep digging it'll find stuff you know
+ 
+
+ align:start position:0%
+keep digging it'll find stuff you know
+without you telling them to do anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else what what what else spits this
+
+ align:start position:0%
+what else what what what else spits this
+ 
+
+ align:start position:0%
+what else what what what else spits this
+kind of description of a something that
+
+ align:start position:0%
+kind of description of a something that
+ 
+
+ align:start position:0%
+kind of description of a something that
+arises still kind of mechanically uh out
+
+ align:start position:0%
+arises still kind of mechanically uh out
+ 
+
+ align:start position:0%
+arises still kind of mechanically uh out
+of all out of a combination of all of
+
+ align:start position:0%
+of all out of a combination of all of
+ 
+
+ align:start position:0%
+of all out of a combination of all of
+these Dietetics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take combat for instance when the
+
+ align:start position:0%
+let's take combat for instance when the
+ 
+
+ align:start position:0%
+let's take combat for instance when the
+red forces and your blue forces start
+
+ align:start position:0%
+red forces and your blue forces start
+ 
+
+ align:start position:0%
+red forces and your blue forces start
+you know like no ants stop facing off
+
+ align:start position:0%
+you know like no ants stop facing off
+ 
+
+ align:start position:0%
+you know like no ants stop facing off
+against each other what happens this
+
+ align:start position:0%
+against each other what happens this
+ 
+
+ align:start position:0%
+against each other what happens this
+squashed right okay so so it has
+
+ align:start position:0%
+squashed right okay so so it has
+ 
+
+ align:start position:0%
+squashed right okay so so it has
+interesting curve on like a successful
+
+ align:start position:0%
+interesting curve on like a successful
+ 
+
+ align:start position:0%
+interesting curve on like a successful
+defense like the barbarians are usually
+
+ align:start position:0%
+defense like the barbarians are usually
+ 
+
+ align:start position:0%
+defense like the barbarians are usually
+here and the followers you know usually
+
+ align:start position:0%
+here and the followers you know usually
+ 
+
+ align:start position:0%
+here and the followers you know usually
+on the slightly lower number because
+
+ align:start position:0%
+on the slightly lower number because
+ 
+
+ align:start position:0%
+on the slightly lower number because
+this huge upper barbarians they show up
+
+ align:start position:0%
+this huge upper barbarians they show up
+ 
+
+ align:start position:0%
+this huge upper barbarians they show up
+obviously off huh yeah but but often
+
+ align:start position:0%
+obviously off huh yeah but but often
+ 
+
+ align:start position:0%
+obviously off huh yeah but but often
+what happens is that you've got a number
+
+ align:start position:0%
+what happens is that you've got a number
+ 
+
+ align:start position:0%
+what happens is that you've got a number
+like that and it kind of goes like like
+
+ align:start position:0%
+like that and it kind of goes like like
+ 
+
+ align:start position:0%
+like that and it kind of goes like like
+that right your response off kind of
+
+ align:start position:0%
+that right your response off kind of
+ 
+
+ align:start position:0%
+that right your response off kind of
+like a you know the barbarians still
+
+ align:start position:0%
+like a you know the barbarians still
+ 
+
+ align:start position:0%
+like a you know the barbarians still
+maintained your numbers in all sudden
+
+ align:start position:0%
+maintained your numbers in all sudden
+ 
+
+ align:start position:0%
+maintained your numbers in all sudden
+just collapses this is what a successful
+
+ align:start position:0%
+just collapses this is what a successful
+ 
+
+ align:start position:0%
+just collapses this is what a successful
+defense at that yeah yeah kill me yeah
+
+ align:start position:0%
+defense at that yeah yeah kill me yeah
+ 
+
+ align:start position:0%
+defense at that yeah yeah kill me yeah
+yeah that's that would be what it took
+
+ align:start position:0%
+yeah that's that would be what it took
+ 
+
+ align:start position:0%
+yeah that's that would be what it took
+this will be Facebook yeah I mean that
+
+ align:start position:0%
+this will be Facebook yeah I mean that
+ 
+
+ align:start position:0%
+this will be Facebook yeah I mean that
+that will look more like like like that
+
+ align:start position:0%
+that will look more like like like that
+ 
+
+ align:start position:0%
+that will look more like like like that
+attendants like oh right so this is all
+
+ align:start position:0%
+attendants like oh right so this is all
+ 
+
+ align:start position:0%
+attendants like oh right so this is all
+arising out of the gate mechanics right
+
+ align:start position:0%
+arising out of the gate mechanics right
+ 
+
+ align:start position:0%
+arising out of the gate mechanics right
+this is still this is not a this is not
+
+ align:start position:0%
+this is still this is not a this is not
+ 
+
+ align:start position:0%
+this is still this is not a this is not
+an aesthetic experience all by itself
+
+ align:start position:0%
+an aesthetic experience all by itself
+ 
+
+ align:start position:0%
+an aesthetic experience all by itself
+this is just how the numbers if you plot
+
+ align:start position:0%
+this is just how the numbers if you plot
+ 
+
+ align:start position:0%
+this is just how the numbers if you plot
+it by a fraction of a second by a
+
+ align:start position:0%
+it by a fraction of a second by a
+ 
+
+ align:start position:0%
+it by a fraction of a second by a
+fraction of a second you get a graph
+
+ align:start position:0%
+fraction of a second you get a graph
+ 
+
+ align:start position:0%
+fraction of a second you get a graph
+like this this is just the outdoors and
+
+ align:start position:0%
+like this this is just the outdoors and
+ 
+
+ align:start position:0%
+like this this is just the outdoors and
+doing its thing
+
+ align:start position:0%
+doing its thing
+ 
+
+ align:start position:0%
+doing its thing
+all right what is what did this kind of
+
+ align:start position:0%
+all right what is what did this kind of
+ 
+
+ align:start position:0%
+all right what is what did this kind of
+is that I couldn't go go back to like a
+
+ align:start position:0%
+is that I couldn't go go back to like a
+ 
+
+ align:start position:0%
+is that I couldn't go go back to like a
+successful defense
+
+ align:start position:0%
+successful defense
+ 
+
+ align:start position:0%
+successful defense
+so these writers are not the mechanics
+
+ align:start position:0%
+so these writers are not the mechanics
+ 
+
+ align:start position:0%
+so these writers are not the mechanics
+of the game
+
+ align:start position:0%
+of the game
+ 
+
+ align:start position:0%
+of the game
+you know everything that you know in the
+
+ align:start position:0%
+you know everything that you know in the
+ 
+
+ align:start position:0%
+you know everything that you know in the
+game - if I get thought get followers
+
+ align:start position:0%
+game - if I get thought get followers
+ 
+
+ align:start position:0%
+game - if I get thought get followers
+into a city give them technologies
+
+ align:start position:0%
+into a city give them technologies
+ 
+
+ align:start position:0%
+into a city give them technologies
+buying stuff you know such cities you
+
+ align:start position:0%
+buying stuff you know such cities you
+ 
+
+ align:start position:0%
+buying stuff you know such cities you
+know make sure that I enough followers
+
+ align:start position:0%
+know make sure that I enough followers
+ 
+
+ align:start position:0%
+know make sure that I enough followers
+by connecting the cities up with rural
+
+ align:start position:0%
+by connecting the cities up with rural
+ 
+
+ align:start position:0%
+by connecting the cities up with rural
+it's the other thing that rules allow
+
+ align:start position:0%
+it's the other thing that rules allow
+ 
+
+ align:start position:0%
+it's the other thing that rules allow
+you to do is we distribute followers
+
+ align:start position:0%
+you to do is we distribute followers
+ 
+
+ align:start position:0%
+you to do is we distribute followers
+between cities that I've been connected
+
+ align:start position:0%
+between cities that I've been connected
+ 
+
+ align:start position:0%
+between cities that I've been connected
+that's the thing that you get to do in
+
+ align:start position:0%
+that's the thing that you get to do in
+ 
+
+ align:start position:0%
+that's the thing that you get to do in
+those last ten seconds is that you don't
+
+ align:start position:0%
+those last ten seconds is that you don't
+ 
+
+ align:start position:0%
+those last ten seconds is that you don't
+just assign everybody that you've got
+
+ align:start position:0%
+just assign everybody that you've got
+ 
+
+ align:start position:0%
+just assign everybody that you've got
+you think all the people go into this
+
+ align:start position:0%
+you think all the people go into this
+ 
+
+ align:start position:0%
+you think all the people go into this
+one city you can actually do that you
+
+ align:start position:0%
+one city you can actually do that you
+ 
+
+ align:start position:0%
+one city you can actually do that you
+connect them up with roads
+
+ align:start position:0%
+connect them up with roads
+ 
+
+ align:start position:0%
+connect them up with roads
+ten seconds to do that so everything
+
+ align:start position:0%
+ten seconds to do that so everything
+ 
+
+ align:start position:0%
+ten seconds to do that so everything
+leads up to how many followers you've
+
+ align:start position:0%
+leads up to how many followers you've
+ 
+
+ align:start position:0%
+leads up to how many followers you've
+got it a city that a barbarians about
+
+ align:start position:0%
+got it a city that a barbarians about
+ 
+
+ align:start position:0%
+got it a city that a barbarians about
+that back the barbarians are gonna
+
+ align:start position:0%
+that back the barbarians are gonna
+ 
+
+ align:start position:0%
+that back the barbarians are gonna
+attack right you know this is good this
+
+ align:start position:0%
+attack right you know this is good this
+ 
+
+ align:start position:0%
+attack right you know this is good this
+interaction that keeps going on into all
+
+ align:start position:0%
+interaction that keeps going on into all
+ 
+
+ align:start position:0%
+interaction that keeps going on into all
+barbarians are destroyed then you get
+
+ align:start position:0%
+barbarians are destroyed then you get
+ 
+
+ align:start position:0%
+barbarians are destroyed then you get
+this curve and what sort of a static
+
+ align:start position:0%
+this curve and what sort of a static
+ 
+
+ align:start position:0%
+this curve and what sort of a static
+does it generate but what is the player
+
+ align:start position:0%
+does it generate but what is the player
+ 
+
+ align:start position:0%
+does it generate but what is the player
+hopefully experience because of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and then and then when they pull
+
+ align:start position:0%
+yeah and then and then when they pull
+ 
+
+ align:start position:0%
+yeah and then and then when they pull
+out of it because it was like yeah it's
+
+ align:start position:0%
+out of it because it was like yeah it's
+ 
+
+ align:start position:0%
+out of it because it was like yeah it's
+like at this point I says oh no we're
+
+ align:start position:0%
+like at this point I says oh no we're
+ 
+
+ align:start position:0%
+like at this point I says oh no we're
+both kind of in the same trajectory yeah
+
+ align:start position:0%
+both kind of in the same trajectory yeah
+ 
+
+ align:start position:0%
+both kind of in the same trajectory yeah
+sure they're dropping but we're dropping
+
+ align:start position:0%
+sure they're dropping but we're dropping
+ 
+
+ align:start position:0%
+sure they're dropping but we're dropping
+too and it's not no it's a girl so well
+
+ align:start position:0%
+too and it's not no it's a girl so well
+ 
+
+ align:start position:0%
+too and it's not no it's a girl so well
+they off suddenly your your hopes come
+
+ align:start position:0%
+they off suddenly your your hopes come
+ 
+
+ align:start position:0%
+they off suddenly your your hopes come
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+right you know and we were cheering we
+
+ align:start position:0%
+right you know and we were cheering we
+ 
+
+ align:start position:0%
+right you know and we were cheering we
+were shouting a heads up as if our
+
+ align:start position:0%
+were shouting a heads up as if our
+ 
+
+ align:start position:0%
+were shouting a heads up as if our
+cheers had any influence on a not quite
+
+ align:start position:0%
+cheers had any influence on a not quite
+ 
+
+ align:start position:0%
+cheers had any influence on a not quite
+sure what to it is how to describe that
+
+ align:start position:0%
+sure what to it is how to describe that
+ 
+
+ align:start position:0%
+sure what to it is how to describe that
+aesthetic but that's the players that's
+
+ align:start position:0%
+aesthetic but that's the players that's
+ 
+
+ align:start position:0%
+aesthetic but that's the players that's
+what the player takes away from this
+
+ align:start position:0%
+what the player takes away from this
+ 
+
+ align:start position:0%
+what the player takes away from this
+game right there's this tiny little
+
+ align:start position:0%
+game right there's this tiny little
+ 
+
+ align:start position:0%
+game right there's this tiny little
+moment of the game it's actually very
+
+ align:start position:0%
+moment of the game it's actually very
+ 
+
+ align:start position:0%
+moment of the game it's actually very
+finely tuned to generate exactly that
+
+ align:start position:0%
+finely tuned to generate exactly that
+ 
+
+ align:start position:0%
+finely tuned to generate exactly that
+experience off the you're not quite sure
+
+ align:start position:0%
+experience off the you're not quite sure
+ 
+
+ align:start position:0%
+experience off the you're not quite sure
+what the outcome of this battle is going
+
+ align:start position:0%
+what the outcome of this battle is going
+ 
+
+ align:start position:0%
+what the outcome of this battle is going
+to be unless you play the game like for
+
+ align:start position:0%
+to be unless you play the game like for
+ 
+
+ align:start position:0%
+to be unless you play the game like for
+hours and hours and hours and then you
+
+ align:start position:0%
+hours and hours and hours and then you
+ 
+
+ align:start position:0%
+hours and hours and hours and then you
+can kind of predict what's going to
+
+ align:start position:0%
+can kind of predict what's going to
+ 
+
+ align:start position:0%
+can kind of predict what's going to
+happen the moment the battle starts
+
+ align:start position:0%
+happen the moment the battle starts
+ 
+
+ align:start position:0%
+happen the moment the battle starts
+because you already know what each
+
+ align:start position:0%
+because you already know what each
+ 
+
+ align:start position:0%
+because you already know what each
+technology actually does but at this
+
+ align:start position:0%
+technology actually does but at this
+ 
+
+ align:start position:0%
+technology actually does but at this
+point of time what you're still learning
+
+ align:start position:0%
+point of time what you're still learning
+ 
+
+ align:start position:0%
+point of time what you're still learning
+the game you don't know why you
+
+ align:start position:0%
+the game you don't know why you
+ 
+
+ align:start position:0%
+the game you don't know why you
+technology does you don't know how the
+
+ align:start position:0%
+technology does you don't know how the
+ 
+
+ align:start position:0%
+technology does you don't know how the
+battles are done it turned out it gets
+
+ align:start position:0%
+battles are done it turned out it gets
+ 
+
+ align:start position:0%
+battles are done it turned out it gets
+really really excited so maybe it
+
+ align:start position:0%
+really really excited so maybe it
+ 
+
+ align:start position:0%
+really really excited so maybe it
+doesn't kind of like that the what matt
+
+ align:start position:0%
+doesn't kind of like that the what matt
+ 
+
+ align:start position:0%
+doesn't kind of like that the what matt
+LeBlanc the designer of this game
+
+ align:start position:0%
+LeBlanc the designer of this game
+ 
+
+ align:start position:0%
+LeBlanc the designer of this game
+describes it was dramatic tension I'm
+
+ align:start position:0%
+describes it was dramatic tension I'm
+ 
+
+ align:start position:0%
+describes it was dramatic tension I'm
+not quite sure he's using that term like
+
+ align:start position:0%
+not quite sure he's using that term like
+ 
+
+ align:start position:0%
+not quite sure he's using that term like
+exactly the way how it will be used in
+
+ align:start position:0%
+exactly the way how it will be used in
+ 
+
+ align:start position:0%
+exactly the way how it will be used in
+literary convention but but it is whew
+
+ align:start position:0%
+literary convention but but it is whew
+ 
+
+ align:start position:0%
+literary convention but but it is whew
+it does feel tense because this is out
+
+ align:start position:0%
+it does feel tense because this is out
+ 
+
+ align:start position:0%
+it does feel tense because this is out
+this is uncertain outcome about who's
+
+ align:start position:0%
+this is uncertain outcome about who's
+ 
+
+ align:start position:0%
+this is uncertain outcome about who's
+going to come out ahead and then when it
+
+ align:start position:0%
+going to come out ahead and then when it
+ 
+
+ align:start position:0%
+going to come out ahead and then when it
+resolves in your favor you feel great
+
+ align:start position:0%
+resolves in your favor you feel great
+ 
+
+ align:start position:0%
+resolves in your favor you feel great
+that's basically one dissection using
+
+ align:start position:0%
+that's basically one dissection using
+ 
+
+ align:start position:0%
+that's basically one dissection using
+the MDA framework that we just went
+
+ align:start position:0%
+the MDA framework that we just went
+ 
+
+ align:start position:0%
+the MDA framework that we just went
+through there's a whole bunch of
+
+ align:start position:0%
+through there's a whole bunch of
+ 
+
+ align:start position:0%
+through there's a whole bunch of
+mechanics create a dynamic they creates
+
+ align:start position:0%
+mechanics create a dynamic they creates
+ 
+
+ align:start position:0%
+mechanics create a dynamic they creates
+this a static experience which is the
+
+ align:start position:0%
+this a static experience which is the
+ 
+
+ align:start position:0%
+this a static experience which is the
+thing that you want your players to have
+
+ align:start position:0%
+thing that you want your players to have
+ 
+
+ align:start position:0%
+thing that you want your players to have
+in this particular case this was
+
+ align:start position:0%
+in this particular case this was
+ 
+
+ align:start position:0%
+in this particular case this was
+explicitly what Matt LeBlanc wanted his
+
+ align:start position:0%
+explicitly what Matt LeBlanc wanted his
+ 
+
+ align:start position:0%
+explicitly what Matt LeBlanc wanted his
+players to experience he wanted them to
+
+ align:start position:0%
+players to experience he wanted them to
+ 
+
+ align:start position:0%
+players to experience he wanted them to
+cheer for the followers even though that
+
+ align:start position:0%
+cheer for the followers even though that
+ 
+
+ align:start position:0%
+cheer for the followers even though that
+has no impact on the final result of the
+
+ align:start position:0%
+has no impact on the final result of the
+ 
+
+ align:start position:0%
+has no impact on the final result of the
+fight so when you look at your games I
+
+ align:start position:0%
+fight so when you look at your games I
+ 
+
+ align:start position:0%
+fight so when you look at your games I
+want you to be asking your play testers
+
+ align:start position:0%
+want you to be asking your play testers
+ 
+
+ align:start position:0%
+want you to be asking your play testers
+what they are feeling about the game
+
+ align:start position:0%
+what they are feeling about the game
+ 
+
+ align:start position:0%
+what they are feeling about the game
+usually after they're done you know it's
+
+ align:start position:0%
+usually after they're done you know it's
+ 
+
+ align:start position:0%
+usually after they're done you know it's
+like how do you feel about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know what did you like about the
+
+ align:start position:0%
+you know what did you like about the
+ 
+
+ align:start position:0%
+you know what did you like about the
+game what didn't you like about the game
+
+ align:start position:0%
+game what didn't you like about the game
+ 
+
+ align:start position:0%
+game what didn't you like about the game
+both both are aesthetic experiences that
+
+ align:start position:0%
+both both are aesthetic experiences that
+ 
+
+ align:start position:0%
+both both are aesthetic experiences that
+come out from the play of the game this
+
+ align:start position:0%
+come out from the play of the game this
+ 
+
+ align:start position:0%
+come out from the play of the game this
+is much easier to do with people who are
+
+ align:start position:0%
+is much easier to do with people who are
+ 
+
+ align:start position:0%
+is much easier to do with people who are
+actually not in this class because
+
+ align:start position:0%
+actually not in this class because
+ 
+
+ align:start position:0%
+actually not in this class because
+you're all thinking about the games or
+
+ align:start position:0%
+you're all thinking about the games or
+ 
+
+ align:start position:0%
+you're all thinking about the games or
+the rules level if you go to somebody to
+
+ align:start position:0%
+the rules level if you go to somebody to
+ 
+
+ align:start position:0%
+the rules level if you go to somebody to
+plays games but doesn't really make
+
+ align:start position:0%
+plays games but doesn't really make
+ 
+
+ align:start position:0%
+plays games but doesn't really make
+games or is it in the process of
+
+ align:start position:0%
+games or is it in the process of
+ 
+
+ align:start position:0%
+games or is it in the process of
+learning about how to make games it's a
+
+ align:start position:0%
+learning about how to make games it's a
+ 
+
+ align:start position:0%
+learning about how to make games it's a
+lot easier for them to just think about
+
+ align:start position:0%
+lot easier for them to just think about
+ 
+
+ align:start position:0%
+lot easier for them to just think about
+well I kind of felt crappy because I
+
+ align:start position:0%
+well I kind of felt crappy because I
+ 
+
+ align:start position:0%
+well I kind of felt crappy because I
+didn't feel that was any way for me to
+
+ align:start position:0%
+didn't feel that was any way for me to
+ 
+
+ align:start position:0%
+didn't feel that was any way for me to
+come back in this game you know oh yeah
+
+ align:start position:0%
+come back in this game you know oh yeah
+ 
+
+ align:start position:0%
+come back in this game you know oh yeah
+I felt like you know I would ruffle
+
+ align:start position:0%
+I felt like you know I would ruffle
+ 
+
+ align:start position:0%
+I felt like you know I would ruffle
+stomping everybody ruffle stop based on
+
+ align:start position:0%
+stomping everybody ruffle stop based on
+ 
+
+ align:start position:0%
+stomping everybody ruffle stop based on
+aesthetic
+
+ align:start position:0%
+aesthetic
+ 
+
+ align:start position:0%
+aesthetic
+you know those those are things that you
+
+ align:start position:0%
+you know those those are things that you
+ 
+
+ align:start position:0%
+you know those those are things that you
+can sort of take you can sort of take
+
+ align:start position:0%
+can sort of take you can sort of take
+ 
+
+ align:start position:0%
+can sort of take you can sort of take
+acid game designers give you clues on
+
+ align:start position:0%
+acid game designers give you clues on
+ 
+
+ align:start position:0%
+acid game designers give you clues on
+whether your game is doing what you
+
+ align:start position:0%
+whether your game is doing what you
+ 
+
+ align:start position:0%
+whether your game is doing what you
+wanted to do from the mechanics that
+
+ align:start position:0%
+wanted to do from the mechanics that
+ 
+
+ align:start position:0%
+wanted to do from the mechanics that
+you're designing whether the game is not
+
+ align:start position:0%
+you're designing whether the game is not
+ 
+
+ align:start position:0%
+you're designing whether the game is not
+doing what you wanted to do because
+
+ align:start position:0%
+doing what you wanted to do because
+ 
+
+ align:start position:0%
+doing what you wanted to do because
+maybe the mechanics are interacting in a
+
+ align:start position:0%
+maybe the mechanics are interacting in a
+ 
+
+ align:start position:0%
+maybe the mechanics are interacting in a
+way that creates a dynamic that you
+
+ align:start position:0%
+way that creates a dynamic that you
+ 
+
+ align:start position:0%
+way that creates a dynamic that you
+didn't want or maybe the game is doing
+
+ align:start position:0%
+didn't want or maybe the game is doing
+ 
+
+ align:start position:0%
+didn't want or maybe the game is doing
+not what you wanted to do and it's
+
+ align:start position:0%
+not what you wanted to do and it's
+ 
+
+ align:start position:0%
+not what you wanted to do and it's
+actually pretty cool there's always the
+
+ align:start position:0%
+actually pretty cool there's always the
+ 
+
+ align:start position:0%
+actually pretty cool there's always the
+accidental discovery of your mechanics
+
+ align:start position:0%
+accidental discovery of your mechanics
+ 
+
+ align:start position:0%
+accidental discovery of your mechanics
+doing something that you didn't quite
+
+ align:start position:0%
+doing something that you didn't quite
+ 
+
+ align:start position:0%
+doing something that you didn't quite
+expect you know maybe you expected
+
+ align:start position:0%
+expect you know maybe you expected
+ 
+
+ align:start position:0%
+expect you know maybe you expected
+something to be kind of like like cool
+
+ align:start position:0%
+something to be kind of like like cool
+ 
+
+ align:start position:0%
+something to be kind of like like cool
+and strategic and detached but then your
+
+ align:start position:0%
+and strategic and detached but then your
+ 
+
+ align:start position:0%
+and strategic and detached but then your
+players end up feeling very really
+
+ align:start position:0%
+players end up feeling very really
+ 
+
+ align:start position:0%
+players end up feeling very really
+tensed and and feeling that everything's
+
+ align:start position:0%
+tensed and and feeling that everything's
+ 
+
+ align:start position:0%
+tensed and and feeling that everything's
+on the line and everything could go
+
+ align:start position:0%
+on the line and everything could go
+ 
+
+ align:start position:0%
+on the line and everything could go
+wrong and every ball and any moment I
+
+ align:start position:0%
+wrong and every ball and any moment I
+ 
+
+ align:start position:0%
+wrong and every ball and any moment I
+didn't like that then okay all right you
+
+ align:start position:0%
+didn't like that then okay all right you
+ 
+
+ align:start position:0%
+didn't like that then okay all right you
+know that's that's something you can
+
+ align:start position:0%
+know that's that's something you can
+ 
+
+ align:start position:0%
+know that's that's something you can
+work with but you may not necessarily
+
+ align:start position:0%
+work with but you may not necessarily
+ 
+
+ align:start position:0%
+work with but you may not necessarily
+understand that's what your game is
+
+ align:start position:0%
+understand that's what your game is
+ 
+
+ align:start position:0%
+understand that's what your game is
+doing if you're not asking your players
+
+ align:start position:0%
+doing if you're not asking your players
+ 
+
+ align:start position:0%
+doing if you're not asking your players
+what's the sensation in to getting out
+
+ align:start position:0%
+what's the sensation in to getting out
+ 
+
+ align:start position:0%
+what's the sensation in to getting out
+of the game purely from the rules when
+
+ align:start position:0%
+of the game purely from the rules when
+ 
+
+ align:start position:0%
+of the game purely from the rules when
+you're working with the prototypes in
+
+ align:start position:0%
+you're working with the prototypes in
+ 
+
+ align:start position:0%
+you're working with the prototypes in
+particular it's very easy for them for
+
+ align:start position:0%
+particular it's very easy for them for
+ 
+
+ align:start position:0%
+particular it's very easy for them for
+you to make this connection back your
+
+ align:start position:0%
+you to make this connection back your
+ 
+
+ align:start position:0%
+you to make this connection back your
+mechanics because they can't be
+
+ align:start position:0%
+mechanics because they can't be
+ 
+
+ align:start position:0%
+mechanics because they can't be
+experiencing terribly much from your
+
+ align:start position:0%
+experiencing terribly much from your
+ 
+
+ align:start position:0%
+experiencing terribly much from your
+artwork or for their sound effects right
+
+ align:start position:0%
+artwork or for their sound effects right
+ 
+
+ align:start position:0%
+artwork or for their sound effects right
+you know unless it make you sound
+
+ align:start position:0%
+you know unless it make you sound
+ 
+
+ align:start position:0%
+you know unless it make you sound
+effects with your mouth or something it
+
+ align:start position:0%
+effects with your mouth or something it
+ 
+
+ align:start position:0%
+effects with your mouth or something it
+probably sounds pretty goofy but you
+
+ align:start position:0%
+probably sounds pretty goofy but you
+ 
+
+ align:start position:0%
+probably sounds pretty goofy but you
+know they can only really sort of get an
+
+ align:start position:0%
+know they can only really sort of get an
+ 
+
+ align:start position:0%
+know they can only really sort of get an
+aesthetic experience out of your rules
+
+ align:start position:0%
+aesthetic experience out of your rules
+ 
+
+ align:start position:0%
+aesthetic experience out of your rules
+obviously this is not the only way that
+
+ align:start position:0%
+obviously this is not the only way that
+ 
+
+ align:start position:0%
+obviously this is not the only way that
+you can convey an aesthetic experience
+
+ align:start position:0%
+you can convey an aesthetic experience
+ 
+
+ align:start position:0%
+you can convey an aesthetic experience
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+things from art sound storytelling
+
+ align:start position:0%
+things from art sound storytelling
+ 
+
+ align:start position:0%
+things from art sound storytelling
+characters plot and everything we'll go
+
+ align:start position:0%
+characters plot and everything we'll go
+ 
+
+ align:start position:0%
+characters plot and everything we'll go
+into that a little bit more before
+
+ align:start position:0%
+into that a little bit more before
+ 
+
+ align:start position:0%
+into that a little bit more before
+assignment 2 because you're going to be
+
+ align:start position:0%
+assignment 2 because you're going to be
+ 
+
+ align:start position:0%
+assignment 2 because you're going to be
+exploring that wave assignment too but
+
+ align:start position:0%
+exploring that wave assignment too but
+ 
+
+ align:start position:0%
+exploring that wave assignment too but
+this is one particular kind of aesthetic
+
+ align:start position:0%
+this is one particular kind of aesthetic
+ 
+
+ align:start position:0%
+this is one particular kind of aesthetic
+that which I will refer to it in clay in
+
+ align:start position:0%
+that which I will refer to it in clay in
+ 
+
+ align:start position:0%
+that which I will refer to it in clay in
+this class as system aesthetics the
+
+ align:start position:0%
+this class as system aesthetics the
+ 
+
+ align:start position:0%
+this class as system aesthetics the
+aesthetics that come out from the system
+
+ align:start position:0%
+aesthetics that come out from the system
+ 
+
+ align:start position:0%
+aesthetics that come out from the system
+of all of your mechanics working
+
+ align:start position:0%
+of all of your mechanics working
+ 
+
+ align:start position:0%
+of all of your mechanics working
+together and in this project this first
+
+ align:start position:0%
+together and in this project this first
+ 
+
+ align:start position:0%
+together and in this project this first
+assignment you don't have to worry about
+
+ align:start position:0%
+assignment you don't have to worry about
+ 
+
+ align:start position:0%
+assignment you don't have to worry about
+hitting the design aesthetic you don't
+
+ align:start position:0%
+hitting the design aesthetic you don't
+ 
+
+ align:start position:0%
+hitting the design aesthetic you don't
+really have to that's not the goal of
+
+ align:start position:0%
+really have to that's not the goal of
+ 
+
+ align:start position:0%
+really have to that's not the goal of
+this project I want you to figure out
+
+ align:start position:0%
+this project I want you to figure out
+ 
+
+ align:start position:0%
+this project I want you to figure out
+everything that y'all gave McKenna can
+
+ align:start position:0%
+everything that y'all gave McKenna can
+ 
+
+ align:start position:0%
+everything that y'all gave McKenna can
+do and by the way there was a question
+
+ align:start position:0%
+do and by the way there was a question
+ 
+
+ align:start position:0%
+do and by the way there was a question
+be at the beginning of class what if we
+
+ align:start position:0%
+be at the beginning of class what if we
+ 
+
+ align:start position:0%
+be at the beginning of class what if we
+wanted to change that by coming because
+
+ align:start position:0%
+wanted to change that by coming because
+ 
+
+ align:start position:0%
+wanted to change that by coming because
+you discovered something along the way
+
+ align:start position:0%
+you discovered something along the way
+ 
+
+ align:start position:0%
+you discovered something along the way
+that's fine but whatever you change it
+
+ align:start position:0%
+that's fine but whatever you change it
+ 
+
+ align:start position:0%
+that's fine but whatever you change it
+to make sure that you're going deep into
+
+ align:start position:0%
+to make sure that you're going deep into
+ 
+
+ align:start position:0%
+to make sure that you're going deep into
+that thing make sure that you're not
+
+ align:start position:0%
+that thing make sure that you're not
+ 
+
+ align:start position:0%
+that thing make sure that you're not
+just like running with what you stumbled
+
+ align:start position:0%
+just like running with what you stumbled
+ 
+
+ align:start position:0%
+just like running with what you stumbled
+with this and then not developing it any
+
+ align:start position:0%
+with this and then not developing it any
+ 
+
+ align:start position:0%
+with this and then not developing it any
+further
+
+ align:start position:0%
+further
+ 
+
+ align:start position:0%
+further
+try to really really explore what what
+
+ align:start position:0%
+try to really really explore what what
+ 
+
+ align:start position:0%
+try to really really explore what what
+you eventually will declare that you're
+
+ align:start position:0%
+you eventually will declare that you're
+ 
+
+ align:start position:0%
+you eventually will declare that you're
+looking at the reason for that is that I
+
+ align:start position:0%
+looking at the reason for that is that I
+ 
+
+ align:start position:0%
+looking at the reason for that is that I
+want you all to have like the experience
+
+ align:start position:0%
+want you all to have like the experience
+ 
+
+ align:start position:0%
+want you all to have like the experience
+of going really deep into mechanics and
+
+ align:start position:0%
+of going really deep into mechanics and
+ 
+
+ align:start position:0%
+of going really deep into mechanics and
+figuring out all the different things
+
+ align:start position:0%
+figuring out all the different things
+ 
+
+ align:start position:0%
+figuring out all the different things
+that one mechanic can do so that later
+
+ align:start position:0%
+that one mechanic can do so that later
+ 
+
+ align:start position:0%
+that one mechanic can do so that later
+on when you all mix and match and form
+
+ align:start position:0%
+on when you all mix and match and form
+ 
+
+ align:start position:0%
+on when you all mix and match and form
+them into assignment 2 and assignment 3
+
+ align:start position:0%
+them into assignment 2 and assignment 3
+ 
+
+ align:start position:0%
+them into assignment 2 and assignment 3
+teams you've got like a pool of
+
+ align:start position:0%
+teams you've got like a pool of
+ 
+
+ align:start position:0%
+teams you've got like a pool of
+knowledge and more importantly a pool of
+
+ align:start position:0%
+knowledge and more importantly a pool of
+ 
+
+ align:start position:0%
+knowledge and more importantly a pool of
+experience and sort of exploring what a
+
+ align:start position:0%
+experience and sort of exploring what a
+ 
+
+ align:start position:0%
+experience and sort of exploring what a
+mechanic can do so that you can take on
+
+ align:start position:0%
+mechanic can do so that you can take on
+ 
+
+ align:start position:0%
+mechanic can do so that you can take on
+new mechanics you can share information
+
+ align:start position:0%
+new mechanics you can share information
+ 
+
+ align:start position:0%
+new mechanics you can share information
+with each other and use that later to
+
+ align:start position:0%
+with each other and use that later to
+ 
+
+ align:start position:0%
+with each other and use that later to
+generate interesting and starting
+
+ align:start position:0%
+generate interesting and starting
+ 
+
+ align:start position:0%
+generate interesting and starting
+experiences I said yeah and this is what
+
+ align:start position:0%
+experiences I said yeah and this is what
+ 
+
+ align:start position:0%
+experiences I said yeah and this is what
+the players are here for they don't care
+
+ align:start position:0%
+the players are here for they don't care
+ 
+
+ align:start position:0%
+the players are here for they don't care
+about the amount of work that you put
+
+ align:start position:0%
+about the amount of work that you put
+ 
+
+ align:start position:0%
+about the amount of work that you put
+into here they only care about whether
+
+ align:start position:0%
+into here they only care about whether
+ 
+
+ align:start position:0%
+into here they only care about whether
+the game makes them feel the way they
+
+ align:start position:0%
+the game makes them feel the way they
+ 
+
+ align:start position:0%
+the game makes them feel the way they
+didn't want to feel right now for a
+
+ align:start position:0%
+didn't want to feel right now for a
+ 
+
+ align:start position:0%
+didn't want to feel right now for a
+while they're playing joking so any
+
+ align:start position:0%
+while they're playing joking so any
+ 
+
+ align:start position:0%
+while they're playing joking so any
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we'll probably go a little bit more
+
+ align:start position:0%
+well we'll probably go a little bit more
+ 
+
+ align:start position:0%
+well we'll probably go a little bit more
+into things about mechanics later this
+
+ align:start position:0%
+into things about mechanics later this
+ 
+
+ align:start position:0%
+into things about mechanics later this
+this month but right now the rest of the
+
+ align:start position:0%
+this month but right now the rest of the
+ 
+
+ align:start position:0%
+this month but right now the rest of the
+class is actually time for you to work
+
+ align:start position:0%
+class is actually time for you to work
+ 
+
+ align:start position:0%
+class is actually time for you to work
+as a team some of you probably haven't
+
+ align:start position:0%
+as a team some of you probably haven't
+ 
+
+ align:start position:0%
+as a team some of you probably haven't
+seen each other since Wednesday and may
+
+ align:start position:0%
+seen each other since Wednesday and may
+ 
+
+ align:start position:0%
+seen each other since Wednesday and may
+not necessarily even have talked to each
+
+ align:start position:0%
+not necessarily even have talked to each
+ 
+
+ align:start position:0%
+not necessarily even have talked to each
+other so that's fine take time now if
+
+ align:start position:0%
+other so that's fine take time now if
+ 
+
+ align:start position:0%
+other so that's fine take time now if
+you then you've got something that you
+
+ align:start position:0%
+you then you've got something that you
+ 
+
+ align:start position:0%
+you then you've got something that you
+need test it you have two options one
+
+ align:start position:0%
+need test it you have two options one
+ 
+
+ align:start position:0%
+need test it you have two options one
+you can grab Rick and I or two you can
+
+ align:start position:0%
+you can grab Rick and I or two you can
+ 
+
+ align:start position:0%
+you can grab Rick and I or two you can
+Rick so you can grab other people in the
+
+ align:start position:0%
+Rick so you can grab other people in the
+ 
+
+ align:start position:0%
+Rick so you can grab other people in the
+classroom who don't necessarily have
+
+ align:start position:0%
+classroom who don't necessarily have
+ 
+
+ align:start position:0%
+classroom who don't necessarily have
+played a game I would suggest asking
+
+ align:start position:0%
+played a game I would suggest asking
+ 
+
+ align:start position:0%
+played a game I would suggest asking
+people who haven't played your game
+
+ align:start position:0%
+people who haven't played your game
+ 
+
+ align:start position:0%
+people who haven't played your game
+before for two tests tomorrow is
+
+ align:start position:0%
+before for two tests tomorrow is
+ 
+
+ align:start position:0%
+before for two tests tomorrow is
+actually the formal play test so what
+
+ align:start position:0%
+actually the formal play test so what
+ 
+
+ align:start position:0%
+actually the formal play test so what
+you absolutely have to have by the end
+
+ align:start position:0%
+you absolutely have to have by the end
+ 
+
+ align:start position:0%
+you absolutely have to have by the end
+of this class all right all right or by
+
+ align:start position:0%
+of this class all right all right or by
+ 
+
+ align:start position:0%
+of this class all right all right or by
+the what you have to have by the
+
+ align:start position:0%
+the what you have to have by the
+ 
+
+ align:start position:0%
+the what you have to have by the
+beginning of tomorrow to twelve to us is
+
+ align:start position:0%
+beginning of tomorrow to twelve to us is
+ 
+
+ align:start position:0%
+beginning of tomorrow to twelve to us is
+something that you'll be played at
+
+ align:start position:0%
+something that you'll be played at
+ 
+
+ align:start position:0%
+something that you'll be played at
+something class so today that's no
+
+ align:start position:0%
+something class so today that's no
+ 
+
+ align:start position:0%
+something class so today that's no
+required play test tomorrow Darius
+
+ align:start position:0%
+required play test tomorrow Darius
+ 
+
+ align:start position:0%
+required play test tomorrow Darius
+alright and that's also reading for
+
+ align:start position:0%
+alright and that's also reading for
+ 
+
+ align:start position:0%
+alright and that's also reading for
+tomorrow but it's not that bad I think
+
+ align:start position:0%
+tomorrow but it's not that bad I think
+ 
+
+ align:start position:0%
+tomorrow but it's not that bad I think
+it'll be okay and I was doing a partner
+
+ align:start position:0%
+it'll be okay and I was doing a partner
+ 
+
+ align:start position:0%
+it'll be okay and I was doing a partner
+yeah it's going to be just looking at
+
+ align:start position:0%
+yeah it's going to be just looking at
+ 
+
+ align:start position:0%
+yeah it's going to be just looking at
+one thing which is the randomizing and
+
+ align:start position:0%
+one thing which is the randomizing and
+ 
+
+ align:start position:0%
+one thing which is the randomizing and
+if I had a functional dice in games so
+
+ align:start position:0%
+if I had a functional dice in games so
+ 
+
+ align:start position:0%
+if I had a functional dice in games so
+okay what are your tips and all the
+
+ align:start position:0%
+okay what are your tips and all the
+ 
+
+ align:start position:0%
+okay what are your tips and all the
+materials are here we'll put it on the
+
+ align:start position:0%
+materials are here we'll put it on the
+ 
+
+ align:start position:0%
+materials are here we'll put it on the
+table content from the following sources
+
+ align:start position:0%
+table content from the following sources
+ 
+
+ align:start position:0%
+table content from the following sources
+is copyright of the respective holders
+
+ align:start position:0%
+is copyright of the respective holders
+ 
+
+ align:start position:0%
+is copyright of the respective holders
+all rights reserved
+
+ align:start position:0%
+all rights reserved
+ 
+
+ align:start position:0%
+all rights reserved
+excluded from our Creative Commons
+
+ align:start position:0%
+excluded from our Creative Commons
+ 
+
+ align:start position:0%
+excluded from our Creative Commons
+license for more information see
+
+ align:start position:0%
+license for more information see
+ 
+
+ align:start position:0%
+license for more information see
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+slash fair use erases play first 2005
+
+ align:start position:0%
+slash fair use erases play first 2005
+ 
+
+ align:start position:0%
+slash fair use erases play first 2005
+video game
\ No newline at end of file
diff --git a/H5m39G-FAwE.txt b/H5m39G-FAwE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8cd9ed3221e7fdeb217e8982ae0cb1c5f203731a
--- /dev/null
+++ b/H5m39G-FAwE.txt
@@ -0,0 +1,4741 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: All right.
+
+Hi, everyone.
+
+AUDIENCE: Hi.
+
+PROFESSOR: We're getting
+towards the end of the semester.
+
+Things are starting to
+cohere and come together.
+
+We have one more midterm exam.
+
+So there is an exam
+next Thursday, the 18th.
+
+OK?
+
+There will be a problem set due.
+
+It'll be posted later today,
+and it will be due next week
+
+on Tuesday as usual.
+
+Of course, next week on Tuesday
+is a holiday technically,
+
+so we'll actually make the
+due date be on Wednesday.
+
+So on Wednesday at 10 o'clock.
+
+You should think
+of this problem set
+
+as part of the
+review for the exam.
+
+Material that is covered
+today and on Thursday
+
+will be fair game for the exam.
+
+So the format of
+the exam is going
+
+to be much more canonical.
+
+It's going to be a
+series of short answer
+
+plus a series of computations.
+
+They'll be, roughly speaking,
+at the level of the problem
+
+sets, and a practice
+exam will be
+
+posted in the next
+couple of days.
+
+The practice exam is going
+to be of the same general
+
+intellectual
+difficulty, but it's
+
+going to be considerably
+longer than the actual exam.
+
+So as a check for yourself
+here's what I would recommend.
+
+I would recommend sitting
+down and giving yourself
+
+an hour and a half or two
+hours with the practice exam
+
+and see how that goes.
+
+OK?
+
+Try to give yourself
+the time constraint.
+
+And here's one of the
+things that-- there's
+
+a very strong correlation
+between having
+
+nailed the problem sets, and
+worked through all the practice
+
+exams, and just done
+a lot of problems,
+
+and doing well on exams.
+
+You'll be more confident.
+
+The only way to study
+for these things is just
+
+do a lot of problems.
+
+So on Stellar, for example,
+are a bunch of previous problem
+
+sets, and previous
+exams and practice
+
+exams from previous years.
+
+I would encourage you to
+look at those also on OCW
+
+and use those as practice.
+
+OK, any practical
+questions before we
+
+get on to the physics.
+
+Yeah?
+
+AUDIENCE: Will the exam
+cover all the material,
+
+or all the material [INAUDIBLE]?
+
+PROFESSOR: This is
+a cumulative topic.
+
+So the question is does it
+cover everything, or just
+
+last couple of weeks.
+
+And it's a cumulative topic,
+so the entire semester
+
+is necessary in order
+to answer the problems.
+
+Other questions?
+
+OK.
+
+Anything else?
+
+So quick couple of
+review questions
+
+before we launch into the
+main material of today.
+
+These are going to
+turn out to be useful
+
+reminders later on
+in today's lecture.
+
+So first, suppose
+I tell you I have
+
+a system with energy operator
+E, which has an operator A such
+
+that the commutator of E with
+A would say plus h bar A. OK?
+
+What does that tell you about
+the spectrum of the energy
+
+operator?
+
+AUDIENCE: It's a ladder.
+
+PROFESSOR: It's a
+ladder, exactly.
+
+So this tells you that the
+spectrum of E, or the energy
+
+eigenvalues En,
+are evenly spaced--
+
+and we need a dimensional
+constant here,
+
+omega-- evenly spaced
+by h bar omega.
+
+And more precisely, that
+given a state phi E,
+
+we can act on it
+with the operator A
+
+to give us a new state, which
+is also an energy eigenstate,
+
+with energy E plus h bar omega.
+
+right?
+
+So any time you see that
+commutation relation,
+
+you know this fact to be true.
+
+Second statement.
+
+Suppose I have an
+operator B which
+
+commutes with the
+energy operator.
+
+OK?
+
+So that the commutator vanishes.
+
+What does that tell
+you about the system?
+
+AUDIENCE: Simultaneous
+eigenfunctions [INAUDIBLE].
+
+PROFESSOR: Excellent.
+
+So one one consequence
+is that there
+
+exists simultaneous
+eigenfunctions phi sub E, B,
+
+which are simultaneous
+eigenfunctions of both E and B.
+
+What else does it tell you?
+
+Well, notice the following.
+
+Notice that if we took this
+computation relation and set
+
+omega to 0, we get this
+commutation relation.
+
+So this commutation relation is
+of the form of this commutation
+
+relation with omega equals 0.
+
+So what does that tell
+you about the states?
+
+About the energy eigenvalues?
+
+What happens if I
+take a state phi sub E
+
+and I act on it with B?
+
+What do I get?
+
+What can you say
+about this function?
+
+Well, what is its
+eigenvalue under E?
+
+It's E. It's the same
+thing, because they commute.
+
+You can pull the E
+through, multiply it,
+
+you get the constant E,
+you pull it back out.
+
+This is still an
+eigenfunction of phi
+
+of the energy operator
+with the same eigenvalue.
+
+But is it necessarily
+the same eigenfunction?
+
+No, because B may act
+on phi and just give you
+
+a different state.
+
+So this is some eigenfunction
+with the same energy,
+
+but it may be a
+different eigenfunction.
+
+OK?
+
+So let's think of
+an example of this.
+
+An example of this is
+consider a free particle.
+
+In the case of a
+free particle, we
+
+have E is equal to
+P squared upon 2m.
+
+And as a consequence
+E and P commute.
+
+Everyone agree with that?
+
+Everyone happy with
+that statement?
+
+They commute.
+
+So plus 0 if you will.
+
+And here what I wanted to say
+is when you have an operator
+
+that commutes with
+the energy, then
+
+there can be multiple states
+with the same energy which
+
+are different states, right?
+
+Different states entirely.
+
+So for example,
+in this case, what
+
+are the energy eigenfunctions?
+
+Well, e to the ikx.
+
+And this has energy h bar
+squared k squared upon 2m.
+
+But there's another state, which
+is a different state, which
+
+has the same energy.
+
+e to the minus ikx.
+
+OK?
+
+So when you have an operator
+that commutes with the energy
+
+operator, you can have
+simultaneous eigenfunctions.
+
+And you can also have
+multiple eigenfunctions
+
+that have the same
+energy eigenvalue,
+
+but are different functions.
+
+For example, this.
+
+Everyone cool with that?
+
+Now, just to make clear
+that it's actually
+
+the commuting that
+matters, imagine
+
+we took not the free particle,
+but the harmonic oscillator.
+
+E is p squared upon 2m plus m
+omega squared upon 2 x squared.
+
+Is it true that E-- I'll call
+this harmonic oscillator--
+
+does E harmonic
+oscillator commute with P?
+
+No, you're going to
+get a term that's
+
+m omega squared x
+from the commutator.
+
+The potential is not
+translationally invariant.
+
+It does not commute
+with momentum.
+
+So this is not equal to 0.
+
+So that suggests that this
+degeneracy, two states having
+
+the same energy,
+should not be present.
+
+And indeed, are the
+states degenerate
+
+for the harmonic oscillator.
+
+No.
+
+No degeneracy.
+
+Yeah?
+
+AUDIENCE: We did
+something [INAUDIBLE]
+
+where I think it said that the
+eigenfunctions were complete.
+
+PROFESSOR: Yes.
+
+AUDIENCE: What does that mean?
+
+PROFESSOR: What does it
+mean for the eigenfunctions
+
+to be complete?
+
+What that means is
+that they form a basis.
+
+AUDIENCE: So the basis
+doesn't necessarily
+
+mean not [INAUDIBLE].
+
+PROFESSOR: Yeah, no one told you
+the basis had to be degenerate,
+
+and in particular,
+that's a excellent--
+
+so the question here
+is, wait a minute,
+
+I thought a basis had to be
+a complete set-- if you had
+
+an energy operator and you
+constructed the energy eigen--
+
+this is a very good question.
+
+Thank you.
+
+If I have the energy operator
+and I construct it's energy
+
+eigenfunctions, then those
+energy eigenfunctions
+
+form a complete basis for
+any arbitrary function.
+
+Any function can be
+expanded in it, right?
+
+So for example, for
+the free particle,
+
+the energy eigenfunctions
+are e to the ikx,
+
+the momentum eigenfunctions
+for any value of k.
+
+But wait, how can there
+be multiple states
+
+with the same energy?
+
+Isn't that double
+counting or something?
+
+And the important thing is
+those guys have the same energy,
+
+but they have different momenta.
+
+They're different states.
+
+One has momentum h bar k.
+
+One has momentum minus h bar k.
+
+And you know that
+that has to be true,
+
+because the Fourier
+theorem tells you,
+
+in order to form a complete
+basis, you need all of them,
+
+all possible values of k.
+
+So there's no problem with
+being a complete basis
+
+and having states have the
+same energy eigenvalue, OK?
+
+It's a good question.
+
+Other questions?
+
+Yeah?
+
+AUDIENCE: So if we have a
+potential that only admits
+
+bound states, we'll never
+have this commutation
+
+happen basically?
+
+PROFESSOR: Yeah, exactly.
+
+Excellent.
+
+So the observation is this.
+
+Look, imagine I have a
+potential that's not trivial.
+
+It's not 0, OK?
+
+Will the momentum commute
+with the energy operator.
+
+No, because it's got
+a potential that's
+
+going to be acted upon by P, so
+you'll get a derivative term.
+
+But more precisely, if I have
+a system with bound states,
+
+I have to have a
+potential, right?
+
+And then I can't have P
+commuting with the energy
+
+operator, which means I
+can't have degeneracies.
+
+So indeed, if you
+have bound states,
+
+you cannot have degeneracies.
+
+That's exactly right.
+
+Yeah?
+
+AUDIENCE: But doesn't this
+break down in higher dimensions?
+
+PROFESSOR: Excellent,
+so we're going
+
+to come back to higher
+dimensions later.
+
+So the question
+predicts what's going
+
+to happen in the
+rest of the lecture.
+
+What we're going to
+do in just a minute
+
+is we're going to
+start working in three
+
+dimensions for the first time.
+
+We're going to leave 1D behind.
+
+We're going to take our
+tripped out tricycle
+
+and replace it with a Yamaha.
+
+As you'll see, it has the
+same basic physics driving
+
+its, well, self.
+
+It's the same dynamics.
+
+But I want to emphasize
+a couple things that
+
+are going to show up.
+
+So the question is,
+isn't this story
+
+different in three dimensions?
+
+And we shall see exactly what
+happens in higher dimensions.
+
+We'll work in two dimensions.
+
+We'll work in three dimensions.
+
+We'll work in more.
+
+Doesn't really matter how
+many dimensions we work in.
+
+You'll see it.
+
+OK, third thing.
+
+You studied this in some
+detail in your problem set.
+
+Suppose I have an
+energy operator
+
+that commutes with a
+unitary operator, U, OK?
+
+So it commutes to 0.
+
+And U is unitary, so U dagger
+U is one, is the identity.
+
+So what does this tell you?
+
+Well, first off
+from these guys it
+
+tells us that we can have
+simultaneous eigenfunctions.
+
+It also tells us too that
+if we take our state phi
+
+and we act on it with
+U, this could give us
+
+a new state, phi tilde sub
+E, which will necessarily
+
+have the same energy eigenvalue,
+because U and E commute.
+
+But it may be a different state.
+
+We'll come to this
+in more detail later.
+
+But the third thing, and
+I want to emphasize this,
+
+is this tells us, look, we
+have a unitary operator.
+
+We can always write the
+unitary operator as e
+
+to the i of a
+Hermitian operator.
+
+So what is the meaning of
+the Hermitian operator?
+
+What is this guy?
+
+So in your problem
+set, you looked
+
+at what unitary operators are.
+
+And in the problem set, it's
+discussed in some detail
+
+that there's a
+relationship between
+
+a unitary transformation,
+or unitary operator,
+
+and the symmetry.
+
+A symmetry is when
+you take your system
+
+and you do something to it,
+like a rotation or translation,
+
+and it's a symmetry if it
+doesn't change anything,
+
+if the energy remains invariant.
+
+So if the energy doesn't change
+under this transformation,
+
+we call that a symmetry.
+
+And we also showed that
+symmetries, or translations,
+
+are generated by
+unitary operators.
+
+For example, my favorite
+examples are the translate by L
+
+operator, which is unitary.
+
+And also e to the minus dxl.
+
+And the boost by
+q operator, which
+
+similarly is e to the minus qdp.
+
+And the time translation
+operator, U sub t,
+
+which is equal to e to the minus
+i t over h bar energy operator.
+
+OK?
+
+So these are
+transformation operators.
+
+These are symmetry operators,
+which translate you by L,
+
+boost or speed you
+up by momentum q,
+
+evolve you forward in time t.
+
+And they can all be expressed
+as e to the unitary operator.
+
+So this in particular
+is l i over h bar p.
+
+And this is similarly x.
+
+And earlier we understood
+the role of momentum
+
+having to do translations
+in the following way.
+
+There's a beautiful
+theorem about this.
+
+If you take a system and
+its translation invariant,
+
+the classical statement
+of Noether's theorem
+
+is that there's a conserved
+quantity associated
+
+with that translation.
+
+That conserved quantity
+is the momentum.
+
+And quantum mechanically,
+the generator
+
+of that transformation
+the Hermitian operator
+
+that goes upstairs
+in the unitary
+
+is the operator associated
+to that conserved quantity,
+
+associated to that observable.
+
+You have translations.
+
+There's a conserved
+quantity, which is momentum.
+
+And the thing that generates
+translations, the operator that
+
+generates translations, is the
+operator representing momentum.
+
+So each of these are going
+to come up later in today,
+
+and I just wanted to flag
+them down before the moment.
+
+OK, questions before we move on?
+
+Yeah?
+
+AUDIENCE: So you made the claim
+that every unitary operator can
+
+be expressed as p to
+the eigenfunction.
+
+PROFESSOR: OK, I should be a
+little bit careful, but yes.
+
+That's right.
+
+AUDIENCE: But if I
+take the [INAUDIBLE] I
+
+should be able to
+figure out what it is,
+
+but you can't take
+the [INAUDIBLE]
+
+PROFESSOR: The more
+precise statement
+
+is that any unitary--
+any one parameter
+
+family of unitary operators
+can be expressed in that form.
+
+And then you can
+take a derivative.
+
+And that's the theory
+of [INAUDIBLE],
+
+which is beyond the scope.
+
+Let me make a very
+specific statement, which
+
+is that one parameter
+of [INAUDIBLE]
+
+unitary transformation.
+
+So translations by l,
+where you can vary l,
+
+can be expressed in that form.
+
+And that's a very
+general statement.
+
+OK, so with all that as
+prelude, let's go back to 3D.
+
+So in 3D, the energy operator--
+so what's going to change?
+
+Now instead of just having
+position and its momentum,
+
+we now also have-- I'll call
+this P sub x-- we can also
+
+have a y-coordinate and
+we have a z-coordinate.
+
+And each of them
+has its momentum.
+
+P sub z and P sub y.
+
+And here's just a quick
+practical question.
+
+We know that x with Px
+is equal to i h bar.
+
+So what do you expect
+to be true of x with y?
+
+AUDIENCE: 0.
+
+PROFESSOR: Why?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: What does
+this equation tell you?
+
+What is its physical content?
+
+Well, that they
+don't commute, good.
+
+What does that tell
+you physically?
+
+Yes?
+
+AUDIENCE: That there's
+an uncertainty principle
+
+connecting the two.
+
+PROFESSOR: Excellent.
+
+So that's one statement.
+
+So the consequence of
+this is that there's
+
+an uncertainty principle.
+
+Delta x delta Px must be greater
+than or equal to h bar upon 2.
+
+What's another way
+of saying this?
+
+Do there exist simultaneous
+eigenfunctions of x and P?
+
+AUDIENCE: No.
+
+PROFESSOR: No.
+
+No simultaneous eigenfunctions.
+
+OK, so you can't
+have a definite value
+
+of x and a definite value
+of P simultaneously.
+
+There's no such state.
+
+It's not that you can't know.
+
+It's that there's no such state.
+
+Do you expect to be able
+to know the position in x
+
+and the position in
+y simultaneously?
+
+Sure.
+
+OK, so this turns out to be 0.
+
+And in some sense,
+you can take that
+
+as a definition of
+quantum mechanics.
+
+x and y need to be 0.
+
+And similarly, Px
+and Py commute.
+
+The momenta are independent.
+
+However, Py and y should
+be equal to minus i h bar.
+
+Good.
+
+Exactly.
+
+So the commutators
+work out exactly
+
+as you'd naively expect.
+
+Every pair of position and its
+momenta commute canonically
+
+to i h bar.
+
+And every pair of
+coordinates commute to 0.
+
+Every pair of
+momenta commute to 0.
+
+Cool?
+
+So what kind of systems are
+we going to interested in?
+
+Well, we're going to be
+interested in systems
+
+where the energy
+operator is equal to P
+
+vector hat squared upon 2m plus
+U of x and y and z, hat, hat.
+
+You can see why dropping
+the hats becomes almost /
+
+So in this language, we can
+write the Schrodinger equation.
+
+This is just a direct extension
+of the 1D Schrodinger equation.
+
+i h bar dt of psi.
+
+Now our wave function is a
+function of x and y and z.
+
+There's some finite
+probability then
+
+to find a particle
+at some position.
+
+That position is labeled
+by the three coordinates.
+
+Is equal to-- and of t.
+
+Is equal to-- well,
+I'm actually write
+
+this in slightly different form.
+
+This is going to be easier
+if I use vector notation.
+
+So I'm going to write
+this as psi of r and t,
+
+where r denotes the
+position vector,
+
+is equal to the energy
+operator acting on it.
+
+And P is just equal to
+minus i h bar the gradient.
+
+So this is minus i h bar
+squared, or minus h bar squared
+
+upon 2m gradient squared plus
+u of x or now u of r psi of r
+
+and t.
+
+Quick question, what
+are the units or what
+
+are the dimensions
+of psi of r in 3D?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, one over
+length to the root three halves.
+
+And the reason is this norm
+squared gives us a probability
+
+density, something
+that when we integrated
+
+over all positions in a
+region integral d 3x is going
+
+to give us a number,
+a probability.
+
+So its actual
+magnitude must be--
+
+or its dimension must
+be 1 over L to the 3/2.
+
+Just the cube of
+what it was in 1D.
+
+And as you'll see
+on the problems set
+
+and as we'll do in a couple
+lectures down the road,
+
+it's convenient sometimes
+to work in Cartesian,
+
+but it's also
+sometimes convenient
+
+to work in spherical
+coordinates.
+
+And it does not matter.
+
+And here's a really
+deep statement
+
+that goes way beyond
+quantum mechanics.
+
+It does not matter which
+coordinates you work in.
+
+You cannot possibly get a
+different answer by using
+
+different coordinates.
+
+So we're going to be ruthless
+in exploiting coordinates that
+
+will simplify our problem
+throughout the rest
+
+of this course.
+
+In the notes is it a short
+discussion of the form
+
+of the Laplacian,
+or the gradient
+
+squared in Cartesian spherical
+and cylindrical coordinates.
+
+You should feel free to use
+any coordinate system you
+
+want at any point.
+
+You just have to be
+consistent about it.
+
+So let's work out a
+couple of examples.
+
+And here are all
+we're going to do
+
+is apply exactly the same
+logic that we see over
+
+and over in 1D to
+our 3D problems.
+
+So the first example is
+a free particle in 3D.
+
+So before I get started
+on this, any questions?
+
+Just in general 3D questions?
+
+OK.
+
+So this stuff starts off easy.
+
+And I'm going to work in
+Cartesian coordinates.
+
+And a fun problem is
+to repeat this analysis
+
+in spherical coordinates,
+and we'll do that later on.
+
+OK, so free particle
+in 3D, so what
+
+is the energy eigenfunction
+equation look like?
+
+We want to find-- the
+Schrodinger equation has
+
+exactly the same
+structure as before.
+
+It's a linear
+differential equation.
+
+So if we find the eigenfunctions
+of the energy operator,
+
+we can use superposition to
+construct the general solution,
+
+right?
+
+So exactly as in 1D, I'm going
+to construct first the energy
+
+eigenfunctions , and then use
+them in superposition to find
+
+a general solution to
+the Schrodinger equation.
+
+OK?
+
+So let's construct the
+energy eigenfunctions.
+
+So what is the energy
+eigenvalue equation look like?
+
+Well, E on psi is equal to
+minus h bar squared upon 2m.
+
+And in Cartesian, the
+Laplacian is derivative respect
+
+to x squared plus
+derivative with respect
+
+to y squared plus derivative
+with respect to z squared.
+
+And we have no potential,
+so this is just psi.
+
+So that would be energy
+operator acting on it.
+
+And the eigenvalue
+equation is at a constant,
+
+the energy E on psi
+satisfies this equation.
+
+I'm going to write
+this phi sub e
+
+to continue with
+our notation of phi
+
+being the energy eigenfunctions.
+
+It of course, doesn't
+matter what I call it,
+
+but just for consistency I'm
+going to use the letter phi.
+
+So this is a very easy
+equation to solve.
+
+In particular, it has
+a lovely property,
+
+which is that it's separable.
+
+OK?
+
+So separable means
+the following.
+
+It means, look, I note, I just
+observed that this differential
+
+equation can be written
+as a sum of terms
+
+where there's a derivative with
+respect to only one variable.
+
+There's a differential
+operator with respect
+
+to only one variable and
+another differential operator
+
+with respect to only one
+variable added together.
+
+And when you see that,
+you can separate.
+
+And here's what I
+mean by separate.
+
+I'm going to just construct.
+
+I'm not going to say that
+this is a general solution.
+
+I'm just going to
+try to construct
+
+a set of solutions of
+the following form.
+
+Psi E of x, y, and
+z is equal to psi
+
+E-- I will call this psi
+sub x of x times phi sub
+
+y of y times phi sub z of z.
+
+And if we take this and we plug
+it in, let's see what we get.
+
+This gives us that E on phi E
+is equal to minus h bar squared
+
+upon 2m.
+
+Well the dx squared
+acting on phi sub e
+
+is only going to hit this guy.
+
+So I'm going to get phi x
+prime prime phi y phi z.
+
+Plus from the next term phi
+y prime prime phi x phi z.
+
+And from the next term phi
+z prime prime phi x phi y.
+
+But now I can do a sneaky thing
+and divide the entire equation
+
+by phi sub e.
+
+Phi sub e is phi x phi y phi z.
+
+So if I do so, I lose the phi
+y phi z, and I divide by phi x.
+
+And in this term, when I
+divide by phi x phi y phi z,
+
+I lose the x and z, and I have
+a left over phi sub y, or phi y.
+
+And similarly here,
+phi sub z upon phi z.
+
+Everyone cool with that?
+
+Yeah?
+
+AUDIENCE: Can we also
+lose the [INAUDIBLE]?
+
+PROFESSOR: I don't think so.
+
+Minus h bar squared over 2m
+just hangs out for the ride.
+
+So when I take the
+derivatives, I get these guys.
+
+And I have E times the function.
+
+We could certainly write
+this as 2m over h bar squared
+
+and put it over here.
+
+That's fine.
+
+OK, so this is the form
+of the equation we have,
+
+and what does this give us?
+
+What content does this give us?
+
+Well, note the following.
+
+This is a funny system.
+
+This is a function of x.
+
+This is a function of y, g
+of y only, and not of x or z.
+
+And this is a function only
+of z, and not of x or y.
+
+Yeah?
+
+So we have that E,
+and let's put this
+
+as minus 2m over
+h bar squared is
+
+equal to a function of
+x plus a function of y
+
+plus a function of h.
+
+What does this tell you?
+
+AUDIENCE: They're all constant.
+
+PROFESSOR: They're
+all constant, right.
+
+So the important
+thing is this equation
+
+has to be true for every
+value of x, y, and z.
+
+It's a differential equation.
+
+It's true everywhere.
+
+It's true here.
+
+It's true there.
+
+It's true at every point.
+
+Yeah?
+
+So for any value of x, y, and
+z, this equation must be true.
+
+So now imagine I have a
+particular solution g at h.
+
+I'm going to fix y and z
+to some particular point.
+
+I'm going to look right here.
+
+And here that fixes y and z.
+
+So these are just some numbers.
+
+And suppose we
+satisfy this equation.
+
+Then there's a very x
+leaving y and z fixed.
+
+What must be true of f of x?
+
+AUDIENCE: Constant.
+
+PROFESSOR: It's got to
+be constant, exactly.
+
+So this tells us that
+f of x is a constant.
+
+I.e.
+
+phi x prime prime of
+over phi x is a constant.
+
+I'll call it epsilon x.
+
+And phi y prime prime
+of over phi y and this
+
+is a function of y of x
+is equal to epsilon y.
+
+And actually for--
+yeah, that's fine.
+
+For fun I'm going
+to put in a minus.
+
+It doesn't matter what
+I call this coefficient.
+
+And similarly for phi z
+prime prime z over phi z
+
+is equal to minus epsilon z.
+
+So this tells us that
+minus 2m upon h bar squared
+
+e is equal to minus epsilon x
+minus epsilon y minus epsilon
+
+z.
+
+And any solutions
+of these equations
+
+with some constant value
+of epsilon x, epsilon
+
+y, and epsilon z
+is going to give me
+
+a solution of my original energy
+eigenvalue equation, where
+
+the value of capital
+E is equal to the sum.
+
+And I can take the minus
+signs make this plus plus.
+
+Yeah?
+
+AUDIENCE: Can
+epsilon x, epsilon y,
+
+and epsilon z-- can
+one of them be negative
+
+if the other's are sufficiently
+positive or vice versa?
+
+Or is that [INAUDIBLE]?
+
+PROFESSOR: Let's check.
+
+Let's check.
+
+So what are the solutions
+of this equation?
+
+Yeah.
+
+So solutions to
+this equation phi
+
+double-- so let's write this in
+a slightly more familiar form.
+
+This says that phi prime
+prime plus epsilon x
+
+phi is equal to 0, OK?
+
+But this just tells you
+that phi is exponential.
+
+Phi is equal to a e
+to the Ikx kxx plus B
+
+e to the minus ikxx,
+where k squared is
+
+equal to kx squared
+is equal to epsilon x.
+
+OK?
+
+So this becomes-- and similarly
+for epsilon y and epsilon z,
+
+each with their own
+value of ky and kz
+
+who squares the
+epsilon accordingly.
+
+So what can you say
+about these epsilons?
+
+Well, the epsilons are
+strictly positive numbers.
+
+So to answer your question.
+
+So the epsilons
+have to be positive.
+
+OK, so this equation becomes,
+though, E is equal to-- I'm
+
+going to put the h bar squared
+over 2m back on the other side.
+
+h bar squared upon 2m.
+
+Epsilon x, epsilon y, epsilon z.
+
+But those are just
+Kx squared plus Ky
+
+squared plus Kz squared.
+
+Kx squared plus
+Ky squared plus Kz
+
+squared, also known as
+h bar squared upon 2m k
+
+vector squared, where the
+wave function, phi sub
+
+E is equal to some overall
+normalization constant times,
+
+for the first function--
+where did the definition go?
+
+Right here.
+
+So from here, phi x is
+the exponential with Kx.
+
+This is an
+exponential y with Ky.
+
+And then the exponential
+in z with Kz.
+
+e to the ikx times x plus
+Ky times y plus Kz times z.
+
+Let me write this as e to the i.
+
+e to the i.
+
+Also known as some normalization
+constant e to the i k vector
+
+dot r vector.
+
+OK?
+
+So the energy, if we have
+a free particle, the energy
+
+eigenfunctions can
+be put in the form,
+
+or at least we can build energy
+eigenfunctions of the form,
+
+plane waves with some 3D
+momentum with energy E
+
+is equal to h bar squared
+k squared upon 2m,
+
+just as we saw for the free
+particle in one dimension.
+
+And the actual wave
+function is nothing
+
+but a product of
+wave functions in 1D.
+
+Yeah?
+
+AUDIENCE: What happened
+to the minus ikx minus iky
+
+minus ikz terms?
+
+PROFESSOR: Good, so here
+I just dropped these guys.
+
+So I just picked examples where
+we just picked e to the ikz.
+
+That's an excellent question.
+
+So I've done something here.
+
+In particular, I looked
+at a special case.
+
+And here's an important
+lesson from the theory
+
+of the separable
+equations, which
+
+is that once I separate-- so
+if I have a separable equation
+
+and I find it
+separated solution,
+
+phi E is equal to phi x of
+x, phi y of y phi z of z,
+
+not all functions-- not all
+solutions of the equation
+
+are of this form.
+
+They're not.
+
+I had to make that assumption.
+
+I said suppose it's of
+this form right here.
+
+So this is an assumption.
+
+OK?
+
+However, these
+form a good basis.
+
+By taking suitable
+linear combinations
+
+of them, suitable
+super positions,
+
+I can build a completely
+general solution.
+
+For example, as was noted, the
+true solution of this equation,
+
+even just focusing on
+the x, is a superposition
+
+of plus and minus
+waves, waves with
+
+plus positive negative momentum.
+
+So how do we get that?
+
+Well, we could
+write that as phi is
+
+equal to e to the ikx
+phi y phi z plus e
+
+to the minus ikx phi y phi z
+with the same phi y and phi z.
+
+So these are actually in there.
+
+Yeah?
+
+AUDIENCE: My other
+question is so I still
+
+don't see why any
+of the epsilons
+
+can't have a negative sign.
+
+You have an exponential,
+a real exponential as one
+
+of your products.
+
+PROFESSOR: OK, so if we
+had a negative epsilon,
+
+is that wave function
+going to be normalizable?
+
+AUDIENCE: Oh, as r
+goes to-- but can you
+
+just keep the minus term?
+
+PROFESSOR: In which direction?
+
+AUDIENCE: Oh, right.
+
+PROFESSOR: So if it's
+converging in this direction,
+
+it's got to be growing
+in this direction.
+
+And that's not going
+to be normalizable.
+
+And so as usual
+with the plane wave,
+
+we can pick the oscillating
+solutions that are also
+
+not normalizable
+to one, but they're
+
+delta function normalizable.
+
+And so that's what
+we've done here.
+
+It's exactly the
+same thing as in 1D.
+
+Yeah?
+
+AUDIENCE: So does this mean
+that any superposition of plane
+
+waves with wave vector
+equal in magnitude
+
+will also be an eigenfunction
+of the same energy?
+
+PROFESSOR: Absolutely.
+
+Awesome.
+
+Great observation.
+
+So the observation is this.
+
+Suppose I take K,
+I'll call it K1.
+
+So this is a vector
+such that K1 squared
+
+times h bar squared
+over 2m is equal to E.
+
+Now there are many vectors k
+which have the same magnitude,
+
+but not the same direction.
+
+So we could also make this equal
+to h bar squared K2 squared
+
+vector squared over 2m where K2
+is not equal to K1 as a vector,
+
+although they share
+the same magnitude.
+
+So that's interesting.
+
+So that looks a lot like before.
+
+In 1D, we saw that if
+we have k or minus k,
+
+these have the same energy.
+
+All right?
+
+Now if we have any K,
+K1-- so this is 1D.
+
+In 3D, if we have K1 and
+K2 with the same magnitude
+
+and the same energy,
+they're degenerate.
+
+That's interesting.
+
+Why?
+
+Why do we have this
+gigantic degeneracy
+
+of the energy eigenfunctions
+for the free particle in three
+
+dimensions?
+
+Yeah?
+
+AUDIENCE: Well, there
+are an infinite number
+
+of directions it could be going
+in with the same momentum.
+
+PROFESSOR: Awesome.
+
+So this is clearly true that
+there are an infinite number
+
+of momenta with
+the same magnitude.
+
+So there are many,
+many, but why?
+
+Why do they have
+the same energy?
+
+Couldn't they have
+different energy?
+
+Couldn't this one have
+a different energy?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Excellent,
+it's symmetric.
+
+The system is invariant
+under rotation.
+
+Who are you to say this
+is the x direction?
+
+I call it y.
+
+Right?
+
+So the system has a symmetry.
+
+The symmetry is rotations.
+
+And when we have
+a symmetry, that
+
+means there's an operator,
+a unitary operator, which
+
+affects that rotation,
+the rotation operator.
+
+It's the operator
+that takes a vector
+
+and rotates in some
+particular way.
+
+We have a unitary
+operator that's
+
+a symmetry that means it
+commutes with the energy
+
+operator.
+
+But if it commutes with
+the energy operator,
+
+we get can degeneracies.
+
+We can get states that are
+different states mapped
+
+to each other under our unitary
+operator, under our rotation.
+
+We get states which are
+different states manifestly.
+
+But which have the
+same energy, which
+
+are shared energy eigenvalues.
+
+Cool?
+
+And this is a really lovely
+example, both in 1D and 3D,
+
+that when you have a symmetry,
+you get degeneracies.
+
+And when you have
+a degeneracy, you
+
+should be very
+suspicious that there's
+
+a symmetry hanging around,
+lurking around ensuring it, OK?
+
+And this is an
+important general lesson
+
+that goes way beyond the
+specifics of the free particle.
+
+Yeah?
+
+AUDIENCE: So that
+occurs in systems
+
+with bound states [INAUDIBLE]?
+
+PROFESSOR: Yeah, it occurs
+in systems with bound states
+
+and systems with
+non bound states.
+
+So here we're talking
+about a free particle.
+
+Certainly not bound.
+
+And its true.
+
+For bound states, we'll
+also see that there
+
+will be a degeneracy
+associated with symmetry.
+
+Now your question is a
+really, really good one,
+
+because what we found-- let
+me rephrase the question.
+
+The question is, look, in
+1D when we had bound states,
+
+there was no degeneracy.
+
+Didn't matter what
+you did to the system.
+
+When you had bound states, bound
+states were non degenerate.
+
+In 3D, we see that when
+you have a free particle,
+
+you again get degeneracy.
+
+In fact, you get a heck
+of a lot more degeneracy.
+
+You get a sphere's worth.
+
+Although actually, that's a
+sphere in 0 dimension, right?
+
+It's a 0 dimensional
+sphere, two points.
+
+So you get a sphere's
+worth of degenerate states
+
+for the free particle.
+
+Well, what about bound states?
+
+Are bound states non
+degenerate still?
+
+Fantastic question.
+
+Let's find out.
+
+So let's do the
+harmonic oscillator.
+
+Let's do the 3D harmonic
+oscillator to check.
+
+So the 3D harmonic oscillator,
+the potential is h bar squared.
+
+And let's pick for fun the
+rotationally symmetric 3D
+
+harmonic oscillator.
+
+m omega squared upon 2 x squared
+plus y squared plus z squared.
+
+This could also be written m
+omega squared upon 2 r squared.
+
+So I could write it in
+spherical coordinates
+
+or in Cartesian coordinates.
+
+This is really in
+vector notation.
+
+Doesn't matter.
+
+It's the same thing.
+
+3D harmonic oscillator.
+
+So what you immediately deduce
+about the form of the energy
+
+eigenfunctions?
+
+Well, we have that E phi E
+is equal to P squared over
+
+minus h bar squared
+over 2m-- so here's
+
+the energy eigenvalue
+equation-- times
+
+dx squared plus dy squared plus
+dz squared plus m omega squared
+
+upon 2 times x squared plus y
+squared plus z squared phi E.
+
+But I can put this
+together in a nice way.
+
+This is minus h bar
+squared upon 2m dx squared
+
+plus m omega squared upon 2
+x squared plus ditto for y
+
+plus ditto for z phi E. Yeah?
+
+Everyone agree?
+
+So this is differential
+operator that only involves x.
+
+Doesn't involve y or z.
+
+Ditto y, but no x or z.
+
+And ditto z, but no x or y.
+
+Aha, this is separable
+just as before.
+
+So now we have a
+nice separable system
+
+where I want to solve the
+equations 3 times, once
+
+for x, y, and z.
+
+And I'm just going
+to write it for x, y,
+
+and z epsilon sub x phi x is
+equal to minus h bar squared
+
+over 2m dx squared plus
+m omega squared upon 2 x
+
+squared phi sub x.
+
+And ditto for x, y, z.
+
+And then phi E is going
+to be equal to phi
+
+x of x, phi y of y,
+and phi z of z, OK?
+
+Where E is equal to epsilon x
+plus epsilon y plus epsilon z.
+
+Note that I've used a slightly
+different definition of epsilon
+
+here as before.
+
+Here it's explicitly
+the energy eigenvalue.
+
+So what this is
+telling is, look,
+
+we know what this equation is.
+
+This equation is
+the same equation
+
+we ran into in the 1D
+harmonic oscillator.
+
+It's exactly the 1D
+harmonic oscillator problem.
+
+So the solution to the 3D
+harmonic oscillator problem
+
+can be written for
+energy eigenfunctions,
+
+can be constructed
+by taking a harmonic
+
+oscillator in the x direction--
+and we know what those are.
+
+There's a tower of them.
+
+There's a ladder of them
+created by the raising operator
+
+and lowered by the
+lowering operator.
+
+And similarly for y,
+and similarly for z.
+
+So I'm going to write
+this slightly differently
+
+in the same place as phi sub
+E is equal to phi sub nx of x.
+
+The state with energy E sub nx.
+
+Phi sub ny of y.
+
+Phi sub nz of z.
+
+Where these are all
+the single dimension,
+
+one dimensional harmonic
+oscillator eigenfunctions.
+
+And E is equal to Ex E sub nx
+plus E sub ny plus E sub nz.
+
+OK?
+
+So let's look at the
+consequences of this.
+
+So first off, does anyone
+have any questions?
+
+I went through
+the kind of quick.
+
+Any questions about that?
+
+If you're not comfortable
+with separable equations,
+
+you need to become super
+comfortable with separable
+
+equations.
+
+It's an important technique.
+
+We're going to use it a lot.
+
+So the upshot is that
+if I write-- in fact,
+
+I'm going to write that in
+slightly different notation.
+
+If I write phi E
+is equal to phi n
+
+of x, where it's the-- and phi
+l of y and phi m of z-- actually
+
+that's a stupid ordering.
+
+Let's try that again.
+
+l, m, n.
+
+That is the
+alphabetical ordering.
+
+With the energy is
+now equal to-- we
+
+know the energy is of a
+state with of the harmonic
+
+oscillator with
+excitation number l.
+
+It's h bar omega, the overall
+omega, times l plus 1/2.
+
+But from this guy it's
+got excitation number m,
+
+so energy of that is h bar
+omega m plus 1/2 plus m.
+
+And so now that's plus 1.
+
+And for this guy
+similarly, h bar omega
+
+n plus n and now plus
+1/2 again plus 3/2.
+
+This is a basis of solutions
+of the energy eigenfunction
+
+equations.
+
+These are the solutions of
+the energy eigenfunctions
+
+for the 3D harmonic oscillator.
+
+And now here's the question.
+
+The question that
+was asked is, look,
+
+there are no degeneracies
+in bound states in 1D.
+
+Here we have manifestly
+a 3D bound state system.
+
+Are there degeneracies?
+
+AUDIENCE: Yes.
+
+PROFESSOR: Yeah,
+obviously, right?
+
+So for example, if I call
+l1 this 0 and this 0.
+
+Or if I call this 010 or 001,
+those all have the same energy.
+
+They have the energy h bar
+omega 0 times 1 plus 3/2 or 5/2.
+
+So let's look at this
+in a little more detail.
+
+Let's write a list
+of the degeneracies
+
+as a function of the energy.
+
+So at energy what's
+the ground state energy
+
+for the 3D harmonic oscillator?
+
+3 halves h bar omega.
+
+It's three times
+the ground state
+
+energy for the single
+1D harmonic oscillator.
+
+So 3/2 h bar omega.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Good, the way
+we arrived that this was we
+
+found that the energy-- so
+the energy operator acting
+
+on the 3D wave
+function is what I
+
+get by taking the
+energy operator in 1D
+
+and acting on the wave function,
+and the energy operator in y
+
+acting on the wave function,
+the energy operator in z acting
+
+on the wave function, where
+the energy operator for each
+
+of those is the 1D
+harmonic oscillator
+
+with the same frequency.
+
+OK?
+
+And then I separated.
+
+I said look, let
+the wave function,
+
+the 3D wave function, since
+I know this is separable
+
+and each separated part
+of the wave function
+
+satisfies the 1D harmonic
+oscillator equation,
+
+I know what the eigenfunctions
+of the 1D harmonic oscillator
+
+energy eigenvalue problem are.
+
+They are the phi n's.
+
+And so I can just take
+my 3D wave function.
+
+I can say the 3D wave function
+is going to be the separated
+
+form, the product
+of 1D wave function
+
+in x, a 1D wave function in
+y, and 1D wave function in z.
+
+Cool?
+
+So now let's look back
+at what let's think
+
+about what happens when I
+take the energy operator
+
+and I act on that [INAUDIBLE].
+
+When I take the 3D
+energy operator, which
+
+is the sum of the three
+1D energy operators,
+
+harmonic oscillator
+energy operators.
+
+When thinking I'm going
+to act on this guy,
+
+the first one, which only
+knows about the x direction,
+
+sees the y and z
+parts as constants.
+
+And it's a phi x, and
+what does it give us back?
+
+E on phi x is just h bar
+omega n plus one half.
+
+Ditto for this guy.
+
+And then the energy
+operator in 3D
+
+is the sum of the three
+1D energy operators.
+
+So that tells us the energy is
+the sum of the three energies.
+
+Is that cool?
+
+OK good.
+
+Other questions?
+
+Yeah?
+
+AUDIENCE: Is the number of
+degeneracies essentially
+
+[INAUDIBLE] of number theory.
+
+PROFESSOR: Ask me
+that after class.
+
+So let's look at
+the degeneracies
+
+as a function of the energy.
+
+So at the lowest possible
+energy, 3/2 omega, what states
+
+can I possibly have?
+
+I'm going to label the states by
+the three numbers, l, m, and n.
+
+So this is just the
+ground state 0 0 0.
+
+So is that degenerate?
+
+No, because there's
+just the one state.
+
+What about at the next level?
+
+What's the next allowed energy?
+
+AUDIENCE: 5/2.
+
+PROFESSOR: 5/2.
+
+OK, 5/2.
+
+So at 5/2 what
+states do we have?
+
+Well, we have 1 0 0.
+
+But we also have 0, 1, 0.
+
+And we also 0 0 1.
+
+Aha, this is looking good.
+
+What does this
+correspond to physically?
+
+This says you have
+excitation, so you've
+
+got a node in the x direction.
+
+But your Gaussian in
+the y and z directions.
+
+This one says your Gaussian
+in the x direction.
+
+You have a node in the y
+direction as a function of y,
+
+because it's phi 1 of y.
+
+And you're Gaussian
+in the z directions.
+
+And this one says you have 1
+excitation in the z direction.
+
+So they sound sort of
+rotated from each other.
+
+That sounds promising.
+
+But in particular, what
+we just discovered sort of
+
+by construction
+is that there can
+
+be degeneracies among
+bound states in 3D.
+
+This was not possible
+in 1D, but it
+
+is possible in
+3D, which is cool.
+
+But we've actually learned more.
+
+What's the form of
+the degeneracies?
+
+So here it looks like they're
+just rotations of each other.
+
+You call this x, I call it
+y, someone else calls it z.
+
+These can't possibly
+look different functions
+
+because they're just
+rotations of each other.
+
+However, things get
+a little more messy
+
+when you write, well,
+what's the next level?
+
+What's the next energy
+after 5/2 h bar omega?
+
+7/2 h bar omega, exactly.
+
+7/2.
+
+And that's not so bad.
+
+So for that one, we get
+2 0 0, 0 2 0, 0 0 2.
+
+But is that it?
+
+AUDIENCE: No.
+
+PROFESSOR: What else do we get?
+
+1 1 0, 0 1 1, 1 0 1.
+
+So first off, let's
+look at the number.
+
+The degeneracy number
+here-- I'll call this d sub
+
+0-- the degeneracy of the
+ground state is 1, OK?
+
+The degeneracy--
+and in fact, I'm
+
+going to write this as a table--
+the degeneracy as level n.
+
+So for d0 is equal to 1.
+
+d1 is equal to 3.
+
+And d2 is equal to 6.
+
+Now it's less clear
+here what's going on,
+
+because is this just
+this guy relabelled?
+
+No.
+
+So this is weird,
+because we already
+
+said that the reason we expect
+that there might be degeneracy,
+
+is because of
+rotational symmetry.
+
+The system is
+rotationally invariant.
+
+The potential, which is the
+harmonic oscillator potential,
+
+doesn't care in what direction
+the radial displacement
+
+vector is pointing.
+
+It's rotationally symmetrical.
+
+When we have symmetry--
+on general grounds, when
+
+we have a symmetry, we
+expect to have degeneracies.
+
+But this are kind of
+weird, because these
+
+don't seem to be simple
+rotations of each other,
+
+and yet they're degenerate.
+
+So what's up with that?
+
+Question?
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE] Gaussian
+in certain directions?
+
+PROFESSOR: Yeah, sure OK.
+
+So let me just explain what
+this notation means again.
+
+So by 1 0 0, what I mean is
+that the number l is equal to 1,
+
+the number m is equal
+to 0, n is equal to 0.
+
+That means that
+the wave function
+
+phi 3D is equal to phi 1 of
+x, phi 0 of y, phi 0 of z.
+
+But what's phi 0 of z?
+
+What's a Gaussian
+in the z direction?
+
+Phi 0 of y.
+
+That's the ground state
+in the y direction
+
+of the harmonic oscillator.
+
+It's Gaussian in
+the y direction.
+
+If I wanted x, that's
+not the ground state.
+
+That's the excited state.
+
+And in particular, sort of being
+a Gaussian it goes through 0.
+
+It has a node.
+
+So this wave function is
+not rotationally invariant.
+
+It as a node in the x direction,
+but no nodes and y and z
+
+direction.
+
+And similarly for these guys.
+
+Did that answer your questions?
+
+Great.
+
+OK, so we have
+these degeneracies,
+
+and they beg an explanation.
+
+And if you look
+at the next level,
+
+it turns out that d3-- and
+you can do this quickly
+
+on a scrap of
+paper-- d3 is 10, OK?
+
+And they go on.
+
+And if you keep
+writing this list out,
+
+I guess it goes up--
+what's the next one?
+
+15.
+
+21, yeah.
+
+So this has a simple
+mathematical structure,
+
+and you can very quickly
+convince yourself
+
+of the form of this degeneracy.
+
+dn is n n plus 1 over 2.
+
+So let's just make
+sure that works.
+
+1 1 plus 1 over 2.
+
+Sorry I should
+really call this 1.
+
+n plus 1, n plus 2
+if I count from 0.
+
+So for 0, this is going to
+give us 1 times 2 over 2.
+
+That's 1.
+
+That works.
+
+So for 1 that gives
+2 times 3 over 2,
+
+which is 3, and so
+on and so forth.
+
+So where did this come from?
+
+This is something we're
+going to have to answer.
+
+Why that degeneracy?
+
+That seems important.
+
+Why is it that number?
+
+Why do we have that
+much degeneracy?
+
+But the thing I really want
+to emphasize at this point
+
+is that there's an absolutely
+essential deep connection
+
+between symmetries
+and degeneracies.
+
+If we didn't have symmetry,
+we wouldn't have degeneracy,
+
+and we can see that
+very easily here.
+
+Imagine that this potential
+was not exactly symmetric.
+
+Imagine we made it slightly
+different by adding
+
+a little bit of extra
+frequency to z direction.
+
+Make the z frequency
+slightly different.
+
+Plus m omega tilde
+squared upon 2 z
+
+squared, where omega tilde
+is not equal to omega 0.
+
+OK?
+
+The system is still
+separable, but this guy
+
+has frequency omega 0.
+
+The x part has omega 0.
+
+This has omega 0.
+
+But this has omega tilde.
+
+OK?
+
+And so exactly the same
+argument is going to go through,
+
+but the energy now is going
+to have a different form.
+
+The energy is going to have h
+bar omega-- h bar omega 0 times
+
+l plus m plus 1.
+
+But from the z part
+it's going to have
+
+plus h bar omega tilde
+times n plus 1/2.
+
+And now these
+degeneracies are going
+
+to be broken, because
+this state will not
+
+have the same
+energy as these two.
+
+Everyone see that?
+
+When you have symmetry,
+you get to degeneracy.
+
+When you don't have a symmetry,
+you do not get degeneracy.
+
+This connection is
+extremely important,
+
+because it allows
+you to do two things.
+
+It allows you to
+first not solve things
+
+you don't need to solve for.
+
+If you know there's a symmetry,
+solve it once and then compute
+
+the degeneracy and you're done.
+
+On the other hand,
+if you have a system
+
+and you see just manifestly
+you measure the energies,
+
+and you measure that the
+energies are degenerate,
+
+you know there's a symmetry
+protecting those degeneracies.
+
+You actually can't
+be 100% confident,
+
+because I didn't prove
+that these are related
+
+to each other, but you
+should be highly suspicious.
+
+And in fact, this is an
+incredibly powerful tool
+
+in building models
+of physical systems.
+
+If you see a degeneracy or
+an approximate degeneracy,
+
+you can exploit that to learn
+things about the underlying
+
+system.
+
+Yeah?
+
+AUDIENCE: So we just
+add the different omega
+
+to each omega
+[INAUDIBLE] number there
+
+is still a possibility
+to get a degeneracy.
+
+PROFESSOR: Exactly.
+
+So it's possible for these
+omegas to be specially tuned
+
+so that rational combinations
+of them give you a degeneracy.
+
+But it's extraordinarily
+unlikely for that
+
+to happen accidentally,
+because they
+
+have to be rationally
+related to each other,
+
+and the rationals are a set
+of measures 0 in the reels.
+
+So if you just randomly
+pick some frequencies,
+
+they'll be totally
+incommensurate,
+
+and you'll never
+get a degeneracy.
+
+So it is possible to have
+an accidental degeneracy.
+
+Whoops, just pure coincidence.
+
+But it's extraordinarily
+unlikely.
+
+And as you'll see when you
+get to perturbation theory,
+
+it's more than unlikely.
+
+It's almost impossible.
+
+So it's very rare that you
+get accidental degeneracy.
+
+It happens, but it's rare.
+
+Other questions?
+
+OK, nothing?
+
+OK so here we're now
+going to launch into--
+
+so this leads us into
+a very simple question.
+
+At the end of the
+day, the degeneracies
+
+that we see for the 3D
+free particle, which
+
+is a whole sphere's
+worth of degeneracy,
+
+and the degeneracy we see for
+the 3D harmonic oscillator,
+
+the bound states,
+which is discrete,
+
+but with more and
+more degeneracy
+
+the higher and
+higher energy you go.
+
+Those we're blaming,
+at the moment,
+
+on a symmetry, on
+rotational symmetry,
+
+rotational invariance.
+
+So it seems wise
+to study rotations,
+
+to study rotational invariance
+and rotational transformations
+
+in the first place.
+
+In the first part of the
+course, in 1D quantum mechanics,
+
+we got an awful lot of juice
+out of studying translations.
+
+And the generator of
+translations was momentum.
+
+So we're going to do
+the same thing now.
+
+We're going to study
+rotations and the generators
+
+of rotations, which are the
+angular momentum operators,
+
+and that's going to occupy
+us for the rest of today
+
+and Thursday.
+
+Yeah?
+
+AUDIENCE: So your
+rotational symmetry
+
+will explain a factor of three
+in your degeneracy, right?
+
+But what's the symmetry that
+explains the way this grows.
+
+Because this very
+clearly appears
+
+there's 1 up to a
+factor of three.
+
+And then there's 2 up
+to a factor of three.
+
+And there's even more that's
+not even a multiple of three.
+
+PROFESSOR: Right,
+actually so here's
+
+a very tempting
+bit of intuition.
+
+Very tempting bit of intuition
+is going to say the following.
+
+Look, rotational invariance,
+there's x, there's y,
+
+and there's z.
+
+It's going to explain
+rotations amongst those three.
+
+So that could only possibly
+give you a factor of three.
+
+But it's important
+to keep in mind
+
+that that's not
+correct intuition.
+
+It's tempting intuition,
+but it's not correct.
+
+And an easy way to see
+that its not correct
+
+is that for the
+free particle, there
+
+is a continuum, a
+whole sphere's worth
+
+of degenerate states
+in any energy.
+
+And all of those are related to
+each other by simple rotation
+
+of the k vector, of
+the wave vector, right?
+
+So the rotational
+symmetry is giving us
+
+a lot more than a
+factor of three.
+
+And in fact, as
+we'll see, it's going
+
+to explain exactly the n
+plus 1 n plus 2 over 2.
+
+OK, so with that
+motivation let's
+
+start talking about
+angular momentum.
+
+So I found this topic
+to be not obviously
+
+the most powerful or interesting
+thing in the world when I first
+
+studied it.
+
+And my professor
+was like no, no, no.
+
+This is the deepest thing.
+
+And recently I had a fun
+conversation with one
+
+of my colleagues,
+Frank Wilczeck,
+
+who said yeah, in intro
+to quantum mechanics
+
+the single most interesting
+thing is the angular momentum
+
+and the addition of
+angular momentum.
+
+And something has happened to
+me in the intervening 20 years
+
+that I totally agree with him.
+
+So I will attempt to convey to
+you the awesomeness of this.
+
+But you have to buy in a little.
+
+So work with me in the math
+at the beginning of this,
+
+and it has a great payoff.
+
+OK so the question is,
+what is the operator.
+
+So we're going to talk
+about angular momentum now.
+
+And I want to start with
+the following question.
+
+In the same sense
+as we started out
+
+by asking what
+represents position
+
+and momentum, linear momentum,
+in quantum mechanics, what
+
+represents what operator by
+our first, second, or third
+
+postulate-- I don't even
+remember the order now.
+
+What operator represents angular
+momentum in quantum mechanics?
+
+And let's start by remembering
+what angular momentum is
+
+in classical mechanics.
+
+So L in classical
+mechanics is r cross p.
+
+In classical mechanics.
+
+So let's just try this.
+
+Let's construct that operator.
+
+This is not the world's most
+beautiful way of deriving this,
+
+but let's just write
+down natural guess.
+
+For in quantum mechanics
+what's the operator we want?
+
+Well, we want a vectors
+worth of operators,
+
+because angular
+momentum is a vector.
+
+It's a vector of
+operators, three operators.
+
+And I'm going to write these
+as r vector the operators x, y,
+
+z cross p the vector
+of momentum operators.
+
+So at this point, you
+should really worry,
+
+because do r and p commute?
+
+Not so much, right?
+
+However, the situation is
+better than it first appears.
+
+Let's write this out
+in terms of components.
+
+So this is in components.
+
+And I'm going to
+work, for the moment,
+
+in Cartesian coordinates.
+
+So Lx is equal to?
+
+Lx is equal to?
+
+You all took mechanics.
+
+Lx is equal to?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Thank you.
+
+YPz minus ZPy.
+
+And that's the curl, the
+x component of the curl.
+
+And similarly, the x component--
+so the way to remember this
+
+is that its cyclic.
+
+x, y, z.
+
+y, z, x.
+
+So z, p, y.
+
+PX minus XPz.
+
+And then we have
+z XPy minus YPx.
+
+So we were worried here about
+maybe an ordering problem.
+
+Is there an ordering
+problem here?
+
+Does it matter if
+I write YPz or PZy?
+
+AUDIENCE: No.
+
+PROFESSOR: No, because they
+commute with each other.
+
+PZ is momentum for
+the z-coordinate, not
+
+the y-coordinate, and they
+commute with each other.
+
+So there's no ambiguity.
+
+It's perfectly well defined.
+
+So we're just going
+to take this to be
+
+the definition of the components
+of the angular momentum
+
+operator Lx, Ly, and Lz.
+
+And just for fun, I
+want to write this out.
+
+So because we know that Px,
+Py, and Pz can be expressed
+
+in terms of derivatives
+or differential operators,
+
+we can write the same operator
+in Cartesian coordinates
+
+in the following way.
+
+So clearly we could
+write this as Y d dx i
+
+upon h bar-- or
+sorry, h bar upon i.
+
+And z h bar upon i d dy.
+
+So we could write that
+in Cartesian coordinates
+
+as a differential operator.
+
+But we can also write this
+in spherical coordinates.
+
+I'm just going to take
+a quick side note just
+
+to write down what it is.
+
+If we did this
+spherical coordinates,
+
+it's particularly
+convenient to write--
+
+let me just write
+Lz for the moment.
+
+This is equal to minus i h bar
+derivative with respect to phi,
+
+where the coordinates,
+[INAUDIBLE]
+
+coordinates and spherical
+coordinates in this class
+
+is theta is going
+to be the angle down
+
+from the vertical
+axis, from the z-axis.
+
+And phi is going to be
+the angle of a period 2pi
+
+that goes around
+the equator, OK?
+
+Just to give you a name.
+
+This is typically what
+physicists call them.
+
+This is typically not what
+mathematicians call them.
+
+This leads to
+enormous confusion.
+
+I apologize for my field.
+
+So here it is.
+
+I can also construct
+the operator associated
+
+with the square of the momentum.
+
+And why would we care about
+the square of the momentum?
+
+Well, that's what shows up
+in the Hamiltonian, that's
+
+what shows up in the energy.
+
+So I can construct the operator
+for the square of the momentum
+
+and write it, and it takes
+a surprisingly simple form.
+
+When I see surprisingly simple,
+you might disagree with me,
+
+but if you actually do
+the derivation of this,
+
+it's much worse in between.
+
+1 over sine theta
+d theta sine theta
+
+d theta plus 1 over sine
+squared theta d phi.
+
+Couple quick things.
+
+What are the dimensions
+of angular momentum?
+
+Length and momentum.
+
+What else has units
+of angular momentum?
+
+AUDIENCE: h bar.
+
+PROFESSOR: Solid. h
+bar, dimensionless.
+
+Angular momentum squared,
+angular momentum squared.
+
+OK, great.
+
+So that's going to
+be very convenient.
+
+h bars are just going to
+float around willy nilly.
+
+OK, so suppose I ask you
+the following-- bless you.
+
+Suppose I ask you the
+following questions.
+
+I say look, here are the
+operators of angular momentum.
+
+This is Lz.
+
+We could have written down
+the same expression for Lx,
+
+and a Ly, and L squared.
+
+What are the eigenfunctions
+of these operators?
+
+Suppose I ask you this question.
+
+You all know how to
+answer this question.
+
+You take these operators--
+so for example,
+
+if I ask you what are
+the eigenfunctions of Lz?
+
+Well, that's not so bad, right?
+
+The eigenfunction
+of Lz is something
+
+where Lz on phi--
+I'll call little m--
+
+is equal to minus I h
+bar d d theta phi sub m.
+
+But I want the
+eigenvalue, so I'll
+
+call this h bar
+times some number.
+
+Let's call it m, because
+Lz is an angular momentum.
+
+It carries units of
+h bar, and its h bar
+
+times some number which is
+dimensional, so we'll call it
+
+m.
+
+And we all know the
+solution of this equation.
+
+The derivative is equal
+to a constant times--
+
+we can lose the h bar.
+
+We get a minus i,
+so we pick up an i.
+
+So therefore phi sub m is
+equal to some constant times e
+
+to the im phi.
+
+What can we say about m?
+
+Well, heres an important
+thing-- oh shoot.
+
+I'm using phi in so many
+different ways here.
+
+Let's call this not
+phi, because it's
+
+going to confuse
+the heck out of us.
+
+Let's call it Y. So
+we'll call it Y sub m.
+
+Why not?
+
+It's not my joke.
+
+This goes back to a bunch of--
+yeah well, it goes way back.
+
+So phi is the variable.
+
+Y is the deciding eigenfunction
+of Lz, and that's great.
+
+But what can you say about m?
+
+Well phi is the variable
+around the equator
+
+is periodic with period 2pi.
+
+And our wave function had
+better be single valued.
+
+So what does that
+tell you about m?
+
+Well, under phi goes
+to phi plus 2pi.
+
+This shifts by im 2pi.
+
+And that's only one to
+make a single valued
+
+if m is an integer.
+
+So m has to be an integer.
+
+m is an integer.
+
+Now we did that for Lz.
+
+We found the
+eigenfunctions of Lz.
+
+What about finding the
+eigenfunctions L squared?
+
+Exactly the same thing.
+
+We're going to solve
+the eigenvalue equation,
+
+but it's going to be
+horrible, horrible to find
+
+these functions, right?
+
+Because look at this.
+
+1 over sine squared d d phi.
+
+And then 1 over sine
+d theta sine d theta.
+
+This is not going to
+be a fun thing to do.
+
+So we could just brute
+force this, but let's not.
+
+Let's all agree that
+that's probably a bad idea.
+
+Let's find a better way to
+construct the eigenfunctions
+
+of the angular
+momentum operators.
+
+So let's do it.
+
+So we ran into a
+situation like this
+
+before when we dealt with
+the harmonic oscillator.
+
+There was a
+differential equation
+
+that we wanted to solve.
+
+And OK, this one isn't nearly
+as bad, not nearly as bad
+
+as that one would have been.
+
+But still it was more useful
+to work with operator methods.
+
+So let's take a hint from that
+and work with operator methods.
+
+So now we need to study the
+operators of angular momentum.
+
+So let's study them in
+a little more detail.
+
+So something you're going
+to show in your problem set
+
+is the following.
+
+The commutator of Lx with Ly
+takes a really simple form.
+
+This is equal to i h bar--
+let's just do this out.
+
+Let's do this commutator.
+
+We're OK.
+
+So Lx with Ly, this is
+equal to the commutator
+
+of YPz minus ZPy with
+Ly ZPx minus XPz.
+
+So let's look at
+these term by term.
+
+So the first one is YPz ZPx.
+
+YPz ZPx.
+
+That's a Px.
+
+Sorry, ZPy.
+
+ZPx, this term.
+
+X, good.
+
+That's the first commutator.
+
+The second commutator, it can
+be YPz an XPz minus YPz XPz.
+
+And then these
+commutators, the next two,
+
+are going to be ZPy with ZPx.
+
+And finally ZPy.
+
+And that's minus
+and this is a plus.
+
+ZPy and XPz.
+
+OK, so let's look at these.
+
+These look kind
+of scary at first.
+
+But in this one
+notice the following.
+
+This is XPz ZPx minus ZPx YPz.
+
+But what you say about Y with
+all these other operators?
+
+Y commutes with all of them.
+
+So in each term I
+could just pull Y
+
+all the way out to one side.
+
+Yeah?
+
+So I could just pull out this
+Y. So for the first term,
+
+I'm going to write this as
+Y commutator PZ with ZPx.
+
+And let me just do
+that explicitly.
+
+There's no reason to.
+
+So this is YPz
+ZPx minus ZPx YPz.
+
+And I can pull the Y out front,
+because this commutes with Px
+
+and with Z. So I can make this
+Y times PZ ZPx minus ZPx Pz.
+
+But now note that I can
+do exactly the same thing
+
+with the Px.
+
+Px commutes with z.
+
+Px commutes with Pz.
+
+And it commutes with y.
+
+So I can pull the px
+from each term out.
+
+Px Y. And now I lose the Px.
+
+I lose the Px.
+
+But now this is looking good.
+
+This is Px times Y. And Pz
+minus ZPz PZz minus ZPz.
+
+This is also known as PXy
+times commutator of PZ with Z.
+
+And what is this equal to?
+
+Let's get our signs right.
+
+This is Px with Y
+time-- OK, we all
+
+agree that this is going
+to have an h bar in it.
+
+Let's write units.
+
+There's going to be an i.
+
+And is it a plus or minus?
+
+Minus.
+
+OK, good.
+
+So we get minus h bar XPy.
+
+So this term is going to give
+us minus i h bar Py XPx times Y.
+
+And let's look at this term.
+
+OK, this is Y, and Y commutes
+with PZx and PZ, right?
+
+So I could just pull out the y.
+
+And x commutes with everything,
+so I can pull out the x.
+
+And I'm left with the
+commutator of Pz with Pz.
+
+What's the commutator
+of Pz with Pz?
+
+AUDIENCE: 0.
+
+PROFESSOR: 0.
+
+This term gives me a 0.
+
+Similarly here, Py
+commutes with everything.
+
+Z ZPx.
+
+Px commutes with everything.
+
+Z ZPy.
+
+So I can pull out the Px Py,
+and I get Z commutator Z,
+
+and what's that?
+
+AUDIENCE: 0.
+
+PROFESSOR: 0.
+
+So this gives me 0.
+
+And now this term, ZPy
+XPz, the only two things
+
+that don't commute with each
+other are the Z and the Pz.
+
+The Py and the X
+I pull out, so I
+
+get it a term that's XPy and
+the commutator of Z with Pz.
+
+And what is that
+going to give me?
+
+PyX i h bar.
+
+Aha, look at what we got.
+
+This is equal to i h bar times--
+did I screw up the signs?
+
+XPy minus YPz.
+
+Oh sorry, Px.
+
+And what is this equal to?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, i h bar Lz.
+
+And more generally, as you'll
+show on the problem set,
+
+you get the following
+commutators.
+
+Once you've done this once, you
+can do the rest very easily.
+
+Lx Ly is-- so Lx with
+Ly is i h bar Lz.
+
+And then the rest can be
+got from cyclic rotations
+
+Ly with Lz is i h bar Lx and
+Lz with Lx is i h bar Ly.
+
+And now here's a fancier one.
+
+This is less obvious, but
+exactly the same machinations
+
+will give you this result,
+and you'll do this again
+
+on the problems set.
+
+If I take L squared,
+k and L squared
+
+here is going to be
+L squared, I just
+
+mean Lx squared plus Ly
+squared plus Lz squared.
+
+This is the norm squared of
+the vector, the operator form.
+
+L squared with Lz--
+or sorry, with Lx.
+
+Yeah, fine.
+
+Lx is equal to 0.
+
+So Lx commutes with the
+magnitude L squared.
+
+Similarly L squared, now just
+by rotational invariance,
+
+if Lx commutes
+with it, Ly and Lz
+
+had better also commute
+with it, because
+
+of who you to see what's Lx.
+
+And L squared with Lz
+must be equal to 0.
+
+Yeah?
+
+Everyone cool with that?
+
+And the thing is
+we've just-- and I'm
+
+going to put big
+flags around this.
+
+We've just learned
+a tremendous amount
+
+about the eigenfunctions of
+the angular momentum operators.
+
+Why?
+
+Let's leave that up.
+
+So what have we just learned
+about the eigenfunctions
+
+of the angular momentum
+operators Lx, Ly, Lz, and L
+
+squared?
+
+Anyone?
+
+We just learned something
+totally awesome about them.
+
+Anyone?
+
+So can you find simultaneous
+eigenfunctions of Lx and Ly?
+
+AUDIENCE: No.
+
+PROFESSOR: Not so much.
+
+They don't commute to 0.
+
+What about Ly and Lz?
+
+Nope.
+
+Lz Lx, nope.
+
+So you cannot find simultaneous
+eigenfunctions of Lx and Ly.
+
+What about Lx and L squared?
+
+Yes.
+
+So we can find
+simultaneously eigenfunctions
+
+of L squared and Lx.
+
+OK, what about can we find
+simultaneous eigenfunctions
+
+of L squared and Ly?
+
+Yep.
+
+Exactly.
+
+What about L
+squared, Ly, and Lz?
+
+Nope.
+
+No such luck.
+
+And this leads us to
+the following idea.
+
+The idea is a complete set
+of commuting observables.
+
+And here's what this
+idea is meant to contain.
+
+You can always write
+down a lot of operators.
+
+So let me step back and
+ask a classical question.
+
+Classically, suppose I have a
+particle in three dimensions,
+
+a particle moving around in
+this room, non relativistic,
+
+familiar 801.
+
+I have a particle moving
+around in this room.
+
+How much data must
+I specify to specify
+
+the configuration
+of this system?
+
+Well, I have to tell you
+where the particle is,
+
+and I have to tell you what
+its momentum is, right?
+
+So I have to tell you the
+three coordinates and the three
+
+momenta.
+
+If I give you five numbers,
+that's not enough, right?
+
+I need to give you
+six bits of data.
+
+On the other hand, if I
+give you seven numbers,
+
+like I give x, y, z, Px, Py,
+Pz, and e, that's over complete.
+
+Right?
+
+That was unnecessary.
+
+So in classical
+mechanics, you can
+
+ask what data must you
+specify to completely specify
+
+the state of the system.
+
+And that's usually pretty easy.
+
+You specify the
+number coordinates
+
+and the number of momenta.
+
+In quantum mechanics, we ask
+a slightly different question.
+
+We ask, in order to specify
+the state of a system,
+
+we say we want to specify
+which state it is.
+
+You can specify
+that by saying which
+
+superposition in a
+particular basis.
+
+So you pick a basis,
+and you specify
+
+which particular
+superposition, what
+
+are the eigenvalues of
+the operators you've
+
+diagonalized in that basis?
+
+So another way to phrase
+this is for a 1D problem,
+
+say we have just a
+simple 1D problem.
+
+We have X and we have P. What
+is a complete set of commuting
+
+operators?
+
+Well, you have to
+have enough operators
+
+so that the eigenvalue
+specifies a state.
+
+So X would be-- is that enough?
+
+So if I take the operator
+X and I say look,
+
+my system is in the state
+with an eigenvalue X not of X,
+
+does that specify the
+state of the system?
+
+It tells you the particles
+are in a delta function state
+
+right here.
+
+Does that specify the state?
+
+AUDIENCE: Yes.
+
+PROFESSOR: Fantastic, it does.
+
+Now what if I tell
+you instead, oh it's
+
+in a state of definite P.
+Does that specify the state?
+
+Absolutely.
+
+Can I say it's in a state with
+definite X and definite P?
+
+AUDIENCE: No.
+
+PROFESSOR: No.
+
+These don't commute.
+
+So a complete set of commuting
+observables in this case
+
+would be either X
+or P, but not both.
+
+Yeah?
+
+Now if we're in three
+dimensions, is x a complete set
+
+of commuting observables?
+
+AUDIENCE: No.
+
+PROFESSOR: No, because
+it's not enough.
+
+You tell me that it's
+X, that doesn't tell me
+
+what state it is
+because it could
+
+have y dependence
+or z dependence.
+
+So in 3D, we take, for
+example, x, and y, and z.
+
+Or Px, and Py, and Pz.
+
+We could also pick
+z, and Px, and y.
+
+Are these complete?
+
+If I tell you I have
+definite position in z,
+
+definite position in y,
+and definite momentum in x?
+
+Does that completely
+specify my state?
+
+AUDIENCE: Yes.
+
+PROFESSOR: Yeah,
+totally unambiguously.
+
+e to the ikx delta of y delta
+of z totally fixes my function,
+
+completely specifies it.
+
+If I'd only picked
+two of these, it
+
+would not have been complete.
+
+It would have told
+me, for example,
+
+e to the ikx delta of y,
+but it doesn't tell me
+
+how it depends on z, how
+the wave functions on z.
+
+And if I added another
+operator, for example, Py,
+
+this is no longer commuting.
+
+These two operators
+don't commute.
+
+So a complete set of
+commuting observables
+
+can be thought of as
+the most operators
+
+you can write down that
+all commute with each other
+
+and the minimum number
+whose eigenvalues completely
+
+specify the state of the system.
+
+Cool?
+
+OK.
+
+So with all that said,
+what is a complete set
+
+of commuting observables for
+the angular momentum system?
+
+Well, it can't be any
+two of Lx, Ly, and Lz.
+
+So let's just pick one.
+
+I'll call it Lz.
+
+I could've called it Lx.
+
+It doesn't matter.
+
+It's up to you
+what axis is what.
+
+I'll just call it
+Lz conventionally.
+
+And then L squared
+also commutes,
+
+because L squared
+commutes with Lx.
+
+It commutes Ly and with Lz.
+
+So this actually
+forms a complete set
+
+of commuting observables for
+the angular momentum system.
+
+Complete set of
+commuting observables
+
+for angular momentum.
+
+So this idea will come
+up more in the future.
+
+And here is going to
+be the key [INAUDIBLE].
+
+So we'd like to use
+the following fact.
+
+We want to construct
+the eigenfunctions
+
+of our complete set
+of-- yeah, question?
+
+AUDIENCE: Really
+quick can you explain
+
+how you got that L
+squared and Lx commute?
+
+PROFESSOR: Yeah, I
+got it by knowing
+
+what you're going to write
+on your solution set.
+
+So this is on your problem set.
+
+So the way it goes-- so there
+are fancy ways of doing it,
+
+but the just direct
+way of doing,
+
+how do you construct
+these commutators?
+
+Is you know what
+the operators are.
+
+You know what L squared is.
+
+And you know that L
+squared is Lx squared
+
+plus Ly squared plus Lz squared.
+
+It's built in that
+fashion out of x and Py.
+
+And then I literally just put
+in the definitions of Lx, Ly,
+
+and Lz into that
+expression for L squared
+
+and compute the
+commutator with Lx, again,
+
+using the definition
+in terms of Py and z.
+
+And then you just chug
+through the commutators.
+
+Yeah, it just works out.
+
+So it's not obvious from
+the way I just phrased it
+
+that it works out like that.
+
+Later on you'll probably
+develop some intuition
+
+that it should be obvious.
+
+But for the moment,
+I'm just going
+
+to call it a brute
+force computation.
+
+And that's how you're going
+to do it on your problem set.
+
+So let me tell you
+where we're going next.
+
+So the question I
+really want to deal with
+
+is what are the eigenfunctions?
+
+So this is where
+we're leaving off.
+
+What are the eigenfunctions
+of our complete set
+
+of commuting variable
+L squared and Lz.
+
+What are these guys?
+
+And we know that
+we could solve them
+
+by solving the differential
+equations using
+
+those operators, but
+that would be horrible.
+
+We'd like to do something
+a little smarter.
+
+We'd like to use the commutation
+relations and the algebra.
+
+And here a really beautiful
+thing is going to happen.
+
+When you look at these
+commutation relations,
+
+one thing they're telling us
+is that we can't simultaneously
+
+have eigenfunctions
+of Lx and Ly.
+
+However, the way that Lx and Ly
+commute together is to form Lz.
+
+That gives us some information.
+
+That gives us some
+magic, some power.
+
+And in particular, much like
+that moment in the harmonic
+
+oscillator I said, well
+look, we could write down
+
+these operators as a.
+
+Well look, we can write
+down these operators,
+
+which I'm going to call
+L plus and L minus.
+
+L plus is going to be
+equal to Lx plus i Ly.
+
+And L minus is going to
+be equal to Lx minus I Ly.
+
+Now Lx, Ly, those
+are observables?
+
+What can you say about
+them as operators?
+
+What kind of operators are
+they since they're observables?
+
+Hermitian, exactly.
+
+So what's the Hermitian adjoint
+of Hermitian plus i Hermitian?
+
+Hermitian minus i Hermitian.
+
+OK, good.
+
+So L minus is the
+adjoint of L plus.
+
+So this is just going
+to be a definition.
+
+Let's take these to be the
+definitions of these guys.
+
+If we take their commutator,
+something totally lovely
+
+happens.
+
+I'm not going to write
+all the commutators.
+
+I'm just going to
+write a couple.
+
+The first is if I take L squared
+and I commute with L plus,
+
+well, L plus is Lx
+plus Ly, and we already
+
+know that L squared
+commutes with Lx
+
+and it commutes with Ly.
+
+So L squared
+commutes with L plus.
+
+And similarly for L minus,
+it commutes with each term.
+
+Question?
+
+Oh, I'm sorry.
+
+Lx.
+
+Shoot, that was an x.
+
+It just didn't look like it.
+
+Lx minus i Ly.
+
+So it commutes both
+L plus and L minus.
+
+But here's the
+real beauty of it.
+
+Lz with L plus is
+equal to-- well,
+
+let's just do
+dimensional analysis.
+
+L plus is Lx plus i Ly.
+
+We know that Lz with Lx
+is something like Ly.
+
+And Lz with Ly is
+something like Lx.
+
+With factors of i's an h bars.
+
+And when you work out the
+commutator, which should only
+
+take you second, you
+get i h bar L plus.
+
+And similarly, when we
+construct Lz and L minus,
+
+we get minus h bar L minus.
+
+Are L plus an L minus Hermitian?
+
+No, they're each
+other's adjoints.
+
+Lz is Hermitian.
+
+And look at this
+commutation relation.
+
+What does that tell you?
+
+From the first observation,
+if we have an energy
+
+or if we have an operator
+e and an operator a
+
+that commute in this
+fashion, then this
+
+tells you that the
+eigenfunctions of this operator
+
+are staggered in a the
+ladder spaced by h bar.
+
+The eigenvalues of Lz come
+in a ladder spaced by h bar.
+
+We can raise with
+L plus, and we can
+
+lower with L minus just like
+in the harmonic oscillator
+
+problem.
+
+And we'll exploit the
+rest of the-- we'll
+
+deduce the rest of the structure
+of the angular momentum
+
+operator eigenfunctions next
+time using this computation
+
+relation.
+
+See you next time.
\ No newline at end of file
diff --git a/Het_nd5x4hs.txt b/Het_nd5x4hs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5f7fc97023d8d4b0768f498548db04b09f7e1007
--- /dev/null
+++ b/Het_nd5x4hs.txt
@@ -0,0 +1,14344 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
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+and mit opencourseware in general is
+ 
+
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+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line engineers a line engineer is
+
+ align:start position:0%
+line engineers a line engineer is
+ 
+
+ align:start position:0%
+line engineers a line engineer is
+what you and i would call a practicing
+
+ align:start position:0%
+what you and i would call a practicing
+ 
+
+ align:start position:0%
+what you and i would call a practicing
+engineer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that term is used in distinction to
+
+ align:start position:0%
+that term is used in distinction to
+ 
+
+ align:start position:0%
+that term is used in distinction to
+management
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh who are people who were at one time
+
+ align:start position:0%
+uh who are people who were at one time
+ 
+
+ align:start position:0%
+uh who are people who were at one time
+line engineers
+
+ align:start position:0%
+line engineers
+ 
+
+ align:start position:0%
+line engineers
+for the most part
+
+ align:start position:0%
+for the most part
+ 
+
+ align:start position:0%
+for the most part
+when i say engineer management i'm
+
+ align:start position:0%
+when i say engineer management i'm
+ 
+
+ align:start position:0%
+when i say engineer management i'm
+saying engineering management
+
+ align:start position:0%
+saying engineering management
+ 
+
+ align:start position:0%
+saying engineering management
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+as you recall from the uh
+
+ align:start position:0%
+as you recall from the uh
+ 
+
+ align:start position:0%
+as you recall from the uh
+challenger case when this vice president
+
+ align:start position:0%
+challenger case when this vice president
+ 
+
+ align:start position:0%
+challenger case when this vice president
+took off his engineering hat and put on
+
+ align:start position:0%
+took off his engineering hat and put on
+ 
+
+ align:start position:0%
+took off his engineering hat and put on
+his management hat and changed the
+
+ align:start position:0%
+his management hat and changed the
+ 
+
+ align:start position:0%
+his management hat and changed the
+decision
+
+ align:start position:0%
+decision
+ 
+
+ align:start position:0%
+decision
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+different points of view
+
+ align:start position:0%
+different points of view
+ 
+
+ align:start position:0%
+different points of view
+and different professional
+
+ align:start position:0%
+and different professional
+ 
+
+ align:start position:0%
+and different professional
+responsibilities that engineers line
+
+ align:start position:0%
+responsibilities that engineers line
+ 
+
+ align:start position:0%
+responsibilities that engineers line
+engineers have as opposed to
+
+ align:start position:0%
+engineers have as opposed to
+ 
+
+ align:start position:0%
+engineers have as opposed to
+engineering managers
+
+ align:start position:0%
+engineering managers
+ 
+
+ align:start position:0%
+engineering managers
+and engineering managers have
+
+ align:start position:0%
+and engineering managers have
+ 
+
+ align:start position:0%
+and engineering managers have
+the greater authority
+
+ align:start position:0%
+the greater authority
+ 
+
+ align:start position:0%
+the greater authority
+uh but uh there is definitely a
+
+ align:start position:0%
+uh but uh there is definitely a
+ 
+
+ align:start position:0%
+uh but uh there is definitely a
+difference in
+
+ align:start position:0%
+difference in
+ 
+
+ align:start position:0%
+difference in
+uh job requirement and
+
+ align:start position:0%
+uh job requirement and
+ 
+
+ align:start position:0%
+uh job requirement and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and for this class
+
+ align:start position:0%
+and for this class
+ 
+
+ align:start position:0%
+and for this class
+contract and
+
+ align:start position:0%
+contract and
+ 
+
+ align:start position:0%
+contract and
+uh point of view
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the professional societies
+
+ align:start position:0%
+the professional societies
+ 
+
+ align:start position:0%
+the professional societies
+are largely
+
+ align:start position:0%
+are largely
+ 
+
+ align:start position:0%
+are largely
+line engineers
+
+ align:start position:0%
+line engineers
+ 
+
+ align:start position:0%
+line engineers
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+the leadership
+
+ align:start position:0%
+the leadership
+ 
+
+ align:start position:0%
+the leadership
+of these leaderships of these
+
+ align:start position:0%
+of these leaderships of these
+ 
+
+ align:start position:0%
+of these leaderships of these
+professional societies
+
+ align:start position:0%
+professional societies
+ 
+
+ align:start position:0%
+professional societies
+are largely managed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the nspe came along
+
+ align:start position:0%
+so the nspe came along
+ 
+
+ align:start position:0%
+so the nspe came along
+they were young engineers they were
+
+ align:start position:0%
+they were young engineers they were
+ 
+
+ align:start position:0%
+they were young engineers they were
+almost all line engineers
+
+ align:start position:0%
+almost all line engineers
+ 
+
+ align:start position:0%
+almost all line engineers
+they were idealistic
+
+ align:start position:0%
+they were idealistic
+ 
+
+ align:start position:0%
+they were idealistic
+and they wanted engineering to do all of
+
+ align:start position:0%
+and they wanted engineering to do all of
+ 
+
+ align:start position:0%
+and they wanted engineering to do all of
+the right things even if it meant some
+
+ align:start position:0%
+the right things even if it meant some
+ 
+
+ align:start position:0%
+the right things even if it meant some
+bad things for their client
+
+ align:start position:0%
+bad things for their client
+ 
+
+ align:start position:0%
+bad things for their client
+or employer
+
+ align:start position:0%
+or employer
+ 
+
+ align:start position:0%
+or employer
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and they
+
+ align:start position:0%
+and they
+ 
+
+ align:start position:0%
+and they
+set the mode with this code of ethics
+
+ align:start position:0%
+set the mode with this code of ethics
+ 
+
+ align:start position:0%
+set the mode with this code of ethics
+and in the 60s
+
+ align:start position:0%
+and in the 60s
+ 
+
+ align:start position:0%
+and in the 60s
+the late 60s uh when we had
+
+ align:start position:0%
+the late 60s uh when we had
+ 
+
+ align:start position:0%
+the late 60s uh when we had
+and then when we had all of the uh
+
+ align:start position:0%
+and then when we had all of the uh
+ 
+
+ align:start position:0%
+and then when we had all of the uh
+social movements that led to the
+
+ align:start position:0%
+social movements that led to the
+ 
+
+ align:start position:0%
+social movements that led to the
+creation of the sts and then engineering
+
+ align:start position:0%
+creation of the sts and then engineering
+ 
+
+ align:start position:0%
+creation of the sts and then engineering
+ethics
+
+ align:start position:0%
+ethics
+ 
+
+ align:start position:0%
+ethics
+that movement was sympathetic to the
+
+ align:start position:0%
+that movement was sympathetic to the
+ 
+
+ align:start position:0%
+that movement was sympathetic to the
+nspe
+
+ align:start position:0%
+nspe
+ 
+
+ align:start position:0%
+nspe
+code not to the asc and the others
+
+ align:start position:0%
+code not to the asc and the others
+ 
+
+ align:start position:0%
+code not to the asc and the others
+so eventually they all came as close to
+
+ align:start position:0%
+so eventually they all came as close to
+ 
+
+ align:start position:0%
+so eventually they all came as close to
+nspe as they could get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you find this difference between
+
+ align:start position:0%
+so you find this difference between
+ 
+
+ align:start position:0%
+so you find this difference between
+management and line engineer
+
+ align:start position:0%
+management and line engineer
+ 
+
+ align:start position:0%
+management and line engineer
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the university
+
+ align:start position:0%
+in the university
+ 
+
+ align:start position:0%
+in the university
+you can if you observe
+
+ align:start position:0%
+you can if you observe
+ 
+
+ align:start position:0%
+you can if you observe
+uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+faculty and administration
+
+ align:start position:0%
+faculty and administration
+ 
+
+ align:start position:0%
+faculty and administration
+uh then the likenesses and the
+
+ align:start position:0%
+uh then the likenesses and the
+ 
+
+ align:start position:0%
+uh then the likenesses and the
+differences are going to be very much
+
+ align:start position:0%
+differences are going to be very much
+ 
+
+ align:start position:0%
+differences are going to be very much
+the same between line engineers
+
+ align:start position:0%
+the same between line engineers
+ 
+
+ align:start position:0%
+the same between line engineers
+and managers
+
+ align:start position:0%
+and managers
+ 
+
+ align:start position:0%
+and managers
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there's this book
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there was some books that were very uh
+
+ align:start position:0%
+there was some books that were very uh
+ 
+
+ align:start position:0%
+there was some books that were very uh
+scathing on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the academy
+
+ align:start position:0%
+the academy
+ 
+
+ align:start position:0%
+the academy
+that came out in the 60s
+
+ align:start position:0%
+that came out in the 60s
+ 
+
+ align:start position:0%
+that came out in the 60s
+one was called the professor scam
+
+ align:start position:0%
+one was called the professor scam
+ 
+
+ align:start position:0%
+one was called the professor scam
+and there were a bunch of others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of them had on the cover
+
+ align:start position:0%
+and one of them had on the cover
+ 
+
+ align:start position:0%
+and one of them had on the cover
+uh that um
+
+ align:start position:0%
+uh that um
+ 
+
+ align:start position:0%
+uh that um
+what are we talking about here
+
+ align:start position:0%
+what are we talking about here
+ 
+
+ align:start position:0%
+what are we talking about here
+when we
+
+ align:start position:0%
+when we
+ 
+
+ align:start position:0%
+when we
+when we say uh
+
+ align:start position:0%
+when we say uh
+ 
+
+ align:start position:0%
+when we say uh
+administration versus faculty
+
+ align:start position:0%
+administration versus faculty
+ 
+
+ align:start position:0%
+administration versus faculty
+this is written for the general public
+
+ align:start position:0%
+this is written for the general public
+ 
+
+ align:start position:0%
+this is written for the general public
+they're all the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what this is what this person was
+
+ align:start position:0%
+that's what this is what this person was
+ 
+
+ align:start position:0%
+that's what this is what this person was
+trying to create in the eyes of the
+
+ align:start position:0%
+trying to create in the eyes of the
+ 
+
+ align:start position:0%
+trying to create in the eyes of the
+general public and had good reasons
+
+ align:start position:0%
+general public and had good reasons
+ 
+
+ align:start position:0%
+general public and had good reasons
+he said they're all the same he said so
+
+ align:start position:0%
+he said they're all the same he said so
+ 
+
+ align:start position:0%
+he said they're all the same he said so
+far as we're concerned they all got phd
+
+ align:start position:0%
+far as we're concerned they all got phd
+ 
+
+ align:start position:0%
+far as we're concerned they all got phd
+they were all faculty members at least
+
+ align:start position:0%
+they were all faculty members at least
+ 
+
+ align:start position:0%
+they were all faculty members at least
+at one time
+
+ align:start position:0%
+at one time
+ 
+
+ align:start position:0%
+at one time
+you know when you talk about a college
+
+ align:start position:0%
+you know when you talk about a college
+ 
+
+ align:start position:0%
+you know when you talk about a college
+president can't get a presidency without
+
+ align:start position:0%
+president can't get a presidency without
+ 
+
+ align:start position:0%
+president can't get a presidency without
+having a full professorship
+
+ align:start position:0%
+having a full professorship
+ 
+
+ align:start position:0%
+having a full professorship
+in one of the academic departments at
+
+ align:start position:0%
+in one of the academic departments at
+ 
+
+ align:start position:0%
+in one of the academic departments at
+most places at all places that i know of
+
+ align:start position:0%
+most places at all places that i know of
+ 
+
+ align:start position:0%
+most places at all places that i know of
+right so from the outside what are you
+
+ align:start position:0%
+right so from the outside what are you
+ 
+
+ align:start position:0%
+right so from the outside what are you
+doing we're splitting hands
+
+ align:start position:0%
+doing we're splitting hands
+ 
+
+ align:start position:0%
+doing we're splitting hands
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so someone can say the same thing
+
+ align:start position:0%
+and so someone can say the same thing
+ 
+
+ align:start position:0%
+and so someone can say the same thing
+about engineering the profession that
+
+ align:start position:0%
+about engineering the profession that
+ 
+
+ align:start position:0%
+about engineering the profession that
+we're splitting hairs when you talk
+
+ align:start position:0%
+we're splitting hairs when you talk
+ 
+
+ align:start position:0%
+we're splitting hairs when you talk
+about engineering management versus
+
+ align:start position:0%
+about engineering management versus
+ 
+
+ align:start position:0%
+about engineering management versus
+engineers and there is a great area in
+
+ align:start position:0%
+engineers and there is a great area in
+ 
+
+ align:start position:0%
+engineers and there is a great area in
+the university where it's hard for
+
+ align:start position:0%
+the university where it's hard for
+ 
+
+ align:start position:0%
+the university where it's hard for
+everybody to decide
+
+ align:start position:0%
+everybody to decide
+ 
+
+ align:start position:0%
+everybody to decide
+whether
+
+ align:start position:0%
+whether
+ 
+
+ align:start position:0%
+whether
+whether this
+
+ align:start position:0%
+whether this
+ 
+
+ align:start position:0%
+whether this
+whether it whether department chairs
+
+ align:start position:0%
+whether it whether department chairs
+ 
+
+ align:start position:0%
+whether it whether department chairs
+or managers or faculty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+varies from institutional institution
+
+ align:start position:0%
+varies from institutional institution
+ 
+
+ align:start position:0%
+varies from institutional institution
+from time to time
+
+ align:start position:0%
+from time to time
+ 
+
+ align:start position:0%
+from time to time
+uh but even and from department to
+
+ align:start position:0%
+uh but even and from department to
+ 
+
+ align:start position:0%
+uh but even and from department to
+department
+
+ align:start position:0%
+department
+ 
+
+ align:start position:0%
+department
+but even there's this real gray area
+
+ align:start position:0%
+but even there's this real gray area
+ 
+
+ align:start position:0%
+but even there's this real gray area
+that's hard to deal with
+
+ align:start position:0%
+that's hard to deal with
+ 
+
+ align:start position:0%
+that's hard to deal with
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+at many institutions a department chair
+
+ align:start position:0%
+at many institutions a department chair
+ 
+
+ align:start position:0%
+at many institutions a department chair
+has to be reviewed by
+
+ align:start position:0%
+has to be reviewed by
+ 
+
+ align:start position:0%
+has to be reviewed by
+her faculty
+
+ align:start position:0%
+her faculty
+ 
+
+ align:start position:0%
+her faculty
+every so often if the review is bad
+
+ align:start position:0%
+every so often if the review is bad
+ 
+
+ align:start position:0%
+every so often if the review is bad
+you're out
+
+ align:start position:0%
+you're out
+ 
+
+ align:start position:0%
+you're out
+the department chair has to be reviewed
+
+ align:start position:0%
+the department chair has to be reviewed
+ 
+
+ align:start position:0%
+the department chair has to be reviewed
+by the dean
+
+ align:start position:0%
+by the dean
+ 
+
+ align:start position:0%
+by the dean
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+day the department chairs in the sort of
+
+ align:start position:0%
+day the department chairs in the sort of
+ 
+
+ align:start position:0%
+day the department chairs in the sort of
+in between case and i'm certain that and
+
+ align:start position:0%
+in between case and i'm certain that and
+ 
+
+ align:start position:0%
+in between case and i'm certain that and
+then all the places that i have worked
+
+ align:start position:0%
+then all the places that i have worked
+ 
+
+ align:start position:0%
+then all the places that i have worked
+not many but we're talking about nasa
+
+ align:start position:0%
+not many but we're talking about nasa
+ 
+
+ align:start position:0%
+not many but we're talking about nasa
+nuclear regulatory commission
+
+ align:start position:0%
+nuclear regulatory commission
+ 
+
+ align:start position:0%
+nuclear regulatory commission
+uh and the u.s army corps of engineers
+
+ align:start position:0%
+uh and the u.s army corps of engineers
+ 
+
+ align:start position:0%
+uh and the u.s army corps of engineers
+uh there is a
+
+ align:start position:0%
+uh there is a
+ 
+
+ align:start position:0%
+uh there is a
+position of responsibility that i liken
+
+ align:start position:0%
+position of responsibility that i liken
+ 
+
+ align:start position:0%
+position of responsibility that i liken
+to depart to department chairs kind of
+
+ align:start position:0%
+to depart to department chairs kind of
+ 
+
+ align:start position:0%
+to depart to department chairs kind of
+hard to decide
+
+ align:start position:0%
+hard to decide
+ 
+
+ align:start position:0%
+hard to decide
+where they fit
+
+ align:start position:0%
+where they fit
+ 
+
+ align:start position:0%
+where they fit
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh so uh the
+
+ align:start position:0%
+uh so uh the
+ 
+
+ align:start position:0%
+uh so uh the
+the other important thing is to remember
+
+ align:start position:0%
+the other important thing is to remember
+ 
+
+ align:start position:0%
+the other important thing is to remember
+that i did say and that is that the
+
+ align:start position:0%
+that i did say and that is that the
+ 
+
+ align:start position:0%
+that i did say and that is that the
+sentiments of the late 60s that brought
+
+ align:start position:0%
+sentiments of the late 60s that brought
+ 
+
+ align:start position:0%
+sentiments of the late 60s that brought
+sts and thus engineering ethics into
+
+ align:start position:0%
+sts and thus engineering ethics into
+ 
+
+ align:start position:0%
+sts and thus engineering ethics into
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+were on the side of nspe and the line
+
+ align:start position:0%
+were on the side of nspe and the line
+ 
+
+ align:start position:0%
+were on the side of nspe and the line
+engineers
+
+ align:start position:0%
+engineers
+ 
+
+ align:start position:0%
+engineers
+because that's where you get mainly the
+
+ align:start position:0%
+because that's where you get mainly the
+ 
+
+ align:start position:0%
+because that's where you get mainly the
+whistleblowers from and all of that
+
+ align:start position:0%
+whistleblowers from and all of that
+ 
+
+ align:start position:0%
+whistleblowers from and all of that
+okay things can change
+
+ align:start position:0%
+okay things can change
+ 
+
+ align:start position:0%
+okay things can change
+things had changed but that's where we
+
+ align:start position:0%
+things had changed but that's where we
+ 
+
+ align:start position:0%
+things had changed but that's where we
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+and the importance of nspe is that
+
+ align:start position:0%
+and the importance of nspe is that
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+
+ align:start position:0%
+and the importance of nspe is that
+most of the codes i think it's fair to
+
+ align:start position:0%
+most of the codes i think it's fair to
+ 
+
+ align:start position:0%
+most of the codes i think it's fair to
+say the line share of the codes
+
+ align:start position:0%
+say the line share of the codes
+ 
+
+ align:start position:0%
+say the line share of the codes
+that are out
+
+ align:start position:0%
+that are out
+ 
+
+ align:start position:0%
+that are out
+that are enforced today
+
+ align:start position:0%
+that are enforced today
+ 
+
+ align:start position:0%
+that are enforced today
+use the nsp code as a starting point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of the things you said
+
+ align:start position:0%
+and one of the things you said
+ 
+
+ align:start position:0%
+and one of the things you said
+in terms of your goals for the quality
+
+ align:start position:0%
+in terms of your goals for the quality
+ 
+
+ align:start position:0%
+in terms of your goals for the quality
+for the aaes is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+that's right and
+
+ align:start position:0%
+that's right and
+ 
+
+ align:start position:0%
+that's right and
+uh i don't know what word is best to
+
+ align:start position:0%
+uh i don't know what word is best to
+ 
+
+ align:start position:0%
+uh i don't know what word is best to
+describe
+
+ align:start position:0%
+describe
+ 
+
+ align:start position:0%
+describe
+the relationship between the two
+
+ align:start position:0%
+the relationship between the two
+ 
+
+ align:start position:0%
+the relationship between the two
+uh various from time to time place to
+
+ align:start position:0%
+uh various from time to time place to
+ 
+
+ align:start position:0%
+uh various from time to time place to
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+but you need to be aware that there is a
+
+ align:start position:0%
+but you need to be aware that there is a
+ 
+
+ align:start position:0%
+but you need to be aware that there is a
+line and if you want to be
+
+ align:start position:0%
+line and if you want to be
+ 
+
+ align:start position:0%
+line and if you want to be
+vice president for engineering you're
+
+ align:start position:0%
+vice president for engineering you're
+ 
+
+ align:start position:0%
+vice president for engineering you're
+going to have to go up through the
+
+ align:start position:0%
+going to have to go up through the
+ 
+
+ align:start position:0%
+going to have to go up through the
+management line and you're going to have
+
+ align:start position:0%
+management line and you're going to have
+ 
+
+ align:start position:0%
+management line and you're going to have
+to deal with these people
+
+ align:start position:0%
+to deal with these people
+ 
+
+ align:start position:0%
+to deal with these people
+people who that you were a part of
+
+ align:start position:0%
+people who that you were a part of
+ 
+
+ align:start position:0%
+people who that you were a part of
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they're going to have to deal with
+
+ align:start position:0%
+and they're going to have to deal with
+ 
+
+ align:start position:0%
+and they're going to have to deal with
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+oh there's another subtlety and that is
+
+ align:start position:0%
+oh there's another subtlety and that is
+ 
+
+ align:start position:0%
+oh there's another subtlety and that is
+that once you decide to go the
+
+ align:start position:0%
+that once you decide to go the
+ 
+
+ align:start position:0%
+that once you decide to go the
+management route
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's very difficult to come back
+
+ align:start position:0%
+it's very difficult to come back
+ 
+
+ align:start position:0%
+it's very difficult to come back
+because you lose those skills
+
+ align:start position:0%
+because you lose those skills
+ 
+
+ align:start position:0%
+because you lose those skills
+it's easy
+
+ align:start position:0%
+it's easy
+ 
+
+ align:start position:0%
+it's easy
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+a person who is not a professional is
+
+ align:start position:0%
+a person who is not a professional is
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+
+ align:start position:0%
+a person who is not a professional is
+going to find what i'm about to say
+
+ align:start position:0%
+going to find what i'm about to say
+ 
+
+ align:start position:0%
+going to find what i'm about to say
+impossible to believe
+
+ align:start position:0%
+impossible to believe
+ 
+
+ align:start position:0%
+impossible to believe
+you do not have
+
+ align:start position:0%
+you do not have
+ 
+
+ align:start position:0%
+you do not have
+to know more or even as much as the
+
+ align:start position:0%
+to know more or even as much as the
+ 
+
+ align:start position:0%
+to know more or even as much as the
+people know that you manage in order to
+
+ align:start position:0%
+people know that you manage in order to
+ 
+
+ align:start position:0%
+people know that you manage in order to
+manage them well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a good place to learn it
+
+ align:start position:0%
+a good place to learn it
+ 
+
+ align:start position:0%
+a good place to learn it
+is in the army second lieutenant
+
+ align:start position:0%
+is in the army second lieutenant
+ 
+
+ align:start position:0%
+is in the army second lieutenant
+22 years old sergeant 40 years old
+
+ align:start position:0%
+22 years old sergeant 40 years old
+ 
+
+ align:start position:0%
+22 years old sergeant 40 years old
+second two lieutenant doesn't know
+
+ align:start position:0%
+second two lieutenant doesn't know
+ 
+
+ align:start position:0%
+second two lieutenant doesn't know
+one-tenth of what the sergeant knows
+
+ align:start position:0%
+one-tenth of what the sergeant knows
+ 
+
+ align:start position:0%
+one-tenth of what the sergeant knows
+but the lieutenant is not supposed to
+
+ align:start position:0%
+but the lieutenant is not supposed to
+ 
+
+ align:start position:0%
+but the lieutenant is not supposed to
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+the lieutenant is supposed to know when
+
+ align:start position:0%
+the lieutenant is supposed to know when
+ 
+
+ align:start position:0%
+the lieutenant is supposed to know when
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+
+ align:start position:0%
+the job is done right and when it's
+ 
+
+ align:start position:0%
+the job is done right and when it's
+wrong and when the pastor ordered down
+
+ align:start position:0%
+wrong and when the pastor ordered down
+ 
+
+ align:start position:0%
+wrong and when the pastor ordered down
+from the higher interface
+
+ align:start position:0%
+from the higher interface
+ 
+
+ align:start position:0%
+from the higher interface
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+
+ align:start position:0%
+that unit with the higher unit
+ 
+
+ align:start position:0%
+that unit with the higher unit
+but the sergeant's supposed to know all
+
+ align:start position:0%
+but the sergeant's supposed to know all
+ 
+
+ align:start position:0%
+but the sergeant's supposed to know all
+this other stuff
+
+ align:start position:0%
+this other stuff
+ 
+
+ align:start position:0%
+this other stuff
+and the lieutenant tells the sergeant
+
+ align:start position:0%
+and the lieutenant tells the sergeant
+ 
+
+ align:start position:0%
+and the lieutenant tells the sergeant
+what to do and the sergeant get the men
+
+ align:start position:0%
+what to do and the sergeant get the men
+ 
+
+ align:start position:0%
+what to do and the sergeant get the men
+order
+
+ align:start position:0%
+order
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+
+ align:start position:0%
+order
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+
+ align:start position:0%
+tell them what to do and do all of that
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+
+ align:start position:0%
+tell them what to do and do all of that
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+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so you have to learn and appreciate that
+
+ align:start position:0%
+so you have to learn and appreciate that
+ 
+
+ align:start position:0%
+so you have to learn and appreciate that
+that's engineering is set up the same
+
+ align:start position:0%
+that's engineering is set up the same
+ 
+
+ align:start position:0%
+that's engineering is set up the same
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+that when that you don't know as much
+
+ align:start position:0%
+that when that you don't know as much
+ 
+
+ align:start position:0%
+that when that you don't know as much
+about putting steel in concrete as the
+
+ align:start position:0%
+about putting steel in concrete as the
+ 
+
+ align:start position:0%
+about putting steel in concrete as the
+steel workers do
+
+ align:start position:0%
+steel workers do
+ 
+
+ align:start position:0%
+steel workers do
+the manager
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even if you did know
+
+ align:start position:0%
+even if you did know
+ 
+
+ align:start position:0%
+even if you did know
+right even if you did know
+
+ align:start position:0%
+right even if you did know
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+
+ align:start position:0%
+right even if you did know
+even if you were a steel worker and now
+
+ align:start position:0%
+even if you were a steel worker and now
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+
+ align:start position:0%
+even if you were a steel worker and now
+a manager
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+ align:start position:0%
+a manager
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+
+ align:start position:0%
+a manager
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+
+ align:start position:0%
+a couple years down the line you're
+ 
+
+ align:start position:0%
+a couple years down the line you're
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+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
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+
+ align:start position:0%
+not be you're going to lose your
+ 
+
+ align:start position:0%
+not be you're going to lose your
+competency
+
+ align:start position:0%
+competency
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+
+ align:start position:0%
+competency
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+ align:start position:0%
+things are going to change
+ 
+
+ align:start position:0%
+things are going to change
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+ align:start position:0%
+especially
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+
+ align:start position:0%
+especially
+so that's another thing you have to do
+
+ align:start position:0%
+so that's another thing you have to do
+ 
+
+ align:start position:0%
+so that's another thing you have to do
+so uh let's see let's see if we can't uh
+
+ align:start position:0%
+so uh let's see let's see if we can't uh
+ 
+
+ align:start position:0%
+so uh let's see let's see if we can't uh
+interrogate this code how is it
+
+ align:start position:0%
+interrogate this code how is it
+ 
+
+ align:start position:0%
+interrogate this code how is it
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+
+ align:start position:0%
+organized does it have a preamble does
+ 
+
+ align:start position:0%
+organized does it have a preamble does
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+have sections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are divided
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's read the parable
+
+ align:start position:0%
+let's read the parable
+ 
+
+ align:start position:0%
+let's read the parable
+and then let's go through the the
+
+ align:start position:0%
+and then let's go through the the
+ 
+
+ align:start position:0%
+and then let's go through the the
+cannons they are uh how many six or
+
+ align:start position:0%
+cannons they are uh how many six or
+ 
+
+ align:start position:0%
+cannons they are uh how many six or
+seven of
+
+ align:start position:0%
+seven of
+ 
+
+ align:start position:0%
+seven of
+six uh let's go through the cannons and
+
+ align:start position:0%
+six uh let's go through the cannons and
+ 
+
+ align:start position:0%
+six uh let's go through the cannons and
+then let's pick out
+
+ align:start position:0%
+then let's pick out
+ 
+
+ align:start position:0%
+then let's pick out
+any of the other parts that we want to
+
+ align:start position:0%
+any of the other parts that we want to
+ 
+
+ align:start position:0%
+any of the other parts that we want to
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+so somebody read the korean
+
+ align:start position:0%
+so somebody read the korean
+ 
+
+ align:start position:0%
+so somebody read the korean
+please engineering is an important and
+
+ align:start position:0%
+please engineering is an important and
+ 
+
+ align:start position:0%
+please engineering is an important and
+learning profession
+
+ align:start position:0%
+learning profession
+ 
+
+ align:start position:0%
+learning profession
+as members of this profession engineers
+
+ align:start position:0%
+as members of this profession engineers
+ 
+
+ align:start position:0%
+as members of this profession engineers
+are expected to exhibit the highest
+
+ align:start position:0%
+are expected to exhibit the highest
+ 
+
+ align:start position:0%
+are expected to exhibit the highest
+standards of honesty and integrity
+
+ align:start position:0%
+standards of honesty and integrity
+ 
+
+ align:start position:0%
+standards of honesty and integrity
+engineering has a direct and vital
+
+ align:start position:0%
+engineering has a direct and vital
+ 
+
+ align:start position:0%
+engineering has a direct and vital
+impact
+
+ align:start position:0%
+impact
+ 
+
+ align:start position:0%
+impact
+accordingly the services provided by
+
+ align:start position:0%
+accordingly the services provided by
+ 
+
+ align:start position:0%
+accordingly the services provided by
+engineers require honesty impartiality
+
+ align:start position:0%
+engineers require honesty impartiality
+ 
+
+ align:start position:0%
+engineers require honesty impartiality
+fairness and equity and must be
+
+ align:start position:0%
+fairness and equity and must be
+ 
+
+ align:start position:0%
+fairness and equity and must be
+dedicated to the protection of the
+
+ align:start position:0%
+dedicated to the protection of the
+ 
+
+ align:start position:0%
+dedicated to the protection of the
+public health safety and welfare
+
+ align:start position:0%
+public health safety and welfare
+ 
+
+ align:start position:0%
+public health safety and welfare
+engineers must perform under a standard
+
+ align:start position:0%
+engineers must perform under a standard
+ 
+
+ align:start position:0%
+engineers must perform under a standard
+of professional behavior that requires
+
+ align:start position:0%
+of professional behavior that requires
+ 
+
+ align:start position:0%
+of professional behavior that requires
+adherence to the highest principles of
+
+ align:start position:0%
+adherence to the highest principles of
+ 
+
+ align:start position:0%
+adherence to the highest principles of
+ethical conduct
+
+ align:start position:0%
+ethical conduct
+ 
+
+ align:start position:0%
+ethical conduct
+okay so there's a statement of what the
+
+ align:start position:0%
+okay so there's a statement of what the
+ 
+
+ align:start position:0%
+okay so there's a statement of what the
+profession is
+
+ align:start position:0%
+profession is
+ 
+
+ align:start position:0%
+profession is
+subject to debate but that's the
+
+ align:start position:0%
+subject to debate but that's the
+ 
+
+ align:start position:0%
+subject to debate but that's the
+statement that is uh authorized by this
+
+ align:start position:0%
+statement that is uh authorized by this
+ 
+
+ align:start position:0%
+statement that is uh authorized by this
+organization
+
+ align:start position:0%
+organization
+ 
+
+ align:start position:0%
+organization
+all right uh do we have any problems
+
+ align:start position:0%
+all right uh do we have any problems
+ 
+
+ align:start position:0%
+all right uh do we have any problems
+with that statement yeah we got a
+
+ align:start position:0%
+with that statement yeah we got a
+ 
+
+ align:start position:0%
+with that statement yeah we got a
+problem with the statement uh do we
+
+ align:start position:0%
+problem with the statement uh do we
+ 
+
+ align:start position:0%
+problem with the statement uh do we
+think that that
+
+ align:start position:0%
+think that that
+ 
+
+ align:start position:0%
+think that that
+when i say we have problems you come in
+
+ align:start position:0%
+when i say we have problems you come in
+ 
+
+ align:start position:0%
+when i say we have problems you come in
+any way you want but i really want to
+
+ align:start position:0%
+any way you want but i really want to
+ 
+
+ align:start position:0%
+any way you want but i really want to
+know if you think there's anything about
+
+ align:start position:0%
+know if you think there's anything about
+ 
+
+ align:start position:0%
+know if you think there's anything about
+that statement that should not be in a
+
+ align:start position:0%
+that statement that should not be in a
+ 
+
+ align:start position:0%
+that statement that should not be in a
+professional organization's preamble up
+
+ align:start position:0%
+professional organization's preamble up
+ 
+
+ align:start position:0%
+professional organization's preamble up
+to its code of ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have they deceived anybody about the
+
+ align:start position:0%
+have they deceived anybody about the
+ 
+
+ align:start position:0%
+have they deceived anybody about the
+greatness of engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i either believe or are given the
+
+ align:start position:0%
+i either believe or are given the
+ 
+
+ align:start position:0%
+i either believe or are given the
+opportunity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that doesn't answer your questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay i'm sorry
+
+ align:start position:0%
+oh okay i'm sorry
+ 
+
+ align:start position:0%
+oh okay i'm sorry
+is it rubbing up against this pen i
+
+ align:start position:0%
+is it rubbing up against this pen i
+ 
+
+ align:start position:0%
+is it rubbing up against this pen i
+think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+okay thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah if there's anything wrong with it
+
+ align:start position:0%
+yeah if there's anything wrong with it
+ 
+
+ align:start position:0%
+yeah if there's anything wrong with it
+it might be too idealistic and that it's
+
+ align:start position:0%
+it might be too idealistic and that it's
+ 
+
+ align:start position:0%
+it might be too idealistic and that it's
+all right to shoot after
+
+ align:start position:0%
+all right to shoot after
+ 
+
+ align:start position:0%
+all right to shoot after
+as a goal
+
+ align:start position:0%
+as a goal
+ 
+
+ align:start position:0%
+as a goal
+yeah that's good i think that's a good
+
+ align:start position:0%
+yeah that's good i think that's a good
+ 
+
+ align:start position:0%
+yeah that's good i think that's a good
+way to think about it
+
+ align:start position:0%
+way to think about it
+ 
+
+ align:start position:0%
+way to think about it
+uh as to whether or not all the
+
+ align:start position:0%
+uh as to whether or not all the
+ 
+
+ align:start position:0%
+uh as to whether or not all the
+engineers buy into it
+
+ align:start position:0%
+engineers buy into it
+ 
+
+ align:start position:0%
+engineers buy into it
+well the question is what is their um
+
+ align:start position:0%
+well the question is what is their um
+ 
+
+ align:start position:0%
+well the question is what is their um
+decision-making method i don't think
+
+ align:start position:0%
+decision-making method i don't think
+ 
+
+ align:start position:0%
+decision-making method i don't think
+that they use
+
+ align:start position:0%
+that they use
+ 
+
+ align:start position:0%
+that they use
+a plebiscite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh where you go out and and take the
+
+ align:start position:0%
+uh where you go out and and take the
+ 
+
+ align:start position:0%
+uh where you go out and and take the
+majority of everybody
+
+ align:start position:0%
+majority of everybody
+ 
+
+ align:start position:0%
+majority of everybody
+no they get a committee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Laughter]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+well there's another thing to a way to
+
+ align:start position:0%
+well there's another thing to a way to
+ 
+
+ align:start position:0%
+well there's another thing to a way to
+think about it uh they've got it
+
+ align:start position:0%
+think about it uh they've got it
+ 
+
+ align:start position:0%
+think about it uh they've got it
+published
+
+ align:start position:0%
+published
+ 
+
+ align:start position:0%
+published
+and if you don't like it you don't have
+
+ align:start position:0%
+and if you don't like it you don't have
+ 
+
+ align:start position:0%
+and if you don't like it you don't have
+to join nspe that's another way to think
+
+ align:start position:0%
+to join nspe that's another way to think
+ 
+
+ align:start position:0%
+to join nspe that's another way to think
+about it doesn't mean that you agree
+
+ align:start position:0%
+about it doesn't mean that you agree
+ 
+
+ align:start position:0%
+about it doesn't mean that you agree
+with it but if you still want to join
+
+ align:start position:0%
+with it but if you still want to join
+ 
+
+ align:start position:0%
+with it but if you still want to join
+nspe you have to take responsibility
+
+ align:start position:0%
+nspe you have to take responsibility
+ 
+
+ align:start position:0%
+nspe you have to take responsibility
+for that statement some way or another
+
+ align:start position:0%
+for that statement some way or another
+ 
+
+ align:start position:0%
+for that statement some way or another
+you did it with your eyes open it's
+
+ align:start position:0%
+you did it with your eyes open it's
+ 
+
+ align:start position:0%
+you did it with your eyes open it's
+published
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+none of us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+the price you pay for that or not the
+
+ align:start position:0%
+the price you pay for that or not the
+ 
+
+ align:start position:0%
+the price you pay for that or not the
+price but a price that you pay for that
+
+ align:start position:0%
+price but a price that you pay for that
+ 
+
+ align:start position:0%
+price but a price that you pay for that
+is if you go to court the judge is going
+
+ align:start position:0%
+is if you go to court the judge is going
+ 
+
+ align:start position:0%
+is if you go to court the judge is going
+to take that position
+
+ align:start position:0%
+to take that position
+ 
+
+ align:start position:0%
+to take that position
+literally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the judge is going to say here it is
+
+ align:start position:0%
+the judge is going to say here it is
+ 
+
+ align:start position:0%
+the judge is going to say here it is
+it's published i got a copy of it
+
+ align:start position:0%
+it's published i got a copy of it
+ 
+
+ align:start position:0%
+it's published i got a copy of it
+everybody's got a copy of it
+
+ align:start position:0%
+everybody's got a copy of it
+ 
+
+ align:start position:0%
+everybody's got a copy of it
+over here i see where your application
+
+ align:start position:0%
+over here i see where your application
+ 
+
+ align:start position:0%
+over here i see where your application
+you asked to be a member nobody came
+
+ align:start position:0%
+you asked to be a member nobody came
+ 
+
+ align:start position:0%
+you asked to be a member nobody came
+down and said you've got to be one or
+
+ align:start position:0%
+down and said you've got to be one or
+ 
+
+ align:start position:0%
+down and said you've got to be one or
+else we'll fire you nobody said that
+
+ align:start position:0%
+else we'll fire you nobody said that
+ 
+
+ align:start position:0%
+else we'll fire you nobody said that
+you're paid your dues every year for the
+
+ align:start position:0%
+you're paid your dues every year for the
+ 
+
+ align:start position:0%
+you're paid your dues every year for the
+last 10 years you had time to change
+
+ align:start position:0%
+last 10 years you had time to change
+ 
+
+ align:start position:0%
+last 10 years you had time to change
+your mind
+
+ align:start position:0%
+your mind
+ 
+
+ align:start position:0%
+your mind
+after you got experience but no you kept
+
+ align:start position:0%
+after you got experience but no you kept
+ 
+
+ align:start position:0%
+after you got experience but no you kept
+your mouth shut you got to pay the price
+
+ align:start position:0%
+your mouth shut you got to pay the price
+ 
+
+ align:start position:0%
+your mouth shut you got to pay the price
+you gotta have to live up to that
+
+ align:start position:0%
+you gotta have to live up to that
+ 
+
+ align:start position:0%
+you gotta have to live up to that
+so that's another way
+
+ align:start position:0%
+so that's another way
+ 
+
+ align:start position:0%
+so that's another way
+to think about this whole thing so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah they decide to subscribe to it
+
+ align:start position:0%
+yeah they decide to subscribe to it
+ 
+
+ align:start position:0%
+yeah they decide to subscribe to it
+and so therefore if they come before
+
+ align:start position:0%
+and so therefore if they come before
+ 
+
+ align:start position:0%
+and so therefore if they come before
+let's say
+
+ align:start position:0%
+let's say
+ 
+
+ align:start position:0%
+let's say
+a community group or high school
+
+ align:start position:0%
+a community group or high school
+ 
+
+ align:start position:0%
+a community group or high school
+uh pta
+
+ align:start position:0%
+uh pta
+ 
+
+ align:start position:0%
+uh pta
+and they say well what is what do you
+
+ align:start position:0%
+and they say well what is what do you
+ 
+
+ align:start position:0%
+and they say well what is what do you
+stand for what is engineering and you
+
+ align:start position:0%
+stand for what is engineering and you
+ 
+
+ align:start position:0%
+stand for what is engineering and you
+look like a liar if you don't say
+
+ align:start position:0%
+look like a liar if you don't say
+ 
+
+ align:start position:0%
+look like a liar if you don't say
+something like this
+
+ align:start position:0%
+something like this
+ 
+
+ align:start position:0%
+something like this
+so because you belong you ask to be lost
+
+ align:start position:0%
+so because you belong you ask to be lost
+ 
+
+ align:start position:0%
+so because you belong you ask to be lost
+free country you don't have to belong
+
+ align:start position:0%
+free country you don't have to belong
+ 
+
+ align:start position:0%
+free country you don't have to belong
+all right so there is the goal
+
+ align:start position:0%
+all right so there is the goal
+ 
+
+ align:start position:0%
+all right so there is the goal
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+now the fundamental cannons
+
+ align:start position:0%
+now the fundamental cannons
+ 
+
+ align:start position:0%
+now the fundamental cannons
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+are more or less
+
+ align:start position:0%
+are more or less
+ 
+
+ align:start position:0%
+are more or less
+that's the that's the this the the
+
+ align:start position:0%
+that's the that's the this the the
+ 
+
+ align:start position:0%
+that's the that's the this the the
+preamble is sort of the end
+
+ align:start position:0%
+preamble is sort of the end
+ 
+
+ align:start position:0%
+preamble is sort of the end
+and the fundamental cannons are the
+
+ align:start position:0%
+and the fundamental cannons are the
+ 
+
+ align:start position:0%
+and the fundamental cannons are the
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+uh laid out in general terms
+
+ align:start position:0%
+uh laid out in general terms
+ 
+
+ align:start position:0%
+uh laid out in general terms
+and we get specifics later
+
+ align:start position:0%
+and we get specifics later
+ 
+
+ align:start position:0%
+and we get specifics later
+and the idea with the specifics is that
+
+ align:start position:0%
+and the idea with the specifics is that
+ 
+
+ align:start position:0%
+and the idea with the specifics is that
+when we uh
+
+ align:start position:0%
+when we uh
+ 
+
+ align:start position:0%
+when we uh
+review the code
+
+ align:start position:0%
+review the code
+ 
+
+ align:start position:0%
+review the code
+and makes decide to make changes or make
+
+ align:start position:0%
+and makes decide to make changes or make
+ 
+
+ align:start position:0%
+and makes decide to make changes or make
+additions
+
+ align:start position:0%
+additions
+ 
+
+ align:start position:0%
+additions
+if we've done things right the preamble
+
+ align:start position:0%
+if we've done things right the preamble
+ 
+
+ align:start position:0%
+if we've done things right the preamble
+and the fundamental cannons remain the
+
+ align:start position:0%
+and the fundamental cannons remain the
+ 
+
+ align:start position:0%
+and the fundamental cannons remain the
+same we only change the rest of
+
+ align:start position:0%
+same we only change the rest of
+ 
+
+ align:start position:0%
+same we only change the rest of
+the details
+
+ align:start position:0%
+the details
+ 
+
+ align:start position:0%
+the details
+in other words there's something that's
+
+ align:start position:0%
+in other words there's something that's
+ 
+
+ align:start position:0%
+in other words there's something that's
+about our organization
+
+ align:start position:0%
+about our organization
+ 
+
+ align:start position:0%
+about our organization
+one would say
+
+ align:start position:0%
+one would say
+ 
+
+ align:start position:0%
+one would say
+who is a who is a member one would say
+
+ align:start position:0%
+who is a who is a member one would say
+ 
+
+ align:start position:0%
+who is a who is a member one would say
+that has lasting value
+
+ align:start position:0%
+that has lasting value
+ 
+
+ align:start position:0%
+that has lasting value
+and the preamble and the fundamental
+
+ align:start position:0%
+and the preamble and the fundamental
+ 
+
+ align:start position:0%
+and the preamble and the fundamental
+canons of you if you're doing things
+
+ align:start position:0%
+canons of you if you're doing things
+ 
+
+ align:start position:0%
+canons of you if you're doing things
+right have lasting value
+
+ align:start position:0%
+right have lasting value
+ 
+
+ align:start position:0%
+right have lasting value
+and that the details about how you carry
+
+ align:start position:0%
+and that the details about how you carry
+ 
+
+ align:start position:0%
+and that the details about how you carry
+it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+may change from time to time
+
+ align:start position:0%
+may change from time to time
+ 
+
+ align:start position:0%
+may change from time to time
+and another way to think about it is
+
+ align:start position:0%
+and another way to think about it is
+ 
+
+ align:start position:0%
+and another way to think about it is
+that the fundamental cannons
+
+ align:start position:0%
+that the fundamental cannons
+ 
+
+ align:start position:0%
+that the fundamental cannons
+uh lay down your strategy
+
+ align:start position:0%
+uh lay down your strategy
+ 
+
+ align:start position:0%
+uh lay down your strategy
+and the rules of pr practice and the
+
+ align:start position:0%
+and the rules of pr practice and the
+ 
+
+ align:start position:0%
+and the rules of pr practice and the
+other the last part are your tactics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see it all fits right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember the basketball metaphor
+
+ align:start position:0%
+remember the basketball metaphor
+ 
+
+ align:start position:0%
+remember the basketball metaphor
+did we do that in this class yeah we did
+
+ align:start position:0%
+did we do that in this class yeah we did
+ 
+
+ align:start position:0%
+did we do that in this class yeah we did
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+big guys can go for the yeah
+
+ align:start position:0%
+big guys can go for the yeah
+ 
+
+ align:start position:0%
+big guys can go for the yeah
+right so the strategy
+
+ align:start position:0%
+right so the strategy
+ 
+
+ align:start position:0%
+right so the strategy
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+uh achieving this goal is laid down in
+
+ align:start position:0%
+uh achieving this goal is laid down in
+ 
+
+ align:start position:0%
+uh achieving this goal is laid down in
+your four the six fundamental cannons
+
+ align:start position:0%
+your four the six fundamental cannons
+ 
+
+ align:start position:0%
+your four the six fundamental cannons
+and your tactics are laid down in the
+
+ align:start position:0%
+and your tactics are laid down in the
+ 
+
+ align:start position:0%
+and your tactics are laid down in the
+rest of it
+
+ align:start position:0%
+rest of it
+ 
+
+ align:start position:0%
+rest of it
+uh now uh
+
+ align:start position:0%
+uh now uh
+ 
+
+ align:start position:0%
+uh now uh
+let's go through these canons it's only
+
+ align:start position:0%
+let's go through these canons it's only
+ 
+
+ align:start position:0%
+let's go through these canons it's only
+six seven let's go through them one by
+
+ align:start position:0%
+six seven let's go through them one by
+ 
+
+ align:start position:0%
+six seven let's go through them one by
+one because as you said we're going to
+
+ align:start position:0%
+one because as you said we're going to
+ 
+
+ align:start position:0%
+one because as you said we're going to
+find them elsewhere
+
+ align:start position:0%
+find them elsewhere
+ 
+
+ align:start position:0%
+find them elsewhere
+what's the first one say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now whatever you do in this life for the
+
+ align:start position:0%
+now whatever you do in this life for the
+ 
+
+ align:start position:0%
+now whatever you do in this life for the
+asterisk beside that statement
+
+ align:start position:0%
+asterisk beside that statement
+ 
+
+ align:start position:0%
+asterisk beside that statement
+because that is
+
+ align:start position:0%
+because that is
+ 
+
+ align:start position:0%
+because that is
+the fundamental point of controversy
+
+ align:start position:0%
+the fundamental point of controversy
+ 
+
+ align:start position:0%
+the fundamental point of controversy
+over engineering ethics
+
+ align:start position:0%
+over engineering ethics
+ 
+
+ align:start position:0%
+over engineering ethics
+in the 20
+
+ align:start position:0%
+in the 20
+ 
+
+ align:start position:0%
+in the 20
+in the 20th century
+
+ align:start position:0%
+in the 20th century
+ 
+
+ align:start position:0%
+in the 20th century
+it is number one
+
+ align:start position:0%
+it is number one
+ 
+
+ align:start position:0%
+it is number one
+i do not stand alone when
+
+ align:start position:0%
+i do not stand alone when
+ 
+
+ align:start position:0%
+i do not stand alone when
+using that superlative
+
+ align:start position:0%
+using that superlative
+ 
+
+ align:start position:0%
+using that superlative
+it is the
+
+ align:start position:0%
+it is the
+ 
+
+ align:start position:0%
+it is the
+most debated highest debated issue
+
+ align:start position:0%
+most debated highest debated issue
+ 
+
+ align:start position:0%
+most debated highest debated issue
+and the nspe was the first one to come
+
+ align:start position:0%
+and the nspe was the first one to come
+ 
+
+ align:start position:0%
+and the nspe was the first one to come
+out early and say
+
+ align:start position:0%
+out early and say
+ 
+
+ align:start position:0%
+out early and say
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+responsibility for the public is more
+
+ align:start position:0%
+responsibility for the public is more
+ 
+
+ align:start position:0%
+responsibility for the public is more
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+than responsibility for the client and
+
+ align:start position:0%
+than responsibility for the client and
+ 
+
+ align:start position:0%
+than responsibility for the client and
+the employee they were the first to jump
+
+ align:start position:0%
+the employee they were the first to jump
+ 
+
+ align:start position:0%
+the employee they were the first to jump
+out and say that
+
+ align:start position:0%
+out and say that
+ 
+
+ align:start position:0%
+out and say that
+and uh that and
+
+ align:start position:0%
+and uh that and
+ 
+
+ align:start position:0%
+and uh that and
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+you can see that if an organization
+
+ align:start position:0%
+you can see that if an organization
+ 
+
+ align:start position:0%
+you can see that if an organization
+is controlled by managers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they were going to have problems with
+
+ align:start position:0%
+they were going to have problems with
+ 
+
+ align:start position:0%
+they were going to have problems with
+that state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the typical uh response from a
+
+ align:start position:0%
+and the typical uh response from a
+ 
+
+ align:start position:0%
+and the typical uh response from a
+management point of view is
+
+ align:start position:0%
+management point of view is
+ 
+
+ align:start position:0%
+management point of view is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+there are competing interests that are
+
+ align:start position:0%
+there are competing interests that are
+ 
+
+ align:start position:0%
+there are competing interests that are
+in that an engineer has to satisfy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is the public one is the client and
+
+ align:start position:0%
+one is the public one is the client and
+ 
+
+ align:start position:0%
+one is the public one is the client and
+the other one's the employee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and nspe comes right out and uses this
+
+ align:start position:0%
+and nspe comes right out and uses this
+ 
+
+ align:start position:0%
+and nspe comes right out and uses this
+word paramount
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and by the way arnie veselan's last book
+
+ align:start position:0%
+and by the way arnie veselan's last book
+ 
+
+ align:start position:0%
+and by the way arnie veselan's last book
+latest it's not he got a new one i just
+
+ align:start position:0%
+latest it's not he got a new one i just
+ 
+
+ align:start position:0%
+latest it's not he got a new one i just
+heard
+
+ align:start position:0%
+heard
+ 
+
+ align:start position:0%
+heard
+but let's put let's say it this way his
+
+ align:start position:0%
+but let's put let's say it this way his
+ 
+
+ align:start position:0%
+but let's put let's say it this way his
+latest book is entitled hold paramount
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that means that now you have
+
+ align:start position:0%
+okay so that means that now you have
+ 
+
+ align:start position:0%
+okay so that means that now you have
+what is called a super principle
+
+ align:start position:0%
+what is called a super principle
+ 
+
+ align:start position:0%
+what is called a super principle
+that principle number one is more
+
+ align:start position:0%
+that principle number one is more
+ 
+
+ align:start position:0%
+that principle number one is more
+overriding over the next five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and most of the code and most of the
+
+ align:start position:0%
+and most of the code and most of the
+ 
+
+ align:start position:0%
+and most of the code and most of the
+and certainly the one i was in with the
+
+ align:start position:0%
+and certainly the one i was in with the
+ 
+
+ align:start position:0%
+and certainly the one i was in with the
+aaes and when i was in the one with the
+
+ align:start position:0%
+aaes and when i was in the one with the
+ 
+
+ align:start position:0%
+aaes and when i was in the one with the
+aes i was very much aware of what the
+
+ align:start position:0%
+aes i was very much aware of what the
+ 
+
+ align:start position:0%
+aes i was very much aware of what the
+other ones were doing
+
+ align:start position:0%
+other ones were doing
+ 
+
+ align:start position:0%
+other ones were doing
+because we would have we would call it
+
+ align:start position:0%
+because we would have we would call it
+ 
+
+ align:start position:0%
+because we would have we would call it
+all that kind of stuff
+
+ align:start position:0%
+all that kind of stuff
+ 
+
+ align:start position:0%
+all that kind of stuff
+i had i had to go out and give all of
+
+ align:start position:0%
+i had i had to go out and give all of
+ 
+
+ align:start position:0%
+i had i had to go out and give all of
+these speeches on behalf of my committee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we all had the same problem
+
+ align:start position:0%
+we all had the same problem
+ 
+
+ align:start position:0%
+we all had the same problem
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+we did we worked at aaes when we get to
+
+ align:start position:0%
+we did we worked at aaes when we get to
+ 
+
+ align:start position:0%
+we did we worked at aaes when we get to
+it i just have a burning issue to say
+
+ align:start position:0%
+it i just have a burning issue to say
+ 
+
+ align:start position:0%
+it i just have a burning issue to say
+this right now we worked on that that
+
+ align:start position:0%
+this right now we worked on that that
+ 
+
+ align:start position:0%
+this right now we worked on that that
+thing for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+must have been about five years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh i was on the committee the last
+
+ align:start position:0%
+and uh i was on the committee the last
+ 
+
+ align:start position:0%
+and uh i was on the committee the last
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+three years of it and i was chair of it
+
+ align:start position:0%
+three years of it and i was chair of it
+ 
+
+ align:start position:0%
+three years of it and i was chair of it
+the last
+
+ align:start position:0%
+the last
+ 
+
+ align:start position:0%
+the last
+two years of it
+
+ align:start position:0%
+two years of it
+ 
+
+ align:start position:0%
+two years of it
+and we did not get a code of ethics
+
+ align:start position:0%
+and we did not get a code of ethics
+ 
+
+ align:start position:0%
+and we did not get a code of ethics
+until
+
+ align:start position:0%
+until
+ 
+
+ align:start position:0%
+until
+we passed this paramounty rule and then
+
+ align:start position:0%
+we passed this paramounty rule and then
+ 
+
+ align:start position:0%
+we passed this paramounty rule and then
+we had one
+
+ align:start position:0%
+we had one
+ 
+
+ align:start position:0%
+we had one
+we were not the committee was not
+
+ align:start position:0%
+we were not the committee was not
+ 
+
+ align:start position:0%
+we were not the committee was not
+willing to submit anything
+
+ align:start position:0%
+willing to submit anything
+ 
+
+ align:start position:0%
+willing to submit anything
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+until we resolved the issue among
+
+ align:start position:0%
+until we resolved the issue among
+ 
+
+ align:start position:0%
+until we resolved the issue among
+ourselves
+
+ align:start position:0%
+ourselves
+ 
+
+ align:start position:0%
+ourselves
+it was fought that hard hard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'll tell you what happened i'll
+
+ align:start position:0%
+and i'll tell you what happened i'll
+ 
+
+ align:start position:0%
+and i'll tell you what happened i'll
+tell you what happened there this is
+
+ align:start position:0%
+tell you what happened there this is
+ 
+
+ align:start position:0%
+tell you what happened there this is
+open i'll call names
+
+ align:start position:0%
+open i'll call names
+ 
+
+ align:start position:0%
+open i'll call names
+uh there was a guy who was a manager
+
+ align:start position:0%
+uh there was a guy who was a manager
+ 
+
+ align:start position:0%
+uh there was a guy who was a manager
+named bill middleton
+
+ align:start position:0%
+named bill middleton
+ 
+
+ align:start position:0%
+named bill middleton
+was on the committee and
+
+ align:start position:0%
+was on the committee and
+ 
+
+ align:start position:0%
+was on the committee and
+he was a very thoughtful person
+
+ align:start position:0%
+he was a very thoughtful person
+ 
+
+ align:start position:0%
+he was a very thoughtful person
+and he was very strong on the side of
+
+ align:start position:0%
+and he was very strong on the side of
+ 
+
+ align:start position:0%
+and he was very strong on the side of
+balancing those that's the term
+
+ align:start position:0%
+balancing those that's the term
+ 
+
+ align:start position:0%
+balancing those that's the term
+balancing competing interests and for a
+
+ align:start position:0%
+balancing competing interests and for a
+ 
+
+ align:start position:0%
+balancing competing interests and for a
+long time
+
+ align:start position:0%
+long time
+ 
+
+ align:start position:0%
+long time
+and then i don't know who said it wasn't
+
+ align:start position:0%
+and then i don't know who said it wasn't
+ 
+
+ align:start position:0%
+and then i don't know who said it wasn't
+me but somebody said something in there
+
+ align:start position:0%
+me but somebody said something in there
+ 
+
+ align:start position:0%
+me but somebody said something in there
+that worked on his heart i don't know
+
+ align:start position:0%
+that worked on his heart i don't know
+ 
+
+ align:start position:0%
+that worked on his heart i don't know
+what it was
+
+ align:start position:0%
+what it was
+ 
+
+ align:start position:0%
+what it was
+but he got on the train going back
+
+ align:start position:0%
+but he got on the train going back
+ 
+
+ align:start position:0%
+but he got on the train going back
+home to philadelphia and he wrote up
+
+ align:start position:0%
+home to philadelphia and he wrote up
+ 
+
+ align:start position:0%
+home to philadelphia and he wrote up
+what he thought should be
+
+ align:start position:0%
+what he thought should be
+ 
+
+ align:start position:0%
+what he thought should be
+our fundamental canons and he put
+
+ align:start position:0%
+our fundamental canons and he put
+ 
+
+ align:start position:0%
+our fundamental canons and he put
+a paramouncy rule in there he did i
+
+ align:start position:0%
+a paramouncy rule in there he did i
+ 
+
+ align:start position:0%
+a paramouncy rule in there he did i
+don't think he used the word paramount
+
+ align:start position:0%
+don't think he used the word paramount
+ 
+
+ align:start position:0%
+don't think he used the word paramount
+but he but he made it more paramount
+
+ align:start position:0%
+but he but he made it more paramount
+ 
+
+ align:start position:0%
+but he but he made it more paramount
+and he
+
+ align:start position:0%
+and he
+ 
+
+ align:start position:0%
+and he
+sent it back to me and said he got it to
+
+ align:start position:0%
+sent it back to me and said he got it to
+ 
+
+ align:start position:0%
+sent it back to me and said he got it to
+him on the train
+
+ align:start position:0%
+him on the train
+ 
+
+ align:start position:0%
+him on the train
+when i got it
+
+ align:start position:0%
+when i got it
+ 
+
+ align:start position:0%
+when i got it
+i put it in the code
+
+ align:start position:0%
+i put it in the code
+ 
+
+ align:start position:0%
+i put it in the code
+and i called the president of the
+
+ align:start position:0%
+and i called the president of the
+ 
+
+ align:start position:0%
+and i called the president of the
+organization i said we finished the cup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i said i have to tell you
+
+ align:start position:0%
+i said i have to tell you
+ 
+
+ align:start position:0%
+i said i have to tell you
+i don't have the the vote in writing
+
+ align:start position:0%
+i don't have the the vote in writing
+ 
+
+ align:start position:0%
+i don't have the the vote in writing
+he said we've been waiting on this thing
+
+ align:start position:0%
+he said we've been waiting on this thing
+ 
+
+ align:start position:0%
+he said we've been waiting on this thing
+for six years he said well you take
+
+ align:start position:0%
+for six years he said well you take
+ 
+
+ align:start position:0%
+for six years he said well you take
+responsibility for it i said i will i
+
+ align:start position:0%
+responsibility for it i said i will i
+ 
+
+ align:start position:0%
+responsibility for it i said i will i
+sent it up man we had it nobody objected
+
+ align:start position:0%
+sent it up man we had it nobody objected
+ 
+
+ align:start position:0%
+sent it up man we had it nobody objected
+once it went in because it came out of
+
+ align:start position:0%
+once it went in because it came out of
+ 
+
+ align:start position:0%
+once it went in because it came out of
+this man's
+
+ align:start position:0%
+this man's
+ 
+
+ align:start position:0%
+this man's
+heart he found some correlation between
+
+ align:start position:0%
+heart he found some correlation between
+ 
+
+ align:start position:0%
+heart he found some correlation between
+what was in his unconscious and his
+
+ align:start position:0%
+what was in his unconscious and his
+ 
+
+ align:start position:0%
+what was in his unconscious and his
+conscience and i said what
+
+ align:start position:0%
+conscience and i said what
+ 
+
+ align:start position:0%
+conscience and i said what
+when that thing comes out everybody's
+
+ align:start position:0%
+when that thing comes out everybody's
+ 
+
+ align:start position:0%
+when that thing comes out everybody's
+going to buy it or
+
+ align:start position:0%
+going to buy it or
+ 
+
+ align:start position:0%
+going to buy it or
+a person who doesn't buy it is not going
+
+ align:start position:0%
+a person who doesn't buy it is not going
+ 
+
+ align:start position:0%
+a person who doesn't buy it is not going
+to fight against it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+and it hurts business
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and um
+
+ align:start position:0%
+uh and um
+ 
+
+ align:start position:0%
+uh and um
+people argue
+
+ align:start position:0%
+people argue
+ 
+
+ align:start position:0%
+people argue
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+and um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that and then you then you get into
+
+ align:start position:0%
+and that and then you then you get into
+ 
+
+ align:start position:0%
+and that and then you then you get into
+this whole thing about gray areas and
+
+ align:start position:0%
+this whole thing about gray areas and
+ 
+
+ align:start position:0%
+this whole thing about gray areas and
+complexity
+
+ align:start position:0%
+complexity
+ 
+
+ align:start position:0%
+complexity
+and most of the issues weren't gray and
+
+ align:start position:0%
+and most of the issues weren't gray and
+ 
+
+ align:start position:0%
+and most of the issues weren't gray and
+they weren't complex
+
+ align:start position:0%
+they weren't complex
+ 
+
+ align:start position:0%
+they weren't complex
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they really wanted to wanted a
+
+ align:start position:0%
+they really wanted to wanted a
+ 
+
+ align:start position:0%
+they really wanted to wanted a
+profession
+
+ align:start position:0%
+profession
+ 
+
+ align:start position:0%
+profession
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in which
+
+ align:start position:0%
+in which
+ 
+
+ align:start position:0%
+in which
+every member
+
+ align:start position:0%
+every member
+ 
+
+ align:start position:0%
+every member
+felt a deep sense of loyalty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to whoever was putting the paycheck on
+
+ align:start position:0%
+to whoever was putting the paycheck on
+ 
+
+ align:start position:0%
+to whoever was putting the paycheck on
+the table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+thought that you could not that that
+
+ align:start position:0%
+thought that you could not that that
+ 
+
+ align:start position:0%
+thought that you could not that that
+that the profession would break down
+
+ align:start position:0%
+that the profession would break down
+ 
+
+ align:start position:0%
+that the profession would break down
+because people would not be loyal
+
+ align:start position:0%
+because people would not be loyal
+ 
+
+ align:start position:0%
+because people would not be loyal
+to the ones they worked for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right there was this question is the way
+
+ align:start position:0%
+right there was this question is the way
+ 
+
+ align:start position:0%
+right there was this question is the way
+not you should serve the public or
+
+ align:start position:0%
+not you should serve the public or
+ 
+
+ align:start position:0%
+not you should serve the public or
+whether it was somebody else's problem
+
+ align:start position:0%
+whether it was somebody else's problem
+ 
+
+ align:start position:0%
+whether it was somebody else's problem
+to serve the public
+
+ align:start position:0%
+to serve the public
+ 
+
+ align:start position:0%
+to serve the public
+or whether you just needed to balance
+
+ align:start position:0%
+or whether you just needed to balance
+ 
+
+ align:start position:0%
+or whether you just needed to balance
+quote-unquote these competing interests
+
+ align:start position:0%
+quote-unquote these competing interests
+ 
+
+ align:start position:0%
+quote-unquote these competing interests
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+my position on there when it came to the
+
+ align:start position:0%
+my position on there when it came to the
+ 
+
+ align:start position:0%
+my position on there when it came to the
+word balance is you got to have a rule
+
+ align:start position:0%
+word balance is you got to have a rule
+ 
+
+ align:start position:0%
+word balance is you got to have a rule
+for what establishes a balance
+
+ align:start position:0%
+for what establishes a balance
+ 
+
+ align:start position:0%
+for what establishes a balance
+all right what is that rule then nobody
+
+ align:start position:0%
+all right what is that rule then nobody
+ 
+
+ align:start position:0%
+all right what is that rule then nobody
+could give me the rule because that goes
+
+ align:start position:0%
+could give me the rule because that goes
+ 
+
+ align:start position:0%
+could give me the rule because that goes
+back to a paramount c
+
+ align:start position:0%
+back to a paramount c
+ 
+
+ align:start position:0%
+back to a paramount c
+something got to be paramount
+
+ align:start position:0%
+something got to be paramount
+ 
+
+ align:start position:0%
+something got to be paramount
+so if you use that word rule what do you
+
+ align:start position:0%
+so if you use that word rule what do you
+ 
+
+ align:start position:0%
+so if you use that word rule what do you
+mean by balance what constitutes a
+
+ align:start position:0%
+mean by balance what constitutes a
+ 
+
+ align:start position:0%
+mean by balance what constitutes a
+balance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that confused the issue for
+
+ align:start position:0%
+well that confused the issue for
+ 
+
+ align:start position:0%
+well that confused the issue for
+everybody enough
+
+ align:start position:0%
+everybody enough
+ 
+
+ align:start position:0%
+everybody enough
+for us to start thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paramount clause
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+because they don't use the word
+
+ align:start position:0%
+because they don't use the word
+ 
+
+ align:start position:0%
+because they don't use the word
+paramount right
+
+ align:start position:0%
+paramount right
+ 
+
+ align:start position:0%
+paramount right
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+their first canon says
+
+ align:start position:0%
+their first canon says
+ 
+
+ align:start position:0%
+their first canon says
+to accept responsibility and making
+
+ align:start position:0%
+to accept responsibility and making
+ 
+
+ align:start position:0%
+to accept responsibility and making
+engineering decisions consistent with
+
+ align:start position:0%
+engineering decisions consistent with
+ 
+
+ align:start position:0%
+engineering decisions consistent with
+the safety health and welfare of the
+
+ align:start position:0%
+the safety health and welfare of the
+ 
+
+ align:start position:0%
+the safety health and welfare of the
+public
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+is that an alternative is that an
+
+ align:start position:0%
+is that an alternative is that an
+ 
+
+ align:start position:0%
+is that an alternative is that an
+alternative that you all were
+
+ align:start position:0%
+alternative that you all were
+ 
+
+ align:start position:0%
+alternative that you all were
+considering
+
+ align:start position:0%
+considering
+ 
+
+ align:start position:0%
+considering
+aaes something like that
+
+ align:start position:0%
+aaes something like that
+ 
+
+ align:start position:0%
+aaes something like that
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah tripoli um well let's say a few
+
+ align:start position:0%
+yeah tripoli um well let's say a few
+ 
+
+ align:start position:0%
+yeah tripoli um well let's say a few
+things about the ieee first of all
+
+ align:start position:0%
+things about the ieee first of all
+ 
+
+ align:start position:0%
+things about the ieee first of all
+what they had to say back in those days
+
+ align:start position:0%
+what they had to say back in those days
+ 
+
+ align:start position:0%
+what they had to say back in those days
+was very important because they were the
+
+ align:start position:0%
+was very important because they were the
+ 
+
+ align:start position:0%
+was very important because they were the
+largest
+
+ align:start position:0%
+largest
+ 
+
+ align:start position:0%
+largest
+engineering professional organization
+
+ align:start position:0%
+engineering professional organization
+ 
+
+ align:start position:0%
+engineering professional organization
+and secondly they were the largest
+
+ align:start position:0%
+and secondly they were the largest
+ 
+
+ align:start position:0%
+and secondly they were the largest
+partly because
+
+ align:start position:0%
+partly because
+ 
+
+ align:start position:0%
+partly because
+in those in those days the electrical
+
+ align:start position:0%
+in those in those days the electrical
+ 
+
+ align:start position:0%
+in those in those days the electrical
+engineering departments in colleges were
+
+ align:start position:0%
+engineering departments in colleges were
+ 
+
+ align:start position:0%
+engineering departments in colleges were
+the largest
+
+ align:start position:0%
+the largest
+ 
+
+ align:start position:0%
+the largest
+most of the students were in most of the
+
+ align:start position:0%
+most of the students were in most of the
+ 
+
+ align:start position:0%
+most of the students were in most of the
+jobs were in electrical engineering now
+
+ align:start position:0%
+jobs were in electrical engineering now
+ 
+
+ align:start position:0%
+jobs were in electrical engineering now
+that's sort of shifted to computer
+
+ align:start position:0%
+that's sort of shifted to computer
+ 
+
+ align:start position:0%
+that's sort of shifted to computer
+science i believe
+
+ align:start position:0%
+science i believe
+ 
+
+ align:start position:0%
+science i believe
+computer engineering and computer
+
+ align:start position:0%
+computer engineering and computer
+ 
+
+ align:start position:0%
+computer engineering and computer
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+but electrical was the biggest one
+
+ align:start position:0%
+but electrical was the biggest one
+ 
+
+ align:start position:0%
+but electrical was the biggest one
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+lastly
+
+ align:start position:0%
+lastly
+ 
+
+ align:start position:0%
+lastly
+ieee was an international organization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it wasn't the americans
+
+ align:start position:0%
+it wasn't the americans
+ 
+
+ align:start position:0%
+it wasn't the americans
+so they had to be concerned about
+
+ align:start position:0%
+so they had to be concerned about
+ 
+
+ align:start position:0%
+so they had to be concerned about
+international concerns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+all of that weighed in with them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it looked for a while as though ieee
+
+ align:start position:0%
+so it looked for a while as though ieee
+ 
+
+ align:start position:0%
+so it looked for a while as though ieee
+was going to
+
+ align:start position:0%
+was going to
+ 
+
+ align:start position:0%
+was going to
+control is not the right word dominate
+
+ align:start position:0%
+control is not the right word dominate
+ 
+
+ align:start position:0%
+control is not the right word dominate
+is the right word dominate everybody
+
+ align:start position:0%
+is the right word dominate everybody
+ 
+
+ align:start position:0%
+is the right word dominate everybody
+else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh it didn't work
+
+ align:start position:0%
+and uh it didn't work
+ 
+
+ align:start position:0%
+and uh it didn't work
+so ieee has has stood by
+
+ align:start position:0%
+so ieee has has stood by
+ 
+
+ align:start position:0%
+so ieee has has stood by
+what they wrote all of these years and
+
+ align:start position:0%
+what they wrote all of these years and
+ 
+
+ align:start position:0%
+what they wrote all of these years and
+they are just
+
+ align:start position:0%
+they are just
+ 
+
+ align:start position:0%
+they are just
+separate from most from the rest
+
+ align:start position:0%
+separate from most from the rest
+ 
+
+ align:start position:0%
+separate from most from the rest
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to accept responsibility in making
+
+ align:start position:0%
+to accept responsibility in making
+ 
+
+ align:start position:0%
+to accept responsibility in making
+decisions consistent with the public
+
+ align:start position:0%
+decisions consistent with the public
+ 
+
+ align:start position:0%
+decisions consistent with the public
+safety
+
+ align:start position:0%
+safety
+ 
+
+ align:start position:0%
+safety
+is so different than saying
+
+ align:start position:0%
+is so different than saying
+ 
+
+ align:start position:0%
+is so different than saying
+like hold paramount
+
+ align:start position:0%
+like hold paramount
+ 
+
+ align:start position:0%
+like hold paramount
+exactly does it mean to accept
+
+ align:start position:0%
+exactly does it mean to accept
+ 
+
+ align:start position:0%
+exactly does it mean to accept
+responsibility does that mean you can
+
+ align:start position:0%
+responsibility does that mean you can
+ 
+
+ align:start position:0%
+responsibility does that mean you can
+still make a bad decision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it uh
+
+ align:start position:0%
+yeah it uh
+ 
+
+ align:start position:0%
+yeah it uh
+well it there's one thing that is good
+
+ align:start position:0%
+well it there's one thing that is good
+ 
+
+ align:start position:0%
+well it there's one thing that is good
+about it uh that
+
+ align:start position:0%
+about it uh that
+ 
+
+ align:start position:0%
+about it uh that
+that i take a lesson from
+
+ align:start position:0%
+that i take a lesson from
+ 
+
+ align:start position:0%
+that i take a lesson from
+uh but i don't and that is that it
+
+ align:start position:0%
+uh but i don't and that is that it
+ 
+
+ align:start position:0%
+uh but i don't and that is that it
+presupposes that you can do engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and not have to sacrifice
+
+ align:start position:0%
+uh and not have to sacrifice
+ 
+
+ align:start position:0%
+uh and not have to sacrifice
+your employer or client to do the right
+
+ align:start position:0%
+your employer or client to do the right
+ 
+
+ align:start position:0%
+your employer or client to do the right
+thing that they're always compatible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the lesson that i take from that is that
+
+ align:start position:0%
+the lesson that i take from that is that
+ 
+
+ align:start position:0%
+the lesson that i take from that is that
+well i don't believe that they're always
+
+ align:start position:0%
+well i don't believe that they're always
+ 
+
+ align:start position:0%
+well i don't believe that they're always
+compatible
+
+ align:start position:0%
+compatible
+ 
+
+ align:start position:0%
+compatible
+but what i do believe is that competency
+
+ align:start position:0%
+but what i do believe is that competency
+ 
+
+ align:start position:0%
+but what i do believe is that competency
+is almost always compatible i mean if
+
+ align:start position:0%
+is almost always compatible i mean if
+ 
+
+ align:start position:0%
+is almost always compatible i mean if
+you're really good at what you do you
+
+ align:start position:0%
+you're really good at what you do you
+ 
+
+ align:start position:0%
+you're really good at what you do you
+should be able to do it and do the right
+
+ align:start position:0%
+should be able to do it and do the right
+ 
+
+ align:start position:0%
+should be able to do it and do the right
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what i'm really after in that
+
+ align:start position:0%
+now what i'm really after in that
+ 
+
+ align:start position:0%
+now what i'm really after in that
+argument to be to be uh quite
+
+ align:start position:0%
+argument to be to be uh quite
+ 
+
+ align:start position:0%
+argument to be to be uh quite
+honest and specific about it is i am
+
+ align:start position:0%
+honest and specific about it is i am
+ 
+
+ align:start position:0%
+honest and specific about it is i am
+less concerned as to whether or not you
+
+ align:start position:0%
+less concerned as to whether or not you
+ 
+
+ align:start position:0%
+less concerned as to whether or not you
+can do both
+
+ align:start position:0%
+can do both
+ 
+
+ align:start position:0%
+can do both
+then i am concerned that to do one or
+
+ align:start position:0%
+then i am concerned that to do one or
+ 
+
+ align:start position:0%
+then i am concerned that to do one or
+the other is definitely incompetent i
+
+ align:start position:0%
+the other is definitely incompetent i
+ 
+
+ align:start position:0%
+the other is definitely incompetent i
+mean it builds into
+
+ align:start position:0%
+mean it builds into
+ 
+
+ align:start position:0%
+mean it builds into
+the culture
+
+ align:start position:0%
+the culture
+ 
+
+ align:start position:0%
+the culture
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh you're doing you're real smart
+
+ align:start position:0%
+uh you're doing you're real smart
+ 
+
+ align:start position:0%
+uh you're doing you're real smart
+if you can kill all of the enemy and
+
+ align:start position:0%
+if you can kill all of the enemy and
+ 
+
+ align:start position:0%
+if you can kill all of the enemy and
+their babies and their dogs and
+
+ align:start position:0%
+their babies and their dogs and
+ 
+
+ align:start position:0%
+their babies and their dogs and
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+uh and say that well i had to do it
+
+ align:start position:0%
+uh and say that well i had to do it
+ 
+
+ align:start position:0%
+uh and say that well i had to do it
+confident you say well i'm just going to
+
+ align:start position:0%
+confident you say well i'm just going to
+ 
+
+ align:start position:0%
+confident you say well i'm just going to
+kill the soldiers the ones that are
+
+ align:start position:0%
+kill the soldiers the ones that are
+ 
+
+ align:start position:0%
+kill the soldiers the ones that are
+armed
+
+ align:start position:0%
+armed
+ 
+
+ align:start position:0%
+armed
+and uh not and we're not going to hit
+
+ align:start position:0%
+and uh not and we're not going to hit
+ 
+
+ align:start position:0%
+and uh not and we're not going to hit
+the civilians and i will be as effective
+
+ align:start position:0%
+the civilians and i will be as effective
+ 
+
+ align:start position:0%
+the civilians and i will be as effective
+as you are with that murder of everybody
+
+ align:start position:0%
+as you are with that murder of everybody
+ 
+
+ align:start position:0%
+as you are with that murder of everybody
+okay so it builds
+
+ align:start position:0%
+okay so it builds
+ 
+
+ align:start position:0%
+okay so it builds
+in a culture that going back to culture
+
+ align:start position:0%
+in a culture that going back to culture
+ 
+
+ align:start position:0%
+in a culture that going back to culture
+again it builds in what i call a bad
+
+ align:start position:0%
+again it builds in what i call a bad
+ 
+
+ align:start position:0%
+again it builds in what i call a bad
+culture
+
+ align:start position:0%
+culture
+ 
+
+ align:start position:0%
+culture
+now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so i think that that that we have the
+
+ align:start position:0%
+uh so i think that that that we have the
+ 
+
+ align:start position:0%
+uh so i think that that that we have the
+lay of the land ieee
+
+ align:start position:0%
+lay of the land ieee
+ 
+
+ align:start position:0%
+lay of the land ieee
+is really trying to say something that i
+
+ align:start position:0%
+is really trying to say something that i
+ 
+
+ align:start position:0%
+is really trying to say something that i
+don't think everybody can believe and
+
+ align:start position:0%
+don't think everybody can believe and
+ 
+
+ align:start position:0%
+don't think everybody can believe and
+that is that you can always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do these things the right way i think
+
+ align:start position:0%
+do these things the right way i think
+ 
+
+ align:start position:0%
+do these things the right way i think
+that it's the right
+
+ align:start position:0%
+that it's the right
+ 
+
+ align:start position:0%
+that it's the right
+in other words here's what i would say
+
+ align:start position:0%
+in other words here's what i would say
+ 
+
+ align:start position:0%
+in other words here's what i would say
+now emphasize i'm taking a stand
+
+ align:start position:0%
+now emphasize i'm taking a stand
+ 
+
+ align:start position:0%
+now emphasize i'm taking a stand
+okay now you can take your stance but i
+
+ align:start position:0%
+okay now you can take your stance but i
+ 
+
+ align:start position:0%
+okay now you can take your stance but i
+can justify my stance
+
+ align:start position:0%
+can justify my stance
+ 
+
+ align:start position:0%
+can justify my stance
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i would take that statement
+
+ align:start position:0%
+i would take that statement
+ 
+
+ align:start position:0%
+i would take that statement
+and put it in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preamble as an ideal that we shoot for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the whole cannon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the whole idea
+
+ align:start position:0%
+the whole idea
+ 
+
+ align:start position:0%
+the whole idea
+i would take the cannon out i would put
+
+ align:start position:0%
+i would take the cannon out i would put
+ 
+
+ align:start position:0%
+i would take the cannon out i would put
+it up there
+
+ align:start position:0%
+it up there
+ 
+
+ align:start position:0%
+it up there
+as the first draft and then i'd work on
+
+ align:start position:0%
+as the first draft and then i'd work on
+ 
+
+ align:start position:0%
+as the first draft and then i'd work on
+it until it all came out made sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+can we go back to nspe
+
+ align:start position:0%
+can we go back to nspe
+ 
+
+ align:start position:0%
+can we go back to nspe
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+hi tony
+
+ align:start position:0%
+hi tony
+ 
+
+ align:start position:0%
+hi tony
+we're doing the uh nspe code
+
+ align:start position:0%
+we're doing the uh nspe code
+ 
+
+ align:start position:0%
+we're doing the uh nspe code
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+what's the second canon
+
+ align:start position:0%
+what's the second canon
+ 
+
+ align:start position:0%
+what's the second canon
+are we done with the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+we've talked about what or read about
+
+ align:start position:0%
+we've talked about what or read about
+ 
+
+ align:start position:0%
+we've talked about what or read about
+what welfare means yeah
+
+ align:start position:0%
+what welfare means yeah
+ 
+
+ align:start position:0%
+what welfare means yeah
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+do the people who subscribe to this code
+
+ align:start position:0%
+do the people who subscribe to this code
+ 
+
+ align:start position:0%
+do the people who subscribe to this code
+of ethics like how are they sure that
+
+ align:start position:0%
+of ethics like how are they sure that
+ 
+
+ align:start position:0%
+of ethics like how are they sure that
+they know what welfare means that was a
+
+ align:start position:0%
+they know what welfare means that was a
+ 
+
+ align:start position:0%
+they know what welfare means that was a
+hotly debated word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+well that was a that was a
+
+ align:start position:0%
+well that was a that was a
+ 
+
+ align:start position:0%
+well that was a that was a
+i was in a meeting when um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some engineers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um three of them
+
+ align:start position:0%
+um three of them
+ 
+
+ align:start position:0%
+um three of them
+uh from the same state
+
+ align:start position:0%
+uh from the same state
+ 
+
+ align:start position:0%
+uh from the same state
+got up and walked out of the meeting
+
+ align:start position:0%
+got up and walked out of the meeting
+ 
+
+ align:start position:0%
+got up and walked out of the meeting
+said and we can't find a substitute for
+
+ align:start position:0%
+said and we can't find a substitute for
+ 
+
+ align:start position:0%
+said and we can't find a substitute for
+that word welfare we're not going to
+
+ align:start position:0%
+that word welfare we're not going to
+ 
+
+ align:start position:0%
+that word welfare we're not going to
+even participate those counters in it
+
+ align:start position:0%
+even participate those counters in it
+ 
+
+ align:start position:0%
+even participate those counters in it
+they got them walked out never came back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it had too many political
+
+ align:start position:0%
+because it had too many political
+ 
+
+ align:start position:0%
+because it had too many political
+connotations
+
+ align:start position:0%
+connotations
+ 
+
+ align:start position:0%
+connotations
+now the political connotation was
+
+ align:start position:0%
+now the political connotation was
+ 
+
+ align:start position:0%
+now the political connotation was
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the government is i mean this this was
+
+ align:start position:0%
+the government is i mean this this was
+ 
+
+ align:start position:0%
+the government is i mean this this was
+the connotation that was applied
+
+ align:start position:0%
+the connotation that was applied
+ 
+
+ align:start position:0%
+the connotation that was applied
+to the word welfare
+
+ align:start position:0%
+to the word welfare
+ 
+
+ align:start position:0%
+to the word welfare
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+these discussions
+
+ align:start position:0%
+these discussions
+ 
+
+ align:start position:0%
+these discussions
+the connotation was that the government
+
+ align:start position:0%
+the connotation was that the government
+ 
+
+ align:start position:0%
+the connotation was that the government
+is giving money to somebody not to work
+
+ align:start position:0%
+is giving money to somebody not to work
+ 
+
+ align:start position:0%
+is giving money to somebody not to work
+and they can live just as well as i am
+
+ align:start position:0%
+and they can live just as well as i am
+ 
+
+ align:start position:0%
+and they can live just as well as i am
+and i am working
+
+ align:start position:0%
+and i am working
+ 
+
+ align:start position:0%
+and i am working
+now that was
+
+ align:start position:0%
+now that was
+ 
+
+ align:start position:0%
+now that was
+the nightmare in the american psyche
+
+ align:start position:0%
+the nightmare in the american psyche
+ 
+
+ align:start position:0%
+the nightmare in the american psyche
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+was um
+
+ align:start position:0%
+was um
+ 
+
+ align:start position:0%
+was um
+that was built into the uh
+
+ align:start position:0%
+that was built into the uh
+ 
+
+ align:start position:0%
+that was built into the uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+movements in the in the middle and late
+
+ align:start position:0%
+movements in the in the middle and late
+ 
+
+ align:start position:0%
+movements in the in the middle and late
+60s
+
+ align:start position:0%
+60s
+ 
+
+ align:start position:0%
+60s
+and the movement said that welfare was
+
+ align:start position:0%
+and the movement said that welfare was
+ 
+
+ align:start position:0%
+and the movement said that welfare was
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+uh people
+
+ align:start position:0%
+uh people
+ 
+
+ align:start position:0%
+uh people
+who either did not get their civil
+
+ align:start position:0%
+who either did not get their civil
+ 
+
+ align:start position:0%
+who either did not get their civil
+rights and therefore needed
+
+ align:start position:0%
+rights and therefore needed
+ 
+
+ align:start position:0%
+rights and therefore needed
+subsistence
+
+ align:start position:0%
+subsistence
+ 
+
+ align:start position:0%
+subsistence
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+that you really don't want to have a
+
+ align:start position:0%
+that you really don't want to have a
+ 
+
+ align:start position:0%
+that you really don't want to have a
+country
+
+ align:start position:0%
+country
+ 
+
+ align:start position:0%
+country
+where in people are suffering and have
+
+ align:start position:0%
+where in people are suffering and have
+ 
+
+ align:start position:0%
+where in people are suffering and have
+every reason to rise up against the
+
+ align:start position:0%
+every reason to rise up against the
+ 
+
+ align:start position:0%
+every reason to rise up against the
+country
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean no matter what your failure in
+
+ align:start position:0%
+i mean no matter what your failure in
+ 
+
+ align:start position:0%
+i mean no matter what your failure in
+life may be you don't want your child to
+
+ align:start position:0%
+life may be you don't want your child to
+ 
+
+ align:start position:0%
+life may be you don't want your child to
+starve
+
+ align:start position:0%
+starve
+ 
+
+ align:start position:0%
+starve
+and you will become a communist all of
+
+ align:start position:0%
+and you will become a communist all of
+ 
+
+ align:start position:0%
+and you will become a communist all of
+these other things okay
+
+ align:start position:0%
+these other things okay
+ 
+
+ align:start position:0%
+these other things okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+branch dravidian
+
+ align:start position:0%
+branch dravidian
+ 
+
+ align:start position:0%
+branch dravidian
+all of these groups that break out
+
+ align:start position:0%
+all of these groups that break out
+ 
+
+ align:start position:0%
+all of these groups that break out
+uh are people who are sore
+
+ align:start position:0%
+uh are people who are sore
+ 
+
+ align:start position:0%
+uh are people who are sore
+about failure
+
+ align:start position:0%
+about failure
+ 
+
+ align:start position:0%
+about failure
+and you don't want a country
+
+ align:start position:0%
+and you don't want a country
+ 
+
+ align:start position:0%
+and you don't want a country
+particularly one that is that's what the
+
+ align:start position:0%
+particularly one that is that's what the
+ 
+
+ align:start position:0%
+particularly one that is that's what the
+argument went particularly when it's
+
+ align:start position:0%
+argument went particularly when it's
+ 
+
+ align:start position:0%
+argument went particularly when it's
+profitable i mean as rich as ours to
+
+ align:start position:0%
+profitable i mean as rich as ours to
+ 
+
+ align:start position:0%
+profitable i mean as rich as ours to
+have that problem
+
+ align:start position:0%
+have that problem
+ 
+
+ align:start position:0%
+have that problem
+okay so those were the two sides of it
+
+ align:start position:0%
+okay so those were the two sides of it
+ 
+
+ align:start position:0%
+okay so those were the two sides of it
+when they got it into
+
+ align:start position:0%
+when they got it into
+ 
+
+ align:start position:0%
+when they got it into
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+debates uh
+
+ align:start position:0%
+debates uh
+ 
+
+ align:start position:0%
+debates uh
+frankly i'll tell you uh
+
+ align:start position:0%
+frankly i'll tell you uh
+ 
+
+ align:start position:0%
+frankly i'll tell you uh
+i just don't know why uh the people who
+
+ align:start position:0%
+i just don't know why uh the people who
+ 
+
+ align:start position:0%
+i just don't know why uh the people who
+used the word welfare
+
+ align:start position:0%
+used the word welfare
+ 
+
+ align:start position:0%
+used the word welfare
+were not going to yield
+
+ align:start position:0%
+were not going to yield
+ 
+
+ align:start position:0%
+were not going to yield
+on that point
+
+ align:start position:0%
+on that point
+ 
+
+ align:start position:0%
+on that point
+i tried some other words
+
+ align:start position:0%
+i tried some other words
+ 
+
+ align:start position:0%
+i tried some other words
+i couldn't find it i didn't see where
+
+ align:start position:0%
+i couldn't find it i didn't see where
+ 
+
+ align:start position:0%
+i couldn't find it i didn't see where
+welfare
+
+ align:start position:0%
+welfare
+ 
+
+ align:start position:0%
+welfare
+was a necessary word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the people who
+
+ align:start position:0%
+and the people who
+ 
+
+ align:start position:0%
+and the people who
+were dissatisfied with it at the time of
+
+ align:start position:0%
+were dissatisfied with it at the time of
+ 
+
+ align:start position:0%
+were dissatisfied with it at the time of
+still dissatisfied they don't like that
+
+ align:start position:0%
+still dissatisfied they don't like that
+ 
+
+ align:start position:0%
+still dissatisfied they don't like that
+word
+
+ align:start position:0%
+word
+ 
+
+ align:start position:0%
+word
+the good news is the time has passed and
+
+ align:start position:0%
+the good news is the time has passed and
+ 
+
+ align:start position:0%
+the good news is the time has passed and
+a whole lot we've got a whole generation
+
+ align:start position:0%
+a whole lot we've got a whole generation
+ 
+
+ align:start position:0%
+a whole lot we've got a whole generation
+out here really doesn't know what that
+
+ align:start position:0%
+out here really doesn't know what that
+ 
+
+ align:start position:0%
+out here really doesn't know what that
+doesn't feel though
+
+ align:start position:0%
+doesn't feel though
+ 
+
+ align:start position:0%
+doesn't feel though
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+they'll happen to say well look in the
+
+ align:start position:0%
+they'll happen to say well look in the
+ 
+
+ align:start position:0%
+they'll happen to say well look in the
+dictionary
+
+ align:start position:0%
+dictionary
+ 
+
+ align:start position:0%
+dictionary
+get say okay
+
+ align:start position:0%
+get say okay
+ 
+
+ align:start position:0%
+get say okay
+so the good news is it no longer makes
+
+ align:start position:0%
+so the good news is it no longer makes
+ 
+
+ align:start position:0%
+so the good news is it no longer makes
+uh seems seems to me to make a
+
+ align:start position:0%
+uh seems seems to me to make a
+ 
+
+ align:start position:0%
+uh seems seems to me to make a
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+but it was loaded and like i said
+
+ align:start position:0%
+but it was loaded and like i said
+ 
+
+ align:start position:0%
+but it was loaded and like i said
+i really i really wasn't uh
+
+ align:start position:0%
+i really i really wasn't uh
+ 
+
+ align:start position:0%
+i really i really wasn't uh
+i really i like the word welfare but i
+
+ align:start position:0%
+i really i like the word welfare but i
+ 
+
+ align:start position:0%
+i really i like the word welfare but i
+could find a substitute
+
+ align:start position:0%
+could find a substitute
+ 
+
+ align:start position:0%
+could find a substitute
+all right if that makes you mad
+
+ align:start position:0%
+all right if that makes you mad
+ 
+
+ align:start position:0%
+all right if that makes you mad
+i'll find another one that means the
+
+ align:start position:0%
+i'll find another one that means the
+ 
+
+ align:start position:0%
+i'll find another one that means the
+same thing
+
+ align:start position:0%
+same thing
+ 
+
+ align:start position:0%
+same thing
+and if that makes you mad then i see
+
+ align:start position:0%
+and if that makes you mad then i see
+ 
+
+ align:start position:0%
+and if that makes you mad then i see
+there's no way for us to
+
+ align:start position:0%
+there's no way for us to
+ 
+
+ align:start position:0%
+there's no way for us to
+come to any conclusion but
+
+ align:start position:0%
+come to any conclusion but
+ 
+
+ align:start position:0%
+come to any conclusion but
+i was willing to find a substitute but
+
+ align:start position:0%
+i was willing to find a substitute but
+ 
+
+ align:start position:0%
+i was willing to find a substitute but
+the people who
+
+ align:start position:0%
+the people who
+ 
+
+ align:start position:0%
+the people who
+laid on that word welfare bang there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right and they were going to do
+
+ align:start position:0%
+that's right and they were going to do
+ 
+
+ align:start position:0%
+that's right and they were going to do
+it and it won if you want to put it in
+
+ align:start position:0%
+it and it won if you want to put it in
+ 
+
+ align:start position:0%
+it and it won if you want to put it in
+terms of winning and losing
+
+ align:start position:0%
+terms of winning and losing
+ 
+
+ align:start position:0%
+terms of winning and losing
+uh so yeah welfare was a that's a good
+
+ align:start position:0%
+uh so yeah welfare was a that's a good
+ 
+
+ align:start position:0%
+uh so yeah welfare was a that's a good
+term it
+
+ align:start position:0%
+term it
+ 
+
+ align:start position:0%
+term it
+was a loaded term in those days loaded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it came out
+
+ align:start position:0%
+but it came out
+ 
+
+ align:start position:0%
+but it came out
+okay where else are we now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somebody read number two
+
+ align:start position:0%
+somebody read number two
+ 
+
+ align:start position:0%
+somebody read number two
+you have a longer version i have
+
+ align:start position:0%
+you have a longer version i have
+ 
+
+ align:start position:0%
+you have a longer version i have
+performed services only in areas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now that was a
+
+ align:start position:0%
+now that was a
+ 
+
+ align:start position:0%
+now that was a
+contested one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i thought a lot about that one
+
+ align:start position:0%
+i thought a lot about that one
+ 
+
+ align:start position:0%
+i thought a lot about that one
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+highly contested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+i'll tell you why
+
+ align:start position:0%
+i'll tell you why
+ 
+
+ align:start position:0%
+i'll tell you why
+uh the people
+
+ align:start position:0%
+uh the people
+ 
+
+ align:start position:0%
+uh the people
+there was one guy i can't remember his
+
+ align:start position:0%
+there was one guy i can't remember his
+ 
+
+ align:start position:0%
+there was one guy i can't remember his
+name or worry what organization he
+
+ align:start position:0%
+name or worry what organization he
+ 
+
+ align:start position:0%
+name or worry what organization he
+represented because in the aaes
+
+ align:start position:0%
+represented because in the aaes
+ 
+
+ align:start position:0%
+represented because in the aaes
+everybody was a representative of one of
+
+ align:start position:0%
+everybody was a representative of one of
+ 
+
+ align:start position:0%
+everybody was a representative of one of
+the member organizations
+
+ align:start position:0%
+the member organizations
+ 
+
+ align:start position:0%
+the member organizations
+uh i can't remember what organization
+
+ align:start position:0%
+uh i can't remember what organization
+ 
+
+ align:start position:0%
+uh i can't remember what organization
+but he put it very articulately and he
+
+ align:start position:0%
+but he put it very articulately and he
+ 
+
+ align:start position:0%
+but he put it very articulately and he
+fought very hard for it
+
+ align:start position:0%
+fought very hard for it
+ 
+
+ align:start position:0%
+fought very hard for it
+lost in the end but he brought fair his
+
+ align:start position:0%
+lost in the end but he brought fair his
+ 
+
+ align:start position:0%
+lost in the end but he brought fair his
+uh his argument was
+
+ align:start position:0%
+uh his argument was
+ 
+
+ align:start position:0%
+uh his argument was
+that the two kinds
+
+ align:start position:0%
+that the two kinds
+ 
+
+ align:start position:0%
+that the two kinds
+of engineering organizations big ones
+
+ align:start position:0%
+of engineering organizations big ones
+ 
+
+ align:start position:0%
+of engineering organizations big ones
+and little ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you got a small company out here
+
+ align:start position:0%
+so if you got a small company out here
+ 
+
+ align:start position:0%
+so if you got a small company out here
+let's say the three of you all get
+
+ align:start position:0%
+let's say the three of you all get
+ 
+
+ align:start position:0%
+let's say the three of you all get
+together and say you're gonna
+
+ align:start position:0%
+together and say you're gonna
+ 
+
+ align:start position:0%
+together and say you're gonna
+get incorporated
+
+ align:start position:0%
+get incorporated
+ 
+
+ align:start position:0%
+get incorporated
+and you wind up hiring 20 people
+
+ align:start position:0%
+and you wind up hiring 20 people
+ 
+
+ align:start position:0%
+and you wind up hiring 20 people
+and you're making good money all right
+
+ align:start position:0%
+and you're making good money all right
+ 
+
+ align:start position:0%
+and you're making good money all right
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+something on the job
+
+ align:start position:0%
+something on the job
+ 
+
+ align:start position:0%
+something on the job
+a fuse bus
+
+ align:start position:0%
+a fuse bus
+ 
+
+ align:start position:0%
+a fuse bus
+loose and you have to fix that
+
+ align:start position:0%
+loose and you have to fix that
+ 
+
+ align:start position:0%
+loose and you have to fix that
+electrical wiring you don't have the
+
+ align:start position:0%
+electrical wiring you don't have the
+ 
+
+ align:start position:0%
+electrical wiring you don't have the
+money to be going out to hire an
+
+ align:start position:0%
+money to be going out to hire an
+ 
+
+ align:start position:0%
+money to be going out to hire an
+electrical engineer
+
+ align:start position:0%
+electrical engineer
+ 
+
+ align:start position:0%
+electrical engineer
+to come in on the spot because you got
+
+ align:start position:0%
+to come in on the spot because you got
+ 
+
+ align:start position:0%
+to come in on the spot because you got
+your critical pass schedule you got to
+
+ align:start position:0%
+your critical pass schedule you got to
+ 
+
+ align:start position:0%
+your critical pass schedule you got to
+finish this job today somebody's got to
+
+ align:start position:0%
+finish this job today somebody's got to
+ 
+
+ align:start position:0%
+finish this job today somebody's got to
+go to crawl down and then fix that wire
+
+ align:start position:0%
+go to crawl down and then fix that wire
+ 
+
+ align:start position:0%
+go to crawl down and then fix that wire
+so um the the idea was that uh
+
+ align:start position:0%
+so um the the idea was that uh
+ 
+
+ align:start position:0%
+so um the the idea was that uh
+requiring engineers to perform only in
+
+ align:start position:0%
+requiring engineers to perform only in
+ 
+
+ align:start position:0%
+requiring engineers to perform only in
+the areas of their competence was going
+
+ align:start position:0%
+the areas of their competence was going
+ 
+
+ align:start position:0%
+the areas of their competence was going
+to put the small business engineers out
+
+ align:start position:0%
+to put the small business engineers out
+ 
+
+ align:start position:0%
+to put the small business engineers out
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+can small business sort of find a way
+
+ align:start position:0%
+can small business sort of find a way
+ 
+
+ align:start position:0%
+can small business sort of find a way
+around this campaign
+
+ align:start position:0%
+around this campaign
+ 
+
+ align:start position:0%
+around this campaign
+what happened i think in the end was the
+
+ align:start position:0%
+what happened i think in the end was the
+ 
+
+ align:start position:0%
+what happened i think in the end was the
+small business just kept doing what they
+
+ align:start position:0%
+small business just kept doing what they
+ 
+
+ align:start position:0%
+small business just kept doing what they
+were doing and
+
+ align:start position:0%
+were doing and
+ 
+
+ align:start position:0%
+were doing and
+and they uh
+
+ align:start position:0%
+and they uh
+ 
+
+ align:start position:0%
+and they uh
+no big cases come up
+
+ align:start position:0%
+no big cases come up
+ 
+
+ align:start position:0%
+no big cases come up
+and the basic attitude that we talked
+
+ align:start position:0%
+and the basic attitude that we talked
+ 
+
+ align:start position:0%
+and the basic attitude that we talked
+about when i was chair of the committee
+
+ align:start position:0%
+about when i was chair of the committee
+ 
+
+ align:start position:0%
+about when i was chair of the committee
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+that look um
+
+ align:start position:0%
+that look um
+ 
+
+ align:start position:0%
+that look um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+judges and juries
+
+ align:start position:0%
+judges and juries
+ 
+
+ align:start position:0%
+judges and juries
+are reasonable to some level at some
+
+ align:start position:0%
+are reasonable to some level at some
+ 
+
+ align:start position:0%
+are reasonable to some level at some
+level they
+
+ align:start position:0%
+level they
+ 
+
+ align:start position:0%
+level they
+they're going to know that
+
+ align:start position:0%
+they're going to know that
+ 
+
+ align:start position:0%
+they're going to know that
+you know you're not a concrete foreman
+
+ align:start position:0%
+you know you're not a concrete foreman
+ 
+
+ align:start position:0%
+you know you're not a concrete foreman
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+some you wanted to pour just enough
+
+ align:start position:0%
+some you wanted to pour just enough
+ 
+
+ align:start position:0%
+some you wanted to pour just enough
+concrete in here
+
+ align:start position:0%
+concrete in here
+ 
+
+ align:start position:0%
+concrete in here
+to put
+
+ align:start position:0%
+to put
+ 
+
+ align:start position:0%
+to put
+an electrical apparatus that your
+
+ align:start position:0%
+an electrical apparatus that your
+ 
+
+ align:start position:0%
+an electrical apparatus that your
+company makes on top of
+
+ align:start position:0%
+company makes on top of
+ 
+
+ align:start position:0%
+company makes on top of
+and nobody came in here on time you got
+
+ align:start position:0%
+and nobody came in here on time you got
+ 
+
+ align:start position:0%
+and nobody came in here on time you got
+to do it so somebody said well let's go
+
+ align:start position:0%
+to do it so somebody said well let's go
+ 
+
+ align:start position:0%
+to do it so somebody said well let's go
+mix the concrete i did it for my son's
+
+ align:start position:0%
+mix the concrete i did it for my son's
+ 
+
+ align:start position:0%
+mix the concrete i did it for my son's
+dog house you know
+
+ align:start position:0%
+dog house you know
+ 
+
+ align:start position:0%
+dog house you know
+and you throw it in there somebody the
+
+ align:start position:0%
+and you throw it in there somebody the
+ 
+
+ align:start position:0%
+and you throw it in there somebody the
+jury some jury is going to be
+
+ align:start position:0%
+jury some jury is going to be
+ 
+
+ align:start position:0%
+jury some jury is going to be
+sympathetic to that
+
+ align:start position:0%
+sympathetic to that
+ 
+
+ align:start position:0%
+sympathetic to that
+and just don't let it get out of hand
+
+ align:start position:0%
+and just don't let it get out of hand
+ 
+
+ align:start position:0%
+and just don't let it get out of hand
+don't don't have a nuclear device
+
+ align:start position:0%
+don't don't have a nuclear device
+ 
+
+ align:start position:0%
+don't don't have a nuclear device
+in the product you make that goes bad
+
+ align:start position:0%
+in the product you make that goes bad
+ 
+
+ align:start position:0%
+in the product you make that goes bad
+and you try to fix it
+
+ align:start position:0%
+and you try to fix it
+ 
+
+ align:start position:0%
+and you try to fix it
+don't go crazy so i think that uh what
+
+ align:start position:0%
+don't go crazy so i think that uh what
+ 
+
+ align:start position:0%
+don't go crazy so i think that uh what
+happened with that case was that cooler
+
+ align:start position:0%
+happened with that case was that cooler
+ 
+
+ align:start position:0%
+happened with that case was that cooler
+heads prevailed in the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i think that resolved
+
+ align:start position:0%
+yeah i think that resolved
+ 
+
+ align:start position:0%
+yeah i think that resolved
+some issues because at first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ethical but that's not really what it's
+
+ align:start position:0%
+ethical but that's not really what it's
+ 
+
+ align:start position:0%
+ethical but that's not really what it's
+saying it's saying
+
+ align:start position:0%
+saying it's saying
+ 
+
+ align:start position:0%
+saying it's saying
+it's unethical
+
+ align:start position:0%
+it's unethical
+ 
+
+ align:start position:0%
+it's unethical
+to do something that you're not
+
+ align:start position:0%
+to do something that you're not
+ 
+
+ align:start position:0%
+to do something that you're not
+confident like it's not unethical or not
+
+ align:start position:0%
+confident like it's not unethical or not
+ 
+
+ align:start position:0%
+confident like it's not unethical or not
+you know how to do something until you
+
+ align:start position:0%
+you know how to do something until you
+ 
+
+ align:start position:0%
+you know how to do something until you
+ignore something so maybe that's the
+
+ align:start position:0%
+ignore something so maybe that's the
+ 
+
+ align:start position:0%
+ignore something so maybe that's the
+idea that i play with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you thought more was this at first
+
+ align:start position:0%
+you thought more was this at first
+ 
+
+ align:start position:0%
+you thought more was this at first
+glance i think we've had a conversation
+
+ align:start position:0%
+glance i think we've had a conversation
+ 
+
+ align:start position:0%
+glance i think we've had a conversation
+before about i think it was going to
+
+ align:start position:0%
+before about i think it was going to
+ 
+
+ align:start position:0%
+before about i think it was going to
+know what we were talking about
+
+ align:start position:0%
+know what we were talking about
+ 
+
+ align:start position:0%
+know what we were talking about
+yeah competency came up in chernobyl
+
+ align:start position:0%
+yeah competency came up in chernobyl
+ 
+
+ align:start position:0%
+yeah competency came up in chernobyl
+so yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that that's what's unethical attention
+
+ align:start position:0%
+that that's what's unethical attention
+ 
+
+ align:start position:0%
+that that's what's unethical attention
+to not necessarily that
+
+ align:start position:0%
+to not necessarily that
+ 
+
+ align:start position:0%
+to not necessarily that
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+maybe you're not great at it and you try
+
+ align:start position:0%
+maybe you're not great at it and you try
+ 
+
+ align:start position:0%
+maybe you're not great at it and you try
+and fail nothing ethically is wrong it's
+
+ align:start position:0%
+and fail nothing ethically is wrong it's
+ 
+
+ align:start position:0%
+and fail nothing ethically is wrong it's
+just you've actually tried an attempt to
+
+ align:start position:0%
+just you've actually tried an attempt to
+ 
+
+ align:start position:0%
+just you've actually tried an attempt to
+do something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that's that was one of the big
+
+ align:start position:0%
+well that's that was one of the big
+ 
+
+ align:start position:0%
+well that's that was one of the big
+issues that i brought to the table as a
+
+ align:start position:0%
+issues that i brought to the table as a
+ 
+
+ align:start position:0%
+issues that i brought to the table as a
+person who had studied ethics formally
+
+ align:start position:0%
+person who had studied ethics formally
+ 
+
+ align:start position:0%
+person who had studied ethics formally
+uh that
+
+ align:start position:0%
+uh that
+ 
+
+ align:start position:0%
+uh that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+but engineers had very strong sentiments
+
+ align:start position:0%
+but engineers had very strong sentiments
+ 
+
+ align:start position:0%
+but engineers had very strong sentiments
+that if you didn't know
+
+ align:start position:0%
+that if you didn't know
+ 
+
+ align:start position:0%
+that if you didn't know
+how to solve a certain kind of problem
+
+ align:start position:0%
+how to solve a certain kind of problem
+ 
+
+ align:start position:0%
+how to solve a certain kind of problem
+you were unethical
+
+ align:start position:0%
+you were unethical
+ 
+
+ align:start position:0%
+you were unethical
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+and i tried to tell them no
+
+ align:start position:0%
+and i tried to tell them no
+ 
+
+ align:start position:0%
+and i tried to tell them no
+you got to separate that out
+
+ align:start position:0%
+you got to separate that out
+ 
+
+ align:start position:0%
+you got to separate that out
+and in the end cooler heads prevailed on
+
+ align:start position:0%
+and in the end cooler heads prevailed on
+ 
+
+ align:start position:0%
+and in the end cooler heads prevailed on
+that one too
+
+ align:start position:0%
+that one too
+ 
+
+ align:start position:0%
+that one too
+but uh there was a basic sentiment among
+
+ align:start position:0%
+but uh there was a basic sentiment among
+ 
+
+ align:start position:0%
+but uh there was a basic sentiment among
+engineers that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if there were certain things you
+
+ align:start position:0%
+that if there were certain things you
+ 
+
+ align:start position:0%
+that if there were certain things you
+didn't know
+
+ align:start position:0%
+didn't know
+ 
+
+ align:start position:0%
+didn't know
+and you shouldn't be practicing
+
+ align:start position:0%
+and you shouldn't be practicing
+ 
+
+ align:start position:0%
+and you shouldn't be practicing
+and it was unethical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i'll tell you what made their arguments
+
+ align:start position:0%
+i'll tell you what made their arguments
+ 
+
+ align:start position:0%
+i'll tell you what made their arguments
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strong if not entirely compelling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they would make a metaphor with
+
+ align:start position:0%
+they would make a metaphor with
+ 
+
+ align:start position:0%
+they would make a metaphor with
+physicians
+
+ align:start position:0%
+physicians
+ 
+
+ align:start position:0%
+physicians
+okay so you're sitting up there your
+
+ align:start position:0%
+okay so you're sitting up there your
+ 
+
+ align:start position:0%
+okay so you're sitting up there your
+heart is going bad you're about to die
+
+ align:start position:0%
+heart is going bad you're about to die
+ 
+
+ align:start position:0%
+heart is going bad you're about to die
+the physician comes in saying well i
+
+ align:start position:0%
+the physician comes in saying well i
+ 
+
+ align:start position:0%
+the physician comes in saying well i
+never studied the heart but i i will cut
+
+ align:start position:0%
+never studied the heart but i i will cut
+ 
+
+ align:start position:0%
+never studied the heart but i i will cut
+your heart out today anyway i mean you
+
+ align:start position:0%
+your heart out today anyway i mean you
+ 
+
+ align:start position:0%
+your heart out today anyway i mean you
+know part of it i now there's there's
+
+ align:start position:0%
+know part of it i now there's there's
+ 
+
+ align:start position:0%
+know part of it i now there's there's
+something unethical and competency tied
+
+ align:start position:0%
+something unethical and competency tied
+ 
+
+ align:start position:0%
+something unethical and competency tied
+into that
+
+ align:start position:0%
+into that
+ 
+
+ align:start position:0%
+into that
+and then they make the metaphor back to
+
+ align:start position:0%
+and then they make the metaphor back to
+ 
+
+ align:start position:0%
+and then they make the metaphor back to
+engineering and engineers start thinking
+
+ align:start position:0%
+engineering and engineers start thinking
+ 
+
+ align:start position:0%
+engineering and engineers start thinking
+and we have to hold it maybe cooler
+
+ align:start position:0%
+and we have to hold it maybe cooler
+ 
+
+ align:start position:0%
+and we have to hold it maybe cooler
+heads have prevailed in these situations
+
+ align:start position:0%
+heads have prevailed in these situations
+ 
+
+ align:start position:0%
+heads have prevailed in these situations
+okay but that was hot that was a hot
+
+ align:start position:0%
+okay but that was hot that was a hot
+ 
+
+ align:start position:0%
+okay but that was hot that was a hot
+issue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and we're not pouring concrete for a
+
+ align:start position:0%
+and we're not pouring concrete for a
+ 
+
+ align:start position:0%
+and we're not pouring concrete for a
+column that's going to sustain
+
+ align:start position:0%
+column that's going to sustain
+ 
+
+ align:start position:0%
+column that's going to sustain
+30 stories
+
+ align:start position:0%
+30 stories
+ 
+
+ align:start position:0%
+30 stories
+of stuff on top we just have a little
+
+ align:start position:0%
+of stuff on top we just have a little
+ 
+
+ align:start position:0%
+of stuff on top we just have a little
+thing over
+
+ align:start position:0%
+thing over
+ 
+
+ align:start position:0%
+thing over
+if it cracks
+
+ align:start position:0%
+if it cracks
+ 
+
+ align:start position:0%
+if it cracks
+then we'll pay for it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you try to work that's
+
+ align:start position:0%
+you try to work that's
+ 
+
+ align:start position:0%
+you try to work that's
+you know cooler has prevail in the
+
+ align:start position:0%
+you know cooler has prevail in the
+ 
+
+ align:start position:0%
+you know cooler has prevail in the
+courtroom sometimes take your
+
+ align:start position:0%
+courtroom sometimes take your
+ 
+
+ align:start position:0%
+courtroom sometimes take your
+chances but um i think that underneath
+
+ align:start position:0%
+chances but um i think that underneath
+ 
+
+ align:start position:0%
+chances but um i think that underneath
+the surface
+
+ align:start position:0%
+the surface
+ 
+
+ align:start position:0%
+the surface
+remember i told you there are certain
+
+ align:start position:0%
+remember i told you there are certain
+ 
+
+ align:start position:0%
+remember i told you there are certain
+things operating
+
+ align:start position:0%
+things operating
+ 
+
+ align:start position:0%
+things operating
+uh underneath the surface of discussion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that nobody would deny and sometimes
+
+ align:start position:0%
+that nobody would deny and sometimes
+ 
+
+ align:start position:0%
+that nobody would deny and sometimes
+some of it has been written one is that
+
+ align:start position:0%
+some of it has been written one is that
+ 
+
+ align:start position:0%
+some of it has been written one is that
+engineers always felt
+
+ align:start position:0%
+engineers always felt
+ 
+
+ align:start position:0%
+engineers always felt
+and probably still feel
+
+ align:start position:0%
+and probably still feel
+ 
+
+ align:start position:0%
+and probably still feel
+that they are not uh accepted as
+
+ align:start position:0%
+that they are not uh accepted as
+ 
+
+ align:start position:0%
+that they are not uh accepted as
+professionals like doctors and lawyers
+
+ align:start position:0%
+professionals like doctors and lawyers
+ 
+
+ align:start position:0%
+professionals like doctors and lawyers
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and they're proud of their profession
+
+ align:start position:0%
+and they're proud of their profession
+ 
+
+ align:start position:0%
+and they're proud of their profession
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+mainly
+
+ align:start position:0%
+mainly
+ 
+
+ align:start position:0%
+mainly
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+not because of the good things that are
+
+ align:start position:0%
+not because of the good things that are
+ 
+
+ align:start position:0%
+not because of the good things that are
+here in this preamble
+
+ align:start position:0%
+here in this preamble
+ 
+
+ align:start position:0%
+here in this preamble
+but because actually what you had said
+
+ align:start position:0%
+but because actually what you had said
+ 
+
+ align:start position:0%
+but because actually what you had said
+ms best yeah a couple classes ago and
+
+ align:start position:0%
+ms best yeah a couple classes ago and
+ 
+
+ align:start position:0%
+ms best yeah a couple classes ago and
+that was they know what it was like to
+
+ align:start position:0%
+that was they know what it was like to
+ 
+
+ align:start position:0%
+that was they know what it was like to
+be in school
+
+ align:start position:0%
+be in school
+ 
+
+ align:start position:0%
+be in school
+and take hard courses when everybody
+
+ align:start position:0%
+and take hard courses when everybody
+ 
+
+ align:start position:0%
+and take hard courses when everybody
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+could not pass these courses and we not
+
+ align:start position:0%
+could not pass these courses and we not
+ 
+
+ align:start position:0%
+could not pass these courses and we not
+only had to pass them but do well in
+
+ align:start position:0%
+only had to pass them but do well in
+ 
+
+ align:start position:0%
+only had to pass them but do well in
+them in order to get a degree
+
+ align:start position:0%
+them in order to get a degree
+ 
+
+ align:start position:0%
+them in order to get a degree
+and there's a lot and there's a and
+
+ align:start position:0%
+and there's a lot and there's a and
+ 
+
+ align:start position:0%
+and there's a lot and there's a and
+there is under the surface
+
+ align:start position:0%
+there is under the surface
+ 
+
+ align:start position:0%
+there is under the surface
+in engineering
+
+ align:start position:0%
+in engineering
+ 
+
+ align:start position:0%
+in engineering
+there is a little bit of bitterness
+
+ align:start position:0%
+there is a little bit of bitterness
+ 
+
+ align:start position:0%
+there is a little bit of bitterness
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+all of that
+
+ align:start position:0%
+all of that
+ 
+
+ align:start position:0%
+all of that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i know of one case
+
+ align:start position:0%
+i know of one case
+ 
+
+ align:start position:0%
+i know of one case
+where there was this professor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh who had something like two or three
+
+ align:start position:0%
+uh who had something like two or three
+ 
+
+ align:start position:0%
+uh who had something like two or three
+hundred publications
+
+ align:start position:0%
+hundred publications
+ 
+
+ align:start position:0%
+hundred publications
+was editor of three journals actually
+
+ align:start position:0%
+was editor of three journals actually
+ 
+
+ align:start position:0%
+was editor of three journals actually
+the guy who told me said it was in her
+
+ align:start position:0%
+the guy who told me said it was in her
+ 
+
+ align:start position:0%
+the guy who told me said it was in her
+four journals
+
+ align:start position:0%
+four journals
+ 
+
+ align:start position:0%
+four journals
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+was a consultant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you want the answer
+
+ align:start position:0%
+you want the answer
+ 
+
+ align:start position:0%
+you want the answer
+it is a term it has two words it's
+
+ align:start position:0%
+it is a term it has two words it's
+ 
+
+ align:start position:0%
+it is a term it has two words it's
+called graduate students
+
+ align:start position:0%
+called graduate students
+ 
+
+ align:start position:0%
+called graduate students
+[Laughter]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+and uh he's at the top of his profession
+
+ align:start position:0%
+and uh he's at the top of his profession
+ 
+
+ align:start position:0%
+and uh he's at the top of his profession
+he had this one student
+
+ align:start position:0%
+he had this one student
+ 
+
+ align:start position:0%
+he had this one student
+that got a master's degree under him
+
+ align:start position:0%
+that got a master's degree under him
+ 
+
+ align:start position:0%
+that got a master's degree under him
+just barely got through
+
+ align:start position:0%
+just barely got through
+ 
+
+ align:start position:0%
+just barely got through
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+five or six ten years later that
+
+ align:start position:0%
+five or six ten years later that
+ 
+
+ align:start position:0%
+five or six ten years later that
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+former student gave a party to his house
+
+ align:start position:0%
+former student gave a party to his house
+ 
+
+ align:start position:0%
+former student gave a party to his house
+he had gone out and had made a little
+
+ align:start position:0%
+he had gone out and had made a little
+ 
+
+ align:start position:0%
+he had gone out and had made a little
+gotten a little business and
+
+ align:start position:0%
+gotten a little business and
+ 
+
+ align:start position:0%
+gotten a little business and
+became successful
+
+ align:start position:0%
+became successful
+ 
+
+ align:start position:0%
+became successful
+and when the professor went to the party
+
+ align:start position:0%
+and when the professor went to the party
+ 
+
+ align:start position:0%
+and when the professor went to the party
+the house was three times as big as the
+
+ align:start position:0%
+the house was three times as big as the
+ 
+
+ align:start position:0%
+the house was three times as big as the
+professor's house
+
+ align:start position:0%
+professor's house
+ 
+
+ align:start position:0%
+professor's house
+had a rolls royce
+
+ align:start position:0%
+had a rolls royce
+ 
+
+ align:start position:0%
+had a rolls royce
+and you know one of the four parking
+
+ align:start position:0%
+and you know one of the four parking
+ 
+
+ align:start position:0%
+and you know one of the four parking
+garages had four full chimneys you know
+
+ align:start position:0%
+garages had four full chimneys you know
+ 
+
+ align:start position:0%
+garages had four full chimneys you know
+the whole bit
+
+ align:start position:0%
+the whole bit
+ 
+
+ align:start position:0%
+the whole bit
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the story goes on about how this man
+
+ align:start position:0%
+the story goes on about how this man
+ 
+
+ align:start position:0%
+the story goes on about how this man
+began to drink and wound up in
+
+ align:start position:0%
+began to drink and wound up in
+ 
+
+ align:start position:0%
+began to drink and wound up in
+a in a home
+
+ align:start position:0%
+a in a home
+ 
+
+ align:start position:0%
+a in a home
+the professor
+
+ align:start position:0%
+the professor
+ 
+
+ align:start position:0%
+the professor
+i just tore him up so you get one story
+
+ align:start position:0%
+i just tore him up so you get one story
+ 
+
+ align:start position:0%
+i just tore him up so you get one story
+out there there was another story that
+
+ align:start position:0%
+out there there was another story that
+ 
+
+ align:start position:0%
+out there there was another story that
+hit the newspapers i know about this
+
+ align:start position:0%
+hit the newspapers i know about this
+ 
+
+ align:start position:0%
+hit the newspapers i know about this
+story personally
+
+ align:start position:0%
+story personally
+ 
+
+ align:start position:0%
+story personally
+uh because this particular professor
+
+ align:start position:0%
+uh because this particular professor
+ 
+
+ align:start position:0%
+uh because this particular professor
+taught me a class in graduate school
+
+ align:start position:0%
+taught me a class in graduate school
+ 
+
+ align:start position:0%
+taught me a class in graduate school
+it turns out that this particular i
+
+ align:start position:0%
+it turns out that this particular i
+ 
+
+ align:start position:0%
+it turns out that this particular i
+won't call a name because in order to
+
+ align:start position:0%
+won't call a name because in order to
+ 
+
+ align:start position:0%
+won't call a name because in order to
+call the name i have to get all my facts
+
+ align:start position:0%
+call the name i have to get all my facts
+ 
+
+ align:start position:0%
+call the name i have to get all my facts
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but the facts are not only
+
+ align:start position:0%
+but the facts are not only
+ 
+
+ align:start position:0%
+but the facts are not only
+on the record in the courts but they're
+
+ align:start position:0%
+on the record in the courts but they're
+ 
+
+ align:start position:0%
+on the record in the courts but they're
+in the newspapers this was nnaaup
+
+ align:start position:0%
+in the newspapers this was nnaaup
+ 
+
+ align:start position:0%
+in the newspapers this was nnaaup
+all kinds of stuff but this professor
+
+ align:start position:0%
+all kinds of stuff but this professor
+ 
+
+ align:start position:0%
+all kinds of stuff but this professor
+turns out he was um
+
+ align:start position:0%
+turns out he was um
+ 
+
+ align:start position:0%
+turns out he was um
+a very good teacher
+
+ align:start position:0%
+a very good teacher
+ 
+
+ align:start position:0%
+a very good teacher
+and had published some textbooks i'm
+
+ align:start position:0%
+and had published some textbooks i'm
+ 
+
+ align:start position:0%
+and had published some textbooks i'm
+talking about springer verlag
+
+ align:start position:0%
+talking about springer verlag
+ 
+
+ align:start position:0%
+talking about springer verlag
+top of the line textbooks required
+
+ align:start position:0%
+top of the line textbooks required
+ 
+
+ align:start position:0%
+top of the line textbooks required
+reading at mit stanford berkeley
+
+ align:start position:0%
+reading at mit stanford berkeley
+ 
+
+ align:start position:0%
+reading at mit stanford berkeley
+princeton okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and but he did not have any research
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+none whatsoever he was just a teacher
+
+ align:start position:0%
+none whatsoever he was just a teacher
+ 
+
+ align:start position:0%
+none whatsoever he was just a teacher
+then it came out
+
+ align:start position:0%
+then it came out
+ 
+
+ align:start position:0%
+then it came out
+that he was a full professor
+
+ align:start position:0%
+that he was a full professor
+ 
+
+ align:start position:0%
+that he was a full professor
+with tenure
+
+ align:start position:0%
+with tenure
+ 
+
+ align:start position:0%
+with tenure
+with a full-time appointment at three
+
+ align:start position:0%
+with a full-time appointment at three
+ 
+
+ align:start position:0%
+with a full-time appointment at three
+different universities
+
+ align:start position:0%
+different universities
+ 
+
+ align:start position:0%
+different universities
+simultaneously
+
+ align:start position:0%
+simultaneously
+ 
+
+ align:start position:0%
+simultaneously
+and he had his schedule made out so that
+
+ align:start position:0%
+and he had his schedule made out so that
+ 
+
+ align:start position:0%
+and he had his schedule made out so that
+at one place he had courses only monday
+
+ align:start position:0%
+at one place he had courses only monday
+ 
+
+ align:start position:0%
+at one place he had courses only monday
+wednesday and friday in the morning
+
+ align:start position:0%
+wednesday and friday in the morning
+ 
+
+ align:start position:0%
+wednesday and friday in the morning
+and other places monday wednesday and
+
+ align:start position:0%
+and other places monday wednesday and
+ 
+
+ align:start position:0%
+and other places monday wednesday and
+friday in the afternoon
+
+ align:start position:0%
+friday in the afternoon
+ 
+
+ align:start position:0%
+friday in the afternoon
+and then the one that was out of town in
+
+ align:start position:0%
+and then the one that was out of town in
+ 
+
+ align:start position:0%
+and then the one that was out of town in
+pennsylvania he was in washington
+
+ align:start position:0%
+pennsylvania he was in washington
+ 
+
+ align:start position:0%
+pennsylvania he was in washington
+was in uh tuesday thursday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they called him and uh they roasted
+
+ align:start position:0%
+and they called him and uh they roasted
+ 
+
+ align:start position:0%
+and they called him and uh they roasted
+him on a spit but
+
+ align:start position:0%
+him on a spit but
+ 
+
+ align:start position:0%
+him on a spit but
+there was a lot of sympathy for his case
+
+ align:start position:0%
+there was a lot of sympathy for his case
+ 
+
+ align:start position:0%
+there was a lot of sympathy for his case
+a lot of other factors came in
+
+ align:start position:0%
+a lot of other factors came in
+ 
+
+ align:start position:0%
+a lot of other factors came in
+he had a daughter that was sick and his
+
+ align:start position:0%
+he had a daughter that was sick and his
+ 
+
+ align:start position:0%
+he had a daughter that was sick and his
+wife was dead you know about all of
+
+ align:start position:0%
+wife was dead you know about all of
+ 
+
+ align:start position:0%
+wife was dead you know about all of
+these things but there was one other
+
+ align:start position:0%
+these things but there was one other
+ 
+
+ align:start position:0%
+these things but there was one other
+factor that came in there that really
+
+ align:start position:0%
+factor that came in there that really
+ 
+
+ align:start position:0%
+factor that came in there that really
+worked on the academic profession very
+
+ align:start position:0%
+worked on the academic profession very
+ 
+
+ align:start position:0%
+worked on the academic profession very
+hard and that was
+
+ align:start position:0%
+hard and that was
+ 
+
+ align:start position:0%
+hard and that was
+is this what a good teacher has to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order just to make pay bills and
+
+ align:start position:0%
+in order just to make pay bills and
+ 
+
+ align:start position:0%
+in order just to make pay bills and
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+you know maybe we're doing too much to
+
+ align:start position:0%
+you know maybe we're doing too much to
+ 
+
+ align:start position:0%
+you know maybe we're doing too much to
+emphasize the research part of it
+
+ align:start position:0%
+emphasize the research part of it
+ 
+
+ align:start position:0%
+emphasize the research part of it
+and so uh his his case has never been
+
+ align:start position:0%
+and so uh his his case has never been
+ 
+
+ align:start position:0%
+and so uh his his case has never been
+forgotten
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh under excuse me underneath the
+
+ align:start position:0%
+so uh under excuse me underneath the
+ 
+
+ align:start position:0%
+so uh under excuse me underneath the
+surface you have all of these currents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the issue was that it was uh that it was
+
+ align:start position:0%
+the issue was that it was uh that it was
+ 
+
+ align:start position:0%
+the issue was that it was uh that it was
+illegal
+
+ align:start position:0%
+illegal
+ 
+
+ align:start position:0%
+illegal
+that you cannot the issue was that the
+
+ align:start position:0%
+that you cannot the issue was that the
+ 
+
+ align:start position:0%
+that you cannot the issue was that the
+pro
+
+ align:start position:0%
+pro
+ 
+
+ align:start position:0%
+pro
+they want
+
+ align:start position:0%
+they want
+ 
+
+ align:start position:0%
+they want
+the president want to fire him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh what and
+
+ align:start position:0%
+uh what and
+ 
+
+ align:start position:0%
+uh what and
+there was a lot of debate on one side or
+
+ align:start position:0%
+there was a lot of debate on one side or
+ 
+
+ align:start position:0%
+there was a lot of debate on one side or
+the other as to whether or not
+
+ align:start position:0%
+the other as to whether or not
+ 
+
+ align:start position:0%
+the other as to whether or not
+a faculty member can have more than one
+
+ align:start position:0%
+a faculty member can have more than one
+ 
+
+ align:start position:0%
+a faculty member can have more than one
+job and
+
+ align:start position:0%
+job and
+ 
+
+ align:start position:0%
+job and
+they they pointed to this
+
+ align:start position:0%
+they they pointed to this
+ 
+
+ align:start position:0%
+they they pointed to this
+tradition of the one day a week
+
+ align:start position:0%
+tradition of the one day a week
+ 
+
+ align:start position:0%
+tradition of the one day a week
+consulting
+
+ align:start position:0%
+consulting
+ 
+
+ align:start position:0%
+consulting
+that when you that there's this
+
+ align:start position:0%
+that when you that there's this
+ 
+
+ align:start position:0%
+that when you that there's this
+understanding
+
+ align:start position:0%
+understanding
+ 
+
+ align:start position:0%
+understanding
+that when you take on a faculty position
+
+ align:start position:0%
+that when you take on a faculty position
+ 
+
+ align:start position:0%
+that when you take on a faculty position
+you've got one day a week
+
+ align:start position:0%
+you've got one day a week
+ 
+
+ align:start position:0%
+you've got one day a week
+to do what you want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that usually means
+
+ align:start position:0%
+and that usually means
+ 
+
+ align:start position:0%
+and that usually means
+consulting or doing something that
+
+ align:start position:0%
+consulting or doing something that
+ 
+
+ align:start position:0%
+consulting or doing something that
+will enhance your abilities to do
+
+ align:start position:0%
+will enhance your abilities to do
+ 
+
+ align:start position:0%
+will enhance your abilities to do
+teaching and research
+
+ align:start position:0%
+teaching and research
+ 
+
+ align:start position:0%
+teaching and research
+you're not going to the beach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but it's up to you to decide is that
+
+ align:start position:0%
+but but it's up to you to decide is that
+ 
+
+ align:start position:0%
+but but it's up to you to decide is that
+it's just an understanding that has been
+
+ align:start position:0%
+it's just an understanding that has been
+ 
+
+ align:start position:0%
+it's just an understanding that has been
+the case for many many years and it has
+
+ align:start position:0%
+the case for many many years and it has
+ 
+
+ align:start position:0%
+the case for many many years and it has
+influence in the courts
+
+ align:start position:0%
+influence in the courts
+ 
+
+ align:start position:0%
+influence in the courts
+courts say this is they'll get all of
+
+ align:start position:0%
+courts say this is they'll get all of
+ 
+
+ align:start position:0%
+courts say this is they'll get all of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+college presidents and people get up and
+
+ align:start position:0%
+college presidents and people get up and
+ 
+
+ align:start position:0%
+college presidents and people get up and
+say yeah that's it's just understood
+
+ align:start position:0%
+say yeah that's it's just understood
+ 
+
+ align:start position:0%
+say yeah that's it's just understood
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you get you suppose you're supposed to
+
+ align:start position:0%
+you get you suppose you're supposed to
+ 
+
+ align:start position:0%
+you get you suppose you're supposed to
+get that one day but to go and have two
+
+ align:start position:0%
+get that one day but to go and have two
+ 
+
+ align:start position:0%
+get that one day but to go and have two
+other full-time jobs
+
+ align:start position:0%
+other full-time jobs
+ 
+
+ align:start position:0%
+other full-time jobs
+and not only that but when you take a
+
+ align:start position:0%
+and not only that but when you take a
+ 
+
+ align:start position:0%
+and not only that but when you take a
+job there's some kind of form you sign
+
+ align:start position:0%
+job there's some kind of form you sign
+ 
+
+ align:start position:0%
+job there's some kind of form you sign
+about are you employed someplace else so
+
+ align:start position:0%
+about are you employed someplace else so
+ 
+
+ align:start position:0%
+about are you employed someplace else so
+they'll talk about conflicts of interest
+
+ align:start position:0%
+they'll talk about conflicts of interest
+ 
+
+ align:start position:0%
+they'll talk about conflicts of interest
+now right and
+
+ align:start position:0%
+now right and
+ 
+
+ align:start position:0%
+now right and
+for example uh here i'm on this
+
+ align:start position:0%
+for example uh here i'm on this
+ 
+
+ align:start position:0%
+for example uh here i'm on this
+sabbatical
+
+ align:start position:0%
+sabbatical
+ 
+
+ align:start position:0%
+sabbatical
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i'm asked to join the editorial board of
+
+ align:start position:0%
+i'm asked to join the editorial board of
+ 
+
+ align:start position:0%
+i'm asked to join the editorial board of
+this journal
+
+ align:start position:0%
+this journal
+ 
+
+ align:start position:0%
+this journal
+they say how should we list you howard
+
+ align:start position:0%
+they say how should we list you howard
+ 
+
+ align:start position:0%
+they say how should we list you howard
+or mit
+
+ align:start position:0%
+or mit
+ 
+
+ align:start position:0%
+or mit
+well i learned long time ago
+
+ align:start position:0%
+well i learned long time ago
+ 
+
+ align:start position:0%
+well i learned long time ago
+that if you are on sabbatical from
+
+ align:start position:0%
+that if you are on sabbatical from
+ 
+
+ align:start position:0%
+that if you are on sabbatical from
+howard
+
+ align:start position:0%
+howard
+ 
+
+ align:start position:0%
+howard
+to another institution that year you're
+
+ align:start position:0%
+to another institution that year you're
+ 
+
+ align:start position:0%
+to another institution that year you're
+at the other institution
+
+ align:start position:0%
+at the other institution
+ 
+
+ align:start position:0%
+at the other institution
+when you go back
+
+ align:start position:0%
+when you go back
+ 
+
+ align:start position:0%
+when you go back
+then you go back on the other one
+
+ align:start position:0%
+then you go back on the other one
+ 
+
+ align:start position:0%
+then you go back on the other one
+uh and and the the institution
+
+ align:start position:0%
+uh and and the the institution
+ 
+
+ align:start position:0%
+uh and and the the institution
+where you are uh on the sabbatical two
+
+ align:start position:0%
+where you are uh on the sabbatical two
+ 
+
+ align:start position:0%
+where you are uh on the sabbatical two
+uh will have some
+
+ align:start position:0%
+uh will have some
+ 
+
+ align:start position:0%
+uh will have some
+mean-spirited ideas if you uh don't give
+
+ align:start position:0%
+mean-spirited ideas if you uh don't give
+ 
+
+ align:start position:0%
+mean-spirited ideas if you uh don't give
+them the recognition and don't give them
+
+ align:start position:0%
+them the recognition and don't give them
+ 
+
+ align:start position:0%
+them the recognition and don't give them
+the prominent recognition
+
+ align:start position:0%
+the prominent recognition
+ 
+
+ align:start position:0%
+the prominent recognition
+and they don't even like it if they say
+
+ align:start position:0%
+and they don't even like it if they say
+ 
+
+ align:start position:0%
+and they don't even like it if they say
+mit slash howard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um so i might by dean and understand
+
+ align:start position:0%
+so um so i might by dean and understand
+ 
+
+ align:start position:0%
+so um so i might by dean and understand
+and i understand it what had oh i tell
+
+ align:start position:0%
+and i understand it what had oh i tell
+ 
+
+ align:start position:0%
+and i understand it what had oh i tell
+you what even set him up one day i
+
+ align:start position:0%
+you what even set him up one day i
+ 
+
+ align:start position:0%
+you what even set him up one day i
+published a paper and put down duke
+
+ align:start position:0%
+published a paper and put down duke
+ 
+
+ align:start position:0%
+published a paper and put down duke
+university
+
+ align:start position:0%
+university
+ 
+
+ align:start position:0%
+university
+he said wait
+
+ align:start position:0%
+he said wait
+ 
+
+ align:start position:0%
+he said wait
+are you going to submit that for uh for
+
+ align:start position:0%
+are you going to submit that for uh for
+ 
+
+ align:start position:0%
+are you going to submit that for uh for
+a raise
+
+ align:start position:0%
+a raise
+ 
+
+ align:start position:0%
+a raise
+so yeah i said well it's got duke
+
+ align:start position:0%
+so yeah i said well it's got duke
+ 
+
+ align:start position:0%
+so yeah i said well it's got duke
+university on there i said yeah
+
+ align:start position:0%
+university on there i said yeah
+ 
+
+ align:start position:0%
+university on there i said yeah
+sabbatical from howard university and
+
+ align:start position:0%
+sabbatical from howard university and
+ 
+
+ align:start position:0%
+sabbatical from howard university and
+here's my
+
+ align:start position:0%
+here's my
+ 
+
+ align:start position:0%
+here's my
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in other words there are some lower
+
+ align:start position:0%
+so in other words there are some lower
+ 
+
+ align:start position:0%
+so in other words there are some lower
+level issues
+
+ align:start position:0%
+level issues
+ 
+
+ align:start position:0%
+level issues
+that are not contested they have legal
+
+ align:start position:0%
+that are not contested they have legal
+ 
+
+ align:start position:0%
+that are not contested they have legal
+standing and this particular one with
+
+ align:start position:0%
+standing and this particular one with
+ 
+
+ align:start position:0%
+standing and this particular one with
+this professor was sort of on the cusp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he found out that what they did in the
+
+ align:start position:0%
+he found out that what they did in the
+ 
+
+ align:start position:0%
+he found out that what they did in the
+end was they just all three of them
+
+ align:start position:0%
+end was they just all three of them
+ 
+
+ align:start position:0%
+end was they just all three of them
+all three universities fired him but
+
+ align:start position:0%
+all three universities fired him but
+ 
+
+ align:start position:0%
+all three universities fired him but
+they get what one of they gave him his
+
+ align:start position:0%
+they get what one of they gave him his
+ 
+
+ align:start position:0%
+they get what one of they gave him his
+return
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but uh it remains
+
+ align:start position:0%
+but uh it remains
+ 
+
+ align:start position:0%
+but uh it remains
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+you know the term uh skeletons in the
+
+ align:start position:0%
+you know the term uh skeletons in the
+ 
+
+ align:start position:0%
+you know the term uh skeletons in the
+closet
+
+ align:start position:0%
+closet
+ 
+
+ align:start position:0%
+closet
+where you've got a family and they're
+
+ align:start position:0%
+where you've got a family and they're
+ 
+
+ align:start position:0%
+where you've got a family and they're
+little things that everybody knows about
+
+ align:start position:0%
+little things that everybody knows about
+ 
+
+ align:start position:0%
+little things that everybody knows about
+but you don't want everybody else to
+
+ align:start position:0%
+but you don't want everybody else to
+ 
+
+ align:start position:0%
+but you don't want everybody else to
+know about
+
+ align:start position:0%
+know about
+ 
+
+ align:start position:0%
+know about
+in the academic profession he's a
+
+ align:start position:0%
+in the academic profession he's a
+ 
+
+ align:start position:0%
+in the academic profession he's a
+skeleton in our closet we
+
+ align:start position:0%
+skeleton in our closet we
+ 
+
+ align:start position:0%
+skeleton in our closet we
+really don't want other people to know
+
+ align:start position:0%
+really don't want other people to know
+ 
+
+ align:start position:0%
+really don't want other people to know
+about his case
+
+ align:start position:0%
+about his case
+ 
+
+ align:start position:0%
+about his case
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the only thing about it that i am i
+
+ align:start position:0%
+the only thing about it that i am i
+ 
+
+ align:start position:0%
+the only thing about it that i am i
+suffer some bitterness over that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and um
+
+ align:start position:0%
+uh and um
+ 
+
+ align:start position:0%
+uh and um
+i made one or two phone calls about it
+
+ align:start position:0%
+i made one or two phone calls about it
+ 
+
+ align:start position:0%
+i made one or two phone calls about it
+because i was a former student
+
+ align:start position:0%
+because i was a former student
+ 
+
+ align:start position:0%
+because i was a former student
+uh and i was bitter that there just
+
+ align:start position:0%
+uh and i was bitter that there just
+ 
+
+ align:start position:0%
+uh and i was bitter that there just
+didn't seem to be interest among
+
+ align:start position:0%
+didn't seem to be interest among
+ 
+
+ align:start position:0%
+didn't seem to be interest among
+students
+
+ align:start position:0%
+students
+ 
+
+ align:start position:0%
+students
+that here's a teacher
+
+ align:start position:0%
+that here's a teacher
+ 
+
+ align:start position:0%
+that here's a teacher
+that quote unquote just can't make it
+
+ align:start position:0%
+that quote unquote just can't make it
+ 
+
+ align:start position:0%
+that quote unquote just can't make it
+in his life
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so anyway but a whole lot of other
+
+ align:start position:0%
+so anyway but a whole lot of other
+ 
+
+ align:start position:0%
+so anyway but a whole lot of other
+issues got involved and they were nasty
+
+ align:start position:0%
+issues got involved and they were nasty
+ 
+
+ align:start position:0%
+issues got involved and they were nasty
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+and people just want to sweep it under
+
+ align:start position:0%
+and people just want to sweep it under
+ 
+
+ align:start position:0%
+and people just want to sweep it under
+the table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and but i think one thing they've done
+
+ align:start position:0%
+and but i think one thing they've done
+ 
+
+ align:start position:0%
+and but i think one thing they've done
+about that here at mit is
+
+ align:start position:0%
+about that here at mit is
+ 
+
+ align:start position:0%
+about that here at mit is
+they have a rank called a teaching
+
+ align:start position:0%
+they have a rank called a teaching
+ 
+
+ align:start position:0%
+they have a rank called a teaching
+professor
+
+ align:start position:0%
+professor
+ 
+
+ align:start position:0%
+professor
+i know that there's a person in esd
+
+ align:start position:0%
+i know that there's a person in esd
+ 
+
+ align:start position:0%
+i know that there's a person in esd
+that's called
+
+ align:start position:0%
+that's called
+ 
+
+ align:start position:0%
+that's called
+that has a
+
+ align:start position:0%
+that has a
+ 
+
+ align:start position:0%
+that has a
+rank of teaching yeah
+
+ align:start position:0%
+rank of teaching yeah
+ 
+
+ align:start position:0%
+rank of teaching yeah
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+it's called teaching professor
+
+ align:start position:0%
+it's called teaching professor
+ 
+
+ align:start position:0%
+it's called teaching professor
+uh it's chris mcgee
+
+ align:start position:0%
+uh it's chris mcgee
+ 
+
+ align:start position:0%
+uh it's chris mcgee
+no no he's called professor of the pro
+
+ align:start position:0%
+no no he's called professor of the pro
+ 
+
+ align:start position:0%
+no no he's called professor of the pro
+of the professional practice of
+
+ align:start position:0%
+of the professional practice of
+ 
+
+ align:start position:0%
+of the professional practice of
+engineering yeah
+
+ align:start position:0%
+engineering yeah
+ 
+
+ align:start position:0%
+engineering yeah
+but there's another one that is i think
+
+ align:start position:0%
+but there's another one that is i think
+ 
+
+ align:start position:0%
+but there's another one that is i think
+an esd that had well you all checked
+
+ align:start position:0%
+an esd that had well you all checked
+ 
+
+ align:start position:0%
+an esd that had well you all checked
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+out but anyway uh one way to get around
+
+ align:start position:0%
+out but anyway uh one way to get around
+ 
+
+ align:start position:0%
+out but anyway uh one way to get around
+it where uh at institutions that could
+
+ align:start position:0%
+it where uh at institutions that could
+ 
+
+ align:start position:0%
+it where uh at institutions that could
+afford to do it
+
+ align:start position:0%
+afford to do it
+ 
+
+ align:start position:0%
+afford to do it
+was to create uh teaching
+
+ align:start position:0%
+was to create uh teaching
+ 
+
+ align:start position:0%
+was to create uh teaching
+rank uh
+
+ align:start position:0%
+rank uh
+ 
+
+ align:start position:0%
+rank uh
+rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you could have a person distinguished
+
+ align:start position:0%
+so you could have a person distinguished
+ 
+
+ align:start position:0%
+so you could have a person distinguished
+professor for teaching
+
+ align:start position:0%
+professor for teaching
+ 
+
+ align:start position:0%
+professor for teaching
+at some place and all they have to do is
+
+ align:start position:0%
+at some place and all they have to do is
+ 
+
+ align:start position:0%
+at some place and all they have to do is
+teach they can get their raises without
+
+ align:start position:0%
+teach they can get their raises without
+ 
+
+ align:start position:0%
+teach they can get their raises without
+submitting
+
+ align:start position:0%
+submitting
+ 
+
+ align:start position:0%
+submitting
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+grants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but uh that's as far as they've gone
+
+ align:start position:0%
+but uh that's as far as they've gone
+ 
+
+ align:start position:0%
+but uh that's as far as they've gone
+with that kind of thing but i'm just
+
+ align:start position:0%
+with that kind of thing but i'm just
+ 
+
+ align:start position:0%
+with that kind of thing but i'm just
+trying to say that these things are not
+
+ align:start position:0%
+trying to say that these things are not
+ 
+
+ align:start position:0%
+trying to say that these things are not
+secret
+
+ align:start position:0%
+secret
+ 
+
+ align:start position:0%
+secret
+you can document all of this
+
+ align:start position:0%
+you can document all of this
+ 
+
+ align:start position:0%
+you can document all of this
+but it still operates below the level of
+
+ align:start position:0%
+but it still operates below the level of
+ 
+
+ align:start position:0%
+but it still operates below the level of
+what i call the collective unconscious a
+
+ align:start position:0%
+what i call the collective unconscious a
+ 
+
+ align:start position:0%
+what i call the collective unconscious a
+collective consciousness nobody really
+
+ align:start position:0%
+collective consciousness nobody really
+ 
+
+ align:start position:0%
+collective consciousness nobody really
+wants to talk about it
+
+ align:start position:0%
+wants to talk about it
+ 
+
+ align:start position:0%
+wants to talk about it
+and underneath what they say and do
+
+ align:start position:0%
+and underneath what they say and do
+ 
+
+ align:start position:0%
+and underneath what they say and do
+will be some of that dust
+
+ align:start position:0%
+will be some of that dust
+ 
+
+ align:start position:0%
+will be some of that dust
+and you have that here with this curve
+
+ align:start position:0%
+and you have that here with this curve
+ 
+
+ align:start position:0%
+and you have that here with this curve
+okay uh let's sweat it out
+
+ align:start position:0%
+okay uh let's sweat it out
+ 
+
+ align:start position:0%
+okay uh let's sweat it out
+let's finish these six and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statements only in an objective and
+
+ align:start position:0%
+statements only in an objective and
+ 
+
+ align:start position:0%
+statements only in an objective and
+truthful manner
+
+ align:start position:0%
+truthful manner
+ 
+
+ align:start position:0%
+truthful manner
+i'll tell you what that was about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll tell you what that was about
+
+ align:start position:0%
+i'll tell you what that was about
+ 
+
+ align:start position:0%
+i'll tell you what that was about
+all of a sudden
+
+ align:start position:0%
+all of a sudden
+ 
+
+ align:start position:0%
+all of a sudden
+the ordinary engineer became someone
+
+ align:start position:0%
+the ordinary engineer became someone
+ 
+
+ align:start position:0%
+the ordinary engineer became someone
+that the big
+
+ align:start position:0%
+that the big
+ 
+
+ align:start position:0%
+that the big
+news media wanted to interview
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh that was that was terrifying
+
+ align:start position:0%
+uh that was that was terrifying
+ 
+
+ align:start position:0%
+uh that was that was terrifying
+you know it's terrifying for university
+
+ align:start position:0%
+you know it's terrifying for university
+ 
+
+ align:start position:0%
+you know it's terrifying for university
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+all of a sudden some ordinary professor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is on nightline or
+
+ align:start position:0%
+is on nightline or
+ 
+
+ align:start position:0%
+is on nightline or
+or i was interviewed by uh some the new
+
+ align:start position:0%
+or i was interviewed by uh some the new
+ 
+
+ align:start position:0%
+or i was interviewed by uh some the new
+york times you know stuff like that
+
+ align:start position:0%
+york times you know stuff like that
+ 
+
+ align:start position:0%
+york times you know stuff like that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh so they uh
+
+ align:start position:0%
+uh so they uh
+ 
+
+ align:start position:0%
+uh so they uh
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+they really uh struggled over who could
+
+ align:start position:0%
+they really uh struggled over who could
+ 
+
+ align:start position:0%
+they really uh struggled over who could
+speak for the company
+
+ align:start position:0%
+speak for the company
+ 
+
+ align:start position:0%
+speak for the company
+when there was a question of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nuclear waste or something like that
+
+ align:start position:0%
+nuclear waste or something like that
+ 
+
+ align:start position:0%
+nuclear waste or something like that
+what can a person say
+
+ align:start position:0%
+what can a person say
+ 
+
+ align:start position:0%
+what can a person say
+and the lawyers got involved in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free speech
+
+ align:start position:0%
+free speech
+ 
+
+ align:start position:0%
+free speech
+not that they were defending it but they
+
+ align:start position:0%
+not that they were defending it but they
+ 
+
+ align:start position:0%
+not that they were defending it but they
+were trying to tell
+
+ align:start position:0%
+were trying to tell
+ 
+
+ align:start position:0%
+were trying to tell
+the presidents the ceos of corporations
+
+ align:start position:0%
+the presidents the ceos of corporations
+ 
+
+ align:start position:0%
+the presidents the ceos of corporations
+that you cannot suppress these employees
+
+ align:start position:0%
+that you cannot suppress these employees
+ 
+
+ align:start position:0%
+that you cannot suppress these employees
+because then the employee will take you
+
+ align:start position:0%
+because then the employee will take you
+ 
+
+ align:start position:0%
+because then the employee will take you
+to court and win big time
+
+ align:start position:0%
+to court and win big time
+ 
+
+ align:start position:0%
+to court and win big time
+right so what can you do so that was
+
+ align:start position:0%
+right so what can you do so that was
+ 
+
+ align:start position:0%
+right so what can you do so that was
+that issue there was uh really to cover
+
+ align:start position:0%
+that issue there was uh really to cover
+ 
+
+ align:start position:0%
+that issue there was uh really to cover
+ordinary people
+
+ align:start position:0%
+ordinary people
+ 
+
+ align:start position:0%
+ordinary people
+who now become celebrities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and some of them let's face it some of
+
+ align:start position:0%
+and some of them let's face it some of
+ 
+
+ align:start position:0%
+and some of them let's face it some of
+them get drunk with being the celebrity
+
+ align:start position:0%
+them get drunk with being the celebrity
+ 
+
+ align:start position:0%
+them get drunk with being the celebrity
+you know what i mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look i mean let's think about it the
+
+ align:start position:0%
+look i mean let's think about it the
+ 
+
+ align:start position:0%
+look i mean let's think about it the
+ordinary things we've all been through
+
+ align:start position:0%
+ordinary things we've all been through
+ 
+
+ align:start position:0%
+ordinary things we've all been through
+this i've been through it
+
+ align:start position:0%
+this i've been through it
+ 
+
+ align:start position:0%
+this i've been through it
+you know when when the challenger went
+
+ align:start position:0%
+you know when when the challenger went
+ 
+
+ align:start position:0%
+you know when when the challenger went
+down howard university has a tv station
+
+ align:start position:0%
+down howard university has a tv station
+ 
+
+ align:start position:0%
+down howard university has a tv station
+so they had this call in program so they
+
+ align:start position:0%
+so they had this call in program so they
+ 
+
+ align:start position:0%
+so they had this call in program so they
+asked me to come in and take the calls
+
+ align:start position:0%
+asked me to come in and take the calls
+ 
+
+ align:start position:0%
+asked me to come in and take the calls
+and just before the calls come in i'm
+
+ align:start position:0%
+and just before the calls come in i'm
+ 
+
+ align:start position:0%
+and just before the calls come in i'm
+sitting down and they got a makeup
+
+ align:start position:0%
+sitting down and they got a makeup
+ 
+
+ align:start position:0%
+sitting down and they got a makeup
+artist
+
+ align:start position:0%
+artist
+ 
+
+ align:start position:0%
+artist
+so what you can let that stuff go to
+
+ align:start position:0%
+so what you can let that stuff go to
+ 
+
+ align:start position:0%
+so what you can let that stuff go to
+your head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+uh it was easy for me i just did my job
+
+ align:start position:0%
+uh it was easy for me i just did my job
+ 
+
+ align:start position:0%
+uh it was easy for me i just did my job
+and went back to the library of congress
+
+ align:start position:0%
+and went back to the library of congress
+ 
+
+ align:start position:0%
+and went back to the library of congress
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+some people
+
+ align:start position:0%
+some people
+ 
+
+ align:start position:0%
+some people
+that stuff goes to their heads and they
+
+ align:start position:0%
+that stuff goes to their heads and they
+ 
+
+ align:start position:0%
+that stuff goes to their heads and they
+start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+making life miserable for a lot of
+
+ align:start position:0%
+making life miserable for a lot of
+ 
+
+ align:start position:0%
+making life miserable for a lot of
+people unnecessarily
+
+ align:start position:0%
+people unnecessarily
+ 
+
+ align:start position:0%
+people unnecessarily
+so there was a lot of that underneath
+
+ align:start position:0%
+so there was a lot of that underneath
+ 
+
+ align:start position:0%
+so there was a lot of that underneath
+the surface that came to the surface
+
+ align:start position:0%
+the surface that came to the surface
+ 
+
+ align:start position:0%
+the surface that came to the surface
+everybody said well
+
+ align:start position:0%
+everybody said well
+ 
+
+ align:start position:0%
+everybody said well
+what they did was there's a term
+
+ align:start position:0%
+what they did was there's a term
+ 
+
+ align:start position:0%
+what they did was there's a term
+i don't know if it's a term of art
+
+ align:start position:0%
+i don't know if it's a term of art
+ 
+
+ align:start position:0%
+i don't know if it's a term of art
+but you're going to get it and it's
+
+ align:start position:0%
+but you're going to get it and it's
+ 
+
+ align:start position:0%
+but you're going to get it and it's
+called word smithing
+
+ align:start position:0%
+called word smithing
+ 
+
+ align:start position:0%
+called word smithing
+everybody knew what we had to do
+
+ align:start position:0%
+everybody knew what we had to do
+ 
+
+ align:start position:0%
+everybody knew what we had to do
+everybody agreed what we had to do still
+
+ align:start position:0%
+everybody agreed what we had to do still
+ 
+
+ align:start position:0%
+everybody agreed what we had to do still
+what words can we do right down here
+
+ align:start position:0%
+what words can we do right down here
+ 
+
+ align:start position:0%
+what words can we do right down here
+and so we so that particular one was a
+
+ align:start position:0%
+and so we so that particular one was a
+ 
+
+ align:start position:0%
+and so we so that particular one was a
+turned out for i i think it's fair to
+
+ align:start position:0%
+turned out for i i think it's fair to
+ 
+
+ align:start position:0%
+turned out for i i think it's fair to
+say for people who are writing codes of
+
+ align:start position:0%
+say for people who are writing codes of
+ 
+
+ align:start position:0%
+say for people who are writing codes of
+ethics
+
+ align:start position:0%
+ethics
+ 
+
+ align:start position:0%
+ethics
+to be a wordsmithing
+
+ align:start position:0%
+to be a wordsmithing
+ 
+
+ align:start position:0%
+to be a wordsmithing
+challenge
+
+ align:start position:0%
+challenge
+ 
+
+ align:start position:0%
+challenge
+particularly to get a lawyer in there
+
+ align:start position:0%
+particularly to get a lawyer in there
+ 
+
+ align:start position:0%
+particularly to get a lawyer in there
+so that we didn't go over the line but
+
+ align:start position:0%
+so that we didn't go over the line but
+ 
+
+ align:start position:0%
+so that we didn't go over the line but
+everybody sort of agreed on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle is to present the company
+
+ align:start position:0%
+principle is to present the company
+ 
+
+ align:start position:0%
+principle is to present the company
+maybe in a more positive manner so you
+
+ align:start position:0%
+maybe in a more positive manner so you
+ 
+
+ align:start position:0%
+maybe in a more positive manner so you
+can't get an employee and get all the
+
+ align:start position:0%
+can't get an employee and get all the
+ 
+
+ align:start position:0%
+can't get an employee and get all the
+names
+
+ align:start position:0%
+names
+ 
+
+ align:start position:0%
+names
+and trash right maybe like underlined
+
+ align:start position:0%
+and trash right maybe like underlined
+ 
+
+ align:start position:0%
+and trash right maybe like underlined
+but it seems like that's not necessarily
+
+ align:start position:0%
+but it seems like that's not necessarily
+ 
+
+ align:start position:0%
+but it seems like that's not necessarily
+you could adhere to that and be truthful
+
+ align:start position:0%
+you could adhere to that and be truthful
+ 
+
+ align:start position:0%
+you could adhere to that and be truthful
+and maybe say something that
+
+ align:start position:0%
+and maybe say something that
+ 
+
+ align:start position:0%
+and maybe say something that
+you know management might not like and
+
+ align:start position:0%
+you know management might not like and
+ 
+
+ align:start position:0%
+you know management might not like and
+you are being
+
+ align:start position:0%
+you are being
+ 
+
+ align:start position:0%
+you are being
+objective and truthful right but maybe
+
+ align:start position:0%
+objective and truthful right but maybe
+ 
+
+ align:start position:0%
+objective and truthful right but maybe
+that is one of the other
+
+ align:start position:0%
+that is one of the other
+ 
+
+ align:start position:0%
+that is one of the other
+assumptions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well definitely that's true i mean the
+
+ align:start position:0%
+well definitely that's true i mean the
+ 
+
+ align:start position:0%
+well definitely that's true i mean the
+way the way
+
+ align:start position:0%
+way the way
+ 
+
+ align:start position:0%
+way the way
+big organizations deal with that
+
+ align:start position:0%
+big organizations deal with that
+ 
+
+ align:start position:0%
+big organizations deal with that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+when they do it
+
+ align:start position:0%
+when they do it
+ 
+
+ align:start position:0%
+when they do it
+is not to come out and tell everybody
+
+ align:start position:0%
+is not to come out and tell everybody
+ 
+
+ align:start position:0%
+is not to come out and tell everybody
+that they have to say things that put
+
+ align:start position:0%
+that they have to say things that put
+ 
+
+ align:start position:0%
+that they have to say things that put
+the company in the best light
+
+ align:start position:0%
+the company in the best light
+ 
+
+ align:start position:0%
+the company in the best light
+what they do is
+
+ align:start position:0%
+what they do is
+ 
+
+ align:start position:0%
+what they do is
+you're just not going to make it up the
+
+ align:start position:0%
+you're just not going to make it up the
+ 
+
+ align:start position:0%
+you're just not going to make it up the
+management level unless you really feel
+
+ align:start position:0%
+management level unless you really feel
+ 
+
+ align:start position:0%
+management level unless you really feel
+that way
+
+ align:start position:0%
+that way
+ 
+
+ align:start position:0%
+that way
+so it becomes an honest so
+
+ align:start position:0%
+so it becomes an honest so
+ 
+
+ align:start position:0%
+so it becomes an honest so
+so if you get a manager update a manager
+
+ align:start position:0%
+so if you get a manager update a manager
+ 
+
+ align:start position:0%
+so if you get a manager update a manager
+is not lying the manager is the person
+
+ align:start position:0%
+is not lying the manager is the person
+ 
+
+ align:start position:0%
+is not lying the manager is the person
+who was chosen because he or she really
+
+ align:start position:0%
+who was chosen because he or she really
+ 
+
+ align:start position:0%
+who was chosen because he or she really
+feels that way has that real outlook
+
+ align:start position:0%
+feels that way has that real outlook
+ 
+
+ align:start position:0%
+feels that way has that real outlook
+everybody believes and
+
+ align:start position:0%
+everybody believes and
+ 
+
+ align:start position:0%
+everybody believes and
+can portray it as something really
+
+ align:start position:0%
+can portray it as something really
+ 
+
+ align:start position:0%
+can portray it as something really
+something truthful and objective right
+
+ align:start position:0%
+something truthful and objective right
+ 
+
+ align:start position:0%
+something truthful and objective right
+somebody who feels differently is just
+
+ align:start position:0%
+somebody who feels differently is just
+ 
+
+ align:start position:0%
+somebody who feels differently is just
+not going to make it
+
+ align:start position:0%
+not going to make it
+ 
+
+ align:start position:0%
+not going to make it
+along those lines all right and you hope
+
+ align:start position:0%
+along those lines all right and you hope
+ 
+
+ align:start position:0%
+along those lines all right and you hope
+when i say you i mean the ceo
+
+ align:start position:0%
+when i say you i mean the ceo
+ 
+
+ align:start position:0%
+when i say you i mean the ceo
+hopes
+
+ align:start position:0%
+hopes
+ 
+
+ align:start position:0%
+hopes
+that somebody who is not in that line
+
+ align:start position:0%
+that somebody who is not in that line
+ 
+
+ align:start position:0%
+that somebody who is not in that line
+is not being interviewed and no the
+
+ align:start position:0%
+is not being interviewed and no the
+ 
+
+ align:start position:0%
+is not being interviewed and no the
+newspapers know
+
+ align:start position:0%
+newspapers know
+ 
+
+ align:start position:0%
+newspapers know
+the structure they know to get one
+
+ align:start position:0%
+the structure they know to get one
+ 
+
+ align:start position:0%
+the structure they know to get one
+person to say the party line they want
+
+ align:start position:0%
+person to say the party line they want
+ 
+
+ align:start position:0%
+person to say the party line they want
+to get another person to say something
+
+ align:start position:0%
+to get another person to say something
+ 
+
+ align:start position:0%
+to get another person to say something
+else and they play it against each other
+
+ align:start position:0%
+else and they play it against each other
+ 
+
+ align:start position:0%
+else and they play it against each other
+and it's hard to deal with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what happens in the end i think is
+
+ align:start position:0%
+uh what happens in the end i think is
+ 
+
+ align:start position:0%
+uh what happens in the end i think is
+that uh if you have to do anything like
+
+ align:start position:0%
+that uh if you have to do anything like
+ 
+
+ align:start position:0%
+that uh if you have to do anything like
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+and i've learned
+
+ align:start position:0%
+and i've learned
+ 
+
+ align:start position:0%
+and i've learned
+from experience
+
+ align:start position:0%
+from experience
+ 
+
+ align:start position:0%
+from experience
+uh is just to say that you are not a
+
+ align:start position:0%
+uh is just to say that you are not a
+ 
+
+ align:start position:0%
+uh is just to say that you are not a
+spokesman
+
+ align:start position:0%
+spokesman
+ 
+
+ align:start position:0%
+spokesman
+for your corporation
+
+ align:start position:0%
+for your corporation
+ 
+
+ align:start position:0%
+for your corporation
+you are an engineer there and you're
+
+ align:start position:0%
+you are an engineer there and you're
+ 
+
+ align:start position:0%
+you are an engineer there and you're
+speaking from the perspective of
+
+ align:start position:0%
+speaking from the perspective of
+ 
+
+ align:start position:0%
+speaking from the perspective of
+an engineer there and this is my
+
+ align:start position:0%
+an engineer there and this is my
+ 
+
+ align:start position:0%
+an engineer there and this is my
+perspective and my outlook and my
+
+ align:start position:0%
+perspective and my outlook and my
+ 
+
+ align:start position:0%
+perspective and my outlook and my
+experience but you don't drag
+
+ align:start position:0%
+experience but you don't drag
+ 
+
+ align:start position:0%
+experience but you don't drag
+you don't take credit for saying well at
+
+ align:start position:0%
+you don't take credit for saying well at
+ 
+
+ align:start position:0%
+you don't take credit for saying well at
+my company we
+
+ align:start position:0%
+my company we
+ 
+
+ align:start position:0%
+my company we
+you don't make statements like that
+
+ align:start position:0%
+you don't make statements like that
+ 
+
+ align:start position:0%
+you don't make statements like that
+somebody else can do it but you can't do
+
+ align:start position:0%
+somebody else can do it but you can't do
+ 
+
+ align:start position:0%
+somebody else can do it but you can't do
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+okay how many more we got
+
+ align:start position:0%
+okay how many more we got
+ 
+
+ align:start position:0%
+okay how many more we got
+three let's knock him out
+
+ align:start position:0%
+three let's knock him out
+ 
+
+ align:start position:0%
+three let's knock him out
+each employer or client
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+what is a faithful agent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's that's uh we got that from the
+
+ align:start position:0%
+that's that's uh we got that from the
+ 
+
+ align:start position:0%
+that's that's uh we got that from the
+lawyers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the specifics
+
+ align:start position:0%
+so in the specifics
+ 
+
+ align:start position:0%
+so in the specifics
+of practice it talks about disclosing
+
+ align:start position:0%
+of practice it talks about disclosing
+ 
+
+ align:start position:0%
+of practice it talks about disclosing
+all known or potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not accepting compensation
+
+ align:start position:0%
+not accepting compensation
+ 
+
+ align:start position:0%
+not accepting compensation
+for more than one party for services on
+
+ align:start position:0%
+for more than one party for services on
+ 
+
+ align:start position:0%
+for more than one party for services on
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not soliciting or accepting financial
+
+ align:start position:0%
+not soliciting or accepting financial
+ 
+
+ align:start position:0%
+not soliciting or accepting financial
+consideration from outside agents right
+
+ align:start position:0%
+consideration from outside agents right
+ 
+
+ align:start position:0%
+consideration from outside agents right
+so those are the particulars on this
+
+ align:start position:0%
+so those are the particulars on this
+ 
+
+ align:start position:0%
+so those are the particulars on this
+issue of faithful agent
+
+ align:start position:0%
+issue of faithful agent
+ 
+
+ align:start position:0%
+issue of faithful agent
+agency
+
+ align:start position:0%
+agency
+ 
+
+ align:start position:0%
+agency
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so when you uh go work when you go to um
+
+ align:start position:0%
+so when you uh go work when you go to um
+ 
+
+ align:start position:0%
+so when you uh go work when you go to um
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh no i mean
+
+ align:start position:0%
+oh no i mean
+ 
+
+ align:start position:0%
+oh no i mean
+you you might go to
+
+ align:start position:0%
+you you might go to
+ 
+
+ align:start position:0%
+you you might go to
+to a contractor say i need another wing
+
+ align:start position:0%
+to a contractor say i need another wing
+ 
+
+ align:start position:0%
+to a contractor say i need another wing
+put on my house
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you want to believe that the contractor
+
+ align:start position:0%
+you want to believe that the contractor
+ 
+
+ align:start position:0%
+you want to believe that the contractor
+has your interest in
+
+ align:start position:0%
+has your interest in
+ 
+
+ align:start position:0%
+has your interest in
+paramount okay
+
+ align:start position:0%
+paramount okay
+ 
+
+ align:start position:0%
+paramount okay
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+and that the person is not saying well
+
+ align:start position:0%
+and that the person is not saying well
+ 
+
+ align:start position:0%
+and that the person is not saying well
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+real estate agency
+
+ align:start position:0%
+real estate agency
+ 
+
+ align:start position:0%
+real estate agency
+thinks that the market in this
+
+ align:start position:0%
+thinks that the market in this
+ 
+
+ align:start position:0%
+thinks that the market in this
+neighborhood
+
+ align:start position:0%
+neighborhood
+ 
+
+ align:start position:0%
+neighborhood
+will be higher
+
+ align:start position:0%
+will be higher
+ 
+
+ align:start position:0%
+will be higher
+if we don't have a whole lot of uh
+
+ align:start position:0%
+if we don't have a whole lot of uh
+ 
+
+ align:start position:0%
+if we don't have a whole lot of uh
+extensions put on these homes
+
+ align:start position:0%
+extensions put on these homes
+ 
+
+ align:start position:0%
+extensions put on these homes
+i don't know why they would say that but
+
+ align:start position:0%
+i don't know why they would say that but
+ 
+
+ align:start position:0%
+i don't know why they would say that but
+i'm making up a case
+
+ align:start position:0%
+i'm making up a case
+ 
+
+ align:start position:0%
+i'm making up a case
+and so they go to this meeting with the
+
+ align:start position:0%
+and so they go to this meeting with the
+ 
+
+ align:start position:0%
+and so they go to this meeting with the
+contractors and say well look uh
+
+ align:start position:0%
+contractors and say well look uh
+ 
+
+ align:start position:0%
+contractors and say well look uh
+it's not in our interest with having all
+
+ align:start position:0%
+it's not in our interest with having all
+ 
+
+ align:start position:0%
+it's not in our interest with having all
+of these things up so what the
+
+ align:start position:0%
+of these things up so what the
+ 
+
+ align:start position:0%
+of these things up so what the
+contractor does is come back let's say
+
+ align:start position:0%
+contractor does is come back let's say
+ 
+
+ align:start position:0%
+contractor does is come back let's say
+and says well you know quote you the
+
+ align:start position:0%
+and says well you know quote you the
+ 
+
+ align:start position:0%
+and says well you know quote you the
+highest prices on everything try to
+
+ align:start position:0%
+highest prices on everything try to
+ 
+
+ align:start position:0%
+highest prices on everything try to
+discourage you from doing it
+
+ align:start position:0%
+discourage you from doing it
+ 
+
+ align:start position:0%
+discourage you from doing it
+we don't want that okay the contract is
+
+ align:start position:0%
+we don't want that okay the contract is
+ 
+
+ align:start position:0%
+we don't want that okay the contract is
+supposed to say no matter what
+
+ align:start position:0%
+supposed to say no matter what
+ 
+
+ align:start position:0%
+supposed to say no matter what
+the other interests are i am your agent
+
+ align:start position:0%
+the other interests are i am your agent
+ 
+
+ align:start position:0%
+the other interests are i am your agent
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh you
+
+ align:start position:0%
+uh you
+ 
+
+ align:start position:0%
+uh you
+if you want this house thing put on here
+
+ align:start position:0%
+if you want this house thing put on here
+ 
+
+ align:start position:0%
+if you want this house thing put on here
+are the prices these are the best prices
+
+ align:start position:0%
+are the prices these are the best prices
+ 
+
+ align:start position:0%
+are the prices these are the best prices
+you don't need to have steel put in as a
+
+ align:start position:0%
+you don't need to have steel put in as a
+ 
+
+ align:start position:0%
+you don't need to have steel put in as a
+column for a one-story
+
+ align:start position:0%
+column for a one-story
+ 
+
+ align:start position:0%
+column for a one-story
+extension of your kitchen we can do that
+
+ align:start position:0%
+extension of your kitchen we can do that
+ 
+
+ align:start position:0%
+extension of your kitchen we can do that
+with a four five by four piece of
+
+ align:start position:0%
+with a four five by four piece of
+ 
+
+ align:start position:0%
+with a four five by four piece of
+wood all right
+
+ align:start position:0%
+wood all right
+ 
+
+ align:start position:0%
+wood all right
+uh and but you got to get a good piece
+
+ align:start position:0%
+uh and but you got to get a good piece
+ 
+
+ align:start position:0%
+uh and but you got to get a good piece
+of wood
+
+ align:start position:0%
+of wood
+ 
+
+ align:start position:0%
+of wood
+so this is the kind you get save
+
+ align:start position:0%
+so this is the kind you get save
+ 
+
+ align:start position:0%
+so this is the kind you get save
+yourself two or three thousand dollars
+
+ align:start position:0%
+yourself two or three thousand dollars
+ 
+
+ align:start position:0%
+yourself two or three thousand dollars
+okay so they don't want you playing that
+
+ align:start position:0%
+okay so they don't want you playing that
+ 
+
+ align:start position:0%
+okay so they don't want you playing that
+those kinds of games
+
+ align:start position:0%
+those kinds of games
+ 
+
+ align:start position:0%
+those kinds of games
+they want the client
+
+ align:start position:0%
+they want the client
+ 
+
+ align:start position:0%
+they want the client
+or whoever you're working for
+
+ align:start position:0%
+or whoever you're working for
+ 
+
+ align:start position:0%
+or whoever you're working for
+the good example is with the legal
+
+ align:start position:0%
+the good example is with the legal
+ 
+
+ align:start position:0%
+the good example is with the legal
+profession
+
+ align:start position:0%
+profession
+ 
+
+ align:start position:0%
+profession
+a lot of them believe that their client
+
+ align:start position:0%
+a lot of them believe that their client
+ 
+
+ align:start position:0%
+a lot of them believe that their client
+you know they're going to be agents for
+
+ align:start position:0%
+you know they're going to be agents for
+ 
+
+ align:start position:0%
+you know they're going to be agents for
+their client
+
+ align:start position:0%
+their client
+ 
+
+ align:start position:0%
+their client
+so i mean you could be
+
+ align:start position:0%
+so i mean you could be
+ 
+
+ align:start position:0%
+so i mean you could be
+a notorious killer if you're supposed to
+
+ align:start position:0%
+a notorious killer if you're supposed to
+ 
+
+ align:start position:0%
+a notorious killer if you're supposed to
+defend that client guess what you're
+
+ align:start position:0%
+defend that client guess what you're
+ 
+
+ align:start position:0%
+defend that client guess what you're
+supposed to do do your best
+
+ align:start position:0%
+supposed to do do your best
+ 
+
+ align:start position:0%
+supposed to do do your best
+to defend that client
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one is that is that what we would
+
+ align:start position:0%
+that one is that is that what we would
+ 
+
+ align:start position:0%
+that one is that is that what we would
+call it easy one give us some specifics
+
+ align:start position:0%
+call it easy one give us some specifics
+ 
+
+ align:start position:0%
+call it easy one give us some specifics
+what are the specific one or
+
+ align:start position:0%
+what are the specific one or
+ 
+
+ align:start position:0%
+what are the specific one or
+two qualifications
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Laughter]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we had a case at howard
+
+ align:start position:0%
+we had a case at howard
+ 
+
+ align:start position:0%
+we had a case at howard
+where a faculty member in engineering
+
+ align:start position:0%
+where a faculty member in engineering
+ 
+
+ align:start position:0%
+where a faculty member in engineering
+all this was a terrible case for other
+
+ align:start position:0%
+all this was a terrible case for other
+ 
+
+ align:start position:0%
+all this was a terrible case for other
+reasons that if if you want to know
+
+ align:start position:0%
+reasons that if if you want to know
+ 
+
+ align:start position:0%
+reasons that if if you want to know
+about we got time to go in
+
+ align:start position:0%
+about we got time to go in
+ 
+
+ align:start position:0%
+about we got time to go in
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+what he did was he submitted credentials
+
+ align:start position:0%
+what he did was he submitted credentials
+ 
+
+ align:start position:0%
+what he did was he submitted credentials
+of 200 publications
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adam nicely sit down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he came in from another university
+
+ align:start position:0%
+and he came in from another university
+ 
+
+ align:start position:0%
+and he came in from another university
+and they the department gave him uh
+
+ align:start position:0%
+and they the department gave him uh
+ 
+
+ align:start position:0%
+and they the department gave him uh
+full professional full professional 10
+
+ align:start position:0%
+full professional full professional 10
+ 
+
+ align:start position:0%
+full professional full professional 10
+based on his presentation
+
+ align:start position:0%
+based on his presentation
+ 
+
+ align:start position:0%
+based on his presentation
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+mainly
+
+ align:start position:0%
+mainly
+ 
+
+ align:start position:0%
+mainly
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh there were some questions why he
+
+ align:start position:0%
+uh there were some questions why he
+ 
+
+ align:start position:0%
+uh there were some questions why he
+never made
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+full at
+
+ align:start position:0%
+full at
+ 
+
+ align:start position:0%
+full at
+any of his previous places but
+
+ align:start position:0%
+any of his previous places but
+ 
+
+ align:start position:0%
+any of his previous places but
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+usually uh answered by
+
+ align:start position:0%
+usually uh answered by
+ 
+
+ align:start position:0%
+usually uh answered by
+the real
+
+ align:start position:0%
+the real
+ 
+
+ align:start position:0%
+the real
+problem of the real case that maybe just
+
+ align:start position:0%
+problem of the real case that maybe just
+ 
+
+ align:start position:0%
+problem of the real case that maybe just
+didn't fit in
+
+ align:start position:0%
+didn't fit in
+ 
+
+ align:start position:0%
+didn't fit in
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i can think of some
+
+ align:start position:0%
+so i can think of some
+ 
+
+ align:start position:0%
+so i can think of some
+very talented professors
+
+ align:start position:0%
+very talented professors
+ 
+
+ align:start position:0%
+very talented professors
+that will not fit in at howard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we brought the professor down
+
+ align:start position:0%
+so we brought the professor down
+ 
+
+ align:start position:0%
+so we brought the professor down
+well he did something else
+
+ align:start position:0%
+well he did something else
+ 
+
+ align:start position:0%
+well he did something else
+that was totally irrelevant to that
+
+ align:start position:0%
+that was totally irrelevant to that
+ 
+
+ align:start position:0%
+that was totally irrelevant to that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+everybody wanted to fire him for
+
+ align:start position:0%
+everybody wanted to fire him for
+ 
+
+ align:start position:0%
+everybody wanted to fire him for
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the department is building up a case
+
+ align:start position:0%
+the department is building up a case
+ 
+
+ align:start position:0%
+the department is building up a case
+against him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so they go back through his resume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what they found out was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that almost all of his publications
+
+ align:start position:0%
+that almost all of his publications
+ 
+
+ align:start position:0%
+that almost all of his publications
+were what you call commentaries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you publish an article
+
+ align:start position:0%
+so you publish an article
+ 
+
+ align:start position:0%
+so you publish an article
+that comes out
+
+ align:start position:0%
+that comes out
+ 
+
+ align:start position:0%
+that comes out
+and in many journals will allow
+
+ align:start position:0%
+and in many journals will allow
+ 
+
+ align:start position:0%
+and in many journals will allow
+a certain period of time like a year
+
+ align:start position:0%
+a certain period of time like a year
+ 
+
+ align:start position:0%
+a certain period of time like a year
+calendar year for the rest of us to say
+
+ align:start position:0%
+calendar year for the rest of us to say
+ 
+
+ align:start position:0%
+calendar year for the rest of us to say
+well you know i think that the equation
+
+ align:start position:0%
+well you know i think that the equation
+ 
+
+ align:start position:0%
+well you know i think that the equation
+3.2
+
+ align:start position:0%
+3.2
+ 
+
+ align:start position:0%
+3.2
+in her report was incorrect
+
+ align:start position:0%
+in her report was incorrect
+ 
+
+ align:start position:0%
+in her report was incorrect
+it left out the square term you put in
+
+ align:start position:0%
+it left out the square term you put in
+ 
+
+ align:start position:0%
+it left out the square term you put in
+the square term and send it back and
+
+ align:start position:0%
+the square term and send it back and
+ 
+
+ align:start position:0%
+the square term and send it back and
+they publish it right along
+
+ align:start position:0%
+they publish it right along
+ 
+
+ align:start position:0%
+they publish it right along
+he had 200 commentary papers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we felt deceived
+
+ align:start position:0%
+now we felt deceived
+ 
+
+ align:start position:0%
+now we felt deceived
+we had made a contract with uh
+
+ align:start position:0%
+we had made a contract with uh
+ 
+
+ align:start position:0%
+we had made a contract with uh
+mephistopheles and stuff he
+
+ align:start position:0%
+mephistopheles and stuff he
+ 
+
+ align:start position:0%
+mephistopheles and stuff he
+we thought that
+
+ align:start position:0%
+we thought that
+ 
+
+ align:start position:0%
+we thought that
+he should have put in
+
+ align:start position:0%
+he should have put in
+ 
+
+ align:start position:0%
+he should have put in
+now i may comment do commentary papers
+
+ align:start position:0%
+now i may comment do commentary papers
+ 
+
+ align:start position:0%
+now i may comment do commentary papers
+but when i put all of the credentials
+
+ align:start position:0%
+but when i put all of the credentials
+ 
+
+ align:start position:0%
+but when i put all of the credentials
+down in for the commentary commentary i
+
+ align:start position:0%
+down in for the commentary commentary i
+ 
+
+ align:start position:0%
+down in for the commentary commentary i
+have a square bracket at the end it says
+
+ align:start position:0%
+have a square bracket at the end it says
+ 
+
+ align:start position:0%
+have a square bracket at the end it says
+commentary oh actually what i do in my
+
+ align:start position:0%
+commentary oh actually what i do in my
+ 
+
+ align:start position:0%
+commentary oh actually what i do in my
+resume i think you should look at my
+
+ align:start position:0%
+resume i think you should look at my
+ 
+
+ align:start position:0%
+resume i think you should look at my
+resume
+
+ align:start position:0%
+resume
+ 
+
+ align:start position:0%
+resume
+uh i got commentary paper i think right
+
+ align:start position:0%
+uh i got commentary paper i think right
+ 
+
+ align:start position:0%
+uh i got commentary paper i think right
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+after the title but i make sure that
+
+ align:start position:0%
+after the title but i make sure that
+ 
+
+ align:start position:0%
+after the title but i make sure that
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+commentary paper now what i do to give a
+
+ align:start position:0%
+commentary paper now what i do to give a
+ 
+
+ align:start position:0%
+commentary paper now what i do to give a
+little bit of credit for myself
+
+ align:start position:0%
+little bit of credit for myself
+ 
+
+ align:start position:0%
+little bit of credit for myself
+is that the commentary papers i've
+
+ align:start position:0%
+is that the commentary papers i've
+ 
+
+ align:start position:0%
+is that the commentary papers i've
+written were what they call invited
+
+ align:start position:0%
+written were what they call invited
+ 
+
+ align:start position:0%
+written were what they call invited
+commentaries
+
+ align:start position:0%
+commentaries
+ 
+
+ align:start position:0%
+commentaries
+the editor will send me a copy of the
+
+ align:start position:0%
+the editor will send me a copy of the
+ 
+
+ align:start position:0%
+the editor will send me a copy of the
+paper and say look we need a commentary
+
+ align:start position:0%
+paper and say look we need a commentary
+ 
+
+ align:start position:0%
+paper and say look we need a commentary
+on it i'm not sitting there
+
+ align:start position:0%
+on it i'm not sitting there
+ 
+
+ align:start position:0%
+on it i'm not sitting there
+saying oh i think this equation 3.2 is
+
+ align:start position:0%
+saying oh i think this equation 3.2 is
+ 
+
+ align:start position:0%
+saying oh i think this equation 3.2 is
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+not that i wouldn't it just not has not
+
+ align:start position:0%
+not that i wouldn't it just not has not
+ 
+
+ align:start position:0%
+not that i wouldn't it just not has not
+happened
+
+ align:start position:0%
+happened
+ 
+
+ align:start position:0%
+happened
+for me in my career to do that so i will
+
+ align:start position:0%
+for me in my career to do that so i will
+ 
+
+ align:start position:0%
+for me in my career to do that so i will
+put invited commentary down there to
+
+ align:start position:0%
+put invited commentary down there to
+ 
+
+ align:start position:0%
+put invited commentary down there to
+give it a little more status
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+so that's a deception that that
+
+ align:start position:0%
+so that's a deception that that
+ 
+
+ align:start position:0%
+so that's a deception that that
+this was an engineer so i'm looking at
+
+ align:start position:0%
+this was an engineer so i'm looking at
+ 
+
+ align:start position:0%
+this was an engineer so i'm looking at
+it as not just academic profession but
+
+ align:start position:0%
+it as not just academic profession but
+ 
+
+ align:start position:0%
+it as not just academic profession but
+as engineering
+
+ align:start position:0%
+as engineering
+ 
+
+ align:start position:0%
+as engineering
+this guy deceived us as we were
+
+ align:start position:0%
+this guy deceived us as we were
+ 
+
+ align:start position:0%
+this guy deceived us as we were
+engineering colleagues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another one that's interesting is
+
+ align:start position:0%
+another one that's interesting is
+ 
+
+ align:start position:0%
+another one that's interesting is
+engineers shall advise their clients or
+
+ align:start position:0%
+engineers shall advise their clients or
+ 
+
+ align:start position:0%
+engineers shall advise their clients or
+employers when they believe that a
+
+ align:start position:0%
+employers when they believe that a
+ 
+
+ align:start position:0%
+employers when they believe that a
+project will not be successful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which i thought was an interesting one i
+
+ align:start position:0%
+which i thought was an interesting one i
+ 
+
+ align:start position:0%
+which i thought was an interesting one i
+mean it goes back to you know mandatory
+
+ align:start position:0%
+mean it goes back to you know mandatory
+ 
+
+ align:start position:0%
+mean it goes back to you know mandatory
+new engineer but it is the engineering
+
+ align:start position:0%
+new engineer but it is the engineering
+ 
+
+ align:start position:0%
+new engineer but it is the engineering
+job to say you know this is going to
+
+ align:start position:0%
+job to say you know this is going to
+ 
+
+ align:start position:0%
+job to say you know this is going to
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's also a
+
+ align:start position:0%
+it's also a
+ 
+
+ align:start position:0%
+it's also a
+scary situation to be in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so read it please
+
+ align:start position:0%
+so read it please
+ 
+
+ align:start position:0%
+so read it please
+well okay so the sticks can well
+
+ align:start position:0%
+well okay so the sticks can well
+ 
+
+ align:start position:0%
+well okay so the sticks can well
+because that could be really obvious no
+
+ align:start position:0%
+because that could be really obvious no
+ 
+
+ align:start position:0%
+because that could be really obvious no
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+so we just did the fifth cannon which is
+
+ align:start position:0%
+so we just did the fifth cannon which is
+ 
+
+ align:start position:0%
+so we just did the fifth cannon which is
+avoid deceptive acts and then the sixth
+
+ align:start position:0%
+avoid deceptive acts and then the sixth
+ 
+
+ align:start position:0%
+avoid deceptive acts and then the sixth
+cannon is
+
+ align:start position:0%
+cannon is
+ 
+
+ align:start position:0%
+cannon is
+conduct themselves honorably responsibly
+
+ align:start position:0%
+conduct themselves honorably responsibly
+ 
+
+ align:start position:0%
+conduct themselves honorably responsibly
+ethically and lawfully
+
+ align:start position:0%
+ethically and lawfully
+ 
+
+ align:start position:0%
+ethically and lawfully
+so as to enhance the honorable
+
+ align:start position:0%
+so as to enhance the honorable
+ 
+
+ align:start position:0%
+so as to enhance the honorable
+reputation and usefulness of the
+
+ align:start position:0%
+reputation and usefulness of the
+ 
+
+ align:start position:0%
+reputation and usefulness of the
+president
+
+ align:start position:0%
+president
+ 
+
+ align:start position:0%
+president
+yeah i always had an objection to that
+
+ align:start position:0%
+yeah i always had an objection to that
+ 
+
+ align:start position:0%
+yeah i always had an objection to that
+i don't have any obligation to enhance
+
+ align:start position:0%
+i don't have any obligation to enhance
+ 
+
+ align:start position:0%
+i don't have any obligation to enhance
+the profession
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what you just brought up is under
+
+ align:start position:0%
+and what you just brought up is under
+ 
+
+ align:start position:0%
+and what you just brought up is under
+professional obligations so it says
+
+ align:start position:0%
+professional obligations so it says
+ 
+
+ align:start position:0%
+professional obligations so it says
+engineers shall advise their clients or
+
+ align:start position:0%
+engineers shall advise their clients or
+ 
+
+ align:start position:0%
+engineers shall advise their clients or
+employers when they believe a project
+
+ align:start position:0%
+employers when they believe a project
+ 
+
+ align:start position:0%
+employers when they believe a project
+will not be successful
+
+ align:start position:0%
+will not be successful
+ 
+
+ align:start position:0%
+will not be successful
+okay well and so far let me let me
+
+ align:start position:0%
+okay well and so far let me let me
+ 
+
+ align:start position:0%
+okay well and so far let me let me
+mention this that i i stand almost alone
+
+ align:start position:0%
+mention this that i i stand almost alone
+ 
+
+ align:start position:0%
+mention this that i i stand almost alone
+in this when it comes to enhancing the
+
+ align:start position:0%
+in this when it comes to enhancing the
+ 
+
+ align:start position:0%
+in this when it comes to enhancing the
+profession i don't believe that i have
+
+ align:start position:0%
+profession i don't believe that i have
+ 
+
+ align:start position:0%
+profession i don't believe that i have
+any obligation but i i have been
+
+ align:start position:0%
+any obligation but i i have been
+ 
+
+ align:start position:0%
+any obligation but i i have been
+overruled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+i was thinking of a metaphor let me just
+
+ align:start position:0%
+i was thinking of a metaphor let me just
+ 
+
+ align:start position:0%
+i was thinking of a metaphor let me just
+put the argument down
+
+ align:start position:0%
+put the argument down
+ 
+
+ align:start position:0%
+put the argument down
+uh if if if if a profession
+
+ align:start position:0%
+uh if if if if a profession
+ 
+
+ align:start position:0%
+uh if if if if a profession
+is going to be honorable it has to be
+
+ align:start position:0%
+is going to be honorable it has to be
+ 
+
+ align:start position:0%
+is going to be honorable it has to be
+honorable without our making it
+
+ align:start position:0%
+honorable without our making it
+ 
+
+ align:start position:0%
+honorable without our making it
+honorable
+
+ align:start position:0%
+honorable
+ 
+
+ align:start position:0%
+honorable
+but i shouldn't have to do anything
+
+ align:start position:0%
+but i shouldn't have to do anything
+ 
+
+ align:start position:0%
+but i shouldn't have to do anything
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+than the minimum to make it honorable i
+
+ align:start position:0%
+than the minimum to make it honorable i
+ 
+
+ align:start position:0%
+than the minimum to make it honorable i
+don't going
+
+ align:start position:0%
+don't going
+ 
+
+ align:start position:0%
+don't going
+going beyond and saying i have some
+
+ align:start position:0%
+going beyond and saying i have some
+ 
+
+ align:start position:0%
+going beyond and saying i have some
+respect for the honor of the profession
+
+ align:start position:0%
+respect for the honor of the profession
+ 
+
+ align:start position:0%
+respect for the honor of the profession
+well that's
+
+ align:start position:0%
+well that's
+ 
+
+ align:start position:0%
+well that's
+that's sort of um circular if the
+
+ align:start position:0%
+that's sort of um circular if the
+ 
+
+ align:start position:0%
+that's sort of um circular if the
+profession
+
+ align:start position:0%
+profession
+ 
+
+ align:start position:0%
+profession
+is honorable it's got to earn it
+
+ align:start position:0%
+is honorable it's got to earn it
+ 
+
+ align:start position:0%
+is honorable it's got to earn it
+i shouldn't have to go around and do
+
+ align:start position:0%
+i shouldn't have to go around and do
+ 
+
+ align:start position:0%
+i shouldn't have to go around and do
+something extra to make it honorable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it should be honorable because of what
+
+ align:start position:0%
+it should be honorable because of what
+ 
+
+ align:start position:0%
+it should be honorable because of what
+it because of what it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following all of those things yeah
+
+ align:start position:0%
+following all of those things yeah
+ 
+
+ align:start position:0%
+following all of those things yeah
+make it honorable right
+
+ align:start position:0%
+make it honorable right
+ 
+
+ align:start position:0%
+make it honorable right
+i shouldn't have to go outside of that
+
+ align:start position:0%
+i shouldn't have to go outside of that
+ 
+
+ align:start position:0%
+i shouldn't have to go outside of that
+to enhance the honor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if you say that engineering is
+
+ align:start position:0%
+because if you say that engineering is
+ 
+
+ align:start position:0%
+because if you say that engineering is
+honorable then i should only have to do
+
+ align:start position:0%
+honorable then i should only have to do
+ 
+
+ align:start position:0%
+honorable then i should only have to do
+engineering and it will be honorable
+
+ align:start position:0%
+engineering and it will be honorable
+ 
+
+ align:start position:0%
+engineering and it will be honorable
+then you have this deceived me
+
+ align:start position:0%
+then you have this deceived me
+ 
+
+ align:start position:0%
+then you have this deceived me
+if i have to do more than that to make
+
+ align:start position:0%
+if i have to do more than that to make
+ 
+
+ align:start position:0%
+if i have to do more than that to make
+it honorable
+
+ align:start position:0%
+it honorable
+ 
+
+ align:start position:0%
+it honorable
+so i um
+
+ align:start position:0%
+so i um
+ 
+
+ align:start position:0%
+so i um
+i stand firm on my position but i'm the
+
+ align:start position:0%
+i stand firm on my position but i'm the
+ 
+
+ align:start position:0%
+i stand firm on my position but i'm the
+only one out there saying this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i guess i i think maybe that
+
+ align:start position:0%
+yeah i guess i i think maybe that
+ 
+
+ align:start position:0%
+yeah i guess i i think maybe that
+enhancing the honor or enhancing the
+
+ align:start position:0%
+enhancing the honor or enhancing the
+ 
+
+ align:start position:0%
+enhancing the honor or enhancing the
+public reputation
+
+ align:start position:0%
+public reputation
+ 
+
+ align:start position:0%
+public reputation
+enhancing it not just maintaining it
+
+ align:start position:0%
+enhancing it not just maintaining it
+ 
+
+ align:start position:0%
+enhancing it not just maintaining it
+it's more something that belongs in a
+
+ align:start position:0%
+it's more something that belongs in a
+ 
+
+ align:start position:0%
+it's more something that belongs in a
+recommendation a request
+
+ align:start position:0%
+recommendation a request
+ 
+
+ align:start position:0%
+recommendation a request
+i don't know like
+
+ align:start position:0%
+i don't know like
+ 
+
+ align:start position:0%
+i don't know like
+letter to colleagues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the code of ethics should be the minimum
+
+ align:start position:0%
+the code of ethics should be the minimum
+ 
+
+ align:start position:0%
+the code of ethics should be the minimum
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and the minimum should be good enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and anything that i do above the minimum
+
+ align:start position:0%
+and anything that i do above the minimum
+ 
+
+ align:start position:0%
+and anything that i do above the minimum
+is my business but not an obligation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of these words in ethics duty
+
+ align:start position:0%
+all of these words in ethics duty
+ 
+
+ align:start position:0%
+all of these words in ethics duty
+obligation they're talking about
+
+ align:start position:0%
+obligation they're talking about
+ 
+
+ align:start position:0%
+obligation they're talking about
+minimums
+
+ align:start position:0%
+minimums
+ 
+
+ align:start position:0%
+minimums
+if you go beyond that that's good but i
+
+ align:start position:0%
+if you go beyond that that's good but i
+ 
+
+ align:start position:0%
+if you go beyond that that's good but i
+don't have to go beyond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes and i was overruled
+
+ align:start position:0%
+yes and i was overruled
+ 
+
+ align:start position:0%
+yes and i was overruled
+everywhere
+
+ align:start position:0%
+everywhere
+ 
+
+ align:start position:0%
+everywhere
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh we've got two more minutes uh i
+
+ align:start position:0%
+okay uh we've got two more minutes uh i
+ 
+
+ align:start position:0%
+okay uh we've got two more minutes uh i
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+i think that you've already picked up
+
+ align:start position:0%
+i think that you've already picked up
+ 
+
+ align:start position:0%
+i think that you've already picked up
+that the other codes of ethics do not
+
+ align:start position:0%
+that the other codes of ethics do not
+ 
+
+ align:start position:0%
+that the other codes of ethics do not
+differ substantially or if they do is
+
+ align:start position:0%
+differ substantially or if they do is
+ 
+
+ align:start position:0%
+differ substantially or if they do is
+mainly by abbreviation
+
+ align:start position:0%
+mainly by abbreviation
+ 
+
+ align:start position:0%
+mainly by abbreviation
+of this code
+
+ align:start position:0%
+of this code
+ 
+
+ align:start position:0%
+of this code
+the aaes code is uh
+
+ align:start position:0%
+the aaes code is uh
+ 
+
+ align:start position:0%
+the aaes code is uh
+is unique in as much as it
+
+ align:start position:0%
+is unique in as much as it
+ 
+
+ align:start position:0%
+is unique in as much as it
+stands it it offers it's it's called
+
+ align:start position:0%
+stands it it offers it's it's called
+ 
+
+ align:start position:0%
+stands it it offers it's it's called
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+guide or code
+
+ align:start position:0%
+guide or code
+ 
+
+ align:start position:0%
+guide or code
+and it tries to get
+
+ align:start position:0%
+and it tries to get
+ 
+
+ align:start position:0%
+and it tries to get
+some kind of coherence among all of the
+
+ align:start position:0%
+some kind of coherence among all of the
+ 
+
+ align:start position:0%
+some kind of coherence among all of the
+professional societies that belong to
+
+ align:start position:0%
+professional societies that belong to
+ 
+
+ align:start position:0%
+professional societies that belong to
+the aaes
+
+ align:start position:0%
+the aaes
+ 
+
+ align:start position:0%
+the aaes
+individuals don't belong
+
+ align:start position:0%
+individuals don't belong
+ 
+
+ align:start position:0%
+individuals don't belong
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just a model but but the the reason for
+
+ align:start position:0%
+just a model but but the the reason for
+ 
+
+ align:start position:0%
+just a model but but the the reason for
+it is that
+
+ align:start position:0%
+it is that
+ 
+
+ align:start position:0%
+it is that
+engineers were advised by high-level
+
+ align:start position:0%
+engineers were advised by high-level
+ 
+
+ align:start position:0%
+engineers were advised by high-level
+people in congress
+
+ align:start position:0%
+people in congress
+ 
+
+ align:start position:0%
+people in congress
+that engineering does not have
+
+ align:start position:0%
+that engineering does not have
+ 
+
+ align:start position:0%
+that engineering does not have
+uh force
+
+ align:start position:0%
+uh force
+ 
+
+ align:start position:0%
+uh force
+among
+
+ align:start position:0%
+among
+ 
+
+ align:start position:0%
+among
+uh in congress like the ama has
+
+ align:start position:0%
+uh in congress like the ama has
+ 
+
+ align:start position:0%
+uh in congress like the ama has
+because the ama can speak for the whole
+
+ align:start position:0%
+because the ama can speak for the whole
+ 
+
+ align:start position:0%
+because the ama can speak for the whole
+profession in engineering you got 10 12
+
+ align:start position:0%
+profession in engineering you got 10 12
+ 
+
+ align:start position:0%
+profession in engineering you got 10 12
+different organizations saying different
+
+ align:start position:0%
+different organizations saying different
+ 
+
+ align:start position:0%
+different organizations saying different
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+so if you believe that engineering
+
+ align:start position:0%
+so if you believe that engineering
+ 
+
+ align:start position:0%
+so if you believe that engineering
+should have some force among
+
+ align:start position:0%
+should have some force among
+ 
+
+ align:start position:0%
+should have some force among
+congressional people lobby
+
+ align:start position:0%
+congressional people lobby
+ 
+
+ align:start position:0%
+congressional people lobby
+should have a lobbying
+
+ align:start position:0%
+should have a lobbying
+ 
+
+ align:start position:0%
+should have a lobbying
+uh dimension
+
+ align:start position:0%
+uh dimension
+ 
+
+ align:start position:0%
+uh dimension
+then try to make your code
+
+ align:start position:0%
+then try to make your code
+ 
+
+ align:start position:0%
+then try to make your code
+as consistent with the
+
+ align:start position:0%
+as consistent with the
+ 
+
+ align:start position:0%
+as consistent with the
+aaes model code as you can and that gets
+
+ align:start position:0%
+aaes model code as you can and that gets
+ 
+
+ align:start position:0%
+aaes model code as you can and that gets
+us closer to that other than that you're
+
+ align:start position:0%
+us closer to that other than that you're
+ 
+
+ align:start position:0%
+us closer to that other than that you're
+free to do whatever you want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're going to have a special
+
+ align:start position:0%
+okay so we're going to have a special
+ 
+
+ align:start position:0%
+okay so we're going to have a special
+event coming up friday for those of us
+
+ align:start position:0%
+event coming up friday for those of us
+ 
+
+ align:start position:0%
+event coming up friday for those of us
+who want to go i want to go i'll be
+
+ align:start position:0%
+who want to go i want to go i'll be
+ 
+
+ align:start position:0%
+who want to go i want to go i'll be
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+give us a little five minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i hadn't thought about it
+
+ align:start position:0%
+i hadn't thought about it
+ 
+
+ align:start position:0%
+i hadn't thought about it
+will you email us
+
+ align:start position:0%
+will you email us
+ 
+
+ align:start position:0%
+will you email us
+yeah if i think of i won't be um if i
+
+ align:start position:0%
+yeah if i think of i won't be um if i
+ 
+
+ align:start position:0%
+yeah if i think of i won't be um if i
+think of something on
+
+ align:start position:0%
+think of something on
+ 
+
+ align:start position:0%
+think of something on
+sunday night i won't that'll be too late
+
+ align:start position:0%
+sunday night i won't that'll be too late
+ 
+
+ align:start position:0%
+sunday night i won't that'll be too late
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+actually uh unless i get a brilliant
+
+ align:start position:0%
+actually uh unless i get a brilliant
+ 
+
+ align:start position:0%
+actually uh unless i get a brilliant
+idea which and i think my brain is not
+
+ align:start position:0%
+idea which and i think my brain is not
+ 
+
+ align:start position:0%
+idea which and i think my brain is not
+ready for any brilliant ideas right now
+
+ align:start position:0%
+ready for any brilliant ideas right now
+ 
+
+ align:start position:0%
+ready for any brilliant ideas right now
+unless i get a brilliant idea i'll just
+
+ align:start position:0%
+unless i get a brilliant idea i'll just
+ 
+
+ align:start position:0%
+unless i get a brilliant idea i'll just
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+close out the discussion with codes of
+
+ align:start position:0%
+close out the discussion with codes of
+ 
+
+ align:start position:0%
+close out the discussion with codes of
+ethics
+
+ align:start position:0%
+ethics
+ 
+
+ align:start position:0%
+ethics
+and profession and professionalism
+
+ align:start position:0%
+and profession and professionalism
+ 
+
+ align:start position:0%
+and profession and professionalism
+can we talk about just
+
+ align:start position:0%
+can we talk about just
+ 
+
+ align:start position:0%
+can we talk about just
+in general the the basis of ethics
+
+ align:start position:0%
+in general the the basis of ethics
+ 
+
+ align:start position:0%
+in general the the basis of ethics
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+yeah i mean
+
+ align:start position:0%
+yeah i mean
+ 
+
+ align:start position:0%
+yeah i mean
+it's nice to just take the principle of
+
+ align:start position:0%
+it's nice to just take the principle of
+ 
+
+ align:start position:0%
+it's nice to just take the principle of
+approach and just say this but i think
+
+ align:start position:0%
+approach and just say this but i think
+ 
+
+ align:start position:0%
+approach and just say this but i think
+there are probably some arguments that
+
+ align:start position:0%
+there are probably some arguments that
+ 
+
+ align:start position:0%
+there are probably some arguments that
+can be made i mean use the example of a
+
+ align:start position:0%
+can be made i mean use the example of a
+ 
+
+ align:start position:0%
+can be made i mean use the example of a
+professor who again violate
+
+ align:start position:0%
+professor who again violate
+ 
+
+ align:start position:0%
+professor who again violate
+various
+
+ align:start position:0%
+various
+ 
+
+ align:start position:0%
+various
+aspects of a certain code right but did
+
+ align:start position:0%
+aspects of a certain code right but did
+ 
+
+ align:start position:0%
+aspects of a certain code right but did
+he really do anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by all means bring it up and
+
+ align:start position:0%
+by all means bring it up and
+ 
+
+ align:start position:0%
+by all means bring it up and
+oh i've got some stuff to say on that
+
+ align:start position:0%
+oh i've got some stuff to say on that
+ 
+
+ align:start position:0%
+oh i've got some stuff to say on that
+you know me by now i got something to
+
+ align:start position:0%
+you know me by now i got something to
+ 
+
+ align:start position:0%
+you know me by now i got something to
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+thank you
\ No newline at end of file
diff --git a/JYuMimF6bu0.txt b/JYuMimF6bu0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5c31cd6f36666793828d80262fc79176d8326989
--- /dev/null
+++ b/JYuMimF6bu0.txt
@@ -0,0 +1,8099 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what we're going to do today is
+
+ align:start position:0%
+okay so what we're going to do today is
+ 
+
+ align:start position:0%
+okay so what we're going to do today is
+we're going to finish our coverage of
+
+ align:start position:0%
+we're going to finish our coverage of
+ 
+
+ align:start position:0%
+we're going to finish our coverage of
+statistical thermodynamics
+
+ align:start position:0%
+statistical thermodynamics
+ 
+
+ align:start position:0%
+statistical thermodynamics
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and then we're going to do a couple
+
+ align:start position:0%
+and then we're going to do a couple
+ 
+
+ align:start position:0%
+and then we're going to do a couple
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+starting Monday remember tomorrow's uh
+
+ align:start position:0%
+starting Monday remember tomorrow's uh
+ 
+
+ align:start position:0%
+starting Monday remember tomorrow's uh
+Friday's a holiday so we'll do a couple
+
+ align:start position:0%
+Friday's a holiday so we'll do a couple
+ 
+
+ align:start position:0%
+Friday's a holiday so we'll do a couple
+lectures uh starting Monday on
+
+ align:start position:0%
+lectures uh starting Monday on
+ 
+
+ align:start position:0%
+lectures uh starting Monday on
+reacting systems and that includes
+
+ align:start position:0%
+reacting systems and that includes
+ 
+
+ align:start position:0%
+reacting systems and that includes
+oxidation processes
+
+ align:start position:0%
+oxidation processes
+ 
+
+ align:start position:0%
+oxidation processes
+and that's mainly to half chapter 11 and
+
+ align:start position:0%
+and that's mainly to half chapter 11 and
+ 
+
+ align:start position:0%
+and that's mainly to half chapter 11 and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um and then that'll be it then we're
+
+ align:start position:0%
+um and then that'll be it then we're
+ 
+
+ align:start position:0%
+um and then that'll be it then we're
+going to have one more hour uh in on
+
+ align:start position:0%
+going to have one more hour uh in on
+ 
+
+ align:start position:0%
+going to have one more hour uh in on
+social and personal then we're going to
+
+ align:start position:0%
+social and personal then we're going to
+ 
+
+ align:start position:0%
+social and personal then we're going to
+have a game show which I don't know how
+
+ align:start position:0%
+have a game show which I don't know how
+ 
+
+ align:start position:0%
+have a game show which I don't know how
+to run a resume we're going to try it
+
+ align:start position:0%
+to run a resume we're going to try it
+ 
+
+ align:start position:0%
+to run a resume we're going to try it
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and then uh
+
+ align:start position:0%
+and then uh
+ 
+
+ align:start position:0%
+and then uh
+and then uh and then the the last exam
+
+ align:start position:0%
+and then uh and then the the last exam
+ 
+
+ align:start position:0%
+and then uh and then the the last exam
+which is non-cumulative okay so let's
+
+ align:start position:0%
+which is non-cumulative okay so let's
+ 
+
+ align:start position:0%
+which is non-cumulative okay so let's
+pick up where we left off
+
+ align:start position:0%
+pick up where we left off
+ 
+
+ align:start position:0%
+pick up where we left off
+Max entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the boltzmann distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continued from last lecture so
+
+ align:start position:0%
+continued from last lecture so
+ 
+
+ align:start position:0%
+continued from last lecture so
+I don't like to do this where I sort of
+
+ align:start position:0%
+I don't like to do this where I sort of
+ 
+
+ align:start position:0%
+I don't like to do this where I sort of
+continue with derivation and something
+
+ align:start position:0%
+continue with derivation and something
+ 
+
+ align:start position:0%
+continue with derivation and something
+across two lectures but um that's how it
+
+ align:start position:0%
+across two lectures but um that's how it
+ 
+
+ align:start position:0%
+across two lectures but um that's how it
+broke
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from last time just um at a high
+
+ align:start position:0%
+so from last time just um at a high
+ 
+
+ align:start position:0%
+so from last time just um at a high
+level we decided that we wanted to
+
+ align:start position:0%
+level we decided that we wanted to
+ 
+
+ align:start position:0%
+level we decided that we wanted to
+optimize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy
+
+ align:start position:0%
+entropy
+ 
+
+ align:start position:0%
+entropy
+for an isolated system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we had both an entropy formula so we
+
+ align:start position:0%
+and we had both an entropy formula so we
+ 
+
+ align:start position:0%
+and we had both an entropy formula so we
+could do some some math and we could uh
+
+ align:start position:0%
+could do some some math and we could uh
+ 
+
+ align:start position:0%
+could do some some math and we could uh
+write down the S equals zero
+
+ align:start position:0%
+write down the S equals zero
+ 
+
+ align:start position:0%
+write down the S equals zero
+subject
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the constraints being conservation
+
+ align:start position:0%
+and the constraints being conservation
+ 
+
+ align:start position:0%
+and the constraints being conservation
+of energy
+
+ align:start position:0%
+of energy
+ 
+
+ align:start position:0%
+of energy
+and conservation of mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to do this using the
+
+ align:start position:0%
+and we're going to do this using the
+ 
+
+ align:start position:0%
+and we're going to do this using the
+method of LaGrange multipliers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we had two of them because we had
+
+ align:start position:0%
+and we had two of them because we had
+ 
+
+ align:start position:0%
+and we had two of them because we had
+two constraints
+
+ align:start position:0%
+two constraints
+ 
+
+ align:start position:0%
+two constraints
+Alpha and beta and we ended up with an
+
+ align:start position:0%
+Alpha and beta and we ended up with an
+ 
+
+ align:start position:0%
+Alpha and beta and we ended up with an
+expression like this
+
+ align:start position:0%
+expression like this
+ 
+
+ align:start position:0%
+expression like this
+some stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so coefficient
+
+ align:start position:0%
+so coefficient
+ 
+
+ align:start position:0%
+so coefficient
+independent variables and in order to
+
+ align:start position:0%
+independent variables and in order to
+ 
+
+ align:start position:0%
+independent variables and in order to
+get our Max entropy condition I should
+
+ align:start position:0%
+get our Max entropy condition I should
+ 
+
+ align:start position:0%
+get our Max entropy condition I should
+say optimize entropy we had to set these
+
+ align:start position:0%
+say optimize entropy we had to set these
+ 
+
+ align:start position:0%
+say optimize entropy we had to set these
+coefficients to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a very sort of familiar
+
+ align:start position:0%
+so there's a very sort of familiar
+ 
+
+ align:start position:0%
+so there's a very sort of familiar
+thermodynamic thing that we did
+
+ align:start position:0%
+thermodynamic thing that we did
+ 
+
+ align:start position:0%
+thermodynamic thing that we did
+and what
+
+ align:start position:0%
+and what
+ 
+
+ align:start position:0%
+and what
+we determined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first multiplier by normalization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is um where we left off where we
+
+ align:start position:0%
+so this is um where we left off where we
+ 
+
+ align:start position:0%
+so this is um where we left off where we
+left off was the following we had ni
+
+ align:start position:0%
+left off was the following we had ni
+ 
+
+ align:start position:0%
+left off was the following we had ni
+Over N total so this is a distribution
+
+ align:start position:0%
+Over N total so this is a distribution
+ 
+
+ align:start position:0%
+Over N total so this is a distribution
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+of fractional distributions of particles
+
+ align:start position:0%
+of fractional distributions of particles
+ 
+
+ align:start position:0%
+of fractional distributions of particles
+in state I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normalized by the total number of
+
+ align:start position:0%
+normalized by the total number of
+ 
+
+ align:start position:0%
+normalized by the total number of
+particles and it was like this
+
+ align:start position:0%
+particles and it was like this
+ 
+
+ align:start position:0%
+particles and it was like this
+this multiplier beta as yet undetermined
+
+ align:start position:0%
+this multiplier beta as yet undetermined
+ 
+
+ align:start position:0%
+this multiplier beta as yet undetermined
+energy of State I
+
+ align:start position:0%
+energy of State I
+ 
+
+ align:start position:0%
+energy of State I
+normalized by Boltzmann's constant
+
+ align:start position:0%
+normalized by Boltzmann's constant
+ 
+
+ align:start position:0%
+normalized by Boltzmann's constant
+and that whole thing normalized by Q
+
+ align:start position:0%
+and that whole thing normalized by Q
+ 
+
+ align:start position:0%
+and that whole thing normalized by Q
+which was the partition function and
+
+ align:start position:0%
+which was the partition function and
+ 
+
+ align:start position:0%
+which was the partition function and
+this was the sum over all possible
+
+ align:start position:0%
+this was the sum over all possible
+ 
+
+ align:start position:0%
+this was the sum over all possible
+States e to the beta
+
+ align:start position:0%
+States e to the beta
+ 
+
+ align:start position:0%
+States e to the beta
+Epsilon I over Boltzmann's Constant and
+
+ align:start position:0%
+Epsilon I over Boltzmann's Constant and
+ 
+
+ align:start position:0%
+Epsilon I over Boltzmann's Constant and
+so this is where we left things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so now what we're going to do is we're
+
+ align:start position:0%
+so now what we're going to do is we're
+ 
+
+ align:start position:0%
+so now what we're going to do is we're
+going to determine beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to determine beta by
+
+ align:start position:0%
+we're going to determine beta by
+ 
+
+ align:start position:0%
+we're going to determine beta by
+considering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a microscopic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reversible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+where some of the particles change their
+
+ align:start position:0%
+where some of the particles change their
+ 
+
+ align:start position:0%
+where some of the particles change their
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+so we're going to do is we're going to
+
+ align:start position:0%
+so we're going to do is we're going to
+ 
+
+ align:start position:0%
+so we're going to do is we're going to
+analyze the s for a process of some
+
+ align:start position:0%
+analyze the s for a process of some
+ 
+
+ align:start position:0%
+analyze the s for a process of some
+State changes
+
+ align:start position:0%
+State changes
+ 
+
+ align:start position:0%
+State changes
+I'm going to just go ahead and write
+
+ align:start position:0%
+I'm going to just go ahead and write
+ 
+
+ align:start position:0%
+I'm going to just go ahead and write
+down the equations that we've been using
+
+ align:start position:0%
+down the equations that we've been using
+ 
+
+ align:start position:0%
+down the equations that we've been using
+and developing for this the S equals log
+
+ align:start position:0%
+and developing for this the S equals log
+ 
+
+ align:start position:0%
+and developing for this the S equals log
+n of I over n total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DN of I you can pull that from
+
+ align:start position:0%
+DN of I you can pull that from
+ 
+
+ align:start position:0%
+DN of I you can pull that from
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know the last two lectures but now
+
+ align:start position:0%
+you know the last two lectures but now
+ 
+
+ align:start position:0%
+you know the last two lectures but now
+we actually have an expression for this
+
+ align:start position:0%
+we actually have an expression for this
+ 
+
+ align:start position:0%
+we actually have an expression for this
+distribution so we're going to use that
+
+ align:start position:0%
+distribution so we're going to use that
+ 
+
+ align:start position:0%
+distribution so we're going to use that
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+KB sum
+
+ align:start position:0%
+KB sum
+ 
+
+ align:start position:0%
+KB sum
+over I
+
+ align:start position:0%
+over I
+ 
+
+ align:start position:0%
+over I
+that distribution is e to the beta
+
+ align:start position:0%
+that distribution is e to the beta
+ 
+
+ align:start position:0%
+that distribution is e to the beta
+Epsilon I over boltzmann constant
+
+ align:start position:0%
+Epsilon I over boltzmann constant
+ 
+
+ align:start position:0%
+Epsilon I over boltzmann constant
+over Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we have some logs of exponentials
+
+ align:start position:0%
+then we have some logs of exponentials
+ 
+
+ align:start position:0%
+then we have some logs of exponentials
+and things so we can simplify this a
+
+ align:start position:0%
+and things so we can simplify this a
+ 
+
+ align:start position:0%
+and things so we can simplify this a
+little bit and this equals
+
+ align:start position:0%
+little bit and this equals
+ 
+
+ align:start position:0%
+little bit and this equals
+minus beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum over I
+
+ align:start position:0%
+sum over I
+ 
+
+ align:start position:0%
+sum over I
+Epsilon I
+
+ align:start position:0%
+Epsilon I
+ 
+
+ align:start position:0%
+Epsilon I
+d n of I
+
+ align:start position:0%
+d n of I
+ 
+
+ align:start position:0%
+d n of I
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+K beta
+
+ align:start position:0%
+K beta
+ 
+
+ align:start position:0%
+K beta
+log of Q
+
+ align:start position:0%
+log of Q
+ 
+
+ align:start position:0%
+log of Q
+sum over I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d n of I
+
+ align:start position:0%
+d n of I
+ 
+
+ align:start position:0%
+d n of I
+and taking our definitions this equals
+
+ align:start position:0%
+and taking our definitions this equals
+ 
+
+ align:start position:0%
+and taking our definitions this equals
+minus beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+k b
+
+ align:start position:0%
+k b
+ 
+
+ align:start position:0%
+k b
+log of Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d n total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um first thing to note
+
+ align:start position:0%
+um first thing to note
+ 
+
+ align:start position:0%
+um first thing to note
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+right this is zero by construction right
+
+ align:start position:0%
+right this is zero by construction right
+ 
+
+ align:start position:0%
+right this is zero by construction right
+this is the LaGrange multiplier uh
+
+ align:start position:0%
+this is the LaGrange multiplier uh
+ 
+
+ align:start position:0%
+this is the LaGrange multiplier uh
+working
+
+ align:start position:0%
+working
+ 
+
+ align:start position:0%
+working
+right because we we wanted DS to be zero
+
+ align:start position:0%
+right because we we wanted DS to be zero
+ 
+
+ align:start position:0%
+right because we we wanted DS to be zero
+under conditions where D U was zero and
+
+ align:start position:0%
+under conditions where D U was zero and
+ 
+
+ align:start position:0%
+under conditions where D U was zero and
+DN total were zero
+
+ align:start position:0%
+DN total were zero
+ 
+
+ align:start position:0%
+DN total were zero
+and we see that for this distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it works out
+
+ align:start position:0%
+it works out
+ 
+
+ align:start position:0%
+it works out
+so the garage multiplier worked the
+
+ align:start position:0%
+so the garage multiplier worked the
+ 
+
+ align:start position:0%
+so the garage multiplier worked the
+method worked
+
+ align:start position:0%
+method worked
+ 
+
+ align:start position:0%
+method worked
+so I'm going to say 0 by Construction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if if you um I really like this
+
+ align:start position:0%
+and if if you um I really like this
+ 
+
+ align:start position:0%
+and if if you um I really like this
+orange pen but life is too short for
+
+ align:start position:0%
+orange pen but life is too short for
+ 
+
+ align:start position:0%
+orange pen but life is too short for
+fading Sharpies okay I I
+
+ align:start position:0%
+fading Sharpies okay I I
+ 
+
+ align:start position:0%
+fading Sharpies okay I I
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so by construction this is zero now if
+
+ align:start position:0%
+so by construction this is zero now if
+ 
+
+ align:start position:0%
+so by construction this is zero now if
+you like you can convince yourself that
+
+ align:start position:0%
+you like you can convince yourself that
+ 
+
+ align:start position:0%
+you like you can convince yourself that
+if you have a different distribution
+
+ align:start position:0%
+if you have a different distribution
+ 
+
+ align:start position:0%
+if you have a different distribution
+function here if you have a different
+
+ align:start position:0%
+function here if you have a different
+ 
+
+ align:start position:0%
+function here if you have a different
+distribution function not this
+
+ align:start position:0%
+distribution function not this
+ 
+
+ align:start position:0%
+distribution function not this
+distribution let's say a flat
+
+ align:start position:0%
+distribution let's say a flat
+ 
+
+ align:start position:0%
+distribution let's say a flat
+distribution function a distribution
+
+ align:start position:0%
+distribution function a distribution
+ 
+
+ align:start position:0%
+distribution function a distribution
+function that doesn't depend on energy
+
+ align:start position:0%
+function that doesn't depend on energy
+ 
+
+ align:start position:0%
+function that doesn't depend on energy
+or has some other functional dependence
+
+ align:start position:0%
+or has some other functional dependence
+ 
+
+ align:start position:0%
+or has some other functional dependence
+of energy like I don't know what if some
+
+ align:start position:0%
+of energy like I don't know what if some
+ 
+
+ align:start position:0%
+of energy like I don't know what if some
+polynomial it could be anything in there
+
+ align:start position:0%
+polynomial it could be anything in there
+ 
+
+ align:start position:0%
+polynomial it could be anything in there
+you can show that in that case DS
+
+ align:start position:0%
+you can show that in that case DS
+ 
+
+ align:start position:0%
+you can show that in that case DS
+um will not be zero
+
+ align:start position:0%
+um will not be zero
+ 
+
+ align:start position:0%
+um will not be zero
+yeah so again LaGrange multiplier method
+
+ align:start position:0%
+yeah so again LaGrange multiplier method
+ 
+
+ align:start position:0%
+yeah so again LaGrange multiplier method
+works but here's here's the takeaway we
+
+ align:start position:0%
+works but here's here's the takeaway we
+ 
+
+ align:start position:0%
+works but here's here's the takeaway we
+want to compare this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to what we have uh derived two months
+
+ align:start position:0%
+to what we have uh derived two months
+ 
+
+ align:start position:0%
+to what we have uh derived two months
+ago
+
+ align:start position:0%
+ago
+ 
+
+ align:start position:0%
+ago
+from the combined statement
+
+ align:start position:0%
+from the combined statement
+ 
+
+ align:start position:0%
+from the combined statement
+which is a DS equals 1 over t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d u
+
+ align:start position:0%
+d u
+ 
+
+ align:start position:0%
+d u
+plus p over t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DV
+
+ align:start position:0%
+DV
+ 
+
+ align:start position:0%
+DV
+minus mu over t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b m
+
+ align:start position:0%
+b m
+ 
+
+ align:start position:0%
+b m
+and this is really the important thing
+
+ align:start position:0%
+and this is really the important thing
+ 
+
+ align:start position:0%
+and this is really the important thing
+here we are comparing
+
+ align:start position:0%
+here we are comparing
+ 
+
+ align:start position:0%
+here we are comparing
+the coefficients
+
+ align:start position:0%
+the coefficients
+ 
+
+ align:start position:0%
+the coefficients
+we're comparing the coefficients and if
+
+ align:start position:0%
+we're comparing the coefficients and if
+ 
+
+ align:start position:0%
+we're comparing the coefficients and if
+you remember
+
+ align:start position:0%
+you remember
+ 
+
+ align:start position:0%
+you remember
+this is almost like General strategy
+
+ align:start position:0%
+this is almost like General strategy
+ 
+
+ align:start position:0%
+this is almost like General strategy
+stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you compare coefficients you can buy
+
+ align:start position:0%
+if you compare coefficients you can buy
+ 
+
+ align:start position:0%
+if you compare coefficients you can buy
+inspection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right set like coefficients to like
+
+ align:start position:0%
+right set like coefficients to like
+ 
+
+ align:start position:0%
+right set like coefficients to like
+so what is DS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at fixed volume
+
+ align:start position:0%
+at fixed volume
+ 
+
+ align:start position:0%
+at fixed volume
+and fixed particle number
+
+ align:start position:0%
+and fixed particle number
+ 
+
+ align:start position:0%
+and fixed particle number
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+from our statistical method
+
+ align:start position:0%
+from our statistical method
+ 
+
+ align:start position:0%
+from our statistical method
+that's minus beta
+
+ align:start position:0%
+that's minus beta
+ 
+
+ align:start position:0%
+that's minus beta
+but from the classical method
+
+ align:start position:0%
+but from the classical method
+ 
+
+ align:start position:0%
+but from the classical method
+that's one over temperature
+
+ align:start position:0%
+that's one over temperature
+ 
+
+ align:start position:0%
+that's one over temperature
+and so we can simply conclude that beta
+
+ align:start position:0%
+and so we can simply conclude that beta
+ 
+
+ align:start position:0%
+and so we can simply conclude that beta
+equals minus one
+
+ align:start position:0%
+equals minus one
+ 
+
+ align:start position:0%
+equals minus one
+over temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now with that identified we have the
+
+ align:start position:0%
+so now with that identified we have the
+ 
+
+ align:start position:0%
+so now with that identified we have the
+Bolton distribution oh
+
+ align:start position:0%
+Bolton distribution oh
+ 
+
+ align:start position:0%
+Bolton distribution oh
+there's more paper so with
+
+ align:start position:0%
+there's more paper so with
+ 
+
+ align:start position:0%
+there's more paper so with
+beta equals minus 1 over temperature
+
+ align:start position:0%
+beta equals minus 1 over temperature
+ 
+
+ align:start position:0%
+beta equals minus 1 over temperature
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the both distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number of particles in state I
+
+ align:start position:0%
+number of particles in state I
+ 
+
+ align:start position:0%
+number of particles in state I
+normalized by the total number of
+
+ align:start position:0%
+normalized by the total number of
+ 
+
+ align:start position:0%
+normalized by the total number of
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+equals e to the minus E I
+
+ align:start position:0%
+equals e to the minus E I
+ 
+
+ align:start position:0%
+equals e to the minus E I
+over k b
+
+ align:start position:0%
+over k b
+ 
+
+ align:start position:0%
+over k b
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+normalized by the rotation function or
+
+ align:start position:0%
+normalized by the rotation function or
+ 
+
+ align:start position:0%
+normalized by the rotation function or
+the partition function
+
+ align:start position:0%
+the partition function
+ 
+
+ align:start position:0%
+the partition function
+equals the sum over all states e to the
+
+ align:start position:0%
+equals the sum over all states e to the
+ 
+
+ align:start position:0%
+equals the sum over all states e to the
+minus E I over k
+
+ align:start position:0%
+minus E I over k
+ 
+
+ align:start position:0%
+minus E I over k
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+and this generally has a a falling
+
+ align:start position:0%
+and this generally has a a falling
+ 
+
+ align:start position:0%
+and this generally has a a falling
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+with State energy
+
+ align:start position:0%
+with State energy
+ 
+
+ align:start position:0%
+with State energy
+so State energy e of I
+
+ align:start position:0%
+so State energy e of I
+ 
+
+ align:start position:0%
+so State energy e of I
+occupation n of I
+
+ align:start position:0%
+occupation n of I
+ 
+
+ align:start position:0%
+occupation n of I
+right it's a falling exponential
+
+ align:start position:0%
+right it's a falling exponential
+ 
+
+ align:start position:0%
+right it's a falling exponential
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in words this is the distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that maximizes entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for an isolated system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+and total particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distributed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with fixed energy levels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so unchanging energy levels
+
+ align:start position:0%
+so unchanging energy levels
+ 
+
+ align:start position:0%
+so unchanging energy levels
+according to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that set of occupation numbers
+
+ align:start position:0%
+that set of occupation numbers
+ 
+
+ align:start position:0%
+that set of occupation numbers
+and what is maximum what is the state of
+
+ align:start position:0%
+and what is maximum what is the state of
+ 
+
+ align:start position:0%
+and what is maximum what is the state of
+Maximum entropy for an isolated system
+
+ align:start position:0%
+Maximum entropy for an isolated system
+ 
+
+ align:start position:0%
+Maximum entropy for an isolated system
+we have a name for that
+
+ align:start position:0%
+we have a name for that
+ 
+
+ align:start position:0%
+we have a name for that
+what's the state of Max entropy for an
+
+ align:start position:0%
+what's the state of Max entropy for an
+ 
+
+ align:start position:0%
+what's the state of Max entropy for an
+isolated system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think way back
+
+ align:start position:0%
+I think way back
+ 
+
+ align:start position:0%
+I think way back
+to late February even
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is an equilibrium distribution
+
+ align:start position:0%
+so this is an equilibrium distribution
+ 
+
+ align:start position:0%
+so this is an equilibrium distribution
+so we have an equilibrium distribution
+
+ align:start position:0%
+so we have an equilibrium distribution
+ 
+
+ align:start position:0%
+so we have an equilibrium distribution
+of single particle energy levels or
+
+ align:start position:0%
+of single particle energy levels or
+ 
+
+ align:start position:0%
+of single particle energy levels or
+single particle Energies
+
+ align:start position:0%
+single particle Energies
+ 
+
+ align:start position:0%
+single particle Energies
+and again
+
+ align:start position:0%
+and again
+ 
+
+ align:start position:0%
+and again
+um you know you knew this uh already but
+
+ align:start position:0%
+um you know you knew this uh already but
+ 
+
+ align:start position:0%
+um you know you knew this uh already but
+you know equilibrium does not mean
+
+ align:start position:0%
+you know equilibrium does not mean
+ 
+
+ align:start position:0%
+you know equilibrium does not mean
+everything is at the lowest energy all
+
+ align:start position:0%
+everything is at the lowest energy all
+ 
+
+ align:start position:0%
+everything is at the lowest energy all
+semester we've been exploring that
+
+ align:start position:0%
+semester we've been exploring that
+ 
+
+ align:start position:0%
+semester we've been exploring that
+consequence so you know if you were if
+
+ align:start position:0%
+consequence so you know if you were if
+ 
+
+ align:start position:0%
+consequence so you know if you were if
+you were at zero Kelvin
+
+ align:start position:0%
+you were at zero Kelvin
+ 
+
+ align:start position:0%
+you were at zero Kelvin
+if you're at zero Kelvin
+
+ align:start position:0%
+if you're at zero Kelvin
+ 
+
+ align:start position:0%
+if you're at zero Kelvin
+uh or you're a physicist which means
+
+ align:start position:0%
+uh or you're a physicist which means
+ 
+
+ align:start position:0%
+uh or you're a physicist which means
+you're a frigid heart you're a zero
+
+ align:start position:0%
+you're a frigid heart you're a zero
+ 
+
+ align:start position:0%
+you're a frigid heart you're a zero
+Kelvin this is your distribution
+
+ align:start position:0%
+Kelvin this is your distribution
+ 
+
+ align:start position:0%
+Kelvin this is your distribution
+function everything's piled up
+
+ align:start position:0%
+function everything's piled up
+ 
+
+ align:start position:0%
+function everything's piled up
+has zero energy
+
+ align:start position:0%
+has zero energy
+ 
+
+ align:start position:0%
+has zero energy
+right but at any real temperature
+
+ align:start position:0%
+right but at any real temperature
+ 
+
+ align:start position:0%
+right but at any real temperature
+you you can have you get energetic
+
+ align:start position:0%
+you you can have you get energetic
+ 
+
+ align:start position:0%
+you you can have you get energetic
+particles and you get them with a
+
+ align:start position:0%
+particles and you get them with a
+ 
+
+ align:start position:0%
+particles and you get them with a
+distribution function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so a couple observations here the
+
+ align:start position:0%
+okay so a couple observations here the
+ 
+
+ align:start position:0%
+okay so a couple observations here the
+first observation is
+
+ align:start position:0%
+first observation is
+ 
+
+ align:start position:0%
+first observation is
+Maxwell distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry it said boltzmann
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and likelihood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+likelihood
+
+ align:start position:0%
+likelihood
+ 
+
+ align:start position:0%
+likelihood
+um this is a stealth class on statistics
+
+ align:start position:0%
+um this is a stealth class on statistics
+ 
+
+ align:start position:0%
+um this is a stealth class on statistics
+right that's what statistical
+
+ align:start position:0%
+right that's what statistical
+ 
+
+ align:start position:0%
+right that's what statistical
+thermodynamics is it's like a stealth
+
+ align:start position:0%
+thermodynamics is it's like a stealth
+ 
+
+ align:start position:0%
+thermodynamics is it's like a stealth
+class on statistics so we'll ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how much less likely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to find
+
+ align:start position:0%
+to find
+ 
+
+ align:start position:0%
+to find
+a particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say
+
+ align:start position:0%
+let's say
+ 
+
+ align:start position:0%
+let's say
+e let's say e m
+
+ align:start position:0%
+e let's say e m
+ 
+
+ align:start position:0%
+e let's say e m
+that's an ugly Epsilon equals e l plus
+
+ align:start position:0%
+that's an ugly Epsilon equals e l plus
+ 
+
+ align:start position:0%
+that's an ugly Epsilon equals e l plus
+Delta e
+
+ align:start position:0%
+Delta e
+ 
+
+ align:start position:0%
+Delta e
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+in state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+El
+
+ align:start position:0%
+El
+ 
+
+ align:start position:0%
+El
+F so that's a typical thing that you
+
+ align:start position:0%
+F so that's a typical thing that you
+ 
+
+ align:start position:0%
+F so that's a typical thing that you
+might need to analyze
+
+ align:start position:0%
+might need to analyze
+ 
+
+ align:start position:0%
+might need to analyze
+so let's see
+
+ align:start position:0%
+so let's see
+ 
+
+ align:start position:0%
+so let's see
+NM over NL right that's how you turn the
+
+ align:start position:0%
+NM over NL right that's how you turn the
+ 
+
+ align:start position:0%
+NM over NL right that's how you turn the
+word problem into a math problem how
+
+ align:start position:0%
+word problem into a math problem how
+ 
+
+ align:start position:0%
+word problem into a math problem how
+much less likely is it to find this
+
+ align:start position:0%
+much less likely is it to find this
+ 
+
+ align:start position:0%
+much less likely is it to find this
+distribution and this distribution or
+
+ align:start position:0%
+distribution and this distribution or
+ 
+
+ align:start position:0%
+distribution and this distribution or
+you know within within the equilibrium
+
+ align:start position:0%
+you know within within the equilibrium
+ 
+
+ align:start position:0%
+you know within within the equilibrium
+distribution how much smaller is this
+
+ align:start position:0%
+distribution how much smaller is this
+ 
+
+ align:start position:0%
+distribution how much smaller is this
+number than this number and um you'll
+
+ align:start position:0%
+number than this number and um you'll
+ 
+
+ align:start position:0%
+number than this number and um you'll
+find the
+
+ align:start position:0%
+find the
+ 
+
+ align:start position:0%
+find the
+the partition functions cancel out
+
+ align:start position:0%
+the partition functions cancel out
+ 
+
+ align:start position:0%
+the partition functions cancel out
+and you get the following
+
+ align:start position:0%
+and you get the following
+ 
+
+ align:start position:0%
+and you get the following
+El plus Delta e
+
+ align:start position:0%
+El plus Delta e
+ 
+
+ align:start position:0%
+El plus Delta e
+over K T over e
+
+ align:start position:0%
+over K T over e
+ 
+
+ align:start position:0%
+over K T over e
+to the minus e l
+
+ align:start position:0%
+to the minus e l
+ 
+
+ align:start position:0%
+to the minus e l
+over KT
+
+ align:start position:0%
+over KT
+ 
+
+ align:start position:0%
+over KT
+and so the e to the minus e l's cancel
+
+ align:start position:0%
+and so the e to the minus e l's cancel
+ 
+
+ align:start position:0%
+and so the e to the minus e l's cancel
+and you get e to the minus
+
+ align:start position:0%
+and you get e to the minus
+ 
+
+ align:start position:0%
+and you get e to the minus
+Delta e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over KT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this depends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depends on Delta Epsilon
+
+ align:start position:0%
+depends on Delta Epsilon
+ 
+
+ align:start position:0%
+depends on Delta Epsilon
+over KT clearly right
+
+ align:start position:0%
+over KT clearly right
+ 
+
+ align:start position:0%
+over KT clearly right
+it becomes less likely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with increasing energy splitting Delta e
+
+ align:start position:0%
+with increasing energy splitting Delta e
+ 
+
+ align:start position:0%
+with increasing energy splitting Delta e
+and it becomes
+
+ align:start position:0%
+and it becomes
+ 
+
+ align:start position:0%
+and it becomes
+more likely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so you're going to explore
+
+ align:start position:0%
+right okay so you're going to explore
+ 
+
+ align:start position:0%
+right okay so you're going to explore
+this a little bit uh on the pset and the
+
+ align:start position:0%
+this a little bit uh on the pset and the
+ 
+
+ align:start position:0%
+this a little bit uh on the pset and the
+context of um semiconductors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the thermal energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this quantity is really important
+
+ align:start position:0%
+right this quantity is really important
+ 
+
+ align:start position:0%
+right this quantity is really important
+it shows up in the Natural Sciences over
+
+ align:start position:0%
+it shows up in the Natural Sciences over
+ 
+
+ align:start position:0%
+it shows up in the Natural Sciences over
+and over and over again
+
+ align:start position:0%
+and over and over again
+ 
+
+ align:start position:0%
+and over and over again
+and we're starting to see why right the
+
+ align:start position:0%
+and we're starting to see why right the
+ 
+
+ align:start position:0%
+and we're starting to see why right the
+why is what we've just shown right
+
+ align:start position:0%
+why is what we've just shown right
+ 
+
+ align:start position:0%
+why is what we've just shown right
+um but the implications are really broad
+
+ align:start position:0%
+um but the implications are really broad
+ 
+
+ align:start position:0%
+um but the implications are really broad
+you're going to see this all over the
+
+ align:start position:0%
+you're going to see this all over the
+ 
+
+ align:start position:0%
+you're going to see this all over the
+place so let's remind ourselves with
+
+ align:start position:0%
+place so let's remind ourselves with
+ 
+
+ align:start position:0%
+place so let's remind ourselves with
+both swing constant is it's R Over N A
+
+ align:start position:0%
+both swing constant is it's R Over N A
+ 
+
+ align:start position:0%
+both swing constant is it's R Over N A
+oh that's finally RNA so it's it's the
+
+ align:start position:0%
+oh that's finally RNA so it's it's the
+ 
+
+ align:start position:0%
+oh that's finally RNA so it's it's the
+ideal gas constant divided by Avogadro's
+
+ align:start position:0%
+ideal gas constant divided by Avogadro's
+ 
+
+ align:start position:0%
+ideal gas constant divided by Avogadro's
+number we have that from before
+
+ align:start position:0%
+number we have that from before
+ 
+
+ align:start position:0%
+number we have that from before
+and this is something uh let's see
+
+ align:start position:0%
+and this is something uh let's see
+ 
+
+ align:start position:0%
+and this is something uh let's see
+1.380e to the minus 23 joules per Kelvin
+
+ align:start position:0%
+1.380e to the minus 23 joules per Kelvin
+ 
+
+ align:start position:0%
+1.380e to the minus 23 joules per Kelvin
+so it has units of entropy
+
+ align:start position:0%
+so it has units of entropy
+ 
+
+ align:start position:0%
+so it has units of entropy
+um but but that's not a number that I
+
+ align:start position:0%
+um but but that's not a number that I
+ 
+
+ align:start position:0%
+um but but that's not a number that I
+remember here's a number I do remember
+
+ align:start position:0%
+remember here's a number I do remember
+ 
+
+ align:start position:0%
+remember here's a number I do remember
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and if you work on uh molecular systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or semiconductor systems
+
+ align:start position:0%
+or semiconductor systems
+ 
+
+ align:start position:0%
+or semiconductor systems
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+pretty much well gee a lot of systems
+
+ align:start position:0%
+pretty much well gee a lot of systems
+ 
+
+ align:start position:0%
+pretty much well gee a lot of systems
+that we work on in dmse this is a useful
+
+ align:start position:0%
+that we work on in dmse this is a useful
+ 
+
+ align:start position:0%
+that we work on in dmse this is a useful
+number to have memorized Bozeman's
+
+ align:start position:0%
+number to have memorized Bozeman's
+ 
+
+ align:start position:0%
+number to have memorized Bozeman's
+constant in units of EV for Kelvin 8.617
+
+ align:start position:0%
+constant in units of EV for Kelvin 8.617
+ 
+
+ align:start position:0%
+constant in units of EV for Kelvin 8.617
+e minus five
+
+ align:start position:0%
+e minus five
+ 
+
+ align:start position:0%
+e minus five
+why on Earth would you memorize that
+
+ align:start position:0%
+why on Earth would you memorize that
+ 
+
+ align:start position:0%
+why on Earth would you memorize that
+it sets
+
+ align:start position:0%
+it sets
+ 
+
+ align:start position:0%
+it sets
+the energy scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for likely
+
+ align:start position:0%
+for likely
+ 
+
+ align:start position:0%
+for likely
+fluctuations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and we have
+
+ align:start position:0%
+right and we have
+ 
+
+ align:start position:0%
+right and we have
+all these words are have meaning right
+
+ align:start position:0%
+all these words are have meaning right
+ 
+
+ align:start position:0%
+all these words are have meaning right
+likely
+
+ align:start position:0%
+likely
+ 
+
+ align:start position:0%
+likely
+fluctuations right those words kind of
+
+ align:start position:0%
+fluctuations right those words kind of
+ 
+
+ align:start position:0%
+fluctuations right those words kind of
+carry a lot of weight so fluctuation
+
+ align:start position:0%
+carry a lot of weight so fluctuation
+ 
+
+ align:start position:0%
+carry a lot of weight so fluctuation
+single particle fluctuations with energy
+
+ align:start position:0%
+single particle fluctuations with energy
+ 
+
+ align:start position:0%
+single particle fluctuations with energy
+on the order of k b t r
+
+ align:start position:0%
+on the order of k b t r
+ 
+
+ align:start position:0%
+on the order of k b t r
+they're likely
+
+ align:start position:0%
+they're likely
+ 
+
+ align:start position:0%
+they're likely
+it's something you're going to find
+
+ align:start position:0%
+it's something you're going to find
+ 
+
+ align:start position:0%
+it's something you're going to find
+naturally occurring
+
+ align:start position:0%
+naturally occurring
+ 
+
+ align:start position:0%
+naturally occurring
+as opposed to fluctuations which are
+
+ align:start position:0%
+as opposed to fluctuations which are
+ 
+
+ align:start position:0%
+as opposed to fluctuations which are
+much much larger than the thermally
+
+ align:start position:0%
+much much larger than the thermally
+ 
+
+ align:start position:0%
+much much larger than the thermally
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+those are unlikely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have all sorts of language for this
+
+ align:start position:0%
+we have all sorts of language for this
+ 
+
+ align:start position:0%
+we have all sorts of language for this
+that comes up in all sorts of contexts
+
+ align:start position:0%
+that comes up in all sorts of contexts
+ 
+
+ align:start position:0%
+that comes up in all sorts of contexts
+for example these fluctuations
+
+ align:start position:0%
+for example these fluctuations
+ 
+
+ align:start position:0%
+for example these fluctuations
+might be called thermally activated
+
+ align:start position:0%
+might be called thermally activated
+ 
+
+ align:start position:0%
+might be called thermally activated
+processes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you need a little bit of thermal
+
+ align:start position:0%
+right you need a little bit of thermal
+ 
+
+ align:start position:0%
+right you need a little bit of thermal
+energy to activate it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so not only is this a number
+
+ align:start position:0%
+all right so not only is this a number
+ 
+
+ align:start position:0%
+all right so not only is this a number
+you should know but
+
+ align:start position:0%
+you should know but
+ 
+
+ align:start position:0%
+you should know but
+the thermal energy at room temperature
+
+ align:start position:0%
+the thermal energy at room temperature
+ 
+
+ align:start position:0%
+the thermal energy at room temperature
+is a number you should know
+
+ align:start position:0%
+is a number you should know
+ 
+
+ align:start position:0%
+is a number you should know
+a 298 Kelvin
+
+ align:start position:0%
+a 298 Kelvin
+ 
+
+ align:start position:0%
+a 298 Kelvin
+KBT equals well in joules it's not a
+
+ align:start position:0%
+KBT equals well in joules it's not a
+ 
+
+ align:start position:0%
+KBT equals well in joules it's not a
+number that I know because it's kind of
+
+ align:start position:0%
+number that I know because it's kind of
+ 
+
+ align:start position:0%
+number that I know because it's kind of
+unwieldy
+
+ align:start position:0%
+unwieldy
+ 
+
+ align:start position:0%
+unwieldy
+but in EV it is a number I know that's
+
+ align:start position:0%
+but in EV it is a number I know that's
+ 
+
+ align:start position:0%
+but in EV it is a number I know that's
+the Natural Energy scale of molecular
+
+ align:start position:0%
+the Natural Energy scale of molecular
+ 
+
+ align:start position:0%
+the Natural Energy scale of molecular
+processes so it's
+
+ align:start position:0%
+processes so it's
+ 
+
+ align:start position:0%
+processes so it's
+0.0257 electron volts or
+
+ align:start position:0%
+0.0257 electron volts or
+ 
+
+ align:start position:0%
+0.0257 electron volts or
+25.7 milli electron volts so
+
+ align:start position:0%
+25.7 milli electron volts so
+ 
+
+ align:start position:0%
+25.7 milli electron volts so
+approximately 25 ml electron volts is
+
+ align:start position:0%
+approximately 25 ml electron volts is
+ 
+
+ align:start position:0%
+approximately 25 ml electron volts is
+the thermal energy at room temperature
+
+ align:start position:0%
+the thermal energy at room temperature
+ 
+
+ align:start position:0%
+the thermal energy at room temperature
+so if you have a molecular system or an
+
+ align:start position:0%
+so if you have a molecular system or an
+ 
+
+ align:start position:0%
+so if you have a molecular system or an
+atomic system or an electronic system
+
+ align:start position:0%
+atomic system or an electronic system
+ 
+
+ align:start position:0%
+atomic system or an electronic system
+processes of that energy are likely to
+
+ align:start position:0%
+processes of that energy are likely to
+ 
+
+ align:start position:0%
+processes of that energy are likely to
+be happening spontaneously at ambient
+
+ align:start position:0%
+be happening spontaneously at ambient
+ 
+
+ align:start position:0%
+be happening spontaneously at ambient
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+processes which much much higher energy
+
+ align:start position:0%
+processes which much much higher energy
+ 
+
+ align:start position:0%
+processes which much much higher energy
+are not likely to be happening
+
+ align:start position:0%
+are not likely to be happening
+ 
+
+ align:start position:0%
+are not likely to be happening
+spontaneously at ambient temperature
+
+ align:start position:0%
+spontaneously at ambient temperature
+ 
+
+ align:start position:0%
+spontaneously at ambient temperature
+so you can see how powerful this is
+
+ align:start position:0%
+so you can see how powerful this is
+ 
+
+ align:start position:0%
+so you can see how powerful this is
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+it's the foundation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+the Arrhenius rate equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right the Arrhenius rate equation I'm
+
+ align:start position:0%
+right the Arrhenius rate equation I'm
+ 
+
+ align:start position:0%
+right the Arrhenius rate equation I'm
+going to use this the notation from a
+
+ align:start position:0%
+going to use this the notation from a
+ 
+
+ align:start position:0%
+going to use this the notation from a
+chemistry class here a rate k equals a
+
+ align:start position:0%
+chemistry class here a rate k equals a
+ 
+
+ align:start position:0%
+chemistry class here a rate k equals a
+pre-factor times e to the minus
+
+ align:start position:0%
+pre-factor times e to the minus
+ 
+
+ align:start position:0%
+pre-factor times e to the minus
+activation energy
+
+ align:start position:0%
+activation energy
+ 
+
+ align:start position:0%
+activation energy
+divided by Boltzmann's constant
+
+ align:start position:0%
+divided by Boltzmann's constant
+ 
+
+ align:start position:0%
+divided by Boltzmann's constant
+times temperature right now this this is
+
+ align:start position:0%
+times temperature right now this this is
+ 
+
+ align:start position:0%
+times temperature right now this this is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is a rate
+
+ align:start position:0%
+this is a rate
+ 
+
+ align:start position:0%
+this is a rate
+percent activation energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and activation energy and we are going
+
+ align:start position:0%
+and activation energy and we are going
+ 
+
+ align:start position:0%
+and activation energy and we are going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+say hello to 3091 here
+
+ align:start position:0%
+say hello to 3091 here
+ 
+
+ align:start position:0%
+say hello to 3091 here
+they may have seen that there so just
+
+ align:start position:0%
+they may have seen that there so just
+ 
+
+ align:start position:0%
+they may have seen that there so just
+another context where you're going to
+
+ align:start position:0%
+another context where you're going to
+ 
+
+ align:start position:0%
+another context where you're going to
+see these exponentials and say why where
+
+ align:start position:0%
+see these exponentials and say why where
+ 
+
+ align:start position:0%
+see these exponentials and say why where
+right where'd that come from it comes
+
+ align:start position:0%
+right where'd that come from it comes
+ 
+
+ align:start position:0%
+right where'd that come from it comes
+from the spokesman distribution that we
+
+ align:start position:0%
+from the spokesman distribution that we
+ 
+
+ align:start position:0%
+from the spokesman distribution that we
+just arrived
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk about
+
+ align:start position:0%
+let's talk about
+ 
+
+ align:start position:0%
+let's talk about
+um and for one side only this is a
+
+ align:start position:0%
+um and for one side only this is a
+ 
+
+ align:start position:0%
+um and for one side only this is a
+little dense but this is to help you
+
+ align:start position:0%
+little dense but this is to help you
+ 
+
+ align:start position:0%
+little dense but this is to help you
+with like with lad let's talk about the
+
+ align:start position:0%
+with like with lad let's talk about the
+ 
+
+ align:start position:0%
+with like with lad let's talk about the
+Maxwell Voltron distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I posted the wiki entry for this on
+
+ align:start position:0%
+and I posted the wiki entry for this on
+ 
+
+ align:start position:0%
+and I posted the wiki entry for this on
+on the on the website um so it's a good
+
+ align:start position:0%
+on the on the website um so it's a good
+ 
+
+ align:start position:0%
+on the on the website um so it's a good
+it's a good article to read and I think
+
+ align:start position:0%
+it's a good article to read and I think
+ 
+
+ align:start position:0%
+it's a good article to read and I think
+that the lab instructors refer to it as
+
+ align:start position:0%
+that the lab instructors refer to it as
+ 
+
+ align:start position:0%
+that the lab instructors refer to it as
+well so we're going to consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kinetic energy right kinetic energy is
+
+ align:start position:0%
+kinetic energy right kinetic energy is
+ 
+
+ align:start position:0%
+kinetic energy right kinetic energy is
+momentum vector modulus squared
+
+ align:start position:0%
+momentum vector modulus squared
+ 
+
+ align:start position:0%
+momentum vector modulus squared
+divided by two times the mass that's
+
+ align:start position:0%
+divided by two times the mass that's
+ 
+
+ align:start position:0%
+divided by two times the mass that's
+kinetic energy of a particle of mass m
+
+ align:start position:0%
+kinetic energy of a particle of mass m
+ 
+
+ align:start position:0%
+kinetic energy of a particle of mass m
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um we're in Three space so this is p x
+
+ align:start position:0%
+um we're in Three space so this is p x
+ 
+
+ align:start position:0%
+um we're in Three space so this is p x
+squared plus p y squared plus p z
+
+ align:start position:0%
+squared plus p y squared plus p z
+ 
+
+ align:start position:0%
+squared plus p y squared plus p z
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+divided by 2m so that's the energy per
+
+ align:start position:0%
+divided by 2m so that's the energy per
+ 
+
+ align:start position:0%
+divided by 2m so that's the energy per
+particle in state of momentum p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what we want to do is we want to
+
+ align:start position:0%
+okay so what we want to do is we want to
+ 
+
+ align:start position:0%
+okay so what we want to do is we want to
+figure out the distribution of particles
+
+ align:start position:0%
+figure out the distribution of particles
+ 
+
+ align:start position:0%
+figure out the distribution of particles
+as a function of energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution of uh distribution
+
+ align:start position:0%
+distribution of uh distribution
+ 
+
+ align:start position:0%
+distribution of uh distribution
+in energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll use f of B for consistency with
+
+ align:start position:0%
+I'll use f of B for consistency with
+ 
+
+ align:start position:0%
+I'll use f of B for consistency with
+Wikipedia
+
+ align:start position:0%
+Wikipedia
+ 
+
+ align:start position:0%
+Wikipedia
+it depends on both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Maxwell sorry the boltzmann
+
+ align:start position:0%
+the Maxwell sorry the boltzmann
+ 
+
+ align:start position:0%
+the Maxwell sorry the boltzmann
+distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I had an error in my nuts there
+
+ align:start position:0%
+I had an error in my nuts there
+ 
+
+ align:start position:0%
+I had an error in my nuts there
+the Boston distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n of I
+
+ align:start position:0%
+n of I
+ 
+
+ align:start position:0%
+n of I
+and for n total
+
+ align:start position:0%
+and for n total
+ 
+
+ align:start position:0%
+and for n total
+equals Q to the minus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponent
+
+ align:start position:0%
+exponent
+ 
+
+ align:start position:0%
+exponent
+and it's going to be minus momentum
+
+ align:start position:0%
+and it's going to be minus momentum
+ 
+
+ align:start position:0%
+and it's going to be minus momentum
+of State I
+
+ align:start position:0%
+of State I
+ 
+
+ align:start position:0%
+of State I
+modulus squared over two
+
+ align:start position:0%
+modulus squared over two
+ 
+
+ align:start position:0%
+modulus squared over two
+m k t
+
+ align:start position:0%
+m k t
+ 
+
+ align:start position:0%
+m k t
+right so it depends on that they're both
+
+ align:start position:0%
+right so it depends on that they're both
+ 
+
+ align:start position:0%
+right so it depends on that they're both
+in distribution and also it depends on
+
+ align:start position:0%
+in distribution and also it depends on
+ 
+
+ align:start position:0%
+in distribution and also it depends on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this concept of density of states is not
+
+ align:start position:0%
+this concept of density of states is not
+ 
+
+ align:start position:0%
+this concept of density of states is not
+something that we've covered
+
+ align:start position:0%
+something that we've covered
+ 
+
+ align:start position:0%
+something that we've covered
+in this class if you are in um O2 o29
+
+ align:start position:0%
+in this class if you are in um O2 o29
+ 
+
+ align:start position:0%
+in this class if you are in um O2 o29
+you've discussed this you're going to
+
+ align:start position:0%
+you've discussed this you're going to
+ 
+
+ align:start position:0%
+you've discussed this you're going to
+see it in the in the in the lab but this
+
+ align:start position:0%
+see it in the in the in the lab but this
+ 
+
+ align:start position:0%
+see it in the in the in the lab but this
+really is a preview of what comes
+
+ align:start position:0%
+really is a preview of what comes
+ 
+
+ align:start position:0%
+really is a preview of what comes
+um in the fall when density of States
+
+ align:start position:0%
+um in the fall when density of States
+ 
+
+ align:start position:0%
+um in the fall when density of States
+becomes kind of uh
+
+ align:start position:0%
+becomes kind of uh
+ 
+
+ align:start position:0%
+becomes kind of uh
+um will be second nature for you in the
+
+ align:start position:0%
+um will be second nature for you in the
+ 
+
+ align:start position:0%
+um will be second nature for you in the
+context of quantum mechanics but density
+
+ align:start position:0%
+context of quantum mechanics but density
+ 
+
+ align:start position:0%
+context of quantum mechanics but density
+of States means well this is the
+
+ align:start position:0%
+of States means well this is the
+ 
+
+ align:start position:0%
+of States means well this is the
+bolstered distribution for a given State
+
+ align:start position:0%
+bolstered distribution for a given State
+ 
+
+ align:start position:0%
+bolstered distribution for a given State
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+with this energy
+
+ align:start position:0%
+with this energy
+ 
+
+ align:start position:0%
+with this energy
+how many such states are there
+
+ align:start position:0%
+how many such states are there
+ 
+
+ align:start position:0%
+how many such states are there
+right how many such states are there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3D differential
+
+ align:start position:0%
+3D differential
+ 
+
+ align:start position:0%
+3D differential
+four equals four pi
+
+ align:start position:0%
+four equals four pi
+ 
+
+ align:start position:0%
+four equals four pi
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+P quantity squared DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to get the 4 Pi there because I
+
+ align:start position:0%
+to get the 4 Pi there because I
+ 
+
+ align:start position:0%
+to get the 4 Pi there because I
+integrated the spherical coordinates so
+
+ align:start position:0%
+integrated the spherical coordinates so
+ 
+
+ align:start position:0%
+integrated the spherical coordinates so
+four Pi stradians all around the sphere
+
+ align:start position:0%
+four Pi stradians all around the sphere
+ 
+
+ align:start position:0%
+four Pi stradians all around the sphere
+and that equals 4 Pi m
+
+ align:start position:0%
+and that equals 4 Pi m
+ 
+
+ align:start position:0%
+and that equals 4 Pi m
+root 2 m e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d e
+
+ align:start position:0%
+d e
+ 
+
+ align:start position:0%
+d e
+so this is a distribution of states
+
+ align:start position:0%
+so this is a distribution of states
+ 
+
+ align:start position:0%
+so this is a distribution of states
+in energy e
+
+ align:start position:0%
+in energy e
+ 
+
+ align:start position:0%
+in energy e
+and you combine these two things you
+
+ align:start position:0%
+and you combine these two things you
+ 
+
+ align:start position:0%
+and you combine these two things you
+combine the density of states and the
+
+ align:start position:0%
+combine the density of states and the
+ 
+
+ align:start position:0%
+combine the density of states and the
+bolts and distribution and you get V
+
+ align:start position:0%
+bolts and distribution and you get V
+ 
+
+ align:start position:0%
+bolts and distribution and you get V
+Maxwell volts in distribution
+
+ align:start position:0%
+Maxwell volts in distribution
+ 
+
+ align:start position:0%
+Maxwell volts in distribution
+distribution of energetic particles
+
+ align:start position:0%
+distribution of energetic particles
+ 
+
+ align:start position:0%
+distribution of energetic particles
+zipping around on the kinetic energy
+
+ align:start position:0%
+zipping around on the kinetic energy
+ 
+
+ align:start position:0%
+zipping around on the kinetic energy
+included
+
+ align:start position:0%
+included
+ 
+
+ align:start position:0%
+included
+as a function of energy
+
+ align:start position:0%
+as a function of energy
+ 
+
+ align:start position:0%
+as a function of energy
+and it's two e over pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 over KT to the three halves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e to the minus E over k
+
+ align:start position:0%
+e to the minus E over k
+ 
+
+ align:start position:0%
+e to the minus E over k
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+so this is uh this is the the Maxwell
+
+ align:start position:0%
+so this is uh this is the the Maxwell
+ 
+
+ align:start position:0%
+so this is uh this is the the Maxwell
+boltzmann distribution
+
+ align:start position:0%
+boltzmann distribution
+ 
+
+ align:start position:0%
+boltzmann distribution
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you plot for example speed particle
+
+ align:start position:0%
+if you plot for example speed particle
+ 
+
+ align:start position:0%
+if you plot for example speed particle
+speed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over probability
+
+ align:start position:0%
+over probability
+ 
+
+ align:start position:0%
+over probability
+right here's a low temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have something that's pretty sharply
+
+ align:start position:0%
+you have something that's pretty sharply
+ 
+
+ align:start position:0%
+you have something that's pretty sharply
+spiked here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the intermediate temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+at high temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a series of
+
+ align:start position:0%
+this is a series of
+ 
+
+ align:start position:0%
+this is a series of
+increasing temp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so this has this has the
+
+ align:start position:0%
+okay and so this has this has the
+ 
+
+ align:start position:0%
+okay and so this has this has the
+feature that
+
+ align:start position:0%
+feature that
+ 
+
+ align:start position:0%
+feature that
+um there are more particles that that go
+
+ align:start position:0%
+um there are more particles that that go
+ 
+
+ align:start position:0%
+um there are more particles that that go
+faster at higher temperature
+
+ align:start position:0%
+faster at higher temperature
+ 
+
+ align:start position:0%
+faster at higher temperature
+right you can see that coming from from
+
+ align:start position:0%
+right you can see that coming from from
+ 
+
+ align:start position:0%
+right you can see that coming from from
+this exponential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's also a vanishingly small
+
+ align:start position:0%
+and there's also a vanishingly small
+ 
+
+ align:start position:0%
+and there's also a vanishingly small
+number of particles at zero speed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and there's going to be some
+
+ align:start position:0%
+right and there's going to be some
+ 
+
+ align:start position:0%
+right and there's going to be some
+mean speed
+
+ align:start position:0%
+mean speed
+ 
+
+ align:start position:0%
+mean speed
+that characterizes the distribution and
+
+ align:start position:0%
+that characterizes the distribution and
+ 
+
+ align:start position:0%
+that characterizes the distribution and
+that mean moves with temperature
+
+ align:start position:0%
+that mean moves with temperature
+ 
+
+ align:start position:0%
+that mean moves with temperature
+okay so I haven't derived this in detail
+
+ align:start position:0%
+okay so I haven't derived this in detail
+ 
+
+ align:start position:0%
+okay so I haven't derived this in detail
+because you know we haven't spent time
+
+ align:start position:0%
+because you know we haven't spent time
+ 
+
+ align:start position:0%
+because you know we haven't spent time
+on density of States but we're just
+
+ align:start position:0%
+on density of States but we're just
+ 
+
+ align:start position:0%
+on density of States but we're just
+exploring implications of that of that
+
+ align:start position:0%
+exploring implications of that of that
+ 
+
+ align:start position:0%
+exploring implications of that of that
+Baltimore distribution
+
+ align:start position:0%
+Baltimore distribution
+ 
+
+ align:start position:0%
+Baltimore distribution
+here's another implication
+
+ align:start position:0%
+here's another implication
+ 
+
+ align:start position:0%
+here's another implication
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um the last thing I want to cover which
+
+ align:start position:0%
+um the last thing I want to cover which
+ 
+
+ align:start position:0%
+um the last thing I want to cover which
+with only a couple slides to go is the
+
+ align:start position:0%
+with only a couple slides to go is the
+ 
+
+ align:start position:0%
+with only a couple slides to go is the
+concept of ensembles which is really
+
+ align:start position:0%
+concept of ensembles which is really
+ 
+
+ align:start position:0%
+concept of ensembles which is really
+just um
+
+ align:start position:0%
+just um
+ 
+
+ align:start position:0%
+just um
+3030 Readiness right we're doing this
+
+ align:start position:0%
+3030 Readiness right we're doing this
+ 
+
+ align:start position:0%
+3030 Readiness right we're doing this
+just to show you that you know some
+
+ align:start position:0%
+just to show you that you know some
+ 
+
+ align:start position:0%
+just to show you that you know some
+Concepts which you're not going to use
+
+ align:start position:0%
+Concepts which you're not going to use
+ 
+
+ align:start position:0%
+Concepts which you're not going to use
+in this class but
+
+ align:start position:0%
+in this class but
+ 
+
+ align:start position:0%
+in this class but
+um you will use in in kinetics and
+
+ align:start position:0%
+um you will use in in kinetics and
+ 
+
+ align:start position:0%
+um you will use in in kinetics and
+macrostructure in the fall so before I
+
+ align:start position:0%
+macrostructure in the fall so before I
+ 
+
+ align:start position:0%
+macrostructure in the fall so before I
+move on to discuss ensembles I want to
+
+ align:start position:0%
+move on to discuss ensembles I want to
+ 
+
+ align:start position:0%
+move on to discuss ensembles I want to
+pause and take questions on the
+
+ align:start position:0%
+pause and take questions on the
+ 
+
+ align:start position:0%
+pause and take questions on the
+boltzmann distribution or Maxwell
+
+ align:start position:0%
+boltzmann distribution or Maxwell
+ 
+
+ align:start position:0%
+boltzmann distribution or Maxwell
+boltzmann or anything else Arenas or
+
+ align:start position:0%
+boltzmann or anything else Arenas or
+ 
+
+ align:start position:0%
+boltzmann or anything else Arenas or
+anything else related
+
+ align:start position:0%
+anything else related
+ 
+
+ align:start position:0%
+anything else related
+who's seen the boltzmann distribution or
+
+ align:start position:0%
+who's seen the boltzmann distribution or
+ 
+
+ align:start position:0%
+who's seen the boltzmann distribution or
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay who's seeing the Arrhenius rate law
+
+ align:start position:0%
+okay who's seeing the Arrhenius rate law
+ 
+
+ align:start position:0%
+okay who's seeing the Arrhenius rate law
+there's not a lot of participation on
+
+ align:start position:0%
+there's not a lot of participation on
+ 
+
+ align:start position:0%
+there's not a lot of participation on
+zoom and so I understand that
+
+ align:start position:0%
+zoom and so I understand that
+ 
+
+ align:start position:0%
+zoom and so I understand that
+um I'm guessing that a large number of
+
+ align:start position:0%
+um I'm guessing that a large number of
+ 
+
+ align:start position:0%
+um I'm guessing that a large number of
+people raise their hands
+
+ align:start position:0%
+people raise their hands
+ 
+
+ align:start position:0%
+people raise their hands
+um and then if I asked you about the
+
+ align:start position:0%
+um and then if I asked you about the
+ 
+
+ align:start position:0%
+um and then if I asked you about the
+Bolton distribution to be a small number
+
+ align:start position:0%
+Bolton distribution to be a small number
+ 
+
+ align:start position:0%
+Bolton distribution to be a small number
+and if I ask you about the Maxwell
+
+ align:start position:0%
+and if I ask you about the Maxwell
+ 
+
+ align:start position:0%
+and if I ask you about the Maxwell
+bullets and distribution it'd probably
+
+ align:start position:0%
+bullets and distribution it'd probably
+ 
+
+ align:start position:0%
+bullets and distribution it'd probably
+be an even smaller number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I bet that everyone's seen something
+
+ align:start position:0%
+but I bet that everyone's seen something
+ 
+
+ align:start position:0%
+but I bet that everyone's seen something
+of this form somewhere before so I hope
+
+ align:start position:0%
+of this form somewhere before so I hope
+ 
+
+ align:start position:0%
+of this form somewhere before so I hope
+it's a little bit satisfying for you to
+
+ align:start position:0%
+it's a little bit satisfying for you to
+ 
+
+ align:start position:0%
+it's a little bit satisfying for you to
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+where it comes from right and to
+
+ align:start position:0%
+where it comes from right and to
+ 
+
+ align:start position:0%
+where it comes from right and to
+understand the principles behind it
+
+ align:start position:0%
+understand the principles behind it
+ 
+
+ align:start position:0%
+understand the principles behind it
+maximum entropy
+
+ align:start position:0%
+maximum entropy
+ 
+
+ align:start position:0%
+maximum entropy
+okay so let's talk about ensembles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ensembles are
+
+ align:start position:0%
+ensembles are
+ 
+
+ align:start position:0%
+ensembles are
+what I look up a different definition of
+
+ align:start position:0%
+what I look up a different definition of
+ 
+
+ align:start position:0%
+what I look up a different definition of
+Cambridge Dictionary it says a group of
+
+ align:start position:0%
+Cambridge Dictionary it says a group of
+ 
+
+ align:start position:0%
+Cambridge Dictionary it says a group of
+things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acting together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or taken as a whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is um
+
+ align:start position:0%
+so this is um
+ 
+
+ align:start position:0%
+so this is um
+you know a concept and and we're going
+
+ align:start position:0%
+you know a concept and and we're going
+ 
+
+ align:start position:0%
+you know a concept and and we're going
+to use it a lot in statistical
+
+ align:start position:0%
+to use it a lot in statistical
+ 
+
+ align:start position:0%
+to use it a lot in statistical
+thermodynamics if not necessarily in
+
+ align:start position:0%
+thermodynamics if not necessarily in
+ 
+
+ align:start position:0%
+thermodynamics if not necessarily in
+this class but you know like I said this
+
+ align:start position:0%
+this class but you know like I said this
+ 
+
+ align:start position:0%
+this class but you know like I said this
+is 3030 Readiness here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right if I didn't tell you about
+
+ align:start position:0%
+all right if I didn't tell you about
+ 
+
+ align:start position:0%
+all right if I didn't tell you about
+this again trouble with Professor who
+
+ align:start position:0%
+this again trouble with Professor who
+ 
+
+ align:start position:0%
+this again trouble with Professor who
+all right so we're going to start with
+
+ align:start position:0%
+all right so we're going to start with
+ 
+
+ align:start position:0%
+all right so we're going to start with
+the micro canonical Ensemble and this is
+
+ align:start position:0%
+the micro canonical Ensemble and this is
+ 
+
+ align:start position:0%
+the micro canonical Ensemble and this is
+something that you've seen before micro
+
+ align:start position:0%
+something that you've seen before micro
+ 
+
+ align:start position:0%
+something that you've seen before micro
+canonical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something called the micro canonical
+
+ align:start position:0%
+something called the micro canonical
+ 
+
+ align:start position:0%
+something called the micro canonical
+ensemble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the set
+
+ align:start position:0%
+this is the set
+ 
+
+ align:start position:0%
+this is the set
+of all possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+microstates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the type of stuff that we've been
+
+ align:start position:0%
+so the type of stuff that we've been
+ 
+
+ align:start position:0%
+so the type of stuff that we've been
+doing instead of all possible
+
+ align:start position:0%
+doing instead of all possible
+ 
+
+ align:start position:0%
+doing instead of all possible
+microstates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+and particle number
+
+ align:start position:0%
+and particle number
+ 
+
+ align:start position:0%
+and particle number
+right so a system with fixed energy
+
+ align:start position:0%
+right so a system with fixed energy
+ 
+
+ align:start position:0%
+right so a system with fixed energy
+volume and particle number that is um
+
+ align:start position:0%
+volume and particle number that is um
+ 
+
+ align:start position:0%
+volume and particle number that is um
+that's an isolated system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right for an isolated system equilibrium
+
+ align:start position:0%
+right for an isolated system equilibrium
+ 
+
+ align:start position:0%
+right for an isolated system equilibrium
+is state of Max entropy that's what we
+
+ align:start position:0%
+is state of Max entropy that's what we
+ 
+
+ align:start position:0%
+is state of Max entropy that's what we
+were just analyzing
+
+ align:start position:0%
+were just analyzing
+ 
+
+ align:start position:0%
+were just analyzing
+all right so this thing which we've been
+
+ align:start position:0%
+all right so this thing which we've been
+ 
+
+ align:start position:0%
+all right so this thing which we've been
+doing for the last two and a half
+
+ align:start position:0%
+doing for the last two and a half
+ 
+
+ align:start position:0%
+doing for the last two and a half
+lectures this is called the micro
+
+ align:start position:0%
+lectures this is called the micro
+ 
+
+ align:start position:0%
+lectures this is called the micro
+canonical Ensemble just gave a name to
+
+ align:start position:0%
+canonical Ensemble just gave a name to
+ 
+
+ align:start position:0%
+canonical Ensemble just gave a name to
+it and so the partition function that
+
+ align:start position:0%
+it and so the partition function that
+ 
+
+ align:start position:0%
+it and so the partition function that
+we've been analyzing is actually better
+
+ align:start position:0%
+we've been analyzing is actually better
+ 
+
+ align:start position:0%
+we've been analyzing is actually better
+known as a micro
+
+ align:start position:0%
+known as a micro
+ 
+
+ align:start position:0%
+known as a micro
+canonical
+
+ align:start position:0%
+canonical
+ 
+
+ align:start position:0%
+canonical
+partition function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normally written as Q as we've been
+
+ align:start position:0%
+normally written as Q as we've been
+ 
+
+ align:start position:0%
+normally written as Q as we've been
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+and it is a sum over
+
+ align:start position:0%
+and it is a sum over
+ 
+
+ align:start position:0%
+and it is a sum over
+single particle energy states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Over All
+
+ align:start position:0%
+Over All
+ 
+
+ align:start position:0%
+Over All
+possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know that we're at equilibrium
+
+ align:start position:0%
+and we know that we're at equilibrium
+ 
+
+ align:start position:0%
+and we know that we're at equilibrium
+equilibrium with s
+
+ align:start position:0%
+equilibrium with s
+ 
+
+ align:start position:0%
+equilibrium with s
+maximized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for what
+
+ align:start position:0%
+for what
+ 
+
+ align:start position:0%
+for what
+for the Boltzmann's distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the probability of finding particle
+
+ align:start position:0%
+so the probability of finding particle
+ 
+
+ align:start position:0%
+so the probability of finding particle
+on state I
+
+ align:start position:0%
+on state I
+ 
+
+ align:start position:0%
+on state I
+equals number of particles that say I at
+
+ align:start position:0%
+equals number of particles that say I at
+ 
+
+ align:start position:0%
+equals number of particles that say I at
+that distribution over the total number
+
+ align:start position:0%
+that distribution over the total number
+ 
+
+ align:start position:0%
+that distribution over the total number
+of particles equals e to the minus e i
+
+ align:start position:0%
+of particles equals e to the minus e i
+ 
+
+ align:start position:0%
+of particles equals e to the minus e i
+you're getting sick of seeing me write
+
+ align:start position:0%
+you're getting sick of seeing me write
+ 
+
+ align:start position:0%
+you're getting sick of seeing me write
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+by now
+
+ align:start position:0%
+by now
+ 
+
+ align:start position:0%
+by now
+right prob
+
+ align:start position:0%
+right prob
+ 
+
+ align:start position:0%
+right prob
+of finding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a single particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in state
+
+ align:start position:0%
+in state
+ 
+
+ align:start position:0%
+in state
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+with energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um this is a repeat of
+
+ align:start position:0%
+okay so um this is a repeat of
+ 
+
+ align:start position:0%
+okay so um this is a repeat of
+everything we just did I just give it a
+
+ align:start position:0%
+everything we just did I just give it a
+ 
+
+ align:start position:0%
+everything we just did I just give it a
+new name I called it micro canonical so
+
+ align:start position:0%
+new name I called it micro canonical so
+ 
+
+ align:start position:0%
+new name I called it micro canonical so
+again that name's kind of
+
+ align:start position:0%
+again that name's kind of
+ 
+
+ align:start position:0%
+again that name's kind of
+kind of highfalutin but here you have it
+
+ align:start position:0%
+kind of highfalutin but here you have it
+ 
+
+ align:start position:0%
+kind of highfalutin but here you have it
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can generalize
+
+ align:start position:0%
+we can generalize
+ 
+
+ align:start position:0%
+we can generalize
+so now I'm going to tell you about a
+
+ align:start position:0%
+so now I'm going to tell you about a
+ 
+
+ align:start position:0%
+so now I'm going to tell you about a
+different type of Ensemble so we've been
+
+ align:start position:0%
+different type of Ensemble so we've been
+ 
+
+ align:start position:0%
+different type of Ensemble so we've been
+analyzing the micro canonical now I'm
+
+ align:start position:0%
+analyzing the micro canonical now I'm
+ 
+
+ align:start position:0%
+analyzing the micro canonical now I'm
+simply going to tell you about the
+
+ align:start position:0%
+simply going to tell you about the
+ 
+
+ align:start position:0%
+simply going to tell you about the
+existence
+
+ align:start position:0%
+existence
+ 
+
+ align:start position:0%
+existence
+of a canonical ensemble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and please don't ask me where these
+
+ align:start position:0%
+and please don't ask me where these
+ 
+
+ align:start position:0%
+and please don't ask me where these
+names come from
+
+ align:start position:0%
+names come from
+ 
+
+ align:start position:0%
+names come from
+a canonical ensemble
+
+ align:start position:0%
+a canonical ensemble
+ 
+
+ align:start position:0%
+a canonical ensemble
+is the set
+
+ align:start position:0%
+is the set
+ 
+
+ align:start position:0%
+is the set
+of all possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+microstates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and n
+
+ align:start position:0%
+and n
+ 
+
+ align:start position:0%
+and n
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+so now we're allowing the system to
+
+ align:start position:0%
+so now we're allowing the system to
+ 
+
+ align:start position:0%
+so now we're allowing the system to
+exchange energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the system
+
+ align:start position:0%
+the system
+ 
+
+ align:start position:0%
+the system
+is closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's rigid
+
+ align:start position:0%
+it's rigid
+ 
+
+ align:start position:0%
+it's rigid
+and closed
+
+ align:start position:0%
+and closed
+ 
+
+ align:start position:0%
+and closed
+so volume and mass are conserved system
+
+ align:start position:0%
+so volume and mass are conserved system
+ 
+
+ align:start position:0%
+so volume and mass are conserved system
+is rigid and closed
+
+ align:start position:0%
+is rigid and closed
+ 
+
+ align:start position:0%
+is rigid and closed
+but can
+
+ align:start position:0%
+but can
+ 
+
+ align:start position:0%
+but can
+Exchange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy and form
+
+ align:start position:0%
+energy and form
+ 
+
+ align:start position:0%
+energy and form
+of heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with surroundings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the system energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we're now going to give a label to
+
+ align:start position:0%
+which we're now going to give a label to
+ 
+
+ align:start position:0%
+which we're now going to give a label to
+U sub Nu
+
+ align:start position:0%
+U sub Nu
+ 
+
+ align:start position:0%
+U sub Nu
+the system energy can fluctuate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I want to draw for you a
+
+ align:start position:0%
+so I want to draw for you a
+ 
+
+ align:start position:0%
+so I want to draw for you a
+representation of the micro of the
+
+ align:start position:0%
+representation of the micro of the
+ 
+
+ align:start position:0%
+representation of the micro of the
+canonical Ensemble so we're going to
+
+ align:start position:0%
+canonical Ensemble so we're going to
+ 
+
+ align:start position:0%
+canonical Ensemble so we're going to
+imagine
+
+ align:start position:0%
+imagine
+ 
+
+ align:start position:0%
+imagine
+um grab a
+
+ align:start position:0%
+um grab a
+ 
+
+ align:start position:0%
+um grab a
+defined tip marker we're going to
+
+ align:start position:0%
+defined tip marker we're going to
+ 
+
+ align:start position:0%
+defined tip marker we're going to
+imagine system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+labeled I with energy U
+
+ align:start position:0%
+labeled I with energy U
+ 
+
+ align:start position:0%
+labeled I with energy U
+sub I but this thing is
+
+ align:start position:0%
+sub I but this thing is
+ 
+
+ align:start position:0%
+sub I but this thing is
+um in thermal contact with
+
+ align:start position:0%
+um in thermal contact with
+ 
+
+ align:start position:0%
+um in thermal contact with
+a lot of other systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to imagine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a whole
+
+ align:start position:0%
+a whole
+ 
+
+ align:start position:0%
+a whole
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+or if you like an ensemble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of systems
+
+ align:start position:0%
+of systems
+ 
+
+ align:start position:0%
+of systems
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+with fixed volume and fixed particle
+
+ align:start position:0%
+with fixed volume and fixed particle
+ 
+
+ align:start position:0%
+with fixed volume and fixed particle
+number but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with diathermal walls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if heat is like sound you have to
+
+ align:start position:0%
+so if heat is like sound you have to
+ 
+
+ align:start position:0%
+so if heat is like sound you have to
+imagine this is an apartment building
+
+ align:start position:0%
+imagine this is an apartment building
+ 
+
+ align:start position:0%
+imagine this is an apartment building
+that's really really noisy you hear all
+
+ align:start position:0%
+that's really really noisy you hear all
+ 
+
+ align:start position:0%
+that's really really noisy you hear all
+your neighbors so the volume the volume
+
+ align:start position:0%
+your neighbors so the volume the volume
+ 
+
+ align:start position:0%
+your neighbors so the volume the volume
+mistakes and the particle number is
+
+ align:start position:0%
+mistakes and the particle number is
+ 
+
+ align:start position:0%
+mistakes and the particle number is
+fixed but you're exchanging energy right
+
+ align:start position:0%
+fixed but you're exchanging energy right
+ 
+
+ align:start position:0%
+fixed but you're exchanging energy right
+through the walls
+
+ align:start position:0%
+through the walls
+ 
+
+ align:start position:0%
+through the walls
+but this Ensemble as a whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I've drawn an ensemble right I've
+
+ align:start position:0%
+so I've drawn an ensemble right I've
+ 
+
+ align:start position:0%
+so I've drawn an ensemble right I've
+drawn a set or a group considered as a
+
+ align:start position:0%
+drawn a set or a group considered as a
+ 
+
+ align:start position:0%
+drawn a set or a group considered as a
+whole right I've drawn a bunch of
+
+ align:start position:0%
+whole right I've drawn a bunch of
+ 
+
+ align:start position:0%
+whole right I've drawn a bunch of
+subsystems now that can exchange energy
+
+ align:start position:0%
+subsystems now that can exchange energy
+ 
+
+ align:start position:0%
+subsystems now that can exchange energy
+with each other
+
+ align:start position:0%
+with each other
+ 
+
+ align:start position:0%
+with each other
+they each have the same volume well not
+
+ align:start position:0%
+they each have the same volume well not
+ 
+
+ align:start position:0%
+they each have the same volume well not
+as I've drawn it but you can imagine
+
+ align:start position:0%
+as I've drawn it but you can imagine
+ 
+
+ align:start position:0%
+as I've drawn it but you can imagine
+they each have the same volume each have
+
+ align:start position:0%
+they each have the same volume each have
+ 
+
+ align:start position:0%
+they each have the same volume each have
+the same particle number
+
+ align:start position:0%
+the same particle number
+ 
+
+ align:start position:0%
+the same particle number
+but the insoluble as a whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is isolated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so all these ensembles you have to
+
+ align:start position:0%
+so all these ensembles you have to
+ 
+
+ align:start position:0%
+so all these ensembles you have to
+imagine this being a very very large
+
+ align:start position:0%
+imagine this being a very very large
+ 
+
+ align:start position:0%
+imagine this being a very very large
+number here not just four by six or
+
+ align:start position:0%
+number here not just four by six or
+ 
+
+ align:start position:0%
+number here not just four by six or
+whatever I've drawn
+
+ align:start position:0%
+whatever I've drawn
+ 
+
+ align:start position:0%
+whatever I've drawn
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is isolated
+
+ align:start position:0%
+is isolated
+ 
+
+ align:start position:0%
+is isolated
+and so this is an ensemble and this is
+
+ align:start position:0%
+and so this is an ensemble and this is
+ 
+
+ align:start position:0%
+and so this is an ensemble and this is
+an ensemble has its own partition
+
+ align:start position:0%
+an ensemble has its own partition
+ 
+
+ align:start position:0%
+an ensemble has its own partition
+function it's known as the canonical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protection function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's typically written as Z
+
+ align:start position:0%
+and that's typically written as Z
+ 
+
+ align:start position:0%
+and that's typically written as Z
+and this is now a sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as before a sum Over States but we're
+
+ align:start position:0%
+as before a sum Over States but we're
+ 
+
+ align:start position:0%
+as before a sum Over States but we're
+not summoning over single particle
+
+ align:start position:0%
+not summoning over single particle
+ 
+
+ align:start position:0%
+not summoning over single particle
+States we're summing over
+
+ align:start position:0%
+States we're summing over
+ 
+
+ align:start position:0%
+States we're summing over
+system energy states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over all possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's distinct from before we were
+
+ align:start position:0%
+so it's distinct from before we were
+ 
+
+ align:start position:0%
+so it's distinct from before we were
+summing over single particle States
+
+ align:start position:0%
+summing over single particle States
+ 
+
+ align:start position:0%
+summing over single particle States
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hold on
+
+ align:start position:0%
+hold on
+ 
+
+ align:start position:0%
+hold on
+when we have equilibrium in an isolated
+
+ align:start position:0%
+when we have equilibrium in an isolated
+ 
+
+ align:start position:0%
+when we have equilibrium in an isolated
+system it was Max entropy
+
+ align:start position:0%
+system it was Max entropy
+ 
+
+ align:start position:0%
+system it was Max entropy
+now I think back two months ago when we
+
+ align:start position:0%
+now I think back two months ago when we
+ 
+
+ align:start position:0%
+now I think back two months ago when we
+had equilibrium for fixed temperature
+
+ align:start position:0%
+had equilibrium for fixed temperature
+ 
+
+ align:start position:0%
+had equilibrium for fixed temperature
+and fixed pressure
+
+ align:start position:0%
+and fixed pressure
+ 
+
+ align:start position:0%
+and fixed pressure
+that was minimum Gibbs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there was another case which we
+
+ align:start position:0%
+but there was another case which we
+ 
+
+ align:start position:0%
+but there was another case which we
+haven't spent a lot of time on it was
+
+ align:start position:0%
+haven't spent a lot of time on it was
+ 
+
+ align:start position:0%
+haven't spent a lot of time on it was
+equilibrium at fixed volume and fixed
+
+ align:start position:0%
+equilibrium at fixed volume and fixed
+ 
+
+ align:start position:0%
+equilibrium at fixed volume and fixed
+temperature do you remember what
+
+ align:start position:0%
+temperature do you remember what
+ 
+
+ align:start position:0%
+temperature do you remember what
+thermodynamic potential we use when we
+
+ align:start position:0%
+thermodynamic potential we use when we
+ 
+
+ align:start position:0%
+thermodynamic potential we use when we
+have a system at fixed volume and fixed
+
+ align:start position:0%
+have a system at fixed volume and fixed
+ 
+
+ align:start position:0%
+have a system at fixed volume and fixed
+temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it Heim Holtz
+
+ align:start position:0%
+is it Heim Holtz
+ 
+
+ align:start position:0%
+is it Heim Holtz
+equilibrium at minimum
+
+ align:start position:0%
+equilibrium at minimum
+ 
+
+ align:start position:0%
+equilibrium at minimum
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+again we haven't used that this course
+
+ align:start position:0%
+again we haven't used that this course
+ 
+
+ align:start position:0%
+again we haven't used that this course
+basically is minimized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability of finding system in state
+
+ align:start position:0%
+probability of finding system in state
+ 
+
+ align:start position:0%
+probability of finding system in state
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+e to the minus U Nu
+
+ align:start position:0%
+e to the minus U Nu
+ 
+
+ align:start position:0%
+e to the minus U Nu
+over KT over Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it has the same functional form as
+
+ align:start position:0%
+so it has the same functional form as
+ 
+
+ align:start position:0%
+so it has the same functional form as
+the Bolton distribution
+
+ align:start position:0%
+the Bolton distribution
+ 
+
+ align:start position:0%
+the Bolton distribution
+except
+
+ align:start position:0%
+except
+ 
+
+ align:start position:0%
+except
+instead of single particle energy this
+
+ align:start position:0%
+instead of single particle energy this
+ 
+
+ align:start position:0%
+instead of single particle energy this
+is energy of the system as a whole
+
+ align:start position:0%
+is energy of the system as a whole
+ 
+
+ align:start position:0%
+is energy of the system as a whole
+and instead of maximizing entropy it
+
+ align:start position:0%
+and instead of maximizing entropy it
+ 
+
+ align:start position:0%
+and instead of maximizing entropy it
+minimizes how much free energy
+
+ align:start position:0%
+minimizes how much free energy
+ 
+
+ align:start position:0%
+minimizes how much free energy
+so there's something very similar that's
+
+ align:start position:0%
+so there's something very similar that's
+ 
+
+ align:start position:0%
+so there's something very similar that's
+happening here similar to when we
+
+ align:start position:0%
+happening here similar to when we
+ 
+
+ align:start position:0%
+happening here similar to when we
+started with entropy and then we moved
+
+ align:start position:0%
+started with entropy and then we moved
+ 
+
+ align:start position:0%
+started with entropy and then we moved
+to helmhot's energy and then we move
+
+ align:start position:0%
+to helmhot's energy and then we move
+ 
+
+ align:start position:0%
+to helmhot's energy and then we move
+through Gibbs energy as we change the
+
+ align:start position:0%
+through Gibbs energy as we change the
+ 
+
+ align:start position:0%
+through Gibbs energy as we change the
+boundary conditions of the system and I
+
+ align:start position:0%
+boundary conditions of the system and I
+ 
+
+ align:start position:0%
+boundary conditions of the system and I
+think you'll remember in problem set two
+
+ align:start position:0%
+think you'll remember in problem set two
+ 
+
+ align:start position:0%
+think you'll remember in problem set two
+we really dove into this
+
+ align:start position:0%
+we really dove into this
+ 
+
+ align:start position:0%
+we really dove into this
+so there's something very similar that
+
+ align:start position:0%
+so there's something very similar that
+ 
+
+ align:start position:0%
+so there's something very similar that
+happens in statistical thermodynamics
+
+ align:start position:0%
+happens in statistical thermodynamics
+ 
+
+ align:start position:0%
+happens in statistical thermodynamics
+where you start with the micro canonical
+
+ align:start position:0%
+where you start with the micro canonical
+ 
+
+ align:start position:0%
+where you start with the micro canonical
+Ensemble and its partition function and
+
+ align:start position:0%
+Ensemble and its partition function and
+ 
+
+ align:start position:0%
+Ensemble and its partition function and
+then you go to the canonical Ensemble
+
+ align:start position:0%
+then you go to the canonical Ensemble
+ 
+
+ align:start position:0%
+then you go to the canonical Ensemble
+and its partition function and there's
+
+ align:start position:0%
+and its partition function and there's
+ 
+
+ align:start position:0%
+and its partition function and there's
+more there are other ensembles the next
+
+ align:start position:0%
+more there are other ensembles the next
+ 
+
+ align:start position:0%
+more there are other ensembles the next
+one is called the Grand canonical
+
+ align:start position:0%
+one is called the Grand canonical
+ 
+
+ align:start position:0%
+one is called the Grand canonical
+Ensemble and that corresponds to
+
+ align:start position:0%
+Ensemble and that corresponds to
+ 
+
+ align:start position:0%
+Ensemble and that corresponds to
+situations with fixed pressure and
+
+ align:start position:0%
+situations with fixed pressure and
+ 
+
+ align:start position:0%
+situations with fixed pressure and
+temperature We're Not Gonna
+
+ align:start position:0%
+temperature We're Not Gonna
+ 
+
+ align:start position:0%
+temperature We're Not Gonna
+bother to introduce that
+
+ align:start position:0%
+bother to introduce that
+ 
+
+ align:start position:0%
+bother to introduce that
+so this is the boltzmann distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's for
+
+ align:start position:0%
+but it's for
+ 
+
+ align:start position:0%
+but it's for
+the canonical ensemble in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case what was it that you
+
+ align:start position:0%
+so in this case what was it that you
+ 
+
+ align:start position:0%
+so in this case what was it that you
+thought you held constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so this is equilibrium at fixed
+
+ align:start position:0%
+um so this is equilibrium at fixed
+ 
+
+ align:start position:0%
+um so this is equilibrium at fixed
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+right when you have when you have
+
+ align:start position:0%
+right when you have when you have
+ 
+
+ align:start position:0%
+right when you have when you have
+um an ensemble of systems
+
+ align:start position:0%
+um an ensemble of systems
+ 
+
+ align:start position:0%
+um an ensemble of systems
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+can't exchange volume
+
+ align:start position:0%
+can't exchange volume
+ 
+
+ align:start position:0%
+can't exchange volume
+and they can't exchange particle number
+
+ align:start position:0%
+and they can't exchange particle number
+ 
+
+ align:start position:0%
+and they can't exchange particle number
+but they can exchange heat energy
+
+ align:start position:0%
+but they can exchange heat energy
+ 
+
+ align:start position:0%
+but they can exchange heat energy
+they reach equilibrium
+
+ align:start position:0%
+they reach equilibrium
+ 
+
+ align:start position:0%
+they reach equilibrium
+when the temperature becomes constant
+
+ align:start position:0%
+when the temperature becomes constant
+ 
+
+ align:start position:0%
+when the temperature becomes constant
+right that's thermal equilibrium
+
+ align:start position:0%
+right that's thermal equilibrium
+ 
+
+ align:start position:0%
+right that's thermal equilibrium
+and so that's what we've done here we've
+
+ align:start position:0%
+and so that's what we've done here we've
+ 
+
+ align:start position:0%
+and so that's what we've done here we've
+set up a system a collection an ensemble
+
+ align:start position:0%
+set up a system a collection an ensemble
+ 
+
+ align:start position:0%
+set up a system a collection an ensemble
+of subsystems that reach thermody
+
+ align:start position:0%
+of subsystems that reach thermody
+ 
+
+ align:start position:0%
+of subsystems that reach thermody
+thermal equilibrium with each other
+
+ align:start position:0%
+thermal equilibrium with each other
+ 
+
+ align:start position:0%
+thermal equilibrium with each other
+because they can exchange heat energy
+
+ align:start position:0%
+because they can exchange heat energy
+ 
+
+ align:start position:0%
+because they can exchange heat energy
+it all works out
+
+ align:start position:0%
+it all works out
+ 
+
+ align:start position:0%
+it all works out
+you end up getting minimum f for this
+
+ align:start position:0%
+you end up getting minimum f for this
+ 
+
+ align:start position:0%
+you end up getting minimum f for this
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+this is the probability
+
+ align:start position:0%
+this is the probability
+ 
+
+ align:start position:0%
+this is the probability
+probability of finding
+
+ align:start position:0%
+probability of finding
+ 
+
+ align:start position:0%
+probability of finding
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in state
+
+ align:start position:0%
+in state
+ 
+
+ align:start position:0%
+in state
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+with energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+have new
+
+ align:start position:0%
+have new
+ 
+
+ align:start position:0%
+have new
+that's what that probability is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I want to leave you with some
+
+ align:start position:0%
+okay so I want to leave you with some
+ 
+
+ align:start position:0%
+okay so I want to leave you with some
+final words on partition functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've seen some partition functions
+
+ align:start position:0%
+we've seen some partition functions
+ 
+
+ align:start position:0%
+we've seen some partition functions
+Q
+
+ align:start position:0%
+Q
+ 
+
+ align:start position:0%
+Q
+and z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and there's there are others which
+
+ align:start position:0%
+and and there's there are others which
+ 
+
+ align:start position:0%
+and and there's there are others which
+we won't cover in this class right
+
+ align:start position:0%
+we won't cover in this class right
+ 
+
+ align:start position:0%
+we won't cover in this class right
+we haven't really covered these and this
+
+ align:start position:0%
+we haven't really covered these and this
+ 
+
+ align:start position:0%
+we haven't really covered these and this
+won't be on the exam I mean there's just
+
+ align:start position:0%
+won't be on the exam I mean there's just
+ 
+
+ align:start position:0%
+won't be on the exam I mean there's just
+sort of commenting on what comes next
+
+ align:start position:0%
+sort of commenting on what comes next
+ 
+
+ align:start position:0%
+sort of commenting on what comes next
+again this is this is in service to
+
+ align:start position:0%
+again this is this is in service to
+ 
+
+ align:start position:0%
+again this is this is in service to
+later classes in our curriculum so the
+
+ align:start position:0%
+later classes in our curriculum so the
+ 
+
+ align:start position:0%
+later classes in our curriculum so the
+partition functions they describe they
+
+ align:start position:0%
+partition functions they describe they
+ 
+
+ align:start position:0%
+partition functions they describe they
+describe
+
+ align:start position:0%
+describe
+ 
+
+ align:start position:0%
+describe
+they describe equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+fluctuations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the partition functions really describe
+
+ align:start position:0%
+the partition functions really describe
+ 
+
+ align:start position:0%
+the partition functions really describe
+the entire thermodynamic properties of
+
+ align:start position:0%
+the entire thermodynamic properties of
+ 
+
+ align:start position:0%
+the entire thermodynamic properties of
+the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so for instance they are the basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for calculating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamic properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and expectation values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is most likely quantity so for
+
+ align:start position:0%
+that is most likely quantity so for
+ 
+
+ align:start position:0%
+that is most likely quantity so for
+example for example
+
+ align:start position:0%
+example for example
+ 
+
+ align:start position:0%
+example for example
+the mean energy of a system
+
+ align:start position:0%
+the mean energy of a system
+ 
+
+ align:start position:0%
+the mean energy of a system
+can be shown
+
+ align:start position:0%
+can be shown
+ 
+
+ align:start position:0%
+can be shown
+to be this derivative d
+
+ align:start position:0%
+to be this derivative d
+ 
+
+ align:start position:0%
+to be this derivative d
+log Z
+
+ align:start position:0%
+log Z
+ 
+
+ align:start position:0%
+log Z
+1 over KT
+
+ align:start position:0%
+1 over KT
+ 
+
+ align:start position:0%
+1 over KT
+so that's a little bit formal can't
+
+ align:start position:0%
+so that's a little bit formal can't
+ 
+
+ align:start position:0%
+so that's a little bit formal can't
+necessarily calculate anything yet but
+
+ align:start position:0%
+necessarily calculate anything yet but
+ 
+
+ align:start position:0%
+necessarily calculate anything yet but
+in principle if you know the partition
+
+ align:start position:0%
+in principle if you know the partition
+ 
+
+ align:start position:0%
+in principle if you know the partition
+function you can calculate the mean
+
+ align:start position:0%
+function you can calculate the mean
+ 
+
+ align:start position:0%
+function you can calculate the mean
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+the heat capacity of a system
+
+ align:start position:0%
+the heat capacity of a system
+ 
+
+ align:start position:0%
+the heat capacity of a system
+is 1 over KT squared
+
+ align:start position:0%
+is 1 over KT squared
+ 
+
+ align:start position:0%
+is 1 over KT squared
+D Squared log z d
+
+ align:start position:0%
+D Squared log z d
+ 
+
+ align:start position:0%
+D Squared log z d
+1 over k t
+
+ align:start position:0%
+1 over k t
+ 
+
+ align:start position:0%
+1 over k t
+squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the entropy of a system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can be shown to be mean energy divided
+
+ align:start position:0%
+can be shown to be mean energy divided
+ 
+
+ align:start position:0%
+can be shown to be mean energy divided
+by temperature
+
+ align:start position:0%
+by temperature
+ 
+
+ align:start position:0%
+by temperature
+plus k b
+
+ align:start position:0%
+plus k b
+ 
+
+ align:start position:0%
+plus k b
+log
+
+ align:start position:0%
+log
+ 
+
+ align:start position:0%
+log
+Z
+
+ align:start position:0%
+Z
+ 
+
+ align:start position:0%
+Z
+the helmo three energy of a system
+
+ align:start position:0%
+the helmo three energy of a system
+ 
+
+ align:start position:0%
+the helmo three energy of a system
+is minus k b t log Z
+
+ align:start position:0%
+is minus k b t log Z
+ 
+
+ align:start position:0%
+is minus k b t log Z
+and it's not just equilibrium properties
+
+ align:start position:0%
+and it's not just equilibrium properties
+ 
+
+ align:start position:0%
+and it's not just equilibrium properties
+it's properties of fluctuations
+
+ align:start position:0%
+it's properties of fluctuations
+ 
+
+ align:start position:0%
+it's properties of fluctuations
+so this gets really fun uh in a later
+
+ align:start position:0%
+so this gets really fun uh in a later
+ 
+
+ align:start position:0%
+so this gets really fun uh in a later
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+and has a lot of implications so for
+
+ align:start position:0%
+and has a lot of implications so for
+ 
+
+ align:start position:0%
+and has a lot of implications so for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+the root mean squared energy fluctuation
+
+ align:start position:0%
+the root mean squared energy fluctuation
+ 
+
+ align:start position:0%
+the root mean squared energy fluctuation
+of a system is another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantity that can be calculated from the
+
+ align:start position:0%
+quantity that can be calculated from the
+ 
+
+ align:start position:0%
+quantity that can be calculated from the
+partition functions
+
+ align:start position:0%
+partition functions
+ 
+
+ align:start position:0%
+partition functions
+so you know I'm just showing you things
+
+ align:start position:0%
+so you know I'm just showing you things
+ 
+
+ align:start position:0%
+so you know I'm just showing you things
+but you know
+
+ align:start position:0%
+but you know
+ 
+
+ align:start position:0%
+but you know
+if you have the partition function for a
+
+ align:start position:0%
+if you have the partition function for a
+ 
+
+ align:start position:0%
+if you have the partition function for a
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+you can calculate the entire
+
+ align:start position:0%
+you can calculate the entire
+ 
+
+ align:start position:0%
+you can calculate the entire
+thermodynamic properties of that system
+
+ align:start position:0%
+thermodynamic properties of that system
+ 
+
+ align:start position:0%
+thermodynamic properties of that system
+so another example is in in the textbook
+
+ align:start position:0%
+so another example is in in the textbook
+ 
+
+ align:start position:0%
+so another example is in in the textbook
+if you look into Hoff uh they calculate
+
+ align:start position:0%
+if you look into Hoff uh they calculate
+ 
+
+ align:start position:0%
+if you look into Hoff uh they calculate
+the partition function for a couple
+
+ align:start position:0%
+the partition function for a couple
+ 
+
+ align:start position:0%
+the partition function for a couple
+different systems a two level system and
+
+ align:start position:0%
+different systems a two level system and
+ 
+
+ align:start position:0%
+different systems a two level system and
+then a system of um
+
+ align:start position:0%
+then a system of um
+ 
+
+ align:start position:0%
+then a system of um
+a monoatomic gas
+
+ align:start position:0%
+a monoatomic gas
+ 
+
+ align:start position:0%
+a monoatomic gas
+and then by applying formulas such as
+
+ align:start position:0%
+and then by applying formulas such as
+ 
+
+ align:start position:0%
+and then by applying formulas such as
+these they derive the ideal gas law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's sort of the ideal gas law from
+
+ align:start position:0%
+so it's sort of the ideal gas law from
+ 
+
+ align:start position:0%
+so it's sort of the ideal gas law from
+first principles right it's no longer
+
+ align:start position:0%
+first principles right it's no longer
+ 
+
+ align:start position:0%
+first principles right it's no longer
+empirical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm going to leave you with some
+
+ align:start position:0%
+so I'm going to leave you with some
+ 
+
+ align:start position:0%
+so I'm going to leave you with some
+thoughts
+
+ align:start position:0%
+thoughts
+ 
+
+ align:start position:0%
+thoughts
+um at this point often students say ah
+
+ align:start position:0%
+um at this point often students say ah
+ 
+
+ align:start position:0%
+um at this point often students say ah
+this is the real stuff this is somehow
+
+ align:start position:0%
+this is the real stuff this is somehow
+ 
+
+ align:start position:0%
+this is the real stuff this is somehow
+the most fundamental
+
+ align:start position:0%
+the most fundamental
+ 
+
+ align:start position:0%
+the most fundamental
+knowledge of thermodynamics is a
+
+ align:start position:0%
+knowledge of thermodynamics is a
+ 
+
+ align:start position:0%
+knowledge of thermodynamics is a
+partition functions
+
+ align:start position:0%
+partition functions
+ 
+
+ align:start position:0%
+partition functions
+right so why did we mess around with all
+
+ align:start position:0%
+right so why did we mess around with all
+ 
+
+ align:start position:0%
+right so why did we mess around with all
+that classical thermodynamics right if
+
+ align:start position:0%
+that classical thermodynamics right if
+ 
+
+ align:start position:0%
+that classical thermodynamics right if
+the partition functions are the keys to
+
+ align:start position:0%
+the partition functions are the keys to
+ 
+
+ align:start position:0%
+the partition functions are the keys to
+the kingdom
+
+ align:start position:0%
+the kingdom
+ 
+
+ align:start position:0%
+the kingdom
+right why not just start there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the answer is that although this
+
+ align:start position:0%
+and the answer is that although this
+ 
+
+ align:start position:0%
+and the answer is that although this
+this approach is beautiful and elegant
+
+ align:start position:0%
+this approach is beautiful and elegant
+ 
+
+ align:start position:0%
+this approach is beautiful and elegant
+and very powerful in instances it also
+
+ align:start position:0%
+and very powerful in instances it also
+ 
+
+ align:start position:0%
+and very powerful in instances it also
+is extremely limited because we don't
+
+ align:start position:0%
+is extremely limited because we don't
+ 
+
+ align:start position:0%
+is extremely limited because we don't
+know and we can't calculate the
+
+ align:start position:0%
+know and we can't calculate the
+ 
+
+ align:start position:0%
+know and we can't calculate the
+partition functions
+
+ align:start position:0%
+partition functions
+ 
+
+ align:start position:0%
+partition functions
+for all but the most toy problems
+
+ align:start position:0%
+for all but the most toy problems
+ 
+
+ align:start position:0%
+for all but the most toy problems
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you can see that we if you take
+
+ align:start position:0%
+you can see that we if you take
+ 
+
+ align:start position:0%
+you can see that we if you take
+thermodynamics in a physics department
+
+ align:start position:0%
+thermodynamics in a physics department
+ 
+
+ align:start position:0%
+thermodynamics in a physics department
+you sort of start from this approach you
+
+ align:start position:0%
+you sort of start from this approach you
+ 
+
+ align:start position:0%
+you sort of start from this approach you
+start from the statistical
+
+ align:start position:0%
+start from the statistical
+ 
+
+ align:start position:0%
+start from the statistical
+thermodynamics approach because
+
+ align:start position:0%
+thermodynamics approach because
+ 
+
+ align:start position:0%
+thermodynamics approach because
+um physicists Love Story problems right
+
+ align:start position:0%
+um physicists Love Story problems right
+ 
+
+ align:start position:0%
+um physicists Love Story problems right
+things that's intellectually rich but
+
+ align:start position:0%
+things that's intellectually rich but
+ 
+
+ align:start position:0%
+things that's intellectually rich but
+you know may or may not apply to the
+
+ align:start position:0%
+you know may or may not apply to the
+ 
+
+ align:start position:0%
+you know may or may not apply to the
+real world
+
+ align:start position:0%
+real world
+ 
+
+ align:start position:0%
+real world
+we're a little bit more applied
+
+ align:start position:0%
+we're a little bit more applied
+ 
+
+ align:start position:0%
+we're a little bit more applied
+to give you an example there's a there's
+
+ align:start position:0%
+to give you an example there's a there's
+ 
+
+ align:start position:0%
+to give you an example there's a there's
+a toy model of magnetism known as the
+
+ align:start position:0%
+a toy model of magnetism known as the
+ 
+
+ align:start position:0%
+a toy model of magnetism known as the
+ising model
+
+ align:start position:0%
+ising model
+ 
+
+ align:start position:0%
+ising model
+and the ising model says that you can
+
+ align:start position:0%
+and the ising model says that you can
+ 
+
+ align:start position:0%
+and the ising model says that you can
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+spins
+
+ align:start position:0%
+spins
+ 
+
+ align:start position:0%
+spins
+on a lattice or magnetic moments I
+
+ align:start position:0%
+on a lattice or magnetic moments I
+ 
+
+ align:start position:0%
+on a lattice or magnetic moments I
+should say on the lattice
+
+ align:start position:0%
+should say on the lattice
+ 
+
+ align:start position:0%
+should say on the lattice
+and they can face up or down that's it
+
+ align:start position:0%
+and they can face up or down that's it
+ 
+
+ align:start position:0%
+and they can face up or down that's it
+so they have a one-dimensional chain and
+
+ align:start position:0%
+so they have a one-dimensional chain and
+ 
+
+ align:start position:0%
+so they have a one-dimensional chain and
+each spin can face up or down and the
+
+ align:start position:0%
+each spin can face up or down and the
+ 
+
+ align:start position:0%
+each spin can face up or down and the
+energy of the system depends on on the
+
+ align:start position:0%
+energy of the system depends on on the
+ 
+
+ align:start position:0%
+energy of the system depends on on the
+orientation of the nearest neighbor it's
+
+ align:start position:0%
+orientation of the nearest neighbor it's
+ 
+
+ align:start position:0%
+orientation of the nearest neighbor it's
+a very simple model of a magnet
+
+ align:start position:0%
+a very simple model of a magnet
+ 
+
+ align:start position:0%
+a very simple model of a magnet
+and so if you if you take a course on
+
+ align:start position:0%
+and so if you if you take a course on
+ 
+
+ align:start position:0%
+and so if you if you take a course on
+magnetism or you take a thermodynamics
+
+ align:start position:0%
+magnetism or you take a thermodynamics
+ 
+
+ align:start position:0%
+magnetism or you take a thermodynamics
+course in the physics department you'll
+
+ align:start position:0%
+course in the physics department you'll
+ 
+
+ align:start position:0%
+course in the physics department you'll
+probably calculate the partition
+
+ align:start position:0%
+probably calculate the partition
+ 
+
+ align:start position:0%
+probably calculate the partition
+function for a 1D eising chain it's not
+
+ align:start position:0%
+function for a 1D eising chain it's not
+ 
+
+ align:start position:0%
+function for a 1D eising chain it's not
+that hard it's kind of fun
+
+ align:start position:0%
+that hard it's kind of fun
+ 
+
+ align:start position:0%
+that hard it's kind of fun
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however if we simply make it a
+
+ align:start position:0%
+however if we simply make it a
+ 
+
+ align:start position:0%
+however if we simply make it a
+two-dimensionalizing system and I'm
+
+ align:start position:0%
+two-dimensionalizing system and I'm
+ 
+
+ align:start position:0%
+two-dimensionalizing system and I'm
+drawing the direction of the arrows at
+
+ align:start position:0%
+drawing the direction of the arrows at
+ 
+
+ align:start position:0%
+drawing the direction of the arrows at
+random here just sort of showing you
+
+ align:start position:0%
+random here just sort of showing you
+ 
+
+ align:start position:0%
+random here just sort of showing you
+right so we just made this from one
+
+ align:start position:0%
+right so we just made this from one
+ 
+
+ align:start position:0%
+right so we just made this from one
+dimensional which is definitely an
+
+ align:start position:0%
+dimensional which is definitely an
+ 
+
+ align:start position:0%
+dimensional which is definitely an
+imaginary thing to a two-dimensional
+
+ align:start position:0%
+imaginary thing to a two-dimensional
+ 
+
+ align:start position:0%
+imaginary thing to a two-dimensional
+which is still imaginary but we're
+
+ align:start position:0%
+which is still imaginary but we're
+ 
+
+ align:start position:0%
+which is still imaginary but we're
+getting there right we're at least
+
+ align:start position:0%
+getting there right we're at least
+ 
+
+ align:start position:0%
+getting there right we're at least
+getting close to real space calculating
+
+ align:start position:0%
+getting close to real space calculating
+ 
+
+ align:start position:0%
+getting close to real space calculating
+a partition function for this model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um is one of the grand intellectual
+
+ align:start position:0%
+um is one of the grand intellectual
+ 
+
+ align:start position:0%
+um is one of the grand intellectual
+achievements of 20th century physics and
+
+ align:start position:0%
+achievements of 20th century physics and
+ 
+
+ align:start position:0%
+achievements of 20th century physics and
+one large answer in Nobel Prize
+
+ align:start position:0%
+one large answer in Nobel Prize
+ 
+
+ align:start position:0%
+one large answer in Nobel Prize
+it's horrendously complicated
+
+ align:start position:0%
+it's horrendously complicated
+ 
+
+ align:start position:0%
+it's horrendously complicated
+mathematically um I've never been able
+
+ align:start position:0%
+mathematically um I've never been able
+ 
+
+ align:start position:0%
+mathematically um I've never been able
+to follow even the first page of that
+
+ align:start position:0%
+to follow even the first page of that
+ 
+
+ align:start position:0%
+to follow even the first page of that
+it's not in any textbooks it's too long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so let's say I want to model a real
+
+ align:start position:0%
+um so let's say I want to model a real
+ 
+
+ align:start position:0%
+um so let's say I want to model a real
+magnet in three dimensions forget it I
+
+ align:start position:0%
+magnet in three dimensions forget it I
+ 
+
+ align:start position:0%
+magnet in three dimensions forget it I
+mean unless you're kind of Nobel Prize
+
+ align:start position:0%
+mean unless you're kind of Nobel Prize
+ 
+
+ align:start position:0%
+mean unless you're kind of Nobel Prize
+quality um that's that's an open problem
+
+ align:start position:0%
+quality um that's that's an open problem
+ 
+
+ align:start position:0%
+quality um that's that's an open problem
+you have at it but basically the point
+
+ align:start position:0%
+you have at it but basically the point
+ 
+
+ align:start position:0%
+you have at it but basically the point
+is that for real systems that we care
+
+ align:start position:0%
+is that for real systems that we care
+ 
+
+ align:start position:0%
+is that for real systems that we care
+about as Engineers this
+
+ align:start position:0%
+about as Engineers this
+ 
+
+ align:start position:0%
+about as Engineers this
+sort of is a magical construct in theory
+
+ align:start position:0%
+sort of is a magical construct in theory
+ 
+
+ align:start position:0%
+sort of is a magical construct in theory
+this exists
+
+ align:start position:0%
+this exists
+ 
+
+ align:start position:0%
+this exists
+in theory it allows you to calculate all
+
+ align:start position:0%
+in theory it allows you to calculate all
+ 
+
+ align:start position:0%
+in theory it allows you to calculate all
+the properties of the system from first
+
+ align:start position:0%
+the properties of the system from first
+ 
+
+ align:start position:0%
+the properties of the system from first
+principles but in practice it just
+
+ align:start position:0%
+principles but in practice it just
+ 
+
+ align:start position:0%
+principles but in practice it just
+Remains the intellectual exercise
+
+ align:start position:0%
+Remains the intellectual exercise
+ 
+
+ align:start position:0%
+Remains the intellectual exercise
+in practice we have to if you like go
+
+ align:start position:0%
+in practice we have to if you like go
+ 
+
+ align:start position:0%
+in practice we have to if you like go
+with a much more powerful which is the
+
+ align:start position:0%
+with a much more powerful which is the
+ 
+
+ align:start position:0%
+with a much more powerful which is the
+root of classical thermodynamics with
+
+ align:start position:0%
+root of classical thermodynamics with
+ 
+
+ align:start position:0%
+root of classical thermodynamics with
+its postulates and and observations and
+
+ align:start position:0%
+its postulates and and observations and
+ 
+
+ align:start position:0%
+its postulates and and observations and
+data and models
\ No newline at end of file
diff --git a/Ja9eEQQzTic.txt b/Ja9eEQQzTic.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42e57655c262a35dc296428b6a28f2b981af6ebf
--- /dev/null
+++ b/Ja9eEQQzTic.txt
@@ -0,0 +1,7323 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay all right let's just
+
+ align:start position:0%
+ocw.mit.edu okay all right let's just
+ 
+
+ align:start position:0%
+ocw.mit.edu okay all right let's just
+take got 10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds all right 92% I like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it that's great I told you there would
+
+ align:start position:0%
+it that's great I told you there would
+ 
+
+ align:start position:0%
+it that's great I told you there would
+be a formal charge question and there
+
+ align:start position:0%
+be a formal charge question and there
+ 
+
+ align:start position:0%
+be a formal charge question and there
+was and you learned it
+
+ align:start position:0%
+was and you learned it
+ 
+
+ align:start position:0%
+was and you learned it
+awesome that's what I like all right so
+
+ align:start position:0%
+awesome that's what I like all right so
+ 
+
+ align:start position:0%
+awesome that's what I like all right so
+that was uh carbon had four no loone
+
+ align:start position:0%
+that was uh carbon had four no loone
+ 
+
+ align:start position:0%
+that was uh carbon had four no loone
+pairs so four minus 0 find minus half of
+
+ align:start position:0%
+pairs so four minus 0 find minus half of
+ 
+
+ align:start position:0%
+pairs so four minus 0 find minus half of
+eight bonding electrons which is four so
+
+ align:start position:0%
+eight bonding electrons which is four so
+ 
+
+ align:start position:0%
+eight bonding electrons which is four so
+four minus 4 is
+
+ align:start position:0%
+four minus 4 is
+ 
+
+ align:start position:0%
+four minus 4 is
+zero okay so today we are having a
+
+ align:start position:0%
+zero okay so today we are having a
+ 
+
+ align:start position:0%
+zero okay so today we are having a
+clicker
+
+ align:start position:0%
+clicker
+ 
+
+ align:start position:0%
+clicker
+competition and problem set four will be
+
+ align:start position:0%
+competition and problem set four will be
+ 
+
+ align:start position:0%
+competition and problem set four will be
+posted later today and today's goal is
+
+ align:start position:0%
+posted later today and today's goal is
+ 
+
+ align:start position:0%
+posted later today and today's goal is
+for all recitations but recitation 12 to
+
+ align:start position:0%
+for all recitations but recitation 12 to
+ 
+
+ align:start position:0%
+for all recitations but recitation 12 to
+try try to uh unseat recitation 12 and
+
+ align:start position:0%
+try try to uh unseat recitation 12 and
+ 
+
+ align:start position:0%
+try try to uh unseat recitation 12 and
+the goal of recitation 12 is of course
+
+ align:start position:0%
+the goal of recitation 12 is of course
+ 
+
+ align:start position:0%
+the goal of recitation 12 is of course
+to win an unprecedented third week in a
+
+ align:start position:0%
+to win an unprecedented third week in a
+ 
+
+ align:start position:0%
+to win an unprecedented third week in a
+row um so that's that's the goal for
+
+ align:start position:0%
+row um so that's that's the goal for
+ 
+
+ align:start position:0%
+row um so that's that's the goal for
+everyone today now remember recitations
+
+ align:start position:0%
+everyone today now remember recitations
+ 
+
+ align:start position:0%
+everyone today now remember recitations
+that win a multiple weeks will be in the
+
+ align:start position:0%
+that win a multiple weeks will be in the
+ 
+
+ align:start position:0%
+that win a multiple weeks will be in the
+playoffs for the clicker competition at
+
+ align:start position:0%
+playoffs for the clicker competition at
+ 
+
+ align:start position:0%
+playoffs for the clicker competition at
+the end of the semester for a specially
+
+ align:start position:0%
+the end of the semester for a specially
+ 
+
+ align:start position:0%
+the end of the semester for a specially
+designed t-shirt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay more on clicker competitions
+
+ align:start position:0%
+okay more on clicker competitions
+ 
+
+ align:start position:0%
+okay more on clicker competitions
+actually later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today so if we can uh get settled in I
+
+ align:start position:0%
+today so if we can uh get settled in I
+ 
+
+ align:start position:0%
+today so if we can uh get settled in I
+know it's exciting and you are allowed
+
+ align:start position:0%
+know it's exciting and you are allowed
+ 
+
+ align:start position:0%
+know it's exciting and you are allowed
+to talk to your recitations uh other
+
+ align:start position:0%
+to talk to your recitations uh other
+ 
+
+ align:start position:0%
+to talk to your recitations uh other
+recitation members during the clicker
+
+ align:start position:0%
+recitation members during the clicker
+ 
+
+ align:start position:0%
+recitation members during the clicker
+questions that is allowed um but uh
+
+ align:start position:0%
+questions that is allowed um but uh
+ 
+
+ align:start position:0%
+questions that is allowed um but uh
+we'll uh need to cover a little material
+
+ align:start position:0%
+we'll uh need to cover a little material
+ 
+
+ align:start position:0%
+we'll uh need to cover a little material
+first so today we're going to talk about
+
+ align:start position:0%
+first so today we're going to talk about
+ 
+
+ align:start position:0%
+first so today we're going to talk about
+shapes of molecules and I brought uh
+
+ align:start position:0%
+shapes of molecules and I brought uh
+ 
+
+ align:start position:0%
+shapes of molecules and I brought uh
+some molecules with me today to help me
+
+ align:start position:0%
+some molecules with me today to help me
+ 
+
+ align:start position:0%
+some molecules with me today to help me
+out um and we're going to be talking
+
+ align:start position:0%
+out um and we're going to be talking
+ 
+
+ align:start position:0%
+out um and we're going to be talking
+about Vesper Theory
+
+ align:start position:0%
+about Vesper Theory
+ 
+
+ align:start position:0%
+about Vesper Theory
+so why is shapes of molecules
+
+ align:start position:0%
+so why is shapes of molecules
+ 
+
+ align:start position:0%
+so why is shapes of molecules
+important so shape which we can also
+
+ align:start position:0%
+important so shape which we can also
+ 
+
+ align:start position:0%
+important so shape which we can also
+call geometry so you're going to ask
+
+ align:start position:0%
+call geometry so you're going to ask
+ 
+
+ align:start position:0%
+call geometry so you're going to ask
+about the geometry of a molecule you're
+
+ align:start position:0%
+about the geometry of a molecule you're
+ 
+
+ align:start position:0%
+about the geometry of a molecule you're
+asking what is its shape is particularly
+
+ align:start position:0%
+asking what is its shape is particularly
+ 
+
+ align:start position:0%
+asking what is its shape is particularly
+important in chemistry because shape can
+
+ align:start position:0%
+important in chemistry because shape can
+ 
+
+ align:start position:0%
+important in chemistry because shape can
+dictate properties of a particular
+
+ align:start position:0%
+dictate properties of a particular
+ 
+
+ align:start position:0%
+dictate properties of a particular
+molecule it can tell you about or
+
+ align:start position:0%
+molecule it can tell you about or
+ 
+
+ align:start position:0%
+molecule it can tell you about or
+dictate melting points or boiling points
+
+ align:start position:0%
+dictate melting points or boiling points
+ 
+
+ align:start position:0%
+dictate melting points or boiling points
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+reactivity and I'm a biological chemist
+
+ align:start position:0%
+reactivity and I'm a biological chemist
+ 
+
+ align:start position:0%
+reactivity and I'm a biological chemist
+so I care a a lot about shapes of
+
+ align:start position:0%
+so I care a a lot about shapes of
+ 
+
+ align:start position:0%
+so I care a a lot about shapes of
+molecules because in in biology shape is
+
+ align:start position:0%
+molecules because in in biology shape is
+ 
+
+ align:start position:0%
+molecules because in in biology shape is
+really important so you have enzymes in
+
+ align:start position:0%
+really important so you have enzymes in
+ 
+
+ align:start position:0%
+really important so you have enzymes in
+your body catalyzing reactions and for
+
+ align:start position:0%
+your body catalyzing reactions and for
+ 
+
+ align:start position:0%
+your body catalyzing reactions and for
+those enzymes to work they are specially
+
+ align:start position:0%
+those enzymes to work they are specially
+ 
+
+ align:start position:0%
+those enzymes to work they are specially
+designed to react with one particular
+
+ align:start position:0%
+designed to react with one particular
+ 
+
+ align:start position:0%
+designed to react with one particular
+kind of molecule and not any molecule in
+
+ align:start position:0%
+kind of molecule and not any molecule in
+ 
+
+ align:start position:0%
+kind of molecule and not any molecule in
+the cell so they're designed to uh
+
+ align:start position:0%
+the cell so they're designed to uh
+ 
+
+ align:start position:0%
+the cell so they're designed to uh
+recognize the shape of that molecule so
+
+ align:start position:0%
+recognize the shape of that molecule so
+ 
+
+ align:start position:0%
+recognize the shape of that molecule so
+biochemistry really works by shape
+
+ align:start position:0%
+biochemistry really works by shape
+ 
+
+ align:start position:0%
+biochemistry really works by shape
+recognition so shape is very
+
+ align:start position:0%
+recognition so shape is very
+ 
+
+ align:start position:0%
+recognition so shape is very
+important so there's a lot of ways to
+
+ align:start position:0%
+important so there's a lot of ways to
+ 
+
+ align:start position:0%
+important so there's a lot of ways to
+get information about shape
+
+ align:start position:0%
+get information about shape
+ 
+
+ align:start position:0%
+get information about shape
+but there's one very simple theory that
+
+ align:start position:0%
+but there's one very simple theory that
+ 
+
+ align:start position:0%
+but there's one very simple theory that
+does exceedingly well in predicting the
+
+ align:start position:0%
+does exceedingly well in predicting the
+ 
+
+ align:start position:0%
+does exceedingly well in predicting the
+shapes of small molecules and that is
+
+ align:start position:0%
+shapes of small molecules and that is
+ 
+
+ align:start position:0%
+shapes of small molecules and that is
+called the veence shell electron pair
+
+ align:start position:0%
+called the veence shell electron pair
+ 
+
+ align:start position:0%
+called the veence shell electron pair
+repulsion Theory which is known as
+
+ align:start position:0%
+repulsion Theory which is known as
+ 
+
+ align:start position:0%
+repulsion Theory which is known as
+Vesper and is also known as the
+
+ align:start position:0%
+Vesper and is also known as the
+ 
+
+ align:start position:0%
+Vesper and is also known as the
+V Theory I will call it Vesper because
+
+ align:start position:0%
+V Theory I will call it Vesper because
+ 
+
+ align:start position:0%
+V Theory I will call it Vesper because
+it is really hard to say
+
+ align:start position:0%
+it is really hard to say
+ 
+
+ align:start position:0%
+it is really hard to say
+V Theory so Vesper is the topic today
+
+ align:start position:0%
+V Theory so Vesper is the topic today
+ 
+
+ align:start position:0%
+V Theory so Vesper is the topic today
+and this is based on Lewis structures So
+
+ align:start position:0%
+and this is based on Lewis structures So
+ 
+
+ align:start position:0%
+and this is based on Lewis structures So
+This is highly exciting because you just
+
+ align:start position:0%
+This is highly exciting because you just
+ 
+
+ align:start position:0%
+This is highly exciting because you just
+finished a problem set that had you draw
+
+ align:start position:0%
+finished a problem set that had you draw
+ 
+
+ align:start position:0%
+finished a problem set that had you draw
+lots of Lewis structures and now on the
+
+ align:start position:0%
+lots of Lewis structures and now on the
+ 
+
+ align:start position:0%
+lots of Lewis structures and now on the
+next problem set you can draw more Lewis
+
+ align:start position:0%
+next problem set you can draw more Lewis
+ 
+
+ align:start position:0%
+next problem set you can draw more Lewis
+structures and then tell us about his
+
+ align:start position:0%
+structures and then tell us about his
+ 
+
+ align:start position:0%
+structures and then tell us about his
+shape so uh so that's very exciting so
+
+ align:start position:0%
+shape so uh so that's very exciting so
+ 
+
+ align:start position:0%
+shape so uh so that's very exciting so
+you're going to retain all of the
+
+ align:start position:0%
+you're going to retain all of the
+ 
+
+ align:start position:0%
+you're going to retain all of the
+knowledge that you've gained in the last
+
+ align:start position:0%
+knowledge that you've gained in the last
+ 
+
+ align:start position:0%
+knowledge that you've gained in the last
+problem set and continue on with that
+
+ align:start position:0%
+problem set and continue on with that
+ 
+
+ align:start position:0%
+problem set and continue on with that
+problems all right so this is a very
+
+ align:start position:0%
+problems all right so this is a very
+ 
+
+ align:start position:0%
+problems all right so this is a very
+Simple Theory and it's based on the idea
+
+ align:start position:0%
+Simple Theory and it's based on the idea
+ 
+
+ align:start position:0%
+Simple Theory and it's based on the idea
+that valence shell valence electron
+
+ align:start position:0%
+that valence shell valence electron
+ 
+
+ align:start position:0%
+that valence shell valence electron
+pairs repel each
+
+ align:start position:0%
+pairs repel each
+ 
+
+ align:start position:0%
+pairs repel each
+other electrons repel each other they're
+
+ align:start position:0%
+other electrons repel each other they're
+ 
+
+ align:start position:0%
+other electrons repel each other they're
+negatively charged they repel each other
+
+ align:start position:0%
+negatively charged they repel each other
+ 
+
+ align:start position:0%
+negatively charged they repel each other
+that is the heart of this Theory very
+
+ align:start position:0%
+that is the heart of this Theory very
+ 
+
+ align:start position:0%
+that is the heart of this Theory very
+simple and as many of you may have
+
+ align:start position:0%
+simple and as many of you may have
+ 
+
+ align:start position:0%
+simple and as many of you may have
+gathered I love it when very simple
+
+ align:start position:0%
+gathered I love it when very simple
+ 
+
+ align:start position:0%
+gathered I love it when very simple
+theories explain a lot of stuff I enjoy
+
+ align:start position:0%
+theories explain a lot of stuff I enjoy
+ 
+
+ align:start position:0%
+theories explain a lot of stuff I enjoy
+that gets it this doesn't get rate 100%
+
+ align:start position:0%
+that gets it this doesn't get rate 100%
+ 
+
+ align:start position:0%
+that gets it this doesn't get rate 100%
+of the time I'm okay with that I'm good
+
+ align:start position:0%
+of the time I'm okay with that I'm good
+ 
+
+ align:start position:0%
+of the time I'm okay with that I'm good
+with about 90% so this works really
+
+ align:start position:0%
+with about 90% so this works really
+ 
+
+ align:start position:0%
+with about 90% so this works really
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+well so again we're talking about the
+
+ align:start position:0%
+well so again we're talking about the
+ 
+
+ align:start position:0%
+well so again we're talking about the
+geometry around a central atom and the
+
+ align:start position:0%
+geometry around a central atom and the
+ 
+
+ align:start position:0%
+geometry around a central atom and the
+idea is that the atoms are lone pairs
+
+ align:start position:0%
+idea is that the atoms are lone pairs
+ 
+
+ align:start position:0%
+idea is that the atoms are lone pairs
+around that Central atom are going to
+
+ align:start position:0%
+around that Central atom are going to
+ 
+
+ align:start position:0%
+around that Central atom are going to
+move in such a way attain such a shape
+
+ align:start position:0%
+move in such a way attain such a shape
+ 
+
+ align:start position:0%
+move in such a way attain such a shape
+such that the repulsion is minimized so
+
+ align:start position:0%
+such that the repulsion is minimized so
+ 
+
+ align:start position:0%
+such that the repulsion is minimized so
+this is all about minimizing repulsion
+
+ align:start position:0%
+this is all about minimizing repulsion
+ 
+
+ align:start position:0%
+this is all about minimizing repulsion
+minimizing stress again I'm a big fan of
+
+ align:start position:0%
+minimizing stress again I'm a big fan of
+ 
+
+ align:start position:0%
+minimizing stress again I'm a big fan of
+minimizing stress so I also like Vesper
+
+ align:start position:0%
+minimizing stress so I also like Vesper
+ 
+
+ align:start position:0%
+minimizing stress so I also like Vesper
+for that reason as
+
+ align:start position:0%
+for that reason as
+ 
+
+ align:start position:0%
+for that reason as
+well leis
+
+ align:start position:0%
+well leis
+ 
+
+ align:start position:0%
+well leis
+structures what causes stress problem
+
+ align:start position:0%
+structures what causes stress problem
+ 
+
+ align:start position:0%
+structures what causes stress problem
+sets oh but they build
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+character all
+
+ align:start position:0%
+character all
+ 
+
+ align:start position:0%
+character all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+Vesper very simple nomenclature again I
+
+ align:start position:0%
+Vesper very simple nomenclature again I
+ 
+
+ align:start position:0%
+Vesper very simple nomenclature again I
+like simple nomenclature a is the
+
+ align:start position:0%
+like simple nomenclature a is the
+ 
+
+ align:start position:0%
+like simple nomenclature a is the
+central atom maybe should be C but Adam
+
+ align:start position:0%
+central atom maybe should be C but Adam
+ 
+
+ align:start position:0%
+central atom maybe should be C but Adam
+is there so so Central atom is a x is
+
+ align:start position:0%
+is there so so Central atom is a x is
+ 
+
+ align:start position:0%
+is there so so Central atom is a x is
+the bonding atom and E is the lone pair
+
+ align:start position:0%
+the bonding atom and E is the lone pair
+ 
+
+ align:start position:0%
+the bonding atom and E is the lone pair
+of electrons so e lone pair electrons X
+
+ align:start position:0%
+of electrons so e lone pair electrons X
+ 
+
+ align:start position:0%
+of electrons so e lone pair electrons X
+is whatever bonding atom and a a is in
+
+ align:start position:0%
+is whatever bonding atom and a a is in
+ 
+
+ align:start position:0%
+is whatever bonding atom and a a is in
+the center a is the central
+
+ align:start position:0%
+the center a is the central
+ 
+
+ align:start position:0%
+the center a is the central
+atom there's one more term you need to
+
+ align:start position:0%
+atom there's one more term you need to
+ 
+
+ align:start position:0%
+atom there's one more term you need to
+know for
+
+ align:start position:0%
+know for
+ 
+
+ align:start position:0%
+know for
+Vesper and that's steric number
+
+ align:start position:0%
+Vesper and that's steric number
+ 
+
+ align:start position:0%
+Vesper and that's steric number
+SN and that's used to predict geometries
+
+ align:start position:0%
+SN and that's used to predict geometries
+ 
+
+ align:start position:0%
+SN and that's used to predict geometries
+so what is steric number
+
+ align:start position:0%
+so what is steric number
+ 
+
+ align:start position:0%
+so what is steric number
+equal steric number is the number of
+
+ align:start position:0%
+equal steric number is the number of
+ 
+
+ align:start position:0%
+equal steric number is the number of
+atoms bonded to the central
+
+ align:start position:0%
+atoms bonded to the central
+ 
+
+ align:start position:0%
+atoms bonded to the central
+atom plus the number of lone pair
+
+ align:start position:0%
+atom plus the number of lone pair
+ 
+
+ align:start position:0%
+atom plus the number of lone pair
+electrons and you count one pair as
+
+ align:start position:0%
+electrons and you count one pair as
+ 
+
+ align:start position:0%
+electrons and you count one pair as
+one and so we want to note when
+
+ align:start position:0%
+one and so we want to note when
+ 
+
+ align:start position:0%
+one and so we want to note when
+considering vasper double triple bonds
+
+ align:start position:0%
+considering vasper double triple bonds
+ 
+
+ align:start position:0%
+considering vasper double triple bonds
+are all and single bonds all the same so
+
+ align:start position:0%
+are all and single bonds all the same so
+ 
+
+ align:start position:0%
+are all and single bonds all the same so
+you don't have to worry about double
+
+ align:start position:0%
+you don't have to worry about double
+ 
+
+ align:start position:0%
+you don't have to worry about double
+triple bonds right now they're all
+
+ align:start position:0%
+triple bonds right now they're all
+ 
+
+ align:start position:0%
+triple bonds right now they're all
+they're all counts the same it's only
+
+ align:start position:0%
+they're all counts the same it's only
+ 
+
+ align:start position:0%
+they're all counts the same it's only
+the number of bonded atoms and the
+
+ align:start position:0%
+the number of bonded atoms and the
+ 
+
+ align:start position:0%
+the number of bonded atoms and the
+number of Lone pairs so let's look at
+
+ align:start position:0%
+number of Lone pairs so let's look at
+ 
+
+ align:start position:0%
+number of Lone pairs so let's look at
+some examples of this so we have our
+
+ align:start position:0%
+some examples of this so we have our
+ 
+
+ align:start position:0%
+some examples of this so we have our
+Central atom a bonded to two bonding
+
+ align:start position:0%
+Central atom a bonded to two bonding
+ 
+
+ align:start position:0%
+Central atom a bonded to two bonding
+atoms x with one lone pair of electrons
+
+ align:start position:0%
+atoms x with one lone pair of electrons
+ 
+
+ align:start position:0%
+atoms x with one lone pair of electrons
+so if you were asked what is the formula
+
+ align:start position:0%
+so if you were asked what is the formula
+ 
+
+ align:start position:0%
+so if you were asked what is the formula
+for this the Vesper formula it would be
+
+ align:start position:0%
+for this the Vesper formula it would be
+ 
+
+ align:start position:0%
+for this the Vesper formula it would be
+a X2 e as shown there and then you might
+
+ align:start position:0%
+a X2 e as shown there and then you might
+ 
+
+ align:start position:0%
+a X2 e as shown there and then you might
+be asked the steric number and the
+
+ align:start position:0%
+be asked the steric number and the
+ 
+
+ align:start position:0%
+be asked the steric number and the
+steric number in this case would be what
+
+ align:start position:0%
+steric number in this case would be what
+ 
+
+ align:start position:0%
+steric number in this case would be what
+three we have two bonding atoms one lone
+
+ align:start position:0%
+three we have two bonding atoms one lone
+ 
+
+ align:start position:0%
+three we have two bonding atoms one lone
+pair of electrons again the lone pair is
+
+ align:start position:0%
+pair of electrons again the lone pair is
+ 
+
+ align:start position:0%
+pair of electrons again the lone pair is
+just counts as
+
+ align:start position:0%
+just counts as
+ 
+
+ align:start position:0%
+just counts as
+one so I could also draw this structure
+
+ align:start position:0%
+one so I could also draw this structure
+ 
+
+ align:start position:0%
+one so I could also draw this structure
+with a double bond to one of the
+
+ align:start position:0%
+with a double bond to one of the
+ 
+
+ align:start position:0%
+with a double bond to one of the
+x's and this would have the equation a
+
+ align:start position:0%
+x's and this would have the equation a
+ 
+
+ align:start position:0%
+x's and this would have the equation a
+x2e exactly the same formula because we
+
+ align:start position:0%
+x2e exactly the same formula because we
+ 
+
+ align:start position:0%
+x2e exactly the same formula because we
+don't care about the double bond in the
+
+ align:start position:0%
+don't care about the double bond in the
+ 
+
+ align:start position:0%
+don't care about the double bond in the
+formula only the number of bonding atoms
+
+ align:start position:0%
+formula only the number of bonding atoms
+ 
+
+ align:start position:0%
+formula only the number of bonding atoms
+only the number of Lone Pairs and this
+
+ align:start position:0%
+only the number of Lone Pairs and this
+ 
+
+ align:start position:0%
+only the number of Lone Pairs and this
+would have an SN number of what three
+
+ align:start position:0%
+would have an SN number of what three
+ 
+
+ align:start position:0%
+would have an SN number of what three
+right because it only matters about the
+
+ align:start position:0%
+right because it only matters about the
+ 
+
+ align:start position:0%
+right because it only matters about the
+lone Pairs and the atoms that's all we
+
+ align:start position:0%
+lone Pairs and the atoms that's all we
+ 
+
+ align:start position:0%
+lone Pairs and the atoms that's all we
+care about here we don't care about the
+
+ align:start position:0%
+care about here we don't care about the
+ 
+
+ align:start position:0%
+care about here we don't care about the
+double bonds triple bonds whatever we'll
+
+ align:start position:0%
+double bonds triple bonds whatever we'll
+ 
+
+ align:start position:0%
+double bonds triple bonds whatever we'll
+care about them later but for right now
+
+ align:start position:0%
+care about them later but for right now
+ 
+
+ align:start position:0%
+care about them later but for right now
+for geometry we're only caring about
+
+ align:start position:0%
+for geometry we're only caring about
+ 
+
+ align:start position:0%
+for geometry we're only caring about
+bonded atoms and lone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairs some of you will be very happy
+
+ align:start position:0%
+pairs some of you will be very happy
+ 
+
+ align:start position:0%
+pairs some of you will be very happy
+after doing the last problem set to know
+
+ align:start position:0%
+after doing the last problem set to know
+ 
+
+ align:start position:0%
+after doing the last problem set to know
+that you can
+
+ align:start position:0%
+that you can
+ 
+
+ align:start position:0%
+that you can
+apply Vesper Theory to all the resonance
+
+ align:start position:0%
+apply Vesper Theory to all the resonance
+ 
+
+ align:start position:0%
+apply Vesper Theory to all the resonance
+structures that you may come up with
+
+ align:start position:0%
+structures that you may come up with
+ 
+
+ align:start position:0%
+structures that you may come up with
+when you're doing Lew structures so if a
+
+ align:start position:0%
+when you're doing Lew structures so if a
+ 
+
+ align:start position:0%
+when you're doing Lew structures so if a
+molecule has one or more resonance
+
+ align:start position:0%
+molecule has one or more resonance
+ 
+
+ align:start position:0%
+molecule has one or more resonance
+structures that's okay Vesper can be
+
+ align:start position:0%
+structures that's okay Vesper can be
+ 
+
+ align:start position:0%
+structures that's okay Vesper can be
+applied to any one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them also if there's more than one
+
+ align:start position:0%
+them also if there's more than one
+ 
+
+ align:start position:0%
+them also if there's more than one
+Central atom you need to consider those
+
+ align:start position:0%
+Central atom you need to consider those
+ 
+
+ align:start position:0%
+Central atom you need to consider those
+atoms separately so in this case you
+
+ align:start position:0%
+atoms separately so in this case you
+ 
+
+ align:start position:0%
+atoms separately so in this case you
+would be asked about the geometry around
+
+ align:start position:0%
+would be asked about the geometry around
+ 
+
+ align:start position:0%
+would be asked about the geometry around
+the carbon and the geometry around the
+
+ align:start position:0%
+the carbon and the geometry around the
+ 
+
+ align:start position:0%
+the carbon and the geometry around the
+oxygen
+
+ align:start position:0%
+oxygen
+ 
+
+ align:start position:0%
+oxygen
+but a lot of the examples we have today
+
+ align:start position:0%
+but a lot of the examples we have today
+ 
+
+ align:start position:0%
+but a lot of the examples we have today
+just have one Central atom all right so
+
+ align:start position:0%
+just have one Central atom all right so
+ 
+
+ align:start position:0%
+just have one Central atom all right so
+that's just a little introduction to
+
+ align:start position:0%
+that's just a little introduction to
+ 
+
+ align:start position:0%
+that's just a little introduction to
+Vesper now there are two cases that
+
+ align:start position:0%
+Vesper now there are two cases that
+ 
+
+ align:start position:0%
+Vesper now there are two cases that
+we're going to consider today one are
+
+ align:start position:0%
+we're going to consider today one are
+ 
+
+ align:start position:0%
+we're going to consider today one are
+molecules without loone Pairs and one
+
+ align:start position:0%
+molecules without loone Pairs and one
+ 
+
+ align:start position:0%
+molecules without loone Pairs and one
+are molecules with loone pairs without
+
+ align:start position:0%
+are molecules with loone pairs without
+ 
+
+ align:start position:0%
+are molecules with loone pairs without
+loone pairs is a little bit easier than
+
+ align:start position:0%
+loone pairs is a little bit easier than
+ 
+
+ align:start position:0%
+loone pairs is a little bit easier than
+with loone pairs so let's start
+
+ align:start position:0%
+with loone pairs so let's start
+ 
+
+ align:start position:0%
+with loone pairs so let's start
+there and we have a nice table for you
+
+ align:start position:0%
+there and we have a nice table for you
+ 
+
+ align:start position:0%
+there and we have a nice table for you
+I'll tell you that these lecture notes
+
+ align:start position:0%
+I'll tell you that these lecture notes
+ 
+
+ align:start position:0%
+I'll tell you that these lecture notes
+are of high value I've had people who've
+
+ align:start position:0%
+are of high value I've had people who've
+ 
+
+ align:start position:0%
+are of high value I've had people who've
+taken this course want to come back it's
+
+ align:start position:0%
+taken this course want to come back it's
+ 
+
+ align:start position:0%
+taken this course want to come back it's
+a nice summary of all these shapes so
+
+ align:start position:0%
+a nice summary of all these shapes so
+ 
+
+ align:start position:0%
+a nice summary of all these shapes so
+you want to keep this in a nice secure
+
+ align:start position:0%
+you want to keep this in a nice secure
+ 
+
+ align:start position:0%
+you want to keep this in a nice secure
+location um highly desirable notes okay
+
+ align:start position:0%
+location um highly desirable notes okay
+ 
+
+ align:start position:0%
+location um highly desirable notes okay
+so let's look at a formula type the
+
+ align:start position:0%
+so let's look at a formula type the
+ 
+
+ align:start position:0%
+so let's look at a formula type the
+simplest we have ax2 here so that has an
+
+ align:start position:0%
+simplest we have ax2 here so that has an
+ 
+
+ align:start position:0%
+simplest we have ax2 here so that has an
+SN number of two because it has two
+
+ align:start position:0%
+SN number of two because it has two
+ 
+
+ align:start position:0%
+SN number of two because it has two
+bonded atoms and it has this molecular
+
+ align:start position:0%
+bonded atoms and it has this molecular
+ 
+
+ align:start position:0%
+bonded atoms and it has this molecular
+shape and I brought an example
+
+ align:start position:0%
+shape and I brought an example
+ 
+
+ align:start position:0%
+shape and I brought an example
+here and this is of course a linear
+
+ align:start position:0%
+here and this is of course a linear
+ 
+
+ align:start position:0%
+here and this is of course a linear
+molecule and therefore the angle and
+
+ align:start position:0%
+molecule and therefore the angle and
+ 
+
+ align:start position:0%
+molecule and therefore the angle and
+here we're talking about the angle
+
+ align:start position:0%
+here we're talking about the angle
+ 
+
+ align:start position:0%
+here we're talking about the angle
+around the central atom so from this a
+
+ align:start position:0%
+around the central atom so from this a
+ 
+
+ align:start position:0%
+around the central atom so from this a
+black atom to that black atom we'd have
+
+ align:start position:0%
+black atom to that black atom we'd have
+ 
+
+ align:start position:0%
+black atom to that black atom we'd have
+180 so that's the simplest linear
+
+ align:start position:0%
+180 so that's the simplest linear
+ 
+
+ align:start position:0%
+180 so that's the simplest linear
+molecule so let's get a little more
+
+ align:start position:0%
+molecule so let's get a little more
+ 
+
+ align:start position:0%
+molecule so let's get a little more
+complicated and add three bonding
+
+ align:start position:0%
+complicated and add three bonding
+ 
+
+ align:start position:0%
+complicated and add three bonding
+atoms so here we have a case of a
+
+ align:start position:0%
+atoms so here we have a case of a
+ 
+
+ align:start position:0%
+atoms so here we have a case of a
+X3 it has an SN number of three there're
+
+ align:start position:0%
+X3 it has an SN number of three there're
+ 
+
+ align:start position:0%
+X3 it has an SN number of three there're
+three things bonded to the central atom
+
+ align:start position:0%
+three things bonded to the central atom
+ 
+
+ align:start position:0%
+three things bonded to the central atom
+and it shapes is trigonal planer
+
+ align:start position:0%
+and it shapes is trigonal planer
+ 
+
+ align:start position:0%
+and it shapes is trigonal planer
+trigonal should be remembered it looks
+
+ align:start position:0%
+trigonal should be remembered it looks
+ 
+
+ align:start position:0%
+trigonal should be remembered it looks
+like a triangle and you should also
+
+ align:start position:0%
+like a triangle and you should also
+ 
+
+ align:start position:0%
+like a triangle and you should also
+remember that it's planer you can hold
+
+ align:start position:0%
+remember that it's planer you can hold
+ 
+
+ align:start position:0%
+remember that it's planer you can hold
+it this way and see all of the atoms are
+
+ align:start position:0%
+it this way and see all of the atoms are
+ 
+
+ align:start position:0%
+it this way and see all of the atoms are
+in one plane and I'm making some of this
+
+ align:start position:0%
+in one plane and I'm making some of this
+ 
+
+ align:start position:0%
+in one plane and I'm making some of this
+point because later on the exam when
+
+ align:start position:0%
+point because later on the exam when
+ 
+
+ align:start position:0%
+point because later on the exam when
+you're asked to name geometries of
+
+ align:start position:0%
+you're asked to name geometries of
+ 
+
+ align:start position:0%
+you're asked to name geometries of
+things people come up with all sorts of
+
+ align:start position:0%
+things people come up with all sorts of
+ 
+
+ align:start position:0%
+things people come up with all sorts of
+crazy things so if I spend a little time
+
+ align:start position:0%
+crazy things so if I spend a little time
+ 
+
+ align:start position:0%
+crazy things so if I spend a little time
+doing uh my demonstration here of the
+
+ align:start position:0%
+doing uh my demonstration here of the
+ 
+
+ align:start position:0%
+doing uh my demonstration here of the
+shapes of molecules um it'll pay off
+
+ align:start position:0%
+shapes of molecules um it'll pay off
+ 
+
+ align:start position:0%
+shapes of molecules um it'll pay off
+later in the exam it'll it'll sear in
+
+ align:start position:0%
+later in the exam it'll it'll sear in
+ 
+
+ align:start position:0%
+later in the exam it'll it'll sear in
+your brain it'll be hard to forget
+
+ align:start position:0%
+your brain it'll be hard to forget
+ 
+
+ align:start position:0%
+your brain it'll be hard to forget
+trigonal planer what are the
+
+ align:start position:0%
+trigonal planer what are the
+ 
+
+ align:start position:0%
+trigonal planer what are the
+angles
+
+ align:start position:0%
+angles
+ 
+
+ align:start position:0%
+angles
+120 right okay let's move on we'll have
+
+ align:start position:0%
+120 right okay let's move on we'll have
+ 
+
+ align:start position:0%
+120 right okay let's move on we'll have
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+atoms SN number of four
+
+ align:start position:0%
+atoms SN number of four
+ 
+
+ align:start position:0%
+atoms SN number of four
+ax4 so this is our tetrahedral
+
+ align:start position:0%
+ax4 so this is our tetrahedral
+ 
+
+ align:start position:0%
+ax4 so this is our tetrahedral
+geometry and I'm going to just note as
+
+ align:start position:0%
+geometry and I'm going to just note as
+ 
+
+ align:start position:0%
+geometry and I'm going to just note as
+it says down here that when you have a
+
+ align:start position:0%
+it says down here that when you have a
+ 
+
+ align:start position:0%
+it says down here that when you have a
+thick um Arrow coming out at you
+
+ align:start position:0%
+thick um Arrow coming out at you
+ 
+
+ align:start position:0%
+thick um Arrow coming out at you
+like this Bond and a thin one going back
+
+ align:start position:0%
+like this Bond and a thin one going back
+ 
+
+ align:start position:0%
+like this Bond and a thin one going back
+that means the one coming out is coming
+
+ align:start position:0%
+that means the one coming out is coming
+ 
+
+ align:start position:0%
+that means the one coming out is coming
+straight out toward you the dashed line
+
+ align:start position:0%
+straight out toward you the dashed line
+ 
+
+ align:start position:0%
+straight out toward you the dashed line
+is going back into the screen and the
+
+ align:start position:0%
+is going back into the screen and the
+ 
+
+ align:start position:0%
+is going back into the screen and the
+two that are not um thickened or dashed
+
+ align:start position:0%
+two that are not um thickened or dashed
+ 
+
+ align:start position:0%
+two that are not um thickened or dashed
+are in the plane so if I hold it like
+
+ align:start position:0%
+are in the plane so if I hold it like
+ 
+
+ align:start position:0%
+are in the plane so if I hold it like
+this we have two atoms in the plane one
+
+ align:start position:0%
+this we have two atoms in the plane one
+ 
+
+ align:start position:0%
+this we have two atoms in the plane one
+coming out one going back and so that's
+
+ align:start position:0%
+coming out one going back and so that's
+ 
+
+ align:start position:0%
+coming out one going back and so that's
+the uh that's how if you see that drawn
+
+ align:start position:0%
+the uh that's how if you see that drawn
+ 
+
+ align:start position:0%
+the uh that's how if you see that drawn
+that way and you will um you can think
+
+ align:start position:0%
+that way and you will um you can think
+ 
+
+ align:start position:0%
+that way and you will um you can think
+about it in three dimensions all right
+
+ align:start position:0%
+about it in three dimensions all right
+ 
+
+ align:start position:0%
+about it in three dimensions all right
+so what what's the angle of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tetrahedral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+109.5 so a lot of people have already
+
+ align:start position:0%
+109.5 so a lot of people have already
+ 
+
+ align:start position:0%
+109.5 so a lot of people have already
+familiar with this is great if you're
+
+ align:start position:0%
+familiar with this is great if you're
+ 
+
+ align:start position:0%
+familiar with this is great if you're
+not you will learn it quickly when you
+
+ align:start position:0%
+not you will learn it quickly when you
+ 
+
+ align:start position:0%
+not you will learn it quickly when you
+do the problems all right we'll keep
+
+ align:start position:0%
+do the problems all right we'll keep
+ 
+
+ align:start position:0%
+do the problems all right we'll keep
+going we have five I'm going to move
+
+ align:start position:0%
+going we have five I'm going to move
+ 
+
+ align:start position:0%
+going we have five I'm going to move
+over here so SN number of five we have
+
+ align:start position:0%
+over here so SN number of five we have
+ 
+
+ align:start position:0%
+over here so SN number of five we have
+ax5 and here is our shape so this is
+
+ align:start position:0%
+ax5 and here is our shape so this is
+ 
+
+ align:start position:0%
+ax5 and here is our shape so this is
+trigonal by paramal so if you think
+
+ align:start position:0%
+trigonal by paramal so if you think
+ 
+
+ align:start position:0%
+trigonal by paramal so if you think
+about the shape of your trigonal planer
+
+ align:start position:0%
+about the shape of your trigonal planer
+ 
+
+ align:start position:0%
+about the shape of your trigonal planer
+you see along here we have our trigonal
+
+ align:start position:0%
+you see along here we have our trigonal
+ 
+
+ align:start position:0%
+you see along here we have our trigonal
+planer so we have our trigonal shape but
+
+ align:start position:0%
+planer so we have our trigonal shape but
+ 
+
+ align:start position:0%
+planer so we have our trigonal shape but
+we also now have an atom above and an
+
+ align:start position:0%
+we also now have an atom above and an
+ 
+
+ align:start position:0%
+we also now have an atom above and an
+atom below and that forms kind of a a
+
+ align:start position:0%
+atom below and that forms kind of a a
+ 
+
+ align:start position:0%
+atom below and that forms kind of a a
+pyramid on top and pyramid on the bottom
+
+ align:start position:0%
+pyramid on top and pyramid on the bottom
+ 
+
+ align:start position:0%
+pyramid on top and pyramid on the bottom
+so it's trigonal by
+
+ align:start position:0%
+so it's trigonal by
+ 
+
+ align:start position:0%
+so it's trigonal by
+paramal and there are two sets of angles
+
+ align:start position:0%
+paramal and there are two sets of angles
+ 
+
+ align:start position:0%
+paramal and there are two sets of angles
+now what are the angles in the
+
+ align:start position:0%
+now what are the angles in the
+ 
+
+ align:start position:0%
+now what are the angles in the
+equatorial
+
+ align:start position:0%
+equatorial
+ 
+
+ align:start position:0%
+equatorial
+120 I love when people yell things out
+
+ align:start position:0%
+120 I love when people yell things out
+ 
+
+ align:start position:0%
+120 I love when people yell things out
+it's awesome angle from the axial to the
+
+ align:start position:0%
+it's awesome angle from the axial to the
+ 
+
+ align:start position:0%
+it's awesome angle from the axial to the
+equatorial 90
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+awesome all right and one more basic
+
+ align:start position:0%
+awesome all right and one more basic
+ 
+
+ align:start position:0%
+awesome all right and one more basic
+shape
+
+ align:start position:0%
+shape
+ 
+
+ align:start position:0%
+shape
+group and that's this one here we have
+
+ align:start position:0%
+group and that's this one here we have
+ 
+
+ align:start position:0%
+group and that's this one here we have
+six atoms bonded to the central atom
+
+ align:start position:0%
+six atoms bonded to the central atom
+ 
+
+ align:start position:0%
+six atoms bonded to the central atom
+ax6 and we have this shape so now I'm
+
+ align:start position:0%
+ax6 and we have this shape so now I'm
+ 
+
+ align:start position:0%
+ax6 and we have this shape so now I'm
+holding it to axial atoms two atoms
+
+ align:start position:0%
+holding it to axial atoms two atoms
+ 
+
+ align:start position:0%
+holding it to axial atoms two atoms
+coming out toward you two going back
+
+ align:start position:0%
+coming out toward you two going back
+ 
+
+ align:start position:0%
+coming out toward you two going back
+octahedral geometry and what are all the
+
+ align:start position:0%
+octahedral geometry and what are all the
+ 
+
+ align:start position:0%
+octahedral geometry and what are all the
+angles here 90
+
+ align:start position:0%
+angles here 90
+ 
+
+ align:start position:0%
+angles here 90
+awesome all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so let's look at some examples
+
+ align:start position:0%
+right so let's look at some examples
+ 
+
+ align:start position:0%
+right so let's look at some examples
+hopefully everyone got the 90 and can
+
+ align:start position:0%
+hopefully everyone got the 90 and can
+ 
+
+ align:start position:0%
+hopefully everyone got the 90 and can
+write it down if not I'm sure someone
+
+ align:start position:0%
+write it down if not I'm sure someone
+ 
+
+ align:start position:0%
+write it down if not I'm sure someone
+will yell it out again for you all right
+
+ align:start position:0%
+will yell it out again for you all right
+ 
+
+ align:start position:0%
+will yell it out again for you all right
+so let's look at some examples we were
+
+ align:start position:0%
+so let's look at some examples we were
+ 
+
+ align:start position:0%
+so let's look at some examples we were
+talking about CO2 and you calculated the
+
+ align:start position:0%
+talking about CO2 and you calculated the
+ 
+
+ align:start position:0%
+talking about CO2 and you calculated the
+formal charge on it for me um so we have
+
+ align:start position:0%
+formal charge on it for me um so we have
+ 
+
+ align:start position:0%
+formal charge on it for me um so we have
+ax2 SN number of two this is linear and
+
+ align:start position:0%
+ax2 SN number of two this is linear and
+ 
+
+ align:start position:0%
+ax2 SN number of two this is linear and
+and our angle is 180 and now we can
+
+ align:start position:0%
+and our angle is 180 and now we can
+ 
+
+ align:start position:0%
+and our angle is 180 and now we can
+explain why this is non-polar we learned
+
+ align:start position:0%
+explain why this is non-polar we learned
+ 
+
+ align:start position:0%
+explain why this is non-polar we learned
+before that we had polar bonds where we
+
+ align:start position:0%
+before that we had polar bonds where we
+ 
+
+ align:start position:0%
+before that we had polar bonds where we
+had difference of electro negativity
+
+ align:start position:0%
+had difference of electro negativity
+ 
+
+ align:start position:0%
+had difference of electro negativity
+between the carbon and the oxygen which
+
+ align:start position:0%
+between the carbon and the oxygen which
+ 
+
+ align:start position:0%
+between the carbon and the oxygen which
+should make a polar bond so you have two
+
+ align:start position:0%
+should make a polar bond so you have two
+ 
+
+ align:start position:0%
+should make a polar bond so you have two
+polar bonds so why is this not a polar
+
+ align:start position:0%
+polar bonds so why is this not a polar
+ 
+
+ align:start position:0%
+polar bonds so why is this not a polar
+molecule and it's not a polar molecule
+
+ align:start position:0%
+molecule and it's not a polar molecule
+ 
+
+ align:start position:0%
+molecule and it's not a polar molecule
+because this Oxygen's pulling this way
+
+ align:start position:0%
+because this Oxygen's pulling this way
+ 
+
+ align:start position:0%
+because this Oxygen's pulling this way
+this one's pulling that way and that
+
+ align:start position:0%
+this one's pulling that way and that
+ 
+
+ align:start position:0%
+this one's pulling that way and that
+makes it non planer because there's no
+
+ align:start position:0%
+makes it non planer because there's no
+ 
+
+ align:start position:0%
+makes it non planer because there's no
+net dipole so shape is important for
+
+ align:start position:0%
+net dipole so shape is important for
+ 
+
+ align:start position:0%
+net dipole so shape is important for
+this all right let's look at the next
+
+ align:start position:0%
+this all right let's look at the next
+ 
+
+ align:start position:0%
+this all right let's look at the next
+example we've seen a lot of these
+
+ align:start position:0%
+example we've seen a lot of these
+ 
+
+ align:start position:0%
+example we've seen a lot of these
+examples before um we were talking about
+
+ align:start position:0%
+examples before um we were talking about
+ 
+
+ align:start position:0%
+examples before um we were talking about
+Lewis structure what was Boron an
+
+ align:start position:0%
+Lewis structure what was Boron an
+ 
+
+ align:start position:0%
+Lewis structure what was Boron an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+of INE incomplete OCT that's right so
+
+ align:start position:0%
+of INE incomplete OCT that's right so
+ 
+
+ align:start position:0%
+of INE incomplete OCT that's right so
+here is an example it has three things
+
+ align:start position:0%
+here is an example it has three things
+ 
+
+ align:start position:0%
+here is an example it has three things
+bound bound to it and it has the shape
+
+ align:start position:0%
+bound bound to it and it has the shape
+ 
+
+ align:start position:0%
+bound bound to it and it has the shape
+of trigonal
+
+ align:start position:0%
+of trigonal
+ 
+
+ align:start position:0%
+of trigonal
+planer and the middle atom is incomplete
+
+ align:start position:0%
+planer and the middle atom is incomplete
+ 
+
+ align:start position:0%
+planer and the middle atom is incomplete
+octet but it's okay Boron and which
+
+ align:start position:0%
+octet but it's okay Boron and which
+ 
+
+ align:start position:0%
+octet but it's okay Boron and which
+other one are okay being incomplete
+
+ align:start position:0%
+other one are okay being incomplete
+ 
+
+ align:start position:0%
+other one are okay being incomplete
+octets aluminum
+
+ align:start position:0%
+octets aluminum
+ 
+
+ align:start position:0%
+octets aluminum
+right so the angles are 120
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here now we move on we have this
+
+ align:start position:0%
+here now we move on we have this
+ 
+
+ align:start position:0%
+here now we move on we have this
+molecule CH4 and if someone tell me what
+
+ align:start position:0%
+molecule CH4 and if someone tell me what
+ 
+
+ align:start position:0%
+molecule CH4 and if someone tell me what
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+methane so we have ax4 SN number of four
+
+ align:start position:0%
+methane so we have ax4 SN number of four
+ 
+
+ align:start position:0%
+methane so we have ax4 SN number of four
+and we have our tetrahedral shape and
+
+ align:start position:0%
+and we have our tetrahedral shape and
+ 
+
+ align:start position:0%
+and we have our tetrahedral shape and
+our angles
+
+ align:start position:0%
+our angles
+ 
+
+ align:start position:0%
+our angles
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+109.5 right so methane we should all
+
+ align:start position:0%
+109.5 right so methane we should all
+ 
+
+ align:start position:0%
+109.5 right so methane we should all
+care about greenhouse gas but also some
+
+ align:start position:0%
+care about greenhouse gas but also some
+ 
+
+ align:start position:0%
+care about greenhouse gas but also some
+people believe will be the Salvation to
+
+ align:start position:0%
+people believe will be the Salvation to
+ 
+
+ align:start position:0%
+people believe will be the Salvation to
+our biofuels and energy problem we will
+
+ align:start position:0%
+our biofuels and energy problem we will
+ 
+
+ align:start position:0%
+our biofuels and energy problem we will
+see if that's true or not okay another
+
+ align:start position:0%
+see if that's true or not okay another
+ 
+
+ align:start position:0%
+see if that's true or not okay another
+example over here so we have phosphorus
+
+ align:start position:0%
+example over here so we have phosphorus
+ 
+
+ align:start position:0%
+example over here so we have phosphorus
+in the middle and five chlorines so what
+
+ align:start position:0%
+in the middle and five chlorines so what
+ 
+
+ align:start position:0%
+in the middle and five chlorines so what
+is this an example of in terms of Lewis
+
+ align:start position:0%
+is this an example of in terms of Lewis
+ 
+
+ align:start position:0%
+is this an example of in terms of Lewis
+structures yeah so this is trigonal
+
+ align:start position:0%
+structures yeah so this is trigonal
+ 
+
+ align:start position:0%
+structures yeah so this is trigonal
+b paramal or
+
+ align:start position:0%
+b paramal or
+ 
+
+ align:start position:0%
+b paramal or
+bipyramidal um I think both are right I
+
+ align:start position:0%
+bipyramidal um I think both are right I
+ 
+
+ align:start position:0%
+bipyramidal um I think both are right I
+don't know um and so we have our 120 and
+
+ align:start position:0%
+don't know um and so we have our 120 and
+ 
+
+ align:start position:0%
+don't know um and so we have our 120 and
+R 90 and this was an example we had in
+
+ align:start position:0%
+R 90 and this was an example we had in
+ 
+
+ align:start position:0%
+R 90 and this was an example we had in
+Lewis structures or something very
+
+ align:start position:0%
+Lewis structures or something very
+ 
+
+ align:start position:0%
+Lewis structures or something very
+similar of an expanded octet so we have
+
+ align:start position:0%
+similar of an expanded octet so we have
+ 
+
+ align:start position:0%
+similar of an expanded octet so we have
+more we have five bonds around the
+
+ align:start position:0%
+more we have five bonds around the
+ 
+
+ align:start position:0%
+more we have five bonds around the
+phosphorus and that's okay because it's
+
+ align:start position:0%
+phosphorus and that's okay because it's
+ 
+
+ align:start position:0%
+phosphorus and that's okay because it's
+um n equals 3 or greater so we have
+
+ align:start position:0%
+um n equals 3 or greater so we have
+ 
+
+ align:start position:0%
+um n equals 3 or greater so we have
+example again of an expanded octet and
+
+ align:start position:0%
+example again of an expanded octet and
+ 
+
+ align:start position:0%
+example again of an expanded octet and
+if we keep going we'll have another
+
+ align:start position:0%
+if we keep going we'll have another
+ 
+
+ align:start position:0%
+if we keep going we'll have another
+expanded octet so here we have
+
+ align:start position:0%
+expanded octet so here we have
+ 
+
+ align:start position:0%
+expanded octet so here we have
+ax6 so we have six bonds around the
+
+ align:start position:0%
+ax6 so we have six bonds around the
+ 
+
+ align:start position:0%
+ax6 so we have six bonds around the
+sulfur sulfur is okay with that and what
+
+ align:start position:0%
+sulfur sulfur is okay with that and what
+ 
+
+ align:start position:0%
+sulfur sulfur is okay with that and what
+is the geometry here octahedral
+
+ align:start position:0%
+is the geometry here octahedral
+ 
+
+ align:start position:0%
+is the geometry here octahedral
+angles 90 yep all right so we have
+
+ align:start position:0%
+angles 90 yep all right so we have
+ 
+
+ align:start position:0%
+angles 90 yep all right so we have
+several examples here of things with
+
+ align:start position:0%
+several examples here of things with
+ 
+
+ align:start position:0%
+several examples here of things with
+expanded octets and also um deficient um
+
+ align:start position:0%
+expanded octets and also um deficient um
+ 
+
+ align:start position:0%
+expanded octets and also um deficient um
+uh octets all right so this is pretty
+
+ align:start position:0%
+uh octets all right so this is pretty
+ 
+
+ align:start position:0%
+uh octets all right so this is pretty
+straightforward people get a lot of
+
+ align:start position:0%
+straightforward people get a lot of
+ 
+
+ align:start position:0%
+straightforward people get a lot of
+points on exams except when they come up
+
+ align:start position:0%
+points on exams except when they come up
+ 
+
+ align:start position:0%
+points on exams except when they come up
+with all sorts of weird kind of shapes
+
+ align:start position:0%
+with all sorts of weird kind of shapes
+ 
+
+ align:start position:0%
+with all sorts of weird kind of shapes
+that don't exist but most of the time
+
+ align:start position:0%
+that don't exist but most of the time
+ 
+
+ align:start position:0%
+that don't exist but most of the time
+you can learn this and it's great with
+
+ align:start position:0%
+you can learn this and it's great with
+ 
+
+ align:start position:0%
+you can learn this and it's great with
+with lone pairs is a little more
+
+ align:start position:0%
+with lone pairs is a little more
+ 
+
+ align:start position:0%
+with lone pairs is a little more
+complicated but also much more fun all
+
+ align:start position:0%
+complicated but also much more fun all
+ 
+
+ align:start position:0%
+complicated but also much more fun all
+right so let's talk now about what
+
+ align:start position:0%
+right so let's talk now about what
+ 
+
+ align:start position:0%
+right so let's talk now about what
+happens when we have lone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairs so electrons in
+
+ align:start position:0%
+pairs so electrons in
+ 
+
+ align:start position:0%
+pairs so electrons in
+bonds are hanging out in their bond and
+
+ align:start position:0%
+bonds are hanging out in their bond and
+ 
+
+ align:start position:0%
+bonds are hanging out in their bond and
+they're not really doing much but being
+
+ align:start position:0%
+they're not really doing much but being
+ 
+
+ align:start position:0%
+they're not really doing much but being
+in their bond so they have less spatial
+
+ align:start position:0%
+in their bond so they have less spatial
+ 
+
+ align:start position:0%
+in their bond so they have less spatial
+distribution than lone pairs meaning
+
+ align:start position:0%
+distribution than lone pairs meaning
+ 
+
+ align:start position:0%
+distribution than lone pairs meaning
+that electrons in bonds take up less
+
+ align:start position:0%
+that electrons in bonds take up less
+ 
+
+ align:start position:0%
+that electrons in bonds take up less
+space and electrons in Lone pairs they
+
+ align:start position:0%
+space and electrons in Lone pairs they
+ 
+
+ align:start position:0%
+space and electrons in Lone pairs they
+can be kind of anywhere they're not
+
+ align:start position:0%
+can be kind of anywhere they're not
+ 
+
+ align:start position:0%
+can be kind of anywhere they're not
+restricted to their bond so they take up
+
+ align:start position:0%
+restricted to their bond so they take up
+ 
+
+ align:start position:0%
+restricted to their bond so they take up
+more space and therefore cause more
+
+ align:start position:0%
+more space and therefore cause more
+ 
+
+ align:start position:0%
+more space and therefore cause more
+repulsion so the whole idea of when
+
+ align:start position:0%
+repulsion so the whole idea of when
+ 
+
+ align:start position:0%
+repulsion so the whole idea of when
+you're talking about Vesper with lone
+
+ align:start position:0%
+you're talking about Vesper with lone
+ 
+
+ align:start position:0%
+you're talking about Vesper with lone
+pairs is you're thinking about electron
+
+ align:start position:0%
+pairs is you're thinking about electron
+ 
+
+ align:start position:0%
+pairs is you're thinking about electron
+pair repulsion and if you have a lone
+
+ align:start position:0%
+pair repulsion and if you have a lone
+ 
+
+ align:start position:0%
+pair repulsion and if you have a lone
+pair that's going to give you more
+
+ align:start position:0%
+pair that's going to give you more
+ 
+
+ align:start position:0%
+pair that's going to give you more
+repulsion than bonded electrons because
+
+ align:start position:0%
+repulsion than bonded electrons because
+ 
+
+ align:start position:0%
+repulsion than bonded electrons because
+lone pair electrons can take up more
+
+ align:start position:0%
+lone pair electrons can take up more
+ 
+
+ align:start position:0%
+lone pair electrons can take up more
+space so it's a very simple idea but it
+
+ align:start position:0%
+space so it's a very simple idea but it
+ 
+
+ align:start position:0%
+space so it's a very simple idea but it
+actually works to explain a lot of stuff
+
+ align:start position:0%
+actually works to explain a lot of stuff
+ 
+
+ align:start position:0%
+actually works to explain a lot of stuff
+and again the geometry rearranges to
+
+ align:start position:0%
+and again the geometry rearranges to
+ 
+
+ align:start position:0%
+and again the geometry rearranges to
+minimize that
+
+ align:start position:0%
+minimize that
+ 
+
+ align:start position:0%
+minimize that
+repulsion so when we're talking about
+
+ align:start position:0%
+repulsion so when we're talking about
+ 
+
+ align:start position:0%
+repulsion so when we're talking about
+repulsive forces then we go from the mo
+
+ align:start position:0%
+repulsive forces then we go from the mo
+ 
+
+ align:start position:0%
+repulsive forces then we go from the mo
+most repulsion lone pair lone
+
+ align:start position:0%
+most repulsion lone pair lone
+ 
+
+ align:start position:0%
+most repulsion lone pair lone
+pair that's like two messy roommates
+
+ align:start position:0%
+pair that's like two messy roommates
+ 
+
+ align:start position:0%
+pair that's like two messy roommates
+living together that's very repulsive
+
+ align:start position:0%
+living together that's very repulsive
+ 
+
+ align:start position:0%
+living together that's very repulsive
+situation lone pair bonding pair and
+
+ align:start position:0%
+situation lone pair bonding pair and
+ 
+
+ align:start position:0%
+situation lone pair bonding pair and
+then bonding pair bonding pair is the
+
+ align:start position:0%
+then bonding pair bonding pair is the
+ 
+
+ align:start position:0%
+then bonding pair bonding pair is the
+least repulsive to neat roommates that
+
+ align:start position:0%
+least repulsive to neat roommates that
+ 
+
+ align:start position:0%
+least repulsive to neat roommates that
+usually works out quite well so if we
+
+ align:start position:0%
+usually works out quite well so if we
+ 
+
+ align:start position:0%
+usually works out quite well so if we
+keep this in mind we can now predict
+
+ align:start position:0%
+keep this in mind we can now predict
+ 
+
+ align:start position:0%
+keep this in mind we can now predict
+shapes of molecules based on this
+
+ align:start position:0%
+shapes of molecules based on this
+ 
+
+ align:start position:0%
+shapes of molecules based on this
+repulsion so we can rationalize shapes
+
+ align:start position:0%
+repulsion so we can rationalize shapes
+ 
+
+ align:start position:0%
+repulsion so we can rationalize shapes
+based on Vesper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory so now we can think about
+
+ align:start position:0%
+Theory so now we can think about
+ 
+
+ align:start position:0%
+Theory so now we can think about
+ax4e has a seesaw shape which of these
+
+ align:start position:0%
+ax4e has a seesaw shape which of these
+ 
+
+ align:start position:0%
+ax4e has a seesaw shape which of these
+two shapes is seesaw so we have one
+
+ align:start position:0%
+two shapes is seesaw so we have one
+ 
+
+ align:start position:0%
+two shapes is seesaw so we have one
+case I'll make this one where we have
+
+ align:start position:0%
+case I'll make this one where we have
+ 
+
+ align:start position:0%
+case I'll make this one where we have
+the lone pair in an axial position and
+
+ align:start position:0%
+the lone pair in an axial position and
+ 
+
+ align:start position:0%
+the lone pair in an axial position and
+we have another case where we have the
+
+ align:start position:0%
+we have another case where we have the
+ 
+
+ align:start position:0%
+we have another case where we have the
+lone pair in an equatorial
+
+ align:start position:0%
+lone pair in an equatorial
+ 
+
+ align:start position:0%
+lone pair in an equatorial
+position so when you have
+
+ align:start position:0%
+position so when you have
+ 
+
+ align:start position:0%
+position so when you have
+it in the axial position here
+
+ align:start position:0%
+it in the axial position here
+ 
+
+ align:start position:0%
+it in the axial position here
+here you have three bonding pairs of
+
+ align:start position:0%
+here you have three bonding pairs of
+ 
+
+ align:start position:0%
+here you have three bonding pairs of
+bonding electrons pretty close they're
+
+ align:start position:0%
+bonding electrons pretty close they're
+ 
+
+ align:start position:0%
+bonding electrons pretty close they're
+90° away from each other so there are
+
+ align:start position:0%
+90° away from each other so there are
+ 
+
+ align:start position:0%
+90° away from each other so there are
+three sets of bonding electrons that
+
+ align:start position:0%
+three sets of bonding electrons that
+ 
+
+ align:start position:0%
+three sets of bonding electrons that
+will be repelled pretty
+
+ align:start position:0%
+will be repelled pretty
+ 
+
+ align:start position:0%
+will be repelled pretty
+strongly now clicker question think
+
+ align:start position:0%
+strongly now clicker question think
+ 
+
+ align:start position:0%
+strongly now clicker question think
+about what's going to be true here how
+
+ align:start position:0%
+about what's going to be true here how
+ 
+
+ align:start position:0%
+about what's going to be true here how
+many things with an equatorial loone
+
+ align:start position:0%
+many things with an equatorial loone
+ 
+
+ align:start position:0%
+many things with an equatorial loone
+pair will be repelled strongly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very repulsive those lone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairs okay so that was the answer we're
+
+ align:start position:0%
+pairs okay so that was the answer we're
+ 
+
+ align:start position:0%
+pairs okay so that was the answer we're
+going for two because there are two sets
+
+ align:start position:0%
+going for two because there are two sets
+ 
+
+ align:start position:0%
+going for two because there are two sets
+of bonding electrons here that are 90
+
+ align:start position:0%
+of bonding electrons here that are 90
+ 
+
+ align:start position:0%
+of bonding electrons here that are 90
+Dees away there're two that are 120 but
+
+ align:start position:0%
+Dees away there're two that are 120 but
+ 
+
+ align:start position:0%
+Dees away there're two that are 120 but
+120 is bigger than 90 so they're two
+
+ align:start position:0%
+120 is bigger than 90 so they're two
+ 
+
+ align:start position:0%
+120 is bigger than 90 so they're two
+that are close whereas with this
+
+ align:start position:0%
+that are close whereas with this
+ 
+
+ align:start position:0%
+that are close whereas with this
+geometry they're three um sets of
+
+ align:start position:0%
+geometry they're three um sets of
+ 
+
+ align:start position:0%
+geometry they're three um sets of
+bonding electrons that are 90 degrees
+
+ align:start position:0%
+bonding electrons that are 90 degrees
+ 
+
+ align:start position:0%
+bonding electrons that are 90 degrees
+away so it turns out that the equatorial
+
+ align:start position:0%
+away so it turns out that the equatorial
+ 
+
+ align:start position:0%
+away so it turns out that the equatorial
+lone pair is more favorable it has a
+
+ align:start position:0%
+lone pair is more favorable it has a
+ 
+
+ align:start position:0%
+lone pair is more favorable it has a
+little bit more room in the equatorial
+
+ align:start position:0%
+little bit more room in the equatorial
+ 
+
+ align:start position:0%
+little bit more room in the equatorial
+area to spread out and so this is the
+
+ align:start position:0%
+area to spread out and so this is the
+ 
+
+ align:start position:0%
+area to spread out and so this is the
+shape that we find we never see this
+
+ align:start position:0%
+shape that we find we never see this
+ 
+
+ align:start position:0%
+shape that we find we never see this
+shape does not exist we'll just take
+
+ align:start position:0%
+shape does not exist we'll just take
+ 
+
+ align:start position:0%
+shape does not exist we'll just take
+that away it doesn't exist and this is
+
+ align:start position:0%
+that away it doesn't exist and this is
+ 
+
+ align:start position:0%
+that away it doesn't exist and this is
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+seesaw and let me demonstrate to you why
+
+ align:start position:0%
+seesaw and let me demonstrate to you why
+ 
+
+ align:start position:0%
+seesaw and let me demonstrate to you why
+that is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case maybe I'll do it this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so how many of you had seesaws in a
+
+ align:start position:0%
+way so how many of you had seesaws in a
+ 
+
+ align:start position:0%
+way so how many of you had seesaws in a
+playground quite a number seesaws are
+
+ align:start position:0%
+playground quite a number seesaws are
+ 
+
+ align:start position:0%
+playground quite a number seesaws are
+not considered that safe you know the
+
+ align:start position:0%
+not considered that safe you know the
+ 
+
+ align:start position:0%
+not considered that safe you know the
+heavy kid sits on it keep keeps you up
+
+ align:start position:0%
+heavy kid sits on it keep keeps you up
+ 
+
+ align:start position:0%
+heavy kid sits on it keep keeps you up
+in the air for days or whatever until
+
+ align:start position:0%
+in the air for days or whatever until
+ 
+
+ align:start position:0%
+in the air for days or whatever until
+your mom comes and gets you from the
+
+ align:start position:0%
+your mom comes and gets you from the
+ 
+
+ align:start position:0%
+your mom comes and gets you from the
+playground or gets off suddenly and the
+
+ align:start position:0%
+playground or gets off suddenly and the
+ 
+
+ align:start position:0%
+playground or gets off suddenly and the
+Seesaw flips and you go flying in the
+
+ align:start position:0%
+Seesaw flips and you go flying in the
+ 
+
+ align:start position:0%
+Seesaw flips and you go flying in the
+air um but studies show actually that
+
+ align:start position:0%
+air um but studies show actually that
+ 
+
+ align:start position:0%
+air um but studies show actually that
+dangerous playground equipment builds uh
+
+ align:start position:0%
+dangerous playground equipment builds uh
+ 
+
+ align:start position:0%
+dangerous playground equipment builds uh
+neural networks and is good for uh
+
+ align:start position:0%
+neural networks and is good for uh
+ 
+
+ align:start position:0%
+neural networks and is good for uh
+cognitive development so um I think we
+
+ align:start position:0%
+cognitive development so um I think we
+ 
+
+ align:start position:0%
+cognitive development so um I think we
+could do a survey here and see if
+
+ align:start position:0%
+could do a survey here and see if
+ 
+
+ align:start position:0%
+could do a survey here and see if
+there's a correlation between how many
+
+ align:start position:0%
+there's a correlation between how many
+ 
+
+ align:start position:0%
+there's a correlation between how many
+of you played with seesaws when you were
+
+ align:start position:0%
+of you played with seesaws when you were
+ 
+
+ align:start position:0%
+of you played with seesaws when you were
+a kid and whether you ended up as an MIT
+
+ align:start position:0%
+a kid and whether you ended up as an MIT
+ 
+
+ align:start position:0%
+a kid and whether you ended up as an MIT
+student or not that could be that could
+
+ align:start position:0%
+student or not that could be that could
+ 
+
+ align:start position:0%
+student or not that could be that could
+be interesting but now none of you will
+
+ align:start position:0%
+be interesting but now none of you will
+ 
+
+ align:start position:0%
+be interesting but now none of you will
+ever forget that this shape is seesaw
+
+ align:start position:0%
+ever forget that this shape is seesaw
+ 
+
+ align:start position:0%
+ever forget that this shape is seesaw
+right you'll remember this forever
+
+ align:start position:0%
+right you'll remember this forever
+ 
+
+ align:start position:0%
+right you'll remember this forever
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+so this idea also is
+
+ align:start position:0%
+so this idea also is
+ 
+
+ align:start position:0%
+so this idea also is
+responsible um for a t-shaped
+
+ align:start position:0%
+responsible um for a t-shaped
+ 
+
+ align:start position:0%
+responsible um for a t-shaped
+molecule so we'll add another one and I
+
+ align:start position:0%
+molecule so we'll add another one and I
+ 
+
+ align:start position:0%
+molecule so we'll add another one and I
+think this is a little harder to
+
+ align:start position:0%
+think this is a little harder to
+ 
+
+ align:start position:0%
+think this is a little harder to
+rationalize why it wouldn't go in a
+
+ align:start position:0%
+rationalize why it wouldn't go in a
+ 
+
+ align:start position:0%
+rationalize why it wouldn't go in a
+different place but it does this is how
+
+ align:start position:0%
+different place but it does this is how
+ 
+
+ align:start position:0%
+different place but it does this is how
+it goes both the lone pairs are in
+
+ align:start position:0%
+it goes both the lone pairs are in
+ 
+
+ align:start position:0%
+it goes both the lone pairs are in
+equatorial positions and we get
+
+ align:start position:0%
+equatorial positions and we get
+ 
+
+ align:start position:0%
+equatorial positions and we get
+something that looks like a t so if you
+
+ align:start position:0%
+something that looks like a t so if you
+ 
+
+ align:start position:0%
+something that looks like a t so if you
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+X3 or ax3 E2 sn5 number it's a t-shaped
+
+ align:start position:0%
+X3 or ax3 E2 sn5 number it's a t-shaped
+ 
+
+ align:start position:0%
+X3 or ax3 E2 sn5 number it's a t-shaped
+molecule we can also think about our
+
+ align:start position:0%
+molecule we can also think about our
+ 
+
+ align:start position:0%
+molecule we can also think about our
+core octahedral
+
+ align:start position:0%
+core octahedral
+ 
+
+ align:start position:0%
+core octahedral
+geometry and if you have two lone pairs
+
+ align:start position:0%
+geometry and if you have two lone pairs
+ 
+
+ align:start position:0%
+geometry and if you have two lone pairs
+so here's our octahedral with six
+
+ align:start position:0%
+so here's our octahedral with six
+ 
+
+ align:start position:0%
+so here's our octahedral with six
+bonding atoms and if you have two lone
+
+ align:start position:0%
+bonding atoms and if you have two lone
+ 
+
+ align:start position:0%
+bonding atoms and if you have two lone
+Pairs and four bonding atoms if you have
+
+ align:start position:0%
+Pairs and four bonding atoms if you have
+ 
+
+ align:start position:0%
+Pairs and four bonding atoms if you have
+ax4 E2 it has this shape the lone pairs
+
+ align:start position:0%
+ax4 E2 it has this shape the lone pairs
+ 
+
+ align:start position:0%
+ax4 E2 it has this shape the lone pairs
+go on opposite sides and now they have
+
+ align:start position:0%
+go on opposite sides and now they have
+ 
+
+ align:start position:0%
+go on opposite sides and now they have
+they're repelling the bonding electrons
+
+ align:start position:0%
+they're repelling the bonding electrons
+ 
+
+ align:start position:0%
+they're repelling the bonding electrons
+here but they're far away from each
+
+ align:start position:0%
+here but they're far away from each
+ 
+
+ align:start position:0%
+here but they're far away from each
+other which is favorable and this is
+
+ align:start position:0%
+other which is favorable and this is
+ 
+
+ align:start position:0%
+other which is favorable and this is
+called Square planer so it's square and
+
+ align:start position:0%
+called Square planer so it's square and
+ 
+
+ align:start position:0%
+called Square planer so it's square and
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+planer Square planer okay the two lone
+
+ align:start position:0%
+planer Square planer okay the two lone
+ 
+
+ align:start position:0%
+planer Square planer okay the two lone
+pairs are far apart on the opposite
+
+ align:start position:0%
+pairs are far apart on the opposite
+ 
+
+ align:start position:0%
+pairs are far apart on the opposite
+sides of the
+
+ align:start position:0%
+sides of the
+ 
+
+ align:start position:0%
+sides of the
+bond so in addition to predicting these
+
+ align:start position:0%
+bond so in addition to predicting these
+ 
+
+ align:start position:0%
+bond so in addition to predicting these
+shapes which work pretty well we can
+
+ align:start position:0%
+shapes which work pretty well we can
+ 
+
+ align:start position:0%
+shapes which work pretty well we can
+also think about the geometries and when
+
+ align:start position:0%
+also think about the geometries and when
+ 
+
+ align:start position:0%
+also think about the geometries and when
+you get lone pairs you find deviations
+
+ align:start position:0%
+you get lone pairs you find deviations
+ 
+
+ align:start position:0%
+you get lone pairs you find deviations
+from your standard geometries so let's
+
+ align:start position:0%
+from your standard geometries so let's
+ 
+
+ align:start position:0%
+from your standard geometries so let's
+look at some examples so with molecules
+
+ align:start position:0%
+look at some examples so with molecules
+ 
+
+ align:start position:0%
+look at some examples so with molecules
+with lone pairs such as
+
+ align:start position:0%
+with lone pairs such as
+ 
+
+ align:start position:0%
+with lone pairs such as
+NH3 the angles tend to be
+
+ align:start position:0%
+NH3 the angles tend to be
+ 
+
+ align:start position:0%
+NH3 the angles tend to be
+smaller so we saw methane before it was
+
+ align:start position:0%
+smaller so we saw methane before it was
+ 
+
+ align:start position:0%
+smaller so we saw methane before it was
+109.5 you yelled that nicely out for
+
+ align:start position:0%
+109.5 you yelled that nicely out for
+ 
+
+ align:start position:0%
+109.5 you yelled that nicely out for
+me these are both sn4
+
+ align:start position:0%
+me these are both sn4
+ 
+
+ align:start position:0%
+me these are both sn4
+this is ax4 this is ax uh 3 e but it's
+
+ align:start position:0%
+this is ax4 this is ax uh 3 e but it's
+ 
+
+ align:start position:0%
+this is ax4 this is ax uh 3 e but it's
+still an sn4 system so it looks like
+
+ align:start position:0%
+still an sn4 system so it looks like
+ 
+
+ align:start position:0%
+still an sn4 system so it looks like
+this we have here we have methane here
+
+ align:start position:0%
+this we have here we have methane here
+ 
+
+ align:start position:0%
+this we have here we have methane here
+we have NH3 and now we want to think
+
+ align:start position:0%
+we have NH3 and now we want to think
+ 
+
+ align:start position:0%
+we have NH3 and now we want to think
+about which would be more repulsive the
+
+ align:start position:0%
+about which would be more repulsive the
+ 
+
+ align:start position:0%
+about which would be more repulsive the
+bonded electrons or the lone pair
+
+ align:start position:0%
+bonded electrons or the lone pair
+ 
+
+ align:start position:0%
+bonded electrons or the lone pair
+electrons in terms of the geometries
+
+ align:start position:0%
+electrons in terms of the geometries
+ 
+
+ align:start position:0%
+electrons in terms of the geometries
+around so if we have hydrogen carbon
+
+ align:start position:0%
+around so if we have hydrogen carbon
+ 
+
+ align:start position:0%
+around so if we have hydrogen carbon
+hydrogen angle of 109.5 here then here
+
+ align:start position:0%
+hydrogen angle of 109.5 here then here
+ 
+
+ align:start position:0%
+hydrogen angle of 109.5 here then here
+with nitrogen we're thinking about
+
+ align:start position:0%
+with nitrogen we're thinking about
+ 
+
+ align:start position:0%
+with nitrogen we're thinking about
+hydrogen nitrogen hydrogen and this lone
+
+ align:start position:0%
+hydrogen nitrogen hydrogen and this lone
+ 
+
+ align:start position:0%
+hydrogen nitrogen hydrogen and this lone
+pair is pushing on those um bonded
+
+ align:start position:0%
+pair is pushing on those um bonded
+ 
+
+ align:start position:0%
+pair is pushing on those um bonded
+electrons and it's taken up a lot of
+
+ align:start position:0%
+electrons and it's taken up a lot of
+ 
+
+ align:start position:0%
+electrons and it's taken up a lot of
+space this is the messy roommate the
+
+ align:start position:0%
+space this is the messy roommate the
+ 
+
+ align:start position:0%
+space this is the messy roommate the
+messy roommate it has a lot of stuff
+
+ align:start position:0%
+messy roommate it has a lot of stuff
+ 
+
+ align:start position:0%
+messy roommate it has a lot of stuff
+that's spreading out all over your room
+
+ align:start position:0%
+that's spreading out all over your room
+ 
+
+ align:start position:0%
+that's spreading out all over your room
+and so instead of having 109.5 amount of
+
+ align:start position:0%
+and so instead of having 109.5 amount of
+ 
+
+ align:start position:0%
+and so instead of having 109.5 amount of
+space you now have
+
+ align:start position:0%
+space you now have
+ 
+
+ align:start position:0%
+space you now have
+106.7 amount of space in your room
+
+ align:start position:0%
+106.7 amount of space in your room
+ 
+
+ align:start position:0%
+106.7 amount of space in your room
+because it's just the messy roommates
+
+ align:start position:0%
+because it's just the messy roommates
+ 
+
+ align:start position:0%
+because it's just the messy roommates
+just spreading out all over price
+
+ align:start position:0%
+just spreading out all over price
+ 
+
+ align:start position:0%
+just spreading out all over price
+pushing down on those bonds and the
+
+ align:start position:0%
+pushing down on those bonds and the
+ 
+
+ align:start position:0%
+pushing down on those bonds and the
+bonds
+
+ align:start position:0%
+bonds
+ 
+
+ align:start position:0%
+bonds
+contract all right now let's go back to
+
+ align:start position:0%
+contract all right now let's go back to
+ 
+
+ align:start position:0%
+contract all right now let's go back to
+Trends in the periodic table for a
+
+ align:start position:0%
+Trends in the periodic table for a
+ 
+
+ align:start position:0%
+Trends in the periodic table for a
+minute we learned that atomic size
+
+ align:start position:0%
+minute we learned that atomic size
+ 
+
+ align:start position:0%
+minute we learned that atomic size
+increases as we go down the periodic
+
+ align:start position:0%
+increases as we go down the periodic
+ 
+
+ align:start position:0%
+increases as we go down the periodic
+table because what
+
+ align:start position:0%
+table because what
+ 
+
+ align:start position:0%
+table because what
+increases n principal quantum number n
+
+ align:start position:0%
+increases n principal quantum number n
+ 
+
+ align:start position:0%
+increases n principal quantum number n
+increases so atomic size increases as we
+
+ align:start position:0%
+increases so atomic size increases as we
+ 
+
+ align:start position:0%
+increases so atomic size increases as we
+go down think of this as a messy
+
+ align:start position:0%
+go down think of this as a messy
+ 
+
+ align:start position:0%
+go down think of this as a messy
+roommate having more
+
+ align:start position:0%
+roommate having more
+ 
+
+ align:start position:0%
+roommate having more
+stuff so the lone pairs now occupy a
+
+ align:start position:0%
+stuff so the lone pairs now occupy a
+ 
+
+ align:start position:0%
+stuff so the lone pairs now occupy a
+larger volume still messy but now messy
+
+ align:start position:0%
+larger volume still messy but now messy
+ 
+
+ align:start position:0%
+larger volume still messy but now messy
+with a lot more stuff and this stuff
+
+ align:start position:0%
+with a lot more stuff and this stuff
+ 
+
+ align:start position:0%
+with a lot more stuff and this stuff
+impedes in your
+
+ align:start position:0%
+impedes in your
+ 
+
+ align:start position:0%
+impedes in your
+space so the angles tend to be even
+
+ align:start position:0%
+space so the angles tend to be even
+ 
+
+ align:start position:0%
+space so the angles tend to be even
+smaller between the bonded atoms so we
+
+ align:start position:0%
+smaller between the bonded atoms so we
+ 
+
+ align:start position:0%
+smaller between the bonded atoms so we
+had NH3 before at 106
+
+ align:start position:0%
+had NH3 before at 106
+ 
+
+ align:start position:0%
+had NH3 before at 106
+7 but nitrogen is up here phosphorus is
+
+ align:start position:0%
+7 but nitrogen is up here phosphorus is
+ 
+
+ align:start position:0%
+7 but nitrogen is up here phosphorus is
+below it so it has a bigger atomic size
+
+ align:start position:0%
+below it so it has a bigger atomic size
+ 
+
+ align:start position:0%
+below it so it has a bigger atomic size
+and it has lone pairs that occupy larger
+
+ align:start position:0%
+and it has lone pairs that occupy larger
+ 
+
+ align:start position:0%
+and it has lone pairs that occupy larger
+volumes so this is what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens some of you may have experienced
+
+ align:start position:0%
+happens some of you may have experienced
+ 
+
+ align:start position:0%
+happens some of you may have experienced
+that that is a messy roommate with a lot
+
+ align:start position:0%
+that that is a messy roommate with a lot
+ 
+
+ align:start position:0%
+that that is a messy roommate with a lot
+of stuff now if you have a roommate
+
+ align:start position:0%
+of stuff now if you have a roommate
+ 
+
+ align:start position:0%
+of stuff now if you have a roommate
+that's very neat they're putting their
+
+ align:start position:0%
+that's very neat they're putting their
+ 
+
+ align:start position:0%
+that's very neat they're putting their
+clothes in drawers when the clothes are
+
+ align:start position:0%
+clothes in drawers when the clothes are
+ 
+
+ align:start position:0%
+clothes in drawers when the clothes are
+in drawers just like electon and bonds
+
+ align:start position:0%
+in drawers just like electon and bonds
+ 
+
+ align:start position:0%
+in drawers just like electon and bonds
+they don't really go any place but when
+
+ align:start position:0%
+they don't really go any place but when
+ 
+
+ align:start position:0%
+they don't really go any place but when
+the messy roommate does not put their
+
+ align:start position:0%
+the messy roommate does not put their
+ 
+
+ align:start position:0%
+the messy roommate does not put their
+clothes when their lone pair clothes
+
+ align:start position:0%
+clothes when their lone pair clothes
+ 
+
+ align:start position:0%
+clothes when their lone pair clothes
+then they go and this is what
+
+ align:start position:0%
+then they go and this is what
+ 
+
+ align:start position:0%
+then they go and this is what
+happens okay so we can predict Now by
+
+ align:start position:0%
+happens okay so we can predict Now by
+ 
+
+ align:start position:0%
+happens okay so we can predict Now by
+looking at periodic trends and thinking
+
+ align:start position:0%
+looking at periodic trends and thinking
+ 
+
+ align:start position:0%
+looking at periodic trends and thinking
+about how much room those lone pair
+
+ align:start position:0%
+about how much room those lone pair
+ 
+
+ align:start position:0%
+about how much room those lone pair
+electrons are taking up we can think
+
+ align:start position:0%
+electrons are taking up we can think
+ 
+
+ align:start position:0%
+electrons are taking up we can think
+about and predict the angle between the
+
+ align:start position:0%
+about and predict the angle between the
+ 
+
+ align:start position:0%
+about and predict the angle between the
+bonded
+
+ align:start position:0%
+bonded
+ 
+
+ align:start position:0%
+bonded
+atoms all right so this is pretty cool
+
+ align:start position:0%
+atoms all right so this is pretty cool
+ 
+
+ align:start position:0%
+atoms all right so this is pretty cool
+but can it save the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world what do you think can veser save
+
+ align:start position:0%
+world what do you think can veser save
+ 
+
+ align:start position:0%
+world what do you think can veser save
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+world do something important of course
+
+ align:start position:0%
+world do something important of course
+ 
+
+ align:start position:0%
+world do something important of course
+it can it's part of
+
+ align:start position:0%
+it can it's part of
+ 
+
+ align:start position:0%
+it can it's part of
+chemistr so let's think about a pressing
+
+ align:start position:0%
+chemistr so let's think about a pressing
+ 
+
+ align:start position:0%
+chemistr so let's think about a pressing
+problem in the world right now and how
+
+ align:start position:0%
+problem in the world right now and how
+ 
+
+ align:start position:0%
+problem in the world right now and how
+Vesper can address it and if you listen
+
+ align:start position:0%
+Vesper can address it and if you listen
+ 
+
+ align:start position:0%
+Vesper can address it and if you listen
+to NPR or open a newspaper these days
+
+ align:start position:0%
+to NPR or open a newspaper these days
+ 
+
+ align:start position:0%
+to NPR or open a newspaper these days
+you're hearing about a lot of car bomb
+
+ align:start position:0%
+you're hearing about a lot of car bomb
+ 
+
+ align:start position:0%
+you're hearing about a lot of car bomb
+explosions things are not good in the
+
+ align:start position:0%
+explosions things are not good in the
+ 
+
+ align:start position:0%
+explosions things are not good in the
+Middle East um we're hearing about all
+
+ align:start position:0%
+Middle East um we're hearing about all
+ 
+
+ align:start position:0%
+Middle East um we're hearing about all
+sorts I heard on the news about bombs
+
+ align:start position:0%
+sorts I heard on the news about bombs
+ 
+
+ align:start position:0%
+sorts I heard on the news about bombs
+going off at a school and then when
+
+ align:start position:0%
+going off at a school and then when
+ 
+
+ align:start position:0%
+going off at a school and then when
+parents rushed toward the school more
+
+ align:start position:0%
+parents rushed toward the school more
+ 
+
+ align:start position:0%
+parents rushed toward the school more
+bombs went off I mean just really
+
+ align:start position:0%
+bombs went off I mean just really
+ 
+
+ align:start position:0%
+bombs went off I mean just really
+horrible stories um and even when the
+
+ align:start position:0%
+horrible stories um and even when the
+ 
+
+ align:start position:0%
+horrible stories um and even when the
+conflict is over a lot of times those
+
+ align:start position:0%
+conflict is over a lot of times those
+ 
+
+ align:start position:0%
+conflict is over a lot of times those
+improvised explosives are still there
+
+ align:start position:0%
+improvised explosives are still there
+ 
+
+ align:start position:0%
+improvised explosives are still there
+they still exist in the countries and
+
+ align:start position:0%
+they still exist in the countries and
+ 
+
+ align:start position:0%
+they still exist in the countries and
+it's estimated by the UN by the United
+
+ align:start position:0%
+it's estimated by the UN by the United
+ 
+
+ align:start position:0%
+it's estimated by the UN by the United
+Nations that land kill 15,000 to 20,000
+
+ align:start position:0%
+Nations that land kill 15,000 to 20,000
+ 
+
+ align:start position:0%
+Nations that land kill 15,000 to 20,000
+people mostly children uh women elderly
+
+ align:start position:0%
+people mostly children uh women elderly
+ 
+
+ align:start position:0%
+people mostly children uh women elderly
+who are out in the farm Fields trying to
+
+ align:start position:0%
+who are out in the farm Fields trying to
+ 
+
+ align:start position:0%
+who are out in the farm Fields trying to
+uh grow food for their family and they
+
+ align:start position:0%
+uh grow food for their family and they
+ 
+
+ align:start position:0%
+uh grow food for their family and they
+step on something and blow up so how do
+
+ align:start position:0%
+step on something and blow up so how do
+ 
+
+ align:start position:0%
+step on something and blow up so how do
+you find these explosive devices how do
+
+ align:start position:0%
+you find these explosive devices how do
+ 
+
+ align:start position:0%
+you find these explosive devices how do
+you find explosive devices that are
+
+ align:start position:0%
+you find explosive devices that are
+ 
+
+ align:start position:0%
+you find explosive devices that are
+actively being used now in dangerous
+
+ align:start position:0%
+actively being used now in dangerous
+ 
+
+ align:start position:0%
+actively being used now in dangerous
+parts of the world and how do you find
+
+ align:start position:0%
+parts of the world and how do you find
+ 
+
+ align:start position:0%
+parts of the world and how do you find
+the explosive devices Left Behind when
+
+ align:start position:0%
+the explosive devices Left Behind when
+ 
+
+ align:start position:0%
+the explosive devices Left Behind when
+the war is over so if you are Stephanie
+
+ align:start position:0%
+the war is over so if you are Stephanie
+ 
+
+ align:start position:0%
+the war is over so if you are Stephanie
+um you use Vesper that's what you do to
+
+ align:start position:0%
+um you use Vesper that's what you do to
+ 
+
+ align:start position:0%
+um you use Vesper that's what you do to
+find those explosives so in her own
+
+ align:start position:0%
+find those explosives so in her own
+ 
+
+ align:start position:0%
+find those explosives so in her own
+words now I'm G to tell you or she's
+
+ align:start position:0%
+words now I'm G to tell you or she's
+ 
+
+ align:start position:0%
+words now I'm G to tell you or she's
+going to tell you why Vesper which she
+
+ align:start position:0%
+going to tell you why Vesper which she
+ 
+
+ align:start position:0%
+going to tell you why Vesper which she
+calls
+
+ align:start position:0%
+calls
+ 
+
+ align:start position:0%
+calls
+vspr because she can say that better
+
+ align:start position:0%
+vspr because she can say that better
+ 
+
+ align:start position:0%
+vspr because she can say that better
+than I can um to uh find explosives my
+
+ align:start position:0%
+than I can um to uh find explosives my
+ 
+
+ align:start position:0%
+than I can um to uh find explosives my
+name is Stephanie s and I am a graduate
+
+ align:start position:0%
+name is Stephanie s and I am a graduate
+ 
+
+ align:start position:0%
+name is Stephanie s and I am a graduate
+student in Tim swaggers research group
+
+ align:start position:0%
+student in Tim swaggers research group
+ 
+
+ align:start position:0%
+student in Tim swaggers research group
+at MIT the research that we're perhaps
+
+ align:start position:0%
+at MIT the research that we're perhaps
+ 
+
+ align:start position:0%
+at MIT the research that we're perhaps
+the most well known for is for sensing
+
+ align:start position:0%
+the most well known for is for sensing
+ 
+
+ align:start position:0%
+the most well known for is for sensing
+explosives such as
+
+ align:start position:0%
+explosives such as
+ 
+
+ align:start position:0%
+explosives such as
+TNT new bigger better explosives have
+
+ align:start position:0%
+TNT new bigger better explosives have
+ 
+
+ align:start position:0%
+TNT new bigger better explosives have
+been developed and two of these are RDX
+
+ align:start position:0%
+been developed and two of these are RDX
+ 
+
+ align:start position:0%
+been developed and two of these are RDX
+and petn and these kind of have more
+
+ align:start position:0%
+and petn and these kind of have more
+ 
+
+ align:start position:0%
+and petn and these kind of have more
+bang for your buck if you will
+
+ align:start position:0%
+bang for your buck if you will
+ 
+
+ align:start position:0%
+bang for your buck if you will
+Unfortunately they have an even lower
+
+ align:start position:0%
+Unfortunately they have an even lower
+ 
+
+ align:start position:0%
+Unfortunately they have an even lower
+vapor pressure than TNT which means
+
+ align:start position:0%
+vapor pressure than TNT which means
+ 
+
+ align:start position:0%
+vapor pressure than TNT which means
+there's even less molecules of the
+
+ align:start position:0%
+there's even less molecules of the
+ 
+
+ align:start position:0%
+there's even less molecules of the
+explosive in the air and it makes them
+
+ align:start position:0%
+explosive in the air and it makes them
+ 
+
+ align:start position:0%
+explosive in the air and it makes them
+even harder to detect the dogs that they
+
+ align:start position:0%
+even harder to detect the dogs that they
+ 
+
+ align:start position:0%
+even harder to detect the dogs that they
+would send out are actually sensing
+
+ align:start position:0%
+would send out are actually sensing
+ 
+
+ align:start position:0%
+would send out are actually sensing
+cyclohexanone and acetone which are
+
+ align:start position:0%
+cyclohexanone and acetone which are
+ 
+
+ align:start position:0%
+cyclohexanone and acetone which are
+molecules that are used in the
+
+ align:start position:0%
+molecules that are used in the
+ 
+
+ align:start position:0%
+molecules that are used in the
+purification of these two
+
+ align:start position:0%
+purification of these two
+ 
+
+ align:start position:0%
+purification of these two
+explosives both cyclohexanone and
+
+ align:start position:0%
+explosives both cyclohexanone and
+ 
+
+ align:start position:0%
+explosives both cyclohexanone and
+acetone have a carbonal in them and this
+
+ align:start position:0%
+acetone have a carbonal in them and this
+ 
+
+ align:start position:0%
+acetone have a carbonal in them and this
+carbonal then can interact with a group
+
+ align:start position:0%
+carbonal then can interact with a group
+ 
+
+ align:start position:0%
+carbonal then can interact with a group
+known as the
+
+ align:start position:0%
+known as the
+ 
+
+ align:start position:0%
+known as the
+Ura we have two nitrogens connected to a
+
+ align:start position:0%
+Ura we have two nitrogens connected to a
+ 
+
+ align:start position:0%
+Ura we have two nitrogens connected to a
+carbon that has a double bond to an
+
+ align:start position:0%
+carbon that has a double bond to an
+ 
+
+ align:start position:0%
+carbon that has a double bond to an
+oxygen between them and these nitrogens
+
+ align:start position:0%
+oxygen between them and these nitrogens
+ 
+
+ align:start position:0%
+oxygen between them and these nitrogens
+have hydrogens on it that that can
+
+ align:start position:0%
+have hydrogens on it that that can
+ 
+
+ align:start position:0%
+have hydrogens on it that that can
+hydrogen bond with the acetone or the
+
+ align:start position:0%
+hydrogen bond with the acetone or the
+ 
+
+ align:start position:0%
+hydrogen bond with the acetone or the
+cyclohexanone that we're looking for
+
+ align:start position:0%
+cyclohexanone that we're looking for
+ 
+
+ align:start position:0%
+cyclohexanone that we're looking for
+what happens is that the lone pair from
+
+ align:start position:0%
+what happens is that the lone pair from
+ 
+
+ align:start position:0%
+what happens is that the lone pair from
+the carbonal reaches out and grabs those
+
+ align:start position:0%
+the carbonal reaches out and grabs those
+ 
+
+ align:start position:0%
+the carbonal reaches out and grabs those
+hydrogens and pulls them away from the
+
+ align:start position:0%
+hydrogens and pulls them away from the
+ 
+
+ align:start position:0%
+hydrogens and pulls them away from the
+nitrogens and this makes the nitrogen
+
+ align:start position:0%
+nitrogens and this makes the nitrogen
+ 
+
+ align:start position:0%
+nitrogens and this makes the nitrogen
+hydrogen bond more lone pair likee as it
+
+ align:start position:0%
+hydrogen bond more lone pair likee as it
+ 
+
+ align:start position:0%
+hydrogen bond more lone pair likee as it
+becomes more lone pair likee we see more
+
+ align:start position:0%
+becomes more lone pair likee we see more
+ 
+
+ align:start position:0%
+becomes more lone pair likee we see more
+repulsion between the lone pair like
+
+ align:start position:0%
+repulsion between the lone pair like
+ 
+
+ align:start position:0%
+repulsion between the lone pair like
+Bond of electrons and the neighboring
+
+ align:start position:0%
+Bond of electrons and the neighboring
+ 
+
+ align:start position:0%
+Bond of electrons and the neighboring
+bonds and by the espr Theory we know
+
+ align:start position:0%
+bonds and by the espr Theory we know
+ 
+
+ align:start position:0%
+bonds and by the espr Theory we know
+that this is going to cause the bond
+
+ align:start position:0%
+that this is going to cause the bond
+ 
+
+ align:start position:0%
+that this is going to cause the bond
+angle to become larger between the
+
+ align:start position:0%
+angle to become larger between the
+ 
+
+ align:start position:0%
+angle to become larger between the
+nitrogen hydrogen bond and the
+
+ align:start position:0%
+nitrogen hydrogen bond and the
+ 
+
+ align:start position:0%
+nitrogen hydrogen bond and the
+accompanying bonds and smaller between
+
+ align:start position:0%
+accompanying bonds and smaller between
+ 
+
+ align:start position:0%
+accompanying bonds and smaller between
+the other bonds around the nitrogen and
+
+ align:start position:0%
+the other bonds around the nitrogen and
+ 
+
+ align:start position:0%
+the other bonds around the nitrogen and
+this causes large scale changes in the
+
+ align:start position:0%
+this causes large scale changes in the
+ 
+
+ align:start position:0%
+this causes large scale changes in the
+polymer so we can see differences in the
+
+ align:start position:0%
+polymer so we can see differences in the
+ 
+
+ align:start position:0%
+polymer so we can see differences in the
+way in the large scale the polymer
+
+ align:start position:0%
+way in the large scale the polymer
+ 
+
+ align:start position:0%
+way in the large scale the polymer
+interacts with light as fluorescence so
+
+ align:start position:0%
+interacts with light as fluorescence so
+ 
+
+ align:start position:0%
+interacts with light as fluorescence so
+it will start to Glow or a refractive
+
+ align:start position:0%
+it will start to Glow or a refractive
+ 
+
+ align:start position:0%
+it will start to Glow or a refractive
+index change which is also a different
+
+ align:start position:0%
+index change which is also a different
+ 
+
+ align:start position:0%
+index change which is also a different
+way that the polymer interacts with
+
+ align:start position:0%
+way that the polymer interacts with
+ 
+
+ align:start position:0%
+way that the polymer interacts with
+light we have instruments that can very
+
+ align:start position:0%
+light we have instruments that can very
+ 
+
+ align:start position:0%
+light we have instruments that can very
+easily measure both fluorescence and
+
+ align:start position:0%
+easily measure both fluorescence and
+ 
+
+ align:start position:0%
+easily measure both fluorescence and
+refractive index and with these very
+
+ align:start position:0%
+refractive index and with these very
+ 
+
+ align:start position:0%
+refractive index and with these very
+easy signals we now know that our
+
+ align:start position:0%
+easy signals we now know that our
+ 
+
+ align:start position:0%
+easy signals we now know that our
+acetone or cyclohexanone and therefore
+
+ align:start position:0%
+acetone or cyclohexanone and therefore
+ 
+
+ align:start position:0%
+acetone or cyclohexanone and therefore
+the explosive is there for soldiers this
+
+ align:start position:0%
+the explosive is there for soldiers this
+ 
+
+ align:start position:0%
+the explosive is there for soldiers this
+is a really big deal in Iraq and
+
+ align:start position:0%
+is a really big deal in Iraq and
+ 
+
+ align:start position:0%
+is a really big deal in Iraq and
+Afghanistan there are Mine Fields and
+
+ align:start position:0%
+Afghanistan there are Mine Fields and
+ 
+
+ align:start position:0%
+Afghanistan there are Mine Fields and
+kind of improvised explosive devices
+
+ align:start position:0%
+kind of improvised explosive devices
+ 
+
+ align:start position:0%
+kind of improvised explosive devices
+almost everywhere and the soldiers over
+
+ align:start position:0%
+almost everywhere and the soldiers over
+ 
+
+ align:start position:0%
+almost everywhere and the soldiers over
+there really have to watch where they
+
+ align:start position:0%
+there really have to watch where they
+ 
+
+ align:start position:0%
+there really have to watch where they
+step so if we can come up with a
+
+ align:start position:0%
+step so if we can come up with a
+ 
+
+ align:start position:0%
+step so if we can come up with a
+handheld device and we have in the past
+
+ align:start position:0%
+handheld device and we have in the past
+ 
+
+ align:start position:0%
+handheld device and we have in the past
+come up with some and I'm hoping that my
+
+ align:start position:0%
+come up with some and I'm hoping that my
+ 
+
+ align:start position:0%
+come up with some and I'm hoping that my
+technology might in the future also go
+
+ align:start position:0%
+technology might in the future also go
+ 
+
+ align:start position:0%
+technology might in the future also go
+towards these types of devices that will
+
+ align:start position:0%
+towards these types of devices that will
+ 
+
+ align:start position:0%
+towards these types of devices that will
+be kind of attached to a robot and sent
+
+ align:start position:0%
+be kind of attached to a robot and sent
+ 
+
+ align:start position:0%
+be kind of attached to a robot and sent
+out to kind of sniff out the area before
+
+ align:start position:0%
+out to kind of sniff out the area before
+ 
+
+ align:start position:0%
+out to kind of sniff out the area before
+the soldiers go there you can really
+
+ align:start position:0%
+the soldiers go there you can really
+ 
+
+ align:start position:0%
+the soldiers go there you can really
+save a lot of the soldiers lives as well
+
+ align:start position:0%
+save a lot of the soldiers lives as well
+ 
+
+ align:start position:0%
+save a lot of the soldiers lives as well
+it's very cool to kind of do the
+
+ align:start position:0%
+it's very cool to kind of do the
+ 
+
+ align:start position:0%
+it's very cool to kind of do the
+Hands-On work in the chemistry
+
+ align:start position:0%
+Hands-On work in the chemistry
+ 
+
+ align:start position:0%
+Hands-On work in the chemistry
+laboratory and then know that what
+
+ align:start position:0%
+laboratory and then know that what
+ 
+
+ align:start position:0%
+laboratory and then know that what
+you've done at your bench will then one
+
+ align:start position:0%
+you've done at your bench will then one
+ 
+
+ align:start position:0%
+you've done at your bench will then one
+day be actually used by someone and
+
+ align:start position:0%
+day be actually used by someone and
+ 
+
+ align:start position:0%
+day be actually used by someone and
+potentially save their life
+
+ align:start position:0%
+potentially save their life
+ 
+
+ align:start position:0%
+potentially save their life
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so back to
+
+ align:start position:0%
+so back to
+ 
+
+ align:start position:0%
+so back to
+Vesper and loone pairs let's look at
+
+ align:start position:0%
+Vesper and loone pairs let's look at
+ 
+
+ align:start position:0%
+Vesper and loone pairs let's look at
+some examples and think about the shapes
+
+ align:start position:0%
+some examples and think about the shapes
+ 
+
+ align:start position:0%
+some examples and think about the shapes
+we've seen some of these already but
+
+ align:start position:0%
+we've seen some of these already but
+ 
+
+ align:start position:0%
+we've seen some of these already but
+let's look at some more so now we can
+
+ align:start position:0%
+let's look at some more so now we can
+ 
+
+ align:start position:0%
+let's look at some more so now we can
+have ax2 e SN number of three so two
+
+ align:start position:0%
+have ax2 e SN number of three so two
+ 
+
+ align:start position:0%
+have ax2 e SN number of three so two
+bonded atoms one lone pair this has bent
+
+ align:start position:0%
+bonded atoms one lone pair this has bent
+ 
+
+ align:start position:0%
+bonded atoms one lone pair this has bent
+geometry
+
+ align:start position:0%
+geometry
+ 
+
+ align:start position:0%
+geometry
+but again think about this lone pair now
+
+ align:start position:0%
+but again think about this lone pair now
+ 
+
+ align:start position:0%
+but again think about this lone pair now
+we're going to talk about the Angles and
+
+ align:start position:0%
+we're going to talk about the Angles and
+ 
+
+ align:start position:0%
+we're going to talk about the Angles and
+when we're talking about angles in this
+
+ align:start position:0%
+when we're talking about angles in this
+ 
+
+ align:start position:0%
+when we're talking about angles in this
+class we're talking about the angles
+
+ align:start position:0%
+class we're talking about the angles
+ 
+
+ align:start position:0%
+class we're talking about the angles
+between the bonded atoms so the angle
+
+ align:start position:0%
+between the bonded atoms so the angle
+ 
+
+ align:start position:0%
+between the bonded atoms so the angle
+from the lone pair down is going to be
+
+ align:start position:0%
+from the lone pair down is going to be
+ 
+
+ align:start position:0%
+from the lone pair down is going to be
+bigger because the lone pair is really
+
+ align:start position:0%
+bigger because the lone pair is really
+ 
+
+ align:start position:0%
+bigger because the lone pair is really
+repulsive but we're going to be thinking
+
+ align:start position:0%
+repulsive but we're going to be thinking
+ 
+
+ align:start position:0%
+repulsive but we're going to be thinking
+about the angle between the atoms you
+
+ align:start position:0%
+about the angle between the atoms you
+ 
+
+ align:start position:0%
+about the angle between the atoms you
+see so when we ask about angle we're
+
+ align:start position:0%
+see so when we ask about angle we're
+ 
+
+ align:start position:0%
+see so when we ask about angle we're
+asking about this angle between one
+
+ align:start position:0%
+asking about this angle between one
+ 
+
+ align:start position:0%
+asking about this angle between one
+bonded atom Central atom and the other
+
+ align:start position:0%
+bonded atom Central atom and the other
+ 
+
+ align:start position:0%
+bonded atom Central atom and the other
+bonded atom so this really this lone
+
+ align:start position:0%
+bonded atom so this really this lone
+ 
+
+ align:start position:0%
+bonded atom so this really this lone
+pair doesn't look that repulsive so I
+
+ align:start position:0%
+pair doesn't look that repulsive so I
+ 
+
+ align:start position:0%
+pair doesn't look that repulsive so I
+just want you to sort of think more
+
+ align:start position:0%
+just want you to sort of think more
+ 
+
+ align:start position:0%
+just want you to sort of think more
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+this so keep this in mind this is really
+
+ align:start position:0%
+this so keep this in mind this is really
+ 
+
+ align:start position:0%
+this so keep this in mind this is really
+more what a messy roommate is all about
+
+ align:start position:0%
+more what a messy roommate is all about
+ 
+
+ align:start position:0%
+more what a messy roommate is all about
+so if this is your lone pair pressing
+
+ align:start position:0%
+so if this is your lone pair pressing
+ 
+
+ align:start position:0%
+so if this is your lone pair pressing
+down on those bonds what do you expect
+
+ align:start position:0%
+down on those bonds what do you expect
+ 
+
+ align:start position:0%
+down on those bonds what do you expect
+the angle is going to
+
+ align:start position:0%
+the angle is going to
+ 
+
+ align:start position:0%
+the angle is going to
+be what's the angle in the normal case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first so we have 120 bonding oh and now
+
+ align:start position:0%
+first so we have 120 bonding oh and now
+ 
+
+ align:start position:0%
+first so we have 120 bonding oh and now
+think and actually that's a clicker
+
+ align:start position:0%
+think and actually that's a clicker
+ 
+
+ align:start position:0%
+think and actually that's a clicker
+question think about what the answer is
+
+ align:start position:0%
+question think about what the answer is
+ 
+
+ align:start position:0%
+question think about what the answer is
+going to be we talked about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normal all right 10 more 10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds all right yes less than
+
+ align:start position:0%
+seconds all right yes less than
+ 
+
+ align:start position:0%
+seconds all right yes less than
+120 so you don't know exactly you can't
+
+ align:start position:0%
+120 so you don't know exactly you can't
+ 
+
+ align:start position:0%
+120 so you don't know exactly you can't
+say oh that's going to be
+
+ align:start position:0%
+say oh that's going to be
+ 
+
+ align:start position:0%
+say oh that's going to be
+118.5 or something but you can say less
+
+ align:start position:0%
+118.5 or something but you can say less
+ 
+
+ align:start position:0%
+118.5 or something but you can say less
+than 120 that's the that's how you would
+
+ align:start position:0%
+than 120 that's the that's how you would
+ 
+
+ align:start position:0%
+than 120 that's the that's how you would
+express it and I'll just remind myself
+
+ align:start position:0%
+express it and I'll just remind myself
+ 
+
+ align:start position:0%
+express it and I'll just remind myself
+to say if you like these model kits and
+
+ align:start position:0%
+to say if you like these model kits and
+ 
+
+ align:start position:0%
+to say if you like these model kits and
+want your own some toothpicks and
+
+ align:start position:0%
+want your own some toothpicks and
+ 
+
+ align:start position:0%
+want your own some toothpicks and
+gumdrops can create some awesome Vesper
+
+ align:start position:0%
+gumdrops can create some awesome Vesper
+ 
+
+ align:start position:0%
+gumdrops can create some awesome Vesper
+model kits and we'll try to bring some
+
+ align:start position:0%
+model kits and we'll try to bring some
+ 
+
+ align:start position:0%
+model kits and we'll try to bring some
+of these into a recitation for people
+
+ align:start position:0%
+of these into a recitation for people
+ 
+
+ align:start position:0%
+of these into a recitation for people
+who want to have gumdrops and toothpicks
+
+ align:start position:0%
+who want to have gumdrops and toothpicks
+ 
+
+ align:start position:0%
+who want to have gumdrops and toothpicks
+for making
+
+ align:start position:0%
+for making
+ 
+
+ align:start position:0%
+for making
+models okay so let's keep going going so
+
+ align:start position:0%
+models okay so let's keep going going so
+ 
+
+ align:start position:0%
+models okay so let's keep going going so
+now we have our tetrahedral based system
+
+ align:start position:0%
+now we have our tetrahedral based system
+ 
+
+ align:start position:0%
+now we have our tetrahedral based system
+ax um and but we have
+
+ align:start position:0%
+ax um and but we have
+ 
+
+ align:start position:0%
+ax um and but we have
+ax 3
+
+ align:start position:0%
+ax 3
+ 
+
+ align:start position:0%
+ax 3
+e and an SN number of four So based on T
+
+ align:start position:0%
+e and an SN number of four So based on T
+ 
+
+ align:start position:0%
+e and an SN number of four So based on T
+on uh on
+
+ align:start position:0%
+on uh on
+ 
+
+ align:start position:0%
+on uh on
+tetrahedral and so here now we have
+
+ align:start position:0%
+tetrahedral and so here now we have
+ 
+
+ align:start position:0%
+tetrahedral and so here now we have
+trigonal paramal so we have a bunch this
+
+ align:start position:0%
+trigonal paramal so we have a bunch this
+ 
+
+ align:start position:0%
+trigonal paramal so we have a bunch this
+is why it's confusing it's not bip
+
+ align:start position:0%
+is why it's confusing it's not bip
+ 
+
+ align:start position:0%
+is why it's confusing it's not bip
+paramal there's only one pyramid here
+
+ align:start position:0%
+paramal there's only one pyramid here
+ 
+
+ align:start position:0%
+paramal there's only one pyramid here
+and it looks like a triangle so trigonal
+
+ align:start position:0%
+and it looks like a triangle so trigonal
+ 
+
+ align:start position:0%
+and it looks like a triangle so trigonal
+paramal and now what are the angles
+
+ align:start position:0%
+paramal and now what are the angles
+ 
+
+ align:start position:0%
+paramal and now what are the angles
+going to be and you can just yell this
+
+ align:start position:0%
+going to be and you can just yell this
+ 
+
+ align:start position:0%
+going to be and you can just yell this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+out yeah lesson
+
+ align:start position:0%
+out yeah lesson
+ 
+
+ align:start position:0%
+out yeah lesson
+109.5 and now let's keep going and we
+
+ align:start position:0%
+109.5 and now let's keep going and we
+ 
+
+ align:start position:0%
+109.5 and now let's keep going and we
+have another clicker
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question all right 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh so the trick here was to
+
+ align:start position:0%
+okay so uh so the trick here was to
+ 
+
+ align:start position:0%
+okay so uh so the trick here was to
+think about the parent geometry of the
+
+ align:start position:0%
+think about the parent geometry of the
+ 
+
+ align:start position:0%
+think about the parent geometry of the
+system and so this is the parent
+
+ align:start position:0%
+system and so this is the parent
+ 
+
+ align:start position:0%
+system and so this is the parent
+geometry is the tetrahedral system and
+
+ align:start position:0%
+geometry is the tetrahedral system and
+ 
+
+ align:start position:0%
+geometry is the tetrahedral system and
+we know that because it has an SN number
+
+ align:start position:0%
+we know that because it has an SN number
+ 
+
+ align:start position:0%
+we know that because it has an SN number
+of four and so when you have an SN
+
+ align:start position:0%
+of four and so when you have an SN
+ 
+
+ align:start position:0%
+of four and so when you have an SN
+number of four then it's going to be
+
+ align:start position:0%
+number of four then it's going to be
+ 
+
+ align:start position:0%
+number of four then it's going to be
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+109.5 and this is called a bent geometry
+
+ align:start position:0%
+109.5 and this is called a bent geometry
+ 
+
+ align:start position:0%
+109.5 and this is called a bent geometry
+so again you can think about it with in
+
+ align:start position:0%
+so again you can think about it with in
+ 
+
+ align:start position:0%
+so again you can think about it with in
+terms of those uh you know if you have
+
+ align:start position:0%
+terms of those uh you know if you have
+ 
+
+ align:start position:0%
+terms of those uh you know if you have
+some whole cans those lone pairs are
+
+ align:start position:0%
+some whole cans those lone pairs are
+ 
+
+ align:start position:0%
+some whole cans those lone pairs are
+pressing down on the bonds and
+
+ align:start position:0%
+pressing down on the bonds and
+ 
+
+ align:start position:0%
+pressing down on the bonds and
+compressing them so it's less than 109.5
+
+ align:start position:0%
+compressing them so it's less than 109.5
+ 
+
+ align:start position:0%
+compressing them so it's less than 109.5
+I just teach chemistry because I like to
+
+ align:start position:0%
+I just teach chemistry because I like to
+ 
+
+ align:start position:0%
+I just teach chemistry because I like to
+buy whole cans and have a justification
+
+ align:start position:0%
+buy whole cans and have a justification
+ 
+
+ align:start position:0%
+buy whole cans and have a justification
+for it it's really the bottom line okay
+
+ align:start position:0%
+for it it's really the bottom line okay
+ 
+
+ align:start position:0%
+for it it's really the bottom line okay
+so if we keep going now we have our
+
+ align:start position:0%
+so if we keep going now we have our
+ 
+
+ align:start position:0%
+so if we keep going now we have our
+friend seesaw which you're never going
+
+ align:start position:0%
+friend seesaw which you're never going
+ 
+
+ align:start position:0%
+friend seesaw which you're never going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+forget and I'll rebuild my my uh oops
+
+ align:start position:0%
+forget and I'll rebuild my my uh oops
+ 
+
+ align:start position:0%
+forget and I'll rebuild my my uh oops
+wrong one rebuild my seesaw over
+
+ align:start position:0%
+wrong one rebuild my seesaw over
+ 
+
+ align:start position:0%
+wrong one rebuild my seesaw over
+here so now what are the angles
+
+ align:start position:0%
+here so now what are the angles
+ 
+
+ align:start position:0%
+here so now what are the angles
+here there's two of them think about the
+
+ align:start position:0%
+here there's two of them think about the
+ 
+
+ align:start position:0%
+here there's two of them think about the
+uh the equatorial
+
+ align:start position:0%
+uh the equatorial
+ 
+
+ align:start position:0%
+uh the equatorial
+angles yep I'm hearing it less than 120
+
+ align:start position:0%
+angles yep I'm hearing it less than 120
+ 
+
+ align:start position:0%
+angles yep I'm hearing it less than 120
+and the axial would be less than 90 so
+
+ align:start position:0%
+and the axial would be less than 90 so
+ 
+
+ align:start position:0%
+and the axial would be less than 90 so
+the lone pair is pressing down both on
+
+ align:start position:0%
+the lone pair is pressing down both on
+ 
+
+ align:start position:0%
+the lone pair is pressing down both on
+the 90 and on the 120 it's probably more
+
+ align:start position:0%
+the 90 and on the 120 it's probably more
+ 
+
+ align:start position:0%
+the 90 and on the 120 it's probably more
+repulsive for the 90 but all you have to
+
+ align:start position:0%
+repulsive for the 90 but all you have to
+ 
+
+ align:start position:0%
+repulsive for the 90 but all you have to
+do is say less than for both of them so
+
+ align:start position:0%
+do is say less than for both of them so
+ 
+
+ align:start position:0%
+do is say less than for both of them so
+the trick is just think about the parent
+
+ align:start position:0%
+the trick is just think about the parent
+ 
+
+ align:start position:0%
+the trick is just think about the parent
+geometry what are the angles in the
+
+ align:start position:0%
+geometry what are the angles in the
+ 
+
+ align:start position:0%
+geometry what are the angles in the
+parent geometry and then it's less
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than um and if we keep going with this
+
+ align:start position:0%
+than um and if we keep going with this
+ 
+
+ align:start position:0%
+than um and if we keep going with this
+we had our t-shaped
+
+ align:start position:0%
+we had our t-shaped
+ 
+
+ align:start position:0%
+we had our t-shaped
+molecule as well so we added another
+
+ align:start position:0%
+molecule as well so we added another
+ 
+
+ align:start position:0%
+molecule as well so we added another
+lone pair to our sn5 case and what's the
+
+ align:start position:0%
+lone pair to our sn5 case and what's the
+ 
+
+ align:start position:0%
+lone pair to our sn5 case and what's the
+angle now going to be with those two
+
+ align:start position:0%
+angle now going to be with those two
+ 
+
+ align:start position:0%
+angle now going to be with those two
+loone
+
+ align:start position:0%
+loone
+ 
+
+ align:start position:0%
+loone
+pairs less than less than 90 right all
+
+ align:start position:0%
+pairs less than less than 90 right all
+ 
+
+ align:start position:0%
+pairs less than less than 90 right all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so there are so many possibilities for
+
+ align:start position:0%
+so there are so many possibilities for
+ 
+
+ align:start position:0%
+so there are so many possibilities for
+loan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairs if we add yet another loone pair
+
+ align:start position:0%
+pairs if we add yet another loone pair
+ 
+
+ align:start position:0%
+pairs if we add yet another loone pair
+to the system what's my
+
+ align:start position:0%
+to the system what's my
+ 
+
+ align:start position:0%
+to the system what's my
+geometry yep so this is going to be now
+
+ align:start position:0%
+geometry yep so this is going to be now
+ 
+
+ align:start position:0%
+geometry yep so this is going to be now
+a linear
+
+ align:start position:0%
+a linear
+ 
+
+ align:start position:0%
+a linear
+geometry and what's the angle going to
+
+ align:start position:0%
+geometry and what's the angle going to
+ 
+
+ align:start position:0%
+geometry and what's the angle going to
+be yeah it's just going to be 180 so we
+
+ align:start position:0%
+be yeah it's just going to be 180 so we
+ 
+
+ align:start position:0%
+be yeah it's just going to be 180 so we
+don't have a less than here because
+
+ align:start position:0%
+don't have a less than here because
+ 
+
+ align:start position:0%
+don't have a less than here because
+whatever way it would bend it would be
+
+ align:start position:0%
+whatever way it would bend it would be
+ 
+
+ align:start position:0%
+whatever way it would bend it would be
+just moving toward more repulsive loone
+
+ align:start position:0%
+just moving toward more repulsive loone
+ 
+
+ align:start position:0%
+just moving toward more repulsive loone
+pairs so there's no way you can minimize
+
+ align:start position:0%
+pairs so there's no way you can minimize
+ 
+
+ align:start position:0%
+pairs so there's no way you can minimize
+the repulsion in this case so it's just
+
+ align:start position:0%
+the repulsion in this case so it's just
+ 
+
+ align:start position:0%
+the repulsion in this case so it's just
+going to be a linear molecule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we're going to move into our
+
+ align:start position:0%
+so now we're going to move into our
+ 
+
+ align:start position:0%
+so now we're going to move into our
+sn6 category and we're going to talk
+
+ align:start position:0%
+sn6 category and we're going to talk
+ 
+
+ align:start position:0%
+sn6 category and we're going to talk
+about a shape that we haven't talked
+
+ align:start position:0%
+about a shape that we haven't talked
+ 
+
+ align:start position:0%
+about a shape that we haven't talked
+about yet
+
+ align:start position:0%
+about yet
+ 
+
+ align:start position:0%
+about yet
+so based on this what happens we have
+
+ align:start position:0%
+so based on this what happens we have
+ 
+
+ align:start position:0%
+so based on this what happens we have
+our parent geometry of octahedral and so
+
+ align:start position:0%
+our parent geometry of octahedral and so
+ 
+
+ align:start position:0%
+our parent geometry of octahedral and so
+this has six bonded atoms sn6 but now
+
+ align:start position:0%
+this has six bonded atoms sn6 but now
+ 
+
+ align:start position:0%
+this has six bonded atoms sn6 but now
+we're going to take off one of the
+
+ align:start position:0%
+we're going to take off one of the
+ 
+
+ align:start position:0%
+we're going to take off one of the
+bonds put it the same as the figure
+
+ align:start position:0%
+bonds put it the same as the figure
+ 
+
+ align:start position:0%
+bonds put it the same as the figure
+we're going to going to take off one of
+
+ align:start position:0%
+we're going to going to take off one of
+ 
+
+ align:start position:0%
+we're going to going to take off one of
+the bonds and put on a lone pair and
+
+ align:start position:0%
+the bonds and put on a lone pair and
+ 
+
+ align:start position:0%
+the bonds and put on a lone pair and
+this is called Square paramal because
+
+ align:start position:0%
+this is called Square paramal because
+ 
+
+ align:start position:0%
+this is called Square paramal because
+you have this Square here in your axial
+
+ align:start position:0%
+you have this Square here in your axial
+ 
+
+ align:start position:0%
+you have this Square here in your axial
+it looks like a square but when you
+
+ align:start position:0%
+it looks like a square but when you
+ 
+
+ align:start position:0%
+it looks like a square but when you
+consider you have an atom on top coming
+
+ align:start position:0%
+consider you have an atom on top coming
+ 
+
+ align:start position:0%
+consider you have an atom on top coming
+down to these
+
+ align:start position:0%
+down to these
+ 
+
+ align:start position:0%
+down to these
+four atoms on the side that again looks
+
+ align:start position:0%
+four atoms on the side that again looks
+ 
+
+ align:start position:0%
+four atoms on the side that again looks
+like a pyramid so this is square
+
+ align:start position:0%
+like a pyramid so this is square
+ 
+
+ align:start position:0%
+like a pyramid so this is square
+paramal and what angle do you think
+
+ align:start position:0%
+paramal and what angle do you think
+ 
+
+ align:start position:0%
+paramal and what angle do you think
+you're going to have here for these
+
+ align:start position:0%
+you're going to have here for these
+ 
+
+ align:start position:0%
+you're going to have here for these
+bonded
+
+ align:start position:0%
+bonded
+ 
+
+ align:start position:0%
+bonded
+atoms yep that'll be less than
+
+ align:start position:0%
+atoms yep that'll be less than
+ 
+
+ align:start position:0%
+atoms yep that'll be less than
+90 all right so we can keep going and we
+
+ align:start position:0%
+90 all right so we can keep going and we
+ 
+
+ align:start position:0%
+90 all right so we can keep going and we
+saw this one before if we take off
+
+ align:start position:0%
+saw this one before if we take off
+ 
+
+ align:start position:0%
+saw this one before if we take off
+another bonded electron and put in a
+
+ align:start position:0%
+another bonded electron and put in a
+ 
+
+ align:start position:0%
+another bonded electron and put in a
+second lone pair as we saw before those
+
+ align:start position:0%
+second lone pair as we saw before those
+ 
+
+ align:start position:0%
+second lone pair as we saw before those
+lone pairs want to be far apart from
+
+ align:start position:0%
+lone pairs want to be far apart from
+ 
+
+ align:start position:0%
+lone pairs want to be far apart from
+each other as they can so one goes on
+
+ align:start position:0%
+each other as they can so one goes on
+ 
+
+ align:start position:0%
+each other as they can so one goes on
+top one goes on the bottom and this was
+
+ align:start position:0%
+top one goes on the bottom and this was
+ 
+
+ align:start position:0%
+top one goes on the bottom and this was
+our Square planer geometry because it's
+
+ align:start position:0%
+our Square planer geometry because it's
+ 
+
+ align:start position:0%
+our Square planer geometry because it's
+a square and it's planer now what do you
+
+ align:start position:0%
+a square and it's planer now what do you
+ 
+
+ align:start position:0%
+a square and it's planer now what do you
+think the angles are
+
+ align:start position:0%
+think the angles are
+ 
+
+ align:start position:0%
+think the angles are
+90 right there's no there's nowhere to
+
+ align:start position:0%
+90 right there's no there's nowhere to
+ 
+
+ align:start position:0%
+90 right there's no there's nowhere to
+escape when you have a messy roommate on
+
+ align:start position:0%
+escape when you have a messy roommate on
+ 
+
+ align:start position:0%
+escape when you have a messy roommate on
+top and a Ry roommate on the bottom if
+
+ align:start position:0%
+top and a Ry roommate on the bottom if
+ 
+
+ align:start position:0%
+top and a Ry roommate on the bottom if
+you're in a triple between messy
+
+ align:start position:0%
+you're in a triple between messy
+ 
+
+ align:start position:0%
+you're in a triple between messy
+roommates there's just nothing you can
+
+ align:start position:0%
+roommates there's just nothing you can
+ 
+
+ align:start position:0%
+roommates there's just nothing you can
+do um and you can't you can't minimize
+
+ align:start position:0%
+do um and you can't you can't minimize
+ 
+
+ align:start position:0%
+do um and you can't you can't minimize
+the repulsion at all you just have to
+
+ align:start position:0%
+the repulsion at all you just have to
+ 
+
+ align:start position:0%
+the repulsion at all you just have to
+live with it okay so if we keep going
+
+ align:start position:0%
+live with it okay so if we keep going
+ 
+
+ align:start position:0%
+live with it okay so if we keep going
+again and now we're going to add another
+
+ align:start position:0%
+again and now we're going to add another
+ 
+
+ align:start position:0%
+again and now we're going to add another
+lone pair and it really doesn't matter
+
+ align:start position:0%
+lone pair and it really doesn't matter
+ 
+
+ align:start position:0%
+lone pair and it really doesn't matter
+where we put that it's all equivalent
+
+ align:start position:0%
+where we put that it's all equivalent
+ 
+
+ align:start position:0%
+where we put that it's all equivalent
+and it comes up with a shape that's
+
+ align:start position:0%
+and it comes up with a shape that's
+ 
+
+ align:start position:0%
+and it comes up with a shape that's
+t-shaped again that makes sense when you
+
+ align:start position:0%
+t-shaped again that makes sense when you
+ 
+
+ align:start position:0%
+t-shaped again that makes sense when you
+look at the structure and now what do
+
+ align:start position:0%
+look at the structure and now what do
+ 
+
+ align:start position:0%
+look at the structure and now what do
+you think the angles
+
+ align:start position:0%
+you think the angles
+ 
+
+ align:start position:0%
+you think the angles
+are less than 90 and you would be
+
+ align:start position:0%
+are less than 90 and you would be
+ 
+
+ align:start position:0%
+are less than 90 and you would be
+correct in that all right so if we put
+
+ align:start position:0%
+correct in that all right so if we put
+ 
+
+ align:start position:0%
+correct in that all right so if we put
+on yet one more lone pair and take off a
+
+ align:start position:0%
+on yet one more lone pair and take off a
+ 
+
+ align:start position:0%
+on yet one more lone pair and take off a
+bonded electron or take off one more
+
+ align:start position:0%
+bonded electron or take off one more
+ 
+
+ align:start position:0%
+bonded electron or take off one more
+bonded at bonded atom and put on
+
+ align:start position:0%
+bonded at bonded atom and put on
+ 
+
+ align:start position:0%
+bonded at bonded atom and put on
+electron what's our
+
+ align:start position:0%
+electron what's our
+ 
+
+ align:start position:0%
+electron what's our
+geometry right so we have this structure
+
+ align:start position:0%
+geometry right so we have this structure
+ 
+
+ align:start position:0%
+geometry right so we have this structure
+it's linear 180 no place to go so we
+
+ align:start position:0%
+it's linear 180 no place to go so we
+ 
+
+ align:start position:0%
+it's linear 180 no place to go so we
+keep going far enough we come back to
+
+ align:start position:0%
+keep going far enough we come back to
+ 
+
+ align:start position:0%
+keep going far enough we come back to
+linear a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lot now let's just look at a couple um
+
+ align:start position:0%
+lot now let's just look at a couple um
+ 
+
+ align:start position:0%
+lot now let's just look at a couple um
+more some real life examples of
+
+ align:start position:0%
+more some real life examples of
+ 
+
+ align:start position:0%
+more some real life examples of
+molecules and think about their think
+
+ align:start position:0%
+molecules and think about their think
+ 
+
+ align:start position:0%
+molecules and think about their think
+about their geometries and shapes have a
+
+ align:start position:0%
+about their geometries and shapes have a
+ 
+
+ align:start position:0%
+about their geometries and shapes have a
+couple more clicker questions um so
+
+ align:start position:0%
+couple more clicker questions um so
+ 
+
+ align:start position:0%
+couple more clicker questions um so
+let's start with our friend
+
+ align:start position:0%
+let's start with our friend
+ 
+
+ align:start position:0%
+let's start with our friend
+water and I had water
+
+ align:start position:0%
+water and I had water
+ 
+
+ align:start position:0%
+water and I had water
+here so now let's think about what the
+
+ align:start position:0%
+here so now let's think about what the
+ 
+
+ align:start position:0%
+here so now let's think about what the
+formula type is going to be for water
+
+ align:start position:0%
+formula type is going to be for water
+ 
+
+ align:start position:0%
+formula type is going to be for water
+and what's our formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type
+
+ align:start position:0%
+type
+ 
+
+ align:start position:0%
+type
+ax y a X2 E2 two bonded atoms two lone
+
+ align:start position:0%
+ax y a X2 E2 two bonded atoms two lone
+ 
+
+ align:start position:0%
+ax y a X2 E2 two bonded atoms two lone
+pairs s a number of four and do you
+
+ align:start position:0%
+pairs s a number of four and do you
+ 
+
+ align:start position:0%
+pairs s a number of four and do you
+remember what this geometry is called
+
+ align:start position:0%
+remember what this geometry is called
+ 
+
+ align:start position:0%
+remember what this geometry is called
+bent yeah and this explains then what we
+
+ align:start position:0%
+bent yeah and this explains then what we
+ 
+
+ align:start position:0%
+bent yeah and this explains then what we
+talked about before that this is a polar
+
+ align:start position:0%
+talked about before that this is a polar
+ 
+
+ align:start position:0%
+talked about before that this is a polar
+molecule so these are polar bonds
+
+ align:start position:0%
+molecule so these are polar bonds
+ 
+
+ align:start position:0%
+molecule so these are polar bonds
+between the oxygen and the hydro
+
+ align:start position:0%
+between the oxygen and the hydro
+ 
+
+ align:start position:0%
+between the oxygen and the hydro
+hydrogen and but in this case it's not a
+
+ align:start position:0%
+hydrogen and but in this case it's not a
+ 
+
+ align:start position:0%
+hydrogen and but in this case it's not a
+linear molecule it's a bent molecule so
+
+ align:start position:0%
+linear molecule it's a bent molecule so
+ 
+
+ align:start position:0%
+linear molecule it's a bent molecule so
+it creates a net dipole and so that
+
+ align:start position:0%
+it creates a net dipole and so that
+ 
+
+ align:start position:0%
+it creates a net dipole and so that
+makes it a polar molecule and if water
+
+ align:start position:0%
+makes it a polar molecule and if water
+ 
+
+ align:start position:0%
+makes it a polar molecule and if water
+had any other shape and was not a polar
+
+ align:start position:0%
+had any other shape and was not a polar
+ 
+
+ align:start position:0%
+had any other shape and was not a polar
+molecule then life would be entirely
+
+ align:start position:0%
+molecule then life would be entirely
+ 
+
+ align:start position:0%
+molecule then life would be entirely
+different because water is the solvent
+
+ align:start position:0%
+different because water is the solvent
+ 
+
+ align:start position:0%
+different because water is the solvent
+of life so uh this shape pretty pretty
+
+ align:start position:0%
+of life so uh this shape pretty pretty
+ 
+
+ align:start position:0%
+of life so uh this shape pretty pretty
+important for anything actually they
+
+ align:start position:0%
+important for anything actually they
+ 
+
+ align:start position:0%
+important for anything actually they
+researched on what what medical doctors
+
+ align:start position:0%
+researched on what what medical doctors
+ 
+
+ align:start position:0%
+researched on what what medical doctors
+thought was the most important topic to
+
+ align:start position:0%
+thought was the most important topic to
+ 
+
+ align:start position:0%
+thought was the most important topic to
+learn as an undergraduate and Premed
+
+ align:start position:0%
+learn as an undergraduate and Premed
+ 
+
+ align:start position:0%
+learn as an undergraduate and Premed
+education and the number one topic that
+
+ align:start position:0%
+education and the number one topic that
+ 
+
+ align:start position:0%
+education and the number one topic that
+was most important was water there and
+
+ align:start position:0%
+was most important was water there and
+ 
+
+ align:start position:0%
+was most important was water there and
+you just learned about it okay so we
+
+ align:start position:0%
+you just learned about it okay so we
+ 
+
+ align:start position:0%
+you just learned about it okay so we
+keep going now and you have to answer a
+
+ align:start position:0%
+keep going now and you have to answer a
+ 
+
+ align:start position:0%
+keep going now and you have to answer a
+lot of things about this on a clicker
+
+ align:start position:0%
+lot of things about this on a clicker
+ 
+
+ align:start position:0%
+lot of things about this on a clicker
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right just 10 more seconds we got to
+
+ align:start position:0%
+all right just 10 more seconds we got to
+ 
+
+ align:start position:0%
+all right just 10 more seconds we got to
+finish our hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out all right so let's go take a look at
+
+ align:start position:0%
+out all right so let's go take a look at
+ 
+
+ align:start position:0%
+out all right so let's go take a look at
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+and fill it
+
+ align:start position:0%
+and fill it
+ 
+
+ align:start position:0%
+and fill it
+in so we have our
+
+ align:start position:0%
+in so we have our
+ 
+
+ align:start position:0%
+in so we have our
+ax4 which is an sn5 system because we
+
+ align:start position:0%
+ax4 which is an sn5 system because we
+ 
+
+ align:start position:0%
+ax4 which is an sn5 system because we
+have one
+
+ align:start position:0%
+have one
+ 
+
+ align:start position:0%
+have one
+e and then we have our seesaw
+
+ align:start position:0%
+e and then we have our seesaw
+ 
+
+ align:start position:0%
+e and then we have our seesaw
+geometry all right so let's just fill in
+
+ align:start position:0%
+geometry all right so let's just fill in
+ 
+
+ align:start position:0%
+geometry all right so let's just fill in
+the in the rest here and see who's won
+
+ align:start position:0%
+the in the rest here and see who's won
+ 
+
+ align:start position:0%
+the in the rest here and see who's won
+the clicker competition so for the next
+
+ align:start position:0%
+the clicker competition so for the next
+ 
+
+ align:start position:0%
+the clicker competition so for the next
+system we have BR now it's it's expanded
+
+ align:start position:0%
+system we have BR now it's it's expanded
+ 
+
+ align:start position:0%
+system we have BR now it's it's expanded
+so we have ax3 E2 sn5 we've added
+
+ align:start position:0%
+so we have ax3 E2 sn5 we've added
+ 
+
+ align:start position:0%
+so we have ax3 E2 sn5 we've added
+another lone pair and now this makes a
+
+ align:start position:0%
+another lone pair and now this makes a
+ 
+
+ align:start position:0%
+another lone pair and now this makes a
+t-shape but it's kind of a little bent
+
+ align:start position:0%
+t-shape but it's kind of a little bent
+ 
+
+ align:start position:0%
+t-shape but it's kind of a little bent
+t-shape because of the repulsion we come
+
+ align:start position:0%
+t-shape because of the repulsion we come
+ 
+
+ align:start position:0%
+t-shape because of the repulsion we come
+down we have ax2 E5 sn5 we've added
+
+ align:start position:0%
+down we have ax2 E5 sn5 we've added
+ 
+
+ align:start position:0%
+down we have ax2 E5 sn5 we've added
+three more with Xenon Xenon is expanded
+
+ align:start position:0%
+three more with Xenon Xenon is expanded
+ 
+
+ align:start position:0%
+three more with Xenon Xenon is expanded
+here we have our linear shape we also
+
+ align:start position:0%
+here we have our linear shape we also
+ 
+
+ align:start position:0%
+here we have our linear shape we also
+have Xenon with four things
+
+ align:start position:0%
+have Xenon with four things
+ 
+
+ align:start position:0%
+have Xenon with four things
+um bound and if we did the Lewis
+
+ align:start position:0%
+um bound and if we did the Lewis
+ 
+
+ align:start position:0%
+um bound and if we did the Lewis
+structure of that we'd realize there's
+
+ align:start position:0%
+structure of that we'd realize there's
+ 
+
+ align:start position:0%
+structure of that we'd realize there's
+lone pairs on the top and the bottom ax4
+
+ align:start position:0%
+lone pairs on the top and the bottom ax4
+ 
+
+ align:start position:0%
+lone pairs on the top and the bottom ax4
+E2
+
+ align:start position:0%
+E2
+ 
+
+ align:start position:0%
+E2
+sn6 and this is our Square planer
+
+ align:start position:0%
+sn6 and this is our Square planer
+ 
+
+ align:start position:0%
+sn6 and this is our Square planer
+geometry so you can predict a lot about
+
+ align:start position:0%
+geometry so you can predict a lot about
+ 
+
+ align:start position:0%
+geometry so you can predict a lot about
+just doing a Lewis structure thinking
+
+ align:start position:0%
+just doing a Lewis structure thinking
+ 
+
+ align:start position:0%
+just doing a Lewis structure thinking
+about where the loan pairs You can
+
+ align:start position:0%
+about where the loan pairs You can
+ 
+
+ align:start position:0%
+about where the loan pairs You can
+predict geometries and let's see who has
+
+ align:start position:0%
+predict geometries and let's see who has
+ 
+
+ align:start position:0%
+predict geometries and let's see who has
+won
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today we have an upset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+Sam all right see everybody on Monday
\ No newline at end of file
diff --git a/JneQrFoLq18.txt b/JneQrFoLq18.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ba2111d5663468394f54dd7c8353cad7333c0c81
--- /dev/null
+++ b/JneQrFoLq18.txt
@@ -0,0 +1,10591 @@
+align:start position:0%
+ 
+let's get started uh welcome back 21m
+
+ align:start position:0%
+let's get started uh welcome back 21m
+ 
+
+ align:start position:0%
+let's get started uh welcome back 21m
+383 computational music theory and
+
+ align:start position:0%
+383 computational music theory and
+ 
+
+ align:start position:0%
+383 computational music theory and
+Analysis went through probably one of
+
+ align:start position:0%
+Analysis went through probably one of
+ 
+
+ align:start position:0%
+Analysis went through probably one of
+the most slide heavy one of the fastest
+
+ align:start position:0%
+the most slide heavy one of the fastest
+ 
+
+ align:start position:0%
+the most slide heavy one of the fastest
+classes ever on Wednesday that I'll be
+
+ align:start position:0%
+classes ever on Wednesday that I'll be
+ 
+
+ align:start position:0%
+classes ever on Wednesday that I'll be
+doing uh this semester today we're going
+
+ align:start position:0%
+doing uh this semester today we're going
+ 
+
+ align:start position:0%
+doing uh this semester today we're going
+to switch gears we're going to do one of
+
+ align:start position:0%
+to switch gears we're going to do one of
+ 
+
+ align:start position:0%
+to switch gears we're going to do one of
+the least Tech uh heavy classes in this
+
+ align:start position:0%
+the least Tech uh heavy classes in this
+ 
+
+ align:start position:0%
+the least Tech uh heavy classes in this
+semester and then we'll probably keep
+
+ align:start position:0%
+semester and then we'll probably keep
+ 
+
+ align:start position:0%
+semester and then we'll probably keep
+going back and forth this is the only
+
+ align:start position:0%
+going back and forth this is the only
+ 
+
+ align:start position:0%
+going back and forth this is the only
+one that in my particular notes it for
+
+ align:start position:0%
+one that in my particular notes it for
+ 
+
+ align:start position:0%
+one that in my particular notes it for
+my lecture it says mike Don't Panic
+
+ align:start position:0%
+my lecture it says mike Don't Panic
+ 
+
+ align:start position:0%
+my lecture it says mike Don't Panic
+there actually is no power point because
+
+ align:start position:0%
+there actually is no power point because
+ 
+
+ align:start position:0%
+there actually is no power point because
+I was panicking the other day when I was
+
+ align:start position:0%
+I was panicking the other day when I was
+ 
+
+ align:start position:0%
+I was panicking the other day when I was
+preparing this I was like wait wait wait
+
+ align:start position:0%
+preparing this I was like wait wait wait
+ 
+
+ align:start position:0%
+preparing this I was like wait wait wait
+wait I did I delete it no there is
+
+ align:start position:0%
+wait I did I delete it no there is
+ 
+
+ align:start position:0%
+wait I did I delete it no there is
+nothing because I want us to step back
+
+ align:start position:0%
+nothing because I want us to step back
+ 
+
+ align:start position:0%
+nothing because I want us to step back
+for a little bit and think about some of
+
+ align:start position:0%
+for a little bit and think about some of
+ 
+
+ align:start position:0%
+for a little bit and think about some of
+the things and do some work on um some
+
+ align:start position:0%
+the things and do some work on um some
+ 
+
+ align:start position:0%
+the things and do some work on um some
+of the things to do with what we mean by
+
+ align:start position:0%
+of the things to do with what we mean by
+ 
+
+ align:start position:0%
+of the things to do with what we mean by
+music because various musical points
+
+ align:start position:0%
+music because various musical points
+ 
+
+ align:start position:0%
+music because various musical points
+because there's a lot of things that we
+
+ align:start position:0%
+because there's a lot of things that we
+ 
+
+ align:start position:0%
+because there's a lot of things that we
+can know that are um you know just sort
+
+ align:start position:0%
+can know that are um you know just sort
+ 
+
+ align:start position:0%
+can know that are um you know just sort
+of um uh just just sort of intuitively
+
+ align:start position:0%
+of um uh just just sort of intuitively
+ 
+
+ align:start position:0%
+of um uh just just sort of intuitively
+we all know what that is but then um we
+
+ align:start position:0%
+we all know what that is but then um we
+ 
+
+ align:start position:0%
+we all know what that is but then um we
+might not um you know we might not be
+
+ align:start position:0%
+might not um you know we might not be
+ 
+
+ align:start position:0%
+might not um you know we might not be
+able to explain it to a computer because
+
+ align:start position:0%
+able to explain it to a computer because
+ 
+
+ align:start position:0%
+able to explain it to a computer because
+computers are smart or computers are
+
+ align:start position:0%
+computers are smart or computers are
+ 
+
+ align:start position:0%
+computers are smart or computers are
+dumb what do you think shout it out dumb
+
+ align:start position:0%
+dumb what do you think shout it out dumb
+ 
+
+ align:start position:0%
+dumb what do you think shout it out dumb
+neither no neither dumb neither no no
+
+ align:start position:0%
+neither no neither dumb neither no no
+ 
+
+ align:start position:0%
+neither no neither dumb neither no no
+smart okay I think computers are really
+
+ align:start position:0%
+smart okay I think computers are really
+ 
+
+ align:start position:0%
+smart okay I think computers are really
+really dumb until we make them smart so
+
+ align:start position:0%
+really dumb until we make them smart so
+ 
+
+ align:start position:0%
+really dumb until we make them smart so
+or something like that great there's
+
+ align:start position:0%
+or something like that great there's
+ 
+
+ align:start position:0%
+or something like that great there's
+some people in the back that whose names
+
+ align:start position:0%
+some people in the back that whose names
+ 
+
+ align:start position:0%
+some people in the back that whose names
+I don't know could you take a sheet of
+
+ align:start position:0%
+I don't know could you take a sheet of
+ 
+
+ align:start position:0%
+I don't know could you take a sheet of
+paper you can also use your outline to
+
+ align:start position:0%
+paper you can also use your outline to
+ 
+
+ align:start position:0%
+paper you can also use your outline to
+put your name on it because uh the
+
+ align:start position:0%
+put your name on it because uh the
+ 
+
+ align:start position:0%
+put your name on it because uh the
+outlines for reading later and it's kind
+
+ align:start position:0%
+outlines for reading later and it's kind
+ 
+
+ align:start position:0%
+outlines for reading later and it's kind
+of nice that this way you have it for
+
+ align:start position:0%
+of nice that this way you have it for
+ 
+
+ align:start position:0%
+of nice that this way you have it for
+later and this way you won't um sort of
+
+ align:start position:0%
+later and this way you won't um sort of
+ 
+
+ align:start position:0%
+later and this way you won't um sort of
+get me if I go out of order right um
+
+ align:start position:0%
+get me if I go out of order right um
+ 
+
+ align:start position:0%
+get me if I go out of order right um
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I'm seeing who your names are can you
+
+ align:start position:0%
+so I'm seeing who your names are can you
+ 
+
+ align:start position:0%
+so I'm seeing who your names are can you
+take a second and at least the person
+
+ align:start position:0%
+take a second and at least the person
+ 
+
+ align:start position:0%
+take a second and at least the person
+you're sharing a table or sharing the
+
+ align:start position:0%
+you're sharing a table or sharing the
+ 
+
+ align:start position:0%
+you're sharing a table or sharing the
+invisible table with um and introduce
+
+ align:start position:0%
+invisible table with um and introduce
+ 
+
+ align:start position:0%
+invisible table with um and introduce
+yourself if you don't know that
+
+ align:start position:0%
+yourself if you don't know that
+ 
+
+ align:start position:0%
+yourself if you don't know that
+where okay now add into your
+
+ align:start position:0%
+where okay now add into your
+ 
+
+ align:start position:0%
+where okay now add into your
+conversation add into your conversation
+
+ align:start position:0%
+conversation add into your conversation
+ 
+
+ align:start position:0%
+conversation add into your conversation
+what you think a note is you can also
+
+ align:start position:0%
+what you think a note is you can also
+ 
+
+ align:start position:0%
+what you think a note is you can also
+keep getting to know each other the same
+
+ align:start position:0%
+keep getting to know each other the same
+ 
+
+ align:start position:0%
+keep getting to know each other the same
+time but what you think a note
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is okay I'm going to be asking you for
+
+ align:start position:0%
+is okay I'm going to be asking you for
+ 
+
+ align:start position:0%
+is okay I'm going to be asking you for
+for some definitions in a second but
+
+ align:start position:0%
+for some definitions in a second but
+ 
+
+ align:start position:0%
+for some definitions in a second but
+before we get to that um all I want you
+
+ align:start position:0%
+before we get to that um all I want you
+ 
+
+ align:start position:0%
+before we get to that um all I want you
+to do is take your definitions you've
+
+ align:start position:0%
+to do is take your definitions you've
+ 
+
+ align:start position:0%
+to do is take your definitions you've
+kind of got them first thing and you
+
+ align:start position:0%
+kind of got them first thing and you
+ 
+
+ align:start position:0%
+kind of got them first thing and you
+just got to count notes okay so I'm
+
+ align:start position:0%
+just got to count notes okay so I'm
+ 
+
+ align:start position:0%
+just got to count notes okay so I'm
+going to sing some things and you tell
+
+ align:start position:0%
+going to sing some things and you tell
+ 
+
+ align:start position:0%
+going to sing some things and you tell
+me how many notes I sing so write them
+
+ align:start position:0%
+me how many notes I sing so write them
+ 
+
+ align:start position:0%
+me how many notes I sing so write them
+down and then I'll ask them later
+
+ align:start position:0%
+down and then I'll ask them later
+ 
+
+ align:start position:0%
+down and then I'll ask them later
+um first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set pretty easy right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one third
+
+ align:start position:0%
+one third
+ 
+
+ align:start position:0%
+one third
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one fourth one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and fifth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one great talk with your talk with your
+
+ align:start position:0%
+one great talk with your talk with your
+ 
+
+ align:start position:0%
+one great talk with your talk with your
+neighbor and see how many if you got
+
+ align:start position:0%
+neighbor and see how many if you got
+ 
+
+ align:start position:0%
+neighbor and see how many if you got
+answers that line up with each
+
+ align:start position:0%
+answers that line up with each
+ 
+
+ align:start position:0%
+answers that line up with each
+other okay let's let's come back
+
+ align:start position:0%
+other okay let's let's come back
+ 
+
+ align:start position:0%
+other okay let's let's come back
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+um let's come back together we have um
+
+ align:start position:0%
+um let's come back together we have um
+ 
+
+ align:start position:0%
+um let's come back together we have um
+uh I believe that the normal
+
+ align:start position:0%
+uh I believe that the normal
+ 
+
+ align:start position:0%
+uh I believe that the normal
+distribution of names in this class is
+
+ align:start position:0%
+distribution of names in this class is
+ 
+
+ align:start position:0%
+distribution of names in this class is
+kind of like the uh letters in the
+
+ align:start position:0%
+kind of like the uh letters in the
+ 
+
+ align:start position:0%
+kind of like the uh letters in the
+alphabet so we we'll start with J's I'll
+
+ align:start position:0%
+alphabet so we we'll start with J's I'll
+ 
+
+ align:start position:0%
+alphabet so we we'll start with J's I'll
+call who's the alphabetically first J is
+
+ align:start position:0%
+call who's the alphabetically first J is
+ 
+
+ align:start position:0%
+call who's the alphabetically first J is
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+Jason Jason um something something like
+
+ align:start position:0%
+Jason Jason um something something like
+ 
+
+ align:start position:0%
+Jason Jason um something something like
+and if I change the things I'm doing it
+
+ align:start position:0%
+and if I change the things I'm doing it
+ 
+
+ align:start position:0%
+and if I change the things I'm doing it
+accidentally because I don't remember
+
+ align:start position:0%
+accidentally because I don't remember
+ 
+
+ align:start position:0%
+accidentally because I don't remember
+what I saying but um the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one three notes three notes how many
+
+ align:start position:0%
+one three notes three notes how many
+ 
+
+ align:start position:0%
+one three notes three notes how many
+agree how many disagree
+
+ align:start position:0%
+agree how many disagree
+ 
+
+ align:start position:0%
+agree how many disagree
+agrees
+
+ align:start position:0%
+agrees
+ 
+
+ align:start position:0%
+agrees
+disagrees okay good that was the right
+
+ align:start position:0%
+disagrees okay good that was the right
+ 
+
+ align:start position:0%
+disagrees okay good that was the right
+answer I saying three notes good who's
+
+ align:start position:0%
+answer I saying three notes good who's
+ 
+
+ align:start position:0%
+answer I saying three notes good who's
+alphabetically next after Jason we have
+
+ align:start position:0%
+alphabetically next after Jason we have
+ 
+
+ align:start position:0%
+alphabetically next after Jason we have
+we have some Jonathan Jordans we have
+
+ align:start position:0%
+we have some Jonathan Jordans we have
+ 
+
+ align:start position:0%
+we have some Jonathan Jordans we have
+Jake oh okay you we went out sorry about
+
+ align:start position:0%
+Jake oh okay you we went out sorry about
+ 
+
+ align:start position:0%
+Jake oh okay you we went out sorry about
+that Jake um no even if we do Jacob or
+
+ align:start position:0%
+that Jake um no even if we do Jacob or
+ 
+
+ align:start position:0%
+that Jake um no even if we do Jacob or
+something it's still I'm still wrong
+
+ align:start position:0%
+something it's still I'm still wrong
+ 
+
+ align:start position:0%
+something it's still I'm still wrong
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+Jake this is what I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+saying one note agree or disagree who
+
+ align:start position:0%
+saying one note agree or disagree who
+ 
+
+ align:start position:0%
+saying one note agree or disagree who
+agrees who
+
+ align:start position:0%
+agrees who
+ 
+
+ align:start position:0%
+agrees who
+disagrees good everybody is wrong I
+
+ align:start position:0%
+disagrees good everybody is wrong I
+ 
+
+ align:start position:0%
+disagrees good everybody is wrong I
+Sayang four
+
+ align:start position:0%
+Sayang four
+ 
+
+ align:start position:0%
+Sayang four
+um okay next note well next one I did I
+
+ align:start position:0%
+um okay next note well next one I did I
+ 
+
+ align:start position:0%
+um okay next note well next one I did I
+I went I went up
+
+ align:start position:0%
+I went I went up
+ 
+
+ align:start position:0%
+I went I went up
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+right uh next up alphabetically would be
+
+ align:start position:0%
+right uh next up alphabetically would be
+ 
+
+ align:start position:0%
+right uh next up alphabetically would be
+uh Jonathan comes before John and comes
+
+ align:start position:0%
+uh Jonathan comes before John and comes
+ 
+
+ align:start position:0%
+uh Jonathan comes before John and comes
+before Jordan so
+
+ align:start position:0%
+before Jordan so
+ 
+
+ align:start position:0%
+before Jordan so
+Jonathan okay uh my was two notes two
+
+ align:start position:0%
+Jonathan okay uh my was two notes two
+ 
+
+ align:start position:0%
+Jonathan okay uh my was two notes two
+notes good uh who
+
+ align:start position:0%
+notes good uh who
+ 
+
+ align:start position:0%
+notes good uh who
+agrees okay we got some agrees um who
+
+ align:start position:0%
+agrees okay we got some agrees um who
+ 
+
+ align:start position:0%
+agrees okay we got some agrees um who
+dis
+
+ align:start position:0%
+dis
+ 
+
+ align:start position:0%
+dis
+agrees okay good we'll we'll continue
+
+ align:start position:0%
+agrees okay good we'll we'll continue
+ 
+
+ align:start position:0%
+agrees okay good we'll we'll continue
+with the J's on that John you disagreed
+
+ align:start position:0%
+with the J's on that John you disagreed
+ 
+
+ align:start position:0%
+with the J's on that John you disagreed
+what's the number you came up with uh I
+
+ align:start position:0%
+what's the number you came up with uh I
+ 
+
+ align:start position:0%
+what's the number you came up with uh I
+thought because you sing a lot I think
+
+ align:start position:0%
+thought because you sing a lot I think
+ 
+
+ align:start position:0%
+thought because you sing a lot I think
+you Sayang at least one note oh okay
+
+ align:start position:0%
+you Sayang at least one note oh okay
+ 
+
+ align:start position:0%
+you Sayang at least one note oh okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well greater than one note no greater
+
+ align:start position:0%
+well greater than one note no greater
+ 
+
+ align:start position:0%
+well greater than one note no greater
+than or equal to one note right okay so
+
+ align:start position:0%
+than or equal to one note right okay so
+ 
+
+ align:start position:0%
+than or equal to one note right okay so
+that that takes a little that's that's a
+
+ align:start position:0%
+that that takes a little that's that's a
+ 
+
+ align:start position:0%
+that that takes a little that's that's a
+pretty pretty broad spectrum I like that
+
+ align:start position:0%
+pretty pretty broad spectrum I like that
+ 
+
+ align:start position:0%
+pretty pretty broad spectrum I like that
+it's always good um who who agrees with
+
+ align:start position:0%
+it's always good um who who agrees with
+ 
+
+ align:start position:0%
+it's always good um who who agrees with
+greater than or equal to one note or or
+
+ align:start position:0%
+greater than or equal to one note or or
+ 
+
+ align:start position:0%
+greater than or equal to one note or or
+wants more disagree if you want more
+
+ align:start position:0%
+wants more disagree if you want more
+ 
+
+ align:start position:0%
+wants more disagree if you want more
+specificity than that who agrees with
+
+ align:start position:0%
+specificity than that who agrees with
+ 
+
+ align:start position:0%
+specificity than that who agrees with
+greater than or equal to one note good
+
+ align:start position:0%
+greater than or equal to one note good
+ 
+
+ align:start position:0%
+greater than or equal to one note good
+Jordan's on your side and you just got
+
+ align:start position:0%
+Jordan's on your side and you just got
+ 
+
+ align:start position:0%
+Jordan's on your side and you just got
+some some people good so who disagrees
+
+ align:start position:0%
+some some people good so who disagrees
+ 
+
+ align:start position:0%
+some some people good so who disagrees
+with that with everything beforehand up
+
+ align:start position:0%
+with that with everything beforehand up
+ 
+
+ align:start position:0%
+with that with everything beforehand up
+till now great so um I think we have um
+
+ align:start position:0%
+till now great so um I think we have um
+ 
+
+ align:start position:0%
+till now great so um I think we have um
+no Jason we've already gone through who
+
+ align:start position:0%
+no Jason we've already gone through who
+ 
+
+ align:start position:0%
+no Jason we've already gone through who
+who raise your hands again if you
+
+ align:start position:0%
+who raise your hands again if you
+ 
+
+ align:start position:0%
+who raise your hands again if you
+disagree I want to keep going
+
+ align:start position:0%
+disagree I want to keep going
+ 
+
+ align:start position:0%
+disagree I want to keep going
+alphabetically next among the disagreer
+
+ align:start position:0%
+alphabetically next among the disagreer
+ 
+
+ align:start position:0%
+alphabetically next among the disagreer
+and that would that might be uh Kara
+
+ align:start position:0%
+and that would that might be uh Kara
+ 
+
+ align:start position:0%
+and that would that might be uh Kara
+Karima yeah yeah uh I I wrote na na okay
+
+ align:start position:0%
+Karima yeah yeah uh I I wrote na na okay
+ 
+
+ align:start position:0%
+Karima yeah yeah uh I I wrote na na okay
+well well na a or we we'll we'll make it
+
+ align:start position:0%
+well well na a or we we'll we'll make it
+ 
+
+ align:start position:0%
+well well na a or we we'll we'll make it
+so it parses in Python not a number is
+
+ align:start position:0%
+so it parses in Python not a number is
+ 
+
+ align:start position:0%
+so it parses in Python not a number is
+that okay okay good good and any um
+
+ align:start position:0%
+that okay okay good good and any um
+ 
+
+ align:start position:0%
+that okay okay good good and any um
+anybody still still have your number not
+
+ align:start position:0%
+anybody still still have your number not
+ 
+
+ align:start position:0%
+anybody still still have your number not
+said Adam yeah I said 14 or 15 14 or 15
+
+ align:start position:0%
+said Adam yeah I said 14 or 15 14 or 15
+ 
+
+ align:start position:0%
+said Adam yeah I said 14 or 15 14 or 15
+okay very very specific um what did you
+
+ align:start position:0%
+okay very very specific um what did you
+ 
+
+ align:start position:0%
+okay very very specific um what did you
+base that on so you went from a c to
+
+ align:start position:0%
+base that on so you went from a c to
+ 
+
+ align:start position:0%
+base that on so you went from a c to
+either a c or a d so it's like if you go
+
+ align:start position:0%
+either a c or a d so it's like if you go
+ 
+
+ align:start position:0%
+either a c or a d so it's like if you go
+all the chromatic notes and slur them
+
+ align:start position:0%
+all the chromatic notes and slur them
+ 
+
+ align:start position:0%
+all the chromatic notes and slur them
+all that's what you get okay okay good
+
+ align:start position:0%
+all that's what you get okay okay good
+ 
+
+ align:start position:0%
+all that's what you get okay okay good
+so we have we have a range extension um
+
+ align:start position:0%
+so we have we have a range extension um
+ 
+
+ align:start position:0%
+so we have we have a range extension um
+good uh anybody else have a number that
+
+ align:start position:0%
+good uh anybody else have a number that
+ 
+
+ align:start position:0%
+good uh anybody else have a number that
+doesn't hasn't been done
+
+ align:start position:0%
+doesn't hasn't been done
+ 
+
+ align:start position:0%
+doesn't hasn't been done
+yet okay um so that's that's
+
+ align:start position:0%
+yet okay um so that's that's
+ 
+
+ align:start position:0%
+yet okay um so that's that's
+particularly good um this one I went
+
+ align:start position:0%
+particularly good um this one I went
+ 
+
+ align:start position:0%
+particularly good um this one I went
+with INF oh sorry I wasn't telling you
+
+ align:start position:0%
+with INF oh sorry I wasn't telling you
+ 
+
+ align:start position:0%
+with INF oh sorry I wasn't telling you
+what what my numbers were yet okay well
+
+ align:start position:0%
+what what my numbers were yet okay well
+ 
+
+ align:start position:0%
+what what my numbers were yet okay well
+that one that's what I went with um and
+
+ align:start position:0%
+that one that's what I went with um and
+ 
+
+ align:start position:0%
+that one that's what I went with um and
+then uh next one D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we have
+
+ align:start position:0%
+um we have
+ 
+
+ align:start position:0%
+um we have
+some you want we have a a listener but
+
+ align:start position:0%
+some you want we have a a listener but
+ 
+
+ align:start position:0%
+some you want we have a a listener but
+you want to be a participant or also
+
+ align:start position:0%
+you want to be a participant or also
+ 
+
+ align:start position:0%
+you want to be a participant or also
+yeah go ahead so with that one I wrote
+
+ align:start position:0%
+yeah go ahead so with that one I wrote
+ 
+
+ align:start position:0%
+yeah go ahead so with that one I wrote
+six
+
+ align:start position:0%
+six
+ 
+
+ align:start position:0%
+six
+six anybody agree yep anybody
+
+ align:start position:0%
+six anybody agree yep anybody
+ 
+
+ align:start position:0%
+six anybody agree yep anybody
+disagree good
+
+ align:start position:0%
+disagree good
+ 
+
+ align:start position:0%
+disagree good
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+um yep and now oh no I was giving I was
+
+ align:start position:0%
+um yep and now oh no I was giving I was
+ 
+
+ align:start position:0%
+um yep and now oh no I was giving I was
+giving the right numbers yep so I'm
+
+ align:start position:0%
+giving the right numbers yep so I'm
+ 
+
+ align:start position:0%
+giving the right numbers yep so I'm
+going to say I did that I did that uh
+
+ align:start position:0%
+going to say I did that I did that uh
+ 
+
+ align:start position:0%
+going to say I did that I did that uh
+nobody disagreed the correct answer
+
+ align:start position:0%
+nobody disagreed the correct answer
+ 
+
+ align:start position:0%
+nobody disagreed the correct answer
+there was
+
+ align:start position:0%
+there was
+ 
+
+ align:start position:0%
+there was
+two and don't worry don't worry this is
+
+ align:start position:0%
+two and don't worry don't worry this is
+ 
+
+ align:start position:0%
+two and don't worry don't worry this is
+frustrating be frustrating and
+
+ align:start position:0%
+frustrating be frustrating and
+ 
+
+ align:start position:0%
+frustrating be frustrating and
+then uh who's also around K or do I hear
+
+ align:start position:0%
+then uh who's also around K or do I hear
+ 
+
+ align:start position:0%
+then uh who's also around K or do I hear
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero anybody
+
+ align:start position:0%
+zero anybody
+ 
+
+ align:start position:0%
+zero anybody
+disagree great uh uh person who's
+
+ align:start position:0%
+disagree great uh uh person who's
+ 
+
+ align:start position:0%
+disagree great uh uh person who's
+disagreed who has to speak um I just
+
+ align:start position:0%
+disagreed who has to speak um I just
+ 
+
+ align:start position:0%
+disagreed who has to speak um I just
+said one one good good who agrees with
+
+ align:start position:0%
+said one one good good who agrees with
+ 
+
+ align:start position:0%
+said one one good good who agrees with
+one good how many people have heard
+
+ align:start position:0%
+one good how many people have heard
+ 
+
+ align:start position:0%
+one good how many people have heard
+neither zero nor
+
+ align:start position:0%
+neither zero nor
+ 
+
+ align:start position:0%
+neither zero nor
+one y so when I was not writing a lot of
+
+ align:start position:0%
+one y so when I was not writing a lot of
+ 
+
+ align:start position:0%
+one y so when I was not writing a lot of
+these I put two answers to a lot of them
+
+ align:start position:0%
+these I put two answers to a lot of them
+ 
+
+ align:start position:0%
+these I put two answers to a lot of them
+depending on okay but you can only give
+
+ align:start position:0%
+depending on okay but you can only give
+ 
+
+ align:start position:0%
+depending on okay but you can only give
+one right now well I was how I not how
+
+ align:start position:0%
+one right now well I was how I not how
+ 
+
+ align:start position:0%
+one right now well I was how I not how
+i' like pitch wise and I was I was
+
+ align:start position:0%
+i' like pitch wise and I was I was
+ 
+
+ align:start position:0%
+i' like pitch wise and I was I was
+taking I I was taking perception
+
+ align:start position:0%
+taking I I was taking perception
+ 
+
+ align:start position:0%
+taking I I was taking perception
+spectrograms and a clap has like all of
+
+ align:start position:0%
+spectrograms and a clap has like all of
+ 
+
+ align:start position:0%
+spectrograms and a clap has like all of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+so so so give me a number so that one
+
+ align:start position:0%
+so so so give me a number so that one
+ 
+
+ align:start position:0%
+so so so give me a number so that one
+would also be INF INF okay
+
+ align:start position:0%
+would also be INF INF okay
+ 
+
+ align:start position:0%
+would also be INF INF okay
+good this one I'm going to go with
+
+ align:start position:0%
+good this one I'm going to go with
+ 
+
+ align:start position:0%
+good this one I'm going to go with
+zero and I will tell you um there isn't
+
+ align:start position:0%
+zero and I will tell you um there isn't
+ 
+
+ align:start position:0%
+zero and I will tell you um there isn't
+a single answer on here that I couldn't
+
+ align:start position:0%
+a single answer on here that I couldn't
+ 
+
+ align:start position:0%
+a single answer on here that I couldn't
+that you couldn't argue for and be
+
+ align:start position:0%
+that you couldn't argue for and be
+ 
+
+ align:start position:0%
+that you couldn't argue for and be
+correct so um why three notes I think we
+
+ align:start position:0%
+correct so um why three notes I think we
+ 
+
+ align:start position:0%
+correct so um why three notes I think we
+all agreed because I think I saying bom
+
+ align:start position:0%
+all agreed because I think I saying bom
+ 
+
+ align:start position:0%
+all agreed because I think I saying bom
+bom bom I count each of those as one
+
+ align:start position:0%
+bom bom I count each of those as one
+ 
+
+ align:start position:0%
+bom bom I count each of those as one
+note right second one was four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cuz was a half a whole note tied to a
+
+ align:start position:0%
+cuz was a half a whole note tied to a
+ 
+
+ align:start position:0%
+cuz was a half a whole note tied to a
+quarter note tied to uh a 60th note tied
+
+ align:start position:0%
+quarter note tied to uh a 60th note tied
+ 
+
+ align:start position:0%
+quarter note tied to uh a 60th note tied
+to a 64th
+
+ align:start position:0%
+to a 64th
+ 
+
+ align:start position:0%
+to a 64th
+note and I do believe that is the
+
+ align:start position:0%
+note and I do believe that is the
+ 
+
+ align:start position:0%
+note and I do believe that is the
+closest shortest representation I can do
+
+ align:start position:0%
+closest shortest representation I can do
+ 
+
+ align:start position:0%
+closest shortest representation I can do
+notationally so I was thinking in a
+
+ align:start position:0%
+notationally so I was thinking in a
+ 
+
+ align:start position:0%
+notationally so I was thinking in a
+notational sphere
+
+ align:start position:0%
+notational sphere
+ 
+
+ align:start position:0%
+notational sphere
+here this time with the gando I was
+
+ align:start position:0%
+here this time with the gando I was
+ 
+
+ align:start position:0%
+here this time with the gando I was
+thinking of it as an infinite number of
+
+ align:start position:0%
+thinking of it as an infinite number of
+ 
+
+ align:start position:0%
+thinking of it as an infinite number of
+notes because if it's continuous it
+
+ align:start position:0%
+notes because if it's continuous it
+ 
+
+ align:start position:0%
+notes because if it's continuous it
+could be but on the other hand it any of
+
+ align:start position:0%
+could be but on the other hand it any of
+ 
+
+ align:start position:0%
+could be but on the other hand it any of
+these other ones could be correct now
+
+ align:start position:0%
+these other ones could be correct now
+ 
+
+ align:start position:0%
+these other ones could be correct now
+let's see if anyone can come up with how
+
+ align:start position:0%
+let's see if anyone can come up with how
+ 
+
+ align:start position:0%
+let's see if anyone can come up with how
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+D I came up with
+
+ align:start position:0%
+D I came up with
+ 
+
+ align:start position:0%
+D I came up with
+two the two different pitches that's one
+
+ align:start position:0%
+two the two different pitches that's one
+ 
+
+ align:start position:0%
+two the two different pitches that's one
+good way to do it um I'm glad I I hit
+
+ align:start position:0%
+good way to do it um I'm glad I I hit
+ 
+
+ align:start position:0%
+good way to do it um I'm glad I I hit
+the same pitch each time maybe I'm close
+
+ align:start position:0%
+the same pitch each time maybe I'm close
+ 
+
+ align:start position:0%
+the same pitch each time maybe I'm close
+um that's not the reason why I was
+
+ align:start position:0%
+um that's not the reason why I was
+ 
+
+ align:start position:0%
+um that's not the reason why I was
+thinking yeah it's like the trol trevolo
+
+ align:start position:0%
+thinking yeah it's like the trol trevolo
+ 
+
+ align:start position:0%
+thinking yeah it's like the trol trevolo
+yeah it was something like I know well
+
+ align:start position:0%
+yeah it was something like I know well
+ 
+
+ align:start position:0%
+yeah it was something like I know well
+don't know what thing we're in but yeah
+
+ align:start position:0%
+don't know what thing we're in but yeah
+ 
+
+ align:start position:0%
+don't know what thing we're in but yeah
+I was thinking it has something like
+
+ align:start position:0%
+I was thinking it has something like
+ 
+
+ align:start position:0%
+I was thinking it has something like
+that or actually would be measured
+
+ align:start position:0%
+that or actually would be measured
+ 
+
+ align:start position:0%
+that or actually would be measured
+tremolo wouldn't it be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like anyone know this sign where you
+
+ align:start position:0%
+like anyone know this sign where you
+ 
+
+ align:start position:0%
+like anyone know this sign where you
+have a beamed or no just one beam right
+
+ align:start position:0%
+have a beamed or no just one beam right
+ 
+
+ align:start position:0%
+have a beamed or no just one beam right
+two beamed dotted half notes you see it
+
+ align:start position:0%
+two beamed dotted half notes you see it
+ 
+
+ align:start position:0%
+two beamed dotted half notes you see it
+everywhere every once a while when
+
+ align:start position:0%
+everywhere every once a while when
+ 
+
+ align:start position:0%
+everywhere every once a while when
+you're playing like POF off or or uh or
+
+ align:start position:0%
+you're playing like POF off or or uh or
+ 
+
+ align:start position:0%
+you're playing like POF off or or uh or
+shert and stuff and I always like oh I
+
+ align:start position:0%
+shert and stuff and I always like oh I
+ 
+
+ align:start position:0%
+shert and stuff and I always like oh I
+have to remember what that is but that
+
+ align:start position:0%
+have to remember what that is but that
+ 
+
+ align:start position:0%
+have to remember what that is but that
+means fill in the space of one dotted
+
+ align:start position:0%
+means fill in the space of one dotted
+ 
+
+ align:start position:0%
+means fill in the space of one dotted
+half note with as many eighth notes as
+
+ align:start position:0%
+half note with as many eighth notes as
+ 
+
+ align:start position:0%
+half note with as many eighth notes as
+it takes to fill it in alternating
+
+ align:start position:0%
+it takes to fill it in alternating
+ 
+
+ align:start position:0%
+it takes to fill it in alternating
+between the top one and the bottom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and
+
+ align:start position:0%
+one and
+ 
+
+ align:start position:0%
+one and
+clap I thought a note to me had to have
+
+ align:start position:0%
+clap I thought a note to me had to have
+ 
+
+ align:start position:0%
+clap I thought a note to me had to have
+some sort of specifiable
+
+ align:start position:0%
+some sort of specifiable
+ 
+
+ align:start position:0%
+some sort of specifiable
+pitch so I count zero
+
+ align:start position:0%
+pitch so I count zero
+ 
+
+ align:start position:0%
+pitch so I count zero
+now everything that somebody said uh one
+
+ align:start position:0%
+now everything that somebody said uh one
+ 
+
+ align:start position:0%
+now everything that somebody said uh one
+for for this or infinite are all valid
+
+ align:start position:0%
+for for this or infinite are all valid
+ 
+
+ align:start position:0%
+for for this or infinite are all valid
+definitions of what we're going to be
+
+ align:start position:0%
+definitions of what we're going to be
+ 
+
+ align:start position:0%
+definitions of what we're going to be
+talking
+
+ align:start position:0%
+talking
+ 
+
+ align:start position:0%
+talking
+about and here's the thing 99% of the
+
+ align:start position:0%
+about and here's the thing 99% of the
+ 
+
+ align:start position:0%
+about and here's the thing 99% of the
+time when I'm not trying to set up an
+
+ align:start position:0%
+time when I'm not trying to set up an
+ 
+
+ align:start position:0%
+time when I'm not trying to set up an
+example for um you know for kind having
+
+ align:start position:0%
+example for um you know for kind having
+ 
+
+ align:start position:0%
+example for um you know for kind having
+fun in the first week of class with you
+
+ align:start position:0%
+fun in the first week of class with you
+ 
+
+ align:start position:0%
+fun in the first week of class with you
+all uh there's no way I would call that
+
+ align:start position:0%
+all uh there's no way I would call that
+ 
+
+ align:start position:0%
+all uh there's no way I would call that
+second one four notes right I mean if I
+
+ align:start position:0%
+second one four notes right I mean if I
+ 
+
+ align:start position:0%
+second one four notes right I mean if I
+hear it I'm going to be one
+
+ align:start position:0%
+hear it I'm going to be one
+ 
+
+ align:start position:0%
+hear it I'm going to be one
+so one of the things that's going to
+
+ align:start position:0%
+so one of the things that's going to
+ 
+
+ align:start position:0%
+so one of the things that's going to
+come up quite often is that depending on
+
+ align:start position:0%
+come up quite often is that depending on
+ 
+
+ align:start position:0%
+come up quite often is that depending on
+what purpose you want to do with
+
+ align:start position:0%
+what purpose you want to do with
+ 
+
+ align:start position:0%
+what purpose you want to do with
+something you're not going to be able to
+
+ align:start position:0%
+something you're not going to be able to
+ 
+
+ align:start position:0%
+something you're not going to be able to
+um necessarily even know how many notes
+
+ align:start position:0%
+um necessarily even know how many notes
+ 
+
+ align:start position:0%
+um necessarily even know how many notes
+or how many of something there is let
+
+ align:start position:0%
+or how many of something there is let
+ 
+
+ align:start position:0%
+or how many of something there is let
+alone what's the correct spelling of
+
+ align:start position:0%
+alone what's the correct spelling of
+ 
+
+ align:start position:0%
+alone what's the correct spelling of
+something or not
+
+ align:start position:0%
+something or not
+ 
+
+ align:start position:0%
+something or not
+um so I think we're just going to be
+
+ align:start position:0%
+um so I think we're just going to be
+ 
+
+ align:start position:0%
+um so I think we're just going to be
+playing around with something like this
+
+ align:start position:0%
+playing around with something like this
+ 
+
+ align:start position:0%
+playing around with something like this
+now go back to your definitions of notes
+
+ align:start position:0%
+now go back to your definitions of notes
+ 
+
+ align:start position:0%
+now go back to your definitions of notes
+that you had before and let's grab into
+
+ align:start position:0%
+that you had before and let's grab into
+ 
+
+ align:start position:0%
+that you had before and let's grab into
+groups of four so your two groups that
+
+ align:start position:0%
+groups of four so your two groups that
+ 
+
+ align:start position:0%
+groups of four so your two groups that
+are the same joining with a group behind
+
+ align:start position:0%
+are the same joining with a group behind
+ 
+
+ align:start position:0%
+are the same joining with a group behind
+you so that's we're going to get good
+
+ align:start position:0%
+you so that's we're going to get good
+ 
+
+ align:start position:0%
+you so that's we're going to get good
+spinning over here we'll create a group
+
+ align:start position:0%
+spinning over here we'll create a group
+ 
+
+ align:start position:0%
+spinning over here we'll create a group
+of three here and three here and we'll
+
+ align:start position:0%
+of three here and three here and we'll
+ 
+
+ align:start position:0%
+of three here and three here and we'll
+we'll break up uh this this group and
+
+ align:start position:0%
+we'll break up uh this this group and
+ 
+
+ align:start position:0%
+we'll break up uh this this group and
+talk about what your definitions of the
+
+ align:start position:0%
+talk about what your definitions of the
+ 
+
+ align:start position:0%
+talk about what your definitions of the
+notes were with the other group and then
+
+ align:start position:0%
+notes were with the other group and then
+ 
+
+ align:start position:0%
+notes were with the other group and then
+try to figure out a if you had correct
+
+ align:start position:0%
+try to figure out a if you had correct
+ 
+
+ align:start position:0%
+try to figure out a if you had correct
+definitions or if you had compatible not
+
+ align:start position:0%
+definitions or if you had compatible not
+ 
+
+ align:start position:0%
+definitions or if you had compatible not
+a correct definition compatible
+
+ align:start position:0%
+a correct definition compatible
+ 
+
+ align:start position:0%
+a correct definition compatible
+definitions of notes before that with
+
+ align:start position:0%
+definitions of notes before that with
+ 
+
+ align:start position:0%
+definitions of notes before that with
+each other's group and then also if you
+
+ align:start position:0%
+each other's group and then also if you
+ 
+
+ align:start position:0%
+each other's group and then also if you
+want to change definition based on all
+
+ align:start position:0%
+want to change definition based on all
+ 
+
+ align:start position:0%
+want to change definition based on all
+the weird numbers that we came up with
+
+ align:start position:0%
+the weird numbers that we came up with
+ 
+
+ align:start position:0%
+the weird numbers that we came up with
+here so go ahead and let's take a couple
+
+ align:start position:0%
+here so go ahead and let's take a couple
+ 
+
+ align:start position:0%
+here so go ahead and let's take a couple
+minutes to do that great let's let's all
+
+ align:start position:0%
+minutes to do that great let's let's all
+ 
+
+ align:start position:0%
+minutes to do that great let's let's all
+come back together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um there was one word that I just kept
+
+ align:start position:0%
+um there was one word that I just kept
+ 
+
+ align:start position:0%
+um there was one word that I just kept
+hearing as I was going around and it
+
+ align:start position:0%
+hearing as I was going around and it
+ 
+
+ align:start position:0%
+hearing as I was going around and it
+begins like this I want any any group
+
+ align:start position:0%
+begins like this I want any any group
+ 
+
+ align:start position:0%
+begins like this I want any any group
+use a word that begins with this in
+
+ align:start position:0%
+use a word that begins with this in
+ 
+
+ align:start position:0%
+use a word that begins with this in
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+definition yeah John go ahead
+
+ align:start position:0%
+definition yeah John go ahead
+ 
+
+ align:start position:0%
+definition yeah John go ahead
+representation representation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so we can kind of start with
+
+ align:start position:0%
+yeah so we can kind of start with
+ 
+
+ align:start position:0%
+yeah so we can kind of start with
+a is
+
+ align:start position:0%
+a is
+ 
+
+ align:start position:0%
+a is
+uh of
+
+ align:start position:0%
+uh of
+ 
+
+ align:start position:0%
+uh of
+is any anybody's definition um
+
+ align:start position:0%
+is any anybody's definition um
+ 
+
+ align:start position:0%
+is any anybody's definition um
+completely incompatible with this
+
+ align:start position:0%
+completely incompatible with this
+ 
+
+ align:start position:0%
+completely incompatible with this
+opening like couldn't be put in is no
+
+ align:start position:0%
+opening like couldn't be put in is no
+ 
+
+ align:start position:0%
+opening like couldn't be put in is no
+smile of thing okay so what are some of
+
+ align:start position:0%
+smile of thing okay so what are some of
+ 
+
+ align:start position:0%
+smile of thing okay so what are some of
+the ways that your groups could have um
+
+ align:start position:0%
+the ways that your groups could have um
+ 
+
+ align:start position:0%
+the ways that your groups could have um
+could have uh done this I didn't think I
+
+ align:start position:0%
+could have uh done this I didn't think I
+ 
+
+ align:start position:0%
+could have uh done this I didn't think I
+heard um because it's physically
+
+ align:start position:0%
+heard um because it's physically
+ 
+
+ align:start position:0%
+heard um because it's physically
+difficult what uh Jonathan Kara Jordan
+
+ align:start position:0%
+difficult what uh Jonathan Kara Jordan
+ 
+
+ align:start position:0%
+difficult what uh Jonathan Kara Jordan
+and Misha's group um came up with what
+
+ align:start position:0%
+and Misha's group um came up with what
+ 
+
+ align:start position:0%
+and Misha's group um came up with what
+do you How would how would somebody in
+
+ align:start position:0%
+do you How would how would somebody in
+ 
+
+ align:start position:0%
+do you How would how would somebody in
+this group uh continue that uh everybody
+
+ align:start position:0%
+this group uh continue that uh everybody
+ 
+
+ align:start position:0%
+this group uh continue that uh everybody
+has oh you guys are all normally
+
+ align:start position:0%
+has oh you guys are all normally
+ 
+
+ align:start position:0%
+has oh you guys are all normally
+distributed names so I've heard from
+
+ align:start position:0%
+distributed names so I've heard from
+ 
+
+ align:start position:0%
+distributed names so I've heard from
+everybody so um would you like
+
+ align:start position:0%
+everybody so um would you like
+ 
+
+ align:start position:0%
+everybody so um would you like
+to is a representation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything with a
+
+ align:start position:0%
+anything with a
+ 
+
+ align:start position:0%
+anything with a
+pitch and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+duration I groups disagree with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so I'm coming at this from the
+
+ align:start position:0%
+yeah so I'm coming at this from the
+ 
+
+ align:start position:0%
+yeah so I'm coming at this from the
+percussion perspective where a note
+
+ align:start position:0%
+percussion perspective where a note
+ 
+
+ align:start position:0%
+percussion perspective where a note
+doesn't necessarily need a pitch and it
+
+ align:start position:0%
+doesn't necessarily need a pitch and it
+ 
+
+ align:start position:0%
+doesn't necessarily need a pitch and it
+doesn't necessarily need a duration okay
+
+ align:start position:0%
+doesn't necessarily need a duration okay
+ 
+
+ align:start position:0%
+doesn't necessarily need a duration okay
+so so we have um not necessarily on that
+
+ align:start position:0%
+so so we have um not necessarily on that
+ 
+
+ align:start position:0%
+so so we have um not necessarily on that
+so do you have a positive did your group
+
+ align:start position:0%
+so do you have a positive did your group
+ 
+
+ align:start position:0%
+so do you have a positive did your group
+come up with a positive
+
+ align:start position:0%
+come up with a positive
+ 
+
+ align:start position:0%
+come up with a positive
+um uh definition from that I don't think
+
+ align:start position:0%
+um uh definition from that I don't think
+ 
+
+ align:start position:0%
+um uh definition from that I don't think
+our group came into agreement good let's
+
+ align:start position:0%
+our group came into agreement good let's
+ 
+
+ align:start position:0%
+our group came into agreement good let's
+hear something is a note as a
+
+ align:start position:0%
+hear something is a note as a
+ 
+
+ align:start position:0%
+hear something is a note as a
+representation of an instance of stri in
+
+ align:start position:0%
+representation of an instance of stri in
+ 
+
+ align:start position:0%
+representation of an instance of stri in
+something an instance of striking
+
+ align:start position:0%
+something an instance of striking
+ 
+
+ align:start position:0%
+something an instance of striking
+something okay anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so it's Matthew anybody um want
+
+ align:start position:0%
+um so it's Matthew anybody um want
+ 
+
+ align:start position:0%
+um so it's Matthew anybody um want
+to want to um go
+
+ align:start position:0%
+to want to um go
+ 
+
+ align:start position:0%
+to want to um go
+forward with that like sorry I can't
+
+ align:start position:0%
+forward with that like sorry I can't
+ 
+
+ align:start position:0%
+forward with that like sorry I can't
+talk and write something else at the
+
+ align:start position:0%
+talk and write something else at the
+ 
+
+ align:start position:0%
+talk and write something else at the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+anybody's that's um perfect to for out
+
+ align:start position:0%
+anybody's that's um perfect to for out
+ 
+
+ align:start position:0%
+anybody's that's um perfect to for out
+things while you're speaking uh anything
+
+ align:start position:0%
+things while you're speaking uh anything
+ 
+
+ align:start position:0%
+things while you're speaking uh anything
+with a pitch and a duration I think an
+
+ align:start position:0%
+with a pitch and a duration I think an
+ 
+
+ align:start position:0%
+with a pitch and a duration I think an
+airplane on a airline flight has its
+
+ align:start position:0%
+airplane on a airline flight has its
+ 
+
+ align:start position:0%
+airplane on a airline flight has its
+pitch and duration right so we I'll
+
+ align:start position:0%
+pitch and duration right so we I'll
+ 
+
+ align:start position:0%
+pitch and duration right so we I'll
+start calling them Notes too no I'm just
+
+ align:start position:0%
+start calling them Notes too no I'm just
+ 
+
+ align:start position:0%
+start calling them Notes too no I'm just
+just having fun just trying to just
+
+ align:start position:0%
+just having fun just trying to just
+ 
+
+ align:start position:0%
+just having fun just trying to just
+trying to get us to think so we can
+
+ align:start position:0%
+trying to get us to think so we can
+ 
+
+ align:start position:0%
+trying to get us to think so we can
+start making things how we're going to
+
+ align:start position:0%
+start making things how we're going to
+ 
+
+ align:start position:0%
+start making things how we're going to
+make this happen for a computer I I like
+
+ align:start position:0%
+make this happen for a computer I I like
+ 
+
+ align:start position:0%
+make this happen for a computer I I like
+both of these an instance of striking
+
+ align:start position:0%
+both of these an instance of striking
+ 
+
+ align:start position:0%
+both of these an instance of striking
+something so yeah I feel like that
+
+ align:start position:0%
+something so yeah I feel like that
+ 
+
+ align:start position:0%
+something so yeah I feel like that
+doesn't really apply to certain
+
+ align:start position:0%
+doesn't really apply to certain
+ 
+
+ align:start position:0%
+doesn't really apply to certain
+instruments like violence for example
+
+ align:start position:0%
+instruments like violence for example
+ 
+
+ align:start position:0%
+instruments like violence for example
+you don't have to anything to issue next
+
+ align:start position:0%
+you don't have to anything to issue next
+ 
+
+ align:start position:0%
+you don't have to anything to issue next
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+good so it's somebody who hasn't spoken
+
+ align:start position:0%
+good so it's somebody who hasn't spoken
+ 
+
+ align:start position:0%
+good so it's somebody who hasn't spoken
+want to defend an instance of striking
+
+ align:start position:0%
+want to defend an instance of striking
+ 
+
+ align:start position:0%
+want to defend an instance of striking
+something as applying to the
+
+ align:start position:0%
+something as applying to the
+ 
+
+ align:start position:0%
+something as applying to the
+violin yeah go ahead Vanessa so I mean
+
+ align:start position:0%
+violin yeah go ahead Vanessa so I mean
+ 
+
+ align:start position:0%
+violin yeah go ahead Vanessa so I mean
+if you want to be annoying you can use
+
+ align:start position:0%
+if you want to be annoying you can use
+ 
+
+ align:start position:0%
+if you want to be annoying you can use
+like a version of striking in a much
+
+ align:start position:0%
+like a version of striking in a much
+ 
+
+ align:start position:0%
+like a version of striking in a much
+more General sense necessarily be like
+
+ align:start position:0%
+more General sense necessarily be like
+ 
+
+ align:start position:0%
+more General sense necessarily be like
+hitting anything just be when you're
+
+ align:start position:0%
+hitting anything just be when you're
+ 
+
+ align:start position:0%
+hitting anything just be when you're
+moving a bow across strings you can say
+
+ align:start position:0%
+moving a bow across strings you can say
+ 
+
+ align:start position:0%
+moving a bow across strings you can say
+that that counts as like a form of
+
+ align:start position:0%
+that that counts as like a form of
+ 
+
+ align:start position:0%
+that that counts as like a form of
+striking even if it's not like the most
+
+ align:start position:0%
+striking even if it's not like the most
+ 
+
+ align:start position:0%
+striking even if it's not like the most
+straightforward definition okay about a
+
+ align:start position:0%
+straightforward definition okay about a
+ 
+
+ align:start position:0%
+straightforward definition okay about a
+wind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instrument
+
+ align:start position:0%
+instrument
+ 
+
+ align:start position:0%
+instrument
+okay who's you y all most of you are are
+
+ align:start position:0%
+okay who's you y all most of you are are
+ 
+
+ align:start position:0%
+okay who's you y all most of you are are
+Juniors and seniors and things so y all
+
+ align:start position:0%
+Juniors and seniors and things so y all
+ 
+
+ align:start position:0%
+Juniors and seniors and things so y all
+most of you all have gotten through your
+
+ align:start position:0%
+most of you all have gotten through your
+ 
+
+ align:start position:0%
+most of you all have gotten through your
+um physics mechanics uh General
+
+ align:start position:0%
+um physics mechanics uh General
+ 
+
+ align:start position:0%
+um physics mechanics uh General
+Institute requirement anybody want to
+
+ align:start position:0%
+Institute requirement anybody want to
+ 
+
+ align:start position:0%
+Institute requirement anybody want to
+say how do what's how's sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+produced or perceived maybe moving
+
+ align:start position:0%
+produced or perceived maybe moving
+ 
+
+ align:start position:0%
+produced or perceived maybe moving
+vibrations of air vibrations of air good
+
+ align:start position:0%
+vibrations of air vibrations of air good
+ 
+
+ align:start position:0%
+vibrations of air vibrations of air good
+and and so there's a lot of air
+
+ align:start position:0%
+and and so there's a lot of air
+ 
+
+ align:start position:0%
+and and so there's a lot of air
+vibrating way way down the street why
+
+ align:start position:0%
+vibrating way way down the street why
+ 
+
+ align:start position:0%
+vibrating way way down the street why
+why do I not hear
+
+ align:start position:0%
+why do I not hear
+ 
+
+ align:start position:0%
+why do I not hear
+it the inverse Square law yes that might
+
+ align:start position:0%
+it the inverse Square law yes that might
+ 
+
+ align:start position:0%
+it the inverse Square law yes that might
+that might be but what what is not
+
+ align:start position:0%
+that might be but what what is not
+ 
+
+ align:start position:0%
+that might be but what what is not
+happening with the movement of air it's
+
+ align:start position:0%
+happening with the movement of air it's
+ 
+
+ align:start position:0%
+happening with the movement of air it's
+not reaching our ears it's not reaching
+
+ align:start position:0%
+not reaching our ears it's not reaching
+ 
+
+ align:start position:0%
+not reaching our ears it's not reaching
+our ears it's
+
+ align:start position:0%
+our ears it's
+ 
+
+ align:start position:0%
+our ears it's
+not what what what is the what is one of
+
+ align:start position:0%
+not what what what is the what is one of
+ 
+
+ align:start position:0%
+not what what what is the what is one of
+the first thing it reaches in our ears e
+
+ align:start position:0%
+the first thing it reaches in our ears e
+ 
+
+ align:start position:0%
+the first thing it reaches in our ears e
+drum ear drum oh so maybe there is a way
+
+ align:start position:0%
+drum ear drum oh so maybe there is a way
+ 
+
+ align:start position:0%
+drum ear drum oh so maybe there is a way
+so we could say an instance of something
+
+ align:start position:0%
+so we could say an instance of something
+ 
+
+ align:start position:0%
+so we could say an instance of something
+striking something um such as air
+
+ align:start position:0%
+striking something um such as air
+ 
+
+ align:start position:0%
+striking something um such as air
+striking a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drum
+
+ align:start position:0%
+drum
+ 
+
+ align:start position:0%
+drum
+before half an hour of you ago how many
+
+ align:start position:0%
+before half an hour of you ago how many
+ 
+
+ align:start position:0%
+before half an hour of you ago how many
+of you would have said that that's a
+
+ align:start position:0%
+of you would have said that that's a
+ 
+
+ align:start position:0%
+of you would have said that that's a
+note
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+striking it doesn't need a strike you
+
+ align:start position:0%
+striking it doesn't need a strike you
+ 
+
+ align:start position:0%
+striking it doesn't need a strike you
+said it's a representation of oh it's a
+
+ align:start position:0%
+said it's a representation of oh it's a
+ 
+
+ align:start position:0%
+said it's a representation of oh it's a
+representation of something striking
+
+ align:start position:0%
+representation of something striking
+ 
+
+ align:start position:0%
+representation of something striking
+good good okay any other things that we
+
+ align:start position:0%
+good good okay any other things that we
+ 
+
+ align:start position:0%
+good good okay any other things that we
+want to do with confusing confusing
+
+ align:start position:0%
+want to do with confusing confusing
+ 
+
+ align:start position:0%
+want to do with confusing confusing
+definitions before we get to the one of
+
+ align:start position:0%
+definitions before we get to the one of
+ 
+
+ align:start position:0%
+definitions before we get to the one of
+the points of this
+
+ align:start position:0%
+the points of this
+ 
+
+ align:start position:0%
+the points of this
+class any other really um great
+
+ align:start position:0%
+class any other really um great
+ 
+
+ align:start position:0%
+class any other really um great
+beautiful things that wasn't covered
+
+ align:start position:0%
+beautiful things that wasn't covered
+ 
+
+ align:start position:0%
+beautiful things that wasn't covered
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the way I I forgot to do this part on
+
+ align:start position:0%
+by the way I I forgot to do this part on
+ 
+
+ align:start position:0%
+by the way I I forgot to do this part on
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um how many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notes okay so if there's something when
+
+ align:start position:0%
+notes okay so if there's something when
+ 
+
+ align:start position:0%
+notes okay so if there's something when
+you play that the three different sounds
+
+ align:start position:0%
+you play that the three different sounds
+ 
+
+ align:start position:0%
+you play that the three different sounds
+being done could be considered three
+
+ align:start position:0%
+being done could be considered three
+ 
+
+ align:start position:0%
+being done could be considered three
+different notes so is a chord a note or
+
+ align:start position:0%
+different notes so is a chord a note or
+ 
+
+ align:start position:0%
+different notes so is a chord a note or
+is a chord a bunch of notes not or is a
+
+ align:start position:0%
+is a chord a bunch of notes not or is a
+ 
+
+ align:start position:0%
+is a chord a bunch of notes not or is a
+chord something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else I'd say this because we're going to
+
+ align:start position:0%
+else I'd say this because we're going to
+ 
+
+ align:start position:0%
+else I'd say this because we're going to
+spend the a lot of the first problem set
+
+ align:start position:0%
+spend the a lot of the first problem set
+ 
+
+ align:start position:0%
+spend the a lot of the first problem set
+in the next week is going to be on how
+
+ align:start position:0%
+in the next week is going to be on how
+ 
+
+ align:start position:0%
+in the next week is going to be on how
+to represent music for the computers for
+
+ align:start position:0%
+to represent music for the computers for
+ 
+
+ align:start position:0%
+to represent music for the computers for
+the computers as as
+
+ align:start position:0%
+the computers as as
+ 
+
+ align:start position:0%
+the computers as as
+1960s for a computer so how do we um how
+
+ align:start position:0%
+1960s for a computer so how do we um how
+ 
+
+ align:start position:0%
+1960s for a computer so how do we um how
+do what kinds of choices will lead us
+
+ align:start position:0%
+do what kinds of choices will lead us
+ 
+
+ align:start position:0%
+do what kinds of choices will lead us
+into bad places fastest and which Ones
+
+ align:start position:0%
+into bad places fastest and which Ones
+ 
+
+ align:start position:0%
+into bad places fastest and which Ones
+Will Keep Us in good and useful places
+
+ align:start position:0%
+Will Keep Us in good and useful places
+ 
+
+ align:start position:0%
+Will Keep Us in good and useful places
+for the longest amount of time notice I
+
+ align:start position:0%
+for the longest amount of time notice I
+ 
+
+ align:start position:0%
+for the longest amount of time notice I
+didn't say which ones will never lead
+
+ align:start position:0%
+didn't say which ones will never lead
+ 
+
+ align:start position:0%
+didn't say which ones will never lead
+you astray because you're always every
+
+ align:start position:0%
+you astray because you're always every
+ 
+
+ align:start position:0%
+you astray because you're always every
+definition that you're going to encode
+
+ align:start position:0%
+definition that you're going to encode
+ 
+
+ align:start position:0%
+definition that you're going to encode
+into a computer at some point is going
+
+ align:start position:0%
+into a computer at some point is going
+ 
+
+ align:start position:0%
+into a computer at some point is going
+to completely screw up something for
+
+ align:start position:0%
+to completely screw up something for
+ 
+
+ align:start position:0%
+to completely screw up something for
+instance
+
+ align:start position:0%
+instance
+ 
+
+ align:start position:0%
+instance
+um we might say one
+
+ align:start position:0%
+um we might say one
+ 
+
+ align:start position:0%
+um we might say one
+note add a little ornament to
+
+ align:start position:0%
+note add a little ornament to
+ 
+
+ align:start position:0%
+note add a little ornament to
+it still one note in some certain senses
+
+ align:start position:0%
+it still one note in some certain senses
+ 
+
+ align:start position:0%
+it still one note in some certain senses
+but y that kind of turn can really
+
+ align:start position:0%
+but y that kind of turn can really
+ 
+
+ align:start position:0%
+but y that kind of turn can really
+change everything so those are going to
+
+ align:start position:0%
+change everything so those are going to
+ 
+
+ align:start position:0%
+change everything so those are going to
+be coming up over and over and over
+
+ align:start position:0%
+be coming up over and over and over
+ 
+
+ align:start position:0%
+be coming up over and over and over
+again how to represent for a computer
+
+ align:start position:0%
+again how to represent for a computer
+ 
+
+ align:start position:0%
+again how to represent for a computer
+and whether or not any one
+
+ align:start position:0%
+and whether or not any one
+ 
+
+ align:start position:0%
+and whether or not any one
+representation is going to work um
+
+ align:start position:0%
+representation is going to work um
+ 
+
+ align:start position:0%
+representation is going to work um
+somebody said a note is a representation
+
+ align:start position:0%
+somebody said a note is a representation
+ 
+
+ align:start position:0%
+somebody said a note is a representation
+of anything with a pitch and a
+
+ align:start position:0%
+of anything with a pitch and a
+ 
+
+ align:start position:0%
+of anything with a pitch and a
+duration um there are some people who
+
+ align:start position:0%
+duration um there are some people who
+ 
+
+ align:start position:0%
+duration um there are some people who
+use the term note and the term pitch
+
+ align:start position:0%
+use the term note and the term pitch
+ 
+
+ align:start position:0%
+use the term note and the term pitch
+absolutely interchangeably
+
+ align:start position:0%
+absolutely interchangeably
+ 
+
+ align:start position:0%
+absolutely interchangeably
+and I do it sometimes also you what
+
+ align:start position:0%
+and I do it sometimes also you what
+ 
+
+ align:start position:0%
+and I do it sometimes also you what
+pitch was that what note what note did
+
+ align:start position:0%
+pitch was that what note what note did
+ 
+
+ align:start position:0%
+pitch was that what note what note did
+you play um things and other people use
+
+ align:start position:0%
+you play um things and other people use
+ 
+
+ align:start position:0%
+you play um things and other people use
+a note to mean the pitch and the
+
+ align:start position:0%
+a note to mean the pitch and the
+ 
+
+ align:start position:0%
+a note to mean the pitch and the
+duration as two different
+
+ align:start position:0%
+duration as two different
+ 
+
+ align:start position:0%
+duration as two different
+entities now
+
+ align:start position:0%
+entities now
+ 
+
+ align:start position:0%
+entities now
+obviously that also leads to certain
+
+ align:start position:0%
+obviously that also leads to certain
+ 
+
+ align:start position:0%
+obviously that also leads to certain
+contradictions I would hope that we
+
+ align:start position:0%
+contradictions I would hope that we
+ 
+
+ align:start position:0%
+contradictions I would hope that we
+think that an eighth note is a
+
+ align:start position:0%
+think that an eighth note is a
+ 
+
+ align:start position:0%
+think that an eighth note is a
+note right I mean it has the word note
+
+ align:start position:0%
+note right I mean it has the word note
+ 
+
+ align:start position:0%
+note right I mean it has the word note
+in its name we're not we're not talking
+
+ align:start position:0%
+in its name we're not we're not talking
+ 
+
+ align:start position:0%
+in its name we're not we're not talking
+about uh Quavers in in Britain I mean at
+
+ align:start position:0%
+about uh Quavers in in Britain I mean at
+ 
+
+ align:start position:0%
+about uh Quavers in in Britain I mean at
+least here in good old us OFA we put the
+
+ align:start position:0%
+least here in good old us OFA we put the
+ 
+
+ align:start position:0%
+least here in good old us OFA we put the
+word note in our eighth notes but by
+
+ align:start position:0%
+word note in our eighth notes but by
+ 
+
+ align:start position:0%
+word note in our eighth notes but by
+this definition pitch and duration and
+
+ align:start position:0%
+this definition pitch and duration and
+ 
+
+ align:start position:0%
+this definition pitch and duration and
+eighth note itself is not a
+
+ align:start position:0%
+eighth note itself is not a
+ 
+
+ align:start position:0%
+eighth note itself is not a
+note because it doesn't have a pitch so
+
+ align:start position:0%
+note because it doesn't have a pitch so
+ 
+
+ align:start position:0%
+note because it doesn't have a pitch so
+we're going to be finding that we're
+
+ align:start position:0%
+we're going to be finding that we're
+ 
+
+ align:start position:0%
+we're going to be finding that we're
+going to going back and forth quite
+
+ align:start position:0%
+going to going back and forth quite
+ 
+
+ align:start position:0%
+going to going back and forth quite
+often now let's um your problem set is
+
+ align:start position:0%
+often now let's um your problem set is
+ 
+
+ align:start position:0%
+often now let's um your problem set is
+going to be dealing with certain
+
+ align:start position:0%
+going to be dealing with certain
+ 
+
+ align:start position:0%
+going to be dealing with certain
+representations of pitch at least the
+
+ align:start position:0%
+representations of pitch at least the
+ 
+
+ align:start position:0%
+representations of pitch at least the
+non duration part of something I I will
+
+ align:start position:0%
+non duration part of something I I will
+ 
+
+ align:start position:0%
+non duration part of something I I will
+say uh I some will pop ahead when when
+
+ align:start position:0%
+say uh I some will pop ahead when when
+ 
+
+ align:start position:0%
+say uh I some will pop ahead when when
+the um when the lecture is getting too
+
+ align:start position:0%
+the um when the lecture is getting too
+ 
+
+ align:start position:0%
+the um when the lecture is getting too
+cerebral and things like that um in
+
+ align:start position:0%
+cerebral and things like that um in
+ 
+
+ align:start position:0%
+cerebral and things like that um in
+music 21 the software we're going to be
+
+ align:start position:0%
+music 21 the software we're going to be
+ 
+
+ align:start position:0%
+music 21 the software we're going to be
+using quite often this is probably the
+
+ align:start position:0%
+using quite often this is probably the
+ 
+
+ align:start position:0%
+using quite often this is probably the
+best closest definition to how music 21
+
+ align:start position:0%
+best closest definition to how music 21
+ 
+
+ align:start position:0%
+best closest definition to how music 21
+Associates um things it's something with
+
+ align:start position:0%
+Associates um things it's something with
+ 
+
+ align:start position:0%
+Associates um things it's something with
+a conceived of single pitch and it
+
+ align:start position:0%
+a conceived of single pitch and it
+ 
+
+ align:start position:0%
+a conceived of single pitch and it
+conceived of single
+
+ align:start position:0%
+conceived of single
+ 
+
+ align:start position:0%
+conceived of single
+duration and that might mean that
+
+ align:start position:0%
+duration and that might mean that
+ 
+
+ align:start position:0%
+duration and that might mean that
+something like this is conceived of as
+
+ align:start position:0%
+something like this is conceived of as
+ 
+
+ align:start position:0%
+something like this is conceived of as
+having a single pitch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or this is conceived of as having a
+
+ align:start position:0%
+or this is conceived of as having a
+ 
+
+ align:start position:0%
+or this is conceived of as having a
+single pitch that's a Trill sign um but
+
+ align:start position:0%
+single pitch that's a Trill sign um but
+ 
+
+ align:start position:0%
+single pitch that's a Trill sign um but
+there are other times when we don't
+
+ align:start position:0%
+there are other times when we don't
+ 
+
+ align:start position:0%
+there are other times when we don't
+conceive of something as a single pitch
+
+ align:start position:0%
+conceive of something as a single pitch
+ 
+
+ align:start position:0%
+conceive of something as a single pitch
+um and duration so let's talk about
+
+ align:start position:0%
+um and duration so let's talk about
+ 
+
+ align:start position:0%
+um and duration so let's talk about
+representations of duration so we've
+
+ align:start position:0%
+representations of duration so we've
+ 
+
+ align:start position:0%
+representations of duration so we've
+gone from the trick questions and now um
+
+ align:start position:0%
+gone from the trick questions and now um
+ 
+
+ align:start position:0%
+gone from the trick questions and now um
+now I hope I haven't like uh ended your
+
+ align:start position:0%
+now I hope I haven't like uh ended your
+ 
+
+ align:start position:0%
+now I hope I haven't like uh ended your
+faith in humanity in the class now I
+
+ align:start position:0%
+faith in humanity in the class now I
+ 
+
+ align:start position:0%
+faith in humanity in the class now I
+want to go to some a little bit um more
+
+ align:start position:0%
+want to go to some a little bit um more
+ 
+
+ align:start position:0%
+want to go to some a little bit um more
+thinking about standard situations and
+
+ align:start position:0%
+thinking about standard situations and
+ 
+
+ align:start position:0%
+thinking about standard situations and
+not weird tremolos and gandos and all
+
+ align:start position:0%
+not weird tremolos and gandos and all
+ 
+
+ align:start position:0%
+not weird tremolos and gandos and all
+that stuff um want to think about how
+
+ align:start position:0%
+that stuff um want to think about how
+ 
+
+ align:start position:0%
+that stuff um want to think about how
+are some ways you might represent pitch
+
+ align:start position:0%
+are some ways you might represent pitch
+ 
+
+ align:start position:0%
+are some ways you might represent pitch
+uh duration for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computer and we'll
+
+ align:start position:0%
+computer and we'll
+ 
+
+ align:start position:0%
+computer and we'll
+say um
+
+ align:start position:0%
+say um
+ 
+
+ align:start position:0%
+say um
+I'm going to put the term here
+
+ align:start position:0%
+I'm going to put the term here
+ 
+
+ align:start position:0%
+I'm going to put the term here
+musical as if somehow there's a
+
+ align:start position:0%
+musical as if somehow there's a
+ 
+
+ align:start position:0%
+musical as if somehow there's a
+different world of time in music than
+
+ align:start position:0%
+different world of time in music than
+ 
+
+ align:start position:0%
+different world of time in music than
+there is in everywhere else it's sort of
+
+ align:start position:0%
+there is in everywhere else it's sort of
+ 
+
+ align:start position:0%
+there is in everywhere else it's sort of
+there's three kinds of time in the world
+
+ align:start position:0%
+there's three kinds of time in the world
+ 
+
+ align:start position:0%
+there's three kinds of time in the world
+there's one on your clock there's one on
+
+ align:start position:0%
+there's one on your clock there's one on
+ 
+
+ align:start position:0%
+there's one on your clock there's one on
+music and there's the one they teach you
+
+ align:start position:0%
+music and there's the one they teach you
+ 
+
+ align:start position:0%
+music and there's the one they teach you
+about in relativity class that you hope
+
+ align:start position:0%
+about in relativity class that you hope
+ 
+
+ align:start position:0%
+about in relativity class that you hope
+you never hear again right um so
+
+ align:start position:0%
+you never hear again right um so
+ 
+
+ align:start position:0%
+you never hear again right um so
+thinking about this what are some ways
+
+ align:start position:0%
+thinking about this what are some ways
+ 
+
+ align:start position:0%
+thinking about this what are some ways
+that you might do I think we've we've
+
+ align:start position:0%
+that you might do I think we've we've
+ 
+
+ align:start position:0%
+that you might do I think we've we've
+grouped enough I think people want to be
+
+ align:start position:0%
+grouped enough I think people want to be
+ 
+
+ align:start position:0%
+grouped enough I think people want to be
+able to shout and some people whose
+
+ align:start position:0%
+able to shout and some people whose
+ 
+
+ align:start position:0%
+able to shout and some people whose
+names are toward the beginning and end
+
+ align:start position:0%
+names are toward the beginning and end
+ 
+
+ align:start position:0%
+names are toward the beginning and end
+of the alphabet might want to be able to
+
+ align:start position:0%
+of the alphabet might want to be able to
+ 
+
+ align:start position:0%
+of the alphabet might want to be able to
+say so what are some of the things that
+
+ align:start position:0%
+say so what are some of the things that
+ 
+
+ align:start position:0%
+say so what are some of the things that
+a musical duration representation might
+
+ align:start position:0%
+a musical duration representation might
+ 
+
+ align:start position:0%
+a musical duration representation might
+include okay I think that's that's good
+
+ align:start position:0%
+include okay I think that's that's good
+ 
+
+ align:start position:0%
+include okay I think that's that's good
+enough I I I think it's it's sort of
+
+ align:start position:0%
+enough I I I think it's it's sort of
+ 
+
+ align:start position:0%
+enough I I I think it's it's sort of
+like doing jumping jacks you just you
+
+ align:start position:0%
+like doing jumping jacks you just you
+ 
+
+ align:start position:0%
+like doing jumping jacks you just you
+know sort of get get the thinking
+
+ align:start position:0%
+know sort of get get the thinking
+ 
+
+ align:start position:0%
+know sort of get get the thinking
+calisthenics going so um what what's
+
+ align:start position:0%
+calisthenics going so um what what's
+ 
+
+ align:start position:0%
+calisthenics going so um what what's
+some of the things that you might do for
+
+ align:start position:0%
+some of the things that you might do for
+ 
+
+ align:start position:0%
+some of the things that you might do for
+representing duration Jordan said saying
+
+ align:start position:0%
+representing duration Jordan said saying
+ 
+
+ align:start position:0%
+representing duration Jordan said saying
+yeah yeah like seconds or seconds good
+
+ align:start position:0%
+yeah yeah like seconds or seconds good
+ 
+
+ align:start position:0%
+yeah yeah like seconds or seconds good
+now let's think about it um
+
+ align:start position:0%
+now let's think about it um
+ 
+
+ align:start position:0%
+now let's think about it um
+we we'll make our default assumption for
+
+ align:start position:0%
+we we'll make our default assumption for
+ 
+
+ align:start position:0%
+we we'll make our default assumption for
+this class that we're thinking in Python
+
+ align:start position:0%
+this class that we're thinking in Python
+ 
+
+ align:start position:0%
+this class that we're thinking in Python
+of course obviously any halfway decent
+
+ align:start position:0%
+of course obviously any halfway decent
+ 
+
+ align:start position:0%
+of course obviously any halfway decent
+programming language can go for another
+
+ align:start position:0%
+programming language can go for another
+ 
+
+ align:start position:0%
+programming language can go for another
+so how are we going to represent seconds
+
+ align:start position:0%
+so how are we going to represent seconds
+ 
+
+ align:start position:0%
+so how are we going to represent seconds
+for a note yeah go ahead oh was that I
+
+ align:start position:0%
+for a note yeah go ahead oh was that I
+ 
+
+ align:start position:0%
+for a note yeah go ahead oh was that I
+guess like typically don't we use like
+
+ align:start position:0%
+guess like typically don't we use like
+ 
+
+ align:start position:0%
+guess like typically don't we use like
+TI and that kind of like well we'll get
+
+ align:start position:0%
+TI and that kind of like well we'll get
+ 
+
+ align:start position:0%
+TI and that kind of like well we'll get
+to that keep that word there for a
+
+ align:start position:0%
+to that keep that word there for a
+ 
+
+ align:start position:0%
+to that keep that word there for a
+second great but what kind of um what
+
+ align:start position:0%
+second great but what kind of um what
+ 
+
+ align:start position:0%
+second great but what kind of um what
+kind of is string a good
+
+ align:start position:0%
+kind of is string a good
+ 
+
+ align:start position:0%
+kind of is string a good
+one array how are we going to represent
+
+ align:start position:0%
+one array how are we going to represent
+ 
+
+ align:start position:0%
+one array how are we going to represent
+seconds yeah go ahead like a float float
+
+ align:start position:0%
+seconds yeah go ahead like a float float
+ 
+
+ align:start position:0%
+seconds yeah go ahead like a float float
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good why not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+int yeah just shout out yep go ahead
+
+ align:start position:0%
+int yeah just shout out yep go ahead
+ 
+
+ align:start position:0%
+int yeah just shout out yep go ahead
+because we can have in between like good
+
+ align:start position:0%
+because we can have in between like good
+ 
+
+ align:start position:0%
+because we can have in between like good
+good we can have in between great super
+
+ align:start position:0%
+good we can have in between great super
+ 
+
+ align:start position:0%
+good we can have in between great super
+um other other things I'm going to uh
+
+ align:start position:0%
+um other other things I'm going to uh
+ 
+
+ align:start position:0%
+um other other things I'm going to uh
+other things you might want ways you
+
+ align:start position:0%
+other things you might want ways you
+ 
+
+ align:start position:0%
+other things you might want ways you
+might want to represent
+
+ align:start position:0%
+might want to represent
+ 
+
+ align:start position:0%
+might want to represent
+duration yeah go ahead Matthew fraction
+
+ align:start position:0%
+duration yeah go ahead Matthew fraction
+ 
+
+ align:start position:0%
+duration yeah go ahead Matthew fraction
+fraction good that fractions seconds as
+
+ align:start position:0%
+fraction good that fractions seconds as
+ 
+
+ align:start position:0%
+fraction good that fractions seconds as
+a fraction or or so thinking both uh
+
+ align:start position:0%
+a fraction or or so thinking both uh
+ 
+
+ align:start position:0%
+a fraction or or so thinking both uh
+represent section seconds as a fraction
+
+ align:start position:0%
+represent section seconds as a fraction
+ 
+
+ align:start position:0%
+represent section seconds as a fraction
+instead of a float so you don't have the
+
+ align:start position:0%
+instead of a float so you don't have the
+ 
+
+ align:start position:0%
+instead of a float so you don't have the
+Precision issues of a float uh um I also
+
+ align:start position:0%
+Precision issues of a float uh um I also
+ 
+
+ align:start position:0%
+Precision issues of a float uh um I also
+think it might make sense to represent
+
+ align:start position:0%
+think it might make sense to represent
+ 
+
+ align:start position:0%
+think it might make sense to represent
+it as a beat and fr okay okay well okay
+
+ align:start position:0%
+it as a beat and fr okay okay well okay
+ 
+
+ align:start position:0%
+it as a beat and fr okay okay well okay
+we go that's that's two things we have
+
+ align:start position:0%
+we go that's that's two things we have
+ 
+
+ align:start position:0%
+we go that's that's two things we have
+beat there good good we'll keep keep
+
+ align:start position:0%
+beat there good good we'll keep keep
+ 
+
+ align:start position:0%
+beat there good good we'll keep keep
+going what are some other things CU um
+
+ align:start position:0%
+going what are some other things CU um
+ 
+
+ align:start position:0%
+going what are some other things CU um
+that we might do yeah I was also
+
+ align:start position:0%
+that we might do yeah I was also
+ 
+
+ align:start position:0%
+that we might do yeah I was also
+thinking fraction but like fraction of
+
+ align:start position:0%
+thinking fraction but like fraction of
+ 
+
+ align:start position:0%
+thinking fraction but like fraction of
+whatever measure you're looking at
+
+ align:start position:0%
+whatever measure you're looking at
+ 
+
+ align:start position:0%
+whatever measure you're looking at
+fraction of measure so if you have like
+
+ align:start position:0%
+fraction of measure so if you have like
+ 
+
+ align:start position:0%
+fraction of measure so if you have like
+a three four
+
+ align:start position:0%
+a three four
+ 
+
+ align:start position:0%
+a three four
+measure and you had a half note that
+
+ align:start position:0%
+measure and you had a half note that
+ 
+
+ align:start position:0%
+measure and you had a half note that
+would be 2/3 of the yep okay so good 2/3
+
+ align:start position:0%
+would be 2/3 of the yep okay so good 2/3
+ 
+
+ align:start position:0%
+would be 2/3 of the yep okay so good 2/3
+that's a particular place where the
+
+ align:start position:0%
+that's a particular place where the
+ 
+
+ align:start position:0%
+that's a particular place where the
+difference between float accuracy and
+
+ align:start position:0%
+difference between float accuracy and
+ 
+
+ align:start position:0%
+difference between float accuracy and
+fraction uh came can can be very very
+
+ align:start position:0%
+fraction uh came can can be very very
+ 
+
+ align:start position:0%
+fraction uh came can can be very very
+important good our beat and fraction of
+
+ align:start position:0%
+important good our beat and fraction of
+ 
+
+ align:start position:0%
+important good our beat and fraction of
+measure um basically saying the same
+
+ align:start position:0%
+measure um basically saying the same
+ 
+
+ align:start position:0%
+measure um basically saying the same
+thing uh with a reciprocal relationship
+
+ align:start position:0%
+thing uh with a reciprocal relationship
+ 
+
+ align:start position:0%
+thing uh with a reciprocal relationship
+can somebody come up with a reason not
+
+ align:start position:0%
+can somebody come up with a reason not
+ 
+
+ align:start position:0%
+can somebody come up with a reason not
+to yess I mean not necessarily because
+
+ align:start position:0%
+to yess I mean not necessarily because
+ 
+
+ align:start position:0%
+to yess I mean not necessarily because
+like something could be on the second
+
+ align:start position:0%
+like something could be on the second
+ 
+
+ align:start position:0%
+like something could be on the second
+beat and have like a duration of one or
+
+ align:start position:0%
+beat and have like a duration of one or
+ 
+
+ align:start position:0%
+beat and have like a duration of one or
+it could be a second beat and have a
+
+ align:start position:0%
+it could be a second beat and have a
+ 
+
+ align:start position:0%
+it could be a second beat and have a
+duration of Two And if it was a fraction
+
+ align:start position:0%
+duration of Two And if it was a fraction
+ 
+
+ align:start position:0%
+duration of Two And if it was a fraction
+of a measure their values would be okay
+
+ align:start position:0%
+of a measure their values would be okay
+ 
+
+ align:start position:0%
+of a measure their values would be okay
+good so we have beat as in what beat is
+
+ align:start position:0%
+good so we have beat as in what beat is
+ 
+
+ align:start position:0%
+good so we have beat as in what beat is
+it on and and that would be very
+
+ align:start position:0%
+it on and and that would be very
+ 
+
+ align:start position:0%
+it on and and that would be very
+different um if we thinking about how
+
+ align:start position:0%
+different um if we thinking about how
+ 
+
+ align:start position:0%
+different um if we thinking about how
+many beats does it last though because
+
+ align:start position:0%
+many beats does it last though because
+ 
+
+ align:start position:0%
+many beats does it last though because
+so thank you Vanessa fantastic um is
+
+ align:start position:0%
+so thank you Vanessa fantastic um is
+ 
+
+ align:start position:0%
+so thank you Vanessa fantastic um is
+that basically the same as what fraction
+
+ align:start position:0%
+that basically the same as what fraction
+ 
+
+ align:start position:0%
+that basically the same as what fraction
+of the measure is
+
+ align:start position:0%
+of the measure is
+ 
+
+ align:start position:0%
+of the measure is
+it thank I see Matthew but I want to
+
+ align:start position:0%
+it thank I see Matthew but I want to
+ 
+
+ align:start position:0%
+it thank I see Matthew but I want to
+want to get I think I'm going this way
+
+ align:start position:0%
+want to get I think I'm going this way
+ 
+
+ align:start position:0%
+want to get I think I'm going this way
+cuz I'm camera shy uh so let me let me
+
+ align:start position:0%
+cuz I'm camera shy uh so let me let me
+ 
+
+ align:start position:0%
+cuz I'm camera shy uh so let me let me
+lean in over here see if there's things
+
+ align:start position:0%
+lean in over here see if there's things
+ 
+
+ align:start position:0%
+lean in over here see if there's things
+are anyone want to who who says it's
+
+ align:start position:0%
+are anyone want to who who says it's
+ 
+
+ align:start position:0%
+are anyone want to who who says it's
+basically the same
+
+ align:start position:0%
+basically the same
+ 
+
+ align:start position:0%
+basically the same
+thing and we can go all the whole room
+
+ align:start position:0%
+thing and we can go all the whole room
+ 
+
+ align:start position:0%
+thing and we can go all the whole room
+who says it's it's it's could be quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different okay go ahead I guess it was
+
+ align:start position:0%
+different okay go ahead I guess it was
+ 
+
+ align:start position:0%
+different okay go ahead I guess it was
+like depends on what you define the beat
+
+ align:start position:0%
+like depends on what you define the beat
+ 
+
+ align:start position:0%
+like depends on what you define the beat
+as so it's like 58 time or something oh
+
+ align:start position:0%
+as so it's like 58 time or something oh
+ 
+
+ align:start position:0%
+as so it's like 58 time or something oh
+okay so five eight we'll say we'll do it
+
+ align:start position:0%
+okay so five eight we'll say we'll do it
+ 
+
+ align:start position:0%
+okay so five eight we'll say we'll do it
+as this I don't know if people know that
+
+ align:start position:0%
+as this I don't know if people know that
+ 
+
+ align:start position:0%
+as this I don't know if people know that
+symbol um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how many beats does this
+
+ align:start position:0%
+so how many beats does this
+ 
+
+ align:start position:0%
+so how many beats does this
+get two in some ways and how many this
+
+ align:start position:0%
+get two in some ways and how many this
+ 
+
+ align:start position:0%
+get two in some ways and how many this
+one three good and now give me another
+
+ align:start position:0%
+one three good and now give me another
+ 
+
+ align:start position:0%
+one three good and now give me another
+number that we could use instead of that
+
+ align:start position:0%
+number that we could use instead of that
+ 
+
+ align:start position:0%
+number that we could use instead of that
+for a lot of five8 yeah 106 106 yeah we
+
+ align:start position:0%
+for a lot of five8 yeah 106 106 yeah we
+ 
+
+ align:start position:0%
+for a lot of five8 yeah 106 106 yeah we
+could we could do any other good good we
+
+ align:start position:0%
+could we could do any other good good we
+ 
+
+ align:start position:0%
+could we could do any other good good we
+have an infinite number of non-reduced
+
+ align:start position:0%
+have an infinite number of non-reduced
+ 
+
+ align:start position:0%
+have an infinite number of non-reduced
+fractions we can do great I love that
+
+ align:start position:0%
+fractions we can do great I love that
+ 
+
+ align:start position:0%
+fractions we can do great I love that
+that um how about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this no I won't write that yet
+
+ align:start position:0%
+this no I won't write that yet
+ 
+
+ align:start position:0%
+this no I won't write that yet
+um how many beats does this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get three three is a good answer and
+
+ align:start position:0%
+get three three is a good answer and
+ 
+
+ align:start position:0%
+get three three is a good answer and
+there's another good answer one one from
+
+ align:start position:0%
+there's another good answer one one from
+ 
+
+ align:start position:0%
+there's another good answer one one from
+one one two right so how many beats does
+
+ align:start position:0%
+one one two right so how many beats does
+ 
+
+ align:start position:0%
+one one two right so how many beats does
+this get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's some ways of doing it when I
+
+ align:start position:0%
+so there's some ways of doing it when I
+ 
+
+ align:start position:0%
+so there's some ways of doing it when I
+put this symbol I'm saying I'm going to
+
+ align:start position:0%
+put this symbol I'm saying I'm going to
+ 
+
+ align:start position:0%
+put this symbol I'm saying I'm going to
+go one one two one two and they're
+
+ align:start position:0%
+go one one two one two and they're
+ 
+
+ align:start position:0%
+go one one two one two and they're
+they're not so a beat can actually
+
+ align:start position:0%
+they're not so a beat can actually
+ 
+
+ align:start position:0%
+they're not so a beat can actually
+change its length during a measure in
+
+ align:start position:0%
+change its length during a measure in
+ 
+
+ align:start position:0%
+change its length during a measure in
+some representation so this this is one
+
+ align:start position:0%
+some representation so this this is one
+ 
+
+ align:start position:0%
+some representation so this this is one
+of the ways I was thinking not exactly
+
+ align:start position:0%
+of the ways I was thinking not exactly
+ 
+
+ align:start position:0%
+of the ways I was thinking not exactly
+the same same thing but pretty pretty
+
+ align:start position:0%
+the same same thing but pretty pretty
+ 
+
+ align:start position:0%
+the same same thing but pretty pretty
+close good let's see what are some other
+
+ align:start position:0%
+close good let's see what are some other
+ 
+
+ align:start position:0%
+close good let's see what are some other
+ways we might represent duration for a
+
+ align:start position:0%
+ways we might represent duration for a
+ 
+
+ align:start position:0%
+ways we might represent duration for a
+computer
+
+ align:start position:0%
+computer
+ 
+
+ align:start position:0%
+computer
+I'm going to go back to the uh in just a
+
+ align:start position:0%
+I'm going to go back to the uh in just a
+ 
+
+ align:start position:0%
+I'm going to go back to the uh in just a
+little bit the um the names the some of
+
+ align:start position:0%
+little bit the um the names the some of
+ 
+
+ align:start position:0%
+little bit the um the names the some of
+the things I've heard otherwise I heard
+
+ align:start position:0%
+the things I've heard otherwise I heard
+ 
+
+ align:start position:0%
+the things I've heard otherwise I heard
+I heard something over here that um I
+
+ align:start position:0%
+I heard something over here that um I
+ 
+
+ align:start position:0%
+I heard something over here that um I
+think I think Adam or say one of you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Derek like an attribute like a DOT is
+
+ align:start position:0%
+Derek like an attribute like a DOT is
+ 
+
+ align:start position:0%
+Derek like an attribute like a DOT is
+like an attribute great so we might keep
+
+ align:start position:0%
+like an attribute great so we might keep
+ 
+
+ align:start position:0%
+like an attribute great so we might keep
+cheack of attributes like how many dots
+
+ align:start position:0%
+cheack of attributes like how many dots
+ 
+
+ align:start position:0%
+cheack of attributes like how many dots
+does it
+
+ align:start position:0%
+does it
+ 
+
+ align:start position:0%
+does it
+have good anything else like that thank
+
+ align:start position:0%
+have good anything else like that thank
+ 
+
+ align:start position:0%
+have good anything else like that thank
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+super yeah yeah you take a number for
+
+ align:start position:0%
+super yeah yeah you take a number for
+ 
+
+ align:start position:0%
+super yeah yeah you take a number for
+the nth note it is so if it's an eighth
+
+ align:start position:0%
+the nth note it is so if it's an eighth
+ 
+
+ align:start position:0%
+the nth note it is so if it's an eighth
+note you say eight okay dots would be an
+
+ align:start position:0%
+note you say eight okay dots would be an
+ 
+
+ align:start position:0%
+note you say eight okay dots would be an
+eight dot eight okay so we can represent
+
+ align:start position:0%
+eight dot eight okay so we can represent
+ 
+
+ align:start position:0%
+eight dot eight okay so we can represent
+it as now
+
+ align:start position:0%
+it as now
+ 
+
+ align:start position:0%
+it as now
+um eight dot works pretty well as a
+
+ align:start position:0%
+um eight dot works pretty well as a
+ 
+
+ align:start position:0%
+um eight dot works pretty well as a
+float but is there another way we might
+
+ align:start position:0%
+float but is there another way we might
+ 
+
+ align:start position:0%
+float but is there another way we might
+consider that if we're talking it works
+
+ align:start position:0%
+consider that if we're talking it works
+ 
+
+ align:start position:0%
+consider that if we're talking it works
+well as a string it works better as a
+
+ align:start position:0%
+well as a string it works better as a
+ 
+
+ align:start position:0%
+well as a string it works better as a
+string right because eight dot dot
+
+ align:start position:0%
+string right because eight dot dot
+ 
+
+ align:start position:0%
+string right because eight dot dot
+suddenly you're you're kind of getting a
+
+ align:start position:0%
+suddenly you're you're kind of getting a
+ 
+
+ align:start position:0%
+suddenly you're you're kind of getting a
+crash error right so that's one way you
+
+ align:start position:0%
+crash error right so that's one way you
+ 
+
+ align:start position:0%
+crash error right so that's one way you
+can do it um other
+
+ align:start position:0%
+can do it um other
+ 
+
+ align:start position:0%
+can do it um other
+ways and then so we would say 16 dot or
+
+ align:start position:0%
+ways and then so we would say 16 dot or
+ 
+
+ align:start position:0%
+ways and then so we would say 16 dot or
+something like that good good what are
+
+ align:start position:0%
+something like that good good what are
+ 
+
+ align:start position:0%
+something like that good good what are
+other attributes we might want to
+
+ align:start position:0%
+other attributes we might want to
+ 
+
+ align:start position:0%
+other attributes we might want to
+represent to talk about the duration of
+
+ align:start position:0%
+represent to talk about the duration of
+ 
+
+ align:start position:0%
+represent to talk about the duration of
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note are all notes um yeah you could you
+
+ align:start position:0%
+note are all notes um yeah you could you
+ 
+
+ align:start position:0%
+note are all notes um yeah you could you
+could also have things in the triplet
+
+ align:start position:0%
+could also have things in the triplet
+ 
+
+ align:start position:0%
+could also have things in the triplet
+you could have things in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triplet yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good you can also have things in a
+
+ align:start position:0%
+good you can also have things in a
+ 
+
+ align:start position:0%
+good you can also have things in a
+quintuplet right see if I can squeeze
+
+ align:start position:0%
+quintuplet right see if I can squeeze
+ 
+
+ align:start position:0%
+quintuplet right see if I can squeeze
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+in and you can also have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things in a triplet within a
+
+ align:start position:0%
+things in a triplet within a
+ 
+
+ align:start position:0%
+things in a triplet within a
+quintuplet this is called nested tuplets
+
+ align:start position:0%
+quintuplet this is called nested tuplets
+ 
+
+ align:start position:0%
+quintuplet this is called nested tuplets
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so I will guarantee you I have seen at
+
+ align:start position:0%
+so I will guarantee you I have seen at
+ 
+
+ align:start position:0%
+so I will guarantee you I have seen at
+least 20 representations of notated
+
+ align:start position:0%
+least 20 representations of notated
+ 
+
+ align:start position:0%
+least 20 representations of notated
+durations where the tuplet was
+
+ align:start position:0%
+durations where the tuplet was
+ 
+
+ align:start position:0%
+durations where the tuplet was
+originally created as an attribute and
+
+ align:start position:0%
+originally created as an attribute and
+ 
+
+ align:start position:0%
+originally created as an attribute and
+then it needed to be represented as a
+
+ align:start position:0%
+then it needed to be represented as a
+ 
+
+ align:start position:0%
+then it needed to be represented as a
+list array uh tupple something like that
+
+ align:start position:0%
+list array uh tupple something like that
+ 
+
+ align:start position:0%
+list array uh tupple something like that
+of a tupple of tuplets try to say that
+
+ align:start position:0%
+of a tupple of tuplets try to say that
+ 
+
+ align:start position:0%
+of a tupple of tuplets try to say that
+10 times fast um for a indeterminate
+
+ align:start position:0%
+10 times fast um for a indeterminate
+ 
+
+ align:start position:0%
+10 times fast um for a indeterminate
+number of tuplets that might be applied
+
+ align:start position:0%
+number of tuplets that might be applied
+ 
+
+ align:start position:0%
+number of tuplets that might be applied
+to a certain notes so these might be
+
+ align:start position:0%
+to a certain notes so these might be
+ 
+
+ align:start position:0%
+to a certain notes so these might be
+certain things good uh anything else
+
+ align:start position:0%
+certain things good uh anything else
+ 
+
+ align:start position:0%
+certain things good uh anything else
+that we might use to represent duration
+
+ align:start position:0%
+that we might use to represent duration
+ 
+
+ align:start position:0%
+that we might use to represent duration
+yeah go ahead certain markings like
+
+ align:start position:0%
+yeah go ahead certain markings like
+ 
+
+ align:start position:0%
+yeah go ahead certain markings like
+Stato or like good so we might have um
+
+ align:start position:0%
+Stato or like good so we might have um
+ 
+
+ align:start position:0%
+Stato or like good so we might have um
+modifying Ying uh I don't know
+
+ align:start position:0%
+modifying Ying uh I don't know
+ 
+
+ align:start position:0%
+modifying Ying uh I don't know
+articulations and expressions or
+
+ align:start position:0%
+articulations and expressions or
+ 
+
+ align:start position:0%
+articulations and expressions or
+markings well it's called markings
+
+ align:start position:0%
+markings well it's called markings
+ 
+
+ align:start position:0%
+markings well it's called markings
+because who knows what they are
+
+ align:start position:0%
+because who knows what they are
+ 
+
+ align:start position:0%
+because who knows what they are
+markings I'll make a formada on my eye
+
+ align:start position:0%
+markings I'll make a formada on my eye
+ 
+
+ align:start position:0%
+markings I'll make a formada on my eye
+good so um yeah we have our dots
+
+ align:start position:0%
+good so um yeah we have our dots
+ 
+
+ align:start position:0%
+good so um yeah we have our dots
+maybe more defin
+
+ align:start position:0%
+maybe more defin
+ 
+
+ align:start position:0%
+maybe more defin
+good so we can think of tudos that those
+
+ align:start position:0%
+good so we can think of tudos that those
+ 
+
+ align:start position:0%
+good so we can think of tudos that those
+affect the duration great now I don't
+
+ align:start position:0%
+affect the duration great now I don't
+ 
+
+ align:start position:0%
+affect the duration great now I don't
+want to um go too much further on this
+
+ align:start position:0%
+want to um go too much further on this
+ 
+
+ align:start position:0%
+want to um go too much further on this
+um now our music is on uh I was going to
+
+ align:start position:0%
+um now our music is on uh I was going to
+ 
+
+ align:start position:0%
+um now our music is on uh I was going to
+use obsolete formats a CD or streaming
+
+ align:start position:0%
+use obsolete formats a CD or streaming
+ 
+
+ align:start position:0%
+use obsolete formats a CD or streaming
+what are the most um useful
+
+ align:start position:0%
+what are the most um useful
+ 
+
+ align:start position:0%
+what are the most um useful
+representations of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+duration of notes let's
+
+ align:start position:0%
+duration of notes let's
+ 
+
+ align:start position:0%
+duration of notes let's
+say or other things which ones of these
+
+ align:start position:0%
+say or other things which ones of these
+ 
+
+ align:start position:0%
+say or other things which ones of these
+are most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful yeah I've heard you a couple
+
+ align:start position:0%
+useful yeah I've heard you a couple
+ 
+
+ align:start position:0%
+useful yeah I've heard you a couple
+times from you so great super Ms got it
+
+ align:start position:0%
+times from you so great super Ms got it
+ 
+
+ align:start position:0%
+times from you so great super Ms got it
+who else got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is this a great duration that you a
+
+ align:start position:0%
+one is this a great duration that you a
+ 
+
+ align:start position:0%
+one is this a great duration that you a
+representation that you're hearing of
+
+ align:start position:0%
+representation that you're hearing of
+ 
+
+ align:start position:0%
+representation that you're hearing of
+the duration of a note when you're
+
+ align:start position:0%
+the duration of a note when you're
+ 
+
+ align:start position:0%
+the duration of a note when you're
+listening to streaming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+music maybe not but but boy that could
+
+ align:start position:0%
+music maybe not but but boy that could
+ 
+
+ align:start position:0%
+music maybe not but but boy that could
+be useful for other things what about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds that's going to depend
+
+ align:start position:0%
+seconds that's going to depend
+ 
+
+ align:start position:0%
+seconds that's going to depend
+on let's say you're listening just for
+
+ align:start position:0%
+on let's say you're listening just for
+ 
+
+ align:start position:0%
+on let's say you're listening just for
+fun seconds very good no maybe not I
+
+ align:start position:0%
+fun seconds very good no maybe not I
+ 
+
+ align:start position:0%
+fun seconds very good no maybe not I
+don't I don't usually hear seconds but
+
+ align:start position:0%
+don't I don't usually hear seconds but
+ 
+
+ align:start position:0%
+don't I don't usually hear seconds but
+who's somebody who involved in the
+
+ align:start position:0%
+who's somebody who involved in the
+ 
+
+ align:start position:0%
+who's somebody who involved in the
+streaming music process who might really
+
+ align:start position:0%
+streaming music process who might really
+ 
+
+ align:start position:0%
+streaming music process who might really
+care about seconds of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notes I guess like computers the
+
+ align:start position:0%
+notes I guess like computers the
+ 
+
+ align:start position:0%
+notes I guess like computers the
+computers why yep and and but what kind
+
+ align:start position:0%
+computers why yep and and but what kind
+ 
+
+ align:start position:0%
+computers why yep and and but what kind
+of human might might be really
+
+ align:start position:0%
+of human might might be really
+ 
+
+ align:start position:0%
+of human might might be really
+interested yeah some editor person the
+
+ align:start position:0%
+interested yeah some editor person the
+ 
+
+ align:start position:0%
+interested yeah some editor person the
+editor yeah the um the person who's
+
+ align:start position:0%
+editor yeah the um the person who's
+ 
+
+ align:start position:0%
+editor yeah the um the person who's
+doing the recording editing they're
+
+ align:start position:0%
+doing the recording editing they're
+ 
+
+ align:start position:0%
+doing the recording editing they're
+always going to be thinking about uh
+
+ align:start position:0%
+always going to be thinking about uh
+ 
+
+ align:start position:0%
+always going to be thinking about uh
+okay let's clip from 22.4 6 to 22.0 48
+
+ align:start position:0%
+okay let's clip from 22.4 6 to 22.0 48
+ 
+
+ align:start position:0%
+okay let's clip from 22.4 6 to 22.0 48
+when somebody coughed and will will'll
+
+ align:start position:0%
+when somebody coughed and will will'll
+ 
+
+ align:start position:0%
+when somebody coughed and will will'll
+come up with something right so those
+
+ align:start position:0%
+come up with something right so those
+ 
+
+ align:start position:0%
+come up with something right so those
+types of things come up quite a bit in
+
+ align:start position:0%
+types of things come up quite a bit in
+ 
+
+ align:start position:0%
+types of things come up quite a bit in
+in that type of World um now what if
+
+ align:start position:0%
+in that type of World um now what if
+ 
+
+ align:start position:0%
+in that type of World um now what if
+we're um you've written your Great Piece
+
+ align:start position:0%
+we're um you've written your Great Piece
+ 
+
+ align:start position:0%
+we're um you've written your Great Piece
+it's already been recorded performed and
+
+ align:start position:0%
+it's already been recorded performed and
+ 
+
+ align:start position:0%
+it's already been recorded performed and
+things and now youve send it off to your
+
+ align:start position:0%
+things and now youve send it off to your
+ 
+
+ align:start position:0%
+things and now youve send it off to your
+sheet music publisher what are the ones
+
+ align:start position:0%
+sheet music publisher what are the ones
+ 
+
+ align:start position:0%
+sheet music publisher what are the ones
+they're going to Care the most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about's some what's a representation
+
+ align:start position:0%
+about's some what's a representation
+ 
+
+ align:start position:0%
+about's some what's a representation
+yeah John PCH dur duration the pitch and
+
+ align:start position:0%
+yeah John PCH dur duration the pitch and
+ 
+
+ align:start position:0%
+yeah John PCH dur duration the pitch and
+the duration good and how are they going
+
+ align:start position:0%
+the duration good and how are they going
+ 
+
+ align:start position:0%
+the duration good and how are they going
+to be thinking about duration how's the
+
+ align:start position:0%
+to be thinking about duration how's the
+ 
+
+ align:start position:0%
+to be thinking about duration how's the
+engraver um that's the person who who
+
+ align:start position:0%
+engraver um that's the person who who
+ 
+
+ align:start position:0%
+engraver um that's the person who who
+makes musical scores the term for that
+
+ align:start position:0%
+makes musical scores the term for that
+ 
+
+ align:start position:0%
+makes musical scores the term for that
+um what's what's the engraver what's she
+
+ align:start position:0%
+um what's what's the engraver what's she
+ 
+
+ align:start position:0%
+um what's what's the engraver what's she
+going to be um thinking about in terms
+
+ align:start position:0%
+going to be um thinking about in terms
+ 
+
+ align:start position:0%
+going to be um thinking about in terms
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+duration what do you think about when
+
+ align:start position:0%
+duration what do you think about when
+ 
+
+ align:start position:0%
+duration what do you think about when
+you when you're looking at musical score
+
+ align:start position:0%
+you when you're looking at musical score
+ 
+
+ align:start position:0%
+you when you're looking at musical score
+yeah um the beat and the modifying the
+
+ align:start position:0%
+yeah um the beat and the modifying the
+ 
+
+ align:start position:0%
+yeah um the beat and the modifying the
+beats the modifi good good the um what
+
+ align:start position:0%
+beats the modifi good good the um what
+ 
+
+ align:start position:0%
+beats the modifi good good the um what
+do what are we going to call something
+
+ align:start position:0%
+do what are we going to call something
+ 
+
+ align:start position:0%
+do what are we going to call something
+uh the difference between an eighth note
+
+ align:start position:0%
+uh the difference between an eighth note
+ 
+
+ align:start position:0%
+uh the difference between an eighth note
+a quarter note a half note St all that
+
+ align:start position:0%
+a quarter note a half note St all that
+ 
+
+ align:start position:0%
+a quarter note a half note St all that
+stuff what do what do we want to call
+
+ align:start position:0%
+stuff what do what do we want to call
+ 
+
+ align:start position:0%
+stuff what do what do we want to call
+that do we we all have been doing music
+
+ align:start position:0%
+that do we we all have been doing music
+ 
+
+ align:start position:0%
+that do we we all have been doing music
+for a very long time we all must know
+
+ align:start position:0%
+for a very long time we all must know
+ 
+
+ align:start position:0%
+for a very long time we all must know
+the term for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right there is no generalized term for
+
+ align:start position:0%
+right there is no generalized term for
+ 
+
+ align:start position:0%
+right there is no generalized term for
+it so what do we want to call it in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class somebody shout out something or
+
+ align:start position:0%
+class somebody shout out something or
+ 
+
+ align:start position:0%
+class somebody shout out something or
+we'll call it the the the note animal
+
+ align:start position:0%
+we'll call it the the the note animal
+ 
+
+ align:start position:0%
+we'll call it the the the note animal
+what what animal is this note or what
+
+ align:start position:0%
+what what animal is this note or what
+ 
+
+ align:start position:0%
+what what animal is this note or what
+flavor is this note that's a good one
+
+ align:start position:0%
+flavor is this note that's a good one
+ 
+
+ align:start position:0%
+flavor is this note that's a good one
+actually I wish I had gone with that um
+
+ align:start position:0%
+actually I wish I had gone with that um
+ 
+
+ align:start position:0%
+actually I wish I had gone with that um
+16th notes are really really tasty
+
+ align:start position:0%
+16th notes are really really tasty
+ 
+
+ align:start position:0%
+16th notes are really really tasty
+today anybody have a suggestion of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term Essence the essence what essence of
+
+ align:start position:0%
+term Essence the essence what essence of
+ 
+
+ align:start position:0%
+term Essence the essence what essence of
+note is good good I will tell you that
+
+ align:start position:0%
+note is good good I will tell you that
+ 
+
+ align:start position:0%
+note is good good I will tell you that
+Essence is better than animal probably
+
+ align:start position:0%
+Essence is better than animal probably
+ 
+
+ align:start position:0%
+Essence is better than animal probably
+as a term it's probably better than
+
+ align:start position:0%
+as a term it's probably better than
+ 
+
+ align:start position:0%
+as a term it's probably better than
+flavor and it's better than what all the
+
+ align:start position:0%
+flavor and it's better than what all the
+ 
+
+ align:start position:0%
+flavor and it's better than what all the
+rest of us didn't say because the first
+
+ align:start position:0%
+rest of us didn't say because the first
+ 
+
+ align:start position:0%
+rest of us didn't say because the first
+thing you have to do when you're
+
+ align:start position:0%
+thing you have to do when you're
+ 
+
+ align:start position:0%
+thing you have to do when you're
+representing for a computer is come up
+
+ align:start position:0%
+representing for a computer is come up
+ 
+
+ align:start position:0%
+representing for a computer is come up
+with a name for everything yeah Vanessa
+
+ align:start position:0%
+with a name for everything yeah Vanessa
+ 
+
+ align:start position:0%
+with a name for everything yeah Vanessa
+oh no okay but come up with a name for
+
+ align:start position:0%
+oh no okay but come up with a name for
+ 
+
+ align:start position:0%
+oh no okay but come up with a name for
+it what duration the duration okay so we
+
+ align:start position:0%
+it what duration the duration okay so we
+ 
+
+ align:start position:0%
+it what duration the duration okay so we
+might have the duration of a duration is
+
+ align:start position:0%
+might have the duration of a duration is
+ 
+
+ align:start position:0%
+might have the duration of a duration is
+a quarter and the number of dots is two
+
+ align:start position:0%
+a quarter and the number of dots is two
+ 
+
+ align:start position:0%
+a quarter and the number of dots is two
+a lot of representations do that the um
+
+ align:start position:0%
+a lot of representations do that the um
+ 
+
+ align:start position:0%
+a lot of representations do that the um
+I think Mei calls that part A duration
+
+ align:start position:0%
+I think Mei calls that part A duration
+ 
+
+ align:start position:0%
+I think Mei calls that part A duration
+so that's a very good term for it other
+
+ align:start position:0%
+so that's a very good term for it other
+ 
+
+ align:start position:0%
+so that's a very good term for it other
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms get good at naming things come up
+
+ align:start position:0%
+terms get good at naming things come up
+ 
+
+ align:start position:0%
+terms get good at naming things come up
+with names fast in this class so let's
+
+ align:start position:0%
+with names fast in this class so let's
+ 
+
+ align:start position:0%
+with names fast in this class so let's
+let's just pepper pepper some pepper
+
+ align:start position:0%
+let's just pepper pepper some pepper
+ 
+
+ align:start position:0%
+let's just pepper pepper some pepper
+some bad names for it Jonathan what's
+
+ align:start position:0%
+some bad names for it Jonathan what's
+ 
+
+ align:start position:0%
+some bad names for it Jonathan what's
+what's that almond the Almond what
+
+ align:start position:0%
+what's that almond the Almond what
+ 
+
+ align:start position:0%
+what's that almond the Almond what
+Almond is it I
+
+ align:start position:0%
+Almond is it I
+ 
+
+ align:start position:0%
+Almond is it I
+think I mean I the length what length
+
+ align:start position:0%
+think I mean I the length what length
+ 
+
+ align:start position:0%
+think I mean I the length what length
+good what length does that not it's a
+
+ align:start position:0%
+good what length does that not it's a
+ 
+
+ align:start position:0%
+good what length does that not it's a
+quarter note what length does that know
+
+ align:start position:0%
+quarter note what length does that know
+ 
+
+ align:start position:0%
+quarter note what length does that know
+it's an eth note there might be a better
+
+ align:start position:0%
+it's an eth note there might be a better
+ 
+
+ align:start position:0%
+it's an eth note there might be a better
+term but that's a pretty good one that's
+
+ align:start position:0%
+term but that's a pretty good one that's
+ 
+
+ align:start position:0%
+term but that's a pretty good one that's
+good yeah I feel like span isn't what
+
+ align:start position:0%
+good yeah I feel like span isn't what
+ 
+
+ align:start position:0%
+good yeah I feel like span isn't what
+span I like that what span I it might
+
+ align:start position:0%
+span I like that what span I it might
+ 
+
+ align:start position:0%
+span I like that what span I it might
+not be so so perfect but you know it's
+
+ align:start position:0%
+not be so so perfect but you know it's
+ 
+
+ align:start position:0%
+not be so so perfect but you know it's
+it gets us when you think think about
+
+ align:start position:0%
+it gets us when you think think about
+ 
+
+ align:start position:0%
+it gets us when you think think about
+things what's something that expands um
+
+ align:start position:0%
+things what's something that expands um
+ 
+
+ align:start position:0%
+things what's something that expands um
+things that people uh spend a lot of
+
+ align:start position:0%
+things that people uh spend a lot of
+ 
+
+ align:start position:0%
+things that people uh spend a lot of
+time especially what course three uh
+
+ align:start position:0%
+time especially what course three uh
+ 
+
+ align:start position:0%
+time especially what course three uh
+thinking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about bridges good and when you start
+
+ align:start position:0%
+about bridges good and when you start
+ 
+
+ align:start position:0%
+about bridges good and when you start
+thinking about bridges what's something
+
+ align:start position:0%
+thinking about bridges what's something
+ 
+
+ align:start position:0%
+thinking about bridges what's something
+that we haven't even thought of that
+
+ align:start position:0%
+that we haven't even thought of that
+ 
+
+ align:start position:0%
+that we haven't even thought of that
+looks like a bridge when we think about
+
+ align:start position:0%
+looks like a bridge when we think about
+ 
+
+ align:start position:0%
+looks like a bridge when we think about
+durations and notes slurs slurs ties
+
+ align:start position:0%
+durations and notes slurs slurs ties
+ 
+
+ align:start position:0%
+durations and notes slurs slurs ties
+good slurs ties I was also thinking of
+
+ align:start position:0%
+good slurs ties I was also thinking of
+ 
+
+ align:start position:0%
+good slurs ties I was also thinking of
+beams any of those good so start when we
+
+ align:start position:0%
+beams any of those good so start when we
+ 
+
+ align:start position:0%
+beams any of those good so start when we
+start thinking of terms like this we
+
+ align:start position:0%
+start thinking of terms like this we
+ 
+
+ align:start position:0%
+start thinking of terms like this we
+start thinking of cases who had thought
+
+ align:start position:0%
+start thinking of cases who had thought
+ 
+
+ align:start position:0%
+start thinking of cases who had thought
+about ties and slurs in your
+
+ align:start position:0%
+about ties and slurs in your
+ 
+
+ align:start position:0%
+about ties and slurs in your
+definition who had thought about
+
+ align:start position:0%
+definition who had thought about
+ 
+
+ align:start position:0%
+definition who had thought about
+Beams I I hadn't thought of TI and so
+
+ align:start position:0%
+Beams I I hadn't thought of TI and so
+ 
+
+ align:start position:0%
+Beams I I hadn't thought of TI and so
+when we do these types of things
+
+ align:start position:0%
+when we do these types of things
+ 
+
+ align:start position:0%
+when we do these types of things
+suddenly why something is a good name or
+
+ align:start position:0%
+suddenly why something is a good name or
+ 
+
+ align:start position:0%
+suddenly why something is a good name or
+might not be a good name can help us
+
+ align:start position:0%
+might not be a good name can help us
+ 
+
+ align:start position:0%
+might not be a good name can help us
+think about what other things we're
+
+ align:start position:0%
+think about what other things we're
+ 
+
+ align:start position:0%
+think about what other things we're
+going to have to represent I'm looking
+
+ align:start position:0%
+going to have to represent I'm looking
+ 
+
+ align:start position:0%
+going to have to represent I'm looking
+at the time we're not going to be able
+
+ align:start position:0%
+at the time we're not going to be able
+ 
+
+ align:start position:0%
+at the time we're not going to be able
+to get through all the different types
+
+ align:start position:0%
+to get through all the different types
+ 
+
+ align:start position:0%
+to get through all the different types
+of representations here but but good now
+
+ align:start position:0%
+of representations here but but good now
+ 
+
+ align:start position:0%
+of representations here but but good now
+what would it
+
+ align:start position:0%
+what would it
+ 
+
+ align:start position:0%
+what would it
+take let's say you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this what's it going to take that's a
+
+ align:start position:0%
+this what's it going to take that's a
+ 
+
+ align:start position:0%
+this what's it going to take that's a
+dotted quarter note that's not a not a
+
+ align:start position:0%
+dotted quarter note that's not a not a
+ 
+
+ align:start position:0%
+dotted quarter note that's not a not a
+trick question what's it going to take
+
+ align:start position:0%
+trick question what's it going to take
+ 
+
+ align:start position:0%
+trick question what's it going to take
+for you to figure out how many seconds
+
+ align:start position:0%
+for you to figure out how many seconds
+ 
+
+ align:start position:0%
+for you to figure out how many seconds
+that is who has performed music from
+
+ align:start position:0%
+that is who has performed music from
+ 
+
+ align:start position:0%
+that is who has performed music from
+sheet music in this class in your life
+
+ align:start position:0%
+sheet music in this class in your life
+ 
+
+ align:start position:0%
+sheet music in this class in your life
+okay it's basically
+
+ align:start position:0%
+okay it's basically
+ 
+
+ align:start position:0%
+okay it's basically
+everybody so when you do that you have
+
+ align:start position:0%
+everybody so when you do that you have
+ 
+
+ align:start position:0%
+everybody so when you do that you have
+to decide how long you're going to play
+
+ align:start position:0%
+to decide how long you're going to play
+ 
+
+ align:start position:0%
+to decide how long you're going to play
+that right you might not even be
+
+ align:start position:0%
+that right you might not even be
+ 
+
+ align:start position:0%
+that right you might not even be
+thinking it in your head I've never been
+
+ align:start position:0%
+thinking it in your head I've never been
+ 
+
+ align:start position:0%
+thinking it in your head I've never been
+like okay I'm going to play that for3 3
+
+ align:start position:0%
+like okay I'm going to play that for3 3
+ 
+
+ align:start position:0%
+like okay I'm going to play that for3 3
+six5
+
+ align:start position:0%
+six5
+ 
+
+ align:start position:0%
+six5
+seconds um how do we how do we go from
+
+ align:start position:0%
+seconds um how do we how do we go from
+ 
+
+ align:start position:0%
+seconds um how do we how do we go from
+this to a number of
+
+ align:start position:0%
+this to a number of
+ 
+
+ align:start position:0%
+this to a number of
+seconds yeah good oh sorry there was two
+
+ align:start position:0%
+seconds yeah good oh sorry there was two
+ 
+
+ align:start position:0%
+seconds yeah good oh sorry there was two
+in a row going behind first U well it's
+
+ align:start position:0%
+in a row going behind first U well it's
+ 
+
+ align:start position:0%
+in a row going behind first U well it's
+based off the tempo based off the tempo
+
+ align:start position:0%
+based off the tempo based off the tempo
+ 
+
+ align:start position:0%
+based off the tempo based off the tempo
+good has Tempo been included I suppose
+
+ align:start position:0%
+good has Tempo been included I suppose
+ 
+
+ align:start position:0%
+good has Tempo been included I suppose
+it's almost implicitly included in beat
+
+ align:start position:0%
+it's almost implicitly included in beat
+ 
+
+ align:start position:0%
+it's almost implicitly included in beat
+but Tempo is this particular term so we
+
+ align:start position:0%
+but Tempo is this particular term so we
+ 
+
+ align:start position:0%
+but Tempo is this particular term so we
+have Tempo how do we measure tempos
+
+ align:start position:0%
+have Tempo how do we measure tempos
+ 
+
+ align:start position:0%
+have Tempo how do we measure tempos
+Tempe Tempe
+
+ align:start position:0%
+Tempe Tempe
+ 
+
+ align:start position:0%
+Tempe Tempe
+what's that be beat per minute
+
+ align:start position:0%
+what's that be beat per minute
+ 
+
+ align:start position:0%
+what's that be beat per minute
+good beat per
+
+ align:start position:0%
+good beat per
+ 
+
+ align:start position:0%
+good beat per
+minute so what do we need to know also
+
+ align:start position:0%
+minute so what do we need to know also
+ 
+
+ align:start position:0%
+minute so what do we need to know also
+in addition to Tempo in order to figure
+
+ align:start position:0%
+in addition to Tempo in order to figure
+ 
+
+ align:start position:0%
+in addition to Tempo in order to figure
+out how many beats something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is we all think of 44 right so yeah Jake
+
+ align:start position:0%
+is we all think of 44 right so yeah Jake
+ 
+
+ align:start position:0%
+is we all think of 44 right so yeah Jake
+you intentionally say 365 because it's
+
+ align:start position:0%
+you intentionally say 365 because it's
+ 
+
+ align:start position:0%
+you intentionally say 365 because it's
+38 of
+
+ align:start position:0%
+38 of
+ 
+
+ align:start position:0%
+38 of
+the7 375 but yeah whatever I I don't
+
+ align:start position:0%
+the7 375 but yeah whatever I I don't
+ 
+
+ align:start position:0%
+the7 375 but yeah whatever I I don't
+know it was something something like
+
+ align:start position:0%
+know it was something something like
+ 
+
+ align:start position:0%
+know it was something something like
+that yeah I I I I very rarely do
+
+ align:start position:0%
+that yeah I I I I very rarely do
+ 
+
+ align:start position:0%
+that yeah I I I I very rarely do
+anything intentionally so so maybe it's
+
+ align:start position:0%
+anything intentionally so so maybe it's
+ 
+
+ align:start position:0%
+anything intentionally so so maybe it's
+karma um uh what do we need to do to get
+
+ align:start position:0%
+karma um uh what do we need to do to get
+ 
+
+ align:start position:0%
+karma um uh what do we need to do to get
+beats per minute how many beats is
+
+ align:start position:0%
+beats per minute how many beats is
+ 
+
+ align:start position:0%
+beats per minute how many beats is
+this depends depends good depends on the
+
+ align:start position:0%
+this depends depends good depends on the
+ 
+
+ align:start position:0%
+this depends depends good depends on the
+everybody shout it out time signature
+
+ align:start position:0%
+everybody shout it out time signature
+ 
+
+ align:start position:0%
+everybody shout it out time signature
+good so suddenly moving from this
+
+ align:start position:0%
+good so suddenly moving from this
+ 
+
+ align:start position:0%
+good so suddenly moving from this
+representation of notes to seconds we
+
+ align:start position:0%
+representation of notes to seconds we
+ 
+
+ align:start position:0%
+representation of notes to seconds we
+need Tempo in beats per minute and a
+
+ align:start position:0%
+need Tempo in beats per minute and a
+ 
+
+ align:start position:0%
+need Tempo in beats per minute and a
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+signature
+
+ align:start position:0%
+signature
+ 
+
+ align:start position:0%
+signature
+good let me give you another one what if
+
+ align:start position:0%
+good let me give you another one what if
+ 
+
+ align:start position:0%
+good let me give you another one what if
+I said the tempo here
+
+ align:start position:0%
+I said the tempo here
+ 
+
+ align:start position:0%
+I said the tempo here
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+Alro ma non
+
+ align:start position:0%
+Alro ma non
+ 
+
+ align:start position:0%
+Alro ma non
+tropo okay the other thing if it gets
+
+ align:start position:0%
+tropo okay the other thing if it gets
+ 
+
+ align:start position:0%
+tropo okay the other thing if it gets
+too much longer than that the other
+
+ align:start position:0%
+too much longer than that the other
+ 
+
+ align:start position:0%
+too much longer than that the other
+thing we need is an Italian dictionary
+
+ align:start position:0%
+thing we need is an Italian dictionary
+ 
+
+ align:start position:0%
+thing we need is an Italian dictionary
+right U algro but not too Allegro not
+
+ align:start position:0%
+right U algro but not too Allegro not
+ 
+
+ align:start position:0%
+right U algro but not too Allegro not
+too much um so what do we need also in
+
+ align:start position:0%
+too much um so what do we need also in
+ 
+
+ align:start position:0%
+too much um so what do we need also in
+order to convert this to seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take a take a stab at it you guys
+
+ align:start position:0%
+let's take a take a stab at it you guys
+ 
+
+ align:start position:0%
+let's take a take a stab at it you guys
+have all been speaking pretty well
+
+ align:start position:0%
+have all been speaking pretty well
+ 
+
+ align:start position:0%
+have all been speaking pretty well
+Hannah I don't think I've heard from you
+
+ align:start position:0%
+Hannah I don't think I've heard from you
+ 
+
+ align:start position:0%
+Hannah I don't think I've heard from you
+in a little bit what would you say you
+
+ align:start position:0%
+in a little bit what would you say you
+ 
+
+ align:start position:0%
+in a little bit what would you say you
+need in order to convert this to I say
+
+ align:start position:0%
+need in order to convert this to I say
+ 
+
+ align:start position:0%
+need in order to convert this to I say
+knowledge of
+
+ align:start position:0%
+knowledge of
+ 
+
+ align:start position:0%
+knowledge of
+what knowledge of like what it means in
+
+ align:start position:0%
+what knowledge of like what it means in
+ 
+
+ align:start position:0%
+what knowledge of like what it means in
+terms of the temp knowledge of good
+
+ align:start position:0%
+terms of the temp knowledge of good
+ 
+
+ align:start position:0%
+terms of the temp knowledge of good
+knowledge of a conversion do can you
+
+ align:start position:0%
+knowledge of a conversion do can you
+ 
+
+ align:start position:0%
+knowledge of a conversion do can you
+give me a conversion maybe what it means
+
+ align:start position:0%
+give me a conversion maybe what it means
+ 
+
+ align:start position:0%
+give me a conversion maybe what it means
+what it a conversion to let's say
+
+ align:start position:0%
+what it a conversion to let's say
+ 
+
+ align:start position:0%
+what it a conversion to let's say
+BPM what would be uh what's somebody uh
+
+ align:start position:0%
+BPM what would be uh what's somebody uh
+ 
+
+ align:start position:0%
+BPM what would be uh what's somebody uh
+Hannah if you want to or pass it along
+
+ align:start position:0%
+Hannah if you want to or pass it along
+ 
+
+ align:start position:0%
+Hannah if you want to or pass it along
+to somebody else take stab what are you
+
+ align:start position:0%
+to somebody else take stab what are you
+ 
+
+ align:start position:0%
+to somebody else take stab what are you
+going to name
+
+ align:start position:0%
+going to name
+ 
+
+ align:start position:0%
+going to name
+that algro
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximately seven no okay two million
+
+ align:start position:0%
+approximately seven no okay two million
+ 
+
+ align:start position:0%
+approximately seven no okay two million
+no okay good we we're we're narrowing it
+
+ align:start position:0%
+no okay good we we're we're narrowing it
+ 
+
+ align:start position:0%
+no okay good we we're we're narrowing it
+down uhbe around like 110 110
+
+ align:start position:0%
+down uhbe around like 110 110
+ 
+
+ align:start position:0%
+down uhbe around like 110 110
+good anybody want to go higher than 110
+
+ align:start position:0%
+good anybody want to go higher than 110
+ 
+
+ align:start position:0%
+good anybody want to go higher than 110
+what do you want to go with 126
+
+ align:start position:0%
+what do you want to go with 126
+ 
+
+ align:start position:0%
+what do you want to go with 126
+126 very specific number um any anyone
+
+ align:start position:0%
+126 very specific number um any anyone
+ 
+
+ align:start position:0%
+126 very specific number um any anyone
+want to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lower I'm going to go a little bit lower
+
+ align:start position:0%
+lower I'm going to go a little bit lower
+ 
+
+ align:start position:0%
+lower I'm going to go a little bit lower
+and say
+
+ align:start position:0%
+and say
+ 
+
+ align:start position:0%
+and say
+90 because the other thing that you need
+
+ align:start position:0%
+90 because the other thing that you need
+ 
+
+ align:start position:0%
+90 because the other thing that you need
+to know is the cultural
+
+ align:start position:0%
+to know is the cultural
+ 
+
+ align:start position:0%
+to know is the cultural
+context and
+
+ align:start position:0%
+context and
+ 
+
+ align:start position:0%
+context and
+because each of these
+
+ align:start position:0%
+because each of these
+ 
+
+ align:start position:0%
+because each of these
+things changes so much handle has a
+
+ align:start position:0%
+things changes so much handle has a
+ 
+
+ align:start position:0%
+things changes so much handle has a
+Tempo marking of Allegro
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Adagio what does that mean those are
+
+ align:start position:0%
+Adagio what does that mean those are
+ 
+
+ align:start position:0%
+Adagio what does that mean those are
+like contradictions that's like you know
+
+ align:start position:0%
+like contradictions that's like you know
+ 
+
+ align:start position:0%
+like contradictions that's like you know
+how how do you like your cereal I like a
+
+ align:start position:0%
+how how do you like your cereal I like a
+ 
+
+ align:start position:0%
+how how do you like your cereal I like a
+hot cold um yeah but at a particular
+
+ align:start position:0%
+hot cold um yeah but at a particular
+ 
+
+ align:start position:0%
+hot cold um yeah but at a particular
+time that is so sometimes we ignore
+
+ align:start position:0%
+time that is so sometimes we ignore
+ 
+
+ align:start position:0%
+time that is so sometimes we ignore
+quite a lot of these right uh I know I
+
+ align:start position:0%
+quite a lot of these right uh I know I
+ 
+
+ align:start position:0%
+quite a lot of these right uh I know I
+use uh and by the way Han I pretty close
+
+ align:start position:0%
+use uh and by the way Han I pretty close
+ 
+
+ align:start position:0%
+use uh and by the way Han I pretty close
+I think I use 118 in a lookup table when
+
+ align:start position:0%
+I think I use 118 in a lookup table when
+ 
+
+ align:start position:0%
+I think I use 118 in a lookup table when
+I have no idea what I want to do from
+
+ align:start position:0%
+I have no idea what I want to do from
+ 
+
+ align:start position:0%
+I have no idea what I want to do from
+Allegro um or sometimes I've used 126
+
+ align:start position:0%
+Allegro um or sometimes I've used 126
+ 
+
+ align:start position:0%
+Allegro um or sometimes I've used 126
+I've used other things 110 110 I usually
+
+ align:start position:0%
+I've used other things 110 110 I usually
+ 
+
+ align:start position:0%
+I've used other things 110 110 I usually
+use as the the it depends on whether or
+
+ align:start position:0%
+use as the the it depends on whether or
+ 
+
+ align:start position:0%
+use as the the it depends on whether or
+not I have a conception of the term Alig
+
+ align:start position:0%
+not I have a conception of the term Alig
+ 
+
+ align:start position:0%
+not I have a conception of the term Alig
+gretto in which case I need to make room
+
+ align:start position:0%
+gretto in which case I need to make room
+ 
+
+ align:start position:0%
+gretto in which case I need to make room
+for that but yeah 11's also very good uh
+
+ align:start position:0%
+for that but yeah 11's also very good uh
+ 
+
+ align:start position:0%
+for that but yeah 11's also very good uh
+good by the way every guess that people
+
+ align:start position:0%
+good by the way every guess that people
+ 
+
+ align:start position:0%
+good by the way every guess that people
+are doing has been really really really
+
+ align:start position:0%
+are doing has been really really really
+ 
+
+ align:start position:0%
+are doing has been really really really
+good in this class so just just keep
+
+ align:start position:0%
+good in this class so just just keep
+ 
+
+ align:start position:0%
+good in this class so just just keep
+taking the guess and I'll when we start
+
+ align:start position:0%
+taking the guess and I'll when we start
+ 
+
+ align:start position:0%
+taking the guess and I'll when we start
+talking too much then I'll you know then
+
+ align:start position:0%
+talking too much then I'll you know then
+ 
+
+ align:start position:0%
+talking too much then I'll you know then
+I'll I'll slow it down but good so these
+
+ align:start position:0%
+I'll I'll slow it down but good so these
+ 
+
+ align:start position:0%
+I'll I'll slow it down but good so these
+are all the various things that we might
+
+ align:start position:0%
+are all the various things that we might
+ 
+
+ align:start position:0%
+are all the various things that we might
+do to convert from one to another um
+
+ align:start position:0%
+do to convert from one to another um
+ 
+
+ align:start position:0%
+do to convert from one to another um
+there was one other Tempo um uh one
+
+ align:start position:0%
+there was one other Tempo um uh one
+ 
+
+ align:start position:0%
+there was one other Tempo um uh one
+other way that we could measure duration
+
+ align:start position:0%
+other way that we could measure duration
+ 
+
+ align:start position:0%
+other way that we could measure duration
+that I think uh Marlin said um that I
+
+ align:start position:0%
+that I think uh Marlin said um that I
+ 
+
+ align:start position:0%
+that I think uh Marlin said um that I
+was like sh not yet not yet not yet but
+
+ align:start position:0%
+was like sh not yet not yet not yet but
+ 
+
+ align:start position:0%
+was like sh not yet not yet not yet but
+comes very important do you remember
+
+ align:start position:0%
+comes very important do you remember
+ 
+
+ align:start position:0%
+comes very important do you remember
+what we said tick ticks good so you can
+
+ align:start position:0%
+what we said tick ticks good so you can
+ 
+
+ align:start position:0%
+what we said tick ticks good so you can
+measure on the number of bugs that get
+
+ align:start position:0%
+measure on the number of bugs that get
+ 
+
+ align:start position:0%
+measure on the number of bugs that get
+into your hair when you go hiking right
+
+ align:start position:0%
+into your hair when you go hiking right
+ 
+
+ align:start position:0%
+into your hair when you go hiking right
+no what do we what do we mean by a tick
+
+ align:start position:0%
+no what do we what do we mean by a tick
+ 
+
+ align:start position:0%
+no what do we what do we mean by a tick
+this has a different meaning than from
+
+ align:start position:0%
+this has a different meaning than from
+ 
+
+ align:start position:0%
+this has a different meaning than from
+my understanding is how like the
+
+ align:start position:0%
+my understanding is how like the
+ 
+
+ align:start position:0%
+my understanding is how like the
+computers process like whatever program
+
+ align:start position:0%
+computers process like whatever program
+ 
+
+ align:start position:0%
+computers process like whatever program
+or application and that me kind of like
+
+ align:start position:0%
+or application and that me kind of like
+ 
+
+ align:start position:0%
+or application and that me kind of like
+tis and so that kind of dictates how
+
+ align:start position:0%
+tis and so that kind of dictates how
+ 
+
+ align:start position:0%
+tis and so that kind of dictates how
+what a second is based on great yeah so
+
+ align:start position:0%
+what a second is based on great yeah so
+ 
+
+ align:start position:0%
+what a second is based on great yeah so
+what we can do is we can think of time
+
+ align:start position:0%
+what we can do is we can think of time
+ 
+
+ align:start position:0%
+what we can do is we can think of time
+as somehow
+
+ align:start position:0%
+as somehow
+ 
+
+ align:start position:0%
+as somehow
+discreet that time moves forward and by
+
+ align:start position:0%
+discreet that time moves forward and by
+ 
+
+ align:start position:0%
+discreet that time moves forward and by
+the way there's some there's some uh
+
+ align:start position:0%
+the way there's some there's some uh
+ 
+
+ align:start position:0%
+the way there's some there's some uh
+theoretical physicists who've been uh
+
+ align:start position:0%
+theoretical physicists who've been uh
+ 
+
+ align:start position:0%
+theoretical physicists who've been uh
+trying to study whether time actually is
+
+ align:start position:0%
+trying to study whether time actually is
+ 
+
+ align:start position:0%
+trying to study whether time actually is
+discrete and moves forward in know 10 to
+
+ align:start position:0%
+discrete and moves forward in know 10 to
+ 
+
+ align:start position:0%
+discrete and moves forward in know 10 to
+the Nega
+
+ align:start position:0%
+the Nega
+ 
+
+ align:start position:0%
+the Nega
+58 seconds or not um but but that we can
+
+ align:start position:0%
+58 seconds or not um but but that we can
+ 
+
+ align:start position:0%
+58 seconds or not um but but that we can
+think of musical time as a screet number
+
+ align:start position:0%
+think of musical time as a screet number
+ 
+
+ align:start position:0%
+think of musical time as a screet number
+of something in a purely computer world
+
+ align:start position:0%
+of something in a purely computer world
+ 
+
+ align:start position:0%
+of something in a purely computer world
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+tix which is both brilliant and a way of
+
+ align:start position:0%
+tix which is both brilliant and a way of
+ 
+
+ align:start position:0%
+tix which is both brilliant and a way of
+just um shuffling later to some other
+
+ align:start position:0%
+just um shuffling later to some other
+ 
+
+ align:start position:0%
+just um shuffling later to some other
+later part of the program the actual
+
+ align:start position:0%
+later part of the program the actual
+ 
+
+ align:start position:0%
+later part of the program the actual
+conversion of this to seconds or to
+
+ align:start position:0%
+conversion of this to seconds or to
+ 
+
+ align:start position:0%
+conversion of this to seconds or to
+quarter notes or to eighth notes or
+
+ align:start position:0%
+quarter notes or to eighth notes or
+ 
+
+ align:start position:0%
+quarter notes or to eighth notes or
+anything like that
+
+ align:start position:0%
+anything like that
+ 
+
+ align:start position:0%
+anything like that
+um but it's very very useful the one um
+
+ align:start position:0%
+um but it's very very useful the one um
+ 
+
+ align:start position:0%
+um but it's very very useful the one um
+thing that you term that you may have
+
+ align:start position:0%
+thing that you term that you may have
+ 
+
+ align:start position:0%
+thing that you term that you may have
+heard of before midi the midi file
+
+ align:start position:0%
+heard of before midi the midi file
+ 
+
+ align:start position:0%
+heard of before midi the midi file
+format the midi things midi tends to
+
+ align:start position:0%
+format the midi things midi tends to
+ 
+
+ align:start position:0%
+format the midi things midi tends to
+measure everything in ticks um there's
+
+ align:start position:0%
+measure everything in ticks um there's
+ 
+
+ align:start position:0%
+measure everything in ticks um there's
+there's some some things are not and
+
+ align:start position:0%
+there's some some things are not and
+ 
+
+ align:start position:0%
+there's some some things are not and
+it's a little bit of a simplification so
+
+ align:start position:0%
+it's a little bit of a simplification so
+ 
+
+ align:start position:0%
+it's a little bit of a simplification so
+ticks end up being sort of ticks per
+
+ align:start position:0%
+ticks end up being sort of ticks per
+ 
+
+ align:start position:0%
+ticks end up being sort of ticks per
+second or ticks per tick per second is a
+
+ align:start position:0%
+second or ticks per tick per second is a
+ 
+
+ align:start position:0%
+second or ticks per tick per second is a
+pretty good one for Tempo and the other
+
+ align:start position:0%
+pretty good one for Tempo and the other
+ 
+
+ align:start position:0%
+pretty good one for Tempo and the other
+one ticks per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+per per quarter note comes up quite a
+
+ align:start position:0%
+per per quarter note comes up quite a
+ 
+
+ align:start position:0%
+per per quarter note comes up quite a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+intriguingly because of the problem of
+
+ align:start position:0%
+intriguingly because of the problem of
+ 
+
+ align:start position:0%
+intriguingly because of the problem of
+68 and 5'8 and these weird things um
+
+ align:start position:0%
+68 and 5'8 and these weird things um
+ 
+
+ align:start position:0%
+68 and 5'8 and these weird things um
+measure fundamental measurements in
+
+ align:start position:0%
+measure fundamental measurements in
+ 
+
+ align:start position:0%
+measure fundamental measurements in
+terms of Beats have not primarily been
+
+ align:start position:0%
+terms of Beats have not primarily been
+ 
+
+ align:start position:0%
+terms of Beats have not primarily been
+taken on by um by comp by people who do
+
+ align:start position:0%
+taken on by um by comp by people who do
+ 
+
+ align:start position:0%
+taken on by um by comp by people who do
+um musical representation it's generally
+
+ align:start position:0%
+um musical representation it's generally
+ 
+
+ align:start position:0%
+um musical representation it's generally
+seen as a slightly higher representation
+
+ align:start position:0%
+seen as a slightly higher representation
+ 
+
+ align:start position:0%
+seen as a slightly higher representation
+which is ironic because it's one of our
+
+ align:start position:0%
+which is ironic because it's one of our
+ 
+
+ align:start position:0%
+which is ironic because it's one of our
+fundamental ones for as musicians right
+
+ align:start position:0%
+fundamental ones for as musicians right
+ 
+
+ align:start position:0%
+fundamental ones for as musicians right
+me you think of that oh that lasts half
+
+ align:start position:0%
+me you think of that oh that lasts half
+ 
+
+ align:start position:0%
+me you think of that oh that lasts half
+note it lasts two beats right and then
+
+ align:start position:0%
+note it lasts two beats right and then
+ 
+
+ align:start position:0%
+note it lasts two beats right and then
+somebody reminds you oh what about cut
+
+ align:start position:0%
+somebody reminds you oh what about cut
+ 
+
+ align:start position:0%
+somebody reminds you oh what about cut
+timeing like uh you ruin everything
+
+ align:start position:0%
+timeing like uh you ruin everything
+ 
+
+ align:start position:0%
+timeing like uh you ruin everything
+right you know because we generally do
+
+ align:start position:0%
+right you know because we generally do
+ 
+
+ align:start position:0%
+right you know because we generally do
+some things like this
+
+ align:start position:0%
+some things like this
+ 
+
+ align:start position:0%
+some things like this
+um I will share now what um I ended up
+
+ align:start position:0%
+um I will share now what um I ended up
+ 
+
+ align:start position:0%
+um I will share now what um I ended up
+in my program in music 21 deciding
+
+ align:start position:0%
+in my program in music 21 deciding
+ 
+
+ align:start position:0%
+in my program in music 21 deciding
+that for some reason the quarter
+
+ align:start position:0%
+that for some reason the quarter
+ 
+
+ align:start position:0%
+that for some reason the quarter
+note is the fundamental measure of
+
+ align:start position:0%
+note is the fundamental measure of
+ 
+
+ align:start position:0%
+note is the fundamental measure of
+everything else so that um everything
+
+ align:start position:0%
+everything else so that um everything
+ 
+
+ align:start position:0%
+everything else so that um everything
+send to get measured in quarter
+
+ align:start position:0%
+send to get measured in quarter
+ 
+
+ align:start position:0%
+send to get measured in quarter
+lengths which is a terrible term boy I
+
+ align:start position:0%
+lengths which is a terrible term boy I
+ 
+
+ align:start position:0%
+lengths which is a terrible term boy I
+wish I had come up with something better
+
+ align:start position:0%
+wish I had come up with something better
+ 
+
+ align:start position:0%
+wish I had come up with something better
+uh Essence that's almonds I wish I had
+
+ align:start position:0%
+uh Essence that's almonds I wish I had
+ 
+
+ align:start position:0%
+uh Essence that's almonds I wish I had
+measured in Almond because quarter
+
+ align:start position:0%
+measured in Almond because quarter
+ 
+
+ align:start position:0%
+measured in Almond because quarter
+length takes a very long time to type
+
+ align:start position:0%
+length takes a very long time to type
+ 
+
+ align:start position:0%
+length takes a very long time to type
+with the camel case in the middle um and
+
+ align:start position:0%
+with the camel case in the middle um and
+ 
+
+ align:start position:0%
+with the camel case in the middle um and
+and we didn't have uh what is it get
+
+ align:start position:0%
+and we didn't have uh what is it get
+ 
+
+ align:start position:0%
+and we didn't have uh what is it get
+GitHub autopilot and things like that um
+
+ align:start position:0%
+GitHub autopilot and things like that um
+ 
+
+ align:start position:0%
+GitHub autopilot and things like that um
+um yeah by the way I didn't mean to put
+
+ align:start position:0%
+um yeah by the way I didn't mean to put
+ 
+
+ align:start position:0%
+um yeah by the way I didn't mean to put
+um no chat GPT on the syllabus I put it
+
+ align:start position:0%
+um no chat GPT on the syllabus I put it
+ 
+
+ align:start position:0%
+um no chat GPT on the syllabus I put it
+on uh the thing later today you have fun
+
+ align:start position:0%
+on uh the thing later today you have fun
+ 
+
+ align:start position:0%
+on uh the thing later today you have fun
+with it but not when we're doing any
+
+ align:start position:0%
+with it but not when we're doing any
+ 
+
+ align:start position:0%
+with it but not when we're doing any
+sort of um writing your essay or
+
+ align:start position:0%
+sort of um writing your essay or
+ 
+
+ align:start position:0%
+sort of um writing your essay or
+anything like that but we maybe we'll
+
+ align:start position:0%
+anything like that but we maybe we'll
+ 
+
+ align:start position:0%
+anything like that but we maybe we'll
+come up with a music a chat music or
+
+ align:start position:0%
+come up with a music a chat music or
+ 
+
+ align:start position:0%
+come up with a music a chat music or
+something later on the semester and try
+
+ align:start position:0%
+something later on the semester and try
+ 
+
+ align:start position:0%
+something later on the semester and try
+to see how we can um do things like that
+
+ align:start position:0%
+to see how we can um do things like that
+ 
+
+ align:start position:0%
+to see how we can um do things like that
+but yeah uh I wish I had come up with a
+
+ align:start position:0%
+but yeah uh I wish I had come up with a
+ 
+
+ align:start position:0%
+but yeah uh I wish I had come up with a
+better thing but almost everything
+
+ align:start position:0%
+better thing but almost everything
+ 
+
+ align:start position:0%
+better thing but almost everything
+measured in quarter lengths what's nice
+
+ align:start position:0%
+measured in quarter lengths what's nice
+ 
+
+ align:start position:0%
+measured in quarter lengths what's nice
+about that is how many quarter lengths
+
+ align:start position:0%
+about that is how many quarter lengths
+ 
+
+ align:start position:0%
+about that is how many quarter lengths
+is a quarter
+
+ align:start position:0%
+is a quarter
+ 
+
+ align:start position:0%
+is a quarter
+note one one good good good we're all
+
+ align:start position:0%
+note one one good good good we're all
+ 
+
+ align:start position:0%
+note one one good good good we're all
+we're all still awake I know it's Friday
+
+ align:start position:0%
+we're all still awake I know it's Friday
+ 
+
+ align:start position:0%
+we're all still awake I know it's Friday
+late and things but yeah so I don't um
+
+ align:start position:0%
+late and things but yeah so I don't um
+ 
+
+ align:start position:0%
+late and things but yeah so I don't um
+what how many quarter lengths is a
+
+ align:start position:0%
+what how many quarter lengths is a
+ 
+
+ align:start position:0%
+what how many quarter lengths is a
+quarter note in
+
+ align:start position:0%
+quarter note in
+ 
+
+ align:start position:0%
+quarter note in
+68 one one how many quarter lengths is a
+
+ align:start position:0%
+68 one one how many quarter lengths is a
+ 
+
+ align:start position:0%
+68 one one how many quarter lengths is a
+quarter note in algro one so so these
+
+ align:start position:0%
+quarter note in algro one so so these
+ 
+
+ align:start position:0%
+quarter note in algro one so so these
+things but then how many seconds is
+
+ align:start position:0%
+things but then how many seconds is
+ 
+
+ align:start position:0%
+things but then how many seconds is
+something that's 1.5 quarter lengths ah
+
+ align:start position:0%
+something that's 1.5 quarter lengths ah
+ 
+
+ align:start position:0%
+something that's 1.5 quarter lengths ah
+now you have to keep up with everything
+
+ align:start position:0%
+now you have to keep up with everything
+ 
+
+ align:start position:0%
+now you have to keep up with everything
+so you can kind of think about when
+
+ align:start position:0%
+so you can kind of think about when
+ 
+
+ align:start position:0%
+so you can kind of think about when
+you're thinking about now let's get to
+
+ align:start position:0%
+you're thinking about now let's get to
+ 
+
+ align:start position:0%
+you're thinking about now let's get to
+the first word in this class it's not
+
+ align:start position:0%
+the first word in this class it's not
+ 
+
+ align:start position:0%
+the first word in this class it's not
+representational music theory it's
+
+ align:start position:0%
+representational music theory it's
+ 
+
+ align:start position:0%
+representational music theory it's
+computational when you're starting to
+
+ align:start position:0%
+computational when you're starting to
+ 
+
+ align:start position:0%
+computational when you're starting to
+think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about I'll abbreviate it quite often as
+
+ align:start position:0%
+about I'll abbreviate it quite often as
+ 
+
+ align:start position:0%
+about I'll abbreviate it quite often as
+Q L um
+
+ align:start position:0%
+Q L um
+ 
+
+ align:start position:0%
+Q L um
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SEC and maybe we'll say sex are floats
+
+ align:start position:0%
+SEC and maybe we'll say sex are floats
+ 
+
+ align:start position:0%
+SEC and maybe we'll say sex are floats
+in this case
+
+ align:start position:0%
+in this case
+ 
+
+ align:start position:0%
+in this case
+case uh I've use a lot of typed python
+
+ align:start position:0%
+case uh I've use a lot of typed python
+ 
+
+ align:start position:0%
+case uh I've use a lot of typed python
+by the way where if you haven't ever
+
+ align:start position:0%
+by the way where if you haven't ever
+ 
+
+ align:start position:0%
+by the way where if you haven't ever
+seen this um you'll put put this in to
+
+ align:start position:0%
+seen this um you'll put put this in to
+ 
+
+ align:start position:0%
+seen this um you'll put put this in to
+say what I expect to do so it's sort of
+
+ align:start position:0%
+say what I expect to do so it's sort of
+ 
+
+ align:start position:0%
+say what I expect to do so it's sort of
+you know the uh you know all the all the
+
+ align:start position:0%
+you know the uh you know all the all the
+ 
+
+ align:start position:0%
+you know the uh you know all the all the
+um all the joys of having to type more
+
+ align:start position:0%
+um all the joys of having to type more
+ 
+
+ align:start position:0%
+um all the joys of having to type more
+things without type safety um it's not
+
+ align:start position:0%
+things without type safety um it's not
+ 
+
+ align:start position:0%
+things without type safety um it's not
+so good but what do we want to put in as
+
+ align:start position:0%
+so good but what do we want to put in as
+ 
+
+ align:start position:0%
+so good but what do we want to put in as
+our attribute or attributes here we're
+
+ align:start position:0%
+our attribute or attributes here we're
+ 
+
+ align:start position:0%
+our attribute or attributes here we're
+going to return a
+
+ align:start position:0%
+going to return a
+ 
+
+ align:start position:0%
+going to return a
+float what's the first thing that we
+
+ align:start position:0%
+float what's the first thing that we
+ 
+
+ align:start position:0%
+float what's the first thing that we
+that we need ql to
+
+ align:start position:0%
+that we need ql to
+ 
+
+ align:start position:0%
+that we need ql to
+seconds many how many qls yeah so maybe
+
+ align:start position:0%
+seconds many how many qls yeah so maybe
+ 
+
+ align:start position:0%
+seconds many how many qls yeah so maybe
+it'll be ql some people like to do ql in
+
+ align:start position:0%
+it'll be ql some people like to do ql in
+ 
+
+ align:start position:0%
+it'll be ql some people like to do ql in
+and that's going to be measured in what
+
+ align:start position:0%
+and that's going to be measured in what
+ 
+
+ align:start position:0%
+and that's going to be measured in what
+do we want to make
+
+ align:start position:0%
+do we want to make
+ 
+
+ align:start position:0%
+do we want to make
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+float good could be a float in probably
+
+ align:start position:0%
+float good could be a float in probably
+ 
+
+ align:start position:0%
+float good could be a float in probably
+not good enough name something not
+
+ align:start position:0%
+not good enough name something not
+ 
+
+ align:start position:0%
+not good enough name something not
+representational um as an INT in in
+
+ align:start position:0%
+representational um as an INT in in
+ 
+
+ align:start position:0%
+representational um as an INT in in
+quarter lengths eighth note good good um
+
+ align:start position:0%
+quarter lengths eighth note good good um
+ 
+
+ align:start position:0%
+quarter lengths eighth note good good um
+the issue I tend to sometimes use the
+
+ align:start position:0%
+the issue I tend to sometimes use the
+ 
+
+ align:start position:0%
+the issue I tend to sometimes use the
+fraction class if you haven't ever done
+
+ align:start position:0%
+fraction class if you haven't ever done
+ 
+
+ align:start position:0%
+fraction class if you haven't ever done
+that because uh the first time they had
+
+ align:start position:0%
+that because uh the first time they had
+ 
+
+ align:start position:0%
+that because uh the first time they had
+three uh triplets add up actually
+
+ align:start position:0%
+three uh triplets add up actually
+ 
+
+ align:start position:0%
+three uh triplets add up actually
+triplets work fine five quintuplets adds
+
+ align:start position:0%
+triplets work fine five quintuplets adds
+ 
+
+ align:start position:0%
+triplets work fine five quintuplets adds
+up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.1 uh quarter notes that's um why I
+
+ align:start position:0%
+1.1 uh quarter notes that's um why I
+ 
+
+ align:start position:0%
+1.1 uh quarter notes that's um why I
+started moving that but floats pretty
+
+ align:start position:0%
+started moving that but floats pretty
+ 
+
+ align:start position:0%
+started moving that but floats pretty
+good good what so that's attribute one
+
+ align:start position:0%
+good good what so that's attribute one
+ 
+
+ align:start position:0%
+good good what so that's attribute one
+is that anybody want another attribute
+
+ align:start position:0%
+is that anybody want another attribute
+ 
+
+ align:start position:0%
+is that anybody want another attribute
+in there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qu length seconds yes the Tempo Tempo
+
+ align:start position:0%
+qu length seconds yes the Tempo Tempo
+ 
+
+ align:start position:0%
+qu length seconds yes the Tempo Tempo
+good so we can define a Tempo object and
+
+ align:start position:0%
+good so we can define a Tempo object and
+ 
+
+ align:start position:0%
+good so we can define a Tempo object and
+now we're going to see um or struct or
+
+ align:start position:0%
+now we're going to see um or struct or
+ 
+
+ align:start position:0%
+now we're going to see um or struct or
+some some kind of a thing well Temple
+
+ align:start position:0%
+some some kind of a thing well Temple
+ 
+
+ align:start position:0%
+some some kind of a thing well Temple
+could be a a basic thing it could be a
+
+ align:start position:0%
+could be a a basic thing it could be a
+ 
+
+ align:start position:0%
+could be a a basic thing it could be a
+float right what else could it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be what do we if we're not thinking
+
+ align:start position:0%
+be what do we if we're not thinking
+ 
+
+ align:start position:0%
+be what do we if we're not thinking
+about algro monopo as used by handle as
+
+ align:start position:0%
+about algro monopo as used by handle as
+ 
+
+ align:start position:0%
+about algro monopo as used by handle as
+opposed to uh mlon or something like
+
+ align:start position:0%
+opposed to uh mlon or something like
+ 
+
+ align:start position:0%
+opposed to uh mlon or something like
+that what do we
+
+ align:start position:0%
+that what do we
+ 
+
+ align:start position:0%
+that what do we
+yeah beats per minute beats per minute
+
+ align:start position:0%
+yeah beats per minute beats per minute
+ 
+
+ align:start position:0%
+yeah beats per minute beats per minute
+okay so we have beats per minute that's
+
+ align:start position:0%
+okay so we have beats per minute that's
+ 
+
+ align:start position:0%
+okay so we have beats per minute that's
+the most common one right so that's
+
+ align:start position:0%
+the most common one right so that's
+ 
+
+ align:start position:0%
+the most common one right so that's
+going to be what do how do you measure
+
+ align:start position:0%
+going to be what do how do you measure
+ 
+
+ align:start position:0%
+going to be what do how do you measure
+beats per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute oh sorry sorry what what how do
+
+ align:start position:0%
+minute oh sorry sorry what what how do
+ 
+
+ align:start position:0%
+minute oh sorry sorry what what how do
+we want to represent it float
+
+ align:start position:0%
+we want to represent it float
+ 
+
+ align:start position:0%
+we want to represent it float
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so we passed in first thing a quarter
+
+ align:start position:0%
+so we passed in first thing a quarter
+ 
+
+ align:start position:0%
+so we passed in first thing a quarter
+length second thing a Tempo um is that
+
+ align:start position:0%
+length second thing a Tempo um is that
+ 
+
+ align:start position:0%
+length second thing a Tempo um is that
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+why not time signature time signature in
+
+ align:start position:0%
+why not time signature time signature in
+ 
+
+ align:start position:0%
+why not time signature time signature in
+order to Define what what are we
+
+ align:start position:0%
+order to Define what what are we
+ 
+
+ align:start position:0%
+order to Define what what are we
+defining by the time signature how many
+
+ align:start position:0%
+defining by the time signature how many
+ 
+
+ align:start position:0%
+defining by the time signature how many
+beats in quarter length is great beats
+
+ align:start position:0%
+beats in quarter length is great beats
+ 
+
+ align:start position:0%
+beats in quarter length is great beats
+per quarter
+
+ align:start position:0%
+per quarter
+ 
+
+ align:start position:0%
+per quarter
+length so TS will measure in beats per
+
+ align:start position:0%
+length so TS will measure in beats per
+ 
+
+ align:start position:0%
+length so TS will measure in beats per
+quarter
+
+ align:start position:0%
+quarter
+ 
+
+ align:start position:0%
+quarter
+length and what do we want to make that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also float
+
+ align:start position:0%
+also float
+ 
+
+ align:start position:0%
+also float
+good let's let's do this you don't need
+
+ align:start position:0%
+good let's let's do this you don't need
+ 
+
+ align:start position:0%
+good let's let's do this you don't need
+any sort of go ahead grab laptops let's
+
+ align:start position:0%
+any sort of go ahead grab laptops let's
+ 
+
+ align:start position:0%
+any sort of go ahead grab laptops let's
+Implement quarter length to
+
+ align:start position:0%
+Implement quarter length to
+ 
+
+ align:start position:0%
+Implement quarter length to
+Second let's do it as paired programming
+
+ align:start position:0%
+Second let's do it as paired programming
+ 
+
+ align:start position:0%
+Second let's do it as paired programming
+so we learn from each other so um the
+
+ align:start position:0%
+so we learn from each other so um the
+ 
+
+ align:start position:0%
+so we learn from each other so um the
+person on the left is the who who's done
+
+ align:start position:0%
+person on the left is the who who's done
+ 
+
+ align:start position:0%
+person on the left is the who who's done
+paired programming person on the left is
+
+ align:start position:0%
+paired programming person on the left is
+ 
+
+ align:start position:0%
+paired programming person on the left is
+the driver unless unless the person on
+
+ align:start position:0%
+the driver unless unless the person on
+ 
+
+ align:start position:0%
+the driver unless unless the person on
+the left doesn't have the thing and
+
+ align:start position:0%
+the left doesn't have the thing and
+ 
+
+ align:start position:0%
+the left doesn't have the thing and
+that's your your left not my left um and
+
+ align:start position:0%
+that's your your left not my left um and
+ 
+
+ align:start position:0%
+that's your your left not my left um and
+everybody else will that it's 4:34 will
+
+ align:start position:0%
+everybody else will that it's 4:34 will
+ 
+
+ align:start position:0%
+everybody else will that it's 4:34 will
+take about 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minutes okay just just just before we we
+
+ align:start position:0%
+minutes okay just just just before we we
+ 
+
+ align:start position:0%
+minutes okay just just just before we we
+continue and start going on things how
+
+ align:start position:0%
+continue and start going on things how
+ 
+
+ align:start position:0%
+continue and start going on things how
+many people wrote five test cases before
+
+ align:start position:0%
+many people wrote five test cases before
+ 
+
+ align:start position:0%
+many people wrote five test cases before
+you started how many people wrote 10
+
+ align:start position:0%
+you started how many people wrote 10
+ 
+
+ align:start position:0%
+you started how many people wrote 10
+test cases how many people wrote one
+
+ align:start position:0%
+test cases how many people wrote one
+ 
+
+ align:start position:0%
+test cases how many people wrote one
+test case one test case how many people
+
+ align:start position:0%
+test case one test case how many people
+ 
+
+ align:start position:0%
+test case one test case how many people
+wrote zero test cases okay this is
+
+ align:start position:0%
+wrote zero test cases okay this is
+ 
+
+ align:start position:0%
+wrote zero test cases okay this is
+you're going to hear this a couple times
+
+ align:start position:0%
+you're going to hear this a couple times
+ 
+
+ align:start position:0%
+you're going to hear this a couple times
+the next class and stuff and this is
+
+ align:start position:0%
+the next class and stuff and this is
+ 
+
+ align:start position:0%
+the next class and stuff and this is
+very different guys just one second you
+
+ align:start position:0%
+very different guys just one second you
+ 
+
+ align:start position:0%
+very different guys just one second you
+get back into it very different from a
+
+ align:start position:0%
+get back into it very different from a
+ 
+
+ align:start position:0%
+get back into it very different from a
+lot of the especially intro level CS
+
+ align:start position:0%
+lot of the especially intro level CS
+ 
+
+ align:start position:0%
+lot of the especially intro level CS
+class at MIT but because this isn't a
+
+ align:start position:0%
+class at MIT but because this isn't a
+ 
+
+ align:start position:0%
+class at MIT but because this isn't a
+really big established field I I I told
+
+ align:start position:0%
+really big established field I I I told
+ 
+
+ align:start position:0%
+really big established field I I I told
+all yall that you're really you this one
+
+ align:start position:0%
+all yall that you're really you this one
+ 
+
+ align:start position:0%
+all yall that you're really you this one
+of the very few classes like this right
+
+ align:start position:0%
+of the very few classes like this right
+ 
+
+ align:start position:0%
+of the very few classes like this right
+one of the really important things is
+
+ align:start position:0%
+one of the really important things is
+ 
+
+ align:start position:0%
+one of the really important things is
+writing test cases and especially
+
+ align:start position:0%
+writing test cases and especially
+ 
+
+ align:start position:0%
+writing test cases and especially
+looking at corner cases so get in the
+
+ align:start position:0%
+looking at corner cases so get in the
+ 
+
+ align:start position:0%
+looking at corner cases so get in the
+habit of this you're going to if I'm
+
+ align:start position:0%
+habit of this you're going to if I'm
+ 
+
+ align:start position:0%
+habit of this you're going to if I'm
+feeling nice I might give one or to test
+
+ align:start position:0%
+feeling nice I might give one or to test
+ 
+
+ align:start position:0%
+feeling nice I might give one or to test
+cases with correct answers on things but
+
+ align:start position:0%
+cases with correct answers on things but
+ 
+
+ align:start position:0%
+cases with correct answers on things but
+a lot of it is sit down and think at 60
+
+ align:start position:0%
+a lot of it is sit down and think at 60
+ 
+
+ align:start position:0%
+a lot of it is sit down and think at 60
+beats per minute at um 44 how many how
+
+ align:start position:0%
+beats per minute at um 44 how many how
+ 
+
+ align:start position:0%
+beats per minute at um 44 how many how
+long what's the answer for a quarter
+
+ align:start position:0%
+long what's the answer for a quarter
+ 
+
+ align:start position:0%
+long what's the answer for a quarter
+note for
+
+ align:start position:0%
+note for
+ 
+
+ align:start position:0%
+note for
+one one good least make sure your code
+
+ align:start position:0%
+one one good least make sure your code
+ 
+
+ align:start position:0%
+one one good least make sure your code
+does that before we go on so keep going
+
+ align:start position:0%
+does that before we go on so keep going
+ 
+
+ align:start position:0%
+does that before we go on so keep going
+try try some running and try
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some okay let's let's all come back
+
+ align:start position:0%
+some okay let's let's all come back
+ 
+
+ align:start position:0%
+some okay let's let's all come back
+together for a bit because this this
+
+ align:start position:0%
+together for a bit because this this
+ 
+
+ align:start position:0%
+together for a bit because this this
+isn't the problem set and I want to want
+
+ align:start position:0%
+isn't the problem set and I want to want
+ 
+
+ align:start position:0%
+isn't the problem set and I want to want
+to kind of move on and things
+
+ align:start position:0%
+to kind of move on and things
+ 
+
+ align:start position:0%
+to kind of move on and things
+what one of the terms I heard a lot um
+
+ align:start position:0%
+what one of the terms I heard a lot um
+ 
+
+ align:start position:0%
+what one of the terms I heard a lot um
+for uh was this one let's do a
+
+ align:start position:0%
+for uh was this one let's do a
+ 
+
+ align:start position:0%
+for uh was this one let's do a
+dimensional analysis or things like that
+
+ align:start position:0%
+dimensional analysis or things like that
+ 
+
+ align:start position:0%
+dimensional analysis or things like that
+for somebody who didn't use that term or
+
+ align:start position:0%
+for somebody who didn't use that term or
+ 
+
+ align:start position:0%
+for somebody who didn't use that term or
+who doesn't we're all coming from
+
+ align:start position:0%
+who doesn't we're all coming from
+ 
+
+ align:start position:0%
+who doesn't we're all coming from
+different backgrounds and things what's
+
+ align:start position:0%
+different backgrounds and things what's
+ 
+
+ align:start position:0%
+different backgrounds and things what's
+a dimensional analysis sto geometry
+
+ align:start position:0%
+a dimensional analysis sto geometry
+ 
+
+ align:start position:0%
+a dimensional analysis sto geometry
+story geometry well thank you for
+
+ align:start position:0%
+story geometry well thank you for
+ 
+
+ align:start position:0%
+story geometry well thank you for
+obviously skating for
+
+ align:start position:0%
+obviously skating for
+ 
+
+ align:start position:0%
+obviously skating for
+there uh we'll get you other the called
+
+ align:start position:0%
+there uh we'll get you other the called
+ 
+
+ align:start position:0%
+there uh we'll get you other the called
+what's that called stochiometry
+
+ align:start position:0%
+what's that called stochiometry
+ 
+
+ align:start position:0%
+what's that called stochiometry
+stochiometry I i' I have I I must have
+
+ align:start position:0%
+stochiometry I i' I have I I must have
+ 
+
+ align:start position:0%
+stochiometry I i' I have I I must have
+failed trigonometry so I didn't get to
+
+ align:start position:0%
+failed trigonometry so I didn't get to
+ 
+
+ align:start position:0%
+failed trigonometry so I didn't get to
+that one what what is
+
+ align:start position:0%
+that one what what is
+ 
+
+ align:start position:0%
+that one what what is
+what okay what what what what what what
+
+ align:start position:0%
+what okay what what what what what what
+ 
+
+ align:start position:0%
+what okay what what what what what what
+that mean I honestly I just learned a
+
+ align:start position:0%
+that mean I honestly I just learned a
+ 
+
+ align:start position:0%
+that mean I honestly I just learned a
+new word thank you that's just
+
+ align:start position:0%
+new word thank you that's just
+ 
+
+ align:start position:0%
+new word thank you that's just
+dimensional analysis for chemistry
+
+ align:start position:0%
+dimensional analysis for chemistry
+ 
+
+ align:start position:0%
+dimensional analysis for chemistry
+that's just dimensional analysis for
+
+ align:start position:0%
+that's just dimensional analysis for
+ 
+
+ align:start position:0%
+that's just dimensional analysis for
+chemistry okay good I I we remember I I
+
+ align:start position:0%
+chemistry okay good I I we remember I I
+ 
+
+ align:start position:0%
+chemistry okay good I I we remember I I
+was up the river so we didn't we didn't
+
+ align:start position:0%
+was up the river so we didn't we didn't
+ 
+
+ align:start position:0%
+was up the river so we didn't we didn't
+learn these things um uh what's the um
+
+ align:start position:0%
+learn these things um uh what's the um
+ 
+
+ align:start position:0%
+learn these things um uh what's the um
+what what do we mean when we're talking
+
+ align:start position:0%
+what what do we mean when we're talking
+ 
+
+ align:start position:0%
+what what do we mean when we're talking
+about dimensional analysis yeah it's
+
+ align:start position:0%
+about dimensional analysis yeah it's
+ 
+
+ align:start position:0%
+about dimensional analysis yeah it's
+like a conversion between equivalent
+
+ align:start position:0%
+like a conversion between equivalent
+ 
+
+ align:start position:0%
+like a conversion between equivalent
+units conversion between equivalent
+
+ align:start position:0%
+units conversion between equivalent
+ 
+
+ align:start position:0%
+units conversion between equivalent
+units good what are some of dimensional
+
+ align:start position:0%
+units good what are some of dimensional
+ 
+
+ align:start position:0%
+units good what are some of dimensional
+analysis things you uh you've done
+
+ align:start position:0%
+analysis things you uh you've done
+ 
+
+ align:start position:0%
+analysis things you uh you've done
+before this
+
+ align:start position:0%
+before this
+ 
+
+ align:start position:0%
+before this
+class other things Yeahs physics so so
+
+ align:start position:0%
+class other things Yeahs physics so so
+ 
+
+ align:start position:0%
+class other things Yeahs physics so so
+what's what's a dimension what's kind
+
+ align:start position:0%
+what's what's a dimension what's kind
+ 
+
+ align:start position:0%
+what's what's a dimension what's kind
+try convert like um where Str is like
+
+ align:start position:0%
+try convert like um where Str is like
+ 
+
+ align:start position:0%
+try convert like um where Str is like
+meters per second like miles per hour
+
+ align:start position:0%
+meters per second like miles per hour
+ 
+
+ align:start position:0%
+meters per second like miles per hour
+great meters per second to miles per
+
+ align:start position:0%
+great meters per second to miles per
+ 
+
+ align:start position:0%
+great meters per second to miles per
+hour and absolutely thank thank you so
+
+ align:start position:0%
+hour and absolutely thank thank you so
+ 
+
+ align:start position:0%
+hour and absolutely thank thank you so
+we have the particular conversion there
+
+ align:start position:0%
+we have the particular conversion there
+ 
+
+ align:start position:0%
+we have the particular conversion there
+so we have meters seconds miles hours
+
+ align:start position:0%
+so we have meters seconds miles hours
+ 
+
+ align:start position:0%
+so we have meters seconds miles hours
+what what were some dimensionality
+
+ align:start position:0%
+what what were some dimensionality
+ 
+
+ align:start position:0%
+what what were some dimensionality
+things uh uh Dimensions that that you
+
+ align:start position:0%
+things uh uh Dimensions that that you
+ 
+
+ align:start position:0%
+things uh uh Dimensions that that you
+use now that you might not have used in
+
+ align:start position:0%
+use now that you might not have used in
+ 
+
+ align:start position:0%
+use now that you might not have used in
+your past
+
+ align:start position:0%
+your past
+ 
+
+ align:start position:0%
+your past
+before yeah beats quarter lengths beats
+
+ align:start position:0%
+before yeah beats quarter lengths beats
+ 
+
+ align:start position:0%
+before yeah beats quarter lengths beats
+per quarter length it beats quarter L
+
+ align:start position:0%
+per quarter length it beats quarter L
+ 
+
+ align:start position:0%
+per quarter length it beats quarter L
+quarter length per beat good beats
+
+ align:start position:0%
+quarter length per beat good beats
+ 
+
+ align:start position:0%
+quarter length per beat good beats
+quarter lengths absolutely um you've
+
+ align:start position:0%
+quarter lengths absolutely um you've
+ 
+
+ align:start position:0%
+quarter lengths absolutely um you've
+probably done heard beats per minute not
+
+ align:start position:0%
+probably done heard beats per minute not
+ 
+
+ align:start position:0%
+probably done heard beats per minute not
+everybody has thought of it as okay then
+
+ align:start position:0%
+everybody has thought of it as okay then
+ 
+
+ align:start position:0%
+everybody has thought of it as okay then
+I have to convert to um beats
+
+ align:start position:0%
+I have to convert to um beats
+ 
+
+ align:start position:0%
+I have to convert to um beats
+per beats per second which is not
+
+ align:start position:0%
+per beats per second which is not
+ 
+
+ align:start position:0%
+per beats per second which is not
+something we think about we're very very
+
+ align:start position:0%
+something we think about we're very very
+ 
+
+ align:start position:0%
+something we think about we're very very
+good at think about beats per minute as
+
+ align:start position:0%
+good at think about beats per minute as
+ 
+
+ align:start position:0%
+good at think about beats per minute as
+musicians we're very very bad at think
+
+ align:start position:0%
+musicians we're very very bad at think
+ 
+
+ align:start position:0%
+musicians we're very very bad at think
+about beats per second or seconds per
+
+ align:start position:0%
+about beats per second or seconds per
+ 
+
+ align:start position:0%
+about beats per second or seconds per
+beat and then beats per what was the
+
+ align:start position:0%
+beat and then beats per what was the
+ 
+
+ align:start position:0%
+beat and then beats per what was the
+other thing beats per quarter
+
+ align:start position:0%
+other thing beats per quarter
+ 
+
+ align:start position:0%
+other thing beats per quarter
+length awesome so that came up quite a
+
+ align:start position:0%
+length awesome so that came up quite a
+ 
+
+ align:start position:0%
+length awesome so that came up quite a
+bit on on things going on what were some
+
+ align:start position:0%
+bit on on things going on what were some
+ 
+
+ align:start position:0%
+bit on on things going on what were some
+other things that seemed to um stump or
+
+ align:start position:0%
+other things that seemed to um stump or
+ 
+
+ align:start position:0%
+other things that seemed to um stump or
+be be fun or interesting or that you
+
+ align:start position:0%
+be be fun or interesting or that you
+ 
+
+ align:start position:0%
+be be fun or interesting or that you
+learned from programming this I heard a
+
+ align:start position:0%
+learned from programming this I heard a
+ 
+
+ align:start position:0%
+learned from programming this I heard a
+lot of we don't need the time signature
+
+ align:start position:0%
+lot of we don't need the time signature
+ 
+
+ align:start position:0%
+lot of we don't need the time signature
+I think I think I heard that aloud at
+
+ align:start position:0%
+I think I think I heard that aloud at
+ 
+
+ align:start position:0%
+I think I think I heard that aloud at
+least three or four times so but what do
+
+ align:start position:0%
+least three or four times so but what do
+ 
+
+ align:start position:0%
+least three or four times so but what do
+you do if you have the time signature
+
+ align:start position:0%
+you do if you have the time signature
+ 
+
+ align:start position:0%
+you do if you have the time signature
+and the problem let's say we're leaving
+
+ align:start position:0%
+and the problem let's say we're leaving
+ 
+
+ align:start position:0%
+and the problem let's say we're leaving
+out that 5'8 where the beat changes
+
+ align:start position:0%
+out that 5'8 where the beat changes
+ 
+
+ align:start position:0%
+out that 5'8 where the beat changes
+stuff how do we convert from um time
+
+ align:start position:0%
+stuff how do we convert from um time
+ 
+
+ align:start position:0%
+stuff how do we convert from um time
+signature let's let's think of time
+
+ align:start position:0%
+signature let's let's think of time
+ 
+
+ align:start position:0%
+signature let's let's think of time
+signature first as a struct as a as a
+
+ align:start position:0%
+signature first as a struct as a as a
+ 
+
+ align:start position:0%
+signature first as a struct as a as a
+two Tuple of numerator and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denominator how do you convert a
+
+ align:start position:0%
+denominator how do you convert a
+ 
+
+ align:start position:0%
+denominator how do you convert a
+numerator to denominator into um beats
+
+ align:start position:0%
+numerator to denominator into um beats
+ 
+
+ align:start position:0%
+numerator to denominator into um beats
+per quarter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length what is 44 how many beats per
+
+ align:start position:0%
+length what is 44 how many beats per
+ 
+
+ align:start position:0%
+length what is 44 how many beats per
+quarter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length good what is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+22 how many
+
+ align:start position:0%
+22 how many
+ 
+
+ align:start position:0%
+22 how many
+beats oh good I I did I did hear it but
+
+ align:start position:0%
+beats oh good I I did I did hear it but
+ 
+
+ align:start position:0%
+beats oh good I I did I did hear it but
+I heard a lot of I love it this is this
+
+ align:start position:0%
+I heard a lot of I love it this is this
+ 
+
+ align:start position:0%
+I heard a lot of I love it this is this
+is why I'm hoping to get to his class I
+
+ align:start position:0%
+is why I'm hoping to get to his class I
+ 
+
+ align:start position:0%
+is why I'm hoping to get to his class I
+heard a lot of very loud wrong answers
+
+ align:start position:0%
+heard a lot of very loud wrong answers
+ 
+
+ align:start position:0%
+heard a lot of very loud wrong answers
+and then very very trickling right at
+
+ align:start position:0%
+and then very very trickling right at
+ 
+
+ align:start position:0%
+and then very very trickling right at
+the end of little whispered right answer
+
+ align:start position:0%
+the end of little whispered right answer
+ 
+
+ align:start position:0%
+the end of little whispered right answer
+uh how many how many beats per quarter
+
+ align:start position:0%
+uh how many how many beats per quarter
+ 
+
+ align:start position:0%
+uh how many how many beats per quarter
+length for cut time for two
+
+ align:start position:0%
+length for cut time for two
+ 
+
+ align:start position:0%
+length for cut time for two
+two two two and I also heard
+
+ align:start position:0%
+two two two and I also heard
+ 
+
+ align:start position:0%
+two two two and I also heard
+whispered somebody had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 12 how many beats does it take to play
+
+ align:start position:0%
+1 12 how many beats does it take to play
+ 
+
+ align:start position:0%
+1 12 how many beats does it take to play
+a quarter note in 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two how long does each of these is that
+
+ align:start position:0%
+two how long does each of these is that
+ 
+
+ align:start position:0%
+two how long does each of these is that
+correct am I wrong this
+
+ align:start position:0%
+correct am I wrong this
+ 
+
+ align:start position:0%
+correct am I wrong this
+time half a beat this is half a beat and
+
+ align:start position:0%
+time half a beat this is half a beat and
+ 
+
+ align:start position:0%
+time half a beat this is half a beat and
+it gets a quarter note this is half a
+
+ align:start position:0%
+it gets a quarter note this is half a
+ 
+
+ align:start position:0%
+it gets a quarter note this is half a
+beat and it gets a quarter note okay
+
+ align:start position:0%
+beat and it gets a quarter note okay
+ 
+
+ align:start position:0%
+beat and it gets a quarter note okay
+what about in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+32 half 1 half so what do what part do
+
+ align:start position:0%
+32 half 1 half so what do what part do
+ 
+
+ align:start position:0%
+32 half 1 half so what do what part do
+we not need
+
+ align:start position:0%
+we not need
+ 
+
+ align:start position:0%
+we not need
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+numerator so for this particular thing
+
+ align:start position:0%
+numerator so for this particular thing
+ 
+
+ align:start position:0%
+numerator so for this particular thing
+we don't need the numerator we would if
+
+ align:start position:0%
+we don't need the numerator we would if
+ 
+
+ align:start position:0%
+we don't need the numerator we would if
+we yeah go ahead Matthew don't we need
+
+ align:start position:0%
+we yeah go ahead Matthew don't we need
+ 
+
+ align:start position:0%
+we yeah go ahead Matthew don't we need
+the numerator in 68 do we need the
+
+ align:start position:0%
+the numerator in 68 do we need the
+ 
+
+ align:start position:0%
+the numerator in 68 do we need the
+numerator in 68 yes so what do we need
+
+ align:start position:0%
+numerator in 68 yes so what do we need
+ 
+
+ align:start position:0%
+numerator in 68 yes so what do we need
+the numerator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four we only need the numerator to do a
+
+ align:start position:0%
+four we only need the numerator to do a
+ 
+
+ align:start position:0%
+four we only need the numerator to do a
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+operation to see compare if it equal Z
+
+ align:start position:0%
+operation to see compare if it equal Z
+ 
+
+ align:start position:0%
+operation to see compare if it equal Z
+but is that good enough because because
+
+ align:start position:0%
+but is that good enough because because
+ 
+
+ align:start position:0%
+but is that good enough because because
+68 98 128 these all generally default in
+
+ align:start position:0%
+68 98 128 these all generally default in
+ 
+
+ align:start position:0%
+68 98 128 these all generally default in
+most conceptions not all but in most
+
+ align:start position:0%
+most conceptions not all but in most
+ 
+
+ align:start position:0%
+most conceptions not all but in most
+conceptions as the the number of Beats
+
+ align:start position:0%
+conceptions as the the number of Beats
+ 
+
+ align:start position:0%
+conceptions as the the number of Beats
+is divided by three on that so is that
+
+ align:start position:0%
+is divided by three on that so is that
+ 
+
+ align:start position:0%
+is divided by three on that so is that
+good enough does everyone know modulo
+
+ align:start position:0%
+good enough does everyone know modulo
+ 
+
+ align:start position:0%
+good enough does everyone know modulo
+notation like the remainder when divided
+
+ align:start position:0%
+notation like the remainder when divided
+ 
+
+ align:start position:0%
+notation like the remainder when divided
+by three equals zero so does that work
+
+ align:start position:0%
+by three equals zero so does that work
+ 
+
+ align:start position:0%
+by three equals zero so does that work
+68 great uh 88 nope that's a normal one
+
+ align:start position:0%
+68 great uh 88 nope that's a normal one
+ 
+
+ align:start position:0%
+68 great uh 88 nope that's a normal one
+98 great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so 64 great that six how many beats does
+
+ align:start position:0%
+so 64 great that six how many beats does
+ 
+
+ align:start position:0%
+so 64 great that six how many beats does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have in in treated in this in this
+
+ align:start position:0%
+have in in treated in this in this
+ 
+
+ align:start position:0%
+have in in treated in this in this
+way two two one two one dot dot two dot
+
+ align:start position:0%
+way two two one two one dot dot two dot
+ 
+
+ align:start position:0%
+way two two one two one dot dot two dot
+dot yeah I say it has two in I one two
+
+ align:start position:0%
+dot yeah I say it has two in I one two
+ 
+
+ align:start position:0%
+dot yeah I say it has two in I one two
+three four but I I'm giving you the big
+
+ align:start position:0%
+three four but I I'm giving you the big
+ 
+
+ align:start position:0%
+three four but I I'm giving you the big
+one great so six 64 How many does 916
+
+ align:start position:0%
+one great so six 64 How many does 916
+ 
+
+ align:start position:0%
+one great so six 64 How many does 916
+have three three great so this this
+
+ align:start position:0%
+have three three great so this this
+ 
+
+ align:start position:0%
+have three three great so this this
+works right we've we we have all our
+
+ align:start position:0%
+works right we've we we have all our
+ 
+
+ align:start position:0%
+works right we've we we have all our
+good test cases
+
+ align:start position:0%
+good test cases
+ 
+
+ align:start position:0%
+good test cases
+there yeah you're smiling big anyone
+
+ align:start position:0%
+there yeah you're smiling big anyone
+ 
+
+ align:start position:0%
+there yeah you're smiling big anyone
+else smiling big you're smiling big what
+
+ align:start position:0%
+else smiling big you're smiling big what
+ 
+
+ align:start position:0%
+else smiling big you're smiling big what
+what's the test case we've missed 34
+
+ align:start position:0%
+what's the test case we've missed 34
+ 
+
+ align:start position:0%
+what's the test case we've missed 34
+34 so 34 has one
+
+ align:start position:0%
+34 so 34 has one
+ 
+
+ align:start position:0%
+34 so 34 has one
+beat right because you divide by three
+
+ align:start position:0%
+beat right because you divide by three
+ 
+
+ align:start position:0%
+beat right because you divide by three
+so what what do we have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do this if the numerator modu 3 equals
+
+ align:start position:0%
+do this if the numerator modu 3 equals
+ 
+
+ align:start position:0%
+do this if the numerator modu 3 equals
+0 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+num not equals
+
+ align:start position:0%
+num not equals
+ 
+
+ align:start position:0%
+num not equals
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+right that's assuming we've already done
+
+ align:start position:0%
+right that's assuming we've already done
+ 
+
+ align:start position:0%
+right that's assuming we've already done
+our assertion that n numerator is
+
+ align:start position:0%
+our assertion that n numerator is
+ 
+
+ align:start position:0%
+our assertion that n numerator is
+positive and all the other things right
+
+ align:start position:0%
+positive and all the other things right
+ 
+
+ align:start position:0%
+positive and all the other things right
+so these are the algorithms that you
+
+ align:start position:0%
+so these are the algorithms that you
+ 
+
+ align:start position:0%
+so these are the algorithms that you
+already know in your head for music by
+
+ align:start position:0%
+already know in your head for music by
+ 
+
+ align:start position:0%
+already know in your head for music by
+being musicians but they are not the
+
+ align:start position:0%
+being musicians but they are not the
+ 
+
+ align:start position:0%
+being musicians but they are not the
+algorithms that you have been
+
+ align:start position:0%
+algorithms that you have been
+ 
+
+ align:start position:0%
+algorithms that you have been
+programming before here's a particular
+
+ align:start position:0%
+programming before here's a particular
+ 
+
+ align:start position:0%
+programming before here's a particular
+one that's that I always like to do and
+
+ align:start position:0%
+one that's that I always like to do and
+ 
+
+ align:start position:0%
+one that's that I always like to do and
+I don't think we're going to have time
+
+ align:start position:0%
+I don't think we're going to have time
+ 
+
+ align:start position:0%
+I don't think we're going to have time
+to go through it today because you guys
+
+ align:start position:0%
+to go through it today because you guys
+ 
+
+ align:start position:0%
+to go through it today because you guys
+have been such great participants in my
+
+ align:start position:0%
+have been such great participants in my
+ 
+
+ align:start position:0%
+have been such great participants in my
+um in my terrible uh employees and
+
+ align:start position:0%
+um in my terrible uh employees and
+ 
+
+ align:start position:0%
+um in my terrible uh employees and
+things um given a a note given a quarter
+
+ align:start position:0%
+things um given a a note given a quarter
+ 
+
+ align:start position:0%
+things um given a a note given a quarter
+note let's say we we'll keep it really
+
+ align:start position:0%
+note let's say we we'll keep it really
+ 
+
+ align:start position:0%
+note let's say we we'll keep it really
+simple because we're already in we'll
+
+ align:start position:0%
+simple because we're already in we'll
+ 
+
+ align:start position:0%
+simple because we're already in we'll
+call the quarter note one one quarter L
+
+ align:start position:0%
+call the quarter note one one quarter L
+ 
+
+ align:start position:0%
+call the quarter note one one quarter L
+one beat or
+
+ align:start position:0%
+one beat or
+ 
+
+ align:start position:0%
+one beat or
+something given a DOT how many
+
+ align:start position:0%
+something given a DOT how many
+ 
+
+ align:start position:0%
+something given a DOT how many
+beats 1.5 given two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dots three
+
+ align:start position:0%
+dots three
+ 
+
+ align:start position:0%
+dots three
+dots oh somebody had is Trail off good
+
+ align:start position:0%
+dots oh somebody had is Trail off good
+ 
+
+ align:start position:0%
+dots oh somebody had is Trail off good
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+dots what is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula yeah so so working this out and
+
+ align:start position:0%
+formula yeah so so working this out and
+ 
+
+ align:start position:0%
+formula yeah so so working this out and
+if you want I'll put a link online uh
+
+ align:start position:0%
+if you want I'll put a link online uh
+ 
+
+ align:start position:0%
+if you want I'll put a link online uh
+once I originally had to write out this
+
+ align:start position:0%
+once I originally had to write out this
+ 
+
+ align:start position:0%
+once I originally had to write out this
+formula because I kind of needed it it
+
+ align:start position:0%
+formula because I kind of needed it it
+ 
+
+ align:start position:0%
+formula because I kind of needed it it
+becomes kind of fun so um yeah so it and
+
+ align:start position:0%
+becomes kind of fun so um yeah so it and
+ 
+
+ align:start position:0%
+becomes kind of fun so um yeah so it and
+end up being uh what do you call them
+
+ align:start position:0%
+end up being uh what do you call them
+ 
+
+ align:start position:0%
+end up being uh what do you call them
+these are meren numbers which are not
+
+ align:start position:0%
+these are meren numbers which are not
+ 
+
+ align:start position:0%
+these are meren numbers which are not
+the same as meren primes they end up
+
+ align:start position:0%
+the same as meren primes they end up
+ 
+
+ align:start position:0%
+the same as meren primes they end up
+being um sort of n minus one uh what is
+
+ align:start position:0%
+being um sort of n minus one uh what is
+ 
+
+ align:start position:0%
+being um sort of n minus one uh what is
+it 2 to the N - one over 2 to the N so
+
+ align:start position:0%
+it 2 to the N - one over 2 to the N so
+ 
+
+ align:start position:0%
+it 2 to the N - one over 2 to the N so
+you end up one and one half slightly
+
+ align:start position:0%
+you end up one and one half slightly
+ 
+
+ align:start position:0%
+you end up one and one half slightly
+under one and 3/4 1 and 78 so 2 to the N
+
+ align:start position:0%
+under one and 3/4 1 and 78 so 2 to the N
+ 
+
+ align:start position:0%
+under one and 3/4 1 and 78 so 2 to the N
+whatever so you can to figure out okay
+
+ align:start position:0%
+whatever so you can to figure out okay
+ 
+
+ align:start position:0%
+whatever so you can to figure out okay
+and hopefully that works um two to the
+
+ align:start position:0%
+and hopefully that works um two to the
+ 
+
+ align:start position:0%
+and hopefully that works um two to the
+zero sorry that that goes down below
+
+ align:start position:0%
+zero sorry that that goes down below
+ 
+
+ align:start position:0%
+zero sorry that that goes down below
+that's not part of the exponent I should
+
+ align:start position:0%
+that's not part of the exponent I should
+ 
+
+ align:start position:0%
+that's not part of the exponent I should
+make that nicer 2 to the N minus one
+
+ align:start position:0%
+make that nicer 2 to the N minus one
+ 
+
+ align:start position:0%
+make that nicer 2 to the N minus one
+over 2 to the N sorry I haven't been
+
+ align:start position:0%
+over 2 to the N sorry I haven't been
+ 
+
+ align:start position:0%
+over 2 to the N sorry I haven't been
+writing on whiteboards in a year so My
+
+ align:start position:0%
+writing on whiteboards in a year so My
+ 
+
+ align:start position:0%
+writing on whiteboards in a year so My
+technique is a little low so does that
+
+ align:start position:0%
+technique is a little low so does that
+ 
+
+ align:start position:0%
+technique is a little low so does that
+does that work or one plus right yeah so
+
+ align:start position:0%
+does that work or one plus right yeah so
+ 
+
+ align:start position:0%
+does that work or one plus right yeah so
+uh does that work for zero dots what's
+
+ align:start position:0%
+uh does that work for zero dots what's
+ 
+
+ align:start position:0%
+uh does that work for zero dots what's
+two to the
+
+ align:start position:0%
+two to the
+ 
+
+ align:start position:0%
+two to the
+zeroth what's two to the Zer one one
+
+ align:start position:0%
+zeroth what's two to the Zer one one
+ 
+
+ align:start position:0%
+zeroth what's two to the Zer one one
+minus one is zero so that cancels that
+
+ align:start position:0%
+minus one is zero so that cancels that
+ 
+
+ align:start position:0%
+minus one is zero so that cancels that
+out as long as that's not zero there
+
+ align:start position:0%
+out as long as that's not zero there
+ 
+
+ align:start position:0%
+out as long as that's not zero there
+good so we get one what happens if you
+
+ align:start position:0%
+good so we get one what happens if you
+ 
+
+ align:start position:0%
+good so we get one what happens if you
+have a negative one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot 2 to the
+
+ align:start position:0%
+dot 2 to the
+ 
+
+ align:start position:0%
+dot 2 to the
+1 12 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one2 over two to the um over 2 to
+
+ align:start position:0%
+one2 over two to the um over 2 to
+ 
+
+ align:start position:0%
+one2 over two to the um over 2 to
+thetive
+
+ align:start position:0%
+thetive
+ 
+
+ align:start position:0%
+thetive
+1 over2 and what's that end up2 over2 1
+
+ align:start position:0%
+1 over2 and what's that end up2 over2 1
+ 
+
+ align:start position:0%
+1 over2 and what's that end up2 over2 1
++ 1 equal zero zero so every time you
+
+ align:start position:0%
++ 1 equal zero zero so every time you
+ 
+
+ align:start position:0%
++ 1 equal zero zero so every time you
+don't hear any music no you're hearing
+
+ align:start position:0%
+don't hear any music no you're hearing
+ 
+
+ align:start position:0%
+don't hear any music no you're hearing
+the grand Symphony of negative one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dots I think that's a good place to wrap
+
+ align:start position:0%
+dots I think that's a good place to wrap
+ 
+
+ align:start position:0%
+dots I think that's a good place to wrap
+up
\ No newline at end of file
diff --git a/KfmQr8gcBL0.txt b/KfmQr8gcBL0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb9ef8cf9cccbcc5a2e0ab988c975c602aa8c5cc
--- /dev/null
+++ b/KfmQr8gcBL0.txt
@@ -0,0 +1,1323 @@
+align:start position:0%
+ 
+I just wanted to tell you a little bit
+
+ align:start position:0%
+I just wanted to tell you a little bit
+ 
+
+ align:start position:0%
+I just wanted to tell you a little bit
+more about grocery shopping in Italy oh
+
+ align:start position:0%
+more about grocery shopping in Italy oh
+ 
+
+ align:start position:0%
+more about grocery shopping in Italy oh
+while we are
+
+ align:start position:0%
+while we are
+ 
+
+ align:start position:0%
+while we are
+waiting yeah we will say cop cop yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not it's it's a supermarket oh oh yeah
+
+ align:start position:0%
+not it's it's a supermarket oh oh yeah
+ 
+
+ align:start position:0%
+not it's it's a supermarket oh oh yeah
+say say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C okay so do you remember how to say um
+
+ align:start position:0%
+C okay so do you remember how to say um
+ 
+
+ align:start position:0%
+C okay so do you remember how to say um
+I'm going or I go grocery shopping okay
+
+ align:start position:0%
+I'm going or I go grocery shopping okay
+ 
+
+ align:start position:0%
+I'm going or I go grocery shopping okay
+you can say V super okay okay when you
+
+ align:start position:0%
+you can say V super okay okay when you
+ 
+
+ align:start position:0%
+you can say V super okay okay when you
+say I'm I'm I'm getting my groceries
+
+ align:start position:0%
+say I'm I'm I'm getting my groceries
+ 
+
+ align:start position:0%
+say I'm I'm I'm getting my groceries
+usually you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say so it's
+
+ align:start position:0%
+say so it's
+ 
+
+ align:start position:0%
+say so it's
+for so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+repat and is an irregular ver very very
+
+ align:start position:0%
+repat and is an irregular ver very very
+ 
+
+ align:start position:0%
+repat and is an irregular ver very very
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+okay so let's try to review it we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you remember why I'm putting the
+
+ align:start position:0%
+yes you remember why I'm putting the
+ 
+
+ align:start position:0%
+yes you remember why I'm putting the
+subject in parenthesis see because you
+
+ align:start position:0%
+subject in parenthesis see because you
+ 
+
+ align:start position:0%
+subject in parenthesis see because you
+don't usually say yeah we don't usually
+
+ align:start position:0%
+don't usually say yeah we don't usually
+ 
+
+ align:start position:0%
+don't usually say yeah we don't usually
+say unless you really want want to
+
+ align:start position:0%
+say unless you really want want to
+ 
+
+ align:start position:0%
+say unless you really want want to
+emphasize now if you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+upset why don't you
+
+ align:start position:0%
+upset why don't you
+ 
+
+ align:start position:0%
+upset why don't you
+say that's it would be it could be fine
+
+ align:start position:0%
+say that's it would be it could be fine
+ 
+
+ align:start position:0%
+say that's it would be it could be fine
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+say if you really want to emphasize
+
+ align:start position:0%
+say if you really want to emphasize
+ 
+
+ align:start position:0%
+say if you really want to emphasize
+that I am
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going which implies not you
+
+ align:start position:0%
+going which implies not you
+ 
+
+ align:start position:0%
+going which implies not you
+okay yeah see wow you remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything it's a v no don't ruin the
+
+ align:start position:0%
+everything it's a v no don't ruin the
+ 
+
+ align:start position:0%
+everything it's a v no don't ruin the
+magic come on you have one left it's a
+
+ align:start position:0%
+magic come on you have one left it's a
+ 
+
+ align:start position:0%
+magic come on you have one left it's a
+it has to be with the V it's with a V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+yeah okay so let's try like try to read
+
+ align:start position:0%
+yeah okay so let's try like try to read
+ 
+
+ align:start position:0%
+yeah okay so let's try like try to read
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aloud let's do without the subject
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just we have different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+options
+
+ align:start position:0%
+options
+ 
+
+ align:start position:0%
+options
+super marato is a big grocery store like
+
+ align:start position:0%
+super marato is a big grocery store like
+ 
+
+ align:start position:0%
+super marato is a big grocery store like
+you would find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here super
+
+ align:start position:0%
+here super
+ 
+
+ align:start position:0%
+here super
+super super super good a super or maybe
+
+ align:start position:0%
+super super super good a super or maybe
+ 
+
+ align:start position:0%
+super super super good a super or maybe
+you prefer to do your grocery shopping
+
+ align:start position:0%
+you prefer to do your grocery shopping
+ 
+
+ align:start position:0%
+you prefer to do your grocery shopping
+in smaller shops so you have different
+
+ align:start position:0%
+in smaller shops so you have different
+ 
+
+ align:start position:0%
+in smaller shops so you have different
+options that is yes that is in merato
+
+ align:start position:0%
+options that is yes that is in merato
+ 
+
+ align:start position:0%
+options that is yes that is in merato
+but you know what is in merato like the
+
+ align:start position:0%
+but you know what is in merato like the
+ 
+
+ align:start position:0%
+but you know what is in merato like the
+F yes the difference is that that the
+
+ align:start position:0%
+F yes the difference is that that the
+ 
+
+ align:start position:0%
+F yes the difference is that that the
+farmers market usually you get good
+
+ align:start position:0%
+farmers market usually you get good
+ 
+
+ align:start position:0%
+farmers market usually you get good
+stuff but it's kind of expensive if you
+
+ align:start position:0%
+stuff but it's kind of expensive if you
+ 
+
+ align:start position:0%
+stuff but it's kind of expensive if you
+get if you go on Mercato then usually
+
+ align:start position:0%
+get if you go on Mercato then usually
+ 
+
+ align:start position:0%
+get if you go on Mercato then usually
+it's good stuff and it's not more
+
+ align:start position:0%
+it's good stuff and it's not more
+ 
+
+ align:start position:0%
+it's good stuff and it's not more
+expensive every town or every
+
+ align:start position:0%
+expensive every town or every
+ 
+
+ align:start position:0%
+expensive every town or every
+neighborhood has a day of the week when
+
+ align:start position:0%
+neighborhood has a day of the week when
+ 
+
+ align:start position:0%
+neighborhood has a day of the week when
+there is
+
+ align:start position:0%
+there is
+ 
+
+ align:start position:0%
+there is
+inato for example in my hometown inato
+
+ align:start position:0%
+inato for example in my hometown inato
+ 
+
+ align:start position:0%
+inato for example in my hometown inato
+ATB which day Saturday morning yes
+
+ align:start position:0%
+ATB which day Saturday morning yes
+ 
+
+ align:start position:0%
+ATB which day Saturday morning yes
+usually it's always in the morning so
+
+ align:start position:0%
+usually it's always in the morning so
+ 
+
+ align:start position:0%
+usually it's always in the morning so
+when I go visit I always try to be there
+
+ align:start position:0%
+when I go visit I always try to be there
+ 
+
+ align:start position:0%
+when I go visit I always try to be there
+on Saturday morning cuz I love going
+
+ align:start position:0%
+on Saturday morning cuz I love going
+ 
+
+ align:start position:0%
+on Saturday morning cuz I love going
+there you get the best fruits vegetables
+
+ align:start position:0%
+there you get the best fruits vegetables
+ 
+
+ align:start position:0%
+there you get the best fruits vegetables
+the best cheese
+
+ align:start position:0%
+the best cheese
+ 
+
+ align:start position:0%
+the best cheese
+everything and and you don't find only
+
+ align:start position:0%
+everything and and you don't find only
+ 
+
+ align:start position:0%
+everything and and you don't find only
+food you also find clothes and shoes
+
+ align:start position:0%
+food you also find clothes and shoes
+ 
+
+ align:start position:0%
+food you also find clothes and shoes
+really old kind of some so if you go to
+
+ align:start position:0%
+really old kind of some so if you go to
+ 
+
+ align:start position:0%
+really old kind of some so if you go to
+visit some place in Italy you should
+
+ align:start position:0%
+visit some place in Italy you should
+ 
+
+ align:start position:0%
+visit some place in Italy you should
+check when is in the Catt well then you
+
+ align:start position:0%
+check when is in the Catt well then you
+ 
+
+ align:start position:0%
+check when is in the Catt well then you
+can you have different options there are
+
+ align:start position:0%
+can you have different options there are
+ 
+
+ align:start position:0%
+can you have different options there are
+small shops that sell food and they're
+
+ align:start position:0%
+small shops that sell food and they're
+ 
+
+ align:start position:0%
+small shops that sell food and they're
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alimar 1 2 3 element yes El and they
+
+ align:start position:0%
+alimar 1 2 3 element yes El and they
+ 
+
+ align:start position:0%
+alimar 1 2 3 element yes El and they
+tend to be a little bit more expensive
+
+ align:start position:0%
+tend to be a little bit more expensive
+ 
+
+ align:start position:0%
+tend to be a little bit more expensive
+so for some specific um sorts of food
+
+ align:start position:0%
+so for some specific um sorts of food
+ 
+
+ align:start position:0%
+so for some specific um sorts of food
+you would go in a specific shop so if
+
+ align:start position:0%
+you would go in a specific shop so if
+ 
+
+ align:start position:0%
+you would go in a specific shop so if
+you want to
+
+ align:start position:0%
+you want to
+ 
+
+ align:start position:0%
+you want to
+buy buy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p you want to buy meat
+
+ align:start position:0%
+p you want to buy meat
+ 
+
+ align:start position:0%
+p you want to buy meat
+you K is where they actually make it it
+
+ align:start position:0%
+you K is where they actually make it it
+ 
+
+ align:start position:0%
+you K is where they actually make it it
+would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mach and the store wouldn't be the Mach
+
+ align:start position:0%
+Mach and the store wouldn't be the Mach
+ 
+
+ align:start position:0%
+Mach and the store wouldn't be the Mach
+yes yeah Mach yeah the Macha is the
+
+ align:start position:0%
+yes yeah Mach yeah the Macha is the
+ 
+
+ align:start position:0%
+yes yeah Mach yeah the Macha is the
+first I'm sorry I got distracted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mach no we don't have Pia that's Pia P
+
+ align:start position:0%
+Mach no we don't have Pia that's Pia P
+ 
+
+ align:start position:0%
+Mach no we don't have Pia that's Pia P
+you want to buy pastries you're going
+
+ align:start position:0%
+you want to buy pastries you're going
+ 
+
+ align:start position:0%
+you want to buy pastries you're going
+PTI
+
+ align:start position:0%
+PTI
+ 
+
+ align:start position:0%
+PTI
+cheria but now you know how to make them
+
+ align:start position:0%
+cheria but now you know how to make them
+ 
+
+ align:start position:0%
+cheria but now you know how to make them
+so you don't need to what about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seafood and you can get fresh fruits and
+
+ align:start position:0%
+seafood and you can get fresh fruits and
+ 
+
+ align:start position:0%
+seafood and you can get fresh fruits and
+vegetable at
+
+ align:start position:0%
+vegetable at
+ 
+
+ align:start position:0%
+vegetable at
+theato theato yeah or you can go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+fr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you have a lot of different
+
+ align:start position:0%
+okay so you have a lot of different
+ 
+
+ align:start position:0%
+okay so you have a lot of different
+options one another thing that you
+
+ align:start position:0%
+options one another thing that you
+ 
+
+ align:start position:0%
+options one another thing that you
+should keep in mind is that both the
+
+ align:start position:0%
+should keep in mind is that both the
+ 
+
+ align:start position:0%
+should keep in mind is that both the
+super and the smaller neot neio is a
+
+ align:start position:0%
+super and the smaller neot neio is a
+ 
+
+ align:start position:0%
+super and the smaller neot neio is a
+store neio where you
+
+ align:start position:0%
+store neio where you
+ 
+
+ align:start position:0%
+store neio where you
+negotiate yeah you negotiate a lot you
+
+ align:start position:0%
+negotiate yeah you negotiate a lot you
+ 
+
+ align:start position:0%
+negotiate yeah you negotiate a lot you
+can always
+
+ align:start position:0%
+can always
+ 
+
+ align:start position:0%
+can always
+hugle
+
+ align:start position:0%
+hugle
+ 
+
+ align:start position:0%
+hugle
+okay so both super and neot they're
+
+ align:start position:0%
+okay so both super and neot they're
+ 
+
+ align:start position:0%
+okay so both super and neot they're
+usually not open like here
+
+ align:start position:0%
+usually not open like here
+ 
+
+ align:start position:0%
+usually not open like here
+247 so typically they close if you're
+
+ align:start position:0%
+247 so typically they close if you're
+ 
+
+ align:start position:0%
+247 so typically they close if you're
+lucky at 8:00 p.m. or
+
+ align:start position:0%
+lucky at 8:00 p.m. or
+ 
+
+ align:start position:0%
+lucky at 8:00 p.m. or
+earlier they might be closed on Sunday
+
+ align:start position:0%
+earlier they might be closed on Sunday
+ 
+
+ align:start position:0%
+earlier they might be closed on Sunday
+and sometimes they closed on like Monday
+
+ align:start position:0%
+and sometimes they closed on like Monday
+ 
+
+ align:start position:0%
+and sometimes they closed on like Monday
+or Wednesday and some cities they have
+
+ align:start position:0%
+or Wednesday and some cities they have
+ 
+
+ align:start position:0%
+or Wednesday and some cities they have
+different things yeah then another thing
+
+ align:start position:0%
+different things yeah then another thing
+ 
+
+ align:start position:0%
+different things yeah then another thing
+is that the
+
+ align:start position:0%
+is that the
+ 
+
+ align:start position:0%
+is that the
+inotti usually they're closed after
+
+ align:start position:0%
+inotti usually they're closed after
+ 
+
+ align:start position:0%
+inotti usually they're closed after
+lunch so there are another a few things
+
+ align:start position:0%
+lunch so there are another a few things
+ 
+
+ align:start position:0%
+lunch so there are another a few things
+that you should know if you go a super
+
+ align:start position:0%
+that you should know if you go a super
+ 
+
+ align:start position:0%
+that you should know if you go a super
+Med in italan
+
+ align:start position:0%
+Med in italan
+ 
+
+ align:start position:0%
+Med in italan
+okay one thing is that you need to bring
+
+ align:start position:0%
+okay one thing is that you need to bring
+ 
+
+ align:start position:0%
+okay one thing is that you need to bring
+with you a coin
+
+ align:start position:0%
+with you a coin
+ 
+
+ align:start position:0%
+with you a coin
+of or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+what I'm joking we don't we always Sayo
+
+ align:start position:0%
+what I'm joking we don't we always Sayo
+ 
+
+ align:start position:0%
+what I'm joking we don't we always Sayo
+you don't conjugate the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coin okay but you need a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coin yeah see what is
+
+ align:start position:0%
+coin yeah see what is
+ 
+
+ align:start position:0%
+coin yeah see what is
+car yes for the shopping and another
+
+ align:start position:0%
+car yes for the shopping and another
+ 
+
+ align:start position:0%
+car yes for the shopping and another
+thing that's important is that say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+super okay they provide you with gloves
+
+ align:start position:0%
+super okay they provide you with gloves
+ 
+
+ align:start position:0%
+super okay they provide you with gloves
+oh wow plastic gloves for Hygiene so you
+
+ align:start position:0%
+oh wow plastic gloves for Hygiene so you
+ 
+
+ align:start position:0%
+oh wow plastic gloves for Hygiene so you
+can't just touch things you have to wear
+
+ align:start position:0%
+can't just touch things you have to wear
+ 
+
+ align:start position:0%
+can't just touch things you have to wear
+these plastic gloves and then you can
+
+ align:start position:0%
+these plastic gloves and then you can
+ 
+
+ align:start position:0%
+these plastic gloves and then you can
+pick your FRA a Vera and then you also
+
+ align:start position:0%
+pick your FRA a Vera and then you also
+ 
+
+ align:start position:0%
+pick your FRA a Vera and then you also
+have to wait
+
+ align:start position:0%
+have to wait
+ 
+
+ align:start position:0%
+have to wait
+it and and tag it price it yourself and
+
+ align:start position:0%
+it and and tag it price it yourself and
+ 
+
+ align:start position:0%
+it and and tag it price it yourself and
+one last thing nobody will help
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you what did I say you put the into your
+
+ align:start position:0%
+you what did I say you put the into your
+ 
+
+ align:start position:0%
+you what did I say you put the into your
+nobody's going to help you to put
+
+ align:start position:0%
+nobody's going to help you to put
+ 
+
+ align:start position:0%
+nobody's going to help you to put
+lasa grocer
+
+ align:start position:0%
+lasa grocer
+ 
+
+ align:start position:0%
+lasa grocer
+groceries and the bag well so um you
+
+ align:start position:0%
+groceries and the bag well so um you
+ 
+
+ align:start position:0%
+groceries and the bag well so um you
+either bring your own
+
+ align:start position:0%
+either bring your own
+ 
+
+ align:start position:0%
+either bring your own
+STI or what you do you can get them in
+
+ align:start position:0%
+STI or what you do you can get them in
+ 
+
+ align:start position:0%
+STI or what you do you can get them in
+the supermarket and you pay them they're
+
+ align:start position:0%
+the supermarket and you pay them they're
+ 
+
+ align:start position:0%
+the supermarket and you pay them they're
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+expensive don't remember a few cents but
+
+ align:start position:0%
+expensive don't remember a few cents but
+ 
+
+ align:start position:0%
+expensive don't remember a few cents but
+the idea is that so people do not use
+
+ align:start position:0%
+the idea is that so people do not use
+ 
+
+ align:start position:0%
+the idea is that so people do not use
+too many plastic bags but if you payto
+
+ align:start position:0%
+too many plastic bags but if you payto
+ 
+
+ align:start position:0%
+too many plastic bags but if you payto
+you still have to put the groceries on
+
+ align:start position:0%
+you still have to put the groceries on
+ 
+
+ align:start position:0%
+you still have to put the groceries on
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+own yeah y okay one last thing let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so there there are different
+
+ align:start position:0%
+that okay so there there are different
+ 
+
+ align:start position:0%
+that okay so there there are different
+sectors of the
+
+ align:start position:0%
+sectors of the
+ 
+
+ align:start position:0%
+sectors of the
+supermarket the okay so let's say that
+
+ align:start position:0%
+supermarket the okay so let's say that
+ 
+
+ align:start position:0%
+supermarket the okay so let's say that
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+want 100 gr cuz you have to use grams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so instead of
+
+ align:start position:0%
+so instead of
+ 
+
+ align:start position:0%
+so instead of
+saying we would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say you know that ETO is the praic that
+
+ align:start position:0%
+say you know that ETO is the praic that
+ 
+
+ align:start position:0%
+say you know that ETO is the praic that
+you use for 100 isn't it
+
+ align:start position:0%
+you use for 100 isn't it
+ 
+
+ align:start position:0%
+you use for 100 isn't it
+so would
+
+ align:start position:0%
+so would
+ 
+
+ align:start position:0%
+so would
+be so I think it's good to keep in mind
+
+ align:start position:0%
+be so I think it's good to keep in mind
+ 
+
+ align:start position:0%
+be so I think it's good to keep in mind
+because maybe you're asking I would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like and then they may
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is too much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
\ No newline at end of file
diff --git a/Kqf0uO0oV6s.txt b/Kqf0uO0oV6s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3c9f817f83595e98f0bdcea92378b72ba858539a
--- /dev/null
+++ b/Kqf0uO0oV6s.txt
@@ -0,0 +1,11889 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer high quality educational
+
+ align:start position:0%
+to offer high quality educational
+ 
+
+ align:start position:0%
+to offer high quality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu this week uh we're going to
+
+ align:start position:0%
+ocw.mit.edu this week uh we're going to
+ 
+
+ align:start position:0%
+ocw.mit.edu this week uh we're going to
+talk about recurrences how to set them
+
+ align:start position:0%
+talk about recurrences how to set them
+ 
+
+ align:start position:0%
+talk about recurrences how to set them
+up how to model a problem as a recurrent
+
+ align:start position:0%
+up how to model a problem as a recurrent
+ 
+
+ align:start position:0%
+up how to model a problem as a recurrent
+problem and then how to solve them uh
+
+ align:start position:0%
+problem and then how to solve them uh
+ 
+
+ align:start position:0%
+problem and then how to solve them uh
+this stuff is really useful when you get
+
+ align:start position:0%
+this stuff is really useful when you get
+ 
+
+ align:start position:0%
+this stuff is really useful when you get
+into algorithm design and algorithm
+
+ align:start position:0%
+into algorithm design and algorithm
+ 
+
+ align:start position:0%
+into algorithm design and algorithm
+analysis 66 and 6046 we use this stuff a
+
+ align:start position:0%
+analysis 66 and 6046 we use this stuff a
+ 
+
+ align:start position:0%
+analysis 66 and 6046 we use this stuff a
+lot we're going to start with a very
+
+ align:start position:0%
+lot we're going to start with a very
+ 
+
+ align:start position:0%
+lot we're going to start with a very
+famous recurrent problem known as the
+
+ align:start position:0%
+famous recurrent problem known as the
+ 
+
+ align:start position:0%
+famous recurrent problem known as the
+towers of Hanoi problem and I'm guessing
+
+ align:start position:0%
+towers of Hanoi problem and I'm guessing
+ 
+
+ align:start position:0%
+towers of Hanoi problem and I'm guessing
+that many of you have seen this problem
+
+ align:start position:0%
+that many of you have seen this problem
+ 
+
+ align:start position:0%
+that many of you have seen this problem
+one form or another uh in the tower of
+
+ align:start position:0%
+one form or another uh in the tower of
+ 
+
+ align:start position:0%
+one form or another uh in the tower of
+Hanoi problem you got three pegs and N
+
+ align:start position:0%
+Hanoi problem you got three pegs and N
+ 
+
+ align:start position:0%
+Hanoi problem you got three pegs and N
+discs these little guys here all
+
+ align:start position:0%
+discs these little guys here all
+ 
+
+ align:start position:0%
+discs these little guys here all
+different sizes and the object is to
+
+ align:start position:0%
+different sizes and the object is to
+ 
+
+ align:start position:0%
+different sizes and the object is to
+start with a stack like this and move
+
+ align:start position:0%
+start with a stack like this and move
+ 
+
+ align:start position:0%
+start with a stack like this and move
+the discs around so they wind up with
+
+ align:start position:0%
+the discs around so they wind up with
+ 
+
+ align:start position:0%
+the discs around so they wind up with
+the stack on another disc now the rules
+
+ align:start position:0%
+the stack on another disc now the rules
+ 
+
+ align:start position:0%
+the stack on another disc now the rules
+are you can only move one disc at a
+
+ align:start position:0%
+are you can only move one disc at a
+ 
+
+ align:start position:0%
+are you can only move one disc at a
+time and you can never put a big disc
+
+ align:start position:0%
+time and you can never put a big disc
+ 
+
+ align:start position:0%
+time and you can never put a big disc
+over a little disc so that you can't do
+
+ align:start position:0%
+over a little disc so that you can't do
+ 
+
+ align:start position:0%
+over a little disc so that you can't do
+so that would have to go there then you
+
+ align:start position:0%
+so that would have to go there then you
+ 
+
+ align:start position:0%
+so that would have to go there then you
+could do this and now I've got gotten
+
+ align:start position:0%
+could do this and now I've got gotten
+ 
+
+ align:start position:0%
+could do this and now I've got gotten
+the top two moved over to here and the
+
+ align:start position:0%
+the top two moved over to here and the
+ 
+
+ align:start position:0%
+the top two moved over to here and the
+goal is to take the minimum number of
+
+ align:start position:0%
+goal is to take the minimum number of
+ 
+
+ align:start position:0%
+goal is to take the minimum number of
+moves to get the whole stack moved over
+
+ align:start position:0%
+moves to get the whole stack moved over
+ 
+
+ align:start position:0%
+moves to get the whole stack moved over
+to here and to even figure out if that's
+
+ align:start position:0%
+to here and to even figure out if that's
+ 
+
+ align:start position:0%
+to here and to even figure out if that's
+doable
+
+ align:start position:0%
+doable
+ 
+
+ align:start position:0%
+doable
+now this was invented by a famous French
+
+ align:start position:0%
+now this was invented by a famous French
+ 
+
+ align:start position:0%
+now this was invented by a famous French
+mathematician named Edward Lucas in
+
+ align:start position:0%
+mathematician named Edward Lucas in
+ 
+
+ align:start position:0%
+mathematician named Edward Lucas in
+1883 and in the original Legend around
+
+ align:start position:0%
+1883 and in the original Legend around
+ 
+
+ align:start position:0%
+1883 and in the original Legend around
+this puzzle there were 64 four discs
+
+ align:start position:0%
+this puzzle there were 64 four discs
+ 
+
+ align:start position:0%
+this puzzle there were 64 four discs
+this one has just seven on
+
+ align:start position:0%
+this one has just seven on
+ 
+
+ align:start position:0%
+this one has just seven on
+it and the story was at the beginning of
+
+ align:start position:0%
+it and the story was at the beginning of
+ 
+
+ align:start position:0%
+it and the story was at the beginning of
+time God placed the 64 discs on one of
+
+ align:start position:0%
+time God placed the 64 discs on one of
+ 
+
+ align:start position:0%
+time God placed the 64 discs on one of
+the three golden pegs and he or got an
+
+ align:start position:0%
+the three golden pegs and he or got an
+ 
+
+ align:start position:0%
+the three golden pegs and he or got an
+order of monks whose lifelong mission
+
+ align:start position:0%
+order of monks whose lifelong mission
+ 
+
+ align:start position:0%
+order of monks whose lifelong mission
+was to move the disc one at a time so at
+
+ align:start position:0%
+was to move the disc one at a time so at
+ 
+
+ align:start position:0%
+was to move the disc one at a time so at
+the end all 64 discs were lined up on an
+
+ align:start position:0%
+the end all 64 discs were lined up on an
+ 
+
+ align:start position:0%
+the end all 64 discs were lined up on an
+adjacent Peg and according to Legend
+
+ align:start position:0%
+adjacent Peg and according to Legend
+ 
+
+ align:start position:0%
+adjacent Peg and according to Legend
+when that task was done the tower would
+
+ align:start position:0%
+when that task was done the tower would
+ 
+
+ align:start position:0%
+when that task was done the tower would
+crumble and the world would end uh sort
+
+ align:start position:0%
+crumble and the world would end uh sort
+ 
+
+ align:start position:0%
+crumble and the world would end uh sort
+of explains why MOS why monks are never
+
+ align:start position:0%
+of explains why MOS why monks are never
+ 
+
+ align:start position:0%
+of explains why MOS why monks are never
+smiling because they work forever and
+
+ align:start position:0%
+smiling because they work forever and
+ 
+
+ align:start position:0%
+smiling because they work forever and
+then just something bad happens now the
+
+ align:start position:0%
+then just something bad happens now the
+ 
+
+ align:start position:0%
+then just something bad happens now the
+question we want to be able to answer is
+
+ align:start position:0%
+question we want to be able to answer is
+ 
+
+ align:start position:0%
+question we want to be able to answer is
+how long till the world
+
+ align:start position:0%
+how long till the world
+ 
+
+ align:start position:0%
+how long till the world
+ends so we could start with a simpler
+
+ align:start position:0%
+ends so we could start with a simpler
+ 
+
+ align:start position:0%
+ends so we could start with a simpler
+version
+
+ align:start position:0%
+version
+ 
+
+ align:start position:0%
+version
+say let's take three discs and start
+
+ align:start position:0%
+say let's take three discs and start
+ 
+
+ align:start position:0%
+say let's take three discs and start
+with that and let's see you know is a
+
+ align:start position:0%
+with that and let's see you know is a
+ 
+
+ align:start position:0%
+with that and let's see you know is a
+doable well we could that's
+
+ align:start position:0%
+doable well we could that's
+ 
+
+ align:start position:0%
+doable well we could that's
+one that's
+
+ align:start position:0%
+one that's
+ 
+
+ align:start position:0%
+one that's
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+6 7 so it's doable with three discs and
+
+ align:start position:0%
+6 7 so it's doable with three discs and
+ 
+
+ align:start position:0%
+6 7 so it's doable with three discs and
+we took seven moves maybe maybe there's
+
+ align:start position:0%
+we took seven moves maybe maybe there's
+ 
+
+ align:start position:0%
+we took seven moves maybe maybe there's
+a better way and that's part of what
+
+ align:start position:0%
+a better way and that's part of what
+ 
+
+ align:start position:0%
+a better way and that's part of what
+we'll try to study today um in fact what
+
+ align:start position:0%
+we'll try to study today um in fact what
+ 
+
+ align:start position:0%
+we'll try to study today um in fact what
+we'd like to know is how many moves
+
+ align:start position:0%
+we'd like to know is how many moves
+ 
+
+ align:start position:0%
+we'd like to know is how many moves
+moves for n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discs and is it even finite so we're
+
+ align:start position:0%
+discs and is it even finite so we're
+ 
+
+ align:start position:0%
+discs and is it even finite so we're
+going to define t subn to be the minimum
+
+ align:start position:0%
+going to define t subn to be the minimum
+ 
+
+ align:start position:0%
+going to define t subn to be the minimum
+number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moves for n diss so to take a stack of
+
+ align:start position:0%
+moves for n diss so to take a stack of
+ 
+
+ align:start position:0%
+moves for n diss so to take a stack of
+end discs and move them to an adjacent
+
+ align:start position:0%
+end discs and move them to an adjacent
+ 
+
+ align:start position:0%
+end discs and move them to an adjacent
+Peg so for example what's
+
+ align:start position:0%
+Peg so for example what's
+ 
+
+ align:start position:0%
+Peg so for example what's
+T1 one I got one peg I just move it
+
+ align:start position:0%
+T1 one I got one peg I just move it
+ 
+
+ align:start position:0%
+T1 one I got one peg I just move it
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+easy
+
+ align:start position:0%
+easy
+ 
+
+ align:start position:0%
+easy
+T2 three move the little guy move the
+
+ align:start position:0%
+T2 three move the little guy move the
+ 
+
+ align:start position:0%
+T2 three move the little guy move the
+base move the little guy back on top
+
+ align:start position:0%
+base move the little guy back on top
+ 
+
+ align:start position:0%
+base move the little guy back on top
+that's the best you can do and we've
+
+ align:start position:0%
+that's the best you can do and we've
+ 
+
+ align:start position:0%
+that's the best you can do and we've
+seen that T3 is at most
+
+ align:start position:0%
+seen that T3 is at most
+ 
+
+ align:start position:0%
+seen that T3 is at most
+seven maybe maybe there's a better way
+
+ align:start position:0%
+seven maybe maybe there's a better way
+ 
+
+ align:start position:0%
+seven maybe maybe there's a better way
+but let's try to first get an upper
+
+ align:start position:0%
+but let's try to first get an upper
+ 
+
+ align:start position:0%
+but let's try to first get an upper
+bound on
+
+ align:start position:0%
+bound on
+ 
+
+ align:start position:0%
+bound on
+this any thoughts about how we might go
+
+ align:start position:0%
+this any thoughts about how we might go
+ 
+
+ align:start position:0%
+this any thoughts about how we might go
+about a general upper Bound for
+
+ align:start position:0%
+about a general upper Bound for
+ 
+
+ align:start position:0%
+about a general upper Bound for
+n for this
+
+ align:start position:0%
+n for this
+ 
+
+ align:start position:0%
+n for this
+problem like say I had four discs any
+
+ align:start position:0%
+problem like say I had four discs any
+ 
+
+ align:start position:0%
+problem like say I had four discs any
+thoughts about a strategy where we might
+
+ align:start position:0%
+thoughts about a strategy where we might
+ 
+
+ align:start position:0%
+thoughts about a strategy where we might
+be able to analyze or get an upper bound
+
+ align:start position:0%
+be able to analyze or get an upper bound
+ 
+
+ align:start position:0%
+be able to analyze or get an upper bound
+on the number of steps for four discs
+
+ align:start position:0%
+on the number of steps for four discs
+ 
+
+ align:start position:0%
+on the number of steps for four discs
+here or more discs any thoughts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah all right look at the three disk
+
+ align:start position:0%
+yeah all right look at the three disk
+ 
+
+ align:start position:0%
+yeah all right look at the three disk
+problem that's a good idea in fact
+
+ align:start position:0%
+problem that's a good idea in fact
+ 
+
+ align:start position:0%
+problem that's a good idea in fact
+fact you know I could look at the three
+
+ align:start position:0%
+fact you know I could look at the three
+ 
+
+ align:start position:0%
+fact you know I could look at the three
+dis problem recursively I got these
+
+ align:start position:0%
+dis problem recursively I got these
+ 
+
+ align:start position:0%
+dis problem recursively I got these
+three discs say I move them over a
+
+ align:start position:0%
+three discs say I move them over a
+ 
+
+ align:start position:0%
+three discs say I move them over a
+series of steps seven steps at most to
+
+ align:start position:0%
+series of steps seven steps at most to
+ 
+
+ align:start position:0%
+series of steps seven steps at most to
+put them
+
+ align:start position:0%
+put them
+ 
+
+ align:start position:0%
+put them
+here what would I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next move the lower one and then do this
+
+ align:start position:0%
+next move the lower one and then do this
+ 
+
+ align:start position:0%
+next move the lower one and then do this
+recurrent problem again
+
+ align:start position:0%
+recurrent problem again
+ 
+
+ align:start position:0%
+recurrent problem again
+back all right so we can take a problem
+
+ align:start position:0%
+back all right so we can take a problem
+ 
+
+ align:start position:0%
+back all right so we can take a problem
+with n Diss and solve it recursively
+
+ align:start position:0%
+with n Diss and solve it recursively
+ 
+
+ align:start position:0%
+with n Diss and solve it recursively
+let's see what happens when we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so let's look at a recursive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution and let's draw it for n so the
+
+ align:start position:0%
+solution and let's draw it for n so the
+ 
+
+ align:start position:0%
+solution and let's draw it for n so the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+phase that you described is I start here
+
+ align:start position:0%
+phase that you described is I start here
+ 
+
+ align:start position:0%
+phase that you described is I start here
+are my three pegs and I start with this
+
+ align:start position:0%
+are my three pegs and I start with this
+ 
+
+ align:start position:0%
+are my three pegs and I start with this
+one 2 three down to n here and nothing
+
+ align:start position:0%
+one 2 three down to n here and nothing
+ 
+
+ align:start position:0%
+one 2 three down to n here and nothing
+on these
+
+ align:start position:0%
+on these
+ 
+
+ align:start position:0%
+on these
+pegs and I'm going to use cursion to
+
+ align:start position:0%
+pegs and I'm going to use cursion to
+ 
+
+ align:start position:0%
+pegs and I'm going to use cursion to
+take the top n minus one and move them
+
+ align:start position:0%
+take the top n minus one and move them
+ 
+
+ align:start position:0%
+take the top n minus one and move them
+out here so I leave the nth guy there
+
+ align:start position:0%
+out here so I leave the nth guy there
+ 
+
+ align:start position:0%
+out here so I leave the nth guy there
+nothing here and I go one two to n minus
+
+ align:start position:0%
+nothing here and I go one two to n minus
+ 
+
+ align:start position:0%
+nothing here and I go one two to n minus
+one how many steps does that move take
+
+ align:start position:0%
+one how many steps does that move take
+ 
+
+ align:start position:0%
+one how many steps does that move take
+that series of moves take that
+
+ align:start position:0%
+that series of moves take that
+ 
+
+ align:start position:0%
+that series of moves take that
+phase in terms of
+
+ align:start position:0%
+phase in terms of
+ 
+
+ align:start position:0%
+phase in terms of
+t t of n minus one because I'm taking an
+
+ align:start position:0%
+t t of n minus one because I'm taking an
+ 
+
+ align:start position:0%
+t t of n minus one because I'm taking an
+N minus one dis stack and moving it so
+
+ align:start position:0%
+N minus one dis stack and moving it so
+ 
+
+ align:start position:0%
+N minus one dis stack and moving it so
+that is is TN minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps all right now my next
+
+ align:start position:0%
+steps all right now my next
+ 
+
+ align:start position:0%
+steps all right now my next
+move is to take this guy and stick him
+
+ align:start position:0%
+move is to take this guy and stick him
+ 
+
+ align:start position:0%
+move is to take this guy and stick him
+here so we'll draw that over here so the
+
+ align:start position:0%
+here so we'll draw that over here so the
+ 
+
+ align:start position:0%
+here so we'll draw that over here so the
+nth guy moves there and I leave all
+
+ align:start position:0%
+nth guy moves there and I leave all
+ 
+
+ align:start position:0%
+nth guy moves there and I leave all
+these guys
+
+ align:start position:0%
+these guys
+ 
+
+ align:start position:0%
+these guys
+here that's going to be phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two I move the largest disc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how many steps did that
+
+ align:start position:0%
+and how many steps did that
+ 
+
+ align:start position:0%
+and how many steps did that
+take one step just move one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dis one step for that and then my last
+
+ align:start position:0%
+dis one step for that and then my last
+ 
+
+ align:start position:0%
+dis one step for that and then my last
+phase is to take all these and move them
+
+ align:start position:0%
+phase is to take all these and move them
+ 
+
+ align:start position:0%
+phase is to take all these and move them
+on to here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so then it looks like final result 1
+
+ align:start position:0%
+and so then it looks like final result 1
+ 
+
+ align:start position:0%
+and so then it looks like final result 1
+2 over n minus one over n and how many
+
+ align:start position:0%
+2 over n minus one over n and how many
+ 
+
+ align:start position:0%
+2 over n minus one over n and how many
+steps does phase three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take TN minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good all right so we've got an algorithm
+
+ align:start position:0%
+good all right so we've got an algorithm
+ 
+
+ align:start position:0%
+good all right so we've got an algorithm
+now recursive algorithm and the total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time the number of moves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+TN is at
+
+ align:start position:0%
+TN is at
+ 
+
+ align:start position:0%
+TN is at
+most TN minus1 plus tnus one is 2 TN
+
+ align:start position:0%
+most TN minus1 plus tnus one is 2 TN
+ 
+
+ align:start position:0%
+most TN minus1 plus tnus one is 2 TN
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one plus the one step up
+
+ align:start position:0%
+one plus the one step up
+ 
+
+ align:start position:0%
+one plus the one step up
+there for example which we already know
+
+ align:start position:0%
+there for example which we already know
+ 
+
+ align:start position:0%
+there for example which we already know
+T3 is at most T 2 T2 + 1 which is 2 * 3
+
+ align:start position:0%
+T3 is at most T 2 T2 + 1 which is 2 * 3
+ 
+
+ align:start position:0%
+T3 is at most T 2 T2 + 1 which is 2 * 3
++ one is
+
+ align:start position:0%
++ one is
+ 
+
+ align:start position:0%
++ one is
+seven so we already knew we could do it
+
+ align:start position:0%
+seven so we already knew we could do it
+ 
+
+ align:start position:0%
+seven so we already knew we could do it
+in Seven what's an upper bound on the
+
+ align:start position:0%
+in Seven what's an upper bound on the
+ 
+
+ align:start position:0%
+in Seven what's an upper bound on the
+time to move four
+
+ align:start position:0%
+time to move four
+ 
+
+ align:start position:0%
+time to move four
+discs
+
+ align:start position:0%
+discs
+ 
+
+ align:start position:0%
+discs
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay all right so T4 is at most
+
+ align:start position:0%
+okay all right so T4 is at most
+ 
+
+ align:start position:0%
+okay all right so T4 is at most
+15 but maybe there's a better way this
+
+ align:start position:0%
+15 but maybe there's a better way this
+ 
+
+ align:start position:0%
+15 but maybe there's a better way this
+is just one way to do it in fact how
+
+ align:start position:0%
+is just one way to do it in fact how
+ 
+
+ align:start position:0%
+is just one way to do it in fact how
+many people think there's a better way
+
+ align:start position:0%
+many people think there's a better way
+ 
+
+ align:start position:0%
+many people think there's a better way
+than this
+
+ align:start position:0%
+than this
+ 
+
+ align:start position:0%
+than this
+approach all right how many people think
+
+ align:start position:0%
+approach all right how many people think
+ 
+
+ align:start position:0%
+approach all right how many people think
+there is no better way all right very
+
+ align:start position:0%
+there is no better way all right very
+ 
+
+ align:start position:0%
+there is no better way all right very
+good yeah this is the best you can do
+
+ align:start position:0%
+good yeah this is the best you can do
+ 
+
+ align:start position:0%
+good yeah this is the best you can do
+and let's prove that let's get a lower B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+found all right to see why this is
+
+ align:start position:0%
+found all right to see why this is
+ 
+
+ align:start position:0%
+found all right to see why this is
+optimal think about the step where the
+
+ align:start position:0%
+optimal think about the step where the
+ 
+
+ align:start position:0%
+optimal think about the step where the
+nth disc moves at some point in our
+
+ align:start position:0%
+nth disc moves at some point in our
+ 
+
+ align:start position:0%
+nth disc moves at some point in our
+procedure the biggest disc has to
+
+ align:start position:0%
+procedure the biggest disc has to
+ 
+
+ align:start position:0%
+procedure the biggest disc has to
+move now it could move to this Peg or
+
+ align:start position:0%
+move now it could move to this Peg or
+ 
+
+ align:start position:0%
+move now it could move to this Peg or
+that Peg doesn't really matter but when
+
+ align:start position:0%
+that Peg doesn't really matter but when
+ 
+
+ align:start position:0%
+that Peg doesn't really matter but when
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+moves what do I know had to have
+
+ align:start position:0%
+moves what do I know had to have
+ 
+
+ align:start position:0%
+moves what do I know had to have
+happened before that guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moved everything on top of it had to
+
+ align:start position:0%
+moved everything on top of it had to
+ 
+
+ align:start position:0%
+moved everything on top of it had to
+move to the other
+
+ align:start position:0%
+move to the other
+ 
+
+ align:start position:0%
+move to the other
+Peg I started with one through n minus
+
+ align:start position:0%
+Peg I started with one through n minus
+ 
+
+ align:start position:0%
+Peg I started with one through n minus
+one here none of them can be here they
+
+ align:start position:0%
+one here none of them can be here they
+ 
+
+ align:start position:0%
+one here none of them can be here they
+all have to be
+
+ align:start position:0%
+all have to be
+ 
+
+ align:start position:0%
+all have to be
+here okay so that means that I have to
+
+ align:start position:0%
+here okay so that means that I have to
+ 
+
+ align:start position:0%
+here okay so that means that I have to
+have had TN minus one
+
+ align:start position:0%
+have had TN minus one
+ 
+
+ align:start position:0%
+have had TN minus one
+steps so at least TN minus one steps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before the big disc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moves all right then there is the step
+
+ align:start position:0%
+moves all right then there is the step
+ 
+
+ align:start position:0%
+moves all right then there is the step
+when the big guy
+
+ align:start position:0%
+when the big guy
+ 
+
+ align:start position:0%
+when the big guy
+moves all right one step for the big guy
+
+ align:start position:0%
+moves all right one step for the big guy
+ 
+
+ align:start position:0%
+moves all right one step for the big guy
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+move cuz it's got to move at least once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then after it moves I got to get
+
+ align:start position:0%
+and then after it moves I got to get
+ 
+
+ align:start position:0%
+and then after it moves I got to get
+everything else one way or another on
+
+ align:start position:0%
+everything else one way or another on
+ 
+
+ align:start position:0%
+everything else one way or another on
+top of
+
+ align:start position:0%
+top of
+ 
+
+ align:start position:0%
+top of
+it at some point after the last time the
+
+ align:start position:0%
+it at some point after the last time the
+ 
+
+ align:start position:0%
+it at some point after the last time the
+big guy moves everything else has to go
+
+ align:start position:0%
+big guy moves everything else has to go
+ 
+
+ align:start position:0%
+big guy moves everything else has to go
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+top and that's another TN minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps so after the last time the big guy
+
+ align:start position:0%
+steps so after the last time the big guy
+ 
+
+ align:start position:0%
+steps so after the last time the big guy
+moves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you got to take TN minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps okay so that means there's a lower
+
+ align:start position:0%
+steps okay so that means there's a lower
+ 
+
+ align:start position:0%
+steps okay so that means there's a lower
+bound that no matter what you
+
+ align:start position:0%
+bound that no matter what you
+ 
+
+ align:start position:0%
+bound that no matter what you
+do TN is at least 2 TN minus one +
+
+ align:start position:0%
+do TN is at least 2 TN minus one +
+ 
+
+ align:start position:0%
+do TN is at least 2 TN minus one +
+one and so in fact it's
+
+ align:start position:0%
+one and so in fact it's
+ 
+
+ align:start position:0%
+one and so in fact it's
+equal TN equal 2 TN minus1 + 1
+
+ align:start position:0%
+equal TN equal 2 TN minus1 + 1
+ 
+
+ align:start position:0%
+equal TN equal 2 TN minus1 + 1
+so T3 is seven T4 is
+
+ align:start position:0%
+so T3 is seven T4 is
+ 
+
+ align:start position:0%
+so T3 is seven T4 is
+15 any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all right well we'd like to know
+
+ align:start position:0%
+that all right well we'd like to know
+ 
+
+ align:start position:0%
+that all right well we'd like to know
+how long till the world ends which is T
+
+ align:start position:0%
+how long till the world ends which is T
+ 
+
+ align:start position:0%
+how long till the world ends which is T
+64 so we'd like to get a formula for T
+
+ align:start position:0%
+64 so we'd like to get a formula for T
+ 
+
+ align:start position:0%
+64 so we'd like to get a formula for T
+of n we could just compute it 64 times
+
+ align:start position:0%
+of n we could just compute it 64 times
+ 
+
+ align:start position:0%
+of n we could just compute it 64 times
+and see um but much nicer just to get a
+
+ align:start position:0%
+and see um but much nicer just to get a
+ 
+
+ align:start position:0%
+and see um but much nicer just to get a
+formula and that's what we're going to
+
+ align:start position:0%
+formula and that's what we're going to
+ 
+
+ align:start position:0%
+formula and that's what we're going to
+learn how to do this week is to get
+
+ align:start position:0%
+learn how to do this week is to get
+ 
+
+ align:start position:0%
+learn how to do this week is to get
+formulas close form Expressions to solve
+
+ align:start position:0%
+formulas close form Expressions to solve
+ 
+
+ align:start position:0%
+formulas close form Expressions to solve
+recurrences and there's a bunch of
+
+ align:start position:0%
+recurrences and there's a bunch of
+ 
+
+ align:start position:0%
+recurrences and there's a bunch of
+different methods you can use and we're
+
+ align:start position:0%
+different methods you can use and we're
+ 
+
+ align:start position:0%
+different methods you can use and we're
+going to talk about them the uh simplest
+
+ align:start position:0%
+going to talk about them the uh simplest
+ 
+
+ align:start position:0%
+going to talk about them the uh simplest
+is to guess the answer and then check it
+
+ align:start position:0%
+is to guess the answer and then check it
+ 
+
+ align:start position:0%
+is to guess the answer and then check it
+it's called guess and
+
+ align:start position:0%
+it's called guess and
+ 
+
+ align:start position:0%
+it's called guess and
+verify also known as the substitution
+
+ align:start position:0%
+verify also known as the substitution
+ 
+
+ align:start position:0%
+verify also known as the substitution
+method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what's a good guess for T of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n 2 the N minus one you got T of one is
+
+ align:start position:0%
+n 2 the N minus one you got T of one is
+ 
+
+ align:start position:0%
+n 2 the N minus one you got T of one is
+1 T of two is three T of3 is seven T of
+
+ align:start position:0%
+1 T of two is three T of3 is seven T of
+ 
+
+ align:start position:0%
+1 T of two is three T of3 is seven T of
+four is 15 you know you won't compute
+
+ align:start position:0%
+four is 15 you know you won't compute
+ 
+
+ align:start position:0%
+four is 15 you know you won't compute
+too many before you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess that t of n is 2 the N minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now that doesn't mean it's
+
+ align:start position:0%
+all right now that doesn't mean it's
+ 
+
+ align:start position:0%
+all right now that doesn't mean it's
+true so how are we going to verify that
+
+ align:start position:0%
+true so how are we going to verify that
+ 
+
+ align:start position:0%
+true so how are we going to verify that
+guess what proof
+
+ align:start position:0%
+guess what proof
+ 
+
+ align:start position:0%
+guess what proof
+technique induction it just keeps coming
+
+ align:start position:0%
+technique induction it just keeps coming
+ 
+
+ align:start position:0%
+technique induction it just keeps coming
+back just never never finish with
+
+ align:start position:0%
+back just never never finish with
+ 
+
+ align:start position:0%
+back just never never finish with
+induction so we're going to verify
+
+ align:start position:0%
+induction so we're going to verify
+ 
+
+ align:start position:0%
+induction so we're going to verify
+this by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction what what's our induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypothesis any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thoughts right there P of n is going to
+
+ align:start position:0%
+thoughts right there P of n is going to
+ 
+
+ align:start position:0%
+thoughts right there P of n is going to
+be that tnal 2 the N minus one all right
+
+ align:start position:0%
+be that tnal 2 the N minus one all right
+ 
+
+ align:start position:0%
+be that tnal 2 the N minus one all right
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+typical so the predicate is that t of n
+
+ align:start position:0%
+typical so the predicate is that t of n
+ 
+
+ align:start position:0%
+typical so the predicate is that t of n
+is 2 the N minus one base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case we'll pick Nal 1
+
+ align:start position:0%
+case we'll pick Nal 1
+ 
+
+ align:start position:0%
+case we'll pick Nal 1
+T of 1 is 1 and that is 2 1us 1 so the
+
+ align:start position:0%
+T of 1 is 1 and that is 2 1us 1 so the
+ 
+
+ align:start position:0%
+T of 1 is 1 and that is 2 1us 1 so the
+base case
+
+ align:start position:0%
+base case
+ 
+
+ align:start position:0%
+base case
+works now we'll do the inductive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step we're going to
+
+ align:start position:0%
+step we're going to
+ 
+
+ align:start position:0%
+step we're going to
+assume P of n we're going to assume that
+
+ align:start position:0%
+assume P of n we're going to assume that
+ 
+
+ align:start position:0%
+assume P of n we're going to assume that
+TN equals 2 to the N minus1 to prove PN
+
+ align:start position:0%
+TN equals 2 to the N minus1 to prove PN
+ 
+
+ align:start position:0%
+TN equals 2 to the N minus1 to prove PN
+minus1 which is T n + 1 = 2 n + 1us 1 so
+
+ align:start position:0%
+minus1 which is T n + 1 = 2 n + 1us 1 so
+ 
+
+ align:start position:0%
+minus1 which is T n + 1 = 2 n + 1us 1 so
+very standard induction so let's look at
+
+ align:start position:0%
+very standard induction so let's look at
+ 
+
+ align:start position:0%
+very standard induction so let's look at
+TN + one
+
+ align:start position:0%
+TN + one
+ 
+
+ align:start position:0%
+TN + one
+now TN + 1 equal 2
+
+ align:start position:0%
+now TN + 1 equal 2
+ 
+
+ align:start position:0%
+now TN + 1 equal 2
+TN + 1 uh yeah 2 tn+
+
+ align:start position:0%
+TN + 1 uh yeah 2 tn+
+ 
+
+ align:start position:0%
+TN + 1 uh yeah 2 tn+
+one now we plug in here that's just the
+
+ align:start position:0%
+one now we plug in here that's just the
+ 
+
+ align:start position:0%
+one now we plug in here that's just the
+recurrence now we plug in using our
+
+ align:start position:0%
+recurrence now we plug in using our
+ 
+
+ align:start position:0%
+recurrence now we plug in using our
+assumption from the induction this is
+
+ align:start position:0%
+assumption from the induction this is
+ 
+
+ align:start position:0%
+assumption from the induction this is
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 the N - 1 + 1 multiply the two that's
+
+ align:start position:0%
+2 the N - 1 + 1 multiply the two that's
+ 
+
+ align:start position:0%
+2 the N - 1 + 1 multiply the two that's
+2 the n + 1 -2 + 1 is
+
+ align:start position:0%
+2 the n + 1 -2 + 1 is
+ 
+
+ align:start position:0%
+2 the n + 1 -2 + 1 is
+minus1 and so we're
+
+ align:start position:0%
+minus1 and so we're
+ 
+
+ align:start position:0%
+minus1 and so we're
+done all right so we guessed the answer
+
+ align:start position:0%
+done all right so we guessed the answer
+ 
+
+ align:start position:0%
+done all right so we guessed the answer
+it was a pretty easy guess very simple
+
+ align:start position:0%
+it was a pretty easy guess very simple
+ 
+
+ align:start position:0%
+it was a pretty easy guess very simple
+to prove it by
+
+ align:start position:0%
+to prove it by
+ 
+
+ align:start position:0%
+to prove it by
+induction any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions all right how long would it
+
+ align:start position:0%
+questions all right how long would it
+ 
+
+ align:start position:0%
+questions all right how long would it
+take me to do all seven discs on this
+
+ align:start position:0%
+take me to do all seven discs on this
+ 
+
+ align:start position:0%
+take me to do all seven discs on this
+puzzle here
+
+ align:start position:0%
+puzzle here
+ 
+
+ align:start position:0%
+puzzle here
+how many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps 127 steps how long till the end of
+
+ align:start position:0%
+steps 127 steps how long till the end of
+ 
+
+ align:start position:0%
+steps 127 steps how long till the end of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+world a long time 2 to the 64th minus 1
+
+ align:start position:0%
+world a long time 2 to the 64th minus 1
+ 
+
+ align:start position:0%
+world a long time 2 to the 64th minus 1
+is 18 billion billion moves so going to
+
+ align:start position:0%
+is 18 billion billion moves so going to
+ 
+
+ align:start position:0%
+is 18 billion billion moves so going to
+keep those monks busy for a little
+
+ align:start position:0%
+keep those monks busy for a little
+ 
+
+ align:start position:0%
+keep those monks busy for a little
+while before the world
+
+ align:start position:0%
+while before the world
+ 
+
+ align:start position:0%
+while before the world
+ends now in general this method is sort
+
+ align:start position:0%
+ends now in general this method is sort
+ 
+
+ align:start position:0%
+ends now in general this method is sort
+of the best method for solving a
+
+ align:start position:0%
+of the best method for solving a
+ 
+
+ align:start position:0%
+of the best method for solving a
+recurrence we'll see lots of examples
+
+ align:start position:0%
+recurrence we'll see lots of examples
+ 
+
+ align:start position:0%
+recurrence we'll see lots of examples
+where it works great the only problem is
+
+ align:start position:0%
+where it works great the only problem is
+ 
+
+ align:start position:0%
+where it works great the only problem is
+it requires that Divine Insight thing
+
+ align:start position:0%
+it requires that Divine Insight thing
+ 
+
+ align:start position:0%
+it requires that Divine Insight thing
+that guess to guess the right answer
+
+ align:start position:0%
+that guess to guess the right answer
+ 
+
+ align:start position:0%
+that guess to guess the right answer
+obviously if you guess the wrong answer
+
+ align:start position:0%
+obviously if you guess the wrong answer
+ 
+
+ align:start position:0%
+obviously if you guess the wrong answer
+it's not going to not going to work
+
+ align:start position:0%
+it's not going to not going to work
+ 
+
+ align:start position:0%
+it's not going to not going to work
+guessing is many times easy but not
+
+ align:start position:0%
+guessing is many times easy but not
+ 
+
+ align:start position:0%
+guessing is many times easy but not
+always um so you need other methods when
+
+ align:start position:0%
+always um so you need other methods when
+ 
+
+ align:start position:0%
+always um so you need other methods when
+you can't guess it the next most common
+
+ align:start position:0%
+you can't guess it the next most common
+ 
+
+ align:start position:0%
+you can't guess it the next most common
+method is called has a lot of names
+
+ align:start position:0%
+method is called has a lot of names
+ 
+
+ align:start position:0%
+method is called has a lot of names
+called plug and
+
+ align:start position:0%
+called plug and
+ 
+
+ align:start position:0%
+called plug and
+chug uh expansion iteration Brute Force
+
+ align:start position:0%
+chug uh expansion iteration Brute Force
+ 
+
+ align:start position:0%
+chug uh expansion iteration Brute Force
+exhaustion
+
+ align:start position:0%
+exhaustion
+ 
+
+ align:start position:0%
+exhaustion
+um let me show you how that works on
+
+ align:start position:0%
+um let me show you how that works on
+ 
+
+ align:start position:0%
+um let me show you how that works on
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example okay so plug and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chug so we'll solve the same
+
+ align:start position:0%
+chug so we'll solve the same
+ 
+
+ align:start position:0%
+chug so we'll solve the same
+recurrence so we've got TN equals and
+
+ align:start position:0%
+recurrence so we've got TN equals and
+ 
+
+ align:start position:0%
+recurrence so we've got TN equals and
+I'm going to write it just reverse 1
+
+ align:start position:0%
+I'm going to write it just reverse 1
+ 
+
+ align:start position:0%
+I'm going to write it just reverse 1
+plus 2 TN because I'm going to expand
+
+ align:start position:0%
+plus 2 TN because I'm going to expand
+ 
+
+ align:start position:0%
+plus 2 TN because I'm going to expand
+out the recurrent term it's why it's
+
+ align:start position:0%
+out the recurrent term it's why it's
+ 
+
+ align:start position:0%
+out the recurrent term it's why it's
+called expansion
+
+ align:start position:0%
+called expansion
+ 
+
+ align:start position:0%
+called expansion
+also well that's equal to 1 + 2 now I
+
+ align:start position:0%
+also well that's equal to 1 + 2 now I
+ 
+
+ align:start position:0%
+also well that's equal to 1 + 2 now I
+expand this out using the recurrence 1 +
+
+ align:start position:0%
+expand this out using the recurrence 1 +
+ 
+
+ align:start position:0%
+expand this out using the recurrence 1 +
+2 TN minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all right now I do a little chugging
+
+ align:start position:0%
+one all right now I do a little chugging
+ 
+
+ align:start position:0%
+one all right now I do a little chugging
+here so I plugged
+
+ align:start position:0%
+here so I plugged
+ 
+
+ align:start position:0%
+here so I plugged
+here now I'll do
+
+ align:start position:0%
+here now I'll do
+ 
+
+ align:start position:0%
+here now I'll do
+chug that's 1 + 2 + 4 TN
+
+ align:start position:0%
+chug that's 1 + 2 + 4 TN
+ 
+
+ align:start position:0%
+chug that's 1 + 2 + 4 TN
+minus1 now I'm going to plug in
+
+ align:start position:0%
+minus1 now I'm going to plug in
+ 
+
+ align:start position:0%
+minus1 now I'm going to plug in
+again what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that you're
+
+ align:start position:0%
+that you're
+ 
+
+ align:start position:0%
+that you're
+right you're right I got to get minus
+
+ align:start position:0%
+right you're right I got to get minus
+ 
+
+ align:start position:0%
+right you're right I got to get minus
+one here and minus two here that is
+
+ align:start position:0%
+one here and minus two here that is
+ 
+
+ align:start position:0%
+one here and minus two here that is
+correct very good I would have run into
+
+ align:start position:0%
+correct very good I would have run into
+ 
+
+ align:start position:0%
+correct very good I would have run into
+trouble that's
+
+ align:start position:0%
+trouble that's
+ 
+
+ align:start position:0%
+trouble that's
+good all right now I plug in here 1 + 2
+
+ align:start position:0%
+good all right now I plug in here 1 + 2
+ 
+
+ align:start position:0%
+good all right now I plug in here 1 + 2
++ 4 4 1 + 2 tnus
+
+ align:start position:0%
++ 4 4 1 + 2 tnus
+ 
+
+ align:start position:0%
++ 4 4 1 + 2 tnus
+3 then we do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chug 1 + 2 + 4 + 8 TN minus
+
+ align:start position:0%
+Chug 1 + 2 + 4 + 8 TN minus
+ 
+
+ align:start position:0%
+Chug 1 + 2 + 4 + 8 TN minus
+3 all right and now we're going to try
+
+ align:start position:0%
+3 all right and now we're going to try
+ 
+
+ align:start position:0%
+3 all right and now we're going to try
+to observe the pattern we're getting so
+
+ align:start position:0%
+to observe the pattern we're getting so
+ 
+
+ align:start position:0%
+to observe the pattern we're getting so
+there's a little bit of a guess going on
+
+ align:start position:0%
+there's a little bit of a guess going on
+ 
+
+ align:start position:0%
+there's a little bit of a guess going on
+in this context still but you see the
+
+ align:start position:0%
+in this context still but you see the
+ 
+
+ align:start position:0%
+in this context still but you see the
+pattern we got powers of two pretty easy
+
+ align:start position:0%
+pattern we got powers of two pretty easy
+ 
+
+ align:start position:0%
+pattern we got powers of two pretty easy
+pattern so you might say if I keep on
+
+ align:start position:0%
+pattern so you might say if I keep on
+ 
+
+ align:start position:0%
+pattern so you might say if I keep on
+doing this I'm going to get 1+ 2+ 4 plus
+
+ align:start position:0%
+doing this I'm going to get 1+ 2+ 4 plus
+ 
+
+ align:start position:0%
+doing this I'm going to get 1+ 2+ 4 plus
+dot dot dot plus 2 to the I -1 + 2 to
+
+ align:start position:0%
+dot dot dot plus 2 to the I -1 + 2 to
+ 
+
+ align:start position:0%
+dot dot dot plus 2 to the I -1 + 2 to
+the i t nus
+
+ align:start position:0%
+the i t nus
+ 
+
+ align:start position:0%
+the i t nus
+i so got 2 3 TN minus 3
+
+ align:start position:0%
+i so got 2 3 TN minus 3
+ 
+
+ align:start position:0%
+i so got 2 3 TN minus 3
+there and then I take this all the way
+
+ align:start position:0%
+there and then I take this all the way
+ 
+
+ align:start position:0%
+there and then I take this all the way
+down to I = nus 1 1 + 2 +
+
+ align:start position:0%
+down to I = nus 1 1 + 2 +
+ 
+
+ align:start position:0%
+down to I = nus 1 1 + 2 +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
++ 2 to the nus 2 + 2 to the
+
+ align:start position:0%
++ 2 to the nus 2 + 2 to the
+ 
+
+ align:start position:0%
++ 2 to the nus 2 + 2 to the
+nus1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T1 and T1 is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so I'm just getting the sum of the
+
+ align:start position:0%
+one so I'm just getting the sum of the
+ 
+
+ align:start position:0%
+one so I'm just getting the sum of the
+powers of two up to 2 the N minus one
+
+ align:start position:0%
+powers of two up to 2 the N minus one
+ 
+
+ align:start position:0%
+powers of two up to 2 the N minus one
+and we know what that is from
+
+ align:start position:0%
+and we know what that is from
+ 
+
+ align:start position:0%
+and we know what that is from
+last time for sure that's just 2 the N
+
+ align:start position:0%
+last time for sure that's just 2 the N
+ 
+
+ align:start position:0%
+last time for sure that's just 2 the N
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one all right so we've derived the
+
+ align:start position:0%
+one all right so we've derived the
+ 
+
+ align:start position:0%
+one all right so we've derived the
+answer with only a little bit of a we
+
+ align:start position:0%
+answer with only a little bit of a we
+ 
+
+ align:start position:0%
+answer with only a little bit of a we
+had to observe the pattern here which is
+
+ align:start position:0%
+had to observe the pattern here which is
+ 
+
+ align:start position:0%
+had to observe the pattern here which is
+often easy to do but now we've derived
+
+ align:start position:0%
+often easy to do but now we've derived
+ 
+
+ align:start position:0%
+often easy to do but now we've derived
+the answer now to be really safe we got
+
+ align:start position:0%
+the answer now to be really safe we got
+ 
+
+ align:start position:0%
+the answer now to be really safe we got
+to go back and still do verify just to
+
+ align:start position:0%
+to go back and still do verify just to
+ 
+
+ align:start position:0%
+to go back and still do verify just to
+make sure that we didn't make a mistake
+
+ align:start position:0%
+make sure that we didn't make a mistake
+ 
+
+ align:start position:0%
+make sure that we didn't make a mistake
+in how we you know did the derivation
+
+ align:start position:0%
+in how we you know did the derivation
+ 
+
+ align:start position:0%
+in how we you know did the derivation
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay any
+
+ align:start position:0%
+okay any
+ 
+
+ align:start position:0%
+okay any
+questions about that approach roach you
+
+ align:start position:0%
+questions about that approach roach you
+ 
+
+ align:start position:0%
+questions about that approach roach you
+just keep plugging it back into the
+
+ align:start position:0%
+just keep plugging it back into the
+ 
+
+ align:start position:0%
+just keep plugging it back into the
+recurrence look at the pattern you get
+
+ align:start position:0%
+recurrence look at the pattern you get
+ 
+
+ align:start position:0%
+recurrence look at the pattern you get
+and try to guess it from from that point
+
+ align:start position:0%
+and try to guess it from from that point
+ 
+
+ align:start position:0%
+and try to guess it from from that point
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+solve all right let's do a little more
+
+ align:start position:0%
+solve all right let's do a little more
+ 
+
+ align:start position:0%
+solve all right let's do a little more
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+recurrence fact this is a fairly famous
+
+ align:start position:0%
+recurrence fact this is a fairly famous
+ 
+
+ align:start position:0%
+recurrence fact this is a fairly famous
+one that comes up in a well-known
+
+ align:start position:0%
+one that comes up in a well-known
+ 
+
+ align:start position:0%
+one that comes up in a well-known
+algorithm for sorting called merge sort
+
+ align:start position:0%
+algorithm for sorting called merge sort
+ 
+
+ align:start position:0%
+algorithm for sorting called merge sort
+this is an algorithm you'll look at in
+
+ align:start position:0%
+this is an algorithm you'll look at in
+ 
+
+ align:start position:0%
+this is an algorithm you'll look at in
+6046 one of the many sorting algorithms
+
+ align:start position:0%
+6046 one of the many sorting algorithms
+ 
+
+ align:start position:0%
+6046 one of the many sorting algorithms
+you'll study when you take an
+
+ align:start position:0%
+you'll study when you take an
+ 
+
+ align:start position:0%
+you'll study when you take an
+algorithm's class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you you give you're given n numbers
+
+ align:start position:0%
+so you you give you're given n numbers
+ 
+
+ align:start position:0%
+so you you give you're given n numbers
+and your task is to sort them put them
+
+ align:start position:0%
+and your task is to sort them put them
+ 
+
+ align:start position:0%
+and your task is to sort them put them
+in order and you're allowed to do
+
+ align:start position:0%
+in order and you're allowed to do
+ 
+
+ align:start position:0%
+in order and you're allowed to do
+comparisons between the numbers you
+
+ align:start position:0%
+comparisons between the numbers you
+ 
+
+ align:start position:0%
+comparisons between the numbers you
+could think of them as you got a A list
+
+ align:start position:0%
+could think of them as you got a A list
+ 
+
+ align:start position:0%
+could think of them as you got a A list
+of names putting them in alphabetical
+
+ align:start position:0%
+of names putting them in alphabetical
+ 
+
+ align:start position:0%
+of names putting them in alphabetical
+order uh how many comparisons do you
+
+ align:start position:0%
+order uh how many comparisons do you
+ 
+
+ align:start position:0%
+order uh how many comparisons do you
+have to do to make that
+
+ align:start position:0%
+have to do to make that
+ 
+
+ align:start position:0%
+have to do to make that
+happen and this is one way to do it
+
+ align:start position:0%
+happen and this is one way to do it
+ 
+
+ align:start position:0%
+happen and this is one way to do it
+that's very
+
+ align:start position:0%
+that's very
+ 
+
+ align:start position:0%
+that's very
+efficient so to sort n items in fact
+
+ align:start position:0%
+efficient so to sort n items in fact
+ 
+
+ align:start position:0%
+efficient so to sort n items in fact
+we're going to look at n being a power
+
+ align:start position:0%
+we're going to look at n being a power
+ 
+
+ align:start position:0%
+we're going to look at n being a power
+of two call the items X1
+
+ align:start position:0%
+of two call the items X1
+ 
+
+ align:start position:0%
+of two call the items X1
+X2
+
+ align:start position:0%
+X2
+ 
+
+ align:start position:0%
+X2
+xn n is going to be power of two to make
+
+ align:start position:0%
+xn n is going to be power of two to make
+ 
+
+ align:start position:0%
+xn n is going to be power of two to make
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+simple for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the first thing we're going to do is
+
+ align:start position:0%
+now the first thing we're going to do is
+ 
+
+ align:start position:0%
+now the first thing we're going to do is
+recursively sort the first half of the
+
+ align:start position:0%
+recursively sort the first half of the
+ 
+
+ align:start position:0%
+recursively sort the first half of the
+items and the second half
+
+ align:start position:0%
+items and the second half
+ 
+
+ align:start position:0%
+items and the second half
+so we use recursion to sort the first n/
+
+ align:start position:0%
+so we use recursion to sort the first n/
+ 
+
+ align:start position:0%
+so we use recursion to sort the first n/
+two items and the last n/ two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+items and then we're going to merge
+
+ align:start position:0%
+items and then we're going to merge
+ 
+
+ align:start position:0%
+items and then we're going to merge
+those two sorted lists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together so we're going to merge this
+
+ align:start position:0%
+together so we're going to merge this
+ 
+
+ align:start position:0%
+together so we're going to merge this
+list and that list so let's see how this
+
+ align:start position:0%
+list and that list so let's see how this
+ 
+
+ align:start position:0%
+list and that list so let's see how this
+works and figure out how many
+
+ align:start position:0%
+works and figure out how many
+ 
+
+ align:start position:0%
+works and figure out how many
+comparisons we have to do to sort the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+list for
+
+ align:start position:0%
+list for
+ 
+
+ align:start position:0%
+list for
+example let's say we're
+
+ align:start position:0%
+example let's say we're
+ 
+
+ align:start position:0%
+example let's say we're
+sorting this list
+
+ align:start position:0%
+sorting this list
+ 
+
+ align:start position:0%
+sorting this list
+10 7
+
+ align:start position:0%
+10 7
+ 
+
+ align:start position:0%
+10 7
+23 5 2 4 three and nine so I've got
+
+ align:start position:0%
+23 5 2 4 three and nine so I've got
+ 
+
+ align:start position:0%
+23 5 2 4 three and nine so I've got
+eight numbers that I'm going to sort
+
+ align:start position:0%
+eight numbers that I'm going to sort
+ 
+
+ align:start position:0%
+eight numbers that I'm going to sort
+so the first step is to recursively sort
+
+ align:start position:0%
+so the first step is to recursively sort
+ 
+
+ align:start position:0%
+so the first step is to recursively sort
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+list and when I do that I produce I'm
+
+ align:start position:0%
+list and when I do that I produce I'm
+ 
+
+ align:start position:0%
+list and when I do that I produce I'm
+sorting 10 7 23 and
+
+ align:start position:0%
+sorting 10 7 23 and
+ 
+
+ align:start position:0%
+sorting 10 7 23 and
+five and that produces let's see I'm
+
+ align:start position:0%
+five and that produces let's see I'm
+ 
+
+ align:start position:0%
+five and that produces let's see I'm
+going to get 5 7 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+23 and then I recursively sort these
+
+ align:start position:0%
+23 and then I recursively sort these
+ 
+
+ align:start position:0%
+23 and then I recursively sort these
+guys
+
+ align:start position:0%
+guys
+ 
+
+ align:start position:0%
+guys
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+produces 2 3 4 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nine I've done comparisons but haven't
+
+ align:start position:0%
+nine I've done comparisons but haven't
+ 
+
+ align:start position:0%
+nine I've done comparisons but haven't
+counted them because they're in the
+
+ align:start position:0%
+counted them because they're in the
+ 
+
+ align:start position:0%
+counted them because they're in the
+recursion now I'm going to use
+
+ align:start position:0%
+recursion now I'm going to use
+ 
+
+ align:start position:0%
+recursion now I'm going to use
+comparisons to merge the list and the
+
+ align:start position:0%
+comparisons to merge the list and the
+ 
+
+ align:start position:0%
+comparisons to merge the list and the
+way I'm going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is to look at the smallest item in
+
+ align:start position:0%
+that is to look at the smallest item in
+ 
+
+ align:start position:0%
+that is to look at the smallest item in
+each list and compare
+
+ align:start position:0%
+each list and compare
+ 
+
+ align:start position:0%
+each list and compare
+them because I know the smallest item
+
+ align:start position:0%
+them because I know the smallest item
+ 
+
+ align:start position:0%
+them because I know the smallest item
+overall is either this one or that one
+
+ align:start position:0%
+overall is either this one or that one
+ 
+
+ align:start position:0%
+overall is either this one or that one
+and when I compare two to five two is
+
+ align:start position:0%
+and when I compare two to five two is
+ 
+
+ align:start position:0%
+and when I compare two to five two is
+the smaller one so I start with two and
+
+ align:start position:0%
+the smaller one so I start with two and
+ 
+
+ align:start position:0%
+the smaller one so I start with two and
+I strike
+
+ align:start position:0%
+I strike
+ 
+
+ align:start position:0%
+I strike
+it what two items do I compare next to
+
+ align:start position:0%
+it what two items do I compare next to
+ 
+
+ align:start position:0%
+it what two items do I compare next to
+get the next smallest
+
+ align:start position:0%
+get the next smallest
+ 
+
+ align:start position:0%
+get the next smallest
+item five and three smallest remaining
+
+ align:start position:0%
+item five and three smallest remaining
+ 
+
+ align:start position:0%
+item five and three smallest remaining
+guys I get three scratch that guy and I
+
+ align:start position:0%
+guys I get three scratch that guy and I
+ 
+
+ align:start position:0%
+guys I get three scratch that guy and I
+compare five and four get four scratch
+
+ align:start position:0%
+compare five and four get four scratch
+ 
+
+ align:start position:0%
+compare five and four get four scratch
+him and five and
+
+ align:start position:0%
+him and five and
+ 
+
+ align:start position:0%
+him and five and
+nine five is the
+
+ align:start position:0%
+nine five is the
+ 
+
+ align:start position:0%
+nine five is the
+smallest seven and
+
+ align:start position:0%
+smallest seven and
+ 
+
+ align:start position:0%
+smallest seven and
+nine seven nine and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 and actually now I don't really have
+
+ align:start position:0%
+10 and actually now I don't really have
+ 
+
+ align:start position:0%
+10 and actually now I don't really have
+to do any more comparisons all I've got
+
+ align:start position:0%
+to do any more comparisons all I've got
+ 
+
+ align:start position:0%
+to do any more comparisons all I've got
+is one list left so I can
+
+ align:start position:0%
+is one list left so I can
+ 
+
+ align:start position:0%
+is one list left so I can
+just send these guys
+
+ align:start position:0%
+just send these guys
+ 
+
+ align:start position:0%
+just send these guys
+down and I produced a sorted
+
+ align:start position:0%
+down and I produced a sorted
+ 
+
+ align:start position:0%
+down and I produced a sorted
+list
+
+ align:start position:0%
+list
+ 
+
+ align:start position:0%
+list
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+how many comparisons do I have to do in
+
+ align:start position:0%
+how many comparisons do I have to do in
+ 
+
+ align:start position:0%
+how many comparisons do I have to do in
+the worst case if this is n/ two items
+
+ align:start position:0%
+the worst case if this is n/ two items
+ 
+
+ align:start position:0%
+the worst case if this is n/ two items
+here and this is n over2
+
+ align:start position:0%
+here and this is n over2
+ 
+
+ align:start position:0%
+here and this is n over2
+here how many comparisons do I have to
+
+ align:start position:0%
+here how many comparisons do I have to
+ 
+
+ align:start position:0%
+here how many comparisons do I have to
+do to produce the N item sorted list
+
+ align:start position:0%
+do to produce the N item sorted list
+ 
+
+ align:start position:0%
+do to produce the N item sorted list
+after I have the Su list
+
+ align:start position:0%
+after I have the Su list
+ 
+
+ align:start position:0%
+after I have the Su list
+sorted what is it n very close n minus
+
+ align:start position:0%
+sorted what is it n very close n minus
+ 
+
+ align:start position:0%
+sorted what is it n very close n minus
+one is right okay because I do every
+
+ align:start position:0%
+one is right okay because I do every
+ 
+
+ align:start position:0%
+one is right okay because I do every
+time I do comparison I pull an item and
+
+ align:start position:0%
+time I do comparison I pull an item and
+ 
+
+ align:start position:0%
+time I do comparison I pull an item and
+stick it in the
+
+ align:start position:0%
+stick it in the
+ 
+
+ align:start position:0%
+stick it in the
+list but once I get down to the very
+
+ align:start position:0%
+list but once I get down to the very
+ 
+
+ align:start position:0%
+list but once I get down to the very
+last item just one guy sitting there I
+
+ align:start position:0%
+last item just one guy sitting there I
+ 
+
+ align:start position:0%
+last item just one guy sitting there I
+don't have to do a comparison it's just
+
+ align:start position:0%
+don't have to do a comparison it's just
+ 
+
+ align:start position:0%
+don't have to do a comparison it's just
+the last guy I know he's the
+
+ align:start position:0%
+the last guy I know he's the
+ 
+
+ align:start position:0%
+the last guy I know he's the
+largest so it it could go up to n minus
+
+ align:start position:0%
+largest so it it could go up to n minus
+ 
+
+ align:start position:0%
+largest so it it could go up to n minus
+one in the worst case in this situation
+
+ align:start position:0%
+one in the worst case in this situation
+ 
+
+ align:start position:0%
+one in the worst case in this situation
+I actually did n minus two because I was
+
+ align:start position:0%
+I actually did n minus two because I was
+ 
+
+ align:start position:0%
+I actually did n minus two because I was
+left with two guys at the end I just
+
+ align:start position:0%
+left with two guys at the end I just
+ 
+
+ align:start position:0%
+left with two guys at the end I just
+bring them down but it might have been
+
+ align:start position:0%
+bring them down but it might have been
+ 
+
+ align:start position:0%
+bring them down but it might have been
+that the next largest thing the 23 was
+
+ align:start position:0%
+that the next largest thing the 23 was
+ 
+
+ align:start position:0%
+that the next largest thing the 23 was
+here and then I would have done n minus
+
+ align:start position:0%
+here and then I would have done n minus
+ 
+
+ align:start position:0%
+here and then I would have done n minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah otherist that make it faster well
+
+ align:start position:0%
+yeah otherist that make it faster well
+ 
+
+ align:start position:0%
+yeah otherist that make it faster well
+that's what's going to happen with the
+
+ align:start position:0%
+that's what's going to happen with the
+ 
+
+ align:start position:0%
+that's what's going to happen with the
+recursion because the first thing we're
+
+ align:start position:0%
+recursion because the first thing we're
+ 
+
+ align:start position:0%
+recursion because the first thing we're
+going to do is when we unfold the
+
+ align:start position:0%
+going to do is when we unfold the
+ 
+
+ align:start position:0%
+going to do is when we unfold the
+recursion is you're going to take the
+
+ align:start position:0%
+recursion is you're going to take the
+ 
+
+ align:start position:0%
+recursion is you're going to take the
+first half split it in half recursively
+
+ align:start position:0%
+first half split it in half recursively
+ 
+
+ align:start position:0%
+first half split it in half recursively
+sort them and then merge them so the
+
+ align:start position:0%
+sort them and then merge them so the
+ 
+
+ align:start position:0%
+sort them and then merge them so the
+answer is that's going to happen but
+
+ align:start position:0%
+answer is that's going to happen but
+ 
+
+ align:start position:0%
+answer is that's going to happen but
+we're sort of going to hide it by the
+
+ align:start position:0%
+we're sort of going to hide it by the
+ 
+
+ align:start position:0%
+we're sort of going to hide it by the
+recursion all right you didn't see me
+
+ align:start position:0%
+recursion all right you didn't see me
+ 
+
+ align:start position:0%
+recursion all right you didn't see me
+produ
+
+ align:start position:0%
+produ
+ 
+
+ align:start position:0%
+produ
+that sorted list but I would have done
+
+ align:start position:0%
+that sorted list but I would have done
+ 
+
+ align:start position:0%
+that sorted list but I would have done
+it by taking 10 and seven sorting them 5
+
+ align:start position:0%
+it by taking 10 and seven sorting them 5
+ 
+
+ align:start position:0%
+it by taking 10 and seven sorting them 5
+and 23 and sorting them and then merging
+
+ align:start position:0%
+and 23 and sorting them and then merging
+ 
+
+ align:start position:0%
+and 23 and sorting them and then merging
+them okay any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions all right well let's set up
+
+ align:start position:0%
+questions all right well let's set up
+ 
+
+ align:start position:0%
+questions all right well let's set up
+the recursion to count how many
+
+ align:start position:0%
+the recursion to count how many
+ 
+
+ align:start position:0%
+the recursion to count how many
+comparisons are needed for the whole
+
+ align:start position:0%
+comparisons are needed for the whole
+ 
+
+ align:start position:0%
+comparisons are needed for the whole
+thing not just the last merge phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define and instead of T subn I'm going
+
+ align:start position:0%
+define and instead of T subn I'm going
+ 
+
+ align:start position:0%
+define and instead of T subn I'm going
+to write T of n as a function makes no
+
+ align:start position:0%
+to write T of n as a function makes no
+ 
+
+ align:start position:0%
+to write T of n as a function makes no
+difference but you'll see people do
+
+ align:start position:0%
+difference but you'll see people do
+ 
+
+ align:start position:0%
+difference but you'll see people do
+recurrences both ways T of n or T
+
+ align:start position:0%
+recurrences both ways T of n or T
+ 
+
+ align:start position:0%
+recurrences both ways T of n or T
+subn it's going to be the number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comparisons used by merge sort to sort
+
+ align:start position:0%
+comparisons used by merge sort to sort
+ 
+
+ align:start position:0%
+comparisons used by merge sort to sort
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+numbers in the worst case worst
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case all right so we already know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+merging takes n minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comparisons in the worst
+
+ align:start position:0%
+comparisons in the worst
+ 
+
+ align:start position:0%
+comparisons in the worst
+case and you always want to prepare for
+
+ align:start position:0%
+case and you always want to prepare for
+ 
+
+ align:start position:0%
+case and you always want to prepare for
+the worst case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many comparisons are
+
+ align:start position:0%
+how many comparisons are
+ 
+
+ align:start position:0%
+how many comparisons are
+used in the recursive steps to sort this
+
+ align:start position:0%
+used in the recursive steps to sort this
+ 
+
+ align:start position:0%
+used in the recursive steps to sort this
+list and to sort that list in
+
+ align:start position:0%
+list and to sort that list in
+ 
+
+ align:start position:0%
+list and to sort that list in
+general TN over
+
+ align:start position:0%
+general TN over
+ 
+
+ align:start position:0%
+general TN over
+two to do this
+
+ align:start position:0%
+two to do this
+ 
+
+ align:start position:0%
+two to do this
+list times two because you got two lists
+
+ align:start position:0%
+list times two because you got two lists
+ 
+
+ align:start position:0%
+list times two because you got two lists
+of size n/ two two sub problems of size
+
+ align:start position:0%
+of size n/ two two sub problems of size
+ 
+
+ align:start position:0%
+of size n/ two two sub problems of size
+n over two each takes T of n
+
+ align:start position:0%
+n over two each takes T of n
+ 
+
+ align:start position:0%
+n over two each takes T of n
+/2 all right so you've got 2 TN /2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comparisons for the recursive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorting all right that means
+
+ align:start position:0%
+sorting all right that means
+ 
+
+ align:start position:0%
+sorting all right that means
+that t of
+
+ align:start position:0%
+that t of
+ 
+
+ align:start position:0%
+that t of
+n equals 2 T of n
+
+ align:start position:0%
+n equals 2 T of n
+ 
+
+ align:start position:0%
+n equals 2 T of n
+/2 plus n minus
+
+ align:start position:0%
+/2 plus n minus
+ 
+
+ align:start position:0%
+/2 plus n minus
+one and we should say what T of one is
+
+ align:start position:0%
+one and we should say what T of one is
+ 
+
+ align:start position:0%
+one and we should say what T of one is
+what's that
+
+ align:start position:0%
+what's that
+ 
+
+ align:start position:0%
+what's that
+what's the time to
+
+ align:start position:0%
+what's the time to
+ 
+
+ align:start position:0%
+what's the time to
+sort zero you don't do any comparisons
+
+ align:start position:0%
+sort zero you don't do any comparisons
+ 
+
+ align:start position:0%
+sort zero you don't do any comparisons
+if there's one item so we'll set that as
+
+ align:start position:0%
+if there's one item so we'll set that as
+ 
+
+ align:start position:0%
+if there's one item so we'll set that as
+our base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case all right so let's find the
+
+ align:start position:0%
+case all right so let's find the
+ 
+
+ align:start position:0%
+case all right so let's find the
+answer so the first thing to always do
+
+ align:start position:0%
+answer so the first thing to always do
+ 
+
+ align:start position:0%
+answer so the first thing to always do
+when you see a
+
+ align:start position:0%
+when you see a
+ 
+
+ align:start position:0%
+when you see a
+recurrence is
+
+ align:start position:0%
+recurrence is
+ 
+
+ align:start position:0%
+recurrence is
+to take a few values compute a few
+
+ align:start position:0%
+to take a few values compute a few
+ 
+
+ align:start position:0%
+to take a few values compute a few
+values and try to guess the
+
+ align:start position:0%
+values and try to guess the
+ 
+
+ align:start position:0%
+values and try to guess the
+answer so what's T of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two one plug it in I get 2 T of 1 T of 1
+
+ align:start position:0%
+two one plug it in I get 2 T of 1 T of 1
+ 
+
+ align:start position:0%
+two one plug it in I get 2 T of 1 T of 1
+zero plus 2 minus one that's
+
+ align:start position:0%
+zero plus 2 minus one that's
+ 
+
+ align:start position:0%
+zero plus 2 minus one that's
+one all right what's T of and we're only
+
+ align:start position:0%
+one all right what's T of and we're only
+ 
+
+ align:start position:0%
+one all right what's T of and we're only
+doing powers of four here sorry powers
+
+ align:start position:0%
+doing powers of four here sorry powers
+ 
+
+ align:start position:0%
+doing powers of four here sorry powers
+of two so I go to T of four next what's
+
+ align:start position:0%
+of two so I go to T of four next what's
+ 
+
+ align:start position:0%
+of two so I go to T of four next what's
+T of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+five right because I've got double this
+
+ align:start position:0%
+five right because I've got double this
+ 
+
+ align:start position:0%
+five right because I've got double this
+is two plus four - one that's adding
+
+ align:start position:0%
+is two plus four - one that's adding
+ 
+
+ align:start position:0%
+is two plus four - one that's adding
+three so I get
+
+ align:start position:0%
+three so I get
+ 
+
+ align:start position:0%
+three so I get
+five all right let's look at T of
+
+ align:start position:0%
+five all right let's look at T of
+ 
+
+ align:start position:0%
+five all right let's look at T of
+8 that's twice
+
+ align:start position:0%
+8 that's twice
+ 
+
+ align:start position:0%
+8 that's twice
+5+ 8 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+17 not so clear what to guess
+
+ align:start position:0%
+17 not so clear what to guess
+ 
+
+ align:start position:0%
+17 not so clear what to guess
+here we can try one
+
+ align:start position:0%
+here we can try one
+ 
+
+ align:start position:0%
+here we can try one
+more T is 16 = 2 * 17 + 16 - 1
+
+ align:start position:0%
+more T is 16 = 2 * 17 + 16 - 1
+ 
+
+ align:start position:0%
+more T is 16 = 2 * 17 + 16 - 1
+=
+
+ align:start position:0%
+=
+ 
+
+ align:start position:0%
+=
+34 and
+
+ align:start position:0%
+34 and
+ 
+
+ align:start position:0%
+34 and
+15 is 49 is that
+
+ align:start position:0%
+15 is 49 is that
+ 
+
+ align:start position:0%
+15 is 49 is that
+right 34 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+15 any any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guesses this one's you're not going to
+
+ align:start position:0%
+guesses this one's you're not going to
+ 
+
+ align:start position:0%
+guesses this one's you're not going to
+guess this that's not going to work and
+
+ align:start position:0%
+guess this that's not going to work and
+ 
+
+ align:start position:0%
+guess this that's not going to work and
+that happens Miracle could happen you
+
+ align:start position:0%
+that happens Miracle could happen you
+ 
+
+ align:start position:0%
+that happens Miracle could happen you
+get a Divine insight and guess it but I
+
+ align:start position:0%
+get a Divine insight and guess it but I
+ 
+
+ align:start position:0%
+get a Divine insight and guess it but I
+think it's not likely
+
+ align:start position:0%
+think it's not likely
+ 
+
+ align:start position:0%
+think it's not likely
+all right so let's go to plug and
+
+ align:start position:0%
+all right so let's go to plug and
+ 
+
+ align:start position:0%
+all right so let's go to plug and
+chug see if that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works all right so now plug and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chug all right so we write down T of n
+
+ align:start position:0%
+chug all right so we write down T of n
+ 
+
+ align:start position:0%
+chug all right so we write down T of n
+is and you always write the recurrent
+
+ align:start position:0%
+is and you always write the recurrent
+ 
+
+ align:start position:0%
+is and you always write the recurrent
+part last for plug and chug to keep it
+
+ align:start position:0%
+part last for plug and chug to keep it
+ 
+
+ align:start position:0%
+part last for plug and chug to keep it
+simpler 2 T of N
+
+ align:start position:0%
+simpler 2 T of N
+ 
+
+ align:start position:0%
+simpler 2 T of N
+/2 and then I substitute I plug in for T
+
+ align:start position:0%
+/2 and then I substitute I plug in for T
+ 
+
+ align:start position:0%
+/2 and then I substitute I plug in for T
+of n
+
+ align:start position:0%
+of n
+ 
+
+ align:start position:0%
+of n
+/2 so I have n minus1 +
+
+ align:start position:0%
+/2 so I have n minus1 +
+ 
+
+ align:start position:0%
+/2 so I have n minus1 +
+2 N / 2 - 1 + 2 T of n
+
+ align:start position:0%
+2 N / 2 - 1 + 2 T of n
+ 
+
+ align:start position:0%
+2 N / 2 - 1 + 2 T of n
+over4 then I
+
+ align:start position:0%
+over4 then I
+ 
+
+ align:start position:0%
+over4 then I
+chug so I have n minus one plus that's
+
+ align:start position:0%
+chug so I have n minus one plus that's
+ 
+
+ align:start position:0%
+chug so I have n minus one plus that's
+n minus 2
+
+ align:start position:0%
+n minus 2
+ 
+
+ align:start position:0%
+n minus 2
+plus 4 TN over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 all right then we'll plug in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and I get N over4 -
+
+ align:start position:0%
+here and I get N over4 -
+ 
+
+ align:start position:0%
+here and I get N over4 -
+1+ 4 TN over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8 and now we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chug that's an n here minus a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four I did something wrong I plugged in
+
+ align:start position:0%
+four I did something wrong I plugged in
+ 
+
+ align:start position:0%
+four I did something wrong I plugged in
+that should be two 4 * 2 is 8 TN over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8 all right can you start to guess the
+
+ align:start position:0%
+8 all right can you start to guess the
+ 
+
+ align:start position:0%
+8 all right can you start to guess the
+pattern here
+
+ align:start position:0%
+pattern here
+ 
+
+ align:start position:0%
+pattern here
+maybe you know we probably should do one
+
+ align:start position:0%
+maybe you know we probably should do one
+ 
+
+ align:start position:0%
+maybe you know we probably should do one
+more to be safe but you got an N minus
+
+ align:start position:0%
+more to be safe but you got an N minus
+ 
+
+ align:start position:0%
+more to be safe but you got an N minus
+one plus an nus 2 plus an nus 4 and if
+
+ align:start position:0%
+one plus an nus 2 plus an nus 4 and if
+ 
+
+ align:start position:0%
+one plus an nus 2 plus an nus 4 and if
+we do one more what's the term going to
+
+ align:start position:0%
+we do one more what's the term going to
+ 
+
+ align:start position:0%
+we do one more what's the term going to
+be n minus 8 and this is looking pretty
+
+ align:start position:0%
+be n minus 8 and this is looking pretty
+ 
+
+ align:start position:0%
+be n minus 8 and this is looking pretty
+simple so we could guess now that the
+
+ align:start position:0%
+simple so we could guess now that the
+ 
+
+ align:start position:0%
+simple so we could guess now that the
+pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is n -1 + N - 2 + N - 4 all the way out
+
+ align:start position:0%
+is n -1 + N - 2 + N - 4 all the way out
+ 
+
+ align:start position:0%
+is n -1 + N - 2 + N - 4 all the way out
+to plus n minus 2 the I
+
+ align:start position:0%
+to plus n minus 2 the I
+ 
+
+ align:start position:0%
+to plus n minus 2 the I
+-1 + 2 to the i t n over 2 the
+
+ align:start position:0%
+-1 + 2 to the i t n over 2 the
+ 
+
+ align:start position:0%
+-1 + 2 to the i t n over 2 the
+I and now we go all the way down where I
+
+ align:start position:0%
+I and now we go all the way down where I
+ 
+
+ align:start position:0%
+I and now we go all the way down where I
+equal log n base
+
+ align:start position:0%
+equal log n base
+ 
+
+ align:start position:0%
+equal log n base
+2 all right and and see what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get 1 + N - 2 plus all the way down N -
+
+ align:start position:0%
+get 1 + N - 2 plus all the way down N -
+ 
+
+ align:start position:0%
+get 1 + N - 2 plus all the way down N -
+2 to the log n
+
+ align:start position:0%
+2 to the log n
+ 
+
+ align:start position:0%
+2 to the log n
+-1 plus 2 the log
+
+ align:start position:0%
+-1 plus 2 the log
+ 
+
+ align:start position:0%
+-1 plus 2 the log
+n t of
+
+ align:start position:0%
+n t of
+ 
+
+ align:start position:0%
+n t of
+1 what's T of
+
+ align:start position:0%
+1 what's T of
+ 
+
+ align:start position:0%
+1 what's T of
+one zero that's nice that goes away
+
+ align:start position:0%
+one zero that's nice that goes away
+ 
+
+ align:start position:0%
+one zero that's nice that goes away
+all right so this is not looking so bad
+
+ align:start position:0%
+all right so this is not looking so bad
+ 
+
+ align:start position:0%
+all right so this is not looking so bad
+this equals the
+
+ align:start position:0%
+this equals the
+ 
+
+ align:start position:0%
+this equals the
+sum I equal 0 to log
+
+ align:start position:0%
+sum I equal 0 to log
+ 
+
+ align:start position:0%
+sum I equal 0 to log
+nus1 of nus 2 the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I all right and this will be good
+
+ align:start position:0%
+I all right and this will be good
+ 
+
+ align:start position:0%
+I all right and this will be good
+practice maybe for to get towards the
+
+ align:start position:0%
+practice maybe for to get towards the
+ 
+
+ align:start position:0%
+practice maybe for to get towards the
+test well I can split that sum
+
+ align:start position:0%
+test well I can split that sum
+ 
+
+ align:start position:0%
+test well I can split that sum
+up I = 0 to log n
+
+ align:start position:0%
+up I = 0 to log n
+ 
+
+ align:start position:0%
+up I = 0 to log n
+minus1 of n minus the sum i = 0 Log n
+
+ align:start position:0%
+minus1 of n minus the sum i = 0 Log n
+ 
+
+ align:start position:0%
+minus1 of n minus the sum i = 0 Log n
+minus one of 2 to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I well this is easy I'm just adding n up
+
+ align:start position:0%
+I well this is easy I'm just adding n up
+ 
+
+ align:start position:0%
+I well this is easy I'm just adding n up
+a total of log n times so I have n log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n this is just summing the powers of two
+
+ align:start position:0%
+n this is just summing the powers of two
+ 
+
+ align:start position:0%
+n this is just summing the powers of two
+which we know to do know how to do so
+
+ align:start position:0%
+which we know to do know how to do so
+ 
+
+ align:start position:0%
+which we know to do know how to do so
+that's going to be 2 the log
+
+ align:start position:0%
+that's going to be 2 the log
+ 
+
+ align:start position:0%
+that's going to be 2 the log
+n minus
+
+ align:start position:0%
+n minus
+ 
+
+ align:start position:0%
+n minus
+one and so we get our answer
+
+ align:start position:0%
+one and so we get our answer
+ 
+
+ align:start position:0%
+one and so we get our answer
+is n log
+
+ align:start position:0%
+is n log
+ 
+
+ align:start position:0%
+is n log
+n minus 2 the log n is just n minus
+
+ align:start position:0%
+n minus 2 the log n is just n minus
+ 
+
+ align:start position:0%
+n minus 2 the log n is just n minus
+minus one is+
+
+ align:start position:0%
+minus one is+
+ 
+
+ align:start position:0%
+minus one is+
+one well we derived an
+
+ align:start position:0%
+one well we derived an
+ 
+
+ align:start position:0%
+one well we derived an
+answer let's see let's just go back and
+
+ align:start position:0%
+answer let's see let's just go back and
+ 
+
+ align:start position:0%
+answer let's see let's just go back and
+check some of the
+
+ align:start position:0%
+check some of the
+ 
+
+ align:start position:0%
+check some of the
+values uh n equals 1 that's zero and I
+
+ align:start position:0%
+values uh n equals 1 that's zero and I
+ 
+
+ align:start position:0%
+values uh n equals 1 that's zero and I
+get one minus one it
+
+ align:start position:0%
+get one minus one it
+ 
+
+ align:start position:0%
+get one minus one it
+works n =
+
+ align:start position:0%
+works n =
+ 
+
+ align:start position:0%
+works n =
+2 2 log 2 is 2- 2 +
+
+ align:start position:0%
+2 2 log 2 is 2- 2 +
+ 
+
+ align:start position:0%
+2 2 log 2 is 2- 2 +
+1 Works plug in four I get 4 log 4 is 8
+
+ align:start position:0%
+1 Works plug in four I get 4 log 4 is 8
+ 
+
+ align:start position:0%
+1 Works plug in four I get 4 log 4 is 8
+- 4 is four plus 1 is five so it works
+
+ align:start position:0%
+- 4 is four plus 1 is five so it works
+ 
+
+ align:start position:0%
+- 4 is four plus 1 is five so it works
+all right for those examples now to be
+
+ align:start position:0%
+all right for those examples now to be
+ 
+
+ align:start position:0%
+all right for those examples now to be
+really careful we should prove it by
+
+ align:start position:0%
+really careful we should prove it by
+ 
+
+ align:start position:0%
+really careful we should prove it by
+induction because when you do enough of
+
+ align:start position:0%
+induction because when you do enough of
+ 
+
+ align:start position:0%
+induction because when you do enough of
+these equations you make mistakes like I
+
+ align:start position:0%
+these equations you make mistakes like I
+ 
+
+ align:start position:0%
+these equations you make mistakes like I
+invariably do even up here and even
+
+ align:start position:0%
+invariably do even up here and even
+ 
+
+ align:start position:0%
+invariably do even up here and even
+though it's written down here I'll make
+
+ align:start position:0%
+though it's written down here I'll make
+ 
+
+ align:start position:0%
+though it's written down here I'll make
+mistakes writing it on the board and so
+
+ align:start position:0%
+mistakes writing it on the board and so
+ 
+
+ align:start position:0%
+mistakes writing it on the board and so
+you want to check you know by induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay so this is the answer this is
+
+ align:start position:0%
+uh okay so this is the answer this is
+ 
+
+ align:start position:0%
+uh okay so this is the answer this is
+how many comparisons are done in merge
+
+ align:start position:0%
+how many comparisons are done in merge
+ 
+
+ align:start position:0%
+how many comparisons are done in merge
+sort and the nice thing is this is
+
+ align:start position:0%
+sort and the nice thing is this is
+ 
+
+ align:start position:0%
+sort and the nice thing is this is
+growing nearly linearly it grows as n
+
+ align:start position:0%
+growing nearly linearly it grows as n
+ 
+
+ align:start position:0%
+growing nearly linearly it grows as n
+log n and that's why this algorithm is
+
+ align:start position:0%
+log n and that's why this algorithm is
+ 
+
+ align:start position:0%
+log n and that's why this algorithm is
+used a lot in practice much better than
+
+ align:start position:0%
+used a lot in practice much better than
+ 
+
+ align:start position:0%
+used a lot in practice much better than
+comparing every item to every other item
+
+ align:start position:0%
+comparing every item to every other item
+ 
+
+ align:start position:0%
+comparing every item to every other item
+which would be more like N squared steps
+
+ align:start position:0%
+which would be more like N squared steps
+ 
+
+ align:start position:0%
+which would be more like N squared steps
+right so much better than a naive
+
+ align:start position:0%
+right so much better than a naive
+ 
+
+ align:start position:0%
+right so much better than a naive
+sorting
+
+ align:start position:0%
+sorting
+ 
+
+ align:start position:0%
+sorting
+algorithm any
+
+ align:start position:0%
+algorithm any
+ 
+
+ align:start position:0%
+algorithm any
+questions about what we did there
+
+ align:start position:0%
+questions about what we did there
+ 
+
+ align:start position:0%
+questions about what we did there
+you know just one rule of thumb when
+
+ align:start position:0%
+you know just one rule of thumb when
+ 
+
+ align:start position:0%
+you know just one rule of thumb when
+you're doing the plug and
+
+ align:start position:0%
+you're doing the plug and
+ 
+
+ align:start position:0%
+you're doing the plug and
+chug notice that I didn't try to
+
+ align:start position:0%
+chug notice that I didn't try to
+ 
+
+ align:start position:0%
+chug notice that I didn't try to
+collapse terms along the
+
+ align:start position:0%
+collapse terms along the
+ 
+
+ align:start position:0%
+collapse terms along the
+way it makes it easier sometimes to see
+
+ align:start position:0%
+way it makes it easier sometimes to see
+ 
+
+ align:start position:0%
+way it makes it easier sometimes to see
+the pattern I left it as n minus1 plus n
+
+ align:start position:0%
+the pattern I left it as n minus1 plus n
+ 
+
+ align:start position:0%
+the pattern I left it as n minus1 plus n
+min-2 and then plus n minus 4 rather
+
+ align:start position:0%
+min-2 and then plus n minus 4 rather
+ 
+
+ align:start position:0%
+min-2 and then plus n minus 4 rather
+than saying oh this is 3 n minus 7 which
+
+ align:start position:0%
+than saying oh this is 3 n minus 7 which
+ 
+
+ align:start position:0%
+than saying oh this is 3 n minus 7 which
+might have made it harder to guess the
+
+ align:start position:0%
+might have made it harder to guess the
+ 
+
+ align:start position:0%
+might have made it harder to guess the
+pattern so you don't always when you're
+
+ align:start position:0%
+pattern so you don't always when you're
+ 
+
+ align:start position:0%
+pattern so you don't always when you're
+doing the chugging collapse everything
+
+ align:start position:0%
+doing the chugging collapse everything
+ 
+
+ align:start position:0%
+doing the chugging collapse everything
+down you want to try and see if there's
+
+ align:start position:0%
+down you want to try and see if there's
+ 
+
+ align:start position:0%
+down you want to try and see if there's
+some because this is the amount of work
+
+ align:start position:0%
+some because this is the amount of work
+ 
+
+ align:start position:0%
+some because this is the amount of work
+done at each step and you want to see if
+
+ align:start position:0%
+done at each step and you want to see if
+ 
+
+ align:start position:0%
+done at each step and you want to see if
+you can see a pattern in
+
+ align:start position:0%
+you can see a pattern in
+ 
+
+ align:start position:0%
+you can see a pattern in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay all right so let's write down our
+
+ align:start position:0%
+okay all right so let's write down our
+ 
+
+ align:start position:0%
+okay all right so let's write down our
+two recurrences
+
+ align:start position:0%
+two recurrences
+ 
+
+ align:start position:0%
+two recurrences
+and sort of compare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so first we did towers of Hanoi
+
+ align:start position:0%
+them so first we did towers of Hanoi
+ 
+
+ align:start position:0%
+them so first we did towers of Hanoi
+which was T of Nal 2 2 T of n minus1 + 1
+
+ align:start position:0%
+which was T of Nal 2 2 T of n minus1 + 1
+ 
+
+ align:start position:0%
+which was T of Nal 2 2 T of n minus1 + 1
+and the answer
+
+ align:start position:0%
+and the answer
+ 
+
+ align:start position:0%
+and the answer
+was T of n is Tilda 2 the N it was
+
+ align:start position:0%
+was T of n is Tilda 2 the N it was
+ 
+
+ align:start position:0%
+was T of n is Tilda 2 the N it was
+actually 2 the N minus
+
+ align:start position:0%
+actually 2 the N minus
+ 
+
+ align:start position:0%
+actually 2 the N minus
+one then we did merge sort which is T of
+
+ align:start position:0%
+one then we did merge sort which is T of
+ 
+
+ align:start position:0%
+one then we did merge sort which is T of
+n equals 2 T of n /
+
+ align:start position:0%
+n equals 2 T of n /
+ 
+
+ align:start position:0%
+n equals 2 T of n /
+2 right difference there plus n
+
+ align:start position:0%
+2 right difference there plus n
+ 
+
+ align:start position:0%
+2 right difference there plus n
+minus1 and now the answer was T of n
+
+ align:start position:0%
+minus1 and now the answer was T of n
+ 
+
+ align:start position:0%
+minus1 and now the answer was T of n
+what's the till for this one for merge
+
+ align:start position:0%
+what's the till for this one for merge
+ 
+
+ align:start position:0%
+what's the till for this one for merge
+sort n log n yeah I can I can forget the
+
+ align:start position:0%
+sort n log n yeah I can I can forget the
+ 
+
+ align:start position:0%
+sort n log n yeah I can I can forget the
+rest if I'm doing the TOA n log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+wow these are pretty different answers
+
+ align:start position:0%
+wow these are pretty different answers
+ 
+
+ align:start position:0%
+wow these are pretty different answers
+right this one's nearly linear that
+
+ align:start position:0%
+right this one's nearly linear that
+ 
+
+ align:start position:0%
+right this one's nearly linear that
+one's
+
+ align:start position:0%
+one's
+ 
+
+ align:start position:0%
+one's
+exponential the recurrences looked
+
+ align:start position:0%
+exponential the recurrences looked
+ 
+
+ align:start position:0%
+exponential the recurrences looked
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+similar in fact this one sort of looks
+
+ align:start position:0%
+similar in fact this one sort of looks
+ 
+
+ align:start position:0%
+similar in fact this one sort of looks
+worse because I'm adding in N minus one
+
+ align:start position:0%
+worse because I'm adding in N minus one
+ 
+
+ align:start position:0%
+worse because I'm adding in N minus one
+every time instead of one but the answer
+
+ align:start position:0%
+every time instead of one but the answer
+ 
+
+ align:start position:0%
+every time instead of one but the answer
+is a lot better lot
+
+ align:start position:0%
+is a lot better lot
+ 
+
+ align:start position:0%
+is a lot better lot
+smaller what's the critical difference
+
+ align:start position:0%
+smaller what's the critical difference
+ 
+
+ align:start position:0%
+smaller what's the critical difference
+between these
+
+ align:start position:0%
+between these
+ 
+
+ align:start position:0%
+between these
+recurrences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you dropping the argument of t a
+
+ align:start position:0%
+yeah you dropping the argument of t a
+ 
+
+ align:start position:0%
+yeah you dropping the argument of t a
+lot faster you're cutting it in half
+
+ align:start position:0%
+lot faster you're cutting it in half
+ 
+
+ align:start position:0%
+lot faster you're cutting it in half
+every time instead of subtracting one
+
+ align:start position:0%
+every time instead of subtracting one
+ 
+
+ align:start position:0%
+every time instead of subtracting one
+right so go away faster that's right
+
+ align:start position:0%
+right so go away faster that's right
+ 
+
+ align:start position:0%
+right so go away faster that's right
+here I've got two problems of size one
+
+ align:start position:0%
+here I've got two problems of size one
+ 
+
+ align:start position:0%
+here I've got two problems of size one
+less here I've got two problem of half
+
+ align:start position:0%
+less here I've got two problem of half
+ 
+
+ align:start position:0%
+less here I've got two problem of half
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+size and that makes an enormous
+
+ align:start position:0%
+size and that makes an enormous
+ 
+
+ align:start position:0%
+size and that makes an enormous
+difference in the answer even though I'm
+
+ align:start position:0%
+difference in the answer even though I'm
+ 
+
+ align:start position:0%
+difference in the answer even though I'm
+doing more work after I cut you know did
+
+ align:start position:0%
+doing more work after I cut you know did
+ 
+
+ align:start position:0%
+doing more work after I cut you know did
+the recursive problems much faster
+
+ align:start position:0%
+the recursive problems much faster
+ 
+
+ align:start position:0%
+the recursive problems much faster
+running time or answer if these are
+
+ align:start position:0%
+running time or answer if these are
+ 
+
+ align:start position:0%
+running time or answer if these are
+algorithms that I'm I'm
+
+ align:start position:0%
+algorithms that I'm I'm
+ 
+
+ align:start position:0%
+algorithms that I'm I'm
+analyzing all right uh in fact let's
+
+ align:start position:0%
+analyzing all right uh in fact let's
+ 
+
+ align:start position:0%
+analyzing all right uh in fact let's
+take a look at what happens if
+
+ align:start position:0%
+take a look at what happens if
+ 
+
+ align:start position:0%
+take a look at what happens if
+I didn't use that n minus one I just put
+
+ align:start position:0%
+I didn't use that n minus one I just put
+ 
+
+ align:start position:0%
+I didn't use that n minus one I just put
+a one there let's see what impact that n
+
+ align:start position:0%
+a one there let's see what impact that n
+ 
+
+ align:start position:0%
+a one there let's see what impact that n
+minus one had
+
+ align:start position:0%
+minus one had
+ 
+
+ align:start position:0%
+minus one had
+had uh so let's do the
+
+ align:start position:0%
+had uh so let's do the
+ 
+
+ align:start position:0%
+had uh so let's do the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+recurrence this one's going to be a
+
+ align:start position:0%
+recurrence this one's going to be a
+ 
+
+ align:start position:0%
+recurrence this one's going to be a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+different because I'm not going to stick
+
+ align:start position:0%
+different because I'm not going to stick
+ 
+
+ align:start position:0%
+different because I'm not going to stick
+to powers of two I'm going to get a
+
+ align:start position:0%
+to powers of two I'm going to get a
+ 
+
+ align:start position:0%
+to powers of two I'm going to get a
+little Messier because that often
+
+ align:start position:0%
+little Messier because that often
+ 
+
+ align:start position:0%
+little Messier because that often
+happens in reality and I'm going to
+
+ align:start position:0%
+happens in reality and I'm going to
+ 
+
+ align:start position:0%
+happens in reality and I'm going to
+Define s of one is zero s of
+
+ align:start position:0%
+Define s of one is zero s of
+ 
+
+ align:start position:0%
+Define s of one is zero s of
+n is s of the floor function of n/2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus s of the ceiling function of n
+
+ align:start position:0%
+plus s of the ceiling function of n
+ 
+
+ align:start position:0%
+plus s of the ceiling function of n
+/2 plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one now the ceiling function means the
+
+ align:start position:0%
+one now the ceiling function means the
+ 
+
+ align:start position:0%
+one now the ceiling function means the
+smallest integer that's at least that
+
+ align:start position:0%
+smallest integer that's at least that
+ 
+
+ align:start position:0%
+smallest integer that's at least that
+big so you're sort of rounding up to the
+
+ align:start position:0%
+big so you're sort of rounding up to the
+ 
+
+ align:start position:0%
+big so you're sort of rounding up to the
+next integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the floor function means you're
+
+ align:start position:0%
+and the floor function means you're
+ 
+
+ align:start position:0%
+and the floor function means you're
+rounding down to the next integer so
+
+ align:start position:0%
+rounding down to the next integer so
+ 
+
+ align:start position:0%
+rounding down to the next integer so
+it's the biggest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integer less than equal to
+
+ align:start position:0%
+integer less than equal to
+ 
+
+ align:start position:0%
+integer less than equal to
+n/2 all right now if we had just powers
+
+ align:start position:0%
+n/2 all right now if we had just powers
+ 
+
+ align:start position:0%
+n/2 all right now if we had just powers
+of two this would be much easier to
+
+ align:start position:0%
+of two this would be much easier to
+ 
+
+ align:start position:0%
+of two this would be much easier to
+write it would just be snal 2 SN
+
+ align:start position:0%
+write it would just be snal 2 SN
+ 
+
+ align:start position:0%
+write it would just be snal 2 SN
+/2 + 1 all right so it's analogous to
+
+ align:start position:0%
+/2 + 1 all right so it's analogous to
+ 
+
+ align:start position:0%
+/2 + 1 all right so it's analogous to
+what we're doing up there where we're
+
+ align:start position:0%
+what we're doing up there where we're
+ 
+
+ align:start position:0%
+what we're doing up there where we're
+just adding one instead of n minus one
+
+ align:start position:0%
+just adding one instead of n minus one
+ 
+
+ align:start position:0%
+just adding one instead of n minus one
+but I'm being careful now I'm going to
+
+ align:start position:0%
+but I'm being careful now I'm going to
+ 
+
+ align:start position:0%
+but I'm being careful now I'm going to
+make this recurrence work for
+
+ align:start position:0%
+make this recurrence work for
+ 
+
+ align:start position:0%
+make this recurrence work for
+all natural numbers because sometimes in
+
+ align:start position:0%
+all natural numbers because sometimes in
+ 
+
+ align:start position:0%
+all natural numbers because sometimes in
+reality you're dealing with non-p powers
+
+ align:start position:0%
+reality you're dealing with non-p powers
+ 
+
+ align:start position:0%
+reality you're dealing with non-p powers
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two uh all right let's see if we can
+
+ align:start position:0%
+two uh all right let's see if we can
+ 
+
+ align:start position:0%
+two uh all right let's see if we can
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+this what's the first thing to try to
+
+ align:start position:0%
+this what's the first thing to try to
+ 
+
+ align:start position:0%
+this what's the first thing to try to
+solve this what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do what's the first step when you get a
+
+ align:start position:0%
+do what's the first step when you get a
+ 
+
+ align:start position:0%
+do what's the first step when you get a
+recurrence you try to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solve all right what method should you
+
+ align:start position:0%
+solve all right what method should you
+ 
+
+ align:start position:0%
+solve all right what method should you
+try guess and to guess well you got to
+
+ align:start position:0%
+try guess and to guess well you got to
+ 
+
+ align:start position:0%
+try guess and to guess well you got to
+plug some values in all right sort of
+
+ align:start position:0%
+plug some values in all right sort of
+ 
+
+ align:start position:0%
+plug some values in all right sort of
+hard to guess I mean I don't know
+
+ align:start position:0%
+hard to guess I mean I don't know
+ 
+
+ align:start position:0%
+hard to guess I mean I don't know
+looking at that I guessing nothing comes
+
+ align:start position:0%
+looking at that I guessing nothing comes
+ 
+
+ align:start position:0%
+looking at that I guessing nothing comes
+to mind other than Panic looking at that
+
+ align:start position:0%
+to mind other than Panic looking at that
+ 
+
+ align:start position:0%
+to mind other than Panic looking at that
+all right but if we plug in some values
+
+ align:start position:0%
+all right but if we plug in some values
+ 
+
+ align:start position:0%
+all right but if we plug in some values
+then maybe it won't be so bad so we got
+
+ align:start position:0%
+then maybe it won't be so bad so we got
+ 
+
+ align:start position:0%
+then maybe it won't be so bad so we got
+S1 equals zero what's S2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this not three because this is 2 over
+
+ align:start position:0%
+this not three because this is 2 over
+ 
+
+ align:start position:0%
+this not three because this is 2 over
+two is one floor of one is one s of one
+
+ align:start position:0%
+two is one floor of one is one s of one
+ 
+
+ align:start position:0%
+two is one floor of one is one s of one
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+zero got ceiling of one is one because
+
+ align:start position:0%
+zero got ceiling of one is one because
+ 
+
+ align:start position:0%
+zero got ceiling of one is one because
+it's an integer s of one is zero plus
+
+ align:start position:0%
+it's an integer s of one is zero plus
+ 
+
+ align:start position:0%
+it's an integer s of one is zero plus
+one so s of two is
+
+ align:start position:0%
+one so s of two is
+ 
+
+ align:start position:0%
+one so s of two is
+one what's s of three yikes all right 3
+
+ align:start position:0%
+one what's s of three yikes all right 3
+ 
+
+ align:start position:0%
+one what's s of three yikes all right 3
+over 2 is 1 and A2 what's the floor of
+
+ align:start position:0%
+over 2 is 1 and A2 what's the floor of
+ 
+
+ align:start position:0%
+over 2 is 1 and A2 what's the floor of
+one one and a half One S of one is zero
+
+ align:start position:0%
+one one and a half One S of one is zero
+ 
+
+ align:start position:0%
+one one and a half One S of one is zero
+that's gone what's the ceiling of one
+
+ align:start position:0%
+that's gone what's the ceiling of one
+ 
+
+ align:start position:0%
+that's gone what's the ceiling of one
+and a
+
+ align:start position:0%
+and a
+ 
+
+ align:start position:0%
+and a
+half s of two is
+
+ align:start position:0%
+half s of two is
+ 
+
+ align:start position:0%
+half s of two is
+one plus one what's the answer for S of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three two right because I've got zero
+
+ align:start position:0%
+three two right because I've got zero
+ 
+
+ align:start position:0%
+three two right because I've got zero
+one and
+
+ align:start position:0%
+one and
+ 
+
+ align:start position:0%
+one and
+one all right s of four this one's easy
+
+ align:start position:0%
+one all right s of four this one's easy
+ 
+
+ align:start position:0%
+one all right s of four this one's easy
+because it's
+
+ align:start position:0%
+because it's
+ 
+
+ align:start position:0%
+because it's
+even I get S of two which is 1 plus s of
+
+ align:start position:0%
+even I get S of two which is 1 plus s of
+ 
+
+ align:start position:0%
+even I get S of two which is 1 plus s of
+2 which is 1 + 1 so what's s of four
+
+ align:start position:0%
+2 which is 1 + 1 so what's s of four
+ 
+
+ align:start position:0%
+2 which is 1 + 1 so what's s of four
+three you might try a
+
+ align:start position:0%
+three you might try a
+ 
+
+ align:start position:0%
+three you might try a
+guess what would you
+
+ align:start position:0%
+guess what would you
+ 
+
+ align:start position:0%
+guess what would you
+guess yeah n minus one okay so we're
+
+ align:start position:0%
+guess yeah n minus one okay so we're
+ 
+
+ align:start position:0%
+guess yeah n minus one okay so we're
+going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess s of n = n minus1 and that's not
+
+ align:start position:0%
+guess s of n = n minus1 and that's not
+ 
+
+ align:start position:0%
+guess s of n = n minus1 and that's not
+so bad actually it's pretty simple
+
+ align:start position:0%
+so bad actually it's pretty simple
+ 
+
+ align:start position:0%
+so bad actually it's pretty simple
+looking at that mess you'd never you
+
+ align:start position:0%
+looking at that mess you'd never you
+ 
+
+ align:start position:0%
+looking at that mess you'd never you
+know think of that right away but once
+
+ align:start position:0%
+know think of that right away but once
+ 
+
+ align:start position:0%
+know think of that right away but once
+you plug in some values that's not so
+
+ align:start position:0%
+you plug in some values that's not so
+ 
+
+ align:start position:0%
+you plug in some values that's not so
+bad all right let's verify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and we're going to verify by strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction the induction hypothesis is
+
+ align:start position:0%
+induction the induction hypothesis is
+ 
+
+ align:start position:0%
+induction the induction hypothesis is
+our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess the the base case is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easy because I've got s of
+
+ align:start position:0%
+easy because I've got s of
+ 
+
+ align:start position:0%
+easy because I've got s of
+one is zero and that equals 1 minus
+
+ align:start position:0%
+one is zero and that equals 1 minus
+ 
+
+ align:start position:0%
+one is zero and that equals 1 minus
+one so that's good so let's do the
+
+ align:start position:0%
+one so that's good so let's do the
+ 
+
+ align:start position:0%
+one so that's good so let's do the
+induction step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so the induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step we're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assume that P1 is true P2 is true all
+
+ align:start position:0%
+assume that P1 is true P2 is true all
+ 
+
+ align:start position:0%
+assume that P1 is true P2 is true all
+the way up to
+
+ align:start position:0%
+the way up to
+ 
+
+ align:start position:0%
+the way up to
+PN to prove PN +
+
+ align:start position:0%
+PN to prove PN +
+ 
+
+ align:start position:0%
+PN to prove PN +
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+true for n bigger than equal to one and
+
+ align:start position:0%
+true for n bigger than equal to one and
+ 
+
+ align:start position:0%
+true for n bigger than equal to one and
+then we look at the N plus first
+
+ align:start position:0%
+then we look at the N plus first
+ 
+
+ align:start position:0%
+then we look at the N plus first
+term that equals s of floor n + 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over2 plus s of ceiling n + 1
+
+ align:start position:0%
+over2 plus s of ceiling n + 1
+ 
+
+ align:start position:0%
+over2 plus s of ceiling n + 1
+over2 plus
+
+ align:start position:0%
+over2 plus
+ 
+
+ align:start position:0%
+over2 plus
+one all right
+
+ align:start position:0%
+one all right
+ 
+
+ align:start position:0%
+one all right
+now I don't know what these are exactly
+
+ align:start position:0%
+now I don't know what these are exactly
+ 
+
+ align:start position:0%
+now I don't know what these are exactly
+depending on whether n is even or odd
+
+ align:start position:0%
+depending on whether n is even or odd
+ 
+
+ align:start position:0%
+depending on whether n is even or odd
+but I do well no I can plug first let me
+
+ align:start position:0%
+but I do well no I can plug first let me
+ 
+
+ align:start position:0%
+but I do well no I can plug first let me
+plug in using the induction
+
+ align:start position:0%
+plug in using the induction
+ 
+
+ align:start position:0%
+plug in using the induction
+hypothesis I know that this is n +1 / 2
+
+ align:start position:0%
+hypothesis I know that this is n +1 / 2
+ 
+
+ align:start position:0%
+hypothesis I know that this is n +1 / 2
+-1 this is
+
+ align:start position:0%
+-1 this is
+ 
+
+ align:start position:0%
+-1 this is
+ceiling n + 1 / 2 minus1 and then I
+
+ align:start position:0%
+ceiling n + 1 / 2 minus1 and then I
+ 
+
+ align:start position:0%
+ceiling n + 1 / 2 minus1 and then I
+carry the plus one down that's by the
+
+ align:start position:0%
+carry the plus one down that's by the
+ 
+
+ align:start position:0%
+carry the plus one down that's by the
+induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypothesis all right now I don't know
+
+ align:start position:0%
+hypothesis all right now I don't know
+ 
+
+ align:start position:0%
+hypothesis all right now I don't know
+exactly what either of these values is
+
+ align:start position:0%
+exactly what either of these values is
+ 
+
+ align:start position:0%
+exactly what either of these values is
+unless I know the par of n but I do know
+
+ align:start position:0%
+unless I know the par of n but I do know
+ 
+
+ align:start position:0%
+unless I know the par of n but I do know
+the sum of these two things the floor of
+
+ align:start position:0%
+the sum of these two things the floor of
+ 
+
+ align:start position:0%
+the sum of these two things the floor of
+something plus the ceiling of that
+
+ align:start position:0%
+something plus the ceiling of that
+ 
+
+ align:start position:0%
+something plus the ceiling of that
+something is twice the
+
+ align:start position:0%
+something is twice the
+ 
+
+ align:start position:0%
+something is twice the
+something all right so this this plus
+
+ align:start position:0%
+something all right so this this plus
+ 
+
+ align:start position:0%
+something all right so this this plus
+that equals n+
+
+ align:start position:0%
+that equals n+
+ 
+
+ align:start position:0%
+that equals n+
+one -1 -1 + 1 is min
+
+ align:start position:0%
+one -1 -1 + 1 is min
+ 
+
+ align:start position:0%
+one -1 -1 + 1 is min
+-1 and so in fact we provve that s of n
+
+ align:start position:0%
+-1 and so in fact we provve that s of n
+ 
+
+ align:start position:0%
+-1 and so in fact we provve that s of n
++ 1 equal n
+
+ align:start position:0%
++ 1 equal n
+ 
+
+ align:start position:0%
++ 1 equal n
++1 minus
+
+ align:start position:0%
++1 minus
+ 
+
+ align:start position:0%
++1 minus
+one so we verified the induction
+
+ align:start position:0%
+one so we verified the induction
+ 
+
+ align:start position:0%
+one so we verified the induction
+hypothesis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um let's see I'm not sure so are
+
+ align:start position:0%
+yeah um let's see I'm not sure so are
+ 
+
+ align:start position:0%
+yeah um let's see I'm not sure so are
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+asking why I started SN plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here uh um doesn't matter but uh the
+
+ align:start position:0%
+here uh um doesn't matter but uh the
+ 
+
+ align:start position:0%
+here uh um doesn't matter but uh the
+expression is s of whatever this is the
+
+ align:start position:0%
+expression is s of whatever this is the
+ 
+
+ align:start position:0%
+expression is s of whatever this is the
+induction ioth thesis would be S of
+
+ align:start position:0%
+induction ioth thesis would be S of
+ 
+
+ align:start position:0%
+induction ioth thesis would be S of
+whatever is inside there is what's
+
+ align:start position:0%
+whatever is inside there is what's
+ 
+
+ align:start position:0%
+whatever is inside there is what's
+inside there minus one and so the
+
+ align:start position:0%
+inside there minus one and so the
+ 
+
+ align:start position:0%
+inside there minus one and so the
+induction hypothesis says s of this is
+
+ align:start position:0%
+induction hypothesis says s of this is
+ 
+
+ align:start position:0%
+induction hypothesis says s of this is
+that minus
+
+ align:start position:0%
+that minus
+ 
+
+ align:start position:0%
+that minus
+one okay any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay so let's write that on our table up
+
+ align:start position:0%
+okay so let's write that on our table up
+ 
+
+ align:start position:0%
+okay so let's write that on our table up
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is SN equals s of Floor N
+
+ align:start position:0%
+so this is SN equals s of Floor N
+ 
+
+ align:start position:0%
+so this is SN equals s of Floor N
+/2 plus s of ceiling n
+
+ align:start position:0%
+/2 plus s of ceiling n
+ 
+
+ align:start position:0%
+/2 plus s of ceiling n
+/2 plus one and the answer
+
+ align:start position:0%
+/2 plus one and the answer
+ 
+
+ align:start position:0%
+/2 plus one and the answer
+is SN is Tilda what's a Tilda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of n the answer is n minus one so it's
+
+ align:start position:0%
+of n the answer is n minus one so it's
+ 
+
+ align:start position:0%
+of n the answer is n minus one so it's
+till of n
+
+ align:start position:0%
+till of n
+ 
+
+ align:start position:0%
+till of n
+now this is the same expression as this
+
+ align:start position:0%
+now this is the same expression as this
+ 
+
+ align:start position:0%
+now this is the same expression as this
+if n's a power of two I'd have 2 SN / 2
+
+ align:start position:0%
+if n's a power of two I'd have 2 SN / 2
+ 
+
+ align:start position:0%
+if n's a power of two I'd have 2 SN / 2
+plus one instead of n minus one and so
+
+ align:start position:0%
+plus one instead of n minus one and so
+ 
+
+ align:start position:0%
+plus one instead of n minus one and so
+I'm by going from n minus one to one I
+
+ align:start position:0%
+I'm by going from n minus one to one I
+ 
+
+ align:start position:0%
+I'm by going from n minus one to one I
+got rid of the log
+
+ align:start position:0%
+got rid of the log
+ 
+
+ align:start position:0%
+got rid of the log
+term all right but it's still you know
+
+ align:start position:0%
+term all right but it's still you know
+ 
+
+ align:start position:0%
+term all right but it's still you know
+not exponential and that's because I'm
+
+ align:start position:0%
+not exponential and that's because I'm
+ 
+
+ align:start position:0%
+not exponential and that's because I'm
+cutting down the insides here by a
+
+ align:start position:0%
+cutting down the insides here by a
+ 
+
+ align:start position:0%
+cutting down the insides here by a
+factor of two
+
+ align:start position:0%
+factor of two
+ 
+
+ align:start position:0%
+factor of two
+roughly okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so all the recurrences we've seen so far
+
+ align:start position:0%
+so all the recurrences we've seen so far
+ 
+
+ align:start position:0%
+so all the recurrences we've seen so far
+have been pretty simple uh if guess and
+
+ align:start position:0%
+have been pretty simple uh if guess and
+ 
+
+ align:start position:0%
+have been pretty simple uh if guess and
+verify doesn't work after seeing a few
+
+ align:start position:0%
+verify doesn't work after seeing a few
+ 
+
+ align:start position:0%
+verify doesn't work after seeing a few
+terms you can use plug and chug and you
+
+ align:start position:0%
+terms you can use plug and chug and you
+ 
+
+ align:start position:0%
+terms you can use plug and chug and you
+can figure it out uh the good news is
+
+ align:start position:0%
+can figure it out uh the good news is
+ 
+
+ align:start position:0%
+can figure it out uh the good news is
+that happens a lot in
+
+ align:start position:0%
+that happens a lot in
+ 
+
+ align:start position:0%
+that happens a lot in
+practice the bad news is sometimes it
+
+ align:start position:0%
+practice the bad news is sometimes it
+ 
+
+ align:start position:0%
+practice the bad news is sometimes it
+doesn't and you can get nasty
+
+ align:start position:0%
+doesn't and you can get nasty
+ 
+
+ align:start position:0%
+doesn't and you can get nasty
+recurrences so let me show you a uh a
+
+ align:start position:0%
+recurrences so let me show you a uh a
+ 
+
+ align:start position:0%
+recurrences so let me show you a uh a
+nasty
+
+ align:start position:0%
+nasty
+ 
+
+ align:start position:0%
+nasty
+one that actually was once uh uh asked
+
+ align:start position:0%
+one that actually was once uh uh asked
+ 
+
+ align:start position:0%
+one that actually was once uh uh asked
+in 6046 I think on a uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quiz with disastrous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+results all right
+
+ align:start position:0%
+results all right
+ 
+
+ align:start position:0%
+results all right
+so this one is T of
+
+ align:start position:0%
+so this one is T of
+ 
+
+ align:start position:0%
+so this one is T of
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+equals 2 T of X over 2
+
+ align:start position:0%
+equals 2 T of X over 2
+ 
+
+ align:start position:0%
+equals 2 T of X over 2
+Plus 8
+
+ align:start position:0%
+Plus 8
+ 
+
+ align:start position:0%
+Plus 8
+9th T of 3x over
+
+ align:start position:0%
+9th T of 3x over
+ 
+
+ align:start position:0%
+9th T of 3x over
+4 plus
+
+ align:start position:0%
+4 plus
+ 
+
+ align:start position:0%
+4 plus
+X2 for X bigger than equal to 1 and
+
+ align:start position:0%
+X2 for X bigger than equal to 1 and
+ 
+
+ align:start position:0%
+X2 for X bigger than equal to 1 and
+otherwise it's zero when X is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one now this is nasty for a lot of
+
+ align:start position:0%
+one now this is nasty for a lot of
+ 
+
+ align:start position:0%
+one now this is nasty for a lot of
+reasons first it's not just to find on
+
+ align:start position:0%
+reasons first it's not just to find on
+ 
+
+ align:start position:0%
+reasons first it's not just to find on
+the integers we can make an integer
+
+ align:start position:0%
+the integers we can make an integer
+ 
+
+ align:start position:0%
+the integers we can make an integer
+verion by putting floors or ceilings
+
+ align:start position:0%
+verion by putting floors or ceilings
+ 
+
+ align:start position:0%
+verion by putting floors or ceilings
+here but the way you set it up now it's
+
+ align:start position:0%
+here but the way you set it up now it's
+ 
+
+ align:start position:0%
+here but the way you set it up now it's
+defined on real
+
+ align:start position:0%
+defined on real
+ 
+
+ align:start position:0%
+defined on real
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+uh you can in theory solve it with plug
+
+ align:start position:0%
+uh you can in theory solve it with plug
+ 
+
+ align:start position:0%
+uh you can in theory solve it with plug
+and chug the nasty part is you got a
+
+ align:start position:0%
+and chug the nasty part is you got a
+ 
+
+ align:start position:0%
+and chug the nasty part is you got a
+bunch of things going down by powers of
+
+ align:start position:0%
+bunch of things going down by powers of
+ 
+
+ align:start position:0%
+bunch of things going down by powers of
+Two and a bunch of things going down by
+
+ align:start position:0%
+Two and a bunch of things going down by
+ 
+
+ align:start position:0%
+Two and a bunch of things going down by
+three qus here and so you have to keep
+
+ align:start position:0%
+three qus here and so you have to keep
+ 
+
+ align:start position:0%
+three qus here and so you have to keep
+track of all the terms that are
+
+ align:start position:0%
+track of all the terms that are
+ 
+
+ align:start position:0%
+track of all the terms that are
+decreasing and that's a a nightmare
+
+ align:start position:0%
+decreasing and that's a a nightmare
+ 
+
+ align:start position:0%
+decreasing and that's a a nightmare
+plug-and chug because it's not just one
+
+ align:start position:0%
+plug-and chug because it's not just one
+ 
+
+ align:start position:0%
+plug-and chug because it's not just one
+thing that's unfolding it's two things
+
+ align:start position:0%
+thing that's unfolding it's two things
+ 
+
+ align:start position:0%
+thing that's unfolding it's two things
+things that are
+
+ align:start position:0%
+things that are
+ 
+
+ align:start position:0%
+things that are
+unfolding uh so very
+
+ align:start position:0%
+unfolding uh so very
+ 
+
+ align:start position:0%
+unfolding uh so very
+painful
+
+ align:start position:0%
+painful
+ 
+
+ align:start position:0%
+painful
+now it used to be that was the state of
+
+ align:start position:0%
+now it used to be that was the state of
+ 
+
+ align:start position:0%
+now it used to be that was the state of
+Life 20 years ago I think we started
+
+ align:start position:0%
+Life 20 years ago I think we started
+ 
+
+ align:start position:0%
+Life 20 years ago I think we started
+teaching this course sometime around
+
+ align:start position:0%
+teaching this course sometime around
+ 
+
+ align:start position:0%
+teaching this course sometime around
+then there just was no nothing else to
+
+ align:start position:0%
+then there just was no nothing else to
+ 
+
+ align:start position:0%
+then there just was no nothing else to
+say other then life's tough and
+
+ align:start position:0%
+say other then life's tough and
+ 
+
+ align:start position:0%
+say other then life's tough and
+sometimes you got to do these things and
+
+ align:start position:0%
+sometimes you got to do these things and
+ 
+
+ align:start position:0%
+sometimes you got to do these things and
+it's a it's a pain uh just had to make
+
+ align:start position:0%
+it's a it's a pain uh just had to make
+ 
+
+ align:start position:0%
+it's a it's a pain uh just had to make
+the best of it and then in the mid90s
+
+ align:start position:0%
+the best of it and then in the mid90s
+ 
+
+ align:start position:0%
+the best of it and then in the mid90s
+one day two students at the American
+
+ align:start position:0%
+one day two students at the American
+ 
+
+ align:start position:0%
+one day two students at the American
+University in Beirut came by my office
+
+ align:start position:0%
+University in Beirut came by my office
+ 
+
+ align:start position:0%
+University in Beirut came by my office
+uh they were named Acra and
+
+ align:start position:0%
+uh they were named Acra and
+ 
+
+ align:start position:0%
+uh they were named Acra and
+botsi uh and they'd actually come to
+
+ align:start position:0%
+botsi uh and they'd actually come to
+ 
+
+ align:start position:0%
+botsi uh and they'd actually come to
+Boston to escape the daily bombings this
+
+ align:start position:0%
+Boston to escape the daily bombings this
+ 
+
+ align:start position:0%
+Boston to escape the daily bombings this
+one was all heck was break breaking
+
+ align:start position:0%
+one was all heck was break breaking
+ 
+
+ align:start position:0%
+one was all heck was break breaking
+loose in Bay rout and it was a mess and
+
+ align:start position:0%
+loose in Bay rout and it was a mess and
+ 
+
+ align:start position:0%
+loose in Bay rout and it was a mess and
+they come into my office and they claim
+
+ align:start position:0%
+they come into my office and they claim
+ 
+
+ align:start position:0%
+they come into my office and they claim
+to have a simple formula for solving any
+
+ align:start position:0%
+to have a simple formula for solving any
+ 
+
+ align:start position:0%
+to have a simple formula for solving any
+recurrence like this in fact you could
+
+ align:start position:0%
+recurrence like this in fact you could
+ 
+
+ align:start position:0%
+recurrence like this in fact you could
+even add you know a a 5 T of X over 7
+
+ align:start position:0%
+even add you know a a 5 T of X over 7
+ 
+
+ align:start position:0%
+even add you know a a 5 T of X over 7
+they said no problem their simple
+
+ align:start position:0%
+they said no problem their simple
+ 
+
+ align:start position:0%
+they said no problem their simple
+formula just will always
+
+ align:start position:0%
+formula just will always
+ 
+
+ align:start position:0%
+formula just will always
+work all right and the general form that
+
+ align:start position:0%
+work all right and the general form that
+ 
+
+ align:start position:0%
+work all right and the general form that
+they claim to solve was the
+
+ align:start position:0%
+they claim to solve was the
+ 
+
+ align:start position:0%
+they claim to solve was the
+following it's the general class of
+
+ align:start position:0%
+following it's the general class of
+ 
+
+ align:start position:0%
+following it's the general class of
+divide and conquer recurrences so any
+
+ align:start position:0%
+divide and conquer recurrences so any
+ 
+
+ align:start position:0%
+divide and conquer recurrences so any
+recurrence you get from an algorithm
+
+ align:start position:0%
+recurrence you get from an algorithm
+ 
+
+ align:start position:0%
+recurrence you get from an algorithm
+where you break it into smaller pieces
+
+ align:start position:0%
+where you break it into smaller pieces
+ 
+
+ align:start position:0%
+where you break it into smaller pieces
+by a constant Factor they claim to solve
+
+ align:start position:0%
+by a constant Factor they claim to solve
+ 
+
+ align:start position:0%
+by a constant Factor they claim to solve
+so let me Define this class it's a
+
+ align:start position:0%
+so let me Define this class it's a
+ 
+
+ align:start position:0%
+so let me Define this class it's a
+little painful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a defied and Conquer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence has the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form you know there's a simple version
+
+ align:start position:0%
+form you know there's a simple version
+ 
+
+ align:start position:0%
+form you know there's a simple version
+and the hard version the simple version
+
+ align:start position:0%
+and the hard version the simple version
+ 
+
+ align:start position:0%
+and the hard version the simple version
+is it looks like that all right you got
+
+ align:start position:0%
+is it looks like that all right you got
+ 
+
+ align:start position:0%
+is it looks like that all right you got
+a bunch of terms inside each term you
+
+ align:start position:0%
+a bunch of terms inside each term you
+ 
+
+ align:start position:0%
+a bunch of terms inside each term you
+cut it down by a constant factor and
+
+ align:start position:0%
+cut it down by a constant factor and
+ 
+
+ align:start position:0%
+cut it down by a constant factor and
+then you add something at the end that's
+
+ align:start position:0%
+then you add something at the end that's
+ 
+
+ align:start position:0%
+then you add something at the end that's
+the simple version of what a divide and
+
+ align:start position:0%
+the simple version of what a divide and
+ 
+
+ align:start position:0%
+the simple version of what a divide and
+conquer recurrence is is and you can
+
+ align:start position:0%
+conquer recurrence is is and you can
+ 
+
+ align:start position:0%
+conquer recurrence is is and you can
+throw in floors and ceilings and other
+
+ align:start position:0%
+throw in floors and ceilings and other
+ 
+
+ align:start position:0%
+throw in floors and ceilings and other
+junk tube all right now I'm going to
+
+ align:start position:0%
+junk tube all right now I'm going to
+ 
+
+ align:start position:0%
+junk tube all right now I'm going to
+give you the formal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+version so it has the form T of x equals
+
+ align:start position:0%
+version so it has the form T of x equals
+ 
+
+ align:start position:0%
+version so it has the form T of x equals
+some constant
+
+ align:start position:0%
+some constant
+ 
+
+ align:start position:0%
+some constant
+A1 time T of a constant less than one B1
+
+ align:start position:0%
+A1 time T of a constant less than one B1
+ 
+
+ align:start position:0%
+A1 time T of a constant less than one B1
+ofx plus some slop you're allowed to
+
+ align:start position:0%
+ofx plus some slop you're allowed to
+ 
+
+ align:start position:0%
+ofx plus some slop you're allowed to
+have like floors and ceilings and who
+
+ align:start position:0%
+have like floors and ceilings and who
+ 
+
+ align:start position:0%
+have like floors and ceilings and who
+knows what else and then you get more of
+
+ align:start position:0%
+knows what else and then you get more of
+ 
+
+ align:start position:0%
+knows what else and then you get more of
+these you get
+
+ align:start position:0%
+these you get
+ 
+
+ align:start position:0%
+these you get
+A2 T of
+
+ align:start position:0%
+A2 T of
+ 
+
+ align:start position:0%
+A2 T of
+b2x plus Epsilon
+
+ align:start position:0%
+b2x plus Epsilon
+ 
+
+ align:start position:0%
+b2x plus Epsilon
+2X and so forth and you can have any
+
+ align:start position:0%
+2X and so forth and you can have any
+ 
+
+ align:start position:0%
+2X and so forth and you can have any
+number of these you want up to a
+
+ align:start position:0%
+number of these you want up to a
+ 
+
+ align:start position:0%
+number of these you want up to a
+constant so maybe there's a subk t b sub
+
+ align:start position:0%
+constant so maybe there's a subk t b sub
+ 
+
+ align:start position:0%
+constant so maybe there's a subk t b sub
+KX plus Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KX plus some function of X sitting out
+
+ align:start position:0%
+KX plus some function of X sitting out
+ 
+
+ align:start position:0%
+KX plus some function of X sitting out
+here like the X
+
+ align:start position:0%
+here like the X
+ 
+
+ align:start position:0%
+here like the X
+squ and this happens for X bigger than
+
+ align:start position:0%
+squ and this happens for X bigger than
+ 
+
+ align:start position:0%
+squ and this happens for X bigger than
+some fixed value some constant
+
+ align:start position:0%
+some fixed value some constant
+ 
+
+ align:start position:0%
+some fixed value some constant
+now the constraints
+
+ align:start position:0%
+now the constraints
+ 
+
+ align:start position:0%
+now the constraints
+are well the AI are positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constants the bi are positive and less
+
+ align:start position:0%
+constants the bi are positive and less
+ 
+
+ align:start position:0%
+constants the bi are positive and less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+one you got to cut it down by a constant
+
+ align:start position:0%
+one you got to cut it down by a constant
+ 
+
+ align:start position:0%
+one you got to cut it down by a constant
+factor to be the divide and conquer
+
+ align:start position:0%
+factor to be the divide and conquer
+ 
+
+ align:start position:0%
+factor to be the divide and conquer
+recurrence that's
+
+ align:start position:0%
+recurrence that's
+ 
+
+ align:start position:0%
+recurrence that's
+critical uh K is fixed it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant and these functions can't be
+
+ align:start position:0%
+constant and these functions can't be
+ 
+
+ align:start position:0%
+constant and these functions can't be
+too big uh they can't be bigger than o
+
+ align:start position:0%
+too big uh they can't be bigger than o
+ 
+
+ align:start position:0%
+too big uh they can't be bigger than o
+of X over log s of X almost as big as X
+
+ align:start position:0%
+of X over log s of X almost as big as X
+ 
+
+ align:start position:0%
+of X over log s of X almost as big as X
+but you can't let them be too big or
+
+ align:start position:0%
+but you can't let them be too big or
+ 
+
+ align:start position:0%
+but you can't let them be too big or
+you'll not be cutting things down by a
+
+ align:start position:0%
+you'll not be cutting things down by a
+ 
+
+ align:start position:0%
+you'll not be cutting things down by a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+factor and you don't get too hung up
+
+ align:start position:0%
+factor and you don't get too hung up
+ 
+
+ align:start position:0%
+factor and you don't get too hung up
+over this
+
+ align:start position:0%
+over this
+ 
+
+ align:start position:0%
+over this
+because you know you don't get too deep
+
+ align:start position:0%
+because you know you don't get too deep
+ 
+
+ align:start position:0%
+because you know you don't get too deep
+in the details but this is at most o of
+
+ align:start position:0%
+in the details but this is at most o of
+ 
+
+ align:start position:0%
+in the details but this is at most o of
+X over log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and find finally the G thing it's got
+
+ align:start position:0%
+X and find finally the G thing it's got
+ 
+
+ align:start position:0%
+X and find finally the G thing it's got
+to be polom it can't be an exponent you
+
+ align:start position:0%
+to be polom it can't be an exponent you
+ 
+
+ align:start position:0%
+to be polom it can't be an exponent you
+can't put 2 to the X here and the formal
+
+ align:start position:0%
+can't put 2 to the X here and the formal
+ 
+
+ align:start position:0%
+can't put 2 to the X here and the formal
+way that's expressed is the derivative
+
+ align:start position:0%
+way that's expressed is the derivative
+ 
+
+ align:start position:0%
+way that's expressed is the derivative
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G of X is less than x to the C for some
+
+ align:start position:0%
+G of X is less than x to the C for some
+ 
+
+ align:start position:0%
+G of X is less than x to the C for some
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C that's it so this is a mouthful but
+
+ align:start position:0%
+C that's it so this is a mouthful but
+ 
+
+ align:start position:0%
+C that's it so this is a mouthful but
+like I said before anything that looks
+
+ align:start position:0%
+like I said before anything that looks
+ 
+
+ align:start position:0%
+like I said before anything that looks
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that okay basically as long as you don't
+
+ align:start position:0%
+that okay basically as long as you don't
+ 
+
+ align:start position:0%
+that okay basically as long as you don't
+throw in exponentials or do something
+
+ align:start position:0%
+throw in exponentials or do something
+ 
+
+ align:start position:0%
+throw in exponentials or do something
+too wild to
+
+ align:start position:0%
+too wild to
+ 
+
+ align:start position:0%
+too wild to
+it it works so let's see which of our
+
+ align:start position:0%
+it it works so let's see which of our
+ 
+
+ align:start position:0%
+it it works so let's see which of our
+guys over here are divide and conquer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrences how about this one towers of
+
+ align:start position:0%
+recurrences how about this one towers of
+ 
+
+ align:start position:0%
+recurrences how about this one towers of
+anoi is that a divide and conquer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence some yes some
+
+ align:start position:0%
+recurrence some yes some
+ 
+
+ align:start position:0%
+recurrence some yes some
+no all right who thinks no can tell me
+
+ align:start position:0%
+no all right who thinks no can tell me
+ 
+
+ align:start position:0%
+no all right who thinks no can tell me
+why it's not why isn't that
+
+ align:start position:0%
+why it's not why isn't that
+ 
+
+ align:start position:0%
+why it's not why isn't that
+by any factor that is less than that's
+
+ align:start position:0%
+by any factor that is less than that's
+ 
+
+ align:start position:0%
+by any factor that is less than that's
+right the recurrence problem is n minus
+
+ align:start position:0%
+right the recurrence problem is n minus
+ 
+
+ align:start position:0%
+right the recurrence problem is n minus
+one and we got to make
+
+ align:start position:0%
+one and we got to make
+ 
+
+ align:start position:0%
+one and we got to make
+it down by a constant Factor here the B1
+
+ align:start position:0%
+it down by a constant Factor here the B1
+ 
+
+ align:start position:0%
+it down by a constant Factor here the B1
+is less than one it can't be equal to
+
+ align:start position:0%
+is less than one it can't be equal to
+ 
+
+ align:start position:0%
+is less than one it can't be equal to
+one and this is not big enough to make
+
+ align:start position:0%
+one and this is not big enough to make
+ 
+
+ align:start position:0%
+one and this is not big enough to make
+up for you know the X over two term or
+
+ align:start position:0%
+up for you know the X over two term or
+ 
+
+ align:start position:0%
+up for you know the X over two term or
+something we're missing so whenever you
+
+ align:start position:0%
+something we're missing so whenever you
+ 
+
+ align:start position:0%
+something we're missing so whenever you
+have an N minus one or an N minus two
+
+ align:start position:0%
+have an N minus one or an N minus two
+ 
+
+ align:start position:0%
+have an N minus one or an N minus two
+that is not divide and
+
+ align:start position:0%
+that is not divide and
+ 
+
+ align:start position:0%
+that is not divide and
+conquer uh we'll discuss those next time
+
+ align:start position:0%
+conquer uh we'll discuss those next time
+ 
+
+ align:start position:0%
+conquer uh we'll discuss those next time
+on Thursday how to solve those so that's
+
+ align:start position:0%
+on Thursday how to solve those so that's
+ 
+
+ align:start position:0%
+on Thursday how to solve those so that's
+not divide and
+
+ align:start position:0%
+not divide and
+ 
+
+ align:start position:0%
+not divide and
+conquer what about this one is that
+
+ align:start position:0%
+conquer what about this one is that
+ 
+
+ align:start position:0%
+conquer what about this one is that
+divide and conquer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here yes you've got two problems of half
+
+ align:start position:0%
+here yes you've got two problems of half
+ 
+
+ align:start position:0%
+here yes you've got two problems of half
+the size and you're adding a linear
+
+ align:start position:0%
+the size and you're adding a linear
+ 
+
+ align:start position:0%
+the size and you're adding a linear
+function it's not exponential it's
+
+ align:start position:0%
+function it's not exponential it's
+ 
+
+ align:start position:0%
+function it's not exponential it's
+polinomial that is divide and
+
+ align:start position:0%
+polinomial that is divide and
+ 
+
+ align:start position:0%
+polinomial that is divide and
+conquer what about this this nasty guy
+
+ align:start position:0%
+conquer what about this this nasty guy
+ 
+
+ align:start position:0%
+conquer what about this this nasty guy
+is that divide and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conquer yeah you've got basically n/2
+
+ align:start position:0%
+conquer yeah you've got basically n/2
+ 
+
+ align:start position:0%
+conquer yeah you've got basically n/2
+here two n/2 terms now this is where
+
+ align:start position:0%
+here two n/2 terms now this is where
+ 
+
+ align:start position:0%
+here two n/2 terms now this is where
+that Epsilon thing comes in handy
+
+ align:start position:0%
+that Epsilon thing comes in handy
+ 
+
+ align:start position:0%
+that Epsilon thing comes in handy
+because Epsilon one of n in this case is
+
+ align:start position:0%
+because Epsilon one of n in this case is
+ 
+
+ align:start position:0%
+because Epsilon one of n in this case is
+FL n /
+
+ align:start position:0%
+FL n /
+ 
+
+ align:start position:0%
+FL n /
+2 minus n over two and that's at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all right so we're adding maybe
+
+ align:start position:0%
+one all right so we're adding maybe
+ 
+
+ align:start position:0%
+one all right so we're adding maybe
+we're adding a half here something like
+
+ align:start position:0%
+we're adding a half here something like
+ 
+
+ align:start position:0%
+we're adding a half here something like
+that and we're allowed to add anything
+
+ align:start position:0%
+that and we're allowed to add anything
+ 
+
+ align:start position:0%
+that and we're allowed to add anything
+up to n over log squ of n to fit
+
+ align:start position:0%
+up to n over log squ of n to fit
+ 
+
+ align:start position:0%
+up to n over log squ of n to fit
+all right so you can you can mess around
+
+ align:start position:0%
+all right so you can you can mess around
+ 
+
+ align:start position:0%
+all right so you can you can mess around
+with the low order terms in here and
+
+ align:start position:0%
+with the low order terms in here and
+ 
+
+ align:start position:0%
+with the low order terms in here and
+adding one is fine as well all right so
+
+ align:start position:0%
+adding one is fine as well all right so
+ 
+
+ align:start position:0%
+adding one is fine as well all right so
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+qualifies what about let we should check
+
+ align:start position:0%
+qualifies what about let we should check
+ 
+
+ align:start position:0%
+qualifies what about let we should check
+that this thing
+
+ align:start position:0%
+that this thing
+ 
+
+ align:start position:0%
+that this thing
+qualifies let's check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that well yeah I
+
+ align:start position:0%
+that well yeah I
+ 
+
+ align:start position:0%
+that well yeah I
+got two constant
+
+ align:start position:0%
+got two constant
+ 
+
+ align:start position:0%
+got two constant
+A1 T of half X that's okay 8 9th T of
+
+ align:start position:0%
+A1 T of half X that's okay 8 9th T of
+ 
+
+ align:start position:0%
+A1 T of half X that's okay 8 9th T of
+3/4 x that's okay my G function is a
+
+ align:start position:0%
+3/4 x that's okay my G function is a
+ 
+
+ align:start position:0%
+3/4 x that's okay my G function is a
+polinomial the derivative is 2x that's
+
+ align:start position:0%
+polinomial the derivative is 2x that's
+ 
+
+ align:start position:0%
+polinomial the derivative is 2x that's
+less than x to a power or of x to a
+
+ align:start position:0%
+less than x to a power or of x to a
+ 
+
+ align:start position:0%
+less than x to a power or of x to a
+power so this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fits okay any questions about the
+
+ align:start position:0%
+fits okay any questions about the
+ 
+
+ align:start position:0%
+fits okay any questions about the
+definition of a divide and conquer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence okay and you can see why sort
+
+ align:start position:0%
+recurrence okay and you can see why sort
+ 
+
+ align:start position:0%
+recurrence okay and you can see why sort
+of they come up because whenever you're
+
+ align:start position:0%
+of they come up because whenever you're
+ 
+
+ align:start position:0%
+of they come up because whenever you're
+solving a problem with recursive pieces
+
+ align:start position:0%
+solving a problem with recursive pieces
+ 
+
+ align:start position:0%
+solving a problem with recursive pieces
+that are a constant Factor smaller
+
+ align:start position:0%
+that are a constant Factor smaller
+ 
+
+ align:start position:0%
+that are a constant Factor smaller
+you're going to have something that that
+
+ align:start position:0%
+you're going to have something that that
+ 
+
+ align:start position:0%
+you're going to have something that that
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+that okay so getting back to Acra and
+
+ align:start position:0%
+that okay so getting back to Acra and
+ 
+
+ align:start position:0%
+that okay so getting back to Acra and
+batsi you know they show up in my office
+
+ align:start position:0%
+batsi you know they show up in my office
+ 
+
+ align:start position:0%
+batsi you know they show up in my office
+they claim to have solved anything like
+
+ align:start position:0%
+they claim to have solved anything like
+ 
+
+ align:start position:0%
+they claim to have solved anything like
+this now needless to say I'm a little
+
+ align:start position:0%
+this now needless to say I'm a little
+ 
+
+ align:start position:0%
+this now needless to say I'm a little
+skeptical you know I got to tell you
+
+ align:start position:0%
+skeptical you know I got to tell you
+ 
+
+ align:start position:0%
+skeptical you know I got to tell you
+you're a professor at MIT especially in
+
+ align:start position:0%
+you're a professor at MIT especially in
+ 
+
+ align:start position:0%
+you're a professor at MIT especially in
+mathematics and uh people are always
+
+ align:start position:0%
+mathematics and uh people are always
+ 
+
+ align:start position:0%
+mathematics and uh people are always
+coming by with proofs of you know the
+
+ align:start position:0%
+coming by with proofs of you know the
+ 
+
+ align:start position:0%
+coming by with proofs of you know the
+remon hypothesis P equals NP P doesn't
+
+ align:start position:0%
+remon hypothesis P equals NP P doesn't
+ 
+
+ align:start position:0%
+remon hypothesis P equals NP P doesn't
+equal NP
+
+ align:start position:0%
+equal NP
+ 
+
+ align:start position:0%
+equal NP
+you know and this was a classic problem
+
+ align:start position:0%
+you know and this was a classic problem
+ 
+
+ align:start position:0%
+you know and this was a classic problem
+you know hundreds of researchers had
+
+ align:start position:0%
+you know hundreds of researchers had
+ 
+
+ align:start position:0%
+you know hundreds of researchers had
+studied recurrences for decades and not
+
+ align:start position:0%
+studied recurrences for decades and not
+ 
+
+ align:start position:0%
+studied recurrences for decades and not
+only it wasn't even believed that there
+
+ align:start position:0%
+only it wasn't even believed that there
+ 
+
+ align:start position:0%
+only it wasn't even believed that there
+was possibly a solution it's not like
+
+ align:start position:0%
+was possibly a solution it's not like
+ 
+
+ align:start position:0%
+was possibly a solution it's not like
+it's one of these open questions where
+
+ align:start position:0%
+it's one of these open questions where
+ 
+
+ align:start position:0%
+it's one of these open questions where
+we all believe P doesn't equal NP in a
+
+ align:start position:0%
+we all believe P doesn't equal NP in a
+ 
+
+ align:start position:0%
+we all believe P doesn't equal NP in a
+Sy matter approving it people didn't
+
+ align:start position:0%
+Sy matter approving it people didn't
+ 
+
+ align:start position:0%
+Sy matter approving it people didn't
+think a solution existed that would be
+
+ align:start position:0%
+think a solution existed that would be
+ 
+
+ align:start position:0%
+think a solution existed that would be
+clean I mean look at just the
+
+ align:start position:0%
+clean I mean look at just the
+ 
+
+ align:start position:0%
+clean I mean look at just the
+definitions of mess how could there
+
+ align:start position:0%
+definitions of mess how could there
+ 
+
+ align:start position:0%
+definitions of mess how could there
+possibly be a clean solution to
+
+ align:start position:0%
+possibly be a clean solution to
+ 
+
+ align:start position:0%
+possibly be a clean solution to
+that you know so it's sort of like the
+
+ align:start position:0%
+that you know so it's sort of like the
+ 
+
+ align:start position:0%
+that you know so it's sort of like the
+Holy Grail you know it doesn't exist but
+
+ align:start position:0%
+Holy Grail you know it doesn't exist but
+ 
+
+ align:start position:0%
+Holy Grail you know it doesn't exist but
+it's fun to think about but a fantasy
+
+ align:start position:0%
+it's fun to think about but a fantasy
+ 
+
+ align:start position:0%
+it's fun to think about but a fantasy
+maybe there's a solution and you could
+
+ align:start position:0%
+maybe there's a solution and you could
+ 
+
+ align:start position:0%
+maybe there's a solution and you could
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+it um and much less these aren't
+
+ align:start position:0%
+it um and much less these aren't
+ 
+
+ align:start position:0%
+it um and much less these aren't
+reputable researchers in my office these
+
+ align:start position:0%
+reputable researchers in my office these
+ 
+
+ align:start position:0%
+reputable researchers in my office these
+are two students from Beirut named ACA
+
+ align:start position:0%
+are two students from Beirut named ACA
+ 
+
+ align:start position:0%
+are two students from Beirut named ACA
+and batsi claiming that they've figured
+
+ align:start position:0%
+and batsi claiming that they've figured
+ 
+
+ align:start position:0%
+and batsi claiming that they've figured
+out this thing that all these professors
+
+ align:start position:0%
+out this thing that all these professors
+ 
+
+ align:start position:0%
+out this thing that all these professors
+been teaching this stuff in 6046 for
+
+ align:start position:0%
+been teaching this stuff in 6046 for
+ 
+
+ align:start position:0%
+been teaching this stuff in 6046 for
+years said doesn't you got to do plugin
+
+ align:start position:0%
+years said doesn't you got to do plugin
+ 
+
+ align:start position:0%
+years said doesn't you got to do plugin
+shot um anyway you know they've been
+
+ align:start position:0%
+shot um anyway you know they've been
+ 
+
+ align:start position:0%
+shot um anyway you know they've been
+kicked out of everybody else's office I
+
+ align:start position:0%
+kicked out of everybody else's office I
+ 
+
+ align:start position:0%
+kicked out of everybody else's office I
+said okay let's let's do it show me the
+
+ align:start position:0%
+said okay let's let's do it show me the
+ 
+
+ align:start position:0%
+said okay let's let's do it show me the
+solution and they did and I go holy cow
+
+ align:start position:0%
+solution and they did and I go holy cow
+ 
+
+ align:start position:0%
+solution and they did and I go holy cow
+it's right you know it looks good now
+
+ align:start position:0%
+it's right you know it looks good now
+ 
+
+ align:start position:0%
+it's right you know it looks good now
+they had a few details wrong but oh my
+
+ align:start position:0%
+they had a few details wrong but oh my
+ 
+
+ align:start position:0%
+they had a few details wrong but oh my
+goodness the answer was correct and it's
+
+ align:start position:0%
+goodness the answer was correct and it's
+ 
+
+ align:start position:0%
+goodness the answer was correct and it's
+amazingly
+
+ align:start position:0%
+amazingly
+ 
+
+ align:start position:0%
+amazingly
+simple all right so now we teach
+
+ align:start position:0%
+simple all right so now we teach
+ 
+
+ align:start position:0%
+simple all right so now we teach
+it and uh fact you can write the
+
+ align:start position:0%
+it and uh fact you can write the
+ 
+
+ align:start position:0%
+it and uh fact you can write the
+solution down easier than can you can
+
+ align:start position:0%
+solution down easier than can you can
+ 
+
+ align:start position:0%
+solution down easier than can you can
+write the definition of divide and
+
+ align:start position:0%
+write the definition of divide and
+ 
+
+ align:start position:0%
+write the definition of divide and
+conquer
+
+ align:start position:0%
+conquer
+ 
+
+ align:start position:0%
+conquer
+recurrence really remarkable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the
+
+ align:start position:0%
+right so the
+ 
+
+ align:start position:0%
+right so the
+theorem by AAR and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bobsy in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+96 set p real number so
+
+ align:start position:0%
+96 set p real number so
+ 
+
+ align:start position:0%
+96 set p real number so
+that the sum IAL 1 to
+
+ align:start position:0%
+that the sum IAL 1 to
+ 
+
+ align:start position:0%
+that the sum IAL 1 to
+K of AI I * b i to the P equal 1 so the
+
+ align:start position:0%
+K of AI I * b i to the P equal 1 so the
+ 
+
+ align:start position:0%
+K of AI I * b i to the P equal 1 so the
+AI are these things here the bis are the
+
+ align:start position:0%
+AI are these things here the bis are the
+ 
+
+ align:start position:0%
+AI are these things here the bis are the
+fractions
+
+ align:start position:0%
+fractions
+ 
+
+ align:start position:0%
+fractions
+here all right find a p such that
+
+ align:start position:0%
+here all right find a p such that
+ 
+
+ align:start position:0%
+here all right find a p such that
+this sum is one all right then the
+
+ align:start position:0%
+this sum is one all right then the
+ 
+
+ align:start position:0%
+this sum is one all right then the
+answer is
+
+ align:start position:0%
+answer is
+ 
+
+ align:start position:0%
+answer is
+this then T of
+
+ align:start position:0%
+this then T of
+ 
+
+ align:start position:0%
+this then T of
+x equals Theta we're going to use our
+
+ align:start position:0%
+x equals Theta we're going to use our
+ 
+
+ align:start position:0%
+x equals Theta we're going to use our
+ASM totic notation X the P plus x to the
+
+ align:start position:0%
+ASM totic notation X the P plus x to the
+ 
+
+ align:start position:0%
+ASM totic notation X the P plus x to the
+P time the integral from 1 to x g of u g
+
+ align:start position:0%
+P time the integral from 1 to x g of u g
+ 
+
+ align:start position:0%
+P time the integral from 1 to x g of u g
+is that polinomial thing the thing at
+
+ align:start position:0%
+is that polinomial thing the thing at
+ 
+
+ align:start position:0%
+is that polinomial thing the thing at
+the end over U to the P minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+du that's
+
+ align:start position:0%
+du that's
+ 
+
+ align:start position:0%
+du that's
+it all right this is really great news
+
+ align:start position:0%
+it all right this is really great news
+ 
+
+ align:start position:0%
+it all right this is really great news
+for you guys especially if you go on
+
+ align:start position:0%
+for you guys especially if you go on
+ 
+
+ align:start position:0%
+for you guys especially if you go on
+into algorithms because you don't have
+
+ align:start position:0%
+into algorithms because you don't have
+ 
+
+ align:start position:0%
+into algorithms because you don't have
+to deal with plug and chug on nasty
+
+ align:start position:0%
+to deal with plug and chug on nasty
+ 
+
+ align:start position:0%
+to deal with plug and chug on nasty
+things you just solve the the answer
+
+ align:start position:0%
+things you just solve the the answer
+ 
+
+ align:start position:0%
+things you just solve the the answer
+okay now the proof is by guess and
+
+ align:start position:0%
+okay now the proof is by guess and
+ 
+
+ align:start position:0%
+okay now the proof is by guess and
+verify and they made a really good
+
+ align:start position:0%
+verify and they made a really good
+ 
+
+ align:start position:0%
+verify and they made a really good
+guess right you know you wouldn't think
+
+ align:start position:0%
+guess right you know you wouldn't think
+ 
+
+ align:start position:0%
+guess right you know you wouldn't think
+looking at that oh I'm G to guess this
+
+ align:start position:0%
+looking at that oh I'm G to guess this
+ 
+
+ align:start position:0%
+looking at that oh I'm G to guess this
+you know probably not you know and
+
+ align:start position:0%
+you know probably not you know and
+ 
+
+ align:start position:0%
+you know probably not you know and
+there's no real numbers to try to guess
+
+ align:start position:0%
+there's no real numbers to try to guess
+ 
+
+ align:start position:0%
+there's no real numbers to try to guess
+this it's ASM totic
+
+ align:start position:0%
+this it's ASM totic
+ 
+
+ align:start position:0%
+this it's ASM totic
+notation um but it works when you you
+
+ align:start position:0%
+notation um but it works when you you
+ 
+
+ align:start position:0%
+notation um but it works when you you
+can verify it by induction it's a little
+
+ align:start position:0%
+can verify it by induction it's a little
+ 
+
+ align:start position:0%
+can verify it by induction it's a little
+painful to verify by induction but you
+
+ align:start position:0%
+painful to verify by induction but you
+ 
+
+ align:start position:0%
+painful to verify by induction but you
+can do it we won't do it in class I did
+
+ align:start position:0%
+can do it we won't do it in class I did
+ 
+
+ align:start position:0%
+can do it we won't do it in class I did
+try one year and it was a disaster so we
+
+ align:start position:0%
+try one year and it was a disaster so we
+ 
+
+ align:start position:0%
+try one year and it was a disaster so we
+don't do it in class anymore uh but
+
+ align:start position:0%
+don't do it in class anymore uh but
+ 
+
+ align:start position:0%
+don't do it in class anymore uh but
+let's see some examples of how to apply
+
+ align:start position:0%
+let's see some examples of how to apply
+ 
+
+ align:start position:0%
+let's see some examples of how to apply
+this all right so let's start with a
+
+ align:start position:0%
+this all right so let's start with a
+ 
+
+ align:start position:0%
+this all right so let's start with a
+merge
+
+ align:start position:0%
+merge
+ 
+
+ align:start position:0%
+merge
+sort which is the second one here let's
+
+ align:start position:0%
+sort which is the second one here let's
+ 
+
+ align:start position:0%
+sort which is the second one here let's
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all right so we got an example here
+
+ align:start position:0%
+that all right so we got an example here
+ 
+
+ align:start position:0%
+that all right so we got an example here
+T ofx
+
+ align:start position:0%
+T ofx
+ 
+
+ align:start position:0%
+T ofx
+= 2 T ofx /
+
+ align:start position:0%
+= 2 T ofx /
+ 
+
+ align:start position:0%
+= 2 T ofx /
+2 plus n minus one or xus one X now and
+
+ align:start position:0%
+2 plus n minus one or xus one X now and
+ 
+
+ align:start position:0%
+2 plus n minus one or xus one X now and
+I'm not even going to worry about powers
+
+ align:start position:0%
+I'm not even going to worry about powers
+ 
+
+ align:start position:0%
+I'm not even going to worry about powers
+of two anymore I don't I don't care it's
+
+ align:start position:0%
+of two anymore I don't I don't care it's
+ 
+
+ align:start position:0%
+of two anymore I don't I don't care it's
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+fine all right what is p in this case
+
+ align:start position:0%
+fine all right what is p in this case
+ 
+
+ align:start position:0%
+fine all right what is p in this case
+I've only got one term I don't even need
+
+ align:start position:0%
+I've only got one term I don't even need
+ 
+
+ align:start position:0%
+I've only got one term I don't even need
+a sum from that definition over there
+
+ align:start position:0%
+a sum from that definition over there
+ 
+
+ align:start position:0%
+a sum from that definition over there
+what's the value of
+
+ align:start position:0%
+what's the value of
+ 
+
+ align:start position:0%
+what's the value of
+P for this guy
+
+ align:start position:0%
+P for this guy
+ 
+
+ align:start position:0%
+P for this guy
+so I've got A1 is
+
+ align:start position:0%
+so I've got A1 is
+ 
+
+ align:start position:0%
+so I've got A1 is
+two B1 is a half just one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term what's the value of P such that 2 *
+
+ align:start position:0%
+term what's the value of P such that 2 *
+ 
+
+ align:start position:0%
+term what's the value of P such that 2 *
+a half to the P equals
+
+ align:start position:0%
+a half to the P equals
+ 
+
+ align:start position:0%
+a half to the P equals
+1 one doesn't get much
+
+ align:start position:0%
+1 one doesn't get much
+ 
+
+ align:start position:0%
+1 one doesn't get much
+simpler all right so 2 * a half to the P
+
+ align:start position:0%
+simpler all right so 2 * a half to the P
+ 
+
+ align:start position:0%
+simpler all right so 2 * a half to the P
+equal 1 implies p is
+
+ align:start position:0%
+equal 1 implies p is
+ 
+
+ align:start position:0%
+equal 1 implies p is
+1 all right now I just plug into the
+
+ align:start position:0%
+1 all right now I just plug into the
+ 
+
+ align:start position:0%
+1 all right now I just plug into the
+integral over there
+
+ align:start position:0%
+integral over there
+ 
+
+ align:start position:0%
+integral over there
+all right let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so T of
+
+ align:start position:0%
+that so T of
+ 
+
+ align:start position:0%
+that so T of
+x equals
+
+ align:start position:0%
+x equals
+ 
+
+ align:start position:0%
+x equals
+Theta well X the p is x 1 plus just take
+
+ align:start position:0%
+Theta well X the p is x 1 plus just take
+ 
+
+ align:start position:0%
+Theta well X the p is x 1 plus just take
+off the one plus x * the integral 1 tox
+
+ align:start position:0%
+off the one plus x * the integral 1 tox
+ 
+
+ align:start position:0%
+off the one plus x * the integral 1 tox
+what's the G
+
+ align:start position:0%
+what's the G
+ 
+
+ align:start position:0%
+what's the G
+function what's G of X in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case x
+
+ align:start position:0%
+case x
+ 
+
+ align:start position:0%
+case x
+-1 so I take the integral of G of U is
+
+ align:start position:0%
+-1 so I take the integral of G of U is
+ 
+
+ align:start position:0%
+-1 so I take the integral of G of U is
+just uus one
+
+ align:start position:0%
+just uus one
+ 
+
+ align:start position:0%
+just uus one
+over U to the p +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 P minus
+
+ align:start position:0%
+1 P minus
+ 
+
+ align:start position:0%
+1 P minus
+one uh did I write the formula right is
+
+ align:start position:0%
+one uh did I write the formula right is
+ 
+
+ align:start position:0%
+one uh did I write the formula right is
+it plus one or minus one
+
+ align:start position:0%
+it plus one or minus one
+ 
+
+ align:start position:0%
+it plus one or minus one
+here did I get it p+ one sorry didn't
+
+ align:start position:0%
+here did I get it p+ one sorry didn't
+ 
+
+ align:start position:0%
+here did I get it p+ one sorry didn't
+write that right p + one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here all right so U to the p+ one is
+
+ align:start position:0%
+here all right so U to the p+ one is
+ 
+
+ align:start position:0%
+here all right so U to the p+ one is
+u^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Du all right this
+
+ align:start position:0%
+Du all right this
+ 
+
+ align:start position:0%
+Du all right this
+is Theta of x + x
+
+ align:start position:0%
+is Theta of x + x
+ 
+
+ align:start position:0%
+is Theta of x + x
+integral 1 / U u - 1 / u^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 the integral of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops the integral of one over U is the
+
+ align:start position:0%
+oops the integral of one over U is the
+ 
+
+ align:start position:0%
+oops the integral of one over U is the
+log of
+
+ align:start position:0%
+log of
+ 
+
+ align:start position:0%
+log of
+U the integral of 1 over U2 is one over
+
+ align:start position:0%
+U the integral of 1 over U2 is one over
+ 
+
+ align:start position:0%
+U the integral of 1 over U2 is one over
+U but I changed the sign
+
+ align:start position:0%
+U but I changed the sign
+ 
+
+ align:start position:0%
+U but I changed the sign
+there one to X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so I get Theta of x + x time
+
+ align:start position:0%
+all right so I get Theta of x + x time
+ 
+
+ align:start position:0%
+all right so I get Theta of x + x time
+log of
+
+ align:start position:0%
+log of
+ 
+
+ align:start position:0%
+log of
+x + 1
+
+ align:start position:0%
+x + 1
+ 
+
+ align:start position:0%
+x + 1
+/x minus log of zero that's log of one
+
+ align:start position:0%
+/x minus log of zero that's log of one
+ 
+
+ align:start position:0%
+/x minus log of zero that's log of one
+is nothing minus
+
+ align:start position:0%
+is nothing minus
+ 
+
+ align:start position:0%
+is nothing minus
+one all
+
+ align:start position:0%
+one all
+ 
+
+ align:start position:0%
+one all
+right and I'm doing thetas here so I can
+
+ align:start position:0%
+right and I'm doing thetas here so I can
+ 
+
+ align:start position:0%
+right and I'm doing thetas here so I can
+forget the low order term
+
+ align:start position:0%
+forget the low order term
+ 
+
+ align:start position:0%
+forget the low order term
+terms so I get X log X + 1 -
+
+ align:start position:0%
+terms so I get X log X + 1 -
+ 
+
+ align:start position:0%
+terms so I get X log X + 1 -
+x this is the only term that survives X
+
+ align:start position:0%
+x this is the only term that survives X
+ 
+
+ align:start position:0%
+x this is the only term that survives X
+log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and that's
+
+ align:start position:0%
+X and that's
+ 
+
+ align:start position:0%
+X and that's
+right T of n is fact Tilda n log n so in
+
+ align:start position:0%
+right T of n is fact Tilda n log n so in
+ 
+
+ align:start position:0%
+right T of n is fact Tilda n log n so in
+fact it's Theta n log
+
+ align:start position:0%
+fact it's Theta n log
+ 
+
+ align:start position:0%
+fact it's Theta n log
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay now in this case going through the
+
+ align:start position:0%
+okay now in this case going through the
+ 
+
+ align:start position:0%
+okay now in this case going through the
+integral and all that maybe that was
+
+ align:start position:0%
+integral and all that maybe that was
+ 
+
+ align:start position:0%
+integral and all that maybe that was
+harder than just guessing and verifying
+
+ align:start position:0%
+harder than just guessing and verifying
+ 
+
+ align:start position:0%
+harder than just guessing and verifying
+you know and and by the way guess and
+
+ align:start position:0%
+you know and and by the way guess and
+ 
+
+ align:start position:0%
+you know and and by the way guess and
+verify got it really the exact
+
+ align:start position:0%
+verify got it really the exact
+ 
+
+ align:start position:0%
+verify got it really the exact
+answer um the nice thing
+
+ align:start position:0%
+answer um the nice thing
+ 
+
+ align:start position:0%
+answer um the nice thing
+is this works for the nasty guys
+
+ align:start position:0%
+is this works for the nasty guys
+ 
+
+ align:start position:0%
+is this works for the nasty guys
+too in
+
+ align:start position:0%
+too in
+ 
+
+ align:start position:0%
+too in
+fact let's figure out the solution to
+
+ align:start position:0%
+fact let's figure out the solution to
+ 
+
+ align:start position:0%
+fact let's figure out the solution to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+thing which I guarantee you is a pain to
+
+ align:start position:0%
+thing which I guarantee you is a pain to
+ 
+
+ align:start position:0%
+thing which I guarantee you is a pain to
+do without this method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right the first thing to do is
+
+ align:start position:0%
+all right the first thing to do is
+ 
+
+ align:start position:0%
+all right the first thing to do is
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+P so to do that we need to find a p such
+
+ align:start position:0%
+P so to do that we need to find a p such
+ 
+
+ align:start position:0%
+P so to do that we need to find a p such
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+two * 12 the p + 8
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9th * 3/4 to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P equals 1 I got a find a p for which
+
+ align:start position:0%
+P equals 1 I got a find a p for which
+ 
+
+ align:start position:0%
+P equals 1 I got a find a p for which
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+true any guesses what P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Works P equals 1 not going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it P =
+
+ align:start position:0%
+it P =
+ 
+
+ align:start position:0%
+it P =
+2 let's try
+
+ align:start position:0%
+2 let's try
+ 
+
+ align:start position:0%
+2 let's try
+that I'd have 2 * a
+
+ align:start position:0%
+that I'd have 2 * a
+ 
+
+ align:start position:0%
+that I'd have 2 * a
+quarter Plus 8 9 * 916
+
+ align:start position:0%
+quarter Plus 8 9 * 916
+ 
+
+ align:start position:0%
+quarter Plus 8 9 * 916
+that looks pretty good I get a half plus
+
+ align:start position:0%
+that looks pretty good I get a half plus
+ 
+
+ align:start position:0%
+that looks pretty good I get a half plus
+a half equals
+
+ align:start position:0%
+a half equals
+ 
+
+ align:start position:0%
+a half equals
+1 so P equals 2
+
+ align:start position:0%
+1 so P equals 2
+ 
+
+ align:start position:0%
+1 so P equals 2
+works all
+
+ align:start position:0%
+works all
+ 
+
+ align:start position:0%
+works all
+right all right so let's do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+TX is Theta of X the p + x the P * the
+
+ align:start position:0%
+TX is Theta of X the p + x the P * the
+ 
+
+ align:start position:0%
+TX is Theta of X the p + x the P * the
+integral all right what is g of X in
+
+ align:start position:0%
+integral all right what is g of X in
+ 
+
+ align:start position:0%
+integral all right what is g of X in
+this thing
+
+ align:start position:0%
+this thing
+ 
+
+ align:start position:0%
+this thing
+X squar so the integral is 1 to x g of U
+
+ align:start position:0%
+X squar so the integral is 1 to x g of U
+ 
+
+ align:start position:0%
+X squar so the integral is 1 to x g of U
+is u^2 divided
+
+ align:start position:0%
+is u^2 divided
+ 
+
+ align:start position:0%
+is u^2 divided
+by U to the 1 +
+
+ align:start position:0%
+by U to the 1 +
+ 
+
+ align:start position:0%
+by U to the 1 +
+p u to the 1 + 2 is just U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubed all right this is Theta x^2 + x^2
+
+ align:start position:0%
+cubed all right this is Theta x^2 + x^2
+ 
+
+ align:start position:0%
+cubed all right this is Theta x^2 + x^2
+times well the integral of one over U is
+
+ align:start position:0%
+times well the integral of one over U is
+ 
+
+ align:start position:0%
+times well the integral of one over U is
+just log of U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's just log of
+
+ align:start position:0%
+and that's just log of
+ 
+
+ align:start position:0%
+and that's just log of
+x so the answer is x square Ln of X
+
+ align:start position:0%
+x so the answer is x square Ln of X
+ 
+
+ align:start position:0%
+x so the answer is x square Ln of X
+done so that's pretty good what these
+
+ align:start position:0%
+done so that's pretty good what these
+ 
+
+ align:start position:0%
+done so that's pretty good what these
+guys
+
+ align:start position:0%
+guys
+ 
+
+ align:start position:0%
+guys
+did in fact that
+
+ align:start position:0%
+did in fact that
+ 
+
+ align:start position:0%
+did in fact that
+is uh that is the correct
+
+ align:start position:0%
+is uh that is the correct
+ 
+
+ align:start position:0%
+is uh that is the correct
+answer all right so really easy to plug
+
+ align:start position:0%
+answer all right so really easy to plug
+ 
+
+ align:start position:0%
+answer all right so really easy to plug
+in any
+
+ align:start position:0%
+in any
+ 
+
+ align:start position:0%
+in any
+questions on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it doesn't give you the actual
+
+ align:start position:0%
+yeah it doesn't give you the actual
+ 
+
+ align:start position:0%
+yeah it doesn't give you the actual
+number it just gives you the ASM totic
+
+ align:start position:0%
+number it just gives you the ASM totic
+ 
+
+ align:start position:0%
+number it just gives you the ASM totic
+growth all you know is that the limit of
+
+ align:start position:0%
+growth all you know is that the limit of
+ 
+
+ align:start position:0%
+growth all you know is that the limit of
+TX over x^2 Ln of X is less than
+
+ align:start position:0%
+TX over x^2 Ln of X is less than
+ 
+
+ align:start position:0%
+TX over x^2 Ln of X is less than
+infinity and bigger than zero so it's
+
+ align:start position:0%
+infinity and bigger than zero so it's
+ 
+
+ align:start position:0%
+infinity and bigger than zero so it's
+growing as this you don't know if it's
+
+ align:start position:0%
+growing as this you don't know if it's
+ 
+
+ align:start position:0%
+growing as this you don't know if it's
+10 X2 l x or a million x s l x on the
+
+ align:start position:0%
+10 X2 l x or a million x s l x on the
+ 
+
+ align:start position:0%
+10 X2 l x or a million x s l x on the
+other hand for algorithms
+
+ align:start position:0%
+other hand for algorithms
+ 
+
+ align:start position:0%
+other hand for algorithms
+usually you're forgetting the constant
+
+ align:start position:0%
+usually you're forgetting the constant
+ 
+
+ align:start position:0%
+usually you're forgetting the constant
+factors anyway because they depend on
+
+ align:start position:0%
+factors anyway because they depend on
+ 
+
+ align:start position:0%
+factors anyway because they depend on
+things to do with the CPU you're using
+
+ align:start position:0%
+things to do with the CPU you're using
+ 
+
+ align:start position:0%
+things to do with the CPU you're using
+and stuff like that what you really care
+
+ align:start position:0%
+and stuff like that what you really care
+ 
+
+ align:start position:0%
+and stuff like that what you really care
+about often when you're studying
+
+ align:start position:0%
+about often when you're studying
+ 
+
+ align:start position:0%
+about often when you're studying
+algorithms is the ASM totic growth not
+
+ align:start position:0%
+algorithms is the ASM totic growth not
+ 
+
+ align:start position:0%
+algorithms is the ASM totic growth not
+the actual value
+
+ align:start position:0%
+the actual value
+ 
+
+ align:start position:0%
+the actual value
+yeah natural log is B log Bas e and then
+
+ align:start position:0%
+yeah natural log is B log Bas e and then
+ 
+
+ align:start position:0%
+yeah natural log is B log Bas e and then
+above I see using log which as base two
+
+ align:start position:0%
+above I see using log which as base two
+ 
+
+ align:start position:0%
+above I see using log which as base two
+doesn't matter it does up there because
+
+ align:start position:0%
+doesn't matter it does up there because
+ 
+
+ align:start position:0%
+doesn't matter it does up there because
+I've got a Tilda and in the Tilda the
+
+ align:start position:0%
+I've got a Tilda and in the Tilda the
+ 
+
+ align:start position:0%
+I've got a Tilda and in the Tilda the
+constant Factor matters it doesn't
+
+ align:start position:0%
+constant Factor matters it doesn't
+ 
+
+ align:start position:0%
+constant Factor matters it doesn't
+matter in here because log base 2 and
+
+ align:start position:0%
+matter in here because log base 2 and
+ 
+
+ align:start position:0%
+matter in here because log base 2 and
+log base e are within a constant Factor
+
+ align:start position:0%
+log base e are within a constant Factor
+ 
+
+ align:start position:0%
+log base e are within a constant Factor
+namely log of two L of two is the
+
+ align:start position:0%
+namely log of two L of two is the
+ 
+
+ align:start position:0%
+namely log of two L of two is the
+constant Factor so logs don't matter
+
+ align:start position:0%
+constant Factor so logs don't matter
+ 
+
+ align:start position:0%
+constant Factor so logs don't matter
+what the base is once you're inside a
+
+ align:start position:0%
+what the base is once you're inside a
+ 
+
+ align:start position:0%
+what the base is once you're inside a
+Theta or an o or that kind of thing in a
+
+ align:start position:0%
+Theta or an o or that kind of thing in a
+ 
+
+ align:start position:0%
+Theta or an o or that kind of thing in a
+Tilda they matter because the constant
+
+ align:start position:0%
+Tilda they matter because the constant
+ 
+
+ align:start position:0%
+Tilda they matter because the constant
+Factor matters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah because x s is small compared
+
+ align:start position:0%
+yeah yeah because x s is small compared
+ 
+
+ align:start position:0%
+yeah yeah because x s is small compared
+to X2 Ln of X because it's all by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theeta no uh you could put all sorts of
+
+ align:start position:0%
+theeta no uh you could put all sorts of
+ 
+
+ align:start position:0%
+theeta no uh you could put all sorts of
+other stuff in here and it doesn't
+
+ align:start position:0%
+other stuff in here and it doesn't
+ 
+
+ align:start position:0%
+other stuff in here and it doesn't
+matter because it still equals Theta of
+
+ align:start position:0%
+matter because it still equals Theta of
+ 
+
+ align:start position:0%
+matter because it still equals Theta of
+x^2 Ln of X there's no hidden meanings
+
+ align:start position:0%
+x^2 Ln of X there's no hidden meanings
+ 
+
+ align:start position:0%
+x^2 Ln of X there's no hidden meanings
+by having extra stuff in here okay
+
+ align:start position:0%
+by having extra stuff in here okay
+ 
+
+ align:start position:0%
+by having extra stuff in here okay
+that's that's important in this case
+
+ align:start position:0%
+that's that's important in this case
+ 
+
+ align:start position:0%
+that's that's important in this case
+when you put more stuff in the Theta
+
+ align:start position:0%
+when you put more stuff in the Theta
+ 
+
+ align:start position:0%
+when you put more stuff in the Theta
+doesn't mean a
+
+ align:start position:0%
+doesn't mean a
+ 
+
+ align:start position:0%
+doesn't mean a
+thing any other questions yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah good question um well let's see it
+
+ align:start position:0%
+ah good question um well let's see it
+ 
+
+ align:start position:0%
+ah good question um well let's see it
+goes back to over here if I
+
+ align:start position:0%
+goes back to over here if I
+ 
+
+ align:start position:0%
+goes back to over here if I
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+p if I make see the B's are between zero
+
+ align:start position:0%
+p if I make see the B's are between zero
+ 
+
+ align:start position:0%
+p if I make see the B's are between zero
+and one by making P big enough I drive
+
+ align:start position:0%
+and one by making P big enough I drive
+ 
+
+ align:start position:0%
+and one by making P big enough I drive
+the value down by making P be larger
+
+ align:start position:0%
+the value down by making P be larger
+ 
+
+ align:start position:0%
+the value down by making P be larger
+than negative I draw the value up so
+
+ align:start position:0%
+than negative I draw the value up so
+ 
+
+ align:start position:0%
+than negative I draw the value up so
+there's some value of P but that's a
+
+ align:start position:0%
+there's some value of P but that's a
+ 
+
+ align:start position:0%
+there's some value of P but that's a
+good question let's see what happens
+
+ align:start position:0%
+good question let's see what happens
+ 
+
+ align:start position:0%
+good question let's see what happens
+when p is not so nice because the
+
+ align:start position:0%
+when p is not so nice because the
+ 
+
+ align:start position:0%
+when p is not so nice because the
+examples I gave you in one case P was
+
+ align:start position:0%
+examples I gave you in one case P was
+ 
+
+ align:start position:0%
+examples I gave you in one case P was
+one and one p was two sort of nice let's
+
+ align:start position:0%
+one and one p was two sort of nice let's
+ 
+
+ align:start position:0%
+one and one p was two sort of nice let's
+look at a bad case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there let's look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence 3 T of X over 3 plus 4 T of X
+
+ align:start position:0%
+recurrence 3 T of X over 3 plus 4 T of X
+ 
+
+ align:start position:0%
+recurrence 3 T of X over 3 plus 4 T of X
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+4 plus
+
+ align:start position:0%
+4 plus
+ 
+
+ align:start position:0%
+4 plus
+x^2 all right so that's the recurrence
+
+ align:start position:0%
+x^2 all right so that's the recurrence
+ 
+
+ align:start position:0%
+x^2 all right so that's the recurrence
+and first step is to compute p and this
+
+ align:start position:0%
+and first step is to compute p and this
+ 
+
+ align:start position:0%
+and first step is to compute p and this
+time it's not going to be
+
+ align:start position:0%
+time it's not going to be
+ 
+
+ align:start position:0%
+time it's not going to be
+nice all right so I need to find a p
+
+ align:start position:0%
+nice all right so I need to find a p
+ 
+
+ align:start position:0%
+nice all right so I need to find a p
+such that 3 * a thir the P plus 4 * a 4
+
+ align:start position:0%
+such that 3 * a thir the P plus 4 * a 4
+ 
+
+ align:start position:0%
+such that 3 * a thir the P plus 4 * a 4
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+P equal
+
+ align:start position:0%
+P equal
+ 
+
+ align:start position:0%
+P equal
+1 and you might say okay let's try P
+
+ align:start position:0%
+1 and you might say okay let's try P
+ 
+
+ align:start position:0%
+1 and you might say okay let's try P
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 I get 1 + 1 is two that's too
+
+ align:start position:0%
+1 I get 1 + 1 is two that's too
+ 
+
+ align:start position:0%
+1 I get 1 + 1 is two that's too
+big so which way do I have to go on P do
+
+ align:start position:0%
+big so which way do I have to go on P do
+ 
+
+ align:start position:0%
+big so which way do I have to go on P do
+I need a bigger P or a smaller
+
+ align:start position:0%
+I need a bigger P or a smaller
+ 
+
+ align:start position:0%
+I need a bigger P or a smaller
+P bigger because I gotta get from two
+
+ align:start position:0%
+P bigger because I gotta get from two
+ 
+
+ align:start position:0%
+P bigger because I gotta get from two
+down to one so I gotta I know that P is
+
+ align:start position:0%
+down to one so I gotta I know that P is
+ 
+
+ align:start position:0%
+down to one so I gotta I know that P is
+bigger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all right so the next thing to try
+
+ align:start position:0%
+one all right so the next thing to try
+ 
+
+ align:start position:0%
+one all right so the next thing to try
+would be hoping the world is nice P
+
+ align:start position:0%
+would be hoping the world is nice P
+ 
+
+ align:start position:0%
+would be hoping the world is nice P
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+2 fact maybe I'll do that over here
+
+ align:start position:0%
+2 fact maybe I'll do that over here
+ 
+
+ align:start position:0%
+2 fact maybe I'll do that over here
+let's try P equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so I get 3 * a 9th + 4 * the
+
+ align:start position:0%
+2 so I get 3 * a 9th + 4 * the
+ 
+
+ align:start position:0%
+2 so I get 3 * a 9th + 4 * the
+16th and that equals A3 + a
+
+ align:start position:0%
+16th and that equals A3 + a
+ 
+
+ align:start position:0%
+16th and that equals A3 + a
+4th that's less than
+
+ align:start position:0%
+4th that's less than
+ 
+
+ align:start position:0%
+4th that's less than
+one that didn't work what do I have to
+
+ align:start position:0%
+one that didn't work what do I have to
+ 
+
+ align:start position:0%
+one that didn't work what do I have to
+do now with p is it bigger than two or
+
+ align:start position:0%
+do now with p is it bigger than two or
+ 
+
+ align:start position:0%
+do now with p is it bigger than two or
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+two less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two Ah that's sort of a pain P is
+
+ align:start position:0%
+two Ah that's sort of a pain P is
+ 
+
+ align:start position:0%
+two Ah that's sort of a pain P is
+between one and two so it's not an
+
+ align:start position:0%
+between one and two so it's not an
+ 
+
+ align:start position:0%
+between one and two so it's not an
+integer now you can sort of do divide
+
+ align:start position:0%
+integer now you can sort of do divide
+ 
+
+ align:start position:0%
+integer now you can sort of do divide
+and conquer here next I try p is three
+
+ align:start position:0%
+and conquer here next I try p is three
+ 
+
+ align:start position:0%
+and conquer here next I try p is three
+Hales get my calculator out and see
+
+ align:start position:0%
+Hales get my calculator out and see
+ 
+
+ align:start position:0%
+Hales get my calculator out and see
+which way it goes and you could sort of
+
+ align:start position:0%
+which way it goes and you could sort of
+ 
+
+ align:start position:0%
+which way it goes and you could sort of
+Home in on it but there's something
+
+ align:start position:0%
+Home in on it but there's something
+ 
+
+ align:start position:0%
+Home in on it but there's something
+really nice that happens with
+
+ align:start position:0%
+really nice that happens with
+ 
+
+ align:start position:0%
+really nice that happens with
+acrobat and that is if you ever conclude
+
+ align:start position:0%
+acrobat and that is if you ever conclude
+ 
+
+ align:start position:0%
+acrobat and that is if you ever conclude
+that P is less than your exponent here
+
+ align:start position:0%
+that P is less than your exponent here
+ 
+
+ align:start position:0%
+that P is less than your exponent here
+you don't even have to compute it
+
+ align:start position:0%
+you don't even have to compute it
+ 
+
+ align:start position:0%
+you don't even have to compute it
+all right let's see why Let's do an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example this will happen a
+
+ align:start position:0%
+example this will happen a
+ 
+
+ align:start position:0%
+example this will happen a
+lot there's some P but it's just going
+
+ align:start position:0%
+lot there's some P but it's just going
+ 
+
+ align:start position:0%
+lot there's some P but it's just going
+to be a pain to evaluate but let's see
+
+ align:start position:0%
+to be a pain to evaluate but let's see
+ 
+
+ align:start position:0%
+to be a pain to evaluate but let's see
+what happens
+
+ align:start position:0%
+what happens
+ 
+
+ align:start position:0%
+what happens
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so I'm just going to try to solve
+
+ align:start position:0%
+okay so I'm just going to try to solve
+ 
+
+ align:start position:0%
+okay so I'm just going to try to solve
+it write the solution anyway T ofx
+
+ align:start position:0%
+it write the solution anyway T ofx
+ 
+
+ align:start position:0%
+it write the solution anyway T ofx
+equals Theta X the P plus X the P
+
+ align:start position:0%
+equals Theta X the P plus X the P
+ 
+
+ align:start position:0%
+equals Theta X the P plus X the P
+integral 1 tox what's G of
+
+ align:start position:0%
+integral 1 tox what's G of
+ 
+
+ align:start position:0%
+integral 1 tox what's G of
+X X2 so that's
+
+ align:start position:0%
+X X2 so that's
+ 
+
+ align:start position:0%
+X X2 so that's
+u^2 over u 1 + P I still don't know what
+
+ align:start position:0%
+u^2 over u 1 + P I still don't know what
+ 
+
+ align:start position:0%
+u^2 over u 1 + P I still don't know what
+it is but going to give it a try
+
+ align:start position:0%
+it is but going to give it a try
+ 
+
+ align:start position:0%
+it is but going to give it a try
+here that's Theta x to the P plus X the
+
+ align:start position:0%
+here that's Theta x to the P plus X the
+ 
+
+ align:start position:0%
+here that's Theta x to the P plus X the
+P well this is now the integral of U the
+
+ align:start position:0%
+P well this is now the integral of U the
+ 
+
+ align:start position:0%
+P well this is now the integral of U the
+1 minus P
+
+ align:start position:0%
+1 minus P
+ 
+
+ align:start position:0%
+1 minus P
+du and P is bigger than one I know that
+
+ align:start position:0%
+du and P is bigger than one I know that
+ 
+
+ align:start position:0%
+du and P is bigger than one I know that
+this is Theta x p + x
+
+ align:start position:0%
+this is Theta x p + x
+ 
+
+ align:start position:0%
+this is Theta x p + x
+p well the integral here is x^ the 2
+
+ align:start position:0%
+p well the integral here is x^ the 2
+ 
+
+ align:start position:0%
+p well the integral here is x^ the 2
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+P up to constants I don't even care
+
+ align:start position:0%
+P up to constants I don't even care
+ 
+
+ align:start position:0%
+P up to constants I don't even care
+about dividing by 2 minus P because I
+
+ align:start position:0%
+about dividing by 2 minus P because I
+ 
+
+ align:start position:0%
+about dividing by 2 minus P because I
+got big Theta let's put that P up
+
+ align:start position:0%
+got big Theta let's put that P up
+ 
+
+ align:start position:0%
+got big Theta let's put that P up
+here okay well this equals Theta X the
+
+ align:start position:0%
+here okay well this equals Theta X the
+ 
+
+ align:start position:0%
+here okay well this equals Theta X the
+p+ oh it canceled there x^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what's the answer going to
+
+ align:start position:0%
+and what's the answer going to
+ 
+
+ align:start position:0%
+and what's the answer going to
+be X2 because p is less than two so this
+
+ align:start position:0%
+be X2 because p is less than two so this
+ 
+
+ align:start position:0%
+be X2 because p is less than two so this
+is a small order
+
+ align:start position:0%
+is a small order
+ 
+
+ align:start position:0%
+is a small order
+term so I didn't even know what P was
+
+ align:start position:0%
+term so I didn't even know what P was
+ 
+
+ align:start position:0%
+term so I didn't even know what P was
+just that it was less than two and I got
+
+ align:start position:0%
+just that it was less than two and I got
+ 
+
+ align:start position:0%
+just that it was less than two and I got
+the answer and what do you know the
+
+ align:start position:0%
+the answer and what do you know the
+ 
+
+ align:start position:0%
+the answer and what do you know the
+answer was just this thing that's sort
+
+ align:start position:0%
+answer was just this thing that's sort
+ 
+
+ align:start position:0%
+answer was just this thing that's sort
+of nice and simple and in fact that's a
+
+ align:start position:0%
+of nice and simple and in fact that's a
+ 
+
+ align:start position:0%
+of nice and simple and in fact that's a
+theorem right which will state in
+
+ align:start position:0%
+theorem right which will state in
+ 
+
+ align:start position:0%
+theorem right which will state in
+general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if G of x equals Theta x to the T for
+
+ align:start position:0%
+if G of x equals Theta x to the T for
+ 
+
+ align:start position:0%
+if G of x equals Theta x to the T for
+some T bigger than equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and when you plug that value in and
+
+ align:start position:0%
+zero and when you plug that value in and
+ 
+
+ align:start position:0%
+zero and when you plug that value in and
+take your
+
+ align:start position:0%
+take your
+ 
+
+ align:start position:0%
+take your
+sum Computing trying to compute the P
+
+ align:start position:0%
+sum Computing trying to compute the P
+ 
+
+ align:start position:0%
+sum Computing trying to compute the P
+value so I take AI * B to the T and that
+
+ align:start position:0%
+value so I take AI * B to the T and that
+ 
+
+ align:start position:0%
+value so I take AI * B to the T and that
+comes out to be less than one like it
+
+ align:start position:0%
+comes out to be less than one like it
+ 
+
+ align:start position:0%
+comes out to be less than one like it
+did here when I plugged
+
+ align:start position:0%
+did here when I plugged
+ 
+
+ align:start position:0%
+did here when I plugged
+in I plugged in P equal 2 and I computed
+
+ align:start position:0%
+in I plugged in P equal 2 and I computed
+ 
+
+ align:start position:0%
+in I plugged in P equal 2 and I computed
+it and I was less than one right but if
+
+ align:start position:0%
+it and I was less than one right but if
+ 
+
+ align:start position:0%
+it and I was less than one right but if
+that happens in
+
+ align:start position:0%
+that happens in
+ 
+
+ align:start position:0%
+that happens in
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+then the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is Theta G of
+
+ align:start position:0%
+is Theta G of
+ 
+
+ align:start position:0%
+is Theta G of
+X plain and simple it just turns out to
+
+ align:start position:0%
+X plain and simple it just turns out to
+ 
+
+ align:start position:0%
+X plain and simple it just turns out to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+the the G of X term up to constant
+
+ align:start position:0%
+the the G of X term up to constant
+ 
+
+ align:start position:0%
+the the G of X term up to constant
+factors so you don't even have to
+
+ align:start position:0%
+factors so you don't even have to
+ 
+
+ align:start position:0%
+factors so you don't even have to
+compute it just do that check on the
+
+ align:start position:0%
+compute it just do that check on the
+ 
+
+ align:start position:0%
+compute it just do that check on the
+power here to see is it smaller than
+
+ align:start position:0%
+power here to see is it smaller than
+ 
+
+ align:start position:0%
+power here to see is it smaller than
+that I won't prove that there actually
+
+ align:start position:0%
+that I won't prove that there actually
+ 
+
+ align:start position:0%
+that I won't prove that there actually
+not hard to do it's the proof is pretty
+
+ align:start position:0%
+not hard to do it's the proof is pretty
+ 
+
+ align:start position:0%
+not hard to do it's the proof is pretty
+much what I did with this example so
+
+ align:start position:0%
+much what I did with this example so
+ 
+
+ align:start position:0%
+much what I did with this example so
+it's not too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard okay any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions I want to show you one more
+
+ align:start position:0%
+questions I want to show you one more
+ 
+
+ align:start position:0%
+questions I want to show you one more
+thing but just make sure that's okay and
+
+ align:start position:0%
+thing but just make sure that's okay and
+ 
+
+ align:start position:0%
+thing but just make sure that's okay and
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+something never to
+
+ align:start position:0%
+something never to
+ 
+
+ align:start position:0%
+something never to
+do um with the ASM totic notation like
+
+ align:start position:0%
+do um with the ASM totic notation like
+ 
+
+ align:start position:0%
+do um with the ASM totic notation like
+we talked about last
+
+ align:start position:0%
+we talked about last
+ 
+
+ align:start position:0%
+we talked about last
+time when you're using acrobot and when
+
+ align:start position:0%
+time when you're using acrobot and when
+ 
+
+ align:start position:0%
+time when you're using acrobot and when
+you're doing occurrences with algorithms
+
+ align:start position:0%
+you're doing occurrences with algorithms
+ 
+
+ align:start position:0%
+you're doing occurrences with algorithms
+you always are using ASM totic
+
+ align:start position:0%
+you always are using ASM totic
+ 
+
+ align:start position:0%
+you always are using ASM totic
+notation right your answer is Theta of
+
+ align:start position:0%
+notation right your answer is Theta of
+ 
+
+ align:start position:0%
+notation right your answer is Theta of
+something and in fact what'll start
+
+ align:start position:0%
+something and in fact what'll start
+ 
+
+ align:start position:0%
+something and in fact what'll start
+happening as you do this
+
+ align:start position:0%
+happening as you do this
+ 
+
+ align:start position:0%
+happening as you do this
+stuff because the constant factors don't
+
+ align:start position:0%
+stuff because the constant factors don't
+ 
+
+ align:start position:0%
+stuff because the constant factors don't
+matter they just because you're wiping
+
+ align:start position:0%
+matter they just because you're wiping
+ 
+
+ align:start position:0%
+matter they just because you're wiping
+them out in the Theta notation
+
+ align:start position:0%
+them out in the Theta notation
+ 
+
+ align:start position:0%
+them out in the Theta notation
+what you'll see is things like this your
+
+ align:start position:0%
+what you'll see is things like this your
+ 
+
+ align:start position:0%
+what you'll see is things like this your
+recurrence will be set up to be T of n
+
+ align:start position:0%
+recurrence will be set up to be T of n
+ 
+
+ align:start position:0%
+recurrence will be set up to be T of n
+is 2 T of n / 2 plus o of n or plus
+
+ align:start position:0%
+is 2 T of n / 2 plus o of n or plus
+ 
+
+ align:start position:0%
+is 2 T of n / 2 plus o of n or plus
+Theta of
+
+ align:start position:0%
+Theta of
+ 
+
+ align:start position:0%
+Theta of
+N and then you'll
+
+ align:start position:0%
+N and then you'll
+ 
+
+ align:start position:0%
+N and then you'll
+conclude that t of n is Theta of n log
+
+ align:start position:0%
+conclude that t of n is Theta of n log
+ 
+
+ align:start position:0%
+conclude that t of n is Theta of n log
+n using acrobot or whatever method you
+
+ align:start position:0%
+n using acrobot or whatever method you
+ 
+
+ align:start position:0%
+n using acrobot or whatever method you
+want all right so this because it
+
+ align:start position:0%
+want all right so this because it
+ 
+
+ align:start position:0%
+want all right so this because it
+doesn't really matter what the constant
+
+ align:start position:0%
+doesn't really matter what the constant
+ 
+
+ align:start position:0%
+doesn't really matter what the constant
+is on
+
+ align:start position:0%
+is on
+ 
+
+ align:start position:0%
+is on
+G because the answer the constants
+
+ align:start position:0%
+G because the answer the constants
+ 
+
+ align:start position:0%
+G because the answer the constants
+disapp
+
+ align:start position:0%
+disapp
+ 
+
+ align:start position:0%
+disapp
+appear doesn't matter and so people stop
+
+ align:start position:0%
+appear doesn't matter and so people stop
+ 
+
+ align:start position:0%
+appear doesn't matter and so people stop
+worrying about it early
+
+ align:start position:0%
+worrying about it early
+ 
+
+ align:start position:0%
+worrying about it early
+on all right now here's the bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example let me show you a false proof
+
+ align:start position:0%
+example let me show you a false proof
+ 
+
+ align:start position:0%
+example let me show you a false proof
+like last
+
+ align:start position:0%
+like last
+ 
+
+ align:start position:0%
+like last
+time and this time I think it'll be
+
+ align:start position:0%
+time and this time I think it'll be
+ 
+
+ align:start position:0%
+time and this time I think it'll be
+pretty easy to spot the flaw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not if T of n = 2 T of n / 2 + n minus1
+
+ align:start position:0%
+not if T of n = 2 T of n / 2 + n minus1
+ 
+
+ align:start position:0%
+not if T of n = 2 T of n / 2 + n minus1
+this is the recurrence we had for merge
+
+ align:start position:0%
+this is the recurrence we had for merge
+ 
+
+ align:start position:0%
+this is the recurrence we had for merge
+sort and T of 1 equals
+
+ align:start position:0%
+sort and T of 1 equals
+ 
+
+ align:start position:0%
+sort and T of 1 equals
+zero then I'm going to prove
+
+ align:start position:0%
+zero then I'm going to prove
+ 
+
+ align:start position:0%
+zero then I'm going to prove
+that t of n is O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n now that can't be
+
+ align:start position:0%
+n now that can't be
+ 
+
+ align:start position:0%
+n now that can't be
+right right because we've proved it's
+
+ align:start position:0%
+right right because we've proved it's
+ 
+
+ align:start position:0%
+right right because we've proved it's
+Theta of n log n til of n log n and that
+
+ align:start position:0%
+Theta of n log n til of n log n and that
+ 
+
+ align:start position:0%
+Theta of n log n til of n log n and that
+is not o of n right and log n grows
+
+ align:start position:0%
+is not o of n right and log n grows
+ 
+
+ align:start position:0%
+is not o of n right and log n grows
+faster than
+
+ align:start position:0%
+faster than
+ 
+
+ align:start position:0%
+faster than
+n all right but let's see the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof by strong induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the induction
+
+ align:start position:0%
+the induction
+ 
+
+ align:start position:0%
+the induction
+hypothesis is going to be what we're
+
+ align:start position:0%
+hypothesis is going to be what we're
+ 
+
+ align:start position:0%
+hypothesis is going to be what we're
+trying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay base
+
+ align:start position:0%
+okay base
+ 
+
+ align:start position:0%
+okay base
+case Nal 1 T of 1 is zero zero is surely
+
+ align:start position:0%
+case Nal 1 T of 1 is zero zero is surely
+ 
+
+ align:start position:0%
+case Nal 1 T of 1 is zero zero is surely
+o of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one the induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step all right we're going to assume P1
+
+ align:start position:0%
+step all right we're going to assume P1
+ 
+
+ align:start position:0%
+step all right we're going to assume P1
+P2 P3 up to PN minus one to prove PN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and let's look at P of n so I
+
+ align:start position:0%
+all right and let's look at P of n so I
+ 
+
+ align:start position:0%
+all right and let's look at P of n so I
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+TN is 2 T of n /
+
+ align:start position:0%
+TN is 2 T of n /
+ 
+
+ align:start position:0%
+TN is 2 T of n /
+2 plus
+
+ align:start position:0%
+2 plus
+ 
+
+ align:start position:0%
+2 plus
+nus1 induction hypothesis on N /2 says
+
+ align:start position:0%
+nus1 induction hypothesis on N /2 says
+ 
+
+ align:start position:0%
+nus1 induction hypothesis on N /2 says
+this is 2 * o of n
+
+ align:start position:0%
+this is 2 * o of n
+ 
+
+ align:start position:0%
+this is 2 * o of n
+/2 plus n minus
+
+ align:start position:0%
+/2 plus n minus
+ 
+
+ align:start position:0%
+/2 plus n minus
+one twice o of n over two is O of n plus
+
+ align:start position:0%
+one twice o of n over two is O of n plus
+ 
+
+ align:start position:0%
+one twice o of n over two is O of n plus
+n is O of n this is O of N and I'm
+
+ align:start position:0%
+n is O of n this is O of N and I'm
+ 
+
+ align:start position:0%
+n is O of n this is O of N and I'm
+done I just proved the of n is O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n all right what's the bad step what's
+
+ align:start position:0%
+n all right what's the bad step what's
+ 
+
+ align:start position:0%
+n all right what's the bad step what's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+bug see the bug what is
+
+ align:start position:0%
+bug see the bug what is
+ 
+
+ align:start position:0%
+bug see the bug what is
+it induction hypothesis what's wrong
+
+ align:start position:0%
+it induction hypothesis what's wrong
+ 
+
+ align:start position:0%
+it induction hypothesis what's wrong
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that right the N from the predicate
+
+ align:start position:0%
+that right the N from the predicate
+ 
+
+ align:start position:0%
+that right the N from the predicate
+cannot be in the O of n right because
+
+ align:start position:0%
+cannot be in the O of n right because
+ 
+
+ align:start position:0%
+cannot be in the O of n right because
+remember o of N means this statement
+
+ align:start position:0%
+remember o of N means this statement
+ 
+
+ align:start position:0%
+remember o of N means this statement
+here by it itself means the limit as n
+
+ align:start position:0%
+here by it itself means the limit as n
+ 
+
+ align:start position:0%
+here by it itself means the limit as n
+goes to Infinity of T of n/ n is less
+
+ align:start position:0%
+goes to Infinity of T of n/ n is less
+ 
+
+ align:start position:0%
+goes to Infinity of T of n/ n is less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+infinity okay but the limit this makes
+
+ align:start position:0%
+infinity okay but the limit this makes
+ 
+
+ align:start position:0%
+infinity okay but the limit this makes
+no sense if I specified n in a
+
+ align:start position:0%
+no sense if I specified n in a
+ 
+
+ align:start position:0%
+no sense if I specified n in a
+predicate so what's the rule same rule
+
+ align:start position:0%
+predicate so what's the rule same rule
+ 
+
+ align:start position:0%
+predicate so what's the rule same rule
+as last time same bug what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule never do ASM totic notation and
+
+ align:start position:0%
+rule never do ASM totic notation and
+ 
+
+ align:start position:0%
+rule never do ASM totic notation and
+induction hypothesis never mix Big O and
+
+ align:start position:0%
+induction hypothesis never mix Big O and
+ 
+
+ align:start position:0%
+induction hypothesis never mix Big O and
+a predicate never ever it looks so nice
+
+ align:start position:0%
+a predicate never ever it looks so nice
+ 
+
+ align:start position:0%
+a predicate never ever it looks so nice
+to do but it is so wrong it just makes
+
+ align:start position:0%
+to do but it is so wrong it just makes
+ 
+
+ align:start position:0%
+to do but it is so wrong it just makes
+nonsense all right very good so um
+
+ align:start position:0%
+nonsense all right very good so um
+ 
+
+ align:start position:0%
+nonsense all right very good so um
+remember ice cream tonight recitation
+
+ align:start position:0%
+remember ice cream tonight recitation
+ 
+
+ align:start position:0%
+remember ice cream tonight recitation
+optional tomorrow but study session is
+
+ align:start position:0%
+optional tomorrow but study session is
+ 
+
+ align:start position:0%
+optional tomorrow but study session is
+there
\ No newline at end of file
diff --git a/LGm2fvo-M9g.txt b/LGm2fvo-M9g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..348712fe9417447678f970131ef66f9a0a984a55
--- /dev/null
+++ b/LGm2fvo-M9g.txt
@@ -0,0 +1,1043 @@
+align:start position:0%
+ 
+hello and welcome back to 8701
+
+ align:start position:0%
+hello and welcome back to 8701
+ 
+
+ align:start position:0%
+hello and welcome back to 8701
+um in this class we'll talk about spin
+
+ align:start position:0%
+um in this class we'll talk about spin
+ 
+
+ align:start position:0%
+um in this class we'll talk about spin
+um if you remember the discussion on
+
+ align:start position:0%
+um if you remember the discussion on
+ 
+
+ align:start position:0%
+um if you remember the discussion on
+relativistic kinematics we had
+
+ align:start position:0%
+relativistic kinematics we had
+ 
+
+ align:start position:0%
+relativistic kinematics we had
+last week you notice that
+
+ align:start position:0%
+last week you notice that
+ 
+
+ align:start position:0%
+last week you notice that
+i discussed a decay
+
+ align:start position:0%
+i discussed a decay
+ 
+
+ align:start position:0%
+i discussed a decay
+of a pion say a neutral ion
+
+ align:start position:0%
+of a pion say a neutral ion
+ 
+
+ align:start position:0%
+of a pion say a neutral ion
+into an electron and a positron and an
+
+ align:start position:0%
+into an electron and a positron and an
+ 
+
+ align:start position:0%
+into an electron and a positron and an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+um and we were able to calculate the
+
+ align:start position:0%
+um and we were able to calculate the
+ 
+
+ align:start position:0%
+um and we were able to calculate the
+velocity of those two particles the
+
+ align:start position:0%
+velocity of those two particles the
+ 
+
+ align:start position:0%
+velocity of those two particles the
+electron and the positron
+
+ align:start position:0%
+electron and the positron
+ 
+
+ align:start position:0%
+electron and the positron
+quite easily by knowing the mass of the
+
+ align:start position:0%
+quite easily by knowing the mass of the
+ 
+
+ align:start position:0%
+quite easily by knowing the mass of the
+pion and the masses of the electron and
+
+ align:start position:0%
+pion and the masses of the electron and
+ 
+
+ align:start position:0%
+pion and the masses of the electron and
+the positron
+
+ align:start position:0%
+the positron
+ 
+
+ align:start position:0%
+the positron
+you put yourself into the rest frame of
+
+ align:start position:0%
+you put yourself into the rest frame of
+ 
+
+ align:start position:0%
+you put yourself into the rest frame of
+the ion and you can calculate those
+
+ align:start position:0%
+the ion and you can calculate those
+ 
+
+ align:start position:0%
+the ion and you can calculate those
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+i also told you that this decay is
+
+ align:start position:0%
+i also told you that this decay is
+ 
+
+ align:start position:0%
+i also told you that this decay is
+highly suppressed because of the spins
+
+ align:start position:0%
+highly suppressed because of the spins
+ 
+
+ align:start position:0%
+highly suppressed because of the spins
+of the particles involved the pion has a
+
+ align:start position:0%
+of the particles involved the pion has a
+ 
+
+ align:start position:0%
+of the particles involved the pion has a
+spin
+
+ align:start position:0%
+spin
+ 
+
+ align:start position:0%
+spin
+zero and the electron and the position
+
+ align:start position:0%
+zero and the electron and the position
+ 
+
+ align:start position:0%
+zero and the electron and the position
+have spin one half
+
+ align:start position:0%
+have spin one half
+ 
+
+ align:start position:0%
+have spin one half
+but it is not easily possible to align
+
+ align:start position:0%
+but it is not easily possible to align
+ 
+
+ align:start position:0%
+but it is not easily possible to align
+the electron in the positron such that
+
+ align:start position:0%
+the electron in the positron such that
+ 
+
+ align:start position:0%
+the electron in the positron such that
+the spins align
+
+ align:start position:0%
+the spins align
+ 
+
+ align:start position:0%
+the spins align
+to zero so therefore this decay is not
+
+ align:start position:0%
+to zero so therefore this decay is not
+ 
+
+ align:start position:0%
+to zero so therefore this decay is not
+easily possible let's dive a little bit
+
+ align:start position:0%
+easily possible let's dive a little bit
+ 
+
+ align:start position:0%
+easily possible let's dive a little bit
+into this
+
+ align:start position:0%
+into this
+ 
+
+ align:start position:0%
+into this
+um in quantum mechanics the spin of a
+
+ align:start position:0%
+um in quantum mechanics the spin of a
+ 
+
+ align:start position:0%
+um in quantum mechanics the spin of a
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+of a particle with a vector can is
+
+ align:start position:0%
+of a particle with a vector can is
+ 
+
+ align:start position:0%
+of a particle with a vector can is
+quantized in terms of its length and its
+
+ align:start position:0%
+quantized in terms of its length and its
+ 
+
+ align:start position:0%
+quantized in terms of its length and its
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+we calculate the length of this in
+
+ align:start position:0%
+we calculate the length of this in
+ 
+
+ align:start position:0%
+we calculate the length of this in
+vector s we find that the square root
+
+ align:start position:0%
+vector s we find that the square root
+ 
+
+ align:start position:0%
+vector s we find that the square root
+of s times s plus 1 in units of h bar
+
+ align:start position:0%
+of s times s plus 1 in units of h bar
+ 
+
+ align:start position:0%
+of s times s plus 1 in units of h bar
+the component then along the any axis
+
+ align:start position:0%
+the component then along the any axis
+ 
+
+ align:start position:0%
+the component then along the any axis
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+and in this case here the z-axis have
+
+ align:start position:0%
+and in this case here the z-axis have
+ 
+
+ align:start position:0%
+and in this case here the z-axis have
+eigenvalues
+
+ align:start position:0%
+eigenvalues
+ 
+
+ align:start position:0%
+eigenvalues
+and we you know they're listed here um
+
+ align:start position:0%
+and we you know they're listed here um
+ 
+
+ align:start position:0%
+and we you know they're listed here um
+and we find that there's two s plus one
+
+ align:start position:0%
+and we find that there's two s plus one
+ 
+
+ align:start position:0%
+and we find that there's two s plus one
+possible values
+
+ align:start position:0%
+possible values
+ 
+
+ align:start position:0%
+possible values
+so i'll pick here just arbitrarily the
+
+ align:start position:0%
+so i'll pick here just arbitrarily the
+ 
+
+ align:start position:0%
+so i'll pick here just arbitrarily the
+z-axis
+
+ align:start position:0%
+z-axis
+ 
+
+ align:start position:0%
+z-axis
+but the question is an obvious question
+
+ align:start position:0%
+but the question is an obvious question
+ 
+
+ align:start position:0%
+but the question is an obvious question
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which access is a sendable choice for
+
+ align:start position:0%
+which access is a sendable choice for
+ 
+
+ align:start position:0%
+which access is a sendable choice for
+this problem
+
+ align:start position:0%
+this problem
+ 
+
+ align:start position:0%
+this problem
+so i want you to actually stop here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and think about this what are sensible
+
+ align:start position:0%
+and think about this what are sensible
+ 
+
+ align:start position:0%
+and think about this what are sensible
+options
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know if you want to get an
+
+ align:start position:0%
+you know if you want to get an
+ 
+
+ align:start position:0%
+you know if you want to get an
+eigenvalue the physical states of
+
+ align:start position:0%
+eigenvalue the physical states of
+ 
+
+ align:start position:0%
+eigenvalue the physical states of
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+um which axes are the right ones to
+
+ align:start position:0%
+um which axes are the right ones to
+ 
+
+ align:start position:0%
+um which axes are the right ones to
+choose
+
+ align:start position:0%
+choose
+ 
+
+ align:start position:0%
+choose
+or sensible you know there's no right
+
+ align:start position:0%
+or sensible you know there's no right
+ 
+
+ align:start position:0%
+or sensible you know there's no right
+and one in this discussion
+
+ align:start position:0%
+and one in this discussion
+ 
+
+ align:start position:0%
+and one in this discussion
+let me motivate this um if you look at
+
+ align:start position:0%
+let me motivate this um if you look at
+ 
+
+ align:start position:0%
+let me motivate this um if you look at
+the orbital momentum of a particle
+
+ align:start position:0%
+the orbital momentum of a particle
+ 
+
+ align:start position:0%
+the orbital momentum of a particle
+that's given by
+
+ align:start position:0%
+that's given by
+ 
+
+ align:start position:0%
+that's given by
+r cross p where p is the momentum vector
+
+ align:start position:0%
+r cross p where p is the momentum vector
+ 
+
+ align:start position:0%
+r cross p where p is the momentum vector
+of the particle
+
+ align:start position:0%
+of the particle
+ 
+
+ align:start position:0%
+of the particle
+so now if you're looking at the total
+
+ align:start position:0%
+so now if you're looking at the total
+ 
+
+ align:start position:0%
+so now if you're looking at the total
+momentum we have to add
+
+ align:start position:0%
+momentum we have to add
+ 
+
+ align:start position:0%
+momentum we have to add
+the longer the angular momentum and the
+
+ align:start position:0%
+the longer the angular momentum and the
+ 
+
+ align:start position:0%
+the longer the angular momentum and the
+spin of the particle together
+
+ align:start position:0%
+spin of the particle together
+ 
+
+ align:start position:0%
+spin of the particle together
+so as shown in this picture here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see that the parallel component
+
+ align:start position:0%
+you see that the parallel component
+ 
+
+ align:start position:0%
+you see that the parallel component
+the component in parallel to the fly
+
+ align:start position:0%
+the component in parallel to the fly
+ 
+
+ align:start position:0%
+the component in parallel to the fly
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+is zero by definition because the cross
+
+ align:start position:0%
+is zero by definition because the cross
+ 
+
+ align:start position:0%
+is zero by definition because the cross
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+is defined the longer
+
+ align:start position:0%
+is defined the longer
+ 
+
+ align:start position:0%
+is defined the longer
+the angular momentum is defined as a
+
+ align:start position:0%
+the angular momentum is defined as a
+ 
+
+ align:start position:0%
+the angular momentum is defined as a
+cross product is momentum
+
+ align:start position:0%
+cross product is momentum
+ 
+
+ align:start position:0%
+cross product is momentum
+so this is a nice choice of coordinate
+
+ align:start position:0%
+so this is a nice choice of coordinate
+ 
+
+ align:start position:0%
+so this is a nice choice of coordinate
+system or of
+
+ align:start position:0%
+system or of
+ 
+
+ align:start position:0%
+system or of
+axis namely that the choice of the
+
+ align:start position:0%
+axis namely that the choice of the
+ 
+
+ align:start position:0%
+axis namely that the choice of the
+momentum of the particle
+
+ align:start position:0%
+momentum of the particle
+ 
+
+ align:start position:0%
+momentum of the particle
+so you find that the total momentum
+
+ align:start position:0%
+so you find that the total momentum
+ 
+
+ align:start position:0%
+so you find that the total momentum
+perpendicular
+
+ align:start position:0%
+perpendicular
+ 
+
+ align:start position:0%
+perpendicular
+is the spin of the particle
+
+ align:start position:0%
+is the spin of the particle
+ 
+
+ align:start position:0%
+is the spin of the particle
+perpendicular
+
+ align:start position:0%
+perpendicular
+ 
+
+ align:start position:0%
+perpendicular
+and the transverse component is the
+
+ align:start position:0%
+and the transverse component is the
+ 
+
+ align:start position:0%
+and the transverse component is the
+angular momentum the orbital energy
+
+ align:start position:0%
+angular momentum the orbital energy
+ 
+
+ align:start position:0%
+angular momentum the orbital energy
+momentum and the spin of the particle in
+
+ align:start position:0%
+momentum and the spin of the particle in
+ 
+
+ align:start position:0%
+momentum and the spin of the particle in
+transverse
+
+ align:start position:0%
+transverse
+ 
+
+ align:start position:0%
+transverse
+direction this then immediately gets us
+
+ align:start position:0%
+direction this then immediately gets us
+ 
+
+ align:start position:0%
+direction this then immediately gets us
+to a new definition
+
+ align:start position:0%
+to a new definition
+ 
+
+ align:start position:0%
+to a new definition
+that of helicity you can define the
+
+ align:start position:0%
+that of helicity you can define the
+ 
+
+ align:start position:0%
+that of helicity you can define the
+helicity of a particle
+
+ align:start position:0%
+helicity of a particle
+ 
+
+ align:start position:0%
+helicity of a particle
+as a spin of the particle dotted
+
+ align:start position:0%
+as a spin of the particle dotted
+ 
+
+ align:start position:0%
+as a spin of the particle dotted
+with the momentum of the particle and
+
+ align:start position:0%
+with the momentum of the particle and
+ 
+
+ align:start position:0%
+with the momentum of the particle and
+then normalized by the momentum
+
+ align:start position:0%
+then normalized by the momentum
+ 
+
+ align:start position:0%
+then normalized by the momentum
+so you basically um for a fermion
+
+ align:start position:0%
+so you basically um for a fermion
+ 
+
+ align:start position:0%
+so you basically um for a fermion
+which has a spin one half get on plus
+
+ align:start position:0%
+which has a spin one half get on plus
+ 
+
+ align:start position:0%
+which has a spin one half get on plus
+one half
+
+ align:start position:0%
+one half
+ 
+
+ align:start position:0%
+one half
+if the spin points in the momentum
+
+ align:start position:0%
+if the spin points in the momentum
+ 
+
+ align:start position:0%
+if the spin points in the momentum
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+and minus one half if it points in the
+
+ align:start position:0%
+and minus one half if it points in the
+ 
+
+ align:start position:0%
+and minus one half if it points in the
+opposite direction
+
+ align:start position:0%
+opposite direction
+ 
+
+ align:start position:0%
+opposite direction
+so now if you go back to our particle
+
+ align:start position:0%
+so now if you go back to our particle
+ 
+
+ align:start position:0%
+so now if you go back to our particle
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+of pi zero decaying into an
+
+ align:start position:0%
+of pi zero decaying into an
+ 
+
+ align:start position:0%
+of pi zero decaying into an
+electron and a positron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um spins a one half but you find that an
+
+ align:start position:0%
+um spins a one half but you find that an
+ 
+
+ align:start position:0%
+um spins a one half but you find that an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+is a left-handed particle so its
+
+ align:start position:0%
+is a left-handed particle so its
+ 
+
+ align:start position:0%
+is a left-handed particle so its
+helicity will point in this direction
+
+ align:start position:0%
+helicity will point in this direction
+ 
+
+ align:start position:0%
+helicity will point in this direction
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for the positron sorry for the positron
+
+ align:start position:0%
+for the positron sorry for the positron
+ 
+
+ align:start position:0%
+for the positron sorry for the positron
+it bounces interaction
+
+ align:start position:0%
+it bounces interaction
+ 
+
+ align:start position:0%
+it bounces interaction
+so the pion here is spin zero
+
+ align:start position:0%
+so the pion here is spin zero
+ 
+
+ align:start position:0%
+so the pion here is spin zero
+um and you know if you discuss this in
+
+ align:start position:0%
+um and you know if you discuss this in
+ 
+
+ align:start position:0%
+um and you know if you discuss this in
+the restroom of the pion
+
+ align:start position:0%
+the restroom of the pion
+ 
+
+ align:start position:0%
+the restroom of the pion
+the electron and the positon fly off in
+
+ align:start position:0%
+the electron and the positon fly off in
+ 
+
+ align:start position:0%
+the electron and the positon fly off in
+opposite direction
+
+ align:start position:0%
+opposite direction
+ 
+
+ align:start position:0%
+opposite direction
+and which means that the spin doesn't
+
+ align:start position:0%
+and which means that the spin doesn't
+ 
+
+ align:start position:0%
+and which means that the spin doesn't
+it's well it doesn't align to zero so
+
+ align:start position:0%
+it's well it doesn't align to zero so
+ 
+
+ align:start position:0%
+it's well it doesn't align to zero so
+that's why this is highly suppressed
+
+ align:start position:0%
+that's why this is highly suppressed
+ 
+
+ align:start position:0%
+that's why this is highly suppressed
+um it's not zero um because you can find
+
+ align:start position:0%
+um it's not zero um because you can find
+ 
+
+ align:start position:0%
+um it's not zero um because you can find
+you can put step into rest frame where
+
+ align:start position:0%
+you can put step into rest frame where
+ 
+
+ align:start position:0%
+you can put step into rest frame where
+you're just basically looking
+
+ align:start position:0%
+you're just basically looking
+ 
+
+ align:start position:0%
+you're just basically looking
+both particles from one side that was
+
+ align:start position:0%
+both particles from one side that was
+ 
+
+ align:start position:0%
+both particles from one side that was
+coming to you
+
+ align:start position:0%
+coming to you
+ 
+
+ align:start position:0%
+coming to you
+and in that case it's allowed but the
+
+ align:start position:0%
+and in that case it's allowed but the
+ 
+
+ align:start position:0%
+and in that case it's allowed but the
+spin configuration is highly surprising
\ No newline at end of file
diff --git a/LV3l9yqJwio.txt b/LV3l9yqJwio.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42b102b0dc92b76de375eedf433b27a3d568862e
--- /dev/null
+++ b/LV3l9yqJwio.txt
@@ -0,0 +1,10315 @@
+align:start position:0%
+ 
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+uh we left off last wednesday
+
+ align:start position:0%
+uh we left off last wednesday
+ 
+
+ align:start position:0%
+uh we left off last wednesday
+last week wednesday so it's been a while
+
+ align:start position:0%
+last week wednesday so it's been a while
+ 
+
+ align:start position:0%
+last week wednesday so it's been a while
+so i wanted just to pick up
+
+ align:start position:0%
+so i wanted just to pick up
+ 
+
+ align:start position:0%
+so i wanted just to pick up
+where we left off and then cover some
+
+ align:start position:0%
+where we left off and then cover some
+ 
+
+ align:start position:0%
+where we left off and then cover some
+new things
+
+ align:start position:0%
+new things
+ 
+
+ align:start position:0%
+new things
+um today um
+
+ align:start position:0%
+um today um
+ 
+
+ align:start position:0%
+um today um
+but where we left off was with this
+
+ align:start position:0%
+but where we left off was with this
+ 
+
+ align:start position:0%
+but where we left off was with this
+diagram okay
+
+ align:start position:0%
+diagram okay
+ 
+
+ align:start position:0%
+diagram okay
+and um and i kind of you know i kind of
+
+ align:start position:0%
+and um and i kind of you know i kind of
+ 
+
+ align:start position:0%
+and um and i kind of you know i kind of
+went through it and i went through it so
+
+ align:start position:0%
+went through it and i went through it so
+ 
+
+ align:start position:0%
+went through it and i went through it so
+quickly but i want to make sure you
+
+ align:start position:0%
+quickly but i want to make sure you
+ 
+
+ align:start position:0%
+quickly but i want to make sure you
+understand it
+
+ align:start position:0%
+understand it
+ 
+
+ align:start position:0%
+understand it
+very well because this is such an
+
+ align:start position:0%
+very well because this is such an
+ 
+
+ align:start position:0%
+very well because this is such an
+important kind of diagram
+
+ align:start position:0%
+important kind of diagram
+ 
+
+ align:start position:0%
+important kind of diagram
+and we'll see it again and you may see
+
+ align:start position:0%
+and we'll see it again and you may see
+ 
+
+ align:start position:0%
+and we'll see it again and you may see
+it again in other classes this is a
+
+ align:start position:0%
+it again in other classes this is a
+ 
+
+ align:start position:0%
+it again in other classes this is a
+diagram of attraction
+
+ align:start position:0%
+diagram of attraction
+ 
+
+ align:start position:0%
+diagram of attraction
+and repulsion coming together in a
+
+ align:start position:0%
+and repulsion coming together in a
+ 
+
+ align:start position:0%
+and repulsion coming together in a
+balance
+
+ align:start position:0%
+balance
+ 
+
+ align:start position:0%
+balance
+to form a bond so so you know last
+
+ align:start position:0%
+to form a bond so so you know last
+ 
+
+ align:start position:0%
+to form a bond so so you know last
+wednesday just to remind you we made our
+
+ align:start position:0%
+wednesday just to remind you we made our
+ 
+
+ align:start position:0%
+wednesday just to remind you we made our
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+bond right we made the ionic bond
+
+ align:start position:0%
+bond right we made the ionic bond
+ 
+
+ align:start position:0%
+bond right we made the ionic bond
+and and i showed you how that worked
+
+ align:start position:0%
+and and i showed you how that worked
+ 
+
+ align:start position:0%
+and and i showed you how that worked
+because in this case the attraction
+
+ align:start position:0%
+because in this case the attraction
+ 
+
+ align:start position:0%
+because in this case the attraction
+the force of attraction is the coulomb
+
+ align:start position:0%
+the force of attraction is the coulomb
+ 
+
+ align:start position:0%
+the force of attraction is the coulomb
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+right remember that goes as minus a
+
+ align:start position:0%
+right remember that goes as minus a
+ 
+
+ align:start position:0%
+right remember that goes as minus a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+times uh just write it down because why
+
+ align:start position:0%
+times uh just write it down because why
+ 
+
+ align:start position:0%
+times uh just write it down because why
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+you're using it in your goody bag right
+
+ align:start position:0%
+you're using it in your goody bag right
+ 
+
+ align:start position:0%
+you're using it in your goody bag right
+so the coulomb energy here
+
+ align:start position:0%
+so the coulomb energy here
+ 
+
+ align:start position:0%
+so the coulomb energy here
+goes as minus some constant
+
+ align:start position:0%
+goes as minus some constant
+ 
+
+ align:start position:0%
+goes as minus some constant
+times the charges the two charges
+
+ align:start position:0%
+times the charges the two charges
+ 
+
+ align:start position:0%
+times the charges the two charges
+divided by the distance between those
+
+ align:start position:0%
+divided by the distance between those
+ 
+
+ align:start position:0%
+divided by the distance between those
+charges
+
+ align:start position:0%
+charges
+ 
+
+ align:start position:0%
+charges
+that's an energy it's an energy of
+
+ align:start position:0%
+that's an energy it's an energy of
+ 
+
+ align:start position:0%
+that's an energy it's an energy of
+attraction but you know
+
+ align:start position:0%
+attraction but you know
+ 
+
+ align:start position:0%
+attraction but you know
+so here's the thing though right so if
+
+ align:start position:0%
+so here's the thing though right so if
+ 
+
+ align:start position:0%
+so here's the thing though right so if
+you have a plus and a minus charge those
+
+ align:start position:0%
+you have a plus and a minus charge those
+ 
+
+ align:start position:0%
+you have a plus and a minus charge those
+are each one
+
+ align:start position:0%
+are each one
+ 
+
+ align:start position:0%
+are each one
+right charge of electron um and then the
+
+ align:start position:0%
+right charge of electron um and then the
+ 
+
+ align:start position:0%
+right charge of electron um and then the
+distance between them when it's really
+
+ align:start position:0%
+distance between them when it's really
+ 
+
+ align:start position:0%
+distance between them when it's really
+far
+
+ align:start position:0%
+far
+ 
+
+ align:start position:0%
+far
+this this energy is pretty weak so
+
+ align:start position:0%
+this this energy is pretty weak so
+ 
+
+ align:start position:0%
+this this energy is pretty weak so
+that's this green curve here but as it
+
+ align:start position:0%
+that's this green curve here but as it
+ 
+
+ align:start position:0%
+that's this green curve here but as it
+gets closer and closer
+
+ align:start position:0%
+gets closer and closer
+ 
+
+ align:start position:0%
+gets closer and closer
+that energy gets lower and lower and
+
+ align:start position:0%
+that energy gets lower and lower and
+ 
+
+ align:start position:0%
+that energy gets lower and lower and
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+happiness is lower energy right these
+
+ align:start position:0%
+happiness is lower energy right these
+ 
+
+ align:start position:0%
+happiness is lower energy right these
+atoms want to find their happy place
+
+ align:start position:0%
+atoms want to find their happy place
+ 
+
+ align:start position:0%
+atoms want to find their happy place
+and they see each other like well we can
+
+ align:start position:0%
+and they see each other like well we can
+ 
+
+ align:start position:0%
+and they see each other like well we can
+be happier if we're closer
+
+ align:start position:0%
+be happier if we're closer
+ 
+
+ align:start position:0%
+be happier if we're closer
+until a certain thing happens which is
+
+ align:start position:0%
+until a certain thing happens which is
+ 
+
+ align:start position:0%
+until a certain thing happens which is
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+they've got similar charges like the
+
+ align:start position:0%
+they've got similar charges like the
+ 
+
+ align:start position:0%
+they've got similar charges like the
+electron shells
+
+ align:start position:0%
+electron shells
+ 
+
+ align:start position:0%
+electron shells
+negative charge negative charge shelf
+
+ align:start position:0%
+negative charge negative charge shelf
+ 
+
+ align:start position:0%
+negative charge negative charge shelf
+kind of coming too close
+
+ align:start position:0%
+kind of coming too close
+ 
+
+ align:start position:0%
+kind of coming too close
+that's the the forces of repulsion
+
+ align:start position:0%
+that's the the forces of repulsion
+ 
+
+ align:start position:0%
+that's the the forces of repulsion
+and so that nets in a total energy curve
+
+ align:start position:0%
+and so that nets in a total energy curve
+ 
+
+ align:start position:0%
+and so that nets in a total energy curve
+which is this
+
+ align:start position:0%
+which is this
+ 
+
+ align:start position:0%
+which is this
+this white line here the green and the
+
+ align:start position:0%
+this white line here the green and the
+ 
+
+ align:start position:0%
+this white line here the green and the
+red then you got the the white line
+
+ align:start position:0%
+red then you got the the white line
+ 
+
+ align:start position:0%
+red then you got the the white line
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+which is the total energy because if
+
+ align:start position:0%
+which is the total energy because if
+ 
+
+ align:start position:0%
+which is the total energy because if
+they came too close then
+
+ align:start position:0%
+they came too close then
+ 
+
+ align:start position:0%
+they came too close then
+you're going to be on this thing and
+
+ align:start position:0%
+you're going to be on this thing and
+ 
+
+ align:start position:0%
+you're going to be on this thing and
+you're just going to be you know all
+
+ align:start position:0%
+you're just going to be you know all
+ 
+
+ align:start position:0%
+you're just going to be you know all
+those electrons are going to be
+
+ align:start position:0%
+those electrons are going to be
+ 
+
+ align:start position:0%
+those electrons are going to be
+overlapping each other
+
+ align:start position:0%
+overlapping each other
+ 
+
+ align:start position:0%
+overlapping each other
+and very unhappy right
+
+ align:start position:0%
+and very unhappy right
+ 
+
+ align:start position:0%
+and very unhappy right
+so this is what we do and and we said
+
+ align:start position:0%
+so this is what we do and and we said
+ 
+
+ align:start position:0%
+so this is what we do and and we said
+okay this is the bond
+
+ align:start position:0%
+okay this is the bond
+ 
+
+ align:start position:0%
+okay this is the bond
+of an atom and another atom an ion
+
+ align:start position:0%
+of an atom and another atom an ion
+ 
+
+ align:start position:0%
+of an atom and another atom an ion
+and another ion a cation and an anion
+
+ align:start position:0%
+and another ion a cation and an anion
+ 
+
+ align:start position:0%
+and another ion a cation and an anion
+we did all this wednesday i'm just
+
+ align:start position:0%
+we did all this wednesday i'm just
+ 
+
+ align:start position:0%
+we did all this wednesday i'm just
+getting us back in the mood
+
+ align:start position:0%
+getting us back in the mood
+ 
+
+ align:start position:0%
+getting us back in the mood
+right and what i told you is that that
+
+ align:start position:0%
+right and what i told you is that that
+ 
+
+ align:start position:0%
+right and what i told you is that that
+bond energy
+
+ align:start position:0%
+bond energy
+ 
+
+ align:start position:0%
+bond energy
+is related to the lattice energy right i
+
+ align:start position:0%
+is related to the lattice energy right i
+ 
+
+ align:start position:0%
+is related to the lattice energy right i
+mean now technically
+
+ align:start position:0%
+mean now technically
+ 
+
+ align:start position:0%
+mean now technically
+the lattice energy is
+
+ align:start position:0%
+the lattice energy is
+ 
+
+ align:start position:0%
+the lattice energy is
+and this is something you're playing
+
+ align:start position:0%
+and this is something you're playing
+ 
+
+ align:start position:0%
+and this is something you're playing
+around with the lattice energy
+
+ align:start position:0%
+around with the lattice energy
+ 
+
+ align:start position:0%
+around with the lattice energy
+would be the energy that it takes to go
+
+ align:start position:0%
+would be the energy that it takes to go
+ 
+
+ align:start position:0%
+would be the energy that it takes to go
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+those ions sodium plus in the gas phase
+
+ align:start position:0%
+those ions sodium plus in the gas phase
+ 
+
+ align:start position:0%
+those ions sodium plus in the gas phase
+right we put that little guy there now
+
+ align:start position:0%
+right we put that little guy there now
+ 
+
+ align:start position:0%
+right we put that little guy there now
+that is something that's going to keep
+
+ align:start position:0%
+that is something that's going to keep
+ 
+
+ align:start position:0%
+that is something that's going to keep
+coming too it's a notation i've been
+
+ align:start position:0%
+coming too it's a notation i've been
+ 
+
+ align:start position:0%
+coming too it's a notation i've been
+sneaking in
+
+ align:start position:0%
+sneaking in
+ 
+
+ align:start position:0%
+sneaking in
+gas phase right plus chlorine
+
+ align:start position:0%
+gas phase right plus chlorine
+ 
+
+ align:start position:0%
+gas phase right plus chlorine
+ion gas phase and they came together
+
+ align:start position:0%
+ion gas phase and they came together
+ 
+
+ align:start position:0%
+ion gas phase and they came together
+to make nacl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ran out of room solid but i put it
+
+ align:start position:0%
+ran out of room solid but i put it
+ 
+
+ align:start position:0%
+ran out of room solid but i put it
+underneath
+
+ align:start position:0%
+underneath
+ 
+
+ align:start position:0%
+underneath
+solid sodium that's salt now the lattice
+
+ align:start position:0%
+solid sodium that's salt now the lattice
+ 
+
+ align:start position:0%
+solid sodium that's salt now the lattice
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+is the energy that it takes to go from
+
+ align:start position:0%
+is the energy that it takes to go from
+ 
+
+ align:start position:0%
+is the energy that it takes to go from
+these ions to the solid and
+
+ align:start position:0%
+these ions to the solid and
+ 
+
+ align:start position:0%
+these ions to the solid and
+as you can see well here i just did two
+
+ align:start position:0%
+as you can see well here i just did two
+ 
+
+ align:start position:0%
+as you can see well here i just did two
+ions
+
+ align:start position:0%
+ions
+ 
+
+ align:start position:0%
+ions
+but the lattice energy is going to be
+
+ align:start position:0%
+but the lattice energy is going to be
+ 
+
+ align:start position:0%
+but the lattice energy is going to be
+related to that bond energy
+
+ align:start position:0%
+related to that bond energy
+ 
+
+ align:start position:0%
+related to that bond energy
+right okay so the lattice energy of the
+
+ align:start position:0%
+right okay so the lattice energy of the
+ 
+
+ align:start position:0%
+right okay so the lattice energy of the
+solid that you make
+
+ align:start position:0%
+solid that you make
+ 
+
+ align:start position:0%
+solid that you make
+is going to be and ionic solids there's
+
+ align:start position:0%
+is going to be and ionic solids there's
+ 
+
+ align:start position:0%
+is going to be and ionic solids there's
+a whole bunch of
+
+ align:start position:0%
+a whole bunch of
+ 
+
+ align:start position:0%
+a whole bunch of
+materials that form solids this way
+
+ align:start position:0%
+materials that form solids this way
+ 
+
+ align:start position:0%
+materials that form solids this way
+they're ionic solids they have
+
+ align:start position:0%
+they're ionic solids they have
+ 
+
+ align:start position:0%
+they're ionic solids they have
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+that are general they're not always
+
+ align:start position:0%
+that are general they're not always
+ 
+
+ align:start position:0%
+that are general they're not always
+they're not always these properties but
+
+ align:start position:0%
+they're not always these properties but
+ 
+
+ align:start position:0%
+they're not always these properties but
+for the most part these are the
+
+ align:start position:0%
+for the most part these are the
+ 
+
+ align:start position:0%
+for the most part these are the
+properties of ionic solids right they
+
+ align:start position:0%
+properties of ionic solids right they
+ 
+
+ align:start position:0%
+properties of ionic solids right they
+tend to be
+
+ align:start position:0%
+tend to be
+ 
+
+ align:start position:0%
+tend to be
+solid at room temperature they tend to
+
+ align:start position:0%
+solid at room temperature they tend to
+ 
+
+ align:start position:0%
+solid at room temperature they tend to
+have high
+
+ align:start position:0%
+have high
+ 
+
+ align:start position:0%
+have high
+melting and boiling points they're often
+
+ align:start position:0%
+melting and boiling points they're often
+ 
+
+ align:start position:0%
+melting and boiling points they're often
+transparent and the visible they can
+
+ align:start position:0%
+transparent and the visible they can
+ 
+
+ align:start position:0%
+transparent and the visible they can
+they're mostly electrical insulators
+
+ align:start position:0%
+they're mostly electrical insulators
+ 
+
+ align:start position:0%
+they're mostly electrical insulators
+they're hard and brittle
+
+ align:start position:0%
+they're hard and brittle
+ 
+
+ align:start position:0%
+they're hard and brittle
+soluble in water but you're seeing
+
+ align:start position:0%
+soluble in water but you're seeing
+ 
+
+ align:start position:0%
+soluble in water but you're seeing
+in your goodie bag you're saying that's
+
+ align:start position:0%
+in your goodie bag you're saying that's
+ 
+
+ align:start position:0%
+in your goodie bag you're saying that's
+not always true because
+
+ align:start position:0%
+not always true because
+ 
+
+ align:start position:0%
+not always true because
+sometimes most of the time there but if
+
+ align:start position:0%
+sometimes most of the time there but if
+ 
+
+ align:start position:0%
+sometimes most of the time there but if
+this lattice energy is too high
+
+ align:start position:0%
+this lattice energy is too high
+ 
+
+ align:start position:0%
+this lattice energy is too high
+right then it may not even dissolve it
+
+ align:start position:0%
+right then it may not even dissolve it
+ 
+
+ align:start position:0%
+right then it may not even dissolve it
+may still be an eye but
+
+ align:start position:0%
+may still be an eye but
+ 
+
+ align:start position:0%
+may still be an eye but
+this may be some really really strong
+
+ align:start position:0%
+this may be some really really strong
+ 
+
+ align:start position:0%
+this may be some really really strong
+ionic solid right but these are the
+
+ align:start position:0%
+ionic solid right but these are the
+ 
+
+ align:start position:0%
+ionic solid right but these are the
+general properties
+
+ align:start position:0%
+general properties
+ 
+
+ align:start position:0%
+general properties
+of ionic solids okay we'll come back as
+
+ align:start position:0%
+of ionic solids okay we'll come back as
+ 
+
+ align:start position:0%
+of ionic solids okay we'll come back as
+we learn about other solids
+
+ align:start position:0%
+we learn about other solids
+ 
+
+ align:start position:0%
+we learn about other solids
+wednesday um to
+
+ align:start position:0%
+wednesday um to
+ 
+
+ align:start position:0%
+wednesday um to
+the differences in properties between
+
+ align:start position:0%
+the differences in properties between
+ 
+
+ align:start position:0%
+the differences in properties between
+different types of solids
+
+ align:start position:0%
+different types of solids
+ 
+
+ align:start position:0%
+different types of solids
+okay so that's where we ended now we've
+
+ align:start position:0%
+okay so that's where we ended now we've
+ 
+
+ align:start position:0%
+okay so that's where we ended now we've
+got we've
+
+ align:start position:0%
+got we've
+ 
+
+ align:start position:0%
+got we've
+now to do this to get to here
+
+ align:start position:0%
+now to do this to get to here
+ 
+
+ align:start position:0%
+now to do this to get to here
+we had to make ions and so we've been
+
+ align:start position:0%
+we had to make ions and so we've been
+ 
+
+ align:start position:0%
+we had to make ions and so we've been
+talking about ions and we're going to
+
+ align:start position:0%
+talking about ions and we're going to
+ 
+
+ align:start position:0%
+talking about ions and we're going to
+keep talking about ions because
+
+ align:start position:0%
+keep talking about ions because
+ 
+
+ align:start position:0%
+keep talking about ions because
+that's a very important part of how
+
+ align:start position:0%
+that's a very important part of how
+ 
+
+ align:start position:0%
+that's a very important part of how
+atoms see each other
+
+ align:start position:0%
+atoms see each other
+ 
+
+ align:start position:0%
+atoms see each other
+right am i seeing you as a neutral atom
+
+ align:start position:0%
+right am i seeing you as a neutral atom
+ 
+
+ align:start position:0%
+right am i seeing you as a neutral atom
+with all your electrons in your shell or
+
+ align:start position:0%
+with all your electrons in your shell or
+ 
+
+ align:start position:0%
+with all your electrons in your shell or
+am i seeing you with a charge uh missing
+
+ align:start position:0%
+am i seeing you with a charge uh missing
+ 
+
+ align:start position:0%
+am i seeing you with a charge uh missing
+or not that makes a big difference
+
+ align:start position:0%
+or not that makes a big difference
+ 
+
+ align:start position:0%
+or not that makes a big difference
+right in how they approach each other
+
+ align:start position:0%
+right in how they approach each other
+ 
+
+ align:start position:0%
+right in how they approach each other
+and therefore how they bond
+
+ align:start position:0%
+and therefore how they bond
+ 
+
+ align:start position:0%
+and therefore how they bond
+right which is a critical part of of
+
+ align:start position:0%
+right which is a critical part of of
+ 
+
+ align:start position:0%
+right which is a critical part of of
+what we need to learn this semester
+
+ align:start position:0%
+what we need to learn this semester
+ 
+
+ align:start position:0%
+what we need to learn this semester
+and so you know we showed this which is
+
+ align:start position:0%
+and so you know we showed this which is
+ 
+
+ align:start position:0%
+and so you know we showed this which is
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+sometimes atoms actually don't mind
+
+ align:start position:0%
+sometimes atoms actually don't mind
+ 
+
+ align:start position:0%
+sometimes atoms actually don't mind
+losing
+
+ align:start position:0%
+losing
+ 
+
+ align:start position:0%
+losing
+an electron right don't mind don't mind
+
+ align:start position:0%
+an electron right don't mind don't mind
+ 
+
+ align:start position:0%
+an electron right don't mind don't mind
+is like happiness level which has to do
+
+ align:start position:0%
+is like happiness level which has to do
+ 
+
+ align:start position:0%
+is like happiness level which has to do
+with energy
+
+ align:start position:0%
+with energy
+ 
+
+ align:start position:0%
+with energy
+and so if we want to look at this more
+
+ align:start position:0%
+and so if we want to look at this more
+ 
+
+ align:start position:0%
+and so if we want to look at this more
+formally we would look at for example
+
+ align:start position:0%
+formally we would look at for example
+ 
+
+ align:start position:0%
+formally we would look at for example
+this chart from april which is the first
+
+ align:start position:0%
+this chart from april which is the first
+ 
+
+ align:start position:0%
+this chart from april which is the first
+ionization energy right now that's
+
+ align:start position:0%
+ionization energy right now that's
+ 
+
+ align:start position:0%
+ionization energy right now that's
+exactly that's something that we talked
+
+ align:start position:0%
+exactly that's something that we talked
+ 
+
+ align:start position:0%
+exactly that's something that we talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+right so the first ionization energy
+
+ align:start position:0%
+right so the first ionization energy
+ 
+
+ align:start position:0%
+right so the first ionization energy
+which is how much energy it takes to
+
+ align:start position:0%
+which is how much energy it takes to
+ 
+
+ align:start position:0%
+which is how much energy it takes to
+remove
+
+ align:start position:0%
+remove
+ 
+
+ align:start position:0%
+remove
+an electron from the outer shell the
+
+ align:start position:0%
+an electron from the outer shell the
+ 
+
+ align:start position:0%
+an electron from the outer shell the
+most outer shell electron the first
+
+ align:start position:0%
+most outer shell electron the first
+ 
+
+ align:start position:0%
+most outer shell electron the first
+one you would take away that's the first
+
+ align:start position:0%
+one you would take away that's the first
+ 
+
+ align:start position:0%
+one you would take away that's the first
+ionization energy
+
+ align:start position:0%
+ionization energy
+ 
+
+ align:start position:0%
+ionization energy
+all right and we saw uh again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+getting us back in the mood oh i've got
+
+ align:start position:0%
+getting us back in the mood oh i've got
+ 
+
+ align:start position:0%
+getting us back in the mood oh i've got
+colors there look so if you started for
+
+ align:start position:0%
+colors there look so if you started for
+ 
+
+ align:start position:0%
+colors there look so if you started for
+example let's start let's just take a
+
+ align:start position:0%
+example let's start let's just take a
+ 
+
+ align:start position:0%
+example let's start let's just take a
+look at this
+
+ align:start position:0%
+look at this
+ 
+
+ align:start position:0%
+look at this
+okay so here here we are at lithium
+
+ align:start position:0%
+okay so here here we are at lithium
+ 
+
+ align:start position:0%
+okay so here here we are at lithium
+i'm going to start here and that's first
+
+ align:start position:0%
+i'm going to start here and that's first
+ 
+
+ align:start position:0%
+i'm going to start here and that's first
+ionization energy and this is just the
+
+ align:start position:0%
+ionization energy and this is just the
+ 
+
+ align:start position:0%
+ionization energy and this is just the
+atomic number
+
+ align:start position:0%
+atomic number
+ 
+
+ align:start position:0%
+atomic number
+so there's lithium and remember we
+
+ align:start position:0%
+so there's lithium and remember we
+ 
+
+ align:start position:0%
+so there's lithium and remember we
+looked at this last week
+
+ align:start position:0%
+looked at this last week
+ 
+
+ align:start position:0%
+looked at this last week
+lithium and beryllium okay so if you
+
+ align:start position:0%
+lithium and beryllium okay so if you
+ 
+
+ align:start position:0%
+lithium and beryllium okay so if you
+look at that we say
+
+ align:start position:0%
+look at that we say
+ 
+
+ align:start position:0%
+look at that we say
+okay so for lithium you had three
+
+ align:start position:0%
+okay so for lithium you had three
+ 
+
+ align:start position:0%
+okay so for lithium you had three
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+in the core so there's lithium right and
+
+ align:start position:0%
+in the core so there's lithium right and
+ 
+
+ align:start position:0%
+in the core so there's lithium right and
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+the lithium oh this is so fun because
+
+ align:start position:0%
+the lithium oh this is so fun because
+ 
+
+ align:start position:0%
+the lithium oh this is so fun because
+now we know what to call this
+
+ align:start position:0%
+now we know what to call this
+ 
+
+ align:start position:0%
+now we know what to call this
+1s2 right and then we have another shell
+
+ align:start position:0%
+1s2 right and then we have another shell
+ 
+
+ align:start position:0%
+1s2 right and then we have another shell
+these are just pictor the electron is
+
+ align:start position:0%
+these are just pictor the electron is
+ 
+
+ align:start position:0%
+these are just pictor the electron is
+not in an orbit
+
+ align:start position:0%
+not in an orbit
+ 
+
+ align:start position:0%
+not in an orbit
+it's in an orbital it's not
+
+ align:start position:0%
+it's in an orbital it's not
+ 
+
+ align:start position:0%
+it's in an orbital it's not
+moving around like this that's our
+
+ align:start position:0%
+moving around like this that's our
+ 
+
+ align:start position:0%
+moving around like this that's our
+classical mines
+
+ align:start position:0%
+classical mines
+ 
+
+ align:start position:0%
+classical mines
+fighting and it's got one more electron
+
+ align:start position:0%
+fighting and it's got one more electron
+ 
+
+ align:start position:0%
+fighting and it's got one more electron
+why did i draw a dash it's got one more
+
+ align:start position:0%
+why did i draw a dash it's got one more
+ 
+
+ align:start position:0%
+why did i draw a dash it's got one more
+electron there in the 2s
+
+ align:start position:0%
+electron there in the 2s
+ 
+
+ align:start position:0%
+electron there in the 2s
+shell and that's lithium okay but now
+
+ align:start position:0%
+shell and that's lithium okay but now
+ 
+
+ align:start position:0%
+shell and that's lithium okay but now
+we're going to go from lithium to
+
+ align:start position:0%
+we're going to go from lithium to
+ 
+
+ align:start position:0%
+we're going to go from lithium to
+beryllium and and we talked about
+
+ align:start position:0%
+beryllium and and we talked about
+ 
+
+ align:start position:0%
+beryllium and and we talked about
+so beryllium now is going to add okay
+
+ align:start position:0%
+so beryllium now is going to add okay
+ 
+
+ align:start position:0%
+so beryllium now is going to add okay
+it's going to add a
+
+ align:start position:0%
+it's going to add a
+ 
+
+ align:start position:0%
+it's going to add a
+another proton it's got all of them but
+
+ align:start position:0%
+another proton it's got all of them but
+ 
+
+ align:start position:0%
+another proton it's got all of them but
+i'm showing the one that was added
+
+ align:start position:0%
+i'm showing the one that was added
+ 
+
+ align:start position:0%
+i'm showing the one that was added
+and it's also going to add an electron
+
+ align:start position:0%
+and it's also going to add an electron
+ 
+
+ align:start position:0%
+and it's also going to add an electron
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+but see for beryllium this
+
+ align:start position:0%
+but see for beryllium this
+ 
+
+ align:start position:0%
+but see for beryllium this
+this electron is not
+
+ align:start position:0%
+this electron is not
+ 
+
+ align:start position:0%
+this electron is not
+really not shielded anymore not shielded
+
+ align:start position:0%
+really not shielded anymore not shielded
+ 
+
+ align:start position:0%
+really not shielded anymore not shielded
+more for the most part
+
+ align:start position:0%
+more for the most part
+ 
+
+ align:start position:0%
+more for the most part
+you know it went into the same shell the
+
+ align:start position:0%
+you know it went into the same shell the
+ 
+
+ align:start position:0%
+you know it went into the same shell the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+you know the same n right and the same l
+
+ align:start position:0%
+you know the same n right and the same l
+ 
+
+ align:start position:0%
+you know the same n right and the same l
+same shape same quantum number so it's
+
+ align:start position:0%
+same shape same quantum number so it's
+ 
+
+ align:start position:0%
+same shape same quantum number so it's
+there's nothing else shielding and yet
+
+ align:start position:0%
+there's nothing else shielding and yet
+ 
+
+ align:start position:0%
+there's nothing else shielding and yet
+there's a whole other proton
+
+ align:start position:0%
+there's a whole other proton
+ 
+
+ align:start position:0%
+there's a whole other proton
+and that's why beryllium is smaller
+
+ align:start position:0%
+and that's why beryllium is smaller
+ 
+
+ align:start position:0%
+and that's why beryllium is smaller
+this is all stuff we talked about
+
+ align:start position:0%
+this is all stuff we talked about
+ 
+
+ align:start position:0%
+this is all stuff we talked about
+wednesday but see look that's
+
+ align:start position:0%
+wednesday but see look that's
+ 
+
+ align:start position:0%
+wednesday but see look that's
+also why it's harder to pull
+
+ align:start position:0%
+also why it's harder to pull
+ 
+
+ align:start position:0%
+also why it's harder to pull
+the outer electron off of beryllium
+
+ align:start position:0%
+the outer electron off of beryllium
+ 
+
+ align:start position:0%
+the outer electron off of beryllium
+there it is than lithium
+
+ align:start position:0%
+there it is than lithium
+ 
+
+ align:start position:0%
+there it is than lithium
+so those really go together right the
+
+ align:start position:0%
+so those really go together right the
+ 
+
+ align:start position:0%
+so those really go together right the
+rate all the radius stuff we talked
+
+ align:start position:0%
+rate all the radius stuff we talked
+ 
+
+ align:start position:0%
+rate all the radius stuff we talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+holds you know that same kind of logic
+
+ align:start position:0%
+holds you know that same kind of logic
+ 
+
+ align:start position:0%
+holds you know that same kind of logic
+in terms of how these electrons are with
+
+ align:start position:0%
+in terms of how these electrons are with
+ 
+
+ align:start position:0%
+in terms of how these electrons are with
+respect to their nucleus
+
+ align:start position:0%
+respect to their nucleus
+ 
+
+ align:start position:0%
+respect to their nucleus
+holds for ionization energy now
+
+ align:start position:0%
+holds for ionization energy now
+ 
+
+ align:start position:0%
+holds for ionization energy now
+let's add let's go to boron
+
+ align:start position:0%
+let's add let's go to boron
+ 
+
+ align:start position:0%
+let's add let's go to boron
+so if we go to boron now
+
+ align:start position:0%
+so if we go to boron now
+ 
+
+ align:start position:0%
+so if we go to boron now
+we're going over look at what happened
+
+ align:start position:0%
+we're going over look at what happened
+ 
+
+ align:start position:0%
+we're going over look at what happened
+look at that we went from there to there
+
+ align:start position:0%
+look at that we went from there to there
+ 
+
+ align:start position:0%
+look at that we went from there to there
+and the ionization energy got lower
+
+ align:start position:0%
+and the ionization energy got lower
+ 
+
+ align:start position:0%
+and the ionization energy got lower
+well that's also something we can
+
+ align:start position:0%
+well that's also something we can
+ 
+
+ align:start position:0%
+well that's also something we can
+understand because now
+
+ align:start position:0%
+understand because now
+ 
+
+ align:start position:0%
+understand because now
+we're putting it into the 2p
+
+ align:start position:0%
+we're putting it into the 2p
+ 
+
+ align:start position:0%
+we're putting it into the 2p
+okay so so if i do that it would be
+
+ align:start position:0%
+okay so so if i do that it would be
+ 
+
+ align:start position:0%
+okay so so if i do that it would be
+i'm going to put it under here 2s2
+
+ align:start position:0%
+i'm going to put it under here 2s2
+ 
+
+ align:start position:0%
+i'm going to put it under here 2s2
+right and now if i go to boron
+
+ align:start position:0%
+right and now if i go to boron
+ 
+
+ align:start position:0%
+right and now if i go to boron
+i'm going to put it here in a 2p shell
+
+ align:start position:0%
+i'm going to put it here in a 2p shell
+ 
+
+ align:start position:0%
+i'm going to put it here in a 2p shell
+so i'm starting
+
+ align:start position:0%
+so i'm starting
+ 
+
+ align:start position:0%
+so i'm starting
+a new l now remember
+
+ align:start position:0%
+a new l now remember
+ 
+
+ align:start position:0%
+a new l now remember
+that means the shape the quantum number
+
+ align:start position:0%
+that means the shape the quantum number
+ 
+
+ align:start position:0%
+that means the shape the quantum number
+is still two but the shape of the
+
+ align:start position:0%
+is still two but the shape of the
+ 
+
+ align:start position:0%
+is still two but the shape of the
+orbital is different
+
+ align:start position:0%
+orbital is different
+ 
+
+ align:start position:0%
+orbital is different
+and now we know also from something we
+
+ align:start position:0%
+and now we know also from something we
+ 
+
+ align:start position:0%
+and now we know also from something we
+learned last week
+
+ align:start position:0%
+learned last week
+ 
+
+ align:start position:0%
+learned last week
+that because of orbital penetration the
+
+ align:start position:0%
+that because of orbital penetration the
+ 
+
+ align:start position:0%
+that because of orbital penetration the
+energies of the 2p and 2s orbitals are
+
+ align:start position:0%
+energies of the 2p and 2s orbitals are
+ 
+
+ align:start position:0%
+energies of the 2p and 2s orbitals are
+not the same
+
+ align:start position:0%
+not the same
+ 
+
+ align:start position:0%
+not the same
+right the s energies are a little lower
+
+ align:start position:0%
+right the s energies are a little lower
+ 
+
+ align:start position:0%
+right the s energies are a little lower
+and it's get it lets those electrons get
+
+ align:start position:0%
+and it's get it lets those electrons get
+ 
+
+ align:start position:0%
+and it's get it lets those electrons get
+a little bit closer to that positive
+
+ align:start position:0%
+a little bit closer to that positive
+ 
+
+ align:start position:0%
+a little bit closer to that positive
+charge that they want so badly
+
+ align:start position:0%
+charge that they want so badly
+ 
+
+ align:start position:0%
+charge that they want so badly
+so we know that this is going to be a
+
+ align:start position:0%
+so we know that this is going to be a
+ 
+
+ align:start position:0%
+so we know that this is going to be a
+little further out
+
+ align:start position:0%
+little further out
+ 
+
+ align:start position:0%
+little further out
+and so there's a little bit of shielding
+
+ align:start position:0%
+and so there's a little bit of shielding
+ 
+
+ align:start position:0%
+and so there's a little bit of shielding
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+shielding that you get for this
+
+ align:start position:0%
+shielding that you get for this
+ 
+
+ align:start position:0%
+shielding that you get for this
+plus orbital penetration that we talked
+
+ align:start position:0%
+plus orbital penetration that we talked
+ 
+
+ align:start position:0%
+plus orbital penetration that we talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+and that puts it further out
+
+ align:start position:0%
+and that puts it further out
+ 
+
+ align:start position:0%
+and that puts it further out
+right and therefore the attraction is a
+
+ align:start position:0%
+right and therefore the attraction is a
+ 
+
+ align:start position:0%
+right and therefore the attraction is a
+little less and therefore
+
+ align:start position:0%
+little less and therefore
+ 
+
+ align:start position:0%
+little less and therefore
+the ionization energy went down yeah and
+
+ align:start position:0%
+the ionization energy went down yeah and
+ 
+
+ align:start position:0%
+the ionization energy went down yeah and
+now we're going to fill those up but
+
+ align:start position:0%
+now we're going to fill those up but
+ 
+
+ align:start position:0%
+now we're going to fill those up but
+it's the same thing as before now you're
+
+ align:start position:0%
+it's the same thing as before now you're
+ 
+
+ align:start position:0%
+it's the same thing as before now you're
+not going further out you're just adding
+
+ align:start position:0%
+not going further out you're just adding
+ 
+
+ align:start position:0%
+not going further out you're just adding
+and you're not really screening while
+
+ align:start position:0%
+and you're not really screening while
+ 
+
+ align:start position:0%
+and you're not really screening while
+you add right
+
+ align:start position:0%
+you add right
+ 
+
+ align:start position:0%
+you add right
+and so you're adding electrons into this
+
+ align:start position:0%
+and so you're adding electrons into this
+ 
+
+ align:start position:0%
+and so you're adding electrons into this
+2p orbital but you're also adding all
+
+ align:start position:0%
+2p orbital but you're also adding all
+ 
+
+ align:start position:0%
+2p orbital but you're also adding all
+this positive charge
+
+ align:start position:0%
+this positive charge
+ 
+
+ align:start position:0%
+this positive charge
+salute and and so the ionization energy
+
+ align:start position:0%
+salute and and so the ionization energy
+ 
+
+ align:start position:0%
+salute and and so the ionization energy
+is going to go up
+
+ align:start position:0%
+is going to go up
+ 
+
+ align:start position:0%
+is going to go up
+except look at that oh half filling
+
+ align:start position:0%
+except look at that oh half filling
+ 
+
+ align:start position:0%
+except look at that oh half filling
+right there half filling a little extra
+
+ align:start position:0%
+right there half filling a little extra
+ 
+
+ align:start position:0%
+right there half filling a little extra
+stability remember we talked about
+
+ align:start position:0%
+stability remember we talked about
+ 
+
+ align:start position:0%
+stability remember we talked about
+exceptions right half filling
+
+ align:start position:0%
+exceptions right half filling
+ 
+
+ align:start position:0%
+exceptions right half filling
+half filling and so you see now you can
+
+ align:start position:0%
+half filling and so you see now you can
+ 
+
+ align:start position:0%
+half filling and so you see now you can
+see we can understand these trends that
+
+ align:start position:0%
+see we can understand these trends that
+ 
+
+ align:start position:0%
+see we can understand these trends that
+were being measured
+
+ align:start position:0%
+were being measured
+ 
+
+ align:start position:0%
+were being measured
+right at the time these ionization
+
+ align:start position:0%
+right at the time these ionization
+ 
+
+ align:start position:0%
+right at the time these ionization
+potentials but now we really can
+
+ align:start position:0%
+potentials but now we really can
+ 
+
+ align:start position:0%
+potentials but now we really can
+understand them
+
+ align:start position:0%
+understand them
+ 
+
+ align:start position:0%
+understand them
+and you can group them and you can see
+
+ align:start position:0%
+and you can group them and you can see
+ 
+
+ align:start position:0%
+and you can group them and you can see
+if you group them
+
+ align:start position:0%
+if you group them
+ 
+
+ align:start position:0%
+if you group them
+remember we also grouped the periodic
+
+ align:start position:0%
+remember we also grouped the periodic
+ 
+
+ align:start position:0%
+remember we also grouped the periodic
+table a little bit by electron filling
+
+ align:start position:0%
+table a little bit by electron filling
+ 
+
+ align:start position:0%
+table a little bit by electron filling
+quantum numbers right you had the s and
+
+ align:start position:0%
+quantum numbers right you had the s and
+ 
+
+ align:start position:0%
+quantum numbers right you had the s and
+p blocks
+
+ align:start position:0%
+p blocks
+ 
+
+ align:start position:0%
+p blocks
+those are also often called the main
+
+ align:start position:0%
+those are also often called the main
+ 
+
+ align:start position:0%
+those are also often called the main
+group elements they're
+
+ align:start position:0%
+group elements they're
+ 
+
+ align:start position:0%
+group elements they're
+in the first couple of rows of those
+
+ align:start position:0%
+in the first couple of rows of those
+ 
+
+ align:start position:0%
+in the first couple of rows of those
+they're the the most abundant elements
+
+ align:start position:0%
+they're the the most abundant elements
+ 
+
+ align:start position:0%
+they're the the most abundant elements
+right um and and so those are and those
+
+ align:start position:0%
+right um and and so those are and those
+ 
+
+ align:start position:0%
+right um and and so those are and those
+tr but those trends now you fully
+
+ align:start position:0%
+tr but those trends now you fully
+ 
+
+ align:start position:0%
+tr but those trends now you fully
+understand from
+
+ align:start position:0%
+understand from
+ 
+
+ align:start position:0%
+understand from
+the the quantum mechanical solution to
+
+ align:start position:0%
+the the quantum mechanical solution to
+ 
+
+ align:start position:0%
+the the quantum mechanical solution to
+the atom
+
+ align:start position:0%
+the atom
+ 
+
+ align:start position:0%
+the atom
+right and the electron filling of those
+
+ align:start position:0%
+right and the electron filling of those
+ 
+
+ align:start position:0%
+right and the electron filling of those
+orbitals we can actually really
+
+ align:start position:0%
+orbitals we can actually really
+ 
+
+ align:start position:0%
+orbitals we can actually really
+understand it all right
+
+ align:start position:0%
+understand it all right
+ 
+
+ align:start position:0%
+understand it all right
+and so that's the and then the same
+
+ align:start position:0%
+and so that's the and then the same
+ 
+
+ align:start position:0%
+and so that's the and then the same
+thing happens with the d
+
+ align:start position:0%
+thing happens with the d
+ 
+
+ align:start position:0%
+thing happens with the d
+it's a little more complicated by the
+
+ align:start position:0%
+it's a little more complicated by the
+ 
+
+ align:start position:0%
+it's a little more complicated by the
+way these are often called transition
+
+ align:start position:0%
+way these are often called transition
+ 
+
+ align:start position:0%
+way these are often called transition
+metals
+
+ align:start position:0%
+metals
+ 
+
+ align:start position:0%
+metals
+the d block i told you about the d block
+
+ align:start position:0%
+the d block i told you about the d block
+ 
+
+ align:start position:0%
+the d block i told you about the d block
+last week they're also called transition
+
+ align:start position:0%
+last week they're also called transition
+ 
+
+ align:start position:0%
+last week they're also called transition
+metals
+
+ align:start position:0%
+metals
+ 
+
+ align:start position:0%
+metals
+and the word metal is something we'll
+
+ align:start position:0%
+and the word metal is something we'll
+ 
+
+ align:start position:0%
+and the word metal is something we'll
+talk a lot about in a few weeks when we
+
+ align:start position:0%
+talk a lot about in a few weeks when we
+ 
+
+ align:start position:0%
+talk a lot about in a few weeks when we
+make metals
+
+ align:start position:0%
+make metals
+ 
+
+ align:start position:0%
+make metals
+but they're called transitions because
+
+ align:start position:0%
+but they're called transitions because
+ 
+
+ align:start position:0%
+but they're called transitions because
+literally they transition
+
+ align:start position:0%
+literally they transition
+ 
+
+ align:start position:0%
+literally they transition
+in the filling they transition they you
+
+ align:start position:0%
+in the filling they transition they you
+ 
+
+ align:start position:0%
+in the filling they transition they you
+you're filling d
+
+ align:start position:0%
+you're filling d
+ 
+
+ align:start position:0%
+you're filling d
+orbitals right transition you're kind of
+
+ align:start position:0%
+orbitals right transition you're kind of
+ 
+
+ align:start position:0%
+orbitals right transition you're kind of
+and that makes it a little more complex
+
+ align:start position:0%
+and that makes it a little more complex
+ 
+
+ align:start position:0%
+and that makes it a little more complex
+in terms of what happens
+
+ align:start position:0%
+in terms of what happens
+ 
+
+ align:start position:0%
+in terms of what happens
+but the same trends hold the same trends
+
+ align:start position:0%
+but the same trends hold the same trends
+ 
+
+ align:start position:0%
+but the same trends hold the same trends
+hold you see
+
+ align:start position:0%
+hold you see
+ 
+
+ align:start position:0%
+hold you see
+you as you add more d electrons the
+
+ align:start position:0%
+you as you add more d electrons the
+ 
+
+ align:start position:0%
+you as you add more d electrons the
+ionization energy keeps going up okay
+
+ align:start position:0%
+ionization energy keeps going up okay
+ 
+
+ align:start position:0%
+ionization energy keeps going up okay
+now this is extremely important this
+
+ align:start position:0%
+now this is extremely important this
+ 
+
+ align:start position:0%
+now this is extremely important this
+ionization energy
+
+ align:start position:0%
+ionization energy
+ 
+
+ align:start position:0%
+ionization energy
+the first ionization energy is very
+
+ align:start position:0%
+the first ionization energy is very
+ 
+
+ align:start position:0%
+the first ionization energy is very
+important because it tells you so much
+
+ align:start position:0%
+important because it tells you so much
+ 
+
+ align:start position:0%
+important because it tells you so much
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+you know the outer electron whether an
+
+ align:start position:0%
+you know the outer electron whether an
+ 
+
+ align:start position:0%
+you know the outer electron whether an
+atom is going to be an anion or a cation
+
+ align:start position:0%
+atom is going to be an anion or a cation
+ 
+
+ align:start position:0%
+atom is going to be an anion or a cation
+but all of the ionization you could you
+
+ align:start position:0%
+but all of the ionization you could you
+ 
+
+ align:start position:0%
+but all of the ionization you could you
+could throw a whole lot of energy at
+
+ align:start position:0%
+could throw a whole lot of energy at
+ 
+
+ align:start position:0%
+could throw a whole lot of energy at
+these atoms
+
+ align:start position:0%
+these atoms
+ 
+
+ align:start position:0%
+these atoms
+and they'll all come off right and and
+
+ align:start position:0%
+and they'll all come off right and and
+ 
+
+ align:start position:0%
+and they'll all come off right and and
+so you know
+
+ align:start position:0%
+so you know
+ 
+
+ align:start position:0%
+so you know
+so we we played with this kind of energy
+
+ align:start position:0%
+so we we played with this kind of energy
+ 
+
+ align:start position:0%
+so we we played with this kind of energy
+this is visible light you had your goody
+
+ align:start position:0%
+this is visible light you had your goody
+ 
+
+ align:start position:0%
+this is visible light you had your goody
+bag too
+
+ align:start position:0%
+bag too
+ 
+
+ align:start position:0%
+bag too
+you got a spectrometer you can see lines
+
+ align:start position:0%
+you got a spectrometer you can see lines
+ 
+
+ align:start position:0%
+you got a spectrometer you can see lines
+in here this is a continuous spectrum
+
+ align:start position:0%
+in here this is a continuous spectrum
+ 
+
+ align:start position:0%
+in here this is a continuous spectrum
+but you see you got this whole all these
+
+ align:start position:0%
+but you see you got this whole all these
+ 
+
+ align:start position:0%
+but you see you got this whole all these
+different wavelengths
+
+ align:start position:0%
+different wavelengths
+ 
+
+ align:start position:0%
+different wavelengths
+right and and they have and now you see
+
+ align:start position:0%
+right and and they have and now you see
+ 
+
+ align:start position:0%
+right and and they have and now you see
+this and you don't just think about
+
+ align:start position:0%
+this and you don't just think about
+ 
+
+ align:start position:0%
+this and you don't just think about
+colors
+
+ align:start position:0%
+colors
+ 
+
+ align:start position:0%
+colors
+you think about energies right and and
+
+ align:start position:0%
+you think about energies right and and
+ 
+
+ align:start position:0%
+you think about energies right and and
+so if you think
+
+ align:start position:0%
+so if you think
+ 
+
+ align:start position:0%
+so if you think
+that way because i want to know how can
+
+ align:start position:0%
+that way because i want to know how can
+ 
+
+ align:start position:0%
+that way because i want to know how can
+i measure
+
+ align:start position:0%
+i measure
+ 
+
+ align:start position:0%
+i measure
+how can i measure these things ah stop
+
+ align:start position:0%
+how can i measure these things ah stop
+ 
+
+ align:start position:0%
+how can i measure these things ah stop
+better all right and so if i you know
+
+ align:start position:0%
+better all right and so if i you know
+ 
+
+ align:start position:0%
+better all right and so if i you know
+if i look at energies oh
+
+ align:start position:0%
+if i look at energies oh
+ 
+
+ align:start position:0%
+if i look at energies oh
+enter energies i've got like the visible
+
+ align:start position:0%
+enter energies i've got like the visible
+ 
+
+ align:start position:0%
+enter energies i've got like the visible
+right which is around oh i don't know
+
+ align:start position:0%
+right which is around oh i don't know
+ 
+
+ align:start position:0%
+right which is around oh i don't know
+say 2 to 6 ev
+
+ align:start position:0%
+say 2 to 6 ev
+ 
+
+ align:start position:0%
+say 2 to 6 ev
+that's pretty high energy and then
+
+ align:start position:0%
+that's pretty high energy and then
+ 
+
+ align:start position:0%
+that's pretty high energy and then
+you've got well now
+
+ align:start position:0%
+you've got well now
+ 
+
+ align:start position:0%
+you've got well now
+can i shine visible light and and kick
+
+ align:start position:0%
+can i shine visible light and and kick
+ 
+
+ align:start position:0%
+can i shine visible light and and kick
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+you know a lithium electron well the
+
+ align:start position:0%
+you know a lithium electron well the
+ 
+
+ align:start position:0%
+you know a lithium electron well the
+answer is
+
+ align:start position:0%
+answer is
+ 
+
+ align:start position:0%
+answer is
+roughly yes if it's if it's you know the
+
+ align:start position:0%
+roughly yes if it's if it's you know the
+ 
+
+ align:start position:0%
+roughly yes if it's if it's you know the
+lithium energy ionization
+
+ align:start position:0%
+lithium energy ionization
+ 
+
+ align:start position:0%
+lithium energy ionization
+oh let's just go back and look that
+
+ align:start position:0%
+oh let's just go back and look that
+ 
+
+ align:start position:0%
+oh let's just go back and look that
+first ionization energy
+
+ align:start position:0%
+first ionization energy
+ 
+
+ align:start position:0%
+first ionization energy
+520 kilojoules per mole i know that's
+
+ align:start position:0%
+520 kilojoules per mole i know that's
+ 
+
+ align:start position:0%
+520 kilojoules per mole i know that's
+5.4
+
+ align:start position:0%
+5.4
+ 
+
+ align:start position:0%
+5.4
+ev ish because i don't mind going back
+
+ align:start position:0%
+ev ish because i don't mind going back
+ 
+
+ align:start position:0%
+ev ish because i don't mind going back
+and forth
+
+ align:start position:0%
+and forth
+ 
+
+ align:start position:0%
+and forth
+right kilojoules per mole of electrons
+
+ align:start position:0%
+right kilojoules per mole of electrons
+ 
+
+ align:start position:0%
+right kilojoules per mole of electrons
+joules ev
+
+ align:start position:0%
+joules ev
+ 
+
+ align:start position:0%
+joules ev
+moles you can go back and forth but
+
+ align:start position:0%
+moles you can go back and forth but
+ 
+
+ align:start position:0%
+moles you can go back and forth but
+that's right around here
+
+ align:start position:0%
+that's right around here
+ 
+
+ align:start position:0%
+that's right around here
+so i could shine visible light and
+
+ align:start position:0%
+so i could shine visible light and
+ 
+
+ align:start position:0%
+so i could shine visible light and
+potentially knock that out but see
+
+ align:start position:0%
+potentially knock that out but see
+ 
+
+ align:start position:0%
+potentially knock that out but see
+if i wanted the 1s electron of lithium
+
+ align:start position:0%
+if i wanted the 1s electron of lithium
+ 
+
+ align:start position:0%
+if i wanted the 1s electron of lithium
+well that's it's much much lower in
+
+ align:start position:0%
+well that's it's much much lower in
+ 
+
+ align:start position:0%
+well that's it's much much lower in
+energy because remember we talk about
+
+ align:start position:0%
+energy because remember we talk about
+ 
+
+ align:start position:0%
+energy because remember we talk about
+it goes in and in each time i add charge
+
+ align:start position:0%
+it goes in and in each time i add charge
+ 
+
+ align:start position:0%
+it goes in and in each time i add charge
+and so it would take 122 electron volts
+
+ align:start position:0%
+and so it would take 122 electron volts
+ 
+
+ align:start position:0%
+and so it would take 122 electron volts
+to knock that out
+
+ align:start position:0%
+to knock that out
+ 
+
+ align:start position:0%
+to knock that out
+right and so but we have that kind of
+
+ align:start position:0%
+right and so but we have that kind of
+ 
+
+ align:start position:0%
+right and so but we have that kind of
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+right the uv the uv would be something
+
+ align:start position:0%
+right the uv the uv would be something
+ 
+
+ align:start position:0%
+right the uv the uv would be something
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+oh 10 to 100 and then if we really want
+
+ align:start position:0%
+oh 10 to 100 and then if we really want
+ 
+
+ align:start position:0%
+oh 10 to 100 and then if we really want
+to blast these we could go
+
+ align:start position:0%
+to blast these we could go
+ 
+
+ align:start position:0%
+to blast these we could go
+x-rays are we going to have fun with
+
+ align:start position:0%
+x-rays are we going to have fun with
+ 
+
+ align:start position:0%
+x-rays are we going to have fun with
+x-rays
+
+ align:start position:0%
+x-rays
+ 
+
+ align:start position:0%
+x-rays
+later in the semester and this would go
+
+ align:start position:0%
+later in the semester and this would go
+ 
+
+ align:start position:0%
+later in the semester and this would go
+to something like a hundred thousand
+
+ align:start position:0%
+to something like a hundred thousand
+ 
+
+ align:start position:0%
+to something like a hundred thousand
+and so i got it you know if i wanted to
+
+ align:start position:0%
+and so i got it you know if i wanted to
+ 
+
+ align:start position:0%
+and so i got it you know if i wanted to
+i could shine light
+
+ align:start position:0%
+i could shine light
+ 
+
+ align:start position:0%
+i could shine light
+and ionize the whole thing and that is
+
+ align:start position:0%
+and ionize the whole thing and that is
+ 
+
+ align:start position:0%
+and ionize the whole thing and that is
+in fact
+
+ align:start position:0%
+in fact
+ 
+
+ align:start position:0%
+in fact
+one of the single most important
+
+ align:start position:0%
+one of the single most important
+ 
+
+ align:start position:0%
+one of the single most important
+experiments we do to characterize
+
+ align:start position:0%
+experiments we do to characterize
+ 
+
+ align:start position:0%
+experiments we do to characterize
+materials and so i want you to know
+
+ align:start position:0%
+materials and so i want you to know
+ 
+
+ align:start position:0%
+materials and so i want you to know
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+it's called photoelectron spectroscopy
+
+ align:start position:0%
+it's called photoelectron spectroscopy
+ 
+
+ align:start position:0%
+it's called photoelectron spectroscopy
+photo
+
+ align:start position:0%
+photo
+ 
+
+ align:start position:0%
+photo
+electron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectroscopy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for short we will not
+
+ align:start position:0%
+and for short we will not
+ 
+
+ align:start position:0%
+and for short we will not
+write that out ever again i will write
+
+ align:start position:0%
+write that out ever again i will write
+ 
+
+ align:start position:0%
+write that out ever again i will write
+out pes
+
+ align:start position:0%
+out pes
+ 
+
+ align:start position:0%
+out pes
+photoelectron spectroscopy now this is a
+
+ align:start position:0%
+photoelectron spectroscopy now this is a
+ 
+
+ align:start position:0%
+photoelectron spectroscopy now this is a
+characterization
+
+ align:start position:0%
+characterization
+ 
+
+ align:start position:0%
+characterization
+tool i'm basically saying well what you
+
+ align:start position:0%
+tool i'm basically saying well what you
+ 
+
+ align:start position:0%
+tool i'm basically saying well what you
+know i need energy i'm going to get it
+
+ align:start position:0%
+know i need energy i'm going to get it
+ 
+
+ align:start position:0%
+know i need energy i'm going to get it
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+some photon source but i'm going to get
+
+ align:start position:0%
+some photon source but i'm going to get
+ 
+
+ align:start position:0%
+some photon source but i'm going to get
+enough to just blast all the electrons
+
+ align:start position:0%
+enough to just blast all the electrons
+ 
+
+ align:start position:0%
+enough to just blast all the electrons
+out of this material out of this atom
+
+ align:start position:0%
+out of this material out of this atom
+ 
+
+ align:start position:0%
+out of this material out of this atom
+because for now our material they're
+
+ align:start position:0%
+because for now our material they're
+ 
+
+ align:start position:0%
+because for now our material they're
+just atoms and i want to know about
+
+ align:start position:0%
+just atoms and i want to know about
+ 
+
+ align:start position:0%
+just atoms and i want to know about
+these atoms
+
+ align:start position:0%
+these atoms
+ 
+
+ align:start position:0%
+these atoms
+okay so let's take a look so what
+
+ align:start position:0%
+okay so let's take a look so what
+ 
+
+ align:start position:0%
+okay so let's take a look so what
+happens when i do this well
+
+ align:start position:0%
+happens when i do this well
+ 
+
+ align:start position:0%
+happens when i do this well
+let's see first of all i've got some
+
+ align:start position:0%
+let's see first of all i've got some
+ 
+
+ align:start position:0%
+let's see first of all i've got some
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+that we know is h new it's dependent on
+
+ align:start position:0%
+that we know is h new it's dependent on
+ 
+
+ align:start position:0%
+that we know is h new it's dependent on
+the frequency
+
+ align:start position:0%
+the frequency
+ 
+
+ align:start position:0%
+the frequency
+there are the frequencies they're the no
+
+ align:start position:0%
+there are the frequencies they're the no
+ 
+
+ align:start position:0%
+there are the frequencies they're the no
+they're there
+
+ align:start position:0%
+they're there
+ 
+
+ align:start position:0%
+they're there
+okay and so now i've got some adam
+
+ align:start position:0%
+okay and so now i've got some adam
+ 
+
+ align:start position:0%
+okay and so now i've got some adam
+here and what do i do well i look
+
+ align:start position:0%
+here and what do i do well i look
+ 
+
+ align:start position:0%
+here and what do i do well i look
+does anything happen no what about now i
+
+ align:start position:0%
+does anything happen no what about now i
+ 
+
+ align:start position:0%
+does anything happen no what about now i
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+okay what about now oh all of a sudden
+
+ align:start position:0%
+okay what about now oh all of a sudden
+ 
+
+ align:start position:0%
+okay what about now oh all of a sudden
+they come flying
+
+ align:start position:0%
+they come flying
+ 
+
+ align:start position:0%
+they come flying
+out electrons right
+
+ align:start position:0%
+out electrons right
+ 
+
+ align:start position:0%
+out electrons right
+and i measure their energy
+
+ align:start position:0%
+and i measure their energy
+ 
+
+ align:start position:0%
+and i measure their energy
+it kind of it goes right back to the
+
+ align:start position:0%
+it kind of it goes right back to the
+ 
+
+ align:start position:0%
+it kind of it goes right back to the
+photoelectric effect right that einstein
+
+ align:start position:0%
+photoelectric effect right that einstein
+ 
+
+ align:start position:0%
+photoelectric effect right that einstein
+was doing he was shining visible-ish
+
+ align:start position:0%
+was doing he was shining visible-ish
+ 
+
+ align:start position:0%
+was doing he was shining visible-ish
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+onto metals and seeing one electro but
+
+ align:start position:0%
+onto metals and seeing one electro but
+ 
+
+ align:start position:0%
+onto metals and seeing one electro but
+now i'm shining all sorts of light
+
+ align:start position:0%
+now i'm shining all sorts of light
+ 
+
+ align:start position:0%
+now i'm shining all sorts of light
+onto an atom and i want them all to come
+
+ align:start position:0%
+onto an atom and i want them all to come
+ 
+
+ align:start position:0%
+onto an atom and i want them all to come
+out not just the outer one
+
+ align:start position:0%
+out not just the outer one
+ 
+
+ align:start position:0%
+out not just the outer one
+and so well you can see if i measure
+
+ align:start position:0%
+and so well you can see if i measure
+ 
+
+ align:start position:0%
+and so well you can see if i measure
+so now i'm going to measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the kinetic energy of these and
+
+ align:start position:0%
+the kinetic energy of these and
+ 
+
+ align:start position:0%
+the kinetic energy of these and
+the ionization energy of that electron
+
+ align:start position:0%
+the ionization energy of that electron
+ 
+
+ align:start position:0%
+the ionization energy of that electron
+is going to equal
+
+ align:start position:0%
+is going to equal
+ 
+
+ align:start position:0%
+is going to equal
+how whatever the energy of the incident
+
+ align:start position:0%
+how whatever the energy of the incident
+ 
+
+ align:start position:0%
+how whatever the energy of the incident
+photon was
+
+ align:start position:0%
+photon was
+ 
+
+ align:start position:0%
+photon was
+minus the kinetic energy of the electron
+
+ align:start position:0%
+minus the kinetic energy of the electron
+ 
+
+ align:start position:0%
+minus the kinetic energy of the electron
+right that's what i want i want that
+
+ align:start position:0%
+right that's what i want i want that
+ 
+
+ align:start position:0%
+right that's what i want i want that
+ionization energy
+
+ align:start position:0%
+ionization energy
+ 
+
+ align:start position:0%
+ionization energy
+this is just to be clear ionization
+
+ align:start position:0%
+this is just to be clear ionization
+ 
+
+ align:start position:0%
+this is just to be clear ionization
+energy and like i said i want it all
+
+ align:start position:0%
+energy and like i said i want it all
+ 
+
+ align:start position:0%
+energy and like i said i want it all
+not just the first i want the second the
+
+ align:start position:0%
+not just the first i want the second the
+ 
+
+ align:start position:0%
+not just the first i want the second the
+third so now you see how so this is the
+
+ align:start position:0%
+third so now you see how so this is the
+ 
+
+ align:start position:0%
+third so now you see how so this is the
+experiment that you do what are the
+
+ align:start position:0%
+experiment that you do what are the
+ 
+
+ align:start position:0%
+experiment that you do what are the
+results
+
+ align:start position:0%
+results
+ 
+
+ align:start position:0%
+results
+well the results are really just what
+
+ align:start position:0%
+well the results are really just what
+ 
+
+ align:start position:0%
+well the results are really just what
+we've been doing but you turn it over
+
+ align:start position:0%
+we've been doing but you turn it over
+ 
+
+ align:start position:0%
+we've been doing but you turn it over
+so let's look at hydrogen okay now what
+
+ align:start position:0%
+so let's look at hydrogen okay now what
+ 
+
+ align:start position:0%
+so let's look at hydrogen okay now what
+have we been doing what do i mean by
+
+ align:start position:0%
+have we been doing what do i mean by
+ 
+
+ align:start position:0%
+have we been doing what do i mean by
+that what we've been doing is we've been
+
+ align:start position:0%
+that what we've been doing is we've been
+ 
+
+ align:start position:0%
+that what we've been doing is we've been
+going like this
+
+ align:start position:0%
+going like this
+ 
+
+ align:start position:0%
+going like this
+what's that okay this is hydrogen 1s1 i
+
+ align:start position:0%
+what's that okay this is hydrogen 1s1 i
+ 
+
+ align:start position:0%
+what's that okay this is hydrogen 1s1 i
+could do that or i could just label it
+
+ align:start position:0%
+could do that or i could just label it
+ 
+
+ align:start position:0%
+could do that or i could just label it
+the 1s and then you see the one electron
+
+ align:start position:0%
+the 1s and then you see the one electron
+ 
+
+ align:start position:0%
+the 1s and then you see the one electron
+right there
+
+ align:start position:0%
+right there
+ 
+
+ align:start position:0%
+right there
+now if i if i shine light on this
+
+ align:start position:0%
+now if i if i shine light on this
+ 
+
+ align:start position:0%
+now if i if i shine light on this
+and i measure the way that you do a pes
+
+ align:start position:0%
+and i measure the way that you do a pes
+ 
+
+ align:start position:0%
+and i measure the way that you do a pes
+for hydrogen is you would look at the
+
+ align:start position:0%
+for hydrogen is you would look at the
+ 
+
+ align:start position:0%
+for hydrogen is you would look at the
+ionization energy
+
+ align:start position:0%
+ionization energy
+ 
+
+ align:start position:0%
+ionization energy
+on the x-axis and this would be the
+
+ align:start position:0%
+on the x-axis and this would be the
+ 
+
+ align:start position:0%
+on the x-axis and this would be the
+relative
+
+ align:start position:0%
+relative
+ 
+
+ align:start position:0%
+relative
+electron count on the y-axis so you're
+
+ align:start position:0%
+electron count on the y-axis so you're
+ 
+
+ align:start position:0%
+electron count on the y-axis so you're
+just counting
+
+ align:start position:0%
+just counting
+ 
+
+ align:start position:0%
+just counting
+right and what you would see in hydrogen
+
+ align:start position:0%
+right and what you would see in hydrogen
+ 
+
+ align:start position:0%
+right and what you would see in hydrogen
+is there'd be a peak
+
+ align:start position:0%
+is there'd be a peak
+ 
+
+ align:start position:0%
+is there'd be a peak
+it'd look like this that's it
+
+ align:start position:0%
+it'd look like this that's it
+ 
+
+ align:start position:0%
+it'd look like this that's it
+if all the electrons in hydrogen one
+
+ align:start position:0%
+if all the electrons in hydrogen one
+ 
+
+ align:start position:0%
+if all the electrons in hydrogen one
+are in their ground state 1s then you
+
+ align:start position:0%
+are in their ground state 1s then you
+ 
+
+ align:start position:0%
+are in their ground state 1s then you
+would see a peak and this would be
+
+ align:start position:0%
+would see a peak and this would be
+ 
+
+ align:start position:0%
+would see a peak and this would be
+you know that it would be at minus 13.6
+
+ align:start position:0%
+you know that it would be at minus 13.6
+ 
+
+ align:start position:0%
+you know that it would be at minus 13.6
+right that would be the energy that it
+
+ align:start position:0%
+right that would be the energy that it
+ 
+
+ align:start position:0%
+right that would be the energy that it
+takes to ionize it
+
+ align:start position:0%
+takes to ionize it
+ 
+
+ align:start position:0%
+takes to ionize it
+and and this would be the 1s uh peak
+
+ align:start position:0%
+and and this would be the 1s uh peak
+ 
+
+ align:start position:0%
+and and this would be the 1s uh peak
+and that's what you measure now it gets
+
+ align:start position:0%
+and that's what you measure now it gets
+ 
+
+ align:start position:0%
+and that's what you measure now it gets
+more fun because now
+
+ align:start position:0%
+more fun because now
+ 
+
+ align:start position:0%
+more fun because now
+i can also look at other elements so
+
+ align:start position:0%
+i can also look at other elements so
+ 
+
+ align:start position:0%
+i can also look at other elements so
+let's draw helium
+
+ align:start position:0%
+let's draw helium
+ 
+
+ align:start position:0%
+let's draw helium
+underneath it i'm going to try to
+
+ align:start position:0%
+underneath it i'm going to try to
+ 
+
+ align:start position:0%
+underneath it i'm going to try to
+squeeze it in
+
+ align:start position:0%
+squeeze it in
+ 
+
+ align:start position:0%
+squeeze it in
+if i look at helium well helium is also
+
+ align:start position:0%
+if i look at helium well helium is also
+ 
+
+ align:start position:0%
+if i look at helium well helium is also
+1s and its pes
+
+ align:start position:0%
+1s and its pes
+ 
+
+ align:start position:0%
+1s and its pes
+would be so this is now
+
+ align:start position:0%
+would be so this is now
+ 
+
+ align:start position:0%
+would be so this is now
+ionization energy this is the pes plot
+
+ align:start position:0%
+ionization energy this is the pes plot
+ 
+
+ align:start position:0%
+ionization energy this is the pes plot
+and the pes for helium would be also
+
+ align:start position:0%
+and the pes for helium would be also
+ 
+
+ align:start position:0%
+and the pes for helium would be also
+the 1s but the relative counts
+
+ align:start position:0%
+the 1s but the relative counts
+ 
+
+ align:start position:0%
+the 1s but the relative counts
+would be twice as high so the peak of
+
+ align:start position:0%
+would be twice as high so the peak of
+ 
+
+ align:start position:0%
+would be twice as high so the peak of
+helium would be twice as high
+
+ align:start position:0%
+helium would be twice as high
+ 
+
+ align:start position:0%
+helium would be twice as high
+as the peak of hydrogen because you know
+
+ align:start position:0%
+as the peak of hydrogen because you know
+ 
+
+ align:start position:0%
+as the peak of hydrogen because you know
+for the same
+
+ align:start position:0%
+for the same
+ 
+
+ align:start position:0%
+for the same
+number of photons in i'm getting that
+
+ align:start position:0%
+number of photons in i'm getting that
+ 
+
+ align:start position:0%
+number of photons in i'm getting that
+many more i've got both these electrons
+
+ align:start position:0%
+many more i've got both these electrons
+ 
+
+ align:start position:0%
+many more i've got both these electrons
+coming out
+
+ align:start position:0%
+coming out
+ 
+
+ align:start position:0%
+coming out
+right so the relative peaks
+
+ align:start position:0%
+right so the relative peaks
+ 
+
+ align:start position:0%
+right so the relative peaks
+the relative peaks i got two more that
+
+ align:start position:0%
+the relative peaks i got two more that
+ 
+
+ align:start position:0%
+the relative peaks i got two more that
+can come out
+
+ align:start position:0%
+can come out
+ 
+
+ align:start position:0%
+can come out
+right so this p now if i go to okay now
+
+ align:start position:0%
+right so this p now if i go to okay now
+ 
+
+ align:start position:0%
+right so this p now if i go to okay now
+it gets really interesting because now
+
+ align:start position:0%
+it gets really interesting because now
+ 
+
+ align:start position:0%
+it gets really interesting because now
+i'm oh
+
+ align:start position:0%
+i'm oh
+ 
+
+ align:start position:0%
+i'm oh
+i even have room which is making me very
+
+ align:start position:0%
+i even have room which is making me very
+ 
+
+ align:start position:0%
+i even have room which is making me very
+happy
+
+ align:start position:0%
+happy
+ 
+
+ align:start position:0%
+happy
+because now i can do lithium right here
+
+ align:start position:0%
+because now i can do lithium right here
+ 
+
+ align:start position:0%
+because now i can do lithium right here
+and if you look at lithium
+
+ align:start position:0%
+and if you look at lithium
+ 
+
+ align:start position:0%
+and if you look at lithium
+lithium goes like this
+
+ align:start position:0%
+lithium goes like this
+ 
+
+ align:start position:0%
+lithium goes like this
+right and if i look at a pes
+
+ align:start position:0%
+right and if i look at a pes
+ 
+
+ align:start position:0%
+right and if i look at a pes
+plot of lithium the ionization energy
+
+ align:start position:0%
+plot of lithium the ionization energy
+ 
+
+ align:start position:0%
+plot of lithium the ionization energy
+and the relative
+
+ align:start position:0%
+and the relative
+ 
+
+ align:start position:0%
+and the relative
+electron count okay i'm going to have
+
+ align:start position:0%
+electron count okay i'm going to have
+ 
+
+ align:start position:0%
+electron count okay i'm going to have
+those 1s electrons filled
+
+ align:start position:0%
+those 1s electrons filled
+ 
+
+ align:start position:0%
+those 1s electrons filled
+and there's going to be another energy
+
+ align:start position:0%
+and there's going to be another energy
+ 
+
+ align:start position:0%
+and there's going to be another energy
+where the 2s electrons are so this is
+
+ align:start position:0%
+where the 2s electrons are so this is
+ 
+
+ align:start position:0%
+where the 2s electrons are so this is
+energy here
+
+ align:start position:0%
+energy here
+ 
+
+ align:start position:0%
+energy here
+these are the orbitals and then
+
+ align:start position:0%
+these are the orbitals and then
+ 
+
+ align:start position:0%
+these are the orbitals and then
+somewhere over here is going to be
+
+ align:start position:0%
+somewhere over here is going to be
+ 
+
+ align:start position:0%
+somewhere over here is going to be
+a peak that's exactly half as high
+
+ align:start position:0%
+a peak that's exactly half as high
+ 
+
+ align:start position:0%
+a peak that's exactly half as high
+exactly i mean that makes a lot of sense
+
+ align:start position:0%
+exactly i mean that makes a lot of sense
+ 
+
+ align:start position:0%
+exactly i mean that makes a lot of sense
+because there's half as
+
+ align:start position:0%
+because there's half as
+ 
+
+ align:start position:0%
+because there's half as
+right there's twice as many electrons
+
+ align:start position:0%
+right there's twice as many electrons
+ 
+
+ align:start position:0%
+right there's twice as many electrons
+it's the relative electron count in the
+
+ align:start position:0%
+it's the relative electron count in the
+ 
+
+ align:start position:0%
+it's the relative electron count in the
+atom
+
+ align:start position:0%
+atom
+ 
+
+ align:start position:0%
+atom
+there's twice as many electrons coming
+
+ align:start position:0%
+there's twice as many electrons coming
+ 
+
+ align:start position:0%
+there's twice as many electrons coming
+out of that
+
+ align:start position:0%
+out of that
+ 
+
+ align:start position:0%
+out of that
+1s orbital in the 2s so i'm going to get
+
+ align:start position:0%
+1s orbital in the 2s so i'm going to get
+ 
+
+ align:start position:0%
+1s orbital in the 2s so i'm going to get
+a half as high peak here
+
+ align:start position:0%
+a half as high peak here
+ 
+
+ align:start position:0%
+a half as high peak here
+right and and usually now this i just
+
+ align:start position:0%
+right and and usually now this i just
+ 
+
+ align:start position:0%
+right and and usually now this i just
+told you
+
+ align:start position:0%
+told you
+ 
+
+ align:start position:0%
+told you
+the lithium atom this electron is 5
+
+ align:start position:0%
+the lithium atom this electron is 5
+ 
+
+ align:start position:0%
+the lithium atom this electron is 5
+point something four ish electron volts
+
+ align:start position:0%
+point something four ish electron volts
+ 
+
+ align:start position:0%
+point something four ish electron volts
+to remove
+
+ align:start position:0%
+to remove
+ 
+
+ align:start position:0%
+to remove
+this is 122. so literally for lithium
+
+ align:start position:0%
+this is 122. so literally for lithium
+ 
+
+ align:start position:0%
+this is 122. so literally for lithium
+this would be 122. this would be 5.4
+
+ align:start position:0%
+this would be 122. this would be 5.4
+ 
+
+ align:start position:0%
+this would be 122. this would be 5.4
+and you know it's ionization energy and
+
+ align:start position:0%
+and you know it's ionization energy and
+ 
+
+ align:start position:0%
+and you know it's ionization energy and
+ev
+
+ align:start position:0%
+ev
+ 
+
+ align:start position:0%
+ev
+and what you would do is you would draw
+
+ align:start position:0%
+and what you would do is you would draw
+ 
+
+ align:start position:0%
+and what you would do is you would draw
+the axis like that so you don't have to
+
+ align:start position:0%
+the axis like that so you don't have to
+ 
+
+ align:start position:0%
+the axis like that so you don't have to
+put this all the way over here
+
+ align:start position:0%
+put this all the way over here
+ 
+
+ align:start position:0%
+put this all the way over here
+right so we often what and all this
+
+ align:start position:0%
+right so we often what and all this
+ 
+
+ align:start position:0%
+right so we often what and all this
+means is i've broken up
+
+ align:start position:0%
+means is i've broken up
+ 
+
+ align:start position:0%
+means is i've broken up
+you know the the axis and it's
+
+ align:start position:0%
+you know the the axis and it's
+ 
+
+ align:start position:0%
+you know the the axis and it's
+continuing to count here
+
+ align:start position:0%
+continuing to count here
+ 
+
+ align:start position:0%
+continuing to count here
+in a different scale right
+
+ align:start position:0%
+in a different scale right
+ 
+
+ align:start position:0%
+in a different scale right
+these pes plots are absolutely essential
+
+ align:start position:0%
+these pes plots are absolutely essential
+ 
+
+ align:start position:0%
+these pes plots are absolutely essential
+in understanding uh atoms
+
+ align:start position:0%
+in understanding uh atoms
+ 
+
+ align:start position:0%
+in understanding uh atoms
+and materials because look at what you
+
+ align:start position:0%
+and materials because look at what you
+ 
+
+ align:start position:0%
+and materials because look at what you
+get you get
+
+ align:start position:0%
+get you get
+ 
+
+ align:start position:0%
+get you get
+literally the electron filling plot
+
+ align:start position:0%
+literally the electron filling plot
+ 
+
+ align:start position:0%
+literally the electron filling plot
+turned over
+
+ align:start position:0%
+turned over
+ 
+
+ align:start position:0%
+turned over
+it's incredible you get it turned over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can write this as oh let's just
+
+ align:start position:0%
+and you can write this as oh let's just
+ 
+
+ align:start position:0%
+and you can write this as oh let's just
+do this story you know
+
+ align:start position:0%
+do this story you know
+ 
+
+ align:start position:0%
+do this story you know
+i could write this as 1s2 we have so
+
+ align:start position:0%
+i could write this as 1s2 we have so
+ 
+
+ align:start position:0%
+i could write this as 1s2 we have so
+many options now 2s1
+
+ align:start position:0%
+many options now 2s1
+ 
+
+ align:start position:0%
+many options now 2s1
+right i could write this as
+
+ align:start position:0%
+right i could write this as
+ 
+
+ align:start position:0%
+right i could write this as
+helium 2s1 that would be like using the
+
+ align:start position:0%
+helium 2s1 that would be like using the
+ 
+
+ align:start position:0%
+helium 2s1 that would be like using the
+noble gas
+
+ align:start position:0%
+noble gas
+ 
+
+ align:start position:0%
+noble gas
+right i could make what people you know
+
+ align:start position:0%
+right i could make what people you know
+ 
+
+ align:start position:0%
+right i could make what people you know
+there's so many
+
+ align:start position:0%
+there's so many
+ 
+
+ align:start position:0%
+there's so many
+i can make box plots oh box plots
+
+ align:start position:0%
+i can make box plots oh box plots
+ 
+
+ align:start position:0%
+i can make box plots oh box plots
+you can do this some people really like
+
+ align:start position:0%
+you can do this some people really like
+ 
+
+ align:start position:0%
+you can do this some people really like
+putting things in boxes
+
+ align:start position:0%
+putting things in boxes
+ 
+
+ align:start position:0%
+putting things in boxes
+1s 2s box plots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this is all meaning these
+
+ align:start position:0%
+right so this is all meaning these
+ 
+
+ align:start position:0%
+right so this is all meaning these
+all say the same thing
+
+ align:start position:0%
+all say the same thing
+ 
+
+ align:start position:0%
+all say the same thing
+lithium they all say lithium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right photoelectron spectra so i could
+
+ align:start position:0%
+right photoelectron spectra so i could
+ 
+
+ align:start position:0%
+right photoelectron spectra so i could
+ask you questions like this
+
+ align:start position:0%
+ask you questions like this
+ 
+
+ align:start position:0%
+ask you questions like this
+there's one ionization energy megajoules
+
+ align:start position:0%
+there's one ionization energy megajoules
+ 
+
+ align:start position:0%
+there's one ionization energy megajoules
+per mole
+
+ align:start position:0%
+per mole
+ 
+
+ align:start position:0%
+per mole
+relative number of electrons this
+
+ align:start position:0%
+relative number of electrons this
+ 
+
+ align:start position:0%
+relative number of electrons this
+element has a charge of two plus and the
+
+ align:start position:0%
+element has a charge of two plus and the
+ 
+
+ align:start position:0%
+element has a charge of two plus and the
+pes shown below what is it
+
+ align:start position:0%
+pes shown below what is it
+ 
+
+ align:start position:0%
+pes shown below what is it
+i said well okay i know one s two
+
+ align:start position:0%
+i said well okay i know one s two
+ 
+
+ align:start position:0%
+i said well okay i know one s two
+two s two and since this is going up
+
+ align:start position:0%
+two s two and since this is going up
+ 
+
+ align:start position:0%
+two s two and since this is going up
+three times as high that sure looks like
+
+ align:start position:0%
+three times as high that sure looks like
+ 
+
+ align:start position:0%
+three times as high that sure looks like
+two p
+
+ align:start position:0%
+two p
+ 
+
+ align:start position:0%
+two p
+six doesn't it that looks like two 2p6
+
+ align:start position:0%
+six doesn't it that looks like two 2p6
+ 
+
+ align:start position:0%
+six doesn't it that looks like two 2p6
+remember it's this turned over on its
+
+ align:start position:0%
+remember it's this turned over on its
+ 
+
+ align:start position:0%
+remember it's this turned over on its
+side right where the peak height
+
+ align:start position:0%
+side right where the peak height
+ 
+
+ align:start position:0%
+side right where the peak height
+corresponds to the filling
+
+ align:start position:0%
+corresponds to the filling
+ 
+
+ align:start position:0%
+corresponds to the filling
+that's what that experiment gives you
+
+ align:start position:0%
+that's what that experiment gives you
+ 
+
+ align:start position:0%
+that's what that experiment gives you
+2p6 well then it must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have your periodic table uh-huh
+
+ align:start position:0%
+you have your periodic table uh-huh
+ 
+
+ align:start position:0%
+you have your periodic table uh-huh
+because then tight
+
+ align:start position:0%
+because then tight
+ 
+
+ align:start position:0%
+because then tight
+neon it must be neon
+
+ align:start position:0%
+neon it must be neon
+ 
+
+ align:start position:0%
+neon it must be neon
+no who said no no don't just
+
+ align:start position:0%
+no who said no no don't just
+ 
+
+ align:start position:0%
+no who said no no don't just
+yes it can't be neon because of the
+
+ align:start position:0%
+yes it can't be neon because of the
+ 
+
+ align:start position:0%
+yes it can't be neon because of the
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+it's got a charge of two plus oh
+
+ align:start position:0%
+it's got a charge of two plus oh
+ 
+
+ align:start position:0%
+it's got a charge of two plus oh
+tricky tricky tricky
+
+ align:start position:0%
+tricky tricky tricky
+ 
+
+ align:start position:0%
+tricky tricky tricky
+magnesium it must be magnesium that is
+
+ align:start position:0%
+magnesium it must be magnesium that is
+ 
+
+ align:start position:0%
+magnesium it must be magnesium that is
+the pe
+
+ align:start position:0%
+the pe
+ 
+
+ align:start position:0%
+the pe
+right but it's magnesium two plus
+
+ align:start position:0%
+right but it's magnesium two plus
+ 
+
+ align:start position:0%
+right but it's magnesium two plus
+because i said it had a char
+
+ align:start position:0%
+because i said it had a char
+ 
+
+ align:start position:0%
+because i said it had a char
+thank you shout out i appreciate that
+
+ align:start position:0%
+thank you shout out i appreciate that
+ 
+
+ align:start position:0%
+thank you shout out i appreciate that
+okay so that's how that's the power of
+
+ align:start position:0%
+okay so that's how that's the power of
+ 
+
+ align:start position:0%
+okay so that's how that's the power of
+the photoelectron spectra and we'll be
+
+ align:start position:0%
+the photoelectron spectra and we'll be
+ 
+
+ align:start position:0%
+the photoelectron spectra and we'll be
+using it
+
+ align:start position:0%
+using it
+ 
+
+ align:start position:0%
+using it
+in the class and this tells us about how
+
+ align:start position:0%
+in the class and this tells us about how
+ 
+
+ align:start position:0%
+in the class and this tells us about how
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+leave atoms it tells us about ionization
+
+ align:start position:0%
+leave atoms it tells us about ionization
+ 
+
+ align:start position:0%
+leave atoms it tells us about ionization
+energies not just the first
+
+ align:start position:0%
+energies not just the first
+ 
+
+ align:start position:0%
+energies not just the first
+which is the one all the way out here to
+
+ align:start position:0%
+which is the one all the way out here to
+ 
+
+ align:start position:0%
+which is the one all the way out here to
+the right on the pes plot but all of
+
+ align:start position:0%
+the right on the pes plot but all of
+ 
+
+ align:start position:0%
+the right on the pes plot but all of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+because i shine enough energy light to
+
+ align:start position:0%
+because i shine enough energy light to
+ 
+
+ align:start position:0%
+because i shine enough energy light to
+get them all out
+
+ align:start position:0%
+get them all out
+ 
+
+ align:start position:0%
+get them all out
+now you can also so that's about losing
+
+ align:start position:0%
+now you can also so that's about losing
+ 
+
+ align:start position:0%
+now you can also so that's about losing
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+you can also gain them and um and so
+
+ align:start position:0%
+you can also gain them and um and so
+ 
+
+ align:start position:0%
+you can also gain them and um and so
+i mentioned this um a little bit but i
+
+ align:start position:0%
+i mentioned this um a little bit but i
+ 
+
+ align:start position:0%
+i mentioned this um a little bit but i
+just for completeness i want to come
+
+ align:start position:0%
+just for completeness i want to come
+ 
+
+ align:start position:0%
+just for completeness i want to come
+back to this you have electro
+
+ align:start position:0%
+back to this you have electro
+ 
+
+ align:start position:0%
+back to this you have electro
+you have ionization energy right
+
+ align:start position:0%
+you have ionization energy right
+ 
+
+ align:start position:0%
+you have ionization energy right
+which is how much energy it takes to
+
+ align:start position:0%
+which is how much energy it takes to
+ 
+
+ align:start position:0%
+which is how much energy it takes to
+pull an electron out you also have
+
+ align:start position:0%
+pull an electron out you also have
+ 
+
+ align:start position:0%
+pull an electron out you also have
+electron affinity and because some atoms
+
+ align:start position:0%
+electron affinity and because some atoms
+ 
+
+ align:start position:0%
+electron affinity and because some atoms
+also uh might want electrons
+
+ align:start position:0%
+also uh might want electrons
+ 
+
+ align:start position:0%
+also uh might want electrons
+and so when you look at those plots it's
+
+ align:start position:0%
+and so when you look at those plots it's
+ 
+
+ align:start position:0%
+and so when you look at those plots it's
+actually all makes sense again
+
+ align:start position:0%
+actually all makes sense again
+ 
+
+ align:start position:0%
+actually all makes sense again
+look at this some atoms like chlorine
+
+ align:start position:0%
+look at this some atoms like chlorine
+ 
+
+ align:start position:0%
+look at this some atoms like chlorine
+this is electron affinity by atom number
+
+ align:start position:0%
+this is electron affinity by atom number
+ 
+
+ align:start position:0%
+this is electron affinity by atom number
+some atoms like chlorine really want
+
+ align:start position:0%
+some atoms like chlorine really want
+ 
+
+ align:start position:0%
+some atoms like chlorine really want
+another electron why
+
+ align:start position:0%
+another electron why
+ 
+
+ align:start position:0%
+another electron why
+because it's got an incomplete shell
+
+ align:start position:0%
+because it's got an incomplete shell
+ 
+
+ align:start position:0%
+because it's got an incomplete shell
+it's so it's so close it just needs one
+
+ align:start position:0%
+it's so it's so close it just needs one
+ 
+
+ align:start position:0%
+it's so it's so close it just needs one
+more electron
+
+ align:start position:0%
+more electron
+ 
+
+ align:start position:0%
+more electron
+to fill that outer shell and it wants it
+
+ align:start position:0%
+to fill that outer shell and it wants it
+ 
+
+ align:start position:0%
+to fill that outer shell and it wants it
+and that's the electron affinity is how
+
+ align:start position:0%
+and that's the electron affinity is how
+ 
+
+ align:start position:0%
+and that's the electron affinity is how
+much does it want it now
+
+ align:start position:0%
+much does it want it now
+ 
+
+ align:start position:0%
+much does it want it now
+want happiness happiness lower energy
+
+ align:start position:0%
+want happiness happiness lower energy
+ 
+
+ align:start position:0%
+want happiness happiness lower energy
+that's what this so if you're not going
+
+ align:start position:0%
+that's what this so if you're not going
+ 
+
+ align:start position:0%
+that's what this so if you're not going
+to lower your energy
+
+ align:start position:0%
+to lower your energy
+ 
+
+ align:start position:0%
+to lower your energy
+with another electron then you're just
+
+ align:start position:0%
+with another electron then you're just
+ 
+
+ align:start position:0%
+with another electron then you're just
+saying no you
+
+ align:start position:0%
+saying no you
+ 
+
+ align:start position:0%
+saying no you
+just say no zero i will not take an
+
+ align:start position:0%
+just say no zero i will not take an
+ 
+
+ align:start position:0%
+just say no zero i will not take an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+because if you give me one my energy is
+
+ align:start position:0%
+because if you give me one my energy is
+ 
+
+ align:start position:0%
+because if you give me one my energy is
+going to go up and i will be a less
+
+ align:start position:0%
+going to go up and i will be a less
+ 
+
+ align:start position:0%
+going to go up and i will be a less
+happy atom and you can make
+
+ align:start position:0%
+happy atom and you can make
+ 
+
+ align:start position:0%
+happy atom and you can make
+that makes sense too right filled shells
+
+ align:start position:0%
+that makes sense too right filled shells
+ 
+
+ align:start position:0%
+that makes sense too right filled shells
+they don't nitrogen
+
+ align:start position:0%
+they don't nitrogen
+ 
+
+ align:start position:0%
+they don't nitrogen
+nitrogen's got a a half-filled shell no
+
+ align:start position:0%
+nitrogen's got a a half-filled shell no
+ 
+
+ align:start position:0%
+nitrogen's got a a half-filled shell no
+to that electron
+
+ align:start position:0%
+to that electron
+ 
+
+ align:start position:0%
+to that electron
+i like my half-filled shell it gives me
+
+ align:start position:0%
+i like my half-filled shell it gives me
+ 
+
+ align:start position:0%
+i like my half-filled shell it gives me
+a little added stability
+
+ align:start position:0%
+a little added stability
+ 
+
+ align:start position:0%
+a little added stability
+a little extra kick if you give me that
+
+ align:start position:0%
+a little extra kick if you give me that
+ 
+
+ align:start position:0%
+a little extra kick if you give me that
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+you know i'm gonna have not have that
+
+ align:start position:0%
+you know i'm gonna have not have that
+ 
+
+ align:start position:0%
+you know i'm gonna have not have that
+added stability i don't want it
+
+ align:start position:0%
+added stability i don't want it
+ 
+
+ align:start position:0%
+added stability i don't want it
+zero right zero
+
+ align:start position:0%
+zero right zero
+ 
+
+ align:start position:0%
+zero right zero
+losing electrons gaining electrons
+
+ align:start position:0%
+losing electrons gaining electrons
+ 
+
+ align:start position:0%
+losing electrons gaining electrons
+losing electrons gaining electrons
+
+ align:start position:0%
+losing electrons gaining electrons
+ 
+
+ align:start position:0%
+losing electrons gaining electrons
+why does it matter why does it matter
+
+ align:start position:0%
+why does it matter why does it matter
+ 
+
+ align:start position:0%
+why does it matter why does it matter
+well we made a solid last week today the
+
+ align:start position:0%
+well we made a solid last week today the
+ 
+
+ align:start position:0%
+well we made a solid last week today the
+answer is obvious
+
+ align:start position:0%
+answer is obvious
+ 
+
+ align:start position:0%
+answer is obvious
+it matters because of danish wind
+
+ align:start position:0%
+it matters because of danish wind
+ 
+
+ align:start position:0%
+it matters because of danish wind
+obviously 43
+
+ align:start position:0%
+obviously 43
+ 
+
+ align:start position:0%
+obviously 43
+in 2014 43 of all the electrical energy
+
+ align:start position:0%
+in 2014 43 of all the electrical energy
+ 
+
+ align:start position:0%
+in 2014 43 of all the electrical energy
+in denmark came from wind
+
+ align:start position:0%
+in denmark came from wind
+ 
+
+ align:start position:0%
+in denmark came from wind
+it's higher now but see now this is a
+
+ align:start position:0%
+it's higher now but see now this is a
+ 
+
+ align:start position:0%
+it's higher now but see now this is a
+quarter of the danish wind
+
+ align:start position:0%
+quarter of the danish wind
+ 
+
+ align:start position:0%
+quarter of the danish wind
+i got i only gave you a two minute
+
+ align:start position:0%
+i got i only gave you a two minute
+ 
+
+ align:start position:0%
+i got i only gave you a two minute
+hemodialysis
+
+ align:start position:0%
+hemodialysis
+ 
+
+ align:start position:0%
+hemodialysis
+why this matters on wednesday so i'm
+
+ align:start position:0%
+why this matters on wednesday so i'm
+ 
+
+ align:start position:0%
+why this matters on wednesday so i'm
+going extended today
+
+ align:start position:0%
+going extended today
+ 
+
+ align:start position:0%
+going extended today
+just a little bit but danish wind
+
+ align:start position:0%
+just a little bit but danish wind
+ 
+
+ align:start position:0%
+just a little bit but danish wind
+people are very dependable so over a
+
+ align:start position:0%
+people are very dependable so over a
+ 
+
+ align:start position:0%
+people are very dependable so over a
+three-month period
+
+ align:start position:0%
+three-month period
+ 
+
+ align:start position:0%
+three-month period
+this is how much we need energy
+
+ align:start position:0%
+this is how much we need energy
+ 
+
+ align:start position:0%
+this is how much we need energy
+electricity
+
+ align:start position:0%
+electricity
+ 
+
+ align:start position:0%
+electricity
+but that look at the wind supply that
+
+ align:start position:0%
+but that look at the wind supply that
+ 
+
+ align:start position:0%
+but that look at the wind supply that
+but sometimes it's really there for us
+
+ align:start position:0%
+but sometimes it's really there for us
+ 
+
+ align:start position:0%
+but sometimes it's really there for us
+sometimes it's not at all there
+
+ align:start position:0%
+sometimes it's not at all there
+ 
+
+ align:start position:0%
+sometimes it's not at all there
+sometimes it's predictable sometimes
+
+ align:start position:0%
+sometimes it's predictable sometimes
+ 
+
+ align:start position:0%
+sometimes it's predictable sometimes
+it's not at all predictable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with that much of your electricity
+
+ align:start position:0%
+with that much of your electricity
+ 
+
+ align:start position:0%
+with that much of your electricity
+coming from this type of unreliable
+
+ align:start position:0%
+coming from this type of unreliable
+ 
+
+ align:start position:0%
+coming from this type of unreliable
+resource that is a huge challenge now
+
+ align:start position:0%
+resource that is a huge challenge now
+ 
+
+ align:start position:0%
+resource that is a huge challenge now
+even if you go out to arizona
+
+ align:start position:0%
+even if you go out to arizona
+ 
+
+ align:start position:0%
+even if you go out to arizona
+and you talk about solar system
+
+ align:start position:0%
+and you talk about solar system
+ 
+
+ align:start position:0%
+and you talk about solar system
+arizona's sunny all the time no
+
+ align:start position:0%
+arizona's sunny all the time no
+ 
+
+ align:start position:0%
+arizona's sunny all the time no
+not sunny all the time most of the time
+
+ align:start position:0%
+not sunny all the time most of the time
+ 
+
+ align:start position:0%
+not sunny all the time most of the time
+more than boston
+
+ align:start position:0%
+more than boston
+ 
+
+ align:start position:0%
+more than boston
+but this is the sun in arizona that's
+
+ align:start position:0%
+but this is the sun in arizona that's
+ 
+
+ align:start position:0%
+but this is the sun in arizona that's
+the power you're getting from it
+
+ align:start position:0%
+the power you're getting from it
+ 
+
+ align:start position:0%
+the power you're getting from it
+and look at this these these are just
+
+ align:start position:0%
+and look at this these these are just
+ 
+
+ align:start position:0%
+and look at this these these are just
+clouds because arizona does have clouds
+
+ align:start position:0%
+clouds because arizona does have clouds
+ 
+
+ align:start position:0%
+clouds because arizona does have clouds
+and they passed by and they blocked the
+
+ align:start position:0%
+and they passed by and they blocked the
+ 
+
+ align:start position:0%
+and they passed by and they blocked the
+sun do you know what a nightmare this is
+
+ align:start position:0%
+sun do you know what a nightmare this is
+ 
+
+ align:start position:0%
+sun do you know what a nightmare this is
+for a grid operator
+
+ align:start position:0%
+for a grid operator
+ 
+
+ align:start position:0%
+for a grid operator
+if a lot of your customers get their
+
+ align:start position:0%
+if a lot of your customers get their
+ 
+
+ align:start position:0%
+if a lot of your customers get their
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+in this way yeah and all of a sudden
+
+ align:start position:0%
+in this way yeah and all of a sudden
+ 
+
+ align:start position:0%
+in this way yeah and all of a sudden
+you know half of your supply of energy
+
+ align:start position:0%
+you know half of your supply of energy
+ 
+
+ align:start position:0%
+you know half of your supply of energy
+just turns off
+
+ align:start position:0%
+just turns off
+ 
+
+ align:start position:0%
+just turns off
+right i mean that's a huge problem right
+
+ align:start position:0%
+right i mean that's a huge problem right
+ 
+
+ align:start position:0%
+right i mean that's a huge problem right
+and this is one of the most
+
+ align:start position:0%
+and this is one of the most
+ 
+
+ align:start position:0%
+and this is one of the most
+limiting factors for increasing
+
+ align:start position:0%
+limiting factors for increasing
+ 
+
+ align:start position:0%
+limiting factors for increasing
+to a large extent the amount of
+
+ align:start position:0%
+to a large extent the amount of
+ 
+
+ align:start position:0%
+to a large extent the amount of
+renewables we have on our grid
+
+ align:start position:0%
+renewables we have on our grid
+ 
+
+ align:start position:0%
+renewables we have on our grid
+and so of course i know a lot of you are
+
+ align:start position:0%
+and so of course i know a lot of you are
+ 
+
+ align:start position:0%
+and so of course i know a lot of you are
+thinking well just store it and that's
+
+ align:start position:0%
+thinking well just store it and that's
+ 
+
+ align:start position:0%
+thinking well just store it and that's
+what we need to do
+
+ align:start position:0%
+what we need to do
+ 
+
+ align:start position:0%
+what we need to do
+right but it turns out that really one
+
+ align:start position:0%
+right but it turns out that really one
+ 
+
+ align:start position:0%
+right but it turns out that really one
+of the only ways we have to store energy
+
+ align:start position:0%
+of the only ways we have to store energy
+ 
+
+ align:start position:0%
+of the only ways we have to store energy
+at this large scale
+
+ align:start position:0%
+at this large scale
+ 
+
+ align:start position:0%
+at this large scale
+is pumped hydro and you see we're
+
+ align:start position:0%
+is pumped hydro and you see we're
+ 
+
+ align:start position:0%
+is pumped hydro and you see we're
+pumping water up up a hill
+
+ align:start position:0%
+pumping water up up a hill
+ 
+
+ align:start position:0%
+pumping water up up a hill
+when i have excess i pump water up a
+
+ align:start position:0%
+when i have excess i pump water up a
+ 
+
+ align:start position:0%
+when i have excess i pump water up a
+hill
+
+ align:start position:0%
+hill
+ 
+
+ align:start position:0%
+hill
+and then when i need i roll it back down
+
+ align:start position:0%
+and then when i need i roll it back down
+ 
+
+ align:start position:0%
+and then when i need i roll it back down
+and i turn a turbine with it right i'm
+
+ align:start position:0%
+and i turn a turbine with it right i'm
+ 
+
+ align:start position:0%
+and i turn a turbine with it right i'm
+literally just
+
+ align:start position:0%
+literally just
+ 
+
+ align:start position:0%
+literally just
+trading energy potential energy right
+
+ align:start position:0%
+trading energy potential energy right
+ 
+
+ align:start position:0%
+trading energy potential energy right
+and then i bring it back kinetic energy
+
+ align:start position:0%
+and then i bring it back kinetic energy
+ 
+
+ align:start position:0%
+and then i bring it back kinetic energy
+and then i make electricity
+
+ align:start position:0%
+and then i make electricity
+ 
+
+ align:start position:0%
+and then i make electricity
+now the problem is that pumped hydro you
+
+ align:start position:0%
+now the problem is that pumped hydro you
+ 
+
+ align:start position:0%
+now the problem is that pumped hydro you
+know pump
+
+ align:start position:0%
+know pump
+ 
+
+ align:start position:0%
+know pump
+well as you can see pumped hydra is
+
+ align:start position:0%
+well as you can see pumped hydra is
+ 
+
+ align:start position:0%
+well as you can see pumped hydra is
+going to be good where there's hydro
+
+ align:start position:0%
+going to be good where there's hydro
+ 
+
+ align:start position:0%
+going to be good where there's hydro
+where there's water
+
+ align:start position:0%
+where there's water
+ 
+
+ align:start position:0%
+where there's water
+so that's limiting but it also is a very
+
+ align:start position:0%
+so that's limiting but it also is a very
+ 
+
+ align:start position:0%
+so that's limiting but it also is a very
+low
+
+ align:start position:0%
+low
+ 
+
+ align:start position:0%
+low
+uh aerial density and there are also a
+
+ align:start position:0%
+uh aerial density and there are also a
+ 
+
+ align:start position:0%
+uh aerial density and there are also a
+lot of uh
+
+ align:start position:0%
+lot of uh
+ 
+
+ align:start position:0%
+lot of uh
+environmental challenges with making
+
+ align:start position:0%
+environmental challenges with making
+ 
+
+ align:start position:0%
+environmental challenges with making
+this work in a way that doesn't
+
+ align:start position:0%
+this work in a way that doesn't
+ 
+
+ align:start position:0%
+this work in a way that doesn't
+uh harm the environment so there are a
+
+ align:start position:0%
+uh harm the environment so there are a
+ 
+
+ align:start position:0%
+uh harm the environment so there are a
+lot of issues with scaling up pumped
+
+ align:start position:0%
+lot of issues with scaling up pumped
+ 
+
+ align:start position:0%
+lot of issues with scaling up pumped
+hydro
+
+ align:start position:0%
+hydro
+ 
+
+ align:start position:0%
+hydro
+a lot of issues as a storage and so i
+
+ align:start position:0%
+a lot of issues as a storage and so i
+ 
+
+ align:start position:0%
+a lot of issues as a storage and so i
+asked well what else can we pump up
+
+ align:start position:0%
+asked well what else can we pump up
+ 
+
+ align:start position:0%
+asked well what else can we pump up
+hills
+
+ align:start position:0%
+hills
+ 
+
+ align:start position:0%
+hills
+and we know what the answer is because
+
+ align:start position:0%
+and we know what the answer is because
+ 
+
+ align:start position:0%
+and we know what the answer is because
+it's what we're talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ions where are they ions we can pump
+
+ align:start position:0%
+ions where are they ions we can pump
+ 
+
+ align:start position:0%
+ions where are they ions we can pump
+ions up hills
+
+ align:start position:0%
+ions up hills
+ 
+
+ align:start position:0%
+ions up hills
+there's my picture look at that right
+
+ align:start position:0%
+there's my picture look at that right
+ 
+
+ align:start position:0%
+there's my picture look at that right
+ions and you know what this is it's a
+
+ align:start position:0%
+ions and you know what this is it's a
+ 
+
+ align:start position:0%
+ions and you know what this is it's a
+battery
+
+ align:start position:0%
+battery
+ 
+
+ align:start position:0%
+battery
+a battery is two different materials two
+
+ align:start position:0%
+a battery is two different materials two
+ 
+
+ align:start position:0%
+a battery is two different materials two
+different metals a and b
+
+ align:start position:0%
+different metals a and b
+ 
+
+ align:start position:0%
+different metals a and b
+where one of them has an ion i don't
+
+ align:start position:0%
+where one of them has an ion i don't
+ 
+
+ align:start position:0%
+where one of them has an ion i don't
+know like lithium
+
+ align:start position:0%
+know like lithium
+ 
+
+ align:start position:0%
+know like lithium
+for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can go back and forth and the
+
+ align:start position:0%
+that can go back and forth and the
+ 
+
+ align:start position:0%
+that can go back and forth and the
+electrolyte is this thing in between
+
+ align:start position:0%
+electrolyte is this thing in between
+ 
+
+ align:start position:0%
+electrolyte is this thing in between
+that only allows that ion through okay
+
+ align:start position:0%
+that only allows that ion through okay
+ 
+
+ align:start position:0%
+that only allows that ion through okay
+now here's the thing so if i'm a metal
+
+ align:start position:0%
+now here's the thing so if i'm a metal
+ 
+
+ align:start position:0%
+now here's the thing so if i'm a metal
+and i lose a positively charged atom
+
+ align:start position:0%
+and i lose a positively charged atom
+ 
+
+ align:start position:0%
+and i lose a positively charged atom
+right well then i got to stay neutral
+
+ align:start position:0%
+right well then i got to stay neutral
+ 
+
+ align:start position:0%
+right well then i got to stay neutral
+the only way to stay neutral is to pump
+
+ align:start position:0%
+the only way to stay neutral is to pump
+ 
+
+ align:start position:0%
+the only way to stay neutral is to pump
+an electron out
+
+ align:start position:0%
+an electron out
+ 
+
+ align:start position:0%
+an electron out
+right is to put on so so if i want to
+
+ align:start position:0%
+right is to put on so so if i want to
+ 
+
+ align:start position:0%
+right is to put on so so if i want to
+draw electrons out of this
+
+ align:start position:0%
+draw electrons out of this
+ 
+
+ align:start position:0%
+draw electrons out of this
+that's fine as long as i draw ions out
+
+ align:start position:0%
+that's fine as long as i draw ions out
+ 
+
+ align:start position:0%
+that's fine as long as i draw ions out
+of it and then both of them can do work
+
+ align:start position:0%
+of it and then both of them can do work
+ 
+
+ align:start position:0%
+of it and then both of them can do work
+and then they come back and they roll
+
+ align:start position:0%
+and then they come back and they roll
+ 
+
+ align:start position:0%
+and then they come back and they roll
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+an energy hill that's what they're doing
+
+ align:start position:0%
+an energy hill that's what they're doing
+ 
+
+ align:start position:0%
+an energy hill that's what they're doing
+and going back and forth shuttling
+
+ align:start position:0%
+and going back and forth shuttling
+ 
+
+ align:start position:0%
+and going back and forth shuttling
+back and forth back and forth they're
+
+ align:start position:0%
+back and forth back and forth they're
+ 
+
+ align:start position:0%
+back and forth back and forth they're
+rolling down a hill literally
+
+ align:start position:0%
+rolling down a hill literally
+ 
+
+ align:start position:0%
+rolling down a hill literally
+of energy yeah when it's in one metal
+
+ align:start position:0%
+of energy yeah when it's in one metal
+ 
+
+ align:start position:0%
+of energy yeah when it's in one metal
+it's higher in energy
+
+ align:start position:0%
+it's higher in energy
+ 
+
+ align:start position:0%
+it's higher in energy
+and then when i plug it up you know plug
+
+ align:start position:0%
+and then when i plug it up you know plug
+ 
+
+ align:start position:0%
+and then when i plug it up you know plug
+my phone in
+
+ align:start position:0%
+my phone in
+ 
+
+ align:start position:0%
+my phone in
+it rolls down that energy hill
+
+ align:start position:0%
+it rolls down that energy hill
+ 
+
+ align:start position:0%
+it rolls down that energy hill
+right and as it does it travels across
+
+ align:start position:0%
+right and as it does it travels across
+ 
+
+ align:start position:0%
+right and as it does it travels across
+to the other other metal gets lower in
+
+ align:start position:0%
+to the other other metal gets lower in
+ 
+
+ align:start position:0%
+to the other other metal gets lower in
+energy and the electrons got to come
+
+ align:start position:0%
+energy and the electrons got to come
+ 
+
+ align:start position:0%
+energy and the electrons got to come
+around and do work for me because
+
+ align:start position:0%
+around and do work for me because
+ 
+
+ align:start position:0%
+around and do work for me because
+otherwise
+
+ align:start position:0%
+otherwise
+ 
+
+ align:start position:0%
+otherwise
+it wouldn't stay neutral that's what a
+
+ align:start position:0%
+it wouldn't stay neutral that's what a
+ 
+
+ align:start position:0%
+it wouldn't stay neutral that's what a
+battery is it's all about ions
+
+ align:start position:0%
+battery is it's all about ions
+ 
+
+ align:start position:0%
+battery is it's all about ions
+right it's all about ions it's like a
+
+ align:start position:0%
+right it's all about ions it's like a
+ 
+
+ align:start position:0%
+right it's all about ions it's like a
+ski lift i like to think of it
+
+ align:start position:0%
+ski lift i like to think of it
+ 
+
+ align:start position:0%
+ski lift i like to think of it
+you know it's like these ions are
+
+ align:start position:0%
+you know it's like these ions are
+ 
+
+ align:start position:0%
+you know it's like these ions are
+getting in into a ski lift they're just
+
+ align:start position:0%
+getting in into a ski lift they're just
+ 
+
+ align:start position:0%
+getting in into a ski lift they're just
+getting
+
+ align:start position:0%
+getting
+ 
+
+ align:start position:0%
+getting
+you know up the mountain and then when
+
+ align:start position:0%
+you know up the mountain and then when
+ 
+
+ align:start position:0%
+you know up the mountain and then when
+you plug it in they're ready to ski down
+
+ align:start position:0%
+you plug it in they're ready to ski down
+ 
+
+ align:start position:0%
+you plug it in they're ready to ski down
+and they go down and that's just
+
+ align:start position:0%
+and they go down and that's just
+ 
+
+ align:start position:0%
+and they go down and that's just
+cruising across this electrolyte
+
+ align:start position:0%
+cruising across this electrolyte
+ 
+
+ align:start position:0%
+cruising across this electrolyte
+right and i don't know what the electron
+
+ align:start position:0%
+right and i don't know what the electron
+ 
+
+ align:start position:0%
+right and i don't know what the electron
+is in this analogy but that's all the
+
+ align:start position:0%
+is in this analogy but that's all the
+ 
+
+ align:start position:0%
+is in this analogy but that's all the
+battery is
+
+ align:start position:0%
+battery is
+ 
+
+ align:start position:0%
+battery is
+you plug it in and the ski lift takes it
+
+ align:start position:0%
+you plug it in and the ski lift takes it
+ 
+
+ align:start position:0%
+you plug it in and the ski lift takes it
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+right when you charge it and now you you
+
+ align:start position:0%
+right when you charge it and now you you
+ 
+
+ align:start position:0%
+right when you charge it and now you you
+power your phone on and it
+
+ align:start position:0%
+power your phone on and it
+ 
+
+ align:start position:0%
+power your phone on and it
+rolls back down well see the thing is
+
+ align:start position:0%
+rolls back down well see the thing is
+ 
+
+ align:start position:0%
+rolls back down well see the thing is
+that batteries have seen
+
+ align:start position:0%
+that batteries have seen
+ 
+
+ align:start position:0%
+that batteries have seen
+a moore's law of themselves
+
+ align:start position:0%
+a moore's law of themselves
+ 
+
+ align:start position:0%
+a moore's law of themselves
+if you look at the moore's law for
+
+ align:start position:0%
+if you look at the moore's law for
+ 
+
+ align:start position:0%
+if you look at the moore's law for
+batteries it uh
+
+ align:start position:0%
+batteries it uh
+ 
+
+ align:start position:0%
+batteries it uh
+doubles right so this is the battery
+
+ align:start position:0%
+doubles right so this is the battery
+ 
+
+ align:start position:0%
+doubles right so this is the battery
+energy storage of batteries
+
+ align:start position:0%
+energy storage of batteries
+ 
+
+ align:start position:0%
+energy storage of batteries
+over the last 150-ish years it doubles
+
+ align:start position:0%
+over the last 150-ish years it doubles
+ 
+
+ align:start position:0%
+over the last 150-ish years it doubles
+every 60 years
+
+ align:start position:0%
+every 60 years
+ 
+
+ align:start position:0%
+every 60 years
+that's not a very good more zone but
+
+ align:start position:0%
+that's not a very good more zone but
+ 
+
+ align:start position:0%
+that's not a very good more zone but
+that's completely changed
+
+ align:start position:0%
+that's completely changed
+ 
+
+ align:start position:0%
+that's completely changed
+that's completely changed recently and
+
+ align:start position:0%
+that's completely changed recently and
+ 
+
+ align:start position:0%
+that's completely changed recently and
+the reason is
+
+ align:start position:0%
+the reason is
+ 
+
+ align:start position:0%
+the reason is
+all about ion shuttling materials
+
+ align:start position:0%
+all about ion shuttling materials
+ 
+
+ align:start position:0%
+all about ion shuttling materials
+and ion storing materials this is why
+
+ align:start position:0%
+and ion storing materials this is why
+ 
+
+ align:start position:0%
+and ion storing materials this is why
+this has happened this is why we've had
+
+ align:start position:0%
+this has happened this is why we've had
+ 
+
+ align:start position:0%
+this has happened this is why we've had
+a revolution
+
+ align:start position:0%
+a revolution
+ 
+
+ align:start position:0%
+a revolution
+in electrochemical energy storage right
+
+ align:start position:0%
+in electrochemical energy storage right
+ 
+
+ align:start position:0%
+in electrochemical energy storage right
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+150 years ago we only made batteries out
+
+ align:start position:0%
+150 years ago we only made batteries out
+ 
+
+ align:start position:0%
+150 years ago we only made batteries out
+of about 10 different materials and
+
+ align:start position:0%
+of about 10 different materials and
+ 
+
+ align:start position:0%
+of about 10 different materials and
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+there's well over 80 that are
+
+ align:start position:0%
+there's well over 80 that are
+ 
+
+ align:start position:0%
+there's well over 80 that are
+commercialized
+
+ align:start position:0%
+commercialized
+ 
+
+ align:start position:0%
+commercialized
+there's many hundreds in research labs
+
+ align:start position:0%
+there's many hundreds in research labs
+ 
+
+ align:start position:0%
+there's many hundreds in research labs
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+what is making the difference is that
+
+ align:start position:0%
+what is making the difference is that
+ 
+
+ align:start position:0%
+what is making the difference is that
+those materials now
+
+ align:start position:0%
+those materials now
+ 
+
+ align:start position:0%
+those materials now
+allow the shuttling to happen it allows
+
+ align:start position:0%
+allow the shuttling to happen it allows
+ 
+
+ align:start position:0%
+allow the shuttling to happen it allows
+the shuttling to happen more easily
+
+ align:start position:0%
+the shuttling to happen more easily
+ 
+
+ align:start position:0%
+the shuttling to happen more easily
+maybe faster and it allows more of them
+
+ align:start position:0%
+maybe faster and it allows more of them
+ 
+
+ align:start position:0%
+maybe faster and it allows more of them
+to be stored
+
+ align:start position:0%
+to be stored
+ 
+
+ align:start position:0%
+to be stored
+per volume it's all about the chemistry
+
+ align:start position:0%
+per volume it's all about the chemistry
+ 
+
+ align:start position:0%
+per volume it's all about the chemistry
+that houses those ions all about the
+
+ align:start position:0%
+that houses those ions all about the
+ 
+
+ align:start position:0%
+that houses those ions all about the
+chemistry of the ions
+
+ align:start position:0%
+chemistry of the ions
+ 
+
+ align:start position:0%
+chemistry of the ions
+so that's why this matters now we we uh
+
+ align:start position:0%
+so that's why this matters now we we uh
+ 
+
+ align:start position:0%
+so that's why this matters now we we uh
+we roll things down hills
+
+ align:start position:0%
+we roll things down hills
+ 
+
+ align:start position:0%
+we roll things down hills
+to power our world i told you this
+
+ align:start position:0%
+to power our world i told you this
+ 
+
+ align:start position:0%
+to power our world i told you this
+already in the first or second lecture
+
+ align:start position:0%
+already in the first or second lecture
+ 
+
+ align:start position:0%
+already in the first or second lecture
+we roll things down hills all the time
+
+ align:start position:0%
+we roll things down hills all the time
+ 
+
+ align:start position:0%
+we roll things down hills all the time
+right so like methane is
+
+ align:start position:0%
+right so like methane is
+ 
+
+ align:start position:0%
+right so like methane is
+you know the core ingredient in natural
+
+ align:start position:0%
+you know the core ingredient in natural
+ 
+
+ align:start position:0%
+you know the core ingredient in natural
+gas and what we do and we talk about
+
+ align:start position:0%
+gas and what we do and we talk about
+ 
+
+ align:start position:0%
+gas and what we do and we talk about
+combustion already
+
+ align:start position:0%
+combustion already
+ 
+
+ align:start position:0%
+combustion already
+is we light that methane on fire but see
+
+ align:start position:0%
+is we light that methane on fire but see
+ 
+
+ align:start position:0%
+is we light that methane on fire but see
+the thing is that what
+
+ align:start position:0%
+the thing is that what
+ 
+
+ align:start position:0%
+the thing is that what
+nature has done is it has put all this
+
+ align:start position:0%
+nature has done is it has put all this
+ 
+
+ align:start position:0%
+nature has done is it has put all this
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+up the hell for us right so
+
+ align:start position:0%
+up the hell for us right so
+ 
+
+ align:start position:0%
+up the hell for us right so
+over tens of millions of years nature
+
+ align:start position:0%
+over tens of millions of years nature
+ 
+
+ align:start position:0%
+over tens of millions of years nature
+has pushed
+
+ align:start position:0%
+has pushed
+ 
+
+ align:start position:0%
+has pushed
+the chemistry up a hill that is
+
+ align:start position:0%
+the chemistry up a hill that is
+ 
+
+ align:start position:0%
+the chemistry up a hill that is
+literally what it's done
+
+ align:start position:0%
+literally what it's done
+ 
+
+ align:start position:0%
+literally what it's done
+right in energy because you know it it's
+
+ align:start position:0%
+right in energy because you know it it's
+ 
+
+ align:start position:0%
+right in energy because you know it it's
+made it so that if i have this rea if i
+
+ align:start position:0%
+made it so that if i have this rea if i
+ 
+
+ align:start position:0%
+made it so that if i have this rea if i
+like this on fire it will go down the
+
+ align:start position:0%
+like this on fire it will go down the
+ 
+
+ align:start position:0%
+like this on fire it will go down the
+hill it will roll down the hill
+
+ align:start position:0%
+hill it will roll down the hill
+ 
+
+ align:start position:0%
+hill it will roll down the hill
+and give off energy right
+
+ align:start position:0%
+and give off energy right
+ 
+
+ align:start position:0%
+and give off energy right
+nature has done that for us but see we
+
+ align:start position:0%
+nature has done that for us but see we
+ 
+
+ align:start position:0%
+nature has done that for us but see we
+need to be able to do this
+
+ align:start position:0%
+need to be able to do this
+ 
+
+ align:start position:0%
+need to be able to do this
+as well as nature and uh and so in the
+
+ align:start position:0%
+as well as nature and uh and so in the
+ 
+
+ align:start position:0%
+as well as nature and uh and so in the
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+uh minute of this why this matters i
+
+ align:start position:0%
+uh minute of this why this matters i
+ 
+
+ align:start position:0%
+uh minute of this why this matters i
+want to explain why this is so
+
+ align:start position:0%
+want to explain why this is so
+ 
+
+ align:start position:0%
+want to explain why this is so
+challenging
+
+ align:start position:0%
+challenging
+ 
+
+ align:start position:0%
+challenging
+we need to be able to match because if
+
+ align:start position:0%
+we need to be able to match because if
+ 
+
+ align:start position:0%
+we need to be able to match because if
+you look at the energy per weight
+
+ align:start position:0%
+you look at the energy per weight
+ 
+
+ align:start position:0%
+you look at the energy per weight
+versus the energy per volume of a
+
+ align:start position:0%
+versus the energy per volume of a
+ 
+
+ align:start position:0%
+versus the energy per volume of a
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+that's a very important metric we plot
+
+ align:start position:0%
+that's a very important metric we plot
+ 
+
+ align:start position:0%
+that's a very important metric we plot
+this all the time if you work on energy
+
+ align:start position:0%
+this all the time if you work on energy
+ 
+
+ align:start position:0%
+this all the time if you work on energy
+materials
+
+ align:start position:0%
+materials
+ 
+
+ align:start position:0%
+materials
+the volumetric versus the gravimetric
+
+ align:start position:0%
+the volumetric versus the gravimetric
+ 
+
+ align:start position:0%
+the volumetric versus the gravimetric
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+density this is good a lot of energy per
+
+ align:start position:0%
+density this is good a lot of energy per
+ 
+
+ align:start position:0%
+density this is good a lot of energy per
+weight and volume well look at where
+
+ align:start position:0%
+weight and volume well look at where
+ 
+
+ align:start position:0%
+weight and volume well look at where
+gasoline is
+
+ align:start position:0%
+gasoline is
+ 
+
+ align:start position:0%
+gasoline is
+now i want to do some math here because
+
+ align:start position:0%
+now i want to do some math here because
+ 
+
+ align:start position:0%
+now i want to do some math here because
+i think this
+
+ align:start position:0%
+i think this
+ 
+
+ align:start position:0%
+i think this
+is very important because i want you to
+
+ align:start position:0%
+is very important because i want you to
+ 
+
+ align:start position:0%
+is very important because i want you to
+see now if i take one liter of gasoline
+
+ align:start position:0%
+see now if i take one liter of gasoline
+ 
+
+ align:start position:0%
+see now if i take one liter of gasoline
+so if i take one liter
+
+ align:start position:0%
+so if i take one liter
+ 
+
+ align:start position:0%
+so if i take one liter
+of gasoline
+
+ align:start position:0%
+of gasoline
+ 
+
+ align:start position:0%
+of gasoline
+now the cost of that is around
+
+ align:start position:0%
+now the cost of that is around
+ 
+
+ align:start position:0%
+now the cost of that is around
+the cost is around a dollar uh
+
+ align:start position:0%
+the cost is around a dollar uh
+ 
+
+ align:start position:0%
+the cost is around a dollar uh
+it fluctuates but you know in this
+
+ align:start position:0%
+it fluctuates but you know in this
+ 
+
+ align:start position:0%
+it fluctuates but you know in this
+country right around now it's about a
+
+ align:start position:0%
+country right around now it's about a
+ 
+
+ align:start position:0%
+country right around now it's about a
+dollar
+
+ align:start position:0%
+dollar
+ 
+
+ align:start position:0%
+dollar
+okay now if i look at how much energy
+
+ align:start position:0%
+okay now if i look at how much energy
+ 
+
+ align:start position:0%
+okay now if i look at how much energy
+is in that gasoline the energy
+
+ align:start position:0%
+is in that gasoline the energy
+ 
+
+ align:start position:0%
+is in that gasoline the energy
+stored in those bonds that nature has
+
+ align:start position:0%
+stored in those bonds that nature has
+ 
+
+ align:start position:0%
+stored in those bonds that nature has
+pushed up a hill over millions of years
+
+ align:start position:0%
+pushed up a hill over millions of years
+ 
+
+ align:start position:0%
+pushed up a hill over millions of years
+the energy stored is about 33 megajoules
+
+ align:start position:0%
+the energy stored is about 33 megajoules
+ 
+
+ align:start position:0%
+the energy stored is about 33 megajoules
+okay good now i'm going to make a
+
+ align:start position:0%
+okay good now i'm going to make a
+ 
+
+ align:start position:0%
+okay good now i'm going to make a
+comparison
+
+ align:start position:0%
+comparison
+ 
+
+ align:start position:0%
+comparison
+one mit professor
+
+ align:start position:0%
+one mit professor
+ 
+
+ align:start position:0%
+one mit professor
+one nit
+
+ align:start position:0%
+one nit
+ 
+
+ align:start position:0%
+one nit
+professor operates
+
+ align:start position:0%
+professor operates
+ 
+
+ align:start position:0%
+professor operates
+at around 60 watts now
+
+ align:start position:0%
+at around 60 watts now
+ 
+
+ align:start position:0%
+at around 60 watts now
+this is something like well this is
+
+ align:start position:0%
+this is something like well this is
+ 
+
+ align:start position:0%
+this is something like well this is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+60 joules per second now i know some
+
+ align:start position:0%
+60 joules per second now i know some
+ 
+
+ align:start position:0%
+60 joules per second now i know some
+professors who can operate a little
+
+ align:start position:0%
+professors who can operate a little
+ 
+
+ align:start position:0%
+professors who can operate a little
+higher than that
+
+ align:start position:0%
+higher than that
+ 
+
+ align:start position:0%
+higher than that
+maybe some a little lower but that's
+
+ align:start position:0%
+maybe some a little lower but that's
+ 
+
+ align:start position:0%
+maybe some a little lower but that's
+like the average right
+
+ align:start position:0%
+like the average right
+ 
+
+ align:start position:0%
+like the average right
+60 joules per second now the thing is if
+
+ align:start position:0%
+60 joules per second now the thing is if
+ 
+
+ align:start position:0%
+60 joules per second now the thing is if
+i want to get
+
+ align:start position:0%
+i want to get
+ 
+
+ align:start position:0%
+i want to get
+33 mega joules out of this professor
+
+ align:start position:0%
+33 mega joules out of this professor
+ 
+
+ align:start position:0%
+33 mega joules out of this professor
+then i get i get at this rate 33
+
+ align:start position:0%
+then i get i get at this rate 33
+ 
+
+ align:start position:0%
+then i get i get at this rate 33
+megajoules takes the prof
+
+ align:start position:0%
+megajoules takes the prof
+ 
+
+ align:start position:0%
+megajoules takes the prof
+um uh 153 hours
+
+ align:start position:0%
+um uh 153 hours
+ 
+
+ align:start position:0%
+um uh 153 hours
+now here's why this matters because 153
+
+ align:start position:0%
+now here's why this matters because 153
+ 
+
+ align:start position:0%
+now here's why this matters because 153
+hours will cost about fifteen hundred
+
+ align:start position:0%
+hours will cost about fifteen hundred
+ 
+
+ align:start position:0%
+hours will cost about fifteen hundred
+and thirty dollars at
+
+ align:start position:0%
+and thirty dollars at
+ 
+
+ align:start position:0%
+and thirty dollars at
+the uh mit uh professor salary
+
+ align:start position:0%
+the uh mit uh professor salary
+ 
+
+ align:start position:0%
+the uh mit uh professor salary
+uh which is around
+
+ align:start position:0%
+uh which is around
+ 
+
+ align:start position:0%
+uh which is around
+ten dollars per hour okay
+
+ align:start position:0%
+ten dollars per hour okay
+ 
+
+ align:start position:0%
+ten dollars per hour okay
+and okay but look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i dug something out of the ground that
+
+ align:start position:0%
+i dug something out of the ground that
+ 
+
+ align:start position:0%
+i dug something out of the ground that
+nature spent 100 million years making
+
+ align:start position:0%
+nature spent 100 million years making
+ 
+
+ align:start position:0%
+nature spent 100 million years making
+fine
+
+ align:start position:0%
+fine
+ 
+
+ align:start position:0%
+fine
+okay and i burned it and i got it for a
+
+ align:start position:0%
+okay and i burned it and i got it for a
+ 
+
+ align:start position:0%
+okay and i burned it and i got it for a
+dollar i got the same amount of energy
+
+ align:start position:0%
+dollar i got the same amount of energy
+ 
+
+ align:start position:0%
+dollar i got the same amount of energy
+that it would have taken me
+
+ align:start position:0%
+that it would have taken me
+ 
+
+ align:start position:0%
+that it would have taken me
+literally fifteen hundred and thirty
+
+ align:start position:0%
+literally fifteen hundred and thirty
+ 
+
+ align:start position:0%
+literally fifteen hundred and thirty
+dollars to pay for
+
+ align:start position:0%
+dollars to pay for
+ 
+
+ align:start position:0%
+dollars to pay for
+that's our challenge right that's our
+
+ align:start position:0%
+that's our challenge right that's our
+ 
+
+ align:start position:0%
+that's our challenge right that's our
+because now you can plot other things
+
+ align:start position:0%
+because now you can plot other things
+ 
+
+ align:start position:0%
+because now you can plot other things
+here but look at this ethanol wood okay
+
+ align:start position:0%
+here but look at this ethanol wood okay
+ 
+
+ align:start position:0%
+here but look at this ethanol wood okay
+liquid hydrogen we're still trying to
+
+ align:start position:0%
+liquid hydrogen we're still trying to
+ 
+
+ align:start position:0%
+liquid hydrogen we're still trying to
+compress it get but look at this
+
+ align:start position:0%
+compress it get but look at this
+ 
+
+ align:start position:0%
+compress it get but look at this
+batteries are way down there this is why
+
+ align:start position:0%
+batteries are way down there this is why
+ 
+
+ align:start position:0%
+batteries are way down there this is why
+this matters because we're not even
+
+ align:start position:0%
+this matters because we're not even
+ 
+
+ align:start position:0%
+this matters because we're not even
+close to being done
+
+ align:start position:0%
+close to being done
+ 
+
+ align:start position:0%
+close to being done
+we're not even close see that great
+
+ align:start position:0%
+we're not even close see that great
+ 
+
+ align:start position:0%
+we're not even close see that great
+uptick in electrochemical storage
+
+ align:start position:0%
+uptick in electrochemical storage
+ 
+
+ align:start position:0%
+uptick in electrochemical storage
+we need another order or two of
+
+ align:start position:0%
+we need another order or two of
+ 
+
+ align:start position:0%
+we need another order or two of
+magnitude still
+
+ align:start position:0%
+magnitude still
+ 
+
+ align:start position:0%
+magnitude still
+right in storing energy efficiencies
+
+ align:start position:0%
+right in storing energy efficiencies
+ 
+
+ align:start position:0%
+right in storing energy efficiencies
+costs etc so that's uh that's my why
+
+ align:start position:0%
+costs etc so that's uh that's my why
+ 
+
+ align:start position:0%
+costs etc so that's uh that's my why
+this matters for
+
+ align:start position:0%
+this matters for
+ 
+
+ align:start position:0%
+this matters for
+today now back to ions and electrons and
+
+ align:start position:0%
+today now back to ions and electrons and
+ 
+
+ align:start position:0%
+today now back to ions and electrons and
+atoms
+
+ align:start position:0%
+atoms
+ 
+
+ align:start position:0%
+atoms
+what i want to take the last 15 minutes
+
+ align:start position:0%
+what i want to take the last 15 minutes
+ 
+
+ align:start position:0%
+what i want to take the last 15 minutes
+of class is to introduce a new way of
+
+ align:start position:0%
+of class is to introduce a new way of
+ 
+
+ align:start position:0%
+of class is to introduce a new way of
+looking at this and some of you may have
+
+ align:start position:0%
+looking at this and some of you may have
+ 
+
+ align:start position:0%
+looking at this and some of you may have
+seen the lewis dots
+
+ align:start position:0%
+seen the lewis dots
+ 
+
+ align:start position:0%
+seen the lewis dots
+okay um we're gonna
+
+ align:start position:0%
+okay um we're gonna
+ 
+
+ align:start position:0%
+okay um we're gonna
+i'm gonna introduce them today and then
+
+ align:start position:0%
+i'm gonna introduce them today and then
+ 
+
+ align:start position:0%
+i'm gonna introduce them today and then
+we're gonna make a whole bunch of
+
+ align:start position:0%
+we're gonna make a whole bunch of
+ 
+
+ align:start position:0%
+we're gonna make a whole bunch of
+molecular structures on wednesday
+
+ align:start position:0%
+molecular structures on wednesday
+ 
+
+ align:start position:0%
+molecular structures on wednesday
+um and the reason this is so important
+
+ align:start position:0%
+um and the reason this is so important
+ 
+
+ align:start position:0%
+um and the reason this is so important
+is that it gives us a sense
+
+ align:start position:0%
+is that it gives us a sense
+ 
+
+ align:start position:0%
+is that it gives us a sense
+of these outer electrons it gives us a
+
+ align:start position:0%
+of these outer electrons it gives us a
+ 
+
+ align:start position:0%
+of these outer electrons it gives us a
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+of how those outer electrons look right
+
+ align:start position:0%
+of how those outer electrons look right
+ 
+
+ align:start position:0%
+of how those outer electrons look right
+for the atoms and then very importantly
+
+ align:start position:0%
+for the atoms and then very importantly
+ 
+
+ align:start position:0%
+for the atoms and then very importantly
+how they come together in bonds
+
+ align:start position:0%
+how they come together in bonds
+ 
+
+ align:start position:0%
+how they come together in bonds
+okay how they come together in bots so
+
+ align:start position:0%
+okay how they come together in bots so
+ 
+
+ align:start position:0%
+okay how they come together in bots so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so if i uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just very very simply ask what is
+
+ align:start position:0%
+just very very simply ask what is
+ 
+
+ align:start position:0%
+just very very simply ask what is
+you know what is the lewis dot
+
+ align:start position:0%
+you know what is the lewis dot
+ 
+
+ align:start position:0%
+you know what is the lewis dot
+structure look like well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all the number of dots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to the number of
+
+ align:start position:0%
+is equal to the number of
+ 
+
+ align:start position:0%
+is equal to the number of
+valence electrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is equal to the last digit
+
+ align:start position:0%
+and this is equal to the last digit
+ 
+
+ align:start position:0%
+and this is equal to the last digit
+of the group so
+
+ align:start position:0%
+of the group so
+ 
+
+ align:start position:0%
+of the group so
+of the element group i'll show you that
+
+ align:start position:0%
+of the element group i'll show you that
+ 
+
+ align:start position:0%
+of the element group i'll show you that
+in a second
+
+ align:start position:0%
+in a second
+ 
+
+ align:start position:0%
+in a second
+okay so there's lewis now lewis um
+
+ align:start position:0%
+okay so there's lewis now lewis um
+ 
+
+ align:start position:0%
+okay so there's lewis now lewis um
+you know he's so there's one of his his
+
+ align:start position:0%
+you know he's so there's one of his his
+ 
+
+ align:start position:0%
+you know he's so there's one of his his
+drawings in one of his original papers
+
+ align:start position:0%
+drawings in one of his original papers
+ 
+
+ align:start position:0%
+drawings in one of his original papers
+in the early 1900s
+
+ align:start position:0%
+in the early 1900s
+ 
+
+ align:start position:0%
+in the early 1900s
+he actually was a professor here as well
+
+ align:start position:0%
+he actually was a professor here as well
+ 
+
+ align:start position:0%
+he actually was a professor here as well
+um and then he he went and did some of
+
+ align:start position:0%
+um and then he he went and did some of
+ 
+
+ align:start position:0%
+um and then he he went and did some of
+this a lot of this work out in berkeley
+
+ align:start position:0%
+this a lot of this work out in berkeley
+ 
+
+ align:start position:0%
+this a lot of this work out in berkeley
+so they named the hall after him
+
+ align:start position:0%
+so they named the hall after him
+ 
+
+ align:start position:0%
+so they named the hall after him
+um and his comprehension was absolutely
+
+ align:start position:0%
+um and his comprehension was absolutely
+ 
+
+ align:start position:0%
+um and his comprehension was absolutely
+profound
+
+ align:start position:0%
+profound
+ 
+
+ align:start position:0%
+profound
+because in thinking about
+
+ align:start position:0%
+because in thinking about
+ 
+
+ align:start position:0%
+because in thinking about
+atoms with dots to represent electrons
+
+ align:start position:0%
+atoms with dots to represent electrons
+ 
+
+ align:start position:0%
+atoms with dots to represent electrons
+in the outer valence it gave us a way
+
+ align:start position:0%
+in the outer valence it gave us a way
+ 
+
+ align:start position:0%
+in the outer valence it gave us a way
+to so easily think about bonding
+
+ align:start position:0%
+to so easily think about bonding
+ 
+
+ align:start position:0%
+to so easily think about bonding
+okay now we can think about ionic
+
+ align:start position:0%
+okay now we can think about ionic
+ 
+
+ align:start position:0%
+okay now we can think about ionic
+bonding for sure which is what we've
+
+ align:start position:0%
+bonding for sure which is what we've
+ 
+
+ align:start position:0%
+bonding for sure which is what we've
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+but more importantly what lewis helps us
+
+ align:start position:0%
+but more importantly what lewis helps us
+ 
+
+ align:start position:0%
+but more importantly what lewis helps us
+with is to think about
+
+ align:start position:0%
+with is to think about
+ 
+
+ align:start position:0%
+with is to think about
+covalent bonding and that's the subject
+
+ align:start position:0%
+covalent bonding and that's the subject
+ 
+
+ align:start position:0%
+covalent bonding and that's the subject
+of wednesday okay which is a whole
+
+ align:start position:0%
+of wednesday okay which is a whole
+ 
+
+ align:start position:0%
+of wednesday okay which is a whole
+another type of bonding that we're going
+
+ align:start position:0%
+another type of bonding that we're going
+ 
+
+ align:start position:0%
+another type of bonding that we're going
+to talk about
+
+ align:start position:0%
+to talk about
+ 
+
+ align:start position:0%
+to talk about
+okay now okay so now uh last digit of
+
+ align:start position:0%
+okay now okay so now uh last digit of
+ 
+
+ align:start position:0%
+okay now okay so now uh last digit of
+the element group okay good so there it
+
+ align:start position:0%
+the element group okay good so there it
+ 
+
+ align:start position:0%
+the element group okay good so there it
+predicts the number of bonds formed by
+
+ align:start position:0%
+predicts the number of bonds formed by
+ 
+
+ align:start position:0%
+predicts the number of bonds formed by
+most elements in their compounds good
+
+ align:start position:0%
+most elements in their compounds good
+ 
+
+ align:start position:0%
+most elements in their compounds good
+and there's the dots look at that
+
+ align:start position:0%
+and there's the dots look at that
+ 
+
+ align:start position:0%
+and there's the dots look at that
+example fluorine
+
+ align:start position:0%
+example fluorine
+ 
+
+ align:start position:0%
+example fluorine
+or using noble gas notation
+
+ align:start position:0%
+or using noble gas notation
+ 
+
+ align:start position:0%
+or using noble gas notation
+helium that really saved us time i
+
+ align:start position:0%
+helium that really saved us time i
+ 
+
+ align:start position:0%
+helium that really saved us time i
+didn't have to write one s2
+
+ align:start position:0%
+didn't have to write one s2
+ 
+
+ align:start position:0%
+didn't have to write one s2
+actually this looks like four strokes of
+
+ align:start position:0%
+actually this looks like four strokes of
+ 
+
+ align:start position:0%
+actually this looks like four strokes of
+the pen one s2 would have been three
+
+ align:start position:0%
+the pen one s2 would have been three
+ 
+
+ align:start position:0%
+the pen one s2 would have been three
+i don't know honestly but anyway uh okay
+
+ align:start position:0%
+i don't know honestly but anyway uh okay
+ 
+
+ align:start position:0%
+i don't know honestly but anyway uh okay
+there's fluorine and look one dot no
+
+ align:start position:0%
+there's fluorine and look one dot no
+ 
+
+ align:start position:0%
+there's fluorine and look one dot no
+two dots no because you add a dot for
+
+ align:start position:0%
+two dots no because you add a dot for
+ 
+
+ align:start position:0%
+two dots no because you add a dot for
+the valence so fluorine
+
+ align:start position:0%
+the valence so fluorine
+ 
+
+ align:start position:0%
+the valence so fluorine
+has seven dots until you reach the
+
+ align:start position:0%
+has seven dots until you reach the
+ 
+
+ align:start position:0%
+has seven dots until you reach the
+valence
+
+ align:start position:0%
+valence
+ 
+
+ align:start position:0%
+valence
+until you reach the valence that is the
+
+ align:start position:0%
+until you reach the valence that is the
+ 
+
+ align:start position:0%
+until you reach the valence that is the
+key
+
+ align:start position:0%
+key
+ 
+
+ align:start position:0%
+key
+of the of the lewis picture because we
+
+ align:start position:0%
+of the of the lewis picture because we
+ 
+
+ align:start position:0%
+of the of the lewis picture because we
+and we talked about this before
+
+ align:start position:0%
+and we talked about this before
+ 
+
+ align:start position:0%
+and we talked about this before
+we talked about this before because so
+
+ align:start position:0%
+we talked about this before because so
+ 
+
+ align:start position:0%
+we talked about this before because so
+there are three
+
+ align:start position:0%
+there are three
+ 
+
+ align:start position:0%
+there are three
+really important things that come out of
+
+ align:start position:0%
+really important things that come out of
+ 
+
+ align:start position:0%
+really important things that come out of
+the lewis picture
+
+ align:start position:0%
+the lewis picture
+ 
+
+ align:start position:0%
+the lewis picture
+one is it tells us
+
+ align:start position:0%
+one is it tells us
+ 
+
+ align:start position:0%
+one is it tells us
+as i've just told you it tells us about
+
+ align:start position:0%
+as i've just told you it tells us about
+ 
+
+ align:start position:0%
+as i've just told you it tells us about
+bond formation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tells us about bond formation and
+
+ align:start position:0%
+tells us about bond formation and
+ 
+
+ align:start position:0%
+tells us about bond formation and
+it makes the assumption that the valence
+
+ align:start position:0%
+it makes the assumption that the valence
+ 
+
+ align:start position:0%
+it makes the assumption that the valence
+electrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are what matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for chemistry and this is critical and
+
+ align:start position:0%
+for chemistry and this is critical and
+ 
+
+ align:start position:0%
+for chemistry and this is critical and
+i've alluded to this before
+
+ align:start position:0%
+i've alluded to this before
+ 
+
+ align:start position:0%
+i've alluded to this before
+you now have a real sense of this though
+
+ align:start position:0%
+you now have a real sense of this though
+ 
+
+ align:start position:0%
+you now have a real sense of this though
+from these energy diagrams you have a
+
+ align:start position:0%
+from these energy diagrams you have a
+ 
+
+ align:start position:0%
+from these energy diagrams you have a
+sense of this
+
+ align:start position:0%
+sense of this
+ 
+
+ align:start position:0%
+sense of this
+because look if i want to rip an
+
+ align:start position:0%
+because look if i want to rip an
+ 
+
+ align:start position:0%
+because look if i want to rip an
+electron off of lithium i got to spend
+
+ align:start position:0%
+electron off of lithium i got to spend
+ 
+
+ align:start position:0%
+electron off of lithium i got to spend
+5.4 electron volts
+
+ align:start position:0%
+5.4 electron volts
+ 
+
+ align:start position:0%
+5.4 electron volts
+if i want to rip the next one off i got
+
+ align:start position:0%
+if i want to rip the next one off i got
+ 
+
+ align:start position:0%
+if i want to rip the next one off i got
+to spend over a hundred electron volts
+
+ align:start position:0%
+to spend over a hundred electron volts
+ 
+
+ align:start position:0%
+to spend over a hundred electron volts
+and we say well we'll do pes with all
+
+ align:start position:0%
+and we say well we'll do pes with all
+ 
+
+ align:start position:0%
+and we say well we'll do pes with all
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+energies it doesn't matter i'll get them
+
+ align:start position:0%
+energies it doesn't matter i'll get them
+ 
+
+ align:start position:0%
+energies it doesn't matter i'll get them
+all but what if i just want to say well
+
+ align:start position:0%
+all but what if i just want to say well
+ 
+
+ align:start position:0%
+all but what if i just want to say well
+who's going to you know what what
+
+ align:start position:0%
+who's going to you know what what
+ 
+
+ align:start position:0%
+who's going to you know what what
+electrons are going to be
+
+ align:start position:0%
+electrons are going to be
+ 
+
+ align:start position:0%
+electrons are going to be
+available to participate
+
+ align:start position:0%
+available to participate
+ 
+
+ align:start position:0%
+available to participate
+in something like a bond which ones it's
+
+ align:start position:0%
+in something like a bond which ones it's
+ 
+
+ align:start position:0%
+in something like a bond which ones it's
+going to be these ones
+
+ align:start position:0%
+going to be these ones
+ 
+
+ align:start position:0%
+going to be these ones
+it's not going to be the ones all the
+
+ align:start position:0%
+it's not going to be the ones all the
+ 
+
+ align:start position:0%
+it's not going to be the ones all the
+way in close to the core
+
+ align:start position:0%
+way in close to the core
+ 
+
+ align:start position:0%
+way in close to the core
+that don't want to be bothered and
+
+ align:start position:0%
+that don't want to be bothered and
+ 
+
+ align:start position:0%
+that don't want to be bothered and
+they've got so much energy
+
+ align:start position:0%
+they've got so much energy
+ 
+
+ align:start position:0%
+they've got so much energy
+just to get their attention takes 100 ev
+
+ align:start position:0%
+just to get their attention takes 100 ev
+ 
+
+ align:start position:0%
+just to get their attention takes 100 ev
+and even that's not a but here a little
+
+ align:start position:0%
+and even that's not a but here a little
+ 
+
+ align:start position:0%
+and even that's not a but here a little
+visible light
+
+ align:start position:0%
+visible light
+ 
+
+ align:start position:0%
+visible light
+and i got i got lithium talking to me
+
+ align:start position:0%
+and i got i got lithium talking to me
+ 
+
+ align:start position:0%
+and i got i got lithium talking to me
+well it's the same you know chemically
+
+ align:start position:0%
+well it's the same you know chemically
+ 
+
+ align:start position:0%
+well it's the same you know chemically
+it's the same these
+
+ align:start position:0%
+it's the same these
+ 
+
+ align:start position:0%
+it's the same these
+that's light right these are these ones
+
+ align:start position:0%
+that's light right these are these ones
+ 
+
+ align:start position:0%
+that's light right these are these ones
+are the ones
+
+ align:start position:0%
+are the ones
+ 
+
+ align:start position:0%
+are the ones
+that want to and can participate in
+
+ align:start position:0%
+that want to and can participate in
+ 
+
+ align:start position:0%
+that want to and can participate in
+bonding
+
+ align:start position:0%
+bonding
+ 
+
+ align:start position:0%
+bonding
+the ones all the way down in energy way
+
+ align:start position:0%
+the ones all the way down in energy way
+ 
+
+ align:start position:0%
+the ones all the way down in energy way
+way way low
+
+ align:start position:0%
+way way low
+ 
+
+ align:start position:0%
+way way low
+they're inert they're inert right
+
+ align:start position:0%
+they're inert they're inert right
+ 
+
+ align:start position:0%
+they're inert they're inert right
+so most of chemistry happens in the
+
+ align:start position:0%
+so most of chemistry happens in the
+ 
+
+ align:start position:0%
+so most of chemistry happens in the
+violence and lewis
+
+ align:start position:0%
+violence and lewis
+ 
+
+ align:start position:0%
+violence and lewis
+really nailed that right so these dots
+
+ align:start position:0%
+really nailed that right so these dots
+ 
+
+ align:start position:0%
+really nailed that right so these dots
+are only
+
+ align:start position:0%
+are only
+ 
+
+ align:start position:0%
+are only
+valence electron dots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's one more rule now okay so
+
+ align:start position:0%
+and there's one more rule now okay so
+ 
+
+ align:start position:0%
+and there's one more rule now okay so
+there's those seven dots for fluorine
+
+ align:start position:0%
+there's those seven dots for fluorine
+ 
+
+ align:start position:0%
+there's those seven dots for fluorine
+and then okay sometimes
+
+ align:start position:0%
+and then okay sometimes
+ 
+
+ align:start position:0%
+and then okay sometimes
+you'll see this oh this is just the
+
+ align:start position:0%
+you'll see this oh this is just the
+ 
+
+ align:start position:0%
+you'll see this oh this is just the
+number of dots it's this classification
+
+ align:start position:0%
+number of dots it's this classification
+ 
+
+ align:start position:0%
+number of dots it's this classification
+of the uh of the columns
+
+ align:start position:0%
+of the uh of the columns
+ 
+
+ align:start position:0%
+of the uh of the columns
+right the groups in the pair but no that
+
+ align:start position:0%
+right the groups in the pair but no that
+ 
+
+ align:start position:0%
+right the groups in the pair but no that
+is not okay
+
+ align:start position:0%
+is not okay
+ 
+
+ align:start position:0%
+is not okay
+not standard remember the iupac
+
+ align:start position:0%
+not standard remember the iupac
+ 
+
+ align:start position:0%
+not standard remember the iupac
+which throws the best most lively
+
+ align:start position:0%
+which throws the best most lively
+ 
+
+ align:start position:0%
+which throws the best most lively
+parties
+
+ align:start position:0%
+parties
+ 
+
+ align:start position:0%
+parties
+and conferences they decide on how to
+
+ align:start position:0%
+and conferences they decide on how to
+ 
+
+ align:start position:0%
+and conferences they decide on how to
+name elements and many many
+
+ align:start position:0%
+name elements and many many
+ 
+
+ align:start position:0%
+name elements and many many
+other aspects of our lives are decided
+
+ align:start position:0%
+other aspects of our lives are decided
+ 
+
+ align:start position:0%
+other aspects of our lives are decided
+by them and they said no
+
+ align:start position:0%
+by them and they said no
+ 
+
+ align:start position:0%
+by them and they said no
+that's an old classification it's
+
+ align:start position:0%
+that's an old classification it's
+ 
+
+ align:start position:0%
+that's an old classification it's
+confusing so we're going to go
+
+ align:start position:0%
+confusing so we're going to go
+ 
+
+ align:start position:0%
+confusing so we're going to go
+with the standard which is that we still
+
+ align:start position:0%
+with the standard which is that we still
+ 
+
+ align:start position:0%
+with the standard which is that we still
+count 1 to 18
+
+ align:start position:0%
+count 1 to 18
+ 
+
+ align:start position:0%
+count 1 to 18
+1 to 18 1 2 s block
+
+ align:start position:0%
+1 to 18 1 2 s block
+ 
+
+ align:start position:0%
+1 to 18 1 2 s block
+13 to 18 p block right
+
+ align:start position:0%
+13 to 18 p block right
+ 
+
+ align:start position:0%
+13 to 18 p block right
+right okay that's cool we now right
+
+ align:start position:0%
+right okay that's cool we now right
+ 
+
+ align:start position:0%
+right okay that's cool we now right
+3 to 12. d block oh
+
+ align:start position:0%
+3 to 12. d block oh
+ 
+
+ align:start position:0%
+3 to 12. d block oh
+we go back and forth but it's still but
+
+ align:start position:0%
+we go back and forth but it's still but
+ 
+
+ align:start position:0%
+we go back and forth but it's still but
+you can just take the last digit there
+
+ align:start position:0%
+you can just take the last digit there
+ 
+
+ align:start position:0%
+you can just take the last digit there
+iupac even the periodic table talks
+
+ align:start position:0%
+iupac even the periodic table talks
+ 
+
+ align:start position:0%
+iupac even the periodic table talks
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+it shows it it shows the old
+
+ align:start position:0%
+it shows it it shows the old
+ 
+
+ align:start position:0%
+it shows it it shows the old
+classification there and then it says no
+
+ align:start position:0%
+classification there and then it says no
+ 
+
+ align:start position:0%
+classification there and then it says no
+don't use it it's confusing and then why
+
+ align:start position:0%
+don't use it it's confusing and then why
+ 
+
+ align:start position:0%
+don't use it it's confusing and then why
+do they show it
+
+ align:start position:0%
+do they show it
+ 
+
+ align:start position:0%
+do they show it
+because some textbooks still show it so
+
+ align:start position:0%
+because some textbooks still show it so
+ 
+
+ align:start position:0%
+because some textbooks still show it so
+you so i want
+
+ align:start position:0%
+you so i want
+ 
+
+ align:start position:0%
+you so i want
+you to be aware of that okay
+
+ align:start position:0%
+you to be aware of that okay
+ 
+
+ align:start position:0%
+you to be aware of that okay
+now you can use
+
+ align:start position:0%
+now you can use
+ 
+
+ align:start position:0%
+now you can use
+louis you can use this idea of only
+
+ align:start position:0%
+louis you can use this idea of only
+ 
+
+ align:start position:0%
+louis you can use this idea of only
+thinking about the the valence
+
+ align:start position:0%
+thinking about the the valence
+ 
+
+ align:start position:0%
+thinking about the the valence
+to understand when atoms have similar
+
+ align:start position:0%
+to understand when atoms have similar
+ 
+
+ align:start position:0%
+to understand when atoms have similar
+chemistry
+
+ align:start position:0%
+chemistry
+ 
+
+ align:start position:0%
+chemistry
+right so if the valence of carbon
+
+ align:start position:0%
+right so if the valence of carbon
+ 
+
+ align:start position:0%
+right so if the valence of carbon
+is the same as the balance of silicon
+
+ align:start position:0%
+is the same as the balance of silicon
+ 
+
+ align:start position:0%
+is the same as the balance of silicon
+you bump down one quantum number
+
+ align:start position:0%
+you bump down one quantum number
+ 
+
+ align:start position:0%
+you bump down one quantum number
+but they both have four electrons out
+
+ align:start position:0%
+but they both have four electrons out
+ 
+
+ align:start position:0%
+but they both have four electrons out
+there in the valence
+
+ align:start position:0%
+there in the valence
+ 
+
+ align:start position:0%
+there in the valence
+in this case it's two in this case it's
+
+ align:start position:0%
+in this case it's two in this case it's
+ 
+
+ align:start position:0%
+in this case it's two in this case it's
+three in terms of quantum number but
+
+ align:start position:0%
+three in terms of quantum number but
+ 
+
+ align:start position:0%
+three in terms of quantum number but
+they both have those same
+
+ align:start position:0%
+they both have those same
+ 
+
+ align:start position:0%
+they both have those same
+kinds of and same number of electrons so
+
+ align:start position:0%
+kinds of and same number of electrons so
+ 
+
+ align:start position:0%
+kinds of and same number of electrons so
+you could maybe expect
+
+ align:start position:0%
+you could maybe expect
+ 
+
+ align:start position:0%
+you could maybe expect
+there to be similar chemistry it turns
+
+ align:start position:0%
+there to be similar chemistry it turns
+ 
+
+ align:start position:0%
+there to be similar chemistry it turns
+out in this case
+
+ align:start position:0%
+out in this case
+ 
+
+ align:start position:0%
+out in this case
+there's very different but we'll learn
+
+ align:start position:0%
+there's very different but we'll learn
+ 
+
+ align:start position:0%
+there's very different but we'll learn
+about that carbon hybridization
+
+ align:start position:0%
+about that carbon hybridization
+ 
+
+ align:start position:0%
+about that carbon hybridization
+silicon no we'll get to that
+
+ align:start position:0%
+silicon no we'll get to that
+ 
+
+ align:start position:0%
+silicon no we'll get to that
+but still this is how we see silicon now
+
+ align:start position:0%
+but still this is how we see silicon now
+ 
+
+ align:start position:0%
+but still this is how we see silicon now
+we don't see it this way with lewis
+
+ align:start position:0%
+we don't see it this way with lewis
+ 
+
+ align:start position:0%
+we don't see it this way with lewis
+we see it this way this is how we see
+
+ align:start position:0%
+we see it this way this is how we see
+ 
+
+ align:start position:0%
+we see it this way this is how we see
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+right and so i want you to start seeing
+
+ align:start position:0%
+right and so i want you to start seeing
+ 
+
+ align:start position:0%
+right and so i want you to start seeing
+elements this way
+
+ align:start position:0%
+elements this way
+ 
+
+ align:start position:0%
+elements this way
+okay and so you can look at periodic
+
+ align:start position:0%
+okay and so you can look at periodic
+ 
+
+ align:start position:0%
+okay and so you can look at periodic
+tables and and take images randomly
+
+ align:start position:0%
+tables and and take images randomly
+ 
+
+ align:start position:0%
+tables and and take images randomly
+found online
+
+ align:start position:0%
+found online
+ 
+
+ align:start position:0%
+found online
+with lewis dots and you can start
+
+ align:start position:0%
+with lewis dots and you can start
+ 
+
+ align:start position:0%
+with lewis dots and you can start
+thinking
+
+ align:start position:0%
+thinking
+ 
+
+ align:start position:0%
+thinking
+of atoms as their lewis dot
+
+ align:start position:0%
+of atoms as their lewis dot
+ 
+
+ align:start position:0%
+of atoms as their lewis dot
+representation
+
+ align:start position:0%
+representation
+ 
+
+ align:start position:0%
+representation
+okay and like i said on wednesday we're
+
+ align:start position:0%
+okay and like i said on wednesday we're
+ 
+
+ align:start position:0%
+okay and like i said on wednesday we're
+going to make a whole bunch of
+
+ align:start position:0%
+going to make a whole bunch of
+ 
+
+ align:start position:0%
+going to make a whole bunch of
+structures molecules
+
+ align:start position:0%
+structures molecules
+ 
+
+ align:start position:0%
+structures molecules
+with lewis dots and and show how that
+
+ align:start position:0%
+with lewis dots and and show how that
+ 
+
+ align:start position:0%
+with lewis dots and and show how that
+teaches us
+
+ align:start position:0%
+teaches us
+ 
+
+ align:start position:0%
+teaches us
+not only about how to draw the bonds but
+
+ align:start position:0%
+not only about how to draw the bonds but
+ 
+
+ align:start position:0%
+not only about how to draw the bonds but
+literally about which config which
+
+ align:start position:0%
+literally about which config which
+ 
+
+ align:start position:0%
+literally about which config which
+bonding if i have sodium and chlorine
+
+ align:start position:0%
+bonding if i have sodium and chlorine
+ 
+
+ align:start position:0%
+bonding if i have sodium and chlorine
+it's pretty obvious
+
+ align:start position:0%
+it's pretty obvious
+ 
+
+ align:start position:0%
+it's pretty obvious
+if there's a bond it's between sodium
+
+ align:start position:0%
+if there's a bond it's between sodium
+ 
+
+ align:start position:0%
+if there's a bond it's between sodium
+and chlorine
+
+ align:start position:0%
+and chlorine
+ 
+
+ align:start position:0%
+and chlorine
+right but as i go to more and more atoms
+
+ align:start position:0%
+right but as i go to more and more atoms
+ 
+
+ align:start position:0%
+right but as i go to more and more atoms
+and i'm trying to form molecules
+
+ align:start position:0%
+and i'm trying to form molecules
+ 
+
+ align:start position:0%
+and i'm trying to form molecules
+it's not so obvious what is bonded to
+
+ align:start position:0%
+it's not so obvious what is bonded to
+ 
+
+ align:start position:0%
+it's not so obvious what is bonded to
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+and how right and thinking about
+
+ align:start position:0%
+and how right and thinking about
+ 
+
+ align:start position:0%
+and how right and thinking about
+this and thinking about the third
+
+ align:start position:0%
+this and thinking about the third
+ 
+
+ align:start position:0%
+this and thinking about the third
+part of what lewis did that was so
+
+ align:start position:0%
+part of what lewis did that was so
+ 
+
+ align:start position:0%
+part of what lewis did that was so
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+is what allows us to draw a whole bunch
+
+ align:start position:0%
+is what allows us to draw a whole bunch
+ 
+
+ align:start position:0%
+is what allows us to draw a whole bunch
+of molecules octet rule
+
+ align:start position:0%
+of molecules octet rule
+ 
+
+ align:start position:0%
+of molecules octet rule
+which is that atoms
+
+ align:start position:0%
+which is that atoms
+ 
+
+ align:start position:0%
+which is that atoms
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we now know like means
+
+ align:start position:0%
+and we now know like means
+ 
+
+ align:start position:0%
+and we now know like means
+lower energy to reach eight
+
+ align:start position:0%
+lower energy to reach eight
+ 
+
+ align:start position:0%
+lower energy to reach eight
+electrons in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+their valence okay well we can already
+
+ align:start position:0%
+their valence okay well we can already
+ 
+
+ align:start position:0%
+their valence okay well we can already
+see this
+
+ align:start position:0%
+see this
+ 
+
+ align:start position:0%
+see this
+for the ionic bond that we've talked
+
+ align:start position:0%
+for the ionic bond that we've talked
+ 
+
+ align:start position:0%
+for the ionic bond that we've talked
+about and you can
+
+ align:start position:0%
+about and you can
+ 
+
+ align:start position:0%
+about and you can
+you can write this and i want you to
+
+ align:start position:0%
+you can write this and i want you to
+ 
+
+ align:start position:0%
+you can write this and i want you to
+write ionic bonds
+
+ align:start position:0%
+write ionic bonds
+ 
+
+ align:start position:0%
+write ionic bonds
+using lewis but in this case it's
+
+ align:start position:0%
+using lewis but in this case it's
+ 
+
+ align:start position:0%
+using lewis but in this case it's
+actually pretty
+
+ align:start position:0%
+actually pretty
+ 
+
+ align:start position:0%
+actually pretty
+straightforward right if i had for
+
+ align:start position:0%
+straightforward right if i had for
+ 
+
+ align:start position:0%
+straightforward right if i had for
+example uh let's
+
+ align:start position:0%
+example uh let's
+ 
+
+ align:start position:0%
+example uh let's
+let's get some more board space
+
+ align:start position:0%
+let's get some more board space
+ 
+
+ align:start position:0%
+let's get some more board space
+over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i had for example an ionic bond
+
+ align:start position:0%
+if i had for example an ionic bond
+ 
+
+ align:start position:0%
+if i had for example an ionic bond
+between cesium and fluorine
+
+ align:start position:0%
+between cesium and fluorine
+ 
+
+ align:start position:0%
+between cesium and fluorine
+so if i had cesium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and fluorine then the way i would think
+
+ align:start position:0%
+and fluorine then the way i would think
+ 
+
+ align:start position:0%
+and fluorine then the way i would think
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+in the lewis world would be
+
+ align:start position:0%
+in the lewis world would be
+ 
+
+ align:start position:0%
+in the lewis world would be
+this way and
+
+ align:start position:0%
+this way and
+ 
+
+ align:start position:0%
+this way and
+this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because i've got seven valence electrons
+
+ align:start position:0%
+because i've got seven valence electrons
+ 
+
+ align:start position:0%
+because i've got seven valence electrons
+in fluorine and one in cesium
+
+ align:start position:0%
+in fluorine and one in cesium
+ 
+
+ align:start position:0%
+in fluorine and one in cesium
+and then if i write this as an ionic
+
+ align:start position:0%
+and then if i write this as an ionic
+ 
+
+ align:start position:0%
+and then if i write this as an ionic
+bond the way i would write it is
+
+ align:start position:0%
+bond the way i would write it is
+ 
+
+ align:start position:0%
+bond the way i would write it is
+cesium plus
+
+ align:start position:0%
+cesium plus
+ 
+
+ align:start position:0%
+cesium plus
+with fluorine having taken
+
+ align:start position:0%
+with fluorine having taken
+ 
+
+ align:start position:0%
+with fluorine having taken
+that electron now i'm not
+
+ align:start position:0%
+that electron now i'm not
+ 
+
+ align:start position:0%
+that electron now i'm not
+and so you would write this still with
+
+ align:start position:0%
+and so you would write this still with
+ 
+
+ align:start position:0%
+and so you would write this still with
+the minus sign there that emphasizes
+
+ align:start position:0%
+the minus sign there that emphasizes
+ 
+
+ align:start position:0%
+the minus sign there that emphasizes
+it emphasizes what happened but i see my
+
+ align:start position:0%
+it emphasizes what happened but i see my
+ 
+
+ align:start position:0%
+it emphasizes what happened but i see my
+lewis here
+
+ align:start position:0%
+lewis here
+ 
+
+ align:start position:0%
+lewis here
+you know i see it there but i'm
+
+ align:start position:0%
+you know i see it there but i'm
+ 
+
+ align:start position:0%
+you know i see it there but i'm
+emphasizing that this is an ionic
+
+ align:start position:0%
+emphasizing that this is an ionic
+ 
+
+ align:start position:0%
+emphasizing that this is an ionic
+bond that's happened because fluorine
+
+ align:start position:0%
+bond that's happened because fluorine
+ 
+
+ align:start position:0%
+bond that's happened because fluorine
+has wasn't supposed to have eight but
+
+ align:start position:0%
+has wasn't supposed to have eight but
+ 
+
+ align:start position:0%
+has wasn't supposed to have eight but
+then it did
+
+ align:start position:0%
+then it did
+ 
+
+ align:start position:0%
+then it did
+it's got a super high electron affinity
+
+ align:start position:0%
+it's got a super high electron affinity
+ 
+
+ align:start position:0%
+it's got a super high electron affinity
+cesium has a very low ionization energy
+
+ align:start position:0%
+cesium has a very low ionization energy
+ 
+
+ align:start position:0%
+cesium has a very low ionization energy
+of its first electron
+
+ align:start position:0%
+of its first electron
+ 
+
+ align:start position:0%
+of its first electron
+and so fluorine just took it it
+
+ align:start position:0%
+and so fluorine just took it it
+ 
+
+ align:start position:0%
+and so fluorine just took it it
+literally just took it
+
+ align:start position:0%
+literally just took it
+ 
+
+ align:start position:0%
+literally just took it
+i'll take that thank you very much you
+
+ align:start position:0%
+i'll take that thank you very much you
+ 
+
+ align:start position:0%
+i'll take that thank you very much you
+know i'm not being judgmental
+
+ align:start position:0%
+know i'm not being judgmental
+ 
+
+ align:start position:0%
+know i'm not being judgmental
+but ionic bonds are kind of you know the
+
+ align:start position:0%
+but ionic bonds are kind of you know the
+ 
+
+ align:start position:0%
+but ionic bonds are kind of you know the
+relationship
+
+ align:start position:0%
+relationship
+ 
+
+ align:start position:0%
+relationship
+in a bond and i don't want to judge but
+
+ align:start position:0%
+in a bond and i don't want to judge but
+ 
+
+ align:start position:0%
+in a bond and i don't want to judge but
+the relationship is not even
+
+ align:start position:0%
+the relationship is not even
+ 
+
+ align:start position:0%
+the relationship is not even
+it's not even and it's okay but they
+
+ align:start position:0%
+it's not even and it's okay but they
+ 
+
+ align:start position:0%
+it's not even and it's okay but they
+because what flooring said take
+
+ align:start position:0%
+because what flooring said take
+ 
+
+ align:start position:0%
+because what flooring said take
+take give and see okay fine
+
+ align:start position:0%
+take give and see okay fine
+ 
+
+ align:start position:0%
+take give and see okay fine
+now on wednesday when we do covalent
+
+ align:start position:0%
+now on wednesday when we do covalent
+ 
+
+ align:start position:0%
+now on wednesday when we do covalent
+bonds it's not so then there's a lot
+
+ align:start position:0%
+bonds it's not so then there's a lot
+ 
+
+ align:start position:0%
+bonds it's not so then there's a lot
+more sharing
+
+ align:start position:0%
+more sharing
+ 
+
+ align:start position:0%
+more sharing
+that happens but here and that's why we
+
+ align:start position:0%
+that happens but here and that's why we
+ 
+
+ align:start position:0%
+that happens but here and that's why we
+can model
+
+ align:start position:0%
+can model
+ 
+
+ align:start position:0%
+can model
+it the way that i yes i still left there
+
+ align:start position:0%
+it the way that i yes i still left there
+ 
+
+ align:start position:0%
+it the way that i yes i still left there
+we can model it that way
+
+ align:start position:0%
+we can model it that way
+ 
+
+ align:start position:0%
+we can model it that way
+because it is like a charged atom in
+
+ align:start position:0%
+because it is like a charged atom in
+ 
+
+ align:start position:0%
+because it is like a charged atom in
+another charged atom
+
+ align:start position:0%
+another charged atom
+ 
+
+ align:start position:0%
+another charged atom
+right and it's because flooring took it
+
+ align:start position:0%
+right and it's because flooring took it
+ 
+
+ align:start position:0%
+right and it's because flooring took it
+laureen took it it's okay any kind of
+
+ align:start position:0%
+laureen took it it's okay any kind of
+ 
+
+ align:start position:0%
+laureen took it it's okay any kind of
+relationship
+
+ align:start position:0%
+relationship
+ 
+
+ align:start position:0%
+relationship
+you know they get along they make it
+
+ align:start position:0%
+you know they get along they make it
+ 
+
+ align:start position:0%
+you know they get along they make it
+work now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we can also do and just in thinking
+
+ align:start position:0%
+what we can also do and just in thinking
+ 
+
+ align:start position:0%
+what we can also do and just in thinking
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+just in thinking about this i could go
+
+ align:start position:0%
+just in thinking about this i could go
+ 
+
+ align:start position:0%
+just in thinking about this i could go
+to another example like calcium
+
+ align:start position:0%
+to another example like calcium
+ 
+
+ align:start position:0%
+to another example like calcium
+and if i think about calcium and
+
+ align:start position:0%
+and if i think about calcium and
+ 
+
+ align:start position:0%
+and if i think about calcium and
+fluorine well i know again fluorine
+
+ align:start position:0%
+fluorine well i know again fluorine
+ 
+
+ align:start position:0%
+fluorine well i know again fluorine
+likes to be f minus but see calcium when
+
+ align:start position:0%
+likes to be f minus but see calcium when
+ 
+
+ align:start position:0%
+likes to be f minus but see calcium when
+i think about it as a lewis
+
+ align:start position:0%
+i think about it as a lewis
+ 
+
+ align:start position:0%
+i think about it as a lewis
+atom yeah calcium likes to lose both of
+
+ align:start position:0%
+atom yeah calcium likes to lose both of
+ 
+
+ align:start position:0%
+atom yeah calcium likes to lose both of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+calcium often because remember they want
+
+ align:start position:0%
+calcium often because remember they want
+ 
+
+ align:start position:0%
+calcium often because remember they want
+to get to that
+
+ align:start position:0%
+to get to that
+ 
+
+ align:start position:0%
+to get to that
+the octet rule they want to reach their
+
+ align:start position:0%
+the octet rule they want to reach their
+ 
+
+ align:start position:0%
+the octet rule they want to reach their
+va
+
+ align:start position:0%
+va
+ 
+
+ align:start position:0%
+va
+they're eight electrons but calcium's
+
+ align:start position:0%
+they're eight electrons but calcium's
+ 
+
+ align:start position:0%
+they're eight electrons but calcium's
+got two what do i do either somebody
+
+ align:start position:0%
+got two what do i do either somebody
+ 
+
+ align:start position:0%
+got two what do i do either somebody
+gives me six
+
+ align:start position:0%
+gives me six
+ 
+
+ align:start position:0%
+gives me six
+not going to happen or i can lose two
+
+ align:start position:0%
+not going to happen or i can lose two
+ 
+
+ align:start position:0%
+not going to happen or i can lose two
+and so what you get is that calcium will
+
+ align:start position:0%
+and so what you get is that calcium will
+ 
+
+ align:start position:0%
+and so what you get is that calcium will
+go you know
+
+ align:start position:0%
+go you know
+ 
+
+ align:start position:0%
+go you know
+to ca2 plus and but fluorine is still
+
+ align:start position:0%
+to ca2 plus and but fluorine is still
+ 
+
+ align:start position:0%
+to ca2 plus and but fluorine is still
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+f minus right from this i know that the
+
+ align:start position:0%
+f minus right from this i know that the
+ 
+
+ align:start position:0%
+f minus right from this i know that the
+balanced stoichiometry
+
+ align:start position:0%
+balanced stoichiometry
+ 
+
+ align:start position:0%
+balanced stoichiometry
+that is to say how many calcium atoms i
+
+ align:start position:0%
+that is to say how many calcium atoms i
+ 
+
+ align:start position:0%
+that is to say how many calcium atoms i
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+to stabilize this whole ionic bond
+
+ align:start position:0%
+to stabilize this whole ionic bond
+ 
+
+ align:start position:0%
+to stabilize this whole ionic bond
+situation
+
+ align:start position:0%
+situation
+ 
+
+ align:start position:0%
+situation
+is going to be two right i gotta go to
+
+ align:start position:0%
+is going to be two right i gotta go to
+ 
+
+ align:start position:0%
+is going to be two right i gotta go to
+calcium
+
+ align:start position:0%
+calcium
+ 
+
+ align:start position:0%
+calcium
+f2 and if i were going to write this as
+
+ align:start position:0%
+f2 and if i were going to write this as
+ 
+
+ align:start position:0%
+f2 and if i were going to write this as
+with emphasizing the ionic bond i might
+
+ align:start position:0%
+with emphasizing the ionic bond i might
+ 
+
+ align:start position:0%
+with emphasizing the ionic bond i might
+put brackets around just so it's really
+
+ align:start position:0%
+put brackets around just so it's really
+ 
+
+ align:start position:0%
+put brackets around just so it's really
+easy to see
+
+ align:start position:0%
+easy to see
+ 
+
+ align:start position:0%
+easy to see
+two plus there's no dots left because
+
+ align:start position:0%
+two plus there's no dots left because
+ 
+
+ align:start position:0%
+two plus there's no dots left because
+now i'm writing it in a way where i've
+
+ align:start position:0%
+now i'm writing it in a way where i've
+ 
+
+ align:start position:0%
+now i'm writing it in a way where i've
+emphasized
+
+ align:start position:0%
+emphasized
+ 
+
+ align:start position:0%
+emphasized
+that because in tight that f took it
+
+ align:start position:0%
+that because in tight that f took it
+ 
+
+ align:start position:0%
+that because in tight that f took it
+it took it and it is minus
+
+ align:start position:0%
+it took it and it is minus
+ 
+
+ align:start position:0%
+it took it and it is minus
+and there's two of them you see
+
+ align:start position:0%
+and there's two of them you see
+ 
+
+ align:start position:0%
+and there's two of them you see
+so that would be like thinking about an
+
+ align:start position:0%
+so that would be like thinking about an
+ 
+
+ align:start position:0%
+so that would be like thinking about an
+ionic bond
+
+ align:start position:0%
+ionic bond
+ 
+
+ align:start position:0%
+ionic bond
+right but from the lewis dot advantage
+
+ align:start position:0%
+right but from the lewis dot advantage
+ 
+
+ align:start position:0%
+right but from the lewis dot advantage
+point where i really
+
+ align:start position:0%
+point where i really
+ 
+
+ align:start position:0%
+point where i really
+see that flooring took the charge
+
+ align:start position:0%
+see that flooring took the charge
+ 
+
+ align:start position:0%
+see that flooring took the charge
+okay okay so i think
+
+ align:start position:0%
+okay okay so i think
+ 
+
+ align:start position:0%
+okay okay so i think
+and you can go further
+
+ align:start position:0%
+and you can go further
+ 
+
+ align:start position:0%
+and you can go further
+you can go further i think we'll stop
+
+ align:start position:0%
+you can go further i think we'll stop
+ 
+
+ align:start position:0%
+you can go further i think we'll stop
+there and on wednesday like i said
+
+ align:start position:0%
+there and on wednesday like i said
+ 
+
+ align:start position:0%
+there and on wednesday like i said
+we're going lewis all the way and we're
+
+ align:start position:0%
+we're going lewis all the way and we're
+ 
+
+ align:start position:0%
+we're going lewis all the way and we're
+doing covalent
+
+ align:start position:0%
+doing covalent
+ 
+
+ align:start position:0%
+doing covalent
+molecules covalent bonds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/LVfIS8pBI6Y.txt b/LVfIS8pBI6Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fd8a3548404064c82b2981444021afcfcbff2855
--- /dev/null
+++ b/LVfIS8pBI6Y.txt
@@ -0,0 +1,627 @@
+align:start position:0%
+ 
+here is a simple application of the law
+
+ align:start position:0%
+here is a simple application of the law
+ 
+
+ align:start position:0%
+here is a simple application of the law
+of iterated expectations we revisit the
+
+ align:start position:0%
+of iterated expectations we revisit the
+ 
+
+ align:start position:0%
+of iterated expectations we revisit the
+stick breaking example which we have
+
+ align:start position:0%
+stick breaking example which we have
+ 
+
+ align:start position:0%
+stick breaking example which we have
+seen sometime in the past so in this
+
+ align:start position:0%
+seen sometime in the past so in this
+ 
+
+ align:start position:0%
+seen sometime in the past so in this
+example we start with a stick that has a
+
+ align:start position:0%
+example we start with a stick that has a
+ 
+
+ align:start position:0%
+example we start with a stick that has a
+certain length and which we break at the
+
+ align:start position:0%
+certain length and which we break at the
+ 
+
+ align:start position:0%
+certain length and which we break at the
+point that chosen uniformly at random
+
+ align:start position:0%
+point that chosen uniformly at random
+ 
+
+ align:start position:0%
+point that chosen uniformly at random
+throughout the length of the stick and
+
+ align:start position:0%
+throughout the length of the stick and
+ 
+
+ align:start position:0%
+throughout the length of the stick and
+we call the point at which we cut the
+
+ align:start position:0%
+we call the point at which we cut the
+ 
+
+ align:start position:0%
+we call the point at which we cut the
+stick Capital y so the random variable Y
+
+ align:start position:0%
+stick Capital y so the random variable Y
+ 
+
+ align:start position:0%
+stick Capital y so the random variable Y
+has a uniform distribution on the
+
+ align:start position:0%
+has a uniform distribution on the
+ 
+
+ align:start position:0%
+has a uniform distribution on the
+interval from zero to L and is described
+
+ align:start position:0%
+interval from zero to L and is described
+ 
+
+ align:start position:0%
+interval from zero to L and is described
+by this particular PDF then we take the
+
+ align:start position:0%
+by this particular PDF then we take the
+ 
+
+ align:start position:0%
+by this particular PDF then we take the
+piece of the stick that's left and we
+
+ align:start position:0%
+piece of the stick that's left and we
+ 
+
+ align:start position:0%
+piece of the stick that's left and we
+break it at a point that's chosen
+
+ align:start position:0%
+break it at a point that's chosen
+ 
+
+ align:start position:0%
+break it at a point that's chosen
+uniformly over the length of the stick
+
+ align:start position:0%
+uniformly over the length of the stick
+ 
+
+ align:start position:0%
+uniformly over the length of the stick
+that's left so the stick that was left
+
+ align:start position:0%
+that's left so the stick that was left
+ 
+
+ align:start position:0%
+that's left so the stick that was left
+has a length Y and the place at which we
+
+ align:start position:0%
+has a length Y and the place at which we
+ 
+
+ align:start position:0%
+has a length Y and the place at which we
+cut it X is chosen uniformly over that
+
+ align:start position:0%
+cut it X is chosen uniformly over that
+ 
+
+ align:start position:0%
+cut it X is chosen uniformly over that
+interval so in particular X or rather
+
+ align:start position:0%
+interval so in particular X or rather
+ 
+
+ align:start position:0%
+interval so in particular X or rather
+the conditional distribution of x given
+
+ align:start position:0%
+the conditional distribution of x given
+ 
+
+ align:start position:0%
+the conditional distribution of x given
+Y is uniform on that interval so in this
+
+ align:start position:0%
+Y is uniform on that interval so in this
+ 
+
+ align:start position:0%
+Y is uniform on that interval so in this
+example what is the expected value of X
+
+ align:start position:0%
+example what is the expected value of X
+ 
+
+ align:start position:0%
+example what is the expected value of X
+if I tell you the value of y well given
+
+ align:start position:0%
+if I tell you the value of y well given
+ 
+
+ align:start position:0%
+if I tell you the value of y well given
+the value of y the random variable X is
+
+ align:start position:0%
+the value of y the random variable X is
+ 
+
+ align:start position:0%
+the value of y the random variable X is
+uniform on that range so the expected
+
+ align:start position:0%
+uniform on that range so the expected
+ 
+
+ align:start position:0%
+uniform on that range so the expected
+value is going to be at the midpoint and
+
+ align:start position:0%
+value is going to be at the midpoint and
+ 
+
+ align:start position:0%
+value is going to be at the midpoint and
+is equal to Y over 2 this is an equality
+
+ align:start position:0%
+is equal to Y over 2 this is an equality
+ 
+
+ align:start position:0%
+is equal to Y over 2 this is an equality
+between numbers for any particular
+
+ align:start position:0%
+between numbers for any particular
+ 
+
+ align:start position:0%
+between numbers for any particular
+number little why we have this equality
+
+ align:start position:0%
+number little why we have this equality
+ 
+
+ align:start position:0%
+number little why we have this equality
+now let us convert this concrete
+
+ align:start position:0%
+now let us convert this concrete
+ 
+
+ align:start position:0%
+now let us convert this concrete
+equality between numbers to a more
+
+ align:start position:0%
+equality between numbers to a more
+ 
+
+ align:start position:0%
+equality between numbers to a more
+abstract equality between random
+
+ align:start position:0%
+abstract equality between random
+ 
+
+ align:start position:0%
+abstract equality between random
+variables this object is a random
+
+ align:start position:0%
+variables this object is a random
+ 
+
+ align:start position:0%
+variables this object is a random
+variable that takes this value whenever
+
+ align:start position:0%
+variable that takes this value whenever
+ 
+
+ align:start position:0%
+variable that takes this value whenever
+Capital y is little Y so this is an
+
+ align:start position:0%
+Capital y is little Y so this is an
+ 
+
+ align:start position:0%
+Capital y is little Y so this is an
+object that takes the value little Y
+
+ align:start position:0%
+object that takes the value little Y
+ 
+
+ align:start position:0%
+object that takes the value little Y
+over 2 whenever the random variable
+
+ align:start position:0%
+over 2 whenever the random variable
+ 
+
+ align:start position:0%
+over 2 whenever the random variable
+capital Y happens to be little Y but
+
+ align:start position:0%
+capital Y happens to be little Y but
+ 
+
+ align:start position:0%
+capital Y happens to be little Y but
+that's the same as the random variable
+
+ align:start position:0%
+that's the same as the random variable
+ 
+
+ align:start position:0%
+that's the same as the random variable
+capital y over 2 this is a random
+
+ align:start position:0%
+capital y over 2 this is a random
+ 
+
+ align:start position:0%
+capital y over 2 this is a random
+variable that takes this value whenever
+
+ align:start position:0%
+variable that takes this value whenever
+ 
+
+ align:start position:0%
+variable that takes this value whenever
+capital y happens to be the same as
+
+ align:start position:0%
+capital y happens to be the same as
+ 
+
+ align:start position:0%
+capital y happens to be the same as
+little Y so the conditional expectation
+
+ align:start position:0%
+little Y so the conditional expectation
+ 
+
+ align:start position:0%
+little Y so the conditional expectation
+the abstract conditional expectation is
+
+ align:start position:0%
+the abstract conditional expectation is
+ 
+
+ align:start position:0%
+the abstract conditional expectation is
+a random variable
+
+ align:start position:0%
+a random variable
+ 
+
+ align:start position:0%
+a random variable
+because its value is determined by the
+
+ align:start position:0%
+because its value is determined by the
+ 
+
+ align:start position:0%
+because its value is determined by the
+random variable Capital y and it is this
+
+ align:start position:0%
+random variable Capital y and it is this
+ 
+
+ align:start position:0%
+random variable Capital y and it is this
+particular function of the random
+
+ align:start position:0%
+particular function of the random
+ 
+
+ align:start position:0%
+particular function of the random
+variable Capital y and now we can
+
+ align:start position:0%
+variable Capital y and now we can
+ 
+
+ align:start position:0%
+variable Capital y and now we can
+proceed and calculate the expected value
+
+ align:start position:0%
+proceed and calculate the expected value
+ 
+
+ align:start position:0%
+proceed and calculate the expected value
+of X using the law of iterated
+
+ align:start position:0%
+of X using the law of iterated
+ 
+
+ align:start position:0%
+of X using the law of iterated
+expectations the law of iterated
+
+ align:start position:0%
+expectations the law of iterated
+ 
+
+ align:start position:0%
+expectations the law of iterated
+expectations takes this form we have
+
+ align:start position:0%
+expectations takes this form we have
+ 
+
+ align:start position:0%
+expectations takes this form we have
+already calculated what this random
+
+ align:start position:0%
+already calculated what this random
+ 
+
+ align:start position:0%
+already calculated what this random
+variable is it is the random variable
+
+ align:start position:0%
+variable is it is the random variable
+ 
+
+ align:start position:0%
+variable is it is the random variable
+that's equal to Y over 2 so this is the
+
+ align:start position:0%
+that's equal to Y over 2 so this is the
+ 
+
+ align:start position:0%
+that's equal to Y over 2 so this is the
+same as 1/2 the expected value of Y and
+
+ align:start position:0%
+same as 1/2 the expected value of Y and
+ 
+
+ align:start position:0%
+same as 1/2 the expected value of Y and
+since Y is uniform in the range from 0
+
+ align:start position:0%
+since Y is uniform in the range from 0
+ 
+
+ align:start position:0%
+since Y is uniform in the range from 0
+to 12 the expected value of y is equal
+
+ align:start position:0%
+to 12 the expected value of y is equal
+ 
+
+ align:start position:0%
+to 12 the expected value of y is equal
+to L over 2 which gives us an answer of
+
+ align:start position:0%
+to L over 2 which gives us an answer of
+ 
+
+ align:start position:0%
+to L over 2 which gives us an answer of
+L over 4 this is the same as the answer
+
+ align:start position:0%
+L over 4 this is the same as the answer
+ 
+
+ align:start position:0%
+L over 4 this is the same as the answer
+that we got in the past where we
+
+ align:start position:0%
+that we got in the past where we
+ 
+
+ align:start position:0%
+that we got in the past where we
+actually found it using the total
+
+ align:start position:0%
+actually found it using the total
+ 
+
+ align:start position:0%
+actually found it using the total
+expectation theorem the calculations
+
+ align:start position:0%
+expectation theorem the calculations
+ 
+
+ align:start position:0%
+expectation theorem the calculations
+were exactly the same as what went on
+
+ align:start position:0%
+were exactly the same as what went on
+ 
+
+ align:start position:0%
+were exactly the same as what went on
+here except that here we carry out the
+
+ align:start position:0%
+here except that here we carry out the
+ 
+
+ align:start position:0%
+here except that here we carry out the
+calculation in a more abstract form and
+
+ align:start position:0%
+calculation in a more abstract form and
+ 
+
+ align:start position:0%
+calculation in a more abstract form and
+what is important to appreciate from
+
+ align:start position:0%
+what is important to appreciate from
+ 
+
+ align:start position:0%
+what is important to appreciate from
+this example is the distinction between
+
+ align:start position:0%
+this example is the distinction between
+ 
+
+ align:start position:0%
+this example is the distinction between
+these two lines this is an equality
+
+ align:start position:0%
+these two lines this is an equality
+ 
+
+ align:start position:0%
+these two lines this is an equality
+between numbers which is true for any
+
+ align:start position:0%
+between numbers which is true for any
+ 
+
+ align:start position:0%
+between numbers which is true for any
+specific little Y who are as this is an
+
+ align:start position:0%
+specific little Y who are as this is an
+ 
+
+ align:start position:0%
+specific little Y who are as this is an
+equality between random variables this
+
+ align:start position:0%
+equality between random variables this
+ 
+
+ align:start position:0%
+equality between random variables this
+quantity is random and this quantity is
+
+ align:start position:0%
+quantity is random and this quantity is
+ 
+
+ align:start position:0%
+quantity is random and this quantity is
+also random meaning that their values
+
+ align:start position:0%
+also random meaning that their values
+ 
+
+ align:start position:0%
+also random meaning that their values
+are not known until the experiment is
+
+ align:start position:0%
+are not known until the experiment is
+ 
+
+ align:start position:0%
+are not known until the experiment is
+carried out and the specific value of
+
+ align:start position:0%
+carried out and the specific value of
+ 
+
+ align:start position:0%
+carried out and the specific value of
+capital y is realized
\ No newline at end of file
diff --git a/LhPZwdhutgU.txt b/LhPZwdhutgU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ac046d323d5e64ccb3f7126bb1c5cc7230b34f7e
--- /dev/null
+++ b/LhPZwdhutgU.txt
@@ -0,0 +1,261 @@
+PROFESSOR: Hello.
+
+I'm Ian Hutchinson, and the
+purpose of this short video
+
+is to give you illustration
+of how to use Octave.
+
+I'm certainly not an
+expert at [? Octave, ?]
+
+which is an open source
+equivalent of MATLAB,
+
+but that's part of
+the demonstration.
+
+Here's someone who's
+not an expert who
+
+can use this routine
+for carrying out
+
+the kinds of exercises
+that we want to do.
+
+So I'm going to delete my
+picture from the screen
+
+now, and just show you
+the rest of the screen.
+
+Here I am in a directory.
+
+I'm going to start a new file.
+
+It's going to be called fitting.
+
+Let's say, fitting.m,
+is the correct extension
+
+for a MATLAB or Octave file.
+
+And I've opened Emax, and
+I'm ready to get started.
+
+Actually, I'm going to
+run Octave simultaneously
+
+in the adjacent window.
+
+I run Octave here.
+
+So now I'm in a situation
+where I, essentially,
+
+have my own IDE, integrated
+development environment.
+
+It's not quite the
+same as you would
+
+have if you're
+running MATLAB itself,
+
+but it's pretty similar.
+
+What I'm going to do now is
+develop this fitting program.
+
+I'm going to start
+with some parameters.
+
+Let's, first of all,
+define the number
+
+of points I'm going to fit.
+
+Let's make it a small number,
+so that it's kind of manageable.
+
+And now, let's generate
+some x and y values.
+
+I can set x to be
+equal to an array.
+
+It might be an array
+with six points.
+
+And I'm going to make it
+be run from 1 to endpoints.
+
+And so I do that by saying
+x is equal to 1 colon
+
+endpoints like this.
+
+I can save this file--
+it's called fitting--
+
+and then I can run it in
+Octave by just typing fitting.
+
+If I do that, what
+you see happens is,
+
+it tells me that endpoints is 6.
+
+Tells me that x is
+1, 2, 3, 4, 5, and 6.
+
+Actually, I don't want
+it to run from 1 to 6.
+
+I want it to run
+from, essentially,
+
+a small value up to 1.
+
+So let's divide
+it by end points.
+
+And I can save that file
+again, run it again,
+
+and now, of course,
+my screen shows
+
+that it runs from 1/6 up to 1.
+
+This is, of course,
+a row vector.
+
+It's preferable that I
+have a column vector.
+
+I can transform a row
+vector into a column vector
+
+by taking its transpose.
+
+In MATLAB or Octave,
+transpose is prime.
+
+So I can say,
+transpose the numbers 1
+
+through 6 into a column vector
+and then divide by endpoints.
+
+And if I do that
+and save the file,
+
+then I see I've turned
+it into a column vector.
+
+Let me now make a y variable.
+
+y, I'm going to make
+equal to x, let's say.
+
+That would just give
+me a straight line,
+
+if I made it nothing but x.
+
+Then I'll add to it
+some small fraction--
+
+let's say, 1/10th-- not 0.1
+times the sine of, let us say,
+
+10 x.
+
+I can save that file.
+
+I can run it again.
+
+And it tells me,
+here's x and here's y.
+
+That's given me a start.
+
+Actually, it's a
+bit inconvenient
+
+to see it in quite those terms.
+
+So let's actually
+try to plot it.
+
+So I can say plot x y.
+
+Save that and run it.
+
+And lo and behold,
+it brings up a plot.
+
+The labeling is
+rather too small,
+
+but that's kind of built
+into the rather poor graphics
+
+in Octave and MATLAB,
+for that matter.
+
+That can be fixed in ways
+that I'll go into later,
+
+but we won't worry about it now.
+
+This is a line plot, which
+is a little bit annoying.
+
+So let's change that plot.
+
+I'll put the figure over here.
+
+I'll change that
+plot by telling it
+
+that it's going to have
+points, and those points
+
+are going to have the
+form of a plus sign.
+
+So let's save that
+and run it again.
+
+And Lo and behold, it's changed
+it to a plot with points.
+
+Again, the markers are
+rather unpleasantly small.
+
+I can actually change that
+if I want by telling it
+
+a string marker size.
+
+Making that size larger than
+it would be-- let's say, 20--
+
+and running it again.
+
+And lo and behold,
+the points are bigger.
+
+So we've started, and
+we've made, some data.
+
+And we've used parameters.
+
+And in our next
+video, we'll move on
+
+to finding out how to
+proceed on that basis.
\ No newline at end of file
diff --git a/Lq6Os-qABK4.txt b/Lq6Os-qABK4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..09c511f8b36aed63a374f0fe7262c7834293fa06
--- /dev/null
+++ b/Lq6Os-qABK4.txt
@@ -0,0 +1,1123 @@
+align:start position:0%
+ 
+welcome to lab four the spectrometer lab
+
+ align:start position:0%
+welcome to lab four the spectrometer lab
+ 
+
+ align:start position:0%
+welcome to lab four the spectrometer lab
+in this lab you will learn some basic
+
+ align:start position:0%
+in this lab you will learn some basic
+ 
+
+ align:start position:0%
+in this lab you will learn some basic
+concepts in Optics and
+
+ align:start position:0%
+concepts in Optics and
+ 
+
+ align:start position:0%
+concepts in Optics and
+photonics you will also use a simple
+
+ align:start position:0%
+photonics you will also use a simple
+ 
+
+ align:start position:0%
+photonics you will also use a simple
+spectrometer setup to characterize a die
+
+ align:start position:0%
+spectrometer setup to characterize a die
+ 
+
+ align:start position:0%
+spectrometer setup to characterize a die
+called arthin extra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bluish let's begin with the preab
+
+ align:start position:0%
+bluish let's begin with the preab
+ 
+
+ align:start position:0%
+bluish let's begin with the preab
+building a fiber coupled LED light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the components of the preab
+
+ align:start position:0%
+the components of the preab
+ 
+
+ align:start position:0%
+the components of the preab
+include a super bright white light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LED a 200 Ohm
+
+ align:start position:0%
+LED a 200 Ohm
+ 
+
+ align:start position:0%
+LED a 200 Ohm
+resistor a battery strap and a 9vt
+
+ align:start position:0%
+resistor a battery strap and a 9vt
+ 
+
+ align:start position:0%
+resistor a battery strap and a 9vt
+battery a piece of multimode
+
+ align:start position:0%
+battery a piece of multimode
+ 
+
+ align:start position:0%
+battery a piece of multimode
+fiber some
+
+ align:start position:0%
+fiber some
+ 
+
+ align:start position:0%
+fiber some
+sandpaper epoxy or glue and a stick for
+
+ align:start position:0%
+sandpaper epoxy or glue and a stick for
+ 
+
+ align:start position:0%
+sandpaper epoxy or glue and a stick for
+application
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you will need to sand away the plastic
+
+ align:start position:0%
+you will need to sand away the plastic
+ 
+
+ align:start position:0%
+you will need to sand away the plastic
+in the front of the LED to make better
+
+ align:start position:0%
+in the front of the LED to make better
+ 
+
+ align:start position:0%
+in the front of the LED to make better
+coupling with the fiber start with the
+
+ align:start position:0%
+coupling with the fiber start with the
+ 
+
+ align:start position:0%
+coupling with the fiber start with the
+rough sandpaper and use the finer
+
+ align:start position:0%
+rough sandpaper and use the finer
+ 
+
+ align:start position:0%
+rough sandpaper and use the finer
+sandpaper later you may sand close to
+
+ align:start position:0%
+sandpaper later you may sand close to
+ 
+
+ align:start position:0%
+sandpaper later you may sand close to
+the bond wire but make sure not to break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the first part of the lab you will be
+
+ align:start position:0%
+in the first part of the lab you will be
+ 
+
+ align:start position:0%
+in the first part of the lab you will be
+observing the fernel coefficients
+
+ align:start position:0%
+observing the fernel coefficients
+ 
+
+ align:start position:0%
+observing the fernel coefficients
+you will measure Fel Reflections from a
+
+ align:start position:0%
+you will measure Fel Reflections from a
+ 
+
+ align:start position:0%
+you will measure Fel Reflections from a
+semicircular acrylic
+
+ align:start position:0%
+semicircular acrylic
+ 
+
+ align:start position:0%
+semicircular acrylic
+prism here's the setup as viewed from
+
+ align:start position:0%
+prism here's the setup as viewed from
+ 
+
+ align:start position:0%
+prism here's the setup as viewed from
+the top you will use a red diode laser a
+
+ align:start position:0%
+the top you will use a red diode laser a
+ 
+
+ align:start position:0%
+the top you will use a red diode laser a
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+polarizer the acrylic prism mounted on a
+
+ align:start position:0%
+polarizer the acrylic prism mounted on a
+ 
+
+ align:start position:0%
+polarizer the acrylic prism mounted on a
+rotational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stage and a high sensitivity power meter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Begin by characterizing the
+
+ align:start position:0%
+Begin by characterizing the
+ 
+
+ align:start position:0%
+Begin by characterizing the
+polarizer you can understand the
+
+ align:start position:0%
+polarizer you can understand the
+ 
+
+ align:start position:0%
+polarizer you can understand the
+direction of the polarizer by looking at
+
+ align:start position:0%
+direction of the polarizer by looking at
+ 
+
+ align:start position:0%
+direction of the polarizer by looking at
+how it attenuates light reflected from a
+
+ align:start position:0%
+how it attenuates light reflected from a
+ 
+
+ align:start position:0%
+how it attenuates light reflected from a
+flat surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set the polarizer to pass the TM
+
+ align:start position:0%
+set the polarizer to pass the TM
+ 
+
+ align:start position:0%
+set the polarizer to pass the TM
+polarization align the back reflected
+
+ align:start position:0%
+polarization align the back reflected
+ 
+
+ align:start position:0%
+polarization align the back reflected
+beam toward the incoming Direction this
+
+ align:start position:0%
+beam toward the incoming Direction this
+ 
+
+ align:start position:0%
+beam toward the incoming Direction this
+will calibrate 0° or normal
+
+ align:start position:0%
+will calibrate 0° or normal
+ 
+
+ align:start position:0%
+will calibrate 0° or normal
+incidents now measure the incident
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power change the angle of incidence by
+
+ align:start position:0%
+power change the angle of incidence by
+ 
+
+ align:start position:0%
+power change the angle of incidence by
+rotating the stage and measure the
+
+ align:start position:0%
+rotating the stage and measure the
+ 
+
+ align:start position:0%
+rotating the stage and measure the
+reflected Power Note the critical angle
+
+ align:start position:0%
+reflected Power Note the critical angle
+ 
+
+ align:start position:0%
+reflected Power Note the critical angle
+at which the transmitted power goes to
+
+ align:start position:0%
+at which the transmitted power goes to
+ 
+
+ align:start position:0%
+at which the transmitted power goes to
+zero for the TM polarization there is
+
+ align:start position:0%
+zero for the TM polarization there is
+ 
+
+ align:start position:0%
+zero for the TM polarization there is
+also a Brewster angle at which the
+
+ align:start position:0%
+also a Brewster angle at which the
+ 
+
+ align:start position:0%
+also a Brewster angle at which the
+reflected power goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now use the te polarization and make the
+
+ align:start position:0%
+now use the te polarization and make the
+ 
+
+ align:start position:0%
+now use the te polarization and make the
+same set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measurements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you will observe the index contrast
+
+ align:start position:0%
+now you will observe the index contrast
+ 
+
+ align:start position:0%
+now you will observe the index contrast
+in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fiber using the LED coupled fiber you
+
+ align:start position:0%
+fiber using the LED coupled fiber you
+ 
+
+ align:start position:0%
+fiber using the LED coupled fiber you
+made in the preab the num numerical
+
+ align:start position:0%
+made in the preab the num numerical
+ 
+
+ align:start position:0%
+made in the preab the num numerical
+aperture is easily found by observing
+
+ align:start position:0%
+aperture is easily found by observing
+ 
+
+ align:start position:0%
+aperture is easily found by observing
+the angle of the output light that's
+
+ align:start position:0%
+the angle of the output light that's
+ 
+
+ align:start position:0%
+the angle of the output light that's
+projected on a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protractor the refractive index of the
+
+ align:start position:0%
+protractor the refractive index of the
+ 
+
+ align:start position:0%
+protractor the refractive index of the
+fiber core is given in the handout the
+
+ align:start position:0%
+fiber core is given in the handout the
+ 
+
+ align:start position:0%
+fiber core is given in the handout the
+numerical aperture formula allows you to
+
+ align:start position:0%
+numerical aperture formula allows you to
+ 
+
+ align:start position:0%
+numerical aperture formula allows you to
+easily calculate the refractive index
+
+ align:start position:0%
+easily calculate the refractive index
+ 
+
+ align:start position:0%
+easily calculate the refractive index
+contrast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the next section of the lab you will
+
+ align:start position:0%
+in the next section of the lab you will
+ 
+
+ align:start position:0%
+in the next section of the lab you will
+be working with a liquid core wave guide
+
+ align:start position:0%
+be working with a liquid core wave guide
+ 
+
+ align:start position:0%
+be working with a liquid core wave guide
+filled with ethylene
+
+ align:start position:0%
+filled with ethylene
+ 
+
+ align:start position:0%
+filled with ethylene
+glycol make sure you're wearing gloves
+
+ align:start position:0%
+glycol make sure you're wearing gloves
+ 
+
+ align:start position:0%
+glycol make sure you're wearing gloves
+for this part of the
+
+ align:start position:0%
+for this part of the
+ 
+
+ align:start position:0%
+for this part of the
+experiment start with a length of Teflon
+
+ align:start position:0%
+experiment start with a length of Teflon
+ 
+
+ align:start position:0%
+experiment start with a length of Teflon
+tubing of about 100 mm length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extract some of the ethylene glycol
+
+ align:start position:0%
+extract some of the ethylene glycol
+ 
+
+ align:start position:0%
+extract some of the ethylene glycol
+using a clean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+syringe use the syringe to carefully
+
+ align:start position:0%
+syringe use the syringe to carefully
+ 
+
+ align:start position:0%
+syringe use the syringe to carefully
+fill the Teflon tubing making sure there
+
+ align:start position:0%
+fill the Teflon tubing making sure there
+ 
+
+ align:start position:0%
+fill the Teflon tubing making sure there
+are no
+
+ align:start position:0%
+are no
+ 
+
+ align:start position:0%
+are no
+bubbles it's ideal to have a small
+
+ align:start position:0%
+bubbles it's ideal to have a small
+ 
+
+ align:start position:0%
+bubbles it's ideal to have a small
+droplet at the end of the tubing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now carefully place the wave guide flush
+
+ align:start position:0%
+now carefully place the wave guide flush
+ 
+
+ align:start position:0%
+now carefully place the wave guide flush
+against the piece of glass glued to a
+
+ align:start position:0%
+against the piece of glass glued to a
+ 
+
+ align:start position:0%
+against the piece of glass glued to a
+fiber VG Grove
+
+ align:start position:0%
+fiber VG Grove
+ 
+
+ align:start position:0%
+fiber VG Grove
+holder this effectively seals the end of
+
+ align:start position:0%
+holder this effectively seals the end of
+ 
+
+ align:start position:0%
+holder this effectively seals the end of
+the wave guide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+couple the LED coupled fiber into the
+
+ align:start position:0%
+couple the LED coupled fiber into the
+ 
+
+ align:start position:0%
+couple the LED coupled fiber into the
+end of the wave guide by inserting it
+
+ align:start position:0%
+end of the wave guide by inserting it
+ 
+
+ align:start position:0%
+end of the wave guide by inserting it
+into the Teflon tube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure again the numerical aperture by
+
+ align:start position:0%
+measure again the numerical aperture by
+ 
+
+ align:start position:0%
+measure again the numerical aperture by
+observing the Divergence angle using a
+
+ align:start position:0%
+observing the Divergence angle using a
+ 
+
+ align:start position:0%
+observing the Divergence angle using a
+protractor because the index of the
+
+ align:start position:0%
+protractor because the index of the
+ 
+
+ align:start position:0%
+protractor because the index of the
+Teflon tubing is known this will allow
+
+ align:start position:0%
+Teflon tubing is known this will allow
+ 
+
+ align:start position:0%
+Teflon tubing is known this will allow
+you to calculate the index of ethylene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glycol the final inlab component is an
+
+ align:start position:0%
+glycol the final inlab component is an
+ 
+
+ align:start position:0%
+glycol the final inlab component is an
+experiment using a homebuilt
+
+ align:start position:0%
+experiment using a homebuilt
+ 
+
+ align:start position:0%
+experiment using a homebuilt
+spectrometer setup construct the
+
+ align:start position:0%
+spectrometer setup construct the
+ 
+
+ align:start position:0%
+spectrometer setup construct the
+spectrometer setup according to the
+
+ align:start position:0%
+spectrometer setup according to the
+ 
+
+ align:start position:0%
+spectrometer setup according to the
+drawing in the lab
+
+ align:start position:0%
+drawing in the lab
+ 
+
+ align:start position:0%
+drawing in the lab
+handout the light source will be the
+
+ align:start position:0%
+handout the light source will be the
+ 
+
+ align:start position:0%
+handout the light source will be the
+fiber coupled liquid core wave guide you
+
+ align:start position:0%
+fiber coupled liquid core wave guide you
+ 
+
+ align:start position:0%
+fiber coupled liquid core wave guide you
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+made set up a black screen with an X to
+
+ align:start position:0%
+made set up a black screen with an X to
+ 
+
+ align:start position:0%
+made set up a black screen with an X to
+focus the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+camera a digital
+
+ align:start position:0%
+camera a digital
+ 
+
+ align:start position:0%
+camera a digital
+camera a thin transmitting
+
+ align:start position:0%
+camera a thin transmitting
+ 
+
+ align:start position:0%
+camera a thin transmitting
+grading a flat mounting
+
+ align:start position:0%
+grading a flat mounting
+ 
+
+ align:start position:0%
+grading a flat mounting
+plate and four vials of ithin extra
+
+ align:start position:0%
+plate and four vials of ithin extra
+ 
+
+ align:start position:0%
+plate and four vials of ithin extra
+bluish at different
+
+ align:start position:0%
+bluish at different
+ 
+
+ align:start position:0%
+bluish at different
+concentrations note that V 4 is just
+
+ align:start position:0%
+concentrations note that V 4 is just
+ 
+
+ align:start position:0%
+concentrations note that V 4 is just
+water and used for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calibration e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once the focus of the camera and
+
+ align:start position:0%
+once the focus of the camera and
+ 
+
+ align:start position:0%
+once the focus of the camera and
+position of all components are optimized
+
+ align:start position:0%
+position of all components are optimized
+ 
+
+ align:start position:0%
+position of all components are optimized
+fix them to the table and do not move
+
+ align:start position:0%
+fix them to the table and do not move
+ 
+
+ align:start position:0%
+fix them to the table and do not move
+them for the rest of the
+
+ align:start position:0%
+them for the rest of the
+ 
+
+ align:start position:0%
+them for the rest of the
+experiment the camera should see a
+
+ align:start position:0%
+experiment the camera should see a
+ 
+
+ align:start position:0%
+experiment the camera should see a
+spectrum at the image plane of the black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+screen e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first remove the LED coupled fiber and
+
+ align:start position:0%
+first remove the LED coupled fiber and
+ 
+
+ align:start position:0%
+first remove the LED coupled fiber and
+insert instead a plain piece of fiber
+
+ align:start position:0%
+insert instead a plain piece of fiber
+ 
+
+ align:start position:0%
+insert instead a plain piece of fiber
+into the wave guide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calibrate the spectrometer by taking
+
+ align:start position:0%
+calibrate the spectrometer by taking
+ 
+
+ align:start position:0%
+calibrate the spectrometer by taking
+data for a green laser at 532 nanom and
+
+ align:start position:0%
+data for a green laser at 532 nanom and
+ 
+
+ align:start position:0%
+data for a green laser at 532 nanom and
+a red laser at around 650 nanom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+replace the LED cuple fiber once you're
+
+ align:start position:0%
+replace the LED cuple fiber once you're
+ 
+
+ align:start position:0%
+replace the LED cuple fiber once you're
+finished with the
+
+ align:start position:0%
+finished with the
+ 
+
+ align:start position:0%
+finished with the
+calibration Mount each D concentration
+
+ align:start position:0%
+calibration Mount each D concentration
+ 
+
+ align:start position:0%
+calibration Mount each D concentration
+in front of the light source and take
+
+ align:start position:0%
+in front of the light source and take
+ 
+
+ align:start position:0%
+in front of the light source and take
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Spectrum make sure to position the
+
+ align:start position:0%
+Spectrum make sure to position the
+ 
+
+ align:start position:0%
+Spectrum make sure to position the
+cuvette so the propagation thickness is
+
+ align:start position:0%
+cuvette so the propagation thickness is
+ 
+
+ align:start position:0%
+cuvette so the propagation thickness is
+1 cm long you will calculate the
+
+ align:start position:0%
+1 cm long you will calculate the
+ 
+
+ align:start position:0%
+1 cm long you will calculate the
+absorption and Molar Extinction
+
+ align:start position:0%
+absorption and Molar Extinction
+ 
+
+ align:start position:0%
+absorption and Molar Extinction
+coefficients in the postlab
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e for
\ No newline at end of file
diff --git a/MDcAOTaCXHs.txt b/MDcAOTaCXHs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b049a057b8d88f07e0e078c49c91645c5defdcae
--- /dev/null
+++ b/MDcAOTaCXHs.txt
@@ -0,0 +1,4502 @@
+I'm Erik Demaine.
+
+You can call me Erik.
+
+This is the web
+page for the class.
+
+You should all go there if you
+haven't already, and sign up
+
+on this sheet if you want
+to be on the mailing list.
+
+Good.
+
+So, maybe I'll tell you a little
+bit what this class about.
+
+Then I'll tell you about
+how the class works,
+
+and then we'll do more
+about what it's about.
+
+The idea of lecture 1 is
+to cover the entire class
+
+in one lecture.
+
+Obviously, I will omit
+a few of the details
+
+because we have a
+lot to cover, but I
+
+thought it would
+be fun to give you
+
+a picture what the whole class
+is, what the sort of content
+
+is, so you know whether
+you want to be here.
+
+And my chalk.
+
+So this class is about geometry.
+
+It's about folding.
+
+It's about algorithms.
+
+In general, we are interested in
+the mathematics and algorithms
+
+behind folding things.
+
+And also unfolding things,
+because that turns out
+
+to be pretty interesting.
+
+And the formal term for
+things is geometric objects.
+
+And you think of things
+like your arm folds.
+
+Pieces of paper fold.
+
+All sorts of things
+fold in the world.
+
+A lot of the-- if there's
+any sheet metal objects
+
+in this room, maybe
+some of these parts
+
+are folded out of sheet.
+
+I would guess so.
+
+So folding is everywhere,
+and this class
+
+is all about how that
+works mathematically.
+
+And I'm a theoretical
+computer scientist.
+
+I do algorithms, so my
+slant is towards algorithms,
+
+which is getting computers
+to do all this for you.
+
+How many people here
+are computer scientists?
+
+How many people are-- you've got
+to pick one-- mathematicians?
+
+How many people are
+neither of the above?
+
+Wow, cool.
+
+It's like not a lot of
+mathematicians only,
+
+but a lot of
+computer scientists,
+
+a lot of everyone else.
+
+So I'll go around later
+maybe and find out
+
+what your background is.
+
+You may be interested
+less in the mathematics
+
+and more in the
+applications, so let
+
+me tell you a little
+bit about those.
+
+I have a long list of
+applications, some of which
+
+have been realized,
+some of which
+
+are still in progress
+or just ideas.
+
+Robotics is a big one,
+folding robotic arms.
+
+And I'll show later different
+kinds of transforming robots,
+
+like Transformers or
+Terminator 2-style, where
+
+you want one robot to take on
+many different forms, this idea
+
+of programmable matter,
+where you can program
+
+the geometry of your
+object as well as you
+
+could program the software.
+
+So next time when you
+buy the new iPhone,
+
+you download the
+hardware in addition
+
+to downloading software.
+
+That would be the crazy idea.
+
+That, of course,
+doesn't exist yet.
+
+But it exists in
+some simple forms.
+
+Computer graphics.
+
+If you're making
+Toy Story 4, and you
+
+want to animate your characters
+from one position to another,
+
+you have some skeleton
+which is a foldable object,
+
+and you'd like to interpolate
+between two key frames
+
+that the animator
+draws automatically.
+
+That's a morphing problem,
+and it's a folding morphing
+
+problem.
+
+We have mechanics.
+
+A lot of the early folding
+work is in like 17, 1800s,
+
+and is motivated by
+building mechanical linkages
+
+to do useful things.
+
+This is back before
+electrical computers,
+
+we had mechanical
+computers of sorts.
+
+Things like you could sign
+your name in triplicate
+
+by just signing once,
+and having a linkage that
+
+made many copies of it.
+
+I think Jefferson
+used such a linkage.
+
+We have manufacturing, which
+is a pretty broad term--
+
+things like sheet metal bending.
+
+Nano manufacturing, I think,
+is an exciting context,
+
+where you can-- we're
+really good at building
+
+flat nano-scale
+objects like CPUs.
+
+And if you could
+get them to fold up,
+
+then you could manufacture
+3D nano-scale objects.
+
+I have optics here, Jason.
+
+Sure.
+
+George [INAUDIBLE] group
+does some optical devices
+
+through folding here at MIT.
+
+Medical is a big one.
+
+Imagine folding a
+stent really small,
+
+so it can fit through
+small blood vessels
+
+until it gets to where
+you want in your body
+
+and expands-- do
+non-intrusive heart surgery.
+
+Drug delivery is another one.
+
+You have some object you want
+to deliver, your cancer drug,
+
+so it follows through your body
+until it detects the cancer,
+
+and then it releases
+the drug, for example.
+
+Something we just
+started looking at.
+
+Aero-astro.
+
+You want to deploy something
+out in outer space.
+
+You've got to get it there
+first within the space shuttle.
+
+So how do you fold
+it down small so it
+
+fits in your space
+shuttle, and then expands
+
+when it gets there?
+
+Biology.
+
+Big one.
+
+I'm interested in
+protein folding.
+
+Proteins are the building block
+of all life forms we know,
+
+and we'd like to
+know how they fold.
+
+I'll show you some
+pictures of them later.
+
+We'll talk more
+about it, obviously,
+
+in the rest of the class.
+
+And the goal is to use
+this mathematics of folding
+
+to try to figure out what
+biology might be doing
+
+in real life, though that's
+still obviously very difficult.
+
+Sculpture, sort
+of an obvious one.
+
+Designing cooler
+origami is possible,
+
+thanks to mathematics
+and algorithms.
+
+Hopefully Jason agrees.
+
+Jason Ku is, I guess, the top
+origami designer currently
+
+at MIT.
+
+That's a safe bet.
+
+You could make
+some broader claim.
+
+And we'll get him to
+give a guest lecture
+
+on the more artistic
+side of origami,
+
+and I'll talk about the
+mathematics-- some of which
+
+is currently used
+in origami design
+
+today, either implicitly or
+explicitly, some of which
+
+is yet to be used, but hopefully
+will make cooler sculpture.
+
+You could also imagine
+building interactive sculpture.
+
+Interactive buildings'
+architecture
+
+is another big one.
+
+How many people
+here are architects?
+
+Cool.
+
+A bunch.
+
+So I think this is really
+exciting and underexploited
+
+at the moment,
+reconfigurable buildings.
+
+Hoberman is one
+example of somebody
+
+exploring this, getting the
+building to fold from one shape
+
+to another, or getting your
+shades to fold from one shape
+
+to another, all sorts of things.
+
+That's all I have.
+
+Maybe there are more.
+
+You're welcome to tell me.
+
+But this is somehow
+why you might
+
+care about the mathematics
+of folding things.
+
+And what else do I have?
+
+Yeah, let me tell you a
+little bit about the field.
+
+It's, in some sense, old.
+
+There are some problems in
+this world of geometric folding
+
+that go back four
+or five centuries.
+
+And some of those problems
+are still unsolved,
+
+but a lot of the
+action in the field
+
+has been in the
+last 12 years or so.
+
+And it's been really exciting.
+
+A lot of theorems
+have been proved.
+
+In fact, a lot of
+theorems have been
+
+proved in the context
+of previous iterations
+
+of this class.
+
+And so I always have
+to update things,
+
+because we keep
+getting new results.
+
+And the idea of this class
+is to cover the bleeding
+
+edge, whatever the
+frontiers of what's known,
+
+and also to push
+that edge further.
+
+So there is an open problem
+session, which is optional.
+
+But if you want to come solve
+new problems that haven't been
+
+solved before,
+every week probably
+
+we'll work on a problem related
+to what I cover in class.
+
+So you know what's
+known, and then we
+
+try to prove what's unknown.
+
+That's the idea.
+
+And that's worked
+pretty well in the past.
+
+Let's dive a little
+bit into the sort
+
+of mathematical structures.
+
+So say geometric objects.
+
+There are three main
+things that we typically
+
+think about, linkages, pieces
+of paper, and polyhedra.
+
+A linkage is something like
+your arm or a robotic arm.
+
+You have one-dimensional
+straight links like bones,
+
+and hinges that
+connect them together.
+
+And you'd like to know
+how that thing can fold.
+
+So this is like in the graphics
+world or mechanical linkage
+
+world.
+
+The typical way we
+think about linkages
+
+is that they have rigid bars.
+
+As opposed to a string,
+which is really floppy,
+
+here you have these rigid,
+like maybe metal, parts,
+
+and you can only
+fold at the hinges.
+
+That's typical
+thinking on linkages.
+
+Makes it interesting.
+
+And sometimes we also
+require no crossing.
+
+I'm trying to take a physical
+thing you have intuition for,
+
+and write some of the
+mathematical constraints.
+
+No crossing means you
+can't intersect yourself.
+
+Sometimes that's important.
+
+Sometimes it's not.
+
+In a lot of the
+mechanical linkage world
+
+you can have crossing
+bars, but just
+
+because they're in different
+planes in real life,
+
+if you're making a
+two-dimensional linkage.
+
+Paper.
+
+This is my drawing
+of a piece of paper.
+
+The rules are you
+are not allowed
+
+to stretch the
+material, and you're not
+
+allowed to tear or cut.
+
+So all you can do is fold.
+
+And so intuitively
+this is saying
+
+you can't make paper any longer.
+
+You can't really
+make it shorter.
+
+The only thing you can do
+is change its 3D geometry.
+
+But if you look really closely,
+the geometry is the same.
+
+It has a fixed
+intrinsic geometry.
+
+All the distances on the
+surface are staying the same.
+
+And usually in modern
+origami, you're
+
+not allowed to cut the
+paper, because that
+
+makes things too
+easy, basically.
+
+And I guess also
+no crossing here.
+
+It's a requirement.
+
+This is a pretty informal
+description of paper.
+
+You can formalize it.
+
+We will do that at some point.
+
+But it's pretty intuitive.
+
+You've all done it before.
+
+Polyhedron is something
+more three-dimensional.
+
+So here we had one-dimensional
+things we were folding.
+
+Two-dimensional things
+we were folding.
+
+A three-dimensional thing, or at
+least a two-dimensional surface
+
+in three dimensions,
+a typical thing
+
+you might want to do with
+a polyhedron is build it.
+
+And often you want to
+build something out
+
+of flat material, something
+like-- you've probably
+
+made a cube by building a
+cross, and then folding it up
+
+into that thing.
+
+That's the folding problem.
+
+The unfolding problem
+is, where do I
+
+cut along this surface
+in order to make
+
+one of these nice unfoldings?
+
+I think there's one more
+cut here in the back.
+
+If I did it right, that
+will unfold into the cross.
+
+So if I have some complicated
+3D shape, what 2D shape
+
+do I cut out in order to
+bend it into that 3D shape?
+
+That's the unfolding problem.
+
+There are actually
+lots of different kinds
+
+of polyhedron folding
+problems, but here it
+
+is you want to cut the surface.
+
+You want one piece-- it's
+a little harder to assemble
+
+multiple pieces-- and you'd like
+no overlap in that unfolding.
+
+Because if, when you
+unfold, it overlaps,
+
+then you can't
+actually make it out
+
+of one piece of sheet material.
+
+So these are the sorts
+of things we study.
+
+And I think the
+plan in the class
+
+is I will start with paper,
+because it's kind of the most
+
+fun, origami design,
+computational origami design.
+
+And then we'll talk about
+linkages and polyhedra.
+
+And I'll probably jump around
+from week to week, just
+
+to keep it exciting, because
+they're all interesting.
+
+You might each have
+your favorite one.
+
+And so that we can talk
+about all of them at once.
+
+So what kind of
+mathematical questions
+
+would you ask about
+these structures?
+
+Well, there are two main
+types I like to characterize.
+
+On the one hand, we have what
+I call foldability questions,
+
+where you're given some existing
+structure like a linkage,
+
+or a piece of paper with
+some creases on it maybe,
+
+and you'd like to know,
+how does that thing fold?
+
+So I give you some structure,
+and you'd like to know,
+
+does it fold?
+
+Maybe just does it fold at all?
+
+Or, in some particular
+way, can you
+
+make it fold into
+something interesting?
+
+Or some notion of interesting?
+
+I'm going to be generic
+here, because there's
+
+a lot of different
+questions obviously.
+
+And this is in contrast
+to a design question,
+
+where you're given-- what
+you start with is a goal.
+
+Like I want to make a butterfly.
+
+And then the question is, how
+do I fold a piece of paper
+
+to make that butterfly?
+
+So here you're given
+maybe a crease pattern
+
+and given some structure.
+
+You want to see how it folds.
+
+In design, you're
+given the goal and you
+
+want to figure out
+what you should build,
+
+what folding structure
+should I make
+
+that will achieve this goal?
+
+So what shapes?
+
+Shape is one thing
+you might want.
+
+But in general, you have some
+property you want to achieve.
+
+Can you fold it?
+
+And of course if you
+can, how do you do it?
+
+So this tends-- in
+general you could
+
+think of this as a more
+mathematical question, this
+
+as a more algorithmic question.
+
+But usually actually
+both of them
+
+are addressed with
+algorithms to some extent.
+
+Of course design
+is somehow cooler,
+
+but often we need to
+understand foldability
+
+before we can solve design.
+
+But not always.
+
+It depends.
+
+And just to give
+you like-- I mean
+
+if you looked at the entire
+set of results, the questions
+
+and answers, that we consider,
+and you filter them down,
+
+there would be three
+kinds of things
+
+that we prove in this class.
+
+These are the results.
+
+All the results
+in three bullets.
+
+It could be either
+you get universality.
+
+This is the coolest
+kind of result,
+
+and it's surprisingly common.
+
+Everything can be folded, for
+some notion of everything.
+
+That's always a challenge.
+
+And you get an
+algorithm to do it.
+
+So if you say I want
+to fold a butterfly,
+
+you put the butterfly
+into the algorithm,
+
+out come your design
+for folding a butterfly.
+
+That's the ideal picture when
+you get a universality result.
+
+The next best thing
+you could hope for
+
+is a sort of decision
+result, which
+
+is that there's a fast
+algorithm that will tell you
+
+whether something is foldable.
+
+So we say it
+decides foldability.
+
+So you give it a butterfly.
+
+It says, oh, that's impossible.
+
+That's not true.
+
+But you could imagine that.
+
+Or maybe you give it a
+butterfly, it says yes.
+
+You give it the
+skyline of New York,
+
+and it says no, you
+can't fold that.
+
+That's not true.
+
+But if it's not the case
+that everything is foldable,
+
+the next best thing is you
+could at least distinguish
+
+which things are foldable
+from which things are not.
+
+And then, of course,
+the worst thing that
+
+could happen, in some sense,
+is you get a hardness results
+
+which says, there's no good
+way to even distinguish
+
+foldable things from
+unfoldable things.
+
+So I'm going to
+say computationally
+
+intractable to mean generically
+that there's no good algorithm
+
+to solve a problem.
+
+We're going to be more formal
+about that in the future.
+
+Because different people
+have different backgrounds,
+
+you may know about
+competition complexity.
+
+Many of you don't.
+
+That's cool.
+
+We're going to talk
+about all that here.
+
+All right.
+
+That's the class in a nutshell.
+
+Totally generic.
+
+Any questions so far?
+
+Probably not.
+
+I thought now I would tell you
+a little bit about the class
+
+structure.
+
+The main part of the
+class are these lectures,
+
+and attendance is
+mandatory for classes,
+
+because you're not going to
+learn it unless you come here.
+
+You can have exceptions.
+
+Just email me and
+watch the videos later.
+
+That's one of the fun
+features of the videos,
+
+although the videos are mainly
+to reach the world for fun.
+
+There will be a few problem sets
+in this class, not too many.
+
+And the other main thing that
+you turn in is the project.
+
+So sort of a
+project-focused class.
+
+You will hand in some write up.
+
+You will give some presentation
+in the last few lectures
+
+of class, if you're taking
+the class for credit.
+
+If you're listening, you
+don't have to do this.
+
+You can, if you want.
+
+You can do the problem sets.
+
+Some of them will be fun.
+
+Hopefully all of
+them will be fun.
+
+None of them will
+bee too painful.
+
+But for people who are
+taking the class for credit,
+
+you have to do a project
+and presentation.
+
+The project could be
+about tons of things.
+
+You could build a sculpture.
+
+You could come up with a cool
+virtual design of something
+
+amazing that somehow
+relates to folding.
+
+It doesn't have to be direct.
+
+If you're a coder, you could
+implement some algorithm
+
+we talk about, or make a
+beautiful image or animation
+
+or applet or something.
+
+If you're more theory, you
+could solve an open problem.
+
+Obviously that's a big win.
+
+But even trying to solve
+an open problem is fine.
+
+You can talk about how
+you failed to solve it,
+
+in the unhappy
+case that happens.
+
+But if you want to
+solve an open problem,
+
+I would encourage you to come
+to the open problem session,
+
+so we can all solve it together.
+
+Then you can have
+a joint project
+
+on what we do, but it's totally
+unpredictable, of course.
+
+Even posing an open
+problem in this field
+
+is pretty interesting.
+
+I know a lot of the
+hard open problems.
+
+I would like to find more of
+them, more tractable ones.
+
+And so if you have some
+idea, especially related
+
+to some application field
+that you know a lot about,
+
+it'd be cool to try
+to extract, what
+
+is the mathematical problem
+in a lot of these fields?
+
+Or you can write a survey.
+
+That's a typical project.
+
+You should avoid overlap with--
+I don't actually have it here,
+
+but the textbook
+for this class--
+
+you can imagine it being
+here-- is Geometric Folding
+
+Algorithms.
+
+Here it is.
+
+Thank you, Jason.
+
+That's good.
+
+I ran out of copies.
+
+Now I have one.
+
+No, I'll give it back.
+
+So this is by me and Joe
+O'Rourke at Smith College.
+
+Any questions about
+class structure?
+
+Yeah.
+
+AUDIENCE: Can projects be
+individual? [INAUDIBLE]
+
+PROFESSOR: Projects
+can be with groups.
+
+I forget whether the
+website has a limit
+
+on the number of people.
+
+I don't think so.
+
+But at some point you'll have
+to do a project proposal.
+
+I should mention that also.
+
+And then I will vet
+your project group.
+
+But I think anything's fine.
+
+Just when you have
+more people, you're
+
+expected to do a
+little more, naturally.
+
+Other questions?
+
+Yeah.
+
+I love collaboration.
+
+I think I've never written
+a paper without a co-author.
+
+It wasn't a survey paper.
+
+So collaboration's good.
+
+All right.
+
+Doing well.
+
+So the next thing I
+want to do is actually
+
+dive into actual content.
+
+This was totally generic.
+
+And to me, it's useful.
+
+But maybe to you,
+it's less useful.
+
+This is sort of an organization.
+
+As we go through,
+everything you'll see
+
+will fit almost always into
+one of these three categories.
+
+The question will fit into
+one of these two categories,
+
+and the answer will fit into
+one of these three categories.
+
+Now let's see what some of
+those actual problems, questions
+
+and answers, are.
+
+That's the fun part.
+
+There's so many
+cool results here,
+
+and so many cool open problems.
+
+I thought I'd tell you a bunch
+of the big open problems, too.
+
+So in today's class, I'm
+going to go in order.
+
+We're going to start with
+linkages, and then paper,
+
+and then polyhedra.
+
+And I'm going to start with
+linkages allowing intersection.
+
+So magically, bars of the
+linkage can overlap each other.
+
+And then later I'll
+talk about linkages,
+
+which is most interesting
+in two dimensions,
+
+because you can actually build
+them in three dimensions.
+
+And then we'll go to linkages
+that do not have intersection.
+
+So an early
+motivation here where
+
+a lot of this linkage folding
+came from originally--
+
+this is the 17, 1800s-- is
+converting linear motion
+
+into circular motion.
+
+Actually, it's really--
+yeah, get it right.
+
+Linear motion to
+circular motion.
+
+I don't know what order
+to cover these things.
+
+I'll show you a slide.
+
+My rules are essentially
+no words on any slide.
+
+This is just for
+pretty pictures,
+
+and I'll write
+stuff on the board.
+
+There's this fun book called
+How to Draw a Straight
+
+Line by Kempe in 1877, which
+is all about this problem.
+
+How do I turn a
+circular crank and make
+
+a straight line come
+out as a result?
+
+And the motivation for this
+problem is steam engines.
+
+You have a steam piston,
+which is moving something
+
+up and down along
+a straight line.
+
+And maybe you're building
+a locomotive train,
+
+and you want to turn
+a wheel in a circle,
+
+because wheels are round.
+
+So how do you convert
+this linear motion
+
+into a circular motion?
+
+That is How to Draw a Straight
+Line, affectionately titled.
+
+But you can see that one of
+the earliest linkages for this
+
+is called the Watt
+parallel motion.
+
+And we have a little
+animation here.
+
+So the idea is this vertex in
+the top left is pinned down.
+
+This one in the bottom
+right is pinned down.
+
+And then, I think if I move
+this around the circle,
+
+the green guy moves
+along that figure eight.
+
+And there's a limit
+to how far it can go.
+
+So and if you draw it
+right, the figure eight
+
+is almost a straight line.
+
+So that was mathematics
+back in the day.
+
+No, no one thought
+that that was perfect,
+
+but it was pretty good.
+
+And that actually led Watt--
+you may have heard of Watt.
+
+He's a unit.
+
+And he was very proud
+of this invention.
+
+And he made tons of innovations
+in the steam engine world,
+
+and this was his favorite.
+
+And, I mean, it changed things.
+
+But later on-- I mean this
+is like 100 years later,
+
+1864 versus 1764.
+
+Exactly 100 years later.
+
+Peaucellier a French guy
+in the army, I think,
+
+came up with this linkage.
+
+So again, you have two
+pinned vertices here.
+
+This one's moving
+around a circle.
+
+So you just turn
+the crank, and look.
+
+This guy moves
+along that red line.
+
+Perfect.
+
+Very cool.
+
+Again it has a limit
+how far you can go.
+
+But it's pretty awesome.
+
+I mean you could play
+with this forever.
+
+I won't bore you.
+
+There's this other
+guy you may have heard
+
+of, Kelvin, Lord Kelvin.
+
+Another unit.
+
+There's a story about
+him playing with one.
+
+He wouldn't want to
+give it up, because he
+
+was having too much fun just
+pushing it back and forth.
+
+It's like, wow, a straight
+line out of a circle.
+
+So that's pretty cool.
+
+Making straight lines out
+of circles is pretty neat.
+
+In fact, you could think,
+well, what else could I make?
+
+I can make a straight line.
+
+That's kind of nice.
+
+But could I make, I don't
+know, some other curve?
+
+I mean a straight line is
+a special kind of curve.
+
+Maybe I could make this curve.
+
+That's a nice curve.
+
+In general, there's
+a universality result
+
+which says there's a
+linkage to sign your name.
+
+That's the cute phrasing.
+
+So it's a
+two-dimensional linkage.
+
+You turn one circular crank,
+and it signs your name.
+
+The mathematical
+version is that you
+
+trace a piecewise
+polynomial curve.
+
+Or if you're an architect
+or graphics person,
+
+call this a spline.
+
+Pick your favorite word.
+
+You can make it all
+with one linkage.
+
+It's pretty crazy, and
+not super practical.
+
+Building this would probably
+require thousands of bars.
+
+But hey, who's counting?
+
+At least you can get
+a universality result.
+
+This is actually
+something that goes back,
+
+in particular, to the
+first time this class was
+
+taught six years ago.
+
+We found some better
+ways to do, so it's
+
+known that it could be done.
+
+And I'll talk about
+those ways later on.
+
+Cool.
+
+Open problem.
+
+Not everything is known.
+
+There's a lot of open
+problems here, but one of them
+
+is, what if you
+forbid crossings?
+
+So these linkages, like the
+ones I've been showing here,
+
+like the Peaucellier linkage,
+there's crossing bars.
+
+And yeah, you could do that, but
+what if you forbid crossings?
+
+It'd be really cool to sign
+your name with a linkage that
+
+doesn't even cross itself.
+
+That's totally open.
+
+Getting any kind of
+result, positive result,
+
+maybe not everything,
+but at least
+
+getting some interesting things.
+
+Even drawing a straight
+line, I think, is open.
+
+Could be a fun
+problem to work on.
+
+All right.
+
+That's one.
+
+Let's go over here.
+
+Let's see, is that the end
+of linkages, is crossing?
+
+No.
+
+Next question you might
+ask is-- so that's
+
+sort of a design question.
+
+I was given the goal, which
+was to make a straight line
+
+or sign my name.
+
+And I wanted to find
+the linkage that did it.
+
+The other question, the
+foldability question,
+
+one of them is rigidity, which
+is, does a linkage fold at all?
+
+I should say a given linkage.
+
+So for example, I'll
+give you three examples.
+
+Test you out here.
+
+These are rigid bars
+connected by hinges.
+
+OK, rigid or flexible?
+
+Rigid, I agree.
+
+Rigid or flexible.
+
+Rigid.
+
+Any other answers?
+
+Flexible, correct.
+
+Both are correct.
+
+In two dimensions, OK, it
+depends where you live?
+
+In two dimensions, this
+is rigid no matter what,
+
+in any dimension.
+
+But in three dimensions, this is
+flexible and in two dimensions,
+
+it's rigid.
+
+In three dimensions,
+you can pick this guy up
+
+and it spins around a circle,
+out of the board here.
+
+Or you could pick this guy up.
+
+It spins around a circle.
+
+In two dimensions,
+though, it's rigid
+
+because it's really
+just two triangles.
+
+Triangles are rigid
+in two dimensions.
+
+This is a tetrahedron.
+
+Tetrahedra are rigid
+in three dimensions.
+
+Rigid or flexible?
+
+Everyone agrees.
+
+In both dimensions
+it is flexible.
+
+OK, pretty intuitive
+for four vertices.
+
+But you can ask the
+mathematical question
+
+and give you a linkage.
+
+Is it rigid in 2D?
+
+Is it rigid in 3D?
+
+And there are many
+versions of this question.
+
+But the short version, a
+short answer, let's say,
+
+is that distinguishing rigid
+from flexible two-dimensional
+
+linkages is easy.
+
+There's a good
+algorithm to do it.
+
+It's very powerful, very useful.
+
+In 3D, we have no idea.
+
+Very open.
+
+Tough.
+
+Very tough problem.
+
+A lot of people
+have been thinking
+
+about that for decades.
+
+So that's rigidity.
+
+I'm just going to touch on
+lots of topics very briefly.
+
+All right.
+
+Next we go on to, I
+guess, one and a half.
+
+This is linkages
+forbidding intersection.
+
+And this is more
+interesting when
+
+you're talking about 3D
+linkages like my arm.
+
+I really don't want it
+to penetrate other bars.
+
+It's not possible.
+
+And the first question you
+might ask in this world, which
+
+I guess is a
+foldability question,
+
+sort of a
+reconfiguration question,
+
+let's say I want to fold
+my robotic arm from one
+
+configuration that
+I know-- call it
+
+configuration A-- to some
+other configuration, B.
+
+When is that possible?
+
+Can I go from A to B?
+
+Can I go from some other A
+prime to some other B prime?
+
+Sometimes yes, sometimes no.
+
+It depends.
+
+Sometimes it's not
+foldable at all,
+
+even when you allow
+intersections.
+
+So this is a pretty
+open-ended question.
+
+In general, it's
+computationally intractable.
+
+If I give you a linkage
+and two configurations,
+
+to decide whether you
+can go from A to B
+
+is, for the
+complexity theorists,
+
+piece space complete.
+
+Talk about what
+that means later.
+
+Really, really hard
+is the short version.
+
+But a lot of the times you can
+think about special linkages.
+
+There are a lot of
+interesting special cases.
+
+In particular, we like
+to think about chains
+
+like I drew before.
+
+Also polygons.
+
+That's a little
+messy, but imagine
+
+those don't self-intersect.
+
+So this is what I
+call an open chain,
+
+and this is a closed chain.
+
+In general, these are chains.
+
+And the other thing I might like
+to think about, in particular
+
+because proteins look kind
+of like this, are trees.
+
+Trees are just linkages
+without any cycles in them.
+
+So those are nice and simple.
+
+Here I have no cycles,
+no cycles, one cycle.
+
+Easier to think about.
+
+And sometimes you actually
+get a universality result
+
+that these linkages can
+fold from any configuration
+
+to any configuration.
+
+And that's especially cool.
+
+Let me tell you about them.
+
+Where do I want to go?
+
+So it depends again what
+dimension you live in.
+
+I'm very flexible in this class.
+
+You can live in
+any dimension you
+
+want to, and even
+fictional ones.
+
+And you can think about
+chains and trees, let's say.
+
+You could go more
+general, but this
+
+is where most things
+have been studied.
+
+And the answer is,
+for chains in 2D
+
+you get a universality result.
+
+You can fold from
+anything into anything.
+
+For trees in 2D, you don't.
+
+There are some trees you can't
+get from one configuration
+
+to another.
+
+Which ones?
+
+We don't know.
+
+But at least you don't
+get a universality result.
+
+In 3D chains you do not
+get a universality result.
+
+And so also for trees,
+because that's even harder.
+
+And for 4D, everything's easy.
+
+Also in 5D, any
+higher dimension.
+
+Because the intuition here,
+at least for this column,
+
+is you think about tying knots.
+
+I have a one-dimensional
+linkage here.
+
+Think of it as a
+one-dimensional cord.
+
+It's kind of a kinky cord.
+
+It has kinks-- not the
+other kind of kinky.
+
+And in two dimensions,
+if you draw
+
+a non-self-intersecting
+loop, it's never knotted.
+
+You can't draw a knot
+in two dimensions.
+
+You can drawn a knot
+in three dimensions,
+
+and you cannot draw a knot
+in four dimensions or higher.
+
+You may not know that
+result, but it's true.
+
+So it matches, but things are
+little tricky, even trees.
+
+If this was a piece
+of string, you'd
+
+be able to always fold this
+piece of a tree-shaped piece
+
+of string into
+anything you wanted.
+
+But it's a little
+more complicated.
+
+Let me show you a locked
+tree, I think, is next.
+
+Yeah.
+
+For a long time, these were
+the only known locked trees.
+
+These are configurations of tree
+linkages that cannot reach some
+
+other configuration.
+
+In fact, they can
+barely move at all.
+
+It's less obvious
+for some of them.
+
+But say, in this
+top left one, you
+
+have these little sort of petals
+tucked into their armpits,
+
+I guess, and you can't
+get any of those arms
+
+open unless you had a
+lot of room to open it.
+
+And in order to make
+room, you'd have
+
+to squeeze all the
+others really tight.
+
+And if you draw this
+example tight enough,
+
+also none of the arms can
+get compressed very much.
+
+And so it's locked.
+
+And this is one of the first
+examples actually discovered
+
+in 1998, and publication
+took a while.
+
+There are a few others,
+which you see here.
+
+This one's kind of
+crazy because it
+
+has only one vertex with
+three incident bars.
+
+Everybody else is like a chain.
+
+So it's like three chains
+joined together at that point,
+
+and still it is locked.
+
+And for a long time,
+these were the examples
+
+we would always carry around.
+
+These are the ones that
+appear in the textbook.
+
+But I thought it would
+be neat to see, well,
+
+are there any simpler examples?
+
+And last time this class
+was offered three years ago,
+
+we found what is believed
+to be the smallest
+
+locked tree in existence.
+
+It has 1, 2, 3, 4, 5, 6, 7,
+8 bars, if I counted right.
+
+And it looks curved here,
+just to make it easier to see.
+
+But, in fact, you could
+straighten these out
+
+and it's still locked.
+
+If you squeeze these
+little regions down,
+
+they'd be very tight.
+
+So that was with a bunch of
+students from this class.
+
+Cool.
+
+So that gives you some
+idea of this answer.
+
+Maybe I'll draw you
+a picture for chains,
+
+because it's really simple.
+
+OK, imagine tying a knot, but
+don't actually close the loops.
+
+And make these end lengths
+really, really long.
+
+We call this the
+knitting needles example,
+
+because the intuition was you
+have two long knitting needles,
+
+and then a very short cord
+connecting them in a knot.
+
+Mathematically,
+this is not a knot,
+
+because if it were string, you
+could untie it, no problem.
+
+But because of these really
+long bars, you can't untie it.
+
+So that's why 3D is hard.
+
+Or one example of
+why 3D is hard.
+
+It's pretty much
+our only example.
+
+It is the smallest example, and
+we can prove things about it.
+
+But there's a pretty
+fascinating open question here,
+
+I would say, which
+is, characterize
+
+these bad examples.
+
+Which 3D chains and
+which 2D trees have
+
+locked configurations?
+
+And all that means is that
+there are two configurations,
+
+A and B, for which you
+cannot get from A to B.
+
+So this is an example.
+
+Those locked trees
+are an example.
+
+It'd be really fascinating
+if you could do this.
+
+I would guess that this is a
+hard problem, but I don't know.
+
+It's hard to know
+whether it's hard.
+
+It'd be nice to understand
+3D chains in particular,
+
+because they relate--
+and 3D trees.
+
+Oh, sorry.
+
+I have more animations.
+
+I forgot.
+
+Let me show you some pretty
+pictures for this result.
+
+This was actually my PhD
+thesis, way back in 2001.
+
+And this is a more
+modern algorithm
+
+for solving this problem.
+
+I give you some
+complicated polygon.
+
+First thing you want
+to know is, can you
+
+unfold it into a
+nice convex shape?
+
+Once you get there, you could
+refolded into some other shape
+
+by playing one of these
+motions backwards.
+
+So that's how you
+unfold some teeth.
+
+Here's one of those tree
+examples, but doubled.
+
+For a while, people thought
+that might still be locked,
+
+but it's not.
+
+Can do this crazy fivefold
+rotationally symmetric motion
+
+to unfold that thing.
+
+We're zooming in
+and out, so it looks
+
+like things are getting
+bigger and smaller.
+
+But in fact, each of these bars
+is staying the same length,
+
+and they're never
+crossing each other.
+
+Here's a much more
+complicated example.
+
+This is the first
+algorithm that could
+
+handle examples of this size.
+
+It's pretty fast.
+
+That's like it's
+going to come back.
+
+You can do it.
+
+It's like a spider.
+
+Spooky.
+
+I think it has 500
+vertices, and it probably
+
+took a couple
+minutes to compute.
+
+I'm not computing it live here.
+
+There's an applet
+on the web if you
+
+want to pick your
+favorite polygon
+
+and run this algorithm on it.
+
+It doesn't make quite
+movies like in this style,
+
+but it will show
+you how it unfolds.
+
+We call this the tentacle.
+
+Yeah, so we'll talk about
+this algorithm, how it works.
+
+There's a couple
+other algorithms
+
+for solving this problem.
+
+It's pretty cool,
+and you could imagine
+
+using this for planning the
+motion of a robotic arm in two
+
+dimensions.
+
+But in three dimensions,
+things are a lot harder.
+
+We lack good algorithms.
+
+I would like to study
+four dimensions actually.
+
+There's some pretty
+neat questions here,
+
+but I'm not supposed
+to talk about that.
+
+It's not on my list.
+
+I've got to move quickly, but
+we're doing all right on time.
+
+What I wanted to show
+you was a protein.
+
+This is a particular
+enzyme protein
+
+called hexokinase, whatever.
+
+Embarrassing myself.
+
+It's a particularly
+complicated one.
+
+It is one of a few I could
+find a nice free image of.
+
+But you can see closely,
+if you look closely here,
+
+it's a linkage.
+
+And this one actually
+has lots of cycles.
+
+But the backbone of a
+protein is like a tree,
+
+and so it fits into
+this kind of world.
+
+Unfortunately it
+fits in this world
+
+of three-dimensional trees,
+which are really hard to fold.
+
+Or three-dimensional
+chains, if you really
+
+just look at the backbone.
+
+They're a little bit more
+complicated than the sorts
+
+of linkages we're
+talking about here,
+
+but it makes it even harder
+to fold things like this.
+
+But there's something
+special about proteins
+
+that makes them
+fold really well.
+
+That enzyme over there is
+in every living organism
+
+we have ever tested for the
+existence of that thing, which
+
+I assume is everything.
+
+And yet it's folding.
+
+It's produced by this
+machine-- the Ribosome,
+
+you probably know about it--
+in a sort of straight state,
+
+and then it folds into
+this shape pretty reliably,
+
+less than a second, usually
+like within nanoseconds.
+
+So it's really hard to
+watch what's happening.
+
+It's very hot and jiggly,
+so it's a little hard
+
+to see what's actually
+going on in the real thing.
+
+But somehow, these kinds
+of barriers to foldability
+
+don't happen.
+
+Maybe that's because evolution
+found the right things,
+
+or maybe it's because
+protein chains don't really
+
+look like this.
+
+They don't have these super
+long bars and super short bars.
+
+If you've ever played with a
+chemistry set, all of the bars
+
+are within a factor of
+like 1.5 of each other.
+
+So there's lots of cool
+mathematical questions
+
+that come out of
+protein folding,
+
+and we will talk
+about the ones I know.
+
+I'd love to find more.
+
+But the ones I know
+I will talk about.
+
+And that's linkages.
+
+Let me move on to paper,
+unless there are questions.
+
+All right.
+
+Let's go over here.
+
+So we've seen some universality
+results, some hardness results.
+
+I didn't go into them.
+
+Folding these linkages.
+
+Let's do that for paper.
+
+I think first up I
+have foldability.
+
+And then we'll
+talk about design.
+
+So there are lots of
+questions in both.
+
+But for foldability, the
+sort of first question people
+
+like to ask is, which
+crease patterns fold flat?
+
+So a crease pattern
+is just a graph
+
+drawn on a piece of paper.
+
+So you have some
+collection of lines,
+
+and I think that will fold flat.
+
+But I'm not going to try to
+draw something more complicated,
+
+but you could imagine doing it.
+
+I don't know.
+
+That probably is
+not flat foldable.
+
+It might be.
+
+It's close.
+
+But that's the sort of question.
+
+If you take some
+origami and unfold it,
+
+what kind of
+patterns do you get?
+
+Some flat origami,
+something that
+
+folds into two
+dimensions in the end.
+
+There's some really
+nice structure here.
+
+If I drew it right, this
+angle plus this angle
+
+should equal 180
+degrees, for example.
+
+And that's true everywhere.
+
+And there's all sorts
+of cool properties.
+
+But unfortunately,
+this is really hard.
+
+This is NP hard problem.
+
+You've probably at least
+heard of P versus NP.
+
+Again, I'll define it later.
+
+But it means probably
+there is no good algorithm
+
+to solve this problem.
+
+It's really hard
+to figure out which
+
+crease patterns fold flat.
+
+It's kind of annoying.
+
+One good news is
+that if you just
+
+have an example like the
+original thing I drew,
+
+which is like this-- so it
+has one vertex and a bunch
+
+of creases emanating out,
+that picture we understand.
+
+So it's easy for
+a single vertex.
+
+That may seem kind of trivial,
+but it's actually really useful
+
+because it lets you understand
+the local behavior around one
+
+vertex.
+
+If you check that
+for every vertex,
+
+you don't know that the whole
+thing folds, but at least
+
+you know it mostly
+folds, at least locally.
+
+And you can't tell whether
+it globally folds correctly,
+
+because that's NP hard.
+
+There are so many questions here
+like, what about two vertices?
+
+No one's studied that.
+
+I think it's polynomial,
+but well, it's
+
+certainly polynomial,
+but I think
+
+you could do it in linear time.
+
+Anyway, there's lots
+of open questions
+
+there I haven't
+even listed here.
+
+One of the bigger open
+questions is a particular kind
+
+of crease pattern, which you may
+have encountered in real life
+
+refolding your roadmaps.
+
+The saying goes, the
+easiest way to refold
+
+your road map is differently.
+
+So suppose you have your road
+map, and each of these creases
+
+is marked.
+
+I'm not going to mark
+all them because it's
+
+a little messy with
+black and white chalk.
+
+But some of them are marked
+mountain, some of them
+
+are marked valley, meaning
+you fold-- this is valley.
+
+This is mountain.
+
+So they just have a relative
+orientation to each other.
+
+Suppose you look
+carefully at your map.
+
+You can recover which
+way it was folded last,
+
+hopefully correctly.
+
+And then you want to find,
+does that thing fold flat?
+
+Sometimes it does,
+sometimes it doesn't.
+
+For two by n maps, we don't
+know whether we can even
+
+detect this with an
+efficient algorithm.
+
+Can I decide whether
+this thing folds flat
+
+using those creases
+and those orientations?
+
+For two by n, it's open.
+
+For one by n, it's easy.
+
+Obviously for bigger,
+it's also open.
+
+Two by n is the smallest.
+
+This is a really
+annoying problem.
+
+Worked on it many times.
+
+It's very difficult.
+
+All right, so that's a quick
+overview of foldability.
+
+It's hard, but there are a lot
+of interesting special cases
+
+where we might be
+able to solve it.
+
+Let's move on to design,
+which is probably
+
+where most of the action
+is in the origami world,
+
+in the mathematical
+origami world.
+
+So and there are
+tons of results,
+
+and I had a much
+longer list initially,
+
+but I trimmed just for
+brevity down to a few things.
+
+The central question--
+at least it's
+
+been considered so far-- in
+computational origami design
+
+is, what shapes can you make?
+
+You could imagine other
+properties than just shape,
+
+if you want stability
+in your folding,
+
+lots of practical things--
+not much thickness,
+
+not too many creases, whatever.
+
+But shape has sort of
+been the fun centerpiece.
+
+And there's an early result
+that says universally,
+
+you can make anything you want.
+
+And in the
+mathematical world, you
+
+might try to make a polygon.
+
+Try to make a
+silhouette or something.
+
+You could make a
+polyhedron in 3D.
+
+Maybe you want to wrap a box,
+so you want to fold a box,
+
+or you want to fold a
+3D model of a dragon.
+
+That's all possible.
+
+And for fun, you can even
+make any two-color pattern
+
+on either of those things.
+
+So I have a tiny example
+here, which is-- yeah,
+
+it's still alive-- a four
+by four checkerboard.
+
+And it's made from
+one square paper.
+
+It's white on one side
+and red on the other.
+
+So you get some idea of
+making two-color patterns.
+
+This one's pretty easy to fold.
+
+It even folds itself almost.
+
+That's great.
+
+Usually when I give a
+class like to high school
+
+students or something, I say,
+could you refold this for me?
+
+And they're like, oh, no!
+
+But it actually does it itself.
+
+It's great.
+
+Like magic.
+
+So you could try that at home.
+
+Just take a square paper.
+
+It works.
+
+So this is great.
+
+Super general.
+
+This is something actually
+my dad and I proved
+
+with Joe Mitchell
+back in '99, I think.
+
+I don't remember exactly.
+
+So beginning of modern
+computational origami design.
+
+But the way that we do
+this, while algorithmic,
+
+is completely impractical.
+
+We'd never want to
+use the foldings that
+
+are designed by this algorithm,
+unless you're starting out
+
+with a big ticker tape of paper.
+
+Then it's a great method.
+
+But if you're starting with a
+square, the first thing it does
+
+is fold it down to a
+tiny little narrow strip,
+
+and then wraps the shape.
+
+And we'll see how that's done.
+
+It's interesting to
+do it mathematically,
+
+but it's not how you want
+to do it practically.
+
+Good news is-- that used to be
+sort of the end of the story.
+
+But now you can even do
+it pretty practically--
+
+practically is a
+relative term-- using
+
+something called Origamizer.
+
+And if you've seen the poster
+of this class, you've seen--
+
+and if I'm lucky, it's
+even the next slide,
+
+yes it is-- this rabbit--
+bunny, I should say.
+
+This is the Stanford bunny.
+
+The original Stanford
+bunny is in the top right.
+
+That's a classic model.
+
+Everybody in computer graphics
+does something with that bunny.
+
+It has a zillion triangles.
+
+I don't know offhand how many.
+
+It's been simplified
+here to make
+
+it feasible to fold to
+this mesh of triangles.
+
+So the input to the algorithm
+was this mesh of triangles.
+
+The output of the algorithm--
+and it's a real program,
+
+you can go and download
+it right now for free--
+
+is this crease pattern.
+
+Now it doesn't look
+like a square or paper,
+
+but if you start with
+a square of paper,
+
+you just fold away
+the excess stuff.
+
+You'll get to a piece
+of paper like this.
+
+And then you just fold along
+all those little creases there,
+
+and eight hours later
+you have this bunny.
+
+This is a real photograph
+of a folded bunny
+
+by Tomohiro Tachi, who
+designed this thing.
+
+He came up with the original
+algorithm and computer program.
+
+In the last few
+years, we've been
+
+proving this algorithm
+actually always works.
+
+We still don't know how to
+prove that it's efficient,
+
+or even what
+efficient should mean.
+
+But in practice it's super good.
+
+If you look closely,
+the white parts
+
+are the parts of
+the paper that you
+
+need to use in
+order to make this.
+
+They are the triangles
+of the surface.
+
+These grey regions
+are the excess.
+
+And it's pretty small.
+
+I don't know, maybe 50% of the
+area is used in a useful way
+
+here, which is a lot.
+
+Whereas this method
+over here would use
+
+like a one millionth
+of a percent
+
+of the paper or something.
+
+A very tiny amount.
+
+The Origamizer is
+super efficient.
+
+We don't know how to prove
+that it's super efficient,
+
+but at least we can
+prove that it works.
+
+It will make any 3D
+polyhedron you want.
+
+And in practice, it
+seems really good at it.
+
+Now it's a very different
+style from typical origami,
+
+so this has not yet hit the
+sculpture world, let's say.
+
+But I think it opens the door
+to a lot of new possibilities.
+
+Traditionally
+though-- traditionally
+
+before this Origamizer
+or in practice
+
+today, a much more
+commonly used approach
+
+to computational
+origami design is
+
+something called
+the tree method.
+
+I'm just going to call
+it TreeMaker here.
+
+TreeMaker's the name
+of the program that
+
+implements the tree method,
+and it's made by Robert Lang.
+
+And this is sort of making
+stick figures, which
+
+sounds a little silly.
+
+But TreeMaker or the
+tree method is powerful
+
+for if I want to make what's
+called an origami base, that
+
+has a lot of limbs in different
+places of different lengths--
+
+maybe you want to make
+something like that.
+
+I don't know.
+
+The typical origami base might
+look something like this.
+
+Maybe you want to make a lizard.
+
+It has a head, some forearms,
+some really big hind legs,
+
+a little tail, and some body.
+
+You can abstract
+this into a tree
+
+and then say, well can
+I fold a piece of paper
+
+into some shape
+whose projection is
+
+that tree, with all
+the right edge links?
+
+And the answer is yes.
+
+I mean, you can make
+anything, of course.
+
+But what TreeMaker tries to do
+is find the most efficient way
+
+to make that thing.
+
+Unfortunately, finding
+the most efficient way--
+
+like the smallest square
+paper, so the most paper
+
+usage possible to make
+something with that projection--
+
+finding that is NP complete.
+
+We just proved that this
+year with Robert Lang
+
+and Sandor Fekete.
+
+But there's a theory.
+
+There's a hard problem
+you have to solve,
+
+something related
+to disk packing.
+
+If you solve it, you
+find the best way.
+
+In practice, use some heuristics
+which are really good.
+
+And usually you
+find the optimal way
+
+to make a given stick figure.
+
+But for super complicated
+things, it may not be perfect.
+
+Now a lot of people use this
+method for designing origami.
+
+I have a slide of cool
+origami, just to show you.
+
+Not all of this uses
+the tree method.
+
+These three designs
+by Brian Chan,
+
+who was an MIT grad student,
+graduated last year--
+
+these are all designed
+partly using the tree method.
+
+I'm sure they're more
+complicated than that.
+
+But to get the initial structure
+of the arms in the right place,
+
+the legs in the right place,
+the head, body segments,
+
+fingers-- some of
+these guys have
+
+fingers-- all that stuff
+is done using tree theory,
+
+almost certainly not with
+TreeMaker, the program.
+
+Most origami designers do it by
+hand, in their head, or drawing
+
+pictures with a drawing
+program, to design out the base.
+
+Then they fold by
+hand everything.
+
+But still, the math is in there.
+
+These guys are not yet
+mathematically analyzed,
+
+let's say.
+
+They're experiments by
+[? Garn ?] and Joel Cooper.
+
+[? Garn ?] is a computer
+scientist slash mathematician,
+
+but he doesn't understand
+these yet, and sort of he's
+
+trying to figure it out.
+
+So there's a lot of
+interesting questions,
+
+and you get some really
+cool sculpture as a result,
+
+out of this world.
+
+So this is something
+we've also been working on
+
+with my dad and Robert Lang,
+proving that this actually
+
+works.
+
+It's been around
+for a long time,
+
+but it turns out to
+be really complicated
+
+to prove that it always works.
+
+But it looks like it
+does, so stay tuned.
+
+Some time we will
+publish that paper.
+
+It's still in process.
+
+All right.
+
+I have some more fun things.
+
+This is just a random selection.
+
+There's a ton of work here.
+
+One of my favorites-- this was
+my first result in this field--
+
+is the folding cut
+problem, theorem, whatever.
+
+So you start with a rectangle
+of paper, and you fold it flat.
+
+Now you take your
+scissors-- I know
+
+this is blasphemy
+for most origamists.
+
+But I'm not going to
+make a lot of cuts.
+
+I'm just going to make
+one complete straight cut.
+
+I get two pieces in this case,
+and then I unfold the pieces
+
+and see what I get.
+
+In this case I
+get a little swan.
+
+And the general theorem is you
+can make any polygon you want.
+
+In fact, you can
+make one cut and make
+
+any collection of
+polygons you want.
+
+So like on my website,
+you can make the MIT logo
+
+with all the little rectangles
+with one complete straight cut.
+
+And the outside
+shape will have holes
+
+exactly where you want them.
+
+And you can download
+this, too, if you
+
+want to impress
+all your friends,
+
+especially recommended
+for, like, kids.
+
+It's a good magic trick.
+
+In fact, Harry Houdini
+used to do this trick
+
+in the '20s before he
+was an escape artist.
+
+He did general magic.
+
+Not this trick.
+
+He made stars.
+
+And we thought about it, and we
+proved you could make anything.
+
+So that's fun.
+
+Another universality result.
+
+It's what got us started.
+
+And it relates to things
+like the tree theory,
+
+in fact, because what
+you're really solving here
+
+is, how do I take a polygon
+and-- if I fold this guy back
+
+up-- how do I make all
+the edges of that polygon
+
+lie along-- this
+guy's not very happy,
+
+get rid of that-- lie
+along a straight line.
+
+That actually turns out to be
+important for origami design.
+
+A lot of these things--
+an Origamizer--
+
+it's all over the place.
+
+And so this structure
+is helpful for solving
+
+sort of pure origami
+problems, not with cutting.
+
+So what else do I have?
+
+Curved creases.
+
+You may not know this,
+because most origami
+
+is straight creases.
+
+But if you take
+a piece of paper,
+
+you can put a curved
+crease into it.
+
+It's a little hard to do
+by hand, but there you go.
+
+Curved crease.
+
+Is that allowed?
+
+What can you make like that?
+
+It's not too well studied.
+
+Jeannine Mosely has done some
+of the curved crease stuff.
+
+Early stuff was done
+by David Huffman,
+
+you may know from Huffman codes
+in every cell phone, whatever.
+
+And by Ron Resch.
+
+That's wrong queuing.
+
+All right, I'm going
+to show that later.
+
+This are some of the
+things that we've made,
+
+this is my dad and I,
+out of curved creases.
+
+This is kind of a crazy-- it's
+like a circular piece of paper,
+
+but it goes around
+twice like a ramp.
+
+So you make two circles
+and then join the ends,
+
+and you pleat along
+concentric circles,
+
+alternating mountain and valley.
+
+And you change a few
+different parameters,
+
+and you get these
+three different shapes.
+
+These are in the permanent
+collection at MOMA in New York.
+
+So you can make some really
+cool sculpture out of this.
+
+This is a more
+recent piece we did.
+
+And this is taking just a
+regular circular band of paper
+
+with concentric
+circular creases,
+
+and then taking three of them
+and joining them together
+
+at a few points.
+
+And then you get
+some cool structures.
+
+These are interesting to us
+especially because the paper
+
+actually does fold itself.
+
+You put in these
+circular creases.
+
+You just squeeze
+a little, and it
+
+will make these
+shapes automatically.
+
+It's called
+self-folding origami.
+
+And in that spirit,
+I will show you
+
+a different kind of
+self-folding origami.
+
+I think I need to
+click this button.
+
+Which is approach to making
+paper that folds itself.
+
+This is a self-folding sheet.
+
+It's made of rigid panels
+connected by little rubber
+
+hinges, and there's little
+muscles, you could say,
+
+that are folding
+those creases shut.
+
+By turning on some
+electrical signal,
+
+that thing folds
+itself into a boat.
+
+That same sheet, you can send
+it a different electrical signal
+
+and it will just fold
+along these two creases.
+
+And then there's little
+magnets to hold it into place,
+
+so you can turn off
+that electricity now.
+
+No power.
+
+Then you send it a third signal,
+and it will fold those three
+
+creases, and you get
+a paper airplane.
+
+No origamist required.
+
+So the idea here, this is the
+programmable matter vision,
+
+where you could download
+hardware in the same way
+
+you could download software.
+
+You can make one sheet that
+has lots of panels in it,
+
+enough creases to make
+anything you want.
+
+And then you just push a
+button and some of the creases
+
+turn on.
+
+Then push a button and
+some other creases turn on,
+
+and it folds into some
+complicated origami
+
+all by itself.
+
+You could imagine making
+this building scale.
+
+You could imagine making it
+nano scale, some scale where
+
+an origamist can't
+do it, or you don't
+
+have an origamist
+to do it for you.
+
+This would be the
+self-refolding, transforming
+
+robot thing.
+
+To do it, though, we
+needed to prove new theory.
+
+And this is the world of, call
+it, universal hinge patterns.
+
+And this is the topic of a
+master's thesis just finished
+
+last week, I think,
+by [? Viva Vadia ?]
+
+where-- and maybe
+we'll get him to talk
+
+about it at some point--
+it's one crease pattern.
+
+In that case we were using
+a crease pattern called
+
+box pleating, where
+you take a square grid,
+
+and then you put alternating
+diagonals in those squares.
+
+Get my alternation going here.
+
+So that's the so-called
+box pleating pattern.
+
+We proved that that pattern,
+if you make it big enough,
+
+can fold any 3D shape that's
+made out of little cubes.
+
+I think, yeah, so in fact if
+you take a sort of n by n sheet,
+
+you could make about n cubes.
+
+And in the worst case,
+that's the best you can do.
+
+So that's cool,
+because that tells
+
+you here's one robot you build.
+
+You just make this sheet
+with those creases,
+
+those rubber creases with
+muscles on each of those edges.
+
+And if you can turn those
+edges on and off programmably,
+
+you could make anything you
+want up to some resolution.
+
+If you want to make a
+bunny, you can sort of
+
+build that bunny our of
+little cubes in simulation,
+
+and then fold that cubefied,
+voxillized form of the bunny.
+
+And then you want to
+make something else,
+
+you unfold it and refold
+it all automatically.
+
+AUDIENCE: This is
+like [INAUDIBLE]
+
+no width of the material?
+
+PROFESSOR: Yeah, there's a
+lot of open questions here.
+
+This result assumes 0 thickness.
+
+In fact, every result
+I've talked about
+
+assumes 0 thickness.
+
+I think there's one theorem
+in the literature that
+
+looks at thickness of paper.
+
+That's a great open
+question, and you really
+
+see it in something
+like that video.
+
+That just appeared at PNAS,
+and the video's online.
+
+Because in the
+airplane, you have
+
+to fold through multiple layers.
+
+And that's tricky.
+
+We get around that right now by
+having the creases be a little
+
+bit stretchy, some rubber.
+
+But there's a limit, and it's
+related to the thickness.
+
+So yes, some complicated shapes
+are not going to work this way.
+
+I think one thing that
+would work really well-- we
+
+have another result with Jason
+Ku, which is folding a maze.
+
+This is sort of like folding
+a shallow terrain in this way,
+
+so you could make a rat maze
+out of a square-- just tracks
+
+by 50%, and then
+you have arbitrary
+
+undulation in the middle,
+which is pretty cool.
+
+So some of these things
+are going to be practical.
+
+Some are not.
+
+So there's still interesting
+theory questions to ask about.
+
+I think thickness is
+a really good one.
+
+Other questions?
+
+Yeah.
+
+AUDIENCE: [INAUDIBLE] I thought
+I heard something about how you
+
+can't fold a sheet of
+paper more than like--
+
+PROFESSOR: Yeah, so
+that's the one thing.
+
+The question is, you can't
+fold a piece of paper in half 8
+
+times, 7 times, whatever the
+number is everyone quotes.
+
+The answer was solved by
+someone who was a high school
+
+student a few years ago.
+
+What's her name?
+
+Britney Gallivan.
+
+And so this is the one paper
+that's about thickness,
+
+and she analyzed-- the issue
+is when you fold-- if you have
+
+a folding that is
+1,000 layers thick,
+
+and you want to
+fold in the middle,
+
+you can't just like cut here
+and move it over here and then
+
+be folded.
+
+Paper has to actually
+turn that corner.
+
+And the thicker that thing
+is, the more length of paper
+
+it takes to turn that corner.
+
+And you can compute
+how much that
+
+is if you assume sort of
+a circular trajectory,
+
+and it matches reality.
+
+So she computed how thin does
+a piece of paper need to be,
+
+or how long does
+a piece of paper
+
+have to be-- it's
+that ratio-- in order
+
+to fold it in half 12 times.
+
+So she took a piece of
+paper that was, I think,
+
+three-quarters of a mile long,
+and folded it in half 12 times.
+
+And it's like this big
+monstrosity when it's done.
+
+And it follows the
+theory exactly.
+
+So that seems to
+be the right model,
+
+but that's the only
+paper that analyzes
+
+paper folding in that
+model, because it's so much
+
+easier to think
+about zero thickness.
+
+But that is what we should do.
+
+So that particular
+question we understand,
+
+but everything else is open.
+
+I'll show you some
+pictures of that next time.
+
+Other questions?
+
+All right.
+
+That is paper, and
+then I was going
+
+to show you a little bit
+about polyhedra and hinged
+
+dissections.
+
+All right.
+
+Let's go.
+
+So I mentioned there's a
+bunch of different kinds
+
+of polyhedron folding
+and unfolding problems.
+
+Probably the coolest
+one-- because it's
+
+the oldest problem in
+this entire field--
+
+is unfolding convex polyhedron
+by cutting along the edges.
+
+We call this edge
+unfolding convex polyhedra.
+
+At the beginning of
+class, I showed you
+
+a cube which you could
+unfold into a cross.
+
+I want that.
+
+So I was only cutting
+along edges of the cube.
+
+That's this edge unfolding.
+
+The cube is a convex shape.
+
+It doesn't have any dents.
+
+And I got to unfold it with
+one piece without overlap.
+
+Is that always possible?
+
+We have no idea.
+
+Can every convex polyhedron
+be made in that way?
+
+We don't know.
+
+This problem goes back
+to Albrecht Durer,
+
+this guy on the left.
+
+This is his self-portrait.
+
+In 1525, he wrote this book
+called The Painter's Manual
+
+in German.
+
+And he tried this out for
+a whole bunch of polyhedra.
+
+This is the so-called snub
+cube, and unfolded in his book.
+
+And he has page after page
+after page of these unfoldings.
+
+And they're all edge unfoldings.
+
+Most of them are correct.
+
+There's a couple small
+errors, probably just
+
+transcription errors.
+
+And he did this
+because he wanted
+
+to understand these 3D shapes.
+
+He had to build them.
+
+How do you build them?
+
+So he didn't pose this
+mathematical question.
+
+He was not a mathematician.
+
+But it's sort of implicit
+there, and people
+
+have been thinking about it for
+at least decades if not more.
+
+At least since '65, I think,
+was the first formal posing.
+
+And it's really hard.
+
+A lot of people
+have worked on it.
+
+We'll talk about it.
+
+There are some interesting
+things that are known.
+
+I mean the depressing
+thing is we
+
+have no algorithm which
+we think will work.
+
+Every algorithm we've tried
+has a counter example.
+
+Every counter
+example we've tried
+
+has an algorithm
+for which it works,
+
+but they don't match
+up, so it's frustrating.
+
+If you allow
+non-convex polyhedra,
+
+then the answer is no.
+
+So that's something I did
+with a bunch of people
+
+back in the day.
+
+This was actually
+done in '98, then
+
+it took forever for the
+journal paper to appear.
+
+This is a polyhedron.
+
+All the faces are triangles.
+
+So it's sort of
+topologically convex.
+
+And then if I made the
+spike a little shorter,
+
+it would be a convex polyhedron.
+
+But this particular embedding--
+these are just two views.
+
+If you cross your eyes,
+it's three dimensions.
+
+No, I'm just kidding.
+
+It's not designed for that.
+
+Just two views of
+the same thing.
+
+And if you cut along the
+edges any way you want,
+
+it will overlap itself
+or be multiple pieces.
+
+And we'll prove
+that at some point.
+
+It's not too hard.
+
+Yeah, so good.
+
+That's edge unfolding.
+
+But there's another
+kind of unfolding
+
+called general unfolding.
+
+This seems a lot more
+interesting to me.
+
+Edges are sort of artificial.
+
+What if you let me cut
+anywhere on the surface,
+
+not just at the edges?
+
+Well, then it turns out,
+for convex polyhedra,
+
+you can do it.
+
+It's always possible.
+
+I don't have pictures
+of that here,
+
+but even for some non-convex
+polyhedra you could do it.
+
+For example, this
+polyhedron, if you
+
+let me cut not just at the edges
+but anywhere on the surface,
+
+you can do this crazy thing.
+
+These are the spikes, and you
+cut out a tiny little sliver
+
+out to the side,
+and that lets you
+
+attach one of those spikes
+from one of these witch's hats
+
+to the wrong side.
+
+Like you see, this blue guy, the
+blue spike-- because this edge
+
+ends up being
+glued over here, we
+
+can attach the spike with
+the little sliver that
+
+gets opened up here, over
+there, and avoid overlap.
+
+Even if these spikes
+are super tall,
+
+does this go out to
+infinity and overlap.
+
+That's one example.
+
+Can you do it for every
+non-convex polyhedron?
+
+We don't know.
+
+I would love to
+answer that question.
+
+The one thing we know or
+the big thing that we know
+
+is so-called
+orthogonal polyhedra.
+
+This is always possible.
+
+This the same kind of
+thing I was talking about.
+
+You take any 3D shape
+made of little cubes--
+
+so all the faces are horizontal,
+vertical, or the other way--
+
+then it's also always possible.
+
+The current method takes an
+exponential number of cuts.
+
+It's really impractical.
+
+I think we could
+make it practical.
+
+I think we could generalize
+it to everything.
+
+But those are all
+open questions.
+
+One more picture I
+wanted to show you
+
+is, so here we really want
+to keep the shape connected.
+
+You have to have a
+positive area of connection
+
+between everything.
+
+If you let that connection
+go down to a single point--
+
+sort of cheating, this is
+called vertex unfolding--
+
+and then it's possible for any
+surface made out of triangles.
+
+So it could be
+non-convex, anything.
+
+These happen to be
+convex polyhedra.
+
+It's a little hard to see that
+they're three-dimensional,
+
+but they are.
+
+You cut them up
+into little faces.
+
+Here I'm only
+cutting along edges.
+
+And I string them
+out on a line here.
+
+This thing will not
+overlap, but I'm
+
+kind of cheating because
+the connections are only
+
+at single points.
+
+But hey, we'll take a positive
+result if we can get it.
+
+A lot of these problems
+are really hard.
+
+OK, the next thing
+I want to talk about
+
+is the reverse
+direction folding.
+
+So we know-- this is
+a video I made back
+
+when I was a grad
+student, a long time ago.
+
+So we know you can take
+a cube, and there's
+
+a whole bunch of different ways
+to just cut along its edges
+
+and unfold it into one piece.
+
+And the particular
+unfolding I want to consider
+
+is the cross unfolding,
+because that's our favorite.
+
+So you take this
+cross unfolding,
+
+and ideally don't stutter.
+
+And you say, well what if
+I gave you that polygon?
+
+What 3D shapes
+could it fold into?
+
+One thing is the
+cube, but it can also
+
+make this flat doubly
+covered quadrilateral.
+
+So I'm taking this
+as a piece of paper,
+
+but I can set the
+creases however I want.
+
+I can fold it into this
+five-sided, reflectionally
+
+symmetric polyhedron.
+
+All of these things are
+convex, and they all
+
+have perfect coverage,
+unlike an origami where
+
+I'm allowed to have
+multiple layers.
+
+Here, one layer everywhere.
+
+Like sheet metal bending.
+
+So here, this pocket fits
+perfectly into that tab.
+
+I make a tetrahedron.
+
+And the last thing you can
+make with something called
+
+edge-to-edge [INAUDIBLE]--
+I'll talk about this more.
+
+There's an algorithm here
+which, given a polygon,
+
+will list all of the
+things it can fold into,
+
+in a reasonable amount of time.
+
+This is an octahedron.
+
+Those are the five
+things you can
+
+make by edge-to-edge
+[INAUDIBLE] of the cross.
+
+Let me stop that.
+
+So that's also on the web.
+
+You can watch it.
+
+In fact, all the lecture notes
+I use, my handwritten notes,
+
+are on the class web page.
+
+The slides that I'm showing
+are on the class web page.
+
+And when there's videos,
+there's links to the videos,
+
+so it's all there for your
+perusal if you miss something.
+
+The last thing I wanted to talk
+about, because I've already
+
+done one, two and three,
+there should always
+
+be one more thing.
+
+Fourth thing.
+
+And this is kind of funny,
+because I don't really
+
+know where to put it.
+
+I'm still figuring it out.
+
+We have these
+debates, because it's
+
+so easy when you're
+thinking about linkages.
+
+Oh, that's one dimensional.
+
+Paper, that's two-dimensional.
+
+Polyhedra, well locally
+it's two-dimensional,
+
+but it's three-dimensional.
+
+It's different.
+
+Different questions.
+
+Hinged dissections span
+so many dimensions,
+
+I don't know where to put it.
+
+So four, hinged dissections.
+
+This didn't used to be
+a topic in this class,
+
+and it's not a topic
+in our textbook,
+
+because the result was proved
+like last year or the year
+
+before out of this class.
+
+Three years ago.
+
+And the theorem is you take
+any finite set of polygons,
+
+of the same area,
+they can be folded
+
+from one chain of polygons
+without collision.
+
+I'm going to say this
+first, and but let me
+
+show you a simple example.
+
+Very simple.
+
+This is going to
+be a little boring.
+
+Let me show you more
+interesting example.
+
+Let's take an
+equilateral triangle.
+
+I'm going to cut it
+into two triangles,
+
+and then I'm going to
+hinge them together here.
+
+So this is now a hinged
+chain of polygons.
+
+If I open it up a little
+bit, it looks like this.
+
+It looks a lot like
+those vertex unfoldings
+
+I was showing before.
+
+And you can fold this
+thing into one other shape.
+
+It's going to look like this.
+
+Not a very good drawing,
+but you get the idea.
+
+Something like that.
+
+So this is what we call
+a hinged dissection
+
+from this equilateral triangle
+into this other triangle.
+
+And it's been an open
+question for about 100 years.
+
+Can you always do this for
+polygons of the same area?
+
+Turns out yes, not
+only for two polygons--
+
+you can take seven
+polygons of equal area
+
+and there's one of
+these chains of blocks
+
+that can fold into all of them.
+
+And I think I have
+a little teaser
+
+picture of how the
+construction goes.
+
+It's really crazy.
+
+You have this chain of blocks.
+
+It's changed in a particular
+way and you say, well
+
+I really want that green piece--
+so think of it like this.
+
+You just have three triangles or
+three pieces that you can fold.
+
+You say, well I really like
+that green piece to be up top.
+
+Turns out you can make
+all these crazy cuts.
+
+And if you fold it this
+way, you get the green piece
+
+on the bottom.
+
+If you fold it this way, you
+get the green piece on the top.
+
+It's one hinged dissection that
+can move the pieces around,
+
+and basically pretend as if
+the hinges weren't there,
+
+and make anything you want.
+
+So it's a bit complicated,
+but it's really
+
+cool theory, something that
+we worked on for like 10 years
+
+before finally solving.
+
+And it's practical.
+
+I mean this particular
+construction isn't practical,
+
+but this is another way
+to build transformers.
+
+Also to build sculpture.
+
+This is a sculpture by Laurie
+Palmer that we collaborated on.
+
+It's an interactive sculpture.
+
+You pick up gloves, and
+this is one chain of blocks.
+
+And the theorem is, this
+particular chain of blocks--
+
+about 1,000 blocks here--
+can make any shape made out
+
+of about 250 cubes.
+
+It's slightly skewed, but so
+there's one hinged dissection
+
+that can fold into exponentially
+many different shapes-- again,
+
+anything made out
+of little cubes.
+
+And this is the
+sculpture version.
+
+We also have various
+prototypes of a robot that's
+
+a long chain of little cubes
+or cube-like shapes, that
+
+can fold itself into
+any 3D shape you want.
+
+It's, again, a different
+kind of transformer,
+
+more inspired by
+proteins, the way nature
+
+does it by long chains,
+compared to the sheet-folding,
+
+origami-inspired approach.
+
+But it's all pretty
+exciting and fun.
+
+Any questions?
+
+Jean?
+
+AUDIENCE: This is a 3D version
+you were talking about.
+
+PROFESSOR: Yeah, I
+pulled a fast one.
+
+That picture's 3D.
+
+This is about 2D.
+
+For 3D, you need the same area.
+
+You need one other
+condition just
+
+for them to have a dissection.
+
+It's impossible to go from a
+regular tetrahedron to a cube.
+
+This was one of Hilbert's
+problems from 1900.
+
+And volumetrically
+it's impossible to go
+
+from regular
+tetrahedron to a cube,
+
+because the angles are wrong.
+
+It's an algebraic thing.
+
+And if you make things out
+of little cubes, it's fine.
+
+You get that.
+
+There's no problem.
+
+But in general, there's
+some tricky issues.
+
+It's easier to state for
+2D, which is why I did,
+
+but it works in 3D, too, with
+a little extra condition.
+
+And we'll talk about
+that in the future.
+
+Other questions?
+
+All right, that's the
+end of lecture one.
\ No newline at end of file
diff --git a/N4GOV3kzbdo.txt b/N4GOV3kzbdo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6112d775867afae890ef14f4f2a02fffaad44656
--- /dev/null
+++ b/N4GOV3kzbdo.txt
@@ -0,0 +1,1763 @@
+align:start position:0%
+ 
+okay I'm there yes Bob
+
+ align:start position:0%
+okay I'm there yes Bob
+ 
+
+ align:start position:0%
+okay I'm there yes Bob
+and I'm Kaylen and our project was kind
+
+ align:start position:0%
+and I'm Kaylen and our project was kind
+ 
+
+ align:start position:0%
+and I'm Kaylen and our project was kind
+of a mini RPG I guess escaped from the
+
+ align:start position:0%
+of a mini RPG I guess escaped from the
+ 
+
+ align:start position:0%
+of a mini RPG I guess escaped from the
+zoo
+
+ align:start position:0%
+zoo
+ 
+
+ align:start position:0%
+zoo
+right here's like an opening cutscene so
+
+ align:start position:0%
+right here's like an opening cutscene so
+ 
+
+ align:start position:0%
+right here's like an opening cutscene so
+there's these cute little animals and
+
+ align:start position:0%
+there's these cute little animals and
+ 
+
+ align:start position:0%
+there's these cute little animals and
+they're gonna try and escape the zoo
+
+ align:start position:0%
+they're gonna try and escape the zoo
+ 
+
+ align:start position:0%
+they're gonna try and escape the zoo
+yeah the premise of our idea was that we
+
+ align:start position:0%
+yeah the premise of our idea was that we
+ 
+
+ align:start position:0%
+yeah the premise of our idea was that we
+wanted to have different animals that
+
+ align:start position:0%
+wanted to have different animals that
+ 
+
+ align:start position:0%
+wanted to have different animals that
+you could control that each had
+
+ align:start position:0%
+you could control that each had
+ 
+
+ align:start position:0%
+you could control that each had
+different ways of moving with the Kinect
+
+ align:start position:0%
+different ways of moving with the Kinect
+ 
+
+ align:start position:0%
+different ways of moving with the Kinect
+and we wanted the ways of moving to kind
+
+ align:start position:0%
+and we wanted the ways of moving to kind
+ 
+
+ align:start position:0%
+and we wanted the ways of moving to kind
+of I guess connect with the ways that
+
+ align:start position:0%
+of I guess connect with the ways that
+ 
+
+ align:start position:0%
+of I guess connect with the ways that
+the animals themselves move so we have
+
+ align:start position:0%
+the animals themselves move so we have
+ 
+
+ align:start position:0%
+the animals themselves move so we have
+you know the Gecko and the Frog who move
+
+ align:start position:0%
+you know the Gecko and the Frog who move
+ 
+
+ align:start position:0%
+you know the Gecko and the Frog who move
+very differently the penguin and the
+
+ align:start position:0%
+very differently the penguin and the
+ 
+
+ align:start position:0%
+very differently the penguin and the
+Rhino so we have four different types of
+
+ align:start position:0%
+Rhino so we have four different types of
+ 
+
+ align:start position:0%
+Rhino so we have four different types of
+controls that correspond with each
+
+ align:start position:0%
+controls that correspond with each
+ 
+
+ align:start position:0%
+controls that correspond with each
+animal these are just colored cubes and
+
+ align:start position:0%
+animal these are just colored cubes and
+ 
+
+ align:start position:0%
+animal these are just colored cubes and
+they unlock the respective colored doors
+
+ align:start position:0%
+they unlock the respective colored doors
+ 
+
+ align:start position:0%
+they unlock the respective colored doors
+and so you have you psych each animals a
+
+ align:start position:0%
+and so you have you psych each animals a
+ 
+
+ align:start position:0%
+and so you have you psych each animals a
+gimmick their special power to get each
+
+ align:start position:0%
+gimmick their special power to get each
+ 
+
+ align:start position:0%
+gimmick their special power to get each
+of the four keys you can escape the zoo
+
+ align:start position:0%
+of the four keys you can escape the zoo
+ 
+
+ align:start position:0%
+of the four keys you can escape the zoo
+so there's like a problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is like the backstory yeah so
+
+ align:start position:0%
+and this is like the backstory yeah so
+ 
+
+ align:start position:0%
+and this is like the backstory yeah so
+there's so many Grand Theft Auto yeah so
+
+ align:start position:0%
+there's so many Grand Theft Auto yeah so
+ 
+
+ align:start position:0%
+there's so many Grand Theft Auto yeah so
+cuz things were really interesting to
+
+ align:start position:0%
+cuz things were really interesting to
+ 
+
+ align:start position:0%
+cuz things were really interesting to
+Nathan yeah they quickly ran up we have
+
+ align:start position:0%
+Nathan yeah they quickly ran up we have
+ 
+
+ align:start position:0%
+Nathan yeah they quickly ran up we have
+like all these damaged files
+
+ align:start position:0%
+like all these damaged files
+ 
+
+ align:start position:0%
+like all these damaged files
+and so it ended up being a raw image
+
+ align:start position:0%
+and so it ended up being a raw image
+ 
+
+ align:start position:0%
+and so it ended up being a raw image
+with like 25 images attached to it and
+
+ align:start position:0%
+with like 25 images attached to it and
+ 
+
+ align:start position:0%
+with like 25 images attached to it and
+then a script that looks like every set
+
+ align:start position:0%
+then a script that looks like every set
+ 
+
+ align:start position:0%
+then a script that looks like every set
+amount of time switch to the next image
+
+ align:start position:0%
+amount of time switch to the next image
+ 
+
+ align:start position:0%
+amount of time switch to the next image
+and it's like a giant long piece of code
+
+ align:start position:0%
+and it's like a giant long piece of code
+ 
+
+ align:start position:0%
+and it's like a giant long piece of code
+because it's like if time is greater
+
+ align:start position:0%
+because it's like if time is greater
+ 
+
+ align:start position:0%
+because it's like if time is greater
+than 15 June image 5 okay we're in the
+
+ align:start position:0%
+than 15 June image 5 okay we're in the
+ 
+
+ align:start position:0%
+than 15 June image 5 okay we're in the
+game I'm already moving around penguin
+
+ align:start position:0%
+game I'm already moving around penguin
+ 
+
+ align:start position:0%
+game I'm already moving around penguin
+so Universal actually could be a little
+
+ align:start position:0%
+so Universal actually could be a little
+ 
+
+ align:start position:0%
+so Universal actually could be a little
+slump
+
+ align:start position:0%
+slump
+ 
+
+ align:start position:0%
+slump
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+originally therefore the penguin was too
+
+ align:start position:0%
+originally therefore the penguin was too
+ 
+
+ align:start position:0%
+originally therefore the penguin was too
+kinda like this which is great kind of
+
+ align:start position:0%
+kinda like this which is great kind of
+ 
+
+ align:start position:0%
+kinda like this which is great kind of
+water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however he kinda got hurt because the
+
+ align:start position:0%
+however he kinda got hurt because the
+ 
+
+ align:start position:0%
+however he kinda got hurt because the
+shoulders were really close to each
+
+ align:start position:0%
+shoulders were really close to each
+ 
+
+ align:start position:0%
+shoulders were really close to each
+other so in the code it would be like if
+
+ align:start position:0%
+other so in the code it would be like if
+ 
+
+ align:start position:0%
+other so in the code it would be like if
+one shoulders in front of the other and
+
+ align:start position:0%
+one shoulders in front of the other and
+ 
+
+ align:start position:0%
+one shoulders in front of the other and
+because they're closed we switch you to
+
+ align:start position:0%
+because they're closed we switch you to
+ 
+
+ align:start position:0%
+because they're closed we switch you to
+the hands so you can see I'm pretty
+
+ align:start position:0%
+the hands so you can see I'm pretty
+ 
+
+ align:start position:0%
+the hands so you can see I'm pretty
+loose with my hands just because it
+
+ align:start position:0%
+loose with my hands just because it
+ 
+
+ align:start position:0%
+loose with my hands just because it
+helps of the code so you saw the through
+
+ align:start position:0%
+helps of the code so you saw the through
+ 
+
+ align:start position:0%
+helps of the code so you saw the through
+support animals so part of this is going
+
+ align:start position:0%
+support animals so part of this is going
+ 
+
+ align:start position:0%
+support animals so part of this is going
+to be able to switch to animals
+
+ align:start position:0%
+to be able to switch to animals
+ 
+
+ align:start position:0%
+to be able to switch to animals
+if I could please switch you go frog
+
+ align:start position:0%
+if I could please switch you go frog
+ 
+
+ align:start position:0%
+if I could please switch you go frog
+email right same general controls of the
+
+ align:start position:0%
+email right same general controls of the
+ 
+
+ align:start position:0%
+email right same general controls of the
+left and right the Frog special ability
+
+ align:start position:0%
+left and right the Frog special ability
+ 
+
+ align:start position:0%
+left and right the Frog special ability
+is jumping which we wanted to be jumped
+
+ align:start position:0%
+is jumping which we wanted to be jumped
+ 
+
+ align:start position:0%
+is jumping which we wanted to be jumped
+but like the coach that was a little bit
+
+ align:start position:0%
+but like the coach that was a little bit
+ 
+
+ align:start position:0%
+but like the coach that was a little bit
+harder then I was able to do because we
+
+ align:start position:0%
+harder then I was able to do because we
+ 
+
+ align:start position:0%
+harder then I was able to do because we
+have a thing like the average of like
+
+ align:start position:0%
+have a thing like the average of like
+ 
+
+ align:start position:0%
+have a thing like the average of like
+your head position and then whenever you
+
+ align:start position:0%
+your head position and then whenever you
+ 
+
+ align:start position:0%
+your head position and then whenever you
+have an outlier jump so much so the Frog
+
+ align:start position:0%
+have an outlier jump so much so the Frog
+ 
+
+ align:start position:0%
+have an outlier jump so much so the Frog
+is kind of like a crawling motion from
+
+ align:start position:0%
+is kind of like a crawling motion from
+ 
+
+ align:start position:0%
+is kind of like a crawling motion from
+the other so um yeah we um
+
+ align:start position:0%
+the other so um yeah we um
+ 
+
+ align:start position:0%
+the other so um yeah we um
+so I built this entire world and we also
+
+ align:start position:0%
+so I built this entire world and we also
+ 
+
+ align:start position:0%
+so I built this entire world and we also
+use sort of terraforming one thing I
+
+ align:start position:0%
+use sort of terraforming one thing I
+ 
+
+ align:start position:0%
+use sort of terraforming one thing I
+really wanted I wanted the zoo to be
+
+ align:start position:0%
+really wanted I wanted the zoo to be
+ 
+
+ align:start position:0%
+really wanted I wanted the zoo to be
+like really crappy like like you need to
+
+ align:start position:0%
+like really crappy like like you need to
+ 
+
+ align:start position:0%
+like really crappy like like you need to
+feel like the animals like you want to
+
+ align:start position:0%
+feel like the animals like you want to
+ 
+
+ align:start position:0%
+feel like the animals like you want to
+get out of here so I found the worst
+
+ align:start position:0%
+get out of here so I found the worst
+ 
+
+ align:start position:0%
+get out of here so I found the worst
+clipart I could possibly find and if you
+
+ align:start position:0%
+clipart I could possibly find and if you
+ 
+
+ align:start position:0%
+clipart I could possibly find and if you
+notice the welcome to the zoo sign is in
+
+ align:start position:0%
+notice the welcome to the zoo sign is in
+ 
+
+ align:start position:0%
+notice the welcome to the zoo sign is in
+Comic Sans all of these models as well
+
+ align:start position:0%
+Comic Sans all of these models as well
+ 
+
+ align:start position:0%
+Comic Sans all of these models as well
+are we found them for like between five
+
+ align:start position:0%
+are we found them for like between five
+ 
+
+ align:start position:0%
+are we found them for like between five
+to ten dollars each on the unity asset
+
+ align:start position:0%
+to ten dollars each on the unity asset
+ 
+
+ align:start position:0%
+to ten dollars each on the unity asset
+store and they came fully animated
+
+ align:start position:0%
+store and they came fully animated
+ 
+
+ align:start position:0%
+store and they came fully animated
+there's actually a lot of animations we
+
+ align:start position:0%
+there's actually a lot of animations we
+ 
+
+ align:start position:0%
+there's actually a lot of animations we
+didn't use like the Frog and the penguin
+
+ align:start position:0%
+didn't use like the Frog and the penguin
+ 
+
+ align:start position:0%
+didn't use like the Frog and the penguin
+can like eat things yeah just make sure
+
+ align:start position:0%
+can like eat things yeah just make sure
+ 
+
+ align:start position:0%
+can like eat things yeah just make sure
+he doesn't jump out of the he can't
+
+ align:start position:0%
+he doesn't jump out of the he can't
+ 
+
+ align:start position:0%
+he doesn't jump out of the he can't
+escape yet yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+players shouldn't do kiss on Beijing
+
+ align:start position:0%
+players shouldn't do kiss on Beijing
+ 
+
+ align:start position:0%
+players shouldn't do kiss on Beijing
+morals so this is currently don't do
+
+ align:start position:0%
+morals so this is currently don't do
+ 
+
+ align:start position:0%
+morals so this is currently don't do
+anything they're not collisions oh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens with models and not flat
+
+ align:start position:0%
+happens with models and not flat
+ 
+
+ align:start position:0%
+happens with models and not flat
+surfaces you can see one thing we didn't
+
+ align:start position:0%
+surfaces you can see one thing we didn't
+ 
+
+ align:start position:0%
+surfaces you can see one thing we didn't
+fix is that the horse still runs like
+
+ align:start position:0%
+fix is that the horse still runs like
+ 
+
+ align:start position:0%
+fix is that the horse still runs like
+the horse has like a controller attached
+
+ align:start position:0%
+the horse has like a controller attached
+ 
+
+ align:start position:0%
+the horse has like a controller attached
+to him that makes him run but he runs in
+
+ align:start position:0%
+to him that makes him run but he runs in
+ 
+
+ align:start position:0%
+to him that makes him run but he runs in
+place whenever you move the horse moves
+
+ align:start position:0%
+place whenever you move the horse moves
+ 
+
+ align:start position:0%
+place whenever you move the horse moves
+I like to think it's because he secretly
+
+ align:start position:0%
+I like to think it's because he secretly
+ 
+
+ align:start position:0%
+I like to think it's because he secretly
+wants to leave with you but he's not
+
+ align:start position:0%
+wants to leave with you but he's not
+ 
+
+ align:start position:0%
+wants to leave with you but he's not
+brave enough to do it sorry yeah this is
+
+ align:start position:0%
+brave enough to do it sorry yeah this is
+ 
+
+ align:start position:0%
+brave enough to do it sorry yeah this is
+this is grass there's a lot of grass so
+
+ align:start position:0%
+this is grass there's a lot of grass so
+ 
+
+ align:start position:0%
+this is grass there's a lot of grass so
+it loads slowly it's a pretty big world
+
+ align:start position:0%
+it loads slowly it's a pretty big world
+ 
+
+ align:start position:0%
+it loads slowly it's a pretty big world
+actually do you want to switch the
+
+ align:start position:0%
+actually do you want to switch the
+ 
+
+ align:start position:0%
+actually do you want to switch the
+penguin is probably the slowest this
+
+ align:start position:0%
+penguin is probably the slowest this
+ 
+
+ align:start position:0%
+penguin is probably the slowest this
+motion right here it was pretty fun so
+
+ align:start position:0%
+motion right here it was pretty fun so
+ 
+
+ align:start position:0%
+motion right here it was pretty fun so
+we knew we wanted like a switching
+
+ align:start position:0%
+we knew we wanted like a switching
+ 
+
+ align:start position:0%
+we knew we wanted like a switching
+motion but like logically we didn't want
+
+ align:start position:0%
+motion but like logically we didn't want
+ 
+
+ align:start position:0%
+motion but like logically we didn't want
+the player to be able to just do this
+
+ align:start position:0%
+the player to be able to just do this
+ 
+
+ align:start position:0%
+the player to be able to just do this
+and then I continued going for an effort
+
+ align:start position:0%
+and then I continued going for an effort
+ 
+
+ align:start position:0%
+and then I continued going for an effort
+forever so there has to be a check where
+
+ align:start position:0%
+forever so there has to be a check where
+ 
+
+ align:start position:0%
+forever so there has to be a check where
+if like if you move using left handed
+
+ align:start position:0%
+if like if you move using left handed
+ 
+
+ align:start position:0%
+if like if you move using left handed
+for the right once switch like this
+
+ align:start position:0%
+for the right once switch like this
+ 
+
+ align:start position:0%
+for the right once switch like this
+check the left and then you can't get
+
+ align:start position:0%
+check the left and then you can't get
+ 
+
+ align:start position:0%
+check the left and then you can't get
+back into that piece of code but it was
+
+ align:start position:0%
+back into that piece of code but it was
+ 
+
+ align:start position:0%
+back into that piece of code but it was
+in a update function and that means that
+
+ align:start position:0%
+in a update function and that means that
+ 
+
+ align:start position:0%
+in a update function and that means that
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+every frame so it was running every
+
+ align:start position:0%
+every frame so it was running every
+ 
+
+ align:start position:0%
+every frame so it was running every
+frame but you could only go left or
+
+ align:start position:0%
+frame but you could only go left or
+ 
+
+ align:start position:0%
+frame but you could only go left or
+right one frame so then you're moving
+
+ align:start position:0%
+right one frame so then you're moving
+ 
+
+ align:start position:0%
+right one frame so then you're moving
+one thing at a time
+
+ align:start position:0%
+one thing at a time
+ 
+
+ align:start position:0%
+one thing at a time
+which is hilarious look so the solution
+
+ align:start position:0%
+which is hilarious look so the solution
+ 
+
+ align:start position:0%
+which is hilarious look so the solution
+to that was 250 invisible wall here yes
+
+ align:start position:0%
+to that was 250 invisible wall here yes
+ 
+
+ align:start position:0%
+to that was 250 invisible wall here yes
+I'm gonna show that so paying special
+
+ align:start position:0%
+I'm gonna show that so paying special
+ 
+
+ align:start position:0%
+I'm gonna show that so paying special
+abilities gonna be able to slide down
+
+ align:start position:0%
+abilities gonna be able to slide down
+ 
+
+ align:start position:0%
+abilities gonna be able to slide down
+things so to keep other animals from
+
+ align:start position:0%
+things so to keep other animals from
+ 
+
+ align:start position:0%
+things so to keep other animals from
+using that ability it's a nice little
+
+ align:start position:0%
+using that ability it's a nice little
+ 
+
+ align:start position:0%
+using that ability it's a nice little
+invisible wall so I'm gonna switch back
+
+ align:start position:0%
+invisible wall so I'm gonna switch back
+ 
+
+ align:start position:0%
+invisible wall so I'm gonna switch back
+to penguin and there was like a counter
+
+ align:start position:0%
+to penguin and there was like a counter
+ 
+
+ align:start position:0%
+to penguin and there was like a counter
+they counted how many frames you are
+
+ align:start position:0%
+they counted how many frames you are
+ 
+
+ align:start position:0%
+they counted how many frames you are
+allowed to stick one hand in front of
+
+ align:start position:0%
+allowed to stick one hand in front of
+ 
+
+ align:start position:0%
+allowed to stick one hand in front of
+the other and 30 works pretty well it
+
+ align:start position:0%
+the other and 30 works pretty well it
+ 
+
+ align:start position:0%
+the other and 30 works pretty well it
+was like it's felt kind of natural with
+
+ align:start position:0%
+was like it's felt kind of natural with
+ 
+
+ align:start position:0%
+was like it's felt kind of natural with
+like like a pattern that you would use
+
+ align:start position:0%
+like like a pattern that you would use
+ 
+
+ align:start position:0%
+like like a pattern that you would use
+or a time that you would used to swim
+
+ align:start position:0%
+or a time that you would used to swim
+ 
+
+ align:start position:0%
+or a time that you would used to swim
+let's see other things switch between
+
+ align:start position:0%
+let's see other things switch between
+ 
+
+ align:start position:0%
+let's see other things switch between
+the animals was interesting I originally
+
+ align:start position:0%
+the animals was interesting I originally
+ 
+
+ align:start position:0%
+the animals was interesting I originally
+tried attach them all to a single player
+
+ align:start position:0%
+tried attach them all to a single player
+ 
+
+ align:start position:0%
+tried attach them all to a single player
+and then having them move the player
+
+ align:start position:0%
+and then having them move the player
+ 
+
+ align:start position:0%
+and then having them move the player
+object so that way it moved all four of
+
+ align:start position:0%
+object so that way it moved all four of
+ 
+
+ align:start position:0%
+object so that way it moved all four of
+the models whether or not they were
+
+ align:start position:0%
+the models whether or not they were
+ 
+
+ align:start position:0%
+the models whether or not they were
+invisible at the same time but that kind
+
+ align:start position:0%
+invisible at the same time but that kind
+ 
+
+ align:start position:0%
+invisible at the same time but that kind
+of caused a perpetual motion thing where
+
+ align:start position:0%
+of caused a perpetual motion thing where
+ 
+
+ align:start position:0%
+of caused a perpetual motion thing where
+like one animal would move the player
+
+ align:start position:0%
+like one animal would move the player
+ 
+
+ align:start position:0%
+like one animal would move the player
+object but then because it was attached
+
+ align:start position:0%
+object but then because it was attached
+ 
+
+ align:start position:0%
+object but then because it was attached
+the player object the player object
+
+ align:start position:0%
+the player object the player object
+ 
+
+ align:start position:0%
+the player object the player object
+remove the animal it's like you would
+
+ align:start position:0%
+remove the animal it's like you would
+ 
+
+ align:start position:0%
+remove the animal it's like you would
+hit the game in like Sun
+
+ align:start position:0%
+hit the game in like Sun
+ 
+
+ align:start position:0%
+hit the game in like Sun
+the penguin starts like waltzing off the
+
+ align:start position:0%
+the penguin starts like waltzing off the
+ 
+
+ align:start position:0%
+the penguin starts like waltzing off the
+playing field I think I'm on flat ground
+
+ align:start position:0%
+playing field I think I'm on flat ground
+ 
+
+ align:start position:0%
+playing field I think I'm on flat ground
+message to Rhino please the Rhino school
+
+ align:start position:0%
+message to Rhino please the Rhino school
+ 
+
+ align:start position:0%
+message to Rhino please the Rhino school
+didn't come with a client so it's just
+
+ align:start position:0%
+didn't come with a client so it's just
+ 
+
+ align:start position:0%
+didn't come with a client so it's just
+have a box but right this way a move is
+
+ align:start position:0%
+have a box but right this way a move is
+ 
+
+ align:start position:0%
+have a box but right this way a move is
+to charge forward get those abilities to
+
+ align:start position:0%
+to charge forward get those abilities to
+ 
+
+ align:start position:0%
+to charge forward get those abilities to
+climb up walls
+
+ align:start position:0%
+climb up walls
+ 
+
+ align:start position:0%
+climb up walls
+however due to time constraints and sets
+
+ align:start position:0%
+however due to time constraints and sets
+ 
+
+ align:start position:0%
+however due to time constraints and sets
+planet walls we're gonna need some
+
+ align:start position:0%
+planet walls we're gonna need some
+ 
+
+ align:start position:0%
+planet walls we're gonna need some
+matches
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough you can get his key so would you
+
+ align:start position:0%
+enough you can get his key so would you
+ 
+
+ align:start position:0%
+enough you can get his key so would you
+like to talk about in disease yes so
+
+ align:start position:0%
+like to talk about in disease yes so
+ 
+
+ align:start position:0%
+like to talk about in disease yes so
+we're gonna go visit some of the NPCs
+
+ align:start position:0%
+we're gonna go visit some of the NPCs
+ 
+
+ align:start position:0%
+we're gonna go visit some of the NPCs
+now there are interacts that you engage
+
+ align:start position:0%
+now there are interacts that you engage
+ 
+
+ align:start position:0%
+now there are interacts that you engage
+with by hitting a little invisible
+
+ align:start position:0%
+with by hitting a little invisible
+ 
+
+ align:start position:0%
+with by hitting a little invisible
+Collider box there's a gorilla and a
+
+ align:start position:0%
+Collider box there's a gorilla and a
+ 
+
+ align:start position:0%
+Collider box there's a gorilla and a
+horse neither of whom want to escape
+
+ align:start position:0%
+horse neither of whom want to escape
+ 
+
+ align:start position:0%
+horse neither of whom want to escape
+with you the gorillas in that
+
+ align:start position:0%
+with you the gorillas in that
+ 
+
+ align:start position:0%
+with you the gorillas in that
+sad-looking cage and the horses you know
+
+ align:start position:0%
+sad-looking cage and the horses you know
+ 
+
+ align:start position:0%
+sad-looking cage and the horses you know
+standing behind him and each interact is
+
+ align:start position:0%
+standing behind him and each interact is
+ 
+
+ align:start position:0%
+standing behind him and each interact is
+specific to the animals so we're going
+
+ align:start position:0%
+specific to the animals so we're going
+ 
+
+ align:start position:0%
+specific to the animals so we're going
+to interact with gorilla as right now
+
+ align:start position:0%
+to interact with gorilla as right now
+ 
+
+ align:start position:0%
+to interact with gorilla as right now
+see good exercise
+
+ align:start position:0%
+see good exercise
+ 
+
+ align:start position:0%
+see good exercise
+oh no you keep the horse it could
+
+ align:start position:0%
+oh no you keep the horse it could
+ 
+
+ align:start position:0%
+oh no you keep the horse it could
+actually be the image
+
+ align:start position:0%
+actually be the image
+ 
+
+ align:start position:0%
+actually be the image
+we've we had to make a Harambee
+
+ align:start position:0%
+we've we had to make a Harambee
+ 
+
+ align:start position:0%
+we've we had to make a Harambee
+reference I mean it's a gorilla in a zoo
+
+ align:start position:0%
+reference I mean it's a gorilla in a zoo
+ 
+
+ align:start position:0%
+reference I mean it's a gorilla in a zoo
+what are we gonna do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk about cut scenes cut scenes were
+
+ align:start position:0%
+talk about cut scenes cut scenes were
+ 
+
+ align:start position:0%
+talk about cut scenes cut scenes were
+fun oh it show it automatically goes to
+
+ align:start position:0%
+fun oh it show it automatically goes to
+ 
+
+ align:start position:0%
+fun oh it show it automatically goes to
+the horse well it's okay the horse but
+
+ align:start position:0%
+the horse well it's okay the horse but
+ 
+
+ align:start position:0%
+the horse well it's okay the horse but
+it only did part of the horse cutscene
+
+ align:start position:0%
+it only did part of the horse cutscene
+ 
+
+ align:start position:0%
+it only did part of the horse cutscene
+maybe the images were just put there
+
+ align:start position:0%
+maybe the images were just put there
+ 
+
+ align:start position:0%
+maybe the images were just put there
+back soon
+
+ align:start position:0%
+back soon
+ 
+
+ align:start position:0%
+back soon
+whatever anyways so this is the worst
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so as we'll find out in a minute
+
+ align:start position:0%
+yeah so as we'll find out in a minute
+ 
+
+ align:start position:0%
+yeah so as we'll find out in a minute
+we're gonna leave oh oh well oh we must
+
+ align:start position:0%
+we're gonna leave oh oh well oh we must
+ 
+
+ align:start position:0%
+we're gonna leave oh oh well oh we must
+have still well so we're gonna go
+
+ align:start position:0%
+have still well so we're gonna go
+ 
+
+ align:start position:0%
+have still well so we're gonna go
+interact with all the voices here we'll
+
+ align:start position:0%
+interact with all the voices here we'll
+ 
+
+ align:start position:0%
+interact with all the voices here we'll
+switch with penguin oh that's why yeah
+
+ align:start position:0%
+switch with penguin oh that's why yeah
+ 
+
+ align:start position:0%
+switch with penguin oh that's why yeah
+so now we'll go interact okay we'll have
+
+ align:start position:0%
+so now we'll go interact okay we'll have
+ 
+
+ align:start position:0%
+so now we'll go interact okay we'll have
+frog here we go when I was like testing
+
+ align:start position:0%
+frog here we go when I was like testing
+ 
+
+ align:start position:0%
+frog here we go when I was like testing
+to get around I had to choose like
+
+ align:start position:0%
+to get around I had to choose like
+ 
+
+ align:start position:0%
+to get around I had to choose like
+different animals to get around so hi
+
+ align:start position:0%
+different animals to get around so hi
+ 
+
+ align:start position:0%
+different animals to get around so hi
+frog was convenient because of the
+
+ align:start position:0%
+frog was convenient because of the
+ 
+
+ align:start position:0%
+frog was convenient because of the
+jumping was pretty fast
+
+ align:start position:0%
+jumping was pretty fast
+ 
+
+ align:start position:0%
+jumping was pretty fast
+the rhinos the fastest but because the
+
+ align:start position:0%
+the rhinos the fastest but because the
+ 
+
+ align:start position:0%
+the rhinos the fastest but because the
+Rhino hitbox is literally a box some
+
+ align:start position:0%
+Rhino hitbox is literally a box some
+ 
+
+ align:start position:0%
+Rhino hitbox is literally a box some
+weird things happen where like it would
+
+ align:start position:0%
+weird things happen where like it would
+ 
+
+ align:start position:0%
+weird things happen where like it would
+hit a log and then start flying off into
+
+ align:start position:0%
+hit a log and then start flying off into
+ 
+
+ align:start position:0%
+hit a log and then start flying off into
+space or like flip over and tumble and
+
+ align:start position:0%
+space or like flip over and tumble and
+ 
+
+ align:start position:0%
+space or like flip over and tumble and
+crazy things so it was really like the
+
+ align:start position:0%
+crazy things so it was really like the
+ 
+
+ align:start position:0%
+crazy things so it was really like the
+safe route to get to places but if I was
+
+ align:start position:0%
+safe route to get to places but if I was
+ 
+
+ align:start position:0%
+safe route to get to places but if I was
+going and reading ambitious oh we're
+
+ align:start position:0%
+going and reading ambitious oh we're
+ 
+
+ align:start position:0%
+going and reading ambitious oh we're
+tilted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I would like go to RINO and I have fun
+
+ align:start position:0%
+I would like go to RINO and I have fun
+ 
+
+ align:start position:0%
+I would like go to RINO and I have fun
+pretending to be like an airplane it's
+
+ align:start position:0%
+pretending to be like an airplane it's
+ 
+
+ align:start position:0%
+pretending to be like an airplane it's
+called a Dutch ankle - it's purposeful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is Lasky's we're almost there huh
+
+ align:start position:0%
+this is Lasky's we're almost there huh
+ 
+
+ align:start position:0%
+this is Lasky's we're almost there huh
+should I switch yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is frog faster than gecko because the
+
+ align:start position:0%
+is frog faster than gecko because the
+ 
+
+ align:start position:0%
+is frog faster than gecko because the
+judge right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the Rhino special ability is a
+
+ align:start position:0%
+so the Rhino special ability is a
+ 
+
+ align:start position:0%
+so the Rhino special ability is a
+meeting with break down boxes the key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however the very tight corridors of the
+
+ align:start position:0%
+however the very tight corridors of the
+ 
+
+ align:start position:0%
+however the very tight corridors of the
+club can't really turn to get out yeah
+
+ align:start position:0%
+club can't really turn to get out yeah
+ 
+
+ align:start position:0%
+club can't really turn to get out yeah
+this sort of another part of the premise
+
+ align:start position:0%
+this sort of another part of the premise
+ 
+
+ align:start position:0%
+this sort of another part of the premise
+was that we wanted to make we wanted to
+
+ align:start position:0%
+was that we wanted to make we wanted to
+ 
+
+ align:start position:0%
+was that we wanted to make we wanted to
+make the characters be animals that like
+
+ align:start position:0%
+make the characters be animals that like
+ 
+
+ align:start position:0%
+make the characters be animals that like
+nobody would miss if they left the zoo
+
+ align:start position:0%
+nobody would miss if they left the zoo
+ 
+
+ align:start position:0%
+nobody would miss if they left the zoo
+except for rhino who everybody would
+
+ align:start position:0%
+except for rhino who everybody would
+ 
+
+ align:start position:0%
+except for rhino who everybody would
+miss so rhino needs a lot of help that's
+
+ align:start position:0%
+miss so rhino needs a lot of help that's
+ 
+
+ align:start position:0%
+miss so rhino needs a lot of help that's
+the plot reason so if you know the
+
+ align:start position:0%
+the plot reason so if you know the
+ 
+
+ align:start position:0%
+the plot reason so if you know the
+beginning there were doors near the
+
+ align:start position:0%
+beginning there were doors near the
+ 
+
+ align:start position:0%
+beginning there were doors near the
+entrance here they're all gone
+
+ align:start position:0%
+entrance here they're all gone
+ 
+
+ align:start position:0%
+entrance here they're all gone
+you know the colored keys got rid of the
+
+ align:start position:0%
+you know the colored keys got rid of the
+ 
+
+ align:start position:0%
+you know the colored keys got rid of the
+respective color doors this all silicon
+
+ align:start position:0%
+respective color doors this all silicon
+ 
+
+ align:start position:0%
+respective color doors this all silicon
+short ending cutscene I'm going to make
+
+ align:start position:0%
+short ending cutscene I'm going to make
+ 
+
+ align:start position:0%
+short ending cutscene I'm going to make
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/N4vMgwWT-80.txt b/N4vMgwWT-80.txt
new file mode 100644
index 0000000000000000000000000000000000000000..12fff01f369fee35998ae73820df0899440678b1
--- /dev/null
+++ b/N4vMgwWT-80.txt
@@ -0,0 +1,6251 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so today we're gonna go from the
+
+ align:start position:0%
+so today we're gonna go from the
+ 
+
+ align:start position:0%
+so today we're gonna go from the
+classical mechanical treatment of the
+
+ align:start position:0%
+classical mechanical treatment of the
+ 
+
+ align:start position:0%
+classical mechanical treatment of the
+harmonic oscillator to a quantum
+
+ align:start position:0%
+harmonic oscillator to a quantum
+ 
+
+ align:start position:0%
+harmonic oscillator to a quantum
+mechanical treatment and I warned you
+
+ align:start position:0%
+mechanical treatment and I warned you
+ 
+
+ align:start position:0%
+mechanical treatment and I warned you
+that I intentionally am going to make
+
+ align:start position:0%
+that I intentionally am going to make
+ 
+
+ align:start position:0%
+that I intentionally am going to make
+this look bad because the the the
+
+ align:start position:0%
+this look bad because the the the
+ 
+
+ align:start position:0%
+this look bad because the the the
+semi-classical approach at the begin at
+
+ align:start position:0%
+semi-classical approach at the begin at
+ 
+
+ align:start position:0%
+semi-classical approach at the begin at
+the end of this lecture will make it all
+
+ align:start position:0%
+the end of this lecture will make it all
+ 
+
+ align:start position:0%
+the end of this lecture will make it all
+really simple and then on Monday I'll
+
+ align:start position:0%
+really simple and then on Monday I'll
+ 
+
+ align:start position:0%
+really simple and then on Monday I'll
+introduce creation and annihilation
+
+ align:start position:0%
+introduce creation and annihilation
+ 
+
+ align:start position:0%
+introduce creation and annihilation
+operators which makes the harmonic
+
+ align:start position:0%
+operators which makes the harmonic
+ 
+
+ align:start position:0%
+operators which makes the harmonic
+oscillator simpler than the particle in
+
+ align:start position:0%
+oscillator simpler than the particle in
+ 
+
+ align:start position:0%
+oscillator simpler than the particle in
+a box you can't believe that but alright
+
+ align:start position:0%
+a box you can't believe that but alright
+ 
+
+ align:start position:0%
+a box you can't believe that but alright
+so last time it we treated the the
+
+ align:start position:0%
+so last time it we treated the the
+ 
+
+ align:start position:0%
+so last time it we treated the the
+harmonic oscillator classically and so
+
+ align:start position:0%
+harmonic oscillator classically and so
+ 
+
+ align:start position:0%
+harmonic oscillator classically and so
+we derived the equation of motion from
+
+ align:start position:0%
+we derived the equation of motion from
+ 
+
+ align:start position:0%
+we derived the equation of motion from
+force is equal to mass times
+
+ align:start position:0%
+force is equal to mass times
+ 
+
+ align:start position:0%
+force is equal to mass times
+acceleration and we solved it and we saw
+
+ align:start position:0%
+acceleration and we solved it and we saw
+ 
+
+ align:start position:0%
+acceleration and we solved it and we saw
+that we have this quantity Omega which
+
+ align:start position:0%
+that we have this quantity Omega which
+ 
+
+ align:start position:0%
+that we have this quantity Omega which
+initially I just introduced as a
+
+ align:start position:0%
+initially I just introduced as a
+ 
+
+ align:start position:0%
+initially I just introduced as a
+constant which was a way of combining
+
+ align:start position:0%
+constant which was a way of combining
+ 
+
+ align:start position:0%
+constant which was a way of combining
+the force constant and the mass and then
+
+ align:start position:0%
+the force constant and the mass and then
+ 
+
+ align:start position:0%
+the force constant and the mass and then
+I showed that the period of oscillation
+
+ align:start position:0%
+I showed that the period of oscillation
+ 
+
+ align:start position:0%
+I showed that the period of oscillation
+is 1 over the frequency which is 2 PI
+
+ align:start position:0%
+is 1 over the frequency which is 2 PI
+ 
+
+ align:start position:0%
+is 1 over the frequency which is 2 PI
+over Omega now one of the things that
+
+ align:start position:0%
+over Omega now one of the things that
+ 
+
+ align:start position:0%
+over Omega now one of the things that
+people have trouble remembering under
+
+ align:start position:0%
+people have trouble remembering under
+ 
+
+ align:start position:0%
+people have trouble remembering under
+exam pressure is turning points and this
+
+ align:start position:0%
+exam pressure is turning points and this
+ 
+
+ align:start position:0%
+exam pressure is turning points and this
+comes when the energy is equal to the
+
+ align:start position:0%
+comes when the energy is equal to the
+ 
+
+ align:start position:0%
+comes when the energy is equal to the
+potential at a turning point
+
+ align:start position:0%
+potential at a turning point
+ 
+
+ align:start position:0%
+potential at a turning point
+oops and since the potential is 1/2 KX
+
+ align:start position:0%
+oops and since the potential is 1/2 KX
+ 
+
+ align:start position:0%
+oops and since the potential is 1/2 KX
+squared we get original the equation for
+
+ align:start position:0%
+squared we get original the equation for
+ 
+
+ align:start position:0%
+squared we get original the equation for
+the turning point at a given energy
+
+ align:start position:0%
+the turning point at a given energy
+ 
+
+ align:start position:0%
+the turning point at a given energy
+which is equal to plus or minus the
+
+ align:start position:0%
+which is equal to plus or minus the
+ 
+
+ align:start position:0%
+which is equal to plus or minus the
+square root of 2 e over K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when you're drawing pictures there
+
+ align:start position:0%
+now when you're drawing pictures there
+ 
+
+ align:start position:0%
+now when you're drawing pictures there
+are certain things that anchor the
+
+ align:start position:0%
+are certain things that anchor the
+ 
+
+ align:start position:0%
+are certain things that anchor the
+pictures like turning points okay
+
+ align:start position:0%
+pictures like turning points okay
+ 
+
+ align:start position:0%
+pictures like turning points okay
+and now at the end of the previous
+
+ align:start position:0%
+and now at the end of the previous
+ 
+
+ align:start position:0%
+and now at the end of the previous
+lecture I calculated the classical
+
+ align:start position:0%
+lecture I calculated the classical
+ 
+
+ align:start position:0%
+lecture I calculated the classical
+mechanical average and we use we use
+
+ align:start position:0%
+mechanical average and we use we use
+ 
+
+ align:start position:0%
+mechanical average and we use we use
+this kind of notation in classical
+
+ align:start position:0%
+this kind of notation in classical
+ 
+
+ align:start position:0%
+this kind of notation in classical
+mechanics sometimes we use this notation
+
+ align:start position:0%
+mechanics sometimes we use this notation
+ 
+
+ align:start position:0%
+mechanics sometimes we use this notation
+too but this is what we mean by the
+
+ align:start position:0%
+too but this is what we mean by the
+ 
+
+ align:start position:0%
+too but this is what we mean by the
+average value in quantum mechanics and
+
+ align:start position:0%
+average value in quantum mechanics and
+ 
+
+ align:start position:0%
+average value in quantum mechanics and
+we found that this was the total energy
+
+ align:start position:0%
+we found that this was the total energy
+ 
+
+ align:start position:0%
+we found that this was the total energy
+divided by two and the average momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the energy divided by two and that's
+
+ align:start position:0%
+is the energy divided by two and that's
+ 
+
+ align:start position:0%
+is the energy divided by two and that's
+a basis for some insight because as a
+
+ align:start position:0%
+a basis for some insight because as a
+ 
+
+ align:start position:0%
+a basis for some insight because as a
+harmonic oscillator moves it throws
+
+ align:start position:0%
+harmonic oscillator moves it throws
+ 
+
+ align:start position:0%
+harmonic oscillator moves it throws
+energy back and forth between kinetic
+
+ align:start position:0%
+energy back and forth between kinetic
+ 
+
+ align:start position:0%
+energy back and forth between kinetic
+energy and potential energy and then one
+
+ align:start position:0%
+energy and potential energy and then one
+ 
+
+ align:start position:0%
+energy and potential energy and then one
+of my favorite things and one of my
+
+ align:start position:0%
+of my favorite things and one of my
+ 
+
+ align:start position:0%
+of my favorite things and one of my
+favorite tortures on short answers is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the average values and does anybody want
+
+ align:start position:0%
+the average values and does anybody want
+ 
+
+ align:start position:0%
+the average values and does anybody want
+to remind the class the easy way or the
+
+ align:start position:0%
+to remind the class the easy way or the
+ 
+
+ align:start position:0%
+to remind the class the easy way or the
+two easy ways to know what this is and
+
+ align:start position:0%
+two easy ways to know what this is and
+ 
+
+ align:start position:0%
+two easy ways to know what this is and
+the person who answered the question
+
+ align:start position:0%
+the person who answered the question
+ 
+
+ align:start position:0%
+the person who answered the question
+last time is disqualified
+
+ align:start position:0%
+last time is disqualified
+ 
+
+ align:start position:0%
+last time is disqualified
+yes symmetry but there's a symmetry the
+
+ align:start position:0%
+yes symmetry but there's a symmetry the
+ 
+
+ align:start position:0%
+yes symmetry but there's a symmetry the
+system's symmetrical yes there it'll be
+
+ align:start position:0%
+system's symmetrical yes there it'll be
+ 
+
+ align:start position:0%
+system's symmetrical yes there it'll be
+actually that symmetry point yes so and
+
+ align:start position:0%
+actually that symmetry point yes so and
+ 
+
+ align:start position:0%
+actually that symmetry point yes so and
+the other is the harmonic oscillator
+
+ align:start position:0%
+the other is the harmonic oscillator
+ 
+
+ align:start position:0%
+the other is the harmonic oscillator
+isn't moving and so there's no way that
+
+ align:start position:0%
+isn't moving and so there's no way that
+ 
+
+ align:start position:0%
+isn't moving and so there's no way that
+the coordinate that the average value of
+
+ align:start position:0%
+the coordinate that the average value of
+ 
+
+ align:start position:0%
+the coordinate that the average value of
+either the coordinate or the momentum
+
+ align:start position:0%
+either the coordinate or the momentum
+ 
+
+ align:start position:0%
+either the coordinate or the momentum
+could be different from zero however you
+
+ align:start position:0%
+could be different from zero however you
+ 
+
+ align:start position:0%
+could be different from zero however you
+do it you want to be doing it in seconds
+
+ align:start position:0%
+do it you want to be doing it in seconds
+ 
+
+ align:start position:0%
+do it you want to be doing it in seconds
+not minutes and certainly not my
+
+ align:start position:0%
+not minutes and certainly not my
+ 
+
+ align:start position:0%
+not minutes and certainly not my
+calculated integral and now x squared
+
+ align:start position:0%
+calculated integral and now x squared
+ 
+
+ align:start position:0%
+calculated integral and now x squared
+and P squared they're easy to especially
+
+ align:start position:0%
+and P squared they're easy to especially
+ 
+
+ align:start position:0%
+and P squared they're easy to especially
+if you know T and V
+
+ align:start position:0%
+if you know T and V
+ 
+
+ align:start position:0%
+ 
+and so we then use those to calculate
+
+ align:start position:0%
+and so we then use those to calculate
+ 
+
+ align:start position:0%
+and so we then use those to calculate
+the variance and that's defined as the
+
+ align:start position:0%
+the variance and that's defined as the
+ 
+
+ align:start position:0%
+the variance and that's defined as the
+average value of the square minus the
+
+ align:start position:0%
+average value of the square minus the
+ 
+
+ align:start position:0%
+average value of the square minus the
+square of the average square root and
+
+ align:start position:0%
+square of the average square root and
+ 
+
+ align:start position:0%
+square of the average square root and
+what we find is that the variance of x
+
+ align:start position:0%
+what we find is that the variance of x
+ 
+
+ align:start position:0%
+what we find is that the variance of x
+times the variance of P is equal to e
+
+ align:start position:0%
+times the variance of P is equal to e
+ 
+
+ align:start position:0%
+times the variance of P is equal to e
+over Omega so as you go up in energy
+
+ align:start position:0%
+over Omega so as you go up in energy
+ 
+
+ align:start position:0%
+over Omega so as you go up in energy
+this this joint uncertainty increases
+
+ align:start position:0%
+this this joint uncertainty increases
+ 
+
+ align:start position:0%
+this this joint uncertainty increases
+and we'll find that that also is true
+
+ align:start position:0%
+and we'll find that that also is true
+ 
+
+ align:start position:0%
+and we'll find that that also is true
+for water mechanics so this is this is
+
+ align:start position:0%
+for water mechanics so this is this is
+ 
+
+ align:start position:0%
+for water mechanics so this is this is
+sort of the the kind of questions you
+
+ align:start position:0%
+sort of the the kind of questions you
+ 
+
+ align:start position:0%
+sort of the the kind of questions you
+want to be asking in quantum mechanics
+
+ align:start position:0%
+want to be asking in quantum mechanics
+ 
+
+ align:start position:0%
+want to be asking in quantum mechanics
+and you want to be able to be guided by
+
+ align:start position:0%
+and you want to be able to be guided by
+ 
+
+ align:start position:0%
+and you want to be able to be guided by
+what you know from classical mechanics
+
+ align:start position:0%
+what you know from classical mechanics
+ 
+
+ align:start position:0%
+what you know from classical mechanics
+and you want to be able to do it fast
+
+ align:start position:0%
+and you want to be able to do it fast
+ 
+
+ align:start position:0%
+and you want to be able to do it fast
+okay so today's menu is what I would
+
+ align:start position:0%
+okay so today's menu is what I would
+ 
+
+ align:start position:0%
+okay so today's menu is what I would
+call this lecture is gratuitous
+
+ align:start position:0%
+call this lecture is gratuitous
+ 
+
+ align:start position:0%
+call this lecture is gratuitous
+gratuitous complexity does everybody
+
+ align:start position:0%
+gratuitous complexity does everybody
+ 
+
+ align:start position:0%
+gratuitous complexity does everybody
+know what gratuitous means okay it's
+
+ align:start position:0%
+know what gratuitous means okay it's
+ 
+
+ align:start position:0%
+know what gratuitous means okay it's
+also this is a this is one of my
+
+ align:start position:0%
+also this is a this is one of my
+ 
+
+ align:start position:0%
+also this is a this is one of my
+favorite Bob isms and you'll hear other
+
+ align:start position:0%
+favorite Bob isms and you'll hear other
+ 
+
+ align:start position:0%
+favorite Bob isms and you'll hear other
+Bob isms be during the course of this
+
+ align:start position:0%
+Bob isms be during the course of this
+ 
+
+ align:start position:0%
+Bob isms be during the course of this
+course what I want you to be able to do
+
+ align:start position:0%
+course what I want you to be able to do
+ 
+
+ align:start position:0%
+course what I want you to be able to do
+for a lot of quantum mechanical problems
+
+ align:start position:0%
+for a lot of quantum mechanical problems
+ 
+
+ align:start position:0%
+for a lot of quantum mechanical problems
+is to know the answer or know what
+
+ align:start position:0%
+is to know the answer or know what
+ 
+
+ align:start position:0%
+is to know the answer or know what
+things look like without doing a
+
+ align:start position:0%
+things look like without doing a
+ 
+
+ align:start position:0%
+things look like without doing a
+calculation in particular not solving a
+
+ align:start position:0%
+calculation in particular not solving a
+ 
+
+ align:start position:0%
+calculation in particular not solving a
+differential equation or evaluating any
+
+ align:start position:0%
+differential equation or evaluating any
+ 
+
+ align:start position:0%
+differential equation or evaluating any
+integrals you want to be able to draw
+
+ align:start position:0%
+integrals you want to be able to draw
+ 
+
+ align:start position:0%
+integrals you want to be able to draw
+these pictures instantly now in the
+
+ align:start position:0%
+these pictures instantly now in the
+ 
+
+ align:start position:0%
+these pictures instantly now in the
+modern age everyone has a pocket a cell
+
+ align:start position:0%
+modern age everyone has a pocket a cell
+ 
+
+ align:start position:0%
+modern age everyone has a pocket a cell
+phone and one could have a program in
+
+ align:start position:0%
+phone and one could have a program in
+ 
+
+ align:start position:0%
+phone and one could have a program in
+there to calculate what anything you
+
+ align:start position:0%
+there to calculate what anything you
+ 
+
+ align:start position:0%
+there to calculate what anything you
+wanted for a harmonic oscillator but
+
+ align:start position:0%
+wanted for a harmonic oscillator but
+ 
+
+ align:start position:0%
+wanted for a harmonic oscillator but
+chances are you won't be super
+
+ align:start position:0%
+chances are you won't be super
+ 
+
+ align:start position:0%
+chances are you won't be super
+you won't be prepared for that and if if
+
+ align:start position:0%
+you won't be prepared for that and if if
+ 
+
+ align:start position:0%
+you won't be prepared for that and if if
+you want to have insights into how do
+
+ align:start position:0%
+you want to have insights into how do
+ 
+
+ align:start position:0%
+you want to have insights into how do
+various things you want to know about
+
+ align:start position:0%
+various things you want to know about
+ 
+
+ align:start position:0%
+various things you want to know about
+harmonic harmonic oscillators come about
+
+ align:start position:0%
+harmonic harmonic oscillators come about
+ 
+
+ align:start position:0%
+harmonic harmonic oscillators come about
+you need the pictures as opposed to the
+
+ align:start position:0%
+you need the pictures as opposed to the
+ 
+
+ align:start position:0%
+you need the pictures as opposed to the
+computer program now the pictures
+
+ align:start position:0%
+computer program now the pictures
+ 
+
+ align:start position:0%
+computer program now the pictures
+involved involve an advance investment
+
+ align:start position:0%
+involved involve an advance investment
+ 
+
+ align:start position:0%
+involved involve an advance investment
+of energy you want to understand every
+
+ align:start position:0%
+of energy you want to understand every
+ 
+
+ align:start position:0%
+of energy you want to understand every
+detail of these little pictures ok so
+
+ align:start position:0%
+detail of these little pictures ok so
+ 
+
+ align:start position:0%
+detail of these little pictures ok so
+I'm going to write the Schrodinger
+
+ align:start position:0%
+I'm going to write the Schrodinger
+ 
+
+ align:start position:0%
+I'm going to write the Schrodinger
+equation I'm going to clean it up to get
+
+ align:start position:0%
+equation I'm going to clean it up to get
+ 
+
+ align:start position:0%
+equation I'm going to clean it up to get
+rid of units which makes it universal so
+
+ align:start position:0%
+rid of units which makes it universal so
+ 
+
+ align:start position:0%
+rid of units which makes it universal so
+it becomes a dimension I see
+
+ align:start position:0%
+it becomes a dimension I see
+ 
+
+ align:start position:0%
+it becomes a dimension I see
+dimensionless equation and the unit
+
+ align:start position:0%
+dimensionless equation and the unit
+ 
+
+ align:start position:0%
+dimensionless equation and the unit
+removal or the the the thing that takes
+
+ align:start position:0%
+removal or the the the thing that takes
+ 
+
+ align:start position:0%
+removal or the the the thing that takes
+takes you from a specific problem where
+
+ align:start position:0%
+takes you from a specific problem where
+ 
+
+ align:start position:0%
+takes you from a specific problem where
+there's a particular force constant and
+
+ align:start position:0%
+there's a particular force constant and
+ 
+
+ align:start position:0%
+there's a particular force constant and
+a particular reduced mass and makes it
+
+ align:start position:0%
+a particular reduced mass and makes it
+ 
+
+ align:start position:0%
+a particular reduced mass and makes it
+into a general problem there is one or
+
+ align:start position:0%
+into a general problem there is one or
+ 
+
+ align:start position:0%
+into a general problem there is one or
+two constants that combine those things
+
+ align:start position:0%
+two constants that combine those things
+ 
+
+ align:start position:0%
+two constants that combine those things
+and you've taken them out at the end of
+
+ align:start position:0%
+and you've taken them out at the end of
+ 
+
+ align:start position:0%
+and you've taken them out at the end of
+a calculation if you need to have real
+
+ align:start position:0%
+a calculation if you need to have real
+ 
+
+ align:start position:0%
+a calculation if you need to have real
+units you can put those back in and
+
+ align:start position:0%
+units you can put those back in and
+ 
+
+ align:start position:0%
+units you can put those back in and
+that's a very wonderful thing in that
+
+ align:start position:0%
+that's a very wonderful thing in that
+ 
+
+ align:start position:0%
+that's a very wonderful thing in that
+that enables us to to draw pictures
+
+ align:start position:0%
+that enables us to to draw pictures
+ 
+
+ align:start position:0%
+that enables us to to draw pictures
+without thinking about what is the
+
+ align:start position:0%
+without thinking about what is the
+ 
+
+ align:start position:0%
+without thinking about what is the
+problem ok and then the solution of this
+
+ align:start position:0%
+problem ok and then the solution of this
+ 
+
+ align:start position:0%
+problem ok and then the solution of this
+differential equation which is actually
+
+ align:start position:0%
+differential equation which is actually
+ 
+
+ align:start position:0%
+differential equation which is actually
+quite an awful differential equation at
+
+ align:start position:0%
+quite an awful differential equation at
+ 
+
+ align:start position:0%
+quite an awful differential equation at
+least for people who are not
+
+ align:start position:0%
+least for people who are not
+ 
+
+ align:start position:0%
+least for people who are not
+mathematicians and the solution can be
+
+ align:start position:0%
+mathematicians and the solution can be
+ 
+
+ align:start position:0%
+mathematicians and the solution can be
+expressed as the product of a Gaussian
+
+ align:start position:0%
+expressed as the product of a Gaussian
+ 
+
+ align:start position:0%
+expressed as the product of a Gaussian
+function which goes to 0 at plus and
+
+ align:start position:0%
+function which goes to 0 at plus and
+ 
+
+ align:start position:0%
+function which goes to 0 at plus and
+minus infinity so it makes the function
+
+ align:start position:0%
+minus infinity so it makes the function
+ 
+
+ align:start position:0%
+minus infinity so it makes the function
+well-behaved times something that
+
+ align:start position:0%
+well-behaved times something that
+ 
+
+ align:start position:0%
+well-behaved times something that
+produces nodes a polynomial does anyone
+
+ align:start position:0%
+produces nodes a polynomial does anyone
+ 
+
+ align:start position:0%
+produces nodes a polynomial does anyone
+who are give me a definition of a
+
+ align:start position:0%
+who are give me a definition of a
+ 
+
+ align:start position:0%
+who are give me a definition of a
+polynomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+silence okay your turn the linear
+
+ align:start position:0%
+silence okay your turn the linear
+ 
+
+ align:start position:0%
+silence okay your turn the linear
+combination of some numbers taken two
+
+ align:start position:0%
+combination of some numbers taken two
+ 
+
+ align:start position:0%
+combination of some numbers taken two
+different power write a sum of integer
+
+ align:start position:0%
+different power write a sum of integer
+ 
+
+ align:start position:0%
+different power write a sum of integer
+powers of a variable okay and so when we
+
+ align:start position:0%
+powers of a variable okay and so when we
+ 
+
+ align:start position:0%
+powers of a variable okay and so when we
+take a derivative of a polynomial we
+
+ align:start position:0%
+take a derivative of a polynomial we
+ 
+
+ align:start position:0%
+take a derivative of a polynomial we
+reduce the order of the polynomial a
+
+ align:start position:0%
+reduce the order of the polynomial a
+ 
+
+ align:start position:0%
+reduce the order of the polynomial a
+little bit of thought if you have a
+
+ align:start position:0%
+little bit of thought if you have a
+ 
+
+ align:start position:0%
+little bit of thought if you have a
+first-order polynomial there'll be one
+
+ align:start position:0%
+first-order polynomial there'll be one
+ 
+
+ align:start position:0%
+first-order polynomial there'll be one
+note if there's a second-order there'll
+
+ align:start position:0%
+note if there's a second-order there'll
+ 
+
+ align:start position:0%
+note if there's a second-order there'll
+be two notes and nodes are very
+
+ align:start position:0%
+be two notes and nodes are very
+ 
+
+ align:start position:0%
+be two notes and nodes are very
+important and so when we're we're going
+
+ align:start position:0%
+important and so when we're we're going
+ 
+
+ align:start position:0%
+important and so when we're we're going
+to be dealing with cartoons of the wave
+
+ align:start position:0%
+to be dealing with cartoons of the wave
+ 
+
+ align:start position:0%
+to be dealing with cartoons of the wave
+function and then using semi classical
+
+ align:start position:0%
+function and then using semi classical
+ 
+
+ align:start position:0%
+function and then using semi classical
+ideas to actually semi calculate things
+
+ align:start position:0%
+ideas to actually semi calculate things
+ 
+
+ align:start position:0%
+ideas to actually semi calculate things
+you'd want to know that the nodes are
+
+ align:start position:0%
+you'd want to know that the nodes are
+ 
+
+ align:start position:0%
+you'd want to know that the nodes are
+really important okay and what's going
+
+ align:start position:0%
+really important okay and what's going
+ 
+
+ align:start position:0%
+really important okay and what's going
+to happen on Monday is we'll throw away
+
+ align:start position:0%
+to happen on Monday is we'll throw away
+ 
+
+ align:start position:0%
+to happen on Monday is we'll throw away
+all this garbage and we will replace
+
+ align:start position:0%
+all this garbage and we will replace
+ 
+
+ align:start position:0%
+all this garbage and we will replace
+everything by these creation and
+
+ align:start position:0%
+everything by these creation and
+ 
+
+ align:start position:0%
+everything by these creation and
+annihilation operators which do have
+
+ align:start position:0%
+annihilation operators which do have
+ 
+
+ align:start position:0%
+annihilation operators which do have
+really simple problem properties which
+
+ align:start position:0%
+really simple problem properties which
+ 
+
+ align:start position:0%
+really simple problem properties which
+you can use to do astonishingly
+
+ align:start position:0%
+you can use to do astonishingly
+ 
+
+ align:start position:0%
+you can use to do astonishingly
+complicated things without breaking a
+
+ align:start position:0%
+complicated things without breaking a
+ 
+
+ align:start position:0%
+complicated things without breaking a
+sweat
+
+ align:start position:0%
+sweat
+ 
+
+ align:start position:0%
+sweat
+okay so and the final exam is in this
+
+ align:start position:0%
+okay so and the final exam is in this
+ 
+
+ align:start position:0%
+okay so and the final exam is in this
+room on the first day of exam period at
+
+ align:start position:0%
+room on the first day of exam period at
+ 
+
+ align:start position:0%
+room on the first day of exam period at
+least it's not on Monday and it's in the
+
+ align:start position:0%
+least it's not on Monday and it's in the
+ 
+
+ align:start position:0%
+least it's not on Monday and it's in the
+afternoon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in the non lecture part of the
+
+ align:start position:0%
+okay in the non lecture part of the
+ 
+
+ align:start position:0%
+okay in the non lecture part of the
+notes I replace the mass for one mass on
+
+ align:start position:0%
+notes I replace the mass for one mass on
+ 
+
+ align:start position:0%
+notes I replace the mass for one mass on
+a spring by the reduced mass which is m1
+
+ align:start position:0%
+a spring by the reduced mass which is m1
+ 
+
+ align:start position:0%
+a spring by the reduced mass which is m1
+m2 over m1 plus m2 for two masses
+
+ align:start position:0%
+m2 over m1 plus m2 for two masses
+ 
+
+ align:start position:0%
+m2 over m1 plus m2 for two masses
+connected by a spring and so I go back
+
+ align:start position:0%
+connected by a spring and so I go back
+ 
+
+ align:start position:0%
+connected by a spring and so I go back
+and forth B to Z between using mu n m
+
+ align:start position:0%
+and forth B to Z between using mu n m
+ 
+
+ align:start position:0%
+and forth B to Z between using mu n m
+and that's okay all right so in the
+
+ align:start position:0%
+and that's okay all right so in the
+ 
+
+ align:start position:0%
+and that's okay all right so in the
+notes the differential equations in the
+
+ align:start position:0%
+notes the differential equations in the
+ 
+
+ align:start position:0%
+notes the differential equations in the
+first few pages are expressed as partial
+
+ align:start position:0%
+first few pages are expressed as partial
+ 
+
+ align:start position:0%
+first few pages are expressed as partial
+differential equations there are total
+
+ align:start position:0%
+differential equations there are total
+ 
+
+ align:start position:0%
+differential equations there are total
+differential equations so that'll get
+
+ align:start position:0%
+differential equations so that'll get
+ 
+
+ align:start position:0%
+differential equations so that'll get
+changed but so the Hamiltonian is P plus
+
+ align:start position:0%
+changed but so the Hamiltonian is P plus
+ 
+
+ align:start position:0%
+changed but so the Hamiltonian is P plus
+e and in the usual form T is P squared
+
+ align:start position:0%
+e and in the usual form T is P squared
+ 
+
+ align:start position:0%
+e and in the usual form T is P squared
+over 2 mu and so we get minus h-bar over
+
+ align:start position:0%
+over 2 mu and so we get minus h-bar over
+ 
+
+ align:start position:0%
+over 2 mu and so we get minus h-bar over
+2 mu are not partial I'm so used to
+
+ align:start position:0%
+2 mu are not partial I'm so used to
+ 
+
+ align:start position:0%
+2 mu are not partial I'm so used to
+writing partials that I can't stop
+
+ align:start position:0%
+writing partials that I can't stop
+ 
+
+ align:start position:0%
+writing partials that I can't stop
+second derivative with respect X plus
+
+ align:start position:0%
+second derivative with respect X plus
+ 
+
+ align:start position:0%
+second derivative with respect X plus
+1/2 okay so that's the Hamiltonian now
+
+ align:start position:0%
+1/2 okay so that's the Hamiltonian now
+ 
+
+ align:start position:0%
+1/2 okay so that's the Hamiltonian now
+that looks kind of innocent but it isn't
+
+ align:start position:0%
+that looks kind of innocent but it isn't
+ 
+
+ align:start position:0%
+that looks kind of innocent but it isn't
+and so the first thing we want to do is
+
+ align:start position:0%
+and so the first thing we want to do is
+ 
+
+ align:start position:0%
+and so the first thing we want to do is
+get rid of the dimensionality the units
+
+ align:start position:0%
+get rid of the dimensionality the units
+ 
+
+ align:start position:0%
+get rid of the dimensionality the units
+so this is X I and it's defined as
+
+ align:start position:0%
+so this is X I and it's defined as
+ 
+
+ align:start position:0%
+so this is X I and it's defined as
+square root of alpha times X where alpha
+
+ align:start position:0%
+square root of alpha times X where alpha
+ 
+
+ align:start position:0%
+square root of alpha times X where alpha
+is defined as K mu square root over
+
+ align:start position:0%
+is defined as K mu square root over
+ 
+
+ align:start position:0%
+is defined as K mu square root over
+h-bar now it would be a perfectly
+
+ align:start position:0%
+h-bar now it would be a perfectly
+ 
+
+ align:start position:0%
+h-bar now it would be a perfectly
+reasonable exam question for you to
+
+ align:start position:0%
+reasonable exam question for you to
+ 
+
+ align:start position:0%
+reasonable exam question for you to
+prove that if I take this combination of
+
+ align:start position:0%
+prove that if I take this combination of
+ 
+
+ align:start position:0%
+prove that if I take this combination of
+physical quoi
+
+ align:start position:0%
+physical quoi
+ 
+
+ align:start position:0%
+physical quoi
+this will have dimension of one over
+
+ align:start position:0%
+this will have dimension of one over
+ 
+
+ align:start position:0%
+this will have dimension of one over
+length so that makes psy dimensionless
+
+ align:start position:0%
+length so that makes psy dimensionless
+ 
+
+ align:start position:0%
+length so that makes psy dimensionless
+quantity so I'm not even going to bother
+
+ align:start position:0%
+quantity so I'm not even going to bother
+ 
+
+ align:start position:0%
+quantity so I'm not even going to bother
+going through the derivation the
+
+ align:start position:0%
+going through the derivation the
+ 
+
+ align:start position:0%
+going through the derivation the
+Hamiltonian becomes H bar Omega times
+
+ align:start position:0%
+Hamiltonian becomes H bar Omega times
+ 
+
+ align:start position:0%
+Hamiltonian becomes H bar Omega times
+two minus second derivative with respect
+
+ align:start position:0%
+two minus second derivative with respect
+ 
+
+ align:start position:0%
+two minus second derivative with respect
+to sine plus y squared alright so this
+
+ align:start position:0%
+to sine plus y squared alright so this
+ 
+
+ align:start position:0%
+to sine plus y squared alright so this
+is now a and now this is dimensionless
+
+ align:start position:0%
+is now a and now this is dimensionless
+ 
+
+ align:start position:0%
+is now a and now this is dimensionless
+this has units we divide by H bar Omega
+
+ align:start position:0%
+this has units we divide by H bar Omega
+ 
+
+ align:start position:0%
+this has units we divide by H bar Omega
+to make now everything dimensionless and
+
+ align:start position:0%
+to make now everything dimensionless and
+ 
+
+ align:start position:0%
+to make now everything dimensionless and
+we get a differential equation that has
+
+ align:start position:0%
+we get a differential equation that has
+ 
+
+ align:start position:0%
+we get a differential equation that has
+the form second - the second derivative
+
+ align:start position:0%
+the form second - the second derivative
+ 
+
+ align:start position:0%
+the form second - the second derivative
+with respect
+
+ align:start position:0%
+with respect
+ 
+
+ align:start position:0%
+with respect
+psy plus size squared - 2 e over H bar
+
+ align:start position:0%
+psy plus size squared - 2 e over H bar
+ 
+
+ align:start position:0%
+psy plus size squared - 2 e over H bar
+Omega times the wave function expressed
+
+ align:start position:0%
+Omega times the wave function expressed
+ 
+
+ align:start position:0%
+Omega times the wave function expressed
+as function of because I X I naught X ok
+
+ align:start position:0%
+as function of because I X I naught X ok
+ 
+
+ align:start position:0%
+as function of because I X I naught X ok
+so this is the differential equation we
+
+ align:start position:0%
+so this is the differential equation we
+ 
+
+ align:start position:0%
+so this is the differential equation we
+want to solve and we don't do that in
+
+ align:start position:0%
+want to solve and we don't do that in
+ 
+
+ align:start position:0%
+want to solve and we don't do that in
+561 you're never going to be asked to
+
+ align:start position:0%
+561 you're never going to be asked to
+ 
+
+ align:start position:0%
+561 you're never going to be asked to
+solve a differential equation like this
+
+ align:start position:0%
+solve a differential equation like this
+ 
+
+ align:start position:0%
+solve a differential equation like this
+but you're certainly going to be asked
+
+ align:start position:0%
+but you're certainly going to be asked
+ 
+
+ align:start position:0%
+but you're certainly going to be asked
+to understand what the solution looks
+
+ align:start position:0%
+to understand what the solution looks
+ 
+
+ align:start position:0%
+to understand what the solution looks
+like and perhaps that it is in fact a
+
+ align:start position:0%
+like and perhaps that it is in fact a
+ 
+
+ align:start position:0%
+like and perhaps that it is in fact a
+solution but that's still pretty high
+
+ align:start position:0%
+solution but that's still pretty high
+ 
+
+ align:start position:0%
+solution but that's still pretty high
+value stuff so you wouldn't really have
+
+ align:start position:0%
+value stuff so you wouldn't really have
+ 
+
+ align:start position:0%
+value stuff so you wouldn't really have
+to do that so this is the simplest way
+
+ align:start position:0%
+to do that so this is the simplest way
+ 
+
+ align:start position:0%
+to do that so this is the simplest way
+of writing the differential equation and
+
+ align:start position:0%
+of writing the differential equation and
+ 
+
+ align:start position:0%
+of writing the differential equation and
+it's dimensionless ok the standard way
+
+ align:start position:0%
+it's dimensionless ok the standard way
+ 
+
+ align:start position:0%
+it's dimensionless ok the standard way
+of dealing with many differential
+
+ align:start position:0%
+of dealing with many differential
+ 
+
+ align:start position:0%
+of dealing with many differential
+equations is to say ok we have some
+
+ align:start position:0%
+equations is to say ok we have some
+ 
+
+ align:start position:0%
+equations is to say ok we have some
+function and it's going to be written as
+
+ align:start position:0%
+function and it's going to be written as
+ 
+
+ align:start position:0%
+function and it's going to be written as
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential a Gaussian times some new
+
+ align:start position:0%
+exponential a Gaussian times some new
+ 
+
+ align:start position:0%
+exponential a Gaussian times some new
+function and for quantum mechanics this
+
+ align:start position:0%
+function and for quantum mechanics this
+ 
+
+ align:start position:0%
+function and for quantum mechanics this
+is perfectly reasonable because we have
+
+ align:start position:0%
+is perfectly reasonable because we have
+ 
+
+ align:start position:0%
+is perfectly reasonable because we have
+a function in a well and the wave
+
+ align:start position:0%
+a function in a well and the wave
+ 
+
+ align:start position:0%
+a function in a well and the wave
+functions have to go to zero at plus and
+
+ align:start position:0%
+functions have to go to zero at plus and
+ 
+
+ align:start position:0%
+functions have to go to zero at plus and
+minus infinity and this thing goes to 0
+
+ align:start position:0%
+minus infinity and this thing goes to 0
+ 
+
+ align:start position:0%
+minus infinity and this thing goes to 0
+at plus and minus infinity pretty
+
+ align:start position:0%
+at plus and minus infinity pretty
+ 
+
+ align:start position:0%
+at plus and minus infinity pretty
+strongly so it's a good way of building
+
+ align:start position:0%
+strongly so it's a good way of building
+ 
+
+ align:start position:0%
+strongly so it's a good way of building
+in some of the expected behavior of the
+
+ align:start position:0%
+in some of the expected behavior of the
+ 
+
+ align:start position:0%
+in some of the expected behavior of the
+solution and that's perfectly legal and
+
+ align:start position:0%
+solution and that's perfectly legal and
+ 
+
+ align:start position:0%
+solution and that's perfectly legal and
+it just then defines what is the
+
+ align:start position:0%
+it just then defines what is the
+ 
+
+ align:start position:0%
+it just then defines what is the
+difference of the equation remaining for
+
+ align:start position:0%
+difference of the equation remaining for
+ 
+
+ align:start position:0%
+difference of the equation remaining for
+this and it turns out well we're going
+
+ align:start position:0%
+this and it turns out well we're going
+ 
+
+ align:start position:0%
+this and it turns out well we're going
+to get a the Hermit equation and this
+
+ align:start position:0%
+to get a the Hermit equation and this
+ 
+
+ align:start position:0%
+to get a the Hermit equation and this
+will be a hermit polynomial the
+
+ align:start position:0%
+will be a hermit polynomial the
+ 
+
+ align:start position:0%
+will be a hermit polynomial the
+solutions okay now one way of dealing
+
+ align:start position:0%
+solutions okay now one way of dealing
+ 
+
+ align:start position:0%
+solutions okay now one way of dealing
+with this is is to simply say well we
+
+ align:start position:0%
+with this is is to simply say well we
+ 
+
+ align:start position:0%
+with this is is to simply say well we
+know the solution of this differential
+
+ align:start position:0%
+know the solution of this differential
+ 
+
+ align:start position:0%
+know the solution of this differential
+equation if this term weren't there okay
+
+ align:start position:0%
+equation if this term weren't there okay
+ 
+
+ align:start position:0%
+equation if this term weren't there okay
+because this is now how the equation for
+
+ align:start position:0%
+because this is now how the equation for
+ 
+
+ align:start position:0%
+because this is now how the equation for
+a Gaussian so building in a Gaussian as
+
+ align:start position:0%
+a Gaussian so building in a Gaussian as
+ 
+
+ align:start position:0%
+a Gaussian so building in a Gaussian as
+a factor in the solution it's a
+
+ align:start position:0%
+a factor in the solution it's a
+ 
+
+ align:start position:0%
+a factor in the solution it's a
+perfectly reasonable thing and then we
+
+ align:start position:0%
+perfectly reasonable thing and then we
+ 
+
+ align:start position:0%
+perfectly reasonable thing and then we
+have to say okay what happens now when
+
+ align:start position:0%
+have to say okay what happens now when
+ 
+
+ align:start position:0%
+have to say okay what happens now when
+we put this term back in and when we do
+
+ align:start position:0%
+we put this term back in and when we do
+ 
+
+ align:start position:0%
+we put this term back in and when we do
+we get this thing second derivative with
+
+ align:start position:0%
+we get this thing second derivative with
+ 
+
+ align:start position:0%
+we get this thing second derivative with
+respect to this polynomial of this
+
+ align:start position:0%
+respect to this polynomial of this
+ 
+
+ align:start position:0%
+respect to this polynomial of this
+polynomial is equal to minus 2 sy times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X I plus 2 and H n so this is a famous
+
+ align:start position:0%
+X I plus 2 and H n so this is a famous
+ 
+
+ align:start position:0%
+X I plus 2 and H n so this is a famous
+differential equation the Hermit
+
+ align:start position:0%
+differential equation the Hermit
+ 
+
+ align:start position:0%
+differential equation the Hermit
+equation which is of no interest does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it generates the Hermit polynomials
+
+ align:start position:0%
+and it generates the Hermit polynomials
+ 
+
+ align:start position:0%
+and it generates the Hermit polynomials
+these things are the Hermit polynomials
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they're treated as in some kind of
+
+ align:start position:0%
+and they're treated as in some kind of
+ 
+
+ align:start position:0%
+and they're treated as in some kind of
+sacred manner in most of the textbooks
+
+ align:start position:0%
+sacred manner in most of the textbooks
+ 
+
+ align:start position:0%
+sacred manner in most of the textbooks
+and I think that's really an offense
+
+ align:start position:0%
+and I think that's really an offense
+ 
+
+ align:start position:0%
+and I think that's really an offense
+because well we're not interested in
+
+ align:start position:0%
+because well we're not interested in
+ 
+
+ align:start position:0%
+because well we're not interested in
+mathematical functions we're we're
+
+ align:start position:0%
+mathematical functions we're we're
+ 
+
+ align:start position:0%
+mathematical functions we're we're
+interested in insight and this is just
+
+ align:start position:0%
+interested in insight and this is just
+ 
+
+ align:start position:0%
+interested in insight and this is just
+putting up another barrier so now these
+
+ align:start position:0%
+putting up another barrier so now these
+ 
+
+ align:start position:0%
+putting up another barrier so now these
+with this equation you can derive two
+
+ align:start position:0%
+with this equation you can derive two
+ 
+
+ align:start position:0%
+with this equation you can derive two
+things called recursion relations and
+
+ align:start position:0%
+things called recursion relations and
+ 
+
+ align:start position:0%
+things called recursion relations and
+one of them is the derivative of this
+
+ align:start position:0%
+one of them is the derivative of this
+ 
+
+ align:start position:0%
+one of them is the derivative of this
+polynomial with respect to X I is equal
+
+ align:start position:0%
+polynomial with respect to X I is equal
+ 
+
+ align:start position:0%
+polynomial with respect to X I is equal
+to 2 n times H and minus one obscure
+
+ align:start position:0%
+to 2 n times H and minus one obscure
+ 
+
+ align:start position:0%
+to 2 n times H and minus one obscure
+side now that's not a surprise
+
+ align:start position:0%
+side now that's not a surprise
+ 
+
+ align:start position:0%
+side now that's not a surprise
+because this is a polynomial and if you
+
+ align:start position:0%
+because this is a polynomial and if you
+ 
+
+ align:start position:0%
+because this is a polynomial and if you
+take a derivative of the variable you're
+
+ align:start position:0%
+take a derivative of the variable you're
+ 
+
+ align:start position:0%
+take a derivative of the variable you're
+going to reduce the power of each term
+
+ align:start position:0%
+going to reduce the power of each term
+ 
+
+ align:start position:0%
+going to reduce the power of each term
+by one now it just happens to be lucky
+
+ align:start position:0%
+by one now it just happens to be lucky
+ 
+
+ align:start position:0%
+by one now it just happens to be lucky
+that we're going to reduce it to one you
+
+ align:start position:0%
+that we're going to reduce it to one you
+ 
+
+ align:start position:0%
+that we're going to reduce it to one you
+don't get a sum of many different lower
+
+ align:start position:0%
+don't get a sum of many different lower
+ 
+
+ align:start position:0%
+don't get a sum of many different lower
+order polynomials you just get one and
+
+ align:start position:0%
+order polynomials you just get one and
+ 
+
+ align:start position:0%
+order polynomials you just get one and
+there's another one another recursive
+
+ align:start position:0%
+there's another one another recursive
+ 
+
+ align:start position:0%
+there's another one another recursive
+relation where it tells you if you want
+
+ align:start position:0%
+relation where it tells you if you want
+ 
+
+ align:start position:0%
+relation where it tells you if you want
+to increase the order you can do this
+
+ align:start position:0%
+to increase the order you can do this
+ 
+
+ align:start position:0%
+to increase the order you can do this
+you can multiply H n bikes I and that's
+
+ align:start position:0%
+you can multiply H n bikes I and that's
+ 
+
+ align:start position:0%
+you can multiply H n bikes I and that's
+obviously it is going to increase the
+
+ align:start position:0%
+obviously it is going to increase the
+ 
+
+ align:start position:0%
+obviously it is going to increase the
+order but it might not do it cleanly and
+
+ align:start position:0%
+order but it might not do it cleanly and
+ 
+
+ align:start position:0%
+order but it might not do it cleanly and
+it doesn't and so we get so we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relationship between these three
+
+ align:start position:0%
+relationship between these three
+ 
+
+ align:start position:0%
+relationship between these three
+different polynomials ok now it turns
+
+ align:start position:0%
+different polynomials ok now it turns
+ 
+
+ align:start position:0%
+different polynomials ok now it turns
+out that these two equations are going
+
+ align:start position:0%
+out that these two equations are going
+ 
+
+ align:start position:0%
+out that these two equations are going
+to reappear or at least their progeny
+
+ align:start position:0%
+to reappear or at least their progeny
+ 
+
+ align:start position:0%
+to reappear or at least their progeny
+will reappear on Monday into
+
+ align:start position:0%
+will reappear on Monday into
+ 
+
+ align:start position:0%
+will reappear on Monday into
+terms of raising and lowering operators
+
+ align:start position:0%
+terms of raising and lowering operators
+ 
+
+ align:start position:0%
+terms of raising and lowering operators
+and what you into it about what happens
+
+ align:start position:0%
+and what you into it about what happens
+ 
+
+ align:start position:0%
+and what you into it about what happens
+if you multiply a polynomial by the
+
+ align:start position:0%
+if you multiply a polynomial by the
+ 
+
+ align:start position:0%
+if you multiply a polynomial by the
+variable or what happens if you take its
+
+ align:start position:0%
+variable or what happens if you take its
+ 
+
+ align:start position:0%
+variable or what happens if you take its
+derivative and it is very simple and
+
+ align:start position:0%
+derivative and it is very simple and
+ 
+
+ align:start position:0%
+derivative and it is very simple and
+beautiful but I don't think this is very
+
+ align:start position:0%
+beautiful but I don't think this is very
+ 
+
+ align:start position:0%
+beautiful but I don't think this is very
+beautiful for our purposes at chemists
+
+ align:start position:0%
+beautiful for our purposes at chemists
+ 
+
+ align:start position:0%
+beautiful for our purposes at chemists
+and one of the things that these
+
+ align:start position:0%
+and one of the things that these
+ 
+
+ align:start position:0%
+and one of the things that these
+recursion relationships do which also
+
+ align:start position:0%
+recursion relationships do which also
+ 
+
+ align:start position:0%
+recursion relationships do which also
+hints at what's to come on Monday is it
+
+ align:start position:0%
+hints at what's to come on Monday is it
+ 
+
+ align:start position:0%
+hints at what's to come on Monday is it
+we can calculate integrals like this no
+
+ align:start position:0%
+we can calculate integrals like this no
+ 
+
+ align:start position:0%
+we can calculate integrals like this no
+that's not what I want this is a quantum
+
+ align:start position:0%
+that's not what I want this is a quantum
+ 
+
+ align:start position:0%
+that's not what I want this is a quantum
+number it's an integer it's V not new
+
+ align:start position:0%
+number it's an integer it's V not new
+ 
+
+ align:start position:0%
+number it's an integer it's V not new
+and multiplied by X to the N P to the M
+
+ align:start position:0%
+and multiplied by X to the N P to the M
+ 
+
+ align:start position:0%
+and multiplied by X to the N P to the M
+sy conjugated V Plus L Y X it turns out
+
+ align:start position:0%
+sy conjugated V Plus L Y X it turns out
+ 
+
+ align:start position:0%
+sy conjugated V Plus L Y X it turns out
+for almost everything we want to do with
+
+ align:start position:0%
+for almost everything we want to do with
+ 
+
+ align:start position:0%
+for almost everything we want to do with
+harmonic oscillators we're going to want
+
+ align:start position:0%
+harmonic oscillators we're going to want
+ 
+
+ align:start position:0%
+harmonic oscillators we're going to want
+to know a lot of integrals like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the things we like is when an
+
+ align:start position:0%
+one of the things we like is when an
+ 
+
+ align:start position:0%
+one of the things we like is when an
+integral is promised to be zero so we
+
+ align:start position:0%
+integral is promised to be zero so we
+ 
+
+ align:start position:0%
+integral is promised to be zero so we
+don't ever have to look at it and so
+
+ align:start position:0%
+don't ever have to look at it and so
+ 
+
+ align:start position:0%
+don't ever have to look at it and so
+their selection rules and the selection
+
+ align:start position:0%
+their selection rules and the selection
+ 
+
+ align:start position:0%
+their selection rules and the selection
+rules for the this kind of integral is L
+
+ align:start position:0%
+rules for the this kind of integral is L
+ 
+
+ align:start position:0%
+rules for the this kind of integral is L
+is equal to M plus n m plus n minus 2
+
+ align:start position:0%
+is equal to M plus n m plus n minus 2
+ 
+
+ align:start position:0%
+is equal to M plus n m plus n minus 2
+down to minus M plus n so the only
+
+ align:start position:0%
+down to minus M plus n so the only
+ 
+
+ align:start position:0%
+down to minus M plus n so the only
+possible nonzero integrals of this form
+
+ align:start position:0%
+possible nonzero integrals of this form
+ 
+
+ align:start position:0%
+possible nonzero integrals of this form
+are for the change in quantum number by
+
+ align:start position:0%
+are for the change in quantum number by
+ 
+
+ align:start position:0%
+are for the change in quantum number by
+this L which goes from M plus n down to
+
+ align:start position:0%
+this L which goes from M plus n down to
+ 
+
+ align:start position:0%
+this L which goes from M plus n down to
+minus M plus n in steps of 2 the two
+
+ align:start position:0%
+minus M plus n in steps of 2 the two
+ 
+
+ align:start position:0%
+minus M plus n in steps of 2 the two
+shouldn't be too surprising because
+
+ align:start position:0%
+shouldn't be too surprising because
+ 
+
+ align:start position:0%
+shouldn't be too surprising because
+their symmetry and we have odd functions
+
+ align:start position:0%
+their symmetry and we have odd functions
+ 
+
+ align:start position:0%
+their symmetry and we have odd functions
+for odd quantum numbers and even
+
+ align:start position:0%
+for odd quantum numbers and even
+ 
+
+ align:start position:0%
+for odd quantum numbers and even
+functions for even quantum numbers and
+
+ align:start position:0%
+functions for even quantum numbers and
+ 
+
+ align:start position:0%
+functions for even quantum numbers and
+so something like this is going to have
+
+ align:start position:0%
+so something like this is going to have
+ 
+
+ align:start position:0%
+so something like this is going to have
+a definite symmetry and it's going to
+
+ align:start position:0%
+a definite symmetry and it's going to
+ 
+
+ align:start position:0%
+a definite symmetry and it's going to
+change things within that within a
+
+ align:start position:0%
+change things within that within a
+ 
+
+ align:start position:0%
+change things within that within a
+symmetry and so it's going to change the
+
+ align:start position:0%
+symmetry and so it's going to change the
+ 
+
+ align:start position:0%
+symmetry and so it's going to change the
+selection rule in steps of 2 now you
+
+ align:start position:0%
+selection rule in steps of 2 now you
+ 
+
+ align:start position:0%
+selection rule in steps of 2 now you
+don't know what selection rules are for
+
+ align:start position:0%
+don't know what selection rules are for
+ 
+
+ align:start position:0%
+don't know what selection rules are for
+why you should get excited about these
+
+ align:start position:0%
+why you should get excited about these
+ 
+
+ align:start position:0%
+why you should get excited about these
+thirds of things but it's really nice to
+
+ align:start position:0%
+thirds of things but it's really nice to
+ 
+
+ align:start position:0%
+thirds of things but it's really nice to
+know that almost all the integrals you
+
+ align:start position:0%
+know that almost all the integrals you
+ 
+
+ align:start position:0%
+know that almost all the integrals you
+ever going to face for a particular
+
+ align:start position:0%
+ever going to face for a particular
+ 
+
+ align:start position:0%
+ever going to face for a particular
+problem are 0 and you can focus on a
+
+ align:start position:0%
+problem are 0 and you can focus on a
+ 
+
+ align:start position:0%
+problem are 0 and you can focus on a
+small number of nonzero ones and it just
+
+ align:start position:0%
+small number of nonzero ones and it just
+ 
+
+ align:start position:0%
+small number of nonzero ones and it just
+turns out that the nonzero ones have
+
+ align:start position:0%
+turns out that the nonzero ones have
+ 
+
+ align:start position:0%
+turns out that the nonzero ones have
+really simple values there also exists
+
+ align:start position:0%
+really simple values there also exists
+ 
+
+ align:start position:0%
+really simple values there also exists
+what's called a generating function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the Rodrigues formula and that
+
+ align:start position:0%
+which is the Rodrigues formula and that
+ 
+
+ align:start position:0%
+which is the Rodrigues formula and that
+is the H M of sy is equal to minus 1 to
+
+ align:start position:0%
+is the H M of sy is equal to minus 1 to
+ 
+
+ align:start position:0%
+is the H M of sy is equal to minus 1 to
+the n e to the I squared second
+
+ align:start position:0%
+the n e to the I squared second
+ 
+
+ align:start position:0%
+the n e to the I squared second
+derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eat the - sighs okay so we have one that
+
+ align:start position:0%
+eat the - sighs okay so we have one that
+ 
+
+ align:start position:0%
+eat the - sighs okay so we have one that
+has a positive exponent one has a
+
+ align:start position:0%
+has a positive exponent one has a
+ 
+
+ align:start position:0%
+has a positive exponent one has a
+negative exponent we have this so we
+
+ align:start position:0%
+negative exponent we have this so we
+ 
+
+ align:start position:0%
+negative exponent we have this so we
+could calculate any hermit polynomial
+
+ align:start position:0%
+could calculate any hermit polynomial
+ 
+
+ align:start position:0%
+could calculate any hermit polynomial
+using this formula which you will never
+
+ align:start position:0%
+using this formula which you will never
+ 
+
+ align:start position:0%
+using this formula which you will never
+do but it's treated with great fanfare
+
+ align:start position:0%
+do but it's treated with great fanfare
+ 
+
+ align:start position:0%
+do but it's treated with great fanfare
+in textbooks
+
+ align:start position:0%
+in textbooks
+ 
+
+ align:start position:0%
+in textbooks
+okay now the solution to the harmonic
+
+ align:start position:0%
+okay now the solution to the harmonic
+ 
+
+ align:start position:0%
+okay now the solution to the harmonic
+oscillator wave function in real units
+
+ align:start position:0%
+oscillator wave function in real units
+ 
+
+ align:start position:0%
+oscillator wave function in real units
+as opposed to dimensionless quantities
+
+ align:start position:0%
+as opposed to dimensionless quantities
+ 
+
+ align:start position:0%
+as opposed to dimensionless quantities
+is and I'm just writing this down
+
+ align:start position:0%
+is and I'm just writing this down
+ 
+
+ align:start position:0%
+is and I'm just writing this down
+because I never would ever think about
+
+ align:start position:0%
+because I never would ever think about
+ 
+
+ align:start position:0%
+because I never would ever think about
+it this way but I have to at least you
+
+ align:start position:0%
+it this way but I have to at least you
+ 
+
+ align:start position:0%
+it this way but I have to at least you
+know provide you with guidance so we
+
+ align:start position:0%
+know provide you with guidance so we
+ 
+
+ align:start position:0%
+know provide you with guidance so we
+have a factor two to the V again this is
+
+ align:start position:0%
+have a factor two to the V again this is
+ 
+
+ align:start position:0%
+have a factor two to the V again this is
+V now the reason I'm emphasize
+
+ align:start position:0%
+V now the reason I'm emphasize
+ 
+
+ align:start position:0%
+V now the reason I'm emphasize
+emphasizing this is it in all texts the
+
+ align:start position:0%
+emphasizing this is it in all texts the
+ 
+
+ align:start position:0%
+emphasizing this is it in all texts the
+quantum numbers are italicized and if
+
+ align:start position:0%
+quantum numbers are italicized and if
+ 
+
+ align:start position:0%
+quantum numbers are italicized and if
+you've thought it for of about it for a
+
+ align:start position:0%
+you've thought it for of about it for a
+ 
+
+ align:start position:0%
+you've thought it for of about it for a
+minute and I tell like V for mortals
+
+ align:start position:0%
+minute and I tell like V for mortals
+ 
+
+ align:start position:0%
+minute and I tell like V for mortals
+looks like a new it isn't quite I don't
+
+ align:start position:0%
+looks like a new it isn't quite I don't
+ 
+
+ align:start position:0%
+looks like a new it isn't quite I don't
+know what the difference is but if you
+
+ align:start position:0%
+know what the difference is but if you
+ 
+
+ align:start position:0%
+know what the difference is but if you
+have them side by side they are
+
+ align:start position:0%
+have them side by side they are
+ 
+
+ align:start position:0%
+have them side by side they are
+different and so a large number of
+
+ align:start position:0%
+different and so a large number of
+ 
+
+ align:start position:0%
+different and so a large number of
+people who should know better
+
+ align:start position:0%
+people who should know better
+ 
+
+ align:start position:0%
+people who should know better
+refer to the vibrational quantum number
+
+ align:start position:0%
+refer to the vibrational quantum number
+ 
+
+ align:start position:0%
+refer to the vibrational quantum number
+as nu which marks that person as well I
+
+ align:start position:0%
+as nu which marks that person as well I
+ 
+
+ align:start position:0%
+as nu which marks that person as well I
+won't say but it's not complimentary
+
+ align:start position:0%
+won't say but it's not complimentary
+ 
+
+ align:start position:0%
+won't say but it's not complimentary
+okay so we have this factor coming and
+
+ align:start position:0%
+okay so we have this factor coming and
+ 
+
+ align:start position:0%
+okay so we have this factor coming and
+it's in square root and that's a
+
+ align:start position:0%
+it's in square root and that's a
+ 
+
+ align:start position:0%
+it's in square root and that's a
+normalization factor we got another part
+
+ align:start position:0%
+normalization factor we got another part
+ 
+
+ align:start position:0%
+normalization factor we got another part
+of it alpha over pi to the 1/4 power
+
+ align:start position:0%
+of it alpha over pi to the 1/4 power
+ 
+
+ align:start position:0%
+of it alpha over pi to the 1/4 power
+so that's normalization then we have the
+
+ align:start position:0%
+so that's normalization then we have the
+ 
+
+ align:start position:0%
+so that's normalization then we have the
+hermite polynomial and you notice I've
+
+ align:start position:0%
+hermite polynomial and you notice I've
+ 
+
+ align:start position:0%
+hermite polynomial and you notice I've
+got sy back in here which is really a
+
+ align:start position:0%
+got sy back in here which is really a
+ 
+
+ align:start position:0%
+got sy back in here which is really a
+shame and we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the general solution we have
+
+ align:start position:0%
+so this is the general solution we have
+ 
+
+ align:start position:0%
+so this is the general solution we have
+the exponentially damped function we
+
+ align:start position:0%
+the exponentially damped function we
+ 
+
+ align:start position:0%
+the exponentially damped function we
+have the polynomials these are all the
+
+ align:start position:0%
+have the polynomials these are all the
+ 
+
+ align:start position:0%
+have the polynomials these are all the
+actors that we're going to have to deal
+
+ align:start position:0%
+actors that we're going to have to deal
+ 
+
+ align:start position:0%
+actors that we're going to have to deal
+with and I promise you you will never
+
+ align:start position:0%
+with and I promise you you will never
+ 
+
+ align:start position:0%
+with and I promise you you will never
+use this unless you want to program a
+
+ align:start position:0%
+use this unless you want to program a
+ 
+
+ align:start position:0%
+use this unless you want to program a
+computer to calculate the wave functions
+
+ align:start position:0%
+computer to calculate the wave functions
+ 
+
+ align:start position:0%
+computer to calculate the wave functions
+for god knows what reason
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the quantum numbers V are 0 1 2 and
+
+ align:start position:0%
+okay the quantum numbers V are 0 1 2 and
+ 
+
+ align:start position:0%
+okay the quantum numbers V are 0 1 2 and
+for a harmonic oscillator which goes to
+
+ align:start position:0%
+for a harmonic oscillator which goes to
+ 
+
+ align:start position:0%
+for a harmonic oscillator which goes to
+infinity V goes to infinity 2 there's an
+
+ align:start position:0%
+infinity V goes to infinity 2 there's an
+ 
+
+ align:start position:0%
+infinity V goes to infinity 2 there's an
+infinite number of eigenfunctions of the
+
+ align:start position:0%
+infinite number of eigenfunctions of the
+ 
+
+ align:start position:0%
+infinite number of eigenfunctions of the
+quantum mechanical Hamiltonian of
+
+ align:start position:0%
+quantum mechanical Hamiltonian of
+ 
+
+ align:start position:0%
+quantum mechanical Hamiltonian of
+quantum mechanical harmonic oscillator
+
+ align:start position:0%
+quantum mechanical harmonic oscillator
+ 
+
+ align:start position:0%
+quantum mechanical harmonic oscillator
+so we have and the functions are
+
+ align:start position:0%
+so we have and the functions are
+ 
+
+ align:start position:0%
+so we have and the functions are
+normalized we have side plus and minus
+
+ align:start position:0%
+normalized we have side plus and minus
+ 
+
+ align:start position:0%
+normalized we have side plus and minus
+infinity goes to 0 we have sy V of 0 so
+
+ align:start position:0%
+infinity goes to 0 we have sy V of 0 so
+ 
+
+ align:start position:0%
+infinity goes to 0 we have sy V of 0 so
+this for all VI / wouldn't be there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sy V is 0 for the derivative of side
+
+ align:start position:0%
+sy V is 0 for the derivative of side
+ 
+
+ align:start position:0%
+sy V is 0 for the derivative of side
+with respect to X at x equals 0 is 0 /
+
+ align:start position:0%
+with respect to X at x equals 0 is 0 /
+ 
+
+ align:start position:0%
+with respect to X at x equals 0 is 0 /
+even me so we have symmetric functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have the energy levels is equal
+
+ align:start position:0%
+and we have the energy levels is equal
+ 
+
+ align:start position:0%
+and we have the energy levels is equal
+to H bar Omega B plus 1/2 now this is H
+
+ align:start position:0%
+to H bar Omega B plus 1/2 now this is H
+ 
+
+ align:start position:0%
+to H bar Omega B plus 1/2 now this is H
+over 2 pi and this is nu times 2 pi the
+
+ align:start position:0%
+over 2 pi and this is nu times 2 pi the
+ 
+
+ align:start position:0%
+over 2 pi and this is nu times 2 pi the
+frequency times 2 pi so it could also be
+
+ align:start position:0%
+frequency times 2 pi so it could also be
+ 
+
+ align:start position:0%
+frequency times 2 pi so it could also be
+H nu I have trouble remembering when
+
+ align:start position:0%
+H nu I have trouble remembering when
+ 
+
+ align:start position:0%
+H nu I have trouble remembering when
+there's a 2pi involved okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have this wonderful thing it says
+
+ align:start position:0%
+and we have this wonderful thing it says
+ 
+
+ align:start position:0%
+and we have this wonderful thing it says
+if V prime is equal to V this integral
+
+ align:start position:0%
+if V prime is equal to V this integral
+ 
+
+ align:start position:0%
+if V prime is equal to V this integral
+is 1 it's normalized and a V prime is
+
+ align:start position:0%
+is 1 it's normalized and a V prime is
+ 
+
+ align:start position:0%
+is 1 it's normalized and a V prime is
+not equal to V it's 0 and that stems
+
+ align:start position:0%
+not equal to V it's 0 and that stems
+ 
+
+ align:start position:0%
+not equal to V it's 0 and that stems
+from a theorem I mentioned before is if
+
+ align:start position:0%
+from a theorem I mentioned before is if
+ 
+
+ align:start position:0%
+from a theorem I mentioned before is if
+you have two different two eigenvalues
+
+ align:start position:0%
+you have two different two eigenvalues
+ 
+
+ align:start position:0%
+you have two different two eigenvalues
+of the same hamiltonian eigenfunctions
+
+ align:start position:0%
+of the same hamiltonian eigenfunctions
+ 
+
+ align:start position:0%
+of the same hamiltonian eigenfunctions
+of the same hamiltonian and they belong
+
+ align:start position:0%
+of the same hamiltonian and they belong
+ 
+
+ align:start position:0%
+of the same hamiltonian and they belong
+to different values eigen values their
+
+ align:start position:0%
+to different values eigen values their
+ 
+
+ align:start position:0%
+to different values eigen values their
+overlap integral is 0 we like zeroes we
+
+ align:start position:0%
+overlap integral is 0 we like zeroes we
+ 
+
+ align:start position:0%
+overlap integral is 0 we like zeroes we
+like normalization because the integral
+
+ align:start position:0%
+like normalization because the integral
+ 
+
+ align:start position:0%
+like normalization because the integral
+is just 1 it goes away or the integral
+
+ align:start position:0%
+is just 1 it goes away or the integral
+ 
+
+ align:start position:0%
+is just 1 it goes away or the integral
+is 0 the whole thing goes away so that's
+
+ align:start position:0%
+is 0 the whole thing goes away so that's
+ 
+
+ align:start position:0%
+is 0 the whole thing goes away so that's
+really good ok so we call this that the
+
+ align:start position:0%
+really good ok so we call this that the
+ 
+
+ align:start position:0%
+really good ok so we call this that the
+set of these is orthonormal orthogonal
+
+ align:start position:0%
+set of these is orthonormal orthogonal
+ 
+
+ align:start position:0%
+set of these is orthonormal orthogonal
+and normalized and the orthonormal
+
+ align:start position:0%
+and normalized and the orthonormal
+ 
+
+ align:start position:0%
+and normalized and the orthonormal
+terminology is used a lot and in almost
+
+ align:start position:0%
+terminology is used a lot and in almost
+ 
+
+ align:start position:0%
+terminology is used a lot and in almost
+all quantum mechanical problems we like
+
+ align:start position:0%
+all quantum mechanical problems we like
+ 
+
+ align:start position:0%
+all quantum mechanical problems we like
+using an orthonormal set of functions to
+
+ align:start position:0%
+using an orthonormal set of functions to
+ 
+
+ align:start position:0%
+using an orthonormal set of functions to
+solve everything sometimes we have to do
+
+ align:start position:0%
+solve everything sometimes we have to do
+ 
+
+ align:start position:0%
+solve everything sometimes we have to do
+a little work to establish that and I'll
+
+ align:start position:0%
+a little work to establish that and I'll
+ 
+
+ align:start position:0%
+a little work to establish that and I'll
+show much later in the course how when
+
+ align:start position:0%
+show much later in the course how when
+ 
+
+ align:start position:0%
+show much later in the course how when
+you have functions that are not
+
+ align:start position:0%
+you have functions that are not
+ 
+
+ align:start position:0%
+you have functions that are not
+orthogonal you can and not normalize you
+
+ align:start position:0%
+orthogonal you can and not normalize you
+ 
+
+ align:start position:0%
+orthogonal you can and not normalize you
+can create a set of functions which are
+
+ align:start position:0%
+can create a set of functions which are
+ 
+
+ align:start position:0%
+can create a set of functions which are
+and this is something that a computer
+
+ align:start position:0%
+and this is something that a computer
+ 
+
+ align:start position:0%
+and this is something that a computer
+will do without breaking a sweat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now we're back to my favorite topic
+
+ align:start position:0%
+okay now we're back to my favorite topic
+ 
+
+ align:start position:0%
+okay now we're back to my favorite topic
+semi-classical because it's really easy
+
+ align:start position:0%
+semi-classical because it's really easy
+ 
+
+ align:start position:0%
+semi-classical because it's really easy
+to understand not just to understand the
+
+ align:start position:0%
+to understand not just to understand the
+ 
+
+ align:start position:0%
+to understand not just to understand the
+harmonic oscillator but to use it in
+
+ align:start position:0%
+harmonic oscillator but to use it in
+ 
+
+ align:start position:0%
+harmonic oscillator but to use it in
+many problems so in classic mechanics
+
+ align:start position:0%
+many problems so in classic mechanics
+ 
+
+ align:start position:0%
+many problems so in classic mechanics
+the kinetic energy is e minus V of X or
+
+ align:start position:0%
+the kinetic energy is e minus V of X or
+ 
+
+ align:start position:0%
+the kinetic energy is e minus V of X or
+P squared over 2 mu and so we can derive
+
+ align:start position:0%
+P squared over 2 mu and so we can derive
+ 
+
+ align:start position:0%
+P squared over 2 mu and so we can derive
+an equation for P of X classical
+
+ align:start position:0%
+an equation for P of X classical
+ 
+
+ align:start position:0%
+an equation for P of X classical
+mechanically which is 2 at 2 mu e minus
+
+ align:start position:0%
+mechanically which is 2 at 2 mu e minus
+ 
+
+ align:start position:0%
+mechanically which is 2 at 2 mu e minus
+3 of X its crook'd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is an extremely useful function
+
+ align:start position:0%
+so this is an extremely useful function
+ 
+
+ align:start position:0%
+so this is an extremely useful function
+it's not an operator it's a thing that
+
+ align:start position:0%
+it's not an operator it's a thing that
+ 
+
+ align:start position:0%
+it's not an operator it's a thing that
+we're going to use to make sense of
+
+ align:start position:0%
+we're going to use to make sense of
+ 
+
+ align:start position:0%
+we're going to use to make sense of
+everything but it's not an operator and
+
+ align:start position:0%
+everything but it's not an operator and
+ 
+
+ align:start position:0%
+everything but it's not an operator and
+so this is classic mechanics and then in
+
+ align:start position:0%
+so this is classic mechanics and then in
+ 
+
+ align:start position:0%
+so this is classic mechanics and then in
+quantum mechanics we know that mr. de
+
+ align:start position:0%
+quantum mechanics we know that mr. de
+ 
+
+ align:start position:0%
+quantum mechanics we know that mr. de
+Blois told us that the wave length is
+
+ align:start position:0%
+Blois told us that the wave length is
+ 
+
+ align:start position:0%
+Blois told us that the wave length is
+equal to H over P and we can generalize
+
+ align:start position:0%
+equal to H over P and we can generalize
+ 
+
+ align:start position:0%
+equal to H over P and we can generalize
+to say well maybe the wave length is a
+
+ align:start position:0%
+to say well maybe the wave length is a
+ 
+
+ align:start position:0%
+to say well maybe the wave length is a
+function of X for potential which is not
+
+ align:start position:0%
+function of X for potential which is not
+ 
+
+ align:start position:0%
+function of X for potential which is not
+constant and even though this is not an
+
+ align:start position:0%
+constant and even though this is not an
+ 
+
+ align:start position:0%
+constant and even though this is not an
+operator in quantum mechanics this is
+
+ align:start position:0%
+operator in quantum mechanics this is
+ 
+
+ align:start position:0%
+operator in quantum mechanics this is
+true that you can say the distance
+
+ align:start position:0%
+true that you can say the distance
+ 
+
+ align:start position:0%
+true that you can say the distance
+between consecutive nodes is lambda over
+
+ align:start position:0%
+between consecutive nodes is lambda over
+ 
+
+ align:start position:0%
+between consecutive nodes is lambda over
+2 and so we can use this node
+
+ align:start position:0%
+2 and so we can use this node
+ 
+
+ align:start position:0%
+2 and so we can use this node
+relationship to great advantage okay so
+
+ align:start position:0%
+relationship to great advantage okay so
+ 
+
+ align:start position:0%
+relationship to great advantage okay so
+for the pair of nodes closest to X we
+
+ align:start position:0%
+for the pair of nodes closest to X we
+ 
+
+ align:start position:0%
+for the pair of nodes closest to X we
+can use this to calculate the distance
+
+ align:start position:0%
+can use this to calculate the distance
+ 
+
+ align:start position:0%
+can use this to calculate the distance
+between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very valuable because I also want to
+
+ align:start position:0%
+very valuable because I also want to
+ 
+
+ align:start position:0%
+very valuable because I also want to
+mention something if you have an
+
+ align:start position:0%
+mention something if you have an
+ 
+
+ align:start position:0%
+mention something if you have an
+integrand which is rapidly oscillating
+
+ align:start position:0%
+integrand which is rapidly oscillating
+ 
+
+ align:start position:0%
+integrand which is rapidly oscillating
+or if you have to rapidly oscillating
+
+ align:start position:0%
+or if you have to rapidly oscillating
+ 
+
+ align:start position:0%
+or if you have to rapidly oscillating
+functions and you're multiplying them
+
+ align:start position:0%
+functions and you're multiplying them
+ 
+
+ align:start position:0%
+functions and you're multiplying them
+together that integral will accumulate
+
+ align:start position:0%
+together that integral will accumulate
+ 
+
+ align:start position:0%
+together that integral will accumulate
+to its final value where at the position
+
+ align:start position:0%
+to its final value where at the position
+ 
+
+ align:start position:0%
+to its final value where at the position
+where the two oscillating functions are
+
+ align:start position:0%
+where the two oscillating functions are
+ 
+
+ align:start position:0%
+where the two oscillating functions are
+oscillating at the same frequency
+
+ align:start position:0%
+oscillating at the same frequency
+ 
+
+ align:start position:0%
+oscillating at the same frequency
+that's the stationary phase point and
+
+ align:start position:0%
+that's the stationary phase point and
+ 
+
+ align:start position:0%
+that's the stationary phase point and
+this is also a wonderful thing because
+
+ align:start position:0%
+this is also a wonderful thing because
+ 
+
+ align:start position:0%
+this is also a wonderful thing because
+if you can figure out where the things
+
+ align:start position:0%
+if you can figure out where the things
+ 
+
+ align:start position:0%
+if you can figure out where the things
+you're multiplying together are
+
+ align:start position:0%
+you're multiplying together are
+ 
+
+ align:start position:0%
+you're multiplying together are
+oscillating at the same frequency your
+
+ align:start position:0%
+oscillating at the same frequency your
+ 
+
+ align:start position:0%
+oscillating at the same frequency your
+integral becomes a number no work ever
+
+ align:start position:0%
+integral becomes a number no work ever
+ 
+
+ align:start position:0%
+integral becomes a number no work ever
+and that's a useful thing okay so the
+
+ align:start position:0%
+and that's a useful thing okay so the
+ 
+
+ align:start position:0%
+and that's a useful thing okay so the
+stationary phase method enables you to
+
+ align:start position:0%
+stationary phase method enables you to
+ 
+
+ align:start position:0%
+stationary phase method enables you to
+use this in a really fantastic way and
+
+ align:start position:0%
+use this in a really fantastic way and
+ 
+
+ align:start position:0%
+use this in a really fantastic way and
+it's a little bit like fineman's path
+
+ align:start position:0%
+it's a little bit like fineman's path
+ 
+
+ align:start position:0%
+it's a little bit like fineman's path
+integral idea that you can calculate a
+
+ align:start position:0%
+integral idea that you can calculate a
+ 
+
+ align:start position:0%
+integral idea that you can calculate a
+complicated thing by evaluating a an
+
+ align:start position:0%
+complicated thing by evaluating a an
+ 
+
+ align:start position:0%
+complicated thing by evaluating a an
+integral over a convenient path as
+
+ align:start position:0%
+integral over a convenient path as
+ 
+
+ align:start position:0%
+integral over a convenient path as
+opposed to integrating over all space
+
+ align:start position:0%
+opposed to integrating over all space
+ 
+
+ align:start position:0%
+opposed to integrating over all space
+because everything that you care about
+
+ align:start position:0%
+because everything that you care about
+ 
+
+ align:start position:0%
+because everything that you care about
+comes from stationary phase quantum
+
+ align:start position:0%
+comes from stationary phase quantum
+ 
+
+ align:start position:0%
+comes from stationary phase quantum
+mechanics is full of oscillations
+
+ align:start position:0%
+mechanics is full of oscillations
+ 
+
+ align:start position:0%
+mechanics is full of oscillations
+classic annex doesn't have oscillations
+
+ align:start position:0%
+classic annex doesn't have oscillations
+ 
+
+ align:start position:0%
+classic annex doesn't have oscillations
+and the two meet at the stationary phase
+
+ align:start position:0%
+and the two meet at the stationary phase
+ 
+
+ align:start position:0%
+and the two meet at the stationary phase
+point okay so now we're going to use
+
+ align:start position:0%
+point okay so now we're going to use
+ 
+
+ align:start position:0%
+point okay so now we're going to use
+these ideas to calculate useful stuff
+
+ align:start position:0%
+these ideas to calculate useful stuff
+ 
+
+ align:start position:0%
+these ideas to calculate useful stuff
+for quantum mechanical vibrational wave
+
+ align:start position:0%
+for quantum mechanical vibrational wave
+ 
+
+ align:start position:0%
+for quantum mechanical vibrational wave
+functions so the shapes of Phi of X gets
+
+ align:start position:0%
+functions so the shapes of Phi of X gets
+ 
+
+ align:start position:0%
+functions so the shapes of Phi of X gets
+exponentially damped but it extends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into the classically forbidden II less
+
+ align:start position:0%
+into the classically forbidden II less
+ 
+
+ align:start position:0%
+into the classically forbidden II less
+than V of X so the wave function if we
+
+ align:start position:0%
+than V of X so the wave function if we
+ 
+
+ align:start position:0%
+than V of X so the wave function if we
+have a potential and we have a wave
+
+ align:start position:0%
+have a potential and we have a wave
+ 
+
+ align:start position:0%
+have a potential and we have a wave
+function that wave function is going to
+
+ align:start position:0%
+function that wave function is going to
+ 
+
+ align:start position:0%
+function that wave function is going to
+not go to zero at the edge but it's
+
+ align:start position:0%
+not go to zero at the edge but it's
+ 
+
+ align:start position:0%
+not go to zero at the edge but it's
+going to have a tail and that tail goes
+
+ align:start position:0%
+going to have a tail and that tail goes
+ 
+
+ align:start position:0%
+going to have a tail and that tail goes
+to zero at infinity and so there's some
+
+ align:start position:0%
+to zero at infinity and so there's some
+ 
+
+ align:start position:0%
+to zero at infinity and so there's some
+amplitude in where the particle isn't
+
+ align:start position:0%
+amplitude in where the particle isn't
+ 
+
+ align:start position:0%
+amplitude in where the particle isn't
+allowed to be classically and that's
+
+ align:start position:0%
+allowed to be classically and that's
+ 
+
+ align:start position:0%
+allowed to be classically and that's
+what we're tunneling comes in and but
+
+ align:start position:0%
+what we're tunneling comes in and but
+ 
+
+ align:start position:0%
+what we're tunneling comes in and but
+the important thing the important
+
+ align:start position:0%
+the important thing the important
+ 
+
+ align:start position:0%
+the important thing the important
+insight is that there are no nodes in
+
+ align:start position:0%
+insight is that there are no nodes in
+ 
+
+ align:start position:0%
+insight is that there are no nodes in
+the classically forbidden region there
+
+ align:start position:0%
+the classically forbidden region there
+ 
+
+ align:start position:0%
+the classically forbidden region there
+is only exponential decay towards zero
+
+ align:start position:0%
+is only exponential decay towards zero
+ 
+
+ align:start position:0%
+is only exponential decay towards zero
+and if you've chosen the wrong value of
+
+ align:start position:0%
+and if you've chosen the wrong value of
+ 
+
+ align:start position:0%
+and if you've chosen the wrong value of
+the energy in other words in a place
+
+ align:start position:0%
+the energy in other words in a place
+ 
+
+ align:start position:0%
+the energy in other words in a place
+where there is no no eigen function the
+
+ align:start position:0%
+where there is no no eigen function the
+ 
+
+ align:start position:0%
+where there is no no eigen function the
+wave function in the classically
+
+ align:start position:0%
+wave function in the classically
+ 
+
+ align:start position:0%
+wave function in the classically
+forbidden region will usually go to
+
+ align:start position:0%
+forbidden region will usually go to
+ 
+
+ align:start position:0%
+forbidden region will usually go to
+infinity either over here or over here
+
+ align:start position:0%
+infinity either over here or over here
+ 
+
+ align:start position:0%
+infinity either over here or over here
+and says well it's clearly not a good
+
+ align:start position:0%
+and says well it's clearly not a good
+ 
+
+ align:start position:0%
+and says well it's clearly not a good
+function but there are no zero crossings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's oscillating in E greater than V of
+
+ align:start position:0%
+it's oscillating in E greater than V of
+ 
+
+ align:start position:0%
+it's oscillating in E greater than V of
+X the classically allowed region the
+
+ align:start position:0%
+X the classically allowed region the
+ 
+
+ align:start position:0%
+X the classically allowed region the
+number of nodes is V so we can have V
+
+ align:start position:0%
+number of nodes is V so we can have V
+ 
+
+ align:start position:0%
+number of nodes is V so we can have V
+equals zero function that just goes up
+
+ align:start position:0%
+equals zero function that just goes up
+ 
+
+ align:start position:0%
+equals zero function that just goes up
+and goes down no internal nodes vehicles
+
+ align:start position:0%
+and goes down no internal nodes vehicles
+ 
+
+ align:start position:0%
+and goes down no internal nodes vehicles
+want to crow who crosses zero right in
+
+ align:start position:0%
+want to crow who crosses zero right in
+ 
+
+ align:start position:0%
+want to crow who crosses zero right in
+the middle and we have the even oddness
+
+ align:start position:0%
+the middle and we have the even oddness
+ 
+
+ align:start position:0%
+the middle and we have the even oddness
+even V even function odd V odd function
+
+ align:start position:0%
+even V even function odd V odd function
+ 
+
+ align:start position:0%
+even V even function odd V odd function
+so for an even function you have a
+
+ align:start position:0%
+so for an even function you have a
+ 
+
+ align:start position:0%
+so for an even function you have a
+relative maximum at x equals zero and
+
+ align:start position:0%
+relative maximum at x equals zero and
+ 
+
+ align:start position:0%
+relative maximum at x equals zero and
+for an odd function you have a zero and
+
+ align:start position:0%
+for an odd function you have a zero and
+ 
+
+ align:start position:0%
+for an odd function you have a zero and
+the opposite for their derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the outer lobes the ones on the ends
+
+ align:start position:0%
+so the outer lobes the ones on the ends
+ 
+
+ align:start position:0%
+so the outer lobes the ones on the ends
+just before the particle RIA encounters
+
+ align:start position:0%
+just before the particle RIA encounters
+ 
+
+ align:start position:0%
+just before the particle RIA encounters
+the classically classical wall you get
+
+ align:start position:0%
+the classically classical wall you get
+ 
+
+ align:start position:0%
+the classically classical wall you get
+the maximum amplitude and so you can you
+
+ align:start position:0%
+the maximum amplitude and so you can you
+ 
+
+ align:start position:0%
+the maximum amplitude and so you can you
+can draw cartoons which looks sort of
+
+ align:start position:0%
+can draw cartoons which looks sort of
+ 
+
+ align:start position:0%
+can draw cartoons which looks sort of
+like that there most of the valuable
+
+ align:start position:0%
+like that there most of the valuable
+ 
+
+ align:start position:0%
+like that there most of the valuable
+stuff is at the outer turning point and
+
+ align:start position:0%
+stuff is at the outer turning point and
+ 
+
+ align:start position:0%
+stuff is at the outer turning point and
+there's oscillations in between but
+
+ align:start position:0%
+there's oscillations in between but
+ 
+
+ align:start position:0%
+there's oscillations in between but
+often you really care about these two
+
+ align:start position:0%
+often you really care about these two
+ 
+
+ align:start position:0%
+often you really care about these two
+outer lobes that's a pretty good
+
+ align:start position:0%
+outer lobes that's a pretty good
+ 
+
+ align:start position:0%
+outer lobes that's a pretty good
+simplification now there's a nice
+
+ align:start position:0%
+simplification now there's a nice
+ 
+
+ align:start position:0%
+simplification now there's a nice
+picture in Macquarie on page 226 which
+
+ align:start position:0%
+picture in Macquarie on page 226 which
+ 
+
+ align:start position:0%
+picture in Macquarie on page 226 which
+shows especially for size squared that
+
+ align:start position:0%
+shows especially for size squared that
+ 
+
+ align:start position:0%
+shows especially for size squared that
+the nodes are pretty big but they're not
+
+ align:start position:0%
+the nodes are pretty big but they're not
+ 
+
+ align:start position:0%
+the nodes are pretty big but they're not
+as big for relatively low quantum
+
+ align:start position:0%
+as big for relatively low quantum
+ 
+
+ align:start position:0%
+as big for relatively low quantum
+numbers as I've implied but at really
+
+ align:start position:0%
+numbers as I've implied but at really
+ 
+
+ align:start position:0%
+numbers as I've implied but at really
+high quantum numbers we have a thing
+
+ align:start position:0%
+high quantum numbers we have a thing
+ 
+
+ align:start position:0%
+high quantum numbers we have a thing
+called the correspondence principle and
+
+ align:start position:0%
+called the correspondence principle and
+ 
+
+ align:start position:0%
+called the correspondence principle and
+in the correspondence principle says
+
+ align:start position:0%
+in the correspondence principle says
+ 
+
+ align:start position:0%
+in the correspondence principle says
+that quantum mechanics will do what
+
+ align:start position:0%
+that quantum mechanics will do what
+ 
+
+ align:start position:0%
+that quantum mechanics will do what
+classical mechanics does in the limit of
+
+ align:start position:0%
+classical mechanics does in the limit of
+ 
+
+ align:start position:0%
+classical mechanics does in the limit of
+high quantum numbers and in the limit of
+
+ align:start position:0%
+high quantum numbers and in the limit of
+ 
+
+ align:start position:0%
+high quantum numbers and in the limit of
+high quantum numbers essentially all the
+
+ align:start position:0%
+high quantum numbers essentially all the
+ 
+
+ align:start position:0%
+high quantum numbers essentially all the
+amplitude is at the turning points and
+
+ align:start position:0%
+amplitude is at the turning points and
+ 
+
+ align:start position:0%
+amplitude is at the turning points and
+in classical mechanics the particle is
+
+ align:start position:0%
+in classical mechanics the particle is
+ 
+
+ align:start position:0%
+in classical mechanics the particle is
+moving fast in the middle and stops and
+
+ align:start position:0%
+moving fast in the middle and stops and
+ 
+
+ align:start position:0%
+moving fast in the middle and stops and
+turns around and essentially all the
+
+ align:start position:0%
+turns around and essentially all the
+ 
+
+ align:start position:0%
+turns around and essentially all the
+amplitude is at the turning point so
+
+ align:start position:0%
+amplitude is at the turning point so
+ 
+
+ align:start position:0%
+amplitude is at the turning point so
+this is nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now we're getting into Bob ISM
+
+ align:start position:0%
+okay now we're getting into Bob ISM
+ 
+
+ align:start position:0%
+okay now we're getting into Bob ISM
+territory because I'm really going to
+
+ align:start position:0%
+territory because I'm really going to
+ 
+
+ align:start position:0%
+territory because I'm really going to
+show you how to calculate the whatever
+
+ align:start position:0%
+show you how to calculate the whatever
+ 
+
+ align:start position:0%
+show you how to calculate the whatever
+you need
+
+ align:start position:0%
+you need
+ 
+
+ align:start position:0%
+you need
+using these semi-classical ideas so we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have the probability envelope psy star
+
+ align:start position:0%
+have the probability envelope psy star
+ 
+
+ align:start position:0%
+have the probability envelope psy star
+of X sine of X and we're gonna have both
+
+ align:start position:0%
+of X sine of X and we're gonna have both
+ 
+
+ align:start position:0%
+of X sine of X and we're gonna have both
+of these having the same quantum number
+
+ align:start position:0%
+of these having the same quantum number
+ 
+
+ align:start position:0%
+of these having the same quantum number
+DX so this is the probability of finding
+
+ align:start position:0%
+DX so this is the probability of finding
+ 
+
+ align:start position:0%
+DX so this is the probability of finding
+the particle near X in a region of width
+
+ align:start position:0%
+the particle near X in a region of width
+ 
+
+ align:start position:0%
+the particle near X in a region of width
+DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the same thing as DX over V
+
+ align:start position:0%
+and this is the same thing as DX over V
+ 
+
+ align:start position:0%
+and this is the same thing as DX over V
+classical it's not the same thing
+
+ align:start position:0%
+classical it's not the same thing
+ 
+
+ align:start position:0%
+classical it's not the same thing
+there's a constant here sorry so this
+
+ align:start position:0%
+there's a constant here sorry so this
+ 
+
+ align:start position:0%
+there's a constant here sorry so this
+probability density that you want is
+
+ align:start position:0%
+probability density that you want is
+ 
+
+ align:start position:0%
+probability density that you want is
+basically 1 over the classical velocity
+
+ align:start position:0%
+basically 1 over the classical velocity
+ 
+
+ align:start position:0%
+basically 1 over the classical velocity
+and that was damage I demonstrated that
+
+ align:start position:0%
+and that was damage I demonstrated that
+ 
+
+ align:start position:0%
+and that was damage I demonstrated that
+when I walked across the room when I
+
+ align:start position:0%
+when I walked across the room when I
+ 
+
+ align:start position:0%
+when I walked across the room when I
+walked fast in the middle and slow on
+
+ align:start position:0%
+walked fast in the middle and slow on
+ 
+
+ align:start position:0%
+walked fast in the middle and slow on
+the outside and you get the probability
+
+ align:start position:0%
+the outside and you get the probability
+ 
+
+ align:start position:0%
+the outside and you get the probability
+you get this constant by saying ok how
+
+ align:start position:0%
+you get this constant by saying ok how
+ 
+
+ align:start position:0%
+you get this constant by saying ok how
+long did it take for me to go from one
+
+ align:start position:0%
+long did it take for me to go from one
+ 
+
+ align:start position:0%
+long did it take for me to go from one
+end to the other and comparing that how
+
+ align:start position:0%
+end to the other and comparing that how
+ 
+
+ align:start position:0%
+end to the other and comparing that how
+long it took for me to go in some
+
+ align:start position:0%
+long it took for me to go in some
+ 
+
+ align:start position:0%
+long it took for me to go in some
+differential position so you get this
+
+ align:start position:0%
+differential position so you get this
+ 
+
+ align:start position:0%
+differential position so you get this
+this constant in a simple way so be
+
+ align:start position:0%
+this constant in a simple way so be
+ 
+
+ align:start position:0%
+this constant in a simple way so be
+classical is equal to P classical over
+
+ align:start position:0%
+classical is equal to P classical over
+ 
+
+ align:start position:0%
+classical is equal to P classical over
+the mass or the MU but we know is a
+
+ align:start position:0%
+the mass or the MU but we know is a
+ 
+
+ align:start position:0%
+the mass or the MU but we know is a
+function for P classical so we have 1
+
+ align:start position:0%
+function for P classical so we have 1
+ 
+
+ align:start position:0%
+function for P classical so we have 1
+over mu times 2 nu e minus V of X so we
+
+ align:start position:0%
+over mu times 2 nu e minus V of X so we
+ 
+
+ align:start position:0%
+over mu times 2 nu e minus V of X so we
+know the velocity everywhere and there's
+
+ align:start position:0%
+know the velocity everywhere and there's
+ 
+
+ align:start position:0%
+know the velocity everywhere and there's
+nothing terribly hard about figuring
+
+ align:start position:0%
+nothing terribly hard about figuring
+ 
+
+ align:start position:0%
+nothing terribly hard about figuring
+that out ok and now we want to know what
+
+ align:start position:0%
+that out ok and now we want to know what
+ 
+
+ align:start position:0%
+that out ok and now we want to know what
+this proportionality constant is and so
+
+ align:start position:0%
+this proportionality constant is and so
+ 
+
+ align:start position:0%
+this proportionality constant is and so
+for that we say by the time to go from X
+
+ align:start position:0%
+for that we say by the time to go from X
+ 
+
+ align:start position:0%
+for that we say by the time to go from X
+to X plus DX over the time to go from X
+
+ align:start position:0%
+to X plus DX over the time to go from X
+ 
+
+ align:start position:0%
+to X plus DX over the time to go from X
+minus 2x plus because what's happening
+
+ align:start position:0%
+minus 2x plus because what's happening
+ 
+
+ align:start position:0%
+minus 2x plus because what's happening
+the particle is going back and forth
+
+ align:start position:0%
+the particle is going back and forth
+ 
+
+ align:start position:0%
+the particle is going back and forth
+inside this well and so this is the time
+
+ align:start position:0%
+inside this well and so this is the time
+ 
+
+ align:start position:0%
+inside this well and so this is the time
+it takes to go one pass and this is the
+
+ align:start position:0%
+it takes to go one pass and this is the
+ 
+
+ align:start position:0%
+it takes to go one pass and this is the
+time it takes to go through the it
+
+ align:start position:0%
+time it takes to go through the it
+ 
+
+ align:start position:0%
+time it takes to go through the it
+region of interest and so this ratio is
+
+ align:start position:0%
+region of interest and so this ratio is
+ 
+
+ align:start position:0%
+region of interest and so this ratio is
+the probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so we have the probability
+
+ align:start position:0%
+okay and so we have the probability
+ 
+
+ align:start position:0%
+okay and so we have the probability
+moving to the from from left turning
+
+ align:start position:0%
+moving to the from from left turning
+ 
+
+ align:start position:0%
+moving to the from from left turning
+point to right turning point and we want
+
+ align:start position:0%
+point to right turning point and we want
+ 
+
+ align:start position:0%
+point to right turning point and we want
+to know the probability in that interval
+
+ align:start position:0%
+to know the probability in that interval
+ 
+
+ align:start position:0%
+to know the probability in that interval
+and so that's just the x over the
+
+ align:start position:0%
+and so that's just the x over the
+ 
+
+ align:start position:0%
+and so that's just the x over the
+classical at X over tau order to because
+
+ align:start position:0%
+classical at X over tau order to because
+ 
+
+ align:start position:0%
+classical at X over tau order to because
+tau is the period and we have half of a
+
+ align:start position:0%
+tau is the period and we have half of a
+ 
+
+ align:start position:0%
+tau is the period and we have half of a
+period and so it's all together and so
+
+ align:start position:0%
+period and so it's all together and so
+ 
+
+ align:start position:0%
+period and so it's all together and so
+I'm just gonna skip a little step
+
+ align:start position:0%
+I'm just gonna skip a little step
+ 
+
+ align:start position:0%
+I'm just gonna skip a little step
+because it's taking too long so our side
+
+ align:start position:0%
+because it's taking too long so our side
+ 
+
+ align:start position:0%
+because it's taking too long so our side
+the X is equal to K over 2 pi squared e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is V of X square us DX now so if we know
+
+ align:start position:0%
+is V of X square us DX now so if we know
+ 
+
+ align:start position:0%
+is V of X square us DX now so if we know
+the potential and we know the energy and
+
+ align:start position:0%
+the potential and we know the energy and
+ 
+
+ align:start position:0%
+the potential and we know the energy and
+we know the force constant well we can
+
+ align:start position:0%
+we know the force constant well we can
+ 
+
+ align:start position:0%
+we know the force constant well we can
+say well this is this is the probability
+
+ align:start position:0%
+say well this is this is the probability
+ 
+
+ align:start position:0%
+say well this is this is the probability
+and and so but this is this is the
+
+ align:start position:0%
+and and so but this is this is the
+ 
+
+ align:start position:0%
+and and so but this is this is the
+probability of the class of the
+
+ align:start position:0%
+probability of the class of the
+ 
+
+ align:start position:0%
+probability of the class of the
+semi-classical representation of sy star
+
+ align:start position:0%
+semi-classical representation of sy star
+ 
+
+ align:start position:0%
+semi-classical representation of sy star
+by DX and X now this is oscillating and
+
+ align:start position:0%
+by DX and X now this is oscillating and
+ 
+
+ align:start position:0%
+by DX and X now this is oscillating and
+this is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we really want to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's here's the so if we have psystar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops slow down okay so this is
+
+ align:start position:0%
+oops slow down okay so this is
+ 
+
+ align:start position:0%
+oops slow down okay so this is
+oscillating and what we've calculated
+
+ align:start position:0%
+oscillating and what we've calculated
+ 
+
+ align:start position:0%
+oscillating and what we've calculated
+before is something that looks sort of
+
+ align:start position:0%
+before is something that looks sort of
+ 
+
+ align:start position:0%
+before is something that looks sort of
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+and if we multiply by two we have a
+
+ align:start position:0%
+and if we multiply by two we have a
+ 
+
+ align:start position:0%
+and if we multiply by two we have a
+curve that goes through the maximum of
+
+ align:start position:0%
+curve that goes through the maximum of
+ 
+
+ align:start position:0%
+curve that goes through the maximum of
+all these oscillations so the envelopes
+
+ align:start position:0%
+all these oscillations so the envelopes
+ 
+
+ align:start position:0%
+all these oscillations so the envelopes
+I star psy has the form we've multiplied
+
+ align:start position:0%
+I star psy has the form we've multiplied
+ 
+
+ align:start position:0%
+I star psy has the form we've multiplied
+by two and so we end up getting two okay
+
+ align:start position:0%
+by two and so we end up getting two okay
+ 
+
+ align:start position:0%
+by two and so we end up getting two okay
+over pi square e times V of X square
+
+ align:start position:0%
+over pi square e times V of X square
+ 
+
+ align:start position:0%
+over pi square e times V of X square
+root now you might say well these are
+
+ align:start position:0%
+root now you might say well these are
+ 
+
+ align:start position:0%
+root now you might say well these are
+complicated functions why should I
+
+ align:start position:0%
+complicated functions why should I
+ 
+
+ align:start position:0%
+complicated functions why should I
+bother with them but if you wanted to
+
+ align:start position:0%
+bother with them but if you wanted to
+ 
+
+ align:start position:0%
+bother with them but if you wanted to
+anything starting from the correct
+
+ align:start position:0%
+anything starting from the correct
+ 
+
+ align:start position:0%
+anything starting from the correct
+solution to the harmonic oscillator
+
+ align:start position:0%
+solution to the harmonic oscillator
+ 
+
+ align:start position:0%
+solution to the harmonic oscillator
+using the hermite polynomials this is a
+
+ align:start position:0%
+using the hermite polynomials this is a
+ 
+
+ align:start position:0%
+using the hermite polynomials this is a
+whole lot more overhead notice also this
+
+ align:start position:0%
+whole lot more overhead notice also this
+ 
+
+ align:start position:0%
+whole lot more overhead notice also this
+is a function of X not X I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the overlap function
+
+ align:start position:0%
+so this is the overlap function
+ 
+
+ align:start position:0%
+so this is the overlap function
+it's the curve that it touches the
+
+ align:start position:0%
+it's the curve that it touches the
+ 
+
+ align:start position:0%
+it's the curve that it touches the
+maximum of all these things and it's
+
+ align:start position:0%
+maximum of all these things and it's
+ 
+
+ align:start position:0%
+maximum of all these things and it's
+very useful if you want to know the
+
+ align:start position:0%
+very useful if you want to know the
+ 
+
+ align:start position:0%
+very useful if you want to know the
+probability of finding the system
+
+ align:start position:0%
+probability of finding the system
+ 
+
+ align:start position:0%
+probability of finding the system
+anywhere okay and we get the node
+
+ align:start position:0%
+anywhere okay and we get the node
+ 
+
+ align:start position:0%
+anywhere okay and we get the node
+spacing from the equation H over give X
+
+ align:start position:0%
+spacing from the equation H over give X
+ 
+
+ align:start position:0%
+spacing from the equation H over give X
+and now here comes something really nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's called the semi-classical
+
+ align:start position:0%
+it's called the semi-classical
+ 
+
+ align:start position:0%
+it's called the semi-classical
+quantization integral so if we have a
+
+ align:start position:0%
+quantization integral so if we have a
+ 
+
+ align:start position:0%
+quantization integral so if we have a
+any one dimensional potential and we're
+
+ align:start position:0%
+any one dimensional potential and we're
+ 
+
+ align:start position:0%
+any one dimensional potential and we're
+at some energy we'd like to be able to
+
+ align:start position:0%
+at some energy we'd like to be able to
+ 
+
+ align:start position:0%
+at some energy we'd like to be able to
+know how many levels are are at the
+
+ align:start position:0%
+know how many levels are are at the
+ 
+
+ align:start position:0%
+know how many levels are are at the
+energy that energy or below or where are
+
+ align:start position:0%
+energy that energy or below or where are
+ 
+
+ align:start position:0%
+energy that energy or below or where are
+the energy levels and we get that from
+
+ align:start position:0%
+the energy levels and we get that from
+ 
+
+ align:start position:0%
+the energy levels and we get that from
+this really incredible thing so we want
+
+ align:start position:0%
+this really incredible thing so we want
+ 
+
+ align:start position:0%
+this really incredible thing so we want
+to know that okay this is the difference
+
+ align:start position:0%
+to know that okay this is the difference
+ 
+
+ align:start position:0%
+to know that okay this is the difference
+between nodes right and now if we would
+
+ align:start position:0%
+between nodes right and now if we would
+ 
+
+ align:start position:0%
+between nodes right and now if we would
+like to know X minus 2x plus it's a
+
+ align:start position:0%
+like to know X minus 2x plus it's a
+ 
+
+ align:start position:0%
+like to know X minus 2x plus it's a
+matter we can replace lambda of X by H
+
+ align:start position:0%
+matter we can replace lambda of X by H
+ 
+
+ align:start position:0%
+matter we can replace lambda of X by H
+over P of X and so we get P of X that's
+
+ align:start position:0%
+over P of X and so we get P of X that's
+ 
+
+ align:start position:0%
+over P of X and so we get P of X that's
+that energy over H DX P DX that's called
+
+ align:start position:0%
+that energy over H DX P DX that's called
+ 
+
+ align:start position:0%
+that energy over H DX P DX that's called
+an action integral now I have to tell a
+
+ align:start position:0%
+an action integral now I have to tell a
+ 
+
+ align:start position:0%
+an action integral now I have to tell a
+little story when I was a senior at
+
+ align:start position:0%
+little story when I was a senior at
+ 
+
+ align:start position:0%
+little story when I was a senior at
+Amherst College we had a a oral exam for
+
+ align:start position:0%
+Amherst College we had a a oral exam for
+ 
+
+ align:start position:0%
+Amherst College we had a a oral exam for
+whether my thesis was going to be
+
+ align:start position:0%
+whether my thesis was going to be
+ 
+
+ align:start position:0%
+whether my thesis was going to be
+accepted or not
+
+ align:start position:0%
+accepted or not
+ 
+
+ align:start position:0%
+accepted or not
+and one of my examiner's asked me what
+
+ align:start position:0%
+and one of my examiner's asked me what
+ 
+
+ align:start position:0%
+and one of my examiner's asked me what
+is the unit of H well its energy times
+
+ align:start position:0%
+is the unit of H well its energy times
+ 
+
+ align:start position:0%
+is the unit of H well its energy times
+time and he wouldn't he wouldn't stop he
+
+ align:start position:0%
+time and he wouldn't he wouldn't stop he
+ 
+
+ align:start position:0%
+time and he wouldn't he wouldn't stop he
+said no it went something else
+
+ align:start position:0%
+said no it went something else
+ 
+
+ align:start position:0%
+said no it went something else
+it's called action momentum times
+
+ align:start position:0%
+it's called action momentum times
+ 
+
+ align:start position:0%
+it's called action momentum times
+position this is an action integral and
+
+ align:start position:0%
+position this is an action integral and
+ 
+
+ align:start position:0%
+position this is an action integral and
+so anyway that's just a story I we had
+
+ align:start position:0%
+so anyway that's just a story I we had
+ 
+
+ align:start position:0%
+so anyway that's just a story I we had
+spent a half an hour and I was damn
+
+ align:start position:0%
+spent a half an hour and I was damn
+ 
+
+ align:start position:0%
+spent a half an hour and I was damn
+stubborn I was not you know it was
+
+ align:start position:0%
+stubborn I was not you know it was
+ 
+
+ align:start position:0%
+stubborn I was not you know it was
+energy times time but that it's much
+
+ align:start position:0%
+energy times time but that it's much
+ 
+
+ align:start position:0%
+energy times time but that it's much
+more inside here and that's maybe why I
+
+ align:start position:0%
+more inside here and that's maybe why I
+ 
+
+ align:start position:0%
+more inside here and that's maybe why I
+got so excited about this sort of an
+
+ align:start position:0%
+got so excited about this sort of an
+ 
+
+ align:start position:0%
+got so excited about this sort of an
+integral ok so if we if we want to know
+
+ align:start position:0%
+integral ok so if we if we want to know
+ 
+
+ align:start position:0%
+integral ok so if we if we want to know
+if we have an eigenvalue this integral
+
+ align:start position:0%
+if we have an eigenvalue this integral
+ 
+
+ align:start position:0%
+if we have an eigenvalue this integral
+has to be equal to H over 2 times the
+
+ align:start position:0%
+has to be equal to H over 2 times the
+ 
+
+ align:start position:0%
+has to be equal to H over 2 times the
+number of nodes that's pretty simple and
+
+ align:start position:0%
+number of nodes that's pretty simple and
+ 
+
+ align:start position:0%
+number of nodes that's pretty simple and
+so we can adjust e to satisfy this or if
+
+ align:start position:0%
+so we can adjust e to satisfy this or if
+ 
+
+ align:start position:0%
+so we can adjust e to satisfy this or if
+we wanted to know how many energy levels
+
+ align:start position:0%
+we wanted to know how many energy levels
+ 
+
+ align:start position:0%
+we wanted to know how many energy levels
+are are at an energy below that energy
+
+ align:start position:0%
+are are at an energy below that energy
+ 
+
+ align:start position:0%
+are are at an energy below that energy
+we've chosen we evaluate this integral
+
+ align:start position:0%
+we've chosen we evaluate this integral
+ 
+
+ align:start position:0%
+we've chosen we evaluate this integral
+and we get a number like 13.5 well means
+
+ align:start position:0%
+and we get a number like 13.5 well means
+ 
+
+ align:start position:0%
+and we get a number like 13.5 well means
+there are 13 energy levels below that
+
+ align:start position:0%
+there are 13 energy levels below that
+ 
+
+ align:start position:0%
+there are 13 energy levels below that
+now often you want to know the density
+
+ align:start position:0%
+now often you want to know the density
+ 
+
+ align:start position:0%
+now often you want to know the density
+of states the number of energy levels
+
+ align:start position:0%
+of states the number of energy levels
+ 
+
+ align:start position:0%
+of states the number of energy levels
+per unit energy because that turns out
+
+ align:start position:0%
+per unit energy because that turns out
+ 
+
+ align:start position:0%
+per unit energy because that turns out
+to be the critical quantity in
+
+ align:start position:0%
+to be the critical quantity in
+ 
+
+ align:start position:0%
+to be the critical quantity in
+calculating many things you want to know
+
+ align:start position:0%
+calculating many things you want to know
+ 
+
+ align:start position:0%
+calculating many things you want to know
+and you can get that from the
+
+ align:start position:0%
+and you can get that from the
+ 
+
+ align:start position:0%
+and you can get that from the
+semi-classical quantization okay
+
+ align:start position:0%
+semi-classical quantization okay
+ 
+
+ align:start position:0%
+semi-classical quantization okay
+so we're close to the end I just want to
+
+ align:start position:0%
+so we're close to the end I just want to
+ 
+
+ align:start position:0%
+so we're close to the end I just want to
+say where we're going so we have
+
+ align:start position:0%
+say where we're going so we have
+ 
+
+ align:start position:0%
+say where we're going so we have
+classical pictures and I really really
+
+ align:start position:0%
+classical pictures and I really really
+ 
+
+ align:start position:0%
+classical pictures and I really really
+want you to think about these classical
+
+ align:start position:0%
+want you to think about these classical
+ 
+
+ align:start position:0%
+want you to think about these classical
+pictures and use them rather than
+
+ align:start position:0%
+pictures and use them rather than
+ 
+
+ align:start position:0%
+pictures and use them rather than
+thinking well I'm going to have my cell
+
+ align:start position:0%
+thinking well I'm going to have my cell
+ 
+
+ align:start position:0%
+thinking well I'm going to have my cell
+phone program to evaluate all these
+
+ align:start position:0%
+phone program to evaluate all these
+ 
+
+ align:start position:0%
+phone program to evaluate all these
+necessary stuff
+
+ align:start position:0%
+necessary stuff
+ 
+
+ align:start position:0%
+necessary stuff
+and there are certain things you want to
+
+ align:start position:0%
+and there are certain things you want to
+ 
+
+ align:start position:0%
+and there are certain things you want to
+remember about this semi-classical
+
+ align:start position:0%
+remember about this semi-classical
+ 
+
+ align:start position:0%
+remember about this semi-classical
+picture and now we have the ability to
+
+ align:start position:0%
+picture and now we have the ability to
+ 
+
+ align:start position:0%
+picture and now we have the ability to
+calculate an infinite number of
+
+ align:start position:0%
+calculate an infinite number of
+ 
+
+ align:start position:0%
+calculate an infinite number of
+integrals involving harmonic oscillator
+
+ align:start position:0%
+integrals involving harmonic oscillator
+ 
+
+ align:start position:0%
+integrals involving harmonic oscillator
+functions and certain operators well
+
+ align:start position:0%
+functions and certain operators well
+ 
+
+ align:start position:0%
+functions and certain operators well
+la-dee-da but why do we want them well
+
+ align:start position:0%
+la-dee-da but why do we want them well
+ 
+
+ align:start position:0%
+la-dee-da but why do we want them well
+one of the things we want is to be able
+
+ align:start position:0%
+one of the things we want is to be able
+ 
+
+ align:start position:0%
+one of the things we want is to be able
+to calculate the probability of a
+
+ align:start position:0%
+to calculate the probability of a
+ 
+
+ align:start position:0%
+to calculate the probability of a
+vibrational transition that's called a
+
+ align:start position:0%
+vibrational transition that's called a
+ 
+
+ align:start position:0%
+vibrational transition that's called a
+transition moment and that's an easy
+
+ align:start position:0%
+transition moment and that's an easy
+ 
+
+ align:start position:0%
+transition moment and that's an easy
+thing to calculate another thing we want
+
+ align:start position:0%
+thing to calculate another thing we want
+ 
+
+ align:start position:0%
+thing to calculate another thing we want
+to do is to say well Nature screwed up
+
+ align:start position:0%
+to do is to say well Nature screwed up
+ 
+
+ align:start position:0%
+to do is to say well Nature screwed up
+this oscillator isn't harmonic there's
+
+ align:start position:0%
+this oscillator isn't harmonic there's
+ 
+
+ align:start position:0%
+this oscillator isn't harmonic there's
+an anharmonic term and I would like to
+
+ align:start position:0%
+an anharmonic term and I would like to
+ 
+
+ align:start position:0%
+an anharmonic term and I would like to
+know what is the contribution of a
+
+ align:start position:0%
+know what is the contribution of a
+ 
+
+ align:start position:0%
+know what is the contribution of a
+constant times X cubed in the potential
+
+ align:start position:0%
+constant times X cubed in the potential
+ 
+
+ align:start position:0%
+constant times X cubed in the potential
+to the energy levels and that's called
+
+ align:start position:0%
+to the energy levels and that's called
+ 
+
+ align:start position:0%
+to the energy levels and that's called
+perturbation theory or I want to have
+
+ align:start position:0%
+perturbation theory or I want to have
+ 
+
+ align:start position:0%
+perturbation theory or I want to have
+many harmonic oscillators in a
+
+ align:start position:0%
+many harmonic oscillators in a
+ 
+
+ align:start position:0%
+many harmonic oscillators in a
+polyatomic molecule they talk to each
+
+ align:start position:0%
+polyatomic molecule they talk to each
+ 
+
+ align:start position:0%
+polyatomic molecule they talk to each
+other and I want to calculate the
+
+ align:start position:0%
+other and I want to calculate the
+ 
+
+ align:start position:0%
+other and I want to calculate the
+interaction how the interactions between
+
+ align:start position:0%
+interaction how the interactions between
+ 
+
+ align:start position:0%
+interaction how the interactions between
+these harmonic oscillators affect the
+
+ align:start position:0%
+these harmonic oscillators affect the
+ 
+
+ align:start position:0%
+these harmonic oscillators affect the
+energy level remember when we have a
+
+ align:start position:0%
+energy level remember when we have a
+ 
+
+ align:start position:0%
+energy level remember when we have a
+separable Hamiltonian we could just
+
+ align:start position:0%
+separable Hamiltonian we could just
+ 
+
+ align:start position:0%
+separable Hamiltonian we could just
+write the energy levels as the sum of
+
+ align:start position:0%
+write the energy levels as the sum of
+ 
+
+ align:start position:0%
+write the energy levels as the sum of
+the individual Hamilton and then there's
+
+ align:start position:0%
+the individual Hamilton and then there's
+ 
+
+ align:start position:0%
+the individual Hamilton and then there's
+coupling terms and we deal with those by
+
+ align:start position:0%
+coupling terms and we deal with those by
+ 
+
+ align:start position:0%
+coupling terms and we deal with those by
+perturbation theory so there's all sorts
+
+ align:start position:0%
+perturbation theory so there's all sorts
+ 
+
+ align:start position:0%
+perturbation theory so there's all sorts
+of wonderful things we do but we're
+
+ align:start position:0%
+of wonderful things we do but we're
+ 
+
+ align:start position:0%
+of wonderful things we do but we're
+going to consider these magical
+
+ align:start position:0%
+going to consider these magical
+ 
+
+ align:start position:0%
+going to consider these magical
+operators a creation and annihilation
+
+ align:start position:0%
+operators a creation and annihilation
+ 
+
+ align:start position:0%
+operators a creation and annihilation
+operator where a star a dagger operating
+
+ align:start position:0%
+operator where a star a dagger operating
+ 
+
+ align:start position:0%
+operator where a star a dagger operating
+on IV gives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this current a V plus one times I 3 + 1
+
+ align:start position:0%
+this current a V plus one times I 3 + 1
+ 
+
+ align:start position:0%
+this current a V plus one times I 3 + 1
++ a dagger operating on V gives the
+
+ align:start position:0%
++ a dagger operating on V gives the
+ 
+
+ align:start position:0%
++ a dagger operating on V gives the
+square root of V of this right I mean a
+
+ align:start position:0%
+square root of V of this right I mean a
+ 
+
+ align:start position:0%
+square root of V of this right I mean a
+non Dagger gives v square but that's I
+
+ align:start position:0%
+non Dagger gives v square but that's I
+ 
+
+ align:start position:0%
+non Dagger gives v square but that's I
+the minus 1 and that X is equal to a
+
+ align:start position:0%
+the minus 1 and that X is equal to a
+ 
+
+ align:start position:0%
+the minus 1 and that X is equal to a
+plus a dagger times a constant and so
+
+ align:start position:0%
+plus a dagger times a constant and so
+ 
+
+ align:start position:0%
+plus a dagger times a constant and so
+all of a sudden we can evaluate all
+
+ align:start position:0%
+all of a sudden we can evaluate all
+ 
+
+ align:start position:0%
+all of a sudden we can evaluate all
+integrals involving X or powers of X or
+
+ align:start position:0%
+integrals involving X or powers of X or
+ 
+
+ align:start position:0%
+integrals involving X or powers of X or
+momento or powers of momentum without
+
+ align:start position:0%
+momento or powers of momentum without
+ 
+
+ align:start position:0%
+momento or powers of momentum without
+thinking without ever looking at a
+
+ align:start position:0%
+thinking without ever looking at a
+ 
+
+ align:start position:0%
+thinking without ever looking at a
+function and I guarantee you that this
+
+ align:start position:0%
+function and I guarantee you that this
+ 
+
+ align:start position:0%
+function and I guarantee you that this
+is embodied in the incredible amount of
+
+ align:start position:0%
+is embodied in the incredible amount of
+ 
+
+ align:start position:0%
+is embodied in the incredible amount of
+work done where we've presented almost
+
+ align:start position:0%
+work done where we've presented almost
+ 
+
+ align:start position:0%
+work done where we've presented almost
+every problem is a harmonic oscillator
+
+ align:start position:0%
+every problem is a harmonic oscillator
+ 
+
+ align:start position:0%
+every problem is a harmonic oscillator
+in disguise because these days and a
+
+ align:start position:0%
+in disguise because these days and a
+ 
+
+ align:start position:0%
+in disguise because these days and a
+daggers enable you to generate
+
+ align:start position:0%
+daggers enable you to generate
+ 
+
+ align:start position:0%
+daggers enable you to generate
+everything without ever converting from
+
+ align:start position:0%
+everything without ever converting from
+ 
+
+ align:start position:0%
+everything without ever converting from
+X to X I without ever looking at an
+
+ align:start position:0%
+X to X I without ever looking at an
+ 
+
+ align:start position:0%
+X to X I without ever looking at an
+integral it's all just a manipulation of
+
+ align:start position:0%
+integral it's all just a manipulation of
+ 
+
+ align:start position:0%
+integral it's all just a manipulation of
+algebra and it's not just convenient but
+
+ align:start position:0%
+algebra and it's not just convenient but
+ 
+
+ align:start position:0%
+algebra and it's not just convenient but
+there's insight and so this is what I
+
+ align:start position:0%
+there's insight and so this is what I
+ 
+
+ align:start position:0%
+there's insight and so this is what I
+want to convey that you will get
+
+ align:start position:0%
+want to convey that you will get
+ 
+
+ align:start position:0%
+want to convey that you will get
+tremendous insight so maybe maybe I sold
+
+ align:start position:0%
+tremendous insight so maybe maybe I sold
+ 
+
+ align:start position:0%
+tremendous insight so maybe maybe I sold
+you on semi-classical and I don't I
+
+ align:start position:0%
+you on semi-classical and I don't I
+ 
+
+ align:start position:0%
+you on semi-classical and I don't I
+don't apologize for that because that's
+
+ align:start position:0%
+don't apologize for that because that's
+ 
+
+ align:start position:0%
+don't apologize for that because that's
+very useful but the next lecture when
+
+ align:start position:0%
+very useful but the next lecture when
+ 
+
+ align:start position:0%
+very useful but the next lecture when
+you get the A's and a daggers it'll just
+
+ align:start position:0%
+you get the A's and a daggers it'll just
+ 
+
+ align:start position:0%
+you get the A's and a daggers it'll just
+knock your socks off ok that's it
\ No newline at end of file
diff --git a/NHedXxUO-Bg.txt b/NHedXxUO-Bg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7eb80486ad6cbe03dc0e5bb93280c26469b2a520
--- /dev/null
+++ b/NHedXxUO-Bg.txt
@@ -0,0 +1,10803 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu the technical topic for for
+
+ align:start position:0%
+ocw.mit.edu the technical topic for for
+ 
+
+ align:start position:0%
+ocw.mit.edu the technical topic for for
+today we start I rushed right at the end
+
+ align:start position:0%
+today we start I rushed right at the end
+ 
+
+ align:start position:0%
+today we start I rushed right at the end
+a little bit about tangent and normal
+
+ align:start position:0%
+a little bit about tangent and normal
+ 
+
+ align:start position:0%
+a little bit about tangent and normal
+unit vectors and I'm going just to recap
+
+ align:start position:0%
+unit vectors and I'm going just to recap
+ 
+
+ align:start position:0%
+unit vectors and I'm going just to recap
+that quick
+
+ align:start position:0%
+that quick
+ 
+
+ align:start position:0%
+that quick
+and then we're going to go on really a
+
+ align:start position:0%
+and then we're going to go on really a
+ 
+
+ align:start position:0%
+and then we're going to go on really a
+review which of by review this is the
+
+ align:start position:0%
+review which of by review this is the
+ 
+
+ align:start position:0%
+review which of by review this is the
+sort of stuff that for the most part I'm
+
+ align:start position:0%
+sort of stuff that for the most part I'm
+ 
+
+ align:start position:0%
+sort of stuff that for the most part I'm
+sure you've seen in 801 physics and
+
+ align:start position:0%
+sure you've seen in 801 physics and
+ 
+
+ align:start position:0%
+sure you've seen in 801 physics and
+other physics you've had before and
+
+ align:start position:0%
+other physics you've had before and
+ 
+
+ align:start position:0%
+other physics you've had before and
+that's impulse linear momentum and
+
+ align:start position:0%
+that's impulse linear momentum and
+ 
+
+ align:start position:0%
+that's impulse linear momentum and
+impulse so that'll be a quick review and
+
+ align:start position:0%
+impulse so that'll be a quick review and
+ 
+
+ align:start position:0%
+impulse so that'll be a quick review and
+then the third subject is one that's
+
+ align:start position:0%
+then the third subject is one that's
+ 
+
+ align:start position:0%
+then the third subject is one that's
+much deeper and this is angular momentum
+
+ align:start position:0%
+much deeper and this is angular momentum
+ 
+
+ align:start position:0%
+much deeper and this is angular momentum
+and angular momentum with respect to
+
+ align:start position:0%
+and angular momentum with respect to
+ 
+
+ align:start position:0%
+and angular momentum with respect to
+moving points which you probably haven't
+
+ align:start position:0%
+moving points which you probably haven't
+ 
+
+ align:start position:0%
+moving points which you probably haven't
+encountered before so those are the
+
+ align:start position:0%
+encountered before so those are the
+ 
+
+ align:start position:0%
+encountered before so those are the
+those are the three topics for today
+
+ align:start position:0%
+those are the three topics for today
+ 
+
+ align:start position:0%
+those are the three topics for today
+let's get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+started so last
+
+ align:start position:0%
+started so last
+ 
+
+ align:start position:0%
+started so last
+time the piece that
+
+ align:start position:0%
+time the piece that
+ 
+
+ align:start position:0%
+time the piece that
+I rushed a bit is this notion of tangent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates so I gave this had this
+
+ align:start position:0%
+coordinates so I gave this had this
+ 
+
+ align:start position:0%
+coordinates so I gave this had this
+example you're driving down the road
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you drunk or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever and when you're at this point
+
+ align:start position:0%
+whatever and when you're at this point
+ 
+
+ align:start position:0%
+whatever and when you're at this point
+this point and this point I'd like to
+
+ align:start position:0%
+this point and this point I'd like to
+ 
+
+ align:start position:0%
+this point and this point I'd like to
+know what the accelerations are so I'll
+
+ align:start position:0%
+know what the accelerations are so I'll
+ 
+
+ align:start position:0%
+know what the accelerations are so I'll
+call these one two 3 and this curve Y is
+
+ align:start position:0%
+call these one two 3 and this curve Y is
+ 
+
+ align:start position:0%
+call these one two 3 and this curve Y is
+of the form some y of some f
+
+ align:start position:0%
+of the form some y of some f
+ 
+
+ align:start position:0%
+of the form some y of some f
+ofx and in this case it's a
+
+ align:start position:0%
+ofx and in this case it's a
+ 
+
+ align:start position:0%
+ofx and in this case it's a
+sinine
+
+ align:start position:0%
+sinine
+ 
+
+ align:start position:0%
+sinine
+KX and K a is what's known as wave
+
+ align:start position:0%
+KX and K a is what's known as wave
+ 
+
+ align:start position:0%
+KX and K a is what's known as wave
+number is 2 pi over the wavelength 2 pi
+
+ align:start position:0%
+number is 2 pi over the wavelength 2 pi
+ 
+
+ align:start position:0%
+number is 2 pi over the wavelength 2 pi
+over Lambda and the wavelength then is
+
+ align:start position:0%
+over Lambda and the wavelength then is
+ 
+
+ align:start position:0%
+over Lambda and the wavelength then is
+for example from here to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here now the velocity I'm going pick a
+
+ align:start position:0%
+here now the velocity I'm going pick a
+ 
+
+ align:start position:0%
+here now the velocity I'm going pick a
+point here the velocity at any point we
+
+ align:start position:0%
+point here the velocity at any point we
+ 
+
+ align:start position:0%
+point here the velocity at any point we
+know is just the tangent to the path so
+
+ align:start position:0%
+know is just the tangent to the path so
+ 
+
+ align:start position:0%
+know is just the tangent to the path so
+this is the path and this is horizontal
+
+ align:start position:0%
+this is the path and this is horizontal
+ 
+
+ align:start position:0%
+this is the path and this is horizontal
+so you're driving driving down the road
+
+ align:start position:0%
+so you're driving driving down the road
+ 
+
+ align:start position:0%
+so you're driving driving down the road
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this right that's what we're trying to
+
+ align:start position:0%
+this right that's what we're trying to
+ 
+
+ align:start position:0%
+this right that's what we're trying to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+here the gravity is down into the board
+
+ align:start position:0%
+here the gravity is down into the board
+ 
+
+ align:start position:0%
+here the gravity is down into the board
+doesn't really come into into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem so the
+
+ align:start position:0%
+problem so the
+ 
+
+ align:start position:0%
+problem so the
+velocity at any at any time the vector
+
+ align:start position:0%
+velocity at any at any time the vector
+ 
+
+ align:start position:0%
+velocity at any at any time the vector
+we could describe as a magnitude and a
+
+ align:start position:0%
+we could describe as a magnitude and a
+ 
+
+ align:start position:0%
+we could describe as a magnitude and a
+unit Vector we'll call UT which is the
+
+ align:start position:0%
+unit Vector we'll call UT which is the
+ 
+
+ align:start position:0%
+unit Vector we'll call UT which is the
+tangent unit vector and at any instant
+
+ align:start position:0%
+tangent unit vector and at any instant
+ 
+
+ align:start position:0%
+tangent unit vector and at any instant
+in time it's just aligned with the
+
+ align:start position:0%
+in time it's just aligned with the
+ 
+
+ align:start position:0%
+in time it's just aligned with the
+tangent to to the
+
+ align:start position:0%
+tangent to to the
+ 
+
+ align:start position:0%
+tangent to to the
+curve and its
+
+ align:start position:0%
+curve and its
+ 
+
+ align:start position:0%
+curve and its
+perpendicular uh partner is a normal
+
+ align:start position:0%
+perpendicular uh partner is a normal
+ 
+
+ align:start position:0%
+perpendicular uh partner is a normal
+unit Vector which it points inward on
+
+ align:start position:0%
+unit Vector which it points inward on
+ 
+
+ align:start position:0%
+unit Vector which it points inward on
+the curve and this would be unu
+
+ align:start position:0%
+the curve and this would be unu
+ 
+
+ align:start position:0%
+the curve and this would be unu
+n now we're interested in accelerations
+
+ align:start position:0%
+n now we're interested in accelerations
+ 
+
+ align:start position:0%
+n now we're interested in accelerations
+so we'll need to take a derivative of
+
+ align:start position:0%
+so we'll need to take a derivative of
+ 
+
+ align:start position:0%
+so we'll need to take a derivative of
+this but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so let I was going to say put taking
+
+ align:start position:0%
+uh so let I was going to say put taking
+ 
+
+ align:start position:0%
+uh so let I was going to say put taking
+aside but I won't so the acceleration
+
+ align:start position:0%
+aside but I won't so the acceleration
+ 
+
+ align:start position:0%
+aside but I won't so the acceleration
+vector we have to take a derivative of
+
+ align:start position:0%
+vector we have to take a derivative of
+ 
+
+ align:start position:0%
+vector we have to take a derivative of
+this well it's a v do UT plus a v
+
+ align:start position:0%
+this well it's a v do UT plus a v
+ 
+
+ align:start position:0%
+this well it's a v do UT plus a v
+UT
+
+ align:start position:0%
+UT
+ 
+
+ align:start position:0%
+UT
+dot it's a unit vector and we've
+
+ align:start position:0%
+dot it's a unit vector and we've
+ 
+
+ align:start position:0%
+dot it's a unit vector and we've
+encountered this problem before because
+
+ align:start position:0%
+encountered this problem before because
+ 
+
+ align:start position:0%
+encountered this problem before because
+if this rotates the unit Vector has a
+
+ align:start position:0%
+if this rotates the unit Vector has a
+ 
+
+ align:start position:0%
+if this rotates the unit Vector has a
+nonzero derivative because of its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation and the this derivative
+
+ align:start position:0%
+rotation and the this derivative
+ 
+
+ align:start position:0%
+rotation and the this derivative
+of the unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector is given
+
+ align:start position:0%
+Vector is given
+ 
+
+ align:start position:0%
+Vector is given
+by Theta
+
+ align:start position:0%
+by Theta
+ 
+
+ align:start position:0%
+by Theta
+dot u n hat now what's Theta dot
+
+ align:start position:0%
+dot u n hat now what's Theta dot
+ 
+
+ align:start position:0%
+dot u n hat now what's Theta dot
+well on this curve at any instant in
+
+ align:start position:0%
+well on this curve at any instant in
+ 
+
+ align:start position:0%
+well on this curve at any instant in
+time here's
+
+ align:start position:0%
+time here's
+ 
+
+ align:start position:0%
+time here's
+U can't draw arrows today here's your
+
+ align:start position:0%
+U can't draw arrows today here's your
+ 
+
+ align:start position:0%
+U can't draw arrows today here's your
+UT at any instant when you're traveling
+
+ align:start position:0%
+UT at any instant when you're traveling
+ 
+
+ align:start position:0%
+UT at any instant when you're traveling
+Along on a curve you are going around a
+
+ align:start position:0%
+Along on a curve you are going around a
+ 
+
+ align:start position:0%
+Along on a curve you are going around a
+circle of some radius we'll call row so
+
+ align:start position:0%
+circle of some radius we'll call row so
+ 
+
+ align:start position:0%
+circle of some radius we'll call row so
+there's some radius of curvature at any
+
+ align:start position:0%
+there's some radius of curvature at any
+ 
+
+ align:start position:0%
+there's some radius of curvature at any
+instant in
+
+ align:start position:0%
+instant in
+ 
+
+ align:start position:0%
+instant in
+time and that radius of as you drive
+
+ align:start position:0%
+time and that radius of as you drive
+ 
+
+ align:start position:0%
+time and that radius of as you drive
+along in little time delta T you go
+
+ align:start position:0%
+along in little time delta T you go
+ 
+
+ align:start position:0%
+along in little time delta T you go
+forward and amount
+
+ align:start position:0%
+forward and amount
+ 
+
+ align:start position:0%
+forward and amount
+row Theta
+
+ align:start position:0%
+row Theta
+ 
+
+ align:start position:0%
+row Theta
+dot is the velocity at which you're
+
+ align:start position:0%
+dot is the velocity at which you're
+ 
+
+ align:start position:0%
+dot is the velocity at which you're
+traveling tangent to the
+
+ align:start position:0%
+traveling tangent to the
+ 
+
+ align:start position:0%
+traveling tangent to the
+curve so this is an there's an angle in
+
+ align:start position:0%
+curve so this is an there's an angle in
+ 
+
+ align:start position:0%
+curve so this is an there's an angle in
+here so in here there's some Delta you
+
+ align:start position:0%
+here so in here there's some Delta you
+ 
+
+ align:start position:0%
+here so in here there's some Delta you
+advance some Delta Theta so r r Omega is
+
+ align:start position:0%
+advance some Delta Theta so r r Omega is
+ 
+
+ align:start position:0%
+advance some Delta Theta so r r Omega is
+a velocity right so row Theta dot is a
+
+ align:start position:0%
+a velocity right so row Theta dot is a
+ 
+
+ align:start position:0%
+a velocity right so row Theta dot is a
+velocity and that gives you this
+
+ align:start position:0%
+velocity and that gives you this
+ 
+
+ align:start position:0%
+velocity and that gives you this
+velocity magnitude B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we've gone through I'm not
+
+ align:start position:0%
+okay and we've gone through I'm not
+ 
+
+ align:start position:0%
+okay and we've gone through I'm not
+going to go through that little deriv
+
+ align:start position:0%
+going to go through that little deriv
+ 
+
+ align:start position:0%
+going to go through that little deriv
+that little argument before but the the
+
+ align:start position:0%
+that little argument before but the the
+ 
+
+ align:start position:0%
+that little argument before but the the
+change in direction of this unit Vector
+
+ align:start position:0%
+change in direction of this unit Vector
+ 
+
+ align:start position:0%
+change in direction of this unit Vector
+UT when you go forward a little bit is
+
+ align:start position:0%
+UT when you go forward a little bit is
+ 
+
+ align:start position:0%
+UT when you go forward a little bit is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+inward un n by an amount uh row Theta
+
+ align:start position:0%
+inward un n by an amount uh row Theta
+ 
+
+ align:start position:0%
+inward un n by an amount uh row Theta
+dot or by an amount Theta dot one times
+
+ align:start position:0%
+dot or by an amount Theta dot one times
+ 
+
+ align:start position:0%
+dot or by an amount Theta dot one times
+Theta dot so we've I'm not going to do
+
+ align:start position:0%
+Theta dot so we've I'm not going to do
+ 
+
+ align:start position:0%
+Theta dot so we've I'm not going to do
+that piece of the derivative before but
+
+ align:start position:0%
+that piece of the derivative before but
+ 
+
+ align:start position:0%
+that piece of the derivative before but
+here is this derivative of the unit
+
+ align:start position:0%
+here is this derivative of the unit
+ 
+
+ align:start position:0%
+here is this derivative of the unit
+Vector it's Theta do unu n so if we
+
+ align:start position:0%
+Vector it's Theta do unu n so if we
+ 
+
+ align:start position:0%
+Vector it's Theta do unu n so if we
+substitute those back in here we can get
+
+ align:start position:0%
+substitute those back in here we can get
+ 
+
+ align:start position:0%
+substitute those back in here we can get
+an expression for our acceleration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is just the acceleration along the
+
+ align:start position:0%
+this is just the acceleration along the
+ 
+
+ align:start position:0%
+this is just the acceleration along the
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+plus v Theta dot u
+
+ align:start position:0%
+plus v Theta dot u
+ 
+
+ align:start position:0%
+plus v Theta dot u
+n and then we need to take into account
+
+ align:start position:0%
+n and then we need to take into account
+ 
+
+ align:start position:0%
+n and then we need to take into account
+the fact that we know that
+
+ align:start position:0%
+the fact that we know that
+ 
+
+ align:start position:0%
+the fact that we know that
+V the magnitude of the Velocity the
+
+ align:start position:0%
+V the magnitude of the Velocity the
+ 
+
+ align:start position:0%
+V the magnitude of the Velocity the
+speed in other words is row Theta
+
+ align:start position:0%
+speed in other words is row Theta
+ 
+
+ align:start position:0%
+speed in other words is row Theta
+Dot and that means Theta Dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is V over
+
+ align:start position:0%
+is V over
+ 
+
+ align:start position:0%
+is V over
+row so if we plug that in up here then
+
+ align:start position:0%
+row so if we plug that in up here then
+ 
+
+ align:start position:0%
+row so if we plug that in up here then
+we get an A final expression for our
+
+ align:start position:0%
+we get an A final expression for our
+ 
+
+ align:start position:0%
+we get an A final expression for our
+acceleration V do
+
+ align:start position:0%
+acceleration V do
+ 
+
+ align:start position:0%
+acceleration V do
+UT
+
+ align:start position:0%
+UT
+ 
+
+ align:start position:0%
+UT
+plus v^2 over row u
+
+ align:start position:0%
+plus v^2 over row u
+ 
+
+ align:start position:0%
+plus v^2 over row u
+n and that v^2 over row this is a this
+
+ align:start position:0%
+n and that v^2 over row this is a this
+ 
+
+ align:start position:0%
+n and that v^2 over row this is a this
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+centripetal acceleration term you're
+
+ align:start position:0%
+centripetal acceleration term you're
+ 
+
+ align:start position:0%
+centripetal acceleration term you're
+going around a curve there's an
+
+ align:start position:0%
+going around a curve there's an
+ 
+
+ align:start position:0%
+going around a curve there's an
+acceleration inward it's just like as we
+
+ align:start position:0%
+acceleration inward it's just like as we
+ 
+
+ align:start position:0%
+acceleration inward it's just like as we
+did from Polar coordinates from it comes
+
+ align:start position:0%
+did from Polar coordinates from it comes
+ 
+
+ align:start position:0%
+did from Polar coordinates from it comes
+from rotating things well as soon as you
+
+ align:start position:0%
+from rotating things well as soon as you
+ 
+
+ align:start position:0%
+from rotating things well as soon as you
+go around a curve you're going to
+
+ align:start position:0%
+go around a curve you're going to
+ 
+
+ align:start position:0%
+go around a curve you're going to
+generate an acceleration that is of the
+
+ align:start position:0%
+generate an acceleration that is of the
+ 
+
+ align:start position:0%
+generate an acceleration that is of the
+same kind but now we because you tend to
+
+ align:start position:0%
+same kind but now we because you tend to
+ 
+
+ align:start position:0%
+same kind but now we because you tend to
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+speed it's easier to express it this way
+
+ align:start position:0%
+speed it's easier to express it this way
+ 
+
+ align:start position:0%
+speed it's easier to express it this way
+when you're doing these tangent normal
+
+ align:start position:0%
+when you're doing these tangent normal
+ 
+
+ align:start position:0%
+when you're doing these tangent normal
+problems and this is just the
+
+ align:start position:0%
+problems and this is just the
+ 
+
+ align:start position:0%
+problems and this is just the
+acceleration along the path the usual
+
+ align:start position:0%
+acceleration along the path the usual
+ 
+
+ align:start position:0%
+acceleration along the path the usual
+hit the gas pedal and speed up that's
+
+ align:start position:0%
+hit the gas pedal and speed up that's
+ 
+
+ align:start position:0%
+hit the gas pedal and speed up that's
+this term
+
+ align:start position:0%
+this term
+ 
+
+ align:start position:0%
+this term
+okay so the the piece that I didn't have
+
+ align:start position:0%
+okay so the the piece that I didn't have
+ 
+
+ align:start position:0%
+okay so the the piece that I didn't have
+time to put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up last time which is in the book as is
+
+ align:start position:0%
+up last time which is in the book as is
+ 
+
+ align:start position:0%
+up last time which is in the book as is
+this little derivative the derivation of
+
+ align:start position:0%
+this little derivative the derivation of
+ 
+
+ align:start position:0%
+this little derivative the derivation of
+that is one page in the one of the early
+
+ align:start position:0%
+that is one page in the one of the early
+ 
+
+ align:start position:0%
+that is one page in the one of the early
+chapters of the book how do you get
+
+ align:start position:0%
+chapters of the book how do you get
+ 
+
+ align:start position:0%
+chapters of the book how do you get
+row and row when you have y as a
+
+ align:start position:0%
+row and row when you have y as a
+ 
+
+ align:start position:0%
+row and row when you have y as a
+function of X there's just this formula
+
+ align:start position:0%
+function of X there's just this formula
+ 
+
+ align:start position:0%
+function of X there's just this formula
+from mathematics from calculus that says
+
+ align:start position:0%
+from mathematics from calculus that says
+ 
+
+ align:start position:0%
+from mathematics from calculus that says
+row is dy
+
+ align:start position:0%
+row is dy
+ 
+
+ align:start position:0%
+row is dy
+DX 1 + dydx 2ar to the 3es
+
+ align:start position:0%
+DX 1 + dydx 2ar to the 3es
+ 
+
+ align:start position:0%
+DX 1 + dydx 2ar to the 3es
+power all over the magnitude of
+
+ align:start position:0%
+power all over the magnitude of
+ 
+
+ align:start position:0%
+power all over the magnitude of
+d2y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dx2 and you just calculate these
+
+ align:start position:0%
+dx2 and you just calculate these
+ 
+
+ align:start position:0%
+dx2 and you just calculate these
+quantities and plug them in so
+
+ align:start position:0%
+quantities and plug them in so
+ 
+
+ align:start position:0%
+quantities and plug them in so
+for y = a sin KX X then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dydx is a
+
+ align:start position:0%
+dydx is a
+ 
+
+ align:start position:0%
+dydx is a
+k cosine
+
+ align:start position:0%
+k cosine
+ 
+
+ align:start position:0%
+k cosine
+KX and
+
+ align:start position:0%
+KX and
+ 
+
+ align:start position:0%
+KX and
+D2 Y dx^
+
+ align:start position:0%
+D2 Y dx^
+ 
+
+ align:start position:0%
+D2 Y dx^
+2 is minus a k
+
+ align:start position:0%
+2 is minus a k
+ 
+
+ align:start position:0%
+2 is minus a k
+2 sin
+
+ align:start position:0%
+2 sin
+ 
+
+ align:start position:0%
+2 sin
+KX so we now have these two quantities
+
+ align:start position:0%
+KX so we now have these two quantities
+ 
+
+ align:start position:0%
+KX so we now have these two quantities
+we pick a value of x at which we want to
+
+ align:start position:0%
+we pick a value of x at which we want to
+ 
+
+ align:start position:0%
+we pick a value of x at which we want to
+know the answer like
+
+ align:start position:0%
+know the answer like
+ 
+
+ align:start position:0%
+know the answer like
+0.1 so at 0.1 KX is pi over two right
+
+ align:start position:0%
+0.1 so at 0.1 KX is pi over two right
+ 
+
+ align:start position:0%
+0.1 so at 0.1 KX is pi over two right
+because s's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximum X is Lambda over
+
+ align:start position:0%
+maximum X is Lambda over
+ 
+
+ align:start position:0%
+maximum X is Lambda over
+4 KX is Pi /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 sin KX is 1
+
+ align:start position:0%
+2 sin KX is 1
+ 
+
+ align:start position:0%
+2 sin KX is 1
+cosine
+
+ align:start position:0%
+cosine
+ 
+
+ align:start position:0%
+cosine
+KX zero and so we can calculate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row
+
+ align:start position:0%
+row
+ 
+
+ align:start position:0%
+row
+1+
+
+ align:start position:0%
+1+
+ 
+
+ align:start position:0%
+1+
+and dydx the derivative is cosine that's
+
+ align:start position:0%
+and dydx the derivative is cosine that's
+ 
+
+ align:start position:0%
+and dydx the derivative is cosine that's
+zero so this term in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is zero this is to the three halves
+
+ align:start position:0%
+here is zero this is to the three halves
+ 
+
+ align:start position:0%
+here is zero this is to the three halves
+that's pretty easy to calculate this
+
+ align:start position:0%
+that's pretty easy to calculate this
+ 
+
+ align:start position:0%
+that's pretty easy to calculate this
+term down here D2 Y dx^ 2 well s of KX
+
+ align:start position:0%
+term down here D2 Y dx^ 2 well s of KX
+ 
+
+ align:start position:0%
+term down here D2 Y dx^ 2 well s of KX
+is 1 so that's uh minus a^ 2 but this is
+
+ align:start position:0%
+is 1 so that's uh minus a^ 2 but this is
+ 
+
+ align:start position:0%
+is 1 so that's uh minus a^ 2 but this is
+an absolute value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign so this just turns out to be one
+
+ align:start position:0%
+sign so this just turns out to be one
+ 
+
+ align:start position:0%
+sign so this just turns out to be one
+over a k
+
+ align:start position:0%
+over a k
+ 
+
+ align:start position:0%
+over a k
+2 and we plug in some
+
+ align:start position:0%
+2 and we plug in some
+ 
+
+ align:start position:0%
+2 and we plug in some
+numbers I'm going to let
+
+ align:start position:0%
+numbers I'm going to let
+ 
+
+ align:start position:0%
+numbers I'm going to let
+uh my Lambda be 150 m
+
+ align:start position:0%
+uh my Lambda be 150 m
+ 
+
+ align:start position:0%
+uh my Lambda be 150 m
+M my amplitude here that I'm swerving
+
+ align:start position:0%
+M my amplitude here that I'm swerving
+ 
+
+ align:start position:0%
+M my amplitude here that I'm swerving
+back and forth let's make that 5
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m uh we need
+
+ align:start position:0%
+m uh we need
+ 
+
+ align:start position:0%
+m uh we need
+a that's all we need to get row so Row
+
+ align:start position:0%
+a that's all we need to get row so Row
+ 
+
+ align:start position:0%
+a that's all we need to get row so Row
+in this case works out to be
+
+ align:start position:0%
+in this case works out to be
+ 
+
+ align:start position:0%
+in this case works out to be
+114 m so the radius of curvature of this
+
+ align:start position:0%
+114 m so the radius of curvature of this
+ 
+
+ align:start position:0%
+114 m so the radius of curvature of this
+road that I'm driving down at that that
+
+ align:start position:0%
+road that I'm driving down at that that
+ 
+
+ align:start position:0%
+road that I'm driving down at that that
+point right at the peak in the curve is
+
+ align:start position:0%
+point right at the peak in the curve is
+ 
+
+ align:start position:0%
+point right at the peak in the curve is
+114 m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+acceleration that I'm looking for a well
+
+ align:start position:0%
+acceleration that I'm looking for a well
+ 
+
+ align:start position:0%
+acceleration that I'm looking for a well
+it's V
+
+ align:start position:0%
+it's V
+ 
+
+ align:start position:0%
+it's V
+Dot UT and if I'm not accelera I'm not
+
+ align:start position:0%
+Dot UT and if I'm not accelera I'm not
+ 
+
+ align:start position:0%
+Dot UT and if I'm not accelera I'm not
+hitting the gas pedal constant speed
+
+ align:start position:0%
+hitting the gas pedal constant speed
+ 
+
+ align:start position:0%
+hitting the gas pedal constant speed
+I'll let that one be
+
+ align:start position:0%
+I'll let that one be
+ 
+
+ align:start position:0%
+I'll let that one be
+zero and the other one then is v^2 over
+
+ align:start position:0%
+zero and the other one then is v^2 over
+ 
+
+ align:start position:0%
+zero and the other one then is v^2 over
+row in the unu direction and let's let
+
+ align:start position:0%
+row in the unu direction and let's let
+ 
+
+ align:start position:0%
+row in the unu direction and let's let
+V equal
+
+ align:start position:0%
+V equal
+ 
+
+ align:start position:0%
+V equal
+um I have here in my example 20 meters
+
+ align:start position:0%
+um I have here in my example 20 meters
+ 
+
+ align:start position:0%
+um I have here in my example 20 meters
+per
+
+ align:start position:0%
+per
+ 
+
+ align:start position:0%
+per
+second which is about 40 knots and a
+
+ align:start position:0%
+second which is about 40 knots and a
+ 
+
+ align:start position:0%
+second which is about 40 knots and a
+knot is 15% more than a mile per hour so
+
+ align:start position:0%
+knot is 15% more than a mile per hour so
+ 
+
+ align:start position:0%
+knot is 15% more than a mile per hour so
+it's somewhere about 45 miles an hour so
+
+ align:start position:0%
+it's somewhere about 45 miles an hour so
+ 
+
+ align:start position:0%
+it's somewhere about 45 miles an hour so
+a typical Road speed driving down the
+
+ align:start position:0%
+a typical Road speed driving down the
+ 
+
+ align:start position:0%
+a typical Road speed driving down the
+road 20 m/ second now you can plug in
+
+ align:start position:0%
+road 20 m/ second now you can plug in
+ 
+
+ align:start position:0%
+road 20 m/ second now you can plug in
+here you can plug in here and you can
+
+ align:start position:0%
+here you can plug in here and you can
+ 
+
+ align:start position:0%
+here you can plug in here and you can
+find that the
+
+ align:start position:0%
+find that the
+ 
+
+ align:start position:0%
+find that the
+acceleration I work out here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3.51 m/s squar
+
+ align:start position:0%
+3.51 m/s squar
+ 
+
+ align:start position:0%
+3.51 m/s squar
+and in what direction is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it what direction is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration the normal it's in the
+
+ align:start position:0%
+acceleration the normal it's in the
+ 
+
+ align:start position:0%
+acceleration the normal it's in the
+normal direction is it to the inside of
+
+ align:start position:0%
+normal direction is it to the inside of
+ 
+
+ align:start position:0%
+normal direction is it to the inside of
+the curve or the outside of the curve
+
+ align:start position:0%
+the curve or the outside of the curve
+ 
+
+ align:start position:0%
+the curve or the outside of the curve
+inside always to the inside of the curve
+
+ align:start position:0%
+inside always to the inside of the curve
+ 
+
+ align:start position:0%
+inside always to the inside of the curve
+so these tangent this tangent normal
+
+ align:start position:0%
+so these tangent this tangent normal
+ 
+
+ align:start position:0%
+so these tangent this tangent normal
+coordinates are really simple
+
+ align:start position:0%
+coordinates are really simple
+ 
+
+ align:start position:0%
+coordinates are really simple
+coordinates they're they're meant for a
+
+ align:start position:0%
+coordinates they're they're meant for a
+ 
+
+ align:start position:0%
+coordinates they're they're meant for a
+particular kind of simple problem when
+
+ align:start position:0%
+particular kind of simple problem when
+ 
+
+ align:start position:0%
+particular kind of simple problem when
+you know the
+
+ align:start position:0%
+you know the
+ 
+
+ align:start position:0%
+you know the
+path and it's just defined the normal
+
+ align:start position:0%
+path and it's just defined the normal
+ 
+
+ align:start position:0%
+path and it's just defined the normal
+unu is positive always inward to the
+
+ align:start position:0%
+unu is positive always inward to the
+ 
+
+ align:start position:0%
+unu is positive always inward to the
+center of the curve pointing toward
+
+ align:start position:0%
+center of the curve pointing toward
+ 
+
+ align:start position:0%
+center of the curve pointing toward
+where the center of rotation where that
+
+ align:start position:0%
+where the center of rotation where that
+ 
+
+ align:start position:0%
+where the center of rotation where that
+radius of where your radius of curve is
+
+ align:start position:0%
+radius of where your radius of curve is
+ 
+
+ align:start position:0%
+radius of where your radius of curve is
+always pointing at the origin of that
+
+ align:start position:0%
+always pointing at the origin of that
+ 
+
+ align:start position:0%
+always pointing at the origin of that
+radius of your curve okay so G is order
+
+ align:start position:0%
+radius of your curve okay so G is order
+ 
+
+ align:start position:0%
+radius of your curve okay so G is order
+of 10 m/s squared so that's about a
+
+ align:start position:0%
+of 10 m/s squared so that's about a
+ 
+
+ align:start position:0%
+of 10 m/s squared so that's about a
+third of a g would
+
+ align:start position:0%
+third of a g would
+ 
+
+ align:start position:0%
+third of a g would
+you third of a g enough to notice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah absolutely you get you get pushed
+
+ align:start position:0%
+yeah absolutely you get you get pushed
+ 
+
+ align:start position:0%
+yeah absolutely you get you get pushed
+to the side of the car if you do that
+
+ align:start position:0%
+to the side of the car if you do that
+ 
+
+ align:start position:0%
+to the side of the car if you do that
+okay all
+
+ align:start position:0%
+okay all
+ 
+
+ align:start position:0%
+okay all
+right so let's we'll any questions about
+
+ align:start position:0%
+right so let's we'll any questions about
+ 
+
+ align:start position:0%
+right so let's we'll any questions about
+that I'm going to move on next if not
+
+ align:start position:0%
+that I'm going to move on next if not
+ 
+
+ align:start position:0%
+that I'm going to move on next if not
+I'm going to move on to linear impulse
+
+ align:start position:0%
+I'm going to move on to linear impulse
+ 
+
+ align:start position:0%
+I'm going to move on to linear impulse
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum and this will be a quick review
+
+ align:start position:0%
+momentum and this will be a quick review
+ 
+
+ align:start position:0%
+momentum and this will be a quick review
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is is consists of the physics the
+
+ align:start position:0%
+this is is consists of the physics the
+ 
+
+ align:start position:0%
+this is is consists of the physics the
+kind of physics that you've done lots of
+
+ align:start position:0%
+kind of physics that you've done lots of
+ 
+
+ align:start position:0%
+kind of physics that you've done lots of
+times so I'm going to hit it quickly and
+
+ align:start position:0%
+times so I'm going to hit it quickly and
+ 
+
+ align:start position:0%
+times so I'm going to hit it quickly and
+then move on to angular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum so we know for a particle this
+
+ align:start position:0%
+momentum so we know for a particle this
+ 
+
+ align:start position:0%
+momentum so we know for a particle this
+is what Newton told us you've got a
+
+ align:start position:0%
+is what Newton told us you've got a
+ 
+
+ align:start position:0%
+is what Newton told us you've got a
+particle here that's some mass m we know
+
+ align:start position:0%
+particle here that's some mass m we know
+ 
+
+ align:start position:0%
+particle here that's some mass m we know
+for a part it has some external forces
+
+ align:start position:0%
+for a part it has some external forces
+ 
+
+ align:start position:0%
+for a part it has some external forces
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it we know for a particle that the sum
+
+ align:start position:0%
+it we know for a particle that the sum
+ 
+
+ align:start position:0%
+it we know for a particle that the sum
+of these external forces a vector
+
+ align:start position:0%
+of these external forces a vector
+ 
+
+ align:start position:0%
+of these external forces a vector
+sum is equal to the mass times the
+
+ align:start position:0%
+sum is equal to the mass times the
+ 
+
+ align:start position:0%
+sum is equal to the mass times the
+acceleration for the particle Newton
+
+ align:start position:0%
+acceleration for the particle Newton
+ 
+
+ align:start position:0%
+acceleration for the particle Newton
+Second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Law and that's the mass times the
+
+ align:start position:0%
+Law and that's the mass times the
+ 
+
+ align:start position:0%
+Law and that's the mass times the
+derivative of the Velocity with respect
+
+ align:start position:0%
+derivative of the Velocity with respect
+ 
+
+ align:start position:0%
+derivative of the Velocity with respect
+to time that's where we get
+
+ align:start position:0%
+to time that's where we get
+ 
+
+ align:start position:0%
+to time that's where we get
+acceleration so this formula we can just
+
+ align:start position:0%
+acceleration so this formula we can just
+ 
+
+ align:start position:0%
+acceleration so this formula we can just
+rearrange the DTs a little bit so the
+
+ align:start position:0%
+rearrange the DTs a little bit so the
+ 
+
+ align:start position:0%
+rearrange the DTs a little bit so the
+summation of the forces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT is M DV and I want to integrate
+
+ align:start position:0%
+DT is M DV and I want to integrate
+ 
+
+ align:start position:0%
+DT is M DV and I want to integrate
+these so if I integrate this over time
+
+ align:start position:0%
+these so if I integrate this over time
+ 
+
+ align:start position:0%
+these so if I integrate this over time
+from some T1 to T2 this equality says
+
+ align:start position:0%
+from some T1 to T2 this equality says
+ 
+
+ align:start position:0%
+from some T1 to T2 this equality says
+we're going to find some change in
+
+ align:start position:0%
+we're going to find some change in
+ 
+
+ align:start position:0%
+we're going to find some change in
+velocity from V1 to
+
+ align:start position:0%
+velocity from V1 to
+ 
+
+ align:start position:0%
+velocity from V1 to
+V2 and this is our this is kind of the
+
+ align:start position:0%
+V2 and this is our this is kind of the
+ 
+
+ align:start position:0%
+V2 and this is our this is kind of the
+beginning of our impulse momentum
+
+ align:start position:0%
+beginning of our impulse momentum
+ 
+
+ align:start position:0%
+beginning of our impulse momentum
+relationship we tend to call the
+
+ align:start position:0%
+relationship we tend to call the
+ 
+
+ align:start position:0%
+relationship we tend to call the
+integration of forces over time
+
+ align:start position:0%
+integration of forces over time
+ 
+
+ align:start position:0%
+integration of forces over time
+impulse and if you have a nonzero
+
+ align:start position:0%
+impulse and if you have a nonzero
+ 
+
+ align:start position:0%
+impulse and if you have a nonzero
+impulse that leads to a change in the
+
+ align:start position:0%
+impulse that leads to a change in the
+ 
+
+ align:start position:0%
+impulse that leads to a change in the
+linear momentum
+
+ align:start position:0%
+linear momentum
+ 
+
+ align:start position:0%
+linear momentum
+okay so when you carry out
+
+ align:start position:0%
+okay so when you carry out
+ 
+
+ align:start position:0%
+okay so when you carry out
+so so they're writing this a little bit
+
+ align:start position:0%
+so so they're writing this a little bit
+ 
+
+ align:start position:0%
+so so they're writing this a little bit
+different way you can do summation
+
+ align:start position:0%
+different way you can do summation
+ 
+
+ align:start position:0%
+different way you can do summation
+because these are vectors and we have
+
+ align:start position:0%
+because these are vectors and we have
+ 
+
+ align:start position:0%
+because these are vectors and we have
+rules about vectors you can bring the
+
+ align:start position:0%
+rules about vectors you can bring the
+ 
+
+ align:start position:0%
+rules about vectors you can bring the
+summation outside of the integral
+
+ align:start position:0%
+summation outside of the integral
+ 
+
+ align:start position:0%
+summation outside of the integral
+so that this says the
+
+ align:start position:0%
+so that this says the
+ 
+
+ align:start position:0%
+so that this says the
+summation of the integral from T1 to T2
+
+ align:start position:0%
+summation of the integral from T1 to T2
+ 
+
+ align:start position:0%
+summation of the integral from T1 to T2
+of these external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forces is just
+
+ align:start position:0%
+forces is just
+ 
+
+ align:start position:0%
+forces is just
+m V2 minus mv1 because the integral on
+
+ align:start position:0%
+m V2 minus mv1 because the integral on
+ 
+
+ align:start position:0%
+m V2 minus mv1 because the integral on
+the right hand side
+
+ align:start position:0%
+the right hand side
+ 
+
+ align:start position:0%
+the right hand side
+is really
+
+ align:start position:0%
+is really
+ 
+
+ align:start position:0%
+is really
+simple and we'll finally State this in a
+
+ align:start position:0%
+simple and we'll finally State this in a
+ 
+
+ align:start position:0%
+simple and we'll finally State this in a
+uh way that we most commonly use it
+
+ align:start position:0%
+uh way that we most commonly use it
+ 
+
+ align:start position:0%
+uh way that we most commonly use it
+moving this term to the left so you
+
+ align:start position:0%
+moving this term to the left so you
+ 
+
+ align:start position:0%
+moving this term to the left so you
+start off with an initial momentum
+
+ align:start position:0%
+start off with an initial momentum
+ 
+
+ align:start position:0%
+start off with an initial momentum
+mv1 you add to
+
+ align:start position:0%
+mv1 you add to
+ 
+
+ align:start position:0%
+mv1 you add to
+it the summation of the impulses that
+
+ align:start position:0%
+it the summation of the impulses that
+ 
+
+ align:start position:0%
+it the summation of the impulses that
+you that occur over
+
+ align:start position:0%
+you that occur over
+ 
+
+ align:start position:0%
+you that occur over
+time T1 to T2 of the external
+
+ align:start position:0%
+time T1 to T2 of the external
+ 
+
+ align:start position:0%
+time T1 to T2 of the external
+forces and you get the final momentum
+
+ align:start position:0%
+forces and you get the final momentum
+ 
+
+ align:start position:0%
+forces and you get the final momentum
+mv2 and this is the way you usually use
+
+ align:start position:0%
+mv2 and this is the way you usually use
+ 
+
+ align:start position:0%
+mv2 and this is the way you usually use
+the formula so what happens if there's
+
+ align:start position:0%
+the formula so what happens if there's
+ 
+
+ align:start position:0%
+the formula so what happens if there's
+no external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forces that's that's where we get the
+
+ align:start position:0%
+forces that's that's where we get the
+ 
+
+ align:start position:0%
+forces that's that's where we get the
+law of conservation of momentum if there
+
+ align:start position:0%
+law of conservation of momentum if there
+ 
+
+ align:start position:0%
+law of conservation of momentum if there
+are no external forces on the particle
+
+ align:start position:0%
+are no external forces on the particle
+ 
+
+ align:start position:0%
+are no external forces on the particle
+the momentum doesn't change and mv1 is
+
+ align:start position:0%
+the momentum doesn't change and mv1 is
+ 
+
+ align:start position:0%
+the momentum doesn't change and mv1 is
+got to be equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mv2 whoops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just a a really trivial
+
+ align:start position:0%
+so just a a really trivial
+ 
+
+ align:start position:0%
+so just a a really trivial
+example drawing for something that we've
+
+ align:start position:0%
+example drawing for something that we've
+ 
+
+ align:start position:0%
+example drawing for something that we've
+done before you get the block sliding
+
+ align:start position:0%
+done before you get the block sliding
+ 
+
+ align:start position:0%
+done before you get the block sliding
+down the
+
+ align:start position:0%
+down the
+ 
+
+ align:start position:0%
+down the
+hill draw your free body
+
+ align:start position:0%
+hill draw your free body
+ 
+
+ align:start position:0%
+hill draw your free body
+diagram got
+
+ align:start position:0%
+diagram got
+ 
+
+ align:start position:0%
+diagram got
+friction got
+
+ align:start position:0%
+friction got
+ 
+
+ align:start position:0%
+friction got
+gravity got a normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+force and we'll set ourselves up with a
+
+ align:start position:0%
+force and we'll set ourselves up with a
+ 
+
+ align:start position:0%
+force and we'll set ourselves up with a
+coordinat system aligned with the motion
+
+ align:start position:0%
+coordinat system aligned with the motion
+ 
+
+ align:start position:0%
+coordinat system aligned with the motion
+we're interested in so this is an
+
+ align:start position:0%
+we're interested in so this is an
+ 
+
+ align:start position:0%
+we're interested in so this is an
+inertial
+
+ align:start position:0%
+inertial
+ 
+
+ align:start position:0%
+inertial
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XY and we've done this problem before so
+
+ align:start position:0%
+XY and we've done this problem before so
+ 
+
+ align:start position:0%
+XY and we've done this problem before so
+we said the summation we found out that
+
+ align:start position:0%
+we said the summation we found out that
+ 
+
+ align:start position:0%
+we said the summation we found out that
+the summation of the
+
+ align:start position:0%
+the summation of the
+ 
+
+ align:start position:0%
+the summation of the
+forces in the X Direction and ah this is
+
+ align:start position:0%
+forces in the X Direction and ah this is
+ 
+
+ align:start position:0%
+forces in the X Direction and ah this is
+a good moment to take an aside for a
+
+ align:start position:0%
+a good moment to take an aside for a
+ 
+
+ align:start position:0%
+a good moment to take an aside for a
+second this was a
+
+ align:start position:0%
+second this was a
+ 
+
+ align:start position:0%
+second this was a
+vector expression but you can break it
+
+ align:start position:0%
+vector expression but you can break it
+ 
+
+ align:start position:0%
+vector expression but you can break it
+you can implement it you can break it
+
+ align:start position:0%
+you can implement it you can break it
+ 
+
+ align:start position:0%
+you can implement it you can break it
+down into its individ idual Vector
+
+ align:start position:0%
+down into its individ idual Vector
+ 
+
+ align:start position:0%
+down into its individ idual Vector
+components so that equation gives you
+
+ align:start position:0%
+components so that equation gives you
+ 
+
+ align:start position:0%
+components so that equation gives you
+for particles gives you
+
+ align:start position:0%
+for particles gives you
+ 
+
+ align:start position:0%
+for particles gives you
+three sub equations one in the X one in
+
+ align:start position:0%
+three sub equations one in the X one in
+ 
+
+ align:start position:0%
+three sub equations one in the X one in
+the Y one in the Z and you can use them
+
+ align:start position:0%
+the Y one in the Z and you can use them
+ 
+
+ align:start position:0%
+the Y one in the Z and you can use them
+each independently so in this case we're
+
+ align:start position:0%
+each independently so in this case we're
+ 
+
+ align:start position:0%
+each independently so in this case we're
+going to use the only need the X
+
+ align:start position:0%
+going to use the only need the X
+ 
+
+ align:start position:0%
+going to use the only need the X
+component in order to do the problem so
+
+ align:start position:0%
+component in order to do the problem so
+ 
+
+ align:start position:0%
+component in order to do the problem so
+the sum of the forces in the X Direction
+
+ align:start position:0%
+the sum of the forces in the X Direction
+ 
+
+ align:start position:0%
+the sum of the forces in the X Direction
+now and this problem we've we which we
+
+ align:start position:0%
+now and this problem we've we which we
+ 
+
+ align:start position:0%
+now and this problem we've we which we
+have done
+
+ align:start position:0%
+have done
+ 
+
+ align:start position:0%
+have done
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+mg sin Theta that component of gravity
+
+ align:start position:0%
+mg sin Theta that component of gravity
+ 
+
+ align:start position:0%
+mg sin Theta that component of gravity
+pulling it down the hip
+
+ align:start position:0%
+pulling it down the hip
+ 
+
+ align:start position:0%
+pulling it down the hip
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+mu mg cosine Theta and that's the
+
+ align:start position:0%
+mu mg cosine Theta and that's the
+ 
+
+ align:start position:0%
+mu mg cosine Theta and that's the
+friction and none of these are functions
+
+ align:start position:0%
+friction and none of these are functions
+ 
+
+ align:start position:0%
+friction and none of these are functions
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+time so that whole thing is just some
+
+ align:start position:0%
+time so that whole thing is just some
+ 
+
+ align:start position:0%
+time so that whole thing is just some
+constant I'll just call it
+
+ align:start position:0%
+constant I'll just call it
+ 
+
+ align:start position:0%
+constant I'll just call it
+K right so the total forces on this
+
+ align:start position:0%
+K right so the total forces on this
+ 
+
+ align:start position:0%
+K right so the total forces on this
+system in the X direction is just some
+
+ align:start position:0%
+system in the X direction is just some
+ 
+
+ align:start position:0%
+system in the X direction is just some
+constant and that makes this integral up
+
+ align:start position:0%
+constant and that makes this integral up
+ 
+
+ align:start position:0%
+constant and that makes this integral up
+here pretty trivial to uh Implement so
+
+ align:start position:0%
+here pretty trivial to uh Implement so
+ 
+
+ align:start position:0%
+here pretty trivial to uh Implement so
+now we can say that m
+
+ align:start position:0%
+now we can say that m
+ 
+
+ align:start position:0%
+now we can say that m
+V1 I'll just make it v1x to emphasize
+
+ align:start position:0%
+V1 I'll just make it v1x to emphasize
+ 
+
+ align:start position:0%
+V1 I'll just make it v1x to emphasize
+that integral from zero or T1 to T2 but
+
+ align:start position:0%
+that integral from zero or T1 to T2 but
+ 
+
+ align:start position:0%
+that integral from zero or T1 to T2 but
+I'm going to let T1 be zero usually
+
+ align:start position:0%
+I'm going to let T1 be zero usually
+ 
+
+ align:start position:0%
+I'm going to let T1 be zero usually
+makes it problems easier so from Zer to
+
+ align:start position:0%
+makes it problems easier so from Zer to
+ 
+
+ align:start position:0%
+makes it problems easier so from Zer to
+t 0 to T of
+
+ align:start position:0%
+t 0 to T of
+ 
+
+ align:start position:0%
+t 0 to T of
+kdt equals
+
+ align:start position:0%
+kdt equals
+ 
+
+ align:start position:0%
+kdt equals
+mv2 I can't write this morning in the X
+
+ align:start position:0%
+mv2 I can't write this morning in the X
+ 
+
+ align:start position:0%
+mv2 I can't write this morning in the X
+Direction and if V1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is zero starts off at zero
+
+ align:start position:0%
+X is zero starts off at zero
+ 
+
+ align:start position:0%
+X is zero starts off at zero
+time and zero velocity when you let it
+
+ align:start position:0%
+time and zero velocity when you let it
+ 
+
+ align:start position:0%
+time and zero velocity when you let it
+go to start with then you this then this
+
+ align:start position:0%
+go to start with then you this then this
+ 
+
+ align:start position:0%
+go to start with then you this then this
+term will go away and we can just
+
+ align:start position:0%
+term will go away and we can just
+ 
+
+ align:start position:0%
+term will go away and we can just
+implement this integral and the integral
+
+ align:start position:0%
+implement this integral and the integral
+ 
+
+ align:start position:0%
+implement this integral and the integral
+of kdt
+
+ align:start position:0%
+of kdt
+ 
+
+ align:start position:0%
+of kdt
+is KT right so this says then
+
+ align:start position:0%
+is KT right so this says then
+ 
+
+ align:start position:0%
+is KT right so this says then
+that KT evaluated from zero to
+
+ align:start position:0%
+that KT evaluated from zero to
+ 
+
+ align:start position:0%
+that KT evaluated from zero to
+some time that we want to know the
+
+ align:start position:0%
+some time that we want to know the
+ 
+
+ align:start position:0%
+some time that we want to know the
+answer is m
+
+ align:start position:0%
+answer is m
+ 
+
+ align:start position:0%
+answer is m
+V2 in the X Direction and so let's
+
+ align:start position:0%
+V2 in the X Direction and so let's
+ 
+
+ align:start position:0%
+V2 in the X Direction and so let's
+let T = 3
+
+ align:start position:0%
+let T = 3
+ 
+
+ align:start position:0%
+let T = 3
+seconds you find out that
+
+ align:start position:0%
+seconds you find out that
+ 
+
+ align:start position:0%
+seconds you find out that
+v2x
+
+ align:start position:0%
+v2x
+ 
+
+ align:start position:0%
+v2x
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+3 K Over
+
+ align:start position:0%
+3 K Over
+ 
+
+ align:start position:0%
+3 K Over
+M
+
+ align:start position:0%
+M
+ 
+
+ align:start position:0%
+M
+right and in this problem then that
+
+ align:start position:0%
+right and in this problem then that
+ 
+
+ align:start position:0%
+right and in this problem then that
+looks like 3 G
+
+ align:start position:0%
+looks like 3 G
+ 
+
+ align:start position:0%
+looks like 3 G
+sin Theta
+
+ align:start position:0%
+sin Theta
+ 
+
+ align:start position:0%
+sin Theta
+minus mu cosine Theta so this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really a trivial almost trivial example
+
+ align:start position:0%
+really a trivial almost trivial example
+ 
+
+ align:start position:0%
+really a trivial almost trivial example
+it's not a hard example but it
+
+ align:start position:0%
+it's not a hard example but it
+ 
+
+ align:start position:0%
+it's not a hard example but it
+emphasizes all of the key points in the
+
+ align:start position:0%
+emphasizes all of the key points in the
+ 
+
+ align:start position:0%
+emphasizes all of the key points in the
+problem start off with a vector equation
+
+ align:start position:0%
+problem start off with a vector equation
+ 
+
+ align:start position:0%
+problem start off with a vector equation
+you can apply it in any one of the three
+
+ align:start position:0%
+you can apply it in any one of the three
+ 
+
+ align:start position:0%
+you can apply it in any one of the three
+Vector d three Vector component
+
+ align:start position:0%
+Vector d three Vector component
+ 
+
+ align:start position:0%
+Vector d three Vector component
+directions you integrate the forces the
+
+ align:start position:0%
+directions you integrate the forces the
+ 
+
+ align:start position:0%
+directions you integrate the forces the
+sum of the forces on the object in that
+
+ align:start position:0%
+sum of the forces on the object in that
+ 
+
+ align:start position:0%
+sum of the forces on the object in that
+direction Direction over time and you
+
+ align:start position:0%
+direction Direction over time and you
+ 
+
+ align:start position:0%
+direction Direction over time and you
+apply the impulse momentum formula and
+
+ align:start position:0%
+apply the impulse momentum formula and
+ 
+
+ align:start position:0%
+apply the impulse momentum formula and
+you get the answer you can do that so
+
+ align:start position:0%
+you get the answer you can do that so
+ 
+
+ align:start position:0%
+you get the answer you can do that so
+that basic step-by-step process is how
+
+ align:start position:0%
+that basic step-by-step process is how
+ 
+
+ align:start position:0%
+that basic step-by-step process is how
+you basically most impulse momentum
+
+ align:start position:0%
+you basically most impulse momentum
+ 
+
+ align:start position:0%
+you basically most impulse momentum
+problems are done and if there's no
+
+ align:start position:0%
+problems are done and if there's no
+ 
+
+ align:start position:0%
+problems are done and if there's no
+forces then you have conservation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum okay so let's do uh there's
+
+ align:start position:0%
+momentum okay so let's do uh there's
+ 
+
+ align:start position:0%
+momentum okay so let's do uh there's
+this was for particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just a
+
+ align:start position:0%
+just a
+ 
+
+ align:start position:0%
+just a
+quick reminder of we need to ask
+
+ align:start position:0%
+quick reminder of we need to ask
+ 
+
+ align:start position:0%
+quick reminder of we need to ask
+ourselves does this apply to groups of
+
+ align:start position:0%
+ourselves does this apply to groups of
+ 
+
+ align:start position:0%
+ourselves does this apply to groups of
+particles systems of particles well
+
+ align:start position:0%
+particles systems of particles well
+ 
+
+ align:start position:0%
+particles systems of particles well
+remember that we said if you've got a
+
+ align:start position:0%
+remember that we said if you've got a
+ 
+
+ align:start position:0%
+remember that we said if you've got a
+bunch of
+
+ align:start position:0%
+bunch of
+ 
+
+ align:start position:0%
+bunch of
+particles a
+
+ align:start position:0%
+particles a
+ 
+
+ align:start position:0%
+particles a
+system all of these are the M
+
+ align:start position:0%
+system all of these are the M
+ 
+
+ align:start position:0%
+system all of these are the M
+eyes we've already figured out that the
+
+ align:start position:0%
+eyes we've already figured out that the
+ 
+
+ align:start position:0%
+eyes we've already figured out that the
+total mass of the system times the
+
+ align:start position:0%
+total mass of the system times the
+ 
+
+ align:start position:0%
+total mass of the system times the
+velocity of the center of mass this is G
+
+ align:start position:0%
+velocity of the center of mass this is G
+ 
+
+ align:start position:0%
+velocity of the center of mass this is G
+is my center of
+
+ align:start position:0%
+is my center of
+ 
+
+ align:start position:0%
+is my center of
+mass with respect to
+
+ align:start position:0%
+mass with respect to
+ 
+
+ align:start position:0%
+mass with respect to
+my inertial
+
+ align:start position:0%
+my inertial
+ 
+
+ align:start position:0%
+my inertial
+frame so this is the momentum of the
+
+ align:start position:0%
+frame so this is the momentum of the
+ 
+
+ align:start position:0%
+frame so this is the momentum of the
+system that was just the summation of
+
+ align:start position:0%
+system that was just the summation of
+ 
+
+ align:start position:0%
+system that was just the summation of
+the individual Mi VI I with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O and further more we took the
+
+ align:start position:0%
+O and further more we took the
+ 
+
+ align:start position:0%
+O and further more we took the
+derivative of this so this is the
+
+ align:start position:0%
+derivative of this so this is the
+ 
+
+ align:start position:0%
+derivative of this so this is the
+momentum of the system the time
+
+ align:start position:0%
+momentum of the system the time
+ 
+
+ align:start position:0%
+momentum of the system the time
+derivative of the momentum should be the
+
+ align:start position:0%
+derivative of the momentum should be the
+ 
+
+ align:start position:0%
+derivative of the momentum should be the
+external forces so that we were able to
+
+ align:start position:0%
+external forces so that we were able to
+ 
+
+ align:start position:0%
+external forces so that we were able to
+by taking that derivative you get Mt the
+
+ align:start position:0%
+by taking that derivative you get Mt the
+ 
+
+ align:start position:0%
+by taking that derivative you get Mt the
+total masstimes v g with respect to O
+
+ align:start position:0%
+total masstimes v g with respect to O
+ 
+
+ align:start position:0%
+total masstimes v g with respect to O
+DOT and that
+
+ align:start position:0%
+DOT and that
+ 
+
+ align:start position:0%
+DOT and that
+had better give you be equal to the
+
+ align:start position:0%
+had better give you be equal to the
+ 
+
+ align:start position:0%
+had better give you be equal to the
+summation of the
+
+ align:start position:0%
+summation of the
+ 
+
+ align:start position:0%
+summation of the
+external forces
+
+ align:start position:0%
+external forces
+ 
+
+ align:start position:0%
+external forces
+on all the particles because you can do
+
+ align:start position:0%
+on all the particles because you can do
+ 
+
+ align:start position:0%
+on all the particles because you can do
+it one particle at a time and they all
+
+ align:start position:0%
+it one particle at a time and they all
+ 
+
+ align:start position:0%
+it one particle at a time and they all
+add each each of these particles has
+
+ align:start position:0%
+add each each of these particles has
+ 
+
+ align:start position:0%
+add each each of these particles has
+forces you sum them all up you get these
+
+ align:start position:0%
+forces you sum them all up you get these
+ 
+
+ align:start position:0%
+forces you sum them all up you get these
+forces
+
+ align:start position:0%
+forces
+ 
+
+ align:start position:0%
+forces
+and this is this allows you to say that
+
+ align:start position:0%
+and this is this allows you to say that
+ 
+
+ align:start position:0%
+and this is this allows you to say that
+the sum of all of the external forces on
+
+ align:start position:0%
+the sum of all of the external forces on
+ 
+
+ align:start position:0%
+the sum of all of the external forces on
+the system is equal to the total mass of
+
+ align:start position:0%
+the system is equal to the total mass of
+ 
+
+ align:start position:0%
+the system is equal to the total mass of
+the system times the acceleration of the
+
+ align:start position:0%
+the system times the acceleration of the
+ 
+
+ align:start position:0%
+the system times the acceleration of the
+center of
+
+ align:start position:0%
+center of
+ 
+
+ align:start position:0%
+center of
+mass so this formula now can it looks
+
+ align:start position:0%
+mass so this formula now can it looks
+ 
+
+ align:start position:0%
+mass so this formula now can it looks
+very similar to where we started with
+
+ align:start position:0%
+very similar to where we started with
+ 
+
+ align:start position:0%
+very similar to where we started with
+this little derivation for a particle
+
+ align:start position:0%
+this little derivation for a particle
+ 
+
+ align:start position:0%
+this little derivation for a particle
+you can now say that the summation this
+
+ align:start position:0%
+you can now say that the summation this
+ 
+
+ align:start position:0%
+you can now say that the summation this
+all leads to the
+
+ align:start position:0%
+all leads to the
+ 
+
+ align:start position:0%
+all leads to the
+summation of the integral from T1 to
+
+ align:start position:0%
+summation of the integral from T1 to
+ 
+
+ align:start position:0%
+summation of the integral from T1 to
+T2 of all of
+
+ align:start position:0%
+T2 of all of
+ 
+
+ align:start position:0%
+T2 of all of
+these forces over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time gives you the
+
+ align:start position:0%
+time gives you the
+ 
+
+ align:start position:0%
+time gives you the
+change in the total linear momentum of
+
+ align:start position:0%
+change in the total linear momentum of
+ 
+
+ align:start position:0%
+change in the total linear momentum of
+the system system v g with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+o1 two rather minus VG with respect to
+
+ align:start position:0%
+o1 two rather minus VG with respect to
+ 
+
+ align:start position:0%
+o1 two rather minus VG with respect to
+o 2 the second one so this is exactly
+
+ align:start position:0%
+o 2 the second one so this is exactly
+ 
+
+ align:start position:0%
+o 2 the second one so this is exactly
+the same kind of formulation the change
+
+ align:start position:0%
+the same kind of formulation the change
+ 
+
+ align:start position:0%
+the same kind of formulation the change
+in the linear momentum of the
+
+ align:start position:0%
+in the linear momentum of the
+ 
+
+ align:start position:0%
+in the linear momentum of the
+system is equal to the integral of the
+
+ align:start position:0%
+system is equal to the integral of the
+ 
+
+ align:start position:0%
+system is equal to the integral of the
+forces on the system over time so the
+
+ align:start position:0%
+forces on the system over time so the
+ 
+
+ align:start position:0%
+forces on the system over time so the
+impulse to the system so it all this
+
+ align:start position:0%
+impulse to the system so it all this
+ 
+
+ align:start position:0%
+impulse to the system so it all this
+allows you to do problems that you might
+
+ align:start position:0%
+allows you to do problems that you might
+ 
+
+ align:start position:0%
+allows you to do problems that you might
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+have thought about before so I've think
+
+ align:start position:0%
+have thought about before so I've think
+ 
+
+ align:start position:0%
+have thought about before so I've think
+about uh something like this I've got an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+old uh back re you know Revolutionary
+
+ align:start position:0%
+old uh back re you know Revolutionary
+ 
+
+ align:start position:0%
+old uh back re you know Revolutionary
+War earlier period
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Canon I can't I'm trying to
+
+ align:start position:0%
+Canon I can't I'm trying to
+ 
+
+ align:start position:0%
+Canon I can't I'm trying to
+draw so here's my Cannon barrel and back
+
+ align:start position:0%
+draw so here's my Cannon barrel and back
+ 
+
+ align:start position:0%
+draw so here's my Cannon barrel and back
+in those days
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+draw a little better job here so we got
+
+ align:start position:0%
+draw a little better job here so we got
+ 
+
+ align:start position:0%
+draw a little better job here so we got
+this cannon sitting here and in the
+
+ align:start position:0%
+this cannon sitting here and in the
+ 
+
+ align:start position:0%
+this cannon sitting here and in the
+barrel you've got a bunch of what's
+
+ align:start position:0%
+barrel you've got a bunch of what's
+ 
+
+ align:start position:0%
+barrel you've got a bunch of what's
+known as in the old days known as grape
+
+ align:start position:0%
+known as in the old days known as grape
+ 
+
+ align:start position:0%
+known as in the old days known as grape
+shot so sometimes for kind for anti
+
+ align:start position:0%
+shot so sometimes for kind for anti
+ 
+
+ align:start position:0%
+shot so sometimes for kind for anti
+Personnel kind of stuff they would just
+
+ align:start position:0%
+Personnel kind of stuff they would just
+ 
+
+ align:start position:0%
+Personnel kind of stuff they would just
+throw a whole bunch of metal and junk
+
+ align:start position:0%
+throw a whole bunch of metal and junk
+ 
+
+ align:start position:0%
+throw a whole bunch of metal and junk
+into it but just imagine a bunch of iron
+
+ align:start position:0%
+into it but just imagine a bunch of iron
+ 
+
+ align:start position:0%
+into it but just imagine a bunch of iron
+balls or lead balls or rocks or whatever
+
+ align:start position:0%
+balls or lead balls or rocks or whatever
+ 
+
+ align:start position:0%
+balls or lead balls or rocks or whatever
+you want to put in there and you put a
+
+ align:start position:0%
+you want to put in there and you put a
+ 
+
+ align:start position:0%
+you want to put in there and you put a
+whole mess of them in here and you have
+
+ align:start position:0%
+whole mess of them in here and you have
+ 
+
+ align:start position:0%
+whole mess of them in here and you have
+a charge
+
+ align:start position:0%
+a charge
+ 
+
+ align:start position:0%
+a charge
+you set it off and it shoots them out
+
+ align:start position:0%
+you set it off and it shoots them out
+ 
+
+ align:start position:0%
+you set it off and it shoots them out
+the end of the gun I want to know what's
+
+ align:start position:0%
+the end of the gun I want to know what's
+ 
+
+ align:start position:0%
+the end of the gun I want to know what's
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction what's the reaction force on
+
+ align:start position:0%
+reaction what's the reaction force on
+ 
+
+ align:start position:0%
+reaction what's the reaction force on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+gun now how much what's when that gun
+
+ align:start position:0%
+gun now how much what's when that gun
+ 
+
+ align:start position:0%
+gun now how much what's when that gun
+when that charge goes off if you ever if
+
+ align:start position:0%
+when that charge goes off if you ever if
+ 
+
+ align:start position:0%
+when that charge goes off if you ever if
+you go down to the Constitution which is
+
+ align:start position:0%
+you go down to the Constitution which is
+ 
+
+ align:start position:0%
+you go down to the Constitution which is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+oldest commissioned warship in the US
+
+ align:start position:0%
+oldest commissioned warship in the US
+ 
+
+ align:start position:0%
+oldest commissioned warship in the US
+Navy still afloat it's that I don't know
+
+ align:start position:0%
+Navy still afloat it's that I don't know
+ 
+
+ align:start position:0%
+Navy still afloat it's that I don't know
+if any of you have seen it down here in
+
+ align:start position:0%
+if any of you have seen it down here in
+ 
+
+ align:start position:0%
+if any of you have seen it down here in
+the dock in Chelsea was built around
+
+ align:start position:0%
+the dock in Chelsea was built around
+ 
+
+ align:start position:0%
+the dock in Chelsea was built around
+1799 but when one of those when they
+
+ align:start position:0%
+1799 but when one of those when they
+ 
+
+ align:start position:0%
+1799 but when one of those when they
+shot one of those guns the gun would
+
+ align:start position:0%
+shot one of those guns the gun would
+ 
+
+ align:start position:0%
+shot one of those guns the gun would
+roll back several feet and get dragged
+
+ align:start position:0%
+roll back several feet and get dragged
+ 
+
+ align:start position:0%
+roll back several feet and get dragged
+to a stop by a bunch of restraining
+
+ align:start position:0%
+to a stop by a bunch of restraining
+ 
+
+ align:start position:0%
+to a stop by a bunch of restraining
+lines and then dragged back up for
+
+ align:start position:0%
+lines and then dragged back up for
+ 
+
+ align:start position:0%
+lines and then dragged back up for
+another for another load so the reaction
+
+ align:start position:0%
+another for another load so the reaction
+ 
+
+ align:start position:0%
+another for another load so the reaction
+force the force pushing back these
+
+ align:start position:0%
+force the force pushing back these
+ 
+
+ align:start position:0%
+force the force pushing back these
+things are used to sitting on
+
+ align:start position:0%
+things are used to sitting on
+ 
+
+ align:start position:0%
+things are used to sitting on
+Wheels could be pretty large let let's
+
+ align:start position:0%
+Wheels could be pretty large let let's
+ 
+
+ align:start position:0%
+Wheels could be pretty large let let's
+take an estimate of it so this is going
+
+ align:start position:0%
+take an estimate of it so this is going
+ 
+
+ align:start position:0%
+take an estimate of it so this is going
+to be a relatively small
+
+ align:start position:0%
+to be a relatively small
+ 
+
+ align:start position:0%
+to be a relatively small
+gun the
+
+ align:start position:0%
+gun the
+ 
+
+ align:start position:0%
+gun the
+uh mass of the total mass of the shot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here time G is 10
+
+ align:start position:0%
+here time G is 10
+ 
+
+ align:start position:0%
+here time G is 10
+lb so 10 lbs a shot a gallon of milk
+
+ align:start position:0%
+lb so 10 lbs a shot a gallon of milk
+ 
+
+ align:start position:0%
+lb so 10 lbs a shot a gallon of milk
+weighs eight pounds we're not this isn't
+
+ align:start position:0%
+weighs eight pounds we're not this isn't
+ 
+
+ align:start position:0%
+weighs eight pounds we're not this isn't
+a very big uh very big load and let's
+
+ align:start position:0%
+a very big uh very big load and let's
+ 
+
+ align:start position:0%
+a very big uh very big load and let's
+say that this Barrel here from here to
+
+ align:start position:0%
+say that this Barrel here from here to
+ 
+
+ align:start position:0%
+say that this Barrel here from here to
+here the acceleration length is 7 feet
+
+ align:start position:0%
+here the acceleration length is 7 feet
+ 
+
+ align:start position:0%
+here the acceleration length is 7 feet
+so that shots accelerated out the barrel
+
+ align:start position:0%
+so that shots accelerated out the barrel
+ 
+
+ align:start position:0%
+so that shots accelerated out the barrel
+over a distance of
+
+ align:start position:0%
+over a distance of
+ 
+
+ align:start position:0%
+over a distance of
+7t and it has a muzzle velocity an exit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocity of
+
+ align:start position:0%
+velocity of
+ 
+
+ align:start position:0%
+velocity of
+700 feet per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second are most guns subsonic supersonic
+
+ align:start position:0%
+second are most guns subsonic supersonic
+ 
+
+ align:start position:0%
+second are most guns subsonic supersonic
+projectiles when they come out of guns
+
+ align:start position:0%
+projectiles when they come out of guns
+ 
+
+ align:start position:0%
+projectiles when they come out of guns
+thought about that I'm just asking
+
+ align:start position:0%
+thought about that I'm just asking
+ 
+
+ align:start position:0%
+thought about that I'm just asking
+seeing if you have a feeling for Speed
+
+ align:start position:0%
+seeing if you have a feeling for Speed
+ 
+
+ align:start position:0%
+seeing if you have a feeling for Speed
+how close to the speed of sound is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so speed of sound is about 1100 ft
+
+ align:start position:0%
+that so speed of sound is about 1100 ft
+ 
+
+ align:start position:0%
+that so speed of sound is about 1100 ft
+per second 340 m/ second so this is
+
+ align:start position:0%
+per second 340 m/ second so this is
+ 
+
+ align:start position:0%
+per second 340 m/ second so this is
+order of mack6 or something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that something like 6 not 06 0.6 so
+
+ align:start position:0%
+that something like 6 not 06 0.6 so
+ 
+
+ align:start position:0%
+that something like 6 not 06 0.6 so
+about 60% of the speed is down that's
+
+ align:start position:0%
+about 60% of the speed is down that's
+ 
+
+ align:start position:0%
+about 60% of the speed is down that's
+kind of slow actually as guns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go so it the uh initial velocity the
+
+ align:start position:0%
+go so it the uh initial velocity the
+ 
+
+ align:start position:0%
+go so it the uh initial velocity the
+shots just sitting
+
+ align:start position:0%
+shots just sitting
+ 
+
+ align:start position:0%
+shots just sitting
+there is zero the final
+
+ align:start position:0%
+there is zero the final
+ 
+
+ align:start position:0%
+there is zero the final
+velocity is
+
+ align:start position:0%
+velocity is
+ 
+
+ align:start position:0%
+velocity is
+700 feet per second the average velocity
+
+ align:start position:0%
+700 feet per second the average velocity
+ 
+
+ align:start position:0%
+700 feet per second the average velocity
+which I'm going to need for a second
+
+ align:start position:0%
+which I'm going to need for a second
+ 
+
+ align:start position:0%
+which I'm going to need for a second
+because I'm just making some estimates
+
+ align:start position:0%
+because I'm just making some estimates
+ 
+
+ align:start position:0%
+because I'm just making some estimates
+here the average velocity average of 0 +
+
+ align:start position:0%
+here the average velocity average of 0 +
+ 
+
+ align:start position:0%
+here the average velocity average of 0 +
+700 is 350 ft per
+
+ align:start position:0%
+700 is 350 ft per
+ 
+
+ align:start position:0%
+700 is 350 ft per
+second to do the reason I need this is I
+
+ align:start position:0%
+second to do the reason I need this is I
+ 
+
+ align:start position:0%
+second to do the reason I need this is I
+need to estimate the delta T how long
+
+ align:start position:0%
+need to estimate the delta T how long
+ 
+
+ align:start position:0%
+need to estimate the delta T how long
+does it take to get the shot out of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+barrel so distance equals rate times
+
+ align:start position:0%
+barrel so distance equals rate times
+ 
+
+ align:start position:0%
+barrel so distance equals rate times
+time right so the uh uh V
+
+ align:start position:0%
+time right so the uh uh V
+ 
+
+ align:start position:0%
+time right so the uh uh V
+average time delta T equals 7
+
+ align:start position:0%
+average time delta T equals 7
+ 
+
+ align:start position:0%
+average time delta T equals 7
+ft at 350 ft per second you find out
+
+ align:start position:0%
+ft at 350 ft per second you find out
+ 
+
+ align:start position:0%
+ft at 350 ft per second you find out
+delta T is about 02
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds so it gets out the barrel pretty
+
+ align:start position:0%
+seconds so it gets out the barrel pretty
+ 
+
+ align:start position:0%
+seconds so it gets out the barrel pretty
+quickly 0.02 seconds 20
+
+ align:start position:0%
+quickly 0.02 seconds 20
+ 
+
+ align:start position:0%
+quickly 0.02 seconds 20
+milliseconds now that powder when it
+
+ align:start position:0%
+milliseconds now that powder when it
+ 
+
+ align:start position:0%
+milliseconds now that powder when it
+goes off it's putting a lot of forces on
+
+ align:start position:0%
+goes off it's putting a lot of forces on
+ 
+
+ align:start position:0%
+goes off it's putting a lot of forces on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+shot so the total force on the shots
+
+ align:start position:0%
+shot so the total force on the shots
+ 
+
+ align:start position:0%
+shot so the total force on the shots
+5,000 PBS what's the reaction force on
+
+ align:start position:0%
+5,000 PBS what's the reaction force on
+ 
+
+ align:start position:0%
+5,000 PBS what's the reaction force on
+the cannon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to going to apply a
+
+ align:start position:0%
+so we're going to going to apply a
+ 
+
+ align:start position:0%
+so we're going to going to apply a
+principle here that we talked about
+
+ align:start position:0%
+principle here that we talked about
+ 
+
+ align:start position:0%
+principle here that we talked about
+earlier Newton Newton had three
+
+ align:start position:0%
+earlier Newton Newton had three
+ 
+
+ align:start position:0%
+earlier Newton Newton had three
+laws this is a group this is this
+
+ align:start position:0%
+laws this is a group this is this
+ 
+
+ align:start position:0%
+laws this is a group this is this
+massive balls in
+
+ align:start position:0%
+massive balls in
+ 
+
+ align:start position:0%
+massive balls in
+there the hot exploding gases are
+
+ align:start position:0%
+there the hot exploding gases are
+ 
+
+ align:start position:0%
+there the hot exploding gases are
+pushing them out the barrel what must be
+
+ align:start position:0%
+pushing them out the barrel what must be
+ 
+
+ align:start position:0%
+pushing them out the barrel what must be
+the push of the same gas on the cannon
+
+ align:start position:0%
+the push of the same gas on the cannon
+ 
+
+ align:start position:0%
+the push of the same gas on the cannon
+that's containing it equal opposite
+
+ align:start position:0%
+that's containing it equal opposite
+ 
+
+ align:start position:0%
+that's containing it equal opposite
+equal and opposite Newton's third law
+
+ align:start position:0%
+equal and opposite Newton's third law
+ 
+
+ align:start position:0%
+equal and opposite Newton's third law
+right so the reaction the reaction force
+
+ align:start position:0%
+right so the reaction the reaction force
+ 
+
+ align:start position:0%
+right so the reaction the reaction force
+that we're looking for is minus the
+
+ align:start position:0%
+that we're looking for is minus the
+ 
+
+ align:start position:0%
+that we're looking for is minus the
+force that it takes to get the shot out
+
+ align:start position:0%
+force that it takes to get the shot out
+ 
+
+ align:start position:0%
+force that it takes to get the shot out
+the barrel
+
+ align:start position:0%
+the barrel
+ 
+
+ align:start position:0%
+the barrel
+okay so force on the
+
+ align:start position:0%
+okay so force on the
+ 
+
+ align:start position:0%
+okay so force on the
+balls on the
+
+ align:start position:0%
+balls on the
+ 
+
+ align:start position:0%
+balls on the
+shot minus the reaction force and that's
+
+ align:start position:0%
+shot minus the reaction force and that's
+ 
+
+ align:start position:0%
+shot minus the reaction force and that's
+Newton's third law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're almost
+
+ align:start position:0%
+okay so we're almost
+ 
+
+ align:start position:0%
+okay so we're almost
+there but just applying now this concept
+
+ align:start position:0%
+there but just applying now this concept
+ 
+
+ align:start position:0%
+there but just applying now this concept
+of impulse and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum so now we can say the integral
+
+ align:start position:0%
+momentum so now we can say the integral
+ 
+
+ align:start position:0%
+momentum so now we can say the integral
+and this is the summation you got a
+
+ align:start position:0%
+and this is the summation you got a
+ 
+
+ align:start position:0%
+and this is the summation you got a
+whole bunch of balls in there they're
+
+ align:start position:0%
+whole bunch of balls in there they're
+ 
+
+ align:start position:0%
+whole bunch of balls in there they're
+all got forces on them but we're
+
+ align:start position:0%
+all got forces on them but we're
+ 
+
+ align:start position:0%
+all got forces on them but we're
+treating the group of balls as a system
+
+ align:start position:0%
+treating the group of balls as a system
+ 
+
+ align:start position:0%
+treating the group of balls as a system
+so we can we can use this notion of the
+
+ align:start position:0%
+so we can we can use this notion of the
+ 
+
+ align:start position:0%
+so we can we can use this notion of the
+ma total mass times velocity of the
+
+ align:start position:0%
+ma total mass times velocity of the
+ 
+
+ align:start position:0%
+ma total mass times velocity of the
+center of gravity to do this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the force on all of these
+
+ align:start position:0%
+so this is the force on all of these
+ 
+
+ align:start position:0%
+so this is the force on all of these
+little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balls integrated over
+
+ align:start position:0%
+balls integrated over
+ 
+
+ align:start position:0%
+balls integrated over
+time it's going to be the mass total of
+
+ align:start position:0%
+time it's going to be the mass total of
+ 
+
+ align:start position:0%
+time it's going to be the mass total of
+the balls times the change in the
+
+ align:start position:0%
+the balls times the change in the
+ 
+
+ align:start position:0%
+the balls times the change in the
+velocity of the center of gravity the
+
+ align:start position:0%
+velocity of the center of gravity the
+ 
+
+ align:start position:0%
+velocity of the center of gravity the
+final velocity minus the initial
+
+ align:start position:0%
+final velocity minus the initial
+ 
+
+ align:start position:0%
+final velocity minus the initial
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+zero okay we know this we know
+
+ align:start position:0%
+zero okay we know this we know
+ 
+
+ align:start position:0%
+zero okay we know this we know
+this so This Mt is the 10 lbs over G we
+
+ align:start position:0%
+this so This Mt is the 10 lbs over G we
+ 
+
+ align:start position:0%
+this so This Mt is the 10 lbs over G we
+know this is 700 feet per second we know
+
+ align:start position:0%
+know this is 700 feet per second we know
+ 
+
+ align:start position:0%
+know this is 700 feet per second we know
+that all of this mounts up to the force
+
+ align:start position:0%
+that all of this mounts up to the force
+ 
+
+ align:start position:0%
+that all of this mounts up to the force
+external on the
+
+ align:start position:0%
+external on the
+ 
+
+ align:start position:0%
+external on the
+group delta T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the weight of the ball W
+
+ align:start position:0%
+and this is the weight of the ball W
+ 
+
+ align:start position:0%
+and this is the weight of the ball W
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+G and this is
+
+ align:start position:0%
+G and this is
+ 
+
+ align:start position:0%
+G and this is
+700 feet per
+
+ align:start position:0%
+700 feet per
+ 
+
+ align:start position:0%
+700 feet per
+second that's 10 PBS divided by gravity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+700 ft per second and if you work out
+
+ align:start position:0%
+700 ft per second and if you work out
+ 
+
+ align:start position:0%
+700 ft per second and if you work out
+those numbers you
+
+ align:start position:0%
+those numbers you
+ 
+
+ align:start position:0%
+those numbers you
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+10,870
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lb now is this is an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+average force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because we at delta T is the
+
+ align:start position:0%
+right because we at delta T is the
+ 
+
+ align:start position:0%
+right because we at delta T is the
+length of time it took assuming we had
+
+ align:start position:0%
+length of time it took assuming we had
+ 
+
+ align:start position:0%
+length of time it took assuming we had
+some one we assumed an average velocity
+
+ align:start position:0%
+some one we assumed an average velocity
+ 
+
+ align:start position:0%
+some one we assumed an average velocity
+going down the barrel so the peak force
+
+ align:start position:0%
+going down the barrel so the peak force
+ 
+
+ align:start position:0%
+going down the barrel so the peak force
+is probably higher than this and the
+
+ align:start position:0%
+is probably higher than this and the
+ 
+
+ align:start position:0%
+is probably higher than this and the
+pressure of the barrel probably isn't
+
+ align:start position:0%
+pressure of the barrel probably isn't
+ 
+
+ align:start position:0%
+pressure of the barrel probably isn't
+constant this actually isn't a bad
+
+ align:start position:0%
+constant this actually isn't a bad
+ 
+
+ align:start position:0%
+constant this actually isn't a bad
+estimate if you know the muzzle velocity
+
+ align:start position:0%
+estimate if you know the muzzle velocity
+ 
+
+ align:start position:0%
+estimate if you know the muzzle velocity
+which you could figure out probably from
+
+ align:start position:0%
+which you could figure out probably from
+ 
+
+ align:start position:0%
+which you could figure out probably from
+the distance it goes and things like
+
+ align:start position:0%
+the distance it goes and things like
+ 
+
+ align:start position:0%
+the distance it goes and things like
+that you can make this estimate so
+
+ align:start position:0%
+that you can make this estimate so
+ 
+
+ align:start position:0%
+that you can make this estimate so
+10,000 pounds of reaction force
+
+ align:start position:0%
+10,000 pounds of reaction force
+ 
+
+ align:start position:0%
+10,000 pounds of reaction force
+is quite a lot this is this is a dinky
+
+ align:start position:0%
+is quite a lot this is this is a dinky
+ 
+
+ align:start position:0%
+is quite a lot this is this is a dinky
+gun 10 this is 10 lbs of shot is not
+
+ align:start position:0%
+gun 10 this is 10 lbs of shot is not
+ 
+
+ align:start position:0%
+gun 10 this is 10 lbs of shot is not
+much so that's this is this is the force
+
+ align:start position:0%
+much so that's this is this is the force
+ 
+
+ align:start position:0%
+much so that's this is this is the force
+to get the balls out the barrel if it's
+
+ align:start position:0%
+to get the balls out the barrel if it's
+ 
+
+ align:start position:0%
+to get the balls out the barrel if it's
+positive what's the reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+force minus
+
+ align:start position:0%
+force minus
+ 
+
+ align:start position:0%
+force minus
+10,870 and all through this I've been
+
+ align:start position:0%
+10,870 and all through this I've been
+ 
+
+ align:start position:0%
+10,870 and all through this I've been
+doing this in a single Vector Direction
+
+ align:start position:0%
+doing this in a single Vector Direction
+ 
+
+ align:start position:0%
+doing this in a single Vector Direction
+so I would have set up my coordinate
+
+ align:start position:0%
+so I would have set up my coordinate
+ 
+
+ align:start position:0%
+so I would have set up my coordinate
+system like here's o this is the X
+
+ align:start position:0%
+system like here's o this is the X
+ 
+
+ align:start position:0%
+system like here's o this is the X
+Direction y direction so this is
+
+ align:start position:0%
+Direction y direction so this is
+ 
+
+ align:start position:0%
+Direction y direction so this is
+obviously in the positive X direction is
+
+ align:start position:0%
+obviously in the positive X direction is
+ 
+
+ align:start position:0%
+obviously in the positive X direction is
+what I've lined up my positive
+
+ align:start position:0%
+what I've lined up my positive
+ 
+
+ align:start position:0%
+what I've lined up my positive
+velocities and positive forces to be so
+
+ align:start position:0%
+velocities and positive forces to be so
+ 
+
+ align:start position:0%
+velocities and positive forces to be so
+just a really simple way one of the kind
+
+ align:start position:0%
+just a really simple way one of the kind
+ 
+
+ align:start position:0%
+just a really simple way one of the kind
+of ways in which you use this notion of
+
+ align:start position:0%
+of ways in which you use this notion of
+ 
+
+ align:start position:0%
+of ways in which you use this notion of
+impulse and momentum but you can use it
+
+ align:start position:0%
+impulse and momentum but you can use it
+ 
+
+ align:start position:0%
+impulse and momentum but you can use it
+to make estimates too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and if you ever fired a
+
+ align:start position:0%
+okay and if you ever fired a
+ 
+
+ align:start position:0%
+okay and if you ever fired a
+shotgun not yeah any kick right so what
+
+ align:start position:0%
+shotgun not yeah any kick right so what
+ 
+
+ align:start position:0%
+shotgun not yeah any kick right so what
+gauge shotgun did you
+
+ align:start position:0%
+gauge shotgun did you
+ 
+
+ align:start position:0%
+gauge shotgun did you
+fire you know know
+
+ align:start position:0%
+fire you know know
+ 
+
+ align:start position:0%
+fire you know know
+okay okay 12 gaug shotgun you know the
+
+ align:start position:0%
+okay okay 12 gaug shotgun you know the
+ 
+
+ align:start position:0%
+okay okay 12 gaug shotgun you know the
+the the cartridge is about 3/4 of an
+
+ align:start position:0%
+the the cartridge is about 3/4 of an
+ 
+
+ align:start position:0%
+the the cartridge is about 3/4 of an
+inch diameter and it probably has a
+
+ align:start position:0%
+inch diameter and it probably has a
+ 
+
+ align:start position:0%
+inch diameter and it probably has a
+little amount of powder in there it
+
+ align:start position:0%
+little amount of powder in there it
+ 
+
+ align:start position:0%
+little amount of powder in there it
+amounts up to about that much stuff but
+
+ align:start position:0%
+amounts up to about that much stuff but
+ 
+
+ align:start position:0%
+amounts up to about that much stuff but
+it can give you a bruise in the shoulder
+
+ align:start position:0%
+it can give you a bruise in the shoulder
+ 
+
+ align:start position:0%
+it can give you a bruise in the shoulder
+if you don't hold it
+
+ align:start position:0%
+if you don't hold it
+ 
+
+ align:start position:0%
+if you don't hold it
+right so that's what that's what this is
+
+ align:start position:0%
+right so that's what that's what this is
+ 
+
+ align:start position:0%
+right so that's what that's what this is
+about all right so this kind of a quick
+
+ align:start position:0%
+about all right so this kind of a quick
+ 
+
+ align:start position:0%
+about all right so this kind of a quick
+review uh you've done lots of
+
+ align:start position:0%
+review uh you've done lots of
+ 
+
+ align:start position:0%
+review uh you've done lots of
+conservational momentum problems in your
+
+ align:start position:0%
+conservational momentum problems in your
+ 
+
+ align:start position:0%
+conservational momentum problems in your
+time the homework set this this time has
+
+ align:start position:0%
+time the homework set this this time has
+ 
+
+ align:start position:0%
+time the homework set this this time has
+two or three problems on it that are
+
+ align:start position:0%
+two or three problems on it that are
+ 
+
+ align:start position:0%
+two or three problems on it that are
+conservation or momentum linear momentum
+
+ align:start position:0%
+conservation or momentum linear momentum
+ 
+
+ align:start position:0%
+conservation or momentum linear momentum
+but now I want to move on to talking
+
+ align:start position:0%
+but now I want to move on to talking
+ 
+
+ align:start position:0%
+but now I want to move on to talking
+about angular momentum and angular
+
+ align:start position:0%
+about angular momentum and angular
+ 
+
+ align:start position:0%
+about angular momentum and angular
+momentum in a way in which you probably
+
+ align:start position:0%
+momentum in a way in which you probably
+ 
+
+ align:start position:0%
+momentum in a way in which you probably
+haven't done angular momentum problems
+
+ align:start position:0%
+haven't done angular momentum problems
+ 
+
+ align:start position:0%
+haven't done angular momentum problems
+before so anything about La last thing
+
+ align:start position:0%
+before so anything about La last thing
+ 
+
+ align:start position:0%
+before so anything about La last thing
+on this so mostly this I want you to
+
+ align:start position:0%
+on this so mostly this I want you to
+ 
+
+ align:start position:0%
+on this so mostly this I want you to
+read the read the chapter I think it's
+
+ align:start position:0%
+read the read the chapter I think it's
+ 
+
+ align:start position:0%
+read the read the chapter I think it's
+chapter
+
+ align:start position:0%
+chapter
+ 
+
+ align:start position:0%
+chapter
+15 first few sections of it are on
+
+ align:start position:0%
+15 first few sections of it are on
+ 
+
+ align:start position:0%
+15 first few sections of it are on
+linear momentum the last few sections on
+
+ align:start position:0%
+linear momentum the last few sections on
+ 
+
+ align:start position:0%
+linear momentum the last few sections on
+angular momentum go read them and just
+
+ align:start position:0%
+angular momentum go read them and just
+ 
+
+ align:start position:0%
+angular momentum go read them and just
+work the problems that's where they
+
+ align:start position:0%
+work the problems that's where they
+ 
+
+ align:start position:0%
+work the problems that's where they
+that's where you'll get most of your
+
+ align:start position:0%
+that's where you'll get most of your
+ 
+
+ align:start position:0%
+that's where you'll get most of your
+refresher is work is doing the practice
+
+ align:start position:0%
+refresher is work is doing the practice
+ 
+
+ align:start position:0%
+refresher is work is doing the practice
+problems okay angular momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll start with particle we're very
+
+ align:start position:0%
+so we'll start with particle we're very
+ 
+
+ align:start position:0%
+so we'll start with particle we're very
+rapidly going to get to rigid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bodies now Mo many times you've done
+
+ align:start position:0%
+bodies now Mo many times you've done
+ 
+
+ align:start position:0%
+bodies now Mo many times you've done
+angular momentum problems before mostly
+
+ align:start position:0%
+angular momentum problems before mostly
+ 
+
+ align:start position:0%
+angular momentum problems before mostly
+rotations about fixed axes so here's our
+
+ align:start position:0%
+rotations about fixed axes so here's our
+ 
+
+ align:start position:0%
+rotations about fixed axes so here's our
+inertial frame fixed
+
+ align:start position:0%
+inertial frame fixed
+ 
+
+ align:start position:0%
+inertial frame fixed
+XY and you have a particle out
+
+ align:start position:0%
+XY and you have a particle out
+ 
+
+ align:start position:0%
+XY and you have a particle out
+here and and it just has some mass
+
+ align:start position:0%
+here and and it just has some mass
+ 
+
+ align:start position:0%
+here and and it just has some mass
+m and it has some total force on it the
+
+ align:start position:0%
+m and it has some total force on it the
+ 
+
+ align:start position:0%
+m and it has some total force on it the
+force and this is the particle is
+
+ align:start position:0%
+force and this is the particle is
+ 
+
+ align:start position:0%
+force and this is the particle is
+located at B here so the force at B
+
+ align:start position:0%
+located at B here so the force at B
+ 
+
+ align:start position:0%
+located at B here so the force at B
+total Force at B just some
+
+ align:start position:0%
+total Force at B just some
+ 
+
+ align:start position:0%
+total Force at B just some
+Vector it also is traveling with some
+
+ align:start position:0%
+Vector it also is traveling with some
+ 
+
+ align:start position:0%
+Vector it also is traveling with some
+velocity at that instant in time so it
+
+ align:start position:0%
+velocity at that instant in time so it
+ 
+
+ align:start position:0%
+velocity at that instant in time so it
+has momentum okay and the momentum is
+
+ align:start position:0%
+has momentum okay and the momentum is
+ 
+
+ align:start position:0%
+has momentum okay and the momentum is
+p of this particle at
+
+ align:start position:0%
+p of this particle at
+ 
+
+ align:start position:0%
+p of this particle at
+B with respect to 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O and I'd like to the standard
+
+ align:start position:0%
+O and I'd like to the standard
+ 
+
+ align:start position:0%
+O and I'd like to the standard
+expression then for the angular
+
+ align:start position:0%
+expression then for the angular
+ 
+
+ align:start position:0%
+expression then for the angular
+momentum of this particle at
+
+ align:start position:0%
+momentum of this particle at
+ 
+
+ align:start position:0%
+momentum of this particle at
+B with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O we have a position Vector here
+
+ align:start position:0%
+O we have a position Vector here
+ 
+
+ align:start position:0%
+O we have a position Vector here
+RB which we've used lots of times by now
+
+ align:start position:0%
+RB which we've used lots of times by now
+ 
+
+ align:start position:0%
+RB which we've used lots of times by now
+is just the cross product of the
+
+ align:start position:0%
+is just the cross product of the
+ 
+
+ align:start position:0%
+is just the cross product of the
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+Vector with the linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum and that's just that's the
+
+ align:start position:0%
+momentum and that's just that's the
+ 
+
+ align:start position:0%
+momentum and that's just that's the
+definition of angular momentum I'm using
+
+ align:start position:0%
+definition of angular momentum I'm using
+ 
+
+ align:start position:0%
+definition of angular momentum I'm using
+a lowercase H here because I'm going to
+
+ align:start position:0%
+a lowercase H here because I'm going to
+ 
+
+ align:start position:0%
+a lowercase H here because I'm going to
+do that to indicate single particles and
+
+ align:start position:0%
+do that to indicate single particles and
+ 
+
+ align:start position:0%
+do that to indicate single particles and
+I use a capital H later on when we're
+
+ align:start position:0%
+I use a capital H later on when we're
+ 
+
+ align:start position:0%
+I use a capital H later on when we're
+referring to rigid bodies so the angular
+
+ align:start position:0%
+referring to rigid bodies so the angular
+ 
+
+ align:start position:0%
+referring to rigid bodies so the angular
+momentum of this particle
+
+ align:start position:0%
+momentum of this particle
+ 
+
+ align:start position:0%
+momentum of this particle
+with respect to this point is given by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and you've where you've used this
+
+ align:start position:0%
+that and you've where you've used this
+ 
+
+ align:start position:0%
+that and you've where you've used this
+before then is the derivative of HB with
+
+ align:start position:0%
+before then is the derivative of HB with
+ 
+
+ align:start position:0%
+before then is the derivative of HB with
+respect to
+
+ align:start position:0%
+respect to
+ 
+
+ align:start position:0%
+respect to
+O DT
+
+ align:start position:0%
+O DT
+ 
+
+ align:start position:0%
+O DT
+is what is that and remember what does
+
+ align:start position:0%
+is what is that and remember what does
+ 
+
+ align:start position:0%
+is what is that and remember what does
+this give you the time rate of change of
+
+ align:start position:0%
+this give you the time rate of change of
+ 
+
+ align:start position:0%
+this give you the time rate of change of
+the angular momentum is the torque right
+
+ align:start position:0%
+the angular momentum is the torque right
+ 
+
+ align:start position:0%
+the angular momentum is the torque right
+and it's the torque it's a sum of the
+
+ align:start position:0%
+and it's the torque it's a sum of the
+ 
+
+ align:start position:0%
+and it's the torque it's a sum of the
+torqus
+
+ align:start position:0%
+torqus
+ 
+
+ align:start position:0%
+torqus
+applied on that object with respect
+
+ align:start position:0%
+applied on that object with respect
+ 
+
+ align:start position:0%
+applied on that object with respect
+to the coordinate system in which you're
+
+ align:start position:0%
+to the coordinate system in which you're
+ 
+
+ align:start position:0%
+to the coordinate system in which you're
+Computing the angular momentum so that's
+
+ align:start position:0%
+Computing the angular momentum so that's
+ 
+
+ align:start position:0%
+Computing the angular momentum so that's
+you've used this formula many times and
+
+ align:start position:0%
+you've used this formula many times and
+ 
+
+ align:start position:0%
+you've used this formula many times and
+in planer motion where you only have one
+
+ align:start position:0%
+in planer motion where you only have one
+ 
+
+ align:start position:0%
+in planer motion where you only have one
+axis of rotation usually the z-axis of
+
+ align:start position:0%
+axis of rotation usually the z-axis of
+ 
+
+ align:start position:0%
+axis of rotation usually the z-axis of
+rotation you usually usually would write
+
+ align:start position:0%
+rotation you usually usually would write
+ 
+
+ align:start position:0%
+rotation you usually usually would write
+this as I Theta double dot right in the
+
+ align:start position:0%
+this as I Theta double dot right in the
+ 
+
+ align:start position:0%
+this as I Theta double dot right in the
+simplest form if it's a rigid body it
+
+ align:start position:0%
+simplest form if it's a rigid body it
+ 
+
+ align:start position:0%
+simplest form if it's a rigid body it
+has the mass moment of inertia times
+
+ align:start position:0%
+has the mass moment of inertia times
+ 
+
+ align:start position:0%
+has the mass moment of inertia times
+Theta double dot is equal to the sum of
+
+ align:start position:0%
+Theta double dot is equal to the sum of
+ 
+
+ align:start position:0%
+Theta double dot is equal to the sum of
+the external torque so that's where
+
+ align:start position:0%
+the external torque so that's where
+ 
+
+ align:start position:0%
+the external torque so that's where
+you've met this before but for the
+
+ align:start position:0%
+you've met this before but for the
+ 
+
+ align:start position:0%
+you've met this before but for the
+moment this is just a particle let's
+
+ align:start position:0%
+moment this is just a particle let's
+ 
+
+ align:start position:0%
+moment this is just a particle let's
+stick with a
+
+ align:start position:0%
+stick with a
+ 
+
+ align:start position:0%
+stick with a
+particle so the piece that's new here
+
+ align:start position:0%
+particle so the piece that's new here
+ 
+
+ align:start position:0%
+particle so the piece that's new here
+probably new for you is that um what if
+
+ align:start position:0%
+probably new for you is that um what if
+ 
+
+ align:start position:0%
+probably new for you is that um what if
+I want to
+
+ align:start position:0%
+I want to
+ 
+
+ align:start position:0%
+I want to
+know the angular momentum with respect
+
+ align:start position:0%
+know the angular momentum with respect
+ 
+
+ align:start position:0%
+know the angular momentum with respect
+to another point so here's a point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a and I'd like to compute
+
+ align:start position:0%
+a and I'd like to compute
+ 
+
+ align:start position:0%
+a and I'd like to compute
+h of B with respect to
+
+ align:start position:0%
+h of B with respect to
+ 
+
+ align:start position:0%
+h of B with respect to
+a well that's
+
+ align:start position:0%
+a well that's
+ 
+
+ align:start position:0%
+a well that's
+r b with respect to
+
+ align:start position:0%
+r b with respect to
+ 
+
+ align:start position:0%
+r b with respect to
+a cross p
+
+ align:start position:0%
+a cross p
+ 
+
+ align:start position:0%
+a cross p
+b with respect to O and this is really
+
+ align:start position:0%
+b with respect to O and this is really
+ 
+
+ align:start position:0%
+b with respect to O and this is really
+easy to forget the momentum is always
+
+ align:start position:0%
+easy to forget the momentum is always
+ 
+
+ align:start position:0%
+easy to forget the momentum is always
+calculated with respect to your inertial
+
+ align:start position:0%
+calculated with respect to your inertial
+ 
+
+ align:start position:0%
+calculated with respect to your inertial
+frame and that's why I keeping this with
+
+ align:start position:0%
+frame and that's why I keeping this with
+ 
+
+ align:start position:0%
+frame and that's why I keeping this with
+respect to and telling you what the
+
+ align:start position:0%
+respect to and telling you what the
+ 
+
+ align:start position:0%
+respect to and telling you what the
+frame name is is pretty important but
+
+ align:start position:0%
+frame name is is pretty important but
+ 
+
+ align:start position:0%
+frame name is is pretty important but
+we're out here at some arbitrary Point
+
+ align:start position:0%
+we're out here at some arbitrary Point
+ 
+
+ align:start position:0%
+we're out here at some arbitrary Point
+Computing the C the cross product of the
+
+ align:start position:0%
+Computing the C the cross product of the
+ 
+
+ align:start position:0%
+Computing the C the cross product of the
+position Vector from this arbitrary
+
+ align:start position:0%
+position Vector from this arbitrary
+ 
+
+ align:start position:0%
+position Vector from this arbitrary
+point to this moving mass and we're
+
+ align:start position:0%
+point to this moving mass and we're
+ 
+
+ align:start position:0%
+point to this moving mass and we're
+defining this is just a definition
+
+ align:start position:0%
+defining this is just a definition
+ 
+
+ align:start position:0%
+defining this is just a definition
+defining the angular momentum with
+
+ align:start position:0%
+defining the angular momentum with
+ 
+
+ align:start position:0%
+defining the angular momentum with
+respect to this point a as RBA cross p p
+
+ align:start position:0%
+respect to this point a as RBA cross p p
+ 
+
+ align:start position:0%
+respect to this point a as RBA cross p p
+with respect to O all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what I want to get to is now is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+torque on this system on this part
+
+ align:start position:0%
+torque on this system on this part
+ 
+
+ align:start position:0%
+torque on this system on this part
+around this particle B with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is the time rate of change of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+HBA with respect to T but now it's a
+
+ align:start position:0%
+HBA with respect to T but now it's a
+ 
+
+ align:start position:0%
+HBA with respect to T but now it's a
+little more complicated plus the
+
+ align:start position:0%
+little more complicated plus the
+ 
+
+ align:start position:0%
+little more complicated plus the
+velocity of a with respect to
+
+ align:start position:0%
+velocity of a with respect to
+ 
+
+ align:start position:0%
+velocity of a with respect to
+O all vectors
+
+ align:start position:0%
+O all vectors
+ 
+
+ align:start position:0%
+O all vectors
+cross p b with respect to O messy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term I was trying to think of an example
+
+ align:start position:0%
+term I was trying to think of an example
+ 
+
+ align:start position:0%
+term I was trying to think of an example
+where you
+
+ align:start position:0%
+where you
+ 
+
+ align:start position:0%
+where you
+uh you might want to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so imagine that you've got an arm which
+
+ align:start position:0%
+so imagine that you've got an arm which
+ 
+
+ align:start position:0%
+so imagine that you've got an arm which
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+rotate you know might be on a robot or
+
+ align:start position:0%
+rotate you know might be on a robot or
+ 
+
+ align:start position:0%
+rotate you know might be on a robot or
+something like that and it has attached
+
+ align:start position:0%
+something like that and it has attached
+ 
+
+ align:start position:0%
+something like that and it has attached
+to it another arm with a mass on
+
+ align:start position:0%
+to it another arm with a mass on
+ 
+
+ align:start position:0%
+to it another arm with a mass on
+it and you've got a motor here which can
+
+ align:start position:0%
+it and you've got a motor here which can
+ 
+
+ align:start position:0%
+it and you've got a motor here which can
+make this
+
+ align:start position:0%
+make this
+ 
+
+ align:start position:0%
+make this
+rotate and you're trying to design the
+
+ align:start position:0%
+rotate and you're trying to design the
+ 
+
+ align:start position:0%
+rotate and you're trying to design the
+motor has has to be able to put out a
+
+ align:start position:0%
+motor has has to be able to put out a
+ 
+
+ align:start position:0%
+motor has has to be able to put out a
+certain amount of
+
+ align:start position:0%
+certain amount of
+ 
+
+ align:start position:0%
+certain amount of
+torque so this is O this is B this is a
+
+ align:start position:0%
+torque so this is O this is B this is a
+ 
+
+ align:start position:0%
+torque so this is O this is B this is a
+and you actually I want to know the
+
+ align:start position:0%
+and you actually I want to know the
+ 
+
+ align:start position:0%
+and you actually I want to know the
+torque required in this motor to drive
+
+ align:start position:0%
+torque required in this motor to drive
+ 
+
+ align:start position:0%
+torque required in this motor to drive
+this thing around but the motor is here
+
+ align:start position:0%
+this thing around but the motor is here
+ 
+
+ align:start position:0%
+this thing around but the motor is here
+and it only cares about what it feels so
+
+ align:start position:0%
+and it only cares about what it feels so
+ 
+
+ align:start position:0%
+and it only cares about what it feels so
+the torque at this point to drive this
+
+ align:start position:0%
+the torque at this point to drive this
+ 
+
+ align:start position:0%
+the torque at this point to drive this
+thing but this whole system is now in
+
+ align:start position:0%
+thing but this whole system is now in
+ 
+
+ align:start position:0%
+thing but this whole system is now in
+motion you'd have to use this formula
+
+ align:start position:0%
+motion you'd have to use this formula
+ 
+
+ align:start position:0%
+motion you'd have to use this formula
+okay so there are practical times when
+
+ align:start position:0%
+okay so there are practical times when
+ 
+
+ align:start position:0%
+okay so there are practical times when
+you'd like to be able to be able to
+
+ align:start position:0%
+you'd like to be able to be able to
+ 
+
+ align:start position:0%
+you'd like to be able to be able to
+calculate something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so there's a I'm going to show you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the a very brief derivation of this and
+
+ align:start position:0%
+the a very brief derivation of this and
+ 
+
+ align:start position:0%
+the a very brief derivation of this and
+but just so you get a feeling for where
+
+ align:start position:0%
+but just so you get a feeling for where
+ 
+
+ align:start position:0%
+but just so you get a feeling for where
+this comes from because there's a couple
+
+ align:start position:0%
+this comes from because there's a couple
+ 
+
+ align:start position:0%
+this comes from because there's a couple
+of outcomes that are very important to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us so the sum of the forces there at
+
+ align:start position:0%
+us so the sum of the forces there at
+ 
+
+ align:start position:0%
+us so the sum of the forces there at
+those forces at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B give you the time rate of
+
+ align:start position:0%
+B give you the time rate of
+ 
+
+ align:start position:0%
+B give you the time rate of
+change of the
+
+ align:start position:0%
+change of the
+ 
+
+ align:start position:0%
+change of the
+momentum at B with respect to O this is
+
+ align:start position:0%
+momentum at B with respect to O this is
+ 
+
+ align:start position:0%
+momentum at B with respect to O this is
+that moment momentum Vector of our
+
+ align:start position:0%
+that moment momentum Vector of our
+ 
+
+ align:start position:0%
+that moment momentum Vector of our
+particle okay and this FB this is a
+
+ align:start position:0%
+particle okay and this FB this is a
+ 
+
+ align:start position:0%
+particle okay and this FB this is a
+total external forces acting on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle we know that's
+
+ align:start position:0%
+particle we know that's
+ 
+
+ align:start position:0%
+particle we know that's
+m a single particle times the
+
+ align:start position:0%
+m a single particle times the
+ 
+
+ align:start position:0%
+m a single particle times the
+velocity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that certainly could be right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times that's our familiar formula for
+
+ align:start position:0%
+times that's our familiar formula for
+ 
+
+ align:start position:0%
+times that's our familiar formula for
+fals ma right so the time derivative of
+
+ align:start position:0%
+fals ma right so the time derivative of
+ 
+
+ align:start position:0%
+fals ma right so the time derivative of
+the linear momentum gives you this and
+
+ align:start position:0%
+the linear momentum gives you this and
+ 
+
+ align:start position:0%
+the linear momentum gives you this and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+torque of B with respect to
+
+ align:start position:0%
+torque of B with respect to
+ 
+
+ align:start position:0%
+torque of B with respect to
+a is r b a cross I'm this total I'm
+
+ align:start position:0%
+a is r b a cross I'm this total I'm
+ 
+
+ align:start position:0%
+a is r b a cross I'm this total I'm
+going let this just be a total Vector
+
+ align:start position:0%
+going let this just be a total Vector
+ 
+
+ align:start position:0%
+going let this just be a total Vector
+I'll call it f
+
+ align:start position:0%
+I'll call it f
+ 
+
+ align:start position:0%
+I'll call it f
+B it's a vector the torque with respect
+
+ align:start position:0%
+B it's a vector the torque with respect
+ 
+
+ align:start position:0%
+B it's a vector the torque with respect
+to a is just RBA cross this total
+
+ align:start position:0%
+to a is just RBA cross this total
+ 
+
+ align:start position:0%
+to a is just RBA cross this total
+external Force
+
+ align:start position:0%
+external Force
+ 
+
+ align:start position:0%
+external Force
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+ba
+
+ align:start position:0%
+ba
+ 
+
+ align:start position:0%
+ba
+cross the time
+
+ align:start position:0%
+cross the time
+ 
+
+ align:start position:0%
+cross the time
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PBO because the forces give us R which
+
+ align:start position:0%
+PBO because the forces give us R which
+ 
+
+ align:start position:0%
+PBO because the forces give us R which
+is from the time rate of change of the
+
+ align:start position:0%
+is from the time rate of change of the
+ 
+
+ align:start position:0%
+is from the time rate of change of the
+linear momentum of that
+
+ align:start position:0%
+linear momentum of that
+ 
+
+ align:start position:0%
+linear momentum of that
+particle so I can say it like this but
+
+ align:start position:0%
+particle so I can say it like this but
+ 
+
+ align:start position:0%
+particle so I can say it like this but
+now this there's just a little
+
+ align:start position:0%
+now this there's just a little
+ 
+
+ align:start position:0%
+now this there's just a little
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+identity
+
+ align:start position:0%
+identity
+ 
+
+ align:start position:0%
+identity
+for products of vectors that I'm going
+
+ align:start position:0%
+for products of vectors that I'm going
+ 
+
+ align:start position:0%
+for products of vectors that I'm going
+to take advantage of and I'll call this
+
+ align:start position:0%
+to take advantage of and I'll call this
+ 
+
+ align:start position:0%
+to take advantage of and I'll call this
+Q so Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Q is of the form and I'm going to say
+
+ align:start position:0%
+so Q is of the form and I'm going to say
+ 
+
+ align:start position:0%
+so Q is of the form and I'm going to say
+m this is a Quant a vector a and this is
+
+ align:start position:0%
+m this is a Quant a vector a and this is
+ 
+
+ align:start position:0%
+m this is a Quant a vector a and this is
+a quantity a vector time derivative of a
+
+ align:start position:0%
+a quantity a vector time derivative of a
+ 
+
+ align:start position:0%
+a quantity a vector time derivative of a
+vector B it's a cross
+
+ align:start position:0%
+vector B it's a cross
+ 
+
+ align:start position:0%
+vector B it's a cross
+dbdt
+
+ align:start position:0%
+dbdt
+ 
+
+ align:start position:0%
+dbdt
+so there's a little identity that you
+
+ align:start position:0%
+so there's a little identity that you
+ 
+
+ align:start position:0%
+so there's a little identity that you
+can use it says a
+
+ align:start position:0%
+can use it says a
+ 
+
+ align:start position:0%
+can use it says a
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+DB
+
+ align:start position:0%
+DB
+ 
+
+ align:start position:0%
+DB
+DT you can you can alternatively write
+
+ align:start position:0%
+DT you can you can alternatively write
+ 
+
+ align:start position:0%
+DT you can you can alternatively write
+that as the time
+
+ align:start position:0%
+that as the time
+ 
+
+ align:start position:0%
+that as the time
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+of A cross
+
+ align:start position:0%
+of A cross
+ 
+
+ align:start position:0%
+of A cross
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+minus time derivative of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A cross
+
+ align:start position:0%
+A cross
+ 
+
+ align:start position:0%
+A cross
+B and if we're we're going to take
+
+ align:start position:0%
+B and if we're we're going to take
+ 
+
+ align:start position:0%
+B and if we're we're going to take
+advantage of this and just
+
+ align:start position:0%
+advantage of this and just
+ 
+
+ align:start position:0%
+advantage of this and just
+re construct this formula using
+
+ align:start position:0%
+re construct this formula using
+ 
+
+ align:start position:0%
+re construct this formula using
+this expression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that says torque with of B with
+
+ align:start position:0%
+so that says torque with of B with
+ 
+
+ align:start position:0%
+so that says torque with of B with
+respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a the time derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+RBA
+
+ align:start position:0%
+RBA
+ 
+
+ align:start position:0%
+RBA
+cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PBO minus the derivative of RBA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+PBF so we've just made this substitution
+
+ align:start position:0%
+PBF so we've just made this substitution
+ 
+
+ align:start position:0%
+PBF so we've just made this substitution
+down here in terms of RBA and
+
+ align:start position:0%
+down here in terms of RBA and
+ 
+
+ align:start position:0%
+down here in terms of RBA and
+PBO all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors but we know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RBA from all the previous work we've
+
+ align:start position:0%
+RBA from all the previous work we've
+ 
+
+ align:start position:0%
+RBA from all the previous work we've
+done is just rbo minus r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AO so the derivative of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RBA with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time is
+
+ align:start position:0%
+time is
+ 
+
+ align:start position:0%
+time is
+VB minus
+
+ align:start position:0%
+VB minus
+ 
+
+ align:start position:0%
+VB minus
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+AO all right we're almost there we're
+
+ align:start position:0%
+AO all right we're almost there we're
+ 
+
+ align:start position:0%
+AO all right we're almost there we're
+almost there I'm going to need another
+
+ align:start position:0%
+almost there I'm going to need another
+ 
+
+ align:start position:0%
+almost there I'm going to need another
+board though
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this quantity here this is just
+
+ align:start position:0%
+this quantity here this is just
+ 
+
+ align:start position:0%
+this quantity here this is just
+h b a this is the angular momentum of
+
+ align:start position:0%
+h b a this is the angular momentum of
+ 
+
+ align:start position:0%
+h b a this is the angular momentum of
+the particle with respect to a it's just
+
+ align:start position:0%
+the particle with respect to a it's just
+ 
+
+ align:start position:0%
+the particle with respect to a it's just
+R cross B if you recall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then we can rewrite this expression
+
+ align:start position:0%
+so then we can rewrite this expression
+ 
+
+ align:start position:0%
+so then we can rewrite this expression
+for the torque
+
+ align:start position:0%
+for the torque
+ 
+
+ align:start position:0%
+for the torque
+as the time
+
+ align:start position:0%
+as the time
+ 
+
+ align:start position:0%
+as the time
+derivative of H of B with respect to a
+
+ align:start position:0%
+derivative of H of B with respect to a
+ 
+
+ align:start position:0%
+derivative of H of B with respect to a
+that's because of what I pointed out
+
+ align:start position:0%
+that's because of what I pointed out
+ 
+
+ align:start position:0%
+that's because of what I pointed out
+there and now this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus VB o minus B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AO cross P Bo o
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so P of B with respect to O is just
+
+ align:start position:0%
+so P of B with respect to O is just
+ 
+
+ align:start position:0%
+so P of B with respect to O is just
+m velocity of B with respect to O
+
+ align:start position:0%
+m velocity of B with respect to O
+ 
+
+ align:start position:0%
+m velocity of B with respect to O
+right so vbo cross PBO gives you what
+
+ align:start position:0%
+right so vbo cross PBO gives you what
+ 
+
+ align:start position:0%
+right so vbo cross PBO gives you what
+nothing get you zero because they're
+
+ align:start position:0%
+nothing get you zero because they're
+ 
+
+ align:start position:0%
+nothing get you zero because they're
+parallel to going they're exact they're
+
+ align:start position:0%
+parallel to going they're exact they're
+ 
+
+ align:start position:0%
+parallel to going they're exact they're
+in the same direction so this you only
+
+ align:start position:0%
+in the same direction so this you only
+ 
+
+ align:start position:0%
+in the same direction so this you only
+get a nonzero piece out of this minus
+
+ align:start position:0%
+get a nonzero piece out of this minus
+ 
+
+ align:start position:0%
+get a nonzero piece out of this minus
+time minus gives you a plus and you end
+
+ align:start position:0%
+time minus gives you a plus and you end
+ 
+
+ align:start position:0%
+time minus gives you a plus and you end
+up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's what we set out to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find I said this is where I was trying
+
+ align:start position:0%
+find I said this is where I was trying
+ 
+
+ align:start position:0%
+find I said this is where I was trying
+to get and now we're
+
+ align:start position:0%
+to get and now we're
+ 
+
+ align:start position:0%
+to get and now we're
+there now the import importantly there's
+
+ align:start position:0%
+there now the import importantly there's
+ 
+
+ align:start position:0%
+there now the import importantly there's
+a couple of special cases of
+
+ align:start position:0%
+a couple of special cases of
+ 
+
+ align:start position:0%
+a couple of special cases of
+this this can be kind of a nuisance term
+
+ align:start position:0%
+this this can be kind of a nuisance term
+ 
+
+ align:start position:0%
+this this can be kind of a nuisance term
+to have to deal with lots of times you'd
+
+ align:start position:0%
+to have to deal with lots of times you'd
+ 
+
+ align:start position:0%
+to have to deal with lots of times you'd
+like to be able to get rid of it and
+
+ align:start position:0%
+like to be able to get rid of it and
+ 
+
+ align:start position:0%
+like to be able to get rid of it and
+just be able to go back to that Old
+
+ align:start position:0%
+just be able to go back to that Old
+ 
+
+ align:start position:0%
+just be able to go back to that Old
+Reliable formula torque is time rate of
+
+ align:start position:0%
+Reliable formula torque is time rate of
+ 
+
+ align:start position:0%
+Reliable formula torque is time rate of
+change of angular
+
+ align:start position:0%
+change of angular
+ 
+
+ align:start position:0%
+change of angular
+momentum so there are two obvious almost
+
+ align:start position:0%
+momentum so there are two obvious almost
+ 
+
+ align:start position:0%
+momentum so there are two obvious almost
+maybe obvious conditions in which this
+
+ align:start position:0%
+maybe obvious conditions in which this
+ 
+
+ align:start position:0%
+maybe obvious conditions in which this
+will go
+
+ align:start position:0%
+will go
+ 
+
+ align:start position:0%
+will go
+away what's the most obvious one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of terms Zer something what did you say
+
+ align:start position:0%
+of terms Zer something what did you say
+ 
+
+ align:start position:0%
+of terms Zer something what did you say
+is zero one of the terms well yeah this
+
+ align:start position:0%
+is zero one of the terms well yeah this
+ 
+
+ align:start position:0%
+is zero one of the terms well yeah this
+this this term presumably not this guy
+
+ align:start position:0%
+this this term presumably not this guy
+ 
+
+ align:start position:0%
+this this term presumably not this guy
+if this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero is just back to our old familiar
+
+ align:start position:0%
+zero is just back to our old familiar
+ 
+
+ align:start position:0%
+zero is just back to our old familiar
+formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's one case the case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one but now actually this this is a
+
+ align:start position:0%
+one but now actually this this is a
+ 
+
+ align:start position:0%
+one but now actually this this is a
+really important
+
+ align:start position:0%
+really important
+ 
+
+ align:start position:0%
+really important
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+because a can be
+
+ align:start position:0%
+because a can be
+ 
+
+ align:start position:0%
+because a can be
+anywhere as long as it's not
+
+ align:start position:0%
+anywhere as long as it's not
+ 
+
+ align:start position:0%
+anywhere as long as it's not
+moving and so this allows you to do
+
+ align:start position:0%
+moving and so this allows you to do
+ 
+
+ align:start position:0%
+moving and so this allows you to do
+things talk about rotations about fixed
+
+ align:start position:0%
+things talk about rotations about fixed
+ 
+
+ align:start position:0%
+things talk about rotations about fixed
+axes that aren't at the center of
+
+ align:start position:0%
+axes that aren't at the center of
+ 
+
+ align:start position:0%
+axes that aren't at the center of
+mass right so if you have a fixed axis
+
+ align:start position:0%
+mass right so if you have a fixed axis
+ 
+
+ align:start position:0%
+mass right so if you have a fixed axis
+of rotation and something going around
+
+ align:start position:0%
+of rotation and something going around
+ 
+
+ align:start position:0%
+of rotation and something going around
+it that's what this allows you to
+
+ align:start position:0%
+it that's what this allows you to
+ 
+
+ align:start position:0%
+it that's what this allows you to
+do okay that's one case so this is typ
+
+ align:start position:0%
+do okay that's one case so this is typ
+ 
+
+ align:start position:0%
+do okay that's one case so this is typ
+this we'll soon get the rigid bodies
+
+ align:start position:0%
+this we'll soon get the rigid bodies
+ 
+
+ align:start position:0%
+this we'll soon get the rigid bodies
+rigid bodies obey exactly the same
+
+ align:start position:0%
+rigid bodies obey exactly the same
+ 
+
+ align:start position:0%
+rigid bodies obey exactly the same
+formulas and you can have a rigid body
+
+ align:start position:0%
+formulas and you can have a rigid body
+ 
+
+ align:start position:0%
+formulas and you can have a rigid body
+now that it's not rotating about its
+
+ align:start position:0%
+now that it's not rotating about its
+ 
+
+ align:start position:0%
+now that it's not rotating about its
+Center but rotating maybe about its end
+
+ align:start position:0%
+Center but rotating maybe about its end
+ 
+
+ align:start position:0%
+Center but rotating maybe about its end
+like this that formul applies if the
+
+ align:start position:0%
+like this that formul applies if the
+ 
+
+ align:start position:0%
+like this that formul applies if the
+velocity of that axis about which it's
+
+ align:start position:0%
+velocity of that axis about which it's
+ 
+
+ align:start position:0%
+velocity of that axis about which it's
+rotating about which you're Computing
+
+ align:start position:0%
+rotating about which you're Computing
+ 
+
+ align:start position:0%
+rotating about which you're Computing
+this is not moving then you can just use
+
+ align:start position:0%
+this is not moving then you can just use
+ 
+
+ align:start position:0%
+this is not moving then you can just use
+you don't have to deal with that messy
+
+ align:start position:0%
+you don't have to deal with that messy
+ 
+
+ align:start position:0%
+you don't have to deal with that messy
+term so this is one case in which this
+
+ align:start position:0%
+term so this is one case in which this
+ 
+
+ align:start position:0%
+term so this is one case in which this
+term goes
+
+ align:start position:0%
+term goes
+ 
+
+ align:start position:0%
+term goes
+away the other case is if this velocity
+
+ align:start position:0%
+away the other case is if this velocity
+ 
+
+ align:start position:0%
+away the other case is if this velocity
+is parallel to the direction of the
+
+ align:start position:0%
+is parallel to the direction of the
+ 
+
+ align:start position:0%
+is parallel to the direction of the
+momentum and there's a really useful
+
+ align:start position:0%
+momentum and there's a really useful
+ 
+
+ align:start position:0%
+momentum and there's a really useful
+time that that happens
+
+ align:start position:0%
+time that that happens
+ 
+
+ align:start position:0%
+time that that happens
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+also this formula is true case
+
+ align:start position:0%
+also this formula is true case
+ 
+
+ align:start position:0%
+also this formula is true case
+two is when
+
+ align:start position:0%
+two is when
+ 
+
+ align:start position:0%
+two is when
+vao is parallel to PBO the direction
+
+ align:start position:0%
+vao is parallel to PBO the direction
+ 
+
+ align:start position:0%
+vao is parallel to PBO the direction
+they're going in the same direction now
+
+ align:start position:0%
+they're going in the same direction now
+ 
+
+ align:start position:0%
+they're going in the same direction now
+that happens when a is guaranteed to be
+
+ align:start position:0%
+that happens when a is guaranteed to be
+ 
+
+ align:start position:0%
+that happens when a is guaranteed to be
+true if a is at the center of
+
+ align:start position:0%
+true if a is at the center of
+ 
+
+ align:start position:0%
+true if a is at the center of
+mass because momentum is defined as the
+
+ align:start position:0%
+mass because momentum is defined as the
+ 
+
+ align:start position:0%
+mass because momentum is defined as the
+mass of the object object times the
+
+ align:start position:0%
+mass of the object object times the
+ 
+
+ align:start position:0%
+mass of the object object times the
+velocity of its Center of
+
+ align:start position:0%
+velocity of its Center of
+ 
+
+ align:start position:0%
+velocity of its Center of
+mass right even for rigid bodies
+
+ align:start position:0%
+mass right even for rigid bodies
+ 
+
+ align:start position:0%
+mass right even for rigid bodies
+so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when a is and I'll call it
+
+ align:start position:0%
+when a is and I'll call it
+ 
+
+ align:start position:0%
+when a is and I'll call it
+g at the center of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass so this gives
+
+ align:start position:0%
+mass so this gives
+ 
+
+ align:start position:0%
+mass so this gives
+us another really important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generalization that we'll use that we
+
+ align:start position:0%
+generalization that we'll use that we
+ 
+
+ align:start position:0%
+generalization that we'll use that we
+make great use of in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dynamics and that says that the torque
+
+ align:start position:0%
+Dynamics and that says that the torque
+ 
+
+ align:start position:0%
+Dynamics and that says that the torque
+with respect to the center of
+
+ align:start position:0%
+with respect to the center of
+ 
+
+ align:start position:0%
+with respect to the center of
+mass is time rate of
+
+ align:start position:0%
+mass is time rate of
+ 
+
+ align:start position:0%
+mass is time rate of
+change of H with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G now I'm not going to go I did the
+
+ align:start position:0%
+G now I'm not going to go I did the
+ 
+
+ align:start position:0%
+G now I'm not going to go I did the
+proof this went through this little
+
+ align:start position:0%
+proof this went through this little
+ 
+
+ align:start position:0%
+proof this went through this little
+proof just for a particle but by summing
+
+ align:start position:0%
+proof just for a particle but by summing
+ 
+
+ align:start position:0%
+proof just for a particle but by summing
+a bunch of particles and kind of going
+
+ align:start position:0%
+a bunch of particles and kind of going
+ 
+
+ align:start position:0%
+a bunch of particles and kind of going
+through all the summations as we did to
+
+ align:start position:0%
+through all the summations as we did to
+ 
+
+ align:start position:0%
+through all the summations as we did to
+prove the center of mass formula you can
+
+ align:start position:0%
+prove the center of mass formula you can
+ 
+
+ align:start position:0%
+prove the center of mass formula you can
+show this allows you to very
+
+ align:start position:0%
+show this allows you to very
+ 
+
+ align:start position:0%
+show this allows you to very
+quickly show that this formulation is
+
+ align:start position:0%
+quickly show that this formulation is
+ 
+
+ align:start position:0%
+quickly show that this formulation is
+also true for rigid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bodies so your way you say it for rigid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bodies is that the sum of the torqus
+
+ align:start position:0%
+bodies is that the sum of the torqus
+ 
+
+ align:start position:0%
+bodies is that the sum of the torqus
+about with respect to some point for
+
+ align:start position:0%
+about with respect to some point for
+ 
+
+ align:start position:0%
+about with respect to some point for
+rigid
+
+ align:start position:0%
+rigid
+ 
+
+ align:start position:0%
+rigid
+body
+
+ align:start position:0%
+body
+ 
+
+ align:start position:0%
+body
+is H now Capital H H dot with respect to
+
+ align:start position:0%
+is H now Capital H H dot with respect to
+ 
+
+ align:start position:0%
+is H now Capital H H dot with respect to
+a plus the velocity of a with respect to
+
+ align:start position:0%
+a plus the velocity of a with respect to
+ 
+
+ align:start position:0%
+a plus the velocity of a with respect to
+O
+
+ align:start position:0%
+O
+ 
+
+ align:start position:0%
+O
+cross p and now I'm going to say G it's
+
+ align:start position:0%
+cross p and now I'm going to say G it's
+ 
+
+ align:start position:0%
+cross p and now I'm going to say G it's
+Center of Mass center of gravity with
+
+ align:start position:0%
+Center of Mass center of gravity with
+ 
+
+ align:start position:0%
+Center of Mass center of gravity with
+respect to
+
+ align:start position:0%
+respect to
+ 
+
+ align:start position:0%
+respect to
+O So the same statement for a rigid body
+
+ align:start position:0%
+O So the same statement for a rigid body
+ 
+
+ align:start position:0%
+O So the same statement for a rigid body
+is it's a torque with respect to some
+
+ align:start position:0%
+is it's a torque with respect to some
+ 
+
+ align:start position:0%
+is it's a torque with respect to some
+point a which can be moving now even
+
+ align:start position:0%
+point a which can be moving now even
+ 
+
+ align:start position:0%
+point a which can be moving now even
+accelerating is the time rate of change
+
+ align:start position:0%
+accelerating is the time rate of change
+ 
+
+ align:start position:0%
+accelerating is the time rate of change
+of the angular momentum with respect to
+
+ align:start position:0%
+of the angular momentum with respect to
+ 
+
+ align:start position:0%
+of the angular momentum with respect to
+a of that rigid body plus vao cross
+
+ align:start position:0%
+a of that rigid body plus vao cross
+ 
+
+ align:start position:0%
+a of that rigid body plus vao cross
+PG okay and again when would this te
+
+ align:start position:0%
+PG okay and again when would this te
+ 
+
+ align:start position:0%
+PG okay and again when would this te
+what would this messy second term go to
+
+ align:start position:0%
+what would this messy second term go to
+ 
+
+ align:start position:0%
+what would this messy second term go to
+zero when the velocity of a is zero
+
+ align:start position:0%
+zero when the velocity of a is zero
+ 
+
+ align:start position:0%
+zero when the velocity of a is zero
+fixed axis
+
+ align:start position:0%
+fixed axis
+ 
+
+ align:start position:0%
+fixed axis
+rotation or when this is parallel to
+
+ align:start position:0%
+rotation or when this is parallel to
+ 
+
+ align:start position:0%
+rotation or when this is parallel to
+that which is true for the center of
+
+ align:start position:0%
+that which is true for the center of
+ 
+
+ align:start position:0%
+that which is true for the center of
+mass always so the same same two special
+
+ align:start position:0%
+mass always so the same same two special
+ 
+
+ align:start position:0%
+mass always so the same same two special
+cases apply for rigid bodies
+
+ align:start position:0%
+cases apply for rigid bodies
+ 
+
+ align:start position:0%
+cases apply for rigid bodies
+when velocity of a with respect to O
+
+ align:start position:0%
+when velocity of a with respect to O
+ 
+
+ align:start position:0%
+when velocity of a with respect to O
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+or when the velocity of a with respect
+
+ align:start position:0%
+or when the velocity of a with respect
+ 
+
+ align:start position:0%
+or when the velocity of a with respect
+to O is parallel to the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p and this the the most important case
+
+ align:start position:0%
+p and this the the most important case
+ 
+
+ align:start position:0%
+p and this the the most important case
+of that is all always
+
+ align:start position:0%
+of that is all always
+ 
+
+ align:start position:0%
+of that is all always
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true that's always the case and in these
+
+ align:start position:0%
+true that's always the case and in these
+ 
+
+ align:start position:0%
+true that's always the case and in these
+when you can say this then the torque
+
+ align:start position:0%
+when you can say this then the torque
+ 
+
+ align:start position:0%
+when you can say this then the torque
+with respect to a is d
+
+ align:start position:0%
+with respect to a is d
+ 
+
+ align:start position:0%
+with respect to a is d
+h respect to a DT no second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms and it's those kinds of this
+
+ align:start position:0%
+terms and it's those kinds of this
+ 
+
+ align:start position:0%
+terms and it's those kinds of this
+you've applied generally in your physics
+
+ align:start position:0%
+you've applied generally in your physics
+ 
+
+ align:start position:0%
+you've applied generally in your physics
+like in 801 you've used formulas like
+
+ align:start position:0%
+like in 801 you've used formulas like
+ 
+
+ align:start position:0%
+like in 801 you've used formulas like
+this a
+
+ align:start position:0%
+this a
+ 
+
+ align:start position:0%
+this a
+lot done problems either with respect to
+
+ align:start position:0%
+lot done problems either with respect to
+ 
+
+ align:start position:0%
+lot done problems either with respect to
+the center of
+
+ align:start position:0%
+the center of
+ 
+
+ align:start position:0%
+the center of
+mass so objects run doing things like
+
+ align:start position:0%
+mass so objects run doing things like
+ 
+
+ align:start position:0%
+mass so objects run doing things like
+that you'll do the torque formulas with
+
+ align:start position:0%
+that you'll do the torque formulas with
+ 
+
+ align:start position:0%
+that you'll do the torque formulas with
+respect to the center of mass or
+
+ align:start position:0%
+respect to the center of mass or
+ 
+
+ align:start position:0%
+respect to the center of mass or
+when you have things that are pinned to
+
+ align:start position:0%
+when you have things that are pinned to
+ 
+
+ align:start position:0%
+when you have things that are pinned to
+points and rotate about fixed
+
+ align:start position:0%
+points and rotate about fixed
+ 
+
+ align:start position:0%
+points and rotate about fixed
+axes then you use the other formulation
+
+ align:start position:0%
+axes then you use the other formulation
+ 
+
+ align:start position:0%
+axes then you use the other formulation
+where it's with respect to a
+
+ align:start position:0%
+where it's with respect to a
+ 
+
+ align:start position:0%
+where it's with respect to a
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+non-moving point so this is fixed axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that's kind of the dry
+
+ align:start position:0%
+all right so that's kind of the dry
+ 
+
+ align:start position:0%
+all right so that's kind of the dry
+derivation part of it I'm going to see
+
+ align:start position:0%
+derivation part of it I'm going to see
+ 
+
+ align:start position:0%
+derivation part of it I'm going to see
+if I can find an example
+
+ align:start position:0%
+if I can find an example
+ 
+
+ align:start position:0%
+if I can find an example
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay this is quite a bit like a
+
+ align:start position:0%
+here okay this is quite a bit like a
+ 
+
+ align:start position:0%
+here okay this is quite a bit like a
+number of the homework problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I've got a carnival
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ride got a bar
+
+ align:start position:0%
+ride got a bar
+ 
+
+ align:start position:0%
+ride got a bar
+and it's got a seat out
+
+ align:start position:0%
+and it's got a seat out
+ 
+
+ align:start position:0%
+and it's got a seat out
+here you're riding in it right so you're
+
+ align:start position:0%
+here you're riding in it right so you're
+ 
+
+ align:start position:0%
+here you're riding in it right so you're
+taking this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ride it's
+
+ align:start position:0%
+ride it's
+ 
+
+ align:start position:0%
+ride it's
+rotating this is some fixed axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and
+
+ align:start position:0%
+here and
+ 
+
+ align:start position:0%
+here and
+they you have a fixed coordinate system
+
+ align:start position:0%
+they you have a fixed coordinate system
+ 
+
+ align:start position:0%
+they you have a fixed coordinate system
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+o XYZ and then you'd probably have some
+
+ align:start position:0%
+o XYZ and then you'd probably have some
+ 
+
+ align:start position:0%
+o XYZ and then you'd probably have some
+rotating coordinate system with the
+
+ align:start position:0%
+rotating coordinate system with the
+ 
+
+ align:start position:0%
+rotating coordinate system with the
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a fixed here at the axis of
+
+ align:start position:0%
+a fixed here at the axis of
+ 
+
+ align:start position:0%
+a fixed here at the axis of
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+and this is going the what's what's
+
+ align:start position:0%
+and this is going the what's what's
+ 
+
+ align:start position:0%
+and this is going the what's what's
+unusual about this ride not only can go
+
+ align:start position:0%
+unusual about this ride not only can go
+ 
+
+ align:start position:0%
+unusual about this ride not only can go
+around and round but the arm can go in
+
+ align:start position:0%
+around and round but the arm can go in
+ 
+
+ align:start position:0%
+around and round but the arm can go in
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out so it might take a path inwards like
+
+ align:start position:0%
+out so it might take a path inwards like
+ 
+
+ align:start position:0%
+out so it might take a path inwards like
+if you pull the arm in as you're going
+
+ align:start position:0%
+if you pull the arm in as you're going
+ 
+
+ align:start position:0%
+if you pull the arm in as you're going
+around what are the forces that you feel
+
+ align:start position:0%
+around what are the forces that you feel
+ 
+
+ align:start position:0%
+around what are the forces that you feel
+in the ride
+
+ align:start position:0%
+in the ride
+ 
+
+ align:start position:0%
+in the ride
+okay so this is my point B out here it's
+
+ align:start position:0%
+okay so this is my point B out here it's
+ 
+
+ align:start position:0%
+okay so this is my point B out here it's
+where the person's at have some
+
+ align:start position:0%
+where the person's at have some
+ 
+
+ align:start position:0%
+where the person's at have some
+mass
+
+ align:start position:0%
+mass
+ 
+
+ align:start position:0%
+mass
+m and let's let for now first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case Theta dot let that be constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a constant angular rate here here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta and r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot all
+
+ align:start position:0%
+dot all
+ 
+
+ align:start position:0%
+dot all
+right now you already know quite a bit
+
+ align:start position:0%
+right now you already know quite a bit
+ 
+
+ align:start position:0%
+right now you already know quite a bit
+about things like this what forces if
+
+ align:start position:0%
+about things like this what forces if
+ 
+
+ align:start position:0%
+about things like this what forces if
+you're riding in that
+
+ align:start position:0%
+you're riding in that
+ 
+
+ align:start position:0%
+you're riding in that
+bucket what forces do you think you
+
+ align:start position:0%
+bucket what forces do you think you
+ 
+
+ align:start position:0%
+bucket what forces do you think you
+would feel or I should say it in more
+
+ align:start position:0%
+would feel or I should say it in more
+ 
+
+ align:start position:0%
+would feel or I should say it in more
+carefully
+
+ align:start position:0%
+carefully
+ 
+
+ align:start position:0%
+carefully
+there will be accelerations that you
+
+ align:start position:0%
+there will be accelerations that you
+ 
+
+ align:start position:0%
+there will be accelerations that you
+feel in that bucket you'll feel like
+
+ align:start position:0%
+feel in that bucket you'll feel like
+ 
+
+ align:start position:0%
+feel in that bucket you'll feel like
+forces on you but what are the
+
+ align:start position:0%
+forces on you but what are the
+ 
+
+ align:start position:0%
+forces on you but what are the
+accelerations that you will feel you
+
+ align:start position:0%
+accelerations that you will feel you
+ 
+
+ align:start position:0%
+accelerations that you will feel you
+expect to be if you're riding in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I hear one here Cal acceleration so
+
+ align:start position:0%
+it I hear one here Cal acceleration so
+ 
+
+ align:start position:0%
+it I hear one here Cal acceleration so
+there'll be centripetal acceleration
+
+ align:start position:0%
+there'll be centripetal acceleration
+ 
+
+ align:start position:0%
+there'll be centripetal acceleration
+right everybody agree with that how
+
+ align:start position:0%
+right everybody agree with that how
+ 
+
+ align:start position:0%
+right everybody agree with that how
+anything else acceler it's going to be
+
+ align:start position:0%
+anything else acceler it's going to be
+ 
+
+ align:start position:0%
+anything else acceler it's going to be
+some coris because our DOT is not zero
+
+ align:start position:0%
+some coris because our DOT is not zero
+ 
+
+ align:start position:0%
+some coris because our DOT is not zero
+right it's changing in position and when
+
+ align:start position:0%
+right it's changing in position and when
+ 
+
+ align:start position:0%
+right it's changing in position and when
+the length of the arm of something
+
+ align:start position:0%
+the length of the arm of something
+ 
+
+ align:start position:0%
+the length of the arm of something
+rotating at constant speed changes what
+
+ align:start position:0%
+rotating at constant speed changes what
+ 
+
+ align:start position:0%
+rotating at constant speed changes what
+momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changes angular for sure how about
+
+ align:start position:0%
+changes angular for sure how about
+ 
+
+ align:start position:0%
+changes angular for sure how about
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+momentum yeah it's changing too because
+
+ align:start position:0%
+momentum yeah it's changing too because
+ 
+
+ align:start position:0%
+momentum yeah it's changing too because
+R cross p is angular momentum so both
+
+ align:start position:0%
+R cross p is angular momentum so both
+ 
+
+ align:start position:0%
+R cross p is angular momentum so both
+linear and angular momentum are changing
+
+ align:start position:0%
+linear and angular momentum are changing
+ 
+
+ align:start position:0%
+linear and angular momentum are changing
+as this radius gets longer or shorter
+
+ align:start position:0%
+as this radius gets longer or shorter
+ 
+
+ align:start position:0%
+as this radius gets longer or shorter
+and if the if that angular momentum
+
+ align:start position:0%
+and if the if that angular momentum
+ 
+
+ align:start position:0%
+and if the if that angular momentum
+changes it takes torque to drive it and
+
+ align:start position:0%
+changes it takes torque to drive it and
+ 
+
+ align:start position:0%
+changes it takes torque to drive it and
+so we ought to be able to use the
+
+ align:start position:0%
+so we ought to be able to use the
+ 
+
+ align:start position:0%
+so we ought to be able to use the
+formulas that we've just derived to
+
+ align:start position:0%
+formulas that we've just derived to
+ 
+
+ align:start position:0%
+formulas that we've just derived to
+calculate something about the torqus
+
+ align:start position:0%
+calculate something about the torqus
+ 
+
+ align:start position:0%
+calculate something about the torqus
+required to make this happen and the
+
+ align:start position:0%
+required to make this happen and the
+ 
+
+ align:start position:0%
+required to make this happen and the
+forces on the rider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we'll treat this one as a
+
+ align:start position:0%
+okay so we'll treat this one as a
+ 
+
+ align:start position:0%
+okay so we'll treat this one as a
+particle so H the angular momentum of
+
+ align:start position:0%
+particle so H the angular momentum of
+ 
+
+ align:start position:0%
+particle so H the angular momentum of
+that of the rider out here at B with
+
+ align:start position:0%
+that of the rider out here at B with
+ 
+
+ align:start position:0%
+that of the rider out here at B with
+respect to O
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's going to be
+
+ align:start position:0%
+it's going to be
+ 
+
+ align:start position:0%
+it's going to be
+rvo
+
+ align:start position:0%
+rvo
+ 
+
+ align:start position:0%
+rvo
+cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p and in this problem I'll use polar
+
+ align:start position:0%
+p and in this problem I'll use polar
+ 
+
+ align:start position:0%
+p and in this problem I'll use polar
+coordinates pretty easy this is a planer
+
+ align:start position:0%
+coordinates pretty easy this is a planer
+ 
+
+ align:start position:0%
+coordinates pretty easy this is a planer
+motion problem it's confined to the XY
+
+ align:start position:0%
+motion problem it's confined to the XY
+ 
+
+ align:start position:0%
+motion problem it's confined to the XY
+plane and rotation in Z so polar
+
+ align:start position:0%
+plane and rotation in Z so polar
+ 
+
+ align:start position:0%
+plane and rotation in Z so polar
+coordinates are pretty convenient so
+
+ align:start position:0%
+coordinates are pretty convenient so
+ 
+
+ align:start position:0%
+coordinates are pretty convenient so
+this should look like radius r r
+
+ align:start position:0%
+this should look like radius r r
+ 
+
+ align:start position:0%
+this should look like radius r r
+Hat Cross and the the linear momentum of
+
+ align:start position:0%
+Hat Cross and the the linear momentum of
+ 
+
+ align:start position:0%
+Hat Cross and the the linear momentum of
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+masstimes r dot R hat that's the
+
+ align:start position:0%
+masstimes r dot R hat that's the
+ 
+
+ align:start position:0%
+masstimes r dot R hat that's the
+extension
+
+ align:start position:0%
+extension
+ 
+
+ align:start position:0%
+extension
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+but it also has velocity in
+
+ align:start position:0%
+but it also has velocity in
+ 
+
+ align:start position:0%
+but it also has velocity in
+the Theta hat
+
+ align:start position:0%
+the Theta hat
+ 
+
+ align:start position:0%
+the Theta hat
+Direction R Theta hat so this is
+
+ align:start position:0%
+Direction R Theta hat so this is
+ 
+
+ align:start position:0%
+Direction R Theta hat so this is
+p with respect to o m v and this is the
+
+ align:start position:0%
+p with respect to o m v and this is the
+ 
+
+ align:start position:0%
+p with respect to o m v and this is the
+rad this is the r crossed into it now r
+
+ align:start position:0%
+rad this is the r crossed into it now r
+ 
+
+ align:start position:0%
+rad this is the r crossed into it now r
+r Hat Cross R hat gives you zero so you
+
+ align:start position:0%
+r Hat Cross R hat gives you zero so you
+ 
+
+ align:start position:0%
+r Hat Cross R hat gives you zero so you
+only get a single term out of this and
+
+ align:start position:0%
+only get a single term out of this and
+ 
+
+ align:start position:0%
+only get a single term out of this and
+you get an R cross R Hat Cross Theta hat
+
+ align:start position:0%
+you get an R cross R Hat Cross Theta hat
+ 
+
+ align:start position:0%
+you get an R cross R Hat Cross Theta hat
+positive K so this looks like plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 Theta
+
+ align:start position:0%
+2 Theta
+ 
+
+ align:start position:0%
+2 Theta
+dot k
+
+ align:start position:0%
+dot k
+ 
+
+ align:start position:0%
+dot k
+hat that's my H Bo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+o now I would that's my first piece that
+
+ align:start position:0%
+o now I would that's my first piece that
+ 
+
+ align:start position:0%
+o now I would that's my first piece that
+I wanted to get that's the a part that's
+
+ align:start position:0%
+I wanted to get that's the a part that's
+ 
+
+ align:start position:0%
+I wanted to get that's the a part that's
+find the angular momentum so this is
+
+ align:start position:0%
+find the angular momentum so this is
+ 
+
+ align:start position:0%
+find the angular momentum so this is
+a B I want to know the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+torque
+
+ align:start position:0%
+torque
+ 
+
+ align:start position:0%
+torque
+okay well which formula can we
+
+ align:start position:0%
+okay well which formula can we
+ 
+
+ align:start position:0%
+okay well which formula can we
+use are we allowed to use do we have to
+
+ align:start position:0%
+use are we allowed to use do we have to
+ 
+
+ align:start position:0%
+use are we allowed to use do we have to
+account for that second
+
+ align:start position:0%
+account for that second
+ 
+
+ align:start position:0%
+account for that second
+term no why yeah the velocity of the
+
+ align:start position:0%
+term no why yeah the velocity of the
+ 
+
+ align:start position:0%
+term no why yeah the velocity of the
+point about which we're Computing the
+
+ align:start position:0%
+point about which we're Computing the
+ 
+
+ align:start position:0%
+point about which we're Computing the
+angular momentum and therefore the
+
+ align:start position:0%
+angular momentum and therefore the
+ 
+
+ align:start position:0%
+angular momentum and therefore the
+torque is not moving so you only have to
+
+ align:start position:0%
+torque is not moving so you only have to
+ 
+
+ align:start position:0%
+torque is not moving so you only have to
+deal with the first term so the
+
+ align:start position:0%
+deal with the first term so the
+ 
+
+ align:start position:0%
+deal with the first term so the
+torque required to move that particle at
+
+ align:start position:0%
+torque required to move that particle at
+ 
+
+ align:start position:0%
+torque required to move that particle at
+B with respect to O is just the time
+
+ align:start position:0%
+B with respect to O is just the time
+ 
+
+ align:start position:0%
+B with respect to O is just the time
+rate of change d by DT of h b with
+
+ align:start position:0%
+rate of change d by DT of h b with
+ 
+
+ align:start position:0%
+rate of change d by DT of h b with
+respect to O and that's d by DT
+
+ align:start position:0%
+respect to O and that's d by DT
+ 
+
+ align:start position:0%
+respect to O and that's d by DT
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+m r
+
+ align:start position:0%
+m r
+ 
+
+ align:start position:0%
+m r
+2 Theta
+
+ align:start position:0%
+2 Theta
+ 
+
+ align:start position:0%
+2 Theta
+dot k
+
+ align:start position:0%
+dot k
+ 
+
+ align:start position:0%
+dot k
+hat so what are the constants in this
+
+ align:start position:0%
+hat so what are the constants in this
+ 
+
+ align:start position:0%
+hat so what are the constants in this
+expression so we don't have to worry
+
+ align:start position:0%
+expression so we don't have to worry
+ 
+
+ align:start position:0%
+expression so we don't have to worry
+about their derivatives K hat change
+
+ align:start position:0%
+about their derivatives K hat change
+ 
+
+ align:start position:0%
+about their derivatives K hat change
+length no change direction no Theta dot
+
+ align:start position:0%
+length no change direction no Theta dot
+ 
+
+ align:start position:0%
+length no change direction no Theta dot
+does it change change in this
+
+ align:start position:0%
+does it change change in this
+ 
+
+ align:start position:0%
+does it change change in this
+problem no we fixed it we said it
+
+ align:start position:0%
+problem no we fixed it we said it
+ 
+
+ align:start position:0%
+problem no we fixed it we said it
+arbitrarily started off saying that
+
+ align:start position:0%
+arbitrarily started off saying that
+ 
+
+ align:start position:0%
+arbitrarily started off saying that
+we'll just let Theta dot be constant R
+
+ align:start position:0%
+we'll just let Theta dot be constant R
+ 
+
+ align:start position:0%
+we'll just let Theta dot be constant R
+though is changing so the time
+
+ align:start position:0%
+though is changing so the time
+ 
+
+ align:start position:0%
+though is changing so the time
+derivative of this particular one only
+
+ align:start position:0%
+derivative of this particular one only
+ 
+
+ align:start position:0%
+derivative of this particular one only
+we have to only have to deal with the r
+
+ align:start position:0%
+we have to only have to deal with the r
+ 
+
+ align:start position:0%
+we have to only have to deal with the r
+actually I'll I'll forget that for a
+
+ align:start position:0%
+actually I'll I'll forget that for a
+ 
+
+ align:start position:0%
+actually I'll I'll forget that for a
+second because I want to get both terms
+
+ align:start position:0%
+second because I want to get both terms
+ 
+
+ align:start position:0%
+second because I want to get both terms
+and then we'll let it be zero so this
+
+ align:start position:0%
+and then we'll let it be zero so this
+ 
+
+ align:start position:0%
+and then we'll let it be zero so this
+time derivative then when you work it
+
+ align:start position:0%
+time derivative then when you work it
+ 
+
+ align:start position:0%
+time derivative then when you work it
+out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right the derivative of the r term gives
+
+ align:start position:0%
+right the derivative of the r term gives
+ 
+
+ align:start position:0%
+right the derivative of the r term gives
+you 2 m r r do theta
+
+ align:start position:0%
+you 2 m r r do theta
+ 
+
+ align:start position:0%
+you 2 m r r do theta
+dot k hat
+
+ align:start position:0%
+dot k hat
+ 
+
+ align:start position:0%
+dot k hat
+and I'll just go ahead and forget for a
+
+ align:start position:0%
+and I'll just go ahead and forget for a
+ 
+
+ align:start position:0%
+and I'll just go ahead and forget for a
+minute that I said that's constant let's
+
+ align:start position:0%
+minute that I said that's constant let's
+ 
+
+ align:start position:0%
+minute that I said that's constant let's
+get the other term that might be
+
+ align:start position:0%
+get the other term that might be
+ 
+
+ align:start position:0%
+get the other term that might be
+there that term gives us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh m r 2 Theta double dot k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hat this term comes from what we'll
+
+ align:start position:0%
+hat this term comes from what we'll
+ 
+
+ align:start position:0%
+hat this term comes from what we'll
+we'll find is the cholis one and this is
+
+ align:start position:0%
+we'll find is the cholis one and this is
+ 
+
+ align:start position:0%
+we'll find is the cholis one and this is
+from what we'd call the oil Arian
+
+ align:start position:0%
+from what we'd call the oil Arian
+ 
+
+ align:start position:0%
+from what we'd call the oil Arian
+acceleration this torque must the
+
+ align:start position:0%
+acceleration this torque must the
+ 
+
+ align:start position:0%
+acceleration this torque must the
+torque get this up a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+higher we should be able to write as
+
+ align:start position:0%
+higher we should be able to write as
+ 
+
+ align:start position:0%
+higher we should be able to write as
+some R
+
+ align:start position:0%
+some R
+ 
+
+ align:start position:0%
+some R
+cross F right and so the r cross F terms
+
+ align:start position:0%
+cross F right and so the r cross F terms
+ 
+
+ align:start position:0%
+cross F right and so the r cross F terms
+this will
+
+ align:start position:0%
+this will
+ 
+
+ align:start position:0%
+this will
+be from the coris force and this would
+
+ align:start position:0%
+be from the coris force and this would
+ 
+
+ align:start position:0%
+be from the coris force and this would
+be from that or oian
+
+ align:start position:0%
+be from that or oian
+ 
+
+ align:start position:0%
+be from that or oian
+Force so this will look like r r hat
+
+ align:start position:0%
+Force so this will look like r r hat
+ 
+
+ align:start position:0%
+Force so this will look like r r hat
+crossed I'm just factoring this back out
+
+ align:start position:0%
+crossed I'm just factoring this back out
+ 
+
+ align:start position:0%
+crossed I'm just factoring this back out
+into its cross products RR Hat Cross 2 m
+
+ align:start position:0%
+into its cross products RR Hat Cross 2 m
+ 
+
+ align:start position:0%
+into its cross products RR Hat Cross 2 m
+r dot Theta dot in the Theta hat
+
+ align:start position:0%
+r dot Theta dot in the Theta hat
+ 
+
+ align:start position:0%
+r dot Theta dot in the Theta hat
+Direction plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r Theta double dot in the Theta hat
+
+ align:start position:0%
+r Theta double dot in the Theta hat
+ 
+
+ align:start position:0%
+r Theta double dot in the Theta hat
+Direction so there's two terms in this
+
+ align:start position:0%
+Direction so there's two terms in this
+ 
+
+ align:start position:0%
+Direction so there's two terms in this
+torque expression they come from R cross
+
+ align:start position:0%
+torque expression they come from R cross
+ 
+
+ align:start position:0%
+torque expression they come from R cross
+two Force
+
+ align:start position:0%
+two Force
+ 
+
+ align:start position:0%
+two Force
+terms the first Force term is what we
+
+ align:start position:0%
+terms the first Force term is what we
+ 
+
+ align:start position:0%
+terms the first Force term is what we
+know to be the cholis force and the
+
+ align:start position:0%
+know to be the cholis force and the
+ 
+
+ align:start position:0%
+know to be the cholis force and the
+second Force term I'm missing an M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here RM Theta double do theta hat that's
+
+ align:start position:0%
+here RM Theta double do theta hat that's
+ 
+
+ align:start position:0%
+here RM Theta double do theta hat that's
+the force that takes to if the thing
+
+ align:start position:0%
+the force that takes to if the thing
+ 
+
+ align:start position:0%
+the force that takes to if the thing
+were're accelerating
+
+ align:start position:0%
+were're accelerating
+ 
+
+ align:start position:0%
+were're accelerating
+just to accelerate that ball Theta
+
+ align:start position:0%
+just to accelerate that ball Theta
+ 
+
+ align:start position:0%
+just to accelerate that ball Theta
+double dot takes that takes a force you
+
+ align:start position:0%
+double dot takes that takes a force you
+ 
+
+ align:start position:0%
+double dot takes that takes a force you
+do these cross products R cross Theta
+
+ align:start position:0%
+do these cross products R cross Theta
+ 
+
+ align:start position:0%
+do these cross products R cross Theta
+hat gives you k r cross Theta hat gives
+
+ align:start position:0%
+hat gives you k r cross Theta hat gives
+ 
+
+ align:start position:0%
+hat gives you k r cross Theta hat gives
+you K it all comes out in the right
+
+ align:start position:0%
+you K it all comes out in the right
+ 
+
+ align:start position:0%
+you K it all comes out in the right
+directions and now to do the problem we
+
+ align:start position:0%
+directions and now to do the problem we
+ 
+
+ align:start position:0%
+directions and now to do the problem we
+had we said oh yeah but this one's zero
+
+ align:start position:0%
+had we said oh yeah but this one's zero
+ 
+
+ align:start position:0%
+had we said oh yeah but this one's zero
+so we'll let this term go to
+
+ align:start position:0%
+so we'll let this term go to
+ 
+
+ align:start position:0%
+so we'll let this term go to
+zero we're left with a single term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we plugged in some numbers let's
+
+ align:start position:0%
+and if we plugged in some numbers let's
+ 
+
+ align:start position:0%
+and if we plugged in some numbers let's
+just see if how this works out and this
+
+ align:start position:0%
+just see if how this works out and this
+ 
+
+ align:start position:0%
+just see if how this works out and this
+we know it's just R cross the coris
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well let's let M you let M be 100
+
+ align:start position:0%
+well let's let M you let M be 100
+ 
+
+ align:start position:0%
+well let's let M you let M be 100
+kilogram and R be 5
+
+ align:start position:0%
+kilogram and R be 5
+ 
+
+ align:start position:0%
+kilogram and R be 5
+M and R
+
+ align:start position:0%
+M and R
+ 
+
+ align:start position:0%
+M and R
+dot
+
+ align:start position:0%
+dot
+ 
+
+ align:start position:0%
+dot
+0.4 m/ second all kind of perfectly
+
+ align:start position:0%
+0.4 m/ second all kind of perfectly
+ 
+
+ align:start position:0%
+0.4 m/ second all kind of perfectly
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+dimensions and Theta
+
+ align:start position:0%
+dimensions and Theta
+ 
+
+ align:start position:0%
+dimensions and Theta
+dot equals 3
+
+ align:start position:0%
+dot equals 3
+ 
+
+ align:start position:0%
+dot equals 3
+radians per second so 2 pi radians per
+
+ align:start position:0%
+radians per second so 2 pi radians per
+ 
+
+ align:start position:0%
+radians per second so 2 pi radians per
+second means it goes around once once a
+
+ align:start position:0%
+second means it goes around once once a
+ 
+
+ align:start position:0%
+second means it goes around once once a
+second right say a little less than half
+
+ align:start position:0%
+second right say a little less than half
+ 
+
+ align:start position:0%
+second right say a little less than half
+a REV per second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+probably yeah good catch got to have an
+
+ align:start position:0%
+probably yeah good catch got to have an
+ 
+
+ align:start position:0%
+probably yeah good catch got to have an
+r in it because that R comes from here
+
+ align:start position:0%
+r in it because that R comes from here
+ 
+
+ align:start position:0%
+r in it because that R comes from here
+right so I had the coris force written
+
+ align:start position:0%
+right so I had the coris force written
+ 
+
+ align:start position:0%
+right so I had the coris force written
+down but not the r you have to multiply
+
+ align:start position:0%
+down but not the r you have to multiply
+ 
+
+ align:start position:0%
+down but not the r you have to multiply
+it by so now we got if you plug in all
+
+ align:start position:0%
+it by so now we got if you plug in all
+ 
+
+ align:start position:0%
+it by so now we got if you plug in all
+of these numbers let's see if it see if
+
+ align:start position:0%
+of these numbers let's see if it see if
+ 
+
+ align:start position:0%
+of these numbers let's see if it see if
+it's ride you could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+survive I actually computed the Coriolis
+
+ align:start position:0%
+survive I actually computed the Coriolis
+ 
+
+ align:start position:0%
+survive I actually computed the Coriolis
+Force first it's just a I think it's
+
+ align:start position:0%
+Force first it's just a I think it's
+ 
+
+ align:start position:0%
+Force first it's just a I think it's
+just interesting to get a physical
+
+ align:start position:0%
+just interesting to get a physical
+ 
+
+ align:start position:0%
+just interesting to get a physical
+feeling for how whether or not you can
+
+ align:start position:0%
+feeling for how whether or not you can
+ 
+
+ align:start position:0%
+feeling for how whether or not you can
+feel these forces so the Coriolis force
+
+ align:start position:0%
+feel these forces so the Coriolis force
+ 
+
+ align:start position:0%
+feel these forces so the Coriolis force
+is just everything but the r 2m r. Theta
+
+ align:start position:0%
+is just everything but the r 2m r. Theta
+ 
+
+ align:start position:0%
+is just everything but the r 2m r. Theta
+dot so if you calculate that you get
+
+ align:start position:0%
+dot so if you calculate that you get
+ 
+
+ align:start position:0%
+dot so if you calculate that you get
+240 Newtons
+
+ align:start position:0%
+240 Newtons
+ 
+
+ align:start position:0%
+240 Newtons
+and R times that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+torque five times that about uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1,200 Newton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M and the acceleration how do we gets
+
+ align:start position:0%
+M and the acceleration how do we gets
+ 
+
+ align:start position:0%
+M and the acceleration how do we gets
+acceleration well F core Corola force is
+
+ align:start position:0%
+acceleration well F core Corola force is
+ 
+
+ align:start position:0%
+acceleration well F core Corola force is
+some mass times an acceleration so we
+
+ align:start position:0%
+some mass times an acceleration so we
+ 
+
+ align:start position:0%
+some mass times an acceleration so we
+can solve from that 240 Newtons the ma
+
+ align:start position:0%
+can solve from that 240 Newtons the ma
+ 
+
+ align:start position:0%
+can solve from that 240 Newtons the ma
+the acceleration of the system
+
+ align:start position:0%
+the acceleration of the system
+ 
+
+ align:start position:0%
+the acceleration of the system
+acceleration of a b with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O 240
+
+ align:start position:0%
+O 240
+ 
+
+ align:start position:0%
+O 240
+Newtons divided 100
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kilogram
+
+ align:start position:0%
+kilogram
+ 
+
+ align:start position:0%
+kilogram
+2.4 m/ second s
+
+ align:start position:0%
+2.4 m/ second s
+ 
+
+ align:start position:0%
+2.4 m/ second s
+square and what's that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G's yeah about quarter of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g and again would you feel that so now
+
+ align:start position:0%
+g and again would you feel that so now
+ 
+
+ align:start position:0%
+g and again would you feel that so now
+you're riding so now you're riding in
+
+ align:start position:0%
+you're riding so now you're riding in
+ 
+
+ align:start position:0%
+you're riding so now you're riding in
+the bucket right let's say it's just
+
+ align:start position:0%
+the bucket right let's say it's just
+ 
+
+ align:start position:0%
+the bucket right let's say it's just
+spinning around the arm's not going in
+
+ align:start position:0%
+spinning around the arm's not going in
+ 
+
+ align:start position:0%
+spinning around the arm's not going in
+and out at all so you're riding in it
+
+ align:start position:0%
+and out at all so you're riding in it
+ 
+
+ align:start position:0%
+and out at all so you're riding in it
+what what force would you
+
+ align:start position:0%
+what what force would you
+ 
+
+ align:start position:0%
+what what force would you
+feel would you feel any forces pushing
+
+ align:start position:0%
+feel would you feel any forces pushing
+ 
+
+ align:start position:0%
+feel would you feel any forces pushing
+you into your
+
+ align:start position:0%
+you into your
+ 
+
+ align:start position:0%
+you into your
+seat constant speed r dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero somebody out there would you feel
+
+ align:start position:0%
+zero somebody out there would you feel
+ 
+
+ align:start position:0%
+zero somebody out there would you feel
+any Force if you're going around and
+
+ align:start position:0%
+any Force if you're going around and
+ 
+
+ align:start position:0%
+any Force if you're going around and
+around in this thing sitting in the seat
+
+ align:start position:0%
+around in this thing sitting in the seat
+ 
+
+ align:start position:0%
+around in this thing sitting in the seat
+okay what's it come from centripetal
+
+ align:start position:0%
+okay what's it come from centripetal
+ 
+
+ align:start position:0%
+okay what's it come from centripetal
+acceleration right all right so and that
+
+ align:start position:0%
+acceleration right all right so and that
+ 
+
+ align:start position:0%
+acceleration right all right so and that
+is in what
+
+ align:start position:0%
+is in what
+ 
+
+ align:start position:0%
+is in what
+direction the acceleration is inward
+
+ align:start position:0%
+direction the acceleration is inward
+ 
+
+ align:start position:0%
+direction the acceleration is inward
+what would you actually feel
+
+ align:start position:0%
+what would you actually feel
+ 
+
+ align:start position:0%
+what would you actually feel
+you you'd feel if this but if this seat
+
+ align:start position:0%
+you you'd feel if this but if this seat
+ 
+
+ align:start position:0%
+you you'd feel if this but if this seat
+could swing out so you're facing in
+
+ align:start position:0%
+could swing out so you're facing in
+ 
+
+ align:start position:0%
+could swing out so you're facing in
+you'd feel like you're being thrown out
+
+ align:start position:0%
+you'd feel like you're being thrown out
+ 
+
+ align:start position:0%
+you'd feel like you're being thrown out
+in your seat
+
+ align:start position:0%
+in your seat
+ 
+
+ align:start position:0%
+in your seat
+right because you have to have a force
+
+ align:start position:0%
+right because you have to have a force
+ 
+
+ align:start position:0%
+right because you have to have a force
+on you to make that acceleration happen
+
+ align:start position:0%
+on you to make that acceleration happen
+ 
+
+ align:start position:0%
+on you to make that acceleration happen
+the acceleration is inward the force it
+
+ align:start position:0%
+the acceleration is inward the force it
+ 
+
+ align:start position:0%
+the acceleration is inward the force it
+better be pushing you inward so it's
+
+ align:start position:0%
+better be pushing you inward so it's
+ 
+
+ align:start position:0%
+better be pushing you inward so it's
+pushing on your back if you're looking
+
+ align:start position:0%
+pushing on your back if you're looking
+ 
+
+ align:start position:0%
+pushing on your back if you're looking
+in going around so that's the you know
+
+ align:start position:0%
+in going around so that's the you know
+ 
+
+ align:start position:0%
+in going around so that's the you know
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh forgotten the term for but you know
+
+ align:start position:0%
+uh forgotten the term for but you know
+ 
+
+ align:start position:0%
+uh forgotten the term for but you know
+they put the astronauts in a centrifuge
+
+ align:start position:0%
+they put the astronauts in a centrifuge
+ 
+
+ align:start position:0%
+they put the astronauts in a centrifuge
+right spin them around to see if they
+
+ align:start position:0%
+right spin them around to see if they
+ 
+
+ align:start position:0%
+right spin them around to see if they
+can take High G's okay that's the that's
+
+ align:start position:0%
+can take High G's okay that's the that's
+ 
+
+ align:start position:0%
+can take High G's okay that's the that's
+the G the inward high G acceleration due
+
+ align:start position:0%
+the G the inward high G acceleration due
+ 
+
+ align:start position:0%
+the G the inward high G acceleration due
+to the centripetal acceleration make you
+
+ align:start position:0%
+to the centripetal acceleration make you
+ 
+
+ align:start position:0%
+to the centripetal acceleration make you
+going in a circle but now not only are
+
+ align:start position:0%
+going in a circle but now not only are
+ 
+
+ align:start position:0%
+going in a circle but now not only are
+you going to feel that but now you start
+
+ align:start position:0%
+you going to feel that but now you start
+ 
+
+ align:start position:0%
+you going to feel that but now you start
+changing the length of the arm and if
+
+ align:start position:0%
+changing the length of the arm and if
+ 
+
+ align:start position:0%
+changing the length of the arm and if
+you change and if you change our DOT and
+
+ align:start position:0%
+you change and if you change our DOT and
+ 
+
+ align:start position:0%
+you change and if you change our DOT and
+make it positive so the arm is getting
+
+ align:start position:0%
+make it positive so the arm is getting
+ 
+
+ align:start position:0%
+make it positive so the arm is getting
+longer and we made this4 m/ second so
+
+ align:start position:0%
+longer and we made this4 m/ second so
+ 
+
+ align:start position:0%
+longer and we made this4 m/ second so
+it's moving out you know about like that
+
+ align:start position:0%
+it's moving out you know about like that
+ 
+
+ align:start position:0%
+it's moving out you know about like that
+it's not real fast but it's going to
+
+ align:start position:0%
+it's not real fast but it's going to
+ 
+
+ align:start position:0%
+it's not real fast but it's going to
+create a quarter of a g acceleration on
+
+ align:start position:0%
+create a quarter of a g acceleration on
+ 
+
+ align:start position:0%
+create a quarter of a g acceleration on
+you and and if R Dot's positive which
+
+ align:start position:0%
+you and and if R Dot's positive which
+ 
+
+ align:start position:0%
+you and and if R Dot's positive which
+direction is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration I was careful we walked all
+
+ align:start position:0%
+acceleration I was careful we walked all
+ 
+
+ align:start position:0%
+acceleration I was careful we walked all
+the way through this the acceleration is
+
+ align:start position:0%
+the way through this the acceleration is
+ 
+
+ align:start position:0%
+the way through this the acceleration is
+positive but in what
+
+ align:start position:0%
+positive but in what
+ 
+
+ align:start position:0%
+positive but in what
+direction for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coris Theta hat positive Theta hat so
+
+ align:start position:0%
+coris Theta hat positive Theta hat so
+ 
+
+ align:start position:0%
+coris Theta hat positive Theta hat so
+it's in direction of increasing Theta so
+
+ align:start position:0%
+it's in direction of increasing Theta so
+ 
+
+ align:start position:0%
+it's in direction of increasing Theta so
+this one is perpendicular to the arm
+
+ align:start position:0%
+this one is perpendicular to the arm
+ 
+
+ align:start position:0%
+this one is perpendicular to the arm
+right and this is this is the uh you
+
+ align:start position:0%
+right and this is this is the uh you
+ 
+
+ align:start position:0%
+right and this is this is the uh you
+know when my pingpong ball in here the
+
+ align:start position:0%
+know when my pingpong ball in here the
+ 
+
+ align:start position:0%
+know when my pingpong ball in here the
+force that actually causes it to speed
+
+ align:start position:0%
+force that actually causes it to speed
+ 
+
+ align:start position:0%
+force that actually causes it to speed
+up is partly cholis and partly orer and
+
+ align:start position:0%
+up is partly cholis and partly orer and
+ 
+
+ align:start position:0%
+up is partly cholis and partly orer and
+if I can make this go at constant speed
+
+ align:start position:0%
+if I can make this go at constant speed
+ 
+
+ align:start position:0%
+if I can make this go at constant speed
+the force that drives that the force
+
+ align:start position:0%
+the force that drives that the force
+ 
+
+ align:start position:0%
+the force that drives that the force
+that actually speeds that up is it going
+
+ align:start position:0%
+that actually speeds that up is it going
+ 
+
+ align:start position:0%
+that actually speeds that up is it going
+out is the coris force the normal one so
+
+ align:start position:0%
+out is the coris force the normal one so
+ 
+
+ align:start position:0%
+out is the coris force the normal one so
+if you were on this ride you'd be
+
+ align:start position:0%
+if you were on this ride you'd be
+ 
+
+ align:start position:0%
+if you were on this ride you'd be
+feeling about a quarter of a g
+
+ align:start position:0%
+feeling about a quarter of a g
+ 
+
+ align:start position:0%
+feeling about a quarter of a g
+perpendicular to the arm you'd be
+
+ align:start position:0%
+perpendicular to the arm you'd be
+ 
+
+ align:start position:0%
+perpendicular to the arm you'd be
+feeling another Force inward that's the
+
+ align:start position:0%
+feeling another Force inward that's the
+ 
+
+ align:start position:0%
+feeling another Force inward that's the
+Cent due to caused by the centripetal
+
+ align:start position:0%
+Cent due to caused by the centripetal
+ 
+
+ align:start position:0%
+Cent due to caused by the centripetal
+acceleration so you'd be feeling both of
+
+ align:start position:0%
+acceleration so you'd be feeling both of
+ 
+
+ align:start position:0%
+acceleration so you'd be feeling both of
+them how big is the centripetal
+
+ align:start position:0%
+them how big is the centripetal
+ 
+
+ align:start position:0%
+them how big is the centripetal
+acceleration
+
+ align:start position:0%
+acceleration
+ 
+
+ align:start position:0%
+acceleration
+sort of like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh R Omega squ right yeah R is 5 Omega
+
+ align:start position:0%
+uh R Omega squ right yeah R is 5 Omega
+ 
+
+ align:start position:0%
+uh R Omega squ right yeah R is 5 Omega
+is 3 3^ 2 is 9 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+5 9 * 5
+
+ align:start position:0%
+5 9 * 5
+ 
+
+ align:start position:0%
+5 9 * 5
+45 divided by 10 4 and a half
+
+ align:start position:0%
+45 divided by 10 4 and a half
+ 
+
+ align:start position:0%
+45 divided by 10 4 and a half
+gez you wouldn't notice the cor you
+
+ align:start position:0%
+gez you wouldn't notice the cor you
+ 
+
+ align:start position:0%
+gez you wouldn't notice the cor you
+wouldn't notice the cholis very much
+
+ align:start position:0%
+wouldn't notice the cholis very much
+ 
+
+ align:start position:0%
+wouldn't notice the cholis very much
+it'd be kind of this' be kind of a tough
+
+ align:start position:0%
+it'd be kind of this' be kind of a tough
+ 
+
+ align:start position:0%
+it'd be kind of this' be kind of a tough
+tough ride on the uh on that side of
+
+ align:start position:0%
+tough ride on the uh on that side of
+ 
+
+ align:start position:0%
+tough ride on the uh on that side of
+things Okay so we've now we've done that
+
+ align:start position:0%
+things Okay so we've now we've done that
+ 
+
+ align:start position:0%
+things Okay so we've now we've done that
+uh you've seen a simple application
+
+ align:start position:0%
+uh you've seen a simple application
+ 
+
+ align:start position:0%
+uh you've seen a simple application
+pretty straightforward application of
+
+ align:start position:0%
+pretty straightforward application of
+ 
+
+ align:start position:0%
+pretty straightforward application of
+using time derivative of angular
+
+ align:start position:0%
+using time derivative of angular
+ 
+
+ align:start position:0%
+using time derivative of angular
+momentum to calculate
+
+ align:start position:0%
+momentum to calculate
+ 
+
+ align:start position:0%
+momentum to calculate
+torqus so homework again there's a
+
+ align:start position:0%
+torqus so homework again there's a
+ 
+
+ align:start position:0%
+torqus so homework again there's a
+couple problems you know very similar to
+
+ align:start position:0%
+couple problems you know very similar to
+ 
+
+ align:start position:0%
+couple problems you know very similar to
+the one I just did things going around
+
+ align:start position:0%
+the one I just did things going around
+ 
+
+ align:start position:0%
+the one I just did things going around
+Circus rides that kind of stuff so
+
+ align:start position:0%
+Circus rides that kind of stuff so
+ 
+
+ align:start position:0%
+Circus rides that kind of stuff so
+so have a good weekend see you on
+
+ align:start position:0%
+so have a good weekend see you on
+ 
+
+ align:start position:0%
+so have a good weekend see you on
+Tuesday
\ No newline at end of file
diff --git a/NS0pxSF0Kmo.txt b/NS0pxSF0Kmo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..238ffbd7c7c697185813f3826f70b293d02c8502
--- /dev/null
+++ b/NS0pxSF0Kmo.txt
@@ -0,0 +1,827 @@
+align:start position:0%
+ 
+so now let's talk about how we go from I
+
+ align:start position:0%
+so now let's talk about how we go from I
+ 
+
+ align:start position:0%
+so now let's talk about how we go from I
+have a passion to a technology or an
+
+ align:start position:0%
+have a passion to a technology or an
+ 
+
+ align:start position:0%
+have a passion to a technology or an
+idea what are the factors even within a
+
+ align:start position:0%
+idea what are the factors even within a
+ 
+
+ align:start position:0%
+idea what are the factors even within a
+technology or an idea that would you
+
+ align:start position:0%
+technology or an idea that would you
+ 
+
+ align:start position:0%
+technology or an idea that would you
+would decide with your team now we
+
+ align:start position:0%
+would decide with your team now we
+ 
+
+ align:start position:0%
+would decide with your team now we
+talked about joining with the team um
+
+ align:start position:0%
+talked about joining with the team um
+ 
+
+ align:start position:0%
+talked about joining with the team um
+what are those things that you would
+
+ align:start position:0%
+what are those things that you would
+ 
+
+ align:start position:0%
+what are those things that you would
+make a factors to decide first of all
+
+ align:start position:0%
+make a factors to decide first of all
+ 
+
+ align:start position:0%
+make a factors to decide first of all
+you would start with knowledge you want
+
+ align:start position:0%
+you would start with knowledge you want
+ 
+
+ align:start position:0%
+you would start with knowledge you want
+to be working in a
+
+ align:start position:0%
+to be working in a
+ 
+
+ align:start position:0%
+to be working in a
+in a area or technology or Marketplace
+
+ align:start position:0%
+in a area or technology or Marketplace
+ 
+
+ align:start position:0%
+in a area or technology or Marketplace
+that you understand that you have a
+
+ align:start position:0%
+that you understand that you have a
+ 
+
+ align:start position:0%
+that you understand that you have a
+knowledge about um but that's necessary
+
+ align:start position:0%
+knowledge about um but that's necessary
+ 
+
+ align:start position:0%
+knowledge about um but that's necessary
+but not sufficient the next thing is
+
+ align:start position:0%
+but not sufficient the next thing is
+ 
+
+ align:start position:0%
+but not sufficient the next thing is
+that you have to have a
+
+ align:start position:0%
+that you have to have a
+ 
+
+ align:start position:0%
+that you have to have a
+Capa ability there something that that's
+
+ align:start position:0%
+Capa ability there something that that's
+ 
+
+ align:start position:0%
+Capa ability there something that that's
+special to you you might be good at
+
+ align:start position:0%
+special to you you might be good at
+ 
+
+ align:start position:0%
+special to you you might be good at
+Material Science and that would allow
+
+ align:start position:0%
+Material Science and that would allow
+ 
+
+ align:start position:0%
+Material Science and that would allow
+you to do energy storage you might not
+
+ align:start position:0%
+you to do energy storage you might not
+ 
+
+ align:start position:0%
+you to do energy storage you might not
+have that expertise but you might have
+
+ align:start position:0%
+have that expertise but you might have
+ 
+
+ align:start position:0%
+have that expertise but you might have
+um an understanding after having worked
+
+ align:start position:0%
+um an understanding after having worked
+ 
+
+ align:start position:0%
+um an understanding after having worked
+rathon for 10 years of what the
+
+ align:start position:0%
+rathon for 10 years of what the
+ 
+
+ align:start position:0%
+rathon for 10 years of what the
+Aerospace industry is about and the
+
+ align:start position:0%
+Aerospace industry is about and the
+ 
+
+ align:start position:0%
+Aerospace industry is about and the
+issues that they face so that's a
+
+ align:start position:0%
+issues that they face so that's a
+ 
+
+ align:start position:0%
+issues that they face so that's a
+special capability that you can build up
+
+ align:start position:0%
+special capability that you can build up
+ 
+
+ align:start position:0%
+special capability that you can build up
+the third thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is would
+
+ align:start position:0%
+is would
+ 
+
+ align:start position:0%
+is would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+connections connections you say well
+
+ align:start position:0%
+connections connections you say well
+ 
+
+ align:start position:0%
+connections connections you say well
+that's something that's easy no that
+
+ align:start position:0%
+that's something that's easy no that
+ 
+
+ align:start position:0%
+that's something that's easy no that
+actually is an asset that you and your
+
+ align:start position:0%
+actually is an asset that you and your
+ 
+
+ align:start position:0%
+actually is an asset that you and your
+team would have do you know the proper
+
+ align:start position:0%
+team would have do you know the proper
+ 
+
+ align:start position:0%
+team would have do you know the proper
+people in this industry do you know the
+
+ align:start position:0%
+people in this industry do you know the
+ 
+
+ align:start position:0%
+people in this industry do you know the
+the people who really understand energy
+
+ align:start position:0%
+the people who really understand energy
+ 
+
+ align:start position:0%
+the people who really understand energy
+storage or whatever the other technology
+
+ align:start position:0%
+storage or whatever the other technology
+ 
+
+ align:start position:0%
+storage or whatever the other technology
+is that you might be working on having
+
+ align:start position:0%
+is that you might be working on having
+ 
+
+ align:start position:0%
+is that you might be working on having
+the right connections is a valuable
+
+ align:start position:0%
+the right connections is a valuable
+ 
+
+ align:start position:0%
+the right connections is a valuable
+asset that should not be
+
+ align:start position:0%
+asset that should not be
+ 
+
+ align:start position:0%
+asset that should not be
+overlooked the next one number four
+
+ align:start position:0%
+overlooked the next one number four
+ 
+
+ align:start position:0%
+overlooked the next one number four
+would be an Financial assets you might
+
+ align:start position:0%
+would be an Financial assets you might
+ 
+
+ align:start position:0%
+would be an Financial assets you might
+have very few Financial assets or you
+
+ align:start position:0%
+have very few Financial assets or you
+ 
+
+ align:start position:0%
+have very few Financial assets or you
+might have a lot of financial assets
+
+ align:start position:0%
+might have a lot of financial assets
+ 
+
+ align:start position:0%
+might have a lot of financial assets
+understanding the level of financial
+
+ align:start position:0%
+understanding the level of financial
+ 
+
+ align:start position:0%
+understanding the level of financial
+assets you have be it very small medium
+
+ align:start position:0%
+assets you have be it very small medium
+ 
+
+ align:start position:0%
+assets you have be it very small medium
+or large will dictate what markets are
+
+ align:start position:0%
+or large will dictate what markets are
+ 
+
+ align:start position:0%
+or large will dictate what markets are
+good for you if you if you don't have a
+
+ align:start position:0%
+good for you if you if you don't have a
+ 
+
+ align:start position:0%
+good for you if you if you don't have a
+lot of assets it's very hard to play in
+
+ align:start position:0%
+lot of assets it's very hard to play in
+ 
+
+ align:start position:0%
+lot of assets it's very hard to play in
+Industries where such as clean energy
+
+ align:start position:0%
+Industries where such as clean energy
+ 
+
+ align:start position:0%
+Industries where such as clean energy
+where the price of Poker is very high
+
+ align:start position:0%
+where the price of Poker is very high
+ 
+
+ align:start position:0%
+where the price of Poker is very high
+where the price of Entry is very high so
+
+ align:start position:0%
+where the price of Entry is very high so
+ 
+
+ align:start position:0%
+where the price of Entry is very high so
+the next one is name recognition
+
+ align:start position:0%
+the next one is name recognition
+ 
+
+ align:start position:0%
+the next one is name recognition
+so when you when you look at these
+
+ align:start position:0%
+so when you when you look at these
+ 
+
+ align:start position:0%
+so when you when you look at these
+um markets you might know the market you
+
+ align:start position:0%
+um markets you might know the market you
+ 
+
+ align:start position:0%
+um markets you might know the market you
+might have capability in that market you
+
+ align:start position:0%
+might have capability in that market you
+ 
+
+ align:start position:0%
+might have capability in that market you
+might know the right people you might
+
+ align:start position:0%
+might know the right people you might
+ 
+
+ align:start position:0%
+might know the right people you might
+have the financial but did the people in
+
+ align:start position:0%
+have the financial but did the people in
+ 
+
+ align:start position:0%
+have the financial but did the people in
+that market know someone on your team
+
+ align:start position:0%
+that market know someone on your team
+ 
+
+ align:start position:0%
+that market know someone on your team
+will they return the call when you when
+
+ align:start position:0%
+will they return the call when you when
+ 
+
+ align:start position:0%
+will they return the call when you when
+you contact them um inherent in this is
+
+ align:start position:0%
+you contact them um inherent in this is
+ 
+
+ align:start position:0%
+you contact them um inherent in this is
+credibility that you would have as well
+
+ align:start position:0%
+credibility that you would have as well
+ 
+
+ align:start position:0%
+credibility that you would have as well
+and that credibility would come from
+
+ align:start position:0%
+and that credibility would come from
+ 
+
+ align:start position:0%
+and that credibility would come from
+past work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experience now past work
+
+ align:start position:0%
+experience now past work
+ 
+
+ align:start position:0%
+experience now past work
+experience could contribute as well to
+
+ align:start position:0%
+experience could contribute as well to
+ 
+
+ align:start position:0%
+experience could contribute as well to
+capability and knowledge and connections
+
+ align:start position:0%
+capability and knowledge and connections
+ 
+
+ align:start position:0%
+capability and knowledge and connections
+but I bring that out because there's
+
+ align:start position:0%
+but I bring that out because there's
+ 
+
+ align:start position:0%
+but I bring that out because there's
+other things that would come from past
+
+ align:start position:0%
+other things that would come from past
+ 
+
+ align:start position:0%
+other things that would come from past
+work work experience that I might not
+
+ align:start position:0%
+work work experience that I might not
+ 
+
+ align:start position:0%
+work work experience that I might not
+have included in here um number
+
+ align:start position:0%
+have included in here um number
+ 
+
+ align:start position:0%
+have included in here um number
+seven would be a
+
+ align:start position:0%
+seven would be a
+ 
+
+ align:start position:0%
+seven would be a
+passion what you're going to be doing
+
+ align:start position:0%
+passion what you're going to be doing
+ 
+
+ align:start position:0%
+passion what you're going to be doing
+when you choose it you better love
+
+ align:start position:0%
+when you choose it you better love
+ 
+
+ align:start position:0%
+when you choose it you better love
+because you're if you can't see yourself
+
+ align:start position:0%
+because you're if you can't see yourself
+ 
+
+ align:start position:0%
+because you're if you can't see yourself
+doing this for the next six years you're
+
+ align:start position:0%
+doing this for the next six years you're
+ 
+
+ align:start position:0%
+doing this for the next six years you're
+very likely not going to be a successful
+
+ align:start position:0%
+very likely not going to be a successful
+ 
+
+ align:start position:0%
+very likely not going to be a successful
+entrepreneur you have got to have a lot
+
+ align:start position:0%
+entrepreneur you have got to have a lot
+ 
+
+ align:start position:0%
+entrepreneur you have got to have a lot
+of passion for what you're doing so I
+
+ align:start position:0%
+of passion for what you're doing so I
+ 
+
+ align:start position:0%
+of passion for what you're doing so I
+said there were eight eight items that
+
+ align:start position:0%
+said there were eight eight items that
+ 
+
+ align:start position:0%
+said there were eight eight items that
+that we would consider knowledge
+
+ align:start position:0%
+that we would consider knowledge
+ 
+
+ align:start position:0%
+that we would consider knowledge
+capability connections Financial assets
+
+ align:start position:0%
+capability connections Financial assets
+ 
+
+ align:start position:0%
+capability connections Financial assets
+name recognition past work experience
+
+ align:start position:0%
+name recognition past work experience
+ 
+
+ align:start position:0%
+name recognition past work experience
+which might contribute other ones and
+
+ align:start position:0%
+which might contribute other ones and
+ 
+
+ align:start position:0%
+which might contribute other ones and
+passion we need to have passion the last
+
+ align:start position:0%
+passion we need to have passion the last
+ 
+
+ align:start position:0%
+passion we need to have passion the last
+thing is even if you have all those
+
+ align:start position:0%
+thing is even if you have all those
+ 
+
+ align:start position:0%
+thing is even if you have all those
+things the last one you need is
+
+ align:start position:0%
+things the last one you need is
+ 
+
+ align:start position:0%
+things the last one you need is
+commitment um when we look at who will
+
+ align:start position:0%
+commitment um when we look at who will
+ 
+
+ align:start position:0%
+commitment um when we look at who will
+succeed and who will not succeed who we
+
+ align:start position:0%
+succeed and who will not succeed who we
+ 
+
+ align:start position:0%
+succeed and who will not succeed who we
+take in our founder skills accelerator
+
+ align:start position:0%
+take in our founder skills accelerator
+ 
+
+ align:start position:0%
+take in our founder skills accelerator
+who we take into our more select classes
+
+ align:start position:0%
+who we take into our more select classes
+ 
+
+ align:start position:0%
+who we take into our more select classes
+one of the number one things we look at
+
+ align:start position:0%
+one of the number one things we look at
+ 
+
+ align:start position:0%
+one of the number one things we look at
+is commitment cuz the person who is
+
+ align:start position:0%
+is commitment cuz the person who is
+ 
+
+ align:start position:0%
+is commitment cuz the person who is
+committed to this they're burning the
+
+ align:start position:0%
+committed to this they're burning the
+ 
+
+ align:start position:0%
+committed to this they're burning the
+boats this is what they're going to do
+
+ align:start position:0%
+boats this is what they're going to do
+ 
+
+ align:start position:0%
+boats this is what they're going to do
+is going to be more successful other
+
+ align:start position:0%
+is going to be more successful other
+ 
+
+ align:start position:0%
+is going to be more successful other
+people might start off with better
+
+ align:start position:0%
+people might start off with better
+ 
+
+ align:start position:0%
+people might start off with better
+technology but in the end the person who
+
+ align:start position:0%
+technology but in the end the person who
+ 
+
+ align:start position:0%
+technology but in the end the person who
+has the commitment is going to pass pass
+
+ align:start position:0%
+has the commitment is going to pass pass
+ 
+
+ align:start position:0%
+has the commitment is going to pass pass
+them all so those are the things that we
+
+ align:start position:0%
+them all so those are the things that we
+ 
+
+ align:start position:0%
+them all so those are the things that we
+look at as you go from a passion to a
+
+ align:start position:0%
+look at as you go from a passion to a
+ 
+
+ align:start position:0%
+look at as you go from a passion to a
+technology or an idea and then within
+
+ align:start position:0%
+technology or an idea and then within
+ 
+
+ align:start position:0%
+technology or an idea and then within
+the technology or idea which one are you
+
+ align:start position:0%
+the technology or idea which one are you
+ 
+
+ align:start position:0%
+the technology or idea which one are you
+going to choose these are some of the
+
+ align:start position:0%
+going to choose these are some of the
+ 
+
+ align:start position:0%
+going to choose these are some of the
+important factors that you must think
+
+ align:start position:0%
+important factors that you must think
+ 
+
+ align:start position:0%
+important factors that you must think
+about
\ No newline at end of file
diff --git a/OAI8C20E7R4.txt b/OAI8C20E7R4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..08d347fda95ee60a13802b1ef5b4d7dd499ac6d7
--- /dev/null
+++ b/OAI8C20E7R4.txt
@@ -0,0 +1,11195 @@
+align:start position:0%
+ 
+Okay everyone. Um so so today uh we're
+
+ align:start position:0%
+Okay everyone. Um so so today uh we're
+ 
+
+ align:start position:0%
+Okay everyone. Um so so today uh we're
+going to learn some of the fundamental
+
+ align:start position:0%
+going to learn some of the fundamental
+ 
+
+ align:start position:0%
+going to learn some of the fundamental
+estimates of projection theory for balls
+
+ align:start position:0%
+estimates of projection theory for balls
+ 
+
+ align:start position:0%
+estimates of projection theory for balls
+in the plane for the setting of real
+
+ align:start position:0%
+in the plane for the setting of real
+ 
+
+ align:start position:0%
+in the plane for the setting of real
+analysis. Um there are kind of two goals
+
+ align:start position:0%
+analysis. Um there are kind of two goals
+ 
+
+ align:start position:0%
+analysis. Um there are kind of two goals
+of the class. The first goal is to adapt
+
+ align:start position:0%
+of the class. The first goal is to adapt
+ 
+
+ align:start position:0%
+of the class. The first goal is to adapt
+the techniques that we learned last time
+
+ align:start position:0%
+the techniques that we learned last time
+ 
+
+ align:start position:0%
+the techniques that we learned last time
+in finite fields. So the double counting
+
+ align:start position:0%
+in finite fields. So the double counting
+ 
+
+ align:start position:0%
+in finite fields. So the double counting
+technique and the forier technique to
+
+ align:start position:0%
+technique and the forier technique to
+ 
+
+ align:start position:0%
+technique and the forier technique to
+uklitian space. Um and the second goal
+
+ align:start position:0%
+uklitian space. Um and the second goal
+ 
+
+ align:start position:0%
+uklitian space. Um and the second goal
+is to start to explore. So there's a
+
+ align:start position:0%
+is to start to explore. So there's a
+ 
+
+ align:start position:0%
+is to start to explore. So there's a
+difference between uklidian space and
+
+ align:start position:0%
+difference between uklidian space and
+ 
+
+ align:start position:0%
+difference between uklidian space and
+finite fields is that in uklidian space
+
+ align:start position:0%
+finite fields is that in uklidian space
+ 
+
+ align:start position:0%
+finite fields is that in uklidian space
+we have to pay attention to how the how
+
+ align:start position:0%
+we have to pay attention to how the how
+ 
+
+ align:start position:0%
+we have to pay attention to how the how
+our sets are clustered. And so the
+
+ align:start position:0%
+our sets are clustered. And so the
+ 
+
+ align:start position:0%
+our sets are clustered. And so the
+second goal of the class is to start to
+
+ align:start position:0%
+second goal of the class is to start to
+ 
+
+ align:start position:0%
+second goal of the class is to start to
+explore uh clustering can cl information
+
+ align:start position:0%
+explore uh clustering can cl information
+ 
+
+ align:start position:0%
+explore uh clustering can cl information
+about how the sets are clustered and and
+
+ align:start position:0%
+about how the sets are clustered and and
+ 
+
+ align:start position:0%
+about how the sets are clustered and and
+how that comes into the store.
+
+ align:start position:0%
+how that comes into the store.
+ 
+
+ align:start position:0%
+how that comes into the store.
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's our setup.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We'll have X will be a set
+
+ align:start position:0%
+We'll have X will be a set
+ 
+
+ align:start position:0%
+We'll have X will be a set
+of disjoint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unit balls
+
+ align:start position:0%
+unit balls
+ 
+
+ align:start position:0%
+unit balls
+in um in the ball of radius R in the
+
+ align:start position:0%
+in um in the ball of radius R in the
+ 
+
+ align:start position:0%
+in um in the ball of radius R in the
+plane.
+
+ align:start position:0%
+plane.
+ 
+
+ align:start position:0%
+plane.
+Okay, so that's our set of points, set
+
+ align:start position:0%
+Okay, so that's our set of points, set
+ 
+
+ align:start position:0%
+Okay, so that's our set of points, set
+of balls. And then we're going to have a
+
+ align:start position:0%
+of balls. And then we're going to have a
+ 
+
+ align:start position:0%
+of balls. And then we're going to have a
+set of directions called D. So D is a
+
+ align:start position:0%
+set of directions called D. So D is a
+ 
+
+ align:start position:0%
+set of directions called D. So D is a
+finite subset of S1. It's 1 / R
+
+ align:start position:0%
+finite subset of S1. It's 1 / R
+ 
+
+ align:start position:0%
+finite subset of S1. It's 1 / R
+separated. So the distance between any
+
+ align:start position:0%
+separated. So the distance between any
+ 
+
+ align:start position:0%
+separated. So the distance between any
+two points of D is at least one / R
+
+ align:start position:0%
+two points of D is at least one / R
+ 
+
+ align:start position:0%
+two points of D is at least one / R
+D. Um and then S which depends on X and
+
+ align:start position:0%
+D. Um and then S which depends on X and
+ 
+
+ align:start position:0%
+D. Um and then S which depends on X and
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+is the maximum size of the projection.
+
+ align:start position:0%
+is the maximum size of the projection.
+ 
+
+ align:start position:0%
+is the maximum size of the projection.
+So I look at all the ang all the
+
+ align:start position:0%
+So I look at all the ang all the
+ 
+
+ align:start position:0%
+So I look at all the ang all the
+directions in D and I project the set X
+
+ align:start position:0%
+directions in D and I project the set X
+ 
+
+ align:start position:0%
+directions in D and I project the set X
+in that direction and I take its measure
+
+ align:start position:0%
+in that direction and I take its measure
+ 
+
+ align:start position:0%
+in that direction and I take its measure
+and the maximum of that is called S.
+
+ align:start position:0%
+and the maximum of that is called S.
+ 
+
+ align:start position:0%
+and the maximum of that is called S.
+Okay. So projection theory we try to
+
+ align:start position:0%
+Okay. So projection theory we try to
+ 
+
+ align:start position:0%
+Okay. So projection theory we try to
+understand how these things are related
+
+ align:start position:0%
+understand how these things are related
+ 
+
+ align:start position:0%
+understand how these things are related
+to each other and in this uklidian
+
+ align:start position:0%
+to each other and in this uklidian
+ 
+
+ align:start position:0%
+to each other and in this uklidian
+setting we also need to care about how
+
+ align:start position:0%
+setting we also need to care about how
+ 
+
+ align:start position:0%
+setting we also need to care about how
+this set X and how the set D are
+
+ align:start position:0%
+this set X and how the set D are
+ 
+
+ align:start position:0%
+this set X and how the set D are
+clustered.
+
+ align:start position:0%
+clustered.
+ 
+
+ align:start position:0%
+clustered.
+So that's measured by I guess call them
+
+ align:start position:0%
+So that's measured by I guess call them
+ 
+
+ align:start position:0%
+So that's measured by I guess call them
+clustering functions. So n subx of
+
+ align:start position:0%
+clustering functions. So n subx of
+ 
+
+ align:start position:0%
+clustering functions. So n subx of
+little r is the measures the most amount
+
+ align:start position:0%
+little r is the measures the most amount
+ 
+
+ align:start position:0%
+little r is the measures the most amount
+of x in any ball of radius little r. So
+
+ align:start position:0%
+of x in any ball of radius little r. So
+ 
+
+ align:start position:0%
+of x in any ball of radius little r. So
+this is the maximum
+
+ align:start position:0%
+this is the maximum
+ 
+
+ align:start position:0%
+this is the maximum
+over c in r2 or um of the size of x
+
+ align:start position:0%
+over c in r2 or um of the size of x
+ 
+
+ align:start position:0%
+over c in r2 or um of the size of x
+intersected with the ball around c of
+
+ align:start position:0%
+intersected with the ball around c of
+ 
+
+ align:start position:0%
+intersected with the ball around c of
+radius r.
+
+ align:start position:0%
+radius r.
+ 
+
+ align:start position:0%
+radius r.
+So this measures how x is clustered and
+
+ align:start position:0%
+So this measures how x is clustered and
+ 
+
+ align:start position:0%
+So this measures how x is clustered and
+we're also going to measure how d is
+
+ align:start position:0%
+we're also going to measure how d is
+ 
+
+ align:start position:0%
+we're also going to measure how d is
+cluster clustered. So n subd of row
+
+ align:start position:0%
+cluster clustered. So n subd of row
+ 
+
+ align:start position:0%
+cluster clustered. So n subd of row
+is the maximum
+
+ align:start position:0%
+is the maximum
+ 
+
+ align:start position:0%
+is the maximum
+over any uh so sigma in s1 and arc
+
+ align:start position:0%
+over any uh so sigma in s1 and arc
+ 
+
+ align:start position:0%
+over any uh so sigma in s1 and arc
+of length row of d intersect zip.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So our big goal is in terms of
+
+ align:start position:0%
+Okay. So our big goal is in terms of
+ 
+
+ align:start position:0%
+Okay. So our big goal is in terms of
+this information and and how big d is
+
+ align:start position:0%
+this information and and how big d is
+ 
+
+ align:start position:0%
+this information and and how big d is
+and how big x is. What can we say about
+
+ align:start position:0%
+and how big x is. What can we say about
+ 
+
+ align:start position:0%
+and how big x is. What can we say about
+S?
+
+ align:start position:0%
+S?
+ 
+
+ align:start position:0%
+S?
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, we're first going to do the
+
+ align:start position:0%
+Okay. So, we're first going to do the
+ 
+
+ align:start position:0%
+Okay. So, we're first going to do the
+double counting approach.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the argument is in in spirit the
+
+ align:start position:0%
+And the argument is in in spirit the
+ 
+
+ align:start position:0%
+And the argument is in in spirit the
+same as last time. But we'll see that
+
+ align:start position:0%
+same as last time. But we'll see that
+ 
+
+ align:start position:0%
+same as last time. But we'll see that
+when we try to do the double counting
+
+ align:start position:0%
+when we try to do the double counting
+ 
+
+ align:start position:0%
+when we try to do the double counting
+that we did last time that the n subx
+
+ align:start position:0%
+that we did last time that the n subx
+ 
+
+ align:start position:0%
+that we did last time that the n subx
+function and the n subd function will
+
+ align:start position:0%
+function and the n subd function will
+ 
+
+ align:start position:0%
+function and the n subd function will
+come into the store and it leads to the
+
+ align:start position:0%
+come into the store and it leads to the
+ 
+
+ align:start position:0%
+come into the store and it leads to the
+following bound. So theorem one I'll
+
+ align:start position:0%
+following bound. So theorem one I'll
+ 
+
+ align:start position:0%
+following bound. So theorem one I'll
+call it theorem 1 r r r r r r r r r r r
+
+ align:start position:0%
+call it theorem 1 r r r r r r r r r r r
+ 
+
+ align:start position:0%
+call it theorem 1 r r r r r r r r r r r
+r r r r r r r r r r for the real case.
+
+ align:start position:0%
+r r r r r r r r r r for the real case.
+ 
+
+ align:start position:0%
+r r r r r r r r r r for the real case.
+Uh whereas last time we had something
+
+ align:start position:0%
+Uh whereas last time we had something
+ 
+
+ align:start position:0%
+Uh whereas last time we had something
+called theorem one which when I do it
+
+ align:start position:0%
+called theorem one which when I do it
+ 
+
+ align:start position:0%
+called theorem one which when I do it
+again it'll be theorem 1 f for the
+
+ align:start position:0%
+again it'll be theorem 1 f for the
+ 
+
+ align:start position:0%
+again it'll be theorem 1 f for the
+finite field case and eventually we'll
+
+ align:start position:0%
+finite field case and eventually we'll
+ 
+
+ align:start position:0%
+finite field case and eventually we'll
+compare them.
+
+ align:start position:0%
+compare them.
+ 
+
+ align:start position:0%
+compare them.
+Okay. So if we have this setup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the number of directions is bounded by
+
+ align:start position:0%
+the number of directions is bounded by
+ 
+
+ align:start position:0%
+the number of directions is bounded by
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you'll notice that this is not a
+
+ align:start position:0%
+okay so you'll notice that this is not a
+ 
+
+ align:start position:0%
+okay so you'll notice that this is not a
+formula that I have memorized
+
+ align:start position:0%
+formula that I have memorized
+ 
+
+ align:start position:0%
+formula that I have memorized
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+s overx times the sum over different
+
+ align:start position:0%
+s overx times the sum over different
+ 
+
+ align:start position:0%
+s overx times the sum over different
+scales else.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. Okay. So, it's a sum over
+
+ align:start position:0%
+Cool. Okay. So, it's a sum over
+ 
+
+ align:start position:0%
+Cool. Okay. So, it's a sum over
+different scales and we often in this
+
+ align:start position:0%
+different scales and we often in this
+ 
+
+ align:start position:0%
+different scales and we often in this
+class will sum over a diadic sequence of
+
+ align:start position:0%
+class will sum over a diadic sequence of
+ 
+
+ align:start position:0%
+class will sum over a diadic sequence of
+scales, powers of two or whatever. Um uh
+
+ align:start position:0%
+scales, powers of two or whatever. Um uh
+ 
+
+ align:start position:0%
+scales, powers of two or whatever. Um uh
+okay and um and the so the formula
+
+ align:start position:0%
+okay and um and the so the formula
+ 
+
+ align:start position:0%
+okay and um and the so the formula
+doesn't yet look that similar but the
+
+ align:start position:0%
+doesn't yet look that similar but the
+ 
+
+ align:start position:0%
+doesn't yet look that similar but the
+the idea is the same as last time and
+
+ align:start position:0%
+the idea is the same as last time and
+ 
+
+ align:start position:0%
+the idea is the same as last time and
+then eventually we'll compare the
+
+ align:start position:0%
+then eventually we'll compare the
+ 
+
+ align:start position:0%
+then eventually we'll compare the
+formulas and see that under certain
+
+ align:start position:0%
+formulas and see that under certain
+ 
+
+ align:start position:0%
+formulas and see that under certain
+assumptions on this it's actually very
+
+ align:start position:0%
+assumptions on this it's actually very
+ 
+
+ align:start position:0%
+assumptions on this it's actually very
+similar to last time.
+
+ align:start position:0%
+similar to last time.
+ 
+
+ align:start position:0%
+similar to last time.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the proof is to double count a
+
+ align:start position:0%
+So the proof is to double count a
+ 
+
+ align:start position:0%
+So the proof is to double count a
+certain quantity which which we which we
+
+ align:start position:0%
+certain quantity which which we which we
+ 
+
+ align:start position:0%
+certain quantity which which we which we
+called coincidences last time. So the
+
+ align:start position:0%
+called coincidences last time. So the
+ 
+
+ align:start position:0%
+called coincidences last time. So the
+key quantity called star
+
+ align:start position:0%
+key quantity called star
+ 
+
+ align:start position:0%
+key quantity called star
+is the number of
+
+ align:start position:0%
+is the number of
+ 
+
+ align:start position:0%
+is the number of
+b1 and b2 in x. So these are these are
+
+ align:start position:0%
+b1 and b2 in x. So these are these are
+ 
+
+ align:start position:0%
+b1 and b2 in x. So these are these are
+unit balls.
+
+ align:start position:0%
+unit balls.
+ 
+
+ align:start position:0%
+unit balls.
+So remember x is a set of unit balls. So
+
+ align:start position:0%
+So remember x is a set of unit balls. So
+ 
+
+ align:start position:0%
+So remember x is a set of unit balls. So
+these are two of the unit balls. Um and
+
+ align:start position:0%
+these are two of the unit balls. Um and
+ 
+
+ align:start position:0%
+these are two of the unit balls. Um and
+um theta and d I guess we'll say they're
+
+ align:start position:0%
+um theta and d I guess we'll say they're
+ 
+
+ align:start position:0%
+um theta and d I guess we'll say they're
+not equal to each other although that
+
+ align:start position:0%
+not equal to each other although that
+ 
+
+ align:start position:0%
+not equal to each other although that
+won't matter as much this time. um
+
+ align:start position:0%
+won't matter as much this time. um
+ 
+
+ align:start position:0%
+won't matter as much this time. um
+uh so that pi theta of b1 and pi theta
+
+ align:start position:0%
+uh so that pi theta of b1 and pi theta
+ 
+
+ align:start position:0%
+uh so that pi theta of b1 and pi theta
+of b2 are similar to each other and in
+
+ align:start position:0%
+of b2 are similar to each other and in
+ 
+
+ align:start position:0%
+of b2 are similar to each other and in
+this setting we won't count they don't
+
+ align:start position:0%
+this setting we won't count they don't
+ 
+
+ align:start position:0%
+this setting we won't count they don't
+have to be exactly the same I would just
+
+ align:start position:0%
+have to be exactly the same I would just
+ 
+
+ align:start position:0%
+have to be exactly the same I would just
+like them to overlap so my condition
+
+ align:start position:0%
+like them to overlap so my condition
+ 
+
+ align:start position:0%
+like them to overlap so my condition
+will be that the intersection of these
+
+ align:start position:0%
+will be that the intersection of these
+ 
+
+ align:start position:0%
+will be that the intersection of these
+is non empty so that's my key quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+actually in this setup. I'm going to I'm
+
+ align:start position:0%
+actually in this setup. I'm going to I'm
+ 
+
+ align:start position:0%
+actually in this setup. I'm going to I'm
+going to allow them to be equal to each
+
+ align:start position:0%
+going to allow them to be equal to each
+ 
+
+ align:start position:0%
+going to allow them to be equal to each
+other. Um that makes the double counting
+
+ align:start position:0%
+other. Um that makes the double counting
+ 
+
+ align:start position:0%
+other. Um that makes the double counting
+a little easier and in a sense it's
+
+ align:start position:0%
+a little easier and in a sense it's
+ 
+
+ align:start position:0%
+a little easier and in a sense it's
+we'll see it's it's part of what's up
+
+ align:start position:0%
+we'll see it's it's part of what's up
+ 
+
+ align:start position:0%
+we'll see it's it's part of what's up
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+Okay. So um so there's a lower bound
+
+ align:start position:0%
+Okay. So um so there's a lower bound
+ 
+
+ align:start position:0%
+Okay. So um so there's a lower bound
+which is straightforward.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The lower bound says that this this star
+
+ align:start position:0%
+The lower bound says that this this star
+ 
+
+ align:start position:0%
+The lower bound says that this this star
+is at least the number of directions
+
+ align:start position:0%
+is at least the number of directions
+ 
+
+ align:start position:0%
+is at least the number of directions
+times in each direction
+
+ align:start position:0%
+times in each direction
+ 
+
+ align:start position:0%
+times in each direction
+x over s^2
+
+ align:start position:0%
+x over s^2
+ 
+
+ align:start position:0%
+x over s^2
+* s.
+
+ align:start position:0%
+* s.
+ 
+
+ align:start position:0%
+* s.
+So in each direction these x different
+
+ align:start position:0%
+So in each direction these x different
+ 
+
+ align:start position:0%
+So in each direction these x different
+balls have been projected into only s
+
+ align:start position:0%
+balls have been projected into only s
+ 
+
+ align:start position:0%
+balls have been projected into only s
+slots. So a typical slot has x over s
+
+ align:start position:0%
+slots. So a typical slot has x over s
+ 
+
+ align:start position:0%
+slots. So a typical slot has x over s
+balls in its fiber. And so we have this
+
+ align:start position:0%
+balls in its fiber. And so we have this
+ 
+
+ align:start position:0%
+balls in its fiber. And so we have this
+many squared choices for to pick B1 and
+
+ align:start position:0%
+many squared choices for to pick B1 and
+ 
+
+ align:start position:0%
+many squared choices for to pick B1 and
+B2 in the same five
+
+ align:start position:0%
+B2 in the same five
+ 
+
+ align:start position:0%
+B2 in the same five
+s times. So lower bound is is really the
+
+ align:start position:0%
+s times. So lower bound is is really the
+ 
+
+ align:start position:0%
+s times. So lower bound is is really the
+same as last time.
+
+ align:start position:0%
+same as last time.
+ 
+
+ align:start position:0%
+same as last time.
+Same as last time, same as the homework.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now let's look at the upper
+
+ align:start position:0%
+Okay. So now let's look at the upper
+ 
+
+ align:start position:0%
+Okay. So now let's look at the upper
+bound.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I will uh for now I'll fix B1 B2 and
+
+ align:start position:0%
+So I will uh for now I'll fix B1 B2 and
+ 
+
+ align:start position:0%
+So I will uh for now I'll fix B1 B2 and
+I'll say that the distance between B1
+
+ align:start position:0%
+I'll say that the distance between B1
+ 
+
+ align:start position:0%
+I'll say that the distance between B1
+and B2 is around R.
+
+ align:start position:0%
+and B2 is around R.
+ 
+
+ align:start position:0%
+and B2 is around R.
+Um so here's my picture
+
+ align:start position:0%
+Um so here's my picture
+ 
+
+ align:start position:0%
+Um so here's my picture
+B1 and B2 and the distance between them
+
+ align:start position:0%
+B1 and B2 and the distance between them
+ 
+
+ align:start position:0%
+B1 and B2 and the distance between them
+is around R.
+
+ align:start position:0%
+is around R.
+ 
+
+ align:start position:0%
+is around R.
+Okay. So now I'm interested in
+
+ align:start position:0%
+Okay. So now I'm interested in
+ 
+
+ align:start position:0%
+Okay. So now I'm interested in
+projections where the projection of B1
+
+ align:start position:0%
+projections where the projection of B1
+ 
+
+ align:start position:0%
+projections where the projection of B1
+and the projection of B2 overlap. And so
+
+ align:start position:0%
+and the projection of B2 overlap. And so
+ 
+
+ align:start position:0%
+and the projection of B2 overlap. And so
+the angles for those projections are in
+
+ align:start position:0%
+the angles for those projections are in
+ 
+
+ align:start position:0%
+the angles for those projections are in
+a little angular range. The angle of the
+
+ align:start position:0%
+a little angular range. The angle of the
+ 
+
+ align:start position:0%
+a little angular range. The angle of the
+projection must be somewhere in this
+
+ align:start position:0%
+projection must be somewhere in this
+ 
+
+ align:start position:0%
+projection must be somewhere in this
+range here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what um what I'll say is let's say
+
+ align:start position:0%
+So what um what I'll say is let's say
+ 
+
+ align:start position:0%
+So what um what I'll say is let's say
+that V is the direction from B1 to to to
+
+ align:start position:0%
+that V is the direction from B1 to to to
+ 
+
+ align:start position:0%
+that V is the direction from B1 to to to
+B2. So v is um center of b2 minus center
+
+ align:start position:0%
+B2. So v is um center of b2 minus center
+ 
+
+ align:start position:0%
+B2. So v is um center of b2 minus center
+of b1
+
+ align:start position:0%
+of b1
+ 
+
+ align:start position:0%
+of b1
+over the norm of that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+if pi theta of b1 intersect pi theta b2
+
+ align:start position:0%
+if pi theta of b1 intersect pi theta b2
+ 
+
+ align:start position:0%
+if pi theta of b1 intersect pi theta b2
+is not empty
+
+ align:start position:0%
+is not empty
+ 
+
+ align:start position:0%
+is not empty
+um then
+
+ align:start position:0%
+um then
+ 
+
+ align:start position:0%
+um then
+theta must be pretty close to v. What
+
+ align:start position:0%
+theta must be pretty close to v. What
+ 
+
+ align:start position:0%
+theta must be pretty close to v. What
+I'll say is that the angle
+
+ align:start position:0%
+I'll say is that the angle
+ 
+
+ align:start position:0%
+I'll say is that the angle
+between theta and v is smaller than
+
+ align:start position:0%
+between theta and v is smaller than
+ 
+
+ align:start position:0%
+between theta and v is smaller than
+around 1 / r.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um so now
+
+ align:start position:0%
+Um so now
+ 
+
+ align:start position:0%
+Um so now
+the number of theta so that pi theta of
+
+ align:start position:0%
+the number of theta so that pi theta of
+ 
+
+ align:start position:0%
+the number of theta so that pi theta of
+b1 intersect pi theta of b2 is not empty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that would be bounded by well the number
+
+ align:start position:0%
+that would be bounded by well the number
+ 
+
+ align:start position:0%
+that would be bounded by well the number
+of directions in this little arc. So
+
+ align:start position:0%
+of directions in this little arc. So
+ 
+
+ align:start position:0%
+of directions in this little arc. So
+that would be nd of 1 / r. So we see the
+
+ align:start position:0%
+that would be nd of 1 / r. So we see the
+ 
+
+ align:start position:0%
+that would be nd of 1 / r. So we see the
+spacing uh the spacing function of the
+
+ align:start position:0%
+spacing uh the spacing function of the
+ 
+
+ align:start position:0%
+spacing uh the spacing function of the
+set d comes into play here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's what happens when we fix
+
+ align:start position:0%
+Okay, so that's what happens when we fix
+ 
+
+ align:start position:0%
+Okay, so that's what happens when we fix
+B1 and B2.
+
+ align:start position:0%
+B1 and B2.
+ 
+
+ align:start position:0%
+B1 and B2.
+And the case B1 equals B2 is allowed.
+
+ align:start position:0%
+And the case B1 equals B2 is allowed.
+ 
+
+ align:start position:0%
+And the case B1 equals B2 is allowed.
+And I'll make the slightly funny
+
+ align:start position:0%
+And I'll make the slightly funny
+ 
+
+ align:start position:0%
+And I'll make the slightly funny
+convention that then R is one. They're
+
+ align:start position:0%
+convention that then R is one. They're
+ 
+
+ align:start position:0%
+convention that then R is one. They're
+unit ball. So the distance between them
+
+ align:start position:0%
+unit ball. So the distance between them
+ 
+
+ align:start position:0%
+unit ball. So the distance between them
+is sort of one. And this is true. Then I
+
+ align:start position:0%
+is sort of one. And this is true. Then I
+ 
+
+ align:start position:0%
+is sort of one. And this is true. Then I
+mean V is not well defined, but this
+
+ align:start position:0%
+mean V is not well defined, but this
+ 
+
+ align:start position:0%
+mean V is not well defined, but this
+condition includes the whole range of
+
+ align:start position:0%
+condition includes the whole range of
+ 
+
+ align:start position:0%
+condition includes the whole range of
+angles. So it's it's true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So look if B1 equals B2 we take little R
+
+ align:start position:0%
+So look if B1 equals B2 we take little R
+ 
+
+ align:start position:0%
+So look if B1 equals B2 we take little R
+equals 1 and it's slightly exceptional
+
+ align:start position:0%
+equals 1 and it's slightly exceptional
+ 
+
+ align:start position:0%
+equals 1 and it's slightly exceptional
+but but all the bounds are true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So if we want to upper bound star now we
+
+ align:start position:0%
+So if we want to upper bound star now we
+ 
+
+ align:start position:0%
+So if we want to upper bound star now we
+need to count the number of choices for
+
+ align:start position:0%
+need to count the number of choices for
+ 
+
+ align:start position:0%
+need to count the number of choices for
+B1 and B2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now I'm interested in the number of
+
+ align:start position:0%
+So now I'm interested in the number of
+ 
+
+ align:start position:0%
+So now I'm interested in the number of
+pairs
+
+ align:start position:0%
+pairs
+ 
+
+ align:start position:0%
+pairs
+B1, B2, and X with the property that the
+
+ align:start position:0%
+B1, B2, and X with the property that the
+ 
+
+ align:start position:0%
+B1, B2, and X with the property that the
+distance from B1 to B2 is at most R.
+
+ align:start position:0%
+distance from B1 to B2 is at most R.
+ 
+
+ align:start position:0%
+distance from B1 to B2 is at most R.
+Okay, how big is that? Well, I have norm
+
+ align:start position:0%
+Okay, how big is that? Well, I have norm
+ 
+
+ align:start position:0%
+Okay, how big is that? Well, I have norm
+of X choices for B1.
+
+ align:start position:0%
+of X choices for B1.
+ 
+
+ align:start position:0%
+of X choices for B1.
+But once I choose B1, I don't have all
+
+ align:start position:0%
+But once I choose B1, I don't have all
+ 
+
+ align:start position:0%
+But once I choose B1, I don't have all
+that many choices for B2 because B2 has
+
+ align:start position:0%
+that many choices for B2 because B2 has
+ 
+
+ align:start position:0%
+that many choices for B2 because B2 has
+to be close to B1. It has to be in a
+
+ align:start position:0%
+to be close to B1. It has to be in a
+ 
+
+ align:start position:0%
+to be close to B1. It has to be in a
+little R ball.
+
+ align:start position:0%
+little R ball.
+ 
+
+ align:start position:0%
+little R ball.
+So the number of choices for B2 is at
+
+ align:start position:0%
+So the number of choices for B2 is at
+ 
+
+ align:start position:0%
+So the number of choices for B2 is at
+most nx of R. So at this moment the
+
+ align:start position:0%
+most nx of R. So at this moment the
+ 
+
+ align:start position:0%
+most nx of R. So at this moment the
+spacing function of X comes into play.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now we can combine these to to
+
+ align:start position:0%
+Okay. So now we can combine these to to
+ 
+
+ align:start position:0%
+Okay. So now we can combine these to to
+upper bound star.
+
+ align:start position:0%
+upper bound star.
+ 
+
+ align:start position:0%
+upper bound star.
+So star is um is now upper bounded by
+
+ align:start position:0%
+So star is um is now upper bounded by
+ 
+
+ align:start position:0%
+So star is um is now upper bounded by
+x * nx of r time n d of 1 / r
+
+ align:start position:0%
+x * nx of r time n d of 1 / r
+ 
+
+ align:start position:0%
+x * nx of r time n d of 1 / r
+uh ah sorry so star
+
+ align:start position:0%
+uh ah sorry so star
+ 
+
+ align:start position:0%
+uh ah sorry so star
+is upperbounded by the sum over the
+
+ align:start position:0%
+is upperbounded by the sum over the
+ 
+
+ align:start position:0%
+is upperbounded by the sum over the
+diatic r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this quantity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let me say why. So star is this
+
+ align:start position:0%
+Okay, so let me say why. So star is this
+ 
+
+ align:start position:0%
+Okay, so let me say why. So star is this
+set of coincidences.
+
+ align:start position:0%
+set of coincidences.
+ 
+
+ align:start position:0%
+set of coincidences.
+It's a B1 and B2 and a theta. And for
+
+ align:start position:0%
+It's a B1 and B2 and a theta. And for
+ 
+
+ align:start position:0%
+It's a B1 and B2 and a theta. And for
+each coincidence, I know I I sort these
+
+ align:start position:0%
+each coincidence, I know I I sort these
+ 
+
+ align:start position:0%
+each coincidence, I know I I sort these
+coincidences by the distance from B1 to
+
+ align:start position:0%
+coincidences by the distance from B1 to
+ 
+
+ align:start position:0%
+coincidences by the distance from B1 to
+B2, which I call R. So I take the the
+
+ align:start position:0%
+B2, which I call R. So I take the the
+ 
+
+ align:start position:0%
+B2, which I call R. So I take the the
+coincidences where the distance is
+
+ align:start position:0%
+coincidences where the distance is
+ 
+
+ align:start position:0%
+coincidences where the distance is
+around R, and I sum over the possible
+
+ align:start position:0%
+around R, and I sum over the possible
+ 
+
+ align:start position:0%
+around R, and I sum over the possible
+Rs. Once I fixed R, um, I have this many
+
+ align:start position:0%
+Rs. Once I fixed R, um, I have this many
+ 
+
+ align:start position:0%
+Rs. Once I fixed R, um, I have this many
+choices for the pair B1 B2. And once I
+
+ align:start position:0%
+choices for the pair B1 B2. And once I
+ 
+
+ align:start position:0%
+choices for the pair B1 B2. And once I
+fixed B1 and B2, I have this many
+
+ align:start position:0%
+fixed B1 and B2, I have this many
+ 
+
+ align:start position:0%
+fixed B1 and B2, I have this many
+choices for theta.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Uh, the rest is algebra. I'll sketch it
+
+ align:start position:0%
+Uh, the rest is algebra. I'll sketch it
+ 
+
+ align:start position:0%
+Uh, the rest is algebra. I'll sketch it
+quickly on the board and that'll be the
+
+ align:start position:0%
+quickly on the board and that'll be the
+ 
+
+ align:start position:0%
+quickly on the board and that'll be the
+end of the proof and then we'll pause to
+
+ align:start position:0%
+end of the proof and then we'll pause to
+ 
+
+ align:start position:0%
+end of the proof and then we'll pause to
+digest and check it.
+
+ align:start position:0%
+digest and check it.
+ 
+
+ align:start position:0%
+digest and check it.
+Okay. So al together
+
+ align:start position:0%
+Okay. So al together
+ 
+
+ align:start position:0%
+Okay. So al together
+we have x^2 s inverse d is bounded by
+
+ align:start position:0%
+we have x^2 s inverse d is bounded by
+ 
+
+ align:start position:0%
+we have x^2 s inverse d is bounded by
+star which is bounded by
+
+ align:start position:0%
+star which is bounded by
+ 
+
+ align:start position:0%
+star which is bounded by
+the sum over r datic
+
+ align:start position:0%
+the sum over r datic
+ 
+
+ align:start position:0%
+the sum over r datic
+of x nx of r and d of 1 / r and then I
+
+ align:start position:0%
+of x nx of r and d of 1 / r and then I
+ 
+
+ align:start position:0%
+of x nx of r and d of 1 / r and then I
+just get the d by itself.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you move this stuff over to the other
+
+ align:start position:0%
+If you move this stuff over to the other
+ 
+
+ align:start position:0%
+If you move this stuff over to the other
+side, you get the formula on the board.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let's pause there for questions
+
+ align:start position:0%
+Okay, so let's pause there for questions
+ 
+
+ align:start position:0%
+Okay, so let's pause there for questions
+and comments.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+All right. So, um, so I wanted to, uh,
+
+ align:start position:0%
+All right. So, um, so I wanted to, uh,
+ 
+
+ align:start position:0%
+All right. So, um, so I wanted to, uh,
+get a sense of start to explore this
+
+ align:start position:0%
+get a sense of start to explore this
+ 
+
+ align:start position:0%
+get a sense of start to explore this
+function nx of r by looking at a few
+
+ align:start position:0%
+function nx of r by looking at a few
+ 
+
+ align:start position:0%
+function nx of r by looking at a few
+different examples of sets x and writing
+
+ align:start position:0%
+different examples of sets x and writing
+ 
+
+ align:start position:0%
+different examples of sets x and writing
+down what is nx of r. It's not
+
+ align:start position:0%
+down what is nx of r. It's not
+ 
+
+ align:start position:0%
+down what is nx of r. It's not
+difficult, but having a few different
+
+ align:start position:0%
+difficult, but having a few different
+ 
+
+ align:start position:0%
+difficult, but having a few different
+examples in our mind, it'll help to
+
+ align:start position:0%
+examples in our mind, it'll help to
+ 
+
+ align:start position:0%
+examples in our mind, it'll help to
+orient us as we keep going.
+
+ align:start position:0%
+orient us as we keep going.
+ 
+
+ align:start position:0%
+orient us as we keep going.
+um and and actually will help also to
+
+ align:start position:0%
+um and and actually will help also to
+ 
+
+ align:start position:0%
+um and and actually will help also to
+digest this formula. So this this proof
+
+ align:start position:0%
+digest this formula. So this this proof
+ 
+
+ align:start position:0%
+digest this formula. So this this proof
+was clean. This formula is a little bit
+
+ align:start position:0%
+was clean. This formula is a little bit
+ 
+
+ align:start position:0%
+was clean. This formula is a little bit
+messy. So after looking at some
+
+ align:start position:0%
+messy. So after looking at some
+ 
+
+ align:start position:0%
+messy. So after looking at some
+examples, we'll digest this formula and
+
+ align:start position:0%
+examples, we'll digest this formula and
+ 
+
+ align:start position:0%
+examples, we'll digest this formula and
+think about a situation where it works
+
+ align:start position:0%
+think about a situation where it works
+ 
+
+ align:start position:0%
+think about a situation where it works
+out a little more cleanly.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So examples
+
+ align:start position:0%
+All right. So examples
+ 
+
+ align:start position:0%
+All right. So examples
+for n sub x sub rar.
+
+ align:start position:0%
+for n sub x sub rar.
+ 
+
+ align:start position:0%
+for n sub x sub rar.
+Okay. So number one, x is the one
+
+ align:start position:0%
+Okay. So number one, x is the one
+ 
+
+ align:start position:0%
+Okay. So number one, x is the one
+neighborhood
+
+ align:start position:0%
+neighborhood
+ 
+
+ align:start position:0%
+neighborhood
+of a curve like a nice like a circle or
+
+ align:start position:0%
+of a curve like a nice like a circle or
+ 
+
+ align:start position:0%
+of a curve like a nice like a circle or
+parabola or something. So here's the
+
+ align:start position:0%
+parabola or something. So here's the
+ 
+
+ align:start position:0%
+parabola or something. So here's the
+ball of radius r and inside of there I
+
+ align:start position:0%
+ball of radius r and inside of there I
+ 
+
+ align:start position:0%
+ball of radius r and inside of there I
+have a nice curve and all along the
+
+ align:start position:0%
+have a nice curve and all along the
+ 
+
+ align:start position:0%
+have a nice curve and all along the
+curve I have unit balls.
+
+ align:start position:0%
+curve I have unit balls.
+ 
+
+ align:start position:0%
+curve I have unit balls.
+That's x.
+
+ align:start position:0%
+That's x.
+ 
+
+ align:start position:0%
+That's x.
+So if I have this set, how many unit
+
+ align:start position:0%
+So if I have this set, how many unit
+ 
+
+ align:start position:0%
+So if I have this set, how many unit
+balls do I have in a ball of radius
+
+ align:start position:0%
+balls do I have in a ball of radius
+ 
+
+ align:start position:0%
+balls do I have in a ball of radius
+little r?
+
+ align:start position:0%
+little r?
+ 
+
+ align:start position:0%
+little r?
+That would be around r.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Do a second example. Um
+
+ align:start position:0%
+Do a second example. Um
+ 
+
+ align:start position:0%
+Do a second example. Um
+second example, it would be very spread
+
+ align:start position:0%
+second example, it would be very spread
+ 
+
+ align:start position:0%
+second example, it would be very spread
+out. You know, if you imagine that these
+
+ align:start position:0%
+out. You know, if you imagine that these
+ 
+
+ align:start position:0%
+out. You know, if you imagine that these
+points are like positive charges that
+
+ align:start position:0%
+points are like positive charges that
+ 
+
+ align:start position:0%
+points are like positive charges that
+repel each other and they push as far
+
+ align:start position:0%
+repel each other and they push as far
+ 
+
+ align:start position:0%
+repel each other and they push as far
+away from each other as possible, they
+
+ align:start position:0%
+away from each other as possible, they
+ 
+
+ align:start position:0%
+away from each other as possible, they
+would arrange themselves in something
+
+ align:start position:0%
+would arrange themselves in something
+ 
+
+ align:start position:0%
+would arrange themselves in something
+like a lattice inside of here.
+
+ align:start position:0%
+like a lattice inside of here.
+ 
+
+ align:start position:0%
+like a lattice inside of here.
+So, okay. So, I'll call this the uh well
+
+ align:start position:0%
+So, okay. So, I'll call this the uh well
+ 
+
+ align:start position:0%
+So, okay. So, I'll call this the uh well
+spaced example, the most spread out
+
+ align:start position:0%
+spaced example, the most spread out
+ 
+
+ align:start position:0%
+spaced example, the most spread out
+example. So, it looks like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it's a let's say it's a well spaced n
+
+ align:start position:0%
+So it's a let's say it's a well spaced n
+ 
+
+ align:start position:0%
+So it's a let's say it's a well spaced n
+byn grid
+
+ align:start position:0%
+byn grid
+ 
+
+ align:start position:0%
+byn grid
+and so the distance between neighboring
+
+ align:start position:0%
+and so the distance between neighboring
+ 
+
+ align:start position:0%
+and so the distance between neighboring
+balls would be like r /n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so now what would nx of r be like?
+
+ align:start position:0%
+Okay so now what would nx of r be like?
+ 
+
+ align:start position:0%
+Okay so now what would nx of r be like?
+Um well it would be one for quite a
+
+ align:start position:0%
+Um well it would be one for quite a
+ 
+
+ align:start position:0%
+Um well it would be one for quite a
+while if our radius is less than rn. um
+
+ align:start position:0%
+while if our radius is less than rn. um
+ 
+
+ align:start position:0%
+while if our radius is less than rn. um
+then this would be one but then
+
+ align:start position:0%
+then this would be one but then
+ 
+
+ align:start position:0%
+then this would be one but then
+eventually as the radius gets bigger it
+
+ align:start position:0%
+eventually as the radius gets bigger it
+ 
+
+ align:start position:0%
+eventually as the radius gets bigger it
+would get bigger than one and at that
+
+ align:start position:0%
+would get bigger than one and at that
+ 
+
+ align:start position:0%
+would get bigger than one and at that
+point it would be um its fair share of
+
+ align:start position:0%
+point it would be um its fair share of
+ 
+
+ align:start position:0%
+point it would be um its fair share of
+the total number total size of x. So
+
+ align:start position:0%
+the total number total size of x. So
+ 
+
+ align:start position:0%
+the total number total size of x. So
+once once r is bigger than this
+
+ align:start position:0%
+once once r is bigger than this
+ 
+
+ align:start position:0%
+once once r is bigger than this
+threshold, every little r ball contains
+
+ align:start position:0%
+threshold, every little r ball contains
+ 
+
+ align:start position:0%
+threshold, every little r ball contains
+the same amount of x. And so the density
+
+ align:start position:0%
+the same amount of x. And so the density
+ 
+
+ align:start position:0%
+the same amount of x. And so the density
+of x is like n^2 r 2. The area of the
+
+ align:start position:0%
+of x is like n^2 r 2. The area of the
+ 
+
+ align:start position:0%
+of x is like n^2 r 2. The area of the
+ball is like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And um I'll do a third example
+
+ align:start position:0%
+Okay. And um I'll do a third example
+ 
+
+ align:start position:0%
+Okay. And um I'll do a third example
+which is the points could be very um uh
+
+ align:start position:0%
+which is the points could be very um uh
+ 
+
+ align:start position:0%
+which is the points could be very um uh
+clustered
+
+ align:start position:0%
+clustered
+ 
+
+ align:start position:0%
+clustered
+cluster.
+
+ align:start position:0%
+cluster.
+ 
+
+ align:start position:0%
+cluster.
+So we could have n squared unit balls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in um in an n ball. So the the picture
+
+ align:start position:0%
+in um in an n ball. So the the picture
+ 
+
+ align:start position:0%
+in um in an n ball. So the the picture
+would be like this. We have our ball of
+
+ align:start position:0%
+would be like this. We have our ball of
+ 
+
+ align:start position:0%
+would be like this. We have our ball of
+radius r. Inside of there we have a
+
+ align:start position:0%
+radius r. Inside of there we have a
+ 
+
+ align:start position:0%
+radius r. Inside of there we have a
+smaller ball of radius n and we pack the
+
+ align:start position:0%
+smaller ball of radius n and we pack the
+ 
+
+ align:start position:0%
+smaller ball of radius n and we pack the
+smaller ball with unit balls of x.
+
+ align:start position:0%
+smaller ball with unit balls of x.
+ 
+
+ align:start position:0%
+smaller ball with unit balls of x.
+Okay. So now what is uh n subx of r?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well it grows like r 2 until r is as big
+
+ align:start position:0%
+Well it grows like r 2 until r is as big
+ 
+
+ align:start position:0%
+Well it grows like r 2 until r is as big
+as this n ball. And after that there are
+
+ align:start position:0%
+as this n ball. And after that there are
+ 
+
+ align:start position:0%
+as this n ball. And after that there are
+only n squared balls at all. So you can
+
+ align:start position:0%
+only n squared balls at all. So you can
+ 
+
+ align:start position:0%
+only n squared balls at all. So you can
+make a little r bigger. It doesn't grow
+
+ align:start position:0%
+make a little r bigger. It doesn't grow
+ 
+
+ align:start position:0%
+make a little r bigger. It doesn't grow
+anymore. So it caps off at n^ squ if r
+
+ align:start position:0%
+anymore. So it caps off at n^ squ if r
+ 
+
+ align:start position:0%
+anymore. So it caps off at n^ squ if r
+is bigger than n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So now I will draw um some pictures of
+
+ align:start position:0%
+So now I will draw um some pictures of
+ 
+
+ align:start position:0%
+So now I will draw um some pictures of
+of of these three functions.
+
+ align:start position:0%
+of of these three functions.
+ 
+
+ align:start position:0%
+of of these three functions.
+You can compare them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we'll do some pictures.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to normalize in my pictures. I
+
+ align:start position:0%
+I'm going to normalize in my pictures. I
+ 
+
+ align:start position:0%
+I'm going to normalize in my pictures. I
+have to choose an n. I'm going to choose
+
+ align:start position:0%
+have to choose an n. I'm going to choose
+ 
+
+ align:start position:0%
+have to choose an n. I'm going to choose
+n= r to the half. Uh, and that's helpful
+
+ align:start position:0%
+n= r to the half. Uh, and that's helpful
+ 
+
+ align:start position:0%
+n= r to the half. Uh, and that's helpful
+because it says that the total size of x
+
+ align:start position:0%
+because it says that the total size of x
+ 
+
+ align:start position:0%
+because it says that the total size of x
+is around r in all three examples. It
+
+ align:start position:0%
+is around r in all three examples. It
+ 
+
+ align:start position:0%
+is around r in all three examples. It
+makes them a little easier to compare
+
+ align:start position:0%
+makes them a little easier to compare
+ 
+
+ align:start position:0%
+makes them a little easier to compare
+with each other.
+
+ align:start position:0%
+with each other.
+ 
+
+ align:start position:0%
+with each other.
+Okay. So now I'll make a graph.
+
+ align:start position:0%
+Okay. So now I'll make a graph.
+ 
+
+ align:start position:0%
+Okay. So now I'll make a graph.
+Basically I'd like to put on this axis
+
+ align:start position:0%
+Basically I'd like to put on this axis
+ 
+
+ align:start position:0%
+Basically I'd like to put on this axis
+little r and on this axis n subx of
+
+ align:start position:0%
+little r and on this axis n subx of
+ 
+
+ align:start position:0%
+little r and on this axis n subx of
+little r. Um but this graph like many
+
+ align:start position:0%
+little r. Um but this graph like many
+ 
+
+ align:start position:0%
+little r. Um but this graph like many
+graphs in math looks nicer if we use log
+
+ align:start position:0%
+graphs in math looks nicer if we use log
+ 
+
+ align:start position:0%
+graphs in math looks nicer if we use log
+is a log log plot. So on this on this
+
+ align:start position:0%
+is a log log plot. So on this on this
+ 
+
+ align:start position:0%
+is a log log plot. So on this on this
+axis I'm going to put the log of little
+
+ align:start position:0%
+axis I'm going to put the log of little
+ 
+
+ align:start position:0%
+axis I'm going to put the log of little
+r and then the nicest base for that is
+
+ align:start position:0%
+r and then the nicest base for that is
+ 
+
+ align:start position:0%
+r and then the nicest base for that is
+big r. This goes from 0 to one. And on
+
+ align:start position:0%
+big r. This goes from 0 to one. And on
+ 
+
+ align:start position:0%
+big r. This goes from 0 to one. And on
+this axis, I'm going to put the log of n
+
+ align:start position:0%
+this axis, I'm going to put the log of n
+ 
+
+ align:start position:0%
+this axis, I'm going to put the log of n
+subx of r. And it's natural to use the
+
+ align:start position:0%
+subx of r. And it's natural to use the
+ 
+
+ align:start position:0%
+subx of r. And it's natural to use the
+same base. So this goes from 0 to one.
+
+ align:start position:0%
+same base. So this goes from 0 to one.
+ 
+
+ align:start position:0%
+same base. So this goes from 0 to one.
+This could go above one potentially, but
+
+ align:start position:0%
+This could go above one potentially, but
+ 
+
+ align:start position:0%
+This could go above one potentially, but
+because the size of x happens to be r,
+
+ align:start position:0%
+because the size of x happens to be r,
+ 
+
+ align:start position:0%
+because the size of x happens to be r,
+we're going to stop there.
+
+ align:start position:0%
+we're going to stop there.
+ 
+
+ align:start position:0%
+we're going to stop there.
+Okay. So now what do these three
+
+ align:start position:0%
+Okay. So now what do these three
+ 
+
+ align:start position:0%
+Okay. So now what do these three
+examples look like? The first example is
+
+ align:start position:0%
+examples look like? The first example is
+ 
+
+ align:start position:0%
+examples look like? The first example is
+a straight line.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's example one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second example grows more slowly
+
+ align:start position:0%
+the second example grows more slowly
+ 
+
+ align:start position:0%
+the second example grows more slowly
+than the straight line for a while. It
+
+ align:start position:0%
+than the straight line for a while. It
+ 
+
+ align:start position:0%
+than the straight line for a while. It
+doesn't grow at all for a while and then
+
+ align:start position:0%
+doesn't grow at all for a while and then
+ 
+
+ align:start position:0%
+doesn't grow at all for a while and then
+it grows quickly to catch up. So that's
+
+ align:start position:0%
+it grows quickly to catch up. So that's
+ 
+
+ align:start position:0%
+it grows quickly to catch up. So that's
+the second example. It lies below the
+
+ align:start position:0%
+the second example. It lies below the
+ 
+
+ align:start position:0%
+the second example. It lies below the
+straight line. Uh and then the third
+
+ align:start position:0%
+straight line. Uh and then the third
+ 
+
+ align:start position:0%
+straight line. Uh and then the third
+example grows more quickly than the
+
+ align:start position:0%
+example grows more quickly than the
+ 
+
+ align:start position:0%
+example grows more quickly than the
+first example and then it reaches a
+
+ align:start position:0%
+first example and then it reaches a
+ 
+
+ align:start position:0%
+first example and then it reaches a
+certain point and it stops growing. So
+
+ align:start position:0%
+certain point and it stops growing. So
+ 
+
+ align:start position:0%
+certain point and it stops growing. So
+it looks like this and it lies above the
+
+ align:start position:0%
+it looks like this and it lies above the
+ 
+
+ align:start position:0%
+it looks like this and it lies above the
+straight line.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So um so in this theory there
+
+ align:start position:0%
+Okay. So um so in this theory there
+ 
+
+ align:start position:0%
+Okay. So um so in this theory there
+turns out to be that things that grow
+
+ align:start position:0%
+turns out to be that things that grow
+ 
+
+ align:start position:0%
+turns out to be that things that grow
+the the straight line case is an
+
+ align:start position:0%
+the the straight line case is an
+ 
+
+ align:start position:0%
+the the straight line case is an
+important case and then there's an
+
+ align:start position:0%
+important case and then there's an
+ 
+
+ align:start position:0%
+important case and then there's an
+important distinction between things
+
+ align:start position:0%
+important distinction between things
+ 
+
+ align:start position:0%
+important distinction between things
+that are below the straight line things
+
+ align:start position:0%
+that are below the straight line things
+ 
+
+ align:start position:0%
+that are below the straight line things
+that are above the straight line.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so the straight line case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would be that n that that the size of x
+
+ align:start position:0%
+would be that n that that the size of x
+ 
+
+ align:start position:0%
+would be that n that that the size of x
+would be r to the alpha for some alpha
+
+ align:start position:0%
+would be r to the alpha for some alpha
+ 
+
+ align:start position:0%
+would be r to the alpha for some alpha
+and then n sub little r of x or n subx
+
+ align:start position:0%
+and then n sub little r of x or n subx
+ 
+
+ align:start position:0%
+and then n sub little r of x or n subx
+of little r
+
+ align:start position:0%
+of little r
+ 
+
+ align:start position:0%
+of little r
+would be little r to the alpha. That
+
+ align:start position:0%
+would be little r to the alpha. That
+ 
+
+ align:start position:0%
+would be little r to the alpha. That
+would be the straight line case.
+
+ align:start position:0%
+would be the straight line case.
+ 
+
+ align:start position:0%
+would be the straight line case.
+And the uh below the straight line case,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh x would still be r to the alpha. So
+
+ align:start position:0%
+uh x would still be r to the alpha. So
+ 
+
+ align:start position:0%
+uh x would still be r to the alpha. So
+the end point would be the same, but now
+
+ align:start position:0%
+the end point would be the same, but now
+ 
+
+ align:start position:0%
+the end point would be the same, but now
+in the middle, we're going to go below
+
+ align:start position:0%
+in the middle, we're going to go below
+ 
+
+ align:start position:0%
+in the middle, we're going to go below
+what we had before. So n subx of r would
+
+ align:start position:0%
+what we had before. So n subx of r would
+ 
+
+ align:start position:0%
+what we had before. So n subx of r would
+be at most r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this thing here is called a
+
+ align:start position:0%
+Okay. So this thing here is called a
+ 
+
+ align:start position:0%
+Okay. So this thing here is called a
+regular alpha dimensional
+
+ align:start position:0%
+regular alpha dimensional
+ 
+
+ align:start position:0%
+regular alpha dimensional
+spacing
+
+ align:start position:0%
+spacing
+ 
+
+ align:start position:0%
+spacing
+and this thing is called a alpha
+
+ align:start position:0%
+and this thing is called a alpha
+ 
+
+ align:start position:0%
+and this thing is called a alpha
+dimensional spacing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+I'd like and I'd like to make one more
+
+ align:start position:0%
+I'd like and I'd like to make one more
+ 
+
+ align:start position:0%
+I'd like and I'd like to make one more
+definition. And I'll say that X has a
+
+ align:start position:0%
+definition. And I'll say that X has a
+ 
+
+ align:start position:0%
+definition. And I'll say that X has a
+housegrowth spacing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if it has alpha dimensional spacing for
+
+ align:start position:0%
+if it has alpha dimensional spacing for
+ 
+
+ align:start position:0%
+if it has alpha dimensional spacing for
+some of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but another way of saying that is if you
+
+ align:start position:0%
+but another way of saying that is if you
+ 
+
+ align:start position:0%
+but another way of saying that is if you
+look at how many points of X are in a
+
+ align:start position:0%
+look at how many points of X are in a
+ 
+
+ align:start position:0%
+look at how many points of X are in a
+ball of radius R to the beta it's
+
+ align:start position:0%
+ball of radius R to the beta it's
+ 
+
+ align:start position:0%
+ball of radius R to the beta it's
+bounded by the total number of points of
+
+ align:start position:0%
+bounded by the total number of points of
+ 
+
+ align:start position:0%
+bounded by the total number of points of
+x to the beta.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this is this is equivalent. This is
+
+ align:start position:0%
+And this is this is equivalent. This is
+ 
+
+ align:start position:0%
+And this is this is equivalent. This is
+still below the straight line.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So over here um we would have we
+
+ align:start position:0%
+Okay. So over here um we would have we
+ 
+
+ align:start position:0%
+Okay. So over here um we would have we
+have example one and and in general if
+
+ align:start position:0%
+have example one and and in general if
+ 
+
+ align:start position:0%
+have example one and and in general if
+you have any if you have a submanifold
+
+ align:start position:0%
+you have any if you have a submanifold
+ 
+
+ align:start position:0%
+you have any if you have a submanifold
+in any dimensional space it will behave
+
+ align:start position:0%
+in any dimensional space it will behave
+ 
+
+ align:start position:0%
+in any dimensional space it will behave
+like this and alpha is the dimension of
+
+ align:start position:0%
+like this and alpha is the dimension of
+ 
+
+ align:start position:0%
+like this and alpha is the dimension of
+the sub manifold. Also some self-
+
+ align:start position:0%
+the sub manifold. Also some self-
+ 
+
+ align:start position:0%
+the sub manifold. Also some self-
+similar caner set kind of fractals like
+
+ align:start position:0%
+similar caner set kind of fractals like
+ 
+
+ align:start position:0%
+similar caner set kind of fractals like
+the caner set um have this kind of
+
+ align:start position:0%
+the caner set um have this kind of
+ 
+
+ align:start position:0%
+the caner set um have this kind of
+spacing where alpha would be the
+
+ align:start position:0%
+spacing where alpha would be the
+ 
+
+ align:start position:0%
+spacing where alpha would be the
+dimension of the of your caner set.
+
+ align:start position:0%
+dimension of the of your caner set.
+ 
+
+ align:start position:0%
+dimension of the of your caner set.
+That's why it's called alpha
+
+ align:start position:0%
+That's why it's called alpha
+ 
+
+ align:start position:0%
+That's why it's called alpha
+dimensional.
+
+ align:start position:0%
+dimensional.
+ 
+
+ align:start position:0%
+dimensional.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+and um and these things this thing
+
+ align:start position:0%
+and um and these things this thing
+ 
+
+ align:start position:0%
+and um and these things this thing
+called housedorf spacing I called it
+
+ align:start position:0%
+called housedorf spacing I called it
+ 
+
+ align:start position:0%
+called housedorf spacing I called it
+that because it it appears naturally in
+
+ align:start position:0%
+that because it it appears naturally in
+ 
+
+ align:start position:0%
+that because it it appears naturally in
+the theory of housed dorf dimensions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah, so it's maybe worth saying briefly
+
+ align:start position:0%
+yeah, so it's maybe worth saying briefly
+ 
+
+ align:start position:0%
+yeah, so it's maybe worth saying briefly
+that in the geometric measure theory
+
+ align:start position:0%
+that in the geometric measure theory
+ 
+
+ align:start position:0%
+that in the geometric measure theory
+literature, a lot of the stuff we're
+
+ align:start position:0%
+literature, a lot of the stuff we're
+ 
+
+ align:start position:0%
+literature, a lot of the stuff we're
+talking about today was originally
+
+ align:start position:0%
+talking about today was originally
+ 
+
+ align:start position:0%
+talking about today was originally
+described in the language of housedorf
+
+ align:start position:0%
+described in the language of housedorf
+ 
+
+ align:start position:0%
+described in the language of housedorf
+dimensions. Um but my impression is that
+
+ align:start position:0%
+dimensions. Um but my impression is that
+ 
+
+ align:start position:0%
+dimensions. Um but my impression is that
+that's not really that helpful. Like if
+
+ align:start position:0%
+that's not really that helpful. Like if
+ 
+
+ align:start position:0%
+that's not really that helpful. Like if
+we if we defined housedorf dimensions
+
+ align:start position:0%
+we if we defined housedorf dimensions
+ 
+
+ align:start position:0%
+we if we defined housedorf dimensions
+and then we wanted to prove things about
+
+ align:start position:0%
+and then we wanted to prove things about
+ 
+
+ align:start position:0%
+and then we wanted to prove things about
+housed dorf dimensions we would add an
+
+ align:start position:0%
+housed dorf dimensions we would add an
+ 
+
+ align:start position:0%
+housed dorf dimensions we would add an
+extra layer of definition and then we'd
+
+ align:start position:0%
+extra layer of definition and then we'd
+ 
+
+ align:start position:0%
+extra layer of definition and then we'd
+have to check the extra layer of
+
+ align:start position:0%
+have to check the extra layer of
+ 
+
+ align:start position:0%
+have to check the extra layer of
+definition. Um but then in all the
+
+ align:start position:0%
+definition. Um but then in all the
+ 
+
+ align:start position:0%
+definition. Um but then in all the
+applications that we'll talk about we
+
+ align:start position:0%
+applications that we'll talk about we
+ 
+
+ align:start position:0%
+applications that we'll talk about we
+would never use those definitions. We
+
+ align:start position:0%
+would never use those definitions. We
+ 
+
+ align:start position:0%
+would never use those definitions. We
+would go back to this theorem the way
+
+ align:start position:0%
+would go back to this theorem the way
+ 
+
+ align:start position:0%
+would go back to this theorem the way
+it's stated now and use that. Um, so I
+
+ align:start position:0%
+it's stated now and use that. Um, so I
+ 
+
+ align:start position:0%
+it's stated now and use that. Um, so I
+have a bit tentatively but I've come to
+
+ align:start position:0%
+have a bit tentatively but I've come to
+ 
+
+ align:start position:0%
+have a bit tentatively but I've come to
+the conclusion that house dorf dimension
+
+ align:start position:0%
+the conclusion that house dorf dimension
+ 
+
+ align:start position:0%
+the conclusion that house dorf dimension
+is not really a helpful notion for this
+
+ align:start position:0%
+is not really a helpful notion for this
+ 
+
+ align:start position:0%
+is not really a helpful notion for this
+subject and and so I'm going to leave it
+
+ align:start position:0%
+subject and and so I'm going to leave it
+ 
+
+ align:start position:0%
+subject and and so I'm going to leave it
+out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um, but any questions or comments
+
+ align:start position:0%
+Okay. Um, but any questions or comments
+ 
+
+ align:start position:0%
+Okay. Um, but any questions or comments
+about these
+
+ align:start position:0%
+about these
+ 
+
+ align:start position:0%
+about these
+different ways that a set can be spaced?
+
+ align:start position:0%
+different ways that a set can be spaced?
+ 
+
+ align:start position:0%
+different ways that a set can be spaced?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> I'm wondering like is the And the pro 01
+
+ align:start position:0%
+>> I'm wondering like is the And the pro 01
+ 
+
+ align:start position:0%
+>> I'm wondering like is the And the pro 01
+for the pro lower bound.
+
+ align:start position:0%
+for the pro lower bound.
+ 
+
+ align:start position:0%
+for the pro lower bound.
+If we try to calculate lower bound for
+
+ align:start position:0%
+If we try to calculate lower bound for
+ 
+
+ align:start position:0%
+If we try to calculate lower bound for
+B1 B2 like is distance like somehow
+
+ align:start position:0%
+B1 B2 like is distance like somehow
+ 
+
+ align:start position:0%
+B1 B2 like is distance like somehow
+R from R1 to R2 like with that and
+
+ align:start position:0%
+R from R1 to R2 like with that and
+ 
+
+ align:start position:0%
+R from R1 to R2 like with that and
+compare this with the upper bound with
+
+ align:start position:0%
+compare this with the upper bound with
+ 
+
+ align:start position:0%
+compare this with the upper bound with
+different distance from B1 and B2. that
+
+ align:start position:0%
+different distance from B1 and B2. that
+ 
+
+ align:start position:0%
+different distance from B1 and B2. that
+information that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> yeah okay so the question is um when we
+
+ align:start position:0%
+>> yeah okay so the question is um when we
+ 
+
+ align:start position:0%
+>> yeah okay so the question is um when we
+were processing the upper bound for this
+
+ align:start position:0%
+were processing the upper bound for this
+ 
+
+ align:start position:0%
+were processing the upper bound for this
+we sorted it according to the distance
+
+ align:start position:0%
+we sorted it according to the distance
+ 
+
+ align:start position:0%
+we sorted it according to the distance
+so we really have a set star sub r where
+
+ align:start position:0%
+so we really have a set star sub r where
+ 
+
+ align:start position:0%
+so we really have a set star sub r where
+we add the condition that the distance
+
+ align:start position:0%
+we add the condition that the distance
+ 
+
+ align:start position:0%
+we add the condition that the distance
+from b1 to b2 is around r and the
+
+ align:start position:0%
+from b1 to b2 is around r and the
+ 
+
+ align:start position:0%
+from b1 to b2 is around r and the
+question is if if we looked at the lower
+
+ align:start position:0%
+question is if if we looked at the lower
+ 
+
+ align:start position:0%
+question is if if we looked at the lower
+bound we could also sort it by r and and
+
+ align:start position:0%
+bound we could also sort it by r and and
+ 
+
+ align:start position:0%
+bound we could also sort it by r and and
+would that be helpful yeah Um
+
+ align:start position:0%
+would that be helpful yeah Um
+ 
+
+ align:start position:0%
+would that be helpful yeah Um
+um yeah I that is a a good thing to look
+
+ align:start position:0%
+um yeah I that is a a good thing to look
+ 
+
+ align:start position:0%
+um yeah I that is a a good thing to look
+into. Off the top of my head I don't
+
+ align:start position:0%
+into. Off the top of my head I don't
+ 
+
+ align:start position:0%
+into. Off the top of my head I don't
+know if it would be helpful. Um you know
+
+ align:start position:0%
+know if it would be helpful. Um you know
+ 
+
+ align:start position:0%
+know if it would be helpful. Um you know
+it's uh our our lower bound with this s
+
+ align:start position:0%
+it's uh our our lower bound with this s
+ 
+
+ align:start position:0%
+it's uh our our lower bound with this s
+here depends on taking all of them. Um
+
+ align:start position:0%
+here depends on taking all of them. Um
+ 
+
+ align:start position:0%
+here depends on taking all of them. Um
+but it would be interesting. Yeah it
+
+ align:start position:0%
+but it would be interesting. Yeah it
+ 
+
+ align:start position:0%
+but it would be interesting. Yeah it
+would be interesting to think about.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Other questions or comments?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Okay. So, let me show you uh so so
+
+ align:start position:0%
+Okay. Okay. So, let me show you uh so so
+ 
+
+ align:start position:0%
+Okay. Okay. So, let me show you uh so so
+I so I claim so okay it seems that um
+
+ align:start position:0%
+I so I claim so okay it seems that um
+ 
+
+ align:start position:0%
+I so I claim so okay it seems that um
+this spacing condition
+
+ align:start position:0%
+this spacing condition
+ 
+
+ align:start position:0%
+this spacing condition
+say housedorf spacing is helpful in the
+
+ align:start position:0%
+say housedorf spacing is helpful in the
+ 
+
+ align:start position:0%
+say housedorf spacing is helpful in the
+theory. Um and one way that comes about
+
+ align:start position:0%
+theory. Um and one way that comes about
+ 
+
+ align:start position:0%
+theory. Um and one way that comes about
+is that a lot of the theorem statements
+
+ align:start position:0%
+is that a lot of the theorem statements
+ 
+
+ align:start position:0%
+is that a lot of the theorem statements
+become a lot cleaner if you put in house
+
+ align:start position:0%
+become a lot cleaner if you put in house
+ 
+
+ align:start position:0%
+become a lot cleaner if you put in house
+spacing.
+
+ align:start position:0%
+spacing.
+ 
+
+ align:start position:0%
+spacing.
+Um so let's do that here. Let's suppose
+
+ align:start position:0%
+Um so let's do that here. Let's suppose
+ 
+
+ align:start position:0%
+Um so let's do that here. Let's suppose
+that X and D have housed doororf spacing
+
+ align:start position:0%
+that X and D have housed doororf spacing
+ 
+
+ align:start position:0%
+that X and D have housed doororf spacing
+and we'll use that to simplify this
+
+ align:start position:0%
+and we'll use that to simplify this
+ 
+
+ align:start position:0%
+and we'll use that to simplify this
+thing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So corollary one real is that if
+
+ align:start position:0%
+Okay. So corollary one real is that if
+ 
+
+ align:start position:0%
+Okay. So corollary one real is that if
+we have the the setup
+
+ align:start position:0%
+we have the the setup
+ 
+
+ align:start position:0%
+we have the the setup
+and x and d are housedorf spacing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we get a simpler inequality which
+
+ align:start position:0%
+then we get a simpler inequality which
+ 
+
+ align:start position:0%
+then we get a simpler inequality which
+matches quite well what happens in
+
+ align:start position:0%
+matches quite well what happens in
+ 
+
+ align:start position:0%
+matches quite well what happens in
+finite fields.
+
+ align:start position:0%
+finite fields.
+ 
+
+ align:start position:0%
+finite fields.
+Then d is bounded by um s plus x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So, I'll prove this and then I'll try to
+
+ align:start position:0%
+So, I'll prove this and then I'll try to
+ 
+
+ align:start position:0%
+So, I'll prove this and then I'll try to
+argue actually. So, so okay. So, this
+
+ align:start position:0%
+argue actually. So, so okay. So, this
+ 
+
+ align:start position:0%
+argue actually. So, so okay. So, this
+looks a little nicer than before. It
+
+ align:start position:0%
+looks a little nicer than before. It
+ 
+
+ align:start position:0%
+looks a little nicer than before. It
+might still not look that nice to you.
+
+ align:start position:0%
+might still not look that nice to you.
+ 
+
+ align:start position:0%
+might still not look that nice to you.
+Um but I would summarize it like this.
+
+ align:start position:0%
+Um but I would summarize it like this.
+ 
+
+ align:start position:0%
+Um but I would summarize it like this.
+Um either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+either s e either s is pretty close to x
+
+ align:start position:0%
+either s e either s is pretty close to x
+ 
+
+ align:start position:0%
+either s e either s is pretty close to x
+or d is smaller than s and that's what
+
+ align:start position:0%
+or d is smaller than s and that's what
+ 
+
+ align:start position:0%
+or d is smaller than s and that's what
+we had in finite fields. So why is it if
+
+ align:start position:0%
+we had in finite fields. So why is it if
+ 
+
+ align:start position:0%
+we had in finite fields. So why is it if
+s is a lot smaller than x? This is much
+
+ align:start position:0%
+s is a lot smaller than x? This is much
+ 
+
+ align:start position:0%
+s is a lot smaller than x? This is much
+less than one. So we can rearrange that
+
+ align:start position:0%
+less than one. So we can rearrange that
+ 
+
+ align:start position:0%
+less than one. So we can rearrange that
+and we get that d is less than s.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, what's the proof? Well, um,
+
+ align:start position:0%
+Okay. So, what's the proof? Well, um,
+ 
+
+ align:start position:0%
+Okay. So, what's the proof? Well, um,
+we're going to have an expression like
+
+ align:start position:0%
+we're going to have an expression like
+ 
+
+ align:start position:0%
+we're going to have an expression like
+nx of r n d of 1 / r.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now let's suppose
+
+ align:start position:0%
+And so now let's suppose
+ 
+
+ align:start position:0%
+And so now let's suppose
+that little r is big r to the beta.
+
+ align:start position:0%
+that little r is big r to the beta.
+ 
+
+ align:start position:0%
+that little r is big r to the beta.
+And um and then being housedorf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it tells us that nx of r the beta n d of
+
+ align:start position:0%
+it tells us that nx of r the beta n d of
+ 
+
+ align:start position:0%
+it tells us that nx of r the beta n d of
+r the minus beta
+
+ align:start position:0%
+r the minus beta
+ 
+
+ align:start position:0%
+r the minus beta
+there that is bounded by x to the beta *
+
+ align:start position:0%
+there that is bounded by x to the beta *
+ 
+
+ align:start position:0%
+there that is bounded by x to the beta *
+d to the 1 - beta.
+
+ align:start position:0%
+d to the 1 - beta.
+ 
+
+ align:start position:0%
+d to the 1 - beta.
+That's what being housed tells us.
+
+ align:start position:0%
+That's what being housed tells us.
+ 
+
+ align:start position:0%
+That's what being housed tells us.
+So being house of dwarf allows us to to
+
+ align:start position:0%
+So being house of dwarf allows us to to
+ 
+
+ align:start position:0%
+So being house of dwarf allows us to to
+relate nx of r for any r to the size of
+
+ align:start position:0%
+relate nx of r for any r to the size of
+ 
+
+ align:start position:0%
+relate nx of r for any r to the size of
+x which is nx of big r and algebraically
+
+ align:start position:0%
+x which is nx of big r and algebraically
+ 
+
+ align:start position:0%
+x which is nx of big r and algebraically
+it works out like this and for d it
+
+ align:start position:0%
+it works out like this and for d it
+ 
+
+ align:start position:0%
+it works out like this and for d it
+works out like that.
+
+ align:start position:0%
+works out like that.
+ 
+
+ align:start position:0%
+works out like that.
+Okay. And then by amg this is smaller
+
+ align:start position:0%
+Okay. And then by amg this is smaller
+ 
+
+ align:start position:0%
+Okay. And then by amg this is smaller
+than x plus d.
+
+ align:start position:0%
+than x plus d.
+ 
+
+ align:start position:0%
+than x plus d.
+So every one of these complicated things
+
+ align:start position:0%
+So every one of these complicated things
+ 
+
+ align:start position:0%
+So every one of these complicated things
+they're all bounded by x plus d
+
+ align:start position:0%
+they're all bounded by x plus d
+ 
+
+ align:start position:0%
+they're all bounded by x plus d
+and the number of them is only log of r.
+
+ align:start position:0%
+and the number of them is only log of r.
+ 
+
+ align:start position:0%
+and the number of them is only log of r.
+So, okay, sorry. So, I should put a log
+
+ align:start position:0%
+So, okay, sorry. So, I should put a log
+ 
+
+ align:start position:0%
+So, okay, sorry. So, I should put a log
+of R here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+okay. So, now we're just going to plug
+
+ align:start position:0%
+okay. So, now we're just going to plug
+ 
+
+ align:start position:0%
+okay. So, now we're just going to plug
+this in up there. I'll have an x plus d
+
+ align:start position:0%
+this in up there. I'll have an x plus d
+ 
+
+ align:start position:0%
+this in up there. I'll have an x plus d
+up there
+
+ align:start position:0%
+up there
+ 
+
+ align:start position:0%
+up there
+and a log r factor. The x in the x plus
+
+ align:start position:0%
+and a log r factor. The x in the x plus
+ 
+
+ align:start position:0%
+and a log r factor. The x in the x plus
+d gives me this and the d and the x plus
+
+ align:start position:0%
+d gives me this and the d and the x plus
+ 
+
+ align:start position:0%
+d gives me this and the d and the x plus
+d gives me that. It's just algebra.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now let's compare this with the
+
+ align:start position:0%
+Okay. Now let's compare this with the
+ 
+
+ align:start position:0%
+Okay. Now let's compare this with the
+theorem we proved last time in finite
+
+ align:start position:0%
+theorem we proved last time in finite
+ 
+
+ align:start position:0%
+theorem we proved last time in finite
+fields.
+
+ align:start position:0%
+fields.
+ 
+
+ align:start position:0%
+fields.
+So theorem one in finite fields said
+
+ align:start position:0%
+So theorem one in finite fields said
+ 
+
+ align:start position:0%
+So theorem one in finite fields said
+that if we had x in fq2
+
+ align:start position:0%
+that if we had x in fq2
+ 
+
+ align:start position:0%
+that if we had x in fq2
+and d in fq
+
+ align:start position:0%
+and d in fq
+ 
+
+ align:start position:0%
+and d in fq
+and s is the maximum
+
+ align:start position:0%
+and s is the maximum
+ 
+
+ align:start position:0%
+and s is the maximum
+theta and d size is pi theta of x.
+
+ align:start position:0%
+theta and d size is pi theta of x.
+ 
+
+ align:start position:0%
+theta and d size is pi theta of x.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+either S is around X or D is bounded by
+
+ align:start position:0%
+either S is around X or D is bounded by
+ 
+
+ align:start position:0%
+either S is around X or D is bounded by
+S.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the numerology is now the same in
+
+ align:start position:0%
+And the numerology is now the same in
+ 
+
+ align:start position:0%
+And the numerology is now the same in
+finite fields or or or if you have balls
+
+ align:start position:0%
+finite fields or or or if you have balls
+ 
+
+ align:start position:0%
+finite fields or or or if you have balls
+with the house space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um so in general the numerology in a lot
+
+ align:start position:0%
+Um so in general the numerology in a lot
+ 
+
+ align:start position:0%
+Um so in general the numerology in a lot
+of things is the same between finite
+
+ align:start position:0%
+of things is the same between finite
+ 
+
+ align:start position:0%
+of things is the same between finite
+fields and balls with housedorf spacing
+
+ align:start position:0%
+fields and balls with housedorf spacing
+ 
+
+ align:start position:0%
+fields and balls with housedorf spacing
+and so now I'll so this was theorem one
+
+ align:start position:0%
+and so now I'll so this was theorem one
+ 
+
+ align:start position:0%
+and so now I'll so this was theorem one
+from last time I'll track through also
+
+ align:start position:0%
+from last time I'll track through also
+ 
+
+ align:start position:0%
+from last time I'll track through also
+theorem two from last time and the
+
+ align:start position:0%
+theorem two from last time and the
+ 
+
+ align:start position:0%
+theorem two from last time and the
+conjecture from last time and we'll see
+
+ align:start position:0%
+conjecture from last time and we'll see
+ 
+
+ align:start position:0%
+conjecture from last time and we'll see
+that they all match up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So I have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projection theory
+
+ align:start position:0%
+projection theory
+ 
+
+ align:start position:0%
+projection theory
+in FQ2
+
+ align:start position:0%
+in FQ2
+ 
+
+ align:start position:0%
+in FQ2
+versus um in
+
+ align:start position:0%
+versus um in
+ 
+
+ align:start position:0%
+versus um in
+versus unit balls in B2R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and B2R with housed door space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so here was theorem two last time
+
+ align:start position:0%
+Okay, so here was theorem two last time
+ 
+
+ align:start position:0%
+Okay, so here was theorem two last time
+in finite fields.
+
+ align:start position:0%
+in finite fields.
+ 
+
+ align:start position:0%
+in finite fields.
+So if we have our finite field setup
+
+ align:start position:0%
+So if we have our finite field setup
+ 
+
+ align:start position:0%
+So if we have our finite field setup
+which is over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and S is smaller than Q.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um then conclusion is that the number of
+
+ align:start position:0%
+Um then conclusion is that the number of
+ 
+
+ align:start position:0%
+Um then conclusion is that the number of
+directions is smaller than SQX.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And here's what we'll prove in the real
+
+ align:start position:0%
+And here's what we'll prove in the real
+ 
+
+ align:start position:0%
+And here's what we'll prove in the real
+case correlary to R. So if we have our
+
+ align:start position:0%
+case correlary to R. So if we have our
+ 
+
+ align:start position:0%
+case correlary to R. So if we have our
+setup of the day and X and D are housed
+
+ align:start position:0%
+setup of the day and X and D are housed
+ 
+
+ align:start position:0%
+setup of the day and X and D are housed
+and S is a good bit smaller than R.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then maybe this needs a little bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um than d
+
+ align:start position:0%
+um than d
+ 
+
+ align:start position:0%
+um than d
+smaller than sr /x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So I I use this symbol with the
+
+ align:start position:0%
+Okay. So I I use this symbol with the
+ 
+
+ align:start position:0%
+Okay. So I I use this symbol with the
+extra tilda that's hiding something like
+
+ align:start position:0%
+extra tilda that's hiding something like
+ 
+
+ align:start position:0%
+extra tilda that's hiding something like
+a log factor similar to the log factor
+
+ align:start position:0%
+a log factor similar to the log factor
+ 
+
+ align:start position:0%
+a log factor similar to the log factor
+that appeared over here. Like if you if
+
+ align:start position:0%
+that appeared over here. Like if you if
+ 
+
+ align:start position:0%
+that appeared over here. Like if you if
+you compare the real case theorem one
+
+ align:start position:0%
+you compare the real case theorem one
+ 
+
+ align:start position:0%
+you compare the real case theorem one
+and the finite field case we lost an
+
+ align:start position:0%
+and the finite field case we lost an
+ 
+
+ align:start position:0%
+and the finite field case we lost an
+extra log r factor and that h that will
+
+ align:start position:0%
+extra log r factor and that h that will
+ 
+
+ align:start position:0%
+extra log r factor and that h that will
+happen sometimes. Um
+
+ align:start position:0%
+happen sometimes. Um
+ 
+
+ align:start position:0%
+happen sometimes. Um
+so uh notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a less sum b means
+
+ align:start position:0%
+a less sum b means
+ 
+
+ align:start position:0%
+a less sum b means
+for every epsilon bigger than zero there
+
+ align:start position:0%
+for every epsilon bigger than zero there
+ 
+
+ align:start position:0%
+for every epsilon bigger than zero there
+exists c epsilon. So a is less than or
+
+ align:start position:0%
+exists c epsilon. So a is less than or
+ 
+
+ align:start position:0%
+exists c epsilon. So a is less than or
+equal to c epsilon r the epsilon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. But if you compare these um Q
+
+ align:start position:0%
+Okay. But if you compare these um Q
+ 
+
+ align:start position:0%
+Okay. But if you compare these um Q
+corresponds to R.
+
+ align:start position:0%
+corresponds to R.
+ 
+
+ align:start position:0%
+corresponds to R.
+That makes sense. There are Q ^2 points
+
+ align:start position:0%
+That makes sense. There are Q ^2 points
+ 
+
+ align:start position:0%
+That makes sense. There are Q ^2 points
+here and there are R squar unit balls
+
+ align:start position:0%
+here and there are R squar unit balls
+ 
+
+ align:start position:0%
+here and there are R squar unit balls
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and these basically match up except
+
+ align:start position:0%
+Um and these basically match up except
+ 
+
+ align:start position:0%
+Um and these basically match up except
+that there's a minor sort of loss here.
+
+ align:start position:0%
+that there's a minor sort of loss here.
+ 
+
+ align:start position:0%
+that there's a minor sort of loss here.
+Okay. And so this is this is the forier
+
+ align:start position:0%
+Okay. And so this is this is the forier
+ 
+
+ align:start position:0%
+Okay. And so this is this is the forier
+method that we'll turn to in a little
+
+ align:start position:0%
+method that we'll turn to in a little
+ 
+
+ align:start position:0%
+method that we'll turn to in a little
+bit. Um there is also a conjecture about
+
+ align:start position:0%
+bit. Um there is also a conjecture about
+ 
+
+ align:start position:0%
+bit. Um there is also a conjecture about
+the sharp behavior.
+
+ align:start position:0%
+the sharp behavior.
+ 
+
+ align:start position:0%
+the sharp behavior.
+So conjecture
+
+ align:start position:0%
+So conjecture
+ 
+
+ align:start position:0%
+So conjecture
+if P is prime
+
+ align:start position:0%
+if P is prime
+ 
+
+ align:start position:0%
+if P is prime
+and we have our finite field setup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and S is smaller than the minimum of Q
+
+ align:start position:0%
+and S is smaller than the minimum of Q
+ 
+
+ align:start position:0%
+and S is smaller than the minimum of Q
+and X. So either of these are sort of
+
+ align:start position:0%
+and X. So either of these are sort of
+ 
+
+ align:start position:0%
+and X. So either of these are sort of
+trivial. S is always at most Q and it's
+
+ align:start position:0%
+trivial. S is always at most Q and it's
+ 
+
+ align:start position:0%
+trivial. S is always at most Q and it's
+always at most X. So we're make it less
+
+ align:start position:0%
+always at most X. So we're make it less
+ 
+
+ align:start position:0%
+always at most X. So we're make it less
+than that. So we're sort of in a
+
+ align:start position:0%
+than that. So we're sort of in a
+ 
+
+ align:start position:0%
+than that. So we're sort of in a
+non-trivial range.
+
+ align:start position:0%
+non-trivial range.
+ 
+
+ align:start position:0%
+non-trivial range.
+um then
+
+ align:start position:0%
+um then
+ 
+
+ align:start position:0%
+um then
+b should be bounded by s^2 overx which
+
+ align:start position:0%
+b should be bounded by s^2 overx which
+ 
+
+ align:start position:0%
+b should be bounded by s^2 overx which
+would be sharp if it's true and it
+
+ align:start position:0%
+would be sharp if it's true and it
+ 
+
+ align:start position:0%
+would be sharp if it's true and it
+matches the behavior in an integer grid.
+
+ align:start position:0%
+matches the behavior in an integer grid.
+ 
+
+ align:start position:0%
+matches the behavior in an integer grid.
+Okay, this conjecture has an analog
+
+ align:start position:0%
+Okay, this conjecture has an analog
+ 
+
+ align:start position:0%
+Okay, this conjecture has an analog
+uh over in the real case and the real
+
+ align:start position:0%
+uh over in the real case and the real
+ 
+
+ align:start position:0%
+uh over in the real case and the real
+analog is uh is due to fenberg. It's
+
+ align:start position:0%
+analog is uh is due to fenberg. It's
+ 
+
+ align:start position:0%
+analog is uh is due to fenberg. It's
+called the fenber set conjecture. So it
+
+ align:start position:0%
+called the fenber set conjecture. So it
+ 
+
+ align:start position:0%
+called the fenber set conjecture. So it
+says if we have the setup and X and B
+
+ align:start position:0%
+says if we have the setup and X and B
+ 
+
+ align:start position:0%
+says if we have the setup and X and B
+are housed dorf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and S is significantly less than the
+
+ align:start position:0%
+um and S is significantly less than the
+ 
+
+ align:start position:0%
+um and S is significantly less than the
+minimum of R and X. So again S is always
+
+ align:start position:0%
+minimum of R and X. So again S is always
+ 
+
+ align:start position:0%
+minimum of R and X. So again S is always
+smaller than R. It's always smaller than
+
+ align:start position:0%
+smaller than R. It's always smaller than
+ 
+
+ align:start position:0%
+smaller than R. It's always smaller than
+X and we're saying it's significantly
+
+ align:start position:0%
+X and we're saying it's significantly
+ 
+
+ align:start position:0%
+X and we're saying it's significantly
+less than that. So it's sort of
+
+ align:start position:0%
+less than that. So it's sort of
+ 
+
+ align:start position:0%
+less than that. So it's sort of
+non-trivial.
+
+ align:start position:0%
+non-trivial.
+ 
+
+ align:start position:0%
+non-trivial.
+um then
+
+ align:start position:0%
+um then
+ 
+
+ align:start position:0%
+um then
+the number of directions would be less
+
+ align:start position:0%
+the number of directions would be less
+ 
+
+ align:start position:0%
+the number of directions would be less
+than tilda tilda s^2 overx.
+
+ align:start position:0%
+than tilda tilda s^2 overx.
+ 
+
+ align:start position:0%
+than tilda tilda s^2 overx.
+You see that these conjectures again
+
+ align:start position:0%
+You see that these conjectures again
+ 
+
+ align:start position:0%
+You see that these conjectures again
+match up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool.
+
+ align:start position:0%
+Cool.
+ 
+
+ align:start position:0%
+Cool.
+Okay. Now I mentioned on the first day
+
+ align:start position:0%
+Okay. Now I mentioned on the first day
+ 
+
+ align:start position:0%
+Okay. Now I mentioned on the first day
+that one of the fundamental thought
+
+ align:start position:0%
+that one of the fundamental thought
+ 
+
+ align:start position:0%
+that one of the fundamental thought
+problems of projection theory recently
+
+ align:start position:0%
+problems of projection theory recently
+ 
+
+ align:start position:0%
+problems of projection theory recently
+had been solved. This is the problem. So
+
+ align:start position:0%
+had been solved. This is the problem. So
+ 
+
+ align:start position:0%
+had been solved. This is the problem. So
+this conjecture has been proven. Um so
+
+ align:start position:0%
+this conjecture has been proven. Um so
+ 
+
+ align:start position:0%
+this conjecture has been proven. Um so
+this is a theorem from 2024
+
+ align:start position:0%
+this is a theorem from 2024
+ 
+
+ align:start position:0%
+this is a theorem from 2024
+of Orpinan
+
+ align:start position:0%
+of Orpinan
+ 
+
+ align:start position:0%
+of Orpinan
+Schmurkin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ran and Wong
+
+ align:start position:0%
+Ran and Wong
+ 
+
+ align:start position:0%
+Ran and Wong
+conjecture is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the first but finite field is still
+
+ align:start position:0%
+in the first but finite field is still
+ 
+
+ align:start position:0%
+in the first but finite field is still
+open.
+
+ align:start position:0%
+open.
+ 
+
+ align:start position:0%
+open.
+>> Yes, thank you. Yeah, conjecture R is
+
+ align:start position:0%
+>> Yes, thank you. Yeah, conjecture R is
+ 
+
+ align:start position:0%
+>> Yes, thank you. Yeah, conjecture R is
+true. Finite field is still wide open.
+
+ align:start position:0%
+true. Finite field is still wide open.
+ 
+
+ align:start position:0%
+true. Finite field is still wide open.
+Yes.
+
+ align:start position:0%
+Yes.
+ 
+
+ align:start position:0%
+Yes.
+Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. So actually another reason I was
+
+ align:start position:0%
+Cool. So actually another reason I was
+ 
+
+ align:start position:0%
+Cool. So actually another reason I was
+excited to do projection theory this
+
+ align:start position:0%
+excited to do projection theory this
+ 
+
+ align:start position:0%
+excited to do projection theory this
+semester is that a bunch of the
+
+ align:start position:0%
+semester is that a bunch of the
+ 
+
+ align:start position:0%
+semester is that a bunch of the
+architects of the recent developments
+
+ align:start position:0%
+architects of the recent developments
+ 
+
+ align:start position:0%
+architects of the recent developments
+will be visiting. Pablo Mkin is going to
+
+ align:start position:0%
+will be visiting. Pablo Mkin is going to
+ 
+
+ align:start position:0%
+will be visiting. Pablo Mkin is going to
+be here for about a month. He's going to
+
+ align:start position:0%
+be here for about a month. He's going to
+ 
+
+ align:start position:0%
+be here for about a month. He's going to
+talk in the analysis seminar. I might
+
+ align:start position:0%
+talk in the analysis seminar. I might
+ 
+
+ align:start position:0%
+talk in the analysis seminar. I might
+rope him into talking in this class. Um
+
+ align:start position:0%
+rope him into talking in this class. Um
+ 
+
+ align:start position:0%
+rope him into talking in this class. Um
+Kevin Ran is going to visit and give a
+
+ align:start position:0%
+Kevin Ran is going to visit and give a
+ 
+
+ align:start position:0%
+Kevin Ran is going to visit and give a
+talk. Hung will be here at at some
+
+ align:start position:0%
+talk. Hung will be here at at some
+ 
+
+ align:start position:0%
+talk. Hung will be here at at some
+point, although maybe not during
+
+ align:start position:0%
+point, although maybe not during
+ 
+
+ align:start position:0%
+point, although maybe not during
+classes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, I'll say let me say something very
+
+ align:start position:0%
+Yeah, I'll say let me say something very
+ 
+
+ align:start position:0%
+Yeah, I'll say let me say something very
+briefly. So these these two conjectures
+
+ align:start position:0%
+briefly. So these these two conjectures
+ 
+
+ align:start position:0%
+briefly. So these these two conjectures
+I presented them as being parallel to
+
+ align:start position:0%
+I presented them as being parallel to
+ 
+
+ align:start position:0%
+I presented them as being parallel to
+each other. I think that's fair. Um and
+
+ align:start position:0%
+each other. I think that's fair. Um and
+ 
+
+ align:start position:0%
+each other. I think that's fair. Um and
+they're both quite difficult. Um this
+
+ align:start position:0%
+they're both quite difficult. Um this
+ 
+
+ align:start position:0%
+they're both quite difficult. Um this
+one people have managed to prove which
+
+ align:start position:0%
+one people have managed to prove which
+ 
+
+ align:start position:0%
+one people have managed to prove which
+is exciting and um and this one is still
+
+ align:start position:0%
+is exciting and um and this one is still
+ 
+
+ align:start position:0%
+is exciting and um and this one is still
+open. So uh the difference is that in
+
+ align:start position:0%
+open. So uh the difference is that in
+ 
+
+ align:start position:0%
+open. So uh the difference is that in
+this problem there are many different
+
+ align:start position:0%
+this problem there are many different
+ 
+
+ align:start position:0%
+this problem there are many different
+scales. We've sort of seen the many
+
+ align:start position:0%
+scales. We've sort of seen the many
+ 
+
+ align:start position:0%
+scales. We've sort of seen the many
+different scales in in what we just did
+
+ align:start position:0%
+different scales in in what we just did
+ 
+
+ align:start position:0%
+different scales in in what we just did
+with double counting. We had to think
+
+ align:start position:0%
+with double counting. We had to think
+ 
+
+ align:start position:0%
+with double counting. We had to think
+about all these different scales and
+
+ align:start position:0%
+about all these different scales and
+ 
+
+ align:start position:0%
+about all these different scales and
+we're going to do it again with the
+
+ align:start position:0%
+we're going to do it again with the
+ 
+
+ align:start position:0%
+we're going to do it again with the
+forier method. So far you might have the
+
+ align:start position:0%
+forier method. So far you might have the
+ 
+
+ align:start position:0%
+forier method. So far you might have the
+impression that these different scales
+
+ align:start position:0%
+impression that these different scales
+ 
+
+ align:start position:0%
+impression that these different scales
+are just a nuisance. They make simple
+
+ align:start position:0%
+are just a nuisance. They make simple
+ 
+
+ align:start position:0%
+are just a nuisance. They make simple
+arguments more complicated and the
+
+ align:start position:0%
+arguments more complicated and the
+ 
+
+ align:start position:0%
+arguments more complicated and the
+expressions longer. Um but but actually
+
+ align:start position:0%
+expressions longer. Um but but actually
+ 
+
+ align:start position:0%
+expressions longer. Um but but actually
+having these many different scales will
+
+ align:start position:0%
+having these many different scales will
+ 
+
+ align:start position:0%
+having these many different scales will
+turn out to be a help. Um so they play a
+
+ align:start position:0%
+turn out to be a help. Um so they play a
+ 
+
+ align:start position:0%
+turn out to be a help. Um so they play a
+key role in the proof of this that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somehow because of all these scales if
+
+ align:start position:0%
+somehow because of all these scales if
+ 
+
+ align:start position:0%
+somehow because of all these scales if
+if if something goes wrong something has
+
+ align:start position:0%
+if if something goes wrong something has
+ 
+
+ align:start position:0%
+if if something goes wrong something has
+to go wrong at many different scales. Um
+
+ align:start position:0%
+to go wrong at many different scales. Um
+ 
+
+ align:start position:0%
+to go wrong at many different scales. Um
+the argument also has different cases
+
+ align:start position:0%
+the argument also has different cases
+ 
+
+ align:start position:0%
+the argument also has different cases
+depending upon whether the sets look
+
+ align:start position:0%
+depending upon whether the sets look
+ 
+
+ align:start position:0%
+depending upon whether the sets look
+like set have spacing like number one or
+
+ align:start position:0%
+like set have spacing like number one or
+ 
+
+ align:start position:0%
+like set have spacing like number one or
+spacing like number two. There are
+
+ align:start position:0%
+spacing like number two. There are
+ 
+
+ align:start position:0%
+spacing like number two. There are
+different things to play with. They're
+
+ align:start position:0%
+different things to play with. They're
+ 
+
+ align:start position:0%
+different things to play with. They're
+both helpful in different ways
+
+ align:start position:0%
+both helpful in different ways
+ 
+
+ align:start position:0%
+both helpful in different ways
+and and none of that structure is
+
+ align:start position:0%
+and and none of that structure is
+ 
+
+ align:start position:0%
+and and none of that structure is
+available here. So So probably
+
+ align:start position:0%
+available here. So So probably
+ 
+
+ align:start position:0%
+available here. So So probably
+completely different ideas would be
+
+ align:start position:0%
+completely different ideas would be
+ 
+
+ align:start position:0%
+completely different ideas would be
+needed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, good. So the second half of the
+
+ align:start position:0%
+Okay, good. So the second half of the
+ 
+
+ align:start position:0%
+Okay, good. So the second half of the
+class the goal is to do the forier
+
+ align:start position:0%
+class the goal is to do the forier
+ 
+
+ align:start position:0%
+class the goal is to do the forier
+method in the real case and build up
+
+ align:start position:0%
+method in the real case and build up
+ 
+
+ align:start position:0%
+method in the real case and build up
+towards towards doing this. Um let me
+
+ align:start position:0%
+towards towards doing this. Um let me
+ 
+
+ align:start position:0%
+towards towards doing this. Um let me
+remind you first of the main thing we
+
+ align:start position:0%
+remind you first of the main thing we
+ 
+
+ align:start position:0%
+remind you first of the main thing we
+proved using for analysis over finite
+
+ align:start position:0%
+proved using for analysis over finite
+ 
+
+ align:start position:0%
+proved using for analysis over finite
+fields and then we'll set up a version
+
+ align:start position:0%
+fields and then we'll set up a version
+ 
+
+ align:start position:0%
+fields and then we'll set up a version
+over over the rings.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So part two of the class for a
+
+ align:start position:0%
+Okay. So part two of the class for a
+ 
+
+ align:start position:0%
+Okay. So part two of the class for a
+method.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um okay so the main lema that we proved
+
+ align:start position:0%
+Um okay so the main lema that we proved
+ 
+
+ align:start position:0%
+Um okay so the main lema that we proved
+over finite fields is like this.
+
+ align:start position:0%
+over finite fields is like this.
+ 
+
+ align:start position:0%
+over finite fields is like this.
+So let's say fancy L is a set of lines
+
+ align:start position:0%
+So let's say fancy L is a set of lines
+ 
+
+ align:start position:0%
+So let's say fancy L is a set of lines
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+FQ^2
+
+ align:start position:0%
+FQ^2
+ 
+
+ align:start position:0%
+FQ^2
+and um F
+
+ align:start position:0%
+and um F
+ 
+
+ align:start position:0%
+and um F
+is a sum over all these lines of the
+
+ align:start position:0%
+is a sum over all these lines of the
+ 
+
+ align:start position:0%
+is a sum over all these lines of the
+characteristic function of the line.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, if that's true, then we can break
+
+ align:start position:0%
+Okay, if that's true, then we can break
+ 
+
+ align:start position:0%
+Okay, if that's true, then we can break
+up f into two pieces. a zero frequency
+
+ align:start position:0%
+up f into two pieces. a zero frequency
+ 
+
+ align:start position:0%
+up f into two pieces. a zero frequency
+piece and a nonzero frequency piece. So
+
+ align:start position:0%
+piece and a nonzero frequency piece. So
+ 
+
+ align:start position:0%
+piece and a nonzero frequency piece. So
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+f is equal to f0 plus f we called it f
+
+ align:start position:0%
+f is equal to f0 plus f we called it f
+ 
+
+ align:start position:0%
+f is equal to f0 plus f we called it f
+high zero frequency high frequency.
+
+ align:start position:0%
+high zero frequency high frequency.
+ 
+
+ align:start position:0%
+high zero frequency high frequency.
+So that
+
+ align:start position:0%
+So that
+ 
+
+ align:start position:0%
+So that
+so the support of f0 hat is just zero.
+
+ align:start position:0%
+so the support of f0 hat is just zero.
+ 
+
+ align:start position:0%
+so the support of f0 hat is just zero.
+In other words, f0 is constant.
+
+ align:start position:0%
+In other words, f0 is constant.
+ 
+
+ align:start position:0%
+In other words, f0 is constant.
+Um and we can find out exactly what the
+
+ align:start position:0%
+Um and we can find out exactly what the
+ 
+
+ align:start position:0%
+Um and we can find out exactly what the
+constant is. And based on that we can
+
+ align:start position:0%
+constant is. And based on that we can
+ 
+
+ align:start position:0%
+constant is. And based on that we can
+say that the L2 norm squared of this is
+
+ align:start position:0%
+say that the L2 norm squared of this is
+ 
+
+ align:start position:0%
+say that the L2 norm squared of this is
+the number of lines squared.
+
+ align:start position:0%
+the number of lines squared.
+ 
+
+ align:start position:0%
+the number of lines squared.
+Then the support of the high frequency
+
+ align:start position:0%
+Then the support of the high frequency
+ 
+
+ align:start position:0%
+Then the support of the high frequency
+part is the complement of zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the high frequency part
+
+ align:start position:0%
+And the high frequency part
+ 
+
+ align:start position:0%
+And the high frequency part
+has an L2 bound. L2 2 is L * Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+I remember teaching a intro to real
+
+ align:start position:0%
+I remember teaching a intro to real
+ 
+
+ align:start position:0%
+I remember teaching a intro to real
+analysis class once and I and so I I
+
+ align:start position:0%
+analysis class once and I and so I I
+ 
+
+ align:start position:0%
+analysis class once and I and so I I
+tried to answer the question on the
+
+ align:start position:0%
+tried to answer the question on the
+ 
+
+ align:start position:0%
+tried to answer the question on the
+first day what is real analysis so there
+
+ align:start position:0%
+first day what is real analysis so there
+ 
+
+ align:start position:0%
+first day what is real analysis so there
+are several you know there are lots of
+
+ align:start position:0%
+are several you know there are lots of
+ 
+
+ align:start position:0%
+are several you know there are lots of
+different things you might say something
+
+ align:start position:0%
+different things you might say something
+ 
+
+ align:start position:0%
+different things you might say something
+about convergence and infinity or
+
+ align:start position:0%
+about convergence and infinity or
+ 
+
+ align:start position:0%
+about convergence and infinity or
+whatever but another thing I proposed is
+
+ align:start position:0%
+whatever but another thing I proposed is
+ 
+
+ align:start position:0%
+whatever but another thing I proposed is
+um analysis is complicated equals simple
+
+ align:start position:0%
+um analysis is complicated equals simple
+ 
+
+ align:start position:0%
+um analysis is complicated equals simple
+plus small.
+
+ align:start position:0%
+plus small.
+ 
+
+ align:start position:0%
+plus small.
+We study something complicated. The real
+
+ align:start position:0%
+We study something complicated. The real
+ 
+
+ align:start position:0%
+We study something complicated. The real
+analysis point of view is to try to
+
+ align:start position:0%
+analysis point of view is to try to
+ 
+
+ align:start position:0%
+analysis point of view is to try to
+write it as something simple plus
+
+ align:start position:0%
+write it as something simple plus
+ 
+
+ align:start position:0%
+write it as something simple plus
+something small.
+
+ align:start position:0%
+something small.
+ 
+
+ align:start position:0%
+something small.
+So this is our function that maybe we
+
+ align:start position:0%
+So this is our function that maybe we
+ 
+
+ align:start position:0%
+So this is our function that maybe we
+feel is complicated. We don't understand
+
+ align:start position:0%
+feel is complicated. We don't understand
+ 
+
+ align:start position:0%
+feel is complicated. We don't understand
+it that well yet. We wrote it as
+
+ align:start position:0%
+it that well yet. We wrote it as
+ 
+
+ align:start position:0%
+it that well yet. We wrote it as
+something simple. This is a constant
+
+ align:start position:0%
+something simple. This is a constant
+ 
+
+ align:start position:0%
+something simple. This is a constant
+function which makes it quite simpler
+
+ align:start position:0%
+function which makes it quite simpler
+ 
+
+ align:start position:0%
+function which makes it quite simpler
+than a general function. And then this
+
+ align:start position:0%
+than a general function. And then this
+ 
+
+ align:start position:0%
+than a general function. And then this
+bit and the point here is that this is
+
+ align:start position:0%
+bit and the point here is that this is
+ 
+
+ align:start position:0%
+bit and the point here is that this is
+smaller than fot or f. Now that that
+
+ align:start position:0%
+smaller than fot or f. Now that that
+ 
+
+ align:start position:0%
+smaller than fot or f. Now that that
+only becomes true and this only becomes
+
+ align:start position:0%
+only becomes true and this only becomes
+ 
+
+ align:start position:0%
+only becomes true and this only becomes
+at all interesting when the number of
+
+ align:start position:0%
+at all interesting when the number of
+ 
+
+ align:start position:0%
+at all interesting when the number of
+lines is much bigger than Q. But when
+
+ align:start position:0%
+lines is much bigger than Q. But when
+ 
+
+ align:start position:0%
+lines is much bigger than Q. But when
+that h when that happens this L2 norm is
+
+ align:start position:0%
+that h when that happens this L2 norm is
+ 
+
+ align:start position:0%
+that h when that happens this L2 norm is
+much smaller than that L2 norm. So
+
+ align:start position:0%
+much smaller than that L2 norm. So
+ 
+
+ align:start position:0%
+much smaller than that L2 norm. So
+complicated equals simple plus small.
+
+ align:start position:0%
+complicated equals simple plus small.
+ 
+
+ align:start position:0%
+complicated equals simple plus small.
+Okay. So uh so our goal is I will
+
+ align:start position:0%
+Okay. So uh so our goal is I will
+ 
+
+ align:start position:0%
+Okay. So uh so our goal is I will
+describe to you the version of this lema
+
+ align:start position:0%
+describe to you the version of this lema
+ 
+
+ align:start position:0%
+describe to you the version of this lema
+in over the real numbers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So instead of a line, so infinitely thin
+
+ align:start position:0%
+So instead of a line, so infinitely thin
+ 
+
+ align:start position:0%
+So instead of a line, so infinitely thin
+line, what we're going to talk about is
+
+ align:start position:0%
+line, what we're going to talk about is
+ 
+
+ align:start position:0%
+line, what we're going to talk about is
+a rectangle or I usually call it a tube.
+
+ align:start position:0%
+a rectangle or I usually call it a tube.
+ 
+
+ align:start position:0%
+a rectangle or I usually call it a tube.
+So capital T for tube is a one by R
+
+ align:start position:0%
+So capital T for tube is a one by R
+ 
+
+ align:start position:0%
+So capital T for tube is a one by R
+rectangle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the plane
+
+ align:start position:0%
+in the plane
+ 
+
+ align:start position:0%
+in the plane
+in any direction.
+
+ align:start position:0%
+in any direction.
+ 
+
+ align:start position:0%
+in any direction.
+Okay. And so basically we're going to
+
+ align:start position:0%
+Okay. And so basically we're going to
+ 
+
+ align:start position:0%
+Okay. And so basically we're going to
+add up characteristic functions of
+
+ align:start position:0%
+add up characteristic functions of
+ 
+
+ align:start position:0%
+add up characteristic functions of
+rectangles.
+
+ align:start position:0%
+rectangles.
+ 
+
+ align:start position:0%
+rectangles.
+Um but when you do for analysis
+
+ align:start position:0%
+Um but when you do for analysis
+ 
+
+ align:start position:0%
+Um but when you do for analysis
+characteristic functions of rectangles
+
+ align:start position:0%
+characteristic functions of rectangles
+ 
+
+ align:start position:0%
+characteristic functions of rectangles
+or characteristic functions in general
+
+ align:start position:0%
+or characteristic functions in general
+ 
+
+ align:start position:0%
+or characteristic functions in general
+are not super nice because of the
+
+ align:start position:0%
+are not super nice because of the
+ 
+
+ align:start position:0%
+are not super nice because of the
+discontinuous sharp cut offs their 4A
+
+ align:start position:0%
+discontinuous sharp cut offs their 4A
+ 
+
+ align:start position:0%
+discontinuous sharp cut offs their 4A
+transforms are not very well behaved. So
+
+ align:start position:0%
+transforms are not very well behaved. So
+ 
+
+ align:start position:0%
+transforms are not very well behaved. So
+what we often do is we work with a
+
+ align:start position:0%
+what we often do is we work with a
+ 
+
+ align:start position:0%
+what we often do is we work with a
+smoothed approximation of the
+
+ align:start position:0%
+smoothed approximation of the
+ 
+
+ align:start position:0%
+smoothed approximation of the
+characteristic function.
+
+ align:start position:0%
+characteristic function.
+ 
+
+ align:start position:0%
+characteristic function.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+C subt is a smooth
+
+ align:start position:0%
+C subt is a smooth
+ 
+
+ align:start position:0%
+C subt is a smooth
+approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the characteristic function of T.
+
+ align:start position:0%
+of the characteristic function of T.
+ 
+
+ align:start position:0%
+of the characteristic function of T.
+Okay. Um so another thing about this
+
+ align:start position:0%
+Okay. Um so another thing about this
+ 
+
+ align:start position:0%
+Okay. Um so another thing about this
+step of doing for analysis on R2 instead
+
+ align:start position:0%
+step of doing for analysis on R2 instead
+ 
+
+ align:start position:0%
+step of doing for analysis on R2 instead
+of finite fields is that certain things
+
+ align:start position:0%
+of finite fields is that certain things
+ 
+
+ align:start position:0%
+of finite fields is that certain things
+are a little bit messy. for example,
+
+ align:start position:0%
+are a little bit messy. for example,
+ 
+
+ align:start position:0%
+are a little bit messy. for example,
+it's a little bit messy to write down
+
+ align:start position:0%
+it's a little bit messy to write down
+ 
+
+ align:start position:0%
+it's a little bit messy to write down
+the formula for C subt.
+
+ align:start position:0%
+the formula for C subt.
+ 
+
+ align:start position:0%
+the formula for C subt.
+Um, so I'm going to try the approach of
+
+ align:start position:0%
+Um, so I'm going to try the approach of
+ 
+
+ align:start position:0%
+Um, so I'm going to try the approach of
+not doing the messy details in class. So
+
+ align:start position:0%
+not doing the messy details in class. So
+ 
+
+ align:start position:0%
+not doing the messy details in class. So
+in class I'll give you an overview and
+
+ align:start position:0%
+in class I'll give you an overview and
+ 
+
+ align:start position:0%
+in class I'll give you an overview and
+then on the homework, uh, I'll do all of
+
+ align:start position:0%
+then on the homework, uh, I'll do all of
+ 
+
+ align:start position:0%
+then on the homework, uh, I'll do all of
+the details and and and you can check
+
+ align:start position:0%
+the details and and and you can check
+ 
+
+ align:start position:0%
+the details and and and you can check
+the things and make sure you understand
+
+ align:start position:0%
+the things and make sure you understand
+ 
+
+ align:start position:0%
+the things and make sure you understand
+how it works.
+
+ align:start position:0%
+how it works.
+ 
+
+ align:start position:0%
+how it works.
+And uh and I do that partly because I
+
+ align:start position:0%
+And uh and I do that partly because I
+ 
+
+ align:start position:0%
+And uh and I do that partly because I
+feel like sometimes the messy details
+
+ align:start position:0%
+feel like sometimes the messy details
+ 
+
+ align:start position:0%
+feel like sometimes the messy details
+obscure sort of the main trajectory of
+
+ align:start position:0%
+obscure sort of the main trajectory of
+ 
+
+ align:start position:0%
+obscure sort of the main trajectory of
+what we want to do. It's good to sort of
+
+ align:start position:0%
+what we want to do. It's good to sort of
+ 
+
+ align:start position:0%
+what we want to do. It's good to sort of
+first learn what you want to do and then
+
+ align:start position:0%
+first learn what you want to do and then
+ 
+
+ align:start position:0%
+first learn what you want to do and then
+um once you know where you're trying to
+
+ align:start position:0%
+um once you know where you're trying to
+ 
+
+ align:start position:0%
+um once you know where you're trying to
+go, fill in all the little steps to get
+
+ align:start position:0%
+go, fill in all the little steps to get
+ 
+
+ align:start position:0%
+go, fill in all the little steps to get
+there.
+
+ align:start position:0%
+there.
+ 
+
+ align:start position:0%
+there.
+Okay. So for this class, I won't say
+
+ align:start position:0%
+Okay. So for this class, I won't say
+ 
+
+ align:start position:0%
+Okay. So for this class, I won't say
+anything more precise than C subt is a
+
+ align:start position:0%
+anything more precise than C subt is a
+ 
+
+ align:start position:0%
+anything more precise than C subt is a
+smooth approximation of the
+
+ align:start position:0%
+smooth approximation of the
+ 
+
+ align:start position:0%
+smooth approximation of the
+characteristic function of T.
+
+ align:start position:0%
+characteristic function of T.
+ 
+
+ align:start position:0%
+characteristic function of T.
+Okay. So now here is our
+
+ align:start position:0%
+Okay. So now here is our
+ 
+
+ align:start position:0%
+Okay. So now here is our
+um main lema
+
+ align:start position:0%
+um main lema
+ 
+
+ align:start position:0%
+um main lema
+in the real case.
+
+ align:start position:0%
+in the real case.
+ 
+
+ align:start position:0%
+in the real case.
+Okay. So instead of L is a set of lines,
+
+ align:start position:0%
+Okay. So instead of L is a set of lines,
+ 
+
+ align:start position:0%
+Okay. So instead of L is a set of lines,
+T is a set of 1 by R rectangles
+
+ align:start position:0%
+T is a set of 1 by R rectangles
+ 
+
+ align:start position:0%
+T is a set of 1 by R rectangles
+in the plane R2.
+
+ align:start position:0%
+in the plane R2.
+ 
+
+ align:start position:0%
+in the plane R2.
+And then f is the sum over all the
+
+ align:start position:0%
+And then f is the sum over all the
+ 
+
+ align:start position:0%
+And then f is the sum over all the
+rectangles of this smooth characteristic
+
+ align:start position:0%
+rectangles of this smooth characteristic
+ 
+
+ align:start position:0%
+rectangles of this smooth characteristic
+function. And that plays the role of the
+
+ align:start position:0%
+function. And that plays the role of the
+ 
+
+ align:start position:0%
+function. And that plays the role of the
+function f up there.
+
+ align:start position:0%
+function f up there.
+ 
+
+ align:start position:0%
+function f up there.
+Okay. And then we're going to break this
+
+ align:start position:0%
+Okay. And then we're going to break this
+ 
+
+ align:start position:0%
+Okay. And then we're going to break this
+function up into pieces. There are going
+
+ align:start position:0%
+function up into pieces. There are going
+ 
+
+ align:start position:0%
+function up into pieces. There are going
+to be sort of low frequency pieces that
+
+ align:start position:0%
+to be sort of low frequency pieces that
+ 
+
+ align:start position:0%
+to be sort of low frequency pieces that
+have the advantage of being kind of
+
+ align:start position:0%
+have the advantage of being kind of
+ 
+
+ align:start position:0%
+have the advantage of being kind of
+constant and there are going to be some
+
+ align:start position:0%
+constant and there are going to be some
+ 
+
+ align:start position:0%
+constant and there are going to be some
+high frequency pieces that have the
+
+ align:start position:0%
+high frequency pieces that have the
+ 
+
+ align:start position:0%
+high frequency pieces that have the
+advantage of being small.
+
+ align:start position:0%
+advantage of being small.
+ 
+
+ align:start position:0%
+advantage of being small.
+Uh but the difference between the real
+
+ align:start position:0%
+Uh but the difference between the real
+ 
+
+ align:start position:0%
+Uh but the difference between the real
+world and and FQ is that in FQ there are
+
+ align:start position:0%
+world and and FQ is that in FQ there are
+ 
+
+ align:start position:0%
+world and and FQ is that in FQ there are
+only two kinds of frequencies. There was
+
+ align:start position:0%
+only two kinds of frequencies. There was
+ 
+
+ align:start position:0%
+only two kinds of frequencies. There was
+zero and not zero. Um but uh in in the
+
+ align:start position:0%
+zero and not zero. Um but uh in in the
+ 
+
+ align:start position:0%
+zero and not zero. Um but uh in in the
+reals there are a lot of frequencies.
+
+ align:start position:0%
+reals there are a lot of frequencies.
+ 
+
+ align:start position:0%
+reals there are a lot of frequencies.
+There's large, medium, small, very small
+
+ align:start position:0%
+There's large, medium, small, very small
+ 
+
+ align:start position:0%
+There's large, medium, small, very small
+and all of those are they're each going
+
+ align:start position:0%
+and all of those are they're each going
+ 
+
+ align:start position:0%
+and all of those are they're each going
+to to to be there. Okay. So instead of
+
+ align:start position:0%
+to to to be there. Okay. So instead of
+ 
+
+ align:start position:0%
+to to to be there. Okay. So instead of
+having two pieces, we will have many
+
+ align:start position:0%
+having two pieces, we will have many
+ 
+
+ align:start position:0%
+having two pieces, we will have many
+pieces.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So f is going to be the sum of f little
+
+ align:start position:0%
+So f is going to be the sum of f little
+ 
+
+ align:start position:0%
+So f is going to be the sum of f little
+r little r goes from one up to capital r
+
+ align:start position:0%
+r little r goes from one up to capital r
+ 
+
+ align:start position:0%
+r little r goes from one up to capital r
+and is diatic just like in theorem one.
+
+ align:start position:0%
+and is diatic just like in theorem one.
+ 
+
+ align:start position:0%
+and is diatic just like in theorem one.
+So we'll have log of r many pieces and
+
+ align:start position:0%
+So we'll have log of r many pieces and
+ 
+
+ align:start position:0%
+So we'll have log of r many pieces and
+these are the different scales of the
+
+ align:start position:0%
+these are the different scales of the
+ 
+
+ align:start position:0%
+these are the different scales of the
+frequencies.
+
+ align:start position:0%
+frequencies.
+ 
+
+ align:start position:0%
+frequencies.
+Okay. Uh we'll do this so that
+
+ align:start position:0%
+Okay. Uh we'll do this so that
+ 
+
+ align:start position:0%
+Okay. Uh we'll do this so that
+the support
+
+ align:start position:0%
+the support
+ 
+
+ align:start position:0%
+the support
+of fr hat
+
+ align:start position:0%
+of fr hat
+ 
+
+ align:start position:0%
+of fr hat
+is contained in the ball of radius one
+
+ align:start position:0%
+is contained in the ball of radius one
+ 
+
+ align:start position:0%
+is contained in the ball of radius one
+over little r. So that's the frequency
+
+ align:start position:0%
+over little r. So that's the frequency
+ 
+
+ align:start position:0%
+over little r. So that's the frequency
+information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um we will say something about the
+
+ align:start position:0%
+and um we will say something about the
+ 
+
+ align:start position:0%
+and um we will say something about the
+L2 norm.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now, um, our bounds on the L2 norm
+
+ align:start position:0%
+Now, um, our bounds on the L2 norm
+ 
+
+ align:start position:0%
+Now, um, our bounds on the L2 norm
+before only depended on how many lines
+
+ align:start position:0%
+before only depended on how many lines
+ 
+
+ align:start position:0%
+before only depended on how many lines
+there were, not about how the lines were
+
+ align:start position:0%
+there were, not about how the lines were
+ 
+
+ align:start position:0%
+there were, not about how the lines were
+arranged. Uh, but that won't be quite
+
+ align:start position:0%
+arranged. Uh, but that won't be quite
+ 
+
+ align:start position:0%
+arranged. Uh, but that won't be quite
+true anymore. Like, like we've seen in
+
+ align:start position:0%
+true anymore. Like, like we've seen in
+ 
+
+ align:start position:0%
+true anymore. Like, like we've seen in
+other places, it will matter how these
+
+ align:start position:0%
+other places, it will matter how these
+ 
+
+ align:start position:0%
+other places, it will matter how these
+tubes are clumped. So, if you have many
+
+ align:start position:0%
+tubes are clumped. So, if you have many
+ 
+
+ align:start position:0%
+tubes are clumped. So, if you have many
+tubes that are clumped together inside
+
+ align:start position:0%
+tubes that are clumped together inside
+ 
+
+ align:start position:0%
+tubes that are clumped together inside
+of a um Yeah. Okay. So, let me let me
+
+ align:start position:0%
+of a um Yeah. Okay. So, let me let me
+ 
+
+ align:start position:0%
+of a um Yeah. Okay. So, let me let me
+put the other part of the definition. So
+
+ align:start position:0%
+put the other part of the definition. So
+ 
+
+ align:start position:0%
+put the other part of the definition. So
+n subr of t is the maximum over tilda
+
+ align:start position:0%
+n subr of t is the maximum over tilda
+ 
+
+ align:start position:0%
+n subr of t is the maximum over tilda
+which is like a two little r by two big
+
+ align:start position:0%
+which is like a two little r by two big
+ 
+
+ align:start position:0%
+which is like a two little r by two big
+r rectangle
+
+ align:start position:0%
+r rectangle
+ 
+
+ align:start position:0%
+r rectangle
+of the number of t in our set of t that
+
+ align:start position:0%
+of the number of t in our set of t that
+ 
+
+ align:start position:0%
+of the number of t in our set of t that
+are so that t is contained in t tilda.
+
+ align:start position:0%
+are so that t is contained in t tilda.
+ 
+
+ align:start position:0%
+are so that t is contained in t tilda.
+So here's a picture.
+
+ align:start position:0%
+So here's a picture.
+ 
+
+ align:start position:0%
+So here's a picture.
+So here's tilda.
+
+ align:start position:0%
+So here's tilda.
+ 
+
+ align:start position:0%
+So here's tilda.
+This axis is little r basically and this
+
+ align:start position:0%
+This axis is little r basically and this
+ 
+
+ align:start position:0%
+This axis is little r basically and this
+axis is big r basically. Maybe it's good
+
+ align:start position:0%
+axis is big r basically. Maybe it's good
+ 
+
+ align:start position:0%
+axis is big r basically. Maybe it's good
+to put two big R. Um, and inside of here
+
+ align:start position:0%
+to put two big R. Um, and inside of here
+ 
+
+ align:start position:0%
+to put two big R. Um, and inside of here
+there may be a bunch of R twos.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So just like uh oh and I I guess to be
+
+ align:start position:0%
+So just like uh oh and I I guess to be
+ 
+
+ align:start position:0%
+So just like uh oh and I I guess to be
+consistent with before I should actually
+
+ align:start position:0%
+consistent with before I should actually
+ 
+
+ align:start position:0%
+consistent with before I should actually
+do this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So n subx of r measured whether many of
+
+ align:start position:0%
+So n subx of r measured whether many of
+ 
+
+ align:start position:0%
+So n subx of r measured whether many of
+the balls in x were clumped together and
+
+ align:start position:0%
+the balls in x were clumped together and
+ 
+
+ align:start position:0%
+the balls in x were clumped together and
+n subt of r measures whether many of the
+
+ align:start position:0%
+n subt of r measures whether many of the
+ 
+
+ align:start position:0%
+n subt of r measures whether many of the
+tubes of t are clumped together.
+
+ align:start position:0%
+tubes of t are clumped together.
+ 
+
+ align:start position:0%
+tubes of t are clumped together.
+Okay. So the bound will depend on that
+
+ align:start position:0%
+Okay. So the bound will depend on that
+ 
+
+ align:start position:0%
+Okay. So the bound will depend on that
+thing and it is
+
+ align:start position:0%
+thing and it is
+ 
+
+ align:start position:0%
+thing and it is
+formula is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay.
+
+ align:start position:0%
+okay.
+ 
+
+ align:start position:0%
+okay.
+n subt of little r
+
+ align:start position:0%
+n subt of little r
+ 
+
+ align:start position:0%
+n subt of little r
+um times the number of tubes
+
+ align:start position:0%
+um times the number of tubes
+ 
+
+ align:start position:0%
+um times the number of tubes
+time little r inverse time big.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so you can see that I don't
+
+ align:start position:0%
+Okay, so you can see that I don't
+ 
+
+ align:start position:0%
+Okay, so you can see that I don't
+remember this formula that well. Um but
+
+ align:start position:0%
+remember this formula that well. Um but
+ 
+
+ align:start position:0%
+remember this formula that well. Um but
+one thing to notice about it is that as
+
+ align:start position:0%
+one thing to notice about it is that as
+ 
+
+ align:start position:0%
+one thing to notice about it is that as
+as this number gets bigger then our
+
+ align:start position:0%
+as this number gets bigger then our
+ 
+
+ align:start position:0%
+as this number gets bigger then our
+bound for this gets bigger.
+
+ align:start position:0%
+bound for this gets bigger.
+ 
+
+ align:start position:0%
+bound for this gets bigger.
+Um I also claim that this tracks with
+
+ align:start position:0%
+Um I also claim that this tracks with
+ 
+
+ align:start position:0%
+Um I also claim that this tracks with
+the finite field case. Um so if you plug
+
+ align:start position:0%
+the finite field case. Um so if you plug
+ 
+
+ align:start position:0%
+the finite field case. Um so if you plug
+in little r equals 1 that's the highest
+
+ align:start position:0%
+in little r equals 1 that's the highest
+ 
+
+ align:start position:0%
+in little r equals 1 that's the highest
+frequency part. Um n subt of one is is
+
+ align:start position:0%
+frequency part. Um n subt of one is is
+ 
+
+ align:start position:0%
+frequency part. Um n subt of one is is
+going to be just one. If if the tubes
+
+ align:start position:0%
+going to be just one. If if the tubes
+ 
+
+ align:start position:0%
+going to be just one. If if the tubes
+are disjoint then then or the tubes are
+
+ align:start position:0%
+are disjoint then then or the tubes are
+ 
+
+ align:start position:0%
+are disjoint then then or the tubes are
+distinct then anyway um uh so then if
+
+ align:start position:0%
+distinct then anyway um uh so then if
+ 
+
+ align:start position:0%
+distinct then anyway um uh so then if
+you plug in little r equals 1 this
+
+ align:start position:0%
+you plug in little r equals 1 this
+ 
+
+ align:start position:0%
+you plug in little r equals 1 this
+number will match with the high
+
+ align:start position:0%
+number will match with the high
+ 
+
+ align:start position:0%
+number will match with the high
+frequency case. And if you plug in
+
+ align:start position:0%
+frequency case. And if you plug in
+ 
+
+ align:start position:0%
+frequency case. And if you plug in
+little r equals big r, then this will
+
+ align:start position:0%
+little r equals big r, then this will
+ 
+
+ align:start position:0%
+little r equals big r, then this will
+match with the zero frequency case. But
+
+ align:start position:0%
+match with the zero frequency case. But
+ 
+
+ align:start position:0%
+match with the zero frequency case. But
+now we also have all this in between
+
+ align:start position:0%
+now we also have all this in between
+ 
+
+ align:start position:0%
+now we also have all this in between
+stuff.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+any questions or comments about this
+
+ align:start position:0%
+any questions or comments about this
+ 
+
+ align:start position:0%
+any questions or comments about this
+statement?
+
+ align:start position:0%
+statement?
+ 
+
+ align:start position:0%
+statement?
+So I'm going to do a proof sketch.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof sketch main are details on
+
+ align:start position:0%
+proof sketch main are details on
+ 
+
+ align:start position:0%
+proof sketch main are details on
+homework two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How's homework one going?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you're interested, there are office
+
+ align:start position:0%
+If you're interested, there are office
+ 
+
+ align:start position:0%
+If you're interested, there are office
+hours after class today and after class
+
+ align:start position:0%
+hours after class today and after class
+ 
+
+ align:start position:0%
+hours after class today and after class
+on Thursday.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. There's a fora analysis proof and
+
+ align:start position:0%
+okay. There's a fora analysis proof and
+ 
+
+ align:start position:0%
+okay. There's a fora analysis proof and
+an important character is well we're
+
+ align:start position:0%
+an important character is well we're
+ 
+
+ align:start position:0%
+an important character is well we're
+take the fora transform of each of these
+
+ align:start position:0%
+take the fora transform of each of these
+ 
+
+ align:start position:0%
+take the fora transform of each of these
+ct hat and the support of ct hat is
+
+ align:start position:0%
+ct hat and the support of ct hat is
+ 
+
+ align:start position:0%
+ct hat and the support of ct hat is
+going to be contained in t star where t
+
+ align:start position:0%
+going to be contained in t star where t
+ 
+
+ align:start position:0%
+going to be contained in t star where t
+star is defined as follows
+
+ align:start position:0%
+star is defined as follows
+ 
+
+ align:start position:0%
+star is defined as follows
+it's the set of c and r2
+
+ align:start position:0%
+it's the set of c and r2
+ 
+
+ align:start position:0%
+it's the set of c and r2
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+the dotproduct x1 - x2 c is at most has
+
+ align:start position:0%
+the dotproduct x1 - x2 c is at most has
+ 
+
+ align:start position:0%
+the dotproduct x1 - x2 c is at most has
+norm at most one for any x1 and x2 in t.
+
+ align:start position:0%
+norm at most one for any x1 and x2 in t.
+ 
+
+ align:start position:0%
+norm at most one for any x1 and x2 in t.
+Um here's a picture.
+
+ align:start position:0%
+Um here's a picture.
+ 
+
+ align:start position:0%
+Um here's a picture.
+So in x space here is our tube t and I
+
+ align:start position:0%
+So in x space here is our tube t and I
+ 
+
+ align:start position:0%
+So in x space here is our tube t and I
+take a couple of points in it x1 and x2
+
+ align:start position:0%
+take a couple of points in it x1 and x2
+ 
+
+ align:start position:0%
+take a couple of points in it x1 and x2
+and so so our c is going to have a small
+
+ align:start position:0%
+and so so our c is going to have a small
+ 
+
+ align:start position:0%
+and so so our c is going to have a small
+dotproduct with any vector like that.
+
+ align:start position:0%
+dotproduct with any vector like that.
+ 
+
+ align:start position:0%
+dotproduct with any vector like that.
+And so um okay the dimensions of this t
+
+ align:start position:0%
+And so um okay the dimensions of this t
+ 
+
+ align:start position:0%
+And so um okay the dimensions of this t
+are this is one and this is r.
+
+ align:start position:0%
+are this is one and this is r.
+ 
+
+ align:start position:0%
+are this is one and this is r.
+Okay. Now in csp space um t star is
+
+ align:start position:0%
+Okay. Now in csp space um t star is
+ 
+
+ align:start position:0%
+Okay. Now in csp space um t star is
+going to be sort of perpendicular to t.
+
+ align:start position:0%
+going to be sort of perpendicular to t.
+ 
+
+ align:start position:0%
+going to be sort of perpendicular to t.
+There's t star and it has length one and
+
+ align:start position:0%
+There's t star and it has length one and
+ 
+
+ align:start position:0%
+There's t star and it has length one and
+width like 1 / r.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So geometrically the idea is that if I
+
+ align:start position:0%
+So geometrically the idea is that if I
+ 
+
+ align:start position:0%
+So geometrically the idea is that if I
+take my vector here and my vector there,
+
+ align:start position:0%
+take my vector here and my vector there,
+ 
+
+ align:start position:0%
+take my vector here and my vector there,
+the long component of this one has size
+
+ align:start position:0%
+the long component of this one has size
+ 
+
+ align:start position:0%
+the long component of this one has size
+R and it gets paired with the short
+
+ align:start position:0%
+R and it gets paired with the short
+ 
+
+ align:start position:0%
+R and it gets paired with the short
+component of that one which has size one
+
+ align:start position:0%
+component of that one which has size one
+ 
+
+ align:start position:0%
+component of that one which has size one
+over R which gives me around one and the
+
+ align:start position:0%
+over R which gives me around one and the
+ 
+
+ align:start position:0%
+over R which gives me around one and the
+two short component the short component
+
+ align:start position:0%
+two short component the short component
+ 
+
+ align:start position:0%
+two short component the short component
+here has size one which gets paired with
+
+ align:start position:0%
+here has size one which gets paired with
+ 
+
+ align:start position:0%
+here has size one which gets paired with
+the long component here which has size
+
+ align:start position:0%
+the long component here which has size
+ 
+
+ align:start position:0%
+the long component here which has size
+one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um and this is analogous to the
+
+ align:start position:0%
+Okay. Um and this is analogous to the
+ 
+
+ align:start position:0%
+Okay. Um and this is analogous to the
+lema we had in the finite field case
+
+ align:start position:0%
+lema we had in the finite field case
+ 
+
+ align:start position:0%
+lema we had in the finite field case
+that that the characteristic function of
+
+ align:start position:0%
+that that the characteristic function of
+ 
+
+ align:start position:0%
+that that the characteristic function of
+a line hat was supported in the line per
+
+ align:start position:0%
+a line hat was supported in the line per
+ 
+
+ align:start position:0%
+a line hat was supported in the line per
+which is like star.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the first important ingredient
+
+ align:start position:0%
+so that's the first important ingredient
+ 
+
+ align:start position:0%
+so that's the first important ingredient
+where the 4A transforms live and I guess
+
+ align:start position:0%
+where the 4A transforms live and I guess
+ 
+
+ align:start position:0%
+where the 4A transforms live and I guess
+you're doing the homework now where
+
+ align:start position:0%
+you're doing the homework now where
+ 
+
+ align:start position:0%
+you're doing the homework now where
+you're checking what what line hat looks
+
+ align:start position:0%
+you're checking what what line hat looks
+ 
+
+ align:start position:0%
+you're checking what what line hat looks
+like and then in the next homework
+
+ align:start position:0%
+like and then in the next homework
+ 
+
+ align:start position:0%
+like and then in the next homework
+you'll check what ct hat looks like and
+
+ align:start position:0%
+you'll check what ct hat looks like and
+ 
+
+ align:start position:0%
+you'll check what ct hat looks like and
+you'll see it supported like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now I'll tell you who F subr
+
+ align:start position:0%
+Okay. So now I'll tell you who F subr
+ 
+
+ align:start position:0%
+Okay. So now I'll tell you who F subr
+is. Um
+
+ align:start position:0%
+is. Um
+ 
+
+ align:start position:0%
+is. Um
+so let's next do so the f subr comes
+
+ align:start position:0%
+so let's next do so the f subr comes
+ 
+
+ align:start position:0%
+so let's next do so the f subr comes
+from from littlewood paley theory where
+
+ align:start position:0%
+from from littlewood paley theory where
+ 
+
+ align:start position:0%
+from from littlewood paley theory where
+you can take any function and you can
+
+ align:start position:0%
+you can take any function and you can
+ 
+
+ align:start position:0%
+you can take any function and you can
+break its frequencies into diatic pieces
+
+ align:start position:0%
+break its frequencies into diatic pieces
+ 
+
+ align:start position:0%
+break its frequencies into diatic pieces
+the little wood pale pieces. That's what
+
+ align:start position:0%
+the little wood pale pieces. That's what
+ 
+
+ align:start position:0%
+the little wood pale pieces. That's what
+we're doing here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so little wood pale decomposition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I'm going to write one as a sum on
+
+ align:start position:0%
+So, I'm going to write one as a sum on
+ 
+
+ align:start position:0%
+So, I'm going to write one as a sum on
+my diatic little rs
+
+ align:start position:0%
+my diatic little rs
+ 
+
+ align:start position:0%
+my diatic little rs
+of ad r of c. So this is a a partition
+
+ align:start position:0%
+of ad r of c. So this is a a partition
+ 
+
+ align:start position:0%
+of ad r of c. So this is a a partition
+of unity on in 4A space. It's a
+
+ align:start position:0%
+of unity on in 4A space. It's a
+ 
+
+ align:start position:0%
+of unity on in 4A space. It's a
+partition of unity. So these are all
+
+ align:start position:0%
+partition of unity. So these are all
+ 
+
+ align:start position:0%
+partition of unity. So these are all
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+and um the support
+
+ align:start position:0%
+and um the support
+ 
+
+ align:start position:0%
+and um the support
+of A to R is contained in in an annulus
+
+ align:start position:0%
+of A to R is contained in in an annulus
+ 
+
+ align:start position:0%
+of A to R is contained in in an annulus
+where the norm of C is at most 1 / R and
+
+ align:start position:0%
+where the norm of C is at most 1 / R and
+ 
+
+ align:start position:0%
+where the norm of C is at most 1 / R and
+at least 1 / 10R.
+
+ align:start position:0%
+at least 1 / 10R.
+ 
+
+ align:start position:0%
+at least 1 / 10R.
+And that's true for R strictly between 1
+
+ align:start position:0%
+And that's true for R strictly between 1
+ 
+
+ align:start position:0%
+And that's true for R strictly between 1
+and R. And at the end points we need to
+
+ align:start position:0%
+and R. And at the end points we need to
+ 
+
+ align:start position:0%
+and R. And at the end points we need to
+have not just an annulus but something a
+
+ align:start position:0%
+have not just an annulus but something a
+ 
+
+ align:start position:0%
+have not just an annulus but something a
+little bit bigger to cover all the
+
+ align:start position:0%
+little bit bigger to cover all the
+ 
+
+ align:start position:0%
+little bit bigger to cover all the
+frequencies. So the support
+
+ align:start position:0%
+frequencies. So the support
+ 
+
+ align:start position:0%
+frequencies. So the support
+of ADA capital R
+
+ align:start position:0%
+of ADA capital R
+ 
+
+ align:start position:0%
+of ADA capital R
+is contained in the ball of radius 1 / R
+
+ align:start position:0%
+is contained in the ball of radius 1 / R
+ 
+
+ align:start position:0%
+is contained in the ball of radius 1 / R
+and the support
+
+ align:start position:0%
+and the support
+ 
+
+ align:start position:0%
+and the support
+of ADA1
+
+ align:start position:0%
+of ADA1
+ 
+
+ align:start position:0%
+of ADA1
+is contained in the set of C where the
+
+ align:start position:0%
+is contained in the set of C where the
+ 
+
+ align:start position:0%
+is contained in the set of C where the
+norm of C is bigger than 110.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Oh, I guess one maybe I
+
+ align:start position:0%
+All right. Oh, I guess one maybe I
+ 
+
+ align:start position:0%
+All right. Oh, I guess one maybe I
+should mention one one thing that we see
+
+ align:start position:0%
+should mention one one thing that we see
+ 
+
+ align:start position:0%
+should mention one one thing that we see
+from this
+
+ align:start position:0%
+from this
+ 
+
+ align:start position:0%
+from this
+is that the support of f hat is
+
+ align:start position:0%
+is that the support of f hat is
+ 
+
+ align:start position:0%
+is that the support of f hat is
+contained in the unit ball because every
+
+ align:start position:0%
+contained in the unit ball because every
+ 
+
+ align:start position:0%
+contained in the unit ball because every
+t star is in is in the unit ball.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now I can say who f_sub_r is.
+
+ align:start position:0%
+Okay. So now I can say who f_sub_r is.
+ 
+
+ align:start position:0%
+Okay. So now I can say who f_sub_r is.
+So f is just taking f and taking
+
+ align:start position:0%
+So f is just taking f and taking
+ 
+
+ align:start position:0%
+So f is just taking f and taking
+multiplying on the frequency side by 8
+
+ align:start position:0%
+multiplying on the frequency side by 8
+ 
+
+ align:start position:0%
+multiplying on the frequency side by 8
+r. So I take fhat I multiply it by a r
+
+ align:start position:0%
+r. So I take fhat I multiply it by a r
+ 
+
+ align:start position:0%
+r. So I take fhat I multiply it by a r
+and I take the 4 a transform back.
+
+ align:start position:0%
+and I take the 4 a transform back.
+ 
+
+ align:start position:0%
+and I take the 4 a transform back.
+So this is also equal to f involved with
+
+ align:start position:0%
+So this is also equal to f involved with
+ 
+
+ align:start position:0%
+So this is also equal to f involved with
+a to r inverse 4 a transform.
+
+ align:start position:0%
+a to r inverse 4 a transform.
+ 
+
+ align:start position:0%
+a to r inverse 4 a transform.
+Okay. And because this is a partition of
+
+ align:start position:0%
+Okay. And because this is a partition of
+ 
+
+ align:start position:0%
+Okay. And because this is a partition of
+unity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that tells me that f is indeed the sum
+
+ align:start position:0%
+that tells me that f is indeed the sum
+ 
+
+ align:start position:0%
+that tells me that f is indeed the sum
+over r of fr.
+
+ align:start position:0%
+over r of fr.
+ 
+
+ align:start position:0%
+over r of fr.
+So that so we can check off our first
+
+ align:start position:0%
+So that so we can check off our first
+ 
+
+ align:start position:0%
+So that so we can check off our first
+conclusion.
+
+ align:start position:0%
+conclusion.
+ 
+
+ align:start position:0%
+conclusion.
+Um and from this formula this here is
+
+ align:start position:0%
+Um and from this formula this here is
+ 
+
+ align:start position:0%
+Um and from this formula this here is
+the for transform of FR hat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a R * Fhat and that tells us that the
+
+ align:start position:0%
+is a R * Fhat and that tells us that the
+ 
+
+ align:start position:0%
+is a R * Fhat and that tells us that the
+support of FR hat is contained in the
+
+ align:start position:0%
+support of FR hat is contained in the
+ 
+
+ align:start position:0%
+support of FR hat is contained in the
+ball of radius 1 / R. So we can check
+
+ align:start position:0%
+ball of radius 1 / R. So we can check
+ 
+
+ align:start position:0%
+ball of radius 1 / R. So we can check
+off that part of the conclusion.
+
+ align:start position:0%
+off that part of the conclusion.
+ 
+
+ align:start position:0%
+off that part of the conclusion.
+And then the difficult and interesting
+
+ align:start position:0%
+And then the difficult and interesting
+ 
+
+ align:start position:0%
+And then the difficult and interesting
+part will be to figure out the L2 norm
+
+ align:start position:0%
+part will be to figure out the L2 norm
+ 
+
+ align:start position:0%
+part will be to figure out the L2 norm
+of each of these pieces FR.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um now this operation of
+
+ align:start position:0%
+Okay. Um now this operation of
+ 
+
+ align:start position:0%
+Okay. Um now this operation of
+localizing frequencies to to an annulus
+
+ align:start position:0%
+localizing frequencies to to an annulus
+ 
+
+ align:start position:0%
+localizing frequencies to to an annulus
+around 1 / R you can do it with any
+
+ align:start position:0%
+around 1 / R you can do it with any
+ 
+
+ align:start position:0%
+around 1 / R you can do it with any
+function not just with f. So you can
+
+ align:start position:0%
+function not just with f. So you can
+ 
+
+ align:start position:0%
+function not just with f. So you can
+also do it with each of the ct one at a
+
+ align:start position:0%
+also do it with each of the ct one at a
+ 
+
+ align:start position:0%
+also do it with each of the ct one at a
+time. So ct comma r would be I take ct
+
+ align:start position:0%
+time. So ct comma r would be I take ct
+ 
+
+ align:start position:0%
+time. So ct comma r would be I take ct
+hat I multiply it by a to r I take the
+
+ align:start position:0%
+hat I multiply it by a to r I take the
+ 
+
+ align:start position:0%
+hat I multiply it by a to r I take the
+for a transform back and so f is the sum
+
+ align:start position:0%
+for a transform back and so f is the sum
+ 
+
+ align:start position:0%
+for a transform back and so f is the sum
+over all the t in my set of tubes of ct.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So the next thing I'd like to do is to
+
+ align:start position:0%
+So the next thing I'd like to do is to
+ 
+
+ align:start position:0%
+So the next thing I'd like to do is to
+visualize together this function a to r
+
+ align:start position:0%
+visualize together this function a to r
+ 
+
+ align:start position:0%
+visualize together this function a to r
+check and this function ctr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do a visual
+
+ align:start position:0%
+do a visual
+ 
+
+ align:start position:0%
+do a visual
+of ad r check um and ctr.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so the function A to R itself A to
+
+ align:start position:0%
+Okay, so the function A to R itself A to
+ 
+
+ align:start position:0%
+Okay, so the function A to R itself A to
+R of C that's around one on the annulus
+
+ align:start position:0%
+R of C that's around one on the annulus
+ 
+
+ align:start position:0%
+R of C that's around one on the annulus
+of size 1 / little R.
+
+ align:start position:0%
+of size 1 / little R.
+ 
+
+ align:start position:0%
+of size 1 / little R.
+So when I take its inverse for a
+
+ align:start position:0%
+So when I take its inverse for a
+ 
+
+ align:start position:0%
+So when I take its inverse for a
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+um a to r check of x
+
+ align:start position:0%
+um a to r check of x
+ 
+
+ align:start position:0%
+um a to r check of x
+will be around
+
+ align:start position:0%
+will be around
+ 
+
+ align:start position:0%
+will be around
+it'll be around um 1 / r 2
+
+ align:start position:0%
+it'll be around um 1 / r 2
+ 
+
+ align:start position:0%
+it'll be around um 1 / r 2
+of most of x less than r.
+
+ align:start position:0%
+of most of x less than r.
+ 
+
+ align:start position:0%
+of most of x less than r.
+So the you know the biggest this could
+
+ align:start position:0%
+So the you know the biggest this could
+ 
+
+ align:start position:0%
+So the you know the biggest this could
+possibly be is integrating this would be
+
+ align:start position:0%
+possibly be is integrating this would be
+ 
+
+ align:start position:0%
+possibly be is integrating this would be
+the area of this annulus which is 1 /
+
+ align:start position:0%
+the area of this annulus which is 1 /
+ 
+
+ align:start position:0%
+the area of this annulus which is 1 /
+r^2.
+
+ align:start position:0%
+r^2.
+ 
+
+ align:start position:0%
+r^2.
+Um and then because this is smooth once
+
+ align:start position:0%
+Um and then because this is smooth once
+ 
+
+ align:start position:0%
+Um and then because this is smooth once
+I look at x's that are significantly
+
+ align:start position:0%
+I look at x's that are significantly
+ 
+
+ align:start position:0%
+I look at x's that are significantly
+bigger than r I start to get a lot of
+
+ align:start position:0%
+bigger than r I start to get a lot of
+ 
+
+ align:start position:0%
+bigger than r I start to get a lot of
+cancellation in the integral and let me
+
+ align:start position:0%
+cancellation in the integral and let me
+ 
+
+ align:start position:0%
+cancellation in the integral and let me
+write down the formula for this. So a to
+
+ align:start position:0%
+write down the formula for this. So a to
+ 
+
+ align:start position:0%
+write down the formula for this. So a to
+r check of x is the integral e to the ix
+
+ align:start position:0%
+r check of x is the integral e to the ix
+ 
+
+ align:start position:0%
+r check of x is the integral e to the ix
+a r of c dx c.
+
+ align:start position:0%
+a r of c dx c.
+ 
+
+ align:start position:0%
+a r of c dx c.
+So if x is smaller than r, there's no
+
+ align:start position:0%
+So if x is smaller than r, there's no
+ 
+
+ align:start position:0%
+So if x is smaller than r, there's no
+significant cancellation in this
+
+ align:start position:0%
+significant cancellation in this
+ 
+
+ align:start position:0%
+significant cancellation in this
+integral because the c is around 1 / r.
+
+ align:start position:0%
+integral because the c is around 1 / r.
+ 
+
+ align:start position:0%
+integral because the c is around 1 / r.
+Um but then when x is bigger than r,
+
+ align:start position:0%
+Um but then when x is bigger than r,
+ 
+
+ align:start position:0%
+Um but then when x is bigger than r,
+there starts to be cancellation in this
+
+ align:start position:0%
+there starts to be cancellation in this
+ 
+
+ align:start position:0%
+there starts to be cancellation in this
+integral. And because this is smooth,
+
+ align:start position:0%
+integral. And because this is smooth,
+ 
+
+ align:start position:0%
+integral. And because this is smooth,
+the cancellation is quite dramatic. So
+
+ align:start position:0%
+the cancellation is quite dramatic. So
+ 
+
+ align:start position:0%
+the cancellation is quite dramatic. So
+this is rapidly decaying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's what the size of this
+
+ align:start position:0%
+Okay, so that's what the size of this
+ 
+
+ align:start position:0%
+Okay, so that's what the size of this
+function is like. Um but but also um
+
+ align:start position:0%
+function is like. Um but but also um
+ 
+
+ align:start position:0%
+function is like. Um but but also um
+there's some cancellation in it. So if
+
+ align:start position:0%
+there's some cancellation in it. So if
+ 
+
+ align:start position:0%
+there's some cancellation in it. So if
+you integrate this function
+
+ align:start position:0%
+you integrate this function
+ 
+
+ align:start position:0%
+you integrate this function
+well if you integrate that you get a to
+
+ align:start position:0%
+well if you integrate that you get a to
+ 
+
+ align:start position:0%
+well if you integrate that you get a to
+r of zero which is zero because a to r
+
+ align:start position:0%
+r of zero which is zero because a to r
+ 
+
+ align:start position:0%
+r of zero which is zero because a to r
+is supported on an annulus and not a
+
+ align:start position:0%
+is supported on an annulus and not a
+ 
+
+ align:start position:0%
+is supported on an annulus and not a
+ball. So this function has some
+
+ align:start position:0%
+ball. So this function has some
+ 
+
+ align:start position:0%
+ball. So this function has some
+cancellation in it. It averages to zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so
+
+ align:start position:0%
+Um so
+ 
+
+ align:start position:0%
+Um so
+I I can graph it. Um C sub R check is
+
+ align:start position:0%
+I I can graph it. Um C sub R check is
+ 
+
+ align:start position:0%
+I I can graph it. Um C sub R check is
+radial.
+
+ align:start position:0%
+radial.
+ 
+
+ align:start position:0%
+radial.
+So here is the radius norm of X and
+
+ align:start position:0%
+So here is the radius norm of X and
+ 
+
+ align:start position:0%
+So here is the radius norm of X and
+here's ADA R check of X and it would
+
+ align:start position:0%
+here's ADA R check of X and it would
+ 
+
+ align:start position:0%
+here's ADA R check of X and it would
+look something like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we have to do this carefully but the
+
+ align:start position:0%
+And we have to do this carefully but the
+ 
+
+ align:start position:0%
+And we have to do this carefully but the
+negative part is going to balance the
+
+ align:start position:0%
+negative part is going to balance the
+ 
+
+ align:start position:0%
+negative part is going to balance the
+positive part to integrate to zero. So
+
+ align:start position:0%
+positive part to integrate to zero. So
+ 
+
+ align:start position:0%
+positive part to integrate to zero. So
+imagine rotating this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, and this scale here is is that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. Now, these different exponents
+
+ align:start position:0%
+okay. Now, these different exponents
+ 
+
+ align:start position:0%
+okay. Now, these different exponents
+here are
+
+ align:start position:0%
+here are
+ 
+
+ align:start position:0%
+here are
+work out nicely.
+
+ align:start position:0%
+work out nicely.
+ 
+
+ align:start position:0%
+work out nicely.
+Um and and a a different way a way to
+
+ align:start position:0%
+Um and and a a different way a way to
+ 
+
+ align:start position:0%
+Um and and a a different way a way to
+describe it is that if I take the
+
+ align:start position:0%
+describe it is that if I take the
+ 
+
+ align:start position:0%
+describe it is that if I take the
+integral of the norm of a total r check
+
+ align:start position:0%
+integral of the norm of a total r check
+ 
+
+ align:start position:0%
+integral of the norm of a total r check
+of x dx
+
+ align:start position:0%
+of x dx
+ 
+
+ align:start position:0%
+of x dx
+um well it's around 1 / r^2 times the
+
+ align:start position:0%
+um well it's around 1 / r^2 times the
+ 
+
+ align:start position:0%
+um well it's around 1 / r^2 times the
+area of the ball of radius r which is 1.
+
+ align:start position:0%
+area of the ball of radius r which is 1.
+ 
+
+ align:start position:0%
+area of the ball of radius r which is 1.
+That integral is around 1.
+
+ align:start position:0%
+That integral is around 1.
+ 
+
+ align:start position:0%
+That integral is around 1.
+So um so if I were to take some function
+
+ align:start position:0%
+So um so if I were to take some function
+ 
+
+ align:start position:0%
+So um so if I were to take some function
+and convolve it with the absolute value
+
+ align:start position:0%
+and convolve it with the absolute value
+ 
+
+ align:start position:0%
+and convolve it with the absolute value
+of a total r check of x that would
+
+ align:start position:0%
+of a total r check of x that would
+ 
+
+ align:start position:0%
+of a total r check of x that would
+roughly be the average value of f
+
+ align:start position:0%
+roughly be the average value of f
+ 
+
+ align:start position:0%
+roughly be the average value of f
+on the ball around x of radius r the
+
+ align:start position:0%
+on the ball around x of radius r the
+ 
+
+ align:start position:0%
+on the ball around x of radius r the
+sort of weighted average. It's not
+
+ align:start position:0%
+sort of weighted average. It's not
+ 
+
+ align:start position:0%
+sort of weighted average. It's not
+exactly the standard average but that's
+
+ align:start position:0%
+exactly the standard average but that's
+ 
+
+ align:start position:0%
+exactly the standard average but that's
+roughly what what it is.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So is it the case that like
+
+ align:start position:0%
+So is it the case that like
+ 
+
+ align:start position:0%
+So is it the case that like
+um convoluting with a function on the
+
+ align:start position:0%
+um convoluting with a function on the
+ 
+
+ align:start position:0%
+um convoluting with a function on the
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+like if data r is like on the end
+
+ align:start position:0%
+like if data r is like on the end
+ 
+
+ align:start position:0%
+like if data r is like on the end
+basically behaves the same as if it were
+
+ align:start position:0%
+basically behaves the same as if it were
+ 
+
+ align:start position:0%
+basically behaves the same as if it were
+on the fall radius.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> So the question is how would we compare
+
+ align:start position:0%
+>> So the question is how would we compare
+ 
+
+ align:start position:0%
+>> So the question is how would we compare
+an ad r that's supported on an annulus
+
+ align:start position:0%
+an ad r that's supported on an annulus
+ 
+
+ align:start position:0%
+an ad r that's supported on an annulus
+with a similar function that was
+
+ align:start position:0%
+with a similar function that was
+ 
+
+ align:start position:0%
+with a similar function that was
+supported on the whole ball. Um yeah,
+
+ align:start position:0%
+supported on the whole ball. Um yeah,
+ 
+
+ align:start position:0%
+supported on the whole ball. Um yeah,
+it's mostly similar because of the
+
+ align:start position:0%
+it's mostly similar because of the
+ 
+
+ align:start position:0%
+it's mostly similar because of the
+annulus. There's more cancellation. So
+
+ align:start position:0%
+annulus. There's more cancellation. So
+ 
+
+ align:start position:0%
+annulus. There's more cancellation. So
+if we did it on the whole ball, we
+
+ align:start position:0%
+if we did it on the whole ball, we
+ 
+
+ align:start position:0%
+if we did it on the whole ball, we
+wouldn't have this integral property.
+
+ align:start position:0%
+wouldn't have this integral property.
+ 
+
+ align:start position:0%
+wouldn't have this integral property.
+>> Okay.
+
+ align:start position:0%
+>> Okay.
+ 
+
+ align:start position:0%
+>> Okay.
+>> And the ne there may or may not be a
+
+ align:start position:0%
+>> And the ne there may or may not be a
+ 
+
+ align:start position:0%
+>> And the ne there may or may not be a
+little negative part if we did it on the
+
+ align:start position:0%
+little negative part if we did it on the
+ 
+
+ align:start position:0%
+little negative part if we did it on the
+whole ball, but the negative part would
+
+ align:start position:0%
+whole ball, but the negative part would
+ 
+
+ align:start position:0%
+whole ball, but the negative part would
+probably would be dominated by the
+
+ align:start position:0%
+probably would be dominated by the
+ 
+
+ align:start position:0%
+probably would be dominated by the
+positive part.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's what the function ad
+
+ align:start position:0%
+Okay, so that's what the function ad
+ 
+
+ align:start position:0%
+Okay, so that's what the function ad
+looks like.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now that we understand that we can
+
+ align:start position:0%
+And now that we understand that we can
+ 
+
+ align:start position:0%
+And now that we understand that we can
+understand the function CTR
+
+ align:start position:0%
+understand the function CTR
+ 
+
+ align:start position:0%
+understand the function CTR
+because CTR is equal to CT convolved
+
+ align:start position:0%
+because CTR is equal to CT convolved
+ 
+
+ align:start position:0%
+because CTR is equal to CT convolved
+with ADA R check.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So the norm of ctr of x is around
+
+ align:start position:0%
+Okay. So the norm of ctr of x is around
+ 
+
+ align:start position:0%
+Okay. So the norm of ctr of x is around
+r inverse times the characteristic
+
+ align:start position:0%
+r inverse times the characteristic
+ 
+
+ align:start position:0%
+r inverse times the characteristic
+function of a thickened tube.
+
+ align:start position:0%
+function of a thickened tube.
+ 
+
+ align:start position:0%
+function of a thickened tube.
+So if I take the r neighborhood of t.
+
+ align:start position:0%
+So if I take the r neighborhood of t.
+ 
+
+ align:start position:0%
+So if I take the r neighborhood of t.
+So if this is uh t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I could take a fat neighborhood of that
+
+ align:start position:0%
+I could take a fat neighborhood of that
+ 
+
+ align:start position:0%
+I could take a fat neighborhood of that
+would look sort of like this.
+
+ align:start position:0%
+would look sort of like this.
+ 
+
+ align:start position:0%
+would look sort of like this.
+So that's the R neighborhood of T. Um so
+
+ align:start position:0%
+So that's the R neighborhood of T. Um so
+ 
+
+ align:start position:0%
+So that's the R neighborhood of T. Um so
+PT itself is basically supported on T
+
+ align:start position:0%
+PT itself is basically supported on T
+ 
+
+ align:start position:0%
+PT itself is basically supported on T
+although it's smoothed out a little bit.
+
+ align:start position:0%
+although it's smoothed out a little bit.
+ 
+
+ align:start position:0%
+although it's smoothed out a little bit.
+And then when I take the low frequency
+
+ align:start position:0%
+And then when I take the low frequency
+ 
+
+ align:start position:0%
+And then when I take the low frequency
+part the R the one over R frequency part
+
+ align:start position:0%
+part the R the one over R frequency part
+ 
+
+ align:start position:0%
+part the R the one over R frequency part
+then it gets spread out and it gets
+
+ align:start position:0%
+then it gets spread out and it gets
+ 
+
+ align:start position:0%
+then it gets spread out and it gets
+smaller.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And it also has some cancellation
+
+ align:start position:0%
+Okay. And it also has some cancellation
+ 
+
+ align:start position:0%
+Okay. And it also has some cancellation
+in it. So if the the graph of this
+
+ align:start position:0%
+in it. So if the the graph of this
+ 
+
+ align:start position:0%
+in it. So if the the graph of this
+function mostly depends on the
+
+ align:start position:0%
+function mostly depends on the
+ 
+
+ align:start position:0%
+function mostly depends on the
+transverse direction and then it looks a
+
+ align:start position:0%
+transverse direction and then it looks a
+ 
+
+ align:start position:0%
+transverse direction and then it looks a
+lot like this. So this would be the
+
+ align:start position:0%
+lot like this. So this would be the
+ 
+
+ align:start position:0%
+lot like this. So this would be the
+transverse direction and this would be
+
+ align:start position:0%
+transverse direction and this would be
+ 
+
+ align:start position:0%
+transverse direction and this would be
+the height.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here I'll put that in the picture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this transverse direction maybe I'll
+
+ align:start position:0%
+So this transverse direction maybe I'll
+ 
+
+ align:start position:0%
+So this transverse direction maybe I'll
+call y.
+
+ align:start position:0%
+call y.
+ 
+
+ align:start position:0%
+call y.
+And then we could make a graph where
+
+ align:start position:0%
+And then we could make a graph where
+ 
+
+ align:start position:0%
+And then we could make a graph where
+here we put y and here we put ct
+
+ align:start position:0%
+here we put y and here we put ct
+ 
+
+ align:start position:0%
+here we put y and here we put ct
+r of y and we would see the same thing
+
+ align:start position:0%
+r of y and we would see the same thing
+ 
+
+ align:start position:0%
+r of y and we would see the same thing
+uh positive negative.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And this length scale here is r.
+
+ align:start position:0%
+Okay. And this length scale here is r.
+ 
+
+ align:start position:0%
+Okay. And this length scale here is r.
+the negative part would cancel the
+
+ align:start position:0%
+the negative part would cancel the
+ 
+
+ align:start position:0%
+the negative part would cancel the
+positive part because if you convolve
+
+ align:start position:0%
+positive part because if you convolve
+ 
+
+ align:start position:0%
+positive part because if you convolve
+something who integrates to zero with
+
+ align:start position:0%
+something who integrates to zero with
+ 
+
+ align:start position:0%
+something who integrates to zero with
+something else then the the whole thing
+
+ align:start position:0%
+something else then the the whole thing
+ 
+
+ align:start position:0%
+something else then the the whole thing
+will integrate to zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's what what these
+
+ align:start position:0%
+Okay, so that's what what these
+ 
+
+ align:start position:0%
+Okay, so that's what what these
+functions look like.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So before I erase this maybe I'll say
+
+ align:start position:0%
+So before I erase this maybe I'll say
+ 
+
+ align:start position:0%
+So before I erase this maybe I'll say
+sorry we mentioned earlier that if we
+
+ align:start position:0%
+sorry we mentioned earlier that if we
+ 
+
+ align:start position:0%
+sorry we mentioned earlier that if we
+have a smooth function supported on this
+
+ align:start position:0%
+have a smooth function supported on this
+ 
+
+ align:start position:0%
+have a smooth function supported on this
+tube we take its 4A transform it's
+
+ align:start position:0%
+tube we take its 4A transform it's
+ 
+
+ align:start position:0%
+tube we take its 4A transform it's
+essentially supported on this dual tube.
+
+ align:start position:0%
+essentially supported on this dual tube.
+ 
+
+ align:start position:0%
+essentially supported on this dual tube.
+That proof is a slightly fancier version
+
+ align:start position:0%
+That proof is a slightly fancier version
+ 
+
+ align:start position:0%
+That proof is a slightly fancier version
+of what we were just talking about. So
+
+ align:start position:0%
+of what we were just talking about. So
+ 
+
+ align:start position:0%
+of what we were just talking about. So
+we were just saying that if you have a
+
+ align:start position:0%
+we were just saying that if you have a
+ 
+
+ align:start position:0%
+we were just saying that if you have a
+smooth function on a certain annulus or
+
+ align:start position:0%
+smooth function on a certain annulus or
+ 
+
+ align:start position:0%
+smooth function on a certain annulus or
+a certain ball then its fora transform
+
+ align:start position:0%
+a certain ball then its fora transform
+ 
+
+ align:start position:0%
+a certain ball then its fora transform
+is essentially supported on a dual ball
+
+ align:start position:0%
+is essentially supported on a dual ball
+ 
+
+ align:start position:0%
+is essentially supported on a dual ball
+and then it's rapidly decaying outside.
+
+ align:start position:0%
+and then it's rapidly decaying outside.
+ 
+
+ align:start position:0%
+and then it's rapidly decaying outside.
+So the this first statement is exactly
+
+ align:start position:0%
+So the this first statement is exactly
+ 
+
+ align:start position:0%
+So the this first statement is exactly
+the same as that except that we have a
+
+ align:start position:0%
+the same as that except that we have a
+ 
+
+ align:start position:0%
+the same as that except that we have a
+tube instead of a ball. Having a tube
+
+ align:start position:0%
+tube instead of a ball. Having a tube
+ 
+
+ align:start position:0%
+tube instead of a ball. Having a tube
+instead of a ball makes it a little
+
+ align:start position:0%
+instead of a ball makes it a little
+ 
+
+ align:start position:0%
+instead of a ball makes it a little
+there's a little bit more writing or
+
+ align:start position:0%
+there's a little bit more writing or
+ 
+
+ align:start position:0%
+there's a little bit more writing or
+thinking involved but it's the same
+
+ align:start position:0%
+thinking involved but it's the same
+ 
+
+ align:start position:0%
+thinking involved but it's the same
+idea.
+
+ align:start position:0%
+idea.
+ 
+
+ align:start position:0%
+idea.
+uh and you'll and and it'll be the
+
+ align:start position:0%
+uh and you'll and and it'll be the
+ 
+
+ align:start position:0%
+uh and you'll and and it'll be the
+details will be on the homework.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, um in the finite field case,
+
+ align:start position:0%
+Okay. So, um in the finite field case,
+ 
+
+ align:start position:0%
+Okay. So, um in the finite field case,
+the the the the heart of the argument,
+
+ align:start position:0%
+the the the the heart of the argument,
+ 
+
+ align:start position:0%
+the the the the heart of the argument,
+the key thing called the key lema was an
+
+ align:start position:0%
+the key thing called the key lema was an
+ 
+
+ align:start position:0%
+the key thing called the key lema was an
+orthogonality lema that said that the
+
+ align:start position:0%
+orthogonality lema that said that the
+ 
+
+ align:start position:0%
+orthogonality lema that said that the
+high frequency parts of two different
+
+ align:start position:0%
+high frequency parts of two different
+ 
+
+ align:start position:0%
+high frequency parts of two different
+lines are orthogonal. and um something
+
+ align:start position:0%
+lines are orthogonal. and um something
+ 
+
+ align:start position:0%
+lines are orthogonal. and um something
+like that is true here.
+
+ align:start position:0%
+like that is true here.
+ 
+
+ align:start position:0%
+like that is true here.
+So lema on orthogonality this is like
+
+ align:start position:0%
+So lema on orthogonality this is like
+ 
+
+ align:start position:0%
+So lema on orthogonality this is like
+the key letter. So it says the following
+
+ align:start position:0%
+the key letter. So it says the following
+ 
+
+ align:start position:0%
+the key letter. So it says the following
+um uh t1 and t2 are are are tubes one by
+
+ align:start position:0%
+um uh t1 and t2 are are are tubes one by
+ 
+
+ align:start position:0%
+um uh t1 and t2 are are are tubes one by
+r tubes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um then
+
+ align:start position:0%
+um then
+ 
+
+ align:start position:0%
+um then
+the ctrs are usually orthogonal. So if I
+
+ align:start position:0%
+the ctrs are usually orthogonal. So if I
+ 
+
+ align:start position:0%
+the ctrs are usually orthogonal. So if I
+take the inner product of CT1R
+
+ align:start position:0%
+take the inner product of CT1R
+ 
+
+ align:start position:0%
+take the inner product of CT1R
+with CT2R,
+
+ align:start position:0%
+with CT2R,
+ 
+
+ align:start position:0%
+with CT2R,
+it's usually really small.
+
+ align:start position:0%
+it's usually really small.
+ 
+
+ align:start position:0%
+it's usually really small.
+R the minus a,000, something that's
+
+ align:start position:0%
+R the minus a,000, something that's
+ 
+
+ align:start position:0%
+R the minus a,000, something that's
+really small compared to everything in
+
+ align:start position:0%
+really small compared to everything in
+ 
+
+ align:start position:0%
+really small compared to everything in
+our proof. Uh unless the two tubes are
+
+ align:start position:0%
+our proof. Uh unless the two tubes are
+ 
+
+ align:start position:0%
+our proof. Uh unless the two tubes are
+quite similar. And the way we'll say
+
+ align:start position:0%
+quite similar. And the way we'll say
+ 
+
+ align:start position:0%
+quite similar. And the way we'll say
+this is there exists tilda which is like
+
+ align:start position:0%
+this is there exists tilda which is like
+ 
+
+ align:start position:0%
+this is there exists tilda which is like
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+it's basically a little r by big r two.
+
+ align:start position:0%
+it's basically a little r by big r two.
+ 
+
+ align:start position:0%
+it's basically a little r by big r two.
+I'm going to magnify it just a little
+
+ align:start position:0%
+I'm going to magnify it just a little
+ 
+
+ align:start position:0%
+I'm going to magnify it just a little
+bit.
+
+ align:start position:0%
+bit.
+ 
+
+ align:start position:0%
+bit.
+um that contains them both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tilda and inside of here and I have this
+
+ align:start position:0%
+tilda and inside of here and I have this
+ 
+
+ align:start position:0%
+tilda and inside of here and I have this
+t1 and t2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so we could have some intuition
+
+ align:start position:0%
+Okay, so we could have some intuition
+ 
+
+ align:start position:0%
+Okay, so we could have some intuition
+about this from our visualization of
+
+ align:start position:0%
+about this from our visualization of
+ 
+
+ align:start position:0%
+about this from our visualization of
+ctr.
+
+ align:start position:0%
+ctr.
+ 
+
+ align:start position:0%
+ctr.
+If I were to take T1 and T2 in in the
+
+ align:start position:0%
+If I were to take T1 and T2 in in the
+ 
+
+ align:start position:0%
+If I were to take T1 and T2 in in the
+same Tilda. So this thickened
+
+ align:start position:0%
+same Tilda. So this thickened
+ 
+
+ align:start position:0%
+same Tilda. So this thickened
+neighborhood notice is basically the
+
+ align:start position:0%
+neighborhood notice is basically the
+ 
+
+ align:start position:0%
+neighborhood notice is basically the
+same as Tilda. If I pick T1 and T2
+
+ align:start position:0%
+same as Tilda. If I pick T1 and T2
+ 
+
+ align:start position:0%
+same as Tilda. If I pick T1 and T2
+corresponding to the same Tilda, then
+
+ align:start position:0%
+corresponding to the same Tilda, then
+ 
+
+ align:start position:0%
+corresponding to the same Tilda, then
+when I when I thicken them both, I get
+
+ align:start position:0%
+when I when I thicken them both, I get
+ 
+
+ align:start position:0%
+when I when I thicken them both, I get
+basically the same rectangle.
+
+ align:start position:0%
+basically the same rectangle.
+ 
+
+ align:start position:0%
+basically the same rectangle.
+And in fact, then the functions CT1R and
+
+ align:start position:0%
+And in fact, then the functions CT1R and
+ 
+
+ align:start position:0%
+And in fact, then the functions CT1R and
+CT2R are basically the same function. So
+
+ align:start position:0%
+CT2R are basically the same function. So
+ 
+
+ align:start position:0%
+CT2R are basically the same function. So
+they are not at all orthogonal.
+
+ align:start position:0%
+they are not at all orthogonal.
+ 
+
+ align:start position:0%
+they are not at all orthogonal.
+And that's the only thing that can go
+
+ align:start position:0%
+And that's the only thing that can go
+ 
+
+ align:start position:0%
+And that's the only thing that can go
+wrong.
+
+ align:start position:0%
+wrong.
+ 
+
+ align:start position:0%
+wrong.
+Um if the thickened neighborhoods are
+
+ align:start position:0%
+Um if the thickened neighborhoods are
+ 
+
+ align:start position:0%
+Um if the thickened neighborhoods are
+disjoint they certainly are orthogonal
+
+ align:start position:0%
+disjoint they certainly are orthogonal
+ 
+
+ align:start position:0%
+disjoint they certainly are orthogonal
+and the more interesting part is that if
+
+ align:start position:0%
+and the more interesting part is that if
+ 
+
+ align:start position:0%
+and the more interesting part is that if
+the thickened neighborhoods are
+
+ align:start position:0%
+the thickened neighborhoods are
+ 
+
+ align:start position:0%
+the thickened neighborhoods are
+transverse to each other they are
+
+ align:start position:0%
+transverse to each other they are
+ 
+
+ align:start position:0%
+transverse to each other they are
+orthogonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we we can we check that by by for
+
+ align:start position:0%
+and we we can we check that by by for
+ 
+
+ align:start position:0%
+and we we can we check that by by for
+analysis.
+
+ align:start position:0%
+analysis.
+ 
+
+ align:start position:0%
+analysis.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+so proof sketch.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+if the
+
+ align:start position:0%
+if the
+ 
+
+ align:start position:0%
+if the
+if the angle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between t1 and t2 is bigger than maybe r
+
+ align:start position:0%
+between t1 and t2 is bigger than maybe r
+ 
+
+ align:start position:0%
+between t1 and t2 is bigger than maybe r
+epsilon 1 / r or little r big r.
+
+ align:start position:0%
+epsilon 1 / r or little r big r.
+ 
+
+ align:start position:0%
+epsilon 1 / r or little r big r.
+Um then
+
+ align:start position:0%
+Um then
+ 
+
+ align:start position:0%
+Um then
+the support
+
+ align:start position:0%
+the support
+ 
+
+ align:start position:0%
+the support
+of CTR hat intercepted the support T1 of
+
+ align:start position:0%
+of CTR hat intercepted the support T1 of
+ 
+
+ align:start position:0%
+of CTR hat intercepted the support T1 of
+CT2R
+
+ align:start position:0%
+CT2R
+ 
+
+ align:start position:0%
+CT2R
+hat is empty
+
+ align:start position:0%
+hat is empty
+ 
+
+ align:start position:0%
+hat is empty
+right so the support of CT1
+
+ align:start position:0%
+right so the support of CT1
+ 
+
+ align:start position:0%
+right so the support of CT1
+so this is the support of CT1 hat
+
+ align:start position:0%
+so this is the support of CT1 hat
+ 
+
+ align:start position:0%
+so this is the support of CT1 hat
+intersected with the annulus of size 1 /
+
+ align:start position:0%
+intersected with the annulus of size 1 /
+ 
+
+ align:start position:0%
+intersected with the annulus of size 1 /
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+intersected with the support of CT2 hat
+
+ align:start position:0%
+intersected with the support of CT2 hat
+ 
+
+ align:start position:0%
+intersected with the support of CT2 hat
+and these are two rectangles that are
+
+ align:start position:0%
+and these are two rectangles that are
+ 
+
+ align:start position:0%
+and these are two rectangles that are
+transverse to each other. Uh and so wow
+
+ align:start position:0%
+transverse to each other. Uh and so wow
+ 
+
+ align:start position:0%
+transverse to each other. Uh and so wow
+and you can you can check the
+
+ align:start position:0%
+and you can you can check the
+ 
+
+ align:start position:0%
+and you can you can check the
+intersection.
+
+ align:start position:0%
+intersection.
+ 
+
+ align:start position:0%
+intersection.
+>> Why does it rule out the translations of
+
+ align:start position:0%
+>> Why does it rule out the translations of
+ 
+
+ align:start position:0%
+>> Why does it rule out the translations of
+rectangles?
+
+ align:start position:0%
+rectangles?
+ 
+
+ align:start position:0%
+rectangles?
+>> Yeah. And so that's case one. So the
+
+ align:start position:0%
+>> Yeah. And so that's case one. So the
+ 
+
+ align:start position:0%
+>> Yeah. And so that's case one. So the
+other case is if um the R neighborhood
+
+ align:start position:0%
+other case is if um the R neighborhood
+ 
+
+ align:start position:0%
+other case is if um the R neighborhood
+of T1 is disjoint
+
+ align:start position:0%
+of T1 is disjoint
+ 
+
+ align:start position:0%
+of T1 is disjoint
+from the R neighborhood of T2 or you
+
+ align:start position:0%
+from the R neighborhood of T2 or you
+ 
+
+ align:start position:0%
+from the R neighborhood of T2 or you
+know a little bit more than R. Um then
+
+ align:start position:0%
+know a little bit more than R. Um then
+ 
+
+ align:start position:0%
+know a little bit more than R. Um then
+we use the formula
+
+ align:start position:0%
+we use the formula
+ 
+
+ align:start position:0%
+we use the formula
+CTR is CT1.
+
+ align:start position:0%
+CTR is CT1.
+ 
+
+ align:start position:0%
+CTR is CT1.
+So that so then we have here
+
+ align:start position:0%
+So that so then we have here
+ 
+
+ align:start position:0%
+So that so then we have here
+integral ct1 r c2 r complex conjugate
+
+ align:start position:0%
+integral ct1 r c2 r complex conjugate
+ 
+
+ align:start position:0%
+integral ct1 r c2 r complex conjugate
+it's the integral ct1 convolved with ad1
+
+ align:start position:0%
+it's the integral ct1 convolved with ad1
+ 
+
+ align:start position:0%
+it's the integral ct1 convolved with ad1
+and ct2 convolved
+
+ align:start position:0%
+and ct2 convolved
+ 
+
+ align:start position:0%
+and ct2 convolved
+a r check and and these two guys have
+
+ align:start position:0%
+a r check and and these two guys have
+ 
+
+ align:start position:0%
+a r check and and these two guys have
+disjoint report.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now we are ready to estimate the L2
+
+ align:start position:0%
+So now we are ready to estimate the L2
+ 
+
+ align:start position:0%
+So now we are ready to estimate the L2
+norm. Um so our orthogonality lema says
+
+ align:start position:0%
+norm. Um so our orthogonality lema says
+ 
+
+ align:start position:0%
+norm. Um so our orthogonality lema says
+that these different CTRs
+
+ align:start position:0%
+that these different CTRs
+ 
+
+ align:start position:0%
+that these different CTRs
+are usually orthogonal with a few
+
+ align:start position:0%
+are usually orthogonal with a few
+ 
+
+ align:start position:0%
+are usually orthogonal with a few
+exceptions and we're going to use that
+
+ align:start position:0%
+exceptions and we're going to use that
+ 
+
+ align:start position:0%
+exceptions and we're going to use that
+orthogonality to estimate the L2 norm.
+
+ align:start position:0%
+orthogonality to estimate the L2 norm.
+ 
+
+ align:start position:0%
+orthogonality to estimate the L2 norm.
+But we have to keep track of how many
+
+ align:start position:0%
+But we have to keep track of how many
+ 
+
+ align:start position:0%
+But we have to keep track of how many
+exceptions there are.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, L2 estimate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, the last thing we need to check is
+
+ align:start position:0%
+So, the last thing we need to check is
+ 
+
+ align:start position:0%
+So, the last thing we need to check is
+FR L2 squared. So, FR is the sum over
+
+ align:start position:0%
+FR L2 squared. So, FR is the sum over
+ 
+
+ align:start position:0%
+FR L2 squared. So, FR is the sum over
+all of our T of ctr.
+
+ align:start position:0%
+all of our T of ctr.
+ 
+
+ align:start position:0%
+all of our T of ctr.
+L2 squ.
+
+ align:start position:0%
+L2 squ.
+ 
+
+ align:start position:0%
+L2 squ.
+So that's this thing inner product with
+
+ align:start position:0%
+So that's this thing inner product with
+ 
+
+ align:start position:0%
+So that's this thing inner product with
+itself. So if I expand it out, it's the
+
+ align:start position:0%
+itself. So if I expand it out, it's the
+ 
+
+ align:start position:0%
+itself. So if I expand it out, it's the
+sum T1 T2 of um
+
+ align:start position:0%
+sum T1 T2 of um
+ 
+
+ align:start position:0%
+sum T1 T2 of um
+the inner product of C T1R
+
+ align:start position:0%
+the inner product of C T1R
+ 
+
+ align:start position:0%
+the inner product of C T1R
+C T2R.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And the key point is orthogonality
+
+ align:start position:0%
+Okay. And the key point is orthogonality
+ 
+
+ align:start position:0%
+Okay. And the key point is orthogonality
+lema tells us that most of the inner
+
+ align:start position:0%
+lema tells us that most of the inner
+ 
+
+ align:start position:0%
+lema tells us that most of the inner
+products in this sum are negligible.
+
+ align:start position:0%
+products in this sum are negligible.
+ 
+
+ align:start position:0%
+products in this sum are negligible.
+There's only a few that are not. Let me
+
+ align:start position:0%
+There's only a few that are not. Let me
+ 
+
+ align:start position:0%
+There's only a few that are not. Let me
+give a bit of a name to the ones that
+
+ align:start position:0%
+give a bit of a name to the ones that
+ 
+
+ align:start position:0%
+give a bit of a name to the ones that
+are not.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this scenario
+
+ align:start position:0%
+So this scenario
+ 
+
+ align:start position:0%
+So this scenario
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+I'm going to abbreviate it as saying
+
+ align:start position:0%
+I'm going to abbreviate it as saying
+ 
+
+ align:start position:0%
+I'm going to abbreviate it as saying
+that T1 uh is related to T2. T T T T T T
+
+ align:start position:0%
+that T1 uh is related to T2. T T T T T T
+ 
+
+ align:start position:0%
+that T1 uh is related to T2. T T T T T T
+T T T T T T T T T T T T T T T T T T T T
+
+ align:start position:0%
+T T T T T T T T T T T T T T T T T T T T
+ 
+
+ align:start position:0%
+T T T T T T T T T T T T T T T T T T T T
+T T T T T T T T T T T T T T T1 is close
+
+ align:start position:0%
+T T T T T T T T T T T T T T T1 is close
+ 
+
+ align:start position:0%
+T T T T T T T T T T T T T T T1 is close
+to T2.
+
+ align:start position:0%
+to T2.
+ 
+
+ align:start position:0%
+to T2.
+I guess we could put a little r here.
+
+ align:start position:0%
+I guess we could put a little r here.
+ 
+
+ align:start position:0%
+I guess we could put a little r here.
+So this inner product is negligible
+
+ align:start position:0%
+So this inner product is negligible
+ 
+
+ align:start position:0%
+So this inner product is negligible
+unless T1 is related to T2.
+
+ align:start position:0%
+unless T1 is related to T2.
+ 
+
+ align:start position:0%
+unless T1 is related to T2.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so let's look at our big sum of inner
+
+ align:start position:0%
+so let's look at our big sum of inner
+ 
+
+ align:start position:0%
+so let's look at our big sum of inner
+products
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll break it up into two parts.
+
+ align:start position:0%
+and I'll break it up into two parts.
+ 
+
+ align:start position:0%
+and I'll break it up into two parts.
+It's the sum where T1 is related to T2
+
+ align:start position:0%
+It's the sum where T1 is related to T2
+ 
+
+ align:start position:0%
+It's the sum where T1 is related to T2
+inner product plus the rest of them and
+
+ align:start position:0%
+inner product plus the rest of them and
+ 
+
+ align:start position:0%
+inner product plus the rest of them and
+the rest of them are really tiny by the
+
+ align:start position:0%
+the rest of them are really tiny by the
+ 
+
+ align:start position:0%
+the rest of them are really tiny by the
+orthogonality lema. So the rest of them
+
+ align:start position:0%
+orthogonality lema. So the rest of them
+ 
+
+ align:start position:0%
+orthogonality lema. So the rest of them
+are negligible.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now each of these inner products
+
+ align:start position:0%
+Okay. Now each of these inner products
+ 
+
+ align:start position:0%
+Okay. Now each of these inner products
+I'll arithmetic geometric mean it. So
+
+ align:start position:0%
+I'll arithmetic geometric mean it. So
+ 
+
+ align:start position:0%
+I'll arithmetic geometric mean it. So
+that's less than this sum t1 related to
+
+ align:start position:0%
+that's less than this sum t1 related to
+ 
+
+ align:start position:0%
+that's less than this sum t1 related to
+t2
+
+ align:start position:0%
+t2
+ 
+
+ align:start position:0%
+t2
+of ctr
+
+ align:start position:0%
+of ctr
+ 
+
+ align:start position:0%
+of ctr
+l2
+
+ align:start position:0%
+l2
+ 
+
+ align:start position:0%
+l2
+ct1 r l2 2 plus ct2r l2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So I want to know how many times
+
+ align:start position:0%
+Okay. So I want to know how many times
+ 
+
+ align:start position:0%
+Okay. So I want to know how many times
+does each of these functions ct1 appear
+
+ align:start position:0%
+does each of these functions ct1 appear
+ 
+
+ align:start position:0%
+does each of these functions ct1 appear
+in this sum
+
+ align:start position:0%
+in this sum
+ 
+
+ align:start position:0%
+in this sum
+and the number of times is the number of
+
+ align:start position:0%
+and the number of times is the number of
+ 
+
+ align:start position:0%
+and the number of times is the number of
+different t2s that are related to t1
+
+ align:start position:0%
+different t2s that are related to t1
+ 
+
+ align:start position:0%
+different t2s that are related to t1
+and that number is basically the number
+
+ align:start position:0%
+and that number is basically the number
+ 
+
+ align:start position:0%
+and that number is basically the number
+that appears in our main lema.
+
+ align:start position:0%
+that appears in our main lema.
+ 
+
+ align:start position:0%
+that appears in our main lema.
+This thing that we were counting here
+
+ align:start position:0%
+This thing that we were counting here
+ 
+
+ align:start position:0%
+This thing that we were counting here
+how many tubes lie in a little r by big
+
+ align:start position:0%
+how many tubes lie in a little r by big
+ 
+
+ align:start position:0%
+how many tubes lie in a little r by big
+r big tube. That's exactly how many
+
+ align:start position:0%
+r big tube. That's exactly how many
+ 
+
+ align:start position:0%
+r big tube. That's exactly how many
+tubes t2 are related to t1.
+
+ align:start position:0%
+tubes t2 are related to t1.
+ 
+
+ align:start position:0%
+tubes t2 are related to t1.
+So this thing
+
+ align:start position:0%
+So this thing
+ 
+
+ align:start position:0%
+So this thing
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+we can say the number of t2 so that t2
+
+ align:start position:0%
+we can say the number of t2 so that t2
+ 
+
+ align:start position:0%
+we can say the number of t2 so that t2
+is related to t1
+
+ align:start position:0%
+is related to t1
+ 
+
+ align:start position:0%
+is related to t1
+this is bounded by nr of t. So this
+
+ align:start position:0%
+this is bounded by nr of t. So this
+ 
+
+ align:start position:0%
+this is bounded by nr of t. So this
+whole sum is bounded by
+
+ align:start position:0%
+whole sum is bounded by
+ 
+
+ align:start position:0%
+whole sum is bounded by
+nr of t times just the sum on all the t
+
+ align:start position:0%
+nr of t times just the sum on all the t
+ 
+
+ align:start position:0%
+nr of t times just the sum on all the t
+and t of ctr l2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. And then finally each of these
+
+ align:start position:0%
+Cool. And then finally each of these
+ 
+
+ align:start position:0%
+Cool. And then finally each of these
+functions we've already described.
+
+ align:start position:0%
+functions we've already described.
+ 
+
+ align:start position:0%
+functions we've already described.
+Hopefully I didn't erase it.
+
+ align:start position:0%
+Hopefully I didn't erase it.
+ 
+
+ align:start position:0%
+Hopefully I didn't erase it.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Yeah, so we described it. It has height
+
+ align:start position:0%
+Yeah, so we described it. It has height
+ 
+
+ align:start position:0%
+Yeah, so we described it. It has height
+r inverse and it's supported on a little
+
+ align:start position:0%
+r inverse and it's supported on a little
+ 
+
+ align:start position:0%
+r inverse and it's supported on a little
+r by big r rectangle. So we can compute
+
+ align:start position:0%
+r by big r rectangle. So we can compute
+ 
+
+ align:start position:0%
+r by big r rectangle. So we can compute
+its L2 norm. Um
+
+ align:start position:0%
+its L2 norm. Um
+ 
+
+ align:start position:0%
+its L2 norm. Um
+so this is n subt of r times the number
+
+ align:start position:0%
+so this is n subt of r times the number
+ 
+
+ align:start position:0%
+so this is n subt of r times the number
+of tubes times uh the height was r
+
+ align:start position:0%
+of tubes times uh the height was r
+ 
+
+ align:start position:0%
+of tubes times uh the height was r
+inverse. So that's rus 2 times the
+
+ align:start position:0%
+inverse. So that's rus 2 times the
+ 
+
+ align:start position:0%
+inverse. So that's rus 2 times the
+uh so this is the amplitude squared
+
+ align:start position:0%
+uh so this is the amplitude squared
+ 
+
+ align:start position:0%
+uh so this is the amplitude squared
+and this is the area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for this ptr.
+
+ align:start position:0%
+for this ptr.
+ 
+
+ align:start position:0%
+for this ptr.
+Okay. And that was the thing that was on
+
+ align:start position:0%
+Okay. And that was the thing that was on
+ 
+
+ align:start position:0%
+Okay. And that was the thing that was on
+the right hand side.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Let me summarize the proof for the
+
+ align:start position:0%
+Okay. Let me summarize the proof for the
+ 
+
+ align:start position:0%
+Okay. Let me summarize the proof for the
+last minute. Um let's look back at our
+
+ align:start position:0%
+last minute. Um let's look back at our
+ 
+
+ align:start position:0%
+last minute. Um let's look back at our
+statement here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if we look at this sum of sum of
+
+ align:start position:0%
+So if we look at this sum of sum of
+ 
+
+ align:start position:0%
+So if we look at this sum of sum of
+tubes, we're going to break it into
+
+ align:start position:0%
+tubes, we're going to break it into
+ 
+
+ align:start position:0%
+tubes, we're going to break it into
+different frequency pieces. Littlewood
+
+ align:start position:0%
+different frequency pieces. Littlewood
+ 
+
+ align:start position:0%
+different frequency pieces. Littlewood
+pale theory. And then um the
+
+ align:start position:0%
+pale theory. And then um the
+ 
+
+ align:start position:0%
+pale theory. And then um the
+highfrequency pieces are usually
+
+ align:start position:0%
+highfrequency pieces are usually
+ 
+
+ align:start position:0%
+highfrequency pieces are usually
+orthogonal to each other. If you take if
+
+ align:start position:0%
+orthogonal to each other. If you take if
+ 
+
+ align:start position:0%
+orthogonal to each other. If you take if
+you look at two tubes and you look at
+
+ align:start position:0%
+you look at two tubes and you look at
+ 
+
+ align:start position:0%
+you look at two tubes and you look at
+the frequency one over R part, they're
+
+ align:start position:0%
+the frequency one over R part, they're
+ 
+
+ align:start position:0%
+the frequency one over R part, they're
+orthogonal to each other unless those
+
+ align:start position:0%
+orthogonal to each other unless those
+ 
+
+ align:start position:0%
+orthogonal to each other unless those
+two tubes are in a common fat tube
+
+ align:start position:0%
+two tubes are in a common fat tube
+ 
+
+ align:start position:0%
+two tubes are in a common fat tube
+little R by big R.
+
+ align:start position:0%
+little R by big R.
+ 
+
+ align:start position:0%
+little R by big R.
+And so you take advantage of that
+
+ align:start position:0%
+And so you take advantage of that
+ 
+
+ align:start position:0%
+And so you take advantage of that
+orthogonality where it's available and
+
+ align:start position:0%
+orthogonality where it's available and
+ 
+
+ align:start position:0%
+orthogonality where it's available and
+it gives this bound.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, good. Let's stop there for today.
+
+ align:start position:0%
+Okay, good. Let's stop there for today.
+ 
+
+ align:start position:0%
+Okay, good. Let's stop there for today.
+uh we will wrap this up on Thursday and
+
+ align:start position:0%
+uh we will wrap this up on Thursday and
+ 
+
+ align:start position:0%
+uh we will wrap this up on Thursday and
+and then uh discuss how similar ideas
+
+ align:start position:0%
+and then uh discuss how similar ideas
+ 
+
+ align:start position:0%
+and then uh discuss how similar ideas
+apply in a different looking context in
+
+ align:start position:0%
+apply in a different looking context in
+ 
+
+ align:start position:0%
+apply in a different looking context in
+civ theory in in number theory.
\ No newline at end of file
diff --git a/ONYokXoy04Q.txt b/ONYokXoy04Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bc7d9f1e00b763bb2c4e2004aadee8a1102b2e6a
--- /dev/null
+++ b/ONYokXoy04Q.txt
@@ -0,0 +1,6435 @@
+align:start position:0%
+ 
+so what I want to do today is recap a
+
+ align:start position:0%
+so what I want to do today is recap a
+ 
+
+ align:start position:0%
+so what I want to do today is recap a
+little bit what we talked about last
+
+ align:start position:0%
+little bit what we talked about last
+ 
+
+ align:start position:0%
+little bit what we talked about last
+time um reiterate some of the important
+
+ align:start position:0%
+time um reiterate some of the important
+ 
+
+ align:start position:0%
+time um reiterate some of the important
+points and then um show you uh how we
+
+ align:start position:0%
+points and then um show you uh how we
+ 
+
+ align:start position:0%
+points and then um show you uh how we
+can learn something about microorganisms
+
+ align:start position:0%
+can learn something about microorganisms
+ 
+
+ align:start position:0%
+can learn something about microorganisms
+in the environment by talking about
+
+ align:start position:0%
+in the environment by talking about
+ 
+
+ align:start position:0%
+in the environment by talking about
+inito identification of microorganisms
+
+ align:start position:0%
+inito identification of microorganisms
+ 
+
+ align:start position:0%
+inito identification of microorganisms
+as well as um genomics um we'll first
+
+ align:start position:0%
+as well as um genomics um we'll first
+ 
+
+ align:start position:0%
+as well as um genomics um we'll first
+talk about genomics in general and then
+
+ align:start position:0%
+talk about genomics in general and then
+ 
+
+ align:start position:0%
+talk about genomics in general and then
+talk about some applications of genomics
+
+ align:start position:0%
+talk about some applications of genomics
+ 
+
+ align:start position:0%
+talk about some applications of genomics
+to environmental microbiology because I
+
+ align:start position:0%
+to environmental microbiology because I
+ 
+
+ align:start position:0%
+to environmental microbiology because I
+think there's some of the most exciting
+
+ align:start position:0%
+think there's some of the most exciting
+ 
+
+ align:start position:0%
+think there's some of the most exciting
+new developments are in that area
+
+ align:start position:0%
+new developments are in that area
+ 
+
+ align:start position:0%
+new developments are in that area
+actually so last time um we talked about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Evolution and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ecology and just to recap some of the
+
+ align:start position:0%
+ecology and just to recap some of the
+ 
+
+ align:start position:0%
+ecology and just to recap some of the
+main points where that we can use genes
+
+ align:start position:0%
+main points where that we can use genes
+ 
+
+ align:start position:0%
+main points where that we can use genes
+or Gene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequences for a couple of very
+
+ align:start position:0%
+sequences for a couple of very
+ 
+
+ align:start position:0%
+sequences for a couple of very
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+um uh uh uh questions that we uh want to
+
+ align:start position:0%
+um uh uh uh questions that we uh want to
+ 
+
+ align:start position:0%
+um uh uh uh questions that we uh want to
+explore the first one was Gene sequences
+
+ align:start position:0%
+explore the first one was Gene sequences
+ 
+
+ align:start position:0%
+explore the first one was Gene sequences
+act as evolutionary chronometers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what do we mean by that basically
+
+ align:start position:0%
+now what do we mean by that basically
+ 
+
+ align:start position:0%
+now what do we mean by that basically
+what we said last time is that each gene
+
+ align:start position:0%
+what we said last time is that each gene
+ 
+
+ align:start position:0%
+what we said last time is that each gene
+each sequence in a genome accumulates
+
+ align:start position:0%
+each sequence in a genome accumulates
+ 
+
+ align:start position:0%
+each sequence in a genome accumulates
+mutation with a certain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability so what we mean is that all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accumulate
+
+ align:start position:0%
+accumulate
+ 
+
+ align:start position:0%
+accumulate
+mutations over time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now these of course are the mutations
+
+ align:start position:0%
+now these of course are the mutations
+ 
+
+ align:start position:0%
+now these of course are the mutations
+that do not kill the organism so not the
+
+ align:start position:0%
+that do not kill the organism so not the
+ 
+
+ align:start position:0%
+that do not kill the organism so not the
+delerious mutations but these are
+
+ align:start position:0%
+delerious mutations but these are
+ 
+
+ align:start position:0%
+delerious mutations but these are
+mutations that are either slightly
+
+ align:start position:0%
+mutations that are either slightly
+ 
+
+ align:start position:0%
+mutations that are either slightly
+delerious or don't matter or the
+
+ align:start position:0%
+delerious or don't matter or the
+ 
+
+ align:start position:0%
+delerious or don't matter or the
+beneficial mutations
+
+ align:start position:0%
+beneficial mutations
+ 
+
+ align:start position:0%
+beneficial mutations
+okay and what this entails that each
+
+ align:start position:0%
+okay and what this entails that each
+ 
+
+ align:start position:0%
+okay and what this entails that each
+gene accumulates mutation with a certain
+
+ align:start position:0%
+gene accumulates mutation with a certain
+ 
+
+ align:start position:0%
+gene accumulates mutation with a certain
+probability over time it basically means
+
+ align:start position:0%
+probability over time it basically means
+ 
+
+ align:start position:0%
+probability over time it basically means
+um that two organisms that come from
+
+ align:start position:0%
+um that two organisms that come from
+ 
+
+ align:start position:0%
+um that two organisms that come from
+species that are relatively closely
+
+ align:start position:0%
+species that are relatively closely
+ 
+
+ align:start position:0%
+species that are relatively closely
+related to each other have uh their Gene
+
+ align:start position:0%
+related to each other have uh their Gene
+ 
+
+ align:start position:0%
+related to each other have uh their Gene
+sequences will be much more similar to
+
+ align:start position:0%
+sequences will be much more similar to
+ 
+
+ align:start position:0%
+sequences will be much more similar to
+each other than um genes from an
+
+ align:start position:0%
+each other than um genes from an
+ 
+
+ align:start position:0%
+each other than um genes from an
+organism that comes from a species
+
+ align:start position:0%
+organism that comes from a species
+ 
+
+ align:start position:0%
+organism that comes from a species
+that's much more distantly related so in
+
+ align:start position:0%
+that's much more distantly related so in
+ 
+
+ align:start position:0%
+that's much more distantly related so in
+in Practical terms what this means is
+
+ align:start position:0%
+in Practical terms what this means is
+ 
+
+ align:start position:0%
+in Practical terms what this means is
+your genes are much much more similar to
+
+ align:start position:0%
+your genes are much much more similar to
+ 
+
+ align:start position:0%
+your genes are much much more similar to
+those of a monkey than they are to a
+
+ align:start position:0%
+those of a monkey than they are to a
+ 
+
+ align:start position:0%
+those of a monkey than they are to a
+crocodile for example and we can take
+
+ align:start position:0%
+crocodile for example and we can take
+ 
+
+ align:start position:0%
+crocodile for example and we can take
+advantage of that by applying some
+
+ align:start position:0%
+advantage of that by applying some
+ 
+
+ align:start position:0%
+advantage of that by applying some
+algorithms some mathemat mathematical
+
+ align:start position:0%
+algorithms some mathemat mathematical
+ 
+
+ align:start position:0%
+algorithms some mathemat mathematical
+modeling essentially to constrain these
+
+ align:start position:0%
+modeling essentially to constrain these
+ 
+
+ align:start position:0%
+modeling essentially to constrain these
+relationships in those philogenetic
+
+ align:start position:0%
+relationships in those philogenetic
+ 
+
+ align:start position:0%
+relationships in those philogenetic
+trees that we uh talked about last time
+
+ align:start position:0%
+trees that we uh talked about last time
+ 
+
+ align:start position:0%
+trees that we uh talked about last time
+and I also mentioned that the ribosomal
+
+ align:start position:0%
+and I also mentioned that the ribosomal
+ 
+
+ align:start position:0%
+and I also mentioned that the ribosomal
+RNA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes are particularly important for
+
+ align:start position:0%
+genes are particularly important for
+ 
+
+ align:start position:0%
+genes are particularly important for
+that process in principle you could do
+
+ align:start position:0%
+that process in principle you could do
+ 
+
+ align:start position:0%
+that process in principle you could do
+it with any protein coding gene or any
+
+ align:start position:0%
+it with any protein coding gene or any
+ 
+
+ align:start position:0%
+it with any protein coding gene or any
+kind of gene in a genome but we use the
+
+ align:start position:0%
+kind of gene in a genome but we use the
+ 
+
+ align:start position:0%
+kind of gene in a genome but we use the
+ribosomal RNA genes in particular
+
+ align:start position:0%
+ribosomal RNA genes in particular
+ 
+
+ align:start position:0%
+ribosomal RNA genes in particular
+because all organisms have them they're
+
+ align:start position:0%
+because all organisms have them they're
+ 
+
+ align:start position:0%
+because all organisms have them they're
+part of a handful of genes that are what
+
+ align:start position:0%
+part of a handful of genes that are what
+ 
+
+ align:start position:0%
+part of a handful of genes that are what
+we called universally distributed last
+
+ align:start position:0%
+we called universally distributed last
+ 
+
+ align:start position:0%
+we called universally distributed last
+time and what this allows us to do is
+
+ align:start position:0%
+time and what this allows us to do is
+ 
+
+ align:start position:0%
+time and what this allows us to do is
+then to construct philogenetic
+
+ align:start position:0%
+then to construct philogenetic
+ 
+
+ align:start position:0%
+then to construct philogenetic
+relationships for all living organisms
+
+ align:start position:0%
+relationships for all living organisms
+ 
+
+ align:start position:0%
+relationships for all living organisms
+okay and I just want to remind you of
+
+ align:start position:0%
+okay and I just want to remind you of
+ 
+
+ align:start position:0%
+okay and I just want to remind you of
+the tree of life that I showed last time
+
+ align:start position:0%
+the tree of life that I showed last time
+ 
+
+ align:start position:0%
+the tree of life that I showed last time
+where we can really explore um the
+
+ align:start position:0%
+where we can really explore um the
+ 
+
+ align:start position:0%
+where we can really explore um the
+relationships amongst all living
+
+ align:start position:0%
+relationships amongst all living
+ 
+
+ align:start position:0%
+relationships amongst all living
+organisms and um some of the important
+
+ align:start position:0%
+organisms and um some of the important
+ 
+
+ align:start position:0%
+organisms and um some of the important
+points there that we made where for
+
+ align:start position:0%
+points there that we made where for
+ 
+
+ align:start position:0%
+points there that we made where for
+example that the Tree of Life supports
+
+ align:start position:0%
+example that the Tree of Life supports
+ 
+
+ align:start position:0%
+example that the Tree of Life supports
+the endos Symon theory that when you
+
+ align:start position:0%
+the endos Symon theory that when you
+ 
+
+ align:start position:0%
+the endos Symon theory that when you
+actually look on the tree where the
+
+ align:start position:0%
+actually look on the tree where the
+ 
+
+ align:start position:0%
+actually look on the tree where the
+mitochondria and the chloroplasts tree
+
+ align:start position:0%
+mitochondria and the chloroplasts tree
+ 
+
+ align:start position:0%
+mitochondria and the chloroplasts tree
+they fall into the
+
+ align:start position:0%
+they fall into the
+ 
+
+ align:start position:0%
+they fall into the
+bacteria now there was a question um
+
+ align:start position:0%
+bacteria now there was a question um
+ 
+
+ align:start position:0%
+bacteria now there was a question um
+where somebody asked uh in in your
+
+ align:start position:0%
+where somebody asked uh in in your
+ 
+
+ align:start position:0%
+where somebody asked uh in in your
+online
+
+ align:start position:0%
+online
+ 
+
+ align:start position:0%
+online
+survey um Can the mitochondria and
+
+ align:start position:0%
+survey um Can the mitochondria and
+ 
+
+ align:start position:0%
+survey um Can the mitochondria and
+chloroplast still live outside of the
+
+ align:start position:0%
+chloroplast still live outside of the
+ 
+
+ align:start position:0%
+chloroplast still live outside of the
+eukaryotic cell and the answer is no
+
+ align:start position:0%
+eukaryotic cell and the answer is no
+ 
+
+ align:start position:0%
+eukaryotic cell and the answer is no
+they can't anymore because um the over
+
+ align:start position:0%
+they can't anymore because um the over
+ 
+
+ align:start position:0%
+they can't anymore because um the over
+evolutionary times the two organisms
+
+ align:start position:0%
+evolutionary times the two organisms
+ 
+
+ align:start position:0%
+evolutionary times the two organisms
+have have become so integrated that um
+
+ align:start position:0%
+have have become so integrated that um
+ 
+
+ align:start position:0%
+have have become so integrated that um
+the mitochondria and chloroplasts have
+
+ align:start position:0%
+the mitochondria and chloroplasts have
+ 
+
+ align:start position:0%
+the mitochondria and chloroplasts have
+both lost their ability to live outside
+
+ align:start position:0%
+both lost their ability to live outside
+ 
+
+ align:start position:0%
+both lost their ability to live outside
+of the eukariotic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hostel another important point that we
+
+ align:start position:0%
+hostel another important point that we
+ 
+
+ align:start position:0%
+hostel another important point that we
+made last
+
+ align:start position:0%
+made last
+ 
+
+ align:start position:0%
+made last
+time um that I want to reiterate here is
+
+ align:start position:0%
+time um that I want to reiterate here is
+ 
+
+ align:start position:0%
+time um that I want to reiterate here is
+that Gene sequences when we go into the
+
+ align:start position:0%
+that Gene sequences when we go into the
+ 
+
+ align:start position:0%
+that Gene sequences when we go into the
+environment and obtain them directly
+
+ align:start position:0%
+environment and obtain them directly
+ 
+
+ align:start position:0%
+environment and obtain them directly
+from the environment act as a proxy for
+
+ align:start position:0%
+from the environment act as a proxy for
+ 
+
+ align:start position:0%
+from the environment act as a proxy for
+microbial diversity in the
+
+ align:start position:0%
+microbial diversity in the
+ 
+
+ align:start position:0%
+microbial diversity in the
+environment so the number
+
+ align:start position:0%
+environment so the number
+ 
+
+ align:start position:0%
+environment so the number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+genes recover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directly from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure of diversity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we said that this actually plays a
+
+ align:start position:0%
+and we said that this actually plays a
+ 
+
+ align:start position:0%
+and we said that this actually plays a
+very very important role in the analysis
+
+ align:start position:0%
+very very important role in the analysis
+ 
+
+ align:start position:0%
+very very important role in the analysis
+of microbial communities and I showed
+
+ align:start position:0%
+of microbial communities and I showed
+ 
+
+ align:start position:0%
+of microbial communities and I showed
+you this example here where we went to
+
+ align:start position:0%
+you this example here where we went to
+ 
+
+ align:start position:0%
+you this example here where we went to
+um took some ocean water and basically
+
+ align:start position:0%
+um took some ocean water and basically
+ 
+
+ align:start position:0%
+um took some ocean water and basically
+applied this technique that I outlined
+
+ align:start position:0%
+applied this technique that I outlined
+ 
+
+ align:start position:0%
+applied this technique that I outlined
+last time where we can actually amplify
+
+ align:start position:0%
+last time where we can actually amplify
+ 
+
+ align:start position:0%
+last time where we can actually amplify
+ribosomal RNA genes from environmental
+
+ align:start position:0%
+ribosomal RNA genes from environmental
+ 
+
+ align:start position:0%
+ribosomal RNA genes from environmental
+samples clone them determine the
+
+ align:start position:0%
+samples clone them determine the
+ 
+
+ align:start position:0%
+samples clone them determine the
+sequence and then construct philogenetic
+
+ align:start position:0%
+sequence and then construct philogenetic
+ 
+
+ align:start position:0%
+sequence and then construct philogenetic
+trees and what you see here is a tree
+
+ align:start position:0%
+trees and what you see here is a tree
+ 
+
+ align:start position:0%
+trees and what you see here is a tree
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+we uh uh summarize the major groups that
+
+ align:start position:0%
+we uh uh summarize the major groups that
+ 
+
+ align:start position:0%
+we uh uh summarize the major groups that
+we found in this uh sample and then only
+
+ align:start position:0%
+we found in this uh sample and then only
+ 
+
+ align:start position:0%
+we found in this uh sample and then only
+for two of those groups do we show the
+
+ align:start position:0%
+for two of those groups do we show the
+ 
+
+ align:start position:0%
+for two of those groups do we show the
+entire set of sequences that we actually
+
+ align:start position:0%
+entire set of sequences that we actually
+ 
+
+ align:start position:0%
+entire set of sequences that we actually
+obtained because there were so many of
+
+ align:start position:0%
+obtained because there were so many of
+ 
+
+ align:start position:0%
+obtained because there were so many of
+them out there and what we basically
+
+ align:start position:0%
+them out there and what we basically
+ 
+
+ align:start position:0%
+them out there and what we basically
+found is that over 1,500 bacterial 6s
+
+ align:start position:0%
+found is that over 1,500 bacterial 6s
+ 
+
+ align:start position:0%
+found is that over 1,500 bacterial 6s
+ribosomal RNA Gene sequences coexist in
+
+ align:start position:0%
+ribosomal RNA Gene sequences coexist in
+ 
+
+ align:start position:0%
+ribosomal RNA Gene sequences coexist in
+this in in this environment and what we
+
+ align:start position:0%
+this in in this environment and what we
+ 
+
+ align:start position:0%
+this in in this environment and what we
+said also last time is that analysis
+
+ align:start position:0%
+said also last time is that analysis
+ 
+
+ align:start position:0%
+said also last time is that analysis
+like these have really taught us that
+
+ align:start position:0%
+like these have really taught us that
+ 
+
+ align:start position:0%
+like these have really taught us that
+microorganisms are the most diverse
+
+ align:start position:0%
+microorganisms are the most diverse
+ 
+
+ align:start position:0%
+microorganisms are the most diverse
+organism in the planet so most diversity
+
+ align:start position:0%
+organism in the planet so most diversity
+ 
+
+ align:start position:0%
+organism in the planet so most diversity
+is amongst the microorganisms and one of
+
+ align:start position:0%
+is amongst the microorganisms and one of
+ 
+
+ align:start position:0%
+is amongst the microorganisms and one of
+the big questions now is um what are all
+
+ align:start position:0%
+the big questions now is um what are all
+ 
+
+ align:start position:0%
+the big questions now is um what are all
+those microorganisms doing in the
+
+ align:start position:0%
+those microorganisms doing in the
+ 
+
+ align:start position:0%
+those microorganisms doing in the
+environment and so today what I want to
+
+ align:start position:0%
+environment and so today what I want to
+ 
+
+ align:start position:0%
+environment and so today what I want to
+do with you is basically explore this
+
+ align:start position:0%
+do with you is basically explore this
+ 
+
+ align:start position:0%
+do with you is basically explore this
+question how we can actually figure out
+
+ align:start position:0%
+question how we can actually figure out
+ 
+
+ align:start position:0%
+question how we can actually figure out
+what those microorganisms are all doing
+
+ align:start position:0%
+what those microorganisms are all doing
+ 
+
+ align:start position:0%
+what those microorganisms are all doing
+in environmental samples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can say we're exploring the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function of microbes in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment and first I want to cover
+
+ align:start position:0%
+environment and first I want to cover
+ 
+
+ align:start position:0%
+environment and first I want to cover
+how we can
+
+ align:start position:0%
+how we can
+ 
+
+ align:start position:0%
+how we can
+actually identify them in C2 in the
+
+ align:start position:0%
+actually identify them in C2 in the
+ 
+
+ align:start position:0%
+actually identify them in C2 in the
+environment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want to show you one specific
+
+ align:start position:0%
+and I want to show you one specific
+ 
+
+ align:start position:0%
+and I want to show you one specific
+example and then I want to talk about
+
+ align:start position:0%
+example and then I want to talk about
+ 
+
+ align:start position:0%
+example and then I want to talk about
+genomics in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general and then basically end with an
+
+ align:start position:0%
+general and then basically end with an
+ 
+
+ align:start position:0%
+general and then basically end with an
+application of genomics to environmental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions so let's
+
+ align:start position:0%
+questions so let's
+ 
+
+ align:start position:0%
+questions so let's
+first talk about the Ino identification
+
+ align:start position:0%
+first talk about the Ino identification
+ 
+
+ align:start position:0%
+first talk about the Ino identification
+of microorganisms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the basic problem that I alluded to
+
+ align:start position:0%
+and the basic problem that I alluded to
+ 
+
+ align:start position:0%
+and the basic problem that I alluded to
+already before is that most microbes are
+
+ align:start position:0%
+already before is that most microbes are
+ 
+
+ align:start position:0%
+already before is that most microbes are
+only known
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from 16s ribosomal RNA clone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+libraries and we basically want to
+
+ align:start position:0%
+libraries and we basically want to
+ 
+
+ align:start position:0%
+libraries and we basically want to
+search and identify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them in the environment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and I'll show you a specific
+
+ align:start position:0%
+okay and I'll show you a specific
+ 
+
+ align:start position:0%
+okay and I'll show you a specific
+example of that later
+
+ align:start position:0%
+example of that later
+ 
+
+ align:start position:0%
+example of that later
+on now last time we said that the
+
+ align:start position:0%
+on now last time we said that the
+ 
+
+ align:start position:0%
+on now last time we said that the
+ribosomal RNA sequences consist really
+
+ align:start position:0%
+ribosomal RNA sequences consist really
+ 
+
+ align:start position:0%
+ribosomal RNA sequences consist really
+like all Gene sequences in fact of
+
+ align:start position:0%
+like all Gene sequences in fact of
+ 
+
+ align:start position:0%
+like all Gene sequences in fact of
+several we identified several stretches
+
+ align:start position:0%
+several we identified several stretches
+ 
+
+ align:start position:0%
+several we identified several stretches
+of nucleotides types of stretches that
+
+ align:start position:0%
+of nucleotides types of stretches that
+ 
+
+ align:start position:0%
+of nucleotides types of stretches that
+can be found we said the a type
+
+ align:start position:0%
+can be found we said the a type
+ 
+
+ align:start position:0%
+can be found we said the a type
+stretches and B type stretches that are
+
+ align:start position:0%
+stretches and B type stretches that are
+ 
+
+ align:start position:0%
+stretches and B type stretches that are
+very important for constructing
+
+ align:start position:0%
+very important for constructing
+ 
+
+ align:start position:0%
+very important for constructing
+philogenetic relationship ships because
+
+ align:start position:0%
+philogenetic relationship ships because
+ 
+
+ align:start position:0%
+philogenetic relationship ships because
+we can align them and look for changes
+
+ align:start position:0%
+we can align them and look for changes
+ 
+
+ align:start position:0%
+we can align them and look for changes
+in the nucleotide sequences because um
+
+ align:start position:0%
+in the nucleotide sequences because um
+ 
+
+ align:start position:0%
+in the nucleotide sequences because um
+they're of the same length and only
+
+ align:start position:0%
+they're of the same length and only
+ 
+
+ align:start position:0%
+they're of the same length and only
+differ in um mutations and in single
+
+ align:start position:0%
+differ in um mutations and in single
+ 
+
+ align:start position:0%
+differ in um mutations and in single
+nucleotide uh base pair
+
+ align:start position:0%
+nucleotide uh base pair
+ 
+
+ align:start position:0%
+nucleotide uh base pair
+changes but then there's also those C
+
+ align:start position:0%
+changes but then there's also those C
+ 
+
+ align:start position:0%
+changes but then there's also those C
+type stretches if you remember and those
+
+ align:start position:0%
+type stretches if you remember and those
+ 
+
+ align:start position:0%
+type stretches if you remember and those
+we said vary at much faster rates
+
+ align:start position:0%
+we said vary at much faster rates
+ 
+
+ align:start position:0%
+we said vary at much faster rates
+because they are not functionally
+
+ align:start position:0%
+because they are not functionally
+ 
+
+ align:start position:0%
+because they are not functionally
+constrained in those genes okay so they
+
+ align:start position:0%
+constrained in those genes okay so they
+ 
+
+ align:start position:0%
+constrained in those genes okay so they
+can actually also accumulate um length
+
+ align:start position:0%
+can actually also accumulate um length
+ 
+
+ align:start position:0%
+can actually also accumulate um length
+changes and it's these C type stretches
+
+ align:start position:0%
+changes and it's these C type stretches
+ 
+
+ align:start position:0%
+changes and it's these C type stretches
+that we can use sort of as diagnostic
+
+ align:start position:0%
+that we can use sort of as diagnostic
+ 
+
+ align:start position:0%
+that we can use sort of as diagnostic
+sequence stretches for
+
+ align:start position:0%
+sequence stretches for
+ 
+
+ align:start position:0%
+sequence stretches for
+microorganisms so what we can say is we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organisms by the C type stretches
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ctype sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stretches we call those signature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+okay and they
+
+ align:start position:0%
+okay and they
+ 
+
+ align:start position:0%
+okay and they
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+allow the differentiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of closely related
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organisms because they vary at very fast
+
+ align:start position:0%
+organisms because they vary at very fast
+ 
+
+ align:start position:0%
+organisms because they vary at very fast
+rates between
+
+ align:start position:0%
+rates between
+ 
+
+ align:start position:0%
+rates between
+organisms and the way we do this is we
+
+ align:start position:0%
+organisms and the way we do this is we
+ 
+
+ align:start position:0%
+organisms and the way we do this is we
+construct so-called philogenetic
+
+ align:start position:0%
+construct so-called philogenetic
+ 
+
+ align:start position:0%
+construct so-called philogenetic
+probes I should probably write this over
+
+ align:start position:0%
+probes I should probably write this over
+ 
+
+ align:start position:0%
+probes I should probably write this over
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what are those philogenetic probes
+
+ align:start position:0%
+now what are those philogenetic probes
+ 
+
+ align:start position:0%
+now what are those philogenetic probes
+they're basically short pieces of
+
+ align:start position:0%
+they're basically short pieces of
+ 
+
+ align:start position:0%
+they're basically short pieces of
+DNA that have a fluorescent molecule
+
+ align:start position:0%
+DNA that have a fluorescent molecule
+ 
+
+ align:start position:0%
+DNA that have a fluorescent molecule
+attached to them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DNA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecules that are roughly 20
+
+ align:start position:0%
+molecules that are roughly 20
+ 
+
+ align:start position:0%
+molecules that are roughly 20
+nucleotides in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length and they carry a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fluorescent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecule now what these short single
+
+ align:start position:0%
+molecule now what these short single
+ 
+
+ align:start position:0%
+molecule now what these short single
+stranded stretches of DNA basically are
+
+ align:start position:0%
+stranded stretches of DNA basically are
+ 
+
+ align:start position:0%
+stranded stretches of DNA basically are
+is they are complementary
+
+ align:start position:0%
+is they are complementary
+ 
+
+ align:start position:0%
+is they are complementary
+to those ctype sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stretches in the ribosomal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R and so basically what we can do is we
+
+ align:start position:0%
+R and so basically what we can do is we
+ 
+
+ align:start position:0%
+R and so basically what we can do is we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+collect microbial cells from the
+
+ align:start position:0%
+collect microbial cells from the
+ 
+
+ align:start position:0%
+collect microbial cells from the
+environment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make them permeable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then basically mix them with those
+
+ align:start position:0%
+and then basically mix them with those
+ 
+
+ align:start position:0%
+and then basically mix them with those
+philogenetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probes and these probes will then
+
+ align:start position:0%
+probes and these probes will then
+ 
+
+ align:start position:0%
+probes and these probes will then
+permeate into the cell and bind to their
+
+ align:start position:0%
+permeate into the cell and bind to their
+ 
+
+ align:start position:0%
+permeate into the cell and bind to their
+complimentary sequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we wash away the Unbound probe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we can view it in a microscope under
+
+ align:start position:0%
+and we can view it in a microscope under
+ 
+
+ align:start position:0%
+and we can view it in a microscope under
+UV light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me show you an example of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this what you see here basically is
+
+ align:start position:0%
+this what you see here basically is
+ 
+
+ align:start position:0%
+this what you see here basically is
+a light micrograph so this is what you
+
+ align:start position:0%
+a light micrograph so this is what you
+ 
+
+ align:start position:0%
+a light micrograph so this is what you
+see basically when you collect microbial
+
+ align:start position:0%
+see basically when you collect microbial
+ 
+
+ align:start position:0%
+see basically when you collect microbial
+cells from the environment under the
+
+ align:start position:0%
+cells from the environment under the
+ 
+
+ align:start position:0%
+cells from the environment under the
+microscope most bacteria look the same
+
+ align:start position:0%
+microscope most bacteria look the same
+ 
+
+ align:start position:0%
+microscope most bacteria look the same
+so you cannot actually differentiate
+
+ align:start position:0%
+so you cannot actually differentiate
+ 
+
+ align:start position:0%
+so you cannot actually differentiate
+them at all by just looking at them now
+
+ align:start position:0%
+them at all by just looking at them now
+ 
+
+ align:start position:0%
+them at all by just looking at them now
+but then these cells were fixed and
+
+ align:start position:0%
+but then these cells were fixed and
+ 
+
+ align:start position:0%
+but then these cells were fixed and
+permeabilized and then basically mixed
+
+ align:start position:0%
+permeabilized and then basically mixed
+ 
+
+ align:start position:0%
+permeabilized and then basically mixed
+with two different philogenetic probes
+
+ align:start position:0%
+with two different philogenetic probes
+ 
+
+ align:start position:0%
+with two different philogenetic probes
+that identified two two different types
+
+ align:start position:0%
+that identified two two different types
+ 
+
+ align:start position:0%
+that identified two two different types
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+organisms one was AED with a red FL the
+
+ align:start position:0%
+organisms one was AED with a red FL the
+ 
+
+ align:start position:0%
+organisms one was AED with a red FL the
+other one with a green
+
+ align:start position:0%
+other one with a green
+ 
+
+ align:start position:0%
+other one with a green
+FL and what you see is that you can now
+
+ align:start position:0%
+FL and what you see is that you can now
+ 
+
+ align:start position:0%
+FL and what you see is that you can now
+differentiate those two
+
+ align:start position:0%
+differentiate those two
+ 
+
+ align:start position:0%
+differentiate those two
+organisms now why is this actually
+
+ align:start position:0%
+organisms now why is this actually
+ 
+
+ align:start position:0%
+organisms now why is this actually
+interesting well this here is just a
+
+ align:start position:0%
+interesting well this here is just a
+ 
+
+ align:start position:0%
+interesting well this here is just a
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+example um where people were looking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um bacteria
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capable of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nitrogen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxidation these are bacteria that are
+
+ align:start position:0%
+oxidation these are bacteria that are
+ 
+
+ align:start position:0%
+oxidation these are bacteria that are
+very important in for example sewage
+
+ align:start position:0%
+very important in for example sewage
+ 
+
+ align:start position:0%
+very important in for example sewage
+treatment and it's it was known already
+
+ align:start position:0%
+treatment and it's it was known already
+ 
+
+ align:start position:0%
+treatment and it's it was known already
+that there's two different types out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there one that oxidizes ammonia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nitrite and then a second one that
+
+ align:start position:0%
+nitrite and then a second one that
+ 
+
+ align:start position:0%
+nitrite and then a second one that
+oxidizes nitrite to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nitrate and by doing this type of
+
+ align:start position:0%
+nitrate and by doing this type of
+ 
+
+ align:start position:0%
+nitrate and by doing this type of
+analysis what people basically Learned
+
+ align:start position:0%
+analysis what people basically Learned
+ 
+
+ align:start position:0%
+analysis what people basically Learned
+was that those two organisms live in
+
+ align:start position:0%
+was that those two organisms live in
+ 
+
+ align:start position:0%
+was that those two organisms live in
+very very close proximity at all times
+
+ align:start position:0%
+very very close proximity at all times
+ 
+
+ align:start position:0%
+very very close proximity at all times
+so the organisms that oxidize ammonia to
+
+ align:start position:0%
+so the organisms that oxidize ammonia to
+ 
+
+ align:start position:0%
+so the organisms that oxidize ammonia to
+nitrite are really attached and
+
+ align:start position:0%
+nitrite are really attached and
+ 
+
+ align:start position:0%
+nitrite are really attached and
+oftentimes even surround the organisms
+
+ align:start position:0%
+oftentimes even surround the organisms
+ 
+
+ align:start position:0%
+oftentimes even surround the organisms
+that take the nitrite to nitrate so what
+
+ align:start position:0%
+that take the nitrite to nitrate so what
+ 
+
+ align:start position:0%
+that take the nitrite to nitrate so what
+you have is a very close cooperation
+
+ align:start position:0%
+you have is a very close cooperation
+ 
+
+ align:start position:0%
+you have is a very close cooperation
+between two different types of
+
+ align:start position:0%
+between two different types of
+ 
+
+ align:start position:0%
+between two different types of
+microorganisms and a transfer of one of
+
+ align:start position:0%
+microorganisms and a transfer of one of
+ 
+
+ align:start position:0%
+microorganisms and a transfer of one of
+the substrates um that's a product of
+
+ align:start position:0%
+the substrates um that's a product of
+ 
+
+ align:start position:0%
+the substrates um that's a product of
+the metabolism of one of the organisms
+
+ align:start position:0%
+the metabolism of one of the organisms
+ 
+
+ align:start position:0%
+the metabolism of one of the organisms
+to another one so an extremely efficient
+
+ align:start position:0%
+to another one so an extremely efficient
+ 
+
+ align:start position:0%
+to another one so an extremely efficient
+process that really is very important to
+
+ align:start position:0%
+process that really is very important to
+ 
+
+ align:start position:0%
+process that really is very important to
+take into consideration when you want to
+
+ align:start position:0%
+take into consideration when you want to
+ 
+
+ align:start position:0%
+take into consideration when you want to
+understand processes like sewage
+
+ align:start position:0%
+understand processes like sewage
+ 
+
+ align:start position:0%
+understand processes like sewage
+treatment but also nitrogen um biog
+
+ align:start position:0%
+treatment but also nitrogen um biog
+ 
+
+ align:start position:0%
+treatment but also nitrogen um biog
+geochemistry in the
+
+ align:start position:0%
+geochemistry in the
+ 
+
+ align:start position:0%
+geochemistry in the
+environment any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so um for the remainder
+
+ align:start position:0%
+questions okay so um for the remainder
+ 
+
+ align:start position:0%
+questions okay so um for the remainder
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+lecture I want to talk about um genomics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then in particular also its
+
+ align:start position:0%
+and then in particular also its
+ 
+
+ align:start position:0%
+and then in particular also its
+application to questions of
+
+ align:start position:0%
+application to questions of
+ 
+
+ align:start position:0%
+application to questions of
+environmental
+
+ align:start position:0%
+environmental
+ 
+
+ align:start position:0%
+environmental
+microbiology and uh environmental
+
+ align:start position:0%
+microbiology and uh environmental
+ 
+
+ align:start position:0%
+microbiology and uh environmental
+science so first what I want to do is
+
+ align:start position:0%
+science so first what I want to do is
+ 
+
+ align:start position:0%
+science so first what I want to do is
+give you a little bit of a definition of
+
+ align:start position:0%
+give you a little bit of a definition of
+ 
+
+ align:start position:0%
+give you a little bit of a definition of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+genomics then I want to cover how it is
+
+ align:start position:0%
+genomics then I want to cover how it is
+ 
+
+ align:start position:0%
+genomics then I want to cover how it is
+actually possible that we can sequence
+
+ align:start position:0%
+actually possible that we can sequence
+ 
+
+ align:start position:0%
+actually possible that we can sequence
+entire
+
+ align:start position:0%
+entire
+ 
+
+ align:start position:0%
+entire
+genomes and then I want to give you some
+
+ align:start position:0%
+genomes and then I want to give you some
+ 
+
+ align:start position:0%
+genomes and then I want to give you some
+highlights of what we have found by
+
+ align:start position:0%
+highlights of what we have found by
+ 
+
+ align:start position:0%
+highlights of what we have found by
+comparing different genomes to each
+
+ align:start position:0%
+comparing different genomes to each
+ 
+
+ align:start position:0%
+comparing different genomes to each
+other and then I want to talk about this
+
+ align:start position:0%
+other and then I want to talk about this
+ 
+
+ align:start position:0%
+other and then I want to talk about this
+field about environmental genomics where
+
+ align:start position:0%
+field about environmental genomics where
+ 
+
+ align:start position:0%
+field about environmental genomics where
+we can use genomic techniques to
+
+ align:start position:0%
+we can use genomic techniques to
+ 
+
+ align:start position:0%
+we can use genomic techniques to
+actually learn something about the
+
+ align:start position:0%
+actually learn something about the
+ 
+
+ align:start position:0%
+actually learn something about the
+function of different uncultured
+
+ align:start position:0%
+function of different uncultured
+ 
+
+ align:start position:0%
+function of different uncultured
+microorganisms in the
+
+ align:start position:0%
+microorganisms in the
+ 
+
+ align:start position:0%
+microorganisms in the
+environment so first our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition it's basically to interpret
+
+ align:start position:0%
+definition it's basically to interpret
+ 
+
+ align:start position:0%
+definition it's basically to interpret
+or to sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interpret and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compare whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genomes and as you will see the
+
+ align:start position:0%
+genomes and as you will see the
+ 
+
+ align:start position:0%
+genomes and as you will see the
+comparison part actually plays an
+
+ align:start position:0%
+comparison part actually plays an
+ 
+
+ align:start position:0%
+comparison part actually plays an
+increasingly important role because we
+
+ align:start position:0%
+increasingly important role because we
+ 
+
+ align:start position:0%
+increasingly important role because we
+have now actually genome sequences
+
+ align:start position:0%
+have now actually genome sequences
+ 
+
+ align:start position:0%
+have now actually genome sequences
+available from almost all or from at
+
+ align:start position:0%
+available from almost all or from at
+ 
+
+ align:start position:0%
+available from almost all or from at
+least some of the major groups of life
+
+ align:start position:0%
+least some of the major groups of life
+ 
+
+ align:start position:0%
+least some of the major groups of life
+so we have a lot of um this again is a a
+
+ align:start position:0%
+so we have a lot of um this again is a a
+ 
+
+ align:start position:0%
+so we have a lot of um this again is a a
+different kind of representation of a
+
+ align:start position:0%
+different kind of representation of a
+ 
+
+ align:start position:0%
+different kind of representation of a
+tree of life you have bacteria or ukaria
+
+ align:start position:0%
+tree of life you have bacteria or ukaria
+ 
+
+ align:start position:0%
+tree of life you have bacteria or ukaria
+again and as you can see we have a lot
+
+ align:start position:0%
+again and as you can see we have a lot
+ 
+
+ align:start position:0%
+again and as you can see we have a lot
+of Representatives in fact this doesn't
+
+ align:start position:0%
+of Representatives in fact this doesn't
+ 
+
+ align:start position:0%
+of Representatives in fact this doesn't
+even uh come close to the diversity that
+
+ align:start position:0%
+even uh come close to the diversity that
+ 
+
+ align:start position:0%
+even uh come close to the diversity that
+we have now sequenced there's well over
+
+ align:start position:0%
+we have now sequenced there's well over
+ 
+
+ align:start position:0%
+we have now sequenced there's well over
+100 bacterial genome sequence now
+
+ align:start position:0%
+100 bacterial genome sequence now
+ 
+
+ align:start position:0%
+100 bacterial genome sequence now
+several AR keal genomes and increasingly
+
+ align:start position:0%
+several AR keal genomes and increasingly
+ 
+
+ align:start position:0%
+several AR keal genomes and increasingly
+also UK carot genomes
+
+ align:start position:0%
+also UK carot genomes
+ 
+
+ align:start position:0%
+also UK carot genomes
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genomes so how is this
+
+ align:start position:0%
+genomes so how is this
+ 
+
+ align:start position:0%
+genomes so how is this
+done how can we actually sequence
+
+ align:start position:0%
+done how can we actually sequence
+ 
+
+ align:start position:0%
+done how can we actually sequence
+genomes well on the face of it we use um
+
+ align:start position:0%
+genomes well on the face of it we use um
+ 
+
+ align:start position:0%
+genomes well on the face of it we use um
+very large facilities where you have uh
+
+ align:start position:0%
+very large facilities where you have uh
+ 
+
+ align:start position:0%
+very large facilities where you have uh
+sequencing machines present there's one
+
+ align:start position:0%
+sequencing machines present there's one
+ 
+
+ align:start position:0%
+sequencing machines present there's one
+very important one at MIT actually in um
+
+ align:start position:0%
+very important one at MIT actually in um
+ 
+
+ align:start position:0%
+very important one at MIT actually in um
+the broad Institute and here you see all
+
+ align:start position:0%
+the broad Institute and here you see all
+ 
+
+ align:start position:0%
+the broad Institute and here you see all
+those um really uh industrial scale
+
+ align:start position:0%
+those um really uh industrial scale
+ 
+
+ align:start position:0%
+those um really uh industrial scale
+uction lines
+
+ align:start position:0%
+uction lines
+ 
+
+ align:start position:0%
+uction lines
+actually but the problem the basic
+
+ align:start position:0%
+actually but the problem the basic
+ 
+
+ align:start position:0%
+actually but the problem the basic
+problem is that genomes are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large eoli for
+
+ align:start position:0%
+large eoli for
+ 
+
+ align:start position:0%
+large eoli for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+roughly 4.4 million base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairs and the human genome is even even
+
+ align:start position:0%
+pairs and the human genome is even even
+ 
+
+ align:start position:0%
+pairs and the human genome is even even
+much much larger it has about 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+billion base pairs okay so genomes are
+
+ align:start position:0%
+billion base pairs okay so genomes are
+ 
+
+ align:start position:0%
+billion base pairs okay so genomes are
+very very large but an a single
+
+ align:start position:0%
+very very large but an a single
+ 
+
+ align:start position:0%
+very very large but an a single
+sequencing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction gives you only roughly 500 to
+
+ align:start position:0%
+reaction gives you only roughly 500 to
+ 
+
+ align:start position:0%
+reaction gives you only roughly 500 to
+1,000 nucleotides or base pairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how is it that we can actually
+
+ align:start position:0%
+so how is it that we can actually
+ 
+
+ align:start position:0%
+so how is it that we can actually
+sequence um entire
+
+ align:start position:0%
+sequence um entire
+ 
+
+ align:start position:0%
+sequence um entire
+genomes I want to walk you through this
+
+ align:start position:0%
+genomes I want to walk you through this
+ 
+
+ align:start position:0%
+genomes I want to walk you through this
+and there's some variations on the theme
+
+ align:start position:0%
+and there's some variations on the theme
+ 
+
+ align:start position:0%
+and there's some variations on the theme
+but um this is still um sort of a major
+
+ align:start position:0%
+but um this is still um sort of a major
+ 
+
+ align:start position:0%
+but um this is still um sort of a major
+uh approach that's still used in in some
+
+ align:start position:0%
+uh approach that's still used in in some
+ 
+
+ align:start position:0%
+uh approach that's still used in in some
+of in in a majority of the sequencing
+
+ align:start position:0%
+of in in a majority of the sequencing
+ 
+
+ align:start position:0%
+of in in a majority of the sequencing
+facilities now you start out by
+
+ align:start position:0%
+facilities now you start out by
+ 
+
+ align:start position:0%
+facilities now you start out by
+extracting genomic DNA from organisms
+
+ align:start position:0%
+extracting genomic DNA from organisms
+ 
+
+ align:start position:0%
+extracting genomic DNA from organisms
+and then you use restriction enzymes to
+
+ align:start position:0%
+and then you use restriction enzymes to
+ 
+
+ align:start position:0%
+and then you use restriction enzymes to
+cut the DNA into relatively large pieces
+
+ align:start position:0%
+cut the DNA into relatively large pieces
+ 
+
+ align:start position:0%
+cut the DNA into relatively large pieces
+of DNA so about 160 kilobase pairs long
+
+ align:start position:0%
+of DNA so about 160 kilobase pairs long
+ 
+
+ align:start position:0%
+of DNA so about 160 kilobase pairs long
+on average as is shown here now kilo
+
+ align:start position:0%
+on average as is shown here now kilo
+ 
+
+ align:start position:0%
+on average as is shown here now kilo
+means a th000 so 160,000 base pairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+long these pieces are then cloned into
+
+ align:start position:0%
+long these pieces are then cloned into
+ 
+
+ align:start position:0%
+long these pieces are then cloned into
+specific clone vectors that are called
+
+ align:start position:0%
+specific clone vectors that are called
+ 
+
+ align:start position:0%
+specific clone vectors that are called
+back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors so therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cloning large pieces of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DNA and back stands for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bacterial artificial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chromosome and what they basically are
+
+ align:start position:0%
+chromosome and what they basically are
+ 
+
+ align:start position:0%
+chromosome and what they basically are
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasmids very special
+
+ align:start position:0%
+plasmids very special
+ 
+
+ align:start position:0%
+plasmids very special
+plasmids that can carry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large pieces of genome or large genome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fragments so by cloning into those back
+
+ align:start position:0%
+fragments so by cloning into those back
+ 
+
+ align:start position:0%
+fragments so by cloning into those back
+vectors what you do is you basically
+
+ align:start position:0%
+vectors what you do is you basically
+ 
+
+ align:start position:0%
+vectors what you do is you basically
+divide up the
+
+ align:start position:0%
+divide up the
+ 
+
+ align:start position:0%
+divide up the
+genome and you can then this is Step
+
+ align:start position:0%
+genome and you can then this is Step
+ 
+
+ align:start position:0%
+genome and you can then this is Step
+number three is mostly done for um UK
+
+ align:start position:0%
+number three is mostly done for um UK
+ 
+
+ align:start position:0%
+number three is mostly done for um UK
+carotic genomes because they're so much
+
+ align:start position:0%
+carotic genomes because they're so much
+ 
+
+ align:start position:0%
+carotic genomes because they're so much
+larger you can actually map then those
+
+ align:start position:0%
+larger you can actually map then those
+ 
+
+ align:start position:0%
+larger you can actually map then those
+uh analyze the fragments in map and onto
+
+ align:start position:0%
+uh analyze the fragments in map and onto
+ 
+
+ align:start position:0%
+uh analyze the fragments in map and onto
+maps onto uh genome Maps where you know
+
+ align:start position:0%
+maps onto uh genome Maps where you know
+ 
+
+ align:start position:0%
+maps onto uh genome Maps where you know
+the location of different um restriction
+
+ align:start position:0%
+the location of different um restriction
+ 
+
+ align:start position:0%
+the location of different um restriction
+fragments and different uh genes
+
+ align:start position:0%
+fragments and different uh genes
+ 
+
+ align:start position:0%
+fragments and different uh genes
+actually for bacteria this step is
+
+ align:start position:0%
+actually for bacteria this step is
+ 
+
+ align:start position:0%
+actually for bacteria this step is
+mostly skipped
+
+ align:start position:0%
+mostly skipped
+ 
+
+ align:start position:0%
+mostly skipped
+actually what you do then with each one
+
+ align:start position:0%
+actually what you do then with each one
+ 
+
+ align:start position:0%
+actually what you do then with each one
+of those bags is you cut them further up
+
+ align:start position:0%
+of those bags is you cut them further up
+ 
+
+ align:start position:0%
+of those bags is you cut them further up
+into one kilobase per fragment so
+
+ align:start position:0%
+into one kilobase per fragment so
+ 
+
+ align:start position:0%
+into one kilobase per fragment so
+smaller much smaller fragments and these
+
+ align:start position:0%
+smaller much smaller fragments and these
+ 
+
+ align:start position:0%
+smaller much smaller fragments and these
+are called
+
+ align:start position:0%
+are called
+ 
+
+ align:start position:0%
+are called
+um and this is then actually these are
+
+ align:start position:0%
+um and this is then actually these are
+ 
+
+ align:start position:0%
+um and this is then actually these are
+clone then into normal plasmid vectors
+
+ align:start position:0%
+clone then into normal plasmid vectors
+ 
+
+ align:start position:0%
+clone then into normal plasmid vectors
+and so you generate what is called
+
+ align:start position:0%
+and so you generate what is called
+ 
+
+ align:start position:0%
+and so you generate what is called
+shotgun
+
+ align:start position:0%
+shotgun
+ 
+
+ align:start position:0%
+shotgun
+clones so these are then cloned into
+
+ align:start position:0%
+clones so these are then cloned into
+ 
+
+ align:start position:0%
+clones so these are then cloned into
+Eola and basically you go through the
+
+ align:start position:0%
+Eola and basically you go through the
+ 
+
+ align:start position:0%
+Eola and basically you go through the
+same type of steps that we discussed uh
+
+ align:start position:0%
+same type of steps that we discussed uh
+ 
+
+ align:start position:0%
+same type of steps that we discussed uh
+before already with environmental clone
+
+ align:start position:0%
+before already with environmental clone
+ 
+
+ align:start position:0%
+before already with environmental clone
+libraries and you can actually determine
+
+ align:start position:0%
+libraries and you can actually determine
+ 
+
+ align:start position:0%
+libraries and you can actually determine
+the sequence of each one of those pieces
+
+ align:start position:0%
+the sequence of each one of those pieces
+ 
+
+ align:start position:0%
+the sequence of each one of those pieces
+of DNA and what you will then get is
+
+ align:start position:0%
+of DNA and what you will then get is
+ 
+
+ align:start position:0%
+of DNA and what you will then get is
+small fragments of overlapping DNA
+
+ align:start position:0%
+small fragments of overlapping DNA
+ 
+
+ align:start position:0%
+small fragments of overlapping DNA
+sequence okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is shown here and you will find
+
+ align:start position:0%
+that is shown here and you will find
+ 
+
+ align:start position:0%
+that is shown here and you will find
+overlaps basically which you piece
+
+ align:start position:0%
+overlaps basically which you piece
+ 
+
+ align:start position:0%
+overlaps basically which you piece
+together the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genome and so first you assemble you
+
+ align:start position:0%
+genome and so first you assemble you
+ 
+
+ align:start position:0%
+genome and so first you assemble you
+piece together those large genome
+
+ align:start position:0%
+piece together those large genome
+ 
+
+ align:start position:0%
+piece together those large genome
+fragments that are present in the backs
+
+ align:start position:0%
+fragments that are present in the backs
+ 
+
+ align:start position:0%
+fragments that are present in the backs
+and then finally you piece together the
+
+ align:start position:0%
+and then finally you piece together the
+ 
+
+ align:start position:0%
+and then finally you piece together the
+entire genome um from those large
+
+ align:start position:0%
+entire genome um from those large
+ 
+
+ align:start position:0%
+entire genome um from those large
+sequence pieces and you get a so-called
+
+ align:start position:0%
+sequence pieces and you get a so-called
+ 
+
+ align:start position:0%
+sequence pieces and you get a so-called
+draft genome sequence
+
+ align:start position:0%
+draft genome sequence
+ 
+
+ align:start position:0%
+draft genome sequence
+the next step in this analysis then is
+
+ align:start position:0%
+the next step in this analysis then is
+ 
+
+ align:start position:0%
+the next step in this analysis then is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um do so-called genome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anotation and the first very important
+
+ align:start position:0%
+anotation and the first very important
+ 
+
+ align:start position:0%
+anotation and the first very important
+step is that you translate the um Gene
+
+ align:start position:0%
+step is that you translate the um Gene
+ 
+
+ align:start position:0%
+step is that you translate the um Gene
+sequences into Amino
+
+ align:start position:0%
+sequences into Amino
+ 
+
+ align:start position:0%
+sequences into Amino
+acids so the nucleotide sequence is into
+
+ align:start position:0%
+acids so the nucleotide sequence is into
+ 
+
+ align:start position:0%
+acids so the nucleotide sequence is into
+amino acids particularly in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+procaryotes this step can be done um
+
+ align:start position:0%
+procaryotes this step can be done um
+ 
+
+ align:start position:0%
+procaryotes this step can be done um
+right away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what this allows you to do is you
+
+ align:start position:0%
+and what this allows you to do is you
+ 
+
+ align:start position:0%
+and what this allows you to do is you
+can look for um what we call open
+
+ align:start position:0%
+can look for um what we call open
+ 
+
+ align:start position:0%
+can look for um what we call open
+reading frames or
+
+ align:start position:0%
+reading frames or
+ 
+
+ align:start position:0%
+reading frames or
+ORS and what you look for is a start
+
+ align:start position:0%
+ORS and what you look for is a start
+ 
+
+ align:start position:0%
+ORS and what you look for is a start
+codon and a stop codon that basically
+
+ align:start position:0%
+codon and a stop codon that basically
+ 
+
+ align:start position:0%
+codon and a stop codon that basically
+branches um or frames a stretch of amino
+
+ align:start position:0%
+branches um or frames a stretch of amino
+ 
+
+ align:start position:0%
+branches um or frames a stretch of amino
+acids encoded by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleotides so you
+
+ align:start position:0%
+nucleotides so you
+ 
+
+ align:start position:0%
+nucleotides so you
+look for ORS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these are your putative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes The Next Step that you can do then
+
+ align:start position:0%
+genes The Next Step that you can do then
+ 
+
+ align:start position:0%
+genes The Next Step that you can do then
+is that you go to databases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now you compare your ORS to
+
+ align:start position:0%
+and now you compare your ORS to
+ 
+
+ align:start position:0%
+and now you compare your ORS to
+information that is present in the
+
+ align:start position:0%
+information that is present in the
+ 
+
+ align:start position:0%
+information that is present in the
+databases so basically you inquire the
+
+ align:start position:0%
+databases so basically you inquire the
+ 
+
+ align:start position:0%
+databases so basically you inquire the
+database uh and ask is a gene sequence
+
+ align:start position:0%
+database uh and ask is a gene sequence
+ 
+
+ align:start position:0%
+database uh and ask is a gene sequence
+that is similar to the one that I have
+
+ align:start position:0%
+that is similar to the one that I have
+ 
+
+ align:start position:0%
+that is similar to the one that I have
+statistically significantly similar
+
+ align:start position:0%
+statistically significantly similar
+ 
+
+ align:start position:0%
+statistically significantly similar
+present that allows me to say something
+
+ align:start position:0%
+present that allows me to say something
+ 
+
+ align:start position:0%
+present that allows me to say something
+about the function of this particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gene so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identified by comparison with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+databases that's
+
+ align:start position:0%
+databases that's
+ 
+
+ align:start position:0%
+databases that's
+the any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so and that allows you
+
+ align:start position:0%
+questions okay so and that allows you
+ 
+
+ align:start position:0%
+questions okay so and that allows you
+then basically to um say something uh
+
+ align:start position:0%
+then basically to um say something uh
+ 
+
+ align:start position:0%
+then basically to um say something uh
+about the different genes that are that
+
+ align:start position:0%
+about the different genes that are that
+ 
+
+ align:start position:0%
+about the different genes that are that
+you have found in a genome but to give
+
+ align:start position:0%
+you have found in a genome but to give
+ 
+
+ align:start position:0%
+you have found in a genome but to give
+you an impression of how new this field
+
+ align:start position:0%
+you an impression of how new this field
+ 
+
+ align:start position:0%
+you an impression of how new this field
+really is and how little we still know
+
+ align:start position:0%
+really is and how little we still know
+ 
+
+ align:start position:0%
+really is and how little we still know
+about the diversity of genes in
+
+ align:start position:0%
+about the diversity of genes in
+ 
+
+ align:start position:0%
+about the diversity of genes in
+organisms on average when we sequence a
+
+ align:start position:0%
+organisms on average when we sequence a
+ 
+
+ align:start position:0%
+organisms on average when we sequence a
+new bacterial genome we find about 30%
+
+ align:start position:0%
+new bacterial genome we find about 30%
+ 
+
+ align:start position:0%
+new bacterial genome we find about 30%
+of the genes so a third of the genes
+
+ align:start position:0%
+of the genes so a third of the genes
+ 
+
+ align:start position:0%
+of the genes so a third of the genes
+have no known functional analog in the
+
+ align:start position:0%
+have no known functional analog in the
+ 
+
+ align:start position:0%
+have no known functional analog in the
+databases okay so there's a lot to learn
+
+ align:start position:0%
+databases okay so there's a lot to learn
+ 
+
+ align:start position:0%
+databases okay so there's a lot to learn
+about the diversity of life and about
+
+ align:start position:0%
+about the diversity of life and about
+ 
+
+ align:start position:0%
+about the diversity of life and about
+the functional diversity of life
+
+ align:start position:0%
+the functional diversity of life
+ 
+
+ align:start position:0%
+the functional diversity of life
+okay in UK carots there's a little twist
+
+ align:start position:0%
+okay in UK carots there's a little twist
+ 
+
+ align:start position:0%
+okay in UK carots there's a little twist
+as you all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know and basically that is that genes of
+
+ align:start position:0%
+know and basically that is that genes of
+ 
+
+ align:start position:0%
+know and basically that is that genes of
+course consist of introns and exons
+
+ align:start position:0%
+course consist of introns and exons
+ 
+
+ align:start position:0%
+course consist of introns and exons
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so it's basically relatively
+
+ align:start position:0%
+and so it's basically relatively
+ 
+
+ align:start position:0%
+and so it's basically relatively
+difficult to directly identify those
+
+ align:start position:0%
+difficult to directly identify those
+ 
+
+ align:start position:0%
+difficult to directly identify those
+open reading
+
+ align:start position:0%
+open reading
+ 
+
+ align:start position:0%
+open reading
+frames and what you have to do is that
+
+ align:start position:0%
+frames and what you have to do is that
+ 
+
+ align:start position:0%
+frames and what you have to do is that
+you have to actually often times so
+
+ align:start position:0%
+you have to actually often times so
+ 
+
+ align:start position:0%
+you have to actually often times so
+let's write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down and what people often times do then
+
+ align:start position:0%
+down and what people often times do then
+ 
+
+ align:start position:0%
+down and what people often times do then
+is that that they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+search for matching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequences in so-called cdna
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+libraries now what are cdna libraries
+
+ align:start position:0%
+libraries now what are cdna libraries
+ 
+
+ align:start position:0%
+libraries now what are cdna libraries
+let me just show you this on the next
+
+ align:start position:0%
+let me just show you this on the next
+ 
+
+ align:start position:0%
+let me just show you this on the next
+slide skip this
+
+ align:start position:0%
+slide skip this
+ 
+
+ align:start position:0%
+slide skip this
+basically what you can do is you can
+
+ align:start position:0%
+basically what you can do is you can
+ 
+
+ align:start position:0%
+basically what you can do is you can
+isolate messenger RNA from cells and
+
+ align:start position:0%
+isolate messenger RNA from cells and
+ 
+
+ align:start position:0%
+isolate messenger RNA from cells and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+translate this messenger RNA by a
+
+ align:start position:0%
+translate this messenger RNA by a
+ 
+
+ align:start position:0%
+translate this messenger RNA by a
+process called reverse transcription
+
+ align:start position:0%
+process called reverse transcription
+ 
+
+ align:start position:0%
+process called reverse transcription
+that's a viral enzyme that translates
+
+ align:start position:0%
+that's a viral enzyme that translates
+ 
+
+ align:start position:0%
+that's a viral enzyme that translates
+RNA into DNA so you can translate it
+
+ align:start position:0%
+RNA into DNA so you can translate it
+ 
+
+ align:start position:0%
+RNA into DNA so you can translate it
+into DNA fragments and you can then
+
+ align:start position:0%
+into DNA fragments and you can then
+ 
+
+ align:start position:0%
+into DNA fragments and you can then
+clone those DNA fragments into plasmids
+
+ align:start position:0%
+clone those DNA fragments into plasmids
+ 
+
+ align:start position:0%
+clone those DNA fragments into plasmids
+sequence those and then basically see
+
+ align:start position:0%
+sequence those and then basically see
+ 
+
+ align:start position:0%
+sequence those and then basically see
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+are the pieces that are actually um what
+
+ align:start position:0%
+are the pieces that are actually um what
+ 
+
+ align:start position:0%
+are the pieces that are actually um what
+are the inance in the genes what are the
+
+ align:start position:0%
+are the inance in the genes what are the
+ 
+
+ align:start position:0%
+are the inance in the genes what are the
+pieces that are excised um when the
+
+ align:start position:0%
+pieces that are excised um when the
+ 
+
+ align:start position:0%
+pieces that are excised um when the
+messenger RNA is actually created uh
+
+ align:start position:0%
+messenger RNA is actually created uh
+ 
+
+ align:start position:0%
+messenger RNA is actually created uh
+from uh the genome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me just cover now a few of the
+
+ align:start position:0%
+so let me just cover now a few of the
+ 
+
+ align:start position:0%
+so let me just cover now a few of the
+major insights that people have come up
+
+ align:start position:0%
+major insights that people have come up
+ 
+
+ align:start position:0%
+major insights that people have come up
+with of course it's a
+
+ align:start position:0%
+with of course it's a
+ 
+
+ align:start position:0%
+with of course it's a
+very uh growing field and a lot of
+
+ align:start position:0%
+very uh growing field and a lot of
+ 
+
+ align:start position:0%
+very uh growing field and a lot of
+excitement is is coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out and I first want to talk about
+
+ align:start position:0%
+out and I first want to talk about
+ 
+
+ align:start position:0%
+out and I first want to talk about
+bacteria and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ARA and then say a few words also about
+
+ align:start position:0%
+ARA and then say a few words also about
+ 
+
+ align:start position:0%
+ARA and then say a few words also about
+ukari or
+
+ align:start position:0%
+ukari or
+ 
+
+ align:start position:0%
+ukari or
+ukaria first of all what we learned
+
+ align:start position:0%
+ukaria first of all what we learned
+ 
+
+ align:start position:0%
+ukaria first of all what we learned
+about bacteria and ARA is that their
+
+ align:start position:0%
+about bacteria and ARA is that their
+ 
+
+ align:start position:0%
+about bacteria and ARA is that their
+genomes are very compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whenever they have pieces of DNA that
+
+ align:start position:0%
+whenever they have pieces of DNA that
+ 
+
+ align:start position:0%
+whenever they have pieces of DNA that
+are not frequently used they're actually
+
+ align:start position:0%
+are not frequently used they're actually
+ 
+
+ align:start position:0%
+are not frequently used they're actually
+lost from The genome okay so they lose
+
+ align:start position:0%
+lost from The genome okay so they lose
+ 
+
+ align:start position:0%
+lost from The genome okay so they lose
+genomes or genes I should say uh
+
+ align:start position:0%
+genomes or genes I should say uh
+ 
+
+ align:start position:0%
+genomes or genes I should say uh
+relatively easily and we can see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this that the genome size excuse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me is correlated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to metabolic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diversity so for
+
+ align:start position:0%
+diversity so for
+ 
+
+ align:start position:0%
+diversity so for
+example with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+microplasma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genitalium and streptococus uh excuse me
+
+ align:start position:0%
+genitalium and streptococus uh excuse me
+ 
+
+ align:start position:0%
+genitalium and streptococus uh excuse me
+strepto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+misis
+
+ align:start position:0%
+misis
+ 
+
+ align:start position:0%
+misis
+celic are two very different bacteria
+
+ align:start position:0%
+celic are two very different bacteria
+ 
+
+ align:start position:0%
+celic are two very different bacteria
+the first one is an obligate
+
+ align:start position:0%
+the first one is an obligate
+ 
+
+ align:start position:0%
+the first one is an obligate
+intracellular parasite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so which means it's actually based
+
+ align:start position:0%
+okay so which means it's actually based
+ 
+
+ align:start position:0%
+okay so which means it's actually based
+in a nutrient solution in the eukariotic
+
+ align:start position:0%
+in a nutrient solution in the eukariotic
+ 
+
+ align:start position:0%
+in a nutrient solution in the eukariotic
+cells that it invades it doesn't have to
+
+ align:start position:0%
+cells that it invades it doesn't have to
+ 
+
+ align:start position:0%
+cells that it invades it doesn't have to
+make amino acids it gets it just from
+
+ align:start position:0%
+make amino acids it gets it just from
+ 
+
+ align:start position:0%
+make amino acids it gets it just from
+the host cell and it turns out it has a
+
+ align:start position:0%
+the host cell and it turns out it has a
+ 
+
+ align:start position:0%
+the host cell and it turns out it has a
+very small
+
+ align:start position:0%
+very small
+ 
+
+ align:start position:0%
+very small
+genome so only
+
+ align:start position:0%
+genome so only
+ 
+
+ align:start position:0%
+genome so only
+.58 megabase pairs so um 580,000 base
+
+ align:start position:0%
+.58 megabase pairs so um 580,000 base
+ 
+
+ align:start position:0%
+.58 megabase pairs so um 580,000 base
+Pairs and only 5177
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes and interestingly actually people
+
+ align:start position:0%
+genes and interestingly actually people
+ 
+
+ align:start position:0%
+genes and interestingly actually people
+are now using this organism to try and
+
+ align:start position:0%
+are now using this organism to try and
+ 
+
+ align:start position:0%
+are now using this organism to try and
+ask well what's the minimum number of
+
+ align:start position:0%
+ask well what's the minimum number of
+ 
+
+ align:start position:0%
+ask well what's the minimum number of
+genes that an organism can actually live
+
+ align:start position:0%
+genes that an organism can actually live
+ 
+
+ align:start position:0%
+genes that an organism can actually live
+with and so they're
+
+ align:start position:0%
+with and so they're
+ 
+
+ align:start position:0%
+with and so they're
+deleting in a stepwise fashion the
+
+ align:start position:0%
+deleting in a stepwise fashion the
+ 
+
+ align:start position:0%
+deleting in a stepwise fashion the
+different genes in this organism and it
+
+ align:start position:0%
+different genes in this organism and it
+ 
+
+ align:start position:0%
+different genes in this organism and it
+turns out that um you need about two to
+
+ align:start position:0%
+turns out that um you need about two to
+ 
+
+ align:start position:0%
+turns out that um you need about two to
+300 genes minimum um in order to uh make
+
+ align:start position:0%
+300 genes minimum um in order to uh make
+ 
+
+ align:start position:0%
+300 genes minimum um in order to uh make
+the things uh to
+
+ align:start position:0%
+the things uh to
+ 
+
+ align:start position:0%
+the things uh to
+survive on the other hand streptomyces
+
+ align:start position:0%
+survive on the other hand streptomyces
+ 
+
+ align:start position:0%
+survive on the other hand streptomyces
+is a soil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bacterium has a very complex lifestyle
+
+ align:start position:0%
+bacterium has a very complex lifestyle
+ 
+
+ align:start position:0%
+bacterium has a very complex lifestyle
+can degrade um a lot of uh environmental
+
+ align:start position:0%
+can degrade um a lot of uh environmental
+ 
+
+ align:start position:0%
+can degrade um a lot of uh environmental
+substrates and it has a very big genome
+
+ align:start position:0%
+substrates and it has a very big genome
+ 
+
+ align:start position:0%
+substrates and it has a very big genome
+one of the biggest bacterial genomes and
+
+ align:start position:0%
+one of the biggest bacterial genomes and
+ 
+
+ align:start position:0%
+one of the biggest bacterial genomes and
+so those two or organisms basically span
+
+ align:start position:0%
+so those two or organisms basically span
+ 
+
+ align:start position:0%
+so those two or organisms basically span
+pretty much the
+
+ align:start position:0%
+pretty much the
+ 
+
+ align:start position:0%
+pretty much the
+um the the range of bacterial genome
+
+ align:start position:0%
+um the the range of bacterial genome
+ 
+
+ align:start position:0%
+um the the range of bacterial genome
+sizes and so it's thought that it has
+
+ align:start position:0%
+sizes and so it's thought that it has
+ 
+
+ align:start position:0%
+sizes and so it's thought that it has
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+7,846
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+okay now we also have have a very large
+
+ align:start position:0%
+okay now we also have have a very large
+ 
+
+ align:start position:0%
+okay now we also have have a very large
+genetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diversity between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+species and typically what you find is
+
+ align:start position:0%
+species and typically what you find is
+ 
+
+ align:start position:0%
+species and typically what you find is
+that roughly 15 to 30% of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unique to a spefic specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+species and that's really because
+
+ align:start position:0%
+species and that's really because
+ 
+
+ align:start position:0%
+species and that's really because
+bacteria and
+
+ align:start position:0%
+bacteria and
+ 
+
+ align:start position:0%
+bacteria and
+ARA have the capability to um affect a
+
+ align:start position:0%
+ARA have the capability to um affect a
+ 
+
+ align:start position:0%
+ARA have the capability to um affect a
+lot of chemical reactions that UK carots
+
+ align:start position:0%
+lot of chemical reactions that UK carots
+ 
+
+ align:start position:0%
+lot of chemical reactions that UK carots
+for example cannot there's about um 20
+
+ align:start position:0%
+for example cannot there's about um 20
+ 
+
+ align:start position:0%
+for example cannot there's about um 20
+million known organic substances organic
+
+ align:start position:0%
+million known organic substances organic
+ 
+
+ align:start position:0%
+million known organic substances organic
+chemicals and almost all of them are
+
+ align:start position:0%
+chemicals and almost all of them are
+ 
+
+ align:start position:0%
+chemicals and almost all of them are
+biodegradable by bacteria okay even the
+
+ align:start position:0%
+biodegradable by bacteria okay even the
+ 
+
+ align:start position:0%
+biodegradable by bacteria okay even the
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+nudist compound uh if it were not
+
+ align:start position:0%
+nudist compound uh if it were not
+ 
+
+ align:start position:0%
+nudist compound uh if it were not
+biodegradable by bacteria would build up
+
+ align:start position:0%
+biodegradable by bacteria would build up
+ 
+
+ align:start position:0%
+biodegradable by bacteria would build up
+in the environment okay so if it just
+
+ align:start position:0%
+in the environment okay so if it just
+ 
+
+ align:start position:0%
+in the environment okay so if it just
+were a co-actor that some organism
+
+ align:start position:0%
+were a co-actor that some organism
+ 
+
+ align:start position:0%
+were a co-actor that some organism
+produces because we have such a long
+
+ align:start position:0%
+produces because we have such a long
+ 
+
+ align:start position:0%
+produces because we have such a long
+period of time of evolution on this
+
+ align:start position:0%
+period of time of evolution on this
+ 
+
+ align:start position:0%
+period of time of evolution on this
+planet um and evolutionary history it
+
+ align:start position:0%
+planet um and evolutionary history it
+ 
+
+ align:start position:0%
+planet um and evolutionary history it
+would you would probably be able to dig
+
+ align:start position:0%
+would you would probably be able to dig
+ 
+
+ align:start position:0%
+would you would probably be able to dig
+it up in your backyard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the other very important and
+
+ align:start position:0%
+one of the other very important and
+ 
+
+ align:start position:0%
+one of the other very important and
+interesting insights that has come out
+
+ align:start position:0%
+interesting insights that has come out
+ 
+
+ align:start position:0%
+interesting insights that has come out
+of comparing
+
+ align:start position:0%
+of comparing
+ 
+
+ align:start position:0%
+of comparing
+genomes of microorganisms is that
+
+ align:start position:0%
+genomes of microorganisms is that
+ 
+
+ align:start position:0%
+genomes of microorganisms is that
+lateral Gene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transfer is a very important process
+
+ align:start position:0%
+transfer is a very important process
+ 
+
+ align:start position:0%
+transfer is a very important process
+amongst microorganisms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what do we mean by a lateral Gene
+
+ align:start position:0%
+now what do we mean by a lateral Gene
+ 
+
+ align:start position:0%
+now what do we mean by a lateral Gene
+transfer it basically means that we find
+
+ align:start position:0%
+transfer it basically means that we find
+ 
+
+ align:start position:0%
+transfer it basically means that we find
+evidence amongst bacterial genomes that
+
+ align:start position:0%
+evidence amongst bacterial genomes that
+ 
+
+ align:start position:0%
+evidence amongst bacterial genomes that
+they have actually taken up genes from
+
+ align:start position:0%
+they have actually taken up genes from
+ 
+
+ align:start position:0%
+they have actually taken up genes from
+completely unrelated
+
+ align:start position:0%
+completely unrelated
+ 
+
+ align:start position:0%
+completely unrelated
+organisms and I just want to show you
+
+ align:start position:0%
+organisms and I just want to show you
+ 
+
+ align:start position:0%
+organisms and I just want to show you
+one example here that of thermatoga Mer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which lives in Hot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Springs this is a very interesting
+
+ align:start position:0%
+Springs this is a very interesting
+ 
+
+ align:start position:0%
+Springs this is a very interesting
+bacterium that can live in hot water of
+
+ align:start position:0%
+bacterium that can live in hot water of
+ 
+
+ align:start position:0%
+bacterium that can live in hot water of
+around 80°
+
+ align:start position:0%
+around 80°
+ 
+
+ align:start position:0%
+around 80°
+C and um um thrives only in those kinds
+
+ align:start position:0%
+C and um um thrives only in those kinds
+ 
+
+ align:start position:0%
+C and um um thrives only in those kinds
+of environments and it coexists there
+
+ align:start position:0%
+of environments and it coexists there
+ 
+
+ align:start position:0%
+of environments and it coexists there
+with many
+
+ align:start position:0%
+with many
+ 
+
+ align:start position:0%
+with many
+ARA and when people sequenced the Genome
+
+ align:start position:0%
+ARA and when people sequenced the Genome
+ 
+
+ align:start position:0%
+ARA and when people sequenced the Genome
+of thermotoga what they found was that
+
+ align:start position:0%
+of thermotoga what they found was that
+ 
+
+ align:start position:0%
+of thermotoga what they found was that
+about 25% of the genes have their
+
+ align:start position:0%
+about 25% of the genes have their
+ 
+
+ align:start position:0%
+about 25% of the genes have their
+closest relatives in archal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genomes so roughly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+25% of genes in thermatoga are
+
+ align:start position:0%
+25% of genes in thermatoga are
+ 
+
+ align:start position:0%
+25% of genes in thermatoga are
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Aral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+origin now how can we actually figure
+
+ align:start position:0%
+origin now how can we actually figure
+ 
+
+ align:start position:0%
+origin now how can we actually figure
+something like that out well the most
+
+ align:start position:0%
+something like that out well the most
+ 
+
+ align:start position:0%
+something like that out well the most
+important technique is again uh
+
+ align:start position:0%
+important technique is again uh
+ 
+
+ align:start position:0%
+important technique is again uh
+philogenetic uh tree construction and so
+
+ align:start position:0%
+philogenetic uh tree construction and so
+ 
+
+ align:start position:0%
+philogenetic uh tree construction and so
+when you have for
+
+ align:start position:0%
+when you have for
+ 
+
+ align:start position:0%
+when you have for
+example Gene
+
+ align:start position:0%
+example Gene
+ 
+
+ align:start position:0%
+example Gene
+a well let me draw this actually on a
+
+ align:start position:0%
+a well let me draw this actually on a
+ 
+
+ align:start position:0%
+a well let me draw this actually on a
+new board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're comparing say three
+
+ align:start position:0%
+so you're comparing say three
+ 
+
+ align:start position:0%
+so you're comparing say three
+organisms organism a b and c and you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compare Gene one
+
+ align:start position:0%
+compare Gene one
+ 
+
+ align:start position:0%
+compare Gene one
+with Gene two and you notice that most
+
+ align:start position:0%
+with Gene two and you notice that most
+ 
+
+ align:start position:0%
+with Gene two and you notice that most
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+adhere to this pattern but then every
+
+ align:start position:0%
+adhere to this pattern but then every
+ 
+
+ align:start position:0%
+adhere to this pattern but then every
+now and then there's a gene that gives
+
+ align:start position:0%
+now and then there's a gene that gives
+ 
+
+ align:start position:0%
+now and then there's a gene that gives
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+this type of
+
+ align:start position:0%
+this type of
+ 
+
+ align:start position:0%
+this type of
+pattern what you can then conclude is
+
+ align:start position:0%
+pattern what you can then conclude is
+ 
+
+ align:start position:0%
+pattern what you can then conclude is
+that this Gene C has not co-evolved with
+
+ align:start position:0%
+that this Gene C has not co-evolved with
+ 
+
+ align:start position:0%
+that this Gene C has not co-evolved with
+the other genes in the Genome of these
+
+ align:start position:0%
+the other genes in the Genome of these
+ 
+
+ align:start position:0%
+the other genes in the Genome of these
+organisms but was actually transferred
+
+ align:start position:0%
+organisms but was actually transferred
+ 
+
+ align:start position:0%
+organisms but was actually transferred
+into it from another
+
+ align:start position:0%
+into it from another
+ 
+
+ align:start position:0%
+into it from another
+source and I don't have time to go
+
+ align:start position:0%
+source and I don't have time to go
+ 
+
+ align:start position:0%
+source and I don't have time to go
+actually into the mechanisms um if
+
+ align:start position:0%
+actually into the mechanisms um if
+ 
+
+ align:start position:0%
+actually into the mechanisms um if
+you're interested I teach a a graduate
+
+ align:start position:0%
+you're interested I teach a a graduate
+ 
+
+ align:start position:0%
+you're interested I teach a a graduate
+class um that a lot of undergraduates
+
+ align:start position:0%
+class um that a lot of undergraduates
+ 
+
+ align:start position:0%
+class um that a lot of undergraduates
+actually take in our department
+
+ align:start position:0%
+actually take in our department
+ 
+
+ align:start position:0%
+actually take in our department
+environmental microbiology where we
+
+ align:start position:0%
+environmental microbiology where we
+ 
+
+ align:start position:0%
+environmental microbiology where we
+discuss a lot of the mechanisms it's
+
+ align:start position:0%
+discuss a lot of the mechanisms it's
+ 
+
+ align:start position:0%
+discuss a lot of the mechanisms it's
+basically a lot of viruses can affect
+
+ align:start position:0%
+basically a lot of viruses can affect
+ 
+
+ align:start position:0%
+basically a lot of viruses can affect
+Gene transfer um but also plasmas and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transposons but for bacteria again you
+
+ align:start position:0%
+transposons but for bacteria again you
+ 
+
+ align:start position:0%
+transposons but for bacteria again you
+should remember that new function is
+
+ align:start position:0%
+should remember that new function is
+ 
+
+ align:start position:0%
+should remember that new function is
+actually often times often times arises
+
+ align:start position:0%
+actually often times often times arises
+ 
+
+ align:start position:0%
+actually often times often times arises
+by lateral Gene transfer and one of the
+
+ align:start position:0%
+by lateral Gene transfer and one of the
+ 
+
+ align:start position:0%
+by lateral Gene transfer and one of the
+interesting things is that Lal Gene
+
+ align:start position:0%
+interesting things is that Lal Gene
+ 
+
+ align:start position:0%
+interesting things is that Lal Gene
+transfer is actually very important in
+
+ align:start position:0%
+transfer is actually very important in
+ 
+
+ align:start position:0%
+transfer is actually very important in
+um the evolution of pathogenic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bacteria so the so-called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+virulence genes which are the genes that
+
+ align:start position:0%
+virulence genes which are the genes that
+ 
+
+ align:start position:0%
+virulence genes which are the genes that
+basically um affect
+
+ align:start position:0%
+basically um affect
+ 
+
+ align:start position:0%
+basically um affect
+pathogenesis a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+among pathogenic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bacteria often
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arise bilateral CH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transfer okay
+
+ align:start position:0%
+transfer okay
+ 
+
+ align:start position:0%
+transfer okay
+any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay now for
+
+ align:start position:0%
+questions okay now for
+ 
+
+ align:start position:0%
+questions okay now for
+ukaria I just want to make the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point that their genomes are generally
+
+ align:start position:0%
+point that their genomes are generally
+ 
+
+ align:start position:0%
+point that their genomes are generally
+orders of magnitudes larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+okay and that the exons so the things
+
+ align:start position:0%
+okay and that the exons so the things
+ 
+
+ align:start position:0%
+okay and that the exons so the things
+the stretches that really encode the
+
+ align:start position:0%
+the stretches that really encode the
+ 
+
+ align:start position:0%
+the stretches that really encode the
+protein uh that makes up uh the organism
+
+ align:start position:0%
+protein uh that makes up uh the organism
+ 
+
+ align:start position:0%
+protein uh that makes up uh the organism
+the Exon are typically only
+
+ align:start position:0%
+the Exon are typically only
+ 
+
+ align:start position:0%
+the Exon are typically only
+few
+
+ align:start position:0%
+few
+ 
+
+ align:start position:0%
+few
+perc of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genome that's particularly in higher
+
+ align:start position:0%
+genome that's particularly in higher
+ 
+
+ align:start position:0%
+genome that's particularly in higher
+ukar yeasts for example have a much more
+
+ align:start position:0%
+ukar yeasts for example have a much more
+ 
+
+ align:start position:0%
+ukar yeasts for example have a much more
+compact genome also but um we for
+
+ align:start position:0%
+compact genome also but um we for
+ 
+
+ align:start position:0%
+compact genome also but um we for
+example are full of DNA that people
+
+ align:start position:0%
+example are full of DNA that people
+ 
+
+ align:start position:0%
+example are full of DNA that people
+still have a very hard time figuring out
+
+ align:start position:0%
+still have a very hard time figuring out
+ 
+
+ align:start position:0%
+still have a very hard time figuring out
+what it actually does but it seems that
+
+ align:start position:0%
+what it actually does but it seems that
+ 
+
+ align:start position:0%
+what it actually does but it seems that
+the majority of the genome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soal repeated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequences many of which seem to be
+
+ align:start position:0%
+sequences many of which seem to be
+ 
+
+ align:start position:0%
+sequences many of which seem to be
+ancient retroviruses that have inserted
+
+ align:start position:0%
+ancient retroviruses that have inserted
+ 
+
+ align:start position:0%
+ancient retroviruses that have inserted
+themselves into the genome and have
+
+ align:start position:0%
+themselves into the genome and have
+ 
+
+ align:start position:0%
+themselves into the genome and have
+since then lost actually their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function okay so in the remaining time I
+
+ align:start position:0%
+function okay so in the remaining time I
+ 
+
+ align:start position:0%
+function okay so in the remaining time I
+want to just give you an example of um
+
+ align:start position:0%
+want to just give you an example of um
+ 
+
+ align:start position:0%
+want to just give you an example of um
+how we now can use these techniques that
+
+ align:start position:0%
+how we now can use these techniques that
+ 
+
+ align:start position:0%
+how we now can use these techniques that
+are outlined
+
+ align:start position:0%
+are outlined
+ 
+
+ align:start position:0%
+are outlined
+before to learn something
+
+ align:start position:0%
+before to learn something
+ 
+
+ align:start position:0%
+before to learn something
+about microorganisms in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment called Environmental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically um the way this all was
+
+ align:start position:0%
+basically um the way this all was
+ 
+
+ align:start position:0%
+basically um the way this all was
+started was by going into the
+
+ align:start position:0%
+started was by going into the
+ 
+
+ align:start position:0%
+started was by going into the
+environment and extracting nucleic acids
+
+ align:start position:0%
+environment and extracting nucleic acids
+ 
+
+ align:start position:0%
+environment and extracting nucleic acids
+and treating them exactly the same way
+
+ align:start position:0%
+and treating them exactly the same way
+ 
+
+ align:start position:0%
+and treating them exactly the same way
+as if you had a single genome but again
+
+ align:start position:0%
+as if you had a single genome but again
+ 
+
+ align:start position:0%
+as if you had a single genome but again
+remember we have a very large mixture of
+
+ align:start position:0%
+remember we have a very large mixture of
+ 
+
+ align:start position:0%
+remember we have a very large mixture of
+microorganisms present in the
+
+ align:start position:0%
+microorganisms present in the
+ 
+
+ align:start position:0%
+microorganisms present in the
+environment and where this was mostly
+
+ align:start position:0%
+environment and where this was mostly
+ 
+
+ align:start position:0%
+environment and where this was mostly
+done was in the ocean actually and what
+
+ align:start position:0%
+done was in the ocean actually and what
+ 
+
+ align:start position:0%
+done was in the ocean actually and what
+people did was constructed those back
+
+ align:start position:0%
+people did was constructed those back
+ 
+
+ align:start position:0%
+people did was constructed those back
+clones directly from the environment and
+
+ align:start position:0%
+clones directly from the environment and
+ 
+
+ align:start position:0%
+clones directly from the environment and
+then looked amongst those back clones
+
+ align:start position:0%
+then looked amongst those back clones
+ 
+
+ align:start position:0%
+then looked amongst those back clones
+for specific 16s ribosomal RNA genes
+
+ align:start position:0%
+for specific 16s ribosomal RNA genes
+ 
+
+ align:start position:0%
+for specific 16s ribosomal RNA genes
+remember this is the marker that we have
+
+ align:start position:0%
+remember this is the marker that we have
+ 
+
+ align:start position:0%
+remember this is the marker that we have
+for microorganisms in the environment we
+
+ align:start position:0%
+for microorganisms in the environment we
+ 
+
+ align:start position:0%
+for microorganisms in the environment we
+know the diversity of microorganisms
+
+ align:start position:0%
+know the diversity of microorganisms
+ 
+
+ align:start position:0%
+know the diversity of microorganisms
+through those types of genes and we have
+
+ align:start position:0%
+through those types of genes and we have
+ 
+
+ align:start position:0%
+through those types of genes and we have
+a lot of data available and so in order
+
+ align:start position:0%
+a lot of data available and so in order
+ 
+
+ align:start position:0%
+a lot of data available and so in order
+to link a specific function that such an
+
+ align:start position:0%
+to link a specific function that such an
+ 
+
+ align:start position:0%
+to link a specific function that such an
+organism that we only know from the 16 a
+
+ align:start position:0%
+organism that we only know from the 16 a
+ 
+
+ align:start position:0%
+organism that we only know from the 16 a
+ribosomal RNA genes um so to ask the
+
+ align:start position:0%
+ribosomal RNA genes um so to ask the
+ 
+
+ align:start position:0%
+ribosomal RNA genes um so to ask the
+question what sort of function this
+
+ align:start position:0%
+question what sort of function this
+ 
+
+ align:start position:0%
+question what sort of function this
+organism might be carrying out in the
+
+ align:start position:0%
+organism might be carrying out in the
+ 
+
+ align:start position:0%
+organism might be carrying out in the
+environment it's very useful to sequence
+
+ align:start position:0%
+environment it's very useful to sequence
+ 
+
+ align:start position:0%
+environment it's very useful to sequence
+back clones that have 6 s ribosomal RNA
+
+ align:start position:0%
+back clones that have 6 s ribosomal RNA
+ 
+
+ align:start position:0%
+back clones that have 6 s ribosomal RNA
+genes on them and then determine what
+
+ align:start position:0%
+genes on them and then determine what
+ 
+
+ align:start position:0%
+genes on them and then determine what
+kinds of protein coding genes are on
+
+ align:start position:0%
+kinds of protein coding genes are on
+ 
+
+ align:start position:0%
+kinds of protein coding genes are on
+there that might reveal some of the
+
+ align:start position:0%
+there that might reveal some of the
+ 
+
+ align:start position:0%
+there that might reveal some of the
+function of the organism in the
+
+ align:start position:0%
+function of the organism in the
+ 
+
+ align:start position:0%
+function of the organism in the
+environment and one example that I want
+
+ align:start position:0%
+environment and one example that I want
+ 
+
+ align:start position:0%
+environment and one example that I want
+to show you is that um of the proteo
+
+ align:start position:0%
+to show you is that um of the proteo
+ 
+
+ align:start position:0%
+to show you is that um of the proteo
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ropin so basically the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+initial um task was to sequence back
+
+ align:start position:0%
+initial um task was to sequence back
+ 
+
+ align:start position:0%
+initial um task was to sequence back
+clones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+containing ribosomal RNA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes and look for other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes that might reveal some of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function so you don't want to look for
+
+ align:start position:0%
+function so you don't want to look for
+ 
+
+ align:start position:0%
+function so you don't want to look for
+all the genes that encode proteins that
+
+ align:start position:0%
+all the genes that encode proteins that
+ 
+
+ align:start position:0%
+all the genes that encode proteins that
+are important in the cell cycle or
+
+ align:start position:0%
+are important in the cell cycle or
+ 
+
+ align:start position:0%
+are important in the cell cycle or
+things like that but really sort of
+
+ align:start position:0%
+things like that but really sort of
+ 
+
+ align:start position:0%
+things like that but really sort of
+metabolic genes that might tell you
+
+ align:start position:0%
+metabolic genes that might tell you
+ 
+
+ align:start position:0%
+metabolic genes that might tell you
+something about the um type of
+
+ align:start position:0%
+something about the um type of
+ 
+
+ align:start position:0%
+something about the um type of
+metabolism that this organism carries
+
+ align:start position:0%
+metabolism that this organism carries
+ 
+
+ align:start position:0%
+metabolism that this organism carries
+out in the
+
+ align:start position:0%
+out in the
+ 
+
+ align:start position:0%
+out in the
+environment and so what the first
+
+ align:start position:0%
+environment and so what the first
+ 
+
+ align:start position:0%
+environment and so what the first
+example that turned out to be really
+
+ align:start position:0%
+example that turned out to be really
+ 
+
+ align:start position:0%
+example that turned out to be really
+really important was that people found
+
+ align:start position:0%
+really important was that people found
+ 
+
+ align:start position:0%
+really important was that people found
+uh ropin genes on one of those um back
+
+ align:start position:0%
+uh ropin genes on one of those um back
+ 
+
+ align:start position:0%
+uh ropin genes on one of those um back
+fragments and it turns out this ropin
+
+ align:start position:0%
+fragments and it turns out this ropin
+ 
+
+ align:start position:0%
+fragments and it turns out this ropin
+catalyzes or these ropson genes produce
+
+ align:start position:0%
+catalyzes or these ropson genes produce
+ 
+
+ align:start position:0%
+catalyzes or these ropson genes produce
+a protein that inserts itself into the
+
+ align:start position:0%
+a protein that inserts itself into the
+ 
+
+ align:start position:0%
+a protein that inserts itself into the
+bacterial
+
+ align:start position:0%
+bacterial
+ 
+
+ align:start position:0%
+bacterial
+membrane and is a photo receptor the so
+
+ align:start position:0%
+membrane and is a photo receptor the so
+ 
+
+ align:start position:0%
+membrane and is a photo receptor the so
+when it's hit by light it actually
+
+ align:start position:0%
+when it's hit by light it actually
+ 
+
+ align:start position:0%
+when it's hit by light it actually
+affects uh it's an it becomes a proton
+
+ align:start position:0%
+affects uh it's an it becomes a proton
+ 
+
+ align:start position:0%
+affects uh it's an it becomes a proton
+pump so it expels protons from the cell
+
+ align:start position:0%
+pump so it expels protons from the cell
+ 
+
+ align:start position:0%
+pump so it expels protons from the cell
+interior to the outside and you already
+
+ align:start position:0%
+interior to the outside and you already
+ 
+
+ align:start position:0%
+interior to the outside and you already
+know that this is important in energy
+
+ align:start position:0%
+know that this is important in energy
+ 
+
+ align:start position:0%
+know that this is important in energy
+generation in all living cells so proton
+
+ align:start position:0%
+generation in all living cells so proton
+ 
+
+ align:start position:0%
+generation in all living cells so proton
+gradients across membranes basically
+
+ align:start position:0%
+gradients across membranes basically
+ 
+
+ align:start position:0%
+gradients across membranes basically
+give the cells sort of a battery status
+
+ align:start position:0%
+give the cells sort of a battery status
+ 
+
+ align:start position:0%
+give the cells sort of a battery status
+that can be exploited by atpa molecules
+
+ align:start position:0%
+that can be exploited by atpa molecules
+ 
+
+ align:start position:0%
+that can be exploited by atpa molecules
+or atpa proteins that equalize the
+
+ align:start position:0%
+or atpa proteins that equalize the
+ 
+
+ align:start position:0%
+or atpa proteins that equalize the
+proton gradient and affect ATP synthesis
+
+ align:start position:0%
+proton gradient and affect ATP synthesis
+ 
+
+ align:start position:0%
+proton gradient and affect ATP synthesis
+in doing
+
+ align:start position:0%
+in doing
+ 
+
+ align:start position:0%
+in doing
+so now why is this so important well it
+
+ align:start position:0%
+so now why is this so important well it
+ 
+
+ align:start position:0%
+so now why is this so important well it
+turned out that this type of protein is
+
+ align:start position:0%
+turned out that this type of protein is
+ 
+
+ align:start position:0%
+turned out that this type of protein is
+present in almost all microbial cells
+
+ align:start position:0%
+present in almost all microbial cells
+ 
+
+ align:start position:0%
+present in almost all microbial cells
+that were previously thought to be
+
+ align:start position:0%
+that were previously thought to be
+ 
+
+ align:start position:0%
+that were previously thought to be
+heterotrophs alone in the ocean in the
+
+ align:start position:0%
+heterotrophs alone in the ocean in the
+ 
+
+ align:start position:0%
+heterotrophs alone in the ocean in the
+in the parts of the ocean that uh
+
+ align:start position:0%
+in the parts of the ocean that uh
+ 
+
+ align:start position:0%
+in the parts of the ocean that uh
+receive enough light and what this means
+
+ align:start position:0%
+receive enough light and what this means
+ 
+
+ align:start position:0%
+receive enough light and what this means
+is that our estimates of the global
+
+ align:start position:0%
+is that our estimates of the global
+ 
+
+ align:start position:0%
+is that our estimates of the global
+carbon budget of the ocean were
+
+ align:start position:0%
+carbon budget of the ocean were
+ 
+
+ align:start position:0%
+carbon budget of the ocean were
+basically wrong okay because most
+
+ align:start position:0%
+basically wrong okay because most
+ 
+
+ align:start position:0%
+basically wrong okay because most
+microorganisms in the ocean have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+procaryotes in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocean have a light
+
+ align:start position:0%
+ocean have a light
+ 
+
+ align:start position:0%
+ocean have a light
+driven proton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pump which is called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proteo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ropin and it basically allows them
+
+ align:start position:0%
+ropin and it basically allows them
+ 
+
+ align:start position:0%
+ropin and it basically allows them
+um to gain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy from sunlight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's an increasing number of such
+
+ align:start position:0%
+and there's an increasing number of such
+ 
+
+ align:start position:0%
+and there's an increasing number of such
+examples now where we we're really
+
+ align:start position:0%
+examples now where we we're really
+ 
+
+ align:start position:0%
+examples now where we we're really
+learning to interpret um environmental
+
+ align:start position:0%
+learning to interpret um environmental
+ 
+
+ align:start position:0%
+learning to interpret um environmental
+uh communities and Environ the function
+
+ align:start position:0%
+uh communities and Environ the function
+ 
+
+ align:start position:0%
+uh communities and Environ the function
+of environmental microbial communities
+
+ align:start position:0%
+of environmental microbial communities
+ 
+
+ align:start position:0%
+of environmental microbial communities
+through those genomic approaches and it
+
+ align:start position:0%
+through those genomic approaches and it
+ 
+
+ align:start position:0%
+through those genomic approaches and it
+reveals um
+
+ align:start position:0%
+reveals um
+ 
+
+ align:start position:0%
+reveals um
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+uh an enormous diversity of organisms
+
+ align:start position:0%
+uh an enormous diversity of organisms
+ 
+
+ align:start position:0%
+uh an enormous diversity of organisms
+out there what we're also learning to do
+
+ align:start position:0%
+out there what we're also learning to do
+ 
+
+ align:start position:0%
+out there what we're also learning to do
+now is to assemble entire genomes from
+
+ align:start position:0%
+now is to assemble entire genomes from
+ 
+
+ align:start position:0%
+now is to assemble entire genomes from
+those samples by applying um genomic
+
+ align:start position:0%
+those samples by applying um genomic
+ 
+
+ align:start position:0%
+those samples by applying um genomic
+techniques and this is an example here
+
+ align:start position:0%
+techniques and this is an example here
+ 
+
+ align:start position:0%
+techniques and this is an example here
+where you see uh this was published last
+
+ align:start position:0%
+where you see uh this was published last
+ 
+
+ align:start position:0%
+where you see uh this was published last
+year where people went out and basically
+
+ align:start position:0%
+year where people went out and basically
+ 
+
+ align:start position:0%
+year where people went out and basically
+were able to piece together from pieces
+
+ align:start position:0%
+were able to piece together from pieces
+ 
+
+ align:start position:0%
+were able to piece together from pieces
+of genes obtained from the environment
+
+ align:start position:0%
+of genes obtained from the environment
+ 
+
+ align:start position:0%
+of genes obtained from the environment
+entire genomes or fragments of entire
+
+ align:start position:0%
+entire genomes or fragments of entire
+ 
+
+ align:start position:0%
+entire genomes or fragments of entire
+genomes and that's shown here um those
+
+ align:start position:0%
+genomes and that's shown here um those
+ 
+
+ align:start position:0%
+genomes and that's shown here um those
+contigous
+
+ align:start position:0%
+contigous
+ 
+
+ align:start position:0%
+contigous
+sequences okay so and if you have any
+
+ align:start position:0%
+sequences okay so and if you have any
+ 
+
+ align:start position:0%
+sequences okay so and if you have any
+questions let me know via email or um if
+
+ align:start position:0%
+questions let me know via email or um if
+ 
+
+ align:start position:0%
+questions let me know via email or um if
+you're interested in pursuing this
+
+ align:start position:0%
+you're interested in pursuing this
+ 
+
+ align:start position:0%
+you're interested in pursuing this
+further uh I also teach another class in
+
+ align:start position:0%
+further uh I also teach another class in
+ 
+
+ align:start position:0%
+further uh I also teach another class in
+civil environmental engineering
\ No newline at end of file
diff --git a/OYcdw5vOgIc.txt b/OYcdw5vOgIc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2650172b6bad120810b42b0f2f86152adef5a93a
--- /dev/null
+++ b/OYcdw5vOgIc.txt
@@ -0,0 +1,13939 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencare at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so let's continue uh talking about
+
+ align:start position:0%
+so let's continue uh talking about
+ 
+
+ align:start position:0%
+so let's continue uh talking about
+maximum likelihood estimation in the
+
+ align:start position:0%
+maximum likelihood estimation in the
+ 
+
+ align:start position:0%
+maximum likelihood estimation in the
+context of generalized linear Models All
+
+ align:start position:0%
+context of generalized linear Models All
+ 
+
+ align:start position:0%
+context of generalized linear Models All
+right so in those generalized linear
+
+ align:start position:0%
+right so in those generalized linear
+ 
+
+ align:start position:0%
+right so in those generalized linear
+models what we spend uh most of the past
+
+ align:start position:0%
+models what we spend uh most of the past
+ 
+
+ align:start position:0%
+models what we spend uh most of the past
+lectures uh working on is the
+
+ align:start position:0%
+lectures uh working on is the
+ 
+
+ align:start position:0%
+lectures uh working on is the
+conditional
+
+ align:start position:0%
+conditional
+ 
+
+ align:start position:0%
+conditional
+distribution of Y sorry of Y given
+
+ align:start position:0%
+distribution of Y sorry of Y given
+ 
+
+ align:start position:0%
+distribution of Y sorry of Y given
+X and we're going to assume that this uh
+
+ align:start position:0%
+X and we're going to assume that this uh
+ 
+
+ align:start position:0%
+X and we're going to assume that this uh
+follow some
+
+ align:start position:0%
+follow some
+ 
+
+ align:start position:0%
+follow some
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution in the exponential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+family okay and so what it means is that
+
+ align:start position:0%
+family okay and so what it means is that
+ 
+
+ align:start position:0%
+family okay and so what it means is that
+if I look at the uh the density say or
+
+ align:start position:0%
+if I look at the uh the density say or
+ 
+
+ align:start position:0%
+if I look at the uh the density say or
+the pmf but uh let's talk about
+
+ align:start position:0%
+the pmf but uh let's talk about
+ 
+
+ align:start position:0%
+the pmf but uh let's talk about
+densities to make things clear we're
+
+ align:start position:0%
+densities to make things clear we're
+ 
+
+ align:start position:0%
+densities to make things clear we're
+going to assume that uh y given f x as
+
+ align:start position:0%
+going to assume that uh y given f x as
+ 
+
+ align:start position:0%
+going to assume that uh y given f x as
+distribution so X is now fixed because
+
+ align:start position:0%
+distribution so X is now fixed because
+ 
+
+ align:start position:0%
+distribution so X is now fixed because
+we're conditioning on it and it has a
+
+ align:start position:0%
+we're conditioning on it and it has a
+ 
+
+ align:start position:0%
+we're conditioning on it and it has a
+density which is of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form C of y
+
+ align:start position:0%
+form C of y
+ 
+
+ align:start position:0%
+form C of y
+i okay so the C again we don't really
+
+ align:start position:0%
+i okay so the C again we don't really
+ 
+
+ align:start position:0%
+i okay so the C again we don't really
+need to think about it this is something
+
+ align:start position:0%
+need to think about it this is something
+ 
+
+ align:start position:0%
+need to think about it this is something
+that's going to come out naturally as
+
+ align:start position:0%
+that's going to come out naturally as
+ 
+
+ align:start position:0%
+that's going to come out naturally as
+soon as you need a normalization factor
+
+ align:start position:0%
+soon as you need a normalization factor
+ 
+
+ align:start position:0%
+soon as you need a normalization factor
+and so here what it means so if this is
+
+ align:start position:0%
+and so here what it means so if this is
+ 
+
+ align:start position:0%
+and so here what it means so if this is
+the distribution of Y given x i so
+
+ align:start position:0%
+the distribution of Y given x i so
+ 
+
+ align:start position:0%
+the distribution of Y given x i so
+that's the density of
+
+ align:start position:0%
+that's the density of
+ 
+
+ align:start position:0%
+that's the density of
+y i given x i is equal to Little X I so
+
+ align:start position:0%
+y i given x i is equal to Little X I so
+ 
+
+ align:start position:0%
+y i given x i is equal to Little X I so
+if it's the conditional distribution of
+
+ align:start position:0%
+if it's the conditional distribution of
+ 
+
+ align:start position:0%
+if it's the conditional distribution of
+Yi given x i it should depend on XI
+
+ align:start position:0%
+Yi given x i it should depend on XI
+ 
+
+ align:start position:0%
+Yi given x i it should depend on XI
+somehow and it does not appear to depend
+
+ align:start position:0%
+somehow and it does not appear to depend
+ 
+
+ align:start position:0%
+somehow and it does not appear to depend
+on XI and here the model is going to be
+
+ align:start position:0%
+on XI and here the model is going to be
+ 
+
+ align:start position:0%
+on XI and here the model is going to be
+on Theta I which is just a function
+
+ align:start position:0%
+on Theta I which is just a function
+ 
+
+ align:start position:0%
+on Theta I which is just a function
+Theta I of x i and we're going to make a
+
+ align:start position:0%
+Theta I of x i and we're going to make a
+ 
+
+ align:start position:0%
+Theta I of x i and we're going to make a
+very specific one it's going to be a
+
+ align:start position:0%
+very specific one it's going to be a
+ 
+
+ align:start position:0%
+very specific one it's going to be a
+function of a linear uh uh uh a linear
+
+ align:start position:0%
+function of a linear uh uh uh a linear
+ 
+
+ align:start position:0%
+function of a linear uh uh uh a linear
+uh um form of the XI so really we're
+
+ align:start position:0%
+uh um form of the XI so really we're
+ 
+
+ align:start position:0%
+uh um form of the XI so really we're
+going to take something which is of the
+
+ align:start position:0%
+going to take something which is of the
+ 
+
+ align:start position:0%
+going to take something which is of the
+form Theta I which is really just this
+
+ align:start position:0%
+form Theta I which is really just this
+ 
+
+ align:start position:0%
+form Theta I which is really just this
+Theta does not depend on XI of XI
+
+ align:start position:0%
+Theta does not depend on XI of XI
+ 
+
+ align:start position:0%
+Theta does not depend on XI of XI
+transpose some beta okay so all these
+
+ align:start position:0%
+transpose some beta okay so all these
+ 
+
+ align:start position:0%
+transpose some beta okay so all these
+parts here this is really some modeling
+
+ align:start position:0%
+parts here this is really some modeling
+ 
+
+ align:start position:0%
+parts here this is really some modeling
+assumptions that we're
+
+ align:start position:0%
+assumptions that we're
+ 
+
+ align:start position:0%
+assumptions that we're
+making once we've agreed on what
+
+ align:start position:0%
+making once we've agreed on what
+ 
+
+ align:start position:0%
+making once we've agreed on what
+distribution we want okay so to do that
+
+ align:start position:0%
+distribution we want okay so to do that
+ 
+
+ align:start position:0%
+distribution we want okay so to do that
+so our goal of course is going to try to
+
+ align:start position:0%
+so our goal of course is going to try to
+ 
+
+ align:start position:0%
+so our goal of course is going to try to
+understand understand what this beta is
+
+ align:start position:0%
+understand understand what this beta is
+ 
+
+ align:start position:0%
+understand understand what this beta is
+there's one beta here what's important
+
+ align:start position:0%
+there's one beta here what's important
+ 
+
+ align:start position:0%
+there's one beta here what's important
+is that this beta does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+depend on I so if I observe pairs x i y
+
+ align:start position:0%
+depend on I so if I observe pairs x i y
+ 
+
+ align:start position:0%
+depend on I so if I observe pairs x i y
+i let's say I observe n of them IAL 1 to
+
+ align:start position:0%
+i let's say I observe n of them IAL 1 to
+ 
+
+ align:start position:0%
+i let's say I observe n of them IAL 1 to
+n The Hope is that as I accumulate more
+
+ align:start position:0%
+n The Hope is that as I accumulate more
+ 
+
+ align:start position:0%
+n The Hope is that as I accumulate more
+and more pairs of this form where
+
+ align:start position:0%
+and more pairs of this form where
+ 
+
+ align:start position:0%
+and more pairs of this form where
+there's always the same parameter that
+
+ align:start position:0%
+there's always the same parameter that
+ 
+
+ align:start position:0%
+there's always the same parameter that
+links XI to Yi that's this parameter
+
+ align:start position:0%
+links XI to Yi that's this parameter
+ 
+
+ align:start position:0%
+links XI to Yi that's this parameter
+beta then I should have a better and
+
+ align:start position:0%
+beta then I should have a better and
+ 
+
+ align:start position:0%
+beta then I should have a better and
+better estimation of this beta because
+
+ align:start position:0%
+better estimation of this beta because
+ 
+
+ align:start position:0%
+better estimation of this beta because
+it's always the same and that's
+
+ align:start position:0%
+it's always the same and that's
+ 
+
+ align:start position:0%
+it's always the same and that's
+essentially what couples all of our
+
+ align:start position:0%
+essentially what couples all of our
+ 
+
+ align:start position:0%
+essentially what couples all of our
+distribution if I did not assume this
+
+ align:start position:0%
+distribution if I did not assume this
+ 
+
+ align:start position:0%
+distribution if I did not assume this
+then I could have a different
+
+ align:start position:0%
+then I could have a different
+ 
+
+ align:start position:0%
+then I could have a different
+distribution for each pair XI given Yi
+
+ align:start position:0%
+distribution for each pair XI given Yi
+ 
+
+ align:start position:0%
+distribution for each pair XI given Yi
+and I would not be able to do any
+
+ align:start position:0%
+and I would not be able to do any
+ 
+
+ align:start position:0%
+and I would not be able to do any
+statistics there would nothing nothing
+
+ align:start position:0%
+statistics there would nothing nothing
+ 
+
+ align:start position:0%
+statistics there would nothing nothing
+would average in the end but here I have
+
+ align:start position:0%
+would average in the end but here I have
+ 
+
+ align:start position:0%
+would average in the end but here I have
+the same beta which means that I can
+
+ align:start position:0%
+the same beta which means that I can
+ 
+
+ align:start position:0%
+the same beta which means that I can
+hope to do statistics and average errors
+
+ align:start position:0%
+hope to do statistics and average errors
+ 
+
+ align:start position:0%
+hope to do statistics and average errors
+Z okay so I'm going to collect so uh
+
+ align:start position:0%
+Z okay so I'm going to collect so uh
+ 
+
+ align:start position:0%
+Z okay so I'm going to collect so uh
+I'll back to this so but as usual in the
+
+ align:start position:0%
+I'll back to this so but as usual in the
+ 
+
+ align:start position:0%
+I'll back to this so but as usual in the
+linear regression model we're going to
+
+ align:start position:0%
+linear regression model we're going to
+ 
+
+ align:start position:0%
+linear regression model we're going to
+collect all our observations Yi so here
+
+ align:start position:0%
+collect all our observations Yi so here
+ 
+
+ align:start position:0%
+collect all our observations Yi so here
+I'm going to assume that they're real
+
+ align:start position:0%
+I'm going to assume that they're real
+ 
+
+ align:start position:0%
+I'm going to assume that they're real
+valued and that my X eyes are val takes
+
+ align:start position:0%
+valued and that my X eyes are val takes
+ 
+
+ align:start position:0%
+valued and that my X eyes are val takes
+value in RP just like in the regression
+
+ align:start position:0%
+value in RP just like in the regression
+ 
+
+ align:start position:0%
+value in RP just like in the regression
+model and I'm going to collect all my y
+
+ align:start position:0%
+model and I'm going to collect all my y
+ 
+
+ align:start position:0%
+model and I'm going to collect all my y
+eyes into one big Vector Y in RN and all
+
+ align:start position:0%
+eyes into one big Vector Y in RN and all
+ 
+
+ align:start position:0%
+eyes into one big Vector Y in RN and all
+my x's into one big Matrix in RN *
+
+ align:start position:0%
+my x's into one big Matrix in RN *
+ 
+
+ align:start position:0%
+my x's into one big Matrix in RN *
+P okay just like for the linear
+
+ align:start position:0%
+P okay just like for the linear
+ 
+
+ align:start position:0%
+P okay just like for the linear
+aggression
+
+ align:start position:0%
+aggression
+ 
+
+ align:start position:0%
+aggression
+model all right
+
+ align:start position:0%
+model all right
+ 
+
+ align:start position:0%
+model all right
+so again what I'm interested in here
+
+ align:start position:0%
+so again what I'm interested in here
+ 
+
+ align:start position:0%
+so again what I'm interested in here
+here is the conditional
+
+ align:start position:0%
+here is the conditional
+ 
+
+ align:start position:0%
+here is the conditional
+distribution of Yi given XI okay and I
+
+ align:start position:0%
+distribution of Yi given XI okay and I
+ 
+
+ align:start position:0%
+distribution of Yi given XI okay and I
+said this is this distribution when
+
+ align:start position:0%
+said this is this distribution when
+ 
+
+ align:start position:0%
+said this is this distribution when
+we're talking about regression I defined
+
+ align:start position:0%
+we're talking about regression I defined
+ 
+
+ align:start position:0%
+we're talking about regression I defined
+last time what the definition of a
+
+ align:start position:0%
+last time what the definition of a
+ 
+
+ align:start position:0%
+last time what the definition of a
+regression function was it's just one
+
+ align:start position:0%
+regression function was it's just one
+ 
+
+ align:start position:0%
+regression function was it's just one
+particular aspect of this conditional
+
+ align:start position:0%
+particular aspect of this conditional
+ 
+
+ align:start position:0%
+particular aspect of this conditional
+distribution is the conditional
+
+ align:start position:0%
+distribution is the conditional
+ 
+
+ align:start position:0%
+distribution is the conditional
+expectation of y i given
+
+ align:start position:0%
+expectation of y i given
+ 
+
+ align:start position:0%
+expectation of y i given
+XI okay and so this conditional
+
+ align:start position:0%
+XI okay and so this conditional
+ 
+
+ align:start position:0%
+XI okay and so this conditional
+expectation I will denote it
+
+ align:start position:0%
+expectation I will denote it
+ 
+
+ align:start position:0%
+expectation I will denote it
+by so if I talk about the conditional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's I'm going to call it say muui
+
+ align:start position:0%
+so that's I'm going to call it say muui
+ 
+
+ align:start position:0%
+so that's I'm going to call it say muui
+which is the conditional expectation of
+
+ align:start position:0%
+which is the conditional expectation of
+ 
+
+ align:start position:0%
+which is the conditional expectation of
+Yi given x i equals some little X I
+
+ align:start position:0%
+Yi given x i equals some little X I
+ 
+
+ align:start position:0%
+Yi given x i equals some little X I
+say you can forget about this part if
+
+ align:start position:0%
+say you can forget about this part if
+ 
+
+ align:start position:0%
+say you can forget about this part if
+you find it confusing it really doesn't
+
+ align:start position:0%
+you find it confusing it really doesn't
+ 
+
+ align:start position:0%
+you find it confusing it really doesn't
+matter it's just so that this is just
+
+ align:start position:0%
+matter it's just so that this is just
+ 
+
+ align:start position:0%
+matter it's just so that this is just
+this means that this is a function of
+
+ align:start position:0%
+this means that this is a function of
+ 
+
+ align:start position:0%
+this means that this is a function of
+little XI but if I only had expectation
+
+ align:start position:0%
+little XI but if I only had expectation
+ 
+
+ align:start position:0%
+little XI but if I only had expectation
+of Yi given big XI this would be just a
+
+ align:start position:0%
+of Yi given big XI this would be just a
+ 
+
+ align:start position:0%
+of Yi given big XI this would be just a
+function of big XI right so it really
+
+ align:start position:0%
+function of big XI right so it really
+ 
+
+ align:start position:0%
+function of big XI right so it really
+doesn't change anything it's just a
+
+ align:start position:0%
+doesn't change anything it's just a
+ 
+
+ align:start position:0%
+doesn't change anything it's just a
+matter of
+
+ align:start position:0%
+matter of
+ 
+
+ align:start position:0%
+matter of
+notation okay so just uh forget about
+
+ align:start position:0%
+notation okay so just uh forget about
+ 
+
+ align:start position:0%
+notation okay so just uh forget about
+this part but uh I'll just uh do it like
+
+ align:start position:0%
+this part but uh I'll just uh do it like
+ 
+
+ align:start position:0%
+this part but uh I'll just uh do it like
+that here okay so this is just the
+
+ align:start position:0%
+that here okay so this is just the
+ 
+
+ align:start position:0%
+that here okay so this is just the
+conditional expectation of y i given XI
+
+ align:start position:0%
+conditional expectation of y i given XI
+ 
+
+ align:start position:0%
+conditional expectation of y i given XI
+all right it just depends on XI so I
+
+ align:start position:0%
+all right it just depends on XI so I
+ 
+
+ align:start position:0%
+all right it just depends on XI so I
+particularly depends on I and so I will
+
+ align:start position:0%
+particularly depends on I and so I will
+ 
+
+ align:start position:0%
+particularly depends on I and so I will
+call it mui but I know that since I'm in
+
+ align:start position:0%
+call it mui but I know that since I'm in
+ 
+
+ align:start position:0%
+call it mui but I know that since I'm in
+a canonical exponential
+
+ align:start position:0%
+a canonical exponential
+ 
+
+ align:start position:0%
+a canonical exponential
+family then I know that mui is actually
+
+ align:start position:0%
+family then I know that mui is actually
+ 
+
+ align:start position:0%
+family then I know that mui is actually
+B Prime of theta I
+
+ align:start position:0%
+B Prime of theta I
+ 
+
+ align:start position:0%
+B Prime of theta I
+okay so there's a onetoone link between
+
+ align:start position:0%
+okay so there's a onetoone link between
+ 
+
+ align:start position:0%
+okay so there's a onetoone link between
+the canonical parameter of my
+
+ align:start position:0%
+the canonical parameter of my
+ 
+
+ align:start position:0%
+the canonical parameter of my
+exponential family and the mean mui the
+
+ align:start position:0%
+exponential family and the mean mui the
+ 
+
+ align:start position:0%
+exponential family and the mean mui the
+conditional
+
+ align:start position:0%
+conditional
+ 
+
+ align:start position:0%
+conditional
+expectation and the modeling assumption
+
+ align:start position:0%
+expectation and the modeling assumption
+ 
+
+ align:start position:0%
+expectation and the modeling assumption
+we're going to make is not directly
+
+ align:start position:0%
+we're going to make is not directly
+ 
+
+ align:start position:0%
+we're going to make is not directly
+that's we remember that was the second
+
+ align:start position:0%
+that's we remember that was the second
+ 
+
+ align:start position:0%
+that's we remember that was the second
+aspect of the generalized linear model
+
+ align:start position:0%
+aspect of the generalized linear model
+ 
+
+ align:start position:0%
+aspect of the generalized linear model
+we're not going to assume that Theta I
+
+ align:start position:0%
+we're not going to assume that Theta I
+ 
+
+ align:start position:0%
+we're not going to assume that Theta I
+itself directly depends on XI we're
+
+ align:start position:0%
+itself directly depends on XI we're
+ 
+
+ align:start position:0%
+itself directly depends on XI we're
+going to assume that mui has a
+
+ align:start position:0%
+going to assume that mui has a
+ 
+
+ align:start position:0%
+going to assume that mui has a
+particular dependence on XI through the
+
+ align:start position:0%
+particular dependence on XI through the
+ 
+
+ align:start position:0%
+particular dependence on XI through the
+link function right so again we're back
+
+ align:start position:0%
+link function right so again we're back
+ 
+
+ align:start position:0%
+link function right so again we're back
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+modeling so we have a link function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G and we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assume that
+
+ align:start position:0%
+assume that
+ 
+
+ align:start position:0%
+assume that
+mui
+
+ align:start position:0%
+mui
+ 
+
+ align:start position:0%
+mui
+depends on
+
+ align:start position:0%
+depends on
+ 
+
+ align:start position:0%
+depends on
+XI as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follows G of mui and remember G all G
+
+ align:start position:0%
+follows G of mui and remember G all G
+ 
+
+ align:start position:0%
+follows G of mui and remember G all G
+does for us is really map the space in
+
+ align:start position:0%
+does for us is really map the space in
+ 
+
+ align:start position:0%
+does for us is really map the space in
+which mui lives which could be just the
+
+ align:start position:0%
+which mui lives which could be just the
+ 
+
+ align:start position:0%
+which mui lives which could be just the
+interval 01 to the entire real line all
+
+ align:start position:0%
+interval 01 to the entire real line all
+ 
+
+ align:start position:0%
+interval 01 to the entire real line all
+right and we're going to assume that
+
+ align:start position:0%
+right and we're going to assume that
+ 
+
+ align:start position:0%
+right and we're going to assume that
+this thing that lives in the real line
+
+ align:start position:0%
+this thing that lives in the real line
+ 
+
+ align:start position:0%
+this thing that lives in the real line
+is just X I transpose beta I should
+
+ align:start position:0%
+is just X I transpose beta I should
+ 
+
+ align:start position:0%
+is just X I transpose beta I should
+maybe put a small One X I transpose beta
+
+ align:start position:0%
+maybe put a small One X I transpose beta
+ 
+
+ align:start position:0%
+maybe put a small One X I transpose beta
+okay so we're making indeed some
+
+ align:start position:0%
+okay so we're making indeed some
+ 
+
+ align:start position:0%
+okay so we're making indeed some
+modeling assumption but compared to uh
+
+ align:start position:0%
+modeling assumption but compared to uh
+ 
+
+ align:start position:0%
+modeling assumption but compared to uh
+in the linear regression model we only
+
+ align:start position:0%
+in the linear regression model we only
+ 
+
+ align:start position:0%
+in the linear regression model we only
+assume that mui was XI transpose beta so
+
+ align:start position:0%
+assume that mui was XI transpose beta so
+ 
+
+ align:start position:0%
+assume that mui was XI transpose beta so
+if you want to make a parallel between
+
+ align:start position:0%
+if you want to make a parallel between
+ 
+
+ align:start position:0%
+if you want to make a parallel between
+generalized linear models and linear
+
+ align:start position:0%
+generalized linear models and linear
+ 
+
+ align:start position:0%
+generalized linear models and linear
+model is just the the only difference is
+
+ align:start position:0%
+model is just the the only difference is
+ 
+
+ align:start position:0%
+model is just the the only difference is
+that g is not the identity necessarily
+
+ align:start position:0%
+that g is not the identity necessarily
+ 
+
+ align:start position:0%
+that g is not the identity necessarily
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+case and all that g does for us is to
+
+ align:start position:0%
+case and all that g does for us is to
+ 
+
+ align:start position:0%
+case and all that g does for us is to
+just make this thing compatible that
+
+ align:start position:0%
+just make this thing compatible that
+ 
+
+ align:start position:0%
+just make this thing compatible that
+those two things on the left and the
+
+ align:start position:0%
+those two things on the left and the
+ 
+
+ align:start position:0%
+those two things on the left and the
+right of this equality live in the same
+
+ align:start position:0%
+right of this equality live in the same
+ 
+
+ align:start position:0%
+right of this equality live in the same
+space so in a way we're not making a
+
+ align:start position:0%
+space so in a way we're not making a
+ 
+
+ align:start position:0%
+space so in a way we're not making a
+much you know bigger leap of faith uh uh
+
+ align:start position:0%
+much you know bigger leap of faith uh uh
+ 
+
+ align:start position:0%
+much you know bigger leap of faith uh uh
+by assuming a linear model the linear
+
+ align:start position:0%
+by assuming a linear model the linear
+ 
+
+ align:start position:0%
+by assuming a linear model the linear
+link is already here we're just making
+
+ align:start position:0%
+link is already here we're just making
+ 
+
+ align:start position:0%
+link is already here we're just making
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+compatible all right and
+
+ align:start position:0%
+compatible all right and
+ 
+
+ align:start position:0%
+compatible all right and
+so uh this is going to be uh what the so
+
+ align:start position:0%
+so uh this is going to be uh what the so
+ 
+
+ align:start position:0%
+so uh this is going to be uh what the so
+it's always the same link function so
+
+ align:start position:0%
+it's always the same link function so
+ 
+
+ align:start position:0%
+it's always the same link function so
+now if I want to uh go back to uh beta
+
+ align:start position:0%
+now if I want to uh go back to uh beta
+ 
+
+ align:start position:0%
+now if I want to uh go back to uh beta
+right because I'm going to want to
+
+ align:start position:0%
+right because I'm going to want to
+ 
+
+ align:start position:0%
+right because I'm going to want to
+express my likelihood right so if I were
+
+ align:start position:0%
+express my likelihood right so if I were
+ 
+
+ align:start position:0%
+express my likelihood right so if I were
+to express my likelihood from this it
+
+ align:start position:0%
+to express my likelihood from this it
+ 
+
+ align:start position:0%
+to express my likelihood from this it
+would just be a function of theta right
+
+ align:start position:0%
+would just be a function of theta right
+ 
+
+ align:start position:0%
+would just be a function of theta right
+and so if I want to maximize my
+
+ align:start position:0%
+and so if I want to maximize my
+ 
+
+ align:start position:0%
+and so if I want to maximize my
+likelihood I don't want to maximize it
+
+ align:start position:0%
+likelihood I don't want to maximize it
+ 
+
+ align:start position:0%
+likelihood I don't want to maximize it
+in Theta I want to maximize it in beta
+
+ align:start position:0%
+in Theta I want to maximize it in beta
+ 
+
+ align:start position:0%
+in Theta I want to maximize it in beta
+so if I can write my density as a
+
+ align:start position:0%
+so if I can write my density as a
+ 
+
+ align:start position:0%
+so if I can write my density as a
+function of beta then I will be able to
+
+ align:start position:0%
+function of beta then I will be able to
+ 
+
+ align:start position:0%
+function of beta then I will be able to
+write my likelihood as a function of
+
+ align:start position:0%
+write my likelihood as a function of
+ 
+
+ align:start position:0%
+write my likelihood as a function of
+beta and then talk about my maximum
+
+ align:start position:0%
+beta and then talk about my maximum
+ 
+
+ align:start position:0%
+beta and then talk about my maximum
+likelihood as the matter and so all I
+
+ align:start position:0%
+likelihood as the matter and so all I
+ 
+
+ align:start position:0%
+likelihood as the matter and so all I
+need to do is to just say okay how do I
+
+ align:start position:0%
+need to do is to just say okay how do I
+ 
+
+ align:start position:0%
+need to do is to just say okay how do I
+replace Theta by what is I know that
+
+ align:start position:0%
+replace Theta by what is I know that
+ 
+
+ align:start position:0%
+replace Theta by what is I know that
+Theta is a function of beta right I
+
+ align:start position:0%
+Theta is a function of beta right I
+ 
+
+ align:start position:0%
+Theta is a function of beta right I
+wrote it
+
+ align:start position:0%
+wrote it
+ 
+
+ align:start position:0%
+wrote it
+here so the question is what what is
+
+ align:start position:0%
+here so the question is what what is
+ 
+
+ align:start position:0%
+here so the question is what what is
+this function and I actually have access
+
+ align:start position:0%
+this function and I actually have access
+ 
+
+ align:start position:0%
+this function and I actually have access
+to all of this so what I know is that
+
+ align:start position:0%
+to all of this so what I know is that
+ 
+
+ align:start position:0%
+to all of this so what I know is that
+Theta right so mu is B Prime of theta
+
+ align:start position:0%
+Theta right so mu is B Prime of theta
+ 
+
+ align:start position:0%
+Theta right so mu is B Prime of theta
+which means that Theta I is B Prime
+
+ align:start position:0%
+which means that Theta I is B Prime
+ 
+
+ align:start position:0%
+which means that Theta I is B Prime
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+mui okay so that's what we got from this
+
+ align:start position:0%
+mui okay so that's what we got from this
+ 
+
+ align:start position:0%
+mui okay so that's what we got from this
+you know derivative of the log
+
+ align:start position:0%
+you know derivative of the log
+ 
+
+ align:start position:0%
+you know derivative of the log
+likelihood equal to zero that gave us
+
+ align:start position:0%
+likelihood equal to zero that gave us
+ 
+
+ align:start position:0%
+likelihood equal to zero that gave us
+this guy I invert it and now I know that
+
+ align:start position:0%
+this guy I invert it and now I know that
+ 
+
+ align:start position:0%
+this guy I invert it and now I know that
+mui is G inverse of x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta so this composition of B Prime
+
+ align:start position:0%
+beta so this composition of B Prime
+ 
+
+ align:start position:0%
+beta so this composition of B Prime
+inverse and G inverse is actually just
+
+ align:start position:0%
+inverse and G inverse is actually just
+ 
+
+ align:start position:0%
+inverse and G inverse is actually just
+the composition of G with B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime everybody's comfortable with this
+
+ align:start position:0%
+Prime everybody's comfortable with this
+ 
+
+ align:start position:0%
+Prime everybody's comfortable with this
+notation the little
+
+ align:start position:0%
+notation the little
+ 
+
+ align:start position:0%
+notation the little
+circle any question about this all right
+
+ align:start position:0%
+circle any question about this all right
+ 
+
+ align:start position:0%
+circle any question about this all right
+just means that I first apply B Prime
+
+ align:start position:0%
+just means that I first apply B Prime
+ 
+
+ align:start position:0%
+just means that I first apply B Prime
+well actually it's the inverse but if I
+
+ align:start position:0%
+well actually it's the inverse but if I
+ 
+
+ align:start position:0%
+well actually it's the inverse but if I
+look at a function G composed with B
+
+ align:start position:0%
+look at a function G composed with B
+ 
+
+ align:start position:0%
+look at a function G composed with B
+Prime I first apply g g b Prime of X is
+
+ align:start position:0%
+Prime I first apply g g b Prime of X is
+ 
+
+ align:start position:0%
+Prime I first apply g g b Prime of X is
+just G of B Prime of
+
+ align:start position:0%
+just G of B Prime of
+ 
+
+ align:start position:0%
+just G of B Prime of
+X okay okay and then I take the inverse
+
+ align:start position:0%
+X okay okay and then I take the inverse
+ 
+
+ align:start position:0%
+X okay okay and then I take the inverse
+of this function which is first take G
+
+ align:start position:0%
+of this function which is first take G
+ 
+
+ align:start position:0%
+of this function which is first take G
+inverse and then take B Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse okay so now I have everywhere I
+
+ align:start position:0%
+inverse okay so now I have everywhere I
+ 
+
+ align:start position:0%
+inverse okay so now I have everywhere I
+saw Theta now I see this function of
+
+ align:start position:0%
+saw Theta now I see this function of
+ 
+
+ align:start position:0%
+saw Theta now I see this function of
+beta so I could technically plug that in
+
+ align:start position:0%
+beta so I could technically plug that in
+ 
+
+ align:start position:0%
+beta so I could technically plug that in
+of course it's a little painful to have
+
+ align:start position:0%
+of course it's a little painful to have
+ 
+
+ align:start position:0%
+of course it's a little painful to have
+to write G Circle beta Prime all the
+
+ align:start position:0%
+to write G Circle beta Prime all the
+ 
+
+ align:start position:0%
+to write G Circle beta Prime all the
+time so I'm going to give this guy name
+
+ align:start position:0%
+time so I'm going to give this guy name
+ 
+
+ align:start position:0%
+time so I'm going to give this guy name
+and uh so you're just going to Define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H which is g b Prime
+
+ align:start position:0%
+H which is g b Prime
+ 
+
+ align:start position:0%
+H which is g b Prime
+inverse so that Theta I is simply h of
+
+ align:start position:0%
+inverse so that Theta I is simply h of
+ 
+
+ align:start position:0%
+inverse so that Theta I is simply h of
+XI transpose
+
+ align:start position:0%
+XI transpose
+ 
+
+ align:start position:0%
+XI transpose
+beta okay I could give it a name you
+
+ align:start position:0%
+beta okay I could give it a name you
+ 
+
+ align:start position:0%
+beta okay I could give it a name you
+know let's call but let's just call it
+
+ align:start position:0%
+know let's call but let's just call it
+ 
+
+ align:start position:0%
+know let's call but let's just call it
+that on the H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function so there's something which is
+
+ align:start position:0%
+function so there's something which is
+ 
+
+ align:start position:0%
+function so there's something which is
+nice about this H function is that
+
+ align:start position:0%
+nice about this H function is that
+ 
+
+ align:start position:0%
+nice about this H function is that
+f g is is the canonical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+link what is the canonical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+link right so it's what is it canonical
+
+ align:start position:0%
+link right so it's what is it canonical
+ 
+
+ align:start position:0%
+link right so it's what is it canonical
+to canonical link is canonical to a
+
+ align:start position:0%
+to canonical link is canonical to a
+ 
+
+ align:start position:0%
+to canonical link is canonical to a
+particular distribution in the canonical
+
+ align:start position:0%
+particular distribution in the canonical
+ 
+
+ align:start position:0%
+particular distribution in the canonical
+exponential family right a canonical
+
+ align:start position:0%
+exponential family right a canonical
+ 
+
+ align:start position:0%
+exponential family right a canonical
+exponential family is completely
+
+ align:start position:0%
+exponential family is completely
+ 
+
+ align:start position:0%
+exponential family is completely
+characterized by the function B which
+
+ align:start position:0%
+characterized by the function B which
+ 
+
+ align:start position:0%
+characterized by the function B which
+means that if if I want to talk about
+
+ align:start position:0%
+means that if if I want to talk about
+ 
+
+ align:start position:0%
+means that if if I want to talk about
+DEC canonical link all I need to tell
+
+ align:start position:0%
+DEC canonical link all I need to tell
+ 
+
+ align:start position:0%
+DEC canonical link all I need to tell
+you is how it depends on
+
+ align:start position:0%
+you is how it depends on
+ 
+
+ align:start position:0%
+you is how it depends on
+B so what is g as a function of
+
+ align:start position:0%
+B so what is g as a function of
+ 
+
+ align:start position:0%
+B so what is g as a function of
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+what B
+
+ align:start position:0%
+what B
+ 
+
+ align:start position:0%
+what B
+inverse B Prime inverse right so this is
+
+ align:start position:0%
+inverse B Prime inverse right so this is
+ 
+
+ align:start position:0%
+inverse B Prime inverse right so this is
+G is equal to B Prime inverse which
+
+ align:start position:0%
+G is equal to B Prime inverse which
+ 
+
+ align:start position:0%
+G is equal to B Prime inverse which
+means that if G is composed with B Prime
+
+ align:start position:0%
+means that if G is composed with B Prime
+ 
+
+ align:start position:0%
+means that if G is composed with B Prime
+that means this is just the identity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so H is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identity so
+
+ align:start position:0%
+identity so
+ 
+
+ align:start position:0%
+identity so
+h of X I transpose beta is simply X I
+
+ align:start position:0%
+h of X I transpose beta is simply X I
+ 
+
+ align:start position:0%
+h of X I transpose beta is simply X I
+transpose beta and it's true that the
+
+ align:start position:0%
+transpose beta and it's true that the
+ 
+
+ align:start position:0%
+transpose beta and it's true that the
+way we introduced the canonical length
+
+ align:start position:0%
+way we introduced the canonical length
+ 
+
+ align:start position:0%
+way we introduced the canonical length
+was just the function for which we model
+
+ align:start position:0%
+was just the function for which we model
+ 
+
+ align:start position:0%
+was just the function for which we model
+directly Theta I as X I transpose beta
+
+ align:start position:0%
+directly Theta I as X I transpose beta
+ 
+
+ align:start position:0%
+directly Theta I as X I transpose beta
+right which is we can read off here
+
+ align:start position:0%
+right which is we can read off here
+ 
+
+ align:start position:0%
+right which is we can read off here
+right so Theta I is simply XI transpose
+
+ align:start position:0%
+right so Theta I is simply XI transpose
+ 
+
+ align:start position:0%
+right so Theta I is simply XI transpose
+beta so now for example if I go back to
+
+ align:start position:0%
+beta so now for example if I go back to
+ 
+
+ align:start position:0%
+beta so now for example if I go back to
+this uh to my log
+
+ align:start position:0%
+this uh to my log
+ 
+
+ align:start position:0%
+this uh to my log
+likelihood uh which I know so if I go
+
+ align:start position:0%
+likelihood uh which I know so if I go
+ 
+
+ align:start position:0%
+likelihood uh which I know so if I go
+back to my log likelihood right so if I
+
+ align:start position:0%
+back to my log likelihood right so if I
+ 
+
+ align:start position:0%
+back to my log likelihood right so if I
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likelihood so the log likelihood is sum
+
+ align:start position:0%
+likelihood so the log likelihood is sum
+ 
+
+ align:start position:0%
+likelihood so the log likelihood is sum
+of the log of the
+
+ align:start position:0%
+of the log of the
+ 
+
+ align:start position:0%
+of the log of the
+densities so it's sum from I = 1 to n of
+
+ align:start position:0%
+densities so it's sum from I = 1 to n of
+ 
+
+ align:start position:0%
+densities so it's sum from I = 1 to n of
+log of
+
+ align:start position:0%
+log of
+ 
+
+ align:start position:0%
+log of
+exponential y i Theta I minus B Theta I
+
+ align:start position:0%
+exponential y i Theta I minus B Theta I
+ 
+
+ align:start position:0%
+exponential y i Theta I minus B Theta I
+/ 5 plus C of y i
+
+ align:start position:0%
+/ 5 plus C of y i
+ 
+
+ align:start position:0%
+/ 5 plus C of y i
+f right so this term that does not
+
+ align:start position:0%
+f right so this term that does not
+ 
+
+ align:start position:0%
+f right so this term that does not
+depend on
+
+ align:start position:0%
+depend on
+ 
+
+ align:start position:0%
+depend on
+Theta so I have two things first of all
+
+ align:start position:0%
+Theta so I have two things first of all
+ 
+
+ align:start position:0%
+Theta so I have two things first of all
+the log and the and the exponential are
+
+ align:start position:0%
+the log and the and the exponential are
+ 
+
+ align:start position:0%
+the log and the and the exponential are
+going to cancel each other and second I
+
+ align:start position:0%
+going to cancel each other and second I
+ 
+
+ align:start position:0%
+going to cancel each other and second I
+actually know that Theta is just a
+
+ align:start position:0%
+actually know that Theta is just a
+ 
+
+ align:start position:0%
+actually know that Theta is just a
+function of B
+
+ align:start position:0%
+function of B
+ 
+
+ align:start position:0%
+function of B
+and it has this form Theta I is H of X I
+
+ align:start position:0%
+and it has this form Theta I is H of X I
+ 
+
+ align:start position:0%
+and it has this form Theta I is H of X I
+transpose beta and that's my modeling
+
+ align:start position:0%
+transpose beta and that's my modeling
+ 
+
+ align:start position:0%
+transpose beta and that's my modeling
+assumption so this is actually equal to
+
+ align:start position:0%
+assumption so this is actually equal to
+ 
+
+ align:start position:0%
+assumption so this is actually equal to
+the sum from I 1 to n of
+
+ align:start position:0%
+the sum from I 1 to n of
+ 
+
+ align:start position:0%
+the sum from I 1 to n of
+Yi and then here I'm going to write h of
+
+ align:start position:0%
+Yi and then here I'm going to write h of
+ 
+
+ align:start position:0%
+Yi and then here I'm going to write h of
+XI transpose beta minus B of H of X I
+
+ align:start position:0%
+XI transpose beta minus B of H of X I
+ 
+
+ align:start position:0%
+XI transpose beta minus B of H of X I
+transpose beta divided by
+
+ align:start position:0%
+transpose beta divided by
+ 
+
+ align:start position:0%
+transpose beta divided by
+F and then I have again this
+
+ align:start position:0%
+F and then I have again this
+ 
+
+ align:start position:0%
+F and then I have again this
+function C of Yi
+
+ align:start position:0%
+function C of Yi
+ 
+
+ align:start position:0%
+function C of Yi
+which again won't matter because when
+
+ align:start position:0%
+which again won't matter because when
+ 
+
+ align:start position:0%
+which again won't matter because when
+I'm going to try to maximize this thing
+
+ align:start position:0%
+I'm going to try to maximize this thing
+ 
+
+ align:start position:0%
+I'm going to try to maximize this thing
+this is just playing the role of a
+
+ align:start position:0%
+this is just playing the role of a
+ 
+
+ align:start position:0%
+this is just playing the role of a
+constant that's Shifting the entire
+
+ align:start position:0%
+constant that's Shifting the entire
+ 
+
+ align:start position:0%
+constant that's Shifting the entire
+function so in particular the org Max is
+
+ align:start position:0%
+function so in particular the org Max is
+ 
+
+ align:start position:0%
+function so in particular the org Max is
+going to be exactly what it was okay so
+
+ align:start position:0%
+going to be exactly what it was okay so
+ 
+
+ align:start position:0%
+going to be exactly what it was okay so
+this thing is really not going to matter
+
+ align:start position:0%
+this thing is really not going to matter
+ 
+
+ align:start position:0%
+this thing is really not going to matter
+for me I'm keeping track of it and
+
+ align:start position:0%
+for me I'm keeping track of it and
+ 
+
+ align:start position:0%
+for me I'm keeping track of it and
+actually if you look here it's
+
+ align:start position:0%
+actually if you look here it's
+ 
+
+ align:start position:0%
+actually if you look here it's
+gone right it's gone because it does not
+
+ align:start position:0%
+gone right it's gone because it does not
+ 
+
+ align:start position:0%
+gone right it's gone because it does not
+matter so let's just pretend it's not
+
+ align:start position:0%
+matter so let's just pretend it's not
+ 
+
+ align:start position:0%
+matter so let's just pretend it's not
+here because it won't matter when I'm
+
+ align:start position:0%
+here because it won't matter when I'm
+ 
+
+ align:start position:0%
+here because it won't matter when I'm
+trying to maximize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lik
+
+ align:start position:0%
+lik
+ 
+
+ align:start position:0%
+lik
+okay well it's here up to a constant
+
+ align:start position:0%
+okay well it's here up to a constant
+ 
+
+ align:start position:0%
+okay well it's here up to a constant
+term it says that's the constant
+
+ align:start position:0%
+term it says that's the constant
+ 
+
+ align:start position:0%
+term it says that's the constant
+term all right any
+
+ align:start position:0%
+term all right any
+ 
+
+ align:start position:0%
+term all right any
+question all I'm doing here is
+
+ align:start position:0%
+question all I'm doing here is
+ 
+
+ align:start position:0%
+question all I'm doing here is
+replacing my likelihood as a function of
+
+ align:start position:0%
+replacing my likelihood as a function of
+ 
+
+ align:start position:0%
+replacing my likelihood as a function of
+theta I so if I had one Theta I per
+
+ align:start position:0%
+theta I so if I had one Theta I per
+ 
+
+ align:start position:0%
+theta I so if I had one Theta I per
+observation again this would not help me
+
+ align:start position:0%
+observation again this would not help me
+ 
+
+ align:start position:0%
+observation again this would not help me
+very much but if I assume that they're
+
+ align:start position:0%
+very much but if I assume that they're
+ 
+
+ align:start position:0%
+very much but if I assume that they're
+all linked together by saying that Theta
+
+ align:start position:0%
+all linked together by saying that Theta
+ 
+
+ align:start position:0%
+all linked together by saying that Theta
+I is of the form XI transpose beta or h
+
+ align:start position:0%
+I is of the form XI transpose beta or h
+ 
+
+ align:start position:0%
+I is of the form XI transpose beta or h
+of XI transpose beta if I'm not using
+
+ align:start position:0%
+of XI transpose beta if I'm not using
+ 
+
+ align:start position:0%
+of XI transpose beta if I'm not using
+the the canonical length then I can hope
+
+ align:start position:0%
+the the canonical length then I can hope
+ 
+
+ align:start position:0%
+the the canonical length then I can hope
+to make some
+
+ align:start position:0%
+to make some
+ 
+
+ align:start position:0%
+to make some
+estimation all right
+
+ align:start position:0%
+estimation all right
+ 
+
+ align:start position:0%
+estimation all right
+so again if I have the canonical link H
+
+ align:start position:0%
+so again if I have the canonical link H
+ 
+
+ align:start position:0%
+so again if I have the canonical link H
+is the identity so I'm left only with y
+
+ align:start position:0%
+is the identity so I'm left only with y
+ 
+
+ align:start position:0%
+is the identity so I'm left only with y
+i time x I transpose beta and then I
+
+ align:start position:0%
+i time x I transpose beta and then I
+ 
+
+ align:start position:0%
+i time x I transpose beta and then I
+have B of XI transpose beta not B
+
+ align:start position:0%
+have B of XI transpose beta not B
+ 
+
+ align:start position:0%
+have B of XI transpose beta not B
+composed with
+
+ align:start position:0%
+composed with
+ 
+
+ align:start position:0%
+composed with
+h because H is the
+
+ align:start position:0%
+h because H is the
+ 
+
+ align:start position:0%
+h because H is the
+identity which is fairly simple right
+
+ align:start position:0%
+identity which is fairly simple right
+ 
+
+ align:start position:0%
+identity which is fairly simple right
+why is it it simple well let's actually
+
+ align:start position:0%
+why is it it simple well let's actually
+ 
+
+ align:start position:0%
+why is it it simple well let's actually
+focus on this guy for one
+
+ align:start position:0%
+focus on this guy for one
+ 
+
+ align:start position:0%
+focus on this guy for one
+second uh so let me write it down so we
+
+ align:start position:0%
+second uh so let me write it down so we
+ 
+
+ align:start position:0%
+second uh so let me write it down so we
+know what we're talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about so we just showed that the log
+
+ align:start position:0%
+about so we just showed that the log
+ 
+
+ align:start position:0%
+about so we just showed that the log
+likelihood when I
+
+ align:start position:0%
+likelihood when I
+ 
+
+ align:start position:0%
+likelihood when I
+use the canonical link so that H is
+
+ align:start position:0%
+use the canonical link so that H is
+ 
+
+ align:start position:0%
+use the canonical link so that H is
+equal to the identity the log likelihood
+
+ align:start position:0%
+equal to the identity the log likelihood
+ 
+
+ align:start position:0%
+equal to the identity the log likelihood
+actually takes the form Ln and it
+
+ align:start position:0%
+actually takes the form Ln and it
+ 
+
+ align:start position:0%
+actually takes the form Ln and it
+depends on a bunch of stuff but let's
+
+ align:start position:0%
+depends on a bunch of stuff but let's
+ 
+
+ align:start position:0%
+depends on a bunch of stuff but let's
+just make it depend only on the
+
+ align:start position:0%
+just make it depend only on the
+ 
+
+ align:start position:0%
+just make it depend only on the
+parameter that we care about which is
+
+ align:start position:0%
+parameter that we care about which is
+ 
+
+ align:start position:0%
+parameter that we care about which is
+beta all right so this is of the form L
+
+ align:start position:0%
+beta all right so this is of the form L
+ 
+
+ align:start position:0%
+beta all right so this is of the form L
+of beta and that's equal to what is the
+
+ align:start position:0%
+of beta and that's equal to what is the
+ 
+
+ align:start position:0%
+of beta and that's equal to what is the
+sum from I = 1 to n of y i x i transpose
+
+ align:start position:0%
+sum from I = 1 to n of y i x i transpose
+ 
+
+ align:start position:0%
+sum from I = 1 to n of y i x i transpose
+beta minus let me put the F here and
+
+ align:start position:0%
+beta minus let me put the F here and
+ 
+
+ align:start position:0%
+beta minus let me put the F here and
+then I'm going to have minus B of X
+
+ align:start position:0%
+then I'm going to have minus B of X
+ 
+
+ align:start position:0%
+then I'm going to have minus B of X
+I transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta okay okay and Fe we know is uh some
+
+ align:start position:0%
+beta okay okay and Fe we know is uh some
+ 
+
+ align:start position:0%
+beta okay okay and Fe we know is uh some
+known positive term so again optimizing
+
+ align:start position:0%
+known positive term so again optimizing
+ 
+
+ align:start position:0%
+known positive term so again optimizing
+a function plus some constant or
+
+ align:start position:0%
+a function plus some constant or
+ 
+
+ align:start position:0%
+a function plus some constant or
+optimizing a function times a constant
+
+ align:start position:0%
+optimizing a function times a constant
+ 
+
+ align:start position:0%
+optimizing a function times a constant
+that's not going to change much either
+
+ align:start position:0%
+that's not going to change much either
+ 
+
+ align:start position:0%
+that's not going to change much either
+so it won't really matter to think about
+
+ align:start position:0%
+so it won't really matter to think about
+ 
+
+ align:start position:0%
+so it won't really matter to think about
+whether this F is here or not but let's
+
+ align:start position:0%
+whether this F is here or not but let's
+ 
+
+ align:start position:0%
+whether this F is here or not but let's
+just think about what this function
+
+ align:start position:0%
+just think about what this function
+ 
+
+ align:start position:0%
+just think about what this function
+looks like all right I'm trying to
+
+ align:start position:0%
+looks like all right I'm trying to
+ 
+
+ align:start position:0%
+looks like all right I'm trying to
+maximize a function I'm trying to
+
+ align:start position:0%
+maximize a function I'm trying to
+ 
+
+ align:start position:0%
+maximize a function I'm trying to
+maximize a log likelihood if it look
+
+ align:start position:0%
+maximize a log likelihood if it look
+ 
+
+ align:start position:0%
+maximize a log likelihood if it look
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this that would be a serious problem but
+
+ align:start position:0%
+this that would be a serious problem but
+ 
+
+ align:start position:0%
+this that would be a serious problem but
+we can do like a basic you know back of
+
+ align:start position:0%
+we can do like a basic you know back of
+ 
+
+ align:start position:0%
+we can do like a basic you know back of
+the envelope uh uh guess of what the
+
+ align:start position:0%
+the envelope uh uh guess of what the
+ 
+
+ align:start position:0%
+the envelope uh uh guess of what the
+variations of this function is this
+
+ align:start position:0%
+variations of this function is this
+ 
+
+ align:start position:0%
+variations of this function is this
+first term here
+
+ align:start position:0%
+first term here
+ 
+
+ align:start position:0%
+first term here
+is in as a function of beta it's what
+
+ align:start position:0%
+is in as a function of beta it's what
+ 
+
+ align:start position:0%
+is in as a function of beta it's what
+kind of function is
+
+ align:start position:0%
+kind of function is
+ 
+
+ align:start position:0%
+kind of function is
+it it's linear right this is just X I
+
+ align:start position:0%
+it it's linear right this is just X I
+ 
+
+ align:start position:0%
+it it's linear right this is just X I
+transpose beta If I multiply beta by two
+
+ align:start position:0%
+transpose beta If I multiply beta by two
+ 
+
+ align:start position:0%
+transpose beta If I multiply beta by two
+I get twice if I add something to Beta
+
+ align:start position:0%
+I get twice if I add something to Beta
+ 
+
+ align:start position:0%
+I get twice if I add something to Beta
+it just gets added so it's a linear
+
+ align:start position:0%
+it just gets added so it's a linear
+ 
+
+ align:start position:0%
+it just gets added so it's a linear
+function of beta and so this thing is
+
+ align:start position:0%
+function of beta and so this thing is
+ 
+
+ align:start position:0%
+function of beta and so this thing is
+both convex and concave in the
+
+ align:start position:0%
+both convex and concave in the
+ 
+
+ align:start position:0%
+both convex and concave in the
+onedimensional case so think about p as
+
+ align:start position:0%
+onedimensional case so think about p as
+ 
+
+ align:start position:0%
+onedimensional case so think about p as
+being one diens that beta is a
+
+ align:start position:0%
+being one diens that beta is a
+ 
+
+ align:start position:0%
+being one diens that beta is a
+onedimensional thing those are just the
+
+ align:start position:0%
+onedimensional thing those are just the
+ 
+
+ align:start position:0%
+onedimensional thing those are just the
+function that look like this right those
+
+ align:start position:0%
+function that look like this right those
+ 
+
+ align:start position:0%
+function that look like this right those
+are linear functions they are both
+
+ align:start position:0%
+are linear functions they are both
+ 
+
+ align:start position:0%
+are linear functions they are both
+convex and
+
+ align:start position:0%
+convex and
+ 
+
+ align:start position:0%
+convex and
+concave so this is not going to matter
+
+ align:start position:0%
+concave so this is not going to matter
+ 
+
+ align:start position:0%
+concave so this is not going to matter
+when it comes to the convexity of My
+
+ align:start position:0%
+when it comes to the convexity of My
+ 
+
+ align:start position:0%
+when it comes to the convexity of My
+overall function because I'm just adding
+
+ align:start position:0%
+overall function because I'm just adding
+ 
+
+ align:start position:0%
+overall function because I'm just adding
+something which is just a line and so if
+
+ align:start position:0%
+something which is just a line and so if
+ 
+
+ align:start position:0%
+something which is just a line and so if
+I started with convex it's going to stay
+
+ align:start position:0%
+I started with convex it's going to stay
+ 
+
+ align:start position:0%
+I started with convex it's going to stay
+convex if I started with concave it's
+
+ align:start position:0%
+convex if I started with concave it's
+ 
+
+ align:start position:0%
+convex if I started with concave it's
+going to stay concave and if I started
+
+ align:start position:0%
+going to stay concave and if I started
+ 
+
+ align:start position:0%
+going to stay concave and if I started
+with something which is both is going to
+
+ align:start position:0%
+with something which is both is going to
+ 
+
+ align:start position:0%
+with something which is both is going to
+stay both meaning neither cannot be both
+
+ align:start position:0%
+stay both meaning neither cannot be both
+ 
+
+ align:start position:0%
+stay both meaning neither cannot be both
+ah yeah so if you're neither conx or
+
+ align:start position:0%
+ah yeah so if you're neither conx or
+ 
+
+ align:start position:0%
+ah yeah so if you're neither conx or
+concave adding this linear so this will
+
+ align:start position:0%
+concave adding this linear so this will
+ 
+
+ align:start position:0%
+concave adding this linear so this will
+not really matter if I want to
+
+ align:start position:0%
+not really matter if I want to
+ 
+
+ align:start position:0%
+not really matter if I want to
+understand what my function looks like I
+
+ align:start position:0%
+understand what my function looks like I
+ 
+
+ align:start position:0%
+understand what my function looks like I
+need to understand what B of XI
+
+ align:start position:0%
+need to understand what B of XI
+ 
+
+ align:start position:0%
+need to understand what B of XI
+transpose beta does again the XI
+
+ align:start position:0%
+transpose beta does again the XI
+ 
+
+ align:start position:0%
+transpose beta does again the XI
+transpose beta no impact it's a linear
+
+ align:start position:0%
+transpose beta no impact it's a linear
+ 
+
+ align:start position:0%
+transpose beta no impact it's a linear
+function in terms of convexity it's not
+
+ align:start position:0%
+function in terms of convexity it's not
+ 
+
+ align:start position:0%
+function in terms of convexity it's not
+going to play any role so I really need
+
+ align:start position:0%
+going to play any role so I really need
+ 
+
+ align:start position:0%
+going to play any role so I really need
+to understand what my function B looks
+
+ align:start position:0%
+to understand what my function B looks
+ 
+
+ align:start position:0%
+to understand what my function B looks
+like what do we know about B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again so we know that b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime of theta is equal to Mu
+
+ align:start position:0%
+Prime of theta is equal to Mu
+ 
+
+ align:start position:0%
+Prime of theta is equal to Mu
+right well you know the mean of um of a
+
+ align:start position:0%
+right well you know the mean of um of a
+ 
+
+ align:start position:0%
+right well you know the mean of um of a
+random variable in the canonical
+
+ align:start position:0%
+random variable in the canonical
+ 
+
+ align:start position:0%
+random variable in the canonical
+exponential family can be a positive or
+
+ align:start position:0%
+exponential family can be a positive or
+ 
+
+ align:start position:0%
+exponential family can be a positive or
+negative number this really does not
+
+ align:start position:0%
+negative number this really does not
+ 
+
+ align:start position:0%
+negative number this really does not
+tell me anything that can be really
+
+ align:start position:0%
+tell me anything that can be really
+ 
+
+ align:start position:0%
+tell me anything that can be really
+anything however if I look at the second
+
+ align:start position:0%
+anything however if I look at the second
+ 
+
+ align:start position:0%
+anything however if I look at the second
+derivative of uh of B I know that this
+
+ align:start position:0%
+derivative of uh of B I know that this
+ 
+
+ align:start position:0%
+derivative of uh of B I know that this
+is what this is the
+
+ align:start position:0%
+is what this is the
+ 
+
+ align:start position:0%
+is what this is the
+variance of Y divided by
+
+ align:start position:0%
+variance of Y divided by
+ 
+
+ align:start position:0%
+variance of Y divided by
+five right that was my dispersion
+
+ align:start position:0%
+five right that was my dispersion
+ 
+
+ align:start position:0%
+five right that was my dispersion
+parameter the variance was equal to 5 *
+
+ align:start position:0%
+parameter the variance was equal to 5 *
+ 
+
+ align:start position:0%
+parameter the variance was equal to 5 *
+B prime prime so we know that if Theta
+
+ align:start position:0%
+B prime prime so we know that if Theta
+ 
+
+ align:start position:0%
+B prime prime so we know that if Theta
+is not degenerate meaning that you know
+
+ align:start position:0%
+is not degenerate meaning that you know
+ 
+
+ align:start position:0%
+is not degenerate meaning that you know
+the density does not take value Infinity
+
+ align:start position:0%
+the density does not take value Infinity
+ 
+
+ align:start position:0%
+the density does not take value Infinity
+at only one point this thing is actually
+
+ align:start position:0%
+at only one point this thing is actually
+ 
+
+ align:start position:0%
+at only one point this thing is actually
+positive and clearly when you have
+
+ align:start position:0%
+positive and clearly when you have
+ 
+
+ align:start position:0%
+positive and clearly when you have
+something that looks like this unless
+
+ align:start position:0%
+something that looks like this unless
+ 
+
+ align:start position:0%
+something that looks like this unless
+you have some crazy stuff happening with
+
+ align:start position:0%
+you have some crazy stuff happening with
+ 
+
+ align:start position:0%
+you have some crazy stuff happening with
+five being equal to zero or anything
+
+ align:start position:0%
+five being equal to zero or anything
+ 
+
+ align:start position:0%
+five being equal to zero or anything
+that's not normal then you will see that
+
+ align:start position:0%
+that's not normal then you will see that
+ 
+
+ align:start position:0%
+that's not normal then you will see that
+you're not degenerate so this thing is
+
+ align:start position:0%
+you're not degenerate so this thing is
+ 
+
+ align:start position:0%
+you're not degenerate so this thing is
+strictly positive and we've said several
+
+ align:start position:0%
+strictly positive and we've said several
+ 
+
+ align:start position:0%
+strictly positive and we've said several
+time that if B prime prime is positive
+
+ align:start position:0%
+time that if B prime prime is positive
+ 
+
+ align:start position:0%
+time that if B prime prime is positive
+then that means that's you know that's
+
+ align:start position:0%
+then that means that's you know that's
+ 
+
+ align:start position:0%
+then that means that's you know that's
+the derivative of B prime meaning that b
+
+ align:start position:0%
+the derivative of B prime meaning that b
+ 
+
+ align:start position:0%
+the derivative of B prime meaning that b
+Prime is increasing and B Prime is
+
+ align:start position:0%
+Prime is increasing and B Prime is
+ 
+
+ align:start position:0%
+Prime is increasing and B Prime is
+increasing is just the same thing as
+
+ align:start position:0%
+increasing is just the same thing as
+ 
+
+ align:start position:0%
+increasing is just the same thing as
+saying that b is convex right so that
+
+ align:start position:0%
+saying that b is convex right so that
+ 
+
+ align:start position:0%
+saying that b is convex right so that
+implies that
+
+ align:start position:0%
+implies that
+ 
+
+ align:start position:0%
+implies that
+b is strictly convex and the strictly
+
+ align:start position:0%
+b is strictly convex and the strictly
+ 
+
+ align:start position:0%
+b is strictly convex and the strictly
+means comes from the fact that this is a
+
+ align:start position:0%
+means comes from the fact that this is a
+ 
+
+ align:start position:0%
+means comes from the fact that this is a
+strict sign well I should not do that
+
+ align:start position:0%
+strict sign well I should not do that
+ 
+
+ align:start position:0%
+strict sign well I should not do that
+because now it's no longer all right so
+
+ align:start position:0%
+because now it's no longer all right so
+ 
+
+ align:start position:0%
+because now it's no longer all right so
+it's just a strict sign meaning that the
+
+ align:start position:0%
+it's just a strict sign meaning that the
+ 
+
+ align:start position:0%
+it's just a strict sign meaning that the
+function this is not strictly convex
+
+ align:start position:0%
+function this is not strictly convex
+ 
+
+ align:start position:0%
+function this is not strictly convex
+because it's linear strictly convex
+
+ align:start position:0%
+because it's linear strictly convex
+ 
+
+ align:start position:0%
+because it's linear strictly convex
+means there's always some curvature
+
+ align:start position:0%
+means there's always some curvature
+ 
+
+ align:start position:0%
+means there's always some curvature
+everywhere so now I have this thing
+
+ align:start position:0%
+everywhere so now I have this thing
+ 
+
+ align:start position:0%
+everywhere so now I have this thing
+that's linear minus something that's
+
+ align:start position:0%
+that's linear minus something that's
+ 
+
+ align:start position:0%
+that's linear minus something that's
+convex something that's negative
+
+ align:start position:0%
+convex something that's negative
+ 
+
+ align:start position:0%
+convex something that's negative
+something convex is concave so this
+
+ align:start position:0%
+something convex is concave so this
+ 
+
+ align:start position:0%
+something convex is concave so this
+thing is linear plus concave so it is
+
+ align:start position:0%
+thing is linear plus concave so it is
+ 
+
+ align:start position:0%
+thing is linear plus concave so it is
+concave so I know just by looking at
+
+ align:start position:0%
+concave so I know just by looking at
+ 
+
+ align:start position:0%
+concave so I know just by looking at
+this that Ln of beta which of course is
+
+ align:start position:0%
+this that Ln of beta which of course is
+ 
+
+ align:start position:0%
+this that Ln of beta which of course is
+something that lives in RP but if I saw
+
+ align:start position:0%
+something that lives in RP but if I saw
+ 
+
+ align:start position:0%
+something that lives in RP but if I saw
+it living in R1 it would look like this
+
+ align:start position:0%
+it living in R1 it would look like this
+ 
+
+ align:start position:0%
+it living in R1 it would look like this
+and if I saw living it in R2 it would
+
+ align:start position:0%
+and if I saw living it in R2 it would
+ 
+
+ align:start position:0%
+and if I saw living it in R2 it would
+look like a dome like this and it the
+
+ align:start position:0%
+look like a dome like this and it the
+ 
+
+ align:start position:0%
+look like a dome like this and it the
+fact that it's strict is also telling me
+
+ align:start position:0%
+fact that it's strict is also telling me
+ 
+
+ align:start position:0%
+fact that it's strict is also telling me
+that there's actually unique
+
+ align:start position:0%
+that there's actually unique
+ 
+
+ align:start position:0%
+that there's actually unique
+maximizer so there's unique maximizer in
+
+ align:start position:0%
+maximizer so there's unique maximizer in
+ 
+
+ align:start position:0%
+maximizer so there's unique maximizer in
+XI transpose beta but not in beta
+
+ align:start position:0%
+XI transpose beta but not in beta
+ 
+
+ align:start position:0%
+XI transpose beta but not in beta
+necessarily we're going to need extra
+
+ align:start position:0%
+necessarily we're going to need extra
+ 
+
+ align:start position:0%
+necessarily we're going to need extra
+assumptions for
+
+ align:start position:0%
+assumptions for
+ 
+
+ align:start position:0%
+assumptions for
+this okay so this is what I say here the
+
+ align:start position:0%
+this okay so this is what I say here the
+ 
+
+ align:start position:0%
+this okay so this is what I say here the
+log likelihood is strictly concave and
+
+ align:start position:0%
+log likelihood is strictly concave and
+ 
+
+ align:start position:0%
+log likelihood is strictly concave and
+so as a consequence under extra
+
+ align:start position:0%
+so as a consequence under extra
+ 
+
+ align:start position:0%
+so as a consequence under extra
+assumptions on the XI because of course
+
+ align:start position:0%
+assumptions on the XI because of course
+ 
+
+ align:start position:0%
+assumptions on the XI because of course
+if the XIs are not uh if the XIs are all
+
+ align:start position:0%
+if the XIs are not uh if the XIs are all
+ 
+
+ align:start position:0%
+if the XIs are not uh if the XIs are all
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+same right so that like if the entries
+
+ align:start position:0%
+same right so that like if the entries
+ 
+
+ align:start position:0%
+same right so that like if the entries
+of XIs so if x I is equal to
+
+ align:start position:0%
+of XIs so if x I is equal to
+ 
+
+ align:start position:0%
+of XIs so if x I is equal to
+11111 then X I transpose beta is just
+
+ align:start position:0%
+11111 then X I transpose beta is just
+ 
+
+ align:start position:0%
+11111 then X I transpose beta is just
+the sum of the betas and I will be of
+
+ align:start position:0%
+the sum of the betas and I will be of
+ 
+
+ align:start position:0%
+the sum of the betas and I will be of
+the beta eyes I will be strictly concave
+
+ align:start position:0%
+the beta eyes I will be strictly concave
+ 
+
+ align:start position:0%
+the beta eyes I will be strictly concave
+in those guys but certainly not in the
+
+ align:start position:0%
+in those guys but certainly not in the
+ 
+
+ align:start position:0%
+in those guys but certainly not in the
+individual entries okay so I need extra
+
+ align:start position:0%
+individual entries okay so I need extra
+ 
+
+ align:start position:0%
+individual entries okay so I need extra
+thing on my XI so that this happens just
+
+ align:start position:0%
+thing on my XI so that this happens just
+ 
+
+ align:start position:0%
+thing on my XI so that this happens just
+like we needed the Matrix capital X in
+
+ align:start position:0%
+like we needed the Matrix capital X in
+ 
+
+ align:start position:0%
+like we needed the Matrix capital X in
+the linear regression case to be a full
+
+ align:start position:0%
+the linear regression case to be a full
+ 
+
+ align:start position:0%
+the linear regression case to be a full
+rank so we could actually identify what
+
+ align:start position:0%
+rank so we could actually identify what
+ 
+
+ align:start position:0%
+rank so we could actually identify what
+beta was okay it's going to be exactly
+
+ align:start position:0%
+beta was okay it's going to be exactly
+ 
+
+ align:start position:0%
+beta was okay it's going to be exactly
+the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh uh so here this is when we have
+
+ align:start position:0%
+so uh uh so here this is when we have
+ 
+
+ align:start position:0%
+so uh uh so here this is when we have
+this very specific uh uh
+
+ align:start position:0%
+this very specific uh uh
+ 
+
+ align:start position:0%
+this very specific uh uh
+parameterization and the question is uh
+
+ align:start position:0%
+parameterization and the question is uh
+ 
+
+ align:start position:0%
+parameterization and the question is uh
+uh but it might not be the case if we
+
+ align:start position:0%
+uh but it might not be the case if we
+ 
+
+ align:start position:0%
+uh but it might not be the case if we
+change the parameter beta into something
+
+ align:start position:0%
+change the parameter beta into something
+ 
+
+ align:start position:0%
+change the parameter beta into something
+else okay so here the fact that we use
+
+ align:start position:0%
+else okay so here the fact that we use
+ 
+
+ align:start position:0%
+else okay so here the fact that we use
+the canonical link and Etc everything
+
+ align:start position:0%
+the canonical link and Etc everything
+ 
+
+ align:start position:0%
+the canonical link and Etc everything
+actually works really to our advantage
+
+ align:start position:0%
+actually works really to our advantage
+ 
+
+ align:start position:0%
+actually works really to our advantage
+right so that everything becomes
+
+ align:start position:0%
+right so that everything becomes
+ 
+
+ align:start position:0%
+right so that everything becomes
+strictly concave and we know exactly
+
+ align:start position:0%
+strictly concave and we know exactly
+ 
+
+ align:start position:0%
+strictly concave and we know exactly
+what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happening all right so I understand I
+
+ align:start position:0%
+happening all right so I understand I
+ 
+
+ align:start position:0%
+happening all right so I understand I
+went a bit fast on playing with convex
+
+ align:start position:0%
+went a bit fast on playing with convex
+ 
+
+ align:start position:0%
+went a bit fast on playing with convex
+and concave function this is not the
+
+ align:start position:0%
+and concave function this is not the
+ 
+
+ align:start position:0%
+and concave function this is not the
+purpose uh you know I could spend a
+
+ align:start position:0%
+purpose uh you know I could spend a
+ 
+
+ align:start position:0%
+purpose uh you know I could spend a
+lecture telling you oh if I add two
+
+ align:start position:0%
+lecture telling you oh if I add two
+ 
+
+ align:start position:0%
+lecture telling you oh if I add two
+concave functions then the result
+
+ align:start position:0%
+concave functions then the result
+ 
+
+ align:start position:0%
+concave functions then the result
+remains concave if I had a you know
+
+ align:start position:0%
+remains concave if I had a you know
+ 
+
+ align:start position:0%
+remains concave if I had a you know
+concave and a strictly concave then the
+
+ align:start position:0%
+concave and a strictly concave then the
+ 
+
+ align:start position:0%
+concave and a strictly concave then the
+result Still Remains strictly concave
+
+ align:start position:0%
+result Still Remains strictly concave
+ 
+
+ align:start position:0%
+result Still Remains strictly concave
+and we could spend time proving this
+
+ align:start position:0%
+and we could spend time proving this
+ 
+
+ align:start position:0%
+and we could spend time proving this
+this is was just for you to get an
+
+ align:start position:0%
+this is was just for you to get an
+ 
+
+ align:start position:0%
+this is was just for you to get an
+intuition as to why this is correct but
+
+ align:start position:0%
+intuition as to why this is correct but
+ 
+
+ align:start position:0%
+intuition as to why this is correct but
+we don't really have time to go into too
+
+ align:start position:0%
+we don't really have time to go into too
+ 
+
+ align:start position:0%
+we don't really have time to go into too
+much details one thing you can do a
+
+ align:start position:0%
+much details one thing you can do a
+ 
+
+ align:start position:0%
+much details one thing you can do a
+strictly concave function if it's in one
+
+ align:start position:0%
+strictly concave function if it's in one
+ 
+
+ align:start position:0%
+strictly concave function if it's in one
+dimension all I need to have is that the
+
+ align:start position:0%
+dimension all I need to have is that the
+ 
+
+ align:start position:0%
+dimension all I need to have is that the
+second der
+
+ align:start position:0%
+second der
+ 
+
+ align:start position:0%
+second der
+ative is strictly is strictly negative
+
+ align:start position:0%
+ative is strictly is strictly negative
+ 
+
+ align:start position:0%
+ative is strictly is strictly negative
+right that's a strictly concave function
+
+ align:start position:0%
+right that's a strictly concave function
+ 
+
+ align:start position:0%
+right that's a strictly concave function
+that was the analytic definition we had
+
+ align:start position:0%
+that was the analytic definition we had
+ 
+
+ align:start position:0%
+that was the analytic definition we had
+for strict concavity so if this was in
+
+ align:start position:0%
+for strict concavity so if this was in
+ 
+
+ align:start position:0%
+for strict concavity so if this was in
+one dimension it would look like
+
+ align:start position:0%
+one dimension it would look like
+ 
+
+ align:start position:0%
+one dimension it would look like
+this y i * x i Time beta Now Beta is
+
+ align:start position:0%
+this y i * x i Time beta Now Beta is
+ 
+
+ align:start position:0%
+this y i * x i Time beta Now Beta is
+just one number and then I would have
+
+ align:start position:0%
+just one number and then I would have
+ 
+
+ align:start position:0%
+just one number and then I would have
+minus beta x i * B and this is over all
+
+ align:start position:0%
+minus beta x i * B and this is over all
+ 
+
+ align:start position:0%
+minus beta x i * B and this is over all
+over five you take second derivatives
+
+ align:start position:0%
+over five you take second derivatives
+ 
+
+ align:start position:0%
+over five you take second derivatives
+the fact that this is linear in beta
+
+ align:start position:0%
+the fact that this is linear in beta
+ 
+
+ align:start position:0%
+the fact that this is linear in beta
+this is going to go way and here I'm
+
+ align:start position:0%
+this is going to go way and here I'm
+ 
+
+ align:start position:0%
+this is going to go way and here I'm
+just going to be left with
+
+ align:start position:0%
+just going to be left with
+ 
+
+ align:start position:0%
+just going to be left with
+minus so if I take the second
+
+ align:start position:0%
+minus so if I take the second
+ 
+
+ align:start position:0%
+minus so if I take the second
+derivative with respect to Beta this is
+
+ align:start position:0%
+derivative with respect to Beta this is
+ 
+
+ align:start position:0%
+derivative with respect to Beta this is
+going to be equal to minus B prime prime
+
+ align:start position:0%
+going to be equal to minus B prime prime
+ 
+
+ align:start position:0%
+going to be equal to minus B prime prime
+x i beta time x i^ 2 divided five so
+
+ align:start position:0%
+x i beta time x i^ 2 divided five so
+ 
+
+ align:start position:0%
+x i beta time x i^ 2 divided five so
+this is clearly positive that's that's
+
+ align:start position:0%
+this is clearly positive that's that's
+ 
+
+ align:start position:0%
+this is clearly positive that's that's
+where if XI is zero this is the generate
+
+ align:start position:0%
+where if XI is zero this is the generate
+ 
+
+ align:start position:0%
+where if XI is zero this is the generate
+so I would not get it uh then I have the
+
+ align:start position:0%
+so I would not get it uh then I have the
+ 
+
+ align:start position:0%
+so I would not get it uh then I have the
+second derivative of B Prime which I
+
+ align:start position:0%
+second derivative of B Prime which I
+ 
+
+ align:start position:0%
+second derivative of B Prime which I
+know is positive because of the variance
+
+ align:start position:0%
+know is positive because of the variance
+ 
+
+ align:start position:0%
+know is positive because of the variance
+thing that I have here divided by five
+
+ align:start position:0%
+thing that I have here divided by five
+ 
+
+ align:start position:0%
+thing that I have here divided by five
+and so that would all be fine that's for
+
+ align:start position:0%
+and so that would all be fine that's for
+ 
+
+ align:start position:0%
+and so that would all be fine that's for
+one dimension if I wanted to do this in
+
+ align:start position:0%
+one dimension if I wanted to do this in
+ 
+
+ align:start position:0%
+one dimension if I wanted to do this in
+higher dimensions and would have to say
+
+ align:start position:0%
+higher dimensions and would have to say
+ 
+
+ align:start position:0%
+higher dimensions and would have to say
+that the hen is a positive definite
+
+ align:start position:0%
+that the hen is a positive definite
+ 
+
+ align:start position:0%
+that the hen is a positive definite
+Matrix and that's maybe a bit beyond
+
+ align:start position:0%
+Matrix and that's maybe a bit beyond
+ 
+
+ align:start position:0%
+Matrix and that's maybe a bit beyond
+what this course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+okay so in the rest of this
+
+ align:start position:0%
+okay so in the rest of this
+ 
+
+ align:start position:0%
+okay so in the rest of this
+chapter uh I will do what I did not do
+
+ align:start position:0%
+chapter uh I will do what I did not do
+ 
+
+ align:start position:0%
+chapter uh I will do what I did not do
+uh when we talked about maximum
+
+ align:start position:0%
+uh when we talked about maximum
+ 
+
+ align:start position:0%
+uh when we talked about maximum
+likelihood and and uh what we're going
+
+ align:start position:0%
+likelihood and and uh what we're going
+ 
+
+ align:start position:0%
+likelihood and and uh what we're going
+to do is we're going to actually show
+
+ align:start position:0%
+to do is we're going to actually show
+ 
+
+ align:start position:0%
+to do is we're going to actually show
+how to do this maximization right so
+
+ align:start position:0%
+how to do this maximization right so
+ 
+
+ align:start position:0%
+how to do this maximization right so
+here we know that the function is
+
+ align:start position:0%
+here we know that the function is
+ 
+
+ align:start position:0%
+here we know that the function is
+concave but what it looks like
+
+ align:start position:0%
+concave but what it looks like
+ 
+
+ align:start position:0%
+concave but what it looks like
+specifically depends on what B is and
+
+ align:start position:0%
+specifically depends on what B is and
+ 
+
+ align:start position:0%
+specifically depends on what B is and
+for different B's I'm going to have
+
+ align:start position:0%
+for different B's I'm going to have
+ 
+
+ align:start position:0%
+for different B's I'm going to have
+different things to do just like when I
+
+ align:start position:0%
+different things to do just like when I
+ 
+
+ align:start position:0%
+different things to do just like when I
+was talking about maximum likelihood
+
+ align:start position:0%
+was talking about maximum likelihood
+ 
+
+ align:start position:0%
+was talking about maximum likelihood
+estimation if I had a concave uh log
+
+ align:start position:0%
+estimation if I had a concave uh log
+ 
+
+ align:start position:0%
+estimation if I had a concave uh log
+likelihood function I could optimize it
+
+ align:start position:0%
+likelihood function I could optimize it
+ 
+
+ align:start position:0%
+likelihood function I could optimize it
+but depending on what the function is I
+
+ align:start position:0%
+but depending on what the function is I
+ 
+
+ align:start position:0%
+but depending on what the function is I
+would actually need some algorithms
+
+ align:start position:0%
+would actually need some algorithms
+ 
+
+ align:start position:0%
+would actually need some algorithms
+that's maybe working better on some
+
+ align:start position:0%
+that's maybe working better on some
+ 
+
+ align:start position:0%
+that's maybe working better on some
+function than others now here I don't
+
+ align:start position:0%
+function than others now here I don't
+ 
+
+ align:start position:0%
+function than others now here I don't
+have random things I have the B is the
+
+ align:start position:0%
+have random things I have the B is the
+ 
+
+ align:start position:0%
+have random things I have the B is the
+cumulant generating function of a
+
+ align:start position:0%
+cumulant generating function of a
+ 
+
+ align:start position:0%
+cumulant generating function of a
+canonical exponential family and there
+
+ align:start position:0%
+canonical exponential family and there
+ 
+
+ align:start position:0%
+canonical exponential family and there
+is a way for me to sort of Leverage that
+
+ align:start position:0%
+is a way for me to sort of Leverage that
+ 
+
+ align:start position:0%
+is a way for me to sort of Leverage that
+right so not only is there's the the B
+
+ align:start position:0%
+right so not only is there's the the B
+ 
+
+ align:start position:0%
+right so not only is there's the the B
+part but there's also the linear part
+
+ align:start position:0%
+part but there's also the linear part
+ 
+
+ align:start position:0%
+part but there's also the linear part
+and if I start trying to use that I'm
+
+ align:start position:0%
+and if I start trying to use that I'm
+ 
+
+ align:start position:0%
+and if I start trying to use that I'm
+actually going to be able to devise very
+
+ align:start position:0%
+actually going to be able to devise very
+ 
+
+ align:start position:0%
+actually going to be able to devise very
+specific optimization algorithms and the
+
+ align:start position:0%
+specific optimization algorithms and the
+ 
+
+ align:start position:0%
+specific optimization algorithms and the
+way I'm going to be able to do this is
+
+ align:start position:0%
+way I'm going to be able to do this is
+ 
+
+ align:start position:0%
+way I'm going to be able to do this is
+by thinking of simple blackbox
+
+ align:start position:0%
+by thinking of simple blackbox
+ 
+
+ align:start position:0%
+by thinking of simple blackbox
+optimization to which I can actually
+
+ align:start position:0%
+optimization to which I can actually
+ 
+
+ align:start position:0%
+optimization to which I can actually
+technically feed any function but it's
+
+ align:start position:0%
+technically feed any function but it's
+ 
+
+ align:start position:0%
+technically feed any function but it's
+going to turn out that the iterations of
+
+ align:start position:0%
+going to turn out that the iterations of
+ 
+
+ align:start position:0%
+going to turn out that the iterations of
+this iterative algorithms are going to
+
+ align:start position:0%
+this iterative algorithms are going to
+ 
+
+ align:start position:0%
+this iterative algorithms are going to
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+very familiar uh when we uh when we just
+
+ align:start position:0%
+very familiar uh when we uh when we just
+ 
+
+ align:start position:0%
+very familiar uh when we uh when we just
+plug in the particular values of B of
+
+ align:start position:0%
+plug in the particular values of B of
+ 
+
+ align:start position:0%
+plug in the particular values of B of
+the log likelihood that we have for this
+
+ align:start position:0%
+the log likelihood that we have for this
+ 
+
+ align:start position:0%
+the log likelihood that we have for this
+problem and so the three methods we're
+
+ align:start position:0%
+problem and so the three methods we're
+ 
+
+ align:start position:0%
+problem and so the three methods we're
+going to talk about going from more
+
+ align:start position:0%
+going to talk about going from more
+ 
+
+ align:start position:0%
+going to talk about going from more
+black box meaning you can basically
+
+ align:start position:0%
+black box meaning you can basically
+ 
+
+ align:start position:0%
+black box meaning you can basically
+stuff it any function is going to work
+
+ align:start position:0%
+stuff it any function is going to work
+ 
+
+ align:start position:0%
+stuff it any function is going to work
+any concave function is going to work
+
+ align:start position:0%
+any concave function is going to work
+ 
+
+ align:start position:0%
+any concave function is going to work
+all the way to this is working
+
+ align:start position:0%
+all the way to this is working
+ 
+
+ align:start position:0%
+all the way to this is working
+specifically for General linear models
+
+ align:start position:0%
+specifically for General linear models
+ 
+
+ align:start position:0%
+specifically for General linear models
+are Newton rafon method who's already
+
+ align:start position:0%
+are Newton rafon method who's already
+ 
+
+ align:start position:0%
+are Newton rafon method who's already
+heard about the Newton rafon method
+
+ align:start position:0%
+heard about the Newton rafon method
+ 
+
+ align:start position:0%
+heard about the Newton rafon method
+right so you know any that's probably
+
+ align:start position:0%
+right so you know any that's probably
+ 
+
+ align:start position:0%
+right so you know any that's probably
+some people actually learned this
+
+ align:start position:0%
+some people actually learned this
+ 
+
+ align:start position:0%
+some people actually learned this
+algorithm without even knowing the word
+
+ align:start position:0%
+algorithm without even knowing the word
+ 
+
+ align:start position:0%
+algorithm without even knowing the word
+algorithm right it's a function that I
+
+ align:start position:0%
+algorithm right it's a function that I
+ 
+
+ align:start position:0%
+algorithm right it's a function that I
+mean typically it's supposed to be
+
+ align:start position:0%
+mean typically it's supposed to be
+ 
+
+ align:start position:0%
+mean typically it's supposed to be
+finding roots of functions but finding
+
+ align:start position:0%
+finding roots of functions but finding
+ 
+
+ align:start position:0%
+finding roots of functions but finding
+the root of a function of a derivative
+
+ align:start position:0%
+the root of a function of a derivative
+ 
+
+ align:start position:0%
+the root of a function of a derivative
+is the same as finding the minimum of a
+
+ align:start position:0%
+is the same as finding the minimum of a
+ 
+
+ align:start position:0%
+is the same as finding the minimum of a
+function uh so uh that's the first
+
+ align:start position:0%
+function uh so uh that's the first
+ 
+
+ align:start position:0%
+function uh so uh that's the first
+blackbox method I mean uh it's it's it's
+
+ align:start position:0%
+blackbox method I mean uh it's it's it's
+ 
+
+ align:start position:0%
+blackbox method I mean uh it's it's it's
+pretty old and then there's something
+
+ align:start position:0%
+pretty old and then there's something
+ 
+
+ align:start position:0%
+pretty old and then there's something
+that's very specific to what we're doing
+
+ align:start position:0%
+that's very specific to what we're doing
+ 
+
+ align:start position:0%
+that's very specific to what we're doing
+which is called so this Newton raon
+
+ align:start position:0%
+which is called so this Newton raon
+ 
+
+ align:start position:0%
+which is called so this Newton raon
+method is going to involve the hhen of
+
+ align:start position:0%
+method is going to involve the hhen of
+ 
+
+ align:start position:0%
+method is going to involve the hhen of
+our log likelihood and uh since we know
+
+ align:start position:0%
+our log likelihood and uh since we know
+ 
+
+ align:start position:0%
+our log likelihood and uh since we know
+something about the hhen for a
+
+ align:start position:0%
+something about the hhen for a
+ 
+
+ align:start position:0%
+something about the hhen for a
+particular problem we're going to be
+
+ align:start position:0%
+particular problem we're going to be
+ 
+
+ align:start position:0%
+particular problem we're going to be
+able to move on to Fisher scoring and
+
+ align:start position:0%
+able to move on to Fisher scoring and
+ 
+
+ align:start position:0%
+able to move on to Fisher scoring and
+the word Fisher here is actually exactly
+
+ align:start position:0%
+the word Fisher here is actually exactly
+ 
+
+ align:start position:0%
+the word Fisher here is actually exactly
+coming from Fisher information so the
+
+ align:start position:0%
+coming from Fisher information so the
+ 
+
+ align:start position:0%
+coming from Fisher information so the
+hen is going to involve the Fisher
+
+ align:start position:0%
+hen is going to involve the Fisher
+ 
+
+ align:start position:0%
+hen is going to involve the Fisher
+information and uh finally uh we will
+
+ align:start position:0%
+information and uh finally uh we will
+ 
+
+ align:start position:0%
+information and uh finally uh we will
+talk about iteratively Reed Le squares
+
+ align:start position:0%
+talk about iteratively Reed Le squares
+ 
+
+ align:start position:0%
+talk about iteratively Reed Le squares
+and that's not for any function it's
+
+ align:start position:0%
+and that's not for any function it's
+ 
+
+ align:start position:0%
+and that's not for any function it's
+when we're trying to use the fact that
+
+ align:start position:0%
+when we're trying to use the fact that
+ 
+
+ align:start position:0%
+when we're trying to use the fact that
+there is this linear dependence on the
+
+ align:start position:0%
+there is this linear dependence on the
+ 
+
+ align:start position:0%
+there is this linear dependence on the
+XIs and this is essentially going to
+
+ align:start position:0%
+XIs and this is essentially going to
+ 
+
+ align:start position:0%
+XIs and this is essentially going to
+tell us well you know you can use lead
+
+ align:start position:0%
+tell us well you know you can use lead
+ 
+
+ align:start position:0%
+tell us well you know you can use lead
+squares for linear regression here you
+
+ align:start position:0%
+squares for linear regression here you
+ 
+
+ align:start position:0%
+squares for linear regression here you
+can use Le squares but locally and you
+
+ align:start position:0%
+can use Le squares but locally and you
+ 
+
+ align:start position:0%
+can use Le squares but locally and you
+have to iterate okay and uh this last
+
+ align:start position:0%
+have to iterate okay and uh this last
+ 
+
+ align:start position:0%
+have to iterate okay and uh this last
+part is essentially a trick by
+
+ align:start position:0%
+part is essentially a trick by
+ 
+
+ align:start position:0%
+part is essentially a trick by
+statisticians to be able to solve the
+
+ align:start position:0%
+statisticians to be able to solve the
+ 
+
+ align:start position:0%
+statisticians to be able to solve the
+Newton rafson updates without actually
+
+ align:start position:0%
+Newton rafson updates without actually
+ 
+
+ align:start position:0%
+Newton rafson updates without actually
+uh having a dedicated software for this
+
+ align:start position:0%
+uh having a dedicated software for this
+ 
+
+ align:start position:0%
+uh having a dedicated software for this
+but just being able to reuse some Le
+
+ align:start position:0%
+but just being able to reuse some Le
+ 
+
+ align:start position:0%
+but just being able to reuse some Le
+squares software
+
+ align:start position:0%
+squares software
+ 
+
+ align:start position:0%
+squares software
+okay so you know uh we've talked about
+
+ align:start position:0%
+okay so you know uh we've talked about
+ 
+
+ align:start position:0%
+okay so you know uh we've talked about
+this many times I just want to make sure
+
+ align:start position:0%
+this many times I just want to make sure
+ 
+
+ align:start position:0%
+this many times I just want to make sure
+that uh we're all on the same page here
+
+ align:start position:0%
+that uh we're all on the same page here
+ 
+
+ align:start position:0%
+that uh we're all on the same page here
+uh we have a function f we're going to
+
+ align:start position:0%
+uh we have a function f we're going to
+ 
+
+ align:start position:0%
+uh we have a function f we're going to
+assume that it has two derivatives and
+
+ align:start position:0%
+assume that it has two derivatives and
+ 
+
+ align:start position:0%
+assume that it has two derivatives and
+it's a function from RM to R so its
+
+ align:start position:0%
+it's a function from RM to R so its
+ 
+
+ align:start position:0%
+it's a function from RM to R so its
+first derivative is called gradient
+
+ align:start position:0%
+first derivative is called gradient
+ 
+
+ align:start position:0%
+first derivative is called gradient
+that's just the vector that collects all
+
+ align:start position:0%
+that's just the vector that collects all
+ 
+
+ align:start position:0%
+that's just the vector that collects all
+the partial derivatives with respect to
+
+ align:start position:0%
+the partial derivatives with respect to
+ 
+
+ align:start position:0%
+the partial derivatives with respect to
+each of the coordinates it's Dimension M
+
+ align:start position:0%
+each of the coordinates it's Dimension M
+ 
+
+ align:start position:0%
+each of the coordinates it's Dimension M
+of course and the second derivative is
+
+ align:start position:0%
+of course and the second derivative is
+ 
+
+ align:start position:0%
+of course and the second derivative is
+an M by m matx is called the hen and on
+
+ align:start position:0%
+an M by m matx is called the hen and on
+ 
+
+ align:start position:0%
+an M by m matx is called the hen and on
+the i j on the I row and jth column you
+
+ align:start position:0%
+the i j on the I row and jth column you
+ 
+
+ align:start position:0%
+the i j on the I row and jth column you
+see the second partial derivative with
+
+ align:start position:0%
+see the second partial derivative with
+ 
+
+ align:start position:0%
+see the second partial derivative with
+respect to the I component and the J
+
+ align:start position:0%
+respect to the I component and the J
+ 
+
+ align:start position:0%
+respect to the I component and the J
+component okay we've seen that several
+
+ align:start position:0%
+component okay we've seen that several
+ 
+
+ align:start position:0%
+component okay we've seen that several
+times this is just multivariable
+
+ align:start position:0%
+times this is just multivariable
+ 
+
+ align:start position:0%
+times this is just multivariable
+calculus uh but uh really the point here
+
+ align:start position:0%
+calculus uh but uh really the point here
+ 
+
+ align:start position:0%
+calculus uh but uh really the point here
+is to uh maybe the notation is slightly
+
+ align:start position:0%
+is to uh maybe the notation is slightly
+ 
+
+ align:start position:0%
+is to uh maybe the notation is slightly
+different because I want to keep track
+
+ align:start position:0%
+different because I want to keep track
+ 
+
+ align:start position:0%
+different because I want to keep track
+of f so when I write gradient I write
+
+ align:start position:0%
+of f so when I write gradient I write
+ 
+
+ align:start position:0%
+of f so when I write gradient I write
+nabla sub F and and when I write hen I
+
+ align:start position:0%
+nabla sub F and and when I write hen I
+ 
+
+ align:start position:0%
+nabla sub F and and when I write hen I
+write Naas sub H sub
+
+ align:start position:0%
+write Naas sub H sub
+ 
+
+ align:start position:0%
+write Naas sub H sub
+F and if as I said if f is strictly
+
+ align:start position:0%
+F and if as I said if f is strictly
+ 
+
+ align:start position:0%
+F and if as I said if f is strictly
+concave then HF ofx is negative definite
+
+ align:start position:0%
+concave then HF ofx is negative definite
+ 
+
+ align:start position:0%
+concave then HF ofx is negative definite
+what it means is that if I take
+
+ align:start position:0%
+what it means is that if I take
+ 
+
+ align:start position:0%
+what it means is that if I take
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+X in
+
+ align:start position:0%
+X in
+ 
+
+ align:start position:0%
+X in
+RM then X transpose
+
+ align:start position:0%
+RM then X transpose
+ 
+
+ align:start position:0%
+RM then X transpose
+HF uh well that's for any
+
+ align:start position:0%
+HF uh well that's for any
+ 
+
+ align:start position:0%
+HF uh well that's for any
+x0 X this is actually strictly
+
+ align:start position:0%
+x0 X this is actually strictly
+ 
+
+ align:start position:0%
+x0 X this is actually strictly
+negative that's what it means to be
+
+ align:start position:0%
+negative that's what it means to be
+ 
+
+ align:start position:0%
+negative that's what it means to be
+negative definite okay so every time I
+
+ align:start position:0%
+negative definite okay so every time I
+ 
+
+ align:start position:0%
+negative definite okay so every time I
+do X transpose so if I so this is like a
+
+ align:start position:0%
+do X transpose so if I so this is like a
+ 
+
+ align:start position:0%
+do X transpose so if I so this is like a
+quadratic form and I want it to be
+
+ align:start position:0%
+quadratic form and I want it to be
+ 
+
+ align:start position:0%
+quadratic form and I want it to be
+negative for all values of x0 and X both
+
+ align:start position:0%
+negative for all values of x0 and X both
+ 
+
+ align:start position:0%
+negative for all values of x0 and X both
+of them that's very strong
+
+ align:start position:0%
+of them that's very strong
+ 
+
+ align:start position:0%
+of them that's very strong
+clearly uh but for us actually this is
+
+ align:start position:0%
+clearly uh but for us actually this is
+ 
+
+ align:start position:0%
+clearly uh but for us actually this is
+what happens just because of the
+
+ align:start position:0%
+what happens just because of the
+ 
+
+ align:start position:0%
+what happens just because of the
+properties of
+
+ align:start position:0%
+properties of
+ 
+
+ align:start position:0%
+properties of
+B uh well at least the fact that it's
+
+ align:start position:0%
+B uh well at least the fact that it's
+ 
+
+ align:start position:0%
+B uh well at least the fact that it's
+negative less than or equal to if I want
+
+ align:start position:0%
+negative less than or equal to if I want
+ 
+
+ align:start position:0%
+negative less than or equal to if I want
+it to be strictly less I need some
+
+ align:start position:0%
+it to be strictly less I need some
+ 
+
+ align:start position:0%
+it to be strictly less I need some
+properties on
+
+ align:start position:0%
+properties on
+ 
+
+ align:start position:0%
+properties on
+X and then I will call the H map the
+
+ align:start position:0%
+X and then I will call the H map the
+ 
+
+ align:start position:0%
+X and then I will call the H map the
+function that Maps X to this Matrix
+
+ align:start position:0%
+function that Maps X to this Matrix
+ 
+
+ align:start position:0%
+function that Maps X to this Matrix
+HF of X okay so that's just a second
+
+ align:start position:0%
+HF of X okay so that's just a second
+ 
+
+ align:start position:0%
+HF of X okay so that's just a second
+derivative at X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah where do I say
+
+ align:start position:0%
+yeah where do I say
+ 
+
+ align:start position:0%
+yeah where do I say
+smooth oh yeah uh I mean you know you
+
+ align:start position:0%
+smooth oh yeah uh I mean you know you
+ 
+
+ align:start position:0%
+smooth oh yeah uh I mean you know you
+need to be able to apply Schwarz Lama
+
+ align:start position:0%
+need to be able to apply Schwarz Lama
+ 
+
+ align:start position:0%
+need to be able to apply Schwarz Lama
+let's say two continuous derivatives
+
+ align:start position:0%
+let's say two continuous derivatives
+ 
+
+ align:start position:0%
+let's say two continuous derivatives
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smooth no that's fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so how does the Newton rafon uh
+
+ align:start position:0%
+okay so how does the Newton rafon uh
+ 
+
+ align:start position:0%
+okay so how does the Newton rafon uh
+method work well what it does is that it
+
+ align:start position:0%
+method work well what it does is that it
+ 
+
+ align:start position:0%
+method work well what it does is that it
+forms a quadratic approximation to your
+
+ align:start position:0%
+forms a quadratic approximation to your
+ 
+
+ align:start position:0%
+forms a quadratic approximation to your
+function and that's the one it optimizes
+
+ align:start position:0%
+function and that's the one it optimizes
+ 
+
+ align:start position:0%
+function and that's the one it optimizes
+at every single point okay and the
+
+ align:start position:0%
+at every single point okay and the
+ 
+
+ align:start position:0%
+at every single point okay and the
+reason is because we have a close form
+
+ align:start position:0%
+reason is because we have a close form
+ 
+
+ align:start position:0%
+reason is because we have a close form
+solution to Def finding the minimum of a
+
+ align:start position:0%
+solution to Def finding the minimum of a
+ 
+
+ align:start position:0%
+solution to Def finding the minimum of a
+quadratic function so if I give you a
+
+ align:start position:0%
+quadratic function so if I give you a
+ 
+
+ align:start position:0%
+quadratic function so if I give you a
+function that's of the form ax2 plus b x
+
+ align:start position:0%
+function that's of the form ax2 plus b x
+ 
+
+ align:start position:0%
+function that's of the form ax2 plus b x
+plus C you know exactly a close form for
+
+ align:start position:0%
+plus C you know exactly a close form for
+ 
+
+ align:start position:0%
+plus C you know exactly a close form for
+its minimum and but if I give you any
+
+ align:start position:0%
+its minimum and but if I give you any
+ 
+
+ align:start position:0%
+its minimum and but if I give you any
+function or let's say yeah so here it's
+
+ align:start position:0%
+function or let's say yeah so here it's
+ 
+
+ align:start position:0%
+function or let's say yeah so here it's
+all about maximum I'm sorry I'm going to
+
+ align:start position:0%
+all about maximum I'm sorry I'm going to
+ 
+
+ align:start position:0%
+all about maximum I'm sorry I'm going to
+try to if you're confused with me using
+
+ align:start position:0%
+try to if you're confused with me using
+ 
+
+ align:start position:0%
+try to if you're confused with me using
+the word minimum just assume that it was
+
+ align:start position:0%
+the word minimum just assume that it was
+ 
+
+ align:start position:0%
+the word minimum just assume that it was
+the word maximum um so this is how it
+
+ align:start position:0%
+the word maximum um so this is how it
+ 
+
+ align:start position:0%
+the word maximum um so this is how it
+works okay if I give
+
+ align:start position:0%
+works okay if I give
+ 
+
+ align:start position:0%
+works okay if I give
+you a function which is concave and
+
+ align:start position:0%
+you a function which is concave and
+ 
+
+ align:start position:0%
+you a function which is concave and
+that's quadratic okay so it's going to
+
+ align:start position:0%
+that's quadratic okay so it's going to
+ 
+
+ align:start position:0%
+that's quadratic okay so it's going to
+look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this all right so that's of the form ax2
+
+ align:start position:0%
+this all right so that's of the form ax2
+ 
+
+ align:start position:0%
+this all right so that's of the form ax2
+where a is negative of course plus BX
+
+ align:start position:0%
+where a is negative of course plus BX
+ 
+
+ align:start position:0%
+where a is negative of course plus BX
+plus C then you know you can solve your
+
+ align:start position:0%
+plus C then you know you can solve your
+ 
+
+ align:start position:0%
+plus C then you know you can solve your
+uh whatever you can take the derivative
+
+ align:start position:0%
+uh whatever you can take the derivative
+ 
+
+ align:start position:0%
+uh whatever you can take the derivative
+of this guy set it equal to zero and you
+
+ align:start position:0%
+of this guy set it equal to zero and you
+ 
+
+ align:start position:0%
+of this guy set it equal to zero and you
+will have an exact equation into what
+
+ align:start position:0%
+will have an exact equation into what
+ 
+
+ align:start position:0%
+will have an exact equation into what
+the value of x is that realizes this
+
+ align:start position:0%
+the value of x is that realizes this
+ 
+
+ align:start position:0%
+the value of x is that realizes this
+maximum if I give you any function
+
+ align:start position:0%
+maximum if I give you any function
+ 
+
+ align:start position:0%
+maximum if I give you any function
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concave that's not clear right I mean
+
+ align:start position:0%
+concave that's not clear right I mean
+ 
+
+ align:start position:0%
+concave that's not clear right I mean
+you know if I tell you the function that
+
+ align:start position:0%
+you know if I tell you the function that
+ 
+
+ align:start position:0%
+you know if I tell you the function that
+we have here is of the form ax minus B
+
+ align:start position:0%
+we have here is of the form ax minus B
+ 
+
+ align:start position:0%
+we have here is of the form ax minus B
+of X right then I'm just going to have
+
+ align:start position:0%
+of X right then I'm just going to have
+ 
+
+ align:start position:0%
+of X right then I'm just going to have
+something that inverts uh B Prime but
+
+ align:start position:0%
+something that inverts uh B Prime but
+ 
+
+ align:start position:0%
+something that inverts uh B Prime but
+you know how do I do it exactly it's not
+
+ align:start position:0%
+you know how do I do it exactly it's not
+ 
+
+ align:start position:0%
+you know how do I do it exactly it's not
+clear and so what we do is we do a
+
+ align:start position:0%
+clear and so what we do is we do a
+ 
+
+ align:start position:0%
+clear and so what we do is we do a
+quadratic approximation which should be
+
+ align:start position:0%
+quadratic approximation which should be
+ 
+
+ align:start position:0%
+quadratic approximation which should be
+true approximately everywhere right so
+
+ align:start position:0%
+true approximately everywhere right so
+ 
+
+ align:start position:0%
+true approximately everywhere right so
+if I'm at this point here I'm going to
+
+ align:start position:0%
+if I'm at this point here I'm going to
+ 
+
+ align:start position:0%
+if I'm at this point here I'm going to
+say oh I'm close to being that
+
+ align:start position:0%
+say oh I'm close to being that
+ 
+
+ align:start position:0%
+say oh I'm close to being that
+function and if I'm at this point here
+
+ align:start position:0%
+function and if I'm at this point here
+ 
+
+ align:start position:0%
+function and if I'm at this point here
+I'm going to be close to being that
+
+ align:start position:0%
+I'm going to be close to being that
+ 
+
+ align:start position:0%
+I'm going to be close to being that
+function and for this functions I can
+
+ align:start position:0%
+function and for this functions I can
+ 
+
+ align:start position:0%
+function and for this functions I can
+actually optimize and so if I'm not
+
+ align:start position:0%
+actually optimize and so if I'm not
+ 
+
+ align:start position:0%
+actually optimize and so if I'm not
+moving too far from one to the other I
+
+ align:start position:0%
+moving too far from one to the other I
+ 
+
+ align:start position:0%
+moving too far from one to the other I
+should actually get something so here's
+
+ align:start position:0%
+should actually get something so here's
+ 
+
+ align:start position:0%
+should actually get something so here's
+how the quadratic approximation works
+
+ align:start position:0%
+how the quadratic approximation works
+ 
+
+ align:start position:0%
+how the quadratic approximation works
+I'm going to write the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order tailor expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so that's just going to be my
+
+ align:start position:0%
+okay and so that's just going to be my
+ 
+
+ align:start position:0%
+okay and so that's just going to be my
+quadratic approximation is going to say
+
+ align:start position:0%
+quadratic approximation is going to say
+ 
+
+ align:start position:0%
+quadratic approximation is going to say
+oh F ofx when X is close to some point
+
+ align:start position:0%
+oh F ofx when X is close to some point
+ 
+
+ align:start position:0%
+oh F ofx when X is close to some point
+x0 is going to be close to F of x0 plus
+
+ align:start position:0%
+x0 is going to be close to F of x0 plus
+ 
+
+ align:start position:0%
+x0 is going to be close to F of x0 plus
+the gradient of F at x0 transpose x -
+
+ align:start position:0%
+the gradient of F at x0 transpose x -
+ 
+
+ align:start position:0%
+the gradient of F at x0 transpose x -
+x0 and then I'm going to have plus 12 x
+
+ align:start position:0%
+x0 and then I'm going to have plus 12 x
+ 
+
+ align:start position:0%
+x0 and then I'm going to have plus 12 x
+- x0 transpose HF at x0 x - x transpose
+
+ align:start position:0%
+- x0 transpose HF at x0 x - x transpose
+ 
+
+ align:start position:0%
+- x0 transpose HF at x0 x - x transpose
+right x- x0 so that's just my second
+
+ align:start position:0%
+right x- x0 so that's just my second
+ 
+
+ align:start position:0%
+right x- x0 so that's just my second
+order tailor expansion multivariate one
+
+ align:start position:0%
+order tailor expansion multivariate one
+ 
+
+ align:start position:0%
+order tailor expansion multivariate one
+and that's let's say if x0 is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy now what I'm going to do is say okay
+
+ align:start position:0%
+guy now what I'm going to do is say okay
+ 
+
+ align:start position:0%
+guy now what I'm going to do is say okay
+if I wanted to set this the derivative
+
+ align:start position:0%
+if I wanted to set this the derivative
+ 
+
+ align:start position:0%
+if I wanted to set this the derivative
+of this guy equal to zero I would just
+
+ align:start position:0%
+of this guy equal to zero I would just
+ 
+
+ align:start position:0%
+of this guy equal to zero I would just
+have to solve well you know frime of x
+
+ align:start position:0%
+have to solve well you know frime of x
+ 
+
+ align:start position:0%
+have to solve well you know frime of x
+equals z meaning that X has to be F
+
+ align:start position:0%
+equals z meaning that X has to be F
+ 
+
+ align:start position:0%
+equals z meaning that X has to be F
+Prime inverse of zero and really apart
+
+ align:start position:0%
+Prime inverse of zero and really apart
+ 
+
+ align:start position:0%
+Prime inverse of zero and really apart
+from like being some notation
+
+ align:start position:0%
+from like being some notation
+ 
+
+ align:start position:0%
+from like being some notation
+manipulations this is really not helping
+
+ align:start position:0%
+manipulations this is really not helping
+ 
+
+ align:start position:0%
+manipulations this is really not helping
+me okay because I don't know what fime
+
+ align:start position:0%
+me okay because I don't know what fime
+ 
+
+ align:start position:0%
+me okay because I don't know what fime
+inverse of zero is in many instances
+
+ align:start position:0%
+inverse of zero is in many instances
+ 
+
+ align:start position:0%
+inverse of zero is in many instances
+however if F has a very specific form
+
+ align:start position:0%
+however if F has a very specific form
+ 
+
+ align:start position:0%
+however if F has a very specific form
+which is something that depends on X in
+
+ align:start position:0%
+which is something that depends on X in
+ 
+
+ align:start position:0%
+which is something that depends on X in
+a very specific way there's just a
+
+ align:start position:0%
+a very specific way there's just a
+ 
+
+ align:start position:0%
+a very specific way there's just a
+linear term and then a quadratic term
+
+ align:start position:0%
+linear term and then a quadratic term
+ 
+
+ align:start position:0%
+linear term and then a quadratic term
+then I can actually do something right
+
+ align:start position:0%
+then I can actually do something right
+ 
+
+ align:start position:0%
+then I can actually do something right
+so let's forget about this approach and
+
+ align:start position:0%
+so let's forget about this approach and
+ 
+
+ align:start position:0%
+so let's forget about this approach and
+rather than minimizing F let's just
+
+ align:start position:0%
+rather than minimizing F let's just
+ 
+
+ align:start position:0%
+rather than minimizing F let's just
+minimize the right hand
+
+ align:start position:0%
+minimize the right hand
+ 
+
+ align:start position:0%
+minimize the right hand
+side okay
+
+ align:start position:0%
+side okay
+ 
+
+ align:start position:0%
+side okay
+so sorry maximize so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximize the right hand
+
+ align:start position:0%
+maximize the right hand
+ 
+
+ align:start position:0%
+maximize the right hand
+side and so how do I get this well I
+
+ align:start position:0%
+side and so how do I get this well I
+ 
+
+ align:start position:0%
+side and so how do I get this well I
+just set the
+
+ align:start position:0%
+just set the
+ 
+
+ align:start position:0%
+just set the
+gradient equal to zero so what is the
+
+ align:start position:0%
+gradient equal to zero so what is the
+ 
+
+ align:start position:0%
+gradient equal to zero so what is the
+gradient the first term does not uh
+
+ align:start position:0%
+gradient the first term does not uh
+ 
+
+ align:start position:0%
+gradient the first term does not uh
+depend on X okay so that means that this
+
+ align:start position:0%
+depend on X okay so that means that this
+ 
+
+ align:start position:0%
+depend on X okay so that means that this
+is going to be
+
+ align:start position:0%
+is going to be
+ 
+
+ align:start position:0%
+is going to be
+zero plus what is the gradient of this
+
+ align:start position:0%
+zero plus what is the gradient of this
+ 
+
+ align:start position:0%
+zero plus what is the gradient of this
+thing of uh the gradient of F at x0
+
+ align:start position:0%
+thing of uh the gradient of F at x0
+ 
+
+ align:start position:0%
+thing of uh the gradient of F at x0
+transpose x - x0 what is the gradient of
+
+ align:start position:0%
+transpose x - x0 what is the gradient of
+ 
+
+ align:start position:0%
+transpose x - x0 what is the gradient of
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy so I have a function of the Form B
+
+ align:start position:0%
+guy so I have a function of the Form B
+ 
+
+ align:start position:0%
+guy so I have a function of the Form B
+transpose x what is the gradient of this
+
+ align:start position:0%
+transpose x what is the gradient of this
+ 
+
+ align:start position:0%
+transpose x what is the gradient of this
+thing I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry I'm writing everything into column
+
+ align:start position:0%
+sorry I'm writing everything into column
+ 
+
+ align:start position:0%
+sorry I'm writing everything into column
+form right so it's just B okay so here
+
+ align:start position:0%
+form right so it's just B okay so here
+ 
+
+ align:start position:0%
+form right so it's just B okay so here
+what is B well it's
+
+ align:start position:0%
+what is B well it's
+ 
+
+ align:start position:0%
+what is B well it's
+gradient of F at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x0 okay on this term here gradient of F
+
+ align:start position:0%
+x0 okay on this term here gradient of F
+ 
+
+ align:start position:0%
+x0 okay on this term here gradient of F
+at x0 transpose x0 is just a constant
+
+ align:start position:0%
+at x0 transpose x0 is just a constant
+ 
+
+ align:start position:0%
+at x0 transpose x0 is just a constant
+this thing is going away as well and
+
+ align:start position:0%
+this thing is going away as well and
+ 
+
+ align:start position:0%
+this thing is going away as well and
+then I'm looking at the derivative of
+
+ align:start position:0%
+then I'm looking at the derivative of
+ 
+
+ align:start position:0%
+then I'm looking at the derivative of
+this guy here and this is like a
+
+ align:start position:0%
+this guy here and this is like a
+ 
+
+ align:start position:0%
+this guy here and this is like a
+quadratic term it's like H * x - x0 2 so
+
+ align:start position:0%
+quadratic term it's like H * x - x0 2 so
+ 
+
+ align:start position:0%
+quadratic term it's like H * x - x0 2 so
+when I'm going to take the derivative
+
+ align:start position:0%
+when I'm going to take the derivative
+ 
+
+ align:start position:0%
+when I'm going to take the derivative
+I'm going to have a factor two that's
+
+ align:start position:0%
+I'm going to have a factor two that's
+ 
+
+ align:start position:0%
+I'm going to have a factor two that's
+going to pop out and cancel this one
+
+ align:start position:0%
+going to pop out and cancel this one
+ 
+
+ align:start position:0%
+going to pop out and cancel this one
+half and then I'm going to be left only
+
+ align:start position:0%
+half and then I'm going to be left only
+ 
+
+ align:start position:0%
+half and then I'm going to be left only
+with this part times this part
+
+ align:start position:0%
+with this part times this part
+ 
+
+ align:start position:0%
+with this part times this part
+okay so that's
+
+ align:start position:0%
+okay so that's
+ 
+
+ align:start position:0%
+okay so that's
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+HF x -
+
+ align:start position:0%
+HF x -
+ 
+
+ align:start position:0%
+HF x -
+x0 okay so that's just the gradient and
+
+ align:start position:0%
+x0 okay so that's just the gradient and
+ 
+
+ align:start position:0%
+x0 okay so that's just the gradient and
+I want it to be equal to zero so I'm
+
+ align:start position:0%
+I want it to be equal to zero so I'm
+ 
+
+ align:start position:0%
+I want it to be equal to zero so I'm
+just going to solve this equal to
+
+ align:start position:0%
+just going to solve this equal to
+ 
+
+ align:start position:0%
+just going to solve this equal to
+zero okay so that means that if I want
+
+ align:start position:0%
+zero okay so that means that if I want
+ 
+
+ align:start position:0%
+zero okay so that means that if I want
+to find the minimum this is just going
+
+ align:start position:0%
+to find the minimum this is just going
+ 
+
+ align:start position:0%
+to find the minimum this is just going
+to be the X star that satisfies this so
+
+ align:start position:0%
+to be the X star that satisfies this so
+ 
+
+ align:start position:0%
+to be the X star that satisfies this so
+that's actually equivalent to
+
+ align:start position:0%
+that's actually equivalent to
+ 
+
+ align:start position:0%
+that's actually equivalent to
+HF * X
+
+ align:start position:0%
+HF * X
+ 
+
+ align:start position:0%
+HF * X
+star is equal
+
+ align:start position:0%
+star is equal
+ 
+
+ align:start position:0%
+star is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+HF
+
+ align:start position:0%
+HF
+ 
+
+ align:start position:0%
+HF
+x0 minus gradient F at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x0 now this is a much easier thing to
+
+ align:start position:0%
+x0 now this is a much easier thing to
+ 
+
+ align:start position:0%
+x0 now this is a much easier thing to
+solve what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this this is just a system of linear
+
+ align:start position:0%
+this this is just a system of linear
+ 
+
+ align:start position:0%
+this this is just a system of linear
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+right I just need to find the X star so
+
+ align:start position:0%
+right I just need to find the X star so
+ 
+
+ align:start position:0%
+right I just need to find the X star so
+that when I premultiply it by a matrix I
+
+ align:start position:0%
+that when I premultiply it by a matrix I
+ 
+
+ align:start position:0%
+that when I premultiply it by a matrix I
+get this Vector on the right hand side
+
+ align:start position:0%
+get this Vector on the right hand side
+ 
+
+ align:start position:0%
+get this Vector on the right hand side
+this is just something of the form ax
+
+ align:start position:0%
+this is just something of the form ax
+ 
+
+ align:start position:0%
+this is just something of the form ax
+equals B and I have many ways I can do
+
+ align:start position:0%
+equals B and I have many ways I can do
+ 
+
+ align:start position:0%
+equals B and I have many ways I can do
+this I could do gaussin elimination or I
+
+ align:start position:0%
+this I could do gaussin elimination or I
+ 
+
+ align:start position:0%
+this I could do gaussin elimination or I
+could use you know spillman's fast
+
+ align:start position:0%
+could use you know spillman's fast
+ 
+
+ align:start position:0%
+could use you know spillman's fast
+lassan solvers if I had some particular
+
+ align:start position:0%
+lassan solvers if I had some particular
+ 
+
+ align:start position:0%
+lassan solvers if I had some particular
+properties of H I mean there's huge
+
+ align:start position:0%
+properties of H I mean there's huge
+ 
+
+ align:start position:0%
+properties of H I mean there's huge
+activity in terms of how to solve those
+
+ align:start position:0%
+activity in terms of how to solve those
+ 
+
+ align:start position:0%
+activity in terms of how to solve those
+systems but let's say I don't I have
+
+ align:start position:0%
+systems but let's say I don't I have
+ 
+
+ align:start position:0%
+systems but let's say I don't I have
+some time it's not a huge problem
+
+ align:start position:0%
+some time it's not a huge problem
+ 
+
+ align:start position:0%
+some time it's not a huge problem
+I can actually just use linear algebra
+
+ align:start position:0%
+I can actually just use linear algebra
+ 
+
+ align:start position:0%
+I can actually just use linear algebra
+and linear algebra just tells me that
+
+ align:start position:0%
+and linear algebra just tells me that
+ 
+
+ align:start position:0%
+and linear algebra just tells me that
+xar is equal to HF
+
+ align:start position:0%
+xar is equal to HF
+ 
+
+ align:start position:0%
+xar is equal to HF
+inverse times this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy which those two guys are going to
+
+ align:start position:0%
+guy which those two guys are going to
+ 
+
+ align:start position:0%
+guy which those two guys are going to
+cancel so this actually equal to x0
+
+ align:start position:0%
+cancel so this actually equal to x0
+ 
+
+ align:start position:0%
+cancel so this actually equal to x0
+minus HF inverse gradient F at
+
+ align:start position:0%
+minus HF inverse gradient F at
+ 
+
+ align:start position:0%
+minus HF inverse gradient F at
+x0 and that's just what's called a
+
+ align:start position:0%
+x0 and that's just what's called a
+ 
+
+ align:start position:0%
+x0 and that's just what's called a
+Newton iterations I started at some
+
+ align:start position:0%
+Newton iterations I started at some
+ 
+
+ align:start position:0%
+Newton iterations I started at some
+x0 I'm at some x0 where I make my
+
+ align:start position:0%
+x0 I'm at some x0 where I make my
+ 
+
+ align:start position:0%
+x0 I'm at some x0 where I make my
+approximation and it's telling me if
+
+ align:start position:0%
+approximation and it's telling me if
+ 
+
+ align:start position:0%
+approximation and it's telling me if
+starting from this x zero I wanted to
+
+ align:start position:0%
+starting from this x zero I wanted to
+ 
+
+ align:start position:0%
+starting from this x zero I wanted to
+fully optimize the quadratic
+
+ align:start position:0%
+fully optimize the quadratic
+ 
+
+ align:start position:0%
+fully optimize the quadratic
+approximation I would just have to take
+
+ align:start position:0%
+approximation I would just have to take
+ 
+
+ align:start position:0%
+approximation I would just have to take
+the X star that's this guy and then I
+
+ align:start position:0%
+the X star that's this guy and then I
+ 
+
+ align:start position:0%
+the X star that's this guy and then I
+could just use this guy as my X zero and
+
+ align:start position:0%
+could just use this guy as my X zero and
+ 
+
+ align:start position:0%
+could just use this guy as my X zero and
+do it again and again and again and
+
+ align:start position:0%
+do it again and again and again and
+ 
+
+ align:start position:0%
+do it again and again and again and
+again and those are called Newton
+
+ align:start position:0%
+again and those are called Newton
+ 
+
+ align:start position:0%
+again and those are called Newton
+iterations and they're basically the
+
+ align:start position:0%
+iterations and they're basically the
+ 
+
+ align:start position:0%
+iterations and they're basically the
+working hor the Workhorse of of uh you
+
+ align:start position:0%
+working hor the Workhorse of of uh you
+ 
+
+ align:start position:0%
+working hor the Workhorse of of uh you
+know interior Point methods for example
+
+ align:start position:0%
+know interior Point methods for example
+ 
+
+ align:start position:0%
+know interior Point methods for example
+a lot of optimization algorithms and
+
+ align:start position:0%
+a lot of optimization algorithms and
+ 
+
+ align:start position:0%
+a lot of optimization algorithms and
+that's what you can you see here xar is
+
+ align:start position:0%
+that's what you can you see here xar is
+ 
+
+ align:start position:0%
+that's what you can you see here xar is
+equal to x0 minus the inverse hen times
+
+ align:start position:0%
+equal to x0 minus the inverse hen times
+ 
+
+ align:start position:0%
+equal to x0 minus the inverse hen times
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+gradient we briefly mentioned gradient
+
+ align:start position:0%
+gradient we briefly mentioned gradient
+ 
+
+ align:start position:0%
+gradient we briefly mentioned gradient
+descent we briefly mention gradient
+
+ align:start position:0%
+descent we briefly mention gradient
+ 
+
+ align:start position:0%
+descent we briefly mention gradient
+descent right at some point to optimize
+
+ align:start position:0%
+descent right at some point to optimize
+ 
+
+ align:start position:0%
+descent right at some point to optimize
+a convex function right and if I wanted
+
+ align:start position:0%
+a convex function right and if I wanted
+ 
+
+ align:start position:0%
+a convex function right and if I wanted
+to use gradient
+
+ align:start position:0%
+to use gradient
+ 
+
+ align:start position:0%
+to use gradient
+descent
+
+ align:start position:0%
+descent
+ 
+
+ align:start position:0%
+descent
+again H is a matrix but if I wanted to
+
+ align:start position:0%
+again H is a matrix but if I wanted to
+ 
+
+ align:start position:0%
+again H is a matrix but if I wanted to
+think of H as being a scalar would it be
+
+ align:start position:0%
+think of H as being a scalar would it be
+ 
+
+ align:start position:0%
+think of H as being a scalar would it be
+a positive or negative number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why yeah so that would be this so I want
+
+ align:start position:0%
+why yeah so that would be this so I want
+ 
+
+ align:start position:0%
+why yeah so that would be this so I want
+to move against the gradient to do what
+
+ align:start position:0%
+to move against the gradient to do what
+ 
+
+ align:start position:0%
+to move against the gradient to do what
+to minimize but I'm maximizing here
+
+ align:start position:0%
+to minimize but I'm maximizing here
+ 
+
+ align:start position:0%
+to minimize but I'm maximizing here
+right everything is maximized right so I
+
+ align:start position:0%
+right everything is maximized right so I
+ 
+
+ align:start position:0%
+right everything is maximized right so I
+know that H is actually negative
+
+ align:start position:0%
+know that H is actually negative
+ 
+
+ align:start position:0%
+know that H is actually negative
+definite so it's a negative number okay
+
+ align:start position:0%
+definite so it's a negative number okay
+ 
+
+ align:start position:0%
+definite so it's a negative number okay
+so that's you're making the same uh you
+
+ align:start position:0%
+so that's you're making the same uh you
+ 
+
+ align:start position:0%
+so that's you're making the same uh you
+have the same confusion as I do we're
+
+ align:start position:0%
+have the same confusion as I do we're
+ 
+
+ align:start position:0%
+have the same confusion as I do we're
+maximizing a concave function here so H
+
+ align:start position:0%
+maximizing a concave function here so H
+ 
+
+ align:start position:0%
+maximizing a concave function here so H
+is negative so this is something of the
+
+ align:start position:0%
+is negative so this is something of the
+ 
+
+ align:start position:0%
+is negative so this is something of the
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+x0 plus something times the
+
+ align:start position:0%
+x0 plus something times the
+ 
+
+ align:start position:0%
+x0 plus something times the
+gradient and this is what your gradient
+
+ align:start position:0%
+gradient and this is what your gradient
+ 
+
+ align:start position:0%
+gradient and this is what your gradient
+Ascent rather than descent would look
+
+ align:start position:0%
+Ascent rather than descent would look
+ 
+
+ align:start position:0%
+Ascent rather than descent would look
+like and all it's saying Newton is
+
+ align:start position:0%
+like and all it's saying Newton is
+ 
+
+ align:start position:0%
+like and all it's saying Newton is
+telling you don't take the gradient for
+
+ align:start position:0%
+telling you don't take the gradient for
+ 
+
+ align:start position:0%
+telling you don't take the gradient for
+granted as a direction in which you want
+
+ align:start position:0%
+granted as a direction in which you want
+ 
+
+ align:start position:0%
+granted as a direction in which you want
+to go it says do a slight change of
+
+ align:start position:0%
+to go it says do a slight change of
+ 
+
+ align:start position:0%
+to go it says do a slight change of
+coordinates before you do this according
+
+ align:start position:0%
+coordinates before you do this according
+ 
+
+ align:start position:0%
+coordinates before you do this according
+to what you're
+
+ align:start position:0%
+to what you're
+ 
+
+ align:start position:0%
+to what you're
+hashen looks
+
+ align:start position:0%
+hashen looks
+ 
+
+ align:start position:0%
+hashen looks
+like all right and that's what uh those
+
+ align:start position:0%
+like all right and that's what uh those
+ 
+
+ align:start position:0%
+like all right and that's what uh those
+are called second order methods that
+
+ align:start position:0%
+are called second order methods that
+ 
+
+ align:start position:0%
+are called second order methods that
+require knowing what the hashen is but
+
+ align:start position:0%
+require knowing what the hashen is but
+ 
+
+ align:start position:0%
+require knowing what the hashen is but
+uh those are actually much more powerful
+
+ align:start position:0%
+uh those are actually much more powerful
+ 
+
+ align:start position:0%
+uh those are actually much more powerful
+than the gradient descent because
+
+ align:start position:0%
+than the gradient descent because
+ 
+
+ align:start position:0%
+than the gradient descent because
+they're using all of the local geometry
+
+ align:start position:0%
+they're using all of the local geometry
+ 
+
+ align:start position:0%
+they're using all of the local geometry
+of the problem all of the local geometry
+
+ align:start position:0%
+of the problem all of the local geometry
+ 
+
+ align:start position:0%
+of the problem all of the local geometry
+of your function is completely encoded
+
+ align:start position:0%
+of your function is completely encoded
+ 
+
+ align:start position:0%
+of your function is completely encoded
+in this hashen and in particular it
+
+ align:start position:0%
+in this hashen and in particular it
+ 
+
+ align:start position:0%
+in this hashen and in particular it
+implies that it tells you where to
+
+ align:start position:0%
+implies that it tells you where to
+ 
+
+ align:start position:0%
+implies that it tells you where to
+switch and not uh go slower in some
+
+ align:start position:0%
+switch and not uh go slower in some
+ 
+
+ align:start position:0%
+switch and not uh go slower in some
+places or go faster in other places now
+
+ align:start position:0%
+places or go faster in other places now
+ 
+
+ align:start position:0%
+places or go faster in other places now
+this in practice for say say modern
+
+ align:start position:0%
+this in practice for say say modern
+ 
+
+ align:start position:0%
+this in practice for say say modern
+large scale machine learning problems
+
+ align:start position:0%
+large scale machine learning problems
+ 
+
+ align:start position:0%
+large scale machine learning problems
+inverting this Matrix H is extremely
+
+ align:start position:0%
+inverting this Matrix H is extremely
+ 
+
+ align:start position:0%
+inverting this Matrix H is extremely
+painful it's it takes too much time the
+
+ align:start position:0%
+painful it's it takes too much time the
+ 
+
+ align:start position:0%
+painful it's it takes too much time the
+Matrix is too big and computers cannot
+
+ align:start position:0%
+Matrix is too big and computers cannot
+ 
+
+ align:start position:0%
+Matrix is too big and computers cannot
+do it and people resort to what's called
+
+ align:start position:0%
+do it and people resort to what's called
+ 
+
+ align:start position:0%
+do it and people resort to what's called
+uh pseudo uh Newton methods which
+
+ align:start position:0%
+uh pseudo uh Newton methods which
+ 
+
+ align:start position:0%
+uh pseudo uh Newton methods which
+essentially try to emulate what this guy
+
+ align:start position:0%
+essentially try to emulate what this guy
+ 
+
+ align:start position:0%
+essentially try to emulate what this guy
+is and there's many ways you can do this
+
+ align:start position:0%
+is and there's many ways you can do this
+ 
+
+ align:start position:0%
+is and there's many ways you can do this
+some of them is by using gradients that
+
+ align:start position:0%
+some of them is by using gradients that
+ 
+
+ align:start position:0%
+some of them is by using gradients that
+you've collected in the
+
+ align:start position:0%
+you've collected in the
+ 
+
+ align:start position:0%
+you've collected in the
+past uh some of them is using the fact
+
+ align:start position:0%
+past uh some of them is using the fact
+ 
+
+ align:start position:0%
+past uh some of them is using the fact
+that uh uh just say well let's just
+
+ align:start position:0%
+that uh uh just say well let's just
+ 
+
+ align:start position:0%
+that uh uh just say well let's just
+pretend is diagonal uh just there's a
+
+ align:start position:0%
+pretend is diagonal uh just there's a
+ 
+
+ align:start position:0%
+pretend is diagonal uh just there's a
+lot of things you can do to just play
+
+ align:start position:0%
+lot of things you can do to just play
+ 
+
+ align:start position:0%
+lot of things you can do to just play
+around this and not actually have to
+
+ align:start position:0%
+around this and not actually have to
+ 
+
+ align:start position:0%
+around this and not actually have to
+invert this Matrix
+
+ align:start position:0%
+invert this Matrix
+ 
+
+ align:start position:0%
+invert this Matrix
+okay so once you have this you started
+
+ align:start position:0%
+okay so once you have this you started
+ 
+
+ align:start position:0%
+okay so once you have this you started
+from Edge zero it tells you which H star
+
+ align:start position:0%
+from Edge zero it tells you which H star
+ 
+
+ align:start position:0%
+from Edge zero it tells you which H star
+you can get uh as the maximizer of the
+
+ align:start position:0%
+you can get uh as the maximizer of the
+ 
+
+ align:start position:0%
+you can get uh as the maximizer of the
+local quadratic approximation to your
+
+ align:start position:0%
+local quadratic approximation to your
+ 
+
+ align:start position:0%
+local quadratic approximation to your
+function you can actually just iterate
+
+ align:start position:0%
+function you can actually just iterate
+ 
+
+ align:start position:0%
+function you can actually just iterate
+that all right so you start at some X
+
+ align:start position:0%
+that all right so you start at some X
+ 
+
+ align:start position:0%
+that all right so you start at some X
+zero somewhere and then once you get to
+
+ align:start position:0%
+zero somewhere and then once you get to
+ 
+
+ align:start position:0%
+zero somewhere and then once you get to
+some XK you just do the Iration we just
+
+ align:start position:0%
+some XK you just do the Iration we just
+ 
+
+ align:start position:0%
+some XK you just do the Iration we just
+described which is just find k + 1 which
+
+ align:start position:0%
+described which is just find k + 1 which
+ 
+
+ align:start position:0%
+described which is just find k + 1 which
+is the maximizer of the local quadratic
+
+ align:start position:0%
+is the maximizer of the local quadratic
+ 
+
+ align:start position:0%
+is the maximizer of the local quadratic
+approximation to your function at XK and
+
+ align:start position:0%
+approximation to your function at XK and
+ 
+
+ align:start position:0%
+approximation to your function at XK and
+repeat until
+
+ align:start position:0%
+repeat until
+ 
+
+ align:start position:0%
+repeat until
+convergence okay so if this was an
+
+ align:start position:0%
+convergence okay so if this was an
+ 
+
+ align:start position:0%
+convergence okay so if this was an
+optimization class we would prove that
+
+ align:start position:0%
+optimization class we would prove that
+ 
+
+ align:start position:0%
+optimization class we would prove that
+convergence actually eventually happens
+
+ align:start position:0%
+convergence actually eventually happens
+ 
+
+ align:start position:0%
+convergence actually eventually happens
+for a uh strictly concave function uh
+
+ align:start position:0%
+for a uh strictly concave function uh
+ 
+
+ align:start position:0%
+for a uh strictly concave function uh
+this is a stas class you're just going
+
+ align:start position:0%
+this is a stas class you're just going
+ 
+
+ align:start position:0%
+this is a stas class you're just going
+to have to trust me that this is the
+
+ align:start position:0%
+to have to trust me that this is the
+ 
+
+ align:start position:0%
+to have to trust me that this is the
+case and it's globally convergent
+
+ align:start position:0%
+case and it's globally convergent
+ 
+
+ align:start position:0%
+case and it's globally convergent
+meaning that you can start wherever you
+
+ align:start position:0%
+meaning that you can start wherever you
+ 
+
+ align:start position:0%
+meaning that you can start wherever you
+want and uh and it's going to work and
+
+ align:start position:0%
+want and uh and it's going to work and
+ 
+
+ align:start position:0%
+want and uh and it's going to work and
+uh uh for under minor conditions on F in
+
+ align:start position:0%
+uh uh for under minor conditions on F in
+ 
+
+ align:start position:0%
+uh uh for under minor conditions on F in
+particular those conditions are
+
+ align:start position:0%
+particular those conditions are
+ 
+
+ align:start position:0%
+particular those conditions are
+satisfied for the uh log likelihood
+
+ align:start position:0%
+satisfied for the uh log likelihood
+ 
+
+ align:start position:0%
+satisfied for the uh log likelihood
+functions we have in mind okay and it
+
+ align:start position:0%
+functions we have in mind okay and it
+ 
+
+ align:start position:0%
+functions we have in mind okay and it
+converges at an extremely fast rate
+
+ align:start position:0%
+converges at an extremely fast rate
+ 
+
+ align:start position:0%
+converges at an extremely fast rate
+usually it's quadratic conversions which
+
+ align:start position:0%
+usually it's quadratic conversions which
+ 
+
+ align:start position:0%
+usually it's quadratic conversions which
+means that every time you make one step
+
+ align:start position:0%
+means that every time you make one step
+ 
+
+ align:start position:0%
+means that every time you make one step
+you improve the accuracy of your
+
+ align:start position:0%
+you improve the accuracy of your
+ 
+
+ align:start position:0%
+you improve the accuracy of your
+Solution by two
+
+ align:start position:0%
+Solution by two
+ 
+
+ align:start position:0%
+Solution by two
+digits
+
+ align:start position:0%
+digits
+ 
+
+ align:start position:0%
+digits
+okay uh if that's something you you're
+
+ align:start position:0%
+okay uh if that's something you you're
+ 
+
+ align:start position:0%
+okay uh if that's something you you're
+vely interested in I highly recommend
+
+ align:start position:0%
+vely interested in I highly recommend
+ 
+
+ align:start position:0%
+vely interested in I highly recommend
+that you take a class on nonlinear
+
+ align:start position:0%
+that you take a class on nonlinear
+ 
+
+ align:start position:0%
+that you take a class on nonlinear
+optimization it's a fascinating topic
+
+ align:start position:0%
+optimization it's a fascinating topic
+ 
+
+ align:start position:0%
+optimization it's a fascinating topic
+unfortunately we don't have much time
+
+ align:start position:0%
+unfortunately we don't have much time
+ 
+
+ align:start position:0%
+unfortunately we don't have much time
+but it starts to in being more and more
+
+ align:start position:0%
+but it starts to in being more and more
+ 
+
+ align:start position:0%
+but it starts to in being more and more
+intertwined with high dimensional
+
+ align:start position:0%
+intertwined with high dimensional
+ 
+
+ align:start position:0%
+intertwined with high dimensional
+statistics and and machine
+
+ align:start position:0%
+statistics and and machine
+ 
+
+ align:start position:0%
+statistics and and machine
+learning that's about div I mean it's
+
+ align:start position:0%
+learning that's about div I mean it's
+ 
+
+ align:start position:0%
+learning that's about div I mean it's
+it's an algorithm's class typically but
+
+ align:start position:0%
+it's an algorithm's class typically but
+ 
+
+ align:start position:0%
+it's an algorithm's class typically but
+it's very much um uh maybe more
+
+ align:start position:0%
+it's very much um uh maybe more
+ 
+
+ align:start position:0%
+it's very much um uh maybe more
+principled it's not a bunch of
+
+ align:start position:0%
+principled it's not a bunch of
+ 
+
+ align:start position:0%
+principled it's not a bunch of
+algorithms that solve a bunch of
+
+ align:start position:0%
+algorithms that solve a bunch of
+ 
+
+ align:start position:0%
+algorithms that solve a bunch of
+problems there's basically one basic
+
+ align:start position:0%
+problems there's basically one basic
+ 
+
+ align:start position:0%
+problems there's basically one basic
+idea which is if I have a convex
+
+ align:start position:0%
+idea which is if I have a convex
+ 
+
+ align:start position:0%
+idea which is if I have a convex
+function I can actually minimize it if I
+
+ align:start position:0%
+function I can actually minimize it if I
+ 
+
+ align:start position:0%
+function I can actually minimize it if I
+have a convex concave function I can
+
+ align:start position:0%
+have a convex concave function I can
+ 
+
+ align:start position:0%
+have a convex concave function I can
+maximize it then there's it evolves
+
+ align:start position:0%
+maximize it then there's it evolves
+ 
+
+ align:start position:0%
+maximize it then there's it evolves
+around similar thing all right so let's
+
+ align:start position:0%
+around similar thing all right so let's
+ 
+
+ align:start position:0%
+around similar thing all right so let's
+stare at this iterative step for a
+
+ align:start position:0%
+stare at this iterative step for a
+ 
+
+ align:start position:0%
+stare at this iterative step for a
+second and pause and ask me let me know
+
+ align:start position:0%
+second and pause and ask me let me know
+ 
+
+ align:start position:0%
+second and pause and ask me let me know
+if you have any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so of course in a second
+
+ align:start position:0%
+questions okay so of course in a second
+ 
+
+ align:start position:0%
+questions okay so of course in a second
+we will plug in for the L likelihood
+
+ align:start position:0%
+we will plug in for the L likelihood
+ 
+
+ align:start position:0%
+we will plug in for the L likelihood
+this is just a general thing for a
+
+ align:start position:0%
+this is just a general thing for a
+ 
+
+ align:start position:0%
+this is just a general thing for a
+general function f but in a in a second
+
+ align:start position:0%
+general function f but in a in a second
+ 
+
+ align:start position:0%
+general function f but in a in a second
+f is going to be Ln
+
+ align:start position:0%
+f is going to be Ln
+ 
+
+ align:start position:0%
+f is going to be Ln
+okay so if I wanted to implement that
+
+ align:start position:0%
+okay so if I wanted to implement that
+ 
+
+ align:start position:0%
+okay so if I wanted to implement that
+for real I would have to compute the
+
+ align:start position:0%
+for real I would have to compute the
+ 
+
+ align:start position:0%
+for real I would have to compute the
+gradient of Ln at a point XK and I would
+
+ align:start position:0%
+gradient of Ln at a point XK and I would
+ 
+
+ align:start position:0%
+gradient of Ln at a point XK and I would
+have to compute the Hasen at a given
+
+ align:start position:0%
+have to compute the Hasen at a given
+ 
+
+ align:start position:0%
+have to compute the Hasen at a given
+point and
+
+ align:start position:0%
+point and
+ 
+
+ align:start position:0%
+point and
+inverted okay so this is just a basic
+
+ align:start position:0%
+inverted okay so this is just a basic
+ 
+
+ align:start position:0%
+inverted okay so this is just a basic
+algorithm and this as as you can tell
+
+ align:start position:0%
+algorithm and this as as you can tell
+ 
+
+ align:start position:0%
+algorithm and this as as you can tell
+used in no place the fact that Ln was
+
+ align:start position:0%
+used in no place the fact that Ln was
+ 
+
+ align:start position:0%
+used in no place the fact that Ln was
+the log likelihood Associated to some
+
+ align:start position:0%
+the log likelihood Associated to some
+ 
+
+ align:start position:0%
+the log likelihood Associated to some
+canonical exponential family in a
+
+ align:start position:0%
+canonical exponential family in a
+ 
+
+ align:start position:0%
+canonical exponential family in a
+generalized linear model right this
+
+ align:start position:0%
+generalized linear model right this
+ 
+
+ align:start position:0%
+generalized linear model right this
+never showed up so can we use that
+
+ align:start position:0%
+never showed up so can we use that
+ 
+
+ align:start position:0%
+never showed up so can we use that
+somehow uh optimization for long longest
+
+ align:start position:0%
+somehow uh optimization for long longest
+ 
+
+ align:start position:0%
+somehow uh optimization for long longest
+time was about making your problems as
+
+ align:start position:0%
+time was about making your problems as
+ 
+
+ align:start position:0%
+time was about making your problems as
+general as possible accumulating maybe
+
+ align:start position:0%
+general as possible accumulating maybe
+ 
+
+ align:start position:0%
+general as possible accumulating maybe
+in the Inter Point method Theory and
+
+ align:start position:0%
+in the Inter Point method Theory and
+ 
+
+ align:start position:0%
+in the Inter Point method Theory and
+conic programming in the mid 90s and now
+
+ align:start position:0%
+conic programming in the mid 90s and now
+ 
+
+ align:start position:0%
+conic programming in the mid 90s and now
+what optimization is doing is that it's
+
+ align:start position:0%
+what optimization is doing is that it's
+ 
+
+ align:start position:0%
+what optimization is doing is that it's
+very general it says okay if I want to
+
+ align:start position:0%
+very general it says okay if I want to
+ 
+
+ align:start position:0%
+very general it says okay if I want to
+start to go fast I need to exploit as
+
+ align:start position:0%
+start to go fast I need to exploit as
+ 
+
+ align:start position:0%
+start to go fast I need to exploit as
+much structure about my problem as I can
+
+ align:start position:0%
+much structure about my problem as I can
+ 
+
+ align:start position:0%
+much structure about my problem as I can
+and the beauty is that as statisticians
+
+ align:start position:0%
+and the beauty is that as statisticians
+ 
+
+ align:start position:0%
+and the beauty is that as statisticians
+or machine learning people we do have a
+
+ align:start position:0%
+or machine learning people we do have a
+ 
+
+ align:start position:0%
+or machine learning people we do have a
+bunch of very specific problem that we
+
+ align:start position:0%
+bunch of very specific problem that we
+ 
+
+ align:start position:0%
+bunch of very specific problem that we
+want optimizers to solve and they can
+
+ align:start position:0%
+want optimizers to solve and they can
+ 
+
+ align:start position:0%
+want optimizers to solve and they can
+make things run much faster but this did
+
+ align:start position:0%
+make things run much faster but this did
+ 
+
+ align:start position:0%
+make things run much faster but this did
+not require to wait until the 21st
+
+ align:start position:0%
+not require to wait until the 21st
+ 
+
+ align:start position:0%
+not require to wait until the 21st
+century problem with very specific
+
+ align:start position:0%
+century problem with very specific
+ 
+
+ align:start position:0%
+century problem with very specific
+structure of Ros already in the this
+
+ align:start position:0%
+structure of Ros already in the this
+ 
+
+ align:start position:0%
+structure of Ros already in the this
+generalized linear model so what do we
+
+ align:start position:0%
+generalized linear model so what do we
+ 
+
+ align:start position:0%
+generalized linear model so what do we
+know well we know that this log
+
+ align:start position:0%
+know well we know that this log
+ 
+
+ align:start position:0%
+know well we know that this log
+likelihood is really one thing that
+
+ align:start position:0%
+likelihood is really one thing that
+ 
+
+ align:start position:0%
+likelihood is really one thing that
+comes when we're trying to replace an
+
+ align:start position:0%
+comes when we're trying to replace an
+ 
+
+ align:start position:0%
+comes when we're trying to replace an
+expectation by an average and then doing
+
+ align:start position:0%
+expectation by an average and then doing
+ 
+
+ align:start position:0%
+expectation by an average and then doing
+something fency right that was our
+
+ align:start position:0%
+something fency right that was our
+ 
+
+ align:start position:0%
+something fency right that was our
+statistical hammer and remember when we
+
+ align:start position:0%
+statistical hammer and remember when we
+ 
+
+ align:start position:0%
+statistical hammer and remember when we
+introduced likelihood maximization we
+
+ align:start position:0%
+introduced likelihood maximization we
+ 
+
+ align:start position:0%
+introduced likelihood maximization we
+just said what we really want to do is
+
+ align:start position:0%
+just said what we really want to do is
+ 
+
+ align:start position:0%
+just said what we really want to do is
+to minimize the K right that's the thing
+
+ align:start position:0%
+to minimize the K right that's the thing
+ 
+
+ align:start position:0%
+to minimize the K right that's the thing
+we wanted to minimize the K Divergence
+
+ align:start position:0%
+we wanted to minimize the K Divergence
+ 
+
+ align:start position:0%
+we wanted to minimize the K Divergence
+between two distributions the true one
+
+ align:start position:0%
+between two distributions the true one
+ 
+
+ align:start position:0%
+between two distributions the true one
+and the one that's parameterized by some
+
+ align:start position:0%
+and the one that's parameterized by some
+ 
+
+ align:start position:0%
+and the one that's parameterized by some
+unknown Theta and we're trying to
+
+ align:start position:0%
+unknown Theta and we're trying to
+ 
+
+ align:start position:0%
+unknown Theta and we're trying to
+minimize that over Theta and we said
+
+ align:start position:0%
+minimize that over Theta and we said
+ 
+
+ align:start position:0%
+minimize that over Theta and we said
+well I don't know what this is because
+
+ align:start position:0%
+well I don't know what this is because
+ 
+
+ align:start position:0%
+well I don't know what this is because
+it's an expectation with respect to some
+
+ align:start position:0%
+it's an expectation with respect to some
+ 
+
+ align:start position:0%
+it's an expectation with respect to some
+unknown distribution so let me just
+
+ align:start position:0%
+unknown distribution so let me just
+ 
+
+ align:start position:0%
+unknown distribution so let me just
+replace the expectation with respect to
+
+ align:start position:0%
+replace the expectation with respect to
+ 
+
+ align:start position:0%
+replace the expectation with respect to
+my unknown distribution by an average
+
+ align:start position:0%
+my unknown distribution by an average
+ 
+
+ align:start position:0%
+my unknown distribution by an average
+over my data points and that's how we
+
+ align:start position:0%
+over my data points and that's how we
+ 
+
+ align:start position:0%
+over my data points and that's how we
+Justified the existence of the log
+
+ align:start position:0%
+Justified the existence of the log
+ 
+
+ align:start position:0%
+Justified the existence of the log
+likelihood maximization
+
+ align:start position:0%
+likelihood maximization
+ 
+
+ align:start position:0%
+likelihood maximization
+problem but
+
+ align:start position:0%
+problem but
+ 
+
+ align:start position:0%
+problem but
+here I actually
+
+ align:start position:0%
+here I actually
+ 
+
+ align:start position:0%
+here I actually
+I might be able to compute this
+
+ align:start position:0%
+I might be able to compute this
+ 
+
+ align:start position:0%
+I might be able to compute this
+expectation at least partially where I
+
+ align:start position:0%
+expectation at least partially where I
+ 
+
+ align:start position:0%
+expectation at least partially where I
+need it and what we're going to do is
+
+ align:start position:0%
+need it and what we're going to do is
+ 
+
+ align:start position:0%
+need it and what we're going to do is
+we're going to say
+
+ align:start position:0%
+we're going to say
+ 
+
+ align:start position:0%
+we're going to say
+okay since at a given point XK say let
+
+ align:start position:0%
+okay since at a given point XK say let
+ 
+
+ align:start position:0%
+okay since at a given point XK say let
+me call it here Theta I'm trying to find
+
+ align:start position:0%
+me call it here Theta I'm trying to find
+ 
+
+ align:start position:0%
+me call it here Theta I'm trying to find
+the inverse of the
+
+ align:start position:0%
+the inverse of the
+ 
+
+ align:start position:0%
+the inverse of the
+hashen of my log likelihood right so if
+
+ align:start position:0%
+hashen of my log likelihood right so if
+ 
+
+ align:start position:0%
+hashen of my log likelihood right so if
+you look at the previous one as I said
+
+ align:start position:0%
+you look at the previous one as I said
+ 
+
+ align:start position:0%
+you look at the previous one as I said
+we're going to have to compute the
+
+ align:start position:0%
+we're going to have to compute the
+ 
+
+ align:start position:0%
+we're going to have to compute the
+hashen H sub Ln of XK and then invert it
+
+ align:start position:0%
+hashen H sub Ln of XK and then invert it
+ 
+
+ align:start position:0%
+hashen H sub Ln of XK and then invert it
+but let's forget about the inversion
+
+ align:start position:0%
+but let's forget about the inversion
+ 
+
+ align:start position:0%
+but let's forget about the inversion
+step for a second we have to compute the
+
+ align:start position:0%
+step for a second we have to compute the
+ 
+
+ align:start position:0%
+step for a second we have to compute the
+Hasen this is because we're trying this
+
+ align:start position:0%
+Hasen this is because we're trying this
+ 
+
+ align:start position:0%
+Hasen this is because we're trying this
+is the Hasen of the function we're
+
+ align:start position:0%
+is the Hasen of the function we're
+ 
+
+ align:start position:0%
+is the Hasen of the function we're
+trying to minimize but if I could
+
+ align:start position:0%
+trying to minimize but if I could
+ 
+
+ align:start position:0%
+trying to minimize but if I could
+actually replace it not by the function
+
+ align:start position:0%
+actually replace it not by the function
+ 
+
+ align:start position:0%
+actually replace it not by the function
+I'm trying to minimize to maximize sorry
+
+ align:start position:0%
+I'm trying to minimize to maximize sorry
+ 
+
+ align:start position:0%
+I'm trying to minimize to maximize sorry
+the log likelihood but really by the
+
+ align:start position:0%
+the log likelihood but really by the
+ 
+
+ align:start position:0%
+the log likelihood but really by the
+function I wish I was actually Maxim
+
+ align:start position:0%
+function I wish I was actually Maxim
+ 
+
+ align:start position:0%
+function I wish I was actually Maxim
+minimizing which is the K right then
+
+ align:start position:0%
+minimizing which is the K right then
+ 
+
+ align:start position:0%
+minimizing which is the K right then
+that would be really nice and what
+
+ align:start position:0%
+that would be really nice and what
+ 
+
+ align:start position:0%
+that would be really nice and what
+happens is that since I'm actually
+
+ align:start position:0%
+happens is that since I'm actually
+ 
+
+ align:start position:0%
+happens is that since I'm actually
+trying to find this at a given XK I can
+
+ align:start position:0%
+trying to find this at a given XK I can
+ 
+
+ align:start position:0%
+trying to find this at a given XK I can
+always pretend that this x key that I
+
+ align:start position:0%
+always pretend that this x key that I
+ 
+
+ align:start position:0%
+always pretend that this x key that I
+have in my current iteration is the true
+
+ align:start position:0%
+have in my current iteration is the true
+ 
+
+ align:start position:0%
+have in my current iteration is the true
+one and compute my expectations respect
+
+ align:start position:0%
+one and compute my expectations respect
+ 
+
+ align:start position:0%
+one and compute my expectations respect
+to that guy and what happens is that I
+
+ align:start position:0%
+to that guy and what happens is that I
+ 
+
+ align:start position:0%
+to that guy and what happens is that I
+know that when I compute the expectation
+
+ align:start position:0%
+know that when I compute the expectation
+ 
+
+ align:start position:0%
+know that when I compute the expectation
+of the Hasen of the log likelihood at a
+
+ align:start position:0%
+of the Hasen of the log likelihood at a
+ 
+
+ align:start position:0%
+of the Hasen of the log likelihood at a
+given Theta and when I take the
+
+ align:start position:0%
+given Theta and when I take the
+ 
+
+ align:start position:0%
+given Theta and when I take the
+expectation with respect to the same
+
+ align:start position:0%
+expectation with respect to the same
+ 
+
+ align:start position:0%
+expectation with respect to the same
+Theta what I get out is negative Fisher
+
+ align:start position:0%
+Theta what I get out is negative Fisher
+ 
+
+ align:start position:0%
+Theta what I get out is negative Fisher
+information right the Fisher information
+
+ align:start position:0%
+information right the Fisher information
+ 
+
+ align:start position:0%
+information right the Fisher information
+was defined in two ways as the
+
+ align:start position:0%
+was defined in two ways as the
+ 
+
+ align:start position:0%
+was defined in two ways as the
+expectation of the square of the
+
+ align:start position:0%
+expectation of the square of the
+ 
+
+ align:start position:0%
+expectation of the square of the
+derivative or the um expectation
+
+ align:start position:0%
+derivative or the um expectation
+ 
+
+ align:start position:0%
+derivative or the um expectation
+negative the expectation of the second
+
+ align:start position:0%
+negative the expectation of the second
+ 
+
+ align:start position:0%
+negative the expectation of the second
+dtive of the log
+
+ align:start position:0%
+dtive of the log
+ 
+
+ align:start position:0%
+dtive of the log
+like and
+
+ align:start position:0%
+like and
+ 
+
+ align:start position:0%
+like and
+so now I'm doing some sort of a leap of
+
+ align:start position:0%
+so now I'm doing some sort of a leap of
+ 
+
+ align:start position:0%
+so now I'm doing some sort of a leap of
+faith here because this Theta there's no
+
+ align:start position:0%
+faith here because this Theta there's no
+ 
+
+ align:start position:0%
+faith here because this Theta there's no
+way the Theta which is the current XK
+
+ align:start position:0%
+way the Theta which is the current XK
+ 
+
+ align:start position:0%
+way the Theta which is the current XK
+that's the current Theta at which I'm
+
+ align:start position:0%
+that's the current Theta at which I'm
+ 
+
+ align:start position:0%
+that's the current Theta at which I'm
+actually doing this optimization I'm
+
+ align:start position:0%
+actually doing this optimization I'm
+ 
+
+ align:start position:0%
+actually doing this optimization I'm
+actually pretending that this is the
+
+ align:start position:0%
+actually pretending that this is the
+ 
+
+ align:start position:0%
+actually pretending that this is the
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one but uh what's going to change by
+
+ align:start position:0%
+one but uh what's going to change by
+ 
+
+ align:start position:0%
+one but uh what's going to change by
+doing this is that it's going to make my
+
+ align:start position:0%
+doing this is that it's going to make my
+ 
+
+ align:start position:0%
+doing this is that it's going to make my
+life easier because when I take
+
+ align:start position:0%
+life easier because when I take
+ 
+
+ align:start position:0%
+life easier because when I take
+expectations I tend to have when I will
+
+ align:start position:0%
+expectations I tend to have when I will
+ 
+
+ align:start position:0%
+expectations I tend to have when I will
+see that when we look at the
+
+ align:start position:0%
+see that when we look at the
+ 
+
+ align:start position:0%
+see that when we look at the
+hhen it's so the hhen as essentially the
+
+ align:start position:0%
+hhen it's so the hhen as essentially the
+ 
+
+ align:start position:0%
+hhen it's so the hhen as essentially the
+derivative of uh say a product is going
+
+ align:start position:0%
+derivative of uh say a product is going
+ 
+
+ align:start position:0%
+derivative of uh say a product is going
+to be the sum of two terms right the
+
+ align:start position:0%
+to be the sum of two terms right the
+ 
+
+ align:start position:0%
+to be the sum of two terms right the
+derivative of U * V is U Prime V plus UV
+
+ align:start position:0%
+derivative of U * V is U Prime V plus UV
+ 
+
+ align:start position:0%
+derivative of U * V is U Prime V plus UV
+prime one of those two terms is actually
+
+ align:start position:0%
+prime one of those two terms is actually
+ 
+
+ align:start position:0%
+prime one of those two terms is actually
+going to have expectations zero and
+
+ align:start position:0%
+going to have expectations zero and
+ 
+
+ align:start position:0%
+going to have expectations zero and
+that's going to make my life very easy
+
+ align:start position:0%
+that's going to make my life very easy
+ 
+
+ align:start position:0%
+that's going to make my life very easy
+when I take expectations and basically
+
+ align:start position:0%
+when I take expectations and basically
+ 
+
+ align:start position:0%
+when I take expectations and basically
+going to just have one term that's going
+
+ align:start position:0%
+going to just have one term that's going
+ 
+
+ align:start position:0%
+going to just have one term that's going
+to go away and so in particular my
+
+ align:start position:0%
+to go away and so in particular my
+ 
+
+ align:start position:0%
+to go away and so in particular my
+formula is just by the virtue of taking
+
+ align:start position:0%
+formula is just by the virtue of taking
+ 
+
+ align:start position:0%
+formula is just by the virtue of taking
+this expectation before inverting the
+
+ align:start position:0%
+this expectation before inverting the
+ 
+
+ align:start position:0%
+this expectation before inverting the
+Hess is going to just shrink the size of
+
+ align:start position:0%
+Hess is going to just shrink the size of
+ 
+
+ align:start position:0%
+Hess is going to just shrink the size of
+my formulas by
+
+ align:start position:0%
+my formulas by
+ 
+
+ align:start position:0%
+my formulas by
+half okay so let's see how this works
+
+ align:start position:0%
+half okay so let's see how this works
+ 
+
+ align:start position:0%
+half okay so let's see how this works
+you don't have to believe me uh is there
+
+ align:start position:0%
+you don't have to believe me uh is there
+ 
+
+ align:start position:0%
+you don't have to believe me uh is there
+any question about this slide you gu
+
+ align:start position:0%
+any question about this slide you gu
+ 
+
+ align:start position:0%
+any question about this slide you gu
+remember when we were doing maximum
+
+ align:start position:0%
+remember when we were doing maximum
+ 
+
+ align:start position:0%
+remember when we were doing maximum
+likelihood estimation and you know
+
+ align:start position:0%
+likelihood estimation and you know
+ 
+
+ align:start position:0%
+likelihood estimation and you know
+Fisher information and the KE Divergence
+
+ align:start position:0%
+Fisher information and the KE Divergence
+ 
+
+ align:start position:0%
+Fisher information and the KE Divergence
+Etc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah because that's what we're really
+
+ align:start position:0%
+yeah because that's what we're really
+ 
+
+ align:start position:0%
+yeah because that's what we're really
+trying to minimize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so there's something you need to uh
+
+ align:start position:0%
+so there's something you need to uh
+ 
+
+ align:start position:0%
+so there's something you need to uh
+trust me with which is that the
+
+ align:start position:0%
+trust me with which is that the
+ 
+
+ align:start position:0%
+trust me with which is that the
+expectation of H of Ln is actually h of
+
+ align:start position:0%
+expectation of H of Ln is actually h of
+ 
+
+ align:start position:0%
+expectation of H of Ln is actually h of
+the expectation of
+
+ align:start position:0%
+the expectation of
+ 
+
+ align:start position:0%
+the expectation of
+Ln all
+
+ align:start position:0%
+Ln all
+ 
+
+ align:start position:0%
+Ln all
+right yeah it's true right because the
+
+ align:start position:0%
+right yeah it's true right because the
+ 
+
+ align:start position:0%
+right yeah it's true right because the
+derivative taking derivative is a linear
+
+ align:start position:0%
+derivative taking derivative is a linear
+ 
+
+ align:start position:0%
+derivative taking derivative is a linear
+operator and we actually used that
+
+ align:start position:0%
+operator and we actually used that
+ 
+
+ align:start position:0%
+operator and we actually used that
+several times when we said expectation
+
+ align:start position:0%
+several times when we said expectation
+ 
+
+ align:start position:0%
+several times when we said expectation
+of second derivative well actually
+
+ align:start position:0%
+of second derivative well actually
+ 
+
+ align:start position:0%
+of second derivative well actually
+expectation of partial of L with respect
+
+ align:start position:0%
+expectation of partial of L with respect
+ 
+
+ align:start position:0%
+expectation of partial of L with respect
+to Theta is equal to zero remember we
+
+ align:start position:0%
+to Theta is equal to zero remember we
+ 
+
+ align:start position:0%
+to Theta is equal to zero remember we
+did that it's basically what we use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's the log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likelihood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+actually Ln is typically not normalized
+
+ align:start position:0%
+actually Ln is typically not normalized
+ 
+
+ align:start position:0%
+actually Ln is typically not normalized
+so I really should talk about Ln Over N
+
+ align:start position:0%
+so I really should talk about Ln Over N
+ 
+
+ align:start position:0%
+so I really should talk about Ln Over N
+okay but let's see that okay
+
+ align:start position:0%
+okay but let's see that okay
+ 
+
+ align:start position:0%
+okay but let's see that okay
+so if I have IID observations that
+
+ align:start position:0%
+so if I have IID observations that
+ 
+
+ align:start position:0%
+so if I have IID observations that
+should be pretty obvious okay so if I
+
+ align:start position:0%
+should be pretty obvious okay so if I
+ 
+
+ align:start position:0%
+should be pretty obvious okay so if I
+have IID say X1 xn with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density F Theta and if I look at log F
+
+ align:start position:0%
+density F Theta and if I look at log F
+ 
+
+ align:start position:0%
+density F Theta and if I look at log F
+Theta of x i sum from I one to n as I
+
+ align:start position:0%
+Theta of x i sum from I one to n as I
+ 
+
+ align:start position:0%
+Theta of x i sum from I one to n as I
+said I need to actually have a one over
+
+ align:start position:0%
+said I need to actually have a one over
+ 
+
+ align:start position:0%
+said I need to actually have a one over
+n here when I look at the expectation
+
+ align:start position:0%
+n here when I look at the expectation
+ 
+
+ align:start position:0%
+n here when I look at the expectation
+they all have the same expectation right
+
+ align:start position:0%
+they all have the same expectation right
+ 
+
+ align:start position:0%
+they all have the same expectation right
+so this is actually indeed equal to um
+
+ align:start position:0%
+so this is actually indeed equal to um
+ 
+
+ align:start position:0%
+so this is actually indeed equal to um
+negative KL plus a constant okay and
+
+ align:start position:0%
+negative KL plus a constant okay and
+ 
+
+ align:start position:0%
+negative KL plus a constant okay and
+negative K is because this if I sorry if
+
+ align:start position:0%
+negative K is because this if I sorry if
+ 
+
+ align:start position:0%
+negative K is because this if I sorry if
+I look at the expectation so the
+
+ align:start position:0%
+I look at the expectation so the
+ 
+
+ align:start position:0%
+I look at the expectation so the
+expectation of this guy is just the
+
+ align:start position:0%
+expectation of this guy is just the
+ 
+
+ align:start position:0%
+expectation of this guy is just the
+expectation of one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them all right so I just do expectation
+
+ align:start position:0%
+them all right so I just do expectation
+ 
+
+ align:start position:0%
+them all right so I just do expectation
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+agreed the K remember the K was
+
+ align:start position:0%
+agreed the K remember the K was
+ 
+
+ align:start position:0%
+agreed the K remember the K was
+expectation Theta log F Theta divided by
+
+ align:start position:0%
+expectation Theta log F Theta divided by
+ 
+
+ align:start position:0%
+expectation Theta log F Theta divided by
+F so that's between P Theta and P Theta
+
+ align:start position:0%
+F so that's between P Theta and P Theta
+ 
+
+ align:start position:0%
+F so that's between P Theta and P Theta
+Prime and that's uh well no sorry that's
+
+ align:start position:0%
+Prime and that's uh well no sorry that's
+ 
+
+ align:start position:0%
+Prime and that's uh well no sorry that's
+the true
+
+ align:start position:0%
+the true
+ 
+
+ align:start position:0%
+the true
+p and let's call it f p Theta right so
+
+ align:start position:0%
+p and let's call it f p Theta right so
+ 
+
+ align:start position:0%
+p and let's call it f p Theta right so
+that's the that's what showed up which
+
+ align:start position:0%
+that's the that's what showed up which
+ 
+
+ align:start position:0%
+that's the that's what showed up which
+is indeed equal to expect minus
+
+ align:start position:0%
+is indeed equal to expect minus
+ 
+
+ align:start position:0%
+is indeed equal to expect minus
+expectation Theta log F theta plus log
+
+ align:start position:0%
+expectation Theta log F theta plus log
+ 
+
+ align:start position:0%
+expectation Theta log F theta plus log
+of f which is just a
+
+ align:start position:0%
+of f which is just a
+ 
+
+ align:start position:0%
+of f which is just a
+constant with respect to Theta right
+
+ align:start position:0%
+constant with respect to Theta right
+ 
+
+ align:start position:0%
+constant with respect to Theta right
+that's just the thing that's up there it
+
+ align:start position:0%
+that's just the thing that's up there it
+ 
+
+ align:start position:0%
+that's just the thing that's up there it
+doesn't matter
+
+ align:start position:0%
+doesn't matter
+ 
+
+ align:start position:0%
+doesn't matter
+okay so this is uh what shows up here
+
+ align:start position:0%
+okay so this is uh what shows up here
+ 
+
+ align:start position:0%
+okay so this is uh what shows up here
+and just the fact that I have this one
+
+ align:start position:0%
+and just the fact that I have this one
+ 
+
+ align:start position:0%
+and just the fact that I have this one
+over n doesn't change because they're
+
+ align:start position:0%
+over n doesn't change because they're
+ 
+
+ align:start position:0%
+over n doesn't change because they're
+IID now when I have things that are not
+
+ align:start position:0%
+IID now when I have things that are not
+ 
+
+ align:start position:0%
+IID now when I have things that are not
+IID because what I really had was y1 YN
+
+ align:start position:0%
+IID because what I really had was y1 YN
+ 
+
+ align:start position:0%
+IID because what I really had was y1 YN
+and Yi at at density F Theta I which is
+
+ align:start position:0%
+and Yi at at density F Theta I which is
+ 
+
+ align:start position:0%
+and Yi at at density F Theta I which is
+just the conditional density given XI
+
+ align:start position:0%
+just the conditional density given XI
+ 
+
+ align:start position:0%
+just the conditional density given XI
+then I could still write this and now
+
+ align:start position:0%
+then I could still write this and now
+ 
+
+ align:start position:0%
+then I could still write this and now
+when I look at the expectation of this
+
+ align:start position:0%
+when I look at the expectation of this
+ 
+
+ align:start position:0%
+when I look at the expectation of this
+guy what I'm going to be left with is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just 1/ n sum from I = 1 to n of the
+
+ align:start position:0%
+just 1/ n sum from I = 1 to n of the
+ 
+
+ align:start position:0%
+just 1/ n sum from I = 1 to n of the
+expectation of
+
+ align:start position:0%
+expectation of
+ 
+
+ align:start position:0%
+expectation of
+log F Theta I of
+
+ align:start position:0%
+log F Theta I of
+ 
+
+ align:start position:0%
+log F Theta I of
+Yi okay and it's basically the same
+
+ align:start position:0%
+Yi okay and it's basically the same
+ 
+
+ align:start position:0%
+Yi okay and it's basically the same
+thing except that I have a one over n
+
+ align:start position:0%
+thing except that I have a one over n
+ 
+
+ align:start position:0%
+thing except that I have a one over n
+expectation in front and I didn't tell
+
+ align:start position:0%
+expectation in front and I didn't tell
+ 
+
+ align:start position:0%
+expectation in front and I didn't tell
+you this because I only show show you
+
+ align:start position:0%
+you this because I only show show you
+ 
+
+ align:start position:0%
+you this because I only show show you
+what the k Divergence was for between
+
+ align:start position:0%
+what the k Divergence was for between
+ 
+
+ align:start position:0%
+what the k Divergence was for between
+one between two uh distributions but
+
+ align:start position:0%
+one between two uh distributions but
+ 
+
+ align:start position:0%
+one between two uh distributions but
+here I'm telling you what the k uh is
+
+ align:start position:0%
+here I'm telling you what the k uh is
+ 
+
+ align:start position:0%
+here I'm telling you what the k uh is
+between uh two products of distributions
+
+ align:start position:0%
+between uh two products of distributions
+ 
+
+ align:start position:0%
+between uh two products of distributions
+that might that are independent but not
+
+ align:start position:0%
+that might that are independent but not
+ 
+
+ align:start position:0%
+that might that are independent but not
+necessarily identically
+
+ align:start position:0%
+necessarily identically
+ 
+
+ align:start position:0%
+necessarily identically
+distributed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but that's what's going to show up
+
+ align:start position:0%
+okay but that's what's going to show up
+ 
+
+ align:start position:0%
+okay but that's what's going to show up
+just because it's a product of things so
+
+ align:start position:0%
+just because it's a product of things so
+ 
+
+ align:start position:0%
+just because it's a product of things so
+when you have the log it's just going to
+
+ align:start position:0%
+when you have the log it's just going to
+ 
+
+ align:start position:0%
+when you have the log it's just going to
+be a sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions all right so what do we do
+
+ align:start position:0%
+questions all right so what do we do
+ 
+
+ align:start position:0%
+questions all right so what do we do
+here well as I said now we know that the
+
+ align:start position:0%
+here well as I said now we know that the
+ 
+
+ align:start position:0%
+here well as I said now we know that the
+uh expectation of H is negative Fisher
+
+ align:start position:0%
+uh expectation of H is negative Fisher
+ 
+
+ align:start position:0%
+uh expectation of H is negative Fisher
+information so rather than putting H
+
+ align:start position:0%
+information so rather than putting H
+ 
+
+ align:start position:0%
+information so rather than putting H
+inverse in my iterates for Newton rafson
+
+ align:start position:0%
+inverse in my iterates for Newton rafson
+ 
+
+ align:start position:0%
+inverse in my iterates for Newton rafson
+I just should I'm just going to put the
+
+ align:start position:0%
+I just should I'm just going to put the
+ 
+
+ align:start position:0%
+I just should I'm just going to put the
+inverse fissure information and uh
+
+ align:start position:0%
+inverse fissure information and uh
+ 
+
+ align:start position:0%
+inverse fissure information and uh
+remember I had a minus sign in front so
+
+ align:start position:0%
+remember I had a minus sign in front so
+ 
+
+ align:start position:0%
+remember I had a minus sign in front so
+I'm just going to pick up a plus sign
+
+ align:start position:0%
+I'm just going to pick up a plus sign
+ 
+
+ align:start position:0%
+I'm just going to pick up a plus sign
+now just because I is negative the
+
+ align:start position:0%
+now just because I is negative the
+ 
+
+ align:start position:0%
+now just because I is negative the
+expectation of the of the
+
+ align:start position:0%
+expectation of the of the
+ 
+
+ align:start position:0%
+expectation of the of the
+H and this guy has essentially the same
+
+ align:start position:0%
+H and this guy has essentially the same
+ 
+
+ align:start position:0%
+H and this guy has essentially the same
+conversions properties uh and it just
+
+ align:start position:0%
+conversions properties uh and it just
+ 
+
+ align:start position:0%
+conversions properties uh and it just
+happens that it's easier to compute I
+
+ align:start position:0%
+happens that it's easier to compute I
+ 
+
+ align:start position:0%
+happens that it's easier to compute I
+than HLM and uh that's it that's really
+
+ align:start position:0%
+than HLM and uh that's it that's really
+ 
+
+ align:start position:0%
+than HLM and uh that's it that's really
+why you want to do this
+
+ align:start position:0%
+why you want to do this
+ 
+
+ align:start position:0%
+why you want to do this
+now you might say that well if I use
+
+ align:start position:0%
+now you might say that well if I use
+ 
+
+ align:start position:0%
+now you might say that well if I use
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+information uh I should do better right
+
+ align:start position:0%
+information uh I should do better right
+ 
+
+ align:start position:0%
+information uh I should do better right
+but it's actually not necessarily true
+
+ align:start position:0%
+but it's actually not necessarily true
+ 
+
+ align:start position:0%
+but it's actually not necessarily true
+for several reasons but let's say that
+
+ align:start position:0%
+for several reasons but let's say that
+ 
+
+ align:start position:0%
+for several reasons but let's say that
+one is probably the fact that I did not
+
+ align:start position:0%
+one is probably the fact that I did not
+ 
+
+ align:start position:0%
+one is probably the fact that I did not
+use more information every step when I
+
+ align:start position:0%
+use more information every step when I
+ 
+
+ align:start position:0%
+use more information every step when I
+was Computing this thing at XK I
+
+ align:start position:0%
+was Computing this thing at XK I
+ 
+
+ align:start position:0%
+was Computing this thing at XK I
+actually pretended that at Theta K the
+
+ align:start position:0%
+actually pretended that at Theta K the
+ 
+
+ align:start position:0%
+actually pretended that at Theta K the
+true distribution was the one
+
+ align:start position:0%
+true distribution was the one
+ 
+
+ align:start position:0%
+true distribution was the one
+distributed according to Theta K and
+
+ align:start position:0%
+distributed according to Theta K and
+ 
+
+ align:start position:0%
+distributed according to Theta K and
+that was not true this is only true at
+
+ align:start position:0%
+that was not true this is only true at
+ 
+
+ align:start position:0%
+that was not true this is only true at
+when Theta K becomes close to the true
+
+ align:start position:0%
+when Theta K becomes close to the true
+ 
+
+ align:start position:0%
+when Theta K becomes close to the true
+Theta and so in a way I what I gained I
+
+ align:start position:0%
+Theta and so in a way I what I gained I
+ 
+
+ align:start position:0%
+Theta and so in a way I what I gained I
+lost again by making this uh this thing
+
+ align:start position:0%
+lost again by making this uh this thing
+ 
+
+ align:start position:0%
+lost again by making this uh this thing
+it's just really a matter of simple
+
+ align:start position:0%
+it's just really a matter of simple
+ 
+
+ align:start position:0%
+it's just really a matter of simple
+computation so let's just see it on a
+
+ align:start position:0%
+computation so let's just see it on a
+ 
+
+ align:start position:0%
+computation so let's just see it on a
+particular example actually on this
+
+ align:start position:0%
+particular example actually on this
+ 
+
+ align:start position:0%
+particular example actually on this
+example it's not going to look much
+
+ align:start position:0%
+example it's not going to look much
+ 
+
+ align:start position:0%
+example it's not going to look much
+simpler uh it's actually going to be the
+
+ align:start position:0%
+simpler uh it's actually going to be the
+ 
+
+ align:start position:0%
+simpler uh it's actually going to be the
+same um all right so I'm going to have
+
+ align:start position:0%
+same um all right so I'm going to have
+ 
+
+ align:start position:0%
+same um all right so I'm going to have
+the uh Burnley example right so we know
+
+ align:start position:0%
+the uh Burnley example right so we know
+ 
+
+ align:start position:0%
+the uh Burnley example right so we know
+that Burnley belongs to the
+
+ align:start position:0%
+that Burnley belongs to the
+ 
+
+ align:start position:0%
+that Burnley belongs to the
+canonical exponential
+
+ align:start position:0%
+canonical exponential
+ 
+
+ align:start position:0%
+canonical exponential
+family and uh essentially all I need to
+
+ align:start position:0%
+family and uh essentially all I need to
+ 
+
+ align:start position:0%
+family and uh essentially all I need to
+tell you is what B is and
+
+ align:start position:0%
+tell you is what B is and
+ 
+
+ align:start position:0%
+tell you is what B is and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+B of theta for Burn only is log 1+ e
+
+ align:start position:0%
+B of theta for Burn only is log 1+ e
+ 
+
+ align:start position:0%
+B of theta for Burn only is log 1+ e
+Theta right we computed that
+
+ align:start position:0%
+Theta right we computed that
+ 
+
+ align:start position:0%
+Theta right we computed that
+okay and so when I look at my log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likelihood it's going to look like the
+
+ align:start position:0%
+likelihood it's going to look like the
+ 
+
+ align:start position:0%
+likelihood it's going to look like the
+sum from I = one to
+
+ align:start position:0%
+sum from I = one to
+ 
+
+ align:start position:0%
+sum from I = one to
+n of y
+
+ align:start position:0%
+n of y
+ 
+
+ align:start position:0%
+n of y
+i okay so here I'm going to actually use
+
+ align:start position:0%
+i okay so here I'm going to actually use
+ 
+
+ align:start position:0%
+i okay so here I'm going to actually use
+the canonical length so it's going to be
+
+ align:start position:0%
+the canonical length so it's going to be
+ 
+
+ align:start position:0%
+the canonical length so it's going to be
+X I transpose beta minus log 1 +
+
+ align:start position:0%
+X I transpose beta minus log 1 +
+ 
+
+ align:start position:0%
+X I transpose beta minus log 1 +
+exponential X I transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta and five for this guy is equal to
+
+ align:start position:0%
+beta and five for this guy is equal to
+ 
+
+ align:start position:0%
+beta and five for this guy is equal to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+is it clear for everyone what I did okay
+
+ align:start position:0%
+is it clear for everyone what I did okay
+ 
+
+ align:start position:0%
+is it clear for everyone what I did okay
+so this remember the the the density
+
+ align:start position:0%
+so this remember the the the density
+ 
+
+ align:start position:0%
+so this remember the the the density
+right so that was really just uh so the
+
+ align:start position:0%
+right so that was really just uh so the
+ 
+
+ align:start position:0%
+right so that was really just uh so the
+pmf was
+
+ align:start position:0%
+pmf was
+ 
+
+ align:start position:0%
+pmf was
+exponential y Theta minus log 1 + e
+
+ align:start position:0%
+exponential y Theta minus log 1 + e
+ 
+
+ align:start position:0%
+exponential y Theta minus log 1 + e
+Theta there was actually no
+
+ align:start position:0%
+Theta there was actually no
+ 
+
+ align:start position:0%
+Theta there was actually no
+normalization that's just the density of
+
+ align:start position:0%
+normalization that's just the density of
+ 
+
+ align:start position:0%
+normalization that's just the density of
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+burnly and Theta is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually log p over 1 minus
+
+ align:start position:0%
+actually log p over 1 minus
+ 
+
+ align:start position:0%
+actually log p over 1 minus
+p and so that's what actually gives me
+
+ align:start position:0%
+p and so that's what actually gives me
+ 
+
+ align:start position:0%
+p and so that's what actually gives me
+what my uh since p is the expectation
+
+ align:start position:0%
+what my uh since p is the expectation
+ 
+
+ align:start position:0%
+what my uh since p is the expectation
+this is actually giving me also my
+
+ align:start position:0%
+this is actually giving me also my
+ 
+
+ align:start position:0%
+this is actually giving me also my
+canonical link which is the logit link
+
+ align:start position:0%
+canonical link which is the logit link
+ 
+
+ align:start position:0%
+canonical link which is the logit link
+we saw that last time and so if I start
+
+ align:start position:0%
+we saw that last time and so if I start
+ 
+
+ align:start position:0%
+we saw that last time and so if I start
+taking the log of this guy and summing
+
+ align:start position:0%
+taking the log of this guy and summing
+ 
+
+ align:start position:0%
+taking the log of this guy and summing
+over n and replacing Theta by X I
+
+ align:start position:0%
+over n and replacing Theta by X I
+ 
+
+ align:start position:0%
+over n and replacing Theta by X I
+transpose beta which is the what the
+
+ align:start position:0%
+transpose beta which is the what the
+ 
+
+ align:start position:0%
+transpose beta which is the what the
+canonical link tells me to do I get this
+
+ align:start position:0%
+canonical link tells me to do I get this
+ 
+
+ align:start position:0%
+canonical link tells me to do I get this
+guy is that clear for everyone if it's
+
+ align:start position:0%
+guy is that clear for everyone if it's
+ 
+
+ align:start position:0%
+guy is that clear for everyone if it's
+not please redo this step on your own
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I want to maximize this function
+
+ align:start position:0%
+okay so I want to maximize this function
+ 
+
+ align:start position:0%
+okay so I want to maximize this function
+sorry so I want to maximize this
+
+ align:start position:0%
+sorry so I want to maximize this
+ 
+
+ align:start position:0%
+sorry so I want to maximize this
+function over there on the first line as
+
+ align:start position:0%
+function over there on the first line as
+ 
+
+ align:start position:0%
+function over there on the first line as
+a function of
+
+ align:start position:0%
+a function of
+ 
+
+ align:start position:0%
+a function of
+beta and so to do this I want to use
+
+ align:start position:0%
+beta and so to do this I want to use
+ 
+
+ align:start position:0%
+beta and so to do this I want to use
+either um Newton rafson or what I call
+
+ align:start position:0%
+either um Newton rafson or what I call
+ 
+
+ align:start position:0%
+either um Newton rafson or what I call
+fisser scoring so Fisher scoring is the
+
+ align:start position:0%
+fisser scoring so Fisher scoring is the
+ 
+
+ align:start position:0%
+fisser scoring so Fisher scoring is the
+second one when you replace the hen by
+
+ align:start position:0%
+second one when you replace the hen by
+ 
+
+ align:start position:0%
+second one when you replace the hen by
+negative Fisher
+
+ align:start position:0%
+negative Fisher
+ 
+
+ align:start position:0%
+negative Fisher
+information right so I replace these two
+
+ align:start position:0%
+information right so I replace these two
+ 
+
+ align:start position:0%
+information right so I replace these two
+things and so I first take the gradient
+
+ align:start position:0%
+things and so I first take the gradient
+ 
+
+ align:start position:0%
+things and so I first take the gradient
+okay so let's take the gradient R of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ln
+
+ align:start position:0%
+Ln
+ 
+
+ align:start position:0%
+Ln
+uh so the gradient of Ln is going to be
+
+ align:start position:0%
+uh so the gradient of Ln is going to be
+ 
+
+ align:start position:0%
+uh so the gradient of Ln is going to be
+sum so here this is of the form Yi which
+
+ align:start position:0%
+sum so here this is of the form Yi which
+ 
+
+ align:start position:0%
+sum so here this is of the form Yi which
+is a scalar times a vector x i beta
+
+ align:start position:0%
+is a scalar times a vector x i beta
+ 
+
+ align:start position:0%
+is a scalar times a vector x i beta
+that's what I erase from here the
+
+ align:start position:0%
+that's what I erase from here the
+ 
+
+ align:start position:0%
+that's what I erase from here the
+derivative of B transpose X the gradient
+
+ align:start position:0%
+derivative of B transpose X the gradient
+ 
+
+ align:start position:0%
+derivative of B transpose X the gradient
+of B transpose X is just B so here I
+
+ align:start position:0%
+of B transpose X is just B so here I
+ 
+
+ align:start position:0%
+of B transpose X is just B so here I
+have just y
+
+ align:start position:0%
+have just y
+ 
+
+ align:start position:0%
+have just y
+ixi okay so that's of the form Yi which
+
+ align:start position:0%
+ixi okay so that's of the form Yi which
+ 
+
+ align:start position:0%
+ixi okay so that's of the form Yi which
+is a scalar time x i which is a
+
+ align:start position:0%
+is a scalar time x i which is a
+ 
+
+ align:start position:0%
+is a scalar time x i which is a
+vector now what about this guy well here
+
+ align:start position:0%
+vector now what about this guy well here
+ 
+
+ align:start position:0%
+vector now what about this guy well here
+I have a function so I'm going to have
+
+ align:start position:0%
+I have a function so I'm going to have
+ 
+
+ align:start position:0%
+I have a function so I'm going to have
+just the usual rule that the the chain
+
+ align:start position:0%
+just the usual rule that the the chain
+ 
+
+ align:start position:0%
+just the usual rule that the the chain
+rule right so that's just going to be
+
+ align:start position:0%
+rule right so that's just going to be
+ 
+
+ align:start position:0%
+rule right so that's just going to be
+one over this
+
+ align:start position:0%
+one over this
+ 
+
+ align:start position:0%
+one over this
+guy and then I need to find the hashen
+
+ align:start position:0%
+guy and then I need to find the hashen
+ 
+
+ align:start position:0%
+guy and then I need to find the hashen
+of this thing so the one is going away
+
+ align:start position:0%
+of this thing so the one is going away
+ 
+
+ align:start position:0%
+of this thing so the one is going away
+and then I apply the chain rule again so
+
+ align:start position:0%
+and then I apply the chain rule again so
+ 
+
+ align:start position:0%
+and then I apply the chain rule again so
+I get e of X I transpose beta and then
+
+ align:start position:0%
+I get e of X I transpose beta and then
+ 
+
+ align:start position:0%
+I get e of X I transpose beta and then
+the HH of this thing
+
+ align:start position:0%
+the HH of this thing
+ 
+
+ align:start position:0%
+the HH of this thing
+which is x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so my hen I can actually my
+
+ align:start position:0%
+okay so my hen I can actually my
+ 
+
+ align:start position:0%
+okay so my hen I can actually my
+gradient sorry I can actually factor out
+
+ align:start position:0%
+gradient sorry I can actually factor out
+ 
+
+ align:start position:0%
+gradient sorry I can actually factor out
+all my XIs and it's going to look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this my
+
+ align:start position:0%
+this my
+ 
+
+ align:start position:0%
+this my
+gradient is a weighted average or
+
+ align:start position:0%
+gradient is a weighted average or
+ 
+
+ align:start position:0%
+gradient is a weighted average or
+weighted sum of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XI this will always happen when you have
+
+ align:start position:0%
+XI this will always happen when you have
+ 
+
+ align:start position:0%
+XI this will always happen when you have
+a canonical when you have an generalized
+
+ align:start position:0%
+a canonical when you have an generalized
+ 
+
+ align:start position:0%
+a canonical when you have an generalized
+in your mod and that's pretty clear
+
+ align:start position:0%
+in your mod and that's pretty clear
+ 
+
+ align:start position:0%
+in your mod and that's pretty clear
+where did the XI show up whether it's
+
+ align:start position:0%
+where did the XI show up whether it's
+ 
+
+ align:start position:0%
+where did the XI show up whether it's
+from this guy or that guy the XI came
+
+ align:start position:0%
+from this guy or that guy the XI came
+ 
+
+ align:start position:0%
+from this guy or that guy the XI came
+from the fact that when I take the
+
+ align:start position:0%
+from the fact that when I take the
+ 
+
+ align:start position:0%
+from the fact that when I take the
+gradient of XI transposed beta I have
+
+ align:start position:0%
+gradient of XI transposed beta I have
+ 
+
+ align:start position:0%
+gradient of XI transposed beta I have
+this Vector XI that comes out it's
+
+ align:start position:0%
+this Vector XI that comes out it's
+ 
+
+ align:start position:0%
+this Vector XI that comes out it's
+always going to be the thing that comes
+
+ align:start position:0%
+always going to be the thing that comes
+ 
+
+ align:start position:0%
+always going to be the thing that comes
+out so I will always have something that
+
+ align:start position:0%
+out so I will always have something that
+ 
+
+ align:start position:0%
+out so I will always have something that
+looks like some sum with some weights
+
+ align:start position:0%
+looks like some sum with some weights
+ 
+
+ align:start position:0%
+looks like some sum with some weights
+here of the
+
+ align:start position:0%
+here of the
+ 
+
+ align:start position:0%
+here of the
+X now when I look at the second
+
+ align:start position:0%
+X now when I look at the second
+ 
+
+ align:start position:0%
+X now when I look at the second
+derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so same thing I'm just going to take the
+
+ align:start position:0%
+so same thing I'm just going to take the
+ 
+
+ align:start position:0%
+so same thing I'm just going to take the
+derivative of this guy since nothing
+
+ align:start position:0%
+derivative of this guy since nothing
+ 
+
+ align:start position:0%
+derivative of this guy since nothing
+depends on beta here or here I'm just
+
+ align:start position:0%
+depends on beta here or here I'm just
+ 
+
+ align:start position:0%
+depends on beta here or here I'm just
+going to have to take the derivative of
+
+ align:start position:0%
+going to have to take the derivative of
+ 
+
+ align:start position:0%
+going to have to take the derivative of
+this thing and so it's going to be equal
+
+ align:start position:0%
+this thing and so it's going to be equal
+ 
+
+ align:start position:0%
+this thing and so it's going to be equal
+so if I look now at the hen Ln as a
+
+ align:start position:0%
+so if I look now at the hen Ln as a
+ 
+
+ align:start position:0%
+so if I look now at the hen Ln as a
+function of beta I'm going to have sum
+
+ align:start position:0%
+function of beta I'm going to have sum
+ 
+
+ align:start position:0%
+function of beta I'm going to have sum
+from I = 1 to n of well y i what is the
+
+ align:start position:0%
+from I = 1 to n of well y i what is the
+ 
+
+ align:start position:0%
+from I = 1 to n of well y i what is the
+derivative of Yi with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+yeah zero okay it doesn't depend on beta
+
+ align:start position:0%
+yeah zero okay it doesn't depend on beta
+ 
+
+ align:start position:0%
+yeah zero okay it doesn't depend on beta
+I mean it's distribution does but y
+
+ align:start position:0%
+I mean it's distribution does but y
+ 
+
+ align:start position:0%
+I mean it's distribution does but y
+itself is just a it's just number right
+
+ align:start position:0%
+itself is just a it's just number right
+ 
+
+ align:start position:0%
+itself is just a it's just number right
+so uh this is zero so I'm going to get
+
+ align:start position:0%
+so uh this is zero so I'm going to get
+ 
+
+ align:start position:0%
+so uh this is zero so I'm going to get
+minus and then I'm going to have again
+
+ align:start position:0%
+minus and then I'm going to have again
+ 
+
+ align:start position:0%
+minus and then I'm going to have again
+the chain rule that shows up so I need
+
+ align:start position:0%
+the chain rule that shows up so I need
+ 
+
+ align:start position:0%
+the chain rule that shows up so I need
+to find the derivative of x over 1 + x
+
+ align:start position:0%
+to find the derivative of x over 1 + x
+ 
+
+ align:start position:0%
+to find the derivative of x over 1 + x
+what is the derivative of x over 1 plus
+
+ align:start position:0%
+what is the derivative of x over 1 plus
+ 
+
+ align:start position:0%
+what is the derivative of x over 1 plus
+X actually don't even
+
+ align:start position:0%
+X actually don't even
+ 
+
+ align:start position:0%
+X actually don't even
+know uh so it gives me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay so that's 1 over 1 + x s so
+
+ align:start position:0%
+uh okay so that's 1 over 1 + x s so
+ 
+
+ align:start position:0%
+uh okay so that's 1 over 1 + x s so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+minus E XI transpose beta sorry no one
+
+ align:start position:0%
+minus E XI transpose beta sorry no one
+ 
+
+ align:start position:0%
+minus E XI transpose beta sorry no one
+divided 1 + E X I transpose beta squar
+
+ align:start position:0%
+divided 1 + E X I transpose beta squar
+ 
+
+ align:start position:0%
+divided 1 + E X I transpose beta squar
+times the derivative of the exponential
+
+ align:start position:0%
+times the derivative of the exponential
+ 
+
+ align:start position:0%
+times the derivative of the exponential
+which is E X I transpose beta and again
+
+ align:start position:0%
+which is E X I transpose beta and again
+ 
+
+ align:start position:0%
+which is E X I transpose beta and again
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+i and then I have this XI that shows up
+
+ align:start position:0%
+i and then I have this XI that shows up
+ 
+
+ align:start position:0%
+i and then I have this XI that shows up
+but since I'm looking for a matrix I'm
+
+ align:start position:0%
+but since I'm looking for a matrix I'm
+ 
+
+ align:start position:0%
+but since I'm looking for a matrix I'm
+going to have x i x i transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+just I know I'm going to need something
+
+ align:start position:0%
+just I know I'm going to need something
+ 
+
+ align:start position:0%
+just I know I'm going to need something
+that looks like a matrix in the end and
+
+ align:start position:0%
+that looks like a matrix in the end and
+ 
+
+ align:start position:0%
+that looks like a matrix in the end and
+so one way you want to think about it is
+
+ align:start position:0%
+so one way you want to think about it is
+ 
+
+ align:start position:0%
+so one way you want to think about it is
+you know this is going to spit out an XI
+
+ align:start position:0%
+you know this is going to spit out an XI
+ 
+
+ align:start position:0%
+you know this is going to spit out an XI
+there's already an XI here so I need to
+
+ align:start position:0%
+there's already an XI here so I need to
+ 
+
+ align:start position:0%
+there's already an XI here so I need to
+so I'm going to have something that
+
+ align:start position:0%
+so I'm going to have something that
+ 
+
+ align:start position:0%
+so I'm going to have something that
+looks like XI and I'm going to have to
+
+ align:start position:0%
+looks like XI and I'm going to have to
+ 
+
+ align:start position:0%
+looks like XI and I'm going to have to
+multiply by another Vector x i and I
+
+ align:start position:0%
+multiply by another Vector x i and I
+ 
+
+ align:start position:0%
+multiply by another Vector x i and I
+want it to form a matrix and so what you
+
+ align:start position:0%
+want it to form a matrix and so what you
+ 
+
+ align:start position:0%
+want it to form a matrix and so what you
+need to do is to take an outer
+
+ align:start position:0%
+need to do is to take an outer
+ 
+
+ align:start position:0%
+need to do is to take an outer
+product and that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so now well as a result the
+
+ align:start position:0%
+right so now well as a result the
+ 
+
+ align:start position:0%
+right so now well as a result the
+updating rule is this honestly this is
+
+ align:start position:0%
+updating rule is this honestly this is
+ 
+
+ align:start position:0%
+updating rule is this honestly this is
+not a result of anything I actually
+
+ align:start position:0%
+not a result of anything I actually
+ 
+
+ align:start position:0%
+not a result of anything I actually
+rewrote everything that I had before
+
+ align:start position:0%
+rewrote everything that I had before
+ 
+
+ align:start position:0%
+rewrote everything that I had before
+with a Theta replaced by Beta because
+
+ align:start position:0%
+with a Theta replaced by Beta because
+ 
+
+ align:start position:0%
+with a Theta replaced by Beta because
+it's just painful to rewrite this entire
+
+ align:start position:0%
+it's just painful to rewrite this entire
+ 
+
+ align:start position:0%
+it's just painful to rewrite this entire
+thing put some big parentheses and put
+
+ align:start position:0%
+thing put some big parentheses and put
+ 
+
+ align:start position:0%
+thing put some big parentheses and put
+minus one here
+
+ align:start position:0%
+minus one here
+ 
+
+ align:start position:0%
+minus one here
+okay and uh then I would have to put the
+
+ align:start position:0%
+okay and uh then I would have to put the
+ 
+
+ align:start position:0%
+okay and uh then I would have to put the
+gradient which is this thing
+
+ align:start position:0%
+gradient which is this thing
+ 
+
+ align:start position:0%
+gradient which is this thing
+here so as you can imagine this is not
+
+ align:start position:0%
+here so as you can imagine this is not
+ 
+
+ align:start position:0%
+here so as you can imagine this is not
+super
+
+ align:start position:0%
+super
+ 
+
+ align:start position:0%
+super
+nice um actually uh what's interesting
+
+ align:start position:0%
+nice um actually uh what's interesting
+ 
+
+ align:start position:0%
+nice um actually uh what's interesting
+is you know at some point I mentioned
+
+ align:start position:0%
+is you know at some point I mentioned
+ 
+
+ align:start position:0%
+is you know at some point I mentioned
+those pseudo Newton um method they're
+
+ align:start position:0%
+those pseudo Newton um method they're
+ 
+
+ align:start position:0%
+those pseudo Newton um method they're
+actually doing exactly this they're
+
+ align:start position:0%
+actually doing exactly this they're
+ 
+
+ align:start position:0%
+actually doing exactly this they're
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+oh I'm actually at it each iterations
+
+ align:start position:0%
+oh I'm actually at it each iterations
+ 
+
+ align:start position:0%
+oh I'm actually at it each iterations
+I'm actually going to just take those
+
+ align:start position:0%
+I'm actually going to just take those
+ 
+
+ align:start position:0%
+I'm actually going to just take those
+guys if I'm at iteration K I'm actually
+
+ align:start position:0%
+guys if I'm at iteration K I'm actually
+ 
+
+ align:start position:0%
+guys if I'm at iteration K I'm actually
+just going to sum those guys up to K
+
+ align:start position:0%
+just going to sum those guys up to K
+ 
+
+ align:start position:0%
+just going to sum those guys up to K
+rather than going all the way to n and
+
+ align:start position:0%
+rather than going all the way to n and
+ 
+
+ align:start position:0%
+rather than going all the way to n and
+look at everyone so you're just looking
+
+ align:start position:0%
+look at everyone so you're just looking
+ 
+
+ align:start position:0%
+look at everyone so you're just looking
+at your observations one at a time based
+
+ align:start position:0%
+at your observations one at a time based
+ 
+
+ align:start position:0%
+at your observations one at a time based
+on where you were
+
+ align:start position:0%
+on where you were
+ 
+
+ align:start position:0%
+on where you were
+before okay so you know you have a
+
+ align:start position:0%
+before okay so you know you have a
+ 
+
+ align:start position:0%
+before okay so you know you have a
+matrix you need to invert it so if you
+
+ align:start position:0%
+matrix you need to invert it so if you
+ 
+
+ align:start position:0%
+matrix you need to invert it so if you
+want to be able to invert it you need to
+
+ align:start position:0%
+want to be able to invert it you need to
+ 
+
+ align:start position:0%
+want to be able to invert it you need to
+make sure that the sum with those
+
+ align:start position:0%
+make sure that the sum with those
+ 
+
+ align:start position:0%
+make sure that the sum with those
+weights of XI outer XI or X ixi
+
+ align:start position:0%
+weights of XI outer XI or X ixi
+ 
+
+ align:start position:0%
+weights of XI outer XI or X ixi
+transpose is invertible so that's a
+
+ align:start position:0%
+transpose is invertible so that's a
+ 
+
+ align:start position:0%
+transpose is invertible so that's a
+condition that you need to have and uh
+
+ align:start position:0%
+condition that you need to have and uh
+ 
+
+ align:start position:0%
+condition that you need to have and uh
+well I mean you don't have to because
+
+ align:start position:0%
+well I mean you don't have to because
+ 
+
+ align:start position:0%
+well I mean you don't have to because
+technically you don't need to invert you
+
+ align:start position:0%
+technically you don't need to invert you
+ 
+
+ align:start position:0%
+technically you don't need to invert you
+just need to solve the linear system
+
+ align:start position:0%
+just need to solve the linear system
+ 
+
+ align:start position:0%
+just need to solve the linear system
+uh but that's uh that's actually
+
+ align:start position:0%
+uh but that's uh that's actually
+ 
+
+ align:start position:0%
+uh but that's uh that's actually
+guaranteed in most of the cases if n is
+
+ align:start position:0%
+guaranteed in most of the cases if n is
+ 
+
+ align:start position:0%
+guaranteed in most of the cases if n is
+large enough all right so everybody sees
+
+ align:start position:0%
+large enough all right so everybody sees
+ 
+
+ align:start position:0%
+large enough all right so everybody sees
+what we're doing here okay so now that's
+
+ align:start position:0%
+what we're doing here okay so now that's
+ 
+
+ align:start position:0%
+what we're doing here okay so now that's
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+um Newton rafon if I wanted to actually
+
+ align:start position:0%
+um Newton rafon if I wanted to actually
+ 
+
+ align:start position:0%
+um Newton rafon if I wanted to actually
+do the um Fisher
+
+ align:start position:0%
+do the um Fisher
+ 
+
+ align:start position:0%
+do the um Fisher
+scoring all I would need to do is to
+
+ align:start position:0%
+scoring all I would need to do is to
+ 
+
+ align:start position:0%
+scoring all I would need to do is to
+replace the Hasen here by its
+
+ align:start position:0%
+replace the Hasen here by its
+ 
+
+ align:start position:0%
+replace the Hasen here by its
+expectation when I pretend that the beta
+
+ align:start position:0%
+expectation when I pretend that the beta
+ 
+
+ align:start position:0%
+expectation when I pretend that the beta
+that I have atation k is the true
+
+ align:start position:0%
+that I have atation k is the true
+ 
+
+ align:start position:0%
+that I have atation k is the true
+one what is the expectation of this
+
+ align:start position:0%
+one what is the expectation of this
+ 
+
+ align:start position:0%
+one what is the expectation of this
+thing and when I say
+
+ align:start position:0%
+thing and when I say
+ 
+
+ align:start position:0%
+thing and when I say
+expectation here I'm always talking
+
+ align:start position:0%
+expectation here I'm always talking
+ 
+
+ align:start position:0%
+expectation here I'm always talking
+about conditional expectation of Y given
+
+ align:start position:0%
+about conditional expectation of Y given
+ 
+
+ align:start position:0%
+about conditional expectation of Y given
+X the only distributions that matter
+
+ align:start position:0%
+X the only distributions that matter
+ 
+
+ align:start position:0%
+X the only distributions that matter
+that have mattered in this entire
+
+ align:start position:0%
+that have mattered in this entire
+ 
+
+ align:start position:0%
+that have mattered in this entire
+chapter are condition conditional
+
+ align:start position:0%
+chapter are condition conditional
+ 
+
+ align:start position:0%
+chapter are condition conditional
+expectation of Y given X the conditional
+
+ align:start position:0%
+expectation of Y given X the conditional
+ 
+
+ align:start position:0%
+expectation of Y given X the conditional
+expectation of this thing given X is
+
+ align:start position:0%
+expectation of this thing given X is
+ 
+
+ align:start position:0%
+expectation of this thing given X is
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's itself it does not depend on y it
+
+ align:start position:0%
+it's itself it does not depend on y it
+ 
+
+ align:start position:0%
+it's itself it does not depend on y it
+only depends on the X's so conditionally
+
+ align:start position:0%
+only depends on the X's so conditionally
+ 
+
+ align:start position:0%
+only depends on the X's so conditionally
+on X this thing as far as we're
+
+ align:start position:0%
+on X this thing as far as we're
+ 
+
+ align:start position:0%
+on X this thing as far as we're
+concerned is completely deterministic so
+
+ align:start position:0%
+concerned is completely deterministic so
+ 
+
+ align:start position:0%
+concerned is completely deterministic so
+it's actually equal to its
+
+ align:start position:0%
+it's actually equal to its
+ 
+
+ align:start position:0%
+it's actually equal to its
+expectation and so in this particular
+
+ align:start position:0%
+expectation and so in this particular
+ 
+
+ align:start position:0%
+expectation and so in this particular
+example there's no
+
+ align:start position:0%
+example there's no
+ 
+
+ align:start position:0%
+example there's no
+difference between Fisher
+
+ align:start position:0%
+difference between Fisher
+ 
+
+ align:start position:0%
+difference between Fisher
+scoring and uh uh Newton rafson and the
+
+ align:start position:0%
+scoring and uh uh Newton rafson and the
+ 
+
+ align:start position:0%
+scoring and uh uh Newton rafson and the
+reason is because the gradient no longer
+
+ align:start position:0%
+reason is because the gradient no longer
+ 
+
+ align:start position:0%
+reason is because the gradient no longer
+depends on why I sorry the h no longer
+
+ align:start position:0%
+depends on why I sorry the h no longer
+ 
+
+ align:start position:0%
+depends on why I sorry the h no longer
+depends on on
+
+ align:start position:0%
+depends on on
+ 
+
+ align:start position:0%
+depends on on
+Yi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this slide is just repeating
+
+ align:start position:0%
+okay so this slide is just repeating
+ 
+
+ align:start position:0%
+okay so this slide is just repeating
+some stuff that I've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I think this is probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's go through this
+
+ align:start position:0%
+okay let's go through this
+ 
+
+ align:start position:0%
+okay let's go through this
+actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um at some point I said that uh Newton
+
+ align:start position:0%
+um at some point I said that uh Newton
+ 
+
+ align:start position:0%
+um at some point I said that uh Newton
+rapson do you have a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not when you have a canonical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+link
+
+ align:start position:0%
+link
+ 
+
+ align:start position:0%
+link
+no uh yeah so you
+
+ align:start position:0%
+no uh yeah so you
+ 
+
+ align:start position:0%
+no uh yeah so you
+know yeah maybe maybe I wanted you to
+
+ align:start position:0%
+know yeah maybe maybe I wanted you to
+ 
+
+ align:start position:0%
+know yeah maybe maybe I wanted you to
+figure that out for yourself but uh okay
+
+ align:start position:0%
+figure that out for yourself but uh okay
+ 
+
+ align:start position:0%
+figure that out for yourself but uh okay
+so Yi times XI transpose beta so
+
+ align:start position:0%
+so Yi times XI transpose beta so
+ 
+
+ align:start position:0%
+so Yi times XI transpose beta so
+essentially you know when I have a
+
+ align:start position:0%
+essentially you know when I have a
+ 
+
+ align:start position:0%
+essentially you know when I have a
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+family what is referring to is that this
+
+ align:start position:0%
+family what is referring to is that this
+ 
+
+ align:start position:0%
+family what is referring to is that this
+is just B of XI transpose beta so I'm
+
+ align:start position:0%
+is just B of XI transpose beta so I'm
+ 
+
+ align:start position:0%
+is just B of XI transpose beta so I'm
+going to take some derivatives and
+
+ align:start position:0%
+going to take some derivatives and
+ 
+
+ align:start position:0%
+going to take some derivatives and
+there's going to be something
+
+ align:start position:0%
+there's going to be something
+ 
+
+ align:start position:0%
+there's going to be something
+complicated coming out of this but I'm
+
+ align:start position:0%
+complicated coming out of this but I'm
+ 
+
+ align:start position:0%
+complicated coming out of this but I'm
+certainly not going to have some Yi
+
+ align:start position:0%
+certainly not going to have some Yi
+ 
+
+ align:start position:0%
+certainly not going to have some Yi
+showing up the only place where Yi shows
+
+ align:start position:0%
+showing up the only place where Yi shows
+ 
+
+ align:start position:0%
+showing up the only place where Yi shows
+up is here now if I take two derivatives
+
+ align:start position:0%
+up is here now if I take two derivatives
+ 
+
+ align:start position:0%
+up is here now if I take two derivatives
+this thing is gone because it's linear
+
+ align:start position:0%
+this thing is gone because it's linear
+ 
+
+ align:start position:0%
+this thing is gone because it's linear
+the first one is going to keep only this
+
+ align:start position:0%
+the first one is going to keep only this
+ 
+
+ align:start position:0%
+the first one is going to keep only this
+guy and the second one is going to make
+
+ align:start position:0%
+guy and the second one is going to make
+ 
+
+ align:start position:0%
+guy and the second one is going to make
+it gone the only way this actually shows
+
+ align:start position:0%
+it gone the only way this actually shows
+ 
+
+ align:start position:0%
+it gone the only way this actually shows
+up is when I have an H here and if I
+
+ align:start position:0%
+up is when I have an H here and if I
+ 
+
+ align:start position:0%
+up is when I have an H here and if I
+have an H then I I can take second
+
+ align:start position:0%
+have an H then I I can take second
+ 
+
+ align:start position:0%
+have an H then I I can take second
+derivatives and this thing is not not
+
+ align:start position:0%
+derivatives and this thing is not not
+ 
+
+ align:start position:0%
+derivatives and this thing is not not
+going to be completely independent of uh
+
+ align:start position:0%
+going to be completely independent of uh
+ 
+
+ align:start position:0%
+going to be completely independent of uh
+beta uh sorry yeah this thing is still
+
+ align:start position:0%
+beta uh sorry yeah this thing is still
+ 
+
+ align:start position:0%
+beta uh sorry yeah this thing is still
+going to depend on beta which means that
+
+ align:start position:0%
+going to depend on beta which means that
+ 
+
+ align:start position:0%
+going to depend on beta which means that
+this Yi term is not going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disappear I believe we'll see an example
+
+ align:start position:0%
+disappear I believe we'll see an example
+ 
+
+ align:start position:0%
+disappear I believe we'll see an example
+of that or maybe I removed I'm not sure
+
+ align:start position:0%
+of that or maybe I removed I'm not sure
+ 
+
+ align:start position:0%
+of that or maybe I removed I'm not sure
+actually I think we we will see an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example all
+
+ align:start position:0%
+example all
+ 
+
+ align:start position:0%
+example all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so let us do uh
+
+ align:start position:0%
+so let us do uh
+ 
+
+ align:start position:0%
+so let us do uh
+iteratively uh Reed Le squares
+
+ align:start position:0%
+iteratively uh Reed Le squares
+ 
+
+ align:start position:0%
+iteratively uh Reed Le squares
+or IR LS which I've actually recently
+
+ align:start position:0%
+or IR LS which I've actually recently
+ 
+
+ align:start position:0%
+or IR LS which I've actually recently
+learned is a term that even though it
+
+ align:start position:0%
+learned is a term that even though it
+ 
+
+ align:start position:0%
+learned is a term that even though it
+was defined in the 50s people still feel
+
+ align:start position:0%
+was defined in the 50s people still feel
+ 
+
+ align:start position:0%
+was defined in the 50s people still feel
+free to use to define to call their new
+
+ align:start position:0%
+free to use to define to call their new
+ 
+
+ align:start position:0%
+free to use to define to call their new
+algorithms which have nothing to do with
+
+ align:start position:0%
+algorithms which have nothing to do with
+ 
+
+ align:start position:0%
+algorithms which have nothing to do with
+this uh this is really something where
+
+ align:start position:0%
+this uh this is really something where
+ 
+
+ align:start position:0%
+this uh this is really something where
+you actually do iteratively reweighted
+
+ align:start position:0%
+you actually do iteratively reweighted
+ 
+
+ align:start position:0%
+you actually do iteratively reweighted
+disir um and so which means that every
+
+ align:start position:0%
+disir um and so which means that every
+ 
+
+ align:start position:0%
+disir um and so which means that every
+step okay let's just actually go through
+
+ align:start position:0%
+step okay let's just actually go through
+ 
+
+ align:start position:0%
+step okay let's just actually go through
+this quickly what is going to be
+
+ align:start position:0%
+this quickly what is going to be
+ 
+
+ align:start position:0%
+this quickly what is going to be
+iteratively weedly SES the way the steps
+
+ align:start position:0%
+iteratively weedly SES the way the steps
+ 
+
+ align:start position:0%
+iteratively weedly SES the way the steps
+that we had here here showed
+
+ align:start position:0%
+that we had here here showed
+ 
+
+ align:start position:0%
+that we had here here showed
+up let's say those
+
+ align:start position:0%
+up let's say those
+ 
+
+ align:start position:0%
+up let's say those
+guys
+
+ align:start position:0%
+guys
+ 
+
+ align:start position:0%
+guys
+xstar is this is when we were actually
+
+ align:start position:0%
+xstar is this is when we were actually
+ 
+
+ align:start position:0%
+xstar is this is when we were actually
+solving this linear
+
+ align:start position:0%
+solving this linear
+ 
+
+ align:start position:0%
+solving this linear
+system right that was the linear system
+
+ align:start position:0%
+system right that was the linear system
+ 
+
+ align:start position:0%
+system right that was the linear system
+we were trying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solve but solving a linear system can be
+
+ align:start position:0%
+solve but solving a linear system can be
+ 
+
+ align:start position:0%
+solve but solving a linear system can be
+done by Just Trying to minimize right if
+
+ align:start position:0%
+done by Just Trying to minimize right if
+ 
+
+ align:start position:0%
+done by Just Trying to minimize right if
+I have X A and B is the same as
+
+ align:start position:0%
+I have X A and B is the same as
+ 
+
+ align:start position:0%
+I have X A and B is the same as
+minimizing the norm of ax minus b^ 2
+
+ align:start position:0%
+minimizing the norm of ax minus b^ 2
+ 
+
+ align:start position:0%
+minimizing the norm of ax minus b^ 2
+right over
+
+ align:start position:0%
+right over
+ 
+
+ align:start position:0%
+right over
+X right if I can actually find an X for
+
+ align:start position:0%
+X right if I can actually find an X for
+ 
+
+ align:start position:0%
+X right if I can actually find an X for
+which is zero it means that I've
+
+ align:start position:0%
+which is zero it means that I've
+ 
+
+ align:start position:0%
+which is zero it means that I've
+actually solved my problem and so that
+
+ align:start position:0%
+actually solved my problem and so that
+ 
+
+ align:start position:0%
+actually solved my problem and so that
+means that this is actually there's
+
+ align:start position:0%
+means that this is actually there's
+ 
+
+ align:start position:0%
+means that this is actually there's
+actually I can solve linear systems by
+
+ align:start position:0%
+actually I can solve linear systems by
+ 
+
+ align:start position:0%
+actually I can solve linear systems by
+solving least course problems and least
+
+ align:start position:0%
+solving least course problems and least
+ 
+
+ align:start position:0%
+solving least course problems and least
+SES problems are things that
+
+ align:start position:0%
+SES problems are things that
+ 
+
+ align:start position:0%
+SES problems are things that
+statisticians are comfortable solving
+
+ align:start position:0%
+statisticians are comfortable solving
+ 
+
+ align:start position:0%
+statisticians are comfortable solving
+and so all I have to do is to rephrase
+
+ align:start position:0%
+and so all I have to do is to rephrase
+ 
+
+ align:start position:0%
+and so all I have to do is to rephrase
+this as a least ques problem okay and
+
+ align:start position:0%
+this as a least ques problem okay and
+ 
+
+ align:start position:0%
+this as a least ques problem okay and
+you know I could just write it directly
+
+ align:start position:0%
+you know I could just write it directly
+ 
+
+ align:start position:0%
+you know I could just write it directly
+like this but there's a way to
+
+ align:start position:0%
+like this but there's a way to
+ 
+
+ align:start position:0%
+like this but there's a way to
+streamline it a little bit and that's
+
+ align:start position:0%
+streamline it a little bit and that's
+ 
+
+ align:start position:0%
+streamline it a little bit and that's
+actually by using uh that's actually by
+
+ align:start position:0%
+actually by using uh that's actually by
+ 
+
+ align:start position:0%
+actually by using uh that's actually by
+using weights okay so I'll come in the
+
+ align:start position:0%
+using weights okay so I'll come in the
+ 
+
+ align:start position:0%
+using weights okay so I'll come in the
+weights in this uh well not today
+
+ align:start position:0%
+weights in this uh well not today
+ 
+
+ align:start position:0%
+weights in this uh well not today
+actually but uh uh very soon all right
+
+ align:start position:0%
+actually but uh uh very soon all right
+ 
+
+ align:start position:0%
+actually but uh uh very soon all right
+so this is just a reminder of what we
+
+ align:start position:0%
+so this is just a reminder of what we
+ 
+
+ align:start position:0%
+so this is just a reminder of what we
+had we have that Yi given XI as a
+
+ align:start position:0%
+had we have that Yi given XI as a
+ 
+
+ align:start position:0%
+had we have that Yi given XI as a
+distribution distributed According to
+
+ align:start position:0%
+distribution distributed According to
+ 
+
+ align:start position:0%
+distribution distributed According to
+some distribution in the canonical
+
+ align:start position:0%
+some distribution in the canonical
+ 
+
+ align:start position:0%
+some distribution in the canonical
+exponential family so that means that
+
+ align:start position:0%
+exponential family so that means that
+ 
+
+ align:start position:0%
+exponential family so that means that
+the log likelihood looks like this again
+
+ align:start position:0%
+the log likelihood looks like this again
+ 
+
+ align:start position:0%
+the log likelihood looks like this again
+this does not matter to us this is the
+
+ align:start position:0%
+this does not matter to us this is the
+ 
+
+ align:start position:0%
+this does not matter to us this is the
+form that matters and we have a bunch of
+
+ align:start position:0%
+form that matters and we have a bunch of
+ 
+
+ align:start position:0%
+form that matters and we have a bunch of
+relationship ships that we actually
+
+ align:start position:0%
+relationship ships that we actually
+ 
+
+ align:start position:0%
+relationship ships that we actually
+spent some time Computing the first one
+
+ align:start position:0%
+spent some time Computing the first one
+ 
+
+ align:start position:0%
+spent some time Computing the first one
+is that mu is B Prime of theta I the
+
+ align:start position:0%
+is that mu is B Prime of theta I the
+ 
+
+ align:start position:0%
+is that mu is B Prime of theta I the
+second one is that if I take g g of mui
+
+ align:start position:0%
+second one is that if I take g g of mui
+ 
+
+ align:start position:0%
+second one is that if I take g g of mui
+I get this uh systematic component XI
+
+ align:start position:0%
+I get this uh systematic component XI
+ 
+
+ align:start position:0%
+I get this uh systematic component XI
+transpose beta that's modeling now if I
+
+ align:start position:0%
+transpose beta that's modeling now if I
+ 
+
+ align:start position:0%
+transpose beta that's modeling now if I
+look at the derivative mui with respect
+
+ align:start position:0%
+look at the derivative mui with respect
+ 
+
+ align:start position:0%
+look at the derivative mui with respect
+to Theta I this is the derivative of B
+
+ align:start position:0%
+to Theta I this is the derivative of B
+ 
+
+ align:start position:0%
+to Theta I this is the derivative of B
+Prime of theta I with respect to Theta I
+
+ align:start position:0%
+Prime of theta I with respect to Theta I
+ 
+
+ align:start position:0%
+Prime of theta I with respect to Theta I
+so that's the second derivative and if
+
+ align:start position:0%
+so that's the second derivative and if
+ 
+
+ align:start position:0%
+so that's the second derivative and if
+uh I'm going to call it VI if f is equal
+
+ align:start position:0%
+uh I'm going to call it VI if f is equal
+ 
+
+ align:start position:0%
+uh I'm going to call it VI if f is equal
+to one this is actually the variance and
+
+ align:start position:0%
+to one this is actually the variance and
+ 
+
+ align:start position:0%
+to one this is actually the variance and
+then I have uh this function H which
+
+ align:start position:0%
+then I have uh this function H which
+ 
+
+ align:start position:0%
+then I have uh this function H which
+allows me to bypass alog together the
+
+ align:start position:0%
+allows me to bypass alog together the
+ 
+
+ align:start position:0%
+allows me to bypass alog together the
+existence of this parameter mu which
+
+ align:start position:0%
+existence of this parameter mu which
+ 
+
+ align:start position:0%
+existence of this parameter mu which
+says if I want to go from X I transpose
+
+ align:start position:0%
+says if I want to go from X I transpose
+ 
+
+ align:start position:0%
+says if I want to go from X I transpose
+beta all the way to Theta I I have to
+
+ align:start position:0%
+beta all the way to Theta I I have to
+ 
+
+ align:start position:0%
+beta all the way to Theta I I have to
+first do G inverse and then B Prime
+
+ align:start position:0%
+first do G inverse and then B Prime
+ 
+
+ align:start position:0%
+first do G inverse and then B Prime
+inverse if I stopped here I would just
+
+ align:start position:0%
+inverse if I stopped here I would just
+ 
+
+ align:start position:0%
+inverse if I stopped here I would just
+have me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so now if I uh what I'm going
+
+ align:start position:0%
+okay okay so now if I uh what I'm going
+ 
+
+ align:start position:0%
+okay okay so now if I uh what I'm going
+to do is I'm going to apply the chain
+
+ align:start position:0%
+to do is I'm going to apply the chain
+ 
+
+ align:start position:0%
+to do is I'm going to apply the chain
+Rule and I'm going to try to uh compute
+
+ align:start position:0%
+Rule and I'm going to try to uh compute
+ 
+
+ align:start position:0%
+Rule and I'm going to try to uh compute
+the derivative of my likelihood log
+
+ align:start position:0%
+the derivative of my likelihood log
+ 
+
+ align:start position:0%
+the derivative of my likelihood log
+likelihood with respect to to Beta so
+
+ align:start position:0%
+likelihood with respect to to Beta so
+ 
+
+ align:start position:0%
+likelihood with respect to to Beta so
+again the the log likelihood is much
+
+ align:start position:0%
+again the the log likelihood is much
+ 
+
+ align:start position:0%
+again the the log likelihood is much
+nicer when I write it as a function of
+
+ align:start position:0%
+nicer when I write it as a function of
+ 
+
+ align:start position:0%
+nicer when I write it as a function of
+theta than a function of beta but it's
+
+ align:start position:0%
+theta than a function of beta but it's
+ 
+
+ align:start position:0%
+theta than a function of beta but it's
+basically what we've been doing by hand
+
+ align:start position:0%
+basically what we've been doing by hand
+ 
+
+ align:start position:0%
+basically what we've been doing by hand
+you can write it as a derivative with
+
+ align:start position:0%
+you can write it as a derivative with
+ 
+
+ align:start position:0%
+you can write it as a derivative with
+respect to Theta first and then multiply
+
+ align:start position:0%
+respect to Theta first and then multiply
+ 
+
+ align:start position:0%
+respect to Theta first and then multiply
+by the derivative of theta with respect
+
+ align:start position:0%
+by the derivative of theta with respect
+ 
+
+ align:start position:0%
+by the derivative of theta with respect
+to Beta okay and we know that Theta
+
+ align:start position:0%
+to Beta okay and we know that Theta
+ 
+
+ align:start position:0%
+to Beta okay and we know that Theta
+depends on beta as h of X I transpose
+
+ align:start position:0%
+depends on beta as h of X I transpose
+ 
+
+ align:start position:0%
+depends on beta as h of X I transpose
+beta okay I mean that's basically what
+
+ align:start position:0%
+beta okay I mean that's basically what
+ 
+
+ align:start position:0%
+beta okay I mean that's basically what
+we've been doing for the the burnly case
+
+ align:start position:0%
+we've been doing for the the burnly case
+ 
+
+ align:start position:0%
+we've been doing for the the burnly case
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+I mean we use the chain rule without
+
+ align:start position:0%
+I mean we use the chain rule without
+ 
+
+ align:start position:0%
+I mean we use the chain rule without
+actually saying it but this is going to
+
+ align:start position:0%
+actually saying it but this is going to
+ 
+
+ align:start position:0%
+actually saying it but this is going to
+be convenient to actually make it
+
+ align:start position:0%
+be convenient to actually make it
+ 
+
+ align:start position:0%
+be convenient to actually make it
+explicitly show up okay so when I first
+
+ align:start position:0%
+explicitly show up okay so when I first
+ 
+
+ align:start position:0%
+explicitly show up okay so when I first
+take the derivative of my log likelihood
+
+ align:start position:0%
+take the derivative of my log likelihood
+ 
+
+ align:start position:0%
+take the derivative of my log likelihood
+with respect to Theta I'm going to use
+
+ align:start position:0%
+with respect to Theta I'm going to use
+ 
+
+ align:start position:0%
+with respect to Theta I'm going to use
+the fact that my canonical family is
+
+ align:start position:0%
+the fact that my canonical family is
+ 
+
+ align:start position:0%
+the fact that my canonical family is
+super simple okay so what I have is that
+
+ align:start position:0%
+super simple okay so what I have is that
+ 
+
+ align:start position:0%
+super simple okay so what I have is that
+my log
+
+ align:start position:0%
+my log
+ 
+
+ align:start position:0%
+my log
+likelihood l
+
+ align:start position:0%
+likelihood l
+ 
+
+ align:start position:0%
+likelihood l
+n is the sum from I = 1 to n of y i
+
+ align:start position:0%
+n is the sum from I = 1 to n of y i
+ 
+
+ align:start position:0%
+n is the sum from I = 1 to n of y i
+Theta IUS B
+
+ align:start position:0%
+Theta IUS B
+ 
+
+ align:start position:0%
+Theta IUS B
+of theta I / f plus some constant which
+
+ align:start position:0%
+of theta I / f plus some constant which
+ 
+
+ align:start position:0%
+of theta I / f plus some constant which
+I will will go away as soon as I'm going
+
+ align:start position:0%
+I will will go away as soon as I'm going
+ 
+
+ align:start position:0%
+I will will go away as soon as I'm going
+to take my first derivative so if I take
+
+ align:start position:0%
+to take my first derivative so if I take
+ 
+
+ align:start position:0%
+to take my first derivative so if I take
+the derivative with respect to Theta
+
+ align:start position:0%
+the derivative with respect to Theta
+ 
+
+ align:start position:0%
+the derivative with respect to Theta
+I uh of this guy this is actually going
+
+ align:start position:0%
+I uh of this guy this is actually going
+ 
+
+ align:start position:0%
+I uh of this guy this is actually going
+to be equal to y i minus B Prime Theta
+
+ align:start position:0%
+to be equal to y i minus B Prime Theta
+ 
+
+ align:start position:0%
+to be equal to y i minus B Prime Theta
+I divided
+
+ align:start position:0%
+I divided
+ 
+
+ align:start position:0%
+I divided
+by and then I need to multiply with the
+
+ align:start position:0%
+by and then I need to multiply with the
+ 
+
+ align:start position:0%
+by and then I need to multiply with the
+by the derivative of theta I with
+
+ align:start position:0%
+by the derivative of theta I with
+ 
+
+ align:start position:0%
+by the derivative of theta I with
+respect to Beta And remember Theta is H
+
+ align:start position:0%
+respect to Beta And remember Theta is H
+ 
+
+ align:start position:0%
+respect to Beta And remember Theta is H
+of X I transpose beta so the derivative
+
+ align:start position:0%
+of X I transpose beta so the derivative
+ 
+
+ align:start position:0%
+of X I transpose beta so the derivative
+of theta I with respect to Beta
+
+ align:start position:0%
+of theta I with respect to Beta
+ 
+
+ align:start position:0%
+of theta I with respect to Beta
+J this is equal to H Prime of X I
+
+ align:start position:0%
+J this is equal to H Prime of X I
+ 
+
+ align:start position:0%
+J this is equal to H Prime of X I
+transpose beta and then I have uh the
+
+ align:start position:0%
+transpose beta and then I have uh the
+ 
+
+ align:start position:0%
+transpose beta and then I have uh the
+derivative of this guy actually let me
+
+ align:start position:0%
+derivative of this guy actually let me
+ 
+
+ align:start position:0%
+derivative of this guy actually let me
+just do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradients of theta I at beta
+
+ align:start position:0%
+gradients of theta I at beta
+ 
+
+ align:start position:0%
+gradients of theta I at beta
+right that's what we did and just
+
+ align:start position:0%
+right that's what we did and just
+ 
+
+ align:start position:0%
+right that's what we did and just
+calling Theta I I'm just thinking of
+
+ align:start position:0%
+calling Theta I I'm just thinking of
+ 
+
+ align:start position:0%
+calling Theta I I'm just thinking of
+theta I as being a function of theta so
+
+ align:start position:0%
+theta I as being a function of theta so
+ 
+
+ align:start position:0%
+theta I as being a function of theta so
+what should I add here
+
+ align:start position:0%
+what should I add here
+ 
+
+ align:start position:0%
+what should I add here
+was just the vector
+
+ align:start position:0%
+was just the vector
+ 
+
+ align:start position:0%
+was just the vector
+XI which is just the chinal
+
+ align:start position:0%
+XI which is just the chinal
+ 
+
+ align:start position:0%
+XI which is just the chinal
+again that's H Prime right so we don't
+
+ align:start position:0%
+again that's H Prime right so we don't
+ 
+
+ align:start position:0%
+again that's H Prime right so we don't
+see it but there's a prime here it's
+
+ align:start position:0%
+see it but there's a prime here it's
+ 
+
+ align:start position:0%
+see it but there's a prime here it's
+derivative okay we've done that without
+
+ align:start position:0%
+derivative okay we've done that without
+ 
+
+ align:start position:0%
+derivative okay we've done that without
+saying it
+
+ align:start position:0%
+saying it
+ 
+
+ align:start position:0%
+saying it
+explicitly so now if I multiply those
+
+ align:start position:0%
+explicitly so now if I multiply those
+ 
+
+ align:start position:0%
+explicitly so now if I multiply those
+two things I have this Yi minus B Prime
+
+ align:start position:0%
+two things I have this Yi minus B Prime
+ 
+
+ align:start position:0%
+two things I have this Yi minus B Prime
+of theta I which I call by its good name
+
+ align:start position:0%
+of theta I which I call by its good name
+ 
+
+ align:start position:0%
+of theta I which I call by its good name
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+mui right B Prime of the I is the
+
+ align:start position:0%
+mui right B Prime of the I is the
+ 
+
+ align:start position:0%
+mui right B Prime of the I is the
+expectation of Yi conditionally on XI
+
+ align:start position:0%
+expectation of Yi conditionally on XI
+ 
+
+ align:start position:0%
+expectation of Yi conditionally on XI
+and then I multiply by this thing here
+
+ align:start position:0%
+and then I multiply by this thing here
+ 
+
+ align:start position:0%
+and then I multiply by this thing here
+so here this thing is written coordinate
+
+ align:start position:0%
+so here this thing is written coordinate
+ 
+
+ align:start position:0%
+so here this thing is written coordinate
+by coordinate but I can write it as a
+
+ align:start position:0%
+by coordinate but I can write it as a
+ 
+
+ align:start position:0%
+by coordinate but I can write it as a
+big uh Vector when I stack them
+
+ align:start position:0%
+big uh Vector when I stack them
+ 
+
+ align:start position:0%
+big uh Vector when I stack them
+together and so what I claim is that
+
+ align:start position:0%
+together and so what I claim is that
+ 
+
+ align:start position:0%
+together and so what I claim is that
+this thing here is of the form y minus
+
+ align:start position:0%
+this thing here is of the form y minus
+ 
+
+ align:start position:0%
+this thing here is of the form y minus
+mu but here I put some tildas because
+
+ align:start position:0%
+mu but here I put some tildas because
+ 
+
+ align:start position:0%
+mu but here I put some tildas because
+what I did is that I first I um I uh uh
+
+ align:start position:0%
+what I did is that I first I um I uh uh
+ 
+
+ align:start position:0%
+what I did is that I first I um I uh uh
+divided this I multiply everything by G
+
+ align:start position:0%
+divided this I multiply everything by G
+ 
+
+ align:start position:0%
+divided this I multiply everything by G
+Prime of
+
+ align:start position:0%
+Prime of
+ 
+
+ align:start position:0%
+Prime of
+me for each me okay so why not okay so I
+
+ align:start position:0%
+me for each me okay so why not okay so I
+ 
+
+ align:start position:0%
+me for each me okay so why not okay so I
+uh actually on this slide it will make
+
+ align:start position:0%
+uh actually on this slide it will make
+ 
+
+ align:start position:0%
+uh actually on this slide it will make
+no sense why I do this right I basically
+
+ align:start position:0%
+no sense why I do this right I basically
+ 
+
+ align:start position:0%
+no sense why I do this right I basically
+multiply by G Prime on one side and
+
+ align:start position:0%
+multiply by G Prime on one side and
+ 
+
+ align:start position:0%
+multiply by G Prime on one side and
+divide by G Prime on the other side okay
+
+ align:start position:0%
+divide by G Prime on the other side okay
+ 
+
+ align:start position:0%
+divide by G Prime on the other side okay
+so what I write so far is that the the
+
+ align:start position:0%
+so what I write so far is that the the
+ 
+
+ align:start position:0%
+so what I write so far is that the the
+gradient of Ln sorry the gradient of Ln
+
+ align:start position:0%
+gradient of Ln sorry the gradient of Ln
+ 
+
+ align:start position:0%
+gradient of Ln sorry the gradient of Ln
+with respect to Beta is the
+
+ align:start position:0%
+with respect to Beta is the
+ 
+
+ align:start position:0%
+with respect to Beta is the
+sum from I = 1 to n of y i minus mui
+
+ align:start position:0%
+sum from I = 1 to n of y i minus mui
+ 
+
+ align:start position:0%
+sum from I = 1 to n of y i minus mui
+let's call it divided 5 times H Prime of
+
+ align:start position:0%
+let's call it divided 5 times H Prime of
+ 
+
+ align:start position:0%
+let's call it divided 5 times H Prime of
+X I transpose beta x i okay so I just
+
+ align:start position:0%
+X I transpose beta x i okay so I just
+ 
+
+ align:start position:0%
+X I transpose beta x i okay so I just
+stacked everything that's here and now
+
+ align:start position:0%
+stacked everything that's here and now
+ 
+
+ align:start position:0%
+stacked everything that's here and now
+I'm going to start calling things the
+
+ align:start position:0%
+I'm going to start calling things the
+ 
+
+ align:start position:0%
+I'm going to start calling things the
+first thing I'm going to do is I'm going
+
+ align:start position:0%
+first thing I'm going to do is I'm going
+ 
+
+ align:start position:0%
+first thing I'm going to do is I'm going
+to divide so this guy here I'm going to
+
+ align:start position:0%
+to divide so this guy here I'm going to
+ 
+
+ align:start position:0%
+to divide so this guy here I'm going to
+push
+
+ align:start position:0%
+push
+ 
+
+ align:start position:0%
+push
+here now this guy here I'm actually
+
+ align:start position:0%
+here now this guy here I'm actually
+ 
+
+ align:start position:0%
+here now this guy here I'm actually
+going to multiply by G
+
+ align:start position:0%
+going to multiply by G
+ 
+
+ align:start position:0%
+going to multiply by G
+Prime of
+
+ align:start position:0%
+Prime of
+ 
+
+ align:start position:0%
+Prime of
+mui and this guy I'm going to divide by
+
+ align:start position:0%
+mui and this guy I'm going to divide by
+ 
+
+ align:start position:0%
+mui and this guy I'm going to divide by
+G Prime of mui so there's really nothing
+
+ align:start position:0%
+G Prime of mui so there's really nothing
+ 
+
+ align:start position:0%
+G Prime of mui so there's really nothing
+that happened here I just took took G
+
+ align:start position:0%
+that happened here I just took took G
+ 
+
+ align:start position:0%
+that happened here I just took took G
+Prime and multiply and divide it by G
+
+ align:start position:0%
+Prime and multiply and divide it by G
+ 
+
+ align:start position:0%
+Prime and multiply and divide it by G
+Prime why do I do this well that's
+
+ align:start position:0%
+Prime why do I do this well that's
+ 
+
+ align:start position:0%
+Prime why do I do this well that's
+actually going to be clear when we talk
+
+ align:start position:0%
+actually going to be clear when we talk
+ 
+
+ align:start position:0%
+actually going to be clear when we talk
+about um iteratively Reed Le squares but
+
+ align:start position:0%
+about um iteratively Reed Le squares but
+ 
+
+ align:start position:0%
+about um iteratively Reed Le squares but
+now essentially I have a new mu a new Y
+
+ align:start position:0%
+now essentially I have a new mu a new Y
+ 
+
+ align:start position:0%
+now essentially I have a new mu a new Y
+which is so this thing now is going to
+
+ align:start position:0%
+which is so this thing now is going to
+ 
+
+ align:start position:0%
+which is so this thing now is going to
+be y Tilda minus
+
+ align:start position:0%
+be y Tilda minus
+ 
+
+ align:start position:0%
+be y Tilda minus
+mulda so I
+
+ align:start position:0%
+mulda so I
+ 
+
+ align:start position:0%
+mulda so I
+I now this guy
+
+ align:start position:0%
+I now this guy
+ 
+
+ align:start position:0%
+I now this guy
+here I'm going to call WI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh and uh I have the XI that's there
+
+ align:start position:0%
+and uh and uh I have the XI that's there
+ 
+
+ align:start position:0%
+and uh and uh I have the XI that's there
+which means that now the thing that I
+
+ align:start position:0%
+which means that now the thing that I
+ 
+
+ align:start position:0%
+which means that now the thing that I
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I can write as
+
+ align:start position:0%
+here I can write as
+ 
+
+ align:start position:0%
+here I can write as
+follows
+
+ align:start position:0%
+follows
+ 
+
+ align:start position:0%
+follows
+gradient
+
+ align:start position:0%
+gradient
+ 
+
+ align:start position:0%
+gradient
+Ln of beta is equal to what well I'm
+
+ align:start position:0%
+Ln of beta is equal to what well I'm
+ 
+
+ align:start position:0%
+Ln of beta is equal to what well I'm
+going to write it in Matrix
+
+ align:start position:0%
+going to write it in Matrix
+ 
+
+ align:start position:0%
+going to write it in Matrix
+forms so I have the sum over I of
+
+ align:start position:0%
+forms so I have the sum over I of
+ 
+
+ align:start position:0%
+forms so I have the sum over I of
+something multipli by x i so I'm going
+
+ align:start position:0%
+something multipli by x i so I'm going
+ 
+
+ align:start position:0%
+something multipli by x i so I'm going
+to write it as X
+
+ align:start position:0%
+to write it as X
+ 
+
+ align:start position:0%
+to write it as X
+transpose then I'm going to have this
+
+ align:start position:0%
+transpose then I'm going to have this
+ 
+
+ align:start position:0%
+transpose then I'm going to have this
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+W1 w n and then zero
+
+ align:start position:0%
+W1 w n and then zero
+ 
+
+ align:start position:0%
+W1 w n and then zero
+elsewhere and then I'm going to have my
+
+ align:start position:0%
+elsewhere and then I'm going to have my
+ 
+
+ align:start position:0%
+elsewhere and then I'm going to have my
+yelda minus mu and remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is the Matrix with uh sorry it should
+
+ align:start position:0%
+X is the Matrix with uh sorry it should
+ 
+
+ align:start position:0%
+X is the Matrix with uh sorry it should
+be a bit narrow I have n and then p and
+
+ align:start position:0%
+be a bit narrow I have n and then p and
+ 
+
+ align:start position:0%
+be a bit narrow I have n and then p and
+here I have my x i j in this Matrix on
+
+ align:start position:0%
+here I have my x i j in this Matrix on
+ 
+
+ align:start position:0%
+here I have my x i j in this Matrix on
+row I and column J
+
+ align:start position:0%
+row I and column J
+ 
+
+ align:start position:0%
+row I and column J
+J and uh this is just the Matrix that
+
+ align:start position:0%
+J and uh this is just the Matrix that
+ 
+
+ align:start position:0%
+J and uh this is just the Matrix that
+has the W eyes on the diagonal and then
+
+ align:start position:0%
+has the W eyes on the diagonal and then
+ 
+
+ align:start position:0%
+has the W eyes on the diagonal and then
+I have whitea minus me so this is just
+
+ align:start position:0%
+I have whitea minus me so this is just
+ 
+
+ align:start position:0%
+I have whitea minus me so this is just
+the Matrix rewriting of this formula all
+
+ align:start position:0%
+the Matrix rewriting of this formula all
+ 
+
+ align:start position:0%
+the Matrix rewriting of this formula all
+right so it's just saying that if I look
+
+ align:start position:0%
+right so it's just saying that if I look
+ 
+
+ align:start position:0%
+right so it's just saying that if I look
+at the sum of weighted things of my
+
+ align:start position:0%
+at the sum of weighted things of my
+ 
+
+ align:start position:0%
+at the sum of weighted things of my
+colums of XI it's basically the same
+
+ align:start position:0%
+colums of XI it's basically the same
+ 
+
+ align:start position:0%
+colums of XI it's basically the same
+thing right when I'm going to multiply
+
+ align:start position:0%
+thing right when I'm going to multiply
+ 
+
+ align:start position:0%
+thing right when I'm going to multiply
+this by my Matrix I'm going to get
+
+ align:start position:0%
+this by my Matrix I'm going to get
+ 
+
+ align:start position:0%
+this by my Matrix I'm going to get
+exactly those terms right y i minus mui
+
+ align:start position:0%
+exactly those terms right y i minus mui
+ 
+
+ align:start position:0%
+exactly those terms right y i minus mui
+telda time w i and then when I actually
+
+ align:start position:0%
+telda time w i and then when I actually
+ 
+
+ align:start position:0%
+telda time w i and then when I actually
+take this X I transpose time this guy
+
+ align:start position:0%
+take this X I transpose time this guy
+ 
+
+ align:start position:0%
+take this X I transpose time this guy
+I'm really just getting the sum of the
+
+ align:start position:0%
+I'm really just getting the sum of the
+ 
+
+ align:start position:0%
+I'm really just getting the sum of the
+columns uh uh with
+
+ align:start position:0%
+columns uh uh with
+ 
+
+ align:start position:0%
+columns uh uh with
+the with the weights right agree so if I
+
+ align:start position:0%
+the with the weights right agree so if I
+ 
+
+ align:start position:0%
+the with the weights right agree so if I
+look at this thing here this is a vector
+
+ align:start position:0%
+look at this thing here this is a vector
+ 
+
+ align:start position:0%
+look at this thing here this is a vector
+that has s
+
+ align:start position:0%
+that has s
+ 
+
+ align:start position:0%
+that has s
+coordinate y i w i * yielda minus mu
+
+ align:start position:0%
+coordinate y i w i * yielda minus mu
+ 
+
+ align:start position:0%
+coordinate y i w i * yielda minus mu
+IA and I have n of them so when I
+
+ align:start position:0%
+IA and I have n of them so when I
+ 
+
+ align:start position:0%
+IA and I have n of them so when I
+multiply X transpose by this guy I'm
+
+ align:start position:0%
+multiply X transpose by this guy I'm
+ 
+
+ align:start position:0%
+multiply X transpose by this guy I'm
+just looking at a weighted sum of The
+
+ align:start position:0%
+just looking at a weighted sum of The
+ 
+
+ align:start position:0%
+just looking at a weighted sum of The
+Columns of X transpose which is a
+
+ align:start position:0%
+Columns of X transpose which is a
+ 
+
+ align:start position:0%
+Columns of X transpose which is a
+weighted sum of the rows of X which are
+
+ align:start position:0%
+weighted sum of the rows of X which are
+ 
+
+ align:start position:0%
+weighted sum of the rows of X which are
+exactly my x
+
+ align:start position:0%
+exactly my x
+ 
+
+ align:start position:0%
+exactly my x
+i right and that's this weed Su of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XI okay so here as I said the fact that
+
+ align:start position:0%
+XI okay so here as I said the fact that
+ 
+
+ align:start position:0%
+XI okay so here as I said the fact that
+we decided to put this G Prime of mui
+
+ align:start position:0%
+we decided to put this G Prime of mui
+ 
+
+ align:start position:0%
+we decided to put this G Prime of mui
+here and G Prime of mui here we could
+
+ align:start position:0%
+here and G Prime of mui here we could
+ 
+
+ align:start position:0%
+here and G Prime of mui here we could
+have not done this right we could have
+
+ align:start position:0%
+have not done this right we could have
+ 
+
+ align:start position:0%
+have not done this right we could have
+just said this I call I don't even for I
+
+ align:start position:0%
+just said this I call I don't even for I
+ 
+
+ align:start position:0%
+just said this I call I don't even for I
+forget about the T I just call it y i
+
+ align:start position:0%
+forget about the T I just call it y i
+ 
+
+ align:start position:0%
+forget about the T I just call it y i
+minus mui and here I just put everything
+
+ align:start position:0%
+minus mui and here I just put everything
+ 
+
+ align:start position:0%
+minus mui and here I just put everything
+I don't know into some W and so why do I
+
+ align:start position:0%
+I don't know into some W and so why do I
+ 
+
+ align:start position:0%
+I don't know into some W and so why do I
+do this well it's because when I
+
+ align:start position:0%
+do this well it's because when I
+ 
+
+ align:start position:0%
+do this well it's because when I
+actually start looking at the
+
+ align:start position:0%
+actually start looking at the
+ 
+
+ align:start position:0%
+actually start looking at the
+hashen what's going to
+
+ align:start position:0%
+hashen what's going to
+ 
+
+ align:start position:0%
+hashen what's going to
+happen uh yeah we'll do that next time
+
+ align:start position:0%
+happen uh yeah we'll do that next time
+ 
+
+ align:start position:0%
+happen uh yeah we'll do that next time
+but uh let's just look quickly at the
+
+ align:start position:0%
+but uh let's just look quickly at the
+ 
+
+ align:start position:0%
+but uh let's just look quickly at the
+outcome of the computation of my
+
+ align:start position:0%
+outcome of the computation of my
+ 
+
+ align:start position:0%
+outcome of the computation of my
+Hasen so I compute a bunch of second
+
+ align:start position:0%
+Hasen so I compute a bunch of second
+ 
+
+ align:start position:0%
+Hasen so I compute a bunch of second
+derivatives and here I have two terms
+
+ align:start position:0%
+derivatives and here I have two terms
+ 
+
+ align:start position:0%
+derivatives and here I have two terms
+right well he's gone right so I have two
+
+ align:start position:0%
+right well he's gone right so I have two
+ 
+
+ align:start position:0%
+right well he's gone right so I have two
+terms and when I take the uh expectation
+
+ align:start position:0%
+terms and when I take the uh expectation
+ 
+
+ align:start position:0%
+terms and when I take the uh expectation
+now it's G to actually change right this
+
+ align:start position:0%
+now it's G to actually change right this
+ 
+
+ align:start position:0%
+now it's G to actually change right this
+thing is actually going to depend on Yi
+
+ align:start position:0%
+thing is actually going to depend on Yi
+ 
+
+ align:start position:0%
+thing is actually going to depend on Yi
+because I have an H which is not the
+
+ align:start position:0%
+because I have an H which is not the
+ 
+
+ align:start position:0%
+because I have an H which is not the
+identity Oh no you're here sorry and uh
+
+ align:start position:0%
+identity Oh no you're here sorry and uh
+ 
+
+ align:start position:0%
+identity Oh no you're here sorry and uh
+so when I start looking at the
+
+ align:start position:0%
+so when I start looking at the
+ 
+
+ align:start position:0%
+so when I start looking at the
+expectation so I look at the conditional
+
+ align:start position:0%
+expectation so I look at the conditional
+ 
+
+ align:start position:0%
+expectation so I look at the conditional
+expectation given XI the first term here
+
+ align:start position:0%
+expectation given XI the first term here
+ 
+
+ align:start position:0%
+expectation given XI the first term here
+has a Yi minus its
+
+ align:start position:0%
+has a Yi minus its
+ 
+
+ align:start position:0%
+has a Yi minus its
+expectation so when I take the
+
+ align:start position:0%
+expectation so when I take the
+ 
+
+ align:start position:0%
+expectation so when I take the
+conditional expectation this is going to
+
+ align:start position:0%
+conditional expectation this is going to
+ 
+
+ align:start position:0%
+conditional expectation this is going to
+be zero the first term is going away
+
+ align:start position:0%
+be zero the first term is going away
+ 
+
+ align:start position:0%
+be zero the first term is going away
+when I take the conditional expectation
+
+ align:start position:0%
+when I take the conditional expectation
+ 
+
+ align:start position:0%
+when I take the conditional expectation
+but this was actually gone already if we
+
+ align:start position:0%
+but this was actually gone already if we
+ 
+
+ align:start position:0%
+but this was actually gone already if we
+had the iCal term because the second
+
+ align:start position:0%
+had the iCal term because the second
+ 
+
+ align:start position:0%
+had the iCal term because the second
+derivative of H when H is the identity
+
+ align:start position:0%
+derivative of H when H is the identity
+ 
+
+ align:start position:0%
+derivative of H when H is the identity
+is zero but if H is not the identity H
+
+ align:start position:0%
+is zero but if H is not the identity H
+ 
+
+ align:start position:0%
+is zero but if H is not the identity H
+prime prime may not be zero and so I
+
+ align:start position:0%
+prime prime may not be zero and so I
+ 
+
+ align:start position:0%
+prime prime may not be zero and so I
+need that part to remove that
+
+ align:start position:0%
+need that part to remove that
+ 
+
+ align:start position:0%
+need that part to remove that
+term and so now you know I work a little
+
+ align:start position:0%
+term and so now you know I work a little
+ 
+
+ align:start position:0%
+term and so now you know I work a little
+bit and I get this term it's not very
+
+ align:start position:0%
+bit and I get this term it's not very
+ 
+
+ align:start position:0%
+bit and I get this term it's not very
+surprising in the second derivative I
+
+ align:start position:0%
+surprising in the second derivative I
+ 
+
+ align:start position:0%
+surprising in the second derivative I
+see I have terms in B prime prime I have
+
+ align:start position:0%
+see I have terms in B prime prime I have
+ 
+
+ align:start position:0%
+see I have terms in B prime prime I have
+term in h Prime but square and then I
+
+ align:start position:0%
+term in h Prime but square and then I
+ 
+
+ align:start position:0%
+term in h Prime but square and then I
+have my XI outer XI X ixi transpose
+
+ align:start position:0%
+have my XI outer XI X ixi transpose
+ 
+
+ align:start position:0%
+have my XI outer XI X ixi transpose
+which we know we would see okay so we'll
+
+ align:start position:0%
+which we know we would see okay so we'll
+ 
+
+ align:start position:0%
+which we know we would see okay so we'll
+go through those things next time but
+
+ align:start position:0%
+go through those things next time but
+ 
+
+ align:start position:0%
+go through those things next time but
+what I wanted to show you is that now uh
+
+ align:start position:0%
+what I wanted to show you is that now uh
+ 
+
+ align:start position:0%
+what I wanted to show you is that now uh
+once I compute
+
+ align:start position:0%
+once I compute
+ 
+
+ align:start position:0%
+once I compute
+this uh I can actually show that if I
+
+ align:start position:0%
+this uh I can actually show that if I
+ 
+
+ align:start position:0%
+this uh I can actually show that if I
+look at this product that showed up
+
+ align:start position:0%
+look at this product that showed up
+ 
+
+ align:start position:0%
+look at this product that showed up
+right I had B prime prime time H H Prime
+
+ align:start position:0%
+right I had B prime prime time H H Prime
+ 
+
+ align:start position:0%
+right I had B prime prime time H H Prime
+squared one of those terms is actually
+
+ align:start position:0%
+squared one of those terms is actually
+ 
+
+ align:start position:0%
+squared one of those terms is actually
+one over G
+
+ align:start position:0%
+one over G
+ 
+
+ align:start position:0%
+one over G
+Prime and so I can rewrite it as one of
+
+ align:start position:0%
+Prime and so I can rewrite it as one of
+ 
+
+ align:start position:0%
+Prime and so I can rewrite it as one of
+the H primes because I had a square
+
+ align:start position:0%
+the H primes because I had a square
+ 
+
+ align:start position:0%
+the H primes because I had a square
+divided by G Prime and now I have this
+
+ align:start position:0%
+divided by G Prime and now I have this
+ 
+
+ align:start position:0%
+divided by G Prime and now I have this
+XI XI transpose so if I did not put the
+
+ align:start position:0%
+XI XI transpose so if I did not put the
+ 
+
+ align:start position:0%
+XI XI transpose so if I did not put the
+if I did not put the G Prime in the W
+
+ align:start position:0%
+if I did not put the G Prime in the W
+ 
+
+ align:start position:0%
+if I did not put the G Prime in the W
+that I put here completely artificially
+
+ align:start position:0%
+that I put here completely artificially
+ 
+
+ align:start position:0%
+that I put here completely artificially
+I would not be able to call this guy
+
+ align:start position:0%
+I would not be able to call this guy
+ 
+
+ align:start position:0%
+I would not be able to call this guy
+W which is exactly what it is from this
+
+ align:start position:0%
+W which is exactly what it is from this
+ 
+
+ align:start position:0%
+W which is exactly what it is from this
+board and now that this guy is w I can
+
+ align:start position:0%
+board and now that this guy is w I can
+ 
+
+ align:start position:0%
+board and now that this guy is w I can
+actually write this thing here as X
+
+ align:start position:0%
+actually write this thing here as X
+ 
+
+ align:start position:0%
+actually write this thing here as X
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+WX okay and that's why I really wanted
+
+ align:start position:0%
+WX okay and that's why I really wanted
+ 
+
+ align:start position:0%
+WX okay and that's why I really wanted
+my w to have this G Prime of mui in the
+
+ align:start position:0%
+my w to have this G Prime of mui in the
+ 
+
+ align:start position:0%
+my w to have this G Prime of mui in the
+denominator because now I can actually
+
+ align:start position:0%
+denominator because now I can actually
+ 
+
+ align:start position:0%
+denominator because now I can actually
+write a term that depends on W now you
+
+ align:start position:0%
+write a term that depends on W now you
+ 
+
+ align:start position:0%
+write a term that depends on W now you
+might say how do I reconcile those two
+
+ align:start position:0%
+might say how do I reconcile those two
+ 
+
+ align:start position:0%
+might say how do I reconcile those two
+things what the hell are you doing and
+
+ align:start position:0%
+things what the hell are you doing and
+ 
+
+ align:start position:0%
+things what the hell are you doing and
+the what the hell I'm doing is
+
+ align:start position:0%
+the what the hell I'm doing is
+ 
+
+ align:start position:0%
+the what the hell I'm doing is
+essentially that I'm saying that if you
+
+ align:start position:0%
+essentially that I'm saying that if you
+ 
+
+ align:start position:0%
+essentially that I'm saying that if you
+write beta
+
+ align:start position:0%
+write beta
+ 
+
+ align:start position:0%
+write beta
+K according to the Fisher scoring
+
+ align:start position:0%
+K according to the Fisher scoring
+ 
+
+ align:start position:0%
+K according to the Fisher scoring
+iterations you can actually write it as
+
+ align:start position:0%
+iterations you can actually write it as
+ 
+
+ align:start position:0%
+iterations you can actually write it as
+just this term here which is of the form
+
+ align:start position:0%
+just this term here which is of the form
+ 
+
+ align:start position:0%
+just this term here which is of the form
+X transpose X inverse X transpose y but
+
+ align:start position:0%
+X transpose X inverse X transpose y but
+ 
+
+ align:start position:0%
+X transpose X inverse X transpose y but
+where I actually squeezed in this
+
+ align:start position:0%
+where I actually squeezed in this
+ 
+
+ align:start position:0%
+where I actually squeezed in this
+W's and that's actually a weighted Le
+
+ align:start position:0%
+W's and that's actually a weighted Le
+ 
+
+ align:start position:0%
+W's and that's actually a weighted Le
+squares and it's applied to this
+
+ align:start position:0%
+squares and it's applied to this
+ 
+
+ align:start position:0%
+squares and it's applied to this
+particular guy so we'll talk about those
+
+ align:start position:0%
+particular guy so we'll talk about those
+ 
+
+ align:start position:0%
+particular guy so we'll talk about those
+weighted Le squares but remember Le
+
+ align:start position:0%
+weighted Le squares but remember Le
+ 
+
+ align:start position:0%
+weighted Le squares but remember Le
+squares is of the form X beta hat is X
+
+ align:start position:0%
+squares is of the form X beta hat is X
+ 
+
+ align:start position:0%
+squares is of the form X beta hat is X
+transpose X inverse X transpose Y and
+
+ align:start position:0%
+transpose X inverse X transpose Y and
+ 
+
+ align:start position:0%
+transpose X inverse X transpose Y and
+here is basically the same thing except
+
+ align:start position:0%
+here is basically the same thing except
+ 
+
+ align:start position:0%
+here is basically the same thing except
+that I squeeze in some W after my X
+
+ align:start position:0%
+that I squeeze in some W after my X
+ 
+
+ align:start position:0%
+that I squeeze in some W after my X
+transpose okay so that's how we're going
+
+ align:start position:0%
+transpose okay so that's how we're going
+ 
+
+ align:start position:0%
+transpose okay so that's how we're going
+to solve uh I don't want to go into the
+
+ align:start position:0%
+to solve uh I don't want to go into the
+ 
+
+ align:start position:0%
+to solve uh I don't want to go into the
+details now and uh because mostly
+
+ align:start position:0%
+details now and uh because mostly
+ 
+
+ align:start position:0%
+details now and uh because mostly
+because we're running out of time are
+
+ align:start position:0%
+because we're running out of time are
+ 
+
+ align:start position:0%
+because we're running out of time are
+there any questions
\ No newline at end of file
diff --git a/OgGTJIgNewE.txt b/OgGTJIgNewE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eae7cb2e5c0c0f3d3b53d2d1bfdcab3143d7489b
--- /dev/null
+++ b/OgGTJIgNewE.txt
@@ -0,0 +1,15120 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right guys let's uh get
+
+ align:start position:0%
+ocw.mit.edu all right guys let's uh get
+ 
+
+ align:start position:0%
+ocw.mit.edu all right guys let's uh get
+started so today we're going to talk
+
+ align:start position:0%
+started so today we're going to talk
+ 
+
+ align:start position:0%
+started so today we're going to talk
+about tour and we actually have one of
+
+ align:start position:0%
+about tour and we actually have one of
+ 
+
+ align:start position:0%
+about tour and we actually have one of
+the authors of the paper you guys read
+
+ align:start position:0%
+the authors of the paper you guys read
+ 
+
+ align:start position:0%
+the authors of the paper you guys read
+for today uh Nick Matthew he's also one
+
+ align:start position:0%
+for today uh Nick Matthew he's also one
+ 
+
+ align:start position:0%
+for today uh Nick Matthew he's also one
+of the main developers of tour he's
+
+ align:start position:0%
+of the main developers of tour he's
+ 
+
+ align:start position:0%
+of the main developers of tour he's
+going to tell you more about it thank
+
+ align:start position:0%
+going to tell you more about it thank
+ 
+
+ align:start position:0%
+going to tell you more about it thank
+you um so at this point I could start
+
+ align:start position:0%
+you um so at this point I could start
+ 
+
+ align:start position:0%
+you um so at this point I could start
+out by saying please put your hand dos
+
+ align:start position:0%
+out by saying please put your hand dos
+ 
+
+ align:start position:0%
+out by saying please put your hand dos
+up if you didn't read the paper but that
+
+ align:start position:0%
+up if you didn't read the paper but that
+ 
+
+ align:start position:0%
+up if you didn't read the paper but that
+wouldn't work because it's embarrassing
+
+ align:start position:0%
+wouldn't work because it's embarrassing
+ 
+
+ align:start position:0%
+wouldn't work because it's embarrassing
+not to have read a paper you're supposed
+
+ align:start position:0%
+not to have read a paper you're supposed
+ 
+
+ align:start position:0%
+not to have read a paper you're supposed
+to to have read so instead what I will
+
+ align:start position:0%
+to to have read so instead what I will
+ 
+
+ align:start position:0%
+to to have read so instead what I will
+ask is think of your birthday think of
+
+ align:start position:0%
+ask is think of your birthday think of
+ 
+
+ align:start position:0%
+ask is think of your birthday think of
+the date of your birth if the last digit
+
+ align:start position:0%
+the date of your birth if the last digit
+ 
+
+ align:start position:0%
+the date of your birth if the last digit
+of the date of your birth is mod or you
+
+ align:start position:0%
+of the date of your birth is mod or you
+ 
+
+ align:start position:0%
+of the date of your birth is mod or you
+didn't read the paper please raise your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hand okay that's not far from half so
+
+ align:start position:0%
+hand okay that's not far from half so
+ 
+
+ align:start position:0%
+hand okay that's not far from half so
+I'm guessing most people read the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paper means of
+
+ align:start position:0%
+paper means of
+ 
+
+ align:start position:0%
+paper means of
+communicating that preserve our privacy
+
+ align:start position:0%
+communicating that preserve our privacy
+ 
+
+ align:start position:0%
+communicating that preserve our privacy
+enable to us to communicate more
+
+ align:start position:0%
+enable to us to communicate more
+ 
+
+ align:start position:0%
+enable to us to communicate more
+honestly to gather better information
+
+ align:start position:0%
+honestly to gather better information
+ 
+
+ align:start position:0%
+honestly to gather better information
+about the world when we are less
+
+ align:start position:0%
+about the world when we are less
+ 
+
+ align:start position:0%
+about the world when we are less
+disinhibited from speaking because of of
+
+ align:start position:0%
+disinhibited from speaking because of of
+ 
+
+ align:start position:0%
+disinhibited from speaking because of of
+possibly Justified possibly unjustified
+
+ align:start position:0%
+possibly Justified possibly unjustified
+ 
+
+ align:start position:0%
+possibly Justified possibly unjustified
+social and other
+
+ align:start position:0%
+social and other
+ 
+
+ align:start position:0%
+social and other
+consequences so which this brings us to
+
+ align:start position:0%
+consequences so which this brings us to
+ 
+
+ align:start position:0%
+consequences so which this brings us to
+tour which is an anonymity Network that
+
+ align:start position:0%
+tour which is an anonymity Network that
+ 
+
+ align:start position:0%
+tour which is an anonymity Network that
+I've been working on for the last 10
+
+ align:start position:0%
+I've been working on for the last 10
+ 
+
+ align:start position:0%
+I've been working on for the last 10
+years with some friends and colleagues
+
+ align:start position:0%
+years with some friends and colleagues
+ 
+
+ align:start position:0%
+years with some friends and colleagues
+and so on um General overview there
+
+ align:start position:0%
+and so on um General overview there
+ 
+
+ align:start position:0%
+and so on um General overview there
+there's a set of volunteer operated
+
+ align:start position:0%
+there's a set of volunteer operated
+ 
+
+ align:start position:0%
+there's a set of volunteer operated
+servers about 6,000 of them at first it
+
+ align:start position:0%
+servers about 6,000 of them at first it
+ 
+
+ align:start position:0%
+servers about 6,000 of them at first it
+was just um friends of ours that we knew
+
+ align:start position:0%
+was just um friends of ours that we knew
+ 
+
+ align:start position:0%
+was just um friends of ours that we knew
+from that Roger dingledine and I knew
+
+ align:start position:0%
+from that Roger dingledine and I knew
+ 
+
+ align:start position:0%
+from that Roger dingledine and I knew
+from MIT after that um
+
+ align:start position:0%
+from MIT after that um
+ 
+
+ align:start position:0%
+from MIT after that um
+we we got more publicity more people
+
+ align:start position:0%
+we we got more publicity more people
+ 
+
+ align:start position:0%
+we we got more publicity more people
+started running servers we now it's run
+
+ align:start position:0%
+started running servers we now it's run
+ 
+
+ align:start position:0%
+started running servers we now it's run
+by nonprofits private individuals some
+
+ align:start position:0%
+by nonprofits private individuals some
+ 
+
+ align:start position:0%
+by nonprofits private individuals some
+University teams possibly some of you
+
+ align:start position:0%
+University teams possibly some of you
+ 
+
+ align:start position:0%
+University teams possibly some of you
+here today
+
+ align:start position:0%
+here today
+ 
+
+ align:start position:0%
+here today
+and and no doubt some very sketchy
+
+ align:start position:0%
+and and no doubt some very sketchy
+ 
+
+ align:start position:0%
+and and no doubt some very sketchy
+people we're serving we got about 6,000
+
+ align:start position:0%
+people we're serving we got about 6,000
+ 
+
+ align:start position:0%
+people we're serving we got about 6,000
+nodes we're serving on the order of
+
+ align:start position:0%
+nodes we're serving on the order of
+ 
+
+ align:start position:0%
+nodes we're serving on the order of
+hundreds of thousands to millions of
+
+ align:start position:0%
+hundreds of thousands to millions of
+ 
+
+ align:start position:0%
+hundreds of thousands to millions of
+users depending on how you count it's
+
+ align:start position:0%
+users depending on how you count it's
+ 
+
+ align:start position:0%
+users depending on how you count it's
+kind of hard to count because they're
+
+ align:start position:0%
+kind of hard to count because they're
+ 
+
+ align:start position:0%
+kind of hard to count because they're
+Anonymous so you have to use statistical
+
+ align:start position:0%
+Anonymous so you have to use statistical
+ 
+
+ align:start position:0%
+Anonymous so you have to use statistical
+techniques to estimate and doing on the
+
+ align:start position:0%
+techniques to estimate and doing on the
+ 
+
+ align:start position:0%
+techniques to estimate and doing on the
+order of terabytes per second worth of
+
+ align:start position:0%
+order of terabytes per second worth of
+ 
+
+ align:start position:0%
+order of terabytes per second worth of
+traffic uh lots of people need anonymity
+
+ align:start position:0%
+traffic uh lots of people need anonymity
+ 
+
+ align:start position:0%
+traffic uh lots of people need anonymity
+for their regular work not everyone who
+
+ align:start position:0%
+for their regular work not everyone who
+ 
+
+ align:start position:0%
+for their regular work not everyone who
+needs anonymity though thinks of it as
+
+ align:start position:0%
+needs anonymity though thinks of it as
+ 
+
+ align:start position:0%
+needs anonymity though thinks of it as
+anonymity some people say um I I don't
+
+ align:start position:0%
+anonymity some people say um I I don't
+ 
+
+ align:start position:0%
+anonymity some people say um I I don't
+need anonymity I'm perfectly fine
+
+ align:start position:0%
+need anonymity I'm perfectly fine
+ 
+
+ align:start position:0%
+need anonymity I'm perfectly fine
+identifying myself but there's broad
+
+ align:start position:0%
+identifying myself but there's broad
+ 
+
+ align:start position:0%
+identifying myself but there's broad
+perceptions though that
+
+ align:start position:0%
+perceptions though that
+ 
+
+ align:start position:0%
+perceptions though that
+privacy is necessary or useful and when
+
+ align:start position:0%
+privacy is necessary or useful and when
+ 
+
+ align:start position:0%
+privacy is necessary or useful and when
+regular citizens use anonymity stuff
+
+ align:start position:0%
+regular citizens use anonymity stuff
+ 
+
+ align:start position:0%
+regular citizens use anonymity stuff
+they tend to be doing it because they
+
+ align:start position:0%
+they tend to be doing it because they
+ 
+
+ align:start position:0%
+they tend to be doing it because they
+want privacy in search results privacy
+
+ align:start position:0%
+want privacy in search results privacy
+ 
+
+ align:start position:0%
+want privacy in search results privacy
+in doing research on the internet they
+
+ align:start position:0%
+in doing research on the internet they
+ 
+
+ align:start position:0%
+in doing research on the internet they
+want to be able to engage in local
+
+ align:start position:0%
+want to be able to engage in local
+ 
+
+ align:start position:0%
+want to be able to engage in local
+politics while not offending local
+
+ align:start position:0%
+politics while not offending local
+ 
+
+ align:start position:0%
+politics while not offending local
+politicians and so
+
+ align:start position:0%
+politicians and so
+ 
+
+ align:start position:0%
+politicians and so
+on researchers frequently use
+
+ align:start position:0%
+on researchers frequently use
+ 
+
+ align:start position:0%
+on researchers frequently use
+anonymizing tools to avoid Gathering
+
+ align:start position:0%
+anonymizing tools to avoid Gathering
+ 
+
+ align:start position:0%
+anonymizing tools to avoid Gathering
+biased data biased by um geolocation
+
+ align:start position:0%
+biased data biased by um geolocation
+ 
+
+ align:start position:0%
+biased data biased by um geolocation
+Based Services that might be serving
+
+ align:start position:0%
+Based Services that might be serving
+ 
+
+ align:start position:0%
+Based Services that might be serving
+them in particular different versions of
+
+ align:start position:0%
+them in particular different versions of
+ 
+
+ align:start position:0%
+them in particular different versions of
+things companies use anonymity
+
+ align:start position:0%
+things companies use anonymity
+ 
+
+ align:start position:0%
+things companies use anonymity
+Technologies for for protection of
+
+ align:start position:0%
+Technologies for for protection of
+ 
+
+ align:start position:0%
+Technologies for for protection of
+sensitive data for instance if you are
+
+ align:start position:0%
+sensitive data for instance if you are
+ 
+
+ align:start position:0%
+sensitive data for instance if you are
+if for instance if I can track all of
+
+ align:start position:0%
+if for instance if I can track all of
+ 
+
+ align:start position:0%
+if for instance if I can track all of
+the movements of the legal team for some
+
+ align:start position:0%
+the movements of the legal team for some
+ 
+
+ align:start position:0%
+the movements of the legal team for some
+major internet company I can probably
+
+ align:start position:0%
+major internet company I can probably
+ 
+
+ align:start position:0%
+major internet company I can probably
+tell a lot about um just by tracking
+
+ align:start position:0%
+tell a lot about um just by tracking
+ 
+
+ align:start position:0%
+tell a lot about um just by tracking
+when when they're visiting their their
+
+ align:start position:0%
+when when they're visiting their their
+ 
+
+ align:start position:0%
+when when they're visiting their their
+web server from different places around
+
+ align:start position:0%
+web server from different places around
+ 
+
+ align:start position:0%
+web server from different places around
+the world I can learn a lot or when
+
+ align:start position:0%
+the world I can learn a lot or when
+ 
+
+ align:start position:0%
+the world I can learn a lot or when
+they're visiting the company VPN from
+
+ align:start position:0%
+they're visiting the company VPN from
+ 
+
+ align:start position:0%
+they're visiting the company VPN from
+different places around the world I can
+
+ align:start position:0%
+different places around the world I can
+ 
+
+ align:start position:0%
+different places around the world I can
+learn a lot about which teams are
+
+ align:start position:0%
+learn a lot about which teams are
+ 
+
+ align:start position:0%
+learn a lot about which teams are
+collaborating with which and this is
+
+ align:start position:0%
+collaborating with which and this is
+ 
+
+ align:start position:0%
+collaborating with which and this is
+information companies would like to keep
+
+ align:start position:0%
+information companies would like to keep
+ 
+
+ align:start position:0%
+information companies would like to keep
+private companies also need anonymity
+
+ align:start position:0%
+private companies also need anonymity
+ 
+
+ align:start position:0%
+private companies also need anonymity
+technology for doing research
+
+ align:start position:0%
+technology for doing research
+ 
+
+ align:start position:0%
+technology for doing research
+so a major router manufacturer for some
+
+ align:start position:0%
+so a major router manufacturer for some
+ 
+
+ align:start position:0%
+so a major router manufacturer for some
+while I don't know if this is still the
+
+ align:start position:0%
+while I don't know if this is still the
+ 
+
+ align:start position:0%
+while I don't know if this is still the
+case would regularly serve different
+
+ align:start position:0%
+case would regularly serve different
+ 
+
+ align:start position:0%
+case would regularly serve different
+versions of its product sheets to IP
+
+ align:start position:0%
+versions of its product sheets to IP
+ 
+
+ align:start position:0%
+versions of its product sheets to IP
+addresses associated with its
+
+ align:start position:0%
+addresses associated with its
+ 
+
+ align:start position:0%
+addresses associated with its
+competitors in order to make reverse
+
+ align:start position:0%
+competitors in order to make reverse
+ 
+
+ align:start position:0%
+competitors in order to make reverse
+engineering
+
+ align:start position:0%
+engineering
+ 
+
+ align:start position:0%
+engineering
+trickier and they found this out by
+
+ align:start position:0%
+trickier and they found this out by
+ 
+
+ align:start position:0%
+trickier and they found this out by
+using our software and saying hey wait a
+
+ align:start position:0%
+using our software and saying hey wait a
+ 
+
+ align:start position:0%
+using our software and saying hey wait a
+minute we got a different product sheet
+
+ align:start position:0%
+minute we got a different product sheet
+ 
+
+ align:start position:0%
+minute we got a different product sheet
+when we came in from tour than we did
+
+ align:start position:0%
+when we came in from tour than we did
+ 
+
+ align:start position:0%
+when we came in from tour than we did
+coming directly and it's also kind of
+
+ align:start position:0%
+coming directly and it's also kind of
+ 
+
+ align:start position:0%
+coming directly and it's also kind of
+normal for some companies to serve other
+
+ align:start position:0%
+normal for some companies to serve other
+ 
+
+ align:start position:0%
+normal for some companies to serve other
+companies versions of their websites to
+
+ align:start position:0%
+companies versions of their websites to
+ 
+
+ align:start position:0%
+companies versions of their websites to
+emphasize the employment opportunity
+
+ align:start position:0%
+emphasize the employment opportunity
+ 
+
+ align:start position:0%
+emphasize the employment opportunity
+sections um Regular law enforcement and
+
+ align:start position:0%
+sections um Regular law enforcement and
+ 
+
+ align:start position:0%
+sections um Regular law enforcement and
+needs anonymity Technologies as well to
+
+ align:start position:0%
+needs anonymity Technologies as well to
+ 
+
+ align:start position:0%
+needs anonymity Technologies as well to
+avoid tipping off people when you're
+
+ align:start position:0%
+avoid tipping off people when you're
+ 
+
+ align:start position:0%
+avoid tipping off people when you're
+doing investigations you do not want the
+
+ align:start position:0%
+doing investigations you do not want the
+ 
+
+ align:start position:0%
+doing investigations you do not want the
+local police station to appear in the
+
+ align:start position:0%
+local police station to appear in the
+ 
+
+ align:start position:0%
+local police station to appear in the
+web logs of somebody you're
+
+ align:start position:0%
+web logs of somebody you're
+ 
+
+ align:start position:0%
+web logs of somebody you're
+investigating and regular folks need it
+
+ align:start position:0%
+investigating and regular folks need it
+ 
+
+ align:start position:0%
+investigating and regular folks need it
+I said for avoiding harassment because
+
+ align:start position:0%
+I said for avoiding harassment because
+ 
+
+ align:start position:0%
+I said for avoiding harassment because
+of online activities to research stuff
+
+ align:start position:0%
+of online activities to research stuff
+ 
+
+ align:start position:0%
+of online activities to research stuff
+that might be embarrassing if you live
+
+ align:start position:0%
+that might be embarrassing if you live
+ 
+
+ align:start position:0%
+that might be embarrassing if you live
+in a country with uncertain healthc care
+
+ align:start position:0%
+in a country with uncertain healthc care
+ 
+
+ align:start position:0%
+in a country with uncertain healthc care
+laws it's a good idea to uh you might
+
+ align:start position:0%
+laws it's a good idea to uh you might
+ 
+
+ align:start position:0%
+laws it's a good idea to uh you might
+want to avoid creating too much public
+
+ align:start position:0%
+want to avoid creating too much public
+ 
+
+ align:start position:0%
+want to avoid creating too much public
+record of what diseases you think you
+
+ align:start position:0%
+record of what diseases you think you
+ 
+
+ align:start position:0%
+record of what diseases you think you
+might have and so on or what any
+
+ align:start position:0%
+might have and so on or what any
+ 
+
+ align:start position:0%
+might have and so on or what any
+dangerous Hobbies you might
+
+ align:start position:0%
+dangerous Hobbies you might
+ 
+
+ align:start position:0%
+dangerous Hobbies you might
+have and um also lots of criminal or bad
+
+ align:start position:0%
+have and um also lots of criminal or bad
+ 
+
+ align:start position:0%
+have and um also lots of criminal or bad
+folks use anonymity technology it's not
+
+ align:start position:0%
+folks use anonymity technology it's not
+ 
+
+ align:start position:0%
+folks use anonymity technology it's not
+their only option but
+
+ align:start position:0%
+their only option but
+ 
+
+ align:start position:0%
+their only option but
+um if you are willing to purchase time
+
+ align:start position:0%
+um if you are willing to purchase time
+ 
+
+ align:start position:0%
+um if you are willing to purchase time
+on a botn net you can buy some pretty
+
+ align:start position:0%
+on a botn net you can buy some pretty
+ 
+
+ align:start position:0%
+on a botn net you can buy some pretty
+good privacy um that is not available to
+
+ align:start position:0%
+good privacy um that is not available to
+ 
+
+ align:start position:0%
+good privacy um that is not available to
+people who think that bot Nets are
+
+ align:start position:0%
+people who think that bot Nets are
+ 
+
+ align:start position:0%
+people who think that bot Nets are
+immoral and tour and anonymity stuff in
+
+ align:start position:0%
+immoral and tour and anonymity stuff in
+ 
+
+ align:start position:0%
+immoral and tour and anonymity stuff in
+general are not the only multi multi-use
+
+ align:start position:0%
+general are not the only multi multi-use
+ 
+
+ align:start position:0%
+general are not the only multi multi-use
+technology out there uh let's see the
+
+ align:start position:0%
+technology out there uh let's see the
+ 
+
+ align:start position:0%
+technology out there uh let's see the
+average under graduate is about 20 so
+
+ align:start position:0%
+average under graduate is about 20 so
+ 
+
+ align:start position:0%
+average under graduate is about 20 so
+you been around when you were born um
+
+ align:start position:0%
+you been around when you were born um
+ 
+
+ align:start position:0%
+you been around when you were born um
+there was have you talked the crypto
+
+ align:start position:0%
+there was have you talked the crypto
+ 
+
+ align:start position:0%
+there was have you talked the crypto
+Wars at all no um during the the 1990s
+
+ align:start position:0%
+Wars at all no um during the the 1990s
+ 
+
+ align:start position:0%
+Wars at all no um during the the 1990s
+it was sort of an up in theair question
+
+ align:start position:0%
+it was sort of an up in theair question
+ 
+
+ align:start position:0%
+it was sort of an up in theair question
+in the United States about to what
+
+ align:start position:0%
+in the United States about to what
+ 
+
+ align:start position:0%
+in the United States about to what
+extent crypto civilian use of non-b
+
+ align:start position:0%
+extent crypto civilian use of non-b
+ 
+
+ align:start position:0%
+extent crypto civilian use of non-b
+backdoored cryptography should be legal
+
+ align:start position:0%
+backdoored cryptography should be legal
+ 
+
+ align:start position:0%
+backdoored cryptography should be legal
+and to what extent it should be
+
+ align:start position:0%
+and to what extent it should be
+ 
+
+ align:start position:0%
+and to what extent it should be
+exported that kind of came down pretty
+
+ align:start position:0%
+exported that kind of came down pretty
+ 
+
+ align:start position:0%
+exported that kind of came down pretty
+decisively on the side of cryptography
+
+ align:start position:0%
+decisively on the side of cryptography
+ 
+
+ align:start position:0%
+decisively on the side of cryptography
+should be legal and exportable during
+
+ align:start position:0%
+should be legal and exportable during
+ 
+
+ align:start position:0%
+should be legal and exportable during
+the '90s and early
+
+ align:start position:0%
+the '90s and early
+ 
+
+ align:start position:0%
+the '90s and early
+2000s and although there's some debate
+
+ align:start position:0%
+2000s and although there's some debate
+ 
+
+ align:start position:0%
+2000s and although there's some debate
+about anonymity technology it's more or
+
+ align:start position:0%
+about anonymity technology it's more or
+ 
+
+ align:start position:0%
+about anonymity technology it's more or
+less the same
+
+ align:start position:0%
+less the same
+ 
+
+ align:start position:0%
+less the same
+debate and I think it's going to end in
+
+ align:start position:0%
+debate and I think it's going to end in
+ 
+
+ align:start position:0%
+debate and I think it's going to end in
+more or less the same way
+
+ align:start position:0%
+more or less the same way
+ 
+
+ align:start position:0%
+more or less the same way
+so here's an outline of my talk going to
+
+ align:start position:0%
+so here's an outline of my talk going to
+ 
+
+ align:start position:0%
+so here's an outline of my talk going to
+give you that little introduction I gave
+
+ align:start position:0%
+give you that little introduction I gave
+ 
+
+ align:start position:0%
+give you that little introduction I gave
+you talk a little bit about what we mean
+
+ align:start position:0%
+you talk a little bit about what we mean
+ 
+
+ align:start position:0%
+you talk a little bit about what we mean
+by anonymity in a technical sense uh
+
+ align:start position:0%
+by anonymity in a technical sense uh
+ 
+
+ align:start position:0%
+by anonymity in a technical sense uh
+talk a little about our motivations for
+
+ align:start position:0%
+talk a little about our motivations for
+ 
+
+ align:start position:0%
+talk a little about our motivations for
+getting into it then I'm going to go to
+
+ align:start position:0%
+getting into it then I'm going to go to
+ 
+
+ align:start position:0%
+getting into it then I'm going to go to
+kind of walk you through stepbystep how
+
+ align:start position:0%
+kind of walk you through stepbystep how
+ 
+
+ align:start position:0%
+kind of walk you through stepbystep how
+you start with the idea of we ought to
+
+ align:start position:0%
+you start with the idea of we ought to
+ 
+
+ align:start position:0%
+you start with the idea of we ought to
+have some anonymity and how you wind up
+
+ align:start position:0%
+have some anonymity and how you wind up
+ 
+
+ align:start position:0%
+have some anonymity and how you wind up
+with the design of Torah from that point
+
+ align:start position:0%
+with the design of Torah from that point
+ 
+
+ align:start position:0%
+with the design of Torah from that point
+and I'll mention some branching off
+
+ align:start position:0%
+and I'll mention some branching off
+ 
+
+ align:start position:0%
+and I'll mention some branching off
+points where you might wind up with
+
+ align:start position:0%
+points where you might wind up with
+ 
+
+ align:start position:0%
+points where you might wind up with
+other designs I'll pause to answer some
+
+ align:start position:0%
+other designs I'll pause to answer some
+ 
+
+ align:start position:0%
+other designs I'll pause to answer some
+of the cool questions that everyone has
+
+ align:start position:0%
+of the cool questions that everyone has
+ 
+
+ align:start position:0%
+of the cool questions that everyone has
+sent in for their class
+
+ align:start position:0%
+sent in for their class
+ 
+
+ align:start position:0%
+sent in for their class
+assignment I'll talk a little bit about
+
+ align:start position:0%
+assignment I'll talk a little bit about
+ 
+
+ align:start position:0%
+assignment I'll talk a little bit about
+how no Discovery Works which is an
+
+ align:start position:0%
+how no Discovery Works which is an
+ 
+
+ align:start position:0%
+how no Discovery Works which is an
+important topic then I'll sort of by
+
+ align:start position:0%
+important topic then I'll sort of by
+ 
+
+ align:start position:0%
+important topic then I'll sort of by
+show of hands pick which of these
+
+ align:start position:0%
+show of hands pick which of these
+ 
+
+ align:start position:0%
+show of hands pick which of these
+Advanced topics to cover I guess I'm
+
+ align:start position:0%
+Advanced topics to cover I guess I'm
+ 
+
+ align:start position:0%
+Advanced topics to cover I guess I'm
+just calling them Advanced because
+
+ align:start position:0%
+just calling them Advanced because
+ 
+
+ align:start position:0%
+just calling them Advanced because
+they're later in the lecture and I can't
+
+ align:start position:0%
+they're later in the lecture and I can't
+ 
+
+ align:start position:0%
+they're later in the lecture and I can't
+cover them all but they're all really
+
+ align:start position:0%
+cover them all but they're all really
+ 
+
+ align:start position:0%
+cover them all but they're all really
+cool I'll mention some related systems
+
+ align:start position:0%
+cool I'll mention some related systems
+ 
+
+ align:start position:0%
+cool I'll mention some related systems
+whose designs you ought to check out if
+
+ align:start position:0%
+whose designs you ought to check out if
+ 
+
+ align:start position:0%
+whose designs you ought to check out if
+this is a topic that interests you and
+
+ align:start position:0%
+this is a topic that interests you and
+ 
+
+ align:start position:0%
+this is a topic that interests you and
+You' like to know more about it I'll
+
+ align:start position:0%
+You' like to know more about it I'll
+ 
+
+ align:start position:0%
+You' like to know more about it I'll
+talk about future work that we want to
+
+ align:start position:0%
+talk about future work that we want to
+ 
+
+ align:start position:0%
+talk about future work that we want to
+back up in tour and I hope we will have
+
+ align:start position:0%
+back up in tour and I hope we will have
+ 
+
+ align:start position:0%
+back up in tour and I hope we will have
+time to do someday and if there's time
+
+ align:start position:0%
+time to do someday and if there's time
+ 
+
+ align:start position:0%
+time to do someday and if there's time
+for questions then I'll take them and
+
+ align:start position:0%
+for questions then I'll take them and
+ 
+
+ align:start position:0%
+for questions then I'll take them and
+I've got nowhere I need to be for the
+
+ align:start position:0%
+I've got nowhere I need to be for the
+ 
+
+ align:start position:0%
+I've got nowhere I need to be for the
+next hour or so so um I and my colleague
+
+ align:start position:0%
+next hour or so so um I and my colleague
+ 
+
+ align:start position:0%
+next hour or so so um I and my colleague
+uh David over there could you wave your
+
+ align:start position:0%
+uh David over there could you wave your
+ 
+
+ align:start position:0%
+uh David over there could you wave your
+hand David we'll be hanging around
+
+ align:start position:0%
+hand David we'll be hanging around
+ 
+
+ align:start position:0%
+hand David we'll be hanging around
+somewhere and talking to anyone who
+
+ align:start position:0%
+somewhere and talking to anyone who
+ 
+
+ align:start position:0%
+somewhere and talking to anyone who
+wants to talk so right anonymity what
+
+ align:start position:0%
+wants to talk so right anonymity what
+ 
+
+ align:start position:0%
+wants to talk so right anonymity what
+what do we mean when we talk about
+
+ align:start position:0%
+what do we mean when we talk about
+ 
+
+ align:start position:0%
+what do we mean when we talk about
+anonymity there are lots of informal
+
+ align:start position:0%
+anonymity there are lots of informal
+ 
+
+ align:start position:0%
+anonymity there are lots of informal
+Notions that get used
+
+ align:start position:0%
+Notions that get used
+ 
+
+ align:start position:0%
+Notions that get used
+in um informal discussions in online and
+
+ align:start position:0%
+in um informal discussions in online and
+ 
+
+ align:start position:0%
+in um informal discussions in online and
+so on some people use anonymous to mean
+
+ align:start position:0%
+so on some people use anonymous to mean
+ 
+
+ align:start position:0%
+so on some people use anonymous to mean
+I didn't write my name on it some people
+
+ align:start position:0%
+I didn't write my name on it some people
+ 
+
+ align:start position:0%
+I didn't write my name on it some people
+use anonymous to mean well no one can
+
+ align:start position:0%
+use anonymous to mean well no one can
+ 
+
+ align:start position:0%
+use anonymous to mean well no one can
+actually prove it's me even if you
+
+ align:start position:0%
+actually prove it's me even if you
+ 
+
+ align:start position:0%
+actually prove it's me even if you
+suspect strongly what we mean is a
+
+ align:start position:0%
+suspect strongly what we mean is a
+ 
+
+ align:start position:0%
+suspect strongly what we mean is a
+number of of Notions expressed in terms
+
+ align:start position:0%
+number of of Notions expressed in terms
+ 
+
+ align:start position:0%
+number of of Notions expressed in terms
+of um of the ability of an observer or
+
+ align:start position:0%
+of um of the ability of an observer or
+ 
+
+ align:start position:0%
+of um of the ability of an observer or
+attacker on a network to link
+
+ align:start position:0%
+attacker on a network to link
+ 
+
+ align:start position:0%
+attacker on a network to link
+participants to actions these Notions
+
+ align:start position:0%
+participants to actions these Notions
+ 
+
+ align:start position:0%
+participants to actions these Notions
+come out of a uh terminology paper by
+
+ align:start position:0%
+come out of a uh terminology paper by
+ 
+
+ align:start position:0%
+come out of a uh terminology paper by
+fitman and Hanson that you can find a
+
+ align:start position:0%
+fitman and Hanson that you can find a
+ 
+
+ align:start position:0%
+fitman and Hanson that you can find a
+link to on freeh haven.nj
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is doing some activity she's
+
+ align:start position:0%
+is doing some activity she's
+ 
+
+ align:start position:0%
+is doing some activity she's
+um uh what should Ellis be doing Ellis
+
+ align:start position:0%
+um uh what should Ellis be doing Ellis
+ 
+
+ align:start position:0%
+um uh what should Ellis be doing Ellis
+is buying new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+socks and there's some attacker here
+
+ align:start position:0%
+socks and there's some attacker here
+ 
+
+ align:start position:0%
+socks and there's some attacker here
+let's call her Eve for
+
+ align:start position:0%
+let's call her Eve for
+ 
+
+ align:start position:0%
+let's call her Eve for
+now Eve can tell that Alice is doing
+
+ align:start position:0%
+now Eve can tell that Alice is doing
+ 
+
+ align:start position:0%
+now Eve can tell that Alice is doing
+something that's not what preventing
+
+ align:start position:0%
+something that's not what preventing
+ 
+
+ align:start position:0%
+something that's not what preventing
+that is not what we mean by anonymity
+
+ align:start position:0%
+that is not what we mean by anonymity
+ 
+
+ align:start position:0%
+that is not what we mean by anonymity
+that's called unobservability you can
+
+ align:start position:0%
+that's called unobservability you can
+ 
+
+ align:start position:0%
+that's called unobservability you can
+tell possibly that someone is buying
+
+ align:start position:0%
+tell possibly that someone is buying
+ 
+
+ align:start position:0%
+tell possibly that someone is buying
+socks again that's not what we mean by
+
+ align:start position:0%
+socks again that's not what we mean by
+ 
+
+ align:start position:0%
+socks again that's not what we mean by
+anonymity but what we hope is that Eve
+
+ align:start position:0%
+anonymity but what we hope is that Eve
+ 
+
+ align:start position:0%
+anonymity but what we hope is that Eve
+cannot tell that Alice in particular is
+
+ align:start position:0%
+cannot tell that Alice in particular is
+ 
+
+ align:start position:0%
+cannot tell that Alice in particular is
+buying socks and we mean that both on a
+
+ align:start position:0%
+buying socks and we mean that both on a
+ 
+
+ align:start position:0%
+buying socks and we mean that both on a
+categorical level Eve should not be able
+
+ align:start position:0%
+categorical level Eve should not be able
+ 
+
+ align:start position:0%
+categorical level Eve should not be able
+to conclude through rigorous
+
+ align:start position:0%
+to conclude through rigorous
+ 
+
+ align:start position:0%
+to conclude through rigorous
+mathematical proof this is Ellis she's
+
+ align:start position:0%
+mathematical proof this is Ellis she's
+ 
+
+ align:start position:0%
+mathematical proof this is Ellis she's
+buying socks but also Eve should not be
+
+ align:start position:0%
+buying socks but also Eve should not be
+ 
+
+ align:start position:0%
+buying socks but also Eve should not be
+able to conclude
+
+ align:start position:0%
+able to conclude
+ 
+
+ align:start position:0%
+able to conclude
+probabilistically it's Liker that Ellis
+
+ align:start position:0%
+probabilistically it's Liker that Ellis
+ 
+
+ align:start position:0%
+probabilistically it's Liker that Ellis
+is buying socks than some randomly
+
+ align:start position:0%
+is buying socks than some randomly
+ 
+
+ align:start position:0%
+is buying socks than some randomly
+selected person and also we would like
+
+ align:start position:0%
+selected person and also we would like
+ 
+
+ align:start position:0%
+selected person and also we would like
+Eve not even not to be able to include
+
+ align:start position:0%
+Eve not even not to be able to include
+ 
+
+ align:start position:0%
+Eve not even not to be able to include
+after observing many Alice activities
+
+ align:start position:0%
+after observing many Alice activities
+ 
+
+ align:start position:0%
+after observing many Alice activities
+Alice sometimes buys socks even if I
+
+ align:start position:0%
+Alice sometimes buys socks even if I
+ 
+
+ align:start position:0%
+Alice sometimes buys socks even if I
+don't know some particular activity of
+
+ align:start position:0%
+don't know some particular activity of
+ 
+
+ align:start position:0%
+don't know some particular activity of
+Alice's is a socks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+purchase there are other ideas that are
+
+ align:start position:0%
+purchase there are other ideas that are
+ 
+
+ align:start position:0%
+purchase there are other ideas that are
+related one idea is unlinkability
+
+ align:start position:0%
+related one idea is unlinkability
+ 
+
+ align:start position:0%
+related one idea is unlinkability
+unlinkability
+
+ align:start position:0%
+unlinkability
+ 
+
+ align:start position:0%
+unlinkability
+is you is there's like a long-term
+
+ align:start position:0%
+is you is there's like a long-term
+ 
+
+ align:start position:0%
+is you is there's like a long-term
+profile you of Alice so for instance
+
+ align:start position:0%
+profile you of Alice so for instance
+ 
+
+ align:start position:0%
+profile you of Alice so for instance
+Alice has been posting as um
+
+ align:start position:0%
+Alice has been posting as um
+ 
+
+ align:start position:0%
+Alice has been posting as um
+um I'm never good at picking names for
+
+ align:start position:0%
+um I'm never good at picking names for
+ 
+
+ align:start position:0%
+um I'm never good at picking names for
+my example Alice has been posting as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bob and writing a political blog that
+
+ align:start position:0%
+Bob and writing a political blog that
+ 
+
+ align:start position:0%
+Bob and writing a political blog that
+would disrupt her career uh that would
+
+ align:start position:0%
+would disrupt her career uh that would
+ 
+
+ align:start position:0%
+would disrupt her career uh that would
+that would offend her department head
+
+ align:start position:0%
+that would offend her department head
+ 
+
+ align:start position:0%
+that would offend her department head
+and disrupt her career as a computer
+
+ align:start position:0%
+and disrupt her career as a computer
+ 
+
+ align:start position:0%
+and disrupt her career as a computer
+security lecturer so um she's been
+
+ align:start position:0%
+security lecturer so um she's been
+ 
+
+ align:start position:0%
+security lecturer so um she's been
+writing as Bob unlinkability
+
+ align:start position:0%
+writing as Bob unlinkability
+ 
+
+ align:start position:0%
+writing as Bob unlinkability
+is the um is Eve's inability to link
+
+ align:start position:0%
+is the um is Eve's inability to link
+ 
+
+ align:start position:0%
+is the um is Eve's inability to link
+Alis to a particular profile uh final
+
+ align:start position:0%
+Alis to a particular profile uh final
+ 
+
+ align:start position:0%
+Alis to a particular profile uh final
+notion unobservability
+
+ align:start position:0%
+notion unobservability
+ 
+
+ align:start position:0%
+notion unobservability
+you some systems try to
+
+ align:start position:0%
+you some systems try to
+ 
+
+ align:start position:0%
+you some systems try to
+provide um try to make it impossible to
+
+ align:start position:0%
+provide um try to make it impossible to
+ 
+
+ align:start position:0%
+provide um try to make it impossible to
+even tell that Ellis is online that
+
+ align:start position:0%
+even tell that Ellis is online that
+ 
+
+ align:start position:0%
+even tell that Ellis is online that
+Ellis is connecting to anybody at all
+
+ align:start position:0%
+Ellis is connecting to anybody at all
+ 
+
+ align:start position:0%
+Ellis is connecting to anybody at all
+the that Alis is doing any activity
+
+ align:start position:0%
+the that Alis is doing any activity
+ 
+
+ align:start position:0%
+the that Alis is doing any activity
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+are rather hard to build I'll talk a
+
+ align:start position:0%
+are rather hard to build I'll talk a
+ 
+
+ align:start position:0%
+are rather hard to build I'll talk a
+little bit more about to what extent
+
+ align:start position:0%
+little bit more about to what extent
+ 
+
+ align:start position:0%
+little bit more about to what extent
+they are useful later uh something that
+
+ align:start position:0%
+they are useful later uh something that
+ 
+
+ align:start position:0%
+they are useful later uh something that
+is useful in that area is you might want
+
+ align:start position:0%
+is useful in that area is you might want
+ 
+
+ align:start position:0%
+is useful in that area is you might want
+to conceal that Alice is using an
+
+ align:start position:0%
+to conceal that Alice is using an
+ 
+
+ align:start position:0%
+to conceal that Alice is using an
+anonymity system but not that she is on
+
+ align:start position:0%
+anonymity system but not that she is on
+ 
+
+ align:start position:0%
+anonymity system but not that she is on
+the internet that's more achievable than
+
+ align:start position:0%
+the internet that's more achievable than
+ 
+
+ align:start position:0%
+the internet that's more achievable than
+concealing the fact that Alice is on the
+
+ align:start position:0%
+concealing the fact that Alice is on the
+ 
+
+ align:start position:0%
+concealing the fact that Alice is on the
+internet
+
+ align:start position:0%
+internet
+ 
+
+ align:start position:0%
+internet
+entirely so why did I start working on
+
+ align:start position:0%
+entirely so why did I start working on
+ 
+
+ align:start position:0%
+entirely so why did I start working on
+this in the first place well partially
+
+ align:start position:0%
+this in the first place well partially
+ 
+
+ align:start position:0%
+this in the first place well partially
+because of the engineers's itch it's a
+
+ align:start position:0%
+because of the engineers's itch it's a
+ 
+
+ align:start position:0%
+because of the engineers's itch it's a
+cool problem it's an interesting problem
+
+ align:start position:0%
+cool problem it's an interesting problem
+ 
+
+ align:start position:0%
+cool problem it's an interesting problem
+nobody else was actually working on it
+
+ align:start position:0%
+nobody else was actually working on it
+ 
+
+ align:start position:0%
+nobody else was actually working on it
+and my friend Roger got a contract to uh
+
+ align:start position:0%
+and my friend Roger got a contract to uh
+ 
+
+ align:start position:0%
+and my friend Roger got a contract to uh
+finish up a stalled research project
+
+ align:start position:0%
+finish up a stalled research project
+ 
+
+ align:start position:0%
+finish up a stalled research project
+before the grant expired and he did it
+
+ align:start position:0%
+before the grant expired and he did it
+ 
+
+ align:start position:0%
+before the grant expired and he did it
+well enough that I said hey I'll join up
+
+ align:start position:0%
+well enough that I said hey I'll join up
+ 
+
+ align:start position:0%
+well enough that I said hey I'll join up
+and you've got some more funding
+
+ align:start position:0%
+and you've got some more funding
+ 
+
+ align:start position:0%
+and you've got some more funding
+foration sure I'll I'll join in after a
+
+ align:start position:0%
+foration sure I'll I'll join in after a
+ 
+
+ align:start position:0%
+foration sure I'll I'll join in after a
+while we formed a nonprofit and G
+
+ align:start position:0%
+while we formed a nonprofit and G
+ 
+
+ align:start position:0%
+while we formed a nonprofit and G
+released everything as open source so
+
+ align:start position:0%
+released everything as open source so
+ 
+
+ align:start position:0%
+released everything as open source so
+that's part of it but for deeper
+
+ align:start position:0%
+that's part of it but for deeper
+ 
+
+ align:start position:0%
+that's part of it but for deeper
+motivations I think Humanity's got a lot
+
+ align:start position:0%
+motivations I think Humanity's got a lot
+ 
+
+ align:start position:0%
+motivations I think Humanity's got a lot
+of problems that can only be solved
+
+ align:start position:0%
+of problems that can only be solved
+ 
+
+ align:start position:0%
+of problems that can only be solved
+through better and more dedicated
+
+ align:start position:0%
+through better and more dedicated
+ 
+
+ align:start position:0%
+through better and more dedicated
+communication Freer expression and more
+
+ align:start position:0%
+communication Freer expression and more
+ 
+
+ align:start position:0%
+communication Freer expression and more
+free of thought and I don't know how to
+
+ align:start position:0%
+free of thought and I don't know how to
+ 
+
+ align:start position:0%
+free of thought and I don't know how to
+solve these
+
+ align:start position:0%
+solve these
+ 
+
+ align:start position:0%
+solve these
+problems all I think I can do is try to
+
+ align:start position:0%
+problems all I think I can do is try to
+ 
+
+ align:start position:0%
+problems all I think I can do is try to
+make sure that what I see as
+
+ align:start position:0%
+make sure that what I see as
+ 
+
+ align:start position:0%
+make sure that what I see as
+inhibiting discussion thought speech
+
+ align:start position:0%
+inhibiting discussion thought speech
+ 
+
+ align:start position:0%
+inhibiting discussion thought speech
+becomes harder to do so that's more or
+
+ align:start position:0%
+becomes harder to do so that's more or
+ 
+
+ align:start position:0%
+becomes harder to do so that's more or
+less where I'm at y uh so I know there
+
+ align:start position:0%
+less where I'm at y uh so I know there
+ 
+
+ align:start position:0%
+less where I'm at y uh so I know there
+are many good reasons to use T please
+
+ align:start position:0%
+are many good reasons to use T please
+ 
+
+ align:start position:0%
+are many good reasons to use T please
+don't see this as criticism I'm just
+
+ align:start position:0%
+don't see this as criticism I'm just
+ 
+
+ align:start position:0%
+don't see this as criticism I'm just
+curious uh what is your opinion as far
+
+ align:start position:0%
+curious uh what is your opinion as far
+ 
+
+ align:start position:0%
+curious uh what is your opinion as far
+as um you know criminal activity what is
+
+ align:start position:0%
+as um you know criminal activity what is
+ 
+
+ align:start position:0%
+as um you know criminal activity what is
+my opinion on criminal activity some
+
+ align:start position:0%
+my opinion on criminal activity some
+ 
+
+ align:start position:0%
+my opinion on criminal activity some
+laws are good some laws are bad my
+
+ align:start position:0%
+laws are good some laws are bad my
+ 
+
+ align:start position:0%
+laws are good some laws are bad my
+lawyers would tell me never to advise
+
+ align:start position:0%
+lawyers would tell me never to advise
+ 
+
+ align:start position:0%
+lawyers would tell me never to advise
+anyone to break the law um I feel my
+
+ align:start position:0%
+anyone to break the law um I feel my
+ 
+
+ align:start position:0%
+anyone to break the law um I feel my
+goal was not to enable criminal activity
+
+ align:start position:0%
+goal was not to enable criminal activity
+ 
+
+ align:start position:0%
+goal was not to enable criminal activity
+against most of the laws I agree with in
+
+ align:start position:0%
+against most of the laws I agree with in
+ 
+
+ align:start position:0%
+against most of the laws I agree with in
+places where criticizing the government
+
+ align:start position:0%
+places where criticizing the government
+ 
+
+ align:start position:0%
+places where criticizing the government
+is illegal then I'm in favor of criminal
+
+ align:start position:0%
+is illegal then I'm in favor of criminal
+ 
+
+ align:start position:0%
+is illegal then I'm in favor of criminal
+activity of that kind I so in that case
+
+ align:start position:0%
+activity of that kind I so in that case
+ 
+
+ align:start position:0%
+activity of that kind I so in that case
+I suppose I was supporting that kind of
+
+ align:start position:0%
+I suppose I was supporting that kind of
+ 
+
+ align:start position:0%
+I suppose I was supporting that kind of
+criminal
+
+ align:start position:0%
+criminal
+ 
+
+ align:start position:0%
+criminal
+activity my stance on whether it's a
+
+ align:start position:0%
+activity my stance on whether it's a
+ 
+
+ align:start position:0%
+activity my stance on whether it's a
+problem that an anonymity Network gets
+
+ align:start position:0%
+problem that an anonymity Network gets
+ 
+
+ align:start position:0%
+problem that an anonymity Network gets
+used for criminal activity in general to
+
+ align:start position:0%
+used for criminal activity in general to
+ 
+
+ align:start position:0%
+used for criminal activity in general to
+the extent that there are good laws I
+
+ align:start position:0%
+the extent that there are good laws I
+ 
+
+ align:start position:0%
+the extent that there are good laws I
+would prefer that people not break them
+
+ align:start position:0%
+would prefer that people not break them
+ 
+
+ align:start position:0%
+would prefer that people not break them
+I would however think that any computer
+
+ align:start position:0%
+I would however think that any computer
+ 
+
+ align:start position:0%
+I would however think that any computer
+security system that does not get used
+
+ align:start position:0%
+security system that does not get used
+ 
+
+ align:start position:0%
+security system that does not get used
+by criminals is probably a very bad
+
+ align:start position:0%
+by criminals is probably a very bad
+ 
+
+ align:start position:0%
+by criminals is probably a very bad
+computer security system if the
+
+ align:start position:0%
+computer security system if the
+ 
+
+ align:start position:0%
+computer security system if the
+computers if the criminals are making
+
+ align:start position:0%
+computers if the criminals are making
+ 
+
+ align:start position:0%
+computers if the criminals are making
+any kind of good decision making policy
+
+ align:start position:0%
+any kind of good decision making policy
+ 
+
+ align:start position:0%
+any kind of good decision making policy
+I think that if we go around Banning
+
+ align:start position:0%
+I think that if we go around Banning
+ 
+
+ align:start position:0%
+I think that if we go around Banning
+security that works for criminals we
+
+ align:start position:0%
+security that works for criminals we
+ 
+
+ align:start position:0%
+security that works for criminals we
+wind up with insecure
+
+ align:start position:0%
+wind up with insecure
+ 
+
+ align:start position:0%
+wind up with insecure
+systems um so that's more or less where
+
+ align:start position:0%
+systems um so that's more or less where
+ 
+
+ align:start position:0%
+systems um so that's more or less where
+I stand on it I'm not really the
+
+ align:start position:0%
+I stand on it I'm not really the
+ 
+
+ align:start position:0%
+I stand on it I'm not really the
+philosopher of it this though I'm more
+
+ align:start position:0%
+philosopher of it this though I'm more
+ 
+
+ align:start position:0%
+philosopher of it this though I'm more
+of the programmer
+
+ align:start position:0%
+of the programmer
+ 
+
+ align:start position:0%
+of the programmer
+so I'm going to be giving really trit
+
+ align:start position:0%
+so I'm going to be giving really trit
+ 
+
+ align:start position:0%
+so I'm going to be giving really trit
+answers to philosophical and legal
+
+ align:start position:0%
+answers to philosophical and legal
+ 
+
+ align:start position:0%
+answers to philosophical and legal
+questions also I am not a lawyer and
+
+ align:start position:0%
+questions also I am not a lawyer and
+ 
+
+ align:start position:0%
+questions also I am not a lawyer and
+cannot offer legal advice do not take
+
+ align:start position:0%
+cannot offer legal advice do not take
+ 
+
+ align:start position:0%
+cannot offer legal advice do not take
+anything I say as legal
+
+ align:start position:0%
+anything I say as legal
+ 
+
+ align:start position:0%
+anything I say as legal
+advice that said um also so at the time
+
+ align:start position:0%
+advice that said um also so at the time
+ 
+
+ align:start position:0%
+advice that said um also so at the time
+we started also a lot of these research
+
+ align:start position:0%
+we started also a lot of these research
+ 
+
+ align:start position:0%
+we started also a lot of these research
+problems I'm going to be talking about
+
+ align:start position:0%
+problems I'm going to be talking about
+ 
+
+ align:start position:0%
+problems I'm going to be talking about
+weren't even close to being solved so
+
+ align:start position:0%
+weren't even close to being solved so
+ 
+
+ align:start position:0%
+weren't even close to being solved so
+why did we start anyway instead of going
+
+ align:start position:0%
+why did we start anyway instead of going
+ 
+
+ align:start position:0%
+why did we start anyway instead of going
+straight into research one of them was
+
+ align:start position:0%
+straight into research one of them was
+ 
+
+ align:start position:0%
+straight into research one of them was
+we thought that a lot of them wouldn't
+
+ align:start position:0%
+we thought that a lot of them wouldn't
+ 
+
+ align:start position:0%
+we thought that a lot of them wouldn't
+get solved unless there was a test bed
+
+ align:start position:0%
+get solved unless there was a test bed
+ 
+
+ align:start position:0%
+get solved unless there was a test bed
+to work on and that's kind of gotten
+
+ align:start position:0%
+to work on and that's kind of gotten
+ 
+
+ align:start position:0%
+to work on and that's kind of gotten
+born out
+
+ align:start position:0%
+born out
+ 
+
+ align:start position:0%
+born out
+because tour has kind of become the
+
+ align:start position:0%
+because tour has kind of become the
+ 
+
+ align:start position:0%
+because tour has kind of become the
+research platform of choice for lots of
+
+ align:start position:0%
+research platform of choice for lots of
+ 
+
+ align:start position:0%
+research platform of choice for lots of
+work on low latency anonymity systems
+
+ align:start position:0%
+work on low latency anonymity systems
+ 
+
+ align:start position:0%
+work on low latency anonymity systems
+and has helped the fied a lot in that
+
+ align:start position:0%
+and has helped the fied a lot in that
+ 
+
+ align:start position:0%
+and has helped the fied a lot in that
+way but also you know 10 years on and a
+
+ align:start position:0%
+way but also you know 10 years on and a
+ 
+
+ align:start position:0%
+way but also you know 10 years on and a
+lot of the big problems still aren't
+
+ align:start position:0%
+lot of the big problems still aren't
+ 
+
+ align:start position:0%
+lot of the big problems still aren't
+solved so if we had waited 10 years for
+
+ align:start position:0%
+solved so if we had waited 10 years for
+ 
+
+ align:start position:0%
+solved so if we had waited 10 years for
+everything to get fixed that we would
+
+ align:start position:0%
+everything to get fixed that we would
+ 
+
+ align:start position:0%
+everything to get fixed that we would
+have been Waiting in
+
+ align:start position:0%
+have been Waiting in
+ 
+
+ align:start position:0%
+have been Waiting in
+Vain
+
+ align:start position:0%
+Vain
+ 
+
+ align:start position:0%
+Vain
+so why do it then partially because we
+
+ align:start position:0%
+so why do it then partially because we
+ 
+
+ align:start position:0%
+so why do it then partially because we
+thought
+
+ align:start position:0%
+thought
+ 
+
+ align:start position:0%
+thought
+that having
+
+ align:start position:0%
+that having
+ 
+
+ align:start position:0%
+that having
+a having a system out there would
+
+ align:start position:0%
+a having a system out there would
+ 
+
+ align:start position:0%
+a having a system out there would
+improve long-term outcomes for the world
+
+ align:start position:0%
+improve long-term outcomes for the world
+ 
+
+ align:start position:0%
+improve long-term outcomes for the world
+that is it's really easy to argue that
+
+ align:start position:0%
+that is it's really easy to argue that
+ 
+
+ align:start position:0%
+that is it's really easy to argue that
+something that doesn't exist should be
+
+ align:start position:0%
+something that doesn't exist should be
+ 
+
+ align:start position:0%
+something that doesn't exist should be
+banned arguments against civilian use of
+
+ align:start position:0%
+banned arguments against civilian use of
+ 
+
+ align:start position:0%
+banned arguments against civilian use of
+cryptography were much easier to make in
+
+ align:start position:0%
+cryptography were much easier to make in
+ 
+
+ align:start position:0%
+cryptography were much easier to make in
+public in 1990 than they are today
+
+ align:start position:0%
+public in 1990 than they are today
+ 
+
+ align:start position:0%
+public in 1990 than they are today
+because there was almost no civilian use
+
+ align:start position:0%
+because there was almost no civilian use
+ 
+
+ align:start position:0%
+because there was almost no civilian use
+of strong cryptography then and you
+
+ align:start position:0%
+of strong cryptography then and you
+ 
+
+ align:start position:0%
+of strong cryptography then and you
+could argue that if that you know if
+
+ align:start position:0%
+could argue that if that you know if
+ 
+
+ align:start position:0%
+could argue that if that you know if
+anything's stronger than Dees is legal
+
+ align:start position:0%
+anything's stronger than Dees is legal
+ 
+
+ align:start position:0%
+anything's stronger than Dees is legal
+then civilization will
+
+ align:start position:0%
+then civilization will
+ 
+
+ align:start position:0%
+then civilization will
+collapse um criminals will never be
+
+ align:start position:0%
+collapse um criminals will never be
+ 
+
+ align:start position:0%
+collapse um criminals will never be
+caught
+
+ align:start position:0%
+caught
+ 
+
+ align:start position:0%
+caught
+and um and organized crime will take
+
+ align:start position:0%
+and um and organized crime will take
+ 
+
+ align:start position:0%
+and um and organized crime will take
+over everything but you couldn't really
+
+ align:start position:0%
+over everything but you couldn't really
+ 
+
+ align:start position:0%
+over everything but you couldn't really
+argue that that was the inevitable
+
+ align:start position:0%
+argue that that was the inevitable
+ 
+
+ align:start position:0%
+argue that that was the inevitable
+consequence of cryptography in 2000
+
+ align:start position:0%
+consequence of cryptography in 2000
+ 
+
+ align:start position:0%
+consequence of cryptography in 2000
+because cryptography had already been
+
+ align:start position:0%
+because cryptography had already been
+ 
+
+ align:start position:0%
+because cryptography had already been
+out there and it turned out not to end
+
+ align:start position:0%
+out there and it turned out not to end
+ 
+
+ align:start position:0%
+out there and it turned out not to end
+the world further it was harder to argue
+
+ align:start position:0%
+the world further it was harder to argue
+ 
+
+ align:start position:0%
+the world further it was harder to argue
+for a cryptography ban in 2000
+
+ align:start position:0%
+for a cryptography ban in 2000
+ 
+
+ align:start position:0%
+for a cryptography ban in 2000
+because there was a large constituency
+
+ align:start position:0%
+because there was a large constituency
+ 
+
+ align:start position:0%
+because there was a large constituency
+in favor of the use of cryptography that
+
+ align:start position:0%
+in favor of the use of cryptography that
+ 
+
+ align:start position:0%
+in favor of the use of cryptography that
+is if someone says if someone in 1985
+
+ align:start position:0%
+is if someone says if someone in 1985
+ 
+
+ align:start position:0%
+is if someone says if someone in 1985
+says let's ban strong cryptography well
+
+ align:start position:0%
+says let's ban strong cryptography well
+ 
+
+ align:start position:0%
+says let's ban strong cryptography well
+banks are using strong cryptography so
+
+ align:start position:0%
+banks are using strong cryptography so
+ 
+
+ align:start position:0%
+banks are using strong cryptography so
+they'll ask for an exemption but other
+
+ align:start position:0%
+they'll ask for an exemption but other
+ 
+
+ align:start position:0%
+they'll ask for an exemption but other
+than that there weren't a lot of users
+
+ align:start position:0%
+than that there weren't a lot of users
+ 
+
+ align:start position:0%
+than that there weren't a lot of users
+of strong cryptography in the civilian
+
+ align:start position:0%
+of strong cryptography in the civilian
+ 
+
+ align:start position:0%
+of strong cryptography in the civilian
+space but if someone in 2000 said let's
+
+ align:start position:0%
+space but if someone in 2000 said let's
+ 
+
+ align:start position:0%
+space but if someone in 2000 said let's
+ban strong cryptography that would be
+
+ align:start position:0%
+ban strong cryptography that would be
+ 
+
+ align:start position:0%
+ban strong cryptography that would be
+every internet
+
+ align:start position:0%
+every internet
+ 
+
+ align:start position:0%
+every internet
+company everyone running an https page
+
+ align:start position:0%
+company everyone running an https page
+ 
+
+ align:start position:0%
+company everyone running an https page
+would start waving their hands and
+
+ align:start position:0%
+would start waving their hands and
+ 
+
+ align:start position:0%
+would start waving their hands and
+shouting about it and and nowadays
+
+ align:start position:0%
+shouting about it and and nowadays
+ 
+
+ align:start position:0%
+shouting about it and and nowadays
+strong cryptography bands are probably
+
+ align:start position:0%
+strong cryptography bands are probably
+ 
+
+ align:start position:0%
+strong cryptography bands are probably
+unfeasible although people keep bringing
+
+ align:start position:0%
+unfeasible although people keep bringing
+ 
+
+ align:start position:0%
+unfeasible although people keep bringing
+back the idea and again I'm not the
+
+ align:start position:0%
+back the idea and again I'm not the
+ 
+
+ align:start position:0%
+back the idea and again I'm not the
+philosopher or political scientist of
+
+ align:start position:0%
+philosopher or political scientist of
+ 
+
+ align:start position:0%
+philosopher or political scientist of
+the movement
+
+ align:start position:0%
+the movement
+ 
+
+ align:start position:0%
+the movement
+so some folks asked me what's your
+
+ align:start position:0%
+so some folks asked me what's your
+ 
+
+ align:start position:0%
+so some folks asked me what's your
+threat model it's good to be thinking in
+
+ align:start position:0%
+threat model it's good to be thinking in
+ 
+
+ align:start position:0%
+threat model it's good to be thinking in
+terms of threat models unfortunately our
+
+ align:start position:0%
+terms of threat models unfortunately our
+ 
+
+ align:start position:0%
+terms of threat models unfortunately our
+threat model is kind of weird we started
+
+ align:start position:0%
+threat model is kind of weird we started
+ 
+
+ align:start position:0%
+threat model is kind of weird we started
+not with a adversary requirement but we
+
+ align:start position:0%
+not with a adversary requirement but we
+ 
+
+ align:start position:0%
+not with a adversary requirement but we
+started with a usability
+
+ align:start position:0%
+started with a usability
+ 
+
+ align:start position:0%
+started with a usability
+requirement the usability requirement we
+
+ align:start position:0%
+requirement the usability requirement we
+ 
+
+ align:start position:0%
+requirement the usability requirement we
+gave ourselves to begin is this has to
+
+ align:start position:0%
+gave ourselves to begin is this has to
+ 
+
+ align:start position:0%
+gave ourselves to begin is this has to
+be useful for web browsing this has to
+
+ align:start position:0%
+be useful for web browsing this has to
+ 
+
+ align:start position:0%
+be useful for web browsing this has to
+be useful for interactive protocols
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it actually needs to see use subject
+
+ align:start position:0%
+and it actually needs to see use subject
+ 
+
+ align:start position:0%
+and it actually needs to see use subject
+to that we want to maximize security so
+
+ align:start position:0%
+to that we want to maximize security so
+ 
+
+ align:start position:0%
+to that we want to maximize security so
+our thread model has lots of weird
+
+ align:start position:0%
+our thread model has lots of weird
+ 
+
+ align:start position:0%
+our thread model has lots of weird
+Corners in it if you actually write it
+
+ align:start position:0%
+Corners in it if you actually write it
+ 
+
+ align:start position:0%
+Corners in it if you actually write it
+out as what can an attacker do what can
+
+ align:start position:0%
+out as what can an attacker do what can
+ 
+
+ align:start position:0%
+out as what can an attacker do what can
+under what circumstances and how and
+
+ align:start position:0%
+under what circumstances and how and
+ 
+
+ align:start position:0%
+under what circumstances and how and
+that's because we've set ourselves the
+
+ align:start position:0%
+that's because we've set ourselves the
+ 
+
+ align:start position:0%
+that's because we've set ourselves the
+goal of it has to work for the
+
+ align:start position:0%
+goal of it has to work for the
+ 
+
+ align:start position:0%
+goal of it has to work for the
+web um and I'll return to that in a
+
+ align:start position:0%
+web um and I'll return to that in a
+ 
+
+ align:start position:0%
+web um and I'll return to that in a
+minute or two but let's sort of talk
+
+ align:start position:0%
+minute or two but let's sort of talk
+ 
+
+ align:start position:0%
+minute or two but let's sort of talk
+about now how we can use
+
+ align:start position:0%
+about now how we can use
+ 
+
+ align:start position:0%
+about now how we can use
+um how we can use forward anony how we
+
+ align:start position:0%
+um how we can use forward anony how we
+ 
+
+ align:start position:0%
+um how we can use forward anony how we
+build forward anonymity
+
+ align:start position:0%
+build forward anonymity
+ 
+
+ align:start position:0%
+build forward anonymity
+so here's Ellis she wants to buy
+
+ align:start position:0%
+so here's Ellis she wants to buy
+ 
+
+ align:start position:0%
+so here's Ellis she wants to buy
+socks so okay let's say that
+
+ align:start position:0%
+socks so okay let's say that
+ 
+
+ align:start position:0%
+socks so okay let's say that
+Alice runs a computer let's call it R
+
+ align:start position:0%
+Alice runs a computer let's call it R
+ 
+
+ align:start position:0%
+Alice runs a computer let's call it R
+for relay and this computer relays her
+
+ align:start position:0%
+for relay and this computer relays her
+ 
+
+ align:start position:0%
+for relay and this computer relays her
+traffic to um I want to say socks.com
+
+ align:start position:0%
+traffic to um I want to say socks.com
+ 
+
+ align:start position:0%
+traffic to um I want to say socks.com
+but I'm afraid that will turn out to be
+
+ align:start position:0%
+but I'm afraid that will turn out to be
+ 
+
+ align:start position:0%
+but I'm afraid that will turn out to be
+something horrible so um.com yeah they
+
+ align:start position:0%
+something horrible so um.com yeah they
+ 
+
+ align:start position:0%
+something horrible so um.com yeah they
+sell socks too all right so Ellis wants
+
+ align:start position:0%
+sell socks too all right so Ellis wants
+ 
+
+ align:start position:0%
+sell socks too all right so Ellis wants
+to buy some socks from z.com and she's
+
+ align:start position:0%
+to buy some socks from z.com and she's
+ 
+
+ align:start position:0%
+to buy some socks from z.com and she's
+going going through a relay um
+
+ align:start position:0%
+going going through a relay um
+ 
+
+ align:start position:0%
+going going through a relay um
+well I said Alice runs a re relay anyone
+
+ align:start position:0%
+well I said Alice runs a re relay anyone
+ 
+
+ align:start position:0%
+well I said Alice runs a re relay anyone
+any EES dropper who's looking at this
+
+ align:start position:0%
+any EES dropper who's looking at this
+ 
+
+ align:start position:0%
+any EES dropper who's looking at this
+will say uh that's Alice's computer it's
+
+ align:start position:0%
+will say uh that's Alice's computer it's
+ 
+
+ align:start position:0%
+will say uh that's Alice's computer it's
+probably Alice all right so let's have
+
+ align:start position:0%
+probably Alice all right so let's have
+ 
+
+ align:start position:0%
+probably Alice all right so let's have
+somebody else run a relay and have lots
+
+ align:start position:0%
+somebody else run a relay and have lots
+ 
+
+ align:start position:0%
+somebody else run a relay and have lots
+of other users all visit it I'll call
+
+ align:start position:0%
+of other users all visit it I'll call
+ 
+
+ align:start position:0%
+of other users all visit it I'll call
+them A2 and A3 because there aren't
+
+ align:start position:0%
+them A2 and A3 because there aren't
+ 
+
+ align:start position:0%
+them A2 and A3 because there aren't
+enough standard cryptography person
+
+ align:start position:0%
+enough standard cryptography person
+ 
+
+ align:start position:0%
+enough standard cryptography person
+names um by books
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tweet cat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pictures this is like 80% of what people
+
+ align:start position:0%
+pictures this is like 80% of what people
+ 
+
+ align:start position:0%
+pictures this is like 80% of what people
+do on the internet right um so now we
+
+ align:start position:0%
+do on the internet right um so now we
+ 
+
+ align:start position:0%
+do on the internet right um so now we
+have three people all going into this
+
+ align:start position:0%
+have three people all going into this
+ 
+
+ align:start position:0%
+have three people all going into this
+relay three streams exiting someone
+
+ align:start position:0%
+relay three streams exiting someone
+ 
+
+ align:start position:0%
+relay three streams exiting someone
+who's watching the relay can't easily
+
+ align:start position:0%
+who's watching the relay can't easily
+ 
+
+ align:start position:0%
+who's watching the relay can't easily
+correlate should not be we hope we we'll
+
+ align:start position:0%
+correlate should not be we hope we we'll
+ 
+
+ align:start position:0%
+correlate should not be we hope we we'll
+return return to that too that this
+
+ align:start position:0%
+return return to that too that this
+ 
+
+ align:start position:0%
+return return to that too that this
+Alice is buying socks this Alice buying
+
+ align:start position:0%
+Alice is buying socks this Alice buying
+ 
+
+ align:start position:0%
+Alice is buying socks this Alice buying
+books this Alice his tweeting
+
+ align:start position:0%
+books this Alice his tweeting
+ 
+
+ align:start position:0%
+books this Alice his tweeting
+CeX well except if they're watching this
+
+ align:start position:0%
+CeX well except if they're watching this
+ 
+
+ align:start position:0%
+CeX well except if they're watching this
+side of the connections they can see
+
+ align:start position:0%
+side of the connections they can see
+ 
+
+ align:start position:0%
+side of the connections they can see
+Alice telling the Relay please connect
+
+ align:start position:0%
+Alice telling the Relay please connect
+ 
+
+ align:start position:0%
+Alice telling the Relay please connect
+me to zap.com all right so we'll add
+
+ align:start position:0%
+me to zap.com all right so we'll add
+ 
+
+ align:start position:0%
+me to zap.com all right so we'll add
+some encryption we'll maybe do TLS on
+
+ align:start position:0%
+some encryption we'll maybe do TLS on
+ 
+
+ align:start position:0%
+some encryption we'll maybe do TLS on
+all of these links so to the extent that
+
+ align:start position:0%
+all of these links so to the extent that
+ 
+
+ align:start position:0%
+all of these links so to the extent that
+you can't break TLS to the extent you
+
+ align:start position:0%
+you can't break TLS to the extent you
+ 
+
+ align:start position:0%
+you can't break TLS to the extent you
+can't correlate this to this then they
+
+ align:start position:0%
+can't correlate this to this then they
+ 
+
+ align:start position:0%
+can't correlate this to this then they
+get some privacy well that's still not
+
+ align:start position:0%
+get some privacy well that's still not
+ 
+
+ align:start position:0%
+get some privacy well that's still not
+good enough though because um first off
+
+ align:start position:0%
+good enough though because um first off
+ 
+
+ align:start position:0%
+good enough though because um first off
+we're assuming that um this relay is
+
+ align:start position:0%
+we're assuming that um this relay is
+ 
+
+ align:start position:0%
+we're assuming that um this relay is
+fully trusted I assume you've done the
+
+ align:start position:0%
+fully trusted I assume you've done the
+ 
+
+ align:start position:0%
+fully trusted I assume you've done the
+definition of of trusted and why it
+
+ align:start position:0%
+definition of of trusted and why it
+ 
+
+ align:start position:0%
+definition of of trusted and why it
+doesn't actually mean trusted okay good
+
+ align:start position:0%
+doesn't actually mean trusted okay good
+ 
+
+ align:start position:0%
+doesn't actually mean trusted okay good
+um this is trusted in the sense that it
+
+ align:start position:0%
+um this is trusted in the sense that it
+ 
+
+ align:start position:0%
+um this is trusted in the sense that it
+can break the whole system trusted in
+
+ align:start position:0%
+can break the whole system trusted in
+ 
+
+ align:start position:0%
+can break the whole system trusted in
+the sense that you can't help but trust
+
+ align:start position:0%
+the sense that you can't help but trust
+ 
+
+ align:start position:0%
+the sense that you can't help but trust
+it not trusted in the sense that is
+
+ align:start position:0%
+it not trusted in the sense that is
+ 
+
+ align:start position:0%
+it not trusted in the sense that is
+actually trustworthy so all right we can
+
+ align:start position:0%
+actually trustworthy so all right we can
+ 
+
+ align:start position:0%
+actually trustworthy so all right we can
+introduce multiple relays we can have
+
+ align:start position:0%
+introduce multiple relays we can have
+ 
+
+ align:start position:0%
+introduce multiple relays we can have
+different relays run by different
+
+ align:start position:0%
+different relays run by different
+ 
+
+ align:start position:0%
+different relays run by different
+people we can have
+
+ align:start position:0%
+people we can have
+ 
+
+ align:start position:0%
+people we can have
+um this is not actually the topology we
+
+ align:start position:0%
+um this is not actually the topology we
+ 
+
+ align:start position:0%
+um this is not actually the topology we
+use but my Blackboard technique is
+
+ align:start position:0%
+use but my Blackboard technique is
+ 
+
+ align:start position:0%
+use but my Blackboard technique is
+terrible and I don't want to read I
+
+ align:start position:0%
+terrible and I don't want to read I
+ 
+
+ align:start position:0%
+terrible and I don't want to read I
+don't want to redraw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything we can imagine tunneling these
+
+ align:start position:0%
+anything we can imagine tunneling these
+ 
+
+ align:start position:0%
+anything we can imagine tunneling these
+connections through multiple relays Each
+
+ align:start position:0%
+connections through multiple relays Each
+ 
+
+ align:start position:0%
+connections through multiple relays Each
+of which removes a single layer of
+
+ align:start position:0%
+of which removes a single layer of
+ 
+
+ align:start position:0%
+of which removes a single layer of
+encryption so this all this relay sees
+
+ align:start position:0%
+encryption so this all this relay sees
+ 
+
+ align:start position:0%
+encryption so this all this relay sees
+is Alice is doing something all this
+
+ align:start position:0%
+is Alice is doing something all this
+ 
+
+ align:start position:0%
+is Alice is doing something all this
+relay sees is someone is buying socks
+
+ align:start position:0%
+relay sees is someone is buying socks
+ 
+
+ align:start position:0%
+relay sees is someone is buying socks
+but this one just sees someone's buying
+
+ align:start position:0%
+but this one just sees someone's buying
+ 
+
+ align:start position:0%
+but this one just sees someone's buying
+socks the connection came from this
+
+ align:start position:0%
+socks the connection came from this
+ 
+
+ align:start position:0%
+socks the connection came from this
+relay this just sees else is doing
+
+ align:start position:0%
+relay this just sees else is doing
+ 
+
+ align:start position:0%
+relay this just sees else is doing
+something and it forwards onto this
+
+ align:start position:0%
+something and it forwards onto this
+ 
+
+ align:start position:0%
+something and it forwards onto this
+relay and no single party ought to be
+
+ align:start position:0%
+relay and no single party ought to be
+ 
+
+ align:start position:0%
+relay and no single party ought to be
+able to correlate the whole
+
+ align:start position:0%
+able to correlate the whole
+ 
+
+ align:start position:0%
+able to correlate the whole
+thing now we come to a major design
+
+ align:start position:0%
+thing now we come to a major design
+ 
+
+ align:start position:0%
+thing now we come to a major design
+Point Let's suppose that that Eve is
+
+ align:start position:0%
+Point Let's suppose that that Eve is
+ 
+
+ align:start position:0%
+Point Let's suppose that that Eve is
+watching here and
+
+ align:start position:0%
+watching here and
+ 
+
+ align:start position:0%
+watching here and
+here nothing I've said so far does
+
+ align:start position:0%
+here nothing I've said so far does
+ 
+
+ align:start position:0%
+here nothing I've said so far does
+anything to obscure the the timing and
+
+ align:start position:0%
+anything to obscure the the timing and
+ 
+
+ align:start position:0%
+anything to obscure the the timing and
+volume of Alice's P packets oh sure
+
+ align:start position:0%
+volume of Alice's P packets oh sure
+ 
+
+ align:start position:0%
+volume of Alice's P packets oh sure
+there will be some some some trivial
+
+ align:start position:0%
+there will be some some some trivial
+ 
+
+ align:start position:0%
+there will be some some some trivial
+noise added from all the computation and
+
+ align:start position:0%
+noise added from all the computation and
+ 
+
+ align:start position:0%
+noise added from all the computation and
+decryption these things do from Network
+
+ align:start position:0%
+decryption these things do from Network
+ 
+
+ align:start position:0%
+decryption these things do from Network
+latency and so on but ultimately if
+
+ align:start position:0%
+latency and so on but ultimately if
+ 
+
+ align:start position:0%
+latency and so on but ultimately if
+Alice is sending a kilobyte in then in
+
+ align:start position:0%
+Alice is sending a kilobyte in then in
+ 
+
+ align:start position:0%
+Alice is sending a kilobyte in then in
+the design I catched out so far a
+
+ align:start position:0%
+the design I catched out so far a
+ 
+
+ align:start position:0%
+the design I catched out so far a
+kilobyte is coming out if Alis is and if
+
+ align:start position:0%
+kilobyte is coming out if Alis is and if
+ 
+
+ align:start position:0%
+kilobyte is coming out if Alis is and if
+the socks web page is 64k long and is
+
+ align:start position:0%
+the socks web page is 64k long and is
+ 
+
+ align:start position:0%
+the socks web page is 64k long and is
+served by this web server at
+
+ align:start position:0%
+served by this web server at
+ 
+
+ align:start position:0%
+served by this web server at
+11:26 then Alice is going to get
+
+ align:start position:0%
+11:26 then Alice is going to get
+ 
+
+ align:start position:0%
+11:26 then Alice is going to get
+something about 64k along at 1126 or
+
+ align:start position:0%
+something about 64k along at 1126 or
+ 
+
+ align:start position:0%
+something about 64k along at 1126 or
+1127 or
+
+ align:start position:0%
+1127 or
+ 
+
+ align:start position:0%
+1127 or
+so now with some statistics Eve can
+
+ align:start position:0%
+so now with some statistics Eve can
+ 
+
+ align:start position:0%
+so now with some statistics Eve can
+correlate some of these streams if we
+
+ align:start position:0%
+correlate some of these streams if we
+ 
+
+ align:start position:0%
+correlate some of these streams if we
+don't obscure volume and timing
+
+ align:start position:0%
+don't obscure volume and timing
+ 
+
+ align:start position:0%
+don't obscure volume and timing
+information there are designs that do
+
+ align:start position:0%
+information there are designs that do
+ 
+
+ align:start position:0%
+information there are designs that do
+obscure volume and timey information the
+
+ align:start position:0%
+obscure volume and timey information the
+ 
+
+ align:start position:0%
+obscure volume and timey information the
+good ones
+
+ align:start position:0%
+good ones
+ 
+
+ align:start position:0%
+good ones
+are usually come out of chow and mix
+
+ align:start position:0%
+are usually come out of chow and mix
+ 
+
+ align:start position:0%
+are usually come out of chow and mix
+Nets although there's some work on DC
+
+ align:start position:0%
+Nets although there's some work on DC
+ 
+
+ align:start position:0%
+Nets although there's some work on DC
+Nets you could have something where each
+
+ align:start position:0%
+Nets you could have something where each
+ 
+
+ align:start position:0%
+Nets you could have something where each
+of these nodes received large number of
+
+ align:start position:0%
+of these nodes received large number of
+ 
+
+ align:start position:0%
+of these nodes received large number of
+requests just bashed up all the requests
+
+ align:start position:0%
+requests just bashed up all the requests
+ 
+
+ align:start position:0%
+requests just bashed up all the requests
+it got for an hour reordered them and
+
+ align:start position:0%
+it got for an hour reordered them and
+ 
+
+ align:start position:0%
+it got for an hour reordered them and
+transmitted them all at once and you
+
+ align:start position:0%
+transmitted them all at once and you
+ 
+
+ align:start position:0%
+transmitted them all at once and you
+could also say all requests must be the
+
+ align:start position:0%
+could also say all requests must be the
+ 
+
+ align:start position:0%
+could also say all requests must be the
+same size requests are 1K responses are
+
+ align:start position:0%
+same size requests are 1K responses are
+ 
+
+ align:start position:0%
+same size requests are 1K responses are
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+Megabyte and with with some more work
+
+ align:start position:0%
+Megabyte and with with some more work
+ 
+
+ align:start position:0%
+Megabyte and with with some more work
+like that you would get something that
+
+ align:start position:0%
+like that you would get something that
+ 
+
+ align:start position:0%
+like that you would get something that
+would let you send an email on the order
+
+ align:start position:0%
+would let you send an email on the order
+ 
+
+ align:start position:0%
+would let you send an email on the order
+of our that would arrive in order of
+
+ align:start position:0%
+of our that would arrive in order of
+ 
+
+ align:start position:0%
+of our that would arrive in order of
+hours or get a web page in order of 2 N
+
+ align:start position:0%
+hours or get a web page in order of 2 N
+ 
+
+ align:start position:0%
+hours or get a web page in order of 2 N
+time assuming that you optimize it to a
+
+ align:start position:0%
+time assuming that you optimize it to a
+ 
+
+ align:start position:0%
+time assuming that you optimize it to a
+single round
+
+ align:start position:0%
+single round
+ 
+
+ align:start position:0%
+single round
+trip these systems exist but and existed
+
+ align:start position:0%
+trip these systems exist but and existed
+ 
+
+ align:start position:0%
+trip these systems exist but and existed
+when we started doing tour they don't
+
+ align:start position:0%
+when we started doing tour they don't
+ 
+
+ align:start position:0%
+when we started doing tour they don't
+get a lot of use though um I actually
+
+ align:start position:0%
+get a lot of use though um I actually
+ 
+
+ align:start position:0%
+get a lot of use though um I actually
+wrote one called mix minion that was a
+
+ align:start position:0%
+wrote one called mix minion that was a
+ 
+
+ align:start position:0%
+wrote one called mix minion that was a
+successor to the Mixmaster
+
+ align:start position:0%
+successor to the Mixmaster
+ 
+
+ align:start position:0%
+successor to the Mixmaster
+remailer I have not gotten a remailer
+
+ align:start position:0%
+remailer I have not gotten a remailer
+ 
+
+ align:start position:0%
+remailer I have not gotten a remailer
+message in the last three
+
+ align:start position:0%
+message in the last three
+ 
+
+ align:start position:0%
+message in the last three
+years uh Tor has millions of users
+
+ align:start position:0%
+years uh Tor has millions of users
+ 
+
+ align:start position:0%
+years uh Tor has millions of users
+remailers it's unclear whether they've
+
+ align:start position:0%
+remailers it's unclear whether they've
+ 
+
+ align:start position:0%
+remailers it's unclear whether they've
+got on the more than on the order of
+
+ align:start position:0%
+got on the more than on the order of
+ 
+
+ align:start position:0%
+got on the more than on the order of
+hundreds so you might think well still
+
+ align:start position:0%
+hundreds so you might think well still
+ 
+
+ align:start position:0%
+hundreds so you might think well still
+though it's better anonymity for the
+
+ align:start position:0%
+though it's better anonymity for the
+ 
+
+ align:start position:0%
+though it's better anonymity for the
+people really need it except if you've
+
+ align:start position:0%
+people really need it except if you've
+ 
+
+ align:start position:0%
+people really need it except if you've
+only got on the order of hundreds of
+
+ align:start position:0%
+only got on the order of hundreds of
+ 
+
+ align:start position:0%
+only got on the order of hundreds of
+users then you're not really providing
+
+ align:start position:0%
+users then you're not really providing
+ 
+
+ align:start position:0%
+users then you're not really providing
+them all that much anonymity against
+
+ align:start position:0%
+them all that much anonymity against
+ 
+
+ align:start position:0%
+them all that much anonymity against
+this kind of adversary anyway because
+
+ align:start position:0%
+this kind of adversary anyway because
+ 
+
+ align:start position:0%
+this kind of adversary anyway because
+this such an adversary can simply go
+
+ align:start position:0%
+this such an adversary can simply go
+ 
+
+ align:start position:0%
+this such an adversary can simply go
+okay there's 100 people well the message
+
+ align:start position:0%
+okay there's 100 people well the message
+ 
+
+ align:start position:0%
+okay there's 100 people well the message
+I want to investigate was looking at a
+
+ align:start position:0%
+I want to investigate was looking at a
+ 
+
+ align:start position:0%
+I want to investigate was looking at a
+Bulgarian website how many of them speak
+
+ align:start position:0%
+Bulgarian website how many of them speak
+ 
+
+ align:start position:0%
+Bulgarian website how many of them speak
+Bulgarian okay that's
+
+ align:start position:0%
+Bulgarian okay that's
+ 
+
+ align:start position:0%
+Bulgarian okay that's
+five uh um the saying is anonymity loves
+
+ align:start position:0%
+five uh um the saying is anonymity loves
+ 
+
+ align:start position:0%
+five uh um the saying is anonymity loves
+company unless you have a large user
+
+ align:start position:0%
+company unless you have a large user
+ 
+
+ align:start position:0%
+company unless you have a large user
+base no system can actually provide
+
+ align:start position:0%
+base no system can actually provide
+ 
+
+ align:start position:0%
+base no system can actually provide
+anonymity and that's why also in this
+
+ align:start position:0%
+anonymity and that's why also in this
+ 
+
+ align:start position:0%
+anonymity and that's why also in this
+design if if these alyses all belong to
+
+ align:start position:0%
+design if if these alyses all belong to
+ 
+
+ align:start position:0%
+design if if these alyses all belong to
+an organization they ought to have a
+
+ align:start position:0%
+an organization they ought to have a
+ 
+
+ align:start position:0%
+an organization they ought to have a
+shared public system rather than a
+
+ align:start position:0%
+shared public system rather than a
+ 
+
+ align:start position:0%
+shared public system rather than a
+private one like if you are if if they
+
+ align:start position:0%
+private one like if you are if if they
+ 
+
+ align:start position:0%
+private one like if you are if if they
+all work
+
+ align:start position:0%
+all work
+ 
+
+ align:start position:0%
+all work
+for MIT legal and they're investigating
+
+ align:start position:0%
+for MIT legal and they're investigating
+ 
+
+ align:start position:0%
+for MIT legal and they're investigating
+some fake MIT website that's um offering
+
+ align:start position:0%
+some fake MIT website that's um offering
+ 
+
+ align:start position:0%
+some fake MIT website that's um offering
+fake
+
+ align:start position:0%
+fake
+ 
+
+ align:start position:0%
+fake
+diplomas then if if they're just using
+
+ align:start position:0%
+diplomas then if if they're just using
+ 
+
+ align:start position:0%
+diplomas then if if they're just using
+the MIT legal anonymizer then it's not
+
+ align:start position:0%
+the MIT legal anonymizer then it's not
+ 
+
+ align:start position:0%
+the MIT legal anonymizer then it's not
+really at all is not really concealing
+
+ align:start position:0%
+really at all is not really concealing
+ 
+
+ align:start position:0%
+really at all is not really concealing
+who they are but if you have a large
+
+ align:start position:0%
+who they are but if you have a large
+ 
+
+ align:start position:0%
+who they are but if you have a large
+number of different parties all using
+
+ align:start position:0%
+number of different parties all using
+ 
+
+ align:start position:0%
+number of different parties all using
+this then it actually can provide some
+
+ align:start position:0%
+this then it actually can provide some
+ 
+
+ align:start position:0%
+this then it actually can provide some
+privacy so we'll return one more time
+
+ align:start position:0%
+privacy so we'll return one more time
+ 
+
+ align:start position:0%
+privacy so we'll return one more time
+to how to resisting this kind of
+
+ align:start position:0%
+to how to resisting this kind of
+ 
+
+ align:start position:0%
+to how to resisting this kind of
+correlation attacks but for now let's
+
+ align:start position:0%
+correlation attacks but for now let's
+ 
+
+ align:start position:0%
+correlation attacks but for now let's
+say that we're not re resisting those
+
+ align:start position:0%
+say that we're not re resisting those
+ 
+
+ align:start position:0%
+say that we're not re resisting those
+correlation attacks and instead we're
+
+ align:start position:0%
+correlation attacks and instead we're
+ 
+
+ align:start position:0%
+correlation attacks and instead we're
+going to try to lower we assume that an
+
+ align:start position:0%
+going to try to lower we assume that an
+ 
+
+ align:start position:0%
+going to try to lower we assume that an
+attacker who sees both ends wins and
+
+ align:start position:0%
+attacker who sees both ends wins and
+ 
+
+ align:start position:0%
+attacker who sees both ends wins and
+we're trying to minimize the probability
+
+ align:start position:0%
+we're trying to minimize the probability
+ 
+
+ align:start position:0%
+we're trying to minimize the probability
+that that happens over
+
+ align:start position:0%
+that that happens over
+ 
+
+ align:start position:0%
+that that happens over
+time all right so I've just talked about
+
+ align:start position:0%
+time all right so I've just talked about
+ 
+
+ align:start position:0%
+time all right so I've just talked about
+message passing
+
+ align:start position:0%
+message passing
+ 
+
+ align:start position:0%
+message passing
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+um well the way you would build that in
+
+ align:start position:0%
+um well the way you would build that in
+ 
+
+ align:start position:0%
+um well the way you would build that in
+something like a mix net is you give
+
+ align:start position:0%
+something like a mix net is you give
+ 
+
+ align:start position:0%
+something like a mix net is you give
+each of these relays a public key um K3
+
+ align:start position:0%
+each of these relays a public key um K3
+ 
+
+ align:start position:0%
+each of these relays a public key um K3
+K2 K1 and when Ellis wants to send
+
+ align:start position:0%
+K2 K1 and when Ellis wants to send
+ 
+
+ align:start position:0%
+K2 K1 and when Ellis wants to send
+something through here she would say
+
+ align:start position:0%
+something through here she would say
+ 
+
+ align:start position:0%
+something through here she would say
+encrypt with
+
+ align:start position:0%
+encrypt with
+ 
+
+ align:start position:0%
+encrypt with
+K3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+socks and then encrypt that with K2
+
+ align:start position:0%
+socks and then encrypt that with K2
+ 
+
+ align:start position:0%
+socks and then encrypt that with K2
+I'm leaving off routing information for
+
+ align:start position:0%
+I'm leaving off routing information for
+ 
+
+ align:start position:0%
+I'm leaving off routing information for
+now and then encrypt with
+
+ align:start position:0%
+now and then encrypt with
+ 
+
+ align:start position:0%
+now and then encrypt with
+K1 but public key as you know is kind of
+
+ align:start position:0%
+K1 but public key as you know is kind of
+ 
+
+ align:start position:0%
+K1 but public key as you know is kind of
+expensive enough that you don't want to
+
+ align:start position:0%
+expensive enough that you don't want to
+ 
+
+ align:start position:0%
+expensive enough that you don't want to
+use it for bulk
+
+ align:start position:0%
+use it for bulk
+ 
+
+ align:start position:0%
+use it for bulk
+traffic so instead what you do and at
+
+ align:start position:0%
+traffic so instead what you do and at
+ 
+
+ align:start position:0%
+traffic so instead what you do and at
+this and if is right instead what you do
+
+ align:start position:0%
+this and if is right instead what you do
+ 
+
+ align:start position:0%
+this and if is right instead what you do
+is you negotiate a set of keys with each
+
+ align:start position:0%
+is you negotiate a set of keys with each
+ 
+
+ align:start position:0%
+is you negotiate a set of keys with each
+server so Alice shares a symmetric key
+
+ align:start position:0%
+server so Alice shares a symmetric key
+ 
+
+ align:start position:0%
+server so Alice shares a symmetric key
+with this relay a different symmetric
+
+ align:start position:0%
+with this relay a different symmetric
+ 
+
+ align:start position:0%
+with this relay a different symmetric
+key with this relay and a different
+
+ align:start position:0%
+key with this relay and a different
+ 
+
+ align:start position:0%
+key with this relay and a different
+symmetric key with this relay associate
+
+ align:start position:0%
+symmetric key with this relay associate
+ 
+
+ align:start position:0%
+symmetric key with this relay associate
+in what we call a circuit which is a
+
+ align:start position:0%
+in what we call a circuit which is a
+ 
+
+ align:start position:0%
+in what we call a circuit which is a
+path through the
+
+ align:start position:0%
+path through the
+ 
+
+ align:start position:0%
+path through the
+network
+
+ align:start position:0%
+network
+ 
+
+ align:start position:0%
+network
+and then and after the initial publicy
+
+ align:start position:0%
+and then and after the initial publicy
+ 
+
+ align:start position:0%
+and then and after the initial publicy
+set up to create those keys Alice can
+
+ align:start position:0%
+set up to create those keys Alice can
+ 
+
+ align:start position:0%
+set up to create those keys Alice can
+then use some Metro crypto to send stuff
+
+ align:start position:0%
+then use some Metro crypto to send stuff
+ 
+
+ align:start position:0%
+then use some Metro crypto to send stuff
+through the network if you stop at that
+
+ align:start position:0%
+through the network if you stop at that
+ 
+
+ align:start position:0%
+through the network if you stop at that
+point then you have onion routing as it
+
+ align:start position:0%
+point then you have onion routing as it
+ 
+
+ align:start position:0%
+point then you have onion routing as it
+was designed in the
+
+ align:start position:0%
+was designed in the
+ 
+
+ align:start position:0%
+was designed in the
+1990s by um cyers gold schlog and Reed I
+
+ align:start position:0%
+1990s by um cyers gold schlog and Reed I
+ 
+
+ align:start position:0%
+1990s by um cyers gold schlog and Reed I
+hope I'm getting the the names right um
+
+ align:start position:0%
+hope I'm getting the the names right um
+ 
+
+ align:start position:0%
+hope I'm getting the the names right um
+Paul cyers is still active the other two
+
+ align:start position:0%
+Paul cyers is still active the other two
+ 
+
+ align:start position:0%
+Paul cyers is still active the other two
+are working on other things
+
+ align:start position:0%
+are working on other things
+ 
+
+ align:start position:0%
+are working on other things
+um also once you've added circuits like
+
+ align:start position:0%
+um also once you've added circuits like
+ 
+
+ align:start position:0%
+um also once you've added circuits like
+that paths medium-term paths through the
+
+ align:start position:0%
+that paths medium-term paths through the
+ 
+
+ align:start position:0%
+that paths medium-term paths through the
+network you can have a easy reply
+
+ align:start position:0%
+network you can have a easy reply
+ 
+
+ align:start position:0%
+network you can have a easy reply
+Channel where things sent back this way
+
+ align:start position:0%
+Channel where things sent back this way
+ 
+
+ align:start position:0%
+Channel where things sent back this way
+get to Alice being encrypted at each
+
+ align:start position:0%
+get to Alice being encrypted at each
+ 
+
+ align:start position:0%
+get to Alice being encrypted at each
+step instead of decrypted at each
+
+ align:start position:0%
+step instead of decrypted at each
+ 
+
+ align:start position:0%
+step instead of decrypted at each
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+and of course you need some kind of
+
+ align:start position:0%
+and of course you need some kind of
+ 
+
+ align:start position:0%
+and of course you need some kind of
+Integrity checking either node by node
+
+ align:start position:0%
+Integrity checking either node by node
+ 
+
+ align:start position:0%
+Integrity checking either node by node
+or end to end because if you don't do
+
+ align:start position:0%
+or end to end because if you don't do
+ 
+
+ align:start position:0%
+or end to end because if you don't do
+Integrity checking then um well let's
+
+ align:start position:0%
+Integrity checking then um well let's
+ 
+
+ align:start position:0%
+Integrity checking then um well let's
+say uh let's say you're using a exor
+
+ align:start position:0%
+say uh let's say you're using a exor
+ 
+
+ align:start position:0%
+say uh let's say you're using a exor
+based stream Cipher for your encryption
+
+ align:start position:0%
+based stream Cipher for your encryption
+ 
+
+ align:start position:0%
+based stream Cipher for your encryption
+if you don't do Integrity checking then
+
+ align:start position:0%
+if you don't do Integrity checking then
+ 
+
+ align:start position:0%
+if you don't do Integrity checking then
+this node can exor in Alis Ellis Alis
+
+ align:start position:0%
+this node can exor in Alis Ellis Alis
+ 
+
+ align:start position:0%
+this node can exor in Alis Ellis Alis
+Alis Alis to the encrypted message and
+
+ align:start position:0%
+Alis Alis to the encrypted message and
+ 
+
+ align:start position:0%
+Alis Alis to the encrypted message and
+then when it is finally decrypted over
+
+ align:start position:0%
+then when it is finally decrypted over
+ 
+
+ align:start position:0%
+then when it is finally decrypted over
+here because that's a malleable crypto
+
+ align:start position:0%
+here because that's a malleable crypto
+ 
+
+ align:start position:0%
+here because that's a malleable crypto
+scheme
+
+ align:start position:0%
+scheme
+ 
+
+ align:start position:0%
+scheme
+if um if the
+
+ align:start position:0%
+if um if the
+ 
+
+ align:start position:0%
+if um if the
+same if the same node happens to if the
+
+ align:start position:0%
+same if the same node happens to if the
+ 
+
+ align:start position:0%
+same if the same node happens to if the
+same attacker is controlling this node
+
+ align:start position:0%
+same attacker is controlling this node
+ 
+
+ align:start position:0%
+same attacker is controlling this node
+as well or if the attacker is observing
+
+ align:start position:0%
+as well or if the attacker is observing
+ 
+
+ align:start position:0%
+as well or if the attacker is observing
+it here
+
+ align:start position:0%
+it here
+ 
+
+ align:start position:0%
+it here
+the attacker will see Alice Alis Alis
+
+ align:start position:0%
+the attacker will see Alice Alis Alis
+ 
+
+ align:start position:0%
+the attacker will see Alice Alis Alis
+Alis Alis exord with a reasonable plain
+
+ align:start position:0%
+Alis Alis exord with a reasonable plain
+ 
+
+ align:start position:0%
+Alis Alis exord with a reasonable plain
+text and be able to use that to identify
+
+ align:start position:0%
+text and be able to use that to identify
+ 
+
+ align:start position:0%
+text and be able to use that to identify
+ah this is the stream that came from
+
+ align:start position:0%
+ah this is the stream that came from
+ 
+
+ align:start position:0%
+ah this is the stream that came from
+Alice so let's do a little more on how
+
+ align:start position:0%
+Alice so let's do a little more on how
+ 
+
+ align:start position:0%
+Alice so let's do a little more on how
+the protocol works because it would be a
+
+ align:start position:0%
+the protocol works because it would be a
+ 
+
+ align:start position:0%
+the protocol works because it would be a
+shame to have everybody read the paper
+
+ align:start position:0%
+shame to have everybody read the paper
+ 
+
+ align:start position:0%
+shame to have everybody read the paper
+and then not talk about the stuff that
+
+ align:start position:0%
+and then not talk about the stuff that
+ 
+
+ align:start position:0%
+and then not talk about the stuff that
+the paper is focused
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on again I apologize for my Blackboard
+
+ align:start position:0%
+on again I apologize for my Blackboard
+ 
+
+ align:start position:0%
+on again I apologize for my Blackboard
+technique this is most of the time I'm
+
+ align:start position:0%
+technique this is most of the time I'm
+ 
+
+ align:start position:0%
+technique this is most of the time I'm
+sitting at home on the uh desktop I
+
+ align:start position:0%
+sitting at home on the uh desktop I
+ 
+
+ align:start position:0%
+sitting at home on the uh desktop I
+don't this is alien
+
+ align:start position:0%
+don't this is alien
+ 
+
+ align:start position:0%
+don't this is alien
+Tech
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's a relay here's
+
+ align:start position:0%
+so here's a relay here's
+ 
+
+ align:start position:0%
+so here's a relay here's
+Alice here's another
+
+ align:start position:0%
+Alice here's another
+ 
+
+ align:start position:0%
+Alice here's another
+relay here's Bob now one else wants to
+
+ align:start position:0%
+relay here's Bob now one else wants to
+ 
+
+ align:start position:0%
+relay here's Bob now one else wants to
+talk to
+
+ align:start position:0%
+talk to
+ 
+
+ align:start position:0%
+talk to
+Bob
+
+ align:start position:0%
+Bob
+ 
+
+ align:start position:0%
+Bob
+so first thing Alice has to do is build
+
+ align:start position:0%
+so first thing Alice has to do is build
+ 
+
+ align:start position:0%
+so first thing Alice has to do is build
+a circuit through these relays to Bob
+
+ align:start position:0%
+a circuit through these relays to Bob
+ 
+
+ align:start position:0%
+a circuit through these relays to Bob
+let's say she's picked these two R1 and
+
+ align:start position:0%
+let's say she's picked these two R1 and
+ 
+
+ align:start position:0%
+let's say she's picked these two R1 and
+R2
+
+ align:start position:0%
+R2
+ 
+
+ align:start position:0%
+R2
+so Alis does first makes a TLS
+
+ align:start position:0%
+so Alis does first makes a TLS
+ 
+
+ align:start position:0%
+so Alis does first makes a TLS
+link to
+
+ align:start position:0%
+link to
+ 
+
+ align:start position:0%
+link to
+R1 R1 let's say already has a TLS link
+
+ align:start position:0%
+R1 R1 let's say already has a TLS link
+ 
+
+ align:start position:0%
+R1 R1 let's say already has a TLS link
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R2 first thing Ellis does is she does an
+
+ align:start position:0%
+R2 first thing Ellis does is she does an
+ 
+
+ align:start position:0%
+R2 first thing Ellis does is she does an
+authenticated
+
+ align:start position:0%
+authenticated
+ 
+
+ align:start position:0%
+authenticated
+um a one-way authenticated one-way
+
+ align:start position:0%
+um a one-way authenticated one-way
+ 
+
+ align:start position:0%
+um a one-way authenticated one-way
+Anonymous key
+
+ align:start position:0%
+Anonymous key
+ 
+
+ align:start position:0%
+Anonymous key
+negotiation uh the old one in tour is
+
+ align:start position:0%
+negotiation uh the old one in tour is
+ 
+
+ align:start position:0%
+negotiation uh the old one in tour is
+called tap the new one is called entor
+
+ align:start position:0%
+called tap the new one is called entor
+ 
+
+ align:start position:0%
+called tap the new one is called entor
+they both have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proofs they both even have correct
+
+ align:start position:0%
+proofs they both even have correct
+ 
+
+ align:start position:0%
+proofs they both even have correct
+proofs although the original proof in
+
+ align:start position:0%
+proofs although the original proof in
+ 
+
+ align:start position:0%
+proofs although the original proof in
+the paper was had a flaw in
+
+ align:start position:0%
+the paper was had a flaw in
+ 
+
+ align:start position:0%
+the paper was had a flaw in
+it but when that's done you know she
+
+ align:start position:0%
+it but when that's done you know she
+ 
+
+ align:start position:0%
+it but when that's done you know she
+basically sends a create she sends a
+
+ align:start position:0%
+basically sends a create she sends a
+ 
+
+ align:start position:0%
+basically sends a create she sends a
+create cell and she picks a circuit ID
+
+ align:start position:0%
+create cell and she picks a circuit ID
+ 
+
+ align:start position:0%
+create cell and she picks a circuit ID
+let's say she picks
+
+ align:start position:0%
+let's say she picks
+ 
+
+ align:start position:0%
+let's say she picks
+three and says create
+
+ align:start position:0%
+three and says create
+ 
+
+ align:start position:0%
+three and says create
+three the relay says created
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now R1 and Ellis share a secret key
+
+ align:start position:0%
+and now R1 and Ellis share a secret key
+ 
+
+ align:start position:0%
+and now R1 and Ellis share a secret key
+which I'm going which a symmetric key
+
+ align:start position:0%
+which I'm going which a symmetric key
+ 
+
+ align:start position:0%
+which I'm going which a symmetric key
+which I'm going to call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S1 and they both have this stored as as
+
+ align:start position:0%
+S1 and they both have this stored as as
+ 
+
+ align:start position:0%
+S1 and they both have this stored as as
+three with respect to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+link now Ellis can use that key to send
+
+ align:start position:0%
+link now Ellis can use that key to send
+ 
+
+ align:start position:0%
+link now Ellis can use that key to send
+messages to R1 so she says on three
+
+ align:start position:0%
+messages to R1 so she says on three
+ 
+
+ align:start position:0%
+messages to R1 so she says on three
+that's the circuit ID that everything
+
+ align:start position:0%
+that's the circuit ID that everything
+ 
+
+ align:start position:0%
+that's the circuit ID that everything
+was talking about in the paper send a
+
+ align:start position:0%
+was talking about in the paper send a
+ 
+
+ align:start position:0%
+was talking about in the paper send a
+send a relay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extend with some contents um the extend
+
+ align:start position:0%
+extend with some contents um the extend
+ 
+
+ align:start position:0%
+extend with some contents um the extend
+cell basically contains the first half
+
+ align:start position:0%
+cell basically contains the first half
+ 
+
+ align:start position:0%
+cell basically contains the first half
+of the create
+
+ align:start position:0%
+of the create
+ 
+
+ align:start position:0%
+of the create
+handshake but this time it's not
+
+ align:start position:0%
+handshake but this time it's not
+ 
+
+ align:start position:0%
+handshake but this time it's not
+encrypted with r1's public key it's
+
+ align:start position:0%
+encrypted with r1's public key it's
+ 
+
+ align:start position:0%
+encrypted with r1's public key it's
+encrypted with r2's public key and it
+
+ align:start position:0%
+encrypted with r2's public key and it
+ 
+
+ align:start position:0%
+encrypted with r2's public key and it
+also says and this one goes to R2 so R1
+
+ align:start position:0%
+also says and this one goes to R2 so R1
+ 
+
+ align:start position:0%
+also says and this one goes to R2 so R1
+knows to open
+
+ align:start position:0%
+knows to open
+ 
+
+ align:start position:0%
+knows to open
+a new circuit to R2 it says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+create and it passes the initial part of
+
+ align:start position:0%
+create and it passes the initial part of
+ 
+
+ align:start position:0%
+create and it passes the initial part of
+the handshake as it came from Alice
+
+ align:start position:0%
+the handshake as it came from Alice
+ 
+
+ align:start position:0%
+the handshake as it came from Alice
+along and it picks the own its own
+
+ align:start position:0%
+along and it picks the own its own
+ 
+
+ align:start position:0%
+along and it picks the own its own
+circuit ID because Al the circuit IDs
+
+ align:start position:0%
+circuit ID because Al the circuit IDs
+ 
+
+ align:start position:0%
+circuit ID because Al the circuit IDs
+identify the different circuits on this
+
+ align:start position:0%
+identify the different circuits on this
+ 
+
+ align:start position:0%
+identify the different circuits on this
+TLS connection and Alice doesn't know
+
+ align:start position:0%
+TLS connection and Alice doesn't know
+ 
+
+ align:start position:0%
+TLS connection and Alice doesn't know
+what other circuit IDs are in use on
+
+ align:start position:0%
+what other circuit IDs are in use on
+ 
+
+ align:start position:0%
+what other circuit IDs are in use on
+this one because this one is private to
+
+ align:start position:0%
+this one because this one is private to
+ 
+
+ align:start position:0%
+this one because this one is private to
+R1 and R2 so it might pick like 95
+
+ align:start position:0%
+R1 and R2 so it might pick like 95
+ 
+
+ align:start position:0%
+R1 and R2 so it might pick like 95
+it actually is very unlikely to pick
+
+ align:start position:0%
+it actually is very unlikely to pick
+ 
+
+ align:start position:0%
+it actually is very unlikely to pick
+that because they're randomly chosen
+
+ align:start position:0%
+that because they're randomly chosen
+ 
+
+ align:start position:0%
+that because they're randomly chosen
+from a 4 byte key from a 4 byte space
+
+ align:start position:0%
+from a 4 byte key from a 4 byte space
+ 
+
+ align:start position:0%
+from a 4 byte key from a 4 byte space
+but I don't want to write out any 32-bit
+
+ align:start position:0%
+but I don't want to write out any 32-bit
+ 
+
+ align:start position:0%
+but I don't want to write out any 32-bit
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+today and this says created in response
+
+ align:start position:0%
+today and this says created in response
+ 
+
+ align:start position:0%
+today and this says created in response
+so this one sends back extended
+
+ align:start position:0%
+so this one sends back extended
+ 
+
+ align:start position:0%
+so this one sends back extended
+encrypted with S1 and now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alice and relay 2 Share S2
+
+ align:start position:0%
+Alice and relay 2 Share S2
+ 
+
+ align:start position:0%
+Alice and relay 2 Share S2
+so now Al sends a me can send messages
+
+ align:start position:0%
+so now Al sends a me can send messages
+ 
+
+ align:start position:0%
+so now Al sends a me can send messages
+encrypted first with S2 and then with S1
+
+ align:start position:0%
+encrypted first with S2 and then with S1
+ 
+
+ align:start position:0%
+encrypted first with S2 and then with S1
+as relay cells so she sends a message
+
+ align:start position:0%
+as relay cells so she sends a message
+ 
+
+ align:start position:0%
+as relay cells so she sends a message
+like that R1 removes the
+
+ align:start position:0%
+like that R1 removes the
+ 
+
+ align:start position:0%
+like that R1 removes the
+S1 encryption and forwards it on it says
+
+ align:start position:0%
+S1 encryption and forwards it on it says
+ 
+
+ align:start position:0%
+S1 encryption and forwards it on it says
+okay it came in on three uh it came in
+
+ align:start position:0%
+okay it came in on three uh it came in
+ 
+
+ align:start position:0%
+okay it came in on three uh it came in
+on circuit three I know that three goes
+
+ align:start position:0%
+on circuit three I know that three goes
+ 
+
+ align:start position:0%
+on circuit three I know that three goes
+to 95 on this one so I sent it on 95 and
+
+ align:start position:0%
+to 95 on this one so I sent it on 95 and
+ 
+
+ align:start position:0%
+to 95 on this one so I sent it on 95 and
+I say whatever I got after decrypting
+
+ align:start position:0%
+I say whatever I got after decrypting
+ 
+
+ align:start position:0%
+I say whatever I got after decrypting
+okay and this one says Ah I came on 95
+
+ align:start position:0%
+okay and this one says Ah I came on 95
+ 
+
+ align:start position:0%
+okay and this one says Ah I came on 95
+95 corresponds to the shared key S2 so
+
+ align:start position:0%
+95 corresponds to the shared key S2 so
+ 
+
+ align:start position:0%
+95 corresponds to the shared key S2 so
+I'll decrypt with that oh that says open
+
+ align:start position:0%
+I'll decrypt with that oh that says open
+ 
+
+ align:start position:0%
+I'll decrypt with that oh that says open
+a connection to Bob and relay 2 opens a
+
+ align:start position:0%
+a connection to Bob and relay 2 opens a
+ 
+
+ align:start position:0%
+a connection to Bob and relay 2 opens a
+TCP connection to Bob and tells Ellis
+
+ align:start position:0%
+TCP connection to Bob and tells Ellis
+ 
+
+ align:start position:0%
+TCP connection to Bob and tells Ellis
+that it did it through the same process
+
+ align:start position:0%
+that it did it through the same process
+ 
+
+ align:start position:0%
+that it did it through the same process
+and ell says great tell Bob um H H tell
+
+ align:start position:0%
+and ell says great tell Bob um H H tell
+ 
+
+ align:start position:0%
+and ell says great tell Bob um H H tell
+Bob
+
+ align:start position:0%
+Bob
+ 
+
+ align:start position:0%
+Bob
+http1 get/
+
+ align:start position:0%
+http1 get/
+ 
+
+ align:start position:0%
+http1 get/
+index.html and the world goes on now
+
+ align:start position:0%
+index.html and the world goes on now
+ 
+
+ align:start position:0%
+index.html and the world goes on now
+let's see what did I leave out oh skip
+
+ align:start position:0%
+let's see what did I leave out oh skip
+ 
+
+ align:start position:0%
+let's see what did I leave out oh skip
+that skip that skip that um so what do
+
+ align:start position:0%
+that skip that skip that um so what do
+ 
+
+ align:start position:0%
+that skip that skip that um so what do
+we actually relay some designs in this
+
+ align:start position:0%
+we actually relay some designs in this
+ 
+
+ align:start position:0%
+we actually relay some designs in this
+area say well you should send IP packets
+
+ align:start position:0%
+area say well you should send IP packets
+ 
+
+ align:start position:0%
+area say well you should send IP packets
+back and forth this should just be a way
+
+ align:start position:0%
+back and forth this should just be a way
+ 
+
+ align:start position:0%
+back and forth this should just be a way
+to transmit IP packets one of the
+
+ align:start position:0%
+to transmit IP packets one of the
+ 
+
+ align:start position:0%
+to transmit IP packets one of the
+problems with that
+
+ align:start position:0%
+problems with that
+ 
+
+ align:start position:0%
+problems with that
+is we want to support as many users as
+
+ align:start position:0%
+is we want to support as many users as
+ 
+
+ align:start position:0%
+is we want to support as many users as
+possible which means that we have to run
+
+ align:start position:0%
+possible which means that we have to run
+ 
+
+ align:start position:0%
+possible which means that we have to run
+on all kinds of operating systems and
+
+ align:start position:0%
+on all kinds of operating systems and
+ 
+
+ align:start position:0%
+on all kinds of operating systems and
+operating systems TCP Stacks do not act
+
+ align:start position:0%
+operating systems TCP Stacks do not act
+ 
+
+ align:start position:0%
+operating systems TCP Stacks do not act
+anything like each other if you've ever
+
+ align:start position:0%
+anything like each other if you've ever
+ 
+
+ align:start position:0%
+anything like each other if you've ever
+used nmap or if you've ever used any
+
+ align:start position:0%
+used nmap or if you've ever used any
+ 
+
+ align:start position:0%
+used nmap or if you've ever used any
+kind of network traffic analysis tool
+
+ align:start position:0%
+kind of network traffic analysis tool
+ 
+
+ align:start position:0%
+kind of network traffic analysis tool
+you can trivially tell Windows T CP from
+
+ align:start position:0%
+you can trivially tell Windows T CP from
+ 
+
+ align:start position:0%
+you can trivially tell Windows T CP from
+FreeBSD from Linux TCP and you can even
+
+ align:start position:0%
+FreeBSD from Linux TCP and you can even
+ 
+
+ align:start position:0%
+FreeBSD from Linux TCP and you can even
+held different versions apart and
+
+ align:start position:0%
+held different versions apart and
+ 
+
+ align:start position:0%
+held different versions apart and
+moreover if you can send raw IP packets
+
+ align:start position:0%
+moreover if you can send raw IP packets
+ 
+
+ align:start position:0%
+moreover if you can send raw IP packets
+to to a chosen host you can provoke
+
+ align:start position:0%
+to to a chosen host you can provoke
+ 
+
+ align:start position:0%
+to to a chosen host you can provoke
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+responses you know in part be in part
+
+ align:start position:0%
+responses you know in part be in part
+ 
+
+ align:start position:0%
+responses you know in part be in part
+based on what the host is doing so if
+
+ align:start position:0%
+based on what the host is doing so if
+ 
+
+ align:start position:0%
+based on what the host is doing so if
+you're doing IP you would actually need
+
+ align:start position:0%
+you're doing IP you would actually need
+ 
+
+ align:start position:0%
+you're doing IP you would actually need
+an IP normalization layer if IP is what
+
+ align:start position:0%
+an IP normalization layer if IP is what
+ 
+
+ align:start position:0%
+an IP normalization layer if IP is what
+you transport back and forth
+
+ align:start position:0%
+you transport back and forth
+ 
+
+ align:start position:0%
+you transport back and forth
+and it seems that anything less than a
+
+ align:start position:0%
+and it seems that anything less than a
+ 
+
+ align:start position:0%
+and it seems that anything less than a
+full IP stack is not actually going to
+
+ align:start position:0%
+full IP stack is not actually going to
+ 
+
+ align:start position:0%
+full IP stack is not actually going to
+work for IP normalization so you
+
+ align:start position:0%
+work for IP normalization so you
+ 
+
+ align:start position:0%
+work for IP normalization so you
+wouldn't want to do
+
+ align:start position:0%
+wouldn't want to do
+ 
+
+ align:start position:0%
+wouldn't want to do
+that instead what we just chose is and
+
+ align:start position:0%
+that instead what we just chose is and
+ 
+
+ align:start position:0%
+that instead what we just chose is and
+this is largely because this is the
+
+ align:start position:0%
+this is largely because this is the
+ 
+
+ align:start position:0%
+this is largely because this is the
+easiest way you take the contents of TCP
+
+ align:start position:0%
+easiest way you take the contents of TCP
+ 
+
+ align:start position:0%
+easiest way you take the contents of TCP
+streams so you just say so you assume
+
+ align:start position:0%
+streams so you just say so you assume
+ 
+
+ align:start position:0%
+streams so you just say so you assume
+each of these things is reliable and in
+
+ align:start position:0%
+each of these things is reliable and in
+ 
+
+ align:start position:0%
+each of these things is reliable and in
+order you
+
+ align:start position:0%
+order you
+ 
+
+ align:start position:0%
+order you
+have the computer at Al's and the
+
+ align:start position:0%
+have the computer at Al's and the
+ 
+
+ align:start position:0%
+have the computer at Al's and the
+program alysis running to do all of this
+
+ align:start position:0%
+program alysis running to do all of this
+ 
+
+ align:start position:0%
+program alysis running to do all of this
+stuff or
+
+ align:start position:0%
+stuff or
+ 
+
+ align:start position:0%
+stuff or
+her except TCP connections from Alice's
+
+ align:start position:0%
+her except TCP connections from Alice's
+ 
+
+ align:start position:0%
+her except TCP connections from Alice's
+applications and then just relay their
+
+ align:start position:0%
+applications and then just relay their
+ 
+
+ align:start position:0%
+applications and then just relay their
+contents and don't do anything trickier
+
+ align:start position:0%
+contents and don't do anything trickier
+ 
+
+ align:start position:0%
+contents and don't do anything trickier
+on the network level you might be able
+
+ align:start position:0%
+on the network level you might be able
+ 
+
+ align:start position:0%
+on the network level you might be able
+to get better performance by trying some
+
+ align:start position:0%
+to get better performance by trying some
+ 
+
+ align:start position:0%
+to get better performance by trying some
+other means and there were some papers
+
+ align:start position:0%
+other means and there were some papers
+ 
+
+ align:start position:0%
+other means and there were some papers
+examining how you would do that but this
+
+ align:start position:0%
+examining how you would do that but this
+ 
+
+ align:start position:0%
+examining how you would do that but this
+is the one that we could actually
+
+ align:start position:0%
+is the one that we could actually
+ 
+
+ align:start position:0%
+is the one that we could actually
+Implement because we paid a lot more
+
+ align:start position:0%
+Implement because we paid a lot more
+ 
+
+ align:start position:0%
+Implement because we paid a lot more
+attention in security and compilers
+
+ align:start position:0%
+attention in security and compilers
+ 
+
+ align:start position:0%
+attention in security and compilers
+classes than we did in networking
+
+ align:start position:0%
+classes than we did in networking
+ 
+
+ align:start position:0%
+classes than we did in networking
+classes
+
+ align:start position:0%
+classes
+ 
+
+ align:start position:0%
+classes
+um now we have networking people but in
+
+ align:start position:0%
+um now we have networking people but in
+ 
+
+ align:start position:0%
+um now we have networking people but in
+in 2003 2004 we did not have any
+
+ align:start position:0%
+in 2003 2004 we did not have any
+ 
+
+ align:start position:0%
+in 2003 2004 we did not have any
+networking
+
+ align:start position:0%
+networking
+ 
+
+ align:start position:0%
+networking
+experts um TCP also seems like the right
+
+ align:start position:0%
+experts um TCP also seems like the right
+ 
+
+ align:start position:0%
+experts um TCP also seems like the right
+level higher level protocols like you
+
+ align:start position:0%
+level higher level protocols like you
+ 
+
+ align:start position:0%
+level higher level protocols like you
+might in some of the original un writing
+
+ align:start position:0%
+might in some of the original un writing
+ 
+
+ align:start position:0%
+might in some of the original un writing
+designs there were separate proxies at
+
+ align:start position:0%
+designs there were separate proxies at
+ 
+
+ align:start position:0%
+designs there were separate proxies at
+this end for HTTP for FTP and so on that
+
+ align:start position:0%
+this end for HTTP for FTP and so on that
+ 
+
+ align:start position:0%
+this end for HTTP for FTP and so on that
+seems to be mostly a bad idea because
+
+ align:start position:0%
+seems to be mostly a bad idea because
+ 
+
+ align:start position:0%
+seems to be mostly a bad idea because
+any interesting protocol is going to
+
+ align:start position:0%
+any interesting protocol is going to
+ 
+
+ align:start position:0%
+any interesting protocol is going to
+have end to-end encryption from Alis all
+
+ align:start position:0%
+have end to-end encryption from Alis all
+ 
+
+ align:start position:0%
+have end to-end encryption from Alis all
+the way to Bob that is if we're lucky
+
+ align:start position:0%
+the way to Bob that is if we're lucky
+ 
+
+ align:start position:0%
+the way to Bob that is if we're lucky
+Alice is doing a TLS connection over
+
+ align:start position:0%
+Alice is doing a TLS connection over
+ 
+
+ align:start position:0%
+Alice is doing a TLS connection over
+this to
+
+ align:start position:0%
+this to
+ 
+
+ align:start position:0%
+this to
+Bob so so that um TLS properties get her
+
+ align:start position:0%
+Bob so so that um TLS properties get her
+ 
+
+ align:start position:0%
+Bob so so that um TLS properties get her
+integrity and um
+
+ align:start position:0%
+integrity and um
+ 
+
+ align:start position:0%
+integrity and um
+secrecy but if that's the case then any
+
+ align:start position:0%
+secrecy but if that's the case then any
+ 
+
+ align:start position:0%
+secrecy but if that's the case then any
+kind of anonymizing Transformations you
+
+ align:start position:0%
+kind of anonymizing Transformations you
+ 
+
+ align:start position:0%
+kind of anonymizing Transformations you
+want to apply to the encrypted data need
+
+ align:start position:0%
+want to apply to the encrypted data need
+ 
+
+ align:start position:0%
+want to apply to the encrypted data need
+to happen in the application Alice is
+
+ align:start position:0%
+to happen in the application Alice is
+ 
+
+ align:start position:0%
+to happen in the application Alice is
+using before the TLs happens
+
+ align:start position:0%
+using before the TLs happens
+ 
+
+ align:start position:0%
+using before the TLs happens
+entirely so you can't really do that in
+
+ align:start position:0%
+entirely so you can't really do that in
+ 
+
+ align:start position:0%
+entirely so you can't really do that in
+a proxy and that's kind of why we came
+
+ align:start position:0%
+a proxy and that's kind of why we came
+ 
+
+ align:start position:0%
+a proxy and that's kind of why we came
+out to okay The Sweet Spot is TCP
+
+ align:start position:0%
+out to okay The Sweet Spot is TCP
+ 
+
+ align:start position:0%
+out to okay The Sweet Spot is TCP
+contents somebody asked me okay but
+
+ align:start position:0%
+contents somebody asked me okay but
+ 
+
+ align:start position:0%
+contents somebody asked me okay but
+where are your security proofs um we do
+
+ align:start position:0%
+where are your security proofs um we do
+ 
+
+ align:start position:0%
+where are your security proofs um we do
+have security proofs for a lot of the
+
+ align:start position:0%
+have security proofs for a lot of the
+ 
+
+ align:start position:0%
+have security proofs for a lot of the
+cryptography that we
+
+ align:start position:0%
+cryptography that we
+ 
+
+ align:start position:0%
+cryptography that we
+use um you know stand standard
+
+ align:start position:0%
+use um you know stand standard
+ 
+
+ align:start position:0%
+use um you know stand standard
+reductions for the protocol as a
+
+ align:start position:0%
+reductions for the protocol as a
+ 
+
+ align:start position:0%
+reductions for the protocol as a
+whole there are proofs in the field
+
+ align:start position:0%
+whole there are proofs in the field
+ 
+
+ align:start position:0%
+whole there are proofs in the field
+about certain aspects of onion routing
+
+ align:start position:0%
+about certain aspects of onion routing
+ 
+
+ align:start position:0%
+about certain aspects of onion routing
+but the models that they have to use in
+
+ align:start position:0%
+but the models that they have to use in
+ 
+
+ align:start position:0%
+but the models that they have to use in
+order to prove this
+
+ align:start position:0%
+order to prove this
+ 
+
+ align:start position:0%
+order to prove this
+provides
+
+ align:start position:0%
+provides
+ 
+
+ align:start position:0%
+provides
+anonymity make assumptions
+
+ align:start position:0%
+anonymity make assumptions
+ 
+
+ align:start position:0%
+anonymity make assumptions
+about the universe the network and the
+
+ align:start position:0%
+about the universe the network and the
+ 
+
+ align:start position:0%
+about the universe the network and the
+attacker's abilities that
+
+ align:start position:0%
+attacker's abilities that
+ 
+
+ align:start position:0%
+attacker's abilities that
+are so weird as to satisfy no one but
+
+ align:start position:0%
+are so weird as to satisfy no one but
+ 
+
+ align:start position:0%
+are so weird as to satisfy no one but
+certain program Committees of more
+
+ align:start position:0%
+certain program Committees of more
+ 
+
+ align:start position:0%
+certain program Committees of more
+theoretical
+
+ align:start position:0%
+theoretical
+ 
+
+ align:start position:0%
+theoretical
+conferences I mean the kind of things
+
+ align:start position:0%
+conferences I mean the kind of things
+ 
+
+ align:start position:0%
+conferences I mean the kind of things
+you can prove is that an attacker who
+
+ align:start position:0%
+you can prove is that an attacker who
+ 
+
+ align:start position:0%
+you can prove is that an attacker who
+sees this who sees a number of strings
+
+ align:start position:0%
+sees this who sees a number of strings
+ 
+
+ align:start position:0%
+sees this who sees a number of strings
+of of this this length but doesn't get
+
+ align:start position:0%
+of of this this length but doesn't get
+ 
+
+ align:start position:0%
+of of this this length but doesn't get
+to see who sees a number of streams here
+
+ align:start position:0%
+to see who sees a number of streams here
+ 
+
+ align:start position:0%
+to see who sees a number of streams here
+all of equal volume and equal timing
+
+ align:start position:0%
+all of equal volume and equal timing
+ 
+
+ align:start position:0%
+all of equal volume and equal timing
+cannot tell which one goes to which Bob
+
+ align:start position:0%
+cannot tell which one goes to which Bob
+ 
+
+ align:start position:0%
+cannot tell which one goes to which Bob
+simply by looking at the bites coming
+
+ align:start position:0%
+simply by looking at the bites coming
+ 
+
+ align:start position:0%
+simply by looking at the bites coming
+out but that's hardly a useful
+
+ align:start position:0%
+out but that's hardly a useful
+ 
+
+ align:start position:0%
+out but that's hardly a useful
+result also the kind of guarantees you
+
+ align:start position:0%
+result also the kind of guarantees you
+ 
+
+ align:start position:0%
+result also the kind of guarantees you
+can get from anonymity systems that we
+
+ align:start position:0%
+can get from anonymity systems that we
+ 
+
+ align:start position:0%
+can get from anonymity systems that we
+know how to build
+
+ align:start position:0%
+know how to build
+ 
+
+ align:start position:0%
+know how to build
+today okay I should be careful here
+
+ align:start position:0%
+today okay I should be careful here
+ 
+
+ align:start position:0%
+today okay I should be careful here
+there are some where you have very
+
+ align:start position:0%
+there are some where you have very
+ 
+
+ align:start position:0%
+there are some where you have very
+strong guarantees that we do know how to
+
+ align:start position:0%
+strong guarantees that we do know how to
+ 
+
+ align:start position:0%
+strong guarantees that we do know how to
+build that you would never actually want
+
+ align:start position:0%
+build that you would never actually want
+ 
+
+ align:start position:0%
+build that you would never actually want
+to use
+
+ align:start position:0%
+to use
+ 
+
+ align:start position:0%
+to use
+like um classical chian D DC nets for
+
+ align:start position:0%
+like um classical chian D DC nets for
+ 
+
+ align:start position:0%
+like um classical chian D DC nets for
+instance provide guaranteed anonymity
+
+ align:start position:0%
+instance provide guaranteed anonymity
+ 
+
+ align:start position:0%
+instance provide guaranteed anonymity
+except any participant can shut down the
+
+ align:start position:0%
+except any participant can shut down the
+ 
+
+ align:start position:0%
+except any participant can shut down the
+whole network by not participating that
+
+ align:start position:0%
+whole network by not participating that
+ 
+
+ align:start position:0%
+whole network by not participating that
+does not scale but for the things that
+
+ align:start position:0%
+does not scale but for the things that
+ 
+
+ align:start position:0%
+does not scale but for the things that
+we do want to build these days what for
+
+ align:start position:0%
+we do want to build these days what for
+ 
+
+ align:start position:0%
+we do want to build these days what for
+the most part you cannot the anonymity
+
+ align:start position:0%
+the most part you cannot the anonymity
+ 
+
+ align:start position:0%
+the most part you cannot the anonymity
+properties are
+
+ align:start position:0%
+properties are
+ 
+
+ align:start position:0%
+properties are
+probabilistic rather than categorically
+
+ align:start position:0%
+probabilistic rather than categorically
+ 
+
+ align:start position:0%
+probabilistic rather than categorically
+guarantee so instead of saying instead
+
+ align:start position:0%
+guarantee so instead of saying instead
+ 
+
+ align:start position:0%
+guarantee so instead of saying instead
+of asking does this protect Alice the
+
+ align:start position:0%
+of asking does this protect Alice the
+ 
+
+ align:start position:0%
+of asking does this protect Alice the
+kind of questions you can ask are under
+
+ align:start position:0%
+kind of questions you can ask are under
+ 
+
+ align:start position:0%
+kind of questions you can ask are under
+this Asser assumption about attacker
+
+ align:start position:0%
+this Asser assumption about attacker
+ 
+
+ align:start position:0%
+this Asser assumption about attacker
+capabilities how much traffic can Alice
+
+ align:start position:0%
+capabilities how much traffic can Alice
+ 
+
+ align:start position:0%
+capabilities how much traffic can Alice
+safely send if she wants a 99% chance of
+
+ align:start position:0%
+safely send if she wants a 99% chance of
+ 
+
+ align:start position:0%
+safely send if she wants a 99% chance of
+not being linked to her
+
+ align:start position:0%
+not being linked to her
+ 
+
+ align:start position:0%
+not being linked to her
+activities so right will anyone actually
+
+ align:start position:0%
+activities so right will anyone actually
+ 
+
+ align:start position:0%
+activities so right will anyone actually
+run these things that was an opening
+
+ align:start position:0%
+run these things that was an opening
+ 
+
+ align:start position:0%
+run these things that was an opening
+question when we started we didn't know
+
+ align:start position:0%
+question when we started we didn't know
+ 
+
+ align:start position:0%
+question when we started we didn't know
+whether the system would actually take
+
+ align:start position:0%
+whether the system would actually take
+ 
+
+ align:start position:0%
+whether the system would actually take
+off or not so the only way to actually
+
+ align:start position:0%
+off or not so the only way to actually
+ 
+
+ align:start position:0%
+off or not so the only way to actually
+find out was proof
+
+ align:start position:0%
+find out was proof
+ 
+
+ align:start position:0%
+find out was proof
+by try it see what happens um we got
+
+ align:start position:0%
+by try it see what happens um we got
+ 
+
+ align:start position:0%
+by try it see what happens um we got
+some a fair amount of of volunteer
+
+ align:start position:0%
+some a fair amount of of volunteer
+ 
+
+ align:start position:0%
+some a fair amount of of volunteer
+operators a fair number of nonprofits
+
+ align:start position:0%
+operators a fair number of nonprofits
+ 
+
+ align:start position:0%
+operators a fair number of nonprofits
+have formed whose sole purpose is just
+
+ align:start position:0%
+have formed whose sole purpose is just
+ 
+
+ align:start position:0%
+have formed whose sole purpose is just
+to take donations and use them to buy
+
+ align:start position:0%
+to take donations and use them to buy
+ 
+
+ align:start position:0%
+to take donations and use them to buy
+bandwidth and Run Tour
+
+ align:start position:0%
+bandwidth and Run Tour
+ 
+
+ align:start position:0%
+bandwidth and Run Tour
+nodes and there are also universities
+
+ align:start position:0%
+nodes and there are also universities
+ 
+
+ align:start position:0%
+nodes and there are also universities
+there's also you know private companies
+
+ align:start position:0%
+there's also you know private companies
+ 
+
+ align:start position:0%
+there's also you know private companies
+for a while aamai was running a tour
+
+ align:start position:0%
+for a while aamai was running a tour
+ 
+
+ align:start position:0%
+for a while aamai was running a tour
+server um out of their security team
+
+ align:start position:0%
+server um out of their security team
+ 
+
+ align:start position:0%
+server um out of their security team
+because they thought it was fun
+
+ align:start position:0%
+because they thought it was fun
+ 
+
+ align:start position:0%
+because they thought it was fun
+um the legal issues there again I'm not
+
+ align:start position:0%
+um the legal issues there again I'm not
+ 
+
+ align:start position:0%
+um the legal issues there again I'm not
+a lawyer I can't offer legal advice but
+
+ align:start position:0%
+a lawyer I can't offer legal advice but
+ 
+
+ align:start position:0%
+a lawyer I can't offer legal advice but
+five different people ask about legal
+
+ align:start position:0%
+five different people ask about legal
+ 
+
+ align:start position:0%
+five different people ask about legal
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+um as far as I can tell in the US at
+
+ align:start position:0%
+um as far as I can tell in the US at
+ 
+
+ align:start position:0%
+um as far as I can tell in the US at
+least there's no legal impediment to
+
+ align:start position:0%
+least there's no legal impediment to
+ 
+
+ align:start position:0%
+least there's no legal impediment to
+running a tour server and that seems to
+
+ align:start position:0%
+running a tour server and that seems to
+ 
+
+ align:start position:0%
+running a tour server and that seems to
+be the case throughout most of Europe as
+
+ align:start position:0%
+be the case throughout most of Europe as
+ 
+
+ align:start position:0%
+be the case throughout most of Europe as
+far as I'm aware in in places that
+
+ align:start position:0%
+far as I'm aware in in places that
+ 
+
+ align:start position:0%
+far as I'm aware in in places that
+generally have less internet Freedom
+
+ align:start position:0%
+generally have less internet Freedom
+ 
+
+ align:start position:0%
+generally have less internet Freedom
+it's a dice your proposition the issues
+
+ align:start position:0%
+it's a dice your proposition the issues
+ 
+
+ align:start position:0%
+it's a dice your proposition the issues
+to be concerned about are not is it
+
+ align:start position:0%
+to be concerned about are not is it
+ 
+
+ align:start position:0%
+to be concerned about are not is it
+illegal to run a tour server
+
+ align:start position:0%
+illegal to run a tour server
+ 
+
+ align:start position:0%
+illegal to run a tour server
+but if I tell if somebody does something
+
+ align:start position:0%
+but if I tell if somebody does something
+ 
+
+ align:start position:0%
+but if I tell if somebody does something
+illegal or undesirable with my tour
+
+ align:start position:0%
+illegal or undesirable with my tour
+ 
+
+ align:start position:0%
+illegal or undesirable with my tour
+server will my ISP shut me down
+
+ align:start position:0%
+server will my ISP shut me down
+ 
+
+ align:start position:0%
+server will my ISP shut me down
+and will my and will law enforcement
+
+ align:start position:0%
+and will my and will law enforcement
+ 
+
+ align:start position:0%
+and will my and will law enforcement
+believe oh you're just running a tour
+
+ align:start position:0%
+believe oh you're just running a tour
+ 
+
+ align:start position:0%
+believe oh you're just running a tour
+server or will they seize the computer
+
+ align:start position:0%
+server or will they seize the computer
+ 
+
+ align:start position:0%
+server or will they seize the computer
+to make sure um for those I would
+
+ align:start position:0%
+to make sure um for those I would
+ 
+
+ align:start position:0%
+to make sure um for those I would
+suggest not running a tour server out of
+
+ align:start position:0%
+suggest not running a tour server out of
+ 
+
+ align:start position:0%
+suggest not running a tour server out of
+your dorm
+
+ align:start position:0%
+your dorm
+ 
+
+ align:start position:0%
+your dorm
+room oh excuse me don't run an exit out
+
+ align:start position:0%
+room oh excuse me don't run an exit out
+ 
+
+ align:start position:0%
+room oh excuse me don't run an exit out
+of your door room dorm room a relay out
+
+ align:start position:0%
+of your door room dorm room a relay out
+ 
+
+ align:start position:0%
+of your door room dorm room a relay out
+of your dorm room assuming that Network
+
+ align:start position:0%
+of your dorm room assuming that Network
+ 
+
+ align:start position:0%
+of your dorm room assuming that Network
+policy allows that I think it I have no
+
+ align:start position:0%
+policy allows that I think it I have no
+ 
+
+ align:start position:0%
+policy allows that I think it I have no
+idea um they've changed so much since I
+
+ align:start position:0%
+idea um they've changed so much since I
+ 
+
+ align:start position:0%
+idea um they've changed so much since I
+was a kid um
+
+ align:start position:0%
+was a kid um
+ 
+
+ align:start position:0%
+was a kid um
+have um running an exit out of your dorm
+
+ align:start position:0%
+have um running an exit out of your dorm
+ 
+
+ align:start position:0%
+have um running an exit out of your dorm
+room could get you in trouble
+
+ align:start position:0%
+room could get you in trouble
+ 
+
+ align:start position:0%
+room could get you in trouble
+um but running running a non-exit relay
+
+ align:start position:0%
+um but running running a non-exit relay
+ 
+
+ align:start position:0%
+um but running running a non-exit relay
+that doesn't deliver traffic to the
+
+ align:start position:0%
+that doesn't deliver traffic to the
+ 
+
+ align:start position:0%
+that doesn't deliver traffic to the
+internet is is is less likely to create
+
+ align:start position:0%
+internet is is is less likely to create
+ 
+
+ align:start position:0%
+internet is is is less likely to create
+those issues in
+
+ align:start position:0%
+those issues in
+ 
+
+ align:start position:0%
+those issues in
+particular the likeliest but you know if
+
+ align:start position:0%
+particular the likeliest but you know if
+ 
+
+ align:start position:0%
+particular the likeliest but you know if
+you do it in a nice Colo site and you
+
+ align:start position:0%
+you do it in a nice Colo site and you
+ 
+
+ align:start position:0%
+you do it in a nice Colo site and you
+get your isp's permission then it's
+
+ align:start position:0%
+get your isp's permission then it's
+ 
+
+ align:start position:0%
+get your isp's permission then it's
+pretty reasonable thing to do let's see
+
+ align:start position:0%
+pretty reasonable thing to do let's see
+ 
+
+ align:start position:0%
+pretty reasonable thing to do let's see
+um someone asked well what if users
+
+ align:start position:0%
+um someone asked well what if users
+ 
+
+ align:start position:0%
+um someone asked well what if users
+don't trust a particular node and this
+
+ align:start position:0%
+don't trust a particular node and this
+ 
+
+ align:start position:0%
+don't trust a particular node and this
+brings me to my next question the my
+
+ align:start position:0%
+brings me to my next question the my
+ 
+
+ align:start position:0%
+brings me to my next question the my
+next topic so the software that clients
+
+ align:start position:0%
+next topic so the software that clients
+ 
+
+ align:start position:0%
+next topic so the software that clients
+use you can tell it don't use this one
+
+ align:start position:0%
+use you can tell it don't use this one
+ 
+
+ align:start position:0%
+use you can tell it don't use this one
+don't use this one only use this one but
+
+ align:start position:0%
+don't use this one only use this one but
+ 
+
+ align:start position:0%
+don't use this one only use this one but
+remember that anonymity loves company
+
+ align:start position:0%
+remember that anonymity loves company
+ 
+
+ align:start position:0%
+remember that anonymity loves company
+principle if I'm the if I am using every
+
+ align:start position:0%
+principle if I'm the if I am using every
+ 
+
+ align:start position:0%
+principle if I'm the if I am using every
+no if I'm only using three nodes and
+
+ align:start position:0%
+no if I'm only using three nodes and
+ 
+
+ align:start position:0%
+no if I'm only using three nodes and
+you're using three different nodes and
+
+ align:start position:0%
+you're using three different nodes and
+ 
+
+ align:start position:0%
+you're using three different nodes and
+you're using three different nodes our
+
+ align:start position:0%
+you're using three different nodes our
+ 
+
+ align:start position:0%
+you're using three different nodes our
+traffic will not mix at all to the
+
+ align:start position:0%
+traffic will not mix at all to the
+ 
+
+ align:start position:0%
+traffic will not mix at all to the
+extent that we partition off which parts
+
+ align:start position:0%
+extent that we partition off which parts
+ 
+
+ align:start position:0%
+extent that we partition off which parts
+of the network we use we are
+
+ align:start position:0%
+of the network we use we are
+ 
+
+ align:start position:0%
+of the network we use we are
+distinguishable from one another now if
+
+ align:start position:0%
+distinguishable from one another now if
+ 
+
+ align:start position:0%
+distinguishable from one another now if
+I just exclude one or two no and you
+
+ align:start position:0%
+I just exclude one or two no and you
+ 
+
+ align:start position:0%
+I just exclude one or two no and you
+just exclude one or two nodes that's not
+
+ align:start position:0%
+just exclude one or two nodes that's not
+ 
+
+ align:start position:0%
+just exclude one or two nodes that's not
+a big partitioning and that doesn't help
+
+ align:start position:0%
+a big partitioning and that doesn't help
+ 
+
+ align:start position:0%
+a big partitioning and that doesn't help
+distinguishability that much
+
+ align:start position:0%
+distinguishability that much
+ 
+
+ align:start position:0%
+distinguishability that much
+but it would be good to the extent
+
+ align:start position:0%
+but it would be good to the extent
+ 
+
+ align:start position:0%
+but it would be good to the extent
+possible to have everyone using the same
+
+ align:start position:0%
+possible to have everyone using the same
+ 
+
+ align:start position:0%
+possible to have everyone using the same
+nodes so right how do we accomplish that
+
+ align:start position:0%
+nodes so right how do we accomplish that
+ 
+
+ align:start position:0%
+nodes so right how do we accomplish that
+so version one in the first version of
+
+ align:start position:0%
+so version one in the first version of
+ 
+
+ align:start position:0%
+so version one in the first version of
+Tor we just chipped a list of all of the
+
+ align:start position:0%
+Tor we just chipped a list of all of the
+ 
+
+ align:start position:0%
+Tor we just chipped a list of all of the
+nodes I think there were three of them
+
+ align:start position:0%
+nodes I think there were three of them
+ 
+
+ align:start position:0%
+nodes I think there were three of them
+or five or something now I think there
+
+ align:start position:0%
+or five or something now I think there
+ 
+
+ align:start position:0%
+or five or something now I think there
+were about six of which three were all
+
+ align:start position:0%
+were about six of which three were all
+ 
+
+ align:start position:0%
+were about six of which three were all
+running on the same computer in a closet
+
+ align:start position:0%
+running on the same computer in a closet
+ 
+
+ align:start position:0%
+running on the same computer in a closet
+at LCS and Tech
+
+ align:start position:0%
+at LCS and Tech
+ 
+
+ align:start position:0%
+at LCS and Tech
+Square um all right so that wasn't a
+
+ align:start position:0%
+Square um all right so that wasn't a
+ 
+
+ align:start position:0%
+Square um all right so that wasn't a
+good idea because nodes can go up and
+
+ align:start position:0%
+good idea because nodes can go up and
+ 
+
+ align:start position:0%
+good idea because nodes can go up and
+down noes change you don't want to have
+
+ align:start position:0%
+down noes change you don't want to have
+ 
+
+ align:start position:0%
+down noes change you don't want to have
+to put out a new release of your
+
+ align:start position:0%
+to put out a new release of your
+ 
+
+ align:start position:0%
+to put out a new release of your
+software every time somebody joins and
+
+ align:start position:0%
+software every time somebody joins and
+ 
+
+ align:start position:0%
+software every time somebody joins and
+leaves the network so you could just
+
+ align:start position:0%
+leaves the network so you could just
+ 
+
+ align:start position:0%
+leaves the network so you could just
+have every node keep a list of all the
+
+ align:start position:0%
+have every node keep a list of all the
+ 
+
+ align:start position:0%
+have every node keep a list of all the
+other nodes that are connected to it and
+
+ align:start position:0%
+other nodes that are connected to it and
+ 
+
+ align:start position:0%
+other nodes that are connected to it and
+all advertise to each other and then
+
+ align:start position:0%
+all advertise to each other and then
+ 
+
+ align:start position:0%
+all advertise to each other and then
+when a client connects to a client just
+
+ align:start position:0%
+when a client connects to a client just
+ 
+
+ align:start position:0%
+when a client connects to a client just
+has to know one node and then says hey
+
+ align:start position:0%
+has to know one node and then says hey
+ 
+
+ align:start position:0%
+has to know one node and then says hey
+who's on the network and actually a lot
+
+ align:start position:0%
+who's on the network and actually a lot
+ 
+
+ align:start position:0%
+who's on the network and actually a lot
+of designs people have built work this
+
+ align:start position:0%
+of designs people have built work this
+ 
+
+ align:start position:0%
+of designs people have built work this
+way a lot of early peer-to-peer
+
+ align:start position:0%
+way a lot of early peer-to-peer
+ 
+
+ align:start position:0%
+way a lot of early peer-to-peer
+anonymity designs that work this way but
+
+ align:start position:0%
+anonymity designs that work this way but
+ 
+
+ align:start position:0%
+anonymity designs that work this way but
+it's a terrible idea because if you go
+
+ align:start position:0%
+it's a terrible idea because if you go
+ 
+
+ align:start position:0%
+it's a terrible idea because if you go
+to one node and say who's on the network
+
+ align:start position:0%
+to one node and say who's on the network
+ 
+
+ align:start position:0%
+to one node and say who's on the network
+and you believe them well if I'm that
+
+ align:start position:0%
+and you believe them well if I'm that
+ 
+
+ align:start position:0%
+and you believe them well if I'm that
+note I can say yes I am on the network
+
+ align:start position:0%
+note I can say yes I am on the network
+ 
+
+ align:start position:0%
+note I can say yes I am on the network
+and my friend over here is on the
+
+ align:start position:0%
+and my friend over here is on the
+ 
+
+ align:start position:0%
+and my friend over here is on the
+network and my friend over here is on
+
+ align:start position:0%
+network and my friend over here is on
+ 
+
+ align:start position:0%
+network and my friend over here is on
+the network and no one else is on the
+
+ align:start position:0%
+the network and no one else is on the
+ 
+
+ align:start position:0%
+the network and no one else is on the
+network and I can tell you any number of
+
+ align:start position:0%
+network and I can tell you any number of
+ 
+
+ align:start position:0%
+network and I can tell you any number of
+fake nodes that are all operated by me
+
+ align:start position:0%
+fake nodes that are all operated by me
+ 
+
+ align:start position:0%
+fake nodes that are all operated by me
+and capture all of your traffic that way
+
+ align:start position:0%
+and capture all of your traffic that way
+ 
+
+ align:start position:0%
+and capture all of your traffic that way
+with what's called a route capture
+
+ align:start position:0%
+with what's called a route capture
+ 
+
+ align:start position:0%
+with what's called a route capture
+attack okay so let's maybe we just have
+
+ align:start position:0%
+attack okay so let's maybe we just have
+ 
+
+ align:start position:0%
+attack okay so let's maybe we just have
+a single directory operated by a trusted
+
+ align:start position:0%
+a single directory operated by a trusted
+ 
+
+ align:start position:0%
+a single directory operated by a trusted
+party that's not so good it's a single
+
+ align:start position:0%
+party that's not so good it's a single
+ 
+
+ align:start position:0%
+party that's not so good it's a single
+point of
+
+ align:start position:0%
+point of
+ 
+
+ align:start position:0%
+point of
+failure so you could have well okay
+
+ align:start position:0%
+failure so you could have well okay
+ 
+
+ align:start position:0%
+failure so you could have well okay
+let's have multiple trusted parties and
+
+ align:start position:0%
+let's have multiple trusted parties and
+ 
+
+ align:start position:0%
+let's have multiple trusted parties and
+clients go to these multiple trusted
+
+ align:start position:0%
+clients go to these multiple trusted
+ 
+
+ align:start position:0%
+clients go to these multiple trusted
+parties and get a list of all of the
+
+ align:start position:0%
+parties and get a list of all of the
+ 
+
+ align:start position:0%
+parties and get a list of all of the
+nodes from all of them and combine those
+
+ align:start position:0%
+nodes from all of them and combine those
+ 
+
+ align:start position:0%
+nodes from all of them and combine those
+lists um then you're actually first off
+
+ align:start position:0%
+lists um then you're actually first off
+ 
+
+ align:start position:0%
+lists um then you're actually first off
+you're partitioned in that case if I
+
+ align:start position:0%
+you're partitioned in that case if I
+ 
+
+ align:start position:0%
+you're partitioned in that case if I
+choose these three and you choose those
+
+ align:start position:0%
+choose these three and you choose those
+ 
+
+ align:start position:0%
+choose these three and you choose those
+three and they say anything different
+
+ align:start position:0%
+three and they say anything different
+ 
+
+ align:start position:0%
+three and they say anything different
+then we'll be using different sets of
+
+ align:start position:0%
+then we'll be using different sets of
+ 
+
+ align:start position:0%
+then we'll be using different sets of
+nodes so that's still not good also
+
+ align:start position:0%
+nodes so that's still not good also
+ 
+
+ align:start position:0%
+nodes so that's still not good also
+there's still a attack attempt where
+
+ align:start position:0%
+there's still a attack attempt where
+ 
+
+ align:start position:0%
+there's still a attack attempt where
+like if I say if I use the intersection
+
+ align:start position:0%
+like if I say if I use the intersection
+ 
+
+ align:start position:0%
+like if I say if I use the intersection
+of the sets they tell
+
+ align:start position:0%
+of the sets they tell
+ 
+
+ align:start position:0%
+of the sets they tell
+me then any one of them can keep me from
+
+ align:start position:0%
+me then any one of them can keep me from
+ 
+
+ align:start position:0%
+me then any one of them can keep me from
+using a node they don't like by not
+
+ align:start position:0%
+using a node they don't like by not
+ 
+
+ align:start position:0%
+using a node they don't like by not
+listing it if I use the union anyone can
+
+ align:start position:0%
+listing it if I use the union anyone can
+ 
+
+ align:start position:0%
+listing it if I use the union anyone can
+flood Me by making 20,000 fake servers
+
+ align:start position:0%
+flood Me by making 20,000 fake servers
+ 
+
+ align:start position:0%
+flood Me by making 20,000 fake servers
+that are all them on the list I might do
+
+ align:start position:0%
+that are all them on the list I might do
+ 
+
+ align:start position:0%
+that are all them on the list I might do
+I might compute the result of some sort
+
+ align:start position:0%
+I might compute the result of some sort
+ 
+
+ align:start position:0%
+I might compute the result of some sort
+of vote on them which would solve those
+
+ align:start position:0%
+of vote on them which would solve those
+ 
+
+ align:start position:0%
+of vote on them which would solve those
+two problems but I'd will be partitioned
+
+ align:start position:0%
+two problems but I'd will be partitioned
+ 
+
+ align:start position:0%
+two problems but I'd will be partitioned
+from everyone who's using different
+
+ align:start position:0%
+from everyone who's using different
+ 
+
+ align:start position:0%
+from everyone who's using different
+trusted
+
+ align:start position:0%
+trusted
+ 
+
+ align:start position:0%
+trusted
+parties um we could do a magical
+
+ align:start position:0%
+parties um we could do a magical
+ 
+
+ align:start position:0%
+parties um we could do a magical
+DHT and have we done distributed hash
+
+ align:start position:0%
+DHT and have we done distributed hash
+ 
+
+ align:start position:0%
+DHT and have we done distributed hash
+tables all right we could do some sort
+
+ align:start position:0%
+tables all right we could do some sort
+ 
+
+ align:start position:0%
+tables all right we could do some sort
+of magical distributed structure run by
+
+ align:start position:0%
+of magical distributed structure run by
+ 
+
+ align:start position:0%
+of magical distributed structure run by
+multiple run across all of the nodes I
+
+ align:start position:0%
+multiple run across all of the nodes I
+ 
+
+ align:start position:0%
+multiple run across all of the nodes I
+say magical because although there are
+
+ align:start position:0%
+say magical because although there are
+ 
+
+ align:start position:0%
+say magical because although there are
+designs in this
+
+ align:start position:0%
+designs in this
+ 
+
+ align:start position:0%
+designs in this
+area um there're and some better than
+
+ align:start position:0%
+area um there're and some better than
+ 
+
+ align:start position:0%
+area um there're and some better than
+others none of them really seems to have
+
+ align:start position:0%
+others none of them really seems to have
+ 
+
+ align:start position:0%
+others none of them really seems to have
+a solid security evidence for it at this
+
+ align:start position:0%
+a solid security evidence for it at this
+ 
+
+ align:start position:0%
+a solid security evidence for it at this
+point to the point where I would be
+
+ align:start position:0%
+point to the point where I would be
+ 
+
+ align:start position:0%
+point to the point where I would be
+comfortable and saying yes this is
+
+ align:start position:0%
+comfortable and saying yes this is
+ 
+
+ align:start position:0%
+comfortable and saying yes this is
+actually secure so the solution we wound
+
+ align:start position:0%
+actually secure so the solution we wound
+ 
+
+ align:start position:0%
+actually secure so the solution we wound
+up with is have multiple hardened
+
+ align:start position:0%
+up with is have multiple hardened
+ 
+
+ align:start position:0%
+up with is have multiple hardened
+trusted authorities run by trusted
+
+ align:start position:0%
+trusted authorities run by trusted
+ 
+
+ align:start position:0%
+trusted authorities run by trusted
+parties that collect lists of nodes that
+
+ align:start position:0%
+parties that collect lists of nodes that
+ 
+
+ align:start position:0%
+parties that collect lists of nodes that
+vote on hourly on which nodes are
+
+ align:start position:0%
+vote on hourly on which nodes are
+ 
+
+ align:start position:0%
+vote on hourly on which nodes are
+running that can exclude no that can
+
+ align:start position:0%
+running that can exclude no that can
+ 
+
+ align:start position:0%
+running that can exclude no that can
+vote to exclude nodes that seem to be
+
+ align:start position:0%
+vote to exclude nodes that seem to be
+ 
+
+ align:start position:0%
+vote to exclude nodes that seem to be
+misbehaving that are all running on the
+
+ align:start position:0%
+misbehaving that are all running on the
+ 
+
+ align:start position:0%
+misbehaving that are all running on the
+slash same
+
+ align:start position:0%
+slash same
+ 
+
+ align:start position:0%
+slash same
+sl6 that are doing strange things to
+
+ align:start position:0%
+sl6 that are doing strange things to
+ 
+
+ align:start position:0%
+sl6 that are doing strange things to
+traffic
+
+ align:start position:0%
+traffic
+ 
+
+ align:start position:0%
+traffic
+and have them form a consensus that's
+
+ align:start position:0%
+and have them form a consensus that's
+ 
+
+ align:start position:0%
+and have them form a consensus that's
+the out that's the result of their votes
+
+ align:start position:0%
+the out that's the result of their votes
+ 
+
+ align:start position:0%
+the out that's the result of their votes
+and everybody signs the consensus and
+
+ align:start position:0%
+and everybody signs the consensus and
+ 
+
+ align:start position:0%
+and everybody signs the consensus and
+clients don't use it unless it's signed
+
+ align:start position:0%
+clients don't use it unless it's signed
+ 
+
+ align:start position:0%
+clients don't use it unless it's signed
+by enough authorities this is not the
+
+ align:start position:0%
+by enough authorities this is not the
+ 
+
+ align:start position:0%
+by enough authorities this is not the
+final design but it's the best we've
+
+ align:start position:0%
+final design but it's the best we've
+ 
+
+ align:start position:0%
+final design but it's the best we've
+managed to get come up with so
+
+ align:start position:0%
+managed to get come up with so
+ 
+
+ align:start position:0%
+managed to get come up with so
+far and this way all you need to
+
+ align:start position:0%
+far and this way all you need to
+ 
+
+ align:start position:0%
+far and this way all you need to
+distribute with clients
+
+ align:start position:0%
+distribute with clients
+ 
+
+ align:start position:0%
+distribute with clients
+is um a list of all of the authorities
+
+ align:start position:0%
+is um a list of all of the authorities
+ 
+
+ align:start position:0%
+is um a list of all of the authorities
+public keys and some places to get the
+
+ align:start position:0%
+public keys and some places to get the
+ 
+
+ align:start position:0%
+public keys and some places to get the
+directories you want to have all of the
+
+ align:start position:0%
+directories you want to have all of the
+ 
+
+ align:start position:0%
+directories you want to have all of the
+nodes cach these directories things
+
+ align:start position:0%
+nodes cach these directories things
+ 
+
+ align:start position:0%
+nodes cach these directories things
+because if you don't the bandwidth load
+
+ align:start position:0%
+because if you don't the bandwidth load
+ 
+
+ align:start position:0%
+because if you don't the bandwidth load
+on authorities is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+catastrophic so I'm going to skip over
+
+ align:start position:0%
+catastrophic so I'm going to skip over
+ 
+
+ align:start position:0%
+catastrophic so I'm going to skip over
+that because uh um I would love to talk
+
+ align:start position:0%
+that because uh um I would love to talk
+ 
+
+ align:start position:0%
+that because uh um I would love to talk
+about how you choose how clients should
+
+ align:start position:0%
+about how you choose how clients should
+ 
+
+ align:start position:0%
+about how you choose how clients should
+choose which paths to build through the
+
+ align:start position:0%
+choose which paths to build through the
+ 
+
+ align:start position:0%
+choose which paths to build through the
+network I would love to talk about
+
+ align:start position:0%
+network I would love to talk about
+ 
+
+ align:start position:0%
+network I would love to talk about
+issues with applications and making
+
+ align:start position:0%
+issues with applications and making
+ 
+
+ align:start position:0%
+issues with applications and making
+applications not de anonymize themselves
+
+ align:start position:0%
+applications not de anonymize themselves
+ 
+
+ align:start position:0%
+applications not de anonymize themselves
+I'd love to talk about abuse I'd love to
+
+ align:start position:0%
+I'd love to talk about abuse I'd love to
+ 
+
+ align:start position:0%
+I'd love to talk about abuse I'd love to
+talk about hidden services and how they
+
+ align:start position:0%
+talk about hidden services and how they
+ 
+
+ align:start position:0%
+talk about hidden services and how they
+work I'd love to talk about censorship
+
+ align:start position:0%
+work I'd love to talk about censorship
+ 
+
+ align:start position:0%
+work I'd love to talk about censorship
+resistance and
+
+ align:start position:0%
+resistance and
+ 
+
+ align:start position:0%
+resistance and
+I'd like to talk about attacks and
+
+ align:start position:0%
+I'd like to talk about attacks and
+ 
+
+ align:start position:0%
+I'd like to talk about attacks and
+defenses but I've only got 35 minutes
+
+ align:start position:0%
+defenses but I've only got 35 minutes
+ 
+
+ align:start position:0%
+defenses but I've only got 35 minutes
+and I can't possibly cover all of these
+
+ align:start position:0%
+and I can't possibly cover all of these
+ 
+
+ align:start position:0%
+and I can't possibly cover all of these
+so show of hands for how many people
+
+ align:start position:0%
+so show of hands for how many people
+ 
+
+ align:start position:0%
+so show of hands for how many people
+think the most important top I think
+
+ align:start position:0%
+think the most important top I think
+ 
+
+ align:start position:0%
+think the most important top I think
+I've got time if you think about what
+
+ align:start position:0%
+I've got time if you think about what
+ 
+
+ align:start position:0%
+I've got time if you think about what
+you think are the two most important
+
+ align:start position:0%
+you think are the two most important
+ 
+
+ align:start position:0%
+you think are the two most important
+topics on this
+
+ align:start position:0%
+topics on this
+ 
+
+ align:start position:0%
+topics on this
+list if one of your two most important
+
+ align:start position:0%
+list if one of your two most important
+ 
+
+ align:start position:0%
+list if one of your two most important
+topics is path selection and how you
+
+ align:start position:0%
+topics is path selection and how you
+ 
+
+ align:start position:0%
+topics is path selection and how you
+choose nodes please raise your
+
+ align:start position:0%
+choose nodes please raise your
+ 
+
+ align:start position:0%
+choose nodes please raise your
+hand if one of your two most important
+
+ align:start position:0%
+hand if one of your two most important
+ 
+
+ align:start position:0%
+hand if one of your two most important
+topics is application issues and how to
+
+ align:start position:0%
+topics is application issues and how to
+ 
+
+ align:start position:0%
+topics is application issues and how to
+make applications not bust your
+
+ align:start position:0%
+make applications not bust your
+ 
+
+ align:start position:0%
+make applications not bust your
+anonymity please raise your
+
+ align:start position:0%
+anonymity please raise your
+ 
+
+ align:start position:0%
+anonymity please raise your
+hand if one of your most important
+
+ align:start position:0%
+hand if one of your most important
+ 
+
+ align:start position:0%
+hand if one of your most important
+issues is abuse and what kind of abuse
+
+ align:start position:0%
+issues is abuse and what kind of abuse
+ 
+
+ align:start position:0%
+issues is abuse and what kind of abuse
+we see how you can prevent it and how
+
+ align:start position:0%
+we see how you can prevent it and how
+ 
+
+ align:start position:0%
+we see how you can prevent it and how
+that works out please raise your
+
+ align:start position:0%
+that works out please raise your
+ 
+
+ align:start position:0%
+that works out please raise your
+hand okay that one's popular um if one
+
+ align:start position:0%
+hand okay that one's popular um if one
+ 
+
+ align:start position:0%
+hand okay that one's popular um if one
+of your most important topics is how
+
+ align:start position:0%
+of your most important topics is how
+ 
+
+ align:start position:0%
+of your most important topics is how
+hidden Services work and how they can be
+
+ align:start position:0%
+hidden Services work and how they can be
+ 
+
+ align:start position:0%
+hidden Services work and how they can be
+made to work better please raise your
+
+ align:start position:0%
+made to work better please raise your
+ 
+
+ align:start position:0%
+made to work better please raise your
+hand that's wow that's much more popular
+
+ align:start position:0%
+hand that's wow that's much more popular
+ 
+
+ align:start position:0%
+hand that's wow that's much more popular
+on this side of the room than that side
+
+ align:start position:0%
+on this side of the room than that side
+ 
+
+ align:start position:0%
+on this side of the room than that side
+of the room I wonder what's going on are
+
+ align:start position:0%
+of the room I wonder what's going on are
+ 
+
+ align:start position:0%
+of the room I wonder what's going on are
+you guys in a club um are you up to
+
+ align:start position:0%
+you guys in a club um are you up to
+ 
+
+ align:start position:0%
+you guys in a club um are you up to
+something censorship who's interested in
+
+ align:start position:0%
+something censorship who's interested in
+ 
+
+ align:start position:0%
+something censorship who's interested in
+censorship okay that's fairly popular
+
+ align:start position:0%
+censorship okay that's fairly popular
+ 
+
+ align:start position:0%
+censorship okay that's fairly popular
+attacks and
+
+ align:start position:0%
+attacks and
+ 
+
+ align:start position:0%
+attacks and
+defenses it's also okay so we're not
+
+ align:start position:0%
+defenses it's also okay so we're not
+ 
+
+ align:start position:0%
+defenses it's also okay so we're not
+doing paths and we're not doing appu
+
+ align:start position:0%
+doing paths and we're not doing appu
+ 
+
+ align:start position:0%
+doing paths and we're not doing appu
+basically paths um guard nodes guard
+
+ align:start position:0%
+basically paths um guard nodes guard
+ 
+
+ align:start position:0%
+basically paths um guard nodes guard
+nodes seard node designs select by
+
+ align:start position:0%
+nodes seard node designs select by
+ 
+
+ align:start position:0%
+nodes seard node designs select by
+bandwidth you need to actually weight by
+
+ align:start position:0%
+bandwidth you need to actually weight by
+ 
+
+ align:start position:0%
+bandwidth you need to actually weight by
+bandwidth but you also need a trusted
+
+ align:start position:0%
+bandwidth but you also need a trusted
+ 
+
+ align:start position:0%
+bandwidth but you also need a trusted
+way to measure
+
+ align:start position:0%
+way to measure
+ 
+
+ align:start position:0%
+way to measure
+bandwidth and that's the too long didn't
+
+ align:start position:0%
+bandwidth and that's the too long didn't
+ 
+
+ align:start position:0%
+bandwidth and that's the too long didn't
+lecture of what would be on path
+
+ align:start position:0%
+lecture of what would be on path
+ 
+
+ align:start position:0%
+lecture of what would be on path
+selection for
+
+ align:start position:0%
+selection for
+ 
+
+ align:start position:0%
+selection for
+issues almost no protocol is actually
+
+ align:start position:0%
+issues almost no protocol is actually
+ 
+
+ align:start position:0%
+issues almost no protocol is actually
+designed to provide anonymity like with
+
+ align:start position:0%
+designed to provide anonymity like with
+ 
+
+ align:start position:0%
+designed to provide anonymity like with
+the assum because almost every protocol
+
+ align:start position:0%
+the assum because almost every protocol
+ 
+
+ align:start position:0%
+the assum because almost every protocol
+that's widely used has the Assumption in
+
+ align:start position:0%
+that's widely used has the Assumption in
+ 
+
+ align:start position:0%
+that's widely used has the Assumption in
+it well you know anyone who wants to can
+
+ align:start position:0%
+it well you know anyone who wants to can
+ 
+
+ align:start position:0%
+it well you know anyone who wants to can
+just see the IPS on this traffic so
+
+ align:start position:0%
+just see the IPS on this traffic so
+ 
+
+ align:start position:0%
+just see the IPS on this traffic so
+there's no point in trying to conceal
+
+ align:start position:0%
+there's no point in trying to conceal
+ 
+
+ align:start position:0%
+there's no point in trying to conceal
+identity so in a particularly complex
+
+ align:start position:0%
+identity so in a particularly complex
+ 
+
+ align:start position:0%
+identity so in a particularly complex
+protocol like the whole stack of
+
+ align:start position:0%
+protocol like the whole stack of
+ 
+
+ align:start position:0%
+protocol like the whole stack of
+protocols a web browser uses there's no
+
+ align:start position:0%
+protocols a web browser uses there's no
+ 
+
+ align:start position:0%
+protocols a web browser uses there's no
+real way to anonymize that just by
+
+ align:start position:0%
+real way to anonymize that just by
+ 
+
+ align:start position:0%
+real way to anonymize that just by
+anonymizing the traffic with something
+
+ align:start position:0%
+anonymizing the traffic with something
+ 
+
+ align:start position:0%
+anonymizing the traffic with something
+like tor you need to hack the web
+
+ align:start position:0%
+like tor you need to hack the web
+ 
+
+ align:start position:0%
+like tor you need to hack the web
+browser pretty hard to make it stop
+
+ align:start position:0%
+browser pretty hard to make it stop
+ 
+
+ align:start position:0%
+browser pretty hard to make it stop
+doing things like leaking the list of
+
+ align:start position:0%
+doing things like leaking the list of
+ 
+
+ align:start position:0%
+doing things like leaking the list of
+all fonts that are identified on your
+
+ align:start position:0%
+all fonts that are identified on your
+ 
+
+ align:start position:0%
+all fonts that are identified on your
+system leaking your exact window size um
+
+ align:start position:0%
+system leaking your exact window size um
+ 
+
+ align:start position:0%
+system leaking your exact window size um
+allowing all kinds of permanent cookie
+
+ align:start position:0%
+allowing all kinds of permanent cookie
+ 
+
+ align:start position:0%
+allowing all kinds of permanent cookie
+like structures leaking what's in the
+
+ align:start position:0%
+like structures leaking what's in the
+ 
+
+ align:start position:0%
+like structures leaking what's in the
+cache and what's not in the cache and
+
+ align:start position:0%
+cache and what's not in the cache and
+ 
+
+ align:start position:0%
+cache and what's not in the cache and
+and so on so your choices there are
+
+ align:start position:0%
+and so on so your choices there are
+ 
+
+ align:start position:0%
+and so on so your choices there are
+basically isolate everything and restart
+
+ align:start position:0%
+basically isolate everything and restart
+ 
+
+ align:start position:0%
+basically isolate everything and restart
+from a fresh VM all the time or rewrite
+
+ align:start position:0%
+from a fresh VM all the time or rewrite
+ 
+
+ align:start position:0%
+from a fresh VM all the time or rewrite
+the browser or both other things are a
+
+ align:start position:0%
+the browser or both other things are a
+ 
+
+ align:start position:0%
+the browser or both other things are a
+lot easier than web browsers but still
+
+ align:start position:0%
+lot easier than web browsers but still
+ 
+
+ align:start position:0%
+lot easier than web browsers but still
+problematic that's all I'm going to say
+
+ align:start position:0%
+problematic that's all I'm going to say
+ 
+
+ align:start position:0%
+problematic that's all I'm going to say
+about app
+
+ align:start position:0%
+about app
+ 
+
+ align:start position:0%
+about app
+issues let's see I think I got the most
+
+ align:start position:0%
+issues let's see I think I got the most
+ 
+
+ align:start position:0%
+issues let's see I think I got the most
+hands did you see what I got the most
+
+ align:start position:0%
+hands did you see what I got the most
+ 
+
+ align:start position:0%
+hands did you see what I got the most
+hands for any opinions abuse and hidden
+
+ align:start position:0%
+hands for any opinions abuse and hidden
+ 
+
+ align:start position:0%
+hands for any opinions abuse and hidden
+Services abuse and hidden Services all
+
+ align:start position:0%
+Services abuse and hidden Services all
+ 
+
+ align:start position:0%
+Services abuse and hidden Services all
+right um I'll talk about abuse hidden
+
+ align:start position:0%
+right um I'll talk about abuse hidden
+ 
+
+ align:start position:0%
+right um I'll talk about abuse hidden
+services and if I've still got time I'll
+
+ align:start position:0%
+services and if I've still got time I'll
+ 
+
+ align:start position:0%
+services and if I've still got time I'll
+do censorship and attacks um so let's go
+
+ align:start position:0%
+do censorship and attacks um so let's go
+ 
+
+ align:start position:0%
+do censorship and attacks um so let's go
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+abuse abuse abuse
+
+ align:start position:0%
+abuse abuse abuse
+ 
+
+ align:start position:0%
+abuse abuse abuse
+abuse um so one problem that
+
+ align:start position:0%
+abuse um so one problem that
+ 
+
+ align:start position:0%
+abuse um so one problem that
+we've fortunately not had all that much
+
+ align:start position:0%
+we've fortunately not had all that much
+ 
+
+ align:start position:0%
+we've fortunately not had all that much
+of so when we were working on this stuff
+
+ align:start position:0%
+of so when we were working on this stuff
+ 
+
+ align:start position:0%
+of so when we were working on this stuff
+the problem that everybody was afraid of
+
+ align:start position:0%
+the problem that everybody was afraid of
+ 
+
+ align:start position:0%
+the problem that everybody was afraid of
+was this horrible stuff that would get
+
+ align:start position:0%
+was this horrible stuff that would get
+ 
+
+ align:start position:0%
+was this horrible stuff that would get
+you kicked off of any ISP and that would
+
+ align:start position:0%
+you kicked off of any ISP and that would
+ 
+
+ align:start position:0%
+you kicked off of any ISP and that would
+create tremendous legal issues in ruing
+
+ align:start position:0%
+create tremendous legal issues in ruing
+ 
+
+ align:start position:0%
+create tremendous legal issues in ruing
+your lives I speak of course of file
+
+ align:start position:0%
+your lives I speak of course of file
+ 
+
+ align:start position:0%
+your lives I speak of course of file
+sharing um we were terrified that people
+
+ align:start position:0%
+sharing um we were terrified that people
+ 
+
+ align:start position:0%
+sharing um we were terrified that people
+would try to bit torrent or Nutella or
+
+ align:start position:0%
+would try to bit torrent or Nutella or
+ 
+
+ align:start position:0%
+would try to bit torrent or Nutella or
+whatever over this thing yes it was a
+
+ align:start position:0%
+whatever over this thing yes it was a
+ 
+
+ align:start position:0%
+whatever over this thing yes it was a
+long time ago and you know we thought
+
+ align:start position:0%
+long time ago and you know we thought
+ 
+
+ align:start position:0%
+long time ago and you know we thought
+about how we can do that well you'll see
+
+ align:start position:0%
+about how we can do that well you'll see
+ 
+
+ align:start position:0%
+about how we can do that well you'll see
+in the paper that we talk a lot about
+
+ align:start position:0%
+in the paper that we talk a lot about
+ 
+
+ align:start position:0%
+in the paper that we talk a lot about
+exit policies about letting exit nodes
+
+ align:start position:0%
+exit policies about letting exit nodes
+ 
+
+ align:start position:0%
+exit policies about letting exit nodes
+say I only allow connections to Port 80
+
+ align:start position:0%
+say I only allow connections to Port 80
+ 
+
+ align:start position:0%
+say I only allow connections to Port 80
+and Port
+
+ align:start position:0%
+and Port
+ 
+
+ align:start position:0%
+and Port
+443 um this doesn't actually help with
+
+ align:start position:0%
+443 um this doesn't actually help with
+ 
+
+ align:start position:0%
+443 um this doesn't actually help with
+abuse at all because
+
+ align:start position:0%
+abuse at all because
+ 
+
+ align:start position:0%
+abuse at all because
+anything because you can
+
+ align:start position:0%
+anything because you can
+ 
+
+ align:start position:0%
+anything because you can
+um you can try to spread um worms over
+
+ align:start position:0%
+um you can try to spread um worms over
+ 
+
+ align:start position:0%
+um you can try to spread um worms over
+Port 80 you
+
+ align:start position:0%
+Port 80 you
+ 
+
+ align:start position:0%
+Port 80 you
+can um post abusive stuff to IRC
+
+ align:start position:0%
+can um post abusive stuff to IRC
+ 
+
+ align:start position:0%
+can um post abusive stuff to IRC
+channels over web to IRC interfaces
+
+ align:start position:0%
+channels over web to IRC interfaces
+ 
+
+ align:start position:0%
+channels over web to IRC interfaces
+everything's got a web interface these
+
+ align:start position:0%
+everything's got a web interface these
+ 
+
+ align:start position:0%
+everything's got a web interface these
+days so you can't really say it's only
+
+ align:start position:0%
+days so you can't really say it's only
+ 
+
+ align:start position:0%
+days so you can't really say it's only
+web it's safe if it's useful it can be
+
+ align:start position:0%
+web it's safe if it's useful it can be
+ 
+
+ align:start position:0%
+web it's safe if it's useful it can be
+abused that said there are people who
+
+ align:start position:0%
+abused that said there are people who
+ 
+
+ align:start position:0%
+abused that said there are people who
+are willing to run exits that deliver 80
+
+ align:start position:0%
+are willing to run exits that deliver 80
+ 
+
+ align:start position:0%
+are willing to run exits that deliver 80
+and 443 who would not be willing to run
+
+ align:start position:0%
+and 443 who would not be willing to run
+ 
+
+ align:start position:0%
+and 443 who would not be willing to run
+exits delivering all ports so that did
+
+ align:start position:0%
+exits delivering all ports so that did
+ 
+
+ align:start position:0%
+exits delivering all ports so that did
+turn out to be useful just didn't turn
+
+ align:start position:0%
+turn out to be useful just didn't turn
+ 
+
+ align:start position:0%
+turn out to be useful just didn't turn
+out to be a
+
+ align:start position:0%
+out to be a
+ 
+
+ align:start position:0%
+out to be a
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+um another thing that creates problems
+
+ align:start position:0%
+um another thing that creates problems
+ 
+
+ align:start position:0%
+um another thing that creates problems
+it is um let's see criminal activity
+
+ align:start position:0%
+it is um let's see criminal activity
+ 
+
+ align:start position:0%
+it is um let's see criminal activity
+generally doesn't create problems for
+
+ align:start position:0%
+generally doesn't create problems for
+ 
+
+ align:start position:0%
+generally doesn't create problems for
+the network operators so much from time
+
+ align:start position:0%
+the network operators so much from time
+ 
+
+ align:start position:0%
+the network operators so much from time
+to time somebody's server gets seized
+
+ align:start position:0%
+to time somebody's server gets seized
+ 
+
+ align:start position:0%
+to time somebody's server gets seized
+and returns 6 months later and they have
+
+ align:start position:0%
+and returns 6 months later and they have
+ 
+
+ align:start position:0%
+and returns 6 months later and they have
+to wipe the thing that's still an
+
+ align:start position:0%
+to wipe the thing that's still an
+ 
+
+ align:start position:0%
+to wipe the thing that's still an
+infrequent enough occurrence that um
+
+ align:start position:0%
+infrequent enough occurrence that um
+ 
+
+ align:start position:0%
+infrequent enough occurrence that um
+it's somewhat surprising when it
+
+ align:start position:0%
+it's somewhat surprising when it
+ 
+
+ align:start position:0%
+it's somewhat surprising when it
+happens and so yeah don't don't run an
+
+ align:start position:0%
+happens and so yeah don't don't run an
+ 
+
+ align:start position:0%
+happens and so yeah don't don't run an
+exit node on a server that you need to
+
+ align:start position:0%
+exit node on a server that you need to
+ 
+
+ align:start position:0%
+exit node on a server that you need to
+graduate
+
+ align:start position:0%
+graduate
+ 
+
+ align:start position:0%
+graduate
+um what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the biggest problem that we have for
+
+ align:start position:0%
+uh the biggest problem that we have for
+ 
+
+ align:start position:0%
+uh the biggest problem that we have for
+abusive stuff is that many websites
+
+ align:start position:0%
+abusive stuff is that many websites
+ 
+
+ align:start position:0%
+abusive stuff is that many websites
+around the world and many IRC servers
+
+ align:start position:0%
+around the world and many IRC servers
+ 
+
+ align:start position:0%
+around the world and many IRC servers
+and so on use IP based blocking in order
+
+ align:start position:0%
+and so on use IP based blocking in order
+ 
+
+ align:start position:0%
+and so on use IP based blocking in order
+to deter and mitigate abusive Behavior
+
+ align:start position:0%
+to deter and mitigate abusive Behavior
+ 
+
+ align:start position:0%
+to deter and mitigate abusive Behavior
+people people
+
+ align:start position:0%
+people people
+ 
+
+ align:start position:0%
+people people
+posting
+
+ align:start position:0%
+posting
+ 
+
+ align:start position:0%
+posting
+um people picture posting roadkill
+
+ align:start position:0%
+um people picture posting roadkill
+ 
+
+ align:start position:0%
+um people picture posting roadkill
+pictures on My Little Pony sites
+
+ align:start position:0%
+pictures on My Little Pony sites
+ 
+
+ align:start position:0%
+pictures on My Little Pony sites
+people flaming everybody on IRC
+
+ align:start position:0%
+people flaming everybody on IRC
+ 
+
+ align:start position:0%
+people flaming everybody on IRC
+channels people making a lot of leave
+
+ align:start position:0%
+channels people making a lot of leave
+ 
+
+ align:start position:0%
+channels people making a lot of leave
+join
+
+ align:start position:0%
+join
+ 
+
+ align:start position:0%
+join
+requests so um people replacing entire
+
+ align:start position:0%
+requests so um people replacing entire
+ 
+
+ align:start position:0%
+requests so um people replacing entire
+Wikipedia pages with um racial slurs
+
+ align:start position:0%
+Wikipedia pages with um racial slurs
+ 
+
+ align:start position:0%
+Wikipedia pages with um racial slurs
+this stuff is real it is problematic
+
+ align:start position:0%
+this stuff is real it is problematic
+ 
+
+ align:start position:0%
+this stuff is real it is problematic
+it's unacceptable to the websites and
+
+ align:start position:0%
+it's unacceptable to the websites and
+ 
+
+ align:start position:0%
+it's unacceptable to the websites and
+services that use IP based blocking um
+
+ align:start position:0%
+services that use IP based blocking um
+ 
+
+ align:start position:0%
+services that use IP based blocking um
+they need a way to keep this from
+
+ align:start position:0%
+they need a way to keep this from
+ 
+
+ align:start position:0%
+they need a way to keep this from
+happening and IP based blocking is a
+
+ align:start position:0%
+happening and IP based blocking is a
+ 
+
+ align:start position:0%
+happening and IP based blocking is a
+cheap way for them to do that so it's
+
+ align:start position:0%
+cheap way for them to do that so it's
+ 
+
+ align:start position:0%
+cheap way for them to do that so it's
+pretty frequent that Tor gets banned
+
+ align:start position:0%
+pretty frequent that Tor gets banned
+ 
+
+ align:start position:0%
+pretty frequent that Tor gets banned
+completely the T users get banned
+
+ align:start position:0%
+completely the T users get banned
+ 
+
+ align:start position:0%
+completely the T users get banned
+completely from some
+
+ align:start position:0%
+completely from some
+ 
+
+ align:start position:0%
+completely from some
+sites this is there's some work on
+
+ align:start position:0%
+sites this is there's some work on
+ 
+
+ align:start position:0%
+sites this is there's some work on
+trying to say
+
+ align:start position:0%
+trying to say
+ 
+
+ align:start position:0%
+trying to say
+well what's why does IP based blocking
+
+ align:start position:0%
+well what's why does IP based blocking
+ 
+
+ align:start position:0%
+well what's why does IP based blocking
+really work is it because IP based block
+
+ align:start position:0%
+really work is it because IP based block
+ 
+
+ align:start position:0%
+really work is it because IP based block
+is it because IPS are people no
+
+ align:start position:0%
+is it because IPS are people no
+ 
+
+ align:start position:0%
+is it because IPS are people no
+everybody in this room knows how to get
+
+ align:start position:0%
+everybody in this room knows how to get
+ 
+
+ align:start position:0%
+everybody in this room knows how to get
+a different IP if they need one
+
+ align:start position:0%
+a different IP if they need one
+ 
+
+ align:start position:0%
+a different IP if they need one
+everybody in this room knows how to get
+
+ align:start position:0%
+everybody in this room knows how to get
+ 
+
+ align:start position:0%
+everybody in this room knows how to get
+like um tens of thousands of different
+
+ align:start position:0%
+like um tens of thousands of different
+ 
+
+ align:start position:0%
+like um tens of thousands of different
+IPS if they need one if they need tens
+
+ align:start position:0%
+IPS if they need one if they need tens
+ 
+
+ align:start position:0%
+IPS if they need one if they need tens
+of thousands but for most people getting
+
+ align:start position:0%
+of thousands but for most people getting
+ 
+
+ align:start position:0%
+of thousands but for most people getting
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+IPS is at least a little time consuming
+
+ align:start position:0%
+IPS is at least a little time consuming
+ 
+
+ align:start position:0%
+IPS is at least a little time consuming
+and at least a little challenging to the
+
+ align:start position:0%
+and at least a little challenging to the
+ 
+
+ align:start position:0%
+and at least a little challenging to the
+extent that it imposes a rate limit and
+
+ align:start position:0%
+extent that it imposes a rate limit and
+ 
+
+ align:start position:0%
+extent that it imposes a rate limit and
+a resource cost on abuse if you don't
+
+ align:start position:0%
+a resource cost on abuse if you don't
+ 
+
+ align:start position:0%
+a resource cost on abuse if you don't
+own a botn net and if they've already
+
+ align:start position:0%
+own a botn net and if they've already
+ 
+
+ align:start position:0%
+own a botn net and if they've already
+blocked T and all the other proxy
+
+ align:start position:0%
+blocked T and all the other proxy
+ 
+
+ align:start position:0%
+blocked T and all the other proxy
+services so for that you need to look at
+
+ align:start position:0%
+services so for that you need to look at
+ 
+
+ align:start position:0%
+services so for that you need to look at
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+ways um to provide other resource costs
+
+ align:start position:0%
+ways um to provide other resource costs
+ 
+
+ align:start position:0%
+ways um to provide other resource costs
+you can either say well you use have you
+
+ align:start position:0%
+you can either say well you use have you
+ 
+
+ align:start position:0%
+you can either say well you use have you
+done blind
+
+ align:start position:0%
+done blind
+ 
+
+ align:start position:0%
+done blind
+signatures okay you can construct things
+
+ align:start position:0%
+signatures okay you can construct things
+ 
+
+ align:start position:0%
+signatures okay you can construct things
+so that you need an IP to make an
+
+ align:start position:0%
+so that you need an IP to make an
+ 
+
+ align:start position:0%
+so that you need an IP to make an
+account but what account you make with
+
+ align:start position:0%
+account but what account you make with
+ 
+
+ align:start position:0%
+account but what account you make with
+an IP is not linkable to your IP and
+
+ align:start position:0%
+an IP is not linkable to your IP and
+ 
+
+ align:start position:0%
+an IP is not linkable to your IP and
+then later on if the account gets banned
+
+ align:start position:0%
+then later on if the account gets banned
+ 
+
+ align:start position:0%
+then later on if the account gets banned
+you need to create a new account from a
+
+ align:start position:0%
+you need to create a new account from a
+ 
+
+ align:start position:0%
+you need to create a new account from a
+different IP that's something you can
+
+ align:start position:0%
+different IP that's something you can
+ 
+
+ align:start position:0%
+different IP that's something you can
+build and we're working with people to
+
+ align:start position:0%
+build and we're working with people to
+ 
+
+ align:start position:0%
+build and we're working with people to
+work on it there's also although it
+
+ align:start position:0%
+work on it there's also although it
+ 
+
+ align:start position:0%
+work on it there's also although it
+needs more hacking on the integration
+
+ align:start position:0%
+needs more hacking on the integration
+ 
+
+ align:start position:0%
+needs more hacking on the integration
+side something also needs more hacking
+
+ align:start position:0%
+side something also needs more hacking
+ 
+
+ align:start position:0%
+side something also needs more hacking
+on the integration side is anonymous
+
+ align:start position:0%
+on the integration side is anonymous
+ 
+
+ align:start position:0%
+on the integration side is anonymous
+black listable credentials they're a
+
+ align:start position:0%
+black listable credentials they're a
+ 
+
+ align:start position:0%
+black listable credentials they're a
+little esoteric but the idea is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that you get something that allows
+
+ align:start position:0%
+um that you get something that allows
+ 
+
+ align:start position:0%
+um that you get something that allows
+you to participate on an IRC server for
+
+ align:start position:0%
+you to participate on an IRC server for
+ 
+
+ align:start position:0%
+you to participate on an IRC server for
+example you can use this as many times
+
+ align:start position:0%
+example you can use this as many times
+ 
+
+ align:start position:0%
+example you can use this as many times
+as you want your using it is not
+
+ align:start position:0%
+as you want your using it is not
+ 
+
+ align:start position:0%
+as you want your using it is not
+linkable until you are banned once you
+
+ align:start position:0%
+linkable until you are banned once you
+ 
+
+ align:start position:0%
+linkable until you are banned once you
+are banned future attempts from the same
+
+ align:start position:0%
+are banned future attempts from the same
+ 
+
+ align:start position:0%
+are banned future attempts from the same
+person with the same credential don't
+
+ align:start position:0%
+person with the same credential don't
+ 
+
+ align:start position:0%
+person with the same credential don't
+work but past activities do not become
+
+ align:start position:0%
+work but past activities do not become
+ 
+
+ align:start position:0%
+work but past activities do not become
+linkable to one
+
+ align:start position:0%
+linkable to one
+ 
+
+ align:start position:0%
+linkable to one
+another these can be built pretty easily
+
+ align:start position:0%
+another these can be built pretty easily
+ 
+
+ align:start position:0%
+another these can be built pretty easily
+they the problem is convincing people
+
+ align:start position:0%
+they the problem is convincing people
+ 
+
+ align:start position:0%
+they the problem is convincing people
+who are more or less satisfied with IP
+
+ align:start position:0%
+who are more or less satisfied with IP
+ 
+
+ align:start position:0%
+who are more or less satisfied with IP
+blocking to actually use them and
+
+ align:start position:0%
+blocking to actually use them and
+ 
+
+ align:start position:0%
+blocking to actually use them and
+actually integrating them with
+
+ align:start position:0%
+actually integrating them with
+ 
+
+ align:start position:0%
+actually integrating them with
+Services uh let's see someone inevitably
+
+ align:start position:0%
+Services uh let's see someone inevitably
+ 
+
+ align:start position:0%
+Services uh let's see someone inevitably
+asks me it's kind of neat um so I I
+
+ align:start position:0%
+asks me it's kind of neat um so I I
+ 
+
+ align:start position:0%
+asks me it's kind of neat um so I I
+started these lectur notes based on my
+
+ align:start position:0%
+started these lectur notes based on my
+ 
+
+ align:start position:0%
+started these lectur notes based on my
+lecture from um
+
+ align:start position:0%
+lecture from um
+ 
+
+ align:start position:0%
+lecture from um
+2013 and there was something about the
+
+ align:start position:0%
+2013 and there was something about the
+ 
+
+ align:start position:0%
+2013 and there was something about the
+inevitable question about Silk Road one
+
+ align:start position:0%
+inevitable question about Silk Road one
+ 
+
+ align:start position:0%
+inevitable question about Silk Road one
+getting busted there's the inevitable
+
+ align:start position:0%
+getting busted there's the inevitable
+ 
+
+ align:start position:0%
+getting busted there's the inevitable
+question about Silk Road 2 getting
+
+ align:start position:0%
+question about Silk Road 2 getting
+ 
+
+ align:start position:0%
+question about Silk Road 2 getting
+busted uh Silk Road 2 was a hidden
+
+ align:start position:0%
+busted uh Silk Road 2 was a hidden
+ 
+
+ align:start position:0%
+busted uh Silk Road 2 was a hidden
+service operating on the tour network uh
+
+ align:start position:0%
+service operating on the tour network uh
+ 
+
+ align:start position:0%
+service operating on the tour network uh
+where people would get together to buy
+
+ align:start position:0%
+where people would get together to buy
+ 
+
+ align:start position:0%
+where people would get together to buy
+and sell illegal things mostly illegal
+
+ align:start position:0%
+and sell illegal things mostly illegal
+ 
+
+ align:start position:0%
+and sell illegal things mostly illegal
+drugs um so as far as we know as far as
+
+ align:start position:0%
+drugs um so as far as we know as far as
+ 
+
+ align:start position:0%
+drugs um so as far as we know as far as
+we can find out the guy got busted
+
+ align:start position:0%
+we can find out the guy got busted
+ 
+
+ align:start position:0%
+we can find out the guy got busted
+through bad UPAC like he made a public
+
+ align:start position:0%
+through bad UPAC like he made a public
+ 
+
+ align:start position:0%
+through bad UPAC like he made a public
+posting with his actual name and then
+
+ align:start position:0%
+posting with his actual name and then
+ 
+
+ align:start position:0%
+posting with his actual name and then
+like went and deleted it and put his his
+
+ align:start position:0%
+like went and deleted it and put his his
+ 
+
+ align:start position:0%
+like went and deleted it and put his his
+pseudonym on it tor can't help people
+
+ align:start position:0%
+pseudonym on it tor can't help people
+ 
+
+ align:start position:0%
+pseudonym on it tor can't help people
+against that kind of stuff on the other
+
+ align:start position:0%
+against that kind of stuff on the other
+ 
+
+ align:start position:0%
+against that kind of stuff on the other
+hand if you've been looking at the NSA
+
+ align:start position:0%
+hand if you've been looking at the NSA
+ 
+
+ align:start position:0%
+hand if you've been looking at the NSA
+leaks you know that law enforcement has
+
+ align:start position:0%
+leaks you know that law enforcement has
+ 
+
+ align:start position:0%
+leaks you know that law enforcement has
+been getting information from
+
+ align:start position:0%
+been getting information from
+ 
+
+ align:start position:0%
+been getting information from
+intelligence and then sanitizing it
+
+ align:start position:0%
+intelligence and then sanitizing it
+ 
+
+ align:start position:0%
+intelligence and then sanitizing it
+through a process called um dual
+
+ align:start position:0%
+through a process called um dual
+ 
+
+ align:start position:0%
+through a process called um dual
+construction where the intelligence
+
+ align:start position:0%
+construction where the intelligence
+ 
+
+ align:start position:0%
+construction where the intelligence
+agency will say to the law enforcement
+
+ align:start position:0%
+agency will say to the law enforcement
+ 
+
+ align:start position:0%
+agency will say to the law enforcement
+agency okay look it's Fred over there he
+
+ align:start position:0%
+agency okay look it's Fred over there he
+ 
+
+ align:start position:0%
+agency okay look it's Fred over there he
+did it but that's not admissible in a
+
+ align:start position:0%
+did it but that's not admissible in a
+ 
+
+ align:start position:0%
+did it but that's not admissible in a
+court and you can never admit that we
+
+ align:start position:0%
+court and you can never admit that we
+ 
+
+ align:start position:0%
+court and you can never admit that we
+told you just find some other way to
+
+ align:start position:0%
+told you just find some other way to
+ 
+
+ align:start position:0%
+told you just find some other way to
+find out that Fred did it but Fred did
+
+ align:start position:0%
+find out that Fred did it but Fred did
+ 
+
+ align:start position:0%
+find out that Fred did it but Fred did
+it um According to some of the Snowden
+
+ align:start position:0%
+it um According to some of the Snowden
+ 
+
+ align:start position:0%
+it um According to some of the Snowden
+leaks and some of the leaks from the
+
+ align:start position:0%
+leaks and some of the leaks from the
+ 
+
+ align:start position:0%
+leaks and some of the leaks from the
+other guy who is still not been caught
+
+ align:start position:0%
+other guy who is still not been caught
+ 
+
+ align:start position:0%
+other guy who is still not been caught
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that's done sometimes so if you look at
+
+ align:start position:0%
+that's done sometimes so if you look at
+ 
+
+ align:start position:0%
+that's done sometimes so if you look at
+um so okay at this point you use your
+
+ align:start position:0%
+um so okay at this point you use your
+ 
+
+ align:start position:0%
+um so okay at this point you use your
+basic basian reasoning skills and you
+
+ align:start position:0%
+basic basian reasoning skills and you
+ 
+
+ align:start position:0%
+basic basian reasoning skills and you
+say well okay would I see this evidence
+
+ align:start position:0%
+say well okay would I see this evidence
+ 
+
+ align:start position:0%
+say well okay would I see this evidence
+if the guy actually got caught because
+
+ align:start position:0%
+if the guy actually got caught because
+ 
+
+ align:start position:0%
+if the guy actually got caught because
+of bad opsac yes I would I would see
+
+ align:start position:0%
+of bad opsac yes I would I would see
+ 
+
+ align:start position:0%
+of bad opsac yes I would I would see
+plenty of I would see bad obsc I would
+
+ align:start position:0%
+plenty of I would see bad obsc I would
+ 
+
+ align:start position:0%
+plenty of I would see bad obsc I would
+see reports that he got caught because
+
+ align:start position:0%
+see reports that he got caught because
+ 
+
+ align:start position:0%
+see reports that he got caught because
+bad obac but what would I see if it were
+
+ align:start position:0%
+bad obac but what would I see if it were
+ 
+
+ align:start position:0%
+bad obac but what would I see if it were
+a dual construction case I would also
+
+ align:start position:0%
+a dual construction case I would also
+ 
+
+ align:start position:0%
+a dual construction case I would also
+see reports that the guy caught by got
+
+ align:start position:0%
+see reports that the guy caught by got
+ 
+
+ align:start position:0%
+see reports that the guy caught by got
+caught by bad
+
+ align:start position:0%
+caught by bad
+ 
+
+ align:start position:0%
+caught by bad
+OPC because the evidence would be that
+
+ align:start position:0%
+OPC because the evidence would be that
+ 
+
+ align:start position:0%
+OPC because the evidence would be that
+we would be available to us is the same
+
+ align:start position:0%
+we would be available to us is the same
+ 
+
+ align:start position:0%
+we would be available to us is the same
+in either case we can't really conclude
+
+ align:start position:0%
+in either case we can't really conclude
+ 
+
+ align:start position:0%
+in either case we can't really conclude
+much from any public reports of that
+
+ align:start position:0%
+much from any public reports of that
+ 
+
+ align:start position:0%
+much from any public reports of that
+that said it does look like the guy got
+
+ align:start position:0%
+that said it does look like the guy got
+ 
+
+ align:start position:0%
+that said it does look like the guy got
+busted by bad opsac it does look like
+
+ align:start position:0%
+busted by bad opsac it does look like
+ 
+
+ align:start position:0%
+busted by bad opsac it does look like
+the kind of bad opsac that you would be
+
+ align:start position:0%
+the kind of bad opsac that you would be
+ 
+
+ align:start position:0%
+the kind of bad opsac that you would be
+looking for if you were trying to catch
+
+ align:start position:0%
+looking for if you were trying to catch
+ 
+
+ align:start position:0%
+looking for if you were trying to catch
+somebody running something like this
+
+ align:start position:0%
+somebody running something like this
+ 
+
+ align:start position:0%
+somebody running something like this
+nevertheless earlier I suggested that
+
+ align:start position:0%
+nevertheless earlier I suggested that
+ 
+
+ align:start position:0%
+nevertheless earlier I suggested that
+nobody please do not use my software to
+
+ align:start position:0%
+nobody please do not use my software to
+ 
+
+ align:start position:0%
+nobody please do not use my software to
+break any laws um also if your life or
+
+ align:start position:0%
+break any laws um also if your life or
+ 
+
+ align:start position:0%
+break any laws um also if your life or
+freedom is at stake from using uh tour
+
+ align:start position:0%
+freedom is at stake from using uh tour
+ 
+
+ align:start position:0%
+freedom is at stake from using uh tour
+or any security
+
+ align:start position:0%
+or any security
+ 
+
+ align:start position:0%
+or any security
+product think do not use that product in
+
+ align:start position:0%
+product think do not use that product in
+ 
+
+ align:start position:0%
+product think do not use that product in
+isolation think of ways to use it to
+
+ align:start position:0%
+isolation think of ways to use it to
+ 
+
+ align:start position:0%
+isolation think of ways to use it to
+construct a series of
+
+ align:start position:0%
+construct a series of
+ 
+
+ align:start position:0%
+construct a series of
+redundant um defenses for yourself if
+
+ align:start position:0%
+redundant um defenses for yourself if
+ 
+
+ align:start position:0%
+redundant um defenses for yourself if
+your if your life or freedom is at stake
+
+ align:start position:0%
+your if your life or freedom is at stake
+ 
+
+ align:start position:0%
+your if your life or freedom is at stake
+or if having the system broken is is
+
+ align:start position:0%
+or if having the system broken is is
+ 
+
+ align:start position:0%
+or if having the system broken is is
+completely unacceptable to you and I'll
+
+ align:start position:0%
+completely unacceptable to you and I'll
+ 
+
+ align:start position:0%
+completely unacceptable to you and I'll
+say that about T and I'll say that about
+
+ align:start position:0%
+say that about T and I'll say that about
+ 
+
+ align:start position:0%
+say that about T and I'll say that about
+TLS and I'll say that about
+
+ align:start position:0%
+TLS and I'll say that about
+ 
+
+ align:start position:0%
+TLS and I'll say that about
+pgp um software is a work in
+
+ align:start position:0%
+pgp um software is a work in
+ 
+
+ align:start position:0%
+pgp um software is a work in
+progress all right so that's the abuse
+
+ align:start position:0%
+progress all right so that's the abuse
+ 
+
+ align:start position:0%
+progress all right so that's the abuse
+section I've got 25
+
+ align:start position:0%
+section I've got 25
+ 
+
+ align:start position:0%
+section I've got 25
+minutes um hidden
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Services where's hidden Services um so
+
+ align:start position:0%
+Services where's hidden Services um so
+ 
+
+ align:start position:0%
+Services where's hidden Services um so
+responder anonymity is a much harder
+
+ align:start position:0%
+responder anonymity is a much harder
+ 
+
+ align:start position:0%
+responder anonymity is a much harder
+problem than initiator anonymity
+
+ align:start position:0%
+problem than initiator anonymity
+ 
+
+ align:start position:0%
+problem than initiator anonymity
+initiator anonymity is what you get when
+
+ align:start position:0%
+initiator anonymity is what you get when
+ 
+
+ align:start position:0%
+initiator anonymity is what you get when
+Ellis wants to buy socks and Ellis wants
+
+ align:start position:0%
+Ellis wants to buy socks and Ellis wants
+ 
+
+ align:start position:0%
+Ellis wants to buy socks and Ellis wants
+to stay Anonymous from the sock vendor
+
+ align:start position:0%
+to stay Anonymous from the sock vendor
+ 
+
+ align:start position:0%
+to stay Anonymous from the sock vendor
+responder anonymity is when Ellis wants
+
+ align:start position:0%
+responder anonymity is when Ellis wants
+ 
+
+ align:start position:0%
+responder anonymity is when Ellis wants
+to publish her poetry online and run a
+
+ align:start position:0%
+to publish her poetry online and run a
+ 
+
+ align:start position:0%
+to publish her poetry online and run a
+web server that has her poetry on it but
+
+ align:start position:0%
+web server that has her poetry on it but
+ 
+
+ align:start position:0%
+web server that has her poetry on it but
+not let anyone know where that web
+
+ align:start position:0%
+not let anyone know where that web
+ 
+
+ align:start position:0%
+not let anyone know where that web
+server is because the Poetry is so
+
+ align:start position:0%
+server is because the Poetry is so
+ 
+
+ align:start position:0%
+server is because the Poetry is so
+embarrassing um and yes there actually
+
+ align:start position:0%
+embarrassing um and yes there actually
+ 
+
+ align:start position:0%
+embarrassing um and yes there actually
+is a hidden service out there of mine
+
+ align:start position:0%
+is a hidden service out there of mine
+ 
+
+ align:start position:0%
+is a hidden service out there of mine
+with bad poetry on it no I don't think
+
+ align:start position:0%
+with bad poetry on it no I don't think
+ 
+
+ align:start position:0%
+with bad poetry on it no I don't think
+anybody's actually published it yet no
+
+ align:start position:0%
+anybody's actually published it yet no
+ 
+
+ align:start position:0%
+anybody's actually published it yet no
+I'm not going to tell anybody where it
+
+ align:start position:0%
+I'm not going to tell anybody where it
+ 
+
+ align:start position:0%
+I'm not going to tell anybody where it
+is I'm waiting for it to go
+
+ align:start position:0%
+is I'm waiting for it to go
+ 
+
+ align:start position:0%
+is I'm waiting for it to go
+public uh let's see
+
+ align:start position:0%
+public uh let's see
+ 
+
+ align:start position:0%
+public uh let's see
+so all right one thing you could do
+
+ align:start position:0%
+so all right one thing you could do
+ 
+
+ align:start position:0%
+so all right one thing you could do
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um so let's see how much time okay I can
+
+ align:start position:0%
+um so let's see how much time okay I can
+ 
+
+ align:start position:0%
+um so let's see how much time okay I can
+do this
+
+ align:start position:0%
+do this
+ 
+
+ align:start position:0%
+do this
+um so um now Ellis wants to publish her
+
+ align:start position:0%
+um so um now Ellis wants to publish her
+ 
+
+ align:start position:0%
+um so um now Ellis wants to publish her
+poetry so I'm going to put Ellis on this
+
+ align:start position:0%
+poetry so I'm going to put Ellis on this
+ 
+
+ align:start position:0%
+poetry so I'm going to put Ellis on this
+end because she's the responder Ellis
+
+ align:start position:0%
+end because she's the responder Ellis
+ 
+
+ align:start position:0%
+end because she's the responder Ellis
+could build a path this represents a lot
+
+ align:start position:0%
+could build a path this represents a lot
+ 
+
+ align:start position:0%
+could build a path this represents a lot
+of relays through the tour Network and
+
+ align:start position:0%
+of relays through the tour Network and
+ 
+
+ align:start position:0%
+of relays through the tour Network and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+just say say to this Relay please accept
+
+ align:start position:0%
+just say say to this Relay please accept
+ 
+
+ align:start position:0%
+just say say to this Relay please accept
+connections you so now anyone who goes
+
+ align:start position:0%
+connections you so now anyone who goes
+ 
+
+ align:start position:0%
+connections you so now anyone who goes
+to this relay could say hey I want to
+
+ align:start position:0%
+to this relay could say hey I want to
+ 
+
+ align:start position:0%
+to this relay could say hey I want to
+talk to Alice and there have been
+
+ align:start position:0%
+talk to Alice and there have been
+ 
+
+ align:start position:0%
+talk to Alice and there have been
+designs that worked this way it has some
+
+ align:start position:0%
+designs that worked this way it has some
+ 
+
+ align:start position:0%
+designs that worked this way it has some
+challenges though One Challenge is this
+
+ align:start position:0%
+challenges though One Challenge is this
+ 
+
+ align:start position:0%
+challenges though One Challenge is this
+relay could man in the middle all the
+
+ align:start position:0%
+relay could man in the middle all the
+ 
+
+ align:start position:0%
+relay could man in the middle all the
+traffic unless there's a well-known TLS
+
+ align:start position:0%
+traffic unless there's a well-known TLS
+ 
+
+ align:start position:0%
+traffic unless there's a well-known TLS
+key another thing is maybe this relay is
+
+ align:start position:0%
+key another thing is maybe this relay is
+ 
+
+ align:start position:0%
+key another thing is maybe this relay is
+even is also embarrassed by The Poetry
+
+ align:start position:0%
+even is also embarrassed by The Poetry
+ 
+
+ align:start position:0%
+even is also embarrassed by The Poetry
+and does not want to be a public contact
+
+ align:start position:0%
+and does not want to be a public contact
+ 
+
+ align:start position:0%
+and does not want to be a public contact
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+for um poetry so
+
+ align:start position:0%
+for um poetry so
+ 
+
+ align:start position:0%
+for um poetry so
+terrible so um this relay could also be
+
+ align:start position:0%
+terrible so um this relay could also be
+ 
+
+ align:start position:0%
+terrible so um this relay could also be
+pressured by other people who hate the
+
+ align:start position:0%
+pressured by other people who hate the
+ 
+
+ align:start position:0%
+pressured by other people who hate the
+Poetry to censor it this relay could
+
+ align:start position:0%
+Poetry to censor it this relay could
+ 
+
+ align:start position:0%
+Poetry to censor it this relay could
+also be makes itself an attack Target so
+
+ align:start position:0%
+also be makes itself an attack Target so
+ 
+
+ align:start position:0%
+also be makes itself an attack Target so
+you want some way where Alice can go to
+
+ align:start position:0%
+you want some way where Alice can go to
+ 
+
+ align:start position:0%
+you want some way where Alice can go to
+different relays over time and no single
+
+ align:start position:0%
+different relays over time and no single
+ 
+
+ align:start position:0%
+different relays over time and no single
+and no single relay is touching un
+
+ align:start position:0%
+and no single relay is touching un
+ 
+
+ align:start position:0%
+and no single relay is touching un
+encrypted traffic of
+
+ align:start position:0%
+encrypted traffic of
+ 
+
+ align:start position:0%
+encrypted traffic of
+alyses all right well that's doable um
+
+ align:start position:0%
+alyses all right well that's doable um
+ 
+
+ align:start position:0%
+alyses all right well that's doable um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+but once you have a lot of different
+
+ align:start position:0%
+but once you have a lot of different
+ 
+
+ align:start position:0%
+but once you have a lot of different
+relays what does Alice actually tell
+
+ align:start position:0%
+relays what does Alice actually tell
+ 
+
+ align:start position:0%
+relays what does Alice actually tell
+people it's kind of got to be a public
+
+ align:start position:0%
+people it's kind of got to be a public
+ 
+
+ align:start position:0%
+people it's kind of got to be a public
+key because if she just says relay X
+
+ align:start position:0%
+key because if she just says relay X
+ 
+
+ align:start position:0%
+key because if she just says relay X
+relay y relay Z but x y and z are
+
+ align:start position:0%
+relay y relay Z but x y and z are
+ 
+
+ align:start position:0%
+relay y relay Z but x y and z are
+changing every five minutes that's kind
+
+ align:start position:0%
+changing every five minutes that's kind
+ 
+
+ align:start position:0%
+changing every five minutes that's kind
+of challenging to know you actually got
+
+ align:start position:0%
+of challenging to know you actually got
+ 
+
+ align:start position:0%
+of challenging to know you actually got
+the right relay so let's say she tells
+
+ align:start position:0%
+the right relay so let's say she tells
+ 
+
+ align:start position:0%
+the right relay so let's say she tells
+everybody a public key and when she gets
+
+ align:start position:0%
+everybody a public key and when she gets
+ 
+
+ align:start position:0%
+everybody a public key and when she gets
+over here she says um hey this is Alice
+
+ align:start position:0%
+over here she says um hey this is Alice
+ 
+
+ align:start position:0%
+over here she says um hey this is Alice
+I'll prove it with my public key so now
+
+ align:start position:0%
+I'll prove it with my public key so now
+ 
+
+ align:start position:0%
+I'll prove it with my public key so now
+this relay knows that um
+
+ align:start position:0%
+this relay knows that um
+ 
+
+ align:start position:0%
+this relay knows that um
+public
+
+ align:start position:0%
+public
+ 
+
+ align:start position:0%
+public
+key uh Z
+
+ align:start position:0%
+key uh Z
+ 
+
+ align:start position:0%
+key uh Z
+is um is running a hidden service here
+
+ align:start position:0%
+is um is running a hidden service here
+ 
+
+ align:start position:0%
+is um is running a hidden service here
+and so if anyone else says Hey connect
+
+ align:start position:0%
+and so if anyone else says Hey connect
+ 
+
+ align:start position:0%
+and so if anyone else says Hey connect
+me to public keyz they can do a
+
+ align:start position:0%
+me to public keyz they can do a
+ 
+
+ align:start position:0%
+me to public keyz they can do a
+handshake and wind up with a shared key
+
+ align:start position:0%
+handshake and wind up with a shared key
+ 
+
+ align:start position:0%
+handshake and wind up with a shared key
+with Ellis and it's the same handshake
+
+ align:start position:0%
+with Ellis and it's the same handshake
+ 
+
+ align:start position:0%
+with Ellis and it's the same handshake
+as the tour circuit extension uses and
+
+ align:start position:0%
+as the tour circuit extension uses and
+ 
+
+ align:start position:0%
+as the tour circuit extension uses and
+now Bob can read Ellis's poetry by
+
+ align:start position:0%
+now Bob can read Ellis's poetry by
+ 
+
+ align:start position:0%
+now Bob can read Ellis's poetry by
+building another path through the tour
+
+ align:start position:0%
+building another path through the tour
+ 
+
+ align:start position:0%
+building another path through the tour
+network over here Bob has to know pkz
+
+ align:start position:0%
+network over here Bob has to know pkz
+ 
+
+ align:start position:0%
+network over here Bob has to know pkz
+and Bob can say hey connect me with PK
+
+ align:start position:0%
+and Bob can say hey connect me with PK
+ 
+
+ align:start position:0%
+and Bob can say hey connect me with PK
+send this thing that's sort of like a
+
+ align:start position:0%
+send this thing that's sort of like a
+ 
+
+ align:start position:0%
+send this thing that's sort of like a
+create cell really it's an introduced
+
+ align:start position:0%
+create cell really it's an introduced
+ 
+
+ align:start position:0%
+create cell really it's an introduced
+cell but let's forget that over to Alice
+
+ align:start position:0%
+cell but let's forget that over to Alice
+ 
+
+ align:start position:0%
+cell but let's forget that over to Alice
+they do the same handshake that you that
+
+ align:start position:0%
+they do the same handshake that you that
+ 
+
+ align:start position:0%
+they do the same handshake that you that
+relays do and now they have a shared key
+
+ align:start position:0%
+relays do and now they have a shared key
+ 
+
+ align:start position:0%
+relays do and now they have a shared key
+that they can use for end to end
+
+ align:start position:0%
+that they can use for end to end
+ 
+
+ align:start position:0%
+that they can use for end to end
+encryption well there's something I left
+
+ align:start position:0%
+encryption well there's something I left
+ 
+
+ align:start position:0%
+encryption well there's something I left
+out though which is how does Bob know
+
+ align:start position:0%
+out though which is how does Bob know
+ 
+
+ align:start position:0%
+out though which is how does Bob know
+how to go here and can we do anything
+
+ align:start position:0%
+how to go here and can we do anything
+ 
+
+ align:start position:0%
+how to go here and can we do anything
+about the fact that this relay has to
+
+ align:start position:0%
+about the fact that this relay has to
+ 
+
+ align:start position:0%
+about the fact that this relay has to
+know this public um learns this public
+
+ align:start position:0%
+know this public um learns this public
+ 
+
+ align:start position:0%
+know this public um learns this public
+Key Well we can we can add a direct some
+
+ align:start position:0%
+Key Well we can we can add a direct some
+ 
+
+ align:start position:0%
+Key Well we can we can add a direct some
+kind of directory system where Alis
+
+ align:start position:0%
+kind of directory system where Alis
+ 
+
+ align:start position:0%
+kind of directory system where Alis
+uploads a sign statement anonymously
+
+ align:start position:0%
+uploads a sign statement anonymously
+ 
+
+ align:start position:0%
+uploads a sign statement anonymously
+over T saying pkz is
+
+ align:start position:0%
+over T saying pkz is
+ 
+
+ align:start position:0%
+over T saying pkz is
+at uh relay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and then Bob says hey give me a sign
+
+ align:start position:0%
+X and then Bob says hey give me a sign
+ 
+
+ align:start position:0%
+X and then Bob says hey give me a sign
+statement to asks the directory system
+
+ align:start position:0%
+statement to asks the directory system
+ 
+
+ align:start position:0%
+statement to asks the directory system
+hey give me a signed statement about
+
+ align:start position:0%
+hey give me a signed statement about
+ 
+
+ align:start position:0%
+hey give me a signed statement about
+pkz and Bob finds out where to go and we
+
+ align:start position:0%
+pkz and Bob finds out where to go and we
+ 
+
+ align:start position:0%
+pkz and Bob finds out where to go and we
+can even do one better and have Alis
+
+ align:start position:0%
+can even do one better and have Alis
+ 
+
+ align:start position:0%
+can even do one better and have Alis
+give a different public key here so this
+
+ align:start position:0%
+give a different public key here so this
+ 
+
+ align:start position:0%
+give a different public key here so this
+can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pkw and the statement she uploads to the
+
+ align:start position:0%
+pkw and the statement she uploads to the
+ 
+
+ align:start position:0%
+pkw and the statement she uploads to the
+directory can say if you want to talk to
+
+ align:start position:0%
+directory can say if you want to talk to
+ 
+
+ align:start position:0%
+directory can say if you want to talk to
+the service with public keyz then go to
+
+ align:start position:0%
+the service with public keyz then go to
+ 
+
+ align:start position:0%
+the service with public keyz then go to
+relay X and use public key W and now um
+
+ align:start position:0%
+relay X and use public key W and now um
+ 
+
+ align:start position:0%
+relay X and use public key W and now um
+public keyz isn't published here you
+
+ align:start position:0%
+public keyz isn't published here you
+ 
+
+ align:start position:0%
+public keyz isn't published here you
+could even go one farther and encrypt
+
+ align:start position:0%
+could even go one farther and encrypt
+ 
+
+ align:start position:0%
+could even go one farther and encrypt
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+with some shared secret known to Alis
+
+ align:start position:0%
+with some shared secret known to Alis
+ 
+
+ align:start position:0%
+with some shared secret known to Alis
+and Bob and if you do that then the
+
+ align:start position:0%
+and Bob and if you do that then the
+ 
+
+ align:start position:0%
+and Bob and if you do that then the
+directory service and people who can
+
+ align:start position:0%
+directory service and people who can
+ 
+
+ align:start position:0%
+directory service and people who can
+contact the directory service can't
+
+ align:start position:0%
+contact the directory service can't
+ 
+
+ align:start position:0%
+contact the directory service can't
+learn how to connect to Alice with
+
+ align:start position:0%
+learn how to connect to Alice with
+ 
+
+ align:start position:0%
+learn how to connect to Alice with
+that that's yo just a quick question
+
+ align:start position:0%
+that that's yo just a quick question
+ 
+
+ align:start position:0%
+that that's yo just a quick question
+there um if that's not encrypted then RX
+
+ align:start position:0%
+there um if that's not encrypted then RX
+ 
+
+ align:start position:0%
+there um if that's not encrypted then RX
+can still find out that it's running a
+
+ align:start position:0%
+can still find out that it's running a
+ 
+
+ align:start position:0%
+can still find out that it's running a
+service for Alis right yeah well not for
+
+ align:start position:0%
+service for Alis right yeah well not for
+ 
+
+ align:start position:0%
+service for Alis right yeah well not for
+ell it can find out that it's running
+
+ align:start position:0%
+ell it can find out that it's running
+ 
+
+ align:start position:0%
+ell it can find out that it's running
+pkz if this is not encrypted we have a
+
+ align:start position:0%
+pkz if this is not encrypted we have a
+ 
+
+ align:start position:0%
+pkz if this is not encrypted we have a
+design for that um that I'm actually
+
+ align:start position:0%
+design for that um that I'm actually
+ 
+
+ align:start position:0%
+design for that um that I'm actually
+going to get to at the end of this but
+
+ align:start position:0%
+going to get to at the end of this but
+ 
+
+ align:start position:0%
+going to get to at the end of this but
+it's not built yet but it's pretty cool
+
+ align:start position:0%
+it's not built yet but it's pretty cool
+ 
+
+ align:start position:0%
+it's not built yet but it's pretty cool
+um so okay and for you don't want to use
+
+ align:start position:0%
+um so okay and for you don't want to use
+ 
+
+ align:start position:0%
+um so okay and for you don't want to use
+a centralized directory for this so we
+
+ align:start position:0%
+a centralized directory for this so we
+ 
+
+ align:start position:0%
+a centralized directory for this so we
+actually do use a DHT W which is you
+
+ align:start position:0%
+actually do use a DHT W which is you
+ 
+
+ align:start position:0%
+actually do use a DHT W which is you
+know again not perfect and has some
+
+ align:start position:0%
+know again not perfect and has some
+ 
+
+ align:start position:0%
+know again not perfect and has some
+censorship opportunities but we are
+
+ align:start position:0%
+censorship opportunities but we are
+ 
+
+ align:start position:0%
+censorship opportunities but we are
+trying to make those less and less and I
+
+ align:start position:0%
+trying to make those less and less and I
+ 
+
+ align:start position:0%
+trying to make those less and less and I
+want to cover more stuff so I can't do
+
+ align:start position:0%
+want to cover more stuff so I can't do
+ 
+
+ align:start position:0%
+want to cover more stuff so I can't do
+the whole details
+
+ align:start position:0%
+the whole details
+ 
+
+ align:start position:0%
+the whole details
+uh so one of the problems there though
+
+ align:start position:0%
+uh so one of the problems there though
+ 
+
+ align:start position:0%
+uh so one of the problems there though
+is if you you are running one of these
+
+ align:start position:0%
+is if you you are running one of these
+ 
+
+ align:start position:0%
+is if you you are running one of these
+directory Services you get a complete
+
+ align:start position:0%
+directory Services you get a complete
+ 
+
+ align:start position:0%
+directory Services you get a complete
+list of these Keys
+
+ align:start position:0%
+list of these Keys
+ 
+
+ align:start position:0%
+list of these Keys
+pretty uh you know over over time just
+
+ align:start position:0%
+pretty uh you know over over time just
+ 
+
+ align:start position:0%
+pretty uh you know over over time just
+you you run a directory service onod and
+
+ align:start position:0%
+you you run a directory service onod and
+ 
+
+ align:start position:0%
+you you run a directory service onod and
+you get a complete list of all these
+
+ align:start position:0%
+you get a complete list of all these
+ 
+
+ align:start position:0%
+you get a complete list of all these
+keys and you can try connecting to all
+
+ align:start position:0%
+keys and you can try connecting to all
+ 
+
+ align:start position:0%
+keys and you can try connecting to all
+of the ones that don't have encrypted
+
+ align:start position:0%
+of the ones that don't have encrypted
+ 
+
+ align:start position:0%
+of the ones that don't have encrypted
+stuff to find out what's there that's
+
+ align:start position:0%
+stuff to find out what's there that's
+ 
+
+ align:start position:0%
+stuff to find out what's there that's
+called an enumeration attack and we
+
+ align:start position:0%
+called an enumeration attack and we
+ 
+
+ align:start position:0%
+called an enumeration attack and we
+didn't list that in our paper because we
+
+ align:start position:0%
+didn't list that in our paper because we
+ 
+
+ align:start position:0%
+didn't list that in our paper because we
+weren't thinking of that we didn't um
+
+ align:start position:0%
+weren't thinking of that we didn't um
+ 
+
+ align:start position:0%
+weren't thinking of that we didn't um
+but it is something we'd like to resist
+
+ align:start position:0%
+but it is something we'd like to resist
+ 
+
+ align:start position:0%
+but it is something we'd like to resist
+so in the design I hope to be to be
+
+ align:start position:0%
+so in the design I hope to be to be
+ 
+
+ align:start position:0%
+so in the design I hope to be to be
+hacking together sometime in 2014 we're
+
+ align:start position:0%
+hacking together sometime in 2014 we're
+ 
+
+ align:start position:0%
+hacking together sometime in 2014 we're
+going to move towards a key blinding
+
+ align:start position:0%
+going to move towards a key blinding
+ 
+
+ align:start position:0%
+going to move towards a key blinding
+approach where um where Alice and Bob
+
+ align:start position:0%
+approach where um where Alice and Bob
+ 
+
+ align:start position:0%
+approach where um where Alice and Bob
+share
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pkw
+
+ align:start position:0%
+pkw
+ 
+
+ align:start position:0%
+pkw
+but sure sorry sh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pkz but this statement is not signed
+
+ align:start position:0%
+pkz but this statement is not signed
+ 
+
+ align:start position:0%
+pkz but this statement is not signed
+with pkz this statement is signed with
+
+ align:start position:0%
+with pkz this statement is signed with
+ 
+
+ align:start position:0%
+with pkz this statement is signed with
+pkz prime where pkz Prime is derived
+
+ align:start position:0%
+pkz prime where pkz Prime is derived
+ 
+
+ align:start position:0%
+pkz prime where pkz Prime is derived
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pkz and say um the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+date s such that if you know pkz and the
+
+ align:start position:0%
+date s such that if you know pkz and the
+ 
+
+ align:start position:0%
+date s such that if you know pkz and the
+date you can derive pkz
+
+ align:start position:0%
+date you can derive pkz
+ 
+
+ align:start position:0%
+date you can derive pkz
+Prime if you if like Alis you know
+
+ align:start position:0%
+Prime if you if like Alis you know
+ 
+
+ align:start position:0%
+Prime if you if like Alis you know
+secret
+
+ align:start position:0%
+secret
+ 
+
+ align:start position:0%
+secret
+KZ you can generate messages that are
+
+ align:start position:0%
+KZ you can generate messages that are
+ 
+
+ align:start position:0%
+KZ you can generate messages that are
+signed by secret K by pkz Prime
+
+ align:start position:0%
+signed by secret K by pkz Prime
+ 
+
+ align:start position:0%
+signed by secret K by pkz Prime
+but if you only see pkz Prime even
+
+ align:start position:0%
+but if you only see pkz Prime even
+ 
+
+ align:start position:0%
+but if you only see pkz Prime even
+knowing the date you cannot rederive pkz
+
+ align:start position:0%
+knowing the date you cannot rederive pkz
+ 
+
+ align:start position:0%
+knowing the date you cannot rederive pkz
+uh we've got a
+
+ align:start position:0%
+uh we've got a
+ 
+
+ align:start position:0%
+uh we've got a
+proof and if you'd like to find out how
+
+ align:start position:0%
+proof and if you'd like to find out how
+ 
+
+ align:start position:0%
+proof and if you'd like to find out how
+this works then like Ping me and I'll
+
+ align:start position:0%
+this works then like Ping me and I'll
+ 
+
+ align:start position:0%
+this works then like Ping me and I'll
+send you the paper it's it's a cool
+
+ align:start position:0%
+send you the paper it's it's a cool
+ 
+
+ align:start position:0%
+send you the paper it's it's a cool
+trick we
+
+ align:start position:0%
+trick we
+ 
+
+ align:start position:0%
+trick we
+didn't we we were not the first ones to
+
+ align:start position:0%
+didn't we we were not the first ones to
+ 
+
+ align:start position:0%
+didn't we we were not the first ones to
+invent this idea but um that is how
+
+ align:start position:0%
+invent this idea but um that is how
+ 
+
+ align:start position:0%
+invent this idea but um that is how
+we're going to solve a numeration attack
+
+ align:start position:0%
+we're going to solve a numeration attack
+ 
+
+ align:start position:0%
+we're going to solve a numeration attack
+sometime in this coming
+
+ align:start position:0%
+sometime in this coming
+ 
+
+ align:start position:0%
+sometime in this coming
+year assuming that I can actually get
+
+ align:start position:0%
+year assuming that I can actually get
+ 
+
+ align:start position:0%
+year assuming that I can actually get
+the time to build it so that's hidden
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Services um attacks and
+
+ align:start position:0%
+Services um attacks and
+ 
+
+ align:start position:0%
+Services um attacks and
+defenses so so far um the biggest
+
+ align:start position:0%
+defenses so so far um the biggest
+ 
+
+ align:start position:0%
+defenses so so far um the biggest
+category of attacks we've seen is
+
+ align:start position:0%
+category of attacks we've seen is
+ 
+
+ align:start position:0%
+category of attacks we've seen is
+attacks at the application Level so if
+
+ align:start position:0%
+attacks at the application Level so if
+ 
+
+ align:start position:0%
+attacks at the application Level so if
+you're running an application over tour
+
+ align:start position:0%
+you're running an application over tour
+ 
+
+ align:start position:0%
+you're running an application over tour
+and it's an unencrypt and it's sending
+
+ align:start position:0%
+and it's an unencrypt and it's sending
+ 
+
+ align:start position:0%
+and it's an unencrypt and it's sending
+unencrypted traffic like regular
+
+ align:start position:0%
+unencrypted traffic like regular
+ 
+
+ align:start position:0%
+unencrypted traffic like regular
+HTTP then
+
+ align:start position:0%
+HTTP then
+ 
+
+ align:start position:0%
+HTTP then
+a hostile exit node just like anyone
+
+ align:start position:0%
+a hostile exit node just like anyone
+ 
+
+ align:start position:0%
+a hostile exit node just like anyone
+else who touches hdtb traffic can
+
+ align:start position:0%
+else who touches hdtb traffic can
+ 
+
+ align:start position:0%
+else who touches hdtb traffic can
+observe and modify the traffic um this
+
+ align:start position:0%
+observe and modify the traffic um this
+ 
+
+ align:start position:0%
+observe and modify the traffic um this
+is the number one attack on the whole
+
+ align:start position:0%
+is the number one attack on the whole
+ 
+
+ align:start position:0%
+is the number one attack on the whole
+system the solution is encrypt your
+
+ align:start position:0%
+system the solution is encrypt your
+ 
+
+ align:start position:0%
+system the solution is encrypt your
+traffic fortunately we're kind of in an
+
+ align:start position:0%
+traffic fortunately we're kind of in an
+ 
+
+ align:start position:0%
+traffic fortunately we're kind of in an
+encryption Renaissance over the last few
+
+ align:start position:0%
+encryption Renaissance over the last few
+ 
+
+ align:start position:0%
+encryption Renaissance over the last few
+years and more and more traffic is
+
+ align:start position:0%
+years and more and more traffic is
+ 
+
+ align:start position:0%
+years and more and more traffic is
+getting encrypted with the Nifty um free
+
+ align:start position:0%
+getting encrypted with the Nifty um free
+ 
+
+ align:start position:0%
+getting encrypted with the Nifty um free
+certificate Authority that eff and
+
+ align:start position:0%
+certificate Authority that eff and
+ 
+
+ align:start position:0%
+certificate Authority that eff and
+Mozilla and Cisco and I forget who else
+
+ align:start position:0%
+Mozilla and Cisco and I forget who else
+ 
+
+ align:start position:0%
+Mozilla and Cisco and I forget who else
+announced a day or two ago there will be
+
+ align:start position:0%
+announced a day or two ago there will be
+ 
+
+ align:start position:0%
+announced a day or two ago there will be
+even less excuse for unencrypted traffic
+
+ align:start position:0%
+even less excuse for unencrypted traffic
+ 
+
+ align:start position:0%
+even less excuse for unencrypted traffic
+in 2015 than there was this year so you
+
+ align:start position:0%
+in 2015 than there was this year so you
+ 
+
+ align:start position:0%
+in 2015 than there was this year so you
+know that solves that more interesting
+
+ align:start position:0%
+know that solves that more interesting
+ 
+
+ align:start position:0%
+know that solves that more interesting
+attacks include things like traffic
+
+ align:start position:0%
+attacks include things like traffic
+ 
+
+ align:start position:0%
+attacks include things like traffic
+tagging so we made a mistake in our
+
+ align:start position:0%
+tagging so we made a mistake in our
+ 
+
+ align:start position:0%
+tagging so we made a mistake in our
+early Integrity checking implementation
+
+ align:start position:0%
+early Integrity checking implementation
+ 
+
+ align:start position:0%
+early Integrity checking implementation
+our early Integrity checking
+
+ align:start position:0%
+our early Integrity checking
+ 
+
+ align:start position:0%
+our early Integrity checking
+implementation um did endtoend checking
+
+ align:start position:0%
+implementation um did endtoend checking
+ 
+
+ align:start position:0%
+implementation um did endtoend checking
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+Alice's program and the exit node
+
+ align:start position:0%
+Alice's program and the exit node
+ 
+
+ align:start position:0%
+Alice's program and the exit node
+but it turns out that that's not quite
+
+ align:start position:0%
+but it turns out that that's not quite
+ 
+
+ align:start position:0%
+but it turns out that that's not quite
+enough because if the first relay messes
+
+ align:start position:0%
+enough because if the first relay messes
+ 
+
+ align:start position:0%
+enough because if the first relay messes
+with the traffic in a way that creates a
+
+ align:start position:0%
+with the traffic in a way that creates a
+ 
+
+ align:start position:0%
+with the traffic in a way that creates a
+a pattern that the exit node can detect
+
+ align:start position:0%
+a pattern that the exit node can detect
+ 
+
+ align:start position:0%
+a pattern that the exit node can detect
+then that's an easy way for the first
+
+ align:start position:0%
+then that's an easy way for the first
+ 
+
+ align:start position:0%
+then that's an easy way for the first
+relay and the last relay to learn that
+
+ align:start position:0%
+relay and the last relay to learn that
+ 
+
+ align:start position:0%
+relay and the last relay to learn that
+they are on the same path and identify
+
+ align:start position:0%
+they are on the same path and identify
+ 
+
+ align:start position:0%
+they are on the same path and identify
+Alice of course if the first relay and
+
+ align:start position:0%
+Alice of course if the first relay and
+ 
+
+ align:start position:0%
+Alice of course if the first relay and
+the last relay happen to be on the same
+
+ align:start position:0%
+the last relay happen to be on the same
+ 
+
+ align:start position:0%
+the last relay happen to be on the same
+path happen to be collaborating anyway
+
+ align:start position:0%
+path happen to be collaborating anyway
+ 
+
+ align:start position:0%
+path happen to be collaborating anyway
+then they can all already identify Alis
+
+ align:start position:0%
+then they can all already identify Alis
+ 
+
+ align:start position:0%
+then they can all already identify Alis
+through traffic correlation we believe
+
+ align:start position:0%
+through traffic correlation we believe
+ 
+
+ align:start position:0%
+through traffic correlation we believe
+but perhaps it should not be so easy for
+
+ align:start position:0%
+but perhaps it should not be so easy for
+ 
+
+ align:start position:0%
+but perhaps it should not be so easy for
+them as as that perhaps traffic
+
+ align:start position:0%
+them as as that perhaps traffic
+ 
+
+ align:start position:0%
+them as as that perhaps traffic
+correlation will someday be harder than
+
+ align:start position:0%
+correlation will someday be harder than
+ 
+
+ align:start position:0%
+correlation will someday be harder than
+we think it would be um it would be good
+
+ align:start position:0%
+we think it would be um it would be good
+ 
+
+ align:start position:0%
+we think it would be um it would be good
+to actually solve that attack for real
+
+ align:start position:0%
+to actually solve that attack for real
+ 
+
+ align:start position:0%
+to actually solve that attack for real
+we've got two solutions for that one is
+
+ align:start position:0%
+we've got two solutions for that one is
+ 
+
+ align:start position:0%
+we've got two solutions for that one is
+the expected out result of this attack
+
+ align:start position:0%
+the expected out result of this attack
+ 
+
+ align:start position:0%
+the expected out result of this attack
+is that periodically circuits will fail
+
+ align:start position:0%
+is that periodically circuits will fail
+ 
+
+ align:start position:0%
+is that periodically circuits will fail
+because the attacker on the first hop
+
+ align:start position:0%
+because the attacker on the first hop
+ 
+
+ align:start position:0%
+because the attacker on the first hop
+guessed wrong about controlling the last
+
+ align:start position:0%
+guessed wrong about controlling the last
+ 
+
+ align:start position:0%
+guessed wrong about controlling the last
+hop so um every Tor client checks for
+
+ align:start position:0%
+hop so um every Tor client checks for
+ 
+
+ align:start position:0%
+hop so um every Tor client checks for
+weird failure rates the real long-term
+
+ align:start position:0%
+weird failure rates the real long-term
+ 
+
+ align:start position:0%
+weird failure rates the real long-term
+fix is to make it so that messing with
+
+ align:start position:0%
+fix is to make it so that messing with
+ 
+
+ align:start position:0%
+fix is to make it so that messing with
+the pattern on the first top doesn't
+
+ align:start position:0%
+the pattern on the first top doesn't
+ 
+
+ align:start position:0%
+the pattern on the first top doesn't
+create more than one bit of information
+
+ align:start position:0%
+create more than one bit of information
+ 
+
+ align:start position:0%
+create more than one bit of information
+on the last toop you can't avoid sending
+
+ align:start position:0%
+on the last toop you can't avoid sending
+ 
+
+ align:start position:0%
+on the last toop you can't avoid sending
+one bit of information because the first
+
+ align:start position:0%
+one bit of information because the first
+ 
+
+ align:start position:0%
+one bit of information because the first
+toop can always just shut down the
+
+ align:start position:0%
+toop can always just shut down the
+ 
+
+ align:start position:0%
+toop can always just shut down the
+connection but if you can limit it to
+
+ align:start position:0%
+connection but if you can limit it to
+ 
+
+ align:start position:0%
+connection but if you can limit it to
+one bit okay two bits because then
+
+ align:start position:0%
+one bit okay two bits because then
+ 
+
+ align:start position:0%
+one bit okay two bits because then
+they'll have the choice to corrupt the
+
+ align:start position:0%
+they'll have the choice to corrupt the
+ 
+
+ align:start position:0%
+they'll have the choice to corrupt the
+data or shut down the
+
+ align:start position:0%
+data or shut down the
+ 
+
+ align:start position:0%
+data or shut down the
+connection but oh I hey I had an idea of
+
+ align:start position:0%
+connection but oh I hey I had an idea of
+ 
+
+ align:start position:0%
+connection but oh I hey I had an idea of
+how to make that better I have to think
+
+ align:start position:0%
+how to make that better I have to think
+ 
+
+ align:start position:0%
+how to make that better I have to think
+about that um let's see do is actually
+
+ align:start position:0%
+about that um let's see do is actually
+ 
+
+ align:start position:0%
+about that um let's see do is actually
+pretty important um there was a paper
+
+ align:start position:0%
+pretty important um there was a paper
+ 
+
+ align:start position:0%
+pretty important um there was a paper
+the other year about something that the
+
+ align:start position:0%
+the other year about something that the
+ 
+
+ align:start position:0%
+the other year about something that the
+author's called the sniper attack where
+
+ align:start position:0%
+author's called the sniper attack where
+ 
+
+ align:start position:0%
+author's called the sniper attack where
+you see traffic coming from a Tor node
+
+ align:start position:0%
+you see traffic coming from a Tor node
+ 
+
+ align:start position:0%
+you see traffic coming from a Tor node
+that you don't control you want to kick
+
+ align:start position:0%
+that you don't control you want to kick
+ 
+
+ align:start position:0%
+that you don't control you want to kick
+everybody off that Tor node so you
+
+ align:start position:0%
+everybody off that Tor node so you
+ 
+
+ align:start position:0%
+everybody off that Tor node so you
+connect to it you fill up all of its
+
+ align:start position:0%
+connect to it you fill up all of its
+ 
+
+ align:start position:0%
+connect to it you fill up all of its
+memory buffers and it
+
+ align:start position:0%
+memory buffers and it
+ 
+
+ align:start position:0%
+memory buffers and it
+crashes then you see whether the traffic
+
+ align:start position:0%
+crashes then you see whether the traffic
+ 
+
+ align:start position:0%
+crashes then you see whether the traffic
+in question gets routed to a node you
+
+ align:start position:0%
+in question gets routed to a node you
+ 
+
+ align:start position:0%
+in question gets routed to a node you
+control or not and your repeat is
+
+ align:start position:0%
+control or not and your repeat is
+ 
+
+ align:start position:0%
+control or not and your repeat is
+necessary
+
+ align:start position:0%
+necessary
+ 
+
+ align:start position:0%
+necessary
+um you can
+
+ align:start position:0%
+um you can
+ 
+
+ align:start position:0%
+um you can
+do for that our best options are um
+
+ align:start position:0%
+do for that our best options are um
+ 
+
+ align:start position:0%
+do for that our best options are um
+first off no longer have memory dos I
+
+ align:start position:0%
+first off no longer have memory dos I
+ 
+
+ align:start position:0%
+first off no longer have memory dos I
+think we have all of the good memory
+
+ align:start position:0%
+think we have all of the good memory
+ 
+
+ align:start position:0%
+think we have all of the good memory
+DS's fixed now there are some bad ones
+
+ align:start position:0%
+DS's fixed now there are some bad ones
+ 
+
+ align:start position:0%
+DS's fixed now there are some bad ones
+that still needed to get addressed but
+
+ align:start position:0%
+that still needed to get addressed but
+ 
+
+ align:start position:0%
+that still needed to get addressed but
+they're screamingly
+
+ align:start position:0%
+they're screamingly
+ 
+
+ align:start position:0%
+they're screamingly
+inefficient the other option for
+
+ align:start position:0%
+inefficient the other option for
+ 
+
+ align:start position:0%
+inefficient the other option for
+resolving this kind of thing is you know
+
+ align:start position:0%
+resolving this kind of thing is you know
+ 
+
+ align:start position:0%
+resolving this kind of thing is you know
+make sure relays are high capacity don't
+
+ align:start position:0%
+make sure relays are high capacity don't
+ 
+
+ align:start position:0%
+make sure relays are high capacity don't
+accept low capacity relays on the
+
+ align:start position:0%
+accept low capacity relays on the
+ 
+
+ align:start position:0%
+accept low capacity relays on the
+network we do that too if you're running
+
+ align:start position:0%
+network we do that too if you're running
+ 
+
+ align:start position:0%
+network we do that too if you're running
+something on your if you're trying to
+
+ align:start position:0%
+something on your if you're trying to
+ 
+
+ align:start position:0%
+something on your if you're trying to
+run a relay on your phone the
+
+ align:start position:0%
+run a relay on your phone the
+ 
+
+ align:start position:0%
+run a relay on your phone the
+authorities won't list
+
+ align:start position:0%
+authorities won't list
+ 
+
+ align:start position:0%
+authorities won't list
+it um but and another is to try to pick
+
+ align:start position:0%
+it um but and another is to try to pick
+ 
+
+ align:start position:0%
+it um but and another is to try to pick
+our circuit scheduling algorithms to so
+
+ align:start position:0%
+our circuit scheduling algorithms to so
+ 
+
+ align:start position:0%
+our circuit scheduling algorithms to so
+that it's hard to starve out circuits
+
+ align:start position:0%
+that it's hard to starve out circuits
+ 
+
+ align:start position:0%
+that it's hard to starve out circuits
+that you don't control that's very hard
+
+ align:start position:0%
+that you don't control that's very hard
+ 
+
+ align:start position:0%
+that you don't control that's very hard
+though and it's it's as yet an unsolved
+
+ align:start position:0%
+though and it's it's as yet an unsolved
+ 
+
+ align:start position:0%
+though and it's it's as yet an unsolved
+problem let's see I should I do an
+
+ align:start position:0%
+problem let's see I should I do an
+ 
+
+ align:start position:0%
+problem let's see I should I do an
+interest attack or an important
+
+ align:start position:0%
+interest attack or an important
+ 
+
+ align:start position:0%
+interest attack or an important
+attack interesting interesting okay um
+
+ align:start position:0%
+attack interesting interesting okay um
+ 
+
+ align:start position:0%
+attack interesting interesting okay um
+so show of hands how many people might
+
+ align:start position:0%
+so show of hands how many people might
+ 
+
+ align:start position:0%
+so show of hands how many people might
+like to write a program that uses
+
+ align:start position:0%
+like to write a program that uses
+ 
+
+ align:start position:0%
+like to write a program that uses
+cryptography
+
+ align:start position:0%
+cryptography
+ 
+
+ align:start position:0%
+cryptography
+someday cool here's what you must learn
+
+ align:start position:0%
+someday cool here's what you must learn
+ 
+
+ align:start position:0%
+someday cool here's what you must learn
+never trust your cryptography
+
+ align:start position:0%
+never trust your cryptography
+ 
+
+ align:start position:0%
+never trust your cryptography
+implementation so even when it's correct
+
+ align:start position:0%
+implementation so even when it's correct
+ 
+
+ align:start position:0%
+implementation so even when it's correct
+it's wrong so long ago there I I think
+
+ align:start position:0%
+it's wrong so long ago there I I think
+ 
+
+ align:start position:0%
+it's wrong so long ago there I I think
+this may be one of the
+
+ align:start position:0%
+this may be one of the
+ 
+
+ align:start position:0%
+this may be one of the
+worst um security bugs that we've had um
+
+ align:start position:0%
+worst um security bugs that we've had um
+ 
+
+ align:start position:0%
+worst um security bugs that we've had um
+any relay could in the middle any
+
+ align:start position:0%
+any relay could in the middle any
+ 
+
+ align:start position:0%
+any relay could in the middle any
+circuit
+
+ align:start position:0%
+circuit
+ 
+
+ align:start position:0%
+circuit
+because we assumed that a correct Diffy
+
+ align:start position:0%
+because we assumed that a correct Diffy
+ 
+
+ align:start position:0%
+because we assumed that a correct Diffy
+Helman
+
+ align:start position:0%
+Helman
+ 
+
+ align:start position:0%
+Helman
+implementation would verify that it was
+
+ align:start position:0%
+implementation would verify that it was
+ 
+
+ align:start position:0%
+implementation would verify that it was
+not being past zero as one of the
+
+ align:start position:0%
+not being past zero as one of the
+ 
+
+ align:start position:0%
+not being past zero as one of the
+inputs the authors of our Diffy helmet
+
+ align:start position:0%
+inputs the authors of our Diffy helmet
+ 
+
+ align:start position:0%
+inputs the authors of our Diffy helmet
+implementation assumed that the proper
+
+ align:start position:0%
+implementation assumed that the proper
+ 
+
+ align:start position:0%
+implementation assumed that the proper
+application would never pass zero to a
+
+ align:start position:0%
+application would never pass zero to a
+ 
+
+ align:start position:0%
+application would never pass zero to a
+Diffy helmet imple
+
+ align:start position:0%
+Diffy helmet imple
+ 
+
+ align:start position:0%
+Diffy helmet imple
+implementation um so so so you know Dy
+
+ align:start position:0%
+implementation um so so so you know Dy
+ 
+
+ align:start position:0%
+implementation um so so so you know Dy
+Helman I say G to the X you say G to the
+
+ align:start position:0%
+Helman I say G to the X you say G to the
+ 
+
+ align:start position:0%
+Helman I say G to the X you say G to the
+Y y I know X you know Y and we can comp
+
+ align:start position:0%
+Y y I know X you know Y and we can comp
+ 
+
+ align:start position:0%
+Y y I know X you know Y and we can comp
+both compute GT thex y now you've done
+
+ align:start position:0%
+both compute GT thex y now you've done
+ 
+
+ align:start position:0%
+both compute GT thex y now you've done
+the fman good um well you know if if
+
+ align:start position:0%
+the fman good um well you know if if
+ 
+
+ align:start position:0%
+the fman good um well you know if if
+Instead The Man in the middle replaces
+
+ align:start position:0%
+Instead The Man in the middle replaces
+ 
+
+ align:start position:0%
+Instead The Man in the middle replaces
+my G to the X with zero and your G to
+
+ align:start position:0%
+my G to the X with zero and your G to
+ 
+
+ align:start position:0%
+my G to the X with zero and your G to
+the X with with zero and then I happily
+
+ align:start position:0%
+the X with with zero and then I happily
+ 
+
+ align:start position:0%
+the X with with zero and then I happily
+compute zero to the X and you compute
+
+ align:start position:0%
+compute zero to the X and you compute
+ 
+
+ align:start position:0%
+compute zero to the X and you compute
+zero to the Y we will have the same key
+
+ align:start position:0%
+zero to the Y we will have the same key
+ 
+
+ align:start position:0%
+zero to the Y we will have the same key
+we will happily talk to each other but
+
+ align:start position:0%
+we will happily talk to each other but
+ 
+
+ align:start position:0%
+we will happily talk to each other but
+this will be an a key that the attacker
+
+ align:start position:0%
+this will be an a key that the attacker
+ 
+
+ align:start position:0%
+this will be an a key that the attacker
+knows because it's zero one also
+
+ align:start position:0%
+knows because it's zero one also
+ 
+
+ align:start position:0%
+knows because it's zero one also
+works p also works p+ one also works so
+
+ align:start position:0%
+works p also works p+ one also works so
+ 
+
+ align:start position:0%
+works p also works p+ one also works so
+you you basically just need to make sure
+
+ align:start position:0%
+you you basically just need to make sure
+ 
+
+ align:start position:0%
+you you basically just need to make sure
+that your values here are within range
+
+ align:start position:0%
+that your values here are within range
+ 
+
+ align:start position:0%
+that your values here are within range
+two and P minus one if you're doing uh
+
+ align:start position:0%
+two and P minus one if you're doing uh
+ 
+
+ align:start position:0%
+two and P minus one if you're doing uh
+Diffy Helman in in Zu
+
+ align:start position:0%
+Diffy Helman in in Zu
+ 
+
+ align:start position:0%
+Diffy Helman in in Zu
+subp okay let's see I would love to talk
+
+ align:start position:0%
+subp okay let's see I would love to talk
+ 
+
+ align:start position:0%
+subp okay let's see I would love to talk
+more about censorship because actually
+
+ align:start position:0%
+more about censorship because actually
+ 
+
+ align:start position:0%
+more about censorship because actually
+it's one of the areas where we can do
+
+ align:start position:0%
+it's one of the areas where we can do
+ 
+
+ align:start position:0%
+it's one of the areas where we can do
+the most good
+
+ align:start position:0%
+the most good
+ 
+
+ align:start position:0%
+the most good
+generally the summarized summarized
+
+ align:start position:0%
+generally the summarized summarized
+ 
+
+ align:start position:0%
+generally the summarized summarized
+version of that was in the earliest
+
+ align:start position:0%
+version of that was in the earliest
+ 
+
+ align:start position:0%
+version of that was in the earliest
+paper you read and in some of the
+
+ align:start position:0%
+paper you read and in some of the
+ 
+
+ align:start position:0%
+paper you read and in some of the
+updates we were still on the idea that
+
+ align:start position:0%
+updates we were still on the idea that
+ 
+
+ align:start position:0%
+updates we were still on the idea that
+we would try to make tour look just like
+
+ align:start position:0%
+we would try to make tour look just like
+ 
+
+ align:start position:0%
+we would try to make tour look just like
+a web client talking to a web server
+
+ align:start position:0%
+a web client talking to a web server
+ 
+
+ align:start position:0%
+a web client talking to a web server
+over https and make that hard to block
+
+ align:start position:0%
+over https and make that hard to block
+ 
+
+ align:start position:0%
+over https and make that hard to block
+turns out that's fantastically difficult
+
+ align:start position:0%
+turns out that's fantastically difficult
+ 
+
+ align:start position:0%
+turns out that's fantastically difficult
+and probably not worth doing uh instead
+
+ align:start position:0%
+and probably not worth doing uh instead
+ 
+
+ align:start position:0%
+and probably not worth doing uh instead
+the approach we take now is using
+
+ align:start position:0%
+the approach we take now is using
+ 
+
+ align:start position:0%
+the approach we take now is using
+different plug-in programs that um a
+
+ align:start position:0%
+different plug-in programs that um a
+ 
+
+ align:start position:0%
+different plug-in programs that um a
+non-listed relay called a bridge can use
+
+ align:start position:0%
+non-listed relay called a bridge can use
+ 
+
+ align:start position:0%
+non-listed relay called a bridge can use
+and a client can use to do different
+
+ align:start position:0%
+and a client can use to do different
+ 
+
+ align:start position:0%
+and a client can use to do different
+traffic transformations
+
+ align:start position:0%
+traffic transformations
+ 
+
+ align:start position:0%
+traffic transformations
+and we manag to keep adding new ones of
+
+ align:start position:0%
+and we manag to keep adding new ones of
+ 
+
+ align:start position:0%
+and we manag to keep adding new ones of
+those faster than the sensors have been
+
+ align:start position:0%
+those faster than the sensors have been
+ 
+
+ align:start position:0%
+those faster than the sensors have been
+able to implement blocking for them and
+
+ align:start position:0%
+able to implement blocking for them and
+ 
+
+ align:start position:0%
+able to implement blocking for them and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+actually a case where um none of the
+
+ align:start position:0%
+actually a case where um none of the
+ 
+
+ align:start position:0%
+actually a case where um none of the
+solutions are actually categorically
+
+ align:start position:0%
+solutions are actually categorically
+ 
+
+ align:start position:0%
+solutions are actually categorically
+workable
+
+ align:start position:0%
+workable
+ 
+
+ align:start position:0%
+workable
+but that's not a well-formed sentence
+
+ align:start position:0%
+but that's not a well-formed sentence
+ 
+
+ align:start position:0%
+but that's not a well-formed sentence
+none of these plugins are inherently
+
+ align:start position:0%
+none of these plugins are inherently
+ 
+
+ align:start position:0%
+none of these plugins are inherently
+unblockable by any Tech imaginable
+
+ align:start position:0%
+unblockable by any Tech imaginable
+ 
+
+ align:start position:0%
+unblockable by any Tech imaginable
+technique so far but they're good enough
+
+ align:start position:0%
+technique so far but they're good enough
+ 
+
+ align:start position:0%
+technique so far but they're good enough
+to keep traffic unblocked for a year or
+
+ align:start position:0%
+to keep traffic unblocked for a year or
+ 
+
+ align:start position:0%
+to keep traffic unblocked for a year or
+two in most places and six or seven
+
+ align:start position:0%
+two in most places and six or seven
+ 
+
+ align:start position:0%
+two in most places and six or seven
+months at a time in
+
+ align:start position:0%
+months at a time in
+ 
+
+ align:start position:0%
+months at a time in
+China China currently has the most
+
+ align:start position:0%
+China China currently has the most
+ 
+
+ align:start position:0%
+China China currently has the most
+competent sensors in the
+
+ align:start position:0%
+competent sensors in the
+ 
+
+ align:start position:0%
+competent sensors in the
+world largely because China doesn't
+
+ align:start position:0%
+world largely because China doesn't
+ 
+
+ align:start position:0%
+world largely because China doesn't
+Outsource most other censoring countries
+
+ align:start position:0%
+Outsource most other censoring countries
+ 
+
+ align:start position:0%
+Outsource most other censoring countries
+Outsource their censorship to dishonest
+
+ align:start position:0%
+Outsource their censorship to dishonest
+ 
+
+ align:start position:0%
+Outsource their censorship to dishonest
+European American and Asian companies
+
+ align:start position:0%
+European American and Asian companies
+ 
+
+ align:start position:0%
+European American and Asian companies
+whose incentives are not actually to
+
+ align:start position:0%
+whose incentives are not actually to
+ 
+
+ align:start position:0%
+whose incentives are not actually to
+sell them good censorship but to keep
+
+ align:start position:0%
+sell them good censorship but to keep
+ 
+
+ align:start position:0%
+sell them good censorship but to keep
+them on an upgrade treadmill so if you
+
+ align:start position:0%
+them on an upgrade treadmill so if you
+ 
+
+ align:start position:0%
+them on an upgrade treadmill so if you
+were buying your censorship software
+
+ align:start position:0%
+were buying your censorship software
+ 
+
+ align:start position:0%
+were buying your censorship software
+from the United States which technically
+
+ align:start position:0%
+from the United States which technically
+ 
+
+ align:start position:0%
+from the United States which technically
+speaking us companies aren't allowed to
+
+ align:start position:0%
+speaking us companies aren't allowed to
+ 
+
+ align:start position:0%
+speaking us companies aren't allowed to
+make censorship software for Nations but
+
+ align:start position:0%
+make censorship software for Nations but
+ 
+
+ align:start position:0%
+make censorship software for Nations but
+they just make you know corporate
+
+ align:start position:0%
+they just make you know corporate
+ 
+
+ align:start position:0%
+they just make you know corporate
+firewall software that happens to scale
+
+ align:start position:0%
+firewall software that happens to scale
+ 
+
+ align:start position:0%
+firewall software that happens to scale
+to 10 million
+
+ align:start position:0%
+to 10 million
+ 
+
+ align:start position:0%
+to 10 million
+people um yeah I think that's unethical
+
+ align:start position:0%
+people um yeah I think that's unethical
+ 
+
+ align:start position:0%
+people um yeah I think that's unethical
+but again I'm not the political
+
+ align:start position:0%
+but again I'm not the political
+ 
+
+ align:start position:0%
+but again I'm not the political
+scientist of the organization or the
+
+ align:start position:0%
+scientist of the organization or the
+ 
+
+ align:start position:0%
+scientist of the organization or the
+philosopher uh Paul cyers one of the
+
+ align:start position:0%
+philosopher uh Paul cyers one of the
+ 
+
+ align:start position:0%
+philosopher uh Paul cyers one of the
+original onion writing authors does have
+
+ align:start position:0%
+original onion writing authors does have
+ 
+
+ align:start position:0%
+original onion writing authors does have
+a degree in Philosophy for what that's
+
+ align:start position:0%
+a degree in Philosophy for what that's
+ 
+
+ align:start position:0%
+a degree in Philosophy for what that's
+worth which means that he can't answer
+
+ align:start position:0%
+worth which means that he can't answer
+ 
+
+ align:start position:0%
+worth which means that he can't answer
+these questions either but he takes a
+
+ align:start position:0%
+these questions either but he takes a
+ 
+
+ align:start position:0%
+these questions either but he takes a
+lot longer not to answer
+
+ align:start position:0%
+lot longer not to answer
+ 
+
+ align:start position:0%
+lot longer not to answer
+them um
+
+ align:start position:0%
+them um
+ 
+
+ align:start position:0%
+them um
+right where was I 90 minutes is a long
+
+ align:start position:0%
+right where was I 90 minutes is a long
+ 
+
+ align:start position:0%
+right where was I 90 minutes is a long
+time um
+
+ align:start position:0%
+time um
+ 
+
+ align:start position:0%
+time um
+censorship right so what what the sensor
+
+ align:start position:0%
+censorship right so what what the sensor
+ 
+
+ align:start position:0%
+censorship right so what what the sensor
+Weare providers do is once Tor gets
+
+ align:start position:0%
+Weare providers do is once Tor gets
+ 
+
+ align:start position:0%
+Weare providers do is once Tor gets
+around their
+
+ align:start position:0%
+around their
+ 
+
+ align:start position:0%
+around their
+censorship they will block the most
+
+ align:start position:0%
+censorship they will block the most
+ 
+
+ align:start position:0%
+censorship they will block the most
+recent version of Tor but they do it in
+
+ align:start position:0%
+recent version of Tor but they do it in
+ 
+
+ align:start position:0%
+recent version of Tor but they do it in
+a way that is the weakest possible block
+
+ align:start position:0%
+a way that is the weakest possible block
+ 
+
+ align:start position:0%
+a way that is the weakest possible block
+so if like we change one bit in one
+
+ align:start position:0%
+so if like we change one bit in one
+ 
+
+ align:start position:0%
+so if like we change one bit in one
+identifier somewhere we get around it we
+
+ align:start position:0%
+identifier somewhere we get around it we
+ 
+
+ align:start position:0%
+identifier somewhere we get around it we
+can't prove that they're doing this on
+
+ align:start position:0%
+can't prove that they're doing this on
+ 
+
+ align:start position:0%
+can't prove that they're doing this on
+purpose to ensure that tour will evade
+
+ align:start position:0%
+purpose to ensure that tour will evade
+ 
+
+ align:start position:0%
+purpose to ensure that tour will evade
+their version so that they can say so
+
+ align:start position:0%
+their version so that they can say so
+ 
+
+ align:start position:0%
+their version so that they can say so
+that they can sell tour blocking and
+
+ align:start position:0%
+that they can sell tour blocking and
+ 
+
+ align:start position:0%
+that they can sell tour blocking and
+then have it not work so they can sell
+
+ align:start position:0%
+then have it not work so they can sell
+ 
+
+ align:start position:0%
+then have it not work so they can sell
+the upgrade and then sell the next
+
+ align:start position:0%
+the upgrade and then sell the next
+ 
+
+ align:start position:0%
+the upgrade and then sell the next
+upgrade and sell the next upgrade but it
+
+ align:start position:0%
+upgrade and sell the next upgrade but it
+ 
+
+ align:start position:0%
+upgrade and sell the next upgrade but it
+sure does seem that way so yeah don't
+
+ align:start position:0%
+sure does seem that way so yeah don't
+ 
+
+ align:start position:0%
+sure does seem that way so yeah don't
+that's another reason not to work for
+
+ align:start position:0%
+that's another reason not to work for
+ 
+
+ align:start position:0%
+that's another reason not to work for
+censorship providers they're
+
+ align:start position:0%
+censorship providers they're
+ 
+
+ align:start position:0%
+censorship providers they're
+tremendously unethical and they don't
+
+ align:start position:0%
+tremendously unethical and they don't
+ 
+
+ align:start position:0%
+tremendously unethical and they don't
+provide very good
+
+ align:start position:0%
+provide very good
+ 
+
+ align:start position:0%
+provide very good
+software um if you interested in writing
+
+ align:start position:0%
+software um if you interested in writing
+ 
+
+ align:start position:0%
+software um if you interested in writing
+any of these pluggable transport things
+
+ align:start position:0%
+any of these pluggable transport things
+ 
+
+ align:start position:0%
+any of these pluggable transport things
+that is an excellent kind of thing to do
+
+ align:start position:0%
+that is an excellent kind of thing to do
+ 
+
+ align:start position:0%
+that is an excellent kind of thing to do
+as a student project
+
+ align:start position:0%
+as a student project
+ 
+
+ align:start position:0%
+as a student project
+loads of fun learn a little bit about
+
+ align:start position:0%
+loads of fun learn a little bit about
+ 
+
+ align:start position:0%
+loads of fun learn a little bit about
+crypto learn a little bit about
+
+ align:start position:0%
+crypto learn a little bit about
+ 
+
+ align:start position:0%
+crypto learn a little bit about
+networking and so long as you do it in a
+
+ align:start position:0%
+networking and so long as you do it in a
+ 
+
+ align:start position:0%
+networking and so long as you do it in a
+memory safe language you can't screw up
+
+ align:start position:0%
+memory safe language you can't screw up
+ 
+
+ align:start position:0%
+memory safe language you can't screw up
+that badly the worst thing that get that
+
+ align:start position:0%
+that badly the worst thing that get that
+ 
+
+ align:start position:0%
+that badly the worst thing that get that
+gets happened is it gets censored after
+
+ align:start position:0%
+gets happened is it gets censored after
+ 
+
+ align:start position:0%
+gets happened is it gets censored after
+a month instead of after a
+
+ align:start position:0%
+a month instead of after a
+ 
+
+ align:start position:0%
+a month instead of after a
+year and that's what I went to oh the
+
+ align:start position:0%
+year and that's what I went to oh the
+ 
+
+ align:start position:0%
+year and that's what I went to oh the
+agenda related to work um Tor is not is
+
+ align:start position:0%
+agenda related to work um Tor is not is
+ 
+
+ align:start position:0%
+agenda related to work um Tor is not is
+the most popular system of its kind but
+
+ align:start position:0%
+the most popular system of its kind but
+ 
+
+ align:start position:0%
+the most popular system of its kind but
+it's not the only one lots of others
+
+ align:start position:0%
+it's not the only one lots of others
+ 
+
+ align:start position:0%
+it's not the only one lots of others
+have really good ideas and you should
+
+ align:start position:0%
+have really good ideas and you should
+ 
+
+ align:start position:0%
+have really good ideas and you should
+check them out too if you're interested
+
+ align:start position:0%
+check them out too if you're interested
+ 
+
+ align:start position:0%
+check them out too if you're interested
+in um learning all of the stuff I'm not
+
+ align:start position:0%
+in um learning all of the stuff I'm not
+ 
+
+ align:start position:0%
+in um learning all of the stuff I'm not
+thinking about enough and all of the
+
+ align:start position:0%
+thinking about enough and all of the
+ 
+
+ align:start position:0%
+thinking about enough and all of the
+reasons I'm wrong uh freeh haven. net
+
+ align:start position:0%
+reasons I'm wrong uh freeh haven. net
+ 
+
+ align:start position:0%
+reasons I'm wrong uh freeh haven. net
+nonb lists the academic research and
+
+ align:start position:0%
+nonb lists the academic research and
+ 
+
+ align:start position:0%
+nonb lists the academic research and
+Publications in this area but not all
+
+ align:start position:0%
+Publications in this area but not all
+ 
+
+ align:start position:0%
+Publications in this area but not all
+the research in this area is academic
+
+ align:start position:0%
+the research in this area is academic
+ 
+
+ align:start position:0%
+the research in this area is academic
+you should also look at
+
+ align:start position:0%
+you should also look at
+ 
+
+ align:start position:0%
+you should also look at
+i2p
+
+ align:start position:0%
+i2p
+ 
+
+ align:start position:0%
+i2p
+gunet
+
+ align:start position:0%
+gunet
+ 
+
+ align:start position:0%
+gunet
+Freedom which is currently defunct no
+
+ align:start position:0%
+Freedom which is currently defunct no
+ 
+
+ align:start position:0%
+Freedom which is currently defunct no
+pun
+
+ align:start position:0%
+pun
+ 
+
+ align:start position:0%
+pun
+intended um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mixmaster mix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minion uh Sphinx with a Y Sphinx with an
+
+ align:start position:0%
+minion uh Sphinx with a Y Sphinx with an
+ 
+
+ align:start position:0%
+minion uh Sphinx with a Y Sphinx with an
+i is something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different um DC
+
+ align:start position:0%
+different um DC
+ 
+
+ align:start position:0%
+different um DC
+Nets particularly the work of um is it
+
+ align:start position:0%
+Nets particularly the work of um is it
+ 
+
+ align:start position:0%
+Nets particularly the work of um is it
+Brian Ford Brian Ford on U making this
+
+ align:start position:0%
+Brian Ford Brian Ford on U making this
+ 
+
+ align:start position:0%
+Brian Ford Brian Ford on U making this
+and also of the team at Technical
+
+ align:start position:0%
+and also of the team at Technical
+ 
+
+ align:start position:0%
+and also of the team at Technical
+University Dresden in make trying to
+
+ align:start position:0%
+University Dresden in make trying to
+ 
+
+ align:start position:0%
+University Dresden in make trying to
+make DC Nets practical they're very
+
+ align:start position:0%
+make DC Nets practical they're very
+ 
+
+ align:start position:0%
+make DC Nets practical they're very
+strong they're just not actually
+
+ align:start position:0%
+strong they're just not actually
+ 
+
+ align:start position:0%
+strong they're just not actually
+Deployable yet and many
+
+ align:start position:0%
+Deployable yet and many
+ 
+
+ align:start position:0%
+Deployable yet and many
+others these tend to
+
+ align:start position:0%
+others these tend to
+ 
+
+ align:start position:0%
+others these tend to
+get why why these get less use or
+
+ align:start position:0%
+get why why these get less use or
+ 
+
+ align:start position:0%
+get why why these get less use or
+attention than tour is a open topic of
+
+ align:start position:0%
+attention than tour is a open topic of
+ 
+
+ align:start position:0%
+attention than tour is a open topic of
+some interest that I don't have a solid
+
+ align:start position:0%
+some interest that I don't have a solid
+ 
+
+ align:start position:0%
+some interest that I don't have a solid
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+for future work
+
+ align:start position:0%
+for future work
+ 
+
+ align:start position:0%
+for future work
+um so one of the reasons I do these is
+
+ align:start position:0%
+um so one of the reasons I do these is
+ 
+
+ align:start position:0%
+um so one of the reasons I do these is
+not just because I would like everybody
+
+ align:start position:0%
+not just because I would like everybody
+ 
+
+ align:start position:0%
+not just because I would like everybody
+to know about the cool software I work
+
+ align:start position:0%
+to know about the cool software I work
+ 
+
+ align:start position:0%
+to know about the cool software I work
+on but also because I know students have
+
+ align:start position:0%
+on but also because I know students have
+ 
+
+ align:start position:0%
+on but also because I know students have
+lots and lots of free time and I'm kind
+
+ align:start position:0%
+lots and lots of free time and I'm kind
+ 
+
+ align:start position:0%
+lots and lots of free time and I'm kind
+of hoping to recruit okay you may think
+
+ align:start position:0%
+of hoping to recruit okay you may think
+ 
+
+ align:start position:0%
+of hoping to recruit okay you may think
+I'm joking but um when I was just
+
+ align:start position:0%
+I'm joking but um when I was just
+ 
+
+ align:start position:0%
+I'm joking but um when I was just
+getting started in this field I was
+
+ align:start position:0%
+getting started in this field I was
+ 
+
+ align:start position:0%
+getting started in this field I was
+complaining about how I was so busy like
+
+ align:start position:0%
+complaining about how I was so busy like
+ 
+
+ align:start position:0%
+complaining about how I was so busy like
+reviewing papers for one conference
+
+ align:start position:0%
+reviewing papers for one conference
+ 
+
+ align:start position:0%
+reviewing papers for one conference
+writing software fixing a bug answering
+
+ align:start position:0%
+writing software fixing a bug answering
+ 
+
+ align:start position:0%
+writing software fixing a bug answering
+email I was complaining to some senior
+
+ align:start position:0%
+email I was complaining to some senior
+ 
+
+ align:start position:0%
+email I was complaining to some senior
+faculty member and he told
+
+ align:start position:0%
+faculty member and he told
+ 
+
+ align:start position:0%
+faculty member and he told
+me you will never have so much free time
+
+ align:start position:0%
+me you will never have so much free time
+ 
+
+ align:start position:0%
+me you will never have so much free time
+as you do
+
+ align:start position:0%
+as you do
+ 
+
+ align:start position:0%
+as you do
+today this is actually you actually have
+
+ align:start position:0%
+today this is actually you actually have
+ 
+
+ align:start position:0%
+today this is actually you actually have
+a lot more free time now than you will
+
+ align:start position:0%
+a lot more free time now than you will
+ 
+
+ align:start position:0%
+a lot more free time now than you will
+in 10 years so this is the great time to
+
+ align:start position:0%
+in 10 years so this is the great time to
+ 
+
+ align:start position:0%
+in 10 years so this is the great time to
+work on crazy software
+
+ align:start position:0%
+work on crazy software
+ 
+
+ align:start position:0%
+work on crazy software
+projects and so let me tell you about
+
+ align:start position:0%
+projects and so let me tell you about
+ 
+
+ align:start position:0%
+projects and so let me tell you about
+future work in tour there's this uh key
+
+ align:start position:0%
+future work in tour there's this uh key
+ 
+
+ align:start position:0%
+future work in tour there's this uh key
+blinding thing and a complete revamp of
+
+ align:start position:0%
+blinding thing and a complete revamp of
+ 
+
+ align:start position:0%
+blinding thing and a complete revamp of
+our hidden Services system which was you
+
+ align:start position:0%
+our hidden Services system which was you
+ 
+
+ align:start position:0%
+our hidden Services system which was you
+know the best we could design when we
+
+ align:start position:0%
+know the best we could design when we
+ 
+
+ align:start position:0%
+know the best we could design when we
+came up with it but there's been a lot
+
+ align:start position:0%
+came up with it but there's been a lot
+ 
+
+ align:start position:0%
+came up with it but there's been a lot
+of research since then maybe some of it
+
+ align:start position:0%
+of research since then maybe some of it
+ 
+
+ align:start position:0%
+of research since then maybe some of it
+will turn out to be a good idea we're
+
+ align:start position:0%
+will turn out to be a good idea we're
+ 
+
+ align:start position:0%
+will turn out to be a good idea we're
+also revamping most of our crypto we
+
+ align:start position:0%
+also revamping most of our crypto we
+ 
+
+ align:start position:0%
+also revamping most of our crypto we
+chose schemes that seemed like a good
+
+ align:start position:0%
+chose schemes that seemed like a good
+ 
+
+ align:start position:0%
+chose schemes that seemed like a good
+security performance tradeoff in 2003
+
+ align:start position:0%
+security performance tradeoff in 2003
+ 
+
+ align:start position:0%
+security performance tradeoff in 2003
+like RSA 1024 we've replaced the really
+
+ align:start position:0%
+like RSA 1024 we've replaced the really
+ 
+
+ align:start position:0%
+like RSA 1024 we've replaced the really
+important uses of RSA 1024 with stronger
+
+ align:start position:0%
+important uses of RSA 1024 with stronger
+ 
+
+ align:start position:0%
+important uses of RSA 1024 with stronger
+stuff uh currently curve 25519 but
+
+ align:start position:0%
+stuff uh currently curve 25519 but
+ 
+
+ align:start position:0%
+stuff uh currently curve 25519 but
+there's still some cases that we want to
+
+ align:start position:0%
+there's still some cases that we want to
+ 
+
+ align:start position:0%
+there's still some cases that we want to
+replace in the protocol that we need
+
+ align:start position:0%
+replace in the protocol that we need
+ 
+
+ align:start position:0%
+replace in the protocol that we need
+some work on um I didn't talk too much
+
+ align:start position:0%
+some work on um I didn't talk too much
+ 
+
+ align:start position:0%
+some work on um I didn't talk too much
+about path selection so I can't talk too
+
+ align:start position:0%
+about path selection so I can't talk too
+ 
+
+ align:start position:0%
+about path selection so I can't talk too
+much about improvements in path
+
+ align:start position:0%
+much about improvements in path
+ 
+
+ align:start position:0%
+much about improvements in path
+selection but our path selection
+
+ align:start position:0%
+selection but our path selection
+ 
+
+ align:start position:0%
+selection but our path selection
+algorithms were chosen pretty naely and
+
+ align:start position:0%
+algorithms were chosen pretty naely and
+ 
+
+ align:start position:0%
+algorithms were chosen pretty naely and
+there's there's been some awesome
+
+ align:start position:0%
+there's there's been some awesome
+ 
+
+ align:start position:0%
+there's there's been some awesome
+research in the past five or six years
+
+ align:start position:0%
+research in the past five or six years
+ 
+
+ align:start position:0%
+research in the past five or six years
+on that that we need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integrate there's a little work that's
+
+ align:start position:0%
+integrate there's a little work that's
+ 
+
+ align:start position:0%
+integrate there's a little work that's
+been done on mixing High latency and low
+
+ align:start position:0%
+been done on mixing High latency and low
+ 
+
+ align:start position:0%
+been done on mixing High latency and low
+latency traffic so that the low latency
+
+ align:start position:0%
+latency traffic so that the low latency
+ 
+
+ align:start position:0%
+latency traffic so that the low latency
+traffic can provide cover for the high
+
+ align:start position:0%
+traffic can provide cover for the high
+ 
+
+ align:start position:0%
+traffic can provide cover for the high
+latency traffic in terms of providing
+
+ align:start position:0%
+latency traffic in terms of providing
+ 
+
+ align:start position:0%
+latency traffic in terms of providing
+lots of users while the high latency
+
+ align:start position:0%
+lots of users while the high latency
+ 
+
+ align:start position:0%
+lots of users while the high latency
+traffic is still very well
+
+ align:start position:0%
+traffic is still very well
+ 
+
+ align:start position:0%
+traffic is still very well
+anonymized um it's not clear whether
+
+ align:start position:0%
+anonymized um it's not clear whether
+ 
+
+ align:start position:0%
+anonymized um it's not clear whether
+this would work or not it's not clear
+
+ align:start position:0%
+this would work or not it's not clear
+ 
+
+ align:start position:0%
+this would work or not it's not clear
+whether would use this or
+
+ align:start position:0%
+whether would use this or
+ 
+
+ align:start position:0%
+whether would use this or
+not and it is clear that unless
+
+ align:start position:0%
+not and it is clear that unless
+ 
+
+ align:start position:0%
+not and it is clear that unless
+something changes or unless some major
+
+ align:start position:0%
+something changes or unless some major
+ 
+
+ align:start position:0%
+something changes or unless some major
+fundinger for that in particular shows
+
+ align:start position:0%
+fundinger for that in particular shows
+ 
+
+ align:start position:0%
+fundinger for that in particular shows
+up I'm not going to have time to work on
+
+ align:start position:0%
+up I'm not going to have time to work on
+ 
+
+ align:start position:0%
+up I'm not going to have time to work on
+it in 2015 but if somebody else wants to
+
+ align:start position:0%
+it in 2015 but if somebody else wants to
+ 
+
+ align:start position:0%
+it in 2015 but if somebody else wants to
+hack on it my God that would be fun um
+
+ align:start position:0%
+hack on it my God that would be fun um
+ 
+
+ align:start position:0%
+hack on it my God that would be fun um
+our congestion control algorithms were
+
+ align:start position:0%
+our congestion control algorithms were
+ 
+
+ align:start position:0%
+our congestion control algorithms were
+chosen questionably based on what we
+
+ align:start position:0%
+chosen questionably based on what we
+ 
+
+ align:start position:0%
+chosen questionably based on what we
+could hack together in a week um we've
+
+ align:start position:0%
+could hack together in a week um we've
+ 
+
+ align:start position:0%
+could hack together in a week um we've
+improved them but they could use a
+
+ align:start position:0%
+improved them but they could use a
+ 
+
+ align:start position:0%
+improved them but they could use a
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+revamp there's some research on scaling
+
+ align:start position:0%
+revamp there's some research on scaling
+ 
+
+ align:start position:0%
+revamp there's some research on scaling
+to hundreds of thousands of nodes so in
+
+ align:start position:0%
+to hundreds of thousands of nodes so in
+ 
+
+ align:start position:0%
+to hundreds of thousands of nodes so in
+the current design
+
+ align:start position:0%
+the current design
+ 
+
+ align:start position:0%
+the current design
+we can probably get up to 10 or 20,000
+
+ align:start position:0%
+we can probably get up to 10 or 20,000
+ 
+
+ align:start position:0%
+we can probably get up to 10 or 20,000
+with no problem but because we assume
+
+ align:start position:0%
+with no problem but because we assume
+ 
+
+ align:start position:0%
+with no problem but because we assume
+that every client knows about every node
+
+ align:start position:0%
+that every client knows about every node
+ 
+
+ align:start position:0%
+that every client knows about every node
+and every node may be connected to every
+
+ align:start position:0%
+and every node may be connected to every
+ 
+
+ align:start position:0%
+and every node may be connected to every
+other node that's going to stop scaling
+
+ align:start position:0%
+other node that's going to stop scaling
+ 
+
+ align:start position:0%
+other node that's going to stop scaling
+before 100,000 and we need to do
+
+ align:start position:0%
+before 100,000 and we need to do
+ 
+
+ align:start position:0%
+before 100,000 and we need to do
+something about that that opens up some
+
+ align:start position:0%
+something about that that opens up some
+ 
+
+ align:start position:0%
+something about that that opens up some
+classes of attacks based on attackers
+
+ align:start position:0%
+classes of attacks based on attackers
+ 
+
+ align:start position:0%
+classes of attacks based on attackers
+learning which clients know which nodes
+
+ align:start position:0%
+learning which clients know which nodes
+ 
+
+ align:start position:0%
+learning which clients know which nodes
+and using that to distinguish clients so
+
+ align:start position:0%
+and using that to distinguish clients so
+ 
+
+ align:start position:0%
+and using that to distinguish clients so
+most of the naive approaches are a bad
+
+ align:start position:0%
+most of the naive approaches are a bad
+ 
+
+ align:start position:0%
+most of the naive approaches are a bad
+idea here but it may be that less naive
+
+ align:start position:0%
+idea here but it may be that less naive
+ 
+
+ align:start position:0%
+idea here but it may be that less naive
+approaches might work out another thing
+
+ align:start position:0%
+approaches might work out another thing
+ 
+
+ align:start position:0%
+approaches might work out another thing
+you might want to do if you're
+
+ align:start position:0%
+you might want to do if you're
+ 
+
+ align:start position:0%
+you might want to do if you're
+approaching 100,000 nodes is get rid of
+
+ align:start position:0%
+approaching 100,000 nodes is get rid of
+ 
+
+ align:start position:0%
+approaching 100,000 nodes is get rid of
+those centralized directory authorities
+
+ align:start position:0%
+those centralized directory authorities
+ 
+
+ align:start position:0%
+those centralized directory authorities
+and go to some kind of peer-to-peer
+
+ align:start position:0%
+and go to some kind of peer-to-peer
+ 
+
+ align:start position:0%
+and go to some kind of peer-to-peer
+design I don't have extremely high
+
+ align:start position:0%
+design I don't have extremely high
+ 
+
+ align:start position:0%
+design I don't have extremely high
+confidence in the peer-to-peer designs I
+
+ align:start position:0%
+confidence in the peer-to-peer designs I
+ 
+
+ align:start position:0%
+confidence in the peer-to-peer designs I
+know of so far
+
+ align:start position:0%
+know of so far
+ 
+
+ align:start position:0%
+know of so far
+but it could be that somebody's about to
+
+ align:start position:0%
+but it could be that somebody's about to
+ 
+
+ align:start position:0%
+but it could be that somebody's about to
+invent the next good one um let's see I
+
+ align:start position:0%
+invent the next good one um let's see I
+ 
+
+ align:start position:0%
+invent the next good one um let's see I
+don't know what that means oh um
+
+ align:start position:0%
+don't know what that means oh um
+ 
+
+ align:start position:0%
+don't know what that means oh um
+somebody asked a question about adding
+
+ align:start position:0%
+somebody asked a question about adding
+ 
+
+ align:start position:0%
+somebody asked a question about adding
+padding traffic or fake traffic to try
+
+ align:start position:0%
+padding traffic or fake traffic to try
+ 
+
+ align:start position:0%
+padding traffic or fake traffic to try
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+deceive um end to- end traffic
+
+ align:start position:0%
+deceive um end to- end traffic
+ 
+
+ align:start position:0%
+deceive um end to- end traffic
+correlation this is an exciting research
+
+ align:start position:0%
+correlation this is an exciting research
+ 
+
+ align:start position:0%
+correlation this is an exciting research
+field that needs someone smarter to work
+
+ align:start position:0%
+field that needs someone smarter to work
+ 
+
+ align:start position:0%
+field that needs someone smarter to work
+on it or someone with a more practical
+
+ align:start position:0%
+on it or someone with a more practical
+ 
+
+ align:start position:0%
+on it or someone with a more practical
+attitude to work on it than has
+
+ align:start position:0%
+attitude to work on it than has
+ 
+
+ align:start position:0%
+attitude to work on it than has
+previously worked on it too many of the
+
+ align:start position:0%
+previously worked on it too many of the
+ 
+
+ align:start position:0%
+previously worked on it too many of the
+results in the research literature there
+
+ align:start position:0%
+results in the research literature there
+ 
+
+ align:start position:0%
+results in the research literature there
+are only about
+
+ align:start position:0%
+are only about
+ 
+
+ align:start position:0%
+are only about
+like distinguishing the traffic of two
+
+ align:start position:0%
+like distinguishing the traffic of two
+ 
+
+ align:start position:0%
+like distinguishing the traffic of two
+users on a network containing one relay
+
+ align:start position:0%
+users on a network containing one relay
+ 
+
+ align:start position:0%
+users on a network containing one relay
+because that's how the math was easy to
+
+ align:start position:0%
+because that's how the math was easy to
+ 
+
+ align:start position:0%
+because that's how the math was easy to
+do instead but so because of this kind
+
+ align:start position:0%
+do instead but so because of this kind
+ 
+
+ align:start position:0%
+do instead but so because of this kind
+of stuff all of the traffic analysis
+
+ align:start position:0%
+of stuff all of the traffic analysis
+ 
+
+ align:start position:0%
+of stuff all of the traffic analysis
+defenses that we know of in this area
+
+ align:start position:0%
+defenses that we know of in this area
+ 
+
+ align:start position:0%
+defenses that we know of in this area
+that are still compatible with web
+
+ align:start position:0%
+that are still compatible with web
+ 
+
+ align:start position:0%
+that are still compatible with web
+browsing they sound good on if you read
+
+ align:start position:0%
+browsing they sound good on if you read
+ 
+
+ align:start position:0%
+browsing they sound good on if you read
+the abstract they'll say hooray this one
+
+ align:start position:0%
+the abstract they'll say hooray this one
+ 
+
+ align:start position:0%
+the abstract they'll say hooray this one
+makes the forces the attacker to gather
+
+ align:start position:0%
+makes the forces the attacker to gather
+ 
+
+ align:start position:0%
+makes the forces the attacker to gather
+three times as much traffic before they
+
+ align:start position:0%
+three times as much traffic before they
+ 
+
+ align:start position:0%
+three times as much traffic before they
+can correlate users except when you
+
+ align:start position:0%
+can correlate users except when you
+ 
+
+ align:start position:0%
+can correlate users except when you
+actually read the paper previously the
+
+ align:start position:0%
+actually read the paper previously the
+ 
+
+ align:start position:0%
+actually read the paper previously the
+attacker needed 2 seconds worth of
+
+ align:start position:0%
+attacker needed 2 seconds worth of
+ 
+
+ align:start position:0%
+attacker needed 2 seconds worth of
+traffic and then they won now the they
+
+ align:start position:0%
+traffic and then they won now the they
+ 
+
+ align:start position:0%
+traffic and then they won now the they
+need six seconds that's not really a
+
+ align:start position:0%
+need six seconds that's not really a
+ 
+
+ align:start position:0%
+need six seconds that's not really a
+defense in this model
+
+ align:start position:0%
+defense in this model
+ 
+
+ align:start position:0%
+defense in this model
+although perhaps against a real Network
+
+ align:start position:0%
+although perhaps against a real Network
+ 
+
+ align:start position:0%
+although perhaps against a real Network
+the numbers would be different and it
+
+ align:start position:0%
+the numbers would be different and it
+ 
+
+ align:start position:0%
+the numbers would be different and it
+might work so we would actually like to
+
+ align:start position:0%
+might work so we would actually like to
+ 
+
+ align:start position:0%
+might work so we would actually like to
+see some stuff done with padding and
+
+ align:start position:0%
+see some stuff done with padding and
+ 
+
+ align:start position:0%
+see some stuff done with padding and
+fake traffic but we don't like to add
+
+ align:start position:0%
+fake traffic but we don't like to add
+ 
+
+ align:start position:0%
+fake traffic but we don't like to add
+Voodoo defenses that we conjecture to
+
+ align:start position:0%
+Voodoo defenses that we conjecture to
+ 
+
+ align:start position:0%
+Voodoo defenses that we conjecture to
+maybe do some good although we can't do
+
+ align:start position:0%
+maybe do some good although we can't do
+ 
+
+ align:start position:0%
+maybe do some good although we can't do
+why we actually like to have evidence
+
+ align:start position:0%
+why we actually like to have evidence
+ 
+
+ align:start position:0%
+why we actually like to have evidence
+that what we're doing is going to that
+
+ align:start position:0%
+that what we're doing is going to that
+ 
+
+ align:start position:0%
+that what we're doing is going to that
+any changes we're going to make are
+
+ align:start position:0%
+any changes we're going to make are
+ 
+
+ align:start position:0%
+any changes we're going to make are
+going to help something I think I'm out
+
+ align:start position:0%
+going to help something I think I'm out
+ 
+
+ align:start position:0%
+going to help something I think I'm out
+of time and there may be a class in here
+
+ align:start position:0%
+of time and there may be a class in here
+ 
+
+ align:start position:0%
+of time and there may be a class in here
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+there's not all right so I'm going to
+
+ align:start position:0%
+there's not all right so I'm going to
+ 
+
+ align:start position:0%
+there's not all right so I'm going to
+hang around for a while and uh thanks
+
+ align:start position:0%
+hang around for a while and uh thanks
+ 
+
+ align:start position:0%
+hang around for a while and uh thanks
+for coming to listen I would take
+
+ align:start position:0%
+for coming to listen I would take
+ 
+
+ align:start position:0%
+for coming to listen I would take
+questions now but it's 12:25 and folks
+
+ align:start position:0%
+questions now but it's 12:25 and folks
+ 
+
+ align:start position:0%
+questions now but it's 12:25 and folks
+may have another class but I'll be
+
+ align:start position:0%
+may have another class but I'll be
+ 
+
+ align:start position:0%
+may have another class but I'll be
+around and so will David thank you very
+
+ align:start position:0%
+around and so will David thank you very
+ 
+
+ align:start position:0%
+around and so will David thank you very
+much for coming
+
+ align:start position:0%
+much for coming
+ 
+
+ align:start position:0%
+much for coming
+[Applause]
\ No newline at end of file
diff --git a/P2hxNOFiBb4.txt b/P2hxNOFiBb4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0d2d83e1810d5b7821292573918aae552863657e
--- /dev/null
+++ b/P2hxNOFiBb4.txt
@@ -0,0 +1,8147 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so this is the first of
+
+ align:start position:0%
+ocw.mit.edu okay so this is the first of
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so this is the first of
+a couple of lectures on group Theory now
+
+ align:start position:0%
+a couple of lectures on group Theory now
+ 
+
+ align:start position:0%
+a couple of lectures on group Theory now
+most of you have seen group Theory and
+
+ align:start position:0%
+most of you have seen group Theory and
+ 
+
+ align:start position:0%
+most of you have seen group Theory and
+no group Theory and so I'm going to go
+
+ align:start position:0%
+no group Theory and so I'm going to go
+ 
+
+ align:start position:0%
+no group Theory and so I'm going to go
+very fast and uh uh I'm
+
+ align:start position:0%
+very fast and uh uh I'm
+ 
+
+ align:start position:0%
+very fast and uh uh I'm
+also probably not going to go very deep
+
+ align:start position:0%
+also probably not going to go very deep
+ 
+
+ align:start position:0%
+also probably not going to go very deep
+because it's really hard to lecture on
+
+ align:start position:0%
+because it's really hard to lecture on
+ 
+
+ align:start position:0%
+because it's really hard to lecture on
+group Theory unless you're going to do
+
+ align:start position:0%
+group Theory unless you're going to do
+ 
+
+ align:start position:0%
+group Theory unless you're going to do
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+right let me just start out with a story
+
+ align:start position:0%
+right let me just start out with a story
+ 
+
+ align:start position:0%
+right let me just start out with a story
+when I was a freshman at Amis
+
+ align:start position:0%
+when I was a freshman at Amis
+ 
+
+ align:start position:0%
+when I was a freshman at Amis
+College I my
+
+ align:start position:0%
+College I my
+ 
+
+ align:start position:0%
+College I my
+uh I ended up uh doing research for a
+
+ align:start position:0%
+uh I ended up uh doing research for a
+ 
+
+ align:start position:0%
+uh I ended up uh doing research for a
+inorganic chemist by the name of Cooper
+
+ align:start position:0%
+inorganic chemist by the name of Cooper
+ 
+
+ align:start position:0%
+inorganic chemist by the name of Cooper
+Langford and in one of my first
+
+ align:start position:0%
+Langford and in one of my first
+ 
+
+ align:start position:0%
+Langford and in one of my first
+conversations with him I don't know
+
+ align:start position:0%
+conversations with him I don't know
+ 
+
+ align:start position:0%
+conversations with him I don't know
+quite why it happened this way but he I
+
+ align:start position:0%
+quite why it happened this way but he I
+ 
+
+ align:start position:0%
+quite why it happened this way but he I
+asked him a question about uh an allow
+
+ align:start position:0%
+asked him a question about uh an allow
+ 
+
+ align:start position:0%
+asked him a question about uh an allow
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+transition uh is allowed or somehow we
+
+ align:start position:0%
+transition uh is allowed or somehow we
+ 
+
+ align:start position:0%
+transition uh is allowed or somehow we
+got to that and he took out a little
+
+ align:start position:0%
+got to that and he took out a little
+ 
+
+ align:start position:0%
+got to that and he took out a little
+scrap of paper and he did a little group
+
+ align:start position:0%
+scrap of paper and he did a little group
+ 
+
+ align:start position:0%
+scrap of paper and he did a little group
+theory on the scrap of paper and and
+
+ align:start position:0%
+theory on the scrap of paper and and
+ 
+
+ align:start position:0%
+theory on the scrap of paper and and
+said this is allowed in this is
+
+ align:start position:0%
+said this is allowed in this is
+ 
+
+ align:start position:0%
+said this is allowed in this is
+forbidden and uh I'm sure there's more
+
+ align:start position:0%
+forbidden and uh I'm sure there's more
+ 
+
+ align:start position:0%
+forbidden and uh I'm sure there's more
+to the story but I just remember that
+
+ align:start position:0%
+to the story but I just remember that
+ 
+
+ align:start position:0%
+to the story but I just remember that
+scrap of paper and being incredibly
+
+ align:start position:0%
+scrap of paper and being incredibly
+ 
+
+ align:start position:0%
+scrap of paper and being incredibly
+impressed and that's really when I
+
+ align:start position:0%
+impressed and that's really when I
+ 
+
+ align:start position:0%
+impressed and that's really when I
+decided that I wanted to be a
+
+ align:start position:0%
+decided that I wanted to be a
+ 
+
+ align:start position:0%
+decided that I wanted to be a
+spectroscopist because uh the the idea
+
+ align:start position:0%
+spectroscopist because uh the the idea
+ 
+
+ align:start position:0%
+spectroscopist because uh the the idea
+of being able to make a decision based
+
+ align:start position:0%
+of being able to make a decision based
+ 
+
+ align:start position:0%
+of being able to make a decision based
+on something you can scribble on a piece
+
+ align:start position:0%
+on something you can scribble on a piece
+ 
+
+ align:start position:0%
+on something you can scribble on a piece
+of paper which was not obvious uh really
+
+ align:start position:0%
+of paper which was not obvious uh really
+ 
+
+ align:start position:0%
+of paper which was not obvious uh really
+appealed to me so this is uh how you do
+
+ align:start position:0%
+appealed to me so this is uh how you do
+ 
+
+ align:start position:0%
+appealed to me so this is uh how you do
+that and uh so let's talk about uh uh
+
+ align:start position:0%
+that and uh so let's talk about uh uh
+ 
+
+ align:start position:0%
+that and uh so let's talk about uh uh
+why we want group Theory um we'd like to
+
+ align:start position:0%
+why we want group Theory um we'd like to
+ 
+
+ align:start position:0%
+why we want group Theory um we'd like to
+be able to know about uh selection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules because everything we do in
+
+ align:start position:0%
+rules because everything we do in
+ 
+
+ align:start position:0%
+rules because everything we do in
+quantum mechanics involves setting up
+
+ align:start position:0%
+quantum mechanics involves setting up
+ 
+
+ align:start position:0%
+quantum mechanics involves setting up
+some kind of a
+
+ align:start position:0%
+some kind of a
+ 
+
+ align:start position:0%
+some kind of a
+matrix uh to represent the structure of
+
+ align:start position:0%
+matrix uh to represent the structure of
+ 
+
+ align:start position:0%
+matrix uh to represent the structure of
+a system or to calculate transition
+
+ align:start position:0%
+a system or to calculate transition
+ 
+
+ align:start position:0%
+a system or to calculate transition
+which transitions are allowed and uh so
+
+ align:start position:0%
+which transitions are allowed and uh so
+ 
+
+ align:start position:0%
+which transitions are allowed and uh so
+we we need to have something that's uh
+
+ align:start position:0%
+we we need to have something that's uh
+ 
+
+ align:start position:0%
+we we need to have something that's uh
+um a generalization on
+
+ align:start position:0%
+um a generalization on
+ 
+
+ align:start position:0%
+um a generalization on
+even versus odd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integrand and so group theory is that
+
+ align:start position:0%
+integrand and so group theory is that
+ 
+
+ align:start position:0%
+integrand and so group theory is that
+generalization
+
+ align:start position:0%
+generalization
+ 
+
+ align:start position:0%
+generalization
+um we'd also like to be able
+
+ align:start position:0%
+um we'd also like to be able
+ 
+
+ align:start position:0%
+um we'd also like to be able
+to uh construct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like to be able to construct functions
+
+ align:start position:0%
+like to be able to construct functions
+ 
+
+ align:start position:0%
+like to be able to construct functions
+which have well- defined symmetry
+
+ align:start position:0%
+which have well- defined symmetry
+ 
+
+ align:start position:0%
+which have well- defined symmetry
+classifications and so projection
+
+ align:start position:0%
+classifications and so projection
+ 
+
+ align:start position:0%
+classifications and so projection
+operators are a convenient way of doing
+
+ align:start position:0%
+operators are a convenient way of doing
+ 
+
+ align:start position:0%
+operators are a convenient way of doing
+that uh one of the main things we're
+
+ align:start position:0%
+that uh one of the main things we're
+ 
+
+ align:start position:0%
+that uh one of the main things we're
+going to do in today's lecture is set up
+
+ align:start position:0%
+going to do in today's lecture is set up
+ 
+
+ align:start position:0%
+going to do in today's lecture is set up
+the structure that enables us to say
+
+ align:start position:0%
+the structure that enables us to say
+ 
+
+ align:start position:0%
+the structure that enables us to say
+what is the uh
+
+ align:start position:0%
+what is the uh
+ 
+
+ align:start position:0%
+what is the uh
+nature of of
+
+ align:start position:0%
+nature of of
+ 
+
+ align:start position:0%
+nature of of
+molecular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibrations so starting out with a
+
+ align:start position:0%
+vibrations so starting out with a
+ 
+
+ align:start position:0%
+vibrations so starting out with a
+picture of the molecule you
+
+ align:start position:0%
+picture of the molecule you
+ 
+
+ align:start position:0%
+picture of the molecule you
+know uh what the geometric structure is
+
+ align:start position:0%
+know uh what the geometric structure is
+ 
+
+ align:start position:0%
+know uh what the geometric structure is
+or might be and sometimes the issue is
+
+ align:start position:0%
+or might be and sometimes the issue is
+ 
+
+ align:start position:0%
+or might be and sometimes the issue is
+well how do we decide among possible
+
+ align:start position:0%
+well how do we decide among possible
+ 
+
+ align:start position:0%
+well how do we decide among possible
+geometric structures qualitatively
+
+ align:start position:0%
+geometric structures qualitatively
+ 
+
+ align:start position:0%
+geometric structures qualitatively
+different ones is there something about
+
+ align:start position:0%
+different ones is there something about
+ 
+
+ align:start position:0%
+different ones is there something about
+the different qual ative structures that
+
+ align:start position:0%
+the different qual ative structures that
+ 
+
+ align:start position:0%
+the different qual ative structures that
+uh provides an
+
+ align:start position:0%
+uh provides an
+ 
+
+ align:start position:0%
+uh provides an
+unambiguous experimental observable that
+
+ align:start position:0%
+unambiguous experimental observable that
+ 
+
+ align:start position:0%
+unambiguous experimental observable that
+says this is
+
+ align:start position:0%
+says this is
+ 
+
+ align:start position:0%
+says this is
+d3h uh uh and uh is d3h a
+
+ align:start position:0%
+d3h uh uh and uh is d3h a
+ 
+
+ align:start position:0%
+d3h uh uh and uh is d3h a
+possibility is that a legal
+
+ align:start position:0%
+possibility is that a legal
+ 
+
+ align:start position:0%
+possibility is that a legal
+C3 c3h is a possibility D3 I don't know
+
+ align:start position:0%
+C3 c3h is a possibility D3 I don't know
+ 
+
+ align:start position:0%
+C3 c3h is a possibility D3 I don't know
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but you you decide between various
+
+ align:start position:0%
+but you you decide between various
+ 
+
+ align:start position:0%
+but you you decide between various
+qualitative
+
+ align:start position:0%
+qualitative
+ 
+
+ align:start position:0%
+qualitative
+geometries and uh
+
+ align:start position:0%
+geometries and uh
+ 
+
+ align:start position:0%
+geometries and uh
+so this lecture is about how do we use
+
+ align:start position:0%
+so this lecture is about how do we use
+ 
+
+ align:start position:0%
+so this lecture is about how do we use
+group Theory
+
+ align:start position:0%
+group Theory
+ 
+
+ align:start position:0%
+group Theory
+to construct and
+
+ align:start position:0%
+to construct and
+ 
+
+ align:start position:0%
+to construct and
+reduce reducible representations which
+
+ align:start position:0%
+reduce reducible representations which
+ 
+
+ align:start position:0%
+reduce reducible representations which
+contain information about what a
+
+ align:start position:0%
+contain information about what a
+ 
+
+ align:start position:0%
+contain information about what a
+molecule can do to irreducible
+
+ align:start position:0%
+molecule can do to irreducible
+ 
+
+ align:start position:0%
+molecule can do to irreducible
+representations that are the more
+
+ align:start position:0%
+representations that are the more
+ 
+
+ align:start position:0%
+representations that are the more
+fundament are the fundamental symmetry
+
+ align:start position:0%
+fundament are the fundamental symmetry
+ 
+
+ align:start position:0%
+fundament are the fundamental symmetry
+species of the various vibrations and
+
+ align:start position:0%
+species of the various vibrations and
+ 
+
+ align:start position:0%
+species of the various vibrations and
+there's all sorts of wonderful tricks
+
+ align:start position:0%
+there's all sorts of wonderful tricks
+ 
+
+ align:start position:0%
+there's all sorts of wonderful tricks
+involved okay so we're off to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+races and so we know that if we have
+
+ align:start position:0%
+races and so we know that if we have
+ 
+
+ align:start position:0%
+races and so we know that if we have
+some operator that commutes with the
+
+ align:start position:0%
+some operator that commutes with the
+ 
+
+ align:start position:0%
+some operator that commutes with the
+hamiltonian then we can simplify the
+
+ align:start position:0%
+hamiltonian then we can simplify the
+ 
+
+ align:start position:0%
+hamiltonian then we can simplify the
+hamiltonian by constructing igen
+
+ align:start position:0%
+hamiltonian by constructing igen
+ 
+
+ align:start position:0%
+hamiltonian by constructing igen
+functions of this simpler operator
+
+ align:start position:0%
+functions of this simpler operator
+ 
+
+ align:start position:0%
+functions of this simpler operator
+because that will enable us to block
+
+ align:start position:0%
+because that will enable us to block
+ 
+
+ align:start position:0%
+because that will enable us to block
+diagonalize the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hamiltonian now there's three different
+
+ align:start position:0%
+hamiltonian now there's three different
+ 
+
+ align:start position:0%
+hamiltonian now there's three different
+levels one is the full hamiltonian
+
+ align:start position:0%
+levels one is the full hamiltonian
+ 
+
+ align:start position:0%
+levels one is the full hamiltonian
+commuting with some
+
+ align:start position:0%
+commuting with some
+ 
+
+ align:start position:0%
+commuting with some
+operator and these are rigorous
+
+ align:start position:0%
+operator and these are rigorous
+ 
+
+ align:start position:0%
+operator and these are rigorous
+symmetries and they're not that many of
+
+ align:start position:0%
+symmetries and they're not that many of
+ 
+
+ align:start position:0%
+symmetries and they're not that many of
+them and usually they're pretty
+
+ align:start position:0%
+them and usually they're pretty
+ 
+
+ align:start position:0%
+them and usually they're pretty
+obvious uh and that's nice but we'd like
+
+ align:start position:0%
+obvious uh and that's nice but we'd like
+ 
+
+ align:start position:0%
+obvious uh and that's nice but we'd like
+to do more often we have some sort of
+
+ align:start position:0%
+to do more often we have some sort of
+ 
+
+ align:start position:0%
+to do more often we have some sort of
+zero order hamiltonian
+
+ align:start position:0%
+zero order hamiltonian
+ 
+
+ align:start position:0%
+zero order hamiltonian
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+approximation and those things generally
+
+ align:start position:0%
+approximation and those things generally
+ 
+
+ align:start position:0%
+approximation and those things generally
+have more Symmetry and it's easier to
+
+ align:start position:0%
+have more Symmetry and it's easier to
+ 
+
+ align:start position:0%
+have more Symmetry and it's easier to
+find operators that commute with the
+
+ align:start position:0%
+find operators that commute with the
+ 
+
+ align:start position:0%
+find operators that commute with the
+zero order hamiltonian and so this
+
+ align:start position:0%
+zero order hamiltonian and so this
+ 
+
+ align:start position:0%
+zero order hamiltonian and so this
+provides a a path towards constructing
+
+ align:start position:0%
+provides a a path towards constructing
+ 
+
+ align:start position:0%
+provides a a path towards constructing
+complete basis
+
+ align:start position:0%
+complete basis
+ 
+
+ align:start position:0%
+complete basis
+sets then there's a third
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing and uh in
+
+ align:start position:0%
+thing and uh in
+ 
+
+ align:start position:0%
+thing and uh in
+particular C2 AB
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C it's always true that the rotational
+
+ align:start position:0%
+C it's always true that the rotational
+ 
+
+ align:start position:0%
+C it's always true that the rotational
+hamiltonian uh commutes with C2
+
+ align:start position:0%
+hamiltonian uh commutes with C2
+ 
+
+ align:start position:0%
+hamiltonian uh commutes with C2
+rotations about the a b or c
+
+ align:start position:0%
+rotations about the a b or c
+ 
+
+ align:start position:0%
+rotations about the a b or c
+axes doesn't matter what the molecular
+
+ align:start position:0%
+axes doesn't matter what the molecular
+ 
+
+ align:start position:0%
+axes doesn't matter what the molecular
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+is the rotational hamiltonian which is
+
+ align:start position:0%
+is the rotational hamiltonian which is
+ 
+
+ align:start position:0%
+is the rotational hamiltonian which is
+expressed in terms of uh uh
+
+ align:start position:0%
+expressed in terms of uh uh
+ 
+
+ align:start position:0%
+expressed in terms of uh uh
+angular momenta
+
+ align:start position:0%
+angular momenta
+ 
+
+ align:start position:0%
+angular momenta
+components multiplying reciprocal
+
+ align:start position:0%
+components multiplying reciprocal
+ 
+
+ align:start position:0%
+components multiplying reciprocal
+inertial tensor
+
+ align:start position:0%
+inertial tensor
+ 
+
+ align:start position:0%
+inertial tensor
+elements uh in the principal axis system
+
+ align:start position:0%
+elements uh in the principal axis system
+ 
+
+ align:start position:0%
+elements uh in the principal axis system
+in the principal axis system the
+
+ align:start position:0%
+in the principal axis system the
+ 
+
+ align:start position:0%
+in the principal axis system the
+rotational uh hamiltonan looks like a
+
+ align:start position:0%
+rotational uh hamiltonan looks like a
+ 
+
+ align:start position:0%
+rotational uh hamiltonan looks like a
+football or a
+
+ align:start position:0%
+football or a
+ 
+
+ align:start position:0%
+football or a
+frisbee doesn't matter whether it's a
+
+ align:start position:0%
+frisbee doesn't matter whether it's a
+ 
+
+ align:start position:0%
+frisbee doesn't matter whether it's a
+symmetric or asymmetric top and you know
+
+ align:start position:0%
+symmetric or asymmetric top and you know
+ 
+
+ align:start position:0%
+symmetric or asymmetric top and you know
+that you take either one of those things
+
+ align:start position:0%
+that you take either one of those things
+ 
+
+ align:start position:0%
+that you take either one of those things
+and it's going to be uh uh it's going to
+
+ align:start position:0%
+and it's going to be uh uh it's going to
+ 
+
+ align:start position:0%
+and it's going to be uh uh it's going to
+have C2 symmetry about any axis and so
+
+ align:start position:0%
+have C2 symmetry about any axis and so
+ 
+
+ align:start position:0%
+have C2 symmetry about any axis and so
+the rotational hamiltonian is going to
+
+ align:start position:0%
+the rotational hamiltonian is going to
+ 
+
+ align:start position:0%
+the rotational hamiltonian is going to
+commute with all these things so there
+
+ align:start position:0%
+commute with all these things so there
+ 
+
+ align:start position:0%
+commute with all these things so there
+is going to be group
+
+ align:start position:0%
+is going to be group
+ 
+
+ align:start position:0%
+is going to be group
+theoretical uh features of rotational
+
+ align:start position:0%
+theoretical uh features of rotational
+ 
+
+ align:start position:0%
+theoretical uh features of rotational
+levels which are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Universal and uh in addition to the
+
+ align:start position:0%
+Universal and uh in addition to the
+ 
+
+ align:start position:0%
+Universal and uh in addition to the
+group theoretical characteristics of uh
+
+ align:start position:0%
+group theoretical characteristics of uh
+ 
+
+ align:start position:0%
+group theoretical characteristics of uh
+the vibrations and translations
+
+ align:start position:0%
+the vibrations and translations
+ 
+
+ align:start position:0%
+the vibrations and translations
+okay yes is that true even if you have
+
+ align:start position:0%
+okay yes is that true even if you have
+ 
+
+ align:start position:0%
+okay yes is that true even if you have
+um axis switching like lude vibrations
+
+ align:start position:0%
+um axis switching like lude vibrations
+ 
+
+ align:start position:0%
+um axis switching like lude vibrations
+and like that to the best of my
+
+ align:start position:0%
+and like that to the best of my
+ 
+
+ align:start position:0%
+and like that to the best of my
+knowledge that well there's a
+
+ align:start position:0%
+knowledge that well there's a
+ 
+
+ align:start position:0%
+knowledge that well there's a
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+uh okay no let me
+
+ align:start position:0%
+uh okay no let me
+ 
+
+ align:start position:0%
+uh okay no let me
+just if we use symmetric
+
+ align:start position:0%
+just if we use symmetric
+ 
+
+ align:start position:0%
+just if we use symmetric
+tops symmetric top basis set then this
+
+ align:start position:0%
+tops symmetric top basis set then this
+ 
+
+ align:start position:0%
+tops symmetric top basis set then this
+is true uh if we have asymmetric tops we
+
+ align:start position:0%
+is true uh if we have asymmetric tops we
+ 
+
+ align:start position:0%
+is true uh if we have asymmetric tops we
+Express the asymmetric top uh functions
+
+ align:start position:0%
+Express the asymmetric top uh functions
+ 
+
+ align:start position:0%
+Express the asymmetric top uh functions
+in terms of linear combinations of
+
+ align:start position:0%
+in terms of linear combinations of
+ 
+
+ align:start position:0%
+in terms of linear combinations of
+symmetric top basis functions and so if
+
+ align:start position:0%
+symmetric top basis functions and so if
+ 
+
+ align:start position:0%
+symmetric top basis functions and so if
+we can classify the symmetric top
+
+ align:start position:0%
+we can classify the symmetric top
+ 
+
+ align:start position:0%
+we can classify the symmetric top
+functions we can classify the asymmetric
+
+ align:start position:0%
+functions we can classify the asymmetric
+ 
+
+ align:start position:0%
+functions we can classify the asymmetric
+top now uh when you talked about large
+
+ align:start position:0%
+top now uh when you talked about large
+ 
+
+ align:start position:0%
+top now uh when you talked about large
+amplitude motion where you're blurring
+
+ align:start position:0%
+amplitude motion where you're blurring
+ 
+
+ align:start position:0%
+amplitude motion where you're blurring
+the distinction between rotation and
+
+ align:start position:0%
+the distinction between rotation and
+ 
+
+ align:start position:0%
+the distinction between rotation and
+vibration I'm still talking about basis
+
+ align:start position:0%
+vibration I'm still talking about basis
+ 
+
+ align:start position:0%
+vibration I'm still talking about basis
+functions and the ability to classify
+
+ align:start position:0%
+functions and the ability to classify
+ 
+
+ align:start position:0%
+functions and the ability to classify
+basis functions
+
+ align:start position:0%
+basis functions
+ 
+
+ align:start position:0%
+basis functions
+and I think that I'd better stop talking
+
+ align:start position:0%
+and I think that I'd better stop talking
+ 
+
+ align:start position:0%
+and I think that I'd better stop talking
+about this because I'm going to end up
+
+ align:start position:0%
+about this because I'm going to end up
+ 
+
+ align:start position:0%
+about this because I'm going to end up
+muddying the
+
+ align:start position:0%
+muddying the
+ 
+
+ align:start position:0%
+muddying the
+water okay so we have this now there's a
+
+ align:start position:0%
+water okay so we have this now there's a
+ 
+
+ align:start position:0%
+water okay so we have this now there's a
+whole bunch we start out and we talk
+
+ align:start position:0%
+whole bunch we start out and we talk
+ 
+
+ align:start position:0%
+whole bunch we start out and we talk
+about Point groups everybody learns
+
+ align:start position:0%
+about Point groups everybody learns
+ 
+
+ align:start position:0%
+about Point groups everybody learns
+group Theory from the point of view of
+
+ align:start position:0%
+group Theory from the point of view of
+ 
+
+ align:start position:0%
+group Theory from the point of view of
+Point groups and point groups are a
+
+ align:start position:0%
+Point groups and point groups are a
+ 
+
+ align:start position:0%
+Point groups and point groups are a
+useful way of dealing with rigid objects
+
+ align:start position:0%
+useful way of dealing with rigid objects
+ 
+
+ align:start position:0%
+useful way of dealing with rigid objects
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and they're not
+
+ align:start position:0%
+and they're not
+ 
+
+ align:start position:0%
+and they're not
+uh they're not useful for describing
+
+ align:start position:0%
+uh they're not useful for describing
+ 
+
+ align:start position:0%
+uh they're not useful for describing
+large amplitude motions or transitions
+
+ align:start position:0%
+large amplitude motions or transitions
+ 
+
+ align:start position:0%
+large amplitude motions or transitions
+between uh St electronic states where
+
+ align:start position:0%
+between uh St electronic states where
+ 
+
+ align:start position:0%
+between uh St electronic states where
+molecules have different shapes
+
+ align:start position:0%
+molecules have different shapes
+ 
+
+ align:start position:0%
+molecules have different shapes
+qualitative shapes a point group is
+
+ align:start position:0%
+qualitative shapes a point group is
+ 
+
+ align:start position:0%
+qualitative shapes a point group is
+called a point group because it consists
+
+ align:start position:0%
+called a point group because it consists
+ 
+
+ align:start position:0%
+called a point group because it consists
+of a bunch of symmetry operations
+
+ align:start position:0%
+of a bunch of symmetry operations
+ 
+
+ align:start position:0%
+of a bunch of symmetry operations
+rotations reflection planes
+
+ align:start position:0%
+rotations reflection planes
+ 
+
+ align:start position:0%
+rotations reflection planes
+uh uh in centers of inversion where all
+
+ align:start position:0%
+uh uh in centers of inversion where all
+ 
+
+ align:start position:0%
+uh uh in centers of inversion where all
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+these uh symmetry operations intersect
+
+ align:start position:0%
+these uh symmetry operations intersect
+ 
+
+ align:start position:0%
+these uh symmetry operations intersect
+with or contain one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point the real symmetries in molecules
+
+ align:start position:0%
+point the real symmetries in molecules
+ 
+
+ align:start position:0%
+point the real symmetries in molecules
+are uh the complete nuclear permutation
+
+ align:start position:0%
+are uh the complete nuclear permutation
+ 
+
+ align:start position:0%
+are uh the complete nuclear permutation
+inversion group nuclear permutations you
+
+ align:start position:0%
+inversion group nuclear permutations you
+ 
+
+ align:start position:0%
+inversion group nuclear permutations you
+have identical nuclei you can permute
+
+ align:start position:0%
+have identical nuclei you can permute
+ 
+
+ align:start position:0%
+have identical nuclei you can permute
+them those have to correspond to
+
+ align:start position:0%
+them those have to correspond to
+ 
+
+ align:start position:0%
+them those have to correspond to
+rigorous symmetries and there's a center
+
+ align:start position:0%
+rigorous symmetries and there's a center
+ 
+
+ align:start position:0%
+rigorous symmetries and there's a center
+there is a uh an inversion symmetry not
+
+ align:start position:0%
+there is a uh an inversion symmetry not
+ 
+
+ align:start position:0%
+there is a uh an inversion symmetry not
+in the body but with respect to the
+
+ align:start position:0%
+in the body but with respect to the
+ 
+
+ align:start position:0%
+in the body but with respect to the
+laboratory and so these are the rigorous
+
+ align:start position:0%
+laboratory and so these are the rigorous
+ 
+
+ align:start position:0%
+laboratory and so these are the rigorous
+symmetry elements now a subset of the
+
+ align:start position:0%
+symmetry elements now a subset of the
+ 
+
+ align:start position:0%
+symmetry elements now a subset of the
+permutations that are possible in a
+
+ align:start position:0%
+permutations that are possible in a
+ 
+
+ align:start position:0%
+permutations that are possible in a
+molecule are not
+
+ align:start position:0%
+molecule are not
+ 
+
+ align:start position:0%
+molecule are not
+feasible because in order to permute
+
+ align:start position:0%
+feasible because in order to permute
+ 
+
+ align:start position:0%
+feasible because in order to permute
+those two things you have to break bonds
+
+ align:start position:0%
+those two things you have to break bonds
+ 
+
+ align:start position:0%
+those two things you have to break bonds
+and so it requires going over a very
+
+ align:start position:0%
+and so it requires going over a very
+ 
+
+ align:start position:0%
+and so it requires going over a very
+high barrier they're not feasible so we
+
+ align:start position:0%
+high barrier they're not feasible so we
+ 
+
+ align:start position:0%
+high barrier they're not feasible so we
+forget about them but that corresponds
+
+ align:start position:0%
+forget about them but that corresponds
+ 
+
+ align:start position:0%
+forget about them but that corresponds
+to a degeneracy or there you have to
+
+ align:start position:0%
+to a degeneracy or there you have to
+ 
+
+ align:start position:0%
+to a degeneracy or there you have to
+somehow build a picture which
+
+ align:start position:0%
+somehow build a picture which
+ 
+
+ align:start position:0%
+somehow build a picture which
+incorporates those nonfeasible
+
+ align:start position:0%
+incorporates those nonfeasible
+ 
+
+ align:start position:0%
+incorporates those nonfeasible
+permutations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so if we exclude those we get What's
+
+ align:start position:0%
+so so if we exclude those we get What's
+ 
+
+ align:start position:0%
+so so if we exclude those we get What's
+called the molecular symmetry group
+
+ align:start position:0%
+called the molecular symmetry group
+ 
+
+ align:start position:0%
+called the molecular symmetry group
+group and the molecular symmetry group
+
+ align:start position:0%
+group and the molecular symmetry group
+ 
+
+ align:start position:0%
+group and the molecular symmetry group
+is isomorphic with the point
+
+ align:start position:0%
+is isomorphic with the point
+ 
+
+ align:start position:0%
+is isomorphic with the point
+group and
+
+ align:start position:0%
+group and
+ 
+
+ align:start position:0%
+group and
+so uh you can usually use Point
+
+ align:start position:0%
+so uh you can usually use Point
+ 
+
+ align:start position:0%
+so uh you can usually use Point
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+operations Point group
+
+ align:start position:0%
+operations Point group
+ 
+
+ align:start position:0%
+operations Point group
+ideas uh even though they are an
+
+ align:start position:0%
+ideas uh even though they are an
+ 
+
+ align:start position:0%
+ideas uh even though they are an
+approximation however when you have
+
+ align:start position:0%
+approximation however when you have
+ 
+
+ align:start position:0%
+approximation however when you have
+really high exitation really large
+
+ align:start position:0%
+really high exitation really large
+ 
+
+ align:start position:0%
+really high exitation really large
+amplitude motions
+
+ align:start position:0%
+amplitude motions
+ 
+
+ align:start position:0%
+amplitude motions
+uh they become more and more of the
+
+ align:start position:0%
+uh they become more and more of the
+ 
+
+ align:start position:0%
+uh they become more and more of the
+elements of the cnpi group that become
+
+ align:start position:0%
+elements of the cnpi group that become
+ 
+
+ align:start position:0%
+elements of the cnpi group that become
+feasible become relevant and levels
+
+ align:start position:0%
+feasible become relevant and levels
+ 
+
+ align:start position:0%
+feasible become relevant and levels
+which you when you when you say I've
+
+ align:start position:0%
+which you when you when you say I've
+ 
+
+ align:start position:0%
+which you when you when you say I've
+neglected uh a symmetry operation
+
+ align:start position:0%
+neglected uh a symmetry operation
+ 
+
+ align:start position:0%
+neglected uh a symmetry operation
+because it's non feasible that really
+
+ align:start position:0%
+because it's non feasible that really
+ 
+
+ align:start position:0%
+because it's non feasible that really
+means that the levels are have a
+
+ align:start position:0%
+means that the levels are have a
+ 
+
+ align:start position:0%
+means that the levels are have a
+built-in this the energy states have a
+
+ align:start position:0%
+built-in this the energy states have a
+ 
+
+ align:start position:0%
+built-in this the energy states have a
+built-in
+
+ align:start position:0%
+built-in
+ 
+
+ align:start position:0%
+built-in
+degeneracy and when what had been
+
+ align:start position:0%
+degeneracy and when what had been
+ 
+
+ align:start position:0%
+degeneracy and when what had been
+non-feasible becomes feasible some of
+
+ align:start position:0%
+non-feasible becomes feasible some of
+ 
+
+ align:start position:0%
+non-feasible becomes feasible some of
+that degeneracy gets lifted and that's
+
+ align:start position:0%
+that degeneracy gets lifted and that's
+ 
+
+ align:start position:0%
+that degeneracy gets lifted and that's
+really what we're interested when we're
+
+ align:start position:0%
+really what we're interested when we're
+ 
+
+ align:start position:0%
+really what we're interested when we're
+looking at bond-breaking isomerization
+
+ align:start position:0%
+looking at bond-breaking isomerization
+ 
+
+ align:start position:0%
+looking at bond-breaking isomerization
+because nothing could be more not
+
+ align:start position:0%
+because nothing could be more not
+ 
+
+ align:start position:0%
+because nothing could be more not
+feasible than Breaking
+
+ align:start position:0%
+feasible than Breaking
+ 
+
+ align:start position:0%
+feasible than Breaking
+bonds and so
+
+ align:start position:0%
+bonds and so
+ 
+
+ align:start position:0%
+bonds and so
+uh you have to get used to the idea that
+
+ align:start position:0%
+uh you have to get used to the idea that
+ 
+
+ align:start position:0%
+uh you have to get used to the idea that
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+neglected a rigorous
+
+ align:start position:0%
+neglected a rigorous
+ 
+
+ align:start position:0%
+neglected a rigorous
+symmetry you have said I'm going to
+
+ align:start position:0%
+symmetry you have said I'm going to
+ 
+
+ align:start position:0%
+symmetry you have said I'm going to
+treat a state as if it were non-
+
+ align:start position:0%
+treat a state as if it were non-
+ 
+
+ align:start position:0%
+treat a state as if it were non-
+degenerate and you can get away with
+
+ align:start position:0%
+degenerate and you can get away with
+ 
+
+ align:start position:0%
+degenerate and you can get away with
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+until that uh non-feasible operation
+
+ align:start position:0%
+until that uh non-feasible operation
+ 
+
+ align:start position:0%
+until that uh non-feasible operation
+becomes relevant so we have the
+
+ align:start position:0%
+becomes relevant so we have the
+ 
+
+ align:start position:0%
+becomes relevant so we have the
+molecular symmetry group and that takes
+
+ align:start position:0%
+molecular symmetry group and that takes
+ 
+
+ align:start position:0%
+molecular symmetry group and that takes
+us back to the point group and usually
+
+ align:start position:0%
+us back to the point group and usually
+ 
+
+ align:start position:0%
+us back to the point group and usually
+there are no surprises if you started
+
+ align:start position:0%
+there are no surprises if you started
+ 
+
+ align:start position:0%
+there are no surprises if you started
+out with with ordinary Point group group
+
+ align:start position:0%
+out with with ordinary Point group group
+ 
+
+ align:start position:0%
+out with with ordinary Point group group
+Theory you can
+
+ align:start position:0%
+Theory you can
+ 
+
+ align:start position:0%
+Theory you can
+classify uh your States quite well but
+
+ align:start position:0%
+classify uh your States quite well but
+ 
+
+ align:start position:0%
+classify uh your States quite well but
+you still have problems when you're
+
+ align:start position:0%
+you still have problems when you're
+ 
+
+ align:start position:0%
+you still have problems when you're
+facing transitions between electronic
+
+ align:start position:0%
+facing transitions between electronic
+ 
+
+ align:start position:0%
+facing transitions between electronic
+states where the equilibrium geometry is
+
+ align:start position:0%
+states where the equilibrium geometry is
+ 
+
+ align:start position:0%
+states where the equilibrium geometry is
+associated with different point groups
+
+ align:start position:0%
+associated with different point groups
+ 
+
+ align:start position:0%
+associated with different point groups
+and there are a lot of ad hoc ways of
+
+ align:start position:0%
+and there are a lot of ad hoc ways of
+ 
+
+ align:start position:0%
+and there are a lot of ad hoc ways of
+trying to find your way
+
+ align:start position:0%
+trying to find your way
+ 
+
+ align:start position:0%
+trying to find your way
+around uh you know what when you're
+
+ align:start position:0%
+around uh you know what when you're
+ 
+
+ align:start position:0%
+around uh you know what when you're
+going from a higher symmetry to a lower
+
+ align:start position:0%
+going from a higher symmetry to a lower
+ 
+
+ align:start position:0%
+going from a higher symmetry to a lower
+symmetry it's usually possible to sort
+
+ align:start position:0%
+symmetry it's usually possible to sort
+ 
+
+ align:start position:0%
+symmetry it's usually possible to sort
+of your way through this but
+
+ align:start position:0%
+of your way through this but
+ 
+
+ align:start position:0%
+of your way through this but
+when you're going say between a c2h and
+
+ align:start position:0%
+when you're going say between a c2h and
+ 
+
+ align:start position:0%
+when you're going say between a c2h and
+a c2v two groups that have the
+
+ align:start position:0%
+a c2v two groups that have the
+ 
+
+ align:start position:0%
+a c2v two groups that have the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+dimensionality uh when you're doing that
+
+ align:start position:0%
+dimensionality uh when you're doing that
+ 
+
+ align:start position:0%
+dimensionality uh when you're doing that
+you really have to be careful and it's
+
+ align:start position:0%
+you really have to be careful and it's
+ 
+
+ align:start position:0%
+you really have to be careful and it's
+there that keeping track of the
+
+ align:start position:0%
+there that keeping track of the
+ 
+
+ align:start position:0%
+there that keeping track of the
+permutations and inversions provide you
+
+ align:start position:0%
+permutations and inversions provide you
+ 
+
+ align:start position:0%
+permutations and inversions provide you
+with guidance and often you have to go
+
+ align:start position:0%
+with guidance and often you have to go
+ 
+
+ align:start position:0%
+with guidance and often you have to go
+to a higher dimensional group in order
+
+ align:start position:0%
+to a higher dimensional group in order
+ 
+
+ align:start position:0%
+to a higher dimensional group in order
+to see the connection between two
+
+ align:start position:0%
+to see the connection between two
+ 
+
+ align:start position:0%
+to see the connection between two
+different point
+
+ align:start position:0%
+different point
+ 
+
+ align:start position:0%
+different point
+groups so this is a beautiful and subtle
+
+ align:start position:0%
+groups so this is a beautiful and subtle
+ 
+
+ align:start position:0%
+groups so this is a beautiful and subtle
+thing but you want to still see the
+
+ align:start position:0%
+thing but you want to still see the
+ 
+
+ align:start position:0%
+thing but you want to still see the
+beauty and power of just simple Point
+
+ align:start position:0%
+beauty and power of just simple Point
+ 
+
+ align:start position:0%
+beauty and power of just simple Point
+group group Theory and that's what I'll
+
+ align:start position:0%
+group group Theory and that's what I'll
+ 
+
+ align:start position:0%
+group group Theory and that's what I'll
+be talking about okay so I assume assum
+
+ align:start position:0%
+be talking about okay so I assume assum
+ 
+
+ align:start position:0%
+be talking about okay so I assume assum
+that everybody has seen plenty of group
+
+ align:start position:0%
+that everybody has seen plenty of group
+ 
+
+ align:start position:0%
+that everybody has seen plenty of group
+theory yes no everybody in the room if
+
+ align:start position:0%
+theory yes no everybody in the room if
+ 
+
+ align:start position:0%
+theory yes no everybody in the room if
+anybody says no I will say
+
+ align:start position:0%
+anybody says no I will say
+ 
+
+ align:start position:0%
+anybody says no I will say
+more so you've seen some group
+
+ align:start position:0%
+more so you've seen some group
+ 
+
+ align:start position:0%
+more so you've seen some group
+Theory okay well let let's just
+
+ align:start position:0%
+Theory okay well let let's just
+ 
+
+ align:start position:0%
+Theory okay well let let's just
+um let's just touch on some high points
+
+ align:start position:0%
+um let's just touch on some high points
+ 
+
+ align:start position:0%
+um let's just touch on some high points
+so we have symmetry operations rotations
+
+ align:start position:0%
+so we have symmetry operations rotations
+ 
+
+ align:start position:0%
+so we have symmetry operations rotations
+are uh denoted with a Capital C and an n
+
+ align:start position:0%
+are uh denoted with a Capital C and an n
+ 
+
+ align:start position:0%
+are uh denoted with a Capital C and an n
+n is the order of the rotation and so if
+
+ align:start position:0%
+n is the order of the rotation and so if
+ 
+
+ align:start position:0%
+n is the order of the rotation and so if
+uh you rotate by pi to uh if that's a
+
+ align:start position:0%
+uh you rotate by pi to uh if that's a
+ 
+
+ align:start position:0%
+uh you rotate by pi to uh if that's a
+symmetry operation that's C2 if you
+
+ align:start position:0%
+symmetry operation that's C2 if you
+ 
+
+ align:start position:0%
+symmetry operation that's C2 if you
+rotate by uh 2 pi over 3 that's C3 the
+
+ align:start position:0%
+rotate by uh 2 pi over 3 that's C3 the
+ 
+
+ align:start position:0%
+rotate by uh 2 pi over 3 that's C3 the
+number of clicks
+
+ align:start position:0%
+number of clicks
+ 
+
+ align:start position:0%
+number of clicks
+along a complete rotation so there are
+
+ align:start position:0%
+along a complete rotation so there are
+ 
+
+ align:start position:0%
+along a complete rotation so there are
+various
+
+ align:start position:0%
+various
+ 
+
+ align:start position:0%
+various
+CNS uh there are planes of symmetry all
+
+ align:start position:0%
+CNS uh there are planes of symmetry all
+ 
+
+ align:start position:0%
+CNS uh there are planes of symmetry all
+of which are called Sigma and there are
+
+ align:start position:0%
+of which are called Sigma and there are
+ 
+
+ align:start position:0%
+of which are called Sigma and there are
+two kinds well there are three kinds of
+
+ align:start position:0%
+two kinds well there are three kinds of
+ 
+
+ align:start position:0%
+two kinds well there are three kinds of
+sigmas Sigma V
+
+ align:start position:0%
+sigmas Sigma V
+ 
+
+ align:start position:0%
+sigmas Sigma V
+Sigma H and sigma
+
+ align:start position:0%
+Sigma H and sigma
+ 
+
+ align:start position:0%
+Sigma H and sigma
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+D most of the Symmetry planes that we
+
+ align:start position:0%
+D most of the Symmetry planes that we
+ 
+
+ align:start position:0%
+D most of the Symmetry planes that we
+see are Sigma V this is a plane that
+
+ align:start position:0%
+see are Sigma V this is a plane that
+ 
+
+ align:start position:0%
+see are Sigma V this is a plane that
+contains the highest order
+
+ align:start position:0%
+contains the highest order
+ 
+
+ align:start position:0%
+contains the highest order
+rotation so uh high order rotation
+
+ align:start position:0%
+rotation so uh high order rotation
+ 
+
+ align:start position:0%
+rotation so uh high order rotation
+Benzene is C6 has a has a C6 rotation
+
+ align:start position:0%
+Benzene is C6 has a has a C6 rotation
+ 
+
+ align:start position:0%
+Benzene is C6 has a has a C6 rotation
+and so Sigma V we always draw the
+
+ align:start position:0%
+and so Sigma V we always draw the
+ 
+
+ align:start position:0%
+and so Sigma V we always draw the
+rotation axis like this and sigma V is a
+
+ align:start position:0%
+rotation axis like this and sigma V is a
+ 
+
+ align:start position:0%
+rotation axis like this and sigma V is a
+vertical plane Sigma H is a horizontal
+
+ align:start position:0%
+vertical plane Sigma H is a horizontal
+ 
+
+ align:start position:0%
+vertical plane Sigma H is a horizontal
+plane and uh Sigma D is a vertical plane
+
+ align:start position:0%
+plane and uh Sigma D is a vertical plane
+ 
+
+ align:start position:0%
+plane and uh Sigma D is a vertical plane
+uh which
+
+ align:start position:0%
+uh which
+ 
+
+ align:start position:0%
+uh which
+bcts uh perpendicular C2
+
+ align:start position:0%
+bcts uh perpendicular C2
+ 
+
+ align:start position:0%
+bcts uh perpendicular C2
+axis so we have those things then we
+
+ align:start position:0%
+axis so we have those things then we
+ 
+
+ align:start position:0%
+axis so we have those things then we
+have I I is inversion in the body
+
+ align:start position:0%
+have I I is inversion in the body
+ 
+
+ align:start position:0%
+have I I is inversion in the body
+frame and that's different from Big I
+
+ align:start position:0%
+frame and that's different from Big I
+ 
+
+ align:start position:0%
+frame and that's different from Big I
+which is inversion in the laboratory and
+
+ align:start position:0%
+which is inversion in the laboratory and
+ 
+
+ align:start position:0%
+which is inversion in the laboratory and
+people do confuse those and uh uh this
+
+ align:start position:0%
+people do confuse those and uh uh this
+ 
+
+ align:start position:0%
+people do confuse those and uh uh this
+has to do with parody and this has to do
+
+ align:start position:0%
+has to do with parody and this has to do
+ 
+
+ align:start position:0%
+has to do with parody and this has to do
+with gu Symmetry and it's very very it's
+
+ align:start position:0%
+with gu Symmetry and it's very very it's
+ 
+
+ align:start position:0%
+with gu Symmetry and it's very very it's
+almost as bad as saying nuclear to get
+
+ align:start position:0%
+almost as bad as saying nuclear to get
+ 
+
+ align:start position:0%
+almost as bad as saying nuclear to get
+to call the Symmetry species associated
+
+ align:start position:0%
+to call the Symmetry species associated
+ 
+
+ align:start position:0%
+to call the Symmetry species associated
+with little I uh as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parody and it's very common okay stop me
+
+ align:start position:0%
+parody and it's very common okay stop me
+ 
+
+ align:start position:0%
+parody and it's very common okay stop me
+I mean this is really
+
+ align:start position:0%
+I mean this is really
+ 
+
+ align:start position:0%
+I mean this is really
+uh you're you're you're sitting here I I
+
+ align:start position:0%
+uh you're you're you're sitting here I I
+ 
+
+ align:start position:0%
+uh you're you're you're sitting here I I
+want you to you know to know all of the
+
+ align:start position:0%
+want you to you know to know all of the
+ 
+
+ align:start position:0%
+want you to you know to know all of the
+actors there's also improper
+
+ align:start position:0%
+actors there's also improper
+ 
+
+ align:start position:0%
+actors there's also improper
+rotations well I should also say c i is
+
+ align:start position:0%
+rotations well I should also say c i is
+ 
+
+ align:start position:0%
+rotations well I should also say c i is
+the same thing as I have to uh look at
+
+ align:start position:0%
+the same thing as I have to uh look at
+ 
+
+ align:start position:0%
+the same thing as I have to uh look at
+that C2 time Sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H and uh so but s SN is
+
+ align:start position:0%
+H and uh so but s SN is
+ 
+
+ align:start position:0%
+H and uh so but s SN is
+CN Sigma H now often you have a this
+
+ align:start position:0%
+CN Sigma H now often you have a this
+ 
+
+ align:start position:0%
+CN Sigma H now often you have a this
+called an improper rotation often you
+
+ align:start position:0%
+called an improper rotation often you
+ 
+
+ align:start position:0%
+called an improper rotation often you
+have a higher order improper rotation
+
+ align:start position:0%
+have a higher order improper rotation
+ 
+
+ align:start position:0%
+have a higher order improper rotation
+than proper rotation so CN doesn't have
+
+ align:start position:0%
+than proper rotation so CN doesn't have
+ 
+
+ align:start position:0%
+than proper rotation so CN doesn't have
+to be a symmetry but the product of two
+
+ align:start position:0%
+to be a symmetry but the product of two
+ 
+
+ align:start position:0%
+to be a symmetry but the product of two
+would be that and so uh the inversion is
+
+ align:start position:0%
+would be that and so uh the inversion is
+ 
+
+ align:start position:0%
+would be that and so uh the inversion is
+S2 but we always give it a special name
+
+ align:start position:0%
+S2 but we always give it a special name
+ 
+
+ align:start position:0%
+S2 but we always give it a special name
+and certain symmetry operations can
+
+ align:start position:0%
+and certain symmetry operations can
+ 
+
+ align:start position:0%
+and certain symmetry operations can
+commute with each other and others don't
+
+ align:start position:0%
+commute with each other and others don't
+ 
+
+ align:start position:0%
+commute with each other and others don't
+and you have to be careful about that
+
+ align:start position:0%
+and you have to be careful about that
+ 
+
+ align:start position:0%
+and you have to be careful about that
+Reflections and uh
+
+ align:start position:0%
+Reflections and uh
+ 
+
+ align:start position:0%
+Reflections and uh
+rotations generally commute but uh at
+
+ align:start position:0%
+rotations generally commute but uh at
+ 
+
+ align:start position:0%
+rotations generally commute but uh at
+least these two commute um
+
+ align:start position:0%
+least these two commute um
+ 
+
+ align:start position:0%
+least these two commute um
+so okay so we have a
+
+ align:start position:0%
+so okay so we have a
+ 
+
+ align:start position:0%
+so okay so we have a
+group and some of the properties of a
+
+ align:start position:0%
+group and some of the properties of a
+ 
+
+ align:start position:0%
+group and some of the properties of a
+group are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closure so we have a bunch of symmetry
+
+ align:start position:0%
+closure so we have a bunch of symmetry
+ 
+
+ align:start position:0%
+closure so we have a bunch of symmetry
+operations
+
+ align:start position:0%
+operations
+ 
+
+ align:start position:0%
+operations
+R and we can multiply R1 *
+
+ align:start position:0%
+R and we can multiply R1 *
+ 
+
+ align:start position:0%
+R and we can multiply R1 *
+R2 and when you do that you get always
+
+ align:start position:0%
+R2 and when you do that you get always
+ 
+
+ align:start position:0%
+R2 and when you do that you get always
+another symmetry operation in the group
+
+ align:start position:0%
+another symmetry operation in the group
+ 
+
+ align:start position:0%
+another symmetry operation in the group
+so there is a multiplication table among
+
+ align:start position:0%
+so there is a multiplication table among
+ 
+
+ align:start position:0%
+so there is a multiplication table among
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+symmetries which is complete you can
+
+ align:start position:0%
+symmetries which is complete you can
+ 
+
+ align:start position:0%
+symmetries which is complete you can
+never get something outside the
+
+ align:start position:0%
+never get something outside the
+ 
+
+ align:start position:0%
+never get something outside the
+group and if you have uh R1 R2 R3 you
+
+ align:start position:0%
+group and if you have uh R1 R2 R3 you
+ 
+
+ align:start position:0%
+group and if you have uh R1 R2 R3 you
+can put parentheses around any two
+
+ align:start position:0%
+can put parentheses around any two
+ 
+
+ align:start position:0%
+can put parentheses around any two
+um there's also an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse so every
+
+ align:start position:0%
+inverse so every
+ 
+
+ align:start position:0%
+inverse so every
+operation in a group in a symmetry group
+
+ align:start position:0%
+operation in a group in a symmetry group
+ 
+
+ align:start position:0%
+operation in a group in a symmetry group
+has to have an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse and so we have uh um and there
+
+ align:start position:0%
+inverse and so we have uh um and there
+ 
+
+ align:start position:0%
+inverse and so we have uh um and there
+is also an identity operation which is
+
+ align:start position:0%
+is also an identity operation which is
+ 
+
+ align:start position:0%
+is also an identity operation which is
+usually denoted e but sometimes I I is
+
+ align:start position:0%
+usually denoted e but sometimes I I is
+ 
+
+ align:start position:0%
+usually denoted e but sometimes I I is
+dangerous because I means something else
+
+ align:start position:0%
+dangerous because I means something else
+ 
+
+ align:start position:0%
+dangerous because I means something else
+but not in point group land but e also
+
+ align:start position:0%
+but not in point group land but e also
+ 
+
+ align:start position:0%
+but not in point group land but e also
+means other things
+
+ align:start position:0%
+means other things
+ 
+
+ align:start position:0%
+means other things
+yeah so uh okay so there's a little bit
+
+ align:start position:0%
+yeah so uh okay so there's a little bit
+ 
+
+ align:start position:0%
+yeah so uh okay so there's a little bit
+of heterogeneity about uh um um notation
+
+ align:start position:0%
+of heterogeneity about uh um um notation
+ 
+
+ align:start position:0%
+of heterogeneity about uh um um notation
+but there's an awful lot of universality
+
+ align:start position:0%
+but there's an awful lot of universality
+ 
+
+ align:start position:0%
+but there's an awful lot of universality
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you look at a molecule and you
+
+ align:start position:0%
+now you look at a molecule and you
+ 
+
+ align:start position:0%
+now you look at a molecule and you
+classify it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+according to symmetry operations
+
+ align:start position:0%
+according to symmetry operations
+ 
+
+ align:start position:0%
+according to symmetry operations
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+now a symmetry operation is one where if
+
+ align:start position:0%
+now a symmetry operation is one where if
+ 
+
+ align:start position:0%
+now a symmetry operation is one where if
+you apply it to the
+
+ align:start position:0%
+you apply it to the
+ 
+
+ align:start position:0%
+you apply it to the
+molecule well uh let me say it
+
+ align:start position:0%
+molecule well uh let me say it
+ 
+
+ align:start position:0%
+molecule well uh let me say it
+again you look at the molecule you leave
+
+ align:start position:0%
+again you look at the molecule you leave
+ 
+
+ align:start position:0%
+again you look at the molecule you leave
+the room somebody your friend applies a
+
+ align:start position:0%
+the room somebody your friend applies a
+ 
+
+ align:start position:0%
+the room somebody your friend applies a
+symmetry operation to the molecule you
+
+ align:start position:0%
+symmetry operation to the molecule you
+ 
+
+ align:start position:0%
+symmetry operation to the molecule you
+come back back you can't tell that
+
+ align:start position:0%
+come back back you can't tell that
+ 
+
+ align:start position:0%
+come back back you can't tell that
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+happened so you classify the molecule
+
+ align:start position:0%
+happened so you classify the molecule
+ 
+
+ align:start position:0%
+happened so you classify the molecule
+According to which symmetry operations
+
+ align:start position:0%
+According to which symmetry operations
+ 
+
+ align:start position:0%
+According to which symmetry operations
+exist and that enables you to to
+
+ align:start position:0%
+exist and that enables you to to
+ 
+
+ align:start position:0%
+exist and that enables you to to
+identify the point group and there is a
+
+ align:start position:0%
+identify the point group and there is a
+ 
+
+ align:start position:0%
+identify the point group and there is a
+logical procedure for doing that uh and
+
+ align:start position:0%
+logical procedure for doing that uh and
+ 
+
+ align:start position:0%
+logical procedure for doing that uh and
+that logical procedure is uh a table in
+
+ align:start position:0%
+that logical procedure is uh a table in
+ 
+
+ align:start position:0%
+that logical procedure is uh a table in
+bernat's book and you can do it it's
+
+ align:start position:0%
+bernat's book and you can do it it's
+ 
+
+ align:start position:0%
+bernat's book and you can do it it's
+it's a usually we deal with such low
+
+ align:start position:0%
+it's a usually we deal with such low
+ 
+
+ align:start position:0%
+it's a usually we deal with such low
+order groups that it's not not a very
+
+ align:start position:0%
+order groups that it's not not a very
+ 
+
+ align:start position:0%
+order groups that it's not not a very
+complicated matter they're always c2h or
+
+ align:start position:0%
+complicated matter they're always c2h or
+ 
+
+ align:start position:0%
+complicated matter they're always c2h or
+c2v or
+
+ align:start position:0%
+c2v or
+ 
+
+ align:start position:0%
+c2v or
+C2 so okay so you classify the
+
+ align:start position:0%
+C2 so okay so you classify the
+ 
+
+ align:start position:0%
+C2 so okay so you classify the
+group so the next thing
+
+ align:start position:0%
+group so the next thing
+ 
+
+ align:start position:0%
+group so the next thing
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+representations so we have objects that
+
+ align:start position:0%
+representations so we have objects that
+ 
+
+ align:start position:0%
+representations so we have objects that
+have a multiplication
+
+ align:start position:0%
+have a multiplication
+ 
+
+ align:start position:0%
+have a multiplication
+table and uh so we'd like to represent
+
+ align:start position:0%
+table and uh so we'd like to represent
+ 
+
+ align:start position:0%
+table and uh so we'd like to represent
+these objects by matrices
+
+ align:start position:0%
+these objects by matrices
+ 
+
+ align:start position:0%
+these objects by matrices
+which have the same multiplication table
+
+ align:start position:0%
+which have the same multiplication table
+ 
+
+ align:start position:0%
+which have the same multiplication table
+now same is a complicated word because
+
+ align:start position:0%
+now same is a complicated word because
+ 
+
+ align:start position:0%
+now same is a complicated word because
+it means that there is nothing in the
+
+ align:start position:0%
+it means that there is nothing in the
+ 
+
+ align:start position:0%
+it means that there is nothing in the
+multiplication table of these
+
+ align:start position:0%
+multiplication table of these
+ 
+
+ align:start position:0%
+multiplication table of these
+matrices which would be
+
+ align:start position:0%
+matrices which would be
+ 
+
+ align:start position:0%
+matrices which would be
+untrue with respect to the
+
+ align:start position:0%
+untrue with respect to the
+ 
+
+ align:start position:0%
+untrue with respect to the
+multiplication table of the operator
+
+ align:start position:0%
+multiplication table of the operator
+ 
+
+ align:start position:0%
+multiplication table of the operator
+sometimes the multiplication table is
+
+ align:start position:0%
+sometimes the multiplication table is
+ 
+
+ align:start position:0%
+sometimes the multiplication table is
+has lost a lot of information so 1 * 1
+
+ align:start position:0%
+has lost a lot of information so 1 * 1
+ 
+
+ align:start position:0%
+has lost a lot of information so 1 * 1
+is always one
+
+ align:start position:0%
+is always one
+ 
+
+ align:start position:0%
+is always one
+and you can represent a lot uh yes so uh
+
+ align:start position:0%
+and you can represent a lot uh yes so uh
+ 
+
+ align:start position:0%
+and you can represent a lot uh yes so uh
+there will be Matrix representations now
+
+ align:start position:0%
+there will be Matrix representations now
+ 
+
+ align:start position:0%
+there will be Matrix representations now
+that we're particularly interested in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geometric
+
+ align:start position:0%
+geometric
+ 
+
+ align:start position:0%
+geometric
+Transformations so what we want to do is
+
+ align:start position:0%
+Transformations so what we want to do is
+ 
+
+ align:start position:0%
+Transformations so what we want to do is
+to to find a set of
+
+ align:start position:0%
+to to find a set of
+ 
+
+ align:start position:0%
+to to find a set of
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+which are equivalent to each of the
+
+ align:start position:0%
+which are equivalent to each of the
+ 
+
+ align:start position:0%
+which are equivalent to each of the
+Symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operations equivalent is a complicated
+
+ align:start position:0%
+operations equivalent is a complicated
+ 
+
+ align:start position:0%
+operations equivalent is a complicated
+thing so one way of doing that is to
+
+ align:start position:0%
+thing so one way of doing that is to
+ 
+
+ align:start position:0%
+thing so one way of doing that is to
+label each of the atoms in a molecule by
+
+ align:start position:0%
+label each of the atoms in a molecule by
+ 
+
+ align:start position:0%
+label each of the atoms in a molecule by
+three cartisian
+
+ align:start position:0%
+three cartisian
+ 
+
+ align:start position:0%
+three cartisian
+coordinates and then we
+
+ align:start position:0%
+coordinates and then we
+ 
+
+ align:start position:0%
+coordinates and then we
+build uh
+
+ align:start position:0%
+build uh
+ 
+
+ align:start position:0%
+build uh
+matrices that transform the coordinates
+
+ align:start position:0%
+matrices that transform the coordinates
+ 
+
+ align:start position:0%
+matrices that transform the coordinates
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+atoms uh
+
+ align:start position:0%
+atoms uh
+ 
+
+ align:start position:0%
+atoms uh
+according to how the Symmetry operation
+
+ align:start position:0%
+according to how the Symmetry operation
+ 
+
+ align:start position:0%
+according to how the Symmetry operation
+would would move
+
+ align:start position:0%
+would would move
+ 
+
+ align:start position:0%
+would would move
+things and that's the the first thing we
+
+ align:start position:0%
+things and that's the the first thing we
+ 
+
+ align:start position:0%
+things and that's the the first thing we
+do we're going to do but the nice thing
+
+ align:start position:0%
+do we're going to do but the nice thing
+ 
+
+ align:start position:0%
+do we're going to do but the nice thing
+about this is
+
+ align:start position:0%
+about this is
+ 
+
+ align:start position:0%
+about this is
+that when we create this 3-end
+
+ align:start position:0%
+that when we create this 3-end
+ 
+
+ align:start position:0%
+that when we create this 3-end
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+representation of the group by uh
+
+ align:start position:0%
+representation of the group by uh
+ 
+
+ align:start position:0%
+representation of the group by uh
+building geometric transformations of
+
+ align:start position:0%
+building geometric transformations of
+ 
+
+ align:start position:0%
+building geometric transformations of
+the 3n cartisian coordinates that
+
+ align:start position:0%
+the 3n cartisian coordinates that
+ 
+
+ align:start position:0%
+the 3n cartisian coordinates that
+correspond to the an
+
+ align:start position:0%
+correspond to the an
+ 
+
+ align:start position:0%
+correspond to the an
+atoms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we're going to want to throw away a
+
+ align:start position:0%
+uh we're going to want to throw away a
+ 
+
+ align:start position:0%
+uh we're going to want to throw away a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+information and this is the beauty of it
+
+ align:start position:0%
+information and this is the beauty of it
+ 
+
+ align:start position:0%
+information and this is the beauty of it
+and this is why my friend Mr
+
+ align:start position:0%
+and this is why my friend Mr
+ 
+
+ align:start position:0%
+and this is why my friend Mr
+Langford uh was able to do this
+
+ align:start position:0%
+Langford uh was able to do this
+ 
+
+ align:start position:0%
+Langford uh was able to do this
+incredible calculation on a little tiny
+
+ align:start position:0%
+incredible calculation on a little tiny
+ 
+
+ align:start position:0%
+incredible calculation on a little tiny
+scrap of paper because we don't care
+
+ align:start position:0%
+scrap of paper because we don't care
+ 
+
+ align:start position:0%
+scrap of paper because we don't care
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+matrices we care about their tra es they
+
+ align:start position:0%
+matrices we care about their tra es they
+ 
+
+ align:start position:0%
+matrices we care about their tra es they
+are characters and there's powerful
+
+ align:start position:0%
+are characters and there's powerful
+ 
+
+ align:start position:0%
+are characters and there's powerful
+things so so what we're going to do
+
+ align:start position:0%
+things so so what we're going to do
+ 
+
+ align:start position:0%
+things so so what we're going to do
+instead of well first we're going to
+
+ align:start position:0%
+instead of well first we're going to
+ 
+
+ align:start position:0%
+instead of well first we're going to
+actually find solve for some of the
+
+ align:start position:0%
+actually find solve for some of the
+ 
+
+ align:start position:0%
+actually find solve for some of the
+matrices but then we're going to learn
+
+ align:start position:0%
+matrices but then we're going to learn
+ 
+
+ align:start position:0%
+matrices but then we're going to learn
+some tricks for what do we really need
+
+ align:start position:0%
+some tricks for what do we really need
+ 
+
+ align:start position:0%
+some tricks for what do we really need
+to know to determine the thing we we
+
+ align:start position:0%
+to know to determine the thing we we
+ 
+
+ align:start position:0%
+to know to determine the thing we we
+really need to know the characters and
+
+ align:start position:0%
+really need to know the characters and
+ 
+
+ align:start position:0%
+really need to know the characters and
+that's much much less and one can
+
+ align:start position:0%
+that's much much less and one can
+ 
+
+ align:start position:0%
+that's much much less and one can
+without being good at uh uh at
+
+ align:start position:0%
+without being good at uh uh at
+ 
+
+ align:start position:0%
+without being good at uh uh at
+geometry uh one can very quickly work
+
+ align:start position:0%
+geometry uh one can very quickly work
+ 
+
+ align:start position:0%
+geometry uh one can very quickly work
+out how to calculate the
+
+ align:start position:0%
+out how to calculate the
+ 
+
+ align:start position:0%
+out how to calculate the
+characters the traces of the matrixes
+
+ align:start position:0%
+characters the traces of the matrixes
+ 
+
+ align:start position:0%
+characters the traces of the matrixes
+that we
+
+ align:start position:0%
+that we
+ 
+
+ align:start position:0%
+that we
+need okay so now I have to do some
+
+ align:start position:0%
+need okay so now I have to do some
+ 
+
+ align:start position:0%
+need okay so now I have to do some
+formal stuff which I don't like very
+
+ align:start position:0%
+formal stuff which I don't like very
+ 
+
+ align:start position:0%
+formal stuff which I don't like very
+much because I often get confused let's
+
+ align:start position:0%
+much because I often get confused let's
+ 
+
+ align:start position:0%
+much because I often get confused let's
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so here is a vector we represented by x
+
+ align:start position:0%
+so here is a vector we represented by x
+ 
+
+ align:start position:0%
+so here is a vector we represented by x
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+z and uh
+
+ align:start position:0%
+z and uh
+ 
+
+ align:start position:0%
+z and uh
+but we can choose a better
+
+ align:start position:0%
+but we can choose a better
+ 
+
+ align:start position:0%
+but we can choose a better
+representation we can we can say this is
+
+ align:start position:0%
+representation we can we can say this is
+ 
+
+ align:start position:0%
+representation we can we can say this is
+X1 E1 unit Factor X2
+
+ align:start position:0%
+X1 E1 unit Factor X2
+ 
+
+ align:start position:0%
+X1 E1 unit Factor X2
+E2 X3
+
+ align:start position:0%
+E2 X3
+ 
+
+ align:start position:0%
+E2 X3
+E3 so E1 E2 and
+
+ align:start position:0%
+E3 so E1 E2 and
+ 
+
+ align:start position:0%
+E3 so E1 E2 and
+E3 Define an axis
+
+ align:start position:0%
+E3 Define an axis
+ 
+
+ align:start position:0%
+E3 Define an axis
+system and X1 X2 and X3 are the uh the
+
+ align:start position:0%
+system and X1 X2 and X3 are the uh the
+ 
+
+ align:start position:0%
+system and X1 X2 and X3 are the uh the
+coordinates in that that axis
+
+ align:start position:0%
+coordinates in that that axis
+ 
+
+ align:start position:0%
+coordinates in that that axis
+system and so we can write this as some
+
+ align:start position:0%
+system and so we can write this as some
+ 
+
+ align:start position:0%
+system and so we can write this as some
+of i x i EI I
+
+ align:start position:0%
+of i x i EI I
+ 
+
+ align:start position:0%
+of i x i EI I
+hat now
+
+ align:start position:0%
+hat now
+ 
+
+ align:start position:0%
+hat now
+uh suppose we have some symmetry
+
+ align:start position:0%
+uh suppose we have some symmetry
+ 
+
+ align:start position:0%
+uh suppose we have some symmetry
+operation operating on X1 X2
+
+ align:start position:0%
+operation operating on X1 X2
+ 
+
+ align:start position:0%
+operation operating on X1 X2
+X3 well that will give us X1 Prime x 2
+
+ align:start position:0%
+X3 well that will give us X1 Prime x 2
+ 
+
+ align:start position:0%
+X3 well that will give us X1 Prime x 2
+Prime X3 Prime
+
+ align:start position:0%
+Prime X3 Prime
+ 
+
+ align:start position:0%
+Prime X3 Prime
+and so we want to find the
+
+ align:start position:0%
+and so we want to find the
+ 
+
+ align:start position:0%
+and so we want to find the
+Matrix that represents this symmetry
+
+ align:start position:0%
+Matrix that represents this symmetry
+ 
+
+ align:start position:0%
+Matrix that represents this symmetry
+operation that when applied to X1 X2 X3
+
+ align:start position:0%
+operation that when applied to X1 X2 X3
+ 
+
+ align:start position:0%
+operation that when applied to X1 X2 X3
+gives us X1 Prime X2 Prime X3 Prime so
+
+ align:start position:0%
+gives us X1 Prime X2 Prime X3 Prime so
+ 
+
+ align:start position:0%
+gives us X1 Prime X2 Prime X3 Prime so
+we want to find this Matrix that does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I guess I don't need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose we're interested in the
+
+ align:start position:0%
+so suppose we're interested in the
+ 
+
+ align:start position:0%
+so suppose we're interested in the
+plane that contains X1 and
+
+ align:start position:0%
+plane that contains X1 and
+ 
+
+ align:start position:0%
+plane that contains X1 and
+X2 well what does that
+
+ align:start position:0%
+X2 well what does that
+ 
+
+ align:start position:0%
+X2 well what does that
+do uh well the plane that contains X1
+
+ align:start position:0%
+do uh well the plane that contains X1
+ 
+
+ align:start position:0%
+do uh well the plane that contains X1
+and X2 takes X1 into X1 X2 into X2 and
+
+ align:start position:0%
+and X2 takes X1 into X1 X2 into X2 and
+ 
+
+ align:start position:0%
+and X2 takes X1 into X1 X2 into X2 and
+X3 into -
+
+ align:start position:0%
+X3 into -
+ 
+
+ align:start position:0%
+X3 into -
+X3
+
+ align:start position:0%
+X3
+ 
+
+ align:start position:0%
+X3
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+d sigma1
+
+ align:start position:0%
+d sigma1
+ 
+
+ align:start position:0%
+d sigma1
+2 is equal to 1 0 0 0 1 0 0 0 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so simply by knowing what each of
+
+ align:start position:0%
+one so simply by knowing what each of
+ 
+
+ align:start position:0%
+one so simply by knowing what each of
+the Symmetry operation does to
+
+ align:start position:0%
+the Symmetry operation does to
+ 
+
+ align:start position:0%
+the Symmetry operation does to
+coordinates uh you can work out uh the
+
+ align:start position:0%
+coordinates uh you can work out uh the
+ 
+
+ align:start position:0%
+coordinates uh you can work out uh the
+matrices and so this
+
+ align:start position:0%
+matrices and so this
+ 
+
+ align:start position:0%
+matrices and so this
+is um and we could also uh work out
+
+ align:start position:0%
+is um and we could also uh work out
+ 
+
+ align:start position:0%
+is um and we could also uh work out
+suppose we have a rotation by Theta
+
+ align:start position:0%
+suppose we have a rotation by Theta
+ 
+
+ align:start position:0%
+suppose we have a rotation by Theta
+about the X3
+
+ align:start position:0%
+about the X3
+ 
+
+ align:start position:0%
+about the X3
+axis so what would that do well if we
+
+ align:start position:0%
+axis so what would that do well if we
+ 
+
+ align:start position:0%
+axis so what would that do well if we
+rotate about the X3 axis X3 goes into X3
+
+ align:start position:0%
+rotate about the X3 axis X3 goes into X3
+ 
+
+ align:start position:0%
+rotate about the X3 axis X3 goes into X3
+but X1 and
+
+ align:start position:0%
+but X1 and
+ 
+
+ align:start position:0%
+but X1 and
+X2 get mixed up and so we can write this
+
+ align:start position:0%
+X2 get mixed up and so we can write this
+ 
+
+ align:start position:0%
+X2 get mixed up and so we can write this
+as cosine and why we don't need to write
+
+ align:start position:0%
+as cosine and why we don't need to write
+ 
+
+ align:start position:0%
+as cosine and why we don't need to write
+all three letters cosine Theta sin Theta
+
+ align:start position:0%
+all three letters cosine Theta sin Theta
+ 
+
+ align:start position:0%
+all three letters cosine Theta sin Theta
+0 minus sin Theta cosine Theta 0 0 0 1
+
+ align:start position:0%
+0 minus sin Theta cosine Theta 0 0 0 1
+ 
+
+ align:start position:0%
+0 minus sin Theta cosine Theta 0 0 0 1
+so you can work
+
+ align:start position:0%
+so you can work
+ 
+
+ align:start position:0%
+so you can work
+out uh what various operations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do well I said that you have to have an
+
+ align:start position:0%
+do well I said that you have to have an
+ 
+
+ align:start position:0%
+do well I said that you have to have an
+inverse of every operation so what does
+
+ align:start position:0%
+inverse of every operation so what does
+ 
+
+ align:start position:0%
+inverse of every operation so what does
+the inverse of this look like so what
+
+ align:start position:0%
+the inverse of this look like so what
+ 
+
+ align:start position:0%
+the inverse of this look like so what
+transformation would do that so we have
+
+ align:start position:0%
+transformation would do that so we have
+ 
+
+ align:start position:0%
+transformation would do that so we have
+c c theta 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus one what would that do what would
+
+ align:start position:0%
+minus one what would that do what would
+ 
+
+ align:start position:0%
+minus one what would that do what would
+that so instead of rotating by Theta we
+
+ align:start position:0%
+that so instead of rotating by Theta we
+ 
+
+ align:start position:0%
+that so instead of rotating by Theta we
+rotate by minus
+
+ align:start position:0%
+rotate by minus
+ 
+
+ align:start position:0%
+rotate by minus
+Theta cosiness don't change they don't
+
+ align:start position:0%
+Theta cosiness don't change they don't
+ 
+
+ align:start position:0%
+Theta cosiness don't change they don't
+care about plus Theta to minus Theta but
+
+ align:start position:0%
+care about plus Theta to minus Theta but
+ 
+
+ align:start position:0%
+care about plus Theta to minus Theta but
+SS do and so we get C Theta minus s
+
+ align:start position:0%
+SS do and so we get C Theta minus s
+ 
+
+ align:start position:0%
+SS do and so we get C Theta minus s
+Theta s Theta C Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 notice that this
+
+ align:start position:0%
+1 notice that this
+ 
+
+ align:start position:0%
+1 notice that this
+is the transpose of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that notice also that the rows and
+
+ align:start position:0%
+that notice also that the rows and
+ 
+
+ align:start position:0%
+that notice also that the rows and
+columns are
+
+ align:start position:0%
+columns are
+ 
+
+ align:start position:0%
+columns are
+normalized to one and the rows and
+
+ align:start position:0%
+normalized to one and the rows and
+ 
+
+ align:start position:0%
+normalized to one and the rows and
+columns are mutually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal those are the properties of a
+
+ align:start position:0%
+orthogonal those are the properties of a
+ 
+
+ align:start position:0%
+orthogonal those are the properties of a
+unitary Matrix
+
+ align:start position:0%
+unitary Matrix
+ 
+
+ align:start position:0%
+unitary Matrix
+we know if we have a unitary
+
+ align:start position:0%
+we know if we have a unitary
+ 
+
+ align:start position:0%
+we know if we have a unitary
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+uh we if we want to perform a similarity
+
+ align:start position:0%
+uh we if we want to perform a similarity
+ 
+
+ align:start position:0%
+uh we if we want to perform a similarity
+transformation we know that's a
+
+ align:start position:0%
+transformation we know that's a
+ 
+
+ align:start position:0%
+transformation we know that's a
+similarity transformation on some uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it's easy to perform a similarity
+
+ align:start position:0%
+that it's easy to perform a similarity
+ 
+
+ align:start position:0%
+that it's easy to perform a similarity
+transformation which involves
+
+ align:start position:0%
+transformation which involves
+ 
+
+ align:start position:0%
+transformation which involves
+sandwiching and operator between U and U
+
+ align:start position:0%
+sandwiching and operator between U and U
+ 
+
+ align:start position:0%
+sandwiching and operator between U and U
+uus one and U if it's if the
+
+ align:start position:0%
+uus one and U if it's if the
+ 
+
+ align:start position:0%
+uus one and U if it's if the
+transformation operator is unitary then
+
+ align:start position:0%
+transformation operator is unitary then
+ 
+
+ align:start position:0%
+transformation operator is unitary then
+you can get the inverse simply by taking
+
+ align:start position:0%
+you can get the inverse simply by taking
+ 
+
+ align:start position:0%
+you can get the inverse simply by taking
+the conjugate transpose if the operator
+
+ align:start position:0%
+the conjugate transpose if the operator
+ 
+
+ align:start position:0%
+the conjugate transpose if the operator
+is uh if the Matrix is real then you
+
+ align:start position:0%
+is uh if the Matrix is real then you
+ 
+
+ align:start position:0%
+is uh if the Matrix is real then you
+don't need the conjugate transpose you
+
+ align:start position:0%
+don't need the conjugate transpose you
+ 
+
+ align:start position:0%
+don't need the conjugate transpose you
+just need the transpose and so uh u- one
+
+ align:start position:0%
+just need the transpose and so uh u- one
+ 
+
+ align:start position:0%
+just need the transpose and so uh u- one
+is equal to U dagger uh U sorry
+
+ align:start position:0%
+is equal to U dagger uh U sorry
+ 
+
+ align:start position:0%
+is equal to U dagger uh U sorry
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we' we know an awful lot we have
+
+ align:start position:0%
+so we' we know an awful lot we have
+ 
+
+ align:start position:0%
+so we' we know an awful lot we have
+Transformations
+
+ align:start position:0%
+Transformations
+ 
+
+ align:start position:0%
+Transformations
+among uh on operators we have
+
+ align:start position:0%
+among uh on operators we have
+ 
+
+ align:start position:0%
+among uh on operators we have
+multiplication of
+
+ align:start position:0%
+multiplication of
+ 
+
+ align:start position:0%
+multiplication of
+operators um we know that the Matrix
+
+ align:start position:0%
+operators um we know that the Matrix
+ 
+
+ align:start position:0%
+operators um we know that the Matrix
+representations have to be
+
+ align:start position:0%
+representations have to be
+ 
+
+ align:start position:0%
+representations have to be
+unitary and we know about un Norm what
+
+ align:start position:0%
+unitary and we know about un Norm what
+ 
+
+ align:start position:0%
+unitary and we know about un Norm what
+unitary is normaliz normalization and
+
+ align:start position:0%
+unitary is normaliz normalization and
+ 
+
+ align:start position:0%
+unitary is normaliz normalization and
+orthogonal okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+now we're beginning to we're ready to be
+
+ align:start position:0%
+now we're beginning to we're ready to be
+ 
+
+ align:start position:0%
+now we're beginning to we're ready to be
+able to set up Matrix
+
+ align:start position:0%
+able to set up Matrix
+ 
+
+ align:start position:0%
+able to set up Matrix
+representations for of symmetry
+
+ align:start position:0%
+representations for of symmetry
+ 
+
+ align:start position:0%
+representations for of symmetry
+operations on a
+
+ align:start position:0%
+operations on a
+ 
+
+ align:start position:0%
+operations on a
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+uh using anything about the molecule
+
+ align:start position:0%
+uh using anything about the molecule
+ 
+
+ align:start position:0%
+uh using anything about the molecule
+that we want to use to generate a
+
+ align:start position:0%
+that we want to use to generate a
+ 
+
+ align:start position:0%
+that we want to use to generate a
+representation so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we uh attach to the molecule a bunch
+
+ align:start position:0%
+uh we uh attach to the molecule a bunch
+ 
+
+ align:start position:0%
+uh we uh attach to the molecule a bunch
+of bases
+
+ align:start position:0%
+of bases
+ 
+
+ align:start position:0%
+of bases
+vectors so at each atom or Each Bond any
+
+ align:start position:0%
+vectors so at each atom or Each Bond any
+ 
+
+ align:start position:0%
+vectors so at each atom or Each Bond any
+play anything we want to do I mean for
+
+ align:start position:0%
+play anything we want to do I mean for
+ 
+
+ align:start position:0%
+play anything we want to do I mean for
+example for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Benzene we could we could uh we can be
+
+ align:start position:0%
+Benzene we could we could uh we can be
+ 
+
+ align:start position:0%
+Benzene we could we could uh we can be
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+masochistic and
+
+ align:start position:0%
+masochistic and
+ 
+
+ align:start position:0%
+masochistic and
+have 3 n uh three cartisian coordinates
+
+ align:start position:0%
+have 3 n uh three cartisian coordinates
+ 
+
+ align:start position:0%
+have 3 n uh three cartisian coordinates
+for each hydrogen and for each carbon or
+
+ align:start position:0%
+for each hydrogen and for each carbon or
+ 
+
+ align:start position:0%
+for each hydrogen and for each carbon or
+we can say I'm only going to be
+
+ align:start position:0%
+we can say I'm only going to be
+ 
+
+ align:start position:0%
+we can say I'm only going to be
+interested in these six
+
+ align:start position:0%
+interested in these six
+ 
+
+ align:start position:0%
+interested in these six
+bonds or in these six
+
+ align:start position:0%
+bonds or in these six
+ 
+
+ align:start position:0%
+bonds or in these six
+bonds or I'm going to uh look at
+
+ align:start position:0%
+bonds or I'm going to uh look at
+ 
+
+ align:start position:0%
+bonds or I'm going to uh look at
+perpendicular uh I'm going to uh I'm
+
+ align:start position:0%
+perpendicular uh I'm going to uh I'm
+ 
+
+ align:start position:0%
+perpendicular uh I'm going to uh I'm
+going to look at motions of the carbon
+
+ align:start position:0%
+going to look at motions of the carbon
+ 
+
+ align:start position:0%
+going to look at motions of the carbon
+atom perpendicular to the plane and
+
+ align:start position:0%
+atom perpendicular to the plane and
+ 
+
+ align:start position:0%
+atom perpendicular to the plane and
+there's six of them or I'm looking at I
+
+ align:start position:0%
+there's six of them or I'm looking at I
+ 
+
+ align:start position:0%
+there's six of them or I'm looking at I
+can look at the hydro motions of the
+
+ align:start position:0%
+can look at the hydro motions of the
+ 
+
+ align:start position:0%
+can look at the hydro motions of the
+hydrogen atom perpendicular to the plane
+
+ align:start position:0%
+hydrogen atom perpendicular to the plane
+ 
+
+ align:start position:0%
+hydrogen atom perpendicular to the plane
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+bending anything you want and it doesn't
+
+ align:start position:0%
+bending anything you want and it doesn't
+ 
+
+ align:start position:0%
+bending anything you want and it doesn't
+have to be linearly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent you can just dress up the
+
+ align:start position:0%
+independent you can just dress up the
+ 
+
+ align:start position:0%
+independent you can just dress up the
+molecule with a bunch of
+
+ align:start position:0%
+molecule with a bunch of
+ 
+
+ align:start position:0%
+molecule with a bunch of
+things that you're going to transform
+
+ align:start position:0%
+things that you're going to transform
+ 
+
+ align:start position:0%
+things that you're going to transform
+using the Symmetry
+
+ align:start position:0%
+using the Symmetry
+ 
+
+ align:start position:0%
+using the Symmetry
+operations and then using the
+
+ align:start position:0%
+operations and then using the
+ 
+
+ align:start position:0%
+operations and then using the
+simplification of not writing the uh the
+
+ align:start position:0%
+simplification of not writing the uh the
+ 
+
+ align:start position:0%
+simplification of not writing the uh the
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+matrices that affect this transformation
+
+ align:start position:0%
+matrices that affect this transformation
+ 
+
+ align:start position:0%
+matrices that affect this transformation
+but the traces of these D matrices one
+
+ align:start position:0%
+but the traces of these D matrices one
+ 
+
+ align:start position:0%
+but the traces of these D matrices one
+can do this amazingly
+
+ align:start position:0%
+can do this amazingly
+ 
+
+ align:start position:0%
+can do this amazingly
+fast and I mean if you have you know if
+
+ align:start position:0%
+fast and I mean if you have you know if
+ 
+
+ align:start position:0%
+fast and I mean if you have you know if
+you have six carboncarbon
+
+ align:start position:0%
+you have six carboncarbon
+ 
+
+ align:start position:0%
+you have six carboncarbon
+bonds uh you can't have six linearly
+
+ align:start position:0%
+bonds uh you can't have six linearly
+ 
+
+ align:start position:0%
+bonds uh you can't have six linearly
+independent Bond lengths because five of
+
+ align:start position:0%
+independent Bond lengths because five of
+ 
+
+ align:start position:0%
+independent Bond lengths because five of
+them will determine the
+
+ align:start position:0%
+them will determine the
+ 
+
+ align:start position:0%
+them will determine the
+sixth so there's going to be some
+
+ align:start position:0%
+sixth so there's going to be some
+ 
+
+ align:start position:0%
+sixth so there's going to be some
+overcompleteness about some of these
+
+ align:start position:0%
+overcompleteness about some of these
+ 
+
+ align:start position:0%
+overcompleteness about some of these
+cartoons but often you want to ask
+
+ align:start position:0%
+cartoons but often you want to ask
+ 
+
+ align:start position:0%
+cartoons but often you want to ask
+questions for example you want to ask
+
+ align:start position:0%
+questions for example you want to ask
+ 
+
+ align:start position:0%
+questions for example you want to ask
+questions how many uh how many modes are
+
+ align:start position:0%
+questions how many uh how many modes are
+ 
+
+ align:start position:0%
+questions how many uh how many modes are
+confined to a
+
+ align:start position:0%
+confined to a
+ 
+
+ align:start position:0%
+confined to a
+plane of the three n minus 6 normal
+
+ align:start position:0%
+plane of the three n minus 6 normal
+ 
+
+ align:start position:0%
+plane of the three n minus 6 normal
+modes which ones conserve planer
+
+ align:start position:0%
+modes which ones conserve planer
+ 
+
+ align:start position:0%
+modes which ones conserve planer
+symmetry which modes uh uh are uniquely
+
+ align:start position:0%
+symmetry which modes uh uh are uniquely
+ 
+
+ align:start position:0%
+symmetry which modes uh uh are uniquely
+bending modes which modes don't invol
+
+ align:start position:0%
+bending modes which modes don't invol
+ 
+
+ align:start position:0%
+bending modes which modes don't invol
+you know involve hydrogens and not
+
+ align:start position:0%
+you know involve hydrogens and not
+ 
+
+ align:start position:0%
+you know involve hydrogens and not
+carbons or something like that if
+
+ align:start position:0%
+carbons or something like that if
+ 
+
+ align:start position:0%
+carbons or something like that if
+there's any well this be hard uh but any
+
+ align:start position:0%
+there's any well this be hard uh but any
+ 
+
+ align:start position:0%
+there's any well this be hard uh but any
+question you want to ask that involves
+
+ align:start position:0%
+question you want to ask that involves
+ 
+
+ align:start position:0%
+question you want to ask that involves
+classifying the normal modes according
+
+ align:start position:0%
+classifying the normal modes according
+ 
+
+ align:start position:0%
+classifying the normal modes according
+to what is their
+
+ align:start position:0%
+to what is their
+ 
+
+ align:start position:0%
+to what is their
+content you will find uh uh amazingly
+
+ align:start position:0%
+content you will find uh uh amazingly
+ 
+
+ align:start position:0%
+content you will find uh uh amazingly
+powerful uh results that come from
+
+ align:start position:0%
+powerful uh results that come from
+ 
+
+ align:start position:0%
+powerful uh results that come from
+practically
+
+ align:start position:0%
+practically
+ 
+
+ align:start position:0%
+practically
+nothing okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm just going to skip over this
+
+ align:start position:0%
+so I'm just going to skip over this
+ 
+
+ align:start position:0%
+so I'm just going to skip over this
+active versus passive because it's been
+
+ align:start position:0%
+active versus passive because it's been
+ 
+
+ align:start position:0%
+active versus passive because it's been
+scaring me and you're going to have to
+
+ align:start position:0%
+scaring me and you're going to have to
+ 
+
+ align:start position:0%
+scaring me and you're going to have to
+sort this out for yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and I'll start so we have matrices
+
+ align:start position:0%
+uh and I'll start so we have matrices
+ 
+
+ align:start position:0%
+uh and I'll start so we have matrices
+and we're going to simplify matrices to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+characters and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so suppose we have a 3n by 3n
+
+ align:start position:0%
+so so suppose we have a 3n by 3n
+ 
+
+ align:start position:0%
+so so suppose we have a 3n by 3n
+dimensional uh Matrix that would be the
+
+ align:start position:0%
+dimensional uh Matrix that would be the
+ 
+
+ align:start position:0%
+dimensional uh Matrix that would be the
+complete thing that you would use and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so we have a matrix which will
+
+ align:start position:0%
+uh so we have a matrix which will
+ 
+
+ align:start position:0%
+uh so we have a matrix which will
+describe what any symmetry operation
+
+ align:start position:0%
+describe what any symmetry operation
+ 
+
+ align:start position:0%
+describe what any symmetry operation
+does to say the
+
+ align:start position:0%
+does to say the
+ 
+
+ align:start position:0%
+does to say the
+3n uh cartisian coordinates attached to
+
+ align:start position:0%
+3n uh cartisian coordinates attached to
+ 
+
+ align:start position:0%
+3n uh cartisian coordinates attached to
+the uh atoms and we can just take the
+
+ align:start position:0%
+the uh atoms and we can just take the
+ 
+
+ align:start position:0%
+the uh atoms and we can just take the
+sum of the diagonal elements of these
+
+ align:start position:0%
+sum of the diagonal elements of these
+ 
+
+ align:start position:0%
+sum of the diagonal elements of these
+matrices and that's called the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+character it turns out
+
+ align:start position:0%
+character it turns out
+ 
+
+ align:start position:0%
+character it turns out
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um we I'm getting ahead of myself but I
+
+ align:start position:0%
+um we I'm getting ahead of myself but I
+ 
+
+ align:start position:0%
+um we I'm getting ahead of myself but I
+just have to say it uh what's unique
+
+ align:start position:0%
+just have to say it uh what's unique
+ 
+
+ align:start position:0%
+just have to say it uh what's unique
+about a
+
+ align:start position:0%
+about a
+ 
+
+ align:start position:0%
+about a
+matrix um suppose you have a a 3n by 3n
+
+ align:start position:0%
+matrix um suppose you have a a 3n by 3n
+ 
+
+ align:start position:0%
+matrix um suppose you have a a 3n by 3n
+dimensional Matrix well it will have 3 n
+
+ align:start position:0%
+dimensional Matrix well it will have 3 n
+ 
+
+ align:start position:0%
+dimensional Matrix well it will have 3 n
+i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values you perform a similarity
+
+ align:start position:0%
+values you perform a similarity
+ 
+
+ align:start position:0%
+values you perform a similarity
+transformation on that Matrix it'll have
+
+ align:start position:0%
+transformation on that Matrix it'll have
+ 
+
+ align:start position:0%
+transformation on that Matrix it'll have
+the same 3n igen
+
+ align:start position:0%
+the same 3n igen
+ 
+
+ align:start position:0%
+the same 3n igen
+values the trace of a
+
+ align:start position:0%
+values the trace of a
+ 
+
+ align:start position:0%
+values the trace of a
+matrix is invariant under similarity
+
+ align:start position:0%
+matrix is invariant under similarity
+ 
+
+ align:start position:0%
+matrix is invariant under similarity
+Transformations it's just the sum of the
+
+ align:start position:0%
+Transformations it's just the sum of the
+ 
+
+ align:start position:0%
+Transformations it's just the sum of the
+I values
+
+ align:start position:0%
+I values
+ 
+
+ align:start position:0%
+I values
+the determinant of a matrix is invariant
+
+ align:start position:0%
+the determinant of a matrix is invariant
+ 
+
+ align:start position:0%
+the determinant of a matrix is invariant
+because it's the product of the igen
+
+ align:start position:0%
+because it's the product of the igen
+ 
+
+ align:start position:0%
+because it's the product of the igen
+values and so uh the
+
+ align:start position:0%
+values and so uh the
+ 
+
+ align:start position:0%
+values and so uh the
+information um that is contained in a
+
+ align:start position:0%
+information um that is contained in a
+ 
+
+ align:start position:0%
+information um that is contained in a
+matrix it may be sufficient to reduce
+
+ align:start position:0%
+matrix it may be sufficient to reduce
+ 
+
+ align:start position:0%
+matrix it may be sufficient to reduce
+our concerns to just the sum of the
+
+ align:start position:0%
+our concerns to just the sum of the
+ 
+
+ align:start position:0%
+our concerns to just the sum of the
+diagonal elements of each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and so with that statement I'm
+
+ align:start position:0%
+Matrix and so with that statement I'm
+ 
+
+ align:start position:0%
+Matrix and so with that statement I'm
+going to to make the
+
+ align:start position:0%
+going to to make the
+ 
+
+ align:start position:0%
+going to to make the
+bold and useful comment that okay how do
+
+ align:start position:0%
+bold and useful comment that okay how do
+ 
+
+ align:start position:0%
+bold and useful comment that okay how do
+we construct a 3n dimensional
+
+ align:start position:0%
+we construct a 3n dimensional
+ 
+
+ align:start position:0%
+we construct a 3n dimensional
+representation of a molecule where the
+
+ align:start position:0%
+representation of a molecule where the
+ 
+
+ align:start position:0%
+representation of a molecule where the
+atoms are not all located at the
+
+ align:start position:0%
+atoms are not all located at the
+ 
+
+ align:start position:0%
+atoms are not all located at the
+center so the first thing that you do is
+
+ align:start position:0%
+center so the first thing that you do is
+ 
+
+ align:start position:0%
+center so the first thing that you do is
+you say Okay suppose atom Alpha and atom
+
+ align:start position:0%
+you say Okay suppose atom Alpha and atom
+ 
+
+ align:start position:0%
+you say Okay suppose atom Alpha and atom
+beta are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exchanged by the Symmetry operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the Matrix that does that is going
+
+ align:start position:0%
+well the Matrix that does that is going
+ 
+
+ align:start position:0%
+well the Matrix that does that is going
+to have an alpha block and a beta
+
+ align:start position:0%
+to have an alpha block and a beta
+ 
+
+ align:start position:0%
+to have an alpha block and a beta
+block and in between there's an alpha
+
+ align:start position:0%
+block and in between there's an alpha
+ 
+
+ align:start position:0%
+block and in between there's an alpha
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+block and uh
+
+ align:start position:0%
+block and uh
+ 
+
+ align:start position:0%
+block and uh
+so all the information about the
+
+ align:start position:0%
+so all the information about the
+ 
+
+ align:start position:0%
+so all the information about the
+exchange of Alpha and beta are out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so if Alpha and beta are
+
+ align:start position:0%
+here so if Alpha and beta are
+ 
+
+ align:start position:0%
+here so if Alpha and beta are
+exchanged the coordinates of Alpha and
+
+ align:start position:0%
+exchanged the coordinates of Alpha and
+ 
+
+ align:start position:0%
+exchanged the coordinates of Alpha and
+the coordinates of beta do not
+
+ align:start position:0%
+the coordinates of beta do not
+ 
+
+ align:start position:0%
+the coordinates of beta do not
+contribute to the uh
+
+ align:start position:0%
+contribute to the uh
+ 
+
+ align:start position:0%
+contribute to the uh
+trace this is the most wonderful thing
+
+ align:start position:0%
+trace this is the most wonderful thing
+ 
+
+ align:start position:0%
+trace this is the most wonderful thing
+because it enables you to look at a
+
+ align:start position:0%
+because it enables you to look at a
+ 
+
+ align:start position:0%
+because it enables you to look at a
+molecule and almost all the Symmetry
+
+ align:start position:0%
+molecule and almost all the Symmetry
+ 
+
+ align:start position:0%
+molecule and almost all the Symmetry
+operations
+
+ align:start position:0%
+operations
+ 
+
+ align:start position:0%
+operations
+involve exchanges of
+
+ align:start position:0%
+involve exchanges of
+ 
+
+ align:start position:0%
+involve exchanges of
+atoms in fact uh only the atoms that lie
+
+ align:start position:0%
+atoms in fact uh only the atoms that lie
+ 
+
+ align:start position:0%
+atoms in fact uh only the atoms that lie
+on a symmetry element like in a plane or
+
+ align:start position:0%
+on a symmetry element like in a plane or
+ 
+
+ align:start position:0%
+on a symmetry element like in a plane or
+along along
+
+ align:start position:0%
+along along
+ 
+
+ align:start position:0%
+along along
+a a rotation Axis or at the center of
+
+ align:start position:0%
+a a rotation Axis or at the center of
+ 
+
+ align:start position:0%
+a a rotation Axis or at the center of
+inversion only those
+
+ align:start position:0%
+inversion only those
+ 
+
+ align:start position:0%
+inversion only those
+atoms uh you have to worry about all the
+
+ align:start position:0%
+atoms uh you have to worry about all the
+ 
+
+ align:start position:0%
+atoms uh you have to worry about all the
+atoms that are
+
+ align:start position:0%
+atoms that are
+ 
+
+ align:start position:0%
+atoms that are
+permuted they don't contribute to the
+
+ align:start position:0%
+permuted they don't contribute to the
+ 
+
+ align:start position:0%
+permuted they don't contribute to the
+trace of this D Matrix for that symmetry
+
+ align:start position:0%
+trace of this D Matrix for that symmetry
+ 
+
+ align:start position:0%
+trace of this D Matrix for that symmetry
+operation and so you can forget about
+
+ align:start position:0%
+operation and so you can forget about
+ 
+
+ align:start position:0%
+operation and so you can forget about
+them and that's
+
+ align:start position:0%
+them and that's
+ 
+
+ align:start position:0%
+them and that's
+fantastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so all you need is a small number of uh
+
+ align:start position:0%
+so all you need is a small number of uh
+ 
+
+ align:start position:0%
+so all you need is a small number of uh
+3x3 matrices that describe what each of
+
+ align:start position:0%
+3x3 matrices that describe what each of
+ 
+
+ align:start position:0%
+3x3 matrices that describe what each of
+the Symmetry operations will do to atoms
+
+ align:start position:0%
+the Symmetry operations will do to atoms
+ 
+
+ align:start position:0%
+the Symmetry operations will do to atoms
+that are located in a plane or on a on
+
+ align:start position:0%
+that are located in a plane or on a on
+ 
+
+ align:start position:0%
+that are located in a plane or on a on
+the rotation axis and you already know
+
+ align:start position:0%
+the rotation axis and you already know
+ 
+
+ align:start position:0%
+the rotation axis and you already know
+that you could work that out yourself so
+
+ align:start position:0%
+that you could work that out yourself so
+ 
+
+ align:start position:0%
+that you could work that out yourself so
+you don't have to be good at uh at
+
+ align:start position:0%
+you don't have to be good at uh at
+ 
+
+ align:start position:0%
+you don't have to be good at uh at
+geometry to figure out what would how to
+
+ align:start position:0%
+geometry to figure out what would how to
+ 
+
+ align:start position:0%
+geometry to figure out what would how to
+write this block in this Matrix because
+
+ align:start position:0%
+write this block in this Matrix because
+ 
+
+ align:start position:0%
+write this block in this Matrix because
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+irrelevant
+
+ align:start position:0%
+irrelevant
+ 
+
+ align:start position:0%
+irrelevant
+so we're going to use a picture of the
+
+ align:start position:0%
+so we're going to use a picture of the
+ 
+
+ align:start position:0%
+so we're going to use a picture of the
+molecule to
+
+ align:start position:0%
+molecule to
+ 
+
+ align:start position:0%
+molecule to
+generate what we call a reducible
+
+ align:start position:0%
+generate what we call a reducible
+ 
+
+ align:start position:0%
+generate what we call a reducible
+representation and this reducible repes
+
+ align:start position:0%
+representation and this reducible repes
+ 
+
+ align:start position:0%
+representation and this reducible repes
+representation will be uh a collection
+
+ align:start position:0%
+representation will be uh a collection
+ 
+
+ align:start position:0%
+representation will be uh a collection
+of D matrices corresponding to the
+
+ align:start position:0%
+of D matrices corresponding to the
+ 
+
+ align:start position:0%
+of D matrices corresponding to the
+different symmetry operations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this we have a all of the
+
+ align:start position:0%
+okay so this we have a all of the
+ 
+
+ align:start position:0%
+okay so this we have a all of the
+Symmetry
+
+ align:start position:0%
+Symmetry
+ 
+
+ align:start position:0%
+Symmetry
+operations and each one is represented
+
+ align:start position:0%
+operations and each one is represented
+ 
+
+ align:start position:0%
+operations and each one is represented
+by a matrix which has the same
+
+ align:start position:0%
+by a matrix which has the same
+ 
+
+ align:start position:0%
+by a matrix which has the same
+Dimension different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+now we can write this reducible Matrix
+
+ align:start position:0%
+now we can write this reducible Matrix
+ 
+
+ align:start position:0%
+now we can write this reducible Matrix
+as a sum of what we call
+
+ align:start position:0%
+as a sum of what we call
+ 
+
+ align:start position:0%
+as a sum of what we call
+irreducible uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+representations which just corresponds
+
+ align:start position:0%
+representations which just corresponds
+ 
+
+ align:start position:0%
+representations which just corresponds
+to basically block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonalizing all of the uh the
+
+ align:start position:0%
+diagonalizing all of the uh the
+ 
+
+ align:start position:0%
+diagonalizing all of the uh the
+Transformations uh so each one of these
+
+ align:start position:0%
+Transformations uh so each one of these
+ 
+
+ align:start position:0%
+Transformations uh so each one of these
+matrices gets Block diagonalized in
+
+ align:start position:0%
+matrices gets Block diagonalized in
+ 
+
+ align:start position:0%
+matrices gets Block diagonalized in
+exactly the same way now you don't know
+
+ align:start position:0%
+exactly the same way now you don't know
+ 
+
+ align:start position:0%
+exactly the same way now you don't know
+that that's guaranteed and the only way
+
+ align:start position:0%
+that that's guaranteed and the only way
+ 
+
+ align:start position:0%
+that that's guaranteed and the only way
+you can prove that it's guaranteed to be
+
+ align:start position:0%
+you can prove that it's guaranteed to be
+ 
+
+ align:start position:0%
+you can prove that it's guaranteed to be
+possible to do this is from What's
+
+ align:start position:0%
+possible to do this is from What's
+ 
+
+ align:start position:0%
+possible to do this is from What's
+called the Great orthogonality theorem
+
+ align:start position:0%
+called the Great orthogonality theorem
+ 
+
+ align:start position:0%
+called the Great orthogonality theorem
+but it is possible to find a
+
+ align:start position:0%
+but it is possible to find a
+ 
+
+ align:start position:0%
+but it is possible to find a
+transformation that block diagonalizes
+
+ align:start position:0%
+transformation that block diagonalizes
+ 
+
+ align:start position:0%
+transformation that block diagonalizes
+all of these
+
+ align:start position:0%
+all of these
+ 
+
+ align:start position:0%
+all of these
+matrices in the same into submatrices of
+
+ align:start position:0%
+matrices in the same into submatrices of
+ 
+
+ align:start position:0%
+matrices in the same into submatrices of
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+Dimension and then we can write the
+
+ align:start position:0%
+Dimension and then we can write the
+ 
+
+ align:start position:0%
+Dimension and then we can write the
+reducible
+
+ align:start position:0%
+reducible
+ 
+
+ align:start position:0%
+reducible
+uh representation that we can generate
+
+ align:start position:0%
+uh representation that we can generate
+ 
+
+ align:start position:0%
+uh representation that we can generate
+very easily by simple it's hardly
+
+ align:start position:0%
+very easily by simple it's hardly
+ 
+
+ align:start position:0%
+very easily by simple it's hardly
+even it's
+
+ align:start position:0%
+even it's
+ 
+
+ align:start position:0%
+even it's
+it's it's magic you you generate this
+
+ align:start position:0%
+it's it's magic you you generate this
+ 
+
+ align:start position:0%
+it's it's magic you you generate this
+thing and then you can uh say that the
+
+ align:start position:0%
+thing and then you can uh say that the
+ 
+
+ align:start position:0%
+thing and then you can uh say that the
+Matrix Matrix is the sum of these
+
+ align:start position:0%
+Matrix Matrix is the sum of these
+ 
+
+ align:start position:0%
+Matrix Matrix is the sum of these
+individual matrices arranged along the
+
+ align:start position:0%
+individual matrices arranged along the
+ 
+
+ align:start position:0%
+individual matrices arranged along the
+diagonal
+
+ align:start position:0%
+diagonal
+ 
+
+ align:start position:0%
+diagonal
+so we should be able to write this
+
+ align:start position:0%
+so we should be able to write this
+ 
+
+ align:start position:0%
+so we should be able to write this
+reducible uh representation as a number
+
+ align:start position:0%
+reducible uh representation as a number
+ 
+
+ align:start position:0%
+reducible uh representation as a number
+how many
+
+ align:start position:0%
+how many
+ 
+
+ align:start position:0%
+how many
+times the
+
+ align:start position:0%
+times the
+ 
+
+ align:start position:0%
+times the
+new irreducible representation appears
+
+ align:start position:0%
+new irreducible representation appears
+ 
+
+ align:start position:0%
+new irreducible representation appears
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+it that so we should be able to
+
+ align:start position:0%
+it that so we should be able to
+ 
+
+ align:start position:0%
+it that so we should be able to
+decompose every reducible representation
+
+ align:start position:0%
+decompose every reducible representation
+ 
+
+ align:start position:0%
+decompose every reducible representation
+into the irreducible representations
+
+ align:start position:0%
+into the irreducible representations
+ 
+
+ align:start position:0%
+into the irreducible representations
+that it's made up out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of okay now the Great orthogonal theorem
+
+ align:start position:0%
+of okay now the Great orthogonal theorem
+ 
+
+ align:start position:0%
+of okay now the Great orthogonal theorem
+tells us how to do this and why we can
+
+ align:start position:0%
+tells us how to do this and why we can
+ 
+
+ align:start position:0%
+tells us how to do this and why we can
+do this and all that wonderful stuff and
+
+ align:start position:0%
+do this and all that wonderful stuff and
+ 
+
+ align:start position:0%
+do this and all that wonderful stuff and
+I'll write it down but we don't use it
+
+ align:start position:0%
+I'll write it down but we don't use it
+ 
+
+ align:start position:0%
+I'll write it down but we don't use it
+we use the reduced form of it which is
+
+ align:start position:0%
+we use the reduced form of it which is
+ 
+
+ align:start position:0%
+we use the reduced form of it which is
+much simpler and easier to remember so
+
+ align:start position:0%
+much simpler and easier to remember so
+ 
+
+ align:start position:0%
+much simpler and easier to remember so
+the great orthogonal theorem from which
+
+ align:start position:0%
+the great orthogonal theorem from which
+ 
+
+ align:start position:0%
+the great orthogonal theorem from which
+all of these group theoretical results
+
+ align:start position:0%
+all of these group theoretical results
+ 
+
+ align:start position:0%
+all of these group theoretical results
+can be derived and which can be proven
+
+ align:start position:0%
+can be derived and which can be proven
+ 
+
+ align:start position:0%
+can be derived and which can be proven
+but in a fairly tedious way uh so this
+
+ align:start position:0%
+but in a fairly tedious way uh so this
+ 
+
+ align:start position:0%
+but in a fairly tedious way uh so this
+is the sum over symmetry
+
+ align:start position:0%
+is the sum over symmetry
+ 
+
+ align:start position:0%
+is the sum over symmetry
+operations and uh so we have now the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so this is a particular irreducible
+
+ align:start position:0%
+uh so this is a particular irreducible
+ 
+
+ align:start position:0%
+uh so this is a particular irreducible
+representation these are the I and K row
+
+ align:start position:0%
+representation these are the I and K row
+ 
+
+ align:start position:0%
+representation these are the I and K row
+and column of that
+
+ align:start position:0%
+and column of that
+ 
+
+ align:start position:0%
+and column of that
+Matrix and then we have another
+
+ align:start position:0%
+Matrix and then we have another
+ 
+
+ align:start position:0%
+Matrix and then we have another
+uh irreducible
+
+ align:start position:0%
+uh irreducible
+ 
+
+ align:start position:0%
+uh irreducible
+representation and we have J and M and R
+
+ align:start position:0%
+representation and we have J and M and R
+ 
+
+ align:start position:0%
+representation and we have J and M and R
+same R complex
+
+ align:start position:0%
+same R complex
+ 
+
+ align:start position:0%
+same R complex
+conjugate so here are
+
+ align:start position:0%
+conjugate so here are
+ 
+
+ align:start position:0%
+conjugate so here are
+two uh sets of Matrix elements the great
+
+ align:start position:0%
+two uh sets of Matrix elements the great
+ 
+
+ align:start position:0%
+two uh sets of Matrix elements the great
+orthogonality theorem tells you that
+
+ align:start position:0%
+orthogonality theorem tells you that
+ 
+
+ align:start position:0%
+orthogonality theorem tells you that
+this product is
+
+ align:start position:0%
+this product is
+ 
+
+ align:start position:0%
+this product is
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+order of the
+
+ align:start position:0%
+order of the
+ 
+
+ align:start position:0%
+order of the
+group and which is the number of
+
+ align:start position:0%
+group and which is the number of
+ 
+
+ align:start position:0%
+group and which is the number of
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elements um and divided by n mu the
+
+ align:start position:0%
+elements um and divided by n mu the
+ 
+
+ align:start position:0%
+elements um and divided by n mu the
+dimension of the Muth irreducible
+
+ align:start position:0%
+dimension of the Muth irreducible
+ 
+
+ align:start position:0%
+dimension of the Muth irreducible
+representation and then
+
+ align:start position:0%
+representation and then
+ 
+
+ align:start position:0%
+representation and then
+Delta uh mu new Delta i j Delta k m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it says if you uh if you have two
+
+ align:start position:0%
+so it says if you uh if you have two
+ 
+
+ align:start position:0%
+so it says if you uh if you have two
+different irreducible
+
+ align:start position:0%
+different irreducible
+ 
+
+ align:start position:0%
+different irreducible
+representations they're orthogonal in
+
+ align:start position:0%
+representations they're orthogonal in
+ 
+
+ align:start position:0%
+representations they're orthogonal in
+the sense of all the rows and all the
+
+ align:start position:0%
+the sense of all the rows and all the
+ 
+
+ align:start position:0%
+the sense of all the rows and all the
+columns and so we have all of this you
+
+ align:start position:0%
+columns and so we have all of this you
+ 
+
+ align:start position:0%
+columns and so we have all of this you
+know all of these orthogonalities in
+
+ align:start position:0%
+know all of these orthogonalities in
+ 
+
+ align:start position:0%
+know all of these orthogonalities in
+this little thing here um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's possible to prove that n new
+
+ align:start position:0%
+okay it's possible to prove that n new
+ 
+
+ align:start position:0%
+okay it's possible to prove that n new
+squar
+
+ align:start position:0%
+squar
+ 
+
+ align:start position:0%
+squar
+is equal to G where this
+
+ align:start position:0%
+is equal to G where this
+ 
+
+ align:start position:0%
+is equal to G where this
+is these this is the dimension of each
+
+ align:start position:0%
+is these this is the dimension of each
+ 
+
+ align:start position:0%
+is these this is the dimension of each
+of this is the dimension of the N
+
+ align:start position:0%
+of this is the dimension of the N
+ 
+
+ align:start position:0%
+of this is the dimension of the N
+irreducible representation there's a
+
+ align:start position:0%
+irreducible representation there's a
+ 
+
+ align:start position:0%
+irreducible representation there's a
+certain number of irreducible
+
+ align:start position:0%
+certain number of irreducible
+ 
+
+ align:start position:0%
+certain number of irreducible
+representations you sum all the orders
+
+ align:start position:0%
+representations you sum all the orders
+ 
+
+ align:start position:0%
+representations you sum all the orders
+of all of them and you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G this great orthogonality theorem can
+
+ align:start position:0%
+G this great orthogonality theorem can
+ 
+
+ align:start position:0%
+G this great orthogonality theorem can
+be simplified by simply taking the sum
+
+ align:start position:0%
+be simplified by simply taking the sum
+ 
+
+ align:start position:0%
+be simplified by simply taking the sum
+over uh uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the diagonal elements and so we can
+
+ align:start position:0%
+the the diagonal elements and so we can
+ 
+
+ align:start position:0%
+the the diagonal elements and so we can
+write this reduced form uh of well let's
+
+ align:start position:0%
+write this reduced form uh of well let's
+ 
+
+ align:start position:0%
+write this reduced form uh of well let's
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so the
+
+ align:start position:0%
+uh so the
+ 
+
+ align:start position:0%
+uh so the
+character of the Muth
+
+ align:start position:0%
+character of the Muth
+ 
+
+ align:start position:0%
+character of the Muth
+representation is just given by the sum
+
+ align:start position:0%
+representation is just given by the sum
+ 
+
+ align:start position:0%
+representation is just given by the sum
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+i d mu I I of
+
+ align:start position:0%
+i d mu I I of
+ 
+
+ align:start position:0%
+i d mu I I of
+R so that's just the sum of the diagonal
+
+ align:start position:0%
+R so that's just the sum of the diagonal
+ 
+
+ align:start position:0%
+R so that's just the sum of the diagonal
+elements and the reduced form of the
+
+ align:start position:0%
+elements and the reduced form of the
+ 
+
+ align:start position:0%
+elements and the reduced form of the
+great orthogonality theorem is sum over
+
+ align:start position:0%
+great orthogonality theorem is sum over
+ 
+
+ align:start position:0%
+great orthogonality theorem is sum over
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+elements Kai mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+Kai
+
+ align:start position:0%
+Kai
+ 
+
+ align:start position:0%
+Kai
+new are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star is equal to
+
+ align:start position:0%
+star is equal to
+ 
+
+ align:start position:0%
+star is equal to
+G time Delta Mu
+
+ align:start position:0%
+G time Delta Mu
+ 
+
+ align:start position:0%
+G time Delta Mu
+new so these
+
+ align:start position:0%
+new so these
+ 
+
+ align:start position:0%
+new so these
+characters are sort of a generalization
+
+ align:start position:0%
+characters are sort of a generalization
+ 
+
+ align:start position:0%
+characters are sort of a generalization
+of vectors these characters are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal because of that and uh when
+
+ align:start position:0%
+orthogonal because of that and uh when
+ 
+
+ align:start position:0%
+orthogonal because of that and uh when
+you when you sum over the Symmetry
+
+ align:start position:0%
+you when you sum over the Symmetry
+ 
+
+ align:start position:0%
+you when you sum over the Symmetry
+elements you get G
+
+ align:start position:0%
+elements you get G
+ 
+
+ align:start position:0%
+elements you get G
+and so this is the thing one uses and it
+
+ align:start position:0%
+and so this is the thing one uses and it
+ 
+
+ align:start position:0%
+and so this is the thing one uses and it
+provides a basis for calculating the uh
+
+ align:start position:0%
+provides a basis for calculating the uh
+ 
+
+ align:start position:0%
+provides a basis for calculating the uh
+decomposition of a reducible
+
+ align:start position:0%
+decomposition of a reducible
+ 
+
+ align:start position:0%
+decomposition of a reducible
+representation into its irreducible
+
+ align:start position:0%
+representation into its irreducible
+ 
+
+ align:start position:0%
+representation into its irreducible
+representations
+
+ align:start position:0%
+representations
+ 
+
+ align:start position:0%
+representations
+so I'm just stating these results
+
+ align:start position:0%
+so I'm just stating these results
+ 
+
+ align:start position:0%
+so I'm just stating these results
+because you could spend weeks deriving
+
+ align:start position:0%
+because you could spend weeks deriving
+ 
+
+ align:start position:0%
+because you could spend weeks deriving
+them but the neat thing is applying them
+
+ align:start position:0%
+them but the neat thing is applying them
+ 
+
+ align:start position:0%
+them but the neat thing is applying them
+what time is it
+
+ align:start position:0%
+what time is it
+ 
+
+ align:start position:0%
+what time is it
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+so the way you apply them
+
+ align:start position:0%
+so the way you apply them
+ 
+
+ align:start position:0%
+so the way you apply them
+is uh we would like to know how many
+
+ align:start position:0%
+is uh we would like to know how many
+ 
+
+ align:start position:0%
+is uh we would like to know how many
+times each irreducible representation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appears in a reducible representation
+
+ align:start position:0%
+appears in a reducible representation
+ 
+
+ align:start position:0%
+appears in a reducible representation
+and so we have a new sum over new Kai
+
+ align:start position:0%
+and so we have a new sum over new Kai
+ 
+
+ align:start position:0%
+and so we have a new sum over new Kai
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+R so
+
+ align:start position:0%
+R so
+ 
+
+ align:start position:0%
+R so
+we want to know what these the the
+
+ align:start position:0%
+we want to know what these the the
+ 
+
+ align:start position:0%
+we want to know what these the the
+number of times each irreducible
+
+ align:start position:0%
+number of times each irreducible
+ 
+
+ align:start position:0%
+number of times each irreducible
+representation appears in a reducible
+
+ align:start position:0%
+representation appears in a reducible
+ 
+
+ align:start position:0%
+representation appears in a reducible
+representation and that's given through
+
+ align:start position:0%
+representation and that's given through
+ 
+
+ align:start position:0%
+representation and that's given through
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um the great orthogonality theorem for
+
+ align:start position:0%
+um the great orthogonality theorem for
+ 
+
+ align:start position:0%
+um the great orthogonality theorem for
+characters as 1 / G and this is the
+
+ align:start position:0%
+characters as 1 / G and this is the
+ 
+
+ align:start position:0%
+characters as 1 / G and this is the
+equation you'll always be
+
+ align:start position:0%
+equation you'll always be
+ 
+
+ align:start position:0%
+equation you'll always be
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+R kind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reducible
+
+ align:start position:0%
+reducible
+ 
+
+ align:start position:0%
+reducible
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star so you have an
+
+ align:start position:0%
+star so you have an
+ 
+
+ align:start position:0%
+star so you have an
+element you
+
+ align:start position:0%
+element you
+ 
+
+ align:start position:0%
+element you
+have for a reducible representation it's
+
+ align:start position:0%
+have for a reducible representation it's
+ 
+
+ align:start position:0%
+have for a reducible representation it's
+it's going to be a set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers what am I going to how am I
+
+ align:start position:0%
+numbers what am I going to how am I
+ 
+
+ align:start position:0%
+numbers what am I going to how am I
+going to call them number number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number corresponding to R1
+
+ align:start position:0%
+number corresponding to R1
+ 
+
+ align:start position:0%
+number corresponding to R1
+R2
+
+ align:start position:0%
+R2
+ 
+
+ align:start position:0%
+R2
+Etc and so
+
+ align:start position:0%
+Etc and so
+ 
+
+ align:start position:0%
+Etc and so
+both the reducible representation and
+
+ align:start position:0%
+both the reducible representation and
+ 
+
+ align:start position:0%
+both the reducible representation and
+the irreducible representation is the
+
+ align:start position:0%
+the irreducible representation is the
+ 
+
+ align:start position:0%
+the irreducible representation is the
+same number of numbers so you just take
+
+ align:start position:0%
+same number of numbers so you just take
+ 
+
+ align:start position:0%
+same number of numbers so you just take
+these vectors and multiply them and
+
+ align:start position:0%
+these vectors and multiply them and
+ 
+
+ align:start position:0%
+these vectors and multiply them and
+divide by the order of the group and you
+
+ align:start position:0%
+divide by the order of the group and you
+ 
+
+ align:start position:0%
+divide by the order of the group and you
+get the number of times a particular
+
+ align:start position:0%
+get the number of times a particular
+ 
+
+ align:start position:0%
+get the number of times a particular
+irreducible representation appears in a
+
+ align:start position:0%
+irreducible representation appears in a
+ 
+
+ align:start position:0%
+irreducible representation appears in a
+reducible representation there's extra
+
+ align:start position:0%
+reducible representation there's extra
+ 
+
+ align:start position:0%
+reducible representation there's extra
+simplification and we
+
+ align:start position:0%
+simplification and we
+ 
+
+ align:start position:0%
+simplification and we
+have you don't need this but since the
+
+ align:start position:0%
+have you don't need this but since the
+ 
+
+ align:start position:0%
+have you don't need this but since the
+character tables are always arranged in
+
+ align:start position:0%
+character tables are always arranged in
+ 
+
+ align:start position:0%
+character tables are always arranged in
+this way we have the
+
+ align:start position:0%
+this way we have the
+ 
+
+ align:start position:0%
+this way we have the
+operations the Symmetry operations can
+
+ align:start position:0%
+operations the Symmetry operations can
+ 
+
+ align:start position:0%
+operations the Symmetry operations can
+be divided into classes how do we know a
+
+ align:start position:0%
+be divided into classes how do we know a
+ 
+
+ align:start position:0%
+be divided into classes how do we know a
+class well what we do is we say okay
+
+ align:start position:0%
+class well what we do is we say okay
+ 
+
+ align:start position:0%
+class well what we do is we say okay
+here is a symmetry
+
+ align:start position:0%
+here is a symmetry
+ 
+
+ align:start position:0%
+here is a symmetry
+operation Let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh oops calculate for all possible
+
+ align:start position:0%
+uh oops calculate for all possible
+ 
+
+ align:start position:0%
+uh oops calculate for all possible
+symmetry elements in the group this
+
+ align:start position:0%
+symmetry elements in the group this
+ 
+
+ align:start position:0%
+symmetry elements in the group this
+transformation and what this will yield
+
+ align:start position:0%
+transformation and what this will yield
+ 
+
+ align:start position:0%
+transformation and what this will yield
+will be all of the members of the class
+
+ align:start position:0%
+will be all of the members of the class
+ 
+
+ align:start position:0%
+will be all of the members of the class
+that contains this
+
+ align:start position:0%
+that contains this
+ 
+
+ align:start position:0%
+that contains this
+guy and so when you see for
+
+ align:start position:0%
+guy and so when you see for
+ 
+
+ align:start position:0%
+guy and so when you see for
+example uh the point group for c3v the
+
+ align:start position:0%
+example uh the point group for c3v the
+ 
+
+ align:start position:0%
+example uh the point group for c3v the
+uh the group that uh is ammonia you
+
+ align:start position:0%
+uh the group that uh is ammonia you
+ 
+
+ align:start position:0%
+uh the group that uh is ammonia you
+see e 2
+
+ align:start position:0%
+see e 2
+ 
+
+ align:start position:0%
+see e 2
+C3 3 Sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V and then you see A1 A2 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E and so there is the identity operation
+
+ align:start position:0%
+E and so there is the identity operation
+ 
+
+ align:start position:0%
+E and so there is the identity operation
+it's in a class by itself there are two
+
+ align:start position:0%
+it's in a class by itself there are two
+ 
+
+ align:start position:0%
+it's in a class by itself there are two
+c3s
+
+ align:start position:0%
+c3s
+ 
+
+ align:start position:0%
+c3s
+C3 uh and uh C3 and C3 squ or C3 and C3
+
+ align:start position:0%
+C3 uh and uh C3 and C3 squ or C3 and C3
+ 
+
+ align:start position:0%
+C3 uh and uh C3 and C3 squ or C3 and C3
+inverse there are three sigma
+
+ align:start position:0%
+inverse there are three sigma
+ 
+
+ align:start position:0%
+inverse there are three sigma
+vs and and so there's a class of
+
+ align:start position:0%
+vs and and so there's a class of
+ 
+
+ align:start position:0%
+vs and and so there's a class of
+Dimension one class of Dimension two
+
+ align:start position:0%
+Dimension one class of Dimension two
+ 
+
+ align:start position:0%
+Dimension one class of Dimension two
+class of Dimension
+
+ align:start position:0%
+class of Dimension
+ 
+
+ align:start position:0%
+class of Dimension
+three and when you do that you discover
+
+ align:start position:0%
+three and when you do that you discover
+ 
+
+ align:start position:0%
+three and when you do that you discover
+that the character table is square
+
+ align:start position:0%
+that the character table is square
+ 
+
+ align:start position:0%
+that the character table is square
+because the same number of class there
+
+ align:start position:0%
+because the same number of class there
+ 
+
+ align:start position:0%
+because the same number of class there
+are the same number of irreducible
+
+ align:start position:0%
+are the same number of irreducible
+ 
+
+ align:start position:0%
+are the same number of irreducible
+representation as there are number of
+
+ align:start position:0%
+representation as there are number of
+ 
+
+ align:start position:0%
+representation as there are number of
+classes and that's
+
+ align:start position:0%
+classes and that's
+ 
+
+ align:start position:0%
+classes and that's
+wonderful and so then
+
+ align:start position:0%
+wonderful and so then
+ 
+
+ align:start position:0%
+wonderful and so then
+uh in this character table you you have
+
+ align:start position:0%
+uh in this character table you you have
+ 
+
+ align:start position:0%
+uh in this character table you you have
+the characters for each of
+
+ align:start position:0%
+the characters for each of
+ 
+
+ align:start position:0%
+the characters for each of
+these and so this is the totally
+
+ align:start position:0%
+these and so this is the totally
+ 
+
+ align:start position:0%
+these and so this is the totally
+symmetric representation nothing happens
+
+ align:start position:0%
+symmetric representation nothing happens
+ 
+
+ align:start position:0%
+symmetric representation nothing happens
+since you just get
+
+ align:start position:0%
+since you just get
+ 
+
+ align:start position:0%
+since you just get
+ones and uh
+
+ align:start position:0%
+ones and uh
+ 
+
+ align:start position:0%
+ones and uh
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+for uh A2 uh
+
+ align:start position:0%
+for uh A2 uh
+ 
+
+ align:start position:0%
+for uh A2 uh
+A2 uh
+
+ align:start position:0%
+A2 uh
+ 
+
+ align:start position:0%
+A2 uh
+is odd with respect to reflection planes
+
+ align:start position:0%
+is odd with respect to reflection planes
+ 
+
+ align:start position:0%
+is odd with respect to reflection planes
+and uh even with respect to uh uh
+
+ align:start position:0%
+and uh even with respect to uh uh
+ 
+
+ align:start position:0%
+and uh even with respect to uh uh
+rotation and he has this
+
+ align:start position:0%
+rotation and he has this
+ 
+
+ align:start position:0%
+rotation and he has this
+form and there's there's some rules
+
+ align:start position:0%
+form and there's there's some rules
+ 
+
+ align:start position:0%
+form and there's there's some rules
+about this but okay so this is the
+
+ align:start position:0%
+about this but okay so this is the
+ 
+
+ align:start position:0%
+about this but okay so this is the
+character table you have a set of
+
+ align:start position:0%
+character table you have a set of
+ 
+
+ align:start position:0%
+character table you have a set of
+numbers that you
+
+ align:start position:0%
+numbers that you
+ 
+
+ align:start position:0%
+numbers that you
+generate by say having a 3n dimensional
+
+ align:start position:0%
+generate by say having a 3n dimensional
+ 
+
+ align:start position:0%
+generate by say having a 3n dimensional
+representation uh and so we get a
+
+ align:start position:0%
+representation uh and so we get a
+ 
+
+ align:start position:0%
+representation uh and so we get a
+reducible represent and then we ask how
+
+ align:start position:0%
+reducible represent and then we ask how
+ 
+
+ align:start position:0%
+reducible represent and then we ask how
+many times does A1 appear in it how many
+
+ align:start position:0%
+many times does A1 appear in it how many
+ 
+
+ align:start position:0%
+many times does A1 appear in it how many
+times is A2 how many times is e appear
+
+ align:start position:0%
+times is A2 how many times is e appear
+ 
+
+ align:start position:0%
+times is A2 how many times is e appear
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+it and it's really mechanical and simple
+
+ align:start position:0%
+it and it's really mechanical and simple
+ 
+
+ align:start position:0%
+it and it's really mechanical and simple
+and the key is not screwing up uh
+
+ align:start position:0%
+and the key is not screwing up uh
+ 
+
+ align:start position:0%
+and the key is not screwing up uh
+because this looks like a product
+
+ align:start position:0%
+because this looks like a product
+ 
+
+ align:start position:0%
+because this looks like a product
+of um the an element and the character
+
+ align:start position:0%
+of um the an element and the character
+ 
+
+ align:start position:0%
+of um the an element and the character
+of the reducible representation and one
+
+ align:start position:0%
+of the reducible representation and one
+ 
+
+ align:start position:0%
+of the reducible representation and one
+goes by classes so you have to multiply
+
+ align:start position:0%
+goes by classes so you have to multiply
+ 
+
+ align:start position:0%
+goes by classes so you have to multiply
+if you're going to sum over classes ra
+
+ align:start position:0%
+if you're going to sum over classes ra
+ 
+
+ align:start position:0%
+if you're going to sum over classes ra
+rather than over the Symmetry operations
+
+ align:start position:0%
+rather than over the Symmetry operations
+ 
+
+ align:start position:0%
+rather than over the Symmetry operations
+you have to remember to multiply by
+
+ align:start position:0%
+you have to remember to multiply by
+ 
+
+ align:start position:0%
+you have to remember to multiply by
+these things 90% of the errors that I've
+
+ align:start position:0%
+these things 90% of the errors that I've
+ 
+
+ align:start position:0%
+these things 90% of the errors that I've
+made in applying group theory has been
+
+ align:start position:0%
+made in applying group theory has been
+ 
+
+ align:start position:0%
+made in applying group theory has been
+forgetting to multiply by the order of
+
+ align:start position:0%
+forgetting to multiply by the order of
+ 
+
+ align:start position:0%
+forgetting to multiply by the order of
+the class the number yes the order of
+
+ align:start position:0%
+the class the number yes the order of
+ 
+
+ align:start position:0%
+the class the number yes the order of
+the classes
+
+ align:start position:0%
+the classes
+ 
+
+ align:start position:0%
+the classes
+and so you get you know it works out
+
+ align:start position:0%
+and so you get you know it works out
+ 
+
+ align:start position:0%
+and so you get you know it works out
+sort of pretty well and all of a sudden
+
+ align:start position:0%
+sort of pretty well and all of a sudden
+ 
+
+ align:start position:0%
+sort of pretty well and all of a sudden
+you get some representation appearing
+
+ align:start position:0%
+you get some representation appearing
+ 
+
+ align:start position:0%
+you get some representation appearing
+three and a half times or you come up
+
+ align:start position:0%
+three and a half times or you come up
+ 
+
+ align:start position:0%
+three and a half times or you come up
+short and that is the error you're going
+
+ align:start position:0%
+short and that is the error you're going
+ 
+
+ align:start position:0%
+short and that is the error you're going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+make okay so I've more or less touched
+
+ align:start position:0%
+make okay so I've more or less touched
+ 
+
+ align:start position:0%
+make okay so I've more or less touched
+on the high points of what I've included
+
+ align:start position:0%
+on the high points of what I've included
+ 
+
+ align:start position:0%
+on the high points of what I've included
+in these notes I do think that it would
+
+ align:start position:0%
+in these notes I do think that it would
+ 
+
+ align:start position:0%
+in these notes I do think that it would
+be useful to play around I'm not going
+
+ align:start position:0%
+be useful to play around I'm not going
+ 
+
+ align:start position:0%
+be useful to play around I'm not going
+to make an assignment but I I recommend
+
+ align:start position:0%
+to make an assignment but I I recommend
+ 
+
+ align:start position:0%
+to make an assignment but I I recommend
+picking a molecule that has uh well
+
+ align:start position:0%
+picking a molecule that has uh well
+ 
+
+ align:start position:0%
+picking a molecule that has uh well
+Benzene is too simple because the
+
+ align:start position:0%
+Benzene is too simple because the
+ 
+
+ align:start position:0%
+Benzene is too simple because the
+carbons and the hydrogens more or less
+
+ align:start position:0%
+carbons and the hydrogens more or less
+ 
+
+ align:start position:0%
+carbons and the hydrogens more or less
+do the same thing there are certainly
+
+ align:start position:0%
+do the same thing there are certainly
+ 
+
+ align:start position:0%
+do the same thing there are certainly
+interesting things but uh you ought to
+
+ align:start position:0%
+interesting things but uh you ought to
+ 
+
+ align:start position:0%
+interesting things but uh you ought to
+pick a molecule that has a relatively
+
+ align:start position:0%
+pick a molecule that has a relatively
+ 
+
+ align:start position:0%
+pick a molecule that has a relatively
+High symmetry but where there's there
+
+ align:start position:0%
+High symmetry but where there's there
+ 
+
+ align:start position:0%
+High symmetry but where there's there
+there's some interesting differences I
+
+ align:start position:0%
+there's some interesting differences I
+ 
+
+ align:start position:0%
+there's some interesting differences I
+can't think of something
+
+ align:start position:0%
+can't think of something
+ 
+
+ align:start position:0%
+can't think of something
+offhand uh but uh I suspect that uh um
+
+ align:start position:0%
+offhand uh but uh I suspect that uh um
+ 
+
+ align:start position:0%
+offhand uh but uh I suspect that uh um
+the the uh uh
+
+ align:start position:0%
+the the uh uh
+ 
+
+ align:start position:0%
+the the uh uh
+cyclohexane uh where you have boat and
+
+ align:start position:0%
+cyclohexane uh where you have boat and
+ 
+
+ align:start position:0%
+cyclohexane uh where you have boat and
+chair forms and so let's say take the
+
+ align:start position:0%
+chair forms and so let's say take the
+ 
+
+ align:start position:0%
+chair forms and so let's say take the
+chair form of cyclohexane and classify
+
+ align:start position:0%
+chair form of cyclohexane and classify
+ 
+
+ align:start position:0%
+chair form of cyclohexane and classify
+it um that's a relatively low Order
+
+ align:start position:0%
+it um that's a relatively low Order
+ 
+
+ align:start position:0%
+it um that's a relatively low Order
+Group um but whatever you do I would
+
+ align:start position:0%
+Group um but whatever you do I would
+ 
+
+ align:start position:0%
+Group um but whatever you do I would
+recommend using various cartoons to
+
+ align:start position:0%
+recommend using various cartoons to
+ 
+
+ align:start position:0%
+recommend using various cartoons to
+descri you know to pick out the kinds of
+
+ align:start position:0%
+descri you know to pick out the kinds of
+ 
+
+ align:start position:0%
+descri you know to pick out the kinds of
+motions that a mole you can have and
+
+ align:start position:0%
+motions that a mole you can have and
+ 
+
+ align:start position:0%
+motions that a mole you can have and
+you'll be able to classify all of the
+
+ align:start position:0%
+you'll be able to classify all of the
+ 
+
+ align:start position:0%
+you'll be able to classify all of the
+vibrations and there'll be certain
+
+ align:start position:0%
+vibrations and there'll be certain
+ 
+
+ align:start position:0%
+vibrations and there'll be certain
+irreducible representations that have
+
+ align:start position:0%
+irreducible representations that have
+ 
+
+ align:start position:0%
+irreducible representations that have
+are pure bending and others that are
+
+ align:start position:0%
+are pure bending and others that are
+ 
+
+ align:start position:0%
+are pure bending and others that are
+pure planer stretching or you know there
+
+ align:start position:0%
+pure planer stretching or you know there
+ 
+
+ align:start position:0%
+pure planer stretching or you know there
+will be certain motions that you can
+
+ align:start position:0%
+will be certain motions that you can
+ 
+
+ align:start position:0%
+will be certain motions that you can
+name simply by doing group Theory and I
+
+ align:start position:0%
+name simply by doing group Theory and I
+ 
+
+ align:start position:0%
+name simply by doing group Theory and I
+don't know if cyclohexane is a good
+
+ align:start position:0%
+don't know if cyclohexane is a good
+ 
+
+ align:start position:0%
+don't know if cyclohexane is a good
+choice but I cannot think off the top of
+
+ align:start position:0%
+choice but I cannot think off the top of
+ 
+
+ align:start position:0%
+choice but I cannot think off the top of
+my head of a good molecule that's that's
+
+ align:start position:0%
+my head of a good molecule that's that's
+ 
+
+ align:start position:0%
+my head of a good molecule that's that's
+that's not trivial but laborious like
+
+ align:start position:0%
+that's not trivial but laborious like
+ 
+
+ align:start position:0%
+that's not trivial but laborious like
+Benzene or trivial and not laborious
+
+ align:start position:0%
+Benzene or trivial and not laborious
+ 
+
+ align:start position:0%
+Benzene or trivial and not laborious
+like form Malahide somewhere in between
+
+ align:start position:0%
+like form Malahide somewhere in between
+ 
+
+ align:start position:0%
+like form Malahide somewhere in between
+there's something really
+
+ align:start position:0%
+there's something really
+ 
+
+ align:start position:0%
+there's something really
+useful and so anyway uh I will continue
+
+ align:start position:0%
+useful and so anyway uh I will continue
+ 
+
+ align:start position:0%
+useful and so anyway uh I will continue
+with this on Wednesday
\ No newline at end of file
diff --git a/PVv4ST8NZaA.txt b/PVv4ST8NZaA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bc9366bb33489e02f34c295d513e50b20874c2a3
--- /dev/null
+++ b/PVv4ST8NZaA.txt
@@ -0,0 +1,1173 @@
+I want to go back a second to the end of last time because in the  
+
+closing moments there,  we, or at least I, got a little bit  
+
+ lost, and where the plusses and  
+
+minuses were at a certain table.    
+
+And, I want to go back and make sure we've got that straight.   
+
+We were talking about a situation where we were trying to use genetics,   
+
+and the phenotypes that might be observed in mutants to try to  
+
+understand the biochemical pathway because we're beginning to try to  
+
+unite the geneticist's point of view who looks only at mutants,   
+
+and the biochemist's point of view who looks at pathways and proteins.   
+
+And, I had hypothesized that there was some biochemists who had thought  
+
+up a possible pathway for the synthesis of arginine that involved  
+
+some precursor,  alpha, beta, gamma,   
+
+where alpha is turned into beta; beta is turned into gamma; and gamma  
+
+is used to turn into arginine.  And, hypothetically,   
+
+there would be some enzymes: enzyme A that converts alpha,   
+
+enzyme B that converts beta,  and enzyme C that converts gamma.   
+
+And, we were just thinking about,  what would the phenotypes look like  
+
+of different arginine auxotrophs that had blocks at different stages  
+
+in the pathway.  If I had an arginine auxotroph that  
+
+had a block here because let's say a mutation in a gene affecting this  
+
+enzyme, or at a block here at a mutation affecting, say,   
+
+the gene that encodes enzyme C,  how would I be able to tell very  
+
+simply that they were in different genes?  Last time,   
+
+we found that we could tell they were in different genes by doing a  
+
+cross between a mutant that had the first mutation,   
+
+and a mutant that had the second mutation, and looking at the double  
+
+heterozygote, right?  And, if in the double heterozygote  
+
+you had a wild type or a normal phenotype, then they had to be in  
+
+different genes, OK?  Remember that?   
+
+That was called a test of complementation.   
+
+That was how we were able to sort out which mutations were in the same  
+
+gene, and which mutations were in different genes.   
+
+Now we can go a step further.  When we've established that they're  
+
+in different genes,  we can try to begin to think,   
+
+how do these genes relate to a biochemical pathway?   
+
+I wanted to begin to introduce,  because it'll be relevant for today,   
+
+this notion: so, suppose I had a mutation that affected enzyme A so  
+
+that this enzymatic step couldn't be carried out.   
+
+Such a mutant,  when I just try to grow it on  
+
+minimal medium won't be able to grow.  If I give it the substrate alpha,   
+
+it doesn't do it any good because it hasn't got the enzyme to convert  
+
+alpha.  So, given alpha,  it won't grow.  But if I give it  
+
+beta, what will happen?  It can grow because I've bypassed  
+
+the defect.  What about if I give it gamma?  Arginine?   
+
+Now, if instead the mutation were affecting enzymatic step here,   
+
+then if I give it on minimal or medium  
+
+but it can grow on gamma.  What about this last line?   
+
+If I have a mutation and the last enzymatic step,   
+
+minimal medium can't grow with alpha,  can't grow with beta,   
+
+can't even grow with gamma.  But, it can grow with arginine  
+
+because I've bypassed that step.  So, I get a different phenotype,   
+
+the inability to grow even on gamma,   
+
+but I can grow on arginine.  Now, here, if I put together those  
+
+mutants and make a double mutant,  a double homozygote, let's say,   
+
+that's defective in both A and B,  which will it look like?  Will it be  
+
+able to grow on minimal medium?  Will it be able to grow on alpha?   
+
+Will it be able to grow on beta?    
+
+Will it be able to grow on gamma and arginine?  What about if I have a  
+
+double mutant in B and C,  minus, minus, minus, minus,   
+
+plus?  So this looks the same as that.  This looks the same as that.   
+
+And so, by looking at different mutant combinations,   
+
+I can see that the phenotype of B here is what occurs in the double  
+
+mutant.  So, this phenotype is epistatic to this phenotype.   
+
+Epistatic means stands upon,  OK?  So, phenotypes, just like  
+
+phenotypes can be recessive or dominant, you can also speak about  
+
+them being epistatic.  And epistatic means when you have  
+
+both of two mutations together at the epistatic  
+
+then one of them is epistatic to the other, perhaps.   
+
+It will, in fact,  be the one that is present.   
+
+So, this is not so easy to do in many cases because if I take  
+
+different kinds of mutation affecting wing development,   
+
+and I put them together in the same fly, I may just get a very messed up  
+
+wing, and it's very hard to tell that the double mutant has a  
+
+phenotype that looks like either of the two single mutants.   
+
+But sometimes, if they fall very nicely in a pathway where this  
+
+affects the first step,  this affects the second step  
+
+this affects the third step,  this affects the fourth step,   
+
+then the double mutant will look like one of those,   
+
+OK?  And, that way you can somehow order things in a biochemical  
+
+pathway.  Now,  notice, this is all indirect,   
+
+right?  This is what geneticists did in the middle of the 20th century to  
+
+try to figure out how to connect up mutants to biochemistry.   
+
+Actually, that's not true.  It's what geneticists still do  
+
+today because you might think that Well, we don't need to do this  
+
+anymore, but in fact geneticists constantly are looking at mutants  
+
+and making connections trying to say,  what does this double combination  
+
+look like?  What does that double combination look like,   
+
+and how does that tell us about the developmental pathway,   
+
+which cell signals which cell?  This turns out to be one of the  
+
+most powerful ways to figure out what mutations do by saying the  
+
+combination of two mutations looks like the same as one of them,   
+
+allowing you to order the mutations in a pathway.   
+
+And, there's no general way to grind up a cell and order things in a  
+
+pathway.  Genetics is a very powerful tool for doing that.   
+
+Now, there are some ways to grind up cells and order things,   
+
+but you need both of these techniques to believe stuff.   
+
+Anyway, I wanted to go over that,  because it is an important concept,   
+
+the concept of epistasis, the concept of relating mutations to  
+
+steps and pathways,  but what I mostly want to do today  
+
+is go on now to talk about genetics not in organisms like yeast or fruit  
+
+flies or even peas,  but genetics in humans.   
+
+So, what's different about genetics in humans than genetics in yeast?   
+
+You can't choose who mates with whom.  Well, you can.   
+
+I mean, in the days of arranged marriages maybe you couldn't,   
+
+but you can choose who mates with whom, but only for yourself,   
+
+right?  What you can't do is arrange other crosses in the human  
+
+population as an experimentalist.  Now, your own choice of mating,   
+
+unfortunately or fortunately perhaps produces too few progeny to be  
+
+statistically significant.  As a parent of three, I think about  
+
+what it would take to raise a statistically significant number of  
+
+offspring to draw any conclusions,  and I don't think I could do that.   
+
+So, you're absolutely right.  We can't arrange the matings that  
+
+we want in the human population.  So, that's the big difference.   
+
+So, can we do genetics anyway?  How do we do genetics even though  
+
+we can't arrange the matings the way we'd like to?  Sorry?   
+
+Well, family trees.  We have to take the matings as we find them in  
+
+the human population.  You can talk to somebody who might  
+
+have an interesting phenotype,  I don't know, attached earlobes,   
+
+or very early heart disease,  or some unusual color of eyes,   
+
+and begin to collect a family history on that person.   
+
+It's a little bit of a dodgy thing because you might just be relying on  
+
+that person's recollection.  So, if you were really industrious  
+
+about this, you'd go check out each of their family members and test for  
+
+yourself whether they have the phenotype.  People who do serious  
+
+human genetic studies often go and do that.  They have to go confirm,   
+
+either by getting hospital records or interviewing the other members of  
+
+the family, etc.  So, this is not as easy as plating  
+
+out lots of yeasts on a Petri plate.   
+
+And then you get pedigrees.  And the pedigrees look like this.   
+
+Here's a pedigree.  Tell me what you make of it.   
+
+Now, symbols: squares are males,  circles are females by convention,   
+
+a colored in symbol means the phenotype that we're  
+
+interested in studying at the moment.  So, in any given problem,   
+
+somebody will tell you, well,  we're studying some interesting  
+
+phenotype.  You often have an index case or a proband,   
+
+meaning the person who comes to clinical attention,   
+
+and then you chase back in the pedigree and try to reconstruct.   
+
+So, suppose I saw a pedigree like this.   
+
+What conclusions could I draw?  Sorry?  Recessive, sex link trait;  
+
+why sex link trait?  So, let's see if we can get your  
+
+model up here.  You think that this represents  
+
+sex-linked inheritance.  So, what would the genotype be of  
+
+this male here?  Mutant: I'll use M to denote a  
+
+mutant carried on the X chromosome,  and a Y on the opposite chromosome.   
+
+What's the genotype of the female here?   
+
+So, it's plus over plus where I'll use plus to denote the gene carried  
+
+on the normal X chromosome.  OK, and then what do you think  
+
+happened over here?  So, mutant over plus,   
+
+you mate to this male who is plus over plus.  Why is that male plus  
+
+over plus?  Oh,  right, good point.   
+
+It's not plus over plus.  It's plus over Y.  Why is that male  
+
+plus over Y as opposed to mutant over Y?   
+
+He'd have the mutant phenotype.  So, he doesn't have the mutant  
+
+phenotype so he can infer he's plus over Y.  OK, and then what happens  
+
+here?  Mutant over Y; this is plus over Y.  How did this person get  
+
+plus over Y?  They just the plus for mom, and the daughters,   
+
+Y from dad, and a plus from mom.  That's cool.  Now, what about the  
+
+daughters there?  They're plus over plus,   
+
+or M over plus?  Is one,  one, and one the other?  Well,   
+
+in textbooks it's always plus over plus and M over plus,   
+
+but in real life?  We don't know,  right?  So, this could be plus over  
+
+plus, or M over plus,  we don't know, OK?  Now,   
+
+what about on this side of the pedigree here?   
+
+What's the genotype here?  Plus over Y, OK.   
+
+Why not mutant over Y?  Because if they got the mutant,   
+
+it would have to come from the, OK,  so here, plus over plus, and then  
+
+here, everybody is normal because there's no mutant allele segregated.   
+
+Yes?  Yeah, couldn't there just be recessive?  I mean,   
+
+it's a nice story about the sex link  
+
+but couldn't it be recessive?  So, walk me through it being  
+
+recessive.  M over plus,  plus over plus.  Wait, wait,   
+
+wait, hang on.  Could this be M over plus, and that person be affected?   
+
+It's got to be M over M, right so mutants over mutants  
+
+but that's possible.  Yeah, OK.  So, what would this  
+
+person be?  Plus over plus,  let's say, come over here.  Now,   
+
+what would this person be?  M plus.  It has to be M plus because, OK,   
+
+and what about this person here?  M plus, now what about the  
+
+offspring?  So, one of them is M over M,   
+
+plus over plus, and two M pluses.  Does it always work out like that?   
+
+[LAUGHTER] No, it doesn't always work out like that at all.   
+
+So, I'm just going to write plus over plus here just to say,   
+
+tough, right?  In real life,  it doesn't always come out like that.   
+
+What about over here?  It would have to be plus over plus.   
+
+Why not?  It doesn't because it could be M over plus and have no  
+
+effect at offspring by chance,  right?  But, you were going to say  
+
+it's plus over plus because in the textbooks it's always plus over plus  
+
+in pictures like this,  right?  And then, it all turns out  
+
+to be pluses and mutants,  and pluses and mutants, and all that,   
+
+right?  Well, which picture's right?   
+
+Sorry?  You don't know.  So,  that's not good.  There's supposed  
+
+to be answers to these things.  Could either be true?  Which is  
+
+more likely?  The one on the left?  Why?  More statistically probable,   
+
+how come?  Because it is.  It may not quite suffice as a fully  
+
+complete scientific answer though.   
+
+Yes?  Yep.  Well,  but I have somebody who is affected  
+
+here.  So, given that I've gotten affected person in the family --  
+
+yeah, so it is actually,  you're right, statistically somewhat  
+
+less likely that you would have two independent M's entering the same  
+
+pedigree particularly if M is relatively rare.   
+
+If M is quite common,  however, suppose M were something  
+
+was a 20% frequency in the population, then it actually might  
+
+be quite reasonable that this could happen.  So, what would you really  
+
+want to do to test this?  Sorry?  Well, if you found any females here  
+
+maybe you'd be able to conclude that it was autosomal recessive because  
+
+females never show a sex-linked trait.  Is that true?   
+
+No, that's not true.  Why not?  You're right.  So, you just have to  
+
+be homozygous for it on the X.  So, having a single  
+
+female won't, I mean,  she's not going to take that as  
+
+evidence.  Get an affected female and demonstrate that all of her male  
+
+offspring show the trait.  Cross her with, wait, wait.   
+
+This is a human pedigree guys [LAUGHTER].  Whew!  There are issues  
+
+involved here,  right?  You could introduce her to a  
+
+normal guy, [LAUGHTER] but whether you can cross her to a normal guy is  
+
+not actually allowed.  So, you see, these are exactly the  
+
+issues in making sense out of pedigrees like this.   
+
+So, what you have to do is you have to collect a lot of data,   
+
+and the kinds of characteristics that you look for in a pedigree,   
+
+but they are statistical characteristics, and  
+
+notwithstanding -- So, this could be colorblindness or  
+
+something, but notwithstanding the pictures in the textbook of  
+
+colorblindness and all that,  you really do have to take a look at  
+
+a number of properties.  What are some properties?   
+
+One you've already referred to which is there's a predominance in  
+
+males if it's X-linked.  Why is there a predominance in  
+
+males?  Well, there's a predominance in males because if I  
+
+have an X over Y and I've got a mutation paired on  
+
+this X chromosome,  males only have to get it on one.   
+
+Females have to get it on both, and therefore it's statistically more  
+
+likely that males will get it.  So, for example, the frequency of  
+
+colorblindness amongst males is what?  Yeah, it's 8-10%,   
+
+something like that.  I think it's about 8% or so.   
+
+And, amongst females, well, if it's 8% to get one,   
+
+what's the chance you're going to get two?   
+
+It's 8% times 8% is a little less than 1% right?   
+
+It's 0.64%, OK,  in females.  So, we'll just go 8%  
+
+squared.  So in males,  8% in females, less than one percent.   
+
+ So, there is a predominance in males  
+
+of these sex-linked traits.  Other things: affected males do not  
+
+transmit the trait to the kids,  in particular do not transmit it to  
+
+their sons, right,  because they are always sending the  
+
+Y chromosomes to their songs.  Carrier females  
+
+transmit to half of their sons,  and affected females transmit to all  
+
+of their sons.  And, the trait appears to skip  
+
+generations, although I don't like this terminology.   
+
+It skips generations.  These are the kinds of properties  
+
+that you have.  So, hemophilia,   
+
+a good example of this,  if I have a child with hemophilia,   
+
+male with hemophilia, would you be surprised if his uncle had  
+
+hemophilia?  Which uncle would it be,  maternal or paternal?   
+
+The maternal uncle would have hemophilia most likely.   
+
+It's always possible it could be paternal.  This is the problem with  
+
+human genetics is you've got to get enough families so the pattern  
+
+becomes overwhelmingly clear,  OK, because otherwise, as you can  
+
+see with small numbers,  it's tough to be absolutely certain.   
+
+So, these are properties of X linked traits.   
+
+How about baldness?  Is baldness, that's a sex-linked  
+
+trait?  How come?  You don't see a lot of bald females.   
+
+Does that prove it's sex linked?  Sorry?  Guys are stressed more.   
+
+[LAUGHTER] Is there evidence that it has anything to do with stress?   
+
+Actually, it has to do with excess testosterone it turns out,   
+
+that high levels of testosterone are correlated with male pattern  
+
+baldness, but does the fact that males become bald indicate that this  
+
+is a sex linked trait?  No.  Just because it's predominant  
+
+in male, we have to check these other properties.   
+
+Is it the case that bald fathers tend to have bald sons?   
+
+Any evidence on this point?  Common-sensical evidence from  
+
+observation?  It's pretty clear.  It's very clearly not a sex-linked  
+
+trait.  It's a sex-limited trait,  because in order to show this you  
+
+need to be male because the high levels of testosterone are not found  
+
+in females even if they have the genotype that might predispose them  
+
+to become bald if they were male.  So, it actually is not a sex-linked  
+
+trait at all, and it's very clear that male pattern baldness does run  
+
+in families more vertically.  So, you've got to be careful about  
+
+the difference between sex linked and sex limited,   
+
+and sex linked you can really pick out from transmission and families.   
+
+OK, here's another one.  New pedigree.   
+
+She married twice here.  OK, what do we got?   
+
+Yep?  She married again.  She married twice.  She didn't have  
+
+any offspring the second time.  But that happens,   
+
+and you have to be able to draw it in the pedigree.   
+
+She's entitled, all right.  OK, so she got married again,   
+
+no offspring from this marriage.  That's her legal symbol.  You guys  
+
+think that's funny.  It's real, you know?   
+
+OK, that doesn't mean she's married to two people at the same time.   
+
+This is not a temporal picture.  So, what do we got here?  Yep?   
+
+Sorry, of this person?  Well, I'm drawing them as an empty  
+
+symbol here, indicating that we do not think they have the trait.   
+
+They're not carriers.  How do you propose to find that out?   
+
+Look at the children.  Well,  the children are affected.  They  
+
+could be carriers.  The data are what they are.   
+
+You've got to interpret it.  Does this person have to be a  
+
+carrier?  What kind of trait do you think this is?   
+
+Dominant?  Does this look like autosomal dominant to you?   
+
+Yep?  Oh, not all the kids have the trait  
+
+in the first generation,  and if this was dominant,   
+
+they'd all have it?  What's a possible genotype for this person?   
+
+Mutant over plus.  And, these kids could be mutant over plus.   
+
+This could be plus over plus,  and this could be plus over plus,   
+
+mutant over plus, plus over plus,  mutant over plus,   
+
+and plus over plus would be one possibility.  On average,   
+
+what fraction of the kids should get the trait?  About half  
+
+the kids, right?  So, let's see what characteristics  
+
+we have here.  We see the trait in every generation.   
+
+On average, half the kids get the trait.   
+
+Half of the offspring of an affected individual are affected.   
+
+What else?  Males and females?  Roughly equal in males and females?   
+
+Sorry?  One, two, three,   
+
+four, five to two.  So, it's a 5:2 ratio?   
+
+Oh, in the offspring it's a 2:1 ratio.  So, this is like Mendel.   
+
+You see this number and you say,  OK, 2:1.  Isn't that trying to tell  
+
+me something?  Not with six offspring.  That's the problem is  
+
+with six offspring,  2:1 might be trying to tell you 1:1.   
+
+And it is.  If I had a dominantly inherited trait where there's a  
+
+50/50 chance of each offspring getting the disease and it was  
+
+autosomal, not sex linked,  there would be very good odds of  
+
+getting two males and one female because it happens: flip coins and  
+
+it happens.  So,  you have to take that into account,   
+
+and here you see what else we have.  Roughly equal numbers of males and  
+
+females, they transmit equally,  and unaffecteds never transmit.   
+
+This would be the classic autosomal dominant trait.   
+
+Right, here this mutant would go mutant over plus,   
+
+mutant over plus, plus over plus,  mutant over plus, plus over plus,   
+
+plus over plus,  and you'd see here that three out of  
+
+the five here,  and one, two, three out of the six  
+
+there: that's a little more than half but it's small numbers  
+
+here, right?  This is a classic autosomal dominant  
+
+as in the textbooks.  Yes?  Turns out not to make too  
+
+much of a difference.  It turns out that there's lots of  
+
+genome that's on either.  And so, it is true that males are  
+
+more susceptible to certain genetic diseases.   
+
+So, it'll be some excess,  but it won't matter for this.   
+
+Now, in real life it doesn't always work so beautifully.   
+
+We'll take an example: colon cancer.  There are particular autosomal  
+
+dominant mutations here that cause a high risk of colon cancer.   
+
+People who have mutations in a certain gene, MLH-1,   
+
+have about a 70% risk of getting colon cancer in their life.   
+
+But notice, it's not 100%.  You might have incomplete penetrance.   
+
+Incompletely penetrance means not everybody who gets the genotype gets  
+
+the phenotype.  Not all people with the M over plus  
+
+genotype show the phenotype.  Once you do that, it messes up our  
+
+picture colossally,  because, tell me,   
+
+how do we know that this person over here is not actually M over plus.   
+
+Maybe they're cryptic.  They haven't shown the phenotype.   
+
+And maybe, it'll appear in the next generation.  That'll screw up  
+
+everything.  It screws up our rule about not transmitting through  
+
+unaffected, it screws up the rule about not being shown in  
+
+every generation,  and it will even screw up our 50/50  
+
+ratio because if half the offspring get M over plus,   
+
+but only 70% of that half show the phenotype, then only 35% of the  
+
+offspring will show the phenotype.  Unfortunately, this is real life.   
+
+When human geneticists really look at traits, many mutations,   
+
+most except the most severe are incompletely penetrant.   
+
+And so you have to really begin to gather a lot of data to demonstrate  
+
+that you're dealing with an autosomal dominant trait that's  
+
+incompletely penetrant.  And then there are other issues.   
+
+There's a gene on chromosome number 17 called BRCA-1,   
+
+mutations in which predisposed to a very high risk of breast cancer but  
+
+only in women.  Males carry the mutation and do not  
+
+have breast cancer.  There are other mutations that do  
+
+cause breast cancer in males.  Males have breast tissue,   
+
+and can have breast cancer,  but the one on chromosome 17 does  
+
+not.  And so, there you would only see this transmitted through females.   
+
+It would skip into males without showing a phenotype,   
+
+etc.  So, in real life,  life's a bit more complicated.   
+
+All right, so autosomal dominance.  Now, let's take one more pedigree.   
+
+Sorry?  Sex limited, but not sex linked.   
+
+So, on chromosome 17,  which is a bona fide autosome,   
+
+but it's sex limited in that phenotype can only show itself in an  
+
+individual who happens to be female.  Yes?  Sorry?  How come autosomal  
+
+recessive?  So,  if that left guy up there is  
+
+actually a heterozygote,  and up there that individual,   
+
+so if we had a homozygote,  homozygote, heterozygote,   
+
+homozygote, ooh,  you can interpret that pedigree if  
+
+you want to as an autosomal recessive, provided that M is pretty  
+
+frequent in the population.  That's right.  Human geneticists,   
+
+in fact, to really prove that they've got the right model,   
+
+collect a lot of pedigrees and run a computer model.   
+
+The computer model first tries out autosomal recessive,   
+
+tries out autosomal dominant,  tries out dominant with incomplete  
+
+penetrance, and for every possible model figures out the statistical  
+
+probability that you would see such data under that model.   
+
+And when the data become overwhelming and you say,   
+
+yeah, with one pedigree, any pedigree I draw on the board,   
+
+it could actually fit almost any for the models.  It doesn't say this in  
+
+the textbooks,  but it's true.  I get enough  
+
+pedigrees, and eventually I say the odds are 105 times more likely that  
+
+this collection of pedigrees would arise from autosomal dominance,   
+
+inheritance with incomplete penetrance of about 80%.   
+
+Then, from autosomal recessive inheritance, then I get to write a  
+
+paper about it.  That's really what human  
+
+geneticists do is they have to collect enough,   
+
+now, any other organism, you'd just set up a cross,   
+
+but you can't.  And,  as long as we have nontrivial models,   
+
+we really have to collect a lot of data.  Let's take the next pedigree,   
+
+great, that you're thinking like a human geneticist.   
+
+It's very good.  Here's the next pedigree.  Actually,   
+
+I'm going to reverse it.  There we go.   
+
+What's that?  Who knows?  You can't tell.  Good, I've got you  
+
+up to training to the point where,  but in textbooks, this would be  
+
+autosomal recessive.  Or it could be anything.   
+
+You know that, right?  But the textbooks would show you this  
+
+picture as an autosomal recessive.  But of course, what else could it  
+
+be?  It could be an autosomal dominant with incomplete penetrance.   
+
+It could be sex linked.  It could be a lot of things.   
+
+It could also be, I haven't told you the phenotype.   
+
+What if the phenotype here was getting hit by a truck?   
+
+[LAUGHTER] Would you tend to observe this?  Yep,   
+
+so getting hit by a truck,  for example, if someone gets hit by  
+
+a truck, it's unlikely either their parents were hit by a truck,   
+
+or going back several generations that their grandparents were hit by  
+
+a truck.  So, how do you tell being hit by a truck from,   
+
+I mean, that is to say,  how do you know that something's  
+
+genetic at all?  When it's relatively rare and it  
+
+pops up in a pedigree,  how do you know it's genetic?   
+
+Because of the DNA.  But, I mean,  it takes a lot of work to find the  
+
+gene and all that as we'll come to the course.  You might want a little  
+
+bit of assurance before you go write the grant to the NIH and say I'm  
+
+going to find the gene for this because you write it and say I'm  
+
+going to find the gene for getting hit by a truck,   
+
+and they're going to write back and say show me that it's worth spending  
+
+money to find that gene.  Show me that it's true.  So,   
+
+what kind of things would we look for?  If we wanted to show something  
+
+was autosomal recessive in a population, what would we do?   
+
+More data.  So,  we collect a lot of families,   
+
+and what would we see?  As we collected more and more families,   
+
+we begin to see what things?  Sometimes we might see families like  
+
+this, or we might see families like this.  [LAUGHTER]  
+
+If both parents were mutants,  all the children would be mutant,   
+
+right?  We'd color them in mutant.  Is that true?  Well, first off, it  
+
+depends.  Some of the things we want to study are extremely severe  
+
+medical genetical phenotypes,  and they're not going to live to  
+
+have children.  So, that's an issue that you have  
+
+to deal with.  But, it is true that if it was  
+
+autosomal recessive,  a mating between two homozygotes for  
+
+that gene would transmit.  [LAUGHTER] What if they were all in  
+
+the same car?  Which is a very important part,   
+
+because we joke about the car,  but diet, things like that, are  
+
+familial correlated environmental factors.  There are environmental  
+
+factors that correlate within a family.   
+
+And so, it's not trivial to make this point.  So,   
+
+all right, we'll be able to demonstrate what's the real proof of  
+
+Mendelian inheritance here?  Because they could all be in the  
+
+same car, or they all eat the same kind of food or something like that,   
+
+which predisposes them a certain way.  So, we're going to want some better  
+
+proofs of these things.  How about Mendelian ratios?   
+
+Mendelian ratios anyone?  No, because it could be incomplete  
+
+autosomal dominance.  I don't want to mess you up.   
+
+On the exams, you guys can think cleanly about simple things.   
+
+But, this could be dominant with incomplete penetrance,   
+
+though the TA's are going to hate me because I'm telling you that,   
+
+anyway, what about Mendelian ratios?  How about something that's a pretty  
+
+good prediction?  What fraction of the offspring will  
+
+be affected?  We get a lot of families,   
+
+line them all up.  What fraction of the offspring?   
+
+A quarter.  Now,  that's a hard and fast prediction.   
+
+One quarter of the offspring are effective.  When I have a mating  
+
+between two homozygotes,  so what am I going to do?   
+
+I'm going to go out.  I'm going to collect a lot of families.   
+
+Maybe I'll collect 100 families because it'll be a particular  
+
+disease, diastrophic dysplasia or something like that,   
+
+xeroderma pygmentosa,  ataxia teleangiectasia,   
+
+and I will go to the disease foundation, and I will get all the  
+
+pedigrees for all the families,  and I'll see how many times it was  
+
+one affected, two affected,  three affected, etc.  And on average,   
+
+the proportion affecteds will be a quarter, except it's not true.   
+
+If I actually do that, I find that the ratio of affecteds is typically  
+
+more like a third.  It isn't a quarter.   
+
+Now, this should disturb you greatly because you know full well  
+
+that M over plus by M over plus should give you a quarter affecteds.   
+
+But when you actually look at human families, it's not.   
+
+Why?  In other words,  when we count up all the matings  
+
+between heterozygotes,  we'll collect all the matings that  
+
+produce one affected child.  We'll collect all the matings that  
+
+produce two affected children.  We'll collect all the matings that  
+
+produce three affected children.  But, we will fail to collect those  
+
+matings between homozygotes that produce zero affected children.   
+
+And so, we will systematically overestimate the proportion.   
+
+Of course, what we really have to do is go out and get all of those  
+
+couples who were both carriers,  but because they had a small number  
+
+of children didn't happen to have an affected child.   
+
+That's not very easy to do especially when you don't know the  
+
+gene in advance.  So, when human geneticists try to  
+
+go out and measure the one-quarter Mendelian ratio,   
+
+you can't.  But what you can do is the following,   
+
+conditional on the first trial being affected, now what will be the  
+
+proportion of subsequent children who are affected?   
+
+A quarter.  If I make it conditional,  conditioning on having a first child  
+
+who's affected,  number one child who's affected,   
+
+then I know I've got a mating between heterozygotes.   
+
+Subsequent offspring now do not have that bias.   
+
+And so, as a matter of fact,  you think this pretty cool thought,   
+
+right?  You've got a condition on one.  It turns out there's a very  
+
+famous paper about cystic fibrosis where somebody forgot this point and  
+
+made a huge big deal in the literature about the fact that a  
+
+third of the kids on average had cystic fibrosis in these  
+
+families, and proposed all sorts of models about how cystic fibrosis  
+
+might be advantageous and would lead to fertility increases and all that.   
+
+In fact, it was just a failure to correct for this little statistical  
+
+bias.  OK, this is what human geneticists do is they've got to  
+
+deal with the popular,  now, there's one other trick that  
+
+you can use to know that something is autosomal recessive.   
+
+That trick is this.  To site this trick,   
+
+I have to go back to a person called Archibald Garrett.   
+
+Archibald Garrett was a physician in London around 1900.   
+
+Garrett studied children with the trait alkoptonuria.   
+
+Alkoptonuria was what alkopton means black.  Uria means urine.   
+
+They had black urine.  This was evident because their urine turned  
+
+black on treatment with alkaline.  How would you treat urine with  
+
+alkaline.  How would people know this?  Sorry?  Outhouses with lime,   
+
+yeah, and who's going to look at the children's urine, or something  
+
+like that?  But you're on the right track.   
+
+How about diapers?  You wash diapers, cloth diapers,   
+
+in alkaline.  They turn black.  This was evident from black diapers.   
+
+The kids' urine would turn black.  So, he observed this, and you know  
+
+what Garrett noticed is when he studied, children alkoptonuria,   
+
+he found that a very large fraction of affected  
+
+offspring were in fact produced from matings of first cousins.   
+
+Consanguineous matings: now you laugh, but in fact consanguinity has  
+
+been something that has been favored in many societies,   
+
+and in Britain,  particularly amongst the upper class  
+
+in Britain in 1900,  marriage or first cousins was quite  
+
+common, but not as common as he observed.  He found that eight out  
+
+of 17 alkoptonuria patients were the products of first cousin marriages.   
+
+That's way off the charts because it's nearly a half,   
+
+when in fact the typical rate in Britain might have been about 5%.   
+
+So, on the basis of that in the early 1900's, Garrett was able to  
+
+show only a few years after the rediscovery of Mendel's work that  
+
+this property of recessive traits,  enrichment in the offspring of  
+
+consanguineous marriages,  was a clear demonstration of  
+
+Mendelian inheritance.  Not only did he do that,   
+
+but Garrett knew because of the work of some biochemists,   
+
+and this is way cool,  that the problem with the urine was  
+
+that these patients put out in their urine a lot of what's called  
+
+homogentisic acid,  HGA, which basically is a phenolic  
+
+ring.  What Garrett did was he,  and that stuff turns black on  
+
+exposure to air.  What might produce from the things  
+
+you've learned already some kind of ring like that?   
+
+What building blocks do you know have rings like that of things  
+
+you've studied already?  Phenylalanine, tyrosine both have  
+
+rings.  Suppose somebody had problems breaking down homogentisic  
+
+acid.  Suppose there was some pathway where proteins were  
+
+broken down into amino acids including phenylalanine  
+
+and tyrosine.  And,  they were broken down into  
+
+homogentisic acid.  And they were broken down into I  
+
+don't know what.  And, suppose like we had up there,   
+
+patients had a mutation in that enzyme.  What would happen if I fed  
+
+patients a lot of protein?  In their urine, you would recover  
+
+lots of homogentisic acid.  Suppose I fed them a lot of tyrosine.   
+
+I'd get a lot of homogentisic acid because the body couldn't break it  
+
+down.  Suppose I fed them a lot of phenylalanine.   
+
+They would excrete a lot of homogentisic acid.   
+
+Suppose I fed them homogentisic acid.  I would get quantitative  
+
+amounts of homogentisic acid.  Garrett did this.  These are the  
+
+days before institutional review boards, you know,   
+
+informed consent.  It turns out it's harmless feeding them proteins and  
+
+things like that.  But in fact, Garrett,   
+
+in 1911, worked out that this trait had to be recessive because of its  
+
+population genetics,  and inferred a biochemical pathway  
+
+by feeding different things along the way and was able to connect a  
+
+mutation in a gene to a problem with a specific biochemical pathway.   
+
+Sorry, 1908: this was his Croonian Lecture in 1908.   
+
+Eight years after the rediscovery of Mendel, he's able to connect  
+
+genetic defect,  showing it's genetic by transmission,   
+
+to biochemical defect showing that he has a pathway that he can feed  
+
+things into.  And,  it all blocks up at the inability to  
+
+metabolize homogentisic acid.  He has connected gene to enzyme by  
+
+1908.  What do you think the reaction to  
+
+this was?  Polite bewilderment,  and it sunk like a stone.  Nobody  
+
+was prepared to hear this.  This is very much like Mendel in my  
+
+opinion.  Now,  he was a distinguished professor.   
+
+It was the Croonian Lecture.  He got lots of accolades and all that,   
+
+and people said, what a lovely lecture that was,   
+
+and proceeded to completely forget this connection between genes and  
+
+enzymes, genes and proteins.  It was not until 40 years later or  
+
+so that Beadle and Tatum,  working with a fungus, actually  
+
+rosper not yeast,  demonstrated that all these mutants  
+
+interfered with the ability to digest or to make particular amino  
+
+acids, and wrote this up as the one gene, one enzyme hypothesis of how  
+
+genes encode enzymes,  and won the Nobel Prize for this  
+
+work, but in fact in their Nobel address,   
+
+Beetle and Tatum noted,  actually, you know, Garrett kind of  
+
+knew all this.  But, people weren't ready,   
+
+yet, to digest it.  Genetics had just come along,   
+
+Biochemistry had just really been invented in the last ten years,   
+
+and the idea of uniting genetics and biochemistry was just something  
+
+people weren't prepared for yet.  More next time.
\ No newline at end of file
diff --git a/PbITFIGLciI.txt b/PbITFIGLciI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bd76f1e9b40d026d42991588fb1621932819db2f
--- /dev/null
+++ b/PbITFIGLciI.txt
@@ -0,0 +1,6627 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think we'll go ahead and get started
+
+ align:start position:0%
+I think we'll go ahead and get started
+ 
+
+ align:start position:0%
+I think we'll go ahead and get started
+hello everyone
+
+ align:start position:0%
+hello everyone
+ 
+
+ align:start position:0%
+hello everyone
+welcome to 8225 which is also
+
+ align:start position:0%
+welcome to 8225 which is also
+ 
+
+ align:start position:0%
+welcome to 8225 which is also
+sts042 physics in the 20th century
+
+ align:start position:0%
+sts042 physics in the 20th century
+ 
+
+ align:start position:0%
+sts042 physics in the 20th century
+uh my name is David Kaiser um today's
+
+ align:start position:0%
+uh my name is David Kaiser um today's
+ 
+
+ align:start position:0%
+uh my name is David Kaiser um today's
+class is um gonna be a little shorter
+
+ align:start position:0%
+class is um gonna be a little shorter
+ 
+
+ align:start position:0%
+class is um gonna be a little shorter
+than average I just want to go over a
+
+ align:start position:0%
+than average I just want to go over a
+ 
+
+ align:start position:0%
+than average I just want to go over a
+kind of quick introduction for the
+
+ align:start position:0%
+kind of quick introduction for the
+ 
+
+ align:start position:0%
+kind of quick introduction for the
+course an overview some Logistics course
+
+ align:start position:0%
+course an overview some Logistics course
+ 
+
+ align:start position:0%
+course an overview some Logistics course
+structure and so on and then we'll jump
+
+ align:start position:0%
+structure and so on and then we'll jump
+ 
+
+ align:start position:0%
+structure and so on and then we'll jump
+in with the first sort of full
+
+ align:start position:0%
+in with the first sort of full
+ 
+
+ align:start position:0%
+in with the first sort of full
+um class session uh next week so I'm
+
+ align:start position:0%
+um class session uh next week so I'm
+ 
+
+ align:start position:0%
+um class session uh next week so I'm
+going to go ahead and share my screen I
+
+ align:start position:0%
+going to go ahead and share my screen I
+ 
+
+ align:start position:0%
+going to go ahead and share my screen I
+have some slides just to help kind of
+
+ align:start position:0%
+have some slides just to help kind of
+ 
+
+ align:start position:0%
+have some slides just to help kind of
+Orient us for today's session
+
+ align:start position:0%
+Orient us for today's session
+ 
+
+ align:start position:0%
+Orient us for today's session
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's do that
+
+ align:start position:0%
+let's do that
+ 
+
+ align:start position:0%
+let's do that
+and that and now hopefully you can see
+
+ align:start position:0%
+and that and now hopefully you can see
+ 
+
+ align:start position:0%
+and that and now hopefully you can see
+my screen there another some nods or
+
+ align:start position:0%
+my screen there another some nods or
+ 
+
+ align:start position:0%
+my screen there another some nods or
+thumbs up so far so good
+
+ align:start position:0%
+thumbs up so far so good
+ 
+
+ align:start position:0%
+thumbs up so far so good
+thank you okay great so welcome to
+
+ align:start position:0%
+thank you okay great so welcome to
+ 
+
+ align:start position:0%
+thank you okay great so welcome to
+um to the new semester uh this is a
+
+ align:start position:0%
+um to the new semester uh this is a
+ 
+
+ align:start position:0%
+um to the new semester uh this is a
+class I've taught many many times I've
+
+ align:start position:0%
+class I've taught many many times I've
+ 
+
+ align:start position:0%
+class I've taught many many times I've
+been teaching at MIT since 2000 which
+
+ align:start position:0%
+been teaching at MIT since 2000 which
+ 
+
+ align:start position:0%
+been teaching at MIT since 2000 which
+itself is now historical it feels like a
+
+ align:start position:0%
+itself is now historical it feels like a
+ 
+
+ align:start position:0%
+itself is now historical it feels like a
+long time and I've taught this course
+
+ align:start position:0%
+long time and I've taught this course
+ 
+
+ align:start position:0%
+long time and I've taught this course
+probably every other year or more or
+
+ align:start position:0%
+probably every other year or more or
+ 
+
+ align:start position:0%
+probably every other year or more or
+less over that time period so I've
+
+ align:start position:0%
+less over that time period so I've
+ 
+
+ align:start position:0%
+less over that time period so I've
+taught at least 10 or 11 times or so and
+
+ align:start position:0%
+taught at least 10 or 11 times or so and
+ 
+
+ align:start position:0%
+taught at least 10 or 11 times or so and
+I have to say
+
+ align:start position:0%
+I have to say
+ 
+
+ align:start position:0%
+I have to say
+um if I may say so myself it's my
+
+ align:start position:0%
+um if I may say so myself it's my
+ 
+
+ align:start position:0%
+um if I may say so myself it's my
+favorite course that I teach um
+
+ align:start position:0%
+favorite course that I teach um
+ 
+
+ align:start position:0%
+favorite course that I teach um
+hopefully it'll be a positive experience
+
+ align:start position:0%
+hopefully it'll be a positive experience
+ 
+
+ align:start position:0%
+hopefully it'll be a positive experience
+for you as well I think it's a really
+
+ align:start position:0%
+for you as well I think it's a really
+ 
+
+ align:start position:0%
+for you as well I think it's a really
+fun opportunity
+
+ align:start position:0%
+fun opportunity
+ 
+
+ align:start position:0%
+fun opportunity
+to um to sort of sit with some material
+
+ align:start position:0%
+to um to sort of sit with some material
+ 
+
+ align:start position:0%
+to um to sort of sit with some material
+that might be familiar to many of you we
+
+ align:start position:0%
+that might be familiar to many of you we
+ 
+
+ align:start position:0%
+that might be familiar to many of you we
+have many folks who are physics Majors
+
+ align:start position:0%
+have many folks who are physics Majors
+ 
+
+ align:start position:0%
+have many folks who are physics Majors
+many of them are Juniors and seniors
+
+ align:start position:0%
+many of them are Juniors and seniors
+ 
+
+ align:start position:0%
+many of them are Juniors and seniors
+it's also um hopefully an interesting
+
+ align:start position:0%
+it's also um hopefully an interesting
+ 
+
+ align:start position:0%
+it's also um hopefully an interesting
+kind of preview for um for students who
+
+ align:start position:0%
+kind of preview for um for students who
+ 
+
+ align:start position:0%
+kind of preview for um for students who
+either are not in the physics department
+
+ align:start position:0%
+either are not in the physics department
+ 
+
+ align:start position:0%
+either are not in the physics department
+or newer to MIT and so on and I think
+
+ align:start position:0%
+or newer to MIT and so on and I think
+ 
+
+ align:start position:0%
+or newer to MIT and so on and I think
+it's just it's a kind of remarkable
+
+ align:start position:0%
+it's just it's a kind of remarkable
+ 
+
+ align:start position:0%
+it's just it's a kind of remarkable
+set of of ideas and institutions and
+
+ align:start position:0%
+set of of ideas and institutions and
+ 
+
+ align:start position:0%
+set of of ideas and institutions and
+events and people that we get to kind of
+
+ align:start position:0%
+events and people that we get to kind of
+ 
+
+ align:start position:0%
+events and people that we get to kind of
+sit with over the course of the semester
+
+ align:start position:0%
+sit with over the course of the semester
+ 
+
+ align:start position:0%
+sit with over the course of the semester
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um so you know it's a new adventure
+
+ align:start position:0%
+um so you know it's a new adventure
+ 
+
+ align:start position:0%
+um so you know it's a new adventure
+doing this remotely by Zoom but I hope
+
+ align:start position:0%
+doing this remotely by Zoom but I hope
+ 
+
+ align:start position:0%
+doing this remotely by Zoom but I hope
+we get to uh to really enjoy the kind of
+
+ align:start position:0%
+we get to uh to really enjoy the kind of
+ 
+
+ align:start position:0%
+we get to uh to really enjoy the kind of
+pretty wacky ideas and some unusual
+
+ align:start position:0%
+pretty wacky ideas and some unusual
+ 
+
+ align:start position:0%
+pretty wacky ideas and some unusual
+times and places that we get to immerse
+
+ align:start position:0%
+times and places that we get to immerse
+ 
+
+ align:start position:0%
+times and places that we get to immerse
+ourselves in as well
+
+ align:start position:0%
+ourselves in as well
+ 
+
+ align:start position:0%
+ourselves in as well
+and I try to just just enjoy that with
+
+ align:start position:0%
+and I try to just just enjoy that with
+ 
+
+ align:start position:0%
+and I try to just just enjoy that with
+some of these opening images here on on
+
+ align:start position:0%
+some of these opening images here on on
+ 
+
+ align:start position:0%
+some of these opening images here on on
+the on the first slide
+
+ align:start position:0%
+the on the first slide
+ 
+
+ align:start position:0%
+the on the first slide
+so today as I mentioned it's not going
+
+ align:start position:0%
+so today as I mentioned it's not going
+ 
+
+ align:start position:0%
+so today as I mentioned it's not going
+to be a full I don't expect to be a full
+
+ align:start position:0%
+to be a full I don't expect to be a full
+ 
+
+ align:start position:0%
+to be a full I don't expect to be a full
+class session
+
+ align:start position:0%
+class session
+ 
+
+ align:start position:0%
+class session
+um but I do want to give an overview of
+
+ align:start position:0%
+um but I do want to give an overview of
+ 
+
+ align:start position:0%
+um but I do want to give an overview of
+kind of where we're going and also some
+
+ align:start position:0%
+kind of where we're going and also some
+ 
+
+ align:start position:0%
+kind of where we're going and also some
+some of the kind of nuts and bolts and
+
+ align:start position:0%
+some of the kind of nuts and bolts and
+ 
+
+ align:start position:0%
+some of the kind of nuts and bolts and
+Logistics
+
+ align:start position:0%
+Logistics
+ 
+
+ align:start position:0%
+Logistics
+so anyway the plan for today we'll talk
+
+ align:start position:0%
+so anyway the plan for today we'll talk
+ 
+
+ align:start position:0%
+so anyway the plan for today we'll talk
+about the course aims we'll talk a bit
+
+ align:start position:0%
+about the course aims we'll talk a bit
+ 
+
+ align:start position:0%
+about the course aims we'll talk a bit
+about the instructors give the teaching
+
+ align:start position:0%
+about the instructors give the teaching
+ 
+
+ align:start position:0%
+about the instructors give the teaching
+assistance a chance to just introduce
+
+ align:start position:0%
+assistance a chance to just introduce
+ 
+
+ align:start position:0%
+assistance a chance to just introduce
+themselves and say quick hello as well
+
+ align:start position:0%
+themselves and say quick hello as well
+ 
+
+ align:start position:0%
+themselves and say quick hello as well
+we'll give we'll talk about the course
+
+ align:start position:0%
+we'll give we'll talk about the course
+ 
+
+ align:start position:0%
+we'll give we'll talk about the course
+structure uh and the requirements of the
+
+ align:start position:0%
+structure uh and the requirements of the
+ 
+
+ align:start position:0%
+structure uh and the requirements of the
+course and then I'll give a kind of
+
+ align:start position:0%
+course and then I'll give a kind of
+ 
+
+ align:start position:0%
+course and then I'll give a kind of
+brief overview of the kinds of material
+
+ align:start position:0%
+brief overview of the kinds of material
+ 
+
+ align:start position:0%
+brief overview of the kinds of material
+that we'll be engaging with in more
+
+ align:start position:0%
+that we'll be engaging with in more
+ 
+
+ align:start position:0%
+that we'll be engaging with in more
+detail starting next week so that's
+
+ align:start position:0%
+detail starting next week so that's
+ 
+
+ align:start position:0%
+detail starting next week so that's
+where we're at
+
+ align:start position:0%
+where we're at
+ 
+
+ align:start position:0%
+where we're at
+so here I'm just taking the subject
+
+ align:start position:0%
+so here I'm just taking the subject
+ 
+
+ align:start position:0%
+so here I'm just taking the subject
+description uh right from the front page
+
+ align:start position:0%
+description uh right from the front page
+ 
+
+ align:start position:0%
+description uh right from the front page
+of the syllabus just to give you a sense
+
+ align:start position:0%
+of the syllabus just to give you a sense
+ 
+
+ align:start position:0%
+of the syllabus just to give you a sense
+of what where we're heading
+
+ align:start position:0%
+of what where we're heading
+ 
+
+ align:start position:0%
+of what where we're heading
+over the term
+
+ align:start position:0%
+over the term
+ 
+
+ align:start position:0%
+over the term
+the class is meant to explore the
+
+ align:start position:0%
+the class is meant to explore the
+ 
+
+ align:start position:0%
+the class is meant to explore the
+changing roles of physics and physicists
+
+ align:start position:0%
+changing roles of physics and physicists
+ 
+
+ align:start position:0%
+changing roles of physics and physicists
+over really not just the 20th century
+
+ align:start position:0%
+over really not just the 20th century
+ 
+
+ align:start position:0%
+over really not just the 20th century
+anymore by now we're going to be up to
+
+ align:start position:0%
+anymore by now we're going to be up to
+ 
+
+ align:start position:0%
+anymore by now we're going to be up to
+just about two centuries worth of
+
+ align:start position:0%
+just about two centuries worth of
+ 
+
+ align:start position:0%
+just about two centuries worth of
+material uh for the first main class
+
+ align:start position:0%
+material uh for the first main class
+ 
+
+ align:start position:0%
+material uh for the first main class
+next week I'll be starting with the
+
+ align:start position:0%
+next week I'll be starting with the
+ 
+
+ align:start position:0%
+next week I'll be starting with the
+1820s which it turns out is now 200
+
+ align:start position:0%
+1820s which it turns out is now 200
+ 
+
+ align:start position:0%
+1820s which it turns out is now 200
+years ago so really it's an expanse of
+
+ align:start position:0%
+years ago so really it's an expanse of
+ 
+
+ align:start position:0%
+years ago so really it's an expanse of
+you not not only uh the 20th century
+
+ align:start position:0%
+you not not only uh the 20th century
+ 
+
+ align:start position:0%
+you not not only uh the 20th century
+we're going to quickly bring ourselves
+
+ align:start position:0%
+we're going to quickly bring ourselves
+ 
+
+ align:start position:0%
+we're going to quickly bring ourselves
+up into what we often call Modern
+
+ align:start position:0%
+up into what we often call Modern
+ 
+
+ align:start position:0%
+up into what we often call Modern
+physics relativity quantum theory again
+
+ align:start position:0%
+physics relativity quantum theory again
+ 
+
+ align:start position:0%
+physics relativity quantum theory again
+which might be familiar to many of you
+
+ align:start position:0%
+which might be familiar to many of you
+ 
+
+ align:start position:0%
+which might be familiar to many of you
+might be new to others
+
+ align:start position:0%
+might be new to others
+ 
+
+ align:start position:0%
+might be new to others
+um and then we're going to zoom forward
+
+ align:start position:0%
+um and then we're going to zoom forward
+ 
+
+ align:start position:0%
+um and then we're going to zoom forward
+even beyond that that early uh ferment
+
+ align:start position:0%
+even beyond that that early uh ferment
+ 
+
+ align:start position:0%
+even beyond that that early uh ferment
+of the early 20th century and uh look at
+
+ align:start position:0%
+of the early 20th century and uh look at
+ 
+
+ align:start position:0%
+of the early 20th century and uh look at
+much more recent developments in high
+
+ align:start position:0%
+much more recent developments in high
+ 
+
+ align:start position:0%
+much more recent developments in high
+energy physics uh in cosmology and
+
+ align:start position:0%
+energy physics uh in cosmology and
+ 
+
+ align:start position:0%
+energy physics uh in cosmology and
+astrophysics my own personal favorite
+
+ align:start position:0%
+astrophysics my own personal favorite
+ 
+
+ align:start position:0%
+astrophysics my own personal favorite
+topics uh and we're going to be
+
+ align:start position:0%
+topics uh and we're going to be
+ 
+
+ align:start position:0%
+topics uh and we're going to be
+examining these intellectual
+
+ align:start position:0%
+examining these intellectual
+ 
+
+ align:start position:0%
+examining these intellectual
+developments these conceptual and
+
+ align:start position:0%
+developments these conceptual and
+ 
+
+ align:start position:0%
+developments these conceptual and
+intellectual developments at each moment
+
+ align:start position:0%
+intellectual developments at each moment
+ 
+
+ align:start position:0%
+intellectual developments at each moment
+we're trying to understand they're kind
+
+ align:start position:0%
+we're trying to understand they're kind
+ 
+
+ align:start position:0%
+we're trying to understand they're kind
+of embedding in a very messy uh human
+
+ align:start position:0%
+of embedding in a very messy uh human
+ 
+
+ align:start position:0%
+of embedding in a very messy uh human
+world in a changing human world so part
+
+ align:start position:0%
+world in a changing human world so part
+ 
+
+ align:start position:0%
+world in a changing human world so part
+of our goal for this semester is both to
+
+ align:start position:0%
+of our goal for this semester is both to
+ 
+
+ align:start position:0%
+of our goal for this semester is both to
+kind of learn or reiterate some pretty
+
+ align:start position:0%
+kind of learn or reiterate some pretty
+ 
+
+ align:start position:0%
+kind of learn or reiterate some pretty
+amazing ideas for modern physics uh
+
+ align:start position:0%
+amazing ideas for modern physics uh
+ 
+
+ align:start position:0%
+amazing ideas for modern physics uh
+might be new to some might be familiar
+
+ align:start position:0%
+might be new to some might be familiar
+ 
+
+ align:start position:0%
+might be new to some might be familiar
+to others who've got to sit with those
+
+ align:start position:0%
+to others who've got to sit with those
+ 
+
+ align:start position:0%
+to others who've got to sit with those
+ideas but also do a lot more work in
+
+ align:start position:0%
+ideas but also do a lot more work in
+ 
+
+ align:start position:0%
+ideas but also do a lot more work in
+practice of embedding those ideas uh in
+
+ align:start position:0%
+practice of embedding those ideas uh in
+ 
+
+ align:start position:0%
+practice of embedding those ideas uh in
+a in an historical
+
+ align:start position:0%
+a in an historical
+ 
+
+ align:start position:0%
+a in an historical
+um kind of a development then that means
+
+ align:start position:0%
+um kind of a development then that means
+ 
+
+ align:start position:0%
+um kind of a development then that means
+looking at institutions at cultural uh
+
+ align:start position:0%
+looking at institutions at cultural uh
+ 
+
+ align:start position:0%
+looking at institutions at cultural uh
+uh features of how people have thought
+
+ align:start position:0%
+uh features of how people have thought
+ 
+
+ align:start position:0%
+uh features of how people have thought
+about physics and physicists physicists
+
+ align:start position:0%
+about physics and physicists physicists
+ 
+
+ align:start position:0%
+about physics and physicists physicists
+and cells have been part of larger
+
+ align:start position:0%
+and cells have been part of larger
+ 
+
+ align:start position:0%
+and cells have been part of larger
+social worlds political context wartime
+
+ align:start position:0%
+social worlds political context wartime
+ 
+
+ align:start position:0%
+social worlds political context wartime
+and so on and so over the course this
+
+ align:start position:0%
+and so on and so over the course this
+ 
+
+ align:start position:0%
+and so on and so over the course this
+semester we're going to be looking at
+
+ align:start position:0%
+semester we're going to be looking at
+ 
+
+ align:start position:0%
+semester we're going to be looking at
+not just a range of ideas but a range of
+
+ align:start position:0%
+not just a range of ideas but a range of
+ 
+
+ align:start position:0%
+not just a range of ideas but a range of
+places in which those ideas have been
+
+ align:start position:0%
+places in which those ideas have been
+ 
+
+ align:start position:0%
+places in which those ideas have been
+pursued or cultivated or argued over or
+
+ align:start position:0%
+pursued or cultivated or argued over or
+ 
+
+ align:start position:0%
+pursued or cultivated or argued over or
+debated or rejected so we'll start
+
+ align:start position:0%
+debated or rejected so we'll start
+ 
+
+ align:start position:0%
+debated or rejected so we'll start
+looking at
+
+ align:start position:0%
+looking at
+ 
+
+ align:start position:0%
+looking at
+Britain from uh in the 19th century
+
+ align:start position:0%
+Britain from uh in the 19th century
+ 
+
+ align:start position:0%
+Britain from uh in the 19th century
+that's where we'll begin much of our
+
+ align:start position:0%
+that's where we'll begin much of our
+ 
+
+ align:start position:0%
+that's where we'll begin much of our
+investigation for this semester we'll
+
+ align:start position:0%
+investigation for this semester we'll
+ 
+
+ align:start position:0%
+investigation for this semester we'll
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+newly unified Germany in the 1870s
+
+ align:start position:0%
+newly unified Germany in the 1870s
+ 
+
+ align:start position:0%
+newly unified Germany in the 1870s
+moving forward in time ultimately to the
+
+ align:start position:0%
+moving forward in time ultimately to the
+ 
+
+ align:start position:0%
+moving forward in time ultimately to the
+first world war to the rise of Nazism to
+
+ align:start position:0%
+first world war to the rise of Nazism to
+ 
+
+ align:start position:0%
+first world war to the rise of Nazism to
+the second world war lots of kind of big
+
+ align:start position:0%
+the second world war lots of kind of big
+ 
+
+ align:start position:0%
+the second world war lots of kind of big
+uh consequential worldly events which as
+
+ align:start position:0%
+uh consequential worldly events which as
+ 
+
+ align:start position:0%
+uh consequential worldly events which as
+I hope we'll we'll get to appreciate
+
+ align:start position:0%
+I hope we'll we'll get to appreciate
+ 
+
+ align:start position:0%
+I hope we'll we'll get to appreciate
+over the course the term had a really
+
+ align:start position:0%
+over the course the term had a really
+ 
+
+ align:start position:0%
+over the course the term had a really
+quite remarkable impact on the
+
+ align:start position:0%
+quite remarkable impact on the
+ 
+
+ align:start position:0%
+quite remarkable impact on the
+intellectual world of physics and
+
+ align:start position:0%
+intellectual world of physics and
+ 
+
+ align:start position:0%
+intellectual world of physics and
+physicists and we'll bring the story up
+
+ align:start position:0%
+physicists and we'll bring the story up
+ 
+
+ align:start position:0%
+physicists and we'll bring the story up
+through the second world war and into
+
+ align:start position:0%
+through the second world war and into
+ 
+
+ align:start position:0%
+through the second world war and into
+the cold war and even Beyond so we have
+
+ align:start position:0%
+the cold war and even Beyond so we have
+ 
+
+ align:start position:0%
+the cold war and even Beyond so we have
+a long timeline uh really as I say the
+
+ align:start position:0%
+a long timeline uh really as I say the
+ 
+
+ align:start position:0%
+a long timeline uh really as I say the
+better part of two Centuries by now to
+
+ align:start position:0%
+better part of two Centuries by now to
+ 
+
+ align:start position:0%
+better part of two Centuries by now to
+to to sample over and I think a pretty
+
+ align:start position:0%
+to to sample over and I think a pretty
+ 
+
+ align:start position:0%
+to to sample over and I think a pretty
+nice broad range of ideas in physics as
+
+ align:start position:0%
+nice broad range of ideas in physics as
+ 
+
+ align:start position:0%
+nice broad range of ideas in physics as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so just sort of pictorially uh some
+
+ align:start position:0%
+and so just sort of pictorially uh some
+ 
+
+ align:start position:0%
+and so just sort of pictorially uh some
+of the early moments will be will be
+
+ align:start position:0%
+of the early moments will be will be
+ 
+
+ align:start position:0%
+of the early moments will be will be
+kind of um thinking about are the turn
+
+ align:start position:0%
+kind of um thinking about are the turn
+ 
+
+ align:start position:0%
+kind of um thinking about are the turn
+of the 19th into the 20th century uh
+
+ align:start position:0%
+of the 19th into the 20th century uh
+ 
+
+ align:start position:0%
+of the 19th into the 20th century uh
+when a lot of research was still
+
+ align:start position:0%
+when a lot of research was still
+ 
+
+ align:start position:0%
+when a lot of research was still
+um sort of tabletop scale here's a
+
+ align:start position:0%
+um sort of tabletop scale here's a
+ 
+
+ align:start position:0%
+um sort of tabletop scale here's a
+photograph of uh Pierre and Marie Curie
+
+ align:start position:0%
+photograph of uh Pierre and Marie Curie
+ 
+
+ align:start position:0%
+photograph of uh Pierre and Marie Curie
+and their uh laboratory in Paris from uh
+
+ align:start position:0%
+and their uh laboratory in Paris from uh
+ 
+
+ align:start position:0%
+and their uh laboratory in Paris from uh
+right around the year 1900 where the
+
+ align:start position:0%
+right around the year 1900 where the
+ 
+
+ align:start position:0%
+right around the year 1900 where the
+scale of apparatus if not phenomenal
+
+ align:start position:0%
+scale of apparatus if not phenomenal
+ 
+
+ align:start position:0%
+scale of apparatus if not phenomenal
+still felt kind of human scaled also a
+
+ align:start position:0%
+still felt kind of human scaled also a
+ 
+
+ align:start position:0%
+still felt kind of human scaled also a
+bit kind of removed from other elements
+
+ align:start position:0%
+bit kind of removed from other elements
+ 
+
+ align:start position:0%
+bit kind of removed from other elements
+of Human Experience this was a a
+
+ align:start position:0%
+of Human Experience this was a a
+ 
+
+ align:start position:0%
+of Human Experience this was a a
+laboratory pursuing esoteric questions
+
+ align:start position:0%
+laboratory pursuing esoteric questions
+ 
+
+ align:start position:0%
+laboratory pursuing esoteric questions
+in a specialized community
+
+ align:start position:0%
+in a specialized community
+ 
+
+ align:start position:0%
+in a specialized community
+before too long as I'm sure many of you
+
+ align:start position:0%
+before too long as I'm sure many of you
+ 
+
+ align:start position:0%
+before too long as I'm sure many of you
+already know
+
+ align:start position:0%
+already know
+ 
+
+ align:start position:0%
+already know
+many of those investigations began
+
+ align:start position:0%
+many of those investigations began
+ 
+
+ align:start position:0%
+many of those investigations began
+having a much more dramatic worldly
+
+ align:start position:0%
+having a much more dramatic worldly
+ 
+
+ align:start position:0%
+having a much more dramatic worldly
+impact it will look quite a bit in this
+
+ align:start position:0%
+impact it will look quite a bit in this
+ 
+
+ align:start position:0%
+impact it will look quite a bit in this
+course at the work on nuclear weapons
+
+ align:start position:0%
+course at the work on nuclear weapons
+ 
+
+ align:start position:0%
+course at the work on nuclear weapons
+the use of nuclear weapons in the second
+
+ align:start position:0%
+the use of nuclear weapons in the second
+ 
+
+ align:start position:0%
+the use of nuclear weapons in the second
+world war a whole different Arrangement
+
+ align:start position:0%
+world war a whole different Arrangement
+ 
+
+ align:start position:0%
+world war a whole different Arrangement
+between scientists engineers nation
+
+ align:start position:0%
+between scientists engineers nation
+ 
+
+ align:start position:0%
+between scientists engineers nation
+states and world affairs So within not a
+
+ align:start position:0%
+states and world affairs So within not a
+ 
+
+ align:start position:0%
+states and world affairs So within not a
+long stretch of time we go from
+
+ align:start position:0%
+long stretch of time we go from
+ 
+
+ align:start position:0%
+long stretch of time we go from
+photographs like the curies over here to
+
+ align:start position:0%
+photographs like the curies over here to
+ 
+
+ align:start position:0%
+photographs like the curies over here to
+something like this where you have
+
+ align:start position:0%
+something like this where you have
+ 
+
+ align:start position:0%
+something like this where you have
+Robert Oppenheimer with his famous pork
+
+ align:start position:0%
+Robert Oppenheimer with his famous pork
+ 
+
+ align:start position:0%
+Robert Oppenheimer with his famous pork
+pie hat working side by side with the
+
+ align:start position:0%
+pie hat working side by side with the
+ 
+
+ align:start position:0%
+pie hat working side by side with the
+Army General uh Leslie Groves at the U.S
+
+ align:start position:0%
+Army General uh Leslie Groves at the U.S
+ 
+
+ align:start position:0%
+Army General uh Leslie Groves at the U.S
+army uh inspecting in this case the site
+
+ align:start position:0%
+army uh inspecting in this case the site
+ 
+
+ align:start position:0%
+army uh inspecting in this case the site
+of the very first test detonation of a
+
+ align:start position:0%
+of the very first test detonation of a
+ 
+
+ align:start position:0%
+of the very first test detonation of a
+nuclear weapon in July 1945.
+
+ align:start position:0%
+nuclear weapon in July 1945.
+ 
+
+ align:start position:0%
+nuclear weapon in July 1945.
+just 75 years ago
+
+ align:start position:0%
+just 75 years ago
+ 
+
+ align:start position:0%
+just 75 years ago
+soon after that as again many of you
+
+ align:start position:0%
+soon after that as again many of you
+ 
+
+ align:start position:0%
+soon after that as again many of you
+probably know
+
+ align:start position:0%
+probably know
+ 
+
+ align:start position:0%
+probably know
+um physics and physicists move into a
+
+ align:start position:0%
+um physics and physicists move into a
+ 
+
+ align:start position:0%
+um physics and physicists move into a
+new kind of Vantage
+
+ align:start position:0%
+new kind of Vantage
+ 
+
+ align:start position:0%
+new kind of Vantage
+um culturally and politically here's a
+
+ align:start position:0%
+um culturally and politically here's a
+ 
+
+ align:start position:0%
+um culturally and politically here's a
+famous Time Magazine cover of Einstein
+
+ align:start position:0%
+famous Time Magazine cover of Einstein
+ 
+
+ align:start position:0%
+famous Time Magazine cover of Einstein
+with uh his most famous equation E
+
+ align:start position:0%
+with uh his most famous equation E
+ 
+
+ align:start position:0%
+with uh his most famous equation E
+equals MC squared appearing eerily in
+
+ align:start position:0%
+equals MC squared appearing eerily in
+ 
+
+ align:start position:0%
+equals MC squared appearing eerily in
+the mushroom cloud of a nuclear
+
+ align:start position:0%
+the mushroom cloud of a nuclear
+ 
+
+ align:start position:0%
+the mushroom cloud of a nuclear
+explosion so the associations between
+
+ align:start position:0%
+explosion so the associations between
+ 
+
+ align:start position:0%
+explosion so the associations between
+physics and physicists were changing
+
+ align:start position:0%
+physics and physicists were changing
+ 
+
+ align:start position:0%
+physics and physicists were changing
+very quickly especially after the second
+
+ align:start position:0%
+very quickly especially after the second
+ 
+
+ align:start position:0%
+very quickly especially after the second
+world war we're going to explore a lot
+
+ align:start position:0%
+world war we're going to explore a lot
+ 
+
+ align:start position:0%
+world war we're going to explore a lot
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+um over the course of semester
+
+ align:start position:0%
+um over the course of semester
+ 
+
+ align:start position:0%
+um over the course of semester
+and then zooming forward we get to where
+
+ align:start position:0%
+and then zooming forward we get to where
+ 
+
+ align:start position:0%
+and then zooming forward we get to where
+the scale of apparatus no longer fits on
+
+ align:start position:0%
+the scale of apparatus no longer fits on
+ 
+
+ align:start position:0%
+the scale of apparatus no longer fits on
+a Parisian tabletop but in fact this is
+
+ align:start position:0%
+a Parisian tabletop but in fact this is
+ 
+
+ align:start position:0%
+a Parisian tabletop but in fact this is
+a a photograph from what would have been
+
+ align:start position:0%
+a a photograph from what would have been
+ 
+
+ align:start position:0%
+a a photograph from what would have been
+the world's largest particle accelerator
+
+ align:start position:0%
+the world's largest particle accelerator
+ 
+
+ align:start position:0%
+the world's largest particle accelerator
+some of you might have heard of it the
+
+ align:start position:0%
+some of you might have heard of it the
+ 
+
+ align:start position:0%
+some of you might have heard of it the
+superconducting super collider or SSC if
+
+ align:start position:0%
+superconducting super collider or SSC if
+ 
+
+ align:start position:0%
+superconducting super collider or SSC if
+you haven't heard about it it's because
+
+ align:start position:0%
+you haven't heard about it it's because
+ 
+
+ align:start position:0%
+you haven't heard about it it's because
+it was never finished this would have
+
+ align:start position:0%
+it was never finished this would have
+ 
+
+ align:start position:0%
+it was never finished this would have
+dwarfed even the Large Hadron Collider
+
+ align:start position:0%
+dwarfed even the Large Hadron Collider
+ 
+
+ align:start position:0%
+dwarfed even the Large Hadron Collider
+that is in operation uh in CERN in
+
+ align:start position:0%
+that is in operation uh in CERN in
+ 
+
+ align:start position:0%
+that is in operation uh in CERN in
+Geneva this was a machine the
+
+ align:start position:0%
+Geneva this was a machine the
+ 
+
+ align:start position:0%
+Geneva this was a machine the
+superconducting super collider that was
+
+ align:start position:0%
+superconducting super collider that was
+ 
+
+ align:start position:0%
+superconducting super collider that was
+under construction in uh Texas not too
+
+ align:start position:0%
+under construction in uh Texas not too
+ 
+
+ align:start position:0%
+under construction in uh Texas not too
+far from Dallas it was actually halted
+
+ align:start position:0%
+far from Dallas it was actually halted
+ 
+
+ align:start position:0%
+far from Dallas it was actually halted
+in 1993 after the engineers had already
+
+ align:start position:0%
+in 1993 after the engineers had already
+ 
+
+ align:start position:0%
+in 1993 after the engineers had already
+dug a 54 mile circumference tunnel
+
+ align:start position:0%
+dug a 54 mile circumference tunnel
+ 
+
+ align:start position:0%
+dug a 54 mile circumference tunnel
+underground roughly three times longer
+
+ align:start position:0%
+underground roughly three times longer
+ 
+
+ align:start position:0%
+underground roughly three times longer
+than the Large Hadron Collider
+
+ align:start position:0%
+than the Large Hadron Collider
+ 
+
+ align:start position:0%
+than the Large Hadron Collider
+so the scale of our apparatus is no
+
+ align:start position:0%
+so the scale of our apparatus is no
+ 
+
+ align:start position:0%
+so the scale of our apparatus is no
+longer fitting on a tabletop and also
+
+ align:start position:0%
+longer fitting on a tabletop and also
+ 
+
+ align:start position:0%
+longer fitting on a tabletop and also
+once you need eight to Fifteen billion
+
+ align:start position:0%
+once you need eight to Fifteen billion
+ 
+
+ align:start position:0%
+once you need eight to Fifteen billion
+dollars to do your experiment now you
+
+ align:start position:0%
+dollars to do your experiment now you
+ 
+
+ align:start position:0%
+dollars to do your experiment now you
+have a different place in the world of
+
+ align:start position:0%
+have a different place in the world of
+ 
+
+ align:start position:0%
+have a different place in the world of
+politics and world affairs as well
+
+ align:start position:0%
+politics and world affairs as well
+ 
+
+ align:start position:0%
+politics and world affairs as well
+and likewise the story didn't end
+
+ align:start position:0%
+and likewise the story didn't end
+ 
+
+ align:start position:0%
+and likewise the story didn't end
+thankfully with the cancellation of the
+
+ align:start position:0%
+thankfully with the cancellation of the
+ 
+
+ align:start position:0%
+thankfully with the cancellation of the
+super collider we have a shift to other
+
+ align:start position:0%
+super collider we have a shift to other
+ 
+
+ align:start position:0%
+super collider we have a shift to other
+kinds of still large-scale research for
+
+ align:start position:0%
+kinds of still large-scale research for
+ 
+
+ align:start position:0%
+kinds of still large-scale research for
+example to push to billion dollar
+
+ align:start position:0%
+example to push to billion dollar
+ 
+
+ align:start position:0%
+example to push to billion dollar
+satellites like the plot satellite shown
+
+ align:start position:0%
+satellites like the plot satellite shown
+ 
+
+ align:start position:0%
+satellites like the plot satellite shown
+here uh in its study of the of the very
+
+ align:start position:0%
+here uh in its study of the of the very
+ 
+
+ align:start position:0%
+here uh in its study of the of the very
+earliest moments of the universe so
+
+ align:start position:0%
+earliest moments of the universe so
+ 
+
+ align:start position:0%
+earliest moments of the universe so
+that's in kind of snapshot
+
+ align:start position:0%
+that's in kind of snapshot
+ 
+
+ align:start position:0%
+that's in kind of snapshot
+um kind of uh picture form the kinds of
+
+ align:start position:0%
+um kind of uh picture form the kinds of
+ 
+
+ align:start position:0%
+um kind of uh picture form the kinds of
+terrain that we're going to cover over
+
+ align:start position:0%
+terrain that we're going to cover over
+ 
+
+ align:start position:0%
+terrain that we're going to cover over
+the course of time and I'll say more
+
+ align:start position:0%
+the course of time and I'll say more
+ 
+
+ align:start position:0%
+the course of time and I'll say more
+about that soon but I just want to give
+
+ align:start position:0%
+about that soon but I just want to give
+ 
+
+ align:start position:0%
+about that soon but I just want to give
+you a kind of preview
+
+ align:start position:0%
+you a kind of preview
+ 
+
+ align:start position:0%
+you a kind of preview
+okay let's talk some nuts and bolts for
+
+ align:start position:0%
+okay let's talk some nuts and bolts for
+ 
+
+ align:start position:0%
+okay let's talk some nuts and bolts for
+a little bit
+
+ align:start position:0%
+a little bit
+ 
+
+ align:start position:0%
+a little bit
+this course has no prerequisites as I'm
+
+ align:start position:0%
+this course has no prerequisites as I'm
+ 
+
+ align:start position:0%
+this course has no prerequisites as I'm
+sure you know it's a Communications
+
+ align:start position:0%
+sure you know it's a Communications
+ 
+
+ align:start position:0%
+sure you know it's a Communications
+intensive subject for physics majors and
+
+ align:start position:0%
+intensive subject for physics majors and
+ 
+
+ align:start position:0%
+intensive subject for physics majors and
+course eight but there's no prior
+
+ align:start position:0%
+course eight but there's no prior
+ 
+
+ align:start position:0%
+course eight but there's no prior
+coursework required it's not limited to
+
+ align:start position:0%
+coursework required it's not limited to
+ 
+
+ align:start position:0%
+coursework required it's not limited to
+students in the physics major it's open
+
+ align:start position:0%
+students in the physics major it's open
+ 
+
+ align:start position:0%
+students in the physics major it's open
+to first year Undeclared students and so
+
+ align:start position:0%
+to first year Undeclared students and so
+ 
+
+ align:start position:0%
+to first year Undeclared students and so
+on there's no prereqs our own is our aim
+
+ align:start position:0%
+on there's no prereqs our own is our aim
+ 
+
+ align:start position:0%
+on there's no prereqs our own is our aim
+uh in the course is really to improve
+
+ align:start position:0%
+uh in the course is really to improve
+ 
+
+ align:start position:0%
+uh in the course is really to improve
+written communication skills rather than
+
+ align:start position:0%
+written communication skills rather than
+ 
+
+ align:start position:0%
+written communication skills rather than
+to worry too much about things like
+
+ align:start position:0%
+to worry too much about things like
+ 
+
+ align:start position:0%
+to worry too much about things like
+problem sets or problem solving which
+
+ align:start position:0%
+problem sets or problem solving which
+ 
+
+ align:start position:0%
+problem sets or problem solving which
+are dearly important to me but this
+
+ align:start position:0%
+are dearly important to me but this
+ 
+
+ align:start position:0%
+are dearly important to me but this
+course has has a different kind of
+
+ align:start position:0%
+course has has a different kind of
+ 
+
+ align:start position:0%
+course has has a different kind of
+center of gravity so to speak
+
+ align:start position:0%
+center of gravity so to speak
+ 
+
+ align:start position:0%
+center of gravity so to speak
+I I should say I've had in the years
+
+ align:start position:0%
+I I should say I've had in the years
+ 
+
+ align:start position:0%
+I I should say I've had in the years
+past I've had high school students take
+
+ align:start position:0%
+past I've had high school students take
+ 
+
+ align:start position:0%
+past I've had high school students take
+the course and do very very well really
+
+ align:start position:0%
+the course and do very very well really
+ 
+
+ align:start position:0%
+the course and do very very well really
+really no prerequisites
+
+ align:start position:0%
+really no prerequisites
+ 
+
+ align:start position:0%
+really no prerequisites
+I want to emphasize that I would
+
+ align:start position:0%
+I want to emphasize that I would
+ 
+
+ align:start position:0%
+I want to emphasize that I would
+emphasize that especially because some
+
+ align:start position:0%
+emphasize that especially because some
+ 
+
+ align:start position:0%
+emphasize that especially because some
+of the very first readings for the term
+
+ align:start position:0%
+of the very first readings for the term
+ 
+
+ align:start position:0%
+of the very first readings for the term
+that you'll have even in advance of this
+
+ align:start position:0%
+that you'll have even in advance of this
+ 
+
+ align:start position:0%
+that you'll have even in advance of this
+coming uh next lecture might look pretty
+
+ align:start position:0%
+coming uh next lecture might look pretty
+ 
+
+ align:start position:0%
+coming uh next lecture might look pretty
+technical or pretty off-putting
+
+ align:start position:0%
+technical or pretty off-putting
+ 
+
+ align:start position:0%
+technical or pretty off-putting
+um some not all of them but some of the
+
+ align:start position:0%
+um some not all of them but some of the
+ 
+
+ align:start position:0%
+um some not all of them but some of the
+readings will have lots of equations
+
+ align:start position:0%
+readings will have lots of equations
+ 
+
+ align:start position:0%
+readings will have lots of equations
+that look like would often be taken from
+
+ align:start position:0%
+that look like would often be taken from
+ 
+
+ align:start position:0%
+that look like would often be taken from
+old textbooks might be on topics you
+
+ align:start position:0%
+old textbooks might be on topics you
+ 
+
+ align:start position:0%
+old textbooks might be on topics you
+haven't had a chance to have a different
+
+ align:start position:0%
+haven't had a chance to have a different
+ 
+
+ align:start position:0%
+haven't had a chance to have a different
+formal course and so on and I want to
+
+ align:start position:0%
+formal course and so on and I want to
+ 
+
+ align:start position:0%
+formal course and so on and I want to
+emphasize that's okay if this looks
+
+ align:start position:0%
+emphasize that's okay if this looks
+ 
+
+ align:start position:0%
+emphasize that's okay if this looks
+strange partly it's designed to look
+
+ align:start position:0%
+strange partly it's designed to look
+ 
+
+ align:start position:0%
+strange partly it's designed to look
+strange actually
+
+ align:start position:0%
+strange actually
+ 
+
+ align:start position:0%
+strange actually
+so the strangeness is meant to trigger
+
+ align:start position:0%
+so the strangeness is meant to trigger
+ 
+
+ align:start position:0%
+so the strangeness is meant to trigger
+some questions about what did people
+
+ align:start position:0%
+some questions about what did people
+ 
+
+ align:start position:0%
+some questions about what did people
+think they were doing when they read
+
+ align:start position:0%
+think they were doing when they read
+ 
+
+ align:start position:0%
+think they were doing when they read
+texts like those so if they look either
+
+ align:start position:0%
+texts like those so if they look either
+ 
+
+ align:start position:0%
+texts like those so if they look either
+very hard or unfamiliar or technical
+
+ align:start position:0%
+very hard or unfamiliar or technical
+ 
+
+ align:start position:0%
+very hard or unfamiliar or technical
+that really is kind of part of the point
+
+ align:start position:0%
+that really is kind of part of the point
+ 
+
+ align:start position:0%
+that really is kind of part of the point
+and part of the point for this
+
+ align:start position:0%
+and part of the point for this
+ 
+
+ align:start position:0%
+and part of the point for this
+particular class is not to worry about
+
+ align:start position:0%
+particular class is not to worry about
+ 
+
+ align:start position:0%
+particular class is not to worry about
+reproducing those calculations or
+
+ align:start position:0%
+reproducing those calculations or
+ 
+
+ align:start position:0%
+reproducing those calculations or
+understanding every single step of the
+
+ align:start position:0%
+understanding every single step of the
+ 
+
+ align:start position:0%
+understanding every single step of the
+mathematics I like to joke that my my
+
+ align:start position:0%
+mathematics I like to joke that my my
+ 
+
+ align:start position:0%
+mathematics I like to joke that my my
+very many friends in the physics
+
+ align:start position:0%
+very many friends in the physics
+ 
+
+ align:start position:0%
+very many friends in the physics
+department it's their job to help you
+
+ align:start position:0%
+department it's their job to help you
+ 
+
+ align:start position:0%
+department it's their job to help you
+all learn how to calculate and many of
+
+ align:start position:0%
+all learn how to calculate and many of
+ 
+
+ align:start position:0%
+all learn how to calculate and many of
+you I'm sure calculated very very well
+
+ align:start position:0%
+you I'm sure calculated very very well
+ 
+
+ align:start position:0%
+you I'm sure calculated very very well
+already and that's incredibly important
+
+ align:start position:0%
+already and that's incredibly important
+ 
+
+ align:start position:0%
+already and that's incredibly important
+this class has a different set of goals
+
+ align:start position:0%
+this class has a different set of goals
+ 
+
+ align:start position:0%
+this class has a different set of goals
+and aims and so I want to really
+
+ align:start position:0%
+and aims and so I want to really
+ 
+
+ align:start position:0%
+and aims and so I want to really
+emphasize uh not to be kind of frankly
+
+ align:start position:0%
+emphasize uh not to be kind of frankly
+ 
+
+ align:start position:0%
+emphasize uh not to be kind of frankly
+scared off if some of the readings look
+
+ align:start position:0%
+scared off if some of the readings look
+ 
+
+ align:start position:0%
+scared off if some of the readings look
+at first blush at least a little
+
+ align:start position:0%
+at first blush at least a little
+ 
+
+ align:start position:0%
+at first blush at least a little
+um overwhelming they should look strange
+
+ align:start position:0%
+um overwhelming they should look strange
+ 
+
+ align:start position:0%
+um overwhelming they should look strange
+and if every step in the derivation is
+
+ align:start position:0%
+and if every step in the derivation is
+ 
+
+ align:start position:0%
+and if every step in the derivation is
+not so clear that's okay in this class
+
+ align:start position:0%
+not so clear that's okay in this class
+ 
+
+ align:start position:0%
+not so clear that's okay in this class
+is special so we're going to be focusing
+
+ align:start position:0%
+is special so we're going to be focusing
+ 
+
+ align:start position:0%
+is special so we're going to be focusing
+on a range of ideas in modern physics
+
+ align:start position:0%
+on a range of ideas in modern physics
+ 
+
+ align:start position:0%
+on a range of ideas in modern physics
+and also they're changing context as I
+
+ align:start position:0%
+and also they're changing context as I
+ 
+
+ align:start position:0%
+and also they're changing context as I
+mentioned of many kinds of contexts and
+
+ align:start position:0%
+mentioned of many kinds of contexts and
+ 
+
+ align:start position:0%
+mentioned of many kinds of contexts and
+it's of course always always okay to ask
+
+ align:start position:0%
+it's of course always always okay to ask
+ 
+
+ align:start position:0%
+it's of course always always okay to ask
+for clarifications uh that formalism is
+
+ align:start position:0%
+for clarifications uh that formalism is
+ 
+
+ align:start position:0%
+for clarifications uh that formalism is
+dear to my heart hopefully dear to many
+
+ align:start position:0%
+dear to my heart hopefully dear to many
+ 
+
+ align:start position:0%
+dear to my heart hopefully dear to many
+of yours I'm not saying ignore the
+
+ align:start position:0%
+of yours I'm not saying ignore the
+ 
+
+ align:start position:0%
+of yours I'm not saying ignore the
+equations mathematics I'm just trying to
+
+ align:start position:0%
+equations mathematics I'm just trying to
+ 
+
+ align:start position:0%
+equations mathematics I'm just trying to
+emphasize not to worry about getting
+
+ align:start position:0%
+emphasize not to worry about getting
+ 
+
+ align:start position:0%
+emphasize not to worry about getting
+hung up if especially on the first
+
+ align:start position:0%
+hung up if especially on the first
+ 
+
+ align:start position:0%
+hung up if especially on the first
+reading things look very strange
+
+ align:start position:0%
+reading things look very strange
+ 
+
+ align:start position:0%
+reading things look very strange
+for a bunch of the of the um lectures
+
+ align:start position:0%
+for a bunch of the of the um lectures
+ 
+
+ align:start position:0%
+for a bunch of the of the um lectures
+not for everyone but for a bunch of them
+
+ align:start position:0%
+not for everyone but for a bunch of them
+ 
+
+ align:start position:0%
+not for everyone but for a bunch of them
+I'm actually writing up separate little
+
+ align:start position:0%
+I'm actually writing up separate little
+ 
+
+ align:start position:0%
+I'm actually writing up separate little
+short lecture notes in addition to these
+
+ align:start position:0%
+short lecture notes in addition to these
+ 
+
+ align:start position:0%
+short lecture notes in addition to these
+lecture slides to go through some more
+
+ align:start position:0%
+lecture slides to go through some more
+ 
+
+ align:start position:0%
+lecture slides to go through some more
+intermediate steps and derivations and
+
+ align:start position:0%
+intermediate steps and derivations and
+ 
+
+ align:start position:0%
+intermediate steps and derivations and
+so on those are always going to be
+
+ align:start position:0%
+so on those are always going to be
+ 
+
+ align:start position:0%
+so on those are always going to be
+optional it really is just to help as a
+
+ align:start position:0%
+optional it really is just to help as a
+ 
+
+ align:start position:0%
+optional it really is just to help as a
+kind of additional resource and also
+
+ align:start position:0%
+kind of additional resource and also
+ 
+
+ align:start position:0%
+kind of additional resource and also
+we'll have office hours and you can
+
+ align:start position:0%
+we'll have office hours and you can
+ 
+
+ align:start position:0%
+we'll have office hours and you can
+always make an appointment to meet with
+
+ align:start position:0%
+always make an appointment to meet with
+ 
+
+ align:start position:0%
+always make an appointment to meet with
+me or your teaching assistants uh
+
+ align:start position:0%
+me or your teaching assistants uh
+ 
+
+ align:start position:0%
+me or your teaching assistants uh
+directly so I just want to emphasize uh
+
+ align:start position:0%
+directly so I just want to emphasize uh
+ 
+
+ align:start position:0%
+directly so I just want to emphasize uh
+the aims course we're going to work on
+
+ align:start position:0%
+the aims course we're going to work on
+ 
+
+ align:start position:0%
+the aims course we're going to work on
+on written communication and we'll get
+
+ align:start position:0%
+on written communication and we'll get
+ 
+
+ align:start position:0%
+on written communication and we'll get
+to do it with some I think really juicy
+
+ align:start position:0%
+to do it with some I think really juicy
+ 
+
+ align:start position:0%
+to do it with some I think really juicy
+amazing fun material that's our that's
+
+ align:start position:0%
+amazing fun material that's our that's
+ 
+
+ align:start position:0%
+amazing fun material that's our that's
+our overarching aim for the semester
+
+ align:start position:0%
+our overarching aim for the semester
+ 
+
+ align:start position:0%
+our overarching aim for the semester
+I like to think of this class as a kind
+
+ align:start position:0%
+I like to think of this class as a kind
+ 
+
+ align:start position:0%
+I like to think of this class as a kind
+of road map and it turns out roadmaps
+
+ align:start position:0%
+of road map and it turns out roadmaps
+ 
+
+ align:start position:0%
+of road map and it turns out roadmaps
+work in at least two directions it could
+
+ align:start position:0%
+work in at least two directions it could
+ 
+
+ align:start position:0%
+work in at least two directions it could
+be a map of where you're heading if
+
+ align:start position:0%
+be a map of where you're heading if
+ 
+
+ align:start position:0%
+be a map of where you're heading if
+you're new to MIT you're new to the
+
+ align:start position:0%
+you're new to MIT you're new to the
+ 
+
+ align:start position:0%
+you're new to MIT you're new to the
+physics department or just curious and
+
+ align:start position:0%
+physics department or just curious and
+ 
+
+ align:start position:0%
+physics department or just curious and
+coming in from a different field it can
+
+ align:start position:0%
+coming in from a different field it can
+ 
+
+ align:start position:0%
+coming in from a different field it can
+be a kind of preview of some pretty
+
+ align:start position:0%
+be a kind of preview of some pretty
+ 
+
+ align:start position:0%
+be a kind of preview of some pretty
+awesome cool stuff that could be ahead
+
+ align:start position:0%
+awesome cool stuff that could be ahead
+ 
+
+ align:start position:0%
+awesome cool stuff that could be ahead
+of you it could also be a kind of look
+
+ align:start position:0%
+of you it could also be a kind of look
+ 
+
+ align:start position:0%
+of you it could also be a kind of look
+in the rear view mirror for Junior's
+
+ align:start position:0%
+in the rear view mirror for Junior's
+ 
+
+ align:start position:0%
+in the rear view mirror for Junior's
+estate or seniors in the physics
+
+ align:start position:0%
+estate or seniors in the physics
+ 
+
+ align:start position:0%
+estate or seniors in the physics
+department you will have seen some of
+
+ align:start position:0%
+department you will have seen some of
+ 
+
+ align:start position:0%
+department you will have seen some of
+this material in other courses already
+
+ align:start position:0%
+this material in other courses already
+ 
+
+ align:start position:0%
+this material in other courses already
+but this is a chance to begin kind of
+
+ align:start position:0%
+but this is a chance to begin kind of
+ 
+
+ align:start position:0%
+but this is a chance to begin kind of
+seeing perhaps how different pieces fit
+
+ align:start position:0%
+seeing perhaps how different pieces fit
+ 
+
+ align:start position:0%
+seeing perhaps how different pieces fit
+together to kind of synthesize a map of
+
+ align:start position:0%
+together to kind of synthesize a map of
+ 
+
+ align:start position:0%
+together to kind of synthesize a map of
+what might have been kind of separated
+
+ align:start position:0%
+what might have been kind of separated
+ 
+
+ align:start position:0%
+what might have been kind of separated
+or disparate Parts until now so I like
+
+ align:start position:0%
+or disparate Parts until now so I like
+ 
+
+ align:start position:0%
+or disparate Parts until now so I like
+this idea of a road map either whether
+
+ align:start position:0%
+this idea of a road map either whether
+ 
+
+ align:start position:0%
+this idea of a road map either whether
+you're whether you're starting a journey
+
+ align:start position:0%
+you're whether you're starting a journey
+ 
+
+ align:start position:0%
+you're whether you're starting a journey
+or looking back uh how you got to where
+
+ align:start position:0%
+or looking back uh how you got to where
+ 
+
+ align:start position:0%
+or looking back uh how you got to where
+you are now hopefully this course will
+
+ align:start position:0%
+you are now hopefully this course will
+ 
+
+ align:start position:0%
+you are now hopefully this course will
+help with some of that as well
+
+ align:start position:0%
+help with some of that as well
+ 
+
+ align:start position:0%
+help with some of that as well
+okay so let me pause and ask for any
+
+ align:start position:0%
+okay so let me pause and ask for any
+ 
+
+ align:start position:0%
+okay so let me pause and ask for any
+questions if you do have questions
+
+ align:start position:0%
+questions if you do have questions
+ 
+
+ align:start position:0%
+questions if you do have questions
+please try to raise your your blue hand
+
+ align:start position:0%
+please try to raise your your blue hand
+ 
+
+ align:start position:0%
+please try to raise your your blue hand
+and ask the teaching assistants who are
+
+ align:start position:0%
+and ask the teaching assistants who are
+ 
+
+ align:start position:0%
+and ask the teaching assistants who are
+co-hosts of this Zoom session uh to to
+
+ align:start position:0%
+co-hosts of this Zoom session uh to to
+ 
+
+ align:start position:0%
+co-hosts of this Zoom session uh to to
+kind of recognize you and then they can
+
+ align:start position:0%
+kind of recognize you and then they can
+ 
+
+ align:start position:0%
+kind of recognize you and then they can
+uh ask you to unmute yourself any
+
+ align:start position:0%
+uh ask you to unmute yourself any
+ 
+
+ align:start position:0%
+uh ask you to unmute yourself any
+questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I hear a resounding silence uh so I'm
+
+ align:start position:0%
+I hear a resounding silence uh so I'm
+ 
+
+ align:start position:0%
+I hear a resounding silence uh so I'm
+gonna I'm gonna charge ahead but if you
+
+ align:start position:0%
+gonna I'm gonna charge ahead but if you
+ 
+
+ align:start position:0%
+gonna I'm gonna charge ahead but if you
+do have questions again please feel free
+
+ align:start position:0%
+do have questions again please feel free
+ 
+
+ align:start position:0%
+do have questions again please feel free
+to use the chat or the or the blue hand
+
+ align:start position:0%
+to use the chat or the or the blue hand
+ 
+
+ align:start position:0%
+to use the chat or the or the blue hand
+uh raise hand icon
+
+ align:start position:0%
+uh raise hand icon
+ 
+
+ align:start position:0%
+uh raise hand icon
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+okay so for this part sorry I want to
+
+ align:start position:0%
+okay so for this part sorry I want to
+ 
+
+ align:start position:0%
+okay so for this part sorry I want to
+just take a few moments and introduce
+
+ align:start position:0%
+just take a few moments and introduce
+ 
+
+ align:start position:0%
+just take a few moments and introduce
+um the the whole team I'm very excited
+
+ align:start position:0%
+um the the whole team I'm very excited
+ 
+
+ align:start position:0%
+um the the whole team I'm very excited
+to work with uh I think a really
+
+ align:start position:0%
+to work with uh I think a really
+ 
+
+ align:start position:0%
+to work with uh I think a really
+terrific team uh of instructors for this
+
+ align:start position:0%
+terrific team uh of instructors for this
+ 
+
+ align:start position:0%
+terrific team uh of instructors for this
+class it's a big group we have uh four
+
+ align:start position:0%
+class it's a big group we have uh four
+ 
+
+ align:start position:0%
+class it's a big group we have uh four
+teaching assistants in addition to
+
+ align:start position:0%
+teaching assistants in addition to
+ 
+
+ align:start position:0%
+teaching assistants in addition to
+myself so I'll just say a little bit
+
+ align:start position:0%
+myself so I'll just say a little bit
+ 
+
+ align:start position:0%
+myself so I'll just say a little bit
+about my own um research uh I am a
+
+ align:start position:0%
+about my own um research uh I am a
+ 
+
+ align:start position:0%
+about my own um research uh I am a
+professor at MIT I teach both in our
+
+ align:start position:0%
+professor at MIT I teach both in our
+ 
+
+ align:start position:0%
+professor at MIT I teach both in our
+program in science technology and
+
+ align:start position:0%
+program in science technology and
+ 
+
+ align:start position:0%
+program in science technology and
+Society STS in that department I uh
+
+ align:start position:0%
+Society STS in that department I uh
+ 
+
+ align:start position:0%
+Society STS in that department I uh
+conduct research and work with students
+
+ align:start position:0%
+conduct research and work with students
+ 
+
+ align:start position:0%
+conduct research and work with students
+uh in the history of Science and
+
+ align:start position:0%
+uh in the history of Science and
+ 
+
+ align:start position:0%
+uh in the history of Science and
+particular history of modern physics
+
+ align:start position:0%
+particular history of modern physics
+ 
+
+ align:start position:0%
+particular history of modern physics
+I've written a few books I've edited
+
+ align:start position:0%
+I've written a few books I've edited
+ 
+
+ align:start position:0%
+I've written a few books I've edited
+other books a lot of the material that
+
+ align:start position:0%
+other books a lot of the material that
+ 
+
+ align:start position:0%
+other books a lot of the material that
+we'll cover in this semester on this
+
+ align:start position:0%
+we'll cover in this semester on this
+ 
+
+ align:start position:0%
+we'll cover in this semester on this
+term comes not surprisingly from things
+
+ align:start position:0%
+term comes not surprisingly from things
+ 
+
+ align:start position:0%
+term comes not surprisingly from things
+that I have a particular interest in
+
+ align:start position:0%
+that I have a particular interest in
+ 
+
+ align:start position:0%
+that I have a particular interest in
+I've written about or who are very dear
+
+ align:start position:0%
+I've written about or who are very dear
+ 
+
+ align:start position:0%
+I've written about or who are very dear
+friends of mine have written about so
+
+ align:start position:0%
+friends of mine have written about so
+ 
+
+ align:start position:0%
+friends of mine have written about so
+I'm sort of uh I like I'm very lucky to
+
+ align:start position:0%
+I'm sort of uh I like I'm very lucky to
+ 
+
+ align:start position:0%
+I'm sort of uh I like I'm very lucky to
+get to be immersed in the history of
+
+ align:start position:0%
+get to be immersed in the history of
+ 
+
+ align:start position:0%
+get to be immersed in the history of
+modern science uh when I wear my STS cap
+
+ align:start position:0%
+modern science uh when I wear my STS cap
+ 
+
+ align:start position:0%
+modern science uh when I wear my STS cap
+I'm also a member of the physics
+
+ align:start position:0%
+I'm also a member of the physics
+ 
+
+ align:start position:0%
+I'm also a member of the physics
+department Professor physics uh up here
+
+ align:start position:0%
+department Professor physics uh up here
+ 
+
+ align:start position:0%
+department Professor physics uh up here
+I have a picture of my research group
+
+ align:start position:0%
+I have a picture of my research group
+ 
+
+ align:start position:0%
+I have a picture of my research group
+there's actually somewhat old photo you
+
+ align:start position:0%
+there's actually somewhat old photo you
+ 
+
+ align:start position:0%
+there's actually somewhat old photo you
+probably won't recognize the faces
+
+ align:start position:0%
+probably won't recognize the faces
+ 
+
+ align:start position:0%
+probably won't recognize the faces
+because even the Europe students in this
+
+ align:start position:0%
+because even the Europe students in this
+ 
+
+ align:start position:0%
+because even the Europe students in this
+photo have all graduated by now I work
+
+ align:start position:0%
+photo have all graduated by now I work
+ 
+
+ align:start position:0%
+photo have all graduated by now I work
+very closely with Alan Guth in our
+
+ align:start position:0%
+very closely with Alan Guth in our
+ 
+
+ align:start position:0%
+very closely with Alan Guth in our
+Center for theoretical physics within
+
+ align:start position:0%
+Center for theoretical physics within
+ 
+
+ align:start position:0%
+Center for theoretical physics within
+the department uh we work on many
+
+ align:start position:0%
+the department uh we work on many
+ 
+
+ align:start position:0%
+the department uh we work on many
+aspects of early Universe cosmology uh
+
+ align:start position:0%
+aspects of early Universe cosmology uh
+ 
+
+ align:start position:0%
+aspects of early Universe cosmology uh
+we'll actually come to some of those
+
+ align:start position:0%
+we'll actually come to some of those
+ 
+
+ align:start position:0%
+we'll actually come to some of those
+topics near the end of this semester
+
+ align:start position:0%
+topics near the end of this semester
+ 
+
+ align:start position:0%
+topics near the end of this semester
+because I couldn't resist I love it so
+
+ align:start position:0%
+because I couldn't resist I love it so
+ 
+
+ align:start position:0%
+because I couldn't resist I love it so
+much I've also I've been working for a
+
+ align:start position:0%
+much I've also I've been working for a
+ 
+
+ align:start position:0%
+much I've also I've been working for a
+number of years on foundations of
+
+ align:start position:0%
+number of years on foundations of
+ 
+
+ align:start position:0%
+number of years on foundations of
+quantum theory including new
+
+ align:start position:0%
+quantum theory including new
+ 
+
+ align:start position:0%
+quantum theory including new
+experimental tests of topics like
+
+ align:start position:0%
+experimental tests of topics like
+ 
+
+ align:start position:0%
+experimental tests of topics like
+quantum entanglement we'll talk about
+
+ align:start position:0%
+quantum entanglement we'll talk about
+ 
+
+ align:start position:0%
+quantum entanglement we'll talk about
+some of that this semester as well so on
+
+ align:start position:0%
+some of that this semester as well so on
+ 
+
+ align:start position:0%
+some of that this semester as well so on
+the physics side I
+
+ align:start position:0%
+the physics side I
+ 
+
+ align:start position:0%
+the physics side I
+especially interested in theoretical
+
+ align:start position:0%
+especially interested in theoretical
+ 
+
+ align:start position:0%
+especially interested in theoretical
+early Universe cosmology and
+
+ align:start position:0%
+early Universe cosmology and
+ 
+
+ align:start position:0%
+early Universe cosmology and
+astrophysics and also uh various aspects
+
+ align:start position:0%
+astrophysics and also uh various aspects
+ 
+
+ align:start position:0%
+astrophysics and also uh various aspects
+of quantum theory and even some uh
+
+ align:start position:0%
+of quantum theory and even some uh
+ 
+
+ align:start position:0%
+of quantum theory and even some uh
+interesting new recent work on Quantum
+
+ align:start position:0%
+interesting new recent work on Quantum
+ 
+
+ align:start position:0%
+interesting new recent work on Quantum
+information science so that's uh that's
+
+ align:start position:0%
+information science so that's uh that's
+ 
+
+ align:start position:0%
+information science so that's uh that's
+where I'm coming from
+
+ align:start position:0%
+where I'm coming from
+ 
+
+ align:start position:0%
+where I'm coming from
+now let's get to uh what are you gonna
+
+ align:start position:0%
+now let's get to uh what are you gonna
+ 
+
+ align:start position:0%
+now let's get to uh what are you gonna
+do in this class what the one things
+
+ align:start position:0%
+do in this class what the one things
+ 
+
+ align:start position:0%
+do in this class what the one things
+you're going to do is read not a ton
+
+ align:start position:0%
+you're going to do is read not a ton
+ 
+
+ align:start position:0%
+you're going to do is read not a ton
+we've worked very carefully to make the
+
+ align:start position:0%
+we've worked very carefully to make the
+ 
+
+ align:start position:0%
+we've worked very carefully to make the
+reading list we think really kind of
+
+ align:start position:0%
+reading list we think really kind of
+ 
+
+ align:start position:0%
+reading list we think really kind of
+curated and uh and not overwhelm
+
+ align:start position:0%
+curated and uh and not overwhelm
+ 
+
+ align:start position:0%
+curated and uh and not overwhelm
+students with with a large page count
+
+ align:start position:0%
+students with with a large page count
+ 
+
+ align:start position:0%
+students with with a large page count
+and so the best thing you can do is read
+
+ align:start position:0%
+and so the best thing you can do is read
+ 
+
+ align:start position:0%
+and so the best thing you can do is read
+the genuine January generally rather
+
+ align:start position:0%
+the genuine January generally rather
+ 
+
+ align:start position:0%
+the genuine January generally rather
+brief reading assignments in advance of
+
+ align:start position:0%
+brief reading assignments in advance of
+ 
+
+ align:start position:0%
+brief reading assignments in advance of
+the of the class with which they're
+
+ align:start position:0%
+the of the class with which they're
+ 
+
+ align:start position:0%
+the of the class with which they're
+Associated it'll help if you've been
+
+ align:start position:0%
+Associated it'll help if you've been
+ 
+
+ align:start position:0%
+Associated it'll help if you've been
+able to do the readings ahead of the
+
+ align:start position:0%
+able to do the readings ahead of the
+ 
+
+ align:start position:0%
+able to do the readings ahead of the
+class session
+
+ align:start position:0%
+class session
+ 
+
+ align:start position:0%
+class session
+what are the actual subject requirements
+
+ align:start position:0%
+what are the actual subject requirements
+ 
+
+ align:start position:0%
+what are the actual subject requirements
+in addition to keeping up the reading as
+
+ align:start position:0%
+in addition to keeping up the reading as
+ 
+
+ align:start position:0%
+in addition to keeping up the reading as
+I mentioned this is a CI course for uh
+
+ align:start position:0%
+I mentioned this is a CI course for uh
+ 
+
+ align:start position:0%
+I mentioned this is a CI course for uh
+for physics Majors so our main emphasis
+
+ align:start position:0%
+for physics Majors so our main emphasis
+ 
+
+ align:start position:0%
+for physics Majors so our main emphasis
+is on written communication it will not
+
+ align:start position:0%
+is on written communication it will not
+ 
+
+ align:start position:0%
+is on written communication it will not
+be on oral communication partly because
+
+ align:start position:0%
+be on oral communication partly because
+ 
+
+ align:start position:0%
+be on oral communication partly because
+there's a hundred of us by Zoo so it
+
+ align:start position:0%
+there's a hundred of us by Zoo so it
+ 
+
+ align:start position:0%
+there's a hundred of us by Zoo so it
+really will be on written communication
+
+ align:start position:0%
+really will be on written communication
+ 
+
+ align:start position:0%
+really will be on written communication
+which had always been the overwhelming
+
+ align:start position:0%
+which had always been the overwhelming
+ 
+
+ align:start position:0%
+which had always been the overwhelming
+majority of the course structure even in
+
+ align:start position:0%
+majority of the course structure even in
+ 
+
+ align:start position:0%
+majority of the course structure even in
+previous years
+
+ align:start position:0%
+previous years
+ 
+
+ align:start position:0%
+previous years
+so like nearly all CI courses we have
+
+ align:start position:0%
+so like nearly all CI courses we have
+ 
+
+ align:start position:0%
+so like nearly all CI courses we have
+um a number of pages of writing over the
+
+ align:start position:0%
+um a number of pages of writing over the
+ 
+
+ align:start position:0%
+um a number of pages of writing over the
+course of the semester the way we do it
+
+ align:start position:0%
+course of the semester the way we do it
+ 
+
+ align:start position:0%
+course of the semester the way we do it
+in this term is to break it up into a
+
+ align:start position:0%
+in this term is to break it up into a
+ 
+
+ align:start position:0%
+in this term is to break it up into a
+number of assignments that kind of build
+
+ align:start position:0%
+number of assignments that kind of build
+ 
+
+ align:start position:0%
+number of assignments that kind of build
+up they build both in length but also in
+
+ align:start position:0%
+up they build both in length but also in
+ 
+
+ align:start position:0%
+up they build both in length but also in
+the nature of the assignment in the type
+
+ align:start position:0%
+the nature of the assignment in the type
+ 
+
+ align:start position:0%
+the nature of the assignment in the type
+of writing that we'll be working on and
+
+ align:start position:0%
+of writing that we'll be working on and
+ 
+
+ align:start position:0%
+of writing that we'll be working on and
+the nature of say the kinds of sources
+
+ align:start position:0%
+the nature of say the kinds of sources
+ 
+
+ align:start position:0%
+the nature of say the kinds of sources
+we'll be working with or the nature the
+
+ align:start position:0%
+we'll be working with or the nature the
+ 
+
+ align:start position:0%
+we'll be working with or the nature the
+argument we want to be able to
+
+ align:start position:0%
+argument we want to be able to
+ 
+
+ align:start position:0%
+argument we want to be able to
+articulate and these really quite
+
+ align:start position:0%
+articulate and these really quite
+ 
+
+ align:start position:0%
+articulate and these really quite
+amazing teaching assistants are here to
+
+ align:start position:0%
+amazing teaching assistants are here to
+ 
+
+ align:start position:0%
+amazing teaching assistants are here to
+work very closely with you on each of
+
+ align:start position:0%
+work very closely with you on each of
+ 
+
+ align:start position:0%
+work very closely with you on each of
+these papers so we're not going to
+
+ align:start position:0%
+these papers so we're not going to
+ 
+
+ align:start position:0%
+these papers so we're not going to
+expect you to do it uh every step on
+
+ align:start position:0%
+expect you to do it uh every step on
+ 
+
+ align:start position:0%
+expect you to do it uh every step on
+your own so you can see now the due
+
+ align:start position:0%
+your own so you can see now the due
+ 
+
+ align:start position:0%
+your own so you can see now the due
+dates uh the structure the first bit
+
+ align:start position:0%
+dates uh the structure the first bit
+ 
+
+ align:start position:0%
+dates uh the structure the first bit
+will of course we'll hand out the
+
+ align:start position:0%
+will of course we'll hand out the
+ 
+
+ align:start position:0%
+will of course we'll hand out the
+assignments uh well in advance of each
+
+ align:start position:0%
+assignments uh well in advance of each
+ 
+
+ align:start position:0%
+assignments uh well in advance of each
+of the due dates uh the actual kind of
+
+ align:start position:0%
+of the due dates uh the actual kind of
+ 
+
+ align:start position:0%
+of the due dates uh the actual kind of
+prompt
+
+ align:start position:0%
+prompt
+ 
+
+ align:start position:0%
+prompt
+so pretty soon we'll finalize a prompt
+
+ align:start position:0%
+so pretty soon we'll finalize a prompt
+ 
+
+ align:start position:0%
+so pretty soon we'll finalize a prompt
+for paper one we'll make sure it's easy
+
+ align:start position:0%
+for paper one we'll make sure it's easy
+ 
+
+ align:start position:0%
+for paper one we'll make sure it's easy
+for you to find on the canvas site that
+
+ align:start position:0%
+for you to find on the canvas site that
+ 
+
+ align:start position:0%
+for you to find on the canvas site that
+one will be four or five double spaced
+
+ align:start position:0%
+one will be four or five double spaced
+ 
+
+ align:start position:0%
+one will be four or five double spaced
+Pages really a handful of paragraphs not
+
+ align:start position:0%
+Pages really a handful of paragraphs not
+ 
+
+ align:start position:0%
+Pages really a handful of paragraphs not
+a very long essay that'll be due um
+
+ align:start position:0%
+a very long essay that'll be due um
+ 
+
+ align:start position:0%
+a very long essay that'll be due um
+electronically uh near the end of
+
+ align:start position:0%
+electronically uh near the end of
+ 
+
+ align:start position:0%
+electronically uh near the end of
+September the second paper we do a
+
+ align:start position:0%
+September the second paper we do a
+ 
+
+ align:start position:0%
+September the second paper we do a
+couple weeks after that a little bit
+
+ align:start position:0%
+couple weeks after that a little bit
+ 
+
+ align:start position:0%
+couple weeks after that a little bit
+longer six or seven doubles for these
+
+ align:start position:0%
+longer six or seven doubles for these
+ 
+
+ align:start position:0%
+longer six or seven doubles for these
+pages and a little more complicated a
+
+ align:start position:0%
+pages and a little more complicated a
+ 
+
+ align:start position:0%
+pages and a little more complicated a
+range of types of sources to to uh to to
+
+ align:start position:0%
+range of types of sources to to uh to to
+ 
+
+ align:start position:0%
+range of types of sources to to uh to to
+make use of as you build your argument
+
+ align:start position:0%
+make use of as you build your argument
+ 
+
+ align:start position:0%
+make use of as you build your argument
+because it's a CI course like usual
+
+ align:start position:0%
+because it's a CI course like usual
+ 
+
+ align:start position:0%
+because it's a CI course like usual
+we'll have a mandatory rewrite of that
+
+ align:start position:0%
+we'll have a mandatory rewrite of that
+ 
+
+ align:start position:0%
+we'll have a mandatory rewrite of that
+paper to assignment
+
+ align:start position:0%
+paper to assignment
+ 
+
+ align:start position:0%
+paper to assignment
+that'll be due handed in separately
+
+ align:start position:0%
+that'll be due handed in separately
+ 
+
+ align:start position:0%
+that'll be due handed in separately
+several weeks after the first iteration
+
+ align:start position:0%
+several weeks after the first iteration
+ 
+
+ align:start position:0%
+several weeks after the first iteration
+and then finally the the final paper is
+
+ align:start position:0%
+and then finally the the final paper is
+ 
+
+ align:start position:0%
+and then finally the the final paper is
+due on the last day of classes uh
+
+ align:start position:0%
+due on the last day of classes uh
+ 
+
+ align:start position:0%
+due on the last day of classes uh
+December 9th so please note there is no
+
+ align:start position:0%
+December 9th so please note there is no
+ 
+
+ align:start position:0%
+December 9th so please note there is no
+midterm there are no problem sets
+
+ align:start position:0%
+midterm there are no problem sets
+ 
+
+ align:start position:0%
+midterm there are no problem sets
+there's no final exam the student work
+
+ align:start position:0%
+there's no final exam the student work
+ 
+
+ align:start position:0%
+there's no final exam the student work
+you'll be handed in will be exclusively
+
+ align:start position:0%
+you'll be handed in will be exclusively
+ 
+
+ align:start position:0%
+you'll be handed in will be exclusively
+these essays the series of essays and
+
+ align:start position:0%
+these essays the series of essays and
+ 
+
+ align:start position:0%
+these essays the series of essays and
+again we'll be working with you along
+
+ align:start position:0%
+again we'll be working with you along
+ 
+
+ align:start position:0%
+again we'll be working with you along
+the way
+
+ align:start position:0%
+the way
+ 
+
+ align:start position:0%
+the way
+you can see the kind of distribution uh
+
+ align:start position:0%
+you can see the kind of distribution uh
+ 
+
+ align:start position:0%
+you can see the kind of distribution uh
+here about how the different papers
+
+ align:start position:0%
+here about how the different papers
+ 
+
+ align:start position:0%
+here about how the different papers
+contribute to your overall final course
+
+ align:start position:0%
+contribute to your overall final course
+ 
+
+ align:start position:0%
+contribute to your overall final course
+grade obviously if any questions come up
+
+ align:start position:0%
+grade obviously if any questions come up
+ 
+
+ align:start position:0%
+grade obviously if any questions come up
+along the way of course of course please
+
+ align:start position:0%
+along the way of course of course please
+ 
+
+ align:start position:0%
+along the way of course of course please
+don't hesitate uh to ask me about it or
+
+ align:start position:0%
+don't hesitate uh to ask me about it or
+ 
+
+ align:start position:0%
+don't hesitate uh to ask me about it or
+your teaching assistant that's the sort
+
+ align:start position:0%
+your teaching assistant that's the sort
+ 
+
+ align:start position:0%
+your teaching assistant that's the sort
+of stuff you'll be working on uh
+
+ align:start position:0%
+of stuff you'll be working on uh
+ 
+
+ align:start position:0%
+of stuff you'll be working on uh
+concretely over the course of the term
+
+ align:start position:0%
+concretely over the course of the term
+ 
+
+ align:start position:0%
+concretely over the course of the term
+so again I'll pause any questions on any
+
+ align:start position:0%
+so again I'll pause any questions on any
+ 
+
+ align:start position:0%
+so again I'll pause any questions on any
+of of those items
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so far so good
+
+ align:start position:0%
+so far so good
+ 
+
+ align:start position:0%
+so far so good
+and so good so so uh Saba asked a
+
+ align:start position:0%
+and so good so so uh Saba asked a
+ 
+
+ align:start position:0%
+and so good so so uh Saba asked a
+question there's zero difference uh for
+
+ align:start position:0%
+question there's zero difference uh for
+ 
+
+ align:start position:0%
+question there's zero difference uh for
+the mechanics of the course between
+
+ align:start position:0%
+the mechanics of the course between
+ 
+
+ align:start position:0%
+the mechanics of the course between
+grading or homework or content between
+
+ align:start position:0%
+grading or homework or content between
+ 
+
+ align:start position:0%
+grading or homework or content between
+SDS and and Corset version it is
+
+ align:start position:0%
+SDS and and Corset version it is
+ 
+
+ align:start position:0%
+SDS and and Corset version it is
+literally one class it's just jointly
+
+ align:start position:0%
+literally one class it's just jointly
+ 
+
+ align:start position:0%
+literally one class it's just jointly
+listed and in fact I don't even know I
+
+ align:start position:0%
+listed and in fact I don't even know I
+ 
+
+ align:start position:0%
+listed and in fact I don't even know I
+mean like I'd have it would take work
+
+ align:start position:0%
+mean like I'd have it would take work
+ 
+
+ align:start position:0%
+mean like I'd have it would take work
+for me to figure out which version of
+
+ align:start position:0%
+for me to figure out which version of
+ 
+
+ align:start position:0%
+for me to figure out which version of
+given students actually registered in we
+
+ align:start position:0%
+given students actually registered in we
+ 
+
+ align:start position:0%
+given students actually registered in we
+we just we treated as one class as one
+
+ align:start position:0%
+we just we treated as one class as one
+ 
+
+ align:start position:0%
+we just we treated as one class as one
+set of materials one set of course aims
+
+ align:start position:0%
+set of materials one set of course aims
+ 
+
+ align:start position:0%
+set of materials one set of course aims
+so as far as we're concerned sort of on
+
+ align:start position:0%
+so as far as we're concerned sort of on
+ 
+
+ align:start position:0%
+so as far as we're concerned sort of on
+this shared screen it's one class we're
+
+ align:start position:0%
+this shared screen it's one class we're
+ 
+
+ align:start position:0%
+this shared screen it's one class we're
+going to work on this cool stuff
+
+ align:start position:0%
+going to work on this cool stuff
+ 
+
+ align:start position:0%
+going to work on this cool stuff
+together the tricky part gets you know
+
+ align:start position:0%
+together the tricky part gets you know
+ 
+
+ align:start position:0%
+together the tricky part gets you know
+how to out of the different
+
+ align:start position:0%
+how to out of the different
+ 
+
+ align:start position:0%
+how to out of the different
+um uh kind of uh requirements get it get
+
+ align:start position:0%
+um uh kind of uh requirements get it get
+ 
+
+ align:start position:0%
+um uh kind of uh requirements get it get
+get counted um for different kinds of
+
+ align:start position:0%
+get counted um for different kinds of
+ 
+
+ align:start position:0%
+get counted um for different kinds of
+students but it's one class one one set
+
+ align:start position:0%
+students but it's one class one one set
+ 
+
+ align:start position:0%
+students but it's one class one one set
+of aims one set of materials
+
+ align:start position:0%
+of aims one set of materials
+ 
+
+ align:start position:0%
+of aims one set of materials
+any other questions on this is all
+
+ align:start position:0%
+any other questions on this is all
+ 
+
+ align:start position:0%
+any other questions on this is all
+excellent questions
+
+ align:start position:0%
+excellent questions
+ 
+
+ align:start position:0%
+excellent questions
+yes definitely flood Sean's inbox I see
+
+ align:start position:0%
+yes definitely flood Sean's inbox I see
+ 
+
+ align:start position:0%
+yes definitely flood Sean's inbox I see
+Sean someone helpfully put Sean's um uh
+
+ align:start position:0%
+Sean someone helpfully put Sean's um uh
+ 
+
+ align:start position:0%
+Sean someone helpfully put Sean's um uh
+email address in there
+
+ align:start position:0%
+email address in there
+ 
+
+ align:start position:0%
+email address in there
+okay I'm gonna I'm gonna move on if you
+
+ align:start position:0%
+okay I'm gonna I'm gonna move on if you
+ 
+
+ align:start position:0%
+okay I'm gonna I'm gonna move on if you
+have more questions again please keep
+
+ align:start position:0%
+have more questions again please keep
+ 
+
+ align:start position:0%
+have more questions again please keep
+chiming in but I think I'll go back to
+
+ align:start position:0%
+chiming in but I think I'll go back to
+ 
+
+ align:start position:0%
+chiming in but I think I'll go back to
+uh screen sharing those are excellent
+
+ align:start position:0%
+uh screen sharing those are excellent
+ 
+
+ align:start position:0%
+uh screen sharing those are excellent
+good questions to get us going
+
+ align:start position:0%
+good questions to get us going
+ 
+
+ align:start position:0%
+good questions to get us going
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so hopefully you can see my screen again
+
+ align:start position:0%
+so hopefully you can see my screen again
+ 
+
+ align:start position:0%
+so hopefully you can see my screen again
+so last part again I won't take too too
+
+ align:start position:0%
+so last part again I won't take too too
+ 
+
+ align:start position:0%
+so last part again I won't take too too
+long we'll finish up early today
+
+ align:start position:0%
+long we'll finish up early today
+ 
+
+ align:start position:0%
+long we'll finish up early today
+I just want to tell you a little bit
+
+ align:start position:0%
+I just want to tell you a little bit
+ 
+
+ align:start position:0%
+I just want to tell you a little bit
+more about the kinds of material that
+
+ align:start position:0%
+more about the kinds of material that
+ 
+
+ align:start position:0%
+more about the kinds of material that
+we'll get to really kind of um kind of
+
+ align:start position:0%
+we'll get to really kind of um kind of
+ 
+
+ align:start position:0%
+we'll get to really kind of um kind of
+chew on get to really explore uh over
+
+ align:start position:0%
+chew on get to really explore uh over
+ 
+
+ align:start position:0%
+chew on get to really explore uh over
+the coming weeks so we'll be starting
+
+ align:start position:0%
+the coming weeks so we'll be starting
+ 
+
+ align:start position:0%
+the coming weeks so we'll be starting
+with a 19th century Legacy in fact
+
+ align:start position:0%
+with a 19th century Legacy in fact
+ 
+
+ align:start position:0%
+with a 19th century Legacy in fact
+starting fairly early in the 19th
+
+ align:start position:0%
+starting fairly early in the 19th
+ 
+
+ align:start position:0%
+starting fairly early in the 19th
+century going back to the 1820s and 30s
+
+ align:start position:0%
+century going back to the 1820s and 30s
+ 
+
+ align:start position:0%
+century going back to the 1820s and 30s
+not for too long we'll kind of gallop
+
+ align:start position:0%
+not for too long we'll kind of gallop
+ 
+
+ align:start position:0%
+not for too long we'll kind of gallop
+forward in time pretty quickly but the
+
+ align:start position:0%
+forward in time pretty quickly but the
+ 
+
+ align:start position:0%
+forward in time pretty quickly but the
+main question We'll be asking that unit
+
+ align:start position:0%
+main question We'll be asking that unit
+ 
+
+ align:start position:0%
+main question We'll be asking that unit
+is what did people think the world was
+
+ align:start position:0%
+is what did people think the world was
+ 
+
+ align:start position:0%
+is what did people think the world was
+made of what did they think it was their
+
+ align:start position:0%
+made of what did they think it was their
+ 
+
+ align:start position:0%
+made of what did they think it was their
+job to study and what what counted as a
+
+ align:start position:0%
+job to study and what what counted as a
+ 
+
+ align:start position:0%
+job to study and what what counted as a
+compelling explanation and equally
+
+ align:start position:0%
+compelling explanation and equally
+ 
+
+ align:start position:0%
+compelling explanation and equally
+interesting I think or equally important
+
+ align:start position:0%
+interesting I think or equally important
+ 
+
+ align:start position:0%
+interesting I think or equally important
+who are the kinds of people who did that
+
+ align:start position:0%
+who are the kinds of people who did that
+ 
+
+ align:start position:0%
+who are the kinds of people who did that
+and where do they do it and what kinds
+
+ align:start position:0%
+and where do they do it and what kinds
+ 
+
+ align:start position:0%
+and where do they do it and what kinds
+of settings or institutions how do they
+
+ align:start position:0%
+of settings or institutions how do they
+ 
+
+ align:start position:0%
+of settings or institutions how do they
+work together what they think their job
+
+ align:start position:0%
+work together what they think their job
+ 
+
+ align:start position:0%
+work together what they think their job
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if all the many topics we could focus
+
+ align:start position:0%
+so if all the many topics we could focus
+ 
+
+ align:start position:0%
+so if all the many topics we could focus
+on Within
+
+ align:start position:0%
+on Within
+ 
+
+ align:start position:0%
+on Within
+the study of uh the Natural Sciences of
+
+ align:start position:0%
+the study of uh the Natural Sciences of
+ 
+
+ align:start position:0%
+the study of uh the Natural Sciences of
+physical sciences in the 19th century
+
+ align:start position:0%
+physical sciences in the 19th century
+ 
+
+ align:start position:0%
+physical sciences in the 19th century
+we're going to look fairly narrowly at
+
+ align:start position:0%
+we're going to look fairly narrowly at
+ 
+
+ align:start position:0%
+we're going to look fairly narrowly at
+examples from electricity and magnetism
+
+ align:start position:0%
+examples from electricity and magnetism
+ 
+
+ align:start position:0%
+examples from electricity and magnetism
+and Optics partly because that becomes
+
+ align:start position:0%
+and Optics partly because that becomes
+ 
+
+ align:start position:0%
+and Optics partly because that becomes
+super important for things like
+
+ align:start position:0%
+super important for things like
+ 
+
+ align:start position:0%
+super important for things like
+relativity and we do want to get too
+
+ align:start position:0%
+relativity and we do want to get too
+ 
+
+ align:start position:0%
+relativity and we do want to get too
+fairly quickly
+
+ align:start position:0%
+fairly quickly
+ 
+
+ align:start position:0%
+fairly quickly
+uh and also because I think they're just
+
+ align:start position:0%
+uh and also because I think they're just
+ 
+
+ align:start position:0%
+uh and also because I think they're just
+fascinating uh in their own right so
+
+ align:start position:0%
+fascinating uh in their own right so
+ 
+
+ align:start position:0%
+fascinating uh in their own right so
+we'll be talking about some names and
+
+ align:start position:0%
+we'll be talking about some names and
+ 
+
+ align:start position:0%
+we'll be talking about some names and
+some some ideas that again are likely
+
+ align:start position:0%
+some some ideas that again are likely
+ 
+
+ align:start position:0%
+some some ideas that again are likely
+familiar to many of you we'll start with
+
+ align:start position:0%
+familiar to many of you we'll start with
+ 
+
+ align:start position:0%
+familiar to many of you we'll start with
+some discussions of of Michael Faraday
+
+ align:start position:0%
+some discussions of of Michael Faraday
+ 
+
+ align:start position:0%
+some discussions of of Michael Faraday
+and his ideas about lines of force and
+
+ align:start position:0%
+and his ideas about lines of force and
+ 
+
+ align:start position:0%
+and his ideas about lines of force and
+The luminiferous Ether will spend a long
+
+ align:start position:0%
+The luminiferous Ether will spend a long
+ 
+
+ align:start position:0%
+The luminiferous Ether will spend a long
+time talking about The Ether we'll talk
+
+ align:start position:0%
+time talking about The Ether we'll talk
+ 
+
+ align:start position:0%
+time talking about The Ether we'll talk
+about James Clark Maxwell you can read a
+
+ align:start position:0%
+about James Clark Maxwell you can read a
+ 
+
+ align:start position:0%
+about James Clark Maxwell you can read a
+short excerpt from uh from his famous
+
+ align:start position:0%
+short excerpt from uh from his famous
+ 
+
+ align:start position:0%
+short excerpt from uh from his famous
+Treatise on electricity magnetism I'm
+
+ align:start position:0%
+Treatise on electricity magnetism I'm
+ 
+
+ align:start position:0%
+Treatise on electricity magnetism I'm
+talking about William Thompson later
+
+ align:start position:0%
+talking about William Thompson later
+ 
+
+ align:start position:0%
+talking about William Thompson later
+known as Lord Calvin and others we'll
+
+ align:start position:0%
+known as Lord Calvin and others we'll
+ 
+
+ align:start position:0%
+known as Lord Calvin and others we'll
+also talk about
+
+ align:start position:0%
+also talk about
+ 
+
+ align:start position:0%
+also talk about
+how do those folks get into their line
+
+ align:start position:0%
+how do those folks get into their line
+ 
+
+ align:start position:0%
+how do those folks get into their line
+of work especially the generation of
+
+ align:start position:0%
+of work especially the generation of
+ 
+
+ align:start position:0%
+of work especially the generation of
+Maxwell Thompson and some of their own
+
+ align:start position:0%
+Maxwell Thompson and some of their own
+ 
+
+ align:start position:0%
+Maxwell Thompson and some of their own
+uh colleagues so what was it like to
+
+ align:start position:0%
+uh colleagues so what was it like to
+ 
+
+ align:start position:0%
+uh colleagues so what was it like to
+become a young uh say mathematical
+
+ align:start position:0%
+become a young uh say mathematical
+ 
+
+ align:start position:0%
+become a young uh say mathematical
+physicist or eventually theoretical
+
+ align:start position:0%
+physicist or eventually theoretical
+ 
+
+ align:start position:0%
+physicist or eventually theoretical
+physicist during the second half of the
+
+ align:start position:0%
+physicist during the second half of the
+ 
+
+ align:start position:0%
+physicist during the second half of the
+19th century how they do that where why
+
+ align:start position:0%
+19th century how they do that where why
+ 
+
+ align:start position:0%
+19th century how they do that where why
+according to whose criteria another
+
+ align:start position:0%
+according to whose criteria another
+ 
+
+ align:start position:0%
+according to whose criteria another
+thing I want to really emphasize this
+
+ align:start position:0%
+thing I want to really emphasize this
+ 
+
+ align:start position:0%
+thing I want to really emphasize this
+one I find incredibly fun is that many
+
+ align:start position:0%
+one I find incredibly fun is that many
+ 
+
+ align:start position:0%
+one I find incredibly fun is that many
+who probably own Master's equations on a
+
+ align:start position:0%
+who probably own Master's equations on a
+ 
+
+ align:start position:0%
+who probably own Master's equations on a
+t-shirt always in fashion we still use
+
+ align:start position:0%
+t-shirt always in fashion we still use
+ 
+
+ align:start position:0%
+t-shirt always in fashion we still use
+Maxwell's equations there are so-called
+
+ align:start position:0%
+Maxwell's equations there are so-called
+ 
+
+ align:start position:0%
+Maxwell's equations there are so-called
+his equations but what I want to sit
+
+ align:start position:0%
+his equations but what I want to sit
+ 
+
+ align:start position:0%
+his equations but what I want to sit
+with for the first few classes is how
+
+ align:start position:0%
+with for the first few classes is how
+ 
+
+ align:start position:0%
+with for the first few classes is how
+remarkably different Maxwell and his
+
+ align:start position:0%
+remarkably different Maxwell and his
+ 
+
+ align:start position:0%
+remarkably different Maxwell and his
+contemporaries interpreted those very
+
+ align:start position:0%
+contemporaries interpreted those very
+ 
+
+ align:start position:0%
+contemporaries interpreted those very
+same mathematical symbols so we still
+
+ align:start position:0%
+same mathematical symbols so we still
+ 
+
+ align:start position:0%
+same mathematical symbols so we still
+put his equations on our t-shirts so to
+
+ align:start position:0%
+put his equations on our t-shirts so to
+ 
+
+ align:start position:0%
+put his equations on our t-shirts so to
+speak
+
+ align:start position:0%
+speak
+ 
+
+ align:start position:0%
+speak
+yeah what we think they mean or what we
+
+ align:start position:0%
+yeah what we think they mean or what we
+ 
+
+ align:start position:0%
+yeah what we think they mean or what we
+think they're good for what we think
+
+ align:start position:0%
+think they're good for what we think
+ 
+
+ align:start position:0%
+think they're good for what we think
+they're talking about what they tell us
+
+ align:start position:0%
+they're talking about what they tell us
+ 
+
+ align:start position:0%
+they're talking about what they tell us
+about the world is almost exactly
+
+ align:start position:0%
+about the world is almost exactly
+ 
+
+ align:start position:0%
+about the world is almost exactly
+opposite to how Maxwell himself imagined
+
+ align:start position:0%
+opposite to how Maxwell himself imagined
+ 
+
+ align:start position:0%
+opposite to how Maxwell himself imagined
+them or how generations of maxwellians
+
+ align:start position:0%
+them or how generations of maxwellians
+ 
+
+ align:start position:0%
+them or how generations of maxwellians
+treated them so we have this kind of
+
+ align:start position:0%
+treated them so we have this kind of
+ 
+
+ align:start position:0%
+treated them so we have this kind of
+continuity in some instances in the in
+
+ align:start position:0%
+continuity in some instances in the in
+ 
+
+ align:start position:0%
+continuity in some instances in the in
+the equations we use sometimes even the
+
+ align:start position:0%
+the equations we use sometimes even the
+ 
+
+ align:start position:0%
+the equations we use sometimes even the
+t-shirts we wear and yet what we think
+
+ align:start position:0%
+t-shirts we wear and yet what we think
+ 
+
+ align:start position:0%
+t-shirts we wear and yet what we think
+those equations or those ideas tell us
+
+ align:start position:0%
+those equations or those ideas tell us
+ 
+
+ align:start position:0%
+those equations or those ideas tell us
+about the world those actually have been
+
+ align:start position:0%
+about the world those actually have been
+ 
+
+ align:start position:0%
+about the world those actually have been
+anything but static or constant over
+
+ align:start position:0%
+anything but static or constant over
+ 
+
+ align:start position:0%
+anything but static or constant over
+time I find that just mind-boggling to
+
+ align:start position:0%
+time I find that just mind-boggling to
+ 
+
+ align:start position:0%
+time I find that just mind-boggling to
+be honest I love that we're going to
+
+ align:start position:0%
+be honest I love that we're going to
+ 
+
+ align:start position:0%
+be honest I love that we're going to
+have a bunch of examples of that
+
+ align:start position:0%
+have a bunch of examples of that
+ 
+
+ align:start position:0%
+have a bunch of examples of that
+throughout this whole semester and one
+
+ align:start position:0%
+throughout this whole semester and one
+ 
+
+ align:start position:0%
+throughout this whole semester and one
+of the first kind of Juicy ones we get
+
+ align:start position:0%
+of the first kind of Juicy ones we get
+ 
+
+ align:start position:0%
+of the first kind of Juicy ones we get
+is with Maxwell's equations so we'll sit
+
+ align:start position:0%
+is with Maxwell's equations so we'll sit
+ 
+
+ align:start position:0%
+is with Maxwell's equations so we'll sit
+with Maxwell and electromagnetism for
+
+ align:start position:0%
+with Maxwell and electromagnetism for
+ 
+
+ align:start position:0%
+with Maxwell and electromagnetism for
+the first couple of lectures the first
+
+ align:start position:0%
+the first couple of lectures the first
+ 
+
+ align:start position:0%
+the first couple of lectures the first
+few few sessions
+
+ align:start position:0%
+few few sessions
+ 
+
+ align:start position:0%
+few few sessions
+okay before too long we'll get into what
+
+ align:start position:0%
+okay before too long we'll get into what
+ 
+
+ align:start position:0%
+okay before too long we'll get into what
+is often called modern physics the the
+
+ align:start position:0%
+is often called modern physics the the
+ 
+
+ align:start position:0%
+is often called modern physics the the
+quite dramatic intellectual changes uh
+
+ align:start position:0%
+quite dramatic intellectual changes uh
+ 
+
+ align:start position:0%
+quite dramatic intellectual changes uh
+taking place roughly speaking in the
+
+ align:start position:0%
+taking place roughly speaking in the
+ 
+
+ align:start position:0%
+taking place roughly speaking in the
+first 25 years of the 20th century
+
+ align:start position:0%
+first 25 years of the 20th century
+ 
+
+ align:start position:0%
+first 25 years of the 20th century
+roughly with with some error bars on
+
+ align:start position:0%
+roughly with with some error bars on
+ 
+
+ align:start position:0%
+roughly with with some error bars on
+that estimate so we'll talk quickly
+
+ align:start position:0%
+that estimate so we'll talk quickly
+ 
+
+ align:start position:0%
+that estimate so we'll talk quickly
+about uh work by Albert Einstein and
+
+ align:start position:0%
+about uh work by Albert Einstein and
+ 
+
+ align:start position:0%
+about uh work by Albert Einstein and
+indeed a circle of colleagues what
+
+ align:start position:0%
+indeed a circle of colleagues what
+ 
+
+ align:start position:0%
+indeed a circle of colleagues what
+became known as uh the special theory of
+
+ align:start position:0%
+became known as uh the special theory of
+ 
+
+ align:start position:0%
+became known as uh the special theory of
+relativity and even some general
+
+ align:start position:0%
+relativity and even some general
+ 
+
+ align:start position:0%
+relativity and even some general
+relativity very near to my heart
+
+ align:start position:0%
+relativity very near to my heart
+ 
+
+ align:start position:0%
+relativity very near to my heart
+Tiffany's heart
+
+ align:start position:0%
+Tiffany's heart
+ 
+
+ align:start position:0%
+Tiffany's heart
+maybe to many of your hearts uh well how
+
+ align:start position:0%
+maybe to many of your hearts uh well how
+ 
+
+ align:start position:0%
+maybe to many of your hearts uh well how
+did Einstein come to these ideas with
+
+ align:start position:0%
+did Einstein come to these ideas with
+ 
+
+ align:start position:0%
+did Einstein come to these ideas with
+whom to what end what was he doing
+
+ align:start position:0%
+whom to what end what was he doing
+ 
+
+ align:start position:0%
+whom to what end what was he doing
+literally what path was he walking each
+
+ align:start position:0%
+literally what path was he walking each
+ 
+
+ align:start position:0%
+literally what path was he walking each
+day as he began contemplating space-time
+
+ align:start position:0%
+day as he began contemplating space-time
+ 
+
+ align:start position:0%
+day as he began contemplating space-time
+and matter uh well then shift to early
+
+ align:start position:0%
+and matter uh well then shift to early
+ 
+
+ align:start position:0%
+and matter uh well then shift to early
+quantum theory as the next main kind of
+
+ align:start position:0%
+quantum theory as the next main kind of
+ 
+
+ align:start position:0%
+quantum theory as the next main kind of
+set within this unit uh and again some
+
+ align:start position:0%
+set within this unit uh and again some
+ 
+
+ align:start position:0%
+set within this unit uh and again some
+some remarkable familiarities some
+
+ align:start position:0%
+some remarkable familiarities some
+ 
+
+ align:start position:0%
+some remarkable familiarities some
+equations we still use 100 to 120 years
+
+ align:start position:0%
+equations we still use 100 to 120 years
+ 
+
+ align:start position:0%
+equations we still use 100 to 120 years
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+I mean but what we think those equations
+
+ align:start position:0%
+I mean but what we think those equations
+ 
+
+ align:start position:0%
+I mean but what we think those equations
+are telling us that actually has not
+
+ align:start position:0%
+are telling us that actually has not
+ 
+
+ align:start position:0%
+are telling us that actually has not
+been so constant where people were
+
+ align:start position:0%
+been so constant where people were
+ 
+
+ align:start position:0%
+been so constant where people were
+working or coming up with the ideas or
+
+ align:start position:0%
+working or coming up with the ideas or
+ 
+
+ align:start position:0%
+working or coming up with the ideas or
+with whom they're interacting is also
+
+ align:start position:0%
+with whom they're interacting is also
+ 
+
+ align:start position:0%
+with whom they're interacting is also
+not so constant so we'll talk about some
+
+ align:start position:0%
+not so constant so we'll talk about some
+ 
+
+ align:start position:0%
+not so constant so we'll talk about some
+shifting institutions like the physic
+
+ align:start position:0%
+shifting institutions like the physic
+ 
+
+ align:start position:0%
+shifting institutions like the physic
+College technician hi Sean stop that
+
+ align:start position:0%
+College technician hi Sean stop that
+ 
+
+ align:start position:0%
+College technician hi Sean stop that
+reminds me to apologize to any people on
+
+ align:start position:0%
+reminds me to apologize to any people on
+ 
+
+ align:start position:0%
+reminds me to apologize to any people on
+the call who actually speak German I
+
+ align:start position:0%
+the call who actually speak German I
+ 
+
+ align:start position:0%
+the call who actually speak German I
+speak incredibly bad German but I love
+
+ align:start position:0%
+speak incredibly bad German but I love
+ 
+
+ align:start position:0%
+speak incredibly bad German but I love
+trying we'll have especially in this
+
+ align:start position:0%
+trying we'll have especially in this
+ 
+
+ align:start position:0%
+trying we'll have especially in this
+first unit a lot of German that I will
+
+ align:start position:0%
+first unit a lot of German that I will
+ 
+
+ align:start position:0%
+first unit a lot of German that I will
+likely mangle
+
+ align:start position:0%
+likely mangle
+ 
+
+ align:start position:0%
+likely mangle
+if you know zero German then you're
+
+ align:start position:0%
+if you know zero German then you're
+ 
+
+ align:start position:0%
+if you know zero German then you're
+actually closer to me than you might
+
+ align:start position:0%
+actually closer to me than you might
+ 
+
+ align:start position:0%
+actually closer to me than you might
+think but nonetheless we'll have some
+
+ align:start position:0%
+think but nonetheless we'll have some
+ 
+
+ align:start position:0%
+think but nonetheless we'll have some
+German stuff don't worry if it's uh if
+
+ align:start position:0%
+German stuff don't worry if it's uh if
+ 
+
+ align:start position:0%
+German stuff don't worry if it's uh if
+it literally sounds foreign or
+
+ align:start position:0%
+it literally sounds foreign or
+ 
+
+ align:start position:0%
+it literally sounds foreign or
+unfamiliar the point is there were some
+
+ align:start position:0%
+unfamiliar the point is there were some
+ 
+
+ align:start position:0%
+unfamiliar the point is there were some
+new institutions new priorities new
+
+ align:start position:0%
+new institutions new priorities new
+ 
+
+ align:start position:0%
+new institutions new priorities new
+national scale uh investment and things
+
+ align:start position:0%
+national scale uh investment and things
+ 
+
+ align:start position:0%
+national scale uh investment and things
+like physics and related fields of
+
+ align:start position:0%
+like physics and related fields of
+ 
+
+ align:start position:0%
+like physics and related fields of
+engineering what role did that play in
+
+ align:start position:0%
+engineering what role did that play in
+ 
+
+ align:start position:0%
+engineering what role did that play in
+the kind of heady years of the early
+
+ align:start position:0%
+the kind of heady years of the early
+ 
+
+ align:start position:0%
+the kind of heady years of the early
+onset of quantum theory and modern
+
+ align:start position:0%
+onset of quantum theory and modern
+ 
+
+ align:start position:0%
+onset of quantum theory and modern
+physics and then where did those ideas
+
+ align:start position:0%
+physics and then where did those ideas
+ 
+
+ align:start position:0%
+physics and then where did those ideas
+lead some of the leading thinkers we'll
+
+ align:start position:0%
+lead some of the leading thinkers we'll
+ 
+
+ align:start position:0%
+lead some of the leading thinkers we'll
+talk of course of course about things
+
+ align:start position:0%
+talk of course of course about things
+ 
+
+ align:start position:0%
+talk of course of course about things
+like Schrodinger's cat or quantum
+
+ align:start position:0%
+like Schrodinger's cat or quantum
+ 
+
+ align:start position:0%
+like Schrodinger's cat or quantum
+entanglement or Einstein podelski Rose
+
+ align:start position:0%
+entanglement or Einstein podelski Rose
+ 
+
+ align:start position:0%
+entanglement or Einstein podelski Rose
+and uh and many many really quite
+
+ align:start position:0%
+and uh and many many really quite
+ 
+
+ align:start position:0%
+and uh and many many really quite
+delicious and delightful elements of
+
+ align:start position:0%
+delicious and delightful elements of
+ 
+
+ align:start position:0%
+delicious and delightful elements of
+quantum theory that I still um wrestle
+
+ align:start position:0%
+quantum theory that I still um wrestle
+ 
+
+ align:start position:0%
+quantum theory that I still um wrestle
+with and get to play with with my own
+
+ align:start position:0%
+with and get to play with with my own
+ 
+
+ align:start position:0%
+with and get to play with with my own
+students and colleagues to this day so
+
+ align:start position:0%
+students and colleagues to this day so
+ 
+
+ align:start position:0%
+students and colleagues to this day so
+that's the the first kind of main unit
+
+ align:start position:0%
+that's the the first kind of main unit
+ 
+
+ align:start position:0%
+that's the the first kind of main unit
+we'll we'll have a kind of quick
+
+ align:start position:0%
+we'll we'll have a kind of quick
+ 
+
+ align:start position:0%
+we'll we'll have a kind of quick
+um uh introduction with his 19th century
+
+ align:start position:0%
+um uh introduction with his 19th century
+ 
+
+ align:start position:0%
+um uh introduction with his 19th century
+Legacy really to set the stage for what
+
+ align:start position:0%
+Legacy really to set the stage for what
+ 
+
+ align:start position:0%
+Legacy really to set the stage for what
+we might call the emergence of modern
+
+ align:start position:0%
+we might call the emergence of modern
+ 
+
+ align:start position:0%
+we might call the emergence of modern
+physics as was recognized even in its
+
+ align:start position:0%
+physics as was recognized even in its
+ 
+
+ align:start position:0%
+physics as was recognized even in its
+day that's the first main unit the
+
+ align:start position:0%
+day that's the first main unit the
+ 
+
+ align:start position:0%
+day that's the first main unit the
+second year of the class
+
+ align:start position:0%
+second year of the class
+ 
+
+ align:start position:0%
+second year of the class
+them we're going to shift again in
+
+ align:start position:0%
+them we're going to shift again in
+ 
+
+ align:start position:0%
+them we're going to shift again in
+remarkably rapid order I mean to an
+
+ align:start position:0%
+remarkably rapid order I mean to an
+ 
+
+ align:start position:0%
+remarkably rapid order I mean to an
+historian the time delay was vanishingly
+
+ align:start position:0%
+historian the time delay was vanishingly
+ 
+
+ align:start position:0%
+historian the time delay was vanishingly
+short a matter of of 10 to 20 years
+
+ align:start position:0%
+short a matter of of 10 to 20 years
+ 
+
+ align:start position:0%
+short a matter of of 10 to 20 years
+being on how one counts
+
+ align:start position:0%
+being on how one counts
+ 
+
+ align:start position:0%
+being on how one counts
+some of those previously very heady very
+
+ align:start position:0%
+some of those previously very heady very
+ 
+
+ align:start position:0%
+some of those previously very heady very
+very esoteric or abstract ideas about
+
+ align:start position:0%
+very esoteric or abstract ideas about
+ 
+
+ align:start position:0%
+very esoteric or abstract ideas about
+atoms about parts of atoms about nuclei
+
+ align:start position:0%
+atoms about parts of atoms about nuclei
+ 
+
+ align:start position:0%
+atoms about parts of atoms about nuclei
+and nuclear forces they began having an
+
+ align:start position:0%
+and nuclear forces they began having an
+ 
+
+ align:start position:0%
+and nuclear forces they began having an
+import and and a priority well beyond uh
+
+ align:start position:0%
+import and and a priority well beyond uh
+ 
+
+ align:start position:0%
+import and and a priority well beyond uh
+professional physicists and chemists or
+
+ align:start position:0%
+professional physicists and chemists or
+ 
+
+ align:start position:0%
+professional physicists and chemists or
+other uh engineers and so on in a way
+
+ align:start position:0%
+other uh engineers and so on in a way
+ 
+
+ align:start position:0%
+other uh engineers and so on in a way
+that again I'm sure are at least in part
+
+ align:start position:0%
+that again I'm sure are at least in part
+ 
+
+ align:start position:0%
+that again I'm sure are at least in part
+familiar to you we're going to sit quite
+
+ align:start position:0%
+familiar to you we're going to sit quite
+ 
+
+ align:start position:0%
+familiar to you we're going to sit quite
+a while with the development of nuclear
+
+ align:start position:0%
+a while with the development of nuclear
+ 
+
+ align:start position:0%
+a while with the development of nuclear
+weapons
+
+ align:start position:0%
+weapons
+ 
+
+ align:start position:0%
+weapons
+Nuclear Physics more broadly but
+
+ align:start position:0%
+Nuclear Physics more broadly but
+ 
+
+ align:start position:0%
+Nuclear Physics more broadly but
+especially the weapons projects during
+
+ align:start position:0%
+especially the weapons projects during
+ 
+
+ align:start position:0%
+especially the weapons projects during
+the second World War uh The Unbelievable
+
+ align:start position:0%
+the second World War uh The Unbelievable
+ 
+
+ align:start position:0%
+the second World War uh The Unbelievable
+transformation of the kind of research
+
+ align:start position:0%
+transformation of the kind of research
+ 
+
+ align:start position:0%
+transformation of the kind of research
+and development infrastructure which
+
+ align:start position:0%
+and development infrastructure which
+ 
+
+ align:start position:0%
+and development infrastructure which
+really starts setting a kind of um
+
+ align:start position:0%
+really starts setting a kind of um
+ 
+
+ align:start position:0%
+really starts setting a kind of um
+blueprint for many features that we
+
+ align:start position:0%
+blueprint for many features that we
+ 
+
+ align:start position:0%
+blueprint for many features that we
+would recognize today even though there
+
+ align:start position:0%
+would recognize today even though there
+ 
+
+ align:start position:0%
+would recognize today even though there
+were forged during a war that itself
+
+ align:start position:0%
+were forged during a war that itself
+ 
+
+ align:start position:0%
+were forged during a war that itself
+ended 75 years ago so we see a change in
+
+ align:start position:0%
+ended 75 years ago so we see a change in
+ 
+
+ align:start position:0%
+ended 75 years ago so we see a change in
+what it means to try to do physics for
+
+ align:start position:0%
+what it means to try to do physics for
+ 
+
+ align:start position:0%
+what it means to try to do physics for
+whom to what ends with what kind of
+
+ align:start position:0%
+whom to what ends with what kind of
+ 
+
+ align:start position:0%
+whom to what ends with what kind of
+support uh and and with what kind of
+
+ align:start position:0%
+support uh and and with what kind of
+ 
+
+ align:start position:0%
+support uh and and with what kind of
+institutional settings uh leading to
+
+ align:start position:0%
+institutional settings uh leading to
+ 
+
+ align:start position:0%
+institutional settings uh leading to
+among other things the use of these very
+
+ align:start position:0%
+among other things the use of these very
+ 
+
+ align:start position:0%
+among other things the use of these very
+new types of weapons again just 75 years
+
+ align:start position:0%
+new types of weapons again just 75 years
+ 
+
+ align:start position:0%
+new types of weapons again just 75 years
+ago against the Japanese cities of
+
+ align:start position:0%
+ago against the Japanese cities of
+ 
+
+ align:start position:0%
+ago against the Japanese cities of
+Hiroshima and Nagasaki in the summer of
+
+ align:start position:0%
+Hiroshima and Nagasaki in the summer of
+ 
+
+ align:start position:0%
+Hiroshima and Nagasaki in the summer of
+1945. so that second main unit third
+
+ align:start position:0%
+1945. so that second main unit third
+ 
+
+ align:start position:0%
+1945. so that second main unit third
+unit of the course the second kind of
+
+ align:start position:0%
+unit of the course the second kind of
+ 
+
+ align:start position:0%
+unit of the course the second kind of
+big juicy thick unit that will sit with
+
+ align:start position:0%
+big juicy thick unit that will sit with
+ 
+
+ align:start position:0%
+big juicy thick unit that will sit with
+for quite a while
+
+ align:start position:0%
+for quite a while
+ 
+
+ align:start position:0%
+for quite a while
+is the kind of new enrollment the new
+
+ align:start position:0%
+is the kind of new enrollment the new
+ 
+
+ align:start position:0%
+is the kind of new enrollment the new
+engagement of physicists chemists
+
+ align:start position:0%
+engagement of physicists chemists
+ 
+
+ align:start position:0%
+engagement of physicists chemists
+various kinds of Engineers with the
+
+ align:start position:0%
+various kinds of Engineers with the
+ 
+
+ align:start position:0%
+various kinds of Engineers with the
+nation-state in times of War and what
+
+ align:start position:0%
+nation-state in times of War and what
+ 
+
+ align:start position:0%
+nation-state in times of War and what
+does that mean for the ideas of physics
+
+ align:start position:0%
+does that mean for the ideas of physics
+ 
+
+ align:start position:0%
+does that mean for the ideas of physics
+for the population of physicists for the
+
+ align:start position:0%
+for the population of physicists for the
+ 
+
+ align:start position:0%
+for the population of physicists for the
+institutions of physics and so on that's
+
+ align:start position:0%
+institutions of physics and so on that's
+ 
+
+ align:start position:0%
+institutions of physics and so on that's
+a big there's a lot to try to really
+
+ align:start position:0%
+a big there's a lot to try to really
+ 
+
+ align:start position:0%
+a big there's a lot to try to really
+understand including a lot of again
+
+ align:start position:0%
+understand including a lot of again
+ 
+
+ align:start position:0%
+understand including a lot of again
+frankly very fascinating uh Cutting Edge
+
+ align:start position:0%
+frankly very fascinating uh Cutting Edge
+ 
+
+ align:start position:0%
+frankly very fascinating uh Cutting Edge
+science and engineering but it was being
+
+ align:start position:0%
+science and engineering but it was being
+ 
+
+ align:start position:0%
+science and engineering but it was being
+done in very specific
+
+ align:start position:0%
+done in very specific
+ 
+
+ align:start position:0%
+done in very specific
+um contexts toward very particular
+
+ align:start position:0%
+um contexts toward very particular
+ 
+
+ align:start position:0%
+um contexts toward very particular
+ethics so we'll spend some some time uh
+
+ align:start position:0%
+ethics so we'll spend some some time uh
+ 
+
+ align:start position:0%
+ethics so we'll spend some some time uh
+around middle of the semester on that
+
+ align:start position:0%
+around middle of the semester on that
+ 
+
+ align:start position:0%
+around middle of the semester on that
+material
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the last main unit
+
+ align:start position:0%
+the last main unit
+ 
+
+ align:start position:0%
+the last main unit
+is that expanding outward from the end
+
+ align:start position:0%
+is that expanding outward from the end
+ 
+
+ align:start position:0%
+is that expanding outward from the end
+of World War II
+
+ align:start position:0%
+of World War II
+ 
+
+ align:start position:0%
+of World War II
+here I was a little more selective I
+
+ align:start position:0%
+here I was a little more selective I
+ 
+
+ align:start position:0%
+here I was a little more selective I
+wanted to cover topics that frankly I
+
+ align:start position:0%
+wanted to cover topics that frankly I
+ 
+
+ align:start position:0%
+wanted to cover topics that frankly I
+like most so uh and that means the
+
+ align:start position:0%
+like most so uh and that means the
+ 
+
+ align:start position:0%
+like most so uh and that means the
+topics are very much biased towards um
+
+ align:start position:0%
+topics are very much biased towards um
+ 
+
+ align:start position:0%
+topics are very much biased towards um
+particle physics uh high energy physics
+
+ align:start position:0%
+particle physics uh high energy physics
+ 
+
+ align:start position:0%
+particle physics uh high energy physics
+and astrophysics and cosmology because
+
+ align:start position:0%
+and astrophysics and cosmology because
+ 
+
+ align:start position:0%
+and astrophysics and cosmology because
+first of all this is objectively the
+
+ align:start position:0%
+first of all this is objectively the
+ 
+
+ align:start position:0%
+first of all this is objectively the
+most interesting that was a joke I just
+
+ align:start position:0%
+most interesting that was a joke I just
+ 
+
+ align:start position:0%
+most interesting that was a joke I just
+think they're actually awesome those are
+
+ align:start position:0%
+think they're actually awesome those are
+ 
+
+ align:start position:0%
+think they're actually awesome those are
+the areas that I am most familiar with
+
+ align:start position:0%
+the areas that I am most familiar with
+ 
+
+ align:start position:0%
+the areas that I am most familiar with
+both historically and also in terms of
+
+ align:start position:0%
+both historically and also in terms of
+ 
+
+ align:start position:0%
+both historically and also in terms of
+more contemporary research and so again
+
+ align:start position:0%
+more contemporary research and so again
+ 
+
+ align:start position:0%
+more contemporary research and so again
+it's an opportunity to kind of take a
+
+ align:start position:0%
+it's an opportunity to kind of take a
+ 
+
+ align:start position:0%
+it's an opportunity to kind of take a
+sample to explore some material that
+
+ align:start position:0%
+sample to explore some material that
+ 
+
+ align:start position:0%
+sample to explore some material that
+that might be quite new uh to many of
+
+ align:start position:0%
+that might be quite new uh to many of
+ 
+
+ align:start position:0%
+that might be quite new uh to many of
+you you might not have had a chance to
+
+ align:start position:0%
+you you might not have had a chance to
+ 
+
+ align:start position:0%
+you you might not have had a chance to
+have a full semester course on Quantum
+
+ align:start position:0%
+have a full semester course on Quantum
+ 
+
+ align:start position:0%
+have a full semester course on Quantum
+field Theory or particle theory or uh
+
+ align:start position:0%
+field Theory or particle theory or uh
+ 
+
+ align:start position:0%
+field Theory or particle theory or uh
+contemporary cosmology some of you might
+
+ align:start position:0%
+contemporary cosmology some of you might
+ 
+
+ align:start position:0%
+contemporary cosmology some of you might
+have but there's again no no need to
+
+ align:start position:0%
+have but there's again no no need to
+ 
+
+ align:start position:0%
+have but there's again no no need to
+have already seen this material and
+
+ align:start position:0%
+have already seen this material and
+ 
+
+ align:start position:0%
+have already seen this material and
+we'll we'll be able to kind of sample
+
+ align:start position:0%
+we'll we'll be able to kind of sample
+ 
+
+ align:start position:0%
+we'll we'll be able to kind of sample
+some of these uh Inc still changing
+
+ align:start position:0%
+some of these uh Inc still changing
+ 
+
+ align:start position:0%
+some of these uh Inc still changing
+ideas within again some still changing
+
+ align:start position:0%
+ideas within again some still changing
+ 
+
+ align:start position:0%
+ideas within again some still changing
+institutions who wanted to pursue those
+
+ align:start position:0%
+institutions who wanted to pursue those
+ 
+
+ align:start position:0%
+institutions who wanted to pursue those
+questions why to what ends and in what
+
+ align:start position:0%
+questions why to what ends and in what
+ 
+
+ align:start position:0%
+questions why to what ends and in what
+facilities so now we get to a place uh
+
+ align:start position:0%
+facilities so now we get to a place uh
+ 
+
+ align:start position:0%
+facilities so now we get to a place uh
+in time like uh the Large Hadron
+
+ align:start position:0%
+in time like uh the Large Hadron
+ 
+
+ align:start position:0%
+in time like uh the Large Hadron
+Collider CERN uh the device was
+
+ align:start position:0%
+Collider CERN uh the device was
+ 
+
+ align:start position:0%
+Collider CERN uh the device was
+completed in the uh first decade of the
+
+ align:start position:0%
+completed in the uh first decade of the
+ 
+
+ align:start position:0%
+completed in the uh first decade of the
+21st century you see an aerial shot here
+
+ align:start position:0%
+21st century you see an aerial shot here
+ 
+
+ align:start position:0%
+21st century you see an aerial shot here
+what brought us from an arrow in
+
+ align:start position:0%
+what brought us from an arrow in
+ 
+
+ align:start position:0%
+what brought us from an arrow in
+particle acceler is still where on the
+
+ align:start position:0%
+particle acceler is still where on the
+ 
+
+ align:start position:0%
+particle acceler is still where on the
+size of a kind of person more or less to
+
+ align:start position:0%
+size of a kind of person more or less to
+ 
+
+ align:start position:0%
+size of a kind of person more or less to
+when they when they actually cross
+
+ align:start position:0%
+when they when they actually cross
+ 
+
+ align:start position:0%
+when they when they actually cross
+National borders where the accelerated
+
+ align:start position:0%
+National borders where the accelerated
+ 
+
+ align:start position:0%
+National borders where the accelerated
+protons cross between the Swiss and
+
+ align:start position:0%
+protons cross between the Swiss and
+ 
+
+ align:start position:0%
+protons cross between the Swiss and
+French borders billions of times per
+
+ align:start position:0%
+French borders billions of times per
+ 
+
+ align:start position:0%
+French borders billions of times per
+second so we'll end the course looking
+
+ align:start position:0%
+second so we'll end the course looking
+ 
+
+ align:start position:0%
+second so we'll end the course looking
+outward toward the cosmos uh that way
+
+ align:start position:0%
+outward toward the cosmos uh that way
+ 
+
+ align:start position:0%
+outward toward the cosmos uh that way
+so here's the very last slide I always
+
+ align:start position:0%
+so here's the very last slide I always
+ 
+
+ align:start position:0%
+so here's the very last slide I always
+like to say this course has one actual
+
+ align:start position:0%
+like to say this course has one actual
+ 
+
+ align:start position:0%
+like to say this course has one actual
+goal which is to make sense of this
+
+ align:start position:0%
+goal which is to make sense of this
+ 
+
+ align:start position:0%
+goal which is to make sense of this
+quotation I never Tire of repeating this
+
+ align:start position:0%
+quotation I never Tire of repeating this
+ 
+
+ align:start position:0%
+quotation I never Tire of repeating this
+quotation it was published in Harper's
+
+ align:start position:0%
+quotation it was published in Harper's
+ 
+
+ align:start position:0%
+quotation it was published in Harper's
+magazine just months after the end of
+
+ align:start position:0%
+magazine just months after the end of
+ 
+
+ align:start position:0%
+magazine just months after the end of
+the second world war observing what had
+
+ align:start position:0%
+the second world war observing what had
+ 
+
+ align:start position:0%
+the second world war observing what had
+become a real sea change in the place of
+
+ align:start position:0%
+become a real sea change in the place of
+ 
+
+ align:start position:0%
+become a real sea change in the place of
+physics and especially physicists in
+
+ align:start position:0%
+physics and especially physicists in
+ 
+
+ align:start position:0%
+physics and especially physicists in
+broader Society so this kind of witty uh
+
+ align:start position:0%
+broader Society so this kind of witty uh
+ 
+
+ align:start position:0%
+broader Society so this kind of witty uh
+kind of pundit colonists wrote in in the
+
+ align:start position:0%
+kind of pundit colonists wrote in in the
+ 
+
+ align:start position:0%
+kind of pundit colonists wrote in in the
+spring of 46 the physical scientists are
+
+ align:start position:0%
+spring of 46 the physical scientists are
+ 
+
+ align:start position:0%
+spring of 46 the physical scientists are
+in Vogue these days no dinner party is a
+
+ align:start position:0%
+in Vogue these days no dinner party is a
+ 
+
+ align:start position:0%
+in Vogue these days no dinner party is a
+success but at least when physicists and
+
+ align:start position:0%
+success but at least when physicists and
+ 
+
+ align:start position:0%
+success but at least when physicists and
+really I want to know what happened how
+
+ align:start position:0%
+really I want to know what happened how
+ 
+
+ align:start position:0%
+really I want to know what happened how
+come so many people have dinner now
+
+ align:start position:0%
+come so many people have dinner now
+ 
+
+ align:start position:0%
+come so many people have dinner now
+without inviting us that's really why I
+
+ align:start position:0%
+without inviting us that's really why I
+ 
+
+ align:start position:0%
+without inviting us that's really why I
+put this whole course together together
+
+ align:start position:0%
+put this whole course together together
+ 
+
+ align:start position:0%
+put this whole course together together
+we'll try to answer that question that's
+
+ align:start position:0%
+we'll try to answer that question that's
+ 
+
+ align:start position:0%
+we'll try to answer that question that's
+only modestly tongue-in-cheek any
+
+ align:start position:0%
+only modestly tongue-in-cheek any
+ 
+
+ align:start position:0%
+only modestly tongue-in-cheek any
+questions about any of the of that
+
+ align:start position:0%
+questions about any of the of that
+ 
+
+ align:start position:0%
+questions about any of the of that
+material of course Logistics course
+
+ align:start position:0%
+material of course Logistics course
+ 
+
+ align:start position:0%
+material of course Logistics course
+overview any of that any of that kind of
+
+ align:start position:0%
+overview any of that any of that kind of
+ 
+
+ align:start position:0%
+overview any of that any of that kind of
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+alrighty well thank you everyone uh good
+
+ align:start position:0%
+alrighty well thank you everyone uh good
+ 
+
+ align:start position:0%
+alrighty well thank you everyone uh good
+to see you at least in small little
+
+ align:start position:0%
+to see you at least in small little
+ 
+
+ align:start position:0%
+to see you at least in small little
+squares uh stay well good luck with the
+
+ align:start position:0%
+squares uh stay well good luck with the
+ 
+
+ align:start position:0%
+squares uh stay well good luck with the
+rest of the start of the term and uh and
+
+ align:start position:0%
+rest of the start of the term and uh and
+ 
+
+ align:start position:0%
+rest of the start of the term and uh and
+I look forward to uh to seeing you next
+
+ align:start position:0%
+I look forward to uh to seeing you next
+ 
+
+ align:start position:0%
+I look forward to uh to seeing you next
+week
+
+ align:start position:0%
+week
+ 
+
+ align:start position:0%
+week
+stay well everyone take care
\ No newline at end of file
diff --git a/PqZj8pySQiU.txt b/PqZj8pySQiU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c6e0b5746a145c183eb5b56fa6ea2b53b30bf2e6
--- /dev/null
+++ b/PqZj8pySQiU.txt
@@ -0,0 +1,346 @@
+Previously, we learned the
+concept of independent
+
+experiments.
+
+In this exercise, we'll see how
+the seemingly simple idea
+
+of independence can help us
+understand the behavior of
+
+quite complex systems.
+
+In particular, we'll combined
+the concept of independence
+
+with the idea of divide and
+conquer, where we break a
+
+larger system into smaller
+components, and then using
+
+independent properties to
+glue them back together.
+
+Now, let's take a look
+at the problem.
+
+We are given a network of
+connected components, and each
+
+component can be good with
+
+probability P or bad otherwise.
+
+All components are independent
+from each other.
+
+We say the system is operational
+if there exists a
+
+path connecting point A here
+to point B that go through
+
+only the good components.
+
+And we'd like to understand,
+what is the probability that
+
+system is operational?
+
+Which we'll denote
+by P of A to B.
+
+Although the problem might seem
+a little complicated at
+
+the beginning, it turns
+out only two
+
+structures really matter.
+
+So let's look at each of them.
+
+In the first structure, which we
+call the serial structure,
+
+we have a collection of k
+components, each one having
+
+probability P being good,
+connected one next to each
+
+other in a serial line.
+
+Now, in this structure, in order
+for there to be a good
+
+path from A to B, every
+single one of the
+
+components must be working.
+
+So the probability of having
+a good path from A to B is
+
+simply P times P, so on and so,
+repeated k times, which is
+
+P raised to the k power.
+
+Know that the reason we can
+write the probability this
+
+way, in terms of this product,
+is because of the
+
+independence property.
+
+ 
+
+Now, the second useful
+
+structure is parallel structure.
+
+Here again, we have k components
+one, two, through
+
+k, but this time they're
+connected in parallel to each
+
+other, namely they start from
+one point here and ends at
+
+another point here,
+and this holds for
+
+every single component.
+
+Now, for the parallel structure
+to work, namely for
+
+there to exist a good path from
+A to B, it's easy to see
+
+that as long as one of these
+components works the whole
+
+thing will work.
+
+So the probability of A to B
+is the probability that at
+
+least one of these
+components works.
+
+Or in the other word, the
+probability of the complement
+
+of the event where all
+components fail.
+
+Now, if each component has
+probability P to be good, then
+
+the probability that all key
+components fail is 1 minus P
+
+raised to the kth power.
+
+Again, having this expression
+means that we have used the
+
+property of independence, and
+that is probability of having
+
+a good parallel structure.
+
+Now, there's one more
+observation that will be
+
+useful for us.
+
+Just like how we define two
+components to be independent,
+
+we can also find two collections
+of components to
+
+be independent from
+each other.
+
+For example, in this diagram,
+if we call the components
+
+between points C and E as
+collection two, and the
+
+components between E and
+B as collection three.
+
+Now, if we assume that each
+component in both
+
+collections--
+
+they're completely independent
+from each other, then it's not
+
+hard to see that collection
+two and three behave
+
+independently.
+
+And this will be very helpful
+in getting us the breakdown
+
+from complex networks
+to simpler elements.
+
+Now, let's go back to the
+original problem of
+
+calculating the probability of
+having a good path from point
+
+big A to point big B
+in this diagram.
+
+Based on that argument of
+independent collections, we
+
+can first divide the whole
+network into three
+
+collections, as you see here,
+from A to C, C to E and E to
+
+B. Now, because they're
+independent and in a serial
+
+structure, as seen by the
+definition of a serial
+
+structure here, we see that the
+probability of A to B can
+
+be written as a probability of
+A to C multiplied by C to E,
+
+and finally, E to B.
+
+Now, the probability of A to
+C is simply P because the
+
+collection contains
+only one element.
+
+And similarly, the probability
+of E to B is not that hard
+
+knowing the parallel
+structure here.
+
+We see that collection three
+has two components in
+
+parallel, so this probability
+will be given by 1 minus 1
+
+minus P squared.
+
+ 
+
+And it remains to calculate just
+the probability of having
+
+a good path from point C to
+point E. To get a value for P
+
+C to E, we notice again, that
+this area can be treated as
+
+two components, C1 to E and C2
+to E connected in parallel.
+
+And using the parallel law we
+get this probability is 1
+
+minus 1 minus P C1 to E
+multiplied by the 1 minus P C2
+
+to E. Know that I'm using two
+different characters, C1 and
+
+C2, to denote the same node,
+which is C. This is simply for
+
+making it easier to analyze
+two branches where they
+
+actually do note
+the same node.
+
+Now P C1 to E is another serial
+connection of these
+
+three elements here with
+another component.
+
+So the first three elements are
+connected in parallel, and
+
+we know the probability of that
+being successful is 1
+
+minus P3, and the
+last one is P.
+
+And finally, P C2 to E. It's
+just a single element
+
+component with probability of
+successful being P. At this
+
+point, there is no longer any
+unknown variables, and we have
+
+indeed obtained exact values
+for all the quantities that
+
+we're interested in.
+
+So starting from this equation,
+we can plug in the
+
+values for P C2 to E, P C1 to E
+back here, and then further
+
+plug in P C to E back here.
+
+That will give us the final
+solution, which is given by
+
+the following somewhat
+complicated formula.
+
+So in summary, in this problem,
+we learned how to use
+
+the independence property among
+different components to
+
+break down the entire fairly
+complex network into simple
+
+modular components, and use the
+law of serial and parallel
+
+connections to put the
+probabilities back together in
+
+common with the overall success
+probability of finding
+
+a path from A to B.
\ No newline at end of file
diff --git a/QTdJiG7mV40.txt b/QTdJiG7mV40.txt
new file mode 100644
index 0000000000000000000000000000000000000000..58a0ada2987186170605a351f74a6d5da3f41646
--- /dev/null
+++ b/QTdJiG7mV40.txt
@@ -0,0 +1,7659 @@
+align:start position:0%
+ 
+so what are we going to do today so
+
+ align:start position:0%
+so what are we going to do today so
+ 
+
+ align:start position:0%
+so what are we going to do today so
+today we're going to continue with amino
+
+ align:start position:0%
+today we're going to continue with amino
+ 
+
+ align:start position:0%
+today we're going to continue with amino
+acids peptides and proteins and I'm
+
+ align:start position:0%
+acids peptides and proteins and I'm
+ 
+
+ align:start position:0%
+acids peptides and proteins and I'm
+going to talk about a different protein
+
+ align:start position:0%
+going to talk about a different protein
+ 
+
+ align:start position:0%
+going to talk about a different protein
+variant that is the causative the cause
+
+ align:start position:0%
+variant that is the causative the cause
+ 
+
+ align:start position:0%
+variant that is the causative the cause
+of sickle cell anemia and it's a very
+
+ align:start position:0%
+of sickle cell anemia and it's a very
+ 
+
+ align:start position:0%
+of sickle cell anemia and it's a very
+interesting structural issue but let me
+
+ align:start position:0%
+interesting structural issue but let me
+ 
+
+ align:start position:0%
+interesting structural issue but let me
+very briefly recap what we did last time
+
+ align:start position:0%
+very briefly recap what we did last time
+ 
+
+ align:start position:0%
+very briefly recap what we did last time
+and then talk to you a little bit about
+
+ align:start position:0%
+and then talk to you a little bit about
+ 
+
+ align:start position:0%
+and then talk to you a little bit about
+a process known as denaturation so last
+
+ align:start position:0%
+a process known as denaturation so last
+ 
+
+ align:start position:0%
+a process known as denaturation so last
+time we discussed how the primary
+
+ align:start position:0%
+time we discussed how the primary
+ 
+
+ align:start position:0%
+time we discussed how the primary
+sequence of a polypeptide chain defines
+
+ align:start position:0%
+sequence of a polypeptide chain defines
+ 
+
+ align:start position:0%
+sequence of a polypeptide chain defines
+its folded structure the folded
+
+ align:start position:0%
+its folded structure the folded
+ 
+
+ align:start position:0%
+its folded structure the folded
+structure is put in place with secondary
+
+ align:start position:0%
+structure is put in place with secondary
+ 
+
+ align:start position:0%
+structure is put in place with secondary
+and tertiary interactions non covalent
+
+ align:start position:0%
+and tertiary interactions non covalent
+ 
+
+ align:start position:0%
+and tertiary interactions non covalent
+interactions secondary just between
+
+ align:start position:0%
+interactions secondary just between
+ 
+
+ align:start position:0%
+interactions secondary just between
+amongst backbone and its tertiary sort
+
+ align:start position:0%
+amongst backbone and its tertiary sort
+ 
+
+ align:start position:0%
+amongst backbone and its tertiary sort
+of everything else even including
+
+ align:start position:0%
+of everything else even including
+ 
+
+ align:start position:0%
+of everything else even including
+backbone omits but either with water or
+
+ align:start position:0%
+backbone omits but either with water or
+ 
+
+ align:start position:0%
+backbone omits but either with water or
+a side chain and so on and then there
+
+ align:start position:0%
+a side chain and so on and then there
+ 
+
+ align:start position:0%
+a side chain and so on and then there
+are some proteins that associate into
+
+ align:start position:0%
+are some proteins that associate into
+ 
+
+ align:start position:0%
+are some proteins that associate into
+quaternary structure so these monomer
+
+ align:start position:0%
+quaternary structure so these monomer
+ 
+
+ align:start position:0%
+quaternary structure so these monomer
+subunits as they would be called and I'm
+
+ align:start position:0%
+subunits as they would be called and I'm
+ 
+
+ align:start position:0%
+subunits as they would be called and I'm
+gonna depict this as like a closed
+
+ align:start position:0%
+gonna depict this as like a closed
+ 
+
+ align:start position:0%
+gonna depict this as like a closed
+circle or an open circle may form dimers
+
+ align:start position:0%
+circle or an open circle may form dimers
+ 
+
+ align:start position:0%
+circle or an open circle may form dimers
+of some kind
+
+ align:start position:0%
+of some kind
+ 
+
+ align:start position:0%
+of some kind
+the dimers may be heterodimers or they
+
+ align:start position:0%
+the dimers may be heterodimers or they
+ 
+
+ align:start position:0%
+the dimers may be heterodimers or they
+may be homo dimers or you could form
+
+ align:start position:0%
+may be homo dimers or you could form
+ 
+
+ align:start position:0%
+may be homo dimers or you could form
+trimers tetra MERS and so on and when we
+
+ align:start position:0%
+trimers tetra MERS and so on and when we
+ 
+
+ align:start position:0%
+trimers tetra MERS and so on and when we
+talk about hemoglobin which is the
+
+ align:start position:0%
+talk about hemoglobin which is the
+ 
+
+ align:start position:0%
+talk about hemoglobin which is the
+protein that gets that it has a problem
+
+ align:start position:0%
+protein that gets that it has a problem
+ 
+
+ align:start position:0%
+protein that gets that it has a problem
+is the cause of sickle cell anemia it
+
+ align:start position:0%
+is the cause of sickle cell anemia it
+ 
+
+ align:start position:0%
+is the cause of sickle cell anemia it
+will what you'll see that at is a hetero
+
+ align:start position:0%
+will what you'll see that at is a hetero
+ 
+
+ align:start position:0%
+will what you'll see that at is a hetero
+tetrameric protein so in this sort of
+
+ align:start position:0%
+tetrameric protein so in this sort of
+ 
+
+ align:start position:0%
+tetrameric protein so in this sort of
+rendition you kind of draw it like this
+
+ align:start position:0%
+rendition you kind of draw it like this
+ 
+
+ align:start position:0%
+rendition you kind of draw it like this
+where there are four subunits tour of
+
+ align:start position:0%
+where there are four subunits tour of
+ 
+
+ align:start position:0%
+where there are four subunits tour of
+one flavor and tour of the other and
+
+ align:start position:0%
+one flavor and tour of the other and
+ 
+
+ align:start position:0%
+one flavor and tour of the other and
+that's the quaternary structure of
+
+ align:start position:0%
+that's the quaternary structure of
+ 
+
+ align:start position:0%
+that's the quaternary structure of
+hemoglobin now proteins fold they are
+
+ align:start position:0%
+hemoglobin now proteins fold they are
+ 
+
+ align:start position:0%
+hemoglobin now proteins fold they are
+weak forces that are holding them
+
+ align:start position:0%
+weak forces that are holding them
+ 
+
+ align:start position:0%
+weak forces that are holding them
+together but there's a lot of weak
+
+ align:start position:0%
+together but there's a lot of weak
+ 
+
+ align:start position:0%
+together but there's a lot of weak
+forces but if you subjects a protein to
+
+ align:start position:0%
+forces but if you subjects a protein to
+ 
+
+ align:start position:0%
+forces but if you subjects a protein to
+various treatments that may break up
+
+ align:start position:0%
+various treatments that may break up
+ 
+
+ align:start position:0%
+various treatments that may break up
+those weak forces the protein will
+
+ align:start position:0%
+those weak forces the protein will
+ 
+
+ align:start position:0%
+those weak forces the protein will
+undergo a process of denaturation so
+
+ align:start position:0%
+undergo a process of denaturation so
+ 
+
+ align:start position:0%
+undergo a process of denaturation so
+anyone think of what kinds of things
+
+ align:start position:0%
+anyone think of what kinds of things
+ 
+
+ align:start position:0%
+anyone think of what kinds of things
+would cause protein denaturation yes
+
+ align:start position:0%
+would cause protein denaturation yes
+ 
+
+ align:start position:0%
+would cause protein denaturation yes
+heat is a bad WA is a serious one
+
+ align:start position:0%
+heat is a bad WA is a serious one
+ 
+
+ align:start position:0%
+heat is a bad WA is a serious one
+obviously and heat yes I'll write them
+
+ align:start position:0%
+obviously and heat yes I'll write them
+ 
+
+ align:start position:0%
+obviously and heat yes I'll write them
+all down
+
+ align:start position:0%
+all down
+ 
+
+ align:start position:0%
+all down
+what's your pH so peach acidity basicity
+
+ align:start position:0%
+what's your pH so peach acidity basicity
+ 
+
+ align:start position:0%
+what's your pH so peach acidity basicity
+and we'll talk about why those things
+
+ align:start position:0%
+and we'll talk about why those things
+ 
+
+ align:start position:0%
+and we'll talk about why those things
+cause changes any other thoughts yes oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so for example salt organic
+
+ align:start position:0%
+yeah so for example salt organic
+ 
+
+ align:start position:0%
+yeah so for example salt organic
+solvents a process that a lot of people
+
+ align:start position:0%
+solvents a process that a lot of people
+ 
+
+ align:start position:0%
+solvents a process that a lot of people
+don't necessarily think about but as
+
+ align:start position:0%
+don't necessarily think about but as
+ 
+
+ align:start position:0%
+don't necessarily think about but as
+engineers some of you will is shear
+
+ align:start position:0%
+engineers some of you will is shear
+ 
+
+ align:start position:0%
+engineers some of you will is shear
+forces so if you're shooting a protein
+
+ align:start position:0%
+forces so if you're shooting a protein
+ 
+
+ align:start position:0%
+forces so if you're shooting a protein
+through a very narrow tubing and there's
+
+ align:start position:0%
+through a very narrow tubing and there's
+ 
+
+ align:start position:0%
+through a very narrow tubing and there's
+high shear forces those who are also
+
+ align:start position:0%
+high shear forces those who are also
+ 
+
+ align:start position:0%
+high shear forces those who are also
+denature proteins so with eat it's very
+
+ align:start position:0%
+denature proteins so with eat it's very
+ 
+
+ align:start position:0%
+denature proteins so with eat it's very
+clear you're gonna break those weak
+
+ align:start position:0%
+clear you're gonna break those weak
+ 
+
+ align:start position:0%
+clear you're gonna break those weak
+bonds and then they you know they can
+
+ align:start position:0%
+bonds and then they you know they can
+ 
+
+ align:start position:0%
+bonds and then they you know they can
+either reform or if you go to to high
+
+ align:start position:0%
+either reform or if you go to to high
+ 
+
+ align:start position:0%
+either reform or if you go to to high
+heat the unfolded protein starts to form
+
+ align:start position:0%
+heat the unfolded protein starts to form
+ 
+
+ align:start position:0%
+heat the unfolded protein starts to form
+aggregates and anyone who has ever
+
+ align:start position:0%
+aggregates and anyone who has ever
+ 
+
+ align:start position:0%
+aggregates and anyone who has ever
+scrambled an egg knows that that is an
+
+ align:start position:0%
+scrambled an egg knows that that is an
+ 
+
+ align:start position:0%
+scrambled an egg knows that that is an
+irreversible process you don't get to
+
+ align:start position:0%
+irreversible process you don't get to
+ 
+
+ align:start position:0%
+irreversible process you don't get to
+cram the egg back into the shell it's
+
+ align:start position:0%
+cram the egg back into the shell it's
+ 
+
+ align:start position:0%
+cram the egg back into the shell it's
+not the same anymore because what you're
+
+ align:start position:0%
+not the same anymore because what you're
+ 
+
+ align:start position:0%
+not the same anymore because what you're
+doing when you're scrambling eggs is
+
+ align:start position:0%
+doing when you're scrambling eggs is
+ 
+
+ align:start position:0%
+doing when you're scrambling eggs is
+denaturing proteins through heat
+
+ align:start position:0%
+denaturing proteins through heat
+ 
+
+ align:start position:0%
+denaturing proteins through heat
+treatment so that's what heat does it
+
+ align:start position:0%
+treatment so that's what heat does it
+ 
+
+ align:start position:0%
+treatment so that's what heat does it
+breaks the forces the the proteins
+
+ align:start position:0%
+breaks the forces the the proteins
+ 
+
+ align:start position:0%
+breaks the forces the the proteins
+stretch out into their denatured state
+
+ align:start position:0%
+stretch out into their denatured state
+ 
+
+ align:start position:0%
+stretch out into their denatured state
+and instead of refolding to a compact
+
+ align:start position:0%
+and instead of refolding to a compact
+ 
+
+ align:start position:0%
+and instead of refolding to a compact
+structure they just start aggregating
+
+ align:start position:0%
+structure they just start aggregating
+ 
+
+ align:start position:0%
+structure they just start aggregating
+with each other and that's pretty much
+
+ align:start position:0%
+with each other and that's pretty much
+ 
+
+ align:start position:0%
+with each other and that's pretty much
+your reverse 'fl ph is interesting why
+
+ align:start position:0%
+your reverse 'fl ph is interesting why
+ 
+
+ align:start position:0%
+your reverse 'fl ph is interesting why
+would pH break up a low temperature why
+
+ align:start position:0%
+would pH break up a low temperature why
+ 
+
+ align:start position:0%
+would pH break up a low temperature why
+would pH cause changes yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so pH perfect so pH will change the
+
+ align:start position:0%
+okay so pH perfect so pH will change the
+ 
+
+ align:start position:0%
+okay so pH perfect so pH will change the
+charge state of many of your site chains
+
+ align:start position:0%
+charge state of many of your site chains
+ 
+
+ align:start position:0%
+charge state of many of your site chains
+and once you've changed it you might
+
+ align:start position:0%
+and once you've changed it you might
+ 
+
+ align:start position:0%
+and once you've changed it you might
+have had a lovely electrostatic
+
+ align:start position:0%
+have had a lovely electrostatic
+ 
+
+ align:start position:0%
+have had a lovely electrostatic
+interaction but then you go and
+
+ align:start position:0%
+interaction but then you go and
+ 
+
+ align:start position:0%
+interaction but then you go and
+protonate the carboxylic acid and it
+
+ align:start position:0%
+protonate the carboxylic acid and it
+ 
+
+ align:start position:0%
+protonate the carboxylic acid and it
+can't fall in fact it wants the former
+
+ align:start position:0%
+can't fall in fact it wants the former
+ 
+
+ align:start position:0%
+can't fall in fact it wants the former
+it wants to break a partisan as opposed
+
+ align:start position:0%
+it wants to break a partisan as opposed
+ 
+
+ align:start position:0%
+it wants to break a partisan as opposed
+to come together so that is changing
+
+ align:start position:0%
+to come together so that is changing
+ 
+
+ align:start position:0%
+to come together so that is changing
+charge state which causes denaturation
+
+ align:start position:0%
+charge state which causes denaturation
+ 
+
+ align:start position:0%
+charge state which causes denaturation
+salts and organics for example they make
+
+ align:start position:0%
+salts and organics for example they make
+ 
+
+ align:start position:0%
+salts and organics for example they make
+interactions with parts of the protein
+
+ align:start position:0%
+interactions with parts of the protein
+ 
+
+ align:start position:0%
+interactions with parts of the protein
+for example organics organic molecules
+
+ align:start position:0%
+for example organics organic molecules
+ 
+
+ align:start position:0%
+for example organics organic molecules
+may slip into a hydrophobic core and
+
+ align:start position:0%
+may slip into a hydrophobic core and
+ 
+
+ align:start position:0%
+may slip into a hydrophobic core and
+break them up just push them apart they
+
+ align:start position:0%
+break them up just push them apart they
+ 
+
+ align:start position:0%
+break them up just push them apart they
+want to be there and then too many too
+
+ align:start position:0%
+want to be there and then too many too
+ 
+
+ align:start position:0%
+want to be there and then too many too
+much of a high concentration of an
+
+ align:start position:0%
+much of a high concentration of an
+ 
+
+ align:start position:0%
+much of a high concentration of an
+organic solvent that is miscible with
+
+ align:start position:0%
+organic solvent that is miscible with
+ 
+
+ align:start position:0%
+organic solvent that is miscible with
+water and we would say ethanol Osito
+
+ align:start position:0%
+water and we would say ethanol Osito
+ 
+
+ align:start position:0%
+water and we would say ethanol Osito
+nitrile DMSO but you don't need to worry
+
+ align:start position:0%
+nitrile DMSO but you don't need to worry
+ 
+
+ align:start position:0%
+nitrile DMSO but you don't need to worry
+about too much of which details well
+
+ align:start position:0%
+about too much of which details well
+ 
+
+ align:start position:0%
+about too much of which details well
+actually once you get above 10 percent
+
+ align:start position:0%
+actually once you get above 10 percent
+ 
+
+ align:start position:0%
+actually once you get above 10 percent
+or so we'll just start denaturing
+
+ align:start position:0%
+or so we'll just start denaturing
+ 
+
+ align:start position:0%
+or so we'll just start denaturing
+proteins sometimes reversibly but often
+
+ align:start position:0%
+proteins sometimes reversibly but often
+ 
+
+ align:start position:0%
+proteins sometimes reversibly but often
+irreversibly so this is very important
+
+ align:start position:0%
+irreversibly so this is very important
+ 
+
+ align:start position:0%
+irreversibly so this is very important
+to know the proteins are stable but you
+
+ align:start position:0%
+to know the proteins are stable but you
+ 
+
+ align:start position:0%
+to know the proteins are stable but you
+got to treat them nicely there are some
+
+ align:start position:0%
+got to treat them nicely there are some
+ 
+
+ align:start position:0%
+got to treat them nicely there are some
+human diseases that are a result of Mis
+
+ align:start position:0%
+human diseases that are a result of Mis
+ 
+
+ align:start position:0%
+human diseases that are a result of Mis
+folded or aggregated proteins so for
+
+ align:start position:0%
+folded or aggregated proteins so for
+ 
+
+ align:start position:0%
+folded or aggregated proteins so for
+example all the prion diseases are
+
+ align:start position:0%
+example all the prion diseases are
+ 
+
+ align:start position:0%
+example all the prion diseases are
+proteins gone bad pretty much where they
+
+ align:start position:0%
+proteins gone bad pretty much where they
+ 
+
+ align:start position:0%
+proteins gone bad pretty much where they
+not in a folded structure anymore but
+
+ align:start position:0%
+not in a folded structure anymore but
+ 
+
+ align:start position:0%
+not in a folded structure anymore but
+they are in aggregates that cause
+
+ align:start position:0%
+they are in aggregates that cause
+ 
+
+ align:start position:0%
+they are in aggregates that cause
+problems with cellular processes and
+
+ align:start position:0%
+problems with cellular processes and
+ 
+
+ align:start position:0%
+problems with cellular processes and
+toxicity so Alzheimer's disease mad cow
+
+ align:start position:0%
+toxicity so Alzheimer's disease mad cow
+ 
+
+ align:start position:0%
+toxicity so Alzheimer's disease mad cow
+disease a lot of those neurologic
+
+ align:start position:0%
+disease a lot of those neurologic
+ 
+
+ align:start position:0%
+disease a lot of those neurologic
+disorders caused by poorly folded or
+
+ align:start position:0%
+disorders caused by poorly folded or
+ 
+
+ align:start position:0%
+disorders caused by poorly folded or
+very miss folded proteins for examples
+
+ align:start position:0%
+very miss folded proteins for examples
+ 
+
+ align:start position:0%
+very miss folded proteins for examples
+so these are the things we talked about
+
+ align:start position:0%
+so these are the things we talked about
+ 
+
+ align:start position:0%
+so these are the things we talked about
+last time with respect to the flux from
+
+ align:start position:0%
+last time with respect to the flux from
+ 
+
+ align:start position:0%
+last time with respect to the flux from
+primary to secondary to tertiary to
+
+ align:start position:0%
+primary to secondary to tertiary to
+ 
+
+ align:start position:0%
+primary to secondary to tertiary to
+quaternary and that's a perfect time for
+
+ align:start position:0%
+quaternary and that's a perfect time for
+ 
+
+ align:start position:0%
+quaternary and that's a perfect time for
+me to introduce to you what we'll talk
+
+ align:start position:0%
+me to introduce to you what we'll talk
+ 
+
+ align:start position:0%
+me to introduce to you what we'll talk
+about today so last time we talked about
+
+ align:start position:0%
+about today so last time we talked about
+ 
+
+ align:start position:0%
+about today so last time we talked about
+structural proteins and I showed you how
+
+ align:start position:0%
+structural proteins and I showed you how
+ 
+
+ align:start position:0%
+structural proteins and I showed you how
+collagen just with a simple defect
+
+ align:start position:0%
+collagen just with a simple defect
+ 
+
+ align:start position:0%
+collagen just with a simple defect
+changing a glycine to an alanine in one
+
+ align:start position:0%
+changing a glycine to an alanine in one
+ 
+
+ align:start position:0%
+changing a glycine to an alanine in one
+of its subunits really alters the
+
+ align:start position:0%
+of its subunits really alters the
+ 
+
+ align:start position:0%
+of its subunits really alters the
+tertiary the quaternary structure
+
+ align:start position:0%
+tertiary the quaternary structure
+ 
+
+ align:start position:0%
+tertiary the quaternary structure
+the protein to make very weak collagen
+
+ align:start position:0%
+the protein to make very weak collagen
+ 
+
+ align:start position:0%
+the protein to make very weak collagen
+that's no longer supportive of bone
+
+ align:start position:0%
+that's no longer supportive of bone
+ 
+
+ align:start position:0%
+that's no longer supportive of bone
+strength but what I'm going to talk to
+
+ align:start position:0%
+strength but what I'm going to talk to
+ 
+
+ align:start position:0%
+strength but what I'm going to talk to
+you about today is a defect in a
+
+ align:start position:0%
+you about today is a defect in a
+ 
+
+ align:start position:0%
+you about today is a defect in a
+transport protein that carries oxygen
+
+ align:start position:0%
+transport protein that carries oxygen
+ 
+
+ align:start position:0%
+transport protein that carries oxygen
+around the body so we're gonna talk
+
+ align:start position:0%
+around the body so we're gonna talk
+ 
+
+ align:start position:0%
+around the body so we're gonna talk
+about hemoglobin these diseases are what
+
+ align:start position:0%
+about hemoglobin these diseases are what
+ 
+
+ align:start position:0%
+about hemoglobin these diseases are what
+are known as inborn errors of metabolism
+
+ align:start position:0%
+are known as inborn errors of metabolism
+ 
+
+ align:start position:0%
+are known as inborn errors of metabolism
+or that's kind of a complex term or
+
+ align:start position:0%
+or that's kind of a complex term or
+ 
+
+ align:start position:0%
+or that's kind of a complex term or
+genetically linked diseases because
+
+ align:start position:0%
+genetically linked diseases because
+ 
+
+ align:start position:0%
+genetically linked diseases because
+there is a single defect in a DNA strand
+
+ align:start position:0%
+there is a single defect in a DNA strand
+ 
+
+ align:start position:0%
+there is a single defect in a DNA strand
+that then gets transcribed into an RNA
+
+ align:start position:0%
+that then gets transcribed into an RNA
+ 
+
+ align:start position:0%
+that then gets transcribed into an RNA
+strand so one base defect that then
+
+ align:start position:0%
+strand so one base defect that then
+ 
+
+ align:start position:0%
+strand so one base defect that then
+becomes an amino acid defect in your
+
+ align:start position:0%
+becomes an amino acid defect in your
+ 
+
+ align:start position:0%
+becomes an amino acid defect in your
+protein strand so these are tiny changes
+
+ align:start position:0%
+protein strand so these are tiny changes
+ 
+
+ align:start position:0%
+protein strand so these are tiny changes
+in the protein of the cause dramatic
+
+ align:start position:0%
+in the protein of the cause dramatic
+ 
+
+ align:start position:0%
+in the protein of the cause dramatic
+changes in the structure and function of
+
+ align:start position:0%
+changes in the structure and function of
+ 
+
+ align:start position:0%
+changes in the structure and function of
+the protein and what you will see with
+
+ align:start position:0%
+the protein and what you will see with
+ 
+
+ align:start position:0%
+the protein and what you will see with
+hemoglobin is it causes a real problem
+
+ align:start position:0%
+hemoglobin is it causes a real problem
+ 
+
+ align:start position:0%
+hemoglobin is it causes a real problem
+with the quaternary structure and then
+
+ align:start position:0%
+with the quaternary structure and then
+ 
+
+ align:start position:0%
+with the quaternary structure and then
+causes proteins to aggregate so
+
+ align:start position:0%
+causes proteins to aggregate so
+ 
+
+ align:start position:0%
+causes proteins to aggregate so
+hemoglobin is the dominant protein in
+
+ align:start position:0%
+hemoglobin is the dominant protein in
+ 
+
+ align:start position:0%
+hemoglobin is the dominant protein in
+red blood cells or erythrocytes
+
+ align:start position:0%
+red blood cells or erythrocytes
+ 
+
+ align:start position:0%
+red blood cells or erythrocytes
+and in fact the differentiation of the
+
+ align:start position:0%
+and in fact the differentiation of the
+ 
+
+ align:start position:0%
+and in fact the differentiation of the
+red blood cell as it comes from
+
+ align:start position:0%
+red blood cell as it comes from
+ 
+
+ align:start position:0%
+red blood cell as it comes from
+progenitor cells goes through a process
+
+ align:start position:0%
+progenitor cells goes through a process
+ 
+
+ align:start position:0%
+progenitor cells goes through a process
+where the red blood cell dumps out its
+
+ align:start position:0%
+where the red blood cell dumps out its
+ 
+
+ align:start position:0%
+where the red blood cell dumps out its
+nucleus so it can't divide anymore and
+
+ align:start position:0%
+nucleus so it can't divide anymore and
+ 
+
+ align:start position:0%
+nucleus so it can't divide anymore and
+basically the content of the cell is
+
+ align:start position:0%
+basically the content of the cell is
+ 
+
+ align:start position:0%
+basically the content of the cell is
+extremely high in hemoglobin you've
+
+ align:start position:0%
+extremely high in hemoglobin you've
+ 
+
+ align:start position:0%
+extremely high in hemoglobin you've
+packed the hemoglobin into the red blood
+
+ align:start position:0%
+packed the hemoglobin into the red blood
+ 
+
+ align:start position:0%
+packed the hemoglobin into the red blood
+cell at the cost of losing the nucleus
+
+ align:start position:0%
+cell at the cost of losing the nucleus
+ 
+
+ align:start position:0%
+cell at the cost of losing the nucleus
+so that's terminally differentiated
+
+ align:start position:0%
+so that's terminally differentiated
+ 
+
+ align:start position:0%
+so that's terminally differentiated
+can't become a red blood cell and can't
+
+ align:start position:0%
+can't become a red blood cell and can't
+ 
+
+ align:start position:0%
+can't become a red blood cell and can't
+divide anymore and it has about a half
+
+ align:start position:0%
+divide anymore and it has about a half
+ 
+
+ align:start position:0%
+divide anymore and it has about a half
+life they have about a half life 100
+
+ align:start position:0%
+life they have about a half life 100
+ 
+
+ align:start position:0%
+life they have about a half life 100
+days so they turn over and then that's
+
+ align:start position:0%
+days so they turn over and then that's
+ 
+
+ align:start position:0%
+days so they turn over and then that's
+it and when red blood cells turn over
+
+ align:start position:0%
+it and when red blood cells turn over
+ 
+
+ align:start position:0%
+it and when red blood cells turn over
+the hemoglobin has to be taken care of
+
+ align:start position:0%
+the hemoglobin has to be taken care of
+ 
+
+ align:start position:0%
+the hemoglobin has to be taken care of
+in order that is not toxic red blood
+
+ align:start position:0%
+in order that is not toxic red blood
+ 
+
+ align:start position:0%
+in order that is not toxic red blood
+cells are red because of a particular
+
+ align:start position:0%
+cells are red because of a particular
+ 
+
+ align:start position:0%
+cells are red because of a particular
+molecule that's in the hemoglobin
+
+ align:start position:0%
+molecule that's in the hemoglobin
+ 
+
+ align:start position:0%
+molecule that's in the hemoglobin
+called ahima molecule which is bound to
+
+ align:start position:0%
+called ahima molecule which is bound to
+ 
+
+ align:start position:0%
+called ahima molecule which is bound to
+iron which provides the hemoglobin with
+
+ align:start position:0%
+iron which provides the hemoglobin with
+ 
+
+ align:start position:0%
+iron which provides the hemoglobin with
+the capacity to pick up oxygen in your
+
+ align:start position:0%
+the capacity to pick up oxygen in your
+ 
+
+ align:start position:0%
+the capacity to pick up oxygen in your
+lungs travel it around the body and then
+
+ align:start position:0%
+lungs travel it around the body and then
+ 
+
+ align:start position:0%
+lungs travel it around the body and then
+leave it where it's needed and then
+
+ align:start position:0%
+leave it where it's needed and then
+ 
+
+ align:start position:0%
+leave it where it's needed and then
+replace the oxygen with co2 and take the
+
+ align:start position:0%
+replace the oxygen with co2 and take the
+ 
+
+ align:start position:0%
+replace the oxygen with co2 and take the
+co2 back to the lungs in order for you
+
+ align:start position:0%
+co2 back to the lungs in order for you
+ 
+
+ align:start position:0%
+co2 back to the lungs in order for you
+to respire it out okay so he made the
+
+ align:start position:0%
+to respire it out okay so he made the
+ 
+
+ align:start position:0%
+to respire it out okay so he made the
+team aglow beam carries oxygen and co2
+
+ align:start position:0%
+team aglow beam carries oxygen and co2
+ 
+
+ align:start position:0%
+team aglow beam carries oxygen and co2
+from oxygen from the lungs co2 back to
+
+ align:start position:0%
+from oxygen from the lungs co2 back to
+ 
+
+ align:start position:0%
+from oxygen from the lungs co2 back to
+the lungs and the reason why you need
+
+ align:start position:0%
+the lungs and the reason why you need
+ 
+
+ align:start position:0%
+the lungs and the reason why you need
+the iron is that the iron is coordinated
+
+ align:start position:0%
+the iron is that the iron is coordinated
+ 
+
+ align:start position:0%
+the iron is that the iron is coordinated
+to the oxygen so the heme molecule I
+
+ align:start position:0%
+to the oxygen so the heme molecule I
+ 
+
+ align:start position:0%
+to the oxygen so the heme molecule I
+won't draw it if you want to see it it's
+
+ align:start position:0%
+won't draw it if you want to see it it's
+ 
+
+ align:start position:0%
+won't draw it if you want to see it it's
+a big complex organic structure a very
+
+ align:start position:0%
+a big complex organic structure a very
+ 
+
+ align:start position:0%
+a big complex organic structure a very
+interesting structure but something for
+
+ align:start position:0%
+interesting structure but something for
+ 
+
+ align:start position:0%
+interesting structure but something for
+another day here look but I want to
+
+ align:start position:0%
+another day here look but I want to
+ 
+
+ align:start position:0%
+another day here look but I want to
+stress to you that the iron heme complex
+
+ align:start position:0%
+stress to you that the iron heme complex
+ 
+
+ align:start position:0%
+stress to you that the iron heme complex
+is red that's why your blood cells are
+
+ align:start position:0%
+is red that's why your blood cells are
+ 
+
+ align:start position:0%
+is red that's why your blood cells are
+red your blood cells don't have a
+
+ align:start position:0%
+red your blood cells don't have a
+ 
+
+ align:start position:0%
+red your blood cells don't have a
+nucleus so they can cram in lots more
+
+ align:start position:0%
+nucleus so they can cram in lots more
+ 
+
+ align:start position:0%
+nucleus so they can cram in lots more
+hemoglobin so it's kind of a fascinating
+
+ align:start position:0%
+hemoglobin so it's kind of a fascinating
+ 
+
+ align:start position:0%
+hemoglobin so it's kind of a fascinating
+situations so hemoglobin is an example
+
+ align:start position:0%
+situations so hemoglobin is an example
+ 
+
+ align:start position:0%
+situations so hemoglobin is an example
+of a homo tetrameric protein and it has
+
+ align:start position:0%
+of a homo tetrameric protein and it has
+ 
+
+ align:start position:0%
+of a homo tetrameric protein and it has
+four subunits two of one flavor and two
+
+ align:start position:0%
+four subunits two of one flavor and two
+ 
+
+ align:start position:0%
+four subunits two of one flavor and two
+of another so we call this an alpha 2
+
+ align:start position:0%
+of another so we call this an alpha 2
+ 
+
+ align:start position:0%
+of another so we call this an alpha 2
+beta 2 protein differentiating the alpha
+
+ align:start position:0%
+beta 2 protein differentiating the alpha
+ 
+
+ align:start position:0%
+beta 2 protein differentiating the alpha
+subunits and the beat ones yes why isn't
+
+ align:start position:0%
+subunits and the beat ones yes why isn't
+ 
+
+ align:start position:0%
+subunits and the beat ones yes why isn't
+it homo tetrameric this you could ask
+
+ align:start position:0%
+it homo tetrameric this you could ask
+ 
+
+ align:start position:0%
+it homo tetrameric this you could ask
+why is it I don't know I mean there will
+
+ align:start position:0%
+why is it I don't know I mean there will
+ 
+
+ align:start position:0%
+why is it I don't know I mean there will
+be interactions amongst the subunits
+
+ align:start position:0%
+be interactions amongst the subunits
+ 
+
+ align:start position:0%
+be interactions amongst the subunits
+that favor that particular packaging the
+
+ align:start position:0%
+that favor that particular packaging the
+ 
+
+ align:start position:0%
+that favor that particular packaging the
+subunits are kind of similar in shape
+
+ align:start position:0%
+subunits are kind of similar in shape
+ 
+
+ align:start position:0%
+subunits are kind of similar in shape
+they have what's called a globe in fold
+
+ align:start position:0%
+they have what's called a globe in fold
+ 
+
+ align:start position:0%
+they have what's called a globe in fold
+you could more or less pick out those
+
+ align:start position:0%
+you could more or less pick out those
+ 
+
+ align:start position:0%
+you could more or less pick out those
+tubes remember our alpha helixes they
+
+ align:start position:0%
+tubes remember our alpha helixes they
+ 
+
+ align:start position:0%
+tubes remember our alpha helixes they
+could form tetramers that are all the
+
+ align:start position:0%
+could form tetramers that are all the
+ 
+
+ align:start position:0%
+could form tetramers that are all the
+same but the energetically favored form
+
+ align:start position:0%
+same but the energetically favored form
+ 
+
+ align:start position:0%
+same but the energetically favored form
+is the two and two hemoglobin is a
+
+ align:start position:0%
+is the two and two hemoglobin is a
+ 
+
+ align:start position:0%
+is the two and two hemoglobin is a
+tetrameric protein because that's really
+
+ align:start position:0%
+tetrameric protein because that's really
+ 
+
+ align:start position:0%
+tetrameric protein because that's really
+advantageous for picking up
+
+ align:start position:0%
+advantageous for picking up
+ 
+
+ align:start position:0%
+advantageous for picking up
+Sigyn and dropping off oxygen in a very
+
+ align:start position:0%
+Sigyn and dropping off oxygen in a very
+ 
+
+ align:start position:0%
+Sigyn and dropping off oxygen in a very
+narrow oxygen range so there are
+
+ align:start position:0%
+narrow oxygen range so there are
+ 
+
+ align:start position:0%
+narrow oxygen range so there are
+proteins called globins that just one of
+
+ align:start position:0%
+proteins called globins that just one of
+ 
+
+ align:start position:0%
+proteins called globins that just one of
+these that can bind oxygen hemoglobin is
+
+ align:start position:0%
+these that can bind oxygen hemoglobin is
+ 
+
+ align:start position:0%
+these that can bind oxygen hemoglobin is
+tetrameric because it has a cooperative
+
+ align:start position:0%
+tetrameric because it has a cooperative
+ 
+
+ align:start position:0%
+tetrameric because it has a cooperative
+oxygen binding so in a very narrow range
+
+ align:start position:0%
+oxygen binding so in a very narrow range
+ 
+
+ align:start position:0%
+oxygen binding so in a very narrow range
+of oxygen it fills all four sites in the
+
+ align:start position:0%
+of oxygen it fills all four sites in the
+ 
+
+ align:start position:0%
+of oxygen it fills all four sites in the
+tetrameric protein with an oxygen
+
+ align:start position:0%
+tetrameric protein with an oxygen
+ 
+
+ align:start position:0%
+tetrameric protein with an oxygen
+molecule so it's very advantageous in
+
+ align:start position:0%
+molecule so it's very advantageous in
+ 
+
+ align:start position:0%
+molecule so it's very advantageous in
+from a physics perspective that it
+
+ align:start position:0%
+from a physics perspective that it
+ 
+
+ align:start position:0%
+from a physics perspective that it
+responds to very narrow changes in
+
+ align:start position:0%
+responds to very narrow changes in
+ 
+
+ align:start position:0%
+responds to very narrow changes in
+oxygen does that make sense to everyone
+
+ align:start position:0%
+oxygen does that make sense to everyone
+ 
+
+ align:start position:0%
+oxygen does that make sense to everyone
+yeah okay it means cut anything that's
+
+ align:start position:0%
+yeah okay it means cut anything that's
+ 
+
+ align:start position:0%
+yeah okay it means cut anything that's
+cooperative means that one let's say
+
+ align:start position:0%
+cooperative means that one let's say
+ 
+
+ align:start position:0%
+cooperative means that one let's say
+I've got a tetramer of hemoglobin one
+
+ align:start position:0%
+I've got a tetramer of hemoglobin one
+ 
+
+ align:start position:0%
+I've got a tetramer of hemoglobin one
+oxygen binds to one of them so I'm a
+
+ align:start position:0%
+oxygen binds to one of them so I'm a
+ 
+
+ align:start position:0%
+oxygen binds to one of them so I'm a
+binding oxygen here and then binding to
+
+ align:start position:0%
+binding oxygen here and then binding to
+ 
+
+ align:start position:0%
+binding oxygen here and then binding to
+the next the next and the next gets
+
+ align:start position:0%
+the next the next and the next gets
+ 
+
+ align:start position:0%
+the next the next and the next gets
+easier and easier so it's they sort of
+
+ align:start position:0%
+easier and easier so it's they sort of
+ 
+
+ align:start position:0%
+easier and easier so it's they sort of
+want to come in as a team and that's
+
+ align:start position:0%
+want to come in as a team and that's
+ 
+
+ align:start position:0%
+want to come in as a team and that's
+handy for maximizing oxygen transport
+
+ align:start position:0%
+handy for maximizing oxygen transport
+ 
+
+ align:start position:0%
+handy for maximizing oxygen transport
+around the body in a narrow oxygen range
+
+ align:start position:0%
+around the body in a narrow oxygen range
+ 
+
+ align:start position:0%
+around the body in a narrow oxygen range
+which we can only deal with what's out
+
+ align:start position:0%
+which we can only deal with what's out
+ 
+
+ align:start position:0%
+which we can only deal with what's out
+there in the atmosphere so we have to
+
+ align:start position:0%
+there in the atmosphere so we have to
+ 
+
+ align:start position:0%
+there in the atmosphere so we have to
+make this work does that answer your
+
+ align:start position:0%
+make this work does that answer your
+ 
+
+ align:start position:0%
+make this work does that answer your
+question okay all right so where was I
+
+ align:start position:0%
+question okay all right so where was I
+ 
+
+ align:start position:0%
+question okay all right so where was I
+okay so so what we're gonna do today
+
+ align:start position:0%
+okay so so what we're gonna do today
+ 
+
+ align:start position:0%
+okay so so what we're gonna do today
+we're gonna look at hemoglobin
+
+ align:start position:0%
+we're gonna look at hemoglobin
+ 
+
+ align:start position:0%
+we're gonna look at hemoglobin
+it's the tetra mer those discoid
+
+ align:start position:0%
+it's the tetra mer those discoid
+ 
+
+ align:start position:0%
+it's the tetra mer those discoid
+structures are the heme that I just
+
+ align:start position:0%
+structures are the heme that I just
+ 
+
+ align:start position:0%
+structures are the heme that I just
+mentioned I've drawn them as this sort
+
+ align:start position:0%
+mentioned I've drawn them as this sort
+ 
+
+ align:start position:0%
+mentioned I've drawn them as this sort
+of four leaf clover here just for
+
+ align:start position:0%
+of four leaf clover here just for
+ 
+
+ align:start position:0%
+of four leaf clover here just for
+simplicity and there is a single defect
+
+ align:start position:0%
+simplicity and there is a single defect
+ 
+
+ align:start position:0%
+simplicity and there is a single defect
+in the sequence of the single monomer
+
+ align:start position:0%
+in the sequence of the single monomer
+ 
+
+ align:start position:0%
+in the sequence of the single monomer
+subunits in hemoglobin so each of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are four proteins betta globin
+
+ align:start position:0%
+so there are four proteins betta globin
+ 
+
+ align:start position:0%
+so there are four proteins betta globin
+two copies of beta globin and two copies
+
+ align:start position:0%
+two copies of beta globin and two copies
+ 
+
+ align:start position:0%
+two copies of beta globin and two copies
+of alpha globin they are all let me see
+
+ align:start position:0%
+of alpha globin they are all let me see
+ 
+
+ align:start position:0%
+of alpha globin they are all let me see
+what's the size did you deluded it to
+
+ align:start position:0%
+what's the size did you deluded it to
+ 
+
+ align:start position:0%
+what's the size did you deluded it to
+pretty subjective you know I could never
+
+ align:start position:0%
+pretty subjective you know I could never
+ 
+
+ align:start position:0%
+pretty subjective you know I could never
+see things when I'm up at the screen but
+
+ align:start position:0%
+see things when I'm up at the screen but
+ 
+
+ align:start position:0%
+see things when I'm up at the screen but
+they're about 160 156 okay so they're
+
+ align:start position:0%
+they're about 160 156 okay so they're
+ 
+
+ align:start position:0%
+they're about 160 156 okay so they're
+about 146 amino acids long in each of
+
+ align:start position:0%
+about 146 amino acids long in each of
+ 
+
+ align:start position:0%
+about 146 amino acids long in each of
+them and a single defect in a beta
+
+ align:start position:0%
+them and a single defect in a beta
+ 
+
+ align:start position:0%
+them and a single defect in a beta
+globin where you have a change from
+
+ align:start position:0%
+globin where you have a change from
+ 
+
+ align:start position:0%
+globin where you have a change from
+glutamic acid residue 6 to valine
+
+ align:start position:0%
+glutamic acid residue 6 to valine
+ 
+
+ align:start position:0%
+glutamic acid residue 6 to valine
+residue 6 one change in beta globin
+
+ align:start position:0%
+residue 6 one change in beta globin
+ 
+
+ align:start position:0%
+residue 6 one change in beta globin
+which means two changes in the whole
+
+ align:start position:0%
+which means two changes in the whole
+ 
+
+ align:start position:0%
+which means two changes in the whole
+structure because there are two beta
+
+ align:start position:0%
+structure because there are two beta
+ 
+
+ align:start position:0%
+structure because there are two beta
+globin alters the properties of the
+
+ align:start position:0%
+globin alters the properties of the
+ 
+
+ align:start position:0%
+globin alters the properties of the
+hemoglobin and causes what's called
+
+ align:start position:0%
+hemoglobin and causes what's called
+ 
+
+ align:start position:0%
+hemoglobin and causes what's called
+sickling of your red blood cells so
+
+ align:start position:0%
+sickling of your red blood cells so
+ 
+
+ align:start position:0%
+sickling of your red blood cells so
+let's take a look at what that would
+
+ align:start position:0%
+let's take a look at what that would
+ 
+
+ align:start position:0%
+let's take a look at what that would
+look like at the amino acid level
+
+ align:start position:0%
+look like at the amino acid level
+ 
+
+ align:start position:0%
+look like at the amino acid level
+glutamic acid is one of your charged
+
+ align:start position:0%
+glutamic acid is one of your charged
+ 
+
+ align:start position:0%
+glutamic acid is one of your charged
+amino acids I'm just going to draw a
+
+ align:start position:0%
+amino acids I'm just going to draw a
+ 
+
+ align:start position:0%
+amino acids I'm just going to draw a
+little bit of it as it were in a peptide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's at position six in the sequence
+
+ align:start position:0%
+and it's at position six in the sequence
+ 
+
+ align:start position:0%
+and it's at position six in the sequence
+so it's six residues from the amino
+
+ align:start position:0%
+so it's six residues from the amino
+ 
+
+ align:start position:0%
+so it's six residues from the amino
+terminus because we always write things
+
+ align:start position:0%
+terminus because we always write things
+ 
+
+ align:start position:0%
+terminus because we always write things
+in this direction and the change takes
+
+ align:start position:0%
+in this direction and the change takes
+ 
+
+ align:start position:0%
+in this direction and the change takes
+place to put in place a valine and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a pretty big change in identity
+
+ align:start position:0%
+there's a pretty big change in identity
+ 
+
+ align:start position:0%
+there's a pretty big change in identity
+and personality of those residues you've
+
+ align:start position:0%
+and personality of those residues you've
+ 
+
+ align:start position:0%
+and personality of those residues you've
+gone from polar charged to neutral big
+
+ align:start position:0%
+gone from polar charged to neutral big
+ 
+
+ align:start position:0%
+gone from polar charged to neutral big
+fluffy hydrophobic residue and it's
+
+ align:start position:0%
+fluffy hydrophobic residue and it's
+ 
+
+ align:start position:0%
+fluffy hydrophobic residue and it's
+really amazing so the beta globin is
+
+ align:start position:0%
+really amazing so the beta globin is
+ 
+
+ align:start position:0%
+really amazing so the beta globin is
+expressed on chromosome 11 it's a
+
+ align:start position:0%
+expressed on chromosome 11 it's a
+ 
+
+ align:start position:0%
+expressed on chromosome 11 it's a
+hundred and thirty-four million base
+
+ align:start position:0%
+hundred and thirty-four million base
+ 
+
+ align:start position:0%
+hundred and thirty-four million base
+pairs one base is changed so what you
+
+ align:start position:0%
+pairs one base is changed so what you
+ 
+
+ align:start position:0%
+pairs one base is changed so what you
+have in the DNA in the normal DNA that
+
+ align:start position:0%
+have in the DNA in the normal DNA that
+ 
+
+ align:start position:0%
+have in the DNA in the normal DNA that
+encodes the No
+
+ align:start position:0%
+encodes the No
+ 
+
+ align:start position:0%
+encodes the No
+more beta-globin gene there's a
+
+ align:start position:0%
+more beta-globin gene there's a
+ 
+
+ align:start position:0%
+more beta-globin gene there's a
+particular sequence of nucleic acids
+
+ align:start position:0%
+particular sequence of nucleic acids
+ 
+
+ align:start position:0%
+particular sequence of nucleic acids
+this is what the double strand would
+
+ align:start position:0%
+this is what the double strand would
+ 
+
+ align:start position:0%
+this is what the double strand would
+look like we're gonna see way more about
+
+ align:start position:0%
+look like we're gonna see way more about
+ 
+
+ align:start position:0%
+look like we're gonna see way more about
+nucleic acids next week when that gets
+
+ align:start position:0%
+nucleic acids next week when that gets
+ 
+
+ align:start position:0%
+nucleic acids next week when that gets
+converted to the messenger RNA you get a
+
+ align:start position:0%
+converted to the messenger RNA you get a
+ 
+
+ align:start position:0%
+converted to the messenger RNA you get a
+particular code that in the genetic code
+
+ align:start position:0%
+particular code that in the genetic code
+ 
+
+ align:start position:0%
+particular code that in the genetic code
+codes for glutamic acids everything's
+
+ align:start position:0%
+codes for glutamic acids everything's
+ 
+
+ align:start position:0%
+codes for glutamic acids everything's
+normal a single change if we change the
+
+ align:start position:0%
+normal a single change if we change the
+ 
+
+ align:start position:0%
+normal a single change if we change the
+center nucleic acid within the DNA it
+
+ align:start position:0%
+center nucleic acid within the DNA it
+ 
+
+ align:start position:0%
+center nucleic acid within the DNA it
+makes a different messenger RNA and one
+
+ align:start position:0%
+makes a different messenger RNA and one
+ 
+
+ align:start position:0%
+makes a different messenger RNA and one
+base pair puts in valine instead of
+
+ align:start position:0%
+base pair puts in valine instead of
+ 
+
+ align:start position:0%
+base pair puts in valine instead of
+glutamic acid out of a hundred and
+
+ align:start position:0%
+glutamic acid out of a hundred and
+ 
+
+ align:start position:0%
+glutamic acid out of a hundred and
+thirty-four million base pairs so what
+
+ align:start position:0%
+thirty-four million base pairs so what
+ 
+
+ align:start position:0%
+thirty-four million base pairs so what
+happens in the normal normal hemoglobin
+
+ align:start position:0%
+happens in the normal normal hemoglobin
+ 
+
+ align:start position:0%
+happens in the normal normal hemoglobin
+you have normal behavior you have this
+
+ align:start position:0%
+you have normal behavior you have this
+ 
+
+ align:start position:0%
+you have normal behavior you have this
+tetrameric structure false commits
+
+ align:start position:0%
+tetrameric structure false commits
+ 
+
+ align:start position:0%
+tetrameric structure false commits
+cooperativity carries oxygen it moves
+
+ align:start position:0%
+cooperativity carries oxygen it moves
+ 
+
+ align:start position:0%
+cooperativity carries oxygen it moves
+around the blood low problem excuse me
+
+ align:start position:0%
+around the blood low problem excuse me
+ 
+
+ align:start position:0%
+around the blood low problem excuse me
+it sits in the erythrocytes or red blood
+
+ align:start position:0%
+it sits in the erythrocytes or red blood
+ 
+
+ align:start position:0%
+it sits in the erythrocytes or red blood
+cells no problem the minute you have
+
+ align:start position:0%
+cells no problem the minute you have
+ 
+
+ align:start position:0%
+cells no problem the minute you have
+that mutation the hemoglobin molecules
+
+ align:start position:0%
+that mutation the hemoglobin molecules
+ 
+
+ align:start position:0%
+that mutation the hemoglobin molecules
+start to associate into clusters like
+
+ align:start position:0%
+start to associate into clusters like
+ 
+
+ align:start position:0%
+start to associate into clusters like
+fiber lacrosse thus because each tetra
+
+ align:start position:0%
+fiber lacrosse thus because each tetra
+ 
+
+ align:start position:0%
+fiber lacrosse thus because each tetra
+mer gets glued to another tetra mer and
+
+ align:start position:0%
+mer gets glued to another tetra mer and
+ 
+
+ align:start position:0%
+mer gets glued to another tetra mer and
+another one and another one so you have
+
+ align:start position:0%
+another one and another one so you have
+ 
+
+ align:start position:0%
+another one and another one so you have
+hemoglobin not behaving as this
+
+ align:start position:0%
+hemoglobin not behaving as this
+ 
+
+ align:start position:0%
+hemoglobin not behaving as this
+beautiful independent quaternary
+
+ align:start position:0%
+beautiful independent quaternary
+ 
+
+ align:start position:0%
+beautiful independent quaternary
+structure but rather sticking to
+
+ align:start position:0%
+structure but rather sticking to
+ 
+
+ align:start position:0%
+structure but rather sticking to
+physically sticking to other molecules
+
+ align:start position:0%
+physically sticking to other molecules
+ 
+
+ align:start position:0%
+physically sticking to other molecules
+and those tangles get those molecules
+
+ align:start position:0%
+and those tangles get those molecules
+ 
+
+ align:start position:0%
+and those tangles get those molecules
+get so so large that they start to form
+
+ align:start position:0%
+get so so large that they start to form
+ 
+
+ align:start position:0%
+get so so large that they start to form
+long and inflexible chains and it's such
+
+ align:start position:0%
+long and inflexible chains and it's such
+ 
+
+ align:start position:0%
+long and inflexible chains and it's such
+a dramatic change that that discoid
+
+ align:start position:0%
+a dramatic change that that discoid
+ 
+
+ align:start position:0%
+a dramatic change that that discoid
+structure you're that you're familiar
+
+ align:start position:0%
+structure you're that you're familiar
+ 
+
+ align:start position:0%
+structure you're that you're familiar
+with for red blood cells suddenly
+
+ align:start position:0%
+with for red blood cells suddenly
+ 
+
+ align:start position:0%
+with for red blood cells suddenly
+becomes a sickle shape so that would be
+
+ align:start position:0%
+becomes a sickle shape so that would be
+ 
+
+ align:start position:0%
+becomes a sickle shape so that would be
+the normal cell with normal hemoglobin
+
+ align:start position:0%
+the normal cell with normal hemoglobin
+ 
+
+ align:start position:0%
+the normal cell with normal hemoglobin
+but sickle cell they look like this
+
+ align:start position:0%
+but sickle cell they look like this
+ 
+
+ align:start position:0%
+but sickle cell they look like this
+they're kind of curved odd a very odd
+
+ align:start position:0%
+they're kind of curved odd a very odd
+ 
+
+ align:start position:0%
+they're kind of curved odd a very odd
+shape and the problem is red blood cells
+
+ align:start position:0%
+shape and the problem is red blood cells
+ 
+
+ align:start position:0%
+shape and the problem is red blood cells
+that have evolved to move really
+
+ align:start position:0%
+that have evolved to move really
+ 
+
+ align:start position:0%
+that have evolved to move really
+smoothly through your capillaries as
+
+ align:start position:0%
+smoothly through your capillaries as
+ 
+
+ align:start position:0%
+smoothly through your capillaries as
+soon as you get a different shape that's
+
+ align:start position:0%
+soon as you get a different shape that's
+ 
+
+ align:start position:0%
+soon as you get a different shape that's
+sort of you know not that discoid
+
+ align:start position:0%
+sort of you know not that discoid
+ 
+
+ align:start position:0%
+sort of you know not that discoid
+structure they start clogging in the
+
+ align:start position:0%
+structure they start clogging in the
+ 
+
+ align:start position:0%
+structure they start clogging in the
+capillaries and when you have the defect
+
+ align:start position:0%
+capillaries and when you have the defect
+ 
+
+ align:start position:0%
+capillaries and when you have the defect
+where all of your hemoglobin is messed
+
+ align:start position:0%
+where all of your hemoglobin is messed
+ 
+
+ align:start position:0%
+where all of your hemoglobin is messed
+up with this variation it's incredibly
+
+ align:start position:0%
+up with this variation it's incredibly
+ 
+
+ align:start position:0%
+up with this variation it's incredibly
+painful because think of all your
+
+ align:start position:0%
+painful because think of all your
+ 
+
+ align:start position:0%
+painful because think of all your
+capillary
+
+ align:start position:0%
+capillary
+ 
+
+ align:start position:0%
+capillary
+is going out to the Father reaches of
+
+ align:start position:0%
+is going out to the Father reaches of
+ 
+
+ align:start position:0%
+is going out to the Father reaches of
+your joints there is thin blood vessels
+
+ align:start position:0%
+your joints there is thin blood vessels
+ 
+
+ align:start position:0%
+your joints there is thin blood vessels
+blocked up with the sick old red blood
+
+ align:start position:0%
+blocked up with the sick old red blood
+ 
+
+ align:start position:0%
+blocked up with the sick old red blood
+cells that are caused by the variation
+
+ align:start position:0%
+cells that are caused by the variation
+ 
+
+ align:start position:0%
+cells that are caused by the variation
+in hemoglobin so that one little defect
+
+ align:start position:0%
+in hemoglobin so that one little defect
+ 
+
+ align:start position:0%
+in hemoglobin so that one little defect
+takes us all the way to a serious
+
+ align:start position:0%
+takes us all the way to a serious
+ 
+
+ align:start position:0%
+takes us all the way to a serious
+disease all right so what I want to do
+
+ align:start position:0%
+disease all right so what I want to do
+ 
+
+ align:start position:0%
+disease all right so what I want to do
+very briefly is show you the molecular
+
+ align:start position:0%
+very briefly is show you the molecular
+ 
+
+ align:start position:0%
+very briefly is show you the molecular
+basis for this all right and the defect
+
+ align:start position:0%
+basis for this all right and the defect
+ 
+
+ align:start position:0%
+basis for this all right and the defect
+actually appears on the two beta globin
+
+ align:start position:0%
+actually appears on the two beta globin
+ 
+
+ align:start position:0%
+actually appears on the two beta globin
+chains but right on the outside of the
+
+ align:start position:0%
+chains but right on the outside of the
+ 
+
+ align:start position:0%
+chains but right on the outside of the
+protein not in the middle of the protein
+
+ align:start position:0%
+protein not in the middle of the protein
+ 
+
+ align:start position:0%
+protein not in the middle of the protein
+because this is a defect that affects
+
+ align:start position:0%
+because this is a defect that affects
+ 
+
+ align:start position:0%
+because this is a defect that affects
+how proteins interact with other
+
+ align:start position:0%
+how proteins interact with other
+ 
+
+ align:start position:0%
+how proteins interact with other
+proteins not the function of the protein
+
+ align:start position:0%
+proteins not the function of the protein
+ 
+
+ align:start position:0%
+proteins not the function of the protein
+on its own probably still carries oxygen
+
+ align:start position:0%
+on its own probably still carries oxygen
+ 
+
+ align:start position:0%
+on its own probably still carries oxygen
+just fine but it's the mechanical change
+
+ align:start position:0%
+just fine but it's the mechanical change
+ 
+
+ align:start position:0%
+just fine but it's the mechanical change
+in the hemoglobin that causes the
+
+ align:start position:0%
+in the hemoglobin that causes the
+ 
+
+ align:start position:0%
+in the hemoglobin that causes the
+disease
+
+ align:start position:0%
+disease
+ 
+
+ align:start position:0%
+disease
+okay so sickle cell anemia the
+
+ align:start position:0%
+okay so sickle cell anemia the
+ 
+
+ align:start position:0%
+okay so sickle cell anemia the
+hemoglobin is now called hemoglobin s
+
+ align:start position:0%
+hemoglobin is now called hemoglobin s
+ 
+
+ align:start position:0%
+hemoglobin is now called hemoglobin s
+with that mutation that I just described
+
+ align:start position:0%
+with that mutation that I just described
+ 
+
+ align:start position:0%
+with that mutation that I just described
+and when people have a heterozygous it
+
+ align:start position:0%
+and when people have a heterozygous it
+ 
+
+ align:start position:0%
+and when people have a heterozygous it
+means they have one good copy of the
+
+ align:start position:0%
+means they have one good copy of the
+ 
+
+ align:start position:0%
+means they have one good copy of the
+gene that's normal and the copy of the
+
+ align:start position:0%
+gene that's normal and the copy of the
+ 
+
+ align:start position:0%
+gene that's normal and the copy of the
+gene that's the variant and you'll learn
+
+ align:start position:0%
+gene that's the variant and you'll learn
+ 
+
+ align:start position:0%
+gene that's the variant and you'll learn
+much more about this in human genetics
+
+ align:start position:0%
+much more about this in human genetics
+ 
+
+ align:start position:0%
+much more about this in human genetics
+when we talk about that later on so you
+
+ align:start position:0%
+when we talk about that later on so you
+ 
+
+ align:start position:0%
+when we talk about that later on so you
+have a lecture of the okay hemoglobin
+
+ align:start position:0%
+have a lecture of the okay hemoglobin
+ 
+
+ align:start position:0%
+have a lecture of the okay hemoglobin
+and the bad and the sickle cell
+
+ align:start position:0%
+and the bad and the sickle cell
+ 
+
+ align:start position:0%
+and the bad and the sickle cell
+hemoglobin people who are homozygous for
+
+ align:start position:0%
+hemoglobin people who are homozygous for
+ 
+
+ align:start position:0%
+hemoglobin people who are homozygous for
+the defect all of their hemoglobin is is
+
+ align:start position:0%
+the defect all of their hemoglobin is is
+ 
+
+ align:start position:0%
+the defect all of their hemoglobin is is
+disrupted and those are the people who
+
+ align:start position:0%
+disrupted and those are the people who
+ 
+
+ align:start position:0%
+disrupted and those are the people who
+really end up in hospital with a lot of
+
+ align:start position:0%
+really end up in hospital with a lot of
+ 
+
+ align:start position:0%
+really end up in hospital with a lot of
+transfusions and so on
+
+ align:start position:0%
+transfusions and so on
+ 
+
+ align:start position:0%
+transfusions and so on
+the heterozygous actually you can manage
+
+ align:start position:0%
+the heterozygous actually you can manage
+ 
+
+ align:start position:0%
+the heterozygous actually you can manage
+quite well with and I'm going to show
+
+ align:start position:0%
+quite well with and I'm going to show
+ 
+
+ align:start position:0%
+quite well with and I'm going to show
+you in a minute that in some parts of
+
+ align:start position:0%
+you in a minute that in some parts of
+ 
+
+ align:start position:0%
+you in a minute that in some parts of
+the world being heterozygous I having
+
+ align:start position:0%
+the world being heterozygous I having
+ 
+
+ align:start position:0%
+the world being heterozygous I having
+some of your hemoglobin with the defect
+
+ align:start position:0%
+some of your hemoglobin with the defect
+ 
+
+ align:start position:0%
+some of your hemoglobin with the defect
+and some without it actually comes with
+
+ align:start position:0%
+and some without it actually comes with
+ 
+
+ align:start position:0%
+and some without it actually comes with
+an advantage it's a really cool story
+
+ align:start position:0%
+an advantage it's a really cool story
+ 
+
+ align:start position:0%
+an advantage it's a really cool story
+okay so what I'm going to do is quickly
+
+ align:start position:0%
+okay so what I'm going to do is quickly
+ 
+
+ align:start position:0%
+okay so what I'm going to do is quickly
+show you the wire structure okay so this
+
+ align:start position:0%
+show you the wire structure okay so this
+ 
+
+ align:start position:0%
+show you the wire structure okay so this
+is the structure that elucidated the
+
+ align:start position:0%
+is the structure that elucidated the
+ 
+
+ align:start position:0%
+is the structure that elucidated the
+real reason for this for the the
+
+ align:start position:0%
+real reason for this for the the
+ 
+
+ align:start position:0%
+real reason for this for the the
+interaction what happens when you have
+
+ align:start position:0%
+interaction what happens when you have
+ 
+
+ align:start position:0%
+interaction what happens when you have
+this mutation okay and it was a
+
+ align:start position:0%
+this mutation okay and it was a
+ 
+
+ align:start position:0%
+this mutation okay and it was a
+structure that was captured of a dimer
+
+ align:start position:0%
+structure that was captured of a dimer
+ 
+
+ align:start position:0%
+structure that was captured of a dimer
+of hemoglobin molecules where you
+
+ align:start position:0%
+of hemoglobin molecules where you
+ 
+
+ align:start position:0%
+of hemoglobin molecules where you
+really see what was happening at the
+
+ align:start position:0%
+really see what was happening at the
+ 
+
+ align:start position:0%
+really see what was happening at the
+interface and the sorts of changes that
+
+ align:start position:0%
+interface and the sorts of changes that
+ 
+
+ align:start position:0%
+interface and the sorts of changes that
+have been put in place by that variation
+
+ align:start position:0%
+have been put in place by that variation
+ 
+
+ align:start position:0%
+have been put in place by that variation
+from the charged to the neutral
+
+ align:start position:0%
+from the charged to the neutral
+ 
+
+ align:start position:0%
+from the charged to the neutral
+structure so for any of you who want to
+
+ align:start position:0%
+structure so for any of you who want to
+ 
+
+ align:start position:0%
+structure so for any of you who want to
+pop by I can start to show you how to
+
+ align:start position:0%
+pop by I can start to show you how to
+ 
+
+ align:start position:0%
+pop by I can start to show you how to
+manipulate pi mol we can do that
+
+ align:start position:0%
+manipulate pi mol we can do that
+ 
+
+ align:start position:0%
+manipulate pi mol we can do that
+separately from class but this is a
+
+ align:start position:0%
+separately from class but this is a
+ 
+
+ align:start position:0%
+separately from class but this is a
+dimer of tetramers and if I just show
+
+ align:start position:0%
+dimer of tetramers and if I just show
+ 
+
+ align:start position:0%
+dimer of tetramers and if I just show
+you just some of the subunits I can
+
+ align:start position:0%
+you just some of the subunits I can
+ 
+
+ align:start position:0%
+you just some of the subunits I can
+actually show you how there's two of
+
+ align:start position:0%
+actually show you how there's two of
+ 
+
+ align:start position:0%
+actually show you how there's two of
+each subunit in each structure so if I
+
+ align:start position:0%
+each subunit in each structure so if I
+ 
+
+ align:start position:0%
+each subunit in each structure so if I
+go I can pick some out every other 1g
+
+ align:start position:0%
+go I can pick some out every other 1g
+ 
+
+ align:start position:0%
+go I can pick some out every other 1g
+and then I can color them a different
+
+ align:start position:0%
+and then I can color them a different
+ 
+
+ align:start position:0%
+and then I can color them a different
+color you can see where the globins
+
+ align:start position:0%
+color you can see where the globins
+ 
+
+ align:start position:0%
+color you can see where the globins
+where the beta globin czar and where the
+
+ align:start position:0%
+where the beta globin czar and where the
+ 
+
+ align:start position:0%
+where the beta globin czar and where the
+alpha globin czar that still looks like
+
+ align:start position:0%
+alpha globin czar that still looks like
+ 
+
+ align:start position:0%
+alpha globin czar that still looks like
+chicken wire it's very unsatisfactory so
+
+ align:start position:0%
+chicken wire it's very unsatisfactory so
+ 
+
+ align:start position:0%
+chicken wire it's very unsatisfactory so
+what I can do is I can show you
+
+ align:start position:0%
+what I can do is I can show you
+ 
+
+ align:start position:0%
+what I can do is I can show you
+everything as a cartoon and get rid of
+
+ align:start position:0%
+everything as a cartoon and get rid of
+ 
+
+ align:start position:0%
+everything as a cartoon and get rid of
+all those little lines and then you can
+
+ align:start position:0%
+all those little lines and then you can
+ 
+
+ align:start position:0%
+all those little lines and then you can
+see perfectly the to the structure where
+
+ align:start position:0%
+see perfectly the to the structure where
+ 
+
+ align:start position:0%
+see perfectly the to the structure where
+you see two beta globin z' and two alpha
+
+ align:start position:0%
+you see two beta globin z' and two alpha
+ 
+
+ align:start position:0%
+you see two beta globin z' and two alpha
+globin x' in each structure okay so what
+
+ align:start position:0%
+globin x' in each structure okay so what
+ 
+
+ align:start position:0%
+globin x' in each structure okay so what
+we're gonna do next is zoom in to see
+
+ align:start position:0%
+we're gonna do next is zoom in to see
+ 
+
+ align:start position:0%
+we're gonna do next is zoom in to see
+what's happening where we've done this
+
+ align:start position:0%
+what's happening where we've done this
+ 
+
+ align:start position:0%
+what's happening where we've done this
+mutation what's going on with the
+
+ align:start position:0%
+mutation what's going on with the
+ 
+
+ align:start position:0%
+mutation what's going on with the
+placement of the baleen in that
+
+ align:start position:0%
+placement of the baleen in that
+ 
+
+ align:start position:0%
+placement of the baleen in that
+structure all right and wherever I put a
+
+ align:start position:0%
+structure all right and wherever I put a
+ 
+
+ align:start position:0%
+structure all right and wherever I put a
+fork four letter code so that one was
+
+ align:start position:0%
+fork four letter code so that one was
+ 
+
+ align:start position:0%
+fork four letter code so that one was
+two HBS that's what's known as the
+
+ align:start position:0%
+two HBS that's what's known as the
+ 
+
+ align:start position:0%
+two HBS that's what's known as the
+protein databank code and it enables you
+
+ align:start position:0%
+protein databank code and it enables you
+ 
+
+ align:start position:0%
+protein databank code and it enables you
+to go fetch the coordinates of that
+
+ align:start position:0%
+to go fetch the coordinates of that
+ 
+
+ align:start position:0%
+to go fetch the coordinates of that
+protein so if any of you for the late
+
+ align:start position:0%
+protein so if any of you for the late
+ 
+
+ align:start position:0%
+protein so if any of you for the late
+project want to do a protein structure
+
+ align:start position:0%
+project want to do a protein structure
+ 
+
+ align:start position:0%
+project want to do a protein structure
+and print it come to me and I'll explain
+
+ align:start position:0%
+and print it come to me and I'll explain
+ 
+
+ align:start position:0%
+and print it come to me and I'll explain
+a lot more about that or all the TAS can
+
+ align:start position:0%
+a lot more about that or all the TAS can
+ 
+
+ align:start position:0%
+a lot more about that or all the TAS can
+also do that so let me now move you to
+
+ align:start position:0%
+also do that so let me now move you to
+ 
+
+ align:start position:0%
+also do that so let me now move you to
+looking in closely to the variations so
+
+ align:start position:0%
+looking in closely to the variations so
+ 
+
+ align:start position:0%
+looking in closely to the variations so
+what I've done here is I've actually
+
+ align:start position:0%
+what I've done here is I've actually
+ 
+
+ align:start position:0%
+what I've done here is I've actually
+colored the beta globin spurple and the
+
+ align:start position:0%
+colored the beta globin spurple and the
+ 
+
+ align:start position:0%
+colored the beta globin spurple and the
+Alpha globin is a cyan colored you can
+
+ align:start position:0%
+Alpha globin is a cyan colored you can
+ 
+
+ align:start position:0%
+Alpha globin is a cyan colored you can
+see the hems in each of the subunits
+
+ align:start position:0%
+see the hems in each of the subunits
+ 
+
+ align:start position:0%
+see the hems in each of the subunits
+those are those red wire things and now
+
+ align:start position:0%
+those are those red wire things and now
+ 
+
+ align:start position:0%
+those are those red wire things and now
+we've zoomed in to the place where the
+
+ align:start position:0%
+we've zoomed in to the place where the
+ 
+
+ align:start position:0%
+we've zoomed in to the place where the
+mutation is where you have a baleen
+
+ align:start position:0%
+mutation is where you have a baleen
+ 
+
+ align:start position:0%
+mutation is where you have a baleen
+instead of a carboxylic acid
+
+ align:start position:0%
+instead of a carboxylic acid
+ 
+
+ align:start position:0%
+instead of a carboxylic acid
+and what you can see from this image
+
+ align:start position:0%
+and what you can see from this image
+ 
+
+ align:start position:0%
+and what you can see from this image
+which should stop is that the baleen on
+
+ align:start position:0%
+which should stop is that the baleen on
+ 
+
+ align:start position:0%
+which should stop is that the baleen on
+one subunit in one homo tetramer
+
+ align:start position:0%
+one subunit in one homo tetramer
+ 
+
+ align:start position:0%
+one subunit in one homo tetramer
+interacts with a sticky patch on another
+
+ align:start position:0%
+interacts with a sticky patch on another
+ 
+
+ align:start position:0%
+interacts with a sticky patch on another
+subunit that's made up of phenylalanine
+
+ align:start position:0%
+subunit that's made up of phenylalanine
+ 
+
+ align:start position:0%
+subunit that's made up of phenylalanine
+85 in the adjacent protein and leucine
+
+ align:start position:0%
+85 in the adjacent protein and leucine
+ 
+
+ align:start position:0%
+85 in the adjacent protein and leucine
+88 in the adjacent protein so this
+
+ align:start position:0%
+88 in the adjacent protein so this
+ 
+
+ align:start position:0%
+88 in the adjacent protein so this
+sticky patch on one surface glues on to
+
+ align:start position:0%
+sticky patch on one surface glues on to
+ 
+
+ align:start position:0%
+sticky patch on one surface glues on to
+a sticky patch on the surface of another
+
+ align:start position:0%
+a sticky patch on the surface of another
+ 
+
+ align:start position:0%
+a sticky patch on the surface of another
+tetra mer if you had glutamic glutamate
+
+ align:start position:0%
+tetra mer if you had glutamic glutamate
+ 
+
+ align:start position:0%
+tetra mer if you had glutamic glutamate
+there would that form no in fact it
+
+ align:start position:0%
+there would that form no in fact it
+ 
+
+ align:start position:0%
+there would that form no in fact it
+would be quite deterred from forming
+
+ align:start position:0%
+would be quite deterred from forming
+ 
+
+ align:start position:0%
+would be quite deterred from forming
+because you don't want to cram that
+
+ align:start position:0%
+because you don't want to cram that
+ 
+
+ align:start position:0%
+because you don't want to cram that
+negatively charged element into those
+
+ align:start position:0%
+negatively charged element into those
+ 
+
+ align:start position:0%
+negatively charged element into those
+two hydrophobic residues so what you've
+
+ align:start position:0%
+two hydrophobic residues so what you've
+ 
+
+ align:start position:0%
+two hydrophobic residues so what you've
+gone from is a situation where this
+
+ align:start position:0%
+gone from is a situation where this
+ 
+
+ align:start position:0%
+gone from is a situation where this
+really is fine on a surface it's
+
+ align:start position:0%
+really is fine on a surface it's
+ 
+
+ align:start position:0%
+really is fine on a surface it's
+hydrated it's not sticking to anything
+
+ align:start position:0%
+hydrated it's not sticking to anything
+ 
+
+ align:start position:0%
+hydrated it's not sticking to anything
+to another situation where you have
+
+ align:start position:0%
+to another situation where you have
+ 
+
+ align:start position:0%
+to another situation where you have
+phenylalanine and leucine which are both
+
+ align:start position:0%
+phenylalanine and leucine which are both
+ 
+
+ align:start position:0%
+phenylalanine and leucine which are both
+hydrophobic providing a catch on the one
+
+ align:start position:0%
+hydrophobic providing a catch on the one
+ 
+
+ align:start position:0%
+hydrophobic providing a catch on the one
+tetramer where the the valine from the
+
+ align:start position:0%
+tetramer where the the valine from the
+ 
+
+ align:start position:0%
+tetramer where the the valine from the
+other tetramer combined and because the
+
+ align:start position:0%
+other tetramer combined and because the
+ 
+
+ align:start position:0%
+other tetramer combined and because the
+molecules are tetra mer on each of the
+
+ align:start position:0%
+molecules are tetra mer on each of the
+ 
+
+ align:start position:0%
+molecules are tetra mer on each of the
+subunits there is also another valine
+
+ align:start position:0%
+subunits there is also another valine
+ 
+
+ align:start position:0%
+subunits there is also another valine
+that will go off and do that elsewhere
+
+ align:start position:0%
+that will go off and do that elsewhere
+ 
+
+ align:start position:0%
+that will go off and do that elsewhere
+and another valine and there's one you
+
+ align:start position:0%
+and another valine and there's one you
+ 
+
+ align:start position:0%
+and another valine and there's one you
+can't see that's tucked behind so that's
+
+ align:start position:0%
+can't see that's tucked behind so that's
+ 
+
+ align:start position:0%
+can't see that's tucked behind so that's
+why the hemoglobin forms these
+
+ align:start position:0%
+why the hemoglobin forms these
+ 
+
+ align:start position:0%
+why the hemoglobin forms these
+structures because every hemoglobin
+
+ align:start position:0%
+structures because every hemoglobin
+ 
+
+ align:start position:0%
+structures because every hemoglobin
+molecule has two places to stick to
+
+ align:start position:0%
+molecule has two places to stick to
+ 
+
+ align:start position:0%
+molecule has two places to stick to
+another hemoglobin tetra mer and so on
+
+ align:start position:0%
+another hemoglobin tetra mer and so on
+ 
+
+ align:start position:0%
+another hemoglobin tetra mer and so on
+so think of the repercussions from one
+
+ align:start position:0%
+so think of the repercussions from one
+ 
+
+ align:start position:0%
+so think of the repercussions from one
+nucleic acid change that's really quite
+
+ align:start position:0%
+nucleic acid change that's really quite
+ 
+
+ align:start position:0%
+nucleic acid change that's really quite
+remarkable so what we've seen here is
+
+ align:start position:0%
+remarkable so what we've seen here is
+ 
+
+ align:start position:0%
+remarkable so what we've seen here is
+that that change occurs so just just a
+
+ align:start position:0%
+that that change occurs so just just a
+ 
+
+ align:start position:0%
+that that change occurs so just just a
+couple of moments for you to think about
+
+ align:start position:0%
+couple of moments for you to think about
+ 
+
+ align:start position:0%
+couple of moments for you to think about
+this you can have variations at that
+
+ align:start position:0%
+this you can have variations at that
+ 
+
+ align:start position:0%
+this you can have variations at that
+site that won't cause a problem which
+
+ align:start position:0%
+site that won't cause a problem which
+ 
+
+ align:start position:0%
+site that won't cause a problem which
+ones of these do you think at least
+
+ align:start position:0%
+ones of these do you think at least
+ 
+
+ align:start position:0%
+ones of these do you think at least
+likely to cause a sickle cell type of
+
+ align:start position:0%
+likely to cause a sickle cell type of
+ 
+
+ align:start position:0%
+likely to cause a sickle cell type of
+phenomenon so tyrosine serine aspartic
+
+ align:start position:0%
+phenomenon so tyrosine serine aspartic
+ 
+
+ align:start position:0%
+phenomenon so tyrosine serine aspartic
+acid and lysine so I'm going to change
+
+ align:start position:0%
+acid and lysine so I'm going to change
+ 
+
+ align:start position:0%
+acid and lysine so I'm going to change
+the glutamate to something else which
+
+ align:start position:0%
+the glutamate to something else which
+ 
+
+ align:start position:0%
+the glutamate to something else which
+one's going to have a perfectly normal
+
+ align:start position:0%
+one's going to have a perfectly normal
+ 
+
+ align:start position:0%
+one's going to have a perfectly normal
+hemoglobin there's one that stands out
+
+ align:start position:0%
+hemoglobin there's one that stands out
+ 
+
+ align:start position:0%
+hemoglobin there's one that stands out
+yeah aspartic that's fine no problem it
+
+ align:start position:0%
+yeah aspartic that's fine no problem it
+ 
+
+ align:start position:0%
+yeah aspartic that's fine no problem it
+just switched it for her it's younger
+
+ align:start position:0%
+just switched it for her it's younger
+ 
+
+ align:start position:0%
+just switched it for her it's younger
+brother wait which one of the others and
+
+ align:start position:0%
+brother wait which one of the others and
+ 
+
+ align:start position:0%
+brother wait which one of the others and
+and in many cases here you could
+
+ align:start position:0%
+and in many cases here you could
+ 
+
+ align:start position:0%
+and in many cases here you could
+probably argue your way to all of them
+
+ align:start position:0%
+probably argue your way to all of them
+ 
+
+ align:start position:0%
+probably argue your way to all of them
+but one would be pretty bad which one
+
+ align:start position:0%
+but one would be pretty bad which one
+ 
+
+ align:start position:0%
+but one would be pretty bad which one
+would be pretty bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tyrosine exactly it's another even
+
+ align:start position:0%
+tyrosine exactly it's another even
+ 
+
+ align:start position:0%
+tyrosine exactly it's another even
+though it's got that Oh H group it's
+
+ align:start position:0%
+though it's got that Oh H group it's
+ 
+
+ align:start position:0%
+though it's got that Oh H group it's
+still pretty hydrophobic because of that
+
+ align:start position:0%
+still pretty hydrophobic because of that
+ 
+
+ align:start position:0%
+still pretty hydrophobic because of that
+ring system there what about the other
+
+ align:start position:0%
+ring system there what about the other
+ 
+
+ align:start position:0%
+ring system there what about the other
+two serine and lysine what do you think
+
+ align:start position:0%
+two serine and lysine what do you think
+ 
+
+ align:start position:0%
+two serine and lysine what do you think
+which one would probably be in fact the
+
+ align:start position:0%
+which one would probably be in fact the
+ 
+
+ align:start position:0%
+which one would probably be in fact the
+least detrimental of those remaining two
+
+ align:start position:0%
+least detrimental of those remaining two
+ 
+
+ align:start position:0%
+least detrimental of those remaining two
+and give me the reason as well yes
+
+ align:start position:0%
+and give me the reason as well yes
+ 
+
+ align:start position:0%
+and give me the reason as well yes
+lysine I think it would be lysine
+
+ align:start position:0%
+lysine I think it would be lysine
+ 
+
+ align:start position:0%
+lysine I think it would be lysine
+because lysine is now positively charged
+
+ align:start position:0%
+because lysine is now positively charged
+ 
+
+ align:start position:0%
+because lysine is now positively charged
+it's equally unlikely to want to do this
+
+ align:start position:0%
+it's equally unlikely to want to do this
+ 
+
+ align:start position:0%
+it's equally unlikely to want to do this
+goofy interaction because it is also
+
+ align:start position:0%
+goofy interaction because it is also
+ 
+
+ align:start position:0%
+goofy interaction because it is also
+charged just charged in the other
+
+ align:start position:0%
+charged just charged in the other
+ 
+
+ align:start position:0%
+charged just charged in the other
+direction but one could also argue that
+
+ align:start position:0%
+direction but one could also argue that
+ 
+
+ align:start position:0%
+direction but one could also argue that
+serine would be okay
+
+ align:start position:0%
+serine would be okay
+ 
+
+ align:start position:0%
+serine would be okay
+because it's got it's a little bit more
+
+ align:start position:0%
+because it's got it's a little bit more
+ 
+
+ align:start position:0%
+because it's got it's a little bit more
+not a polar so it wouldn't cause as much
+
+ align:start position:0%
+not a polar so it wouldn't cause as much
+ 
+
+ align:start position:0%
+not a polar so it wouldn't cause as much
+problem okay
+
+ align:start position:0%
+problem okay
+ 
+
+ align:start position:0%
+problem okay
+finally the this issue with sickle cell
+
+ align:start position:0%
+finally the this issue with sickle cell
+ 
+
+ align:start position:0%
+finally the this issue with sickle cell
+anemia there's some fascinating data
+
+ align:start position:0%
+anemia there's some fascinating data
+ 
+
+ align:start position:0%
+anemia there's some fascinating data
+that shows in parts of the world for
+
+ align:start position:0%
+that shows in parts of the world for
+ 
+
+ align:start position:0%
+that shows in parts of the world for
+example during a drug trial for
+
+ align:start position:0%
+example during a drug trial for
+ 
+
+ align:start position:0%
+example during a drug trial for
+Plasmodium falciparum one of the
+
+ align:start position:0%
+Plasmodium falciparum one of the
+ 
+
+ align:start position:0%
+Plasmodium falciparum one of the
+causative agents of malaria they found
+
+ align:start position:0%
+causative agents of malaria they found
+ 
+
+ align:start position:0%
+causative agents of malaria they found
+that one out of 15 people with the
+
+ align:start position:0%
+that one out of 15 people with the
+ 
+
+ align:start position:0%
+that one out of 15 people with the
+sickle-cell trait was infected with
+
+ align:start position:0%
+sickle-cell trait was infected with
+ 
+
+ align:start position:0%
+sickle-cell trait was infected with
+malaria whereas the the people who were
+
+ align:start position:0%
+malaria whereas the the people who were
+ 
+
+ align:start position:0%
+malaria whereas the the people who were
+healthy normal homozygous for the right
+
+ align:start position:0%
+healthy normal homozygous for the right
+ 
+
+ align:start position:0%
+healthy normal homozygous for the right
+hemoglobin 14 out of 15 were infected
+
+ align:start position:0%
+hemoglobin 14 out of 15 were infected
+ 
+
+ align:start position:0%
+hemoglobin 14 out of 15 were infected
+with Plasmodium falciparum and now what
+
+ align:start position:0%
+with Plasmodium falciparum and now what
+ 
+
+ align:start position:0%
+with Plasmodium falciparum and now what
+do you think why do you think that is
+
+ align:start position:0%
+do you think why do you think that is
+ 
+
+ align:start position:0%
+do you think why do you think that is
+how can we relate the infectivity of a
+
+ align:start position:0%
+how can we relate the infectivity of a
+ 
+
+ align:start position:0%
+how can we relate the infectivity of a
+parasite with the shape of a cell we've
+
+ align:start position:0%
+parasite with the shape of a cell we've
+ 
+
+ align:start position:0%
+parasite with the shape of a cell we've
+gone from these juicy looking red blood
+
+ align:start position:0%
+gone from these juicy looking red blood
+ 
+
+ align:start position:0%
+gone from these juicy looking red blood
+cells nice and round and probably quite
+
+ align:start position:0%
+cells nice and round and probably quite
+ 
+
+ align:start position:0%
+cells nice and round and probably quite
+open to a cell that sort of difficult
+
+ align:start position:0%
+open to a cell that sort of difficult
+ 
+
+ align:start position:0%
+open to a cell that sort of difficult
+shape so it turns out that the parasite
+
+ align:start position:0%
+shape so it turns out that the parasite
+ 
+
+ align:start position:0%
+shape so it turns out that the parasite
+doesn't want to infect the sickle cells
+
+ align:start position:0%
+doesn't want to infect the sickle cells
+ 
+
+ align:start position:0%
+doesn't want to infect the sickle cells
+that cells red blood cells anywhere near
+
+ align:start position:0%
+that cells red blood cells anywhere near
+ 
+
+ align:start position:0%
+that cells red blood cells anywhere near
+as well and there are for example other
+
+ align:start position:0%
+as well and there are for example other
+ 
+
+ align:start position:0%
+as well and there are for example other
+Bloods tested which shows the same
+
+ align:start position:0%
+Bloods tested which shows the same
+ 
+
+ align:start position:0%
+Bloods tested which shows the same
+correlation
+
+ align:start position:0%
+correlation
+ 
+
+ align:start position:0%
+correlation
+and here's a map of Africa where you see
+
+ align:start position:0%
+and here's a map of Africa where you see
+ 
+
+ align:start position:0%
+and here's a map of Africa where you see
+a massive overlap of the prevalence of
+
+ align:start position:0%
+a massive overlap of the prevalence of
+ 
+
+ align:start position:0%
+a massive overlap of the prevalence of
+the sickle cell trait and the and the
+
+ align:start position:0%
+the sickle cell trait and the and the
+ 
+
+ align:start position:0%
+the sickle cell trait and the and the
+presence of Plasmodium falciparum so
+
+ align:start position:0%
+presence of Plasmodium falciparum so
+ 
+
+ align:start position:0%
+presence of Plasmodium falciparum so
+there's there's there is a evolutionary
+
+ align:start position:0%
+there's there's there is a evolutionary
+ 
+
+ align:start position:0%
+there's there's there is a evolutionary
+advantage to having the heterozygous
+
+ align:start position:0%
+advantage to having the heterozygous
+ 
+
+ align:start position:0%
+advantage to having the heterozygous
+variant where you have some normal
+
+ align:start position:0%
+variant where you have some normal
+ 
+
+ align:start position:0%
+variant where you have some normal
+hemoglobin but some of the sickling
+
+ align:start position:0%
+hemoglobin but some of the sickling
+ 
+
+ align:start position:0%
+hemoglobin but some of the sickling
+hemoglobin because it confers you some
+
+ align:start position:0%
+hemoglobin because it confers you some
+ 
+
+ align:start position:0%
+hemoglobin because it confers you some
+resistance to term to malaria it's not
+
+ align:start position:0%
+resistance to term to malaria it's not
+ 
+
+ align:start position:0%
+resistance to term to malaria it's not
+good to have both of them the variant
+
+ align:start position:0%
+good to have both of them the variant
+ 
+
+ align:start position:0%
+good to have both of them the variant
+that causes sickling because that's
+
+ align:start position:0%
+that causes sickling because that's
+ 
+
+ align:start position:0%
+that causes sickling because that's
+painful and it really causes a lot of
+
+ align:start position:0%
+painful and it really causes a lot of
+ 
+
+ align:start position:0%
+painful and it really causes a lot of
+health disorders it's just when you have
+
+ align:start position:0%
+health disorders it's just when you have
+ 
+
+ align:start position:0%
+health disorders it's just when you have
+one of each gene encoding both variants
+
+ align:start position:0%
+one of each gene encoding both variants
+ 
+
+ align:start position:0%
+one of each gene encoding both variants
+okay all right great okay so now we're
+
+ align:start position:0%
+okay all right great okay so now we're
+ 
+
+ align:start position:0%
+okay all right great okay so now we're
+gonna talk about enzymes and these are
+
+ align:start position:0%
+gonna talk about enzymes and these are
+ 
+
+ align:start position:0%
+gonna talk about enzymes and these are
+the proteins that catalyze reactions any
+
+ align:start position:0%
+the proteins that catalyze reactions any
+ 
+
+ align:start position:0%
+the proteins that catalyze reactions any
+questions about that so while a lot of
+
+ align:start position:0%
+questions about that so while a lot of
+ 
+
+ align:start position:0%
+questions about that so while a lot of
+disease states actually might be bred
+
+ align:start position:0%
+disease states actually might be bred
+ 
+
+ align:start position:0%
+disease states actually might be bred
+out because someone would have be at a
+
+ align:start position:0%
+out because someone would have be at a
+ 
+
+ align:start position:0%
+out because someone would have be at a
+disadvantage
+
+ align:start position:0%
+disadvantage
+ 
+
+ align:start position:0%
+disadvantage
+with a particular disease in this case
+
+ align:start position:0%
+with a particular disease in this case
+ 
+
+ align:start position:0%
+with a particular disease in this case
+that trait has been maintained because
+
+ align:start position:0%
+that trait has been maintained because
+ 
+
+ align:start position:0%
+that trait has been maintained because
+it offers a very different advantage
+
+ align:start position:0%
+it offers a very different advantage
+ 
+
+ align:start position:0%
+it offers a very different advantage
+with respect to disease okay let's talk
+
+ align:start position:0%
+with respect to disease okay let's talk
+ 
+
+ align:start position:0%
+with respect to disease okay let's talk
+about enzymes for a moment all for the
+
+ align:start position:0%
+about enzymes for a moment all for the
+ 
+
+ align:start position:0%
+about enzymes for a moment all for the
+rest of the class in fact okay so
+
+ align:start position:0%
+rest of the class in fact okay so
+ 
+
+ align:start position:0%
+rest of the class in fact okay so
+enzymes are the heavy lifters of the
+
+ align:start position:0%
+enzymes are the heavy lifters of the
+ 
+
+ align:start position:0%
+enzymes are the heavy lifters of the
+protein world because they catalyze all
+
+ align:start position:0%
+protein world because they catalyze all
+ 
+
+ align:start position:0%
+protein world because they catalyze all
+the reactions in metabolism in
+
+ align:start position:0%
+the reactions in metabolism in
+ 
+
+ align:start position:0%
+the reactions in metabolism in
+biosynthesis all kinds of
+
+ align:start position:0%
+biosynthesis all kinds of
+ 
+
+ align:start position:0%
+biosynthesis all kinds of
+transformations that make you what you
+
+ align:start position:0%
+transformations that make you what you
+ 
+
+ align:start position:0%
+transformations that make you what you
+are enzymes a protein based catalysts
+
+ align:start position:0%
+are enzymes a protein based catalysts
+ 
+
+ align:start position:0%
+are enzymes a protein based catalysts
+you will know that writing again there
+
+ align:start position:0%
+you will know that writing again there
+ 
+
+ align:start position:0%
+you will know that writing again there
+were a couple of other terms I just
+
+ align:start position:0%
+were a couple of other terms I just
+ 
+
+ align:start position:0%
+were a couple of other terms I just
+quickly want to give you so an enzyme
+
+ align:start position:0%
+quickly want to give you so an enzyme
+ 
+
+ align:start position:0%
+quickly want to give you so an enzyme
+there's also a term known as an ISO xym
+
+ align:start position:0%
+there's also a term known as an ISO xym
+ 
+
+ align:start position:0%
+there's also a term known as an ISO xym
+and an allison you may see them you'll
+
+ align:start position:0%
+and an allison you may see them you'll
+ 
+
+ align:start position:0%
+and an allison you may see them you'll
+see Alice
+
+ align:start position:0%
+see Alice
+ 
+
+ align:start position:0%
+see Alice
+less commonly but you'll see Isis I'm
+
+ align:start position:0%
+less commonly but you'll see Isis I'm
+ 
+
+ align:start position:0%
+less commonly but you'll see Isis I'm
+quite commonly an Isis I'm of one enzyme
+
+ align:start position:0%
+quite commonly an Isis I'm of one enzyme
+ 
+
+ align:start position:0%
+quite commonly an Isis I'm of one enzyme
+is a variation on the enzyme that
+
+ align:start position:0%
+is a variation on the enzyme that
+ 
+
+ align:start position:0%
+is a variation on the enzyme that
+catalyzes the same reaction but it's
+
+ align:start position:0%
+catalyzes the same reaction but it's
+ 
+
+ align:start position:0%
+catalyzes the same reaction but it's
+expressed on a different gene an aloes
+
+ align:start position:0%
+expressed on a different gene an aloes
+ 
+
+ align:start position:0%
+expressed on a different gene an aloes
+I'm is the same enzyme but with a
+
+ align:start position:0%
+I'm is the same enzyme but with a
+ 
+
+ align:start position:0%
+I'm is the same enzyme but with a
+variation in it so it's it's encoded by
+
+ align:start position:0%
+variation in it so it's it's encoded by
+ 
+
+ align:start position:0%
+variation in it so it's it's encoded by
+an allele of one gene so there it's just
+
+ align:start position:0%
+an allele of one gene so there it's just
+ 
+
+ align:start position:0%
+an allele of one gene so there it's just
+a variation of the gene that might have
+
+ align:start position:0%
+a variation of the gene that might have
+ 
+
+ align:start position:0%
+a variation of the gene that might have
+happened through a mutation still
+
+ align:start position:0%
+happened through a mutation still
+ 
+
+ align:start position:0%
+happened through a mutation still
+catalyzes the reaction but there's a
+
+ align:start position:0%
+catalyzes the reaction but there's a
+ 
+
+ align:start position:0%
+catalyzes the reaction but there's a
+change in slight change in the sequence
+
+ align:start position:0%
+change in slight change in the sequence
+ 
+
+ align:start position:0%
+change in slight change in the sequence
+but they're coded by the same gene same
+
+ align:start position:0%
+but they're coded by the same gene same
+ 
+
+ align:start position:0%
+but they're coded by the same gene same
+gene with a variation and as I said you
+
+ align:start position:0%
+gene with a variation and as I said you
+ 
+
+ align:start position:0%
+gene with a variation and as I said you
+will see the isozyme term more commonly
+
+ align:start position:0%
+will see the isozyme term more commonly
+ 
+
+ align:start position:0%
+will see the isozyme term more commonly
+than the al Azim term now why do we need
+
+ align:start position:0%
+than the al Azim term now why do we need
+ 
+
+ align:start position:0%
+than the al Azim term now why do we need
+enzymes well the problem is there are
+
+ align:start position:0%
+enzymes well the problem is there are
+ 
+
+ align:start position:0%
+enzymes well the problem is there are
+reactions physiologic reactions that we
+
+ align:start position:0%
+reactions physiologic reactions that we
+ 
+
+ align:start position:0%
+reactions physiologic reactions that we
+need to carry out that are just too hard
+
+ align:start position:0%
+need to carry out that are just too hard
+ 
+
+ align:start position:0%
+need to carry out that are just too hard
+to carry out at room temperature pH 7 in
+
+ align:start position:0%
+to carry out at room temperature pH 7 in
+ 
+
+ align:start position:0%
+to carry out at room temperature pH 7 in
+water they just don't occur so you need
+
+ align:start position:0%
+water they just don't occur so you need
+ 
+
+ align:start position:0%
+water they just don't occur so you need
+enzyme catalysis for all of your
+
+ align:start position:0%
+enzyme catalysis for all of your
+ 
+
+ align:start position:0%
+enzyme catalysis for all of your
+metabolic reactions let me just give you
+
+ align:start position:0%
+metabolic reactions let me just give you
+ 
+
+ align:start position:0%
+metabolic reactions let me just give you
+one trivial example this bond really no
+
+ align:start position:0%
+one trivial example this bond really no
+ 
+
+ align:start position:0%
+one trivial example this bond really no
+nicely now peptide or amide bond if I
+
+ align:start position:0%
+nicely now peptide or amide bond if I
+ 
+
+ align:start position:0%
+nicely now peptide or amide bond if I
+want to hydrolyze that if I want to
+
+ align:start position:0%
+want to hydrolyze that if I want to
+ 
+
+ align:start position:0%
+want to hydrolyze that if I want to
+break it open pH 7 physiologic
+
+ align:start position:0%
+break it open pH 7 physiologic
+ 
+
+ align:start position:0%
+break it open pH 7 physiologic
+temperatures so 37 see you know in water
+
+ align:start position:0%
+temperatures so 37 see you know in water
+ 
+
+ align:start position:0%
+temperatures so 37 see you know in water
+it would take me how many years is it
+
+ align:start position:0%
+it would take me how many years is it
+ 
+
+ align:start position:0%
+it would take me how many years is it
+the half-life of that bond would be 600
+
+ align:start position:0%
+the half-life of that bond would be 600
+ 
+
+ align:start position:0%
+the half-life of that bond would be 600
+years okay there and that's pretty
+
+ align:start position:0%
+years okay there and that's pretty
+ 
+
+ align:start position:0%
+years okay there and that's pretty
+untenable for digesting a Big Mac even
+
+ align:start position:0%
+untenable for digesting a Big Mac even
+ 
+
+ align:start position:0%
+untenable for digesting a Big Mac even
+even under the best of circumstances
+
+ align:start position:0%
+even under the best of circumstances
+ 
+
+ align:start position:0%
+even under the best of circumstances
+right so we
+
+ align:start position:0%
+right so we
+ 
+
+ align:start position:0%
+right so we
+need enzymes to speed up breaking down
+
+ align:start position:0%
+need enzymes to speed up breaking down
+ 
+
+ align:start position:0%
+need enzymes to speed up breaking down
+proteins carrying out reactions because
+
+ align:start position:0%
+proteins carrying out reactions because
+ 
+
+ align:start position:0%
+proteins carrying out reactions because
+otherwise we just can't we can't do
+
+ align:start position:0%
+otherwise we just can't we can't do
+ 
+
+ align:start position:0%
+otherwise we just can't we can't do
+anything so what I want to describe to
+
+ align:start position:0%
+anything so what I want to describe to
+ 
+
+ align:start position:0%
+anything so what I want to describe to
+you some of the details of how enzymes
+
+ align:start position:0%
+you some of the details of how enzymes
+ 
+
+ align:start position:0%
+you some of the details of how enzymes
+work and then how we can control the
+
+ align:start position:0%
+work and then how we can control the
+ 
+
+ align:start position:0%
+work and then how we can control the
+function of enzymes so typical enzymes
+
+ align:start position:0%
+function of enzymes so typical enzymes
+ 
+
+ align:start position:0%
+function of enzymes so typical enzymes
+take a substrate to a product some
+
+ align:start position:0%
+take a substrate to a product some
+ 
+
+ align:start position:0%
+take a substrate to a product some
+enzymes may take two substrates and make
+
+ align:start position:0%
+enzymes may take two substrates and make
+ 
+
+ align:start position:0%
+enzymes may take two substrates and make
+one product some enzymes may we take one
+
+ align:start position:0%
+one product some enzymes may we take one
+ 
+
+ align:start position:0%
+one product some enzymes may we take one
+substrate and make two products it just
+
+ align:start position:0%
+substrate and make two products it just
+ 
+
+ align:start position:0%
+substrate and make two products it just
+depends on the transformation that
+
+ align:start position:0%
+depends on the transformation that
+ 
+
+ align:start position:0%
+depends on the transformation that
+you're doing enzymes are classified into
+
+ align:start position:0%
+you're doing enzymes are classified into
+ 
+
+ align:start position:0%
+you're doing enzymes are classified into
+a bunch of different families but the
+
+ align:start position:0%
+a bunch of different families but the
+ 
+
+ align:start position:0%
+a bunch of different families but the
+thing that will tell you that something
+
+ align:start position:0%
+thing that will tell you that something
+ 
+
+ align:start position:0%
+thing that will tell you that something
+you're reading about is an enzyme is the
+
+ align:start position:0%
+you're reading about is an enzyme is the
+ 
+
+ align:start position:0%
+you're reading about is an enzyme is the
+suffix a s e at the end of the name of
+
+ align:start position:0%
+suffix a s e at the end of the name of
+ 
+
+ align:start position:0%
+suffix a s e at the end of the name of
+the enzyme so the enzyme that hydrolyzes
+
+ align:start position:0%
+the enzyme so the enzyme that hydrolyzes
+ 
+
+ align:start position:0%
+the enzyme so the enzyme that hydrolyzes
+the peptide bond or hydrolyzes proteins
+
+ align:start position:0%
+the peptide bond or hydrolyzes proteins
+ 
+
+ align:start position:0%
+the peptide bond or hydrolyzes proteins
+is called no big surprise a protease and
+
+ align:start position:0%
+is called no big surprise a protease and
+ 
+
+ align:start position:0%
+is called no big surprise a protease and
+you'll see later on ribonuclease DNA's
+
+ align:start position:0%
+you'll see later on ribonuclease DNA's
+ 
+
+ align:start position:0%
+you'll see later on ribonuclease DNA's
+oxidoreductases all kinds of rare
+
+ align:start position:0%
+oxidoreductases all kinds of rare
+ 
+
+ align:start position:0%
+oxidoreductases all kinds of rare
+reactions where if you see this term at
+
+ align:start position:0%
+reactions where if you see this term at
+ 
+
+ align:start position:0%
+reactions where if you see this term at
+the end of the name it's telling you
+
+ align:start position:0%
+the end of the name it's telling you
+ 
+
+ align:start position:0%
+the end of the name it's telling you
+quite loud and clear that it's an enzyme
+
+ align:start position:0%
+quite loud and clear that it's an enzyme
+ 
+
+ align:start position:0%
+quite loud and clear that it's an enzyme
+it's just a very sort of simple way of
+
+ align:start position:0%
+it's just a very sort of simple way of
+ 
+
+ align:start position:0%
+it's just a very sort of simple way of
+remembering now now enzymes promote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+promote reactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order that we can have them carried
+
+ align:start position:0%
+in order that we can have them carried
+ 
+
+ align:start position:0%
+in order that we can have them carried
+out at room temperature but we want to
+
+ align:start position:0%
+out at room temperature but we want to
+ 
+
+ align:start position:0%
+out at room temperature but we want to
+think about how they they carry out
+
+ align:start position:0%
+think about how they they carry out
+ 
+
+ align:start position:0%
+think about how they they carry out
+these changes and transformations what
+
+ align:start position:0%
+these changes and transformations what
+ 
+
+ align:start position:0%
+these changes and transformations what
+is it about the structure of the protein
+
+ align:start position:0%
+is it about the structure of the protein
+ 
+
+ align:start position:0%
+is it about the structure of the protein
+that enables these reactions but the
+
+ align:start position:0%
+that enables these reactions but the
+ 
+
+ align:start position:0%
+that enables these reactions but the
+first thing we have to do is take a look
+
+ align:start position:0%
+first thing we have to do is take a look
+ 
+
+ align:start position:0%
+first thing we have to do is take a look
+and the thermodynamics and kinetics of a
+
+ align:start position:0%
+and the thermodynamics and kinetics of a
+ 
+
+ align:start position:0%
+and the thermodynamics and kinetics of a
+transformation so before I go anywhere
+
+ align:start position:0%
+transformation so before I go anywhere
+ 
+
+ align:start position:0%
+transformation so before I go anywhere
+what I want to do is describe to you how
+
+ align:start position:0%
+what I want to do is describe to you how
+ 
+
+ align:start position:0%
+what I want to do is describe to you how
+enzymes work by thinking about the
+
+ align:start position:0%
+enzymes work by thinking about the
+ 
+
+ align:start position:0%
+enzymes work by thinking about the
+physical parameters that we describe the
+
+ align:start position:0%
+physical parameters that we describe the
+ 
+
+ align:start position:0%
+physical parameters that we describe the
+energetics of a transformation so in in
+
+ align:start position:0%
+energetics of a transformation so in in
+ 
+
+ align:start position:0%
+energetics of a transformation so in in
+thermodynamics you'll know Delta G is
+
+ align:start position:0%
+thermodynamics you'll know Delta G is
+ 
+
+ align:start position:0%
+thermodynamics you'll know Delta G is
+Delta H minus T Delta s and we're really
+
+ align:start position:0%
+Delta H minus T Delta s and we're really
+ 
+
+ align:start position:0%
+Delta H minus T Delta s and we're really
+only gonna worry about one of these
+
+ align:start position:0%
+only gonna worry about one of these
+ 
+
+ align:start position:0%
+only gonna worry about one of these
+terms we're gonna worry about Delta G
+
+ align:start position:0%
+terms we're gonna worry about Delta G
+ 
+
+ align:start position:0%
+terms we're gonna worry about Delta G
+and I'll explain why so Delta G is the
+
+ align:start position:0%
+and I'll explain why so Delta G is the
+ 
+
+ align:start position:0%
+and I'll explain why so Delta G is the
+Gibbs free energy H is the enthalpy T is
+
+ align:start position:0%
+Gibbs free energy H is the enthalpy T is
+ 
+
+ align:start position:0%
+Gibbs free energy H is the enthalpy T is
+the temperature in Kelvin and then s is
+
+ align:start position:0%
+the temperature in Kelvin and then s is
+ 
+
+ align:start position:0%
+the temperature in Kelvin and then s is
+entropy so these are two terms when
+
+ align:start position:0%
+entropy so these are two terms when
+ 
+
+ align:start position:0%
+entropy so these are two terms when
+you're looking at an energy diagram we
+
+ align:start position:0%
+you're looking at an energy diagram we
+ 
+
+ align:start position:0%
+you're looking at an energy diagram we
+generally think about reactions where we
+
+ align:start position:0%
+generally think about reactions where we
+ 
+
+ align:start position:0%
+generally think about reactions where we
+describe the y coordinate as the change
+
+ align:start position:0%
+describe the y coordinate as the change
+ 
+
+ align:start position:0%
+describe the y coordinate as the change
+in Delta G the change in the free energy
+
+ align:start position:0%
+in Delta G the change in the free energy
+ 
+
+ align:start position:0%
+in Delta G the change in the free energy
+and the x coordinate is your reaction
+
+ align:start position:0%
+and the x coordinate is your reaction
+ 
+
+ align:start position:0%
+and the x coordinate is your reaction
+coordinate so in going from a substrate
+
+ align:start position:0%
+coordinate so in going from a substrate
+ 
+
+ align:start position:0%
+coordinate so in going from a substrate
+to a product we generally have a
+
+ align:start position:0%
+to a product we generally have a
+ 
+
+ align:start position:0%
+to a product we generally have a
+situation where we have a substrate at a
+
+ align:start position:0%
+situation where we have a substrate at a
+ 
+
+ align:start position:0%
+situation where we have a substrate at a
+certain energy and then maybe a product
+
+ align:start position:0%
+certain energy and then maybe a product
+ 
+
+ align:start position:0%
+certain energy and then maybe a product
+at a different energy and we're going to
+
+ align:start position:0%
+at a different energy and we're going to
+ 
+
+ align:start position:0%
+at a different energy and we're going to
+talk about the details of that so why do
+
+ align:start position:0%
+talk about the details of that so why do
+ 
+
+ align:start position:0%
+talk about the details of that so why do
+we deal with Gibbs free energy not an
+
+ align:start position:0%
+we deal with Gibbs free energy not an
+ 
+
+ align:start position:0%
+we deal with Gibbs free energy not an
+enthalpy does anyone know okay
+
+ align:start position:0%
+enthalpy does anyone know okay
+ 
+
+ align:start position:0%
+enthalpy does anyone know okay
+enthalpy describes the energies of
+
+ align:start position:0%
+enthalpy describes the energies of
+ 
+
+ align:start position:0%
+enthalpy describes the energies of
+all the bonds in a molecule but when
+
+ align:start position:0%
+all the bonds in a molecule but when
+ 
+
+ align:start position:0%
+all the bonds in a molecule but when
+you're doing an enzyme catalyzed
+
+ align:start position:0%
+you're doing an enzyme catalyzed
+ 
+
+ align:start position:0%
+you're doing an enzyme catalyzed
+transformation you're not busting open
+
+ align:start position:0%
+transformation you're not busting open
+ 
+
+ align:start position:0%
+transformation you're not busting open
+all of those bonds you're not breaking
+
+ align:start position:0%
+all of those bonds you're not breaking
+ 
+
+ align:start position:0%
+all of those bonds you're not breaking
+something down to carbon hydrogen and
+
+ align:start position:0%
+something down to carbon hydrogen and
+ 
+
+ align:start position:0%
+something down to carbon hydrogen and
+oxygen you're only dealing with parts of
+
+ align:start position:0%
+oxygen you're only dealing with parts of
+ 
+
+ align:start position:0%
+oxygen you're only dealing with parts of
+the energetics of the molecule you're
+
+ align:start position:0%
+the energetics of the molecule you're
+ 
+
+ align:start position:0%
+the energetics of the molecule you're
+only dealing with what's known as the
+
+ align:start position:0%
+only dealing with what's known as the
+ 
+
+ align:start position:0%
+only dealing with what's known as the
+free energy changes to look at the
+
+ align:start position:0%
+free energy changes to look at the
+ 
+
+ align:start position:0%
+free energy changes to look at the
+enthalpy changes isn't going to get you
+
+ align:start position:0%
+enthalpy changes isn't going to get you
+ 
+
+ align:start position:0%
+enthalpy changes isn't going to get you
+very far it's not going to describe the
+
+ align:start position:0%
+very far it's not going to describe the
+ 
+
+ align:start position:0%
+very far it's not going to describe the
+reaction because the enthalpy changes
+
+ align:start position:0%
+reaction because the enthalpy changes
+ 
+
+ align:start position:0%
+reaction because the enthalpy changes
+would be enormous breaking down that
+
+ align:start position:0%
+would be enormous breaking down that
+ 
+
+ align:start position:0%
+would be enormous breaking down that
+molecule and that's not what you want to
+
+ align:start position:0%
+molecule and that's not what you want to
+ 
+
+ align:start position:0%
+molecule and that's not what you want to
+achieve in a chemical transformation we
+
+ align:start position:0%
+achieve in a chemical transformation we
+ 
+
+ align:start position:0%
+achieve in a chemical transformation we
+care about Delta G now the next thing to
+
+ align:start position:0%
+care about Delta G now the next thing to
+ 
+
+ align:start position:0%
+care about Delta G now the next thing to
+think about is what are the energetics
+
+ align:start position:0%
+think about is what are the energetics
+ 
+
+ align:start position:0%
+think about is what are the energetics
+of the reaction and how does an enzyme
+
+ align:start position:0%
+of the reaction and how does an enzyme
+ 
+
+ align:start position:0%
+of the reaction and how does an enzyme
+catalyzed reaction manipulate those n
+
+ align:start position:0%
+catalyzed reaction manipulate those n
+ 
+
+ align:start position:0%
+catalyzed reaction manipulate those n
+energetics so the key thing here is we
+
+ align:start position:0%
+energetics so the key thing here is we
+ 
+
+ align:start position:0%
+energetics so the key thing here is we
+want to talk about Gibbs free energy
+
+ align:start position:0%
+want to talk about Gibbs free energy
+ 
+
+ align:start position:0%
+want to talk about Gibbs free energy
+shouldn't written quite this much stuff
+
+ align:start position:0%
+shouldn't written quite this much stuff
+ 
+
+ align:start position:0%
+shouldn't written quite this much stuff
+here because I need the blackboard
+
+ align:start position:0%
+here because I need the blackboard
+ 
+
+ align:start position:0%
+here because I need the blackboard
+alright so when you describe a reaction
+
+ align:start position:0%
+alright so when you describe a reaction
+ 
+
+ align:start position:0%
+alright so when you describe a reaction
+you want to understand how far that
+
+ align:start position:0%
+you want to understand how far that
+ 
+
+ align:start position:0%
+you want to understand how far that
+reaction goes and how fast that reaction
+
+ align:start position:0%
+reaction goes and how fast that reaction
+ 
+
+ align:start position:0%
+reaction goes and how fast that reaction
+goes so when you go through a reaction
+
+ align:start position:0%
+goes so when you go through a reaction
+ 
+
+ align:start position:0%
+goes so when you go through a reaction
+we can describe how far the reaction
+
+ align:start position:0%
+we can describe how far the reaction
+ 
+
+ align:start position:0%
+we can describe how far the reaction
+goes by thinking about the free energy
+
+ align:start position:0%
+goes by thinking about the free energy
+ 
+
+ align:start position:0%
+goes by thinking about the free energy
+of the substrates and the products so in
+
+ align:start position:0%
+of the substrates and the products so in
+ 
+
+ align:start position:0%
+of the substrates and the products so in
+this case the substrate is at a higher
+
+ align:start position:0%
+this case the substrate is at a higher
+ 
+
+ align:start position:0%
+this case the substrate is at a higher
+energy than the products so you will go
+
+ align:start position:0%
+energy than the products so you will go
+ 
+
+ align:start position:0%
+energy than the products so you will go
+a long way through the reaction to make
+
+ align:start position:0%
+a long way through the reaction to make
+ 
+
+ align:start position:0%
+a long way through the reaction to make
+mud quite a lot of product in there in a
+
+ align:start position:0%
+mud quite a lot of product in there in a
+ 
+
+ align:start position:0%
+mud quite a lot of product in there in a
+transformation so that describes how far
+
+ align:start position:0%
+transformation so that describes how far
+ 
+
+ align:start position:0%
+transformation so that describes how far
+the reaction goes so that is the
+
+ align:start position:0%
+the reaction goes so that is the
+ 
+
+ align:start position:0%
+the reaction goes so that is the
+difference between the energy of the
+
+ align:start position:0%
+difference between the energy of the
+ 
+
+ align:start position:0%
+difference between the energy of the
+substrate and the product how fast the
+
+ align:start position:0%
+substrate and the product how fast the
+ 
+
+ align:start position:0%
+substrate and the product how fast the
+reaction goes concern is described in
+
+ align:start position:0%
+reaction goes concern is described in
+ 
+
+ align:start position:0%
+reaction goes concern is described in
+and didn't different part of this
+
+ align:start position:0%
+and didn't different part of this
+ 
+
+ align:start position:0%
+and didn't different part of this
+diagram does anyone know what it is yes
+
+ align:start position:0%
+diagram does anyone know what it is yes
+ 
+
+ align:start position:0%
+diagram does anyone know what it is yes
+yes exactly how fast the reaction goes
+
+ align:start position:0%
+yes exactly how fast the reaction goes
+ 
+
+ align:start position:0%
+yes exactly how fast the reaction goes
+is literally how high the mountain is
+
+ align:start position:0%
+is literally how high the mountain is
+ 
+
+ align:start position:0%
+is literally how high the mountain is
+but you have to get over
+
+ align:start position:0%
+but you have to get over
+ 
+
+ align:start position:0%
+but you have to get over
+to carry out the transformation and that
+
+ align:start position:0%
+to carry out the transformation and that
+ 
+
+ align:start position:0%
+to carry out the transformation and that
+height is described as the energy of
+
+ align:start position:0%
+height is described as the energy of
+ 
+
+ align:start position:0%
+height is described as the energy of
+activation so that tells you how fast
+
+ align:start position:0%
+activation so that tells you how fast
+ 
+
+ align:start position:0%
+activation so that tells you how fast
+and the difference here tells you how
+
+ align:start position:0%
+and the difference here tells you how
+ 
+
+ align:start position:0%
+and the difference here tells you how
+far the energy of activation is a really
+
+ align:start position:0%
+far the energy of activation is a really
+ 
+
+ align:start position:0%
+far the energy of activation is a really
+important parameter because it's
+
+ align:start position:0%
+important parameter because it's
+ 
+
+ align:start position:0%
+important parameter because it's
+actually what gets manipulated when
+
+ align:start position:0%
+actually what gets manipulated when
+ 
+
+ align:start position:0%
+actually what gets manipulated when
+you're dealing with catalyzed reactions
+
+ align:start position:0%
+you're dealing with catalyzed reactions
+ 
+
+ align:start position:0%
+you're dealing with catalyzed reactions
+so the energy of activation the higher
+
+ align:start position:0%
+so the energy of activation the higher
+ 
+
+ align:start position:0%
+so the energy of activation the higher
+that mountain is the slower the reaction
+
+ align:start position:0%
+that mountain is the slower the reaction
+ 
+
+ align:start position:0%
+that mountain is the slower the reaction
+will be because it's a much harder
+
+ align:start position:0%
+will be because it's a much harder
+ 
+
+ align:start position:0%
+will be because it's a much harder
+transformation to go through the
+
+ align:start position:0%
+transformation to go through the
+ 
+
+ align:start position:0%
+transformation to go through the
+reactions in our bodies can be of
+
+ align:start position:0%
+reactions in our bodies can be of
+ 
+
+ align:start position:0%
+reactions in our bodies can be of
+different flavors depending on the
+
+ align:start position:0%
+different flavors depending on the
+ 
+
+ align:start position:0%
+different flavors depending on the
+difference in energy of the substrate
+
+ align:start position:0%
+difference in energy of the substrate
+ 
+
+ align:start position:0%
+difference in energy of the substrate
+and the product so shown there substrate
+
+ align:start position:0%
+and the product so shown there substrate
+ 
+
+ align:start position:0%
+and the product so shown there substrate
+going to products where the product is
+
+ align:start position:0%
+going to products where the product is
+ 
+
+ align:start position:0%
+going to products where the product is
+at lower energy than the substrate we
+
+ align:start position:0%
+at lower energy than the substrate we
+ 
+
+ align:start position:0%
+at lower energy than the substrate we
+would call this an exergonic reaction
+
+ align:start position:0%
+would call this an exergonic reaction
+ 
+
+ align:start position:0%
+would call this an exergonic reaction
+because we're releasing energy in the in
+
+ align:start position:0%
+because we're releasing energy in the in
+ 
+
+ align:start position:0%
+because we're releasing energy in the in
+the transformation so as higher than P
+
+ align:start position:0%
+the transformation so as higher than P
+ 
+
+ align:start position:0%
+the transformation so as higher than P
+exergonic and if we have a different
+
+ align:start position:0%
+exergonic and if we have a different
+ 
+
+ align:start position:0%
+exergonic and if we have a different
+reaction and I'll sketch this one in
+
+ align:start position:0%
+reaction and I'll sketch this one in
+ 
+
+ align:start position:0%
+reaction and I'll sketch this one in
+here where the product is higher energy
+
+ align:start position:0%
+here where the product is higher energy
+ 
+
+ align:start position:0%
+here where the product is higher energy
+and this is a reaction coordinate then
+
+ align:start position:0%
+and this is a reaction coordinate then
+ 
+
+ align:start position:0%
+and this is a reaction coordinate then
+that will be an endergonic reaction both
+
+ align:start position:0%
+that will be an endergonic reaction both
+ 
+
+ align:start position:0%
+that will be an endergonic reaction both
+reactions happen in the enzyme catalyzed
+
+ align:start position:0%
+reactions happen in the enzyme catalyzed
+ 
+
+ align:start position:0%
+reactions happen in the enzyme catalyzed
+systems and we'll explain why you're
+
+ align:start position:0%
+systems and we'll explain why you're
+ 
+
+ align:start position:0%
+systems and we'll explain why you're
+able to catalyze even ones that require
+
+ align:start position:0%
+able to catalyze even ones that require
+ 
+
+ align:start position:0%
+able to catalyze even ones that require
+energy so exergonic releases energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and endergonic requires okay what else
+
+ align:start position:0%
+and endergonic requires okay what else
+ 
+
+ align:start position:0%
+and endergonic requires okay what else
+have I got on here we also in the
+
+ align:start position:0%
+have I got on here we also in the
+ 
+
+ align:start position:0%
+have I got on here we also in the
+situations where energy is produced the
+
+ align:start position:0%
+situations where energy is produced the
+ 
+
+ align:start position:0%
+situations where energy is produced the
+exergonic reactions we call these
+
+ align:start position:0%
+exergonic reactions we call these
+ 
+
+ align:start position:0%
+exergonic reactions we call these
+catabolic processes and if you have
+
+ align:start position:0%
+catabolic processes and if you have
+ 
+
+ align:start position:0%
+catabolic processes and if you have
+trouble remembering catabolic and
+
+ align:start position:0%
+trouble remembering catabolic and
+ 
+
+ align:start position:0%
+trouble remembering catabolic and
+anabolic just join me in that because I
+
+ align:start position:0%
+anabolic just join me in that because I
+ 
+
+ align:start position:0%
+anabolic just join me in that because I
+always forget which is which but the
+
+ align:start position:0%
+always forget which is which but the
+ 
+
+ align:start position:0%
+always forget which is which but the
+ones that produce energy a catabolic the
+
+ align:start position:0%
+ones that produce energy a catabolic the
+ 
+
+ align:start position:0%
+ones that produce energy a catabolic the
+ones that require energy are anabolic
+
+ align:start position:0%
+ones that require energy are anabolic
+ 
+
+ align:start position:0%
+ones that require energy are anabolic
+and when we think about metabolism the
+
+ align:start position:0%
+and when we think about metabolism the
+ 
+
+ align:start position:0%
+and when we think about metabolism the
+catabolic reactions are when we're
+
+ align:start position:0%
+catabolic reactions are when we're
+ 
+
+ align:start position:0%
+catabolic reactions are when we're
+breaking molecules down because we need
+
+ align:start position:0%
+breaking molecules down because we need
+ 
+
+ align:start position:0%
+breaking molecules down because we need
+energy we need to use it to do something
+
+ align:start position:0%
+energy we need to use it to do something
+ 
+
+ align:start position:0%
+energy we need to use it to do something
+the anabolic reactions are when we want
+
+ align:start position:0%
+the anabolic reactions are when we want
+ 
+
+ align:start position:0%
+the anabolic reactions are when we want
+to store things store fats build
+
+ align:start position:0%
+to store things store fats build
+ 
+
+ align:start position:0%
+to store things store fats build
+proteins because they're going to be
+
+ align:start position:0%
+proteins because they're going to be
+ 
+
+ align:start position:0%
+proteins because they're going to be
+endergonic they're going to be requiring
+
+ align:start position:0%
+endergonic they're going to be requiring
+ 
+
+ align:start position:0%
+endergonic they're going to be requiring
+energy to take place
+
+ align:start position:0%
+energy to take place
+ 
+
+ align:start position:0%
+energy to take place
+I just forgot one thing that I learned
+
+ align:start position:0%
+I just forgot one thing that I learned
+ 
+
+ align:start position:0%
+I just forgot one thing that I learned
+shamefully done
+
+ align:start position:0%
+shamefully done
+ 
+
+ align:start position:0%
+shamefully done
+remember this axis is kilocalories per
+
+ align:start position:0%
+remember this axis is kilocalories per
+ 
+
+ align:start position:0%
+remember this axis is kilocalories per
+mole most commonly when we're talking
+
+ align:start position:0%
+mole most commonly when we're talking
+ 
+
+ align:start position:0%
+mole most commonly when we're talking
+about Delta G or kilo joules per mole if
+
+ align:start position:0%
+about Delta G or kilo joules per mole if
+ 
+
+ align:start position:0%
+about Delta G or kilo joules per mole if
+you're in a different part of the world
+
+ align:start position:0%
+you're in a different part of the world
+ 
+
+ align:start position:0%
+you're in a different part of the world
+but it's important to have units on
+
+ align:start position:0%
+but it's important to have units on
+ 
+
+ align:start position:0%
+but it's important to have units on
+these diagrams so that tells us a little
+
+ align:start position:0%
+these diagrams so that tells us a little
+ 
+
+ align:start position:0%
+these diagrams so that tells us a little
+bit about enzyme catalyzed reactions we
+
+ align:start position:0%
+bit about enzyme catalyzed reactions we
+ 
+
+ align:start position:0%
+bit about enzyme catalyzed reactions we
+need the enzyme to do something about
+
+ align:start position:0%
+need the enzyme to do something about
+ 
+
+ align:start position:0%
+need the enzyme to do something about
+this energy of activation because if we
+
+ align:start position:0%
+this energy of activation because if we
+ 
+
+ align:start position:0%
+this energy of activation because if we
+didn't have a high energy of activation
+
+ align:start position:0%
+didn't have a high energy of activation
+ 
+
+ align:start position:0%
+didn't have a high energy of activation
+I brought a Snickers bar to eat during
+
+ align:start position:0%
+I brought a Snickers bar to eat during
+ 
+
+ align:start position:0%
+I brought a Snickers bar to eat during
+class which is burst into flames right
+
+ align:start position:0%
+class which is burst into flames right
+ 
+
+ align:start position:0%
+class which is burst into flames right
+it has it needs a high energy of
+
+ align:start position:0%
+it has it needs a high energy of
+ 
+
+ align:start position:0%
+it has it needs a high energy of
+activation to keep it stable regularly
+
+ align:start position:0%
+activation to keep it stable regularly
+ 
+
+ align:start position:0%
+activation to keep it stable regularly
+in under regular conditions but only
+
+ align:start position:0%
+in under regular conditions but only
+ 
+
+ align:start position:0%
+in under regular conditions but only
+break down the bonds under time at times
+
+ align:start position:0%
+break down the bonds under time at times
+ 
+
+ align:start position:0%
+break down the bonds under time at times
+when you require that break down right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so what are the catalysts do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now I've shown you the simple
+
+ align:start position:0%
+okay now I've shown you the simple
+ 
+
+ align:start position:0%
+okay now I've shown you the simple
+reaction the enzyme is a very large
+
+ align:start position:0%
+reaction the enzyme is a very large
+ 
+
+ align:start position:0%
+reaction the enzyme is a very large
+structure it binds to a substrate
+
+ align:start position:0%
+structure it binds to a substrate
+ 
+
+ align:start position:0%
+structure it binds to a substrate
+chemistry happens and it releases a
+
+ align:start position:0%
+chemistry happens and it releases a
+ 
+
+ align:start position:0%
+chemistry happens and it releases a
+product but at the same time you can't
+
+ align:start position:0%
+product but at the same time you can't
+ 
+
+ align:start position:0%
+product but at the same time you can't
+disobey the principles of thermodynamics
+
+ align:start position:0%
+disobey the principles of thermodynamics
+ 
+
+ align:start position:0%
+disobey the principles of thermodynamics
+so there's certain criteria we have to
+
+ align:start position:0%
+so there's certain criteria we have to
+ 
+
+ align:start position:0%
+so there's certain criteria we have to
+think about when we consider an enzyme
+
+ align:start position:0%
+think about when we consider an enzyme
+ 
+
+ align:start position:0%
+think about when we consider an enzyme
+catalyzed reaction so first of all do
+
+ align:start position:0%
+catalyzed reaction so first of all do
+ 
+
+ align:start position:0%
+catalyzed reaction so first of all do
+not disobey whichever law of
+
+ align:start position:0%
+not disobey whichever law of
+ 
+
+ align:start position:0%
+not disobey whichever law of
+thermodynamics is is they do not change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta G Delta G is a property of the two
+
+ align:start position:0%
+Delta G Delta G is a property of the two
+ 
+
+ align:start position:0%
+Delta G Delta G is a property of the two
+reactants you're not going to change it
+
+ align:start position:0%
+reactants you're not going to change it
+ 
+
+ align:start position:0%
+reactants you're not going to change it
+with a catalyst it's it's going to have
+
+ align:start position:0%
+with a catalyst it's it's going to have
+ 
+
+ align:start position:0%
+with a catalyst it's it's going to have
+a much more important impact on a
+
+ align:start position:0%
+a much more important impact on a
+ 
+
+ align:start position:0%
+a much more important impact on a
+different parameter which parameter do
+
+ align:start position:0%
+different parameter which parameter do
+ 
+
+ align:start position:0%
+different parameter which parameter do
+enzymes change and help lower over there
+
+ align:start position:0%
+enzymes change and help lower over there
+ 
+
+ align:start position:0%
+enzymes change and help lower over there
+right so catalysts do to change and in
+
+ align:start position:0%
+right so catalysts do to change and in
+ 
+
+ align:start position:0%
+right so catalysts do to change and in
+fact lower energy of activation and
+
+ align:start position:0%
+fact lower energy of activation and
+ 
+
+ align:start position:0%
+fact lower energy of activation and
+we'll talk about how they do that at the
+
+ align:start position:0%
+we'll talk about how they do that at the
+ 
+
+ align:start position:0%
+we'll talk about how they do that at the
+end and then the last rule about a
+
+ align:start position:0%
+end and then the last rule about a
+ 
+
+ align:start position:0%
+end and then the last rule about a
+catalyst is you can recover them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unchanged after a reaction it would be a
+
+ align:start position:0%
+unchanged after a reaction it would be a
+ 
+
+ align:start position:0%
+unchanged after a reaction it would be a
+lousy catalyst if it did it's chemistry
+
+ align:start position:0%
+lousy catalyst if it did it's chemistry
+ 
+
+ align:start position:0%
+lousy catalyst if it did it's chemistry
+and then you've used up the catalysts so
+
+ align:start position:0%
+and then you've used up the catalysts so
+ 
+
+ align:start position:0%
+and then you've used up the catalysts so
+enzyme catalysts are the ultimate green
+
+ align:start position:0%
+enzyme catalysts are the ultimate green
+ 
+
+ align:start position:0%
+enzyme catalysts are the ultimate green
+reagents you can keep using them
+
+ align:start position:0%
+reagents you can keep using them
+ 
+
+ align:start position:0%
+reagents you can keep using them
+thousands and thousands of times to
+
+ align:start position:0%
+thousands and thousands of times to
+ 
+
+ align:start position:0%
+thousands and thousands of times to
+continuously turn over transformations
+
+ align:start position:0%
+continuously turn over transformations
+ 
+
+ align:start position:0%
+continuously turn over transformations
+so you haven't changed a catalyst so the
+
+ align:start position:0%
+so you haven't changed a catalyst so the
+ 
+
+ align:start position:0%
+so you haven't changed a catalyst so the
+things that we want to think about is
+
+ align:start position:0%
+things that we want to think about is
+ 
+
+ align:start position:0%
+things that we want to think about is
+how what are the processes that that
+
+ align:start position:0%
+how what are the processes that that
+ 
+
+ align:start position:0%
+how what are the processes that that
+enzymes can manipulate and I should
+
+ align:start position:0%
+enzymes can manipulate and I should
+ 
+
+ align:start position:0%
+enzymes can manipulate and I should
+probably just quickly run through these
+
+ align:start position:0%
+probably just quickly run through these
+ 
+
+ align:start position:0%
+probably just quickly run through these
+slides so we've talked about these
+
+ align:start position:0%
+slides so we've talked about these
+ 
+
+ align:start position:0%
+slides so we've talked about these
+entities but I put them on the board
+
+ align:start position:0%
+entities but I put them on the board
+ 
+
+ align:start position:0%
+entities but I put them on the board
+because they're particularly important
+
+ align:start position:0%
+because they're particularly important
+ 
+
+ align:start position:0%
+because they're particularly important
+so the energy of activation of a
+
+ align:start position:0%
+so the energy of activation of a
+ 
+
+ align:start position:0%
+so the energy of activation of a
+catalyzed reaction is lower than the
+
+ align:start position:0%
+catalyzed reaction is lower than the
+ 
+
+ align:start position:0%
+catalyzed reaction is lower than the
+uncatalyzed
+
+ align:start position:0%
+uncatalyzed
+ 
+
+ align:start position:0%
+uncatalyzed
+not going to bore you with these
+
+ align:start position:0%
+not going to bore you with these
+ 
+
+ align:start position:0%
+not going to bore you with these
+questions because you can work this out
+
+ align:start position:0%
+questions because you can work this out
+ 
+
+ align:start position:0%
+questions because you can work this out
+quite readily so delta g is the free
+
+ align:start position:0%
+quite readily so delta g is the free
+ 
+
+ align:start position:0%
+quite readily so delta g is the free
+energy that changes and these are
+
+ align:start position:0%
+energy that changes and these are
+ 
+
+ align:start position:0%
+energy that changes and these are
+endergonic because the energy of the
+
+ align:start position:0%
+endergonic because the energy of the
+ 
+
+ align:start position:0%
+endergonic because the energy of the
+products is lower so this is the slide I
+
+ align:start position:0%
+products is lower so this is the slide I
+ 
+
+ align:start position:0%
+products is lower so this is the slide I
+want to get to with respect to the
+
+ align:start position:0%
+want to get to with respect to the
+ 
+
+ align:start position:0%
+want to get to with respect to the
+enzyme to enzyme catalyst so we always
+
+ align:start position:0%
+enzyme to enzyme catalyst so we always
+ 
+
+ align:start position:0%
+enzyme to enzyme catalyst so we always
+think well gosh the enzyme is really
+
+ align:start position:0%
+think well gosh the enzyme is really
+ 
+
+ align:start position:0%
+think well gosh the enzyme is really
+large relative to the size of the
+
+ align:start position:0%
+large relative to the size of the
+ 
+
+ align:start position:0%
+large relative to the size of the
+product that's because all that energy
+
+ align:start position:0%
+product that's because all that energy
+ 
+
+ align:start position:0%
+product that's because all that energy
+within the protein folded structure is
+
+ align:start position:0%
+within the protein folded structure is
+ 
+
+ align:start position:0%
+within the protein folded structure is
+very useful for lowering the energy of
+
+ align:start position:0%
+very useful for lowering the energy of
+ 
+
+ align:start position:0%
+very useful for lowering the energy of
+activation of our transformations so
+
+ align:start position:0%
+activation of our transformations so
+ 
+
+ align:start position:0%
+activation of our transformations so
+let's say I have a reaction that
+
+ align:start position:0%
+let's say I have a reaction that
+ 
+
+ align:start position:0%
+let's say I have a reaction that
+involves two substrates coming together
+
+ align:start position:0%
+involves two substrates coming together
+ 
+
+ align:start position:0%
+involves two substrates coming together
+to make a product right if I'm off the
+
+ align:start position:0%
+to make a product right if I'm off the
+ 
+
+ align:start position:0%
+to make a product right if I'm off the
+enzyme these guys it's gonna take them a
+
+ align:start position:0%
+enzyme these guys it's gonna take them a
+ 
+
+ align:start position:0%
+enzyme these guys it's gonna take them a
+long time to bump into each other to do
+
+ align:start position:0%
+long time to bump into each other to do
+ 
+
+ align:start position:0%
+long time to bump into each other to do
+chemistry the way enzymes catalyze those
+
+ align:start position:0%
+chemistry the way enzymes catalyze those
+ 
+
+ align:start position:0%
+chemistry the way enzymes catalyze those
+types of reactions is they have binding
+
+ align:start position:0%
+types of reactions is they have binding
+ 
+
+ align:start position:0%
+types of reactions is they have binding
+sites for both of those compounds in
+
+ align:start position:0%
+sites for both of those compounds in
+ 
+
+ align:start position:0%
+sites for both of those compounds in
+fact the enzyme acts as a stage 1
+
+ align:start position:0%
+fact the enzyme acts as a stage 1
+ 
+
+ align:start position:0%
+fact the enzyme acts as a stage 1
+substrate binds the other substrate
+
+ align:start position:0%
+substrate binds the other substrate
+ 
+
+ align:start position:0%
+substrate binds the other substrate
+binds their binding close to each other
+
+ align:start position:0%
+binds their binding close to each other
+ 
+
+ align:start position:0%
+binds their binding close to each other
+on the enzyme chemistry can happen it
+
+ align:start position:0%
+on the enzyme chemistry can happen it
+ 
+
+ align:start position:0%
+on the enzyme chemistry can happen it
+favors reactions that involve multiple
+
+ align:start position:0%
+favors reactions that involve multiple
+ 
+
+ align:start position:0%
+favors reactions that involve multiple
+molecules what about another situation
+
+ align:start position:0%
+molecules what about another situation
+ 
+
+ align:start position:0%
+molecules what about another situation
+where you have a bond for example the
+
+ align:start position:0%
+where you have a bond for example the
+ 
+
+ align:start position:0%
+where you have a bond for example the
+amide bond the protease is break it's
+
+ align:start position:0%
+amide bond the protease is break it's
+ 
+
+ align:start position:0%
+amide bond the protease is break it's
+hard to think of how that how can we
+
+ align:start position:0%
+hard to think of how that how can we
+ 
+
+ align:start position:0%
+hard to think of how that how can we
+make that more easy
+
+ align:start position:0%
+make that more easy
+ 
+
+ align:start position:0%
+make that more easy
+well amides are most stable when they
+
+ align:start position:0%
+well amides are most stable when they
+ 
+
+ align:start position:0%
+well amides are most stable when they
+are flat and planar through this
+
+ align:start position:0%
+are flat and planar through this
+ 
+
+ align:start position:0%
+are flat and planar through this
+arrangement of atoms but what can happen
+
+ align:start position:0%
+arrangement of atoms but what can happen
+ 
+
+ align:start position:0%
+arrangement of atoms but what can happen
+on the enzyme is that they can twist
+
+ align:start position:0%
+on the enzyme is that they can twist
+ 
+
+ align:start position:0%
+on the enzyme is that they can twist
+bonds to make them less stable and then
+
+ align:start position:0%
+bonds to make them less stable and then
+ 
+
+ align:start position:0%
+bonds to make them less stable and then
+more easy to hydrolyze
+
+ align:start position:0%
+more easy to hydrolyze
+ 
+
+ align:start position:0%
+more easy to hydrolyze
+so the structure of that enzyme
+
+ align:start position:0%
+so the structure of that enzyme
+ 
+
+ align:start position:0%
+so the structure of that enzyme
+basically holds on to the substrate and
+
+ align:start position:0%
+basically holds on to the substrate and
+ 
+
+ align:start position:0%
+basically holds on to the substrate and
+twists or distorts the bond that you're
+
+ align:start position:0%
+twists or distorts the bond that you're
+ 
+
+ align:start position:0%
+twists or distorts the bond that you're
+trying to do chemistry on to once again
+
+ align:start position:0%
+trying to do chemistry on to once again
+ 
+
+ align:start position:0%
+trying to do chemistry on to once again
+lower the energy of activation another
+
+ align:start position:0%
+lower the energy of activation another
+ 
+
+ align:start position:0%
+lower the energy of activation another
+way enzymes work is in a reaction where
+
+ align:start position:0%
+way enzymes work is in a reaction where
+ 
+
+ align:start position:0%
+way enzymes work is in a reaction where
+you're breaking this bond you might make
+
+ align:start position:0%
+you're breaking this bond you might make
+ 
+
+ align:start position:0%
+you're breaking this bond you might make
+charged intermediates the enzymes there
+
+ align:start position:0%
+charged intermediates the enzymes there
+ 
+
+ align:start position:0%
+charged intermediates the enzymes there
+to hold those charged intermediates in
+
+ align:start position:0%
+to hold those charged intermediates in
+ 
+
+ align:start position:0%
+to hold those charged intermediates in
+order to stabilize them once again to
+
+ align:start position:0%
+order to stabilize them once again to
+ 
+
+ align:start position:0%
+order to stabilize them once again to
+lower energy of activation so it's funny
+
+ align:start position:0%
+lower energy of activation so it's funny
+ 
+
+ align:start position:0%
+lower energy of activation so it's funny
+when you get the question that's well
+
+ align:start position:0%
+when you get the question that's well
+ 
+
+ align:start position:0%
+when you get the question that's well
+how do enzymes catalyze RIA
+
+ align:start position:0%
+how do enzymes catalyze RIA
+ 
+
+ align:start position:0%
+how do enzymes catalyze RIA
+actions there is no one rule you want to
+
+ align:start position:0%
+actions there is no one rule you want to
+ 
+
+ align:start position:0%
+actions there is no one rule you want to
+think about the reactions and then just
+
+ align:start position:0%
+think about the reactions and then just
+ 
+
+ align:start position:0%
+think about the reactions and then just
+think about the ways in which an enzyme
+
+ align:start position:0%
+think about the ways in which an enzyme
+ 
+
+ align:start position:0%
+think about the ways in which an enzyme
+could contribute to that
+
+ align:start position:0%
+could contribute to that
+ 
+
+ align:start position:0%
+could contribute to that
+for example orienting to substrates
+
+ align:start position:0%
+for example orienting to substrates
+ 
+
+ align:start position:0%
+for example orienting to substrates
+ready to do chemistry causing physical
+
+ align:start position:0%
+ready to do chemistry causing physical
+ 
+
+ align:start position:0%
+ready to do chemistry causing physical
+strain in a bond that you want to break
+
+ align:start position:0%
+strain in a bond that you want to break
+ 
+
+ align:start position:0%
+strain in a bond that you want to break
+or comforting electric charges as
+
+ align:start position:0%
+or comforting electric charges as
+ 
+
+ align:start position:0%
+or comforting electric charges as
+charges that form during a reaction
+
+ align:start position:0%
+charges that form during a reaction
+ 
+
+ align:start position:0%
+charges that form during a reaction
+coordinate so their loads and loads of
+
+ align:start position:0%
+coordinate so their loads and loads of
+ 
+
+ align:start position:0%
+coordinate so their loads and loads of
+different principles and it's a really
+
+ align:start position:0%
+different principles and it's a really
+ 
+
+ align:start position:0%
+different principles and it's a really
+important study that's carried that is
+
+ align:start position:0%
+important study that's carried that is
+ 
+
+ align:start position:0%
+important study that's carried that is
+carried out so finally and I think I
+
+ align:start position:0%
+carried out so finally and I think I
+ 
+
+ align:start position:0%
+carried out so finally and I think I
+have a couple you know I have a couple
+
+ align:start position:0%
+have a couple you know I have a couple
+ 
+
+ align:start position:0%
+have a couple you know I have a couple
+of minutes but I want to just describe
+
+ align:start position:0%
+of minutes but I want to just describe
+ 
+
+ align:start position:0%
+of minutes but I want to just describe
+this to you it'll also be covered in the
+
+ align:start position:0%
+this to you it'll also be covered in the
+ 
+
+ align:start position:0%
+this to you it'll also be covered in the
+sections because I'm going to rush it a
+
+ align:start position:0%
+sections because I'm going to rush it a
+ 
+
+ align:start position:0%
+sections because I'm going to rush it a
+bit because this last bit is features a
+
+ align:start position:0%
+bit because this last bit is features a
+ 
+
+ align:start position:0%
+bit because this last bit is features a
+little bit on that on the pset so
+
+ align:start position:0%
+little bit on that on the pset so
+ 
+
+ align:start position:0%
+little bit on that on the pset so
+finally we've enzymes are very commonly
+
+ align:start position:0%
+finally we've enzymes are very commonly
+ 
+
+ align:start position:0%
+finally we've enzymes are very commonly
+the targets of drugs we like to think
+
+ align:start position:0%
+the targets of drugs we like to think
+ 
+
+ align:start position:0%
+the targets of drugs we like to think
+that some drugs are important targets if
+
+ align:start position:0%
+that some drugs are important targets if
+ 
+
+ align:start position:0%
+that some drugs are important targets if
+we deactivate the enzyme we might
+
+ align:start position:0%
+we deactivate the enzyme we might
+ 
+
+ align:start position:0%
+we deactivate the enzyme we might
+mitigate the symptoms of a disease now
+
+ align:start position:0%
+mitigate the symptoms of a disease now
+ 
+
+ align:start position:0%
+mitigate the symptoms of a disease now
+you can't go in and heat the enzyme or
+
+ align:start position:0%
+you can't go in and heat the enzyme or
+ 
+
+ align:start position:0%
+you can't go in and heat the enzyme or
+you know denature the enzyme if you're
+
+ align:start position:0%
+you know denature the enzyme if you're
+ 
+
+ align:start position:0%
+you know denature the enzyme if you're
+trying to treat a person so we do a lot
+
+ align:start position:0%
+trying to treat a person so we do a lot
+ 
+
+ align:start position:0%
+trying to treat a person so we do a lot
+of work to mitigate disease by
+
+ align:start position:0%
+of work to mitigate disease by
+ 
+
+ align:start position:0%
+of work to mitigate disease by
+inhibiting enzymes with small molecules
+
+ align:start position:0%
+inhibiting enzymes with small molecules
+ 
+
+ align:start position:0%
+inhibiting enzymes with small molecules
+so in these slides I described to you
+
+ align:start position:0%
+so in these slides I described to you
+ 
+
+ align:start position:0%
+so in these slides I described to you
+the types of molecules that may alter
+
+ align:start position:0%
+the types of molecules that may alter
+ 
+
+ align:start position:0%
+the types of molecules that may alter
+the chemistry of a transformation so if
+
+ align:start position:0%
+the chemistry of a transformation so if
+ 
+
+ align:start position:0%
+the chemistry of a transformation so if
+a substrate binds to an enzyme active
+
+ align:start position:0%
+a substrate binds to an enzyme active
+ 
+
+ align:start position:0%
+a substrate binds to an enzyme active
+site we often do this pac-man rendition
+
+ align:start position:0%
+site we often do this pac-man rendition
+ 
+
+ align:start position:0%
+site we often do this pac-man rendition
+you could design a molecule that binds
+
+ align:start position:0%
+you could design a molecule that binds
+ 
+
+ align:start position:0%
+you could design a molecule that binds
+there instead and basically inhibits the
+
+ align:start position:0%
+there instead and basically inhibits the
+ 
+
+ align:start position:0%
+there instead and basically inhibits the
+substrate from getting there this would
+
+ align:start position:0%
+substrate from getting there this would
+ 
+
+ align:start position:0%
+substrate from getting there this would
+be called a simple reversible inhibitor
+
+ align:start position:0%
+be called a simple reversible inhibitor
+ 
+
+ align:start position:0%
+be called a simple reversible inhibitor
+that's competitive with the active site
+
+ align:start position:0%
+that's competitive with the active site
+ 
+
+ align:start position:0%
+that's competitive with the active site
+there are other inhibitors that will
+
+ align:start position:0%
+there are other inhibitors that will
+ 
+
+ align:start position:0%
+there are other inhibitors that will
+bind to the enzyme but do chemistry with
+
+ align:start position:0%
+bind to the enzyme but do chemistry with
+ 
+
+ align:start position:0%
+bind to the enzyme but do chemistry with
+it and stay blocked at the enzyme and
+
+ align:start position:0%
+it and stay blocked at the enzyme and
+ 
+
+ align:start position:0%
+it and stay blocked at the enzyme and
+that would be called an irreversible
+
+ align:start position:0%
+that would be called an irreversible
+ 
+
+ align:start position:0%
+that would be called an irreversible
+competitive inhibitor you can't get the
+
+ align:start position:0%
+competitive inhibitor you can't get the
+ 
+
+ align:start position:0%
+competitive inhibitor you can't get the
+inhibitor off and there's differences in
+
+ align:start position:0%
+inhibitor off and there's differences in
+ 
+
+ align:start position:0%
+inhibitor off and there's differences in
+the way you can reverse this because for
+
+ align:start position:0%
+the way you can reverse this because for
+ 
+
+ align:start position:0%
+the way you can reverse this because for
+example up here if I add a lot more
+
+ align:start position:0%
+example up here if I add a lot more
+ 
+
+ align:start position:0%
+example up here if I add a lot more
+substrate and these are equilibria I can
+
+ align:start position:0%
+substrate and these are equilibria I can
+ 
+
+ align:start position:0%
+substrate and these are equilibria I can
+get my reaction to happen anyway but
+
+ align:start position:0%
+get my reaction to happen anyway but
+ 
+
+ align:start position:0%
+get my reaction to happen anyway but
+here I could add as much substrate as
+
+ align:start position:0%
+here I could add as much substrate as
+ 
+
+ align:start position:0%
+here I could add as much substrate as
+possible but it won't help it won't
+
+ align:start position:0%
+possible but it won't help it won't
+ 
+
+ align:start position:0%
+possible but it won't help it won't
+reverse the transformer
+
+ align:start position:0%
+reverse the transformer
+ 
+
+ align:start position:0%
+reverse the transformer
+okay and there's a question here to
+
+ align:start position:0%
+okay and there's a question here to
+ 
+
+ align:start position:0%
+okay and there's a question here to
+restore the reaction the answer really
+
+ align:start position:0%
+restore the reaction the answer really
+ 
+
+ align:start position:0%
+restore the reaction the answer really
+is you just have to start with new
+
+ align:start position:0%
+is you just have to start with new
+ 
+
+ align:start position:0%
+is you just have to start with new
+enzyme because you've covalently changed
+
+ align:start position:0%
+enzyme because you've covalently changed
+ 
+
+ align:start position:0%
+enzyme because you've covalently changed
+the protein structure the last type of
+
+ align:start position:0%
+the protein structure the last type of
+ 
+
+ align:start position:0%
+the protein structure the last type of
+inhibitors that are important the ones
+
+ align:start position:0%
+inhibitors that are important the ones
+ 
+
+ align:start position:0%
+inhibitors that are important the ones
+that bind at different sites on the
+
+ align:start position:0%
+that bind at different sites on the
+ 
+
+ align:start position:0%
+that bind at different sites on the
+enzymes and they are called allosteric
+
+ align:start position:0%
+enzymes and they are called allosteric
+ 
+
+ align:start position:0%
+enzymes and they are called allosteric
+allo always means different so if you
+
+ align:start position:0%
+allo always means different so if you
+ 
+
+ align:start position:0%
+allo always means different so if you
+have a compound that's an allosteric
+
+ align:start position:0%
+have a compound that's an allosteric
+ 
+
+ align:start position:0%
+have a compound that's an allosteric
+inhibitor it might bind on another face
+
+ align:start position:0%
+inhibitor it might bind on another face
+ 
+
+ align:start position:0%
+inhibitor it might bind on another face
+of the enzyme but it'll alter the active
+
+ align:start position:0%
+of the enzyme but it'll alter the active
+ 
+
+ align:start position:0%
+of the enzyme but it'll alter the active
+sites so it doesn't work that's an
+
+ align:start position:0%
+sites so it doesn't work that's an
+ 
+
+ align:start position:0%
+sites so it doesn't work that's an
+allosteric inhibitor and the final type
+
+ align:start position:0%
+allosteric inhibitor and the final type
+ 
+
+ align:start position:0%
+allosteric inhibitor and the final type
+of compound is an allosteric activator
+
+ align:start position:0%
+of compound is an allosteric activator
+ 
+
+ align:start position:0%
+of compound is an allosteric activator
+that may bind somewhere else on the
+
+ align:start position:0%
+that may bind somewhere else on the
+ 
+
+ align:start position:0%
+that may bind somewhere else on the
+enzyme but make it more active so these
+
+ align:start position:0%
+enzyme but make it more active so these
+ 
+
+ align:start position:0%
+enzyme but make it more active so these
+are the way small molecules work I'd
+
+ align:start position:0%
+are the way small molecules work I'd
+ 
+
+ align:start position:0%
+are the way small molecules work I'd
+like to encourage the TAS to just cover
+
+ align:start position:0%
+like to encourage the TAS to just cover
+ 
+
+ align:start position:0%
+like to encourage the TAS to just cover
+this in a little bit more detail because
+
+ align:start position:0%
+this in a little bit more detail because
+ 
+
+ align:start position:0%
+this in a little bit more detail because
+I brushed it and I'll also remain it at
+
+ align:start position:0%
+I brushed it and I'll also remain it at
+ 
+
+ align:start position:0%
+I brushed it and I'll also remain it at
+the beginning of the next class but bear
+
+ align:start position:0%
+the beginning of the next class but bear
+ 
+
+ align:start position:0%
+the beginning of the next class but bear
+in mind we should have everything
+
+ align:start position:0%
+in mind we should have everything
+ 
+
+ align:start position:0%
+in mind we should have everything
+covered now for the problem set one and
+
+ align:start position:0%
+covered now for the problem set one and
+ 
+
+ align:start position:0%
+covered now for the problem set one and
+if you have any questions reach out to
+
+ align:start position:0%
+if you have any questions reach out to
+ 
+
+ align:start position:0%
+if you have any questions reach out to
+us cover them in section and I'll
+
+ align:start position:0%
+us cover them in section and I'll
+ 
+
+ align:start position:0%
+us cover them in section and I'll
+reiterate a little bit of this in the
+
+ align:start position:0%
+reiterate a little bit of this in the
+ 
+
+ align:start position:0%
+reiterate a little bit of this in the
+next class and finally there's a little
+
+ align:start position:0%
+next class and finally there's a little
+ 
+
+ align:start position:0%
+next class and finally there's a little
+bit of reading if you would like to
+
+ align:start position:0%
+bit of reading if you would like to
+ 
+
+ align:start position:0%
+bit of reading if you would like to
+prepare we'll talk about carbohydrates
+
+ align:start position:0%
+prepare we'll talk about carbohydrates
+ 
+
+ align:start position:0%
+prepare we'll talk about carbohydrates
+next time one of my favorite molecules
+
+ align:start position:0%
+next time one of my favorite molecules
+ 
+
+ align:start position:0%
+next time one of my favorite molecules
+and there's also a fabulous set of
+
+ align:start position:0%
+and there's also a fabulous set of
+ 
+
+ align:start position:0%
+and there's also a fabulous set of
+videos on how enzymes work and the
+
+ align:start position:0%
+videos on how enzymes work and the
+ 
+
+ align:start position:0%
+videos on how enzymes work and the
+protein databank a site and you will see
+
+ align:start position:0%
+protein databank a site and you will see
+ 
+
+ align:start position:0%
+protein databank a site and you will see
+this little handout on the slides
+
+ align:start position:0%
+this little handout on the slides
+ 
+
+ align:start position:0%
+this little handout on the slides
+version of the slides that's posted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/QVDLMx0Guiw.txt b/QVDLMx0Guiw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4d50d139b24f4cfc965f3736fe39feec5ead7e29
--- /dev/null
+++ b/QVDLMx0Guiw.txt
@@ -0,0 +1,11288 @@
+align:start position:0%
+ 
+Yeah. So, we're sort of in the last part
+
+ align:start position:0%
+Yeah. So, we're sort of in the last part
+ 
+
+ align:start position:0%
+Yeah. So, we're sort of in the last part
+of the class now and I've been
+
+ align:start position:0%
+of the class now and I've been
+ 
+
+ align:start position:0%
+of the class now and I've been
+reflecting on what what to do together.
+
+ align:start position:0%
+reflecting on what what to do together.
+ 
+
+ align:start position:0%
+reflecting on what what to do together.
+Um and uh I asked everybody for for some
+
+ align:start position:0%
+Um and uh I asked everybody for for some
+ 
+
+ align:start position:0%
+Um and uh I asked everybody for for some
+input, a little survey about what topics
+
+ align:start position:0%
+input, a little survey about what topics
+ 
+
+ align:start position:0%
+input, a little survey about what topics
+to do and how much detail to do.
+
+ align:start position:0%
+to do and how much detail to do.
+ 
+
+ align:start position:0%
+to do and how much detail to do.
+Um there was no consensus in the survey
+
+ align:start position:0%
+Um there was no consensus in the survey
+ 
+
+ align:start position:0%
+Um there was no consensus in the survey
+of of what people wanted to do. Um
+
+ align:start position:0%
+of of what people wanted to do. Um
+ 
+
+ align:start position:0%
+of of what people wanted to do. Um
+but I've decided I would like to do for
+
+ align:start position:0%
+but I've decided I would like to do for
+ 
+
+ align:start position:0%
+but I've decided I would like to do for
+a couple of weeks uh talk about some
+
+ align:start position:0%
+a couple of weeks uh talk about some
+ 
+
+ align:start position:0%
+a couple of weeks uh talk about some
+applications of projection theory in
+
+ align:start position:0%
+applications of projection theory in
+ 
+
+ align:start position:0%
+applications of projection theory in
+other areas. Um and then in the last
+
+ align:start position:0%
+other areas. Um and then in the last
+ 
+
+ align:start position:0%
+other areas. Um and then in the last
+couple weeks try to talk about at least
+
+ align:start position:0%
+couple weeks try to talk about at least
+ 
+
+ align:start position:0%
+couple weeks try to talk about at least
+the some of the main ideas in the proof
+
+ align:start position:0%
+the some of the main ideas in the proof
+ 
+
+ align:start position:0%
+the some of the main ideas in the proof
+of the sharp projection theorem.
+
+ align:start position:0%
+of the sharp projection theorem.
+ 
+
+ align:start position:0%
+of the sharp projection theorem.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+yeah so we recently had been doing uh
+
+ align:start position:0%
+yeah so we recently had been doing uh
+ 
+
+ align:start position:0%
+yeah so we recently had been doing uh
+Burgans's projection theorem and the
+
+ align:start position:0%
+Burgans's projection theorem and the
+ 
+
+ align:start position:0%
+Burgans's projection theorem and the
+burganc cat's projection theorem in
+
+ align:start position:0%
+burganc cat's projection theorem in
+ 
+
+ align:start position:0%
+burganc cat's projection theorem in
+finite fields and um we so
+
+ align:start position:0%
+finite fields and um we so
+ 
+
+ align:start position:0%
+finite fields and um we so
+feeling that that we really had to work
+
+ align:start position:0%
+feeling that that we really had to work
+ 
+
+ align:start position:0%
+feeling that that we really had to work
+pretty hard for those things and it was
+
+ align:start position:0%
+pretty hard for those things and it was
+ 
+
+ align:start position:0%
+pretty hard for those things and it was
+striking that we had to work pretty hard
+
+ align:start position:0%
+striking that we had to work pretty hard
+ 
+
+ align:start position:0%
+striking that we had to work pretty hard
+just to get this like very small uh
+
+ align:start position:0%
+just to get this like very small uh
+ 
+
+ align:start position:0%
+just to get this like very small uh
+improvement um and um so in some of what
+
+ align:start position:0%
+improvement um and um so in some of what
+ 
+
+ align:start position:0%
+improvement um and um so in some of what
+we'll do in the rest of the class I I
+
+ align:start position:0%
+we'll do in the rest of the class I I
+ 
+
+ align:start position:0%
+we'll do in the rest of the class I I
+will try to show that that that small
+
+ align:start position:0%
+will try to show that that that small
+ 
+
+ align:start position:0%
+will try to show that that that small
+improvement is really valuable
+
+ align:start position:0%
+improvement is really valuable
+ 
+
+ align:start position:0%
+improvement is really valuable
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+okay. Um so the yeah so the so so the
+
+ align:start position:0%
+okay. Um so the yeah so the so so the
+ 
+
+ align:start position:0%
+okay. Um so the yeah so the so so the
+the plan for the rest of the class is
+
+ align:start position:0%
+the plan for the rest of the class is
+ 
+
+ align:start position:0%
+the plan for the rest of the class is
+for for about one week we'll talk about
+
+ align:start position:0%
+for for about one week we'll talk about
+ 
+
+ align:start position:0%
+for for about one week we'll talk about
+random walks on groups and then for
+
+ align:start position:0%
+random walks on groups and then for
+ 
+
+ align:start position:0%
+random walks on groups and then for
+about one week we'll talk about
+
+ align:start position:0%
+about one week we'll talk about
+ 
+
+ align:start position:0%
+about one week we'll talk about
+homogeneous dynamics. Um and then at the
+
+ align:start position:0%
+homogeneous dynamics. Um and then at the
+ 
+
+ align:start position:0%
+homogeneous dynamics. Um and then at the
+end we'll talk about the sharp
+
+ align:start position:0%
+end we'll talk about the sharp
+ 
+
+ align:start position:0%
+end we'll talk about the sharp
+projection theorem.
+
+ align:start position:0%
+projection theorem.
+ 
+
+ align:start position:0%
+projection theorem.
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+um cool. And also in the last few
+
+ align:start position:0%
+um cool. And also in the last few
+ 
+
+ align:start position:0%
+um cool. And also in the last few
+classes I felt that we were um doing
+
+ align:start position:0%
+classes I felt that we were um doing
+ 
+
+ align:start position:0%
+classes I felt that we were um doing
+some very technical things and and and
+
+ align:start position:0%
+some very technical things and and and
+ 
+
+ align:start position:0%
+some very technical things and and and
+uh um sometimes a little bit of a
+
+ align:start position:0%
+uh um sometimes a little bit of a
+ 
+
+ align:start position:0%
+uh um sometimes a little bit of a
+struggle. Um so for for today what I
+
+ align:start position:0%
+struggle. Um so for for today what I
+ 
+
+ align:start position:0%
+struggle. Um so for for today what I
+want to do is to give I hope a very
+
+ align:start position:0%
+want to do is to give I hope a very
+ 
+
+ align:start position:0%
+want to do is to give I hope a very
+friendly induct in introduction to
+
+ align:start position:0%
+friendly induct in introduction to
+ 
+
+ align:start position:0%
+friendly induct in introduction to
+random walks on groups and then um next
+
+ align:start position:0%
+random walks on groups and then um next
+ 
+
+ align:start position:0%
+random walks on groups and then um next
+week on Tuesday to explain how
+
+ align:start position:0%
+week on Tuesday to explain how
+ 
+
+ align:start position:0%
+week on Tuesday to explain how
+projection theory helps to figure out
+
+ align:start position:0%
+projection theory helps to figure out
+ 
+
+ align:start position:0%
+projection theory helps to figure out
+some interesting things.
+
+ align:start position:0%
+some interesting things.
+ 
+
+ align:start position:0%
+some interesting things.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+random walks
+
+ align:start position:0%
+random walks
+ 
+
+ align:start position:0%
+random walks
+of groups.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So suppose that G is a finite
+
+ align:start position:0%
+All right. So suppose that G is a finite
+ 
+
+ align:start position:0%
+All right. So suppose that G is a finite
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+and then mu is a probability measure on
+
+ align:start position:0%
+and then mu is a probability measure on
+ 
+
+ align:start position:0%
+and then mu is a probability measure on
+G. So I'll think of it
+
+ align:start position:0%
+G. So I'll think of it
+ 
+
+ align:start position:0%
+G. So I'll think of it
+as a function on G
+
+ align:start position:0%
+as a function on G
+ 
+
+ align:start position:0%
+as a function on G
+which is non- negative and sums to one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So if you have a probability
+
+ align:start position:0%
+Okay. So if you have a probability
+ 
+
+ align:start position:0%
+Okay. So if you have a probability
+measure like this, you can do a random
+
+ align:start position:0%
+measure like this, you can do a random
+ 
+
+ align:start position:0%
+measure like this, you can do a random
+walk where at each step of the random
+
+ align:start position:0%
+walk where at each step of the random
+ 
+
+ align:start position:0%
+walk where at each step of the random
+walk, you pick an element of G by this
+
+ align:start position:0%
+walk, you pick an element of G by this
+ 
+
+ align:start position:0%
+walk, you pick an element of G by this
+probability and then you move by that
+
+ align:start position:0%
+probability and then you move by that
+ 
+
+ align:start position:0%
+probability and then you move by that
+element. So here's how the random walk
+
+ align:start position:0%
+element. So here's how the random walk
+ 
+
+ align:start position:0%
+element. So here's how the random walk
+works.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you start somewhere
+
+ align:start position:0%
+So you start somewhere
+ 
+
+ align:start position:0%
+So you start somewhere
+say at G0 then you sample
+
+ align:start position:0%
+say at G0 then you sample
+ 
+
+ align:start position:0%
+say at G0 then you sample
+a step h from mu
+
+ align:start position:0%
+a step h from mu
+ 
+
+ align:start position:0%
+a step h from mu
+and the next guy g1 is g 0 * h.
+
+ align:start position:0%
+and the next guy g1 is g 0 * h.
+ 
+
+ align:start position:0%
+and the next guy g1 is g 0 * h.
+So that's one step of the random walk
+
+ align:start position:0%
+So that's one step of the random walk
+ 
+
+ align:start position:0%
+So that's one step of the random walk
+and then you can keep doing this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And um so if you do take K steps
+
+ align:start position:0%
+Okay. And um so if you do take K steps
+ 
+
+ align:start position:0%
+Okay. And um so if you do take K steps
+of the random walk then that will be
+
+ align:start position:0%
+of the random walk then that will be
+ 
+
+ align:start position:0%
+of the random walk then that will be
+there will be some probability
+
+ align:start position:0%
+there will be some probability
+ 
+
+ align:start position:0%
+there will be some probability
+distribution of where you end up after k
+
+ align:start position:0%
+distribution of where you end up after k
+ 
+
+ align:start position:0%
+distribution of where you end up after k
+steps and the main question about one
+
+ align:start position:0%
+steps and the main question about one
+ 
+
+ align:start position:0%
+steps and the main question about one
+main question about random walks is how
+
+ align:start position:0%
+main question about random walks is how
+ 
+
+ align:start position:0%
+main question about random walks is how
+evenly distributed is that probability
+
+ align:start position:0%
+evenly distributed is that probability
+ 
+
+ align:start position:0%
+evenly distributed is that probability
+distribution.
+
+ align:start position:0%
+distribution.
+ 
+
+ align:start position:0%
+distribution.
+Um so
+
+ align:start position:0%
+Um so
+ 
+
+ align:start position:0%
+Um so
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+how evenly
+
+ align:start position:0%
+how evenly
+ 
+
+ align:start position:0%
+how evenly
+distributed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uh the random walk after k steps.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And we'll make we'll make this
+
+ align:start position:0%
+Okay. And we'll make we'll make this
+ 
+
+ align:start position:0%
+Okay. And we'll make we'll make this
+more precise in a moment.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So,
+
+ align:start position:0%
+All right. So,
+ 
+
+ align:start position:0%
+All right. So,
+so we um it is helpful to describe this
+
+ align:start position:0%
+so we um it is helpful to describe this
+ 
+
+ align:start position:0%
+so we um it is helpful to describe this
+random walk using uh convolution.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so convolution on a group looks
+
+ align:start position:0%
+Okay, so convolution on a group looks
+ 
+
+ align:start position:0%
+Okay, so convolution on a group looks
+like this. We have two functions f_sub_1
+
+ align:start position:0%
+like this. We have two functions f_sub_1
+ 
+
+ align:start position:0%
+like this. We have two functions f_sub_1
+and f_sub_2 on this group. And then if I
+
+ align:start position:0%
+and f_sub_2 on this group. And then if I
+ 
+
+ align:start position:0%
+and f_sub_2 on this group. And then if I
+convolve them with each other
+
+ align:start position:0%
+convolve them with each other
+ 
+
+ align:start position:0%
+convolve them with each other
+and I evaluate that at g, that's the sum
+
+ align:start position:0%
+and I evaluate that at g, that's the sum
+ 
+
+ align:start position:0%
+and I evaluate that at g, that's the sum
+g1 * g2 = g. f of g1 f_sub_1 of g1
+
+ align:start position:0%
+g1 * g2 = g. f of g1 f_sub_1 of g1
+ 
+
+ align:start position:0%
+g1 * g2 = g. f of g1 f_sub_1 of g1
+f_sub_2 of g2.
+
+ align:start position:0%
+f_sub_2 of g2.
+ 
+
+ align:start position:0%
+f_sub_2 of g2.
+That's the sum over all the g1 and g2
+
+ align:start position:0%
+That's the sum over all the g1 and g2
+ 
+
+ align:start position:0%
+That's the sum over all the g1 and g2
+that multiply to g of of this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um and then for mu we can make an
+
+ align:start position:0%
+Okay. Um and then for mu we can make an
+ 
+
+ align:start position:0%
+Okay. Um and then for mu we can make an
+operator and t mu of f is just f
+
+ align:start position:0%
+operator and t mu of f is just f
+ 
+
+ align:start position:0%
+operator and t mu of f is just f
+convolved with mu. And this operator
+
+ align:start position:0%
+convolved with mu. And this operator
+ 
+
+ align:start position:0%
+convolved with mu. And this operator
+basically describes this random walk.
+
+ align:start position:0%
+basically describes this random walk.
+ 
+
+ align:start position:0%
+basically describes this random walk.
+So let's say how they're related. So
+
+ align:start position:0%
+So let's say how they're related. So
+ 
+
+ align:start position:0%
+So let's say how they're related. So
+suppose I were to take t mu and apply it
+
+ align:start position:0%
+suppose I were to take t mu and apply it
+ 
+
+ align:start position:0%
+suppose I were to take t mu and apply it
+to the delta function at g knot and
+
+ align:start position:0%
+to the delta function at g knot and
+ 
+
+ align:start position:0%
+to the delta function at g knot and
+evaluate that at some g.
+
+ align:start position:0%
+evaluate that at some g.
+ 
+
+ align:start position:0%
+evaluate that at some g.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+okay. So let's let's see what's a good
+
+ align:start position:0%
+okay. So let's let's see what's a good
+ 
+
+ align:start position:0%
+okay. So let's let's see what's a good
+way to write this.
+
+ align:start position:0%
+way to write this.
+ 
+
+ align:start position:0%
+way to write this.
+Um so that's the sum. Um actually let me
+
+ align:start position:0%
+Um so that's the sum. Um actually let me
+ 
+
+ align:start position:0%
+Um so that's the sum. Um actually let me
+look at how I wrote it in my notes. I
+
+ align:start position:0%
+look at how I wrote it in my notes. I
+ 
+
+ align:start position:0%
+look at how I wrote it in my notes. I
+tried writing this a few ways and then I
+
+ align:start position:0%
+tried writing this a few ways and then I
+ 
+
+ align:start position:0%
+tried writing this a few ways and then I
+decided there was a good way to write
+
+ align:start position:0%
+decided there was a good way to write
+ 
+
+ align:start position:0%
+decided there was a good way to write
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+Right? Yeah. Let's write it this way.
+
+ align:start position:0%
+Right? Yeah. Let's write it this way.
+ 
+
+ align:start position:0%
+Right? Yeah. Let's write it this way.
+So suppose I want to evaluate this at g*
+
+ align:start position:0%
+So suppose I want to evaluate this at g*
+ 
+
+ align:start position:0%
+So suppose I want to evaluate this at g*
+h. So that's the sum over g1 * g2 = g *
+
+ align:start position:0%
+h. So that's the sum over g1 * g2 = g *
+ 
+
+ align:start position:0%
+h. So that's the sum over g1 * g2 = g *
+h of delta function at g of g1 time mu
+
+ align:start position:0%
+h of delta function at g of g1 time mu
+ 
+
+ align:start position:0%
+h of delta function at g of g1 time mu
+of g2.
+
+ align:start position:0%
+of g2.
+ 
+
+ align:start position:0%
+of g2.
+All right. So the only way that this sum
+
+ align:start position:0%
+All right. So the only way that this sum
+ 
+
+ align:start position:0%
+All right. So the only way that this sum
+can be not zero is if g1 is g0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there's only one term in this sum.
+
+ align:start position:0%
+So there's only one term in this sum.
+ 
+
+ align:start position:0%
+So there's only one term in this sum.
+So this um g 0 * g2 is g 0 * h of mu of
+
+ align:start position:0%
+So this um g 0 * g2 is g 0 * h of mu of
+ 
+
+ align:start position:0%
+So this um g 0 * g2 is g 0 * h of mu of
+g2.
+
+ align:start position:0%
+g2.
+ 
+
+ align:start position:0%
+g2.
+There's only one term and it's the term
+
+ align:start position:0%
+There's only one term and it's the term
+ 
+
+ align:start position:0%
+There's only one term and it's the term
+where g2 is h.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this thing is the probability
+
+ align:start position:0%
+Okay. So this thing is the probability
+ 
+
+ align:start position:0%
+Okay. So this thing is the probability
+distribution of one step of the random
+
+ align:start position:0%
+distribution of one step of the random
+ 
+
+ align:start position:0%
+distribution of one step of the random
+walk. The probability if I started at g
+
+ align:start position:0%
+walk. The probability if I started at g
+ 
+
+ align:start position:0%
+walk. The probability if I started at g
+that I end up at g* h is mu of h. That's
+
+ align:start position:0%
+that I end up at g* h is mu of h. That's
+ 
+
+ align:start position:0%
+that I end up at g* h is mu of h. That's
+the definition of my random walk. So
+
+ align:start position:0%
+the definition of my random walk. So
+ 
+
+ align:start position:0%
+the definition of my random walk. So
+this operator is performing one step of
+
+ align:start position:0%
+this operator is performing one step of
+ 
+
+ align:start position:0%
+this operator is performing one step of
+the random walker. And therefore if I
+
+ align:start position:0%
+the random walker. And therefore if I
+ 
+
+ align:start position:0%
+the random walker. And therefore if I
+take t mu to the k of delta g0 that's uh
+
+ align:start position:0%
+take t mu to the k of delta g0 that's uh
+ 
+
+ align:start position:0%
+take t mu to the k of delta g0 that's uh
+like k steps of the random walk
+
+ align:start position:0%
+like k steps of the random walk
+ 
+
+ align:start position:0%
+like k steps of the random walk
+starting at g.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um actually let me say this I could say
+
+ align:start position:0%
+Um actually let me say this I could say
+ 
+
+ align:start position:0%
+Um actually let me say this I could say
+this better.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is the probability
+
+ align:start position:0%
+So this is the probability
+ 
+
+ align:start position:0%
+So this is the probability
+that a random walk is at g
+
+ align:start position:0%
+that a random walk is at g
+ 
+
+ align:start position:0%
+that a random walk is at g
+after k steps.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now we can take this question
+
+ align:start position:0%
+Okay. So now we can take this question
+ 
+
+ align:start position:0%
+Okay. So now we can take this question
+how evenly distributed is the random
+
+ align:start position:0%
+how evenly distributed is the random
+ 
+
+ align:start position:0%
+how evenly distributed is the random
+walk. We can write that as a precise
+
+ align:start position:0%
+walk. We can write that as a precise
+ 
+
+ align:start position:0%
+walk. We can write that as a precise
+question about this. I'll call it
+
+ align:start position:0%
+question about this. I'll call it
+ 
+
+ align:start position:0%
+question about this. I'll call it
+question one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I'd like to estimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay t mu to the k of delta g0. So this
+
+ align:start position:0%
+okay t mu to the k of delta g0. So this
+ 
+
+ align:start position:0%
+okay t mu to the k of delta g0. So this
+is the actual probability distribution.
+
+ align:start position:0%
+is the actual probability distribution.
+ 
+
+ align:start position:0%
+is the actual probability distribution.
+And if the probability was completely
+
+ align:start position:0%
+And if the probability was completely
+ 
+
+ align:start position:0%
+And if the probability was completely
+even over the whole group, it would be
+
+ align:start position:0%
+even over the whole group, it would be
+ 
+
+ align:start position:0%
+even over the whole group, it would be
+one over the size of the group
+
+ align:start position:0%
+one over the size of the group
+ 
+
+ align:start position:0%
+one over the size of the group
+everywhere. So I'm going to see how
+
+ align:start position:0%
+everywhere. So I'm going to see how
+ 
+
+ align:start position:0%
+everywhere. So I'm going to see how
+close it is to that by measuring the
+
+ align:start position:0%
+close it is to that by measuring the
+ 
+
+ align:start position:0%
+close it is to that by measuring the
+norm of this difference. So I like to
+
+ align:start position:0%
+norm of this difference. So I like to
+ 
+
+ align:start position:0%
+norm of this difference. So I like to
+estimate that. Okay. And L2 is helpful
+
+ align:start position:0%
+estimate that. Okay. And L2 is helpful
+ 
+
+ align:start position:0%
+estimate that. Okay. And L2 is helpful
+but also perhaps a little arbitrary. You
+
+ align:start position:0%
+but also perhaps a little arbitrary. You
+ 
+
+ align:start position:0%
+but also perhaps a little arbitrary. You
+could also put other norms. So could put
+
+ align:start position:0%
+could also put other norms. So could put
+ 
+
+ align:start position:0%
+could also put other norms. So could put
+or L infinity or maybe some other norm.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this is the kind of question
+
+ align:start position:0%
+Okay. So this is the kind of question
+ 
+
+ align:start position:0%
+Okay. So this is the kind of question
+about random walks on groups that we are
+
+ align:start position:0%
+about random walks on groups that we are
+ 
+
+ align:start position:0%
+about random walks on groups that we are
+going to try to understand.
+
+ align:start position:0%
+going to try to understand.
+ 
+
+ align:start position:0%
+going to try to understand.
+All right. So um to understand this it
+
+ align:start position:0%
+All right. So um to understand this it
+ 
+
+ align:start position:0%
+All right. So um to understand this it
+is helpful to notice that this is a
+
+ align:start position:0%
+is helpful to notice that this is a
+ 
+
+ align:start position:0%
+is helpful to notice that this is a
+linear operator. This t- mu is a linear
+
+ align:start position:0%
+linear operator. This t- mu is a linear
+ 
+
+ align:start position:0%
+linear operator. This t- mu is a linear
+operator. It's basically a matrix. And
+
+ align:start position:0%
+operator. It's basically a matrix. And
+ 
+
+ align:start position:0%
+operator. It's basically a matrix. And
+it's helpful to think about that um in
+
+ align:start position:0%
+it's helpful to think about that um in
+ 
+
+ align:start position:0%
+it's helpful to think about that um in
+terms of matrix ideas like the singular
+
+ align:start position:0%
+terms of matrix ideas like the singular
+ 
+
+ align:start position:0%
+terms of matrix ideas like the singular
+values and singular vectors of this
+
+ align:start position:0%
+values and singular vectors of this
+ 
+
+ align:start position:0%
+values and singular vectors of this
+matrix.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So t mu plus a linear operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to study
+
+ align:start position:0%
+and we're going to study
+ 
+
+ align:start position:0%
+and we're going to study
+singular values and singular vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of t.
+
+ align:start position:0%
+of t.
+ 
+
+ align:start position:0%
+of t.
+Okay. So there is um
+
+ align:start position:0%
+Okay. So there is um
+ 
+
+ align:start position:0%
+Okay. So there is um
+one um simple singular value which is or
+
+ align:start position:0%
+one um simple singular value which is or
+ 
+
+ align:start position:0%
+one um simple singular value which is or
+value I guess that t mu of one is one.
+
+ align:start position:0%
+value I guess that t mu of one is one.
+ 
+
+ align:start position:0%
+value I guess that t mu of one is one.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Are singular values and singular vectors
+
+ align:start position:0%
+>> Are singular values and singular vectors
+ 
+
+ align:start position:0%
+>> Are singular values and singular vectors
+just the same as values and values.
+
+ align:start position:0%
+just the same as values and values.
+ 
+
+ align:start position:0%
+just the same as values and values.
+>> Um they are closely related. Um
+
+ align:start position:0%
+>> Um they are closely related. Um
+ 
+
+ align:start position:0%
+>> Um they are closely related. Um
+so let me do a quick review of singular
+
+ align:start position:0%
+so let me do a quick review of singular
+ 
+
+ align:start position:0%
+so let me do a quick review of singular
+values and values. Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+so if you have a a matrix and you think
+
+ align:start position:0%
+so if you have a a matrix and you think
+ 
+
+ align:start position:0%
+so if you have a a matrix and you think
+about what it does to the unit ball, it
+
+ align:start position:0%
+about what it does to the unit ball, it
+ 
+
+ align:start position:0%
+about what it does to the unit ball, it
+will turn the unit ball into an
+
+ align:start position:0%
+will turn the unit ball into an
+ 
+
+ align:start position:0%
+will turn the unit ball into an
+ellipsoid.
+
+ align:start position:0%
+ellipsoid.
+ 
+
+ align:start position:0%
+ellipsoid.
+Um and the principal axes of this
+
+ align:start position:0%
+Um and the principal axes of this
+ 
+
+ align:start position:0%
+Um and the principal axes of this
+ellipsoid are the singular values sigma
+
+ align:start position:0%
+ellipsoid are the singular values sigma
+ 
+
+ align:start position:0%
+ellipsoid are the singular values sigma
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+sigma 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so if we look at the pre-im images of
+
+ align:start position:0%
+uh so if we look at the pre-im images of
+ 
+
+ align:start position:0%
+uh so if we look at the pre-im images of
+these things those will be the singular
+
+ align:start position:0%
+these things those will be the singular
+ 
+
+ align:start position:0%
+these things those will be the singular
+vectors.
+
+ align:start position:0%
+vectors.
+ 
+
+ align:start position:0%
+vectors.
+So well depending on the matrix they
+
+ align:start position:0%
+So well depending on the matrix they
+ 
+
+ align:start position:0%
+So well depending on the matrix they
+could be pointing any which way but
+
+ align:start position:0%
+could be pointing any which way but
+ 
+
+ align:start position:0%
+could be pointing any which way but
+maybe that's um v2
+
+ align:start position:0%
+maybe that's um v2
+ 
+
+ align:start position:0%
+maybe that's um v2
+and that is v1.
+
+ align:start position:0%
+and that is v1.
+ 
+
+ align:start position:0%
+and that is v1.
+Okay. And they will always be so we'll
+
+ align:start position:0%
+Okay. And they will always be so we'll
+ 
+
+ align:start position:0%
+Okay. And they will always be so we'll
+have um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the the vi or orthonormal
+
+ align:start position:0%
+so the the vi or orthonormal
+ 
+
+ align:start position:0%
+so the the vi or orthonormal
+and the size of mvi
+
+ align:start position:0%
+and the size of mvi
+ 
+
+ align:start position:0%
+and the size of mvi
+is sigma.
+
+ align:start position:0%
+is sigma.
+ 
+
+ align:start position:0%
+is sigma.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+and the mvi are also worth are also
+
+ align:start position:0%
+and the mvi are also worth are also
+ 
+
+ align:start position:0%
+and the mvi are also worth are also
+orthogonal. Those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are the singular vectors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now they are not generally igen
+
+ align:start position:0%
+Okay. Now they are not generally igen
+ 
+
+ align:start position:0%
+Okay. Now they are not generally igen
+vectors in the sense that mvi will not
+
+ align:start position:0%
+vectors in the sense that mvi will not
+ 
+
+ align:start position:0%
+vectors in the sense that mvi will not
+usually be a multiple of vi. Uh but they
+
+ align:start position:0%
+usually be a multiple of vi. Uh but they
+ 
+
+ align:start position:0%
+usually be a multiple of vi. Uh but they
+are closely related to them. Um the vi
+
+ align:start position:0%
+are closely related to them. Um the vi
+ 
+
+ align:start position:0%
+are closely related to them. Um the vi
+are the igen vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of m star or m m star I guess. Um
+
+ align:start position:0%
+of m star or m m star I guess. Um
+ 
+
+ align:start position:0%
+of m star or m m star I guess. Um
+and the uh sigma i squared are the igen
+
+ align:start position:0%
+and the uh sigma i squared are the igen
+ 
+
+ align:start position:0%
+and the uh sigma i squared are the igen
+values of m star mic
+
+ align:start position:0%
+values of m star mic
+ 
+
+ align:start position:0%
+values of m star mic
+mm star.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+so in particular this biggest uh this
+
+ align:start position:0%
+so in particular this biggest uh this
+ 
+
+ align:start position:0%
+so in particular this biggest uh this
+biggest singular vector measures the
+
+ align:start position:0%
+biggest singular vector measures the
+ 
+
+ align:start position:0%
+biggest singular vector measures the
+operator norm of the matrix which is
+
+ align:start position:0%
+operator norm of the matrix which is
+ 
+
+ align:start position:0%
+operator norm of the matrix which is
+that the the um so these are these are
+
+ align:start position:0%
+that the the um so these are these are
+ 
+
+ align:start position:0%
+that the the um so these are these are
+ordered like this and um
+
+ align:start position:0%
+ordered like this and um
+ 
+
+ align:start position:0%
+ordered like this and um
+MV
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is at most sigma 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so the reason we're talking about
+
+ align:start position:0%
+Okay, so the reason we're talking about
+ 
+
+ align:start position:0%
+Okay, so the reason we're talking about
+singular values is we're going to care
+
+ align:start position:0%
+singular values is we're going to care
+ 
+
+ align:start position:0%
+singular values is we're going to care
+about stuff like this. And
+
+ align:start position:0%
+about stuff like this. And
+ 
+
+ align:start position:0%
+about stuff like this. And
+this is naturally associated with
+
+ align:start position:0%
+this is naturally associated with
+ 
+
+ align:start position:0%
+this is naturally associated with
+singular values. If m is not symmetric,
+
+ align:start position:0%
+singular values. If m is not symmetric,
+ 
+
+ align:start position:0%
+singular values. If m is not symmetric,
+it's not necessarily the same as talking
+
+ align:start position:0%
+it's not necessarily the same as talking
+ 
+
+ align:start position:0%
+it's not necessarily the same as talking
+about values.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. So, if we take this tu of the
+
+ align:start position:0%
+okay. So, if we take this tu of the
+ 
+
+ align:start position:0%
+okay. So, if we take this tu of the
+function one, the constant function,
+
+ align:start position:0%
+function one, the constant function,
+ 
+
+ align:start position:0%
+function one, the constant function,
+we'll just get one because this t- mu is
+
+ align:start position:0%
+we'll just get one because this t- mu is
+ 
+
+ align:start position:0%
+we'll just get one because this t- mu is
+is like an averaging operator.
+
+ align:start position:0%
+is like an averaging operator.
+ 
+
+ align:start position:0%
+is like an averaging operator.
+We're averaging t. So, t mu of f at g is
+
+ align:start position:0%
+We're averaging t. So, t mu of f at g is
+ 
+
+ align:start position:0%
+We're averaging t. So, t mu of f at g is
+the average value at of g at some other
+
+ align:start position:0%
+the average value at of g at some other
+ 
+
+ align:start position:0%
+the average value at of g at some other
+places around g that are dictated by mu.
+
+ align:start position:0%
+places around g that are dictated by mu.
+ 
+
+ align:start position:0%
+places around g that are dictated by mu.
+So t mu of one is one.
+
+ align:start position:0%
+So t mu of one is one.
+ 
+
+ align:start position:0%
+So t mu of one is one.
+Okay. And um now it's uh okay. So so
+
+ align:start position:0%
+Okay. And um now it's uh okay. So so
+ 
+
+ align:start position:0%
+Okay. And um now it's uh okay. So so
+that implies that the that the the Okay.
+
+ align:start position:0%
+that implies that the that the the Okay.
+ 
+
+ align:start position:0%
+that implies that the that the the Okay.
+So I'll do a little lema.
+
+ align:start position:0%
+So I'll do a little lema.
+ 
+
+ align:start position:0%
+So I'll do a little lema.
+The the the largest singular value.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Okay. So little lema is that t mu
+
+ align:start position:0%
+Yeah. Okay. So little lema is that t mu
+ 
+
+ align:start position:0%
+Yeah. Okay. So little lema is that t mu
+of f and l2 is at most f and l2 and this
+
+ align:start position:0%
+of f and l2 is at most f and l2 and this
+ 
+
+ align:start position:0%
+of f and l2 is at most f and l2 and this
+is sharp because of this example.
+
+ align:start position:0%
+is sharp because of this example.
+ 
+
+ align:start position:0%
+is sharp because of this example.
+They could be they could be equal.
+
+ align:start position:0%
+They could be they could be equal.
+ 
+
+ align:start position:0%
+They could be they could be equal.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So proving this will help us think
+
+ align:start position:0%
+Okay. So proving this will help us think
+ 
+
+ align:start position:0%
+Okay. So proving this will help us think
+a little bit about what convolution
+
+ align:start position:0%
+a little bit about what convolution
+ 
+
+ align:start position:0%
+a little bit about what convolution
+means. Um so t mu of f is f convolved
+
+ align:start position:0%
+means. Um so t mu of f is f convolved
+ 
+
+ align:start position:0%
+means. Um so t mu of f is f convolved
+with mu
+
+ align:start position:0%
+with mu
+ 
+
+ align:start position:0%
+with mu
+g here.
+
+ align:start position:0%
+g here.
+ 
+
+ align:start position:0%
+g here.
+So that's the sum g1 g2 = g f of g1 mu
+
+ align:start position:0%
+So that's the sum g1 g2 = g f of g1 mu
+ 
+
+ align:start position:0%
+So that's the sum g1 g2 = g f of g1 mu
+of g2.
+
+ align:start position:0%
+of g2.
+ 
+
+ align:start position:0%
+of g2.
+And I'd like to think of this as a sum
+
+ align:start position:0%
+And I'd like to think of this as a sum
+ 
+
+ align:start position:0%
+And I'd like to think of this as a sum
+over g2. So it's the sum over g2 because
+
+ align:start position:0%
+over g2. So it's the sum over g2 because
+ 
+
+ align:start position:0%
+over g2. So it's the sum over g2 because
+I'm thinking of it that way. I can bring
+
+ align:start position:0%
+I'm thinking of it that way. I can bring
+ 
+
+ align:start position:0%
+I'm thinking of it that way. I can bring
+the mu of g2 out front and then what I
+
+ align:start position:0%
+the mu of g2 out front and then what I
+ 
+
+ align:start position:0%
+the mu of g2 out front and then what I
+have left is f of g1 which is g * g2
+
+ align:start position:0%
+have left is f of g1 which is g * g2
+ 
+
+ align:start position:0%
+have left is f of g1 which is g * g2
+inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want to think of this as a linear
+
+ align:start position:0%
+and I want to think of this as a linear
+ 
+
+ align:start position:0%
+and I want to think of this as a linear
+combination of a bunch of different
+
+ align:start position:0%
+combination of a bunch of different
+ 
+
+ align:start position:0%
+combination of a bunch of different
+functions of g.
+
+ align:start position:0%
+functions of g.
+ 
+
+ align:start position:0%
+functions of g.
+Okay, let's give them a name. So this
+
+ align:start position:0%
+Okay, let's give them a name. So this
+ 
+
+ align:start position:0%
+Okay, let's give them a name. So this
+function of g is sort of f but but we
+
+ align:start position:0%
+function of g is sort of f but but we
+ 
+
+ align:start position:0%
+function of g is sort of f but but we
+first did this thing and I want I want
+
+ align:start position:0%
+first did this thing and I want I want
+ 
+
+ align:start position:0%
+first did this thing and I want I want
+you to think of it as taking f and then
+
+ align:start position:0%
+you to think of it as taking f and then
+ 
+
+ align:start position:0%
+you to think of it as taking f and then
+shifting it using the group. So it's the
+
+ align:start position:0%
+shifting it using the group. So it's the
+ 
+
+ align:start position:0%
+shifting it using the group. So it's the
+right translation by g2 of f of g is
+
+ align:start position:0%
+right translation by g2 of f of g is
+ 
+
+ align:start position:0%
+right translation by g2 of f of g is
+defined to be this thing here.
+
+ align:start position:0%
+defined to be this thing here.
+ 
+
+ align:start position:0%
+defined to be this thing here.
+So we could plug that in. Um and this
+
+ align:start position:0%
+So we could plug that in. Um and this
+ 
+
+ align:start position:0%
+So we could plug that in. Um and this
+shifting operation doesn't change the
+
+ align:start position:0%
+shifting operation doesn't change the
+ 
+
+ align:start position:0%
+shifting operation doesn't change the
+norm of g. So, RG2 of F in L2 is the
+
+ align:start position:0%
+norm of g. So, RG2 of F in L2 is the
+ 
+
+ align:start position:0%
+norm of g. So, RG2 of F in L2 is the
+same as F in R2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ah, I've been mentioning L2. What? Yeah,
+
+ align:start position:0%
+Ah, I've been mentioning L2. What? Yeah,
+ 
+
+ align:start position:0%
+Ah, I've been mentioning L2. What? Yeah,
+I should say.
+
+ align:start position:0%
+I should say.
+ 
+
+ align:start position:0%
+I should say.
+Okay, let me pause for a second. I
+
+ align:start position:0%
+Okay, let me pause for a second. I
+ 
+
+ align:start position:0%
+Okay, let me pause for a second. I
+should have said something before.
+
+ align:start position:0%
+should have said something before.
+ 
+
+ align:start position:0%
+should have said something before.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so when we have these functions on
+
+ align:start position:0%
+Okay, so when we have these functions on
+ 
+
+ align:start position:0%
+Okay, so when we have these functions on
+G, we're going to measure their norm.
+
+ align:start position:0%
+G, we're going to measure their norm.
+ 
+
+ align:start position:0%
+G, we're going to measure their norm.
+Um, and if I have f L2 of G, this is
+
+ align:start position:0%
+Um, and if I have f L2 of G, this is
+ 
+
+ align:start position:0%
+Um, and if I have f L2 of G, this is
+going to be some G and G, f of gum
+
+ align:start position:0%
+going to be some G and G, f of gum
+ 
+
+ align:start position:0%
+going to be some G and G, f of gum
+squared to the 12. Or I could take an
+
+ align:start position:0%
+squared to the 12. Or I could take an
+ 
+
+ align:start position:0%
+squared to the 12. Or I could take an
+inner product, the inner product of
+
+ align:start position:0%
+inner product, the inner product of
+ 
+
+ align:start position:0%
+inner product, the inner product of
+f_sub_1 and f_sub_2 is the sum g and g,
+
+ align:start position:0%
+f_sub_1 and f_sub_2 is the sum g and g,
+ 
+
+ align:start position:0%
+f_sub_1 and f_sub_2 is the sum g and g,
+f_sub_1 of g, f_sub_2 of g to that. So
+
+ align:start position:0%
+f_sub_1 of g, f_sub_2 of g to that. So
+ 
+
+ align:start position:0%
+f_sub_1 of g, f_sub_2 of g to that. So
+the functions on g are I hope we're
+
+ align:start position:0%
+the functions on g are I hope we're
+ 
+
+ align:start position:0%
+the functions on g are I hope we're
+spaced with this with this natural
+
+ align:start position:0%
+spaced with this with this natural
+ 
+
+ align:start position:0%
+spaced with this with this natural
+measure. Okay. Um so then if I take a
+
+ align:start position:0%
+measure. Okay. Um so then if I take a
+ 
+
+ align:start position:0%
+measure. Okay. Um so then if I take a
+function and I
+
+ align:start position:0%
+function and I
+ 
+
+ align:start position:0%
+function and I
+translate it or do this right
+
+ align:start position:0%
+translate it or do this right
+ 
+
+ align:start position:0%
+translate it or do this right
+translation um it just sort of permutes
+
+ align:start position:0%
+translation um it just sort of permutes
+ 
+
+ align:start position:0%
+translation um it just sort of permutes
+the value so it doesn't change this
+
+ align:start position:0%
+the value so it doesn't change this
+ 
+
+ align:start position:0%
+the value so it doesn't change this
+thing.
+
+ align:start position:0%
+thing.
+ 
+
+ align:start position:0%
+thing.
+Okay. So now if we look at our t mu of f
+
+ align:start position:0%
+Okay. So now if we look at our t mu of f
+ 
+
+ align:start position:0%
+Okay. So now if we look at our t mu of f
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+um I have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm interested in the norm of t mu of f.
+
+ align:start position:0%
+I'm interested in the norm of t mu of f.
+ 
+
+ align:start position:0%
+I'm interested in the norm of t mu of f.
+This is the norm of the sum on G2 mu of
+
+ align:start position:0%
+This is the norm of the sum on G2 mu of
+ 
+
+ align:start position:0%
+This is the norm of the sum on G2 mu of
+G2
+
+ align:start position:0%
+G2
+ 
+
+ align:start position:0%
+G2
+R subg2 of F.
+
+ align:start position:0%
+R subg2 of F.
+ 
+
+ align:start position:0%
+R subg2 of F.
+It's a linear combination of these
+
+ align:start position:0%
+It's a linear combination of these
+ 
+
+ align:start position:0%
+It's a linear combination of these
+functions which are all translates of F.
+
+ align:start position:0%
+functions which are all translates of F.
+ 
+
+ align:start position:0%
+functions which are all translates of F.
+And L2 is a norm. It obeys the triangle
+
+ align:start position:0%
+And L2 is a norm. It obeys the triangle
+ 
+
+ align:start position:0%
+And L2 is a norm. It obeys the triangle
+inequality. So this is less than the sum
+
+ align:start position:0%
+inequality. So this is less than the sum
+ 
+
+ align:start position:0%
+inequality. So this is less than the sum
+on G2 mu of G2
+
+ align:start position:0%
+on G2 mu of G2
+ 
+
+ align:start position:0%
+on G2 mu of G2
+RG2 of F and L2. All of these have the
+
+ align:start position:0%
+RG2 of F and L2. All of these have the
+ 
+
+ align:start position:0%
+RG2 of F and L2. All of these have the
+same norm.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the L2 norm of F and the L2
+
+ align:start position:0%
+which is the L2 norm of F and the L2
+ 
+
+ align:start position:0%
+which is the L2 norm of F and the L2
+norm and then this adds up to one. So
+
+ align:start position:0%
+norm and then this adds up to one. So
+ 
+
+ align:start position:0%
+norm and then this adds up to one. So
+this is just the L2 norm of F.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so this is a basic fact about averaging
+
+ align:start position:0%
+so this is a basic fact about averaging
+ 
+
+ align:start position:0%
+so this is a basic fact about averaging
+operators. Um and
+
+ align:start position:0%
+operators. Um and
+ 
+
+ align:start position:0%
+operators. Um and
+to understand whether the random walk is
+
+ align:start position:0%
+to understand whether the random walk is
+ 
+
+ align:start position:0%
+to understand whether the random walk is
+mixing things up, we have to care about
+
+ align:start position:0%
+mixing things up, we have to care about
+ 
+
+ align:start position:0%
+mixing things up, we have to care about
+how it behaves on the space orthogonal
+
+ align:start position:0%
+how it behaves on the space orthogonal
+ 
+
+ align:start position:0%
+how it behaves on the space orthogonal
+to one. And the first observation is
+
+ align:start position:0%
+to one. And the first observation is
+ 
+
+ align:start position:0%
+to one. And the first observation is
+that it preserves the space orthogonal
+
+ align:start position:0%
+that it preserves the space orthogonal
+ 
+
+ align:start position:0%
+that it preserves the space orthogonal
+to one. So let's give that space a name.
+
+ align:start position:0%
+to one. So let's give that space a name.
+ 
+
+ align:start position:0%
+to one. So let's give that space a name.
+Say L2 of G KN is the set of F and L2 of
+
+ align:start position:0%
+Say L2 of G KN is the set of F and L2 of
+ 
+
+ align:start position:0%
+Say L2 of G KN is the set of F and L2 of
+G.
+
+ align:start position:0%
+G.
+ 
+
+ align:start position:0%
+G.
+So that
+
+ align:start position:0%
+So that
+ 
+
+ align:start position:0%
+So that
+sum G and G of F of G is zero. This is
+
+ align:start position:0%
+sum G and G of F of G is zero. This is
+ 
+
+ align:start position:0%
+sum G and G of F of G is zero. This is
+saying that f is orthogonal to the
+
+ align:start position:0%
+saying that f is orthogonal to the
+ 
+
+ align:start position:0%
+saying that f is orthogonal to the
+constant function.
+
+ align:start position:0%
+constant function.
+ 
+
+ align:start position:0%
+constant function.
+Okay. So another simple lema is that our
+
+ align:start position:0%
+Okay. So another simple lema is that our
+ 
+
+ align:start position:0%
+Okay. So another simple lema is that our
+operator t mu actually takes this space
+
+ align:start position:0%
+operator t mu actually takes this space
+ 
+
+ align:start position:0%
+operator t mu actually takes this space
+to itself. So it takes the constant
+
+ align:start position:0%
+to itself. So it takes the constant
+ 
+
+ align:start position:0%
+to itself. So it takes the constant
+function to itself and it takes the
+
+ align:start position:0%
+function to itself and it takes the
+ 
+
+ align:start position:0%
+function to itself and it takes the
+perpendicular space to itself which will
+
+ align:start position:0%
+perpendicular space to itself which will
+ 
+
+ align:start position:0%
+perpendicular space to itself which will
+imply that the constant function is one
+
+ align:start position:0%
+imply that the constant function is one
+ 
+
+ align:start position:0%
+imply that the constant function is one
+of the singular vectors of the of of
+
+ align:start position:0%
+of the singular vectors of the of of
+ 
+
+ align:start position:0%
+of the singular vectors of the of of
+this operator.
+
+ align:start position:0%
+this operator.
+ 
+
+ align:start position:0%
+this operator.
+Okay. So proof
+
+ align:start position:0%
+Okay. So proof
+ 
+
+ align:start position:0%
+Okay. So proof
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+so I want to understand the sum g and g
+
+ align:start position:0%
+so I want to understand the sum g and g
+ 
+
+ align:start position:0%
+so I want to understand the sum g and g
+of t team muf of g. Going to imagine
+
+ align:start position:0%
+of t team muf of g. Going to imagine
+ 
+
+ align:start position:0%
+of t team muf of g. Going to imagine
+that the sum of f of g is zero. And I
+
+ align:start position:0%
+that the sum of f of g is zero. And I
+ 
+
+ align:start position:0%
+that the sum of f of g is zero. And I
+want to see if that's still true. All
+
+ align:start position:0%
+want to see if that's still true. All
+ 
+
+ align:start position:0%
+want to see if that's still true. All
+right. So that's the sum g and g sum g1
+
+ align:start position:0%
+right. So that's the sum g and g sum g1
+ 
+
+ align:start position:0%
+right. So that's the sum g and g sum g1
+* g2 equals g. f of g1 mu of g2.
+
+ align:start position:0%
+* g2 equals g. f of g1 mu of g2.
+ 
+
+ align:start position:0%
+* g2 equals g. f of g1 mu of g2.
+And if you think about what we're
+
+ align:start position:0%
+And if you think about what we're
+ 
+
+ align:start position:0%
+And if you think about what we're
+summing over, we're just summing over G1
+
+ align:start position:0%
+summing over, we're just summing over G1
+ 
+
+ align:start position:0%
+summing over, we're just summing over G1
+and G2.
+
+ align:start position:0%
+and G2.
+ 
+
+ align:start position:0%
+and G2.
+So this is the sum over G1 and G2 of F
+
+ align:start position:0%
+So this is the sum over G1 and G2 of F
+ 
+
+ align:start position:0%
+So this is the sum over G1 and G2 of F
+of G1, mu of G2. And now that factors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is one. And if F was in L2 of
+
+ align:start position:0%
+So this is one. And if F was in L2 of
+ 
+
+ align:start position:0%
+So this is one. And if F was in L2 of
+GN, this would be zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is
+
+ align:start position:0%
+This is
+ 
+
+ align:start position:0%
+This is
+so f if f is an l2 of g not then so t mu
+
+ align:start position:0%
+so f if f is an l2 of g not then so t mu
+ 
+
+ align:start position:0%
+so f if f is an l2 of g not then so t mu
+of f will be
+
+ align:start position:0%
+of f will be
+ 
+
+ align:start position:0%
+of f will be
+okay Oh,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right. So, so we've seen that um
+
+ align:start position:0%
+all right. So, so we've seen that um
+ 
+
+ align:start position:0%
+all right. So, so we've seen that um
+t mu of one is one and t mu takes l2 of
+
+ align:start position:0%
+t mu of one is one and t mu takes l2 of
+ 
+
+ align:start position:0%
+t mu of one is one and t mu takes l2 of
+g kn to itself.
+
+ align:start position:0%
+g kn to itself.
+ 
+
+ align:start position:0%
+g kn to itself.
+So this is the largest singular value
+
+ align:start position:0%
+So this is the largest singular value
+ 
+
+ align:start position:0%
+So this is the largest singular value
+we've seen and um and then here there's
+
+ align:start position:0%
+we've seen and um and then here there's
+ 
+
+ align:start position:0%
+we've seen and um and then here there's
+something else. So let's say sigma one
+
+ align:start position:0%
+something else. So let's say sigma one
+ 
+
+ align:start position:0%
+something else. So let's say sigma one
+of t mu.
+
+ align:start position:0%
+of t mu.
+ 
+
+ align:start position:0%
+of t mu.
+So, so this this one could I'll call it
+
+ align:start position:0%
+So, so this this one could I'll call it
+ 
+
+ align:start position:0%
+So, so this this one could I'll call it
+sigma kn of t mu. Somehow in this
+
+ align:start position:0%
+sigma kn of t mu. Somehow in this
+ 
+
+ align:start position:0%
+sigma kn of t mu. Somehow in this
+setting the one is sort of trivial and
+
+ align:start position:0%
+setting the one is sort of trivial and
+ 
+
+ align:start position:0%
+setting the one is sort of trivial and
+everything else will depend on the trace
+
+ align:start position:0%
+everything else will depend on the trace
+ 
+
+ align:start position:0%
+everything else will depend on the trace
+of mu. So sigma 1 of t mu is the largest
+
+ align:start position:0%
+of mu. So sigma 1 of t mu is the largest
+ 
+
+ align:start position:0%
+of mu. So sigma 1 of t mu is the largest
+singular value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of of this part.
+
+ align:start position:0%
+of of this part.
+ 
+
+ align:start position:0%
+of of this part.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+All right. So question two is going to
+
+ align:start position:0%
+All right. So question two is going to
+ 
+
+ align:start position:0%
+All right. So question two is going to
+be to estimate that
+
+ align:start position:0%
+be to estimate that
+ 
+
+ align:start position:0%
+be to estimate that
+estimate sigma one of t and these two
+
+ align:start position:0%
+estimate sigma one of t and these two
+ 
+
+ align:start position:0%
+estimate sigma one of t and these two
+questions are related to each other. Um
+
+ align:start position:0%
+questions are related to each other. Um
+ 
+
+ align:start position:0%
+questions are related to each other. Um
+this thing helps to understand um how I
+
+ align:start position:0%
+this thing helps to understand um how I
+ 
+
+ align:start position:0%
+this thing helps to understand um how I
+mean helps a lot to understand how this
+
+ align:start position:0%
+mean helps a lot to understand how this
+ 
+
+ align:start position:0%
+mean helps a lot to understand how this
+operator behaves and and to and to
+
+ align:start position:0%
+operator behaves and and to and to
+ 
+
+ align:start position:0%
+operator behaves and and to and to
+answer question one. So let me put up a
+
+ align:start position:0%
+answer question one. So let me put up a
+ 
+
+ align:start position:0%
+answer question one. So let me put up a
+simple proposition how question two is
+
+ align:start position:0%
+simple proposition how question two is
+ 
+
+ align:start position:0%
+simple proposition how question two is
+related to question one.
+
+ align:start position:0%
+related to question one.
+ 
+
+ align:start position:0%
+related to question one.
+So proposition if you look at that thing
+
+ align:start position:0%
+So proposition if you look at that thing
+ 
+
+ align:start position:0%
+So proposition if you look at that thing
+t mu to the k delta function g minus 1 /
+
+ align:start position:0%
+t mu to the k delta function g minus 1 /
+ 
+
+ align:start position:0%
+t mu to the k delta function g minus 1 /
+g in l2 this is bounded by sigma 1 of t
+
+ align:start position:0%
+g in l2 this is bounded by sigma 1 of t
+ 
+
+ align:start position:0%
+g in l2 this is bounded by sigma 1 of t
+mu to the k.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so proof.
+
+ align:start position:0%
+Okay so proof.
+ 
+
+ align:start position:0%
+Okay so proof.
+So we want to see what t mu to the k
+
+ align:start position:0%
+So we want to see what t mu to the k
+ 
+
+ align:start position:0%
+So we want to see what t mu to the k
+does to a delta function at a point.
+
+ align:start position:0%
+does to a delta function at a point.
+ 
+
+ align:start position:0%
+does to a delta function at a point.
+Let's take this delta function at a
+
+ align:start position:0%
+Let's take this delta function at a
+ 
+
+ align:start position:0%
+Let's take this delta function at a
+point and t mu splits up the constant
+
+ align:start position:0%
+point and t mu splits up the constant
+ 
+
+ align:start position:0%
+point and t mu splits up the constant
+function is an igen function and then
+
+ align:start position:0%
+function is an igen function and then
+ 
+
+ align:start position:0%
+function is an igen function and then
+and then then the the the things with
+
+ align:start position:0%
+and then then the the the things with
+ 
+
+ align:start position:0%
+and then then the the the things with
+mean zero. So let's split up this delta
+
+ align:start position:0%
+mean zero. So let's split up this delta
+ 
+
+ align:start position:0%
+mean zero. So let's split up this delta
+function. So the the
+
+ align:start position:0%
+function. So the the
+ 
+
+ align:start position:0%
+function. So the the
+constant part of it is like this and
+
+ align:start position:0%
+constant part of it is like this and
+ 
+
+ align:start position:0%
+constant part of it is like this and
+then we have this.
+
+ align:start position:0%
+then we have this.
+ 
+
+ align:start position:0%
+then we have this.
+So the reason we split it up that way is
+
+ align:start position:0%
+So the reason we split it up that way is
+ 
+
+ align:start position:0%
+So the reason we split it up that way is
+that this part which in the beginning of
+
+ align:start position:0%
+that this part which in the beginning of
+ 
+
+ align:start position:0%
+that this part which in the beginning of
+the class we could have we would have
+
+ align:start position:0%
+the class we could have we would have
+ 
+
+ align:start position:0%
+the class we could have we would have
+called like the high part of this um so
+
+ align:start position:0%
+called like the high part of this um so
+ 
+
+ align:start position:0%
+called like the high part of this um so
+I guess I'll do that that's in L2 of G 0
+
+ align:start position:0%
+I guess I'll do that that's in L2 of G 0
+ 
+
+ align:start position:0%
+I guess I'll do that that's in L2 of G 0
+mean zero part okay now what happens
+
+ align:start position:0%
+mean zero part okay now what happens
+ 
+
+ align:start position:0%
+mean zero part okay now what happens
+when we apply this operator well this
+
+ align:start position:0%
+when we apply this operator well this
+ 
+
+ align:start position:0%
+when we apply this operator well this
+operator takes constants to constants
+
+ align:start position:0%
+operator takes constants to constants
+ 
+
+ align:start position:0%
+operator takes constants to constants
+uh it's the identity on the constant
+
+ align:start position:0%
+uh it's the identity on the constant
+ 
+
+ align:start position:0%
+uh it's the identity on the constant
+part um and so I take t mu to the k
+
+ align:start position:0%
+part um and so I take t mu to the k
+ 
+
+ align:start position:0%
+part um and so I take t mu to the k
+delta g kn
+
+ align:start position:0%
+delta g kn
+ 
+
+ align:start position:0%
+delta g kn
+this part will say stay stay like one
+
+ align:start position:0%
+this part will say stay stay like one
+ 
+
+ align:start position:0%
+this part will say stay stay like one
+over one over I'll take the left hand
+
+ align:start position:0%
+over one over I'll take the left hand
+ 
+
+ align:start position:0%
+over one over I'll take the left hand
+side and then if I subtract that it will
+
+ align:start position:0%
+side and then if I subtract that it will
+ 
+
+ align:start position:0%
+side and then if I subtract that it will
+disappear so what I'll be left with is t
+
+ align:start position:0%
+disappear so what I'll be left with is t
+ 
+
+ align:start position:0%
+disappear so what I'll be left with is t
+mu to the k on
+
+ align:start position:0%
+mu to the k on
+ 
+
+ align:start position:0%
+mu to the k on
+this uh high part of the delta g not
+
+ align:start position:0%
+this uh high part of the delta g not
+ 
+
+ align:start position:0%
+this uh high part of the delta g not
+okay how big is that well this part
+
+ align:start position:0%
+okay how big is that well this part
+ 
+
+ align:start position:0%
+okay how big is that well this part
+lives in this space so we can bound the
+
+ align:start position:0%
+lives in this space so we can bound the
+ 
+
+ align:start position:0%
+lives in this space so we can bound the
+size of this thing using the uh singular
+
+ align:start position:0%
+size of this thing using the uh singular
+ 
+
+ align:start position:0%
+size of this thing using the uh singular
+vector. Um and so so
+
+ align:start position:0%
+vector. Um and so so
+ 
+
+ align:start position:0%
+vector. Um and so so
+I get t mu
+
+ align:start position:0%
+I get t mu
+ 
+
+ align:start position:0%
+I get t mu
+to the k
+
+ align:start position:0%
+to the k
+ 
+
+ align:start position:0%
+to the k
+of delta g high
+
+ align:start position:0%
+of delta g high
+ 
+
+ align:start position:0%
+of delta g high
+two that's bounded by
+
+ align:start position:0%
+two that's bounded by
+ 
+
+ align:start position:0%
+two that's bounded by
+sigma 1 of t mu to the k
+
+ align:start position:0%
+sigma 1 of t mu to the k
+ 
+
+ align:start position:0%
+sigma 1 of t mu to the k
+times delta g high2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And now it's it's also now
+
+ align:start position:0%
+Okay. And now it's it's also now
+ 
+
+ align:start position:0%
+Okay. And now it's it's also now
+straightforward to check that this is
+
+ align:start position:0%
+straightforward to check that this is
+ 
+
+ align:start position:0%
+straightforward to check that this is
+smaller than one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So uh it's an application um
+
+ align:start position:0%
+So uh it's an application um
+ 
+
+ align:start position:0%
+So uh it's an application um
+if we were able to arrange that sigma 1
+
+ align:start position:0%
+if we were able to arrange that sigma 1
+ 
+
+ align:start position:0%
+if we were able to arrange that sigma 1
+t mu to the k was less than 1 over 100
+
+ align:start position:0%
+t mu to the k was less than 1 over 100
+ 
+
+ align:start position:0%
+t mu to the k was less than 1 over 100
+times the size of g
+
+ align:start position:0%
+times the size of g
+ 
+
+ align:start position:0%
+times the size of g
+um then well this l2 norm would be less
+
+ align:start position:0%
+um then well this l2 norm would be less
+ 
+
+ align:start position:0%
+um then well this l2 norm would be less
+than one over 100 times the size of g
+
+ align:start position:0%
+than one over 100 times the size of g
+ 
+
+ align:start position:0%
+than one over 100 times the size of g
+and so in particular the l infinity norm
+
+ align:start position:0%
+and so in particular the l infinity norm
+ 
+
+ align:start position:0%
+and so in particular the l infinity norm
+would be less than one over 100 times
+
+ align:start position:0%
+would be less than one over 100 times
+ 
+
+ align:start position:0%
+would be less than one over 100 times
+the size of g. So then I would say that
+
+ align:start position:0%
+the size of g. So then I would say that
+ 
+
+ align:start position:0%
+the size of g. So then I would say that
+for every g um
+
+ align:start position:0%
+for every g um
+ 
+
+ align:start position:0%
+for every g um
+t mu k delta g of g minus one over the
+
+ align:start position:0%
+t mu k delta g of g minus one over the
+ 
+
+ align:start position:0%
+t mu k delta g of g minus one over the
+size of g would be smaller than 1 over
+
+ align:start position:0%
+size of g would be smaller than 1 over
+ 
+
+ align:start position:0%
+size of g would be smaller than 1 over
+100 times the size of g. That would tell
+
+ align:start position:0%
+100 times the size of g. That would tell
+ 
+
+ align:start position:0%
+100 times the size of g. That would tell
+us say that this function is pretty
+
+ align:start position:0%
+us say that this function is pretty
+ 
+
+ align:start position:0%
+us say that this function is pretty
+close to this constant function within
+
+ align:start position:0%
+close to this constant function within
+ 
+
+ align:start position:0%
+close to this constant function within
+1%. So that random walk would now have
+
+ align:start position:0%
+1%. So that random walk would now have
+ 
+
+ align:start position:0%
+1%. So that random walk would now have
+mixed uh pretty thoroughly.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, great. So if we can get our hands
+
+ align:start position:0%
+Okay, great. So if we can get our hands
+ 
+
+ align:start position:0%
+Okay, great. So if we can get our hands
+on sigma 1 of t mu, then we can figure
+
+ align:start position:0%
+on sigma 1 of t mu, then we can figure
+ 
+
+ align:start position:0%
+on sigma 1 of t mu, then we can figure
+out how long it takes this random walk
+
+ align:start position:0%
+out how long it takes this random walk
+ 
+
+ align:start position:0%
+out how long it takes this random walk
+to mix evenly.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now let me mention tell you an
+
+ align:start position:0%
+So now let me mention tell you an
+ 
+
+ align:start position:0%
+So now let me mention tell you an
+interesting example of a particular
+
+ align:start position:0%
+interesting example of a particular
+ 
+
+ align:start position:0%
+interesting example of a particular
+group and a particular mu where there's
+
+ align:start position:0%
+group and a particular mu where there's
+ 
+
+ align:start position:0%
+group and a particular mu where there's
+a cool estimate for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we are going to mostly focus or maybe
+
+ align:start position:0%
+So we are going to mostly focus or maybe
+ 
+
+ align:start position:0%
+So we are going to mostly focus or maybe
+only focus on the group SL2 of FP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um could pick many different
+
+ align:start position:0%
+and um could pick many different
+ 
+
+ align:start position:0%
+and um could pick many different
+measures for a random walk but one nice
+
+ align:start position:0%
+measures for a random walk but one nice
+ 
+
+ align:start position:0%
+measures for a random walk but one nice
+one which has been studied is to take
+
+ align:start position:0%
+one which has been studied is to take
+ 
+
+ align:start position:0%
+one which has been studied is to take
+the set A to be so f so first of all um
+
+ align:start position:0%
+the set A to be so f so first of all um
+ 
+
+ align:start position:0%
+the set A to be so f so first of all um
+if A is a subset of G. There's a natural
+
+ align:start position:0%
+if A is a subset of G. There's a natural
+ 
+
+ align:start position:0%
+if A is a subset of G. There's a natural
+measure on A which is the uniform
+
+ align:start position:0%
+measure on A which is the uniform
+ 
+
+ align:start position:0%
+measure on A which is the uniform
+measure. So measure on A which is one
+
+ align:start position:0%
+measure. So measure on A which is one
+ 
+
+ align:start position:0%
+measure. So measure on A which is one
+over the cardality of A times the sum A
+
+ align:start position:0%
+over the cardality of A times the sum A
+ 
+
+ align:start position:0%
+over the cardality of A times the sum A
+and A of delta A.
+
+ align:start position:0%
+and A of delta A.
+ 
+
+ align:start position:0%
+and A of delta A.
+Okay. Um okay. So there's a nice set A
+
+ align:start position:0%
+Okay. Um okay. So there's a nice set A
+ 
+
+ align:start position:0%
+Okay. Um okay. So there's a nice set A
+inside of here which was studied by
+
+ align:start position:0%
+inside of here which was studied by
+ 
+
+ align:start position:0%
+inside of here which was studied by
+Selberg. A Selberg.
+
+ align:start position:0%
+Selberg. A Selberg.
+ 
+
+ align:start position:0%
+Selberg. A Selberg.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+well okay which is relevant to a theorem
+
+ align:start position:0%
+well okay which is relevant to a theorem
+ 
+
+ align:start position:0%
+well okay which is relevant to a theorem
+of Selberg. P set his third differently.
+
+ align:start position:0%
+of Selberg. P set his third differently.
+ 
+
+ align:start position:0%
+of Selberg. P set his third differently.
+But
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are four elements in this set.
+
+ align:start position:0%
+so there are four elements in this set.
+ 
+
+ align:start position:0%
+so there are four elements in this set.
+Um and these are generators of the group
+
+ align:start position:0%
+Um and these are generators of the group
+ 
+
+ align:start position:0%
+Um and these are generators of the group
+SL2FP. There are many ways you could
+
+ align:start position:0%
+SL2FP. There are many ways you could
+ 
+
+ align:start position:0%
+SL2FP. There are many ways you could
+choose generators for this group, but
+
+ align:start position:0%
+choose generators for this group, but
+ 
+
+ align:start position:0%
+choose generators for this group, but
+this is probably the simplest way.
+
+ align:start position:0%
+this is probably the simplest way.
+ 
+
+ align:start position:0%
+this is probably the simplest way.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+and okay and now I can state a theorem.
+
+ align:start position:0%
+and okay and now I can state a theorem.
+ 
+
+ align:start position:0%
+and okay and now I can state a theorem.
+So theorem one exists a positive c I
+
+ align:start position:0%
+So theorem one exists a positive c I
+ 
+
+ align:start position:0%
+So theorem one exists a positive c I
+think one one over 100 should be fine.
+
+ align:start position:0%
+think one one over 100 should be fine.
+ 
+
+ align:start position:0%
+think one one over 100 should be fine.
+Um so that
+
+ align:start position:0%
+Um so that
+ 
+
+ align:start position:0%
+Um so that
+for every p prime if you take a selberg
+
+ align:start position:0%
+for every p prime if you take a selberg
+ 
+
+ align:start position:0%
+for every p prime if you take a selberg
+and sl2 of fp you make a random walk. Um
+
+ align:start position:0%
+and sl2 of fp you make a random walk. Um
+ 
+
+ align:start position:0%
+and sl2 of fp you make a random walk. Um
+and so in this setting let me write t a
+
+ align:start position:0%
+and so in this setting let me write t a
+ 
+
+ align:start position:0%
+and so in this setting let me write t a
+for t sub mu sub a.
+
+ align:start position:0%
+for t sub mu sub a.
+ 
+
+ align:start position:0%
+for t sub mu sub a.
+um then
+
+ align:start position:0%
+um then
+ 
+
+ align:start position:0%
+um then
+sigma 1 of ta is less than 1 minus c. So
+
+ align:start position:0%
+sigma 1 of ta is less than 1 minus c. So
+ 
+
+ align:start position:0%
+sigma 1 of ta is less than 1 minus c. So
+uniformly for all primes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if this is say 99 over 100 then you
+
+ align:start position:0%
+So if this is say 99 over 100 then you
+ 
+
+ align:start position:0%
+So if this is say 99 over 100 then you
+can just read off uh you know high
+
+ align:start position:0%
+can just read off uh you know high
+ 
+
+ align:start position:0%
+can just read off uh you know high
+powers of this are bounded by something
+
+ align:start position:0%
+powers of this are bounded by something
+ 
+
+ align:start position:0%
+powers of this are bounded by something
+and you can plug that into the
+
+ align:start position:0%
+and you can plug that into the
+ 
+
+ align:start position:0%
+and you can plug that into the
+discussion over here. So it says that
+
+ align:start position:0%
+discussion over here. So it says that
+ 
+
+ align:start position:0%
+discussion over here. So it says that
+that random walk mixes extremely fast.
+
+ align:start position:0%
+that random walk mixes extremely fast.
+ 
+
+ align:start position:0%
+that random walk mixes extremely fast.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+>> How does sigma one behave kind of as it
+
+ align:start position:0%
+>> How does sigma one behave kind of as it
+ 
+
+ align:start position:0%
+>> How does sigma one behave kind of as it
+over time? Does it converge to sub or
+
+ align:start position:0%
+over time? Does it converge to sub or
+ 
+
+ align:start position:0%
+over time? Does it converge to sub or
+oscillate a lot?
+
+ align:start position:0%
+oscillate a lot?
+ 
+
+ align:start position:0%
+oscillate a lot?
+>> Um so the question is how does sigma 1
+
+ align:start position:0%
+>> Um so the question is how does sigma 1
+ 
+
+ align:start position:0%
+>> Um so the question is how does sigma 1
+of ta behave um as as the prime varies?
+
+ align:start position:0%
+of ta behave um as as the prime varies?
+ 
+
+ align:start position:0%
+of ta behave um as as the prime varies?
+I do not know the answer to that
+
+ align:start position:0%
+I do not know the answer to that
+ 
+
+ align:start position:0%
+I do not know the answer to that
+question.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so I should say so let me say that
+
+ align:start position:0%
+Um so I should say so let me say that
+ 
+
+ align:start position:0%
+Um so I should say so let me say that
+this was this is a correlary of a
+
+ align:start position:0%
+this was this is a correlary of a
+ 
+
+ align:start position:0%
+this was this is a correlary of a
+theorem of Selberg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the late 50s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and Selberg act's actual theorem is
+
+ align:start position:0%
+um and Selberg act's actual theorem is
+ 
+
+ align:start position:0%
+um and Selberg act's actual theorem is
+about the first igen value of the
+
+ align:start position:0%
+about the first igen value of the
+ 
+
+ align:start position:0%
+about the first igen value of the
+lelassian on a hyperbolic surface which
+
+ align:start position:0%
+lelassian on a hyperbolic surface which
+ 
+
+ align:start position:0%
+lelassian on a hyperbolic surface which
+is associated to this group
+
+ align:start position:0%
+is associated to this group
+ 
+
+ align:start position:0%
+is associated to this group
+and you can go back and forth. With
+
+ align:start position:0%
+and you can go back and forth. With
+ 
+
+ align:start position:0%
+and you can go back and forth. With
+modern technology, it's considered not
+
+ align:start position:0%
+modern technology, it's considered not
+ 
+
+ align:start position:0%
+modern technology, it's considered not
+very difficult to go back and forth
+
+ align:start position:0%
+very difficult to go back and forth
+ 
+
+ align:start position:0%
+very difficult to go back and forth
+between a bound for the igen value of
+
+ align:start position:0%
+between a bound for the igen value of
+ 
+
+ align:start position:0%
+between a bound for the igen value of
+the surface and a bound here. Uh but
+
+ align:start position:0%
+the surface and a bound here. Uh but
+ 
+
+ align:start position:0%
+the surface and a bound here. Uh but
+when you do go back and forth, you will
+
+ align:start position:0%
+when you do go back and forth, you will
+ 
+
+ align:start position:0%
+when you do go back and forth, you will
+screw up the constants.
+
+ align:start position:0%
+screw up the constants.
+ 
+
+ align:start position:0%
+screw up the constants.
+Um Selberg's theorem was that the first
+
+ align:start position:0%
+Um Selberg's theorem was that the first
+ 
+
+ align:start position:0%
+Um Selberg's theorem was that the first
+igen value of that surface was at least
+
+ align:start position:0%
+igen value of that surface was at least
+ 
+
+ align:start position:0%
+igen value of that surface was at least
+316s
+
+ align:start position:0%
+316s
+ 
+
+ align:start position:0%
+316s
+and that's probably not the right
+
+ align:start position:0%
+and that's probably not the right
+ 
+
+ align:start position:0%
+and that's probably not the right
+answer. And he conjectured that it
+
+ align:start position:0%
+answer. And he conjectured that it
+ 
+
+ align:start position:0%
+answer. And he conjectured that it
+should be a quarter.
+
+ align:start position:0%
+should be a quarter.
+ 
+
+ align:start position:0%
+should be a quarter.
+Um so for his actual problem there was
+
+ align:start position:0%
+Um so for his actual problem there was
+ 
+
+ align:start position:0%
+Um so for his actual problem there was
+there is a beautiful conjecture about
+
+ align:start position:0%
+there is a beautiful conjecture about
+ 
+
+ align:start position:0%
+there is a beautiful conjecture about
+what happens as p goes to infinity which
+
+ align:start position:0%
+what happens as p goes to infinity which
+ 
+
+ align:start position:0%
+what happens as p goes to infinity which
+is that the values should converge to a
+
+ align:start position:0%
+is that the values should converge to a
+ 
+
+ align:start position:0%
+is that the values should converge to a
+quarter
+
+ align:start position:0%
+quarter
+ 
+
+ align:start position:0%
+quarter
+um for this I'm not sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so bounds like this are also
+
+ align:start position:0%
+okay so bounds like this are also
+ 
+
+ align:start position:0%
+okay so bounds like this are also
+related to uh expand standard graphs,
+
+ align:start position:0%
+related to uh expand standard graphs,
+ 
+
+ align:start position:0%
+related to uh expand standard graphs,
+isoparametric inequalities in graphs and
+
+ align:start position:0%
+isoparametric inequalities in graphs and
+ 
+
+ align:start position:0%
+isoparametric inequalities in graphs and
+I thought I would also show that um and
+
+ align:start position:0%
+I thought I would also show that um and
+ 
+
+ align:start position:0%
+I thought I would also show that um and
+um so it it shows that well okay so so
+
+ align:start position:0%
+um so it it shows that well okay so so
+ 
+
+ align:start position:0%
+um so it it shows that well okay so so
+let me explain that. So we can we can if
+
+ align:start position:0%
+let me explain that. So we can we can if
+ 
+
+ align:start position:0%
+let me explain that. So we can we can if
+you have a set of of generators inside
+
+ align:start position:0%
+you have a set of of generators inside
+ 
+
+ align:start position:0%
+you have a set of of generators inside
+of a group we can use that to make a
+
+ align:start position:0%
+of a group we can use that to make a
+ 
+
+ align:start position:0%
+of a group we can use that to make a
+graph called a kaly graph.
+
+ align:start position:0%
+graph called a kaly graph.
+ 
+
+ align:start position:0%
+graph called a kaly graph.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+And this mixing inequality
+
+ align:start position:0%
+And this mixing inequality
+ 
+
+ align:start position:0%
+And this mixing inequality
+can be thought of or implies some
+
+ align:start position:0%
+can be thought of or implies some
+ 
+
+ align:start position:0%
+can be thought of or implies some
+interesting geometric features of the
+
+ align:start position:0%
+interesting geometric features of the
+ 
+
+ align:start position:0%
+interesting geometric features of the
+graph.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So um
+
+ align:start position:0%
+So um
+ 
+
+ align:start position:0%
+So um
+expansion
+
+ align:start position:0%
+expansion
+ 
+
+ align:start position:0%
+expansion
+in graphs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So if G is a finite group
+
+ align:start position:0%
+Okay. So if G is a finite group
+ 
+
+ align:start position:0%
+Okay. So if G is a finite group
+then A is a set of generators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I guess that to have a graph maybe
+
+ align:start position:0%
+and I guess that to have a graph maybe
+ 
+
+ align:start position:0%
+and I guess that to have a graph maybe
+we should say that is a symmetric set of
+
+ align:start position:0%
+we should say that is a symmetric set of
+ 
+
+ align:start position:0%
+we should say that is a symmetric set of
+generators. I don't know if that's
+
+ align:start position:0%
+generators. I don't know if that's
+ 
+
+ align:start position:0%
+generators. I don't know if that's
+important. Yeah, let's leave it.
+
+ align:start position:0%
+important. Yeah, let's leave it.
+ 
+
+ align:start position:0%
+important. Yeah, let's leave it.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+then we'll have a kaly graph kaly graph
+
+ align:start position:0%
+then we'll have a kaly graph kaly graph
+ 
+
+ align:start position:0%
+then we'll have a kaly graph kaly graph
+of GA. This is a graph.
+
+ align:start position:0%
+of GA. This is a graph.
+ 
+
+ align:start position:0%
+of GA. This is a graph.
+The vertices
+
+ align:start position:0%
+The vertices
+ 
+
+ align:start position:0%
+The vertices
+are G and G. And a pair G1, G2
+
+ align:start position:0%
+are G and G. And a pair G1, G2
+ 
+
+ align:start position:0%
+are G and G. And a pair G1, G2
+um is an edge
+
+ align:start position:0%
+um is an edge
+ 
+
+ align:start position:0%
+um is an edge
+if and only if um G2 is G1 * A or vice
+
+ align:start position:0%
+if and only if um G2 is G1 * A or vice
+ 
+
+ align:start position:0%
+if and only if um G2 is G1 * A or vice
+versa.
+
+ align:start position:0%
+versa.
+ 
+
+ align:start position:0%
+versa.
+Um yeah, so I guess we should have it
+
+ align:start position:0%
+Um yeah, so I guess we should have it
+ 
+
+ align:start position:0%
+Um yeah, so I guess we should have it
+symmetric. Um G2= G1 * A where A is in
+
+ align:start position:0%
+symmetric. Um G2= G1 * A where A is in
+ 
+
+ align:start position:0%
+symmetric. Um G2= G1 * A where A is in
+A.
+
+ align:start position:0%
+A.
+ 
+
+ align:start position:0%
+A.
+Okay. And the random walk we've been
+
+ align:start position:0%
+Okay. And the random walk we've been
+ 
+
+ align:start position:0%
+Okay. And the random walk we've been
+imagining is basically the random walk
+
+ align:start position:0%
+imagining is basically the random walk
+ 
+
+ align:start position:0%
+imagining is basically the random walk
+on this graph. You start at a vertex and
+
+ align:start position:0%
+on this graph. You start at a vertex and
+ 
+
+ align:start position:0%
+on this graph. You start at a vertex and
+you move randomly to a neighboring along
+
+ align:start position:0%
+you move randomly to a neighboring along
+ 
+
+ align:start position:0%
+you move randomly to a neighboring along
+the edges. Yeah.
+
+ align:start position:0%
+the edges. Yeah.
+ 
+
+ align:start position:0%
+the edges. Yeah.
+>> How do you identify SL2 of a finite
+
+ align:start position:0%
+>> How do you identify SL2 of a finite
+ 
+
+ align:start position:0%
+>> How do you identify SL2 of a finite
+field with a hyperbolic surface?
+
+ align:start position:0%
+field with a hyperbolic surface?
+ 
+
+ align:start position:0%
+field with a hyperbolic surface?
+>> Um yeah, I I I will Okay, we'll talk
+
+ align:start position:0%
+>> Um yeah, I I I will Okay, we'll talk
+ 
+
+ align:start position:0%
+>> Um yeah, I I I will Okay, we'll talk
+about the connection to hyperbolic
+
+ align:start position:0%
+about the connection to hyperbolic
+ 
+
+ align:start position:0%
+about the connection to hyperbolic
+geometry a little later when we talk
+
+ align:start position:0%
+geometry a little later when we talk
+ 
+
+ align:start position:0%
+geometry a little later when we talk
+about the proof of this theorem, but
+
+ align:start position:0%
+about the proof of this theorem, but
+ 
+
+ align:start position:0%
+about the proof of this theorem, but
+let's do it then.
+
+ align:start position:0%
+let's do it then.
+ 
+
+ align:start position:0%
+let's do it then.
+Yeah. Okay.
+
+ align:start position:0%
+Yeah. Okay.
+ 
+
+ align:start position:0%
+Yeah. Okay.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+okay so that's the kaly graph
+
+ align:start position:0%
+okay so that's the kaly graph
+ 
+
+ align:start position:0%
+okay so that's the kaly graph
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and in this graph if I have subsets s
+
+ align:start position:0%
+and in this graph if I have subsets s
+ 
+
+ align:start position:0%
+and in this graph if I have subsets s
+and t inside of the vertices e of s and
+
+ align:start position:0%
+and t inside of the vertices e of s and
+ 
+
+ align:start position:0%
+and t inside of the vertices e of s and
+t the edges from s to t that's going to
+
+ align:start position:0%
+t the edges from s to t that's going to
+ 
+
+ align:start position:0%
+t the edges from s to t that's going to
+be the set of g1 g2 and s cross t so
+
+ align:start position:0%
+be the set of g1 g2 and s cross t so
+ 
+
+ align:start position:0%
+be the set of g1 g2 and s cross t so
+that g1 g2 is an edge
+
+ align:start position:0%
+that g1 g2 is an edge
+ 
+
+ align:start position:0%
+that g1 g2 is an edge
+a set of edges from fast.
+
+ align:start position:0%
+a set of edges from fast.
+ 
+
+ align:start position:0%
+a set of edges from fast.
+Okay. So, proposition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we have CGA is above then the number
+
+ align:start position:0%
+if we have CGA is above then the number
+ 
+
+ align:start position:0%
+if we have CGA is above then the number
+of edges from S to S complement. So, S
+
+ align:start position:0%
+of edges from S to S complement. So, S
+ 
+
+ align:start position:0%
+of edges from S to S complement. So, S
+is going to be a subset of the vertices.
+
+ align:start position:0%
+is going to be a subset of the vertices.
+ 
+
+ align:start position:0%
+is going to be a subset of the vertices.
+number of these edges is at least one
+
+ align:start position:0%
+number of these edges is at least one
+ 
+
+ align:start position:0%
+number of these edges is at least one
+minus sigma 1 of TA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+a * S * S complement over G.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let's digest this a little bit.
+
+ align:start position:0%
+Okay, so let's digest this a little bit.
+ 
+
+ align:start position:0%
+Okay, so let's digest this a little bit.
+Um so what does this expression mean?
+
+ align:start position:0%
+Um so what does this expression mean?
+ 
+
+ align:start position:0%
+Um so what does this expression mean?
+Well, there are S.
+
+ align:start position:0%
+Well, there are S.
+ 
+
+ align:start position:0%
+Well, there are S.
+This is the this is how many points
+
+ align:start position:0%
+This is the this is how many points
+ 
+
+ align:start position:0%
+This is the this is how many points
+there are in the set S. From each of
+
+ align:start position:0%
+there are in the set S. From each of
+ 
+
+ align:start position:0%
+there are in the set S. From each of
+those points, there are a edges coming
+
+ align:start position:0%
+those points, there are a edges coming
+ 
+
+ align:start position:0%
+those points, there are a edges coming
+out. So, this is how many edges there
+
+ align:start position:0%
+out. So, this is how many edges there
+ 
+
+ align:start position:0%
+out. So, this is how many edges there
+are that are leaving points at S.
+
+ align:start position:0%
+are that are leaving points at S.
+ 
+
+ align:start position:0%
+are that are leaving points at S.
+How many of them do we think end up in S
+
+ align:start position:0%
+How many of them do we think end up in S
+ 
+
+ align:start position:0%
+How many of them do we think end up in S
+complement? Well, we don't really know,
+
+ align:start position:0%
+complement? Well, we don't really know,
+ 
+
+ align:start position:0%
+complement? Well, we don't really know,
+but as a reference point,
+
+ align:start position:0%
+but as a reference point,
+ 
+
+ align:start position:0%
+but as a reference point,
+everything was sort of random. The
+
+ align:start position:0%
+everything was sort of random. The
+ 
+
+ align:start position:0%
+everything was sort of random. The
+fraction of edges that ended up in S
+
+ align:start position:0%
+fraction of edges that ended up in S
+ 
+
+ align:start position:0%
+fraction of edges that ended up in S
+complement might be S complement over G.
+
+ align:start position:0%
+complement might be S complement over G.
+ 
+
+ align:start position:0%
+complement might be S complement over G.
+So this expression here would be the
+
+ align:start position:0%
+So this expression here would be the
+ 
+
+ align:start position:0%
+So this expression here would be the
+typical number of edges from S to S
+
+ align:start position:0%
+typical number of edges from S to S
+ 
+
+ align:start position:0%
+typical number of edges from S to S
+complement if we had a random graph
+
+ align:start position:0%
+complement if we had a random graph
+ 
+
+ align:start position:0%
+complement if we had a random graph
+where each vertex was in this many
+
+ align:start position:0%
+where each vertex was in this many
+ 
+
+ align:start position:0%
+where each vertex was in this many
+edges.
+
+ align:start position:0%
+edges.
+ 
+
+ align:start position:0%
+edges.
+Okay. And then we're going to say that
+
+ align:start position:0%
+Okay. And then we're going to say that
+ 
+
+ align:start position:0%
+Okay. And then we're going to say that
+the actual number of edges is at least
+
+ align:start position:0%
+the actual number of edges is at least
+ 
+
+ align:start position:0%
+the actual number of edges is at least
+some fraction of that.
+
+ align:start position:0%
+some fraction of that.
+ 
+
+ align:start position:0%
+some fraction of that.
+If sigma 1 of TA were one, this would be
+
+ align:start position:0%
+If sigma 1 of TA were one, this would be
+ 
+
+ align:start position:0%
+If sigma 1 of TA were one, this would be
+a trivial inequality. It's bigger than
+
+ align:start position:0%
+a trivial inequality. It's bigger than
+ 
+
+ align:start position:0%
+a trivial inequality. It's bigger than
+zero. But if sigma 1 is is smaller than
+
+ align:start position:0%
+zero. But if sigma 1 is is smaller than
+ 
+
+ align:start position:0%
+zero. But if sigma 1 is is smaller than
+one, then this is a non-trivial
+
+ align:start position:0%
+one, then this is a non-trivial
+ 
+
+ align:start position:0%
+one, then this is a non-trivial
+inequality. and it says that the number
+
+ align:start position:0%
+inequality. and it says that the number
+ 
+
+ align:start position:0%
+inequality. and it says that the number
+of edges is a certain a definite
+
+ align:start position:0%
+of edges is a certain a definite
+ 
+
+ align:start position:0%
+of edges is a certain a definite
+fraction of what you would see in the
+
+ align:start position:0%
+fraction of what you would see in the
+ 
+
+ align:start position:0%
+fraction of what you would see in the
+random model.
+
+ align:start position:0%
+random model.
+ 
+
+ align:start position:0%
+random model.
+Okay, so let's prove this or at least
+
+ align:start position:0%
+Okay, so let's prove this or at least
+ 
+
+ align:start position:0%
+Okay, so let's prove this or at least
+give a proof sketch.
+
+ align:start position:0%
+give a proof sketch.
+ 
+
+ align:start position:0%
+give a proof sketch.
+So the key point is that we can describe
+
+ align:start position:0%
+So the key point is that we can describe
+ 
+
+ align:start position:0%
+So the key point is that we can describe
+this quantity using this operator TA and
+
+ align:start position:0%
+this quantity using this operator TA and
+ 
+
+ align:start position:0%
+this quantity using this operator TA and
+then it becomes not so surprising that
+
+ align:start position:0%
+then it becomes not so surprising that
+ 
+
+ align:start position:0%
+then it becomes not so surprising that
+the singular value of TA is relevant.
+
+ align:start position:0%
+the singular value of TA is relevant.
+ 
+
+ align:start position:0%
+the singular value of TA is relevant.
+How do you do it? The number of edges
+
+ align:start position:0%
+How do you do it? The number of edges
+ 
+
+ align:start position:0%
+How do you do it? The number of edges
+from S to S complement is the inner
+
+ align:start position:0%
+from S to S complement is the inner
+ 
+
+ align:start position:0%
+from S to S complement is the inner
+product is inner product of TA of the
+
+ align:start position:0%
+product is inner product of TA of the
+ 
+
+ align:start position:0%
+product is inner product of TA of the
+characteristic function of S with the
+
+ align:start position:0%
+characteristic function of S with the
+ 
+
+ align:start position:0%
+characteristic function of S with the
+characteristic function of S complement
+
+ align:start position:0%
+characteristic function of S complement
+ 
+
+ align:start position:0%
+characteristic function of S complement
+and there's a factor of a in front. This
+
+ align:start position:0%
+and there's a factor of a in front. This
+ 
+
+ align:start position:0%
+and there's a factor of a in front. This
+is a normalization. If if TA had been
+
+ align:start position:0%
+is a normalization. If if TA had been
+ 
+
+ align:start position:0%
+is a normalization. If if TA had been
+just TA is an averaging operator, but we
+
+ align:start position:0%
+just TA is an averaging operator, but we
+ 
+
+ align:start position:0%
+just TA is an averaging operator, but we
+didn't really want to average. We wanted
+
+ align:start position:0%
+didn't really want to average. We wanted
+ 
+
+ align:start position:0%
+didn't really want to average. We wanted
+to count edges. So there's an extra
+
+ align:start position:0%
+to count edges. So there's an extra
+ 
+
+ align:start position:0%
+to count edges. So there's an extra
+factor.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Does this look plausible to
+
+ align:start position:0%
+Okay. Does this look plausible to
+ 
+
+ align:start position:0%
+Okay. Does this look plausible to
+people? Should we write this?
+
+ align:start position:0%
+people? Should we write this?
+ 
+
+ align:start position:0%
+people? Should we write this?
+Let's write this out a little bit.
+
+ align:start position:0%
+Let's write this out a little bit.
+ 
+
+ align:start position:0%
+Let's write this out a little bit.
+So t a1s
+
+ align:start position:0%
+So t a1s
+ 
+
+ align:start position:0%
+So t a1s
+of g
+
+ align:start position:0%
+of g
+ 
+
+ align:start position:0%
+of g
+is 1 / a sum a and a
+
+ align:start position:0%
+is 1 / a sum a and a
+ 
+
+ align:start position:0%
+is 1 / a sum a and a
+of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s of g
+
+ align:start position:0%
+s of g
+ 
+
+ align:start position:0%
+s of g
+a inverse.
+
+ align:start position:0%
+a inverse.
+ 
+
+ align:start position:0%
+a inverse.
+So that's the definition of the of the
+
+ align:start position:0%
+So that's the definition of the of the
+ 
+
+ align:start position:0%
+So that's the definition of the of the
+convolution.
+
+ align:start position:0%
+convolution.
+ 
+
+ align:start position:0%
+convolution.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we we so then when we take this inner
+
+ align:start position:0%
+so we we so then when we take this inner
+ 
+
+ align:start position:0%
+so we we so then when we take this inner
+product we're going to have the um sum g
+
+ align:start position:0%
+product we're going to have the um sum g
+ 
+
+ align:start position:0%
+product we're going to have the um sum g
+and g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 / a sum a
+
+ align:start position:0%
+1 / a sum a
+ 
+
+ align:start position:0%
+1 / a sum a
+1 s of g a inverse one s complement of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we will only be counting
+
+ align:start position:0%
+So we will only be counting
+ 
+
+ align:start position:0%
+So we will only be counting
+uh we'll be counting G's that are in S
+
+ align:start position:0%
+uh we'll be counting G's that are in S
+ 
+
+ align:start position:0%
+uh we'll be counting G's that are in S
+complement but GA inverse is an S and
+
+ align:start position:0%
+complement but GA inverse is an S and
+ 
+
+ align:start position:0%
+complement but GA inverse is an S and
+that's an edge that starts in S and goes
+
+ align:start position:0%
+that's an edge that starts in S and goes
+ 
+
+ align:start position:0%
+that's an edge that starts in S and goes
+to S complnt.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So S S complement
+
+ align:start position:0%
+So S S complement
+ 
+
+ align:start position:0%
+So S S complement
+over here we have G. Over here we have
+
+ align:start position:0%
+over here we have G. Over here we have
+ 
+
+ align:start position:0%
+over here we have G. Over here we have
+GA inverse and those are connected by an
+
+ align:start position:0%
+GA inverse and those are connected by an
+ 
+
+ align:start position:0%
+GA inverse and those are connected by an
+edge. That's the thing that we're
+
+ align:start position:0%
+edge. That's the thing that we're
+ 
+
+ align:start position:0%
+edge. That's the thing that we're
+counting.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, this double sum here means we're
+
+ align:start position:0%
+Okay, this double sum here means we're
+ 
+
+ align:start position:0%
+Okay, this double sum here means we're
+counting all of the going through all
+
+ align:start position:0%
+counting all of the going through all
+ 
+
+ align:start position:0%
+counting all of the going through all
+the edges, but we're only counting an
+
+ align:start position:0%
+the edges, but we're only counting an
+ 
+
+ align:start position:0%
+the edges, but we're only counting an
+edge if it goes from S to S complement.
+
+ align:start position:0%
+edge if it goes from S to S complement.
+ 
+
+ align:start position:0%
+edge if it goes from S to S complement.
+And we have this, which we didn't really
+
+ align:start position:0%
+And we have this, which we didn't really
+ 
+
+ align:start position:0%
+And we have this, which we didn't really
+want, which is why we multiplied by this
+
+ align:start position:0%
+want, which is why we multiplied by this
+ 
+
+ align:start position:0%
+want, which is why we multiplied by this
+over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, good.
+
+ align:start position:0%
+Okay, good.
+ 
+
+ align:start position:0%
+Okay, good.
+Okay, so now remember that this operator
+
+ align:start position:0%
+Okay, so now remember that this operator
+ 
+
+ align:start position:0%
+Okay, so now remember that this operator
+uh sort of splits we it takes the
+
+ align:start position:0%
+uh sort of splits we it takes the
+ 
+
+ align:start position:0%
+uh sort of splits we it takes the
+constant functions to the constant
+
+ align:start position:0%
+constant functions to the constant
+ 
+
+ align:start position:0%
+constant functions to the constant
+functions and it takes the mean zero
+
+ align:start position:0%
+functions and it takes the mean zero
+ 
+
+ align:start position:0%
+functions and it takes the mean zero
+functions to the mean zero functions. So
+
+ align:start position:0%
+functions to the mean zero functions. So
+ 
+
+ align:start position:0%
+functions to the mean zero functions. So
+we should split everybody in sight into
+
+ align:start position:0%
+we should split everybody in sight into
+ 
+
+ align:start position:0%
+we should split everybody in sight into
+a constant part and a mean zero part.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we split
+
+ align:start position:0%
+So we split
+ 
+
+ align:start position:0%
+So we split
+1 s is s over g that's the constant part
+
+ align:start position:0%
+1 s is s over g that's the constant part
+ 
+
+ align:start position:0%
+1 s is s over g that's the constant part
+plus 1 s minus s over g. So this I'll
+
+ align:start position:0%
+plus 1 s minus s over g. So this I'll
+ 
+
+ align:start position:0%
+plus 1 s minus s over g. So this I'll
+call it 1 s high and it lives in l2 g0.
+
+ align:start position:0%
+call it 1 s high and it lives in l2 g0.
+ 
+
+ align:start position:0%
+call it 1 s high and it lives in l2 g0.
+Okay. Do the same thing for s
+
+ align:start position:0%
+Okay. Do the same thing for s
+ 
+
+ align:start position:0%
+Okay. Do the same thing for s
+complement. So now the number of edges
+
+ align:start position:0%
+complement. So now the number of edges
+ 
+
+ align:start position:0%
+complement. So now the number of edges
+from S to S complement
+
+ align:start position:0%
+from S to S complement
+ 
+
+ align:start position:0%
+from S to S complement
+that is A times
+
+ align:start position:0%
+that is A times
+ 
+
+ align:start position:0%
+that is A times
+um okay we'll have TA of the constant
+
+ align:start position:0%
+um okay we'll have TA of the constant
+ 
+
+ align:start position:0%
+um okay we'll have TA of the constant
+parts so that's SG s complement G
+
+ align:start position:0%
+parts so that's SG s complement G
+ 
+
+ align:start position:0%
+parts so that's SG s complement G
+plus A times the high frequency high
+
+ align:start position:0%
+plus A times the high frequency high
+ 
+
+ align:start position:0%
+plus A times the high frequency high
+frequency parts uh the non the mean zero
+
+ align:start position:0%
+frequency parts uh the non the mean zero
+ 
+
+ align:start position:0%
+frequency parts uh the non the mean zero
+parts um TA of 1s high
+
+ align:start position:0%
+parts um TA of 1s high
+ 
+
+ align:start position:0%
+parts um TA of 1s high
+one as complement.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So let's call this zero and this
+
+ align:start position:0%
+Okay. So let's call this zero and this
+ 
+
+ align:start position:0%
+Okay. So let's call this zero and this
+is the high part or the let's call this
+
+ align:start position:0%
+is the high part or the let's call this
+ 
+
+ align:start position:0%
+is the high part or the let's call this
+the constant part and this is the high
+
+ align:start position:0%
+the constant part and this is the high
+ 
+
+ align:start position:0%
+the constant part and this is the high
+part.
+
+ align:start position:0%
+part.
+ 
+
+ align:start position:0%
+part.
+Okay. So the rest of it is just a
+
+ align:start position:0%
+Okay. So the rest of it is just a
+ 
+
+ align:start position:0%
+Okay. So the rest of it is just a
+computation and I won't do the algebra
+
+ align:start position:0%
+computation and I won't do the algebra
+ 
+
+ align:start position:0%
+computation and I won't do the algebra
+carefully but if you do the constant
+
+ align:start position:0%
+carefully but if you do the constant
+ 
+
+ align:start position:0%
+carefully but if you do the constant
+part you get this as SS complement over
+
+ align:start position:0%
+part you get this as SS complement over
+ 
+
+ align:start position:0%
+part you get this as SS complement over
+G. The constant part exactly tracks what
+
+ align:start position:0%
+G. The constant part exactly tracks what
+ 
+
+ align:start position:0%
+G. The constant part exactly tracks what
+would happen if all the edges were
+
+ align:start position:0%
+would happen if all the edges were
+ 
+
+ align:start position:0%
+would happen if all the edges were
+random. Okay. And then for the high part
+
+ align:start position:0%
+random. Okay. And then for the high part
+ 
+
+ align:start position:0%
+random. Okay. And then for the high part
+of course we won't compute it exactly
+
+ align:start position:0%
+of course we won't compute it exactly
+ 
+
+ align:start position:0%
+of course we won't compute it exactly
+because we have to know what the
+
+ align:start position:0%
+because we have to know what the
+ 
+
+ align:start position:0%
+because we have to know what the
+operator TA is. But we can bound it by
+
+ align:start position:0%
+operator TA is. But we can bound it by
+ 
+
+ align:start position:0%
+operator TA is. But we can bound it by
+the um by the norm of TA sigma 1 of TA
+
+ align:start position:0%
+the um by the norm of TA sigma 1 of TA
+ 
+
+ align:start position:0%
+the um by the norm of TA sigma 1 of TA
+times 1 S high in L2
+
+ align:start position:0%
+times 1 S high in L2
+ 
+
+ align:start position:0%
+times 1 S high in L2
+times 1 S complement high in L2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then those things are
+
+ align:start position:0%
+Okay. And then those things are
+ 
+
+ align:start position:0%
+Okay. And then those things are
+straightforward to compute those L2
+
+ align:start position:0%
+straightforward to compute those L2
+ 
+
+ align:start position:0%
+straightforward to compute those L2
+norms. And if you work if you compute
+
+ align:start position:0%
+norms. And if you work if you compute
+ 
+
+ align:start position:0%
+norms. And if you work if you compute
+them you get that this is a this is I'll
+
+ align:start position:0%
+them you get that this is a this is I'll
+ 
+
+ align:start position:0%
+them you get that this is a this is I'll
+put the sigma one out front.
+
+ align:start position:0%
+put the sigma one out front.
+ 
+
+ align:start position:0%
+put the sigma one out front.
+And then it's the same thing a s S
+
+ align:start position:0%
+And then it's the same thing a s S
+ 
+
+ align:start position:0%
+And then it's the same thing a s S
+complement over G.
+
+ align:start position:0%
+complement over G.
+ 
+
+ align:start position:0%
+complement over G.
+Okay. So the true answer is the constant
+
+ align:start position:0%
+Okay. So the true answer is the constant
+ 
+
+ align:start position:0%
+Okay. So the true answer is the constant
+term plus the high term which is like an
+
+ align:start position:0%
+term plus the high term which is like an
+ 
+
+ align:start position:0%
+term plus the high term which is like an
+error term and whose size is at most
+
+ align:start position:0%
+error term and whose size is at most
+ 
+
+ align:start position:0%
+error term and whose size is at most
+this. And if sigma 1 is strictly less
+
+ align:start position:0%
+this. And if sigma 1 is strictly less
+ 
+
+ align:start position:0%
+this. And if sigma 1 is strictly less
+than one then the error term is strictly
+
+ align:start position:0%
+than one then the error term is strictly
+ 
+
+ align:start position:0%
+than one then the error term is strictly
+smaller than the constant term. So
+
+ align:start position:0%
+smaller than the constant term. So
+ 
+
+ align:start position:0%
+smaller than the constant term. So
+something will be left over and that's
+
+ align:start position:0%
+something will be left over and that's
+ 
+
+ align:start position:0%
+something will be left over and that's
+the inequality.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let me make a little remark.
+
+ align:start position:0%
+Okay, so let me make a little remark.
+ 
+
+ align:start position:0%
+Okay, so let me make a little remark.
+Um, if S is smaller than G over two,
+
+ align:start position:0%
+Um, if S is smaller than G over two,
+ 
+
+ align:start position:0%
+Um, if S is smaller than G over two,
+then S complement is bigger than G
+
+ align:start position:0%
+then S complement is bigger than G
+ 
+
+ align:start position:0%
+then S complement is bigger than G
+over2. So this is more or less without
+
+ align:start position:0%
+over2. So this is more or less without
+ 
+
+ align:start position:0%
+over2. So this is more or less without
+loss of generality. You know, if you
+
+ align:start position:0%
+loss of generality. You know, if you
+ 
+
+ align:start position:0%
+loss of generality. You know, if you
+switch the roles of S and S complement,
+
+ align:start position:0%
+switch the roles of S and S complement,
+ 
+
+ align:start position:0%
+switch the roles of S and S complement,
+but it means S complement is at least G
+
+ align:start position:0%
+but it means S complement is at least G
+ 
+
+ align:start position:0%
+but it means S complement is at least G
+over2, which means that this whole
+
+ align:start position:0%
+over2, which means that this whole
+ 
+
+ align:start position:0%
+over2, which means that this whole
+fraction has order of one. So then we
+
+ align:start position:0%
+fraction has order of one. So then we
+ 
+
+ align:start position:0%
+fraction has order of one. So then we
+get that the number of edges from S to S
+
+ align:start position:0%
+get that the number of edges from S to S
+ 
+
+ align:start position:0%
+get that the number of edges from S to S
+complement is at least half sigma 1 of
+
+ align:start position:0%
+complement is at least half sigma 1 of
+ 
+
+ align:start position:0%
+complement is at least half sigma 1 of
+TA
+
+ align:start position:0%
+TA
+ 
+
+ align:start position:0%
+TA
+A time S. So it's at least uh a definite
+
+ align:start position:0%
+A time S. So it's at least uh a definite
+ 
+
+ align:start position:0%
+A time S. So it's at least uh a definite
+fraction of all of the possible edges
+
+ align:start position:0%
+fraction of all of the possible edges
+ 
+
+ align:start position:0%
+fraction of all of the possible edges
+that it could be living leaving us.
+
+ align:start position:0%
+that it could be living leaving us.
+ 
+
+ align:start position:0%
+that it could be living leaving us.
+Okay. So this property here is called
+
+ align:start position:0%
+Okay. So this property here is called
+ 
+
+ align:start position:0%
+Okay. So this property here is called
+being an expander graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if you take a set that's less
+
+ align:start position:0%
+because if you take a set that's less
+ 
+
+ align:start position:0%
+because if you take a set that's less
+than half of the graph and then you add
+
+ align:start position:0%
+than half of the graph and then you add
+ 
+
+ align:start position:0%
+than half of the graph and then you add
+to it all of the edges that are leaving
+
+ align:start position:0%
+to it all of the edges that are leaving
+ 
+
+ align:start position:0%
+to it all of the edges that are leaving
+it then it will get significantly
+
+ align:start position:0%
+it then it will get significantly
+ 
+
+ align:start position:0%
+it then it will get significantly
+bigger. It will expand. So it's called
+
+ align:start position:0%
+bigger. It will expand. So it's called
+ 
+
+ align:start position:0%
+bigger. It will expand. So it's called
+an expander graph.
+
+ align:start position:0%
+an expander graph.
+ 
+
+ align:start position:0%
+an expander graph.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. Cool.
+
+ align:start position:0%
+Okay. Cool.
+ 
+
+ align:start position:0%
+Okay. Cool.
+Um so so this proposition shows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if this sigma one is strictly less
+
+ align:start position:0%
+that if this sigma one is strictly less
+ 
+
+ align:start position:0%
+that if this sigma one is strictly less
+than one it's something like in Selber's
+
+ align:start position:0%
+than one it's something like in Selber's
+ 
+
+ align:start position:0%
+than one it's something like in Selber's
+theorem then the edges in the graph
+
+ align:start position:0%
+theorem then the edges in the graph
+ 
+
+ align:start position:0%
+theorem then the edges in the graph
+behave in this way that it's an expanded
+
+ align:start position:0%
+behave in this way that it's an expanded
+ 
+
+ align:start position:0%
+behave in this way that it's an expanded
+graph.
+
+ align:start position:0%
+graph.
+ 
+
+ align:start position:0%
+graph.
+Okay, cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, now so Selberg did not state his
+
+ align:start position:0%
+Okay, now so Selberg did not state his
+ 
+
+ align:start position:0%
+Okay, now so Selberg did not state his
+theorem in this way. So this is slightly
+
+ align:start position:0%
+theorem in this way. So this is slightly
+ 
+
+ align:start position:0%
+theorem in this way. So this is slightly
+ahistorical, but Selberg's theorem plus
+
+ align:start position:0%
+ahistorical, but Selberg's theorem plus
+ 
+
+ align:start position:0%
+ahistorical, but Selberg's theorem plus
+things that are not very difficult in
+
+ align:start position:0%
+things that are not very difficult in
+ 
+
+ align:start position:0%
+things that are not very difficult in
+hindsight show that this kaly graph of
+
+ align:start position:0%
+hindsight show that this kaly graph of
+ 
+
+ align:start position:0%
+hindsight show that this kaly graph of
+SL2FP is an expander graph and it is in
+
+ align:start position:0%
+SL2FP is an expander graph and it is in
+ 
+
+ align:start position:0%
+SL2FP is an expander graph and it is in
+a sense the first Zelberg didn't quite
+
+ align:start position:0%
+a sense the first Zelberg didn't quite
+ 
+
+ align:start position:0%
+a sense the first Zelberg didn't quite
+say this but in a sense this was the
+
+ align:start position:0%
+say this but in a sense this was the
+ 
+
+ align:start position:0%
+say this but in a sense this was the
+first proof that any graph was an
+
+ align:start position:0%
+first proof that any graph was an
+ 
+
+ align:start position:0%
+first proof that any graph was an
+expander graph. Um, expander graphs were
+
+ align:start position:0%
+expander graph. Um, expander graphs were
+ 
+
+ align:start position:0%
+expander graph. Um, expander graphs were
+officially defined in 1970 by Pinsker
+
+ align:start position:0%
+officially defined in 1970 by Pinsker
+ 
+
+ align:start position:0%
+officially defined in 1970 by Pinsker
+and something pretty close by Koma Garf
+
+ align:start position:0%
+and something pretty close by Koma Garf
+ 
+
+ align:start position:0%
+and something pretty close by Koma Garf
+and Bars in the 60s and all of those
+
+ align:start position:0%
+and Bars in the 60s and all of those
+ 
+
+ align:start position:0%
+and Bars in the 60s and all of those
+people realized that um random graphs
+
+ align:start position:0%
+people realized that um random graphs
+ 
+
+ align:start position:0%
+people realized that um random graphs
+were expander graphs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+yeah. So I maybe many people have seen
+
+ align:start position:0%
+yeah. So I maybe many people have seen
+ 
+
+ align:start position:0%
+yeah. So I maybe many people have seen
+but it's really a remarkable thing. So,
+
+ align:start position:0%
+but it's really a remarkable thing. So,
+ 
+
+ align:start position:0%
+but it's really a remarkable thing. So,
+so just for comparison, like a simple
+
+ align:start position:0%
+so just for comparison, like a simple
+ 
+
+ align:start position:0%
+so just for comparison, like a simple
+graph that we might think of that we can
+
+ align:start position:0%
+graph that we might think of that we can
+ 
+
+ align:start position:0%
+graph that we might think of that we can
+easily visualize would be like a like an
+
+ align:start position:0%
+easily visualize would be like a like an
+ 
+
+ align:start position:0%
+easily visualize would be like a like an
+n byn grid and that kind of graph is not
+
+ align:start position:0%
+n byn grid and that kind of graph is not
+ 
+
+ align:start position:0%
+n byn grid and that kind of graph is not
+an expander at all. So an n byn grid has
+
+ align:start position:0%
+an expander at all. So an n byn grid has
+ 
+
+ align:start position:0%
+an expander at all. So an n byn grid has
+n squared vertices but you can cut it in
+
+ align:start position:0%
+n squared vertices but you can cut it in
+ 
+
+ align:start position:0%
+n squared vertices but you can cut it in
+half with a vertical line and you only
+
+ align:start position:0%
+half with a vertical line and you only
+ 
+
+ align:start position:0%
+half with a vertical line and you only
+cut n edges. So the number of edges so s
+
+ align:start position:0%
+cut n edges. So the number of edges so s
+ 
+
+ align:start position:0%
+cut n edges. So the number of edges so s
+and s complement are each about half of
+
+ align:start position:0%
+and s complement are each about half of
+ 
+
+ align:start position:0%
+and s complement are each about half of
+the graph. The number of edges between
+
+ align:start position:0%
+the graph. The number of edges between
+ 
+
+ align:start position:0%
+the graph. The number of edges between
+them is is much smaller than s. Um so
+
+ align:start position:0%
+them is is much smaller than s. Um so
+ 
+
+ align:start position:0%
+them is is much smaller than s. Um so
+these are very large graphs but the
+
+ align:start position:0%
+these are very large graphs but the
+ 
+
+ align:start position:0%
+these are very large graphs but the
+number of edges it takes to cut it in
+
+ align:start position:0%
+number of edges it takes to cut it in
+ 
+
+ align:start position:0%
+number of edges it takes to cut it in
+half is comparable to all of the edges
+
+ align:start position:0%
+half is comparable to all of the edges
+ 
+
+ align:start position:0%
+half is comparable to all of the edges
+and um it most graphs are like that but
+
+ align:start position:0%
+and um it most graphs are like that but
+ 
+
+ align:start position:0%
+and um it most graphs are like that but
+before people realized it it was
+
+ align:start position:0%
+before people realized it it was
+ 
+
+ align:start position:0%
+before people realized it it was
+surprising and counterintuitive that any
+
+ align:start position:0%
+surprising and counterintuitive that any
+ 
+
+ align:start position:0%
+surprising and counterintuitive that any
+graphs were like that and it's very
+
+ align:start position:0%
+graphs were like that and it's very
+ 
+
+ align:start position:0%
+graphs were like that and it's very
+significant fact in many domains of math
+
+ align:start position:0%
+significant fact in many domains of math
+ 
+
+ align:start position:0%
+significant fact in many domains of math
+and science.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Uh okay, let me pause there and
+
+ align:start position:0%
+Uh okay, let me pause there and
+ 
+
+ align:start position:0%
+Uh okay, let me pause there and
+questions about about Selberg's theorem
+
+ align:start position:0%
+questions about about Selberg's theorem
+ 
+
+ align:start position:0%
+questions about about Selberg's theorem
+and this setup mixing and expansion.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> The point of a generators is just so
+
+ align:start position:0%
+>> The point of a generators is just so
+ 
+
+ align:start position:0%
+>> The point of a generators is just so
+that it's connected.
+
+ align:start position:0%
+that it's connected.
+ 
+
+ align:start position:0%
+that it's connected.
+>> Yes, that's right. So um so the question
+
+ align:start position:0%
+>> Yes, that's right. So um so the question
+ 
+
+ align:start position:0%
+>> Yes, that's right. So um so the question
+is uh is what what is the point of a
+
+ align:start position:0%
+is uh is what what is the point of a
+ 
+
+ align:start position:0%
+is uh is what what is the point of a
+being generators?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So if a did not generate the group then
+
+ align:start position:0%
+So if a did not generate the group then
+ 
+
+ align:start position:0%
+So if a did not generate the group then
+this graph would be disconnected and
+
+ align:start position:0%
+this graph would be disconnected and
+ 
+
+ align:start position:0%
+this graph would be disconnected and
+then it wouldn't mix at all. Um so make
+
+ align:start position:0%
+then it wouldn't mix at all. Um so make
+ 
+
+ align:start position:0%
+then it wouldn't mix at all. Um so make
+a remark
+
+ align:start position:0%
+a remark
+ 
+
+ align:start position:0%
+a remark
+suppose that A is in a finite group and
+
+ align:start position:0%
+suppose that A is in a finite group and
+ 
+
+ align:start position:0%
+suppose that A is in a finite group and
+that H
+
+ align:start position:0%
+that H
+ 
+
+ align:start position:0%
+that H
+the so the the subgroup
+
+ align:start position:0%
+the so the the subgroup
+ 
+
+ align:start position:0%
+the so the the subgroup
+generated by A is H which is a proper
+
+ align:start position:0%
+generated by A is H which is a proper
+ 
+
+ align:start position:0%
+generated by A is H which is a proper
+subgroup.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So then if we take TA and we apply
+
+ align:start position:0%
+Okay. So then if we take TA and we apply
+ 
+
+ align:start position:0%
+Okay. So then if we take TA and we apply
+it to the characteristic function of
+
+ align:start position:0%
+it to the characteristic function of
+ 
+
+ align:start position:0%
+it to the characteristic function of
+this subgroup since all of these guys
+
+ align:start position:0%
+this subgroup since all of these guys
+ 
+
+ align:start position:0%
+this subgroup since all of these guys
+are in the subgroup we would just stay
+
+ align:start position:0%
+are in the subgroup we would just stay
+ 
+
+ align:start position:0%
+are in the subgroup we would just stay
+in the subgroup. So this would be 1 H.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And um and that implies with a
+
+ align:start position:0%
+Okay. And um and that implies with a
+ 
+
+ align:start position:0%
+Okay. And um and that implies with a
+teeny bit of work that sigma 1 of TA
+
+ align:start position:0%
+teeny bit of work that sigma 1 of TA
+ 
+
+ align:start position:0%
+teeny bit of work that sigma 1 of TA
+would be one.
+
+ align:start position:0%
+would be one.
+ 
+
+ align:start position:0%
+would be one.
+Right? So, okay, one thing we could see
+
+ align:start position:0%
+Right? So, okay, one thing we could see
+ 
+
+ align:start position:0%
+Right? So, okay, one thing we could see
+is that no matter how many times we
+
+ align:start position:0%
+is that no matter how many times we
+ 
+
+ align:start position:0%
+is that no matter how many times we
+repeat this operation, we will never mix
+
+ align:start position:0%
+repeat this operation, we will never mix
+ 
+
+ align:start position:0%
+repeat this operation, we will never mix
+over the whole group because we'll never
+
+ align:start position:0%
+over the whole group because we'll never
+ 
+
+ align:start position:0%
+over the whole group because we'll never
+get out of H. And so, based on what
+
+ align:start position:0%
+get out of H. And so, based on what
+ 
+
+ align:start position:0%
+get out of H. And so, based on what
+we've seen before, um, this should be
+
+ align:start position:0%
+we've seen before, um, this should be
+ 
+
+ align:start position:0%
+we've seen before, um, this should be
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+>> Just make a big does it just make the
+
+ align:start position:0%
+>> Just make a big does it just make the
+ 
+
+ align:start position:0%
+>> Just make a big does it just make the
+graph more
+
+ align:start position:0%
+graph more
+ 
+
+ align:start position:0%
+graph more
+likely to be an expander?
+
+ align:start position:0%
+likely to be an expander?
+ 
+
+ align:start position:0%
+likely to be an expander?
+>> Yeah. So, the question is, if we make a
+
+ align:start position:0%
+>> Yeah. So, the question is, if we make a
+ 
+
+ align:start position:0%
+>> Yeah. So, the question is, if we make a
+big, is the graph more likely to be an
+
+ align:start position:0%
+big, is the graph more likely to be an
+ 
+
+ align:start position:0%
+big, is the graph more likely to be an
+expander? Um
+
+ align:start position:0%
+expander? Um
+ 
+
+ align:start position:0%
+expander? Um
+perhaps if we so we could we could take
+
+ align:start position:0%
+perhaps if we so we could we could take
+ 
+
+ align:start position:0%
+perhaps if we so we could we could take
+a big and then it would um so we're so
+
+ align:start position:0%
+a big and then it would um so we're so
+ 
+
+ align:start position:0%
+a big and then it would um so we're so
+we're allowed to take a big and um we
+
+ align:start position:0%
+we're allowed to take a big and um we
+ 
+
+ align:start position:0%
+we're allowed to take a big and um we
+will talk in a little bit about what
+
+ align:start position:0%
+will talk in a little bit about what
+ 
+
+ align:start position:0%
+will talk in a little bit about what
+what we can say if we just know that a
+
+ align:start position:0%
+what we can say if we just know that a
+ 
+
+ align:start position:0%
+what we can say if we just know that a
+is big what does that tell us about
+
+ align:start position:0%
+is big what does that tell us about
+ 
+
+ align:start position:0%
+is big what does that tell us about
+sigma of ta we'll we'll talk about that
+
+ align:start position:0%
+sigma of ta we'll we'll talk about that
+ 
+
+ align:start position:0%
+sigma of ta we'll we'll talk about that
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay so another remark I wanted to make
+
+ align:start position:0%
+okay so another remark I wanted to make
+ 
+
+ align:start position:0%
+okay so another remark I wanted to make
+is that the first proof of this theorem
+
+ align:start position:0%
+is that the first proof of this theorem
+ 
+
+ align:start position:0%
+is that the first proof of this theorem
+was very difficult so the first proof
+
+ align:start position:0%
+was very difficult so the first proof
+ 
+
+ align:start position:0%
+was very difficult so the first proof
+depended on. So it had some interesting
+
+ align:start position:0%
+depended on. So it had some interesting
+ 
+
+ align:start position:0%
+depended on. So it had some interesting
+analysis related to hyperbolic geometry
+
+ align:start position:0%
+analysis related to hyperbolic geometry
+ 
+
+ align:start position:0%
+analysis related to hyperbolic geometry
+but then it depended on the remon
+
+ align:start position:0%
+but then it depended on the remon
+ 
+
+ align:start position:0%
+but then it depended on the remon
+hypothesis for curves over finite
+
+ align:start position:0%
+hypothesis for curves over finite
+ 
+
+ align:start position:0%
+hypothesis for curves over finite
+fields.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's a you know a beautiful and
+
+ align:start position:0%
+So that's a you know a beautiful and
+ 
+
+ align:start position:0%
+So that's a you know a beautiful and
+important theorem but if you wanted to
+
+ align:start position:0%
+important theorem but if you wanted to
+ 
+
+ align:start position:0%
+important theorem but if you wanted to
+include the whole proof of that then the
+
+ align:start position:0%
+include the whole proof of that then the
+ 
+
+ align:start position:0%
+include the whole proof of that then the
+proof of this theorem is effectively
+
+ align:start position:0%
+proof of this theorem is effectively
+ 
+
+ align:start position:0%
+proof of this theorem is effectively
+several hundred pages long and has a lot
+
+ align:start position:0%
+several hundred pages long and has a lot
+ 
+
+ align:start position:0%
+several hundred pages long and has a lot
+of algebraic geometry. Um and in around
+
+ align:start position:0%
+of algebraic geometry. Um and in around
+ 
+
+ align:start position:0%
+of algebraic geometry. Um and in around
+the early 1990s, Sarnac and Shuer gave a
+
+ align:start position:0%
+the early 1990s, Sarnac and Shuer gave a
+ 
+
+ align:start position:0%
+the early 1990s, Sarnac and Shuer gave a
+much simpler proof.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh which is the proof that we'll talk
+
+ align:start position:0%
+Uh which is the proof that we'll talk
+ 
+
+ align:start position:0%
+Uh which is the proof that we'll talk
+about.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Okay. So in the rest of the class
+
+ align:start position:0%
+Okay. Okay. So in the rest of the class
+ 
+
+ align:start position:0%
+Okay. Okay. So in the rest of the class
+I will start to describe the uh proof by
+
+ align:start position:0%
+I will start to describe the uh proof by
+ 
+
+ align:start position:0%
+I will start to describe the uh proof by
+Sarn and and Shuer um uh and and
+
+ align:start position:0%
+Sarn and and Shuer um uh and and
+ 
+
+ align:start position:0%
+Sarn and and Shuer um uh and and
+introduce the first the first key idea.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first idea
+
+ align:start position:0%
+so first idea
+ 
+
+ align:start position:0%
+so first idea
+this idea has to do with the
+
+ align:start position:0%
+this idea has to do with the
+ 
+
+ align:start position:0%
+this idea has to do with the
+representation theory
+
+ align:start position:0%
+representation theory
+ 
+
+ align:start position:0%
+representation theory
+of the group SL2FP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a proposition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if we have a representation so a
+
+ align:start position:0%
+okay so if we have a representation so a
+ 
+
+ align:start position:0%
+okay so if we have a representation so a
+representation is a group homorphism
+
+ align:start position:0%
+representation is a group homorphism
+ 
+
+ align:start position:0%
+representation is a group homorphism
+to uh this is a unitary representation
+
+ align:start position:0%
+to uh this is a unitary representation
+ 
+
+ align:start position:0%
+to uh this is a unitary representation
+so to the unitary group in D dimensions.
+
+ align:start position:0%
+so to the unitary group in D dimensions.
+ 
+
+ align:start position:0%
+so to the unitary group in D dimensions.
+So this is a representation
+
+ align:start position:0%
+So this is a representation
+ 
+
+ align:start position:0%
+So this is a representation
+need a group homorphism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and okay and let me so there there's
+
+ align:start position:0%
+um and okay and let me so there there's
+ 
+
+ align:start position:0%
+um and okay and let me so there there's
+the trivial representation where
+
+ align:start position:0%
+the trivial representation where
+ 
+
+ align:start position:0%
+the trivial representation where
+everything goes to the identity but let
+
+ align:start position:0%
+everything goes to the identity but let
+ 
+
+ align:start position:0%
+everything goes to the identity but let
+me say it is a non-trivial
+
+ align:start position:0%
+me say it is a non-trivial
+ 
+
+ align:start position:0%
+me say it is a non-trivial
+representation
+
+ align:start position:0%
+representation
+ 
+
+ align:start position:0%
+representation
+um then actually d needs to be quite big
+
+ align:start position:0%
+um then actually d needs to be quite big
+ 
+
+ align:start position:0%
+um then actually d needs to be quite big
+d is at least p + 1 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so before we prove this theorem, let's
+
+ align:start position:0%
+so before we prove this theorem, let's
+ 
+
+ align:start position:0%
+so before we prove this theorem, let's
+try to put it in context by trying to
+
+ align:start position:0%
+try to put it in context by trying to
+ 
+
+ align:start position:0%
+try to put it in context by trying to
+think about group representations.
+
+ align:start position:0%
+think about group representations.
+ 
+
+ align:start position:0%
+think about group representations.
+Um, where would we find a group
+
+ align:start position:0%
+Um, where would we find a group
+ 
+
+ align:start position:0%
+Um, where would we find a group
+representation?
+
+ align:start position:0%
+representation?
+ 
+
+ align:start position:0%
+representation?
+Okay, well SL2FP acts on itself. So it
+
+ align:start position:0%
+Okay, well SL2FP acts on itself. So it
+ 
+
+ align:start position:0%
+Okay, well SL2FP acts on itself. So it
+acts on the space that we started with
+
+ align:start position:0%
+acts on the space that we started with
+ 
+
+ align:start position:0%
+acts on the space that we started with
+L2 of G. So, so any so any group G
+
+ align:start position:0%
+L2 of G. So, so any so any group G
+ 
+
+ align:start position:0%
+L2 of G. So, so any so any group G
+acts on L2 G by the action that we sort
+
+ align:start position:0%
+acts on L2 G by the action that we sort
+ 
+
+ align:start position:0%
+acts on L2 G by the action that we sort
+of wrote down. You take a function and
+
+ align:start position:0%
+of wrote down. You take a function and
+ 
+
+ align:start position:0%
+of wrote down. You take a function and
+you like shift the space under it.
+
+ align:start position:0%
+you like shift the space under it.
+ 
+
+ align:start position:0%
+you like shift the space under it.
+Okay, that action is not trivial. So the
+
+ align:start position:0%
+Okay, that action is not trivial. So the
+ 
+
+ align:start position:0%
+Okay, that action is not trivial. So the
+only only the constant functions are
+
+ align:start position:0%
+only only the constant functions are
+ 
+
+ align:start position:0%
+only only the constant functions are
+fixed. So that's a non-trivial action.
+
+ align:start position:0%
+fixed. So that's a non-trivial action.
+ 
+
+ align:start position:0%
+fixed. So that's a non-trivial action.
+And the dimension of this space is the
+
+ align:start position:0%
+And the dimension of this space is the
+ 
+
+ align:start position:0%
+And the dimension of this space is the
+cardality of G. So for this group that
+
+ align:start position:0%
+cardality of G. So for this group that
+ 
+
+ align:start position:0%
+cardality of G. So for this group that
+would be about P cubed.
+
+ align:start position:0%
+would be about P cubed.
+ 
+
+ align:start position:0%
+would be about P cubed.
+So cardality of SL2
+
+ align:start position:0%
+So cardality of SL2
+ 
+
+ align:start position:0%
+So cardality of SL2
+FP.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+what else? Well, if you have a subgroup
+
+ align:start position:0%
+what else? Well, if you have a subgroup
+ 
+
+ align:start position:0%
+what else? Well, if you have a subgroup
+of G,
+
+ align:start position:0%
+of G,
+ 
+
+ align:start position:0%
+of G,
+H is a subgroup
+
+ align:start position:0%
+H is a subgroup
+ 
+
+ align:start position:0%
+H is a subgroup
+of G. Then um G acts
+
+ align:start position:0%
+of G. Then um G acts
+ 
+
+ align:start position:0%
+of G. Then um G acts
+on G mod H and so it acts
+
+ align:start position:0%
+on G mod H and so it acts
+ 
+
+ align:start position:0%
+on G mod H and so it acts
+acts on this as a set and so it acts on
+
+ align:start position:0%
+acts on this as a set and so it acts on
+ 
+
+ align:start position:0%
+acts on this as a set and so it acts on
+L2 of G mod H by a unitary
+
+ align:start position:0%
+L2 of G mod H by a unitary
+ 
+
+ align:start position:0%
+L2 of G mod H by a unitary
+representation and so the dimension
+
+ align:start position:0%
+representation and so the dimension
+ 
+
+ align:start position:0%
+representation and so the dimension
+of L2 of GH
+
+ align:start position:0%
+of L2 of GH
+ 
+
+ align:start position:0%
+of L2 of GH
+is the cardality of G mod which is the
+
+ align:start position:0%
+is the cardality of G mod which is the
+ 
+
+ align:start position:0%
+is the cardality of G mod which is the
+cardality of G divided by the cardality
+
+ align:start position:0%
+cardality of G divided by the cardality
+ 
+
+ align:start position:0%
+cardality of G divided by the cardality
+of H.
+
+ align:start position:0%
+of H.
+ 
+
+ align:start position:0%
+of H.
+Okay, so let's think of some subgroups
+
+ align:start position:0%
+Okay, so let's think of some subgroups
+ 
+
+ align:start position:0%
+Okay, so let's think of some subgroups
+of SL2FP.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Think of there's the diagonal subgroup
+
+ align:start position:0%
+Think of there's the diagonal subgroup
+ 
+
+ align:start position:0%
+Think of there's the diagonal subgroup
+looks like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The size of the diagonal subgroup is
+
+ align:start position:0%
+The size of the diagonal subgroup is
+ 
+
+ align:start position:0%
+The size of the diagonal subgroup is
+around P. There's the unipotent subgroup
+
+ align:start position:0%
+around P. There's the unipotent subgroup
+ 
+
+ align:start position:0%
+around P. There's the unipotent subgroup
+looks like this. Size of the unipotent
+
+ align:start position:0%
+looks like this. Size of the unipotent
+ 
+
+ align:start position:0%
+looks like this. Size of the unipotent
+subgroup is P.
+
+ align:start position:0%
+subgroup is P.
+ 
+
+ align:start position:0%
+subgroup is P.
+And you could sort of mix these
+
+ align:start position:0%
+And you could sort of mix these
+ 
+
+ align:start position:0%
+And you could sort of mix these
+together. So there's the upper
+
+ align:start position:0%
+together. So there's the upper
+ 
+
+ align:start position:0%
+together. So there's the upper
+triangular subgroup. Uh but we already
+
+ align:start position:0%
+triangular subgroup. Uh but we already
+ 
+
+ align:start position:0%
+triangular subgroup. Uh but we already
+used the letter U. So I'm going to call
+
+ align:start position:0%
+used the letter U. So I'm going to call
+ 
+
+ align:start position:0%
+used the letter U. So I'm going to call
+this B for Burell. Uh so I'll write it A
+
+ align:start position:0%
+this B for Burell. Uh so I'll write it A
+ 
+
+ align:start position:0%
+this B for Burell. Uh so I'll write it A
+A inverse T.
+
+ align:start position:0%
+A inverse T.
+ 
+
+ align:start position:0%
+A inverse T.
+That's a subgroup. And the size of the
+
+ align:start position:0%
+That's a subgroup. And the size of the
+ 
+
+ align:start position:0%
+That's a subgroup. And the size of the
+upper triangle subgroup is around P^
+
+ align:start position:0%
+upper triangle subgroup is around P^
+ 
+
+ align:start position:0%
+upper triangle subgroup is around P^
+squ. So that's the biggest one that we
+
+ align:start position:0%
+squ. So that's the biggest one that we
+ 
+
+ align:start position:0%
+squ. So that's the biggest one that we
+have come up with here. And if you plug
+
+ align:start position:0%
+have come up with here. And if you plug
+ 
+
+ align:start position:0%
+have come up with here. And if you plug
+this in here, uh so if you take SL2FP,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's around P. And so this is uh the
+
+ align:start position:0%
+that's around P. And so this is uh the
+ 
+
+ align:start position:0%
+that's around P. And so this is uh the
+right order of magnitude.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And this is an interesting fact
+
+ align:start position:0%
+Okay. And this is an interesting fact
+ 
+
+ align:start position:0%
+Okay. And this is an interesting fact
+about this group which is extremely
+
+ align:start position:0%
+about this group which is extremely
+ 
+
+ align:start position:0%
+about this group which is extremely
+different from a billion groups. So for
+
+ align:start position:0%
+different from a billion groups. So for
+ 
+
+ align:start position:0%
+different from a billion groups. So for
+for an aelion group uh every irreducible
+
+ align:start position:0%
+for an aelion group uh every irreducible
+ 
+
+ align:start position:0%
+for an aelion group uh every irreducible
+representation is onedimensional. So
+
+ align:start position:0%
+representation is onedimensional. So
+ 
+
+ align:start position:0%
+representation is onedimensional. So
+there are lots and lots of
+
+ align:start position:0%
+there are lots and lots of
+ 
+
+ align:start position:0%
+there are lots and lots of
+representations where D is one. But for
+
+ align:start position:0%
+representations where D is one. But for
+ 
+
+ align:start position:0%
+representations where D is one. But for
+SL2FP life is very different. All of
+
+ align:start position:0%
+SL2FP life is very different. All of
+ 
+
+ align:start position:0%
+SL2FP life is very different. All of
+them have very large dimension.
+
+ align:start position:0%
+them have very large dimension.
+ 
+
+ align:start position:0%
+them have very large dimension.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So let's prove this theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh so I had heard about this theorem
+
+ align:start position:0%
+Uh so I had heard about this theorem
+ 
+
+ align:start position:0%
+Uh so I had heard about this theorem
+years ago and I always assumed that to
+
+ align:start position:0%
+years ago and I always assumed that to
+ 
+
+ align:start position:0%
+years ago and I always assumed that to
+prove this theorem one had to study a
+
+ align:start position:0%
+prove this theorem one had to study a
+ 
+
+ align:start position:0%
+prove this theorem one had to study a
+lot of representation theory and I was a
+
+ align:start position:0%
+lot of representation theory and I was a
+ 
+
+ align:start position:0%
+lot of representation theory and I was a
+little intimidated by it. Uh but then I
+
+ align:start position:0%
+little intimidated by it. Uh but then I
+ 
+
+ align:start position:0%
+little intimidated by it. Uh but then I
+read the proof as I was getting ready to
+
+ align:start position:0%
+read the proof as I was getting ready to
+ 
+
+ align:start position:0%
+read the proof as I was getting ready to
+teach this class and actually it it
+
+ align:start position:0%
+teach this class and actually it it
+ 
+
+ align:start position:0%
+teach this class and actually it it
+doesn't require anything that's outside
+
+ align:start position:0%
+doesn't require anything that's outside
+ 
+
+ align:start position:0%
+doesn't require anything that's outside
+of uh you know a good a good
+
+ align:start position:0%
+of uh you know a good a good
+ 
+
+ align:start position:0%
+of uh you know a good a good
+undergraduate algebra curriculum
+
+ align:start position:0%
+undergraduate algebra curriculum
+ 
+
+ align:start position:0%
+undergraduate algebra curriculum
+and it's quite elegant.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So here's the proof. Um,
+
+ align:start position:0%
+All right. So here's the proof. Um,
+ 
+
+ align:start position:0%
+All right. So here's the proof. Um,
+so we're going to focus on this matrix
+
+ align:start position:0%
+so we're going to focus on this matrix
+ 
+
+ align:start position:0%
+so we're going to focus on this matrix
+for a little while and try to figure out
+
+ align:start position:0%
+for a little while and try to figure out
+ 
+
+ align:start position:0%
+for a little while and try to figure out
+what the representation does with this
+
+ align:start position:0%
+what the representation does with this
+ 
+
+ align:start position:0%
+what the representation does with this
+matrix.
+
+ align:start position:0%
+matrix.
+ 
+
+ align:start position:0%
+matrix.
+So let's suppose for now
+
+ align:start position:0%
+So let's suppose for now
+ 
+
+ align:start position:0%
+So let's suppose for now
+that row of this matrix is not just the
+
+ align:start position:0%
+that row of this matrix is not just the
+ 
+
+ align:start position:0%
+that row of this matrix is not just the
+identity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+actually let me let me say it in a
+
+ align:start position:0%
+actually let me let me say it in a
+ 
+
+ align:start position:0%
+actually let me let me say it in a
+different order. So let's say so U is
+
+ align:start position:0%
+different order. So let's say so U is
+ 
+
+ align:start position:0%
+different order. So let's say so U is
+that matrix and V is this matrix which
+
+ align:start position:0%
+that matrix and V is this matrix which
+ 
+
+ align:start position:0%
+that matrix and V is this matrix which
+is very similar to U and we'll make the
+
+ align:start position:0%
+is very similar to U and we'll make the
+ 
+
+ align:start position:0%
+is very similar to U and we'll make the
+remark that so exercise this point I
+
+ align:start position:0%
+remark that so exercise this point I
+ 
+
+ align:start position:0%
+remark that so exercise this point I
+won't include the details U and V
+
+ align:start position:0%
+won't include the details U and V
+ 
+
+ align:start position:0%
+won't include the details U and V
+generate
+
+ align:start position:0%
+generate
+ 
+
+ align:start position:0%
+generate
+SL2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you play around a little bit you
+
+ align:start position:0%
+okay if you play around a little bit you
+ 
+
+ align:start position:0%
+okay if you play around a little bit you
+you can see this all right so therefore
+
+ align:start position:0%
+you can see this all right so therefore
+ 
+
+ align:start position:0%
+you can see this all right so therefore
+if we have a non-trivial representation
+
+ align:start position:0%
+if we have a non-trivial representation
+ 
+
+ align:start position:0%
+if we have a non-trivial representation
+these cannot both go to the identity.
+
+ align:start position:0%
+these cannot both go to the identity.
+ 
+
+ align:start position:0%
+these cannot both go to the identity.
+So row is non-trivial.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So either row of u or row of v is not
+
+ align:start position:0%
+So either row of u or row of v is not
+ 
+
+ align:start position:0%
+So either row of u or row of v is not
+the identity. And u and v are so similar
+
+ align:start position:0%
+the identity. And u and v are so similar
+ 
+
+ align:start position:0%
+the identity. And u and v are so similar
+to each other it doesn't really matter
+
+ align:start position:0%
+to each other it doesn't really matter
+ 
+
+ align:start position:0%
+to each other it doesn't really matter
+which one. So I'm going to say
+
+ align:start position:0%
+which one. So I'm going to say
+ 
+
+ align:start position:0%
+which one. So I'm going to say
+essentially without loss of generality
+
+ align:start position:0%
+essentially without loss of generality
+ 
+
+ align:start position:0%
+essentially without loss of generality
+row of u is not the identity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Now let's think about row of
+
+ align:start position:0%
+All right. Now let's think about row of
+ 
+
+ align:start position:0%
+All right. Now let's think about row of
+u. Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's something quite special about
+
+ align:start position:0%
+there's something quite special about
+ 
+
+ align:start position:0%
+there's something quite special about
+this matrix which is um
+
+ align:start position:0%
+this matrix which is um
+ 
+
+ align:start position:0%
+this matrix which is um
+um that it is conjugate
+
+ align:start position:0%
+um that it is conjugate
+ 
+
+ align:start position:0%
+um that it is conjugate
+to powers of itself.
+
+ align:start position:0%
+to powers of itself.
+ 
+
+ align:start position:0%
+to powers of itself.
+Let me write that down. So suppose take
+
+ align:start position:0%
+Let me write that down. So suppose take
+ 
+
+ align:start position:0%
+Let me write that down. So suppose take
+a diagonal matrix A a inverse. I put
+
+ align:start position:0%
+a diagonal matrix A a inverse. I put
+ 
+
+ align:start position:0%
+a diagonal matrix A a inverse. I put
+this matrix in the middle
+
+ align:start position:0%
+this matrix in the middle
+ 
+
+ align:start position:0%
+this matrix in the middle
+and then I want to conjugate it. So now
+
+ align:start position:0%
+and then I want to conjugate it. So now
+ 
+
+ align:start position:0%
+and then I want to conjugate it. So now
+I put on the other side the inverse.
+
+ align:start position:0%
+I put on the other side the inverse.
+ 
+
+ align:start position:0%
+I put on the other side the inverse.
+Right? So this is the conjugate of my
+
+ align:start position:0%
+Right? So this is the conjugate of my
+ 
+
+ align:start position:0%
+Right? So this is the conjugate of my
+matrix U.
+
+ align:start position:0%
+matrix U.
+ 
+
+ align:start position:0%
+matrix U.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So I multiply this by this. Uh I
+
+ align:start position:0%
+So I multiply this by this. Uh I
+ 
+
+ align:start position:0%
+So I multiply this by this. Uh I
+multiply the top row by a and the bottom
+
+ align:start position:0%
+multiply the top row by a and the bottom
+ 
+
+ align:start position:0%
+multiply the top row by a and the bottom
+row by a inverse. So I get a a z a
+
+ align:start position:0%
+row by a inverse. So I get a a z a
+ 
+
+ align:start position:0%
+row by a inverse. So I get a a z a
+inverse. And then I still have this guy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now when I multiply these matrices
+
+ align:start position:0%
+Now when I multiply these matrices
+ 
+
+ align:start position:0%
+Now when I multiply these matrices
+together, I multiply the left column by
+
+ align:start position:0%
+together, I multiply the left column by
+ 
+
+ align:start position:0%
+together, I multiply the left column by
+a inverse and the right column by a.
+
+ align:start position:0%
+a inverse and the right column by a.
+ 
+
+ align:start position:0%
+a inverse and the right column by a.
+The diagonals cancel, but I get one 01
+
+ align:start position:0%
+The diagonals cancel, but I get one 01
+ 
+
+ align:start position:0%
+The diagonals cancel, but I get one 01
+a².
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So see that u is conjugate
+
+ align:start position:0%
+So see that u is conjugate
+ 
+
+ align:start position:0%
+So see that u is conjugate
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+u to the power a squ
+
+ align:start position:0%
+u to the power a squ
+ 
+
+ align:start position:0%
+u to the power a squ
+and this is for any a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+So that is a special and really
+
+ align:start position:0%
+So that is a special and really
+ 
+
+ align:start position:0%
+So that is a special and really
+interesting feature of this element of
+
+ align:start position:0%
+interesting feature of this element of
+ 
+
+ align:start position:0%
+interesting feature of this element of
+my group.
+
+ align:start position:0%
+my group.
+ 
+
+ align:start position:0%
+my group.
+And so now I have a representation and
+
+ align:start position:0%
+And so now I have a representation and
+ 
+
+ align:start position:0%
+And so now I have a representation and
+row of u is conjugate to row of u of a 2
+
+ align:start position:0%
+row of u is conjugate to row of u of a 2
+ 
+
+ align:start position:0%
+row of u is conjugate to row of u of a 2
+which is row of u to the a 2. So now I
+
+ align:start position:0%
+which is row of u to the a 2. So now I
+ 
+
+ align:start position:0%
+which is row of u to the a 2. So now I
+have a matrix I have a unitary matrix
+
+ align:start position:0%
+have a matrix I have a unitary matrix
+ 
+
+ align:start position:0%
+have a matrix I have a unitary matrix
+and it is conjugate to a big power of
+
+ align:start position:0%
+and it is conjugate to a big power of
+ 
+
+ align:start position:0%
+and it is conjugate to a big power of
+itself.
+
+ align:start position:0%
+itself.
+ 
+
+ align:start position:0%
+itself.
+Okay, in the world of matrices, it's not
+
+ align:start position:0%
+Okay, in the world of matrices, it's not
+ 
+
+ align:start position:0%
+Okay, in the world of matrices, it's not
+so easy to get that to happen. So, this
+
+ align:start position:0%
+so easy to get that to happen. So, this
+ 
+
+ align:start position:0%
+so easy to get that to happen. So, this
+group has a has an interesting property
+
+ align:start position:0%
+group has a has an interesting property
+ 
+
+ align:start position:0%
+group has a has an interesting property
+that has an element which is conjugate
+
+ align:start position:0%
+that has an element which is conjugate
+ 
+
+ align:start position:0%
+that has an element which is conjugate
+to many different powers of itself.
+
+ align:start position:0%
+to many different powers of itself.
+ 
+
+ align:start position:0%
+to many different powers of itself.
+And in matrices, it's not so easy to
+
+ align:start position:0%
+And in matrices, it's not so easy to
+ 
+
+ align:start position:0%
+And in matrices, it's not so easy to
+find a matrix which is conjugate to many
+
+ align:start position:0%
+find a matrix which is conjugate to many
+ 
+
+ align:start position:0%
+find a matrix which is conjugate to many
+different powers of itself.
+
+ align:start position:0%
+different powers of itself.
+ 
+
+ align:start position:0%
+different powers of itself.
+Why? because
+
+ align:start position:0%
+Why? because
+ 
+
+ align:start position:0%
+Why? because
+uh uh- because of how the igen values
+
+ align:start position:0%
+uh uh- because of how the igen values
+ 
+
+ align:start position:0%
+uh uh- because of how the igen values
+behave.
+
+ align:start position:0%
+behave.
+ 
+
+ align:start position:0%
+behave.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+okay. So so now let's think about IGEN
+
+ align:start position:0%
+okay. So so now let's think about IGEN
+ 
+
+ align:start position:0%
+okay. So so now let's think about IGEN
+values.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+row of U is U of D is a matrix.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if row of u is conjugate to row of u
+
+ align:start position:0%
+And if row of u is conjugate to row of u
+ 
+
+ align:start position:0%
+And if row of u is conjugate to row of u
+to the a^2
+
+ align:start position:0%
+to the a^2
+ 
+
+ align:start position:0%
+to the a^2
+then that tells us that the igen values
+
+ align:start position:0%
+then that tells us that the igen values
+ 
+
+ align:start position:0%
+then that tells us that the igen values
+the spectrum of row of u is the same as
+
+ align:start position:0%
+the spectrum of row of u is the same as
+ 
+
+ align:start position:0%
+the spectrum of row of u is the same as
+the igen values of row of u to the a^ 2.
+
+ align:start position:0%
+the igen values of row of u to the a^ 2.
+ 
+
+ align:start position:0%
+the igen values of row of u to the a^ 2.
+Two conjugate matrices have the same
+
+ align:start position:0%
+Two conjugate matrices have the same
+ 
+
+ align:start position:0%
+Two conjugate matrices have the same
+igen values.
+
+ align:start position:0%
+igen values.
+ 
+
+ align:start position:0%
+igen values.
+But if you take a matrix and raise it to
+
+ align:start position:0%
+But if you take a matrix and raise it to
+ 
+
+ align:start position:0%
+But if you take a matrix and raise it to
+a power, the igen values are all raised
+
+ align:start position:0%
+a power, the igen values are all raised
+ 
+
+ align:start position:0%
+a power, the igen values are all raised
+to a power. So this is the igen values
+
+ align:start position:0%
+to a power. So this is the igen values
+ 
+
+ align:start position:0%
+to a power. So this is the igen values
+of row of u to the a 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. So for instance, you could take a
+
+ align:start position:0%
+Okay. So for instance, you could take a
+ 
+
+ align:start position:0%
+Okay. So for instance, you could take a
+to be two and it tells you if you have
+
+ align:start position:0%
+to be two and it tells you if you have
+ 
+
+ align:start position:0%
+to be two and it tells you if you have
+an igen value of row of u you raise it
+
+ align:start position:0%
+an igen value of row of u you raise it
+ 
+
+ align:start position:0%
+an igen value of row of u you raise it
+to the fourth power that will also be an
+
+ align:start position:0%
+to the fourth power that will also be an
+ 
+
+ align:start position:0%
+to the fourth power that will also be an
+igen value of row of u. And you can keep
+
+ align:start position:0%
+igen value of row of u. And you can keep
+ 
+
+ align:start position:0%
+igen value of row of u. And you can keep
+doing that. And it's not just four. We
+
+ align:start position:0%
+doing that. And it's not just four. We
+ 
+
+ align:start position:0%
+doing that. And it's not just four. We
+have many choices for a squ.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So let's think about what the igen
+
+ align:start position:0%
+Okay. So let's think about what the igen
+ 
+
+ align:start position:0%
+Okay. So let's think about what the igen
+values of row of u may be like. So study
+
+ align:start position:0%
+values of row of u may be like. So study
+ 
+
+ align:start position:0%
+values of row of u may be like. So study
+values of row of u. So this is an an
+
+ align:start position:0%
+values of row of u. So this is an an
+ 
+
+ align:start position:0%
+values of row of u. So this is an an
+amazing fact about them. And there's a
+
+ align:start position:0%
+amazing fact about them. And there's a
+ 
+
+ align:start position:0%
+amazing fact about them. And there's a
+more pedestrian fact that we should also
+
+ align:start position:0%
+more pedestrian fact that we should also
+ 
+
+ align:start position:0%
+more pedestrian fact that we should also
+observe. We know that u to the p is the
+
+ align:start position:0%
+observe. We know that u to the p is the
+ 
+
+ align:start position:0%
+observe. We know that u to the p is the
+identity.
+
+ align:start position:0%
+identity.
+ 
+
+ align:start position:0%
+identity.
+And therefore
+
+ align:start position:0%
+And therefore
+ 
+
+ align:start position:0%
+And therefore
+row of u to the p is the identity. So
+
+ align:start position:0%
+row of u to the p is the identity. So
+ 
+
+ align:start position:0%
+row of u to the p is the identity. So
+then if lambda is an igen value of row
+
+ align:start position:0%
+then if lambda is an igen value of row
+ 
+
+ align:start position:0%
+then if lambda is an igen value of row
+of u then we get that lambda to the p is
+
+ align:start position:0%
+of u then we get that lambda to the p is
+ 
+
+ align:start position:0%
+of u then we get that lambda to the p is
+the is one. Okay. So the igen values of
+
+ align:start position:0%
+the is one. Okay. So the igen values of
+ 
+
+ align:start position:0%
+the is one. Okay. So the igen values of
+row of u they're all p roots of unity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+right so we get the following. If lambda
+
+ align:start position:0%
+right so we get the following. If lambda
+ 
+
+ align:start position:0%
+right so we get the following. If lambda
+is an igen value of row of u then lambda
+
+ align:start position:0%
+is an igen value of row of u then lambda
+ 
+
+ align:start position:0%
+is an igen value of row of u then lambda
+to the p is one and lambda to the a 2 is
+
+ align:start position:0%
+to the p is one and lambda to the a 2 is
+ 
+
+ align:start position:0%
+to the p is one and lambda to the a 2 is
+also an igen value of row of u.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+um since lambda to the p is one, we only
+
+ align:start position:0%
+um since lambda to the p is one, we only
+ 
+
+ align:start position:0%
+um since lambda to the p is one, we only
+care about a^2 mod p. So could put mod p
+
+ align:start position:0%
+care about a^2 mod p. So could put mod p
+ 
+
+ align:start position:0%
+care about a^2 mod p. So could put mod p
+there.
+
+ align:start position:0%
+there.
+ 
+
+ align:start position:0%
+there.
+Um and um
+
+ align:start position:0%
+Um and um
+ 
+
+ align:start position:0%
+Um and um
+there are p min -1 / 2 quadratic
+
+ align:start position:0%
+there are p min -1 / 2 quadratic
+ 
+
+ align:start position:0%
+there are p min -1 / 2 quadratic
+residues
+
+ align:start position:0%
+residues
+ 
+
+ align:start position:0%
+residues
+mod p.
+
+ align:start position:0%
+mod p.
+ 
+
+ align:start position:0%
+mod p.
+So this a^ squ mod p. It could be any
+
+ align:start position:0%
+So this a^ squ mod p. It could be any
+ 
+
+ align:start position:0%
+So this a^ squ mod p. It could be any
+quadratic residue mod p. There are p
+
+ align:start position:0%
+quadratic residue mod p. There are p
+ 
+
+ align:start position:0%
+quadratic residue mod p. There are p
+minus one over two of them. And if you
+
+ align:start position:0%
+minus one over two of them. And if you
+ 
+
+ align:start position:0%
+minus one over two of them. And if you
+take a p of unity and you raise it to a
+
+ align:start position:0%
+take a p of unity and you raise it to a
+ 
+
+ align:start position:0%
+take a p of unity and you raise it to a
+power it's between one and p you'll
+
+ align:start position:0%
+power it's between one and p you'll
+ 
+
+ align:start position:0%
+power it's between one and p you'll
+you'll change it. So so lambda is a
+
+ align:start position:0%
+you'll change it. So so lambda is a
+ 
+
+ align:start position:0%
+you'll change it. So so lambda is a
+primitive. So if lambda is not one
+
+ align:start position:0%
+primitive. So if lambda is not one
+ 
+
+ align:start position:0%
+primitive. So if lambda is not one
+then lambda is a primitive p root of
+
+ align:start position:0%
+then lambda is a primitive p root of
+ 
+
+ align:start position:0%
+then lambda is a primitive p root of
+unity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that tells us that the lambda to the
+
+ align:start position:0%
+and that tells us that the lambda to the
+ 
+
+ align:start position:0%
+and that tells us that the lambda to the
+a^ 2 mod p are all distinct
+
+ align:start position:0%
+a^ 2 mod p are all distinct
+ 
+
+ align:start position:0%
+a^ 2 mod p are all distinct
+for the p minus one over two quadratic
+
+ align:start position:0%
+for the p minus one over two quadratic
+ 
+
+ align:start position:0%
+for the p minus one over two quadratic
+reserves.
+
+ align:start position:0%
+reserves.
+ 
+
+ align:start position:0%
+reserves.
+Okay, so we now have seen that that
+
+ align:start position:0%
+Okay, so we now have seen that that
+ 
+
+ align:start position:0%
+Okay, so we now have seen that that
+there are an awful lot of different igen
+
+ align:start position:0%
+there are an awful lot of different igen
+ 
+
+ align:start position:0%
+there are an awful lot of different igen
+values which can only happen if the
+
+ align:start position:0%
+values which can only happen if the
+ 
+
+ align:start position:0%
+values which can only happen if the
+matrix is in a large dimension.
+
+ align:start position:0%
+matrix is in a large dimension.
+ 
+
+ align:start position:0%
+matrix is in a large dimension.
+So that gives us that d is at least p +
+
+ align:start position:0%
+So that gives us that d is at least p +
+ 
+
+ align:start position:0%
+So that gives us that d is at least p +
+1 / 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, actually I so how do we know that
+
+ align:start position:0%
+Okay, actually I so how do we know that
+ 
+
+ align:start position:0%
+Okay, actually I so how do we know that
+row of u has a not an igen value that's
+
+ align:start position:0%
+row of u has a not an igen value that's
+ 
+
+ align:start position:0%
+row of u has a not an igen value that's
+not one? Well, if all the igen values
+
+ align:start position:0%
+not one? Well, if all the igen values
+ 
+
+ align:start position:0%
+not one? Well, if all the igen values
+were one, then row of u you you could is
+
+ align:start position:0%
+were one, then row of u you you could is
+ 
+
+ align:start position:0%
+were one, then row of u you you could is
+conjugate to a matrix with ones on the
+
+ align:start position:0%
+conjugate to a matrix with ones on the
+ 
+
+ align:start position:0%
+conjugate to a matrix with ones on the
+diagonals and some upper triangular
+
+ align:start position:0%
+diagonals and some upper triangular
+ 
+
+ align:start position:0%
+diagonals and some upper triangular
+stuff. And if you raise that to a power,
+
+ align:start position:0%
+stuff. And if you raise that to a power,
+ 
+
+ align:start position:0%
+stuff. And if you raise that to a power,
+you'll never get the identity. Um
+
+ align:start position:0%
+you'll never get the identity. Um
+ 
+
+ align:start position:0%
+you'll never get the identity. Um
+an exercise. So there's a little a
+
+ align:start position:0%
+an exercise. So there's a little a
+ 
+
+ align:start position:0%
+an exercise. So there's a little a
+little something where exercise.
+
+ align:start position:0%
+little something where exercise.
+ 
+
+ align:start position:0%
+little something where exercise.
+If um the igen values of row of u are
+
+ align:start position:0%
+If um the igen values of row of u are
+ 
+
+ align:start position:0%
+If um the igen values of row of u are
+exactly the set one
+
+ align:start position:0%
+exactly the set one
+ 
+
+ align:start position:0%
+exactly the set one
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+row of u to the p = 1 then row of u is
+
+ align:start position:0%
+row of u to the p = 1 then row of u is
+ 
+
+ align:start position:0%
+row of u to the p = 1 then row of u is
+the identity
+
+ align:start position:0%
+the identity
+ 
+
+ align:start position:0%
+the identity
+I I'll leave the matrix details.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So all the representations of SL2 are
+
+ align:start position:0%
+So all the representations of SL2 are
+ 
+
+ align:start position:0%
+So all the representations of SL2 are
+really big. Why does that matter?
+
+ align:start position:0%
+really big. Why does that matter?
+ 
+
+ align:start position:0%
+really big. Why does that matter?
+Let's do another proposition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So proposition two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you take sigma 1 of t mu. So mu is a
+
+ align:start position:0%
+you take sigma 1 of t mu. So mu is a
+ 
+
+ align:start position:0%
+you take sigma 1 of t mu. So mu is a
+measure on
+
+ align:start position:0%
+measure on
+ 
+
+ align:start position:0%
+measure on
+probability measure on SL2 FP.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then sigma 1 of this guy if you square
+
+ align:start position:0%
+Then sigma 1 of this guy if you square
+ 
+
+ align:start position:0%
+Then sigma 1 of this guy if you square
+it and you multiply by D +1 / 2 that is
+
+ align:start position:0%
+it and you multiply by D +1 / 2 that is
+ 
+
+ align:start position:0%
+it and you multiply by D +1 / 2 that is
+at most the size of SL2FP
+
+ align:start position:0%
+at most the size of SL2FP
+ 
+
+ align:start position:0%
+at most the size of SL2FP
+times mu L2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Simplifying the algebra a little bit,
+
+ align:start position:0%
+Simplifying the algebra a little bit,
+ 
+
+ align:start position:0%
+Simplifying the algebra a little bit,
+sigma 1 of t mu^2 is smaller than around
+
+ align:start position:0%
+sigma 1 of t mu^2 is smaller than around
+ 
+
+ align:start position:0%
+sigma 1 of t mu^2 is smaller than around
+1 over p^2
+
+ align:start position:0%
+1 over p^2
+ 
+
+ align:start position:0%
+1 over p^2
+time mu l2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So we come back to the
+
+ align:start position:0%
+All right. So we come back to the
+ 
+
+ align:start position:0%
+All right. So we come back to the
+question from earlier in the class. How
+
+ align:start position:0%
+question from earlier in the class. How
+ 
+
+ align:start position:0%
+question from earlier in the class. How
+are singular values related to igen
+
+ align:start position:0%
+are singular values related to igen
+ 
+
+ align:start position:0%
+are singular values related to igen
+values?
+
+ align:start position:0%
+values?
+ 
+
+ align:start position:0%
+values?
+So sigma i of t mu
+
+ align:start position:0%
+So sigma i of t mu
+ 
+
+ align:start position:0%
+So sigma i of t mu
+squared is lambda i of t mu t mu star.
+
+ align:start position:0%
+squared is lambda i of t mu t mu star.
+ 
+
+ align:start position:0%
+squared is lambda i of t mu t mu star.
+It's the ien value of this matrix.
+
+ align:start position:0%
+It's the ien value of this matrix.
+ 
+
+ align:start position:0%
+It's the ien value of this matrix.
+And the key observation is that the igen
+
+ align:start position:0%
+And the key observation is that the igen
+ 
+
+ align:start position:0%
+And the key observation is that the igen
+spaces of this matrix have a g action on
+
+ align:start position:0%
+spaces of this matrix have a g action on
+ 
+
+ align:start position:0%
+spaces of this matrix have a g action on
+them. And except for the constant
+
+ align:start position:0%
+them. And except for the constant
+ 
+
+ align:start position:0%
+them. And except for the constant
+functions the igen spaces are not
+
+ align:start position:0%
+functions the igen spaces are not
+ 
+
+ align:start position:0%
+functions the igen spaces are not
+trivial. Here's the key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spaces
+
+ align:start position:0%
+spaces
+ 
+
+ align:start position:0%
+spaces
+of t mu t mu star have a g action
+
+ align:start position:0%
+of t mu t mu star have a g action
+ 
+
+ align:start position:0%
+of t mu t mu star have a g action
+and except for
+
+ align:start position:0%
+and except for
+ 
+
+ align:start position:0%
+and except for
+the constant functions. So the constant
+
+ align:start position:0%
+the constant functions. So the constant
+ 
+
+ align:start position:0%
+the constant functions. So the constant
+functions are an igen space of t mu tu
+
+ align:start position:0%
+functions are an igen space of t mu tu
+ 
+
+ align:start position:0%
+functions are an igen space of t mu tu
+star but all the other ones it's a
+
+ align:start position:0%
+star but all the other ones it's a
+ 
+
+ align:start position:0%
+star but all the other ones it's a
+non-trivial action.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's suppose that for a moment and see
+
+ align:start position:0%
+Let's suppose that for a moment and see
+ 
+
+ align:start position:0%
+Let's suppose that for a moment and see
+why it's helpful and then we can think
+
+ align:start position:0%
+why it's helpful and then we can think
+ 
+
+ align:start position:0%
+why it's helpful and then we can think
+more carefully about what exactly are
+
+ align:start position:0%
+more carefully about what exactly are
+ 
+
+ align:start position:0%
+more carefully about what exactly are
+the igen spaces.
+
+ align:start position:0%
+the igen spaces.
+ 
+
+ align:start position:0%
+the igen spaces.
+Um.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um so that tells us that sig each sigma
+
+ align:start position:0%
+Um so that tells us that sig each sigma
+ 
+
+ align:start position:0%
+Um so that tells us that sig each sigma
+i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a multiplicity
+
+ align:start position:0%
+has a multiplicity
+ 
+
+ align:start position:0%
+has a multiplicity
+which is at least d + 1 / 2.
+
+ align:start position:0%
+which is at least d + 1 / 2.
+ 
+
+ align:start position:0%
+which is at least d + 1 / 2.
+So you have and we really care about the
+
+ align:start position:0%
+So you have and we really care about the
+ 
+
+ align:start position:0%
+So you have and we really care about the
+biggest one, this biggest singular
+
+ align:start position:0%
+biggest one, this biggest singular
+ 
+
+ align:start position:0%
+biggest one, this biggest singular
+vector. There's not just one biggest
+
+ align:start position:0%
+vector. There's not just one biggest
+ 
+
+ align:start position:0%
+vector. There's not just one biggest
+singular vector, but there's a a whole
+
+ align:start position:0%
+singular vector, but there's a a whole
+ 
+
+ align:start position:0%
+singular vector, but there's a a whole
+singular subspace of a big dimension and
+
+ align:start position:0%
+singular subspace of a big dimension and
+ 
+
+ align:start position:0%
+singular subspace of a big dimension and
+all of those vectors have have this
+
+ align:start position:0%
+all of those vectors have have this
+ 
+
+ align:start position:0%
+all of those vectors have have this
+large singular value.
+
+ align:start position:0%
+large singular value.
+ 
+
+ align:start position:0%
+large singular value.
+Okay. So now another uh fact from linear
+
+ align:start position:0%
+Okay. So now another uh fact from linear
+ 
+
+ align:start position:0%
+Okay. So now another uh fact from linear
+algebra is that if you add up the
+
+ align:start position:0%
+algebra is that if you add up the
+ 
+
+ align:start position:0%
+algebra is that if you add up the
+singular values squared of a of a matrix
+
+ align:start position:0%
+singular values squared of a of a matrix
+ 
+
+ align:start position:0%
+singular values squared of a of a matrix
+with multiplicity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is the Hilbert Schmidt norm of the
+
+ align:start position:0%
+that is the Hilbert Schmidt norm of the
+ 
+
+ align:start position:0%
+that is the Hilbert Schmidt norm of the
+matrix. So it's the sum of the entries
+
+ align:start position:0%
+matrix. So it's the sum of the entries
+ 
+
+ align:start position:0%
+matrix. So it's the sum of the entries
+of the matrix.
+
+ align:start position:0%
+of the matrix.
+ 
+
+ align:start position:0%
+of the matrix.
+Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a matrix where the rows and
+
+ align:start position:0%
+so this is a matrix where the rows and
+ 
+
+ align:start position:0%
+so this is a matrix where the rows and
+columns are indexed by our group G. So
+
+ align:start position:0%
+columns are indexed by our group G. So
+ 
+
+ align:start position:0%
+columns are indexed by our group G. So
+it has an entry G1 G2 and it's the sum
+
+ align:start position:0%
+it has an entry G1 G2 and it's the sum
+ 
+
+ align:start position:0%
+it has an entry G1 G2 and it's the sum
+of the entries squared.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Does this look familiar to people from
+
+ align:start position:0%
+Does this look familiar to people from
+ 
+
+ align:start position:0%
+Does this look familiar to people from
+linear algebra?
+
+ align:start position:0%
+linear algebra?
+ 
+
+ align:start position:0%
+linear algebra?
+Okay. Okay. Now the entries of our
+
+ align:start position:0%
+Okay. Okay. Now the entries of our
+ 
+
+ align:start position:0%
+Okay. Okay. Now the entries of our
+matrix we can read off. It's the sum g1
+
+ align:start position:0%
+matrix we can read off. It's the sum g1
+ 
+
+ align:start position:0%
+matrix we can read off. It's the sum g1
+g2
+
+ align:start position:0%
+g2
+ 
+
+ align:start position:0%
+g2
+mu of something like g1 g2 inverse. This
+
+ align:start position:0%
+mu of something like g1 g2 inverse. This
+ 
+
+ align:start position:0%
+mu of something like g1 g2 inverse. This
+might not be exactly right but it's the
+
+ align:start position:0%
+might not be exactly right but it's the
+ 
+
+ align:start position:0%
+might not be exactly right but it's the
+right idea.
+
+ align:start position:0%
+right idea.
+ 
+
+ align:start position:0%
+right idea.
+>> Uh that's that's the entry and then
+
+ align:start position:0%
+>> Uh that's that's the entry and then
+ 
+
+ align:start position:0%
+>> Uh that's that's the entry and then
+we're squaring it.
+
+ align:start position:0%
+we're squaring it.
+ 
+
+ align:start position:0%
+we're squaring it.
+Um and so that's the size of the group
+
+ align:start position:0%
+Um and so that's the size of the group
+ 
+
+ align:start position:0%
+Um and so that's the size of the group
+times the sum of mu of g^2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's the right hand side
+
+ align:start position:0%
+Okay, so that's the right hand side
+ 
+
+ align:start position:0%
+Okay, so that's the right hand side
+and over here we're counting with
+
+ align:start position:0%
+and over here we're counting with
+ 
+
+ align:start position:0%
+and over here we're counting with
+multiplicity and the multiplicity is
+
+ align:start position:0%
+multiplicity and the multiplicity is
+ 
+
+ align:start position:0%
+multiplicity and the multiplicity is
+always large. So this is at least d + 1
+
+ align:start position:0%
+always large. So this is at least d + 1
+ 
+
+ align:start position:0%
+always large. So this is at least d + 1
+/ 2 * sigma 1 of t mu^ 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there's an important difference
+
+ align:start position:0%
+So there's an important difference
+ 
+
+ align:start position:0%
+So there's an important difference
+between the sigma 1 and the sigma 0. The
+
+ align:start position:0%
+between the sigma 1 and the sigma 0. The
+ 
+
+ align:start position:0%
+between the sigma 1 and the sigma 0. The
+sigma 0 went with the constant functions
+
+ align:start position:0%
+sigma 0 went with the constant functions
+ 
+
+ align:start position:0%
+sigma 0 went with the constant functions
+that lives in a space of dimension one.
+
+ align:start position:0%
+that lives in a space of dimension one.
+ 
+
+ align:start position:0%
+that lives in a space of dimension one.
+But anybody else lives in a big
+
+ align:start position:0%
+But anybody else lives in a big
+ 
+
+ align:start position:0%
+But anybody else lives in a big
+dimensional space. And so this uh counts
+
+ align:start position:0%
+dimensional space. And so this uh counts
+ 
+
+ align:start position:0%
+dimensional space. And so this uh counts
+get gets counted many times. Um and and
+
+ align:start position:0%
+get gets counted many times. Um and and
+ 
+
+ align:start position:0%
+get gets counted many times. Um and and
+that changes the playing field.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, what is D?
+
+ align:start position:0%
+Um, what is D?
+ 
+
+ align:start position:0%
+Um, what is D?
+>> What is D? Sorry. D is P. Sorry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thank you.
+
+ align:start position:0%
+Thank you.
+ 
+
+ align:start position:0%
+Thank you.
+Okay. Is it right up there? Yeah. So, D
+
+ align:start position:0%
+Okay. Is it right up there? Yeah. So, D
+ 
+
+ align:start position:0%
+Okay. Is it right up there? Yeah. So, D
+is the dimension of the representation,
+
+ align:start position:0%
+is the dimension of the representation,
+ 
+
+ align:start position:0%
+is the dimension of the representation,
+but um that's why I put it, but it's a
+
+ align:start position:0%
+but um that's why I put it, but it's a
+ 
+
+ align:start position:0%
+but um that's why I put it, but it's a
+it was just a mistake. It's supposed to
+
+ align:start position:0%
+it was just a mistake. It's supposed to
+ 
+
+ align:start position:0%
+it was just a mistake. It's supposed to
+be P+ one over two.
+
+ align:start position:0%
+be P+ one over two.
+ 
+
+ align:start position:0%
+be P+ one over two.
+So what needs to be spelled out more
+
+ align:start position:0%
+So what needs to be spelled out more
+ 
+
+ align:start position:0%
+So what needs to be spelled out more
+carefully?
+
+ align:start position:0%
+carefully?
+ 
+
+ align:start position:0%
+carefully?
+I think we should just spell out a
+
+ align:start position:0%
+I think we should just spell out a
+ 
+
+ align:start position:0%
+I think we should just spell out a
+little more carefully why the spaces
+
+ align:start position:0%
+little more carefully why the spaces
+ 
+
+ align:start position:0%
+little more carefully why the spaces
+have this G action.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so first of all, what is T mu
+
+ align:start position:0%
+Okay, so first of all, what is T mu
+ 
+
+ align:start position:0%
+Okay, so first of all, what is T mu
+star? Let's say mu star of g is just mu
+
+ align:start position:0%
+star? Let's say mu star of g is just mu
+ 
+
+ align:start position:0%
+star? Let's say mu star of g is just mu
+of g inverse. And if you write down the
+
+ align:start position:0%
+of g inverse. And if you write down the
+ 
+
+ align:start position:0%
+of g inverse. And if you write down the
+definition of the adjint and play around
+
+ align:start position:0%
+definition of the adjint and play around
+ 
+
+ align:start position:0%
+definition of the adjint and play around
+a little bit, you'll see that t mu star
+
+ align:start position:0%
+a little bit, you'll see that t mu star
+ 
+
+ align:start position:0%
+a little bit, you'll see that t mu star
+is just t of u star convoling with you.
+
+ align:start position:0%
+is just t of u star convoling with you.
+ 
+
+ align:start position:0%
+is just t of u star convoling with you.
+So t mu t mu star of that is just you
+
+ align:start position:0%
+So t mu t mu star of that is just you
+ 
+
+ align:start position:0%
+So t mu t mu star of that is just you
+take f you convolve it with mu star and
+
+ align:start position:0%
+take f you convolve it with mu star and
+ 
+
+ align:start position:0%
+take f you convolve it with mu star and
+then you convolve it with mu. So it's t
+
+ align:start position:0%
+then you convolve it with mu. So it's t
+ 
+
+ align:start position:0%
+then you convolve it with mu. So it's t
+of uh mu convolve with mu star.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so our oper our operator is still
+
+ align:start position:0%
+Okay so our oper our operator is still
+ 
+
+ align:start position:0%
+Okay so our oper our operator is still
+just a convolution operator just
+
+ align:start position:0%
+just a convolution operator just
+ 
+
+ align:start position:0%
+just a convolution operator just
+convolving by something slightly
+
+ align:start position:0%
+convolving by something slightly
+ 
+
+ align:start position:0%
+convolving by something slightly
+different. And now we want to see that
+
+ align:start position:0%
+different. And now we want to see that
+ 
+
+ align:start position:0%
+different. And now we want to see that
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+uh commutes with the some symmetries of
+
+ align:start position:0%
+uh commutes with the some symmetries of
+ 
+
+ align:start position:0%
+uh commutes with the some symmetries of
+of g.
+
+ align:start position:0%
+of g.
+ 
+
+ align:start position:0%
+of g.
+Um okay so our convolution has been
+
+ align:start position:0%
+Um okay so our convolution has been
+ 
+
+ align:start position:0%
+Um okay so our convolution has been
+defined to be on the right and so I
+
+ align:start position:0%
+defined to be on the right and so I
+ 
+
+ align:start position:0%
+defined to be on the right and so I
+think it's supposed to commute with the
+
+ align:start position:0%
+think it's supposed to commute with the
+ 
+
+ align:start position:0%
+think it's supposed to commute with the
+symmetries of of f on the left. So let's
+
+ align:start position:0%
+symmetries of of f on the left. So let's
+ 
+
+ align:start position:0%
+symmetries of of f on the left. So let's
+say f the left action of g on f of h is
+
+ align:start position:0%
+say f the left action of g on f of h is
+ 
+
+ align:start position:0%
+say f the left action of g on f of h is
+f of
+
+ align:start position:0%
+f of
+ 
+
+ align:start position:0%
+f of
+g inverse h.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want to say that uh convolution
+
+ align:start position:0%
+I want to say that uh convolution
+ 
+
+ align:start position:0%
+I want to say that uh convolution
+commutes with this action. So I want to
+
+ align:start position:0%
+commutes with this action. So I want to
+ 
+
+ align:start position:0%
+commutes with this action. So I want to
+say claim
+
+ align:start position:0%
+say claim
+ 
+
+ align:start position:0%
+say claim
+that for for any measure new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I take T new of left action G of F
+
+ align:start position:0%
+if I take T new of left action G of F
+ 
+
+ align:start position:0%
+if I take T new of left action G of F
+this is left action G T new of F.
+
+ align:start position:0%
+this is left action G T new of F.
+ 
+
+ align:start position:0%
+this is left action G T new of F.
+Okay, cross my finger that I wrote
+
+ align:start position:0%
+Okay, cross my finger that I wrote
+ 
+
+ align:start position:0%
+Okay, cross my finger that I wrote
+everything correctly so that this is
+
+ align:start position:0%
+everything correctly so that this is
+ 
+
+ align:start position:0%
+everything correctly so that this is
+true.
+
+ align:start position:0%
+true.
+ 
+
+ align:start position:0%
+true.
+uh t new of left action g of f at some
+
+ align:start position:0%
+uh t new of left action g of f at some
+ 
+
+ align:start position:0%
+uh t new of left action g of f at some
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's say I evaluate that at x.
+
+ align:start position:0%
+let's say I evaluate that at x.
+ 
+
+ align:start position:0%
+let's say I evaluate that at x.
+So the I'm going to convolve this
+
+ align:start position:0%
+So the I'm going to convolve this
+ 
+
+ align:start position:0%
+So the I'm going to convolve this
+function with new. So it's lgf convolved
+
+ align:start position:0%
+function with new. So it's lgf convolved
+ 
+
+ align:start position:0%
+function with new. So it's lgf convolved
+with new at x. So it's the sum x1 x2 = x
+
+ align:start position:0%
+with new at x. So it's the sum x1 x2 = x
+ 
+
+ align:start position:0%
+with new at x. So it's the sum x1 x2 = x
+lf of x1
+
+ align:start position:0%
+lf of x1
+ 
+
+ align:start position:0%
+lf of x1
+new of x2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's the sum x1 x2 = x f of g
+
+ align:start position:0%
+So that's the sum x1 x2 = x f of g
+ 
+
+ align:start position:0%
+So that's the sum x1 x2 = x f of g
+inverse x1
+
+ align:start position:0%
+inverse x1
+ 
+
+ align:start position:0%
+inverse x1
+new of x2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So the product of these two
+
+ align:start position:0%
+All right. So the product of these two
+ 
+
+ align:start position:0%
+All right. So the product of these two
+guys is g inverse x.
+
+ align:start position:0%
+guys is g inverse x.
+ 
+
+ align:start position:0%
+guys is g inverse x.
+So really the product x1 tilda time x2
+
+ align:start position:0%
+So really the product x1 tilda time x2
+ 
+
+ align:start position:0%
+So really the product x1 tilda time x2
+tilda is g inverse x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um f of x1 tilda new of x2 tilda.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that is t new of f evaluated at g
+
+ align:start position:0%
+So that is t new of f evaluated at g
+ 
+
+ align:start position:0%
+So that is t new of f evaluated at g
+inverse x.
+
+ align:start position:0%
+inverse x.
+ 
+
+ align:start position:0%
+inverse x.
+So that's lg of t new of f x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably can see that I'm not a very
+
+ align:start position:0%
+probably can see that I'm not a very
+ 
+
+ align:start position:0%
+probably can see that I'm not a very
+algebraically minded person. I think
+
+ align:start position:0%
+algebraically minded person. I think
+ 
+
+ align:start position:0%
+algebraically minded person. I think
+there's probably a high sort of more
+
+ align:start position:0%
+there's probably a high sort of more
+ 
+
+ align:start position:0%
+there's probably a high sort of more
+highbrow proof of this. So something
+
+ align:start position:0%
+highbrow proof of this. So something
+ 
+
+ align:start position:0%
+highbrow proof of this. So something
+about acting on the left commutes with
+
+ align:start position:0%
+about acting on the left commutes with
+ 
+
+ align:start position:0%
+about acting on the left commutes with
+acting on the right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So,
+
+ align:start position:0%
+Okay. So,
+ 
+
+ align:start position:0%
+Okay. So,
+so the group
+
+ align:start position:0%
+so the group
+ 
+
+ align:start position:0%
+so the group
+commutes the group acts on functions and
+
+ align:start position:0%
+commutes the group acts on functions and
+ 
+
+ align:start position:0%
+commutes the group acts on functions and
+that action commutes with this. So, if
+
+ align:start position:0%
+that action commutes with this. So, if
+ 
+
+ align:start position:0%
+that action commutes with this. So, if
+you have an igen space of this, the
+
+ align:start position:0%
+you have an igen space of this, the
+ 
+
+ align:start position:0%
+you have an igen space of this, the
+group will act on it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if t new of f is lambda f then t new
+
+ align:start position:0%
+So if t new of f is lambda f then t new
+ 
+
+ align:start position:0%
+So if t new of f is lambda f then t new
+of lgf
+
+ align:start position:0%
+of lgf
+ 
+
+ align:start position:0%
+of lgf
+will be lg t new of f which is lg of
+
+ align:start position:0%
+will be lg t new of f which is lg of
+ 
+
+ align:start position:0%
+will be lg t new of f which is lg of
+lambda f which is lambda lg of f.
+
+ align:start position:0%
+lambda f which is lambda lg of f.
+ 
+
+ align:start position:0%
+lambda f which is lambda lg of f.
+So LG so G
+
+ align:start position:0%
+So LG so G
+ 
+
+ align:start position:0%
+So LG so G
+acts on V lambda the space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that fleshes out
+
+ align:start position:0%
+Okay. So that fleshes out
+ 
+
+ align:start position:0%
+Okay. So that fleshes out
+this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. So um let's do a quick application
+
+ align:start position:0%
+Cool. So um let's do a quick application
+ 
+
+ align:start position:0%
+Cool. So um let's do a quick application
+of this to see what we have learned
+
+ align:start position:0%
+of this to see what we have learned
+ 
+
+ align:start position:0%
+of this to see what we have learned
+about mixing.
+
+ align:start position:0%
+about mixing.
+ 
+
+ align:start position:0%
+about mixing.
+So remember that we already know that
+
+ align:start position:0%
+So remember that we already know that
+ 
+
+ align:start position:0%
+So remember that we already know that
+this thing is bounded by one and it's
+
+ align:start position:0%
+this thing is bounded by one and it's
+ 
+
+ align:start position:0%
+this thing is bounded by one and it's
+not at all clear whether this is bigger
+
+ align:start position:0%
+not at all clear whether this is bigger
+ 
+
+ align:start position:0%
+not at all clear whether this is bigger
+or smaller than one. It depends upon mu.
+
+ align:start position:0%
+or smaller than one. It depends upon mu.
+ 
+
+ align:start position:0%
+or smaller than one. It depends upon mu.
+Um if this is bigger than one then this
+
+ align:start position:0%
+Um if this is bigger than one then this
+ 
+
+ align:start position:0%
+Um if this is bigger than one then this
+is kind of useless. But if this is
+
+ align:start position:0%
+is kind of useless. But if this is
+ 
+
+ align:start position:0%
+is kind of useless. But if this is
+smaller than one then it gives us some
+
+ align:start position:0%
+smaller than one then it gives us some
+ 
+
+ align:start position:0%
+smaller than one then it gives us some
+new information.
+
+ align:start position:0%
+new information.
+ 
+
+ align:start position:0%
+new information.
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one question about proposition 2.
+
+ align:start position:0%
+one question about proposition 2.
+ 
+
+ align:start position:0%
+one question about proposition 2.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Does it require the existence of a
+
+ align:start position:0%
+>> Does it require the existence of a
+ 
+
+ align:start position:0%
+>> Does it require the existence of a
+representation of degree P + 1 /2?
+
+ align:start position:0%
+representation of degree P + 1 /2?
+ 
+
+ align:start position:0%
+representation of degree P + 1 /2?
+>> Uh not exactly. I mean this oper this
+
+ align:start position:0%
+>> Uh not exactly. I mean this oper this
+ 
+
+ align:start position:0%
+>> Uh not exactly. I mean this oper this
+operator here has spaces
+
+ align:start position:0%
+operator here has spaces
+ 
+
+ align:start position:0%
+operator here has spaces
+>> and we know that the group acts on them.
+
+ align:start position:0%
+>> and we know that the group acts on them.
+ 
+
+ align:start position:0%
+>> and we know that the group acts on them.
+So therefore there are representations
+
+ align:start position:0%
+So therefore there are representations
+ 
+
+ align:start position:0%
+So therefore there are representations
+of this group.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So application.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So suppose a is a subset of SL2FP.
+
+ align:start position:0%
+So suppose a is a subset of SL2FP.
+ 
+
+ align:start position:0%
+So suppose a is a subset of SL2FP.
+It doesn't have to be a Selberg just any
+
+ align:start position:0%
+It doesn't have to be a Selberg just any
+ 
+
+ align:start position:0%
+It doesn't have to be a Selberg just any
+subset. And remember that mu of A is the
+
+ align:start position:0%
+subset. And remember that mu of A is the
+ 
+
+ align:start position:0%
+subset. And remember that mu of A is the
+uniform measure on A.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So what is mu of a L2 squared?
+
+ align:start position:0%
+Okay. So what is mu of a L2 squared?
+ 
+
+ align:start position:0%
+Okay. So what is mu of a L2 squared?
+Well, we square the amplitude of 1 / a^2
+
+ align:start position:0%
+Well, we square the amplitude of 1 / a^2
+ 
+
+ align:start position:0%
+Well, we square the amplitude of 1 / a^2
+and then we add it up and we'll get a
+
+ align:start position:0%
+and then we add it up and we'll get a
+ 
+
+ align:start position:0%
+and then we add it up and we'll get a
+contribution from a points. So we get
+
+ align:start position:0%
+contribution from a points. So we get
+ 
+
+ align:start position:0%
+contribution from a points. So we get
+one over the cardality of a
+
+ align:start position:0%
+one over the cardality of a
+ 
+
+ align:start position:0%
+one over the cardality of a
+right. So if we just plug in our our uh
+
+ align:start position:0%
+right. So if we just plug in our our uh
+ 
+
+ align:start position:0%
+right. So if we just plug in our our uh
+estimate, proposition two
+
+ align:start position:0%
+estimate, proposition two
+ 
+
+ align:start position:0%
+estimate, proposition two
+tells us that sigma 1 of ta squared is
+
+ align:start position:0%
+tells us that sigma 1 of ta squared is
+ 
+
+ align:start position:0%
+tells us that sigma 1 of ta squared is
+bounded by um
+
+ align:start position:0%
+bounded by um
+ 
+
+ align:start position:0%
+bounded by um
+p ^2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Whoops,
+
+ align:start position:0%
+Whoops,
+ 
+
+ align:start position:0%
+Whoops,
+I did that wrong. That's not good.
+
+ align:start position:0%
+I did that wrong. That's not good.
+ 
+
+ align:start position:0%
+I did that wrong. That's not good.
+This is about p cub. This is about p.
+
+ align:start position:0%
+This is about p cub. This is about p.
+ 
+
+ align:start position:0%
+This is about p cub. This is about p.
+Okay, good. So it's bounded by p ^2 over
+
+ align:start position:0%
+Okay, good. So it's bounded by p ^2 over
+ 
+
+ align:start position:0%
+Okay, good. So it's bounded by p ^2 over
+a.
+
+ align:start position:0%
+a.
+ 
+
+ align:start position:0%
+a.
+So we can see
+
+ align:start position:0%
+So we can see
+ 
+
+ align:start position:0%
+So we can see
+that if a is significantly bigger than p
+
+ align:start position:0%
+that if a is significantly bigger than p
+ 
+
+ align:start position:0%
+that if a is significantly bigger than p
+^2 then sigma 1 of ta is less than one.
+
+ align:start position:0%
+^2 then sigma 1 of ta is less than one.
+ 
+
+ align:start position:0%
+^2 then sigma 1 of ta is less than one.
+So a is 10 p ^2 or even better p 2 plus
+
+ align:start position:0%
+So a is 10 p ^2 or even better p 2 plus
+ 
+
+ align:start position:0%
+So a is 10 p ^2 or even better p 2 plus
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+then sigma 1 is quite a bit less than
+
+ align:start position:0%
+then sigma 1 is quite a bit less than
+ 
+
+ align:start position:0%
+then sigma 1 is quite a bit less than
+one and so this this walk this random
+
+ align:start position:0%
+one and so this this walk this random
+ 
+
+ align:start position:0%
+one and so this this walk this random
+walk will mix. Great.
+
+ align:start position:0%
+walk will mix. Great.
+ 
+
+ align:start position:0%
+walk will mix. Great.
+Um in particular corlary of that is that
+
+ align:start position:0%
+Um in particular corlary of that is that
+ 
+
+ align:start position:0%
+Um in particular corlary of that is that
+if H is a proper subgroup
+
+ align:start position:0%
+if H is a proper subgroup
+ 
+
+ align:start position:0%
+if H is a proper subgroup
+of SL2FP
+
+ align:start position:0%
+of SL2FP
+ 
+
+ align:start position:0%
+of SL2FP
+so we saw earlier take a proper subgroup
+
+ align:start position:0%
+so we saw earlier take a proper subgroup
+ 
+
+ align:start position:0%
+so we saw earlier take a proper subgroup
+and you you walk you just stay in the
+
+ align:start position:0%
+and you you walk you just stay in the
+ 
+
+ align:start position:0%
+and you you walk you just stay in the
+subgroup it won't mix at all sigma 1
+
+ align:start position:0%
+subgroup it won't mix at all sigma 1
+ 
+
+ align:start position:0%
+subgroup it won't mix at all sigma 1
+would be one um then H has size which is
+
+ align:start position:0%
+would be one um then H has size which is
+ 
+
+ align:start position:0%
+would be one um then H has size which is
+smaller than around P ^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we saw earlier that there is a
+
+ align:start position:0%
+and we saw earlier that there is a
+ 
+
+ align:start position:0%
+and we saw earlier that there is a
+subgroup of size about P^2. So this is
+
+ align:start position:0%
+subgroup of size about P^2. So this is
+ 
+
+ align:start position:0%
+subgroup of size about P^2. So this is
+sharp.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this addresses the question
+
+ align:start position:0%
+Okay. So this addresses the question
+ 
+
+ align:start position:0%
+Okay. So this addresses the question
+that was raised earlier. The set A may
+
+ align:start position:0%
+that was raised earlier. The set A may
+ 
+
+ align:start position:0%
+that was raised earlier. The set A may
+be large. If you just know the size of
+
+ align:start position:0%
+be large. If you just know the size of
+ 
+
+ align:start position:0%
+be large. If you just know the size of
+A, can you say whether it mixes or not?
+
+ align:start position:0%
+A, can you say whether it mixes or not?
+ 
+
+ align:start position:0%
+A, can you say whether it mixes or not?
+Um this is essentially a sharp answer to
+
+ align:start position:0%
+Um this is essentially a sharp answer to
+ 
+
+ align:start position:0%
+Um this is essentially a sharp answer to
+that question. If A is significantly
+
+ align:start position:0%
+that question. If A is significantly
+ 
+
+ align:start position:0%
+that question. If A is significantly
+bigger than P^2, then the random walk
+
+ align:start position:0%
+bigger than P^2, then the random walk
+ 
+
+ align:start position:0%
+bigger than P^2, then the random walk
+does mix. And if a is smaller than p ^2,
+
+ align:start position:0%
+does mix. And if a is smaller than p ^2,
+ 
+
+ align:start position:0%
+does mix. And if a is smaller than p ^2,
+a could live in a subgroup and the
+
+ align:start position:0%
+a could live in a subgroup and the
+ 
+
+ align:start position:0%
+a could live in a subgroup and the
+random walk may not mix.
+
+ align:start position:0%
+random walk may not mix.
+ 
+
+ align:start position:0%
+random walk may not mix.
+This whole phenomenon is is is quite
+
+ align:start position:0%
+This whole phenomenon is is is quite
+ 
+
+ align:start position:0%
+This whole phenomenon is is is quite
+different from what would happen in a
+
+ align:start position:0%
+different from what would happen in a
+ 
+
+ align:start position:0%
+different from what would happen in a
+commutive group. Um in a commutive
+
+ align:start position:0%
+commutive group. Um in a commutive
+ 
+
+ align:start position:0%
+commutive group. Um in a commutive
+group, you could take very large subsets
+
+ align:start position:0%
+group, you could take very large subsets
+ 
+
+ align:start position:0%
+group, you could take very large subsets
+and still nothing might mix. Um
+
+ align:start position:0%
+and still nothing might mix. Um
+ 
+
+ align:start position:0%
+and still nothing might mix. Um
+partly because the commutive group might
+
+ align:start position:0%
+partly because the commutive group might
+ 
+
+ align:start position:0%
+partly because the commutive group might
+have very large subgroups, but even if
+
+ align:start position:0%
+have very large subgroups, but even if
+ 
+
+ align:start position:0%
+have very large subgroups, but even if
+it doesn't, it wouldn't work.
+
+ align:start position:0%
+it doesn't, it wouldn't work.
+ 
+
+ align:start position:0%
+it doesn't, it wouldn't work.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Cool.
+
+ align:start position:0%
+Cool.
+ 
+
+ align:start position:0%
+Cool.
+Okay, so that's all very interesting,
+
+ align:start position:0%
+Okay, so that's all very interesting,
+ 
+
+ align:start position:0%
+Okay, so that's all very interesting,
+but it doesn't look very close to this
+
+ align:start position:0%
+but it doesn't look very close to this
+ 
+
+ align:start position:0%
+but it doesn't look very close to this
+theorem yet because this is theorem says
+
+ align:start position:0%
+theorem yet because this is theorem says
+ 
+
+ align:start position:0%
+theorem yet because this is theorem says
+that we get mixing if our subset has
+
+ align:start position:0%
+that we get mixing if our subset has
+ 
+
+ align:start position:0%
+that we get mixing if our subset has
+size larger than P ^2 and this is a
+
+ align:start position:0%
+size larger than P ^2 and this is a
+ 
+
+ align:start position:0%
+size larger than P ^2 and this is a
+subset of size four. So we will have to
+
+ align:start position:0%
+subset of size four. So we will have to
+ 
+
+ align:start position:0%
+subset of size four. So we will have to
+think some more uh about how to do this
+
+ align:start position:0%
+think some more uh about how to do this
+ 
+
+ align:start position:0%
+think some more uh about how to do this
+and we will talk about that uh next
+
+ align:start position:0%
+and we will talk about that uh next
+ 
+
+ align:start position:0%
+and we will talk about that uh next
+time.
\ No newline at end of file
diff --git a/QeHuHti530Q.txt b/QeHuHti530Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cdb39712599105cd87a99c8ecb10982c01e39420
--- /dev/null
+++ b/QeHuHti530Q.txt
@@ -0,0 +1,8363 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+my topic today is they're discussing
+
+ align:start position:0%
+my topic today is they're discussing
+ 
+
+ align:start position:0%
+my topic today is they're discussing
+sensory representations in deep cortex
+
+ align:start position:0%
+sensory representations in deep cortex
+ 
+
+ align:start position:0%
+sensory representations in deep cortex
+like architectures I would say the the
+
+ align:start position:0%
+like architectures I would say the the
+ 
+
+ align:start position:0%
+like architectures I would say the the
+topic is perhaps toward a theory of
+
+ align:start position:0%
+topic is perhaps toward a theory of
+ 
+
+ align:start position:0%
+topic is perhaps toward a theory of
+sensory representations in in deep
+
+ align:start position:0%
+sensory representations in in deep
+ 
+
+ align:start position:0%
+sensory representations in in deep
+networks as you will see the our attempt
+
+ align:start position:0%
+networks as you will see the our attempt
+ 
+
+ align:start position:0%
+networks as you will see the our attempt
+is to develop a systematic theoretical
+
+ align:start position:0%
+is to develop a systematic theoretical
+ 
+
+ align:start position:0%
+is to develop a systematic theoretical
+understanding of the capacity and
+
+ align:start position:0%
+understanding of the capacity and
+ 
+
+ align:start position:0%
+understanding of the capacity and
+limitations of architectures of that of
+
+ align:start position:0%
+limitations of architectures of that of
+ 
+
+ align:start position:0%
+limitations of architectures of that of
+that type the general context is well
+
+ align:start position:0%
+that type the general context is well
+ 
+
+ align:start position:0%
+that type the general context is well
+known in many sensory systems we see
+
+ align:start position:0%
+known in many sensory systems we see
+ 
+
+ align:start position:0%
+known in many sensory systems we see
+information is propagating from from the
+
+ align:start position:0%
+information is propagating from from the
+ 
+
+ align:start position:0%
+information is propagating from from the
+periphery like the retina to visual
+
+ align:start position:0%
+periphery like the retina to visual
+ 
+
+ align:start position:0%
+periphery like the retina to visual
+primary visual cortex and then across
+
+ align:start position:0%
+primary visual cortex and then across
+ 
+
+ align:start position:0%
+primary visual cortex and then across
+many stages up to a very high level or
+
+ align:start position:0%
+many stages up to a very high level or
+ 
+
+ align:start position:0%
+many stages up to a very high level or
+maybe the hippocampal structure it's not
+
+ align:start position:0%
+maybe the hippocampal structure it's not
+ 
+
+ align:start position:0%
+maybe the hippocampal structure it's not
+purely feed-forward
+
+ align:start position:0%
+purely feed-forward
+ 
+
+ align:start position:0%
+purely feed-forward
+there are backward massive backward or
+
+ align:start position:0%
+there are backward massive backward or
+ 
+
+ align:start position:0%
+there are backward massive backward or
+top-down connections that I can't
+
+ align:start position:0%
+top-down connections that I can't
+ 
+
+ align:start position:0%
+top-down connections that I can't
+connections and some of those extra
+
+ align:start position:0%
+connections and some of those extra
+ 
+
+ align:start position:0%
+connections and some of those extra
+features I'll talk about but the most
+
+ align:start position:0%
+features I'll talk about but the most
+ 
+
+ align:start position:0%
+features I'll talk about but the most
+intuitive feature of that is simply
+
+ align:start position:0%
+intuitive feature of that is simply
+ 
+
+ align:start position:0%
+intuitive feature of that is simply
+transformation or filtering of data
+
+ align:start position:0%
+transformation or filtering of data
+ 
+
+ align:start position:0%
+transformation or filtering of data
+across multiple stages
+
+ align:start position:0%
+across multiple stages
+ 
+
+ align:start position:0%
+across multiple stages
+similarly in auditory pathway in other
+
+ align:start position:0%
+similarly in auditory pathway in other
+ 
+
+ align:start position:0%
+similarly in auditory pathway in other
+systems we see a similar structure or
+
+ align:start position:0%
+systems we see a similar structure or
+ 
+
+ align:start position:0%
+systems we see a similar structure or
+aspect of similar structure as well a
+
+ align:start position:0%
+aspect of similar structure as well a
+ 
+
+ align:start position:0%
+aspect of similar structure as well a
+well known and a classical formative
+
+ align:start position:0%
+well known and a classical formative
+ 
+
+ align:start position:0%
+well known and a classical formative
+system for computational science is
+
+ align:start position:0%
+system for computational science is
+ 
+
+ align:start position:0%
+system for computational science is
+bellum where you have information coming
+
+ align:start position:0%
+bellum where you have information coming
+ 
+
+ align:start position:0%
+bellum where you have information coming
+from the mossy fiber layer then expand
+
+ align:start position:0%
+from the mossy fiber layer then expand
+ 
+
+ align:start position:0%
+from the mossy fiber layer then expand
+anonymously into a granule layer and
+
+ align:start position:0%
+anonymously into a granule layer and
+ 
+
+ align:start position:0%
+anonymously into a granule layer and
+then converge to a poke poking yourself
+
+ align:start position:0%
+then converge to a poke poking yourself
+ 
+
+ align:start position:0%
+then converge to a poke poking yourself
+so if you look at a single poke in G
+
+ align:start position:0%
+so if you look at a single poke in G
+ 
+
+ align:start position:0%
+so if you look at a single poke in G
+sell the output of the cerebellum
+
+ align:start position:0%
+sell the output of the cerebellum
+ 
+
+ align:start position:0%
+sell the output of the cerebellum
+as a unit then you see there is a first
+
+ align:start position:0%
+as a unit then you see there is a first
+ 
+
+ align:start position:0%
+as a unit then you see there is a first
+and expansion from one thousand to two
+
+ align:start position:0%
+and expansion from one thousand to two
+ 
+
+ align:start position:0%
+and expansion from one thousand to two
+orders of magnitude or higher in a
+
+ align:start position:0%
+orders of magnitude or higher in a
+ 
+
+ align:start position:0%
+orders of magnitude or higher in a
+granule layer and then convergence of
+
+ align:start position:0%
+granule layer and then convergence of
+ 
+
+ align:start position:0%
+granule layer and then convergence of
+two hundred thousands or so parallel
+
+ align:start position:0%
+two hundred thousands or so parallel
+ 
+
+ align:start position:0%
+two hundred thousands or so parallel
+fibers onto a single poking poking
+
+ align:start position:0%
+fibers onto a single poking poking
+ 
+
+ align:start position:0%
+fibers onto a single poking poking
+yourself and there are those type of
+
+ align:start position:0%
+yourself and there are those type of
+ 
+
+ align:start position:0%
+yourself and there are those type of
+modules many many across the cerebellum
+
+ align:start position:0%
+modules many many across the cerebellum
+ 
+
+ align:start position:0%
+modules many many across the cerebellum
+so again a transformation which involves
+
+ align:start position:0%
+so again a transformation which involves
+ 
+
+ align:start position:0%
+so again a transformation which involves
+in in this case expansion and then
+
+ align:start position:0%
+in in this case expansion and then
+ 
+
+ align:start position:0%
+in in this case expansion and then
+convergence in the basal ganglia which
+
+ align:start position:0%
+convergence in the basal ganglia which
+ 
+
+ align:start position:0%
+convergence in the basal ganglia which
+is not which I wouldn't categorize it as
+
+ align:start position:0%
+is not which I wouldn't categorize it as
+ 
+
+ align:start position:0%
+is not which I wouldn't categorize it as
+a sensory system nevertheless more data
+
+ align:start position:0%
+a sensory system nevertheless more data
+ 
+
+ align:start position:0%
+a sensory system nevertheless more data
+to motor nevertheless you see cortex
+
+ align:start position:0%
+to motor nevertheless you see cortex
+ 
+
+ align:start position:0%
+to motor nevertheless you see cortex
+converging first to various stages of
+
+ align:start position:0%
+converging first to various stages of
+ 
+
+ align:start position:0%
+converging first to various stages of
+the basal ganglia and then expanding
+
+ align:start position:0%
+the basal ganglia and then expanding
+ 
+
+ align:start position:0%
+the basal ganglia and then expanding
+again in to cortex hippocampus has also
+
+ align:start position:0%
+again in to cortex hippocampus has also
+ 
+
+ align:start position:0%
+again in to cortex hippocampus has also
+multiple pathways but some of them
+
+ align:start position:0%
+multiple pathways but some of them
+ 
+
+ align:start position:0%
+multiple pathways but some of them
+include a convergence for instance
+
+ align:start position:0%
+include a convergence for instance
+ 
+
+ align:start position:0%
+include a convergence for instance
+convergence to see a three and then
+
+ align:start position:0%
+convergence to see a three and then
+ 
+
+ align:start position:0%
+convergence to see a three and then
+expansion again to cortex but there are
+
+ align:start position:0%
+expansion again to cortex but there are
+ 
+
+ align:start position:0%
+expansion again to cortex but there are
+other multiple pathways as well
+
+ align:start position:0%
+other multiple pathways as well
+ 
+
+ align:start position:0%
+other multiple pathways as well
+different stages of sensory information
+
+ align:start position:0%
+different stages of sensory information
+ 
+
+ align:start position:0%
+different stages of sensory information
+propagating cause across them okay and
+
+ align:start position:0%
+propagating cause across them okay and
+ 
+
+ align:start position:0%
+propagating cause across them okay and
+finally the artificial network story of
+
+ align:start position:0%
+finally the artificial network story of
+ 
+
+ align:start position:0%
+finally the artificial network story of
+deep neural networks you all of you may
+
+ align:start position:0%
+deep neural networks you all of you may
+ 
+
+ align:start position:0%
+deep neural networks you all of you may
+have heard input layer then sequence of
+
+ align:start position:0%
+have heard input layer then sequence of
+ 
+
+ align:start position:0%
+have heard input layer then sequence of
+stages purely feed-forward and at least
+
+ align:start position:0%
+stages purely feed-forward and at least
+ 
+
+ align:start position:0%
+stages purely feed-forward and at least
+the canonical leading leading network is
+
+ align:start position:0%
+the canonical leading leading network is
+ 
+
+ align:start position:0%
+the canonical leading leading network is
+one that the output layer has object
+
+ align:start position:0%
+one that the output layer has object
+ 
+
+ align:start position:0%
+one that the output layer has object
+recognition object classification task
+
+ align:start position:0%
+recognition object classification task
+ 
+
+ align:start position:0%
+recognition object classification task
+and the whole network is studied by back
+
+ align:start position:0%
+and the whole network is studied by back
+ 
+
+ align:start position:0%
+and the whole network is studied by back
+prop and supervised learning for that
+
+ align:start position:0%
+prop and supervised learning for that
+ 
+
+ align:start position:0%
+prop and supervised learning for that
+what I'll talk about is the more in in
+
+ align:start position:0%
+what I'll talk about is the more in in
+ 
+
+ align:start position:0%
+what I'll talk about is the more in in
+the spirit of the idea that the first
+
+ align:start position:0%
+the spirit of the idea that the first
+ 
+
+ align:start position:0%
+the spirit of the idea that the first
+stages are more general-purpose than the
+
+ align:start position:0%
+stages are more general-purpose than the
+ 
+
+ align:start position:0%
+stages are more general-purpose than the
+specific a classic task in the output
+
+ align:start position:0%
+specific a classic task in the output
+ 
+
+ align:start position:0%
+specific a classic task in the output
+layer okay so there are many issues
+
+ align:start position:0%
+layer okay so there are many issues
+ 
+
+ align:start position:0%
+layer okay so there are many issues
+number of stages that are require the
+
+ align:start position:0%
+number of stages that are require the
+ 
+
+ align:start position:0%
+number of stages that are require the
+size of them why compression or
+
+ align:start position:0%
+size of them why compression or
+ 
+
+ align:start position:0%
+size of them why compression or
+expansion in many system you see that
+
+ align:start position:0%
+expansion in many system you see that
+ 
+
+ align:start position:0%
+expansion in many system you see that
+the fraction
+
+ align:start position:0%
+the fraction
+ 
+
+ align:start position:0%
+the fraction
+of active neurons is is small in the
+
+ align:start position:0%
+of active neurons is is small in the
+ 
+
+ align:start position:0%
+of active neurons is is small in the
+expanded layer that's what we call
+
+ align:start position:0%
+expanded layer that's what we call
+ 
+
+ align:start position:0%
+expanded layer that's what we call
+sparseness so high sparseness means
+
+ align:start position:0%
+sparseness so high sparseness means
+ 
+
+ align:start position:0%
+sparseness so high sparseness means
+small number of neurons activate any
+
+ align:start position:0%
+small number of neurons activate any
+ 
+
+ align:start position:0%
+small number of neurons activate any
+given stimulus
+
+ align:start position:0%
+given stimulus
+ 
+
+ align:start position:0%
+given stimulus
+it's just terminologies somewhat
+
+ align:start position:0%
+it's just terminologies somewhat
+ 
+
+ align:start position:0%
+it's just terminologies somewhat
+confusing so highs partners is small
+
+ align:start position:0%
+confusing so highs partners is small
+ 
+
+ align:start position:0%
+confusing so highs partners is small
+number of active neurons one important
+
+ align:start position:0%
+number of active neurons one important
+ 
+
+ align:start position:0%
+number of active neurons one important
+and crucial questions is how to
+
+ align:start position:0%
+and crucial questions is how to
+ 
+
+ align:start position:0%
+and crucial questions is how to
+transform what are the filters the
+
+ align:start position:0%
+transform what are the filters the
+ 
+
+ align:start position:0%
+transform what are the filters the
+weights that are good for transforming
+
+ align:start position:0%
+weights that are good for transforming
+ 
+
+ align:start position:0%
+weights that are good for transforming
+sensor information from one layer to
+
+ align:start position:0%
+sensor information from one layer to
+ 
+
+ align:start position:0%
+sensor information from one layer to
+another and in particular whether random
+
+ align:start position:0%
+another and in particular whether random
+ 
+
+ align:start position:0%
+another and in particular whether random
+weights is good enough or maybe even
+
+ align:start position:0%
+weights is good enough or maybe even
+ 
+
+ align:start position:0%
+weights is good enough or maybe even
+even optimal in some sense or all one
+
+ align:start position:0%
+even optimal in some sense or all one
+ 
+
+ align:start position:0%
+even optimal in some sense or all one
+needs most structure the more learned a
+
+ align:start position:0%
+needs most structure the more learned a
+ 
+
+ align:start position:0%
+needs most structure the more learned a
+type of synaptic wave this is a crucial
+
+ align:start position:0%
+type of synaptic wave this is a crucial
+ 
+
+ align:start position:0%
+type of synaptic wave this is a crucial
+question perhaps not for machine
+
+ align:start position:0%
+question perhaps not for machine
+ 
+
+ align:start position:0%
+question perhaps not for machine
+learning but for computational science
+
+ align:start position:0%
+learning but for computational science
+ 
+
+ align:start position:0%
+learning but for computational science
+because there is some experimental
+
+ align:start position:0%
+because there is some experimental
+ 
+
+ align:start position:0%
+because there is some experimental
+evidence for at least of some of the
+
+ align:start position:0%
+evidence for at least of some of the
+ 
+
+ align:start position:0%
+evidence for at least of some of the
+systems that are that are studied that
+
+ align:start position:0%
+systems that are that are studied that
+ 
+
+ align:start position:0%
+systems that are that are studied that
+the mapping from the compressed original
+
+ align:start position:0%
+the mapping from the compressed original
+ 
+
+ align:start position:0%
+the mapping from the compressed original
+representation to the space
+
+ align:start position:0%
+representation to the space
+ 
+
+ align:start position:0%
+representation to the space
+representation is is actually done by
+
+ align:start position:0%
+representation is is actually done by
+ 
+
+ align:start position:0%
+representation is is actually done by
+randomly connected weight so one example
+
+ align:start position:0%
+randomly connected weight so one example
+ 
+
+ align:start position:0%
+randomly connected weight so one example
+is all facto a cortex the mapping from
+
+ align:start position:0%
+is all facto a cortex the mapping from
+ 
+
+ align:start position:0%
+is all facto a cortex the mapping from
+of a factory representation from the
+
+ align:start position:0%
+of a factory representation from the
+ 
+
+ align:start position:0%
+of a factory representation from the
+olfactory bulb so come gloom ever lose
+
+ align:start position:0%
+olfactory bulb so come gloom ever lose
+ 
+
+ align:start position:0%
+olfactory bulb so come gloom ever lose
+layer to the period from cortex seems to
+
+ align:start position:0%
+layer to the period from cortex seems to
+ 
+
+ align:start position:0%
+layer to the period from cortex seems to
+be random as far as one can say
+
+ align:start position:0%
+be random as far as one can say
+ 
+
+ align:start position:0%
+be random as far as one can say
+similarly in the cerebellum the example
+
+ align:start position:0%
+similarly in the cerebellum the example
+ 
+
+ align:start position:0%
+similarly in the cerebellum the example
+that I mentioned before when one looks
+
+ align:start position:0%
+that I mentioned before when one looks
+ 
+
+ align:start position:0%
+that I mentioned before when one looks
+at the mapping from the mossy fiber to
+
+ align:start position:0%
+at the mapping from the mossy fiber to
+ 
+
+ align:start position:0%
+at the mapping from the mossy fiber to
+the granule cell again enormous
+
+ align:start position:0%
+the granule cell again enormous
+ 
+
+ align:start position:0%
+the granule cell again enormous
+expansion by a few orders of magnitude
+
+ align:start position:0%
+expansion by a few orders of magnitude
+ 
+
+ align:start position:0%
+expansion by a few orders of magnitude
+nevertheless it they seem to be random
+
+ align:start position:0%
+nevertheless it they seem to be random
+ 
+
+ align:start position:0%
+nevertheless it they seem to be random
+now of course one cannot say exclude
+
+ align:start position:0%
+now of course one cannot say exclude
+ 
+
+ align:start position:0%
+now of course one cannot say exclude
+exclusively that they're random they're
+
+ align:start position:0%
+exclusively that they're random they're
+ 
+
+ align:start position:0%
+exclusively that they're random they're
+not subtle correlations or structures
+
+ align:start position:0%
+not subtle correlations or structures
+ 
+
+ align:start position:0%
+not subtle correlations or structures
+but nevertheless there is a strong
+
+ align:start position:0%
+but nevertheless there is a strong
+ 
+
+ align:start position:0%
+but nevertheless there is a strong
+motivation to ask whether random
+
+ align:start position:0%
+motivation to ask whether random
+ 
+
+ align:start position:0%
+motivation to ask whether random
+projections are good enough and if not
+
+ align:start position:0%
+projections are good enough and if not
+ 
+
+ align:start position:0%
+projections are good enough and if not
+what does it mean structure what kind of
+
+ align:start position:0%
+what does it mean structure what kind of
+ 
+
+ align:start position:0%
+what does it mean structure what kind of
+what kind of structure is
+
+ align:start position:0%
+what kind of structure is
+ 
+
+ align:start position:0%
+what kind of structure is
+is appropriate for this task question of
+
+ align:start position:0%
+is appropriate for this task question of
+ 
+
+ align:start position:0%
+is appropriate for this task question of
+top-down and feedback loops recurrent
+
+ align:start position:0%
+top-down and feedback loops recurrent
+ 
+
+ align:start position:0%
+top-down and feedback loops recurrent
+connections and so on so that all I hope
+
+ align:start position:0%
+connections and so on so that all I hope
+ 
+
+ align:start position:0%
+connections and so on so that all I hope
+to at least briefly mention later on my
+
+ align:start position:0%
+to at least briefly mention later on my
+ 
+
+ align:start position:0%
+to at least briefly mention later on my
+talk okay so before I continue most of
+
+ align:start position:0%
+talk okay so before I continue most of
+ 
+
+ align:start position:0%
+talk okay so before I continue most of
+our large part of my work of the of the
+
+ align:start position:0%
+our large part of my work of the of the
+ 
+
+ align:start position:0%
+our large part of my work of the of the
+talk will be based on published and
+
+ align:start position:0%
+talk will be based on published and
+ 
+
+ align:start position:0%
+talk will be based on published and
+unpublished work with dr. Abadi who was
+
+ align:start position:0%
+unpublished work with dr. Abadi who was
+ 
+
+ align:start position:0%
+unpublished work with dr. Abadi who was
+until recently a postdoctoral a sports
+
+ align:start position:0%
+until recently a postdoctoral a sports
+ 
+
+ align:start position:0%
+until recently a postdoctoral a sports
+fellow at Harvard University when to do
+
+ align:start position:0%
+fellow at Harvard University when to do
+ 
+
+ align:start position:0%
+fellow at Harvard University when to do
+practice medicine any a Franklin master
+
+ align:start position:0%
+practice medicine any a Franklin master
+ 
+
+ align:start position:0%
+practice medicine any a Franklin master
+student at Hebrew University so you know
+
+ align:start position:0%
+student at Hebrew University so you know
+ 
+
+ align:start position:0%
+student at Hebrew University so you know
+who all you know here or at Harvard or
+
+ align:start position:0%
+who all you know here or at Harvard or
+ 
+
+ align:start position:0%
+who all you know here or at Harvard or
+Akoni PhD student at Hebrew University
+
+ align:start position:0%
+Akoni PhD student at Hebrew University
+ 
+
+ align:start position:0%
+Akoni PhD student at Hebrew University
+and and then we from Penn University
+
+ align:start position:0%
+and and then we from Penn University
+ 
+
+ align:start position:0%
+and and then we from Penn University
+okay so here is our formalization of the
+
+ align:start position:0%
+okay so here is our formalization of the
+ 
+
+ align:start position:0%
+okay so here is our formalization of the
+problem we have an input layer the note
+
+ align:start position:0%
+problem we have an input layer the note
+ 
+
+ align:start position:0%
+problem we have an input layer the note
+is 0 typically it's it's a it's a small
+
+ align:start position:0%
+is 0 typically it's it's a it's a small
+ 
+
+ align:start position:0%
+is 0 typically it's it's a it's a small
+it's a compressed layer with dense
+
+ align:start position:0%
+it's a compressed layer with dense
+ 
+
+ align:start position:0%
+it's a compressed layer with dense
+representation so here every input will
+
+ align:start position:0%
+representation so here every input will
+ 
+
+ align:start position:0%
+representation so here every input will
+generate maybe half of the population on
+
+ align:start position:0%
+generate maybe half of the population on
+ 
+
+ align:start position:0%
+generate maybe half of the population on
+average then there is a feed-forward
+
+ align:start position:0%
+average then there is a feed-forward
+ 
+
+ align:start position:0%
+average then there is a feed-forward
+layer of synaptic weights which expand
+
+ align:start position:0%
+layer of synaptic weights which expand
+ 
+
+ align:start position:0%
+layer of synaptic weights which expand
+to a higher dimension layer which we
+
+ align:start position:0%
+to a higher dimension layer which we
+ 
+
+ align:start position:0%
+to a higher dimension layer which we
+call cortical layer it's expanded in
+
+ align:start position:0%
+call cortical layer it's expanded in
+ 
+
+ align:start position:0%
+call cortical layer it's expanded in
+terms of the number of neurons so this
+
+ align:start position:0%
+terms of the number of neurons so this
+ 
+
+ align:start position:0%
+terms of the number of neurons so this
+will be s 1 it is fast because the F the
+
+ align:start position:0%
+will be s 1 it is fast because the F the
+ 
+
+ align:start position:0%
+will be s 1 it is fast because the F the
+fraction of neurons that are active for
+
+ align:start position:0%
+fraction of neurons that are active for
+ 
+
+ align:start position:0%
+fraction of neurons that are active for
+each given input vector will be small so
+
+ align:start position:0%
+each given input vector will be small so
+ 
+
+ align:start position:0%
+each given input vector will be small so
+it is expanded and spouse that was the
+
+ align:start position:0%
+it is expanded and spouse that was the
+ 
+
+ align:start position:0%
+it is expanded and spouse that was the
+that will be the first part of my talk
+
+ align:start position:0%
+that will be the first part of my talk
+ 
+
+ align:start position:0%
+that will be the first part of my talk
+discussing this then a later on I'll
+
+ align:start position:0%
+discussing this then a later on I'll
+ 
+
+ align:start position:0%
+discussing this then a later on I'll
+talk about staging cascading this
+
+ align:start position:0%
+talk about staging cascading this
+ 
+
+ align:start position:0%
+talk about staging cascading this
+transformation to several stages and
+
+ align:start position:0%
+transformation to several stages and
+ 
+
+ align:start position:0%
+transformation to several stages and
+ultimately there is a readout will be
+
+ align:start position:0%
+ultimately there is a readout will be
+ 
+
+ align:start position:0%
+ultimately there is a readout will be
+some classification task our one will be
+
+ align:start position:0%
+some classification task our one will be
+ 
+
+ align:start position:0%
+some classification task our one will be
+one classification our two will be
+
+ align:start position:0%
+one classification our two will be
+ 
+
+ align:start position:0%
+one classification our two will be
+another classification rule etc each one
+
+ align:start position:0%
+another classification rule etc each one
+ 
+
+ align:start position:0%
+another classification rule etc each one
+of them with synaptic weight which I'll
+
+ align:start position:0%
+of them with synaptic weight which I'll
+ 
+
+ align:start position:0%
+of them with synaptic weight which I'll
+learn
+
+ align:start position:0%
+learn
+ 
+
+ align:start position:0%
+learn
+perform that task okay so that's so we
+
+ align:start position:0%
+perform that task okay so that's so we
+ 
+
+ align:start position:0%
+perform that task okay so that's so we
+call that a supervised layer and that's
+
+ align:start position:0%
+call that a supervised layer and that's
+ 
+
+ align:start position:0%
+call that a supervised layer and that's
+the unsupervised layer okay so that's a
+
+ align:start position:0%
+the unsupervised layer okay so that's a
+ 
+
+ align:start position:0%
+the unsupervised layer okay so that's a
+formalization of the problem and as you
+
+ align:start position:0%
+formalization of the problem and as you
+ 
+
+ align:start position:0%
+formalization of the problem and as you
+will see we'll make enormous Lea
+
+ align:start position:0%
+will see we'll make enormous Lea
+ 
+
+ align:start position:0%
+will see we'll make enormous Lea
+simplifying abstraction of the real
+
+ align:start position:0%
+simplifying abstraction of the real
+ 
+
+ align:start position:0%
+simplifying abstraction of the real
+biological system in order to try to
+
+ align:start position:0%
+biological system in order to try to
+ 
+
+ align:start position:0%
+biological system in order to try to
+gain some insight about the
+
+ align:start position:0%
+gain some insight about the
+ 
+
+ align:start position:0%
+gain some insight about the
+computational capacity of such systems
+
+ align:start position:0%
+computational capacity of such systems
+ 
+
+ align:start position:0%
+computational capacity of such systems
+okay so the first important question is
+
+ align:start position:0%
+okay so the first important question is
+ 
+
+ align:start position:0%
+okay so the first important question is
+what is the statistics the statistical
+
+ align:start position:0%
+what is the statistics the statistical
+ 
+
+ align:start position:0%
+what is the statistics the statistical
+structure of the input so the input is
+
+ align:start position:0%
+structure of the input so the input is
+ 
+
+ align:start position:0%
+structure of the input so the input is
+kind of n dimensional vector n or n 0
+
+ align:start position:0%
+kind of n dimensional vector n or n 0
+ 
+
+ align:start position:0%
+kind of n dimensional vector n or n 0
+when n is the number of units here
+
+ align:start position:0%
+when n is the number of units here
+ 
+
+ align:start position:0%
+when n is the number of units here
+so each sense of event evokes a pattern
+
+ align:start position:0%
+so each sense of event evokes a pattern
+ 
+
+ align:start position:0%
+so each sense of event evokes a pattern
+of activity here but what is the
+
+ align:start position:0%
+of activity here but what is the
+ 
+
+ align:start position:0%
+of activity here but what is the
+structure that the statistical structure
+
+ align:start position:0%
+structure that the statistical structure
+ 
+
+ align:start position:0%
+structure that the statistical structure
+that we are working with and the
+
+ align:start position:0%
+that we are working with and the
+ 
+
+ align:start position:0%
+that we are working with and the
+simplest one to that we are going to
+
+ align:start position:0%
+simplest one to that we are going to
+ 
+
+ align:start position:0%
+simplest one to that we are going to
+discuss is the following so we assume
+
+ align:start position:0%
+discuss is the following so we assume
+ 
+
+ align:start position:0%
+discuss is the following so we assume
+basically that the input are coming from
+
+ align:start position:0%
+basically that the input are coming from
+ 
+
+ align:start position:0%
+basically that the input are coming from
+a mixture of so to speak a mixture of
+
+ align:start position:0%
+a mixture of so to speak a mixture of
+ 
+
+ align:start position:0%
+a mixture of so to speak a mixture of
+Gaussian statistics it's not going to be
+
+ align:start position:0%
+Gaussian statistics it's not going to be
+ 
+
+ align:start position:0%
+Gaussian statistics it's not going to be
+Gaussian because for simplicity we'll
+
+ align:start position:0%
+Gaussian because for simplicity we'll
+ 
+
+ align:start position:0%
+Gaussian because for simplicity we'll
+assume they're binary but this doesn't
+
+ align:start position:0%
+assume they're binary but this doesn't
+ 
+
+ align:start position:0%
+assume they're binary but this doesn't
+matter actually so imagine that this is
+
+ align:start position:0%
+matter actually so imagine that this is
+ 
+
+ align:start position:0%
+matter actually so imagine that this is
+kind of a graphical representation at or
+
+ align:start position:0%
+kind of a graphical representation at or
+ 
+
+ align:start position:0%
+kind of a graphical representation at or
+of high dimensional space and imagine
+
+ align:start position:0%
+of high dimensional space and imagine
+ 
+
+ align:start position:0%
+of high dimensional space and imagine
+each in the inputs the sensory inputs
+
+ align:start position:0%
+each in the inputs the sensory inputs
+ 
+
+ align:start position:0%
+each in the inputs the sensory inputs
+imagine that there are a clustered
+
+ align:start position:0%
+imagine that there are a clustered
+ 
+
+ align:start position:0%
+imagine that there are a clustered
+around templates or cluster centers in
+
+ align:start position:0%
+around templates or cluster centers in
+ 
+
+ align:start position:0%
+around templates or cluster centers in
+so this would be the centers of this of
+
+ align:start position:0%
+so this would be the centers of this of
+ 
+
+ align:start position:0%
+so this would be the centers of this of
+these balls and the the input itself is
+
+ align:start position:0%
+these balls and the the input itself is
+ 
+
+ align:start position:0%
+these balls and the the input itself is
+coming from the neighborhoods of those
+
+ align:start position:0%
+coming from the neighborhoods of those
+ 
+
+ align:start position:0%
+coming from the neighborhoods of those
+templates so each input will be one
+
+ align:start position:0%
+templates so each input will be one
+ 
+
+ align:start position:0%
+templates so each input will be one
+point in this in this space and it will
+
+ align:start position:0%
+point in this in this space and it will
+ 
+
+ align:start position:0%
+point in this in this space and it will
+be originating from one of those and
+
+ align:start position:0%
+be originating from one of those and
+ 
+
+ align:start position:0%
+be originating from one of those and
+some of one of those states so that's a
+
+ align:start position:0%
+some of one of those states so that's a
+ 
+
+ align:start position:0%
+some of one of those states so that's a
+simple simple architecture and we are
+
+ align:start position:0%
+simple simple architecture and we are
+ 
+
+ align:start position:0%
+simple simple architecture and we are
+going so in in real space nothing it
+
+ align:start position:0%
+going so in in real space nothing it
+ 
+
+ align:start position:0%
+going so in in real space nothing it
+will be mapping from one of those states
+
+ align:start position:0%
+will be mapping from one of those states
+ 
+
+ align:start position:0%
+will be mapping from one of those states
+into another state in the next layer and
+
+ align:start position:0%
+into another state in the next layer and
+ 
+
+ align:start position:0%
+into another state in the next layer and
+then and then finally the
+
+ align:start position:0%
+then and then finally the
+ 
+
+ align:start position:0%
+then and then finally the
+tasks will be to take imagine that some
+
+ align:start position:0%
+tasks will be to take imagine that some
+ 
+
+ align:start position:0%
+tasks will be to take imagine that some
+of those balls are classified as plus
+
+ align:start position:0%
+of those balls are classified as plus
+ 
+
+ align:start position:0%
+of those balls are classified as plus
+let's say though the olfactory stimuli
+
+ align:start position:0%
+let's say though the olfactory stimuli
+ 
+
+ align:start position:0%
+let's say though the olfactory stimuli
+and some of them are classified as a
+
+ align:start position:0%
+and some of them are classified as a
+ 
+
+ align:start position:0%
+and some of them are classified as a
+appetitive some of them as aversive so
+
+ align:start position:0%
+appetitive some of them as aversive so
+ 
+
+ align:start position:0%
+appetitive some of them as aversive so
+the output layer the the readout unit
+
+ align:start position:0%
+the output layer the the readout unit
+ 
+
+ align:start position:0%
+the output layer the the readout unit
+has to classify some of those spheres as
+
+ align:start position:0%
+has to classify some of those spheres as
+ 
+
+ align:start position:0%
+has to classify some of those spheres as
+a class and some of them are - and of
+
+ align:start position:0%
+a class and some of them are - and of
+ 
+
+ align:start position:0%
+a class and some of them are - and of
+course depending on the how many of them
+
+ align:start position:0%
+course depending on the how many of them
+ 
+
+ align:start position:0%
+course depending on the how many of them
+are any dimensionality and their
+
+ align:start position:0%
+are any dimensionality and their
+ 
+
+ align:start position:0%
+are any dimensionality and their
+location this may or may not be an easy
+
+ align:start position:0%
+location this may or may not be an easy
+ 
+
+ align:start position:0%
+location this may or may not be an easy
+problem so for instance here here it's
+
+ align:start position:0%
+problem so for instance here here it's
+ 
+
+ align:start position:0%
+problem so for instance here here it's
+fine there is a linear classifier on the
+
+ align:start position:0%
+fine there is a linear classifier on the
+ 
+
+ align:start position:0%
+fine there is a linear classifier on the
+input space can do it here
+
+ align:start position:0%
+input space can do it here
+ 
+
+ align:start position:0%
+input space can do it here
+I think that should be some mistakes in
+
+ align:start position:0%
+I think that should be some mistakes in
+ 
+
+ align:start position:0%
+I think that should be some mistakes in
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+so here is in a case where the the
+
+ align:start position:0%
+so here is in a case where the the
+ 
+
+ align:start position:0%
+so here is in a case where the the
+linear classifier at the input layer
+
+ align:start position:0%
+linear classifier at the input layer
+ 
+
+ align:start position:0%
+linear classifier at the input layer
+cannot do it and that's our debts and
+
+ align:start position:0%
+cannot do it and that's our debts and
+ 
+
+ align:start position:0%
+cannot do it and that's our debts and
+that's a theme which is very popular
+
+ align:start position:0%
+that's a theme which is very popular
+ 
+
+ align:start position:0%
+that's a theme which is very popular
+both in computational science in and
+
+ align:start position:0%
+both in computational science in and
+ 
+
+ align:start position:0%
+both in computational science in and
+system neuroscience studies in machine
+
+ align:start position:0%
+system neuroscience studies in machine
+ 
+
+ align:start position:0%
+system neuroscience studies in machine
+learning and the following the following
+
+ align:start position:0%
+learning and the following the following
+ 
+
+ align:start position:0%
+learning and the following the following
+question comes up suppose we see that
+
+ align:start position:0%
+question comes up suppose we see that
+ 
+
+ align:start position:0%
+question comes up suppose we see that
+there is a transformation of data from
+
+ align:start position:0%
+there is a transformation of data from
+ 
+
+ align:start position:0%
+there is a transformation of data from
+let's a photo photoreceptor layer in
+
+ align:start position:0%
+let's a photo photoreceptor layer in
+ 
+
+ align:start position:0%
+let's a photo photoreceptor layer in
+vision to the ganglion cells at the
+
+ align:start position:0%
+vision to the ganglion cells at the
+ 
+
+ align:start position:0%
+vision to the ganglion cells at the
+output of the retina then to cortex and
+
+ align:start position:0%
+output of the retina then to cortex and
+ 
+
+ align:start position:0%
+output of the retina then to cortex and
+in several stages how do we gauge how do
+
+ align:start position:0%
+in several stages how do we gauge how do
+ 
+
+ align:start position:0%
+in several stages how do we gauge how do
+we assess what is the what is the
+
+ align:start position:0%
+we assess what is the what is the
+ 
+
+ align:start position:0%
+we assess what is the what is the
+advantage for the brain to transform
+
+ align:start position:0%
+advantage for the brain to transform
+ 
+
+ align:start position:0%
+advantage for the brain to transform
+information from one let's say from
+
+ align:start position:0%
+information from one let's say from
+ 
+
+ align:start position:0%
+information from one let's say from
+retina to v1 and so on so forth
+
+ align:start position:0%
+retina to v1 and so on so forth
+ 
+
+ align:start position:0%
+retina to v1 and so on so forth
+basically after all in this feed forward
+
+ align:start position:0%
+basically after all in this feed forward
+ 
+
+ align:start position:0%
+basically after all in this feed forward
+architecture no net information is
+
+ align:start position:0%
+architecture no net information is
+ 
+
+ align:start position:0%
+architecture no net information is
+generated at the next layer so if known
+
+ align:start position:0%
+generated at the next layer so if known
+ 
+
+ align:start position:0%
+generated at the next layer so if known
+if not information is generated the
+
+ align:start position:0%
+if not information is generated the
+ 
+
+ align:start position:0%
+if not information is generated the
+question is what
+
+ align:start position:0%
+question is what
+ 
+
+ align:start position:0%
+question is what
+what did we gain by these
+
+ align:start position:0%
+what did we gain by these
+ 
+
+ align:start position:0%
+what did we gain by these
+transformations and one one possible
+
+ align:start position:0%
+transformations and one one possible
+ 
+
+ align:start position:0%
+transformations and one one possible
+answer is that it is reformatted we live
+
+ align:start position:0%
+answer is that it is reformatted we live
+ 
+
+ align:start position:0%
+answer is that it is reformatted we live
+formatting the sensory representation in
+
+ align:start position:0%
+formatting the sensory representation in
+ 
+
+ align:start position:0%
+formatting the sensory representation in
+two different representation which will
+
+ align:start position:0%
+two different representation which will
+ 
+
+ align:start position:0%
+two different representation which will
+make subsequent computations simpler so
+
+ align:start position:0%
+make subsequent computations simpler so
+ 
+
+ align:start position:0%
+make subsequent computations simpler so
+what does it mean subset computation
+
+ align:start position:0%
+what does it mean subset computation
+ 
+
+ align:start position:0%
+what does it mean subset computation
+subsequent computations simpler one
+
+ align:start position:0%
+subsequent computations simpler one
+ 
+
+ align:start position:0%
+subsequent computations simpler one
+notion of simplicity is whether
+
+ align:start position:0%
+notion of simplicity is whether
+ 
+
+ align:start position:0%
+notion of simplicity is whether
+subsequent computation can be realized
+
+ align:start position:0%
+subsequent computation can be realized
+ 
+
+ align:start position:0%
+subsequent computation can be realized
+by a simple linear linear readout so
+
+ align:start position:0%
+by a simple linear linear readout so
+ 
+
+ align:start position:0%
+by a simple linear linear readout so
+that's that's the that's the strategy
+
+ align:start position:0%
+that's that's the that's the strategy
+ 
+
+ align:start position:0%
+that's that's the that's the strategy
+that we are going to to adopt here and
+
+ align:start position:0%
+that we are going to to adopt here and
+ 
+
+ align:start position:0%
+that we are going to to adopt here and
+this is to ask as the information as the
+
+ align:start position:0%
+this is to ask as the information as the
+ 
+
+ align:start position:0%
+this is to ask as the information as the
+representation is changing as you go
+
+ align:start position:0%
+representation is changing as you go
+ 
+
+ align:start position:0%
+representation is changing as you go
+from one layer to another how well a
+
+ align:start position:0%
+from one layer to another how well a
+ 
+
+ align:start position:0%
+from one layer to another how well a
+linear readout will be able to perform
+
+ align:start position:0%
+linear readout will be able to perform
+ 
+
+ align:start position:0%
+linear readout will be able to perform
+the task okay so that's the input that's
+
+ align:start position:0%
+the task okay so that's the input that's
+ 
+
+ align:start position:0%
+the task okay so that's the input that's
+the story and another said there is an
+
+ align:start position:0%
+the story and another said there is an
+ 
+
+ align:start position:0%
+the story and another said there is an
+input unsupervised representations and
+
+ align:start position:0%
+input unsupervised representations and
+ 
+
+ align:start position:0%
+input unsupervised representations and
+supervised at the end okay okay now I
+
+ align:start position:0%
+supervised at the end okay okay now I
+ 
+
+ align:start position:0%
+supervised at the end okay okay now I
+mean I need to put two into those
+
+ align:start position:0%
+mean I need to put two into those
+ 
+
+ align:start position:0%
+mean I need to put two into those
+notations bear with me this is a
+
+ align:start position:0%
+notations bear with me this is a
+ 
+
+ align:start position:0%
+notations bear with me this is a
+computational talk I cannot just talk
+
+ align:start position:0%
+computational talk I cannot just talk
+ 
+
+ align:start position:0%
+computational talk I cannot just talk
+about ideas because the the whole thing
+
+ align:start position:0%
+about ideas because the the whole thing
+ 
+
+ align:start position:0%
+about ideas because the the whole thing
+is to be able to actually come up with a
+
+ align:start position:0%
+is to be able to actually come up with a
+ 
+
+ align:start position:0%
+is to be able to actually come up with a
+quantitative theory that test ideas so
+
+ align:start position:0%
+quantitative theory that test ideas so
+ 
+
+ align:start position:0%
+quantitative theory that test ideas so
+let me let me introduce notations so at
+
+ align:start position:0%
+let me let me introduce notations so at
+ 
+
+ align:start position:0%
+let me let me introduce notations so at
+the the centers at each layer you can
+
+ align:start position:0%
+the the centers at each layer you can
+ 
+
+ align:start position:0%
+the the centers at each layer you can
+ask what is the representation of the
+
+ align:start position:0%
+ask what is the representation of the
+ 
+
+ align:start position:0%
+ask what is the representation of the
+centers of this stimuli and I'll denote
+
+ align:start position:0%
+centers of this stimuli and I'll denote
+ 
+
+ align:start position:0%
+centers of this stimuli and I'll denote
+the center by a bar okay and me U is one
+
+ align:start position:0%
+the center by a bar okay and me U is one
+ 
+
+ align:start position:0%
+the center by a bar okay and me U is one
+mu is index of the patterns some u goes
+
+ align:start position:0%
+mu is index of the patterns some u goes
+ 
+
+ align:start position:0%
+mu is index of the patterns some u goes
+from 1 to P P is the number of those
+
+ align:start position:0%
+from 1 to P P is the number of those
+ 
+
+ align:start position:0%
+from 1 to P P is the number of those
+balls number of those fields or number
+
+ align:start position:0%
+balls number of those fields or number
+ 
+
+ align:start position:0%
+balls number of those fields or number
+of those clusters if you think about
+
+ align:start position:0%
+of those clusters if you think about
+ 
+
+ align:start position:0%
+of those clusters if you think about
+clustering some sensory data so P will
+
+ align:start position:0%
+clustering some sensory data so P will
+ 
+
+ align:start position:0%
+clustering some sensory data so P will
+be the number of clusters I from 1 to n
+
+ align:start position:0%
+be the number of clusters I from 1 to n
+ 
+
+ align:start position:0%
+be the number of clusters I from 1 to n
+is simply the neuron of the unit
+
+ align:start position:0%
+is simply the neuron of the unit
+ 
+
+ align:start position:0%
+is simply the neuron of the unit
+activation its mu and n is the layer so
+
+ align:start position:0%
+activation its mu and n is the layer so
+ 
+
+ align:start position:0%
+activation its mu and n is the layer so
+0 is the input layer that's up to Lal ok
+
+ align:start position:0%
+0 is the input layer that's up to Lal ok
+ 
+
+ align:start position:0%
+0 is the input layer that's up to Lal ok
+so this would be 0 1 the mean activation
+
+ align:start position:0%
+so this would be 0 1 the mean activation
+ 
+
+ align:start position:0%
+so this would be 0 1 the mean activation
+at each
+
+ align:start position:0%
+at each
+ 
+
+ align:start position:0%
+at each
+lair from from one on will just kept to
+
+ align:start position:0%
+lair from from one on will just kept to
+ 
+
+ align:start position:0%
+lair from from one on will just kept to
+be constant two BFF goes from zero to
+
+ align:start position:0%
+be constant two BFF goes from zero to
+ 
+
+ align:start position:0%
+be constant two BFF goes from zero to
+one the smaller F is the sponsor the
+
+ align:start position:0%
+one the smaller F is the sponsor the
+ 
+
+ align:start position:0%
+one the smaller F is the sponsor the
+representation is we will assume that
+
+ align:start position:0%
+representation is we will assume that
+ 
+
+ align:start position:0%
+representation is we will assume that
+the input representation is dense of
+
+ align:start position:0%
+the input representation is dense of
+ 
+
+ align:start position:0%
+the input representation is dense of
+this is 0.5 and again will assume to be
+
+ align:start position:0%
+this is 0.5 and again will assume to be
+ 
+
+ align:start position:0%
+this is 0.5 and again will assume to be
+constant PCT constant across layer
+
+ align:start position:0%
+constant PCT constant across layer
+ 
+
+ align:start position:0%
+constant PCT constant across layer
+except for the first level there is
+
+ align:start position:0%
+except for the first level there is
+ 
+
+ align:start position:0%
+except for the first level there is
+expansion
+
+ align:start position:0%
+expansion
+ 
+
+ align:start position:0%
+expansion
+you can vary those parameters and
+
+ align:start position:0%
+you can vary those parameters and
+ 
+
+ align:start position:0%
+you can vary those parameters and
+actually the theory accommodates
+
+ align:start position:0%
+actually the theory accommodates
+ 
+
+ align:start position:0%
+actually the theory accommodates
+variations of those but that's the
+
+ align:start position:0%
+variations of those but that's the
+ 
+
+ align:start position:0%
+variations of those but that's the
+simplest architecture you expand and
+
+ align:start position:0%
+simplest architecture you expand and
+ 
+
+ align:start position:0%
+simplest architecture you expand and
+dense representation into a sparse
+
+ align:start position:0%
+dense representation into a sparse
+ 
+
+ align:start position:0%
+dense representation into a sparse
+higher dimension and you keep doing it
+
+ align:start position:0%
+higher dimension and you keep doing it
+ 
+
+ align:start position:0%
+higher dimension and you keep doing it
+as you go along okay so that's notation
+
+ align:start position:0%
+as you go along okay so that's notation
+ 
+
+ align:start position:0%
+as you go along okay so that's notation
+okay now I how do how do we assess what
+
+ align:start position:0%
+okay now I how do how do we assess what
+ 
+
+ align:start position:0%
+okay now I how do how do we assess what
+is what is the next stage is doing to
+
+ align:start position:0%
+is what is the next stage is doing to
+ 
+
+ align:start position:0%
+is what is the next stage is doing to
+those clusters okay so as I said one
+
+ align:start position:0%
+those clusters okay so as I said one
+ 
+
+ align:start position:0%
+those clusters okay so as I said one
+measure is take a linear classifier and
+
+ align:start position:0%
+measure is take a linear classifier and
+ 
+
+ align:start position:0%
+measure is take a linear classifier and
+see how Lin a classifier performs okay
+
+ align:start position:0%
+see how Lin a classifier performs okay
+ 
+
+ align:start position:0%
+see how Lin a classifier performs okay
+but actually you can you can also look
+
+ align:start position:0%
+but actually you can you can also look
+ 
+
+ align:start position:0%
+but actually you can you can also look
+at the statistics of the injected
+
+ align:start position:0%
+at the statistics of the injected
+ 
+
+ align:start position:0%
+at the statistics of the injected
+sensory stimuli at each layer and learn
+
+ align:start position:0%
+sensory stimuli at each layer and learn
+ 
+
+ align:start position:0%
+sensory stimuli at each layer and learn
+something from it and basically I'm
+
+ align:start position:0%
+something from it and basically I'm
+ 
+
+ align:start position:0%
+something from it and basically I'm
+going to suggest looking at the two
+
+ align:start position:0%
+going to suggest looking at the two
+ 
+
+ align:start position:0%
+going to suggest looking at the two
+major statistical aspects of the data as
+
+ align:start position:0%
+major statistical aspects of the data as
+ 
+
+ align:start position:0%
+major statistical aspects of the data as
+each layer of the transformation one of
+
+ align:start position:0%
+each layer of the transformation one of
+ 
+
+ align:start position:0%
+each layer of the transformation one of
+them is noise and one of them is
+
+ align:start position:0%
+them is noise and one of them is
+ 
+
+ align:start position:0%
+them is noise and one of them is
+correlation so what is what is noise so
+
+ align:start position:0%
+correlation so what is what is noise so
+ 
+
+ align:start position:0%
+correlation so what is what is noise so
+again noise will be simply the the
+
+ align:start position:0%
+again noise will be simply the the
+ 
+
+ align:start position:0%
+again noise will be simply the the
+radius or measure of the radius of this
+
+ align:start position:0%
+radius or measure of the radius of this
+ 
+
+ align:start position:0%
+radius or measure of the radius of this
+of this field so if you had only the
+
+ align:start position:0%
+of this field so if you had only the
+ 
+
+ align:start position:0%
+of this field so if you had only the
+templates as input the problem would be
+
+ align:start position:0%
+templates as input the problem would be
+ 
+
+ align:start position:0%
+templates as input the problem would be
+simple problem would be easy as long as
+
+ align:start position:0%
+simple problem would be easy as long as
+ 
+
+ align:start position:0%
+simple problem would be easy as long as
+we have enough dimension you expand it
+
+ align:start position:0%
+we have enough dimension you expand it
+ 
+
+ align:start position:0%
+we have enough dimension you expand it
+you can easily do linear classifier and
+
+ align:start position:0%
+you can easily do linear classifier and
+ 
+
+ align:start position:0%
+you can easily do linear classifier and
+an end and solve the problem so the
+
+ align:start position:0%
+an end and solve the problem so the
+ 
+
+ align:start position:0%
+an end and solve the problem so the
+problem in our case is the fact that the
+
+ align:start position:0%
+problem in our case is the fact that the
+ 
+
+ align:start position:0%
+problem in our case is the fact that the
+input is actually the infinite number of
+
+ align:start position:0%
+input is actually the infinite number of
+ 
+
+ align:start position:0%
+input is actually the infinite number of
+inputs or exponentially large number of
+
+ align:start position:0%
+inputs or exponentially large number of
+ 
+
+ align:start position:0%
+inputs or exponentially large number of
+possible inputs because they all come
+
+ align:start position:0%
+possible inputs because they all come
+ 
+
+ align:start position:0%
+possible inputs because they all come
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+from from Gaussian or binarized version
+
+ align:start position:0%
+from from Gaussian or binarized version
+ 
+
+ align:start position:0%
+from from Gaussian or binarized version
+of a Gaussian noise around the templates
+
+ align:start position:0%
+of a Gaussian noise around the templates
+ 
+
+ align:start position:0%
+of a Gaussian noise around the templates
+and at the node the noise by Delta zero
+
+ align:start position:0%
+and at the node the noise by Delta zero
+ 
+
+ align:start position:0%
+and at the node the noise by Delta zero
+means no noise one the normalization is
+
+ align:start position:0%
+means no noise one the normalization is
+ 
+
+ align:start position:0%
+means no noise one the normalization is
+such that one means that they are random
+
+ align:start position:0%
+such that one means that they are random
+ 
+
+ align:start position:0%
+such that one means that they are random
+so Delta equals to one means that
+
+ align:start position:0%
+so Delta equals to one means that
+ 
+
+ align:start position:0%
+so Delta equals to one means that
+basically you cannot tell of the input
+
+ align:start position:0%
+basically you cannot tell of the input
+ 
+
+ align:start position:0%
+basically you cannot tell of the input
+whether it's coming from here or from
+
+ align:start position:0%
+whether it's coming from here or from
+ 
+
+ align:start position:0%
+whether it's coming from here or from
+any other points in the input space the
+
+ align:start position:0%
+any other points in the input space the
+ 
+
+ align:start position:0%
+any other points in the input space the
+other thing is correlations is more
+
+ align:start position:0%
+other thing is correlations is more
+ 
+
+ align:start position:0%
+other thing is correlations is more
+subtle so I'm going to assume that those
+
+ align:start position:0%
+subtle so I'm going to assume that those
+ 
+
+ align:start position:0%
+subtle so I'm going to assume that those
+those balls are coming from kind of
+
+ align:start position:0%
+those balls are coming from kind of
+ 
+
+ align:start position:0%
+those balls are coming from kind of
+uniform distribution imagine you take a
+
+ align:start position:0%
+uniform distribution imagine you take a
+ 
+
+ align:start position:0%
+uniform distribution imagine you take a
+template here you draw a ball around it
+
+ align:start position:0%
+template here you draw a ball around it
+ 
+
+ align:start position:0%
+template here you draw a ball around it
+take a template to draw but everything
+
+ align:start position:0%
+take a template to draw but everything
+ 
+
+ align:start position:0%
+take a template to draw but everything
+is kind of uniform distribution you
+
+ align:start position:0%
+is kind of uniform distribution you
+ 
+
+ align:start position:0%
+is kind of uniform distribution you
+distributed the only structure is the
+
+ align:start position:0%
+distributed the only structure is the
+ 
+
+ align:start position:0%
+distributed the only structure is the
+fact that data comes from this mixture
+
+ align:start position:0%
+fact that data comes from this mixture
+ 
+
+ align:start position:0%
+fact that data comes from this mixture
+of gaussians or noisy patterns around or
+
+ align:start position:0%
+of gaussians or noisy patterns around or
+ 
+
+ align:start position:0%
+of gaussians or noisy patterns around or
+centers okay so that's fine but as you
+
+ align:start position:0%
+centers okay so that's fine but as you
+ 
+
+ align:start position:0%
+centers okay so that's fine but as you
+project project this project those those
+
+ align:start position:0%
+project project this project those those
+ 
+
+ align:start position:0%
+project project this project those those
+clusters into the next stage I claim
+
+ align:start position:0%
+clusters into the next stage I claim
+ 
+
+ align:start position:0%
+clusters into the next stage I claim
+that those centers those templates get
+
+ align:start position:0%
+that those centers those templates get
+ 
+
+ align:start position:0%
+that those centers those templates get
+new representation which can actually
+
+ align:start position:0%
+new representation which can actually
+ 
+
+ align:start position:0%
+new representation which can actually
+have structure in them simply by the
+
+ align:start position:0%
+have structure in them simply by the
+ 
+
+ align:start position:0%
+have structure in them simply by the
+fact that you you you put all of them
+
+ align:start position:0%
+fact that you you you put all of them
+ 
+
+ align:start position:0%
+fact that you you you put all of them
+into this common synaptic weights into
+
+ align:start position:0%
+into this common synaptic weights into
+ 
+
+ align:start position:0%
+into this common synaptic weights into
+the next layer and I'm going to measure
+
+ align:start position:0%
+the next layer and I'm going to measure
+ 
+
+ align:start position:0%
+the next layer and I'm going to measure
+this by hue and basically long q0q is
+
+ align:start position:0%
+this by hue and basically long q0q is
+ 
+
+ align:start position:0%
+this by hue and basically long q0q is
+basically a kind of randomly uniformly
+
+ align:start position:0%
+basically a kind of randomly uniformly
+ 
+
+ align:start position:0%
+basically a kind of randomly uniformly
+distributed centers and I'll always
+
+ align:start position:0%
+distributed centers and I'll always
+ 
+
+ align:start position:0%
+distributed centers and I'll always
+start from that at the input layer but
+
+ align:start position:0%
+start from that at the input layer but
+ 
+
+ align:start position:0%
+start from that at the input layer but
+then there is a danger or it might
+
+ align:start position:0%
+then there is a danger or it might
+ 
+
+ align:start position:0%
+then there is a danger or it might
+happen that as you propagate this
+
+ align:start position:0%
+happen that as you propagate this
+ 
+
+ align:start position:0%
+happen that as you propagate this
+information or this representation to
+
+ align:start position:0%
+information or this representation to
+ 
+
+ align:start position:0%
+information or this representation to
+the next layer the centers will look
+
+ align:start position:0%
+the next layer the centers will look
+ 
+
+ align:start position:0%
+the next layer the centers will look
+like that or older than the data
+
+ align:start position:0%
+like that or older than the data
+ 
+
+ align:start position:0%
+like that or older than the data
+structure data look like that so on
+
+ align:start position:0%
+structure data look like that so on
+ 
+
+ align:start position:0%
+structure data look like that so on
+average you know the distance between
+
+ align:start position:0%
+average you know the distance between
+ 
+
+ align:start position:0%
+average you know the distance between
+two centers on average is the same as
+
+ align:start position:0%
+two centers on average is the same as
+ 
+
+ align:start position:0%
+two centers on average is the same as
+here but they are clumped together it's
+
+ align:start position:0%
+here but they are clumped together it's
+ 
+
+ align:start position:0%
+here but they are clumped together it's
+kind of random clustering of the
+
+ align:start position:0%
+kind of random clustering of the
+ 
+
+ align:start position:0%
+kind of random clustering of the
+clusters and that's
+
+ align:start position:0%
+clusters and that's
+ 
+
+ align:start position:0%
+clusters and that's
+can be induced by the fact that the data
+
+ align:start position:0%
+can be induced by the fact that the data
+ 
+
+ align:start position:0%
+can be induced by the fact that the data
+is feed-forward from and from from this
+
+ align:start position:0%
+is feed-forward from and from from this
+ 
+
+ align:start position:0%
+is feed-forward from and from from this
+representation that can pose a problem
+
+ align:start position:0%
+representation that can pose a problem
+ 
+
+ align:start position:0%
+representation that can pose a problem
+if there is no no is then there is again
+
+ align:start position:0%
+if there is no no is then there is again
+ 
+
+ align:start position:0%
+if there is no no is then there is again
+no no problem you can you can
+
+ align:start position:0%
+no no problem you can you can
+ 
+
+ align:start position:0%
+no no problem you can you can
+differentiate between and so on but if
+
+ align:start position:0%
+differentiate between and so on but if
+ 
+
+ align:start position:0%
+differentiate between and so on but if
+there is noise this can aggravate the
+
+ align:start position:0%
+there is noise this can aggravate the
+ 
+
+ align:start position:0%
+there is noise this can aggravate the
+situation because some of the clusters
+
+ align:start position:0%
+situation because some of the clusters
+ 
+
+ align:start position:0%
+situation because some of the clusters
+become may become dangerously close to
+
+ align:start position:0%
+become may become dangerously close to
+ 
+
+ align:start position:0%
+become may become dangerously close to
+each other and will come to it but
+
+ align:start position:0%
+each other and will come to it but
+ 
+
+ align:start position:0%
+each other and will come to it but
+anyway so we have this Delta the noise
+
+ align:start position:0%
+anyway so we have this Delta the noise
+ 
+
+ align:start position:0%
+anyway so we have this Delta the noise
+the size of the of the clusters and we
+
+ align:start position:0%
+the size of the of the clusters and we
+ 
+
+ align:start position:0%
+the size of the of the clusters and we
+have queued the correlations how they
+
+ align:start position:0%
+have queued the correlations how they
+ 
+
+ align:start position:0%
+have queued the correlations how they
+are clumped into in each representation
+
+ align:start position:0%
+are clumped into in each representation
+ 
+
+ align:start position:0%
+are clumped into in each representation
+and now we can ask how Delta evolved
+
+ align:start position:0%
+and now we can ask how Delta evolved
+ 
+
+ align:start position:0%
+and now we can ask how Delta evolved
+when you go from one representation to
+
+ align:start position:0%
+when you go from one representation to
+ 
+
+ align:start position:0%
+when you go from one representation to
+another how you evolve from one
+
+ align:start position:0%
+another how you evolve from one
+ 
+
+ align:start position:0%
+another how you evolve from one
+representation to another and how linear
+
+ align:start position:0%
+representation to another and how linear
+ 
+
+ align:start position:0%
+representation to another and how linear
+classifier performance will change from
+
+ align:start position:0%
+classifier performance will change from
+ 
+
+ align:start position:0%
+classifier performance will change from
+one representation to another so the
+
+ align:start position:0%
+one representation to another so the
+ 
+
+ align:start position:0%
+one representation to another so the
+simplicity of this of this assumption is
+
+ align:start position:0%
+simplicity of this of this assumption is
+ 
+
+ align:start position:0%
+simplicity of this of this assumption is
+allows for allows for kind of a
+
+ align:start position:0%
+allows for allows for kind of a
+ 
+
+ align:start position:0%
+allows for allows for kind of a
+systematic analytical exploration or
+
+ align:start position:0%
+systematic analytical exploration or
+ 
+
+ align:start position:0%
+systematic analytical exploration or
+study of these ok so ok these are
+
+ align:start position:0%
+study of these ok so ok these are
+ 
+
+ align:start position:0%
+study of these ok so ok these are
+definitions let's go ok so what will be
+
+ align:start position:0%
+definitions let's go ok so what will be
+ 
+
+ align:start position:0%
+definitions let's go ok so what will be
+the ideal situation that this situation
+
+ align:start position:0%
+the ideal situation that this situation
+ 
+
+ align:start position:0%
+the ideal situation that this situation
+would be ok so the ideal situation will
+
+ align:start position:0%
+would be ok so the ideal situation will
+ 
+
+ align:start position:0%
+would be ok so the ideal situation will
+be that I start from some level of noise
+
+ align:start position:0%
+be that I start from some level of noise
+ 
+
+ align:start position:0%
+be that I start from some level of noise
+which is the my Gauss my-my-my-my
+
+ align:start position:0%
+which is the my Gauss my-my-my-my
+ 
+
+ align:start position:0%
+which is the my Gauss my-my-my-my
+spheres at the input layer I may or may
+
+ align:start position:0%
+spheres at the input layer I may or may
+ 
+
+ align:start position:0%
+spheres at the input layer I may or may
+not start from with some correlation the
+
+ align:start position:0%
+not start from with some correlation the
+ 
+
+ align:start position:0%
+not start from with some correlation the
+simplest case would be that I start from
+
+ align:start position:0%
+simplest case would be that I start from
+ 
+
+ align:start position:0%
+simplest case would be that I start from
+randomly distributed center so this
+
+ align:start position:0%
+randomly distributed center so this
+ 
+
+ align:start position:0%
+randomly distributed center so this
+would be zero and the best situation
+
+ align:start position:0%
+would be zero and the best situation
+ 
+
+ align:start position:0%
+would be zero and the best situation
+will be that as I Papa gate the sensory
+
+ align:start position:0%
+will be that as I Papa gate the sensory
+ 
+
+ align:start position:0%
+will be that as I Papa gate the sensory
+stimuli Delta the noise will go to zero
+
+ align:start position:0%
+stimuli Delta the noise will go to zero
+ 
+
+ align:start position:0%
+stimuli Delta the noise will go to zero
+okay as I said if the noise goes to zero
+
+ align:start position:0%
+okay as I said if the noise goes to zero
+ 
+
+ align:start position:0%
+okay as I said if the noise goes to zero
+you are left with basically points and
+
+ align:start position:0%
+you are left with basically points and
+ 
+
+ align:start position:0%
+you are left with basically points and
+those points if there is enough
+
+ align:start position:0%
+those points if there is enough
+ 
+
+ align:start position:0%
+those points if there is enough
+dimensionality those points would be
+
+ align:start position:0%
+dimensionality those points would be
+ 
+
+ align:start position:0%
+dimensionality those points would be
+easily classifiable it also be good
+
+ align:start position:0%
+easily classifiable it also be good
+ 
+
+ align:start position:0%
+easily classifiable it also be good
+since if the noise doesn't go to zero to
+
+ align:start position:0%
+since if the noise doesn't go to zero to
+ 
+
+ align:start position:0%
+since if the noise doesn't go to zero to
+have also kind of uniformly spread
+
+ align:start position:0%
+have also kind of uniformly spread
+ 
+
+ align:start position:0%
+have also kind of uniformly spread
+clusters so it will be good to keep Q to
+
+ align:start position:0%
+clusters so it will be good to keep Q to
+ 
+
+ align:start position:0%
+clusters so it will be good to keep Q to
+be small
+
+ align:start position:0%
+be small
+ 
+
+ align:start position:0%
+be small
+okay okay so let's look at one layer so
+
+ align:start position:0%
+okay okay so let's look at one layer so
+ 
+
+ align:start position:0%
+okay okay so let's look at one layer so
+let's look at just we have the input
+
+ align:start position:0%
+let's look at just we have the input
+ 
+
+ align:start position:0%
+let's look at just we have the input
+layer the output layer here and and the
+
+ align:start position:0%
+layer the output layer here and and the
+ 
+
+ align:start position:0%
+layer the output layer here and and the
+readout the first question is what to
+
+ align:start position:0%
+readout the first question is what to
+ 
+
+ align:start position:0%
+readout the first question is what to
+choose for this input layer so the
+
+ align:start position:0%
+choose for this input layer so the
+ 
+
+ align:start position:0%
+choose for this input layer so the
+simplest answer would be choose random
+
+ align:start position:0%
+simplest answer would be choose random
+ 
+
+ align:start position:0%
+simplest answer would be choose random
+okay so what we do is just take Gaussian
+
+ align:start position:0%
+okay so what we do is just take Gaussian
+ 
+
+ align:start position:0%
+okay so what we do is just take Gaussian
+we just IID Gaussian weights in this
+
+ align:start position:0%
+we just IID Gaussian weights in this
+ 
+
+ align:start position:0%
+we just IID Gaussian weights in this
+layer a very simple with zero mean some
+
+ align:start position:0%
+layer a very simple with zero mean some
+ 
+
+ align:start position:0%
+layer a very simple with zero mean some
+normalization doesn't matter then we
+
+ align:start position:0%
+normalization doesn't matter then we
+ 
+
+ align:start position:0%
+normalization doesn't matter then we
+project them into each one of these guys
+
+ align:start position:0%
+project them into each one of these guys
+ 
+
+ align:start position:0%
+project them into each one of these guys
+here and then we add threshold to
+
+ align:start position:0%
+here and then we add threshold to
+ 
+
+ align:start position:0%
+here and then we add threshold to
+enforce the sparsity that that we that
+
+ align:start position:0%
+enforce the sparsity that that we that
+ 
+
+ align:start position:0%
+enforce the sparsity that that we that
+we want okay so whatever the the
+
+ align:start position:0%
+we want okay so whatever the the
+ 
+
+ align:start position:0%
+we want okay so whatever the the
+activation here is whatever the input is
+
+ align:start position:0%
+activation here is whatever the input is
+ 
+
+ align:start position:0%
+activation here is whatever the input is
+here here is the threshold make sure
+
+ align:start position:0%
+here here is the threshold make sure
+ 
+
+ align:start position:0%
+here here is the threshold make sure
+that only the F the with the largest
+
+ align:start position:0%
+that only the F the with the largest
+ 
+
+ align:start position:0%
+that only the F the with the largest
+input will be active and the rest will
+
+ align:start position:0%
+input will be active and the rest will
+ 
+
+ align:start position:0%
+input will be active and the rest will
+be zero so there is a non-linearity
+
+ align:start position:0%
+be zero so there is a non-linearity
+ 
+
+ align:start position:0%
+be zero so there is a non-linearity
+which is the first extremely important
+
+ align:start position:0%
+which is the first extremely important
+ 
+
+ align:start position:0%
+which is the first extremely important
+if you map one layer to another with a
+
+ align:start position:0%
+if you map one layer to another with a
+ 
+
+ align:start position:0%
+if you map one layer to another with a
+linear a linear transformation you don't
+
+ align:start position:0%
+linear a linear transformation you don't
+ 
+
+ align:start position:0%
+linear a linear transformation you don't
+you don't gain anything in terms of
+
+ align:start position:0%
+you don't gain anything in terms of
+ 
+
+ align:start position:0%
+you don't gain anything in terms of
+classification so there is a
+
+ align:start position:0%
+classification so there is a
+ 
+
+ align:start position:0%
+classification so there is a
+non-linearity simply threshold
+
+ align:start position:0%
+non-linearity simply threshold
+ 
+
+ align:start position:0%
+non-linearity simply threshold
+non-linearity after an input input
+
+ align:start position:0%
+non-linearity after an input input
+ 
+
+ align:start position:0%
+non-linearity after an input input
+projection all right so how we're going
+
+ align:start position:0%
+projection all right so how we're going
+ 
+
+ align:start position:0%
+projection all right so how we're going
+to do this so so it's straightforward to
+
+ align:start position:0%
+to do this so so it's straightforward to
+ 
+
+ align:start position:0%
+to do this so so it's straightforward to
+actually compute analytically what will
+
+ align:start position:0%
+actually compute analytically what will
+ 
+
+ align:start position:0%
+actually compute analytically what will
+happen to a noise so imagine you take
+
+ align:start position:0%
+happen to a noise so imagine you take
+ 
+
+ align:start position:0%
+happen to a noise so imagine you take
+two input vectors with some hanging
+
+ align:start position:0%
+two input vectors with some hanging
+ 
+
+ align:start position:0%
+two input vectors with some hanging
+distance apart from each other you map
+
+ align:start position:0%
+distance apart from each other you map
+ 
+
+ align:start position:0%
+distance apart from each other you map
+them into by by by by convolving them
+
+ align:start position:0%
+them into by by by by convolving them
+ 
+
+ align:start position:0%
+them into by by by by convolving them
+Toto speak with with with the Gaussian
+
+ align:start position:0%
+Toto speak with with with the Gaussian
+ 
+
+ align:start position:0%
+Toto speak with with with the Gaussian
+weight and then threshold in them to get
+
+ align:start position:0%
+weight and then threshold in them to get
+ 
+
+ align:start position:0%
+weight and then threshold in them to get
+some sparsity so every the sparsity the
+
+ align:start position:0%
+some sparsity so every the sparsity the
+ 
+
+ align:start position:0%
+some sparsity so every the sparsity the
+smaller the f is that the sparse on it
+
+ align:start position:0%
+smaller the f is that the sparse on it
+ 
+
+ align:start position:0%
+smaller the f is that the sparse on it
+is so this is the noise level the gun or
+
+ align:start position:0%
+is so this is the noise level the gun or
+ 
+
+ align:start position:0%
+is so this is the noise level the gun or
+malaises Gaussian I'm sorry reduce or
+
+ align:start position:0%
+malaises Gaussian I'm sorry reduce or
+ 
+
+ align:start position:0%
+malaises Gaussian I'm sorry reduce or
+Hamming distance in the in the output
+
+ align:start position:0%
+Hamming distance in the in the output
+ 
+
+ align:start position:0%
+Hamming distance in the in the output
+layer versus the input layer well if
+
+ align:start position:0%
+layer versus the input layer well if
+ 
+
+ align:start position:0%
+layer versus the input layer well if
+zero start then of course you started
+
+ align:start position:0%
+zero start then of course you started
+ 
+
+ align:start position:0%
+zero start then of course you started
+the origin if you are random in the
+
+ align:start position:0%
+the origin if you are random in the
+ 
+
+ align:start position:0%
+the origin if you are random in the
+input will be random there so these
+
+ align:start position:0%
+input will be random there so these
+ 
+
+ align:start position:0%
+input will be random there so these
+points are fine but as you see
+
+ align:start position:0%
+points are fine but as you see
+ 
+
+ align:start position:0%
+points are fine but as you see
+immediately there is an amplification of
+
+ align:start position:0%
+immediately there is an amplification of
+ 
+
+ align:start position:0%
+immediately there is an amplification of
+the noise as you go from from the input
+
+ align:start position:0%
+the noise as you go from from the input
+ 
+
+ align:start position:0%
+the noise as you go from from the input
+to the output right so you start from
+
+ align:start position:0%
+to the output right so you start from
+ 
+
+ align:start position:0%
+to the output right so you start from
+point two but you get actually after one
+
+ align:start position:0%
+point two but you get actually after one
+ 
+
+ align:start position:0%
+point two but you get actually after one
+layer two point six okay and actually
+
+ align:start position:0%
+layer two point six okay and actually
+ 
+
+ align:start position:0%
+layer two point six okay and actually
+for loss for the span silk is so this is
+
+ align:start position:0%
+for loss for the span silk is so this is
+ 
+
+ align:start position:0%
+for loss for the span silk is so this is
+a relatively high sparsity or at least
+
+ align:start position:0%
+a relatively high sparsity or at least
+ 
+
+ align:start position:0%
+a relatively high sparsity or at least
+you go from here to here by increasing
+
+ align:start position:0%
+you go from here to here by increasing
+ 
+
+ align:start position:0%
+you go from here to here by increasing
+sparsity namely f becomes smaller and as
+
+ align:start position:0%
+sparsity namely f becomes smaller and as
+ 
+
+ align:start position:0%
+sparsity namely f becomes smaller and as
+have become smaller this curve is
+
+ align:start position:0%
+have become smaller this curve is
+ 
+
+ align:start position:0%
+have become smaller this curve is
+actually steeper and steeper so not only
+
+ align:start position:0%
+actually steeper and steeper so not only
+ 
+
+ align:start position:0%
+actually steeper and steeper so not only
+you amplify noise but you also the
+
+ align:start position:0%
+you amplify noise but you also the
+ 
+
+ align:start position:0%
+you amplify noise but you also the
+amplification becomes worse thus parcel
+
+ align:start position:0%
+amplification becomes worse thus parcel
+ 
+
+ align:start position:0%
+amplification becomes worse thus parcel
+the representation is so that is the
+
+ align:start position:0%
+the representation is so that is the
+ 
+
+ align:start position:0%
+the representation is so that is the
+kind of negative result the idea that
+
+ align:start position:0%
+kind of negative result the idea that
+ 
+
+ align:start position:0%
+kind of negative result the idea that
+you can gain by expanding data to a
+
+ align:start position:0%
+you can gain by expanding data to a
+ 
+
+ align:start position:0%
+you can gain by expanding data to a
+higher dimension and make them more
+
+ align:start position:0%
+higher dimension and make them more
+ 
+
+ align:start position:0%
+higher dimension and make them more
+separable later on it dates back to
+
+ align:start position:0%
+separable later on it dates back to
+ 
+
+ align:start position:0%
+separable later on it dates back to
+David Mouse classical theory of the
+
+ align:start position:0%
+David Mouse classical theory of the
+ 
+
+ align:start position:0%
+David Mouse classical theory of the
+cerebellum but what we show here is that
+
+ align:start position:0%
+cerebellum but what we show here is that
+ 
+
+ align:start position:0%
+cerebellum but what we show here is that
+if you think not about clean data set of
+
+ align:start position:0%
+if you think not about clean data set of
+ 
+
+ align:start position:0%
+if you think not about clean data set of
+point that you want to separate but you
+
+ align:start position:0%
+point that you want to separate but you
+ 
+
+ align:start position:0%
+point that you want to separate but you
+think about the more realistic case of
+
+ align:start position:0%
+think about the more realistic case of
+ 
+
+ align:start position:0%
+think about the more realistic case of
+you have noisy data or data with high
+
+ align:start position:0%
+you have noisy data or data with high
+ 
+
+ align:start position:0%
+you have noisy data or data with high
+variance then then the situation is very
+
+ align:start position:0%
+variance then then the situation is very
+ 
+
+ align:start position:0%
+variance then then the situation is very
+different so a random expansion is
+
+ align:start position:0%
+different so a random expansion is
+ 
+
+ align:start position:0%
+different so a random expansion is
+actually amplify snows and that's that's
+
+ align:start position:0%
+actually amplify snows and that's that's
+ 
+
+ align:start position:0%
+actually amplify snows and that's that's
+a theme that will actually we will live
+
+ align:start position:0%
+a theme that will actually we will live
+ 
+
+ align:start position:0%
+a theme that will actually we will live
+with it as we go along
+
+ align:start position:0%
+with it as we go along
+ 
+
+ align:start position:0%
+with it as we go along
+random expansion is doing the separation
+
+ align:start position:0%
+random expansion is doing the separation
+ 
+
+ align:start position:0%
+random expansion is doing the separation
+of the of the templates but the problem
+
+ align:start position:0%
+of the of the templates but the problem
+ 
+
+ align:start position:0%
+of the of the templates but the problem
+is it also separates two nearby points
+
+ align:start position:0%
+is it also separates two nearby points
+ 
+
+ align:start position:0%
+is it also separates two nearby points
+within a cluster it also separates them
+
+ align:start position:0%
+within a cluster it also separates them
+ 
+
+ align:start position:0%
+within a cluster it also separates them
+so everything becomes separated from
+
+ align:start position:0%
+so everything becomes separated from
+ 
+
+ align:start position:0%
+so everything becomes separated from
+each other and this is why noise is is
+
+ align:start position:0%
+each other and this is why noise is is
+ 
+
+ align:start position:0%
+each other and this is why noise is is
+amplified now what about the most subtle
+
+ align:start position:0%
+amplified now what about the most subtle
+ 
+
+ align:start position:0%
+amplified now what about the most subtle
+thing which is the kind of overlap
+
+ align:start position:0%
+thing which is the kind of overlap
+ 
+
+ align:start position:0%
+thing which is the kind of overlap
+between the center's so on average the
+
+ align:start position:0%
+between the center's so on average the
+ 
+
+ align:start position:0%
+between the center's so on average the
+center's are as far as part as random
+
+ align:start position:0%
+center's are as far as part as random
+ 
+
+ align:start position:0%
+center's are as far as part as random
+things but if you look not on
+
+ align:start position:0%
+things but if you look not on
+ 
+
+ align:start position:0%
+things but if you look not on
+but you look at the individual pairs you
+
+ align:start position:0%
+but you look at the individual pairs you
+ 
+
+ align:start position:0%
+but you look at the individual pairs you
+see that there is an excess correlation
+
+ align:start position:0%
+see that there is an excess correlation
+ 
+
+ align:start position:0%
+see that there is an excess correlation
+so overlap between them so this is
+
+ align:start position:0%
+so overlap between them so this is
+ 
+
+ align:start position:0%
+so overlap between them so this is
+overlap between the Centers again on
+
+ align:start position:0%
+overlap between the Centers again on
+ 
+
+ align:start position:0%
+overlap between the Centers again on
+average it is zero but the violence is
+
+ align:start position:0%
+average it is zero but the violence is
+ 
+
+ align:start position:0%
+average it is zero but the violence is
+not zero on average it's like random but
+
+ align:start position:0%
+not zero on average it's like random but
+ 
+
+ align:start position:0%
+not zero on average it's like random but
+the valence is different is larger than
+
+ align:start position:0%
+the valence is different is larger than
+ 
+
+ align:start position:0%
+the valence is different is larger than
+range or than random and there is a
+
+ align:start position:0%
+range or than random and there is a
+ 
+
+ align:start position:0%
+range or than random and there is a
+there is an amplification there is a
+
+ align:start position:0%
+there is an amplification there is a
+ 
+
+ align:start position:0%
+there is an amplification there is a
+generation of the of the of the success
+
+ align:start position:0%
+generation of the of the of the success
+ 
+
+ align:start position:0%
+generation of the of the of the success
+overlap although it's it's nicely
+
+ align:start position:0%
+overlap although it's it's nicely
+ 
+
+ align:start position:0%
+overlap although it's it's nicely
+controlled by sparsity so as positive
+
+ align:start position:0%
+controlled by sparsity so as positive
+ 
+
+ align:start position:0%
+controlled by sparsity so as positive
+goes down the dis correlations go down
+
+ align:start position:0%
+goes down the dis correlations go down
+ 
+
+ align:start position:0%
+goes down the dis correlations go down
+okay so that's that's that's not a
+
+ align:start position:0%
+okay so that's that's that's not a
+ 
+
+ align:start position:0%
+okay so that's that's that's not a
+tremendous problem the major problem as
+
+ align:start position:0%
+tremendous problem the major problem as
+ 
+
+ align:start position:0%
+tremendous problem the major problem as
+I said is the noise okay by the way you
+
+ align:start position:0%
+I said is the noise okay by the way you
+ 
+
+ align:start position:0%
+I said is the noise okay by the way you
+can you can you can nicely do an
+
+ align:start position:0%
+can you can you can nicely do an
+ 
+
+ align:start position:0%
+can you can you can nicely do an
+exercise where you generate you look at
+
+ align:start position:0%
+exercise where you generate you look at
+ 
+
+ align:start position:0%
+exercise where you generate you look at
+the this cortical layer representation
+
+ align:start position:0%
+the this cortical layer representation
+ 
+
+ align:start position:0%
+the this cortical layer representation
+and you do as BM or PCA you look at the
+
+ align:start position:0%
+and you do as BM or PCA you look at the
+ 
+
+ align:start position:0%
+and you do as BM or PCA you look at the
+eigen value spectrum so if you if you
+
+ align:start position:0%
+eigen value spectrum so if you if you
+ 
+
+ align:start position:0%
+eigen value spectrum so if you if you
+just look at random spouse points and
+
+ align:start position:0%
+just look at random spouse points and
+ 
+
+ align:start position:0%
+just look at random spouse points and
+you look at the SVD this is the angle
+
+ align:start position:0%
+you look at the SVD this is the angle
+ 
+
+ align:start position:0%
+you look at the SVD this is the angle
+values and number rank rank then that's
+
+ align:start position:0%
+values and number rank rank then that's
+ 
+
+ align:start position:0%
+values and number rank rank then that's
+what you find is the famous mung mung
+
+ align:start position:0%
+what you find is the famous mung mung
+ 
+
+ align:start position:0%
+what you find is the famous mung mung
+gain so a store distribution but in our
+
+ align:start position:0%
+gain so a store distribution but in our
+ 
+
+ align:start position:0%
+gain so a store distribution but in our
+case you see there is an external power
+
+ align:start position:0%
+case you see there is an external power
+ 
+
+ align:start position:0%
+case you see there is an external power
+in this case the input layer is hundred
+
+ align:start position:0%
+in this case the input layer is hundred
+ 
+
+ align:start position:0%
+in this case the input layer is hundred
+so the extra power in the input layer in
+
+ align:start position:0%
+so the extra power in the input layer in
+ 
+
+ align:start position:0%
+so the extra power in the input layer in
+the first input eigenvalue now why is it
+
+ align:start position:0%
+the first input eigenvalue now why is it
+ 
+
+ align:start position:0%
+the first input eigenvalue now why is it
+so so so the the what Hugh is telling us
+
+ align:start position:0%
+so so so the the what Hugh is telling us
+ 
+
+ align:start position:0%
+so so so the the what Hugh is telling us
+what Nancy okay telling us is the
+
+ align:start position:0%
+what Nancy okay telling us is the
+ 
+
+ align:start position:0%
+what Nancy okay telling us is the
+following you take random set of you
+
+ align:start position:0%
+following you take random set of you
+ 
+
+ align:start position:0%
+following you take random set of you
+take a set of random points and you
+
+ align:start position:0%
+take a set of random points and you
+ 
+
+ align:start position:0%
+take a set of random points and you
+project them into higher dimension the
+
+ align:start position:0%
+project them into higher dimension the
+ 
+
+ align:start position:0%
+project them into higher dimension the
+start with hundred dimension and you
+
+ align:start position:0%
+start with hundred dimension and you
+ 
+
+ align:start position:0%
+start with hundred dimension and you
+project and in a thousand dimension on
+
+ align:start position:0%
+project and in a thousand dimension on
+ 
+
+ align:start position:0%
+project and in a thousand dimension on
+average they're random but actually so
+
+ align:start position:0%
+average they're random but actually so
+ 
+
+ align:start position:0%
+average they're random but actually so
+you you would imagine that that that
+
+ align:start position:0%
+you you would imagine that that that
+ 
+
+ align:start position:0%
+you you would imagine that that that
+it's a perfect thing you project them
+
+ align:start position:0%
+it's a perfect thing you project them
+ 
+
+ align:start position:0%
+it's a perfect thing you project them
+with random weights then you'll be
+
+ align:start position:0%
+with random weights then you'll be
+ 
+
+ align:start position:0%
+with random weights then you'll be
+imagine that you just created a set of
+
+ align:start position:0%
+imagine that you just created a set of
+ 
+
+ align:start position:0%
+imagine that you just created a set of
+random points in the expanded
+
+ align:start position:0%
+random points in the expanded
+ 
+
+ align:start position:0%
+random points in the expanded
+mention representation if this was so
+
+ align:start position:0%
+mention representation if this was so
+ 
+
+ align:start position:0%
+mention representation if this was so
+then if you do SVM or PCA on dit on this
+
+ align:start position:0%
+then if you do SVM or PCA on dit on this
+ 
+
+ align:start position:0%
+then if you do SVM or PCA on dit on this
+representation you will find what you
+
+ align:start position:0%
+representation you will find what you
+ 
+
+ align:start position:0%
+representation you will find what you
+expect from PCA of a set of random
+
+ align:start position:0%
+expect from PCA of a set of random
+ 
+
+ align:start position:0%
+expect from PCA of a set of random
+points and this is this one in fact
+
+ align:start position:0%
+points and this is this one in fact
+ 
+
+ align:start position:0%
+points and this is this one in fact
+there is a trace of low dimensionality
+
+ align:start position:0%
+there is a trace of low dimensionality
+ 
+
+ align:start position:0%
+there is a trace of low dimensionality
+in the data okay so so I think that's an
+
+ align:start position:0%
+in the data okay so so I think that's an
+ 
+
+ align:start position:0%
+in the data okay so so I think that's an
+important point which I would like to
+
+ align:start position:0%
+important point which I would like to
+ 
+
+ align:start position:0%
+important point which I would like to
+explain you start from a set of points
+
+ align:start position:0%
+explain you start from a set of points
+ 
+
+ align:start position:0%
+explain you start from a set of points
+if you don't threshold them and you just
+
+ align:start position:0%
+if you don't threshold them and you just
+ 
+
+ align:start position:0%
+if you don't threshold them and you just
+map them into one thousand dimensional
+
+ align:start position:0%
+map them into one thousand dimensional
+ 
+
+ align:start position:0%
+map them into one thousand dimensional
+space those hundred dimensional input
+
+ align:start position:0%
+space those hundred dimensional input
+ 
+
+ align:start position:0%
+space those hundred dimensional input
+will remain higher than 100 dimensional
+
+ align:start position:0%
+will remain higher than 100 dimensional
+ 
+
+ align:start position:0%
+will remain higher than 100 dimensional
+just before ten ten and so on but
+
+ align:start position:0%
+just before ten ten and so on but
+ 
+
+ align:start position:0%
+just before ten ten and so on but
+everything will live in in Han hundred
+
+ align:start position:0%
+everything will live in in Han hundred
+ 
+
+ align:start position:0%
+everything will live in in Han hundred
+dimensional space now you add threshold
+
+ align:start position:0%
+dimensional space now you add threshold
+ 
+
+ align:start position:0%
+dimensional space now you add threshold
+a high threshold being by sparsity so
+
+ align:start position:0%
+a high threshold being by sparsity so
+ 
+
+ align:start position:0%
+a high threshold being by sparsity so
+those 100 dimensional subspace becomes
+
+ align:start position:0%
+those 100 dimensional subspace becomes
+ 
+
+ align:start position:0%
+those 100 dimensional subspace becomes
+now thousand dimensional space because
+
+ align:start position:0%
+now thousand dimensional space because
+ 
+
+ align:start position:0%
+now thousand dimensional space because
+of the non-linearity but but this
+
+ align:start position:0%
+of the non-linearity but but this
+ 
+
+ align:start position:0%
+of the non-linearity but but this
+non-linearity although it takes on the
+
+ align:start position:0%
+non-linearity although it takes on the
+ 
+
+ align:start position:0%
+non-linearity although it takes on the
+dimensional input and makes them
+
+ align:start position:0%
+dimensional input and makes them
+ 
+
+ align:start position:0%
+dimensional input and makes them
+thousand dimensional it's still not like
+
+ align:start position:0%
+thousand dimensional it's still not like
+ 
+
+ align:start position:0%
+thousand dimensional it's still not like
+a random there is still this thousand
+
+ align:start position:0%
+a random there is still this thousand
+ 
+
+ align:start position:0%
+a random there is still this thousand
+dimensional cloud is still elongated
+
+ align:start position:0%
+dimensional cloud is still elongated
+ 
+
+ align:start position:0%
+dimensional cloud is still elongated
+it's not simply uniformly distributed
+
+ align:start position:0%
+it's not simply uniformly distributed
+ 
+
+ align:start position:0%
+it's not simply uniformly distributed
+and that this is the this is the
+
+ align:start position:0%
+and that this is the this is the
+ 
+
+ align:start position:0%
+and that this is the this is the
+signature that you see here in the first
+
+ align:start position:0%
+signature that you see here in the first
+ 
+
+ align:start position:0%
+signature that you see here in the first
+largest hundred eigenvalues there is
+
+ align:start position:0%
+largest hundred eigenvalues there is
+ 
+
+ align:start position:0%
+largest hundred eigenvalues there is
+extra power relative to to to the to the
+
+ align:start position:0%
+extra power relative to to to the to the
+ 
+
+ align:start position:0%
+extra power relative to to to the to the
+random okay the rest is not zero so if
+
+ align:start position:0%
+random okay the rest is not zero so if
+ 
+
+ align:start position:0%
+random okay the rest is not zero so if
+you look here you know this is this goes
+
+ align:start position:0%
+you look here you know this is this goes
+ 
+
+ align:start position:0%
+you look here you know this is this goes
+up to thousand the rest is not zero but
+
+ align:start position:0%
+up to thousand the rest is not zero but
+ 
+
+ align:start position:0%
+up to thousand the rest is not zero but
+so the system is strictly speaking
+
+ align:start position:0%
+so the system is strictly speaking
+ 
+
+ align:start position:0%
+so the system is strictly speaking
+thousand dimensional space but it's not
+
+ align:start position:0%
+thousand dimensional space but it's not
+ 
+
+ align:start position:0%
+thousand dimensional space but it's not
+random it is has increased power in
+
+ align:start position:0%
+random it is has increased power in
+ 
+
+ align:start position:0%
+random it is has increased power in
+hundred channels if you do a read out
+
+ align:start position:0%
+hundred channels if you do a read out
+ 
+
+ align:start position:0%
+hundred channels if you do a read out
+linear classifier read out what you find
+
+ align:start position:0%
+linear classifier read out what you find
+ 
+
+ align:start position:0%
+linear classifier read out what you find
+in this again in when you when you
+
+ align:start position:0%
+in this again in when you when you
+ 
+
+ align:start position:0%
+in this again in when you when you
+expand with a random okay with random
+
+ align:start position:0%
+expand with a random okay with random
+ 
+
+ align:start position:0%
+expand with a random okay with random
+with random weights you find that there
+
+ align:start position:0%
+with random weights you find that there
+ 
+
+ align:start position:0%
+with random weights you find that there
+is an optimal an optimal sparsity so
+
+ align:start position:0%
+is an optimal an optimal sparsity so
+ 
+
+ align:start position:0%
+is an optimal an optimal sparsity so
+this is the readout arrow for a
+
+ align:start position:0%
+this is the readout arrow for a
+ 
+
+ align:start position:0%
+this is the readout arrow for a
+classifier the output is a function of
+
+ align:start position:0%
+classifier the output is a function of
+ 
+
+ align:start position:0%
+classifier the output is a function of
+of the sparsity for different level of
+
+ align:start position:0%
+of the sparsity for different level of
+ 
+
+ align:start position:0%
+of the sparsity for different level of
+noise and you see that in the case of
+
+ align:start position:0%
+noise and you see that in the case of
+ 
+
+ align:start position:0%
+noise and you see that in the case of
+random weights there is a very high very
+
+ align:start position:0%
+random weights there is a very high very
+ 
+
+ align:start position:0%
+random weights there is a very high very
+very high sparsity is bad there is an
+
+ align:start position:0%
+very high sparsity is bad there is an
+ 
+
+ align:start position:0%
+very high sparsity is bad there is an
+optimal sparsity of sparseness and then
+
+ align:start position:0%
+optimal sparsity of sparseness and then
+ 
+
+ align:start position:0%
+optimal sparsity of sparseness and then
+there is a shallow increase in the error
+
+ align:start position:0%
+there is a shallow increase in the error
+ 
+
+ align:start position:0%
+there is a shallow increase in the error
+when you go to a denser representation
+
+ align:start position:0%
+when you go to a denser representation
+ 
+
+ align:start position:0%
+when you go to a denser representation
+one important point which I want to
+
+ align:start position:0%
+one important point which I want to
+ 
+
+ align:start position:0%
+one important point which I want to
+emphasize a coming from the null this
+
+ align:start position:0%
+emphasize a coming from the null this
+ 
+
+ align:start position:0%
+emphasize a coming from the null this
+let me skip equations and this is what
+
+ align:start position:0%
+let me skip equations and this is what
+ 
+
+ align:start position:0%
+let me skip equations and this is what
+you see here the question is can I do
+
+ align:start position:0%
+you see here the question is can I do
+ 
+
+ align:start position:0%
+you see here the question is can I do
+better by further increase the layer so
+
+ align:start position:0%
+better by further increase the layer so
+ 
+
+ align:start position:0%
+better by further increase the layer so
+here I plot the readout error as a
+
+ align:start position:0%
+here I plot the readout error as a
+ 
+
+ align:start position:0%
+here I plot the readout error as a
+function of the size of cortical layer
+
+ align:start position:0%
+function of the size of cortical layer
+ 
+
+ align:start position:0%
+function of the size of cortical layer
+can I do better can I make the if I make
+
+ align:start position:0%
+can I do better can I make the if I make
+ 
+
+ align:start position:0%
+can I do better can I make the if I make
+the kernel dimensionality infinite okay
+
+ align:start position:0%
+the kernel dimensionality infinite okay
+ 
+
+ align:start position:0%
+the kernel dimensionality infinite okay
+can I do better okay well you can do
+
+ align:start position:0%
+can I do better okay well you can do
+ 
+
+ align:start position:0%
+can I do better okay well you can do
+better if you start with zero noise but
+
+ align:start position:0%
+better if you start with zero noise but
+ 
+
+ align:start position:0%
+better if you start with zero noise but
+if you have noisy inputs then basically
+
+ align:start position:0%
+if you have noisy inputs then basically
+ 
+
+ align:start position:0%
+if you have noisy inputs then basically
+the basically the the performance
+
+ align:start position:0%
+the basically the the performance
+ 
+
+ align:start position:0%
+the basically the the performance
+saturates and that's kind of surprising
+
+ align:start position:0%
+saturates and that's kind of surprising
+ 
+
+ align:start position:0%
+saturates and that's kind of surprising
+we we were under the we were expected
+
+ align:start position:0%
+we we were under the we were expected
+ 
+
+ align:start position:0%
+we we were under the we were expected
+that if you go to a larger and larger
+
+ align:start position:0%
+that if you go to a larger and larger
+ 
+
+ align:start position:0%
+that if you go to a larger and larger
+representation eventually the error will
+
+ align:start position:0%
+representation eventually the error will
+ 
+
+ align:start position:0%
+representation eventually the error will
+go to zero but it doesn't go to zero and
+
+ align:start position:0%
+go to zero but it doesn't go to zero and
+ 
+
+ align:start position:0%
+go to zero but it doesn't go to zero and
+that actually happens even for what we
+
+ align:start position:0%
+that actually happens even for what we
+ 
+
+ align:start position:0%
+that actually happens even for what we
+call structured representation and
+
+ align:start position:0%
+call structured representation and
+ 
+
+ align:start position:0%
+call structured representation and
+that's the same for different types of
+
+ align:start position:0%
+that's the same for different types of
+ 
+
+ align:start position:0%
+that's the same for different types of
+Linda with our perceptron pseudoinverse
+
+ align:start position:0%
+Linda with our perceptron pseudoinverse
+ 
+
+ align:start position:0%
+Linda with our perceptron pseudoinverse
+SVM all of them show this situation as
+
+ align:start position:0%
+SVM all of them show this situation as
+ 
+
+ align:start position:0%
+SVM all of them show this situation as
+you increase the size of cortical layer
+
+ align:start position:0%
+you increase the size of cortical layer
+ 
+
+ align:start position:0%
+you increase the size of cortical layer
+and that's one of them a very important
+
+ align:start position:0%
+and that's one of them a very important
+ 
+
+ align:start position:0%
+and that's one of them a very important
+outcome of our study that when you talk
+
+ align:start position:0%
+outcome of our study that when you talk
+ 
+
+ align:start position:0%
+outcome of our study that when you talk
+about noisy inputs you can think about
+
+ align:start position:0%
+about noisy inputs you can think about
+ 
+
+ align:start position:0%
+about noisy inputs you can think about
+it as kind of more generalization tasks
+
+ align:start position:0%
+it as kind of more generalization tasks
+ 
+
+ align:start position:0%
+it as kind of more generalization tasks
+then there is the limit about what you
+
+ align:start position:0%
+then there is the limit about what you
+ 
+
+ align:start position:0%
+then there is the limit about what you
+gain by expanding representation if even
+
+ align:start position:0%
+gain by expanding representation if even
+ 
+
+ align:start position:0%
+gain by expanding representation if even
+if you expand in a nonlinear fashion and
+
+ align:start position:0%
+if you expand in a nonlinear fashion and
+ 
+
+ align:start position:0%
+if you expand in a nonlinear fashion and
+you increase the dimensionality you
+
+ align:start position:0%
+you increase the dimensionality you
+ 
+
+ align:start position:0%
+you increase the dimensionality you
+cannot combat the noise
+
+ align:start position:0%
+cannot combat the noise
+ 
+
+ align:start position:0%
+cannot combat the noise
+at least up to some level beyond some
+
+ align:start position:0%
+at least up to some level beyond some
+ 
+
+ align:start position:0%
+at least up to some level beyond some
+level there is no point of further
+
+ align:start position:0%
+level there is no point of further
+ 
+
+ align:start position:0%
+level there is no point of further
+expansion because basically the arrow
+
+ align:start position:0%
+expansion because basically the arrow
+ 
+
+ align:start position:0%
+expansion because basically the arrow
+saturates okay let me let me since times
+
+ align:start position:0%
+saturates okay let me let me since times
+ 
+
+ align:start position:0%
+saturates okay let me let me since times
+goal goes fast let me talk about the
+
+ align:start position:0%
+goal goes fast let me talk about the
+ 
+
+ align:start position:0%
+goal goes fast let me talk about the
+eternity
+
+ align:start position:0%
+eternity
+ 
+
+ align:start position:0%
+eternity
+so if random weights are not doing so
+
+ align:start position:0%
+so if random weights are not doing so
+ 
+
+ align:start position:0%
+so if random weights are not doing so
+well what are the alternatives that
+
+ align:start position:0%
+well what are the alternatives that
+ 
+
+ align:start position:0%
+well what are the alternatives that
+anything is to do some kind of
+
+ align:start position:0%
+anything is to do some kind of
+ 
+
+ align:start position:0%
+anything is to do some kind of
+unsupervised learning here we are doing
+
+ align:start position:0%
+unsupervised learning here we are doing
+ 
+
+ align:start position:0%
+unsupervised learning here we are doing
+it in a kind of a shortcut of
+
+ align:start position:0%
+it in a kind of a shortcut of
+ 
+
+ align:start position:0%
+it in a kind of a shortcut of
+unsupervised learning okay what is the
+
+ align:start position:0%
+unsupervised learning okay what is the
+ 
+
+ align:start position:0%
+unsupervised learning okay what is the
+shortcut we said the following imagine
+
+ align:start position:0%
+shortcut we said the following imagine
+ 
+
+ align:start position:0%
+shortcut we said the following imagine
+that this layers the learner knows about
+
+ align:start position:0%
+that this layers the learner knows about
+ 
+
+ align:start position:0%
+that this layers the learner knows about
+the representation of the clusters it
+
+ align:start position:0%
+the representation of the clusters it
+ 
+
+ align:start position:0%
+the representation of the clusters it
+doesn't know the labels in other words
+
+ align:start position:0%
+doesn't know the labels in other words
+ 
+
+ align:start position:0%
+doesn't know the labels in other words
+whether those are pluses and those are
+
+ align:start position:0%
+whether those are pluses and those are
+ 
+
+ align:start position:0%
+whether those are pluses and those are
+managers which one are pluses and
+
+ align:start position:0%
+managers which one are pluses and
+ 
+
+ align:start position:0%
+managers which one are pluses and
+minuses but it does know about the
+
+ align:start position:0%
+minuses but it does know about the
+ 
+
+ align:start position:0%
+minuses but it does know about the
+statistical structure of the input and
+
+ align:start position:0%
+statistical structure of the input and
+ 
+
+ align:start position:0%
+statistical structure of the input and
+this is this s s bar these are the
+
+ align:start position:0%
+this is this s s bar these are the
+ 
+
+ align:start position:0%
+this is this s s bar these are the
+Centers okay so we want to encode the
+
+ align:start position:0%
+Centers okay so we want to encode the
+ 
+
+ align:start position:0%
+Centers okay so we want to encode the
+statistical structure of the of this
+
+ align:start position:0%
+statistical structure of the of this
+ 
+
+ align:start position:0%
+statistical structure of the of this
+input in this expansion of the of the
+
+ align:start position:0%
+input in this expansion of the of the
+ 
+
+ align:start position:0%
+input in this expansion of the of the
+weight and the way we do the simplest
+
+ align:start position:0%
+weight and the way we do the simplest
+ 
+
+ align:start position:0%
+weight and the way we do the simplest
+way is the kind of head rule we do the
+
+ align:start position:0%
+way is the kind of head rule we do the
+ 
+
+ align:start position:0%
+way is the kind of head rule we do the
+following we say let's first choose a
+
+ align:start position:0%
+following we say let's first choose a
+ 
+
+ align:start position:0%
+following we say let's first choose a
+recruit or allocate a state a spawn
+
+ align:start position:0%
+recruit or allocate a state a spawn
+ 
+
+ align:start position:0%
+recruit or allocate a state a spawn
+state here randomly chosen to associate
+
+ align:start position:0%
+state here randomly chosen to associate
+ 
+
+ align:start position:0%
+state here randomly chosen to associate
+a to represent each one of the clusters
+
+ align:start position:0%
+a to represent each one of the clusters
+ 
+
+ align:start position:0%
+a to represent each one of the clusters
+so these are the are the randomly chosen
+
+ align:start position:0%
+so these are the are the randomly chosen
+ 
+
+ align:start position:0%
+so these are the are the randomly chosen
+patterns here and then we associate
+
+ align:start position:0%
+patterns here and then we associate
+ 
+
+ align:start position:0%
+patterns here and then we associate
+between those randomly chosen
+
+ align:start position:0%
+between those randomly chosen
+ 
+
+ align:start position:0%
+between those randomly chosen
+representations and in the end the
+
+ align:start position:0%
+representations and in the end the
+ 
+
+ align:start position:0%
+representations and in the end the
+actual Centers of the classes at the
+
+ align:start position:0%
+actual Centers of the classes at the
+ 
+
+ align:start position:0%
+actual Centers of the classes at the
+input so this is s bar and R and then we
+
+ align:start position:0%
+input so this is s bar and R and then we
+ 
+
+ align:start position:0%
+input so this is s bar and R and then we
+do the Association by the simple what's
+
+ align:start position:0%
+do the Association by the simple what's
+ 
+
+ align:start position:0%
+do the Association by the simple what's
+called hey bro so this happy enroll
+
+ align:start position:0%
+called hey bro so this happy enroll
+ 
+
+ align:start position:0%
+called hey bro so this happy enroll
+Associate Justice Center with randomly
+
+ align:start position:0%
+Associate Justice Center with randomly
+ 
+
+ align:start position:0%
+Associate Justice Center with randomly
+assign a state in the in the cortical
+
+ align:start position:0%
+assign a state in the in the cortical
+ 
+
+ align:start position:0%
+assign a state in the in the cortical
+layer in in kind of simple summation
+
+ align:start position:0%
+layer in in kind of simple summation
+ 
+
+ align:start position:0%
+layer in in kind of simple summation
+without the product for the hypodermis
+
+ align:start position:0%
+without the product for the hypodermis
+ 
+
+ align:start position:0%
+without the product for the hypodermis
+sofisticated ways to do it but that's
+
+ align:start position:0%
+sofisticated ways to do it but that's
+ 
+
+ align:start position:0%
+sofisticated ways to do it but that's
+the simplest one of doing so it turns
+
+ align:start position:0%
+the simplest one of doing so it turns
+ 
+
+ align:start position:0%
+the simplest one of doing so it turns
+out that this simple rule is
+
+ align:start position:0%
+out that this simple rule is
+ 
+
+ align:start position:0%
+out that this simple rule is
+has enormous potential for suppressing
+
+ align:start position:0%
+has enormous potential for suppressing
+ 
+
+ align:start position:0%
+has enormous potential for suppressing
+noise so it's again this is the input
+
+ align:start position:0%
+noise so it's again this is the input
+ 
+
+ align:start position:0%
+noise so it's again this is the input
+noise than the output noise the humming
+
+ align:start position:0%
+noise than the output noise the humming
+ 
+
+ align:start position:0%
+noise than the output noise the humming
+this distance of the input and the
+
+ align:start position:0%
+this distance of the input and the
+ 
+
+ align:start position:0%
+this distance of the input and the
+output properly normalized and you see
+
+ align:start position:0%
+output properly normalized and you see
+ 
+
+ align:start position:0%
+output properly normalized and you see
+that as you go to higher and higher
+
+ align:start position:0%
+that as you go to higher and higher
+ 
+
+ align:start position:0%
+that as you go to higher and higher
+sparseness toulon low F this is
+
+ align:start position:0%
+sparseness toulon low F this is
+ 
+
+ align:start position:0%
+sparseness toulon low F this is
+basically the the input noise is
+
+ align:start position:0%
+basically the the input noise is
+ 
+
+ align:start position:0%
+basically the the input noise is
+completely quenched whenever an F is
+
+ align:start position:0%
+completely quenched whenever an F is
+ 
+
+ align:start position:0%
+completely quenched whenever an F is
+large when F is 0.01 for instance this
+
+ align:start position:0%
+large when F is 0.01 for instance this
+ 
+
+ align:start position:0%
+large when F is 0.01 for instance this
+is this already stably when at point of
+
+ align:start position:0%
+is this already stably when at point of
+ 
+
+ align:start position:0%
+is this already stably when at point of
+five is here and then and so on so forth
+
+ align:start position:0%
+five is here and then and so on so forth
+ 
+
+ align:start position:0%
+five is here and then and so on so forth
+so sparse representation in particular
+
+ align:start position:0%
+so sparse representation in particular
+ 
+
+ align:start position:0%
+so sparse representation in particular
+are very effective in suppressing noise
+
+ align:start position:0%
+are very effective in suppressing noise
+ 
+
+ align:start position:0%
+are very effective in suppressing noise
+but provided the inputs have kind of
+
+ align:start position:0%
+but provided the inputs have kind of
+ 
+
+ align:start position:0%
+but provided the inputs have kind of
+unsupervised learning encoded into them
+
+ align:start position:0%
+unsupervised learning encoded into them
+ 
+
+ align:start position:0%
+unsupervised learning encoded into them
+which embed into them the cluster
+
+ align:start position:0%
+which embed into them the cluster
+ 
+
+ align:start position:0%
+which embed into them the cluster
+structure of the input okay the same or
+
+ align:start position:0%
+structure of the input okay the same or
+ 
+
+ align:start position:0%
+structure of the input okay the same or
+similar thing is true for Q for these
+
+ align:start position:0%
+similar thing is true for Q for these
+ 
+
+ align:start position:0%
+similar thing is true for Q for these
+correlations if you look at the this was
+
+ align:start position:0%
+correlations if you look at the this was
+ 
+
+ align:start position:0%
+correlations if you look at the this was
+was a random correlation and this is a
+
+ align:start position:0%
+was a random correlation and this is a
+ 
+
+ align:start position:0%
+was a random correlation and this is a
+function of F and this is Q the
+
+ align:start position:0%
+function of F and this is Q the
+ 
+
+ align:start position:0%
+function of F and this is Q the
+correlation
+
+ align:start position:0%
+correlation
+ 
+
+ align:start position:0%
+correlation
+it's a stoical is extremely suppressed
+
+ align:start position:0%
+it's a stoical is extremely suppressed
+ 
+
+ align:start position:0%
+it's a stoical is extremely suppressed
+for for sparse representation basically
+
+ align:start position:0%
+for for sparse representation basically
+ 
+
+ align:start position:0%
+for for sparse representation basically
+it is exponentially small with one over
+
+ align:start position:0%
+it is exponentially small with one over
+ 
+
+ align:start position:0%
+it is exponentially small with one over
+F so it's basically zero for sparse
+
+ align:start position:0%
+F so it's basically zero for sparse
+ 
+
+ align:start position:0%
+F so it's basically zero for sparse
+representation which means that those
+
+ align:start position:0%
+representation which means that those
+ 
+
+ align:start position:0%
+representation which means that those
+centres look like randomly distributed
+
+ align:start position:0%
+centres look like randomly distributed
+ 
+
+ align:start position:0%
+centres look like randomly distributed
+essentially and with very small noise so
+
+ align:start position:0%
+essentially and with very small noise so
+ 
+
+ align:start position:0%
+essentially and with very small noise so
+you took this spheres and you basically
+
+ align:start position:0%
+you took this spheres and you basically
+ 
+
+ align:start position:0%
+you took this spheres and you basically
+map them into random points with a very
+
+ align:start position:0%
+map them into random points with a very
+ 
+
+ align:start position:0%
+map them into random points with a very
+small radius okay so it's not surprising
+
+ align:start position:0%
+small radius okay so it's not surprising
+ 
+
+ align:start position:0%
+small radius okay so it's not surprising
+that in this case the error for small
+
+ align:start position:0%
+that in this case the error for small
+ 
+
+ align:start position:0%
+that in this case the error for small
+for small F the error even for large
+
+ align:start position:0%
+for small F the error even for large
+ 
+
+ align:start position:0%
+for small F the error even for large
+very loud noise value with aro is
+
+ align:start position:0%
+very loud noise value with aro is
+ 
+
+ align:start position:0%
+very loud noise value with aro is
+basically small as zero nevertheless it
+
+ align:start position:0%
+basically small as zero nevertheless it
+ 
+
+ align:start position:0%
+basically small as zero nevertheless it
+is still saturating is function of the
+
+ align:start position:0%
+is still saturating is function of the
+ 
+
+ align:start position:0%
+is still saturating is function of the
+network side of the cortical size okay
+
+ align:start position:0%
+network side of the cortical size okay
+ 
+
+ align:start position:0%
+network side of the cortical size okay
+so the saturation of performance as a
+
+ align:start position:0%
+so the saturation of performance as a
+ 
+
+ align:start position:0%
+so the saturation of performance as a
+function of cortical size is the general
+
+ align:start position:0%
+function of cortical size is the general
+ 
+
+ align:start position:0%
+function of cortical size is the general
+property of such systems nevertheless
+
+ align:start position:0%
+property of such systems nevertheless
+ 
+
+ align:start position:0%
+property of such systems nevertheless
+the performance itself for any given
+
+ align:start position:0%
+the performance itself for any given
+ 
+
+ align:start position:0%
+the performance itself for any given
+size is extremely extremely impressive I
+
+ align:start position:0%
+size is extremely extremely impressive I
+ 
+
+ align:start position:0%
+size is extremely extremely impressive I
+would say when the system is passed
+
+ align:start position:0%
+would say when the system is passed
+ 
+
+ align:start position:0%
+would say when the system is passed
+and nose level is kind of moderate okay
+
+ align:start position:0%
+and nose level is kind of moderate okay
+ 
+
+ align:start position:0%
+and nose level is kind of moderate okay
+okay let me skip this because I don't
+
+ align:start position:0%
+okay let me skip this because I don't
+ 
+
+ align:start position:0%
+okay let me skip this because I don't
+have time let me briefly talk about
+
+ align:start position:0%
+have time let me briefly talk about
+ 
+
+ align:start position:0%
+have time let me briefly talk about
+extension D of this story to two
+
+ align:start position:0%
+extension D of this story to two
+ 
+
+ align:start position:0%
+extension D of this story to two
+multi-layer so we are now briefly
+
+ align:start position:0%
+multi-layer so we are now briefly
+ 
+
+ align:start position:0%
+multi-layer so we are now briefly
+discussing what happens if you take this
+
+ align:start position:0%
+discussing what happens if you take this
+ 
+
+ align:start position:0%
+discussing what happens if you take this
+story and you just propagate it as you
+
+ align:start position:0%
+story and you just propagate it as you
+ 
+
+ align:start position:0%
+story and you just propagate it as you
+go along the along the architecture so
+
+ align:start position:0%
+go along the along the architecture so
+ 
+
+ align:start position:0%
+go along the along the architecture so
+let's start with random eighths so the
+
+ align:start position:0%
+let's start with random eighths so the
+ 
+
+ align:start position:0%
+let's start with random eighths so the
+idea is maybe something is good
+
+ align:start position:0%
+idea is maybe something is good
+ 
+
+ align:start position:0%
+idea is maybe something is good
+happening although initially performance
+
+ align:start position:0%
+happening although initially performance
+ 
+
+ align:start position:0%
+happening although initially performance
+was poor maybe we can improve the
+
+ align:start position:0%
+was poor maybe we can improve the
+ 
+
+ align:start position:0%
+was poor maybe we can improve the
+performance by cascading such layers and
+
+ align:start position:0%
+performance by cascading such layers and
+ 
+
+ align:start position:0%
+performance by cascading such layers and
+the answer is no in particularly the
+
+ align:start position:0%
+the answer is no in particularly the
+ 
+
+ align:start position:0%
+the answer is no in particularly the
+noise level this is now the number of
+
+ align:start position:0%
+noise level this is now the number of
+ 
+
+ align:start position:0%
+noise level this is now the number of
+layers go to discuss before is here and
+
+ align:start position:0%
+layers go to discuss before is here and
+ 
+
+ align:start position:0%
+layers go to discuss before is here and
+you see the problem becomes worse and
+
+ align:start position:0%
+you see the problem becomes worse and
+ 
+
+ align:start position:0%
+you see the problem becomes worse and
+worse as you continue to propagate those
+
+ align:start position:0%
+worse as you continue to propagate those
+ 
+
+ align:start position:0%
+worse as you continue to propagate those
+signals the lowest the noise is
+
+ align:start position:0%
+signals the lowest the noise is
+ 
+
+ align:start position:0%
+signals the lowest the noise is
+amplified and essentially goes to one so
+
+ align:start position:0%
+amplified and essentially goes to one so
+ 
+
+ align:start position:0%
+amplified and essentially goes to one so
+basically you'll get just random
+
+ align:start position:0%
+basically you'll get just random
+ 
+
+ align:start position:0%
+basically you'll get just random
+performance if you keep doing it with
+
+ align:start position:0%
+performance if you keep doing it with
+ 
+
+ align:start position:0%
+performance if you keep doing it with
+random waves and the reason is very the
+
+ align:start position:0%
+random waves and the reason is very the
+ 
+
+ align:start position:0%
+random waves and the reason is very the
+reason the reason is basically that if
+
+ align:start position:0%
+reason the reason is basically that if
+ 
+
+ align:start position:0%
+reason the reason is basically that if
+you think about the mapping from one
+
+ align:start position:0%
+you think about the mapping from one
+ 
+
+ align:start position:0%
+you think about the mapping from one
+layer of noise tune to lab tune another
+
+ align:start position:0%
+layer of noise tune to lab tune another
+ 
+
+ align:start position:0%
+layer of noise tune to lab tune another
+layer of noise there are two fixed point
+
+ align:start position:0%
+layer of noise there are two fixed point
+ 
+
+ align:start position:0%
+layer of noise there are two fixed point
+and zero and one the zero fixed point is
+
+ align:start position:0%
+and zero and one the zero fixed point is
+ 
+
+ align:start position:0%
+and zero and one the zero fixed point is
+unstable
+
+ align:start position:0%
+unstable
+ 
+
+ align:start position:0%
+unstable
+everything goes eventually to one so
+
+ align:start position:0%
+everything goes eventually to one so
+ 
+
+ align:start position:0%
+everything goes eventually to one so
+it's it is a nice I think it's a nice
+
+ align:start position:0%
+it's it is a nice I think it's a nice
+ 
+
+ align:start position:0%
+it's it is a nice I think it's a nice
+this system gives you a nice perspective
+
+ align:start position:0%
+this system gives you a nice perspective
+ 
+
+ align:start position:0%
+this system gives you a nice perspective
+about this a distant deep network by
+
+ align:start position:0%
+about this a distant deep network by
+ 
+
+ align:start position:0%
+about this a distant deep network by
+thinking about is a kind of dynamical
+
+ align:start position:0%
+thinking about is a kind of dynamical
+ 
+
+ align:start position:0%
+thinking about is a kind of dynamical
+system for instance what is the level of
+
+ align:start position:0%
+system for instance what is the level of
+ 
+
+ align:start position:0%
+system for instance what is the level of
+noise at one there and how it is how
+
+ align:start position:0%
+noise at one there and how it is how
+ 
+
+ align:start position:0%
+noise at one there and how it is how
+it's related to the level of noise it
+
+ align:start position:0%
+it's related to the level of noise it
+ 
+
+ align:start position:0%
+it's related to the level of noise it
+previously so it's connect iterative map
+
+ align:start position:0%
+previously so it's connect iterative map
+ 
+
+ align:start position:0%
+previously so it's connect iterative map
+Delta n versus Delta n minus 1 and
+
+ align:start position:0%
+Delta n versus Delta n minus 1 and
+ 
+
+ align:start position:0%
+Delta n versus Delta n minus 1 and
+what's good about it this once you kind
+
+ align:start position:0%
+what's good about it this once you kind
+ 
+
+ align:start position:0%
+what's good about it this once you kind
+of draw this curve what one layer is
+
+ align:start position:0%
+of draw this curve what one layer is
+ 
+
+ align:start position:0%
+of draw this curve what one layer is
+mapped to another layer you can know
+
+ align:start position:0%
+mapped to another layer you can know
+ 
+
+ align:start position:0%
+mapped to another layer you can know
+what happens to a deep network because
+
+ align:start position:0%
+what happens to a deep network because
+ 
+
+ align:start position:0%
+what happens to a deep network because
+just iterate this you have to find what
+
+ align:start position:0%
+just iterate this you have to find what
+ 
+
+ align:start position:0%
+just iterate this you have to find what
+are the fixed points and which one is
+
+ align:start position:0%
+are the fixed points and which one is
+ 
+
+ align:start position:0%
+are the fixed points and which one is
+stable which one is not in this case the
+
+ align:start position:0%
+stable which one is not in this case the
+ 
+
+ align:start position:0%
+stable which one is not in this case the
+one is stable the zero is unstable so
+
+ align:start position:0%
+one is stable the zero is unstable so
+ 
+
+ align:start position:0%
+one is stable the zero is unstable so
+unfortunately from any level of noise
+
+ align:start position:0%
+unfortunately from any level of noise
+ 
+
+ align:start position:0%
+unfortunately from any level of noise
+that you'll start you eventually go to
+
+ align:start position:0%
+that you'll start you eventually go to
+ 
+
+ align:start position:0%
+that you'll start you eventually go to
+two one
+
+ align:start position:0%
+two one
+ 
+
+ align:start position:0%
+two one
+okay correlations is similar story but I
+
+ align:start position:0%
+okay correlations is similar story but I
+ 
+
+ align:start position:0%
+okay correlations is similar story but I
+and the arrow will go to 2.5 okay so
+
+ align:start position:0%
+and the arrow will go to 2.5 okay so
+ 
+
+ align:start position:0%
+and the arrow will go to 2.5 okay so
+that's very bad okay there are cases by
+
+ align:start position:0%
+that's very bad okay there are cases by
+ 
+
+ align:start position:0%
+that's very bad okay there are cases by
+the way that you can find parameters
+
+ align:start position:0%
+the way that you can find parameters
+ 
+
+ align:start position:0%
+the way that you can find parameters
+where initially you improve like here
+
+ align:start position:0%
+where initially you improve like here
+ 
+
+ align:start position:0%
+where initially you improve like here
+but then eventually it will it will go
+
+ align:start position:0%
+but then eventually it will it will go
+ 
+
+ align:start position:0%
+but then eventually it will it will go
+to 0.5 now if we do similar if we
+
+ align:start position:0%
+to 0.5 now if we do similar if we
+ 
+
+ align:start position:0%
+to 0.5 now if we do similar if we
+compare this to what happened to the
+
+ align:start position:0%
+compare this to what happened to the
+ 
+
+ align:start position:0%
+compare this to what happened to the
+structure wait if you keep doing the
+
+ align:start position:0%
+structure wait if you keep doing the
+ 
+
+ align:start position:0%
+structure wait if you keep doing the
+same kind of unsupervised hebbian
+
+ align:start position:0%
+same kind of unsupervised hebbian
+ 
+
+ align:start position:0%
+same kind of unsupervised hebbian
+learning from one layer to another and
+
+ align:start position:0%
+learning from one layer to another and
+ 
+
+ align:start position:0%
+learning from one layer to another and
+and I'll skip the details you see the
+
+ align:start position:0%
+and I'll skip the details you see the
+ 
+
+ align:start position:0%
+and I'll skip the details you see the
+opposite so here are parameters
+
+ align:start position:0%
+opposite so here are parameters
+ 
+
+ align:start position:0%
+opposite so here are parameters
+parameter value in which one stage of
+
+ align:start position:0%
+parameter value in which one stage of
+ 
+
+ align:start position:0%
+parameter value in which one stage of
+expansion stage is is actually
+
+ align:start position:0%
+expansion stage is is actually
+ 
+
+ align:start position:0%
+expansion stage is is actually
+increasing the noise and this is because
+
+ align:start position:0%
+increasing the noise and this is because
+ 
+
+ align:start position:0%
+increasing the noise and this is because
+F is small is not is not too small and
+
+ align:start position:0%
+F is small is not is not too small and
+ 
+
+ align:start position:0%
+F is small is not is not too small and
+the load is large and the noise is
+
+ align:start position:0%
+the load is large and the noise is
+ 
+
+ align:start position:0%
+the load is large and the noise is
+starting so you can have such iteration
+
+ align:start position:0%
+starting so you can have such iteration
+ 
+
+ align:start position:0%
+starting so you can have such iteration
+but even in such situation eventually
+
+ align:start position:0%
+but even in such situation eventually
+ 
+
+ align:start position:0%
+but even in such situation eventually
+the system goes into into stages where
+
+ align:start position:0%
+the system goes into into stages where
+ 
+
+ align:start position:0%
+the system goes into into stages where
+the noise basically goes to zero and if
+
+ align:start position:0%
+the noise basically goes to zero and if
+ 
+
+ align:start position:0%
+the noise basically goes to zero and if
+you compare the the story why it is so
+
+ align:start position:0%
+you compare the the story why it is so
+ 
+
+ align:start position:0%
+you compare the the story why it is so
+two kind of iterative met in my picture
+
+ align:start position:0%
+two kind of iterative met in my picture
+ 
+
+ align:start position:0%
+two kind of iterative met in my picture
+you see that the picture is very
+
+ align:start position:0%
+you see that the picture is very
+ 
+
+ align:start position:0%
+you see that the picture is very
+different you have one fixed point at
+
+ align:start position:0%
+different you have one fixed point at
+ 
+
+ align:start position:0%
+different you have one fixed point at
+zero you have one fixed point at one you
+
+ align:start position:0%
+zero you have one fixed point at one you
+ 
+
+ align:start position:0%
+zero you have one fixed point at one you
+have intermediate fixed point at a high
+
+ align:start position:0%
+have intermediate fixed point at a high
+ 
+
+ align:start position:0%
+have intermediate fixed point at a high
+value but this is an unstable fixed
+
+ align:start position:0%
+value but this is an unstable fixed
+ 
+
+ align:start position:0%
+value but this is an unstable fixed
+point at both of them a stable fixed
+
+ align:start position:0%
+point at both of them a stable fixed
+ 
+
+ align:start position:0%
+point at both of them a stable fixed
+point so if you start from even from
+
+ align:start position:0%
+point so if you start from even from
+ 
+
+ align:start position:0%
+point so if you start from even from
+large values of noise eventually you
+
+ align:start position:0%
+large values of noise eventually you
+ 
+
+ align:start position:0%
+large values of noise eventually you
+will iterate to zero so it does buy you
+
+ align:start position:0%
+will iterate to zero so it does buy you
+ 
+
+ align:start position:0%
+will iterate to zero so it does buy you
+to actually go into several stages of of
+
+ align:start position:0%
+to actually go into several stages of of
+ 
+
+ align:start position:0%
+to actually go into several stages of of
+this deep network to make sure that the
+
+ align:start position:0%
+this deep network to make sure that the
+ 
+
+ align:start position:0%
+this deep network to make sure that the
+noise is suppressed to zero
+
+ align:start position:0%
+noise is suppressed to zero
+ 
+
+ align:start position:0%
+noise is suppressed to zero
+similarly from the correlations even if
+
+ align:start position:0%
+similarly from the correlations even if
+ 
+
+ align:start position:0%
+similarly from the correlations even if
+the parameters are such that initially
+
+ align:start position:0%
+the parameters are such that initially
+ 
+
+ align:start position:0%
+the parameters are such that initially
+correlations are increased and you can
+
+ align:start position:0%
+correlations are increased and you can
+ 
+
+ align:start position:0%
+correlations are increased and you can
+find parameters like that eventually
+
+ align:start position:0%
+find parameters like that eventually
+ 
+
+ align:start position:0%
+find parameters like that eventually
+correlations will go to almost zero okay
+
+ align:start position:0%
+correlations will go to almost zero okay
+ 
+
+ align:start position:0%
+correlations will go to almost zero okay
+and this is comparison of the grid out
+
+ align:start position:0%
+and this is comparison of the grid out
+ 
+
+ align:start position:0%
+and this is comparison of the grid out
+MO as a function of the layers we
+
+ align:start position:0%
+MO as a function of the layers we
+ 
+
+ align:start position:0%
+MO as a function of the layers we
+structured weights and I compare it with
+
+ align:start position:0%
+structured weights and I compare it with
+ 
+
+ align:start position:0%
+structured weights and I compare it with
+the readout error of infinity wide layer
+
+ align:start position:0%
+the readout error of infinity wide layer
+ 
+
+ align:start position:0%
+the readout error of infinity wide layer
+kind of a
+
+ align:start position:0%
+kind of a
+ 
+
+ align:start position:0%
+kind of a
+colonel with infinitely white colonel
+
+ align:start position:0%
+colonel with infinitely white colonel
+ 
+
+ align:start position:0%
+colonel with infinitely white colonel
+and you can see that that at least for
+
+ align:start position:0%
+and you can see that that at least for
+ 
+
+ align:start position:0%
+and you can see that that at least for
+here I compare the same type of
+
+ align:start position:0%
+here I compare the same type of
+ 
+
+ align:start position:0%
+here I compare the same type of
+unsupervised learning but two different
+
+ align:start position:0%
+unsupervised learning but two different
+ 
+
+ align:start position:0%
+unsupervised learning but two different
+architecture one is deep network
+
+ align:start position:0%
+architecture one is deep network
+ 
+
+ align:start position:0%
+architecture one is deep network
+architecture another one is shallow
+
+ align:start position:0%
+architecture another one is shallow
+ 
+
+ align:start position:0%
+architecture another one is shallow
+architecture infinitely wide and I'm not
+
+ align:start position:0%
+architecture infinitely wide and I'm not
+ 
+
+ align:start position:0%
+architecture infinitely wide and I'm not
+claiming that we can show that there is
+
+ align:start position:0%
+claiming that we can show that there is
+ 
+
+ align:start position:0%
+claiming that we can show that there is
+no kernel or shallow architecture which
+
+ align:start position:0%
+no kernel or shallow architecture which
+ 
+
+ align:start position:0%
+no kernel or shallow architecture which
+will do better but I'm saying if we
+
+ align:start position:0%
+will do better but I'm saying if we
+ 
+
+ align:start position:0%
+will do better but I'm saying if we
+compare the same learning rule but with
+
+ align:start position:0%
+compare the same learning rule but with
+ 
+
+ align:start position:0%
+compare the same learning rule but with
+it but with the two different
+
+ align:start position:0%
+it but with the two different
+ 
+
+ align:start position:0%
+it but with the two different
+architecture you find that you do gain
+
+ align:start position:0%
+architecture you find that you do gain
+ 
+
+ align:start position:0%
+architecture you find that you do gain
+by going into multiple stages of
+
+ align:start position:0%
+by going into multiple stages of
+ 
+
+ align:start position:0%
+by going into multiple stages of
+non-linearity then by using an
+
+ align:start position:0%
+non-linearity then by using an
+ 
+
+ align:start position:0%
+non-linearity then by using an
+infinitely wide layer ok I'll skip this
+
+ align:start position:0%
+infinitely wide layer ok I'll skip this
+ 
+
+ align:start position:0%
+infinitely wide layer ok I'll skip this
+I want to go briefly to to two more
+
+ align:start position:0%
+I want to go briefly to to two more
+ 
+
+ align:start position:0%
+I want to go briefly to to two more
+issues one issue is the recurrent
+
+ align:start position:0%
+issues one issue is the recurrent
+ 
+
+ align:start position:0%
+issues one issue is the recurrent
+networks why recurrent networks are the
+
+ align:start position:0%
+networks why recurrent networks are the
+ 
+
+ align:start position:0%
+networks why recurrent networks are the
+primary reason is that in each one of
+
+ align:start position:0%
+primary reason is that in each one of
+ 
+
+ align:start position:0%
+primary reason is that in each one of
+those stages that I have a fail to if
+
+ align:start position:0%
+those stages that I have a fail to if
+ 
+
+ align:start position:0%
+those stages that I have a fail to if
+you look at the biology on most of them
+
+ align:start position:0%
+you look at the biology on most of them
+ 
+
+ align:start position:0%
+you look at the biology on most of them
+maybe not all of them but most of them
+
+ align:start position:0%
+maybe not all of them but most of them
+ 
+
+ align:start position:0%
+maybe not all of them but most of them
+indefinitely in neocortex you'll find
+
+ align:start position:0%
+indefinitely in neocortex you'll find
+ 
+
+ align:start position:0%
+indefinitely in neocortex you'll find
+massive recurrent or lateral
+
+ align:start position:0%
+massive recurrent or lateral
+ 
+
+ align:start position:0%
+massive recurrent or lateral
+interactions between each one of the
+
+ align:start position:0%
+interactions between each one of the
+ 
+
+ align:start position:0%
+interactions between each one of the
+layers so again we would like to ask
+
+ align:start position:0%
+layers so again we would like to ask
+ 
+
+ align:start position:0%
+layers so again we would like to ask
+what is the what is the what is the
+
+ align:start position:0%
+what is the what is the what is the
+ 
+
+ align:start position:0%
+what is the what is the what is the
+computational advantage of having this
+
+ align:start position:0%
+computational advantage of having this
+ 
+
+ align:start position:0%
+computational advantage of having this
+recurrent layer now in in our case we
+
+ align:start position:0%
+recurrent layer now in in our case we
+ 
+
+ align:start position:0%
+recurrent layer now in in our case we
+had an extra motivation and this is
+
+ align:start position:0%
+had an extra motivation and this is
+ 
+
+ align:start position:0%
+had an extra motivation and this is
+remember that I started in saying that
+
+ align:start position:0%
+remember that I started in saying that
+ 
+
+ align:start position:0%
+remember that I started in saying that
+in some cases there is experimental
+
+ align:start position:0%
+in some cases there is experimental
+ 
+
+ align:start position:0%
+in some cases there is experimental
+evidence that the initial projection is
+
+ align:start position:0%
+evidence that the initial projection is
+ 
+
+ align:start position:0%
+evidence that the initial projection is
+random so that we asked ourselves what
+
+ align:start position:0%
+random so that we asked ourselves what
+ 
+
+ align:start position:0%
+random so that we asked ourselves what
+happens if we do this if we start from
+
+ align:start position:0%
+happens if we do this if we start from
+ 
+
+ align:start position:0%
+happens if we do this if we start from
+random projection feed-forward
+
+ align:start position:0%
+random projection feed-forward
+ 
+
+ align:start position:0%
+random projection feed-forward
+projection and then add recurrent
+
+ align:start position:0%
+projection and then add recurrent
+ 
+
+ align:start position:0%
+projection and then add recurrent
+connections think about it as from the
+
+ align:start position:0%
+connections think about it as from the
+ 
+
+ align:start position:0%
+connections think about it as from the
+or factory bomb for instance to perform
+
+ align:start position:0%
+or factory bomb for instance to perform
+ 
+
+ align:start position:0%
+or factory bomb for instance to perform
+cortex perhaps random fitful projections
+
+ align:start position:0%
+cortex perhaps random fitful projections
+ 
+
+ align:start position:0%
+cortex perhaps random fitful projections
+but then the Association recurrent
+
+ align:start position:0%
+but then the Association recurrent
+ 
+
+ align:start position:0%
+but then the Association recurrent
+connections in period from cortex our
+
+ align:start position:0%
+connections in period from cortex our
+ 
+
+ align:start position:0%
+connections in period from cortex our
+structure how do we do that we start we
+
+ align:start position:0%
+structure how do we do that we start we
+ 
+
+ align:start position:0%
+structure how do we do that we start we
+imagine starting from random
+
+ align:start position:0%
+imagine starting from random
+ 
+
+ align:start position:0%
+imagine starting from random
+generating a presentation initial
+
+ align:start position:0%
+generating a presentation initial
+ 
+
+ align:start position:0%
+generating a presentation initial
+presentation by the random projection
+
+ align:start position:0%
+presentation by the random projection
+ 
+
+ align:start position:0%
+presentation by the random projection
+and then stabilizing those of
+
+ align:start position:0%
+and then stabilizing those of
+ 
+
+ align:start position:0%
+and then stabilizing those of
+presentation into attractors by the
+
+ align:start position:0%
+presentation into attractors by the
+ 
+
+ align:start position:0%
+presentation into attractors by the
+recurrent connections and that actually
+
+ align:start position:0%
+recurrent connections and that actually
+ 
+
+ align:start position:0%
+recurrent connections and that actually
+works pretty well it's not it's not it's
+
+ align:start position:0%
+works pretty well it's not it's not it's
+ 
+
+ align:start position:0%
+works pretty well it's not it's not it's
+not the optimal architecture but it's
+
+ align:start position:0%
+not the optimal architecture but it's
+ 
+
+ align:start position:0%
+not the optimal architecture but it's
+pretty well for instance noise which is
+
+ align:start position:0%
+pretty well for instance noise which is
+ 
+
+ align:start position:0%
+pretty well for instance noise which is
+initially increased by the random
+
+ align:start position:0%
+initially increased by the random
+ 
+
+ align:start position:0%
+initially increased by the random
+projections will quenched by convergence
+
+ align:start position:0%
+projections will quenched by convergence
+ 
+
+ align:start position:0%
+projections will quenched by convergence
+two attractor and similarly Q will not
+
+ align:start position:0%
+two attractor and similarly Q will not
+ 
+
+ align:start position:0%
+two attractor and similarly Q will not
+go to zero but will not continue growing
+
+ align:start position:0%
+go to zero but will not continue growing
+ 
+
+ align:start position:0%
+go to zero but will not continue growing
+but we'll go to intimately and and the
+
+ align:start position:0%
+but we'll go to intimately and and the
+ 
+
+ align:start position:0%
+but we'll go to intimately and and the
+arrow is is pretty well so if you look
+
+ align:start position:0%
+arrow is is pretty well so if you look
+ 
+
+ align:start position:0%
+arrow is is pretty well so if you look
+at the in this case the arrow really
+
+ align:start position:0%
+at the in this case the arrow really
+ 
+
+ align:start position:0%
+at the in this case the arrow really
+goes down to very low values but now
+
+ align:start position:0%
+goes down to very low values but now
+ 
+
+ align:start position:0%
+goes down to very low values but now
+it's not layers now it is the number of
+
+ align:start position:0%
+it's not layers now it is the number of
+ 
+
+ align:start position:0%
+it's not layers now it is the number of
+iterations of the recurrent connections
+
+ align:start position:0%
+iterations of the recurrent connections
+ 
+
+ align:start position:0%
+iterations of the recurrent connections
+so you start from just input layer or
+
+ align:start position:0%
+so you start from just input layer or
+ 
+
+ align:start position:0%
+so you start from just input layer or
+put project random projection and then
+
+ align:start position:0%
+put project random projection and then
+ 
+
+ align:start position:0%
+put project random projection and then
+you iterate the dynamics and it goes to
+
+ align:start position:0%
+you iterate the dynamics and it goes to
+ 
+
+ align:start position:0%
+you iterate the dynamics and it goes to
+zero so it's not the layers it's just
+
+ align:start position:0%
+zero so it's not the layers it's just
+ 
+
+ align:start position:0%
+zero so it's not the layers it's just
+the dynamics of the I conversion to
+
+ align:start position:0%
+the dynamics of the I conversion to
+ 
+
+ align:start position:0%
+the dynamics of the I conversion to
+attractor okay my final point I have
+
+ align:start position:0%
+attractor okay my final point I have
+ 
+
+ align:start position:0%
+attractor okay my final point I have
+three from four minutes okay
+
+ align:start position:0%
+three from four minutes okay
+ 
+
+ align:start position:0%
+three from four minutes okay
+my final points are before wrapping up
+
+ align:start position:0%
+my final points are before wrapping up
+ 
+
+ align:start position:0%
+my final points are before wrapping up
+is the question of top-down so we can't
+
+ align:start position:0%
+is the question of top-down so we can't
+ 
+
+ align:start position:0%
+is the question of top-down so we can't
+move really talked about it but
+
+ align:start position:0%
+move really talked about it but
+ 
+
+ align:start position:0%
+move really talked about it but
+incorporating contextual knowledge is a
+
+ align:start position:0%
+incorporating contextual knowledge is a
+ 
+
+ align:start position:0%
+incorporating contextual knowledge is a
+major question how can you improve on
+
+ align:start position:0%
+major question how can you improve on
+ 
+
+ align:start position:0%
+major question how can you improve on
+deep networks by incorporating not
+
+ align:start position:0%
+deep networks by incorporating not
+ 
+
+ align:start position:0%
+deep networks by incorporating not
+simply the feed-forward sensory input
+
+ align:start position:0%
+simply the feed-forward sensory input
+ 
+
+ align:start position:0%
+simply the feed-forward sensory input
+but other sort of knowledge about this
+
+ align:start position:0%
+but other sort of knowledge about this
+ 
+
+ align:start position:0%
+but other sort of knowledge about this
+particular stimulus and it's important
+
+ align:start position:0%
+particular stimulus and it's important
+ 
+
+ align:start position:0%
+particular stimulus and it's important
+that we are not talking about knowledge
+
+ align:start position:0%
+that we are not talking about knowledge
+ 
+
+ align:start position:0%
+that we are not talking about knowledge
+about the statistics of the input which
+
+ align:start position:0%
+about the statistics of the input which
+ 
+
+ align:start position:0%
+about the statistics of the input which
+can be incorporated into the learning of
+
+ align:start position:0%
+can be incorporated into the learning of
+ 
+
+ align:start position:0%
+can be incorporated into the learning of
+the feed-forward one but we're talking
+
+ align:start position:0%
+the feed-forward one but we're talking
+ 
+
+ align:start position:0%
+the feed-forward one but we're talking
+about inputs which our knowledge which
+
+ align:start position:0%
+about inputs which our knowledge which
+ 
+
+ align:start position:0%
+about inputs which our knowledge which
+we have now on the network which already
+
+ align:start position:0%
+we have now on the network which already
+ 
+
+ align:start position:0%
+we have now on the network which already
+has learned whatever it has learned so
+
+ align:start position:0%
+has learned whatever it has learned so
+ 
+
+ align:start position:0%
+has learned whatever it has learned so
+we have a mature Network whatever the
+
+ align:start position:0%
+we have a mature Network whatever the
+ 
+
+ align:start position:0%
+we have a mature Network whatever the
+architecture is we have a sensory input
+
+ align:start position:0%
+architecture is we have a sensory input
+ 
+
+ align:start position:0%
+architecture is we have a sensory input
+gross feed-forward and now we have
+
+ align:start position:0%
+gross feed-forward and now we have
+ 
+
+ align:start position:0%
+gross feed-forward and now we have
+additional information about context for
+
+ align:start position:0%
+additional information about context for
+ 
+
+ align:start position:0%
+additional information about context for
+instance that we want to incorporate
+
+ align:start position:0%
+instance that we want to incorporate
+ 
+
+ align:start position:0%
+instance that we want to incorporate
+with the sensory input to
+
+ align:start position:0%
+with the sensory input to
+ 
+
+ align:start position:0%
+with the sensory input to
+to improve the performance so how do we
+
+ align:start position:0%
+to improve the performance so how do we
+ 
+
+ align:start position:0%
+to improve the performance so how do we
+do that it that's it's a nut it turns
+
+ align:start position:0%
+do that it that's it's a nut it turns
+ 
+
+ align:start position:0%
+do that it that's it's a nut it turns
+out to be non-trivial a computational
+
+ align:start position:0%
+out to be non-trivial a computational
+ 
+
+ align:start position:0%
+out to be non-trivial a computational
+problem it is very straightforward to do
+
+ align:start position:0%
+problem it is very straightforward to do
+ 
+
+ align:start position:0%
+problem it is very straightforward to do
+it in in Bayesian framework where you
+
+ align:start position:0%
+it in in Bayesian framework where you
+ 
+
+ align:start position:0%
+it in in Bayesian framework where you
+simply update the prior of what the
+
+ align:start position:0%
+simply update the prior of what the
+ 
+
+ align:start position:0%
+simply update the prior of what the
+sensory input is by this contextual
+
+ align:start position:0%
+sensory input is by this contextual
+ 
+
+ align:start position:0%
+sensory input is by this contextual
+information but but if you want to
+
+ align:start position:0%
+information but but if you want to
+ 
+
+ align:start position:0%
+information but but if you want to
+implement it in a network you find that
+
+ align:start position:0%
+implement it in a network you find that
+ 
+
+ align:start position:0%
+implement it in a network you find that
+it's not it's not easy to to find the
+
+ align:start position:0%
+it's not it's not easy to to find the
+ 
+
+ align:start position:0%
+it's not it's not easy to to find the
+appropriate architecture so I just
+
+ align:start position:0%
+appropriate architecture so I just
+ 
+
+ align:start position:0%
+appropriate architecture so I just
+briefly talked about I talked about how
+
+ align:start position:0%
+briefly talked about I talked about how
+ 
+
+ align:start position:0%
+briefly talked about I talked about how
+we do it so so imagine you have again
+
+ align:start position:0%
+we do it so so imagine you have again
+ 
+
+ align:start position:0%
+we do it so so imagine you have again
+this sensory input but now there is some
+
+ align:start position:0%
+this sensory input but now there is some
+ 
+
+ align:start position:0%
+this sensory input but now there is some
+context different context and and
+
+ align:start position:0%
+context different context and and
+ 
+
+ align:start position:0%
+context different context and and
+imagine you have an information that the
+
+ align:start position:0%
+imagine you have an information that the
+ 
+
+ align:start position:0%
+imagine you have an information that the
+input is coming from that particular set
+
+ align:start position:0%
+input is coming from that particular set
+ 
+
+ align:start position:0%
+input is coming from that particular set
+of a part of state space so basically
+
+ align:start position:0%
+of a part of state space so basically
+ 
+
+ align:start position:0%
+of a part of state space so basically
+the question is how to amplify
+
+ align:start position:0%
+the question is how to amplify
+ 
+
+ align:start position:0%
+the question is how to amplify
+selectively a specific set of states in
+
+ align:start position:0%
+selectively a specific set of states in
+ 
+
+ align:start position:0%
+selectively a specific set of states in
+a distributed representation so usually
+
+ align:start position:0%
+a distributed representation so usually
+ 
+
+ align:start position:0%
+a distributed representation so usually
+when you talk about attention or gating
+
+ align:start position:0%
+when you talk about attention or gating
+ 
+
+ align:start position:0%
+when you talk about attention or gating
+on questions like that we think about
+
+ align:start position:0%
+on questions like that we think about
+ 
+
+ align:start position:0%
+on questions like that we think about
+okay we have these neurons we suppress
+
+ align:start position:0%
+okay we have these neurons we suppress
+ 
+
+ align:start position:0%
+okay we have these neurons we suppress
+those and amp or maybe amplify other
+
+ align:start position:0%
+those and amp or maybe amplify other
+ 
+
+ align:start position:0%
+those and amp or maybe amplify other
+ones or we have a set of axons or
+
+ align:start position:0%
+ones or we have a set of axons or
+ 
+
+ align:start position:0%
+ones or we have a set of axons or
+pathways we suppress those and amplify
+
+ align:start position:0%
+pathways we suppress those and amplify
+ 
+
+ align:start position:0%
+pathways we suppress those and amplify
+those but what about a representation
+
+ align:start position:0%
+those but what about a representation
+ 
+
+ align:start position:0%
+those but what about a representation
+which is more distributed where you have
+
+ align:start position:0%
+which is more distributed where you have
+ 
+
+ align:start position:0%
+which is more distributed where you have
+to really suppress states rather than
+
+ align:start position:0%
+to really suppress states rather than
+ 
+
+ align:start position:0%
+to really suppress states rather than
+no.11 populations so I just want one go
+
+ align:start position:0%
+no.11 populations so I just want one go
+ 
+
+ align:start position:0%
+no.11 populations so I just want one go
+again it's a complicated architecture
+
+ align:start position:0%
+again it's a complicated architecture
+ 
+
+ align:start position:0%
+again it's a complicated architecture
+but basically we're using some some sort
+
+ align:start position:0%
+but basically we're using some some sort
+ 
+
+ align:start position:0%
+but basically we're using some some sort
+of a mixed representation where we take
+
+ align:start position:0%
+of a mixed representation where we take
+ 
+
+ align:start position:0%
+of a mixed representation where we take
+the sensory input and categorical or
+
+ align:start position:0%
+the sensory input and categorical or
+ 
+
+ align:start position:0%
+the sensory input and categorical or
+contextual input mix them non-linearity
+
+ align:start position:0%
+contextual input mix them non-linearity
+ 
+
+ align:start position:0%
+contextual input mix them non-linearity
+use them to clean it and and propagate
+
+ align:start position:0%
+use them to clean it and and propagate
+ 
+
+ align:start position:0%
+use them to clean it and and propagate
+this so it's a more complicated
+
+ align:start position:0%
+this so it's a more complicated
+ 
+
+ align:start position:0%
+this so it's a more complicated
+architecture but it works beautifully
+
+ align:start position:0%
+architecture but it works beautifully
+ 
+
+ align:start position:0%
+architecture but it works beautifully
+let me show you here an example you have
+
+ align:start position:0%
+let me show you here an example you have
+ 
+
+ align:start position:0%
+let me show you here an example you have
+a flavor of what we are doing so now the
+
+ align:start position:0%
+a flavor of what we are doing so now the
+ 
+
+ align:start position:0%
+a flavor of what we are doing so now the
+input we have we have those 900 spheres
+
+ align:start position:0%
+input we have we have those 900 spheres
+ 
+
+ align:start position:0%
+input we have we have those 900 spheres
+or templates but they are organized
+
+ align:start position:0%
+or templates but they are organized
+ 
+
+ align:start position:0%
+or templates but they are organized
+- with 30 categories and 30 tokens per
+
+ align:start position:0%
+- with 30 categories and 30 tokens per
+ 
+
+ align:start position:0%
+- with 30 categories and 30 tokens per
+category okay
+
+ align:start position:0%
+category okay
+ 
+
+ align:start position:0%
+category okay
+now the the tokens which are the actual
+
+ align:start position:0%
+now the the tokens which are the actual
+ 
+
+ align:start position:0%
+now the the tokens which are the actual
+sensory inputs are represented but let's
+
+ align:start position:0%
+sensory inputs are represented but let's
+ 
+
+ align:start position:0%
+sensory inputs are represented but let's
+say 200 neurons and you have a small
+
+ align:start position:0%
+say 200 neurons and you have a small
+ 
+
+ align:start position:0%
+say 200 neurons and you have a small
+number of neurons representing category
+
+ align:start position:0%
+number of neurons representing category
+ 
+
+ align:start position:0%
+number of neurons representing category
+maybe 20s enough so that's important
+
+ align:start position:0%
+maybe 20s enough so that's important
+ 
+
+ align:start position:0%
+maybe 20s enough so that's important
+that you don't have to really expand
+
+ align:start position:0%
+that you don't have to really expand
+ 
+
+ align:start position:0%
+that you don't have to really expand
+dramatically the representation okay so
+
+ align:start position:0%
+dramatically the representation okay so
+ 
+
+ align:start position:0%
+dramatically the representation okay so
+this is the input and now we have very
+
+ align:start position:0%
+this is the input and now we have very
+ 
+
+ align:start position:0%
+this is the input and now we have very
+noisy inputs if you look at the readout
+
+ align:start position:0%
+noisy inputs if you look at the readout
+ 
+
+ align:start position:0%
+noisy inputs if you look at the readout
+this is layers here and there is read
+
+ align:start position:0%
+this is layers here and there is read
+ 
+
+ align:start position:0%
+this is layers here and there is read
+out arrow if you do it on the input
+
+ align:start position:0%
+out arrow if you do it on the input
+ 
+
+ align:start position:0%
+out arrow if you do it on the input
+layer or any subsequent layer here but
+
+ align:start position:0%
+layer or any subsequent layer here but
+ 
+
+ align:start position:0%
+layer or any subsequent layer here but
+without top-down information we
+
+ align:start position:0%
+without top-down information we
+ 
+
+ align:start position:0%
+without top-down information we
+structured interactions and all that I
+
+ align:start position:0%
+structured interactions and all that I
+ 
+
+ align:start position:0%
+structured interactions and all that I
+told you this is such a noisy input
+
+ align:start position:0%
+told you this is such a noisy input
+ 
+
+ align:start position:0%
+told you this is such a noisy input
+where the performance is basically 0.5
+
+ align:start position:0%
+where the performance is basically 0.5
+ 
+
+ align:start position:0%
+where the performance is basically 0.5
+okay there is nothing that you can do
+
+ align:start position:0%
+okay there is nothing that you can do
+ 
+
+ align:start position:0%
+okay there is nothing that you can do
+without top-down information in this
+
+ align:start position:0%
+without top-down information in this
+ 
+
+ align:start position:0%
+without top-down information in this
+network you can ask what what will be
+
+ align:start position:0%
+network you can ask what what will be
+ 
+
+ align:start position:0%
+network you can ask what what will be
+the performance if you have an ideal
+
+ align:start position:0%
+the performance if you have an ideal
+ 
+
+ align:start position:0%
+the performance if you have an ideal
+observer that looks at the in noisy
+
+ align:start position:0%
+observer that looks at the in noisy
+ 
+
+ align:start position:0%
+observer that looks at the in noisy
+input and makes maximum likelihood
+
+ align:start position:0%
+input and makes maximum likelihood
+ 
+
+ align:start position:0%
+input and makes maximum likelihood
+maximum likelihood categorization well
+
+ align:start position:0%
+maximum likelihood categorization well
+ 
+
+ align:start position:0%
+maximum likelihood categorization well
+then it will do much better also not
+
+ align:start position:0%
+then it will do much better also not
+ 
+
+ align:start position:0%
+then it will do much better also not
+zero so these are this level okay this
+
+ align:start position:0%
+zero so these are this level okay this
+ 
+
+ align:start position:0%
+zero so these are this level okay this
+is this higher error is in virtue of the
+
+ align:start position:0%
+is this higher error is in virtue of the
+ 
+
+ align:start position:0%
+is this higher error is in virtue of the
+fact that this network is still not
+
+ align:start position:0%
+fact that this network is still not
+ 
+
+ align:start position:0%
+fact that this network is still not
+doing what an optimal maximum likelihood
+
+ align:start position:0%
+doing what an optimal maximum likelihood
+ 
+
+ align:start position:0%
+doing what an optimal maximum likelihood
+observer will do okay so this is the
+
+ align:start position:0%
+observer will do okay so this is the
+ 
+
+ align:start position:0%
+observer will do okay so this is the
+network this is a maximum likelihood
+
+ align:start position:0%
+network this is a maximum likelihood
+ 
+
+ align:start position:0%
+network this is a maximum likelihood
+without both of them without extra
+
+ align:start position:0%
+without both of them without extra
+ 
+
+ align:start position:0%
+without both of them without extra
+top-down information and in the network
+
+ align:start position:0%
+top-down information and in the network
+ 
+
+ align:start position:0%
+top-down information and in the network
+that I kind of hinted about if you add
+
+ align:start position:0%
+that I kind of hinted about if you add
+ 
+
+ align:start position:0%
+that I kind of hinted about if you add
+this top-down information by generating
+
+ align:start position:0%
+this top-down information by generating
+ 
+
+ align:start position:0%
+this top-down information by generating
+mixed representations you get the
+
+ align:start position:0%
+mixed representations you get the
+ 
+
+ align:start position:0%
+mixed representations you get the
+performance which is really dramatic
+
+ align:start position:0%
+performance which is really dramatic
+ 
+
+ align:start position:0%
+performance which is really dramatic
+dramatically improves and as you keep
+
+ align:start position:0%
+dramatically improves and as you keep
+ 
+
+ align:start position:0%
+dramatically improves and as you keep
+doing it one layer from another you
+
+ align:start position:0%
+doing it one layer from another you
+ 
+
+ align:start position:0%
+doing it one layer from another you
+really get a very very nice performance
+
+ align:start position:0%
+really get a very very nice performance
+ 
+
+ align:start position:0%
+really get a very very nice performance
+okay so maybe did summarize the day's
+
+ align:start position:0%
+okay so maybe did summarize the day's
+ 
+
+ align:start position:0%
+okay so maybe did summarize the day's
+gonna the whole the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's one more before summarizing yeah
+
+ align:start position:0%
+there's one more before summarizing yeah
+ 
+
+ align:start position:0%
+there's one more before summarizing yeah
+okay before that okay so to two points
+
+ align:start position:0%
+okay before that okay so to two points
+ 
+
+ align:start position:0%
+okay before that okay so to two points
+to bear in mind one of them is that what
+
+ align:start position:0%
+to bear in mind one of them is that what
+ 
+
+ align:start position:0%
+to bear in mind one of them is that what
+I discussed to you today relies on on on
+
+ align:start position:0%
+I discussed to you today relies on on on
+ 
+
+ align:start position:0%
+I discussed to you today relies on on on
+assuming either random comparing random
+
+ align:start position:0%
+assuming either random comparing random
+ 
+
+ align:start position:0%
+assuming either random comparing random
+projection to unsupervised learning of a
+
+ align:start position:0%
+projection to unsupervised learning of a
+ 
+
+ align:start position:0%
+projection to unsupervised learning of a
+very simple type of kind of hedging type
+
+ align:start position:0%
+very simple type of kind of hedging type
+ 
+
+ align:start position:0%
+very simple type of kind of hedging type
+the output can be happier nor perceptron
+
+ align:start position:0%
+the output can be happier nor perceptron
+ 
+
+ align:start position:0%
+the output can be happier nor perceptron
+or SVM and so on you could ask what
+
+ align:start position:0%
+or SVM and so on you could ask what
+ 
+
+ align:start position:0%
+or SVM and so on you could ask what
+happens if you use learning rules more
+
+ align:start position:0%
+happens if you use learning rules more
+ 
+
+ align:start position:0%
+happens if you use learning rules more
+sophisticated learning goals for the
+
+ align:start position:0%
+sophisticated learning goals for the
+ 
+
+ align:start position:0%
+sophisticated learning goals for the
+unsupervised wait some of them we've
+
+ align:start position:0%
+unsupervised wait some of them we've
+ 
+
+ align:start position:0%
+unsupervised wait some of them we've
+studied but anyway that's something
+
+ align:start position:0%
+studied but anyway that's something
+ 
+
+ align:start position:0%
+studied but anyway that's something
+which is important to to explore and and
+
+ align:start position:0%
+which is important to to explore and and
+ 
+
+ align:start position:0%
+which is important to to explore and and
+another very important issue for
+
+ align:start position:0%
+another very important issue for
+ 
+
+ align:start position:0%
+another very important issue for
+thinking about object recognition in
+
+ align:start position:0%
+thinking about object recognition in
+ 
+
+ align:start position:0%
+thinking about object recognition in
+vision and and in other real-life
+
+ align:start position:0%
+vision and and in other real-life
+ 
+
+ align:start position:0%
+vision and and in other real-life
+problem is input statistics because what
+
+ align:start position:0%
+problem is input statistics because what
+ 
+
+ align:start position:0%
+problem is input statistics because what
+we assumed is a very simple mixture of
+
+ align:start position:0%
+we assumed is a very simple mixture of
+ 
+
+ align:start position:0%
+we assumed is a very simple mixture of
+Gaussian model so you can think about
+
+ align:start position:0%
+Gaussian model so you can think about
+ 
+
+ align:start position:0%
+Gaussian model so you can think about
+the task of the network is to take
+
+ align:start position:0%
+the task of the network is to take
+ 
+
+ align:start position:0%
+the task of the network is to take
+they're in violation away from the
+
+ align:start position:0%
+they're in violation away from the
+ 
+
+ align:start position:0%
+they're in violation away from the
+center this spherical valuation and to
+
+ align:start position:0%
+center this spherical valuation and to
+ 
+
+ align:start position:0%
+center this spherical valuation and to
+generate a presentation which is
+
+ align:start position:0%
+generate a presentation which is
+ 
+
+ align:start position:0%
+generate a presentation which is
+environed to that but this is a very
+
+ align:start position:0%
+environed to that but this is a very
+ 
+
+ align:start position:0%
+environed to that but this is a very
+simple invent
+
+ align:start position:0%
+simple invent
+ 
+
+ align:start position:0%
+simple invent
+the invariance was simply restricted to
+
+ align:start position:0%
+the invariance was simply restricted to
+ 
+
+ align:start position:0%
+the invariance was simply restricted to
+this simple geometric structures more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems which are closer to what
+
+ align:start position:0%
+problems which are closer to what
+ 
+
+ align:start position:0%
+problems which are closer to what
+real-life problems are will have inputs
+
+ align:start position:0%
+real-life problems are will have inputs
+ 
+
+ align:start position:0%
+real-life problems are will have inputs
+which are essentially have some
+
+ align:start position:0%
+which are essentially have some
+ 
+
+ align:start position:0%
+which are essentially have some
+structure but the structure can be a
+
+ align:start position:0%
+structure but the structure can be a
+ 
+
+ align:start position:0%
+structure but the structure can be a
+variety of shapes each one of them
+
+ align:start position:0%
+variety of shapes each one of them
+ 
+
+ align:start position:0%
+variety of shapes each one of them
+correspond to an object or cluster or a
+
+ align:start position:0%
+correspond to an object or cluster or a
+ 
+
+ align:start position:0%
+correspond to an object or cluster or a
+manifold representing an entity a
+
+ align:start position:0%
+manifold representing an entity a
+ 
+
+ align:start position:0%
+manifold representing an entity a
+perceptual entity but how you go from
+
+ align:start position:0%
+perceptual entity but how you go from
+ 
+
+ align:start position:0%
+perceptual entity but how you go from
+this nice simple
+
+ align:start position:0%
+this nice simple
+ 
+
+ align:start position:0%
+this nice simple
+problem of this spherical environment
+
+ align:start position:0%
+problem of this spherical environment
+ 
+
+ align:start position:0%
+problem of this spherical environment
+to those problems it's of course a
+
+ align:start position:0%
+to those problems it's of course a
+ 
+
+ align:start position:0%
+to those problems it's of course a
+challenging problem and that's the work
+
+ align:start position:0%
+challenging problem and that's the work
+ 
+
+ align:start position:0%
+challenging problem and that's the work
+which we are now ongoing work also with
+
+ align:start position:0%
+which we are now ongoing work also with
+ 
+
+ align:start position:0%
+which we are now ongoing work also with
+us with so Eun Chun and then Lee but
+
+ align:start position:0%
+us with so Eun Chun and then Lee but
+ 
+
+ align:start position:0%
+us with so Eun Chun and then Lee but
+it's a story which is still at the stage
+
+ align:start position:0%
+it's a story which is still at the stage
+ 
+
+ align:start position:0%
+it's a story which is still at the stage
+of unfolding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/QuWEUrIzZNs.txt b/QuWEUrIzZNs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7337338cd4463ecfa5e555720f5ccc83bfbd40db
--- /dev/null
+++ b/QuWEUrIzZNs.txt
@@ -0,0 +1,11683 @@
+align:start position:0%
+ 
+okay let's go ahead and get
+
+ align:start position:0%
+okay let's go ahead and get
+ 
+
+ align:start position:0%
+okay let's go ahead and get
+started uh today I'm going to talk about
+
+ align:start position:0%
+started uh today I'm going to talk about
+ 
+
+ align:start position:0%
+started uh today I'm going to talk about
+uh start talking about random
+
+ align:start position:0%
+uh start talking about random
+ 
+
+ align:start position:0%
+uh start talking about random
+variables and uh distributions of random
+
+ align:start position:0%
+variables and uh distributions of random
+ 
+
+ align:start position:0%
+variables and uh distributions of random
+variables and uh at the end I will
+
+ align:start position:0%
+variables and uh at the end I will
+ 
+
+ align:start position:0%
+variables and uh at the end I will
+probably also uh get to a discussion of
+
+ align:start position:0%
+probably also uh get to a discussion of
+ 
+
+ align:start position:0%
+probably also uh get to a discussion of
+joint
+
+ align:start position:0%
+joint
+ 
+
+ align:start position:0%
+joint
+distributions um Tuesday then Esther's
+
+ align:start position:0%
+distributions um Tuesday then Esther's
+ 
+
+ align:start position:0%
+distributions um Tuesday then Esther's
+going to be um lecturing she's going to
+
+ align:start position:0%
+going to be um lecturing she's going to
+ 
+
+ align:start position:0%
+going to be um lecturing she's going to
+do a bunch of examples um and also talk
+
+ align:start position:0%
+do a bunch of examples um and also talk
+ 
+
+ align:start position:0%
+do a bunch of examples um and also talk
+about um you know some uh as she as she
+
+ align:start position:0%
+about um you know some uh as she as she
+ 
+
+ align:start position:0%
+about um you know some uh as she as she
+mentioned last time some data sources
+
+ align:start position:0%
+mentioned last time some data sources
+ 
+
+ align:start position:0%
+mentioned last time some data sources
+and techniques for Gathering data such
+
+ align:start position:0%
+and techniques for Gathering data such
+ 
+
+ align:start position:0%
+and techniques for Gathering data such
+as web scraping uh and then um she's
+
+ align:start position:0%
+as web scraping uh and then um she's
+ 
+
+ align:start position:0%
+as web scraping uh and then um she's
+going to play around with data a little
+
+ align:start position:0%
+going to play around with data a little
+ 
+
+ align:start position:0%
+going to play around with data a little
+bit and uh do some uh techniques that
+
+ align:start position:0%
+bit and uh do some uh techniques that
+ 
+
+ align:start position:0%
+bit and uh do some uh techniques that
+that are essentially used histograms
+
+ align:start position:0%
+that are essentially used histograms
+ 
+
+ align:start position:0%
+that are essentially used histograms
+kernel density plots so forth uh some te
+
+ align:start position:0%
+kernel density plots so forth uh some te
+ 
+
+ align:start position:0%
+kernel density plots so forth uh some te
+techniques that we essentially use to um
+
+ align:start position:0%
+techniques that we essentially use to um
+ 
+
+ align:start position:0%
+techniques that we essentially use to um
+to estimate or
+
+ align:start position:0%
+to estimate or
+ 
+
+ align:start position:0%
+to estimate or
+approximate um things like uh
+
+ align:start position:0%
+approximate um things like uh
+ 
+
+ align:start position:0%
+approximate um things like uh
+distributions of random variables okay
+
+ align:start position:0%
+distributions of random variables okay
+ 
+
+ align:start position:0%
+distributions of random variables okay
+and then uh Wednesday I'll be um
+
+ align:start position:0%
+and then uh Wednesday I'll be um
+ 
+
+ align:start position:0%
+and then uh Wednesday I'll be um
+lecturing again we'll talk about
+
+ align:start position:0%
+lecturing again we'll talk about
+ 
+
+ align:start position:0%
+lecturing again we'll talk about
+independence of random variables
+
+ align:start position:0%
+independence of random variables
+ 
+
+ align:start position:0%
+independence of random variables
+conditional distributions and maybe some
+
+ align:start position:0%
+conditional distributions and maybe some
+ 
+
+ align:start position:0%
+conditional distributions and maybe some
+other stuff too okay the recitation on
+
+ align:start position:0%
+other stuff too okay the recitation on
+ 
+
+ align:start position:0%
+other stuff too okay the recitation on
+Friday is going to be Contin uation of
+
+ align:start position:0%
+Friday is going to be Contin uation of
+ 
+
+ align:start position:0%
+Friday is going to be Contin uation of
+uh the sort of our tutorial and there
+
+ align:start position:0%
+uh the sort of our tutorial and there
+ 
+
+ align:start position:0%
+uh the sort of our tutorial and there
+could be um depending on exactly what
+
+ align:start position:0%
+could be um depending on exactly what
+ 
+
+ align:start position:0%
+could be um depending on exactly what
+gets put on the problem set there could
+
+ align:start position:0%
+gets put on the problem set there could
+ 
+
+ align:start position:0%
+gets put on the problem set there could
+be a couple little uh sort of hints
+
+ align:start position:0%
+be a couple little uh sort of hints
+ 
+
+ align:start position:0%
+be a couple little uh sort of hints
+about um you know uh issues in
+
+ align:start position:0%
+about um you know uh issues in
+ 
+
+ align:start position:0%
+about um you know uh issues in
+probability that you might need for the
+
+ align:start position:0%
+probability that you might need for the
+ 
+
+ align:start position:0%
+probability that you might need for the
+problem set in the recitation on Friday
+
+ align:start position:0%
+problem set in the recitation on Friday
+ 
+
+ align:start position:0%
+problem set in the recitation on Friday
+but it's mostly going to be on R okay
+
+ align:start position:0%
+but it's mostly going to be on R okay
+ 
+
+ align:start position:0%
+but it's mostly going to be on R okay
+questions before I get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+started okay so as I I said I'm going to
+
+ align:start position:0%
+started okay so as I I said I'm going to
+ 
+
+ align:start position:0%
+started okay so as I I said I'm going to
+start talking about this uh sort of
+
+ align:start position:0%
+start talking about this uh sort of
+ 
+
+ align:start position:0%
+start talking about this uh sort of
+mathematical construct uh called random
+
+ align:start position:0%
+mathematical construct uh called random
+ 
+
+ align:start position:0%
+mathematical construct uh called random
+variable so often times there's some
+
+ align:start position:0%
+variable so often times there's some
+ 
+
+ align:start position:0%
+variable so often times there's some
+numerical characteristic in the sample
+
+ align:start position:0%
+numerical characteristic in the sample
+ 
+
+ align:start position:0%
+numerical characteristic in the sample
+space that we're interested in so we've
+
+ align:start position:0%
+space that we're interested in so we've
+ 
+
+ align:start position:0%
+space that we're interested in so we've
+talked about a lot of you know we've
+
+ align:start position:0%
+talked about a lot of you know we've
+ 
+
+ align:start position:0%
+talked about a lot of you know we've
+seen examples of different sample spaces
+
+ align:start position:0%
+seen examples of different sample spaces
+ 
+
+ align:start position:0%
+seen examples of different sample spaces
+and some of them have you know we could
+
+ align:start position:0%
+and some of them have you know we could
+ 
+
+ align:start position:0%
+and some of them have you know we could
+we can talk about a numerical
+
+ align:start position:0%
+we can talk about a numerical
+ 
+
+ align:start position:0%
+we can talk about a numerical
+characteristic of the sample space that
+
+ align:start position:0%
+characteristic of the sample space that
+ 
+
+ align:start position:0%
+characteristic of the sample space that
+we might be interested in like the sum
+
+ align:start position:0%
+we might be interested in like the sum
+ 
+
+ align:start position:0%
+we might be interested in like the sum
+of the faces of two dice or the number
+
+ align:start position:0%
+of the faces of two dice or the number
+ 
+
+ align:start position:0%
+of the faces of two dice or the number
+of threep point field goals that Steph
+
+ align:start position:0%
+of threep point field goals that Steph
+ 
+
+ align:start position:0%
+of threep point field goals that Steph
+Curry makes in his next six attempts the
+
+ align:start position:0%
+Curry makes in his next six attempts the
+ 
+
+ align:start position:0%
+Curry makes in his next six attempts the
+number of vegetarian toppings I get on
+
+ align:start position:0%
+number of vegetarian toppings I get on
+ 
+
+ align:start position:0%
+number of vegetarian toppings I get on
+my pizza um and it's uh there's an sort
+
+ align:start position:0%
+my pizza um and it's uh there's an sort
+ 
+
+ align:start position:0%
+my pizza um and it's uh there's an sort
+of an important and useful mathematical
+
+ align:start position:0%
+of an important and useful mathematical
+ 
+
+ align:start position:0%
+of an important and useful mathematical
+construct that we use to analyze those
+
+ align:start position:0%
+construct that we use to analyze those
+ 
+
+ align:start position:0%
+construct that we use to analyze those
+numerical characteristics and it's
+
+ align:start position:0%
+numerical characteristics and it's
+ 
+
+ align:start position:0%
+numerical characteristics and it's
+called a random variable okay so a
+
+ align:start position:0%
+called a random variable okay so a
+ 
+
+ align:start position:0%
+called a random variable okay so a
+random variable is a real valued
+
+ align:start position:0%
+random variable is a real valued
+ 
+
+ align:start position:0%
+random variable is a real valued
+function whose domain is the sample
+
+ align:start position:0%
+function whose domain is the sample
+ 
+
+ align:start position:0%
+function whose domain is the sample
+space and um you know as I said it it
+
+ align:start position:0%
+space and um you know as I said it it
+ 
+
+ align:start position:0%
+space and um you know as I said it it
+sort of uh it it has a uh it's real
+
+ align:start position:0%
+sort of uh it it has a uh it's real
+ 
+
+ align:start position:0%
+sort of uh it it has a uh it's real
+valued
+
+ align:start position:0%
+valued
+ 
+
+ align:start position:0%
+valued
+so it goes from in particular the sample
+
+ align:start position:0%
+so it goes from in particular the sample
+ 
+
+ align:start position:0%
+so it goes from in particular the sample
+space to the real
+
+ align:start position:0%
+space to the real
+ 
+
+ align:start position:0%
+space to the real
+line so I don't know if this graphic
+
+ align:start position:0%
+line so I don't know if this graphic
+ 
+
+ align:start position:0%
+line so I don't know if this graphic
+sort of helps you um kind of think about
+
+ align:start position:0%
+sort of helps you um kind of think about
+ 
+
+ align:start position:0%
+sort of helps you um kind of think about
+the relationship between a probability
+
+ align:start position:0%
+the relationship between a probability
+ 
+
+ align:start position:0%
+the relationship between a probability
+in a random variable in a sample space
+
+ align:start position:0%
+in a random variable in a sample space
+ 
+
+ align:start position:0%
+in a random variable in a sample space
+and and the unit interval and the real
+
+ align:start position:0%
+and and the unit interval and the real
+ 
+
+ align:start position:0%
+and and the unit interval and the real
+line it's all this is probably still
+
+ align:start position:0%
+line it's all this is probably still
+ 
+
+ align:start position:0%
+line it's all this is probably still
+abstra pretty abstract to you and we'll
+
+ align:start position:0%
+abstra pretty abstract to you and we'll
+ 
+
+ align:start position:0%
+abstra pretty abstract to you and we'll
+go through examples but at least for me
+
+ align:start position:0%
+go through examples but at least for me
+ 
+
+ align:start position:0%
+go through examples but at least for me
+this sort of this kind of GRA graic
+
+ align:start position:0%
+this sort of this kind of GRA graic
+ 
+
+ align:start position:0%
+this sort of this kind of GRA graic
+helps me think about what the difference
+
+ align:start position:0%
+helps me think about what the difference
+ 
+
+ align:start position:0%
+helps me think about what the difference
+between a probability like we defined
+
+ align:start position:0%
+between a probability like we defined
+ 
+
+ align:start position:0%
+between a probability like we defined
+last time is and a random variable so a
+
+ align:start position:0%
+last time is and a random variable so a
+ 
+
+ align:start position:0%
+last time is and a random variable so a
+probability goes from the set of all
+
+ align:start position:0%
+probability goes from the set of all
+ 
+
+ align:start position:0%
+probability goes from the set of all
+subsets of the sample space into the
+
+ align:start position:0%
+subsets of the sample space into the
+ 
+
+ align:start position:0%
+subsets of the sample space into the
+unit interval okay so it always has
+
+ align:start position:0%
+unit interval okay so it always has
+ 
+
+ align:start position:0%
+unit interval okay so it always has
+values between zero and one as we saw
+
+ align:start position:0%
+values between zero and one as we saw
+ 
+
+ align:start position:0%
+values between zero and one as we saw
+last time a random variable is um it's
+
+ align:start position:0%
+last time a random variable is um it's
+ 
+
+ align:start position:0%
+last time a random variable is um it's
+it goes from the sample space to the
+
+ align:start position:0%
+it goes from the sample space to the
+ 
+
+ align:start position:0%
+it goes from the sample space to the
+real line line and it's just some
+
+ align:start position:0%
+real line line and it's just some
+ 
+
+ align:start position:0%
+real line line and it's just some
+numerical characteristic of the sample
+
+ align:start position:0%
+numerical characteristic of the sample
+ 
+
+ align:start position:0%
+numerical characteristic of the sample
+space that we care about okay and the
+
+ align:start position:0%
+space that we care about okay and the
+ 
+
+ align:start position:0%
+space that we care about okay and the
+probability on the left
+
+ align:start position:0%
+probability on the left
+ 
+
+ align:start position:0%
+probability on the left
+induces the the the distribution of our
+
+ align:start position:0%
+induces the the the distribution of our
+ 
+
+ align:start position:0%
+induces the the the distribution of our
+random variable okay so I'll be more
+
+ align:start position:0%
+random variable okay so I'll be more
+ 
+
+ align:start position:0%
+random variable okay so I'll be more
+clear about that when we go through
+
+ align:start position:0%
+clear about that when we go through
+ 
+
+ align:start position:0%
+clear about that when we go through
+examples and and that will become much
+
+ align:start position:0%
+examples and and that will become much
+ 
+
+ align:start position:0%
+examples and and that will become much
+more concrete but basically we just
+
+ align:start position:0%
+more concrete but basically we just
+ 
+
+ align:start position:0%
+more concrete but basically we just
+think about um you know sort of the
+
+ align:start position:0%
+think about um you know sort of the
+ 
+
+ align:start position:0%
+think about um you know sort of the
+probability that exists that that's
+
+ align:start position:0%
+probability that exists that that's
+ 
+
+ align:start position:0%
+probability that exists that that's
+defined on this sample space as inducing
+
+ align:start position:0%
+defined on this sample space as inducing
+ 
+
+ align:start position:0%
+defined on this sample space as inducing
+a distribution of our random variable
+
+ align:start position:0%
+a distribution of our random variable
+ 
+
+ align:start position:0%
+a distribution of our random variable
+okay okay so all of the uh examples
+
+ align:start position:0%
+okay okay so all of the uh examples
+ 
+
+ align:start position:0%
+okay okay so all of the uh examples
+we've seen so far all of the probability
+
+ align:start position:0%
+we've seen so far all of the probability
+ 
+
+ align:start position:0%
+we've seen so far all of the probability
+examples uh would give rise to a type of
+
+ align:start position:0%
+examples uh would give rise to a type of
+ 
+
+ align:start position:0%
+examples uh would give rise to a type of
+random variable called discret okay and
+
+ align:start position:0%
+random variable called discret okay and
+ 
+
+ align:start position:0%
+random variable called discret okay and
+that's a t that's a random variable that
+
+ align:start position:0%
+that's a t that's a random variable that
+ 
+
+ align:start position:0%
+that's a t that's a random variable that
+takes on a finite or countably infinite
+
+ align:start position:0%
+takes on a finite or countably infinite
+ 
+
+ align:start position:0%
+takes on a finite or countably infinite
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+values so uh the the examples that I
+
+ align:start position:0%
+values so uh the the examples that I
+ 
+
+ align:start position:0%
+values so uh the the examples that I
+gave you on the previous slide you know
+
+ align:start position:0%
+gave you on the previous slide you know
+ 
+
+ align:start position:0%
+gave you on the previous slide you know
+sort of the number of vegetarian
+
+ align:start position:0%
+sort of the number of vegetarian
+ 
+
+ align:start position:0%
+sort of the number of vegetarian
+toppings that I'm getting it's not going
+
+ align:start position:0%
+toppings that I'm getting it's not going
+ 
+
+ align:start position:0%
+toppings that I'm getting it's not going
+to be you know it's going to be uh an
+
+ align:start position:0%
+to be you know it's going to be uh an
+ 
+
+ align:start position:0%
+to be you know it's going to be uh an
+integer value for instance discrete
+
+ align:start position:0%
+integer value for instance discrete
+ 
+
+ align:start position:0%
+integer value for instance discrete
+random variables don't have to all be
+
+ align:start position:0%
+random variables don't have to all be
+ 
+
+ align:start position:0%
+random variables don't have to all be
+integers but uh something that can only
+
+ align:start position:0%
+integers but uh something that can only
+ 
+
+ align:start position:0%
+integers but uh something that can only
+take on the value of integers for
+
+ align:start position:0%
+take on the value of integers for
+ 
+
+ align:start position:0%
+take on the value of integers for
+instance would be a discrete random
+
+ align:start position:0%
+instance would be a discrete random
+ 
+
+ align:start position:0%
+instance would be a discrete random
+variable okay we can also however
+
+ align:start position:0%
+variable okay we can also however
+ 
+
+ align:start position:0%
+variable okay we can also however
+consider a natural generalization or
+
+ align:start position:0%
+consider a natural generalization or
+ 
+
+ align:start position:0%
+consider a natural generalization or
+kind of depending on the the
+
+ align:start position:0%
+kind of depending on the the
+ 
+
+ align:start position:0%
+kind of depending on the the
+mathematical framework you're using a
+
+ align:start position:0%
+mathematical framework you're using a
+ 
+
+ align:start position:0%
+mathematical framework you're using a
+different flavor of this
+
+ align:start position:0%
+different flavor of this
+ 
+
+ align:start position:0%
+different flavor of this
+construct and um and that's uh allowing
+
+ align:start position:0%
+construct and um and that's uh allowing
+ 
+
+ align:start position:0%
+construct and um and that's uh allowing
+a random variable to take on any value
+
+ align:start position:0%
+a random variable to take on any value
+ 
+
+ align:start position:0%
+a random variable to take on any value
+in some interval bounded or unbounded of
+
+ align:start position:0%
+in some interval bounded or unbounded of
+ 
+
+ align:start position:0%
+in some interval bounded or unbounded of
+the real line okay and this is called a
+
+ align:start position:0%
+the real line okay and this is called a
+ 
+
+ align:start position:0%
+the real line okay and this is called a
+continuous random variable so in this uh
+
+ align:start position:0%
+continuous random variable so in this uh
+ 
+
+ align:start position:0%
+continuous random variable so in this uh
+in this class and in most in a lot of
+
+ align:start position:0%
+in this class and in most in a lot of
+ 
+
+ align:start position:0%
+in this class and in most in a lot of
+Statistics classes in fact um we will
+
+ align:start position:0%
+Statistics classes in fact um we will
+ 
+
+ align:start position:0%
+Statistics classes in fact um we will
+mostly deal with uh continuous random
+
+ align:start position:0%
+mostly deal with uh continuous random
+ 
+
+ align:start position:0%
+mostly deal with uh continuous random
+variables and there are a couple reasons
+
+ align:start position:0%
+variables and there are a couple reasons
+ 
+
+ align:start position:0%
+variables and there are a couple reasons
+for this um this is partly because there
+
+ align:start position:0%
+for this um this is partly because there
+ 
+
+ align:start position:0%
+for this um this is partly because there
+are lots of discrete random variables in
+
+ align:start position:0%
+are lots of discrete random variables in
+ 
+
+ align:start position:0%
+are lots of discrete random variables in
+the real world that can be adequately
+
+ align:start position:0%
+the real world that can be adequately
+ 
+
+ align:start position:0%
+the real world that can be adequately
+approximated with continuous random
+
+ align:start position:0%
+approximated with continuous random
+ 
+
+ align:start position:0%
+approximated with continuous random
+variables okay and so then that that's
+
+ align:start position:0%
+variables okay and so then that that's
+ 
+
+ align:start position:0%
+variables okay and so then that that's
+uh sort of um handy if we're sort of uh
+
+ align:start position:0%
+uh sort of um handy if we're sort of uh
+ 
+
+ align:start position:0%
+uh sort of um handy if we're sort of uh
+we can do everything in the in the
+
+ align:start position:0%
+we can do everything in the in the
+ 
+
+ align:start position:0%
+we can do everything in the in the
+framework of a continuous random
+
+ align:start position:0%
+framework of a continuous random
+ 
+
+ align:start position:0%
+framework of a continuous random
+variable the other thing is that uh
+
+ align:start position:0%
+variable the other thing is that uh
+ 
+
+ align:start position:0%
+variable the other thing is that uh
+sometimes the the sort of math is just
+
+ align:start position:0%
+sometimes the the sort of math is just
+ 
+
+ align:start position:0%
+sometimes the the sort of math is just
+simply easier to do um when you're doing
+
+ align:start position:0%
+simply easier to do um when you're doing
+ 
+
+ align:start position:0%
+simply easier to do um when you're doing
+when you're considering um fun
+
+ align:start position:0%
+when you're considering um fun
+ 
+
+ align:start position:0%
+when you're considering um fun
+complicated functions of random
+
+ align:start position:0%
+complicated functions of random
+ 
+
+ align:start position:0%
+complicated functions of random
+variables uh for instance uh Sometimes
+
+ align:start position:0%
+variables uh for instance uh Sometimes
+ 
+
+ align:start position:0%
+variables uh for instance uh Sometimes
+using continuous random variables is
+
+ align:start position:0%
+using continuous random variables is
+ 
+
+ align:start position:0%
+using continuous random variables is
+just a lot lot simpler than uh doing
+
+ align:start position:0%
+just a lot lot simpler than uh doing
+ 
+
+ align:start position:0%
+just a lot lot simpler than uh doing
+everything with discret random
+
+ align:start position:0%
+everything with discret random
+ 
+
+ align:start position:0%
+everything with discret random
+variables okay so we will uh today we're
+
+ align:start position:0%
+variables okay so we will uh today we're
+ 
+
+ align:start position:0%
+variables okay so we will uh today we're
+going to see examples of discrete random
+
+ align:start position:0%
+going to see examples of discrete random
+ 
+
+ align:start position:0%
+going to see examples of discrete random
+variables continuous random variables
+
+ align:start position:0%
+variables continuous random variables
+ 
+
+ align:start position:0%
+variables continuous random variables
+and we'll continue to see them
+
+ align:start position:0%
+and we'll continue to see them
+ 
+
+ align:start position:0%
+and we'll continue to see them
+throughout the semester but as we go
+
+ align:start position:0%
+throughout the semester but as we go
+ 
+
+ align:start position:0%
+throughout the semester but as we go
+through the semester we'll see more and
+
+ align:start position:0%
+through the semester we'll see more and
+ 
+
+ align:start position:0%
+through the semester we'll see more and
+more examples of continuous random
+
+ align:start position:0%
+more examples of continuous random
+ 
+
+ align:start position:0%
+more examples of continuous random
+variables okay so um for discrete random
+
+ align:start position:0%
+variables okay so um for discrete random
+ 
+
+ align:start position:0%
+variables okay so um for discrete random
+variable we can often start with a
+
+ align:start position:0%
+variable we can often start with a
+ 
+
+ align:start position:0%
+variable we can often start with a
+verbal description and then BAS based on
+
+ align:start position:0%
+verbal description and then BAS based on
+ 
+
+ align:start position:0%
+verbal description and then BAS based on
+that verbal description a verbal
+
+ align:start position:0%
+that verbal description a verbal
+ 
+
+ align:start position:0%
+that verbal description a verbal
+description of some kind of an
+
+ align:start position:0%
+description of some kind of an
+ 
+
+ align:start position:0%
+description of some kind of an
+experiment and then based on that verbal
+
+ align:start position:0%
+experiment and then based on that verbal
+ 
+
+ align:start position:0%
+experiment and then based on that verbal
+description we can calculate
+
+ align:start position:0%
+description we can calculate
+ 
+
+ align:start position:0%
+description we can calculate
+probabilities for each value of the
+
+ align:start position:0%
+probabilities for each value of the
+ 
+
+ align:start position:0%
+probabilities for each value of the
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+variable and then write down a function
+
+ align:start position:0%
+variable and then write down a function
+ 
+
+ align:start position:0%
+variable and then write down a function
+or draw a graph or something like that
+
+ align:start position:0%
+or draw a graph or something like that
+ 
+
+ align:start position:0%
+or draw a graph or something like that
+that describes the probabilities for
+
+ align:start position:0%
+that describes the probabilities for
+ 
+
+ align:start position:0%
+that describes the probabilities for
+different values of the random variable
+
+ align:start position:0%
+different values of the random variable
+ 
+
+ align:start position:0%
+different values of the random variable
+and this is called a probability
+
+ align:start position:0%
+and this is called a probability
+ 
+
+ align:start position:0%
+and this is called a probability
+function now when last time when we saw
+
+ align:start position:0%
+function now when last time when we saw
+ 
+
+ align:start position:0%
+function now when last time when we saw
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+hypergeometric uh example and the
+
+ align:start position:0%
+hypergeometric uh example and the
+ 
+
+ align:start position:0%
+hypergeometric uh example and the
+binomial example
+
+ align:start position:0%
+binomial example
+ 
+
+ align:start position:0%
+binomial example
+we did sort of the first part of this
+
+ align:start position:0%
+we did sort of the first part of this
+ 
+
+ align:start position:0%
+we did sort of the first part of this
+exercise already okay we didn't we
+
+ align:start position:0%
+exercise already okay we didn't we
+ 
+
+ align:start position:0%
+exercise already okay we didn't we
+hadn't defined random variables yet we
+
+ align:start position:0%
+hadn't defined random variables yet we
+ 
+
+ align:start position:0%
+hadn't defined random variables yet we
+did the first part of this exercise and
+
+ align:start position:0%
+did the first part of this exercise and
+ 
+
+ align:start position:0%
+did the first part of this exercise and
+so now the the two examples I'm going to
+
+ align:start position:0%
+so now the the two examples I'm going to
+ 
+
+ align:start position:0%
+so now the the two examples I'm going to
+do are sort of completing this exercise
+
+ align:start position:0%
+do are sort of completing this exercise
+ 
+
+ align:start position:0%
+do are sort of completing this exercise
+uh for um hyper geometric and binomial
+
+ align:start position:0%
+uh for um hyper geometric and binomial
+ 
+
+ align:start position:0%
+uh for um hyper geometric and binomial
+random variables okay so back to the
+
+ align:start position:0%
+random variables okay so back to the
+ 
+
+ align:start position:0%
+random variables okay so back to the
+pizza
+
+ align:start position:0%
+pizza
+ 
+
+ align:start position:0%
+pizza
+example so um we're going to define a
+
+ align:start position:0%
+example so um we're going to define a
+ 
+
+ align:start position:0%
+example so um we're going to define a
+random variable x and x is the number of
+
+ align:start position:0%
+random variable x and x is the number of
+ 
+
+ align:start position:0%
+random variable x and x is the number of
+vegetarian toppings I get on my pizza if
+
+ align:start position:0%
+vegetarian toppings I get on my pizza if
+ 
+
+ align:start position:0%
+vegetarian toppings I get on my pizza if
+I draw the area four toppings randomly
+
+ align:start position:0%
+I draw the area four toppings randomly
+ 
+
+ align:start position:0%
+I draw the area four toppings randomly
+without replacement okay so remember a
+
+ align:start position:0%
+without replacement okay so remember a
+ 
+
+ align:start position:0%
+without replacement okay so remember a
+random variable is some numerical
+
+ align:start position:0%
+random variable is some numerical
+ 
+
+ align:start position:0%
+random variable is some numerical
+characteristic of the sample space we
+
+ align:start position:0%
+characteristic of the sample space we
+ 
+
+ align:start position:0%
+characteristic of the sample space we
+care about in this case number of
+
+ align:start position:0%
+care about in this case number of
+ 
+
+ align:start position:0%
+care about in this case number of
+vegetarian toppings
+
+ align:start position:0%
+vegetarian toppings
+ 
+
+ align:start position:0%
+vegetarian toppings
+okay so last time we calculated the
+
+ align:start position:0%
+okay so last time we calculated the
+ 
+
+ align:start position:0%
+okay so last time we calculated the
+probability I can't remember exactly
+
+ align:start position:0%
+probability I can't remember exactly
+ 
+
+ align:start position:0%
+probability I can't remember exactly
+which probability we calculated the
+
+ align:start position:0%
+which probability we calculated the
+ 
+
+ align:start position:0%
+which probability we calculated the
+probability that I got one vegetarian
+
+ align:start position:0%
+probability that I got one vegetarian
+ 
+
+ align:start position:0%
+probability that I got one vegetarian
+topping when I drew two from R uh two
+
+ align:start position:0%
+topping when I drew two from R uh two
+ 
+
+ align:start position:0%
+topping when I drew two from R uh two
+two uh at random when there were six
+
+ align:start position:0%
+two uh at random when there were six
+ 
+
+ align:start position:0%
+two uh at random when there were six
+nonvegetarian and five vegetarian or
+
+ align:start position:0%
+nonvegetarian and five vegetarian or
+ 
+
+ align:start position:0%
+nonvegetarian and five vegetarian or
+something like that okay so we
+
+ align:start position:0%
+something like that okay so we
+ 
+
+ align:start position:0%
+something like that okay so we
+calculated that probability but what I
+
+ align:start position:0%
+calculated that probability but what I
+ 
+
+ align:start position:0%
+calculated that probability but what I
+want to do now is I want to calculate
+
+ align:start position:0%
+want to do now is I want to calculate
+ 
+
+ align:start position:0%
+want to do now is I want to calculate
+those probabilities for all of the the
+
+ align:start position:0%
+those probabilities for all of the the
+ 
+
+ align:start position:0%
+those probabilities for all of the the
+various possible values of X okay so
+
+ align:start position:0%
+various possible values of X okay so
+ 
+
+ align:start position:0%
+various possible values of X okay so
+instead of just saying what's the
+
+ align:start position:0%
+instead of just saying what's the
+ 
+
+ align:start position:0%
+instead of just saying what's the
+probability that I get one vegetarian
+
+ align:start position:0%
+probability that I get one vegetarian
+ 
+
+ align:start position:0%
+probability that I get one vegetarian
+topping I want to calculate the
+
+ align:start position:0%
+topping I want to calculate the
+ 
+
+ align:start position:0%
+topping I want to calculate the
+probability that I get zero that I get
+
+ align:start position:0%
+probability that I get zero that I get
+ 
+
+ align:start position:0%
+probability that I get zero that I get
+one that I get two and so forth up to
+
+ align:start position:0%
+one that I get two and so forth up to
+ 
+
+ align:start position:0%
+one that I get two and so forth up to
+the maximum number of uh vegetan Aran
+
+ align:start position:0%
+the maximum number of uh vegetan Aran
+ 
+
+ align:start position:0%
+the maximum number of uh vegetan Aran
+topics I can get okay and in this case
+
+ align:start position:0%
+topics I can get okay and in this case
+ 
+
+ align:start position:0%
+topics I can get okay and in this case
+the maximum number is the max of six and
+
+ align:start position:0%
+the maximum number is the max of six and
+ 
+
+ align:start position:0%
+the maximum number is the max of six and
+N why is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so perhaps you don't remember what
+
+ align:start position:0%
+that so perhaps you don't remember what
+ 
+
+ align:start position:0%
+that so perhaps you don't remember what
+um sort of how what the setup of this
+
+ align:start position:0%
+um sort of how what the setup of this
+ 
+
+ align:start position:0%
+um sort of how what the setup of this
+problem was six is the number of
+
+ align:start position:0%
+problem was six is the number of
+ 
+
+ align:start position:0%
+problem was six is the number of
+vegetarian toppings available so I can't
+
+ align:start position:0%
+vegetarian toppings available so I can't
+ 
+
+ align:start position:0%
+vegetarian toppings available so I can't
+get any more than that n is the number
+
+ align:start position:0%
+get any more than that n is the number
+ 
+
+ align:start position:0%
+get any more than that n is the number
+of toppings that I'm choosing at random
+
+ align:start position:0%
+of toppings that I'm choosing at random
+ 
+
+ align:start position:0%
+of toppings that I'm choosing at random
+so I can't get any more than that okay
+
+ align:start position:0%
+so I can't get any more than that okay
+ 
+
+ align:start position:0%
+so I can't get any more than that okay
+so the the um oh sorry up to a sorry the
+
+ align:start position:0%
+so the the um oh sorry up to a sorry the
+ 
+
+ align:start position:0%
+so the the um oh sorry up to a sorry the
+minimum or yeah the the it it yeah the
+
+ align:start position:0%
+minimum or yeah the the it it yeah the
+ 
+
+ align:start position:0%
+minimum or yeah the the it it yeah the
+minimum of of six and N
+
+ align:start position:0%
+minimum of of six and N
+ 
+
+ align:start position:0%
+minimum of of six and N
+okay or yeah sorry I guess I wrote this
+
+ align:start position:0%
+okay or yeah sorry I guess I wrote this
+ 
+
+ align:start position:0%
+okay or yeah sorry I guess I wrote this
+in a somewhat confusing way but I think
+
+ align:start position:0%
+in a somewhat confusing way but I think
+ 
+
+ align:start position:0%
+in a somewhat confusing way but I think
+it's it's actually correct up there so
+
+ align:start position:0%
+it's it's actually correct up there so
+ 
+
+ align:start position:0%
+it's it's actually correct up there so
+up to six or n whichever is
+
+ align:start position:0%
+up to six or n whichever is
+ 
+
+ align:start position:0%
+up to six or n whichever is
+smaller okay so I use this
+
+ align:start position:0%
+smaller okay so I use this
+ 
+
+ align:start position:0%
+smaller okay so I use this
+formula and couple things to note about
+
+ align:start position:0%
+formula and couple things to note about
+ 
+
+ align:start position:0%
+formula and couple things to note about
+it it's a little bit different from the
+
+ align:start position:0%
+it it's a little bit different from the
+ 
+
+ align:start position:0%
+it it's a little bit different from the
+one I had up on the uh screen last time
+
+ align:start position:0%
+one I had up on the uh screen last time
+ 
+
+ align:start position:0%
+one I had up on the uh screen last time
+um first of all I CH well I changed the
+
+ align:start position:0%
+um first of all I CH well I changed the
+ 
+
+ align:start position:0%
+um first of all I CH well I changed the
+notation first of all I changed N1 to X
+
+ align:start position:0%
+notation first of all I changed N1 to X
+ 
+
+ align:start position:0%
+notation first of all I changed N1 to X
+okay and that's just to be uh consistent
+
+ align:start position:0%
+okay and that's just to be uh consistent
+ 
+
+ align:start position:0%
+okay and that's just to be uh consistent
+with my notation for the random variable
+
+ align:start position:0%
+with my notation for the random variable
+ 
+
+ align:start position:0%
+with my notation for the random variable
+and then I noted that uh N1 plus N2 was
+
+ align:start position:0%
+and then I noted that uh N1 plus N2 was
+ 
+
+ align:start position:0%
+and then I noted that uh N1 plus N2 was
+equal to n and so then I just uh since I
+
+ align:start position:0%
+equal to n and so then I just uh since I
+ 
+
+ align:start position:0%
+equal to n and so then I just uh since I
+substituted X for N1 then I just
+
+ align:start position:0%
+substituted X for N1 then I just
+ 
+
+ align:start position:0%
+substituted X for N1 then I just
+substituted n minus X for N2
+
+ align:start position:0%
+substituted n minus X for N2
+ 
+
+ align:start position:0%
+substituted n minus X for N2
+okay so just change the notation a
+
+ align:start position:0%
+okay so just change the notation a
+ 
+
+ align:start position:0%
+okay so just change the notation a
+little bit otherwise it's exactly the
+
+ align:start position:0%
+little bit otherwise it's exactly the
+ 
+
+ align:start position:0%
+little bit otherwise it's exactly the
+same formula and then the other thing I
+
+ align:start position:0%
+same formula and then the other thing I
+ 
+
+ align:start position:0%
+same formula and then the other thing I
+want to note that I forgot to note last
+
+ align:start position:0%
+want to note that I forgot to note last
+ 
+
+ align:start position:0%
+want to note that I forgot to note last
+time is that zero factorial is defined
+
+ align:start position:0%
+time is that zero factorial is defined
+ 
+
+ align:start position:0%
+time is that zero factorial is defined
+as one so when we're using this formula
+
+ align:start position:0%
+as one so when we're using this formula
+ 
+
+ align:start position:0%
+as one so when we're using this formula
+and we're plugging in for x equals 0
+
+ align:start position:0%
+and we're plugging in for x equals 0
+ 
+
+ align:start position:0%
+and we're plugging in for x equals 0
+it's no problem
+
+ align:start position:0%
+it's no problem
+ 
+
+ align:start position:0%
+it's no problem
+okay okay so I go ahead and do that for
+
+ align:start position:0%
+okay okay so I go ahead and do that for
+ 
+
+ align:start position:0%
+okay okay so I go ahead and do that for
+all of the possible values of
+
+ align:start position:0%
+all of the possible values of
+ 
+
+ align:start position:0%
+all of the possible values of
+X of course they're going to be
+
+ align:start position:0%
+X of course they're going to be
+ 
+
+ align:start position:0%
+X of course they're going to be
+functions of n in general but for
+
+ align:start position:0%
+functions of n in general but for
+ 
+
+ align:start position:0%
+functions of n in general but for
+concreteness let me choose a particular
+
+ align:start position:0%
+concreteness let me choose a particular
+ 
+
+ align:start position:0%
+concreteness let me choose a particular
+n so we'll choose n equals 3 so we've
+
+ align:start position:0%
+n so we'll choose n equals 3 so we've
+ 
+
+ align:start position:0%
+n so we'll choose n equals 3 so we've
+got the probability that X is equal to Z
+
+ align:start position:0%
+got the probability that X is equal to Z
+ 
+
+ align:start position:0%
+got the probability that X is equal to Z
+is uh equal when n is three is equal to
+
+ align:start position:0%
+is uh equal when n is three is equal to
+ 
+
+ align:start position:0%
+is uh equal when n is three is equal to
+6 over
+
+ align:start position:0%
+6 over
+ 
+
+ align:start position:0%
+6 over
+99 and then so forth um 36 over 99 for
+
+ align:start position:0%
+99 and then so forth um 36 over 99 for
+ 
+
+ align:start position:0%
+99 and then so forth um 36 over 99 for
+xals one and um and on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and here is a picture of sort of
+
+ align:start position:0%
+okay and here is a picture of sort of
+ 
+
+ align:start position:0%
+okay and here is a picture of sort of
+graphically what this probability
+
+ align:start position:0%
+graphically what this probability
+ 
+
+ align:start position:0%
+graphically what this probability
+function looks like okay so here on the
+
+ align:start position:0%
+function looks like okay so here on the
+ 
+
+ align:start position:0%
+function looks like okay so here on the
+uh horizontal axis I have the different
+
+ align:start position:0%
+uh horizontal axis I have the different
+ 
+
+ align:start position:0%
+uh horizontal axis I have the different
+values that X can take on and then I
+
+ align:start position:0%
+values that X can take on and then I
+ 
+
+ align:start position:0%
+values that X can take on and then I
+have uh the um the probabilities with
+
+ align:start position:0%
+have uh the um the probabilities with
+ 
+
+ align:start position:0%
+have uh the um the probabilities with
+which uh the random variable X takes on
+
+ align:start position:0%
+which uh the random variable X takes on
+ 
+
+ align:start position:0%
+which uh the random variable X takes on
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+okay so uh one thing I want to pause for
+
+ align:start position:0%
+okay so uh one thing I want to pause for
+ 
+
+ align:start position:0%
+okay so uh one thing I want to pause for
+just a second and note um a couple
+
+ align:start position:0%
+just a second and note um a couple
+ 
+
+ align:start position:0%
+just a second and note um a couple
+things about uh about this graph so by
+
+ align:start position:0%
+things about uh about this graph so by
+ 
+
+ align:start position:0%
+things about uh about this graph so by
+con vention we graph um when we graph
+
+ align:start position:0%
+con vention we graph um when we graph
+ 
+
+ align:start position:0%
+con vention we graph um when we graph
+probability functions we put vertical
+
+ align:start position:0%
+probability functions we put vertical
+ 
+
+ align:start position:0%
+probability functions we put vertical
+lines beneath each um point on the graph
+
+ align:start position:0%
+lines beneath each um point on the graph
+ 
+
+ align:start position:0%
+lines beneath each um point on the graph
+okay and I suppose that just makes them
+
+ align:start position:0%
+okay and I suppose that just makes them
+ 
+
+ align:start position:0%
+okay and I suppose that just makes them
+easier to read but in probability that's
+
+ align:start position:0%
+easier to read but in probability that's
+ 
+
+ align:start position:0%
+easier to read but in probability that's
+sort of a very standard convention
+
+ align:start position:0%
+sort of a very standard convention
+ 
+
+ align:start position:0%
+sort of a very standard convention
+you'll see these sort of vertical lines
+
+ align:start position:0%
+you'll see these sort of vertical lines
+ 
+
+ align:start position:0%
+you'll see these sort of vertical lines
+instead of just dots on the graph and
+
+ align:start position:0%
+instead of just dots on the graph and
+ 
+
+ align:start position:0%
+instead of just dots on the graph and
+then also a a piece of terminology that
+
+ align:start position:0%
+then also a a piece of terminology that
+ 
+
+ align:start position:0%
+then also a a piece of terminology that
+you should know is that each one of
+
+ align:start position:0%
+you should know is that each one of
+ 
+
+ align:start position:0%
+you should know is that each one of
+these points is called a point
+
+ align:start position:0%
+these points is called a point
+ 
+
+ align:start position:0%
+these points is called a point
+Mass okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions what we've done here
+
+ align:start position:0%
+okay any questions what we've done here
+ 
+
+ align:start position:0%
+okay any questions what we've done here
+so this is a pretty this is a a pretty
+
+ align:start position:0%
+so this is a pretty this is a a pretty
+ 
+
+ align:start position:0%
+so this is a pretty this is a a pretty
+important thing to understand we started
+
+ align:start position:0%
+important thing to understand we started
+ 
+
+ align:start position:0%
+important thing to understand we started
+from this verbal description of like
+
+ align:start position:0%
+from this verbal description of like
+ 
+
+ align:start position:0%
+from this verbal description of like
+drawing pieces of paper out of a hat and
+
+ align:start position:0%
+drawing pieces of paper out of a hat and
+ 
+
+ align:start position:0%
+drawing pieces of paper out of a hat and
+you know that have uh different pizza
+
+ align:start position:0%
+you know that have uh different pizza
+ 
+
+ align:start position:0%
+you know that have uh different pizza
+toppings on it and from that we were
+
+ align:start position:0%
+toppings on it and from that we were
+ 
+
+ align:start position:0%
+toppings on it and from that we were
+able to write down the probability
+
+ align:start position:0%
+able to write down the probability
+ 
+
+ align:start position:0%
+able to write down the probability
+function of a random variable that we
+
+ align:start position:0%
+function of a random variable that we
+ 
+
+ align:start position:0%
+function of a random variable that we
+defined on that sample
+
+ align:start position:0%
+defined on that sample
+ 
+
+ align:start position:0%
+defined on that sample
+space does that make sense okay
+
+ align:start position:0%
+space does that make sense okay
+ 
+
+ align:start position:0%
+space does that make sense okay
+so we can do this uh in a more General
+
+ align:start position:0%
+so we can do this uh in a more General
+ 
+
+ align:start position:0%
+so we can do this uh in a more General
+way okay so I had I picked the specific
+
+ align:start position:0%
+way okay so I had I picked the specific
+ 
+
+ align:start position:0%
+way okay so I had I picked the specific
+example of the the area 4 menu and that
+
+ align:start position:0%
+example of the the area 4 menu and that
+ 
+
+ align:start position:0%
+example of the the area 4 menu and that
+sort of let us calculate actual you know
+
+ align:start position:0%
+sort of let us calculate actual you know
+ 
+
+ align:start position:0%
+sort of let us calculate actual you know
+sort of numerical values for our
+
+ align:start position:0%
+sort of numerical values for our
+ 
+
+ align:start position:0%
+sort of numerical values for our
+probability function um but it's also
+
+ align:start position:0%
+probability function um but it's also
+ 
+
+ align:start position:0%
+probability function um but it's also
+useful to recognize that this is a
+
+ align:start position:0%
+useful to recognize that this is a
+ 
+
+ align:start position:0%
+useful to recognize that this is a
+general type of um this is a general
+
+ align:start position:0%
+general type of um this is a general
+ 
+
+ align:start position:0%
+general type of um this is a general
+type of uh uh random variable that you
+
+ align:start position:0%
+type of uh uh random variable that you
+ 
+
+ align:start position:0%
+type of uh uh random variable that you
+might run into again okay and and um we
+
+ align:start position:0%
+might run into again okay and and um we
+ 
+
+ align:start position:0%
+might run into again okay and and um we
+call it in particular a hyper geometric
+
+ align:start position:0%
+call it in particular a hyper geometric
+ 
+
+ align:start position:0%
+call it in particular a hyper geometric
+U random variable so we say that X has a
+
+ align:start position:0%
+U random variable so we say that X has a
+ 
+
+ align:start position:0%
+U random variable so we say that X has a
+hyper geometric distribution with
+
+ align:start position:0%
+hyper geometric distribution with
+ 
+
+ align:start position:0%
+hyper geometric distribution with
+parameters capital N where capital N is
+
+ align:start position:0%
+parameters capital N where capital N is
+ 
+
+ align:start position:0%
+parameters capital N where capital N is
+in our case the total number of toppings
+
+ align:start position:0%
+in our case the total number of toppings
+ 
+
+ align:start position:0%
+in our case the total number of toppings
+available for the pizza capital K the
+
+ align:start position:0%
+available for the pizza capital K the
+ 
+
+ align:start position:0%
+available for the pizza capital K the
+total number of vegetarian toppings and
+
+ align:start position:0%
+total number of vegetarian toppings and
+ 
+
+ align:start position:0%
+total number of vegetarian toppings and
+little n the number that we're going to
+
+ align:start position:0%
+little n the number that we're going to
+ 
+
+ align:start position:0%
+little n the number that we're going to
+choose okay so does this make sense to
+
+ align:start position:0%
+choose okay so does this make sense to
+ 
+
+ align:start position:0%
+choose okay so does this make sense to
+everyone is this clear
+
+ align:start position:0%
+everyone is this clear
+ 
+
+ align:start position:0%
+everyone is this clear
+and then afterwards we have to be be
+
+ align:start position:0%
+and then afterwards we have to be be
+ 
+
+ align:start position:0%
+and then afterwards we have to be be
+sure to um note for which values of um
+
+ align:start position:0%
+sure to um note for which values of um
+ 
+
+ align:start position:0%
+sure to um note for which values of um
+for which values of X that there is
+
+ align:start position:0%
+for which values of X that there is
+ 
+
+ align:start position:0%
+for which values of X that there is
+positive probability so for which values
+
+ align:start position:0%
+positive probability so for which values
+ 
+
+ align:start position:0%
+positive probability so for which values
+of X this is the formula to compute the
+
+ align:start position:0%
+of X this is the formula to compute the
+ 
+
+ align:start position:0%
+of X this is the formula to compute the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+probability okay and I've been a little
+
+ align:start position:0%
+probability okay and I've been a little
+ 
+
+ align:start position:0%
+probability okay and I've been a little
+lazy here if I wanted to be
+
+ align:start position:0%
+lazy here if I wanted to be
+ 
+
+ align:start position:0%
+lazy here if I wanted to be
+absolutely um correct I would have have
+
+ align:start position:0%
+absolutely um correct I would have have
+ 
+
+ align:start position:0%
+absolutely um correct I would have have
+written this as f ofx f subx of little X
+
+ align:start position:0%
+written this as f ofx f subx of little X
+ 
+
+ align:start position:0%
+written this as f ofx f subx of little X
+is equal to this formula for these
+
+ align:start position:0%
+is equal to this formula for these
+ 
+
+ align:start position:0%
+is equal to this formula for these
+values of X and it's equal to zero
+
+ align:start position:0%
+values of X and it's equal to zero
+ 
+
+ align:start position:0%
+values of X and it's equal to zero
+otherwise okay sometimes we leave off
+
+ align:start position:0%
+otherwise okay sometimes we leave off
+ 
+
+ align:start position:0%
+otherwise okay sometimes we leave off
+the equals zero otherwise just because
+
+ align:start position:0%
+the equals zero otherwise just because
+ 
+
+ align:start position:0%
+the equals zero otherwise just because
+we're lazy but it's sort of uh
+
+ align:start position:0%
+we're lazy but it's sort of uh
+ 
+
+ align:start position:0%
+we're lazy but it's sort of uh
+understood
+
+ align:start position:0%
+understood
+ 
+
+ align:start position:0%
+understood
+okay okay so what can we say what how
+
+ align:start position:0%
+okay okay so what can we say what how
+ 
+
+ align:start position:0%
+okay okay so what can we say what how
+how do we interpret this um distribution
+
+ align:start position:0%
+how do we interpret this um distribution
+ 
+
+ align:start position:0%
+how do we interpret this um distribution
+sometimes it is useful to think in terms
+
+ align:start position:0%
+sometimes it is useful to think in terms
+ 
+
+ align:start position:0%
+sometimes it is useful to think in terms
+of you know to think in terms of of uh
+
+ align:start position:0%
+of you know to think in terms of of uh
+ 
+
+ align:start position:0%
+of you know to think in terms of of uh
+you know a description of a an
+
+ align:start position:0%
+you know a description of a an
+ 
+
+ align:start position:0%
+you know a description of a an
+experiment or something like that when
+
+ align:start position:0%
+experiment or something like that when
+ 
+
+ align:start position:0%
+experiment or something like that when
+we're thinking about uh random variables
+
+ align:start position:0%
+we're thinking about uh random variables
+ 
+
+ align:start position:0%
+we're thinking about uh random variables
+and the interpretation I put on the
+
+ align:start position:0%
+and the interpretation I put on the
+ 
+
+ align:start position:0%
+and the interpretation I put on the
+hypergeometric is that it describes the
+
+ align:start position:0%
+hypergeometric is that it describes the
+ 
+
+ align:start position:0%
+hypergeometric is that it describes the
+number of quote successes in end trials
+
+ align:start position:0%
+number of quote successes in end trials
+ 
+
+ align:start position:0%
+number of quote successes in end trials
+when you're sampling without replacement
+
+ align:start position:0%
+when you're sampling without replacement
+ 
+
+ align:start position:0%
+when you're sampling without replacement
+from a sample of size n whose initial
+
+ align:start position:0%
+from a sample of size n whose initial
+ 
+
+ align:start position:0%
+from a sample of size n whose initial
+probability is K Over N okay so sampling
+
+ align:start position:0%
+probability is K Over N okay so sampling
+ 
+
+ align:start position:0%
+probability is K Over N okay so sampling
+without replacement we're not putting
+
+ align:start position:0%
+without replacement we're not putting
+ 
+
+ align:start position:0%
+without replacement we're not putting
+the pieces of paper back in the Hat we
+
+ align:start position:0%
+the pieces of paper back in the Hat we
+ 
+
+ align:start position:0%
+the pieces of paper back in the Hat we
+pull them out and we read them and then
+
+ align:start position:0%
+pull them out and we read them and then
+ 
+
+ align:start position:0%
+pull them out and we read them and then
+that's it and the sample the initial
+
+ align:start position:0%
+that's it and the sample the initial
+ 
+
+ align:start position:0%
+that's it and the sample the initial
+sample sizes in and the initial
+
+ align:start position:0%
+sample sizes in and the initial
+ 
+
+ align:start position:0%
+sample sizes in and the initial
+probability of success in in our case a
+
+ align:start position:0%
+probability of success in in our case a
+ 
+
+ align:start position:0%
+probability of success in in our case a
+quote Success is defined as a vegetarian
+
+ align:start position:0%
+quote Success is defined as a vegetarian
+ 
+
+ align:start position:0%
+quote Success is defined as a vegetarian
+topping so the the initial probability
+
+ align:start position:0%
+topping so the the initial probability
+ 
+
+ align:start position:0%
+topping so the the initial probability
+of success is K Over N and then of
+
+ align:start position:0%
+of success is K Over N and then of
+ 
+
+ align:start position:0%
+of success is K Over N and then of
+course that probability of success
+
+ align:start position:0%
+course that probability of success
+ 
+
+ align:start position:0%
+course that probability of success
+changes uh over the course of the
+
+ align:start position:0%
+changes uh over the course of the
+ 
+
+ align:start position:0%
+changes uh over the course of the
+experiment as you're drawing without
+
+ align:start position:0%
+experiment as you're drawing without
+ 
+
+ align:start position:0%
+experiment as you're drawing without
+replacement okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep again
+
+ align:start position:0%
+yep again
+ 
+
+ align:start position:0%
+yep again
+notations what does that okay so it
+
+ align:start position:0%
+notations what does that okay so it
+ 
+
+ align:start position:0%
+notations what does that okay so it
+means that the the these are the values
+
+ align:start position:0%
+means that the the these are the values
+ 
+
+ align:start position:0%
+means that the the these are the values
+for which um X has positive probability
+
+ align:start position:0%
+for which um X has positive probability
+ 
+
+ align:start position:0%
+for which um X has positive probability
+okay so um it can't obviously um you
+
+ align:start position:0%
+okay so um it can't obviously um you
+ 
+
+ align:start position:0%
+okay so um it can't obviously um you
+know have positive probability for
+
+ align:start position:0%
+know have positive probability for
+ 
+
+ align:start position:0%
+know have positive probability for
+anything less than zero and it can't it
+
+ align:start position:0%
+anything less than zero and it can't it
+ 
+
+ align:start position:0%
+anything less than zero and it can't it
+also can't have positive probability if
+
+ align:start position:0%
+also can't have positive probability if
+ 
+
+ align:start position:0%
+also can't have positive probability if
+if uh let me see n + K minus n so if
+
+ align:start position:0%
+if uh let me see n + K minus n so if
+ 
+
+ align:start position:0%
+if uh let me see n + K minus n so if
+Capital if the number vegetarian
+
+ align:start position:0%
+Capital if the number vegetarian
+ 
+
+ align:start position:0%
+Capital if the number vegetarian
+toppings plus the number that you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose minus let me think through this
+
+ align:start position:0%
+choose minus let me think through this
+ 
+
+ align:start position:0%
+choose minus let me think through this
+so the number you choose plus the number
+
+ align:start position:0%
+so the number you choose plus the number
+ 
+
+ align:start position:0%
+so the number you choose plus the number
+of vegetarian toppings minus n is
+
+ align:start position:0%
+of vegetarian toppings minus n is
+ 
+
+ align:start position:0%
+of vegetarian toppings minus n is
+positive then that's the that's the um
+
+ align:start position:0%
+positive then that's the that's the um
+ 
+
+ align:start position:0%
+positive then that's the that's the um
+minimum that the uh X can take on okay
+
+ align:start position:0%
+minimum that the uh X can take on okay
+ 
+
+ align:start position:0%
+minimum that the uh X can take on okay
+and then it it the maximum it can take
+
+ align:start position:0%
+and then it it the maximum it can take
+ 
+
+ align:start position:0%
+and then it it the maximum it can take
+on is either the number of vegetarian
+
+ align:start position:0%
+on is either the number of vegetarian
+ 
+
+ align:start position:0%
+on is either the number of vegetarian
+toppings you're choosing or sorry the
+
+ align:start position:0%
+toppings you're choosing or sorry the
+ 
+
+ align:start position:0%
+toppings you're choosing or sorry the
+number of toppings you're choosing or
+
+ align:start position:0%
+number of toppings you're choosing or
+ 
+
+ align:start position:0%
+number of toppings you're choosing or
+the total number of vegetarian toppings
+
+ align:start position:0%
+the total number of vegetarian toppings
+ 
+
+ align:start position:0%
+the total number of vegetarian toppings
+it can't exceed either of
+
+ align:start position:0%
+it can't exceed either of
+ 
+
+ align:start position:0%
+it can't exceed either of
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay second
+
+ align:start position:0%
+questions okay second
+ 
+
+ align:start position:0%
+questions okay second
+example so um remember that we had in
+
+ align:start position:0%
+example so um remember that we had in
+ 
+
+ align:start position:0%
+example so um remember that we had in
+the staff Curry example we did last time
+
+ align:start position:0%
+the staff Curry example we did last time
+ 
+
+ align:start position:0%
+the staff Curry example we did last time
+uh we talked about how we could uh think
+
+ align:start position:0%
+uh we talked about how we could uh think
+ 
+
+ align:start position:0%
+uh we talked about how we could uh think
+about the number of shots he made the
+
+ align:start position:0%
+about the number of shots he made the
+ 
+
+ align:start position:0%
+about the number of shots he made the
+number of threo uh shots that he made as
+
+ align:start position:0%
+number of threo uh shots that he made as
+ 
+
+ align:start position:0%
+number of threo uh shots that he made as
+having a binomial distribution if we
+
+ align:start position:0%
+having a binomial distribution if we
+ 
+
+ align:start position:0%
+having a binomial distribution if we
+made certain assumptions such as the
+
+ align:start position:0%
+made certain assumptions such as the
+ 
+
+ align:start position:0%
+made certain assumptions such as the
+shots were independent and the
+
+ align:start position:0%
+shots were independent and the
+ 
+
+ align:start position:0%
+shots were independent and the
+probability of making each shot uh was
+
+ align:start position:0%
+probability of making each shot uh was
+ 
+
+ align:start position:0%
+probability of making each shot uh was
+the same uh for for each shot okay so
+
+ align:start position:0%
+the same uh for for each shot okay so
+ 
+
+ align:start position:0%
+the same uh for for each shot okay so
+let's now Define a random variable
+
+ align:start position:0%
+let's now Define a random variable
+ 
+
+ align:start position:0%
+let's now Define a random variable
+that's based on this sort of um
+
+ align:start position:0%
+that's based on this sort of um
+ 
+
+ align:start position:0%
+that's based on this sort of um
+experiment and we'll call this random
+
+ align:start position:0%
+experiment and we'll call this random
+ 
+
+ align:start position:0%
+experiment and we'll call this random
+variable X as well and let it be the
+
+ align:start position:0%
+variable X as well and let it be the
+ 
+
+ align:start position:0%
+variable X as well and let it be the
+number of three-point shots that Steph
+
+ align:start position:0%
+number of three-point shots that Steph
+ 
+
+ align:start position:0%
+number of three-point shots that Steph
+Curry makes in the next six shots he
+
+ align:start position:0%
+Curry makes in the next six shots he
+ 
+
+ align:start position:0%
+Curry makes in the next six shots he
+takes
+
+ align:start position:0%
+takes
+ 
+
+ align:start position:0%
+takes
+okay so just like we did in the previous
+
+ align:start position:0%
+okay so just like we did in the previous
+ 
+
+ align:start position:0%
+okay so just like we did in the previous
+example we can calculate the probability
+
+ align:start position:0%
+example we can calculate the probability
+ 
+
+ align:start position:0%
+example we can calculate the probability
+that x equals 0 x x = 1 x = 2 and so
+
+ align:start position:0%
+that x equals 0 x x = 1 x = 2 and so
+ 
+
+ align:start position:0%
+that x equals 0 x x = 1 x = 2 and so
+forth up to six and we actually
+
+ align:start position:0%
+forth up to six and we actually
+ 
+
+ align:start position:0%
+forth up to six and we actually
+calculated a couple of those last time
+
+ align:start position:0%
+calculated a couple of those last time
+ 
+
+ align:start position:0%
+calculated a couple of those last time
+two or three of them last time in the
+
+ align:start position:0%
+two or three of them last time in the
+ 
+
+ align:start position:0%
+two or three of them last time in the
+example uh but we can we have a formula
+
+ align:start position:0%
+example uh but we can we have a formula
+ 
+
+ align:start position:0%
+example uh but we can we have a formula
+here 6 choose x uh time 44 to the x *
+
+ align:start position:0%
+here 6 choose x uh time 44 to the x *
+ 
+
+ align:start position:0%
+here 6 choose x uh time 44 to the x *
+.56 6 - x and remember where this comes
+
+ align:start position:0%
+.56 6 - x and remember where this comes
+ 
+
+ align:start position:0%
+.56 6 - x and remember where this comes
+from this is the probability that he
+
+ align:start position:0%
+from this is the probability that he
+ 
+
+ align:start position:0%
+from this is the probability that he
+makes any particular shot this is the
+
+ align:start position:0%
+makes any particular shot this is the
+ 
+
+ align:start position:0%
+makes any particular shot this is the
+probability that he misses any
+
+ align:start position:0%
+probability that he misses any
+ 
+
+ align:start position:0%
+probability that he misses any
+particular shot this is
+
+ align:start position:0%
+particular shot this is
+ 
+
+ align:start position:0%
+particular shot this is
+the without this uh coefficient out
+
+ align:start position:0%
+the without this uh coefficient out
+ 
+
+ align:start position:0%
+the without this uh coefficient out
+front that's the probability of any
+
+ align:start position:0%
+front that's the probability of any
+ 
+
+ align:start position:0%
+front that's the probability of any
+particular sequence of X um shots made
+
+ align:start position:0%
+particular sequence of X um shots made
+ 
+
+ align:start position:0%
+particular sequence of X um shots made
+and 6 - x shots missed and then if we
+
+ align:start position:0%
+and 6 - x shots missed and then if we
+ 
+
+ align:start position:0%
+and 6 - x shots missed and then if we
+add this coefficient out in the front
+
+ align:start position:0%
+add this coefficient out in the front
+ 
+
+ align:start position:0%
+add this coefficient out in the front
+that tells us the that counts the number
+
+ align:start position:0%
+that tells us the that counts the number
+ 
+
+ align:start position:0%
+that tells us the that counts the number
+of such sequences there are okay so you
+
+ align:start position:0%
+of such sequences there are okay so you
+ 
+
+ align:start position:0%
+of such sequences there are okay so you
+guys remember this from last time so we
+
+ align:start position:0%
+guys remember this from last time so we
+ 
+
+ align:start position:0%
+guys remember this from last time so we
+just use this formula we plug into it to
+
+ align:start position:0%
+just use this formula we plug into it to
+ 
+
+ align:start position:0%
+just use this formula we plug into it to
+calculate the probabilities for all of
+
+ align:start position:0%
+calculate the probabilities for all of
+ 
+
+ align:start position:0%
+calculate the probabilities for all of
+the various values of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+Okay and like I said some of these look
+
+ align:start position:0%
+Okay and like I said some of these look
+ 
+
+ align:start position:0%
+Okay and like I said some of these look
+probably look familiar because we
+
+ align:start position:0%
+probably look familiar because we
+ 
+
+ align:start position:0%
+probably look familiar because we
+calculated them last time I think we
+
+ align:start position:0%
+calculated them last time I think we
+ 
+
+ align:start position:0%
+calculated them last time I think we
+calculated the probability that x equals
+
+ align:start position:0%
+calculated the probability that x equals
+ 
+
+ align:start position:0%
+calculated the probability that x equals
+3 last time and maybe we calculated the
+
+ align:start position:0%
+3 last time and maybe we calculated the
+ 
+
+ align:start position:0%
+3 last time and maybe we calculated the
+probability that x equals z last time I
+
+ align:start position:0%
+probability that x equals z last time I
+ 
+
+ align:start position:0%
+probability that x equals z last time I
+can't
+
+ align:start position:0%
+can't
+ 
+
+ align:start position:0%
+can't
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+okay so graphically what does this look
+
+ align:start position:0%
+okay so graphically what does this look
+ 
+
+ align:start position:0%
+okay so graphically what does this look
+like there we go and again I sort of
+
+ align:start position:0%
+like there we go and again I sort of
+ 
+
+ align:start position:0%
+like there we go and again I sort of
+graphed each point Mass as you know sort
+
+ align:start position:0%
+graphed each point Mass as you know sort
+ 
+
+ align:start position:0%
+graphed each point Mass as you know sort
+of a DOT and a sort of a vertical line
+
+ align:start position:0%
+of a DOT and a sort of a vertical line
+ 
+
+ align:start position:0%
+of a DOT and a sort of a vertical line
+under it now if you just glance at this
+
+ align:start position:0%
+under it now if you just glance at this
+ 
+
+ align:start position:0%
+under it now if you just glance at this
+you might think it's uh symmetric this
+
+ align:start position:0%
+you might think it's uh symmetric this
+ 
+
+ align:start position:0%
+you might think it's uh symmetric this
+distribution symmetric but in fact it's
+
+ align:start position:0%
+distribution symmetric but in fact it's
+ 
+
+ align:start position:0%
+distribution symmetric but in fact it's
+not I mean if you look at the numbers
+
+ align:start position:0%
+not I mean if you look at the numbers
+ 
+
+ align:start position:0%
+not I mean if you look at the numbers
+you can tell it's not and if if you look
+
+ align:start position:0%
+you can tell it's not and if if you look
+ 
+
+ align:start position:0%
+you can tell it's not and if if you look
+closely at my drawing you can also tell
+
+ align:start position:0%
+closely at my drawing you can also tell
+ 
+
+ align:start position:0%
+closely at my drawing you can also tell
+it's not
+
+ align:start position:0%
+it's not
+ 
+
+ align:start position:0%
+it's not
+um okay and again just like in the last
+
+ align:start position:0%
+um okay and again just like in the last
+ 
+
+ align:start position:0%
+um okay and again just like in the last
+example we can sort of generalize this
+
+ align:start position:0%
+example we can sort of generalize this
+ 
+
+ align:start position:0%
+example we can sort of generalize this
+example so we can say uh instead of
+
+ align:start position:0%
+example so we can say uh instead of
+ 
+
+ align:start position:0%
+example so we can say uh instead of
+uh just uh considering um events where
+
+ align:start position:0%
+uh just uh considering um events where
+ 
+
+ align:start position:0%
+uh just uh considering um events where
+there's a a0 44 probability of a success
+
+ align:start position:0%
+there's a a0 44 probability of a success
+ 
+
+ align:start position:0%
+there's a a0 44 probability of a success
+and a 0.56 probability of a failure we
+
+ align:start position:0%
+and a 0.56 probability of a failure we
+ 
+
+ align:start position:0%
+and a 0.56 probability of a failure we
+can sort of uh use more General notation
+
+ align:start position:0%
+can sort of uh use more General notation
+ 
+
+ align:start position:0%
+can sort of uh use more General notation
+and consider um arbitrary probability of
+
+ align:start position:0%
+and consider um arbitrary probability of
+ 
+
+ align:start position:0%
+and consider um arbitrary probability of
+success as p and also consider an
+
+ align:start position:0%
+success as p and also consider an
+ 
+
+ align:start position:0%
+success as p and also consider an
+arbitrary number of Trials n okay so we
+
+ align:start position:0%
+arbitrary number of Trials n okay so we
+ 
+
+ align:start position:0%
+arbitrary number of Trials n okay so we
+say that uh X has a binomial
+
+ align:start position:0%
+say that uh X has a binomial
+ 
+
+ align:start position:0%
+say that uh X has a binomial
+distribution with parameters n and p
+
+ align:start position:0%
+distribution with parameters n and p
+ 
+
+ align:start position:0%
+distribution with parameters n and p
+and um that's uh denoted using that
+
+ align:start position:0%
+and um that's uh denoted using that
+ 
+
+ align:start position:0%
+and um that's uh denoted using that
+notation okay and then its probability
+
+ align:start position:0%
+notation okay and then its probability
+ 
+
+ align:start position:0%
+notation okay and then its probability
+function looks like this and again I was
+
+ align:start position:0%
+function looks like this and again I was
+ 
+
+ align:start position:0%
+function looks like this and again I was
+sort of uh you know I was too lazy to
+
+ align:start position:0%
+sort of uh you know I was too lazy to
+ 
+
+ align:start position:0%
+sort of uh you know I was too lazy to
+put equals zero otherwise but that's
+
+ align:start position:0%
+put equals zero otherwise but that's
+ 
+
+ align:start position:0%
+put equals zero otherwise but that's
+understood okay does this make sense do
+
+ align:start position:0%
+understood okay does this make sense do
+ 
+
+ align:start position:0%
+understood okay does this make sense do
+do you guys given these two examples do
+
+ align:start position:0%
+do you guys given these two examples do
+ 
+
+ align:start position:0%
+do you guys given these two examples do
+you feel like you have a little bit of a
+
+ align:start position:0%
+you feel like you have a little bit of a
+ 
+
+ align:start position:0%
+you feel like you have a little bit of a
+sense about what a random variable is a
+
+ align:start position:0%
+sense about what a random variable is a
+ 
+
+ align:start position:0%
+sense about what a random variable is a
+little bit of
+
+ align:start position:0%
+little bit of
+ 
+
+ align:start position:0%
+little bit of
+intuition
+
+ align:start position:0%
+intuition
+ 
+
+ align:start position:0%
+intuition
+okay okay but do feel free as I said to
+
+ align:start position:0%
+okay okay but do feel free as I said to
+ 
+
+ align:start position:0%
+okay okay but do feel free as I said to
+stop and ask questions if if we're going
+
+ align:start position:0%
+stop and ask questions if if we're going
+ 
+
+ align:start position:0%
+stop and ask questions if if we're going
+through this material too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quickly okay so the binomial
+
+ align:start position:0%
+quickly okay so the binomial
+ 
+
+ align:start position:0%
+quickly okay so the binomial
+distribution comes up a
+
+ align:start position:0%
+distribution comes up a
+ 
+
+ align:start position:0%
+distribution comes up a
+lot and um it's it's also it can be very
+
+ align:start position:0%
+lot and um it's it's also it can be very
+ 
+
+ align:start position:0%
+lot and um it's it's also it can be very
+useful in lots of different settings uh
+
+ align:start position:0%
+useful in lots of different settings uh
+ 
+
+ align:start position:0%
+useful in lots of different settings uh
+here's a picture of several different um
+
+ align:start position:0%
+here's a picture of several different um
+ 
+
+ align:start position:0%
+here's a picture of several different um
+probability functions from uh binomial
+
+ align:start position:0%
+probability functions from uh binomial
+ 
+
+ align:start position:0%
+probability functions from uh binomial
+distributions with different parameters
+
+ align:start position:0%
+distributions with different parameters
+ 
+
+ align:start position:0%
+distributions with different parameters
+so this picture all in this picture all
+
+ align:start position:0%
+so this picture all in this picture all
+ 
+
+ align:start position:0%
+so this picture all in this picture all
+of the parameters all of the P
+
+ align:start position:0%
+of the parameters all of the P
+ 
+
+ align:start position:0%
+of the parameters all of the P
+parameters are equal to 0.5 so if p is
+
+ align:start position:0%
+parameters are equal to 0.5 so if p is
+ 
+
+ align:start position:0%
+parameters are equal to 0.5 so if p is
+equal to 0.5 you will in fact get a
+
+ align:start position:0%
+equal to 0.5 you will in fact get a
+ 
+
+ align:start position:0%
+equal to 0.5 you will in fact get a
+symmetric distribution if p is not equal
+
+ align:start position:0%
+symmetric distribution if p is not equal
+ 
+
+ align:start position:0%
+symmetric distribution if p is not equal
+to 0.5 you won't get a symmetric
+
+ align:start position:0%
+to 0.5 you won't get a symmetric
+ 
+
+ align:start position:0%
+to 0.5 you won't get a symmetric
+distribution so here all of these PS are
+
+ align:start position:0%
+distribution so here all of these PS are
+ 
+
+ align:start position:0%
+distribution so here all of these PS are
+equal to 0.5 and then you can see how
+
+ align:start position:0%
+equal to 0.5 and then you can see how
+ 
+
+ align:start position:0%
+equal to 0.5 and then you can see how
+the distribution changes as uh n
+
+ align:start position:0%
+the distribution changes as uh n
+ 
+
+ align:start position:0%
+the distribution changes as uh n
+increases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that one
+
+ align:start position:0%
+okay and that one
+ 
+
+ align:start position:0%
+okay and that one
+uh on the right is starting to look like
+
+ align:start position:0%
+uh on the right is starting to look like
+ 
+
+ align:start position:0%
+uh on the right is starting to look like
+another distribution you've probably
+
+ align:start position:0%
+another distribution you've probably
+ 
+
+ align:start position:0%
+another distribution you've probably
+seen before the normal distribution and
+
+ align:start position:0%
+seen before the normal distribution and
+ 
+
+ align:start position:0%
+seen before the normal distribution and
+uh we'll be encountering that uh soon
+
+ align:start position:0%
+uh we'll be encountering that uh soon
+ 
+
+ align:start position:0%
+uh we'll be encountering that uh soon
+enough and we'll also talk about the
+
+ align:start position:0%
+enough and we'll also talk about the
+ 
+
+ align:start position:0%
+enough and we'll also talk about the
+relationship between the binomial
+
+ align:start position:0%
+relationship between the binomial
+ 
+
+ align:start position:0%
+relationship between the binomial
+distribution and the normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution okay so let's step back and
+
+ align:start position:0%
+distribution okay so let's step back and
+ 
+
+ align:start position:0%
+distribution okay so let's step back and
+think a little bit more formally about
+
+ align:start position:0%
+think a little bit more formally about
+ 
+
+ align:start position:0%
+think a little bit more formally about
+this uh this notion of a probability
+
+ align:start position:0%
+this uh this notion of a probability
+ 
+
+ align:start position:0%
+this uh this notion of a probability
+function what is a probability function
+
+ align:start position:0%
+function what is a probability function
+ 
+
+ align:start position:0%
+function what is a probability function
+and you know sort of what properties
+
+ align:start position:0%
+and you know sort of what properties
+ 
+
+ align:start position:0%
+and you know sort of what properties
+does it have well the the probability
+
+ align:start position:0%
+does it have well the the probability
+ 
+
+ align:start position:0%
+does it have well the the probability
+function of X where X is a discrete
+
+ align:start position:0%
+function of X where X is a discrete
+ 
+
+ align:start position:0%
+function of X where X is a discrete
+random variable is defined as the
+
+ align:start position:0%
+random variable is defined as the
+ 
+
+ align:start position:0%
+random variable is defined as the
+function such that for any x f subx of
+
+ align:start position:0%
+function such that for any x f subx of
+ 
+
+ align:start position:0%
+function such that for any x f subx of
+little X is equal to the probability
+
+ align:start position:0%
+little X is equal to the probability
+ 
+
+ align:start position:0%
+little X is equal to the probability
+that X is equal to Little X okay so this
+
+ align:start position:0%
+that X is equal to Little X okay so this
+ 
+
+ align:start position:0%
+that X is equal to Little X okay so this
+is just this is just formalizing what we
+
+ align:start position:0%
+is just this is just formalizing what we
+ 
+
+ align:start position:0%
+is just this is just formalizing what we
+did in the last two examples we just
+
+ align:start position:0%
+did in the last two examples we just
+ 
+
+ align:start position:0%
+did in the last two examples we just
+created these functions we called them
+
+ align:start position:0%
+created these functions we called them
+ 
+
+ align:start position:0%
+created these functions we called them
+little F called them probability
+
+ align:start position:0%
+little F called them probability
+ 
+
+ align:start position:0%
+little F called them probability
+functions and denoted them little F I
+
+ align:start position:0%
+functions and denoted them little F I
+ 
+
+ align:start position:0%
+functions and denoted them little F I
+guess and all we did is we um just you
+
+ align:start position:0%
+guess and all we did is we um just you
+ 
+
+ align:start position:0%
+guess and all we did is we um just you
+know computed probabilities that our
+
+ align:start position:0%
+know computed probabilities that our
+ 
+
+ align:start position:0%
+know computed probabilities that our
+random variable was equal to various uh
+
+ align:start position:0%
+random variable was equal to various uh
+ 
+
+ align:start position:0%
+random variable was equal to various uh
+values and that defined our uh
+
+ align:start position:0%
+values and that defined our uh
+ 
+
+ align:start position:0%
+values and that defined our uh
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+function okay so what are some of the
+
+ align:start position:0%
+function okay so what are some of the
+ 
+
+ align:start position:0%
+function okay so what are some of the
+properties that the probability function
+
+ align:start position:0%
+properties that the probability function
+ 
+
+ align:start position:0%
+properties that the probability function
+is going to have well because because
+
+ align:start position:0%
+is going to have well because because
+ 
+
+ align:start position:0%
+is going to have well because because
+it you know defines Pro the probability
+
+ align:start position:0%
+it you know defines Pro the probability
+ 
+
+ align:start position:0%
+it you know defines Pro the probability
+with which random variables take on
+
+ align:start position:0%
+with which random variables take on
+ 
+
+ align:start position:0%
+with which random variables take on
+various values it it is by its nature
+
+ align:start position:0%
+various values it it is by its nature
+ 
+
+ align:start position:0%
+various values it it is by its nature
+going to have certain properties that it
+
+ align:start position:0%
+going to have certain properties that it
+ 
+
+ align:start position:0%
+going to have certain properties that it
+always satisfies so in
+
+ align:start position:0%
+always satisfies so in
+ 
+
+ align:start position:0%
+always satisfies so in
+particular the value of the probability
+
+ align:start position:0%
+particular the value of the probability
+ 
+
+ align:start position:0%
+particular the value of the probability
+function for any X is going to be
+
+ align:start position:0%
+function for any X is going to be
+ 
+
+ align:start position:0%
+function for any X is going to be
+between zero and one okay and that's
+
+ align:start position:0%
+between zero and one okay and that's
+ 
+
+ align:start position:0%
+between zero and one okay and that's
+just because that's just by definition
+
+ align:start position:0%
+just because that's just by definition
+ 
+
+ align:start position:0%
+just because that's just by definition
+it's a probability okay and you can go
+
+ align:start position:0%
+it's a probability okay and you can go
+ 
+
+ align:start position:0%
+it's a probability okay and you can go
+back and you know we we can uh go back
+
+ align:start position:0%
+back and you know we we can uh go back
+ 
+
+ align:start position:0%
+back and you know we we can uh go back
+and check the examples I did all of the
+
+ align:start position:0%
+and check the examples I did all of the
+ 
+
+ align:start position:0%
+and check the examples I did all of the
+probabilities I computed were between
+
+ align:start position:0%
+probabilities I computed were between
+ 
+
+ align:start position:0%
+probabilities I computed were between
+zero and
+
+ align:start position:0%
+zero and
+ 
+
+ align:start position:0%
+zero and
+one the second um the uh second property
+
+ align:start position:0%
+one the second um the uh second property
+ 
+
+ align:start position:0%
+one the second um the uh second property
+is that if you sum up over all of the
+
+ align:start position:0%
+is that if you sum up over all of the
+ 
+
+ align:start position:0%
+is that if you sum up over all of the
+possible values that the random variable
+
+ align:start position:0%
+possible values that the random variable
+ 
+
+ align:start position:0%
+possible values that the random variable
+can take on then if you sum up the pro
+
+ align:start position:0%
+can take on then if you sum up the pro
+ 
+
+ align:start position:0%
+can take on then if you sum up the pro
+uh the probability function then that uh
+
+ align:start position:0%
+uh the probability function then that uh
+ 
+
+ align:start position:0%
+uh the probability function then that uh
+sum has to equal one okay again this
+
+ align:start position:0%
+sum has to equal one okay again this
+ 
+
+ align:start position:0%
+sum has to equal one okay again this
+follows directly from the fact that the
+
+ align:start position:0%
+follows directly from the fact that the
+ 
+
+ align:start position:0%
+follows directly from the fact that the
+probability function is uh you know sort
+
+ align:start position:0%
+probability function is uh you know sort
+ 
+
+ align:start position:0%
+probability function is uh you know sort
+of described probabilities so let me
+
+ align:start position:0%
+of described probabilities so let me
+ 
+
+ align:start position:0%
+of described probabilities so let me
+just go back and we can just sort of
+
+ align:start position:0%
+just go back and we can just sort of
+ 
+
+ align:start position:0%
+just go back and we can just sort of
+convince ourselves I did double check so
+
+ align:start position:0%
+convince ourselves I did double check so
+ 
+
+ align:start position:0%
+convince ourselves I did double check so
+it is in fact true but we can convince
+
+ align:start position:0%
+it is in fact true but we can convince
+ 
+
+ align:start position:0%
+it is in fact true but we can convince
+ourselves those things do sum to
+
+ align:start position:0%
+ourselves those things do sum to
+ 
+
+ align:start position:0%
+ourselves those things do sum to
+one and in the other
+
+ align:start position:0%
+one and in the other
+ 
+
+ align:start position:0%
+one and in the other
+example those also sum to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and um the third thing that uh very
+
+ align:start position:0%
+okay and um the third thing that uh very
+ 
+
+ align:start position:0%
+okay and um the third thing that uh very
+useful to know about a probability
+
+ align:start position:0%
+useful to know about a probability
+ 
+
+ align:start position:0%
+useful to know about a probability
+function is how to use it to compute
+
+ align:start position:0%
+function is how to use it to compute
+ 
+
+ align:start position:0%
+function is how to use it to compute
+probabilities okay so obviously if you
+
+ align:start position:0%
+probabilities okay so obviously if you
+ 
+
+ align:start position:0%
+probabilities okay so obviously if you
+just want the probability of a
+
+ align:start position:0%
+just want the probability of a
+ 
+
+ align:start position:0%
+just want the probability of a
+particular value of x you just the
+
+ align:start position:0%
+particular value of x you just the
+ 
+
+ align:start position:0%
+particular value of x you just the
+probability function gives it to you you
+
+ align:start position:0%
+probability function gives it to you you
+ 
+
+ align:start position:0%
+probability function gives it to you you
+just read it off but what if you want
+
+ align:start position:0%
+just read it off but what if you want
+ 
+
+ align:start position:0%
+just read it off but what if you want
+the probability of a whole set of
+
+ align:start position:0%
+the probability of a whole set of
+ 
+
+ align:start position:0%
+the probability of a whole set of
+different values of X well not
+
+ align:start position:0%
+different values of X well not
+ 
+
+ align:start position:0%
+different values of X well not
+surprisingly you just sum up the
+
+ align:start position:0%
+surprisingly you just sum up the
+ 
+
+ align:start position:0%
+surprisingly you just sum up the
+probability function over x's in that
+
+ align:start position:0%
+probability function over x's in that
+ 
+
+ align:start position:0%
+probability function over x's in that
+set okay and so that's going to uh
+
+ align:start position:0%
+set okay and so that's going to uh
+ 
+
+ align:start position:0%
+set okay and so that's going to uh
+that's going to be useful when we have
+
+ align:start position:0%
+that's going to be useful when we have
+ 
+
+ align:start position:0%
+that's going to be useful when we have
+when we're given a probability function
+
+ align:start position:0%
+when we're given a probability function
+ 
+
+ align:start position:0%
+when we're given a probability function
+for a random variable and we want to
+
+ align:start position:0%
+for a random variable and we want to
+ 
+
+ align:start position:0%
+for a random variable and we want to
+calculate the probability of a you know
+
+ align:start position:0%
+calculate the probability of a you know
+ 
+
+ align:start position:0%
+calculate the probability of a you know
+that X is in a particular set or region
+
+ align:start position:0%
+that X is in a particular set or region
+ 
+
+ align:start position:0%
+that X is in a particular set or region
+or something like
+
+ align:start position:0%
+or something like
+ 
+
+ align:start position:0%
+or something like
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I briefly mentioned continuous
+
+ align:start position:0%
+okay so I briefly mentioned continuous
+ 
+
+ align:start position:0%
+okay so I briefly mentioned continuous
+random variables a couple minutes ago so
+
+ align:start position:0%
+random variables a couple minutes ago so
+ 
+
+ align:start position:0%
+random variables a couple minutes ago so
+for continuous random variables we're
+
+ align:start position:0%
+for continuous random variables we're
+ 
+
+ align:start position:0%
+for continuous random variables we're
+rarely going to start with a verbal
+
+ align:start position:0%
+rarely going to start with a verbal
+ 
+
+ align:start position:0%
+rarely going to start with a verbal
+description of some kind of uh
+
+ align:start position:0%
+description of some kind of uh
+ 
+
+ align:start position:0%
+description of some kind of uh
+experiment like we with the discrete
+
+ align:start position:0%
+experiment like we with the discrete
+ 
+
+ align:start position:0%
+experiment like we with the discrete
+random variables um and instead we're
+
+ align:start position:0%
+random variables um and instead we're
+ 
+
+ align:start position:0%
+random variables um and instead we're
+typically just given a function that
+
+ align:start position:0%
+typically just given a function that
+ 
+
+ align:start position:0%
+typically just given a function that
+describes sort of the probabilities uh
+
+ align:start position:0%
+describes sort of the probabilities uh
+ 
+
+ align:start position:0%
+describes sort of the probabilities uh
+with which a r you know the
+
+ align:start position:0%
+with which a r you know the
+ 
+
+ align:start position:0%
+with which a r you know the
+probabilities with which uh continuous
+
+ align:start position:0%
+probabilities with which uh continuous
+ 
+
+ align:start position:0%
+probabilities with which uh continuous
+random variable is in various regions
+
+ align:start position:0%
+random variable is in various regions
+ 
+
+ align:start position:0%
+random variable is in various regions
+okay and that function is called a
+
+ align:start position:0%
+okay and that function is called a
+ 
+
+ align:start position:0%
+okay and that function is called a
+density um so all of you have seen lots
+
+ align:start position:0%
+density um so all of you have seen lots
+ 
+
+ align:start position:0%
+density um so all of you have seen lots
+of examples of densities the the over on
+
+ align:start position:0%
+of examples of densities the the over on
+ 
+
+ align:start position:0%
+of examples of densities the the over on
+the left is a normal density this is a a
+
+ align:start position:0%
+the left is a normal density this is a a
+ 
+
+ align:start position:0%
+the left is a normal density this is a a
+triangular density these are examples of
+
+ align:start position:0%
+triangular density these are examples of
+ 
+
+ align:start position:0%
+triangular density these are examples of
+log beta densities so we're you've all
+
+ align:start position:0%
+log beta densities so we're you've all
+ 
+
+ align:start position:0%
+log beta densities so we're you've all
+seen examples of them and we will sort
+
+ align:start position:0%
+seen examples of them and we will sort
+ 
+
+ align:start position:0%
+seen examples of them and we will sort
+of see many additional examples and sort
+
+ align:start position:0%
+of see many additional examples and sort
+ 
+
+ align:start position:0%
+of see many additional examples and sort
+of learn how to man manipulate them in
+
+ align:start position:0%
+of learn how to man manipulate them in
+ 
+
+ align:start position:0%
+of learn how to man manipulate them in
+various ways
+
+ align:start position:0%
+various ways
+ 
+
+ align:start position:0%
+various ways
+um but let me say a little bit more
+
+ align:start position:0%
+um but let me say a little bit more
+ 
+
+ align:start position:0%
+um but let me say a little bit more
+about this function the the density or
+
+ align:start position:0%
+about this function the the density or
+ 
+
+ align:start position:0%
+about this function the the density or
+also known as a probability density
+
+ align:start position:0%
+also known as a probability density
+ 
+
+ align:start position:0%
+also known as a probability density
+function okay so it's a a
+
+ align:start position:0%
+function okay so it's a a
+ 
+
+ align:start position:0%
+function okay so it's a a
+an analog in a lot of ways to the
+
+ align:start position:0%
+an analog in a lot of ways to the
+ 
+
+ align:start position:0%
+an analog in a lot of ways to the
+discrete probability function that we
+
+ align:start position:0%
+discrete probability function that we
+ 
+
+ align:start position:0%
+discrete probability function that we
+were just uh
+
+ align:start position:0%
+were just uh
+ 
+
+ align:start position:0%
+were just uh
+discussing and the next slide uh will
+
+ align:start position:0%
+discussing and the next slide uh will
+ 
+
+ align:start position:0%
+discussing and the next slide uh will
+talk about how they're similar and
+
+ align:start position:0%
+talk about how they're similar and
+ 
+
+ align:start position:0%
+talk about how they're similar and
+different uh but first let me give you
+
+ align:start position:0%
+different uh but first let me give you
+ 
+
+ align:start position:0%
+different uh but first let me give you
+sort of a more formal definition of what
+
+ align:start position:0%
+sort of a more formal definition of what
+ 
+
+ align:start position:0%
+sort of a more formal definition of what
+a a PDF or probability density function
+
+ align:start position:0%
+a a PDF or probability density function
+ 
+
+ align:start position:0%
+a a PDF or probability density function
+or density is okay well so in fact we
+
+ align:start position:0%
+or density is okay well so in fact we
+ 
+
+ align:start position:0%
+or density is okay well so in fact we
+Define The Continuous random variables
+
+ align:start position:0%
+Define The Continuous random variables
+ 
+
+ align:start position:0%
+Define The Continuous random variables
+in terms of this function so let me just
+
+ align:start position:0%
+in terms of this function so let me just
+ 
+
+ align:start position:0%
+in terms of this function so let me just
+uh do that that a random variable X is
+
+ align:start position:0%
+uh do that that a random variable X is
+ 
+
+ align:start position:0%
+uh do that that a random variable X is
+continuous if there exists a non-
+
+ align:start position:0%
+continuous if there exists a non-
+ 
+
+ align:start position:0%
+continuous if there exists a non-
+negative function f subx such that for
+
+ align:start position:0%
+negative function f subx such that for
+ 
+
+ align:start position:0%
+negative function f subx such that for
+any interval a uh in the real line the
+
+ align:start position:0%
+any interval a uh in the real line the
+ 
+
+ align:start position:0%
+any interval a uh in the real line the
+probability that X is an a is just equal
+
+ align:start position:0%
+probability that X is an a is just equal
+ 
+
+ align:start position:0%
+probability that X is an a is just equal
+to the integral over that region a of
+
+ align:start position:0%
+to the integral over that region a of
+ 
+
+ align:start position:0%
+to the integral over that region a of
+the the PDF F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subx okay so note that I've given these
+
+ align:start position:0%
+subx okay so note that I've given these
+ 
+
+ align:start position:0%
+subx okay so note that I've given these
+two functions the the the one the the
+
+ align:start position:0%
+two functions the the the one the the
+ 
+
+ align:start position:0%
+two functions the the the one the the
+one that I said was analogous for the
+
+ align:start position:0%
+one that I said was analogous for the
+ 
+
+ align:start position:0%
+one that I said was analogous for the
+discrete random variable and the
+
+ align:start position:0%
+discrete random variable and the
+ 
+
+ align:start position:0%
+discrete random variable and the
+continuous random variable they have
+
+ align:start position:0%
+continuous random variable they have
+ 
+
+ align:start position:0%
+continuous random variable they have
+different terms one's called a
+
+ align:start position:0%
+different terms one's called a
+ 
+
+ align:start position:0%
+different terms one's called a
+probability function one's called a
+
+ align:start position:0%
+probability function one's called a
+ 
+
+ align:start position:0%
+probability function one's called a
+probability density function okay and we
+
+ align:start position:0%
+probability density function okay and we
+ 
+
+ align:start position:0%
+probability density function okay and we
+do that to emphasize the fact that
+
+ align:start position:0%
+do that to emphasize the fact that
+ 
+
+ align:start position:0%
+do that to emphasize the fact that
+they're not exactly the same they don't
+
+ align:start position:0%
+they're not exactly the same they don't
+ 
+
+ align:start position:0%
+they're not exactly the same they don't
+behave exactly the same way
+
+ align:start position:0%
+behave exactly the same way
+ 
+
+ align:start position:0%
+behave exactly the same way
+mathematically however they're going to
+
+ align:start position:0%
+mathematically however they're going to
+ 
+
+ align:start position:0%
+mathematically however they're going to
+be uh they're analogous in a lot of ways
+
+ align:start position:0%
+be uh they're analogous in a lot of ways
+ 
+
+ align:start position:0%
+be uh they're analogous in a lot of ways
+and they're going to be used in a lot of
+
+ align:start position:0%
+and they're going to be used in a lot of
+ 
+
+ align:start position:0%
+and they're going to be used in a lot of
+the same ways and so that's why we use
+
+ align:start position:0%
+the same ways and so that's why we use
+ 
+
+ align:start position:0%
+the same ways and so that's why we use
+the same notation uh this sort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of f
+
+ align:start position:0%
+of f
+ 
+
+ align:start position:0%
+of f
+subx of little X notation okay so we use
+
+ align:start position:0%
+subx of little X notation okay so we use
+ 
+
+ align:start position:0%
+subx of little X notation okay so we use
+the same notation for both the sort of
+
+ align:start position:0%
+the same notation for both the sort of
+ 
+
+ align:start position:0%
+the same notation for both the sort of
+discrete probability function and the
+
+ align:start position:0%
+discrete probability function and the
+ 
+
+ align:start position:0%
+discrete probability function and the
+continuous probability density
+
+ align:start position:0%
+continuous probability density
+ 
+
+ align:start position:0%
+continuous probability density
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+oh and yes that's the PDF that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F okay so I said I was going to go
+
+ align:start position:0%
+F okay so I said I was going to go
+ 
+
+ align:start position:0%
+F okay so I said I was going to go
+through some of the similarities and the
+
+ align:start position:0%
+through some of the similarities and the
+ 
+
+ align:start position:0%
+through some of the similarities and the
+differences between a probability
+
+ align:start position:0%
+differences between a probability
+ 
+
+ align:start position:0%
+differences between a probability
+function and a probability density
+
+ align:start position:0%
+function and a probability density
+ 
+
+ align:start position:0%
+function and a probability density
+function so just like the probability
+
+ align:start position:0%
+function so just like the probability
+ 
+
+ align:start position:0%
+function so just like the probability
+function the probability density
+
+ align:start position:0%
+function the probability density
+ 
+
+ align:start position:0%
+function the probability density
+function has properties induced by our
+
+ align:start position:0%
+function has properties induced by our
+ 
+
+ align:start position:0%
+function has properties induced by our
+earlier definition of a probability okay
+
+ align:start position:0%
+earlier definition of a probability okay
+ 
+
+ align:start position:0%
+earlier definition of a probability okay
+so in particular it's always going to be
+
+ align:start position:0%
+so in particular it's always going to be
+ 
+
+ align:start position:0%
+so in particular it's always going to be
+non-
+
+ align:start position:0%
+non-
+ 
+
+ align:start position:0%
+non-
+negative now note that um it can be
+
+ align:start position:0%
+negative now note that um it can be
+ 
+
+ align:start position:0%
+negative now note that um it can be
+greater than one okay the probability
+
+ align:start position:0%
+greater than one okay the probability
+ 
+
+ align:start position:0%
+greater than one okay the probability
+function is never going to have a value
+
+ align:start position:0%
+function is never going to have a value
+ 
+
+ align:start position:0%
+function is never going to have a value
+greater than one because it is by
+
+ align:start position:0%
+greater than one because it is by
+ 
+
+ align:start position:0%
+greater than one because it is by
+definition a probability okay each point
+
+ align:start position:0%
+definition a probability okay each point
+ 
+
+ align:start position:0%
+definition a probability okay each point
+is just the probability that a random
+
+ align:start position:0%
+is just the probability that a random
+ 
+
+ align:start position:0%
+is just the probability that a random
+variable is equal to that point the
+
+ align:start position:0%
+variable is equal to that point the
+ 
+
+ align:start position:0%
+variable is equal to that point the
+definition of the probability density
+
+ align:start position:0%
+definition of the probability density
+ 
+
+ align:start position:0%
+definition of the probability density
+function is a little different okay so
+
+ align:start position:0%
+function is a little different okay so
+ 
+
+ align:start position:0%
+function is a little different okay so
+it can there can be regions or areas
+
+ align:start position:0%
+it can there can be regions or areas
+ 
+
+ align:start position:0%
+it can there can be regions or areas
+where the probability density function
+
+ align:start position:0%
+where the probability density function
+ 
+
+ align:start position:0%
+where the probability density function
+exceeds one that's perfectly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fine okay um the probability
+
+ align:start position:0%
+fine okay um the probability
+ 
+
+ align:start position:0%
+fine okay um the probability
+function when you um sum up the the uh
+
+ align:start position:0%
+function when you um sum up the the uh
+ 
+
+ align:start position:0%
+function when you um sum up the the uh
+values for the probability function over
+
+ align:start position:0%
+values for the probability function over
+ 
+
+ align:start position:0%
+values for the probability function over
+all of the uh possible values of X you
+
+ align:start position:0%
+all of the uh possible values of X you
+ 
+
+ align:start position:0%
+all of the uh possible values of X you
+get one here the continuous analog is
+
+ align:start position:0%
+get one here the continuous analog is
+ 
+
+ align:start position:0%
+get one here the continuous analog is
+that we integrate over all the possible
+
+ align:start position:0%
+that we integrate over all the possible
+ 
+
+ align:start position:0%
+that we integrate over all the possible
+values of X and we get one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then again just like when we um
+
+ align:start position:0%
+okay and then again just like when we um
+ 
+
+ align:start position:0%
+okay and then again just like when we um
+when when I had the previous slide up
+
+ align:start position:0%
+when when I had the previous slide up
+ 
+
+ align:start position:0%
+when when I had the previous slide up
+with the uh probability function and I
+
+ align:start position:0%
+with the uh probability function and I
+ 
+
+ align:start position:0%
+with the uh probability function and I
+said if you want to compute the
+
+ align:start position:0%
+said if you want to compute the
+ 
+
+ align:start position:0%
+said if you want to compute the
+probability that X is in a particular
+
+ align:start position:0%
+probability that X is in a particular
+ 
+
+ align:start position:0%
+probability that X is in a particular
+region you just sum up the probability
+
+ align:start position:0%
+region you just sum up the probability
+ 
+
+ align:start position:0%
+region you just sum up the probability
+function over all of the X in that
+
+ align:start position:0%
+function over all of the X in that
+ 
+
+ align:start position:0%
+function over all of the X in that
+region well here you do the continuous
+
+ align:start position:0%
+region well here you do the continuous
+ 
+
+ align:start position:0%
+region well here you do the continuous
+analog which is you integrate over that
+
+ align:start position:0%
+analog which is you integrate over that
+ 
+
+ align:start position:0%
+analog which is you integrate over that
+region okay so we're interested in X um
+
+ align:start position:0%
+region okay so we're interested in X um
+ 
+
+ align:start position:0%
+region okay so we're interested in X um
+the probability that X is between A and
+
+ align:start position:0%
+the probability that X is between A and
+ 
+
+ align:start position:0%
+the probability that X is between A and
+B oh actually oh no I guess I have it
+
+ align:start position:0%
+B oh actually oh no I guess I have it
+ 
+
+ align:start position:0%
+B oh actually oh no I guess I have it
+over here so the probability of that X
+
+ align:start position:0%
+over here so the probability of that X
+ 
+
+ align:start position:0%
+over here so the probability of that X
+is in some region capital A which we
+
+ align:start position:0%
+is in some region capital A which we
+ 
+
+ align:start position:0%
+is in some region capital A which we
+Define as an interval uh between A and B
+
+ align:start position:0%
+Define as an interval uh between A and B
+ 
+
+ align:start position:0%
+Define as an interval uh between A and B
+uh all we do is we just integrate over
+
+ align:start position:0%
+uh all we do is we just integrate over
+ 
+
+ align:start position:0%
+uh all we do is we just integrate over
+that region a okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um a couple things to keep in mind about
+
+ align:start position:0%
+um a couple things to keep in mind about
+ 
+
+ align:start position:0%
+um a couple things to keep in mind about
+a probability density function uh you
+
+ align:start position:0%
+a probability density function uh you
+ 
+
+ align:start position:0%
+a probability density function uh you
+know sort of um relative to the
+
+ align:start position:0%
+know sort of um relative to the
+ 
+
+ align:start position:0%
+know sort of um relative to the
+probability function so the value of a
+
+ align:start position:0%
+probability function so the value of a
+ 
+
+ align:start position:0%
+probability function so the value of a
+probability density function at a
+
+ align:start position:0%
+probability density function at a
+ 
+
+ align:start position:0%
+probability density function at a
+particular X does not have the same
+
+ align:start position:0%
+particular X does not have the same
+ 
+
+ align:start position:0%
+particular X does not have the same
+interpretation as a probability okay in
+
+ align:start position:0%
+interpretation as a probability okay in
+ 
+
+ align:start position:0%
+interpretation as a probability okay in
+fact the probability that the random
+
+ align:start position:0%
+fact the probability that the random
+ 
+
+ align:start position:0%
+fact the probability that the random
+variable X is equal to some number
+
+ align:start position:0%
+variable X is equal to some number
+ 
+
+ align:start position:0%
+variable X is equal to some number
+Little X is equal to zero for any X if x
+
+ align:start position:0%
+Little X is equal to zero for any X if x
+ 
+
+ align:start position:0%
+Little X is equal to zero for any X if x
+if big X is a continuous random
+
+ align:start position:0%
+if big X is a continuous random
+ 
+
+ align:start position:0%
+if big X is a continuous random
+variable okay so this is the this is the
+
+ align:start position:0%
+variable okay so this is the this is the
+ 
+
+ align:start position:0%
+variable okay so this is the this is the
+sort of fundamental difference between a
+
+ align:start position:0%
+sort of fundamental difference between a
+ 
+
+ align:start position:0%
+sort of fundamental difference between a
+discrete random variable and a
+
+ align:start position:0%
+discrete random variable and a
+ 
+
+ align:start position:0%
+discrete random variable and a
+continuous random variable discrete
+
+ align:start position:0%
+continuous random variable discrete
+ 
+
+ align:start position:0%
+continuous random variable discrete
+random variable takes on particular
+
+ align:start position:0%
+random variable takes on particular
+ 
+
+ align:start position:0%
+random variable takes on particular
+values with positive probability an a a
+
+ align:start position:0%
+values with positive probability an a a
+ 
+
+ align:start position:0%
+values with positive probability an a a
+finite or countably infinite number of
+
+ align:start position:0%
+finite or countably infinite number of
+ 
+
+ align:start position:0%
+finite or countably infinite number of
+particular values with positive
+
+ align:start position:0%
+particular values with positive
+ 
+
+ align:start position:0%
+particular values with positive
+probability uh the a continuous random
+
+ align:start position:0%
+probability uh the a continuous random
+ 
+
+ align:start position:0%
+probability uh the a continuous random
+variable is equal to a particular value
+
+ align:start position:0%
+variable is equal to a particular value
+ 
+
+ align:start position:0%
+variable is equal to a particular value
+with probability zero but instead we
+
+ align:start position:0%
+with probability zero but instead we
+ 
+
+ align:start position:0%
+with probability zero but instead we
+talk about it being in a region for
+
+ align:start position:0%
+talk about it being in a region for
+ 
+
+ align:start position:0%
+talk about it being in a region for
+instance with positive
+
+ align:start position:0%
+instance with positive
+ 
+
+ align:start position:0%
+instance with positive
+probability okay yes I have a question
+
+ align:start position:0%
+probability okay yes I have a question
+ 
+
+ align:start position:0%
+probability okay yes I have a question
+where so if we have value of f subx of
+
+ align:start position:0%
+where so if we have value of f subx of
+ 
+
+ align:start position:0%
+where so if we have value of f subx of
+little X is greater than one then how do
+
+ align:start position:0%
+little X is greater than one then how do
+ 
+
+ align:start position:0%
+little X is greater than one then how do
+you integrate everything up to well
+
+ align:start position:0%
+you integrate everything up to well
+ 
+
+ align:start position:0%
+you integrate everything up to well
+because it can it can be greater than
+
+ align:start position:0%
+because it can it can be greater than
+ 
+
+ align:start position:0%
+because it can it can be greater than
+one on an interval that's that's uh uh
+
+ align:start position:0%
+one on an interval that's that's uh uh
+ 
+
+ align:start position:0%
+one on an interval that's that's uh uh
+shorter than one so like for instance
+
+ align:start position:0%
+shorter than one so like for instance
+ 
+
+ align:start position:0%
+shorter than one so like for instance
+let me draw an
+
+ align:start position:0%
+let me draw an
+ 
+
+ align:start position:0%
+let me draw an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+so let's take the unit interval and we
+
+ align:start position:0%
+so let's take the unit interval and we
+ 
+
+ align:start position:0%
+so let's take the unit interval and we
+have a density that's defined on the
+
+ align:start position:0%
+have a density that's defined on the
+ 
+
+ align:start position:0%
+have a density that's defined on the
+unit interval well what uh on the unit
+
+ align:start position:0%
+unit interval well what uh on the unit
+ 
+
+ align:start position:0%
+unit interval well what uh on the unit
+interval can integrate to one well we
+
+ align:start position:0%
+interval can integrate to one well we
+ 
+
+ align:start position:0%
+interval can integrate to one well we
+know if we
+
+ align:start position:0%
+know if we
+ 
+
+ align:start position:0%
+know if we
+just let's
+
+ align:start position:0%
+just let's
+ 
+
+ align:start position:0%
+just let's
+consider this function right that
+
+ align:start position:0%
+consider this function right that
+ 
+
+ align:start position:0%
+consider this function right that
+integrates to one it never exceeds one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but let's see if I can draw this in a
+
+ align:start position:0%
+but let's see if I can draw this in a
+ 
+
+ align:start position:0%
+but let's see if I can draw this in a
+reasonable way
+
+ align:start position:0%
+reasonable way
+ 
+
+ align:start position:0%
+reasonable way
+this function should also integrate to
+
+ align:start position:0%
+this function should also integrate to
+ 
+
+ align:start position:0%
+this function should also integrate to
+one over the unit interval but it does
+
+ align:start position:0%
+one over the unit interval but it does
+ 
+
+ align:start position:0%
+one over the unit interval but it does
+exceed one for part of the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay was there anything else I
+
+ align:start position:0%
+okay okay was there anything else I
+ 
+
+ align:start position:0%
+okay okay was there anything else I
+wanted to say about this any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions no
+
+ align:start position:0%
+questions no
+ 
+
+ align:start position:0%
+questions no
+okay okay so I I do want to pause for a
+
+ align:start position:0%
+okay okay so I I do want to pause for a
+ 
+
+ align:start position:0%
+okay okay so I I do want to pause for a
+second to to um give to say a word about
+
+ align:start position:0%
+second to to um give to say a word about
+ 
+
+ align:start position:0%
+second to to um give to say a word about
+terminology and notation so I sort of
+
+ align:start position:0%
+terminology and notation so I sort of
+ 
+
+ align:start position:0%
+terminology and notation so I sort of
+did a little bit of a search on the
+
+ align:start position:0%
+did a little bit of a search on the
+ 
+
+ align:start position:0%
+did a little bit of a search on the
+internet and tried to find what the
+
+ align:start position:0%
+internet and tried to find what the
+ 
+
+ align:start position:0%
+internet and tried to find what the
+standard terminology and standard
+
+ align:start position:0%
+standard terminology and standard
+ 
+
+ align:start position:0%
+standard terminology and standard
+notation for all of these entities in
+
+ align:start position:0%
+notation for all of these entities in
+ 
+
+ align:start position:0%
+notation for all of these entities in
+probability is and it turns out there
+
+ align:start position:0%
+probability is and it turns out there
+ 
+
+ align:start position:0%
+probability is and it turns out there
+isn't one there is a huge range of
+
+ align:start position:0%
+isn't one there is a huge range of
+ 
+
+ align:start position:0%
+isn't one there is a huge range of
+different terms that different textbooks
+
+ align:start position:0%
+different terms that different textbooks
+ 
+
+ align:start position:0%
+different terms that different textbooks
+use and different websites use and and
+
+ align:start position:0%
+use and different websites use and and
+ 
+
+ align:start position:0%
+use and different websites use and and
+uh you know both formal terms and
+
+ align:start position:0%
+uh you know both formal terms and
+ 
+
+ align:start position:0%
+uh you know both formal terms and
+informal terms so I just want you to be
+
+ align:start position:0%
+informal terms so I just want you to be
+ 
+
+ align:start position:0%
+informal terms so I just want you to be
+aware of that if you're looking if
+
+ align:start position:0%
+aware of that if you're looking if
+ 
+
+ align:start position:0%
+aware of that if you're looking if
+you're using a a book on probability as
+
+ align:start position:0%
+you're using a a book on probability as
+ 
+
+ align:start position:0%
+you're using a a book on probability as
+a resource uh looking things up the
+
+ align:start position:0%
+a resource uh looking things up the
+ 
+
+ align:start position:0%
+a resource uh looking things up the
+terminology um might be different than
+
+ align:start position:0%
+terminology um might be different than
+ 
+
+ align:start position:0%
+terminology um might be different than
+what we're using in class um I'm going
+
+ align:start position:0%
+what we're using in class um I'm going
+ 
+
+ align:start position:0%
+what we're using in class um I'm going
+to try to be consistent internally
+
+ align:start position:0%
+to try to be consistent internally
+ 
+
+ align:start position:0%
+to try to be consistent internally
+consistent but that doesn't mean that I
+
+ align:start position:0%
+consistent but that doesn't mean that I
+ 
+
+ align:start position:0%
+consistent but that doesn't mean that I
+will always be completely formal so for
+
+ align:start position:0%
+will always be completely formal so for
+ 
+
+ align:start position:0%
+will always be completely formal so for
+instance I will try to say probability
+
+ align:start position:0%
+instance I will try to say probability
+ 
+
+ align:start position:0%
+instance I will try to say probability
+function when I'm referring to or sorry
+
+ align:start position:0%
+function when I'm referring to or sorry
+ 
+
+ align:start position:0%
+function when I'm referring to or sorry
+yeah probability function when I'm
+
+ align:start position:0%
+yeah probability function when I'm
+ 
+
+ align:start position:0%
+yeah probability function when I'm
+referring to uh a discrete random
+
+ align:start position:0%
+referring to uh a discrete random
+ 
+
+ align:start position:0%
+referring to uh a discrete random
+variable and I'll try to say probability
+
+ align:start position:0%
+variable and I'll try to say probability
+ 
+
+ align:start position:0%
+variable and I'll try to say probability
+density function when I'm referring to a
+
+ align:start position:0%
+density function when I'm referring to a
+ 
+
+ align:start position:0%
+density function when I'm referring to a
+continuous random variable but sometimes
+
+ align:start position:0%
+continuous random variable but sometimes
+ 
+
+ align:start position:0%
+continuous random variable but sometimes
+I'll just Punt and say
+
+ align:start position:0%
+I'll just Punt and say
+ 
+
+ align:start position:0%
+I'll just Punt and say
+distribution and that's kind of an
+
+ align:start position:0%
+distribution and that's kind of an
+ 
+
+ align:start position:0%
+distribution and that's kind of an
+informal catchall phrase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but do do uh feel free to ask if
+
+ align:start position:0%
+okay but do do uh feel free to ask if
+ 
+
+ align:start position:0%
+okay but do do uh feel free to ask if
+you have uh you know clar if you want
+
+ align:start position:0%
+you have uh you know clar if you want
+ 
+
+ align:start position:0%
+you have uh you know clar if you want
+clarification on these
+
+ align:start position:0%
+clarification on these
+ 
+
+ align:start position:0%
+clarification on these
+points okay yep question you how
+
+ align:start position:0%
+points okay yep question you how
+ 
+
+ align:start position:0%
+points okay yep question you how
+continuous distribution at Point the
+
+ align:start position:0%
+continuous distribution at Point the
+ 
+
+ align:start position:0%
+continuous distribution at Point the
+probably zero so let's say you have a
+
+ align:start position:0%
+probably zero so let's say you have a
+ 
+
+ align:start position:0%
+probably zero so let's say you have a
+spike at that one point maybe goes to
+
+ align:start position:0%
+spike at that one point maybe goes to
+ 
+
+ align:start position:0%
+spike at that one point maybe goes to
+Infinity so you that from distribution
+
+ align:start position:0%
+Infinity so you that from distribution
+ 
+
+ align:start position:0%
+Infinity so you that from distribution
+but had this integration fail or what
+
+ align:start position:0%
+but had this integration fail or what
+ 
+
+ align:start position:0%
+but had this integration fail or what
+problem that yeah I mean it's just it's
+
+ align:start position:0%
+problem that yeah I mean it's just it's
+ 
+
+ align:start position:0%
+problem that yeah I mean it's just it's
+just not sort of a well- behaved um
+
+ align:start position:0%
+just not sort of a well- behaved um
+ 
+
+ align:start position:0%
+just not sort of a well- behaved um
+distribution and so yeah so basically
+
+ align:start position:0%
+distribution and so yeah so basically
+ 
+
+ align:start position:0%
+distribution and so yeah so basically
+you know things like um you know
+
+ align:start position:0%
+you know things like um you know
+ 
+
+ align:start position:0%
+you know things like um you know
+regularity conditions that ensure that
+
+ align:start position:0%
+regularity conditions that ensure that
+ 
+
+ align:start position:0%
+regularity conditions that ensure that
+it's integrable might not uh still exist
+
+ align:start position:0%
+it's integrable might not uh still exist
+ 
+
+ align:start position:0%
+it's integrable might not uh still exist
+so what you're thinking of is like a
+
+ align:start position:0%
+so what you're thinking of is like a
+ 
+
+ align:start position:0%
+so what you're thinking of is like a
+distribution like this that's sort of
+
+ align:start position:0%
+distribution like this that's sort of
+ 
+
+ align:start position:0%
+distribution like this that's sort of
+getting that's kind of uh in the limit
+
+ align:start position:0%
+getting that's kind of uh in the limit
+ 
+
+ align:start position:0%
+getting that's kind of uh in the limit
+going down to a single point getting
+
+ align:start position:0%
+going down to a single point getting
+ 
+
+ align:start position:0%
+going down to a single point getting
+getting more concentrated more
+
+ align:start position:0%
+getting more concentrated more
+ 
+
+ align:start position:0%
+getting more concentrated more
+concentrated like one Break um so you
+
+ align:start position:0%
+concentrated like one Break um so you
+ 
+
+ align:start position:0%
+concentrated like one Break um so you
+have at one point just a
+
+ align:start position:0%
+have at one point just a
+ 
+
+ align:start position:0%
+have at one point just a
+spike so what you're what you're
+
+ align:start position:0%
+spike so what you're what you're
+ 
+
+ align:start position:0%
+spike so what you're what you're
+actually perhaps talking about is a
+
+ align:start position:0%
+actually perhaps talking about is a
+ 
+
+ align:start position:0%
+actually perhaps talking about is a
+mixed distribution so such a so I
+
+ align:start position:0%
+mixed distribution so such a so I
+ 
+
+ align:start position:0%
+mixed distribution so such a so I
+haven't mentioned them but such a thing
+
+ align:start position:0%
+haven't mentioned them but such a thing
+ 
+
+ align:start position:0%
+haven't mentioned them but such a thing
+definitely exists so um tell me if this
+
+ align:start position:0%
+definitely exists so um tell me if this
+ 
+
+ align:start position:0%
+definitely exists so um tell me if this
+is what you mean so you
+
+ align:start position:0%
+is what you mean so you
+ 
+
+ align:start position:0%
+is what you mean so you
+have a distribution for a continuous
+
+ align:start position:0%
+have a distribution for a continuous
+ 
+
+ align:start position:0%
+have a distribution for a continuous
+random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable and then maybe at this one
+
+ align:start position:0%
+variable and then maybe at this one
+ 
+
+ align:start position:0%
+variable and then maybe at this one
+particular well actually let me do a
+
+ align:start position:0%
+particular well actually let me do a
+ 
+
+ align:start position:0%
+particular well actually let me do a
+sort of a example that makes more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense and maybe so maybe this is the
+
+ align:start position:0%
+sense and maybe so maybe this is the
+ 
+
+ align:start position:0%
+sense and maybe so maybe this is the
+distribution of some
+
+ align:start position:0%
+distribution of some
+ 
+
+ align:start position:0%
+distribution of some
+measurement and then our how our
+
+ align:start position:0%
+measurement and then our how our
+ 
+
+ align:start position:0%
+measurement and then our how our
+measuring technology uh can't measure
+
+ align:start position:0%
+measuring technology uh can't measure
+ 
+
+ align:start position:0%
+measuring technology uh can't measure
+anything above this point so everything
+
+ align:start position:0%
+anything above this point so everything
+ 
+
+ align:start position:0%
+anything above this point so everything
+every measurement that we would like to
+
+ align:start position:0%
+every measurement that we would like to
+ 
+
+ align:start position:0%
+every measurement that we would like to
+take at this you know above this point
+
+ align:start position:0%
+take at this you know above this point
+ 
+
+ align:start position:0%
+take at this you know above this point
+gets recorded at this point is that what
+
+ align:start position:0%
+gets recorded at this point is that what
+ 
+
+ align:start position:0%
+gets recorded at this point is that what
+you mean so there is there is a point
+
+ align:start position:0%
+you mean so there is there is a point
+ 
+
+ align:start position:0%
+you mean so there is there is a point
+Mass here this is like we have a
+
+ align:start position:0%
+Mass here this is like we have a
+ 
+
+ align:start position:0%
+Mass here this is like we have a
+continuous part of the random variable
+
+ align:start position:0%
+continuous part of the random variable
+ 
+
+ align:start position:0%
+continuous part of the random variable
+and then this one part of the random
+
+ align:start position:0%
+and then this one part of the random
+ 
+
+ align:start position:0%
+and then this one part of the random
+variable is
+
+ align:start position:0%
+variable is
+ 
+
+ align:start position:0%
+variable is
+discreet and so there is you know sort
+
+ align:start position:0%
+discreet and so there is you know sort
+ 
+
+ align:start position:0%
+discreet and so there is you know sort
+of positive probability at that
+
+ align:start position:0%
+of positive probability at that
+ 
+
+ align:start position:0%
+of positive probability at that
+point so yeah you're absolutely right
+
+ align:start position:0%
+point so yeah you're absolutely right
+ 
+
+ align:start position:0%
+point so yeah you're absolutely right
+it's just called a mixed random variable
+
+ align:start position:0%
+it's just called a mixed random variable
+ 
+
+ align:start position:0%
+it's just called a mixed random variable
+and when we we deal with mixed random
+
+ align:start position:0%
+and when we we deal with mixed random
+ 
+
+ align:start position:0%
+and when we we deal with mixed random
+variables we just have to be cognizant
+
+ align:start position:0%
+variables we just have to be cognizant
+ 
+
+ align:start position:0%
+variables we just have to be cognizant
+of the fact that none of these there's
+
+ align:start position:0%
+of the fact that none of these there's
+ 
+
+ align:start position:0%
+of the fact that none of these there's
+there isn't a positive probability on
+
+ align:start position:0%
+there isn't a positive probability on
+ 
+
+ align:start position:0%
+there isn't a positive probability on
+any of these points but on this one
+
+ align:start position:0%
+any of these points but on this one
+ 
+
+ align:start position:0%
+any of these points but on this one
+particular point there is a point Mass
+
+ align:start position:0%
+particular point there is a point Mass
+ 
+
+ align:start position:0%
+particular point there is a point Mass
+we have to treat that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differently
+
+ align:start position:0%
+differently
+ 
+
+ align:start position:0%
+differently
+yeah okay other questions
+
+ align:start position:0%
+yeah okay other questions
+ 
+
+ align:start position:0%
+yeah okay other questions
+nope okay so let me go through an
+
+ align:start position:0%
+nope okay so let me go through an
+ 
+
+ align:start position:0%
+nope okay so let me go through an
+example so let A and B be real numbers
+
+ align:start position:0%
+example so let A and B be real numbers
+ 
+
+ align:start position:0%
+example so let A and B be real numbers
+uh such that uh a is less than b okay so
+
+ align:start position:0%
+uh such that uh a is less than b okay so
+ 
+
+ align:start position:0%
+uh such that uh a is less than b okay so
+a defines an interval on the real
+
+ align:start position:0%
+a defines an interval on the real
+ 
+
+ align:start position:0%
+a defines an interval on the real
+line and suppose that we have a random
+
+ align:start position:0%
+line and suppose that we have a random
+ 
+
+ align:start position:0%
+line and suppose that we have a random
+variable X and it's defined in such a
+
+ align:start position:0%
+variable X and it's defined in such a
+ 
+
+ align:start position:0%
+variable X and it's defined in such a
+way that the probability of X belonging
+
+ align:start position:0%
+way that the probability of X belonging
+ 
+
+ align:start position:0%
+way that the probability of X belonging
+to any sub interval of s is proportional
+
+ align:start position:0%
+to any sub interval of s is proportional
+ 
+
+ align:start position:0%
+to any sub interval of s is proportional
+to the length of the sub interval
+
+ align:start position:0%
+to the length of the sub interval
+ 
+
+ align:start position:0%
+to the length of the sub interval
+okay so then and you can uh perhaps this
+
+ align:start position:0%
+okay so then and you can uh perhaps this
+ 
+
+ align:start position:0%
+okay so then and you can uh perhaps this
+isn't a formal proof but you might be
+
+ align:start position:0%
+isn't a formal proof but you might be
+ 
+
+ align:start position:0%
+isn't a formal proof but you might be
+able to convince yourself if you think
+
+ align:start position:0%
+able to convince yourself if you think
+ 
+
+ align:start position:0%
+able to convince yourself if you think
+about it the uh the probability density
+
+ align:start position:0%
+about it the uh the probability density
+ 
+
+ align:start position:0%
+about it the uh the probability density
+function of that random variable that
+
+ align:start position:0%
+function of that random variable that
+ 
+
+ align:start position:0%
+function of that random variable that
+I've just described uh will take this
+
+ align:start position:0%
+I've just described uh will take this
+ 
+
+ align:start position:0%
+I've just described uh will take this
+form okay so basically it's going to
+
+ align:start position:0%
+form okay so basically it's going to
+ 
+
+ align:start position:0%
+form okay so basically it's going to
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's going to have a uniform
+
+ align:start position:0%
+it's going to have a uniform
+ 
+
+ align:start position:0%
+it's going to have a uniform
+density at Value 1 over B minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a uh over the interval A to B and it's
+
+ align:start position:0%
+a uh over the interval A to B and it's
+ 
+
+ align:start position:0%
+a uh over the interval A to B and it's
+going to be zero otherwise okay
+
+ align:start position:0%
+going to be zero otherwise okay
+ 
+
+ align:start position:0%
+going to be zero otherwise okay
+so definitely
+
+ align:start position:0%
+so definitely
+ 
+
+ align:start position:0%
+so definitely
+once you write down this uh PDF and you
+
+ align:start position:0%
+once you write down this uh PDF and you
+ 
+
+ align:start position:0%
+once you write down this uh PDF and you
+think about uh this description of the
+
+ align:start position:0%
+think about uh this description of the
+ 
+
+ align:start position:0%
+think about uh this description of the
+random variable you certainly can
+
+ align:start position:0%
+random variable you certainly can
+ 
+
+ align:start position:0%
+random variable you certainly can
+convince yourself I think that um you
+
+ align:start position:0%
+convince yourself I think that um you
+ 
+
+ align:start position:0%
+convince yourself I think that um you
+know any the the the FRA the probability
+
+ align:start position:0%
+know any the the the FRA the probability
+ 
+
+ align:start position:0%
+know any the the the FRA the probability
+that the random variable X is in any sub
+
+ align:start position:0%
+that the random variable X is in any sub
+ 
+
+ align:start position:0%
+that the random variable X is in any sub
+interval of a is going to be
+
+ align:start position:0%
+interval of a is going to be
+ 
+
+ align:start position:0%
+interval of a is going to be
+proportional to the length of that sub
+
+ align:start position:0%
+proportional to the length of that sub
+ 
+
+ align:start position:0%
+proportional to the length of that sub
+interval because this is just a constant
+
+ align:start position:0%
+interval because this is just a constant
+ 
+
+ align:start position:0%
+interval because this is just a constant
+prob ability or yeah constant PDF over
+
+ align:start position:0%
+prob ability or yeah constant PDF over
+ 
+
+ align:start position:0%
+prob ability or yeah constant PDF over
+that interval
+
+ align:start position:0%
+that interval
+ 
+
+ align:start position:0%
+that interval
+okay so this is a special random
+
+ align:start position:0%
+okay so this is a special random
+ 
+
+ align:start position:0%
+okay so this is a special random
+variable we'll see this um again over
+
+ align:start position:0%
+variable we'll see this um again over
+ 
+
+ align:start position:0%
+variable we'll see this um again over
+the course of the semester it is perhaps
+
+ align:start position:0%
+the course of the semester it is perhaps
+ 
+
+ align:start position:0%
+the course of the semester it is perhaps
+my favorite random variable it is the
+
+ align:start position:0%
+my favorite random variable it is the
+ 
+
+ align:start position:0%
+my favorite random variable it is the
+uniform random variable and um it's it
+
+ align:start position:0%
+uniform random variable and um it's it
+ 
+
+ align:start position:0%
+uniform random variable and um it's it
+comes in handy in lots of different uh
+
+ align:start position:0%
+comes in handy in lots of different uh
+ 
+
+ align:start position:0%
+comes in handy in lots of different uh
+circumstances um and oh I think actually
+
+ align:start position:0%
+circumstances um and oh I think actually
+ 
+
+ align:start position:0%
+circumstances um and oh I think actually
+I drew a picture up here on the board
+
+ align:start position:0%
+I drew a picture up here on the board
+ 
+
+ align:start position:0%
+I drew a picture up here on the board
+but I think I made have a picture in my
+
+ align:start position:0%
+but I think I made have a picture in my
+ 
+
+ align:start position:0%
+but I think I made have a picture in my
+next slide yep there's a picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um if you want to compute the
+
+ align:start position:0%
+okay so um if you want to compute the
+ 
+
+ align:start position:0%
+okay so um if you want to compute the
+probability of a uniform AB random
+
+ align:start position:0%
+probability of a uniform AB random
+ 
+
+ align:start position:0%
+probability of a uniform AB random
+variable being in some interval CD which
+
+ align:start position:0%
+variable being in some interval CD which
+ 
+
+ align:start position:0%
+variable being in some interval CD which
+is a sub interval of ab uh well we know
+
+ align:start position:0%
+is a sub interval of ab uh well we know
+ 
+
+ align:start position:0%
+is a sub interval of ab uh well we know
+one way that we can you can do that
+
+ align:start position:0%
+one way that we can you can do that
+ 
+
+ align:start position:0%
+one way that we can you can do that
+because we saw that um uh several slides
+
+ align:start position:0%
+because we saw that um uh several slides
+ 
+
+ align:start position:0%
+because we saw that um uh several slides
+ago you can just
+
+ align:start position:0%
+ago you can just
+ 
+
+ align:start position:0%
+ago you can just
+integrate the value
+
+ align:start position:0%
+integrate the value
+ 
+
+ align:start position:0%
+integrate the value
+of the probability density function over
+
+ align:start position:0%
+of the probability density function over
+ 
+
+ align:start position:0%
+of the probability density function over
+that sub interval okay but in fact
+
+ align:start position:0%
+that sub interval okay but in fact
+ 
+
+ align:start position:0%
+that sub interval okay but in fact
+there's kind of an easier way to do it
+
+ align:start position:0%
+there's kind of an easier way to do it
+ 
+
+ align:start position:0%
+there's kind of an easier way to do it
+with a uniform uh distribution a uniform
+
+ align:start position:0%
+with a uniform uh distribution a uniform
+ 
+
+ align:start position:0%
+with a uniform uh distribution a uniform
+random variable we don't have to
+
+ align:start position:0%
+random variable we don't have to
+ 
+
+ align:start position:0%
+random variable we don't have to
+actually do the integration uh because
+
+ align:start position:0%
+actually do the integration uh because
+ 
+
+ align:start position:0%
+actually do the integration uh because
+this is just constant over the whole
+
+ align:start position:0%
+this is just constant over the whole
+ 
+
+ align:start position:0%
+this is just constant over the whole
+interval so to compute the probability
+
+ align:start position:0%
+interval so to compute the probability
+ 
+
+ align:start position:0%
+interval so to compute the probability
+of any sub interval uh you know as I
+
+ align:start position:0%
+of any sub interval uh you know as I
+ 
+
+ align:start position:0%
+of any sub interval uh you know as I
+said it's just a the length of the sub
+
+ align:start position:0%
+said it's just a the length of the sub
+ 
+
+ align:start position:0%
+said it's just a the length of the sub
+interval over uh the length of the the
+
+ align:start position:0%
+interval over uh the length of the the
+ 
+
+ align:start position:0%
+interval over uh the length of the the
+entire support of the random
+
+ align:start position:0%
+entire support of the random
+ 
+
+ align:start position:0%
+entire support of the random
+variable so we've got probability
+
+ align:start position:0%
+variable so we've got probability
+ 
+
+ align:start position:0%
+variable so we've got probability
+functions and we've got probability
+
+ align:start position:0%
+functions and we've got probability
+ 
+
+ align:start position:0%
+functions and we've got probability
+density functions and for two different
+
+ align:start position:0%
+density functions and for two different
+ 
+
+ align:start position:0%
+density functions and for two different
+kinds of random variables those describe
+
+ align:start position:0%
+kinds of random variables those describe
+ 
+
+ align:start position:0%
+kinds of random variables those describe
+the um the sort of uh probabilities that
+
+ align:start position:0%
+the um the sort of uh probabilities that
+ 
+
+ align:start position:0%
+the um the sort of uh probabilities that
+the random variables are in different
+
+ align:start position:0%
+the random variables are in different
+ 
+
+ align:start position:0%
+the random variables are in different
+regions or take on different values
+
+ align:start position:0%
+regions or take on different values
+ 
+
+ align:start position:0%
+regions or take on different values
+there it's a complete description okay
+
+ align:start position:0%
+there it's a complete description okay
+ 
+
+ align:start position:0%
+there it's a complete description okay
+but sometimes it's going to be handy to
+
+ align:start position:0%
+but sometimes it's going to be handy to
+ 
+
+ align:start position:0%
+but sometimes it's going to be handy to
+express those probabilities related to a
+
+ align:start position:0%
+express those probabilities related to a
+ 
+
+ align:start position:0%
+express those probabilities related to a
+random variable in an alternative form
+
+ align:start position:0%
+random variable in an alternative form
+ 
+
+ align:start position:0%
+random variable in an alternative form
+okay doubly handy is the fact that this
+
+ align:start position:0%
+okay doubly handy is the fact that this
+ 
+
+ align:start position:0%
+okay doubly handy is the fact that this
+alternative form has the same definition
+
+ align:start position:0%
+alternative form has the same definition
+ 
+
+ align:start position:0%
+alternative form has the same definition
+regardless of whether the random
+
+ align:start position:0%
+regardless of whether the random
+ 
+
+ align:start position:0%
+regardless of whether the random
+variable is discret or
+
+ align:start position:0%
+variable is discret or
+ 
+
+ align:start position:0%
+variable is discret or
+continuous okay and this alternative
+
+ align:start position:0%
+continuous okay and this alternative
+ 
+
+ align:start position:0%
+continuous okay and this alternative
+form is the cumulative distribution
+
+ align:start position:0%
+form is the cumulative distribution
+ 
+
+ align:start position:0%
+form is the cumulative distribution
+function so a cumulative distribution
+
+ align:start position:0%
+function so a cumulative distribution
+ 
+
+ align:start position:0%
+function so a cumulative distribution
+function uh which will often abbreviate
+
+ align:start position:0%
+function uh which will often abbreviate
+ 
+
+ align:start position:0%
+function uh which will often abbreviate
+as CDF um it's denoted with a cap
+
+ align:start position:0%
+as CDF um it's denoted with a cap
+ 
+
+ align:start position:0%
+as CDF um it's denoted with a cap
+capital F
+
+ align:start position:0%
+capital F
+ 
+
+ align:start position:0%
+capital F
+subx and um it is defined simply as the
+
+ align:start position:0%
+subx and um it is defined simply as the
+ 
+
+ align:start position:0%
+subx and um it is defined simply as the
+probability that the random variable X
+
+ align:start position:0%
+probability that the random variable X
+ 
+
+ align:start position:0%
+probability that the random variable X
+is less than or equal to some value
+
+ align:start position:0%
+is less than or equal to some value
+ 
+
+ align:start position:0%
+is less than or equal to some value
+Little X okay same definition for both
+
+ align:start position:0%
+Little X okay same definition for both
+ 
+
+ align:start position:0%
+Little X okay same definition for both
+the um uh discrete and continuous random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables and I should say by the way
+
+ align:start position:0%
+variables and I should say by the way
+ 
+
+ align:start position:0%
+variables and I should say by the way
+sometimes I often like to put uh the
+
+ align:start position:0%
+sometimes I often like to put uh the
+ 
+
+ align:start position:0%
+sometimes I often like to put uh the
+random variable as a subscript on either
+
+ align:start position:0%
+random variable as a subscript on either
+ 
+
+ align:start position:0%
+random variable as a subscript on either
+the probability function or the PDF or
+
+ align:start position:0%
+the probability function or the PDF or
+ 
+
+ align:start position:0%
+the probability function or the PDF or
+the CDF just so we you know just to keep
+
+ align:start position:0%
+the CDF just so we you know just to keep
+ 
+
+ align:start position:0%
+the CDF just so we you know just to keep
+things straight um it doesn't have to be
+
+ align:start position:0%
+things straight um it doesn't have to be
+ 
+
+ align:start position:0%
+things straight um it doesn't have to be
+there so sometimes I'll omit there's no
+
+ align:start position:0%
+there so sometimes I'll omit there's no
+ 
+
+ align:start position:0%
+there so sometimes I'll omit there's no
+chance of um ambiguity sometimes I'll
+
+ align:start position:0%
+chance of um ambiguity sometimes I'll
+ 
+
+ align:start position:0%
+chance of um ambiguity sometimes I'll
+omit the subscript and just use the
+
+ align:start position:0%
+omit the subscript and just use the
+ 
+
+ align:start position:0%
+omit the subscript and just use the
+little f for probability function or PDF
+
+ align:start position:0%
+little f for probability function or PDF
+ 
+
+ align:start position:0%
+little f for probability function or PDF
+and then the capital F for uh
+
+ align:start position:0%
+and then the capital F for uh
+ 
+
+ align:start position:0%
+and then the capital F for uh
+CDF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so just like in the case of
+
+ align:start position:0%
+okay okay so just like in the case of
+ 
+
+ align:start position:0%
+okay okay so just like in the case of
+the probability function and the
+
+ align:start position:0%
+the probability function and the
+ 
+
+ align:start position:0%
+the probability function and the
+probability density function the
+
+ align:start position:0%
+probability density function the
+ 
+
+ align:start position:0%
+probability density function the
+properties of probability are going to
+
+ align:start position:0%
+properties of probability are going to
+ 
+
+ align:start position:0%
+properties of probability are going to
+imply certain things about cdfs there's
+
+ align:start position:0%
+imply certain things about cdfs there's
+ 
+
+ align:start position:0%
+imply certain things about cdfs there's
+certain ways that cdfs are going to
+
+ align:start position:0%
+certain ways that cdfs are going to
+ 
+
+ align:start position:0%
+certain ways that cdfs are going to
+behave so uh first of all the CDF is
+
+ align:start position:0%
+behave so uh first of all the CDF is
+ 
+
+ align:start position:0%
+behave so uh first of all the CDF is
+always going to have values between zero
+
+ align:start position:0%
+always going to have values between zero
+ 
+
+ align:start position:0%
+always going to have values between zero
+and one okay and again I mean just you
+
+ align:start position:0%
+and one okay and again I mean just you
+ 
+
+ align:start position:0%
+and one okay and again I mean just you
+can look back at the definition and
+
+ align:start position:0%
+can look back at the definition and
+ 
+
+ align:start position:0%
+can look back at the definition and
+convince yourself that this is
+
+ align:start position:0%
+convince yourself that this is
+ 
+
+ align:start position:0%
+convince yourself that this is
+true uh second thing is that the CDF is
+
+ align:start position:0%
+true uh second thing is that the CDF is
+ 
+
+ align:start position:0%
+true uh second thing is that the CDF is
+always going to be non decreasing in
+
+ align:start position:0%
+always going to be non decreasing in
+ 
+
+ align:start position:0%
+always going to be non decreasing in
+X okay and again if you think about the
+
+ align:start position:0%
+X okay and again if you think about the
+ 
+
+ align:start position:0%
+X okay and again if you think about the
+definition it's just the definition that
+
+ align:start position:0%
+definition it's just the definition that
+ 
+
+ align:start position:0%
+definition it's just the definition that
+X the random variable X is less than or
+
+ align:start position:0%
+X the random variable X is less than or
+ 
+
+ align:start position:0%
+X the random variable X is less than or
+equal to Little X as little X increases
+
+ align:start position:0%
+equal to Little X as little X increases
+ 
+
+ align:start position:0%
+equal to Little X as little X increases
+uh then um you know capital F is not
+
+ align:start position:0%
+uh then um you know capital F is not
+ 
+
+ align:start position:0%
+uh then um you know capital F is not
+ever going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decrease uh the um third property is
+
+ align:start position:0%
+decrease uh the um third property is
+ 
+
+ align:start position:0%
+decrease uh the um third property is
+that the limit as X goes to negative
+
+ align:start position:0%
+that the limit as X goes to negative
+ 
+
+ align:start position:0%
+that the limit as X goes to negative
+Infinity um of the CDF is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and um along with that is the limit
+
+ align:start position:0%
+zero and um along with that is the limit
+ 
+
+ align:start position:0%
+zero and um along with that is the limit
+as X goes to positive Infinity of the
+
+ align:start position:0%
+as X goes to positive Infinity of the
+ 
+
+ align:start position:0%
+as X goes to positive Infinity of the
+CDF is equal to one okay so what are
+
+ align:start position:0%
+CDF is equal to one okay so what are
+ 
+
+ align:start position:0%
+CDF is equal to one okay so what are
+these cdfs going to look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so we know that they're always
+
+ align:start position:0%
+like so we know that they're always
+ 
+
+ align:start position:0%
+like so we know that they're always
+going to start at zero okay so the these
+
+ align:start position:0%
+going to start at zero okay so the these
+ 
+
+ align:start position:0%
+going to start at zero okay so the these
+are just uh you know sort of values that
+
+ align:start position:0%
+are just uh you know sort of values that
+ 
+
+ align:start position:0%
+are just uh you know sort of values that
+X can take on so the CDF is always going
+
+ align:start position:0%
+X can take on so the CDF is always going
+ 
+
+ align:start position:0%
+X can take on so the CDF is always going
+to start at zero it's going to go up
+
+ align:start position:0%
+to start at zero it's going to go up
+ 
+
+ align:start position:0%
+to start at zero it's going to go up
+it's never going to decrease it might
+
+ align:start position:0%
+it's never going to decrease it might
+ 
+
+ align:start position:0%
+it's never going to decrease it might
+have flat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Parts relatively more flat parts and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then in the limit as X goes to Infinity
+
+ align:start position:0%
+then in the limit as X goes to Infinity
+ 
+
+ align:start position:0%
+then in the limit as X goes to Infinity
+it's going to be equal to one
+
+ align:start position:0%
+it's going to be equal to one
+ 
+
+ align:start position:0%
+it's going to be equal to one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now I've drawn a CDF for a continuous
+
+ align:start position:0%
+now I've drawn a CDF for a continuous
+ 
+
+ align:start position:0%
+now I've drawn a CDF for a continuous
+random variable this CDF doesn't have
+
+ align:start position:0%
+random variable this CDF doesn't have
+ 
+
+ align:start position:0%
+random variable this CDF doesn't have
+any jumps in it uh a jump occurs in a
+
+ align:start position:0%
+any jumps in it uh a jump occurs in a
+ 
+
+ align:start position:0%
+any jumps in it uh a jump occurs in a
+CDF when there is positive probability
+
+ align:start position:0%
+CDF when there is positive probability
+ 
+
+ align:start position:0%
+CDF when there is positive probability
+that the random variable takes on a
+
+ align:start position:0%
+that the random variable takes on a
+ 
+
+ align:start position:0%
+that the random variable takes on a
+particular value so for continuous
+
+ align:start position:0%
+particular value so for continuous
+ 
+
+ align:start position:0%
+particular value so for continuous
+random variables the cdfs are always
+
+ align:start position:0%
+random variables the cdfs are always
+ 
+
+ align:start position:0%
+random variables the cdfs are always
+going to be smooth for discret random
+
+ align:start position:0%
+going to be smooth for discret random
+ 
+
+ align:start position:0%
+going to be smooth for discret random
+variables they will always have jumps
+
+ align:start position:0%
+variables they will always have jumps
+ 
+
+ align:start position:0%
+variables they will always have jumps
+and for a mixed random variable they
+
+ align:start position:0%
+and for a mixed random variable they
+ 
+
+ align:start position:0%
+and for a mixed random variable they
+could be sort of a mixture of the two so
+
+ align:start position:0%
+could be sort of a mixture of the two so
+ 
+
+ align:start position:0%
+could be sort of a mixture of the two so
+what does a um CDF a maybe a typical CDF
+
+ align:start position:0%
+what does a um CDF a maybe a typical CDF
+ 
+
+ align:start position:0%
+what does a um CDF a maybe a typical CDF
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see oops I went a little too
+
+ align:start position:0%
+see oops I went a little too
+ 
+
+ align:start position:0%
+see oops I went a little too
+high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here this might be a typical CDF
+
+ align:start position:0%
+okay so here this might be a typical CDF
+ 
+
+ align:start position:0%
+okay so here this might be a typical CDF
+for a discrete random variable how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many at how many points does this
+
+ align:start position:0%
+many at how many points does this
+ 
+
+ align:start position:0%
+many at how many points does this
+discrete random variable have positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability three points right right
+
+ align:start position:0%
+probability three points right right
+ 
+
+ align:start position:0%
+probability three points right right
+here right here and right
+
+ align:start position:0%
+here right here and right
+ 
+
+ align:start position:0%
+here right here and right
+here okay so basically the the the
+
+ align:start position:0%
+here okay so basically the the the
+ 
+
+ align:start position:0%
+here okay so basically the the the
+cumulative distribution function is
+
+ align:start position:0%
+cumulative distribution function is
+ 
+
+ align:start position:0%
+cumulative distribution function is
+doing precisely what we've what its name
+
+ align:start position:0%
+doing precisely what we've what its name
+ 
+
+ align:start position:0%
+doing precisely what we've what its name
+suggests it would do as you go from sort
+
+ align:start position:0%
+suggests it would do as you go from sort
+ 
+
+ align:start position:0%
+suggests it would do as you go from sort
+of negative Infinity up to P positive
+
+ align:start position:0%
+of negative Infinity up to P positive
+ 
+
+ align:start position:0%
+of negative Infinity up to P positive
+Infinity you're accumulating probability
+
+ align:start position:0%
+Infinity you're accumulating probability
+ 
+
+ align:start position:0%
+Infinity you're accumulating probability
+okay so you can think of maybe the the
+
+ align:start position:0%
+okay so you can think of maybe the the
+ 
+
+ align:start position:0%
+okay so you can think of maybe the the
+probability function kind of sitting in
+
+ align:start position:0%
+probability function kind of sitting in
+ 
+
+ align:start position:0%
+probability function kind of sitting in
+the background of the board and we go
+
+ align:start position:0%
+the background of the board and we go
+ 
+
+ align:start position:0%
+the background of the board and we go
+along and we get to the first point mass
+
+ align:start position:0%
+along and we get to the first point mass
+ 
+
+ align:start position:0%
+along and we get to the first point mass
+in the probability function and then at
+
+ align:start position:0%
+in the probability function and then at
+ 
+
+ align:start position:0%
+in the probability function and then at
+that point the CDF jumps up the uh the
+
+ align:start position:0%
+that point the CDF jumps up the uh the
+ 
+
+ align:start position:0%
+that point the CDF jumps up the uh the
+amount of the size of the point Mass
+
+ align:start position:0%
+amount of the size of the point Mass
+ 
+
+ align:start position:0%
+amount of the size of the point Mass
+okay and then we go along this in this
+
+ align:start position:0%
+okay and then we go along this in this
+ 
+
+ align:start position:0%
+okay and then we go along this in this
+whole region um there's zero probability
+
+ align:start position:0%
+whole region um there's zero probability
+ 
+
+ align:start position:0%
+whole region um there's zero probability
+so we're not accumulating any
+
+ align:start position:0%
+so we're not accumulating any
+ 
+
+ align:start position:0%
+so we're not accumulating any
+probability we get to the second Point
+
+ align:start position:0%
+probability we get to the second Point
+ 
+
+ align:start position:0%
+probability we get to the second Point
+Mass in the probability function and
+
+ align:start position:0%
+Mass in the probability function and
+ 
+
+ align:start position:0%
+Mass in the probability function and
+this is the size of the second Point
+
+ align:start position:0%
+this is the size of the second Point
+ 
+
+ align:start position:0%
+this is the size of the second Point
+Mass so our CDF jump jumps up at that
+
+ align:start position:0%
+Mass so our CDF jump jumps up at that
+ 
+
+ align:start position:0%
+Mass so our CDF jump jumps up at that
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the the the PF PDF as I said is
+
+ align:start position:0%
+okay so the the the PF PDF as I said is
+ 
+
+ align:start position:0%
+okay so the the the PF PDF as I said is
+a complete description of the
+
+ align:start position:0%
+a complete description of the
+ 
+
+ align:start position:0%
+a complete description of the
+probability the probabilities associated
+
+ align:start position:0%
+probability the probabilities associated
+ 
+
+ align:start position:0%
+probability the probabilities associated
+with a particular random variable the
+
+ align:start position:0%
+with a particular random variable the
+ 
+
+ align:start position:0%
+with a particular random variable the
+CDF is also a complete description of
+
+ align:start position:0%
+CDF is also a complete description of
+ 
+
+ align:start position:0%
+CDF is also a complete description of
+the probabilities associated with a
+
+ align:start position:0%
+the probabilities associated with a
+ 
+
+ align:start position:0%
+the probabilities associated with a
+random variable and so uh in particular
+
+ align:start position:0%
+random variable and so uh in particular
+ 
+
+ align:start position:0%
+random variable and so uh in particular
+particular they contain the same
+
+ align:start position:0%
+particular they contain the same
+ 
+
+ align:start position:0%
+particular they contain the same
+information about its uh distribution
+
+ align:start position:0%
+information about its uh distribution
+ 
+
+ align:start position:0%
+information about its uh distribution
+just in a different form okay so it
+
+ align:start position:0%
+just in a different form okay so it
+ 
+
+ align:start position:0%
+just in a different form okay so it
+stands to reason then that given the PF
+
+ align:start position:0%
+stands to reason then that given the PF
+ 
+
+ align:start position:0%
+stands to reason then that given the PF
+or the PDF one could recover the CDF and
+
+ align:start position:0%
+or the PDF one could recover the CDF and
+ 
+
+ align:start position:0%
+or the PDF one could recover the CDF and
+given the CDF one can recover the PF or
+
+ align:start position:0%
+given the CDF one can recover the PF or
+ 
+
+ align:start position:0%
+given the CDF one can recover the PF or
+the PDF okay so in the case of a um in
+
+ align:start position:0%
+the PDF okay so in the case of a um in
+ 
+
+ align:start position:0%
+the PDF okay so in the case of a um in
+the case of a discret random variable uh
+
+ align:start position:0%
+the case of a discret random variable uh
+ 
+
+ align:start position:0%
+the case of a discret random variable uh
+that can be a fairly simple process so I
+
+ align:start position:0%
+that can be a fairly simple process so I
+ 
+
+ align:start position:0%
+that can be a fairly simple process so I
+just described it up here right so if I
+
+ align:start position:0%
+just described it up here right so if I
+ 
+
+ align:start position:0%
+just described it up here right so if I
+gave you this CDF you would you would be
+
+ align:start position:0%
+gave you this CDF you would you would be
+ 
+
+ align:start position:0%
+gave you this CDF you would you would be
+able to uh draw the PDF or sorry the PF
+
+ align:start position:0%
+able to uh draw the PDF or sorry the PF
+ 
+
+ align:start position:0%
+able to uh draw the PDF or sorry the PF
+you would be able to say their Point
+
+ align:start position:0%
+you would be able to say their Point
+ 
+
+ align:start position:0%
+you would be able to say their Point
+Mass I'd have to label this I guess so
+
+ align:start position:0%
+Mass I'd have to label this I guess so
+ 
+
+ align:start position:0%
+Mass I'd have to label this I guess so
+you'd know where the point masses are
+
+ align:start position:0%
+you'd know where the point masses are
+ 
+
+ align:start position:0%
+you'd know where the point masses are
+but you know there's a point Mass here a
+
+ align:start position:0%
+but you know there's a point Mass here a
+ 
+
+ align:start position:0%
+but you know there's a point Mass here a
+point Mass here a point Mass here and
+
+ align:start position:0%
+point Mass here a point Mass here and
+ 
+
+ align:start position:0%
+point Mass here a point Mass here and
+you'd know how big this one and how big
+
+ align:start position:0%
+you'd know how big this one and how big
+ 
+
+ align:start position:0%
+you'd know how big this one and how big
+this one and how big this one was okay
+
+ align:start position:0%
+this one and how big this one was okay
+ 
+
+ align:start position:0%
+this one and how big this one was okay
+and you'd be done and likewise if I'd
+
+ align:start position:0%
+and you'd be done and likewise if I'd
+ 
+
+ align:start position:0%
+and you'd be done and likewise if I'd
+given you the PF you could have
+
+ align:start position:0%
+given you the PF you could have
+ 
+
+ align:start position:0%
+given you the PF you could have
+constructed this pretty easily for
+
+ align:start position:0%
+constructed this pretty easily for
+ 
+
+ align:start position:0%
+constructed this pretty easily for
+continuous random VAR Ables uh the these
+
+ align:start position:0%
+continuous random VAR Ables uh the these
+ 
+
+ align:start position:0%
+continuous random VAR Ables uh the these
+are the formulas that tell you how to
+
+ align:start position:0%
+are the formulas that tell you how to
+ 
+
+ align:start position:0%
+are the formulas that tell you how to
+move between a PDF and a CDF okay and
+
+ align:start position:0%
+move between a PDF and a CDF okay and
+ 
+
+ align:start position:0%
+move between a PDF and a CDF okay and
+they they intuitively I think make
+
+ align:start position:0%
+they they intuitively I think make
+ 
+
+ align:start position:0%
+they they intuitively I think make
+complete sense they're just the
+
+ align:start position:0%
+complete sense they're just the
+ 
+
+ align:start position:0%
+complete sense they're just the
+continuous analoges of what I described
+
+ align:start position:0%
+continuous analoges of what I described
+ 
+
+ align:start position:0%
+continuous analoges of what I described
+here uh with the the discrete random
+
+ align:start position:0%
+here uh with the the discrete random
+ 
+
+ align:start position:0%
+here uh with the the discrete random
+variables so the if you want to get the
+
+ align:start position:0%
+variables so the if you want to get the
+ 
+
+ align:start position:0%
+variables so the if you want to get the
+uh CDF uh for a continuous random
+
+ align:start position:0%
+uh CDF uh for a continuous random
+ 
+
+ align:start position:0%
+uh CDF uh for a continuous random
+variable at a particular point then you
+
+ align:start position:0%
+variable at a particular point then you
+ 
+
+ align:start position:0%
+variable at a particular point then you
+integrate the PDF up to that point okay
+
+ align:start position:0%
+integrate the PDF up to that point okay
+ 
+
+ align:start position:0%
+integrate the PDF up to that point okay
+and that's what we have
+
+ align:start position:0%
+and that's what we have
+ 
+
+ align:start position:0%
+and that's what we have
+here and if you have the
+
+ align:start position:0%
+here and if you have the
+ 
+
+ align:start position:0%
+here and if you have the
+CDF uh and you want to get the the PDF
+
+ align:start position:0%
+CDF uh and you want to get the the PDF
+ 
+
+ align:start position:0%
+CDF uh and you want to get the the PDF
+you want to recover the PDF from it um
+
+ align:start position:0%
+you want to recover the PDF from it um
+ 
+
+ align:start position:0%
+you want to recover the PDF from it um
+then you take the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so does this make sense okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good okay oh I should say the second
+
+ align:start position:0%
+good okay oh I should say the second
+ 
+
+ align:start position:0%
+good okay oh I should say the second
+I I have to add this disclaimer this is
+
+ align:start position:0%
+I I have to add this disclaimer this is
+ 
+
+ align:start position:0%
+I I have to add this disclaimer this is
+true provided that X is continuous and
+
+ align:start position:0%
+true provided that X is continuous and
+ 
+
+ align:start position:0%
+true provided that X is continuous and
+f-prime exists at all but a finite
+
+ align:start position:0%
+f-prime exists at all but a finite
+ 
+
+ align:start position:0%
+f-prime exists at all but a finite
+number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points okay
+
+ align:start position:0%
+points okay
+ 
+
+ align:start position:0%
+points okay
+so when we were talking about
+
+ align:start position:0%
+so when we were talking about
+ 
+
+ align:start position:0%
+so when we were talking about
+probability last lecture at some point
+
+ align:start position:0%
+probability last lecture at some point
+ 
+
+ align:start position:0%
+probability last lecture at some point
+during the lecture I said that it was
+
+ align:start position:0%
+during the lecture I said that it was
+ 
+
+ align:start position:0%
+during the lecture I said that it was
+going to be important for us to discuss
+
+ align:start position:0%
+going to be important for us to discuss
+ 
+
+ align:start position:0%
+going to be important for us to discuss
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+relationships uh between stochastic
+
+ align:start position:0%
+relationships uh between stochastic
+ 
+
+ align:start position:0%
+relationships uh between stochastic
+events and then we talked about
+
+ align:start position:0%
+events and then we talked about
+ 
+
+ align:start position:0%
+events and then we talked about
+independence of
+
+ align:start position:0%
+independence of
+ 
+
+ align:start position:0%
+independence of
+of events we talked about conditional
+
+ align:start position:0%
+of events we talked about conditional
+ 
+
+ align:start position:0%
+of events we talked about conditional
+probability and then we sort of segued
+
+ align:start position:0%
+probability and then we sort of segued
+ 
+
+ align:start position:0%
+probability and then we sort of segued
+into Bas theorem and so forth um well
+
+ align:start position:0%
+into Bas theorem and so forth um well
+ 
+
+ align:start position:0%
+into Bas theorem and so forth um well
+we're going to talk about analogous
+
+ align:start position:0%
+we're going to talk about analogous
+ 
+
+ align:start position:0%
+we're going to talk about analogous
+Concepts in the context of random
+
+ align:start position:0%
+Concepts in the context of random
+ 
+
+ align:start position:0%
+Concepts in the context of random
+variables as
+
+ align:start position:0%
+variables as
+ 
+
+ align:start position:0%
+variables as
+well but in order to do that I first
+
+ align:start position:0%
+well but in order to do that I first
+ 
+
+ align:start position:0%
+well but in order to do that I first
+have to define a joint distribution okay
+
+ align:start position:0%
+have to define a joint distribution okay
+ 
+
+ align:start position:0%
+have to define a joint distribution okay
+so in the case where we're only where we
+
+ align:start position:0%
+so in the case where we're only where we
+ 
+
+ align:start position:0%
+so in the case where we're only where we
+only have two random variables where
+
+ align:start position:0%
+only have two random variables where
+ 
+
+ align:start position:0%
+only have two random variables where
+only two random variables are involved
+
+ align:start position:0%
+only two random variables are involved
+ 
+
+ align:start position:0%
+only two random variables are involved
+uh we're going to call that a b variant
+
+ align:start position:0%
+uh we're going to call that a b variant
+ 
+
+ align:start position:0%
+uh we're going to call that a b variant
+distribution we'll see see um sort of uh
+
+ align:start position:0%
+distribution we'll see see um sort of uh
+ 
+
+ align:start position:0%
+distribution we'll see see um sort of uh
+multivariate distributions later on in
+
+ align:start position:0%
+multivariate distributions later on in
+ 
+
+ align:start position:0%
+multivariate distributions later on in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+semester okay so let me pause now to
+
+ align:start position:0%
+semester okay so let me pause now to
+ 
+
+ align:start position:0%
+semester okay so let me pause now to
+sort of uh give you some indication why
+
+ align:start position:0%
+sort of uh give you some indication why
+ 
+
+ align:start position:0%
+sort of uh give you some indication why
+we care about the relationship between
+
+ align:start position:0%
+we care about the relationship between
+ 
+
+ align:start position:0%
+we care about the relationship between
+random variables well maybe you know
+
+ align:start position:0%
+random variables well maybe you know
+ 
+
+ align:start position:0%
+random variables well maybe you know
+exactly why we do and that's why you're
+
+ align:start position:0%
+exactly why we do and that's why you're
+ 
+
+ align:start position:0%
+exactly why we do and that's why you're
+in this class because that's you know
+
+ align:start position:0%
+in this class because that's you know
+ 
+
+ align:start position:0%
+in this class because that's you know
+sort of much of what we do in uh you
+
+ align:start position:0%
+sort of much of what we do in uh you
+ 
+
+ align:start position:0%
+sort of much of what we do in uh you
+know sort of um much of what we do in
+
+ align:start position:0%
+know sort of um much of what we do in
+ 
+
+ align:start position:0%
+know sort of um much of what we do in
+data analysis is gather sort of
+
+ align:start position:0%
+data analysis is gather sort of
+ 
+
+ align:start position:0%
+data analysis is gather sort of
+repeated um uh you know um repeated
+
+ align:start position:0%
+repeated um uh you know um repeated
+ 
+
+ align:start position:0%
+repeated um uh you know um repeated
+observations from particular joint
+
+ align:start position:0%
+observations from particular joint
+ 
+
+ align:start position:0%
+observations from particular joint
+distributions of random variables to try
+
+ align:start position:0%
+distributions of random variables to try
+ 
+
+ align:start position:0%
+distributions of random variables to try
+to figure out what their relationship is
+
+ align:start position:0%
+to figure out what their relationship is
+ 
+
+ align:start position:0%
+to figure out what their relationship is
+okay so we do this all the time and you
+
+ align:start position:0%
+okay so we do this all the time and you
+ 
+
+ align:start position:0%
+okay so we do this all the time and you
+know maybe you don't need need to be
+
+ align:start position:0%
+know maybe you don't need need to be
+ 
+
+ align:start position:0%
+know maybe you don't need need to be
+convinced but here are a couple of
+
+ align:start position:0%
+convinced but here are a couple of
+ 
+
+ align:start position:0%
+convinced but here are a couple of
+examples of sort of random variables
+
+ align:start position:0%
+examples of sort of random variables
+ 
+
+ align:start position:0%
+examples of sort of random variables
+whose joint distributions we might care
+
+ align:start position:0%
+whose joint distributions we might care
+ 
+
+ align:start position:0%
+whose joint distributions we might care
+about so maybe we're interested in for
+
+ align:start position:0%
+about so maybe we're interested in for
+ 
+
+ align:start position:0%
+about so maybe we're interested in for
+instance uh The Joint distribution of
+
+ align:start position:0%
+instance uh The Joint distribution of
+ 
+
+ align:start position:0%
+instance uh The Joint distribution of
+rainfall and crop growth in a particular
+
+ align:start position:0%
+rainfall and crop growth in a particular
+ 
+
+ align:start position:0%
+rainfall and crop growth in a particular
+um field um maybe we care about the
+
+ align:start position:0%
+um field um maybe we care about the
+ 
+
+ align:start position:0%
+um field um maybe we care about the
+length of the regular checkout line and
+
+ align:start position:0%
+length of the regular checkout line and
+ 
+
+ align:start position:0%
+length of the regular checkout line and
+the length of the Express checkout line
+
+ align:start position:0%
+the length of the Express checkout line
+ 
+
+ align:start position:0%
+the length of the Express checkout line
+and the relationship between those two
+
+ align:start position:0%
+and the relationship between those two
+ 
+
+ align:start position:0%
+and the relationship between those two
+okay so in particular maybe we sort of
+
+ align:start position:0%
+okay so in particular maybe we sort of
+ 
+
+ align:start position:0%
+okay so in particular maybe we sort of
+know what the distribution of the length
+
+ align:start position:0%
+know what the distribution of the length
+ 
+
+ align:start position:0%
+know what the distribution of the length
+of the the Express checkout line is but
+
+ align:start position:0%
+of the the Express checkout line is but
+ 
+
+ align:start position:0%
+of the the Express checkout line is but
+um we want to know what the relationship
+
+ align:start position:0%
+um we want to know what the relationship
+ 
+
+ align:start position:0%
+um we want to know what the relationship
+between that distribution and the
+
+ align:start position:0%
+between that distribution and the
+ 
+
+ align:start position:0%
+between that distribution and the
+distribution of the length of the
+
+ align:start position:0%
+distribution of the length of the
+ 
+
+ align:start position:0%
+distribution of the length of the
+regular checkout line is so we know
+
+ align:start position:0%
+regular checkout line is so we know
+ 
+
+ align:start position:0%
+regular checkout line is so we know
+whether to switch or something like that
+
+ align:start position:0%
+whether to switch or something like that
+ 
+
+ align:start position:0%
+whether to switch or something like that
+um we might also be concerned about you
+
+ align:start position:0%
+um we might also be concerned about you
+ 
+
+ align:start position:0%
+um we might also be concerned about you
+know uh if we're interested in investing
+
+ align:start position:0%
+know uh if we're interested in investing
+ 
+
+ align:start position:0%
+know uh if we're interested in investing
+in a stock we might want to know uh The
+
+ align:start position:0%
+in a stock we might want to know uh The
+ 
+
+ align:start position:0%
+in a stock we might want to know uh The
+Joint distribution of the dollar euro
+
+ align:start position:0%
+Joint distribution of the dollar euro
+ 
+
+ align:start position:0%
+Joint distribution of the dollar euro
+exchange rate and um the stock price of
+
+ align:start position:0%
+exchange rate and um the stock price of
+ 
+
+ align:start position:0%
+exchange rate and um the stock price of
+an exporting firm that would be uh that
+
+ align:start position:0%
+an exporting firm that would be uh that
+ 
+
+ align:start position:0%
+an exporting firm that would be uh that
+would be affected by the fluctuations in
+
+ align:start position:0%
+would be affected by the fluctuations in
+ 
+
+ align:start position:0%
+would be affected by the fluctuations in
+the dollar euro exchange rate okay so
+
+ align:start position:0%
+the dollar euro exchange rate okay so
+ 
+
+ align:start position:0%
+the dollar euro exchange rate okay so
+these are just you know a few examples
+
+ align:start position:0%
+these are just you know a few examples
+ 
+
+ align:start position:0%
+these are just you know a few examples
+from you know
+
+ align:start position:0%
+from you know
+ 
+
+ align:start position:0%
+from you know
+uh an infinite number of examples we
+
+ align:start position:0%
+uh an infinite number of examples we
+ 
+
+ align:start position:0%
+uh an infinite number of examples we
+could come up with for why we care about
+
+ align:start position:0%
+could come up with for why we care about
+ 
+
+ align:start position:0%
+could come up with for why we care about
+joint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distributions okay so now
+
+ align:start position:0%
+distributions okay so now
+ 
+
+ align:start position:0%
+distributions okay so now
+definition If X and Y are continuous
+
+ align:start position:0%
+definition If X and Y are continuous
+ 
+
+ align:start position:0%
+definition If X and Y are continuous
+random variables defined on the same
+
+ align:start position:0%
+random variables defined on the same
+ 
+
+ align:start position:0%
+random variables defined on the same
+sample space
+
+ align:start position:0%
+sample space
+ 
+
+ align:start position:0%
+sample space
+s then the joint probability density
+
+ align:start position:0%
+s then the joint probability density
+ 
+
+ align:start position:0%
+s then the joint probability density
+function of X and Y and this is
+
+ align:start position:0%
+function of X and Y and this is
+ 
+
+ align:start position:0%
+function of X and Y and this is
+denoted little F sub
+
+ align:start position:0%
+denoted little F sub
+ 
+
+ align:start position:0%
+denoted little F sub
+XY is the surface such that for any
+
+ align:start position:0%
+XY is the surface such that for any
+ 
+
+ align:start position:0%
+XY is the surface such that for any
+region of the XY plane the probability
+
+ align:start position:0%
+region of the XY plane the probability
+ 
+
+ align:start position:0%
+region of the XY plane the probability
+that XY is contained in some region a is
+
+ align:start position:0%
+that XY is contained in some region a is
+ 
+
+ align:start position:0%
+that XY is contained in some region a is
+equal to the integral of that function
+
+ align:start position:0%
+equal to the integral of that function
+ 
+
+ align:start position:0%
+equal to the integral of that function
+over the region a okay so it's kind of
+
+ align:start position:0%
+over the region a okay so it's kind of
+ 
+
+ align:start position:0%
+over the region a okay so it's kind of
+the natural generalization of the
+
+ align:start position:0%
+the natural generalization of the
+ 
+
+ align:start position:0%
+the natural generalization of the
+continuous the definition of the
+
+ align:start position:0%
+continuous the definition of the
+ 
+
+ align:start position:0%
+continuous the definition of the
+continuous um PDF uh natural generaliz
+
+ align:start position:0%
+continuous um PDF uh natural generaliz
+ 
+
+ align:start position:0%
+continuous um PDF uh natural generaliz
+ation to two random
+
+ align:start position:0%
+ation to two random
+ 
+
+ align:start position:0%
+ation to two random
+variables okay so here we're just um
+
+ align:start position:0%
+variables okay so here we're just um
+ 
+
+ align:start position:0%
+variables okay so here we're just um
+we've got this this uh function here
+
+ align:start position:0%
+we've got this this uh function here
+ 
+
+ align:start position:0%
+we've got this this uh function here
+this small f is a Surface over the XY
+
+ align:start position:0%
+this small f is a Surface over the XY
+ 
+
+ align:start position:0%
+this small f is a Surface over the XY
+plane and in order to calculate
+
+ align:start position:0%
+plane and in order to calculate
+ 
+
+ align:start position:0%
+plane and in order to calculate
+probabilities we're we're going to um be
+
+ align:start position:0%
+probabilities we're we're going to um be
+ 
+
+ align:start position:0%
+probabilities we're we're going to um be
+integrating over sort of regions of the
+
+ align:start position:0%
+integrating over sort of regions of the
+ 
+
+ align:start position:0%
+integrating over sort of regions of the
+XY plane integrating that surface over
+
+ align:start position:0%
+XY plane integrating that surface over
+ 
+
+ align:start position:0%
+XY plane integrating that surface over
+regions of the XY plane okay
+
+ align:start position:0%
+regions of the XY plane okay
+ 
+
+ align:start position:0%
+regions of the XY plane okay
+so like before properties of probability
+
+ align:start position:0%
+so like before properties of probability
+ 
+
+ align:start position:0%
+so like before properties of probability
+imply certain properties of the joint
+
+ align:start position:0%
+imply certain properties of the joint
+ 
+
+ align:start position:0%
+imply certain properties of the joint
+PDF uh such as uh that it's it's got to
+
+ align:start position:0%
+PDF uh such as uh that it's it's got to
+ 
+
+ align:start position:0%
+PDF uh such as uh that it's it's got to
+integrate to one over the XY plane uh
+
+ align:start position:0%
+integrate to one over the XY plane uh
+ 
+
+ align:start position:0%
+integrate to one over the XY plane uh
+any individual point or onedimensional
+
+ align:start position:0%
+any individual point or onedimensional
+ 
+
+ align:start position:0%
+any individual point or onedimensional
+curve has probability zero um Etc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the analogous uh function exists
+
+ align:start position:0%
+okay so the analogous uh function exists
+ 
+
+ align:start position:0%
+okay so the analogous uh function exists
+for discrete random variables as well
+
+ align:start position:0%
+for discrete random variables as well
+ 
+
+ align:start position:0%
+for discrete random variables as well
+and this is how it's defined okay I'm
+
+ align:start position:0%
+and this is how it's defined okay I'm
+ 
+
+ align:start position:0%
+and this is how it's defined okay I'm
+not going to say any more about it right
+
+ align:start position:0%
+not going to say any more about it right
+ 
+
+ align:start position:0%
+not going to say any more about it right
+now and uh sometimes I'm just going to
+
+ align:start position:0%
+now and uh sometimes I'm just going to
+ 
+
+ align:start position:0%
+now and uh sometimes I'm just going to
+give definitions in terms of in terms of
+
+ align:start position:0%
+give definitions in terms of in terms of
+ 
+
+ align:start position:0%
+give definitions in terms of in terms of
+continuous random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so now let's uh let's consider
+
+ align:start position:0%
+okay okay so now let's uh let's consider
+ 
+
+ align:start position:0%
+okay okay so now let's uh let's consider
+an example um where we can uh sort of
+
+ align:start position:0%
+an example um where we can uh sort of
+ 
+
+ align:start position:0%
+an example um where we can uh sort of
+play around with a joint distribution so
+
+ align:start position:0%
+play around with a joint distribution so
+ 
+
+ align:start position:0%
+play around with a joint distribution so
+let's suppose that after hours and hours
+
+ align:start position:0%
+let's suppose that after hours and hours
+ 
+
+ align:start position:0%
+let's suppose that after hours and hours
+of writing lecture notes I develop a
+
+ align:start position:0%
+of writing lecture notes I develop a
+ 
+
+ align:start position:0%
+of writing lecture notes I develop a
+splitting headache by the way this is a
+
+ align:start position:0%
+splitting headache by the way this is a
+ 
+
+ align:start position:0%
+splitting headache by the way this is a
+entirely fictional
+
+ align:start position:0%
+entirely fictional
+ 
+
+ align:start position:0%
+entirely fictional
+account um and after developing that uh
+
+ align:start position:0%
+account um and after developing that uh
+ 
+
+ align:start position:0%
+account um and after developing that uh
+fictional headache I rumage around in my
+
+ align:start position:0%
+fictional headache I rumage around in my
+ 
+
+ align:start position:0%
+fictional headache I rumage around in my
+drawer and I find one tablet of neoen
+
+ align:start position:0%
+drawer and I find one tablet of neoen
+ 
+
+ align:start position:0%
+drawer and I find one tablet of neoen
+and one of acetaminophen okay so those
+
+ align:start position:0%
+and one of acetaminophen okay so those
+ 
+
+ align:start position:0%
+and one of acetaminophen okay so those
+are both uh things that one might take
+
+ align:start position:0%
+are both uh things that one might take
+ 
+
+ align:start position:0%
+are both uh things that one might take
+for a headache and by the way I asked my
+
+ align:start position:0%
+for a headache and by the way I asked my
+ 
+
+ align:start position:0%
+for a headache and by the way I asked my
+sister who who uh who is who went to
+
+ align:start position:0%
+sister who who uh who is who went to
+ 
+
+ align:start position:0%
+sister who who uh who is who went to
+medical school whether this was an
+
+ align:start position:0%
+medical school whether this was an
+ 
+
+ align:start position:0%
+medical school whether this was an
+irresponsible example for me to do in
+
+ align:start position:0%
+irresponsible example for me to do in
+ 
+
+ align:start position:0%
+irresponsible example for me to do in
+class and she said she thought it was
+
+ align:start position:0%
+class and she said she thought it was
+ 
+
+ align:start position:0%
+class and she said she thought it was
+fine
+
+ align:start position:0%
+fine
+ 
+
+ align:start position:0%
+fine
+so okay um so I take both the neoen and
+
+ align:start position:0%
+so okay um so I take both the neoen and
+ 
+
+ align:start position:0%
+so okay um so I take both the neoen and
+the acet acetaminophen okay now let X
+
+ align:start position:0%
+the acet acetaminophen okay now let X
+ 
+
+ align:start position:0%
+the acet acetaminophen okay now let X
+random variable X be the effective
+
+ align:start position:0%
+random variable X be the effective
+ 
+
+ align:start position:0%
+random variable X be the effective
+period of the neoen so I've got this
+
+ align:start position:0%
+period of the neoen so I've got this
+ 
+
+ align:start position:0%
+period of the neoen so I've got this
+headache and I take the nioxin and the
+
+ align:start position:0%
+headache and I take the nioxin and the
+ 
+
+ align:start position:0%
+headache and I take the nioxin and the
+the length of time that it it makes the
+
+ align:start position:0%
+the length of time that it it makes the
+ 
+
+ align:start position:0%
+the length of time that it it makes the
+headache go away is X the random
+
+ align:start position:0%
+headache go away is X the random
+ 
+
+ align:start position:0%
+headache go away is X the random
+variable X and let y be the effective
+
+ align:start position:0%
+variable X and let y be the effective
+ 
+
+ align:start position:0%
+variable X and let y be the effective
+period of the acetam
+
+ align:start position:0%
+period of the acetam
+ 
+
+ align:start position:0%
+period of the acetam
+Menan okay and suppose that this is the
+
+ align:start position:0%
+Menan okay and suppose that this is the
+ 
+
+ align:start position:0%
+Menan okay and suppose that this is the
+joint distribution of for X and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y so I want to ask the following
+
+ align:start position:0%
+Y so I want to ask the following
+ 
+
+ align:start position:0%
+Y so I want to ask the following
+question what's the probability that my
+
+ align:start position:0%
+question what's the probability that my
+ 
+
+ align:start position:0%
+question what's the probability that my
+headache comes back within 3 hours yep
+
+ align:start position:0%
+headache comes back within 3 hours yep
+ 
+
+ align:start position:0%
+headache comes back within 3 hours yep
+do that all depend on the value of
+
+ align:start position:0%
+do that all depend on the value of
+ 
+
+ align:start position:0%
+do that all depend on the value of
+Lambda oh yeah we're going to do all the
+
+ align:start position:0%
+Lambda oh yeah we're going to do all the
+ 
+
+ align:start position:0%
+Lambda oh yeah we're going to do all the
+calculations conditional and Lambda yeah
+
+ align:start position:0%
+calculations conditional and Lambda yeah
+ 
+
+ align:start position:0%
+calculations conditional and Lambda yeah
+I mean I could have put a number in
+
+ align:start position:0%
+I mean I could have put a number in
+ 
+
+ align:start position:0%
+I mean I could have put a number in
+there I don't know maybe I should have
+
+ align:start position:0%
+there I don't know maybe I should have
+ 
+
+ align:start position:0%
+there I don't know maybe I should have
+put a number in there but um yeah no
+
+ align:start position:0%
+put a number in there but um yeah no
+ 
+
+ align:start position:0%
+put a number in there but um yeah no
+we're we'll I I uh decided to just do
+
+ align:start position:0%
+we're we'll I I uh decided to just do
+ 
+
+ align:start position:0%
+we're we'll I I uh decided to just do
+this example in sort of a more General
+
+ align:start position:0%
+this example in sort of a more General
+ 
+
+ align:start position:0%
+this example in sort of a more General
+way and so we'll just do we'll we'll
+
+ align:start position:0%
+way and so we'll just do we'll we'll
+ 
+
+ align:start position:0%
+way and so we'll just do we'll we'll
+calculate all of the probabilities as a
+
+ align:start position:0%
+calculate all of the probabilities as a
+ 
+
+ align:start position:0%
+calculate all of the probabilities as a
+function of Lambda
+
+ align:start position:0%
+function of Lambda
+ 
+
+ align:start position:0%
+function of Lambda
+so so how how would we go about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so if you integrate that that's the
+
+ align:start position:0%
+yeah so if you integrate that that's the
+ 
+
+ align:start position:0%
+yeah so if you integrate that that's the
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+that so that's like
+
+ align:start position:0%
+that so that's like
+ 
+
+ align:start position:0%
+that so that's like
+the would it be
+
+ align:start position:0%
+the would it be
+ 
+
+ align:start position:0%
+the would it be
+one one minus the integral of of
+
+ align:start position:0%
+one one minus the integral of of
+ 
+
+ align:start position:0%
+one one minus the integral of of
+that so I'm I'm not sure exactly what
+
+ align:start position:0%
+that so I'm I'm not sure exactly what
+ 
+
+ align:start position:0%
+that so I'm I'm not sure exactly what
+you're getting at what what I'm what I'm
+
+ align:start position:0%
+you're getting at what what I'm what I'm
+ 
+
+ align:start position:0%
+you're getting at what what I'm what I'm
+uh sort of wanting you to answer is the
+
+ align:start position:0%
+uh sort of wanting you to answer is the
+ 
+
+ align:start position:0%
+uh sort of wanting you to answer is the
+region over which so you're right that
+
+ align:start position:0%
+region over which so you're right that
+ 
+
+ align:start position:0%
+region over which so you're right that
+we're going to integrate this PD this uh
+
+ align:start position:0%
+we're going to integrate this PD this uh
+ 
+
+ align:start position:0%
+we're going to integrate this PD this uh
+joint PDF to get the
+
+ align:start position:0%
+joint PDF to get the
+ 
+
+ align:start position:0%
+joint PDF to get the
+probability and what I'm uh driving at
+
+ align:start position:0%
+probability and what I'm uh driving at
+ 
+
+ align:start position:0%
+probability and what I'm uh driving at
+is what is the can you characterize the
+
+ align:start position:0%
+is what is the can you characterize the
+ 
+
+ align:start position:0%
+is what is the can you characterize the
+region over which we're going to
+
+ align:start position:0%
+region over which we're going to
+ 
+
+ align:start position:0%
+region over which we're going to
+integrate this joint
+
+ align:start position:0%
+integrate this joint
+ 
+
+ align:start position:0%
+integrate this joint
+PDF yep do 0 to 3 and then take one
+
+ align:start position:0%
+PDF yep do 0 to 3 and then take one
+ 
+
+ align:start position:0%
+PDF yep do 0 to 3 and then take one
+minus the probability of that integrate
+
+ align:start position:0%
+minus the probability of that integrate
+ 
+
+ align:start position:0%
+minus the probability of that integrate
+for 0 to 3 hours integrate so remember
+
+ align:start position:0%
+for 0 to 3 hours integrate so remember
+ 
+
+ align:start position:0%
+for 0 to 3 hours integrate so remember
+this is a Surface this is a Surface over
+
+ align:start position:0%
+this is a Surface this is a Surface over
+ 
+
+ align:start position:0%
+this is a Surface this is a Surface over
+the XY plane So when you say integrate
+
+ align:start position:0%
+the XY plane So when you say integrate
+ 
+
+ align:start position:0%
+the XY plane So when you say integrate
+integ from 0 to three do you mean
+
+ align:start position:0%
+integ from 0 to three do you mean
+ 
+
+ align:start position:0%
+integ from 0 to three do you mean
+in The X Dimension
+
+ align:start position:0%
+in The X Dimension
+ 
+
+ align:start position:0%
+in The X Dimension
+oral yeah a double inter oh okay yeah
+
+ align:start position:0%
+oral yeah a double inter oh okay yeah
+ 
+
+ align:start position:0%
+oral yeah a double inter oh okay yeah
+yeah yeah yeah yeah yeah oh okay yes so
+
+ align:start position:0%
+yeah yeah yeah yeah yeah oh okay yes so
+ 
+
+ align:start position:0%
+yeah yeah yeah yeah yeah oh okay yes so
+the double integral is exactly right
+
+ align:start position:0%
+the double integral is exactly right
+ 
+
+ align:start position:0%
+the double integral is exactly right
+yeah yeah so um so the let me see the
+
+ align:start position:0%
+yeah yeah so um so the let me see the
+ 
+
+ align:start position:0%
+yeah yeah so um so the let me see the
+probability my headache comes back
+
+ align:start position:0%
+probability my headache comes back
+ 
+
+ align:start position:0%
+probability my headache comes back
+within three hours
+
+ align:start position:0%
+within three hours
+ 
+
+ align:start position:0%
+within three hours
+is the yes it's one minus this
+
+ align:start position:0%
+is the yes it's one minus this
+ 
+
+ align:start position:0%
+is the yes it's one minus this
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here here i' I've sort of set up the
+
+ align:start position:0%
+so here here i' I've sort of set up the
+ 
+
+ align:start position:0%
+so here here i' I've sort of set up the
+integral so that you can see exactly
+
+ align:start position:0%
+integral so that you can see exactly
+ 
+
+ align:start position:0%
+integral so that you can see exactly
+what we're doing the probability my
+
+ align:start position:0%
+what we're doing the probability my
+ 
+
+ align:start position:0%
+what we're doing the probability my
+headache comes back within 3 hours so
+
+ align:start position:0%
+headache comes back within 3 hours so
+ 
+
+ align:start position:0%
+headache comes back within 3 hours so
+you're right it should be one minus the
+
+ align:start position:0%
+you're right it should be one minus the
+ 
+
+ align:start position:0%
+you're right it should be one minus the
+probability that X is uh less than or
+
+ align:start position:0%
+probability that X is uh less than or
+ 
+
+ align:start position:0%
+probability that X is uh less than or
+equal to three and Y is less than or
+
+ align:start position:0%
+equal to three and Y is less than or
+ 
+
+ align:start position:0%
+equal to three and Y is less than or
+equal to three okay
+
+ align:start position:0%
+equal to three okay
+ 
+
+ align:start position:0%
+equal to three okay
+yep is it correct because if x is less
+
+ align:start position:0%
+yep is it correct because if x is less
+ 
+
+ align:start position:0%
+yep is it correct because if x is less
+than three and Y is less than three that
+
+ align:start position:0%
+than three and Y is less than three that
+ 
+
+ align:start position:0%
+than three and Y is less than three that
+means the of the medicines are not
+
+ align:start position:0%
+means the of the medicines are not
+ 
+
+ align:start position:0%
+means the of the medicines are not
+effective within the 3 hours and you
+
+ align:start position:0%
+effective within the 3 hours and you
+ 
+
+ align:start position:0%
+effective within the 3 hours and you
+will get a headache right so should be
+
+ align:start position:0%
+will get a headache right so should be
+ 
+
+ align:start position:0%
+will get a headache right so should be
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+one or am I
+
+ align:start position:0%
+one or am I
+ 
+
+ align:start position:0%
+one or am I
+understand sorry okay maybe maybe I got
+
+ align:start position:0%
+understand sorry okay maybe maybe I got
+ 
+
+ align:start position:0%
+understand sorry okay maybe maybe I got
+maybe I've got I've I I'm confused with
+
+ align:start position:0%
+maybe I've got I've I I'm confused with
+ 
+
+ align:start position:0%
+maybe I've got I've I I'm confused with
+the uh the negatives so this is this is
+
+ align:start position:0%
+the uh the negatives so this is this is
+ 
+
+ align:start position:0%
+the uh the negatives so this is this is
+giving me the probability oh yeah no
+
+ align:start position:0%
+giving me the probability oh yeah no
+ 
+
+ align:start position:0%
+giving me the probability oh yeah no
+this is giving me the probability that
+
+ align:start position:0%
+this is giving me the probability that
+ 
+
+ align:start position:0%
+this is giving me the probability that
+um my
+
+ align:start position:0%
+um my
+ 
+
+ align:start position:0%
+um my
+headache will come back yeah yeah yeah
+
+ align:start position:0%
+headache will come back yeah yeah yeah
+ 
+
+ align:start position:0%
+headache will come back yeah yeah yeah
+yeah yeah y sorry about that confusion
+
+ align:start position:0%
+yeah yeah y sorry about that confusion
+ 
+
+ align:start position:0%
+yeah yeah y sorry about that confusion
+okay so the probability that my headache
+
+ align:start position:0%
+okay so the probability that my headache
+ 
+
+ align:start position:0%
+okay so the probability that my headache
+comes back within 3 hours is the the
+
+ align:start position:0%
+comes back within 3 hours is the the
+ 
+
+ align:start position:0%
+comes back within 3 hours is the the
+integral over this region okay and I
+
+ align:start position:0%
+integral over this region okay and I
+ 
+
+ align:start position:0%
+integral over this region okay and I
+have a picture of it as well so we all
+
+ align:start position:0%
+have a picture of it as well so we all
+ 
+
+ align:start position:0%
+have a picture of it as well so we all
+we do is we take the joint PDF okay so
+
+ align:start position:0%
+we do is we take the joint PDF okay so
+ 
+
+ align:start position:0%
+we do is we take the joint PDF okay so
+this is the surface over the XY plane
+
+ align:start position:0%
+this is the surface over the XY plane
+ 
+
+ align:start position:0%
+this is the surface over the XY plane
+and we're integrating from uh we're
+
+ align:start position:0%
+and we're integrating from uh we're
+ 
+
+ align:start position:0%
+and we're integrating from uh we're
+doing the double integral over the
+
+ align:start position:0%
+doing the double integral over the
+ 
+
+ align:start position:0%
+doing the double integral over the
+region the sort of um
+
+ align:start position:0%
+region the sort of um
+ 
+
+ align:start position:0%
+region the sort of um
+3x3 box at the origin
+
+ align:start position:0%
+3x3 box at the origin
+ 
+
+ align:start position:0%
+3x3 box at the origin
+okay and those dots mean that I left out
+
+ align:start position:0%
+okay and those dots mean that I left out
+ 
+
+ align:start position:0%
+okay and those dots mean that I left out
+the intermediate steps but you can work
+
+ align:start position:0%
+the intermediate steps but you can work
+ 
+
+ align:start position:0%
+the intermediate steps but you can work
+on them uh work on the details at home
+
+ align:start position:0%
+on them uh work on the details at home
+ 
+
+ align:start position:0%
+on them uh work on the details at home
+and in fact this is what the this is
+
+ align:start position:0%
+and in fact this is what the this is
+ 
+
+ align:start position:0%
+and in fact this is what the this is
+what you get when you do the double
+
+ align:start position:0%
+what you get when you do the double
+ 
+
+ align:start position:0%
+what you get when you do the double
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+okay and here is a picture this is the
+
+ align:start position:0%
+okay and here is a picture this is the
+ 
+
+ align:start position:0%
+okay and here is a picture this is the
+region uh over which we're integrating
+
+ align:start position:0%
+region uh over which we're integrating
+ 
+
+ align:start position:0%
+region uh over which we're integrating
+okay so if I wanted to draw I'm not sure
+
+ align:start position:0%
+okay so if I wanted to draw I'm not sure
+ 
+
+ align:start position:0%
+okay so if I wanted to draw I'm not sure
+if I can do this in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very useful way but let me give it a
+
+ align:start position:0%
+very useful way but let me give it a
+ 
+
+ align:start position:0%
+very useful way but let me give it a
+shot so let's see I have X over here and
+
+ align:start position:0%
+shot so let's see I have X over here and
+ 
+
+ align:start position:0%
+shot so let's see I have X over here and
+Y over here and then I have f subx y
+
+ align:start position:0%
+Y over here and then I have f subx y
+ 
+
+ align:start position:0%
+Y over here and then I have f subx y
+here and this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region over which we're integrating and
+
+ align:start position:0%
+region over which we're integrating and
+ 
+
+ align:start position:0%
+region over which we're integrating and
+the surface looks something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not sure how useful that is
+
+ align:start position:0%
+not sure how useful that is
+ 
+
+ align:start position:0%
+not sure how useful that is
+but and what we want to do is um to
+
+ align:start position:0%
+but and what we want to do is um to
+ 
+
+ align:start position:0%
+but and what we want to do is um to
+calculate the probability just integrate
+
+ align:start position:0%
+calculate the probability just integrate
+ 
+
+ align:start position:0%
+calculate the probability just integrate
+this surface over this area okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep uh only only if you want me to get
+
+ align:start position:0%
+yep uh only only if you want me to get
+ 
+
+ align:start position:0%
+yep uh only only if you want me to get
+confused again and scratch my head okay
+
+ align:start position:0%
+confused again and scratch my head okay
+ 
+
+ align:start position:0%
+confused again and scratch my head okay
+so let's go through this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay so X is the effective period of
+
+ align:start position:0%
+so okay so X is the effective period of
+ 
+
+ align:start position:0%
+so okay so X is the effective period of
+nioxin so if uh if x is equal to 3 so
+
+ align:start position:0%
+nioxin so if uh if x is equal to 3 so
+ 
+
+ align:start position:0%
+nioxin so if uh if x is equal to 3 so
+let's let's just think about it in terms
+
+ align:start position:0%
+let's let's just think about it in terms
+ 
+
+ align:start position:0%
+let's let's just think about it in terms
+of a of of one dimension okay so if if
+
+ align:start position:0%
+of a of of one dimension okay so if if
+ 
+
+ align:start position:0%
+of a of of one dimension okay so if if
+uh X is equal to three my headache comes
+
+ align:start position:0%
+uh X is equal to three my headache comes
+ 
+
+ align:start position:0%
+uh X is equal to three my headache comes
+back uh in 3 hours okay if my or if x is
+
+ align:start position:0%
+back uh in 3 hours okay if my or if x is
+ 
+
+ align:start position:0%
+back uh in 3 hours okay if my or if x is
+less anything less than three my
+
+ align:start position:0%
+less anything less than three my
+ 
+
+ align:start position:0%
+less anything less than three my
+headache will come back within three
+
+ align:start position:0%
+headache will come back within three
+ 
+
+ align:start position:0%
+headache will come back within three
+hours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you had only one then it will
+
+ align:start position:0%
+okay if you had only one then it will
+ 
+
+ align:start position:0%
+okay if you had only one then it will
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+if that one is out
+
+ align:start position:0%
+if that one is out
+ 
+
+ align:start position:0%
+if that one is out
+to be less than three but then you
+
+ align:start position:0%
+to be less than three but then you
+ 
+
+ align:start position:0%
+to be less than three but then you
+always have the other one so that's
+
+ align:start position:0%
+always have the other one so that's
+ 
+
+ align:start position:0%
+always have the other one so that's
+youting Square EV have to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together and perhaps this next example
+
+ align:start position:0%
+together and perhaps this next example
+ 
+
+ align:start position:0%
+together and perhaps this next example
+will so this next example is sort of I'm
+
+ align:start position:0%
+will so this next example is sort of I'm
+ 
+
+ align:start position:0%
+will so this next example is sort of I'm
+changing the question a little bit and
+
+ align:start position:0%
+changing the question a little bit and
+ 
+
+ align:start position:0%
+changing the question a little bit and
+it might clear it actually might clarify
+
+ align:start position:0%
+it might clear it actually might clarify
+ 
+
+ align:start position:0%
+it might clear it actually might clarify
+um the question so or might clarify the
+
+ align:start position:0%
+um the question so or might clarify the
+ 
+
+ align:start position:0%
+um the question so or might clarify the
+previous question
+
+ align:start position:0%
+previous question
+ 
+
+ align:start position:0%
+previous question
+so I'm going to change the question now
+
+ align:start position:0%
+so I'm going to change the question now
+ 
+
+ align:start position:0%
+so I'm going to change the question now
+and ask what if I only took the
+
+ align:start position:0%
+and ask what if I only took the
+ 
+
+ align:start position:0%
+and ask what if I only took the
+acetaminophen after the nepro stopped
+
+ align:start position:0%
+acetaminophen after the nepro stopped
+ 
+
+ align:start position:0%
+acetaminophen after the nepro stopped
+working okay so what uh question what
+
+ align:start position:0%
+working okay so what uh question what
+ 
+
+ align:start position:0%
+working okay so what uh question what
+can we put this in terms of sort of a
+
+ align:start position:0%
+can we put this in terms of sort of a
+ 
+
+ align:start position:0%
+can we put this in terms of sort of a
+question about probability what am I
+
+ align:start position:0%
+question about probability what am I
+ 
+
+ align:start position:0%
+question about probability what am I
+asking
+
+ align:start position:0%
+asking
+ 
+
+ align:start position:0%
+asking
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+y that's right it's the probability that
+
+ align:start position:0%
+y that's right it's the probability that
+ 
+
+ align:start position:0%
+y that's right it's the probability that
+x + y is less than three because I take
+
+ align:start position:0%
+x + y is less than three because I take
+ 
+
+ align:start position:0%
+x + y is less than three because I take
+the neox and as soon as that stops
+
+ align:start position:0%
+the neox and as soon as that stops
+ 
+
+ align:start position:0%
+the neox and as soon as that stops
+working I take the acet acetaminophen so
+
+ align:start position:0%
+working I take the acet acetaminophen so
+ 
+
+ align:start position:0%
+working I take the acet acetaminophen so
+I'm asking the question whether the the
+
+ align:start position:0%
+I'm asking the question whether the the
+ 
+
+ align:start position:0%
+I'm asking the question whether the the
+uh sum of the two lengths is less than
+
+ align:start position:0%
+uh sum of the two lengths is less than
+ 
+
+ align:start position:0%
+uh sum of the two lengths is less than
+or equal to three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so now the region over which
+
+ align:start position:0%
+okay okay so now the region over which
+ 
+
+ align:start position:0%
+okay okay so now the region over which
+we're going to integrate this surface
+
+ align:start position:0%
+we're going to integrate this surface
+ 
+
+ align:start position:0%
+we're going to integrate this surface
+changes obviously um and uh you know
+
+ align:start position:0%
+changes obviously um and uh you know
+ 
+
+ align:start position:0%
+changes obviously um and uh you know
+this is I've set up the the uh
+
+ align:start position:0%
+this is I've set up the the uh
+ 
+
+ align:start position:0%
+this is I've set up the the uh
+integral but I can also show you the
+
+ align:start position:0%
+integral but I can also show you the
+ 
+
+ align:start position:0%
+integral but I can also show you the
+picture how of how it
+
+ align:start position:0%
+picture how of how it
+ 
+
+ align:start position:0%
+picture how of how it
+changes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now yep how do you probability X Y to
+
+ align:start position:0%
+now yep how do you probability X Y to
+ 
+
+ align:start position:0%
+now yep how do you probability X Y to
+that how how do I set up these limits of
+
+ align:start position:0%
+that how how do I set up these limits of
+ 
+
+ align:start position:0%
+that how how do I set up these limits of
+integration well so basically what I'm
+
+ align:start position:0%
+integration well so basically what I'm
+ 
+
+ align:start position:0%
+integration well so basically what I'm
+I'm going to do is I'm going to draw a
+
+ align:start position:0%
+I'm going to do is I'm going to draw a
+ 
+
+ align:start position:0%
+I'm going to do is I'm going to draw a
+line in the XY plane that's def that
+
+ align:start position:0%
+line in the XY plane that's def that
+ 
+
+ align:start position:0%
+line in the XY plane that's def that
+defines sort of x + y being equal to
+
+ align:start position:0%
+defines sort of x + y being equal to
+ 
+
+ align:start position:0%
+defines sort of x + y being equal to
+three and then I've got to set out my
+
+ align:start position:0%
+three and then I've got to set out my
+ 
+
+ align:start position:0%
+three and then I've got to set out my
+limits of integration so this that's
+
+ align:start position:0%
+limits of integration so this that's
+ 
+
+ align:start position:0%
+limits of integration so this that's
+this line here okay and then I've got to
+
+ align:start position:0%
+this line here okay and then I've got to
+ 
+
+ align:start position:0%
+this line here okay and then I've got to
+set out my limits of integration to uh
+
+ align:start position:0%
+set out my limits of integration to uh
+ 
+
+ align:start position:0%
+set out my limits of integration to uh
+to to get that triangle and the the way
+
+ align:start position:0%
+to to get that triangle and the the way
+ 
+
+ align:start position:0%
+to to get that triangle and the the way
+I do it I mean there there's actually
+
+ align:start position:0%
+I do it I mean there there's actually
+ 
+
+ align:start position:0%
+I do it I mean there there's actually
+two different ways to do it but the way
+
+ align:start position:0%
+two different ways to do it but the way
+ 
+
+ align:start position:0%
+two different ways to do it but the way
+I did it was letting X go from 0 to 3
+
+ align:start position:0%
+I did it was letting X go from 0 to 3
+ 
+
+ align:start position:0%
+I did it was letting X go from 0 to 3
+but then when you uh so as X is going
+
+ align:start position:0%
+but then when you uh so as X is going
+ 
+
+ align:start position:0%
+but then when you uh so as X is going
+from 0 to 3 then y uh goes from 0 to 3 -
+
+ align:start position:0%
+from 0 to 3 then y uh goes from 0 to 3 -
+ 
+
+ align:start position:0%
+from 0 to 3 then y uh goes from 0 to 3 -
+x which is which is this line here okay
+
+ align:start position:0%
+x which is which is this line here okay
+ 
+
+ align:start position:0%
+x which is which is this line here okay
+so the the the um the the limits of
+
+ align:start position:0%
+so the the the um the the limits of
+ 
+
+ align:start position:0%
+so the the the um the the limits of
+integration for y depend on X because
+
+ align:start position:0%
+integration for y depend on X because
+ 
+
+ align:start position:0%
+integration for y depend on X because
+it's a triangle and you know you can
+
+ align:start position:0%
+it's a triangle and you know you can
+ 
+
+ align:start position:0%
+it's a triangle and you know you can
+sort of look for each for each value of
+
+ align:start position:0%
+sort of look for each for each value of
+ 
+
+ align:start position:0%
+sort of look for each for each value of
+x what uh the limits of integration for
+
+ align:start position:0%
+x what uh the limits of integration for
+ 
+
+ align:start position:0%
+x what uh the limits of integration for
+y will be does that make sense so I
+
+ align:start position:0%
+y will be does that make sense so I
+ 
+
+ align:start position:0%
+y will be does that make sense so I
+could have done it the other you know I
+
+ align:start position:0%
+could have done it the other you know I
+ 
+
+ align:start position:0%
+could have done it the other you know I
+could have switched the the order of
+
+ align:start position:0%
+could have switched the the order of
+ 
+
+ align:start position:0%
+could have switched the the order of
+integration and I would have had
+
+ align:start position:0%
+integration and I would have had
+ 
+
+ align:start position:0%
+integration and I would have had
+different limits and would have gotten
+
+ align:start position:0%
+different limits and would have gotten
+ 
+
+ align:start position:0%
+different limits and would have gotten
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yep might be a weird question but it
+
+ align:start position:0%
+yep might be a weird question but it
+ 
+
+ align:start position:0%
+yep might be a weird question but it
+seems like to get these two The Joint
+
+ align:start position:0%
+seems like to get these two The Joint
+ 
+
+ align:start position:0%
+seems like to get these two The Joint
+probability just multiplying each
+
+ align:start position:0%
+probability just multiplying each
+ 
+
+ align:start position:0%
+probability just multiplying each
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+probability well you're a step ahead of
+
+ align:start position:0%
+probability well you're a step ahead of
+ 
+
+ align:start position:0%
+probability well you're a step ahead of
+us actually so so so actually that no
+
+ align:start position:0%
+us actually so so so actually that no
+ 
+
+ align:start position:0%
+us actually so so so actually that no
+you're absolutely right and that's a
+
+ align:start position:0%
+you're absolutely right and that's a
+ 
+
+ align:start position:0%
+you're absolutely right and that's a
+that's a um an astute observation um and
+
+ align:start position:0%
+that's a um an astute observation um and
+ 
+
+ align:start position:0%
+that's a um an astute observation um and
+basically this the that means that this
+
+ align:start position:0%
+basically this the that means that this
+ 
+
+ align:start position:0%
+basically this the that means that this
+joint probability is the result of two
+
+ align:start position:0%
+joint probability is the result of two
+ 
+
+ align:start position:0%
+joint probability is the result of two
+uh random variables that are that are
+
+ align:start position:0%
+uh random variables that are that are
+ 
+
+ align:start position:0%
+uh random variables that are that are
+independent and this that's how you get
+
+ align:start position:0%
+independent and this that's how you get
+ 
+
+ align:start position:0%
+independent and this that's how you get
+joint distributions of independent
+
+ align:start position:0%
+joint distributions of independent
+ 
+
+ align:start position:0%
+joint distributions of independent
+random variables is you multiply their
+
+ align:start position:0%
+random variables is you multiply their
+ 
+
+ align:start position:0%
+random variables is you multiply their
+individual uh distributions together
+
+ align:start position:0%
+individual uh distributions together
+ 
+
+ align:start position:0%
+individual uh distributions together
+okay so we didn't you didn't have have
+
+ align:start position:0%
+okay so we didn't you didn't have have
+ 
+
+ align:start position:0%
+okay so we didn't you didn't have have
+to know that for this example I just
+
+ align:start position:0%
+to know that for this example I just
+ 
+
+ align:start position:0%
+to know that for this example I just
+gave you the joint distribution but if
+
+ align:start position:0%
+gave you the joint distribution but if
+ 
+
+ align:start position:0%
+gave you the joint distribution but if
+you knew about independence of random
+
+ align:start position:0%
+you knew about independence of random
+ 
+
+ align:start position:0%
+you knew about independence of random
+variables and you knew how to get joint
+
+ align:start position:0%
+variables and you knew how to get joint
+ 
+
+ align:start position:0%
+variables and you knew how to get joint
+distributions when they were independent
+
+ align:start position:0%
+distributions when they were independent
+ 
+
+ align:start position:0%
+distributions when they were independent
+then I could have given you the
+
+ align:start position:0%
+then I could have given you the
+ 
+
+ align:start position:0%
+then I could have given you the
+individual distributions and you know
+
+ align:start position:0%
+individual distributions and you know
+ 
+
+ align:start position:0%
+individual distributions and you know
+then you could have uh you know computed
+
+ align:start position:0%
+then you could have uh you know computed
+ 
+
+ align:start position:0%
+then you could have uh you know computed
+what the The Joint distribution was and
+
+ align:start position:0%
+what the The Joint distribution was and
+ 
+
+ align:start position:0%
+what the The Joint distribution was and
+then done the problem like that
+
+ align:start position:0%
+then done the problem like that
+ 
+
+ align:start position:0%
+then done the problem like that
+y okay so let's
+
+ align:start position:0%
+y okay so let's
+ 
+
+ align:start position:0%
+y okay so let's
+see okay so one uh one sort of final and
+
+ align:start position:0%
+see okay so one uh one sort of final and
+ 
+
+ align:start position:0%
+see okay so one uh one sort of final and
+important point I want to make about
+
+ align:start position:0%
+important point I want to make about
+ 
+
+ align:start position:0%
+important point I want to make about
+this uh
+
+ align:start position:0%
+this uh
+ 
+
+ align:start position:0%
+this uh
+example is that this example sort of
+
+ align:start position:0%
+example is that this example sort of
+ 
+
+ align:start position:0%
+example is that this example sort of
+suggests something very powerful that we
+
+ align:start position:0%
+suggests something very powerful that we
+ 
+
+ align:start position:0%
+suggests something very powerful that we
+can do with um uh random variables so
+
+ align:start position:0%
+can do with um uh random variables so
+ 
+
+ align:start position:0%
+can do with um uh random variables so
+let's suppose I want to define a new
+
+ align:start position:0%
+let's suppose I want to define a new
+ 
+
+ align:start position:0%
+let's suppose I want to define a new
+random variable and I call my random
+
+ align:start position:0%
+random variable and I call my random
+ 
+
+ align:start position:0%
+random variable and I call my random
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+Z and that's the total effective life of
+
+ align:start position:0%
+Z and that's the total effective life of
+ 
+
+ align:start position:0%
+Z and that's the total effective life of
+the Naproxin and the acetam menen taken
+
+ align:start position:0%
+the Naproxin and the acetam menen taken
+ 
+
+ align:start position:0%
+the Naproxin and the acetam menen taken
+sequentially okay so I mean that's a
+
+ align:start position:0%
+sequentially okay so I mean that's a
+ 
+
+ align:start position:0%
+sequentially okay so I mean that's a
+it's a certainly a reasonable uh random
+
+ align:start position:0%
+it's a certainly a reasonable uh random
+ 
+
+ align:start position:0%
+it's a certainly a reasonable uh random
+variable to Define how could I start to
+
+ align:start position:0%
+variable to Define how could I start to
+ 
+
+ align:start position:0%
+variable to Define how could I start to
+think about how that random variable is
+
+ align:start position:0%
+think about how that random variable is
+ 
+
+ align:start position:0%
+think about how that random variable is
+distributed well in fact we've already
+
+ align:start position:0%
+distributed well in fact we've already
+ 
+
+ align:start position:0%
+distributed well in fact we've already
+figured out exactly how it's distributed
+
+ align:start position:0%
+figured out exactly how it's distributed
+ 
+
+ align:start position:0%
+figured out exactly how it's distributed
+right so were you going to say no Okay
+
+ align:start position:0%
+right so were you going to say no Okay
+ 
+
+ align:start position:0%
+right so were you going to say no Okay
+so we've we've actually already figured
+
+ align:start position:0%
+so we've we've actually already figured
+ 
+
+ align:start position:0%
+so we've we've actually already figured
+out how it's distributed so um the the
+
+ align:start position:0%
+out how it's distributed so um the the
+ 
+
+ align:start position:0%
+out how it's distributed so um the the
+CDF of the new random variable by
+
+ align:start position:0%
+CDF of the new random variable by
+ 
+
+ align:start position:0%
+CDF of the new random variable by
+definition is just equal to the
+
+ align:start position:0%
+definition is just equal to the
+ 
+
+ align:start position:0%
+definition is just equal to the
+probability that Z is less than little
+
+ align:start position:0%
+probability that Z is less than little
+ 
+
+ align:start position:0%
+probability that Z is less than little
+Z okay it's just the definition of a
+
+ align:start position:0%
+Z okay it's just the definition of a
+ 
+
+ align:start position:0%
+Z okay it's just the definition of a
+CDF that is equal to by definition of
+
+ align:start position:0%
+CDF that is equal to by definition of
+ 
+
+ align:start position:0%
+CDF that is equal to by definition of
+our random our new random variable
+
+ align:start position:0%
+our random our new random variable
+ 
+
+ align:start position:0%
+our random our new random variable
+that's equal to the probability that x +
+
+ align:start position:0%
+that's equal to the probability that x +
+ 
+
+ align:start position:0%
+that's equal to the probability that x +
+y is less than or equal to little Z
+
+ align:start position:0%
+y is less than or equal to little Z
+ 
+
+ align:start position:0%
+y is less than or equal to little Z
+okay and that is equal to that quantity
+
+ align:start position:0%
+okay and that is equal to that quantity
+ 
+
+ align:start position:0%
+okay and that is equal to that quantity
+which we just computed okay for Z
+
+ align:start position:0%
+which we just computed okay for Z
+ 
+
+ align:start position:0%
+which we just computed okay for Z
+greater than zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so once we've got the CDF of this
+
+ align:start position:0%
+and so once we've got the CDF of this
+ 
+
+ align:start position:0%
+and so once we've got the CDF of this
+new random variable Z then we know that
+
+ align:start position:0%
+new random variable Z then we know that
+ 
+
+ align:start position:0%
+new random variable Z then we know that
+we can also get the PDF of the new
+
+ align:start position:0%
+we can also get the PDF of the new
+ 
+
+ align:start position:0%
+we can also get the PDF of the new
+random variable Z okay and how do we do
+
+ align:start position:0%
+random variable Z okay and how do we do
+ 
+
+ align:start position:0%
+random variable Z okay and how do we do
+that well we just take the derivative
+
+ align:start position:0%
+that well we just take the derivative
+ 
+
+ align:start position:0%
+that well we just take the derivative
+okay so the PDF of this new random
+
+ align:start position:0%
+okay so the PDF of this new random
+ 
+
+ align:start position:0%
+okay so the PDF of this new random
+variable is just equal to uh Lambda
+
+ align:start position:0%
+variable is just equal to uh Lambda
+ 
+
+ align:start position:0%
+variable is just equal to uh Lambda
+squared z uh time e to the negative Z
+
+ align:start position:0%
+squared z uh time e to the negative Z
+ 
+
+ align:start position:0%
+squared z uh time e to the negative Z
+Lambda okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the the the reason why this is a
+
+ align:start position:0%
+okay so the the the reason why this is a
+ 
+
+ align:start position:0%
+okay so the the the reason why this is a
+a a very important um example and sort
+
+ align:start position:0%
+a a very important um example and sort
+ 
+
+ align:start position:0%
+a a very important um example and sort
+of the concepts embodied in it are going
+
+ align:start position:0%
+of the concepts embodied in it are going
+ 
+
+ align:start position:0%
+of the concepts embodied in it are going
+to come up many times over the course of
+
+ align:start position:0%
+to come up many times over the course of
+ 
+
+ align:start position:0%
+to come up many times over the course of
+the semester the reason why it's so
+
+ align:start position:0%
+the semester the reason why it's so
+ 
+
+ align:start position:0%
+the semester the reason why it's so
+important is that when we start studying
+
+ align:start position:0%
+important is that when we start studying
+ 
+
+ align:start position:0%
+important is that when we start studying
+statistics statistics are a statistic is
+
+ align:start position:0%
+statistics statistics are a statistic is
+ 
+
+ align:start position:0%
+statistics statistics are a statistic is
+nothing other than functions of random
+
+ align:start position:0%
+nothing other than functions of random
+ 
+
+ align:start position:0%
+nothing other than functions of random
+variables that's what statistic is and
+
+ align:start position:0%
+variables that's what statistic is and
+ 
+
+ align:start position:0%
+variables that's what statistic is and
+so if we want to understand how
+
+ align:start position:0%
+so if we want to understand how
+ 
+
+ align:start position:0%
+so if we want to understand how
+statistics behave we have to understand
+
+ align:start position:0%
+statistics behave we have to understand
+ 
+
+ align:start position:0%
+statistics behave we have to understand
+how functions of random variables behave
+
+ align:start position:0%
+how functions of random variables behave
+ 
+
+ align:start position:0%
+how functions of random variables behave
+and this is the first step we're going
+
+ align:start position:0%
+and this is the first step we're going
+ 
+
+ align:start position:0%
+and this is the first step we're going
+to take towards this this is just one
+
+ align:start position:0%
+to take towards this this is just one
+ 
+
+ align:start position:0%
+to take towards this this is just one
+example but this lets us know that if we
+
+ align:start position:0%
+example but this lets us know that if we
+ 
+
+ align:start position:0%
+example but this lets us know that if we
+have two random variables and we uh X
+
+ align:start position:0%
+have two random variables and we uh X
+ 
+
+ align:start position:0%
+have two random variables and we uh X
+and Y and we know how they're
+
+ align:start position:0%
+and Y and we know how they're
+ 
+
+ align:start position:0%
+and Y and we know how they're
+distributed uh we have some hope of
+
+ align:start position:0%
+distributed uh we have some hope of
+ 
+
+ align:start position:0%
+distributed uh we have some hope of
+figuring out out how some arbitrary
+
+ align:start position:0%
+figuring out out how some arbitrary
+ 
+
+ align:start position:0%
+figuring out out how some arbitrary
+function of them is also distributed and
+
+ align:start position:0%
+function of them is also distributed and
+ 
+
+ align:start position:0%
+function of them is also distributed and
+in fact we're you know typically going
+
+ align:start position:0%
+in fact we're you know typically going
+ 
+
+ align:start position:0%
+in fact we're you know typically going
+to be able to figure out how the sum of
+
+ align:start position:0%
+to be able to figure out how the sum of
+ 
+
+ align:start position:0%
+to be able to figure out how the sum of
+random variables is distributed um and
+
+ align:start position:0%
+random variables is distributed um and
+ 
+
+ align:start position:0%
+random variables is distributed um and
+that's going to be very useful for us
+
+ align:start position:0%
+that's going to be very useful for us
+ 
+
+ align:start position:0%
+that's going to be very useful for us
+okay and so uh you know that's sort of
+
+ align:start position:0%
+okay and so uh you know that's sort of
+ 
+
+ align:start position:0%
+okay and so uh you know that's sort of
+um uh you know one reason why I like
+
+ align:start position:0%
+um uh you know one reason why I like
+ 
+
+ align:start position:0%
+um uh you know one reason why I like
+this example a lot is to sort of make
+
+ align:start position:0%
+this example a lot is to sort of make
+ 
+
+ align:start position:0%
+this example a lot is to sort of make
+the point um that you know that that uh
+
+ align:start position:0%
+the point um that you know that that uh
+ 
+
+ align:start position:0%
+the point um that you know that that uh
+we can with the with the tools we have
+
+ align:start position:0%
+we can with the with the tools we have
+ 
+
+ align:start position:0%
+we can with the with the tools we have
+already uh start thinking about how to
+
+ align:start position:0%
+already uh start thinking about how to
+ 
+
+ align:start position:0%
+already uh start thinking about how to
+deal with function of random
+
+ align:start position:0%
+deal with function of random
+ 
+
+ align:start position:0%
+deal with function of random
+variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
\ No newline at end of file
diff --git a/R8k2x5qJgO4.txt b/R8k2x5qJgO4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e5b8612db72811d0e8e8dddb079043badea21dac
--- /dev/null
+++ b/R8k2x5qJgO4.txt
@@ -0,0 +1,12371 @@
+align:start position:0%
+ 
+welcome everyone
+
+ align:start position:0%
+welcome everyone
+ 
+
+ align:start position:0%
+welcome everyone
+try to start on time are there any
+
+ align:start position:0%
+try to start on time are there any
+ 
+
+ align:start position:0%
+try to start on time are there any
+questions from last time
+
+ align:start position:0%
+questions from last time
+ 
+
+ align:start position:0%
+questions from last time
+okay we'll take a look at the
+
+ align:start position:0%
+okay we'll take a look at the
+ 
+
+ align:start position:0%
+okay we'll take a look at the
+class syllabus um we did a theory
+
+ align:start position:0%
+class syllabus um we did a theory
+ 
+
+ align:start position:0%
+class syllabus um we did a theory
+lecture on borisian equilibria and two
+
+ align:start position:0%
+lecture on borisian equilibria and two
+ 
+
+ align:start position:0%
+lecture on borisian equilibria and two
+by two by two
+
+ align:start position:0%
+by two by two
+ 
+
+ align:start position:0%
+by two by two
+trade models in theory last class
+
+ align:start position:0%
+trade models in theory last class
+ 
+
+ align:start position:0%
+trade models in theory last class
+today we're going to begin the first of
+
+ align:start position:0%
+today we're going to begin the first of
+ 
+
+ align:start position:0%
+today we're going to begin the first of
+two applications of that you can see in
+
+ align:start position:0%
+two applications of that you can see in
+ 
+
+ align:start position:0%
+two applications of that you can see in
+fact on the reading list
+
+ align:start position:0%
+fact on the reading list
+ 
+
+ align:start position:0%
+fact on the reading list
+the papers for today which includes this
+
+ align:start position:0%
+the papers for today which includes this
+ 
+
+ align:start position:0%
+the papers for today which includes this
+thing with my thai colleague archer watt
+
+ align:start position:0%
+thing with my thai colleague archer watt
+ 
+
+ align:start position:0%
+thing with my thai colleague archer watt
+which is taking the theory model back to
+
+ align:start position:0%
+which is taking the theory model back to
+ 
+
+ align:start position:0%
+which is taking the theory model back to
+the thai applications
+
+ align:start position:0%
+the thai applications
+ 
+
+ align:start position:0%
+the thai applications
+and there's an additional star reading
+
+ align:start position:0%
+and there's an additional star reading
+ 
+
+ align:start position:0%
+and there's an additional star reading
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+dawkins which is calibration which we
+
+ align:start position:0%
+dawkins which is calibration which we
+ 
+
+ align:start position:0%
+dawkins which is calibration which we
+have done before with the medieval
+
+ align:start position:0%
+have done before with the medieval
+ 
+
+ align:start position:0%
+have done before with the medieval
+villages and dynamics and today we're
+
+ align:start position:0%
+villages and dynamics and today we're
+ 
+
+ align:start position:0%
+villages and dynamics and today we're
+going to do it again but that starred
+
+ align:start position:0%
+going to do it again but that starred
+ 
+
+ align:start position:0%
+going to do it again but that starred
+reading does not appear anywhere
+
+ align:start position:0%
+reading does not appear anywhere
+ 
+
+ align:start position:0%
+reading does not appear anywhere
+particularly in the lectures but still
+
+ align:start position:0%
+particularly in the lectures but still
+ 
+
+ align:start position:0%
+particularly in the lectures but still
+there aren't a lot of new theorems and
+
+ align:start position:0%
+there aren't a lot of new theorems and
+ 
+
+ align:start position:0%
+there aren't a lot of new theorems and
+stuff in the lecture today mostly
+
+ align:start position:0%
+stuff in the lecture today mostly
+ 
+
+ align:start position:0%
+stuff in the lecture today mostly
+concepts so i think you can
+
+ align:start position:0%
+concepts so i think you can
+ 
+
+ align:start position:0%
+concepts so i think you can
+get some time to look at the doc and
+
+ align:start position:0%
+get some time to look at the doc and
+ 
+
+ align:start position:0%
+get some time to look at the doc and
+start article
+
+ align:start position:0%
+start article
+ 
+
+ align:start position:0%
+start article
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+on the class schedule
+
+ align:start position:0%
+on the class schedule
+ 
+
+ align:start position:0%
+on the class schedule
+so after the trade today trade lecture
+
+ align:start position:0%
+so after the trade today trade lecture
+ 
+
+ align:start position:0%
+so after the trade today trade lecture
+application today and the one next
+
+ align:start position:0%
+application today and the one next
+ 
+
+ align:start position:0%
+application today and the one next
+thursday
+
+ align:start position:0%
+thursday
+ 
+
+ align:start position:0%
+thursday
+and then the following week on tuesday
+
+ align:start position:0%
+and then the following week on tuesday
+ 
+
+ align:start position:0%
+and then the following week on tuesday
+i'll conduct with you a review session
+
+ align:start position:0%
+i'll conduct with you a review session
+ 
+
+ align:start position:0%
+i'll conduct with you a review session
+of the material covered in the last one
+
+ align:start position:0%
+of the material covered in the last one
+ 
+
+ align:start position:0%
+of the material covered in the last one
+third of the class
+
+ align:start position:0%
+third of the class
+ 
+
+ align:start position:0%
+third of the class
+so that's the way the schedule looks
+
+ align:start position:0%
+so that's the way the schedule looks
+ 
+
+ align:start position:0%
+so that's the way the schedule looks
+again let me
+
+ align:start position:0%
+again let me
+ 
+
+ align:start position:0%
+again let me
+ask if there are questions otherwise i'm
+
+ align:start position:0%
+ask if there are questions otherwise i'm
+ 
+
+ align:start position:0%
+ask if there are questions otherwise i'm
+going to turn to the study guide in
+
+ align:start position:0%
+going to turn to the study guide in
+ 
+
+ align:start position:0%
+going to turn to the study guide in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+material from last time lecture 13.
+
+ align:start position:0%
+material from last time lecture 13.
+ 
+
+ align:start position:0%
+material from last time lecture 13.
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+review question was in addition to
+
+ align:start position:0%
+review question was in addition to
+ 
+
+ align:start position:0%
+review question was in addition to
+reviewing what it takes
+
+ align:start position:0%
+reviewing what it takes
+ 
+
+ align:start position:0%
+reviewing what it takes
+in general equilibrium terms to describe
+
+ align:start position:0%
+in general equilibrium terms to describe
+ 
+
+ align:start position:0%
+in general equilibrium terms to describe
+an economy
+
+ align:start position:0%
+an economy
+ 
+
+ align:start position:0%
+an economy
+what additional features do we need
+
+ align:start position:0%
+what additional features do we need
+ 
+
+ align:start position:0%
+what additional features do we need
+to put in there to describe a private
+
+ align:start position:0%
+to put in there to describe a private
+ 
+
+ align:start position:0%
+to put in there to describe a private
+ownership
+
+ align:start position:0%
+ownership
+ 
+
+ align:start position:0%
+ownership
+economy
+
+ align:start position:0%
+economy
+ 
+
+ align:start position:0%
+economy
+and let me see
+
+ align:start position:0%
+and let me see
+ 
+
+ align:start position:0%
+and let me see
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+texan do you want to take a stab at that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah so
+
+ align:start position:0%
+uh yeah so
+ 
+
+ align:start position:0%
+uh yeah so
+for a general equilibrium economy we
+
+ align:start position:0%
+for a general equilibrium economy we
+ 
+
+ align:start position:0%
+for a general equilibrium economy we
+need like the consumers like preferences
+
+ align:start position:0%
+need like the consumers like preferences
+ 
+
+ align:start position:0%
+need like the consumers like preferences
+and consumption set
+
+ align:start position:0%
+and consumption set
+ 
+
+ align:start position:0%
+and consumption set
+the firm technology
+
+ align:start position:0%
+the firm technology
+ 
+
+ align:start position:0%
+the firm technology
+um which is the production set and then
+
+ align:start position:0%
+um which is the production set and then
+ 
+
+ align:start position:0%
+um which is the production set and then
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+economy resources
+
+ align:start position:0%
+economy resources
+ 
+
+ align:start position:0%
+economy resources
+um which is endowment
+
+ align:start position:0%
+um which is endowment
+ 
+
+ align:start position:0%
+um which is endowment
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+additionally for the private ownership
+
+ align:start position:0%
+additionally for the private ownership
+ 
+
+ align:start position:0%
+additionally for the private ownership
+we need each consumer has their own
+
+ align:start position:0%
+we need each consumer has their own
+ 
+
+ align:start position:0%
+we need each consumer has their own
+endowment
+
+ align:start position:0%
+endowment
+ 
+
+ align:start position:0%
+endowment
+um and also each consumer has like
+
+ align:start position:0%
+um and also each consumer has like
+ 
+
+ align:start position:0%
+um and also each consumer has like
+complete ownership of like
+
+ align:start position:0%
+complete ownership of like
+ 
+
+ align:start position:0%
+complete ownership of like
+the firm so the
+
+ align:start position:0%
+the firm so the
+ 
+
+ align:start position:0%
+the firm so the
+the firm is made out of like consumer
+
+ align:start position:0%
+the firm is made out of like consumer
+ 
+
+ align:start position:0%
+the firm is made out of like consumer
+ownership
+
+ align:start position:0%
+ownership
+ 
+
+ align:start position:0%
+ownership
+good okay yeah each consumer has shares
+
+ align:start position:0%
+good okay yeah each consumer has shares
+ 
+
+ align:start position:0%
+good okay yeah each consumer has shares
+in firms so those were the theta i j
+
+ align:start position:0%
+in firms so those were the theta i j
+ 
+
+ align:start position:0%
+in firms so those were the theta i j
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+so that the
+
+ align:start position:0%
+so that the
+ 
+
+ align:start position:0%
+so that the
+if there are profits as in decreasing
+
+ align:start position:0%
+if there are profits as in decreasing
+ 
+
+ align:start position:0%
+if there are profits as in decreasing
+returns to scale those profits
+
+ align:start position:0%
+returns to scale those profits
+ 
+
+ align:start position:0%
+returns to scale those profits
+get distributed back to households
+
+ align:start position:0%
+get distributed back to households
+ 
+
+ align:start position:0%
+get distributed back to households
+so they own the returns on the firms
+
+ align:start position:0%
+so they own the returns on the firms
+ 
+
+ align:start position:0%
+so they own the returns on the firms
+that's a great answer thank you so much
+
+ align:start position:0%
+that's a great answer thank you so much
+ 
+
+ align:start position:0%
+that's a great answer thank you so much
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what is the potential difference between
+
+ align:start position:0%
+what is the potential difference between
+ 
+
+ align:start position:0%
+what is the potential difference between
+a volrasian equilibrium
+
+ align:start position:0%
+a volrasian equilibrium
+ 
+
+ align:start position:0%
+a volrasian equilibrium
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a price equilibrium with transfers
+
+ align:start position:0%
+a price equilibrium with transfers
+ 
+
+ align:start position:0%
+a price equilibrium with transfers
+maria sophia do you want to try that one
+
+ align:start position:0%
+maria sophia do you want to try that one
+ 
+
+ align:start position:0%
+maria sophia do you want to try that one
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+um with the price equilibrium with
+
+ align:start position:0%
+um with the price equilibrium with
+ 
+
+ align:start position:0%
+um with the price equilibrium with
+transfers we're looking to see if there
+
+ align:start position:0%
+transfers we're looking to see if there
+ 
+
+ align:start position:0%
+transfers we're looking to see if there
+like exists an assignment
+
+ align:start position:0%
+like exists an assignment
+ 
+
+ align:start position:0%
+like exists an assignment
+um like of wealth levels
+
+ align:start position:0%
+um like of wealth levels
+ 
+
+ align:start position:0%
+um like of wealth levels
+such that the economy will satisfy like
+
+ align:start position:0%
+such that the economy will satisfy like
+ 
+
+ align:start position:0%
+such that the economy will satisfy like
+a set of constraints but in general like
+
+ align:start position:0%
+a set of constraints but in general like
+ 
+
+ align:start position:0%
+a set of constraints but in general like
+a while raising equilibrium
+
+ align:start position:0%
+a while raising equilibrium
+ 
+
+ align:start position:0%
+a while raising equilibrium
+like is a type of price equilibrium with
+
+ align:start position:0%
+like is a type of price equilibrium with
+ 
+
+ align:start position:0%
+like is a type of price equilibrium with
+transfers
+
+ align:start position:0%
+transfers
+ 
+
+ align:start position:0%
+transfers
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+except like we have the condition that
+
+ align:start position:0%
+except like we have the condition that
+ 
+
+ align:start position:0%
+except like we have the condition that
+the wealth is equal to
+
+ align:start position:0%
+the wealth is equal to
+ 
+
+ align:start position:0%
+the wealth is equal to
+um i think it's like the price times the
+
+ align:start position:0%
+um i think it's like the price times the
+ 
+
+ align:start position:0%
+um i think it's like the price times the
+wealth plus the sum of like the profits
+
+ align:start position:0%
+wealth plus the sum of like the profits
+ 
+
+ align:start position:0%
+wealth plus the sum of like the profits
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+the shares that the consumer has in
+
+ align:start position:0%
+the shares that the consumer has in
+ 
+
+ align:start position:0%
+the shares that the consumer has in
+various companies
+
+ align:start position:0%
+various companies
+ 
+
+ align:start position:0%
+various companies
+yes that's right
+
+ align:start position:0%
+yes that's right
+ 
+
+ align:start position:0%
+yes that's right
+so the variant equilibrium
+
+ align:start position:0%
+so the variant equilibrium
+ 
+
+ align:start position:0%
+so the variant equilibrium
+works off of this private ownership
+
+ align:start position:0%
+works off of this private ownership
+ 
+
+ align:start position:0%
+works off of this private ownership
+economy so we have the valuation of the
+
+ align:start position:0%
+economy so we have the valuation of the
+ 
+
+ align:start position:0%
+economy so we have the valuation of the
+household's endowment plus
+
+ align:start position:0%
+household's endowment plus
+ 
+
+ align:start position:0%
+household's endowment plus
+the valuation of the profits that the
+
+ align:start position:0%
+the valuation of the profits that the
+ 
+
+ align:start position:0%
+the valuation of the profits that the
+household
+
+ align:start position:0%
+household
+ 
+
+ align:start position:0%
+household
+has a claim to on the
+
+ align:start position:0%
+has a claim to on the
+ 
+
+ align:start position:0%
+has a claim to on the
+and that is a wealth object
+
+ align:start position:0%
+and that is a wealth object
+ 
+
+ align:start position:0%
+and that is a wealth object
+so technically
+
+ align:start position:0%
+so technically
+ 
+
+ align:start position:0%
+so technically
+it looks like a price equilibrium with
+
+ align:start position:0%
+it looks like a price equilibrium with
+ 
+
+ align:start position:0%
+it looks like a price equilibrium with
+transfers meaning that
+
+ align:start position:0%
+transfers meaning that
+ 
+
+ align:start position:0%
+transfers meaning that
+if we assign that particular wealth
+
+ align:start position:0%
+if we assign that particular wealth
+ 
+
+ align:start position:0%
+if we assign that particular wealth
+we're going to have an equilibrium
+
+ align:start position:0%
+we're going to have an equilibrium
+ 
+
+ align:start position:0%
+we're going to have an equilibrium
+the more general idea behind
+
+ align:start position:0%
+the more general idea behind
+ 
+
+ align:start position:0%
+the more general idea behind
+the price equilibrium is with transfers
+
+ align:start position:0%
+the price equilibrium is with transfers
+ 
+
+ align:start position:0%
+the price equilibrium is with transfers
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+including the transfers part
+
+ align:start position:0%
+including the transfers part
+ 
+
+ align:start position:0%
+including the transfers part
+is that the wealth assignments that we
+
+ align:start position:0%
+is that the wealth assignments that we
+ 
+
+ align:start position:0%
+is that the wealth assignments that we
+give to households
+
+ align:start position:0%
+give to households
+ 
+
+ align:start position:0%
+give to households
+may be greater or less than the va
+
+ align:start position:0%
+may be greater or less than the va
+ 
+
+ align:start position:0%
+may be greater or less than the va
+valuation of the wealth they would have
+
+ align:start position:0%
+valuation of the wealth they would have
+ 
+
+ align:start position:0%
+valuation of the wealth they would have
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+if we had restricted ourselves to
+
+ align:start position:0%
+if we had restricted ourselves to
+ 
+
+ align:start position:0%
+if we had restricted ourselves to
+private ownership
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what i didn't i guess emphasized very
+
+ align:start position:0%
+so what i didn't i guess emphasized very
+ 
+
+ align:start position:0%
+so what i didn't i guess emphasized very
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+is there are going to be two welfare
+
+ align:start position:0%
+is there are going to be two welfare
+ 
+
+ align:start position:0%
+is there are going to be two welfare
+theorems that we will study in detail
+
+ align:start position:0%
+theorems that we will study in detail
+ 
+
+ align:start position:0%
+theorems that we will study in detail
+one is that the volrasian equilibrium is
+
+ align:start position:0%
+one is that the volrasian equilibrium is
+ 
+
+ align:start position:0%
+one is that the volrasian equilibrium is
+pareto optimal
+
+ align:start position:0%
+pareto optimal
+ 
+
+ align:start position:0%
+pareto optimal
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and for that part we need
+
+ align:start position:0%
+and for that part we need
+ 
+
+ align:start position:0%
+and for that part we need
+private ownership only and the second is
+
+ align:start position:0%
+private ownership only and the second is
+ 
+
+ align:start position:0%
+private ownership only and the second is
+going to be that
+
+ align:start position:0%
+going to be that
+ 
+
+ align:start position:0%
+going to be that
+that any pareto optimal allocation can
+
+ align:start position:0%
+that any pareto optimal allocation can
+ 
+
+ align:start position:0%
+that any pareto optimal allocation can
+be achieved with a suitable distribution
+
+ align:start position:0%
+be achieved with a suitable distribution
+ 
+
+ align:start position:0%
+be achieved with a suitable distribution
+of redistribution of wealth
+
+ align:start position:0%
+of redistribution of wealth
+ 
+
+ align:start position:0%
+of redistribution of wealth
+and that's the part where we're going to
+
+ align:start position:0%
+and that's the part where we're going to
+ 
+
+ align:start position:0%
+and that's the part where we're going to
+need this more general
+
+ align:start position:0%
+need this more general
+ 
+
+ align:start position:0%
+need this more general
+concept of price equilibrium with
+
+ align:start position:0%
+concept of price equilibrium with
+ 
+
+ align:start position:0%
+concept of price equilibrium with
+transfers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the ordering of the class
+
+ align:start position:0%
+the ordering of the class
+ 
+
+ align:start position:0%
+the ordering of the class
+was to introduce the small raisin
+
+ align:start position:0%
+was to introduce the small raisin
+ 
+
+ align:start position:0%
+was to introduce the small raisin
+equilibrium notion not dwell on the
+
+ align:start position:0%
+equilibrium notion not dwell on the
+ 
+
+ align:start position:0%
+equilibrium notion not dwell on the
+optimality of it
+
+ align:start position:0%
+optimality of it
+ 
+
+ align:start position:0%
+optimality of it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but rather get into some applications
+
+ align:start position:0%
+but rather get into some applications
+ 
+
+ align:start position:0%
+but rather get into some applications
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+in a couple of weeks we'll be back to
+
+ align:start position:0%
+in a couple of weeks we'll be back to
+ 
+
+ align:start position:0%
+in a couple of weeks we'll be back to
+those welfare theorems and when they are
+
+ align:start position:0%
+those welfare theorems and when they are
+ 
+
+ align:start position:0%
+those welfare theorems and when they are
+true and when they can fail
+
+ align:start position:0%
+true and when they can fail
+ 
+
+ align:start position:0%
+true and when they can fail
+so that's the ordering of the class
+
+ align:start position:0%
+so that's the ordering of the class
+ 
+
+ align:start position:0%
+so that's the ordering of the class
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we got into the two by two by two
+
+ align:start position:0%
+we got into the two by two by two
+ 
+
+ align:start position:0%
+we got into the two by two by two
+all of this stuff at the beginning is
+
+ align:start position:0%
+all of this stuff at the beginning is
+ 
+
+ align:start position:0%
+all of this stuff at the beginning is
+kind of a review
+
+ align:start position:0%
+kind of a review
+ 
+
+ align:start position:0%
+kind of a review
+of the notation
+
+ align:start position:0%
+of the notation
+ 
+
+ align:start position:0%
+of the notation
+where we have uh cost
+
+ align:start position:0%
+where we have uh cost
+ 
+
+ align:start position:0%
+where we have uh cost
+minimizing the cost of achieving a unit
+
+ align:start position:0%
+minimizing the cost of achieving a unit
+ 
+
+ align:start position:0%
+minimizing the cost of achieving a unit
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+given the vector of factor prices w and
+
+ align:start position:0%
+given the vector of factor prices w and
+ 
+
+ align:start position:0%
+given the vector of factor prices w and
+we had the
+
+ align:start position:0%
+we had the
+ 
+
+ align:start position:0%
+we had the
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+minimizing input values
+
+ align:start position:0%
+minimizing input values
+ 
+
+ align:start position:0%
+minimizing input values
+um and at the end of all that i finally
+
+ align:start position:0%
+um and at the end of all that i finally
+ 
+
+ align:start position:0%
+um and at the end of all that i finally
+got around to asking
+
+ align:start position:0%
+got around to asking
+ 
+
+ align:start position:0%
+got around to asking
+define what it means for the production
+
+ align:start position:0%
+define what it means for the production
+ 
+
+ align:start position:0%
+define what it means for the production
+of good one to be relatively
+
+ align:start position:0%
+of good one to be relatively
+ 
+
+ align:start position:0%
+of good one to be relatively
+more intensive in factor one
+
+ align:start position:0%
+more intensive in factor one
+ 
+
+ align:start position:0%
+more intensive in factor one
+than uh
+
+ align:start position:0%
+than uh
+ 
+
+ align:start position:0%
+than uh
+and the production of good two
+
+ align:start position:0%
+and the production of good two
+ 
+
+ align:start position:0%
+and the production of good two
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+see if we can get some how about a
+
+ align:start position:0%
+see if we can get some how about a
+ 
+
+ align:start position:0%
+see if we can get some how about a
+volunteer for that one
+
+ align:start position:0%
+volunteer for that one
+ 
+
+ align:start position:0%
+volunteer for that one
+no i can take this one
+
+ align:start position:0%
+no i can take this one
+ 
+
+ align:start position:0%
+no i can take this one
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+this means that um like the
+
+ align:start position:0%
+this means that um like the
+ 
+
+ align:start position:0%
+this means that um like the
+per for producing a unit of good one
+
+ align:start position:0%
+per for producing a unit of good one
+ 
+
+ align:start position:0%
+per for producing a unit of good one
+versus a unit of good two
+
+ align:start position:0%
+versus a unit of good two
+ 
+
+ align:start position:0%
+versus a unit of good two
+you need like the ratio uh you need a
+
+ align:start position:0%
+you need like the ratio uh you need a
+ 
+
+ align:start position:0%
+you need like the ratio uh you need a
+the ratio of factor one to factor two
+
+ align:start position:0%
+the ratio of factor one to factor two
+ 
+
+ align:start position:0%
+the ratio of factor one to factor two
+that's used to produce one unit of good
+
+ align:start position:0%
+that's used to produce one unit of good
+ 
+
+ align:start position:0%
+that's used to produce one unit of good
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+greater than the ratio of uh
+
+ align:start position:0%
+greater than the ratio of uh
+ 
+
+ align:start position:0%
+greater than the ratio of uh
+factor one to factor two when producing
+
+ align:start position:0%
+factor one to factor two when producing
+ 
+
+ align:start position:0%
+factor one to factor two when producing
+a unit of good two
+
+ align:start position:0%
+a unit of good two
+ 
+
+ align:start position:0%
+a unit of good two
+excellent
+
+ align:start position:0%
+excellent
+ 
+
+ align:start position:0%
+excellent
+perfect answer
+
+ align:start position:0%
+perfect answer
+ 
+
+ align:start position:0%
+perfect answer
+and then implicit let me just add a
+
+ align:start position:0%
+and then implicit let me just add a
+ 
+
+ align:start position:0%
+and then implicit let me just add a
+little bit editorial
+
+ align:start position:0%
+little bit editorial
+ 
+
+ align:start position:0%
+little bit editorial
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+it's defined over the whole domain so
+
+ align:start position:0%
+it's defined over the whole domain so
+ 
+
+ align:start position:0%
+it's defined over the whole domain so
+whatever those factor prices are
+
+ align:start position:0%
+whatever those factor prices are
+ 
+
+ align:start position:0%
+whatever those factor prices are
+w1 and w2 it remains true
+
+ align:start position:0%
+w1 and w2 it remains true
+ 
+
+ align:start position:0%
+w1 and w2 it remains true
+that good one uses relatively more
+
+ align:start position:0%
+that good one uses relatively more
+ 
+
+ align:start position:0%
+that good one uses relatively more
+factor one than factor two and vice
+
+ align:start position:0%
+factor one than factor two and vice
+ 
+
+ align:start position:0%
+factor one than factor two and vice
+versa
+
+ align:start position:0%
+versa
+ 
+
+ align:start position:0%
+versa
+so it's a statement about the whole ring
+
+ align:start position:0%
+so it's a statement about the whole ring
+ 
+
+ align:start position:0%
+so it's a statement about the whole ring
+and we used
+
+ align:start position:0%
+and we used
+ 
+
+ align:start position:0%
+and we used
+that in the analysis in class when we
+
+ align:start position:0%
+that in the analysis in class when we
+ 
+
+ align:start position:0%
+that in the analysis in class when we
+were looking at the cost curves and what
+
+ align:start position:0%
+were looking at the cost curves and what
+ 
+
+ align:start position:0%
+were looking at the cost curves and what
+would happen if
+
+ align:start position:0%
+would happen if
+ 
+
+ align:start position:0%
+would happen if
+if input prices
+
+ align:start position:0%
+if input prices
+ 
+
+ align:start position:0%
+if input prices
+moved
+
+ align:start position:0%
+moved
+ 
+
+ align:start position:0%
+moved
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can someone take a stab at the
+
+ align:start position:0%
+can someone take a stab at the
+ 
+
+ align:start position:0%
+can someone take a stab at the
+stopler samuelson theorem for the
+
+ align:start position:0%
+stopler samuelson theorem for the
+ 
+
+ align:start position:0%
+stopler samuelson theorem for the
+determination of input prices
+
+ align:start position:0%
+determination of input prices
+ 
+
+ align:start position:0%
+determination of input prices
+as output prices change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can
+
+ align:start position:0%
+i can
+ 
+
+ align:start position:0%
+i can
+okay in the
+
+ align:start position:0%
+okay in the
+ 
+
+ align:start position:0%
+okay in the
+yeah in this theory
+
+ align:start position:0%
+yeah in this theory
+ 
+
+ align:start position:0%
+yeah in this theory
+that if the if if we assume that the
+
+ align:start position:0%
+that if the if if we assume that the
+ 
+
+ align:start position:0%
+that if the if if we assume that the
+model was to multiply two
+
+ align:start position:0%
+model was to multiply two
+ 
+
+ align:start position:0%
+model was to multiply two
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+when the output price like the price of
+
+ align:start position:0%
+when the output price like the price of
+ 
+
+ align:start position:0%
+when the output price like the price of
+good one increases than the
+
+ align:start position:0%
+good one increases than the
+ 
+
+ align:start position:0%
+good one increases than the
+intensive factors in producing the
+
+ align:start position:0%
+intensive factors in producing the
+ 
+
+ align:start position:0%
+intensive factors in producing the
+good one world also increases
+
+ align:start position:0%
+good one world also increases
+ 
+
+ align:start position:0%
+good one world also increases
+and the another factor that factored to
+
+ align:start position:0%
+and the another factor that factored to
+ 
+
+ align:start position:0%
+and the another factor that factored to
+and that was not the intensive factor
+
+ align:start position:0%
+and that was not the intensive factor
+ 
+
+ align:start position:0%
+and that was not the intensive factor
+the price of this factor world goes down
+
+ align:start position:0%
+the price of this factor world goes down
+ 
+
+ align:start position:0%
+the price of this factor world goes down
+yeah okay that's good yep
+
+ align:start position:0%
+yeah okay that's good yep
+ 
+
+ align:start position:0%
+yeah okay that's good yep
+so normally it's not a statement about
+
+ align:start position:0%
+so normally it's not a statement about
+ 
+
+ align:start position:0%
+so normally it's not a statement about
+international trade although it is
+
+ align:start position:0%
+international trade although it is
+ 
+
+ align:start position:0%
+international trade although it is
+very useful in that context we're just
+
+ align:start position:0%
+very useful in that context we're just
+ 
+
+ align:start position:0%
+very useful in that context we're just
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+doing some comparative static exercises
+
+ align:start position:0%
+doing some comparative static exercises
+ 
+
+ align:start position:0%
+doing some comparative static exercises
+of what would happen if
+
+ align:start position:0%
+of what would happen if
+ 
+
+ align:start position:0%
+of what would happen if
+these exogenously given output prices
+
+ align:start position:0%
+these exogenously given output prices
+ 
+
+ align:start position:0%
+these exogenously given output prices
+are changing what's going to happen to
+
+ align:start position:0%
+are changing what's going to happen to
+ 
+
+ align:start position:0%
+are changing what's going to happen to
+input prices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we
+
+ align:start position:0%
+and then we
+ 
+
+ align:start position:0%
+and then we
+we did a graph we used those cost curves
+
+ align:start position:0%
+we did a graph we used those cost curves
+ 
+
+ align:start position:0%
+we did a graph we used those cost curves
+to illustrate it
+
+ align:start position:0%
+to illustrate it
+ 
+
+ align:start position:0%
+to illustrate it
+i flagged the last question but i really
+
+ align:start position:0%
+i flagged the last question but i really
+ 
+
+ align:start position:0%
+i flagged the last question but i really
+don't want to ask that one i want to ask
+
+ align:start position:0%
+don't want to ask that one i want to ask
+ 
+
+ align:start position:0%
+don't want to ask that one i want to ask
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little harder to answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we had two countries
+
+ align:start position:0%
+if we had two countries
+ 
+
+ align:start position:0%
+if we had two countries
+and each country had a representative
+
+ align:start position:0%
+and each country had a representative
+ 
+
+ align:start position:0%
+and each country had a representative
+consumer
+
+ align:start position:0%
+consumer
+ 
+
+ align:start position:0%
+consumer
+and there were two goods
+
+ align:start position:0%
+and there were two goods
+ 
+
+ align:start position:0%
+and there were two goods
+each of which can be produced in both
+
+ align:start position:0%
+each of which can be produced in both
+ 
+
+ align:start position:0%
+each of which can be produced in both
+countries
+
+ align:start position:0%
+countries
+ 
+
+ align:start position:0%
+countries
+and there are two factors that can be
+
+ align:start position:0%
+and there are two factors that can be
+ 
+
+ align:start position:0%
+and there are two factors that can be
+used in each good in each country
+
+ align:start position:0%
+used in each good in each country
+ 
+
+ align:start position:0%
+used in each good in each country
+we've got a lot of
+
+ align:start position:0%
+we've got a lot of
+ 
+
+ align:start position:0%
+we've got a lot of
+equations and unknowns we've got
+
+ align:start position:0%
+equations and unknowns we've got
+ 
+
+ align:start position:0%
+equations and unknowns we've got
+the consumer's consumption levels of the
+
+ align:start position:0%
+the consumer's consumption levels of the
+ 
+
+ align:start position:0%
+the consumer's consumption levels of the
+two goods
+
+ align:start position:0%
+two goods
+ 
+
+ align:start position:0%
+two goods
+the input being used to produce outputs
+
+ align:start position:0%
+the input being used to produce outputs
+ 
+
+ align:start position:0%
+the input being used to produce outputs
+of the two goods
+
+ align:start position:0%
+of the two goods
+ 
+
+ align:start position:0%
+of the two goods
+the outputs themselves of the two goods
+
+ align:start position:0%
+the outputs themselves of the two goods
+ 
+
+ align:start position:0%
+the outputs themselves of the two goods
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+prices of each of the two inputs
+
+ align:start position:0%
+prices of each of the two inputs
+ 
+
+ align:start position:0%
+prices of each of the two inputs
+in both countries etc etc
+
+ align:start position:0%
+in both countries etc etc
+ 
+
+ align:start position:0%
+in both countries etc etc
+do you remember can someone tell me how
+
+ align:start position:0%
+do you remember can someone tell me how
+ 
+
+ align:start position:0%
+do you remember can someone tell me how
+we attack this problem in class
+
+ align:start position:0%
+we attack this problem in class
+ 
+
+ align:start position:0%
+we attack this problem in class
+in the sense of an algorithm
+
+ align:start position:0%
+in the sense of an algorithm
+ 
+
+ align:start position:0%
+in the sense of an algorithm
+that you know we broke it into pieces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otherwise it's a very
+
+ align:start position:0%
+otherwise it's a very
+ 
+
+ align:start position:0%
+otherwise it's a very
+high dimensional problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you remember the ordering yeah go
+
+ align:start position:0%
+if you remember the ordering yeah go
+ 
+
+ align:start position:0%
+if you remember the ordering yeah go
+ahead please
+
+ align:start position:0%
+ahead please
+ 
+
+ align:start position:0%
+ahead please
+yeah i think that the the way that we
+
+ align:start position:0%
+yeah i think that the the way that we
+ 
+
+ align:start position:0%
+yeah i think that the the way that we
+did this was kind of like um
+
+ align:start position:0%
+did this was kind of like um
+ 
+
+ align:start position:0%
+did this was kind of like um
+inductively where i i think that the way
+
+ align:start position:0%
+inductively where i i think that the way
+ 
+
+ align:start position:0%
+inductively where i i think that the way
+that we did this was first like pretend
+
+ align:start position:0%
+that we did this was first like pretend
+ 
+
+ align:start position:0%
+that we did this was first like pretend
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh pretend basically that it's just like
+
+ align:start position:0%
+uh pretend basically that it's just like
+ 
+
+ align:start position:0%
+uh pretend basically that it's just like
+the original two by two model and then
+
+ align:start position:0%
+the original two by two model and then
+ 
+
+ align:start position:0%
+the original two by two model and then
+we kind of solve for the what's supposed
+
+ align:start position:0%
+we kind of solve for the what's supposed
+ 
+
+ align:start position:0%
+we kind of solve for the what's supposed
+to happen there and then we build in the
+
+ align:start position:0%
+to happen there and then we build in the
+ 
+
+ align:start position:0%
+to happen there and then we build in the
+like additional thing of i'm pretty sure
+
+ align:start position:0%
+like additional thing of i'm pretty sure
+ 
+
+ align:start position:0%
+like additional thing of i'm pretty sure
+we built in the
+
+ align:start position:0%
+we built in the
+ 
+
+ align:start position:0%
+we built in the
+the different endowments i think was the
+
+ align:start position:0%
+the different endowments i think was the
+ 
+
+ align:start position:0%
+the different endowments i think was the
+difference in the two by two by two
+
+ align:start position:0%
+difference in the two by two by two
+ 
+
+ align:start position:0%
+difference in the two by two by two
+versus the two by two the kind of we saw
+
+ align:start position:0%
+versus the two by two the kind of we saw
+ 
+
+ align:start position:0%
+versus the two by two the kind of we saw
+for the smaller model and then we build
+
+ align:start position:0%
+for the smaller model and then we build
+ 
+
+ align:start position:0%
+for the smaller model and then we build
+it upwards to the bigger one
+
+ align:start position:0%
+it upwards to the bigger one
+ 
+
+ align:start position:0%
+it upwards to the bigger one
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+and what in particular did we focus on
+
+ align:start position:0%
+and what in particular did we focus on
+ 
+
+ align:start position:0%
+and what in particular did we focus on
+first in the smaller model
+
+ align:start position:0%
+first in the smaller model
+ 
+
+ align:start position:0%
+first in the smaller model
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i think uh the way that we did this was
+
+ align:start position:0%
+i think uh the way that we did this was
+ 
+
+ align:start position:0%
+i think uh the way that we did this was
+kind of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+i i don't think i remember this
+
+ align:start position:0%
+i i don't think i remember this
+ 
+
+ align:start position:0%
+i i don't think i remember this
+okay anyone else want to
+
+ align:start position:0%
+okay anyone else want to
+ 
+
+ align:start position:0%
+okay anyone else want to
+take an attempt at it this is a
+
+ align:start position:0%
+take an attempt at it this is a
+ 
+
+ align:start position:0%
+take an attempt at it this is a
+difficult question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to pose and hard to answer because it
+
+ align:start position:0%
+to pose and hard to answer because it
+ 
+
+ align:start position:0%
+to pose and hard to answer because it
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+to do with putting the
+
+ align:start position:0%
+to do with putting the
+ 
+
+ align:start position:0%
+to do with putting the
+pieces of a lot of information in the
+
+ align:start position:0%
+pieces of a lot of information in the
+ 
+
+ align:start position:0%
+pieces of a lot of information in the
+lecture and and sort of
+
+ align:start position:0%
+lecture and and sort of
+ 
+
+ align:start position:0%
+lecture and and sort of
+taking a step backwards and thinking
+
+ align:start position:0%
+taking a step backwards and thinking
+ 
+
+ align:start position:0%
+taking a step backwards and thinking
+about it globally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well it starts
+
+ align:start position:0%
+okay well it starts
+ 
+
+ align:start position:0%
+okay well it starts
+with this stolper samuelson theorem so
+
+ align:start position:0%
+with this stolper samuelson theorem so
+ 
+
+ align:start position:0%
+with this stolper samuelson theorem so
+at this point
+
+ align:start position:0%
+at this point
+ 
+
+ align:start position:0%
+at this point
+early on in the lecture we were taking
+
+ align:start position:0%
+early on in the lecture we were taking
+ 
+
+ align:start position:0%
+early on in the lecture we were taking
+the prices of the goods p1 and p2 as
+
+ align:start position:0%
+the prices of the goods p1 and p2 as
+ 
+
+ align:start position:0%
+the prices of the goods p1 and p2 as
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+we weren't trying to solve for that i
+
+ align:start position:0%
+we weren't trying to solve for that i
+ 
+
+ align:start position:0%
+we weren't trying to solve for that i
+had not yet introduced consumers either
+
+ align:start position:0%
+had not yet introduced consumers either
+ 
+
+ align:start position:0%
+had not yet introduced consumers either
+we didn't even
+
+ align:start position:0%
+we didn't even
+ 
+
+ align:start position:0%
+we didn't even
+attempt to solve for the quantities
+
+ align:start position:0%
+attempt to solve for the quantities
+ 
+
+ align:start position:0%
+attempt to solve for the quantities
+we merely wanted to find
+
+ align:start position:0%
+we merely wanted to find
+ 
+
+ align:start position:0%
+we merely wanted to find
+equilibrium factor prices
+
+ align:start position:0%
+equilibrium factor prices
+ 
+
+ align:start position:0%
+equilibrium factor prices
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so we had
+
+ align:start position:0%
+so we had
+ 
+
+ align:start position:0%
+so we had
+for a given country you could think of
+
+ align:start position:0%
+for a given country you could think of
+ 
+
+ align:start position:0%
+for a given country you could think of
+it that way a given economy
+
+ align:start position:0%
+it that way a given economy
+ 
+
+ align:start position:0%
+it that way a given economy
+we had the
+
+ align:start position:0%
+we had the
+ 
+
+ align:start position:0%
+we had the
+minimized cost of producing one unit of
+
+ align:start position:0%
+minimized cost of producing one unit of
+ 
+
+ align:start position:0%
+minimized cost of producing one unit of
+good one
+
+ align:start position:0%
+good one
+ 
+
+ align:start position:0%
+good one
+the minimized cost of producing one good
+
+ align:start position:0%
+the minimized cost of producing one good
+ 
+
+ align:start position:0%
+the minimized cost of producing one good
+one unit of good two
+
+ align:start position:0%
+one unit of good two
+ 
+
+ align:start position:0%
+one unit of good two
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+we know we know that and that's in the
+
+ align:start position:0%
+we know we know that and that's in the
+ 
+
+ align:start position:0%
+we know we know that and that's in the
+space of input prices w1 and w2
+
+ align:start position:0%
+space of input prices w1 and w2
+ 
+
+ align:start position:0%
+space of input prices w1 and w2
+so we know we're looking for an
+
+ align:start position:0%
+so we know we're looking for an
+ 
+
+ align:start position:0%
+so we know we're looking for an
+equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore the input prices should be the
+
+ align:start position:0%
+therefore the input prices should be the
+ 
+
+ align:start position:0%
+therefore the input prices should be the
+same regardless of whether it's
+
+ align:start position:0%
+same regardless of whether it's
+ 
+
+ align:start position:0%
+same regardless of whether it's
+good one or good two
+
+ align:start position:0%
+good one or good two
+ 
+
+ align:start position:0%
+good one or good two
+so we looked at where those curves
+
+ align:start position:0%
+so we looked at where those curves
+ 
+
+ align:start position:0%
+so we looked at where those curves
+crossed and that you know that's the
+
+ align:start position:0%
+crossed and that you know that's the
+ 
+
+ align:start position:0%
+crossed and that you know that's the
+only point in the diagram
+
+ align:start position:0%
+only point in the diagram
+ 
+
+ align:start position:0%
+only point in the diagram
+where we can both
+
+ align:start position:0%
+where we can both
+ 
+
+ align:start position:0%
+where we can both
+have common input prices
+
+ align:start position:0%
+have common input prices
+ 
+
+ align:start position:0%
+have common input prices
+of the two inputs and
+
+ align:start position:0%
+of the two inputs and
+ 
+
+ align:start position:0%
+of the two inputs and
+beyond those curves where the curves
+
+ align:start position:0%
+beyond those curves where the curves
+ 
+
+ align:start position:0%
+beyond those curves where the curves
+crossed
+
+ align:start position:0%
+crossed
+ 
+
+ align:start position:0%
+crossed
+so that was the very very first part
+
+ align:start position:0%
+so that was the very very first part
+ 
+
+ align:start position:0%
+so that was the very very first part
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+we given those prices
+
+ align:start position:0%
+we given those prices
+ 
+
+ align:start position:0%
+we given those prices
+we moved to
+
+ align:start position:0%
+we moved to
+ 
+
+ align:start position:0%
+we moved to
+a different space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which had isoquants
+
+ align:start position:0%
+which had isoquants
+ 
+
+ align:start position:0%
+which had isoquants
+so there we have
+
+ align:start position:0%
+so there we have
+ 
+
+ align:start position:0%
+so there we have
+the unit output
+
+ align:start position:0%
+the unit output
+ 
+
+ align:start position:0%
+the unit output
+or any output really
+
+ align:start position:0%
+or any output really
+ 
+
+ align:start position:0%
+or any output really
+described by an isoquant
+
+ align:start position:0%
+described by an isoquant
+ 
+
+ align:start position:0%
+described by an isoquant
+a different isoquant for different
+
+ align:start position:0%
+a different isoquant for different
+ 
+
+ align:start position:0%
+a different isoquant for different
+quantities and we had
+
+ align:start position:0%
+quantities and we had
+ 
+
+ align:start position:0%
+quantities and we had
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+inputs on the on the x-axis so there we
+
+ align:start position:0%
+inputs on the on the x-axis so there we
+ 
+
+ align:start position:0%
+inputs on the on the x-axis so there we
+solve for
+
+ align:start position:0%
+solve for
+ 
+
+ align:start position:0%
+solve for
+minimizing unit cost again
+
+ align:start position:0%
+minimizing unit cost again
+ 
+
+ align:start position:0%
+minimizing unit cost again
+but what's on the x and y axis
+
+ align:start position:0%
+but what's on the x and y axis
+ 
+
+ align:start position:0%
+but what's on the x and y axis
+would be the input quantities and we and
+
+ align:start position:0%
+would be the input quantities and we and
+ 
+
+ align:start position:0%
+would be the input quantities and we and
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know that has to align with the
+
+ align:start position:0%
+and we know that has to align with the
+ 
+
+ align:start position:0%
+and we know that has to align with the
+factor prices we already solved for
+
+ align:start position:0%
+factor prices we already solved for
+ 
+
+ align:start position:0%
+factor prices we already solved for
+so there we
+
+ align:start position:0%
+so there we
+ 
+
+ align:start position:0%
+so there we
+we determine both
+
+ align:start position:0%
+we determine both
+ 
+
+ align:start position:0%
+we determine both
+the input quantities as well as the
+
+ align:start position:0%
+the input quantities as well as the
+ 
+
+ align:start position:0%
+the input quantities as well as the
+output quantities
+
+ align:start position:0%
+output quantities
+ 
+
+ align:start position:0%
+output quantities
+where both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+firm 1 and firm 2 could be in
+
+ align:start position:0%
+firm 1 and firm 2 could be in
+ 
+
+ align:start position:0%
+firm 1 and firm 2 could be in
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+and then finally at the very end of the
+
+ align:start position:0%
+and then finally at the very end of the
+ 
+
+ align:start position:0%
+and then finally at the very end of the
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+we zeroed out
+
+ align:start position:0%
+we zeroed out
+ 
+
+ align:start position:0%
+we zeroed out
+to consider
+
+ align:start position:0%
+to consider
+ 
+
+ align:start position:0%
+to consider
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+two countries not just
+
+ align:start position:0%
+two countries not just
+ 
+
+ align:start position:0%
+two countries not just
+one each with a consumer
+
+ align:start position:0%
+one each with a consumer
+ 
+
+ align:start position:0%
+one each with a consumer
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+those countries could be in autarky or
+
+ align:start position:0%
+those countries could be in autarky or
+ 
+
+ align:start position:0%
+those countries could be in autarky or
+potentially trading with one another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both both specifications would be
+
+ align:start position:0%
+both both specifications would be
+ 
+
+ align:start position:0%
+both both specifications would be
+legitimate general equilibrium
+
+ align:start position:0%
+legitimate general equilibrium
+ 
+
+ align:start position:0%
+legitimate general equilibrium
+environments both autarky each country
+
+ align:start position:0%
+environments both autarky each country
+ 
+
+ align:start position:0%
+environments both autarky each country
+separately is one and then
+
+ align:start position:0%
+separately is one and then
+ 
+
+ align:start position:0%
+separately is one and then
+with trade it's another except obviously
+
+ align:start position:0%
+with trade it's another except obviously
+ 
+
+ align:start position:0%
+with trade it's another except obviously
+with trade consumption and production do
+
+ align:start position:0%
+with trade consumption and production do
+ 
+
+ align:start position:0%
+with trade consumption and production do
+not have to be the same because the
+
+ align:start position:0%
+not have to be the same because the
+ 
+
+ align:start position:0%
+not have to be the same because the
+countries
+
+ align:start position:0%
+countries
+ 
+
+ align:start position:0%
+countries
+can export one thing and import another
+
+ align:start position:0%
+can export one thing and import another
+ 
+
+ align:start position:0%
+can export one thing and import another
+sorry that's a rather long winded
+
+ align:start position:0%
+sorry that's a rather long winded
+ 
+
+ align:start position:0%
+sorry that's a rather long winded
+summary but again it's uh
+
+ align:start position:0%
+summary but again it's uh
+ 
+
+ align:start position:0%
+summary but again it's uh
+not the easiest lecture maybe
+
+ align:start position:0%
+not the easiest lecture maybe
+ 
+
+ align:start position:0%
+not the easiest lecture maybe
+potentially the hardest lecture
+
+ align:start position:0%
+potentially the hardest lecture
+ 
+
+ align:start position:0%
+potentially the hardest lecture
+in the whole series of lectures so i
+
+ align:start position:0%
+in the whole series of lectures so i
+ 
+
+ align:start position:0%
+in the whole series of lectures so i
+thought i would
+
+ align:start position:0%
+thought i would
+ 
+
+ align:start position:0%
+thought i would
+take the time to elaborate a bit on what
+
+ align:start position:0%
+take the time to elaborate a bit on what
+ 
+
+ align:start position:0%
+take the time to elaborate a bit on what
+we were doing
+
+ align:start position:0%
+we were doing
+ 
+
+ align:start position:0%
+we were doing
+um okay
+
+ align:start position:0%
+um okay
+ 
+
+ align:start position:0%
+um okay
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+the review
+
+ align:start position:0%
+the review
+ 
+
+ align:start position:0%
+the review
+now we come to
+
+ align:start position:0%
+now we come to
+ 
+
+ align:start position:0%
+now we come to
+applying a very similar theory
+
+ align:start position:0%
+applying a very similar theory
+ 
+
+ align:start position:0%
+applying a very similar theory
+to actual data so this is real and
+
+ align:start position:0%
+to actual data so this is real and
+ 
+
+ align:start position:0%
+to actual data so this is real and
+financial flows in thailand and an
+
+ align:start position:0%
+financial flows in thailand and an
+ 
+
+ align:start position:0%
+financial flows in thailand and an
+outline we're going to talk about
+
+ align:start position:0%
+outline we're going to talk about
+ 
+
+ align:start position:0%
+outline we're going to talk about
+villages again but we're going to embed
+
+ align:start position:0%
+villages again but we're going to embed
+ 
+
+ align:start position:0%
+villages again but we're going to embed
+them in the local
+
+ align:start position:0%
+them in the local
+ 
+
+ align:start position:0%
+them in the local
+economy
+
+ align:start position:0%
+economy
+ 
+
+ align:start position:0%
+economy
+and also their relationship to the
+
+ align:start position:0%
+and also their relationship to the
+ 
+
+ align:start position:0%
+and also their relationship to the
+national economy where we view the
+
+ align:start position:0%
+national economy where we view the
+ 
+
+ align:start position:0%
+national economy where we view the
+financial accounts which you've seen
+
+ align:start position:0%
+financial accounts which you've seen
+ 
+
+ align:start position:0%
+financial accounts which you've seen
+once before when we did sort of the
+
+ align:start position:0%
+once before when we did sort of the
+ 
+
+ align:start position:0%
+once before when we did sort of the
+bitcoin part
+
+ align:start position:0%
+bitcoin part
+ 
+
+ align:start position:0%
+bitcoin part
+we'll review them here balance sheets
+
+ align:start position:0%
+we'll review them here balance sheets
+ 
+
+ align:start position:0%
+we'll review them here balance sheets
+income statement and cash flow then
+
+ align:start position:0%
+income statement and cash flow then
+ 
+
+ align:start position:0%
+income statement and cash flow then
+more general background on these village
+
+ align:start position:0%
+more general background on these village
+ 
+
+ align:start position:0%
+more general background on these village
+economies and heterogeneity within them
+
+ align:start position:0%
+economies and heterogeneity within them
+ 
+
+ align:start position:0%
+economies and heterogeneity within them
+then we'll take
+
+ align:start position:0%
+then we'll take
+ 
+
+ align:start position:0%
+then we'll take
+the village economy as a whole as an
+
+ align:start position:0%
+the village economy as a whole as an
+ 
+
+ align:start position:0%
+the village economy as a whole as an
+entire economy
+
+ align:start position:0%
+entire economy
+ 
+
+ align:start position:0%
+entire economy
+and kind of come up with gdp and
+
+ align:start position:0%
+and kind of come up with gdp and
+ 
+
+ align:start position:0%
+and kind of come up with gdp and
+village
+
+ align:start position:0%
+village
+ 
+
+ align:start position:0%
+village
+income the way we come up with national
+
+ align:start position:0%
+income the way we come up with national
+ 
+
+ align:start position:0%
+income the way we come up with national
+income and the national income and
+
+ align:start position:0%
+income and the national income and
+ 
+
+ align:start position:0%
+income and the national income and
+product accounts
+
+ align:start position:0%
+product accounts
+ 
+
+ align:start position:0%
+product accounts
+and then finally what as a small open
+
+ align:start position:0%
+and then finally what as a small open
+ 
+
+ align:start position:0%
+and then finally what as a small open
+economy
+
+ align:start position:0%
+economy
+ 
+
+ align:start position:0%
+economy
+we can look at flow of funds balance of
+
+ align:start position:0%
+we can look at flow of funds balance of
+ 
+
+ align:start position:0%
+we can look at flow of funds balance of
+payments how open or how closed is the
+
+ align:start position:0%
+payments how open or how closed is the
+ 
+
+ align:start position:0%
+payments how open or how closed is the
+economy
+
+ align:start position:0%
+economy
+ 
+
+ align:start position:0%
+economy
+and then we come to this calibration
+
+ align:start position:0%
+and then we come to this calibration
+ 
+
+ align:start position:0%
+and then we come to this calibration
+part which i already highlighted with
+
+ align:start position:0%
+part which i already highlighted with
+ 
+
+ align:start position:0%
+part which i already highlighted with
+respect to the other start reading
+
+ align:start position:0%
+respect to the other start reading
+ 
+
+ align:start position:0%
+respect to the other start reading
+dawkins at al what does it mean to be
+
+ align:start position:0%
+dawkins at al what does it mean to be
+ 
+
+ align:start position:0%
+dawkins at al what does it mean to be
+calibrating a model which they often did
+
+ align:start position:0%
+calibrating a model which they often did
+ 
+
+ align:start position:0%
+calibrating a model which they often did
+in the trade context as we do here
+
+ align:start position:0%
+in the trade context as we do here
+ 
+
+ align:start position:0%
+in the trade context as we do here
+and we'll look at model predicted data
+
+ align:start position:0%
+and we'll look at model predicted data
+ 
+
+ align:start position:0%
+and we'll look at model predicted data
+and compare directly to actual data
+
+ align:start position:0%
+and compare directly to actual data
+ 
+
+ align:start position:0%
+and compare directly to actual data
+and then look at some counter factuals
+
+ align:start position:0%
+and then look at some counter factuals
+ 
+
+ align:start position:0%
+and then look at some counter factuals
+like uh imposing tariffs and frictions
+
+ align:start position:0%
+like uh imposing tariffs and frictions
+ 
+
+ align:start position:0%
+like uh imposing tariffs and frictions
+so last time and today you could think
+
+ align:start position:0%
+so last time and today you could think
+ 
+
+ align:start position:0%
+so last time and today you could think
+of this question as
+
+ align:start position:0%
+of this question as
+ 
+
+ align:start position:0%
+of this question as
+free trade who are the winners and
+
+ align:start position:0%
+free trade who are the winners and
+ 
+
+ align:start position:0%
+free trade who are the winners and
+losers tariffs
+
+ align:start position:0%
+losers tariffs
+ 
+
+ align:start position:0%
+losers tariffs
+who are the winners and losers and not
+
+ align:start position:0%
+who are the winners and losers and not
+ 
+
+ align:start position:0%
+who are the winners and losers and not
+in the abstract as in last time but
+
+ align:start position:0%
+in the abstract as in last time but
+ 
+
+ align:start position:0%
+in the abstract as in last time but
+actually here in the context of a
+
+ align:start position:0%
+actually here in the context of a
+ 
+
+ align:start position:0%
+actually here in the context of a
+calibrated model you'll actually see the
+
+ align:start position:0%
+calibrated model you'll actually see the
+ 
+
+ align:start position:0%
+calibrated model you'll actually see the
+impact on individual people living in
+
+ align:start position:0%
+impact on individual people living in
+ 
+
+ align:start position:0%
+impact on individual people living in
+these villages
+
+ align:start position:0%
+these villages
+ 
+
+ align:start position:0%
+these villages
+and then when we get to the us we'll do
+
+ align:start position:0%
+and then when we get to the us we'll do
+ 
+
+ align:start position:0%
+and then when we get to the us we'll do
+it all again on thursday which is a
+
+ align:start position:0%
+it all again on thursday which is a
+ 
+
+ align:start position:0%
+it all again on thursday which is a
+different context but the same kind of
+
+ align:start position:0%
+different context but the same kind of
+ 
+
+ align:start position:0%
+different context but the same kind of
+theory okay
+
+ align:start position:0%
+theory okay
+ 
+
+ align:start position:0%
+theory okay
+so you've seen this before let me
+
+ align:start position:0%
+so you've seen this before let me
+ 
+
+ align:start position:0%
+so you've seen this before let me
+highlight the thai map we have these two
+
+ align:start position:0%
+highlight the thai map we have these two
+ 
+
+ align:start position:0%
+highlight the thai map we have these two
+provinces cha chung sao and loperi in
+
+ align:start position:0%
+provinces cha chung sao and loperi in
+ 
+
+ align:start position:0%
+provinces cha chung sao and loperi in
+the central area of the country near if
+
+ align:start position:0%
+the central area of the country near if
+ 
+
+ align:start position:0%
+the central area of the country near if
+not right on top of bangkok and we have
+
+ align:start position:0%
+not right on top of bangkok and we have
+ 
+
+ align:start position:0%
+not right on top of bangkok and we have
+the other two bertram and sisiket
+
+ align:start position:0%
+the other two bertram and sisiket
+ 
+
+ align:start position:0%
+the other two bertram and sisiket
+in the northeast and much more agrarian
+
+ align:start position:0%
+in the northeast and much more agrarian
+ 
+
+ align:start position:0%
+in the northeast and much more agrarian
+area of the country this is sisa cat i
+
+ align:start position:0%
+area of the country this is sisa cat i
+ 
+
+ align:start position:0%
+area of the country this is sisa cat i
+muttered something about not finding
+
+ align:start position:0%
+muttered something about not finding
+ 
+
+ align:start position:0%
+muttered something about not finding
+these monthly starred villages but i
+
+ align:start position:0%
+these monthly starred villages but i
+ 
+
+ align:start position:0%
+these monthly starred villages but i
+knew where they were and now i realize
+
+ align:start position:0%
+knew where they were and now i realize
+ 
+
+ align:start position:0%
+knew where they were and now i realize
+it's still very hard to read but these
+
+ align:start position:0%
+it's still very hard to read but these
+ 
+
+ align:start position:0%
+it's still very hard to read but these
+sort of cheerio circles correspond to
+
+ align:start position:0%
+sort of cheerio circles correspond to
+ 
+
+ align:start position:0%
+sort of cheerio circles correspond to
+baseline survey done in 1997 a subset of
+
+ align:start position:0%
+baseline survey done in 1997 a subset of
+ 
+
+ align:start position:0%
+baseline survey done in 1997 a subset of
+those villages were chosen from 98
+
+ align:start position:0%
+those villages were chosen from 98
+ 
+
+ align:start position:0%
+those villages were chosen from 98
+onward including the data that we're
+
+ align:start position:0%
+onward including the data that we're
+ 
+
+ align:start position:0%
+onward including the data that we're
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+in which case it's a monthly survey so
+
+ align:start position:0%
+in which case it's a monthly survey so
+ 
+
+ align:start position:0%
+in which case it's a monthly survey so
+so the cheerio covers up the star and
+
+ align:start position:0%
+so the cheerio covers up the star and
+ 
+
+ align:start position:0%
+so the cheerio covers up the star and
+produces these green like objects up
+
+ align:start position:0%
+produces these green like objects up
+ 
+
+ align:start position:0%
+produces these green like objects up
+here so that's the cluster so there are
+
+ align:start position:0%
+here so that's the cluster so there are
+ 
+
+ align:start position:0%
+here so that's the cluster so there are
+four villages in cesa cat that
+
+ align:start position:0%
+four villages in cesa cat that
+ 
+
+ align:start position:0%
+four villages in cesa cat that
+constitute the monthly data and likewise
+
+ align:start position:0%
+constitute the monthly data and likewise
+ 
+
+ align:start position:0%
+constitute the monthly data and likewise
+they're going to be four each in the
+
+ align:start position:0%
+they're going to be four each in the
+ 
+
+ align:start position:0%
+they're going to be four each in the
+other three provinces okay so let's
+
+ align:start position:0%
+other three provinces okay so let's
+ 
+
+ align:start position:0%
+other three provinces okay so let's
+take loperi over here
+
+ align:start position:0%
+take loperi over here
+ 
+
+ align:start position:0%
+take loperi over here
+and take a wage earner
+
+ align:start position:0%
+and take a wage earner
+ 
+
+ align:start position:0%
+and take a wage earner
+and look at
+
+ align:start position:0%
+and look at
+ 
+
+ align:start position:0%
+and look at
+this actual
+
+ align:start position:0%
+this actual
+ 
+
+ align:start position:0%
+this actual
+households
+
+ align:start position:0%
+households
+ 
+
+ align:start position:0%
+households
+income statement so you've seen version
+
+ align:start position:0%
+income statement so you've seen version
+ 
+
+ align:start position:0%
+income statement so you've seen version
+of this before and i remember asking you
+
+ align:start position:0%
+of this before and i remember asking you
+ 
+
+ align:start position:0%
+of this before and i remember asking you
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+in the follow-up we've got revenues
+
+ align:start position:0%
+in the follow-up we've got revenues
+ 
+
+ align:start position:0%
+in the follow-up we've got revenues
+and costs in this case
+
+ align:start position:0%
+and costs in this case
+ 
+
+ align:start position:0%
+and costs in this case
+this guy does a little bit of livestock
+
+ align:start position:0%
+this guy does a little bit of livestock
+ 
+
+ align:start position:0%
+this guy does a little bit of livestock
+but mostly it's wage labor
+
+ align:start position:0%
+but mostly it's wage labor
+ 
+
+ align:start position:0%
+but mostly it's wage labor
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in principle could have had interest
+
+ align:start position:0%
+in principle could have had interest
+ 
+
+ align:start position:0%
+in principle could have had interest
+income but didn't
+
+ align:start position:0%
+income but didn't
+ 
+
+ align:start position:0%
+income but didn't
+and on the cost side you know most of
+
+ align:start position:0%
+and on the cost side you know most of
+ 
+
+ align:start position:0%
+and on the cost side you know most of
+these costs are associated with
+
+ align:start position:0%
+these costs are associated with
+ 
+
+ align:start position:0%
+these costs are associated with
+livestock
+
+ align:start position:0%
+livestock
+ 
+
+ align:start position:0%
+livestock
+and in debt has actually has an interest
+
+ align:start position:0%
+and in debt has actually has an interest
+ 
+
+ align:start position:0%
+and in debt has actually has an interest
+expense
+
+ align:start position:0%
+expense
+ 
+
+ align:start position:0%
+expense
+and then does consumption and uh
+
+ align:start position:0%
+and then does consumption and uh
+ 
+
+ align:start position:0%
+and then does consumption and uh
+subtracts that's off of income and has
+
+ align:start position:0%
+subtracts that's off of income and has
+ 
+
+ align:start position:0%
+subtracts that's off of income and has
+some savings so that's the income
+
+ align:start position:0%
+some savings so that's the income
+ 
+
+ align:start position:0%
+some savings so that's the income
+statement of household a
+
+ align:start position:0%
+statement of household a
+ 
+
+ align:start position:0%
+statement of household a
+which we have these kinds of statements
+
+ align:start position:0%
+which we have these kinds of statements
+ 
+
+ align:start position:0%
+which we have these kinds of statements
+for you know roughly 800 households
+
+ align:start position:0%
+for you know roughly 800 households
+ 
+
+ align:start position:0%
+for you know roughly 800 households
+here's what happens over time that labor
+
+ align:start position:0%
+here's what happens over time that labor
+ 
+
+ align:start position:0%
+here's what happens over time that labor
+income which is the dominant source of
+
+ align:start position:0%
+income which is the dominant source of
+ 
+
+ align:start position:0%
+income which is the dominant source of
+income falls
+
+ align:start position:0%
+income falls
+ 
+
+ align:start position:0%
+income falls
+and then gradually increases back up
+
+ align:start position:0%
+and then gradually increases back up
+ 
+
+ align:start position:0%
+and then gradually increases back up
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+other components are largely zero
+
+ align:start position:0%
+other components are largely zero
+ 
+
+ align:start position:0%
+other components are largely zero
+although this they started a business
+
+ align:start position:0%
+although this they started a business
+ 
+
+ align:start position:0%
+although this they started a business
+right in the last year or two
+
+ align:start position:0%
+right in the last year or two
+ 
+
+ align:start position:0%
+right in the last year or two
+cultivation rises and then falls again
+
+ align:start position:0%
+cultivation rises and then falls again
+ 
+
+ align:start position:0%
+cultivation rises and then falls again
+so trying this that or the other but
+
+ align:start position:0%
+so trying this that or the other but
+ 
+
+ align:start position:0%
+so trying this that or the other but
+largely labor income
+
+ align:start position:0%
+largely labor income
+ 
+
+ align:start position:0%
+largely labor income
+this same household has a balance sheet
+
+ align:start position:0%
+this same household has a balance sheet
+ 
+
+ align:start position:0%
+this same household has a balance sheet
+which has
+
+ align:start position:0%
+which has
+ 
+
+ align:start position:0%
+which has
+liabilities on the right-hand side and
+
+ align:start position:0%
+liabilities on the right-hand side and
+ 
+
+ align:start position:0%
+liabilities on the right-hand side and
+assets on the left-hand side since those
+
+ align:start position:0%
+assets on the left-hand side since those
+ 
+
+ align:start position:0%
+assets on the left-hand side since those
+things don't balance hopefully
+
+ align:start position:0%
+things don't balance hopefully
+ 
+
+ align:start position:0%
+things don't balance hopefully
+liabilities are smaller than assets and
+
+ align:start position:0%
+liabilities are smaller than assets and
+ 
+
+ align:start position:0%
+liabilities are smaller than assets and
+the difference is net worth
+
+ align:start position:0%
+the difference is net worth
+ 
+
+ align:start position:0%
+the difference is net worth
+so we have
+
+ align:start position:0%
+so we have
+ 
+
+ align:start position:0%
+so we have
+liabilities in net worth on the right
+
+ align:start position:0%
+liabilities in net worth on the right
+ 
+
+ align:start position:0%
+liabilities in net worth on the right
+hand side and assets on the left
+
+ align:start position:0%
+hand side and assets on the left
+ 
+
+ align:start position:0%
+hand side and assets on the left
+assets consist of financial assets like
+
+ align:start position:0%
+assets consist of financial assets like
+ 
+
+ align:start position:0%
+assets consist of financial assets like
+cash and could have been deposits a
+
+ align:start position:0%
+cash and could have been deposits a
+ 
+
+ align:start position:0%
+cash and could have been deposits a
+little bit of deposits in banks
+
+ align:start position:0%
+little bit of deposits in banks
+ 
+
+ align:start position:0%
+little bit of deposits in banks
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+those are financial assets and then we
+
+ align:start position:0%
+those are financial assets and then we
+ 
+
+ align:start position:0%
+those are financial assets and then we
+have you know real assets like livestock
+
+ align:start position:0%
+have you know real assets like livestock
+ 
+
+ align:start position:0%
+have you know real assets like livestock
+and so on inventories and we have other
+
+ align:start position:0%
+and so on inventories and we have other
+ 
+
+ align:start position:0%
+and so on inventories and we have other
+fixed assets including household assets
+
+ align:start position:0%
+fixed assets including household assets
+ 
+
+ align:start position:0%
+fixed assets including household assets
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you're wondering where i'm going with
+
+ align:start position:0%
+you're wondering where i'm going with
+ 
+
+ align:start position:0%
+you're wondering where i'm going with
+this i'm deliberately highlighting
+
+ align:start position:0%
+this i'm deliberately highlighting
+ 
+
+ align:start position:0%
+this i'm deliberately highlighting
+things they're going to come up
+
+ align:start position:0%
+things they're going to come up
+ 
+
+ align:start position:0%
+things they're going to come up
+momentarily
+
+ align:start position:0%
+momentarily
+ 
+
+ align:start position:0%
+momentarily
+and again
+
+ align:start position:0%
+and again
+ 
+
+ align:start position:0%
+and again
+the balance sheet over time for this
+
+ align:start position:0%
+the balance sheet over time for this
+ 
+
+ align:start position:0%
+the balance sheet over time for this
+household
+
+ align:start position:0%
+household
+ 
+
+ align:start position:0%
+household
+you can see wealth is going
+
+ align:start position:0%
+you can see wealth is going
+ 
+
+ align:start position:0%
+you can see wealth is going
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+mostly because assets are going up
+
+ align:start position:0%
+mostly because assets are going up
+ 
+
+ align:start position:0%
+mostly because assets are going up
+but toward the end when the household
+
+ align:start position:0%
+but toward the end when the household
+ 
+
+ align:start position:0%
+but toward the end when the household
+started that business they borrowed
+
+ align:start position:0%
+started that business they borrowed
+ 
+
+ align:start position:0%
+started that business they borrowed
+liabilities went up and net worth
+
+ align:start position:0%
+liabilities went up and net worth
+ 
+
+ align:start position:0%
+liabilities went up and net worth
+actually went down
+
+ align:start position:0%
+actually went down
+ 
+
+ align:start position:0%
+actually went down
+but anyway this is over time
+
+ align:start position:0%
+but anyway this is over time
+ 
+
+ align:start position:0%
+but anyway this is over time
+finally we have the statement of cash
+
+ align:start position:0%
+finally we have the statement of cash
+ 
+
+ align:start position:0%
+finally we have the statement of cash
+flow which i highlighted when we talked
+
+ align:start position:0%
+flow which i highlighted when we talked
+ 
+
+ align:start position:0%
+flow which i highlighted when we talked
+about bitcoin
+
+ align:start position:0%
+about bitcoin
+ 
+
+ align:start position:0%
+about bitcoin
+we've got cash flow from production cash
+
+ align:start position:0%
+we've got cash flow from production cash
+ 
+
+ align:start position:0%
+we've got cash flow from production cash
+flow from financing investment and
+
+ align:start position:0%
+flow from financing investment and
+ 
+
+ align:start position:0%
+flow from financing investment and
+consumption
+
+ align:start position:0%
+consumption
+ 
+
+ align:start position:0%
+consumption
+and that produces a measure of cash flow
+
+ align:start position:0%
+and that produces a measure of cash flow
+ 
+
+ align:start position:0%
+and that produces a measure of cash flow
+from the flows which has to sync up with
+
+ align:start position:0%
+from the flows which has to sync up with
+ 
+
+ align:start position:0%
+from the flows which has to sync up with
+the change in the cash in the balance
+
+ align:start position:0%
+the change in the cash in the balance
+ 
+
+ align:start position:0%
+the change in the cash in the balance
+sheet
+
+ align:start position:0%
+sheet
+ 
+
+ align:start position:0%
+sheet
+which it does in these data so next i
+
+ align:start position:0%
+which it does in these data so next i
+ 
+
+ align:start position:0%
+which it does in these data so next i
+want to talk about diversity across the
+
+ align:start position:0%
+want to talk about diversity across the
+ 
+
+ align:start position:0%
+want to talk about diversity across the
+households
+
+ align:start position:0%
+households
+ 
+
+ align:start position:0%
+households
+especially for the ones who are actually
+
+ align:start position:0%
+especially for the ones who are actually
+ 
+
+ align:start position:0%
+especially for the ones who are actually
+firms who have decided to go into
+
+ align:start position:0%
+firms who have decided to go into
+ 
+
+ align:start position:0%
+firms who have decided to go into
+business the types of activities
+
+ align:start position:0%
+business the types of activities
+ 
+
+ align:start position:0%
+business the types of activities
+cultivation farming business like retail
+
+ align:start position:0%
+cultivation farming business like retail
+ 
+
+ align:start position:0%
+cultivation farming business like retail
+outlets trucking stuff around livestock
+
+ align:start position:0%
+outlets trucking stuff around livestock
+ 
+
+ align:start position:0%
+outlets trucking stuff around livestock
+fish and shrimp and this is like a cobb
+
+ align:start position:0%
+fish and shrimp and this is like a cobb
+ 
+
+ align:start position:0%
+fish and shrimp and this is like a cobb
+douglas production function written out
+
+ align:start position:0%
+douglas production function written out
+ 
+
+ align:start position:0%
+douglas production function written out
+in logs so delta k is the intensity of
+
+ align:start position:0%
+in logs so delta k is the intensity of
+ 
+
+ align:start position:0%
+in logs so delta k is the intensity of
+the capital good and delta l is the
+
+ align:start position:0%
+the capital good and delta l is the
+ 
+
+ align:start position:0%
+the capital good and delta l is the
+intensity of the labor good
+
+ align:start position:0%
+intensity of the labor good
+ 
+
+ align:start position:0%
+intensity of the labor good
+and what we want to see are those factor
+
+ align:start position:0%
+and what we want to see are those factor
+ 
+
+ align:start position:0%
+and what we want to see are those factor
+intensities so in fact if you look
+
+ align:start position:0%
+intensities so in fact if you look
+ 
+
+ align:start position:0%
+intensities so in fact if you look
+cultivation is labor intensive it will
+
+ align:start position:0%
+cultivation is labor intensive it will
+ 
+
+ align:start position:0%
+cultivation is labor intensive it will
+fit the definition we reviewed at the
+
+ align:start position:0%
+fit the definition we reviewed at the
+ 
+
+ align:start position:0%
+fit the definition we reviewed at the
+beginning of class
+
+ align:start position:0%
+beginning of class
+ 
+
+ align:start position:0%
+beginning of class
+uses relatively more labor than capital
+
+ align:start position:0%
+uses relatively more labor than capital
+ 
+
+ align:start position:0%
+uses relatively more labor than capital
+because of the coefficients delta l and
+
+ align:start position:0%
+because of the coefficients delta l and
+ 
+
+ align:start position:0%
+because of the coefficients delta l and
+delta k
+
+ align:start position:0%
+delta k
+ 
+
+ align:start position:0%
+delta k
+on the other extreme the fish and shrimp
+
+ align:start position:0%
+on the other extreme the fish and shrimp
+ 
+
+ align:start position:0%
+on the other extreme the fish and shrimp
+uses almost no labor at all and uses
+
+ align:start position:0%
+uses almost no labor at all and uses
+ 
+
+ align:start position:0%
+uses almost no labor at all and uses
+tons of capital
+
+ align:start position:0%
+tons of capital
+ 
+
+ align:start position:0%
+tons of capital
+so we've got capital and labor intensive
+
+ align:start position:0%
+so we've got capital and labor intensive
+ 
+
+ align:start position:0%
+so we've got capital and labor intensive
+activities
+
+ align:start position:0%
+activities
+ 
+
+ align:start position:0%
+activities
+we can try to
+
+ align:start position:0%
+we can try to
+ 
+
+ align:start position:0%
+we can try to
+make it simpler and talk about basically
+
+ align:start position:0%
+make it simpler and talk about basically
+ 
+
+ align:start position:0%
+make it simpler and talk about basically
+agricultural goods versus others called
+
+ align:start position:0%
+agricultural goods versus others called
+ 
+
+ align:start position:0%
+agricultural goods versus others called
+manufacturing really means
+
+ align:start position:0%
+manufacturing really means
+ 
+
+ align:start position:0%
+manufacturing really means
+non-agricultural
+
+ align:start position:0%
+non-agricultural
+ 
+
+ align:start position:0%
+non-agricultural
+okay the other thing sitting up here is
+
+ align:start position:0%
+okay the other thing sitting up here is
+ 
+
+ align:start position:0%
+okay the other thing sitting up here is
+this epsilon
+
+ align:start position:0%
+this epsilon
+ 
+
+ align:start position:0%
+this epsilon
+this is quote an error term but it
+
+ align:start position:0%
+this is quote an error term but it
+ 
+
+ align:start position:0%
+this is quote an error term but it
+actually contains
+
+ align:start position:0%
+actually contains
+ 
+
+ align:start position:0%
+actually contains
+not just noisy data but a measurement of
+
+ align:start position:0%
+not just noisy data but a measurement of
+ 
+
+ align:start position:0%
+not just noisy data but a measurement of
+talent
+
+ align:start position:0%
+talent
+ 
+
+ align:start position:0%
+talent
+so if we took the average for a
+
+ align:start position:0%
+so if we took the average for a
+ 
+
+ align:start position:0%
+so if we took the average for a
+particular household eye
+
+ align:start position:0%
+particular household eye
+ 
+
+ align:start position:0%
+particular household eye
+we took the average of these epsilons
+
+ align:start position:0%
+we took the average of these epsilons
+ 
+
+ align:start position:0%
+we took the average of these epsilons
+they don't have to average out to zero
+
+ align:start position:0%
+they don't have to average out to zero
+ 
+
+ align:start position:0%
+they don't have to average out to zero
+they average out to something that is
+
+ align:start position:0%
+they average out to something that is
+ 
+
+ align:start position:0%
+they average out to something that is
+common to the sector that household eye
+
+ align:start position:0%
+common to the sector that household eye
+ 
+
+ align:start position:0%
+common to the sector that household eye
+is engaged in a bar and some other
+
+ align:start position:0%
+is engaged in a bar and some other
+ 
+
+ align:start position:0%
+is engaged in a bar and some other
+household specific talent called z okay
+
+ align:start position:0%
+household specific talent called z okay
+ 
+
+ align:start position:0%
+household specific talent called z okay
+so there's a sector and household
+
+ align:start position:0%
+so there's a sector and household
+ 
+
+ align:start position:0%
+so there's a sector and household
+specific talent variable
+
+ align:start position:0%
+specific talent variable
+ 
+
+ align:start position:0%
+specific talent variable
+that's wrapped up into these epsilons
+
+ align:start position:0%
+that's wrapped up into these epsilons
+ 
+
+ align:start position:0%
+that's wrapped up into these epsilons
+obviously if you're talented the
+
+ align:start position:0%
+obviously if you're talented the
+ 
+
+ align:start position:0%
+obviously if you're talented the
+epsilons are going to tend to be high
+
+ align:start position:0%
+epsilons are going to tend to be high
+ 
+
+ align:start position:0%
+epsilons are going to tend to be high
+meaning output's going to be high
+
+ align:start position:0%
+meaning output's going to be high
+ 
+
+ align:start position:0%
+meaning output's going to be high
+even controlling for capital and labor
+
+ align:start position:0%
+even controlling for capital and labor
+ 
+
+ align:start position:0%
+even controlling for capital and labor
+so if you look across the sectors
+
+ align:start position:0%
+so if you look across the sectors
+ 
+
+ align:start position:0%
+so if you look across the sectors
+at quote sectoral productivity
+
+ align:start position:0%
+at quote sectoral productivity
+ 
+
+ align:start position:0%
+at quote sectoral productivity
+they're pretty similar
+
+ align:start position:0%
+they're pretty similar
+ 
+
+ align:start position:0%
+they're pretty similar
+the highest one here is livestock the
+
+ align:start position:0%
+the highest one here is livestock the
+ 
+
+ align:start position:0%
+the highest one here is livestock the
+lowest one is business
+
+ align:start position:0%
+lowest one is business
+ 
+
+ align:start position:0%
+lowest one is business
+now in terms of the household specific
+
+ align:start position:0%
+now in terms of the household specific
+ 
+
+ align:start position:0%
+now in terms of the household specific
+productivities there's a whole
+
+ align:start position:0%
+productivities there's a whole
+ 
+
+ align:start position:0%
+productivities there's a whole
+cross-sectional dispersion of these zis
+
+ align:start position:0%
+cross-sectional dispersion of these zis
+ 
+
+ align:start position:0%
+cross-sectional dispersion of these zis
+in each sector and so this sigma
+
+ align:start position:0%
+in each sector and so this sigma
+ 
+
+ align:start position:0%
+in each sector and so this sigma
+is a characterization of the
+
+ align:start position:0%
+is a characterization of the
+ 
+
+ align:start position:0%
+is a characterization of the
+a bit like a variance of the
+
+ align:start position:0%
+a bit like a variance of the
+ 
+
+ align:start position:0%
+a bit like a variance of the
+distribution the point being that
+
+ align:start position:0%
+distribution the point being that
+ 
+
+ align:start position:0%
+distribution the point being that
+each household has a particular z
+
+ align:start position:0%
+each household has a particular z
+ 
+
+ align:start position:0%
+each household has a particular z
+depending on the sector in which they
+
+ align:start position:0%
+depending on the sector in which they
+ 
+
+ align:start position:0%
+depending on the sector in which they
+reside and they could be very talented
+
+ align:start position:0%
+reside and they could be very talented
+ 
+
+ align:start position:0%
+reside and they could be very talented
+or not talented at all even though
+
+ align:start position:0%
+or not talented at all even though
+ 
+
+ align:start position:0%
+or not talented at all even though
+they're engaged in that activity
+
+ align:start position:0%
+they're engaged in that activity
+ 
+
+ align:start position:0%
+they're engaged in that activity
+and these are estimated in the data
+
+ align:start position:0%
+and these are estimated in the data
+ 
+
+ align:start position:0%
+and these are estimated in the data
+you're looking at the actual numbers the
+
+ align:start position:0%
+you're looking at the actual numbers the
+ 
+
+ align:start position:0%
+you're looking at the actual numbers the
+other aspect of heterogeneity here in
+
+ align:start position:0%
+other aspect of heterogeneity here in
+ 
+
+ align:start position:0%
+other aspect of heterogeneity here in
+addition to household talent
+
+ align:start position:0%
+addition to household talent
+ 
+
+ align:start position:0%
+addition to household talent
+would be their wealth
+
+ align:start position:0%
+would be their wealth
+ 
+
+ align:start position:0%
+would be their wealth
+or specifically their fixed assets
+
+ align:start position:0%
+or specifically their fixed assets
+ 
+
+ align:start position:0%
+or specifically their fixed assets
+that's why i emphasized that when we
+
+ align:start position:0%
+that's why i emphasized that when we
+ 
+
+ align:start position:0%
+that's why i emphasized that when we
+went through the balance sheet and you
+
+ align:start position:0%
+went through the balance sheet and you
+ 
+
+ align:start position:0%
+went through the balance sheet and you
+can see the cross-sectional distribution
+
+ align:start position:0%
+can see the cross-sectional distribution
+ 
+
+ align:start position:0%
+can see the cross-sectional distribution
+in loperi which is near bangkok versus
+
+ align:start position:0%
+in loperi which is near bangkok versus
+ 
+
+ align:start position:0%
+in loperi which is near bangkok versus
+the cross-sectional distribution in bury
+
+ align:start position:0%
+the cross-sectional distribution in bury
+ 
+
+ align:start position:0%
+the cross-sectional distribution in bury
+rum
+
+ align:start position:0%
+rum
+ 
+
+ align:start position:0%
+rum
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+has a lot more mass over here to the
+
+ align:start position:0%
+has a lot more mass over here to the
+ 
+
+ align:start position:0%
+has a lot more mass over here to the
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+meaning low assets so indeed in the data
+
+ align:start position:0%
+meaning low assets so indeed in the data
+ 
+
+ align:start position:0%
+meaning low assets so indeed in the data
+loperi near bangkok has higher average
+
+ align:start position:0%
+loperi near bangkok has higher average
+ 
+
+ align:start position:0%
+loperi near bangkok has higher average
+fixed assets than does bergeron out in
+
+ align:start position:0%
+fixed assets than does bergeron out in
+ 
+
+ align:start position:0%
+fixed assets than does bergeron out in
+the northeast
+
+ align:start position:0%
+the northeast
+ 
+
+ align:start position:0%
+the northeast
+but again
+
+ align:start position:0%
+but again
+ 
+
+ align:start position:0%
+but again
+it is a whole distribution so a given
+
+ align:start position:0%
+it is a whole distribution so a given
+ 
+
+ align:start position:0%
+it is a whole distribution so a given
+household could have a lot of have
+
+ align:start position:0%
+household could have a lot of have
+ 
+
+ align:start position:0%
+household could have a lot of have
+relatively little wealth or have a lot
+
+ align:start position:0%
+relatively little wealth or have a lot
+ 
+
+ align:start position:0%
+relatively little wealth or have a lot
+of wealth even in burriron this actually
+
+ align:start position:0%
+of wealth even in burriron this actually
+ 
+
+ align:start position:0%
+of wealth even in burriron this actually
+is consistent with the paulson townsend
+
+ align:start position:0%
+is consistent with the paulson townsend
+ 
+
+ align:start position:0%
+is consistent with the paulson townsend
+kharavanov paper
+
+ align:start position:0%
+kharavanov paper
+ 
+
+ align:start position:0%
+kharavanov paper
+which was an application of mechanism
+
+ align:start position:0%
+which was an application of mechanism
+ 
+
+ align:start position:0%
+which was an application of mechanism
+design where we talked about the talent
+
+ align:start position:0%
+design where we talked about the talent
+ 
+
+ align:start position:0%
+design where we talked about the talent
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+being a firm
+
+ align:start position:0%
+being a firm
+ 
+
+ align:start position:0%
+being a firm
+theta i think we had it there
+
+ align:start position:0%
+theta i think we had it there
+ 
+
+ align:start position:0%
+theta i think we had it there
+and also we talked about assets
+
+ align:start position:0%
+and also we talked about assets
+ 
+
+ align:start position:0%
+and also we talked about assets
+separately
+
+ align:start position:0%
+separately
+ 
+
+ align:start position:0%
+separately
+and indeed we talked about a limited
+
+ align:start position:0%
+and indeed we talked about a limited
+ 
+
+ align:start position:0%
+and indeed we talked about a limited
+liability constraint which is coming up
+
+ align:start position:0%
+liability constraint which is coming up
+ 
+
+ align:start position:0%
+liability constraint which is coming up
+so we have this cash thing which as i
+
+ align:start position:0%
+so we have this cash thing which as i
+ 
+
+ align:start position:0%
+so we have this cash thing which as i
+was saying from your previous lecture
+
+ align:start position:0%
+was saying from your previous lecture
+ 
+
+ align:start position:0%
+was saying from your previous lecture
+you know cash holdings don't behave very
+
+ align:start position:0%
+you know cash holdings don't behave very
+ 
+
+ align:start position:0%
+you know cash holdings don't behave very
+well so we just imposed what we see in
+
+ align:start position:0%
+well so we just imposed what we see in
+ 
+
+ align:start position:0%
+well so we just imposed what we see in
+the data that cash holdings that part of
+
+ align:start position:0%
+the data that cash holdings that part of
+ 
+
+ align:start position:0%
+the data that cash holdings that part of
+wealth that they're putting into cash is
+
+ align:start position:0%
+wealth that they're putting into cash is
+ 
+
+ align:start position:0%
+wealth that they're putting into cash is
+fixed it turns out that consumption is
+
+ align:start position:0%
+fixed it turns out that consumption is
+ 
+
+ align:start position:0%
+fixed it turns out that consumption is
+related to that we impose
+
+ align:start position:0%
+related to that we impose
+ 
+
+ align:start position:0%
+related to that we impose
+that consumption is equal to an
+
+ align:start position:0%
+that consumption is equal to an
+ 
+
+ align:start position:0%
+that consumption is equal to an
+intercept
+
+ align:start position:0%
+intercept
+ 
+
+ align:start position:0%
+intercept
+plus profits less that intercept
+
+ align:start position:0%
+plus profits less that intercept
+ 
+
+ align:start position:0%
+plus profits less that intercept
+and gamma here
+
+ align:start position:0%
+and gamma here
+ 
+
+ align:start position:0%
+and gamma here
+has to do with omega which is the
+
+ align:start position:0%
+has to do with omega which is the
+ 
+
+ align:start position:0%
+has to do with omega which is the
+fraction of savings i put into cash i
+
+ align:start position:0%
+fraction of savings i put into cash i
+ 
+
+ align:start position:0%
+fraction of savings i put into cash i
+didn't put the algebra in which i
+
+ align:start position:0%
+didn't put the algebra in which i
+ 
+
+ align:start position:0%
+didn't put the algebra in which i
+probably should have done except all i
+
+ align:start position:0%
+probably should have done except all i
+ 
+
+ align:start position:0%
+probably should have done except all i
+want to say from this is the cash part
+
+ align:start position:0%
+want to say from this is the cash part
+ 
+
+ align:start position:0%
+want to say from this is the cash part
+of savings is just fitted to the model
+
+ align:start position:0%
+of savings is just fitted to the model
+ 
+
+ align:start position:0%
+of savings is just fitted to the model
+it's not something we derive
+
+ align:start position:0%
+it's not something we derive
+ 
+
+ align:start position:0%
+it's not something we derive
+so now i want to go back to those
+
+ align:start position:0%
+so now i want to go back to those
+ 
+
+ align:start position:0%
+so now i want to go back to those
+accounts and
+
+ align:start position:0%
+accounts and
+ 
+
+ align:start position:0%
+accounts and
+show you where
+
+ align:start position:0%
+show you where
+ 
+
+ align:start position:0%
+show you where
+gross national product comes from
+
+ align:start position:0%
+gross national product comes from
+ 
+
+ align:start position:0%
+gross national product comes from
+except that in this case it's going to
+
+ align:start position:0%
+except that in this case it's going to
+ 
+
+ align:start position:0%
+except that in this case it's going to
+be village level product and income
+
+ align:start position:0%
+be village level product and income
+ 
+
+ align:start position:0%
+be village level product and income
+and then we'll go on to
+
+ align:start position:0%
+and then we'll go on to
+ 
+
+ align:start position:0%
+and then we'll go on to
+flow of funds the balance sheet
+
+ align:start position:0%
+flow of funds the balance sheet
+ 
+
+ align:start position:0%
+flow of funds the balance sheet
+balance of payments and so on so the top
+
+ align:start position:0%
+balance of payments and so on so the top
+ 
+
+ align:start position:0%
+balance of payments and so on so the top
+you've seen before
+
+ align:start position:0%
+you've seen before
+ 
+
+ align:start position:0%
+you've seen before
+that's just a statement of income
+
+ align:start position:0%
+that's just a statement of income
+ 
+
+ align:start position:0%
+that's just a statement of income
+revenues less costs but now we start
+
+ align:start position:0%
+revenues less costs but now we start
+ 
+
+ align:start position:0%
+revenues less costs but now we start
+subtracting things from both sides for
+
+ align:start position:0%
+subtracting things from both sides for
+ 
+
+ align:start position:0%
+subtracting things from both sides for
+example to get rid of capital gains
+
+ align:start position:0%
+example to get rid of capital gains
+ 
+
+ align:start position:0%
+example to get rid of capital gains
+capital losses and indemnity
+
+ align:start position:0%
+capital losses and indemnity
+ 
+
+ align:start position:0%
+capital losses and indemnity
+we subtract them off
+
+ align:start position:0%
+we subtract them off
+ 
+
+ align:start position:0%
+we subtract them off
+and then they appear with the opposite
+
+ align:start position:0%
+and then they appear with the opposite
+ 
+
+ align:start position:0%
+and then they appear with the opposite
+sign on the left hand side
+
+ align:start position:0%
+sign on the left hand side
+ 
+
+ align:start position:0%
+sign on the left hand side
+likewise we have expenses from
+
+ align:start position:0%
+likewise we have expenses from
+ 
+
+ align:start position:0%
+likewise we have expenses from
+production
+
+ align:start position:0%
+production
+ 
+
+ align:start position:0%
+production
+which we subtract off of both sides
+
+ align:start position:0%
+which we subtract off of both sides
+ 
+
+ align:start position:0%
+which we subtract off of both sides
+hence it disappears on the hand side and
+
+ align:start position:0%
+hence it disappears on the hand side and
+ 
+
+ align:start position:0%
+hence it disappears on the hand side and
+reappears on the right and it's
+
+ align:start position:0%
+reappears on the right and it's
+ 
+
+ align:start position:0%
+reappears on the right and it's
+subtracted
+
+ align:start position:0%
+subtracted
+ 
+
+ align:start position:0%
+subtracted
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we end up with revenues less expenses in
+
+ align:start position:0%
+we end up with revenues less expenses in
+ 
+
+ align:start position:0%
+we end up with revenues less expenses in
+production
+
+ align:start position:0%
+production
+ 
+
+ align:start position:0%
+production
+which we call output and on the left
+
+ align:start position:0%
+which we call output and on the left
+ 
+
+ align:start position:0%
+which we call output and on the left
+hand side we have the disposition of
+
+ align:start position:0%
+hand side we have the disposition of
+ 
+
+ align:start position:0%
+hand side we have the disposition of
+output output is used to pay interest
+
+ align:start position:0%
+output output is used to pay interest
+ 
+
+ align:start position:0%
+output output is used to pay interest
+it's used to pay interest for capital
+
+ align:start position:0%
+it's used to pay interest for capital
+ 
+
+ align:start position:0%
+it's used to pay interest for capital
+normally you would see wages paid to
+
+ align:start position:0%
+normally you would see wages paid to
+ 
+
+ align:start position:0%
+normally you would see wages paid to
+labor over here
+
+ align:start position:0%
+labor over here
+ 
+
+ align:start position:0%
+labor over here
+i'll come back to that momentarily
+
+ align:start position:0%
+i'll come back to that momentarily
+ 
+
+ align:start position:0%
+i'll come back to that momentarily
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+residual is profits
+
+ align:start position:0%
+residual is profits
+ 
+
+ align:start position:0%
+residual is profits
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+all output gets paid in the sense of
+
+ align:start position:0%
+all output gets paid in the sense of
+ 
+
+ align:start position:0%
+all output gets paid in the sense of
+paying hired factors or what's left over
+
+ align:start position:0%
+paying hired factors or what's left over
+ 
+
+ align:start position:0%
+paying hired factors or what's left over
+accruing to the business owner
+
+ align:start position:0%
+accruing to the business owner
+ 
+
+ align:start position:0%
+accruing to the business owner
+so this is a classic decomposition of
+
+ align:start position:0%
+so this is a classic decomposition of
+ 
+
+ align:start position:0%
+so this is a classic decomposition of
+the national income accounts
+
+ align:start position:0%
+the national income accounts
+ 
+
+ align:start position:0%
+the national income accounts
+from production or from inputs
+
+ align:start position:0%
+from production or from inputs
+ 
+
+ align:start position:0%
+from production or from inputs
+we're really interested in international
+
+ align:start position:0%
+we're really interested in international
+ 
+
+ align:start position:0%
+we're really interested in international
+trade so we're really interested in here
+
+ align:start position:0%
+trade so we're really interested in here
+ 
+
+ align:start position:0%
+trade so we're really interested in here
+in you know how much is labor getting
+
+ align:start position:0%
+in you know how much is labor getting
+ 
+
+ align:start position:0%
+in you know how much is labor getting
+paid how much of the interest being paid
+
+ align:start position:0%
+paid how much of the interest being paid
+ 
+
+ align:start position:0%
+paid how much of the interest being paid
+to capital and so on
+
+ align:start position:0%
+to capital and so on
+ 
+
+ align:start position:0%
+to capital and so on
+as a function of output just a bit like
+
+ align:start position:0%
+as a function of output just a bit like
+ 
+
+ align:start position:0%
+as a function of output just a bit like
+the two by two by two lecture so if
+
+ align:start position:0%
+the two by two by two lecture so if
+ 
+
+ align:start position:0%
+the two by two by two lecture so if
+we're looking at output remember there
+
+ align:start position:0%
+we're looking at output remember there
+ 
+
+ align:start position:0%
+we're looking at output remember there
+are four villages in each province that
+
+ align:start position:0%
+are four villages in each province that
+ 
+
+ align:start position:0%
+are four villages in each province that
+were selected for the monthly data
+
+ align:start position:0%
+were selected for the monthly data
+ 
+
+ align:start position:0%
+were selected for the monthly data
+here you can actually see output going
+
+ align:start position:0%
+here you can actually see output going
+ 
+
+ align:start position:0%
+here you can actually see output going
+down in chat chung sao
+
+ align:start position:0%
+down in chat chung sao
+ 
+
+ align:start position:0%
+down in chat chung sao
+wiggling but going down whereas in
+
+ align:start position:0%
+wiggling but going down whereas in
+ 
+
+ align:start position:0%
+wiggling but going down whereas in
+buriram output's going up um and these
+
+ align:start position:0%
+buriram output's going up um and these
+ 
+
+ align:start position:0%
+buriram output's going up um and these
+are the other two provinces
+
+ align:start position:0%
+are the other two provinces
+ 
+
+ align:start position:0%
+are the other two provinces
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+another point to make is that output is
+
+ align:start position:0%
+another point to make is that output is
+ 
+
+ align:start position:0%
+another point to make is that output is
+different across different villages even
+
+ align:start position:0%
+different across different villages even
+ 
+
+ align:start position:0%
+different across different villages even
+though they're nearby to one another and
+
+ align:start position:0%
+though they're nearby to one another and
+ 
+
+ align:start position:0%
+though they're nearby to one another and
+also you'll miss it if i don't point it
+
+ align:start position:0%
+also you'll miss it if i don't point it
+ 
+
+ align:start position:0%
+also you'll miss it if i don't point it
+out probably
+
+ align:start position:0%
+out probably
+ 
+
+ align:start position:0%
+out probably
+which is the scale in the northeast the
+
+ align:start position:0%
+which is the scale in the northeast the
+ 
+
+ align:start position:0%
+which is the scale in the northeast the
+maximum value is six and five
+
+ align:start position:0%
+maximum value is six and five
+ 
+
+ align:start position:0%
+maximum value is six and five
+whereas in the central the maximum is 15
+
+ align:start position:0%
+whereas in the central the maximum is 15
+ 
+
+ align:start position:0%
+whereas in the central the maximum is 15
+and 12. so yeah place villages near
+
+ align:start position:0%
+and 12. so yeah place villages near
+ 
+
+ align:start position:0%
+and 12. so yeah place villages near
+bangkok have higher output than villages
+
+ align:start position:0%
+bangkok have higher output than villages
+ 
+
+ align:start position:0%
+bangkok have higher output than villages
+in the northeast but there remains
+
+ align:start position:0%
+in the northeast but there remains
+ 
+
+ align:start position:0%
+in the northeast but there remains
+heterogeneity across the villages and
+
+ align:start position:0%
+heterogeneity across the villages and
+ 
+
+ align:start position:0%
+heterogeneity across the villages and
+and you see the ups and downs
+
+ align:start position:0%
+and you see the ups and downs
+ 
+
+ align:start position:0%
+and you see the ups and downs
+the shrimp ponds got hit with a bad
+
+ align:start position:0%
+the shrimp ponds got hit with a bad
+ 
+
+ align:start position:0%
+the shrimp ponds got hit with a bad
+shock that we've talked about previously
+
+ align:start position:0%
+shock that we've talked about previously
+ 
+
+ align:start position:0%
+shock that we've talked about previously
+in the network lecture under risk
+
+ align:start position:0%
+in the network lecture under risk
+ 
+
+ align:start position:0%
+in the network lecture under risk
+sharing so that's part of the decline in
+
+ align:start position:0%
+sharing so that's part of the decline in
+ 
+
+ align:start position:0%
+sharing so that's part of the decline in
+output in in chattering south bury rom
+
+ align:start position:0%
+output in in chattering south bury rom
+ 
+
+ align:start position:0%
+output in in chattering south bury rom
+used to be a bunch of villages we put
+
+ align:start position:0%
+used to be a bunch of villages we put
+ 
+
+ align:start position:0%
+used to be a bunch of villages we put
+rain gauges out there
+
+ align:start position:0%
+rain gauges out there
+ 
+
+ align:start position:0%
+rain gauges out there
+to measure waterfall and so on and then
+
+ align:start position:0%
+to measure waterfall and so on and then
+ 
+
+ align:start position:0%
+to measure waterfall and so on and then
+it experienced sort of a boom
+
+ align:start position:0%
+it experienced sort of a boom
+ 
+
+ align:start position:0%
+it experienced sort of a boom
+and those villages were subsumed by the
+
+ align:start position:0%
+and those villages were subsumed by the
+ 
+
+ align:start position:0%
+and those villages were subsumed by the
+town and you can see that expansion
+
+ align:start position:0%
+town and you can see that expansion
+ 
+
+ align:start position:0%
+town and you can see that expansion
+pretty dramatically in this output
+
+ align:start position:0%
+pretty dramatically in this output
+ 
+
+ align:start position:0%
+pretty dramatically in this output
+diagram
+
+ align:start position:0%
+diagram
+ 
+
+ align:start position:0%
+diagram
+and as i was saying we can decompose
+
+ align:start position:0%
+and as i was saying we can decompose
+ 
+
+ align:start position:0%
+and as i was saying we can decompose
+output into who gets it
+
+ align:start position:0%
+output into who gets it
+ 
+
+ align:start position:0%
+output into who gets it
+and you can see here
+
+ align:start position:0%
+and you can see here
+ 
+
+ align:start position:0%
+and you can see here
+wages which is the darkest line
+
+ align:start position:0%
+wages which is the darkest line
+ 
+
+ align:start position:0%
+wages which is the darkest line
+you know is is the bigger part of the
+
+ align:start position:0%
+you know is is the bigger part of the
+ 
+
+ align:start position:0%
+you know is is the bigger part of the
+disposition of output in very ram and
+
+ align:start position:0%
+disposition of output in very ram and
+ 
+
+ align:start position:0%
+disposition of output in very ram and
+sisa cat
+
+ align:start position:0%
+sisa cat
+ 
+
+ align:start position:0%
+sisa cat
+wages are not as much
+
+ align:start position:0%
+wages are not as much
+ 
+
+ align:start position:0%
+wages are not as much
+they're not trivial
+
+ align:start position:0%
+they're not trivial
+ 
+
+ align:start position:0%
+they're not trivial
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+near bangkok
+
+ align:start position:0%
+near bangkok
+ 
+
+ align:start position:0%
+near bangkok
+chatringshow and loperi instead we have
+
+ align:start position:0%
+chatringshow and loperi instead we have
+ 
+
+ align:start position:0%
+chatringshow and loperi instead we have
+these two sectors the labor intensive
+
+ align:start position:0%
+these two sectors the labor intensive
+ 
+
+ align:start position:0%
+these two sectors the labor intensive
+agricultural sector and
+
+ align:start position:0%
+agricultural sector and
+ 
+
+ align:start position:0%
+agricultural sector and
+the capital intensive manufacturing
+
+ align:start position:0%
+the capital intensive manufacturing
+ 
+
+ align:start position:0%
+the capital intensive manufacturing
+sector
+
+ align:start position:0%
+sector
+ 
+
+ align:start position:0%
+sector
+as sometimes having profit shares
+
+ align:start position:0%
+as sometimes having profit shares
+ 
+
+ align:start position:0%
+as sometimes having profit shares
+which are higher than the wages
+
+ align:start position:0%
+which are higher than the wages
+ 
+
+ align:start position:0%
+which are higher than the wages
+now we come to the savings investment
+
+ align:start position:0%
+now we come to the savings investment
+ 
+
+ align:start position:0%
+now we come to the savings investment
+account we take the balance sheet at a
+
+ align:start position:0%
+account we take the balance sheet at a
+ 
+
+ align:start position:0%
+account we take the balance sheet at a
+point in time and we take the first
+
+ align:start position:0%
+point in time and we take the first
+ 
+
+ align:start position:0%
+point in time and we take the first
+difference so now we'll have the change
+
+ align:start position:0%
+difference so now we'll have the change
+ 
+
+ align:start position:0%
+difference so now we'll have the change
+in liabilities the change in net worth
+
+ align:start position:0%
+in liabilities the change in net worth
+ 
+
+ align:start position:0%
+in liabilities the change in net worth
+on the right
+
+ align:start position:0%
+on the right
+ 
+
+ align:start position:0%
+on the right
+change in financial and real physical
+
+ align:start position:0%
+change in financial and real physical
+ 
+
+ align:start position:0%
+change in financial and real physical
+assets on the left
+
+ align:start position:0%
+assets on the left
+ 
+
+ align:start position:0%
+assets on the left
+we now go through this thing about
+
+ align:start position:0%
+we now go through this thing about
+ 
+
+ align:start position:0%
+we now go through this thing about
+subtracting items on the left and the
+
+ align:start position:0%
+subtracting items on the left and the
+ 
+
+ align:start position:0%
+subtracting items on the left and the
+right-hand side we leave the change in
+
+ align:start position:0%
+right-hand side we leave the change in
+ 
+
+ align:start position:0%
+right-hand side we leave the change in
+net worth on the right-hand side
+
+ align:start position:0%
+net worth on the right-hand side
+ 
+
+ align:start position:0%
+net worth on the right-hand side
+and the disposition of that change into
+
+ align:start position:0%
+and the disposition of that change into
+ 
+
+ align:start position:0%
+and the disposition of that change into
+an increase in financial or real assets
+
+ align:start position:0%
+an increase in financial or real assets
+ 
+
+ align:start position:0%
+an increase in financial or real assets
+or a decrease in liabilities
+
+ align:start position:0%
+or a decrease in liabilities
+ 
+
+ align:start position:0%
+or a decrease in liabilities
+so we can kind of see they're managing
+
+ align:start position:0%
+so we can kind of see they're managing
+ 
+
+ align:start position:0%
+so we can kind of see they're managing
+their portfolio
+
+ align:start position:0%
+their portfolio
+ 
+
+ align:start position:0%
+their portfolio
+in an accounting sense as a function of
+
+ align:start position:0%
+in an accounting sense as a function of
+ 
+
+ align:start position:0%
+in an accounting sense as a function of
+you know what do they do with savings
+
+ align:start position:0%
+you know what do they do with savings
+ 
+
+ align:start position:0%
+you know what do they do with savings
+and likewise if savings are negative
+
+ align:start position:0%
+and likewise if savings are negative
+ 
+
+ align:start position:0%
+and likewise if savings are negative
+because you know they consume more than
+
+ align:start position:0%
+because you know they consume more than
+ 
+
+ align:start position:0%
+because you know they consume more than
+they earn
+
+ align:start position:0%
+they earn
+ 
+
+ align:start position:0%
+they earn
+then they have to draw that value out of
+
+ align:start position:0%
+then they have to draw that value out of
+ 
+
+ align:start position:0%
+then they have to draw that value out of
+something or borrow
+
+ align:start position:0%
+something or borrow
+ 
+
+ align:start position:0%
+something or borrow
+so this is the allocation of savings
+
+ align:start position:0%
+so this is the allocation of savings
+ 
+
+ align:start position:0%
+so this is the allocation of savings
+across the four provinces uh the darkest
+
+ align:start position:0%
+across the four provinces uh the darkest
+ 
+
+ align:start position:0%
+across the four provinces uh the darkest
+line here is savings which is largely
+
+ align:start position:0%
+line here is savings which is largely
+ 
+
+ align:start position:0%
+line here is savings which is largely
+going up although not entirely
+
+ align:start position:0%
+going up although not entirely
+ 
+
+ align:start position:0%
+going up although not entirely
+savings that's going down in chat
+
+ align:start position:0%
+savings that's going down in chat
+ 
+
+ align:start position:0%
+savings that's going down in chat
+transfer as you might have expected
+
+ align:start position:0%
+transfer as you might have expected
+ 
+
+ align:start position:0%
+transfer as you might have expected
+since they gotta finance those losses
+
+ align:start position:0%
+since they gotta finance those losses
+ 
+
+ align:start position:0%
+since they gotta finance those losses
+that declining output from somewhere
+
+ align:start position:0%
+that declining output from somewhere
+ 
+
+ align:start position:0%
+that declining output from somewhere
+they're preserving consumption by taking
+
+ align:start position:0%
+they're preserving consumption by taking
+ 
+
+ align:start position:0%
+they're preserving consumption by taking
+it out of savings likewise
+
+ align:start position:0%
+it out of savings likewise
+ 
+
+ align:start position:0%
+it out of savings likewise
+they can save into fixed assets
+
+ align:start position:0%
+they can save into fixed assets
+ 
+
+ align:start position:0%
+they can save into fixed assets
+save into financial assets the thing
+
+ align:start position:0%
+save into financial assets the thing
+ 
+
+ align:start position:0%
+save into financial assets the thing
+that tracks the best overall
+
+ align:start position:0%
+that tracks the best overall
+ 
+
+ align:start position:0%
+that tracks the best overall
+tracks dark savings overall the best
+
+ align:start position:0%
+tracks dark savings overall the best
+ 
+
+ align:start position:0%
+tracks dark savings overall the best
+is financial and you can see in most of
+
+ align:start position:0%
+is financial and you can see in most of
+ 
+
+ align:start position:0%
+is financial and you can see in most of
+these diagrams the black dotted lines
+
+ align:start position:0%
+these diagrams the black dotted lines
+ 
+
+ align:start position:0%
+these diagrams the black dotted lines
+are close to the solid black line
+
+ align:start position:0%
+are close to the solid black line
+ 
+
+ align:start position:0%
+are close to the solid black line
+so financial asset increase when savings
+
+ align:start position:0%
+so financial asset increase when savings
+ 
+
+ align:start position:0%
+so financial asset increase when savings
+is positive
+
+ align:start position:0%
+is positive
+ 
+
+ align:start position:0%
+is positive
+but these other real physical stuff as
+
+ align:start position:0%
+but these other real physical stuff as
+ 
+
+ align:start position:0%
+but these other real physical stuff as
+well as gifts play a role gifts are not
+
+ align:start position:0%
+well as gifts play a role gifts are not
+ 
+
+ align:start position:0%
+well as gifts play a role gifts are not
+trivial in these economies as you
+
+ align:start position:0%
+trivial in these economies as you
+ 
+
+ align:start position:0%
+trivial in these economies as you
+already know from thinking about
+
+ align:start position:0%
+already know from thinking about
+ 
+
+ align:start position:0%
+already know from thinking about
+insurance and so on so
+
+ align:start position:0%
+insurance and so on so
+ 
+
+ align:start position:0%
+insurance and so on so
+you know all these things add up
+
+ align:start position:0%
+you know all these things add up
+ 
+
+ align:start position:0%
+you know all these things add up
+gifts financial transfers inventory and
+
+ align:start position:0%
+gifts financial transfers inventory and
+ 
+
+ align:start position:0%
+gifts financial transfers inventory and
+so on add up to savings but you know
+
+ align:start position:0%
+so on add up to savings but you know
+ 
+
+ align:start position:0%
+so on add up to savings but you know
+gifts could be negative
+
+ align:start position:0%
+gifts could be negative
+ 
+
+ align:start position:0%
+gifts could be negative
+because they're not incoming but they're
+
+ align:start position:0%
+because they're not incoming but they're
+ 
+
+ align:start position:0%
+because they're not incoming but they're
+outgoing they're not saving it they're
+
+ align:start position:0%
+outgoing they're not saving it they're
+ 
+
+ align:start position:0%
+outgoing they're not saving it they're
+giving it away
+
+ align:start position:0%
+giving it away
+ 
+
+ align:start position:0%
+giving it away
+it's not always negative gifts are
+
+ align:start position:0%
+it's not always negative gifts are
+ 
+
+ align:start position:0%
+it's not always negative gifts are
+positive in some instances but in any
+
+ align:start position:0%
+positive in some instances but in any
+ 
+
+ align:start position:0%
+positive in some instances but in any
+event they're not a trivial order of
+
+ align:start position:0%
+event they're not a trivial order of
+ 
+
+ align:start position:0%
+event they're not a trivial order of
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+and we will look at that subsequently
+
+ align:start position:0%
+and we will look at that subsequently
+ 
+
+ align:start position:0%
+and we will look at that subsequently
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+in terms of financial flows
+
+ align:start position:0%
+in terms of financial flows
+ 
+
+ align:start position:0%
+in terms of financial flows
+you've got something called the current
+
+ align:start position:0%
+you've got something called the current
+ 
+
+ align:start position:0%
+you've got something called the current
+account like for the us for example are
+
+ align:start position:0%
+account like for the us for example are
+ 
+
+ align:start position:0%
+account like for the us for example are
+they running a trade balance or are they
+
+ align:start position:0%
+they running a trade balance or are they
+ 
+
+ align:start position:0%
+they running a trade balance or are they
+earning money from abroad and likewise
+
+ align:start position:0%
+earning money from abroad and likewise
+ 
+
+ align:start position:0%
+earning money from abroad and likewise
+for these villages they export and
+
+ align:start position:0%
+for these villages they export and
+ 
+
+ align:start position:0%
+for these villages they export and
+import stuff we take the trade balance
+
+ align:start position:0%
+import stuff we take the trade balance
+ 
+
+ align:start position:0%
+import stuff we take the trade balance
+as the difference
+
+ align:start position:0%
+as the difference
+ 
+
+ align:start position:0%
+as the difference
+if positive exports exceed imports and
+
+ align:start position:0%
+if positive exports exceed imports and
+ 
+
+ align:start position:0%
+if positive exports exceed imports and
+likewise some member of the household is
+
+ align:start position:0%
+likewise some member of the household is
+ 
+
+ align:start position:0%
+likewise some member of the household is
+in bangkok and earning money and sending
+
+ align:start position:0%
+in bangkok and earning money and sending
+ 
+
+ align:start position:0%
+in bangkok and earning money and sending
+that money back home it's a gift that's
+
+ align:start position:0%
+that money back home it's a gift that's
+ 
+
+ align:start position:0%
+that money back home it's a gift that's
+a factor income earned abroad like in
+
+ align:start position:0%
+a factor income earned abroad like in
+ 
+
+ align:start position:0%
+a factor income earned abroad like in
+china people work in the philippines and
+
+ align:start position:0%
+china people work in the philippines and
+ 
+
+ align:start position:0%
+china people work in the philippines and
+send money back home so so this is
+
+ align:start position:0%
+send money back home so so this is
+ 
+
+ align:start position:0%
+send money back home so so this is
+called the current account now there are
+
+ align:start position:0%
+called the current account now there are
+ 
+
+ align:start position:0%
+called the current account now there are
+corresponding items
+
+ align:start position:0%
+corresponding items
+ 
+
+ align:start position:0%
+corresponding items
+offsetting items on the financial
+
+ align:start position:0%
+offsetting items on the financial
+ 
+
+ align:start position:0%
+offsetting items on the financial
+account basically
+
+ align:start position:0%
+account basically
+ 
+
+ align:start position:0%
+account basically
+if you're running a trade surplus you're
+
+ align:start position:0%
+if you're running a trade surplus you're
+ 
+
+ align:start position:0%
+if you're running a trade surplus you're
+acquiring claims on foreigners which
+
+ align:start position:0%
+acquiring claims on foreigners which
+ 
+
+ align:start position:0%
+acquiring claims on foreigners which
+could be by holding their currency
+
+ align:start position:0%
+could be by holding their currency
+ 
+
+ align:start position:0%
+could be by holding their currency
+holding their financial assets or
+
+ align:start position:0%
+holding their financial assets or
+ 
+
+ align:start position:0%
+holding their financial assets or
+holding their real assets and as we'll
+
+ align:start position:0%
+holding their real assets and as we'll
+ 
+
+ align:start position:0%
+holding their real assets and as we'll
+talk about next time
+
+ align:start position:0%
+talk about next time
+ 
+
+ align:start position:0%
+talk about next time
+the us has been running a trade deficit
+
+ align:start position:0%
+the us has been running a trade deficit
+ 
+
+ align:start position:0%
+the us has been running a trade deficit
+with china which means china is
+
+ align:start position:0%
+with china which means china is
+ 
+
+ align:start position:0%
+with china which means china is
+acquiring claims on the u.s holding u.s
+
+ align:start position:0%
+acquiring claims on the u.s holding u.s
+ 
+
+ align:start position:0%
+acquiring claims on the u.s holding u.s
+treasuries real estate and so on
+
+ align:start position:0%
+treasuries real estate and so on
+ 
+
+ align:start position:0%
+treasuries real estate and so on
+so the names change to protect the
+
+ align:start position:0%
+so the names change to protect the
+ 
+
+ align:start position:0%
+so the names change to protect the
+innocent in the sense of we're not
+
+ align:start position:0%
+innocent in the sense of we're not
+ 
+
+ align:start position:0%
+innocent in the sense of we're not
+looking at countries here we're looking
+
+ align:start position:0%
+looking at countries here we're looking
+ 
+
+ align:start position:0%
+looking at countries here we're looking
+at villages but we're doing all the
+
+ align:start position:0%
+at villages but we're doing all the
+ 
+
+ align:start position:0%
+at villages but we're doing all the
+accounting for the villages the way is
+
+ align:start position:0%
+accounting for the villages the way is
+ 
+
+ align:start position:0%
+accounting for the villages the way is
+done for countries with exactly the same
+
+ align:start position:0%
+done for countries with exactly the same
+ 
+
+ align:start position:0%
+done for countries with exactly the same
+accounting identities
+
+ align:start position:0%
+accounting identities
+ 
+
+ align:start position:0%
+accounting identities
+and the point of all of this is only to
+
+ align:start position:0%
+and the point of all of this is only to
+ 
+
+ align:start position:0%
+and the point of all of this is only to
+tell you where some of these things that
+
+ align:start position:0%
+tell you where some of these things that
+ 
+
+ align:start position:0%
+tell you where some of these things that
+you've heard of are coming from from the
+
+ align:start position:0%
+you've heard of are coming from from the
+ 
+
+ align:start position:0%
+you've heard of are coming from from the
+ground up from each and every household
+
+ align:start position:0%
+ground up from each and every household
+ 
+
+ align:start position:0%
+ground up from each and every household
+we have the financial accounts income
+
+ align:start position:0%
+we have the financial accounts income
+ 
+
+ align:start position:0%
+we have the financial accounts income
+statement balance sheet and so on we can
+
+ align:start position:0%
+statement balance sheet and so on we can
+ 
+
+ align:start position:0%
+statement balance sheet and so on we can
+add it up over all households in the
+
+ align:start position:0%
+add it up over all households in the
+ 
+
+ align:start position:0%
+add it up over all households in the
+village
+
+ align:start position:0%
+village
+ 
+
+ align:start position:0%
+village
+as the sample allows
+
+ align:start position:0%
+as the sample allows
+ 
+
+ align:start position:0%
+as the sample allows
+and get the village level aggregates
+
+ align:start position:0%
+and get the village level aggregates
+ 
+
+ align:start position:0%
+and get the village level aggregates
+this is for all of thailand thailand was
+
+ align:start position:0%
+this is for all of thailand thailand was
+ 
+
+ align:start position:0%
+this is for all of thailand thailand was
+running a
+
+ align:start position:0%
+running a
+ 
+
+ align:start position:0%
+running a
+trade deficit and foreigners
+
+ align:start position:0%
+trade deficit and foreigners
+ 
+
+ align:start position:0%
+trade deficit and foreigners
+were acquiring claims on thailand until
+
+ align:start position:0%
+were acquiring claims on thailand until
+ 
+
+ align:start position:0%
+were acquiring claims on thailand until
+the 1997 financial crisis in which case
+
+ align:start position:0%
+the 1997 financial crisis in which case
+ 
+
+ align:start position:0%
+the 1997 financial crisis in which case
+things reversed and they've been a bit
+
+ align:start position:0%
+things reversed and they've been a bit
+ 
+
+ align:start position:0%
+things reversed and they've been a bit
+unstable ever since uh in this case
+
+ align:start position:0%
+unstable ever since uh in this case
+ 
+
+ align:start position:0%
+unstable ever since uh in this case
+balance of payments are roughly you know
+
+ align:start position:0%
+balance of payments are roughly you know
+ 
+
+ align:start position:0%
+balance of payments are roughly you know
+a certain percent of gdp
+
+ align:start position:0%
+a certain percent of gdp
+ 
+
+ align:start position:0%
+a certain percent of gdp
+maybe ten percent that's a big number
+
+ align:start position:0%
+maybe ten percent that's a big number
+ 
+
+ align:start position:0%
+maybe ten percent that's a big number
+typically five percent
+
+ align:start position:0%
+typically five percent
+ 
+
+ align:start position:0%
+typically five percent
+so when we come to villages you might
+
+ align:start position:0%
+so when we come to villages you might
+ 
+
+ align:start position:0%
+so when we come to villages you might
+ask how big are these flows
+
+ align:start position:0%
+ask how big are these flows
+ 
+
+ align:start position:0%
+ask how big are these flows
+and the answer is typically much bigger
+
+ align:start position:0%
+and the answer is typically much bigger
+ 
+
+ align:start position:0%
+and the answer is typically much bigger
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+in cha chung sao the balance of payments
+
+ align:start position:0%
+in cha chung sao the balance of payments
+ 
+
+ align:start position:0%
+in cha chung sao the balance of payments
+including the trade and the current
+
+ align:start position:0%
+including the trade and the current
+ 
+
+ align:start position:0%
+including the trade and the current
+account you know can be as high as 20
+
+ align:start position:0%
+account you know can be as high as 20
+ 
+
+ align:start position:0%
+account you know can be as high as 20
+percent of gdp
+
+ align:start position:0%
+percent of gdp
+ 
+
+ align:start position:0%
+percent of gdp
+and loperi likewise reaches 15 percent
+
+ align:start position:0%
+and loperi likewise reaches 15 percent
+ 
+
+ align:start position:0%
+and loperi likewise reaches 15 percent
+of gdp so they are small open economies
+
+ align:start position:0%
+of gdp so they are small open economies
+ 
+
+ align:start position:0%
+of gdp so they are small open economies
+these villages are engaged with the rest
+
+ align:start position:0%
+these villages are engaged with the rest
+ 
+
+ align:start position:0%
+these villages are engaged with the rest
+of the country and in fact we can break
+
+ align:start position:0%
+of the country and in fact we can break
+ 
+
+ align:start position:0%
+of the country and in fact we can break
+that down into
+
+ align:start position:0%
+that down into
+ 
+
+ align:start position:0%
+that down into
+the gifts which i showed you a moment
+
+ align:start position:0%
+the gifts which i showed you a moment
+ 
+
+ align:start position:0%
+the gifts which i showed you a moment
+ago as well as here
+
+ align:start position:0%
+ago as well as here
+ 
+
+ align:start position:0%
+ago as well as here
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+measure of openness in terms of trade
+
+ align:start position:0%
+measure of openness in terms of trade
+ 
+
+ align:start position:0%
+measure of openness in terms of trade
+which is exports minus imports so
+
+ align:start position:0%
+which is exports minus imports so
+ 
+
+ align:start position:0%
+which is exports minus imports so
+roughly toxin sound near bangkok
+
+ align:start position:0%
+roughly toxin sound near bangkok
+ 
+
+ align:start position:0%
+roughly toxin sound near bangkok
+is imports and exports are
+
+ align:start position:0%
+is imports and exports are
+ 
+
+ align:start position:0%
+is imports and exports are
+almost matching one another
+
+ align:start position:0%
+almost matching one another
+ 
+
+ align:start position:0%
+almost matching one another
+whereas out in the northeast the imports
+
+ align:start position:0%
+whereas out in the northeast the imports
+ 
+
+ align:start position:0%
+whereas out in the northeast the imports
+are a lot bigger than the exports
+
+ align:start position:0%
+are a lot bigger than the exports
+ 
+
+ align:start position:0%
+are a lot bigger than the exports
+there the imports are for production
+
+ align:start position:0%
+there the imports are for production
+ 
+
+ align:start position:0%
+there the imports are for production
+their inputs acquired for production and
+
+ align:start position:0%
+their inputs acquired for production and
+ 
+
+ align:start position:0%
+their inputs acquired for production and
+they export a little bit of their output
+
+ align:start position:0%
+they export a little bit of their output
+ 
+
+ align:start position:0%
+they export a little bit of their output
+they eat a lot of the rice that they
+
+ align:start position:0%
+they eat a lot of the rice that they
+ 
+
+ align:start position:0%
+they eat a lot of the rice that they
+produce
+
+ align:start position:0%
+produce
+ 
+
+ align:start position:0%
+produce
+and export less
+
+ align:start position:0%
+and export less
+ 
+
+ align:start position:0%
+and export less
+i'm getting ready to show you the model
+
+ align:start position:0%
+i'm getting ready to show you the model
+ 
+
+ align:start position:0%
+i'm getting ready to show you the model
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+what about the relative price at the
+
+ align:start position:0%
+what about the relative price at the
+ 
+
+ align:start position:0%
+what about the relative price at the
+beginning of this class we talked about
+
+ align:start position:0%
+beginning of this class we talked about
+ 
+
+ align:start position:0%
+beginning of this class we talked about
+price of good one the price of good two
+
+ align:start position:0%
+price of good one the price of good two
+ 
+
+ align:start position:0%
+price of good one the price of good two
+we have two sectors for simplicity
+
+ align:start position:0%
+we have two sectors for simplicity
+ 
+
+ align:start position:0%
+we have two sectors for simplicity
+agriculture and manufacturing
+
+ align:start position:0%
+agriculture and manufacturing
+ 
+
+ align:start position:0%
+agriculture and manufacturing
+so from the data we can actually see
+
+ align:start position:0%
+so from the data we can actually see
+ 
+
+ align:start position:0%
+so from the data we can actually see
+overall
+
+ align:start position:0%
+overall
+ 
+
+ align:start position:0%
+overall
+that the price of the agricultural good
+
+ align:start position:0%
+that the price of the agricultural good
+ 
+
+ align:start position:0%
+that the price of the agricultural good
+is going up
+
+ align:start position:0%
+is going up
+ 
+
+ align:start position:0%
+is going up
+the ratio is going down
+
+ align:start position:0%
+the ratio is going down
+ 
+
+ align:start position:0%
+the ratio is going down
+from the standpoint of a typical village
+
+ align:start position:0%
+from the standpoint of a typical village
+ 
+
+ align:start position:0%
+from the standpoint of a typical village
+you know with the possibility of imports
+
+ align:start position:0%
+you know with the possibility of imports
+ 
+
+ align:start position:0%
+you know with the possibility of imports
+and exports
+
+ align:start position:0%
+and exports
+ 
+
+ align:start position:0%
+and exports
+just the way we had countries possibly
+
+ align:start position:0%
+just the way we had countries possibly
+ 
+
+ align:start position:0%
+just the way we had countries possibly
+exporting and importing to each other
+
+ align:start position:0%
+exporting and importing to each other
+ 
+
+ align:start position:0%
+exporting and importing to each other
+in terms of the factor prices remember
+
+ align:start position:0%
+in terms of the factor prices remember
+ 
+
+ align:start position:0%
+in terms of the factor prices remember
+the minimized cost curve well this is
+
+ align:start position:0%
+the minimized cost curve well this is
+ 
+
+ align:start position:0%
+the minimized cost curve well this is
+over time so we can see the wage rate
+
+ align:start position:0%
+over time so we can see the wage rate
+ 
+
+ align:start position:0%
+over time so we can see the wage rate
+and the interest rate both adjusted to
+
+ align:start position:0%
+and the interest rate both adjusted to
+ 
+
+ align:start position:0%
+and the interest rate both adjusted to
+be in units of consumption and surreal
+
+ align:start position:0%
+be in units of consumption and surreal
+ 
+
+ align:start position:0%
+be in units of consumption and surreal
+values as the numerator so in the
+
+ align:start position:0%
+values as the numerator so in the
+ 
+
+ align:start position:0%
+values as the numerator so in the
+areas near bangkok the blue and the red
+
+ align:start position:0%
+areas near bangkok the blue and the red
+ 
+
+ align:start position:0%
+areas near bangkok the blue and the red
+we can see that wages tend to be higher
+
+ align:start position:0%
+we can see that wages tend to be higher
+ 
+
+ align:start position:0%
+we can see that wages tend to be higher
+than they are in the northeast
+
+ align:start position:0%
+than they are in the northeast
+ 
+
+ align:start position:0%
+than they are in the northeast
+now near bangkok you would think this is
+
+ align:start position:0%
+now near bangkok you would think this is
+ 
+
+ align:start position:0%
+now near bangkok you would think this is
+relatively capital abundant because
+
+ align:start position:0%
+relatively capital abundant because
+ 
+
+ align:start position:0%
+relatively capital abundant because
+they're pretty industrialized and short
+
+ align:start position:0%
+they're pretty industrialized and short
+ 
+
+ align:start position:0%
+they're pretty industrialized and short
+of labor
+
+ align:start position:0%
+of labor
+ 
+
+ align:start position:0%
+of labor
+so indeed the relative price of labor to
+
+ align:start position:0%
+so indeed the relative price of labor to
+ 
+
+ align:start position:0%
+so indeed the relative price of labor to
+capital is higher
+
+ align:start position:0%
+capital is higher
+ 
+
+ align:start position:0%
+capital is higher
+in the areas near bangkok reflecting the
+
+ align:start position:0%
+in the areas near bangkok reflecting the
+ 
+
+ align:start position:0%
+in the areas near bangkok reflecting the
+capital abundance and the relative
+
+ align:start position:0%
+capital abundance and the relative
+ 
+
+ align:start position:0%
+capital abundance and the relative
+shortage of labor the reverse is true in
+
+ align:start position:0%
+shortage of labor the reverse is true in
+ 
+
+ align:start position:0%
+shortage of labor the reverse is true in
+the northeast
+
+ align:start position:0%
+the northeast
+ 
+
+ align:start position:0%
+the northeast
+and also we can look at the interest
+
+ align:start position:0%
+and also we can look at the interest
+ 
+
+ align:start position:0%
+and also we can look at the interest
+rate which is like the price of capital
+
+ align:start position:0%
+rate which is like the price of capital
+ 
+
+ align:start position:0%
+rate which is like the price of capital
+and again you can see
+
+ align:start position:0%
+and again you can see
+ 
+
+ align:start position:0%
+and again you can see
+that now the blue and the red are at the
+
+ align:start position:0%
+that now the blue and the red are at the
+ 
+
+ align:start position:0%
+that now the blue and the red are at the
+bottom
+
+ align:start position:0%
+bottom
+ 
+
+ align:start position:0%
+bottom
+because places near bangkok are capital
+
+ align:start position:0%
+because places near bangkok are capital
+ 
+
+ align:start position:0%
+because places near bangkok are capital
+abundant
+
+ align:start position:0%
+abundant
+ 
+
+ align:start position:0%
+abundant
+and so the interest rates tend to be low
+
+ align:start position:0%
+and so the interest rates tend to be low
+ 
+
+ align:start position:0%
+and so the interest rates tend to be low
+we did this experiment for the hectaro
+
+ align:start position:0%
+we did this experiment for the hectaro
+ 
+
+ align:start position:0%
+we did this experiment for the hectaro
+lean model like countries that are
+
+ align:start position:0%
+lean model like countries that are
+ 
+
+ align:start position:0%
+lean model like countries that are
+relatively abundant in a factor should
+
+ align:start position:0%
+relatively abundant in a factor should
+ 
+
+ align:start position:0%
+relatively abundant in a factor should
+be exporting the good which uses that
+
+ align:start position:0%
+be exporting the good which uses that
+ 
+
+ align:start position:0%
+be exporting the good which uses that
+factor relatively intensively so you
+
+ align:start position:0%
+factor relatively intensively so you
+ 
+
+ align:start position:0%
+factor relatively intensively so you
+could imagine you know that places near
+
+ align:start position:0%
+could imagine you know that places near
+ 
+
+ align:start position:0%
+could imagine you know that places near
+bangkok that are abundant in capital
+
+ align:start position:0%
+bangkok that are abundant in capital
+ 
+
+ align:start position:0%
+bangkok that are abundant in capital
+will have a tendency to export the
+
+ align:start position:0%
+will have a tendency to export the
+ 
+
+ align:start position:0%
+will have a tendency to export the
+manufactured good because that's the one
+
+ align:start position:0%
+manufactured good because that's the one
+ 
+
+ align:start position:0%
+manufactured good because that's the one
+that's intensive in capital
+
+ align:start position:0%
+that's intensive in capital
+ 
+
+ align:start position:0%
+that's intensive in capital
+what am i doing today
+
+ align:start position:0%
+what am i doing today
+ 
+
+ align:start position:0%
+what am i doing today
+i'm just getting the labels to be
+
+ align:start position:0%
+i'm just getting the labels to be
+ 
+
+ align:start position:0%
+i'm just getting the labels to be
+realistic in actual context from
+
+ align:start position:0%
+realistic in actual context from
+ 
+
+ align:start position:0%
+realistic in actual context from
+realistic relative to last time
+
+ align:start position:0%
+realistic relative to last time
+ 
+
+ align:start position:0%
+realistic relative to last time
+learn the theory first now we're
+
+ align:start position:0%
+learn the theory first now we're
+ 
+
+ align:start position:0%
+learn the theory first now we're
+applying it although with some
+
+ align:start position:0%
+applying it although with some
+ 
+
+ align:start position:0%
+applying it although with some
+modifications the other thing you can
+
+ align:start position:0%
+modifications the other thing you can
+ 
+
+ align:start position:0%
+modifications the other thing you can
+see here is the interest rates are
+
+ align:start position:0%
+see here is the interest rates are
+ 
+
+ align:start position:0%
+see here is the interest rates are
+converging they're getting really close
+
+ align:start position:0%
+converging they're getting really close
+ 
+
+ align:start position:0%
+converging they're getting really close
+to one another over time so
+
+ align:start position:0%
+to one another over time so
+ 
+
+ align:start position:0%
+to one another over time so
+one imagines that
+
+ align:start position:0%
+one imagines that
+ 
+
+ align:start position:0%
+one imagines that
+if they could x trade in inputs not just
+
+ align:start position:0%
+if they could x trade in inputs not just
+ 
+
+ align:start position:0%
+if they could x trade in inputs not just
+outputs it's pretty easy to do that with
+
+ align:start position:0%
+outputs it's pretty easy to do that with
+ 
+
+ align:start position:0%
+outputs it's pretty easy to do that with
+a capital input but
+
+ align:start position:0%
+a capital input but
+ 
+
+ align:start position:0%
+a capital input but
+the wage rates are not converging so
+
+ align:start position:0%
+the wage rates are not converging so
+ 
+
+ align:start position:0%
+the wage rates are not converging so
+that's also a hint that like the 2x2
+
+ align:start position:0%
+that's also a hint that like the 2x2
+ 
+
+ align:start position:0%
+that's also a hint that like the 2x2
+model we're not going to allow labor to
+
+ align:start position:0%
+model we're not going to allow labor to
+ 
+
+ align:start position:0%
+model we're not going to allow labor to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+moving across borders okay
+
+ align:start position:0%
+moving across borders okay
+ 
+
+ align:start position:0%
+moving across borders okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i'm going to show you the ingredients
+
+ align:start position:0%
+i'm going to show you the ingredients
+ 
+
+ align:start position:0%
+i'm going to show you the ingredients
+for small open economy and then i'm
+
+ align:start position:0%
+for small open economy and then i'm
+ 
+
+ align:start position:0%
+for small open economy and then i'm
+gonna tell you what the difference is
+
+ align:start position:0%
+gonna tell you what the difference is
+ 
+
+ align:start position:0%
+gonna tell you what the difference is
+with the two by two by two that we did
+
+ align:start position:0%
+with the two by two by two that we did
+ 
+
+ align:start position:0%
+with the two by two by two that we did
+last time so
+
+ align:start position:0%
+last time so
+ 
+
+ align:start position:0%
+last time so
+it is two by two
+
+ align:start position:0%
+it is two by two
+ 
+
+ align:start position:0%
+it is two by two
+two goods two factors although it's uh
+
+ align:start position:0%
+two goods two factors although it's uh
+ 
+
+ align:start position:0%
+two goods two factors although it's uh
+you know a village relative to the rest
+
+ align:start position:0%
+you know a village relative to the rest
+ 
+
+ align:start position:0%
+you know a village relative to the rest
+of the country different from last time
+
+ align:start position:0%
+of the country different from last time
+ 
+
+ align:start position:0%
+of the country different from last time
+we're going to have financial frictions
+
+ align:start position:0%
+we're going to have financial frictions
+ 
+
+ align:start position:0%
+we're going to have financial frictions
+like those borrowing to
+
+ align:start position:0%
+like those borrowing to
+ 
+
+ align:start position:0%
+like those borrowing to
+wealth ratios
+
+ align:start position:0%
+wealth ratios
+ 
+
+ align:start position:0%
+wealth ratios
+there's a lot of agents in each village
+
+ align:start position:0%
+there's a lot of agents in each village
+ 
+
+ align:start position:0%
+there's a lot of agents in each village
+and they differ in their wealth and
+
+ align:start position:0%
+and they differ in their wealth and
+ 
+
+ align:start position:0%
+and they differ in their wealth and
+ability levels they can choose to be
+
+ align:start position:0%
+ability levels they can choose to be
+ 
+
+ align:start position:0%
+ability levels they can choose to be
+workers or they could become a firm and
+
+ align:start position:0%
+workers or they could become a firm and
+ 
+
+ align:start position:0%
+workers or they could become a firm and
+if they're an entrepreneur they could be
+
+ align:start position:0%
+if they're an entrepreneur they could be
+ 
+
+ align:start position:0%
+if they're an entrepreneur they could be
+in the manufacturing or agricultural
+
+ align:start position:0%
+in the manufacturing or agricultural
+ 
+
+ align:start position:0%
+in the manufacturing or agricultural
+sector
+
+ align:start position:0%
+sector
+ 
+
+ align:start position:0%
+sector
+so that's the two one of the two tools
+
+ align:start position:0%
+so that's the two one of the two tools
+ 
+
+ align:start position:0%
+so that's the two one of the two tools
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+goods agriculture and manufacturing
+
+ align:start position:0%
+goods agriculture and manufacturing
+ 
+
+ align:start position:0%
+goods agriculture and manufacturing
+to inputs capital and labor
+
+ align:start position:0%
+to inputs capital and labor
+ 
+
+ align:start position:0%
+to inputs capital and labor
+with the factor intensities different
+
+ align:start position:0%
+with the factor intensities different
+ 
+
+ align:start position:0%
+with the factor intensities different
+labor supplied is owned by
+
+ align:start position:0%
+labor supplied is owned by
+ 
+
+ align:start position:0%
+labor supplied is owned by
+households and supplied inelastically
+
+ align:start position:0%
+households and supplied inelastically
+ 
+
+ align:start position:0%
+households and supplied inelastically
+like it was last time
+
+ align:start position:0%
+like it was last time
+ 
+
+ align:start position:0%
+like it was last time
+they get this wage w
+
+ align:start position:0%
+they get this wage w
+ 
+
+ align:start position:0%
+they get this wage w
+wealth is owned by households
+
+ align:start position:0%
+wealth is owned by households
+ 
+
+ align:start position:0%
+wealth is owned by households
+and supplied at an interest rate but
+
+ align:start position:0%
+and supplied at an interest rate but
+ 
+
+ align:start position:0%
+and supplied at an interest rate but
+it's also changing over time
+
+ align:start position:0%
+it's also changing over time
+ 
+
+ align:start position:0%
+it's also changing over time
+unlike what we had last time we've got
+
+ align:start position:0%
+unlike what we had last time we've got
+ 
+
+ align:start position:0%
+unlike what we had last time we've got
+dynamics and a way to save money over
+
+ align:start position:0%
+dynamics and a way to save money over
+ 
+
+ align:start position:0%
+dynamics and a way to save money over
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+they can use their capital or they can
+
+ align:start position:0%
+they can use their capital or they can
+ 
+
+ align:start position:0%
+they can use their capital or they can
+lend it out so we have a borrowing and
+
+ align:start position:0%
+lend it out so we have a borrowing and
+ 
+
+ align:start position:0%
+lend it out so we have a borrowing and
+lending market
+
+ align:start position:0%
+lending market
+ 
+
+ align:start position:0%
+lending market
+but that capital market is imperfect
+
+ align:start position:0%
+but that capital market is imperfect
+ 
+
+ align:start position:0%
+but that capital market is imperfect
+namely you can't necessarily use an
+
+ align:start position:0%
+namely you can't necessarily use an
+ 
+
+ align:start position:0%
+namely you can't necessarily use an
+unlimited amount of capital k
+
+ align:start position:0%
+unlimited amount of capital k
+ 
+
+ align:start position:0%
+unlimited amount of capital k
+you're bounded by your wealth
+
+ align:start position:0%
+you're bounded by your wealth
+ 
+
+ align:start position:0%
+you're bounded by your wealth
+so that for the third time today
+
+ align:start position:0%
+so that for the third time today
+ 
+
+ align:start position:0%
+so that for the third time today
+is mention of the limited liability
+
+ align:start position:0%
+is mention of the limited liability
+ 
+
+ align:start position:0%
+is mention of the limited liability
+constraints
+
+ align:start position:0%
+constraints
+ 
+
+ align:start position:0%
+constraints
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+differences with last time we have
+
+ align:start position:0%
+differences with last time we have
+ 
+
+ align:start position:0%
+differences with last time we have
+decreasing returns to scale
+
+ align:start position:0%
+decreasing returns to scale
+ 
+
+ align:start position:0%
+decreasing returns to scale
+whereas last time in the theory lecture
+
+ align:start position:0%
+whereas last time in the theory lecture
+ 
+
+ align:start position:0%
+whereas last time in the theory lecture
+we used and abused the fact that it was
+
+ align:start position:0%
+we used and abused the fact that it was
+ 
+
+ align:start position:0%
+we used and abused the fact that it was
+constant returns to scale
+
+ align:start position:0%
+constant returns to scale
+ 
+
+ align:start position:0%
+constant returns to scale
+hence unit cost of production which
+
+ align:start position:0%
+hence unit cost of production which
+ 
+
+ align:start position:0%
+hence unit cost of production which
+scale up and down depending on the level
+
+ align:start position:0%
+scale up and down depending on the level
+ 
+
+ align:start position:0%
+scale up and down depending on the level
+of production
+
+ align:start position:0%
+of production
+ 
+
+ align:start position:0%
+of production
+factor mobility is somewhat limited here
+
+ align:start position:0%
+factor mobility is somewhat limited here
+ 
+
+ align:start position:0%
+factor mobility is somewhat limited here
+but the capital good moves around unlike
+
+ align:start position:0%
+but the capital good moves around unlike
+ 
+
+ align:start position:0%
+but the capital good moves around unlike
+last time we have financial variables
+
+ align:start position:0%
+last time we have financial variables
+ 
+
+ align:start position:0%
+last time we have financial variables
+here and real variables
+
+ align:start position:0%
+here and real variables
+ 
+
+ align:start position:0%
+here and real variables
+whereas last time we only had real
+
+ align:start position:0%
+whereas last time we only had real
+ 
+
+ align:start position:0%
+whereas last time we only had real
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+and likewise here we have borrowing
+
+ align:start position:0%
+and likewise here we have borrowing
+ 
+
+ align:start position:0%
+and likewise here we have borrowing
+constraints
+
+ align:start position:0%
+constraints
+ 
+
+ align:start position:0%
+constraints
+and last time we didn't have any of that
+
+ align:start position:0%
+and last time we didn't have any of that
+ 
+
+ align:start position:0%
+and last time we didn't have any of that
+but this model does have the different
+
+ align:start position:0%
+but this model does have the different
+ 
+
+ align:start position:0%
+but this model does have the different
+endowments of the factors
+
+ align:start position:0%
+endowments of the factors
+ 
+
+ align:start position:0%
+endowments of the factors
+it does have the different factor
+
+ align:start position:0%
+it does have the different factor
+ 
+
+ align:start position:0%
+it does have the different factor
+intensities
+
+ align:start position:0%
+intensities
+ 
+
+ align:start position:0%
+intensities
+it keeps the two by two by two well two
+
+ align:start position:0%
+it keeps the two by two by two well two
+ 
+
+ align:start position:0%
+it keeps the two by two by two well two
+by two anyway with small open economy
+
+ align:start position:0%
+by two anyway with small open economy
+ 
+
+ align:start position:0%
+by two anyway with small open economy
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+part of what you're going to see in the
+
+ align:start position:0%
+part of what you're going to see in the
+ 
+
+ align:start position:0%
+part of what you're going to see in the
+simulations
+
+ align:start position:0%
+simulations
+ 
+
+ align:start position:0%
+simulations
+reflects what we learned last time
+
+ align:start position:0%
+reflects what we learned last time
+ 
+
+ align:start position:0%
+reflects what we learned last time
+and part of it is a bit different
+
+ align:start position:0%
+and part of it is a bit different
+ 
+
+ align:start position:0%
+and part of it is a bit different
+because it has
+
+ align:start position:0%
+because it has
+ 
+
+ align:start position:0%
+because it has
+a few additional realistic features
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rather than take you through
+
+ align:start position:0%
+rather than take you through
+ 
+
+ align:start position:0%
+rather than take you through
+the entire model i'll just give you the
+
+ align:start position:0%
+the entire model i'll just give you the
+ 
+
+ align:start position:0%
+the entire model i'll just give you the
+notation at the beginning
+
+ align:start position:0%
+notation at the beginning
+ 
+
+ align:start position:0%
+notation at the beginning
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+each entrepreneur can produce
+
+ align:start position:0%
+each entrepreneur can produce
+ 
+
+ align:start position:0%
+each entrepreneur can produce
+sector a which could be agriculture but
+
+ align:start position:0%
+sector a which could be agriculture but
+ 
+
+ align:start position:0%
+sector a which could be agriculture but
+it's also manufacturing a household has
+
+ align:start position:0%
+it's also manufacturing a household has
+ 
+
+ align:start position:0%
+it's also manufacturing a household has
+a certain talent level z
+
+ align:start position:0%
+a certain talent level z
+ 
+
+ align:start position:0%
+a certain talent level z
+and initial capital stock it will use
+
+ align:start position:0%
+and initial capital stock it will use
+ 
+
+ align:start position:0%
+and initial capital stock it will use
+its inputs
+
+ align:start position:0%
+its inputs
+ 
+
+ align:start position:0%
+its inputs
+capital and higher labor
+
+ align:start position:0%
+capital and higher labor
+ 
+
+ align:start position:0%
+capital and higher labor
+at its productivity level selling it for
+
+ align:start position:0%
+at its productivity level selling it for
+ 
+
+ align:start position:0%
+at its productivity level selling it for
+the price of output but it has to pay
+
+ align:start position:0%
+the price of output but it has to pay
+ 
+
+ align:start position:0%
+the price of output but it has to pay
+input costs for capital labor and the
+
+ align:start position:0%
+input costs for capital labor and the
+ 
+
+ align:start position:0%
+input costs for capital labor and the
+input prices are r and w
+
+ align:start position:0%
+input prices are r and w
+ 
+
+ align:start position:0%
+input prices are r and w
+so you've seen this many times
+
+ align:start position:0%
+so you've seen this many times
+ 
+
+ align:start position:0%
+so you've seen this many times
+this is just a statement of profits for
+
+ align:start position:0%
+this is just a statement of profits for
+ 
+
+ align:start position:0%
+this is just a statement of profits for
+a firm it happens to be a firm owned and
+
+ align:start position:0%
+a firm it happens to be a firm owned and
+ 
+
+ align:start position:0%
+a firm it happens to be a firm owned and
+entirely operated by a given household
+
+ align:start position:0%
+entirely operated by a given household
+ 
+
+ align:start position:0%
+entirely operated by a given household
+because the theta i j equals one and
+
+ align:start position:0%
+because the theta i j equals one and
+ 
+
+ align:start position:0%
+because the theta i j equals one and
+here's the borrowing constraint
+
+ align:start position:0%
+here's the borrowing constraint
+ 
+
+ align:start position:0%
+here's the borrowing constraint
+capital utilized is limited by the
+
+ align:start position:0%
+capital utilized is limited by the
+ 
+
+ align:start position:0%
+capital utilized is limited by the
+pre-existing stock of fixed assets but
+
+ align:start position:0%
+pre-existing stock of fixed assets but
+ 
+
+ align:start position:0%
+pre-existing stock of fixed assets but
+this constant c could be greater than
+
+ align:start position:0%
+this constant c could be greater than
+ 
+
+ align:start position:0%
+this constant c could be greater than
+one which allows them to borrow to
+
+ align:start position:0%
+one which allows them to borrow to
+ 
+
+ align:start position:0%
+one which allows them to borrow to
+borrow to acquire fixed assets and
+
+ align:start position:0%
+borrow to acquire fixed assets and
+ 
+
+ align:start position:0%
+borrow to acquire fixed assets and
+production
+
+ align:start position:0%
+production
+ 
+
+ align:start position:0%
+production
+greater than what they already own
+
+ align:start position:0%
+greater than what they already own
+ 
+
+ align:start position:0%
+greater than what they already own
+labor is non-negative
+
+ align:start position:0%
+labor is non-negative
+ 
+
+ align:start position:0%
+labor is non-negative
+as in that paper with anna paulsen and
+
+ align:start position:0%
+as in that paper with anna paulsen and
+ 
+
+ align:start position:0%
+as in that paper with anna paulsen and
+kuravanov they could choose to be a wage
+
+ align:start position:0%
+kuravanov they could choose to be a wage
+ 
+
+ align:start position:0%
+kuravanov they could choose to be a wage
+earner put all their wealth lend it out
+
+ align:start position:0%
+earner put all their wealth lend it out
+ 
+
+ align:start position:0%
+earner put all their wealth lend it out
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+earn interest on it or they earn money
+
+ align:start position:0%
+earn interest on it or they earn money
+ 
+
+ align:start position:0%
+earn interest on it or they earn money
+from being a wage earner likewise we
+
+ align:start position:0%
+from being a wage earner likewise we
+ 
+
+ align:start position:0%
+from being a wage earner likewise we
+have profits for agriculturalists and
+
+ align:start position:0%
+have profits for agriculturalists and
+ 
+
+ align:start position:0%
+have profits for agriculturalists and
+manufacturers
+
+ align:start position:0%
+manufacturers
+ 
+
+ align:start position:0%
+manufacturers
+and they're
+
+ align:start position:0%
+and they're
+ 
+
+ align:start position:0%
+and they're
+in principle lending stuff out
+
+ align:start position:0%
+in principle lending stuff out
+ 
+
+ align:start position:0%
+in principle lending stuff out
+but they could be borrowing some of it
+
+ align:start position:0%
+but they could be borrowing some of it
+ 
+
+ align:start position:0%
+but they could be borrowing some of it
+back to finance production and then we
+
+ align:start position:0%
+back to finance production and then we
+ 
+
+ align:start position:0%
+back to finance production and then we
+have a utility over
+
+ align:start position:0%
+have a utility over
+ 
+
+ align:start position:0%
+have a utility over
+consumption of agriculture and
+
+ align:start position:0%
+consumption of agriculture and
+ 
+
+ align:start position:0%
+consumption of agriculture and
+manufactured goods
+
+ align:start position:0%
+manufactured goods
+ 
+
+ align:start position:0%
+manufactured goods
+which looks like kind of this cobb
+
+ align:start position:0%
+which looks like kind of this cobb
+ 
+
+ align:start position:0%
+which looks like kind of this cobb
+douglas thing
+
+ align:start position:0%
+douglas thing
+ 
+
+ align:start position:0%
+douglas thing
+where these ada's are cleverly chosen to
+
+ align:start position:0%
+where these ada's are cleverly chosen to
+ 
+
+ align:start position:0%
+where these ada's are cleverly chosen to
+allow us to talk about you know
+
+ align:start position:0%
+allow us to talk about you know
+ 
+
+ align:start position:0%
+allow us to talk about you know
+aggregate savings because in fact
+
+ align:start position:0%
+aggregate savings because in fact
+ 
+
+ align:start position:0%
+aggregate savings because in fact
+there's capital in manufacturing and
+
+ align:start position:0%
+there's capital in manufacturing and
+ 
+
+ align:start position:0%
+there's capital in manufacturing and
+capital in agriculture and we don't want
+
+ align:start position:0%
+capital in agriculture and we don't want
+ 
+
+ align:start position:0%
+capital in agriculture and we don't want
+to keep having to refer to the
+
+ align:start position:0%
+to keep having to refer to the
+ 
+
+ align:start position:0%
+to keep having to refer to the
+distinction about where they're saving
+
+ align:start position:0%
+distinction about where they're saving
+ 
+
+ align:start position:0%
+distinction about where they're saving
+so we come up with this ideal price
+
+ align:start position:0%
+so we come up with this ideal price
+ 
+
+ align:start position:0%
+so we come up with this ideal price
+index don't worry about it too much
+
+ align:start position:0%
+index don't worry about it too much
+ 
+
+ align:start position:0%
+index don't worry about it too much
+it exists that's all we need to know
+
+ align:start position:0%
+it exists that's all we need to know
+ 
+
+ align:start position:0%
+it exists that's all we need to know
+um okay
+
+ align:start position:0%
+um okay
+ 
+
+ align:start position:0%
+um okay
+it's a small open economy
+
+ align:start position:0%
+it's a small open economy
+ 
+
+ align:start position:0%
+it's a small open economy
+households have their capital endowment
+
+ align:start position:0%
+households have their capital endowment
+ 
+
+ align:start position:0%
+households have their capital endowment
+we fit a distribution that fits pretty
+
+ align:start position:0%
+we fit a distribution that fits pretty
+ 
+
+ align:start position:0%
+we fit a distribution that fits pretty
+well relative to the histograms i
+
+ align:start position:0%
+well relative to the histograms i
+ 
+
+ align:start position:0%
+well relative to the histograms i
+already shown you we have the labor
+
+ align:start position:0%
+already shown you we have the labor
+ 
+
+ align:start position:0%
+already shown you we have the labor
+endowments
+
+ align:start position:0%
+endowments
+ 
+
+ align:start position:0%
+endowments
+we help we know how much time they have
+
+ align:start position:0%
+we help we know how much time they have
+ 
+
+ align:start position:0%
+we help we know how much time they have
+we give them a little bit of sleep
+
+ align:start position:0%
+we give them a little bit of sleep
+ 
+
+ align:start position:0%
+we give them a little bit of sleep
+and come up with how many units of labor
+
+ align:start position:0%
+and come up with how many units of labor
+ 
+
+ align:start position:0%
+and come up with how many units of labor
+they can supply over the year which is a
+
+ align:start position:0%
+they can supply over the year which is a
+ 
+
+ align:start position:0%
+they can supply over the year which is a
+fixed and exogenous
+
+ align:start position:0%
+fixed and exogenous
+ 
+
+ align:start position:0%
+fixed and exogenous
+and they have a savings rate which again
+
+ align:start position:0%
+and they have a savings rate which again
+ 
+
+ align:start position:0%
+and they have a savings rate which again
+as i already said that was an omega
+
+ align:start position:0%
+as i already said that was an omega
+ 
+
+ align:start position:0%
+as i already said that was an omega
+we fit to kind of match the data i
+
+ align:start position:0%
+we fit to kind of match the data i
+ 
+
+ align:start position:0%
+we fit to kind of match the data i
+mentioned that in the context of the
+
+ align:start position:0%
+mentioned that in the context of the
+ 
+
+ align:start position:0%
+mentioned that in the context of the
+cash holdings
+
+ align:start position:0%
+cash holdings
+ 
+
+ align:start position:0%
+cash holdings
+one could imagine having these
+
+ align:start position:0%
+one could imagine having these
+ 
+
+ align:start position:0%
+one could imagine having these
+households solve discounted expected
+
+ align:start position:0%
+households solve discounted expected
+ 
+
+ align:start position:0%
+households solve discounted expected
+utility maximization problems over their
+
+ align:start position:0%
+utility maximization problems over their
+ 
+
+ align:start position:0%
+utility maximization problems over their
+lifetime
+
+ align:start position:0%
+lifetime
+ 
+
+ align:start position:0%
+lifetime
+that adds a lot to the complication so
+
+ align:start position:0%
+that adds a lot to the complication so
+ 
+
+ align:start position:0%
+that adds a lot to the complication so
+instead of doing that we just basically
+
+ align:start position:0%
+instead of doing that we just basically
+ 
+
+ align:start position:0%
+instead of doing that we just basically
+impose from the data on to the
+
+ align:start position:0%
+impose from the data on to the
+ 
+
+ align:start position:0%
+impose from the data on to the
+households
+
+ align:start position:0%
+households
+ 
+
+ align:start position:0%
+households
+an estimated savings rate now this is a
+
+ align:start position:0%
+an estimated savings rate now this is a
+ 
+
+ align:start position:0%
+an estimated savings rate now this is a
+kind of interesting diagram because
+
+ align:start position:0%
+kind of interesting diagram because
+ 
+
+ align:start position:0%
+kind of interesting diagram because
+all these parameters like the factor
+
+ align:start position:0%
+all these parameters like the factor
+ 
+
+ align:start position:0%
+all these parameters like the factor
+intensity numbers
+
+ align:start position:0%
+intensity numbers
+ 
+
+ align:start position:0%
+intensity numbers
+and everything else are are going to be
+
+ align:start position:0%
+and everything else are are going to be
+ 
+
+ align:start position:0%
+and everything else are are going to be
+calibrated
+
+ align:start position:0%
+calibrated
+ 
+
+ align:start position:0%
+calibrated
+which i'll tell you about momentarily
+
+ align:start position:0%
+which i'll tell you about momentarily
+ 
+
+ align:start position:0%
+which i'll tell you about momentarily
+and we will generate pictures
+
+ align:start position:0%
+and we will generate pictures
+ 
+
+ align:start position:0%
+and we will generate pictures
+like this so
+
+ align:start position:0%
+like this so
+ 
+
+ align:start position:0%
+like this so
+i mentioned the calibration only because
+
+ align:start position:0%
+i mentioned the calibration only because
+ 
+
+ align:start position:0%
+i mentioned the calibration only because
+you can draw any picture you want
+
+ align:start position:0%
+you can draw any picture you want
+ 
+
+ align:start position:0%
+you can draw any picture you want
+but this is what it's going to look like
+
+ align:start position:0%
+but this is what it's going to look like
+ 
+
+ align:start position:0%
+but this is what it's going to look like
+after the work is done of estimation
+
+ align:start position:0%
+after the work is done of estimation
+ 
+
+ align:start position:0%
+after the work is done of estimation
+over here we have low wealth households
+
+ align:start position:0%
+over here we have low wealth households
+ 
+
+ align:start position:0%
+over here we have low wealth households
+versus high wealth households
+
+ align:start position:0%
+versus high wealth households
+ 
+
+ align:start position:0%
+versus high wealth households
+the other dimension of heterogeneity is
+
+ align:start position:0%
+the other dimension of heterogeneity is
+ 
+
+ align:start position:0%
+the other dimension of heterogeneity is
+low talent
+
+ align:start position:0%
+low talent
+ 
+
+ align:start position:0%
+low talent
+versus high talent and you can see if
+
+ align:start position:0%
+versus high talent and you can see if
+ 
+
+ align:start position:0%
+versus high talent and you can see if
+they're not very talented they're not
+
+ align:start position:0%
+they're not very talented they're not
+ 
+
+ align:start position:0%
+they're not very talented they're not
+going to go into either type of business
+
+ align:start position:0%
+going to go into either type of business
+ 
+
+ align:start position:0%
+going to go into either type of business
+they're going to be workers
+
+ align:start position:0%
+they're going to be workers
+ 
+
+ align:start position:0%
+they're going to be workers
+on the other hand if talent reaches a
+
+ align:start position:0%
+on the other hand if talent reaches a
+ 
+
+ align:start position:0%
+on the other hand if talent reaches a
+higher level
+
+ align:start position:0%
+higher level
+ 
+
+ align:start position:0%
+higher level
+they could decide to go into
+
+ align:start position:0%
+they could decide to go into
+ 
+
+ align:start position:0%
+they could decide to go into
+manufacturing or agriculture
+
+ align:start position:0%
+manufacturing or agriculture
+ 
+
+ align:start position:0%
+manufacturing or agriculture
+and then for a given level of wealth
+
+ align:start position:0%
+and then for a given level of wealth
+ 
+
+ align:start position:0%
+and then for a given level of wealth
+they may be constrained or unconstrained
+
+ align:start position:0%
+they may be constrained or unconstrained
+ 
+
+ align:start position:0%
+they may be constrained or unconstrained
+ironically the more talented they are
+
+ align:start position:0%
+ironically the more talented they are
+ 
+
+ align:start position:0%
+ironically the more talented they are
+given a certain borrowing constraint and
+
+ align:start position:0%
+given a certain borrowing constraint and
+ 
+
+ align:start position:0%
+given a certain borrowing constraint and
+their wealth
+
+ align:start position:0%
+their wealth
+ 
+
+ align:start position:0%
+their wealth
+the more constrained they're going to be
+
+ align:start position:0%
+the more constrained they're going to be
+ 
+
+ align:start position:0%
+the more constrained they're going to be
+because they would like to do more and
+
+ align:start position:0%
+because they would like to do more and
+ 
+
+ align:start position:0%
+because they would like to do more and
+they're not allowed to do it
+
+ align:start position:0%
+they're not allowed to do it
+ 
+
+ align:start position:0%
+they're not allowed to do it
+and here
+
+ align:start position:0%
+and here
+ 
+
+ align:start position:0%
+and here
+it actually moves from being constrained
+
+ align:start position:0%
+it actually moves from being constrained
+ 
+
+ align:start position:0%
+it actually moves from being constrained
+in manufacturing
+
+ align:start position:0%
+in manufacturing
+ 
+
+ align:start position:0%
+in manufacturing
+to being constrained in agriculture
+
+ align:start position:0%
+to being constrained in agriculture
+ 
+
+ align:start position:0%
+to being constrained in agriculture
+so it's the really really talented guys
+
+ align:start position:0%
+so it's the really really talented guys
+ 
+
+ align:start position:0%
+so it's the really really talented guys
+who are sticking on the farm
+
+ align:start position:0%
+who are sticking on the farm
+ 
+
+ align:start position:0%
+who are sticking on the farm
+given the parameters that we estimated
+
+ align:start position:0%
+given the parameters that we estimated
+ 
+
+ align:start position:0%
+given the parameters that we estimated
+this i've already said we're going to
+
+ align:start position:0%
+this i've already said we're going to
+ 
+
+ align:start position:0%
+this i've already said we're going to
+have an open market for capital
+
+ align:start position:0%
+have an open market for capital
+ 
+
+ align:start position:0%
+have an open market for capital
+but a closed market for labor
+
+ align:start position:0%
+but a closed market for labor
+ 
+
+ align:start position:0%
+but a closed market for labor
+then again that's because the interest
+
+ align:start position:0%
+then again that's because the interest
+ 
+
+ align:start position:0%
+then again that's because the interest
+rates are converging so it looks like in
+
+ align:start position:0%
+rates are converging so it looks like in
+ 
+
+ align:start position:0%
+rates are converging so it looks like in
+the end at least capital can
+
+ align:start position:0%
+the end at least capital can
+ 
+
+ align:start position:0%
+the end at least capital can
+be moved across provinces without a cost
+
+ align:start position:0%
+be moved across provinces without a cost
+ 
+
+ align:start position:0%
+be moved across provinces without a cost
+here's finally the calibration slide
+
+ align:start position:0%
+here's finally the calibration slide
+ 
+
+ align:start position:0%
+here's finally the calibration slide
+we have to figure out the relative
+
+ align:start position:0%
+we have to figure out the relative
+ 
+
+ align:start position:0%
+we have to figure out the relative
+prices we need the interest rate
+
+ align:start position:0%
+prices we need the interest rate
+ 
+
+ align:start position:0%
+prices we need the interest rate
+we're going to take it as exogenous
+
+ align:start position:0%
+we're going to take it as exogenous
+ 
+
+ align:start position:0%
+we're going to take it as exogenous
+the relative price of manufacturing
+
+ align:start position:0%
+the relative price of manufacturing
+ 
+
+ align:start position:0%
+the relative price of manufacturing
+versus agriculture
+
+ align:start position:0%
+versus agriculture
+ 
+
+ align:start position:0%
+versus agriculture
+we're going to take as exogenous and
+
+ align:start position:0%
+we're going to take as exogenous and
+ 
+
+ align:start position:0%
+we're going to take as exogenous and
+match it up with what we see
+
+ align:start position:0%
+match it up with what we see
+ 
+
+ align:start position:0%
+match it up with what we see
+in the data
+
+ align:start position:0%
+in the data
+ 
+
+ align:start position:0%
+in the data
+as exogenous i'll come back to how we
+
+ align:start position:0%
+as exogenous i'll come back to how we
+ 
+
+ align:start position:0%
+as exogenous i'll come back to how we
+pick it in a minute and the borrowing
+
+ align:start position:0%
+pick it in a minute and the borrowing
+ 
+
+ align:start position:0%
+pick it in a minute and the borrowing
+rates are exogenous we stick in for the
+
+ align:start position:0%
+rates are exogenous we stick in for the
+ 
+
+ align:start position:0%
+rates are exogenous we stick in for the
+interest rate what we observe the data
+
+ align:start position:0%
+interest rate what we observe the data
+ 
+
+ align:start position:0%
+interest rate what we observe the data
+we don't know about this relative price
+
+ align:start position:0%
+we don't know about this relative price
+ 
+
+ align:start position:0%
+we don't know about this relative price
+of the borrowing limit but we do
+
+ align:start position:0%
+of the borrowing limit but we do
+ 
+
+ align:start position:0%
+of the borrowing limit but we do
+have the profit sharing in each sector
+
+ align:start position:0%
+have the profit sharing in each sector
+ 
+
+ align:start position:0%
+have the profit sharing in each sector
+so we move the relative prices to match
+
+ align:start position:0%
+so we move the relative prices to match
+ 
+
+ align:start position:0%
+so we move the relative prices to match
+the profit share so for example
+
+ align:start position:0%
+the profit share so for example
+ 
+
+ align:start position:0%
+the profit share so for example
+if agriculture has a price pa
+
+ align:start position:0%
+if agriculture has a price pa
+ 
+
+ align:start position:0%
+if agriculture has a price pa
+uh and we observe a lot
+
+ align:start position:0%
+uh and we observe a lot
+ 
+
+ align:start position:0%
+uh and we observe a lot
+a large relative share
+
+ align:start position:0%
+a large relative share
+ 
+
+ align:start position:0%
+a large relative share
+of profits from agriculture
+
+ align:start position:0%
+of profits from agriculture
+ 
+
+ align:start position:0%
+of profits from agriculture
+then we
+
+ align:start position:0%
+then we
+ 
+
+ align:start position:0%
+then we
+imagine that it's a relatively high
+
+ align:start position:0%
+imagine that it's a relatively high
+ 
+
+ align:start position:0%
+imagine that it's a relatively high
+price of the agricultural good relative
+
+ align:start position:0%
+price of the agricultural good relative
+ 
+
+ align:start position:0%
+price of the agricultural good relative
+to the manufacturing good and vice versa
+
+ align:start position:0%
+to the manufacturing good and vice versa
+ 
+
+ align:start position:0%
+to the manufacturing good and vice versa
+likewise we're going to move the
+
+ align:start position:0%
+likewise we're going to move the
+ 
+
+ align:start position:0%
+likewise we're going to move the
+borrowing limit to match the observed
+
+ align:start position:0%
+borrowing limit to match the observed
+ 
+
+ align:start position:0%
+borrowing limit to match the observed
+weight rate
+
+ align:start position:0%
+weight rate
+ 
+
+ align:start position:0%
+weight rate
+the point being that if they can't
+
+ align:start position:0%
+the point being that if they can't
+ 
+
+ align:start position:0%
+the point being that if they can't
+borrow very much
+
+ align:start position:0%
+borrow very much
+ 
+
+ align:start position:0%
+borrow very much
+they're not going to have a very high
+
+ align:start position:0%
+they're not going to have a very high
+ 
+
+ align:start position:0%
+they're not going to have a very high
+scale of production
+
+ align:start position:0%
+scale of production
+ 
+
+ align:start position:0%
+scale of production
+they're not going to hire a lot of labor
+
+ align:start position:0%
+they're not going to hire a lot of labor
+ 
+
+ align:start position:0%
+they're not going to hire a lot of labor
+the demand for labor being low
+
+ align:start position:0%
+the demand for labor being low
+ 
+
+ align:start position:0%
+the demand for labor being low
+means the wage
+
+ align:start position:0%
+means the wage
+ 
+
+ align:start position:0%
+means the wage
+that has to clear the local market is
+
+ align:start position:0%
+that has to clear the local market is
+ 
+
+ align:start position:0%
+that has to clear the local market is
+going to be low
+
+ align:start position:0%
+going to be low
+ 
+
+ align:start position:0%
+going to be low
+the bigger picture here is calibration
+
+ align:start position:0%
+the bigger picture here is calibration
+ 
+
+ align:start position:0%
+the bigger picture here is calibration
+you have objects that matter a lot in
+
+ align:start position:0%
+you have objects that matter a lot in
+ 
+
+ align:start position:0%
+you have objects that matter a lot in
+the model
+
+ align:start position:0%
+the model
+ 
+
+ align:start position:0%
+the model
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+how you pick them
+
+ align:start position:0%
+how you pick them
+ 
+
+ align:start position:0%
+how you pick them
+well here we pick them
+
+ align:start position:0%
+well here we pick them
+ 
+
+ align:start position:0%
+well here we pick them
+by taking the data that we have
+
+ align:start position:0%
+by taking the data that we have
+ 
+
+ align:start position:0%
+by taking the data that we have
+and varying the parameters in the model
+
+ align:start position:0%
+and varying the parameters in the model
+ 
+
+ align:start position:0%
+and varying the parameters in the model
+in such a way that we can fit the model
+
+ align:start position:0%
+in such a way that we can fit the model
+ 
+
+ align:start position:0%
+in such a way that we can fit the model
+generated data to the actual data
+
+ align:start position:0%
+generated data to the actual data
+ 
+
+ align:start position:0%
+generated data to the actual data
+doing that we have to make a choice of
+
+ align:start position:0%
+doing that we have to make a choice of
+ 
+
+ align:start position:0%
+doing that we have to make a choice of
+which part of the actual data to use to
+
+ align:start position:0%
+which part of the actual data to use to
+ 
+
+ align:start position:0%
+which part of the actual data to use to
+calibrate which parameter
+
+ align:start position:0%
+calibrate which parameter
+ 
+
+ align:start position:0%
+calibrate which parameter
+and again read the dawkins thing and
+
+ align:start position:0%
+and again read the dawkins thing and
+ 
+
+ align:start position:0%
+and again read the dawkins thing and
+you'll see a discussion of this
+
+ align:start position:0%
+you'll see a discussion of this
+ 
+
+ align:start position:0%
+you'll see a discussion of this
+much more generally
+
+ align:start position:0%
+much more generally
+ 
+
+ align:start position:0%
+much more generally
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's look at what happens how well are
+
+ align:start position:0%
+let's look at what happens how well are
+ 
+
+ align:start position:0%
+let's look at what happens how well are
+we doing oh these economists they come
+
+ align:start position:0%
+we doing oh these economists they come
+ 
+
+ align:start position:0%
+we doing oh these economists they come
+up with these models god knows how well
+
+ align:start position:0%
+up with these models god knows how well
+ 
+
+ align:start position:0%
+up with these models god knows how well
+they predict so i'll show you how well
+
+ align:start position:0%
+they predict so i'll show you how well
+ 
+
+ align:start position:0%
+they predict so i'll show you how well
+we're doing
+
+ align:start position:0%
+we're doing
+ 
+
+ align:start position:0%
+we're doing
+this is at the calibrated values for
+
+ align:start position:0%
+this is at the calibrated values for
+ 
+
+ align:start position:0%
+this is at the calibrated values for
+lopere i believe doesn't say that on the
+
+ align:start position:0%
+lopere i believe doesn't say that on the
+ 
+
+ align:start position:0%
+lopere i believe doesn't say that on the
+slide
+
+ align:start position:0%
+slide
+ 
+
+ align:start position:0%
+slide
+the actual level of output in the
+
+ align:start position:0%
+the actual level of output in the
+ 
+
+ align:start position:0%
+the actual level of output in the
+predicted level of output model
+
+ align:start position:0%
+predicted level of output model
+ 
+
+ align:start position:0%
+predicted level of output model
+predicted
+
+ align:start position:0%
+predicted
+ 
+
+ align:start position:0%
+predicted
+so we ran a successful experiment if you
+
+ align:start position:0%
+so we ran a successful experiment if you
+ 
+
+ align:start position:0%
+so we ran a successful experiment if you
+think about the model as an experiment
+
+ align:start position:0%
+think about the model as an experiment
+ 
+
+ align:start position:0%
+think about the model as an experiment
+populated by the
+
+ align:start position:0%
+populated by the
+ 
+
+ align:start position:0%
+populated by the
+parameters we calibrate then we are able
+
+ align:start position:0%
+parameters we calibrate then we are able
+ 
+
+ align:start position:0%
+parameters we calibrate then we are able
+to take this stylized model a la lucas
+
+ align:start position:0%
+to take this stylized model a la lucas
+ 
+
+ align:start position:0%
+to take this stylized model a la lucas
+and use it to interpret reality
+
+ align:start position:0%
+and use it to interpret reality
+ 
+
+ align:start position:0%
+and use it to interpret reality
+this is pretty close for consumption
+
+ align:start position:0%
+this is pretty close for consumption
+ 
+
+ align:start position:0%
+this is pretty close for consumption
+the actual being below the model
+
+ align:start position:0%
+the actual being below the model
+ 
+
+ align:start position:0%
+the actual being below the model
+so in this case they're consuming a
+
+ align:start position:0%
+so in this case they're consuming a
+ 
+
+ align:start position:0%
+so in this case they're consuming a
+little bit less than what the model says
+
+ align:start position:0%
+little bit less than what the model says
+ 
+
+ align:start position:0%
+little bit less than what the model says
+they might despite our attempt to fit it
+
+ align:start position:0%
+they might despite our attempt to fit it
+ 
+
+ align:start position:0%
+they might despite our attempt to fit it
+to the data
+
+ align:start position:0%
+to the data
+ 
+
+ align:start position:0%
+to the data
+and this is for
+
+ align:start position:0%
+and this is for
+ 
+
+ align:start position:0%
+and this is for
+assets which is very very close
+
+ align:start position:0%
+assets which is very very close
+ 
+
+ align:start position:0%
+assets which is very very close
+now these last three figures are all
+
+ align:start position:0%
+now these last three figures are all
+ 
+
+ align:start position:0%
+now these last three figures are all
+aggregated across all the households in
+
+ align:start position:0%
+aggregated across all the households in
+ 
+
+ align:start position:0%
+aggregated across all the households in
+a given economy
+
+ align:start position:0%
+a given economy
+ 
+
+ align:start position:0%
+a given economy
+okay so having sort of
+
+ align:start position:0%
+okay so having sort of
+ 
+
+ align:start position:0%
+okay so having sort of
+um oh and this is cash holdings
+
+ align:start position:0%
+um oh and this is cash holdings
+ 
+
+ align:start position:0%
+um oh and this is cash holdings
+which is you know one of our weak points
+
+ align:start position:0%
+which is you know one of our weak points
+ 
+
+ align:start position:0%
+which is you know one of our weak points
+uh and we're pretty close for a while
+
+ align:start position:0%
+uh and we're pretty close for a while
+ 
+
+ align:start position:0%
+uh and we're pretty close for a while
+and then cash holdings and the data
+
+ align:start position:0%
+and then cash holdings and the data
+ 
+
+ align:start position:0%
+and then cash holdings and the data
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+want to be higher than in the model god
+
+ align:start position:0%
+want to be higher than in the model god
+ 
+
+ align:start position:0%
+want to be higher than in the model god
+knows why they want that cash i
+
+ align:start position:0%
+knows why they want that cash i
+ 
+
+ align:start position:0%
+knows why they want that cash i
+we're just still dumbfounded
+
+ align:start position:0%
+we're just still dumbfounded
+ 
+
+ align:start position:0%
+we're just still dumbfounded
+that's the way they're saving
+
+ align:start position:0%
+that's the way they're saving
+ 
+
+ align:start position:0%
+that's the way they're saving
+over time in the aggregate accumulating
+
+ align:start position:0%
+over time in the aggregate accumulating
+ 
+
+ align:start position:0%
+over time in the aggregate accumulating
+claims on foreigners yeah that's the
+
+ align:start position:0%
+claims on foreigners yeah that's the
+ 
+
+ align:start position:0%
+claims on foreigners yeah that's the
+paper currency
+
+ align:start position:0%
+paper currency
+ 
+
+ align:start position:0%
+paper currency
+it's a claim on the central bank
+
+ align:start position:0%
+it's a claim on the central bank
+ 
+
+ align:start position:0%
+it's a claim on the central bank
+and they love it doesn't bear interest
+
+ align:start position:0%
+and they love it doesn't bear interest
+ 
+
+ align:start position:0%
+and they love it doesn't bear interest
+or anything but anyway i'll stop
+
+ align:start position:0%
+or anything but anyway i'll stop
+ 
+
+ align:start position:0%
+or anything but anyway i'll stop
+complaining okay
+
+ align:start position:0%
+complaining okay
+ 
+
+ align:start position:0%
+complaining okay
+so having done pretty well with the
+
+ align:start position:0%
+so having done pretty well with the
+ 
+
+ align:start position:0%
+so having done pretty well with the
+aggregates one hopes
+
+ align:start position:0%
+aggregates one hopes
+ 
+
+ align:start position:0%
+aggregates one hopes
+we've earned the right to talk about
+
+ align:start position:0%
+we've earned the right to talk about
+ 
+
+ align:start position:0%
+we've earned the right to talk about
+individual experiences now needless to
+
+ align:start position:0%
+individual experiences now needless to
+ 
+
+ align:start position:0%
+individual experiences now needless to
+say there are many households in a
+
+ align:start position:0%
+say there are many households in a
+ 
+
+ align:start position:0%
+say there are many households in a
+village and a non-trivial number of
+
+ align:start position:0%
+village and a non-trivial number of
+ 
+
+ align:start position:0%
+village and a non-trivial number of
+households in the sample we're fitting
+
+ align:start position:0%
+households in the sample we're fitting
+ 
+
+ align:start position:0%
+households in the sample we're fitting
+the aggregates you know via calibration
+
+ align:start position:0%
+the aggregates you know via calibration
+ 
+
+ align:start position:0%
+the aggregates you know via calibration
+i wouldn't expect perfect performance
+
+ align:start position:0%
+i wouldn't expect perfect performance
+ 
+
+ align:start position:0%
+i wouldn't expect perfect performance
+for each and every individual that's too
+
+ align:start position:0%
+for each and every individual that's too
+ 
+
+ align:start position:0%
+for each and every individual that's too
+much to hope for but let me show you how
+
+ align:start position:0%
+much to hope for but let me show you how
+ 
+
+ align:start position:0%
+much to hope for but let me show you how
+well we did with household a that labor
+
+ align:start position:0%
+well we did with household a that labor
+ 
+
+ align:start position:0%
+well we did with household a that labor
+household in loperi that we featured at
+
+ align:start position:0%
+household in loperi that we featured at
+ 
+
+ align:start position:0%
+household in loperi that we featured at
+the beginning
+
+ align:start position:0%
+the beginning
+ 
+
+ align:start position:0%
+the beginning
+so this is the actual
+
+ align:start position:0%
+so this is the actual
+ 
+
+ align:start position:0%
+so this is the actual
+darker line
+
+ align:start position:0%
+darker line
+ 
+
+ align:start position:0%
+darker line
+labor income i showed you this path
+
+ align:start position:0%
+labor income i showed you this path
+ 
+
+ align:start position:0%
+labor income i showed you this path
+before actually
+
+ align:start position:0%
+before actually
+ 
+
+ align:start position:0%
+before actually
+in wages and they went into agriculture
+
+ align:start position:0%
+in wages and they went into agriculture
+ 
+
+ align:start position:0%
+in wages and they went into agriculture
+livestock a bit they went into business
+
+ align:start position:0%
+livestock a bit they went into business
+ 
+
+ align:start position:0%
+livestock a bit they went into business
+and borrowed to do it
+
+ align:start position:0%
+and borrowed to do it
+ 
+
+ align:start position:0%
+and borrowed to do it
+this is the actual
+
+ align:start position:0%
+this is the actual
+ 
+
+ align:start position:0%
+this is the actual
+model prediction which is a lot flatter
+
+ align:start position:0%
+model prediction which is a lot flatter
+ 
+
+ align:start position:0%
+model prediction which is a lot flatter
+but it's not that far off
+
+ align:start position:0%
+but it's not that far off
+ 
+
+ align:start position:0%
+but it's not that far off
+matches pretty well at the beginning and
+
+ align:start position:0%
+matches pretty well at the beginning and
+ 
+
+ align:start position:0%
+matches pretty well at the beginning and
+the end
+
+ align:start position:0%
+the end
+ 
+
+ align:start position:0%
+the end
+this is consumption which is horrible
+
+ align:start position:0%
+this is consumption which is horrible
+ 
+
+ align:start position:0%
+this is consumption which is horrible
+so for this household
+
+ align:start position:0%
+so for this household
+ 
+
+ align:start position:0%
+so for this household
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+actual
+
+ align:start position:0%
+actual
+ 
+
+ align:start position:0%
+actual
+numbers drop lower than what the model
+
+ align:start position:0%
+numbers drop lower than what the model
+ 
+
+ align:start position:0%
+numbers drop lower than what the model
+says it ought to be
+
+ align:start position:0%
+says it ought to be
+ 
+
+ align:start position:0%
+says it ought to be
+and fixed assets is closer we do pretty
+
+ align:start position:0%
+and fixed assets is closer we do pretty
+ 
+
+ align:start position:0%
+and fixed assets is closer we do pretty
+well with fixed assets including at the
+
+ align:start position:0%
+well with fixed assets including at the
+ 
+
+ align:start position:0%
+well with fixed assets including at the
+individual household a level and cash
+
+ align:start position:0%
+individual household a level and cash
+ 
+
+ align:start position:0%
+individual household a level and cash
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+under and over going up though for both
+
+ align:start position:0%
+under and over going up though for both
+ 
+
+ align:start position:0%
+under and over going up though for both
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i'm tempted to put this in the u.s
+
+ align:start position:0%
+so i'm tempted to put this in the u.s
+ 
+
+ align:start position:0%
+so i'm tempted to put this in the u.s
+context because
+
+ align:start position:0%
+context because
+ 
+
+ align:start position:0%
+context because
+it may make it seem more real if you
+
+ align:start position:0%
+it may make it seem more real if you
+ 
+
+ align:start position:0%
+it may make it seem more real if you
+haven't been in thai villages
+
+ align:start position:0%
+haven't been in thai villages
+ 
+
+ align:start position:0%
+haven't been in thai villages
+what's the effect on farmers of
+
+ align:start position:0%
+what's the effect on farmers of
+ 
+
+ align:start position:0%
+what's the effect on farmers of
+restricted exports to china when china
+
+ align:start position:0%
+restricted exports to china when china
+ 
+
+ align:start position:0%
+restricted exports to china when china
+retaliated
+
+ align:start position:0%
+retaliated
+ 
+
+ align:start position:0%
+retaliated
+they came to an agreement but still
+
+ align:start position:0%
+they came to an agreement but still
+ 
+
+ align:start position:0%
+they came to an agreement but still
+china's not purchasing as much
+
+ align:start position:0%
+china's not purchasing as much
+ 
+
+ align:start position:0%
+china's not purchasing as much
+the other way around what about
+
+ align:start position:0%
+the other way around what about
+ 
+
+ align:start position:0%
+the other way around what about
+manufactured goods coming in from china
+
+ align:start position:0%
+manufactured goods coming in from china
+ 
+
+ align:start position:0%
+manufactured goods coming in from china
+what's the effect on wage earners
+
+ align:start position:0%
+what's the effect on wage earners
+ 
+
+ align:start position:0%
+what's the effect on wage earners
+that produce the thing which is now
+
+ align:start position:0%
+that produce the thing which is now
+ 
+
+ align:start position:0%
+that produce the thing which is now
+being imported
+
+ align:start position:0%
+being imported
+ 
+
+ align:start position:0%
+being imported
+whereas before had been produced
+
+ align:start position:0%
+whereas before had been produced
+ 
+
+ align:start position:0%
+whereas before had been produced
+domestically
+
+ align:start position:0%
+domestically
+ 
+
+ align:start position:0%
+domestically
+but we're going to talk about those
+
+ align:start position:0%
+but we're going to talk about those
+ 
+
+ align:start position:0%
+but we're going to talk about those
+things next time
+
+ align:start position:0%
+things next time
+ 
+
+ align:start position:0%
+things next time
+but we can already answer questions like
+
+ align:start position:0%
+but we can already answer questions like
+ 
+
+ align:start position:0%
+but we can already answer questions like
+this for thailand
+
+ align:start position:0%
+this for thailand
+ 
+
+ align:start position:0%
+this for thailand
+if for example we take the actual
+
+ align:start position:0%
+if for example we take the actual
+ 
+
+ align:start position:0%
+if for example we take the actual
+estimated model and run counterfactuals
+
+ align:start position:0%
+estimated model and run counterfactuals
+ 
+
+ align:start position:0%
+estimated model and run counterfactuals
+okay so suppose we impose trade
+
+ align:start position:0%
+okay so suppose we impose trade
+ 
+
+ align:start position:0%
+okay so suppose we impose trade
+frictions within the country
+
+ align:start position:0%
+frictions within the country
+ 
+
+ align:start position:0%
+frictions within the country
+what are tariffs going to do basically
+
+ align:start position:0%
+what are tariffs going to do basically
+ 
+
+ align:start position:0%
+what are tariffs going to do basically
+they hurt trade so if a village had been
+
+ align:start position:0%
+they hurt trade so if a village had been
+ 
+
+ align:start position:0%
+they hurt trade so if a village had been
+exporting a lot of agricultural goods
+
+ align:start position:0%
+exporting a lot of agricultural goods
+ 
+
+ align:start position:0%
+exporting a lot of agricultural goods
+and importing a lot of manufactured
+
+ align:start position:0%
+and importing a lot of manufactured
+ 
+
+ align:start position:0%
+and importing a lot of manufactured
+goods as in the northeast
+
+ align:start position:0%
+goods as in the northeast
+ 
+
+ align:start position:0%
+goods as in the northeast
+then the effect of a trade friction will
+
+ align:start position:0%
+then the effect of a trade friction will
+ 
+
+ align:start position:0%
+then the effect of a trade friction will
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+the price of the thing that they they
+
+ align:start position:0%
+the price of the thing that they they
+ 
+
+ align:start position:0%
+the price of the thing that they they
+have been buying the import good
+
+ align:start position:0%
+have been buying the import good
+ 
+
+ align:start position:0%
+have been buying the import good
+and decrease the price of the export
+
+ align:start position:0%
+and decrease the price of the export
+ 
+
+ align:start position:0%
+and decrease the price of the export
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+hurt both ways
+
+ align:start position:0%
+hurt both ways
+ 
+
+ align:start position:0%
+hurt both ways
+we're going to do it by one percent so
+
+ align:start position:0%
+we're going to do it by one percent so
+ 
+
+ align:start position:0%
+we're going to do it by one percent so
+we're going to take these calibrated
+
+ align:start position:0%
+we're going to take these calibrated
+ 
+
+ align:start position:0%
+we're going to take these calibrated
+prices that match were used to match the
+
+ align:start position:0%
+prices that match were used to match the
+ 
+
+ align:start position:0%
+prices that match were used to match the
+payments to factors and profits and now
+
+ align:start position:0%
+payments to factors and profits and now
+ 
+
+ align:start position:0%
+payments to factors and profits and now
+vary them and see what happens
+
+ align:start position:0%
+vary them and see what happens
+ 
+
+ align:start position:0%
+vary them and see what happens
+we're also going to do a financial
+
+ align:start position:0%
+we're also going to do a financial
+ 
+
+ align:start position:0%
+we're also going to do a financial
+experiment in the model we're going to
+
+ align:start position:0%
+experiment in the model we're going to
+ 
+
+ align:start position:0%
+experiment in the model we're going to
+change the interest rate
+
+ align:start position:0%
+change the interest rate
+ 
+
+ align:start position:0%
+change the interest rate
+so it's like we're we're going to impede
+
+ align:start position:0%
+so it's like we're we're going to impede
+ 
+
+ align:start position:0%
+so it's like we're we're going to impede
+financial flows so again the effect of
+
+ align:start position:0%
+financial flows so again the effect of
+ 
+
+ align:start position:0%
+financial flows so again the effect of
+it always hurts so if the village had
+
+ align:start position:0%
+it always hurts so if the village had
+ 
+
+ align:start position:0%
+it always hurts so if the village had
+been in that lender
+
+ align:start position:0%
+been in that lender
+ 
+
+ align:start position:0%
+been in that lender
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+then the effect of the financial
+
+ align:start position:0%
+then the effect of the financial
+ 
+
+ align:start position:0%
+then the effect of the financial
+friction
+
+ align:start position:0%
+friction
+ 
+
+ align:start position:0%
+friction
+is to make the interest rate lower
+
+ align:start position:0%
+is to make the interest rate lower
+ 
+
+ align:start position:0%
+is to make the interest rate lower
+because lenders don't like low interest
+
+ align:start position:0%
+because lenders don't like low interest
+ 
+
+ align:start position:0%
+because lenders don't like low interest
+rates we talked about that
+
+ align:start position:0%
+rates we talked about that
+ 
+
+ align:start position:0%
+rates we talked about that
+when we did the lecture on
+
+ align:start position:0%
+when we did the lecture on
+ 
+
+ align:start position:0%
+when we did the lecture on
+household income and price effects for
+
+ align:start position:0%
+household income and price effects for
+ 
+
+ align:start position:0%
+household income and price effects for
+households in the too good world anyway
+
+ align:start position:0%
+households in the too good world anyway
+ 
+
+ align:start position:0%
+households in the too good world anyway
+so if they're lending they're not going
+
+ align:start position:0%
+so if they're lending they're not going
+ 
+
+ align:start position:0%
+so if they're lending they're not going
+to like it that the interest rate goes
+
+ align:start position:0%
+to like it that the interest rate goes
+ 
+
+ align:start position:0%
+to like it that the interest rate goes
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+and likewise if they had been
+
+ align:start position:0%
+and likewise if they had been
+ 
+
+ align:start position:0%
+and likewise if they had been
+borrowing we would have gone the other
+
+ align:start position:0%
+borrowing we would have gone the other
+ 
+
+ align:start position:0%
+borrowing we would have gone the other
+way and make the loans more expensive so
+
+ align:start position:0%
+way and make the loans more expensive so
+ 
+
+ align:start position:0%
+way and make the loans more expensive so
+that's the effect of
+
+ align:start position:0%
+that's the effect of
+ 
+
+ align:start position:0%
+that's the effect of
+the way we capture in the model in order
+
+ align:start position:0%
+the way we capture in the model in order
+ 
+
+ align:start position:0%
+the way we capture in the model in order
+to run and experiment
+
+ align:start position:0%
+to run and experiment
+ 
+
+ align:start position:0%
+to run and experiment
+uh the impact of trade frictions through
+
+ align:start position:0%
+uh the impact of trade frictions through
+ 
+
+ align:start position:0%
+uh the impact of trade frictions through
+tariffs and
+
+ align:start position:0%
+tariffs and
+ 
+
+ align:start position:0%
+tariffs and
+or internal frictions
+
+ align:start position:0%
+or internal frictions
+ 
+
+ align:start position:0%
+or internal frictions
+and financial frictions okay so
+
+ align:start position:0%
+and financial frictions okay so
+ 
+
+ align:start position:0%
+and financial frictions okay so
+you want to see what happens
+
+ align:start position:0%
+you want to see what happens
+ 
+
+ align:start position:0%
+you want to see what happens
+uh this is in lopere and this is the
+
+ align:start position:0%
+uh this is in lopere and this is the
+ 
+
+ align:start position:0%
+uh this is in lopere and this is the
+effect of that one percent increase in
+
+ align:start position:0%
+effect of that one percent increase in
+ 
+
+ align:start position:0%
+effect of that one percent increase in
+trade frictions
+
+ align:start position:0%
+trade frictions
+ 
+
+ align:start position:0%
+trade frictions
+making exports give less revenue imports
+
+ align:start position:0%
+making exports give less revenue imports
+ 
+
+ align:start position:0%
+making exports give less revenue imports
+now cost more
+
+ align:start position:0%
+now cost more
+ 
+
+ align:start position:0%
+now cost more
+that's going to affect the production
+
+ align:start position:0%
+that's going to affect the production
+ 
+
+ align:start position:0%
+that's going to affect the production
+and profits from the manufactured good
+
+ align:start position:0%
+and profits from the manufactured good
+ 
+
+ align:start position:0%
+and profits from the manufactured good
+and the agricultural good and in turn
+
+ align:start position:0%
+and the agricultural good and in turn
+ 
+
+ align:start position:0%
+and the agricultural good and in turn
+remember the algorithm from last time
+
+ align:start position:0%
+remember the algorithm from last time
+ 
+
+ align:start position:0%
+remember the algorithm from last time
+that i reviewed
+
+ align:start position:0%
+that i reviewed
+ 
+
+ align:start position:0%
+that i reviewed
+those price changes are going to map
+
+ align:start position:0%
+those price changes are going to map
+ 
+
+ align:start position:0%
+those price changes are going to map
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+input quantities are going to map into
+
+ align:start position:0%
+input quantities are going to map into
+ 
+
+ align:start position:0%
+input quantities are going to map into
+relative factor price movements okay but
+
+ align:start position:0%
+relative factor price movements okay but
+ 
+
+ align:start position:0%
+relative factor price movements okay but
+there's a lot of diversity in these
+
+ align:start position:0%
+there's a lot of diversity in these
+ 
+
+ align:start position:0%
+there's a lot of diversity in these
+economies
+
+ align:start position:0%
+economies
+ 
+
+ align:start position:0%
+economies
+as i've been saying households differ by
+
+ align:start position:0%
+as i've been saying households differ by
+ 
+
+ align:start position:0%
+as i've been saying households differ by
+their initial level of capital they
+
+ align:start position:0%
+their initial level of capital they
+ 
+
+ align:start position:0%
+their initial level of capital they
+differ also by their talent so we have
+
+ align:start position:0%
+differ also by their talent so we have
+ 
+
+ align:start position:0%
+differ also by their talent so we have
+capital moving on the x-axis and the
+
+ align:start position:0%
+capital moving on the x-axis and the
+ 
+
+ align:start position:0%
+capital moving on the x-axis and the
+average skill level pretty high skill
+
+ align:start position:0%
+average skill level pretty high skill
+ 
+
+ align:start position:0%
+average skill level pretty high skill
+level and very high skill level and then
+
+ align:start position:0%
+level and very high skill level and then
+ 
+
+ align:start position:0%
+level and very high skill level and then
+what's getting plotted here is the gains
+
+ align:start position:0%
+what's getting plotted here is the gains
+ 
+
+ align:start position:0%
+what's getting plotted here is the gains
+or losses so
+
+ align:start position:0%
+or losses so
+ 
+
+ align:start position:0%
+or losses so
+it's a tariff effectively
+
+ align:start position:0%
+it's a tariff effectively
+ 
+
+ align:start position:0%
+it's a tariff effectively
+so you might expect losses
+
+ align:start position:0%
+so you might expect losses
+ 
+
+ align:start position:0%
+so you might expect losses
+and in fact these average or low skilled
+
+ align:start position:0%
+and in fact these average or low skilled
+ 
+
+ align:start position:0%
+and in fact these average or low skilled
+guys do suffer losses
+
+ align:start position:0%
+guys do suffer losses
+ 
+
+ align:start position:0%
+guys do suffer losses
+arguably because they're wage earners
+
+ align:start position:0%
+arguably because they're wage earners
+ 
+
+ align:start position:0%
+arguably because they're wage earners
+although you can't see that
+
+ align:start position:0%
+although you can't see that
+ 
+
+ align:start position:0%
+although you can't see that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+movement in production
+
+ align:start position:0%
+movement in production
+ 
+
+ align:start position:0%
+movement in production
+from the capital good and the labor
+
+ align:start position:0%
+from the capital good and the labor
+ 
+
+ align:start position:0%
+from the capital good and the labor
+intensive good
+
+ align:start position:0%
+intensive good
+ 
+
+ align:start position:0%
+intensive good
+was such as to hurt the wage so remember
+
+ align:start position:0%
+was such as to hurt the wage so remember
+ 
+
+ align:start position:0%
+was such as to hurt the wage so remember
+we did stolper samuelson where an
+
+ align:start position:0%
+we did stolper samuelson where an
+ 
+
+ align:start position:0%
+we did stolper samuelson where an
+increase in the price causes an increase
+
+ align:start position:0%
+increase in the price causes an increase
+ 
+
+ align:start position:0%
+increase in the price causes an increase
+in the factor price of the good that is
+
+ align:start position:0%
+in the factor price of the good that is
+ 
+
+ align:start position:0%
+in the factor price of the good that is
+used relatively intensively so despite
+
+ align:start position:0%
+used relatively intensively so despite
+ 
+
+ align:start position:0%
+used relatively intensively so despite
+all the differences with the two by two
+
+ align:start position:0%
+all the differences with the two by two
+ 
+
+ align:start position:0%
+all the differences with the two by two
+from last time that ingredient is
+
+ align:start position:0%
+from last time that ingredient is
+ 
+
+ align:start position:0%
+from last time that ingredient is
+playing a role here
+
+ align:start position:0%
+playing a role here
+ 
+
+ align:start position:0%
+playing a role here
+so these wage earners are hurt initially
+
+ align:start position:0%
+so these wage earners are hurt initially
+ 
+
+ align:start position:0%
+so these wage earners are hurt initially
+but then ironically as we move in the
+
+ align:start position:0%
+but then ironically as we move in the
+ 
+
+ align:start position:0%
+but then ironically as we move in the
+cross section for a higher level of
+
+ align:start position:0%
+cross section for a higher level of
+ 
+
+ align:start position:0%
+cross section for a higher level of
+capital they were actually producers not
+
+ align:start position:0%
+capital they were actually producers not
+ 
+
+ align:start position:0%
+capital they were actually producers not
+wage earners and now the lower wage
+
+ align:start position:0%
+wage earners and now the lower wage
+ 
+
+ align:start position:0%
+wage earners and now the lower wage
+helps them because it's an a lowered
+
+ align:start position:0%
+helps them because it's an a lowered
+ 
+
+ align:start position:0%
+helps them because it's an a lowered
+cost of production so their profits go
+
+ align:start position:0%
+cost of production so their profits go
+ 
+
+ align:start position:0%
+cost of production so their profits go
+up now they're they're winning by a
+
+ align:start position:0%
+up now they're they're winning by a
+ 
+
+ align:start position:0%
+up now they're they're winning by a
+little less than one percent and you
+
+ align:start position:0%
+little less than one percent and you
+ 
+
+ align:start position:0%
+little less than one percent and you
+know if they're really really talented
+
+ align:start position:0%
+know if they're really really talented
+ 
+
+ align:start position:0%
+know if they're really really talented
+they've been producing at a higher scale
+
+ align:start position:0%
+they've been producing at a higher scale
+ 
+
+ align:start position:0%
+they've been producing at a higher scale
+all along so the drop in wages you know
+
+ align:start position:0%
+all along so the drop in wages you know
+ 
+
+ align:start position:0%
+all along so the drop in wages you know
+is even better for them
+
+ align:start position:0%
+is even better for them
+ 
+
+ align:start position:0%
+is even better for them
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i'm trying to give you some intuition
+
+ align:start position:0%
+i'm trying to give you some intuition
+ 
+
+ align:start position:0%
+i'm trying to give you some intuition
+here but i decided because time was
+
+ align:start position:0%
+here but i decided because time was
+ 
+
+ align:start position:0%
+here but i decided because time was
+short i wouldn't be able to actually
+
+ align:start position:0%
+short i wouldn't be able to actually
+ 
+
+ align:start position:0%
+short i wouldn't be able to actually
+prove all these assertions
+
+ align:start position:0%
+prove all these assertions
+ 
+
+ align:start position:0%
+prove all these assertions
+i'm just asking you to sort of imagine
+
+ align:start position:0%
+i'm just asking you to sort of imagine
+ 
+
+ align:start position:0%
+i'm just asking you to sort of imagine
+from the two by two by two that we did
+
+ align:start position:0%
+from the two by two by two that we did
+ 
+
+ align:start position:0%
+from the two by two by two that we did
+last time you know why it is we're
+
+ align:start position:0%
+last time you know why it is we're
+ 
+
+ align:start position:0%
+last time you know why it is we're
+seeing all this diversity here
+
+ align:start position:0%
+seeing all this diversity here
+ 
+
+ align:start position:0%
+seeing all this diversity here
+oh the order of magnitude is like less
+
+ align:start position:0%
+oh the order of magnitude is like less
+ 
+
+ align:start position:0%
+oh the order of magnitude is like less
+than one percent here it's one percent
+
+ align:start position:0%
+than one percent here it's one percent
+ 
+
+ align:start position:0%
+than one percent here it's one percent
+so that's pretty small but if you looked
+
+ align:start position:0%
+so that's pretty small but if you looked
+ 
+
+ align:start position:0%
+so that's pretty small but if you looked
+at the financial frictions
+
+ align:start position:0%
+at the financial frictions
+ 
+
+ align:start position:0%
+at the financial frictions
+in lopere
+
+ align:start position:0%
+in lopere
+ 
+
+ align:start position:0%
+in lopere
+in the sense that i described you you
+
+ align:start position:0%
+in the sense that i described you you
+ 
+
+ align:start position:0%
+in the sense that i described you you
+can see bigger numbers first of all you
+
+ align:start position:0%
+can see bigger numbers first of all you
+ 
+
+ align:start position:0%
+can see bigger numbers first of all you
+see winners and losers
+
+ align:start position:0%
+see winners and losers
+ 
+
+ align:start position:0%
+see winners and losers
+you also see that it matters whether
+
+ align:start position:0%
+you also see that it matters whether
+ 
+
+ align:start position:0%
+you also see that it matters whether
+they were wage earners or capitalists
+
+ align:start position:0%
+they were wage earners or capitalists
+ 
+
+ align:start position:0%
+they were wage earners or capitalists
+but above all you see
+
+ align:start position:0%
+but above all you see
+ 
+
+ align:start position:0%
+but above all you see
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+high skilled guys
+
+ align:start position:0%
+high skilled guys
+ 
+
+ align:start position:0%
+high skilled guys
+can benefit up to 10
+
+ align:start position:0%
+can benefit up to 10
+ 
+
+ align:start position:0%
+can benefit up to 10
+from the increase in the interest rate
+
+ align:start position:0%
+from the increase in the interest rate
+ 
+
+ align:start position:0%
+from the increase in the interest rate
+that's associated with
+
+ align:start position:0%
+that's associated with
+ 
+
+ align:start position:0%
+that's associated with
+the uh financial friction
+
+ align:start position:0%
+the uh financial friction
+ 
+
+ align:start position:0%
+the uh financial friction
+because the country had been borrowing
+
+ align:start position:0%
+because the country had been borrowing
+ 
+
+ align:start position:0%
+because the country had been borrowing
+the village had been borrowing but some
+
+ align:start position:0%
+the village had been borrowing but some
+ 
+
+ align:start position:0%
+the village had been borrowing but some
+of those guys don't borrow they lend
+
+ align:start position:0%
+of those guys don't borrow they lend
+ 
+
+ align:start position:0%
+of those guys don't borrow they lend
+and likewise
+
+ align:start position:0%
+and likewise
+ 
+
+ align:start position:0%
+and likewise
+there are other people here
+
+ align:start position:0%
+there are other people here
+ 
+
+ align:start position:0%
+there are other people here
+the average skilled guys who are taking
+
+ align:start position:0%
+the average skilled guys who are taking
+ 
+
+ align:start position:0%
+the average skilled guys who are taking
+big losses of up to 10
+
+ align:start position:0%
+big losses of up to 10
+ 
+
+ align:start position:0%
+big losses of up to 10
+so again one could imagine
+
+ align:start position:0%
+so again one could imagine
+ 
+
+ align:start position:0%
+so again one could imagine
+producing pictures like this
+
+ align:start position:0%
+producing pictures like this
+ 
+
+ align:start position:0%
+producing pictures like this
+and if we go back to household a
+
+ align:start position:0%
+and if we go back to household a
+ 
+
+ align:start position:0%
+and if we go back to household a
+like what happens to
+
+ align:start position:0%
+like what happens to
+ 
+
+ align:start position:0%
+like what happens to
+a wage earner in the u.s with
+
+ align:start position:0%
+a wage earner in the u.s with
+ 
+
+ align:start position:0%
+a wage earner in the u.s with
+manufactured imports
+
+ align:start position:0%
+manufactured imports
+ 
+
+ align:start position:0%
+manufactured imports
+or a farmer in the midwest with
+
+ align:start position:0%
+or a farmer in the midwest with
+ 
+
+ align:start position:0%
+or a farmer in the midwest with
+agricultural exports what happens in
+
+ align:start position:0%
+agricultural exports what happens in
+ 
+
+ align:start position:0%
+agricultural exports what happens in
+loperi
+
+ align:start position:0%
+loperi
+ 
+
+ align:start position:0%
+loperi
+to that wage earner
+
+ align:start position:0%
+to that wage earner
+ 
+
+ align:start position:0%
+to that wage earner
+under you know the trade friction
+
+ align:start position:0%
+under you know the trade friction
+ 
+
+ align:start position:0%
+under you know the trade friction
+or under the financial friction they
+
+ align:start position:0%
+or under the financial friction they
+ 
+
+ align:start position:0%
+or under the financial friction they
+lose
+
+ align:start position:0%
+lose
+ 
+
+ align:start position:0%
+lose
+he lose he or she loses that household
+
+ align:start position:0%
+he lose he or she loses that household
+ 
+
+ align:start position:0%
+he lose he or she loses that household
+loses so we validated the model to try
+
+ align:start position:0%
+loses so we validated the model to try
+ 
+
+ align:start position:0%
+loses so we validated the model to try
+to make this realistic it fit pretty
+
+ align:start position:0%
+to make this realistic it fit pretty
+ 
+
+ align:start position:0%
+to make this realistic it fit pretty
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+very well to the aggregate level it fit
+
+ align:start position:0%
+very well to the aggregate level it fit
+ 
+
+ align:start position:0%
+very well to the aggregate level it fit
+pretty well at the individual level so
+
+ align:start position:0%
+pretty well at the individual level so
+ 
+
+ align:start position:0%
+pretty well at the individual level so
+if for some reason the thai government
+
+ align:start position:0%
+if for some reason the thai government
+ 
+
+ align:start position:0%
+if for some reason the thai government
+had run this experiment or they had
+
+ align:start position:0%
+had run this experiment or they had
+ 
+
+ align:start position:0%
+had run this experiment or they had
+political
+
+ align:start position:0%
+political
+ 
+
+ align:start position:0%
+political
+issues that made the country more
+
+ align:start position:0%
+issues that made the country more
+ 
+
+ align:start position:0%
+issues that made the country more
+isolated you could see the effect of
+
+ align:start position:0%
+isolated you could see the effect of
+ 
+
+ align:start position:0%
+isolated you could see the effect of
+that on individual households through
+
+ align:start position:0%
+that on individual households through
+ 
+
+ align:start position:0%
+that on individual households through
+through the lens of the model okay
+
+ align:start position:0%
+through the lens of the model okay
+ 
+
+ align:start position:0%
+through the lens of the model okay
+any final questions
+
+ align:start position:0%
+any final questions
+ 
+
+ align:start position:0%
+any final questions
+so again we'll kind of do it all over
+
+ align:start position:0%
+so again we'll kind of do it all over
+ 
+
+ align:start position:0%
+so again we'll kind of do it all over
+again when we when we come to the u.s
+
+ align:start position:0%
+again when we when we come to the u.s
+ 
+
+ align:start position:0%
+again when we when we come to the u.s
+next time next thursday
\ No newline at end of file
diff --git a/RoTz_ylFHfY.txt b/RoTz_ylFHfY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6282411dac336a312fe7a4c85e51ce5f8cacbc2e
--- /dev/null
+++ b/RoTz_ylFHfY.txt
@@ -0,0 +1,2363 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+I'd like us to work on the following
+
+ align:start position:0%
+I'd like us to work on the following
+ 
+
+ align:start position:0%
+I'd like us to work on the following
+problem we're going to let capital D
+
+ align:start position:0%
+problem we're going to let capital D
+ 
+
+ align:start position:0%
+problem we're going to let capital D
+denote the portion of the sphere the
+
+ align:start position:0%
+denote the portion of the sphere the
+ 
+
+ align:start position:0%
+denote the portion of the sphere the
+solid sphere of radius one that's
+
+ align:start position:0%
+solid sphere of radius one that's
+ 
+
+ align:start position:0%
+solid sphere of radius one that's
+centered at
+
+ align:start position:0%
+centered at
+ 
+
+ align:start position:0%
+centered at
+001 which also lies above the plane zal
+
+ align:start position:0%
+001 which also lies above the plane zal
+ 
+
+ align:start position:0%
+001 which also lies above the plane zal
+1 and then I'd like us to First Supply
+
+ align:start position:0%
+1 and then I'd like us to First Supply
+ 
+
+ align:start position:0%
+1 and then I'd like us to First Supply
+the limits for D and spherical
+
+ align:start position:0%
+the limits for D and spherical
+ 
+
+ align:start position:0%
+the limits for D and spherical
+coordinates in other words I want you to
+
+ align:start position:0%
+coordinates in other words I want you to
+ 
+
+ align:start position:0%
+coordinates in other words I want you to
+determine the values for row Theta and f
+
+ align:start position:0%
+determine the values for row Theta and f
+ 
+
+ align:start position:0%
+determine the values for row Theta and f
+that will give us all of D and then I
+
+ align:start position:0%
+that will give us all of D and then I
+ 
+
+ align:start position:0%
+that will give us all of D and then I
+would like us to just set up the
+
+ align:start position:0%
+would like us to just set up the
+ 
+
+ align:start position:0%
+would like us to just set up the
+integral for the average distance of a
+
+ align:start position:0%
+integral for the average distance of a
+ 
+
+ align:start position:0%
+integral for the average distance of a
+point in D from the origin so there are
+
+ align:start position:0%
+point in D from the origin so there are
+ 
+
+ align:start position:0%
+point in D from the origin so there are
+two parts to this problem the first is
+
+ align:start position:0%
+two parts to this problem the first is
+ 
+
+ align:start position:0%
+two parts to this problem the first is
+to determine what values of row Theta
+
+ align:start position:0%
+to determine what values of row Theta
+ 
+
+ align:start position:0%
+to determine what values of row Theta
+and Fe describe this region this this
+
+ align:start position:0%
+and Fe describe this region this this
+ 
+
+ align:start position:0%
+and Fe describe this region this this
+solid region D and then second is just
+
+ align:start position:0%
+solid region D and then second is just
+ 
+
+ align:start position:0%
+solid region D and then second is just
+set up the integral for the average
+
+ align:start position:0%
+set up the integral for the average
+ 
+
+ align:start position:0%
+set up the integral for the average
+distance of a point in that region from
+
+ align:start position:0%
+distance of a point in that region from
+ 
+
+ align:start position:0%
+distance of a point in that region from
+the origin so why don't you pause the
+
+ align:start position:0%
+the origin so why don't you pause the
+ 
+
+ align:start position:0%
+the origin so why don't you pause the
+video work on those and then when you're
+
+ align:start position:0%
+video work on those and then when you're
+ 
+
+ align:start position:0%
+video work on those and then when you're
+ready to see my Solutions you can bring
+
+ align:start position:0%
+ready to see my Solutions you can bring
+ 
+
+ align:start position:0%
+ready to see my Solutions you can bring
+the video back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up okay welcome back well I would say
+
+ align:start position:0%
+up okay welcome back well I would say
+ 
+
+ align:start position:0%
+up okay welcome back well I would say
+from looking at this problem actually
+
+ align:start position:0%
+from looking at this problem actually
+ 
+
+ align:start position:0%
+from looking at this problem actually
+part A is potentially a little bit more
+
+ align:start position:0%
+part A is potentially a little bit more
+ 
+
+ align:start position:0%
+part A is potentially a little bit more
+hazardous for some of us than Part B
+
+ align:start position:0%
+hazardous for some of us than Part B
+ 
+
+ align:start position:0%
+hazardous for some of us than Part B
+once we know the the bounds that
+
+ align:start position:0%
+once we know the the bounds that
+ 
+
+ align:start position:0%
+once we know the the bounds that
+describe D it's not too hard to set up
+
+ align:start position:0%
+describe D it's not too hard to set up
+ 
+
+ align:start position:0%
+describe D it's not too hard to set up
+this integral so the hard part of this
+
+ align:start position:0%
+this integral so the hard part of this
+ 
+
+ align:start position:0%
+this integral so the hard part of this
+problem is understanding how to write
+
+ align:start position:0%
+problem is understanding how to write
+ 
+
+ align:start position:0%
+problem is understanding how to write
+this solid region D in spherical
+
+ align:start position:0%
+this solid region D in spherical
+ 
+
+ align:start position:0%
+this solid region D in spherical
+coordinates but it's actually really not
+
+ align:start position:0%
+coordinates but it's actually really not
+ 
+
+ align:start position:0%
+coordinates but it's actually really not
+that hard either so I'm going to try and
+
+ align:start position:0%
+that hard either so I'm going to try and
+ 
+
+ align:start position:0%
+that hard either so I'm going to try and
+take us through it in a reasonable way
+
+ align:start position:0%
+take us through it in a reasonable way
+ 
+
+ align:start position:0%
+take us through it in a reasonable way
+so the first thing I'm going to draw a
+
+ align:start position:0%
+so the first thing I'm going to draw a
+ 
+
+ align:start position:0%
+so the first thing I'm going to draw a
+very rough picture of the region so we
+
+ align:start position:0%
+very rough picture of the region so we
+ 
+
+ align:start position:0%
+very rough picture of the region so we
+understand what it looks like so in
+
+ align:start position:0%
+understand what it looks like so in
+ 
+
+ align:start position:0%
+understand what it looks like so in
+order to do part A and if you did not do
+
+ align:start position:0%
+order to do part A and if you did not do
+ 
+
+ align:start position:0%
+order to do part A and if you did not do
+this I would highly recommend that next
+
+ align:start position:0%
+this I would highly recommend that next
+ 
+
+ align:start position:0%
+this I would highly recommend that next
+time you encounter such a problem you
+
+ align:start position:0%
+time you encounter such a problem you
+ 
+
+ align:start position:0%
+time you encounter such a problem you
+begin by drawing yourself a picture even
+
+ align:start position:0%
+begin by drawing yourself a picture even
+ 
+
+ align:start position:0%
+begin by drawing yourself a picture even
+if it's not a gr picture it will give
+
+ align:start position:0%
+if it's not a gr picture it will give
+ 
+
+ align:start position:0%
+if it's not a gr picture it will give
+you some intuition about what's
+
+ align:start position:0%
+you some intuition about what's
+ 
+
+ align:start position:0%
+you some intuition about what's
+happening so let me first first draw the
+
+ align:start position:0%
+happening so let me first first draw the
+ 
+
+ align:start position:0%
+happening so let me first first draw the
+axes and ultimately what I have is say
+
+ align:start position:0%
+axes and ultimately what I have is say
+ 
+
+ align:start position:0%
+axes and ultimately what I have is say
+here is the
+
+ align:start position:0%
+here is the
+ 
+
+ align:start position:0%
+here is the
+01 I have a
+
+ align:start position:0%
+01 I have a
+ 
+
+ align:start position:0%
+01 I have a
+sphere that's looking in in the x or
+
+ align:start position:0%
+sphere that's looking in in the x or
+ 
+
+ align:start position:0%
+sphere that's looking in in the x or
+sorry in the z y plane it looks
+
+ align:start position:0%
+sorry in the z y plane it looks
+ 
+
+ align:start position:0%
+sorry in the z y plane it looks
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+this and then so it has this depth
+
+ align:start position:0%
+this and then so it has this depth
+ 
+
+ align:start position:0%
+this and then so it has this depth
+here and that's the solid sphere I want
+
+ align:start position:0%
+here and that's the solid sphere I want
+ 
+
+ align:start position:0%
+here and that's the solid sphere I want
+to be considering and then I'm going to
+
+ align:start position:0%
+to be considering and then I'm going to
+ 
+
+ align:start position:0%
+to be considering and then I'm going to
+be removing the bottom half I'm only
+
+ align:start position:0%
+be removing the bottom half I'm only
+ 
+
+ align:start position:0%
+be removing the bottom half I'm only
+going to be looking at the part that is
+
+ align:start position:0%
+going to be looking at the part that is
+ 
+
+ align:start position:0%
+going to be looking at the part that is
+above the zal 1 plane so it's actually
+
+ align:start position:0%
+above the zal 1 plane so it's actually
+ 
+
+ align:start position:0%
+above the zal 1 plane so it's actually
+going to look it's going to be all the
+
+ align:start position:0%
+going to look it's going to be all the
+ 
+
+ align:start position:0%
+going to look it's going to be all the
+circular
+
+ align:start position:0%
+circular
+ 
+
+ align:start position:0%
+circular
+slices that are in the the top half sort
+
+ align:start position:0%
+slices that are in the the top half sort
+ 
+
+ align:start position:0%
+slices that are in the the top half sort
+of the upper hemisphere of this sphere
+
+ align:start position:0%
+of the upper hemisphere of this sphere
+ 
+
+ align:start position:0%
+of the upper hemisphere of this sphere
+and so it's the solid region there
+
+ align:start position:0%
+and so it's the solid region there
+ 
+
+ align:start position:0%
+and so it's the solid region there
+that's D and what I want to do to
+
+ align:start position:0%
+that's D and what I want to do to
+ 
+
+ align:start position:0%
+that's D and what I want to do to
+determine uh row and and Theta and Fe
+
+ align:start position:0%
+determine uh row and and Theta and Fe
+ 
+
+ align:start position:0%
+determine uh row and and Theta and Fe
+actually the Theta is the easy one right
+
+ align:start position:0%
+actually the Theta is the easy one right
+ 
+
+ align:start position:0%
+actually the Theta is the easy one right
+because Theta at each at each value here
+
+ align:start position:0%
+because Theta at each at each value here
+ 
+
+ align:start position:0%
+because Theta at each at each value here
+I go all the way around in the Theta
+
+ align:start position:0%
+I go all the way around in the Theta
+ 
+
+ align:start position:0%
+I go all the way around in the Theta
+Direction so I know I'm going to go at
+
+ align:start position:0%
+Direction so I know I'm going to go at
+ 
+
+ align:start position:0%
+Direction so I know I'm going to go at
+any given at any given height or radius
+
+ align:start position:0%
+any given at any given height or radius
+ 
+
+ align:start position:0%
+any given at any given height or radius
+I want to go all the way around in the
+
+ align:start position:0%
+I want to go all the way around in the
+ 
+
+ align:start position:0%
+I want to go all the way around in the
+Theta direction from 0 to 2 pi so my
+
+ align:start position:0%
+Theta direction from 0 to 2 pi so my
+ 
+
+ align:start position:0%
+Theta direction from 0 to 2 pi so my
+Theta bounds are the easy ones that's
+
+ align:start position:0%
+Theta bounds are the easy ones that's
+ 
+
+ align:start position:0%
+Theta bounds are the easy ones that's
+just I'm covering it I'm covering 0 to 2
+
+ align:start position:0%
+just I'm covering it I'm covering 0 to 2
+ 
+
+ align:start position:0%
+just I'm covering it I'm covering 0 to 2
+pi in Theta I'm not because that would
+
+ align:start position:0%
+pi in Theta I'm not because that would
+ 
+
+ align:start position:0%
+pi in Theta I'm not because that would
+if I cut off the back half of the circle
+
+ align:start position:0%
+if I cut off the back half of the circle
+ 
+
+ align:start position:0%
+if I cut off the back half of the circle
+that would change my values of theta but
+
+ align:start position:0%
+that would change my values of theta but
+ 
+
+ align:start position:0%
+that would change my values of theta but
+because I'm sorry not Circle sphere the
+
+ align:start position:0%
+because I'm sorry not Circle sphere the
+ 
+
+ align:start position:0%
+because I'm sorry not Circle sphere the
+back half of the sphere I'd want to only
+
+ align:start position:0%
+back half of the sphere I'd want to only
+ 
+
+ align:start position:0%
+back half of the sphere I'd want to only
+have a restricted value of theta but
+
+ align:start position:0%
+have a restricted value of theta but
+ 
+
+ align:start position:0%
+have a restricted value of theta but
+because I'm covering sort of all the way
+
+ align:start position:0%
+because I'm covering sort of all the way
+ 
+
+ align:start position:0%
+because I'm covering sort of all the way
+around and my restriction is only sort
+
+ align:start position:0%
+around and my restriction is only sort
+ 
+
+ align:start position:0%
+around and my restriction is only sort
+of bottom half my Theta values haven't
+
+ align:start position:0%
+of bottom half my Theta values haven't
+ 
+
+ align:start position:0%
+of bottom half my Theta values haven't
+changed so Theta is easy 0 and 2
+
+ align:start position:0%
+changed so Theta is easy 0 and 2
+ 
+
+ align:start position:0%
+changed so Theta is easy 0 and 2
+pi now the harder ones are going to be
+
+ align:start position:0%
+pi now the harder ones are going to be
+ 
+
+ align:start position:0%
+pi now the harder ones are going to be
+row and Fe but in fact actually Fe is
+
+ align:start position:0%
+row and Fe but in fact actually Fe is
+ 
+
+ align:start position:0%
+row and Fe but in fact actually Fe is
+not that hard either Fe I notice I'm
+
+ align:start position:0%
+not that hard either Fe I notice I'm
+ 
+
+ align:start position:0%
+not that hard either Fe I notice I'm
+starting Fe is the angle that I make
+
+ align:start position:0%
+starting Fe is the angle that I make
+ 
+
+ align:start position:0%
+starting Fe is the angle that I make
+from the z-axis to any given point so I
+
+ align:start position:0%
+from the z-axis to any given point so I
+ 
+
+ align:start position:0%
+from the z-axis to any given point so I
+notice that I certainly I'm including
+
+ align:start position:0%
+notice that I certainly I'm including
+ 
+
+ align:start position:0%
+notice that I certainly I'm including
+the point where Fe is zero and then I'm
+
+ align:start position:0%
+the point where Fe is zero and then I'm
+ 
+
+ align:start position:0%
+the point where Fe is zero and then I'm
+going all the way down to a point out
+
+ align:start position:0%
+going all the way down to a point out
+ 
+
+ align:start position:0%
+going all the way down to a point out
+here which is 45° angle with the z-axis
+
+ align:start position:0%
+here which is 45° angle with the z-axis
+ 
+
+ align:start position:0%
+here which is 45° angle with the z-axis
+so f is also easy it's actually just
+
+ align:start position:0%
+so f is also easy it's actually just
+ 
+
+ align:start position:0%
+so f is also easy it's actually just
+between 0 and pi over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 and the row will be the slightly
+
+ align:start position:0%
+4 and the row will be the slightly
+ 
+
+ align:start position:0%
+4 and the row will be the slightly
+harder part so that's the really the
+
+ align:start position:0%
+harder part so that's the really the
+ 
+
+ align:start position:0%
+harder part so that's the really the
+only real tricky part in this problem is
+
+ align:start position:0%
+only real tricky part in this problem is
+ 
+
+ align:start position:0%
+only real tricky part in this problem is
+determining the row value now the row
+
+ align:start position:0%
+determining the row value now the row
+ 
+
+ align:start position:0%
+determining the row value now the row
+value to get the outer boundary we'll
+
+ align:start position:0%
+value to get the outer boundary we'll
+ 
+
+ align:start position:0%
+value to get the outer boundary we'll
+look at that part first to get the outer
+
+ align:start position:0%
+look at that part first to get the outer
+ 
+
+ align:start position:0%
+look at that part first to get the outer
+boundary well the boundary of of this
+
+ align:start position:0%
+boundary well the boundary of of this
+ 
+
+ align:start position:0%
+boundary well the boundary of of this
+sphere here has a certain equation in X
+
+ align:start position:0%
+sphere here has a certain equation in X
+ 
+
+ align:start position:0%
+sphere here has a certain equation in X
+Y and Z that we know right it's x^2 +
+
+ align:start position:0%
+Y and Z that we know right it's x^2 +
+ 
+
+ align:start position:0%
+Y and Z that we know right it's x^2 +
+y^2 plus the quantity zus 1^ 2 equals 1
+
+ align:start position:0%
+y^2 plus the quantity zus 1^ 2 equals 1
+ 
+
+ align:start position:0%
+y^2 plus the quantity zus 1^ 2 equals 1
+I mean that's just the the equation for
+
+ align:start position:0%
+I mean that's just the the equation for
+ 
+
+ align:start position:0%
+I mean that's just the the equation for
+a sphere of radius 1 centered at 0 0 1
+
+ align:start position:0%
+a sphere of radius 1 centered at 0 0 1
+ 
+
+ align:start position:0%
+a sphere of radius 1 centered at 0 0 1
+so I'm going to write that here and
+
+ align:start position:0%
+so I'm going to write that here and
+ 
+
+ align:start position:0%
+so I'm going to write that here and
+we're going to show how we can
+
+ align:start position:0%
+we're going to show how we can
+ 
+
+ align:start position:0%
+we're going to show how we can
+manipulate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that right x^2 + y^2 is R 2 R 2 is Row 2
+
+ align:start position:0%
+that right x^2 + y^2 is R 2 R 2 is Row 2
+ 
+
+ align:start position:0%
+that right x^2 + y^2 is R 2 R 2 is Row 2
+sin 2 so I can replace this by Row 2
+
+ align:start position:0%
+sin 2 so I can replace this by Row 2
+ 
+
+ align:start position:0%
+sin 2 so I can replace this by Row 2
+sin^2 if you didn't know that
+
+ align:start position:0%
+sin^2 if you didn't know that
+ 
+
+ align:start position:0%
+sin^2 if you didn't know that
+immediately you could make the
+
+ align:start position:0%
+immediately you could make the
+ 
+
+ align:start position:0%
+immediately you could make the
+substitution for x and y in spherical
+
+ align:start position:0%
+substitution for x and y in spherical
+ 
+
+ align:start position:0%
+substitution for x and y in spherical
+coordinates and it simplifies to this so
+
+ align:start position:0%
+coordinates and it simplifies to this so
+ 
+
+ align:start position:0%
+coordinates and it simplifies to this so
+either way if you didn't know r s was
+
+ align:start position:0%
+either way if you didn't know r s was
+ 
+
+ align:start position:0%
+either way if you didn't know r s was
+this you can you can get it from just
+
+ align:start position:0%
+this you can you can get it from just
+ 
+
+ align:start position:0%
+this you can you can get it from just
+doing the substitution and then Z is
+
+ align:start position:0%
+doing the substitution and then Z is
+ 
+
+ align:start position:0%
+doing the substitution and then Z is
+going to be row cosine Fe so here I'm
+
+ align:start position:0%
+going to be row cosine Fe so here I'm
+ 
+
+ align:start position:0%
+going to be row cosine Fe so here I'm
+going to have a row cosine Fe - 1^ 2 1
+
+ align:start position:0%
+going to have a row cosine Fe - 1^ 2 1
+ 
+
+ align:start position:0%
+going to have a row cosine Fe - 1^ 2 1
+this in the spherical coordinates is
+
+ align:start position:0%
+this in the spherical coordinates is
+ 
+
+ align:start position:0%
+this in the spherical coordinates is
+describing the boundary of this entire
+
+ align:start position:0%
+describing the boundary of this entire
+ 
+
+ align:start position:0%
+describing the boundary of this entire
+sphere right and so I can actually
+
+ align:start position:0%
+sphere right and so I can actually
+ 
+
+ align:start position:0%
+sphere right and so I can actually
+simplify this it's not too hard if I
+
+ align:start position:0%
+simplify this it's not too hard if I
+ 
+
+ align:start position:0%
+simplify this it's not too hard if I
+Square this I get a little cancellation
+
+ align:start position:0%
+Square this I get a little cancellation
+ 
+
+ align:start position:0%
+Square this I get a little cancellation
+and then because I want my row to be I'm
+
+ align:start position:0%
+and then because I want my row to be I'm
+ 
+
+ align:start position:0%
+and then because I want my row to be I'm
+assuming in this region row is greater
+
+ align:start position:0%
+assuming in this region row is greater
+ 
+
+ align:start position:0%
+assuming in this region row is greater
+than zero I can do a little
+
+ align:start position:0%
+than zero I can do a little
+ 
+
+ align:start position:0%
+than zero I can do a little
+simplification I come up with the fact
+
+ align:start position:0%
+simplification I come up with the fact
+ 
+
+ align:start position:0%
+simplification I come up with the fact
+that row is equal to 2 cosine V and
+
+ align:start position:0%
+that row is equal to 2 cosine V and
+ 
+
+ align:start position:0%
+that row is equal to 2 cosine V and
+let's describe exactly where that is
+
+ align:start position:0%
+let's describe exactly where that is
+ 
+
+ align:start position:0%
+let's describe exactly where that is
+that's the entire boundary of this
+
+ align:start position:0%
+that's the entire boundary of this
+ 
+
+ align:start position:0%
+that's the entire boundary of this
+entire sphere is described by row is
+
+ align:start position:0%
+entire sphere is described by row is
+ 
+
+ align:start position:0%
+entire sphere is described by row is
+equal to 2 cosine
+
+ align:start position:0%
+equal to 2 cosine
+ 
+
+ align:start position:0%
+equal to 2 cosine
+V and so if I want to think about what
+
+ align:start position:0%
+V and so if I want to think about what
+ 
+
+ align:start position:0%
+V and so if I want to think about what
+my bounds are for row I'm actually going
+
+ align:start position:0%
+my bounds are for row I'm actually going
+ 
+
+ align:start position:0%
+my bounds are for row I'm actually going
+to grab a piece of colored
+
+ align:start position:0%
+to grab a piece of colored
+ 
+
+ align:start position:0%
+to grab a piece of colored
+chalk if I start at the origin I think
+
+ align:start position:0%
+chalk if I start at the origin I think
+ 
+
+ align:start position:0%
+chalk if I start at the origin I think
+about what is row so this say this is a
+
+ align:start position:0%
+about what is row so this say this is a
+ 
+
+ align:start position:0%
+about what is row so this say this is a
+point on the boundary of the sphere I'm
+
+ align:start position:0%
+point on the boundary of the sphere I'm
+ 
+
+ align:start position:0%
+point on the boundary of the sphere I'm
+going to start my row value whatever it
+
+ align:start position:0%
+going to start my row value whatever it
+ 
+
+ align:start position:0%
+going to start my row value whatever it
+is when it hits the plane Z equals 1 and
+
+ align:start position:0%
+is when it hits the plane Z equals 1 and
+ 
+
+ align:start position:0%
+is when it hits the plane Z equals 1 and
+I'm going to stop it when it hits the
+
+ align:start position:0%
+I'm going to stop it when it hits the
+ 
+
+ align:start position:0%
+I'm going to stop it when it hits the
+boundary of the sphere so my outer
+
+ align:start position:0%
+boundary of the sphere so my outer
+ 
+
+ align:start position:0%
+boundary of the sphere so my outer
+boundary for row is going to be this
+
+ align:start position:0%
+boundary for row is going to be this
+ 
+
+ align:start position:0%
+boundary for row is going to be this
+value it's going to be determined by
+
+ align:start position:0%
+value it's going to be determined by
+ 
+
+ align:start position:0%
+value it's going to be determined by
+Fe right and now I have to determine my
+
+ align:start position:0%
+Fe right and now I have to determine my
+ 
+
+ align:start position:0%
+Fe right and now I have to determine my
+inner boundary right and my inner
+
+ align:start position:0%
+inner boundary right and my inner
+ 
+
+ align:start position:0%
+inner boundary right and my inner
+boundary is actually quite simple it's a
+
+ align:start position:0%
+boundary is actually quite simple it's a
+ 
+
+ align:start position:0%
+boundary is actually quite simple it's a
+very simple geometric thing and so my
+
+ align:start position:0%
+very simple geometric thing and so my
+ 
+
+ align:start position:0%
+very simple geometric thing and so my
+inner boundary deals with the fact that
+
+ align:start position:0%
+inner boundary deals with the fact that
+ 
+
+ align:start position:0%
+inner boundary deals with the fact that
+if this is my plane Z equals 1 and I
+
+ align:start position:0%
+if this is my plane Z equals 1 and I
+ 
+
+ align:start position:0%
+if this is my plane Z equals 1 and I
+look at this triangle I make right
+
+ align:start position:0%
+look at this triangle I make right
+ 
+
+ align:start position:0%
+look at this triangle I make right
+here this this angle down here the
+
+ align:start position:0%
+here this this angle down here the
+ 
+
+ align:start position:0%
+here this this angle down here the
+bottom angle is Fe and this is a right
+
+ align:start position:0%
+bottom angle is Fe and this is a right
+ 
+
+ align:start position:0%
+bottom angle is Fe and this is a right
+angle and this is the row value I'm
+
+ align:start position:0%
+angle and this is the row value I'm
+ 
+
+ align:start position:0%
+angle and this is the row value I'm
+interested in is this hypotenuse right I
+
+ align:start position:0%
+interested in is this hypotenuse right I
+ 
+
+ align:start position:0%
+interested in is this hypotenuse right I
+need to figure out what the length of
+
+ align:start position:0%
+need to figure out what the length of
+ 
+
+ align:start position:0%
+need to figure out what the length of
+this is right here and you can see it
+
+ align:start position:0%
+this is right here and you can see it
+ 
+
+ align:start position:0%
+this is right here and you can see it
+right away from just the fact that this
+
+ align:start position:0%
+right away from just the fact that this
+ 
+
+ align:start position:0%
+right away from just the fact that this
+is Fe is is this little in this angle
+
+ align:start position:0%
+is Fe is is this little in this angle
+ 
+
+ align:start position:0%
+is Fe is is this little in this angle
+here you get Fe is secant sorry Fe row
+
+ align:start position:0%
+here you get Fe is secant sorry Fe row
+ 
+
+ align:start position:0%
+here you get Fe is secant sorry Fe row
+is secant Fe so the the bottom boundary
+
+ align:start position:0%
+is secant Fe so the the bottom boundary
+ 
+
+ align:start position:0%
+is secant Fe so the the bottom boundary
+comes from just simple geometry you get
+
+ align:start position:0%
+comes from just simple geometry you get
+ 
+
+ align:start position:0%
+comes from just simple geometry you get
+this length is one here so you get row
+
+ align:start position:0%
+this length is one here so you get row
+ 
+
+ align:start position:0%
+this length is one here so you get row
+is equal to secant Fe right this length
+
+ align:start position:0%
+is equal to secant Fe right this length
+ 
+
+ align:start position:0%
+is equal to secant Fe right this length
+here is one this is the row I'm
+
+ align:start position:0%
+here is one this is the row I'm
+ 
+
+ align:start position:0%
+here is one this is the row I'm
+interested in the blue part here so row
+
+ align:start position:0%
+interested in the blue part here so row
+ 
+
+ align:start position:0%
+interested in the blue part here so row
+is equal to secant Fe as the lower bound
+
+ align:start position:0%
+is equal to secant Fe as the lower bound
+ 
+
+ align:start position:0%
+is equal to secant Fe as the lower bound
+and it's equal to two cosine Fe as the
+
+ align:start position:0%
+and it's equal to two cosine Fe as the
+ 
+
+ align:start position:0%
+and it's equal to two cosine Fe as the
+upper bound okay and the thing I want to
+
+ align:start position:0%
+upper bound okay and the thing I want to
+ 
+
+ align:start position:0%
+upper bound okay and the thing I want to
+be careful of is I'm not supposed to
+
+ align:start position:0%
+be careful of is I'm not supposed to
+ 
+
+ align:start position:0%
+be careful of is I'm not supposed to
+include it won't matter for the integral
+
+ align:start position:0%
+include it won't matter for the integral
+ 
+
+ align:start position:0%
+include it won't matter for the integral
+but I'm not supposed to include the
+
+ align:start position:0%
+but I'm not supposed to include the
+ 
+
+ align:start position:0%
+but I'm not supposed to include the
+plane so row is going to be let me write
+
+ align:start position:0%
+plane so row is going to be let me write
+ 
+
+ align:start position:0%
+plane so row is going to be let me write
+this and make sure row is going to be
+
+ align:start position:0%
+this and make sure row is going to be
+ 
+
+ align:start position:0%
+this and make sure row is going to be
+greater than secant
+
+ align:start position:0%
+greater than secant
+ 
+
+ align:start position:0%
+greater than secant
+Fe and it's going to be less than or
+
+ align:start position:0%
+Fe and it's going to be less than or
+ 
+
+ align:start position:0%
+Fe and it's going to be less than or
+equal to 2 cosine Fe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right so let me double check and
+
+ align:start position:0%
+right right so let me double check and
+ 
+
+ align:start position:0%
+right right so let me double check and
+make sure I didn't make a geometry
+
+ align:start position:0%
+make sure I didn't make a geometry
+ 
+
+ align:start position:0%
+make sure I didn't make a geometry
+mistake here just to be sure this
+
+ align:start position:0%
+mistake here just to be sure this
+ 
+
+ align:start position:0%
+mistake here just to be sure this
+picture tells me that cosine Fe is equal
+
+ align:start position:0%
+picture tells me that cosine Fe is equal
+ 
+
+ align:start position:0%
+picture tells me that cosine Fe is equal
+to 1 over row that's good so row is
+
+ align:start position:0%
+to 1 over row that's good so row is
+ 
+
+ align:start position:0%
+to 1 over row that's good so row is
+equal to one over cosine Fe so I get
+
+ align:start position:0%
+equal to one over cosine Fe so I get
+ 
+
+ align:start position:0%
+equal to one over cosine Fe so I get
+secant fee there so my row values go all
+
+ align:start position:0%
+secant fee there so my row values go all
+ 
+
+ align:start position:0%
+secant fee there so my row values go all
+the way they start at the secant fee
+
+ align:start position:0%
+the way they start at the secant fee
+ 
+
+ align:start position:0%
+the way they start at the secant fee
+length and they go to the two cosine Fe
+
+ align:start position:0%
+length and they go to the two cosine Fe
+ 
+
+ align:start position:0%
+length and they go to the two cosine Fe
+length I know I maybe I'm beating a dead
+
+ align:start position:0%
+length I know I maybe I'm beating a dead
+ 
+
+ align:start position:0%
+length I know I maybe I'm beating a dead
+horse here but I want to make sure we
+
+ align:start position:0%
+horse here but I want to make sure we
+ 
+
+ align:start position:0%
+horse here but I want to make sure we
+understand where the row values are
+
+ align:start position:0%
+understand where the row values are
+ 
+
+ align:start position:0%
+understand where the row values are
+coming from so have all the bounds I
+
+ align:start position:0%
+coming from so have all the bounds I
+ 
+
+ align:start position:0%
+coming from so have all the bounds I
+need now I have the Theta bounds and I
+
+ align:start position:0%
+need now I have the Theta bounds and I
+ 
+
+ align:start position:0%
+need now I have the Theta bounds and I
+have the and the F bounds and the row
+
+ align:start position:0%
+have the and the F bounds and the row
+ 
+
+ align:start position:0%
+have the and the F bounds and the row
+bounds now you notice that Theta and Fe
+
+ align:start position:0%
+bounds now you notice that Theta and Fe
+ 
+
+ align:start position:0%
+bounds now you notice that Theta and Fe
+don't depend on uh don't depend on the
+
+ align:start position:0%
+don't depend on uh don't depend on the
+ 
+
+ align:start position:0%
+don't depend on uh don't depend on the
+other variables but row depends on Fe so
+
+ align:start position:0%
+other variables but row depends on Fe so
+ 
+
+ align:start position:0%
+other variables but row depends on Fe so
+we're going to have to integrate that
+
+ align:start position:0%
+we're going to have to integrate that
+ 
+
+ align:start position:0%
+we're going to have to integrate that
+first so now we can deal with Part
+
+ align:start position:0%
+first so now we can deal with Part
+ 
+
+ align:start position:0%
+first so now we can deal with Part
+B Part B let's come back over remind
+
+ align:start position:0%
+B Part B let's come back over remind
+ 
+
+ align:start position:0%
+B Part B let's come back over remind
+ourselves what it said it said set up
+
+ align:start position:0%
+ourselves what it said it said set up
+ 
+
+ align:start position:0%
+ourselves what it said it said set up
+the integral for the average distance of
+
+ align:start position:0%
+the integral for the average distance of
+ 
+
+ align:start position:0%
+the integral for the average distance of
+a point in D from the origin so I'm
+
+ align:start position:0%
+a point in D from the origin so I'm
+ 
+
+ align:start position:0%
+a point in D from the origin so I'm
+taking the average value of a function
+
+ align:start position:0%
+taking the average value of a function
+ 
+
+ align:start position:0%
+taking the average value of a function
+function what is that function I'm
+
+ align:start position:0%
+function what is that function I'm
+ 
+
+ align:start position:0%
+function what is that function I'm
+averaging how do I find the distance
+
+ align:start position:0%
+averaging how do I find the distance
+ 
+
+ align:start position:0%
+averaging how do I find the distance
+from the origin well the distance from
+
+ align:start position:0%
+from the origin well the distance from
+ 
+
+ align:start position:0%
+from the origin well the distance from
+the origin is a great function to have
+
+ align:start position:0%
+the origin is a great function to have
+ 
+
+ align:start position:0%
+the origin is a great function to have
+in spherical coordinates because it's
+
+ align:start position:0%
+in spherical coordinates because it's
+ 
+
+ align:start position:0%
+in spherical coordinates because it's
+just row so the function I'm supposed to
+
+ align:start position:0%
+just row so the function I'm supposed to
+ 
+
+ align:start position:0%
+just row so the function I'm supposed to
+average over is the function Row in
+
+ align:start position:0%
+average over is the function Row in
+ 
+
+ align:start position:0%
+average over is the function Row in
+spherical coordinates that's the
+
+ align:start position:0%
+spherical coordinates that's the
+ 
+
+ align:start position:0%
+spherical coordinates that's the
+function so let me write down what we're
+
+ align:start position:0%
+function so let me write down what we're
+ 
+
+ align:start position:0%
+function so let me write down what we're
+going to have here so Part
+
+ align:start position:0%
+going to have here so Part
+ 
+
+ align:start position:0%
+going to have here so Part
+B the average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance is going to equal well it's
+
+ align:start position:0%
+distance is going to equal well it's
+ 
+
+ align:start position:0%
+distance is going to equal well it's
+going to equal 1 / the volume of
+
+ align:start position:0%
+going to equal 1 / the volume of
+ 
+
+ align:start position:0%
+going to equal 1 / the volume of
+D times the triple integral over
+
+ align:start position:0%
+D times the triple integral over
+ 
+
+ align:start position:0%
+D times the triple integral over
+d right of the function
+
+ align:start position:0%
+d right of the function
+ 
+
+ align:start position:0%
+d right of the function
+row DV okay so now I have to write DV in
+
+ align:start position:0%
+row DV okay so now I have to write DV in
+ 
+
+ align:start position:0%
+row DV okay so now I have to write DV in
+the spherical coordinates and I have to
+
+ align:start position:0%
+the spherical coordinates and I have to
+ 
+
+ align:start position:0%
+the spherical coordinates and I have to
+write D in the spherical coordinate
+
+ align:start position:0%
+write D in the spherical coordinate
+ 
+
+ align:start position:0%
+write D in the spherical coordinate
+bounds and then I know I have to figure
+
+ align:start position:0%
+bounds and then I know I have to figure
+ 
+
+ align:start position:0%
+bounds and then I know I have to figure
+out the volume of D so we're going to
+
+ align:start position:0%
+out the volume of D so we're going to
+ 
+
+ align:start position:0%
+out the volume of D so we're going to
+figure out each of these things and then
+
+ align:start position:0%
+figure out each of these things and then
+ 
+
+ align:start position:0%
+figure out each of these things and then
+we'll be done all right so what is first
+
+ align:start position:0%
+we'll be done all right so what is first
+ 
+
+ align:start position:0%
+we'll be done all right so what is first
+what is the volume of D well the volume
+
+ align:start position:0%
+what is the volume of D well the volume
+ 
+
+ align:start position:0%
+what is the volume of D well the volume
+of D let's think about what it is it's
+
+ align:start position:0%
+of D let's think about what it is it's
+ 
+
+ align:start position:0%
+of D let's think about what it is it's
+it's a sphere of radius
+
+ align:start position:0%
+it's a sphere of radius
+ 
+
+ align:start position:0%
+it's a sphere of radius
+one and so the volume of a sphere of
+
+ align:start position:0%
+one and so the volume of a sphere of
+ 
+
+ align:start position:0%
+one and so the volume of a sphere of
+radius 1 is 4 4/3 pi R cubed and I want
+
+ align:start position:0%
+radius 1 is 4 4/3 pi R cubed and I want
+ 
+
+ align:start position:0%
+radius 1 is 4 4/3 pi R cubed and I want
+half of that so I want 2/3 since my
+
+ align:start position:0%
+half of that so I want 2/3 since my
+ 
+
+ align:start position:0%
+half of that so I want 2/3 since my
+radius is one I just have to do 2/3 Pi
+
+ align:start position:0%
+radius is one I just have to do 2/3 Pi
+ 
+
+ align:start position:0%
+radius is one I just have to do 2/3 Pi
+so I just the first part is 1 / 2/3 Pi
+
+ align:start position:0%
+so I just the first part is 1 / 2/3 Pi
+ 
+
+ align:start position:0%
+so I just the first part is 1 / 2/3 Pi
+that's the volume of a half sphere of
+
+ align:start position:0%
+that's the volume of a half sphere of
+ 
+
+ align:start position:0%
+that's the volume of a half sphere of
+radius one and now let's
+
+ align:start position:0%
+radius one and now let's
+ 
+
+ align:start position:0%
+radius one and now let's
+integrate
+
+ align:start position:0%
+integrate
+ 
+
+ align:start position:0%
+integrate
+so I'll leave a little space to write my
+
+ align:start position:0%
+so I'll leave a little space to write my
+ 
+
+ align:start position:0%
+so I'll leave a little space to write my
+bounds DV I'm going to write the bounds
+
+ align:start position:0%
+bounds DV I'm going to write the bounds
+ 
+
+ align:start position:0%
+bounds DV I'm going to write the bounds
+last after I have everything in order
+
+ align:start position:0%
+last after I have everything in order
+ 
+
+ align:start position:0%
+last after I have everything in order
+over here DV is row s sin Fe d r d Theta
+
+ align:start position:0%
+over here DV is row s sin Fe d r d Theta
+ 
+
+ align:start position:0%
+over here DV is row s sin Fe d r d Theta
+D Fe so I'm going to end up with a row
+
+ align:start position:0%
+D Fe so I'm going to end up with a row
+ 
+
+ align:start position:0%
+D Fe so I'm going to end up with a row
+cubed sin v d Row D Theta D
+
+ align:start position:0%
+cubed sin v d Row D Theta D
+ 
+
+ align:start position:0%
+cubed sin v d Row D Theta D
+Fe right the DV gave me an extra row
+
+ align:start position:0%
+Fe right the DV gave me an extra row
+ 
+
+ align:start position:0%
+Fe right the DV gave me an extra row
+squared and a sign Fe and then this
+
+ align:start position:0%
+squared and a sign Fe and then this
+ 
+
+ align:start position:0%
+squared and a sign Fe and then this
+these are the that that whole part is DV
+
+ align:start position:0%
+these are the that that whole part is DV
+ 
+
+ align:start position:0%
+these are the that that whole part is DV
+sorry and then I keep one row from the
+
+ align:start position:0%
+sorry and then I keep one row from the
+ 
+
+ align:start position:0%
+sorry and then I keep one row from the
+fact that the distance function is is
+
+ align:start position:0%
+fact that the distance function is is
+ 
+
+ align:start position:0%
+fact that the distance function is is
+row and so I get a row cubed there so
+
+ align:start position:0%
+row and so I get a row cubed there so
+ 
+
+ align:start position:0%
+row and so I get a row cubed there so
+hopefully that makes sense now D row I
+
+ align:start position:0%
+hopefully that makes sense now D row I
+ 
+
+ align:start position:0%
+hopefully that makes sense now D row I
+know the bounds are secant Fe to 2
+
+ align:start position:0%
+know the bounds are secant Fe to 2
+ 
+
+ align:start position:0%
+know the bounds are secant Fe to 2
+cosine
+
+ align:start position:0%
+cosine
+ 
+
+ align:start position:0%
+cosine
+Fe D Theta my bounds are 0 to 2 pi and D
+
+ align:start position:0%
+Fe D Theta my bounds are 0 to 2 pi and D
+ 
+
+ align:start position:0%
+Fe D Theta my bounds are 0 to 2 pi and D
+Fe my bounds were 0 to Pi
+
+ align:start position:0%
+Fe my bounds were 0 to Pi
+ 
+
+ align:start position:0%
+Fe my bounds were 0 to Pi
+over4 and so that actually I didn't make
+
+ align:start position:0%
+over4 and so that actually I didn't make
+ 
+
+ align:start position:0%
+over4 and so that actually I didn't make
+you evaluate it I'm just making you set
+
+ align:start position:0%
+you evaluate it I'm just making you set
+ 
+
+ align:start position:0%
+you evaluate it I'm just making you set
+it up that actually is the solution we
+
+ align:start position:0%
+it up that actually is the solution we
+ 
+
+ align:start position:0%
+it up that actually is the solution we
+wanted for Part B I wanted to average
+
+ align:start position:0%
+wanted for Part B I wanted to average
+ 
+
+ align:start position:0%
+wanted for Part B I wanted to average
+the distance from any point in D to the
+
+ align:start position:0%
+the distance from any point in D to the
+ 
+
+ align:start position:0%
+the distance from any point in D to the
+origin so I just took the average value
+
+ align:start position:0%
+origin so I just took the average value
+ 
+
+ align:start position:0%
+origin so I just took the average value
+of the function row over that region D
+
+ align:start position:0%
+of the function row over that region D
+ 
+
+ align:start position:0%
+of the function row over that region D
+and so that's how you finish that up so
+
+ align:start position:0%
+and so that's how you finish that up so
+ 
+
+ align:start position:0%
+and so that's how you finish that up so
+this problem basically we want you to
+
+ align:start position:0%
+this problem basically we want you to
+ 
+
+ align:start position:0%
+this problem basically we want you to
+get really familiar with how to do some
+
+ align:start position:0%
+get really familiar with how to do some
+ 
+
+ align:start position:0%
+get really familiar with how to do some
+things in in these spherical coordinates
+
+ align:start position:0%
+things in in these spherical coordinates
+ 
+
+ align:start position:0%
+things in in these spherical coordinates
+which are sometimes a little hard to do
+
+ align:start position:0%
+which are sometimes a little hard to do
+ 
+
+ align:start position:0%
+which are sometimes a little hard to do
+but if you notice what we were doing and
+
+ align:start position:0%
+but if you notice what we were doing and
+ 
+
+ align:start position:0%
+but if you notice what we were doing and
+trying to figure F out the bounds in
+
+ align:start position:0%
+trying to figure F out the bounds in
+ 
+
+ align:start position:0%
+trying to figure F out the bounds in
+particular trying to figure out row we
+
+ align:start position:0%
+particular trying to figure out row we
+ 
+
+ align:start position:0%
+particular trying to figure out row we
+took what we knew in the XYZ coordinates
+
+ align:start position:0%
+took what we knew in the XYZ coordinates
+ 
+
+ align:start position:0%
+took what we knew in the XYZ coordinates
+about certain relationships and then we
+
+ align:start position:0%
+about certain relationships and then we
+ 
+
+ align:start position:0%
+about certain relationships and then we
+we replace the XYZ values by the values
+
+ align:start position:0%
+we replace the XYZ values by the values
+ 
+
+ align:start position:0%
+we replace the XYZ values by the values
+in terms of row and and Theta and Fe and
+
+ align:start position:0%
+in terms of row and and Theta and Fe and
+ 
+
+ align:start position:0%
+in terms of row and and Theta and Fe and
+you can simplify to figure out the
+
+ align:start position:0%
+you can simplify to figure out the
+ 
+
+ align:start position:0%
+you can simplify to figure out the
+relationships you have between row and
+
+ align:start position:0%
+relationships you have between row and
+ 
+
+ align:start position:0%
+relationships you have between row and
+Theta and Fe for say the boundary value
+
+ align:start position:0%
+Theta and Fe for say the boundary value
+ 
+
+ align:start position:0%
+Theta and Fe for say the boundary value
+so that was kind of one of the
+
+ align:start position:0%
+so that was kind of one of the
+ 
+
+ align:start position:0%
+so that was kind of one of the
+techniques we were using there and
+
+ align:start position:0%
+techniques we were using there and
+ 
+
+ align:start position:0%
+techniques we were using there and
+hopefully the geometric understanding of
+
+ align:start position:0%
+hopefully the geometric understanding of
+ 
+
+ align:start position:0%
+hopefully the geometric understanding of
+why these angles go from 0 to 2 pi and 0
+
+ align:start position:0%
+why these angles go from 0 to 2 pi and 0
+ 
+
+ align:start position:0%
+why these angles go from 0 to 2 pi and 0
+to pi over 4 is clear and actually this
+
+ align:start position:0%
+to pi over 4 is clear and actually this
+ 
+
+ align:start position:0%
+to pi over 4 is clear and actually this
+should remind you the fact that this is
+
+ align:start position:0%
+should remind you the fact that this is
+ 
+
+ align:start position:0%
+should remind you the fact that this is
+row equal 2 cosine Fe should remind you
+
+ align:start position:0%
+row equal 2 cosine Fe should remind you
+ 
+
+ align:start position:0%
+row equal 2 cosine Fe should remind you
+of the two dimensional case where you
+
+ align:start position:0%
+of the two dimensional case where you
+ 
+
+ align:start position:0%
+of the two dimensional case where you
+had some problem like R equals 2 cosine
+
+ align:start position:0%
+had some problem like R equals 2 cosine
+ 
+
+ align:start position:0%
+had some problem like R equals 2 cosine
+Theta and that Drew a circle off center
+
+ align:start position:0%
+Theta and that Drew a circle off center
+ 
+
+ align:start position:0%
+Theta and that Drew a circle off center
+from the origin it's the same it's the
+
+ align:start position:0%
+from the origin it's the same it's the
+ 
+
+ align:start position:0%
+from the origin it's the same it's the
+analogous kind of thing happening here
+
+ align:start position:0%
+analogous kind of thing happening here
+ 
+
+ align:start position:0%
+analogous kind of thing happening here
+so maybe I should stop there before I
+
+ align:start position:0%
+so maybe I should stop there before I
+ 
+
+ align:start position:0%
+so maybe I should stop there before I
+say too many things but the again the
+
+ align:start position:0%
+say too many things but the again the
+ 
+
+ align:start position:0%
+say too many things but the again the
+object of this was just to get really
+
+ align:start position:0%
+object of this was just to get really
+ 
+
+ align:start position:0%
+object of this was just to get really
+comfortable with spherical coordinates
+
+ align:start position:0%
+comfortable with spherical coordinates
+ 
+
+ align:start position:0%
+comfortable with spherical coordinates
+and I hope it's helped you I'll stop
+
+ align:start position:0%
+and I hope it's helped you I'll stop
+ 
+
+ align:start position:0%
+and I hope it's helped you I'll stop
+there
\ No newline at end of file
diff --git a/RpeaxINv2Yk.txt b/RpeaxINv2Yk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a4db0075dff6346d488d89474eeb0c440af3f3c
--- /dev/null
+++ b/RpeaxINv2Yk.txt
@@ -0,0 +1,9963 @@
+align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um so I've written up on the board as
+
+ align:start position:0%
+um so I've written up on the board as
+ 
+
+ align:start position:0%
+um so I've written up on the board as
+usual the topics uh or some of the main
+
+ align:start position:0%
+usual the topics uh or some of the main
+ 
+
+ align:start position:0%
+usual the topics uh or some of the main
+topics uh for this lecture uh it it
+
+ align:start position:0%
+topics uh for this lecture uh it it
+ 
+
+ align:start position:0%
+topics uh for this lecture uh it it
+certainly will connect to the next one
+
+ align:start position:0%
+certainly will connect to the next one
+ 
+
+ align:start position:0%
+certainly will connect to the next one
+uh so this is uh least squares
+
+ align:start position:0%
+uh so this is uh least squares
+ 
+
+ align:start position:0%
+uh so this is uh least squares
+estimation and uh uh so I'm interested
+
+ align:start position:0%
+estimation and uh uh so I'm interested
+ 
+
+ align:start position:0%
+estimation and uh uh so I'm interested
+here in waiting in the waiting Matrix
+
+ align:start position:0%
+here in waiting in the waiting Matrix
+ 
+
+ align:start position:0%
+here in waiting in the waiting Matrix
+the the role of The covariance Matrix
+
+ align:start position:0%
+the the role of The covariance Matrix
+ 
+
+ align:start position:0%
+the the role of The covariance Matrix
+and in the recursive
+
+ align:start position:0%
+and in the recursive
+ 
+
+ align:start position:0%
+and in the recursive
+part uh but
+
+ align:start position:0%
+part uh but
+ 
+
+ align:start position:0%
+part uh but
+the number of parameters the parameters
+
+ align:start position:0%
+the number of parameters the parameters
+ 
+
+ align:start position:0%
+the number of parameters the parameters
+I'm looking for you hat well I'm looking
+
+ align:start position:0%
+I'm looking for you hat well I'm looking
+ 
+
+ align:start position:0%
+I'm looking for you hat well I'm looking
+for you and I settle for you
+
+ align:start position:0%
+for you and I settle for you
+ 
+
+ align:start position:0%
+for you and I settle for you
+hat is not changing I mean it's is
+
+ align:start position:0%
+hat is not changing I mean it's is
+ 
+
+ align:start position:0%
+hat is not changing I mean it's is
+improving but but uh
+
+ align:start position:0%
+improving but but uh
+ 
+
+ align:start position:0%
+improving but but uh
+we're we're at a fixed time so to speak
+
+ align:start position:0%
+we're we're at a fixed time so to speak
+ 
+
+ align:start position:0%
+we're we're at a fixed time so to speak
+so we've got these various steps Le
+
+ align:start position:0%
+so we've got these various steps Le
+ 
+
+ align:start position:0%
+so we've got these various steps Le
+squares hi I I think I started a moment
+
+ align:start position:0%
+squares hi I I think I started a moment
+ 
+
+ align:start position:0%
+squares hi I I think I started a moment
+early but I've written I haven't
+
+ align:start position:0%
+early but I've written I haven't
+ 
+
+ align:start position:0%
+early but I've written I haven't
+said anything yet that isn't already
+
+ align:start position:0%
+said anything yet that isn't already
+ 
+
+ align:start position:0%
+said anything yet that isn't already
+written um so this we know
+
+ align:start position:0%
+written um so this we know
+ 
+
+ align:start position:0%
+written um so this we know
+about this this this waiting Matrix I'll
+
+ align:start position:0%
+about this this this waiting Matrix I'll
+ 
+
+ align:start position:0%
+about this this this waiting Matrix I'll
+introduce early and then this recursive
+
+ align:start position:0%
+introduce early and then this recursive
+ 
+
+ align:start position:0%
+introduce early and then this recursive
+aspect so that's the those are the
+
+ align:start position:0%
+aspect so that's the those are the
+ 
+
+ align:start position:0%
+aspect so that's the those are the
+themes of this lecture and then uh on
+
+ align:start position:0%
+themes of this lecture and then uh on
+ 
+
+ align:start position:0%
+themes of this lecture and then uh on
+into the next lecture we'll come a
+
+ align:start position:0%
+into the next lecture we'll come a
+ 
+
+ align:start position:0%
+into the next lecture we'll come a
+dynamic problem in which the U that
+
+ align:start position:0%
+dynamic problem in which the U that
+ 
+
+ align:start position:0%
+dynamic problem in which the U that
+we're looking for is
+
+ align:start position:0%
+we're looking for is
+ 
+
+ align:start position:0%
+we're looking for is
+changing so you know something is moving
+
+ align:start position:0%
+changing so you know something is moving
+ 
+
+ align:start position:0%
+changing so you know something is moving
+we're tracking uh uh a missile whatever
+
+ align:start position:0%
+we're tracking uh uh a missile whatever
+ 
+
+ align:start position:0%
+we're tracking uh uh a missile whatever
+we're doing the the we know something
+
+ align:start position:0%
+we're doing the the we know something
+ 
+
+ align:start position:0%
+we're doing the the we know something
+about the connection between the present
+
+ align:start position:0%
+about the connection between the present
+ 
+
+ align:start position:0%
+about the connection between the present
+State and the previous state but they're
+
+ align:start position:0%
+State and the previous state but they're
+ 
+
+ align:start position:0%
+State and the previous state but they're
+not the same okay and may I say I regret
+
+ align:start position:0%
+not the same okay and may I say I regret
+ 
+
+ align:start position:0%
+not the same okay and may I say I regret
+that kalman's name starts with k because
+
+ align:start position:0%
+that kalman's name starts with k because
+ 
+
+ align:start position:0%
+that kalman's name starts with k because
+I've been using K so widely for uh our a
+
+ align:start position:0%
+I've been using K so widely for uh our a
+ 
+
+ align:start position:0%
+I've been using K so widely for uh our a
+transpose CA Matrix but maybe uh today
+
+ align:start position:0%
+transpose CA Matrix but maybe uh today
+ 
+
+ align:start position:0%
+transpose CA Matrix but maybe uh today
+uh I'll tend to write out a transpose CA
+
+ align:start position:0%
+uh I'll tend to write out a transpose CA
+ 
+
+ align:start position:0%
+uh I'll tend to write out a transpose CA
+or a transpose Sigma inverse a that will
+
+ align:start position:0%
+or a transpose Sigma inverse a that will
+ 
+
+ align:start position:0%
+or a transpose Sigma inverse a that will
+be the Matrix C that's appropriate so
+
+ align:start position:0%
+be the Matrix C that's appropriate so
+ 
+
+ align:start position:0%
+be the Matrix C that's appropriate so
+I'll I'll stay with the of course the
+
+ align:start position:0%
+I'll I'll stay with the of course the
+ 
+
+ align:start position:0%
+I'll I'll stay with the of course the
+world convention that K stands for the
+
+ align:start position:0%
+world convention that K stands for the
+ 
+
+ align:start position:0%
+world convention that K stands for the
+this uh gain Matrix named after
+
+ align:start position:0%
+this uh gain Matrix named after
+ 
+
+ align:start position:0%
+this uh gain Matrix named after
+calman and uh and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll uh
+
+ align:start position:0%
+I'll uh
+ 
+
+ align:start position:0%
+I'll uh
+come to that maybe can I say just a few
+
+ align:start position:0%
+come to that maybe can I say just a few
+ 
+
+ align:start position:0%
+come to that maybe can I say just a few
+words in advance before I
+
+ align:start position:0%
+words in advance before I
+ 
+
+ align:start position:0%
+words in advance before I
+start um well one I I want to say a few
+
+ align:start position:0%
+start um well one I I want to say a few
+ 
+
+ align:start position:0%
+start um well one I I want to say a few
+final things about the
+
+ align:start position:0%
+final things about the
+ 
+
+ align:start position:0%
+final things about the
+SVD or maybe not final but a few just a
+
+ align:start position:0%
+SVD or maybe not final but a few just a
+ 
+
+ align:start position:0%
+SVD or maybe not final but a few just a
+supplementary like a short recap partly
+
+ align:start position:0%
+supplementary like a short recap partly
+ 
+
+ align:start position:0%
+supplementary like a short recap partly
+because I feel it's always good to for
+
+ align:start position:0%
+because I feel it's always good to for
+ 
+
+ align:start position:0%
+because I feel it's always good to for
+the previous lecture to kind of get come
+
+ align:start position:0%
+the previous lecture to kind of get come
+ 
+
+ align:start position:0%
+the previous lecture to kind of get come
+back again uh uh at the start uh
+
+ align:start position:0%
+back again uh uh at the start uh
+ 
+
+ align:start position:0%
+back again uh uh at the start uh
+um secondly to say that this
+
+ align:start position:0%
+um secondly to say that this
+ 
+
+ align:start position:0%
+um secondly to say that this
+area is um well first to say that I'm
+
+ align:start position:0%
+area is um well first to say that I'm
+ 
+
+ align:start position:0%
+area is um well first to say that I'm
+not an expert in it and that I had a
+
+ align:start position:0%
+not an expert in it and that I had a
+ 
+
+ align:start position:0%
+not an expert in it and that I had a
+wild time this morning uh I feel I left
+
+ align:start position:0%
+wild time this morning uh I feel I left
+ 
+
+ align:start position:0%
+wild time this morning uh I feel I left
+home with a head packed full of formulas
+
+ align:start position:0%
+home with a head packed full of formulas
+ 
+
+ align:start position:0%
+home with a head packed full of formulas
+from for the calman filter and
+
+ align:start position:0%
+from for the calman filter and
+ 
+
+ align:start position:0%
+from for the calman filter and
+um uh but one and the formulas are quite
+
+ align:start position:0%
+um uh but one and the formulas are quite
+ 
+
+ align:start position:0%
+um uh but one and the formulas are quite
+wonderful uh and I'll try to organize
+
+ align:start position:0%
+wonderful uh and I'll try to organize
+ 
+
+ align:start position:0%
+wonderful uh and I'll try to organize
+them here but I just have to say that uh
+
+ align:start position:0%
+them here but I just have to say that uh
+ 
+
+ align:start position:0%
+them here but I just have to say that uh
+every exposition of the calman filter
+
+ align:start position:0%
+every exposition of the calman filter
+ 
+
+ align:start position:0%
+every exposition of the calman filter
+has its own way of reaching these
+
+ align:start position:0%
+has its own way of reaching these
+ 
+
+ align:start position:0%
+has its own way of reaching these
+formulas and they always seem
+
+ align:start position:0%
+formulas and they always seem
+ 
+
+ align:start position:0%
+formulas and they always seem
+confusing uh and then the next person
+
+ align:start position:0%
+confusing uh and then the next person
+ 
+
+ align:start position:0%
+confusing uh and then the next person
+tries his his or her own way and feels
+
+ align:start position:0%
+tries his his or her own way and feels
+ 
+
+ align:start position:0%
+tries his his or her own way and feels
+okay now I've finally got it all clear
+
+ align:start position:0%
+okay now I've finally got it all clear
+ 
+
+ align:start position:0%
+okay now I've finally got it all clear
+but of course the next reader says not
+
+ align:start position:0%
+but of course the next reader says not
+ 
+
+ align:start position:0%
+but of course the next reader says not
+the best way and do it again so that
+
+ align:start position:0%
+the best way and do it again so that
+ 
+
+ align:start position:0%
+the best way and do it again so that
+applies uh to myself too um so there's
+
+ align:start position:0%
+applies uh to myself too um so there's
+ 
+
+ align:start position:0%
+applies uh to myself too um so there's
+not uh there's a just a little about the
+
+ align:start position:0%
+not uh there's a just a little about the
+ 
+
+ align:start position:0%
+not uh there's a just a little about the
+calman filter in the course textbook the
+
+ align:start position:0%
+calman filter in the course textbook the
+ 
+
+ align:start position:0%
+calman filter in the course textbook the
+applied math book uh then the latest
+
+ align:start position:0%
+applied math book uh then the latest
+ 
+
+ align:start position:0%
+applied math book uh then the latest
+book that I got involved with was about
+
+ align:start position:0%
+book that I got involved with was about
+ 
+
+ align:start position:0%
+book that I got involved with was about
+um was this one with my friend Kai Bor
+
+ align:start position:0%
+um was this one with my friend Kai Bor
+ 
+
+ align:start position:0%
+um was this one with my friend Kai Bor
+uh it starts with linear algebra so that
+
+ align:start position:0%
+uh it starts with linear algebra so that
+ 
+
+ align:start position:0%
+uh it starts with linear algebra so that
+those chapters are very familiar his
+
+ align:start position:0%
+those chapters are very familiar his
+ 
+
+ align:start position:0%
+those chapters are very familiar his
+subject is geodyssey and then the third
+
+ align:start position:0%
+subject is geodyssey and then the third
+ 
+
+ align:start position:0%
+subject is geodyssey and then the third
+part of of the book is about GPS global
+
+ align:start position:0%
+part of of the book is about GPS global
+ 
+
+ align:start position:0%
+part of of the book is about GPS global
+positioning well for that filtering is
+
+ align:start position:0%
+positioning well for that filtering is
+ 
+
+ align:start position:0%
+positioning well for that filtering is
+all is highly important so had to learn
+
+ align:start position:0%
+all is highly important so had to learn
+ 
+
+ align:start position:0%
+all is highly important so had to learn
+about the calman filter and the final
+
+ align:start position:0%
+about the calman filter and the final
+ 
+
+ align:start position:0%
+about the calman filter and the final
+chapter of that book is now or will be
+
+ align:start position:0%
+chapter of that book is now or will be
+ 
+
+ align:start position:0%
+chapter of that book is now or will be
+this afternoon or early tomorrow morning
+
+ align:start position:0%
+this afternoon or early tomorrow morning
+ 
+
+ align:start position:0%
+this afternoon or early tomorrow morning
+on our website so I felt I wanted to
+
+ align:start position:0%
+on our website so I felt I wanted to
+ 
+
+ align:start position:0%
+on our website so I felt I wanted to
+give you
+
+ align:start position:0%
+give you
+ 
+
+ align:start position:0%
+give you
+uh since we couldn't get all the the
+
+ align:start position:0%
+uh since we couldn't get all the the
+ 
+
+ align:start position:0%
+uh since we couldn't get all the the
+board isn't big enough for all the
+
+ align:start position:0%
+board isn't big enough for all the
+ 
+
+ align:start position:0%
+board isn't big enough for all the
+formulas of of the calman filter but
+
+ align:start position:0%
+formulas of of the calman filter but
+ 
+
+ align:start position:0%
+formulas of of the calman filter but
+uh so that's this chapter 17 cman
+
+ align:start position:0%
+uh so that's this chapter 17 cman
+ 
+
+ align:start position:0%
+uh so that's this chapter 17 cman
+filters from that book is on the
+
+ align:start position:0%
+filters from that book is on the
+ 
+
+ align:start position:0%
+filters from that book is on the
+website and and really uh expresses
+
+ align:start position:0%
+website and and really uh expresses
+ 
+
+ align:start position:0%
+website and and really uh expresses
+my uh starting
+
+ align:start position:0%
+my uh starting
+ 
+
+ align:start position:0%
+my uh starting
+point so what should I say about that
+
+ align:start position:0%
+point so what should I say about that
+ 
+
+ align:start position:0%
+point so what should I say about that
+and I say it here uh there are several
+
+ align:start position:0%
+and I say it here uh there are several
+ 
+
+ align:start position:0%
+and I say it here uh there are several
+ways to start on the calman filter
+
+ align:start position:0%
+ways to start on the calman filter
+ 
+
+ align:start position:0%
+ways to start on the calman filter
+people who are in statistics think of it
+
+ align:start position:0%
+people who are in statistics think of it
+ 
+
+ align:start position:0%
+people who are in statistics think of it
+as regression
+
+ align:start position:0%
+as regression
+ 
+
+ align:start position:0%
+as regression
+people who are in probability think of
+
+ align:start position:0%
+people who are in probability think of
+ 
+
+ align:start position:0%
+people who are in probability think of
+it as Contin conditional probability and
+
+ align:start position:0%
+it as Contin conditional probability and
+ 
+
+ align:start position:0%
+it as Contin conditional probability and
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+two which from a distance seem like they
+
+ align:start position:0%
+two which from a distance seem like they
+ 
+
+ align:start position:0%
+two which from a distance seem like they
+should be able to talk to each other uh
+
+ align:start position:0%
+should be able to talk to each other uh
+ 
+
+ align:start position:0%
+should be able to talk to each other uh
+I can see in the early literature many
+
+ align:start position:0%
+I can see in the early literature many
+ 
+
+ align:start position:0%
+I can see in the early literature many
+references to people
+
+ align:start position:0%
+references to people
+ 
+
+ align:start position:0%
+references to people
+who had to translate of course the main
+
+ align:start position:0%
+who had to translate of course the main
+ 
+
+ align:start position:0%
+who had to translate of course the main
+ideas into their own world so that all
+
+ align:start position:0%
+ideas into their own world so that all
+ 
+
+ align:start position:0%
+ideas into their own world so that all
+these different worlds are
+
+ align:start position:0%
+these different worlds are
+ 
+
+ align:start position:0%
+these different worlds are
+represented um and uh you're everybody
+
+ align:start position:0%
+represented um and uh you're everybody
+ 
+
+ align:start position:0%
+represented um and uh you're everybody
+all of us have different backgrounds uh
+
+ align:start position:0%
+all of us have different backgrounds uh
+ 
+
+ align:start position:0%
+all of us have different backgrounds uh
+so that's one reference sort of from
+
+ align:start position:0%
+so that's one reference sort of from
+ 
+
+ align:start position:0%
+so that's one reference sort of from
+this course and of course my point of
+
+ align:start position:0%
+this course and of course my point of
+ 
+
+ align:start position:0%
+this course and of course my point of
+view is because I don't know the other
+
+ align:start position:0%
+view is because I don't know the other
+ 
+
+ align:start position:0%
+view is because I don't know the other
+stuff well enough
+
+ align:start position:0%
+stuff well enough
+ 
+
+ align:start position:0%
+stuff well enough
+is matrices linear algebra I look at
+
+ align:start position:0%
+is matrices linear algebra I look at
+ 
+
+ align:start position:0%
+is matrices linear algebra I look at
+these as Pro I'll so I'll just look at
+
+ align:start position:0%
+these as Pro I'll so I'll just look at
+ 
+
+ align:start position:0%
+these as Pro I'll so I'll just look at
+these as problems in linear algebra
+
+ align:start position:0%
+these as problems in linear algebra
+ 
+
+ align:start position:0%
+these as problems in linear algebra
+we're looking for that solution you hat
+
+ align:start position:0%
+we're looking for that solution you hat
+ 
+
+ align:start position:0%
+we're looking for that solution you hat
+and new data comes in and we looking for
+
+ align:start position:0%
+and new data comes in and we looking for
+ 
+
+ align:start position:0%
+and new data comes in and we looking for
+the change so we we have a uat old from
+
+ align:start position:0%
+the change so we we have a uat old from
+ 
+
+ align:start position:0%
+the change so we we have a uat old from
+from the from an original set of data
+
+ align:start position:0%
+from the from an original set of data
+ 
+
+ align:start position:0%
+from the from an original set of data
+some new B new comes in I have to update
+
+ align:start position:0%
+some new B new comes in I have to update
+ 
+
+ align:start position:0%
+some new B new comes in I have to update
+it and uh I'm looking for the
+
+ align:start position:0%
+it and uh I'm looking for the
+ 
+
+ align:start position:0%
+it and uh I'm looking for the
+formula so that will be uh sort of
+
+ align:start position:0%
+formula so that will be uh sort of
+ 
+
+ align:start position:0%
+formula so that will be uh sort of
+straightforward matrices I I guess I'm
+
+ align:start position:0%
+straightforward matrices I I guess I'm
+ 
+
+ align:start position:0%
+straightforward matrices I I guess I'm
+hoping that that that's a language that
+
+ align:start position:0%
+hoping that that that's a language that
+ 
+
+ align:start position:0%
+hoping that that that's a language that
+almost everybody
+
+ align:start position:0%
+almost everybody
+ 
+
+ align:start position:0%
+almost everybody
+speaks I hope I mean it's least it's
+
+ align:start position:0%
+speaks I hope I mean it's least it's
+ 
+
+ align:start position:0%
+speaks I hope I mean it's least it's
+like more
+
+ align:start position:0%
+like more
+ 
+
+ align:start position:0%
+like more
+uh it's not Esperanto maybe but it's uh
+
+ align:start position:0%
+uh it's not Esperanto maybe but it's uh
+ 
+
+ align:start position:0%
+uh it's not Esperanto maybe but it's uh
+it's um
+
+ align:start position:0%
+it's um
+ 
+
+ align:start position:0%
+it's um
+uh sort of you don't need to be a
+
+ align:start position:0%
+uh sort of you don't need to be a
+ 
+
+ align:start position:0%
+uh sort of you don't need to be a
+specialist in in these areas to to deal
+
+ align:start position:0%
+specialist in in these areas to to deal
+ 
+
+ align:start position:0%
+specialist in in these areas to to deal
+with the Matrix formulas but I have to
+
+ align:start position:0%
+with the Matrix formulas but I have to
+ 
+
+ align:start position:0%
+with the Matrix formulas but I have to
+admit
+
+ align:start position:0%
+admit
+ 
+
+ align:start position:0%
+admit
+that once I see those formulas or once
+
+ align:start position:0%
+that once I see those formulas or once
+ 
+
+ align:start position:0%
+that once I see those formulas or once
+we see them we can figure them out by
+
+ align:start position:0%
+we see them we can figure them out by
+ 
+
+ align:start position:0%
+we see them we can figure them out by
+regular Matrix methods there's one
+
+ align:start position:0%
+regular Matrix methods there's one
+ 
+
+ align:start position:0%
+regular Matrix methods there's one
+identity one Matrix identity that's that
+
+ align:start position:0%
+identity one Matrix identity that's that
+ 
+
+ align:start position:0%
+identity one Matrix identity that's that
+I've mentioned before and now it's going
+
+ align:start position:0%
+I've mentioned before and now it's going
+ 
+
+ align:start position:0%
+I've mentioned before and now it's going
+to come into its own as the most
+
+ align:start position:0%
+to come into its own as the most
+ 
+
+ align:start position:0%
+to come into its own as the most
+important identity of and least and sort
+
+ align:start position:0%
+important identity of and least and sort
+ 
+
+ align:start position:0%
+important identity of and least and sort
+of most important non-obvious Matrix
+
+ align:start position:0%
+of most important non-obvious Matrix
+ 
+
+ align:start position:0%
+of most important non-obvious Matrix
+identity in the world and uh so that's
+
+ align:start position:0%
+identity in the world and uh so that's
+ 
+
+ align:start position:0%
+identity in the world and uh so that's
+what'll get used um
+
+ align:start position:0%
+what'll get used um
+ 
+
+ align:start position:0%
+what'll get used um
+but if I if if these other people who
+
+ align:start position:0%
+but if I if if these other people who
+ 
+
+ align:start position:0%
+but if I if if these other people who
+knew the who knew the other other the
+
+ align:start position:0%
+knew the who knew the other other the
+ 
+
+ align:start position:0%
+knew the who knew the other other the
+the different ways to look at it hadn't
+
+ align:start position:0%
+the different ways to look at it hadn't
+ 
+
+ align:start position:0%
+the different ways to look at it hadn't
+derived if calman hadn't derived the
+
+ align:start position:0%
+derived if calman hadn't derived the
+ 
+
+ align:start position:0%
+derived if calman hadn't derived the
+calman formulas
+
+ align:start position:0%
+calman formulas
+ 
+
+ align:start position:0%
+calman formulas
+I have to admit I wouldn't
+
+ align:start position:0%
+I have to admit I wouldn't
+ 
+
+ align:start position:0%
+I have to admit I wouldn't
+have been able to to get to them uh so
+
+ align:start position:0%
+have been able to to get to them uh so
+ 
+
+ align:start position:0%
+have been able to to get to them uh so
+it's sort of those so those insights are
+
+ align:start position:0%
+it's sort of those so those insights are
+ 
+
+ align:start position:0%
+it's sort of those so those insights are
+are crucial uh I and so I should mention
+
+ align:start position:0%
+are crucial uh I and so I should mention
+ 
+
+ align:start position:0%
+are crucial uh I and so I should mention
+some authors and you'll know others uh
+
+ align:start position:0%
+some authors and you'll know others uh
+ 
+
+ align:start position:0%
+some authors and you'll know others uh
+one recent book that's I think
+
+ align:start position:0%
+one recent book that's I think
+ 
+
+ align:start position:0%
+one recent book that's I think
+especially
+
+ align:start position:0%
+especially
+ 
+
+ align:start position:0%
+especially
+clear uh is by Brown and hang can I just
+
+ align:start position:0%
+clear uh is by Brown and hang can I just
+ 
+
+ align:start position:0%
+clear uh is by Brown and hang can I just
+I'll just maybe put these over here uh
+
+ align:start position:0%
+I'll just maybe put these over here uh
+ 
+
+ align:start position:0%
+I'll just maybe put these over here uh
+Brown and hang
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it has the words calman applied
+
+ align:start position:0%
+and it has the words calman applied
+ 
+
+ align:start position:0%
+and it has the words calman applied
+calman filtering in the title an earlier
+
+ align:start position:0%
+calman filtering in the title an earlier
+ 
+
+ align:start position:0%
+calman filtering in the title an earlier
+book
+
+ align:start position:0%
+book
+ 
+
+ align:start position:0%
+book
+that was edited by
+
+ align:start position:0%
+that was edited by
+ 
+
+ align:start position:0%
+that was edited by
+gilb and came from uh uh uh
+
+ align:start position:0%
+gilb and came from uh uh uh
+ 
+
+ align:start position:0%
+gilb and came from uh uh uh
+nearby uh is is also uh highly
+
+ align:start position:0%
+nearby uh is is also uh highly
+ 
+
+ align:start position:0%
+nearby uh is is also uh highly
+recommended and I always
+
+ align:start position:0%
+recommended and I always
+ 
+
+ align:start position:0%
+recommended and I always
+enjoy uh the writing of Tom kyth
+
+ align:start position:0%
+enjoy uh the writing of Tom kyth
+ 
+
+ align:start position:0%
+enjoy uh the writing of Tom kyth
+uh who has a number of
+
+ align:start position:0%
+uh who has a number of
+ 
+
+ align:start position:0%
+uh who has a number of
+books uh about uh calman filters in fact
+
+ align:start position:0%
+books uh about uh calman filters in fact
+ 
+
+ align:start position:0%
+books uh about uh calman filters in fact
+I think a couple of new ones and here's
+
+ align:start position:0%
+I think a couple of new ones and here's
+ 
+
+ align:start position:0%
+I think a couple of new ones and here's
+a very old one lectures on weer and cman
+
+ align:start position:0%
+a very old one lectures on weer and cman
+ 
+
+ align:start position:0%
+a very old one lectures on weer and cman
+filtering so I didn't know what weiner
+
+ align:start position:0%
+filtering so I didn't know what weiner
+ 
+
+ align:start position:0%
+filtering so I didn't know what weiner
+filtering is was either is either but uh
+
+ align:start position:0%
+filtering is was either is either but uh
+ 
+
+ align:start position:0%
+filtering is was either is either but uh
+it's the lots of insights in Kyla's book
+
+ align:start position:0%
+it's the lots of insights in Kyla's book
+ 
+
+ align:start position:0%
+it's the lots of insights in Kyla's book
+Lots so those are a few of the
+
+ align:start position:0%
+Lots so those are a few of the
+ 
+
+ align:start position:0%
+Lots so those are a few of the
+possibilities um okay so that's some
+
+ align:start position:0%
+possibilities um okay so that's some
+ 
+
+ align:start position:0%
+possibilities um okay so that's some
+comments about books very
+
+ align:start position:0%
+comments about books very
+ 
+
+ align:start position:0%
+comments about books very
+incomplete uh and uh I'm happy to know
+
+ align:start position:0%
+incomplete uh and uh I'm happy to know
+ 
+
+ align:start position:0%
+incomplete uh and uh I'm happy to know
+of others always I'm I'm beginning to
+
+ align:start position:0%
+of others always I'm I'm beginning to
+ 
+
+ align:start position:0%
+of others always I'm I'm beginning to
+get emails of All Sorts now from you and
+
+ align:start position:0%
+get emails of All Sorts now from you and
+ 
+
+ align:start position:0%
+get emails of All Sorts now from you and
+I'm really appreciating it uh on on
+
+ align:start position:0%
+I'm really appreciating it uh on on
+ 
+
+ align:start position:0%
+I'm really appreciating it uh on on
+topics and on applications for example
+
+ align:start position:0%
+topics and on applications for example
+ 
+
+ align:start position:0%
+topics and on applications for example
+one application that I'd like to follow
+
+ align:start position:0%
+one application that I'd like to follow
+ 
+
+ align:start position:0%
+one application that I'd like to follow
+up that's been significant at lincol lab
+
+ align:start position:0%
+up that's been significant at lincol lab
+ 
+
+ align:start position:0%
+up that's been significant at lincol lab
+uh Bob Nichols got me uh connected a
+
+ align:start position:0%
+uh Bob Nichols got me uh connected a
+ 
+
+ align:start position:0%
+uh Bob Nichols got me uh connected a
+little bit is this St AP the stap um um
+
+ align:start position:0%
+little bit is this St AP the stap um um
+ 
+
+ align:start position:0%
+little bit is this St AP the stap um um
+and so I'm starting with an article from
+
+ align:start position:0%
+and so I'm starting with an article from
+ 
+
+ align:start position:0%
+and so I'm starting with an article from
+Lincoln lab uh journal and what is what
+
+ align:start position:0%
+Lincoln lab uh journal and what is what
+ 
+
+ align:start position:0%
+Lincoln lab uh journal and what is what
+was the key issue in that article it's
+
+ align:start position:0%
+was the key issue in that article it's
+ 
+
+ align:start position:0%
+was the key issue in that article it's
+exactly what we talked about last time
+
+ align:start position:0%
+exactly what we talked about last time
+ 
+
+ align:start position:0%
+exactly what we talked about last time
+we the the uh samples so so this is part
+
+ align:start position:0%
+we the the uh samples so so this is part
+ 
+
+ align:start position:0%
+we the the uh samples so so this is part
+of the recap then this is a recap of the
+
+ align:start position:0%
+of the recap then this is a recap of the
+ 
+
+ align:start position:0%
+of the recap then this is a recap of the
+QR part of the of last time uh in Janice
+
+ align:start position:0%
+QR part of the of last time uh in Janice
+ 
+
+ align:start position:0%
+QR part of the of last time uh in Janice
+McMahon
+
+ align:start position:0%
+McMahon
+ 
+
+ align:start position:0%
+McMahon
+um uh very nicely written paper on step
+
+ align:start position:0%
+um uh very nicely written paper on step
+ 
+
+ align:start position:0%
+um uh very nicely written paper on step
+she's the the central problem is to deal
+
+ align:start position:0%
+she's the the central problem is to deal
+ 
+
+ align:start position:0%
+she's the the central problem is to deal
+with uh to solve a linear system where
+
+ align:start position:0%
+with uh to solve a linear system where
+ 
+
+ align:start position:0%
+with uh to solve a linear system where
+the um coefficient Matrix let's call it
+
+ align:start position:0%
+the um coefficient Matrix let's call it
+ 
+
+ align:start position:0%
+the um coefficient Matrix let's call it
+R to follow her is comes from taking
+
+ align:start position:0%
+R to follow her is comes from taking
+ 
+
+ align:start position:0%
+R to follow her is comes from taking
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+samples so this was this is the
+
+ align:start position:0%
+samples so this was this is the
+ 
+
+ align:start position:0%
+samples so this was this is the
+coefficient Matrix uh the sample Matrix
+
+ align:start position:0%
+coefficient Matrix uh the sample Matrix
+ 
+
+ align:start position:0%
+coefficient Matrix uh the sample Matrix
+you could say coming from by taking many
+
+ align:start position:0%
+you could say coming from by taking many
+ 
+
+ align:start position:0%
+you could say coming from by taking many
+samples of uh from from radar uh data uh
+
+ align:start position:0%
+samples of uh from from radar uh data uh
+ 
+
+ align:start position:0%
+samples of uh from from radar uh data uh
+at different frequencies uh different
+
+ align:start position:0%
+at different frequencies uh different
+ 
+
+ align:start position:0%
+at different frequencies uh different
+Doppler uh Lots uh so X is a very long
+
+ align:start position:0%
+Doppler uh Lots uh so X is a very long
+ 
+
+ align:start position:0%
+Doppler uh Lots uh so X is a very long
+Vector this is probably a full Matrix
+
+ align:start position:0%
+Vector this is probably a full Matrix
+ 
+
+ align:start position:0%
+Vector this is probably a full Matrix
+and what she concludes
+
+ align:start position:0%
+and what she concludes
+ 
+
+ align:start position:0%
+and what she concludes
+is that to use uh
+
+ align:start position:0%
+is that to use uh
+ 
+
+ align:start position:0%
+is that to use uh
+orthogonalization in parallel is uh and
+
+ align:start position:0%
+orthogonalization in parallel is uh and
+ 
+
+ align:start position:0%
+orthogonalization in parallel is uh and
+and using heavy uh Computing of course
+
+ align:start position:0%
+and using heavy uh Computing of course
+ 
+
+ align:start position:0%
+and using heavy uh Computing of course
+is a way to go I'm going to hope to meet
+
+ align:start position:0%
+is a way to go I'm going to hope to meet
+ 
+
+ align:start position:0%
+is a way to go I'm going to hope to meet
+with her and speak more about that can I
+
+ align:start position:0%
+with her and speak more about that can I
+ 
+
+ align:start position:0%
+with her and speak more about that can I
+also just so that was that's just a
+
+ align:start position:0%
+also just so that was that's just a
+ 
+
+ align:start position:0%
+also just so that was that's just a
+touch of what I hope to come back to and
+
+ align:start position:0%
+touch of what I hope to come back to and
+ 
+
+ align:start position:0%
+touch of what I hope to come back to and
+can I also just recap one little point
+
+ align:start position:0%
+can I also just recap one little point
+ 
+
+ align:start position:0%
+can I also just recap one little point
+about one recap the SVD just to say
+
+ align:start position:0%
+about one recap the SVD just to say
+ 
+
+ align:start position:0%
+about one recap the SVD just to say
+again what it tells us just most
+
+ align:start position:0%
+again what it tells us just most
+ 
+
+ align:start position:0%
+again what it tells us just most
+directly so it say the most direct of of
+
+ align:start position:0%
+directly so it say the most direct of of
+ 
+
+ align:start position:0%
+directly so it say the most direct of of
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+of this factorization U times Sigma
+
+ align:start position:0%
+of this factorization U times Sigma
+ 
+
+ align:start position:0%
+of this factorization U times Sigma
+different totally different Sigma oh boy
+
+ align:start position:0%
+different totally different Sigma oh boy
+ 
+
+ align:start position:0%
+different totally different Sigma oh boy
+we applied math is running out of
+
+ align:start position:0%
+we applied math is running out of
+ 
+
+ align:start position:0%
+we applied math is running out of
+letters even help with help from the
+
+ align:start position:0%
+letters even help with help from the
+ 
+
+ align:start position:0%
+letters even help with help from the
+Greeks uh this Sigma of course is so
+
+ align:start position:0%
+Greeks uh this Sigma of course is so
+ 
+
+ align:start position:0%
+Greeks uh this Sigma of course is so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is uh the orthogonal I vectors of uh AA
+
+ align:start position:0%
+is uh the orthogonal I vectors of uh AA
+ 
+
+ align:start position:0%
+is uh the orthogonal I vectors of uh AA
+transpose then these they're not I Val
+
+ align:start position:0%
+transpose then these they're not I Val
+ 
+
+ align:start position:0%
+transpose then these they're not I Val
+values they're singular values and then
+
+ align:start position:0%
+values they're singular values and then
+ 
+
+ align:start position:0%
+values they're singular values and then
+with a lot of
+
+ align:start position:0%
+with a lot of
+ 
+
+ align:start position:0%
+with a lot of
+zeros and then the orthogonal Lan
+
+ align:start position:0%
+zeros and then the orthogonal Lan
+ 
+
+ align:start position:0%
+zeros and then the orthogonal Lan
+vectors of a transpose
+
+ align:start position:0%
+vectors of a transpose
+ 
+
+ align:start position:0%
+vectors of a transpose
+a so maybe they're n of those and M of
+
+ align:start position:0%
+a so maybe they're n of those and M of
+ 
+
+ align:start position:0%
+a so maybe they're n of those and M of
+those if it's uh M byn Matrix and R here
+
+ align:start position:0%
+those if it's uh M byn Matrix and R here
+ 
+
+ align:start position:0%
+those if it's uh M byn Matrix and R here
+is the rank of the of the Matrix the
+
+ align:start position:0%
+is the rank of the of the Matrix the
+ 
+
+ align:start position:0%
+is the rank of the of the Matrix the
+number of uh so the number of
+
+ align:start position:0%
+number of uh so the number of
+ 
+
+ align:start position:0%
+number of uh so the number of
+nonzero igen values of a transpose a the
+
+ align:start position:0%
+nonzero igen values of a transpose a the
+ 
+
+ align:start position:0%
+nonzero igen values of a transpose a the
+number of independent The crucial
+
+ align:start position:0%
+number of independent The crucial
+ 
+
+ align:start position:0%
+number of independent The crucial
+number the number of nonzero values of
+
+ align:start position:0%
+number the number of nonzero values of
+ 
+
+ align:start position:0%
+number the number of nonzero values of
+AA transpose the number of independent
+
+ align:start position:0%
+AA transpose the number of independent
+ 
+
+ align:start position:0%
+AA transpose the number of independent
+rows in a the number of independent
+
+ align:start position:0%
+rows in a the number of independent
+ 
+
+ align:start position:0%
+rows in a the number of independent
+Columns of a it's it's measures the true
+
+ align:start position:0%
+Columns of a it's it's measures the true
+ 
+
+ align:start position:0%
+Columns of a it's it's measures the true
+the size the true size of a because the
+
+ align:start position:0%
+the size the true size of a because the
+ 
+
+ align:start position:0%
+the size the true size of a because the
+rest of a is is
+
+ align:start position:0%
+rest of a is is
+ 
+
+ align:start position:0%
+rest of a is is
+uh is sort of zero if we look at it the
+
+ align:start position:0%
+uh is sort of zero if we look at it the
+ 
+
+ align:start position:0%
+uh is sort of zero if we look at it the
+right way it's it's known from these and
+
+ align:start position:0%
+right way it's it's known from these and
+ 
+
+ align:start position:0%
+right way it's it's known from these and
+now so that's this SVD and I just want
+
+ align:start position:0%
+now so that's this SVD and I just want
+ 
+
+ align:start position:0%
+now so that's this SVD and I just want
+to point
+
+ align:start position:0%
+to point
+ 
+
+ align:start position:0%
+to point
+out what we see from there I could write
+
+ align:start position:0%
+out what we see from there I could write
+ 
+
+ align:start position:0%
+out what we see from there I could write
+that as a sum
+
+ align:start position:0%
+that as a sum
+ 
+
+ align:start position:0%
+that as a sum
+of multiplying column times number time
+
+ align:start position:0%
+of multiplying column times number time
+ 
+
+ align:start position:0%
+of multiplying column times number time
+row would be U1 Sigma 1 V1 transpose
+
+ align:start position:0%
+row would be U1 Sigma 1 V1 transpose
+ 
+
+ align:start position:0%
+row would be U1 Sigma 1 V1 transpose
+that's like the first piece and then the
+
+ align:start position:0%
+that's like the first piece and then the
+ 
+
+ align:start position:0%
+that's like the first piece and then the
+second piece would be U2 V2 so on and
+
+ align:start position:0%
+second piece would be U2 V2 so on and
+ 
+
+ align:start position:0%
+second piece would be U2 V2 so on and
+the last piece would be Ur Sigma R VR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transpose so the beauty is this is the
+
+ align:start position:0%
+transpose so the beauty is this is the
+ 
+
+ align:start position:0%
+transpose so the beauty is this is the
+decomposition of the Matrix a we're all
+
+ align:start position:0%
+decomposition of the Matrix a we're all
+ 
+
+ align:start position:0%
+decomposition of the Matrix a we're all
+we're talking about a everything here is
+
+ align:start position:0%
+we're talking about a everything here is
+ 
+
+ align:start position:0%
+we're talking about a everything here is
+the Matrix
+
+ align:start position:0%
+the Matrix
+ 
+
+ align:start position:0%
+the Matrix
+a so what do we learn from this usually
+
+ align:start position:0%
+a so what do we learn from this usually
+ 
+
+ align:start position:0%
+a so what do we learn from this usually
+we we Sigma 1 is is greater equal Sigma
+
+ align:start position:0%
+we we Sigma 1 is is greater equal Sigma
+ 
+
+ align:start position:0%
+we we Sigma 1 is is greater equal Sigma
+2 greater equal greater equal we usually
+
+ align:start position:0%
+2 greater equal greater equal we usually
+ 
+
+ align:start position:0%
+2 greater equal greater equal we usually
+put them in descending order so this is
+
+ align:start position:0%
+put them in descending order so this is
+ 
+
+ align:start position:0%
+put them in descending order so this is
+Sigma Max here
+
+ align:start position:0%
+Sigma Max here
+ 
+
+ align:start position:0%
+Sigma Max here
+and this is Sigma
+
+ align:start position:0%
+and this is Sigma
+ 
+
+ align:start position:0%
+and this is Sigma
+Min apart from some possible zeros
+
+ align:start position:0%
+Min apart from some possible zeros
+ 
+
+ align:start position:0%
+Min apart from some possible zeros
+so this piece like tells us the most
+
+ align:start position:0%
+so this piece like tells us the most
+ 
+
+ align:start position:0%
+so this piece like tells us the most
+important part of the
+
+ align:start position:0%
+important part of the
+ 
+
+ align:start position:0%
+important part of the
+Matrix for example in images my Matrix
+
+ align:start position:0%
+Matrix for example in images my Matrix
+ 
+
+ align:start position:0%
+Matrix for example in images my Matrix
+could could I could think of it as an
+
+ align:start position:0%
+could could I could think of it as an
+ 
+
+ align:start position:0%
+could could I could think of it as an
+image right I I if you give me an image
+
+ align:start position:0%
+image right I I if you give me an image
+ 
+
+ align:start position:0%
+image right I I if you give me an image
+I could just divide it into pixels and
+
+ align:start position:0%
+I could just divide it into pixels and
+ 
+
+ align:start position:0%
+I could just divide it into pixels and
+then for each pixel I'll say put the uh
+
+ align:start position:0%
+then for each pixel I'll say put the uh
+ 
+
+ align:start position:0%
+then for each pixel I'll say put the uh
+gray level and that gives me a matrix a
+
+ align:start position:0%
+gray level and that gives me a matrix a
+ 
+
+ align:start position:0%
+gray level and that gives me a matrix a
+matrix of gray levels so let let me take
+
+ align:start position:0%
+matrix of gray levels so let let me take
+ 
+
+ align:start position:0%
+matrix of gray levels so let let me take
+a a possible application a is a
+
+ align:start position:0%
+a a possible application a is a
+ 
+
+ align:start position:0%
+a a possible application a is a
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+of gray levels of
+
+ align:start position:0%
+of gray levels of
+ 
+
+ align:start position:0%
+of gray levels of
+pixels
+
+ align:start position:0%
+pixels
+ 
+
+ align:start position:0%
+pixels
+okay so that's got n s or M time n
+
+ align:start position:0%
+okay so that's got n s or M time n
+ 
+
+ align:start position:0%
+okay so that's got n s or M time n
+pixels M * n entries in the matrix it's
+
+ align:start position:0%
+pixels M * n entries in the matrix it's
+ 
+
+ align:start position:0%
+pixels M * n entries in the matrix it's
+a giant Matrix and I want to compress it
+
+ align:start position:0%
+a giant Matrix and I want to compress it
+ 
+
+ align:start position:0%
+a giant Matrix and I want to compress it
+what's the good way to compress a matrix
+
+ align:start position:0%
+what's the good way to compress a matrix
+ 
+
+ align:start position:0%
+what's the good way to compress a matrix
+well this would be a very nice way if I
+
+ align:start position:0%
+well this would be a very nice way if I
+ 
+
+ align:start position:0%
+well this would be a very nice way if I
+do the
+
+ align:start position:0%
+do the
+ 
+
+ align:start position:0%
+do the
+SVD then and keep just this
+
+ align:start position:0%
+SVD then and keep just this
+ 
+
+ align:start position:0%
+SVD then and keep just this
+part say that's a very simple piece to
+
+ align:start position:0%
+part say that's a very simple piece to
+ 
+
+ align:start position:0%
+part say that's a very simple piece to
+keep it's a it's a it's a rectang m byn
+
+ align:start position:0%
+keep it's a it's a it's a rectang m byn
+ 
+
+ align:start position:0%
+keep it's a it's a it's a rectang m byn
+Matrix but it only needs M components of
+
+ align:start position:0%
+Matrix but it only needs M components of
+ 
+
+ align:start position:0%
+Matrix but it only needs M components of
+u n components of v and one number Sigma
+
+ align:start position:0%
+u n components of v and one number Sigma
+ 
+
+ align:start position:0%
+u n components of v and one number Sigma
+and it's keeping
+
+ align:start position:0%
+and it's keeping
+ 
+
+ align:start position:0%
+and it's keeping
+like the biggest piece of a we could
+
+ align:start position:0%
+like the biggest piece of a we could
+ 
+
+ align:start position:0%
+like the biggest piece of a we could
+probably recognize the image from one or
+
+ align:start position:0%
+probably recognize the image from one or
+ 
+
+ align:start position:0%
+probably recognize the image from one or
+a fraction of the total number of pieces
+
+ align:start position:0%
+a fraction of the total number of pieces
+ 
+
+ align:start position:0%
+a fraction of the total number of pieces
+right if we had an M byn Matrix its rank
+
+ align:start position:0%
+right if we had an M byn Matrix its rank
+ 
+
+ align:start position:0%
+right if we had an M byn Matrix its rank
+might be M or n if no reason why it
+
+ align:start position:0%
+might be M or n if no reason why it
+ 
+
+ align:start position:0%
+might be M or n if no reason why it
+wouldn't be full Rank and that might be
+
+ align:start position:0%
+wouldn't be full Rank and that might be
+ 
+
+ align:start position:0%
+wouldn't be full Rank and that might be
+enormous but if we kept maybe 10 the
+
+ align:start position:0%
+enormous but if we kept maybe 10 the
+ 
+
+ align:start position:0%
+enormous but if we kept maybe 10 the
+first the largest 10 uh pieces we could
+
+ align:start position:0%
+first the largest 10 uh pieces we could
+ 
+
+ align:start position:0%
+first the largest 10 uh pieces we could
+recognize the image so they
+
+ align:start position:0%
+recognize the image so they
+ 
+
+ align:start position:0%
+recognize the image so they
+the SVD is somehow taking your Matrix
+
+ align:start position:0%
+the SVD is somehow taking your Matrix
+ 
+
+ align:start position:0%
+the SVD is somehow taking your Matrix
+and separating it into the natural block
+
+ align:start position:0%
+and separating it into the natural block
+ 
+
+ align:start position:0%
+and separating it into the natural block
+building
+
+ align:start position:0%
+building
+ 
+
+ align:start position:0%
+building
+blocks the building blocks are rank
+
+ align:start position:0%
+blocks the building blocks are rank
+ 
+
+ align:start position:0%
+blocks the building blocks are rank
+one column times row and they're
+
+ align:start position:0%
+one column times row and they're
+ 
+
+ align:start position:0%
+one column times row and they're
+multiplied by these numbers that
+
+ align:start position:0%
+multiplied by these numbers that
+ 
+
+ align:start position:0%
+multiplied by these numbers that
+decrease in order and uh so this this
+
+ align:start position:0%
+decrease in order and uh so this this
+ 
+
+ align:start position:0%
+decrease in order and uh so this this
+sort of tells us something about a
+
+ align:start position:0%
+sort of tells us something about a
+ 
+
+ align:start position:0%
+sort of tells us something about a
+inverse how how how difficult it is and
+
+ align:start position:0%
+inverse how how how difficult it is and
+ 
+
+ align:start position:0%
+inverse how how how difficult it is and
+this tells us what's important about a
+
+ align:start position:0%
+this tells us what's important about a
+ 
+
+ align:start position:0%
+this tells us what's important about a
+and the difficulty
+
+ align:start position:0%
+and the difficulty
+ 
+
+ align:start position:0%
+and the difficulty
+is uh as as I was discussing before the
+
+ align:start position:0%
+is uh as as I was discussing before the
+ 
+
+ align:start position:0%
+is uh as as I was discussing before the
+class started the difficulty is if we
+
+ align:start position:0%
+class started the difficulty is if we
+ 
+
+ align:start position:0%
+class started the difficulty is if we
+have a lot of this to do and we have a
+
+ align:start position:0%
+have a lot of this to do and we have a
+ 
+
+ align:start position:0%
+have a lot of this to do and we have a
+have to do it a lot in real time then we
+
+ align:start position:0%
+have to do it a lot in real time then we
+ 
+
+ align:start position:0%
+have to do it a lot in real time then we
+have to consider how quickly can we get
+
+ align:start position:0%
+have to consider how quickly can we get
+ 
+
+ align:start position:0%
+have to consider how quickly can we get
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SVD I'm beginning to think like Lincoln
+
+ align:start position:0%
+SVD I'm beginning to think like Lincoln
+ 
+
+ align:start position:0%
+SVD I'm beginning to think like Lincoln
+Labs needs a department of numerical
+
+ align:start position:0%
+Labs needs a department of numerical
+ 
+
+ align:start position:0%
+Labs needs a department of numerical
+linear algebra because uh the problems
+
+ align:start position:0%
+linear algebra because uh the problems
+ 
+
+ align:start position:0%
+linear algebra because uh the problems
+you're facing are this these questions
+
+ align:start position:0%
+you're facing are this these questions
+ 
+
+ align:start position:0%
+you're facing are this these questions
+of of efficient uh calculation of very
+
+ align:start position:0%
+of of efficient uh calculation of very
+ 
+
+ align:start position:0%
+of of efficient uh calculation of very
+very large systems and uh do you do it
+
+ align:start position:0%
+very large systems and uh do you do it
+ 
+
+ align:start position:0%
+very large systems and uh do you do it
+on uh do you use QR what do you do do
+
+ align:start position:0%
+on uh do you use QR what do you do do
+ 
+
+ align:start position:0%
+on uh do you use QR what do you do do
+you use uh uh elimination do you do you
+
+ align:start position:0%
+you use uh uh elimination do you do you
+ 
+
+ align:start position:0%
+you use uh uh elimination do you do you
+do it in parallel do you do it on what
+
+ align:start position:0%
+do it in parallel do you do it on what
+ 
+
+ align:start position:0%
+do it in parallel do you do it on what
+processors how how to make that
+
+ align:start position:0%
+processors how how to make that
+ 
+
+ align:start position:0%
+processors how how to make that
+efficient I mean it's really uh Central
+
+ align:start position:0%
+efficient I mean it's really uh Central
+ 
+
+ align:start position:0%
+efficient I mean it's really uh Central
+issue and it's certainly part of these
+
+ align:start position:0%
+issue and it's certainly part of these
+ 
+
+ align:start position:0%
+issue and it's certainly part of these
+lectures uh it's not the only
+
+ align:start position:0%
+lectures uh it's not the only
+ 
+
+ align:start position:0%
+lectures uh it's not the only
+part uh but I'm happy to let me say this
+
+ align:start position:0%
+part uh but I'm happy to let me say this
+ 
+
+ align:start position:0%
+part uh but I'm happy to let me say this
+again I'm I'm really happy to know what
+
+ align:start position:0%
+again I'm I'm really happy to know what
+ 
+
+ align:start position:0%
+again I'm I'm really happy to know what
+the problems that are arising are and
+
+ align:start position:0%
+the problems that are arising are and
+ 
+
+ align:start position:0%
+the problems that are arising are and
+especially if I'm able to translate them
+
+ align:start position:0%
+especially if I'm able to translate them
+ 
+
+ align:start position:0%
+especially if I'm able to translate them
+into a familiar language and and sort of
+
+ align:start position:0%
+into a familiar language and and sort of
+ 
+
+ align:start position:0%
+into a familiar language and and sort of
+Rec identify well what is the what is
+
+ align:start position:0%
+Rec identify well what is the what is
+ 
+
+ align:start position:0%
+Rec identify well what is the what is
+the underlying problem here uh is it
+
+ align:start position:0%
+the underlying problem here uh is it
+ 
+
+ align:start position:0%
+the underlying problem here uh is it
+uh and uh with
+
+ align:start position:0%
+uh and uh with
+ 
+
+ align:start position:0%
+uh and uh with
+SVD we have to say clearly that it's
+
+ align:start position:0%
+SVD we have to say clearly that it's
+ 
+
+ align:start position:0%
+SVD we have to say clearly that it's
+even though people have found very good
+
+ align:start position:0%
+even though people have found very good
+ 
+
+ align:start position:0%
+even though people have found very good
+algorithms for it it's still a heck of a
+
+ align:start position:0%
+algorithms for it it's still a heck of a
+ 
+
+ align:start position:0%
+algorithms for it it's still a heck of a
+lot of work uh basically you have an IG
+
+ align:start position:0%
+lot of work uh basically you have an IG
+ 
+
+ align:start position:0%
+lot of work uh basically you have an IG
+value problem to
+
+ align:start position:0%
+value problem to
+ 
+
+ align:start position:0%
+value problem to
+do and igen value problems take you know
+
+ align:start position:0%
+do and igen value problems take you know
+ 
+
+ align:start position:0%
+do and igen value problems take you know
+that bit more time than uh QR or uh uh
+
+ align:start position:0%
+that bit more time than uh QR or uh uh
+ 
+
+ align:start position:0%
+that bit more time than uh QR or uh uh
+LDL transpose
+
+ align:start position:0%
+LDL transpose
+ 
+
+ align:start position:0%
+LDL transpose
+elimination okay uh any comment you feel
+
+ align:start position:0%
+elimination okay uh any comment you feel
+ 
+
+ align:start position:0%
+elimination okay uh any comment you feel
+free to make a comment because this is
+
+ align:start position:0%
+free to make a comment because this is
+ 
+
+ align:start position:0%
+free to make a comment because this is
+like preliminary before I launch into uh
+
+ align:start position:0%
+like preliminary before I launch into uh
+ 
+
+ align:start position:0%
+like preliminary before I launch into uh
+today's
+
+ align:start position:0%
+today's
+ 
+
+ align:start position:0%
+today's
+lecture any or or comments offline um
+
+ align:start position:0%
+lecture any or or comments offline um
+ 
+
+ align:start position:0%
+lecture any or or comments offline um
+are are totally welcome okay ready to go
+
+ align:start position:0%
+are are totally welcome okay ready to go
+ 
+
+ align:start position:0%
+are are totally welcome okay ready to go
+on Lee squares okay so so this part I
+
+ align:start position:0%
+on Lee squares okay so so this part I
+ 
+
+ align:start position:0%
+on Lee squares okay so so this part I
+take as known the the the uh the
+
+ align:start position:0%
+take as known the the the uh the
+ 
+
+ align:start position:0%
+take as known the the the uh the
+um the re we got to that either by a
+
+ align:start position:0%
+um the re we got to that either by a
+ 
+
+ align:start position:0%
+um the re we got to that either by a
+minim
+
+ align:start position:0%
+minim
+ 
+
+ align:start position:0%
+minim
+minimization of the error B minus Au U
+
+ align:start position:0%
+minimization of the error B minus Au U
+ 
+
+ align:start position:0%
+minimization of the error B minus Au U
+squared or geometrically we got to that
+
+ align:start position:0%
+squared or geometrically we got to that
+ 
+
+ align:start position:0%
+squared or geometrically we got to that
+by a
+
+ align:start position:0%
+by a
+ 
+
+ align:start position:0%
+by a
+projection of
+
+ align:start position:0%
+projection of
+ 
+
+ align:start position:0%
+projection of
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+onto the column space of
+
+ align:start position:0%
+onto the column space of
+ 
+
+ align:start position:0%
+onto the column space of
+a but we got there it's in on the
+
+ align:start position:0%
+a but we got there it's in on the
+ 
+
+ align:start position:0%
+a but we got there it's in on the
+videotape so I don't uh it's on the on
+
+ align:start position:0%
+videotape so I don't uh it's on the on
+ 
+
+ align:start position:0%
+videotape so I don't uh it's on the on
+the record now I'm ready to discuss
+
+ align:start position:0%
+the record now I'm ready to discuss
+ 
+
+ align:start position:0%
+the record now I'm ready to discuss
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+two why the weights okay
+
+ align:start position:0%
+two why the weights okay
+ 
+
+ align:start position:0%
+two why the weights okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+okay uh I have to I would like to know
+
+ align:start position:0%
+okay uh I have to I would like to know
+ 
+
+ align:start position:0%
+okay uh I have to I would like to know
+why these are the appropriate weights
+
+ align:start position:0%
+why these are the appropriate weights
+ 
+
+ align:start position:0%
+why these are the appropriate weights
+the the sigma and so let's remember what
+
+ align:start position:0%
+the the sigma and so let's remember what
+ 
+
+ align:start position:0%
+the the sigma and so let's remember what
+Sigma is the The covariance Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sigma and if I'm trying to remember what
+
+ align:start position:0%
+Sigma and if I'm trying to remember what
+ 
+
+ align:start position:0%
+Sigma and if I'm trying to remember what
+is the covariance of I might put a v to
+
+ align:start position:0%
+is the covariance of I might put a v to
+ 
+
+ align:start position:0%
+is the covariance of I might put a v to
+remind myself it's
+
+ align:start position:0%
+remind myself it's
+ 
+
+ align:start position:0%
+remind myself it's
+the our system is coming to us with
+
+ align:start position:0%
+the our system is coming to us with
+ 
+
+ align:start position:0%
+the our system is coming to us with
+noise so we get Au equal B say
+
+ align:start position:0%
+noise so we get Au equal B say
+ 
+
+ align:start position:0%
+noise so we get Au equal B say
+minus noise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e and of course we don't know exactly
+
+ align:start position:0%
+e and of course we don't know exactly
+ 
+
+ align:start position:0%
+e and of course we don't know exactly
+what that noise
+
+ align:start position:0%
+what that noise
+ 
+
+ align:start position:0%
+what that noise
+is but we may
+
+ align:start position:0%
+is but we may
+ 
+
+ align:start position:0%
+is but we may
+know uh sort of what its variance is
+
+ align:start position:0%
+know uh sort of what its variance is
+ 
+
+ align:start position:0%
+know uh sort of what its variance is
+what what what's it what its expectation
+
+ align:start position:0%
+what what what's it what its expectation
+ 
+
+ align:start position:0%
+what what what's it what its expectation
+is is the average noise
+
+ align:start position:0%
+is is the average noise
+ 
+
+ align:start position:0%
+is is the average noise
+zero let's say it is because if the
+
+ align:start position:0%
+zero let's say it is because if the
+ 
+
+ align:start position:0%
+zero let's say it is because if the
+average noise isn't zero we'll subtract
+
+ align:start position:0%
+average noise isn't zero we'll subtract
+ 
+
+ align:start position:0%
+average noise isn't zero we'll subtract
+off that average to to get noise that
+
+ align:start position:0%
+off that average to to get noise that
+ 
+
+ align:start position:0%
+off that average to to get noise that
+has average zero so I'm ass I'm going to
+
+ align:start position:0%
+has average zero so I'm ass I'm going to
+ 
+
+ align:start position:0%
+has average zero so I'm ass I'm going to
+always assume that the expected value of
+
+ align:start position:0%
+always assume that the expected value of
+ 
+
+ align:start position:0%
+always assume that the expected value of
+e of the of this error B minus AU
+
+ align:start position:0%
+e of the of this error B minus AU
+ 
+
+ align:start position:0%
+e of the of this error B minus AU
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+zero let's but
+
+ align:start position:0%
+zero let's but
+ 
+
+ align:start position:0%
+zero let's but
+now but it that doesn't mean we expect
+
+ align:start position:0%
+now but it that doesn't mean we expect
+ 
+
+ align:start position:0%
+now but it that doesn't mean we expect
+it to be zero we expect its average to
+
+ align:start position:0%
+it to be zero we expect its average to
+ 
+
+ align:start position:0%
+it to be zero we expect its average to
+be zero it's more as as as likely to be
+
+ align:start position:0%
+be zero it's more as as as likely to be
+ 
+
+ align:start position:0%
+be zero it's more as as as likely to be
+plus as
+
+ align:start position:0%
+plus as
+ 
+
+ align:start position:0%
+plus as
+minus roughly speaking but but if we
+
+ align:start position:0%
+minus roughly speaking but but if we
+ 
+
+ align:start position:0%
+minus roughly speaking but but if we
+Square it then we get the so the this is
+
+ align:start position:0%
+Square it then we get the so the this is
+ 
+
+ align:start position:0%
+Square it then we get the so the this is
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation the average value of
+
+ align:start position:0%
+expectation the average value of
+ 
+
+ align:start position:0%
+expectation the average value of
+the error squared it's so essentially
+
+ align:start position:0%
+the error squared it's so essentially
+ 
+
+ align:start position:0%
+the error squared it's so essentially
+what I'm going to put in here is e^ squ
+
+ align:start position:0%
+what I'm going to put in here is e^ squ
+ 
+
+ align:start position:0%
+what I'm going to put in here is e^ squ
+right the expectation of e is zero and
+
+ align:start position:0%
+right the expectation of e is zero and
+ 
+
+ align:start position:0%
+right the expectation of e is zero and
+now I'm looking at the expectation of e
+
+ align:start position:0%
+now I'm looking at the expectation of e
+ 
+
+ align:start position:0%
+now I'm looking at the expectation of e
+squ but e is a
+
+ align:start position:0%
+squ but e is a
+ 
+
+ align:start position:0%
+squ but e is a
+vector we've got here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M uh
+
+ align:start position:0%
+M uh
+ 
+
+ align:start position:0%
+M uh
+measurements MBS M
+
+ align:start position:0%
+measurements MBS M
+ 
+
+ align:start position:0%
+measurements MBS M
+errors so this is a and those
+
+ align:start position:0%
+errors so this is a and those
+ 
+
+ align:start position:0%
+errors so this is a and those
+errors those M errors from the from the
+
+ align:start position:0%
+errors those M errors from the from the
+ 
+
+ align:start position:0%
+errors those M errors from the from the
+M measurements may
+
+ align:start position:0%
+M measurements may
+ 
+
+ align:start position:0%
+M measurements may
+be independent and identical just all
+
+ align:start position:0%
+be independent and identical just all
+ 
+
+ align:start position:0%
+be independent and identical just all
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+uh and very frequently very frequently
+
+ align:start position:0%
+uh and very frequently very frequently
+ 
+
+ align:start position:0%
+uh and very frequently very frequently
+uh so they we might use the word white
+
+ align:start position:0%
+uh so they we might use the word white
+ 
+
+ align:start position:0%
+uh so they we might use the word white
+noise or something for the error in that
+
+ align:start position:0%
+noise or something for the error in that
+ 
+
+ align:start position:0%
+noise or something for the error in that
+case uh or they might be correlated so
+
+ align:start position:0%
+case uh or they might be correlated so
+ 
+
+ align:start position:0%
+case uh or they might be correlated so
+this Matrix tells us and you've seen it
+
+ align:start position:0%
+this Matrix tells us and you've seen it
+ 
+
+ align:start position:0%
+this Matrix tells us and you've seen it
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what that's the covariance Matrix
+
+ align:start position:0%
+that's what that's the covariance Matrix
+ 
+
+ align:start position:0%
+that's what that's the covariance Matrix
+so let's just look at a typical entry
+
+ align:start position:0%
+so let's just look at a typical entry
+ 
+
+ align:start position:0%
+so let's just look at a typical entry
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+JJ entry
+
+ align:start position:0%
+JJ entry
+ 
+
+ align:start position:0%
+JJ entry
+is the expected value of the e error
+
+ align:start position:0%
+is the expected value of the e error
+ 
+
+ align:start position:0%
+is the expected value of the e error
+times the J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+error
+
+ align:start position:0%
+error
+ 
+
+ align:start position:0%
+error
+and Independence means that the Matrix
+
+ align:start position:0%
+and Independence means that the Matrix
+ 
+
+ align:start position:0%
+and Independence means that the Matrix
+is what so what's the Matrix so independ
+
+ align:start position:0%
+is what so what's the Matrix so independ
+ 
+
+ align:start position:0%
+is what so what's the Matrix so independ
+observations would mean uh in
+
+ align:start position:0%
+observations would mean uh in
+ 
+
+ align:start position:0%
+observations would mean uh in
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+errors would mean
+
+ align:start position:0%
+errors would mean
+ 
+
+ align:start position:0%
+errors would mean
+what that that that the Matrix is
+
+ align:start position:0%
+what that that that the Matrix is
+ 
+
+ align:start position:0%
+what that that that the Matrix is
+diagonal right that that when I is
+
+ align:start position:0%
+diagonal right that that when I is
+ 
+
+ align:start position:0%
+diagonal right that that when I is
+different from
+
+ align:start position:0%
+different from
+ 
+
+ align:start position:0%
+different from
+J there's no there's no connection
+
+ align:start position:0%
+J there's no there's no connection
+ 
+
+ align:start position:0%
+J there's no there's no connection
+between those two errors The Joint
+
+ align:start position:0%
+between those two errors The Joint
+ 
+
+ align:start position:0%
+between those two errors The Joint
+probability is just one probability
+
+ align:start position:0%
+probability is just one probability
+ 
+
+ align:start position:0%
+probability is just one probability
+times the other in which case we can
+
+ align:start position:0%
+times the other in which case we can
+ 
+
+ align:start position:0%
+times the other in which case we can
+like separate this into two integrals
+
+ align:start position:0%
+like separate this into two integrals
+ 
+
+ align:start position:0%
+like separate this into two integrals
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is our assumption that the
+
+ align:start position:0%
+this is our assumption that the
+ 
+
+ align:start position:0%
+this is our assumption that the
+expectation of a single one is zero so
+
+ align:start position:0%
+expectation of a single one is zero so
+ 
+
+ align:start position:0%
+expectation of a single one is zero so
+we get 0 time 0 we get zero so
+
+ align:start position:0%
+we get 0 time 0 we get zero so
+ 
+
+ align:start position:0%
+we get 0 time 0 we get zero so
+independent independent errors would be
+
+ align:start position:0%
+independent independent errors would be
+ 
+
+ align:start position:0%
+independent independent errors would be
+uh uh Sigma i j would be zero
+
+ align:start position:0%
+uh uh Sigma i j would be zero
+ 
+
+ align:start position:0%
+uh uh Sigma i j would be zero
+okay uh yeah is that or this would be
+
+ align:start position:0%
+okay uh yeah is that or this would be
+ 
+
+ align:start position:0%
+okay uh yeah is that or this would be
+zero anyway yeah yeah the the the JJ
+
+ align:start position:0%
+zero anyway yeah yeah the the the JJ
+ 
+
+ align:start position:0%
+zero anyway yeah yeah the the the JJ
+entry independent errors it you said it
+
+ align:start position:0%
+entry independent errors it you said it
+ 
+
+ align:start position:0%
+entry independent errors it you said it
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+diagonal Sigma and identical errors what
+
+ align:start position:0%
+diagonal Sigma and identical errors what
+ 
+
+ align:start position:0%
+diagonal Sigma and identical errors what
+what would that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean because you often see these words
+
+ align:start position:0%
+mean because you often see these words
+ 
+
+ align:start position:0%
+mean because you often see these words
+in fact they get abbreviated to I I
+
+ align:start position:0%
+in fact they get abbreviated to I I
+ 
+
+ align:start position:0%
+in fact they get abbreviated to I I
+because they this is an assumption this
+
+ align:start position:0%
+because they this is an assumption this
+ 
+
+ align:start position:0%
+because they this is an assumption this
+this whiteness assumption is made so
+
+ align:start position:0%
+this whiteness assumption is made so
+ 
+
+ align:start position:0%
+this whiteness assumption is made so
+often and when they're identical what
+
+ align:start position:0%
+often and when they're identical what
+ 
+
+ align:start position:0%
+often and when they're identical what
+what would that
+
+ align:start position:0%
+what would that
+ 
+
+ align:start position:0%
+what would that
+mean right and and and for their Matrix
+
+ align:start position:0%
+mean right and and and for their Matrix
+ 
+
+ align:start position:0%
+mean right and and and for their Matrix
+that will mean that
+
+ align:start position:0%
+that will mean that
+ 
+
+ align:start position:0%
+that will mean that
+Sigma yeah it's just a multiple of I
+
+ align:start position:0%
+Sigma yeah it's just a multiple of I
+ 
+
+ align:start position:0%
+Sigma yeah it's just a multiple of I
+Sigma equals some whatever this this
+
+ align:start position:0%
+Sigma equals some whatever this this
+ 
+
+ align:start position:0%
+Sigma equals some whatever this this
+common Sigma times I right so that very
+
+ align:start position:0%
+common Sigma times I right so that very
+ 
+
+ align:start position:0%
+common Sigma times I right so that very
+often we we uh assume that and just to
+
+ align:start position:0%
+often we we uh assume that and just to
+ 
+
+ align:start position:0%
+often we we uh assume that and just to
+mention we can always you can always
+
+ align:start position:0%
+mention we can always you can always
+ 
+
+ align:start position:0%
+mention we can always you can always
+look at what we're we we could always
+
+ align:start position:0%
+look at what we're we we could always
+ 
+
+ align:start position:0%
+look at what we're we we could always
+change variables whiten the the the
+
+ align:start position:0%
+change variables whiten the the the
+ 
+
+ align:start position:0%
+change variables whiten the the the
+Errors By by a change of variables we if
+
+ align:start position:0%
+Errors By by a change of variables we if
+ 
+
+ align:start position:0%
+Errors By by a change of variables we if
+we if we uh put part of this Sigma into
+
+ align:start position:0%
+we if we uh put part of this Sigma into
+ 
+
+ align:start position:0%
+we if we uh put part of this Sigma into
+our problem the effect is to whiten the
+
+ align:start position:0%
+our problem the effect is to whiten the
+ 
+
+ align:start position:0%
+our problem the effect is to whiten the
+ears in fact if I put square root of
+
+ align:start position:0%
+ears in fact if I put square root of
+ 
+
+ align:start position:0%
+ears in fact if I put square root of
+Sigma in here that will uh uh have have
+
+ align:start position:0%
+Sigma in here that will uh uh have have
+ 
+
+ align:start position:0%
+Sigma in here that will uh uh have have
+that effect so uh I can get to that if I
+
+ align:start position:0%
+that effect so uh I can get to that if I
+ 
+
+ align:start position:0%
+that effect so uh I can get to that if I
+want to but but uh uh now I better say
+
+ align:start position:0%
+want to but but uh uh now I better say
+ 
+
+ align:start position:0%
+want to but but uh uh now I better say
+something quite important that
+
+ align:start position:0%
+something quite important that
+ 
+
+ align:start position:0%
+something quite important that
+uh that looking ahead we aren't going to
+
+ align:start position:0%
+uh that looking ahead we aren't going to
+ 
+
+ align:start position:0%
+uh that looking ahead we aren't going to
+assume that all our errors are
+
+ align:start position:0%
+assume that all our errors are
+ 
+
+ align:start position:0%
+assume that all our errors are
+independent or identical so I'm not
+
+ align:start position:0%
+independent or identical so I'm not
+ 
+
+ align:start position:0%
+independent or identical so I'm not
+going to assume that Sigma is so simple
+
+ align:start position:0%
+going to assume that Sigma is so simple
+ 
+
+ align:start position:0%
+going to assume that Sigma is so simple
+but when it gets
+
+ align:start position:0%
+but when it gets
+ 
+
+ align:start position:0%
+but when it gets
+to recursive stuff so that sort of
+
+ align:start position:0%
+to recursive stuff so that sort of
+ 
+
+ align:start position:0%
+to recursive stuff so that sort of
+things are
+
+ align:start position:0%
+things are
+ 
+
+ align:start position:0%
+things are
+happening you know we have some
+
+ align:start position:0%
+happening you know we have some
+ 
+
+ align:start position:0%
+happening you know we have some
+information and then we get some new
+
+ align:start position:0%
+information and then we get some new
+ 
+
+ align:start position:0%
+information and then we get some new
+information then I will be
+
+ align:start position:0%
+information then I will be
+ 
+
+ align:start position:0%
+information then I will be
+assuming that the
+
+ align:start position:0%
+assuming that the
+ 
+
+ align:start position:0%
+assuming that the
+sigma for the old
+
+ align:start position:0%
+sigma for the old
+ 
+
+ align:start position:0%
+sigma for the old
+information and for the new are are
+
+ align:start position:0%
+information and for the new are are
+ 
+
+ align:start position:0%
+information and for the new are are
+independent uh I'll assume that the old
+
+ align:start position:0%
+independent uh I'll assume that the old
+ 
+
+ align:start position:0%
+independent uh I'll assume that the old
+errors and the new errors are
+
+ align:start position:0%
+errors and the new errors are
+ 
+
+ align:start position:0%
+errors and the new errors are
+independent so that my so so
+
+ align:start position:0%
+independent so that my so so
+ 
+
+ align:start position:0%
+independent so that my so so
+typically
+
+ align:start position:0%
+typically
+ 
+
+ align:start position:0%
+typically
+so just while I'm discussing
+
+ align:start position:0%
+so just while I'm discussing
+ 
+
+ align:start position:0%
+so just while I'm discussing
+Sigma what if imagine a I hope you're
+
+ align:start position:0%
+Sigma what if imagine a I hope you're
+ 
+
+ align:start position:0%
+Sigma what if imagine a I hope you're
+imagining a situation in which maybe I
+
+ align:start position:0%
+imagining a situation in which maybe I
+ 
+
+ align:start position:0%
+imagining a situation in which maybe I
+better start start writing this uh
+
+ align:start position:0%
+better start start writing this uh
+ 
+
+ align:start position:0%
+better start start writing this uh
+recursive now I'm I'm combining these
+
+ align:start position:0%
+recursive now I'm I'm combining these
+ 
+
+ align:start position:0%
+recursive now I'm I'm combining these
+discussions here so in the recursive
+
+ align:start position:0%
+discussions here so in the recursive
+ 
+
+ align:start position:0%
+discussions here so in the recursive
+stuff what's my problem I have
+
+ align:start position:0%
+stuff what's my problem I have
+ 
+
+ align:start position:0%
+stuff what's my problem I have
+a there's a there's old there's new
+
+ align:start position:0%
+a there's a there's old there's new
+ 
+
+ align:start position:0%
+a there's a there's old there's new
+there's old data and there's new
+
+ align:start position:0%
+there's old data and there's new
+ 
+
+ align:start position:0%
+there's old data and there's new
+data and my U it's the same U same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U so I could maybe I have one set of
+
+ align:start position:0%
+U so I could maybe I have one set of
+ 
+
+ align:start position:0%
+U so I could maybe I have one set of
+measurements where the coefficient
+
+ align:start position:0%
+measurements where the coefficient
+ 
+
+ align:start position:0%
+measurements where the coefficient
+Matrix is some a new a old sorry the old
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy and then a second set of
+
+ align:start position:0%
+guy and then a second set of
+ 
+
+ align:start position:0%
+guy and then a second set of
+measurements where the of the same U so
+
+ align:start position:0%
+measurements where the of the same U so
+ 
+
+ align:start position:0%
+measurements where the of the same U so
+so it's the same U but new errors new
+
+ align:start position:0%
+so it's the same U but new errors new
+ 
+
+ align:start position:0%
+so it's the same U but new errors new
+measurements and and therefore new
+
+ align:start position:0%
+measurements and and therefore new
+ 
+
+ align:start position:0%
+measurements and and therefore new
+errors and what I want to do is I want
+
+ align:start position:0%
+errors and what I want to do is I want
+ 
+
+ align:start position:0%
+errors and what I want to do is I want
+to solve that
+
+ align:start position:0%
+to solve that
+ 
+
+ align:start position:0%
+to solve that
+problem following all the
+
+ align:start position:0%
+problem following all the
+ 
+
+ align:start position:0%
+problem following all the
+rules but getting the answer in this
+
+ align:start position:0%
+rules but getting the answer in this
+ 
+
+ align:start position:0%
+rules but getting the answer in this
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+so the idea is this problem should get
+
+ align:start position:0%
+so the idea is this problem should get
+ 
+
+ align:start position:0%
+so the idea is this problem should get
+me an if I do it right could get me an
+
+ align:start position:0%
+me an if I do it right could get me an
+ 
+
+ align:start position:0%
+me an if I do it right could get me an
+answer in this
+
+ align:start position:0%
+answer in this
+ 
+
+ align:start position:0%
+answer in this
+form but I will have to
+
+ align:start position:0%
+form but I will have to
+ 
+
+ align:start position:0%
+form but I will have to
+assume to make this come out well I'll
+
+ align:start position:0%
+assume to make this come out well I'll
+ 
+
+ align:start position:0%
+assume to make this come out well I'll
+have to assume that the old errors and
+
+ align:start position:0%
+have to assume that the old errors and
+ 
+
+ align:start position:0%
+have to assume that the old errors and
+new errors are not
+
+ align:start position:0%
+new errors are not
+ 
+
+ align:start position:0%
+new errors are not
+correlated okay so the sigma for this
+
+ align:start position:0%
+correlated okay so the sigma for this
+ 
+
+ align:start position:0%
+correlated okay so the sigma for this
+for this like combined problem the sigma
+
+ align:start position:0%
+for this like combined problem the sigma
+ 
+
+ align:start position:0%
+for this like combined problem the sigma
+combined will be will
+
+ align:start position:0%
+combined will be will
+ 
+
+ align:start position:0%
+combined will be will
+be uh a
+
+ align:start position:0%
+be uh a
+ 
+
+ align:start position:0%
+be uh a
+sigma for the
+
+ align:start position:0%
+sigma for the
+ 
+
+ align:start position:0%
+sigma for the
+old errors no correlation to the sigma
+
+ align:start position:0%
+old errors no correlation to the sigma
+ 
+
+ align:start position:0%
+old errors no correlation to the sigma
+for the new
+
+ align:start position:0%
+for the new
+ 
+
+ align:start position:0%
+for the new
+errors do you see what I'm saying I I I
+
+ align:start position:0%
+errors do you see what I'm saying I I I
+ 
+
+ align:start position:0%
+errors do you see what I'm saying I I I
+I won't be required to assume these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonal nor will I required to be to
+
+ align:start position:0%
+diagonal nor will I required to be to
+ 
+
+ align:start position:0%
+diagonal nor will I required to be to
+assume that they're the same in any way
+
+ align:start position:0%
+assume that they're the same in any way
+ 
+
+ align:start position:0%
+assume that they're the same in any way
+in fact we might have four old
+
+ align:start position:0%
+in fact we might have four old
+ 
+
+ align:start position:0%
+in fact we might have four old
+measurements and one new one or 4,000
+
+ align:start position:0%
+measurements and one new one or 4,000
+ 
+
+ align:start position:0%
+measurements and one new one or 4,000
+old measurements and 10 new
+
+ align:start position:0%
+old measurements and 10 new
+ 
+
+ align:start position:0%
+old measurements and 10 new
+ones it wouldn't even be the same size
+
+ align:start position:0%
+ones it wouldn't even be the same size
+ 
+
+ align:start position:0%
+ones it wouldn't even be the same size
+but the you see that what those zeros
+
+ align:start position:0%
+but the you see that what those zeros
+ 
+
+ align:start position:0%
+but the you see that what those zeros
+are saying is that old and new errors
+
+ align:start position:0%
+are saying is that old and new errors
+ 
+
+ align:start position:0%
+are saying is that old and new errors
+are not correlated okay good so that's
+
+ align:start position:0%
+are not correlated okay good so that's
+ 
+
+ align:start position:0%
+are not correlated okay good so that's
+some discussion of Sigma but now let me
+
+ align:start position:0%
+some discussion of Sigma but now let me
+ 
+
+ align:start position:0%
+some discussion of Sigma but now let me
+come back to this weighted
+
+ align:start position:0%
+come back to this weighted
+ 
+
+ align:start position:0%
+come back to this weighted
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+why do we so so I'm now coming back to
+
+ align:start position:0%
+why do we so so I'm now coming back to
+ 
+
+ align:start position:0%
+why do we so so I'm now coming back to
+weighted not ready for a recursive yet
+
+ align:start position:0%
+weighted not ready for a recursive yet
+ 
+
+ align:start position:0%
+weighted not ready for a recursive yet
+I'm I'm trying to identify what's our
+
+ align:start position:0%
+I'm I'm trying to identify what's our
+ 
+
+ align:start position:0%
+I'm I'm trying to identify what's our
+equation then I think about how to solve
+
+ align:start position:0%
+equation then I think about how to solve
+ 
+
+ align:start position:0%
+equation then I think about how to solve
+it recursively but let's why is this our
+
+ align:start position:0%
+it recursively but let's why is this our
+ 
+
+ align:start position:0%
+it recursively but let's why is this our
+this is our Central equation of the
+
+ align:start position:0%
+this is our Central equation of the
+ 
+
+ align:start position:0%
+this is our Central equation of the
+whole of the whole lecture
+
+ align:start position:0%
+whole of the whole lecture
+ 
+
+ align:start position:0%
+whole of the whole lecture
+absolutely so I've made a specific
+
+ align:start position:0%
+absolutely so I've made a specific
+ 
+
+ align:start position:0%
+absolutely so I've made a specific
+choice of of these waiting Matrix M of
+
+ align:start position:0%
+choice of of these waiting Matrix M of
+ 
+
+ align:start position:0%
+choice of of these waiting Matrix M of
+that waiting Matrix and and
+
+ align:start position:0%
+that waiting Matrix and and
+ 
+
+ align:start position:0%
+that waiting Matrix and and
+uh and it's a it will seem a reasonable
+
+ align:start position:0%
+uh and it's a it will seem a reasonable
+ 
+
+ align:start position:0%
+uh and it's a it will seem a reasonable
+choice to you that we Sigma a small
+
+ align:start position:0%
+choice to you that we Sigma a small
+ 
+
+ align:start position:0%
+choice to you that we Sigma a small
+Sigma a small variance so I'm repeating
+
+ align:start position:0%
+Sigma a small variance so I'm repeating
+ 
+
+ align:start position:0%
+Sigma a small variance so I'm repeating
+what I've said back in the Le squares
+
+ align:start position:0%
+what I've said back in the Le squares
+ 
+
+ align:start position:0%
+what I've said back in the Le squares
+lecture a small variance
+
+ align:start position:0%
+lecture a small variance
+ 
+
+ align:start position:0%
+lecture a small variance
+means small errors reliable measurements
+
+ align:start position:0%
+means small errors reliable measurements
+ 
+
+ align:start position:0%
+means small errors reliable measurements
+so we weight those those more heavily so
+
+ align:start position:0%
+so we weight those those more heavily so
+ 
+
+ align:start position:0%
+so we weight those those more heavily so
+small variance and then taking inverses
+
+ align:start position:0%
+small variance and then taking inverses
+ 
+
+ align:start position:0%
+small variance and then taking inverses
+means heavier weight fine but why is
+
+ align:start position:0%
+means heavier weight fine but why is
+ 
+
+ align:start position:0%
+means heavier weight fine but why is
+this exactly the right way so that's one
+
+ align:start position:0%
+this exactly the right way so that's one
+ 
+
+ align:start position:0%
+this exactly the right way so that's one
+point why why is I mean it's sort of the
+
+ align:start position:0%
+point why why is I mean it's sort of the
+ 
+
+ align:start position:0%
+point why why is I mean it's sort of the
+the pattern is reasonable to weit the
+
+ align:start position:0%
+the pattern is reasonable to weit the
+ 
+
+ align:start position:0%
+the pattern is reasonable to weit the
+more reliable measurements with smaller
+
+ align:start position:0%
+more reliable measurements with smaller
+ 
+
+ align:start position:0%
+more reliable measurements with smaller
+errors High heavier weights but that
+
+ align:start position:0%
+errors High heavier weights but that
+ 
+
+ align:start position:0%
+errors High heavier weights but that
+does it just right and what is just
+
+ align:start position:0%
+does it just right and what is just
+ 
+
+ align:start position:0%
+does it just right and what is just
+right about that and then the other key
+
+ align:start position:0%
+right about that and then the other key
+ 
+
+ align:start position:0%
+right about that and then the other key
+point is that in a lot of problems it's
+
+ align:start position:0%
+point is that in a lot of problems it's
+ 
+
+ align:start position:0%
+point is that in a lot of problems it's
+not just you hat the best parameters
+
+ align:start position:0%
+not just you hat the best parameters
+ 
+
+ align:start position:0%
+not just you hat the best parameters
+that we're
+
+ align:start position:0%
+that we're
+ 
+
+ align:start position:0%
+that we're
+after we're after also some information
+
+ align:start position:0%
+after we're after also some information
+ 
+
+ align:start position:0%
+after we're after also some information
+of how reliable they are how reliable is
+
+ align:start position:0%
+of how reliable they are how reliable is
+ 
+
+ align:start position:0%
+of how reliable they are how reliable is
+you hat we so we so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input is measurements B and their
+
+ align:start position:0%
+input is measurements B and their
+ 
+
+ align:start position:0%
+input is measurements B and their
+variances Sigma B what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output the output will be U
+
+ align:start position:0%
+output the output will be U
+ 
+
+ align:start position:0%
+output the output will be U
+hat the
+
+ align:start position:0%
+hat the
+ 
+
+ align:start position:0%
+hat the
+best estimate of the parameters and the
+
+ align:start position:0%
+best estimate of the parameters and the
+ 
+
+ align:start position:0%
+best estimate of the parameters and the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+variance it's variance how reliable is
+
+ align:start position:0%
+variance it's variance how reliable is
+ 
+
+ align:start position:0%
+variance it's variance how reliable is
+that and and there's going to be of
+
+ align:start position:0%
+that and and there's going to be of
+ 
+
+ align:start position:0%
+that and and there's going to be of
+course a connection between
+
+ align:start position:0%
+course a connection between
+ 
+
+ align:start position:0%
+course a connection between
+these and
+
+ align:start position:0%
+these and
+ 
+
+ align:start position:0%
+these and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh but but the formula for this W uh is
+
+ align:start position:0%
+uh but but the formula for this W uh is
+ 
+
+ align:start position:0%
+uh but but the formula for this W uh is
+it maybe more this may this may be more
+
+ align:start position:0%
+it maybe more this may this may be more
+ 
+
+ align:start position:0%
+it maybe more this may this may be more
+important than that is what I'm trying
+
+ align:start position:0%
+important than that is what I'm trying
+ 
+
+ align:start position:0%
+important than that is what I'm trying
+to say this is this thing comes from a
+
+ align:start position:0%
+to say this is this thing comes from a
+ 
+
+ align:start position:0%
+to say this is this thing comes from a
+specific experiment that gave us a
+
+ align:start position:0%
+specific experiment that gave us a
+ 
+
+ align:start position:0%
+specific experiment that gave us a
+specific you know we we made one we made
+
+ align:start position:0%
+specific you know we we made one we made
+ 
+
+ align:start position:0%
+specific you know we we made one we made
+one run one sample we got we got some
+
+ align:start position:0%
+one run one sample we got we got some
+ 
+
+ align:start position:0%
+one run one sample we got we got some
+B's we some measurements we computed you
+
+ align:start position:0%
+B's we some measurements we computed you
+ 
+
+ align:start position:0%
+B's we some measurements we computed you
+hat if we had if we ran it again we
+
+ align:start position:0%
+hat if we had if we ran it again we
+ 
+
+ align:start position:0%
+hat if we had if we ran it again we
+would get a different you hat so then
+
+ align:start position:0%
+would get a different you hat so then
+ 
+
+ align:start position:0%
+would get a different you hat so then
+you naturally ask well wait a minute I
+
+ align:start position:0%
+you naturally ask well wait a minute I
+ 
+
+ align:start position:0%
+you naturally ask well wait a minute I
+can't just run it and run it run it
+
+ align:start position:0%
+can't just run it and run it run it
+ 
+
+ align:start position:0%
+can't just run it and run it run it
+forever what are the statistics of you
+
+ align:start position:0%
+forever what are the statistics of you
+ 
+
+ align:start position:0%
+forever what are the statistics of you
+hat they they tell us like how good is
+
+ align:start position:0%
+hat they they tell us like how good is
+ 
+
+ align:start position:0%
+hat they they tell us like how good is
+the experiment before we run it
+
+ align:start position:0%
+the experiment before we run it
+ 
+
+ align:start position:0%
+the experiment before we run it
+and uh that's the information here so
+
+ align:start position:0%
+and uh that's the information here so
+ 
+
+ align:start position:0%
+and uh that's the information here so
+this information is is is Central okay
+
+ align:start position:0%
+this information is is is Central okay
+ 
+
+ align:start position:0%
+this information is is is Central okay
+so now the beauty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the beauty and in many cases it's
+
+ align:start position:0%
+is the beauty and in many cases it's
+ 
+
+ align:start position:0%
+is the beauty and in many cases it's
+many formulas involve the inverse of
+
+ align:start position:0%
+many formulas involve the inverse of
+ 
+
+ align:start position:0%
+many formulas involve the inverse of
+that so can I introduce a symbol for the
+
+ align:start position:0%
+that so can I introduce a symbol for the
+ 
+
+ align:start position:0%
+that so can I introduce a symbol for the
+inverse of that of that
+
+ align:start position:0%
+inverse of that of that
+ 
+
+ align:start position:0%
+inverse of that of that
+Matrix I I'll let p be the
+
+ align:start position:0%
+Matrix I I'll let p be the
+ 
+
+ align:start position:0%
+Matrix I I'll let p be the
+inverse of this Sigma you have it's the
+
+ align:start position:0%
+inverse of this Sigma you have it's the
+ 
+
+ align:start position:0%
+inverse of this Sigma you have it's the
+inverse is that is that okay I just I'm
+
+ align:start position:0%
+inverse is that is that okay I just I'm
+ 
+
+ align:start position:0%
+inverse is that is that okay I just I'm
+introducing a a a letter for the inverse
+
+ align:start position:0%
+introducing a a a letter for the inverse
+ 
+
+ align:start position:0%
+introducing a a a letter for the inverse
+Matrix okay so that if I know to know p
+
+ align:start position:0%
+Matrix okay so that if I know to know p
+ 
+
+ align:start position:0%
+Matrix okay so that if I know to know p
+is to know Sigma and to know Sigma is to
+
+ align:start position:0%
+is to know Sigma and to know Sigma is to
+ 
+
+ align:start position:0%
+is to know Sigma and to know Sigma is to
+know P one's the inverse of the other
+
+ align:start position:0%
+know P one's the inverse of the other
+ 
+
+ align:start position:0%
+know P one's the inverse of the other
+okay and it just happens that a lot of
+
+ align:start position:0%
+okay and it just happens that a lot of
+ 
+
+ align:start position:0%
+okay and it just happens that a lot of
+formulas come out especially nice for
+
+ align:start position:0%
+formulas come out especially nice for
+ 
+
+ align:start position:0%
+formulas come out especially nice for
+the inverse p and
+
+ align:start position:0%
+the inverse p and
+ 
+
+ align:start position:0%
+the inverse p and
+and okay right all right let me see if I
+
+ align:start position:0%
+and okay right all right let me see if I
+ 
+
+ align:start position:0%
+and okay right all right let me see if I
+can get
+
+ align:start position:0%
+can get
+ 
+
+ align:start position:0%
+can get
+um I want to get the get the main
+
+ align:start position:0%
+um I want to get the get the main
+ 
+
+ align:start position:0%
+um I want to get the get the main
+formula here that connects this to this
+
+ align:start position:0%
+formula here that connects this to this
+ 
+
+ align:start position:0%
+formula here that connects this to this
+okay let's see if I can all right let's
+
+ align:start position:0%
+okay let's see if I can all right let's
+ 
+
+ align:start position:0%
+okay let's see if I can all right let's
+see if I can
+
+ align:start position:0%
+see if I can
+ 
+
+ align:start position:0%
+see if I can
+see if I look at this
+
+ align:start position:0%
+see if I look at this
+ 
+
+ align:start position:0%
+see if I look at this
+equation it gives me U had in terms of B
+
+ align:start position:0%
+equation it gives me U had in terms of B
+ 
+
+ align:start position:0%
+equation it gives me U had in terms of B
+in a linear way right U hat is some L
+
+ align:start position:0%
+in a linear way right U hat is some L
+ 
+
+ align:start position:0%
+in a linear way right U hat is some L
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+Matrix so I I can if I talk about
+
+ align:start position:0%
+Matrix so I I can if I talk about
+ 
+
+ align:start position:0%
+Matrix so I I can if I talk about
+formulas for a moment U hat is if I just
+
+ align:start position:0%
+formulas for a moment U hat is if I just
+ 
+
+ align:start position:0%
+formulas for a moment U hat is if I just
+read all that stuff off it's this a
+
+ align:start position:0%
+read all that stuff off it's this a
+ 
+
+ align:start position:0%
+read all that stuff off it's this a
+transpose Sigma so Sigma B inverse a
+
+ align:start position:0%
+transpose Sigma so Sigma B inverse a
+ 
+
+ align:start position:0%
+transpose Sigma so Sigma B inverse a
+inverse put that all over there times a
+
+ align:start position:0%
+inverse put that all over there times a
+ 
+
+ align:start position:0%
+inverse put that all over there times a
+transpose Sigma
+
+ align:start position:0%
+transpose Sigma
+ 
+
+ align:start position:0%
+transpose Sigma
+B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse time B
+
+ align:start position:0%
+inverse time B
+ 
+
+ align:start position:0%
+inverse time B
+and for convenience I might recognize
+
+ align:start position:0%
+and for convenience I might recognize
+ 
+
+ align:start position:0%
+and for convenience I might recognize
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+some made some
+
+ align:start position:0%
+some made some
+ 
+
+ align:start position:0%
+some made some
+linear some Matrix applied to
+
+ align:start position:0%
+linear some Matrix applied to
+ 
+
+ align:start position:0%
+linear some Matrix applied to
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now that the reason that helps is
+
+ align:start position:0%
+and now that the reason that helps is
+ 
+
+ align:start position:0%
+and now that the reason that helps is
+that if I'm interested in and as I
+
+ align:start position:0%
+that if I'm interested in and as I
+ 
+
+ align:start position:0%
+that if I'm interested in and as I
+certainly am interested in this Sigma U
+
+ align:start position:0%
+certainly am interested in this Sigma U
+ 
+
+ align:start position:0%
+certainly am interested in this Sigma U
+hat so what's Sigma U hat what's this
+
+ align:start position:0%
+hat so what's Sigma U hat what's this
+ 
+
+ align:start position:0%
+hat so what's Sigma U hat what's this
+what's the covariance Matrix for U hat
+
+ align:start position:0%
+what's the covariance Matrix for U hat
+ 
+
+ align:start position:0%
+what's the covariance Matrix for U hat
+it has to be the expectation of U of the
+
+ align:start position:0%
+it has to be the expectation of U of the
+ 
+
+ align:start position:0%
+it has to be the expectation of U of the
+correct U with no errors minus the U hat
+
+ align:start position:0%
+correct U with no errors minus the U hat
+ 
+
+ align:start position:0%
+correct U with no errors minus the U hat
+which came from B that included errors
+
+ align:start position:0%
+which came from B that included errors
+ 
+
+ align:start position:0%
+which came from B that included errors
+oops not the transpose there if I want I
+
+ align:start position:0%
+oops not the transpose there if I want I
+ 
+
+ align:start position:0%
+oops not the transpose there if I want I
+want a column times a row so that I get
+
+ align:start position:0%
+want a column times a row so that I get
+ 
+
+ align:start position:0%
+want a column times a row so that I get
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now can I just see what's going on
+
+ align:start position:0%
+okay now can I just see what's going on
+ 
+
+ align:start position:0%
+okay now can I just see what's going on
+here I claim that this is this is my
+
+ align:start position:0%
+here I claim that this is this is my
+ 
+
+ align:start position:0%
+here I claim that this is this is my
+error in
+
+ align:start position:0%
+error in
+ 
+
+ align:start position:0%
+error in
+U and the error in U is related to the
+
+ align:start position:0%
+U and the error in U is related to the
+ 
+
+ align:start position:0%
+U and the error in U is related to the
+error in B by L so this I I I would like
+
+ align:start position:0%
+error in B by L so this I I I would like
+ 
+
+ align:start position:0%
+error in B by L so this I I I would like
+to see as the expected value of
+
+ align:start position:0%
+to see as the expected value of
+ 
+
+ align:start position:0%
+to see as the expected value of
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+etimes l e trans
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transpose right to go from from my
+
+ align:start position:0%
+transpose right to go from from my
+ 
+
+ align:start position:0%
+transpose right to go from from my
+inputs to my
+
+ align:start position:0%
+inputs to my
+ 
+
+ align:start position:0%
+inputs to my
+outputs to go from B to U hat I'm
+
+ align:start position:0%
+outputs to go from B to U hat I'm
+ 
+
+ align:start position:0%
+outputs to go from B to U hat I'm
+multiplying by
+
+ align:start position:0%
+multiplying by
+ 
+
+ align:start position:0%
+multiplying by
+L what happens to the to the error
+
+ align:start position:0%
+L what happens to the to the error
+ 
+
+ align:start position:0%
+L what happens to the to the error
+covariance Matrix when I multiply by L
+
+ align:start position:0%
+covariance Matrix when I multiply by L
+ 
+
+ align:start position:0%
+covariance Matrix when I multiply by L
+okay so that well the point is that when
+
+ align:start position:0%
+okay so that well the point is that when
+ 
+
+ align:start position:0%
+okay so that well the point is that when
+I remembering this is an expectation of
+
+ align:start position:0%
+I remembering this is an expectation of
+ 
+
+ align:start position:0%
+I remembering this is an expectation of
+something I'm multiplying
+
+ align:start position:0%
+something I'm multiplying
+ 
+
+ align:start position:0%
+something I'm multiplying
+it's it's the the the sample values
+
+ align:start position:0%
+it's it's the the the sample values
+ 
+
+ align:start position:0%
+it's it's the the the sample values
+times the probability of that sample but
+
+ align:start position:0%
+times the probability of that sample but
+ 
+
+ align:start position:0%
+times the probability of that sample but
+everything here is linear and L is a
+
+ align:start position:0%
+everything here is linear and L is a
+ 
+
+ align:start position:0%
+everything here is linear and L is a
+fixed Matrix so I can bring it out this
+
+ align:start position:0%
+fixed Matrix so I can bring it out this
+ 
+
+ align:start position:0%
+fixed Matrix so I can bring it out this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+L bringing out on the left expected
+
+ align:start position:0%
+L bringing out on the left expected
+ 
+
+ align:start position:0%
+L bringing out on the left expected
+value of e
+
+ align:start position:0%
+value of e
+ 
+
+ align:start position:0%
+value of e
+transpose times L transpose do you see
+
+ align:start position:0%
+transpose times L transpose do you see
+ 
+
+ align:start position:0%
+transpose times L transpose do you see
+that I just the usual parentheses that's
+
+ align:start position:0%
+that I just the usual parentheses that's
+ 
+
+ align:start position:0%
+that I just the usual parentheses that's
+l e e transpose
+
+ align:start position:0%
+l e e transpose
+ 
+
+ align:start position:0%
+l e e transpose
+looks like a cross word puzzle L
+
+ align:start position:0%
+looks like a cross word puzzle L
+ 
+
+ align:start position:0%
+looks like a cross word puzzle L
+transpose okay so all I'm saying is I
+
+ align:start position:0%
+transpose okay so all I'm saying is I
+ 
+
+ align:start position:0%
+transpose okay so all I'm saying is I
+can bring the L and the L transpose out
+
+ align:start position:0%
+can bring the L and the L transpose out
+ 
+
+ align:start position:0%
+can bring the L and the L transpose out
+of the expectation because when I
+
+ align:start position:0%
+of the expectation because when I
+ 
+
+ align:start position:0%
+of the expectation because when I
+multiply these values by
+
+ align:start position:0%
+multiply these values by
+ 
+
+ align:start position:0%
+multiply these values by
+probabilities L is
+
+ align:start position:0%
+probabilities L is
+ 
+
+ align:start position:0%
+probabilities L is
+fixed L is the same okay and what's this
+
+ align:start position:0%
+fixed L is the same okay and what's this
+ 
+
+ align:start position:0%
+fixed L is the same okay and what's this
+here that's Sigma that's Sigma B so this
+
+ align:start position:0%
+here that's Sigma that's Sigma B so this
+ 
+
+ align:start position:0%
+here that's Sigma that's Sigma B so this
+is Sigma B okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+um it's our no wait a minute we could
+
+ align:start position:0%
+um it's our no wait a minute we could
+ 
+
+ align:start position:0%
+um it's our no wait a minute we could
+figure out what this is we we know what
+
+ align:start position:0%
+figure out what this is we we know what
+ 
+
+ align:start position:0%
+figure out what this is we we know what
+L is now this is where I
+
+ align:start position:0%
+L is now this is where I
+ 
+
+ align:start position:0%
+L is now this is where I
+feel like a bit of ma a typical bit of
+
+ align:start position:0%
+feel like a bit of ma a typical bit of
+ 
+
+ align:start position:0%
+feel like a bit of ma a typical bit of
+magic in these formulas is going to
+
+ align:start position:0%
+magic in these formulas is going to
+ 
+
+ align:start position:0%
+magic in these formulas is going to
+happen now I'm going to put in this
+
+ align:start position:0%
+happen now I'm going to put in this
+ 
+
+ align:start position:0%
+happen now I'm going to put in this
+awful expression for L and see what I
+
+ align:start position:0%
+awful expression for L and see what I
+ 
+
+ align:start position:0%
+awful expression for L and see what I
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I'm doing now is totally standard
+
+ align:start position:0%
+what I'm doing now is totally standard
+ 
+
+ align:start position:0%
+what I'm doing now is totally standard
+and and maybe familiar to all of you but
+
+ align:start position:0%
+and and maybe familiar to all of you but
+ 
+
+ align:start position:0%
+and and maybe familiar to all of you but
+I think I better take this last step can
+
+ align:start position:0%
+I think I better take this last step can
+ 
+
+ align:start position:0%
+I think I better take this last step can
+I just say okay I'm claiming that this
+
+ align:start position:0%
+I just say okay I'm claiming that this
+ 
+
+ align:start position:0%
+I just say okay I'm claiming that this
+is the right L to choose well gaus said
+
+ align:start position:0%
+is the right L to choose well gaus said
+ 
+
+ align:start position:0%
+is the right L to choose well gaus said
+it was so who's going to argue with gal
+
+ align:start position:0%
+it was so who's going to argue with gal
+ 
+
+ align:start position:0%
+it was so who's going to argue with gal
+okay so there's he he says that the
+
+ align:start position:0%
+okay so there's he he says that the
+ 
+
+ align:start position:0%
+okay so there's he he says that the
+right L to take is Sigma is the right C
+
+ align:start position:0%
+right L to take is Sigma is the right C
+ 
+
+ align:start position:0%
+right L to take is Sigma is the right C
+to take is is Sigma B inverse Okay so
+
+ align:start position:0%
+to take is is Sigma B inverse Okay so
+ 
+
+ align:start position:0%
+to take is is Sigma B inverse Okay so
+can I put that l in here could you do
+
+ align:start position:0%
+can I put that l in here could you do
+ 
+
+ align:start position:0%
+can I put that l in here could you do
+that multiplication and do you know what
+
+ align:start position:0%
+that multiplication and do you know what
+ 
+
+ align:start position:0%
+that multiplication and do you know what
+we're going to get I'll make a little
+
+ align:start position:0%
+we're going to get I'll make a little
+ 
+
+ align:start position:0%
+we're going to get I'll make a little
+room to do it because L is a little long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but okay here comes L okay so so I have
+
+ align:start position:0%
+but okay here comes L okay so so I have
+ 
+
+ align:start position:0%
+but okay here comes L okay so so I have
+a transpose Sigma inverse a all
+
+ align:start position:0%
+a transpose Sigma inverse a all
+ 
+
+ align:start position:0%
+a transpose Sigma inverse a all
+inverse times a transpose Sigma inverse
+
+ align:start position:0%
+inverse times a transpose Sigma inverse
+ 
+
+ align:start position:0%
+inverse times a transpose Sigma inverse
+that was the that's the L finally okay
+
+ align:start position:0%
+that was the that's the L finally okay
+ 
+
+ align:start position:0%
+that was the that's the L finally okay
+okay now comes the sigma Sigma I'll just
+
+ align:start position:0%
+okay now comes the sigma Sigma I'll just
+ 
+
+ align:start position:0%
+okay now comes the sigma Sigma I'll just
+write Sigma skip the B time Sigma and
+
+ align:start position:0%
+write Sigma skip the B time Sigma and
+ 
+
+ align:start position:0%
+write Sigma skip the B time Sigma and
+now comes I need more room for L
+
+ align:start position:0%
+now comes I need more room for L
+ 
+
+ align:start position:0%
+now comes I need more room for L
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+okay this formula will finish before the
+
+ align:start position:0%
+okay this formula will finish before the
+ 
+
+ align:start position:0%
+okay this formula will finish before the
+board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does now that was L can I what's L
+
+ align:start position:0%
+does now that was L can I what's L
+ 
+
+ align:start position:0%
+does now that was L can I what's L
+transpose Sigma by the way of course is
+
+ align:start position:0%
+transpose Sigma by the way of course is
+ 
+
+ align:start position:0%
+transpose Sigma by the way of course is
+symmetric Sigma of course is
+
+ align:start position:0%
+symmetric Sigma of course is
+ 
+
+ align:start position:0%
+symmetric Sigma of course is
+symmetric so when I transpose I don't
+
+ align:start position:0%
+symmetric so when I transpose I don't
+ 
+
+ align:start position:0%
+symmetric so when I transpose I don't
+have to worry about transposing Sigma a
+
+ align:start position:0%
+have to worry about transposing Sigma a
+ 
+
+ align:start position:0%
+have to worry about transposing Sigma a
+of course I do have to and this
+
+ align:start position:0%
+of course I do have to and this
+ 
+
+ align:start position:0%
+of course I do have to and this
+combination is symmetric so I
+
+ align:start position:0%
+combination is symmetric so I
+ 
+
+ align:start position:0%
+combination is symmetric so I
+transposing that no no effect okay so
+
+ align:start position:0%
+transposing that no no effect okay so
+ 
+
+ align:start position:0%
+transposing that no no effect okay so
+now I want to transpose this whole thing
+
+ align:start position:0%
+now I want to transpose this whole thing
+ 
+
+ align:start position:0%
+now I want to transpose this whole thing
+in the opposite order so I transpose
+
+ align:start position:0%
+in the opposite order so I transpose
+ 
+
+ align:start position:0%
+in the opposite order so I transpose
+that it's just Sigma inverse transpose
+
+ align:start position:0%
+that it's just Sigma inverse transpose
+ 
+
+ align:start position:0%
+that it's just Sigma inverse transpose
+that it's an a transpose that that's
+
+ align:start position:0%
+that it's an a transpose that that's
+ 
+
+ align:start position:0%
+that it's an a transpose that that's
+symmetric so it doesn't change a
+
+ align:start position:0%
+symmetric so it doesn't change a
+ 
+
+ align:start position:0%
+symmetric so it doesn't change a
+transpose Sigma inverse a inverse and
+
+ align:start position:0%
+transpose Sigma inverse a inverse and
+ 
+
+ align:start position:0%
+transpose Sigma inverse a inverse and
+what have I got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is following all the rules and
+
+ align:start position:0%
+so this is following all the rules and
+ 
+
+ align:start position:0%
+so this is following all the rules and
+notice well there's a sigma inverse
+
+ align:start position:0%
+notice well there's a sigma inverse
+ 
+
+ align:start position:0%
+notice well there's a sigma inverse
+Sigma identity in the middle there then
+
+ align:start position:0%
+Sigma identity in the middle there then
+ 
+
+ align:start position:0%
+Sigma identity in the middle there then
+there's an a transpose Sigma inverse a
+
+ align:start position:0%
+there's an a transpose Sigma inverse a
+ 
+
+ align:start position:0%
+there's an a transpose Sigma inverse a
+which I'll just put parentheses around
+
+ align:start position:0%
+which I'll just put parentheses around
+ 
+
+ align:start position:0%
+which I'll just put parentheses around
+to call attention and what do I have
+
+ align:start position:0%
+to call attention and what do I have
+ 
+
+ align:start position:0%
+to call attention and what do I have
+I've got this inverse times this thing
+
+ align:start position:0%
+I've got this inverse times this thing
+ 
+
+ align:start position:0%
+I've got this inverse times this thing
+times the inverse again so so this
+
+ align:start position:0%
+times the inverse again so so this
+ 
+
+ align:start position:0%
+times the inverse again so so this
+knocked off this and left me just with
+
+ align:start position:0%
+knocked off this and left me just with
+ 
+
+ align:start position:0%
+knocked off this and left me just with
+this is it all right if I just
+
+ align:start position:0%
+this is it all right if I just
+ 
+
+ align:start position:0%
+this is it all right if I just
+that's the answer what a beautiful
+
+ align:start position:0%
+that's the answer what a beautiful
+ 
+
+ align:start position:0%
+that's the answer what a beautiful
+answer that the the right choice of
+
+ align:start position:0%
+answer that the the right choice of
+ 
+
+ align:start position:0%
+answer that the the right choice of
+Sigma the right choice of the sorry the
+
+ align:start position:0%
+Sigma the right choice of the sorry the
+ 
+
+ align:start position:0%
+Sigma the right choice of the sorry the
+right choice of the waiting Matrix
+
+ align:start position:0%
+right choice of the waiting Matrix
+ 
+
+ align:start position:0%
+right choice of the waiting Matrix
+produced a beautiful answer for the uh
+
+ align:start position:0%
+produced a beautiful answer for the uh
+ 
+
+ align:start position:0%
+produced a beautiful answer for the uh
+variance in the in the in the uh hat and
+
+ align:start position:0%
+variance in the in the in the uh hat and
+ 
+
+ align:start position:0%
+variance in the in the in the uh hat and
+the Beautiful answer is this is the
+
+ align:start position:0%
+the Beautiful answer is this is the
+ 
+
+ align:start position:0%
+the Beautiful answer is this is the
+inverse is p is our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P that's theu Matrix then in fact that's
+
+ align:start position:0%
+P that's theu Matrix then in fact that's
+ 
+
+ align:start position:0%
+P that's theu Matrix then in fact that's
+like the most important thing output so
+
+ align:start position:0%
+like the most important thing output so
+ 
+
+ align:start position:0%
+like the most important thing output so
+that that the most important output is
+
+ align:start position:0%
+that that the most important output is
+ 
+
+ align:start position:0%
+that that the most important output is
+that uh Sigma U hat which we finally
+
+ align:start position:0%
+that uh Sigma U hat which we finally
+ 
+
+ align:start position:0%
+that uh Sigma U hat which we finally
+identified
+
+ align:start position:0%
+identified
+ 
+
+ align:start position:0%
+identified
+as as Sigma U hat we finally identified
+
+ align:start position:0%
+as as Sigma U hat we finally identified
+ 
+
+ align:start position:0%
+as as Sigma U hat we finally identified
+as our Matrix
+
+ align:start position:0%
+as our Matrix
+ 
+
+ align:start position:0%
+as our Matrix
+p is that
+
+ align:start position:0%
+p is that
+ 
+
+ align:start position:0%
+p is that
+right let's see uh I didn't yes sorry I
+
+ align:start position:0%
+right let's see uh I didn't yes sorry I
+ 
+
+ align:start position:0%
+right let's see uh I didn't yes sorry I
+didn't this was wrong just un
+
+ align:start position:0%
+didn't this was wrong just un
+ 
+
+ align:start position:0%
+didn't this was wrong just un
+fortunately I I get to erase it I meant
+
+ align:start position:0%
+fortunately I I get to erase it I meant
+ 
+
+ align:start position:0%
+fortunately I I get to erase it I meant
+P to be exactly this Matrix that we're
+
+ align:start position:0%
+P to be exactly this Matrix that we're
+ 
+
+ align:start position:0%
+P to be exactly this Matrix that we're
+sorry The crucial Matrix for us p
+
+ align:start position:0%
+sorry The crucial Matrix for us p
+ 
+
+ align:start position:0%
+sorry The crucial Matrix for us p
+is is a transpose Sigma B inverse a all
+
+ align:start position:0%
+is is a transpose Sigma B inverse a all
+ 
+
+ align:start position:0%
+is is a transpose Sigma B inverse a all
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+that's that's the key that's the
+
+ align:start position:0%
+that's that's the key that's the
+ 
+
+ align:start position:0%
+that's that's the key that's the
+beautiful Matrix in the whole subject
+
+ align:start position:0%
+beautiful Matrix in the whole subject
+ 
+
+ align:start position:0%
+beautiful Matrix in the whole subject
+and oh I can't help saying this is this
+
+ align:start position:0%
+and oh I can't help saying this is this
+ 
+
+ align:start position:0%
+and oh I can't help saying this is this
+is the inverse of our stiffness Matrix
+
+ align:start position:0%
+is the inverse of our stiffness Matrix
+ 
+
+ align:start position:0%
+is the inverse of our stiffness Matrix
+those early lectures were
+
+ align:start position:0%
+those early lectures were
+ 
+
+ align:start position:0%
+those early lectures were
+about this Matrix right and its
+
+ align:start position:0%
+about this Matrix right and its
+ 
+
+ align:start position:0%
+about this Matrix right and its
+inverse and now we're meeting it as the
+
+ align:start position:0%
+inverse and now we're meeting it as the
+ 
+
+ align:start position:0%
+inverse and now we're meeting it as the
+central output that the inverse of the
+
+ align:start position:0%
+central output that the inverse of the
+ 
+
+ align:start position:0%
+central output that the inverse of the
+stiffness Matrix as the central output
+
+ align:start position:0%
+stiffness Matrix as the central output
+ 
+
+ align:start position:0%
+stiffness Matrix as the central output
+Sigma U hat the it's the variance of the
+
+ align:start position:0%
+Sigma U hat the it's the variance of the
+ 
+
+ align:start position:0%
+Sigma U hat the it's the variance of the
+error in our uh estimated
+
+ align:start position:0%
+error in our uh estimated
+ 
+
+ align:start position:0%
+error in our uh estimated
+parameters it's it's
+
+ align:start position:0%
+parameters it's it's
+ 
+
+ align:start position:0%
+parameters it's it's
+fantastic and
+
+ align:start position:0%
+fantastic and
+ 
+
+ align:start position:0%
+fantastic and
+there's one more Central
+
+ align:start position:0%
+there's one more Central
+ 
+
+ align:start position:0%
+there's one more Central
+Point you remember what was special
+
+ align:start position:0%
+Point you remember what was special
+ 
+
+ align:start position:0%
+Point you remember what was special
+about those matrices in the beginning of
+
+ align:start position:0%
+about those matrices in the beginning of
+ 
+
+ align:start position:0%
+about those matrices in the beginning of
+this course of
+
+ align:start position:0%
+this course of
+ 
+
+ align:start position:0%
+this course of
+lectures they were
+
+ align:start position:0%
+lectures they were
+ 
+
+ align:start position:0%
+lectures they were
+triagonal they were Tri diagonal and
+
+ align:start position:0%
+triagonal they were Tri diagonal and
+ 
+
+ align:start position:0%
+triagonal they were Tri diagonal and
+that and that came for the line of
+
+ align:start position:0%
+that and that came for the line of
+ 
+
+ align:start position:0%
+that and that came for the line of
+Springs
+
+ align:start position:0%
+Springs
+ 
+
+ align:start position:0%
+Springs
+because um each spring was just
+
+ align:start position:0%
+because um each spring was just
+ 
+
+ align:start position:0%
+because um each spring was just
+connected to one spring below and one
+
+ align:start position:0%
+connected to one spring below and one
+ 
+
+ align:start position:0%
+connected to one spring below and one
+above
+
+ align:start position:0%
+above
+ 
+
+ align:start position:0%
+above
+but Springs here were not connected to
+
+ align:start position:0%
+but Springs here were not connected to
+ 
+
+ align:start position:0%
+but Springs here were not connected to
+Springs 10 down or we wouldn't have had
+
+ align:start position:0%
+Springs 10 down or we wouldn't have had
+ 
+
+ align:start position:0%
+Springs 10 down or we wouldn't have had
+tridiagonal
+
+ align:start position:0%
+tridiagonal
+ 
+
+ align:start position:0%
+tridiagonal
+matrices all I want to say is that the
+
+ align:start position:0%
+matrices all I want to say is that the
+ 
+
+ align:start position:0%
+matrices all I want to say is that the
+most important word that's not on this
+
+ align:start position:0%
+most important word that's not on this
+ 
+
+ align:start position:0%
+most important word that's not on this
+Blackboard is
+
+ align:start position:0%
+Blackboard is
+ 
+
+ align:start position:0%
+Blackboard is
+tridiagonal that's it's the I'll have to
+
+ align:start position:0%
+tridiagonal that's it's the I'll have to
+ 
+
+ align:start position:0%
+tridiagonal that's it's the I'll have to
+qualify it for for those first lectures
+
+ align:start position:0%
+qualify it for for those first lectures
+ 
+
+ align:start position:0%
+qualify it for for those first lectures
+it was normal triagonal
+
+ align:start position:0%
+it was normal triagonal
+ 
+
+ align:start position:0%
+it was normal triagonal
+matrices now we're going to have blocks
+
+ align:start position:0%
+matrices now we're going to have blocks
+ 
+
+ align:start position:0%
+matrices now we're going to have blocks
+triagonal that's the central thing that
+
+ align:start position:0%
+triagonal that's the central thing that
+ 
+
+ align:start position:0%
+triagonal that's the central thing that
+makes the whole calman filter process
+
+ align:start position:0%
+makes the whole calman filter process
+ 
+
+ align:start position:0%
+makes the whole calman filter process
+work is that the the the key Matrix in
+
+ align:start position:0%
+work is that the the the key Matrix in
+ 
+
+ align:start position:0%
+work is that the the the key Matrix in
+there this Matrix in the in the giant
+
+ align:start position:0%
+there this Matrix in the in the giant
+ 
+
+ align:start position:0%
+there this Matrix in the in the giant
+process is block Tri diagonal that's I
+
+ align:start position:0%
+process is block Tri diagonal that's I
+ 
+
+ align:start position:0%
+process is block Tri diagonal that's I
+can't overemphasize that that's the key
+
+ align:start position:0%
+can't overemphasize that that's the key
+ 
+
+ align:start position:0%
+can't overemphasize that that's the key
+to all the Matrix formulas and to the
+
+ align:start position:0%
+to all the Matrix formulas and to the
+ 
+
+ align:start position:0%
+to all the Matrix formulas and to the
+recursion and to everything that's and
+
+ align:start position:0%
+recursion and to everything that's and
+ 
+
+ align:start position:0%
+recursion and to everything that's and
+and you can see that it's uh lots of
+
+ align:start position:0%
+and you can see that it's uh lots of
+ 
+
+ align:start position:0%
+and you can see that it's uh lots of
+applications are blocked tried diagonal
+
+ align:start position:0%
+applications are blocked tried diagonal
+ 
+
+ align:start position:0%
+applications are blocked tried diagonal
+the new state comes from the old state
+
+ align:start position:0%
+the new state comes from the old state
+ 
+
+ align:start position:0%
+the new state comes from the old state
+but it doesn't come from 10 old
+
+ align:start position:0%
+but it doesn't come from 10 old
+ 
+
+ align:start position:0%
+but it doesn't come from 10 old
+States or it doesn't go all the way back
+
+ align:start position:0%
+States or it doesn't go all the way back
+ 
+
+ align:start position:0%
+States or it doesn't go all the way back
+to the very beginning state it just it's
+
+ align:start position:0%
+to the very beginning state it just it's
+ 
+
+ align:start position:0%
+to the very beginning state it just it's
+connected to the previous state and it's
+
+ align:start position:0%
+connected to the previous state and it's
+ 
+
+ align:start position:0%
+connected to the previous state and it's
+like you know we have a differential
+
+ align:start position:0%
+like you know we have a differential
+ 
+
+ align:start position:0%
+like you know we have a differential
+equation or a difference equation
+
+ align:start position:0%
+equation or a difference equation
+ 
+
+ align:start position:0%
+equation or a difference equation
+connecting new state to old one I I'll
+
+ align:start position:0%
+connecting new state to old one I I'll
+ 
+
+ align:start position:0%
+connecting new state to old one I I'll
+come back to
+
+ align:start position:0%
+come back to
+ 
+
+ align:start position:0%
+come back to
+that in the in the second lecture of
+
+ align:start position:0%
+that in the in the second lecture of
+ 
+
+ align:start position:0%
+that in the in the second lecture of
+course when when we really get to that
+
+ align:start position:0%
+course when when we really get to that
+ 
+
+ align:start position:0%
+course when when we really get to that
+okay I just didn't didn't want
+
+ align:start position:0%
+okay I just didn't didn't want
+ 
+
+ align:start position:0%
+okay I just didn't didn't want
+to all I can what I can try to do in
+
+ align:start position:0%
+to all I can what I can try to do in
+ 
+
+ align:start position:0%
+to all I can what I can try to do in
+these lectures is to
+
+ align:start position:0%
+these lectures is to
+ 
+
+ align:start position:0%
+these lectures is to
+highlight what seems like to me the key
+
+ align:start position:0%
+highlight what seems like to me the key
+ 
+
+ align:start position:0%
+highlight what seems like to me the key
+points we're going to need we're going
+
+ align:start position:0%
+points we're going to need we're going
+ 
+
+ align:start position:0%
+points we're going to need we're going
+to have formulas and I won't get them
+
+ align:start position:0%
+to have formulas and I won't get them
+ 
+
+ align:start position:0%
+to have formulas and I won't get them
+all on the board but um
+
+ align:start position:0%
+all on the board but um
+ 
+
+ align:start position:0%
+all on the board but um
+we but those can be looked up those will
+
+ align:start position:0%
+we but those can be looked up those will
+ 
+
+ align:start position:0%
+we but those can be looked up those will
+be in this chapter that goes on the web
+
+ align:start position:0%
+be in this chapter that goes on the web
+ 
+
+ align:start position:0%
+be in this chapter that goes on the web
+and and there many other descriptions of
+
+ align:start position:0%
+and and there many other descriptions of
+ 
+
+ align:start position:0%
+and and there many other descriptions of
+them in the references and I have begun
+
+ align:start position:0%
+them in the references and I have begun
+ 
+
+ align:start position:0%
+them in the references and I have begun
+to give all the
+
+ align:start position:0%
+to give all the
+ 
+
+ align:start position:0%
+to give all the
+references uh but the ideas are always
+
+ align:start position:0%
+references uh but the ideas are always
+ 
+
+ align:start position:0%
+references uh but the ideas are always
+not so many and one of them is block
+
+ align:start position:0%
+not so many and one of them is block
+ 
+
+ align:start position:0%
+not so many and one of them is block
+triagonal they're blocks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+B new the new the new uh uh in this
+
+ align:start position:0%
+B new the new the new uh uh in this
+ 
+
+ align:start position:0%
+B new the new the new uh uh in this
+recursive stuff this is a block of bees
+
+ align:start position:0%
+recursive stuff this is a block of bees
+ 
+
+ align:start position:0%
+recursive stuff this is a block of bees
+this is another block of B's this is a
+
+ align:start position:0%
+this is another block of B's this is a
+ 
+
+ align:start position:0%
+this is another block of B's this is a
+block of a this is the rest of a the
+
+ align:start position:0%
+block of a this is the rest of a the
+ 
+
+ align:start position:0%
+block of a this is the rest of a the
+this is the block picture do you want me
+
+ align:start position:0%
+this is the block picture do you want me
+ 
+
+ align:start position:0%
+this is the block picture do you want me
+to write that as a block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture it's the block Matrix is a old a
+
+ align:start position:0%
+picture it's the block Matrix is a old a
+ 
+
+ align:start position:0%
+picture it's the block Matrix is a old a
+new and it multiplies U and the U is not
+
+ align:start position:0%
+new and it multiplies U and the U is not
+ 
+
+ align:start position:0%
+new and it multiplies U and the U is not
+changing length if we have a newer and a
+
+ align:start position:0%
+changing length if we have a newer and a
+ 
+
+ align:start position:0%
+changing length if we have a newer and a
+newer and a brand new Block in the
+
+ align:start position:0%
+newer and a brand new Block in the
+ 
+
+ align:start position:0%
+newer and a brand new Block in the
+recursive setup we're still keeping the
+
+ align:start position:0%
+recursive setup we're still keeping the
+ 
+
+ align:start position:0%
+recursive setup we're still keeping the
+same u in the calman setup we're also
+
+ align:start position:0%
+same u in the calman setup we're also
+ 
+
+ align:start position:0%
+same u in the calman setup we're also
+getting a new U and a newer U and a
+
+ align:start position:0%
+getting a new U and a newer U and a
+ 
+
+ align:start position:0%
+getting a new U and a newer U and a
+brand new U so that's the difference
+
+ align:start position:0%
+brand new U so that's the difference
+ 
+
+ align:start position:0%
+brand new U so that's the difference
+here that
+
+ align:start position:0%
+here that
+ 
+
+ align:start position:0%
+here that
+recursive uh you could say it in Matrix
+
+ align:start position:0%
+recursive uh you could say it in Matrix
+ 
+
+ align:start position:0%
+recursive uh you could say it in Matrix
+language recursively squares we're
+
+ align:start position:0%
+language recursively squares we're
+ 
+
+ align:start position:0%
+language recursively squares we're
+adding new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rows in Dynamic problems we're adding
+
+ align:start position:0%
+rows in Dynamic problems we're adding
+ 
+
+ align:start position:0%
+rows in Dynamic problems we're adding
+new parameters so we're adding new
+
+ align:start position:0%
+new parameters so we're adding new
+ 
+
+ align:start position:0%
+new parameters so we're adding new
+columns too so we're adding new rows and
+
+ align:start position:0%
+columns too so we're adding new rows and
+ 
+
+ align:start position:0%
+columns too so we're adding new rows and
+columns so should I write that down to
+
+ align:start position:0%
+columns so should I write that down to
+ 
+
+ align:start position:0%
+columns so should I write that down to
+get it on the board recursive this stuff
+
+ align:start position:0%
+get it on the board recursive this stuff
+ 
+
+ align:start position:0%
+get it on the board recursive this stuff
+is new rows new rows in
+
+ align:start position:0%
+is new rows new rows in
+ 
+
+ align:start position:0%
+is new rows new rows in
+a and the Dynamics is
+
+ align:start position:0%
+a and the Dynamics is
+ 
+
+ align:start position:0%
+a and the Dynamics is
+new columns
+
+ align:start position:0%
+new columns
+ 
+
+ align:start position:0%
+new columns
+to new
+
+ align:start position:0%
+to new
+ 
+
+ align:start position:0%
+to new
+unknowns okay but this lecture is about
+
+ align:start position:0%
+unknowns okay but this lecture is about
+ 
+
+ align:start position:0%
+unknowns okay but this lecture is about
+new rows is about this problem is about
+
+ align:start position:0%
+new rows is about this problem is about
+ 
+
+ align:start position:0%
+new rows is about this problem is about
+this problem so now I'm ready to turn to
+
+ align:start position:0%
+this problem so now I'm ready to turn to
+ 
+
+ align:start position:0%
+this problem so now I'm ready to turn to
+that problem but first I didn't make
+
+ align:start position:0%
+that problem but first I didn't make
+ 
+
+ align:start position:0%
+that problem but first I didn't make
+the most important comment about this
+
+ align:start position:0%
+the most important comment about this
+ 
+
+ align:start position:0%
+the most important comment about this
+I've never written such a long equation
+
+ align:start position:0%
+I've never written such a long equation
+ 
+
+ align:start position:0%
+I've never written such a long equation
+I'm sure as this one for Sigma
+
+ align:start position:0%
+I'm sure as this one for Sigma
+ 
+
+ align:start position:0%
+I'm sure as this one for Sigma
+U which has turned out to be P which
+
+ align:start position:0%
+U which has turned out to be P which
+ 
+
+ align:start position:0%
+U which has turned out to be P which
+turned out to have this NE
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer what's
+
+ align:start position:0%
+answer what's
+ 
+
+ align:start position:0%
+answer what's
+the the point I haven't made but the
+
+ align:start position:0%
+the the point I haven't made but the
+ 
+
+ align:start position:0%
+the the point I haven't made but the
+it's it's uh established in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+textbook is the reason for this Choice
+
+ align:start position:0%
+textbook is the reason for this Choice
+ 
+
+ align:start position:0%
+textbook is the reason for this Choice
+the reason that choice is the right
+
+ align:start position:0%
+the reason that choice is the right
+ 
+
+ align:start position:0%
+the reason that choice is the right
+one is that it
+
+ align:start position:0%
+one is that it
+ 
+
+ align:start position:0%
+one is that it
+makes this Matrix p as small as
+
+ align:start position:0%
+makes this Matrix p as small as
+ 
+
+ align:start position:0%
+makes this Matrix p as small as
+possible we get the best
+
+ align:start position:0%
+possible we get the best
+ 
+
+ align:start position:0%
+possible we get the best
+estimate in the sense that the variance
+
+ align:start position:0%
+estimate in the sense that the variance
+ 
+
+ align:start position:0%
+estimate in the sense that the variance
+is the the the the the variant
+
+ align:start position:0%
+is the the the the the variant
+ 
+
+ align:start position:0%
+is the the the the the variant
+covariance Matrix is as small as
+
+ align:start position:0%
+covariance Matrix is as small as
+ 
+
+ align:start position:0%
+covariance Matrix is as small as
+possible by making this choice of
+
+ align:start position:0%
+possible by making this choice of
+ 
+
+ align:start position:0%
+possible by making this choice of
+Sigma this Choice sorry this choice of C
+
+ align:start position:0%
+Sigma this Choice sorry this choice of C
+ 
+
+ align:start position:0%
+Sigma this Choice sorry this choice of C
+this by taking that particular waiting
+
+ align:start position:0%
+this by taking that particular waiting
+ 
+
+ align:start position:0%
+this by taking that particular waiting
+Matrix it produced this answer and we
+
+ align:start position:0%
+Matrix it produced this answer and we
+ 
+
+ align:start position:0%
+Matrix it produced this answer and we
+couldn't have got a
+
+ align:start position:0%
+couldn't have got a
+ 
+
+ align:start position:0%
+couldn't have got a
+smaller we couldn't have got a smaller
+
+ align:start position:0%
+smaller we couldn't have got a smaller
+ 
+
+ align:start position:0%
+smaller we couldn't have got a smaller
+Sigma U than
+
+ align:start position:0%
+Sigma U than
+ 
+
+ align:start position:0%
+Sigma U than
+that and uh that's uh that's that's one
+
+ align:start position:0%
+that and uh that's uh that's that's one
+ 
+
+ align:start position:0%
+that and uh that's uh that's that's one
+way to say why it's best so there's an
+
+ align:start position:0%
+way to say why it's best so there's an
+ 
+
+ align:start position:0%
+way to say why it's best so there's an
+optimal property of this of this weight
+
+ align:start position:0%
+optimal property of this of this weight
+ 
+
+ align:start position:0%
+optimal property of this of this weight
+and uh that's one way to justify the
+
+ align:start position:0%
+and uh that's one way to justify the
+ 
+
+ align:start position:0%
+and uh that's one way to justify the
+choice of that of that as our waiting
+
+ align:start position:0%
+choice of that of that as our waiting
+ 
+
+ align:start position:0%
+choice of that of that as our waiting
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+I'm ready to tackle
+
+ align:start position:0%
+I'm ready to tackle
+ 
+
+ align:start position:0%
+I'm ready to tackle
+this this recursion all right so what's
+
+ align:start position:0%
+this this recursion all right so what's
+ 
+
+ align:start position:0%
+this this recursion all right so what's
+the idea we solve the old problem then
+
+ align:start position:0%
+the idea we solve the old problem then
+ 
+
+ align:start position:0%
+the idea we solve the old problem then
+we get new
+
+ align:start position:0%
+we get new
+ 
+
+ align:start position:0%
+we get new
+measurements we
+
+ align:start position:0%
+measurements we
+ 
+
+ align:start position:0%
+measurements we
+have new part of a corresponding new
+
+ align:start position:0%
+have new part of a corresponding new
+ 
+
+ align:start position:0%
+have new part of a corresponding new
+part of the Matrix a and I want to get I
+
+ align:start position:0%
+part of the Matrix a and I want to get I
+ 
+
+ align:start position:0%
+part of the Matrix a and I want to get I
+want to solve the problem
+
+ align:start position:0%
+want to solve the problem
+ 
+
+ align:start position:0%
+want to solve the problem
+again and the point is I want to solve
+
+ align:start position:0%
+again and the point is I want to solve
+ 
+
+ align:start position:0%
+again and the point is I want to solve
+the problem again
+
+ align:start position:0%
+the problem again
+ 
+
+ align:start position:0%
+the problem again
+I don't want to start from the
+
+ align:start position:0%
+I don't want to start from the
+ 
+
+ align:start position:0%
+I don't want to start from the
+beginning that's the that's the
+
+ align:start position:0%
+beginning that's the that's the
+ 
+
+ align:start position:0%
+beginning that's the that's the
+recursive idea I would like to be able
+
+ align:start position:0%
+recursive idea I would like to be able
+ 
+
+ align:start position:0%
+recursive idea I would like to be able
+to say I would like to be able to use my
+
+ align:start position:0%
+to say I would like to be able to use my
+ 
+
+ align:start position:0%
+to say I would like to be able to use my
+the calculation already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+made so I would like to have a update
+
+ align:start position:0%
+made so I would like to have a update
+ 
+
+ align:start position:0%
+made so I would like to have a update
+formula of this type I would like to to
+
+ align:start position:0%
+formula of this type I would like to to
+ 
+
+ align:start position:0%
+formula of this type I would like to to
+see the best you for the combined system
+
+ align:start position:0%
+see the best you for the combined system
+ 
+
+ align:start position:0%
+see the best you for the combined system
+as the best you for the original system
+
+ align:start position:0%
+as the best you for the original system
+ 
+
+ align:start position:0%
+as the best you for the original system
+plus some Matrix and that's going to be
+
+ align:start position:0%
+plus some Matrix and that's going to be
+ 
+
+ align:start position:0%
+plus some Matrix and that's going to be
+a key this common gain Matrix
+
+ align:start position:0%
+a key this common gain Matrix
+ 
+
+ align:start position:0%
+a key this common gain Matrix
+multiplying this quantity now does that
+
+ align:start position:0%
+multiplying this quantity now does that
+ 
+
+ align:start position:0%
+multiplying this quantity now does that
+seem like a reasonable goal before we
+
+ align:start position:0%
+seem like a reasonable goal before we
+ 
+
+ align:start position:0%
+seem like a reasonable goal before we
+reach it let's see if it's let's see
+
+ align:start position:0%
+reach it let's see if it's let's see
+ 
+
+ align:start position:0%
+reach it let's see if it's let's see
+what we're aiming for and
+
+ align:start position:0%
+what we're aiming for and
+ 
+
+ align:start position:0%
+what we're aiming for and
+you'll what would happen
+
+ align:start position:0%
+you'll what would happen
+ 
+
+ align:start position:0%
+you'll what would happen
+if what would happen if
+
+ align:start position:0%
+if what would happen if
+ 
+
+ align:start position:0%
+if what would happen if
+this these new measurements were a
+
+ align:start position:0%
+this these new measurements were a
+ 
+
+ align:start position:0%
+this these new measurements were a
+perfect repeat and this was a perfect
+
+ align:start position:0%
+perfect repeat and this was a perfect
+ 
+
+ align:start position:0%
+perfect repeat and this was a perfect
+repeat if if a new was the same as a old
+
+ align:start position:0%
+repeat if if a new was the same as a old
+ 
+
+ align:start position:0%
+repeat if if a new was the same as a old
+and B knew was the same as B old so we
+
+ align:start position:0%
+and B knew was the same as B old so we
+ 
+
+ align:start position:0%
+and B knew was the same as B old so we
+just ran the experiment
+
+ align:start position:0%
+just ran the experiment
+ 
+
+ align:start position:0%
+just ran the experiment
+twice or just copied the answer and
+
+ align:start position:0%
+twice or just copied the answer and
+ 
+
+ align:start position:0%
+twice or just copied the answer and
+didn't notice or something what would we
+
+ align:start position:0%
+didn't notice or something what would we
+ 
+
+ align:start position:0%
+didn't notice or something what would we
+expect you new the the perfect the best
+
+ align:start position:0%
+expect you new the the perfect the best
+ 
+
+ align:start position:0%
+expect you new the the perfect the best
+U to be for the combined system it' be
+
+ align:start position:0%
+U to be for the combined system it' be
+ 
+
+ align:start position:0%
+U to be for the combined system it' be
+the same right and you see that that's
+
+ align:start position:0%
+the same right and you see that that's
+ 
+
+ align:start position:0%
+the same right and you see that that's
+what would happen with this formula that
+
+ align:start position:0%
+what would happen with this formula that
+ 
+
+ align:start position:0%
+what would happen with this formula that
+you new would be U old plus
+
+ align:start position:0%
+you new would be U old plus
+ 
+
+ align:start position:0%
+you new would be U old plus
+this uh would be
+
+ align:start position:0%
+this uh would be
+ 
+
+ align:start position:0%
+this uh would be
+uh uh the best uh is that is that right
+
+ align:start position:0%
+uh uh the best uh is that is that right
+ 
+
+ align:start position:0%
+uh uh the best uh is that is that right
+we would learn if if if well maybe I'm
+
+ align:start position:0%
+we would learn if if if well maybe I'm
+ 
+
+ align:start position:0%
+we would learn if if if well maybe I'm
+saying it a little should be saying it
+
+ align:start position:0%
+saying it a little should be saying it
+ 
+
+ align:start position:0%
+saying it a little should be saying it
+differently yeah that that the best
+
+ align:start position:0%
+differently yeah that that the best
+ 
+
+ align:start position:0%
+differently yeah that that the best
+uh that if our yeah I I should have so I
+
+ align:start position:0%
+uh that if our yeah I I should have so I
+ 
+
+ align:start position:0%
+uh that if our yeah I I should have so I
+have to wipe out part of what I said and
+
+ align:start position:0%
+have to wipe out part of what I said and
+ 
+
+ align:start position:0%
+have to wipe out part of what I said and
+say it differently although what I said
+
+ align:start position:0%
+say it differently although what I said
+ 
+
+ align:start position:0%
+say it differently although what I said
+would apply but what I wanted to say was
+
+ align:start position:0%
+would apply but what I wanted to say was
+ 
+
+ align:start position:0%
+would apply but what I wanted to say was
+if the new measurements exactly if this
+
+ align:start position:0%
+if the new measurements exactly if this
+ 
+
+ align:start position:0%
+if the new measurements exactly if this
+was Zero we wouldn't make a change right
+
+ align:start position:0%
+was Zero we wouldn't make a change right
+ 
+
+ align:start position:0%
+was Zero we wouldn't make a change right
+that's that's you you see what I'm
+
+ align:start position:0%
+that's that's you you see what I'm
+ 
+
+ align:start position:0%
+that's that's you you see what I'm
+struggling for here that that if our old
+
+ align:start position:0%
+struggling for here that that if our old
+ 
+
+ align:start position:0%
+struggling for here that that if our old
+measurements exactly gave us perfection
+
+ align:start position:0%
+measurements exactly gave us perfection
+ 
+
+ align:start position:0%
+measurements exactly gave us perfection
+in this second in this new system then
+
+ align:start position:0%
+in this second in this new system then
+ 
+
+ align:start position:0%
+in this second in this new system then
+we wouldn't want to change of course but
+
+ align:start position:0%
+we wouldn't want to change of course but
+ 
+
+ align:start position:0%
+we wouldn't want to change of course but
+if they don't give us Perfection then
+
+ align:start position:0%
+if they don't give us Perfection then
+ 
+
+ align:start position:0%
+if they don't give us Perfection then
+this is called The Innovation this is
+
+ align:start position:0%
+this is called The Innovation this is
+ 
+
+ align:start position:0%
+this is called The Innovation this is
+the new
+
+ align:start position:0%
+the new
+ 
+
+ align:start position:0%
+the new
+information this is the Ovation
+
+ align:start position:0%
+information this is the Ovation
+ 
+
+ align:start position:0%
+information this is the Ovation
+here and
+
+ align:start position:0%
+here and
+ 
+
+ align:start position:0%
+here and
+uh and we hope that there should be some
+
+ align:start position:0%
+uh and we hope that there should be some
+ 
+
+ align:start position:0%
+uh and we hope that there should be some
+Matrix that multiplies that Innovation
+
+ align:start position:0%
+Matrix that multiplies that Innovation
+ 
+
+ align:start position:0%
+Matrix that multiplies that Innovation
+to give us the the Delta you hat the the
+
+ align:start position:0%
+to give us the the Delta you hat the the
+ 
+
+ align:start position:0%
+to give us the the Delta you hat the the
+correction okay could we just derive
+
+ align:start position:0%
+correction okay could we just derive
+ 
+
+ align:start position:0%
+correction okay could we just derive
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+formula that's that's what I plan to do
+
+ align:start position:0%
+formula that's that's what I plan to do
+ 
+
+ align:start position:0%
+formula that's that's what I plan to do
+now is just derive it from first
+
+ align:start position:0%
+now is just derive it from first
+ 
+
+ align:start position:0%
+now is just derive it from first
+principles what do I mean by first
+
+ align:start position:0%
+principles what do I mean by first
+ 
+
+ align:start position:0%
+principles what do I mean by first
+principles I mean that I'll I'll write
+
+ align:start position:0%
+principles I mean that I'll I'll write
+ 
+
+ align:start position:0%
+principles I mean that I'll I'll write
+the the answer to this
+
+ align:start position:0%
+the the answer to this
+ 
+
+ align:start position:0%
+the the answer to this
+problem and then I'll manipulate
+
+ align:start position:0%
+problem and then I'll manipulate
+ 
+
+ align:start position:0%
+problem and then I'll manipulate
+to put it in this form is that all right
+
+ align:start position:0%
+to put it in this form is that all right
+ 
+
+ align:start position:0%
+to put it in this form is that all right
+that's so that's the goal so what's the
+
+ align:start position:0%
+that's so that's the goal so what's the
+ 
+
+ align:start position:0%
+that's so that's the goal so what's the
+answer to this
+
+ align:start position:0%
+answer to this
+ 
+
+ align:start position:0%
+answer to this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+okay so we see the we see the problem
+
+ align:start position:0%
+okay so we see the we see the problem
+ 
+
+ align:start position:0%
+okay so we see the we see the problem
+here and we know the equation that we
+
+ align:start position:0%
+here and we know the equation that we
+ 
+
+ align:start position:0%
+here and we know the equation that we
+have to solve and we've decided that
+
+ align:start position:0%
+have to solve and we've decided that
+ 
+
+ align:start position:0%
+have to solve and we've decided that
+Sigma will separate into two pieces
+
+ align:start position:0%
+Sigma will separate into two pieces
+ 
+
+ align:start position:0%
+Sigma will separate into two pieces
+that's you'll see that that's a big help
+
+ align:start position:0%
+that's you'll see that that's a big help
+ 
+
+ align:start position:0%
+that's you'll see that that's a big help
+so actually what is this
+
+ align:start position:0%
+so actually what is this
+ 
+
+ align:start position:0%
+so actually what is this
+left hand side Matrix for this for this
+
+ align:start position:0%
+left hand side Matrix for this for this
+ 
+
+ align:start position:0%
+left hand side Matrix for this for this
+problem yeah let me let me do this in
+
+ align:start position:0%
+problem yeah let me let me do this in
+ 
+
+ align:start position:0%
+problem yeah let me let me do this in
+two steps here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so I'm about to derive this
+
+ align:start position:0%
+okay okay so I'm about to derive this
+ 
+
+ align:start position:0%
+okay okay so I'm about to derive this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so I've got a whole lot of
+
+ align:start position:0%
+okay okay so I've got a whole lot of
+ 
+
+ align:start position:0%
+okay okay so I've got a whole lot of
+pieces here I've got this Matrix and
+
+ align:start position:0%
+pieces here I've got this Matrix and
+ 
+
+ align:start position:0%
+pieces here I've got this Matrix and
+then I've got some changes over here let
+
+ align:start position:0%
+then I've got some changes over here let
+ 
+
+ align:start position:0%
+then I've got some changes over here let
+me deal with that Matrix first so I have
+
+ align:start position:0%
+me deal with that Matrix first so I have
+ 
+
+ align:start position:0%
+me deal with that Matrix first so I have
+a which
+
+ align:start position:0%
+a which
+ 
+
+ align:start position:0%
+a which
+is a old a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new times Sigma inverse which is Sigma
+
+ align:start position:0%
+new times Sigma inverse which is Sigma
+ 
+
+ align:start position:0%
+new times Sigma inverse which is Sigma
+old inverse Sigma new inverse you see
+
+ align:start position:0%
+old inverse Sigma new inverse you see
+ 
+
+ align:start position:0%
+old inverse Sigma new inverse you see
+there it was absolutely critical that we
+
+ align:start position:0%
+there it was absolutely critical that we
+ 
+
+ align:start position:0%
+there it was absolutely critical that we
+had a block diagonal matrix and now a
+
+ align:start position:0%
+had a block diagonal matrix and now a
+ 
+
+ align:start position:0%
+had a block diagonal matrix and now a
+transpose is a
+
+ align:start position:0%
+transpose is a
+ 
+
+ align:start position:0%
+transpose is a
+old transpose
+
+ align:start position:0%
+old transpose
+ 
+
+ align:start position:0%
+old transpose
+next to a new
+
+ align:start position:0%
+next to a new
+ 
+
+ align:start position:0%
+next to a new
+transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good all I'm finding here oh yeah all
+
+ align:start position:0%
+good all I'm finding here oh yeah all
+ 
+
+ align:start position:0%
+good all I'm finding here oh yeah all
+right let's just do that multiplication
+
+ align:start position:0%
+right let's just do that multiplication
+ 
+
+ align:start position:0%
+right let's just do that multiplication
+out so so what do I what do I have then
+
+ align:start position:0%
+out so so what do I what do I have then
+ 
+
+ align:start position:0%
+out so so what do I what do I have then
+I've just got a sigma inverse a
+
+ align:start position:0%
+I've just got a sigma inverse a
+ 
+
+ align:start position:0%
+I've just got a sigma inverse a
+transpose old maybe I maybe I if I'm
+
+ align:start position:0%
+transpose old maybe I maybe I if I'm
+ 
+
+ align:start position:0%
+transpose old maybe I maybe I if I'm
+consistent I write old on every
+
+ align:start position:0%
+consistent I write old on every
+ 
+
+ align:start position:0%
+consistent I write old on every
+Matrix Plus
+
+ align:start position:0%
+Matrix Plus
+ 
+
+ align:start position:0%
+Matrix Plus
+doing that multiplication oh plus a new
+
+ align:start position:0%
+doing that multiplication oh plus a new
+ 
+
+ align:start position:0%
+doing that multiplication oh plus a new
+let me write the answer down what it's
+
+ align:start position:0%
+let me write the answer down what it's
+ 
+
+ align:start position:0%
+let me write the answer down what it's
+maybe not Sigma inverse
+
+ align:start position:0%
+maybe not Sigma inverse
+ 
+
+ align:start position:0%
+maybe not Sigma inverse
+new a
+
+ align:start position:0%
+new a
+ 
+
+ align:start position:0%
+new a
+new do you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a am I am I doing this
+
+ align:start position:0%
+that a am I am I doing this
+ 
+
+ align:start position:0%
+that a am I am I doing this
+right am I the transpose should have
+
+ align:start position:0%
+right am I the transpose should have
+ 
+
+ align:start position:0%
+right am I the transpose should have
+been first shouldn't it yeah absolutely
+
+ align:start position:0%
+been first shouldn't it yeah absolutely
+ 
+
+ align:start position:0%
+been first shouldn't it yeah absolutely
+otherwise all wrong
+
+ align:start position:0%
+otherwise all wrong
+ 
+
+ align:start position:0%
+otherwise all wrong
+thanks you're quite
+
+ align:start position:0%
+thanks you're quite
+ 
+
+ align:start position:0%
+thanks you're quite
+right I can't say that I make errors
+
+ align:start position:0%
+right I can't say that I make errors
+ 
+
+ align:start position:0%
+right I can't say that I make errors
+just to keep you awake but uh you can
+
+ align:start position:0%
+just to keep you awake but uh you can
+ 
+
+ align:start position:0%
+just to keep you awake but uh you can
+see I
+
+ align:start position:0%
+see I
+ 
+
+ align:start position:0%
+see I
+right well yeah but I like to go on
+
+ align:start position:0%
+right well yeah but I like to go on
+ 
+
+ align:start position:0%
+right well yeah but I like to go on
+record with the truth here uh all right
+
+ align:start position:0%
+record with the truth here uh all right
+ 
+
+ align:start position:0%
+record with the truth here uh all right
+and and of course I was going to see
+
+ align:start position:0%
+and and of course I was going to see
+ 
+
+ align:start position:0%
+and and of course I was going to see
+that it was that I was wrong just as
+
+ align:start position:0%
+that it was that I was wrong just as
+ 
+
+ align:start position:0%
+that it was that I was wrong just as
+soon as I tried that multiplications so
+
+ align:start position:0%
+soon as I tried that multiplications so
+ 
+
+ align:start position:0%
+soon as I tried that multiplications so
+you're absolutely right it's a transpose
+
+ align:start position:0%
+you're absolutely right it's a transpose
+ 
+
+ align:start position:0%
+you're absolutely right it's a transpose
+old and a transpose
+
+ align:start position:0%
+old and a transpose
+ 
+
+ align:start position:0%
+old and a transpose
+new that's a transpose put together this
+
+ align:start position:0%
+new that's a transpose put together this
+ 
+
+ align:start position:0%
+new that's a transpose put together this
+is Sigma inverse and this is a good now
+
+ align:start position:0%
+is Sigma inverse and this is a good now
+ 
+
+ align:start position:0%
+is Sigma inverse and this is a good now
+I believe this multiplication do you
+
+ align:start position:0%
+I believe this multiplication do you
+ 
+
+ align:start position:0%
+I believe this multiplication do you
+believe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and do you see what
+
+ align:start position:0%
+it and do you see what
+ 
+
+ align:start position:0%
+it and do you see what
+it's I mean it's quite important to see
+
+ align:start position:0%
+it's I mean it's quite important to see
+ 
+
+ align:start position:0%
+it's I mean it's quite important to see
+what happens because this is like the
+
+ align:start position:0%
+what happens because this is like the
+ 
+
+ align:start position:0%
+what happens because this is like the
+whole point of the lecture we're getting
+
+ align:start position:0%
+whole point of the lecture we're getting
+ 
+
+ align:start position:0%
+whole point of the lecture we're getting
+new new stuff here yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah this you're right of course I
+
+ align:start position:0%
+yeah this you're right of course I
+ 
+
+ align:start position:0%
+yeah this you're right of course I
+didn't correct the last line either
+
+ align:start position:0%
+didn't correct the last line either
+ 
+
+ align:start position:0%
+didn't correct the last line either
+thanks it's a gosh I'm living and dying
+
+ align:start position:0%
+thanks it's a gosh I'm living and dying
+ 
+
+ align:start position:0%
+thanks it's a gosh I'm living and dying
+with a transpose CA here I ought to get
+
+ align:start position:0%
+with a transpose CA here I ought to get
+ 
+
+ align:start position:0%
+with a transpose CA here I ought to get
+the transpose in the right spot there we
+
+ align:start position:0%
+the transpose in the right spot there we
+ 
+
+ align:start position:0%
+the transpose in the right spot there we
+go is that all right
+
+ align:start position:0%
+go is that all right
+ 
+
+ align:start position:0%
+go is that all right
+now yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+you actually the way I would see this
+
+ align:start position:0%
+you actually the way I would see this
+ 
+
+ align:start position:0%
+you actually the way I would see this
+is uh my old columns times
+
+ align:start position:0%
+is uh my old columns times
+ 
+
+ align:start position:0%
+is uh my old columns times
+rows I mean if suppose a new is just one
+
+ align:start position:0%
+rows I mean if suppose a new is just one
+ 
+
+ align:start position:0%
+rows I mean if suppose a new is just one
+new a suppose a new is just one new row
+
+ align:start position:0%
+new a suppose a new is just one new row
+ 
+
+ align:start position:0%
+new a suppose a new is just one new row
+this is like valuable to think of one
+
+ align:start position:0%
+this is like valuable to think of one
+ 
+
+ align:start position:0%
+this is like valuable to think of one
+new measurement has come in so we have
+
+ align:start position:0%
+new measurement has come in so we have
+ 
+
+ align:start position:0%
+new measurement has come in so we have
+one new row of a one new column of a
+
+ align:start position:0%
+one new row of a one new column of a
+ 
+
+ align:start position:0%
+one new row of a one new column of a
+transpose how much does that change this
+
+ align:start position:0%
+transpose how much does that change this
+ 
+
+ align:start position:0%
+transpose how much does that change this
+a transpose Sigma inverse a it changes
+
+ align:start position:0%
+a transpose Sigma inverse a it changes
+ 
+
+ align:start position:0%
+a transpose Sigma inverse a it changes
+us just by the column times the row
+
+ align:start position:0%
+us just by the column times the row
+ 
+
+ align:start position:0%
+us just by the column times the row
+times it would just be a one by one
+
+ align:start position:0%
+times it would just be a one by one
+ 
+
+ align:start position:0%
+times it would just be a one by one
+number in in in what I just described
+
+ align:start position:0%
+number in in in what I just described
+ 
+
+ align:start position:0%
+number in in in what I just described
+you see I'm multiplying
+
+ align:start position:0%
+you see I'm multiplying
+ 
+
+ align:start position:0%
+you see I'm multiplying
+columns by piece by matrix by
+
+ align:start position:0%
+columns by piece by matrix by
+ 
+
+ align:start position:0%
+columns by piece by matrix by
+row and It just fits okay so that's the
+
+ align:start position:0%
+row and It just fits okay so that's the
+ 
+
+ align:start position:0%
+row and It just fits okay so that's the
+that's the uh uh that's the the
+
+ align:start position:0%
+that's the uh uh that's the the
+ 
+
+ align:start position:0%
+that's the uh uh that's the the
+total okay you see all right I that that
+
+ align:start position:0%
+total okay you see all right I that that
+ 
+
+ align:start position:0%
+total okay you see all right I that that
+better be okay because I've got uh uh
+
+ align:start position:0%
+better be okay because I've got uh uh
+ 
+
+ align:start position:0%
+better be okay because I've got uh uh
+now all right now so I'm going to have
+
+ align:start position:0%
+now all right now so I'm going to have
+ 
+
+ align:start position:0%
+now all right now so I'm going to have
+to You'll forgive me if I if I depend on
+
+ align:start position:0%
+to You'll forgive me if I if I depend on
+ 
+
+ align:start position:0%
+to You'll forgive me if I if I depend on
+the author for help here
+
+ align:start position:0%
+the author for help here
+ 
+
+ align:start position:0%
+the author for help here
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right okay now let's see let
+
+ align:start position:0%
+okay right okay now let's see let
+ 
+
+ align:start position:0%
+okay right okay now let's see let
+me so here I'm talking about the this
+
+ align:start position:0%
+me so here I'm talking about the this
+ 
+
+ align:start position:0%
+me so here I'm talking about the this
+will leave to an update of U hat this
+
+ align:start position:0%
+will leave to an update of U hat this
+ 
+
+ align:start position:0%
+will leave to an update of U hat this
+update of U but I haven't written in can
+
+ align:start position:0%
+update of U but I haven't written in can
+ 
+
+ align:start position:0%
+update of U but I haven't written in can
+you maybe tell me what it is what's the
+
+ align:start position:0%
+you maybe tell me what it is what's the
+ 
+
+ align:start position:0%
+you maybe tell me what it is what's the
+update formula for
+
+ align:start position:0%
+update formula for
+ 
+
+ align:start position:0%
+update formula for
+p the the two outputs are U hat and
+
+ align:start position:0%
+p the the two outputs are U hat and
+ 
+
+ align:start position:0%
+p the the two outputs are U hat and
+P and we're looking and we're going to
+
+ align:start position:0%
+P and we're looking and we're going to
+ 
+
+ align:start position:0%
+P and we're looking and we're going to
+write down the right expression here for
+
+ align:start position:0%
+write down the right expression here for
+ 
+
+ align:start position:0%
+write down the right expression here for
+the update in U but we darn well have to
+
+ align:start position:0%
+the update in U but we darn well have to
+ 
+
+ align:start position:0%
+the update in U but we darn well have to
+be able to write down the right
+
+ align:start position:0%
+be able to write down the right
+ 
+
+ align:start position:0%
+be able to write down the right
+expression for the up state in
+
+ align:start position:0%
+expression for the up state in
+ 
+
+ align:start position:0%
+expression for the up state in
+p and what's that what's the new P
+
+ align:start position:0%
+p and what's that what's the new P
+ 
+
+ align:start position:0%
+p and what's that what's the new P
+what's the new Sigma you have what's
+
+ align:start position:0%
+what's the new Sigma you have what's
+ 
+
+ align:start position:0%
+what's the new Sigma you have what's
+here here here's here's P well this is a
+
+ align:start position:0%
+here here here's here's P well this is a
+ 
+
+ align:start position:0%
+here here here's here's P well this is a
+case where it'll be easier to write the
+
+ align:start position:0%
+case where it'll be easier to write the
+ 
+
+ align:start position:0%
+case where it'll be easier to write the
+update in P inverse in in this Matrix
+
+ align:start position:0%
+update in P inverse in in this Matrix
+ 
+
+ align:start position:0%
+update in P inverse in in this Matrix
+without the
+
+ align:start position:0%
+without the
+ 
+
+ align:start position:0%
+without the
+inverse I'll still I'll use so so P
+
+ align:start position:0%
+inverse I'll still I'll use so so P
+ 
+
+ align:start position:0%
+inverse I'll still I'll use so so P
+inverse is our a transpose Sigma inverse
+
+ align:start position:0%
+inverse is our a transpose Sigma inverse
+ 
+
+ align:start position:0%
+inverse is our a transpose Sigma inverse
+a just you can I poke this up here some
+
+ align:start position:0%
+a just you can I poke this up here some
+ 
+
+ align:start position:0%
+a just you can I poke this up here some
+just as a reminder P inverse is a
+
+ align:start position:0%
+just as a reminder P inverse is a
+ 
+
+ align:start position:0%
+just as a reminder P inverse is a
+transpose Sigma inverse a it's it's what
+
+ align:start position:0%
+transpose Sigma inverse a it's it's what
+ 
+
+ align:start position:0%
+transpose Sigma inverse a it's it's what
+we just figured out actually so I I've
+
+ align:start position:0%
+we just figured out actually so I I've
+ 
+
+ align:start position:0%
+we just figured out actually so I I've
+I've really this this
+
+ align:start position:0%
+I've really this this
+ 
+
+ align:start position:0%
+I've really this this
+says this says P
+
+ align:start position:0%
+says this says P
+ 
+
+ align:start position:0%
+says this says P
+inverse this this this formula that we
+
+ align:start position:0%
+inverse this this this formula that we
+ 
+
+ align:start position:0%
+inverse this this this formula that we
+just got says P inverse new that's what
+
+ align:start position:0%
+just got says P inverse new that's what
+ 
+
+ align:start position:0%
+just got says P inverse new that's what
+we were Computing is now what is this
+
+ align:start position:0%
+we were Computing is now what is this
+ 
+
+ align:start position:0%
+we were Computing is now what is this
+what is that quantity
+
+ align:start position:0%
+what is that quantity
+ 
+
+ align:start position:0%
+what is that quantity
+there that's P inverse
+
+ align:start position:0%
+there that's P inverse
+ 
+
+ align:start position:0%
+there that's P inverse
+old so P inverse no I shouldn't say new
+
+ align:start position:0%
+old so P inverse no I shouldn't say new
+ 
+
+ align:start position:0%
+old so P inverse no I shouldn't say new
+I should
+
+ align:start position:0%
+I should
+ 
+
+ align:start position:0%
+I should
+say uh combined or something P inverse
+
+ align:start position:0%
+say uh combined or something P inverse
+ 
+
+ align:start position:0%
+say uh combined or something P inverse
+combined or P1 inverse yeah I I'd be a
+
+ align:start position:0%
+combined or P1 inverse yeah I I'd be a
+ 
+
+ align:start position:0%
+combined or P1 inverse yeah I I'd be a
+lot better if I just use zero and one
+
+ align:start position:0%
+lot better if I just use zero and one
+ 
+
+ align:start position:0%
+lot better if I just use zero and one
+for zero for old one for new I guess
+
+ align:start position:0%
+for zero for old one for new I guess
+ 
+
+ align:start position:0%
+for zero for old one for new I guess
+there's a value to having numbers in
+
+ align:start position:0%
+there's a value to having numbers in
+ 
+
+ align:start position:0%
+there's a value to having numbers in
+this uh World okay so
+
+ align:start position:0%
+this uh World okay so
+ 
+
+ align:start position:0%
+this uh World okay so
+P1 inverse the the combined the the the
+
+ align:start position:0%
+P1 inverse the the combined the the the
+ 
+
+ align:start position:0%
+P1 inverse the the combined the the the
+the one
+
+ align:start position:0%
+the one
+ 
+
+ align:start position:0%
+the one
+that right is according to this formula
+
+ align:start position:0%
+that right is according to this formula
+ 
+
+ align:start position:0%
+that right is according to this formula
+is p the old
+
+ align:start position:0%
+is p the old
+ 
+
+ align:start position:0%
+is p the old
+one inverse because that's P inverse
+
+ align:start position:0%
+one inverse because that's P inverse
+ 
+
+ align:start position:0%
+one inverse because that's P inverse
+plus this correction that's the
+
+ align:start position:0%
+plus this correction that's the
+ 
+
+ align:start position:0%
+plus this correction that's the
+a new inverse a new if we're calling one
+
+ align:start position:0%
+a new inverse a new if we're calling one
+ 
+
+ align:start position:0%
+a new inverse a new if we're calling one
+for that transpose Sigma inverse 1 A1
+
+ align:start position:0%
+for that transpose Sigma inverse 1 A1
+ 
+
+ align:start position:0%
+for that transpose Sigma inverse 1 A1
+that's the update formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the update formula for this
+
+ align:start position:0%
+so that's the update formula for this
+ 
+
+ align:start position:0%
+so that's the update formula for this
+crucial quantity P or in fact for p
+
+ align:start position:0%
+crucial quantity P or in fact for p
+ 
+
+ align:start position:0%
+crucial quantity P or in fact for p
+inverse what we just found so you see
+
+ align:start position:0%
+inverse what we just found so you see
+ 
+
+ align:start position:0%
+inverse what we just found so you see
+that actually as we
+
+ align:start position:0%
+that actually as we
+ 
+
+ align:start position:0%
+that actually as we
+proceed it often happens that we figure
+
+ align:start position:0%
+proceed it often happens that we figure
+ 
+
+ align:start position:0%
+proceed it often happens that we figure
+out the update in the P because that's
+
+ align:start position:0%
+out the update in the P because that's
+ 
+
+ align:start position:0%
+out the update in the P because that's
+because P inverse is the Matrix here
+
+ align:start position:0%
+because P inverse is the Matrix here
+ 
+
+ align:start position:0%
+because P inverse is the Matrix here
+that that leads us to U it's remember
+
+ align:start position:0%
+that that leads us to U it's remember
+ 
+
+ align:start position:0%
+that that leads us to U it's remember
+you hat got this
+
+ align:start position:0%
+you hat got this
+ 
+
+ align:start position:0%
+you hat got this
+this is all this stuff here is
+
+ align:start position:0%
+this is all this stuff here is
+ 
+
+ align:start position:0%
+this is all this stuff here is
+p in there so if it's no surprise that
+
+ align:start position:0%
+p in there so if it's no surprise that
+ 
+
+ align:start position:0%
+p in there so if it's no surprise that
+updating p is a is an important step
+
+ align:start position:0%
+updating p is a is an important step
+ 
+
+ align:start position:0%
+updating p is a is an important step
+toward the update of U and an important
+
+ align:start position:0%
+toward the update of U and an important
+ 
+
+ align:start position:0%
+toward the update of U and an important
+step on its own okay now I'm ready for
+
+ align:start position:0%
+step on its own okay now I'm ready for
+ 
+
+ align:start position:0%
+step on its own okay now I'm ready for
+the update in U okay so what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U so
+
+ align:start position:0%
+U so
+ 
+
+ align:start position:0%
+U so
+you combined you one the the the answer
+
+ align:start position:0%
+you combined you one the the the answer
+ 
+
+ align:start position:0%
+you combined you one the the the answer
+with for the combined problem is okay
+
+ align:start position:0%
+with for the combined problem is okay
+ 
+
+ align:start position:0%
+with for the combined problem is okay
+well let's see what it was here it's
+
+ align:start position:0%
+well let's see what it was here it's
+ 
+
+ align:start position:0%
+well let's see what it was here it's
+P1 that's all this stuff times a what a
+
+ align:start position:0%
+P1 that's all this stuff times a what a
+ 
+
+ align:start position:0%
+P1 that's all this stuff times a what a
+is that that's both A's isn't it yeah
+
+ align:start position:0%
+is that that's both A's isn't it yeah
+ 
+
+ align:start position:0%
+is that that's both A's isn't it yeah
+that's the combined a and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+combined right see have we got it
+
+ align:start position:0%
+combined right see have we got it
+ 
+
+ align:start position:0%
+combined right see have we got it
+this is now I'm looking for yeah what
+
+ align:start position:0%
+this is now I'm looking for yeah what
+ 
+
+ align:start position:0%
+this is now I'm looking for yeah what
+what's in
+
+ align:start position:0%
+what's in
+ 
+
+ align:start position:0%
+what's in
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay is this
+
+ align:start position:0%
+okay is this
+ 
+
+ align:start position:0%
+okay is this
+part which is if I write b as B KN B1
+
+ align:start position:0%
+part which is if I write b as B KN B1
+ 
+
+ align:start position:0%
+part which is if I write b as B KN B1
+and I write Sigma inverse as Sigma not
+
+ align:start position:0%
+and I write Sigma inverse as Sigma not
+ 
+
+ align:start position:0%
+and I write Sigma inverse as Sigma not
+inverse Sigma 1 inverse and I write a as
+
+ align:start position:0%
+inverse Sigma 1 inverse and I write a as
+ 
+
+ align:start position:0%
+inverse Sigma 1 inverse and I write a as
+a A1 I've got two pieces I've got a
+
+ align:start position:0%
+a A1 I've got two pieces I've got a
+ 
+
+ align:start position:0%
+a A1 I've got two pieces I've got a
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+transpose P not
+
+ align:start position:0%
+transpose P not
+ 
+
+ align:start position:0%
+transpose P not
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+inverse oh no
+
+ align:start position:0%
+inverse oh no
+ 
+
+ align:start position:0%
+inverse oh no
+Sigma yep Sigma n
+
+ align:start position:0%
+Sigma yep Sigma n
+ 
+
+ align:start position:0%
+Sigma yep Sigma n
+inverse B not that's the old part
+
+ align:start position:0%
+inverse B not that's the old part
+ 
+
+ align:start position:0%
+inverse B not that's the old part
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+new transpose Sigma inverse B1 the new
+
+ align:start position:0%
+new transpose Sigma inverse B1 the new
+ 
+
+ align:start position:0%
+new transpose Sigma inverse B1 the new
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+okay that's our exact formula that's
+
+ align:start position:0%
+okay that's our exact formula that's
+ 
+
+ align:start position:0%
+okay that's our exact formula that's
+that's we haven't simplified it
+
+ align:start position:0%
+that's we haven't simplified it
+ 
+
+ align:start position:0%
+that's we haven't simplified it
+all this is what we would have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do if we don't use recursion this is the
+
+ align:start position:0%
+do if we don't use recursion this is the
+ 
+
+ align:start position:0%
+do if we don't use recursion this is the
+this is the answer if we just tackle the
+
+ align:start position:0%
+this is the answer if we just tackle the
+ 
+
+ align:start position:0%
+this is the answer if we just tackle the
+the new problem the the combined problem
+
+ align:start position:0%
+the new problem the the combined problem
+ 
+
+ align:start position:0%
+the new problem the the combined problem
+without paying any attention to the work
+
+ align:start position:0%
+without paying any attention to the work
+ 
+
+ align:start position:0%
+without paying any attention to the work
+we did before but now we want to use
+
+ align:start position:0%
+we did before but now we want to use
+ 
+
+ align:start position:0%
+we did before but now we want to use
+that work we did did before so what did
+
+ align:start position:0%
+that work we did did before so what did
+ 
+
+ align:start position:0%
+that work we did did before so what did
+we achieve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before we we figured out P not inverse
+
+ align:start position:0%
+before we we figured out P not inverse
+ 
+
+ align:start position:0%
+before we we figured out P not inverse
+before and we have an update formula for
+
+ align:start position:0%
+before and we have an update formula for
+ 
+
+ align:start position:0%
+before and we have an update formula for
+P1
+
+ align:start position:0%
+P1
+ 
+
+ align:start position:0%
+P1
+inverse okay and we can so I'm going to
+
+ align:start position:0%
+inverse okay and we can so I'm going to
+ 
+
+ align:start position:0%
+inverse okay and we can so I'm going to
+this this update is going to get plugged
+
+ align:start position:0%
+this this update is going to get plugged
+ 
+
+ align:start position:0%
+this this update is going to get plugged
+into here okay why don't
+
+ align:start position:0%
+into here okay why don't
+ 
+
+ align:start position:0%
+into here okay why don't
+I go to the answer I think that's
+
+ align:start position:0%
+I go to the answer I think that's
+ 
+
+ align:start position:0%
+I go to the answer I think that's
+reasonable because the the it's just two
+
+ align:start position:0%
+reasonable because the the it's just two
+ 
+
+ align:start position:0%
+reasonable because the the it's just two
+or three steps
+
+ align:start position:0%
+or three steps
+ 
+
+ align:start position:0%
+or three steps
+that lead to this final answer and I
+
+ align:start position:0%
+that lead to this final answer and I
+ 
+
+ align:start position:0%
+that lead to this final answer and I
+think the The crucial thing is to say
+
+ align:start position:0%
+think the The crucial thing is to say
+ 
+
+ align:start position:0%
+think the The crucial thing is to say
+what is K and that let's complete the
+
+ align:start position:0%
+what is K and that let's complete the
+ 
+
+ align:start position:0%
+what is K and that let's complete the
+lecture with that so I I if that's all
+
+ align:start position:0%
+lecture with that so I I if that's all
+ 
+
+ align:start position:0%
+lecture with that so I I if that's all
+right with you if I just proceed
+
+ align:start position:0%
+right with you if I just proceed
+ 
+
+ align:start position:0%
+right with you if I just proceed
+systematically as the as the uh
+
+ align:start position:0%
+systematically as the as the uh
+ 
+
+ align:start position:0%
+systematically as the as the uh
+Exposition does this is
+
+ align:start position:0%
+Exposition does this is
+ 
+
+ align:start position:0%
+Exposition does this is
+Page um
+
+ align:start position:0%
+Page um
+ 
+
+ align:start position:0%
+Page um
+146 that I'm
+
+ align:start position:0%
+146 that I'm
+ 
+
+ align:start position:0%
+146 that I'm
+using and let me just write down what
+
+ align:start position:0%
+using and let me just write down what
+ 
+
+ align:start position:0%
+using and let me just write down what
+this cman Matrix turns out to be because
+
+ align:start position:0%
+this cman Matrix turns out to be because
+ 
+
+ align:start position:0%
+this cman Matrix turns out to be because
+that's the The crucial quantity it's
+
+ align:start position:0%
+that's the The crucial quantity it's
+ 
+
+ align:start position:0%
+that's the The crucial quantity it's
+P1 the updated
+
+ align:start position:0%
+P1 the updated
+ 
+
+ align:start position:0%
+P1 the updated
+P A1
+
+ align:start position:0%
+P A1
+ 
+
+ align:start position:0%
+P A1
+transpose Sigma
+
+ align:start position:0%
+transpose Sigma
+ 
+
+ align:start position:0%
+transpose Sigma
+1 the new the the new bit of the new bit
+
+ align:start position:0%
+1 the new the the new bit of the new bit
+ 
+
+ align:start position:0%
+1 the new the the new bit of the new bit
+of a the new bit of Sigma and the then
+
+ align:start position:0%
+of a the new bit of Sigma and the then
+ 
+
+ align:start position:0%
+of a the new bit of Sigma and the then
+the combined and the updated Peak that's
+
+ align:start position:0%
+the combined and the updated Peak that's
+ 
+
+ align:start position:0%
+the combined and the updated Peak that's
+the cman game Matrix
+
+ align:start position:0%
+the cman game Matrix
+ 
+
+ align:start position:0%
+the cman game Matrix
+and that's what makes this formula
+
+ align:start position:0%
+and that's what makes this formula
+ 
+
+ align:start position:0%
+and that's what makes this formula
+correct and it's it's
+
+ align:start position:0%
+correct and it's it's
+ 
+
+ align:start position:0%
+correct and it's it's
+uh I feel I've covered the board and
+
+ align:start position:0%
+uh I feel I've covered the board and
+ 
+
+ align:start position:0%
+uh I feel I've covered the board and
+asked you to watch uh a bunch of Matrix
+
+ align:start position:0%
+asked you to watch uh a bunch of Matrix
+ 
+
+ align:start position:0%
+asked you to watch uh a bunch of Matrix
+steps on the other hand what worries me
+
+ align:start position:0%
+steps on the other hand what worries me
+ 
+
+ align:start position:0%
+steps on the other hand what worries me
+is this was nothing compared to
+
+ align:start position:0%
+is this was nothing compared to
+ 
+
+ align:start position:0%
+is this was nothing compared to
+kman cuz we only
+
+ align:start position:0%
+kman cuz we only
+ 
+
+ align:start position:0%
+kman cuz we only
+updated uh we only we only had new B's
+
+ align:start position:0%
+updated uh we only we only had new B's
+ 
+
+ align:start position:0%
+updated uh we only we only had new B's
+and new row in you but not a new not new
+
+ align:start position:0%
+and new row in you but not a new not new
+ 
+
+ align:start position:0%
+and new row in you but not a new not new
+column
+
+ align:start position:0%
+column
+ 
+
+ align:start position:0%
+column
+so the next lecture can only get
+
+ align:start position:0%
+so the next lecture can only get
+ 
+
+ align:start position:0%
+so the next lecture can only get
+worse uh uh but I'll probably have I'll
+
+ align:start position:0%
+worse uh uh but I'll probably have I'll
+ 
+
+ align:start position:0%
+worse uh uh but I'll probably have I'll
+probably shortcut it by again
+
+ align:start position:0%
+probably shortcut it by again
+ 
+
+ align:start position:0%
+probably shortcut it by again
+emphasizing that this this is the thing
+
+ align:start position:0%
+emphasizing that this this is the thing
+ 
+
+ align:start position:0%
+emphasizing that this this is the thing
+to like remember what are the inputs
+
+ align:start position:0%
+to like remember what are the inputs
+ 
+
+ align:start position:0%
+to like remember what are the inputs
+what are the outputs the
+
+ align:start position:0%
+what are the outputs the
+ 
+
+ align:start position:0%
+what are the outputs the
+formulas clearly it's not essential to
+
+ align:start position:0%
+formulas clearly it's not essential to
+ 
+
+ align:start position:0%
+formulas clearly it's not essential to
+couldn't try to memorize or even
+
+ align:start position:0%
+couldn't try to memorize or even
+ 
+
+ align:start position:0%
+couldn't try to memorize or even
+reproduce all of them but what are the
+
+ align:start position:0%
+reproduce all of them but what are the
+ 
+
+ align:start position:0%
+reproduce all of them but what are the
+inputs what are the outputs and then
+
+ align:start position:0%
+inputs what are the outputs and then
+ 
+
+ align:start position:0%
+inputs what are the outputs and then
+what's the
+
+ align:start position:0%
+what's the
+ 
+
+ align:start position:0%
+what's the
+problem what's the goal and here was the
+
+ align:start position:0%
+problem what's the goal and here was the
+ 
+
+ align:start position:0%
+problem what's the goal and here was the
+problem of this lecture which I'm going
+
+ align:start position:0%
+problem of this lecture which I'm going
+ 
+
+ align:start position:0%
+problem of this lecture which I'm going
+to call it quits now and then the second
+
+ align:start position:0%
+to call it quits now and then the second
+ 
+
+ align:start position:0%
+to call it quits now and then the second
+lecture uh should we well let's say
+
+ align:start position:0%
+lecture uh should we well let's say
+ 
+
+ align:start position:0%
+lecture uh should we well let's say
+start at
+
+ align:start position:0%
+start at
+ 
+
+ align:start position:0%
+start at
+3:30 okay 3:30 for the second lecture
+
+ align:start position:0%
+3:30 okay 3:30 for the second lecture
+ 
+
+ align:start position:0%
+3:30 okay 3:30 for the second lecture
+I've learned that uh a guy name guy
+
+ align:start position:0%
+I've learned that uh a guy name guy
+ 
+
+ align:start position:0%
+I've learned that uh a guy name guy
+named Eric Missour from Harvard who's a
+
+ align:start position:0%
+named Eric Missour from Harvard who's a
+ 
+
+ align:start position:0%
+named Eric Missour from Harvard who's a
+who's uh maybe the outstanding person in
+
+ align:start position:0%
+who's uh maybe the outstanding person in
+ 
+
+ align:start position:0%
+who's uh maybe the outstanding person in
+Science Education these these days is
+
+ align:start position:0%
+Science Education these these days is
+ 
+
+ align:start position:0%
+Science Education these these days is
+speaking just right now in the
+
+ align:start position:0%
+speaking just right now in the
+ 
+
+ align:start position:0%
+speaking just right now in the
+auditorium is it yeah so I'm going to at
+
+ align:start position:0%
+auditorium is it yeah so I'm going to at
+ 
+
+ align:start position:0%
+auditorium is it yeah so I'm going to at
+least go and see what he's looks like um
+
+ align:start position:0%
+least go and see what he's looks like um
+ 
+
+ align:start position:0%
+least go and see what he's looks like um
+and um be ready for 3:30 cman filter and
+
+ align:start position:0%
+and um be ready for 3:30 cman filter and
+ 
+
+ align:start position:0%
+and um be ready for 3:30 cman filter and
+ready for advice from you uh offline in
+
+ align:start position:0%
+ready for advice from you uh offline in
+ 
+
+ align:start position:0%
+ready for advice from you uh offline in
+person or uh by email in between okay
+
+ align:start position:0%
+person or uh by email in between okay
+ 
+
+ align:start position:0%
+person or uh by email in between okay
+see you at
+
+ align:start position:0%
+see you at
+ 
+
+ align:start position:0%
+see you at
+3:30 what was that
+
+ align:start position:0%
+3:30 what was that
+ 
+
+ align:start position:0%
+3:30 what was that
+page uh the book you have that that book
+
+ align:start position:0%
+page uh the book you have that that book
+ 
+
+ align:start position:0%
+page uh the book you have that that book
+right yeah that's right page 14 right
+
+ align:start position:0%
+right yeah that's right page 14 right
+ 
+
+ align:start position:0%
+right yeah that's right page 14 right
+right and then
\ No newline at end of file
diff --git a/Rvnv3bPDCs8.txt b/Rvnv3bPDCs8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1a1666a455e7f97dbc7a3ea115cfa0de1402f4ec
--- /dev/null
+++ b/Rvnv3bPDCs8.txt
@@ -0,0 +1,5467 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi our main aim today is to successfully
+
+ align:start position:0%
+hi our main aim today is to successfully
+ 
+
+ align:start position:0%
+hi our main aim today is to successfully
+conclude block three and to set the
+
+ align:start position:0%
+conclude block three and to set the
+ 
+
+ align:start position:0%
+conclude block three and to set the
+stage for introducing block four Now by
+
+ align:start position:0%
+stage for introducing block four Now by
+ 
+
+ align:start position:0%
+stage for introducing block four Now by
+way of Brief Review we may have become
+
+ align:start position:0%
+way of Brief Review we may have become
+ 
+
+ align:start position:0%
+way of Brief Review we may have become
+so involved with our discussion of the
+
+ align:start position:0%
+so involved with our discussion of the
+ 
+
+ align:start position:0%
+so involved with our discussion of the
+last few lessons where we've done the
+
+ align:start position:0%
+last few lessons where we've done the
+ 
+
+ align:start position:0%
+last few lessons where we've done the
+chain rule that we may have forgotten
+
+ align:start position:0%
+chain rule that we may have forgotten
+ 
+
+ align:start position:0%
+chain rule that we may have forgotten
+that the basic ingredient that we had
+
+ align:start position:0%
+that the basic ingredient that we had
+ 
+
+ align:start position:0%
+that the basic ingredient that we had
+arrived at that set up our proof of the
+
+ align:start position:0%
+arrived at that set up our proof of the
+ 
+
+ align:start position:0%
+arrived at that set up our proof of the
+chain Rule and then after that we get
+
+ align:start position:0%
+chain Rule and then after that we get
+ 
+
+ align:start position:0%
+chain Rule and then after that we get
+involved in the computation of how to
+
+ align:start position:0%
+involved in the computation of how to
+ 
+
+ align:start position:0%
+involved in the computation of how to
+use the chain rule but the basic
+
+ align:start position:0%
+use the chain rule but the basic
+ 
+
+ align:start position:0%
+use the chain rule but the basic
+ingredient was the idea that we had
+
+ align:start position:0%
+ingredient was the idea that we had
+ 
+
+ align:start position:0%
+ingredient was the idea that we had
+obtained a linear approximation a Delta
+
+ align:start position:0%
+obtained a linear approximation a Delta
+ 
+
+ align:start position:0%
+obtained a linear approximation a Delta
+W tan idea and this concept leads to the
+
+ align:start position:0%
+W tan idea and this concept leads to the
+ 
+
+ align:start position:0%
+W tan idea and this concept leads to the
+idea of a differential which is an
+
+ align:start position:0%
+idea of a differential which is an
+ 
+
+ align:start position:0%
+idea of a differential which is an
+extension of the idea of differentials
+
+ align:start position:0%
+extension of the idea of differentials
+ 
+
+ align:start position:0%
+extension of the idea of differentials
+as we knew them in part one of our
+
+ align:start position:0%
+as we knew them in part one of our
+ 
+
+ align:start position:0%
+as we knew them in part one of our
+course and what I would like to do is to
+
+ align:start position:0%
+course and what I would like to do is to
+ 
+
+ align:start position:0%
+course and what I would like to do is to
+talk somewhat briefly about this topic
+
+ align:start position:0%
+talk somewhat briefly about this topic
+ 
+
+ align:start position:0%
+talk somewhat briefly about this topic
+to show how it introduces what will be
+
+ align:start position:0%
+to show how it introduces what will be
+ 
+
+ align:start position:0%
+to show how it introduces what will be
+the main body of material in Block four
+
+ align:start position:0%
+the main body of material in Block four
+ 
+
+ align:start position:0%
+the main body of material in Block four
+and an important application that we can
+
+ align:start position:0%
+and an important application that we can
+ 
+
+ align:start position:0%
+and an important application that we can
+handle now that will show why it's worth
+
+ align:start position:0%
+handle now that will show why it's worth
+ 
+
+ align:start position:0%
+handle now that will show why it's worth
+understanding certain things about
+
+ align:start position:0%
+understanding certain things about
+ 
+
+ align:start position:0%
+understanding certain things about
+differentials even on a very Elementary
+
+ align:start position:0%
+differentials even on a very Elementary
+ 
+
+ align:start position:0%
+differentials even on a very Elementary
+level any rate the topic that I've
+
+ align:start position:0%
+level any rate the topic that I've
+ 
+
+ align:start position:0%
+level any rate the topic that I've
+chosen for today is called exact
+
+ align:start position:0%
+chosen for today is called exact
+ 
+
+ align:start position:0%
+chosen for today is called exact
+differentials and the idea again is
+
+ align:start position:0%
+differentials and the idea again is
+ 
+
+ align:start position:0%
+differentials and the idea again is
+completely analogous to what we did in
+
+ align:start position:0%
+completely analogous to what we did in
+ 
+
+ align:start position:0%
+completely analogous to what we did in
+calculus of a single variable we start
+
+ align:start position:0%
+calculus of a single variable we start
+ 
+
+ align:start position:0%
+calculus of a single variable we start
+with wals f ofx y and we showed that if
+
+ align:start position:0%
+with wals f ofx y and we showed that if
+ 
+
+ align:start position:0%
+with wals f ofx y and we showed that if
+W was a continuously differentiable
+
+ align:start position:0%
+W was a continuously differentiable
+ 
+
+ align:start position:0%
+W was a continuously differentiable
+function of X and Y it made sense to
+
+ align:start position:0%
+function of X and Y it made sense to
+ 
+
+ align:start position:0%
+function of X and Y it made sense to
+emphasize the expression called Delta W
+
+ align:start position:0%
+emphasize the expression called Delta W
+ 
+
+ align:start position:0%
+emphasize the expression called Delta W
+tan which was the partial of effort
+
+ align:start position:0%
+tan which was the partial of effort
+ 
+
+ align:start position:0%
+tan which was the partial of effort
+respect to X evaluated a given point
+
+ align:start position:0%
+respect to X evaluated a given point
+ 
+
+ align:start position:0%
+respect to X evaluated a given point
+time Delta X plus the partial of effort
+
+ align:start position:0%
+time Delta X plus the partial of effort
+ 
+
+ align:start position:0%
+time Delta X plus the partial of effort
+respect to Y at that same point times
+
+ align:start position:0%
+respect to Y at that same point times
+ 
+
+ align:start position:0%
+respect to Y at that same point times
+Delta Y and what we do is the same thing
+
+ align:start position:0%
+Delta Y and what we do is the same thing
+ 
+
+ align:start position:0%
+Delta Y and what we do is the same thing
+that we did as I say in calculus of a
+
+ align:start position:0%
+that we did as I say in calculus of a
+ 
+
+ align:start position:0%
+that we did as I say in calculus of a
+single variable we introduce a new
+
+ align:start position:0%
+single variable we introduce a new
+ 
+
+ align:start position:0%
+single variable we introduce a new
+language we write Delta W tan now as DW
+
+ align:start position:0%
+language we write Delta W tan now as DW
+ 
+
+ align:start position:0%
+language we write Delta W tan now as DW
+we write Delta X as DX Delta y as
+
+ align:start position:0%
+we write Delta X as DX Delta y as
+ 
+
+ align:start position:0%
+we write Delta X as DX Delta y as
+Dy and what we say is that DW is the
+
+ align:start position:0%
+Dy and what we say is that DW is the
+ 
+
+ align:start position:0%
+Dy and what we say is that DW is the
+total differential of w to see how this
+
+ align:start position:0%
+total differential of w to see how this
+ 
+
+ align:start position:0%
+total differential of w to see how this
+is analogous to what happened in
+
+ align:start position:0%
+is analogous to what happened in
+ 
+
+ align:start position:0%
+is analogous to what happened in
+calculus of a single variable notice for
+
+ align:start position:0%
+calculus of a single variable notice for
+ 
+
+ align:start position:0%
+calculus of a single variable notice for
+the sake of argument that if F happens
+
+ align:start position:0%
+the sake of argument that if F happens
+ 
+
+ align:start position:0%
+the sake of argument that if F happens
+to be a function of X alone so that
+
+ align:start position:0%
+to be a function of X alone so that
+ 
+
+ align:start position:0%
+to be a function of X alone so that
+there is no second variable in other
+
+ align:start position:0%
+there is no second variable in other
+ 
+
+ align:start position:0%
+there is no second variable in other
+words if f is independent of Y notice
+
+ align:start position:0%
+words if f is independent of Y notice
+ 
+
+ align:start position:0%
+words if f is independent of Y notice
+that the partial of f respect to Y will
+
+ align:start position:0%
+that the partial of f respect to Y will
+ 
+
+ align:start position:0%
+that the partial of f respect to Y will
+be zero and we will then have that W is
+
+ align:start position:0%
+be zero and we will then have that W is
+ 
+
+ align:start position:0%
+be zero and we will then have that W is
+a function of X alone DW then will be
+
+ align:start position:0%
+a function of X alone DW then will be
+ 
+
+ align:start position:0%
+a function of X alone DW then will be
+what well in that case the partial of f
+
+ align:start position:0%
+what well in that case the partial of f
+ 
+
+ align:start position:0%
+what well in that case the partial of f
+respect to X is the the ordinary
+
+ align:start position:0%
+respect to X is the the ordinary
+ 
+
+ align:start position:0%
+respect to X is the the ordinary
+derivative of f respect to X time DX and
+
+ align:start position:0%
+derivative of f respect to X time DX and
+ 
+
+ align:start position:0%
+derivative of f respect to X time DX and
+we're back to our old recipe that DW is
+
+ align:start position:0%
+we're back to our old recipe that DW is
+ 
+
+ align:start position:0%
+we're back to our old recipe that DW is
+dwdx time DX that this is a natural
+
+ align:start position:0%
+dwdx time DX that this is a natural
+ 
+
+ align:start position:0%
+dwdx time DX that this is a natural
+extension of what happened in calculus
+
+ align:start position:0%
+extension of what happened in calculus
+ 
+
+ align:start position:0%
+extension of what happened in calculus
+of a single variable all right now what
+
+ align:start position:0%
+of a single variable all right now what
+ 
+
+ align:start position:0%
+of a single variable all right now what
+leads into the next block and what and
+
+ align:start position:0%
+leads into the next block and what and
+ 
+
+ align:start position:0%
+leads into the next block and what and
+why we're going to drop this for the
+
+ align:start position:0%
+why we're going to drop this for the
+ 
+
+ align:start position:0%
+why we're going to drop this for the
+time being but to go up to a different
+
+ align:start position:0%
+time being but to go up to a different
+ 
+
+ align:start position:0%
+time being but to go up to a different
+aspect of this is notice that if we can
+
+ align:start position:0%
+aspect of this is notice that if we can
+ 
+
+ align:start position:0%
+aspect of this is notice that if we can
+assume that
+
+ align:start position:0%
+assume that
+ 
+
+ align:start position:0%
+assume that
+DW can replace Delta W if we can assume
+
+ align:start position:0%
+DW can replace Delta W if we can assume
+ 
+
+ align:start position:0%
+DW can replace Delta W if we can assume
+as we as we talked about in the case of
+
+ align:start position:0%
+as we as we talked about in the case of
+ 
+
+ align:start position:0%
+as we as we talked about in the case of
+L differentiable functions that the
+
+ align:start position:0%
+L differentiable functions that the
+ 
+
+ align:start position:0%
+L differentiable functions that the
+difference between Delta W and Delta W
+
+ align:start position:0%
+difference between Delta W and Delta W
+ 
+
+ align:start position:0%
+difference between Delta W and Delta W
+tan is negligible for sufficiently small
+
+ align:start position:0%
+tan is negligible for sufficiently small
+ 
+
+ align:start position:0%
+tan is negligible for sufficiently small
+Delta X and Delta y notice that the
+
+ align:start position:0%
+Delta X and Delta y notice that the
+ 
+
+ align:start position:0%
+Delta X and Delta y notice that the
+equation DW equals F subx DX plus F suby
+
+ align:start position:0%
+equation DW equals F subx DX plus F suby
+ 
+
+ align:start position:0%
+equation DW equals F subx DX plus F suby
+Dy since F subx and F suby are computed
+
+ align:start position:0%
+Dy since F subx and F suby are computed
+ 
+
+ align:start position:0%
+Dy since F subx and F suby are computed
+at a given point these become what
+
+ align:start position:0%
+at a given point these become what
+ 
+
+ align:start position:0%
+at a given point these become what
+linear combinations of DX and Dy a
+
+ align:start position:0%
+linear combinations of DX and Dy a
+ 
+
+ align:start position:0%
+linear combinations of DX and Dy a
+constant time DX plus a constant time Dy
+
+ align:start position:0%
+constant time DX plus a constant time Dy
+ 
+
+ align:start position:0%
+constant time DX plus a constant time Dy
+and we're into the subject of linear
+
+ align:start position:0%
+and we're into the subject of linear
+ 
+
+ align:start position:0%
+and we're into the subject of linear
+equations which we will talk about next
+
+ align:start position:0%
+equations which we will talk about next
+ 
+
+ align:start position:0%
+equations which we will talk about next
+time for the the time being all I want
+
+ align:start position:0%
+time for the the time being all I want
+ 
+
+ align:start position:0%
+time for the the time being all I want
+to point out is that DW is called the
+
+ align:start position:0%
+to point out is that DW is called the
+ 
+
+ align:start position:0%
+to point out is that DW is called the
+total differential of w and that
+
+ align:start position:0%
+total differential of w and that
+ 
+
+ align:start position:0%
+total differential of w and that
+conversely starting with any expression
+
+ align:start position:0%
+conversely starting with any expression
+ 
+
+ align:start position:0%
+conversely starting with any expression
+of the form some function M of X and Y *
+
+ align:start position:0%
+of the form some function M of X and Y *
+ 
+
+ align:start position:0%
+of the form some function M of X and Y *
+DX plus some function n of X and Y * Dy
+
+ align:start position:0%
+DX plus some function n of X and Y * Dy
+ 
+
+ align:start position:0%
+DX plus some function n of X and Y * Dy
+in other words M of XY DX plus n of XY
+
+ align:start position:0%
+in other words M of XY DX plus n of XY
+ 
+
+ align:start position:0%
+in other words M of XY DX plus n of XY
+Dy no matter what functions of X and Y M
+
+ align:start position:0%
+Dy no matter what functions of X and Y M
+ 
+
+ align:start position:0%
+Dy no matter what functions of X and Y M
+and N are any expression of this form is
+
+ align:start position:0%
+and N are any expression of this form is
+ 
+
+ align:start position:0%
+and N are any expression of this form is
+called a differential by the way you may
+
+ align:start position:0%
+called a differential by the way you may
+ 
+
+ align:start position:0%
+called a differential by the way you may
+recall that you were used to calling DX
+
+ align:start position:0%
+recall that you were used to calling DX
+ 
+
+ align:start position:0%
+recall that you were used to calling DX
+a differential backend calculus of a
+
+ align:start position:0%
+a differential backend calculus of a
+ 
+
+ align:start position:0%
+a differential backend calculus of a
+single variable notice that in
+
+ align:start position:0%
+single variable notice that in
+ 
+
+ align:start position:0%
+single variable notice that in
+particular one choice of capital N is to
+
+ align:start position:0%
+particular one choice of capital N is to
+ 
+
+ align:start position:0%
+particular one choice of capital N is to
+have n of X Y be identically zero we
+
+ align:start position:0%
+have n of X Y be identically zero we
+ 
+
+ align:start position:0%
+have n of X Y be identically zero we
+could have M of XY be identically one in
+
+ align:start position:0%
+could have M of XY be identically one in
+ 
+
+ align:start position:0%
+could have M of XY be identically one in
+which case MDX plus ndy would simply be
+
+ align:start position:0%
+which case MDX plus ndy would simply be
+ 
+
+ align:start position:0%
+which case MDX plus ndy would simply be
+1 DX + 0 Dy or DX in other words notice
+
+ align:start position:0%
+1 DX + 0 Dy or DX in other words notice
+ 
+
+ align:start position:0%
+1 DX + 0 Dy or DX in other words notice
+that this extended definition of a
+
+ align:start position:0%
+that this extended definition of a
+ 
+
+ align:start position:0%
+that this extended definition of a
+differential for two or more variables
+
+ align:start position:0%
+differential for two or more variables
+ 
+
+ align:start position:0%
+differential for two or more variables
+includes the definition for a single
+
+ align:start position:0%
+includes the definition for a single
+ 
+
+ align:start position:0%
+includes the definition for a single
+variable at any rate any expression of
+
+ align:start position:0%
+variable at any rate any expression of
+ 
+
+ align:start position:0%
+variable at any rate any expression of
+this type is called a differential and
+
+ align:start position:0%
+this type is called a differential and
+ 
+
+ align:start position:0%
+this type is called a differential and
+again a very natural question that comes
+
+ align:start position:0%
+again a very natural question that comes
+ 
+
+ align:start position:0%
+again a very natural question that comes
+up is who wants differentials why do we
+
+ align:start position:0%
+up is who wants differentials why do we
+ 
+
+ align:start position:0%
+up is who wants differentials why do we
+need them and perhaps the best
+
+ align:start position:0%
+need them and perhaps the best
+ 
+
+ align:start position:0%
+need them and perhaps the best
+application comes from the clue that a
+
+ align:start position:0%
+application comes from the clue that a
+ 
+
+ align:start position:0%
+application comes from the clue that a
+certain subject is called differential
+
+ align:start position:0%
+certain subject is called differential
+ 
+
+ align:start position:0%
+certain subject is called differential
+equations rather than derivative
+
+ align:start position:0%
+equations rather than derivative
+ 
+
+ align:start position:0%
+equations rather than derivative
+equations let me illustrate this in
+
+ align:start position:0%
+equations let me illustrate this in
+ 
+
+ align:start position:0%
+equations let me illustrate this in
+terms of a what I think is a rather nice
+
+ align:start position:0%
+terms of a what I think is a rather nice
+ 
+
+ align:start position:0%
+terms of a what I think is a rather nice
+example in the sense that it would be
+
+ align:start position:0%
+example in the sense that it would be
+ 
+
+ align:start position:0%
+example in the sense that it would be
+hard to guess the answer but rather easy
+
+ align:start position:0%
+hard to guess the answer but rather easy
+ 
+
+ align:start position:0%
+hard to guess the answer but rather easy
+to visualize what the problem says at
+
+ align:start position:0%
+to visualize what the problem says at
+ 
+
+ align:start position:0%
+to visualize what the problem says at
+least let's imagine I have a certain
+
+ align:start position:0%
+least let's imagine I have a certain
+ 
+
+ align:start position:0%
+least let's imagine I have a certain
+curve s in the XY plane I don't tell you
+
+ align:start position:0%
+curve s in the XY plane I don't tell you
+ 
+
+ align:start position:0%
+curve s in the XY plane I don't tell you
+anything else about that curve except
+
+ align:start position:0%
+anything else about that curve except
+ 
+
+ align:start position:0%
+anything else about that curve except
+that its slope at any point x comma Y is
+
+ align:start position:0%
+that its slope at any point x comma Y is
+ 
+
+ align:start position:0%
+that its slope at any point x comma Y is
+given by the very interesting
+
+ align:start position:0%
+given by the very interesting
+ 
+
+ align:start position:0%
+given by the very interesting
+relationship that it's the quotient of
+
+ align:start position:0%
+relationship that it's the quotient of
+ 
+
+ align:start position:0%
+relationship that it's the quotient of
+the square of its distance from the
+
+ align:start position:0%
+the square of its distance from the
+ 
+
+ align:start position:0%
+the square of its distance from the
+origin over twice the product of its
+
+ align:start position:0%
+origin over twice the product of its
+ 
+
+ align:start position:0%
+origin over twice the product of its
+coordinates in other words to find the
+
+ align:start position:0%
+coordinates in other words to find the
+ 
+
+ align:start position:0%
+coordinates in other words to find the
+slope of the curve S at the point x
+
+ align:start position:0%
+slope of the curve S at the point x
+ 
+
+ align:start position:0%
+slope of the curve S at the point x
+comma y i Square the
+
+ align:start position:0%
+comma y i Square the
+ 
+
+ align:start position:0%
+comma y i Square the
+distance of the point from the
+
+ align:start position:0%
+distance of the point from the
+ 
+
+ align:start position:0%
+distance of the point from the
+origin take the negative of that divide
+
+ align:start position:0%
+origin take the negative of that divide
+ 
+
+ align:start position:0%
+origin take the negative of that divide
+by twice the product of the coordinates
+
+ align:start position:0%
+by twice the product of the coordinates
+ 
+
+ align:start position:0%
+by twice the product of the coordinates
+and that's going to be the slope now
+
+ align:start position:0%
+and that's going to be the slope now
+ 
+
+ align:start position:0%
+and that's going to be the slope now
+certainly that makes sense geometrically
+
+ align:start position:0%
+certainly that makes sense geometrically
+ 
+
+ align:start position:0%
+certainly that makes sense geometrically
+but what type of a curve would have that
+
+ align:start position:0%
+but what type of a curve would have that
+ 
+
+ align:start position:0%
+but what type of a curve would have that
+property and even assuming that we knew
+
+ align:start position:0%
+property and even assuming that we knew
+ 
+
+ align:start position:0%
+property and even assuming that we knew
+such a curve how in the world can you
+
+ align:start position:0%
+such a curve how in the world can you
+ 
+
+ align:start position:0%
+such a curve how in the world can you
+express it in a convenient manner well
+
+ align:start position:0%
+express it in a convenient manner well
+ 
+
+ align:start position:0%
+express it in a convenient manner well
+here's the idea again back to the same
+
+ align:start position:0%
+here's the idea again back to the same
+ 
+
+ align:start position:0%
+here's the idea again back to the same
+technique that we use in calculus of a
+
+ align:start position:0%
+technique that we use in calculus of a
+ 
+
+ align:start position:0%
+technique that we use in calculus of a
+single variable algebraically this is
+
+ align:start position:0%
+single variable algebraically this is
+ 
+
+ align:start position:0%
+single variable algebraically this is
+our equation if we cross multiply and
+
+ align:start position:0%
+our equation if we cross multiply and
+ 
+
+ align:start position:0%
+our equation if we cross multiply and
+collect all our terms onto one side of
+
+ align:start position:0%
+collect all our terms onto one side of
+ 
+
+ align:start position:0%
+collect all our terms onto one side of
+the equation we obtain what we call the
+
+ align:start position:0%
+the equation we obtain what we call the
+ 
+
+ align:start position:0%
+the equation we obtain what we call the
+differential equation see it's an
+
+ align:start position:0%
+differential equation see it's an
+ 
+
+ align:start position:0%
+differential equation see it's an
+equation involving a differential in
+
+ align:start position:0%
+equation involving a differential in
+ 
+
+ align:start position:0%
+equation involving a differential in
+fact in this case using our general
+
+ align:start position:0%
+fact in this case using our general
+ 
+
+ align:start position:0%
+fact in this case using our general
+notation M of X Y is x^2 + y^2 and N of
+
+ align:start position:0%
+notation M of X Y is x^2 + y^2 and N of
+ 
+
+ align:start position:0%
+notation M of X Y is x^2 + y^2 and N of
+X Y is 2x y we have a differential equal
+
+ align:start position:0%
+X Y is 2x y we have a differential equal
+ 
+
+ align:start position:0%
+X Y is 2x y we have a differential equal
+to zero now without going into this
+
+ align:start position:0%
+to zero now without going into this
+ 
+
+ align:start position:0%
+to zero now without going into this
+right now suppose I just happen to have
+
+ align:start position:0%
+right now suppose I just happen to have
+ 
+
+ align:start position:0%
+right now suppose I just happen to have
+a very quick eye well in fact before I
+
+ align:start position:0%
+a very quick eye well in fact before I
+ 
+
+ align:start position:0%
+a very quick eye well in fact before I
+even say that let me point this out
+
+ align:start position:0%
+even say that let me point this out
+ 
+
+ align:start position:0%
+even say that let me point this out
+we've had problems like this in part one
+
+ align:start position:0%
+we've had problems like this in part one
+ 
+
+ align:start position:0%
+we've had problems like this in part one
+of our course the main difference was is
+
+ align:start position:0%
+of our course the main difference was is
+ 
+
+ align:start position:0%
+of our course the main difference was is
+that we could separate out the variables
+
+ align:start position:0%
+that we could separate out the variables
+ 
+
+ align:start position:0%
+that we could separate out the variables
+we could get the x's and the Y's
+
+ align:start position:0%
+we could get the x's and the Y's
+ 
+
+ align:start position:0%
+we could get the x's and the Y's
+separated remember now Y is implicitly a
+
+ align:start position:0%
+separated remember now Y is implicitly a
+ 
+
+ align:start position:0%
+separated remember now Y is implicitly a
+function of X here in this expression
+
+ align:start position:0%
+function of X here in this expression
+ 
+
+ align:start position:0%
+function of X here in this expression
+because of the equation see X and Y are
+
+ align:start position:0%
+because of the equation see X and Y are
+ 
+
+ align:start position:0%
+because of the equation see X and Y are
+no longer independent when we equate
+
+ align:start position:0%
+no longer independent when we equate
+ 
+
+ align:start position:0%
+no longer independent when we equate
+this to zero the question is though we
+
+ align:start position:0%
+this to zero the question is though we
+ 
+
+ align:start position:0%
+this to zero the question is though we
+cannot solve or separate the x's and the
+
+ align:start position:0%
+cannot solve or separate the x's and the
+ 
+
+ align:start position:0%
+cannot solve or separate the x's and the
+Y's here but if we were lucky that's
+
+ align:start position:0%
+Y's here but if we were lucky that's
+ 
+
+ align:start position:0%
+Y's here but if we were lucky that's
+where luck comes in we would recognize
+
+ align:start position:0%
+where luck comes in we would recognize
+ 
+
+ align:start position:0%
+where luck comes in we would recognize
+that treating y as a function of X the
+
+ align:start position:0%
+that treating y as a function of X the
+ 
+
+ align:start position:0%
+that treating y as a function of X the
+differential on the left hand side is
+
+ align:start position:0%
+differential on the left hand side is
+ 
+
+ align:start position:0%
+differential on the left hand side is
+precisely the differential of 1/3 x Cub
+
+ align:start position:0%
+precisely the differential of 1/3 x Cub
+ 
+
+ align:start position:0%
+precisely the differential of 1/3 x Cub
+Plus x^2 Y in other words the partial of
+
+ align:start position:0%
+Plus x^2 Y in other words the partial of
+ 
+
+ align:start position:0%
+Plus x^2 Y in other words the partial of
+this with respect to X is simply
+
+ align:start position:0%
+this with respect to X is simply
+ 
+
+ align:start position:0%
+this with respect to X is simply
+X2
+
+ align:start position:0%
+X2
+ 
+
+ align:start position:0%
+X2
+uh do I have I think I may have this
+
+ align:start position:0%
+uh do I have I think I may have this
+ 
+
+ align:start position:0%
+uh do I have I think I may have this
+thing in Reverse let me make sure if I
+
+ align:start position:0%
+thing in Reverse let me make sure if I
+ 
+
+ align:start position:0%
+thing in Reverse let me make sure if I
+take the partial of this with respect to
+
+ align:start position:0%
+take the partial of this with respect to
+ 
+
+ align:start position:0%
+take the partial of this with respect to
+X I have 1/3 x cubed plus 2X y right and
+
+ align:start position:0%
+X I have 1/3 x cubed plus 2X y right and
+ 
+
+ align:start position:0%
+X I have 1/3 x cubed plus 2X y right and
+if I take the partial with respect to Y
+
+ align:start position:0%
+if I take the partial with respect to Y
+ 
+
+ align:start position:0%
+if I take the partial with respect to Y
+I simply have X2 at any rate what I'm
+
+ align:start position:0%
+I simply have X2 at any rate what I'm
+ 
+
+ align:start position:0%
+I simply have X2 at any rate what I'm
+saying is if we knew a function who's
+
+ align:start position:0%
+saying is if we knew a function who's
+ 
+
+ align:start position:0%
+saying is if we knew a function who's
+say I have this in Reverse that's what's
+
+ align:start position:0%
+say I have this in Reverse that's what's
+ 
+
+ align:start position:0%
+say I have this in Reverse that's what's
+bothering me here I think the square
+
+ align:start position:0%
+bothering me here I think the square
+ 
+
+ align:start position:0%
+bothering me here I think the square
+should go this way that's not important
+
+ align:start position:0%
+should go this way that's not important
+ 
+
+ align:start position:0%
+should go this way that's not important
+all I'm saying is if I've done this
+
+ align:start position:0%
+all I'm saying is if I've done this
+ 
+
+ align:start position:0%
+all I'm saying is if I've done this
+thing correctly if you take the partial
+
+ align:start position:0%
+thing correctly if you take the partial
+ 
+
+ align:start position:0%
+thing correctly if you take the partial
+of this with respect to Y with respect
+
+ align:start position:0%
+of this with respect to Y with respect
+ 
+
+ align:start position:0%
+of this with respect to Y with respect
+to X you should get this if you take the
+
+ align:start position:0%
+to X you should get this if you take the
+ 
+
+ align:start position:0%
+to X you should get this if you take the
+partial of this with respect to Y you
+
+ align:start position:0%
+partial of this with respect to Y you
+ 
+
+ align:start position:0%
+partial of this with respect to Y you
+should get this and that comes out
+
+ align:start position:0%
+should get this and that comes out
+ 
+
+ align:start position:0%
+should get this and that comes out
+correctly now in other words the partial
+
+ align:start position:0%
+correctly now in other words the partial
+ 
+
+ align:start position:0%
+correctly now in other words the partial
+of this with respect to X is x^2 + y^2
+
+ align:start position:0%
+of this with respect to X is x^2 + y^2
+ 
+
+ align:start position:0%
+of this with respect to X is x^2 + y^2
+the partial of this with respect to Y
+
+ align:start position:0%
+the partial of this with respect to Y
+ 
+
+ align:start position:0%
+the partial of this with respect to Y
+this term drops out and it's just 2x y
+
+ align:start position:0%
+this term drops out and it's just 2x y
+ 
+
+ align:start position:0%
+this term drops out and it's just 2x y
+I'm sorry for that little mistake but I
+
+ align:start position:0%
+I'm sorry for that little mistake but I
+ 
+
+ align:start position:0%
+I'm sorry for that little mistake but I
+won't really apologize for it in the
+
+ align:start position:0%
+won't really apologize for it in the
+ 
+
+ align:start position:0%
+won't really apologize for it in the
+sense that once we found it or even if
+
+ align:start position:0%
+sense that once we found it or even if
+ 
+
+ align:start position:0%
+sense that once we found it or even if
+we didn't find it the key theory is the
+
+ align:start position:0%
+we didn't find it the key theory is the
+ 
+
+ align:start position:0%
+we didn't find it the key theory is the
+same the point is that if we knew a
+
+ align:start position:0%
+same the point is that if we knew a
+ 
+
+ align:start position:0%
+same the point is that if we knew a
+function whose differential was this
+
+ align:start position:0%
+function whose differential was this
+ 
+
+ align:start position:0%
+function whose differential was this
+then the fact that this differential is
+
+ align:start position:0%
+then the fact that this differential is
+ 
+
+ align:start position:0%
+then the fact that this differential is
+zero means the expression itself must be
+
+ align:start position:0%
+zero means the expression itself must be
+ 
+
+ align:start position:0%
+zero means the expression itself must be
+a constant in other words 1/3 x cubed +
+
+ align:start position:0%
+a constant in other words 1/3 x cubed +
+ 
+
+ align:start position:0%
+a constant in other words 1/3 x cubed +
+x y^ 2 must be a
+
+ align:start position:0%
+x y^ 2 must be a
+ 
+
+ align:start position:0%
+x y^ 2 must be a
+constant and therefore what we're saying
+
+ align:start position:0%
+constant and therefore what we're saying
+ 
+
+ align:start position:0%
+constant and therefore what we're saying
+is if we now solve the equation I'm I
+
+ align:start position:0%
+is if we now solve the equation I'm I
+ 
+
+ align:start position:0%
+is if we now solve the equation I'm I
+really am sorry to have botched this for
+
+ align:start position:0%
+really am sorry to have botched this for
+ 
+
+ align:start position:0%
+really am sorry to have botched this for
+you but again as I say the idea
+
+ align:start position:0%
+you but again as I say the idea
+ 
+
+ align:start position:0%
+you but again as I say the idea
+basically comes through unimpeded I now
+
+ align:start position:0%
+basically comes through unimpeded I now
+ 
+
+ align:start position:0%
+basically comes through unimpeded I now
+solve for y in terms of X and I get what
+
+ align:start position:0%
+solve for y in terms of X and I get what
+ 
+
+ align:start position:0%
+solve for y in terms of X and I get what
+that Y is equal to transposing here uh
+
+ align:start position:0%
+that Y is equal to transposing here uh
+ 
+
+ align:start position:0%
+that Y is equal to transposing here uh
+plus or minus the square root of C - 1/3
+
+ align:start position:0%
+plus or minus the square root of C - 1/3
+ 
+
+ align:start position:0%
+plus or minus the square root of C - 1/3
+x Cub all over X in other words the
+
+ align:start position:0%
+x Cub all over X in other words the
+ 
+
+ align:start position:0%
+x Cub all over X in other words the
+family of curves that satisfies this
+
+ align:start position:0%
+family of curves that satisfies this
+ 
+
+ align:start position:0%
+family of curves that satisfies this
+differential equation is precisely this
+
+ align:start position:0%
+differential equation is precisely this
+ 
+
+ align:start position:0%
+differential equation is precisely this
+family here whatever that may look like
+
+ align:start position:0%
+family here whatever that may look like
+ 
+
+ align:start position:0%
+family here whatever that may look like
+in other words this is the family of Cur
+
+ align:start position:0%
+in other words this is the family of Cur
+ 
+
+ align:start position:0%
+in other words this is the family of Cur
+curves that has the interesting slope
+
+ align:start position:0%
+curves that has the interesting slope
+ 
+
+ align:start position:0%
+curves that has the interesting slope
+property that we just discussed now you
+
+ align:start position:0%
+property that we just discussed now you
+ 
+
+ align:start position:0%
+property that we just discussed now you
+see again the reason I say that I wasn't
+
+ align:start position:0%
+see again the reason I say that I wasn't
+ 
+
+ align:start position:0%
+see again the reason I say that I wasn't
+too concerned about what this function
+
+ align:start position:0%
+too concerned about what this function
+ 
+
+ align:start position:0%
+too concerned about what this function
+actually was is notice that I was just
+
+ align:start position:0%
+actually was is notice that I was just
+ 
+
+ align:start position:0%
+actually was is notice that I was just
+pulling it out of the hat for you here
+
+ align:start position:0%
+pulling it out of the hat for you here
+ 
+
+ align:start position:0%
+pulling it out of the hat for you here
+anyway I said suppose we could find a
+
+ align:start position:0%
+anyway I said suppose we could find a
+ 
+
+ align:start position:0%
+anyway I said suppose we could find a
+function W such that DW was this the
+
+ align:start position:0%
+function W such that DW was this the
+ 
+
+ align:start position:0%
+function W such that DW was this the
+major question that comes up and how one
+
+ align:start position:0%
+major question that comes up and how one
+ 
+
+ align:start position:0%
+major question that comes up and how one
+uses differentials and the like is as
+
+ align:start position:0%
+uses differentials and the like is as
+ 
+
+ align:start position:0%
+uses differentials and the like is as
+follows suppose all I told you was that
+
+ align:start position:0%
+follows suppose all I told you was that
+ 
+
+ align:start position:0%
+follows suppose all I told you was that
+we had the differential X2 + y DX + 2xy
+
+ align:start position:0%
+we had the differential X2 + y DX + 2xy
+ 
+
+ align:start position:0%
+we had the differential X2 + y DX + 2xy
+Dy and I said to you find a function W
+
+ align:start position:0%
+Dy and I said to you find a function W
+ 
+
+ align:start position:0%
+Dy and I said to you find a function W
+such that DW will be X2 + Y2 DX plus 2xy
+
+ align:start position:0%
+such that DW will be X2 + Y2 DX plus 2xy
+ 
+
+ align:start position:0%
+such that DW will be X2 + Y2 DX plus 2xy
+Dy the key computational Aid in doing
+
+ align:start position:0%
+Dy the key computational Aid in doing
+ 
+
+ align:start position:0%
+Dy the key computational Aid in doing
+this involves the fact that if u and v
+
+ align:start position:0%
+this involves the fact that if u and v
+ 
+
+ align:start position:0%
+this involves the fact that if u and v
+are independent variables and it's
+
+ align:start position:0%
+are independent variables and it's
+ 
+
+ align:start position:0%
+are independent variables and it's
+crucial that they be independent that if
+
+ align:start position:0%
+crucial that they be independent that if
+ 
+
+ align:start position:0%
+crucial that they be independent that if
+Au U plus BV equals cuu plus DV it must
+
+ align:start position:0%
+Au U plus BV equals cuu plus DV it must
+ 
+
+ align:start position:0%
+Au U plus BV equals cuu plus DV it must
+be that a equals c and b equals D in
+
+ align:start position:0%
+be that a equals c and b equals D in
+ 
+
+ align:start position:0%
+be that a equals c and b equals D in
+other words the only way that two linear
+
+ align:start position:0%
+other words the only way that two linear
+ 
+
+ align:start position:0%
+other words the only way that two linear
+combinations of independent variables
+
+ align:start position:0%
+combinations of independent variables
+ 
+
+ align:start position:0%
+combinations of independent variables
+can be equal is if they're equal
+
+ align:start position:0%
+can be equal is if they're equal
+ 
+
+ align:start position:0%
+can be equal is if they're equal
+coefficient by coefficient you see the
+
+ align:start position:0%
+coefficient by coefficient you see the
+ 
+
+ align:start position:0%
+coefficient by coefficient you see the
+proof is very simple namely after all if
+
+ align:start position:0%
+proof is very simple namely after all if
+ 
+
+ align:start position:0%
+proof is very simple namely after all if
+u and v are independent variables why
+
+ align:start position:0%
+u and v are independent variables why
+ 
+
+ align:start position:0%
+u and v are independent variables why
+can't I pick V to be zero let U be any
+
+ align:start position:0%
+can't I pick V to be zero let U be any
+ 
+
+ align:start position:0%
+can't I pick V to be zero let U be any
+nonzero number then if V is zero when I
+
+ align:start position:0%
+nonzero number then if V is zero when I
+ 
+
+ align:start position:0%
+nonzero number then if V is zero when I
+equate these two it says Au U equals cuu
+
+ align:start position:0%
+equate these two it says Au U equals cuu
+ 
+
+ align:start position:0%
+equate these two it says Au U equals cuu
+Since U is not zero I can cancel and
+
+ align:start position:0%
+Since U is not zero I can cancel and
+ 
+
+ align:start position:0%
+Since U is not zero I can cancel and
+obtain that a equals c and in a similar
+
+ align:start position:0%
+obtain that a equals c and in a similar
+ 
+
+ align:start position:0%
+obtain that a equals c and in a similar
+way letting U equals z i have B V equal
+
+ align:start position:0%
+way letting U equals z i have B V equal
+ 
+
+ align:start position:0%
+way letting U equals z i have B V equal
+DV I can cancel the v's and get that b
+
+ align:start position:0%
+DV I can cancel the v's and get that b
+ 
+
+ align:start position:0%
+DV I can cancel the v's and get that b
+equals D but it's crucial that u and v
+
+ align:start position:0%
+equals D but it's crucial that u and v
+ 
+
+ align:start position:0%
+equals D but it's crucial that u and v
+be independent because if u and v are
+
+ align:start position:0%
+be independent because if u and v are
+ 
+
+ align:start position:0%
+be independent because if u and v are
+not independent how do I know that I can
+
+ align:start position:0%
+not independent how do I know that I can
+ 
+
+ align:start position:0%
+not independent how do I know that I can
+have U equal to zero when V is not zero
+
+ align:start position:0%
+have U equal to zero when V is not zero
+ 
+
+ align:start position:0%
+have U equal to zero when V is not zero
+for example let's suppose that V and U
+
+ align:start position:0%
+for example let's suppose that V and U
+ 
+
+ align:start position:0%
+for example let's suppose that V and U
+Were dependent suppose for example that
+
+ align:start position:0%
+Were dependent suppose for example that
+ 
+
+ align:start position:0%
+Were dependent suppose for example that
+V equals tce U observe in this case that
+
+ align:start position:0%
+V equals tce U observe in this case that
+ 
+
+ align:start position:0%
+V equals tce U observe in this case that
+9 U + 4 V since V is 2 U turns out to be
+
+ align:start position:0%
+9 U + 4 V since V is 2 U turns out to be
+ 
+
+ align:start position:0%
+9 U + 4 V since V is 2 U turns out to be
+17 U on the other hand 7 U + 5 V is 7 U
+
+ align:start position:0%
+17 U on the other hand 7 U + 5 V is 7 U
+ 
+
+ align:start position:0%
+17 U on the other hand 7 U + 5 V is 7 U
++ 10 U which is also 17 U notice that 9
+
+ align:start position:0%
++ 10 U which is also 17 U notice that 9
+ 
+
+ align:start position:0%
++ 10 U which is also 17 U notice that 9
+U + 4 v = 7 U + 5 V even though the
+
+ align:start position:0%
+U + 4 v = 7 U + 5 V even though the
+ 
+
+ align:start position:0%
+U + 4 v = 7 U + 5 V even though the
+coefficients don't line up as far as
+
+ align:start position:0%
+coefficients don't line up as far as
+ 
+
+ align:start position:0%
+coefficients don't line up as far as
+being equal a
+
+ align:start position:0%
+being equal a
+ 
+
+ align:start position:0%
+being equal a
+concern you see in other words notice
+
+ align:start position:0%
+concern you see in other words notice
+ 
+
+ align:start position:0%
+concern you see in other words notice
+that being able to equate things
+
+ align:start position:0%
+that being able to equate things
+ 
+
+ align:start position:0%
+that being able to equate things
+coefficient by coefficient hinges on the
+
+ align:start position:0%
+coefficient by coefficient hinges on the
+ 
+
+ align:start position:0%
+coefficient by coefficient hinges on the
+fact that the variables that we're
+
+ align:start position:0%
+fact that the variables that we're
+ 
+
+ align:start position:0%
+fact that the variables that we're
+dealing with are independent and the key
+
+ align:start position:0%
+dealing with are independent and the key
+ 
+
+ align:start position:0%
+dealing with are independent and the key
+thing going back to this problem is what
+
+ align:start position:0%
+thing going back to this problem is what
+ 
+
+ align:start position:0%
+thing going back to this problem is what
+were DX and Dy they were Delta X and
+
+ align:start position:0%
+were DX and Dy they were Delta X and
+ 
+
+ align:start position:0%
+were DX and Dy they were Delta X and
+Delta Y and as long as X and Y are
+
+ align:start position:0%
+Delta Y and as long as X and Y are
+ 
+
+ align:start position:0%
+Delta Y and as long as X and Y are
+independent variables certainly the
+
+ align:start position:0%
+independent variables certainly the
+ 
+
+ align:start position:0%
+independent variables certainly the
+change in X is independent can be done
+
+ align:start position:0%
+change in X is independent can be done
+ 
+
+ align:start position:0%
+change in X is independent can be done
+independently of the change in y in
+
+ align:start position:0%
+independently of the change in y in
+ 
+
+ align:start position:0%
+independently of the change in y in
+other words DX and Dy are independent
+
+ align:start position:0%
+other words DX and Dy are independent
+ 
+
+ align:start position:0%
+other words DX and Dy are independent
+variables so if we now say let's find
+
+ align:start position:0%
+variables so if we now say let's find
+ 
+
+ align:start position:0%
+variables so if we now say let's find
+that function W such that DW is X2 + y^2
+
+ align:start position:0%
+that function W such that DW is X2 + y^2
+ 
+
+ align:start position:0%
+that function W such that DW is X2 + y^2
+DX is x + y^2 DX + 2x y Dy the one thing
+
+ align:start position:0%
+DX is x + y^2 DX + 2x y Dy the one thing
+ 
+
+ align:start position:0%
+DX is x + y^2 DX + 2x y Dy the one thing
+we know about DW if it exists by our
+
+ align:start position:0%
+we know about DW if it exists by our
+ 
+
+ align:start position:0%
+we know about DW if it exists by our
+basic definition of this section of this
+
+ align:start position:0%
+basic definition of this section of this
+ 
+
+ align:start position:0%
+basic definition of this section of this
+lecture is that DW is the partial of f
+
+ align:start position:0%
+lecture is that DW is the partial of f
+ 
+
+ align:start position:0%
+lecture is that DW is the partial of f
+respect to x * DX plus the partial of f
+
+ align:start position:0%
+respect to x * DX plus the partial of f
+ 
+
+ align:start position:0%
+respect to x * DX plus the partial of f
+respect to y * Dy since DX and Dy are
+
+ align:start position:0%
+respect to y * Dy since DX and Dy are
+ 
+
+ align:start position:0%
+respect to y * Dy since DX and Dy are
+independent variables the only way these
+
+ align:start position:0%
+independent variables the only way these
+ 
+
+ align:start position:0%
+independent variables the only way these
+two expressions can be identical is
+
+ align:start position:0%
+two expressions can be identical is
+ 
+
+ align:start position:0%
+two expressions can be identical is
+coefficient by coefficient that means in
+
+ align:start position:0%
+coefficient by coefficient that means in
+ 
+
+ align:start position:0%
+coefficient by coefficient that means in
+particular therefore that the partial of
+
+ align:start position:0%
+particular therefore that the partial of
+ 
+
+ align:start position:0%
+particular therefore that the partial of
+f respect to X which is the coefficient
+
+ align:start position:0%
+f respect to X which is the coefficient
+ 
+
+ align:start position:0%
+f respect to X which is the coefficient
+of DX here must be x^2 + y² which is the
+
+ align:start position:0%
+of DX here must be x^2 + y² which is the
+ 
+
+ align:start position:0%
+of DX here must be x^2 + y² which is the
+coefficient of DX here and similarly the
+
+ align:start position:0%
+coefficient of DX here and similarly the
+ 
+
+ align:start position:0%
+coefficient of DX here and similarly the
+partial of f respect to Y Must equal 2 X
+
+ align:start position:0%
+partial of f respect to Y Must equal 2 X
+ 
+
+ align:start position:0%
+partial of f respect to Y Must equal 2 X
+Y now armed with this information I can
+
+ align:start position:0%
+Y now armed with this information I can
+ 
+
+ align:start position:0%
+Y now armed with this information I can
+actually go out and construct F and the
+
+ align:start position:0%
+actually go out and construct F and the
+ 
+
+ align:start position:0%
+actually go out and construct F and the
+way I do this is remember as soon as I
+
+ align:start position:0%
+way I do this is remember as soon as I
+ 
+
+ align:start position:0%
+way I do this is remember as soon as I
+see the partial of f with respect to X
+
+ align:start position:0%
+see the partial of f with respect to X
+ 
+
+ align:start position:0%
+see the partial of f with respect to X
+it means I'm treating y as a constant if
+
+ align:start position:0%
+it means I'm treating y as a constant if
+ 
+
+ align:start position:0%
+it means I'm treating y as a constant if
+I'm treating y as a constant I just
+
+ align:start position:0%
+I'm treating y as a constant I just
+ 
+
+ align:start position:0%
+I'm treating y as a constant I just
+integrate this thing as if x were the
+
+ align:start position:0%
+integrate this thing as if x were the
+ 
+
+ align:start position:0%
+integrate this thing as if x were the
+only variable treating X as a variable
+
+ align:start position:0%
+only variable treating X as a variable
+ 
+
+ align:start position:0%
+only variable treating X as a variable
+and Y as a constant the integral of x^2
+
+ align:start position:0%
+and Y as a constant the integral of x^2
+ 
+
+ align:start position:0%
+and Y as a constant the integral of x^2
+is 1/3 x cubed the integral of y^2 is
+
+ align:start position:0%
+is 1/3 x cubed the integral of y^2 is
+ 
+
+ align:start position:0%
+is 1/3 x cubed the integral of y^2 is
+simply y^2 X because Y is being treated
+
+ align:start position:0%
+simply y^2 X because Y is being treated
+ 
+
+ align:start position:0%
+simply y^2 X because Y is being treated
+as a constant and finally there must be
+
+ align:start position:0%
+as a constant and finally there must be
+ 
+
+ align:start position:0%
+as a constant and finally there must be
+a constant of integration but my
+
+ align:start position:0%
+a constant of integration but my
+ 
+
+ align:start position:0%
+a constant of integration but my
+constant now is any function of Y in
+
+ align:start position:0%
+constant now is any function of Y in
+ 
+
+ align:start position:0%
+constant now is any function of Y in
+other words if if I have any function of
+
+ align:start position:0%
+other words if if I have any function of
+ 
+
+ align:start position:0%
+other words if if I have any function of
+Y it's partial with respect to X by
+
+ align:start position:0%
+Y it's partial with respect to X by
+ 
+
+ align:start position:0%
+Y it's partial with respect to X by
+definition of X and Y being independent
+
+ align:start position:0%
+definition of X and Y being independent
+ 
+
+ align:start position:0%
+definition of X and Y being independent
+the partial of any function of Y respect
+
+ align:start position:0%
+the partial of any function of Y respect
+ 
+
+ align:start position:0%
+the partial of any function of Y respect
+to X is zero therefore my constant of
+
+ align:start position:0%
+to X is zero therefore my constant of
+ 
+
+ align:start position:0%
+to X is zero therefore my constant of
+integration in this case is a function
+
+ align:start position:0%
+integration in this case is a function
+ 
+
+ align:start position:0%
+integration in this case is a function
+of Y alone again to look at this in a
+
+ align:start position:0%
+of Y alone again to look at this in a
+ 
+
+ align:start position:0%
+of Y alone again to look at this in a
+different perspective what I'm saying is
+
+ align:start position:0%
+different perspective what I'm saying is
+ 
+
+ align:start position:0%
+different perspective what I'm saying is
+the most General function of two
+
+ align:start position:0%
+the most General function of two
+ 
+
+ align:start position:0%
+the most General function of two
+variables in the whole world whose
+
+ align:start position:0%
+variables in the whole world whose
+ 
+
+ align:start position:0%
+variables in the whole world whose
+derivative with respect to X is x^2 +
+
+ align:start position:0%
+derivative with respect to X is x^2 +
+ 
+
+ align:start position:0%
+derivative with respect to X is x^2 +
+y^2 is 1/3 XB + y^2 x plus a function of
+
+ align:start position:0%
+y^2 is 1/3 XB + y^2 x plus a function of
+ 
+
+ align:start position:0%
+y^2 is 1/3 XB + y^2 x plus a function of
+Y alone now all I don't know so far is
+
+ align:start position:0%
+Y alone now all I don't know so far is
+ 
+
+ align:start position:0%
+Y alone now all I don't know so far is
+what specific function of Y is G in
+
+ align:start position:0%
+what specific function of Y is G in
+ 
+
+ align:start position:0%
+what specific function of Y is G in
+other words I've determined F now up to
+
+ align:start position:0%
+other words I've determined F now up to
+ 
+
+ align:start position:0%
+other words I've determined F now up to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+particular arbitrary constant of
+
+ align:start position:0%
+particular arbitrary constant of
+ 
+
+ align:start position:0%
+particular arbitrary constant of
+integration how do I get a hold of this
+
+ align:start position:0%
+integration how do I get a hold of this
+ 
+
+ align:start position:0%
+integration how do I get a hold of this
+thing notice that as yet I have not used
+
+ align:start position:0%
+thing notice that as yet I have not used
+ 
+
+ align:start position:0%
+thing notice that as yet I have not used
+a piece of information that tells me the
+
+ align:start position:0%
+a piece of information that tells me the
+ 
+
+ align:start position:0%
+a piece of information that tells me the
+partial of effort respect to Y is 2X Y
+
+ align:start position:0%
+partial of effort respect to Y is 2X Y
+ 
+
+ align:start position:0%
+partial of effort respect to Y is 2X Y
+and to utilize that piece of information
+
+ align:start position:0%
+and to utilize that piece of information
+ 
+
+ align:start position:0%
+and to utilize that piece of information
+what I do is I come to this equation and
+
+ align:start position:0%
+what I do is I come to this equation and
+ 
+
+ align:start position:0%
+what I do is I come to this equation and
+I say look at let me from here just
+
+ align:start position:0%
+I say look at let me from here just
+ 
+
+ align:start position:0%
+I say look at let me from here just
+differentiate this with respect to Y
+
+ align:start position:0%
+differentiate this with respect to Y
+ 
+
+ align:start position:0%
+differentiate this with respect to Y
+treating X as a constant if I do that
+
+ align:start position:0%
+treating X as a constant if I do that
+ 
+
+ align:start position:0%
+treating X as a constant if I do that
+this term drops out this term becomes
+
+ align:start position:0%
+this term drops out this term becomes
+ 
+
+ align:start position:0%
+this term drops out this term becomes
+2xy and this being a function of Y alone
+
+ align:start position:0%
+2xy and this being a function of Y alone
+ 
+
+ align:start position:0%
+2xy and this being a function of Y alone
+its derivative with respect to Y is just
+
+ align:start position:0%
+its derivative with respect to Y is just
+ 
+
+ align:start position:0%
+its derivative with respect to Y is just
+G Prime of Y so whatever f is f the Der
+
+ align:start position:0%
+G Prime of Y so whatever f is f the Der
+ 
+
+ align:start position:0%
+G Prime of Y so whatever f is f the Der
+of f with respect to Y is 2x y + G Prime
+
+ align:start position:0%
+of f with respect to Y is 2x y + G Prime
+ 
+
+ align:start position:0%
+of f with respect to Y is 2x y + G Prime
+of Y on the other hand we ALS also know
+
+ align:start position:0%
+of Y on the other hand we ALS also know
+ 
+
+ align:start position:0%
+of Y on the other hand we ALS also know
+that the parti of effort respect to Y is
+
+ align:start position:0%
+that the parti of effort respect to Y is
+ 
+
+ align:start position:0%
+that the parti of effort respect to Y is
+2xy consequently since these are two
+
+ align:start position:0%
+2xy consequently since these are two
+ 
+
+ align:start position:0%
+2xy consequently since these are two
+different expressions for the same
+
+ align:start position:0%
+different expressions for the same
+ 
+
+ align:start position:0%
+different expressions for the same
+quantity they must be equal equating
+
+ align:start position:0%
+quantity they must be equal equating
+ 
+
+ align:start position:0%
+quantity they must be equal equating
+these two the 2 X Y cancel we obtain
+
+ align:start position:0%
+these two the 2 X Y cancel we obtain
+ 
+
+ align:start position:0%
+these two the 2 X Y cancel we obtain
+that g Prime of Y is zero which means in
+
+ align:start position:0%
+that g Prime of Y is zero which means in
+ 
+
+ align:start position:0%
+that g Prime of Y is zero which means in
+this case that g of Y was a Bonafide
+
+ align:start position:0%
+this case that g of Y was a Bonafide
+ 
+
+ align:start position:0%
+this case that g of Y was a Bonafide
+constant that not only is G independent
+
+ align:start position:0%
+constant that not only is G independent
+ 
+
+ align:start position:0%
+constant that not only is G independent
+of X it's also independent of Y and we
+
+ align:start position:0%
+of X it's also independent of Y and we
+ 
+
+ align:start position:0%
+of X it's also independent of Y and we
+see that the most General function f
+
+ align:start position:0%
+see that the most General function f
+ 
+
+ align:start position:0%
+see that the most General function f
+which has the desired property is what
+
+ align:start position:0%
+which has the desired property is what
+ 
+
+ align:start position:0%
+which has the desired property is what
+all we have to do is now go back to this
+
+ align:start position:0%
+all we have to do is now go back to this
+ 
+
+ align:start position:0%
+all we have to do is now go back to this
+expression here which gave us the answer
+
+ align:start position:0%
+expression here which gave us the answer
+ 
+
+ align:start position:0%
+expression here which gave us the answer
+up to G of Y put this value of G of Y in
+
+ align:start position:0%
+up to G of Y put this value of G of Y in
+ 
+
+ align:start position:0%
+up to G of Y put this value of G of Y in
+and we see that the most General
+
+ align:start position:0%
+and we see that the most General
+ 
+
+ align:start position:0%
+and we see that the most General
+function whose total differential is x^2
+
+ align:start position:0%
+function whose total differential is x^2
+ 
+
+ align:start position:0%
+function whose total differential is x^2
++ y^2 DX + 2xy Dy is 1/3 x Cub + y^2 x +
+
+ align:start position:0%
++ y^2 DX + 2xy Dy is 1/3 x Cub + y^2 x +
+ 
+
+ align:start position:0%
++ y^2 DX + 2xy Dy is 1/3 x Cub + y^2 x +
+C and I guess there's a moral to this
+
+ align:start position:0%
+C and I guess there's a moral to this
+ 
+
+ align:start position:0%
+C and I guess there's a moral to this
+story after all you know when I did it
+
+ align:start position:0%
+story after all you know when I did it
+ 
+
+ align:start position:0%
+story after all you know when I did it
+the quick way I made a Kess
+
+ align:start position:0%
+the quick way I made a Kess
+ 
+
+ align:start position:0%
+the quick way I made a Kess
+computational mistake earlier in the
+
+ align:start position:0%
+computational mistake earlier in the
+ 
+
+ align:start position:0%
+computational mistake earlier in the
+lecture that sort of threw me off a bit
+
+ align:start position:0%
+lecture that sort of threw me off a bit
+ 
+
+ align:start position:0%
+lecture that sort of threw me off a bit
+and perplexed me
+
+ align:start position:0%
+and perplexed me
+ 
+
+ align:start position:0%
+and perplexed me
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh it seems it was Poetic Justice
+
+ align:start position:0%
+uh it seems it was Poetic Justice
+ 
+
+ align:start position:0%
+uh it seems it was Poetic Justice
+because you know when I took this method
+
+ align:start position:0%
+because you know when I took this method
+ 
+
+ align:start position:0%
+because you know when I took this method
+where we pretended we didn't know the
+
+ align:start position:0%
+where we pretended we didn't know the
+ 
+
+ align:start position:0%
+where we pretended we didn't know the
+answer in advance and just work the
+
+ align:start position:0%
+answer in advance and just work the
+ 
+
+ align:start position:0%
+answer in advance and just work the
+thing out systematically we came up with
+
+ align:start position:0%
+thing out systematically we came up with
+ 
+
+ align:start position:0%
+thing out systematically we came up with
+the right term in other words it should
+
+ align:start position:0%
+the right term in other words it should
+ 
+
+ align:start position:0%
+the right term in other words it should
+be y^2 X not YX s and that was what we
+
+ align:start position:0%
+be y^2 X not YX s and that was what we
+ 
+
+ align:start position:0%
+be y^2 X not YX s and that was what we
+saw should be the correct answer so
+
+ align:start position:0%
+saw should be the correct answer so
+ 
+
+ align:start position:0%
+saw should be the correct answer so
+maybe there's something to be said about
+
+ align:start position:0%
+maybe there's something to be said about
+ 
+
+ align:start position:0%
+maybe there's something to be said about
+doing things systematically after all
+
+ align:start position:0%
+doing things systematically after all
+ 
+
+ align:start position:0%
+doing things systematically after all
+you see if I can't win them all at least
+
+ align:start position:0%
+you see if I can't win them all at least
+ 
+
+ align:start position:0%
+you see if I can't win them all at least
+I have the gift of rationalizing to
+
+ align:start position:0%
+I have the gift of rationalizing to
+ 
+
+ align:start position:0%
+I have the gift of rationalizing to
+think that I win them all
+
+ align:start position:0%
+think that I win them all
+ 
+
+ align:start position:0%
+think that I win them all
+time after time I snatch defeat from the
+
+ align:start position:0%
+time after time I snatch defeat from the
+ 
+
+ align:start position:0%
+time after time I snatch defeat from the
+jaws of
+
+ align:start position:0%
+jaws of
+ 
+
+ align:start position:0%
+jaws of
+Victory no all right you know what I
+
+ align:start position:0%
+Victory no all right you know what I
+ 
+
+ align:start position:0%
+Victory no all right you know what I
+mean look at anyway the question that
+
+ align:start position:0%
+mean look at anyway the question that
+ 
+
+ align:start position:0%
+mean look at anyway the question that
+we've now solved is what we have worked
+
+ align:start position:0%
+we've now solved is what we have worked
+ 
+
+ align:start position:0%
+we've now solved is what we have worked
+out this routine notice that what we are
+
+ align:start position:0%
+out this routine notice that what we are
+ 
+
+ align:start position:0%
+out this routine notice that what we are
+really doing is the counterpart of
+
+ align:start position:0%
+really doing is the counterpart of
+ 
+
+ align:start position:0%
+really doing is the counterpart of
+calculus of a single variable that
+
+ align:start position:0%
+calculus of a single variable that
+ 
+
+ align:start position:0%
+calculus of a single variable that
+knowing what a partial is we can
+
+ align:start position:0%
+knowing what a partial is we can
+ 
+
+ align:start position:0%
+knowing what a partial is we can
+integrate with respect to that variable
+
+ align:start position:0%
+integrate with respect to that variable
+ 
+
+ align:start position:0%
+integrate with respect to that variable
+treating all the other variables as a
+
+ align:start position:0%
+treating all the other variables as a
+ 
+
+ align:start position:0%
+treating all the other variables as a
+constant and this is the general
+
+ align:start position:0%
+constant and this is the general
+ 
+
+ align:start position:0%
+constant and this is the general
+technique now let's summarize this more
+
+ align:start position:0%
+technique now let's summarize this more
+ 
+
+ align:start position:0%
+technique now let's summarize this more
+generally the general definition is this
+
+ align:start position:0%
+generally the general definition is this
+ 
+
+ align:start position:0%
+generally the general definition is this
+and by the way for the sake of
+
+ align:start position:0%
+and by the way for the sake of
+ 
+
+ align:start position:0%
+and by the way for the sake of
+conserving space I will now abbreviate m
+
+ align:start position:0%
+conserving space I will now abbreviate m
+ 
+
+ align:start position:0%
+conserving space I will now abbreviate m
+ofx y and N of X Y just by m and n but
+
+ align:start position:0%
+ofx y and N of X Y just by m and n but
+ 
+
+ align:start position:0%
+ofx y and N of X Y just by m and n but
+whenever I write M and N here it's
+
+ align:start position:0%
+whenever I write M and N here it's
+ 
+
+ align:start position:0%
+whenever I write M and N here it's
+assumed that M and N are functions of X
+
+ align:start position:0%
+assumed that M and N are functions of X
+ 
+
+ align:start position:0%
+assumed that M and N are functions of X
+and yo what we say is this MDX plus ndy
+
+ align:start position:0%
+and yo what we say is this MDX plus ndy
+ 
+
+ align:start position:0%
+and yo what we say is this MDX plus ndy
+which by the way by a previous
+
+ align:start position:0%
+which by the way by a previous
+ 
+
+ align:start position:0%
+which by the way by a previous
+definition is always a differential but
+
+ align:start position:0%
+definition is always a differential but
+ 
+
+ align:start position:0%
+definition is always a differential but
+this differential is called an exact
+
+ align:start position:0%
+this differential is called an exact
+ 
+
+ align:start position:0%
+this differential is called an exact
+differential if and only if there exists
+
+ align:start position:0%
+differential if and only if there exists
+ 
+
+ align:start position:0%
+differential if and only if there exists
+a function w f of XY such that DW is MDX
+
+ align:start position:0%
+a function w f of XY such that DW is MDX
+ 
+
+ align:start position:0%
+a function w f of XY such that DW is MDX
++ mdy or in terms of our previous
+
+ align:start position:0%
++ mdy or in terms of our previous
+ 
+
+ align:start position:0%
++ mdy or in terms of our previous
+discussion what this means is what
+
+ align:start position:0%
+discussion what this means is what
+ 
+
+ align:start position:0%
+discussion what this means is what
+DW is also equal to F subx DX plus F
+
+ align:start position:0%
+DW is also equal to F subx DX plus F
+ 
+
+ align:start position:0%
+DW is also equal to F subx DX plus F
+suby Dy since X and Y are independent
+
+ align:start position:0%
+suby Dy since X and Y are independent
+ 
+
+ align:start position:0%
+suby Dy since X and Y are independent
+variables DX and Dy are independent
+
+ align:start position:0%
+variables DX and Dy are independent
+ 
+
+ align:start position:0%
+variables DX and Dy are independent
+variables so an alternative definition
+
+ align:start position:0%
+variables so an alternative definition
+ 
+
+ align:start position:0%
+variables so an alternative definition
+is what that MDX plus n Dy is an exact
+
+ align:start position:0%
+is what that MDX plus n Dy is an exact
+ 
+
+ align:start position:0%
+is what that MDX plus n Dy is an exact
+differential if there exists a function
+
+ align:start position:0%
+differential if there exists a function
+ 
+
+ align:start position:0%
+differential if there exists a function
+f such that the partial of f resp
+
+ align:start position:0%
+f such that the partial of f resp
+ 
+
+ align:start position:0%
+f such that the partial of f resp
+respect to X is M and the partial of f
+
+ align:start position:0%
+respect to X is M and the partial of f
+ 
+
+ align:start position:0%
+respect to X is M and the partial of f
+respect to Y is n now by the way let's
+
+ align:start position:0%
+respect to Y is n now by the way let's
+ 
+
+ align:start position:0%
+respect to Y is n now by the way let's
+just pause here for a moment you might
+
+ align:start position:0%
+just pause here for a moment you might
+ 
+
+ align:start position:0%
+just pause here for a moment you might
+suspect that with all the functions to
+
+ align:start position:0%
+suspect that with all the functions to
+ 
+
+ align:start position:0%
+suspect that with all the functions to
+choose from that no matter how M and N
+
+ align:start position:0%
+choose from that no matter how M and N
+ 
+
+ align:start position:0%
+choose from that no matter how M and N
+were given we're bound to find at least
+
+ align:start position:0%
+were given we're bound to find at least
+ 
+
+ align:start position:0%
+were given we're bound to find at least
+one function which satisfies I should
+
+ align:start position:0%
+one function which satisfies I should
+ 
+
+ align:start position:0%
+one function which satisfies I should
+put this in because you want both of
+
+ align:start position:0%
+put this in because you want both of
+ 
+
+ align:start position:0%
+put this in because you want both of
+these conditions fulfilled at the same
+
+ align:start position:0%
+these conditions fulfilled at the same
+ 
+
+ align:start position:0%
+these conditions fulfilled at the same
+time the amazing thing is that it is not
+
+ align:start position:0%
+time the amazing thing is that it is not
+ 
+
+ align:start position:0%
+time the amazing thing is that it is not
+always possible to find a function which
+
+ align:start position:0%
+always possible to find a function which
+ 
+
+ align:start position:0%
+always possible to find a function which
+has a given differential as its total
+
+ align:start position:0%
+has a given differential as its total
+ 
+
+ align:start position:0%
+has a given differential as its total
+differential in fact let me show you why
+
+ align:start position:0%
+differential in fact let me show you why
+ 
+
+ align:start position:0%
+differential in fact let me show you why
+if we can just do something a little bit
+
+ align:start position:0%
+if we can just do something a little bit
+ 
+
+ align:start position:0%
+if we can just do something a little bit
+tricky here let's suppose that the
+
+ align:start position:0%
+tricky here let's suppose that the
+ 
+
+ align:start position:0%
+tricky here let's suppose that the
+function f exists such that it's partial
+
+ align:start position:0%
+function f exists such that it's partial
+ 
+
+ align:start position:0%
+function f exists such that it's partial
+with respect to X as M and it's partial
+
+ align:start position:0%
+with respect to X as M and it's partial
+ 
+
+ align:start position:0%
+with respect to X as M and it's partial
+with respect to Y is n suppose that both
+
+ align:start position:0%
+with respect to Y is n suppose that both
+ 
+
+ align:start position:0%
+with respect to Y is n suppose that both
+of these happen to be differentiable
+
+ align:start position:0%
+of these happen to be differentiable
+ 
+
+ align:start position:0%
+of these happen to be differentiable
+take the partial of f subx with respect
+
+ align:start position:0%
+take the partial of f subx with respect
+ 
+
+ align:start position:0%
+take the partial of f subx with respect
+to Y that tells me that f subx y is the
+
+ align:start position:0%
+to Y that tells me that f subx y is the
+ 
+
+ align:start position:0%
+to Y that tells me that f subx y is the
+partial of M with respect to Y let's
+
+ align:start position:0%
+partial of M with respect to Y let's
+ 
+
+ align:start position:0%
+partial of M with respect to Y let's
+take the partial of f suby with respect
+
+ align:start position:0%
+take the partial of f suby with respect
+ 
+
+ align:start position:0%
+take the partial of f suby with respect
+to X that tells me that the of f sub y
+
+ align:start position:0%
+to X that tells me that the of f sub y
+ 
+
+ align:start position:0%
+to X that tells me that the of f sub y
+respect to X is n subx in other words
+
+ align:start position:0%
+respect to X is n subx in other words
+ 
+
+ align:start position:0%
+respect to X is n subx in other words
+fyx equal n subx now if f is continu see
+
+ align:start position:0%
+fyx equal n subx now if f is continu see
+ 
+
+ align:start position:0%
+fyx equal n subx now if f is continu see
+if if we have the right amount of
+
+ align:start position:0%
+if if we have the right amount of
+ 
+
+ align:start position:0%
+if if we have the right amount of
+continuity and differentiability that
+
+ align:start position:0%
+continuity and differentiability that
+ 
+
+ align:start position:0%
+continuity and differentiability that
+we've talked about in previous lectures
+
+ align:start position:0%
+we've talked about in previous lectures
+ 
+
+ align:start position:0%
+we've talked about in previous lectures
+notice that for most well defined
+
+ align:start position:0%
+notice that for most well defined
+ 
+
+ align:start position:0%
+notice that for most well defined
+functions in particular if these two
+
+ align:start position:0%
+functions in particular if these two
+ 
+
+ align:start position:0%
+functions in particular if these two
+partials see we don't know what f is
+
+ align:start position:0%
+partials see we don't know what f is
+ 
+
+ align:start position:0%
+partials see we don't know what f is
+we're trying to find F and we're
+
+ align:start position:0%
+we're trying to find F and we're
+ 
+
+ align:start position:0%
+we're trying to find F and we're
+assuming it exists the thing that's
+
+ align:start position:0%
+assuming it exists the thing that's
+ 
+
+ align:start position:0%
+assuming it exists the thing that's
+given in our definition M and N so to
+
+ align:start position:0%
+given in our definition M and N so to
+ 
+
+ align:start position:0%
+given in our definition M and N so to
+this more succinctly if it turns out
+
+ align:start position:0%
+this more succinctly if it turns out
+ 
+
+ align:start position:0%
+this more succinctly if it turns out
+that the partial of M respect to Y and
+
+ align:start position:0%
+that the partial of M respect to Y and
+ 
+
+ align:start position:0%
+that the partial of M respect to Y and
+the partial of n with respect to X
+
+ align:start position:0%
+the partial of n with respect to X
+ 
+
+ align:start position:0%
+the partial of n with respect to X
+happen to be continuous functions notice
+
+ align:start position:0%
+happen to be continuous functions notice
+ 
+
+ align:start position:0%
+happen to be continuous functions notice
+that these two things are equal and in
+
+ align:start position:0%
+that these two things are equal and in
+ 
+
+ align:start position:0%
+that these two things are equal and in
+particular that means that the partial
+
+ align:start position:0%
+particular that means that the partial
+ 
+
+ align:start position:0%
+particular that means that the partial
+of n with respect to Y has to equal the
+
+ align:start position:0%
+of n with respect to Y has to equal the
+ 
+
+ align:start position:0%
+of n with respect to Y has to equal the
+partial of n with respect to X coming
+
+ align:start position:0%
+partial of n with respect to X coming
+ 
+
+ align:start position:0%
+partial of n with respect to X coming
+back to the original definition here
+
+ align:start position:0%
+back to the original definition here
+ 
+
+ align:start position:0%
+back to the original definition here
+this is a rather amazing thing it says
+
+ align:start position:0%
+this is a rather amazing thing it says
+ 
+
+ align:start position:0%
+this is a rather amazing thing it says
+that if this differential is exact if
+
+ align:start position:0%
+that if this differential is exact if
+ 
+
+ align:start position:0%
+that if this differential is exact if
+you take the coefficient of DX see think
+
+ align:start position:0%
+you take the coefficient of DX see think
+ 
+
+ align:start position:0%
+you take the coefficient of DX see think
+of M as being the coefficient of DX and
+
+ align:start position:0%
+of M as being the coefficient of DX and
+ 
+
+ align:start position:0%
+of M as being the coefficient of DX and
+n as being the coefficient of Dy if you
+
+ align:start position:0%
+n as being the coefficient of Dy if you
+ 
+
+ align:start position:0%
+n as being the coefficient of Dy if you
+take the coefficient of DX and
+
+ align:start position:0%
+take the coefficient of DX and
+ 
+
+ align:start position:0%
+take the coefficient of DX and
+differentiate that with respect to Y you
+
+ align:start position:0%
+differentiate that with respect to Y you
+ 
+
+ align:start position:0%
+differentiate that with respect to Y you
+must get the same
+
+ align:start position:0%
+must get the same
+ 
+
+ align:start position:0%
+must get the same
+answer as if you took the coefficient of
+
+ align:start position:0%
+answer as if you took the coefficient of
+ 
+
+ align:start position:0%
+answer as if you took the coefficient of
+Dy and differentiated that with respect
+
+ align:start position:0%
+Dy and differentiated that with respect
+ 
+
+ align:start position:0%
+Dy and differentiated that with respect
+to X that's an amazing coincidence if
+
+ align:start position:0%
+to X that's an amazing coincidence if
+ 
+
+ align:start position:0%
+to X that's an amazing coincidence if
+that happens given two arbitrary
+
+ align:start position:0%
+that happens given two arbitrary
+ 
+
+ align:start position:0%
+that happens given two arbitrary
+functions this indeed won't happen now
+
+ align:start position:0%
+functions this indeed won't happen now
+ 
+
+ align:start position:0%
+functions this indeed won't happen now
+before I show you that let's summarize
+
+ align:start position:0%
+before I show you that let's summarize
+ 
+
+ align:start position:0%
+before I show you that let's summarize
+this in words written down so that I
+
+ align:start position:0%
+this in words written down so that I
+ 
+
+ align:start position:0%
+this in words written down so that I
+make sure that you understand what I'm
+
+ align:start position:0%
+make sure that you understand what I'm
+ 
+
+ align:start position:0%
+make sure that you understand what I'm
+saying what I'm saying is if the partial
+
+ align:start position:0%
+saying what I'm saying is if the partial
+ 
+
+ align:start position:0%
+saying what I'm saying is if the partial
+of M with respect to Y and the partial
+
+ align:start position:0%
+of M with respect to Y and the partial
+ 
+
+ align:start position:0%
+of M with respect to Y and the partial
+of n with respect to X are continuous
+
+ align:start position:0%
+of n with respect to X are continuous
+ 
+
+ align:start position:0%
+of n with respect to X are continuous
+then if MDX plus ndy is exact the
+
+ align:start position:0%
+then if MDX plus ndy is exact the
+ 
+
+ align:start position:0%
+then if MDX plus ndy is exact the
+implication is that the partial of n
+
+ align:start position:0%
+implication is that the partial of n
+ 
+
+ align:start position:0%
+implication is that the partial of n
+with respect to Y Must equal the partial
+
+ align:start position:0%
+with respect to Y Must equal the partial
+ 
+
+ align:start position:0%
+with respect to Y Must equal the partial
+of n with respect to X and to invert the
+
+ align:start position:0%
+of n with respect to X and to invert the
+ 
+
+ align:start position:0%
+of n with respect to X and to invert the
+emphasis here another way of saying this
+
+ align:start position:0%
+emphasis here another way of saying this
+ 
+
+ align:start position:0%
+emphasis here another way of saying this
+is that if the partial of n with respect
+
+ align:start position:0%
+is that if the partial of n with respect
+ 
+
+ align:start position:0%
+is that if the partial of n with respect
+to Y is not equal to the partial of n
+
+ align:start position:0%
+to Y is not equal to the partial of n
+ 
+
+ align:start position:0%
+to Y is not equal to the partial of n
+with respect to X then MDX plus ndy is
+
+ align:start position:0%
+with respect to X then MDX plus ndy is
+ 
+
+ align:start position:0%
+with respect to X then MDX plus ndy is
+not exact and let me show you that by
+
+ align:start position:0%
+not exact and let me show you that by
+ 
+
+ align:start position:0%
+not exact and let me show you that by
+means of an example let's look at the
+
+ align:start position:0%
+means of an example let's look at the
+ 
+
+ align:start position:0%
+means of an example let's look at the
+differential a very simple looking one
+
+ align:start position:0%
+differential a very simple looking one
+ 
+
+ align:start position:0%
+differential a very simple looking one
+in fact it looks far less complicated
+
+ align:start position:0%
+in fact it looks far less complicated
+ 
+
+ align:start position:0%
+in fact it looks far less complicated
+than the expression that we worked with
+
+ align:start position:0%
+than the expression that we worked with
+ 
+
+ align:start position:0%
+than the expression that we worked with
+previously let's look simply at Y dxus
+
+ align:start position:0%
+previously let's look simply at Y dxus
+ 
+
+ align:start position:0%
+previously let's look simply at Y dxus
+xdy in this problem the coefficient of
+
+ align:start position:0%
+xdy in this problem the coefficient of
+ 
+
+ align:start position:0%
+xdy in this problem the coefficient of
+DX is y that plays the role of M the
+
+ align:start position:0%
+DX is y that plays the role of M the
+ 
+
+ align:start position:0%
+DX is y that plays the role of M the
+coefficient of Dy is minus X that's what
+
+ align:start position:0%
+coefficient of Dy is minus X that's what
+ 
+
+ align:start position:0%
+coefficient of Dy is minus X that's what
+we're calling n you see and the partial
+
+ align:start position:0%
+we're calling n you see and the partial
+ 
+
+ align:start position:0%
+we're calling n you see and the partial
+of M with respect to Y is just the
+
+ align:start position:0%
+of M with respect to Y is just the
+ 
+
+ align:start position:0%
+of M with respect to Y is just the
+partial of Y with respect to Y which is
+
+ align:start position:0%
+partial of Y with respect to Y which is
+ 
+
+ align:start position:0%
+partial of Y with respect to Y which is
+one the partial of n with respect to X
+
+ align:start position:0%
+one the partial of n with respect to X
+ 
+
+ align:start position:0%
+one the partial of n with respect to X
+is the partial of - x with respect to X
+
+ align:start position:0%
+is the partial of - x with respect to X
+ 
+
+ align:start position:0%
+is the partial of - x with respect to X
+which is minus1 since 1 is not equal to
+
+ align:start position:0%
+which is minus1 since 1 is not equal to
+ 
+
+ align:start position:0%
+which is minus1 since 1 is not equal to
+minus1 this is not exact because if it
+
+ align:start position:0%
+minus1 this is not exact because if it
+ 
+
+ align:start position:0%
+minus1 this is not exact because if it
+were exact these two partials would have
+
+ align:start position:0%
+were exact these two partials would have
+ 
+
+ align:start position:0%
+were exact these two partials would have
+to be equal what does it mean to say if
+
+ align:start position:0%
+to be equal what does it mean to say if
+ 
+
+ align:start position:0%
+to be equal what does it mean to say if
+this is not exact what it means is that
+
+ align:start position:0%
+this is not exact what it means is that
+ 
+
+ align:start position:0%
+this is not exact what it means is that
+there is not a single function in the
+
+ align:start position:0%
+there is not a single function in the
+ 
+
+ align:start position:0%
+there is not a single function in the
+whole world that has the property that
+
+ align:start position:0%
+whole world that has the property that
+ 
+
+ align:start position:0%
+whole world that has the property that
+it's partial with respect to X is y and
+
+ align:start position:0%
+it's partial with respect to X is y and
+ 
+
+ align:start position:0%
+it's partial with respect to X is y and
+it's partial with respect to Y is minus
+
+ align:start position:0%
+it's partial with respect to Y is minus
+ 
+
+ align:start position:0%
+it's partial with respect to Y is minus
+X you can look
+
+ align:start position:0%
+X you can look
+ 
+
+ align:start position:0%
+X you can look
+forever and not only won't you find one
+
+ align:start position:0%
+forever and not only won't you find one
+ 
+
+ align:start position:0%
+forever and not only won't you find one
+there isn't one and by the way let me
+
+ align:start position:0%
+there isn't one and by the way let me
+ 
+
+ align:start position:0%
+there isn't one and by the way let me
+make one very quick aside here notice
+
+ align:start position:0%
+make one very quick aside here notice
+ 
+
+ align:start position:0%
+make one very quick aside here notice
+the difference between saying you can't
+
+ align:start position:0%
+the difference between saying you can't
+ 
+
+ align:start position:0%
+the difference between saying you can't
+find one and there isn't one there may
+
+ align:start position:0%
+find one and there isn't one there may
+ 
+
+ align:start position:0%
+find one and there isn't one there may
+be one and you just not lucky enough to
+
+ align:start position:0%
+be one and you just not lucky enough to
+ 
+
+ align:start position:0%
+be one and you just not lucky enough to
+find it I'm saying that the reason you
+
+ align:start position:0%
+find it I'm saying that the reason you
+ 
+
+ align:start position:0%
+find it I'm saying that the reason you
+don't find an answer here unless you
+
+ align:start position:0%
+don't find an answer here unless you
+ 
+
+ align:start position:0%
+don't find an answer here unless you
+make a mistake and think you found an
+
+ align:start position:0%
+make a mistake and think you found an
+ 
+
+ align:start position:0%
+make a mistake and think you found an
+answer the reason you don't find an
+
+ align:start position:0%
+answer the reason you don't find an
+ 
+
+ align:start position:0%
+answer the reason you don't find an
+answer is there is none and how can I
+
+ align:start position:0%
+answer is there is none and how can I
+ 
+
+ align:start position:0%
+answer is there is none and how can I
+show you that there is none well the
+
+ align:start position:0%
+show you that there is none well the
+ 
+
+ align:start position:0%
+show you that there is none well the
+best way is to do the same thing that we
+
+ align:start position:0%
+best way is to do the same thing that we
+ 
+
+ align:start position:0%
+best way is to do the same thing that we
+did in the previous example and see
+
+ align:start position:0%
+did in the previous example and see
+ 
+
+ align:start position:0%
+did in the previous example and see
+something go wrong let's suppose that
+
+ align:start position:0%
+something go wrong let's suppose that
+ 
+
+ align:start position:0%
+something go wrong let's suppose that
+we're an answer to this well if the
+
+ align:start position:0%
+we're an answer to this well if the
+ 
+
+ align:start position:0%
+we're an answer to this well if the
+partial of effort respect to x equals y
+
+ align:start position:0%
+partial of effort respect to x equals y
+ 
+
+ align:start position:0%
+partial of effort respect to x equals y
+let me integrate this with respect to X
+
+ align:start position:0%
+let me integrate this with respect to X
+ 
+
+ align:start position:0%
+let me integrate this with respect to X
+treating y as a constant it means that
+
+ align:start position:0%
+treating y as a constant it means that
+ 
+
+ align:start position:0%
+treating y as a constant it means that
+the function that I'm looking for must
+
+ align:start position:0%
+the function that I'm looking for must
+ 
+
+ align:start position:0%
+the function that I'm looking for must
+have what form it's x * y plus some
+
+ align:start position:0%
+have what form it's x * y plus some
+ 
+
+ align:start position:0%
+have what form it's x * y plus some
+function of Y alone and now we say gee
+
+ align:start position:0%
+function of Y alone and now we say gee
+ 
+
+ align:start position:0%
+function of Y alone and now we say gee
+we're in pretty good shape all we've got
+
+ align:start position:0%
+we're in pretty good shape all we've got
+ 
+
+ align:start position:0%
+we're in pretty good shape all we've got
+to do is find what G of Y is and we're
+
+ align:start position:0%
+to do is find what G of Y is and we're
+ 
+
+ align:start position:0%
+to do is find what G of Y is and we're
+home free let's continue to mimic what
+
+ align:start position:0%
+home free let's continue to mimic what
+ 
+
+ align:start position:0%
+home free let's continue to mimic what
+we did before knowing this I can take
+
+ align:start position:0%
+we did before knowing this I can take
+ 
+
+ align:start position:0%
+we did before knowing this I can take
+the partial of this with respect to Y
+
+ align:start position:0%
+the partial of this with respect to Y
+ 
+
+ align:start position:0%
+the partial of this with respect to Y
+okay which is what if I take the partial
+
+ align:start position:0%
+okay which is what if I take the partial
+ 
+
+ align:start position:0%
+okay which is what if I take the partial
+of this with respect to Y this is
+
+ align:start position:0%
+of this with respect to Y this is
+ 
+
+ align:start position:0%
+of this with respect to Y this is
+F suby is X Plus G Prime of Y all right
+
+ align:start position:0%
+F suby is X Plus G Prime of Y all right
+ 
+
+ align:start position:0%
+F suby is X Plus G Prime of Y all right
+now this is the partial of f with
+
+ align:start position:0%
+now this is the partial of f with
+ 
+
+ align:start position:0%
+now this is the partial of f with
+respect to Y computed from here I know
+
+ align:start position:0%
+respect to Y computed from here I know
+ 
+
+ align:start position:0%
+respect to Y computed from here I know
+by hypothesis that the function I'm
+
+ align:start position:0%
+by hypothesis that the function I'm
+ 
+
+ align:start position:0%
+by hypothesis that the function I'm
+looking for must have its partial with
+
+ align:start position:0%
+looking for must have its partial with
+ 
+
+ align:start position:0%
+looking for must have its partial with
+respect to y equal to this consequently
+
+ align:start position:0%
+respect to y equal to this consequently
+ 
+
+ align:start position:0%
+respect to y equal to this consequently
+these two expressions must be equal and
+
+ align:start position:0%
+these two expressions must be equal and
+ 
+
+ align:start position:0%
+these two expressions must be equal and
+equating these two expressions says that
+
+ align:start position:0%
+equating these two expressions says that
+ 
+
+ align:start position:0%
+equating these two expressions says that
+g Prime of Y see x + G Prime of Y Must
+
+ align:start position:0%
+g Prime of Y see x + G Prime of Y Must
+ 
+
+ align:start position:0%
+g Prime of Y see x + G Prime of Y Must
+equal - x transposing says that g Prime
+
+ align:start position:0%
+equal - x transposing says that g Prime
+ 
+
+ align:start position:0%
+equal - x transposing says that g Prime
+of Y is - 2 X and this is a
+
+ align:start position:0%
+of Y is - 2 X and this is a
+ 
+
+ align:start position:0%
+of Y is - 2 X and this is a
+contradiction because look at G Prime of
+
+ align:start position:0%
+contradiction because look at G Prime of
+ 
+
+ align:start position:0%
+contradiction because look at G Prime of
+Y is a function of Y alone and here we
+
+ align:start position:0%
+Y is a function of Y alone and here we
+ 
+
+ align:start position:0%
+Y is a function of Y alone and here we
+have it's equal to some function of X or
+
+ align:start position:0%
+have it's equal to some function of X or
+ 
+
+ align:start position:0%
+have it's equal to some function of X or
+another way of looking at it this says
+
+ align:start position:0%
+another way of looking at it this says
+ 
+
+ align:start position:0%
+another way of looking at it this says
+that X depends on y x is some function
+
+ align:start position:0%
+that X depends on y x is some function
+ 
+
+ align:start position:0%
+that X depends on y x is some function
+of Y which is a contradiction since we
+
+ align:start position:0%
+of Y which is a contradiction since we
+ 
+
+ align:start position:0%
+of Y which is a contradiction since we
+assumed that X and Y are independent
+
+ align:start position:0%
+assumed that X and Y are independent
+ 
+
+ align:start position:0%
+assumed that X and Y are independent
+variables by the way just as a quick
+
+ align:start position:0%
+variables by the way just as a quick
+ 
+
+ align:start position:0%
+variables by the way just as a quick
+aside notice that in the case where we
+
+ align:start position:0%
+aside notice that in the case where we
+ 
+
+ align:start position:0%
+aside notice that in the case where we
+were able to succeed at this namely the
+
+ align:start position:0%
+were able to succeed at this namely the
+ 
+
+ align:start position:0%
+were able to succeed at this namely the
+the previous example X2 + y DX + 2x y d
+
+ align:start position:0%
+the previous example X2 + y DX + 2x y d
+ 
+
+ align:start position:0%
+the previous example X2 + y DX + 2x y d
+y m was x^2 + y^2 n was 2x y notice that
+
+ align:start position:0%
+y m was x^2 + y^2 n was 2x y notice that
+ 
+
+ align:start position:0%
+y m was x^2 + y^2 n was 2x y notice that
+the partial of M with respect to Y is 2
+
+ align:start position:0%
+the partial of M with respect to Y is 2
+ 
+
+ align:start position:0%
+the partial of M with respect to Y is 2
+Y and the partial of n with respect to X
+
+ align:start position:0%
+Y and the partial of n with respect to X
+ 
+
+ align:start position:0%
+Y and the partial of n with respect to X
+is also 2 y so it seems that the
+
+ align:start position:0%
+is also 2 y so it seems that the
+ 
+
+ align:start position:0%
+is also 2 y so it seems that the
+deciding factor really seems to be that
+
+ align:start position:0%
+deciding factor really seems to be that
+ 
+
+ align:start position:0%
+deciding factor really seems to be that
+the partial of n with respect to Y has
+
+ align:start position:0%
+the partial of n with respect to Y has
+ 
+
+ align:start position:0%
+the partial of n with respect to Y has
+to equal the partial of n with respect
+
+ align:start position:0%
+to equal the partial of n with respect
+ 
+
+ align:start position:0%
+to equal the partial of n with respect
+to X and the major result is and I
+
+ align:start position:0%
+to X and the major result is and I
+ 
+
+ align:start position:0%
+to X and the major result is and I
+didn't write this in because I didn't
+
+ align:start position:0%
+didn't write this in because I didn't
+ 
+
+ align:start position:0%
+didn't write this in because I didn't
+want to use up too much space but this
+
+ align:start position:0%
+want to use up too much space but this
+ 
+
+ align:start position:0%
+want to use up too much space but this
+is emphasized in the text and in the
+
+ align:start position:0%
+is emphasized in the text and in the
+ 
+
+ align:start position:0%
+is emphasized in the text and in the
+exercises if
+
+ align:start position:0%
+exercises if
+ 
+
+ align:start position:0%
+exercises if
+MN M suby and M subx all exist and are
+
+ align:start position:0%
+MN M suby and M subx all exist and are
+ 
+
+ align:start position:0%
+MN M suby and M subx all exist and are
+continuous then not only can we say that
+
+ align:start position:0%
+continuous then not only can we say that
+ 
+
+ align:start position:0%
+continuous then not only can we say that
+MDX plus ndy is exact implies this part
+
+ align:start position:0%
+MDX plus ndy is exact implies this part
+ 
+
+ align:start position:0%
+MDX plus ndy is exact implies this part
+but we can do the converse too that in
+
+ align:start position:0%
+but we can do the converse too that in
+ 
+
+ align:start position:0%
+but we can do the converse too that in
+particular if m suby equals m subx we
+
+ align:start position:0%
+particular if m suby equals m subx we
+ 
+
+ align:start position:0%
+particular if m suby equals m subx we
+can conclude that this is exact and the
+
+ align:start position:0%
+can conclude that this is exact and the
+ 
+
+ align:start position:0%
+can conclude that this is exact and the
+reason for this I'll go through this
+
+ align:start position:0%
+reason for this I'll go through this
+ 
+
+ align:start position:0%
+reason for this I'll go through this
+very quickly because the proof is given
+
+ align:start position:0%
+very quickly because the proof is given
+ 
+
+ align:start position:0%
+very quickly because the proof is given
+in the text I just want to show you the
+
+ align:start position:0%
+in the text I just want to show you the
+ 
+
+ align:start position:0%
+in the text I just want to show you the
+highlights of what happens is what
+
+ align:start position:0%
+highlights of what happens is what
+ 
+
+ align:start position:0%
+highlights of what happens is what
+really happened when we tried to con
+
+ align:start position:0%
+really happened when we tried to con
+ 
+
+ align:start position:0%
+really happened when we tried to con
+struct F that made things work in one
+
+ align:start position:0%
+struct F that made things work in one
+ 
+
+ align:start position:0%
+struct F that made things work in one
+case but not in the other I think the
+
+ align:start position:0%
+case but not in the other I think the
+ 
+
+ align:start position:0%
+case but not in the other I think the
+best way to do this is to work
+
+ align:start position:0%
+best way to do this is to work
+ 
+
+ align:start position:0%
+best way to do this is to work
+abstractly here without specifying what
+
+ align:start position:0%
+abstractly here without specifying what
+ 
+
+ align:start position:0%
+abstractly here without specifying what
+M and N are and see what happens what we
+
+ align:start position:0%
+M and N are and see what happens what we
+ 
+
+ align:start position:0%
+M and N are and see what happens what we
+were trying to solve was a pair of
+
+ align:start position:0%
+were trying to solve was a pair of
+ 
+
+ align:start position:0%
+were trying to solve was a pair of
+equations we was trying to find F such
+
+ align:start position:0%
+equations we was trying to find F such
+ 
+
+ align:start position:0%
+equations we was trying to find F such
+as the partial of f respect to X is M
+
+ align:start position:0%
+as the partial of f respect to X is M
+ 
+
+ align:start position:0%
+as the partial of f respect to X is M
+partial of f respect to Y is n the first
+
+ align:start position:0%
+partial of f respect to Y is n the first
+ 
+
+ align:start position:0%
+partial of f respect to Y is n the first
+thing that we did was we treated y as a
+
+ align:start position:0%
+thing that we did was we treated y as a
+ 
+
+ align:start position:0%
+thing that we did was we treated y as a
+constant and integrated this with
+
+ align:start position:0%
+constant and integrated this with
+ 
+
+ align:start position:0%
+constant and integrated this with
+respect to X well I can't do this
+
+ align:start position:0%
+respect to X well I can't do this
+ 
+
+ align:start position:0%
+respect to X well I can't do this
+specifically because I don't know what M
+
+ align:start position:0%
+specifically because I don't know what M
+ 
+
+ align:start position:0%
+specifically because I don't know what M
+is so let me just just put the integral
+
+ align:start position:0%
+is so let me just just put the integral
+ 
+
+ align:start position:0%
+is so let me just just put the integral
+sign in here to say what I'm integrating
+
+ align:start position:0%
+sign in here to say what I'm integrating
+ 
+
+ align:start position:0%
+sign in here to say what I'm integrating
+this with respect to X treating y as a
+
+ align:start position:0%
+this with respect to X treating y as a
+ 
+
+ align:start position:0%
+this with respect to X treating y as a
+constant that's some function of X and Y
+
+ align:start position:0%
+constant that's some function of X and Y
+ 
+
+ align:start position:0%
+constant that's some function of X and Y
+you see over here see m is a function of
+
+ align:start position:0%
+you see over here see m is a function of
+ 
+
+ align:start position:0%
+you see over here see m is a function of
+X and Y I'm holding y constant I'm
+
+ align:start position:0%
+X and Y I'm holding y constant I'm
+ 
+
+ align:start position:0%
+X and Y I'm holding y constant I'm
+integrating this plus a constant of
+
+ align:start position:0%
+integrating this plus a constant of
+ 
+
+ align:start position:0%
+integrating this plus a constant of
+integration which depends only on y all
+
+ align:start position:0%
+integration which depends only on y all
+ 
+
+ align:start position:0%
+integration which depends only on y all
+right same as before what was my next
+
+ align:start position:0%
+right same as before what was my next
+ 
+
+ align:start position:0%
+right same as before what was my next
+step I took the partial of this with
+
+ align:start position:0%
+step I took the partial of this with
+ 
+
+ align:start position:0%
+step I took the partial of this with
+respect to F with respect to Y and I was
+
+ align:start position:0%
+respect to F with respect to Y and I was
+ 
+
+ align:start position:0%
+respect to F with respect to Y and I was
+going to compare that with what I knew
+
+ align:start position:0%
+going to compare that with what I knew
+ 
+
+ align:start position:0%
+going to compare that with what I knew
+the partial of f respect to Y had to be
+
+ align:start position:0%
+the partial of f respect to Y had to be
+ 
+
+ align:start position:0%
+the partial of f respect to Y had to be
+namely n so I then took what the partial
+
+ align:start position:0%
+namely n so I then took what the partial
+ 
+
+ align:start position:0%
+namely n so I then took what the partial
+of this with respect to Y that gave me
+
+ align:start position:0%
+of this with respect to Y that gave me
+ 
+
+ align:start position:0%
+of this with respect to Y that gave me
+the partial of this integral with
+
+ align:start position:0%
+the partial of this integral with
+ 
+
+ align:start position:0%
+the partial of this integral with
+respect to Y plus G Prime of Y and
+
+ align:start position:0%
+respect to Y plus G Prime of Y and
+ 
+
+ align:start position:0%
+respect to Y plus G Prime of Y and
+equating that to N I get that g Prime of
+
+ align:start position:0%
+equating that to N I get that g Prime of
+ 
+
+ align:start position:0%
+equating that to N I get that g Prime of
+Y was n minus the partial respect to Y
+
+ align:start position:0%
+Y was n minus the partial respect to Y
+ 
+
+ align:start position:0%
+Y was n minus the partial respect to Y
+integral M DX and again don't be alarmed
+
+ align:start position:0%
+integral M DX and again don't be alarmed
+ 
+
+ align:start position:0%
+integral M DX and again don't be alarmed
+by this expression if M had been given
+
+ align:start position:0%
+by this expression if M had been given
+ 
+
+ align:start position:0%
+by this expression if M had been given
+explicitly I would have solved
+
+ align:start position:0%
+explicitly I would have solved
+ 
+
+ align:start position:0%
+explicitly I would have solved
+explicitly for what this function was
+
+ align:start position:0%
+explicitly for what this function was
+ 
+
+ align:start position:0%
+explicitly for what this function was
+the key point is to notice that this
+
+ align:start position:0%
+the key point is to notice that this
+ 
+
+ align:start position:0%
+the key point is to notice that this
+side here is independent of x
+
+ align:start position:0%
+side here is independent of x
+ 
+
+ align:start position:0%
+side here is independent of x
+consequently this equation will be a
+
+ align:start position:0%
+consequently this equation will be a
+ 
+
+ align:start position:0%
+consequently this equation will be a
+contradiction unless the right hand side
+
+ align:start position:0%
+contradiction unless the right hand side
+ 
+
+ align:start position:0%
+contradiction unless the right hand side
+is a function of X in other words I mean
+
+ align:start position:0%
+is a function of X in other words I mean
+ 
+
+ align:start position:0%
+is a function of X in other words I mean
+is independent of X in other words we
+
+ align:start position:0%
+is independent of X in other words we
+ 
+
+ align:start position:0%
+is independent of X in other words we
+have determined f up to this function G
+
+ align:start position:0%
+have determined f up to this function G
+ 
+
+ align:start position:0%
+have determined f up to this function G
+of Y and what's going to happen is we
+
+ align:start position:0%
+of Y and what's going to happen is we
+ 
+
+ align:start position:0%
+of Y and what's going to happen is we
+are going to be able to compute G of Y
+
+ align:start position:0%
+are going to be able to compute G of Y
+ 
+
+ align:start position:0%
+are going to be able to compute G of Y
+if this expression is independent of X
+
+ align:start position:0%
+if this expression is independent of X
+ 
+
+ align:start position:0%
+if this expression is independent of X
+namely just by integrating this but if
+
+ align:start position:0%
+namely just by integrating this but if
+ 
+
+ align:start position:0%
+namely just by integrating this but if
+if G of Y is not independent of X we are
+
+ align:start position:0%
+if G of Y is not independent of X we are
+ 
+
+ align:start position:0%
+if G of Y is not independent of X we are
+in trouble it means that it's not going
+
+ align:start position:0%
+in trouble it means that it's not going
+ 
+
+ align:start position:0%
+in trouble it means that it's not going
+to exist the key key step is is this
+
+ align:start position:0%
+to exist the key key step is is this
+ 
+
+ align:start position:0%
+to exist the key key step is is this
+independent of X and the answer is the
+
+ align:start position:0%
+independent of X and the answer is the
+ 
+
+ align:start position:0%
+independent of X and the answer is the
+best way to find out in terms of
+
+ align:start position:0%
+best way to find out in terms of
+ 
+
+ align:start position:0%
+best way to find out in terms of
+calculus is to take its derivative with
+
+ align:start position:0%
+calculus is to take its derivative with
+ 
+
+ align:start position:0%
+calculus is to take its derivative with
+respect to X if this depends on y alone
+
+ align:start position:0%
+respect to X if this depends on y alone
+ 
+
+ align:start position:0%
+respect to X if this depends on y alone
+its partial with respect to X must be
+
+ align:start position:0%
+its partial with respect to X must be
+ 
+
+ align:start position:0%
+its partial with respect to X must be
+zero in other words if this partial with
+
+ align:start position:0%
+zero in other words if this partial with
+ 
+
+ align:start position:0%
+zero in other words if this partial with
+respect to X is not zero it means that
+
+ align:start position:0%
+respect to X is not zero it means that
+ 
+
+ align:start position:0%
+respect to X is not zero it means that
+this expression varies with X at any
+
+ align:start position:0%
+this expression varies with X at any
+ 
+
+ align:start position:0%
+this expression varies with X at any
+rate to see what this derivative is we
+
+ align:start position:0%
+rate to see what this derivative is we
+ 
+
+ align:start position:0%
+rate to see what this derivative is we
+just differentiate term by term and then
+
+ align:start position:0%
+just differentiate term by term and then
+ 
+
+ align:start position:0%
+just differentiate term by term and then
+we say you know it's rather interesting
+
+ align:start position:0%
+we say you know it's rather interesting
+ 
+
+ align:start position:0%
+we say you know it's rather interesting
+if this thing had been
+
+ align:start position:0%
+if this thing had been
+ 
+
+ align:start position:0%
+if this thing had been
+first notice that if you integrate with
+
+ align:start position:0%
+first notice that if you integrate with
+ 
+
+ align:start position:0%
+first notice that if you integrate with
+respect to X and then differentiate with
+
+ align:start position:0%
+respect to X and then differentiate with
+ 
+
+ align:start position:0%
+respect to X and then differentiate with
+respect to X you wind up with just the
+
+ align:start position:0%
+respect to X you wind up with just the
+ 
+
+ align:start position:0%
+respect to X you wind up with just the
+integrand well again if we have enough
+
+ align:start position:0%
+integrand well again if we have enough
+ 
+
+ align:start position:0%
+integrand well again if we have enough
+continuity the order of differentiation
+
+ align:start position:0%
+continuity the order of differentiation
+ 
+
+ align:start position:0%
+continuity the order of differentiation
+is irrelevant we can reverse the order
+
+ align:start position:0%
+is irrelevant we can reverse the order
+ 
+
+ align:start position:0%
+is irrelevant we can reverse the order
+without changing anything if we now
+
+ align:start position:0%
+without changing anything if we now
+ 
+
+ align:start position:0%
+without changing anything if we now
+interchange this order take the partial
+
+ align:start position:0%
+interchange this order take the partial
+ 
+
+ align:start position:0%
+interchange this order take the partial
+first with respect to X that will give
+
+ align:start position:0%
+first with respect to X that will give
+ 
+
+ align:start position:0%
+first with respect to X that will give
+us just m and the partial of M with
+
+ align:start position:0%
+us just m and the partial of M with
+ 
+
+ align:start position:0%
+us just m and the partial of M with
+respect to Y is just a partial of M with
+
+ align:start position:0%
+respect to Y is just a partial of M with
+ 
+
+ align:start position:0%
+respect to Y is just a partial of M with
+respect to Y of course what we're saying
+
+ align:start position:0%
+respect to Y of course what we're saying
+ 
+
+ align:start position:0%
+respect to Y of course what we're saying
+is that from this step we get the this
+
+ align:start position:0%
+is that from this step we get the this
+ 
+
+ align:start position:0%
+is that from this step we get the this
+step and this in turn implies this
+
+ align:start position:0%
+step and this in turn implies this
+ 
+
+ align:start position:0%
+step and this in turn implies this
+notice that the only way that this can
+
+ align:start position:0%
+notice that the only way that this can
+ 
+
+ align:start position:0%
+notice that the only way that this can
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+zero is if the partial of n with respect
+
+ align:start position:0%
+zero is if the partial of n with respect
+ 
+
+ align:start position:0%
+zero is if the partial of n with respect
+to x equals the partial of M with
+
+ align:start position:0%
+to x equals the partial of M with
+ 
+
+ align:start position:0%
+to x equals the partial of M with
+respect to Y so in summary then this is
+
+ align:start position:0%
+respect to Y so in summary then this is
+ 
+
+ align:start position:0%
+respect to Y so in summary then this is
+a very interesting device it tells us
+
+ align:start position:0%
+a very interesting device it tells us
+ 
+
+ align:start position:0%
+a very interesting device it tells us
+how to tell whether a differential is
+
+ align:start position:0%
+how to tell whether a differential is
+ 
+
+ align:start position:0%
+how to tell whether a differential is
+exact and the proof is very nice in this
+
+ align:start position:0%
+exact and the proof is very nice in this
+ 
+
+ align:start position:0%
+exact and the proof is very nice in this
+case because the proof exactly imitates
+
+ align:start position:0%
+case because the proof exactly imitates
+ 
+
+ align:start position:0%
+case because the proof exactly imitates
+how we construct the function f if it
+
+ align:start position:0%
+how we construct the function f if it
+ 
+
+ align:start position:0%
+how we construct the function f if it
+turns out to be exact but but the point
+
+ align:start position:0%
+turns out to be exact but but the point
+ 
+
+ align:start position:0%
+turns out to be exact but but the point
+is if given MDX plus ndy if the partial
+
+ align:start position:0%
+is if given MDX plus ndy if the partial
+ 
+
+ align:start position:0%
+is if given MDX plus ndy if the partial
+of M with respect to Y is not equal to
+
+ align:start position:0%
+of M with respect to Y is not equal to
+ 
+
+ align:start position:0%
+of M with respect to Y is not equal to
+the partial of M with respect to X
+
+ align:start position:0%
+the partial of M with respect to X
+ 
+
+ align:start position:0%
+the partial of M with respect to X
+there's no hope that the function will
+
+ align:start position:0%
+there's no hope that the function will
+ 
+
+ align:start position:0%
+there's no hope that the function will
+be exact the differential will be exact
+
+ align:start position:0%
+be exact the differential will be exact
+ 
+
+ align:start position:0%
+be exact the differential will be exact
+any rate we will have sufficient
+
+ align:start position:0%
+any rate we will have sufficient
+ 
+
+ align:start position:0%
+any rate we will have sufficient
+exercises for drill and how one uses
+
+ align:start position:0%
+exercises for drill and how one uses
+ 
+
+ align:start position:0%
+exercises for drill and how one uses
+exact differentials this concludes block
+
+ align:start position:0%
+exact differentials this concludes block
+ 
+
+ align:start position:0%
+exact differentials this concludes block
+three of our material our next block of
+
+ align:start position:0%
+three of our material our next block of
+ 
+
+ align:start position:0%
+three of our material our next block of
+material which will cons which will
+
+ align:start position:0%
+material which will cons which will
+ 
+
+ align:start position:0%
+material which will cons which will
+concern linear systems of equations will
+
+ align:start position:0%
+concern linear systems of equations will
+ 
+
+ align:start position:0%
+concern linear systems of equations will
+be begin with our next lecture and until
+
+ align:start position:0%
+be begin with our next lecture and until
+ 
+
+ align:start position:0%
+be begin with our next lecture and until
+next time
+
+ align:start position:0%
+next time
+ 
+
+ align:start position:0%
+next time
+goodbye funding for the publication of
+
+ align:start position:0%
+goodbye funding for the publication of
+ 
+
+ align:start position:0%
+goodbye funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
+ align:start position:0%
+and Paul rosenbom
+ 
+
+ align:start position:0%
+and Paul rosenbom
+foundation help ocw continue to provide
+
+ align:start position:0%
+foundation help ocw continue to provide
+ 
+
+ align:start position:0%
+foundation help ocw continue to provide
+free and open access to MIT courses by
+
+ align:start position:0%
+free and open access to MIT courses by
+ 
+
+ align:start position:0%
+free and open access to MIT courses by
+making a donation at ocw.mit.edu/donate
\ No newline at end of file
diff --git a/S5HmxtARo8Q.txt b/S5HmxtARo8Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f45e1984594823dfb50b478b6f09e65b4d5312f1
--- /dev/null
+++ b/S5HmxtARo8Q.txt
@@ -0,0 +1,4523 @@
+align:start position:0%
+ 
+we are excited and honored to have
+
+ align:start position:0%
+we are excited and honored to have
+ 
+
+ align:start position:0%
+we are excited and honored to have
+professor Stephen carpenter with us and
+
+ align:start position:0%
+professor Stephen carpenter with us and
+ 
+
+ align:start position:0%
+professor Stephen carpenter with us and
+this is the first of a series of events
+
+ align:start position:0%
+this is the first of a series of events
+ 
+
+ align:start position:0%
+this is the first of a series of events
+on Larry Susskind on the faculty and
+
+ align:start position:0%
+on Larry Susskind on the faculty and
+ 
+
+ align:start position:0%
+on Larry Susskind on the faculty and
+urban studies and planning it's
+
+ align:start position:0%
+urban studies and planning it's
+ 
+
+ align:start position:0%
+urban studies and planning it's
+interesting to me that several people
+
+ align:start position:0%
+interesting to me that several people
+ 
+
+ align:start position:0%
+interesting to me that several people
+here have a water interest several
+
+ align:start position:0%
+here have a water interest several
+ 
+
+ align:start position:0%
+here have a water interest several
+people here of planning interest several
+
+ align:start position:0%
+people here of planning interest several
+ 
+
+ align:start position:0%
+people here of planning interest several
+people here have artistic or arts
+
+ align:start position:0%
+people here have artistic or arts
+ 
+
+ align:start position:0%
+people here have artistic or arts
+methods interest several people here
+
+ align:start position:0%
+methods interest several people here
+ 
+
+ align:start position:0%
+methods interest several people here
+have sort of public education interest
+
+ align:start position:0%
+have sort of public education interest
+ 
+
+ align:start position:0%
+have sort of public education interest
+and and all of those are alive and well
+
+ align:start position:0%
+and and all of those are alive and well
+ 
+
+ align:start position:0%
+and and all of those are alive and well
+in the department of urban studies and
+
+ align:start position:0%
+in the department of urban studies and
+ 
+
+ align:start position:0%
+in the department of urban studies and
+planning in different kinds of ways
+
+ align:start position:0%
+planning in different kinds of ways
+ 
+
+ align:start position:0%
+planning in different kinds of ways
+there is an environmental group in the
+
+ align:start position:0%
+there is an environmental group in the
+ 
+
+ align:start position:0%
+there is an environmental group in the
+department that I have had some
+
+ align:start position:0%
+department that I have had some
+ 
+
+ align:start position:0%
+department that I have had some
+responsibility for and water is
+
+ align:start position:0%
+responsibility for and water is
+ 
+
+ align:start position:0%
+responsibility for and water is
+concerned within the environmental group
+
+ align:start position:0%
+concerned within the environmental group
+ 
+
+ align:start position:0%
+concerned within the environmental group
+not just domestically but
+
+ align:start position:0%
+not just domestically but
+ 
+
+ align:start position:0%
+not just domestically but
+internationally which relates to part of
+
+ align:start position:0%
+internationally which relates to part of
+ 
+
+ align:start position:0%
+internationally which relates to part of
+your work we're interested in water as
+
+ align:start position:0%
+your work we're interested in water as
+ 
+
+ align:start position:0%
+your work we're interested in water as
+environmental justice concern not just a
+
+ align:start position:0%
+environmental justice concern not just a
+ 
+
+ align:start position:0%
+environmental justice concern not just a
+natural resource management concern and
+
+ align:start position:0%
+natural resource management concern and
+ 
+
+ align:start position:0%
+natural resource management concern and
+so when I first learned of some of the
+
+ align:start position:0%
+so when I first learned of some of the
+ 
+
+ align:start position:0%
+so when I first learned of some of the
+ways in which your work is focused on
+
+ align:start position:0%
+ways in which your work is focused on
+ 
+
+ align:start position:0%
+ways in which your work is focused on
+making clean water available to people
+
+ align:start position:0%
+making clean water available to people
+ 
+
+ align:start position:0%
+making clean water available to people
+in different places there was a direct
+
+ align:start position:0%
+in different places there was a direct
+ 
+
+ align:start position:0%
+in different places there was a direct
+connection with that aspect of of what
+
+ align:start position:0%
+connection with that aspect of of what
+ 
+
+ align:start position:0%
+connection with that aspect of of what
+we do I was really interested in how
+
+ align:start position:0%
+we do I was really interested in how
+ 
+
+ align:start position:0%
+we do I was really interested in how
+issues of race could be raised in a way
+
+ align:start position:0%
+issues of race could be raised in a way
+ 
+
+ align:start position:0%
+issues of race could be raised in a way
+the conversation was possible and that
+
+ align:start position:0%
+the conversation was possible and that
+ 
+
+ align:start position:0%
+the conversation was possible and that
+is another very big part of what our
+
+ align:start position:0%
+is another very big part of what our
+ 
+
+ align:start position:0%
+is another very big part of what our
+department and our school are interested
+
+ align:start position:0%
+department and our school are interested
+ 
+
+ align:start position:0%
+department and our school are interested
+in so by way of background those are
+
+ align:start position:0%
+in so by way of background those are
+ 
+
+ align:start position:0%
+in so by way of background those are
+some of the thematic interests that led
+
+ align:start position:0%
+some of the thematic interests that led
+ 
+
+ align:start position:0%
+some of the thematic interests that led
+us to very much want you to be here well
+
+ align:start position:0%
+us to very much want you to be here well
+ 
+
+ align:start position:0%
+us to very much want you to be here well
+thanks Larry
+
+ align:start position:0%
+thanks Larry
+ 
+
+ align:start position:0%
+thanks Larry
+as far back as I can remember I like
+
+ align:start position:0%
+as far back as I can remember I like
+ 
+
+ align:start position:0%
+as far back as I can remember I like
+making stuff I'll just make things you
+
+ align:start position:0%
+making stuff I'll just make things you
+ 
+
+ align:start position:0%
+making stuff I'll just make things you
+know I'm the oldest of four boys and the
+
+ align:start position:0%
+know I'm the oldest of four boys and the
+ 
+
+ align:start position:0%
+know I'm the oldest of four boys and the
+oldest and the youngest were born five
+
+ align:start position:0%
+oldest and the youngest were born five
+ 
+
+ align:start position:0%
+oldest and the youngest were born five
+and a half years apart no twins so we
+
+ align:start position:0%
+and a half years apart no twins so we
+ 
+
+ align:start position:0%
+and a half years apart no twins so we
+were constantly together in doing things
+
+ align:start position:0%
+were constantly together in doing things
+ 
+
+ align:start position:0%
+were constantly together in doing things
+and we make
+
+ align:start position:0%
+and we make
+ 
+
+ align:start position:0%
+and we make
+like a set of golf clubs my dad had golf
+
+ align:start position:0%
+like a set of golf clubs my dad had golf
+ 
+
+ align:start position:0%
+like a set of golf clubs my dad had golf
+clubs we weren't allowed to use them so
+
+ align:start position:0%
+clubs we weren't allowed to use them so
+ 
+
+ align:start position:0%
+clubs we weren't allowed to use them so
+we made them of course we used his
+
+ align:start position:0%
+we made them of course we used his
+ 
+
+ align:start position:0%
+we made them of course we used his
+copper pipe for the the plumbing in the
+
+ align:start position:0%
+copper pipe for the the plumbing in the
+ 
+
+ align:start position:0%
+copper pipe for the the plumbing in the
+house and so making things was always
+
+ align:start position:0%
+house and so making things was always
+ 
+
+ align:start position:0%
+house and so making things was always
+part of what what I did and and have
+
+ align:start position:0%
+part of what what I did and and have
+ 
+
+ align:start position:0%
+part of what what I did and and have
+done and just engaging the one his
+
+ align:start position:0%
+done and just engaging the one his
+ 
+
+ align:start position:0%
+done and just engaging the one his
+shifts and has moved my backgrounds
+
+ align:start position:0%
+shifts and has moved my backgrounds
+ 
+
+ align:start position:0%
+shifts and has moved my backgrounds
+really pottery his really ceramics
+
+ align:start position:0%
+really pottery his really ceramics
+ 
+
+ align:start position:0%
+really pottery his really ceramics
+touching the clay touching the mud
+
+ align:start position:0%
+touching the clay touching the mud
+ 
+
+ align:start position:0%
+touching the clay touching the mud
+making things that's my degree is in
+
+ align:start position:0%
+making things that's my degree is in
+ 
+
+ align:start position:0%
+making things that's my degree is in
+ceramics and fine art I don't know what
+
+ align:start position:0%
+ceramics and fine art I don't know what
+ 
+
+ align:start position:0%
+ceramics and fine art I don't know what
+it was this urge ability interest for
+
+ align:start position:0%
+it was this urge ability interest for
+ 
+
+ align:start position:0%
+it was this urge ability interest for
+teaching for education so that
+
+ align:start position:0%
+teaching for education so that
+ 
+
+ align:start position:0%
+teaching for education so that
+complicated the situation making stuff
+
+ align:start position:0%
+complicated the situation making stuff
+ 
+
+ align:start position:0%
+complicated the situation making stuff
+and teaching stuff but actually you can
+
+ align:start position:0%
+and teaching stuff but actually you can
+ 
+
+ align:start position:0%
+and teaching stuff but actually you can
+do that that's called being an art
+
+ align:start position:0%
+do that that's called being an art
+ 
+
+ align:start position:0%
+do that that's called being an art
+educator or a teacher and the ceramics
+
+ align:start position:0%
+educator or a teacher and the ceramics
+ 
+
+ align:start position:0%
+educator or a teacher and the ceramics
+piece stayed with I couldn't shake the
+
+ align:start position:0%
+piece stayed with I couldn't shake the
+ 
+
+ align:start position:0%
+piece stayed with I couldn't shake the
+clay couldn't get the clay out of my
+
+ align:start position:0%
+clay couldn't get the clay out of my
+ 
+
+ align:start position:0%
+clay couldn't get the clay out of my
+fingernails the making of things had to
+
+ align:start position:0%
+fingernails the making of things had to
+ 
+
+ align:start position:0%
+fingernails the making of things had to
+always be there and I taught elementary
+
+ align:start position:0%
+always be there and I taught elementary
+ 
+
+ align:start position:0%
+always be there and I taught elementary
+school art that was the art teacher in
+
+ align:start position:0%
+school art that was the art teacher in
+ 
+
+ align:start position:0%
+school art that was the art teacher in
+elementary school and that was among the
+
+ align:start position:0%
+elementary school and that was among the
+ 
+
+ align:start position:0%
+elementary school and that was among the
+most invigorating experiences of my life
+
+ align:start position:0%
+most invigorating experiences of my life
+ 
+
+ align:start position:0%
+most invigorating experiences of my life
+because the students are always about
+
+ align:start position:0%
+because the students are always about
+ 
+
+ align:start position:0%
+because the students are always about
+making something their bodies are always
+
+ align:start position:0%
+making something their bodies are always
+ 
+
+ align:start position:0%
+making something their bodies are always
+moving they're constantly in a state of
+
+ align:start position:0%
+moving they're constantly in a state of
+ 
+
+ align:start position:0%
+moving they're constantly in a state of
+absorbing what they're doing in the
+
+ align:start position:0%
+absorbing what they're doing in the
+ 
+
+ align:start position:0%
+absorbing what they're doing in the
+world and seeing other people doing and
+
+ align:start position:0%
+world and seeing other people doing and
+ 
+
+ align:start position:0%
+world and seeing other people doing and
+moving and checking and so that energy
+
+ align:start position:0%
+moving and checking and so that energy
+ 
+
+ align:start position:0%
+moving and checking and so that energy
+was was quite interesting to me followed
+
+ align:start position:0%
+was was quite interesting to me followed
+ 
+
+ align:start position:0%
+was was quite interesting to me followed
+that experience up with a doctoral
+
+ align:start position:0%
+that experience up with a doctoral
+ 
+
+ align:start position:0%
+that experience up with a doctoral
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+
+ align:start position:0%
+degree in art education but the idea was
+ 
+
+ align:start position:0%
+degree in art education but the idea was
+that the making and the teaching and the
+
+ align:start position:0%
+that the making and the teaching and the
+ 
+
+ align:start position:0%
+that the making and the teaching and the
+learning and the asking of questions
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+ align:start position:0%
+learning and the asking of questions
+ 
+
+ align:start position:0%
+learning and the asking of questions
+through art through the visual imagery
+
+ align:start position:0%
+through art through the visual imagery
+ 
+
+ align:start position:0%
+through art through the visual imagery
+that you're talking about that was what
+
+ align:start position:0%
+that you're talking about that was what
+ 
+
+ align:start position:0%
+that you're talking about that was what
+was so important and you mentioned the
+
+ align:start position:0%
+was so important and you mentioned the
+ 
+
+ align:start position:0%
+was so important and you mentioned the
+notion of access
+
+ align:start position:0%
+notion of access
+ 
+
+ align:start position:0%
+notion of access
+well we didn't have golf clubs we didn't
+
+ align:start position:0%
+well we didn't have golf clubs we didn't
+ 
+
+ align:start position:0%
+well we didn't have golf clubs we didn't
+have access to with like we saw we
+
+ align:start position:0%
+have access to with like we saw we
+ 
+
+ align:start position:0%
+have access to with like we saw we
+didn't have access to so making our own
+
+ align:start position:0%
+didn't have access to so making our own
+ 
+
+ align:start position:0%
+didn't have access to so making our own
+access i'm interested in that as well
+
+ align:start position:0%
+access i'm interested in that as well
+ 
+
+ align:start position:0%
+access i'm interested in that as well
+how does one make one's own access so
+
+ align:start position:0%
+how does one make one's own access so
+ 
+
+ align:start position:0%
+how does one make one's own access so
+moving around to a series of different
+
+ align:start position:0%
+moving around to a series of different
+ 
+
+ align:start position:0%
+moving around to a series of different
+universities as an art educator still
+
+ align:start position:0%
+universities as an art educator still
+ 
+
+ align:start position:0%
+universities as an art educator still
+making part of my graduate both graduate
+
+ align:start position:0%
+making part of my graduate both graduate
+ 
+
+ align:start position:0%
+making part of my graduate both graduate
+degrees was about being in the clay
+
+ align:start position:0%
+degrees was about being in the clay
+ 
+
+ align:start position:0%
+degrees was about being in the clay
+studio as much as it was being in the
+
+ align:start position:0%
+studio as much as it was being in the
+ 
+
+ align:start position:0%
+studio as much as it was being in the
+seminar room and that was really the
+
+ align:start position:0%
+seminar room and that was really the
+ 
+
+ align:start position:0%
+seminar room and that was really the
+focus of my dissertation was in the clay
+
+ align:start position:0%
+focus of my dissertation was in the clay
+ 
+
+ align:start position:0%
+focus of my dissertation was in the clay
+studio we were talking and critiquing
+
+ align:start position:0%
+studio we were talking and critiquing
+ 
+
+ align:start position:0%
+studio we were talking and critiquing
+about color and shape and form and how
+
+ align:start position:0%
+about color and shape and form and how
+ 
+
+ align:start position:0%
+about color and shape and form and how
+the glaze works and on the other side of
+
+ align:start position:0%
+the glaze works and on the other side of
+ 
+
+ align:start position:0%
+the glaze works and on the other side of
+the same part of campus on the other
+
+ align:start position:0%
+the same part of campus on the other
+ 
+
+ align:start position:0%
+the same part of campus on the other
+side of the road in the theory class as
+
+ align:start position:0%
+side of the road in the theory class as
+ 
+
+ align:start position:0%
+side of the road in the theory class as
+an art education we're talking about
+
+ align:start position:0%
+an art education we're talking about
+ 
+
+ align:start position:0%
+an art education we're talking about
+postmodern theory and feminist theory
+
+ align:start position:0%
+postmodern theory and feminist theory
+ 
+
+ align:start position:0%
+postmodern theory and feminist theory
+and film theory and
+
+ align:start position:0%
+and film theory and
+ 
+
+ align:start position:0%
+and film theory and
+interpreting installations and and and
+
+ align:start position:0%
+interpreting installations and and and
+ 
+
+ align:start position:0%
+interpreting installations and and and
+performances and then on the other side
+
+ align:start position:0%
+performances and then on the other side
+ 
+
+ align:start position:0%
+performances and then on the other side
+of the road I'd go to my class the next
+
+ align:start position:0%
+of the road I'd go to my class the next
+ 
+
+ align:start position:0%
+of the road I'd go to my class the next
+day we were again critiquing but we were
+
+ align:start position:0%
+day we were again critiquing but we were
+ 
+
+ align:start position:0%
+day we were again critiquing but we were
+talking about oh I like I like that
+
+ align:start position:0%
+talking about oh I like I like that
+ 
+
+ align:start position:0%
+talking about oh I like I like that
+handle show me how you made the handle
+
+ align:start position:0%
+handle show me how you made the handle
+ 
+
+ align:start position:0%
+handle show me how you made the handle
+this handle works and that one doesn't
+
+ align:start position:0%
+this handle works and that one doesn't
+ 
+
+ align:start position:0%
+this handle works and that one doesn't
+we never defined what works meant but
+
+ align:start position:0%
+we never defined what works meant but
+ 
+
+ align:start position:0%
+we never defined what works meant but
+putting those together the making and
+
+ align:start position:0%
+putting those together the making and
+ 
+
+ align:start position:0%
+putting those together the making and
+that interpreting and thinking and
+
+ align:start position:0%
+that interpreting and thinking and
+ 
+
+ align:start position:0%
+that interpreting and thinking and
+theorizing in both registers doesn't
+
+ align:start position:0%
+theorizing in both registers doesn't
+ 
+
+ align:start position:0%
+theorizing in both registers doesn't
+have to be separated so to think of us
+
+ align:start position:0%
+have to be separated so to think of us
+ 
+
+ align:start position:0%
+have to be separated so to think of us
+even with labels I find kind of curious
+
+ align:start position:0%
+even with labels I find kind of curious
+ 
+
+ align:start position:0%
+even with labels I find kind of curious
+like we have to find a place on campus
+
+ align:start position:0%
+like we have to find a place on campus
+ 
+
+ align:start position:0%
+like we have to find a place on campus
+but the understanding that we can move
+
+ align:start position:0%
+but the understanding that we can move
+ 
+
+ align:start position:0%
+but the understanding that we can move
+in and out of those spaces and we can
+
+ align:start position:0%
+in and out of those spaces and we can
+ 
+
+ align:start position:0%
+in and out of those spaces and we can
+start to shed those those identities the
+
+ align:start position:0%
+start to shed those those identities the
+ 
+
+ align:start position:0%
+start to shed those those identities the
+kind of group that has self-assembled
+
+ align:start position:0%
+kind of group that has self-assembled
+ 
+
+ align:start position:0%
+kind of group that has self-assembled
+today speaks to multiple interests that
+
+ align:start position:0%
+today speaks to multiple interests that
+ 
+
+ align:start position:0%
+today speaks to multiple interests that
+I have and trying to weave it into what
+
+ align:start position:0%
+I have and trying to weave it into what
+ 
+
+ align:start position:0%
+I have and trying to weave it into what
+is an art education how does one learn
+
+ align:start position:0%
+is an art education how does one learn
+ 
+
+ align:start position:0%
+is an art education how does one learn
+through the making of things through the
+
+ align:start position:0%
+through the making of things through the
+ 
+
+ align:start position:0%
+through the making of things through the
+to the display of cultural products
+
+ align:start position:0%
+to the display of cultural products
+ 
+
+ align:start position:0%
+to the display of cultural products
+through cultural production what kind of
+
+ align:start position:0%
+through cultural production what kind of
+ 
+
+ align:start position:0%
+through cultural production what kind of
+questions can we ask not just about what
+
+ align:start position:0%
+questions can we ask not just about what
+ 
+
+ align:start position:0%
+questions can we ask not just about what
+someone else has made but what kind of
+
+ align:start position:0%
+someone else has made but what kind of
+ 
+
+ align:start position:0%
+someone else has made but what kind of
+questions can we ask through them the
+
+ align:start position:0%
+questions can we ask through them the
+ 
+
+ align:start position:0%
+questions can we ask through them the
+act of making itself we can make meaning
+
+ align:start position:0%
+act of making itself we can make meaning
+ 
+
+ align:start position:0%
+act of making itself we can make meaning
+through relationships we can make
+
+ align:start position:0%
+through relationships we can make
+ 
+
+ align:start position:0%
+through relationships we can make
+meaning through conversation we can make
+
+ align:start position:0%
+meaning through conversation we can make
+ 
+
+ align:start position:0%
+meaning through conversation we can make
+meaning through verbal or written
+
+ align:start position:0%
+meaning through verbal or written
+ 
+
+ align:start position:0%
+meaning through verbal or written
+responses so it's the the making of
+
+ align:start position:0%
+responses so it's the the making of
+ 
+
+ align:start position:0%
+responses so it's the the making of
+meaning making of cultural product
+
+ align:start position:0%
+meaning making of cultural product
+ 
+
+ align:start position:0%
+meaning making of cultural product
+making of a difference right so this
+
+ align:start position:0%
+making of a difference right so this
+ 
+
+ align:start position:0%
+making of a difference right so this
+notion of making doesn't have to always
+
+ align:start position:0%
+notion of making doesn't have to always
+ 
+
+ align:start position:0%
+notion of making doesn't have to always
+have this physicality to it from saying
+
+ align:start position:0%
+have this physicality to it from saying
+ 
+
+ align:start position:0%
+have this physicality to it from saying
+all that to say that the clay left my
+
+ align:start position:0%
+all that to say that the clay left my
+ 
+
+ align:start position:0%
+all that to say that the clay left my
+fingernails for a while until move to
+
+ align:start position:0%
+fingernails for a while until move to
+ 
+
+ align:start position:0%
+fingernails for a while until move to
+Texas my wife is an engineer mechanical
+
+ align:start position:0%
+Texas my wife is an engineer mechanical
+ 
+
+ align:start position:0%
+Texas my wife is an engineer mechanical
+engineer material science and it's a
+
+ align:start position:0%
+engineer material science and it's a
+ 
+
+ align:start position:0%
+engineer material science and it's a
+great opportunity for her to move there
+
+ align:start position:0%
+great opportunity for her to move there
+ 
+
+ align:start position:0%
+great opportunity for her to move there
+for me there's no art education there at
+
+ align:start position:0%
+for me there's no art education there at
+ 
+
+ align:start position:0%
+for me there's no art education there at
+all they got my CV and didn't know where
+
+ align:start position:0%
+all they got my CV and didn't know where
+ 
+
+ align:start position:0%
+all they got my CV and didn't know where
+to put me send it all over campus and
+
+ align:start position:0%
+to put me send it all over campus and
+ 
+
+ align:start position:0%
+to put me send it all over campus and
+finally the education folks at all will
+
+ align:start position:0%
+finally the education folks at all will
+ 
+
+ align:start position:0%
+finally the education folks at all will
+take him
+
+ align:start position:0%
+take him
+ 
+
+ align:start position:0%
+take him
+it has education in his degree will take
+
+ align:start position:0%
+it has education in his degree will take
+ 
+
+ align:start position:0%
+it has education in his degree will take
+him telling you all that to say I got to
+
+ align:start position:0%
+him telling you all that to say I got to
+ 
+
+ align:start position:0%
+him telling you all that to say I got to
+Texas and art education had to be I had
+
+ align:start position:0%
+Texas and art education had to be I had
+ 
+
+ align:start position:0%
+Texas and art education had to be I had
+to reinvent it or at least I had to
+
+ align:start position:0%
+to reinvent it or at least I had to
+ 
+
+ align:start position:0%
+to reinvent it or at least I had to
+figure out what I meant by it and how I
+
+ align:start position:0%
+figure out what I meant by it and how I
+ 
+
+ align:start position:0%
+figure out what I meant by it and how I
+fit in if you don't have an art
+
+ align:start position:0%
+fit in if you don't have an art
+ 
+
+ align:start position:0%
+fit in if you don't have an art
+department how do you have art education
+
+ align:start position:0%
+department how do you have art education
+ 
+
+ align:start position:0%
+department how do you have art education
+well you just open the studio in your
+
+ align:start position:0%
+well you just open the studio in your
+ 
+
+ align:start position:0%
+well you just open the studio in your
+garage and have people over on Fridays I
+
+ align:start position:0%
+garage and have people over on Fridays I
+ 
+
+ align:start position:0%
+garage and have people over on Fridays I
+did that or you can engage in the work
+
+ align:start position:0%
+did that or you can engage in the work
+ 
+
+ align:start position:0%
+did that or you can engage in the work
+in the curriculum that fixed set of
+
+ align:start position:0%
+in the curriculum that fixed set of
+ 
+
+ align:start position:0%
+in the curriculum that fixed set of
+notions and premeditated concepts terms
+
+ align:start position:0%
+notions and premeditated concepts terms
+ 
+
+ align:start position:0%
+notions and premeditated concepts terms
+practices skills construct that
+
+ align:start position:0%
+practices skills construct that
+ 
+
+ align:start position:0%
+practices skills construct that
+educational experience my entrance into
+
+ align:start position:0%
+educational experience my entrance into
+ 
+
+ align:start position:0%
+educational experience my entrance into
+a more curriculum instruction space was
+
+ align:start position:0%
+a more curriculum instruction space was
+ 
+
+ align:start position:0%
+a more curriculum instruction space was
+through my background as an artist and
+
+ align:start position:0%
+through my background as an artist and
+ 
+
+ align:start position:0%
+through my background as an artist and
+as an art educator the water filter work
+
+ align:start position:0%
+as an art educator the water filter work
+ 
+
+ align:start position:0%
+as an art educator the water filter work
+that I do and have started to do came
+
+ align:start position:0%
+that I do and have started to do came
+ 
+
+ align:start position:0%
+that I do and have started to do came
+about when I was in Texas I met a guy
+
+ align:start position:0%
+about when I was in Texas I met a guy
+ 
+
+ align:start position:0%
+about when I was in Texas I met a guy
+who is name is Oscar muñoz Oscar is in
+
+ align:start position:0%
+who is name is Oscar muñoz Oscar is in
+ 
+
+ align:start position:0%
+who is name is Oscar muñoz Oscar is in
+charge of the Texas A&M colonias
+
+ align:start position:0%
+charge of the Texas A&M colonias
+ 
+
+ align:start position:0%
+charge of the Texas A&M colonias
+programs all along the border
+
+ align:start position:0%
+programs all along the border
+ 
+
+ align:start position:0%
+programs all along the border
+Texas is 1/3 the width of the United
+
+ align:start position:0%
+Texas is 1/3 the width of the United
+ 
+
+ align:start position:0%
+Texas is 1/3 the width of the United
+States so that distance and then 150
+
+ align:start position:0%
+States so that distance and then 150
+ 
+
+ align:start position:0%
+States so that distance and then 150
+miles up is called the border of Texas
+
+ align:start position:0%
+miles up is called the border of Texas
+ 
+
+ align:start position:0%
+miles up is called the border of Texas
+and in that space they live over half a
+
+ align:start position:0%
+and in that space they live over half a
+ 
+
+ align:start position:0%
+and in that space they live over half a
+million people most of whom don't have
+
+ align:start position:0%
+million people most of whom don't have
+ 
+
+ align:start position:0%
+million people most of whom don't have
+access to clean water in their homes and
+
+ align:start position:0%
+access to clean water in their homes and
+ 
+
+ align:start position:0%
+access to clean water in their homes and
+Oscar talk you know let me know this and
+
+ align:start position:0%
+Oscar talk you know let me know this and
+ 
+
+ align:start position:0%
+Oscar talk you know let me know this and
+he works with communities all across
+
+ align:start position:0%
+he works with communities all across
+ 
+
+ align:start position:0%
+he works with communities all across
+that swath and as an art educator that
+
+ align:start position:0%
+that swath and as an art educator that
+ 
+
+ align:start position:0%
+that swath and as an art educator that
+was interesting to me because I had to
+
+ align:start position:0%
+was interesting to me because I had to
+ 
+
+ align:start position:0%
+was interesting to me because I had to
+learn about a lot of the practices that
+
+ align:start position:0%
+learn about a lot of the practices that
+ 
+
+ align:start position:0%
+learn about a lot of the practices that
+that he's up against and faces telling
+
+ align:start position:0%
+that he's up against and faces telling
+ 
+
+ align:start position:0%
+that he's up against and faces telling
+you all it is to say I'm not that I I
+
+ align:start position:0%
+you all it is to say I'm not that I I
+ 
+
+ align:start position:0%
+you all it is to say I'm not that I I
+planned where this has got where my my
+
+ align:start position:0%
+planned where this has got where my my
+ 
+
+ align:start position:0%
+planned where this has got where my my
+work has gone but it it's always my grad
+
+ align:start position:0%
+work has gone but it it's always my grad
+ 
+
+ align:start position:0%
+work has gone but it it's always my grad
+always moved and shifted to new it's
+
+ align:start position:0%
+always moved and shifted to new it's
+ 
+
+ align:start position:0%
+always moved and shifted to new it's
+almost like water water finds its own
+
+ align:start position:0%
+almost like water water finds its own
+ 
+
+ align:start position:0%
+almost like water water finds its own
+level right water fills the this the the
+
+ align:start position:0%
+level right water fills the this the the
+ 
+
+ align:start position:0%
+level right water fills the this the the
+vessel in which it's poured but I've
+
+ align:start position:0%
+vessel in which it's poured but I've
+ 
+
+ align:start position:0%
+vessel in which it's poured but I've
+never lost the clay I've never lost that
+
+ align:start position:0%
+never lost the clay I've never lost that
+ 
+
+ align:start position:0%
+never lost the clay I've never lost that
+notion of making or the ways that
+
+ align:start position:0%
+notion of making or the ways that
+ 
+
+ align:start position:0%
+notion of making or the ways that
+meanings can be made and understandings
+
+ align:start position:0%
+meanings can be made and understandings
+ 
+
+ align:start position:0%
+meanings can be made and understandings
+can be constructed through engagement
+
+ align:start position:0%
+can be constructed through engagement
+ 
+
+ align:start position:0%
+can be constructed through engagement
+with other people that's what education
+
+ align:start position:0%
+with other people that's what education
+ 
+
+ align:start position:0%
+with other people that's what education
+is it's a social space teaching and
+
+ align:start position:0%
+is it's a social space teaching and
+ 
+
+ align:start position:0%
+is it's a social space teaching and
+learning is a social space aren't
+
+ align:start position:0%
+learning is a social space aren't
+ 
+
+ align:start position:0%
+learning is a social space aren't
+education can take up and take on those
+
+ align:start position:0%
+education can take up and take on those
+ 
+
+ align:start position:0%
+education can take up and take on those
+those tasks as well the title for this
+
+ align:start position:0%
+those tasks as well the title for this
+ 
+
+ align:start position:0%
+those tasks as well the title for this
+visit that people have seen and that you
+
+ align:start position:0%
+visit that people have seen and that you
+ 
+
+ align:start position:0%
+visit that people have seen and that you
+gave us is making something from nothing
+
+ align:start position:0%
+gave us is making something from nothing
+ 
+
+ align:start position:0%
+gave us is making something from nothing
+and first of all sort of there's
+
+ align:start position:0%
+and first of all sort of there's
+ 
+
+ align:start position:0%
+and first of all sort of there's
+immediately doubt about whether you can
+
+ align:start position:0%
+immediately doubt about whether you can
+ 
+
+ align:start position:0%
+immediately doubt about whether you can
+actually make I mean you can transform
+
+ align:start position:0%
+actually make I mean you can transform
+ 
+
+ align:start position:0%
+actually make I mean you can transform
+things but the notion that you can make
+
+ align:start position:0%
+things but the notion that you can make
+ 
+
+ align:start position:0%
+things but the notion that you can make
+something out of nothing would sort of
+
+ align:start position:0%
+something out of nothing would sort of
+ 
+
+ align:start position:0%
+something out of nothing would sort of
+defy most of the laws of physics
+
+ align:start position:0%
+defy most of the laws of physics
+ 
+
+ align:start position:0%
+defy most of the laws of physics
+presumably and so you mean something by
+
+ align:start position:0%
+presumably and so you mean something by
+ 
+
+ align:start position:0%
+presumably and so you mean something by
+that and then appropriate technology as
+
+ align:start position:0%
+that and then appropriate technology as
+ 
+
+ align:start position:0%
+that and then appropriate technology as
+intentionally disruptive
+
+ align:start position:0%
+intentionally disruptive
+ 
+
+ align:start position:0%
+intentionally disruptive
+responsibilities
+
+ align:start position:0%
+responsibilities
+ 
+
+ align:start position:0%
+responsibilities
+yeah that is a mouthful that title isn't
+
+ align:start position:0%
+yeah that is a mouthful that title isn't
+ 
+
+ align:start position:0%
+yeah that is a mouthful that title isn't
+I actually had a lot of trouble with it
+
+ align:start position:0%
+I actually had a lot of trouble with it
+ 
+
+ align:start position:0%
+I actually had a lot of trouble with it
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+to the left of the colon making
+
+ align:start position:0%
+to the left of the colon making
+ 
+
+ align:start position:0%
+to the left of the colon making
+something from nothing
+
+ align:start position:0%
+something from nothing
+ 
+
+ align:start position:0%
+something from nothing
+that piece was intentionally provocative
+
+ align:start position:0%
+that piece was intentionally provocative
+ 
+
+ align:start position:0%
+that piece was intentionally provocative
+right I mean you kind of have to do that
+
+ align:start position:0%
+right I mean you kind of have to do that
+ 
+
+ align:start position:0%
+right I mean you kind of have to do that
+in some ways to entice folks to show up
+
+ align:start position:0%
+in some ways to entice folks to show up
+ 
+
+ align:start position:0%
+in some ways to entice folks to show up
+to certain things maybe but the idea of
+
+ align:start position:0%
+to certain things maybe but the idea of
+ 
+
+ align:start position:0%
+to certain things maybe but the idea of
+making of course you know defying laws
+
+ align:start position:0%
+making of course you know defying laws
+ 
+
+ align:start position:0%
+making of course you know defying laws
+of physics yeah I'm with you so no you
+
+ align:start position:0%
+of physics yeah I'm with you so no you
+ 
+
+ align:start position:0%
+of physics yeah I'm with you so no you
+know knowing that there's a problem with
+
+ align:start position:0%
+know knowing that there's a problem with
+ 
+
+ align:start position:0%
+know knowing that there's a problem with
+with that if we think of it in certain
+
+ align:start position:0%
+with that if we think of it in certain
+ 
+
+ align:start position:0%
+with that if we think of it in certain
+realms the idea that there are some
+
+ align:start position:0%
+realms the idea that there are some
+ 
+
+ align:start position:0%
+realms the idea that there are some
+folks who don't necessarily have access
+
+ align:start position:0%
+folks who don't necessarily have access
+ 
+
+ align:start position:0%
+folks who don't necessarily have access
+it's about access maybe it should have
+
+ align:start position:0%
+it's about access maybe it should have
+ 
+
+ align:start position:0%
+it's about access maybe it should have
+said you know making something from
+
+ align:start position:0%
+said you know making something from
+ 
+
+ align:start position:0%
+said you know making something from
+whatever it is that you have right but
+
+ align:start position:0%
+whatever it is that you have right but
+ 
+
+ align:start position:0%
+whatever it is that you have right but
+if we move it to nothing you start to
+
+ align:start position:0%
+if we move it to nothing you start to
+ 
+
+ align:start position:0%
+if we move it to nothing you start to
+think well there's a there's a there's a
+
+ align:start position:0%
+think well there's a there's a there's a
+ 
+
+ align:start position:0%
+think well there's a there's a there's a
+complete and utter lack of something
+
+ align:start position:0%
+complete and utter lack of something
+ 
+
+ align:start position:0%
+complete and utter lack of something
+for example there's some people who have
+
+ align:start position:0%
+for example there's some people who have
+ 
+
+ align:start position:0%
+for example there's some people who have
+no access to clean water we can raise a
+
+ align:start position:0%
+no access to clean water we can raise a
+ 
+
+ align:start position:0%
+no access to clean water we can raise a
+bit of hyperbole there and say they
+
+ align:start position:0%
+bit of hyperbole there and say they
+ 
+
+ align:start position:0%
+bit of hyperbole there and say they
+don't have access or they have nothing
+
+ align:start position:0%
+don't have access or they have nothing
+ 
+
+ align:start position:0%
+don't have access or they have nothing
+there folks you know who we talk about
+
+ align:start position:0%
+there folks you know who we talk about
+ 
+
+ align:start position:0%
+there folks you know who we talk about
+food scarcity we talk about folks who
+
+ align:start position:0%
+food scarcity we talk about folks who
+ 
+
+ align:start position:0%
+food scarcity we talk about folks who
+homeless folks who need shelter I mean
+
+ align:start position:0%
+homeless folks who need shelter I mean
+ 
+
+ align:start position:0%
+homeless folks who need shelter I mean
+so you can take minimum and exaggerate
+
+ align:start position:0%
+so you can take minimum and exaggerate
+ 
+
+ align:start position:0%
+so you can take minimum and exaggerate
+it just a little bit more right it was
+
+ align:start position:0%
+it just a little bit more right it was
+ 
+
+ align:start position:0%
+it just a little bit more right it was
+something called artistic license let's
+
+ align:start position:0%
+something called artistic license let's
+ 
+
+ align:start position:0%
+something called artistic license let's
+let's use that and turn it into nothing
+
+ align:start position:0%
+let's use that and turn it into nothing
+ 
+
+ align:start position:0%
+let's use that and turn it into nothing
+so making something from nothing what
+
+ align:start position:0%
+so making something from nothing what
+ 
+
+ align:start position:0%
+so making something from nothing what
+can we make from what is available to us
+
+ align:start position:0%
+can we make from what is available to us
+ 
+
+ align:start position:0%
+can we make from what is available to us
+so that's the something from nothing and
+
+ align:start position:0%
+so that's the something from nothing and
+ 
+
+ align:start position:0%
+so that's the something from nothing and
+in in the case of this first visit but
+
+ align:start position:0%
+in in the case of this first visit but
+ 
+
+ align:start position:0%
+in in the case of this first visit but
+something is adequate access to clean
+
+ align:start position:0%
+something is adequate access to clean
+ 
+
+ align:start position:0%
+something is adequate access to clean
+water and then nothing is the lack of
+
+ align:start position:0%
+water and then nothing is the lack of
+ 
+
+ align:start position:0%
+water and then nothing is the lack of
+that and the something is a response
+
+ align:start position:0%
+that and the something is a response
+ 
+
+ align:start position:0%
+that and the something is a response
+which would in this case is a ceramic
+
+ align:start position:0%
+which would in this case is a ceramic
+ 
+
+ align:start position:0%
+which would in this case is a ceramic
+water filter made out of clay and
+
+ align:start position:0%
+water filter made out of clay and
+ 
+
+ align:start position:0%
+water filter made out of clay and
+sawdust the nothing is well that's just
+
+ align:start position:0%
+sawdust the nothing is well that's just
+ 
+
+ align:start position:0%
+sawdust the nothing is well that's just
+clay it's it's just in the riverbed
+
+ align:start position:0%
+clay it's it's just in the riverbed
+ 
+
+ align:start position:0%
+clay it's it's just in the riverbed
+that's that's nothing or let's just
+
+ align:start position:0%
+that's that's nothing or let's just
+ 
+
+ align:start position:0%
+that's that's nothing or let's just
+sawdust that's leftover scraps then
+
+ align:start position:0%
+sawdust that's leftover scraps then
+ 
+
+ align:start position:0%
+sawdust that's leftover scraps then
+that's nothing right you see you
+
+ align:start position:0%
+that's nothing right you see you
+ 
+
+ align:start position:0%
+that's nothing right you see you
+understand that play that's going there
+
+ align:start position:0%
+understand that play that's going there
+ 
+
+ align:start position:0%
+understand that play that's going there
+appropriate technology is essentially
+
+ align:start position:0%
+appropriate technology is essentially
+ 
+
+ align:start position:0%
+appropriate technology is essentially
+whatever is available culturally and
+
+ align:start position:0%
+whatever is available culturally and
+ 
+
+ align:start position:0%
+whatever is available culturally and
+locally that fits in with this within
+
+ align:start position:0%
+locally that fits in with this within
+ 
+
+ align:start position:0%
+locally that fits in with this within
+the cultural practices of of a community
+
+ align:start position:0%
+the cultural practices of of a community
+ 
+
+ align:start position:0%
+the cultural practices of of a community
+introducing an external or an unfamiliar
+
+ align:start position:0%
+introducing an external or an unfamiliar
+ 
+
+ align:start position:0%
+introducing an external or an unfamiliar
+substance or chemical or food is not
+
+ align:start position:0%
+substance or chemical or food is not
+ 
+
+ align:start position:0%
+substance or chemical or food is not
+appropriate to certain community because
+
+ align:start position:0%
+appropriate to certain community because
+ 
+
+ align:start position:0%
+appropriate to certain community because
+it's either against one's religion it's
+
+ align:start position:0%
+it's either against one's religion it's
+ 
+
+ align:start position:0%
+it's either against one's religion it's
+against one's history against one's
+
+ align:start position:0%
+against one's history against one's
+ 
+
+ align:start position:0%
+against one's history against one's
+culture it
+
+ align:start position:0%
+culture it
+ 
+
+ align:start position:0%
+culture it
+doesn't fit in so finding something
+
+ align:start position:0%
+doesn't fit in so finding something
+ 
+
+ align:start position:0%
+doesn't fit in so finding something
+that's appropriate for example clay is
+
+ align:start position:0%
+that's appropriate for example clay is
+ 
+
+ align:start position:0%
+that's appropriate for example clay is
+essentially a material that is
+
+ align:start position:0%
+essentially a material that is
+ 
+
+ align:start position:0%
+essentially a material that is
+accessible to almost every single
+
+ align:start position:0%
+accessible to almost every single
+ 
+
+ align:start position:0%
+accessible to almost every single
+culture in the history of this of the
+
+ align:start position:0%
+culture in the history of this of the
+ 
+
+ align:start position:0%
+culture in the history of this of the
+world and clay is a natural naturally
+
+ align:start position:0%
+world and clay is a natural naturally
+ 
+
+ align:start position:0%
+world and clay is a natural naturally
+occurring material in most places around
+
+ align:start position:0%
+occurring material in most places around
+ 
+
+ align:start position:0%
+occurring material in most places around
+the world in some places using plastic
+
+ align:start position:0%
+the world in some places using plastic
+ 
+
+ align:start position:0%
+the world in some places using plastic
+oh that doesn't seem to make sense or
+
+ align:start position:0%
+oh that doesn't seem to make sense or
+ 
+
+ align:start position:0%
+oh that doesn't seem to make sense or
+appropriate technology is using what is
+
+ align:start position:0%
+appropriate technology is using what is
+ 
+
+ align:start position:0%
+appropriate technology is using what is
+that hand philosopher theorist Umberto
+
+ align:start position:0%
+that hand philosopher theorist Umberto
+ 
+
+ align:start position:0%
+that hand philosopher theorist Umberto
+Eco he was a guy who knew everything but
+
+ align:start position:0%
+Eco he was a guy who knew everything but
+ 
+
+ align:start position:0%
+Eco he was a guy who knew everything but
+he didn't know it echo had numerous
+
+ align:start position:0%
+he didn't know it echo had numerous
+ 
+
+ align:start position:0%
+he didn't know it echo had numerous
+theories among them where these in
+
+ align:start position:0%
+theories among them where these in
+ 
+
+ align:start position:0%
+theories among them where these in
+theory of intentions he says that the
+
+ align:start position:0%
+theory of intentions he says that the
+ 
+
+ align:start position:0%
+theory of intentions he says that the
+artist or the author has an intention
+
+ align:start position:0%
+artist or the author has an intention
+ 
+
+ align:start position:0%
+artist or the author has an intention
+and the viewer or the reader has an
+
+ align:start position:0%
+and the viewer or the reader has an
+ 
+
+ align:start position:0%
+and the viewer or the reader has an
+intention but he also says the work has
+
+ align:start position:0%
+intention but he also says the work has
+ 
+
+ align:start position:0%
+intention but he also says the work has
+an intention that comes about through
+
+ align:start position:0%
+an intention that comes about through
+ 
+
+ align:start position:0%
+an intention that comes about through
+the rest process or a series of events
+
+ align:start position:0%
+the rest process or a series of events
+ 
+
+ align:start position:0%
+the rest process or a series of events
+but this idea of having an intention
+
+ align:start position:0%
+but this idea of having an intention
+ 
+
+ align:start position:0%
+but this idea of having an intention
+means it's deliberate so I'm interested
+
+ align:start position:0%
+means it's deliberate so I'm interested
+ 
+
+ align:start position:0%
+means it's deliberate so I'm interested
+in in in thinking about why we're doing
+
+ align:start position:0%
+in in in thinking about why we're doing
+ 
+
+ align:start position:0%
+in in in thinking about why we're doing
+what we're doing that's that's where
+
+ align:start position:0%
+what we're doing that's that's where
+ 
+
+ align:start position:0%
+what we're doing that's that's where
+that intentional piece disruptive you
+
+ align:start position:0%
+that intentional piece disruptive you
+ 
+
+ align:start position:0%
+that intentional piece disruptive you
+know if I pick this up and I threw this
+
+ align:start position:0%
+know if I pick this up and I threw this
+ 
+
+ align:start position:0%
+know if I pick this up and I threw this
+water at the camera that would be
+
+ align:start position:0%
+water at the camera that would be
+ 
+
+ align:start position:0%
+water at the camera that would be
+disruptive in a number of rays or if
+
+ align:start position:0%
+disruptive in a number of rays or if
+ 
+
+ align:start position:0%
+disruptive in a number of rays or if
+you're in a you know in a quiet library
+
+ align:start position:0%
+you're in a you know in a quiet library
+ 
+
+ align:start position:0%
+you're in a you know in a quiet library
+and a stampede of aardvarks comes
+
+ align:start position:0%
+and a stampede of aardvarks comes
+ 
+
+ align:start position:0%
+and a stampede of aardvarks comes
+through the space that's disruption
+
+ align:start position:0%
+through the space that's disruption
+ 
+
+ align:start position:0%
+through the space that's disruption
+right so we understand disruption is
+
+ align:start position:0%
+right so we understand disruption is
+ 
+
+ align:start position:0%
+right so we understand disruption is
+something that is abnormal or not
+
+ align:start position:0%
+something that is abnormal or not
+ 
+
+ align:start position:0%
+something that is abnormal or not
+expected within a particular context
+
+ align:start position:0%
+expected within a particular context
+ 
+
+ align:start position:0%
+expected within a particular context
+that has assumed rules regulations and
+
+ align:start position:0%
+that has assumed rules regulations and
+ 
+
+ align:start position:0%
+that has assumed rules regulations and
+ways of being but I'm also thinking of a
+
+ align:start position:0%
+ways of being but I'm also thinking of a
+ 
+
+ align:start position:0%
+ways of being but I'm also thinking of a
+disruption in the intentional sense of
+
+ align:start position:0%
+disruption in the intentional sense of
+ 
+
+ align:start position:0%
+disruption in the intentional sense of
+to reveal or to poke at or to engage or
+
+ align:start position:0%
+to reveal or to poke at or to engage or
+ 
+
+ align:start position:0%
+to reveal or to poke at or to engage or
+to entice a certain kind of conversation
+
+ align:start position:0%
+to entice a certain kind of conversation
+ 
+
+ align:start position:0%
+to entice a certain kind of conversation
+or relationship and that kind of
+
+ align:start position:0%
+or relationship and that kind of
+ 
+
+ align:start position:0%
+or relationship and that kind of
+conversation relationship is the
+
+ align:start position:0%
+conversation relationship is the
+ 
+
+ align:start position:0%
+conversation relationship is the
+responsibility would you agree that most
+
+ align:start position:0%
+responsibility would you agree that most
+ 
+
+ align:start position:0%
+responsibility would you agree that most
+educational efforts are disruptions
+
+ align:start position:0%
+educational efforts are disruptions
+ 
+
+ align:start position:0%
+educational efforts are disruptions
+aimed at fulfilling a responsibility
+
+ align:start position:0%
+aimed at fulfilling a responsibility
+ 
+
+ align:start position:0%
+aimed at fulfilling a responsibility
+that is defining education that way I
+
+ align:start position:0%
+that is defining education that way I
+ 
+
+ align:start position:0%
+that is defining education that way I
+don't think enough of them are oh you
+
+ align:start position:0%
+don't think enough of them are oh you
+ 
+
+ align:start position:0%
+don't think enough of them are oh you
+think they should be I think they should
+
+ align:start position:0%
+think they should be I think they should
+ 
+
+ align:start position:0%
+think they should be I think they should
+I like to shift that up and question
+
+ align:start position:0%
+I like to shift that up and question
+ 
+
+ align:start position:0%
+I like to shift that up and question
+that and then there's there's it's it's
+
+ align:start position:0%
+that and then there's there's it's it's
+ 
+
+ align:start position:0%
+that and then there's there's it's it's
+very difficult to to get at new ways of
+
+ align:start position:0%
+very difficult to to get at new ways of
+ 
+
+ align:start position:0%
+very difficult to to get at new ways of
+doing something without disrupting a
+
+ align:start position:0%
+doing something without disrupting a
+ 
+
+ align:start position:0%
+doing something without disrupting a
+status quo without without questioning
+
+ align:start position:0%
+status quo without without questioning
+ 
+
+ align:start position:0%
+status quo without without questioning
+it we say it's because we're responsible
+
+ align:start position:0%
+it we say it's because we're responsible
+ 
+
+ align:start position:0%
+it we say it's because we're responsible
+and we have to disrupt but what about
+
+ align:start position:0%
+and we have to disrupt but what about
+ 
+
+ align:start position:0%
+and we have to disrupt but what about
+the choice of the people and the place
+
+ align:start position:0%
+the choice of the people and the place
+ 
+
+ align:start position:0%
+the choice of the people and the place
+whose lives you're disrupting is that
+
+ align:start position:0%
+whose lives you're disrupting is that
+ 
+
+ align:start position:0%
+whose lives you're disrupting is that
+fair to them sure yeah no certainly the
+
+ align:start position:0%
+fair to them sure yeah no certainly the
+ 
+
+ align:start position:0%
+fair to them sure yeah no certainly the
+way you frame it it's not fair to them
+
+ align:start position:0%
+way you frame it it's not fair to them
+ 
+
+ align:start position:0%
+way you frame it it's not fair to them
+but in the disruption of the lives of
+
+ align:start position:0%
+but in the disruption of the lives of
+ 
+
+ align:start position:0%
+but in the disruption of the lives of
+the communities that are mentioned in
+
+ align:start position:0%
+the communities that are mentioned in
+ 
+
+ align:start position:0%
+the communities that are mentioned in
+Texas it's not disrupting uninvited
+
+ align:start position:0%
+Texas it's not disrupting uninvited
+ 
+
+ align:start position:0%
+Texas it's not disrupting uninvited
+it's an invited disruption and second
+
+ align:start position:0%
+it's an invited disruption and second
+ 
+
+ align:start position:0%
+it's an invited disruption and second
+the disruption has to do with whatever
+
+ align:start position:0%
+the disruption has to do with whatever
+ 
+
+ align:start position:0%
+the disruption has to do with whatever
+the current practice was new was not
+
+ align:start position:0%
+the current practice was new was not
+ 
+
+ align:start position:0%
+the current practice was new was not
+fulfilling or were responding to needs
+
+ align:start position:0%
+fulfilling or were responding to needs
+ 
+
+ align:start position:0%
+fulfilling or were responding to needs
+of the community in in their eyes and in
+
+ align:start position:0%
+of the community in in their eyes and in
+ 
+
+ align:start position:0%
+of the community in in their eyes and in
+you know to my eyes as well so my friend
+
+ align:start position:0%
+you know to my eyes as well so my friend
+ 
+
+ align:start position:0%
+you know to my eyes as well so my friend
+as I mentioned Oscar who for years has
+
+ align:start position:0%
+as I mentioned Oscar who for years has
+ 
+
+ align:start position:0%
+as I mentioned Oscar who for years has
+been working in throughout South Texas
+
+ align:start position:0%
+been working in throughout South Texas
+ 
+
+ align:start position:0%
+been working in throughout South Texas
+when he learned to the work I was that I
+
+ align:start position:0%
+when he learned to the work I was that I
+ 
+
+ align:start position:0%
+when he learned to the work I was that I
+was you know at that point still
+
+ align:start position:0%
+was you know at that point still
+ 
+
+ align:start position:0%
+was you know at that point still
+learning how to do he said oh there's
+
+ align:start position:0%
+learning how to do he said oh there's
+ 
+
+ align:start position:0%
+learning how to do he said oh there's
+there's a water issue would you come
+
+ align:start position:0%
+there's a water issue would you come
+ 
+
+ align:start position:0%
+there's a water issue would you come
+down and work with us we talked to us
+
+ align:start position:0%
+down and work with us we talked to us
+ 
+
+ align:start position:0%
+down and work with us we talked to us
+let's see if this would work out that
+
+ align:start position:0%
+let's see if this would work out that
+ 
+
+ align:start position:0%
+let's see if this would work out that
+was my invitation to come in Oscar was
+
+ align:start position:0%
+was my invitation to come in Oscar was
+ 
+
+ align:start position:0%
+was my invitation to come in Oscar was
+already part of that community I would
+
+ align:start position:0%
+already part of that community I would
+ 
+
+ align:start position:0%
+already part of that community I would
+never imagine just driving down there
+
+ align:start position:0%
+never imagine just driving down there
+ 
+
+ align:start position:0%
+never imagine just driving down there
+driving to any community and say hey
+
+ align:start position:0%
+driving to any community and say hey
+ 
+
+ align:start position:0%
+driving to any community and say hey
+Dyke if something you need I'm gonna
+
+ align:start position:0%
+Dyke if something you need I'm gonna
+ 
+
+ align:start position:0%
+Dyke if something you need I'm gonna
+sell you something that's not my
+
+ align:start position:0%
+sell you something that's not my
+ 
+
+ align:start position:0%
+sell you something that's not my
+approach and so that kind of disruption
+
+ align:start position:0%
+approach and so that kind of disruption
+ 
+
+ align:start position:0%
+approach and so that kind of disruption
+I think is on the the unethical side he
+
+ align:start position:0%
+I think is on the the unethical side he
+ 
+
+ align:start position:0%
+I think is on the the unethical side he
+was a bit wary of someone coming in and
+
+ align:start position:0%
+was a bit wary of someone coming in and
+ 
+
+ align:start position:0%
+was a bit wary of someone coming in and
+he's shared and other people have shared
+
+ align:start position:0%
+he's shared and other people have shared
+ 
+
+ align:start position:0%
+he's shared and other people have shared
+stories with me of researchers going
+
+ align:start position:0%
+stories with me of researchers going
+ 
+
+ align:start position:0%
+stories with me of researchers going
+into communities oh yeah I have this
+
+ align:start position:0%
+into communities oh yeah I have this
+ 
+
+ align:start position:0%
+into communities oh yeah I have this
+ideas let me study what you're doing let
+
+ align:start position:0%
+ideas let me study what you're doing let
+ 
+
+ align:start position:0%
+ideas let me study what you're doing let
+me work with you and they take the
+
+ align:start position:0%
+me work with you and they take the
+ 
+
+ align:start position:0%
+me work with you and they take the
+information and there's a report that's
+
+ align:start position:0%
+information and there's a report that's
+ 
+
+ align:start position:0%
+information and there's a report that's
+promised and the report never gets back
+
+ align:start position:0%
+promised and the report never gets back
+ 
+
+ align:start position:0%
+promised and the report never gets back
+to the communities or the results never
+
+ align:start position:0%
+to the communities or the results never
+ 
+
+ align:start position:0%
+to the communities or the results never
+never help and he said he has never he
+
+ align:start position:0%
+never help and he said he has never he
+ 
+
+ align:start position:0%
+never help and he said he has never he
+had never seen a report come back based
+
+ align:start position:0%
+had never seen a report come back based
+ 
+
+ align:start position:0%
+had never seen a report come back based
+on the invitations to the scholars and
+
+ align:start position:0%
+on the invitations to the scholars and
+ 
+
+ align:start position:0%
+on the invitations to the scholars and
+so once we got to know each other he
+
+ align:start position:0%
+so once we got to know each other he
+ 
+
+ align:start position:0%
+so once we got to know each other he
+felt comfortable with me so but then he
+
+ align:start position:0%
+felt comfortable with me so but then he
+ 
+
+ align:start position:0%
+felt comfortable with me so but then he
+had to go through a process of talking
+
+ align:start position:0%
+had to go through a process of talking
+ 
+
+ align:start position:0%
+had to go through a process of talking
+with members of the community to say hey
+
+ align:start position:0%
+with members of the community to say hey
+ 
+
+ align:start position:0%
+with members of the community to say hey
+here's you know have this friend coming
+
+ align:start position:0%
+here's you know have this friend coming
+ 
+
+ align:start position:0%
+here's you know have this friend coming
+down that's the invitation is the
+
+ align:start position:0%
+down that's the invitation is the
+ 
+
+ align:start position:0%
+down that's the invitation is the
+invitation pieces so what is an
+
+ align:start position:0%
+invitation pieces so what is an
+ 
+
+ align:start position:0%
+invitation pieces so what is an
+invitation have to consist of for you to
+
+ align:start position:0%
+invitation have to consist of for you to
+ 
+
+ align:start position:0%
+invitation have to consist of for you to
+be of a sort that you're comfortable
+
+ align:start position:0%
+be of a sort that you're comfortable
+ 
+
+ align:start position:0%
+be of a sort that you're comfortable
+then responding in this rich disruptive
+
+ align:start position:0%
+then responding in this rich disruptive
+ 
+
+ align:start position:0%
+then responding in this rich disruptive
+way you need a vote of the community has
+
+ align:start position:0%
+way you need a vote of the community has
+ 
+
+ align:start position:0%
+way you need a vote of the community has
+to be 100 percent majority rule people
+
+ align:start position:0%
+to be 100 percent majority rule people
+ 
+
+ align:start position:0%
+to be 100 percent majority rule people
+you like say come on down
+
+ align:start position:0%
+you like say come on down
+ 
+
+ align:start position:0%
+you like say come on down
+what what is in your mind about what
+
+ align:start position:0%
+what what is in your mind about what
+ 
+
+ align:start position:0%
+what what is in your mind about what
+legitimizes these kinds of disruptions
+
+ align:start position:0%
+legitimizes these kinds of disruptions
+ 
+
+ align:start position:0%
+legitimizes these kinds of disruptions
+again it has to be that imitation from
+
+ align:start position:0%
+again it has to be that imitation from
+ 
+
+ align:start position:0%
+again it has to be that imitation from
+someone who is positioned within the
+
+ align:start position:0%
+someone who is positioned within the
+ 
+
+ align:start position:0%
+someone who is positioned within the
+community then there has to be for me a
+
+ align:start position:0%
+community then there has to be for me a
+ 
+
+ align:start position:0%
+community then there has to be for me a
+conversation and and so no the entire
+
+ align:start position:0%
+conversation and and so no the entire
+ 
+
+ align:start position:0%
+conversation and and so no the entire
+community because defining who is in the
+
+ align:start position:0%
+community because defining who is in the
+ 
+
+ align:start position:0%
+community because defining who is in the
+community is often difficult to do
+
+ align:start position:0%
+community is often difficult to do
+ 
+
+ align:start position:0%
+community is often difficult to do
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+certainly it's it's often just a leader
+
+ align:start position:0%
+certainly it's it's often just a leader
+ 
+
+ align:start position:0%
+certainly it's it's often just a leader
+or some member of the community who
+
+ align:start position:0%
+or some member of the community who
+ 
+
+ align:start position:0%
+or some member of the community who
+might want to engage a conversation that
+
+ align:start position:0%
+might want to engage a conversation that
+ 
+
+ align:start position:0%
+might want to engage a conversation that
+that then might expand in their own
+
+ align:start position:0%
+that then might expand in their own
+ 
+
+ align:start position:0%
+that then might expand in their own
+circles in this particular case in Texas
+
+ align:start position:0%
+circles in this particular case in Texas
+ 
+
+ align:start position:0%
+circles in this particular case in Texas
+through my colleague we met with a few
+
+ align:start position:0%
+through my colleague we met with a few
+ 
+
+ align:start position:0%
+through my colleague we met with a few
+leaders people who had worked within the
+
+ align:start position:0%
+leaders people who had worked within the
+ 
+
+ align:start position:0%
+leaders people who had worked within the
+communities as promotoras as community
+
+ align:start position:0%
+communities as promotoras as community
+ 
+
+ align:start position:0%
+communities as promotoras as community
+educators and and other senior members
+
+ align:start position:0%
+educators and and other senior members
+ 
+
+ align:start position:0%
+educators and and other senior members
+of the community
+
+ align:start position:0%
+of the community
+ 
+
+ align:start position:0%
+of the community
+a senior meeting they had been doing
+
+ align:start position:0%
+a senior meeting they had been doing
+ 
+
+ align:start position:0%
+a senior meeting they had been doing
+work at the community centers and it was
+
+ align:start position:0%
+work at the community centers and it was
+ 
+
+ align:start position:0%
+work at the community centers and it was
+let's just talk let's see where the
+
+ align:start position:0%
+let's just talk let's see where the
+ 
+
+ align:start position:0%
+let's just talk let's see where the
+conversation goes very much like what
+
+ align:start position:0%
+conversation goes very much like what
+ 
+
+ align:start position:0%
+conversation goes very much like what
+we're doing here having having a
+
+ align:start position:0%
+we're doing here having having a
+ 
+
+ align:start position:0%
+we're doing here having having a
+conversation now it's not my role or
+
+ align:start position:0%
+conversation now it's not my role or
+ 
+
+ align:start position:0%
+conversation now it's not my role or
+position or personality or interest to
+
+ align:start position:0%
+position or personality or interest to
+ 
+
+ align:start position:0%
+position or personality or interest to
+push that after that conversation that's
+
+ align:start position:0%
+push that after that conversation that's
+ 
+
+ align:start position:0%
+push that after that conversation that's
+on that's on whomever to to take that up
+
+ align:start position:0%
+on that's on whomever to to take that up
+ 
+
+ align:start position:0%
+on that's on whomever to to take that up
+so when I speak of community it's it's
+
+ align:start position:0%
+so when I speak of community it's it's
+ 
+
+ align:start position:0%
+so when I speak of community it's it's
+it's not the entirety there's not a
+
+ align:start position:0%
+it's not the entirety there's not a
+ 
+
+ align:start position:0%
+it's not the entirety there's not a
+simple answer in this we all struggle
+
+ align:start position:0%
+simple answer in this we all struggle
+ 
+
+ align:start position:0%
+simple answer in this we all struggle
+with this notion of the artist as the
+
+ align:start position:0%
+with this notion of the artist as the
+ 
+
+ align:start position:0%
+with this notion of the artist as the
+independent thinker as a creator of
+
+ align:start position:0%
+independent thinker as a creator of
+ 
+
+ align:start position:0%
+independent thinker as a creator of
+something that's an expression of an
+
+ align:start position:0%
+something that's an expression of an
+ 
+
+ align:start position:0%
+something that's an expression of an
+individual view when you're calling this
+
+ align:start position:0%
+individual view when you're calling this
+ 
+
+ align:start position:0%
+individual view when you're calling this
+a form of art education but isn't it
+
+ align:start position:0%
+a form of art education but isn't it
+ 
+
+ align:start position:0%
+a form of art education but isn't it
+contrary to artists being artists how
+
+ align:start position:0%
+contrary to artists being artists how
+ 
+
+ align:start position:0%
+contrary to artists being artists how
+was it art yeah so that's not a small
+
+ align:start position:0%
+was it art yeah so that's not a small
+ 
+
+ align:start position:0%
+was it art yeah so that's not a small
+question but it's a very important
+
+ align:start position:0%
+question but it's a very important
+ 
+
+ align:start position:0%
+question but it's a very important
+question it's a central question that
+
+ align:start position:0%
+question it's a central question that
+ 
+
+ align:start position:0%
+question it's a central question that
+I'm still answering for myself but there
+
+ align:start position:0%
+I'm still answering for myself but there
+ 
+
+ align:start position:0%
+I'm still answering for myself but there
+are three realms here one is the work in
+
+ align:start position:0%
+are three realms here one is the work in
+ 
+
+ align:start position:0%
+are three realms here one is the work in
+South Texas that I actually wouldn't
+
+ align:start position:0%
+South Texas that I actually wouldn't
+ 
+
+ align:start position:0%
+South Texas that I actually wouldn't
+call that art or art education okay
+
+ align:start position:0%
+call that art or art education okay
+ 
+
+ align:start position:0%
+call that art or art education okay
+second is the kind of work that I will
+
+ align:start position:0%
+second is the kind of work that I will
+ 
+
+ align:start position:0%
+second is the kind of work that I will
+do tomorrow the performance and that
+
+ align:start position:0%
+do tomorrow the performance and that
+ 
+
+ align:start position:0%
+do tomorrow the performance and that
+moves into the realm of the social
+
+ align:start position:0%
+moves into the realm of the social
+ 
+
+ align:start position:0%
+moves into the realm of the social
+practice and that's where I've I've come
+
+ align:start position:0%
+practice and that's where I've I've come
+ 
+
+ align:start position:0%
+practice and that's where I've I've come
+to an agreement understanding
+
+ align:start position:0%
+to an agreement understanding
+ 
+
+ align:start position:0%
+to an agreement understanding
+comfortable place with myself that
+
+ align:start position:0%
+comfortable place with myself that
+ 
+
+ align:start position:0%
+comfortable place with myself that
+that's where the art education happened
+
+ align:start position:0%
+that's where the art education happened
+ 
+
+ align:start position:0%
+that's where the art education happened
+and then this there's a third piece your
+
+ align:start position:0%
+and then this there's a third piece your
+ 
+
+ align:start position:0%
+and then this there's a third piece your
+definition of an artist and what an
+
+ align:start position:0%
+definition of an artist and what an
+ 
+
+ align:start position:0%
+definition of an artist and what an
+artist does that I want to disrupt down
+
+ align:start position:0%
+artist does that I want to disrupt down
+ 
+
+ align:start position:0%
+artist does that I want to disrupt down
+in South Texas that kind of work for me
+
+ align:start position:0%
+in South Texas that kind of work for me
+ 
+
+ align:start position:0%
+in South Texas that kind of work for me
+is not art education it certainly uses
+
+ align:start position:0%
+is not art education it certainly uses
+ 
+
+ align:start position:0%
+is not art education it certainly uses
+an employ certain artistic practices
+
+ align:start position:0%
+an employ certain artistic practices
+ 
+
+ align:start position:0%
+an employ certain artistic practices
+folks who have access to a kiln know how
+
+ align:start position:0%
+folks who have access to a kiln know how
+ 
+
+ align:start position:0%
+folks who have access to a kiln know how
+to fire kiln and have access to clay
+
+ align:start position:0%
+to fire kiln and have access to clay
+ 
+
+ align:start position:0%
+to fire kiln and have access to clay
+that's where you want to begin your work
+
+ align:start position:0%
+that's where you want to begin your work
+ 
+
+ align:start position:0%
+that's where you want to begin your work
+usually that's the the tile person or
+
+ align:start position:0%
+usually that's the the tile person or
+ 
+
+ align:start position:0%
+usually that's the the tile person or
+the the pot putter or it's the brick
+
+ align:start position:0%
+the the pot putter or it's the brick
+ 
+
+ align:start position:0%
+the the pot putter or it's the brick
+maker but my collaboration and myung
+
+ align:start position:0%
+maker but my collaboration and myung
+ 
+
+ align:start position:0%
+maker but my collaboration and myung
+involvement in that project I wouldn't
+
+ align:start position:0%
+involvement in that project I wouldn't
+ 
+
+ align:start position:0%
+involvement in that project I wouldn't
+call that art that was kind of me shed
+
+ align:start position:0%
+call that art that was kind of me shed
+ 
+
+ align:start position:0%
+call that art that was kind of me shed
+you know that that helps to clarify that
+
+ align:start position:0%
+you know that that helps to clarify that
+ 
+
+ align:start position:0%
+you know that that helps to clarify that
+piece of it so the work that I'm going
+
+ align:start position:0%
+piece of it so the work that I'm going
+ 
+
+ align:start position:0%
+piece of it so the work that I'm going
+to do I will do tomorrow I'm gonna set
+
+ align:start position:0%
+to do I will do tomorrow I'm gonna set
+ 
+
+ align:start position:0%
+to do I will do tomorrow I'm gonna set
+up a water filter production facility in
+
+ align:start position:0%
+up a water filter production facility in
+ 
+
+ align:start position:0%
+up a water filter production facility in
+one of the rooms downstairs and I'm
+
+ align:start position:0%
+one of the rooms downstairs and I'm
+ 
+
+ align:start position:0%
+one of the rooms downstairs and I'm
+gonna make water filters the idea there
+
+ align:start position:0%
+gonna make water filters the idea there
+ 
+
+ align:start position:0%
+gonna make water filters the idea there
+is to engage in a practice that somehow
+
+ align:start position:0%
+is to engage in a practice that somehow
+ 
+
+ align:start position:0%
+is to engage in a practice that somehow
+blurs what might be our conventional
+
+ align:start position:0%
+blurs what might be our conventional
+ 
+
+ align:start position:0%
+blurs what might be our conventional
+notions of art making art practice with
+
+ align:start position:0%
+notions of art making art practice with
+ 
+
+ align:start position:0%
+notions of art making art practice with
+practices from other disciplines we're
+
+ align:start position:0%
+practices from other disciplines we're
+ 
+
+ align:start position:0%
+practices from other disciplines we're
+not quite sure where one ends and one
+
+ align:start position:0%
+not quite sure where one ends and one
+ 
+
+ align:start position:0%
+not quite sure where one ends and one
+begins and it's supposed to remain in
+
+ align:start position:0%
+begins and it's supposed to remain in
+ 
+
+ align:start position:0%
+begins and it's supposed to remain in
+that uncomfortable space if one is
+
+ align:start position:0%
+that uncomfortable space if one is
+ 
+
+ align:start position:0%
+that uncomfortable space if one is
+thinking in that social practice art as
+
+ align:start position:0%
+thinking in that social practice art as
+ 
+
+ align:start position:0%
+thinking in that social practice art as
+social practice register if you can set
+
+ align:start position:0%
+social practice register if you can set
+ 
+
+ align:start position:0%
+social practice register if you can set
+up that practice as an engagement as an
+
+ align:start position:0%
+up that practice as an engagement as an
+ 
+
+ align:start position:0%
+up that practice as an engagement as an
+ongoing set of activities where people
+
+ align:start position:0%
+ongoing set of activities where people
+ 
+
+ align:start position:0%
+ongoing set of activities where people
+can come in and out of that space
+
+ align:start position:0%
+can come in and out of that space
+ 
+
+ align:start position:0%
+can come in and out of that space
+there's an educational component
+
+ align:start position:0%
+there's an educational component
+ 
+
+ align:start position:0%
+there's an educational component
+invariably there'll be a question hey
+
+ align:start position:0%
+invariably there'll be a question hey
+ 
+
+ align:start position:0%
+invariably there'll be a question hey
+man what are you doing that's an
+
+ align:start position:0%
+man what are you doing that's an
+ 
+
+ align:start position:0%
+man what are you doing that's an
+invitation right there for me to respond
+
+ align:start position:0%
+invitation right there for me to respond
+ 
+
+ align:start position:0%
+invitation right there for me to respond
+so we can establish this conversation as
+
+ align:start position:0%
+so we can establish this conversation as
+ 
+
+ align:start position:0%
+so we can establish this conversation as
+a relationship you're not creating art
+
+ align:start position:0%
+a relationship you're not creating art
+ 
+
+ align:start position:0%
+a relationship you're not creating art
+you're creating something that serves a
+
+ align:start position:0%
+you're creating something that serves a
+ 
+
+ align:start position:0%
+you're creating something that serves a
+function in response to the need of a
+
+ align:start position:0%
+function in response to the need of a
+ 
+
+ align:start position:0%
+function in response to the need of a
+client you're saying though it's not art
+
+ align:start position:0%
+client you're saying though it's not art
+ 
+
+ align:start position:0%
+client you're saying though it's not art
+I'm an artist and it's my social
+
+ align:start position:0%
+I'm an artist and it's my social
+ 
+
+ align:start position:0%
+I'm an artist and it's my social
+practice that you should observe here is
+
+ align:start position:0%
+practice that you should observe here is
+ 
+
+ align:start position:0%
+practice that you should observe here is
+art education but the product of my
+
+ align:start position:0%
+art education but the product of my
+ 
+
+ align:start position:0%
+art education but the product of my
+artwork is not art it's more than the
+
+ align:start position:0%
+artwork is not art it's more than the
+ 
+
+ align:start position:0%
+artwork is not art it's more than the
+filter itself that filter is just one
+
+ align:start position:0%
+filter itself that filter is just one
+ 
+
+ align:start position:0%
+filter itself that filter is just one
+component of the work the work being the
+
+ align:start position:0%
+component of the work the work being the
+ 
+
+ align:start position:0%
+component of the work the work being the
+performance education as experience this
+
+ align:start position:0%
+performance education as experience this
+ 
+
+ align:start position:0%
+performance education as experience this
+notion of experience is where the
+
+ align:start position:0%
+notion of experience is where the
+ 
+
+ align:start position:0%
+notion of experience is where the
+education happens for some of us the
+
+ align:start position:0%
+education happens for some of us the
+ 
+
+ align:start position:0%
+education happens for some of us the
+next step is oh and I want to help a
+
+ align:start position:0%
+next step is oh and I want to help a
+ 
+
+ align:start position:0%
+next step is oh and I want to help a
+place in Africa or Latin America in a
+
+ align:start position:0%
+place in Africa or Latin America in a
+ 
+
+ align:start position:0%
+place in Africa or Latin America in a
+community make a factory
+
+ align:start position:0%
+community make a factory
+ 
+
+ align:start position:0%
+community make a factory
+where there are people now without me
+
+ align:start position:0%
+where there are people now without me
+ 
+
+ align:start position:0%
+where there are people now without me
+they're capable of making more filters
+
+ align:start position:0%
+they're capable of making more filters
+ 
+
+ align:start position:0%
+they're capable of making more filters
+and maybe they can sell them for a small
+
+ align:start position:0%
+and maybe they can sell them for a small
+ 
+
+ align:start position:0%
+and maybe they can sell them for a small
+amount to be able to maintain them a
+
+ align:start position:0%
+amount to be able to maintain them a
+ 
+
+ align:start position:0%
+amount to be able to maintain them a
+community business the doing of all of
+
+ align:start position:0%
+community business the doing of all of
+ 
+
+ align:start position:0%
+community business the doing of all of
+that that seems to be a different realm
+
+ align:start position:0%
+that that seems to be a different realm
+ 
+
+ align:start position:0%
+that that seems to be a different realm
+it is yeah and I have not worked closely
+
+ align:start position:0%
+it is yeah and I have not worked closely
+ 
+
+ align:start position:0%
+it is yeah and I have not worked closely
+with communities as you're saying to set
+
+ align:start position:0%
+with communities as you're saying to set
+ 
+
+ align:start position:0%
+with communities as you're saying to set
+up facilities although and in South
+
+ align:start position:0%
+up facilities although and in South
+ 
+
+ align:start position:0%
+up facilities although and in South
+Texas I did I helped laid the groundwork
+
+ align:start position:0%
+Texas I did I helped laid the groundwork
+ 
+
+ align:start position:0%
+Texas I did I helped laid the groundwork
+and that facilities is working you saw
+
+ align:start position:0%
+and that facilities is working you saw
+ 
+
+ align:start position:0%
+and that facilities is working you saw
+pictures right but there are a number of
+
+ align:start position:0%
+pictures right but there are a number of
+ 
+
+ align:start position:0%
+pictures right but there are a number of
+groups who are doing the exact kind of
+
+ align:start position:0%
+groups who are doing the exact kind of
+ 
+
+ align:start position:0%
+groups who are doing the exact kind of
+work that you're mentioning and it's not
+
+ align:start position:0%
+work that you're mentioning and it's not
+ 
+
+ align:start position:0%
+work that you're mentioning and it's not
+from an arts or an art education
+
+ align:start position:0%
+from an arts or an art education
+ 
+
+ align:start position:0%
+from an arts or an art education
+perspective it is from that social
+
+ align:start position:0%
+perspective it is from that social
+ 
+
+ align:start position:0%
+perspective it is from that social
+entrepreneur realm that you're that
+
+ align:start position:0%
+entrepreneur realm that you're that
+ 
+
+ align:start position:0%
+entrepreneur realm that you're that
+you're talking about and I am very
+
+ align:start position:0%
+you're talking about and I am very
+ 
+
+ align:start position:0%
+you're talking about and I am very
+supportive of that piece and that is
+
+ align:start position:0%
+supportive of that piece and that is
+ 
+
+ align:start position:0%
+supportive of that piece and that is
+actually an intriguing component of what
+
+ align:start position:0%
+actually an intriguing component of what
+ 
+
+ align:start position:0%
+actually an intriguing component of what
+comes out of this this work it's that
+
+ align:start position:0%
+comes out of this this work it's that
+ 
+
+ align:start position:0%
+comes out of this this work it's that
+work that then has benefits in terms of
+
+ align:start position:0%
+work that then has benefits in terms of
+ 
+
+ align:start position:0%
+work that then has benefits in terms of
+health economics self-sustaining
+
+ align:start position:0%
+health economics self-sustaining
+ 
+
+ align:start position:0%
+health economics self-sustaining
+capacity that that I find intriguing and
+
+ align:start position:0%
+capacity that that I find intriguing and
+ 
+
+ align:start position:0%
+capacity that that I find intriguing and
+it's something that can be attempted
+
+ align:start position:0%
+it's something that can be attempted
+ 
+
+ align:start position:0%
+it's something that can be attempted
+where it's not intended to be a
+
+ align:start position:0%
+where it's not intended to be a
+ 
+
+ align:start position:0%
+where it's not intended to be a
+moneymaker initially it's intended to to
+
+ align:start position:0%
+moneymaker initially it's intended to to
+ 
+
+ align:start position:0%
+moneymaker initially it's intended to to
+save people's lives and and and to
+
+ align:start position:0%
+save people's lives and and and to
+ 
+
+ align:start position:0%
+save people's lives and and and to
+respond in that way so I'm curious about
+
+ align:start position:0%
+respond in that way so I'm curious about
+ 
+
+ align:start position:0%
+respond in that way so I'm curious about
+the longer term with this community in
+
+ align:start position:0%
+the longer term with this community in
+ 
+
+ align:start position:0%
+the longer term with this community in
+South Texas that you're working with
+
+ align:start position:0%
+South Texas that you're working with
+ 
+
+ align:start position:0%
+South Texas that you're working with
+obviously it sounds like there's a
+
+ align:start position:0%
+obviously it sounds like there's a
+ 
+
+ align:start position:0%
+obviously it sounds like there's a
+really pressing need so these water
+
+ align:start position:0%
+really pressing need so these water
+ 
+
+ align:start position:0%
+really pressing need so these water
+filters can meet that immediate need is
+
+ align:start position:0%
+filters can meet that immediate need is
+ 
+
+ align:start position:0%
+filters can meet that immediate need is
+the long-term goal still to kind of get
+
+ align:start position:0%
+the long-term goal still to kind of get
+ 
+
+ align:start position:0%
+the long-term goal still to kind of get
+a more traditional grid water setup for
+
+ align:start position:0%
+a more traditional grid water setup for
+ 
+
+ align:start position:0%
+a more traditional grid water setup for
+them yeah yes the origin of the filters
+
+ align:start position:0%
+them yeah yes the origin of the filters
+ 
+
+ align:start position:0%
+them yeah yes the origin of the filters
+was that they were supposed to be a
+
+ align:start position:0%
+was that they were supposed to be a
+ 
+
+ align:start position:0%
+was that they were supposed to be a
+first response to natural disaster and
+
+ align:start position:0%
+first response to natural disaster and
+ 
+
+ align:start position:0%
+first response to natural disaster and
+they were not supposed to be long-term
+
+ align:start position:0%
+they were not supposed to be long-term
+ 
+
+ align:start position:0%
+they were not supposed to be long-term
+their point of views temporary solutions
+
+ align:start position:0%
+their point of views temporary solutions
+ 
+
+ align:start position:0%
+their point of views temporary solutions
+unfortunately for some folks around the
+
+ align:start position:0%
+unfortunately for some folks around the
+ 
+
+ align:start position:0%
+unfortunately for some folks around the
+world these become more long-term
+
+ align:start position:0%
+world these become more long-term
+ 
+
+ align:start position:0%
+world these become more long-term
+responses what do you do when you're
+
+ align:start position:0%
+responses what do you do when you're
+ 
+
+ align:start position:0%
+responses what do you do when you're
+just starting out what's your advice for
+
+ align:start position:0%
+just starting out what's your advice for
+ 
+
+ align:start position:0%
+just starting out what's your advice for
+how you go about getting
+
+ align:start position:0%
+how you go about getting
+ 
+
+ align:start position:0%
+how you go about getting
+that's a tough one I think sometimes
+
+ align:start position:0%
+that's a tough one I think sometimes
+ 
+
+ align:start position:0%
+that's a tough one I think sometimes
+it's it's not about poking for the
+
+ align:start position:0%
+it's it's not about poking for the
+ 
+
+ align:start position:0%
+it's it's not about poking for the
+invitation initially sometimes you find
+
+ align:start position:0%
+invitation initially sometimes you find
+ 
+
+ align:start position:0%
+invitation initially sometimes you find
+ways to to become part of the community
+
+ align:start position:0%
+ways to to become part of the community
+ 
+
+ align:start position:0%
+ways to to become part of the community
+it's some level that might sound like oh
+
+ align:start position:0%
+it's some level that might sound like oh
+ 
+
+ align:start position:0%
+it's some level that might sound like oh
+but you're really kind of manipulating
+
+ align:start position:0%
+but you're really kind of manipulating
+ 
+
+ align:start position:0%
+but you're really kind of manipulating
+right because in the back of your mind
+
+ align:start position:0%
+right because in the back of your mind
+ 
+
+ align:start position:0%
+right because in the back of your mind
+you're saying okay at the right moment
+
+ align:start position:0%
+you're saying okay at the right moment
+ 
+
+ align:start position:0%
+you're saying okay at the right moment
+I'm gonna spring the question I'm gonna
+
+ align:start position:0%
+I'm gonna spring the question I'm gonna
+ 
+
+ align:start position:0%
+I'm gonna spring the question I'm gonna
+get the invitation that's not what I'm
+
+ align:start position:0%
+get the invitation that's not what I'm
+ 
+
+ align:start position:0%
+get the invitation that's not what I'm
+talking about what I'm talking about is
+
+ align:start position:0%
+talking about what I'm talking about is
+ 
+
+ align:start position:0%
+talking about what I'm talking about is
+being part of a community in doing the
+
+ align:start position:0%
+being part of a community in doing the
+ 
+
+ align:start position:0%
+being part of a community in doing the
+work in the community where the work
+
+ align:start position:0%
+work in the community where the work
+ 
+
+ align:start position:0%
+work in the community where the work
+that you're doing might be seen by folks
+
+ align:start position:0%
+that you're doing might be seen by folks
+ 
+
+ align:start position:0%
+that you're doing might be seen by folks
+who could invite you again that sounds
+
+ align:start position:0%
+who could invite you again that sounds
+ 
+
+ align:start position:0%
+who could invite you again that sounds
+like it's you some sort of nefarious
+
+ align:start position:0%
+like it's you some sort of nefarious
+ 
+
+ align:start position:0%
+like it's you some sort of nefarious
+manipulative component but not really I
+
+ align:start position:0%
+manipulative component but not really I
+ 
+
+ align:start position:0%
+manipulative component but not really I
+mean I think it's about continuing your
+
+ align:start position:0%
+mean I think it's about continuing your
+ 
+
+ align:start position:0%
+mean I think it's about continuing your
+work and staying visible and the
+
+ align:start position:0%
+work and staying visible and the
+ 
+
+ align:start position:0%
+work and staying visible and the
+invitations come there's a approach
+
+ align:start position:0%
+invitations come there's a approach
+ 
+
+ align:start position:0%
+invitations come there's a approach
+called arts entrepreneurship that is
+
+ align:start position:0%
+called arts entrepreneurship that is
+ 
+
+ align:start position:0%
+called arts entrepreneurship that is
+gaining traction in several universities
+
+ align:start position:0%
+gaining traction in several universities
+ 
+
+ align:start position:0%
+gaining traction in several universities
+have courses in art entrepreneurship
+
+ align:start position:0%
+have courses in art entrepreneurship
+ 
+
+ align:start position:0%
+have courses in art entrepreneurship
+arts entrepreneurship and minors and I
+
+ align:start position:0%
+arts entrepreneurship and minors and I
+ 
+
+ align:start position:0%
+arts entrepreneurship and minors and I
+think a few are starting majors as well
+
+ align:start position:0%
+think a few are starting majors as well
+ 
+
+ align:start position:0%
+think a few are starting majors as well
+or have majors because these other
+
+ align:start position:0%
+or have majors because these other
+ 
+
+ align:start position:0%
+or have majors because these other
+groups are doing this kind of work folks
+
+ align:start position:0%
+groups are doing this kind of work folks
+ 
+
+ align:start position:0%
+groups are doing this kind of work folks
+know about the water filter technology
+
+ align:start position:0%
+know about the water filter technology
+ 
+
+ align:start position:0%
+know about the water filter technology
+is starting to take off and people are
+
+ align:start position:0%
+is starting to take off and people are
+ 
+
+ align:start position:0%
+is starting to take off and people are
+collaborating they're entering into that
+
+ align:start position:0%
+collaborating they're entering into that
+ 
+
+ align:start position:0%
+collaborating they're entering into that
+space and what they're doing is they're
+
+ align:start position:0%
+space and what they're doing is they're
+ 
+
+ align:start position:0%
+space and what they're doing is they're
+they're making available for their
+
+ align:start position:0%
+they're making available for their
+ 
+
+ align:start position:0%
+they're making available for their
+learners k-12 learners possibilities
+
+ align:start position:0%
+learners k-12 learners possibilities
+ 
+
+ align:start position:0%
+learners k-12 learners possibilities
+that they might not have thought it's
+
+ align:start position:0%
+that they might not have thought it's
+ 
+
+ align:start position:0%
+that they might not have thought it's
+the curriculum work that I'm doing with
+
+ align:start position:0%
+the curriculum work that I'm doing with
+ 
+
+ align:start position:0%
+the curriculum work that I'm doing with
+with teachers I think that it becomes
+
+ align:start position:0%
+with teachers I think that it becomes
+ 
+
+ align:start position:0%
+with teachers I think that it becomes
+quite engaging great thank you all very
+
+ align:start position:0%
+quite engaging great thank you all very
+ 
+
+ align:start position:0%
+quite engaging great thank you all very
+much you very much yeah yeah I hope to
+
+ align:start position:0%
+much you very much yeah yeah I hope to
+ 
+
+ align:start position:0%
+much you very much yeah yeah I hope to
+see you tomorrow thank you thank you
\ No newline at end of file
diff --git a/SBe03vJr8-Y.txt b/SBe03vJr8-Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8f5f0babd61748f42aba44e1e34c1024684dbe77
--- /dev/null
+++ b/SBe03vJr8-Y.txt
@@ -0,0 +1,7515 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu good morning uh my talk this
+
+ align:start position:0%
+ocw.mit.edu good morning uh my talk this
+ 
+
+ align:start position:0%
+ocw.mit.edu good morning uh my talk this
+morning is going to be uh as it states
+
+ align:start position:0%
+morning is going to be uh as it states
+ 
+
+ align:start position:0%
+morning is going to be uh as it states
+there uh about pilgrimage and um first
+
+ align:start position:0%
+there uh about pilgrimage and um first
+ 
+
+ align:start position:0%
+there uh about pilgrimage and um first
+question I'd like to do is kind of
+
+ align:start position:0%
+question I'd like to do is kind of
+ 
+
+ align:start position:0%
+question I'd like to do is kind of
+introduce us to the kind of broad scope
+
+ align:start position:0%
+introduce us to the kind of broad scope
+ 
+
+ align:start position:0%
+introduce us to the kind of broad scope
+uh within this kind of mil which when
+
+ align:start position:0%
+uh within this kind of mil which when
+ 
+
+ align:start position:0%
+uh within this kind of mil which when
+within which within we're situated uh
+
+ align:start position:0%
+within which within we're situated uh
+ 
+
+ align:start position:0%
+within which within we're situated uh
+when we talk about pilgrimage as this
+
+ align:start position:0%
+when we talk about pilgrimage as this
+ 
+
+ align:start position:0%
+when we talk about pilgrimage as this
+kind of overarching global phenomenon um
+
+ align:start position:0%
+kind of overarching global phenomenon um
+ 
+
+ align:start position:0%
+kind of overarching global phenomenon um
+and the first question I would pose to
+
+ align:start position:0%
+and the first question I would pose to
+ 
+
+ align:start position:0%
+and the first question I would pose to
+you is um you know besides being
+
+ align:start position:0%
+you is um you know besides being
+ 
+
+ align:start position:0%
+you is um you know besides being
+pilgrims as we kind of as I sort of laid
+
+ align:start position:0%
+pilgrims as we kind of as I sort of laid
+ 
+
+ align:start position:0%
+pilgrims as we kind of as I sort of laid
+out there in the title what do these
+
+ align:start position:0%
+out there in the title what do these
+ 
+
+ align:start position:0%
+out there in the title what do these
+people have in common right
+
+ align:start position:0%
+people have in common right
+ 
+
+ align:start position:0%
+people have in common right
+uh we see people in different um uh sort
+
+ align:start position:0%
+uh we see people in different um uh sort
+ 
+
+ align:start position:0%
+uh we see people in different um uh sort
+of actions here and here are the places
+
+ align:start position:0%
+of actions here and here are the places
+ 
+
+ align:start position:0%
+of actions here and here are the places
+that they're all sort of associated with
+
+ align:start position:0%
+that they're all sort of associated with
+ 
+
+ align:start position:0%
+that they're all sort of associated with
+right so they're all
+
+ align:start position:0%
+right so they're all
+ 
+
+ align:start position:0%
+right so they're all
+going to a certain place right so the
+
+ align:start position:0%
+going to a certain place right so the
+ 
+
+ align:start position:0%
+going to a certain place right so the
+first one obviously on the left here
+
+ align:start position:0%
+first one obviously on the left here
+ 
+
+ align:start position:0%
+first one obviously on the left here
+this is the Kaba in Mecca we have St
+
+ align:start position:0%
+this is the Kaba in Mecca we have St
+ 
+
+ align:start position:0%
+this is the Kaba in Mecca we have St
+James compostella in Spain the mahabi
+
+ align:start position:0%
+James compostella in Spain the mahabi
+ 
+
+ align:start position:0%
+James compostella in Spain the mahabi
+temple in India and of course graceand
+
+ align:start position:0%
+temple in India and of course graceand
+ 
+
+ align:start position:0%
+temple in India and of course graceand
+in Memphis
+
+ align:start position:0%
+in Memphis
+ 
+
+ align:start position:0%
+in Memphis
+Tennessee um so questions I'd like to
+
+ align:start position:0%
+Tennessee um so questions I'd like to
+ 
+
+ align:start position:0%
+Tennessee um so questions I'd like to
+ask to kind of frame our conversation
+
+ align:start position:0%
+ask to kind of frame our conversation
+ 
+
+ align:start position:0%
+ask to kind of frame our conversation
+today really uh center
+
+ align:start position:0%
+today really uh center
+ 
+
+ align:start position:0%
+today really uh center
+around kind of problematizing some of
+
+ align:start position:0%
+around kind of problematizing some of
+ 
+
+ align:start position:0%
+around kind of problematizing some of
+these Notions that we've inherited uh
+
+ align:start position:0%
+these Notions that we've inherited uh
+ 
+
+ align:start position:0%
+these Notions that we've inherited uh
+with this term pilgrimage um we're
+
+ align:start position:0%
+with this term pilgrimage um we're
+ 
+
+ align:start position:0%
+with this term pilgrimage um we're
+surrounded by it uh in our popular
+
+ align:start position:0%
+surrounded by it uh in our popular
+ 
+
+ align:start position:0%
+surrounded by it uh in our popular
+culture today uh we've got all kinds of
+
+ align:start position:0%
+culture today uh we've got all kinds of
+ 
+
+ align:start position:0%
+culture today uh we've got all kinds of
+examples um we've got uh National
+
+ align:start position:0%
+examples um we've got uh National
+ 
+
+ align:start position:0%
+examples um we've got uh National
+Geographic uh magazines and um this is a
+
+ align:start position:0%
+Geographic uh magazines and um this is a
+ 
+
+ align:start position:0%
+Geographic uh magazines and um this is a
+French magazine that's com it's a themed
+
+ align:start position:0%
+French magazine that's com it's a themed
+ 
+
+ align:start position:0%
+French magazine that's com it's a themed
+magazine that just came out a month ago
+
+ align:start position:0%
+magazine that just came out a month ago
+ 
+
+ align:start position:0%
+magazine that just came out a month ago
+um you know and and we're surrounded
+
+ align:start position:0%
+um you know and and we're surrounded
+ 
+
+ align:start position:0%
+um you know and and we're surrounded
+with images uh of pilgrimage people
+
+ align:start position:0%
+with images uh of pilgrimage people
+ 
+
+ align:start position:0%
+with images uh of pilgrimage people
+going on these great travels and
+
+ align:start position:0%
+going on these great travels and
+ 
+
+ align:start position:0%
+going on these great travels and
+Journeys to different places uh
+
+ align:start position:0%
+Journeys to different places uh
+ 
+
+ align:start position:0%
+Journeys to different places uh
+throughout the world and so I just I
+
+ align:start position:0%
+throughout the world and so I just I
+ 
+
+ align:start position:0%
+throughout the world and so I just I
+think that uh this lecture is an
+
+ align:start position:0%
+think that uh this lecture is an
+ 
+
+ align:start position:0%
+think that uh this lecture is an
+opportunity to kind of uh you know try
+
+ align:start position:0%
+opportunity to kind of uh you know try
+ 
+
+ align:start position:0%
+opportunity to kind of uh you know try
+to begin to understand those some of
+
+ align:start position:0%
+to begin to understand those some of
+ 
+
+ align:start position:0%
+to begin to understand those some of
+those issues um
+
+ align:start position:0%
+those issues um
+ 
+
+ align:start position:0%
+those issues um
+it's it is a very contemporary
+
+ align:start position:0%
+it's it is a very contemporary
+ 
+
+ align:start position:0%
+it's it is a very contemporary
+phenomenon still um even though the bulk
+
+ align:start position:0%
+phenomenon still um even though the bulk
+ 
+
+ align:start position:0%
+phenomenon still um even though the bulk
+of this lecture will be a historical uh
+
+ align:start position:0%
+of this lecture will be a historical uh
+ 
+
+ align:start position:0%
+of this lecture will be a historical uh
+discussion the I would like to situate
+
+ align:start position:0%
+discussion the I would like to situate
+ 
+
+ align:start position:0%
+discussion the I would like to situate
+it within a cont temporary framework of
+
+ align:start position:0%
+it within a cont temporary framework of
+ 
+
+ align:start position:0%
+it within a cont temporary framework of
+um because it's very relevant today I
+
+ align:start position:0%
+um because it's very relevant today I
+ 
+
+ align:start position:0%
+um because it's very relevant today I
+mean as this is from the National
+
+ align:start position:0%
+mean as this is from the National
+ 
+
+ align:start position:0%
+mean as this is from the National
+Geographic website which was also
+
+ align:start position:0%
+Geographic website which was also
+ 
+
+ align:start position:0%
+Geographic website which was also
+published in a magazine a few months ago
+
+ align:start position:0%
+published in a magazine a few months ago
+ 
+
+ align:start position:0%
+published in a magazine a few months ago
+which talks about um Global pilgrimage
+
+ align:start position:0%
+which talks about um Global pilgrimage
+ 
+
+ align:start position:0%
+which talks about um Global pilgrimage
+really it tries to kind of elicit uh
+
+ align:start position:0%
+really it tries to kind of elicit uh
+ 
+
+ align:start position:0%
+really it tries to kind of elicit uh
+kind of sort of essentializes a lot of
+
+ align:start position:0%
+kind of sort of essentializes a lot of
+ 
+
+ align:start position:0%
+kind of sort of essentializes a lot of
+different pilgrimages around the world
+
+ align:start position:0%
+different pilgrimages around the world
+ 
+
+ align:start position:0%
+different pilgrimages around the world
+and um it highlights and on their
+
+ align:start position:0%
+and um it highlights and on their
+ 
+
+ align:start position:0%
+and um it highlights and on their
+website they actually have a um an
+
+ align:start position:0%
+website they actually have a um an
+ 
+
+ align:start position:0%
+website they actually have a um an
+interactive map where you can click and
+
+ align:start position:0%
+interactive map where you can click and
+ 
+
+ align:start position:0%
+interactive map where you can click and
+read all about the different types of
+
+ align:start position:0%
+read all about the different types of
+ 
+
+ align:start position:0%
+read all about the different types of
+pilgrimages around the world um and you
+
+ align:start position:0%
+pilgrimages around the world um and you
+ 
+
+ align:start position:0%
+pilgrimages around the world um and you
+know again just to kind of remind us of
+
+ align:start position:0%
+know again just to kind of remind us of
+ 
+
+ align:start position:0%
+know again just to kind of remind us of
+the Contemporary
+
+ align:start position:0%
+the Contemporary
+ 
+
+ align:start position:0%
+the Contemporary
+contemporariness really of the situ of
+
+ align:start position:0%
+contemporariness really of the situ of
+ 
+
+ align:start position:0%
+contemporariness really of the situ of
+of pilgrimage it does have over 300
+
+ align:start position:0%
+of pilgrimage it does have over 300
+ 
+
+ align:start position:0%
+of pilgrimage it does have over 300
+million Travelers per year are traveling
+
+ align:start position:0%
+million Travelers per year are traveling
+ 
+
+ align:start position:0%
+million Travelers per year are traveling
+on some kind of Faith tourism or
+
+ align:start position:0%
+on some kind of Faith tourism or
+ 
+
+ align:start position:0%
+on some kind of Faith tourism or
+religious programm of some sort and it
+
+ align:start position:0%
+religious programm of some sort and it
+ 
+
+ align:start position:0%
+religious programm of some sort and it
+is an $18 billion year Revenue
+
+ align:start position:0%
+is an $18 billion year Revenue
+ 
+
+ align:start position:0%
+is an $18 billion year Revenue
+generating industry so this is something
+
+ align:start position:0%
+generating industry so this is something
+ 
+
+ align:start position:0%
+generating industry so this is something
+that's extremely um um relevant and so
+
+ align:start position:0%
+that's extremely um um relevant and so
+ 
+
+ align:start position:0%
+that's extremely um um relevant and so
+here's the National Geographic
+
+ align:start position:0%
+here's the National Geographic
+ 
+
+ align:start position:0%
+here's the National Geographic
+interactive map and you can kind of
+
+ align:start position:0%
+interactive map and you can kind of
+ 
+
+ align:start position:0%
+interactive map and you can kind of
+click on all these different places and
+
+ align:start position:0%
+click on all these different places and
+ 
+
+ align:start position:0%
+click on all these different places and
+try to gain an understanding uh
+
+ align:start position:0%
+try to gain an understanding uh
+ 
+
+ align:start position:0%
+try to gain an understanding uh
+and so we we can understand pilgrimage
+
+ align:start position:0%
+and so we we can understand pilgrimage
+ 
+
+ align:start position:0%
+and so we we can understand pilgrimage
+as this as you know occurring all over
+
+ align:start position:0%
+as this as you know occurring all over
+ 
+
+ align:start position:0%
+as this as you know occurring all over
+the world but for our sake for this
+
+ align:start position:0%
+the world but for our sake for this
+ 
+
+ align:start position:0%
+the world but for our sake for this
+lecture I think it's very important to
+
+ align:start position:0%
+lecture I think it's very important to
+ 
+
+ align:start position:0%
+lecture I think it's very important to
+kind of hone in on on uh focus on some
+
+ align:start position:0%
+kind of hone in on on uh focus on some
+ 
+
+ align:start position:0%
+kind of hone in on on uh focus on some
+specific Traditions So today we're going
+
+ align:start position:0%
+specific Traditions So today we're going
+ 
+
+ align:start position:0%
+specific Traditions So today we're going
+to be looking at an example from Egypt
+
+ align:start position:0%
+to be looking at an example from Egypt
+ 
+
+ align:start position:0%
+to be looking at an example from Egypt
+uh early Buddhism Islam and
+
+ align:start position:0%
+uh early Buddhism Islam and
+ 
+
+ align:start position:0%
+uh early Buddhism Islam and
+Christianity um but first I'd like to
+
+ align:start position:0%
+Christianity um but first I'd like to
+ 
+
+ align:start position:0%
+Christianity um but first I'd like to
+kind of problematize what pilgrimage is
+
+ align:start position:0%
+kind of problematize what pilgrimage is
+ 
+
+ align:start position:0%
+kind of problematize what pilgrimage is
+what it means uh what's going on here
+
+ align:start position:0%
+what it means uh what's going on here
+ 
+
+ align:start position:0%
+what it means uh what's going on here
+um the um the question is what is a
+
+ align:start position:0%
+um the um the question is what is a
+ 
+
+ align:start position:0%
+um the um the question is what is a
+pilgrimage right so it's usually a
+
+ align:start position:0%
+pilgrimage right so it's usually a
+ 
+
+ align:start position:0%
+pilgrimage right so it's usually a
+journey of some sort somebody's
+
+ align:start position:0%
+journey of some sort somebody's
+ 
+
+ align:start position:0%
+journey of some sort somebody's
+traveling to some degree uh to see some
+
+ align:start position:0%
+traveling to some degree uh to see some
+ 
+
+ align:start position:0%
+traveling to some degree uh to see some
+sacred or some holy either a relic or a
+
+ align:start position:0%
+sacred or some holy either a relic or a
+ 
+
+ align:start position:0%
+sacred or some holy either a relic or a
+space or something um and these people
+
+ align:start position:0%
+space or something um and these people
+ 
+
+ align:start position:0%
+space or something um and these people
+usually pay some kind of homage or
+
+ align:start position:0%
+usually pay some kind of homage or
+ 
+
+ align:start position:0%
+usually pay some kind of homage or
+respect uh and they they they perform
+
+ align:start position:0%
+respect uh and they they they perform
+ 
+
+ align:start position:0%
+respect uh and they they they perform
+this journey um out of some kind of
+
+ align:start position:0%
+this journey um out of some kind of
+ 
+
+ align:start position:0%
+this journey um out of some kind of
+sense of a Duty or some kind of
+
+ align:start position:0%
+sense of a Duty or some kind of
+ 
+
+ align:start position:0%
+sense of a Duty or some kind of
+responsibility there's something that
+
+ align:start position:0%
+responsibility there's something that
+ 
+
+ align:start position:0%
+responsibility there's something that
+kind of you know gets them to go on it
+
+ align:start position:0%
+kind of you know gets them to go on it
+ 
+
+ align:start position:0%
+kind of you know gets them to go on it
+uh and what a pilgrim is is not
+
+ align:start position:0%
+uh and what a pilgrim is is not
+ 
+
+ align:start position:0%
+uh and what a pilgrim is is not
+necessarily um you know we're not really
+
+ align:start position:0%
+necessarily um you know we're not really
+ 
+
+ align:start position:0%
+necessarily um you know we're not really
+going to cover that specifically because
+
+ align:start position:0%
+going to cover that specifically because
+ 
+
+ align:start position:0%
+going to cover that specifically because
+that's more of a sort of an
+
+ align:start position:0%
+that's more of a sort of an
+ 
+
+ align:start position:0%
+that's more of a sort of an
+anthropological thing but we we are
+
+ align:start position:0%
+anthropological thing but we we are
+ 
+
+ align:start position:0%
+anthropological thing but we we are
+going to address a couple issues related
+
+ align:start position:0%
+going to address a couple issues related
+ 
+
+ align:start position:0%
+going to address a couple issues related
+to pilgrims because they are obviously
+
+ align:start position:0%
+to pilgrims because they are obviously
+ 
+
+ align:start position:0%
+to pilgrims because they are obviously
+very diverse and they're the reason that
+
+ align:start position:0%
+very diverse and they're the reason that
+ 
+
+ align:start position:0%
+very diverse and they're the reason that
+pilgrimages exist so um to some extent
+
+ align:start position:0%
+pilgrimages exist so um to some extent
+ 
+
+ align:start position:0%
+pilgrimages exist so um to some extent
+we need to understand that what a
+
+ align:start position:0%
+we need to understand that what a
+ 
+
+ align:start position:0%
+we need to understand that what a
+pilgrim is and who who they are very
+
+ align:start position:0%
+pilgrim is and who who they are very
+ 
+
+ align:start position:0%
+pilgrim is and who who they are very
+basically um and I've tried to kind of
+
+ align:start position:0%
+basically um and I've tried to kind of
+ 
+
+ align:start position:0%
+basically um and I've tried to kind of
+outline or reduce some of the themes of
+
+ align:start position:0%
+outline or reduce some of the themes of
+ 
+
+ align:start position:0%
+outline or reduce some of the themes of
+pilgrimage to three kind of very basic
+
+ align:start position:0%
+pilgrimage to three kind of very basic
+ 
+
+ align:start position:0%
+pilgrimage to three kind of very basic
+um um kind of ideas so there's Faith
+
+ align:start position:0%
+um um kind of ideas so there's Faith
+ 
+
+ align:start position:0%
+um um kind of ideas so there's Faith
+obviously which is involved and this is
+
+ align:start position:0%
+obviously which is involved and this is
+ 
+
+ align:start position:0%
+obviously which is involved and this is
+not necessarily religious uh it can be
+
+ align:start position:0%
+not necessarily religious uh it can be
+ 
+
+ align:start position:0%
+not necessarily religious uh it can be
+uh some kind of spiritual entity or
+
+ align:start position:0%
+uh some kind of spiritual entity or
+ 
+
+ align:start position:0%
+uh some kind of spiritual entity or
+personage as I mentioned can be
+
+ align:start position:0%
+personage as I mentioned can be
+ 
+
+ align:start position:0%
+personage as I mentioned can be
+religious or secular as we saw with
+
+ align:start position:0%
+religious or secular as we saw with
+ 
+
+ align:start position:0%
+religious or secular as we saw with
+Elvis already um people can believe in
+
+ align:start position:0%
+Elvis already um people can believe in
+ 
+
+ align:start position:0%
+Elvis already um people can believe in
+something related to somebody um but
+
+ align:start position:0%
+something related to somebody um but
+ 
+
+ align:start position:0%
+something related to somebody um but
+most importantly there's a desire to do
+
+ align:start position:0%
+most importantly there's a desire to do
+ 
+
+ align:start position:0%
+most importantly there's a desire to do
+something about it and so um that's
+
+ align:start position:0%
+something about it and so um that's
+ 
+
+ align:start position:0%
+something about it and so um that's
+where movement comes in and so Movement
+
+ align:start position:0%
+where movement comes in and so Movement
+ 
+
+ align:start position:0%
+where movement comes in and so Movement
+we can basically understand it as this
+
+ align:start position:0%
+we can basically understand it as this
+ 
+
+ align:start position:0%
+we can basically understand it as this
+this WEA um you know in some traditions
+
+ align:start position:0%
+this WEA um you know in some traditions
+ 
+
+ align:start position:0%
+this WEA um you know in some traditions
+we're going to talk about
+
+ align:start position:0%
+we're going to talk about
+ 
+
+ align:start position:0%
+we're going to talk about
+circumambulation and some some uh
+
+ align:start position:0%
+circumambulation and some some uh
+ 
+
+ align:start position:0%
+circumambulation and some some uh
+Traditions we're going to talk about
+
+ align:start position:0%
+Traditions we're going to talk about
+ 
+
+ align:start position:0%
+Traditions we're going to talk about
+procession there's this constant thread
+
+ align:start position:0%
+procession there's this constant thread
+ 
+
+ align:start position:0%
+procession there's this constant thread
+of movement which is kind of a thread
+
+ align:start position:0%
+of movement which is kind of a thread
+ 
+
+ align:start position:0%
+of movement which is kind of a thread
+within all of these different Traditions
+
+ align:start position:0%
+within all of these different Traditions
+ 
+
+ align:start position:0%
+within all of these different Traditions
+or something's moving right whether it's
+
+ align:start position:0%
+or something's moving right whether it's
+ 
+
+ align:start position:0%
+or something's moving right whether it's
+the sacred or the or the profane or
+
+ align:start position:0%
+the sacred or the or the profane or
+ 
+
+ align:start position:0%
+the sacred or the or the profane or
+whether it's people or whether it's an
+
+ align:start position:0%
+whether it's people or whether it's an
+ 
+
+ align:start position:0%
+whether it's people or whether it's an
+object things are things are constantly
+
+ align:start position:0%
+object things are things are constantly
+ 
+
+ align:start position:0%
+object things are things are constantly
+moving which is obviously very important
+
+ align:start position:0%
+moving which is obviously very important
+ 
+
+ align:start position:0%
+moving which is obviously very important
+for us spatially uh and of course that
+
+ align:start position:0%
+for us spatially uh and of course that
+ 
+
+ align:start position:0%
+for us spatially uh and of course that
+brings me to the differentiation of
+
+ align:start position:0%
+brings me to the differentiation of
+ 
+
+ align:start position:0%
+brings me to the differentiation of
+space and so space really uh as a key to
+
+ align:start position:0%
+space and so space really uh as a key to
+ 
+
+ align:start position:0%
+space and so space really uh as a key to
+this um this understanding uh
+
+ align:start position:0%
+this um this understanding uh
+ 
+
+ align:start position:0%
+this um this understanding uh
+understanding the differences in the
+
+ align:start position:0%
+understanding the differences in the
+ 
+
+ align:start position:0%
+understanding the differences in the
+conceptions of space between these
+
+ align:start position:0%
+conceptions of space between these
+ 
+
+ align:start position:0%
+conceptions of space between these
+different traditions and how the
+
+ align:start position:0%
+different traditions and how the
+ 
+
+ align:start position:0%
+different traditions and how the
+different Traditions understand this
+
+ align:start position:0%
+different Traditions understand this
+ 
+
+ align:start position:0%
+different Traditions understand this
+notion of the Sacred and the profane
+
+ align:start position:0%
+notion of the Sacred and the profane
+ 
+
+ align:start position:0%
+notion of the Sacred and the profane
+right so we we've kind of inherited this
+
+ align:start position:0%
+right so we we've kind of inherited this
+ 
+
+ align:start position:0%
+right so we we've kind of inherited this
+very this you know very dualistic uh
+
+ align:start position:0%
+very this you know very dualistic uh
+ 
+
+ align:start position:0%
+very this you know very dualistic uh
+diagram of the Sacred versus the profane
+
+ align:start position:0%
+diagram of the Sacred versus the profane
+ 
+
+ align:start position:0%
+diagram of the Sacred versus the profane
+right they're always kind of like
+
+ align:start position:0%
+right they're always kind of like
+ 
+
+ align:start position:0%
+right they're always kind of like
+opposed to one another uh in our kind of
+
+ align:start position:0%
+opposed to one another uh in our kind of
+ 
+
+ align:start position:0%
+opposed to one another uh in our kind of
+traditional understanding you're either
+
+ align:start position:0%
+traditional understanding you're either
+ 
+
+ align:start position:0%
+traditional understanding you're either
+sacred or profane spaces can be sacred
+
+ align:start position:0%
+sacred or profane spaces can be sacred
+ 
+
+ align:start position:0%
+sacred or profane spaces can be sacred
+or profane and so what I would really
+
+ align:start position:0%
+or profane and so what I would really
+ 
+
+ align:start position:0%
+or profane and so what I would really
+like to do is challenge our
+
+ align:start position:0%
+like to do is challenge our
+ 
+
+ align:start position:0%
+like to do is challenge our
+understanding of that and this is again
+
+ align:start position:0%
+understanding of that and this is again
+ 
+
+ align:start position:0%
+understanding of that and this is again
+this is the sort of traditional path
+
+ align:start position:0%
+this is the sort of traditional path
+ 
+
+ align:start position:0%
+this is the sort of traditional path
+that a pilgrim takes right they move
+
+ align:start position:0%
+that a pilgrim takes right they move
+ 
+
+ align:start position:0%
+that a pilgrim takes right they move
+from the profane through or into the s
+
+ align:start position:0%
+from the profane through or into the s
+ 
+
+ align:start position:0%
+from the profane through or into the s
+and then they come back to their profane
+
+ align:start position:0%
+and then they come back to their profane
+ 
+
+ align:start position:0%
+and then they come back to their profane
+existence somehow
+
+ align:start position:0%
+existence somehow
+ 
+
+ align:start position:0%
+existence somehow
+transformed so how does that
+
+ align:start position:0%
+transformed so how does that
+ 
+
+ align:start position:0%
+transformed so how does that
+transformation occur again anthropology
+
+ align:start position:0%
+transformation occur again anthropology
+ 
+
+ align:start position:0%
+transformation occur again anthropology
+here does a little bit of a job and they
+
+ align:start position:0%
+here does a little bit of a job and they
+ 
+
+ align:start position:0%
+here does a little bit of a job and they
+sort of help me out with this
+
+ align:start position:0%
+sort of help me out with this
+ 
+
+ align:start position:0%
+sort of help me out with this
+understanding uh the anthropologists
+
+ align:start position:0%
+understanding uh the anthropologists
+ 
+
+ align:start position:0%
+understanding uh the anthropologists
+have been studying this since like
+
+ align:start position:0%
+have been studying this since like
+ 
+
+ align:start position:0%
+have been studying this since like
+really the 60s and so um there's three
+
+ align:start position:0%
+really the 60s and so um there's three
+ 
+
+ align:start position:0%
+really the 60s and so um there's three
+quick stages of of a pilgrimage uh
+
+ align:start position:0%
+quick stages of of a pilgrimage uh
+ 
+
+ align:start position:0%
+quick stages of of a pilgrimage uh
+Journey that I'd like to kind of elicit
+
+ align:start position:0%
+Journey that I'd like to kind of elicit
+ 
+
+ align:start position:0%
+Journey that I'd like to kind of elicit
+here and this is the prelimin Lial and
+
+ align:start position:0%
+here and this is the prelimin Lial and
+ 
+
+ align:start position:0%
+here and this is the prelimin Lial and
+post liin right so we Anthropologist
+
+ align:start position:0%
+post liin right so we Anthropologist
+ 
+
+ align:start position:0%
+post liin right so we Anthropologist
+kind of like this to a graduation
+
+ align:start position:0%
+kind of like this to a graduation
+ 
+
+ align:start position:0%
+kind of like this to a graduation
+ceremony where the prelimin is the
+
+ align:start position:0%
+ceremony where the prelimin is the
+ 
+
+ align:start position:0%
+ceremony where the prelimin is the
+separation phase right where students
+
+ align:start position:0%
+separation phase right where students
+ 
+
+ align:start position:0%
+separation phase right where students
+are with their parents and they're kind
+
+ align:start position:0%
+are with their parents and they're kind
+ 
+
+ align:start position:0%
+are with their parents and they're kind
+of Milling about and then they all kind
+
+ align:start position:0%
+of Milling about and then they all kind
+ 
+
+ align:start position:0%
+of Milling about and then they all kind
+of they get their robes on right so
+
+ align:start position:0%
+of they get their robes on right so
+ 
+
+ align:start position:0%
+of they get their robes on right so
+they're differentiating themselves then
+
+ align:start position:0%
+they're differentiating themselves then
+ 
+
+ align:start position:0%
+they're differentiating themselves then
+they all go sit in the middle of the uh
+
+ align:start position:0%
+they all go sit in the middle of the uh
+ 
+
+ align:start position:0%
+they all go sit in the middle of the uh
+in the middle they are separated from
+
+ align:start position:0%
+in the middle they are separated from
+ 
+
+ align:start position:0%
+in the middle they are separated from
+their parents and families they sit
+
+ align:start position:0%
+their parents and families they sit
+ 
+
+ align:start position:0%
+their parents and families they sit
+there then they're in this Lial phase
+
+ align:start position:0%
+there then they're in this Lial phase
+ 
+
+ align:start position:0%
+there then they're in this Lial phase
+where there's this transitional phase
+
+ align:start position:0%
+where there's this transitional phase
+ 
+
+ align:start position:0%
+where there's this transitional phase
+where people give their you know
+
+ align:start position:0%
+where people give their you know
+ 
+
+ align:start position:0%
+where people give their you know
+lectures and they talk about how great
+
+ align:start position:0%
+lectures and they talk about how great
+ 
+
+ align:start position:0%
+lectures and they talk about how great
+the class is and what happened that year
+
+ align:start position:0%
+the class is and what happened that year
+ 
+
+ align:start position:0%
+the class is and what happened that year
+and all this things and so um then this
+
+ align:start position:0%
+and all this things and so um then this
+ 
+
+ align:start position:0%
+and all this things and so um then this
+notion of communitas kind of evolves out
+
+ align:start position:0%
+notion of communitas kind of evolves out
+ 
+
+ align:start position:0%
+notion of communitas kind of evolves out
+of that right so there's this feeling of
+
+ align:start position:0%
+of that right so there's this feeling of
+ 
+
+ align:start position:0%
+of that right so there's this feeling of
+a community that they're together with
+
+ align:start position:0%
+a community that they're together with
+ 
+
+ align:start position:0%
+a community that they're together with
+people and so um very basically you you
+
+ align:start position:0%
+people and so um very basically you you
+ 
+
+ align:start position:0%
+people and so um very basically you you
+the anthropologists talk about how
+
+ align:start position:0%
+the anthropologists talk about how
+ 
+
+ align:start position:0%
+the anthropologists talk about how
+there's this um together feeling that
+
+ align:start position:0%
+there's this um together feeling that
+ 
+
+ align:start position:0%
+there's this um together feeling that
+they're doing something together and
+
+ align:start position:0%
+they're doing something together and
+ 
+
+ align:start position:0%
+they're doing something together and
+then the post liino is the
+
+ align:start position:0%
+then the post liino is the
+ 
+
+ align:start position:0%
+then the post liino is the
+reincorporation into society you have th
+
+ align:start position:0%
+reincorporation into society you have th
+ 
+
+ align:start position:0%
+reincorporation into society you have th
+graduated you've been given your degree
+
+ align:start position:0%
+graduated you've been given your degree
+ 
+
+ align:start position:0%
+graduated you've been given your degree
+and now you're reincorporated into
+
+ align:start position:0%
+and now you're reincorporated into
+ 
+
+ align:start position:0%
+and now you're reincorporated into
+society as an individual you you're part
+
+ align:start position:0%
+society as an individual you you're part
+ 
+
+ align:start position:0%
+society as an individual you you're part
+of this community of people with a
+
+ align:start position:0%
+of this community of people with a
+ 
+
+ align:start position:0%
+of this community of people with a
+degree right so this is kind of but I'd
+
+ align:start position:0%
+degree right so this is kind of but I'd
+ 
+
+ align:start position:0%
+degree right so this is kind of but I'd
+like us to keep in mind this notion of
+
+ align:start position:0%
+like us to keep in mind this notion of
+ 
+
+ align:start position:0%
+like us to keep in mind this notion of
+communitas as we move forward um the
+
+ align:start position:0%
+communitas as we move forward um the
+ 
+
+ align:start position:0%
+communitas as we move forward um the
+first um kind of example here in um
+
+ align:start position:0%
+first um kind of example here in um
+ 
+
+ align:start position:0%
+first um kind of example here in um
+slide 16 is the uh we're going to look
+
+ align:start position:0%
+slide 16 is the uh we're going to look
+ 
+
+ align:start position:0%
+slide 16 is the uh we're going to look
+at a sort of an ancient example in the
+
+ align:start position:0%
+at a sort of an ancient example in the
+ 
+
+ align:start position:0%
+at a sort of an ancient example in the
+New Kingdom of um in Egypt uh the carac
+
+ align:start position:0%
+New Kingdom of um in Egypt uh the carac
+ 
+
+ align:start position:0%
+New Kingdom of um in Egypt uh the carac
+and so this is B very basically where
+
+ align:start position:0%
+and so this is B very basically where
+ 
+
+ align:start position:0%
+and so this is B very basically where
+it's located um in Africa
+
+ align:start position:0%
+it's located um in Africa
+ 
+
+ align:start position:0%
+it's located um in Africa
+and um this is a procession basically
+
+ align:start position:0%
+and um this is a procession basically
+ 
+
+ align:start position:0%
+and um this is a procession basically
+it's it's it's a very early form of
+
+ align:start position:0%
+it's it's it's a very early form of
+ 
+
+ align:start position:0%
+it's it's it's a very early form of
+pilgrimage and um really it takes on
+
+ align:start position:0%
+pilgrimage and um really it takes on
+ 
+
+ align:start position:0%
+pilgrimage and um really it takes on
+this notion of the of the procession to
+
+ align:start position:0%
+this notion of the of the procession to
+ 
+
+ align:start position:0%
+this notion of the of the procession to
+a very specific um in a very specific
+
+ align:start position:0%
+a very specific um in a very specific
+ 
+
+ align:start position:0%
+a very specific um in a very specific
+manner people aren't necessarily coming
+
+ align:start position:0%
+manner people aren't necessarily coming
+ 
+
+ align:start position:0%
+manner people aren't necessarily coming
+from extremely far distances to come to
+
+ align:start position:0%
+from extremely far distances to come to
+ 
+
+ align:start position:0%
+from extremely far distances to come to
+thieves this general area here that we
+
+ align:start position:0%
+thieves this general area here that we
+ 
+
+ align:start position:0%
+thieves this general area here that we
+can see but um there are people within
+
+ align:start position:0%
+can see but um there are people within
+ 
+
+ align:start position:0%
+can see but um there are people within
+thieves that um and this is a very
+
+ align:start position:0%
+thieves that um and this is a very
+ 
+
+ align:start position:0%
+thieves that um and this is a very
+unique um procession in that the the
+
+ align:start position:0%
+unique um procession in that the the
+ 
+
+ align:start position:0%
+unique um procession in that the the
+notion of our notion of the Sacred that
+
+ align:start position:0%
+notion of our notion of the Sacred that
+ 
+
+ align:start position:0%
+notion of our notion of the Sacred that
+we talked about just briefly earlier uh
+
+ align:start position:0%
+we talked about just briefly earlier uh
+ 
+
+ align:start position:0%
+we talked about just briefly earlier uh
+the sacred is actually very interesting
+
+ align:start position:0%
+the sacred is actually very interesting
+ 
+
+ align:start position:0%
+the sacred is actually very interesting
+because it's cooc there are the temples
+
+ align:start position:0%
+because it's cooc there are the temples
+ 
+
+ align:start position:0%
+because it's cooc there are the temples
+themselves are sacred and the spaces are
+
+ align:start position:0%
+themselves are sacred and the spaces are
+ 
+
+ align:start position:0%
+themselves are sacred and the spaces are
+sacred within them but the there's
+
+ align:start position:0%
+sacred within them but the there's
+ 
+
+ align:start position:0%
+sacred within them but the there's
+something very interesting here where
+
+ align:start position:0%
+something very interesting here where
+ 
+
+ align:start position:0%
+something very interesting here where
+the sacred is actually moved so the the
+
+ align:start position:0%
+the sacred is actually moved so the the
+ 
+
+ align:start position:0%
+the sacred is actually moved so the the
+gods actually leave the temples and are
+
+ align:start position:0%
+gods actually leave the temples and are
+ 
+
+ align:start position:0%
+gods actually leave the temples and are
+processed through these different areas
+
+ align:start position:0%
+processed through these different areas
+ 
+
+ align:start position:0%
+processed through these different areas
+and we can see here from this first uh
+
+ align:start position:0%
+and we can see here from this first uh
+ 
+
+ align:start position:0%
+and we can see here from this first uh
+example this is the there's two main
+
+ align:start position:0%
+example this is the there's two main
+ 
+
+ align:start position:0%
+example this is the there's two main
+festivals I'd like to very briefly talk
+
+ align:start position:0%
+festivals I'd like to very briefly talk
+ 
+
+ align:start position:0%
+festivals I'd like to very briefly talk
+about there's the opet festival which is
+
+ align:start position:0%
+about there's the opet festival which is
+ 
+
+ align:start position:0%
+about there's the opet festival which is
+this essentially this route all right so
+
+ align:start position:0%
+this essentially this route all right so
+ 
+
+ align:start position:0%
+this essentially this route all right so
+very basically uh Carnac Temple here and
+
+ align:start position:0%
+very basically uh Carnac Temple here and
+ 
+
+ align:start position:0%
+very basically uh Carnac Temple here and
+then the um the procession there's two
+
+ align:start position:0%
+then the um the procession there's two
+ 
+
+ align:start position:0%
+then the um the procession there's two
+different there's a couple different
+
+ align:start position:0%
+different there's a couple different
+ 
+
+ align:start position:0%
+different there's a couple different
+ways in which this happens but the
+
+ align:start position:0%
+ways in which this happens but the
+ 
+
+ align:start position:0%
+ways in which this happens but the
+initial the earlier kingdoms uh example
+
+ align:start position:0%
+initial the earlier kingdoms uh example
+ 
+
+ align:start position:0%
+initial the earlier kingdoms uh example
+leaves from Carnac goes takes the land
+
+ align:start position:0%
+leaves from Carnac goes takes the land
+ 
+
+ align:start position:0%
+leaves from Carnac goes takes the land
+route to Luxor then goes in the Nile and
+
+ align:start position:0%
+route to Luxor then goes in the Nile and
+ 
+
+ align:start position:0%
+route to Luxor then goes in the Nile and
+then come so it comes back Thea the Nile
+
+ align:start position:0%
+then come so it comes back Thea the Nile
+ 
+
+ align:start position:0%
+then come so it comes back Thea the Nile
+um and so what's happening is Amun the
+
+ align:start position:0%
+um and so what's happening is Amun the
+ 
+
+ align:start position:0%
+um and so what's happening is Amun the
+god Amun uh is sort of he inhabits
+
+ align:start position:0%
+god Amun uh is sort of he inhabits
+ 
+
+ align:start position:0%
+god Amun uh is sort of he inhabits
+Carnac right so he's removed his image
+
+ align:start position:0%
+Carnac right so he's removed his image
+ 
+
+ align:start position:0%
+Carnac right so he's removed his image
+is removed and thus their understanding
+
+ align:start position:0%
+is removed and thus their understanding
+ 
+
+ align:start position:0%
+is removed and thus their understanding
+of the god so they they put him on a
+
+ align:start position:0%
+of the god so they they put him on a
+ 
+
+ align:start position:0%
+of the god so they they put him on a
+bark and then which is the ship and I'll
+
+ align:start position:0%
+bark and then which is the ship and I'll
+ 
+
+ align:start position:0%
+bark and then which is the ship and I'll
+show you that in a minute but I'd like
+
+ align:start position:0%
+show you that in a minute but I'd like
+ 
+
+ align:start position:0%
+show you that in a minute but I'd like
+to first show you the other this is the
+
+ align:start position:0%
+to first show you the other this is the
+ 
+
+ align:start position:0%
+to first show you the other this is the
+Feast of the valley and this route uh
+
+ align:start position:0%
+Feast of the valley and this route uh
+ 
+
+ align:start position:0%
+Feast of the valley and this route uh
+includes this is a little bit later
+
+ align:start position:0%
+includes this is a little bit later
+ 
+
+ align:start position:0%
+includes this is a little bit later
+because it includes the Temple of Hut
+
+ align:start position:0%
+because it includes the Temple of Hut
+ 
+
+ align:start position:0%
+because it includes the Temple of Hut
+and the med Tabu over here so this again
+
+ align:start position:0%
+and the med Tabu over here so this again
+ 
+
+ align:start position:0%
+and the med Tabu over here so this again
+and and the the are double-headed
+
+ align:start position:0%
+and and the the are double-headed
+ 
+
+ align:start position:0%
+and and the the are double-headed
+because there's different in different
+
+ align:start position:0%
+because there's different in different
+ 
+
+ align:start position:0%
+because there's different in different
+area eras uh The Roots went different
+
+ align:start position:0%
+area eras uh The Roots went different
+ 
+
+ align:start position:0%
+area eras uh The Roots went different
+way sometimes they went out on the water
+
+ align:start position:0%
+way sometimes they went out on the water
+ 
+
+ align:start position:0%
+way sometimes they went out on the water
+and came back on the water and sometimes
+
+ align:start position:0%
+and came back on the water and sometimes
+ 
+
+ align:start position:0%
+and came back on the water and sometimes
+they went over the
+
+ align:start position:0%
+they went over the
+ 
+
+ align:start position:0%
+they went over the
+land um and so here it is a kind of a
+
+ align:start position:0%
+land um and so here it is a kind of a
+ 
+
+ align:start position:0%
+land um and so here it is a kind of a
+plan view again here you can see how
+
+ align:start position:0%
+plan view again here you can see how
+ 
+
+ align:start position:0%
+plan view again here you can see how
+there's multiple Pathways here but the
+
+ align:start position:0%
+there's multiple Pathways here but the
+ 
+
+ align:start position:0%
+there's multiple Pathways here but the
+key to our understanding is and just a
+
+ align:start position:0%
+key to our understanding is and just a
+ 
+
+ align:start position:0%
+key to our understanding is and just a
+couple views here this is of the ram
+
+ align:start position:0%
+couple views here this is of the ram
+ 
+
+ align:start position:0%
+couple views here this is of the ram
+headed spin so this is this you can
+
+ align:start position:0%
+headed spin so this is this you can
+ 
+
+ align:start position:0%
+headed spin so this is this you can
+obviously get a sense of this very
+
+ align:start position:0%
+obviously get a sense of this very
+ 
+
+ align:start position:0%
+obviously get a sense of this very
+hieratic um sort of processional space
+
+ align:start position:0%
+hieratic um sort of processional space
+ 
+
+ align:start position:0%
+hieratic um sort of processional space
+that that was occurring um and so my my
+
+ align:start position:0%
+that that was occurring um and so my my
+ 
+
+ align:start position:0%
+that that was occurring um and so my my
+kind of diagram here sort of tries to
+
+ align:start position:0%
+kind of diagram here sort of tries to
+ 
+
+ align:start position:0%
+kind of diagram here sort of tries to
+understand this notion of the Sacred in
+
+ align:start position:0%
+understand this notion of the Sacred in
+ 
+
+ align:start position:0%
+understand this notion of the Sacred in
+the profane in this Carnac uh example
+
+ align:start position:0%
+the profane in this Carnac uh example
+ 
+
+ align:start position:0%
+the profane in this Carnac uh example
+and so I would put forward that the
+
+ align:start position:0%
+and so I would put forward that the
+ 
+
+ align:start position:0%
+and so I would put forward that the
+sacred is not necess is is not only an
+
+ align:start position:0%
+sacred is not necess is is not only an
+ 
+
+ align:start position:0%
+sacred is not necess is is not only an
+object here the little sacred which is
+
+ align:start position:0%
+object here the little sacred which is
+ 
+
+ align:start position:0%
+object here the little sacred which is
+the image of the god or The God himself
+
+ align:start position:0%
+the image of the god or The God himself
+ 
+
+ align:start position:0%
+the image of the god or The God himself
+uh but he's within the sacred Temple
+
+ align:start position:0%
+uh but he's within the sacred Temple
+ 
+
+ align:start position:0%
+uh but he's within the sacred Temple
+complex and he's literally processed
+
+ align:start position:0%
+complex and he's literally processed
+ 
+
+ align:start position:0%
+complex and he's literally processed
+through profane spaces to go visit his
+
+ align:start position:0%
+through profane spaces to go visit his
+ 
+
+ align:start position:0%
+through profane spaces to go visit his
+son konu or his wife mut so he's going
+
+ align:start position:0%
+son konu or his wife mut so he's going
+ 
+
+ align:start position:0%
+son konu or his wife mut so he's going
+to these different he's processed
+
+ align:start position:0%
+to these different he's processed
+ 
+
+ align:start position:0%
+to these different he's processed
+through these different Temple complexes
+
+ align:start position:0%
+through these different Temple complexes
+ 
+
+ align:start position:0%
+through these different Temple complexes
+and eventually he ends up back in
+
+ align:start position:0%
+and eventually he ends up back in
+ 
+
+ align:start position:0%
+and eventually he ends up back in
+another Sacred Space so uh what happens
+
+ align:start position:0%
+another Sacred Space so uh what happens
+ 
+
+ align:start position:0%
+another Sacred Space so uh what happens
+is that the people of um the people in
+
+ align:start position:0%
+is that the people of um the people in
+ 
+
+ align:start position:0%
+is that the people of um the people in
+the procession actually pick up the bark
+
+ align:start position:0%
+the procession actually pick up the bark
+ 
+
+ align:start position:0%
+the procession actually pick up the bark
+so this is an example here of the bark
+
+ align:start position:0%
+so this is an example here of the bark
+ 
+
+ align:start position:0%
+so this is an example here of the bark
+and then the image of the godhead is
+
+ align:start position:0%
+and then the image of the godhead is
+ 
+
+ align:start position:0%
+and then the image of the godhead is
+inside and thus the belief is that the
+
+ align:start position:0%
+inside and thus the belief is that the
+ 
+
+ align:start position:0%
+inside and thus the belief is that the
+God is there he's present there they've
+
+ align:start position:0%
+God is there he's present there they've
+ 
+
+ align:start position:0%
+God is there he's present there they've
+removed him from the inner sanctum of
+
+ align:start position:0%
+removed him from the inner sanctum of
+ 
+
+ align:start position:0%
+removed him from the inner sanctum of
+the temple and he's processed through
+
+ align:start position:0%
+the temple and he's processed through
+ 
+
+ align:start position:0%
+the temple and he's processed through
+space and so here all the celebrations
+
+ align:start position:0%
+space and so here all the celebrations
+ 
+
+ align:start position:0%
+space and so here all the celebrations
+they people are bringing cattle with
+
+ align:start position:0%
+they people are bringing cattle with
+ 
+
+ align:start position:0%
+they people are bringing cattle with
+them and here we can see play people
+
+ align:start position:0%
+them and here we can see play people
+ 
+
+ align:start position:0%
+them and here we can see play people
+playing a loot likee object so there's
+
+ align:start position:0%
+playing a loot likee object so there's
+ 
+
+ align:start position:0%
+playing a loot likee object so there's
+and this is an artist rendering of the
+
+ align:start position:0%
+and this is an artist rendering of the
+ 
+
+ align:start position:0%
+and this is an artist rendering of the
+of a large bark on the River on the Nile
+
+ align:start position:0%
+of a large bark on the River on the Nile
+ 
+
+ align:start position:0%
+of a large bark on the River on the Nile
+and then within it you can see the small
+
+ align:start position:0%
+and then within it you can see the small
+ 
+
+ align:start position:0%
+and then within it you can see the small
+bark with the image of the god um God
+
+ align:start position:0%
+bark with the image of the god um God
+ 
+
+ align:start position:0%
+bark with the image of the god um God
+within it so and it's very interesting
+
+ align:start position:0%
+within it so and it's very interesting
+ 
+
+ align:start position:0%
+within it so and it's very interesting
+I'd like to just very quickly briefly
+
+ align:start position:0%
+I'd like to just very quickly briefly
+ 
+
+ align:start position:0%
+I'd like to just very quickly briefly
+read um Herodotus saw one of these
+
+ align:start position:0%
+read um Herodotus saw one of these
+ 
+
+ align:start position:0%
+read um Herodotus saw one of these
+processions at one point um our friend
+
+ align:start position:0%
+processions at one point um our friend
+ 
+
+ align:start position:0%
+processions at one point um our friend
+the Greek historian uh and he describes
+
+ align:start position:0%
+the Greek historian uh and he describes
+ 
+
+ align:start position:0%
+the Greek historian uh and he describes
+it very interesting he says the
+
+ align:start position:0%
+it very interesting he says the
+ 
+
+ align:start position:0%
+it very interesting he says the
+Egyptians hold their solemn assemblies
+
+ align:start position:0%
+Egyptians hold their solemn assemblies
+ 
+
+ align:start position:0%
+Egyptians hold their solemn assemblies
+not once in the year but often now when
+
+ align:start position:0%
+not once in the year but often now when
+ 
+
+ align:start position:0%
+not once in the year but often now when
+they are coming to the city of bubastis
+
+ align:start position:0%
+they are coming to the city of bubastis
+ 
+
+ align:start position:0%
+they are coming to the city of bubastis
+they do as follows they sail men and
+
+ align:start position:0%
+they do as follows they sail men and
+ 
+
+ align:start position:0%
+they do as follows they sail men and
+women together in a great multitude of
+
+ align:start position:0%
+women together in a great multitude of
+ 
+
+ align:start position:0%
+women together in a great multitude of
+each sex in every boat and some of the
+
+ align:start position:0%
+each sex in every boat and some of the
+ 
+
+ align:start position:0%
+each sex in every boat and some of the
+men have rattles and rattle with them
+
+ align:start position:0%
+men have rattles and rattle with them
+ 
+
+ align:start position:0%
+men have rattles and rattle with them
+while some of the men play the flute
+
+ align:start position:0%
+while some of the men play the flute
+ 
+
+ align:start position:0%
+while some of the men play the flute
+during the whole time of the voyage and
+
+ align:start position:0%
+during the whole time of the voyage and
+ 
+
+ align:start position:0%
+during the whole time of the voyage and
+the rest both men and women sing and
+
+ align:start position:0%
+the rest both men and women sing and
+ 
+
+ align:start position:0%
+the rest both men and women sing and
+clap their hands and when as and when as
+
+ align:start position:0%
+clap their hands and when as and when as
+ 
+
+ align:start position:0%
+clap their hands and when as and when as
+they sail they come opposite to any City
+
+ align:start position:0%
+they sail they come opposite to any City
+ 
+
+ align:start position:0%
+they sail they come opposite to any City
+on the way they bring the boat to land
+
+ align:start position:0%
+on the way they bring the boat to land
+ 
+
+ align:start position:0%
+on the way they bring the boat to land
+and some of the women continue to do as
+
+ align:start position:0%
+and some of the women continue to do as
+ 
+
+ align:start position:0%
+and some of the women continue to do as
+I have said others cry allow and Jer at
+
+ align:start position:0%
+I have said others cry allow and Jer at
+ 
+
+ align:start position:0%
+I have said others cry allow and Jer at
+the women in the city some dance and
+
+ align:start position:0%
+the women in the city some dance and
+ 
+
+ align:start position:0%
+the women in the city some dance and
+some stand up and pull their pull up
+
+ align:start position:0%
+some stand up and pull their pull up
+ 
+
+ align:start position:0%
+some stand up and pull their pull up
+their garments this they do by every
+
+ align:start position:0%
+their garments this they do by every
+ 
+
+ align:start position:0%
+their garments this they do by every
+city along the riverbank and when they
+
+ align:start position:0%
+city along the riverbank and when they
+ 
+
+ align:start position:0%
+city along the riverbank and when they
+come to basas they hold Festival SE
+
+ align:start position:0%
+come to basas they hold Festival SE
+ 
+
+ align:start position:0%
+come to basas they hold Festival SE
+celebrating great sacrifices and more
+
+ align:start position:0%
+celebrating great sacrifices and more
+ 
+
+ align:start position:0%
+celebrating great sacrifices and more
+wine of grapes is consumed upon that
+
+ align:start position:0%
+wine of grapes is consumed upon that
+ 
+
+ align:start position:0%
+wine of grapes is consumed upon that
+Festival than then during the whole rest
+
+ align:start position:0%
+Festival than then during the whole rest
+ 
+
+ align:start position:0%
+Festival than then during the whole rest
+of the year so um you can see here that
+
+ align:start position:0%
+of the year so um you can see here that
+ 
+
+ align:start position:0%
+of the year so um you can see here that
+these and and um these individuals in
+
+ align:start position:0%
+these and and um these individuals in
+ 
+
+ align:start position:0%
+these and and um these individuals in
+these reliefs that are out of the Luxor
+
+ align:start position:0%
+these reliefs that are out of the Luxor
+ 
+
+ align:start position:0%
+these reliefs that are out of the Luxor
+Temple and the and the carac these are
+
+ align:start position:0%
+Temple and the and the carac these are
+ 
+
+ align:start position:0%
+Temple and the and the carac these are
+just a variety of reliefs kind of
+
+ align:start position:0%
+just a variety of reliefs kind of
+ 
+
+ align:start position:0%
+just a variety of reliefs kind of
+showing kind of outlining this this
+
+ align:start position:0%
+showing kind of outlining this this
+ 
+
+ align:start position:0%
+showing kind of outlining this this
+processional activity and these priests
+
+ align:start position:0%
+processional activity and these priests
+ 
+
+ align:start position:0%
+processional activity and these priests
+are called wob priests um and
+
+ align:start position:0%
+are called wob priests um and
+ 
+
+ align:start position:0%
+are called wob priests um and
+uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um excuse me the the next tradition that
+
+ align:start position:0%
+um excuse me the the next tradition that
+ 
+
+ align:start position:0%
+um excuse me the the next tradition that
+uh we would like to we're going to take
+
+ align:start position:0%
+uh we would like to we're going to take
+ 
+
+ align:start position:0%
+uh we would like to we're going to take
+a look at here um differs to quite some
+
+ align:start position:0%
+a look at here um differs to quite some
+ 
+
+ align:start position:0%
+a look at here um differs to quite some
+extent um and this is Buddhism now we've
+
+ align:start position:0%
+extent um and this is Buddhism now we've
+ 
+
+ align:start position:0%
+extent um and this is Buddhism now we've
+already talked about the Buddha and his
+
+ align:start position:0%
+already talked about the Buddha and his
+ 
+
+ align:start position:0%
+already talked about the Buddha and his
+his um
+
+ align:start position:0%
+his um
+ 
+
+ align:start position:0%
+his um
+his Origins and and the kind of origins
+
+ align:start position:0%
+his Origins and and the kind of origins
+ 
+
+ align:start position:0%
+his Origins and and the kind of origins
+of Buddhism and the the fact that it uh
+
+ align:start position:0%
+of Buddhism and the the fact that it uh
+ 
+
+ align:start position:0%
+of Buddhism and the the fact that it uh
+begins in India and it kind of spreads
+
+ align:start position:0%
+begins in India and it kind of spreads
+ 
+
+ align:start position:0%
+begins in India and it kind of spreads
+uh throughout Asia um and so we've
+
+ align:start position:0%
+uh throughout Asia um and so we've
+ 
+
+ align:start position:0%
+uh throughout Asia um and so we've
+covered that but what I'd like to come
+
+ align:start position:0%
+covered that but what I'd like to come
+ 
+
+ align:start position:0%
+covered that but what I'd like to come
+back to now is this notion of pilgrimage
+
+ align:start position:0%
+back to now is this notion of pilgrimage
+ 
+
+ align:start position:0%
+back to now is this notion of pilgrimage
+with Buddhism and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the um you know as we've talked about
+
+ align:start position:0%
+um the um you know as we've talked about
+ 
+
+ align:start position:0%
+um the um you know as we've talked about
+before we've talked about the eight-fold
+
+ align:start position:0%
+before we've talked about the eight-fold
+ 
+
+ align:start position:0%
+before we've talked about the eight-fold
+path and what it means to you know
+
+ align:start position:0%
+path and what it means to you know
+ 
+
+ align:start position:0%
+path and what it means to you know
+Enlightenment we've discussed
+
+ align:start position:0%
+Enlightenment we've discussed
+ 
+
+ align:start position:0%
+Enlightenment we've discussed
+uh the ideas of the stupa and what those
+
+ align:start position:0%
+uh the ideas of the stupa and what those
+ 
+
+ align:start position:0%
+uh the ideas of the stupa and what those
+are um and the variety of traditions
+
+ align:start position:0%
+are um and the variety of traditions
+ 
+
+ align:start position:0%
+are um and the variety of traditions
+obviously here this is an example from
+
+ align:start position:0%
+obviously here this is an example from
+ 
+
+ align:start position:0%
+obviously here this is an example from
+Thailand of of a Buddhist uh procession
+
+ align:start position:0%
+Thailand of of a Buddhist uh procession
+ 
+
+ align:start position:0%
+Thailand of of a Buddhist uh procession
+this is also an an example um of a um a
+
+ align:start position:0%
+this is also an an example um of a um a
+ 
+
+ align:start position:0%
+this is also an an example um of a um a
+Buddhist Shrine in Myanmar and this this
+
+ align:start position:0%
+Buddhist Shrine in Myanmar and this this
+ 
+
+ align:start position:0%
+Buddhist Shrine in Myanmar and this this
+I just show this slide basically because
+
+ align:start position:0%
+I just show this slide basically because
+ 
+
+ align:start position:0%
+I just show this slide basically because
+um there's this notion in Buddhism that
+
+ align:start position:0%
+um there's this notion in Buddhism that
+ 
+
+ align:start position:0%
+um there's this notion in Buddhism that
+I've come across of
+
+ align:start position:0%
+I've come across of
+ 
+
+ align:start position:0%
+I've come across of
+um the kind of difficulty associated
+
+ align:start position:0%
+um the kind of difficulty associated
+ 
+
+ align:start position:0%
+um the kind of difficulty associated
+with the path
+
+ align:start position:0%
+with the path
+ 
+
+ align:start position:0%
+with the path
+is warrants more and there's like an
+
+ align:start position:0%
+is warrants more and there's like an
+ 
+
+ align:start position:0%
+is warrants more and there's like an
+accumulation of Merit there's this a
+
+ align:start position:0%
+accumulation of Merit there's this a
+ 
+
+ align:start position:0%
+accumulation of Merit there's this a
+kind of accum the harder the path the
+
+ align:start position:0%
+kind of accum the harder the path the
+ 
+
+ align:start position:0%
+kind of accum the harder the path the
+more the struggle the greater the
+
+ align:start position:0%
+more the struggle the greater the
+ 
+
+ align:start position:0%
+more the struggle the greater the
+attainment of some kind of spiritual or
+
+ align:start position:0%
+attainment of some kind of spiritual or
+ 
+
+ align:start position:0%
+attainment of some kind of spiritual or
+um kind of Merit I guess is for lack of
+
+ align:start position:0%
+um kind of Merit I guess is for lack of
+ 
+
+ align:start position:0%
+um kind of Merit I guess is for lack of
+a better term um but really I'd like to
+
+ align:start position:0%
+a better term um but really I'd like to
+ 
+
+ align:start position:0%
+a better term um but really I'd like to
+point us to the uh the scriptural basis
+
+ align:start position:0%
+point us to the uh the scriptural basis
+ 
+
+ align:start position:0%
+point us to the uh the scriptural basis
+and motivation um within Buddhism um and
+
+ align:start position:0%
+and motivation um within Buddhism um and
+ 
+
+ align:start position:0%
+and motivation um within Buddhism um and
+here the Buddha is uh
+
+ align:start position:0%
+here the Buddha is uh
+ 
+
+ align:start position:0%
+here the Buddha is uh
+um believed to have said to called for
+
+ align:start position:0%
+um believed to have said to called for
+ 
+
+ align:start position:0%
+um believed to have said to called for
+the P the pilgrimage to four main sites
+
+ align:start position:0%
+the P the pilgrimage to four main sites
+ 
+
+ align:start position:0%
+the P the pilgrimage to four main sites
+so he says um here the tagata uh which
+
+ align:start position:0%
+so he says um here the tagata uh which
+ 
+
+ align:start position:0%
+so he says um here the tagata uh which
+is um he's referring to himself the
+
+ align:start position:0%
+is um he's referring to himself the
+ 
+
+ align:start position:0%
+is um he's referring to himself the
+perfected one he says that the first is
+
+ align:start position:0%
+perfected one he says that the first is
+ 
+
+ align:start position:0%
+perfected one he says that the first is
+where he was born the second is where he
+
+ align:start position:0%
+where he was born the second is where he
+ 
+
+ align:start position:0%
+where he was born the second is where he
+attained Supreme
+
+ align:start position:0%
+attained Supreme
+ 
+
+ align:start position:0%
+attained Supreme
+Enlightenment uh the fourth is where the
+
+ align:start position:0%
+Enlightenment uh the fourth is where the
+ 
+
+ align:start position:0%
+Enlightenment uh the fourth is where the
+third is where he set in the wheel of
+
+ align:start position:0%
+third is where he set in the wheel of
+ 
+
+ align:start position:0%
+third is where he set in the wheel of
+Dharma the where he gave his first
+
+ align:start position:0%
+Dharma the where he gave his first
+ 
+
+ align:start position:0%
+Dharma the where he gave his first
+lecture and then the fourth is where he
+
+ align:start position:0%
+lecture and then the fourth is where he
+ 
+
+ align:start position:0%
+lecture and then the fourth is where he
+um passed away into Nirvana where he
+
+ align:start position:0%
+um passed away into Nirvana where he
+ 
+
+ align:start position:0%
+um passed away into Nirvana where he
+died and so these uh to to to kind of
+
+ align:start position:0%
+died and so these uh to to to kind of
+ 
+
+ align:start position:0%
+died and so these uh to to to kind of
+illustrate some of the the themes around
+
+ align:start position:0%
+illustrate some of the the themes around
+ 
+
+ align:start position:0%
+illustrate some of the the themes around
+Buddhist pilgrimage that sort of begin
+
+ align:start position:0%
+Buddhist pilgrimage that sort of begin
+ 
+
+ align:start position:0%
+Buddhist pilgrimage that sort of begin
+to Define it um are that the this early
+
+ align:start position:0%
+to Define it um are that the this early
+ 
+
+ align:start position:0%
+to Define it um are that the this early
+notion of Buddhist pilgrimage is based
+
+ align:start position:0%
+notion of Buddhist pilgrimage is based
+ 
+
+ align:start position:0%
+notion of Buddhist pilgrimage is based
+around the Buddha life so many people
+
+ align:start position:0%
+around the Buddha life so many people
+ 
+
+ align:start position:0%
+around the Buddha life so many people
+will travel to these different sacred
+
+ align:start position:0%
+will travel to these different sacred
+ 
+
+ align:start position:0%
+will travel to these different sacred
+places uh in in the order in which they
+
+ align:start position:0%
+places uh in in the order in which they
+ 
+
+ align:start position:0%
+places uh in in the order in which they
+happened not necessarily from what I've
+
+ align:start position:0%
+happened not necessarily from what I've
+ 
+
+ align:start position:0%
+happened not necessarily from what I've
+come across but it is sometimes uh if
+
+ align:start position:0%
+come across but it is sometimes uh if
+ 
+
+ align:start position:0%
+come across but it is sometimes uh if
+somebody's going to do the entire route
+
+ align:start position:0%
+somebody's going to do the entire route
+ 
+
+ align:start position:0%
+somebody's going to do the entire route
+they'll go the they'll go to everyone in
+
+ align:start position:0%
+they'll go the they'll go to everyone in
+ 
+
+ align:start position:0%
+they'll go the they'll go to everyone in
+that order uh and so you're sort of
+
+ align:start position:0%
+that order uh and so you're sort of
+ 
+
+ align:start position:0%
+that order uh and so you're sort of
+traveling in this path of the Buddha of
+
+ align:start position:0%
+traveling in this path of the Buddha of
+ 
+
+ align:start position:0%
+traveling in this path of the Buddha of
+a of a holy individual you're kind of
+
+ align:start position:0%
+a of a holy individual you're kind of
+ 
+
+ align:start position:0%
+a of a holy individual you're kind of
+recreating their you're re trying to
+
+ align:start position:0%
+recreating their you're re trying to
+ 
+
+ align:start position:0%
+recreating their you're re trying to
+re-experience their life essentially um
+
+ align:start position:0%
+re-experience their life essentially um
+ 
+
+ align:start position:0%
+re-experience their life essentially um
+and there are relics Within These
+
+ align:start position:0%
+and there are relics Within These
+ 
+
+ align:start position:0%
+and there are relics Within These
+different places so um the presence or
+
+ align:start position:0%
+different places so um the presence or
+ 
+
+ align:start position:0%
+different places so um the presence or
+the sacred throughout the land is sort
+
+ align:start position:0%
+the sacred throughout the land is sort
+ 
+
+ align:start position:0%
+the sacred throughout the land is sort
+of dispersed throughout the
+
+ align:start position:0%
+of dispersed throughout the
+ 
+
+ align:start position:0%
+of dispersed throughout the
+landscape um and circumambulation is a
+
+ align:start position:0%
+landscape um and circumambulation is a
+ 
+
+ align:start position:0%
+landscape um and circumambulation is a
+big is a key feature to Buddhism there's
+
+ align:start position:0%
+big is a key feature to Buddhism there's
+ 
+
+ align:start position:0%
+big is a key feature to Buddhism there's
+um a lot of circum ulation as a kind of
+
+ align:start position:0%
+um a lot of circum ulation as a kind of
+ 
+
+ align:start position:0%
+um a lot of circum ulation as a kind of
+a spiritual um
+
+ align:start position:0%
+a spiritual um
+ 
+
+ align:start position:0%
+a spiritual um
+um as a sort of spiritual reflection uh
+
+ align:start position:0%
+um as a sort of spiritual reflection uh
+ 
+
+ align:start position:0%
+um as a sort of spiritual reflection uh
+and also the accumulation of Merit for
+
+ align:start position:0%
+and also the accumulation of Merit for
+ 
+
+ align:start position:0%
+and also the accumulation of Merit for
+long and difficult Journeys which I've
+
+ align:start position:0%
+long and difficult Journeys which I've
+ 
+
+ align:start position:0%
+long and difficult Journeys which I've
+already briefly discussed um the four
+
+ align:start position:0%
+already briefly discussed um the four
+ 
+
+ align:start position:0%
+already briefly discussed um the four
+main locations uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops uh are lumini um sarth bodgaya and
+
+ align:start position:0%
+oops uh are lumini um sarth bodgaya and
+ 
+
+ align:start position:0%
+oops uh are lumini um sarth bodgaya and
+um kushnar which um are the sites that
+
+ align:start position:0%
+um kushnar which um are the sites that
+ 
+
+ align:start position:0%
+um kushnar which um are the sites that
+we'll be looking at um specifically but
+
+ align:start position:0%
+we'll be looking at um specifically but
+ 
+
+ align:start position:0%
+we'll be looking at um specifically but
+before we get into that again I would
+
+ align:start position:0%
+before we get into that again I would
+ 
+
+ align:start position:0%
+before we get into that again I would
+like to kind of I'm trying to you know
+
+ align:start position:0%
+like to kind of I'm trying to you know
+ 
+
+ align:start position:0%
+like to kind of I'm trying to you know
+come back to our notion of the Sacred
+
+ align:start position:0%
+come back to our notion of the Sacred
+ 
+
+ align:start position:0%
+come back to our notion of the Sacred
+and the profane with each of these
+
+ align:start position:0%
+and the profane with each of these
+ 
+
+ align:start position:0%
+and the profane with each of these
+examples and this is just another
+
+ align:start position:0%
+examples and this is just another
+ 
+
+ align:start position:0%
+examples and this is just another
+diagram kind of trying to outline the
+
+ align:start position:0%
+diagram kind of trying to outline the
+ 
+
+ align:start position:0%
+diagram kind of trying to outline the
+way in which you know one way at least
+
+ align:start position:0%
+way in which you know one way at least
+ 
+
+ align:start position:0%
+way in which you know one way at least
+in which we can
+
+ align:start position:0%
+in which we can
+ 
+
+ align:start position:0%
+in which we can
+view um an understanding of the Sacred
+
+ align:start position:0%
+view um an understanding of the Sacred
+ 
+
+ align:start position:0%
+view um an understanding of the Sacred
+and profane and early Buddhist
+
+ align:start position:0%
+and profane and early Buddhist
+ 
+
+ align:start position:0%
+and profane and early Buddhist
+pilgrimage and so here again we have
+
+ align:start position:0%
+pilgrimage and so here again we have
+ 
+
+ align:start position:0%
+pilgrimage and so here again we have
+these kind of sacred nodes and we passed
+
+ align:start position:0%
+these kind of sacred nodes and we passed
+ 
+
+ align:start position:0%
+these kind of sacred nodes and we passed
+through them through the profane to get
+
+ align:start position:0%
+through them through the profane to get
+ 
+
+ align:start position:0%
+through them through the profane to get
+to get to each one and and and like I
+
+ align:start position:0%
+to get to each one and and and like I
+ 
+
+ align:start position:0%
+to get to each one and and and like I
+said earlier there's not a a um a
+
+ align:start position:0%
+said earlier there's not a a um a
+ 
+
+ align:start position:0%
+said earlier there's not a a um a
+specific manner in which that happens
+
+ align:start position:0%
+specific manner in which that happens
+ 
+
+ align:start position:0%
+specific manner in which that happens
+but this becomes more complicated when
+
+ align:start position:0%
+but this becomes more complicated when
+ 
+
+ align:start position:0%
+but this becomes more complicated when
+um Buddha's relics are distributed into
+
+ align:start position:0%
+um Buddha's relics are distributed into
+ 
+
+ align:start position:0%
+um Buddha's relics are distributed into
+over 880,000 places and um this it
+
+ align:start position:0%
+over 880,000 places and um this it
+ 
+
+ align:start position:0%
+over 880,000 places and um this it
+becomes a little bit more complicated
+
+ align:start position:0%
+becomes a little bit more complicated
+ 
+
+ align:start position:0%
+becomes a little bit more complicated
+later but for now we're kind of trying
+
+ align:start position:0%
+later but for now we're kind of trying
+ 
+
+ align:start position:0%
+later but for now we're kind of trying
+to focus on the early uh aspects the
+
+ align:start position:0%
+to focus on the early uh aspects the
+ 
+
+ align:start position:0%
+to focus on the early uh aspects the
+um the first um this is the birthplace
+
+ align:start position:0%
+um the first um this is the birthplace
+ 
+
+ align:start position:0%
+um the first um this is the birthplace
+of the Buddha uh in lumini which is
+
+ align:start position:0%
+of the Buddha uh in lumini which is
+ 
+
+ align:start position:0%
+of the Buddha uh in lumini which is
+present day Nepal uh he was born in 563
+
+ align:start position:0%
+present day Nepal uh he was born in 563
+ 
+
+ align:start position:0%
+present day Nepal uh he was born in 563
+approximately and um located in the
+
+ align:start position:0%
+approximately and um located in the
+ 
+
+ align:start position:0%
+approximately and um located in the
+foothills of the Himalayas and uh what
+
+ align:start position:0%
+foothills of the Himalayas and uh what
+ 
+
+ align:start position:0%
+foothills of the Himalayas and uh what
+we see here on the left is an asokan
+
+ align:start position:0%
+we see here on the left is an asokan
+ 
+
+ align:start position:0%
+we see here on the left is an asokan
+pillar uh which marks the birthplace of
+
+ align:start position:0%
+pillar uh which marks the birthplace of
+ 
+
+ align:start position:0%
+pillar uh which marks the birthplace of
+the Buddha and you can see you can see
+
+ align:start position:0%
+the Buddha and you can see you can see
+ 
+
+ align:start position:0%
+the Buddha and you can see you can see
+the uh monks and other pilgrims kind of
+
+ align:start position:0%
+the uh monks and other pilgrims kind of
+ 
+
+ align:start position:0%
+the uh monks and other pilgrims kind of
+circum ulating around it uh and then on
+
+ align:start position:0%
+circum ulating around it uh and then on
+ 
+
+ align:start position:0%
+circum ulating around it uh and then on
+the right we have a reflecting pool with
+
+ align:start position:0%
+the right we have a reflecting pool with
+ 
+
+ align:start position:0%
+the right we have a reflecting pool with
+a a more recent
+
+ align:start position:0%
+a a more recent
+ 
+
+ align:start position:0%
+a a more recent
+Temple this second example is this is
+
+ align:start position:0%
+Temple this second example is this is
+ 
+
+ align:start position:0%
+Temple this second example is this is
+where the Buddha delivered his first
+
+ align:start position:0%
+where the Buddha delivered his first
+ 
+
+ align:start position:0%
+where the Buddha delivered his first
+meeting where people come to pilgrimage
+
+ align:start position:0%
+meeting where people come to pilgrimage
+ 
+
+ align:start position:0%
+meeting where people come to pilgrimage
+they also circum ulate this stupa this
+
+ align:start position:0%
+they also circum ulate this stupa this
+ 
+
+ align:start position:0%
+they also circum ulate this stupa this
+is the dhek stupa uh again built by
+
+ align:start position:0%
+is the dhek stupa uh again built by
+ 
+
+ align:start position:0%
+is the dhek stupa uh again built by
+Asoka uh in the 3D Century so
+
+ align:start position:0%
+Asoka uh in the 3D Century so
+ 
+
+ align:start position:0%
+Asoka uh in the 3D Century so
+essentially the great emperor Oka came
+
+ align:start position:0%
+essentially the great emperor Oka came
+ 
+
+ align:start position:0%
+essentially the great emperor Oka came
+and sort of created all these built all
+
+ align:start position:0%
+and sort of created all these built all
+ 
+
+ align:start position:0%
+and sort of created all these built all
+these monuments to commemorate uh the
+
+ align:start position:0%
+these monuments to commemorate uh the
+ 
+
+ align:start position:0%
+these monuments to commemorate uh the
+Buddha and so
+
+ align:start position:0%
+Buddha and so
+ 
+
+ align:start position:0%
+Buddha and so
+um the third place is one of the most
+
+ align:start position:0%
+um the third place is one of the most
+ 
+
+ align:start position:0%
+um the third place is one of the most
+holy it's where he uh achieved
+
+ align:start position:0%
+holy it's where he uh achieved
+ 
+
+ align:start position:0%
+holy it's where he uh achieved
+Enlightenment uh next under the Bodhi
+
+ align:start position:0%
+Enlightenment uh next under the Bodhi
+ 
+
+ align:start position:0%
+Enlightenment uh next under the Bodhi
+Tree uh which is what this Temple the
+
+ align:start position:0%
+Tree uh which is what this Temple the
+ 
+
+ align:start position:0%
+Tree uh which is what this Temple the
+bodaya the um at bodgaya the mahabodhi
+
+ align:start position:0%
+bodaya the um at bodgaya the mahabodhi
+ 
+
+ align:start position:0%
+bodaya the um at bodgaya the mahabodhi
+temple uh commemorates this is a brick
+
+ align:start position:0%
+temple uh commemorates this is a brick
+ 
+
+ align:start position:0%
+temple uh commemorates this is a brick
+structure um and it
+
+ align:start position:0%
+structure um and it
+ 
+
+ align:start position:0%
+structure um and it
+is approximately 180 ft tall and um the
+
+ align:start position:0%
+is approximately 180 ft tall and um the
+ 
+
+ align:start position:0%
+is approximately 180 ft tall and um the
+brick work um depicts scenes from the
+
+ align:start position:0%
+brick work um depicts scenes from the
+ 
+
+ align:start position:0%
+brick work um depicts scenes from the
+life of the Buddha and this is where he
+
+ align:start position:0%
+life of the Buddha and this is where he
+ 
+
+ align:start position:0%
+life of the Buddha and this is where he
+really is transformed from Prince gatama
+
+ align:start position:0%
+really is transformed from Prince gatama
+ 
+
+ align:start position:0%
+really is transformed from Prince gatama
+to the Lord Buddha um so this is an
+
+ align:start position:0%
+to the Lord Buddha um so this is an
+ 
+
+ align:start position:0%
+to the Lord Buddha um so this is an
+extremely important um location for
+
+ align:start position:0%
+extremely important um location for
+ 
+
+ align:start position:0%
+extremely important um location for
+pilgrims this is a footprint sculpture
+
+ align:start position:0%
+pilgrims this is a footprint sculpture
+ 
+
+ align:start position:0%
+pilgrims this is a footprint sculpture
+of the Buddhist feet uh and also a
+
+ align:start position:0%
+of the Buddhist feet uh and also a
+ 
+
+ align:start position:0%
+of the Buddhist feet uh and also a
+pilgrim inside commemorating uh the life
+
+ align:start position:0%
+pilgrim inside commemorating uh the life
+ 
+
+ align:start position:0%
+pilgrim inside commemorating uh the life
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+Buddha the last place is the is
+
+ align:start position:0%
+Buddha the last place is the is
+ 
+
+ align:start position:0%
+Buddha the last place is the is
+kushinagar which is where the Buddha
+
+ align:start position:0%
+kushinagar which is where the Buddha
+ 
+
+ align:start position:0%
+kushinagar which is where the Buddha
+passed away um on the bottom we see a
+
+ align:start position:0%
+passed away um on the bottom we see a
+ 
+
+ align:start position:0%
+passed away um on the bottom we see a
+six meter long statue that was excavated
+
+ align:start position:0%
+six meter long statue that was excavated
+ 
+
+ align:start position:0%
+six meter long statue that was excavated
+in the 19th century um and um the
+
+ align:start position:0%
+in the 19th century um and um the
+ 
+
+ align:start position:0%
+in the 19th century um and um the
+Buddhist remains were at one point
+
+ align:start position:0%
+Buddhist remains were at one point
+ 
+
+ align:start position:0%
+Buddhist remains were at one point
+deposited here under the Nirvana stupa
+
+ align:start position:0%
+deposited here under the Nirvana stupa
+ 
+
+ align:start position:0%
+deposited here under the Nirvana stupa
+um and um basically this is where he
+
+ align:start position:0%
+um and um basically this is where he
+ 
+
+ align:start position:0%
+um and um basically this is where he
+performed his last sermon and
+
+ align:start position:0%
+performed his last sermon and
+ 
+
+ align:start position:0%
+performed his last sermon and
+subsequently passed
+
+ align:start position:0%
+subsequently passed
+ 
+
+ align:start position:0%
+subsequently passed
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+so as we move forward we we're going to
+
+ align:start position:0%
+so as we move forward we we're going to
+ 
+
+ align:start position:0%
+so as we move forward we we're going to
+take a look at um the tradition of Islam
+
+ align:start position:0%
+take a look at um the tradition of Islam
+ 
+
+ align:start position:0%
+take a look at um the tradition of Islam
+and pilgrimage which I sort of argue
+
+ align:start position:0%
+and pilgrimage which I sort of argue
+ 
+
+ align:start position:0%
+and pilgrimage which I sort of argue
+here in my title is consolidation and
+
+ align:start position:0%
+here in my title is consolidation and
+ 
+
+ align:start position:0%
+here in my title is consolidation and
+globalization of pilgrimage
+
+ align:start position:0%
+globalization of pilgrimage
+ 
+
+ align:start position:0%
+globalization of pilgrimage
+and um I say that
+
+ align:start position:0%
+and um I say that
+ 
+
+ align:start position:0%
+and um I say that
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+um in Islam no matter where you are
+
+ align:start position:0%
+um in Islam no matter where you are
+ 
+
+ align:start position:0%
+um in Islam no matter where you are
+you're essentially required to go to
+
+ align:start position:0%
+you're essentially required to go to
+ 
+
+ align:start position:0%
+you're essentially required to go to
+Mecca to make the pilgrimage or the Hajj
+
+ align:start position:0%
+Mecca to make the pilgrimage or the Hajj
+ 
+
+ align:start position:0%
+Mecca to make the pilgrimage or the Hajj
+um and this obviously entails can can
+
+ align:start position:0%
+um and this obviously entails can can
+ 
+
+ align:start position:0%
+um and this obviously entails can can
+entail quite a bit of um of travel and
+
+ align:start position:0%
+entail quite a bit of um of travel and
+ 
+
+ align:start position:0%
+entail quite a bit of um of travel and
+so uh similar to Buddhism uh Islam is
+
+ align:start position:0%
+so uh similar to Buddhism uh Islam is
+ 
+
+ align:start position:0%
+so uh similar to Buddhism uh Islam is
+scripturally based it's in the Quran
+
+ align:start position:0%
+scripturally based it's in the Quran
+ 
+
+ align:start position:0%
+scripturally based it's in the Quran
+it's also the fifth pillar of Islam
+
+ align:start position:0%
+it's also the fifth pillar of Islam
+ 
+
+ align:start position:0%
+it's also the fifth pillar of Islam
+which uh requires mus all Muslims to go
+
+ align:start position:0%
+which uh requires mus all Muslims to go
+ 
+
+ align:start position:0%
+which uh requires mus all Muslims to go
+make the um Hajj and so here we just
+
+ align:start position:0%
+make the um Hajj and so here we just
+ 
+
+ align:start position:0%
+make the um Hajj and so here we just
+have a very basic very uh quick slide um
+
+ align:start position:0%
+have a very basic very uh quick slide um
+ 
+
+ align:start position:0%
+have a very basic very uh quick slide um
+to slide 38 to indicate um to show the
+
+ align:start position:0%
+to slide 38 to indicate um to show the
+ 
+
+ align:start position:0%
+to slide 38 to indicate um to show the
+significance of of the kabah in Mecca
+
+ align:start position:0%
+significance of of the kabah in Mecca
+ 
+
+ align:start position:0%
+significance of of the kabah in Mecca
+I'm going to get back to this in a
+
+ align:start position:0%
+I'm going to get back to this in a
+ 
+
+ align:start position:0%
+I'm going to get back to this in a
+minute here but what's occurring is
+
+ align:start position:0%
+minute here but what's occurring is
+ 
+
+ align:start position:0%
+minute here but what's occurring is
+circum ulation again we can see with the
+
+ align:start position:0%
+circum ulation again we can see with the
+ 
+
+ align:start position:0%
+circum ulation again we can see with the
+the kind of long exposure f photograph
+
+ align:start position:0%
+the kind of long exposure f photograph
+ 
+
+ align:start position:0%
+the kind of long exposure f photograph
+here of the movement around the
+
+ align:start position:0%
+here of the movement around the
+ 
+
+ align:start position:0%
+here of the movement around the
+Kabab um and so my diagram is naturally
+
+ align:start position:0%
+Kabab um and so my diagram is naturally
+ 
+
+ align:start position:0%
+Kabab um and so my diagram is naturally
+one that is very
+
+ align:start position:0%
+one that is very
+ 
+
+ align:start position:0%
+one that is very
+um very much
+
+ align:start position:0%
+um very much
+ 
+
+ align:start position:0%
+um very much
+about um congregating into one specific
+
+ align:start position:0%
+about um congregating into one specific
+ 
+
+ align:start position:0%
+about um congregating into one specific
+sacred holy place right so it's a very
+
+ align:start position:0%
+sacred holy place right so it's a very
+ 
+
+ align:start position:0%
+sacred holy place right so it's a very
+basic diagram that tries to just at
+
+ align:start position:0%
+basic diagram that tries to just at
+ 
+
+ align:start position:0%
+basic diagram that tries to just at
+least articulate this idea that um we're
+
+ align:start position:0%
+least articulate this idea that um we're
+ 
+
+ align:start position:0%
+least articulate this idea that um we're
+all coming from these different profane
+
+ align:start position:0%
+all coming from these different profane
+ 
+
+ align:start position:0%
+all coming from these different profane
+spaces but we all when we come together
+
+ align:start position:0%
+spaces but we all when we come together
+ 
+
+ align:start position:0%
+spaces but we all when we come together
+uh in Mecca this is the sacred it's the
+
+ align:start position:0%
+uh in Mecca this is the sacred it's the
+ 
+
+ align:start position:0%
+uh in Mecca this is the sacred it's the
+the moment of the Sacred and so just
+
+ align:start position:0%
+the moment of the Sacred and so just
+ 
+
+ align:start position:0%
+the moment of the Sacred and so just
+some very basic uh
+
+ align:start position:0%
+some very basic uh
+ 
+
+ align:start position:0%
+some very basic uh
+characteristics um I don't want to get
+
+ align:start position:0%
+characteristics um I don't want to get
+ 
+
+ align:start position:0%
+characteristics um I don't want to get
+into these too much but um circum
+
+ align:start position:0%
+into these too much but um circum
+ 
+
+ align:start position:0%
+into these too much but um circum
+ulation again but one of the biggest
+
+ align:start position:0%
+ulation again but one of the biggest
+ 
+
+ align:start position:0%
+ulation again but one of the biggest
+things I'd like to uh discuss here is
+
+ align:start position:0%
+things I'd like to uh discuss here is
+ 
+
+ align:start position:0%
+things I'd like to uh discuss here is
+this notion of communitas again um which
+
+ align:start position:0%
+this notion of communitas again um which
+ 
+
+ align:start position:0%
+this notion of communitas again um which
+really the hodj takes place once a year
+
+ align:start position:0%
+really the hodj takes place once a year
+ 
+
+ align:start position:0%
+really the hodj takes place once a year
+and you it is performed communally so
+
+ align:start position:0%
+and you it is performed communally so
+ 
+
+ align:start position:0%
+and you it is performed communally so
+this is a very big aspect to it I mean
+
+ align:start position:0%
+this is a very big aspect to it I mean
+ 
+
+ align:start position:0%
+this is a very big aspect to it I mean
+it's not to say that you can't go on the
+
+ align:start position:0%
+it's not to say that you can't go on the
+ 
+
+ align:start position:0%
+it's not to say that you can't go on the
+hjj the rest of the year but but it's uh
+
+ align:start position:0%
+hjj the rest of the year but but it's uh
+ 
+
+ align:start position:0%
+hjj the rest of the year but but it's uh
+still required that you make the Hajj as
+
+ align:start position:0%
+still required that you make the Hajj as
+ 
+
+ align:start position:0%
+still required that you make the Hajj as
+a as a communal thing um the official
+
+ align:start position:0%
+a as a communal thing um the official
+ 
+
+ align:start position:0%
+a as a communal thing um the official
+Hajj at once and so um this notion is
+
+ align:start position:0%
+Hajj at once and so um this notion is
+ 
+
+ align:start position:0%
+Hajj at once and so um this notion is
+kind of very important it's very Central
+
+ align:start position:0%
+kind of very important it's very Central
+ 
+
+ align:start position:0%
+kind of very important it's very Central
+to Islam and so the three main locations
+
+ align:start position:0%
+to Islam and so the three main locations
+ 
+
+ align:start position:0%
+to Islam and so the three main locations
+which obviously the most important is
+
+ align:start position:0%
+which obviously the most important is
+ 
+
+ align:start position:0%
+which obviously the most important is
+Mecca uh which is the al- Alam which is
+
+ align:start position:0%
+Mecca uh which is the al- Alam which is
+ 
+
+ align:start position:0%
+Mecca uh which is the al- Alam which is
+the sacred mosque uh which is the the
+
+ align:start position:0%
+the sacred mosque uh which is the the
+ 
+
+ align:start position:0%
+the sacred mosque uh which is the the
+kabah is located within that uh the
+
+ align:start position:0%
+kabah is located within that uh the
+ 
+
+ align:start position:0%
+kabah is located within that uh the
+other two main sites for pilgrimage uh
+
+ align:start position:0%
+other two main sites for pilgrimage uh
+ 
+
+ align:start position:0%
+other two main sites for pilgrimage uh
+that are not required for Islam are are
+
+ align:start position:0%
+that are not required for Islam are are
+ 
+
+ align:start position:0%
+that are not required for Islam are are
+uh Medina where the house of the Prophet
+
+ align:start position:0%
+uh Medina where the house of the Prophet
+ 
+
+ align:start position:0%
+uh Medina where the house of the Prophet
+or the mosque of the Prophet is located
+
+ align:start position:0%
+or the mosque of the Prophet is located
+ 
+
+ align:start position:0%
+or the mosque of the Prophet is located
+and also in Jerusalem uh with the Dome
+
+ align:start position:0%
+and also in Jerusalem uh with the Dome
+ 
+
+ align:start position:0%
+and also in Jerusalem uh with the Dome
+of the Rock this is just a quick a brief
+
+ align:start position:0%
+of the Rock this is just a quick a brief
+ 
+
+ align:start position:0%
+of the Rock this is just a quick a brief
+interesting um map from the 10th Century
+
+ align:start position:0%
+interesting um map from the 10th Century
+ 
+
+ align:start position:0%
+interesting um map from the 10th Century
+by the geographer Al jiani who uh
+
+ align:start position:0%
+by the geographer Al jiani who uh
+ 
+
+ align:start position:0%
+by the geographer Al jiani who uh
+indicates to us the viewer how important
+
+ align:start position:0%
+indicates to us the viewer how important
+ 
+
+ align:start position:0%
+indicates to us the viewer how important
+Mecca is to Islam how it's he literally
+
+ align:start position:0%
+Mecca is to Islam how it's he literally
+ 
+
+ align:start position:0%
+Mecca is to Islam how it's he literally
+is drawing it as the center of the
+
+ align:start position:0%
+is drawing it as the center of the
+ 
+
+ align:start position:0%
+is drawing it as the center of the
+world and this is just a quick graphic I
+
+ align:start position:0%
+world and this is just a quick graphic I
+ 
+
+ align:start position:0%
+world and this is just a quick graphic I
+found
+
+ align:start position:0%
+found
+ 
+
+ align:start position:0%
+found
+uh that uh shows again it's it's
+
+ align:start position:0%
+uh that uh shows again it's it's
+ 
+
+ align:start position:0%
+uh that uh shows again it's it's
+interesting because it my diagram sort
+
+ align:start position:0%
+interesting because it my diagram sort
+ 
+
+ align:start position:0%
+interesting because it my diagram sort
+of abstracts this in a way this is
+
+ align:start position:0%
+of abstracts this in a way this is
+ 
+
+ align:start position:0%
+of abstracts this in a way this is
+literally the amount of uh percentage of
+
+ align:start position:0%
+literally the amount of uh percentage of
+ 
+
+ align:start position:0%
+literally the amount of uh percentage of
+people coming from different locations
+
+ align:start position:0%
+people coming from different locations
+ 
+
+ align:start position:0%
+people coming from different locations
+throughout the world uh coming to the
+
+ align:start position:0%
+throughout the world uh coming to the
+ 
+
+ align:start position:0%
+throughout the world uh coming to the
+Hajj in 1982 so it's just a kind of a
+
+ align:start position:0%
+Hajj in 1982 so it's just a kind of a
+ 
+
+ align:start position:0%
+Hajj in 1982 so it's just a kind of a
+quick graphic to so you can easily see
+
+ align:start position:0%
+quick graphic to so you can easily see
+ 
+
+ align:start position:0%
+quick graphic to so you can easily see
+where where the a great number of
+
+ align:start position:0%
+where where the a great number of
+ 
+
+ align:start position:0%
+where where the a great number of
+Muslims are coming from um it would be
+
+ align:start position:0%
+Muslims are coming from um it would be
+ 
+
+ align:start position:0%
+Muslims are coming from um it would be
+interesting to see a more recent version
+
+ align:start position:0%
+interesting to see a more recent version
+ 
+
+ align:start position:0%
+interesting to see a more recent version
+of that obviously um given the change in
+
+ align:start position:0%
+of that obviously um given the change in
+ 
+
+ align:start position:0%
+of that obviously um given the change in
+population locations um this is an this
+
+ align:start position:0%
+population locations um this is an this
+ 
+
+ align:start position:0%
+population locations um this is an this
+is an abstracted uh plan of the mosque
+
+ align:start position:0%
+is an abstracted uh plan of the mosque
+ 
+
+ align:start position:0%
+is an abstracted uh plan of the mosque
+the alh Haram mosque and um really up to
+
+ align:start position:0%
+the alh Haram mosque and um really up to
+ 
+
+ align:start position:0%
+the alh Haram mosque and um really up to
+the year 785 so it's a very basic mosque
+
+ align:start position:0%
+the year 785 so it's a very basic mosque
+ 
+
+ align:start position:0%
+the year 785 so it's a very basic mosque
+the Cabas in the center and it's
+
+ align:start position:0%
+the Cabas in the center and it's
+ 
+
+ align:start position:0%
+the Cabas in the center and it's
+beginning to acquire this kind of
+
+ align:start position:0%
+beginning to acquire this kind of
+ 
+
+ align:start position:0%
+beginning to acquire this kind of
+colonade uh around
+
+ align:start position:0%
+colonade uh around
+ 
+
+ align:start position:0%
+colonade uh around
+it and so by the 18th century um the
+
+ align:start position:0%
+it and so by the 18th century um the
+ 
+
+ align:start position:0%
+it and so by the 18th century um the
+kabah is here located centrally you can
+
+ align:start position:0%
+kabah is here located centrally you can
+ 
+
+ align:start position:0%
+kabah is here located centrally you can
+see the colonade is pretty well
+
+ align:start position:0%
+see the colonade is pretty well
+ 
+
+ align:start position:0%
+see the colonade is pretty well
+established around it and the city is
+
+ align:start position:0%
+established around it and the city is
+ 
+
+ align:start position:0%
+established around it and the city is
+filling in pretty densely around it as
+
+ align:start position:0%
+filling in pretty densely around it as
+ 
+
+ align:start position:0%
+filling in pretty densely around it as
+well and this is what it is basically
+
+ align:start position:0%
+well and this is what it is basically
+ 
+
+ align:start position:0%
+well and this is what it is basically
+contemporarily uh today as it looks
+
+ align:start position:0%
+contemporarily uh today as it looks
+ 
+
+ align:start position:0%
+contemporarily uh today as it looks
+today and so um this is as it is today
+
+ align:start position:0%
+today and so um this is as it is today
+ 
+
+ align:start position:0%
+today and so um this is as it is today
+during the Hajj um full of
+
+ align:start position:0%
+during the Hajj um full of
+ 
+
+ align:start position:0%
+during the Hajj um full of
+pilgrims again another view and this is
+
+ align:start position:0%
+pilgrims again another view and this is
+ 
+
+ align:start position:0%
+pilgrims again another view and this is
+um this is the kiswa this is the the
+
+ align:start position:0%
+um this is the kiswa this is the the
+ 
+
+ align:start position:0%
+um this is the kiswa this is the the
+black silk cloth that covers that this
+
+ align:start position:0%
+black silk cloth that covers that this
+ 
+
+ align:start position:0%
+black silk cloth that covers that this
+site is very sacred to Islam for a
+
+ align:start position:0%
+site is very sacred to Islam for a
+ 
+
+ align:start position:0%
+site is very sacred to Islam for a
+number of reasons but basic very quickly
+
+ align:start position:0%
+number of reasons but basic very quickly
+ 
+
+ align:start position:0%
+number of reasons but basic very quickly
+and basically um ibraim or Abraham is
+
+ align:start position:0%
+and basically um ibraim or Abraham is
+ 
+
+ align:start position:0%
+and basically um ibraim or Abraham is
+said to have uh left his wife and son um
+
+ align:start position:0%
+said to have uh left his wife and son um
+ 
+
+ align:start position:0%
+said to have uh left his wife and son um
+Ismael here very briefly while he went
+
+ align:start position:0%
+Ismael here very briefly while he went
+ 
+
+ align:start position:0%
+Ismael here very briefly while he went
+to Palestine and um Ismael discovered or
+
+ align:start position:0%
+to Palestine and um Ismael discovered or
+ 
+
+ align:start position:0%
+to Palestine and um Ismael discovered or
+you know it's a long story but he
+
+ align:start position:0%
+you know it's a long story but he
+ 
+
+ align:start position:0%
+you know it's a long story but he
+discovered a spring here this holy well
+
+ align:start position:0%
+discovered a spring here this holy well
+ 
+
+ align:start position:0%
+discovered a spring here this holy well
+of Zam Zam and so um not only is that
+
+ align:start position:0%
+of Zam Zam and so um not only is that
+ 
+
+ align:start position:0%
+of Zam Zam and so um not only is that
+significant and then obviously um well
+
+ align:start position:0%
+significant and then obviously um well
+ 
+
+ align:start position:0%
+significant and then obviously um well
+not obviously but Allah instructed
+
+ align:start position:0%
+not obviously but Allah instructed
+ 
+
+ align:start position:0%
+not obviously but Allah instructed
+Ibrahim to create a to build this
+
+ align:start position:0%
+Ibrahim to create a to build this
+ 
+
+ align:start position:0%
+Ibrahim to create a to build this
+structure to commemorate him and so uh
+
+ align:start position:0%
+structure to commemorate him and so uh
+ 
+
+ align:start position:0%
+structure to commemorate him and so uh
+he did that and he this is also uh
+
+ align:start position:0%
+he did that and he this is also uh
+ 
+
+ align:start position:0%
+he did that and he this is also uh
+supposedly the tomb of Abraham as well
+
+ align:start position:0%
+supposedly the tomb of Abraham as well
+ 
+
+ align:start position:0%
+supposedly the tomb of Abraham as well
+so there and there are all kinds of
+
+ align:start position:0%
+so there and there are all kinds of
+ 
+
+ align:start position:0%
+so there and there are all kinds of
+other um significant associations with
+
+ align:start position:0%
+other um significant associations with
+ 
+
+ align:start position:0%
+other um significant associations with
+this um and so here this is just to
+
+ align:start position:0%
+this um and so here this is just to
+ 
+
+ align:start position:0%
+this um and so here this is just to
+quickly show um some pilgrims performing
+
+ align:start position:0%
+quickly show um some pilgrims performing
+ 
+
+ align:start position:0%
+quickly show um some pilgrims performing
+the Hodge where they're coming from and
+
+ align:start position:0%
+the Hodge where they're coming from and
+ 
+
+ align:start position:0%
+the Hodge where they're coming from and
+where they're going and this is
+
+ align:start position:0%
+where they're going and this is
+ 
+
+ align:start position:0%
+where they're going and this is
+obviously a very dense packed Street
+
+ align:start position:0%
+obviously a very dense packed Street
+ 
+
+ align:start position:0%
+obviously a very dense packed Street
+here because there's it's a highly
+
+ align:start position:0%
+here because there's it's a highly
+ 
+
+ align:start position:0%
+here because there's it's a highly
+ritualized um highly
+
+ align:start position:0%
+ritualized um highly
+ 
+
+ align:start position:0%
+ritualized um highly
+ritualized um
+
+ align:start position:0%
+ritualized um
+ 
+
+ align:start position:0%
+ritualized um
+um reenactments and circum ulation
+
+ align:start position:0%
+um reenactments and circum ulation
+ 
+
+ align:start position:0%
+um reenactments and circum ulation
+there's all kinds of interesting things
+
+ align:start position:0%
+there's all kinds of interesting things
+ 
+
+ align:start position:0%
+there's all kinds of interesting things
+going on
+
+ align:start position:0%
+going on
+ 
+
+ align:start position:0%
+going on
+here again this is the well this is the
+
+ align:start position:0%
+here again this is the well this is the
+ 
+
+ align:start position:0%
+here again this is the well this is the
+Village um of tents at Mina near nearby
+
+ align:start position:0%
+Village um of tents at Mina near nearby
+ 
+
+ align:start position:0%
+Village um of tents at Mina near nearby
+Mecca so these are all tents and this
+
+ align:start position:0%
+Mecca so these are all tents and this
+ 
+
+ align:start position:0%
+Mecca so these are all tents and this
+can this space can essentially um
+
+ align:start position:0%
+can this space can essentially um
+ 
+
+ align:start position:0%
+can this space can essentially um
+contain about three million pilgrims
+
+ align:start position:0%
+contain about three million pilgrims
+ 
+
+ align:start position:0%
+contain about three million pilgrims
+when they come to perform the
+
+ align:start position:0%
+when they come to perform the
+ 
+
+ align:start position:0%
+when they come to perform the
+Hodge um and then another quick
+
+ align:start position:0%
+Hodge um and then another quick
+ 
+
+ align:start position:0%
+Hodge um and then another quick
+interesting thing I I found is these are
+
+ align:start position:0%
+interesting thing I I found is these are
+ 
+
+ align:start position:0%
+interesting thing I I found is these are
+all uh images of uh house paintings
+
+ align:start position:0%
+all uh images of uh house paintings
+ 
+
+ align:start position:0%
+all uh images of uh house paintings
+displaying evidence of having completed
+
+ align:start position:0%
+displaying evidence of having completed
+ 
+
+ align:start position:0%
+displaying evidence of having completed
+the Hajj so like if you've completed the
+
+ align:start position:0%
+the Hajj so like if you've completed the
+ 
+
+ align:start position:0%
+the Hajj so like if you've completed the
+Hajj you're and you celebrate that
+
+ align:start position:0%
+Hajj you're and you celebrate that
+ 
+
+ align:start position:0%
+Hajj you're and you celebrate that
+by either a painting or you know at
+
+ align:start position:0%
+by either a painting or you know at
+ 
+
+ align:start position:0%
+by either a painting or you know at
+least in these kind of very localized uh
+
+ align:start position:0%
+least in these kind of very localized uh
+ 
+
+ align:start position:0%
+least in these kind of very localized uh
+examples um and so here's a an image
+
+ align:start position:0%
+examples um and so here's a an image
+ 
+
+ align:start position:0%
+examples um and so here's a an image
+here on the left side of the cabal that
+
+ align:start position:0%
+here on the left side of the cabal that
+ 
+
+ align:start position:0%
+here on the left side of the cabal that
+this person has obviously completed the
+
+ align:start position:0%
+this person has obviously completed the
+ 
+
+ align:start position:0%
+this person has obviously completed the
+Hajj and this is uh this is Bak the the
+
+ align:start position:0%
+Hajj and this is uh this is Bak the the
+ 
+
+ align:start position:0%
+Hajj and this is uh this is Bak the the
+horse that Muhammad rode into um Heaven
+
+ align:start position:0%
+horse that Muhammad rode into um Heaven
+ 
+
+ align:start position:0%
+horse that Muhammad rode into um Heaven
+very briefly this is the prophet's
+
+ align:start position:0%
+very briefly this is the prophet's
+ 
+
+ align:start position:0%
+very briefly this is the prophet's
+mosque in Medina as it looks today so
+
+ align:start position:0%
+mosque in Medina as it looks today so
+ 
+
+ align:start position:0%
+mosque in Medina as it looks today so
+again it's full of pilgrims people are
+
+ align:start position:0%
+again it's full of pilgrims people are
+ 
+
+ align:start position:0%
+again it's full of pilgrims people are
+coming here all throughout the year um
+
+ align:start position:0%
+coming here all throughout the year um
+ 
+
+ align:start position:0%
+coming here all throughout the year um
+another Central
+
+ align:start position:0%
+another Central
+ 
+
+ align:start position:0%
+another Central
+um uh Monument to Islam is the Dome of
+
+ align:start position:0%
+um uh Monument to Islam is the Dome of
+ 
+
+ align:start position:0%
+um uh Monument to Islam is the Dome of
+the Rock which we're really not going to
+
+ align:start position:0%
+the Rock which we're really not going to
+ 
+
+ align:start position:0%
+the Rock which we're really not going to
+spend any time with but I just wanted to
+
+ align:start position:0%
+spend any time with but I just wanted to
+ 
+
+ align:start position:0%
+spend any time with but I just wanted to
+show it very briefly this commemorates
+
+ align:start position:0%
+show it very briefly this commemorates
+ 
+
+ align:start position:0%
+show it very briefly this commemorates
+uh several things as well um this is
+
+ align:start position:0%
+uh several things as well um this is
+ 
+
+ align:start position:0%
+uh several things as well um this is
+where supposedly the uh that Muhammad
+
+ align:start position:0%
+where supposedly the uh that Muhammad
+ 
+
+ align:start position:0%
+where supposedly the uh that Muhammad
+rode the horse up into heaven and also
+
+ align:start position:0%
+rode the horse up into heaven and also
+ 
+
+ align:start position:0%
+rode the horse up into heaven and also
+the point where um it's it's thought
+
+ align:start position:0%
+the point where um it's it's thought
+ 
+
+ align:start position:0%
+the point where um it's it's thought
+that uh Abraham was about to
+
+ align:start position:0%
+that uh Abraham was about to
+ 
+
+ align:start position:0%
+that uh Abraham was about to
+um where Abraham was instructed to kill
+
+ align:start position:0%
+um where Abraham was instructed to kill
+ 
+
+ align:start position:0%
+um where Abraham was instructed to kill
+his son Isaac and then obviously the
+
+ align:start position:0%
+his son Isaac and then obviously the
+ 
+
+ align:start position:0%
+his son Isaac and then obviously the
+angels interceded and prevented that so
+
+ align:start position:0%
+angels interceded and prevented that so
+ 
+
+ align:start position:0%
+angels interceded and prevented that so
+this is also a and here's the rock this
+
+ align:start position:0%
+this is also a and here's the rock this
+ 
+
+ align:start position:0%
+this is also a and here's the rock this
+is just a view of the Rock from
+
+ align:start position:0%
+is just a view of the Rock from
+ 
+
+ align:start position:0%
+is just a view of the Rock from
+above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so that was kind of the Whirlwind
+
+ align:start position:0%
+um so that was kind of the Whirlwind
+ 
+
+ align:start position:0%
+um so that was kind of the Whirlwind
+tour of
+
+ align:start position:0%
+tour of
+ 
+
+ align:start position:0%
+tour of
+Islam um it's obviously you know the the
+
+ align:start position:0%
+Islam um it's obviously you know the the
+ 
+
+ align:start position:0%
+Islam um it's obviously you know the the
+the struggle here is that there is so
+
+ align:start position:0%
+the struggle here is that there is so
+ 
+
+ align:start position:0%
+the struggle here is that there is so
+much culturally loaded in all of these
+
+ align:start position:0%
+much culturally loaded in all of these
+ 
+
+ align:start position:0%
+much culturally loaded in all of these
+examples and so much of a massive
+
+ align:start position:0%
+examples and so much of a massive
+ 
+
+ align:start position:0%
+examples and so much of a massive
+history associated with them that it's
+
+ align:start position:0%
+history associated with them that it's
+ 
+
+ align:start position:0%
+history associated with them that it's
+been very difficult to kind of reduce
+
+ align:start position:0%
+been very difficult to kind of reduce
+ 
+
+ align:start position:0%
+been very difficult to kind of reduce
+the amount of of material
+
+ align:start position:0%
+the amount of of material
+ 
+
+ align:start position:0%
+the amount of of material
+um but that brings me to uh some
+
+ align:start position:0%
+um but that brings me to uh some
+ 
+
+ align:start position:0%
+um but that brings me to uh some
+Christian examples uh and this is really
+
+ align:start position:0%
+Christian examples uh and this is really
+ 
+
+ align:start position:0%
+Christian examples uh and this is really
+uh some medieval my main focus here in
+
+ align:start position:0%
+uh some medieval my main focus here in
+ 
+
+ align:start position:0%
+uh some medieval my main focus here in
+this presentation is the medieval period
+
+ align:start position:0%
+this presentation is the medieval period
+ 
+
+ align:start position:0%
+this presentation is the medieval period
+um in Christianity and this is just on
+
+ align:start position:0%
+um in Christianity and this is just on
+ 
+
+ align:start position:0%
+um in Christianity and this is just on
+the left a drawing from the 15th century
+
+ align:start position:0%
+the left a drawing from the 15th century
+ 
+
+ align:start position:0%
+the left a drawing from the 15th century
+of a pilgrim on his way and on the right
+
+ align:start position:0%
+of a pilgrim on his way and on the right
+ 
+
+ align:start position:0%
+of a pilgrim on his way and on the right
+it's a drawing by Matthew Paris it's a
+
+ align:start position:0%
+it's a drawing by Matthew Paris it's a
+ 
+
+ align:start position:0%
+it's a drawing by Matthew Paris it's a
+sort of a map of a pilgrimage route that
+
+ align:start position:0%
+sort of a map of a pilgrimage route that
+ 
+
+ align:start position:0%
+sort of a map of a pilgrimage route that
+he performed in 1250 that uh is
+
+ align:start position:0%
+he performed in 1250 that uh is
+ 
+
+ align:start position:0%
+he performed in 1250 that uh is
+interesting because it highlights it he
+
+ align:start position:0%
+interesting because it highlights it he
+ 
+
+ align:start position:0%
+interesting because it highlights it he
+actually articulated he drew all the
+
+ align:start position:0%
+actually articulated he drew all the
+ 
+
+ align:start position:0%
+actually articulated he drew all the
+buildings that were along the way um
+
+ align:start position:0%
+buildings that were along the way um
+ 
+
+ align:start position:0%
+buildings that were along the way um
+that he you know all the different
+
+ align:start position:0%
+that he you know all the different
+ 
+
+ align:start position:0%
+that he you know all the different
+buildings that he visited along the way
+
+ align:start position:0%
+buildings that he visited along the way
+ 
+
+ align:start position:0%
+buildings that he visited along the way
+of his pilgrimage route which I found
+
+ align:start position:0%
+of his pilgrimage route which I found
+ 
+
+ align:start position:0%
+of his pilgrimage route which I found
+was very interesting appropriate um um
+
+ align:start position:0%
+was very interesting appropriate um um
+ 
+
+ align:start position:0%
+was very interesting appropriate um um
+the main Center or the focus of the
+
+ align:start position:0%
+the main Center or the focus of the
+ 
+
+ align:start position:0%
+the main Center or the focus of the
+medieval Christian pilgrimage was to St
+
+ align:start position:0%
+medieval Christian pilgrimage was to St
+ 
+
+ align:start position:0%
+medieval Christian pilgrimage was to St
+James of compostella which is located
+
+ align:start position:0%
+James of compostella which is located
+ 
+
+ align:start position:0%
+James of compostella which is located
+out here um in the Iberian Peninsula and
+
+ align:start position:0%
+out here um in the Iberian Peninsula and
+ 
+
+ align:start position:0%
+out here um in the Iberian Peninsula and
+you can see here on this map Paris VI Le
+
+ align:start position:0%
+you can see here on this map Paris VI Le
+ 
+
+ align:start position:0%
+you can see here on this map Paris VI Le
+and AR they all those are the kind of
+
+ align:start position:0%
+and AR they all those are the kind of
+ 
+
+ align:start position:0%
+and AR they all those are the kind of
+main centers of where the pilgrimage
+
+ align:start position:0%
+main centers of where the pilgrimage
+ 
+
+ align:start position:0%
+main centers of where the pilgrimage
+would start and people would progress
+
+ align:start position:0%
+would start and people would progress
+ 
+
+ align:start position:0%
+would start and people would progress
+down these these lines these uh these
+
+ align:start position:0%
+down these these lines these uh these
+ 
+
+ align:start position:0%
+down these these lines these uh these
+essentially these Pilgrim Roots uh
+
+ align:start position:0%
+essentially these Pilgrim Roots uh
+ 
+
+ align:start position:0%
+essentially these Pilgrim Roots uh
+pilgrimage Roots along and hitting
+
+ align:start position:0%
+pilgrimage Roots along and hitting
+ 
+
+ align:start position:0%
+pilgrimage Roots along and hitting
+different holy places along as they go
+
+ align:start position:0%
+different holy places along as they go
+ 
+
+ align:start position:0%
+different holy places along as they go
+uh this is a reconstruction of Santiago
+
+ align:start position:0%
+uh this is a reconstruction of Santiago
+ 
+
+ align:start position:0%
+uh this is a reconstruction of Santiago
+to compostella and um as it would have
+
+ align:start position:0%
+to compostella and um as it would have
+ 
+
+ align:start position:0%
+to compostella and um as it would have
+looked in the 11 around 1100 it's pretty
+
+ align:start position:0%
+looked in the 11 around 1100 it's pretty
+ 
+
+ align:start position:0%
+looked in the 11 around 1100 it's pretty
+interesting it was constructed it was
+
+ align:start position:0%
+interesting it was constructed it was
+ 
+
+ align:start position:0%
+interesting it was constructed it was
+developed by some students and faculty
+
+ align:start position:0%
+developed by some students and faculty
+ 
+
+ align:start position:0%
+developed by some students and faculty
+at UCLA the architecture Department um
+
+ align:start position:0%
+at UCLA the architecture Department um
+ 
+
+ align:start position:0%
+at UCLA the architecture Department um
+I'm not sure how authentic it would be
+
+ align:start position:0%
+I'm not sure how authentic it would be
+ 
+
+ align:start position:0%
+I'm not sure how authentic it would be
+but it's a lot better than the Baroque
+
+ align:start position:0%
+but it's a lot better than the Baroque
+ 
+
+ align:start position:0%
+but it's a lot better than the Baroque
+uh afterthought which is what we have
+
+ align:start position:0%
+uh afterthought which is what we have
+ 
+
+ align:start position:0%
+uh afterthought which is what we have
+right now you can't see the it's um
+
+ align:start position:0%
+right now you can't see the it's um
+ 
+
+ align:start position:0%
+right now you can't see the it's um
+they've the Romanesque structures
+
+ align:start position:0%
+they've the Romanesque structures
+ 
+
+ align:start position:0%
+they've the Romanesque structures
+completely covered with a pretty much a
+
+ align:start position:0%
+completely covered with a pretty much a
+ 
+
+ align:start position:0%
+completely covered with a pretty much a
+broke um structure so this is again we
+
+ align:start position:0%
+broke um structure so this is again we
+ 
+
+ align:start position:0%
+broke um structure so this is again we
+come back to our sacred and profane
+
+ align:start position:0%
+come back to our sacred and profane
+ 
+
+ align:start position:0%
+come back to our sacred and profane
+diagram um
+
+ align:start position:0%
+diagram um
+ 
+
+ align:start position:0%
+diagram um
+and this is sort of how I Envision um
+
+ align:start position:0%
+and this is sort of how I Envision um
+ 
+
+ align:start position:0%
+and this is sort of how I Envision um
+the movement from a Sacred Space uh
+
+ align:start position:0%
+the movement from a Sacred Space uh
+ 
+
+ align:start position:0%
+the movement from a Sacred Space uh
+through the profane to essentially
+
+ align:start position:0%
+through the profane to essentially
+ 
+
+ align:start position:0%
+through the profane to essentially
+there's this very um linear movement to
+
+ align:start position:0%
+there's this very um linear movement to
+ 
+
+ align:start position:0%
+there's this very um linear movement to
+an ultimate sacred place that's you know
+
+ align:start position:0%
+an ultimate sacred place that's you know
+ 
+
+ align:start position:0%
+an ultimate sacred place that's you know
+there's there's some hierarchy here
+
+ align:start position:0%
+there's there's some hierarchy here
+ 
+
+ align:start position:0%
+there's there's some hierarchy here
+there's uh one is process processing
+
+ align:start position:0%
+there's uh one is process processing
+ 
+
+ align:start position:0%
+there's uh one is process processing
+essentially metaphorically through this
+
+ align:start position:0%
+essentially metaphorically through this
+ 
+
+ align:start position:0%
+essentially metaphorically through this
+landscape of the profane and reaches
+
+ align:start position:0%
+landscape of the profane and reaches
+ 
+
+ align:start position:0%
+landscape of the profane and reaches
+these different uh sacred spaces to
+
+ align:start position:0%
+these different uh sacred spaces to
+ 
+
+ align:start position:0%
+these different uh sacred spaces to
+which um they can um you know benefit by
+
+ align:start position:0%
+which um they can um you know benefit by
+ 
+
+ align:start position:0%
+which um they can um you know benefit by
+grace of some sort um and I just we
+
+ align:start position:0%
+grace of some sort um and I just we
+ 
+
+ align:start position:0%
+grace of some sort um and I just we
+can't talk about this without discussing
+
+ align:start position:0%
+can't talk about this without discussing
+ 
+
+ align:start position:0%
+can't talk about this without discussing
+this just massive proliferation of
+
+ align:start position:0%
+this just massive proliferation of
+ 
+
+ align:start position:0%
+this just massive proliferation of
+architecture that just was generated
+
+ align:start position:0%
+architecture that just was generated
+ 
+
+ align:start position:0%
+architecture that just was generated
+around this time and so um this is just
+
+ align:start position:0%
+around this time and so um this is just
+ 
+
+ align:start position:0%
+around this time and so um this is just
+four examples out of the book um
+
+ align:start position:0%
+four examples out of the book um
+ 
+
+ align:start position:0%
+four examples out of the book um
+that show us uh the four examples of
+
+ align:start position:0%
+that show us uh the four examples of
+ 
+
+ align:start position:0%
+that show us uh the four examples of
+pilgrimage churches and you can see
+
+ align:start position:0%
+pilgrimage churches and you can see
+ 
+
+ align:start position:0%
+pilgrimage churches and you can see
+right away the cruciform similarity that
+
+ align:start position:0%
+right away the cruciform similarity that
+ 
+
+ align:start position:0%
+right away the cruciform similarity that
+they share uh the larger abses these AB
+
+ align:start position:0%
+they share uh the larger abses these AB
+ 
+
+ align:start position:0%
+they share uh the larger abses these AB
+cidial which um where relics would be
+
+ align:start position:0%
+cidial which um where relics would be
+ 
+
+ align:start position:0%
+cidial which um where relics would be
+relics would either be located within
+
+ align:start position:0%
+relics would either be located within
+ 
+
+ align:start position:0%
+relics would either be located within
+the apps here or Within These AB cidial
+
+ align:start position:0%
+the apps here or Within These AB cidial
+ 
+
+ align:start position:0%
+the apps here or Within These AB cidial
+uh and so pilgrims would be able to come
+
+ align:start position:0%
+uh and so pilgrims would be able to come
+ 
+
+ align:start position:0%
+uh and so pilgrims would be able to come
+in and and sometimes they would
+
+ align:start position:0%
+in and and sometimes they would
+ 
+
+ align:start position:0%
+in and and sometimes they would
+circumambulate here or they would
+
+ align:start position:0%
+circumambulate here or they would
+ 
+
+ align:start position:0%
+circumambulate here or they would
+process in and out um and very um
+
+ align:start position:0%
+process in and out um and very um
+ 
+
+ align:start position:0%
+process in and out um and very um
+specifically here we have an example
+
+ align:start position:0%
+specifically here we have an example
+ 
+
+ align:start position:0%
+specifically here we have an example
+from sanua in Con in France around
+
+ align:start position:0%
+from sanua in Con in France around
+ 
+
+ align:start position:0%
+from sanua in Con in France around
+11:20 and this is interesting because um
+
+ align:start position:0%
+11:20 and this is interesting because um
+ 
+
+ align:start position:0%
+11:20 and this is interesting because um
+this the the beginning of the story is
+
+ align:start position:0%
+this the the beginning of the story is
+ 
+
+ align:start position:0%
+this the the beginning of the story is
+the um there was a monk who translated
+
+ align:start position:0%
+the um there was a monk who translated
+ 
+
+ align:start position:0%
+the um there was a monk who translated
+or stole um some relics from one place
+
+ align:start position:0%
+or stole um some relics from one place
+ 
+
+ align:start position:0%
+or stole um some relics from one place
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+in um another location in France brought
+
+ align:start position:0%
+in um another location in France brought
+ 
+
+ align:start position:0%
+in um another location in France brought
+them here essentially everybody followed
+
+ align:start position:0%
+them here essentially everybody followed
+ 
+
+ align:start position:0%
+them here essentially everybody followed
+uh and they created this uh large Church
+
+ align:start position:0%
+uh and they created this uh large Church
+ 
+
+ align:start position:0%
+uh and they created this uh large Church
+to kind kind of celebrate the relics of
+
+ align:start position:0%
+to kind kind of celebrate the relics of
+ 
+
+ align:start position:0%
+to kind kind of celebrate the relics of
+s St Faith who was a martyr from the 3rd
+
+ align:start position:0%
+s St Faith who was a martyr from the 3rd
+ 
+
+ align:start position:0%
+s St Faith who was a martyr from the 3rd
+century and here's here's here's her
+
+ align:start position:0%
+century and here's here's here's her
+ 
+
+ align:start position:0%
+century and here's here's here's her
+rendered image and I just wanted to
+
+ align:start position:0%
+rendered image and I just wanted to
+ 
+
+ align:start position:0%
+rendered image and I just wanted to
+quickly read this uh by a clergyman
+
+ align:start position:0%
+quickly read this uh by a clergyman
+ 
+
+ align:start position:0%
+quickly read this uh by a clergyman
+named Berard Doner uh from 1010 he says
+
+ align:start position:0%
+named Berard Doner uh from 1010 he says
+ 
+
+ align:start position:0%
+named Berard Doner uh from 1010 he says
+he's talking about this Relic he says
+
+ align:start position:0%
+he's talking about this Relic he says
+ 
+
+ align:start position:0%
+he's talking about this Relic he says
+when they saw it for the first time all
+
+ align:start position:0%
+when they saw it for the first time all
+ 
+
+ align:start position:0%
+when they saw it for the first time all
+in gold and sparkling with process
+
+ align:start position:0%
+in gold and sparkling with process
+ 
+
+ align:start position:0%
+in gold and sparkling with process
+precious stones and looking like a human
+
+ align:start position:0%
+precious stones and looking like a human
+ 
+
+ align:start position:0%
+precious stones and looking like a human
+face the majority of the peasants
+
+ align:start position:0%
+face the majority of the peasants
+ 
+
+ align:start position:0%
+face the majority of the peasants
+thought that the statue was really
+
+ align:start position:0%
+thought that the statue was really
+ 
+
+ align:start position:0%
+thought that the statue was really
+looking at them and answering their
+
+ align:start position:0%
+looking at them and answering their
+ 
+
+ align:start position:0%
+looking at them and answering their
+prayers with her
+
+ align:start position:0%
+prayers with her
+ 
+
+ align:start position:0%
+prayers with her
+eyes so there's a great deal of Interest
+
+ align:start position:0%
+eyes so there's a great deal of Interest
+ 
+
+ align:start position:0%
+eyes so there's a great deal of Interest
+around these relics the reliquaries and
+
+ align:start position:0%
+around these relics the reliquaries and
+ 
+
+ align:start position:0%
+around these relics the reliquaries and
+the kind of sacredness of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spaces this is San and more
+
+ align:start position:0%
+spaces this is San and more
+ 
+
+ align:start position:0%
+spaces this is San and more
+views
+
+ align:start position:0%
+views
+ 
+
+ align:start position:0%
+views
+um we can't forget that one of the um
+
+ align:start position:0%
+um we can't forget that one of the um
+ 
+
+ align:start position:0%
+um we can't forget that one of the um
+most important pilgrimages in the
+
+ align:start position:0%
+most important pilgrimages in the
+ 
+
+ align:start position:0%
+most important pilgrimages in the
+medieval period was one that is
+
+ align:start position:0%
+medieval period was one that is
+ 
+
+ align:start position:0%
+medieval period was one that is
+obviously um as mixed
+
+ align:start position:0%
+obviously um as mixed
+ 
+
+ align:start position:0%
+obviously um as mixed
+um not so mixed uh it's pretty um rather
+
+ align:start position:0%
+um not so mixed uh it's pretty um rather
+ 
+
+ align:start position:0%
+um not so mixed uh it's pretty um rather
+controversial uh pilgrimage but that is
+
+ align:start position:0%
+controversial uh pilgrimage but that is
+ 
+
+ align:start position:0%
+controversial uh pilgrimage but that is
+the that everyone's familiar with the
+
+ align:start position:0%
+the that everyone's familiar with the
+ 
+
+ align:start position:0%
+the that everyone's familiar with the
+Crusades um which essentially occur
+
+ align:start position:0%
+Crusades um which essentially occur
+ 
+
+ align:start position:0%
+Crusades um which essentially occur
+between around here the dates that I've
+
+ align:start position:0%
+between around here the dates that I've
+ 
+
+ align:start position:0%
+between around here the dates that I've
+sort of shown and the thing I wanted to
+
+ align:start position:0%
+sort of shown and the thing I wanted to
+ 
+
+ align:start position:0%
+sort of shown and the thing I wanted to
+kind of elicit out of the Crusades was
+
+ align:start position:0%
+kind of elicit out of the Crusades was
+ 
+
+ align:start position:0%
+kind of elicit out of the Crusades was
+this notion of exchange uh of
+
+ align:start position:0%
+this notion of exchange uh of
+ 
+
+ align:start position:0%
+this notion of exchange uh of
+architectural uh architectural
+
+ align:start position:0%
+architectural uh architectural
+ 
+
+ align:start position:0%
+architectural uh architectural
+techniques right so one thing I just
+
+ align:start position:0%
+techniques right so one thing I just
+ 
+
+ align:start position:0%
+techniques right so one thing I just
+want to quickly quickly discuss here is
+
+ align:start position:0%
+want to quickly quickly discuss here is
+ 
+
+ align:start position:0%
+want to quickly quickly discuss here is
+this notion obviously the the Crusades
+
+ align:start position:0%
+this notion obviously the the Crusades
+ 
+
+ align:start position:0%
+this notion obviously the the Crusades
+went to the holy lands what they believe
+
+ align:start position:0%
+went to the holy lands what they believe
+ 
+
+ align:start position:0%
+went to the holy lands what they believe
+were the holy lands which were obviously
+
+ align:start position:0%
+were the holy lands which were obviously
+ 
+
+ align:start position:0%
+were the holy lands which were obviously
+Jerusalem and Bethlehem and all these
+
+ align:start position:0%
+Jerusalem and Bethlehem and all these
+ 
+
+ align:start position:0%
+Jerusalem and Bethlehem and all these
+places along associated with the Life of
+
+ align:start position:0%
+places along associated with the Life of
+ 
+
+ align:start position:0%
+places along associated with the Life of
+Christ um and
+
+ align:start position:0%
+Christ um and
+ 
+
+ align:start position:0%
+Christ um and
+so um what I'm showing here depicting is
+
+ align:start position:0%
+so um what I'm showing here depicting is
+ 
+
+ align:start position:0%
+so um what I'm showing here depicting is
+the AL AXA mosque in Jerusalem which uh
+
+ align:start position:0%
+the AL AXA mosque in Jerusalem which uh
+ 
+
+ align:start position:0%
+the AL AXA mosque in Jerusalem which uh
+is using the uh pointed Arch right so
+
+ align:start position:0%
+is using the uh pointed Arch right so
+ 
+
+ align:start position:0%
+is using the uh pointed Arch right so
+very basically um the Crusaders bring
+
+ align:start position:0%
+very basically um the Crusaders bring
+ 
+
+ align:start position:0%
+very basically um the Crusaders bring
+back some of this
+
+ align:start position:0%
+back some of this
+ 
+
+ align:start position:0%
+back some of this
+technology um that uh pre-existed in
+
+ align:start position:0%
+technology um that uh pre-existed in
+ 
+
+ align:start position:0%
+technology um that uh pre-existed in
+Islam for many years before the
+
+ align:start position:0%
+Islam for many years before the
+ 
+
+ align:start position:0%
+Islam for many years before the
+Crusaders bring it back and there's a we
+
+ align:start position:0%
+Crusaders bring it back and there's a we
+ 
+
+ align:start position:0%
+Crusaders bring it back and there's a we
+see a quick steady development of
+
+ align:start position:0%
+see a quick steady development of
+ 
+
+ align:start position:0%
+see a quick steady development of
+different types of arch systems from the
+
+ align:start position:0%
+different types of arch systems from the
+ 
+
+ align:start position:0%
+different types of arch systems from the
+barrel the Roman kind of groin vaults uh
+
+ align:start position:0%
+barrel the Roman kind of groin vaults uh
+ 
+
+ align:start position:0%
+barrel the Roman kind of groin vaults uh
+and of course the importance here is
+
+ align:start position:0%
+and of course the importance here is
+ 
+
+ align:start position:0%
+and of course the importance here is
+there's this relationship between how
+
+ align:start position:0%
+there's this relationship between how
+ 
+
+ align:start position:0%
+there's this relationship between how
+high you go and how wide you are right
+
+ align:start position:0%
+high you go and how wide you are right
+ 
+
+ align:start position:0%
+high you go and how wide you are right
+that's a fixed point of relationship but
+
+ align:start position:0%
+that's a fixed point of relationship but
+ 
+
+ align:start position:0%
+that's a fixed point of relationship but
+once you introduce the pointed Arch that
+
+ align:start position:0%
+once you introduce the pointed Arch that
+ 
+
+ align:start position:0%
+once you introduce the pointed Arch that
+anything's fair right so that brings me
+
+ align:start position:0%
+anything's fair right so that brings me
+ 
+
+ align:start position:0%
+anything's fair right so that brings me
+to the example of
+
+ align:start position:0%
+to the example of
+ 
+
+ align:start position:0%
+to the example of
+s um which is another pilgrimage church
+
+ align:start position:0%
+s um which is another pilgrimage church
+ 
+
+ align:start position:0%
+s um which is another pilgrimage church
+this is an image this is a stained glass
+
+ align:start position:0%
+this is an image this is a stained glass
+ 
+
+ align:start position:0%
+this is an image this is a stained glass
+image of s and so uh this is the plan
+
+ align:start position:0%
+image of s and so uh this is the plan
+ 
+
+ align:start position:0%
+image of s and so uh this is the plan
+and so we can see here in this apps uh
+
+ align:start position:0%
+and so we can see here in this apps uh
+ 
+
+ align:start position:0%
+and so we can see here in this apps uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+ex big additions that um uh that uh
+
+ align:start position:0%
+ex big additions that um uh that uh
+ 
+
+ align:start position:0%
+ex big additions that um uh that uh
+abbid Su uh went through and I wanted to
+
+ align:start position:0%
+abbid Su uh went through and I wanted to
+ 
+
+ align:start position:0%
+abbid Su uh went through and I wanted to
+just quickly read this um videos removed
+
+ align:start position:0%
+just quickly read this um videos removed
+ 
+
+ align:start position:0%
+just quickly read this um videos removed
+due to copyright
+
+ align:start position:0%
+due to copyright
+ 
+
+ align:start position:0%
+due to copyright
+restrictions so he goes on to explain
+
+ align:start position:0%
+restrictions so he goes on to explain
+ 
+
+ align:start position:0%
+restrictions so he goes on to explain
+how horrendous the conditions were in
+
+ align:start position:0%
+how horrendous the conditions were in
+ 
+
+ align:start position:0%
+how horrendous the conditions were in
+viewing these relics so he totally
+
+ align:start position:0%
+viewing these relics so he totally
+ 
+
+ align:start position:0%
+viewing these relics so he totally
+expands the church and you get this
+
+ align:start position:0%
+expands the church and you get this
+ 
+
+ align:start position:0%
+expands the church and you get this
+amazing network of of vaulting going on
+
+ align:start position:0%
+amazing network of of vaulting going on
+ 
+
+ align:start position:0%
+amazing network of of vaulting going on
+here that's brought about essentially by
+
+ align:start position:0%
+here that's brought about essentially by
+ 
+
+ align:start position:0%
+here that's brought about essentially by
+this newer technology of the pointed
+
+ align:start position:0%
+this newer technology of the pointed
+ 
+
+ align:start position:0%
+this newer technology of the pointed
+Arch and I just really wanted to quickly
+
+ align:start position:0%
+Arch and I just really wanted to quickly
+ 
+
+ align:start position:0%
+Arch and I just really wanted to quickly
+briefly go through uh some more recent
+
+ align:start position:0%
+briefly go through uh some more recent
+ 
+
+ align:start position:0%
+briefly go through uh some more recent
+or contemporary things the Santiago to
+
+ align:start position:0%
+or contemporary things the Santiago to
+ 
+
+ align:start position:0%
+or contemporary things the Santiago to
+compostella is still a pilgrimage route
+
+ align:start position:0%
+compostella is still a pilgrimage route
+ 
+
+ align:start position:0%
+compostella is still a pilgrimage route
+that is still practice today these are
+
+ align:start position:0%
+that is still practice today these are
+ 
+
+ align:start position:0%
+that is still practice today these are
+all very contemporary people performing
+
+ align:start position:0%
+all very contemporary people performing
+ 
+
+ align:start position:0%
+all very contemporary people performing
+this this is a sign in France that
+
+ align:start position:0%
+this this is a sign in France that
+ 
+
+ align:start position:0%
+this this is a sign in France that
+indicates it's 953 kilometers um because
+
+ align:start position:0%
+indicates it's 953 kilometers um because
+ 
+
+ align:start position:0%
+indicates it's 953 kilometers um because
+people are still taking these
+
+ align:start position:0%
+people are still taking these
+ 
+
+ align:start position:0%
+people are still taking these
+pilgrimmage frots um and then in Lords
+
+ align:start position:0%
+pilgrimmage frots um and then in Lords
+ 
+
+ align:start position:0%
+pilgrimmage frots um and then in Lords
+in France I wanted to just highlight the
+
+ align:start position:0%
+in France I wanted to just highlight the
+ 
+
+ align:start position:0%
+in France I wanted to just highlight the
+story of bernardet subus who in 1858 saw
+
+ align:start position:0%
+story of bernardet subus who in 1858 saw
+ 
+
+ align:start position:0%
+story of bernardet subus who in 1858 saw
+a sighting of the Virgin Mary
+
+ align:start position:0%
+a sighting of the Virgin Mary
+ 
+
+ align:start position:0%
+a sighting of the Virgin Mary
+um in this nowhere Village uh that
+
+ align:start position:0%
+um in this nowhere Village uh that
+ 
+
+ align:start position:0%
+um in this nowhere Village uh that
+didn't even have a railroad station or
+
+ align:start position:0%
+didn't even have a railroad station or
+ 
+
+ align:start position:0%
+didn't even have a railroad station or
+anything it was extremely difficult to
+
+ align:start position:0%
+anything it was extremely difficult to
+ 
+
+ align:start position:0%
+anything it was extremely difficult to
+get there and she was an uneducated um
+
+ align:start position:0%
+get there and she was an uneducated um
+ 
+
+ align:start position:0%
+get there and she was an uneducated um
+illiterate peasant girl essentially so
+
+ align:start position:0%
+illiterate peasant girl essentially so
+ 
+
+ align:start position:0%
+illiterate peasant girl essentially so
+to speak who saw this vision and turned
+
+ align:start position:0%
+to speak who saw this vision and turned
+ 
+
+ align:start position:0%
+to speak who saw this vision and turned
+this place essentially her vision turned
+
+ align:start position:0%
+this place essentially her vision turned
+ 
+
+ align:start position:0%
+this place essentially her vision turned
+it into this um this key Central
+
+ align:start position:0%
+it into this um this key Central
+ 
+
+ align:start position:0%
+it into this um this key Central
+Christian uh pilgrimage location and
+
+ align:start position:0%
+Christian uh pilgrimage location and
+ 
+
+ align:start position:0%
+Christian uh pilgrimage location and
+here you can see on the bottom right a
+
+ align:start position:0%
+here you can see on the bottom right a
+ 
+
+ align:start position:0%
+here you can see on the bottom right a
+very contemporary view of pilgrims um
+
+ align:start position:0%
+very contemporary view of pilgrims um
+ 
+
+ align:start position:0%
+very contemporary view of pilgrims um
+coming here again and then bernardet
+
+ align:start position:0%
+coming here again and then bernardet
+ 
+
+ align:start position:0%
+coming here again and then bernardet
+dies and they turn her into a Rec Relic
+
+ align:start position:0%
+dies and they turn her into a Rec Relic
+ 
+
+ align:start position:0%
+dies and they turn her into a Rec Relic
+essentially uh so it's sort of it's very
+
+ align:start position:0%
+essentially uh so it's sort of it's very
+ 
+
+ align:start position:0%
+essentially uh so it's sort of it's very
+interesting this whole process that's
+
+ align:start position:0%
+interesting this whole process that's
+ 
+
+ align:start position:0%
+interesting this whole process that's
+occurring um and again in later
+
+ align:start position:0%
+occurring um and again in later
+ 
+
+ align:start position:0%
+occurring um and again in later
+Christianity we have we it's it's
+
+ align:start position:0%
+Christianity we have we it's it's
+ 
+
+ align:start position:0%
+Christianity we have we it's it's
+interesting because we almost come back
+
+ align:start position:0%
+interesting because we almost come back
+ 
+
+ align:start position:0%
+interesting because we almost come back
+in a full circle back to Carnac where
+
+ align:start position:0%
+in a full circle back to Carnac where
+ 
+
+ align:start position:0%
+in a full circle back to Carnac where
+where where we are there's an
+
+ align:start position:0%
+where where we are there's an
+ 
+
+ align:start position:0%
+where where we are there's an
+understanding of the the movement or the
+
+ align:start position:0%
+understanding of the the movement or the
+ 
+
+ align:start position:0%
+understanding of the the movement or the
+procession of the Sacred the sacred
+
+ align:start position:0%
+procession of the Sacred the sacred
+ 
+
+ align:start position:0%
+procession of the Sacred the sacred
+actually is moved from one location to
+
+ align:start position:0%
+actually is moved from one location to
+ 
+
+ align:start position:0%
+actually is moved from one location to
+another and on the left we have an
+
+ align:start position:0%
+another and on the left we have an
+ 
+
+ align:start position:0%
+another and on the left we have an
+example of in Poland on the upper right
+
+ align:start position:0%
+example of in Poland on the upper right
+ 
+
+ align:start position:0%
+example of in Poland on the upper right
+in Italy and then on the bottom right we
+
+ align:start position:0%
+in Italy and then on the bottom right we
+ 
+
+ align:start position:0%
+in Italy and then on the bottom right we
+have the famous s Santa in Spain um the
+
+ align:start position:0%
+have the famous s Santa in Spain um the
+ 
+
+ align:start position:0%
+have the famous s Santa in Spain um the
+holy weeks ceremony where um you have
+
+ align:start position:0%
+holy weeks ceremony where um you have
+ 
+
+ align:start position:0%
+holy weeks ceremony where um you have
+quite an amazing amount proliferation of
+
+ align:start position:0%
+quite an amazing amount proliferation of
+ 
+
+ align:start position:0%
+quite an amazing amount proliferation of
+processions um and more recently we also
+
+ align:start position:0%
+processions um and more recently we also
+ 
+
+ align:start position:0%
+processions um and more recently we also
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+um uh more Christian processions with uh
+
+ align:start position:0%
+um uh more Christian processions with uh
+ 
+
+ align:start position:0%
+um uh more Christian processions with uh
+pilgrimages to see all kinds of things
+
+ align:start position:0%
+pilgrimages to see all kinds of things
+ 
+
+ align:start position:0%
+pilgrimages to see all kinds of things
+right Rome this whole Space is all about
+
+ align:start position:0%
+right Rome this whole Space is all about
+ 
+
+ align:start position:0%
+right Rome this whole Space is all about
+procession and pilgrimage um and if you
+
+ align:start position:0%
+procession and pilgrimage um and if you
+ 
+
+ align:start position:0%
+procession and pilgrimage um and if you
+ever want to go to any of these places
+
+ align:start position:0%
+ever want to go to any of these places
+ 
+
+ align:start position:0%
+ever want to go to any of these places
+you can hop on online and um click if
+
+ align:start position:0%
+you can hop on online and um click if
+ 
+
+ align:start position:0%
+you can hop on online and um click if
+you're Protestant my interest is
+
+ align:start position:0%
+you're Protestant my interest is
+ 
+
+ align:start position:0%
+you're Protestant my interest is
+Protestant or whatever and then um if
+
+ align:start position:0%
+Protestant or whatever and then um if
+ 
+
+ align:start position:0%
+Protestant or whatever and then um if
+you're Buddhist you can find Buddhist
+
+ align:start position:0%
+you're Buddhist you can find Buddhist
+ 
+
+ align:start position:0%
+you're Buddhist you can find Buddhist
+pilgrimages to go to lumini bodaya
+
+ align:start position:0%
+pilgrimages to go to lumini bodaya
+ 
+
+ align:start position:0%
+pilgrimages to go to lumini bodaya
+wherever um the Hajj of course is you
+
+ align:start position:0%
+wherever um the Hajj of course is you
+ 
+
+ align:start position:0%
+wherever um the Hajj of course is you
+know not a problem at all they can do
+
+ align:start position:0%
+know not a problem at all they can do
+ 
+
+ align:start position:0%
+know not a problem at all they can do
+that for you there's packages trips from
+
+ align:start position:0%
+that for you there's packages trips from
+ 
+
+ align:start position:0%
+that for you there's packages trips from
+JFK you can even rent a pilgrim which is
+
+ align:start position:0%
+JFK you can even rent a pilgrim which is
+ 
+
+ align:start position:0%
+JFK you can even rent a pilgrim which is
+a medieval notion the
+
+ align:start position:0%
+a medieval notion the
+ 
+
+ align:start position:0%
+a medieval notion the
+perrino picun CAA which is where you
+
+ align:start position:0%
+perrino picun CAA which is where you
+ 
+
+ align:start position:0%
+perrino picun CAA which is where you
+would pay a pilgrim to go in in your
+
+ align:start position:0%
+would pay a pilgrim to go in in your
+ 
+
+ align:start position:0%
+would pay a pilgrim to go in in your
+stead um and this notion you can do it's
+
+ align:start position:0%
+stead um and this notion you can do it's
+ 
+
+ align:start position:0%
+stead um and this notion you can do it's
+interesting I only I only raised this
+
+ align:start position:0%
+interesting I only I only raised this
+ 
+
+ align:start position:0%
+interesting I only I only raised this
+issue because it's interesting because
+
+ align:start position:0%
+issue because it's interesting because
+ 
+
+ align:start position:0%
+issue because it's interesting because
+it's connected to architecture in a very
+
+ align:start position:0%
+it's connected to architecture in a very
+ 
+
+ align:start position:0%
+it's connected to architecture in a very
+interesting way so if you do go onto
+
+ align:start position:0%
+interesting way so if you do go onto
+ 
+
+ align:start position:0%
+interesting way so if you do go onto
+this website and rent a pilgrim this guy
+
+ align:start position:0%
+this website and rent a pilgrim this guy
+ 
+
+ align:start position:0%
+this website and rent a pilgrim this guy
+will walk for you and you'll pay him and
+
+ align:start position:0%
+will walk for you and you'll pay him and
+ 
+
+ align:start position:0%
+will walk for you and you'll pay him and
+he'll do the walk and the money will go
+
+ align:start position:0%
+he'll do the walk and the money will go
+ 
+
+ align:start position:0%
+he'll do the walk and the money will go
+to fund the renovation of the City
+
+ align:start position:0%
+to fund the renovation of the City
+ 
+
+ align:start position:0%
+to fund the renovation of the City
+Church uh St Jacob in Rottenberg in
+
+ align:start position:0%
+Church uh St Jacob in Rottenberg in
+ 
+
+ align:start position:0%
+Church uh St Jacob in Rottenberg in
+Germany and so it's very interesting and
+
+ align:start position:0%
+Germany and so it's very interesting and
+ 
+
+ align:start position:0%
+Germany and so it's very interesting and
+then of course you get a emblem that you
+
+ align:start position:0%
+then of course you get a emblem that you
+ 
+
+ align:start position:0%
+then of course you get a emblem that you
+went on the pilgrimage right your your
+
+ align:start position:0%
+went on the pilgrimage right your your
+ 
+
+ align:start position:0%
+went on the pilgrimage right your your
+scallop pendant
+
+ align:start position:0%
+scallop pendant
+ 
+
+ align:start position:0%
+scallop pendant
+um and there are all kinds of
+
+ align:start position:0%
+um and there are all kinds of
+ 
+
+ align:start position:0%
+um and there are all kinds of
+contemporary guides to St James uh these
+
+ align:start position:0%
+contemporary guides to St James uh these
+ 
+
+ align:start position:0%
+contemporary guides to St James uh these
+are this is an image of the Buddhists
+
+ align:start position:0%
+are this is an image of the Buddhists
+ 
+
+ align:start position:0%
+are this is an image of the Buddhists
+doing the Santiago de compostella so
+
+ align:start position:0%
+doing the Santiago de compostella so
+ 
+
+ align:start position:0%
+doing the Santiago de compostella so
+there's this kind of very interesting
+
+ align:start position:0%
+there's this kind of very interesting
+ 
+
+ align:start position:0%
+there's this kind of very interesting
+Global thing going on here um you know
+
+ align:start position:0%
+Global thing going on here um you know
+ 
+
+ align:start position:0%
+Global thing going on here um you know
+just this notion of a Sacred Space uh
+
+ align:start position:0%
+just this notion of a Sacred Space uh
+ 
+
+ align:start position:0%
+just this notion of a Sacred Space uh
+following the path of a sacred no matter
+
+ align:start position:0%
+following the path of a sacred no matter
+ 
+
+ align:start position:0%
+following the path of a sacred no matter
+what kind of denomination or whatever it
+
+ align:start position:0%
+what kind of denomination or whatever it
+ 
+
+ align:start position:0%
+what kind of denomination or whatever it
+is um again uh secular pilgrimages not
+
+ align:start position:0%
+is um again uh secular pilgrimages not
+ 
+
+ align:start position:0%
+is um again uh secular pilgrimages not
+the focus necessarily of the talk but
+
+ align:start position:0%
+the focus necessarily of the talk but
+ 
+
+ align:start position:0%
+the focus necessarily of the talk but
+still an important um aspect to popular
+
+ align:start position:0%
+still an important um aspect to popular
+ 
+
+ align:start position:0%
+still an important um aspect to popular
+culture uh that we're surrounded with
+
+ align:start position:0%
+culture uh that we're surrounded with
+ 
+
+ align:start position:0%
+culture uh that we're surrounded with
+today JFK and Vietnam
+
+ align:start position:0%
+today JFK and Vietnam
+ 
+
+ align:start position:0%
+today JFK and Vietnam
+memorial um and of course Elvis we can't
+
+ align:start position:0%
+memorial um and of course Elvis we can't
+ 
+
+ align:start position:0%
+memorial um and of course Elvis we can't
+leave uh hit Grace land out with his
+
+ align:start position:0%
+leave uh hit Grace land out with his
+ 
+
+ align:start position:0%
+leave uh hit Grace land out with his
+tomb here and um there's just if the
+
+ align:start position:0%
+tomb here and um there's just if the
+ 
+
+ align:start position:0%
+tomb here and um there's just if the
+closer you look there's just these very
+
+ align:start position:0%
+closer you look there's just these very
+ 
+
+ align:start position:0%
+closer you look there's just these very
+odd stories about people this is a this
+
+ align:start position:0%
+odd stories about people this is a this
+ 
+
+ align:start position:0%
+odd stories about people this is a this
+is a former military installation in the
+
+ align:start position:0%
+is a former military installation in the
+ 
+
+ align:start position:0%
+is a former military installation in the
+desert that people flock to every year
+
+ align:start position:0%
+desert that people flock to every year
+ 
+
+ align:start position:0%
+desert that people flock to every year
+and do these um interesting
+
+ align:start position:0%
+and do these um interesting
+ 
+
+ align:start position:0%
+and do these um interesting
+sculptures but basically um I think it's
+
+ align:start position:0%
+sculptures but basically um I think it's
+ 
+
+ align:start position:0%
+sculptures but basically um I think it's
+it's important to think about the
+
+ align:start position:0%
+it's important to think about the
+ 
+
+ align:start position:0%
+it's important to think about the
+Contemporary um contemporary pilgrimage
+
+ align:start position:0%
+Contemporary um contemporary pilgrimage
+ 
+
+ align:start position:0%
+Contemporary um contemporary pilgrimage
+and how it relates to our historical
+
+ align:start position:0%
+and how it relates to our historical
+ 
+
+ align:start position:0%
+and how it relates to our historical
+examples that we just discussed and how
+
+ align:start position:0%
+examples that we just discussed and how
+ 
+
+ align:start position:0%
+examples that we just discussed and how
+it's continually readapted and
+
+ align:start position:0%
+it's continually readapted and
+ 
+
+ align:start position:0%
+it's continually readapted and
+interpreted through different world
+
+ align:start position:0%
+interpreted through different world
+ 
+
+ align:start position:0%
+interpreted through different world
+cultures and traditions and um
\ No newline at end of file
diff --git a/SC8K6gNAIL4.txt b/SC8K6gNAIL4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f2c2ae21dbbd6d449c2d8e406ad0514924847b9a
--- /dev/null
+++ b/SC8K6gNAIL4.txt
@@ -0,0 +1,19613 @@
+align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let me sort of just recap what we
+
+ align:start position:0%
+so let me sort of just recap what we
+ 
+
+ align:start position:0%
+so let me sort of just recap what we
+discussed last time
+
+ align:start position:0%
+discussed last time
+ 
+
+ align:start position:0%
+discussed last time
+fairly quickly and then we want to move
+
+ align:start position:0%
+fairly quickly and then we want to move
+ 
+
+ align:start position:0%
+fairly quickly and then we want to move
+to empirical evidence on a variety of
+
+ align:start position:0%
+to empirical evidence on a variety of
+ 
+
+ align:start position:0%
+to empirical evidence on a variety of
+settings
+
+ align:start position:0%
+settings
+ 
+
+ align:start position:0%
+settings
+we might not get through all of the
+
+ align:start position:0%
+we might not get through all of the
+ 
+
+ align:start position:0%
+we might not get through all of the
+slides that's fine
+
+ align:start position:0%
+slides that's fine
+ 
+
+ align:start position:0%
+slides that's fine
+in that case we'll just discuss some of
+
+ align:start position:0%
+in that case we'll just discuss some of
+ 
+
+ align:start position:0%
+in that case we'll just discuss some of
+this in recitation
+
+ align:start position:0%
+this in recitation
+ 
+
+ align:start position:0%
+this in recitation
+so let me sort of recap what
+
+ align:start position:0%
+so let me sort of recap what
+ 
+
+ align:start position:0%
+so let me sort of recap what
+in their 1979 article um were
+
+ align:start position:0%
+in their 1979 article um were
+ 
+
+ align:start position:0%
+in their 1979 article um were
+proposing based on a bunch of
+
+ align:start position:0%
+proposing based on a bunch of
+ 
+
+ align:start position:0%
+proposing based on a bunch of
+experiments and empirical evidence that
+
+ align:start position:0%
+experiments and empirical evidence that
+ 
+
+ align:start position:0%
+experiments and empirical evidence that
+they had collected
+
+ align:start position:0%
+they had collected
+ 
+
+ align:start position:0%
+they had collected
+so their theory
+
+ align:start position:0%
+so their theory
+ 
+
+ align:start position:0%
+so their theory
+is called prospect theory what they
+
+ align:start position:0%
+is called prospect theory what they
+ 
+
+ align:start position:0%
+is called prospect theory what they
+proposed versions of prospect theory is
+
+ align:start position:0%
+proposed versions of prospect theory is
+ 
+
+ align:start position:0%
+proposed versions of prospect theory is
+essentially versions of reference
+
+ align:start position:0%
+essentially versions of reference
+ 
+
+ align:start position:0%
+essentially versions of reference
+dependent utility
+
+ align:start position:0%
+dependent utility
+ 
+
+ align:start position:0%
+dependent utility
+have been used are used prominently now
+
+ align:start position:0%
+have been used are used prominently now
+ 
+
+ align:start position:0%
+have been used are used prominently now
+in economics
+
+ align:start position:0%
+in economics
+ 
+
+ align:start position:0%
+in economics
+so the first thing that they proposed
+
+ align:start position:0%
+so the first thing that they proposed
+ 
+
+ align:start position:0%
+so the first thing that they proposed
+was what matters what the carrier of
+
+ align:start position:0%
+was what matters what the carrier of
+ 
+
+ align:start position:0%
+was what matters what the carrier of
+utility is is
+
+ align:start position:0%
+utility is is
+ 
+
+ align:start position:0%
+utility is is
+changes rather than levels that's to say
+
+ align:start position:0%
+changes rather than levels that's to say
+ 
+
+ align:start position:0%
+changes rather than levels that's to say
+it doesn't matter for you necessarily
+
+ align:start position:0%
+it doesn't matter for you necessarily
+ 
+
+ align:start position:0%
+it doesn't matter for you necessarily
+how warm it is it matters kind of what's
+
+ align:start position:0%
+how warm it is it matters kind of what's
+ 
+
+ align:start position:0%
+how warm it is it matters kind of what's
+the change of temperature compared to
+
+ align:start position:0%
+the change of temperature compared to
+ 
+
+ align:start position:0%
+the change of temperature compared to
+yesterday
+
+ align:start position:0%
+yesterday
+ 
+
+ align:start position:0%
+yesterday
+it doesn't matter that much how much
+
+ align:start position:0%
+it doesn't matter that much how much
+ 
+
+ align:start position:0%
+it doesn't matter that much how much
+money people have in total it matters
+
+ align:start position:0%
+money people have in total it matters
+ 
+
+ align:start position:0%
+money people have in total it matters
+how much the changes
+
+ align:start position:0%
+how much the changes
+ 
+
+ align:start position:0%
+how much the changes
+relative to what they had previously
+
+ align:start position:0%
+relative to what they had previously
+ 
+
+ align:start position:0%
+relative to what they had previously
+more generally what matters for people
+
+ align:start position:0%
+more generally what matters for people
+ 
+
+ align:start position:0%
+more generally what matters for people
+is essentially a certain
+
+ align:start position:0%
+is essentially a certain
+ 
+
+ align:start position:0%
+is essentially a certain
+consumption or the like relative to
+
+ align:start position:0%
+consumption or the like relative to
+ 
+
+ align:start position:0%
+consumption or the like relative to
+reference point as opposed to an
+
+ align:start position:0%
+reference point as opposed to an
+ 
+
+ align:start position:0%
+reference point as opposed to an
+absolute
+
+ align:start position:0%
+absolute
+ 
+
+ align:start position:0%
+absolute
+terms second loss aversion this is
+
+ align:start position:0%
+terms second loss aversion this is
+ 
+
+ align:start position:0%
+terms second loss aversion this is
+losses
+
+ align:start position:0%
+losses
+ 
+
+ align:start position:0%
+losses
+loom larger than gains and we had some
+
+ align:start position:0%
+loom larger than gains and we had some
+ 
+
+ align:start position:0%
+loom larger than gains and we had some
+evidence of that in the last lecture
+
+ align:start position:0%
+evidence of that in the last lecture
+ 
+
+ align:start position:0%
+evidence of that in the last lecture
+that's to say if you lose some money or
+
+ align:start position:0%
+that's to say if you lose some money or
+ 
+
+ align:start position:0%
+that's to say if you lose some money or
+some consumption
+
+ align:start position:0%
+some consumption
+ 
+
+ align:start position:0%
+some consumption
+or anything else grades etc
+
+ align:start position:0%
+or anything else grades etc
+ 
+
+ align:start position:0%
+or anything else grades etc
+a lot relative to either your status quo
+
+ align:start position:0%
+a lot relative to either your status quo
+ 
+
+ align:start position:0%
+a lot relative to either your status quo
+or to your expectation
+
+ align:start position:0%
+or to your expectation
+ 
+
+ align:start position:0%
+or to your expectation
+looms larger is more important hurts
+
+ align:start position:0%
+looms larger is more important hurts
+ 
+
+ align:start position:0%
+looms larger is more important hurts
+more than a gain of the same magnitude
+
+ align:start position:0%
+more than a gain of the same magnitude
+ 
+
+ align:start position:0%
+more than a gain of the same magnitude
+in the positive direction and number
+
+ align:start position:0%
+in the positive direction and number
+ 
+
+ align:start position:0%
+in the positive direction and number
+three which you talked about
+
+ align:start position:0%
+three which you talked about
+ 
+
+ align:start position:0%
+three which you talked about
+quickly is what's referred to as
+
+ align:start position:0%
+quickly is what's referred to as
+ 
+
+ align:start position:0%
+quickly is what's referred to as
+diminishing sensitivity
+
+ align:start position:0%
+diminishing sensitivity
+ 
+
+ align:start position:0%
+diminishing sensitivity
+that is um people are risk averse in the
+
+ align:start position:0%
+that is um people are risk averse in the
+ 
+
+ align:start position:0%
+that is um people are risk averse in the
+gain domain but risk loving in the last
+
+ align:start position:0%
+gain domain but risk loving in the last
+ 
+
+ align:start position:0%
+gain domain but risk loving in the last
+domain
+
+ align:start position:0%
+domain
+ 
+
+ align:start position:0%
+domain
+that's to say um um if you are for
+
+ align:start position:0%
+that's to say um um if you are for
+ 
+
+ align:start position:0%
+that's to say um um if you are for
+example if you think about distance
+
+ align:start position:0%
+example if you think about distance
+ 
+
+ align:start position:0%
+example if you think about distance
+time chance and the like going from zero
+
+ align:start position:0%
+time chance and the like going from zero
+ 
+
+ align:start position:0%
+time chance and the like going from zero
+to one
+
+ align:start position:0%
+to one
+ 
+
+ align:start position:0%
+to one
+or from one to two from two to three is
+
+ align:start position:0%
+or from one to two from two to three is
+ 
+
+ align:start position:0%
+or from one to two from two to three is
+more important for you
+
+ align:start position:0%
+more important for you
+ 
+
+ align:start position:0%
+more important for you
+than going from like 100 to 101 101 102
+
+ align:start position:0%
+than going from like 100 to 101 101 102
+ 
+
+ align:start position:0%
+than going from like 100 to 101 101 102
+and so on essentially
+
+ align:start position:0%
+and so on essentially
+ 
+
+ align:start position:0%
+and so on essentially
+uh the further you'll go away from like
+
+ align:start position:0%
+uh the further you'll go away from like
+ 
+
+ align:start position:0%
+uh the further you'll go away from like
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+status quo your reference point uh any
+
+ align:start position:0%
+status quo your reference point uh any
+ 
+
+ align:start position:0%
+status quo your reference point uh any
+marginal changes like diminishing
+
+ align:start position:0%
+marginal changes like diminishing
+ 
+
+ align:start position:0%
+marginal changes like diminishing
+right and that's true for both the gain
+
+ align:start position:0%
+right and that's true for both the gain
+ 
+
+ align:start position:0%
+right and that's true for both the gain
+domain and um
+
+ align:start position:0%
+domain and um
+ 
+
+ align:start position:0%
+domain and um
+uh the loss domain so these are sort of
+
+ align:start position:0%
+uh the loss domain so these are sort of
+ 
+
+ align:start position:0%
+uh the loss domain so these are sort of
+the main three characteristics
+
+ align:start position:0%
+the main three characteristics
+ 
+
+ align:start position:0%
+the main three characteristics
+related to what kind of first we call
+
+ align:start position:0%
+related to what kind of first we call
+ 
+
+ align:start position:0%
+related to what kind of first we call
+the value function we can think of this
+
+ align:start position:0%
+the value function we can think of this
+ 
+
+ align:start position:0%
+the value function we can think of this
+as essentially a version of the utility
+
+ align:start position:0%
+as essentially a version of the utility
+ 
+
+ align:start position:0%
+as essentially a version of the utility
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+there's a fourth characteristic which is
+
+ align:start position:0%
+there's a fourth characteristic which is
+ 
+
+ align:start position:0%
+there's a fourth characteristic which is
+probability weighting which we're not
+
+ align:start position:0%
+probability weighting which we're not
+ 
+
+ align:start position:0%
+probability weighting which we're not
+going to talk about at least
+
+ align:start position:0%
+going to talk about at least
+ 
+
+ align:start position:0%
+going to talk about at least
+for now are there any questions on these
+
+ align:start position:0%
+for now are there any questions on these
+ 
+
+ align:start position:0%
+for now are there any questions on these
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+things so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now
+
+ align:start position:0%
+okay so now
+ 
+
+ align:start position:0%
+okay so now
+prospect theory is then what kahneman
+
+ align:start position:0%
+prospect theory is then what kahneman
+ 
+
+ align:start position:0%
+prospect theory is then what kahneman
+and versky were proposing they were
+
+ align:start position:0%
+and versky were proposing they were
+ 
+
+ align:start position:0%
+and versky were proposing they were
+essentially saying like
+
+ align:start position:0%
+essentially saying like
+ 
+
+ align:start position:0%
+essentially saying like
+instead of having concave utility which
+
+ align:start position:0%
+instead of having concave utility which
+ 
+
+ align:start position:0%
+instead of having concave utility which
+i showed you um uh
+
+ align:start position:0%
+i showed you um uh
+ 
+
+ align:start position:0%
+i showed you um uh
+last week instead your utility function
+
+ align:start position:0%
+last week instead your utility function
+ 
+
+ align:start position:0%
+last week instead your utility function
+may look like
+
+ align:start position:0%
+may look like
+ 
+
+ align:start position:0%
+may look like
+this and what are sort of the features
+
+ align:start position:0%
+this and what are sort of the features
+ 
+
+ align:start position:0%
+this and what are sort of the features
+of this utility function what what are
+
+ align:start position:0%
+of this utility function what what are
+ 
+
+ align:start position:0%
+of this utility function what what are
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+three key features that i just showed
+
+ align:start position:0%
+three key features that i just showed
+ 
+
+ align:start position:0%
+three key features that i just showed
+you how they're showing up in this
+
+ align:start position:0%
+you how they're showing up in this
+ 
+
+ align:start position:0%
+you how they're showing up in this
+function here
+
+ align:start position:0%
+function here
+ 
+
+ align:start position:0%
+function here
+yes uh c minus where is the changes
+
+ align:start position:0%
+yes uh c minus where is the changes
+ 
+
+ align:start position:0%
+yes uh c minus where is the changes
+right so the carrier of the utility
+
+ align:start position:0%
+right so the carrier of the utility
+ 
+
+ align:start position:0%
+right so the carrier of the utility
+function so what we have here is like c
+
+ align:start position:0%
+function so what we have here is like c
+ 
+
+ align:start position:0%
+function so what we have here is like c
+and r
+
+ align:start position:0%
+and r
+ 
+
+ align:start position:0%
+and r
+uh c is like consumption that could be
+
+ align:start position:0%
+uh c is like consumption that could be
+ 
+
+ align:start position:0%
+uh c is like consumption that could be
+anything that could be apples that could
+
+ align:start position:0%
+anything that could be apples that could
+ 
+
+ align:start position:0%
+anything that could be apples that could
+be bananas that could be uh
+
+ align:start position:0%
+be bananas that could be uh
+ 
+
+ align:start position:0%
+be bananas that could be uh
+sort of how much money people have
+
+ align:start position:0%
+sort of how much money people have
+ 
+
+ align:start position:0%
+sort of how much money people have
+available to consume overall
+
+ align:start position:0%
+available to consume overall
+ 
+
+ align:start position:0%
+available to consume overall
+the carrier of the utility function is
+
+ align:start position:0%
+the carrier of the utility function is
+ 
+
+ align:start position:0%
+the carrier of the utility function is
+not c itself it's c minus r so it's c
+
+ align:start position:0%
+not c itself it's c minus r so it's c
+ 
+
+ align:start position:0%
+not c itself it's c minus r so it's c
+relative to some reference point r
+
+ align:start position:0%
+relative to some reference point r
+ 
+
+ align:start position:0%
+relative to some reference point r
+that's exactly right
+
+ align:start position:0%
+that's exactly right
+ 
+
+ align:start position:0%
+that's exactly right
+so and if r is the status quo if r is
+
+ align:start position:0%
+so and if r is the status quo if r is
+ 
+
+ align:start position:0%
+so and if r is the status quo if r is
+how much do we have right now or the
+
+ align:start position:0%
+how much do we have right now or the
+ 
+
+ align:start position:0%
+how much do we have right now or the
+person has right now
+
+ align:start position:0%
+person has right now
+ 
+
+ align:start position:0%
+person has right now
+c minus r is a change relative to the
+
+ align:start position:0%
+c minus r is a change relative to the
+ 
+
+ align:start position:0%
+c minus r is a change relative to the
+status quo
+
+ align:start position:0%
+status quo
+ 
+
+ align:start position:0%
+status quo
+notice that r uh we're going to talk
+
+ align:start position:0%
+notice that r uh we're going to talk
+ 
+
+ align:start position:0%
+notice that r uh we're going to talk
+about this a little bit could be also
+
+ align:start position:0%
+about this a little bit could be also
+ 
+
+ align:start position:0%
+about this a little bit could be also
+other things it doesn't have to be
+
+ align:start position:0%
+other things it doesn't have to be
+ 
+
+ align:start position:0%
+other things it doesn't have to be
+necessarily the status quo
+
+ align:start position:0%
+necessarily the status quo
+ 
+
+ align:start position:0%
+necessarily the status quo
+it could be also people's expectation or
+
+ align:start position:0%
+it could be also people's expectation or
+ 
+
+ align:start position:0%
+it could be also people's expectation or
+their goals or their aspirations for the
+
+ align:start position:0%
+their goals or their aspirations for the
+ 
+
+ align:start position:0%
+their goals or their aspirations for the
+future
+
+ align:start position:0%
+future
+ 
+
+ align:start position:0%
+future
+right the key part is however what
+
+ align:start position:0%
+right the key part is however what
+ 
+
+ align:start position:0%
+right the key part is however what
+matters is the first thing i was saying
+
+ align:start position:0%
+matters is the first thing i was saying
+ 
+
+ align:start position:0%
+matters is the first thing i was saying
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+it's changes rather than levels changes
+
+ align:start position:0%
+it's changes rather than levels changes
+ 
+
+ align:start position:0%
+it's changes rather than levels changes
+relative to some
+
+ align:start position:0%
+relative to some
+ 
+
+ align:start position:0%
+relative to some
+reference point or consumption relative
+
+ align:start position:0%
+reference point or consumption relative
+ 
+
+ align:start position:0%
+reference point or consumption relative
+to some reference point that's number
+
+ align:start position:0%
+to some reference point that's number
+ 
+
+ align:start position:0%
+to some reference point that's number
+one yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes uh the curve flattens out which is
+
+ align:start position:0%
+yes uh the curve flattens out which is
+ 
+
+ align:start position:0%
+yes uh the curve flattens out which is
+diminishing
+
+ align:start position:0%
+diminishing
+ 
+
+ align:start position:0%
+diminishing
+exactly the curve flattens out in both
+
+ align:start position:0%
+exactly the curve flattens out in both
+ 
+
+ align:start position:0%
+exactly the curve flattens out in both
+directions that's diminishing
+
+ align:start position:0%
+directions that's diminishing
+ 
+
+ align:start position:0%
+directions that's diminishing
+sensitivity
+
+ align:start position:0%
+sensitivity
+ 
+
+ align:start position:0%
+sensitivity
+it's essentially concave in the in the
+
+ align:start position:0%
+it's essentially concave in the in the
+ 
+
+ align:start position:0%
+it's essentially concave in the in the
+gain domain of the domain where like
+
+ align:start position:0%
+gain domain of the domain where like
+ 
+
+ align:start position:0%
+gain domain of the domain where like
+c is larger than r and it's convex in
+
+ align:start position:0%
+c is larger than r and it's convex in
+ 
+
+ align:start position:0%
+c is larger than r and it's convex in
+the last domain where c is
+
+ align:start position:0%
+the last domain where c is
+ 
+
+ align:start position:0%
+the last domain where c is
+smaller than r right
+
+ align:start position:0%
+smaller than r right
+ 
+
+ align:start position:0%
+smaller than r right
+and that's exactly the issue that
+
+ align:start position:0%
+and that's exactly the issue that
+ 
+
+ align:start position:0%
+and that's exactly the issue that
+essentially the first the marginal
+
+ align:start position:0%
+essentially the first the marginal
+ 
+
+ align:start position:0%
+essentially the first the marginal
+change going from like uh say one to two
+
+ align:start position:0%
+change going from like uh say one to two
+ 
+
+ align:start position:0%
+change going from like uh say one to two
+is relatively large compared to a
+
+ align:start position:0%
+is relatively large compared to a
+ 
+
+ align:start position:0%
+is relatively large compared to a
+marginal change going from 10 to 11
+
+ align:start position:0%
+marginal change going from 10 to 11
+ 
+
+ align:start position:0%
+marginal change going from 10 to 11
+that's both going in the right direction
+
+ align:start position:0%
+that's both going in the right direction
+ 
+
+ align:start position:0%
+that's both going in the right direction
+in the gains domain and the left
+
+ align:start position:0%
+in the gains domain and the left
+ 
+
+ align:start position:0%
+in the gains domain and the left
+direction and the last domain
+
+ align:start position:0%
+direction and the last domain
+ 
+
+ align:start position:0%
+direction and the last domain
+uh yes um for the loss of version um the
+
+ align:start position:0%
+uh yes um for the loss of version um the
+ 
+
+ align:start position:0%
+uh yes um for the loss of version um the
+left side is cheaper than the right side
+
+ align:start position:0%
+left side is cheaper than the right side
+ 
+
+ align:start position:0%
+left side is cheaper than the right side
+exactly in particular there's like kink
+
+ align:start position:0%
+exactly in particular there's like kink
+ 
+
+ align:start position:0%
+exactly in particular there's like kink
+in and this function
+
+ align:start position:0%
+in and this function
+ 
+
+ align:start position:0%
+in and this function
+uh when you look at zero where
+
+ align:start position:0%
+uh when you look at zero where
+ 
+
+ align:start position:0%
+uh when you look at zero where
+essentially um
+
+ align:start position:0%
+essentially um
+ 
+
+ align:start position:0%
+essentially um
+the gain and loss domain was c equals r
+
+ align:start position:0%
+the gain and loss domain was c equals r
+ 
+
+ align:start position:0%
+the gain and loss domain was c equals r
+uh the gain and loss domain
+
+ align:start position:0%
+uh the gain and loss domain
+ 
+
+ align:start position:0%
+uh the gain and loss domain
+intersect uh there we have a kink in the
+
+ align:start position:0%
+intersect uh there we have a kink in the
+ 
+
+ align:start position:0%
+intersect uh there we have a kink in the
+in the value function and the utility
+
+ align:start position:0%
+in the value function and the utility
+ 
+
+ align:start position:0%
+in the value function and the utility
+function uh which essentially exactly is
+
+ align:start position:0%
+function uh which essentially exactly is
+ 
+
+ align:start position:0%
+function uh which essentially exactly is
+the last domain
+
+ align:start position:0%
+the last domain
+ 
+
+ align:start position:0%
+the last domain
+at the last aversion which is like going
+
+ align:start position:0%
+at the last aversion which is like going
+ 
+
+ align:start position:0%
+at the last aversion which is like going
+to the right it's less deep than going
+
+ align:start position:0%
+to the right it's less deep than going
+ 
+
+ align:start position:0%
+to the right it's less deep than going
+to the left
+
+ align:start position:0%
+to the left
+ 
+
+ align:start position:0%
+to the left
+but differently if you lose if you're
+
+ align:start position:0%
+but differently if you lose if you're
+ 
+
+ align:start position:0%
+but differently if you lose if you're
+sort of below the reference point
+
+ align:start position:0%
+sort of below the reference point
+ 
+
+ align:start position:0%
+sort of below the reference point
+that's more painful than being the same
+
+ align:start position:0%
+that's more painful than being the same
+ 
+
+ align:start position:0%
+that's more painful than being the same
+amount of uh
+
+ align:start position:0%
+amount of uh
+ 
+
+ align:start position:0%
+amount of uh
+units to be above the reference point
+
+ align:start position:0%
+units to be above the reference point
+ 
+
+ align:start position:0%
+units to be above the reference point
+that's number two that's essentially
+
+ align:start position:0%
+that's number two that's essentially
+ 
+
+ align:start position:0%
+that's number two that's essentially
+exactly the last aversion
+
+ align:start position:0%
+exactly the last aversion
+ 
+
+ align:start position:0%
+exactly the last aversion
+so i just wrote down all of that again
+
+ align:start position:0%
+so i just wrote down all of that again
+ 
+
+ align:start position:0%
+so i just wrote down all of that again
+let me repeat caro the utility has
+
+ align:start position:0%
+let me repeat caro the utility has
+ 
+
+ align:start position:0%
+let me repeat caro the utility has
+changes relative to the reference point
+
+ align:start position:0%
+changes relative to the reference point
+ 
+
+ align:start position:0%
+changes relative to the reference point
+excuse me rather than levels second
+
+ align:start position:0%
+excuse me rather than levels second
+ 
+
+ align:start position:0%
+excuse me rather than levels second
+there's loss of version there's a kink
+
+ align:start position:0%
+there's loss of version there's a kink
+ 
+
+ align:start position:0%
+there's loss of version there's a kink
+at zero in this function and three
+
+ align:start position:0%
+at zero in this function and three
+ 
+
+ align:start position:0%
+at zero in this function and three
+there's diminishing sensitivity which is
+
+ align:start position:0%
+there's diminishing sensitivity which is
+ 
+
+ align:start position:0%
+there's diminishing sensitivity which is
+concavity and gains and convexity in
+
+ align:start position:0%
+concavity and gains and convexity in
+ 
+
+ align:start position:0%
+concavity and gains and convexity in
+losses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now a key question here is i'm going to
+
+ align:start position:0%
+now a key question here is i'm going to
+ 
+
+ align:start position:0%
+now a key question here is i'm going to
+sort of flag this we're going to talk
+
+ align:start position:0%
+sort of flag this we're going to talk
+ 
+
+ align:start position:0%
+sort of flag this we're going to talk
+about this a little bit at the end
+
+ align:start position:0%
+about this a little bit at the end
+ 
+
+ align:start position:0%
+about this a little bit at the end
+of the lecture we're going to talk to
+
+ align:start position:0%
+of the lecture we're going to talk to
+ 
+
+ align:start position:0%
+of the lecture we're going to talk to
+this a little bit in the next problem
+
+ align:start position:0%
+this a little bit in the next problem
+ 
+
+ align:start position:0%
+this a little bit in the next problem
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+is kind of like how is the reference
+
+ align:start position:0%
+is kind of like how is the reference
+ 
+
+ align:start position:0%
+is kind of like how is the reference
+point determined and does it matter
+
+ align:start position:0%
+point determined and does it matter
+ 
+
+ align:start position:0%
+point determined and does it matter
+as i said before in kanaman firski's
+
+ align:start position:0%
+as i said before in kanaman firski's
+ 
+
+ align:start position:0%
+as i said before in kanaman firski's
+work a lot of the reference point is the
+
+ align:start position:0%
+work a lot of the reference point is the
+ 
+
+ align:start position:0%
+work a lot of the reference point is the
+status quo
+
+ align:start position:0%
+status quo
+ 
+
+ align:start position:0%
+status quo
+so they essentially postulated the
+
+ align:start position:0%
+so they essentially postulated the
+ 
+
+ align:start position:0%
+so they essentially postulated the
+status quo is what would really
+
+ align:start position:0%
+status quo is what would really
+ 
+
+ align:start position:0%
+status quo is what would really
+what matters originally i think people
+
+ align:start position:0%
+what matters originally i think people
+ 
+
+ align:start position:0%
+what matters originally i think people
+have moved towards saying like the
+
+ align:start position:0%
+have moved towards saying like the
+ 
+
+ align:start position:0%
+have moved towards saying like the
+reference point and this is what kossig
+
+ align:start position:0%
+reference point and this is what kossig
+ 
+
+ align:start position:0%
+reference point and this is what kossig
+and raven and others have
+
+ align:start position:0%
+and raven and others have
+ 
+
+ align:start position:0%
+and raven and others have
+written down in their models of
+
+ align:start position:0%
+written down in their models of
+ 
+
+ align:start position:0%
+written down in their models of
+reference dependence utility and
+
+ align:start position:0%
+reference dependence utility and
+ 
+
+ align:start position:0%
+reference dependence utility and
+and and recent more economics work is
+
+ align:start position:0%
+and and recent more economics work is
+ 
+
+ align:start position:0%
+and and recent more economics work is
+what really matters is
+
+ align:start position:0%
+what really matters is
+ 
+
+ align:start position:0%
+what really matters is
+expectations so what do you expect
+
+ align:start position:0%
+expectations so what do you expect
+ 
+
+ align:start position:0%
+expectations so what do you expect
+to consume or to have and so on that
+
+ align:start position:0%
+to consume or to have and so on that
+ 
+
+ align:start position:0%
+to consume or to have and so on that
+matters that sometimes coincides with
+
+ align:start position:0%
+matters that sometimes coincides with
+ 
+
+ align:start position:0%
+matters that sometimes coincides with
+the status quo
+
+ align:start position:0%
+the status quo
+ 
+
+ align:start position:0%
+the status quo
+for example if you have a house the
+
+ align:start position:0%
+for example if you have a house the
+ 
+
+ align:start position:0%
+for example if you have a house the
+status quo is that you have a house you
+
+ align:start position:0%
+status quo is that you have a house you
+ 
+
+ align:start position:0%
+status quo is that you have a house you
+probably assume that you have a house in
+
+ align:start position:0%
+probably assume that you have a house in
+ 
+
+ align:start position:0%
+probably assume that you have a house in
+the future
+
+ align:start position:0%
+the future
+ 
+
+ align:start position:0%
+the future
+uh these things coincide if you think
+
+ align:start position:0%
+uh these things coincide if you think
+ 
+
+ align:start position:0%
+uh these things coincide if you think
+about wages et cetera what seems to
+
+ align:start position:0%
+about wages et cetera what seems to
+ 
+
+ align:start position:0%
+about wages et cetera what seems to
+matter often is not so much how
+
+ align:start position:0%
+matter often is not so much how
+ 
+
+ align:start position:0%
+matter often is not so much how
+much what people's wages are right now
+
+ align:start position:0%
+much what people's wages are right now
+ 
+
+ align:start position:0%
+much what people's wages are right now
+what matters is like what wage gains and
+
+ align:start position:0%
+what matters is like what wage gains and
+ 
+
+ align:start position:0%
+what matters is like what wage gains and
+so on do they expect to
+
+ align:start position:0%
+so on do they expect to
+ 
+
+ align:start position:0%
+so on do they expect to
+receive in the future and they evaluate
+
+ align:start position:0%
+receive in the future and they evaluate
+ 
+
+ align:start position:0%
+receive in the future and they evaluate
+their future their their outcomes in the
+
+ align:start position:0%
+their future their their outcomes in the
+ 
+
+ align:start position:0%
+their future their their outcomes in the
+future
+
+ align:start position:0%
+future
+ 
+
+ align:start position:0%
+future
+uh not necessarily to like the current
+
+ align:start position:0%
+uh not necessarily to like the current
+ 
+
+ align:start position:0%
+uh not necessarily to like the current
+wage but rather what they expect they
+
+ align:start position:0%
+wage but rather what they expect they
+ 
+
+ align:start position:0%
+wage but rather what they expect they
+would get
+
+ align:start position:0%
+would get
+ 
+
+ align:start position:0%
+would get
+in the future okay and so here's an
+
+ align:start position:0%
+in the future okay and so here's an
+ 
+
+ align:start position:0%
+in the future okay and so here's an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+and you'll have some problem sets
+
+ align:start position:0%
+and you'll have some problem sets
+ 
+
+ align:start position:0%
+and you'll have some problem sets
+questions again this is problem set
+
+ align:start position:0%
+questions again this is problem set
+ 
+
+ align:start position:0%
+questions again this is problem set
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+which is not posted yet but but will be
+
+ align:start position:0%
+which is not posted yet but but will be
+ 
+
+ align:start position:0%
+which is not posted yet but but will be
+uh of that kind
+
+ align:start position:0%
+uh of that kind
+ 
+
+ align:start position:0%
+uh of that kind
+which is you might have like reference
+
+ align:start position:0%
+which is you might have like reference
+ 
+
+ align:start position:0%
+which is you might have like reference
+dependent utility over
+
+ align:start position:0%
+dependent utility over
+ 
+
+ align:start position:0%
+dependent utility over
+uh this is just a very simple example
+
+ align:start position:0%
+uh this is just a very simple example
+ 
+
+ align:start position:0%
+uh this is just a very simple example
+over shirts and money so you have
+
+ align:start position:0%
+over shirts and money so you have
+ 
+
+ align:start position:0%
+over shirts and money so you have
+essentially two different domains you
+
+ align:start position:0%
+essentially two different domains you
+ 
+
+ align:start position:0%
+essentially two different domains you
+have essentially losses and gains over
+
+ align:start position:0%
+have essentially losses and gains over
+ 
+
+ align:start position:0%
+have essentially losses and gains over
+both of those domains
+
+ align:start position:0%
+both of those domains
+ 
+
+ align:start position:0%
+both of those domains
+you have a reference point which is rs
+
+ align:start position:0%
+you have a reference point which is rs
+ 
+
+ align:start position:0%
+you have a reference point which is rs
+is how many shirts you might have you
+
+ align:start position:0%
+is how many shirts you might have you
+ 
+
+ align:start position:0%
+is how many shirts you might have you
+have a reference point rm how much money
+
+ align:start position:0%
+have a reference point rm how much money
+ 
+
+ align:start position:0%
+have a reference point rm how much money
+you might have
+
+ align:start position:0%
+you might have
+ 
+
+ align:start position:0%
+you might have
+now what's important here is that
+
+ align:start position:0%
+now what's important here is that
+ 
+
+ align:start position:0%
+now what's important here is that
+essentially when you think about buying
+
+ align:start position:0%
+essentially when you think about buying
+ 
+
+ align:start position:0%
+essentially when you think about buying
+a shirt
+
+ align:start position:0%
+a shirt
+ 
+
+ align:start position:0%
+a shirt
+or or selling a shirt there's going to
+
+ align:start position:0%
+or or selling a shirt there's going to
+ 
+
+ align:start position:0%
+or or selling a shirt there's going to
+be two dimensions
+
+ align:start position:0%
+be two dimensions
+ 
+
+ align:start position:0%
+be two dimensions
+which you have to sort of consider if
+
+ align:start position:0%
+which you have to sort of consider if
+ 
+
+ align:start position:0%
+which you have to sort of consider if
+and when you think about the endowment
+
+ align:start position:0%
+and when you think about the endowment
+ 
+
+ align:start position:0%
+and when you think about the endowment
+effect of mugs and so on
+
+ align:start position:0%
+effect of mugs and so on
+ 
+
+ align:start position:0%
+effect of mugs and so on
+you have to consider not only
+
+ align:start position:0%
+you have to consider not only
+ 
+
+ align:start position:0%
+you have to consider not only
+the losses on gains and shirts but also
+
+ align:start position:0%
+the losses on gains and shirts but also
+ 
+
+ align:start position:0%
+the losses on gains and shirts but also
+the losses can gains in money
+
+ align:start position:0%
+the losses can gains in money
+ 
+
+ align:start position:0%
+the losses can gains in money
+so that's to say if you're trying to buy
+
+ align:start position:0%
+so that's to say if you're trying to buy
+ 
+
+ align:start position:0%
+so that's to say if you're trying to buy
+something you're going to get like a
+
+ align:start position:0%
+something you're going to get like a
+ 
+
+ align:start position:0%
+something you're going to get like a
+gain in shirts relative to the reference
+
+ align:start position:0%
+gain in shirts relative to the reference
+ 
+
+ align:start position:0%
+gain in shirts relative to the reference
+point if it's unexpected
+
+ align:start position:0%
+point if it's unexpected
+ 
+
+ align:start position:0%
+point if it's unexpected
+but you'll also have a loss in money
+
+ align:start position:0%
+but you'll also have a loss in money
+ 
+
+ align:start position:0%
+but you'll also have a loss in money
+similarly if you're going to like sell a
+
+ align:start position:0%
+similarly if you're going to like sell a
+ 
+
+ align:start position:0%
+similarly if you're going to like sell a
+shirt you're going to have like a
+
+ align:start position:0%
+shirt you're going to have like a
+ 
+
+ align:start position:0%
+shirt you're going to have like a
+loss in shirts but a gain and money on
+
+ align:start position:0%
+loss in shirts but a gain and money on
+ 
+
+ align:start position:0%
+loss in shirts but a gain and money on
+these things and interact
+
+ align:start position:0%
+these things and interact
+ 
+
+ align:start position:0%
+these things and interact
+now what's the value function the value
+
+ align:start position:0%
+now what's the value function the value
+ 
+
+ align:start position:0%
+now what's the value function the value
+function as i said before it's usually
+
+ align:start position:0%
+function as i said before it's usually
+ 
+
+ align:start position:0%
+function as i said before it's usually
+concave in the gain domain and convex in
+
+ align:start position:0%
+concave in the gain domain and convex in
+ 
+
+ align:start position:0%
+concave in the gain domain and convex in
+the in the last domain
+
+ align:start position:0%
+the in the last domain
+ 
+
+ align:start position:0%
+the in the last domain
+there's a kinkex zero it's deeper on the
+
+ align:start position:0%
+there's a kinkex zero it's deeper on the
+ 
+
+ align:start position:0%
+there's a kinkex zero it's deeper on the
+left uh then on the right usually we
+
+ align:start position:0%
+left uh then on the right usually we
+ 
+
+ align:start position:0%
+left uh then on the right usually we
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+uh the relative slope is about like two
+
+ align:start position:0%
+uh the relative slope is about like two
+ 
+
+ align:start position:0%
+uh the relative slope is about like two
+2.5
+
+ align:start position:0%
+2.5
+ 
+
+ align:start position:0%
+2.5
+okay so um so one version of that would
+
+ align:start position:0%
+okay so um so one version of that would
+ 
+
+ align:start position:0%
+okay so um so one version of that would
+be uh
+
+ align:start position:0%
+be uh
+ 
+
+ align:start position:0%
+be uh
+this function that i wrote down again
+
+ align:start position:0%
+this function that i wrote down again
+ 
+
+ align:start position:0%
+this function that i wrote down again
+there will be some
+
+ align:start position:0%
+there will be some
+ 
+
+ align:start position:0%
+there will be some
+problem such questions etc sort of to
+
+ align:start position:0%
+problem such questions etc sort of to
+ 
+
+ align:start position:0%
+problem such questions etc sort of to
+clarify uh that
+
+ align:start position:0%
+clarify uh that
+ 
+
+ align:start position:0%
+clarify uh that
+but one key question here is then uh
+
+ align:start position:0%
+but one key question here is then uh
+ 
+
+ align:start position:0%
+but one key question here is then uh
+what are the different domains and
+
+ align:start position:0%
+what are the different domains and
+ 
+
+ align:start position:0%
+what are the different domains and
+that's kind of like a question like of
+
+ align:start position:0%
+that's kind of like a question like of
+ 
+
+ align:start position:0%
+that's kind of like a question like of
+mental accounting we'll get to this like
+
+ align:start position:0%
+mental accounting we'll get to this like
+ 
+
+ align:start position:0%
+mental accounting we'll get to this like
+in the second half of the course
+
+ align:start position:0%
+in the second half of the course
+ 
+
+ align:start position:0%
+in the second half of the course
+the question kind of like what are the
+
+ align:start position:0%
+the question kind of like what are the
+ 
+
+ align:start position:0%
+the question kind of like what are the
+different categories do you have like
+
+ align:start position:0%
+different categories do you have like
+ 
+
+ align:start position:0%
+different categories do you have like
+shirts do you have like
+
+ align:start position:0%
+shirts do you have like
+ 
+
+ align:start position:0%
+shirts do you have like
+uh pants uh sweaters or is it just for
+
+ align:start position:0%
+uh pants uh sweaters or is it just for
+ 
+
+ align:start position:0%
+uh pants uh sweaters or is it just for
+clothes overall
+
+ align:start position:0%
+clothes overall
+ 
+
+ align:start position:0%
+clothes overall
+um or like when you think about like
+
+ align:start position:0%
+um or like when you think about like
+ 
+
+ align:start position:0%
+um or like when you think about like
+earnings and uh consumption et cetera is
+
+ align:start position:0%
+earnings and uh consumption et cetera is
+ 
+
+ align:start position:0%
+earnings and uh consumption et cetera is
+it daily consumption is it weekly
+
+ align:start position:0%
+it daily consumption is it weekly
+ 
+
+ align:start position:0%
+it daily consumption is it weekly
+consumption is it monthly consumption
+
+ align:start position:0%
+consumption is it monthly consumption
+ 
+
+ align:start position:0%
+consumption is it monthly consumption
+so there's lots of questions on like how
+
+ align:start position:0%
+so there's lots of questions on like how
+ 
+
+ align:start position:0%
+so there's lots of questions on like how
+to exactly specify this utility function
+
+ align:start position:0%
+to exactly specify this utility function
+ 
+
+ align:start position:0%
+to exactly specify this utility function
+these questions are mostly um unanswered
+
+ align:start position:0%
+these questions are mostly um unanswered
+ 
+
+ align:start position:0%
+these questions are mostly um unanswered
+in the literature so for now for us in
+
+ align:start position:0%
+in the literature so for now for us in
+ 
+
+ align:start position:0%
+in the literature so for now for us in
+our purposes
+
+ align:start position:0%
+our purposes
+ 
+
+ align:start position:0%
+our purposes
+we're going to essentially assume there
+
+ align:start position:0%
+we're going to essentially assume there
+ 
+
+ align:start position:0%
+we're going to essentially assume there
+is a value function given and then
+
+ align:start position:0%
+is a value function given and then
+ 
+
+ align:start position:0%
+is a value function given and then
+sort of work with with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay great so now we're going to talk
+
+ align:start position:0%
+okay great so now we're going to talk
+ 
+
+ align:start position:0%
+okay great so now we're going to talk
+about the number of different
+
+ align:start position:0%
+about the number of different
+ 
+
+ align:start position:0%
+about the number of different
+applications we talked a little bit
+
+ align:start position:0%
+applications we talked a little bit
+ 
+
+ align:start position:0%
+applications we talked a little bit
+about already
+
+ align:start position:0%
+about already
+ 
+
+ align:start position:0%
+about already
+about the endowment effect and about
+
+ align:start position:0%
+about the endowment effect and about
+ 
+
+ align:start position:0%
+about the endowment effect and about
+insurance i'm going to skip this
+
+ align:start position:0%
+insurance i'm going to skip this
+ 
+
+ align:start position:0%
+insurance i'm going to skip this
+um there's some of this already in in
+
+ align:start position:0%
+um there's some of this already in in
+ 
+
+ align:start position:0%
+um there's some of this already in in
+recitation and the problem sets
+
+ align:start position:0%
+recitation and the problem sets
+ 
+
+ align:start position:0%
+recitation and the problem sets
+we're going to particularly talk about
+
+ align:start position:0%
+we're going to particularly talk about
+ 
+
+ align:start position:0%
+we're going to particularly talk about
+labor supply and employment decisions
+
+ align:start position:0%
+labor supply and employment decisions
+ 
+
+ align:start position:0%
+labor supply and employment decisions
+essentially how much do people
+
+ align:start position:0%
+essentially how much do people
+ 
+
+ align:start position:0%
+essentially how much do people
+like to work in is effort or people's
+
+ align:start position:0%
+like to work in is effort or people's
+ 
+
+ align:start position:0%
+like to work in is effort or people's
+work decisions are they reference
+
+ align:start position:0%
+work decisions are they reference
+ 
+
+ align:start position:0%
+work decisions are they reference
+dependent
+
+ align:start position:0%
+dependent
+ 
+
+ align:start position:0%
+dependent
+uh we're gonna talk about finances what
+
+ align:start position:0%
+uh we're gonna talk about finances what
+ 
+
+ align:start position:0%
+uh we're gonna talk about finances what
+was mentioned last time already about
+
+ align:start position:0%
+was mentioned last time already about
+ 
+
+ align:start position:0%
+was mentioned last time already about
+investment decisions when do people sell
+
+ align:start position:0%
+investment decisions when do people sell
+ 
+
+ align:start position:0%
+investment decisions when do people sell
+and buy stocks we're going to talk about
+
+ align:start position:0%
+and buy stocks we're going to talk about
+ 
+
+ align:start position:0%
+and buy stocks we're going to talk about
+housing when do people decide to sell or
+
+ align:start position:0%
+housing when do people decide to sell or
+ 
+
+ align:start position:0%
+housing when do people decide to sell or
+buy a solar house and at what price
+
+ align:start position:0%
+buy a solar house and at what price
+ 
+
+ align:start position:0%
+buy a solar house and at what price
+uh we're gonna talk about sports in
+
+ align:start position:0%
+uh we're gonna talk about sports in
+ 
+
+ align:start position:0%
+uh we're gonna talk about sports in
+particular marathon running uh
+
+ align:start position:0%
+particular marathon running uh
+ 
+
+ align:start position:0%
+particular marathon running uh
+and golf um uh and a little bit about
+
+ align:start position:0%
+and golf um uh and a little bit about
+ 
+
+ align:start position:0%
+and golf um uh and a little bit about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+some papers in domestic violence we're
+
+ align:start position:0%
+some papers in domestic violence we're
+ 
+
+ align:start position:0%
+some papers in domestic violence we're
+gonna talk very briefly about and then
+
+ align:start position:0%
+gonna talk very briefly about and then
+ 
+
+ align:start position:0%
+gonna talk very briefly about and then
+we talk a little bit about firms how do
+
+ align:start position:0%
+we talk a little bit about firms how do
+ 
+
+ align:start position:0%
+we talk a little bit about firms how do
+firms think about pricing
+
+ align:start position:0%
+firms think about pricing
+ 
+
+ align:start position:0%
+firms think about pricing
+um uh and so on and what what is sort of
+
+ align:start position:0%
+um uh and so on and what what is sort of
+ 
+
+ align:start position:0%
+um uh and so on and what what is sort of
+like the market response to
+
+ align:start position:0%
+like the market response to
+ 
+
+ align:start position:0%
+like the market response to
+to reference dependence that's to say
+
+ align:start position:0%
+to reference dependence that's to say
+ 
+
+ align:start position:0%
+to reference dependence that's to say
+given that we know there's lots of
+
+ align:start position:0%
+given that we know there's lots of
+ 
+
+ align:start position:0%
+given that we know there's lots of
+reference dependence on the world
+
+ align:start position:0%
+reference dependence on the world
+ 
+
+ align:start position:0%
+reference dependence on the world
+uh how should we now as a firm or like
+
+ align:start position:0%
+uh how should we now as a firm or like
+ 
+
+ align:start position:0%
+uh how should we now as a firm or like
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh treating other people how should we
+
+ align:start position:0%
+uh treating other people how should we
+ 
+
+ align:start position:0%
+uh treating other people how should we
+think about um how does that affect our
+
+ align:start position:0%
+think about um how does that affect our
+ 
+
+ align:start position:0%
+think about um how does that affect our
+our own behavior
+
+ align:start position:0%
+our own behavior
+ 
+
+ align:start position:0%
+our own behavior
+or how maybe firms interact with us okay
+
+ align:start position:0%
+or how maybe firms interact with us okay
+ 
+
+ align:start position:0%
+or how maybe firms interact with us okay
+so let's start with um a labor supply
+
+ align:start position:0%
+so let's start with um a labor supply
+ 
+
+ align:start position:0%
+so let's start with um a labor supply
+let's start with a very simple
+
+ align:start position:0%
+let's start with a very simple
+ 
+
+ align:start position:0%
+let's start with a very simple
+um example suppose there's a worker in
+
+ align:start position:0%
+um example suppose there's a worker in
+ 
+
+ align:start position:0%
+um example suppose there's a worker in
+the following situation
+
+ align:start position:0%
+the following situation
+ 
+
+ align:start position:0%
+the following situation
+she can work freely choose how many
+
+ align:start position:0%
+she can work freely choose how many
+ 
+
+ align:start position:0%
+she can work freely choose how many
+hours she works every day
+
+ align:start position:0%
+hours she works every day
+ 
+
+ align:start position:0%
+hours she works every day
+and there are frequent temporary changes
+
+ align:start position:0%
+and there are frequent temporary changes
+ 
+
+ align:start position:0%
+and there are frequent temporary changes
+in her hourly
+
+ align:start position:0%
+in her hourly
+ 
+
+ align:start position:0%
+in her hourly
+wage now there's different relationships
+
+ align:start position:0%
+wage now there's different relationships
+ 
+
+ align:start position:0%
+wage now there's different relationships
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+wages and hours per day you could always
+
+ align:start position:0%
+wages and hours per day you could always
+ 
+
+ align:start position:0%
+wages and hours per day you could always
+work the same
+
+ align:start position:0%
+work the same
+ 
+
+ align:start position:0%
+work the same
+number of hours you could work more
+
+ align:start position:0%
+number of hours you could work more
+ 
+
+ align:start position:0%
+number of hours you could work more
+hours on the days when wages are high
+
+ align:start position:0%
+hours on the days when wages are high
+ 
+
+ align:start position:0%
+hours on the days when wages are high
+or you could work a few hours and days
+
+ align:start position:0%
+or you could work a few hours and days
+ 
+
+ align:start position:0%
+or you could work a few hours and days
+when the wages are high
+
+ align:start position:0%
+when the wages are high
+ 
+
+ align:start position:0%
+when the wages are high
+what are sort of standard theory say
+
+ align:start position:0%
+what are sort of standard theory say
+ 
+
+ align:start position:0%
+what are sort of standard theory say
+what should you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes two two why is that um
+
+ align:start position:0%
+yes two two why is that um
+ 
+
+ align:start position:0%
+yes two two why is that um
+because that maximizes your expected
+
+ align:start position:0%
+because that maximizes your expected
+ 
+
+ align:start position:0%
+because that maximizes your expected
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+for time right so if if hours are
+
+ align:start position:0%
+for time right so if if hours are
+ 
+
+ align:start position:0%
+for time right so if if hours are
+effortful you usually don't like to work
+
+ align:start position:0%
+effortful you usually don't like to work
+ 
+
+ align:start position:0%
+effortful you usually don't like to work
+you should work during the hours when uh
+
+ align:start position:0%
+you should work during the hours when uh
+ 
+
+ align:start position:0%
+you should work during the hours when uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+when your payment is the largest uh
+
+ align:start position:0%
+when your payment is the largest uh
+ 
+
+ align:start position:0%
+when your payment is the largest uh
+that's right so
+
+ align:start position:0%
+that's right so
+ 
+
+ align:start position:0%
+that's right so
+what about option number one why might
+
+ align:start position:0%
+what about option number one why might
+ 
+
+ align:start position:0%
+what about option number one why might
+option number one
+
+ align:start position:0%
+option number one
+ 
+
+ align:start position:0%
+option number one
+be optimal so what you're saying is
+
+ align:start position:0%
+be optimal so what you're saying is
+ 
+
+ align:start position:0%
+be optimal so what you're saying is
+exactly right uh depends a little bit on
+
+ align:start position:0%
+exactly right uh depends a little bit on
+ 
+
+ align:start position:0%
+exactly right uh depends a little bit on
+on something else and what is that
+
+ align:start position:0%
+on something else and what is that
+ 
+
+ align:start position:0%
+on something else and what is that
+like why might you choose number one
+
+ align:start position:0%
+like why might you choose number one
+ 
+
+ align:start position:0%
+like why might you choose number one
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+um habit farming is nice
+
+ align:start position:0%
+um habit farming is nice
+ 
+
+ align:start position:0%
+um habit farming is nice
+yeah there could be sort of habits
+
+ align:start position:0%
+yeah there could be sort of habits
+ 
+
+ align:start position:0%
+yeah there could be sort of habits
+exactly or it could just be that it's
+
+ align:start position:0%
+exactly or it could just be that it's
+ 
+
+ align:start position:0%
+exactly or it could just be that it's
+really effortful to work like 12 hours
+
+ align:start position:0%
+really effortful to work like 12 hours
+ 
+
+ align:start position:0%
+really effortful to work like 12 hours
+in one day maybe there's like kids at
+
+ align:start position:0%
+in one day maybe there's like kids at
+ 
+
+ align:start position:0%
+in one day maybe there's like kids at
+home or maybe there's like you know it's
+
+ align:start position:0%
+home or maybe there's like you know it's
+ 
+
+ align:start position:0%
+home or maybe there's like you know it's
+just really
+
+ align:start position:0%
+just really
+ 
+
+ align:start position:0%
+just really
+tedious to work at some point you just
+
+ align:start position:0%
+tedious to work at some point you just
+ 
+
+ align:start position:0%
+tedious to work at some point you just
+want to go home and do other stuff
+
+ align:start position:0%
+want to go home and do other stuff
+ 
+
+ align:start position:0%
+want to go home and do other stuff
+so it could just be that working beyond
+
+ align:start position:0%
+so it could just be that working beyond
+ 
+
+ align:start position:0%
+so it could just be that working beyond
+you know like say eight or nine hours
+
+ align:start position:0%
+you know like say eight or nine hours
+ 
+
+ align:start position:0%
+you know like say eight or nine hours
+per day is really tough to do
+
+ align:start position:0%
+per day is really tough to do
+ 
+
+ align:start position:0%
+per day is really tough to do
+so then you might say i'm always going
+
+ align:start position:0%
+so then you might say i'm always going
+ 
+
+ align:start position:0%
+so then you might say i'm always going
+to work eight hours i'd love to work
+
+ align:start position:0%
+to work eight hours i'd love to work
+ 
+
+ align:start position:0%
+to work eight hours i'd love to work
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+uh but that's difficult to do so
+
+ align:start position:0%
+uh but that's difficult to do so
+ 
+
+ align:start position:0%
+uh but that's difficult to do so
+essentially it's just to say if the
+
+ align:start position:0%
+essentially it's just to say if the
+ 
+
+ align:start position:0%
+essentially it's just to say if the
+effort function if the
+
+ align:start position:0%
+effort function if the
+ 
+
+ align:start position:0%
+effort function if the
+effort as a resp function of hours is
+
+ align:start position:0%
+effort as a resp function of hours is
+ 
+
+ align:start position:0%
+effort as a resp function of hours is
+convex and you might sort of say
+
+ align:start position:0%
+convex and you might sort of say
+ 
+
+ align:start position:0%
+convex and you might sort of say
+keep it the same surely what you don't
+
+ align:start position:0%
+keep it the same surely what you don't
+ 
+
+ align:start position:0%
+keep it the same surely what you don't
+want to do as
+
+ align:start position:0%
+want to do as
+ 
+
+ align:start position:0%
+want to do as
+number three working few hours and days
+
+ align:start position:0%
+number three working few hours and days
+ 
+
+ align:start position:0%
+number three working few hours and days
+and wages are high
+
+ align:start position:0%
+and wages are high
+ 
+
+ align:start position:0%
+and wages are high
+unless you know effort costs are
+
+ align:start position:0%
+unless you know effort costs are
+ 
+
+ align:start position:0%
+unless you know effort costs are
+particularly high on those days so it
+
+ align:start position:0%
+particularly high on those days so it
+ 
+
+ align:start position:0%
+particularly high on those days so it
+could be that it's like really super hot
+
+ align:start position:0%
+could be that it's like really super hot
+ 
+
+ align:start position:0%
+could be that it's like really super hot
+or it could be like it's super tedious
+
+ align:start position:0%
+or it could be like it's super tedious
+ 
+
+ align:start position:0%
+or it could be like it's super tedious
+to work on those days and you might say
+
+ align:start position:0%
+to work on those days and you might say
+ 
+
+ align:start position:0%
+to work on those days and you might say
+then you don't want to do it
+
+ align:start position:0%
+then you don't want to do it
+ 
+
+ align:start position:0%
+then you don't want to do it
+but assuming that's not the case you you
+
+ align:start position:0%
+but assuming that's not the case you you
+ 
+
+ align:start position:0%
+but assuming that's not the case you you
+kind of want to avoid this because
+
+ align:start position:0%
+kind of want to avoid this because
+ 
+
+ align:start position:0%
+kind of want to avoid this because
+for the same number of hours you're
+
+ align:start position:0%
+for the same number of hours you're
+ 
+
+ align:start position:0%
+for the same number of hours you're
+going to make less money um overall
+
+ align:start position:0%
+going to make less money um overall
+ 
+
+ align:start position:0%
+going to make less money um overall
+right and sort of here's a concrete
+
+ align:start position:0%
+right and sort of here's a concrete
+ 
+
+ align:start position:0%
+right and sort of here's a concrete
+example suppose wages
+
+ align:start position:0%
+example suppose wages
+ 
+
+ align:start position:0%
+example suppose wages
+five hours an hour on day one and ten
+
+ align:start position:0%
+five hours an hour on day one and ten
+ 
+
+ align:start position:0%
+five hours an hour on day one and ten
+hours a day on day two
+
+ align:start position:0%
+hours a day on day two
+ 
+
+ align:start position:0%
+hours a day on day two
+so there's three strategies you can work
+
+ align:start position:0%
+so there's three strategies you can work
+ 
+
+ align:start position:0%
+so there's three strategies you can work
+eight hours in both days you can work
+
+ align:start position:0%
+eight hours in both days you can work
+ 
+
+ align:start position:0%
+eight hours in both days you can work
+six hours on day one nine hours on day
+
+ align:start position:0%
+six hours on day one nine hours on day
+ 
+
+ align:start position:0%
+six hours on day one nine hours on day
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+or the opposite nine hours on day one
+
+ align:start position:0%
+or the opposite nine hours on day one
+ 
+
+ align:start position:0%
+or the opposite nine hours on day one
+and six hours on on day two
+
+ align:start position:0%
+and six hours on on day two
+ 
+
+ align:start position:0%
+and six hours on on day two
+so if you do that you can do you sort of
+
+ align:start position:0%
+so if you do that you can do you sort of
+ 
+
+ align:start position:0%
+so if you do that you can do you sort of
+calculate how much that is you can
+
+ align:start position:0%
+calculate how much that is you can
+ 
+
+ align:start position:0%
+calculate how much that is you can
+essentially work eight hours on both
+
+ align:start position:0%
+essentially work eight hours on both
+ 
+
+ align:start position:0%
+essentially work eight hours on both
+days you get 120 hours you can work
+
+ align:start position:0%
+days you get 120 hours you can work
+ 
+
+ align:start position:0%
+days you get 120 hours you can work
+six hours and nine uh uh uh
+
+ align:start position:0%
+six hours and nine uh uh uh
+ 
+
+ align:start position:0%
+six hours and nine uh uh uh
+uh on on days one and two which makes
+
+ align:start position:0%
+uh on on days one and two which makes
+ 
+
+ align:start position:0%
+uh on on days one and two which makes
+120 hours
+
+ align:start position:0%
+120 hours
+ 
+
+ align:start position:0%
+120 hours
+at dollars as well or you can
+
+ align:start position:0%
+at dollars as well or you can
+ 
+
+ align:start position:0%
+at dollars as well or you can
+essentially do um the opposite which
+
+ align:start position:0%
+essentially do um the opposite which
+ 
+
+ align:start position:0%
+essentially do um the opposite which
+makes you 105
+
+ align:start position:0%
+makes you 105
+ 
+
+ align:start position:0%
+makes you 105
+dollars this is what i was saying like
+
+ align:start position:0%
+dollars this is what i was saying like
+ 
+
+ align:start position:0%
+dollars this is what i was saying like
+options three doesn't make a lot of
+
+ align:start position:0%
+options three doesn't make a lot of
+ 
+
+ align:start position:0%
+options three doesn't make a lot of
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+um unless effort costs are particularly
+
+ align:start position:0%
+um unless effort costs are particularly
+ 
+
+ align:start position:0%
+um unless effort costs are particularly
+high on certain days when the wages are
+
+ align:start position:0%
+high on certain days when the wages are
+ 
+
+ align:start position:0%
+high on certain days when the wages are
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+we're assuming that away for now um and
+
+ align:start position:0%
+we're assuming that away for now um and
+ 
+
+ align:start position:0%
+we're assuming that away for now um and
+so now option two
+
+ align:start position:0%
+so now option two
+ 
+
+ align:start position:0%
+so now option two
+and this is what you were saying
+
+ align:start position:0%
+and this is what you were saying
+ 
+
+ align:start position:0%
+and this is what you were saying
+essentially saves you an hour overall
+
+ align:start position:0%
+essentially saves you an hour overall
+ 
+
+ align:start position:0%
+essentially saves you an hour overall
+you work only 15 hours instead of 16
+
+ align:start position:0%
+you work only 15 hours instead of 16
+ 
+
+ align:start position:0%
+you work only 15 hours instead of 16
+hours and you make the same amount of
+
+ align:start position:0%
+hours and you make the same amount of
+ 
+
+ align:start position:0%
+hours and you make the same amount of
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+now unless sort of the effort court
+
+ align:start position:0%
+now unless sort of the effort court
+ 
+
+ align:start position:0%
+now unless sort of the effort court
+unless the ninth hour is extremely
+
+ align:start position:0%
+unless the ninth hour is extremely
+ 
+
+ align:start position:0%
+unless the ninth hour is extremely
+costly for you to do you might not want
+
+ align:start position:0%
+costly for you to do you might not want
+ 
+
+ align:start position:0%
+costly for you to do you might not want
+to to do that
+
+ align:start position:0%
+to to do that
+ 
+
+ align:start position:0%
+to to do that
+okay now why might you do
+
+ align:start position:0%
+okay now why might you do
+ 
+
+ align:start position:0%
+okay now why might you do
+uh something else uh instead or what
+
+ align:start position:0%
+uh something else uh instead or what
+ 
+
+ align:start position:0%
+uh something else uh instead or what
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+where does reference dependence come in
+
+ align:start position:0%
+where does reference dependence come in
+ 
+
+ align:start position:0%
+where does reference dependence come in
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes i see on the high wage day that i've
+
+ align:start position:0%
+yes i see on the high wage day that i've
+ 
+
+ align:start position:0%
+yes i see on the high wage day that i've
+made more than the less waste day so i
+
+ align:start position:0%
+made more than the less waste day so i
+ 
+
+ align:start position:0%
+made more than the less waste day so i
+feel like stopping maybe
+
+ align:start position:0%
+feel like stopping maybe
+ 
+
+ align:start position:0%
+feel like stopping maybe
+and why am i why would you stop like
+
+ align:start position:0%
+and why am i why would you stop like
+ 
+
+ align:start position:0%
+and why am i why would you stop like
+what's what's what's causing you to stop
+
+ align:start position:0%
+what's what's what's causing you to stop
+ 
+
+ align:start position:0%
+what's what's what's causing you to stop
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah and so yes and but
+
+ align:start position:0%
+yeah and so yes and but
+ 
+
+ align:start position:0%
+yeah and so yes and but
+so what's the what are you evaluating or
+
+ align:start position:0%
+so what's the what are you evaluating or
+ 
+
+ align:start position:0%
+so what's the what are you evaluating or
+what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or what happens for example if you work
+
+ align:start position:0%
+or what happens for example if you work
+ 
+
+ align:start position:0%
+or what happens for example if you work
+only six hours on
+
+ align:start position:0%
+only six hours on
+ 
+
+ align:start position:0%
+only six hours on
+on a different day like how much do you
+
+ align:start position:0%
+on a different day like how much do you
+ 
+
+ align:start position:0%
+on a different day like how much do you
+make on the six hour day i guess which
+
+ align:start position:0%
+make on the six hour day i guess which
+ 
+
+ align:start position:0%
+make on the six hour day i guess which
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+uh maybe thirty dollars right and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are you comparing that to i guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose you on average you want to
+
+ align:start position:0%
+so suppose you on average you want to
+ 
+
+ align:start position:0%
+so suppose you on average you want to
+make a certain amount of money which is
+
+ align:start position:0%
+make a certain amount of money which is
+ 
+
+ align:start position:0%
+make a certain amount of money which is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+60 and so on now if on sundays you make
+
+ align:start position:0%
+60 and so on now if on sundays you make
+ 
+
+ align:start position:0%
+60 and so on now if on sundays you make
+a lot of money and on sunday you make
+
+ align:start position:0%
+a lot of money and on sunday you make
+ 
+
+ align:start position:0%
+a lot of money and on sunday you make
+very little money
+
+ align:start position:0%
+very little money
+ 
+
+ align:start position:0%
+very little money
+you might sort of evaluate that
+
+ align:start position:0%
+you might sort of evaluate that
+ 
+
+ align:start position:0%
+you might sort of evaluate that
+separately and say on that day i'm
+
+ align:start position:0%
+separately and say on that day i'm
+ 
+
+ align:start position:0%
+separately and say on that day i'm
+essentially in the last domain i'm like
+
+ align:start position:0%
+essentially in the last domain i'm like
+ 
+
+ align:start position:0%
+essentially in the last domain i'm like
+below my target or
+
+ align:start position:0%
+below my target or
+ 
+
+ align:start position:0%
+below my target or
+below my expectation and so if you
+
+ align:start position:0%
+below my expectation and so if you
+ 
+
+ align:start position:0%
+below my expectation and so if you
+evaluate your
+
+ align:start position:0%
+evaluate your
+ 
+
+ align:start position:0%
+evaluate your
+utility that way you might sort of not
+
+ align:start position:0%
+utility that way you might sort of not
+ 
+
+ align:start position:0%
+utility that way you might sort of not
+want that because it feels essentially
+
+ align:start position:0%
+want that because it feels essentially
+ 
+
+ align:start position:0%
+want that because it feels essentially
+you're below
+
+ align:start position:0%
+you're below
+ 
+
+ align:start position:0%
+you're below
+a certain threshold it feels kind of
+
+ align:start position:0%
+a certain threshold it feels kind of
+ 
+
+ align:start position:0%
+a certain threshold it feels kind of
+like a loss relative to your expectation
+
+ align:start position:0%
+like a loss relative to your expectation
+ 
+
+ align:start position:0%
+like a loss relative to your expectation
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+and you might be inclined to work a lot
+
+ align:start position:0%
+and you might be inclined to work a lot
+ 
+
+ align:start position:0%
+and you might be inclined to work a lot
+of hours
+
+ align:start position:0%
+of hours
+ 
+
+ align:start position:0%
+of hours
+instead on the days when you make a lot
+
+ align:start position:0%
+instead on the days when you make a lot
+ 
+
+ align:start position:0%
+instead on the days when you make a lot
+of money why might you stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you might have like a target that
+
+ align:start position:0%
+yes you might have like a target that
+ 
+
+ align:start position:0%
+yes you might have like a target that
+you expect to hit every day to cover
+
+ align:start position:0%
+you expect to hit every day to cover
+ 
+
+ align:start position:0%
+you expect to hit every day to cover
+your expenses and if you
+
+ align:start position:0%
+your expenses and if you
+ 
+
+ align:start position:0%
+your expenses and if you
+feel like working less you can still
+
+ align:start position:0%
+feel like working less you can still
+ 
+
+ align:start position:0%
+feel like working less you can still
+reach that target
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so if your target your reference
+
+ align:start position:0%
+right so if your target your reference
+ 
+
+ align:start position:0%
+right so if your target your reference
+point is essentially a a certain number
+
+ align:start position:0%
+point is essentially a a certain number
+ 
+
+ align:start position:0%
+point is essentially a a certain number
+you might reach that target quickly
+
+ align:start position:0%
+you might reach that target quickly
+ 
+
+ align:start position:0%
+you might reach that target quickly
+because your wage is pretty high on that
+
+ align:start position:0%
+because your wage is pretty high on that
+ 
+
+ align:start position:0%
+because your wage is pretty high on that
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+now once you reach that target you might
+
+ align:start position:0%
+now once you reach that target you might
+ 
+
+ align:start position:0%
+now once you reach that target you might
+say well like now your utility function
+
+ align:start position:0%
+say well like now your utility function
+ 
+
+ align:start position:0%
+say well like now your utility function
+is relatively
+
+ align:start position:0%
+is relatively
+ 
+
+ align:start position:0%
+is relatively
+not very steep anymore relative to being
+
+ align:start position:0%
+not very steep anymore relative to being
+ 
+
+ align:start position:0%
+not very steep anymore relative to being
+in the last domain so it's like flatter
+
+ align:start position:0%
+in the last domain so it's like flatter
+ 
+
+ align:start position:0%
+in the last domain so it's like flatter
+so then you might just stop relatively
+
+ align:start position:0%
+so then you might just stop relatively
+ 
+
+ align:start position:0%
+so then you might just stop relatively
+soon because essentially any marginal
+
+ align:start position:0%
+soon because essentially any marginal
+ 
+
+ align:start position:0%
+soon because essentially any marginal
+earnings
+
+ align:start position:0%
+earnings
+ 
+
+ align:start position:0%
+earnings
+are not really valuable for you anymore
+
+ align:start position:0%
+are not really valuable for you anymore
+ 
+
+ align:start position:0%
+are not really valuable for you anymore
+okay any questions on that or comments
+
+ align:start position:0%
+okay any questions on that or comments
+ 
+
+ align:start position:0%
+okay any questions on that or comments
+so why do we want the wage changes to be
+
+ align:start position:0%
+so why do we want the wage changes to be
+ 
+
+ align:start position:0%
+so why do we want the wage changes to be
+temporary here what's an issue here when
+
+ align:start position:0%
+temporary here what's an issue here when
+ 
+
+ align:start position:0%
+temporary here what's an issue here when
+you sort of try to look at this in the
+
+ align:start position:0%
+you sort of try to look at this in the
+ 
+
+ align:start position:0%
+you sort of try to look at this in the
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+suppose i had like persistent wage
+
+ align:start position:0%
+suppose i had like persistent wage
+ 
+
+ align:start position:0%
+suppose i had like persistent wage
+changes yeah so you can have like a
+
+ align:start position:0%
+changes yeah so you can have like a
+ 
+
+ align:start position:0%
+changes yeah so you can have like a
+frame of reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you want to kind of keep the
+
+ align:start position:0%
+yeah you want to kind of keep the
+ 
+
+ align:start position:0%
+yeah you want to kind of keep the
+reference constant so in some sense if
+
+ align:start position:0%
+reference constant so in some sense if
+ 
+
+ align:start position:0%
+reference constant so in some sense if
+wage changes are permanent
+
+ align:start position:0%
+wage changes are permanent
+ 
+
+ align:start position:0%
+wage changes are permanent
+uh then you get essentially income
+
+ align:start position:0%
+uh then you get essentially income
+ 
+
+ align:start position:0%
+uh then you get essentially income
+effects you'll be a lot richer overall
+
+ align:start position:0%
+effects you'll be a lot richer overall
+ 
+
+ align:start position:0%
+effects you'll be a lot richer overall
+if they're only temporary essentially
+
+ align:start position:0%
+if they're only temporary essentially
+ 
+
+ align:start position:0%
+if they're only temporary essentially
+you can sort of argue that essentially
+
+ align:start position:0%
+you can sort of argue that essentially
+ 
+
+ align:start position:0%
+you can sort of argue that essentially
+your expectation should be the same
+
+ align:start position:0%
+your expectation should be the same
+ 
+
+ align:start position:0%
+your expectation should be the same
+and once you reach once you have a lot
+
+ align:start position:0%
+and once you reach once you have a lot
+ 
+
+ align:start position:0%
+and once you reach once you have a lot
+more money then your classical model
+
+ align:start position:0%
+more money then your classical model
+ 
+
+ align:start position:0%
+more money then your classical model
+should actually say that there should be
+
+ align:start position:0%
+should actually say that there should be
+ 
+
+ align:start position:0%
+should actually say that there should be
+income effects
+
+ align:start position:0%
+income effects
+ 
+
+ align:start position:0%
+income effects
+the neoclassical model only says
+
+ align:start position:0%
+the neoclassical model only says
+ 
+
+ align:start position:0%
+the neoclassical model only says
+essentially the inner classical model
+
+ align:start position:0%
+essentially the inner classical model
+ 
+
+ align:start position:0%
+essentially the inner classical model
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+you should essentially aggregate all of
+
+ align:start position:0%
+you should essentially aggregate all of
+ 
+
+ align:start position:0%
+you should essentially aggregate all of
+your income and say it doesn't really
+
+ align:start position:0%
+your income and say it doesn't really
+ 
+
+ align:start position:0%
+your income and say it doesn't really
+matter like whether you earn it in
+
+ align:start position:0%
+matter like whether you earn it in
+ 
+
+ align:start position:0%
+matter like whether you earn it in
+monday or tuesday wednesday or thursday
+
+ align:start position:0%
+monday or tuesday wednesday or thursday
+ 
+
+ align:start position:0%
+monday or tuesday wednesday or thursday
+you should look at like how much are you
+
+ align:start position:0%
+you should look at like how much are you
+ 
+
+ align:start position:0%
+you should look at like how much are you
+earning overall depending whether you
+
+ align:start position:0%
+earning overall depending whether you
+ 
+
+ align:start position:0%
+earning overall depending whether you
+earn
+
+ align:start position:0%
+earn
+ 
+
+ align:start position:0%
+earn
+sufficiently much um uh you're gonna
+
+ align:start position:0%
+sufficiently much um uh you're gonna
+ 
+
+ align:start position:0%
+sufficiently much um uh you're gonna
+work fewer or more hours
+
+ align:start position:0%
+work fewer or more hours
+ 
+
+ align:start position:0%
+work fewer or more hours
+now if you earn like a lot because your
+
+ align:start position:0%
+now if you earn like a lot because your
+ 
+
+ align:start position:0%
+now if you earn like a lot because your
+wages doubles or whatever you might
+
+ align:start position:0%
+wages doubles or whatever you might
+ 
+
+ align:start position:0%
+wages doubles or whatever you might
+actually work few hours
+
+ align:start position:0%
+actually work few hours
+ 
+
+ align:start position:0%
+actually work few hours
+not because you reach a reference point
+
+ align:start position:0%
+not because you reach a reference point
+ 
+
+ align:start position:0%
+not because you reach a reference point
+on a given day it's just because you got
+
+ align:start position:0%
+on a given day it's just because you got
+ 
+
+ align:start position:0%
+on a given day it's just because you got
+a lot richer and then you decide it's
+
+ align:start position:0%
+a lot richer and then you decide it's
+ 
+
+ align:start position:0%
+a lot richer and then you decide it's
+not worth for you to work that much
+
+ align:start position:0%
+not worth for you to work that much
+ 
+
+ align:start position:0%
+not worth for you to work that much
+so we're kind of trying to avoid that
+
+ align:start position:0%
+so we're kind of trying to avoid that
+ 
+
+ align:start position:0%
+so we're kind of trying to avoid that
+we're trying to have only permanent
+
+ align:start position:0%
+we're trying to have only permanent
+ 
+
+ align:start position:0%
+we're trying to have only permanent
+temporary changes which is to say
+
+ align:start position:0%
+temporary changes which is to say
+ 
+
+ align:start position:0%
+temporary changes which is to say
+forgiven wealth overall um
+
+ align:start position:0%
+forgiven wealth overall um
+ 
+
+ align:start position:0%
+forgiven wealth overall um
+on any given day it shouldn't matter
+
+ align:start position:0%
+on any given day it shouldn't matter
+ 
+
+ align:start position:0%
+on any given day it shouldn't matter
+whether you earn the money on monday or
+
+ align:start position:0%
+whether you earn the money on monday or
+ 
+
+ align:start position:0%
+whether you earn the money on monday or
+on tuesday
+
+ align:start position:0%
+on tuesday
+ 
+
+ align:start position:0%
+on tuesday
+so essentially if the wage happens to be
+
+ align:start position:0%
+so essentially if the wage happens to be
+ 
+
+ align:start position:0%
+so essentially if the wage happens to be
+really high on tuesday you should be
+
+ align:start position:0%
+really high on tuesday you should be
+ 
+
+ align:start position:0%
+really high on tuesday you should be
+working more earning more on tuesday as
+
+ align:start position:0%
+working more earning more on tuesday as
+ 
+
+ align:start position:0%
+working more earning more on tuesday as
+opposed to on monday
+
+ align:start position:0%
+opposed to on monday
+ 
+
+ align:start position:0%
+opposed to on monday
+uh now what i was saying is if you
+
+ align:start position:0%
+uh now what i was saying is if you
+ 
+
+ align:start position:0%
+uh now what i was saying is if you
+reference the pendant you might actually
+
+ align:start position:0%
+reference the pendant you might actually
+ 
+
+ align:start position:0%
+reference the pendant you might actually
+care about this you might care about on
+
+ align:start position:0%
+care about this you might care about on
+ 
+
+ align:start position:0%
+care about this you might care about on
+monday you didn't reach your target
+
+ align:start position:0%
+monday you didn't reach your target
+ 
+
+ align:start position:0%
+monday you didn't reach your target
+therefore you want to work more
+
+ align:start position:0%
+therefore you want to work more
+ 
+
+ align:start position:0%
+therefore you want to work more
+on tuesday you reach your target very
+
+ align:start position:0%
+on tuesday you reach your target very
+ 
+
+ align:start position:0%
+on tuesday you reach your target very
+quickly and you work
+
+ align:start position:0%
+quickly and you work
+ 
+
+ align:start position:0%
+quickly and you work
+uh uh less even though the wage is
+
+ align:start position:0%
+uh uh less even though the wage is
+ 
+
+ align:start position:0%
+uh uh less even though the wage is
+actually really high
+
+ align:start position:0%
+actually really high
+ 
+
+ align:start position:0%
+actually really high
+okay now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strategy one might be optimal even in
+
+ align:start position:0%
+strategy one might be optimal even in
+ 
+
+ align:start position:0%
+strategy one might be optimal even in
+the neoclassical model if effort costs
+
+ align:start position:0%
+the neoclassical model if effort costs
+ 
+
+ align:start position:0%
+the neoclassical model if effort costs
+uh are convex this is what i was saying
+
+ align:start position:0%
+uh are convex this is what i was saying
+ 
+
+ align:start position:0%
+uh are convex this is what i was saying
+is if it's really sort of costly for you
+
+ align:start position:0%
+is if it's really sort of costly for you
+ 
+
+ align:start position:0%
+is if it's really sort of costly for you
+to work nine hours you might say i
+
+ align:start position:0%
+to work nine hours you might say i
+ 
+
+ align:start position:0%
+to work nine hours you might say i
+always work like eight hours i wanna
+
+ align:start position:0%
+always work like eight hours i wanna
+ 
+
+ align:start position:0%
+always work like eight hours i wanna
+have a certain amount of money for my
+
+ align:start position:0%
+have a certain amount of money for my
+ 
+
+ align:start position:0%
+have a certain amount of money for my
+children and so on
+
+ align:start position:0%
+children and so on
+ 
+
+ align:start position:0%
+children and so on
+um so the extra hour if that's really
+
+ align:start position:0%
+um so the extra hour if that's really
+ 
+
+ align:start position:0%
+um so the extra hour if that's really
+really painful you might not want to do
+
+ align:start position:0%
+really painful you might not want to do
+ 
+
+ align:start position:0%
+really painful you might not want to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh we don't think that's necessarily the
+
+ align:start position:0%
+uh we don't think that's necessarily the
+ 
+
+ align:start position:0%
+uh we don't think that's necessarily the
+case in in so many
+
+ align:start position:0%
+case in in so many
+ 
+
+ align:start position:0%
+case in in so many
+uh situations um the question is like
+
+ align:start position:0%
+uh situations um the question is like
+ 
+
+ align:start position:0%
+uh situations um the question is like
+can we really say that strategy
+
+ align:start position:0%
+can we really say that strategy
+ 
+
+ align:start position:0%
+can we really say that strategy
+three that's the strategy of doing the
+
+ align:start position:0%
+three that's the strategy of doing the
+ 
+
+ align:start position:0%
+three that's the strategy of doing the
+opposite of working like essentially a
+
+ align:start position:0%
+opposite of working like essentially a
+ 
+
+ align:start position:0%
+opposite of working like essentially a
+lot of hours and wages are low and few
+
+ align:start position:0%
+lot of hours and wages are low and few
+ 
+
+ align:start position:0%
+lot of hours and wages are low and few
+hours
+
+ align:start position:0%
+hours
+ 
+
+ align:start position:0%
+hours
+when wages are high can we really say
+
+ align:start position:0%
+when wages are high can we really say
+ 
+
+ align:start position:0%
+when wages are high can we really say
+it's a mistake well it depends on kind
+
+ align:start position:0%
+it's a mistake well it depends on kind
+ 
+
+ align:start position:0%
+it's a mistake well it depends on kind
+of like whether the effort costs are
+
+ align:start position:0%
+of like whether the effort costs are
+ 
+
+ align:start position:0%
+of like whether the effort costs are
+correlated with wages so if cab drivers
+
+ align:start position:0%
+correlated with wages so if cab drivers
+ 
+
+ align:start position:0%
+correlated with wages so if cab drivers
+for example make really high wages on
+
+ align:start position:0%
+for example make really high wages on
+ 
+
+ align:start position:0%
+for example make really high wages on
+some days and low wages on
+
+ align:start position:0%
+some days and low wages on
+ 
+
+ align:start position:0%
+some days and low wages on
+other days it could just be on low low
+
+ align:start position:0%
+other days it could just be on low low
+ 
+
+ align:start position:0%
+other days it could just be on low low
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+wage day it's really um uh it's much
+
+ align:start position:0%
+wage day it's really um uh it's much
+ 
+
+ align:start position:0%
+wage day it's really um uh it's much
+less effortful to drive around
+
+ align:start position:0%
+less effortful to drive around
+ 
+
+ align:start position:0%
+less effortful to drive around
+so you would do like more hours it turns
+
+ align:start position:0%
+so you would do like more hours it turns
+ 
+
+ align:start position:0%
+so you would do like more hours it turns
+out when you actually ask
+
+ align:start position:0%
+out when you actually ask
+ 
+
+ align:start position:0%
+out when you actually ask
+a cab drivers they actually prefer a
+
+ align:start position:0%
+a cab drivers they actually prefer a
+ 
+
+ align:start position:0%
+a cab drivers they actually prefer a
+busy day is actually preferred when
+
+ align:start position:0%
+busy day is actually preferred when
+ 
+
+ align:start position:0%
+busy day is actually preferred when
+they're customers as opposed to just
+
+ align:start position:0%
+they're customers as opposed to just
+ 
+
+ align:start position:0%
+they're customers as opposed to just
+driving around and looking for people so
+
+ align:start position:0%
+driving around and looking for people so
+ 
+
+ align:start position:0%
+driving around and looking for people so
+we don't think that's actually true
+
+ align:start position:0%
+we don't think that's actually true
+ 
+
+ align:start position:0%
+we don't think that's actually true
+but in principle you would have to sort
+
+ align:start position:0%
+but in principle you would have to sort
+ 
+
+ align:start position:0%
+but in principle you would have to sort
+of think about uh that
+
+ align:start position:0%
+of think about uh that
+ 
+
+ align:start position:0%
+of think about uh that
+now uh there's a long literature uh
+
+ align:start position:0%
+now uh there's a long literature uh
+ 
+
+ align:start position:0%
+now uh there's a long literature uh
+starting with camera at all on
+
+ align:start position:0%
+starting with camera at all on
+ 
+
+ align:start position:0%
+starting with camera at all on
+uh cab drivers a lot of that essentially
+
+ align:start position:0%
+uh cab drivers a lot of that essentially
+ 
+
+ align:start position:0%
+uh cab drivers a lot of that essentially
+is pre
+
+ align:start position:0%
+is pre
+ 
+
+ align:start position:0%
+is pre
+uber like uh collecting trip sheets um
+
+ align:start position:0%
+uber like uh collecting trip sheets um
+ 
+
+ align:start position:0%
+uber like uh collecting trip sheets um
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+cab drivers now there's lots of like
+
+ align:start position:0%
+cab drivers now there's lots of like
+ 
+
+ align:start position:0%
+cab drivers now there's lots of like
+uber data that's like essentially much
+
+ align:start position:0%
+uber data that's like essentially much
+ 
+
+ align:start position:0%
+uber data that's like essentially much
+more powerful in some ways
+
+ align:start position:0%
+more powerful in some ways
+ 
+
+ align:start position:0%
+more powerful in some ways
+so there will be probably more papers
+
+ align:start position:0%
+so there will be probably more papers
+ 
+
+ align:start position:0%
+so there will be probably more papers
+using uber and lyft etc data on that
+
+ align:start position:0%
+using uber and lyft etc data on that
+ 
+
+ align:start position:0%
+using uber and lyft etc data on that
+um but what camera doll did at the time
+
+ align:start position:0%
+um but what camera doll did at the time
+ 
+
+ align:start position:0%
+um but what camera doll did at the time
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+they essentially looked at a typical cab
+
+ align:start position:0%
+they essentially looked at a typical cab
+ 
+
+ align:start position:0%
+they essentially looked at a typical cab
+drivers that rent their cab for 12 hour
+
+ align:start position:0%
+drivers that rent their cab for 12 hour
+ 
+
+ align:start position:0%
+drivers that rent their cab for 12 hour
+periods for a fixed fee
+
+ align:start position:0%
+periods for a fixed fee
+ 
+
+ align:start position:0%
+periods for a fixed fee
+and within this 12 hour window a driver
+
+ align:start position:0%
+and within this 12 hour window a driver
+ 
+
+ align:start position:0%
+and within this 12 hour window a driver
+can choose the hours freely so you just
+
+ align:start position:0%
+can choose the hours freely so you just
+ 
+
+ align:start position:0%
+can choose the hours freely so you just
+get your cab that's not yours you rent
+
+ align:start position:0%
+get your cab that's not yours you rent
+ 
+
+ align:start position:0%
+get your cab that's not yours you rent
+it for the day and then you can
+
+ align:start position:0%
+it for the day and then you can
+ 
+
+ align:start position:0%
+it for the day and then you can
+essentially choose how many hours you
+
+ align:start position:0%
+essentially choose how many hours you
+ 
+
+ align:start position:0%
+essentially choose how many hours you
+want to work
+
+ align:start position:0%
+want to work
+ 
+
+ align:start position:0%
+want to work
+and their wages how much money they make
+
+ align:start position:0%
+and their wages how much money they make
+ 
+
+ align:start position:0%
+and their wages how much money they make
+in any given hour varies by a lot
+
+ align:start position:0%
+in any given hour varies by a lot
+ 
+
+ align:start position:0%
+in any given hour varies by a lot
+there's like you know uh the weather
+
+ align:start position:0%
+there's like you know uh the weather
+ 
+
+ align:start position:0%
+there's like you know uh the weather
+varies there's subway breakdowns
+
+ align:start position:0%
+varies there's subway breakdowns
+ 
+
+ align:start position:0%
+varies there's subway breakdowns
+conferences and so on and so forth
+
+ align:start position:0%
+conferences and so on and so forth
+ 
+
+ align:start position:0%
+conferences and so on and so forth
+there's lots of variation in how much
+
+ align:start position:0%
+there's lots of variation in how much
+ 
+
+ align:start position:0%
+there's lots of variation in how much
+money you make on a given
+
+ align:start position:0%
+money you make on a given
+ 
+
+ align:start position:0%
+money you make on a given
+day so then they have like trip sheets
+
+ align:start position:0%
+day so then they have like trip sheets
+ 
+
+ align:start position:0%
+day so then they have like trip sheets
+that look at like how long
+
+ align:start position:0%
+that look at like how long
+ 
+
+ align:start position:0%
+that look at like how long
+cab drivers work and their overall
+
+ align:start position:0%
+cab drivers work and their overall
+ 
+
+ align:start position:0%
+cab drivers work and their overall
+earnings and so they can essentially
+
+ align:start position:0%
+earnings and so they can essentially
+ 
+
+ align:start position:0%
+earnings and so they can essentially
+back out the wages from
+
+ align:start position:0%
+back out the wages from
+ 
+
+ align:start position:0%
+back out the wages from
+from each day and then look at like how
+
+ align:start position:0%
+from each day and then look at like how
+ 
+
+ align:start position:0%
+from each day and then look at like how
+much do people work on uh
+
+ align:start position:0%
+much do people work on uh
+ 
+
+ align:start position:0%
+much do people work on uh
+days when wages are high versus wages
+
+ align:start position:0%
+days when wages are high versus wages
+ 
+
+ align:start position:0%
+days when wages are high versus wages
+are days when wages
+
+ align:start position:0%
+are days when wages
+ 
+
+ align:start position:0%
+are days when wages
+are low and then they essentially find
+
+ align:start position:0%
+are low and then they essentially find
+ 
+
+ align:start position:0%
+are low and then they essentially find
+the basic finding and that's a finding
+
+ align:start position:0%
+the basic finding and that's a finding
+ 
+
+ align:start position:0%
+the basic finding and that's a finding
+that's sort of been contested in the
+
+ align:start position:0%
+that's sort of been contested in the
+ 
+
+ align:start position:0%
+that's sort of been contested in the
+literature and many people are found
+
+ align:start position:0%
+literature and many people are found
+ 
+
+ align:start position:0%
+literature and many people are found
+are confirmed subsequently or and others
+
+ align:start position:0%
+are confirmed subsequently or and others
+ 
+
+ align:start position:0%
+are confirmed subsequently or and others
+have not but i think eventually people
+
+ align:start position:0%
+have not but i think eventually people
+ 
+
+ align:start position:0%
+have not but i think eventually people
+have sort of
+
+ align:start position:0%
+have sort of
+ 
+
+ align:start position:0%
+have sort of
+settled on this hours are negatively
+
+ align:start position:0%
+settled on this hours are negatively
+ 
+
+ align:start position:0%
+settled on this hours are negatively
+correlated with wages so when wages in
+
+ align:start position:0%
+correlated with wages so when wages in
+ 
+
+ align:start position:0%
+correlated with wages so when wages in
+particular are unexpectedly high
+
+ align:start position:0%
+particular are unexpectedly high
+ 
+
+ align:start position:0%
+particular are unexpectedly high
+uh cap drivers tend to work a few hours
+
+ align:start position:0%
+uh cap drivers tend to work a few hours
+ 
+
+ align:start position:0%
+uh cap drivers tend to work a few hours
+and again the and this is like not for
+
+ align:start position:0%
+and again the and this is like not for
+ 
+
+ align:start position:0%
+and again the and this is like not for
+permanent changes but for transitory
+
+ align:start position:0%
+permanent changes but for transitory
+ 
+
+ align:start position:0%
+permanent changes but for transitory
+changes if surprisingly on a given day
+
+ align:start position:0%
+changes if surprisingly on a given day
+ 
+
+ align:start position:0%
+changes if surprisingly on a given day
+people get
+
+ align:start position:0%
+people get
+ 
+
+ align:start position:0%
+people get
+more money then
+
+ align:start position:0%
+more money then
+ 
+
+ align:start position:0%
+more money then
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+drivers work few hours and that's very
+
+ align:start position:0%
+drivers work few hours and that's very
+ 
+
+ align:start position:0%
+drivers work few hours and that's very
+hard to explain for the neoclassical
+
+ align:start position:0%
+hard to explain for the neoclassical
+ 
+
+ align:start position:0%
+hard to explain for the neoclassical
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+because essentially like you shouldn't
+
+ align:start position:0%
+because essentially like you shouldn't
+ 
+
+ align:start position:0%
+because essentially like you shouldn't
+care about like whether you make the
+
+ align:start position:0%
+care about like whether you make the
+ 
+
+ align:start position:0%
+care about like whether you make the
+money on monday on tuesday as i said you
+
+ align:start position:0%
+money on monday on tuesday as i said you
+ 
+
+ align:start position:0%
+money on monday on tuesday as i said you
+should care about how much you money
+
+ align:start position:0%
+should care about how much you money
+ 
+
+ align:start position:0%
+should care about how much you money
+you make overall and how many hours you
+
+ align:start position:0%
+you make overall and how many hours you
+ 
+
+ align:start position:0%
+you make overall and how many hours you
+uh work
+
+ align:start position:0%
+uh work
+ 
+
+ align:start position:0%
+uh work
+and so it's very hard to explain this
+
+ align:start position:0%
+and so it's very hard to explain this
+ 
+
+ align:start position:0%
+and so it's very hard to explain this
+and sort of the explanation
+
+ align:start position:0%
+and sort of the explanation
+ 
+
+ align:start position:0%
+and sort of the explanation
+uh that cameradoll and others um
+
+ align:start position:0%
+uh that cameradoll and others um
+ 
+
+ align:start position:0%
+uh that cameradoll and others um
+we're testing or or arguing is
+
+ align:start position:0%
+we're testing or or arguing is
+ 
+
+ align:start position:0%
+we're testing or or arguing is
+essentially this has to do with um
+
+ align:start position:0%
+essentially this has to do with um
+ 
+
+ align:start position:0%
+essentially this has to do with um
+reference dependence and so what's being
+
+ align:start position:0%
+reference dependence and so what's being
+ 
+
+ align:start position:0%
+reference dependence and so what's being
+evaluated in a reference dependent way
+
+ align:start position:0%
+evaluated in a reference dependent way
+ 
+
+ align:start position:0%
+evaluated in a reference dependent way
+or how do we think about this
+
+ align:start position:0%
+or how do we think about this
+ 
+
+ align:start position:0%
+or how do we think about this
+yeah i have a question yeah um how did
+
+ align:start position:0%
+yeah i have a question yeah um how did
+ 
+
+ align:start position:0%
+yeah i have a question yeah um how did
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+rule out the possibility that like maybe
+
+ align:start position:0%
+rule out the possibility that like maybe
+ 
+
+ align:start position:0%
+rule out the possibility that like maybe
+there's like um
+
+ align:start position:0%
+there's like um
+ 
+
+ align:start position:0%
+there's like um
+reverse causality maybe i'll say where
+
+ align:start position:0%
+reverse causality maybe i'll say where
+ 
+
+ align:start position:0%
+reverse causality maybe i'll say where
+none of the cab drivers want to work
+
+ align:start position:0%
+none of the cab drivers want to work
+ 
+
+ align:start position:0%
+none of the cab drivers want to work
+that much because of supply and demand
+
+ align:start position:0%
+that much because of supply and demand
+ 
+
+ align:start position:0%
+that much because of supply and demand
+but they just go up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so that's to say like effort costs
+
+ align:start position:0%
+so so that's to say like effort costs
+ 
+
+ align:start position:0%
+so so that's to say like effort costs
+are high
+
+ align:start position:0%
+are high
+ 
+
+ align:start position:0%
+are high
+so usually it's to do with like other
+
+ align:start position:0%
+so usually it's to do with like other
+ 
+
+ align:start position:0%
+so usually it's to do with like other
+drivers so let me let me actually get
+
+ align:start position:0%
+drivers so let me let me actually get
+ 
+
+ align:start position:0%
+drivers so let me let me actually get
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+so let me defer this for one second i
+
+ align:start position:0%
+so let me defer this for one second i
+ 
+
+ align:start position:0%
+so let me defer this for one second i
+have like a slide on like confounds
+
+ align:start position:0%
+have like a slide on like confounds
+ 
+
+ align:start position:0%
+have like a slide on like confounds
+and then we can see whether it addresses
+
+ align:start position:0%
+and then we can see whether it addresses
+ 
+
+ align:start position:0%
+and then we can see whether it addresses
+your question and then get get back to
+
+ align:start position:0%
+your question and then get get back to
+ 
+
+ align:start position:0%
+your question and then get get back to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+but that's a good question so
+
+ align:start position:0%
+but that's a good question so
+ 
+
+ align:start position:0%
+but that's a good question so
+uh what is being evaluated in reference
+
+ align:start position:0%
+uh what is being evaluated in reference
+ 
+
+ align:start position:0%
+uh what is being evaluated in reference
+dependent way here what are people
+
+ align:start position:0%
+dependent way here what are people
+ 
+
+ align:start position:0%
+dependent way here what are people
+looking at in terms of
+
+ align:start position:0%
+looking at in terms of
+ 
+
+ align:start position:0%
+looking at in terms of
+where is the reference point in the
+
+ align:start position:0%
+where is the reference point in the
+ 
+
+ align:start position:0%
+where is the reference point in the
+evaluation here
+
+ align:start position:0%
+evaluation here
+ 
+
+ align:start position:0%
+evaluation here
+yes um i guess if you're a cab driver
+
+ align:start position:0%
+yes um i guess if you're a cab driver
+ 
+
+ align:start position:0%
+yes um i guess if you're a cab driver
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+kind of say oh i want to make like this
+
+ align:start position:0%
+kind of say oh i want to make like this
+ 
+
+ align:start position:0%
+kind of say oh i want to make like this
+much money today and then you just kind
+
+ align:start position:0%
+much money today and then you just kind
+ 
+
+ align:start position:0%
+much money today and then you just kind
+of like work until
+
+ align:start position:0%
+of like work until
+ 
+
+ align:start position:0%
+of like work until
+you feel like you've made it up and then
+
+ align:start position:0%
+you feel like you've made it up and then
+ 
+
+ align:start position:0%
+you feel like you've made it up and then
+you just stop right
+
+ align:start position:0%
+you just stop right
+ 
+
+ align:start position:0%
+you just stop right
+exactly you have to pay your fixed fee
+
+ align:start position:0%
+exactly you have to pay your fixed fee
+ 
+
+ align:start position:0%
+exactly you have to pay your fixed fee
+for the day or for the month or whatever
+
+ align:start position:0%
+for the day or for the month or whatever
+ 
+
+ align:start position:0%
+for the day or for the month or whatever
+but like there's an implicit uh
+
+ align:start position:0%
+but like there's an implicit uh
+ 
+
+ align:start position:0%
+but like there's an implicit uh
+fixed fee for the day so you kind of
+
+ align:start position:0%
+fixed fee for the day so you kind of
+ 
+
+ align:start position:0%
+fixed fee for the day so you kind of
+want to make at least that much money to
+
+ align:start position:0%
+want to make at least that much money to
+ 
+
+ align:start position:0%
+want to make at least that much money to
+make not a loss you probably have some
+
+ align:start position:0%
+make not a loss you probably have some
+ 
+
+ align:start position:0%
+make not a loss you probably have some
+positive target in some way and saying
+
+ align:start position:0%
+positive target in some way and saying
+ 
+
+ align:start position:0%
+positive target in some way and saying
+like i want to make uh
+
+ align:start position:0%
+like i want to make uh
+ 
+
+ align:start position:0%
+like i want to make uh
+pay back like my um my fee plus you want
+
+ align:start position:0%
+pay back like my um my fee plus you want
+ 
+
+ align:start position:0%
+pay back like my um my fee plus you want
+to make some money for the day
+
+ align:start position:0%
+to make some money for the day
+ 
+
+ align:start position:0%
+to make some money for the day
+and minus sort of expenses and once you
+
+ align:start position:0%
+and minus sort of expenses and once you
+ 
+
+ align:start position:0%
+and minus sort of expenses and once you
+reach that target
+
+ align:start position:0%
+reach that target
+ 
+
+ align:start position:0%
+reach that target
+you are in the gain domain below that
+
+ align:start position:0%
+you are in the gain domain below that
+ 
+
+ align:start position:0%
+you are in the gain domain below that
+you are in the last domain
+
+ align:start position:0%
+you are in the last domain
+ 
+
+ align:start position:0%
+you are in the last domain
+right and so the daily income
+
+ align:start position:0%
+right and so the daily income
+ 
+
+ align:start position:0%
+right and so the daily income
+essentially and that's essentially sort
+
+ align:start position:0%
+essentially and that's essentially sort
+ 
+
+ align:start position:0%
+essentially and that's essentially sort
+of like
+
+ align:start position:0%
+of like
+ 
+
+ align:start position:0%
+of like
+uh money after paying back the fee but
+
+ align:start position:0%
+uh money after paying back the fee but
+ 
+
+ align:start position:0%
+uh money after paying back the fee but
+you could also get uh it's essentially
+
+ align:start position:0%
+you could also get uh it's essentially
+ 
+
+ align:start position:0%
+you could also get uh it's essentially
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+uh uh what's being evaluated in the
+
+ align:start position:0%
+uh uh what's being evaluated in the
+ 
+
+ align:start position:0%
+uh uh what's being evaluated in the
+reference append network
+
+ align:start position:0%
+reference append network
+ 
+
+ align:start position:0%
+reference append network
+what's the reference point it's some
+
+ align:start position:0%
+what's the reference point it's some
+ 
+
+ align:start position:0%
+what's the reference point it's some
+daily target that you have often it's
+
+ align:start position:0%
+daily target that you have often it's
+ 
+
+ align:start position:0%
+daily target that you have often it's
+like expectation
+
+ align:start position:0%
+like expectation
+ 
+
+ align:start position:0%
+like expectation
+and so on and sort of essentially how
+
+ align:start position:0%
+and so on and sort of essentially how
+ 
+
+ align:start position:0%
+and so on and sort of essentially how
+much you think
+
+ align:start position:0%
+much you think
+ 
+
+ align:start position:0%
+much you think
+you will make and then what's the
+
+ align:start position:0%
+you will make and then what's the
+ 
+
+ align:start position:0%
+you will make and then what's the
+feature of the value of a function that
+
+ align:start position:0%
+feature of the value of a function that
+ 
+
+ align:start position:0%
+feature of the value of a function that
+explains the phenomena well it's loss of
+
+ align:start position:0%
+explains the phenomena well it's loss of
+ 
+
+ align:start position:0%
+explains the phenomena well it's loss of
+version if you're like falling short of
+
+ align:start position:0%
+version if you're like falling short of
+ 
+
+ align:start position:0%
+version if you're like falling short of
+the target
+
+ align:start position:0%
+the target
+ 
+
+ align:start position:0%
+the target
+essentially your marginal utility how
+
+ align:start position:0%
+essentially your marginal utility how
+ 
+
+ align:start position:0%
+essentially your marginal utility how
+much when you drive another hour or
+
+ align:start position:0%
+much when you drive another hour or
+ 
+
+ align:start position:0%
+much when you drive another hour or
+another trip
+
+ align:start position:0%
+another trip
+ 
+
+ align:start position:0%
+another trip
+the marginal utility that you get to see
+
+ align:start position:0%
+the marginal utility that you get to see
+ 
+
+ align:start position:0%
+the marginal utility that you get to see
+it then the value function is very steep
+
+ align:start position:0%
+it then the value function is very steep
+ 
+
+ align:start position:0%
+it then the value function is very steep
+below the target
+
+ align:start position:0%
+below the target
+ 
+
+ align:start position:0%
+below the target
+is very high once you reach the target
+
+ align:start position:0%
+is very high once you reach the target
+ 
+
+ align:start position:0%
+is very high once you reach the target
+it's very flat and then essentially you
+
+ align:start position:0%
+it's very flat and then essentially you
+ 
+
+ align:start position:0%
+it's very flat and then essentially you
+you you tend to stop does that make
+
+ align:start position:0%
+you you tend to stop does that make
+ 
+
+ align:start position:0%
+you you tend to stop does that make
+sense yeah
+
+ align:start position:0%
+sense yeah
+ 
+
+ align:start position:0%
+sense yeah
+okay great so um the main takeaway here
+
+ align:start position:0%
+okay great so um the main takeaway here
+ 
+
+ align:start position:0%
+okay great so um the main takeaway here
+is although if drivers often stop at
+
+ align:start position:0%
+is although if drivers often stop at
+ 
+
+ align:start position:0%
+is although if drivers often stop at
+their daily income target
+
+ align:start position:0%
+their daily income target
+ 
+
+ align:start position:0%
+their daily income target
+um drivers with a higher wage reach
+
+ align:start position:0%
+um drivers with a higher wage reach
+ 
+
+ align:start position:0%
+um drivers with a higher wage reach
+their targets faster and they work few
+
+ align:start position:0%
+their targets faster and they work few
+ 
+
+ align:start position:0%
+their targets faster and they work few
+hours
+
+ align:start position:0%
+hours
+ 
+
+ align:start position:0%
+hours
+again that's like variation uh uh uh
+
+ align:start position:0%
+again that's like variation uh uh uh
+ 
+
+ align:start position:0%
+again that's like variation uh uh uh
+within
+
+ align:start position:0%
+within
+ 
+
+ align:start position:0%
+within
+drivers um across days and so that
+
+ align:start position:0%
+drivers um across days and so that
+ 
+
+ align:start position:0%
+drivers um across days and so that
+there's lots of
+
+ align:start position:0%
+there's lots of
+ 
+
+ align:start position:0%
+there's lots of
+subsequent work and debate regarding
+
+ align:start position:0%
+subsequent work and debate regarding
+ 
+
+ align:start position:0%
+subsequent work and debate regarding
+this finding that the debate is still
+
+ align:start position:0%
+this finding that the debate is still
+ 
+
+ align:start position:0%
+this finding that the debate is still
+ongoing
+
+ align:start position:0%
+ongoing
+ 
+
+ align:start position:0%
+ongoing
+for example one reason paper looks at
+
+ align:start position:0%
+for example one reason paper looks at
+ 
+
+ align:start position:0%
+for example one reason paper looks at
+like tips that people
+
+ align:start position:0%
+like tips that people
+ 
+
+ align:start position:0%
+like tips that people
+uh drivers get unexpectedly so sometimes
+
+ align:start position:0%
+uh drivers get unexpectedly so sometimes
+ 
+
+ align:start position:0%
+uh drivers get unexpectedly so sometimes
+drivers get like large tips sometimes
+
+ align:start position:0%
+drivers get like large tips sometimes
+ 
+
+ align:start position:0%
+drivers get like large tips sometimes
+get small
+
+ align:start position:0%
+get small
+ 
+
+ align:start position:0%
+get small
+tips it depends a lot like when in the
+
+ align:start position:0%
+tips it depends a lot like when in the
+ 
+
+ align:start position:0%
+tips it depends a lot like when in the
+day they receive the tip if they receive
+
+ align:start position:0%
+day they receive the tip if they receive
+ 
+
+ align:start position:0%
+day they receive the tip if they receive
+it really early versus late if they sort
+
+ align:start position:0%
+it really early versus late if they sort
+ 
+
+ align:start position:0%
+it really early versus late if they sort
+of get to their target
+
+ align:start position:0%
+of get to their target
+ 
+
+ align:start position:0%
+of get to their target
+and essentially the target seems to be
+
+ align:start position:0%
+and essentially the target seems to be
+ 
+
+ align:start position:0%
+and essentially the target seems to be
+adjusting over time uh but overall this
+
+ align:start position:0%
+adjusting over time uh but overall this
+ 
+
+ align:start position:0%
+adjusting over time uh but overall this
+is sort of getting a little bit at your
+
+ align:start position:0%
+is sort of getting a little bit at your
+ 
+
+ align:start position:0%
+is sort of getting a little bit at your
+question um
+
+ align:start position:0%
+question um
+ 
+
+ align:start position:0%
+question um
+uh where we think it's not sort of
+
+ align:start position:0%
+uh where we think it's not sort of
+ 
+
+ align:start position:0%
+uh where we think it's not sort of
+aggregate um
+
+ align:start position:0%
+aggregate um
+ 
+
+ align:start position:0%
+aggregate um
+supply but the debate is over are still
+
+ align:start position:0%
+supply but the debate is over are still
+ 
+
+ align:start position:0%
+supply but the debate is over are still
+ongoing but overall we sort of think
+
+ align:start position:0%
+ongoing but overall we sort of think
+ 
+
+ align:start position:0%
+ongoing but overall we sort of think
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+lots of labor supply decisions when
+
+ align:start position:0%
+lots of labor supply decisions when
+ 
+
+ align:start position:0%
+lots of labor supply decisions when
+people have daily decisions of how many
+
+ align:start position:0%
+people have daily decisions of how many
+ 
+
+ align:start position:0%
+people have daily decisions of how many
+hours to work and their
+
+ align:start position:0%
+hours to work and their
+ 
+
+ align:start position:0%
+hours to work and their
+wages vary depend on uh reference points
+
+ align:start position:0%
+wages vary depend on uh reference points
+ 
+
+ align:start position:0%
+wages vary depend on uh reference points
+uh and might sort of potentially be at
+
+ align:start position:0%
+uh and might sort of potentially be at
+ 
+
+ align:start position:0%
+uh and might sort of potentially be at
+least um suboptimal or put differently
+
+ align:start position:0%
+least um suboptimal or put differently
+ 
+
+ align:start position:0%
+least um suboptimal or put differently
+they could people would could work few
+
+ align:start position:0%
+they could people would could work few
+ 
+
+ align:start position:0%
+they could people would could work few
+hours
+
+ align:start position:0%
+hours
+ 
+
+ align:start position:0%
+hours
+um and trying to sort of adjust their
+
+ align:start position:0%
+um and trying to sort of adjust their
+ 
+
+ align:start position:0%
+um and trying to sort of adjust their
+overall amounts you can actually when
+
+ align:start position:0%
+overall amounts you can actually when
+ 
+
+ align:start position:0%
+overall amounts you can actually when
+for a while like this you can ask your
+
+ align:start position:0%
+for a while like this you can ask your
+ 
+
+ align:start position:0%
+for a while like this you can ask your
+uber lyft drivers what they're doing
+
+ align:start position:0%
+uber lyft drivers what they're doing
+ 
+
+ align:start position:0%
+uber lyft drivers what they're doing
+and so on and see whether they're a
+
+ align:start position:0%
+and so on and see whether they're a
+ 
+
+ align:start position:0%
+and so on and see whether they're a
+reference dependent uh a
+
+ align:start position:0%
+reference dependent uh a
+ 
+
+ align:start position:0%
+reference dependent uh a
+driver so they have reference dependent
+
+ align:start position:0%
+driver so they have reference dependent
+ 
+
+ align:start position:0%
+driver so they have reference dependent
+preferences now what are sort of
+
+ align:start position:0%
+preferences now what are sort of
+ 
+
+ align:start position:0%
+preferences now what are sort of
+potential alternative hypotheses one
+
+ align:start position:0%
+potential alternative hypotheses one
+ 
+
+ align:start position:0%
+potential alternative hypotheses one
+question one issue could be like
+
+ align:start position:0%
+question one issue could be like
+ 
+
+ align:start position:0%
+question one issue could be like
+liquidity constraints
+
+ align:start position:0%
+liquidity constraints
+ 
+
+ align:start position:0%
+liquidity constraints
+this is like for example if you just
+
+ align:start position:0%
+this is like for example if you just
+ 
+
+ align:start position:0%
+this is like for example if you just
+don't have enough cash and you have to
+
+ align:start position:0%
+don't have enough cash and you have to
+ 
+
+ align:start position:0%
+don't have enough cash and you have to
+pay back
+
+ align:start position:0%
+pay back
+ 
+
+ align:start position:0%
+pay back
+for uh your fee for the day or for the
+
+ align:start position:0%
+for uh your fee for the day or for the
+ 
+
+ align:start position:0%
+for uh your fee for the day or for the
+next day you might want to not work only
+
+ align:start position:0%
+next day you might want to not work only
+ 
+
+ align:start position:0%
+next day you might want to not work only
+very few hours on a given day
+
+ align:start position:0%
+very few hours on a given day
+ 
+
+ align:start position:0%
+very few hours on a given day
+uh it turns out that drivers who own
+
+ align:start position:0%
+uh it turns out that drivers who own
+ 
+
+ align:start position:0%
+uh it turns out that drivers who own
+their own medallion exhibit the same
+
+ align:start position:0%
+their own medallion exhibit the same
+ 
+
+ align:start position:0%
+their own medallion exhibit the same
+patterns
+
+ align:start position:0%
+patterns
+ 
+
+ align:start position:0%
+patterns
+they could be things like fatigue it's
+
+ align:start position:0%
+they could be things like fatigue it's
+ 
+
+ align:start position:0%
+they could be things like fatigue it's
+let's just say it's really tedious to
+
+ align:start position:0%
+let's just say it's really tedious to
+ 
+
+ align:start position:0%
+let's just say it's really tedious to
+work on certain days
+
+ align:start position:0%
+work on certain days
+ 
+
+ align:start position:0%
+work on certain days
+when wages are high we don't think
+
+ align:start position:0%
+when wages are high we don't think
+ 
+
+ align:start position:0%
+when wages are high we don't think
+that's going on in part because drivers
+
+ align:start position:0%
+that's going on in part because drivers
+ 
+
+ align:start position:0%
+that's going on in part because drivers
+themselves
+
+ align:start position:0%
+themselves
+ 
+
+ align:start position:0%
+themselves
+they say it's actually easier to drive
+
+ align:start position:0%
+they say it's actually easier to drive
+ 
+
+ align:start position:0%
+they say it's actually easier to drive
+with more passengers
+
+ align:start position:0%
+with more passengers
+ 
+
+ align:start position:0%
+with more passengers
+again recent papers in fact can also
+
+ align:start position:0%
+again recent papers in fact can also
+ 
+
+ align:start position:0%
+again recent papers in fact can also
+control for this and so on so we don't
+
+ align:start position:0%
+control for this and so on so we don't
+ 
+
+ align:start position:0%
+control for this and so on so we don't
+think it's actually
+
+ align:start position:0%
+think it's actually
+ 
+
+ align:start position:0%
+think it's actually
+um fatigue and this is i think what
+
+ align:start position:0%
+um fatigue and this is i think what
+ 
+
+ align:start position:0%
+um fatigue and this is i think what
+you're saying uh the last one is
+
+ align:start position:0%
+you're saying uh the last one is
+ 
+
+ align:start position:0%
+you're saying uh the last one is
+unobserved shocks so some shocks that
+
+ align:start position:0%
+unobserved shocks so some shocks that
+ 
+
+ align:start position:0%
+unobserved shocks so some shocks that
+affect all drivers labor supply at the
+
+ align:start position:0%
+affect all drivers labor supply at the
+ 
+
+ align:start position:0%
+affect all drivers labor supply at the
+same time
+
+ align:start position:0%
+same time
+ 
+
+ align:start position:0%
+same time
+example you know there are some days in
+
+ align:start position:0%
+example you know there are some days in
+ 
+
+ align:start position:0%
+example you know there are some days in
+which all drivers get the flu
+
+ align:start position:0%
+which all drivers get the flu
+ 
+
+ align:start position:0%
+which all drivers get the flu
+uh fewer drivers will work and those who
+
+ align:start position:0%
+uh fewer drivers will work and those who
+ 
+
+ align:start position:0%
+uh fewer drivers will work and those who
+will work uh
+
+ align:start position:0%
+will work uh
+ 
+
+ align:start position:0%
+will work uh
+work few hours and those who work get
+
+ align:start position:0%
+work few hours and those who work get
+ 
+
+ align:start position:0%
+work few hours and those who work get
+uh get higher wages
+
+ align:start position:0%
+uh get higher wages
+ 
+
+ align:start position:0%
+uh get higher wages
+we that's a little bit trickier for them
+
+ align:start position:0%
+we that's a little bit trickier for them
+ 
+
+ align:start position:0%
+we that's a little bit trickier for them
+to to
+
+ align:start position:0%
+to to
+ 
+
+ align:start position:0%
+to to
+to to roll out in part there's other
+
+ align:start position:0%
+to to roll out in part there's other
+ 
+
+ align:start position:0%
+to to roll out in part there's other
+papers other studies afterwards that
+
+ align:start position:0%
+papers other studies afterwards that
+ 
+
+ align:start position:0%
+papers other studies afterwards that
+sort of try to
+
+ align:start position:0%
+sort of try to
+ 
+
+ align:start position:0%
+sort of try to
+get at this usually um um
+
+ align:start position:0%
+get at this usually um um
+ 
+
+ align:start position:0%
+get at this usually um um
+yeah for this specific data that's hard
+
+ align:start position:0%
+yeah for this specific data that's hard
+ 
+
+ align:start position:0%
+yeah for this specific data that's hard
+to do i think for the other
+
+ align:start position:0%
+to do i think for the other
+ 
+
+ align:start position:0%
+to do i think for the other
+data where people have essentially not
+
+ align:start position:0%
+data where people have essentially not
+ 
+
+ align:start position:0%
+data where people have essentially not
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+daily so this is essentially trip sheets
+
+ align:start position:0%
+daily so this is essentially trip sheets
+ 
+
+ align:start position:0%
+daily so this is essentially trip sheets
+so they have what they're using mostly
+
+ align:start position:0%
+so they have what they're using mostly
+ 
+
+ align:start position:0%
+so they have what they're using mostly
+is like daily wages overall
+
+ align:start position:0%
+is like daily wages overall
+ 
+
+ align:start position:0%
+is like daily wages overall
+they don't even have the wage they only
+
+ align:start position:0%
+they don't even have the wage they only
+ 
+
+ align:start position:0%
+they don't even have the wage they only
+have the um
+
+ align:start position:0%
+have the um
+ 
+
+ align:start position:0%
+have the um
+the overall um uh earnings and then the
+
+ align:start position:0%
+the overall um uh earnings and then the
+ 
+
+ align:start position:0%
+the overall um uh earnings and then the
+hours and then they sort of impute the
+
+ align:start position:0%
+hours and then they sort of impute the
+ 
+
+ align:start position:0%
+hours and then they sort of impute the
+wage dividing the two which causes some
+
+ align:start position:0%
+wage dividing the two which causes some
+ 
+
+ align:start position:0%
+wage dividing the two which causes some
+other trouble
+
+ align:start position:0%
+other trouble
+ 
+
+ align:start position:0%
+other trouble
+but once you have like uber data once
+
+ align:start position:0%
+but once you have like uber data once
+ 
+
+ align:start position:0%
+but once you have like uber data once
+you have like specific trips in
+
+ align:start position:0%
+you have like specific trips in
+ 
+
+ align:start position:0%
+you have like specific trips in
+particular also tips and so on
+
+ align:start position:0%
+particular also tips and so on
+ 
+
+ align:start position:0%
+particular also tips and so on
+you can look at on a given day uh when i
+
+ align:start position:0%
+you can look at on a given day uh when i
+ 
+
+ align:start position:0%
+you can look at on a given day uh when i
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+like a high tip versus a low tip uh uh
+
+ align:start position:0%
+like a high tip versus a low tip uh uh
+ 
+
+ align:start position:0%
+like a high tip versus a low tip uh uh
+how do
+
+ align:start position:0%
+how do
+ 
+
+ align:start position:0%
+how do
+you can you can look at like you can
+
+ align:start position:0%
+you can you can look at like you can
+ 
+
+ align:start position:0%
+you can you can look at like you can
+predict essentially how much i'm gonna
+
+ align:start position:0%
+predict essentially how much i'm gonna
+ 
+
+ align:start position:0%
+predict essentially how much i'm gonna
+earn on a given day
+
+ align:start position:0%
+earn on a given day
+ 
+
+ align:start position:0%
+earn on a given day
+so suppose you you predict that i'm
+
+ align:start position:0%
+so suppose you you predict that i'm
+ 
+
+ align:start position:0%
+so suppose you you predict that i'm
+gonna uh earn hundred dollars in a given
+
+ align:start position:0%
+gonna uh earn hundred dollars in a given
+ 
+
+ align:start position:0%
+gonna uh earn hundred dollars in a given
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+now i have like say fifty sixty dollars
+
+ align:start position:0%
+now i have like say fifty sixty dollars
+ 
+
+ align:start position:0%
+now i have like say fifty sixty dollars
+now i get like a large trip and like a
+
+ align:start position:0%
+now i get like a large trip and like a
+ 
+
+ align:start position:0%
+now i get like a large trip and like a
+tip and so on that gets me over that
+
+ align:start position:0%
+tip and so on that gets me over that
+ 
+
+ align:start position:0%
+tip and so on that gets me over that
+threshold you can look at where their
+
+ align:start position:0%
+threshold you can look at where their
+ 
+
+ align:start position:0%
+threshold you can look at where their
+stop
+
+ align:start position:0%
+stop
+ 
+
+ align:start position:0%
+stop
+you can look at the exact same thing
+
+ align:start position:0%
+you can look at the exact same thing
+ 
+
+ align:start position:0%
+you can look at the exact same thing
+when i have like only twenty dollars and
+
+ align:start position:0%
+when i have like only twenty dollars and
+ 
+
+ align:start position:0%
+when i have like only twenty dollars and
+they get a large ship to a stop and so
+
+ align:start position:0%
+they get a large ship to a stop and so
+ 
+
+ align:start position:0%
+they get a large ship to a stop and so
+on so you can essentially control for
+
+ align:start position:0%
+on so you can essentially control for
+ 
+
+ align:start position:0%
+on so you can essentially control for
+all of that
+
+ align:start position:0%
+all of that
+ 
+
+ align:start position:0%
+all of that
+and then do within a driver comparisons
+
+ align:start position:0%
+and then do within a driver comparisons
+ 
+
+ align:start position:0%
+and then do within a driver comparisons
+like for trips
+
+ align:start position:0%
+like for trips
+ 
+
+ align:start position:0%
+like for trips
+uh that happen to be large or small that
+
+ align:start position:0%
+uh that happen to be large or small that
+ 
+
+ align:start position:0%
+uh that happen to be large or small that
+you happen to get in a given hour and
+
+ align:start position:0%
+you happen to get in a given hour and
+ 
+
+ align:start position:0%
+you happen to get in a given hour and
+then you can sort of deal with like
+
+ align:start position:0%
+then you can sort of deal with like
+ 
+
+ align:start position:0%
+then you can sort of deal with like
+overall market conditions
+
+ align:start position:0%
+overall market conditions
+ 
+
+ align:start position:0%
+overall market conditions
+i think even better in the future there
+
+ align:start position:0%
+i think even better in the future there
+ 
+
+ align:start position:0%
+i think even better in the future there
+will be sort of like experiments and so
+
+ align:start position:0%
+will be sort of like experiments and so
+ 
+
+ align:start position:0%
+will be sort of like experiments and so
+on where you can look at
+
+ align:start position:0%
+on where you can look at
+ 
+
+ align:start position:0%
+on where you can look at
+when uber and lyft try to incentivize
+
+ align:start position:0%
+when uber and lyft try to incentivize
+ 
+
+ align:start position:0%
+when uber and lyft try to incentivize
+their workers and so just say
+
+ align:start position:0%
+their workers and so just say
+ 
+
+ align:start position:0%
+their workers and so just say
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+sometimes pay people more and unless
+
+ align:start position:0%
+sometimes pay people more and unless
+ 
+
+ align:start position:0%
+sometimes pay people more and unless
+randomly sort of explicitly randomly
+
+ align:start position:0%
+randomly sort of explicitly randomly
+ 
+
+ align:start position:0%
+randomly sort of explicitly randomly
+because they want to kind of learn about
+
+ align:start position:0%
+because they want to kind of learn about
+ 
+
+ align:start position:0%
+because they want to kind of learn about
+how to best incentivize the drivers and
+
+ align:start position:0%
+how to best incentivize the drivers and
+ 
+
+ align:start position:0%
+how to best incentivize the drivers and
+then you can control for everything
+
+ align:start position:0%
+then you can control for everything
+ 
+
+ align:start position:0%
+then you can control for everything
+because it's like explicitly random
+
+ align:start position:0%
+because it's like explicitly random
+ 
+
+ align:start position:0%
+because it's like explicitly random
+whether a certain driver gets like
+
+ align:start position:0%
+whether a certain driver gets like
+ 
+
+ align:start position:0%
+whether a certain driver gets like
+high versus low uh uh wages or sort of
+
+ align:start position:0%
+high versus low uh uh wages or sort of
+ 
+
+ align:start position:0%
+high versus low uh uh wages or sort of
+trip fares yeah okay
+
+ align:start position:0%
+trip fares yeah okay
+ 
+
+ align:start position:0%
+trip fares yeah okay
+um are any questions on the um
+
+ align:start position:0%
+um are any questions on the um
+ 
+
+ align:start position:0%
+um are any questions on the um
+on the uh labor supply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um i'm a bit confused about the
+
+ align:start position:0%
+yes um i'm a bit confused about the
+ 
+
+ align:start position:0%
+yes um i'm a bit confused about the
+unobserved shocks
+
+ align:start position:0%
+unobserved shocks
+ 
+
+ align:start position:0%
+unobserved shocks
+because like if you get like a really
+
+ align:start position:0%
+because like if you get like a really
+ 
+
+ align:start position:0%
+because like if you get like a really
+large tip that doesn't necessarily like
+
+ align:start position:0%
+large tip that doesn't necessarily like
+ 
+
+ align:start position:0%
+large tip that doesn't necessarily like
+predict that the rest of the day you
+
+ align:start position:0%
+predict that the rest of the day you
+ 
+
+ align:start position:0%
+predict that the rest of the day you
+have higher wages if you kept working
+
+ align:start position:0%
+have higher wages if you kept working
+ 
+
+ align:start position:0%
+have higher wages if you kept working
+okay like you just get this really high
+
+ align:start position:0%
+okay like you just get this really high
+ 
+
+ align:start position:0%
+okay like you just get this really high
+tip and then you might be like oh
+
+ align:start position:0%
+tip and then you might be like oh
+ 
+
+ align:start position:0%
+tip and then you might be like oh
+today's a lucky day i can stop early
+
+ align:start position:0%
+today's a lucky day i can stop early
+ 
+
+ align:start position:0%
+today's a lucky day i can stop early
+but if i had worked more this day i
+
+ align:start position:0%
+but if i had worked more this day i
+ 
+
+ align:start position:0%
+but if i had worked more this day i
+wouldn't necessarily be making
+
+ align:start position:0%
+wouldn't necessarily be making
+ 
+
+ align:start position:0%
+wouldn't necessarily be making
+continuously more
+
+ align:start position:0%
+continuously more
+ 
+
+ align:start position:0%
+continuously more
+than normal right so in the unobserved
+
+ align:start position:0%
+than normal right so in the unobserved
+ 
+
+ align:start position:0%
+than normal right so in the unobserved
+in the large tip
+
+ align:start position:0%
+in the large tip
+ 
+
+ align:start position:0%
+in the large tip
+example the assumption is exactly or
+
+ align:start position:0%
+example the assumption is exactly or
+ 
+
+ align:start position:0%
+example the assumption is exactly or
+what they show in the paper this is
+
+ align:start position:0%
+what they show in the paper this is
+ 
+
+ align:start position:0%
+what they show in the paper this is
+subsequent work not this specific work
+
+ align:start position:0%
+subsequent work not this specific work
+ 
+
+ align:start position:0%
+subsequent work not this specific work
+what they exactly show in this type of
+
+ align:start position:0%
+what they exactly show in this type of
+ 
+
+ align:start position:0%
+what they exactly show in this type of
+paper these are sort of random events in
+
+ align:start position:0%
+paper these are sort of random events in
+ 
+
+ align:start position:0%
+paper these are sort of random events in
+a sense it's
+
+ align:start position:0%
+a sense it's
+ 
+
+ align:start position:0%
+a sense it's
+really precisely not predictive of your
+
+ align:start position:0%
+really precisely not predictive of your
+ 
+
+ align:start position:0%
+really precisely not predictive of your
+future uh
+
+ align:start position:0%
+future uh
+ 
+
+ align:start position:0%
+future uh
+uh earnings it's random now one
+
+ align:start position:0%
+uh earnings it's random now one
+ 
+
+ align:start position:0%
+uh earnings it's random now one
+interpretation that you have is to say
+
+ align:start position:0%
+interpretation that you have is to say
+ 
+
+ align:start position:0%
+interpretation that you have is to say
+well it could be that you kind of have
+
+ align:start position:0%
+well it could be that you kind of have
+ 
+
+ align:start position:0%
+well it could be that you kind of have
+some expectations about your future
+
+ align:start position:0%
+some expectations about your future
+ 
+
+ align:start position:0%
+some expectations about your future
+earnings
+
+ align:start position:0%
+earnings
+ 
+
+ align:start position:0%
+earnings
+that could be particularly high or low
+
+ align:start position:0%
+that could be particularly high or low
+ 
+
+ align:start position:0%
+that could be particularly high or low
+it's like i got my lucky day
+
+ align:start position:0%
+it's like i got my lucky day
+ 
+
+ align:start position:0%
+it's like i got my lucky day
+and so on and so forth that is hard to
+
+ align:start position:0%
+and so on and so forth that is hard to
+ 
+
+ align:start position:0%
+and so on and so forth that is hard to
+rule out and sometimes if you had
+
+ align:start position:0%
+rule out and sometimes if you had
+ 
+
+ align:start position:0%
+rule out and sometimes if you had
+rational expectations uh that's hard to
+
+ align:start position:0%
+rational expectations uh that's hard to
+ 
+
+ align:start position:0%
+rational expectations uh that's hard to
+explain for the neoclassical model
+
+ align:start position:0%
+explain for the neoclassical model
+ 
+
+ align:start position:0%
+explain for the neoclassical model
+what's harder to rule out is to say
+
+ align:start position:0%
+what's harder to rule out is to say
+ 
+
+ align:start position:0%
+what's harder to rule out is to say
+you know i now think like i got my lucky
+
+ align:start position:0%
+you know i now think like i got my lucky
+ 
+
+ align:start position:0%
+you know i now think like i got my lucky
+draw for the day and that's it and i'm
+
+ align:start position:0%
+draw for the day and that's it and i'm
+ 
+
+ align:start position:0%
+draw for the day and that's it and i'm
+not gonna
+
+ align:start position:0%
+not gonna
+ 
+
+ align:start position:0%
+not gonna
+uh i get any lucky draw again let's just
+
+ align:start position:0%
+uh i get any lucky draw again let's just
+ 
+
+ align:start position:0%
+uh i get any lucky draw again let's just
+call it a day
+
+ align:start position:0%
+call it a day
+ 
+
+ align:start position:0%
+call it a day
+that is hard to rule out but what is um
+
+ align:start position:0%
+that is hard to rule out but what is um
+ 
+
+ align:start position:0%
+that is hard to rule out but what is um
+hard to explain for the neoclassical uh
+
+ align:start position:0%
+hard to explain for the neoclassical uh
+ 
+
+ align:start position:0%
+hard to explain for the neoclassical uh
+model i think we can sort of reject is
+
+ align:start position:0%
+model i think we can sort of reject is
+ 
+
+ align:start position:0%
+model i think we can sort of reject is
+to say
+
+ align:start position:0%
+to say
+ 
+
+ align:start position:0%
+to say
+if you just think this is a shock which
+
+ align:start position:0%
+if you just think this is a shock which
+ 
+
+ align:start position:0%
+if you just think this is a shock which
+really in reality it is and you just
+
+ align:start position:0%
+really in reality it is and you just
+ 
+
+ align:start position:0%
+really in reality it is and you just
+happen to get a bunch of money on given
+
+ align:start position:0%
+happen to get a bunch of money on given
+ 
+
+ align:start position:0%
+happen to get a bunch of money on given
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+uh just randomly uh that is
+
+ align:start position:0%
+uh just randomly uh that is
+ 
+
+ align:start position:0%
+uh just randomly uh that is
+then the reference dependent model can
+
+ align:start position:0%
+then the reference dependent model can
+ 
+
+ align:start position:0%
+then the reference dependent model can
+sort of explain why you stop early
+
+ align:start position:0%
+sort of explain why you stop early
+ 
+
+ align:start position:0%
+sort of explain why you stop early
+because you it just puts you
+
+ align:start position:0%
+because you it just puts you
+ 
+
+ align:start position:0%
+because you it just puts you
+tips gets you over the reference point
+
+ align:start position:0%
+tips gets you over the reference point
+ 
+
+ align:start position:0%
+tips gets you over the reference point
+the neoclassical model should just say
+
+ align:start position:0%
+the neoclassical model should just say
+ 
+
+ align:start position:0%
+the neoclassical model should just say
+depends on like essentially how many
+
+ align:start position:0%
+depends on like essentially how many
+ 
+
+ align:start position:0%
+depends on like essentially how many
+hours you want to work on a given day
+
+ align:start position:0%
+hours you want to work on a given day
+ 
+
+ align:start position:0%
+hours you want to work on a given day
+it's nothing to do with a target because
+
+ align:start position:0%
+it's nothing to do with a target because
+ 
+
+ align:start position:0%
+it's nothing to do with a target because
+essentially again it doesn't matter
+
+ align:start position:0%
+essentially again it doesn't matter
+ 
+
+ align:start position:0%
+essentially again it doesn't matter
+whether you make money on monday or
+
+ align:start position:0%
+whether you make money on monday or
+ 
+
+ align:start position:0%
+whether you make money on monday or
+tuesday or wednesday you should just
+
+ align:start position:0%
+tuesday or wednesday you should just
+ 
+
+ align:start position:0%
+tuesday or wednesday you should just
+care about like your overall amount of
+
+ align:start position:0%
+care about like your overall amount of
+ 
+
+ align:start position:0%
+care about like your overall amount of
+money that you make
+
+ align:start position:0%
+money that you make
+ 
+
+ align:start position:0%
+money that you make
+overall but that's a good question
+
+ align:start position:0%
+overall but that's a good question
+ 
+
+ align:start position:0%
+overall but that's a good question
+okay so now um a second paper is on the
+
+ align:start position:0%
+okay so now um a second paper is on the
+ 
+
+ align:start position:0%
+okay so now um a second paper is on the
+housing market
+
+ align:start position:0%
+housing market
+ 
+
+ align:start position:0%
+housing market
+so what is the natural reference point
+
+ align:start position:0%
+so what is the natural reference point
+ 
+
+ align:start position:0%
+so what is the natural reference point
+for housing
+
+ align:start position:0%
+for housing
+ 
+
+ align:start position:0%
+for housing
+markets or like how do we think about
+
+ align:start position:0%
+markets or like how do we think about
+ 
+
+ align:start position:0%
+markets or like how do we think about
+housing prices or how do you think about
+
+ align:start position:0%
+housing prices or how do you think about
+ 
+
+ align:start position:0%
+housing prices or how do you think about
+i guess
+
+ align:start position:0%
+i guess
+ 
+
+ align:start position:0%
+i guess
+a few of you will own a house but how
+
+ align:start position:0%
+a few of you will own a house but how
+ 
+
+ align:start position:0%
+a few of you will own a house but how
+would you think about if you if you
+
+ align:start position:0%
+would you think about if you if you
+ 
+
+ align:start position:0%
+would you think about if you if you
+owned a house
+
+ align:start position:0%
+owned a house
+ 
+
+ align:start position:0%
+owned a house
+how do you think about uh selling a
+
+ align:start position:0%
+how do you think about uh selling a
+ 
+
+ align:start position:0%
+how do you think about uh selling a
+house what is a natural reference point
+
+ align:start position:0%
+house what is a natural reference point
+ 
+
+ align:start position:0%
+house what is a natural reference point
+yes uh whatever it was for or like how
+
+ align:start position:0%
+yes uh whatever it was for or like how
+ 
+
+ align:start position:0%
+yes uh whatever it was for or like how
+it changes
+
+ align:start position:0%
+it changes
+ 
+
+ align:start position:0%
+it changes
+yeah so exactly so uh the previous
+
+ align:start position:0%
+yeah so exactly so uh the previous
+ 
+
+ align:start position:0%
+yeah so exactly so uh the previous
+purchase price it turns out it's a very
+
+ align:start position:0%
+purchase price it turns out it's a very
+ 
+
+ align:start position:0%
+purchase price it turns out it's a very
+very salient thing for owners people
+
+ align:start position:0%
+very salient thing for owners people
+ 
+
+ align:start position:0%
+very salient thing for owners people
+really know how much they paid for their
+
+ align:start position:0%
+really know how much they paid for their
+ 
+
+ align:start position:0%
+really know how much they paid for their
+house
+
+ align:start position:0%
+house
+ 
+
+ align:start position:0%
+house
+it's like a huge expense in their life
+
+ align:start position:0%
+it's like a huge expense in their life
+ 
+
+ align:start position:0%
+it's like a huge expense in their life
+they really remember it was like three
+
+ align:start position:0%
+they really remember it was like three
+ 
+
+ align:start position:0%
+they really remember it was like three
+hundred thousand five hundred thousand a
+
+ align:start position:0%
+hundred thousand five hundred thousand a
+ 
+
+ align:start position:0%
+hundred thousand five hundred thousand a
+million et cetera they know exactly how
+
+ align:start position:0%
+million et cetera they know exactly how
+ 
+
+ align:start position:0%
+million et cetera they know exactly how
+much they paid
+
+ align:start position:0%
+much they paid
+ 
+
+ align:start position:0%
+much they paid
+and that even asked people people know
+
+ align:start position:0%
+and that even asked people people know
+ 
+
+ align:start position:0%
+and that even asked people people know
+exactly how much they uh the majority of
+
+ align:start position:0%
+exactly how much they uh the majority of
+ 
+
+ align:start position:0%
+exactly how much they uh the majority of
+people know exactly how much they paid
+
+ align:start position:0%
+people know exactly how much they paid
+ 
+
+ align:start position:0%
+people know exactly how much they paid
+for their um home
+
+ align:start position:0%
+for their um home
+ 
+
+ align:start position:0%
+for their um home
+now one claim is that loss of version
+
+ align:start position:0%
+now one claim is that loss of version
+ 
+
+ align:start position:0%
+now one claim is that loss of version
+makes people unwilling to sell
+
+ align:start position:0%
+makes people unwilling to sell
+ 
+
+ align:start position:0%
+makes people unwilling to sell
+their houses at a loss and so what they
+
+ align:start position:0%
+their houses at a loss and so what they
+ 
+
+ align:start position:0%
+their houses at a loss and so what they
+would then do is they ask essentially
+
+ align:start position:0%
+would then do is they ask essentially
+ 
+
+ align:start position:0%
+would then do is they ask essentially
+for higher prices if a loss relative to
+
+ align:start position:0%
+for higher prices if a loss relative to
+ 
+
+ align:start position:0%
+for higher prices if a loss relative to
+like their their purchase price and
+
+ align:start position:0%
+like their their purchase price and
+ 
+
+ align:start position:0%
+like their their purchase price and
+let me just show you um exactly what i
+
+ align:start position:0%
+let me just show you um exactly what i
+ 
+
+ align:start position:0%
+let me just show you um exactly what i
+mean by that
+
+ align:start position:0%
+mean by that
+ 
+
+ align:start position:0%
+mean by that
+uh gina risa and meier have um boston
+
+ align:start position:0%
+uh gina risa and meier have um boston
+ 
+
+ align:start position:0%
+uh gina risa and meier have um boston
+condominium data from 1990 to 1997.
+
+ align:start position:0%
+condominium data from 1990 to 1997.
+ 
+
+ align:start position:0%
+condominium data from 1990 to 1997.
+um luckily for them there's lots of
+
+ align:start position:0%
+um luckily for them there's lots of
+ 
+
+ align:start position:0%
+um luckily for them there's lots of
+variation or fluctuations in the housing
+
+ align:start position:0%
+variation or fluctuations in the housing
+ 
+
+ align:start position:0%
+variation or fluctuations in the housing
+market during that time so the housing
+
+ align:start position:0%
+market during that time so the housing
+ 
+
+ align:start position:0%
+market during that time so the housing
+market went up a lot and then it went
+
+ align:start position:0%
+market went up a lot and then it went
+ 
+
+ align:start position:0%
+market went up a lot and then it went
+down a lot and went up a lot
+
+ align:start position:0%
+down a lot and went up a lot
+ 
+
+ align:start position:0%
+down a lot and went up a lot
+now suppose you have two sellers a and b
+
+ align:start position:0%
+now suppose you have two sellers a and b
+ 
+
+ align:start position:0%
+now suppose you have two sellers a and b
+who both want to sell their house or
+
+ align:start position:0%
+who both want to sell their house or
+ 
+
+ align:start position:0%
+who both want to sell their house or
+their home in 1994.
+
+ align:start position:0%
+their home in 1994.
+ 
+
+ align:start position:0%
+their home in 1994.
+now what we can do is we can look at
+
+ align:start position:0%
+now what we can do is we can look at
+ 
+
+ align:start position:0%
+now what we can do is we can look at
+these two people who suppose they have
+
+ align:start position:0%
+these two people who suppose they have
+ 
+
+ align:start position:0%
+these two people who suppose they have
+very similar houses
+
+ align:start position:0%
+very similar houses
+ 
+
+ align:start position:0%
+very similar houses
+based on observable characteristics and
+
+ align:start position:0%
+based on observable characteristics and
+ 
+
+ align:start position:0%
+based on observable characteristics and
+location and so on and so forth
+
+ align:start position:0%
+location and so on and so forth
+ 
+
+ align:start position:0%
+location and so on and so forth
+so once they have really comparable
+
+ align:start position:0%
+so once they have really comparable
+ 
+
+ align:start position:0%
+so once they have really comparable
+houses we can now look at
+
+ align:start position:0%
+houses we can now look at
+ 
+
+ align:start position:0%
+houses we can now look at
+people who seller a purchased their
+
+ align:start position:0%
+people who seller a purchased their
+ 
+
+ align:start position:0%
+people who seller a purchased their
+home really early on in 1989 that person
+
+ align:start position:0%
+home really early on in 1989 that person
+ 
+
+ align:start position:0%
+home really early on in 1989 that person
+happens to be quite unlucky because they
+
+ align:start position:0%
+happens to be quite unlucky because they
+ 
+
+ align:start position:0%
+happens to be quite unlucky because they
+just bought the house really at the peak
+
+ align:start position:0%
+just bought the house really at the peak
+ 
+
+ align:start position:0%
+just bought the house really at the peak
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+uh i guess the housing boom at the time
+
+ align:start position:0%
+uh i guess the housing boom at the time
+ 
+
+ align:start position:0%
+uh i guess the housing boom at the time
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+seller number b who purchased in 1991 uh
+
+ align:start position:0%
+seller number b who purchased in 1991 uh
+ 
+
+ align:start position:0%
+seller number b who purchased in 1991 uh
+uh that that person was relatively lucky
+
+ align:start position:0%
+uh that that person was relatively lucky
+ 
+
+ align:start position:0%
+uh that that person was relatively lucky
+the bot essentially had a price where
+
+ align:start position:0%
+the bot essentially had a price where
+ 
+
+ align:start position:0%
+the bot essentially had a price where
+at a time where the housing market was
+
+ align:start position:0%
+at a time where the housing market was
+ 
+
+ align:start position:0%
+at a time where the housing market was
+relatively low and uh
+
+ align:start position:0%
+relatively low and uh
+ 
+
+ align:start position:0%
+relatively low and uh
+appreciated quite a bit so now we can
+
+ align:start position:0%
+appreciated quite a bit so now we can
+ 
+
+ align:start position:0%
+appreciated quite a bit so now we can
+look at these two people
+
+ align:start position:0%
+look at these two people
+ 
+
+ align:start position:0%
+look at these two people
+and ask the question uh is seller a or
+
+ align:start position:0%
+and ask the question uh is seller a or
+ 
+
+ align:start position:0%
+and ask the question uh is seller a or
+seller b
+
+ align:start position:0%
+seller b
+ 
+
+ align:start position:0%
+seller b
+more likely to sell their house and and
+
+ align:start position:0%
+more likely to sell their house and and
+ 
+
+ align:start position:0%
+more likely to sell their house and and
+the hypothesis is that
+
+ align:start position:0%
+the hypothesis is that
+ 
+
+ align:start position:0%
+the hypothesis is that
+seller a will sort of view this as like
+
+ align:start position:0%
+seller a will sort of view this as like
+ 
+
+ align:start position:0%
+seller a will sort of view this as like
+a loss this seller will essentially just
+
+ align:start position:0%
+a loss this seller will essentially just
+ 
+
+ align:start position:0%
+a loss this seller will essentially just
+say i'm losing money here
+
+ align:start position:0%
+say i'm losing money here
+ 
+
+ align:start position:0%
+say i'm losing money here
+i don't want to sell and that seller
+
+ align:start position:0%
+i don't want to sell and that seller
+ 
+
+ align:start position:0%
+i don't want to sell and that seller
+might essentially ask for like a higher
+
+ align:start position:0%
+might essentially ask for like a higher
+ 
+
+ align:start position:0%
+might essentially ask for like a higher
+listing price and wants to like more
+
+ align:start position:0%
+listing price and wants to like more
+ 
+
+ align:start position:0%
+listing price and wants to like more
+money for this house because they don't
+
+ align:start position:0%
+money for this house because they don't
+ 
+
+ align:start position:0%
+money for this house because they don't
+want to make a
+
+ align:start position:0%
+want to make a
+ 
+
+ align:start position:0%
+want to make a
+a loss on that uh sale well seller b
+
+ align:start position:0%
+a loss on that uh sale well seller b
+ 
+
+ align:start position:0%
+a loss on that uh sale well seller b
+says i'm actually gaining money anyway
+
+ align:start position:0%
+says i'm actually gaining money anyway
+ 
+
+ align:start position:0%
+says i'm actually gaining money anyway
+so let's just sort of like uh
+
+ align:start position:0%
+so let's just sort of like uh
+ 
+
+ align:start position:0%
+so let's just sort of like uh
+post whatever you think is actually the
+
+ align:start position:0%
+post whatever you think is actually the
+ 
+
+ align:start position:0%
+post whatever you think is actually the
+expected market price might be happy to
+
+ align:start position:0%
+expected market price might be happy to
+ 
+
+ align:start position:0%
+expected market price might be happy to
+to sell at a lower price
+
+ align:start position:0%
+to sell at a lower price
+ 
+
+ align:start position:0%
+to sell at a lower price
+compared to seller a okay so one thing
+
+ align:start position:0%
+compared to seller a okay so one thing
+ 
+
+ align:start position:0%
+compared to seller a okay so one thing
+we can look at essentially are listing
+
+ align:start position:0%
+we can look at essentially are listing
+ 
+
+ align:start position:0%
+we can look at essentially are listing
+prices how much do people want for the
+
+ align:start position:0%
+prices how much do people want for the
+ 
+
+ align:start position:0%
+prices how much do people want for the
+houses
+
+ align:start position:0%
+houses
+ 
+
+ align:start position:0%
+houses
+effect second thing we can look at is
+
+ align:start position:0%
+effect second thing we can look at is
+ 
+
+ align:start position:0%
+effect second thing we can look at is
+like actual sales prices
+
+ align:start position:0%
+like actual sales prices
+ 
+
+ align:start position:0%
+like actual sales prices
+you know are you now like selling this
+
+ align:start position:0%
+you know are you now like selling this
+ 
+
+ align:start position:0%
+you know are you now like selling this
+at a higher lower price and number three
+
+ align:start position:0%
+at a higher lower price and number three
+ 
+
+ align:start position:0%
+at a higher lower price and number three
+we can look at like how long is the
+
+ align:start position:0%
+we can look at like how long is the
+ 
+
+ align:start position:0%
+we can look at like how long is the
+house on the market
+
+ align:start position:0%
+house on the market
+ 
+
+ align:start position:0%
+house on the market
+how long does it actually take to sell
+
+ align:start position:0%
+how long does it actually take to sell
+ 
+
+ align:start position:0%
+how long does it actually take to sell
+it that's a quite costly thing to do to
+
+ align:start position:0%
+it that's a quite costly thing to do to
+ 
+
+ align:start position:0%
+it that's a quite costly thing to do to
+have your house on the market for quite
+
+ align:start position:0%
+have your house on the market for quite
+ 
+
+ align:start position:0%
+have your house on the market for quite
+a while because essentially
+
+ align:start position:0%
+a while because essentially
+ 
+
+ align:start position:0%
+a while because essentially
+often people then don't already move
+
+ align:start position:0%
+often people then don't already move
+ 
+
+ align:start position:0%
+often people then don't already move
+somewhere else or they don't kind of
+
+ align:start position:0%
+somewhere else or they don't kind of
+ 
+
+ align:start position:0%
+somewhere else or they don't kind of
+live in the house because they have to
+
+ align:start position:0%
+live in the house because they have to
+ 
+
+ align:start position:0%
+live in the house because they have to
+sort of show it and make it available
+
+ align:start position:0%
+sort of show it and make it available
+ 
+
+ align:start position:0%
+sort of show it and make it available
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+showings and so on so it's a costly
+
+ align:start position:0%
+showings and so on so it's a costly
+ 
+
+ align:start position:0%
+showings and so on so it's a costly
+thing to do you really
+
+ align:start position:0%
+thing to do you really
+ 
+
+ align:start position:0%
+thing to do you really
+don't want to you have your house on the
+
+ align:start position:0%
+don't want to you have your house on the
+ 
+
+ align:start position:0%
+don't want to you have your house on the
+market for like several months
+
+ align:start position:0%
+market for like several months
+ 
+
+ align:start position:0%
+market for like several months
+but it's sort of the broad idea claire
+
+ align:start position:0%
+but it's sort of the broad idea claire
+ 
+
+ align:start position:0%
+but it's sort of the broad idea claire
+what we're trying to do
+
+ align:start position:0%
+what we're trying to do
+ 
+
+ align:start position:0%
+what we're trying to do
+okay so what predictions um
+
+ align:start position:0%
+okay so what predictions um
+ 
+
+ align:start position:0%
+okay so what predictions um
+do you want to test but you want to test
+
+ align:start position:0%
+do you want to test but you want to test
+ 
+
+ align:start position:0%
+do you want to test but you want to test
+whether house owners are reluctant to
+
+ align:start position:0%
+whether house owners are reluctant to
+ 
+
+ align:start position:0%
+whether house owners are reluctant to
+sell their house when the current market
+
+ align:start position:0%
+sell their house when the current market
+ 
+
+ align:start position:0%
+sell their house when the current market
+price is below
+
+ align:start position:0%
+price is below
+ 
+
+ align:start position:0%
+price is below
+the purchase price so the ideal
+
+ align:start position:0%
+the purchase price so the ideal
+ 
+
+ align:start position:0%
+the purchase price so the ideal
+specification is essentially the
+
+ align:start position:0%
+specification is essentially the
+ 
+
+ align:start position:0%
+specification is essentially the
+following we look at the list price on
+
+ align:start position:0%
+following we look at the list price on
+ 
+
+ align:start position:0%
+following we look at the list price on
+the left-hand side
+
+ align:start position:0%
+the left-hand side
+ 
+
+ align:start position:0%
+the left-hand side
+and then we are going to run a
+
+ align:start position:0%
+and then we are going to run a
+ 
+
+ align:start position:0%
+and then we are going to run a
+regression that looks at some constant
+
+ align:start position:0%
+regression that looks at some constant
+ 
+
+ align:start position:0%
+regression that looks at some constant
+that's just kind of like time trends et
+
+ align:start position:0%
+that's just kind of like time trends et
+ 
+
+ align:start position:0%
+that's just kind of like time trends et
+cetera
+
+ align:start position:0%
+cetera
+ 
+
+ align:start position:0%
+cetera
+plus a beta which is the coefficient of
+
+ align:start position:0%
+plus a beta which is the coefficient of
+ 
+
+ align:start position:0%
+plus a beta which is the coefficient of
+interest or one coefficient
+
+ align:start position:0%
+interest or one coefficient
+ 
+
+ align:start position:0%
+interest or one coefficient
+of interest is of the actual market
+
+ align:start position:0%
+of interest is of the actual market
+ 
+
+ align:start position:0%
+of interest is of the actual market
+price how much is the thing worth
+
+ align:start position:0%
+price how much is the thing worth
+ 
+
+ align:start position:0%
+price how much is the thing worth
+and then delta on the loss is like how
+
+ align:start position:0%
+and then delta on the loss is like how
+ 
+
+ align:start position:0%
+and then delta on the loss is like how
+much do you lose relative to your
+
+ align:start position:0%
+much do you lose relative to your
+ 
+
+ align:start position:0%
+much do you lose relative to your
+purchase price now if people were not
+
+ align:start position:0%
+purchase price now if people were not
+ 
+
+ align:start position:0%
+purchase price now if people were not
+reference dependent what should we find
+
+ align:start position:0%
+reference dependent what should we find
+ 
+
+ align:start position:0%
+reference dependent what should we find
+what would be the predictions
+
+ align:start position:0%
+what would be the predictions
+ 
+
+ align:start position:0%
+what would be the predictions
+like the neoclassical model what should
+
+ align:start position:0%
+like the neoclassical model what should
+ 
+
+ align:start position:0%
+like the neoclassical model what should
+we find here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+exactly delta should not matter it
+
+ align:start position:0%
+exactly delta should not matter it
+ 
+
+ align:start position:0%
+exactly delta should not matter it
+shouldn't matter how much you lost or
+
+ align:start position:0%
+shouldn't matter how much you lost or
+ 
+
+ align:start position:0%
+shouldn't matter how much you lost or
+gained in that house
+
+ align:start position:0%
+gained in that house
+ 
+
+ align:start position:0%
+gained in that house
+uh what should matter is like what is
+
+ align:start position:0%
+uh what should matter is like what is
+ 
+
+ align:start position:0%
+uh what should matter is like what is
+the actual market value you should
+
+ align:start position:0%
+the actual market value you should
+ 
+
+ align:start position:0%
+the actual market value you should
+essentially try to
+
+ align:start position:0%
+essentially try to
+ 
+
+ align:start position:0%
+essentially try to
+be willing to sell it or not beta could
+
+ align:start position:0%
+be willing to sell it or not beta could
+ 
+
+ align:start position:0%
+be willing to sell it or not beta could
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+you know it doesn't have to be one it
+
+ align:start position:0%
+you know it doesn't have to be one it
+ 
+
+ align:start position:0%
+you know it doesn't have to be one it
+could be like everybody
+
+ align:start position:0%
+could be like everybody
+ 
+
+ align:start position:0%
+could be like everybody
+pays above the actual market for some
+
+ align:start position:0%
+pays above the actual market for some
+ 
+
+ align:start position:0%
+pays above the actual market for some
+housing bubble or whatever beta could be
+
+ align:start position:0%
+housing bubble or whatever beta could be
+ 
+
+ align:start position:0%
+housing bubble or whatever beta could be
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+1.1 or whatever you might be uh that
+
+ align:start position:0%
+1.1 or whatever you might be uh that
+ 
+
+ align:start position:0%
+1.1 or whatever you might be uh that
+depends on essentially sort of aggregate
+
+ align:start position:0%
+depends on essentially sort of aggregate
+ 
+
+ align:start position:0%
+depends on essentially sort of aggregate
+conditions and so on
+
+ align:start position:0%
+conditions and so on
+ 
+
+ align:start position:0%
+conditions and so on
+but delta really should not matter when
+
+ align:start position:0%
+but delta really should not matter when
+ 
+
+ align:start position:0%
+but delta really should not matter when
+i'm trying to sell you a house you
+
+ align:start position:0%
+i'm trying to sell you a house you
+ 
+
+ align:start position:0%
+i'm trying to sell you a house you
+should ask like what's the
+
+ align:start position:0%
+should ask like what's the
+ 
+
+ align:start position:0%
+should ask like what's the
+actual market value and i should um
+
+ align:start position:0%
+actual market value and i should um
+ 
+
+ align:start position:0%
+actual market value and i should um
+essentially then based on that
+
+ align:start position:0%
+essentially then based on that
+ 
+
+ align:start position:0%
+essentially then based on that
+uh uh put it under market um on that
+
+ align:start position:0%
+uh uh put it under market um on that
+ 
+
+ align:start position:0%
+uh uh put it under market um on that
+listing price
+
+ align:start position:0%
+listing price
+ 
+
+ align:start position:0%
+listing price
+uh but what might be the case is that
+
+ align:start position:0%
+uh but what might be the case is that
+ 
+
+ align:start position:0%
+uh but what might be the case is that
+the loss actually um
+
+ align:start position:0%
+the loss actually um
+ 
+
+ align:start position:0%
+the loss actually um
+matters now one problem here is that the
+
+ align:start position:0%
+matters now one problem here is that the
+ 
+
+ align:start position:0%
+matters now one problem here is that the
+actual market value is not observable
+
+ align:start position:0%
+actual market value is not observable
+ 
+
+ align:start position:0%
+actual market value is not observable
+right so i don't actually know what the
+
+ align:start position:0%
+right so i don't actually know what the
+ 
+
+ align:start position:0%
+right so i don't actually know what the
+market value is because that's like
+
+ align:start position:0%
+market value is because that's like
+ 
+
+ align:start position:0%
+market value is because that's like
+endogenous that's part of like the
+
+ align:start position:0%
+endogenous that's part of like the
+ 
+
+ align:start position:0%
+endogenous that's part of like the
+transaction
+
+ align:start position:0%
+transaction
+ 
+
+ align:start position:0%
+transaction
+so what can i do instead or how do i do
+
+ align:start position:0%
+so what can i do instead or how do i do
+ 
+
+ align:start position:0%
+so what can i do instead or how do i do
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes by asking people like would you like
+
+ align:start position:0%
+yes by asking people like would you like
+ 
+
+ align:start position:0%
+yes by asking people like would you like
+would you take this trade
+
+ align:start position:0%
+would you take this trade
+ 
+
+ align:start position:0%
+would you take this trade
+what they say right so you can look at
+
+ align:start position:0%
+what they say right so you can look at
+ 
+
+ align:start position:0%
+what they say right so you can look at
+actually the market
+
+ align:start position:0%
+actually the market
+ 
+
+ align:start position:0%
+actually the market
+outcome overall you can look at like who
+
+ align:start position:0%
+outcome overall you can look at like who
+ 
+
+ align:start position:0%
+outcome overall you can look at like who
+buys it and what's the actual purchase
+
+ align:start position:0%
+buys it and what's the actual purchase
+ 
+
+ align:start position:0%
+buys it and what's the actual purchase
+price
+
+ align:start position:0%
+price
+ 
+
+ align:start position:0%
+price
+now that might also be endogenous to
+
+ align:start position:0%
+now that might also be endogenous to
+ 
+
+ align:start position:0%
+now that might also be endogenous to
+like the listing price right so if you
+
+ align:start position:0%
+like the listing price right so if you
+ 
+
+ align:start position:0%
+like the listing price right so if you
+think you know the people who are lost a
+
+ align:start position:0%
+think you know the people who are lost a
+ 
+
+ align:start position:0%
+think you know the people who are lost a
+verse are
+
+ align:start position:0%
+verse are
+ 
+
+ align:start position:0%
+verse are
+listing their houses too high relatively
+
+ align:start position:0%
+listing their houses too high relatively
+ 
+
+ align:start position:0%
+listing their houses too high relatively
+compared to what the market value
+
+ align:start position:0%
+compared to what the market value
+ 
+
+ align:start position:0%
+compared to what the market value
+actually is
+
+ align:start position:0%
+actually is
+ 
+
+ align:start position:0%
+actually is
+it might actually be sold at a higher
+
+ align:start position:0%
+it might actually be sold at a higher
+ 
+
+ align:start position:0%
+it might actually be sold at a higher
+price so that could
+
+ align:start position:0%
+price so that could
+ 
+
+ align:start position:0%
+price so that could
+that's hard to interpret it could just
+
+ align:start position:0%
+that's hard to interpret it could just
+ 
+
+ align:start position:0%
+that's hard to interpret it could just
+be that if you sell it at a high
+
+ align:start position:0%
+be that if you sell it at a high
+ 
+
+ align:start position:0%
+be that if you sell it at a high
+if you list it at a very high price and
+
+ align:start position:0%
+if you list it at a very high price and
+ 
+
+ align:start position:0%
+if you list it at a very high price and
+wait for a long time you also sell it at
+
+ align:start position:0%
+wait for a long time you also sell it at
+ 
+
+ align:start position:0%
+wait for a long time you also sell it at
+a higher price
+
+ align:start position:0%
+a higher price
+ 
+
+ align:start position:0%
+a higher price
+but doesn't mean that it's actually
+
+ align:start position:0%
+but doesn't mean that it's actually
+ 
+
+ align:start position:0%
+but doesn't mean that it's actually
+worth that much it just means that like
+
+ align:start position:0%
+worth that much it just means that like
+ 
+
+ align:start position:0%
+worth that much it just means that like
+you happen to find
+
+ align:start position:0%
+you happen to find
+ 
+
+ align:start position:0%
+you happen to find
+a buyer who happens to be willing to pay
+
+ align:start position:0%
+a buyer who happens to be willing to pay
+ 
+
+ align:start position:0%
+a buyer who happens to be willing to pay
+a lot and that's more likely when you
+
+ align:start position:0%
+a lot and that's more likely when you
+ 
+
+ align:start position:0%
+a lot and that's more likely when you
+wait for a long time
+
+ align:start position:0%
+wait for a long time
+ 
+
+ align:start position:0%
+wait for a long time
+which is not necessarily optimal because
+
+ align:start position:0%
+which is not necessarily optimal because
+ 
+
+ align:start position:0%
+which is not necessarily optimal because
+it's actually quite costly to do that
+
+ align:start position:0%
+it's actually quite costly to do that
+ 
+
+ align:start position:0%
+it's actually quite costly to do that
+but you're saying something else which
+
+ align:start position:0%
+but you're saying something else which
+ 
+
+ align:start position:0%
+but you're saying something else which
+is like asking them about what they
+
+ align:start position:0%
+is like asking them about what they
+ 
+
+ align:start position:0%
+is like asking them about what they
+think but what are the characteristics
+
+ align:start position:0%
+think but what are the characteristics
+ 
+
+ align:start position:0%
+think but what are the characteristics
+that we could look at or what data
+
+ align:start position:0%
+that we could look at or what data
+ 
+
+ align:start position:0%
+that we could look at or what data
+could we look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like if you had like zillow data or data
+
+ align:start position:0%
+like if you had like zillow data or data
+ 
+
+ align:start position:0%
+like if you had like zillow data or data
+on like essentially a bunch of these
+
+ align:start position:0%
+on like essentially a bunch of these
+ 
+
+ align:start position:0%
+on like essentially a bunch of these
+apps where you can look at houses
+
+ align:start position:0%
+apps where you can look at houses
+ 
+
+ align:start position:0%
+apps where you can look at houses
+what data could you get yes you'd look
+
+ align:start position:0%
+what data could you get yes you'd look
+ 
+
+ align:start position:0%
+what data could you get yes you'd look
+at like the houses like in the
+
+ align:start position:0%
+at like the houses like in the
+ 
+
+ align:start position:0%
+at like the houses like in the
+neighborhood like similar
+
+ align:start position:0%
+neighborhood like similar
+ 
+
+ align:start position:0%
+neighborhood like similar
+houses exactly what redfin and zillow et
+
+ align:start position:0%
+houses exactly what redfin and zillow et
+ 
+
+ align:start position:0%
+houses exactly what redfin and zillow et
+cetera do these days is essentially they
+
+ align:start position:0%
+cetera do these days is essentially they
+ 
+
+ align:start position:0%
+cetera do these days is essentially they
+have these algorithms that try to
+
+ align:start position:0%
+have these algorithms that try to
+ 
+
+ align:start position:0%
+have these algorithms that try to
+predict
+
+ align:start position:0%
+predict
+ 
+
+ align:start position:0%
+predict
+uh the actual market sales price and
+
+ align:start position:0%
+uh the actual market sales price and
+ 
+
+ align:start position:0%
+uh the actual market sales price and
+what they tend to do essentially is look
+
+ align:start position:0%
+what they tend to do essentially is look
+ 
+
+ align:start position:0%
+what they tend to do essentially is look
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+exactly as you say surrounding houses
+
+ align:start position:0%
+exactly as you say surrounding houses
+ 
+
+ align:start position:0%
+exactly as you say surrounding houses
+that are similar in some characteristics
+
+ align:start position:0%
+that are similar in some characteristics
+ 
+
+ align:start position:0%
+that are similar in some characteristics
+they look at the number of they look at
+
+ align:start position:0%
+they look at the number of they look at
+ 
+
+ align:start position:0%
+they look at the number of they look at
+the square footage they look at the
+
+ align:start position:0%
+the square footage they look at the
+ 
+
+ align:start position:0%
+the square footage they look at the
+number of uh
+
+ align:start position:0%
+number of uh
+ 
+
+ align:start position:0%
+number of uh
+bathrooms and rooms in general they look
+
+ align:start position:0%
+bathrooms and rooms in general they look
+ 
+
+ align:start position:0%
+bathrooms and rooms in general they look
+at like sort of like location and so on
+
+ align:start position:0%
+at like sort of like location and so on
+ 
+
+ align:start position:0%
+at like sort of like location and so on
+and so forth
+
+ align:start position:0%
+and so forth
+ 
+
+ align:start position:0%
+and so forth
+and then you can predict um uh
+
+ align:start position:0%
+and then you can predict um uh
+ 
+
+ align:start position:0%
+and then you can predict um uh
+how much uh and sort of they look at
+
+ align:start position:0%
+how much uh and sort of they look at
+ 
+
+ align:start position:0%
+how much uh and sort of they look at
+also time trends and so on
+
+ align:start position:0%
+also time trends and so on
+ 
+
+ align:start position:0%
+also time trends and so on
+how much is the actual market value but
+
+ align:start position:0%
+how much is the actual market value but
+ 
+
+ align:start position:0%
+how much is the actual market value but
+it's essentially fundamentally it's like
+
+ align:start position:0%
+it's essentially fundamentally it's like
+ 
+
+ align:start position:0%
+it's essentially fundamentally it's like
+a prediction exercise you can try to
+
+ align:start position:0%
+a prediction exercise you can try to
+ 
+
+ align:start position:0%
+a prediction exercise you can try to
+predict
+
+ align:start position:0%
+predict
+ 
+
+ align:start position:0%
+predict
+uh what the actual value is and that's
+
+ align:start position:0%
+uh what the actual value is and that's
+ 
+
+ align:start position:0%
+uh what the actual value is and that's
+exactly what uh genovese and meyer do
+
+ align:start position:0%
+exactly what uh genovese and meyer do
+ 
+
+ align:start position:0%
+exactly what uh genovese and meyer do
+they do
+
+ align:start position:0%
+they do
+ 
+
+ align:start position:0%
+they do
+some more fancy things that try to get
+
+ align:start position:0%
+some more fancy things that try to get
+ 
+
+ align:start position:0%
+some more fancy things that try to get
+at like other
+
+ align:start position:0%
+at like other
+ 
+
+ align:start position:0%
+at like other
+unobservable characteristics and so on
+
+ align:start position:0%
+unobservable characteristics and so on
+ 
+
+ align:start position:0%
+unobservable characteristics and so on
+but the essence of this is exactly a
+
+ align:start position:0%
+but the essence of this is exactly a
+ 
+
+ align:start position:0%
+but the essence of this is exactly a
+prediction exercise where they say
+
+ align:start position:0%
+prediction exercise where they say
+ 
+
+ align:start position:0%
+prediction exercise where they say
+let's just look at uh the
+
+ align:start position:0%
+let's just look at uh the
+ 
+
+ align:start position:0%
+let's just look at uh the
+characteristics of this house let's try
+
+ align:start position:0%
+characteristics of this house let's try
+ 
+
+ align:start position:0%
+characteristics of this house let's try
+to predict what the market value is
+
+ align:start position:0%
+to predict what the market value is
+ 
+
+ align:start position:0%
+to predict what the market value is
+and then look at the loss which is
+
+ align:start position:0%
+and then look at the loss which is
+ 
+
+ align:start position:0%
+and then look at the loss which is
+essentially the difference between the
+
+ align:start position:0%
+essentially the difference between the
+ 
+
+ align:start position:0%
+essentially the difference between the
+previous selling price and the expected
+
+ align:start position:0%
+previous selling price and the expected
+ 
+
+ align:start position:0%
+previous selling price and the expected
+selling
+
+ align:start position:0%
+selling
+ 
+
+ align:start position:0%
+selling
+price truncated from zero because
+
+ align:start position:0%
+price truncated from zero because
+ 
+
+ align:start position:0%
+price truncated from zero because
+otherwise it's a gain
+
+ align:start position:0%
+otherwise it's a gain
+ 
+
+ align:start position:0%
+otherwise it's a gain
+and then we can look at uh does it
+
+ align:start position:0%
+and then we can look at uh does it
+ 
+
+ align:start position:0%
+and then we can look at uh does it
+really seem that like when people are in
+
+ align:start position:0%
+really seem that like when people are in
+ 
+
+ align:start position:0%
+really seem that like when people are in
+the lost domain when their losses
+
+ align:start position:0%
+the lost domain when their losses
+ 
+
+ align:start position:0%
+the lost domain when their losses
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+are they now um selling their house or
+
+ align:start position:0%
+are they now um selling their house or
+ 
+
+ align:start position:0%
+are they now um selling their house or
+trying to sell their house
+
+ align:start position:0%
+trying to sell their house
+ 
+
+ align:start position:0%
+trying to sell their house
+at a higher um price yes
+
+ align:start position:0%
+at a higher um price yes
+ 
+
+ align:start position:0%
+at a higher um price yes
+how would you account for something like
+
+ align:start position:0%
+how would you account for something like
+ 
+
+ align:start position:0%
+how would you account for something like
+recent renovations like since the last
+
+ align:start position:0%
+recent renovations like since the last
+ 
+
+ align:start position:0%
+recent renovations like since the last
+listing and
+
+ align:start position:0%
+listing and
+ 
+
+ align:start position:0%
+listing and
+relative to any other similar units or
+
+ align:start position:0%
+relative to any other similar units or
+ 
+
+ align:start position:0%
+relative to any other similar units or
+causes
+
+ align:start position:0%
+causes
+ 
+
+ align:start position:0%
+causes
+and nearby right
+
+ align:start position:0%
+and nearby right
+ 
+
+ align:start position:0%
+and nearby right
+so um that's tricky to do and i don't
+
+ align:start position:0%
+so um that's tricky to do and i don't
+ 
+
+ align:start position:0%
+so um that's tricky to do and i don't
+think they have this in their data so
+
+ align:start position:0%
+think they have this in their data so
+ 
+
+ align:start position:0%
+think they have this in their data so
+what you'd have to assume here and
+
+ align:start position:0%
+what you'd have to assume here and
+ 
+
+ align:start position:0%
+what you'd have to assume here and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+perhaps reasonable is to say that when
+
+ align:start position:0%
+perhaps reasonable is to say that when
+ 
+
+ align:start position:0%
+perhaps reasonable is to say that when
+you look at sort of this picture
+
+ align:start position:0%
+you look at sort of this picture
+ 
+
+ align:start position:0%
+you look at sort of this picture
+that um seller a and zellerb did not do
+
+ align:start position:0%
+that um seller a and zellerb did not do
+ 
+
+ align:start position:0%
+that um seller a and zellerb did not do
+differential renovation depending on
+
+ align:start position:0%
+differential renovation depending on
+ 
+
+ align:start position:0%
+differential renovation depending on
+when they bought the house right so if
+
+ align:start position:0%
+when they bought the house right so if
+ 
+
+ align:start position:0%
+when they bought the house right so if
+you said
+
+ align:start position:0%
+you said
+ 
+
+ align:start position:0%
+you said
+it's fine if people have done
+
+ align:start position:0%
+it's fine if people have done
+ 
+
+ align:start position:0%
+it's fine if people have done
+renovations for example this is what i
+
+ align:start position:0%
+renovations for example this is what i
+ 
+
+ align:start position:0%
+renovations for example this is what i
+was saying about the beta on the actual
+
+ align:start position:0%
+was saying about the beta on the actual
+ 
+
+ align:start position:0%
+was saying about the beta on the actual
+market value
+
+ align:start position:0%
+market value
+ 
+
+ align:start position:0%
+market value
+if you systematically underestimate or
+
+ align:start position:0%
+if you systematically underestimate or
+ 
+
+ align:start position:0%
+if you systematically underestimate or
+overestimate how much people renovate
+
+ align:start position:0%
+overestimate how much people renovate
+ 
+
+ align:start position:0%
+overestimate how much people renovate
+and so on or maybe you know the housing
+
+ align:start position:0%
+and so on or maybe you know the housing
+ 
+
+ align:start position:0%
+and so on or maybe you know the housing
+market is really hot or whatever
+
+ align:start position:0%
+market is really hot or whatever
+ 
+
+ align:start position:0%
+market is really hot or whatever
+that's okay the main issue is like that
+
+ align:start position:0%
+that's okay the main issue is like that
+ 
+
+ align:start position:0%
+that's okay the main issue is like that
+can't be correlated with the
+
+ align:start position:0%
+can't be correlated with the
+ 
+
+ align:start position:0%
+can't be correlated with the
+uh uh the loss here so if it's the case
+
+ align:start position:0%
+uh uh the loss here so if it's the case
+ 
+
+ align:start position:0%
+uh uh the loss here so if it's the case
+that people who may
+
+ align:start position:0%
+that people who may
+ 
+
+ align:start position:0%
+that people who may
+who lost a bunch of money in terms of
+
+ align:start position:0%
+who lost a bunch of money in terms of
+ 
+
+ align:start position:0%
+who lost a bunch of money in terms of
+like their housing prices sort of like
+
+ align:start position:0%
+like their housing prices sort of like
+ 
+
+ align:start position:0%
+like their housing prices sort of like
+tanked
+
+ align:start position:0%
+tanked
+ 
+
+ align:start position:0%
+tanked
+uh if those people have done more or
+
+ align:start position:0%
+uh if those people have done more or
+ 
+
+ align:start position:0%
+uh if those people have done more or
+less renovations then you're in trouble
+
+ align:start position:0%
+less renovations then you're in trouble
+ 
+
+ align:start position:0%
+less renovations then you're in trouble
+with your estimates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah is the expected selling price the
+
+ align:start position:0%
+yeah is the expected selling price the
+ 
+
+ align:start position:0%
+yeah is the expected selling price the
+estimation of actual work value
+
+ align:start position:0%
+estimation of actual work value
+ 
+
+ align:start position:0%
+estimation of actual work value
+correct okay yes
+
+ align:start position:0%
+correct okay yes
+ 
+
+ align:start position:0%
+correct okay yes
+um so now what what generation meyer
+
+ align:start position:0%
+um so now what what generation meyer
+ 
+
+ align:start position:0%
+um so now what what generation meyer
+find is and there's more detail to that
+
+ align:start position:0%
+find is and there's more detail to that
+ 
+
+ align:start position:0%
+find is and there's more detail to that
+but essentially the main finding is and
+
+ align:start position:0%
+but essentially the main finding is and
+ 
+
+ align:start position:0%
+but essentially the main finding is and
+that's a
+
+ align:start position:0%
+that's a
+ 
+
+ align:start position:0%
+that's a
+fairly solid one there's a bunch of
+
+ align:start position:0%
+fairly solid one there's a bunch of
+ 
+
+ align:start position:0%
+fairly solid one there's a bunch of
+different specifications is a 10
+
+ align:start position:0%
+different specifications is a 10
+ 
+
+ align:start position:0%
+different specifications is a 10
+increase in a perspective loss if this
+
+ align:start position:0%
+increase in a perspective loss if this
+ 
+
+ align:start position:0%
+increase in a perspective loss if this
+loss coefficient the difference between
+
+ align:start position:0%
+loss coefficient the difference between
+ 
+
+ align:start position:0%
+loss coefficient the difference between
+the expected selling price and the uh
+
+ align:start position:0%
+the expected selling price and the uh
+ 
+
+ align:start position:0%
+the expected selling price and the uh
+purchase price
+
+ align:start position:0%
+purchase price
+ 
+
+ align:start position:0%
+purchase price
+uh if that's 10 percent higher than
+
+ align:start position:0%
+uh if that's 10 percent higher than
+ 
+
+ align:start position:0%
+uh if that's 10 percent higher than
+essentially the list price is 2.5 to 3
+
+ align:start position:0%
+essentially the list price is 2.5 to 3
+ 
+
+ align:start position:0%
+essentially the list price is 2.5 to 3
+percent
+
+ align:start position:0%
+percent
+ 
+
+ align:start position:0%
+percent
+uh 3.5 percent higher and then these
+
+ align:start position:0%
+uh 3.5 percent higher and then these
+ 
+
+ align:start position:0%
+uh 3.5 percent higher and then these
+effects so like people list the price
+
+ align:start position:0%
+effects so like people list the price
+ 
+
+ align:start position:0%
+effects so like people list the price
+the house at a higher price if the house
+
+ align:start position:0%
+the house at a higher price if the house
+ 
+
+ align:start position:0%
+the house at a higher price if the house
+is at a loss compared to like a similar
+
+ align:start position:0%
+is at a loss compared to like a similar
+ 
+
+ align:start position:0%
+is at a loss compared to like a similar
+house who's not at a loss or like
+
+ align:start position:0%
+house who's not at a loss or like
+ 
+
+ align:start position:0%
+house who's not at a loss or like
+it was in the game domain these effects
+
+ align:start position:0%
+it was in the game domain these effects
+ 
+
+ align:start position:0%
+it was in the game domain these effects
+then translate
+
+ align:start position:0%
+then translate
+ 
+
+ align:start position:0%
+then translate
+into higher uh sales prices and the
+
+ align:start position:0%
+into higher uh sales prices and the
+ 
+
+ align:start position:0%
+into higher uh sales prices and the
+lower hazard rate of sale
+
+ align:start position:0%
+lower hazard rate of sale
+ 
+
+ align:start position:0%
+lower hazard rate of sale
+that's to say people actually sell it at
+
+ align:start position:0%
+that's to say people actually sell it at
+ 
+
+ align:start position:0%
+that's to say people actually sell it at
+a higher price
+
+ align:start position:0%
+a higher price
+ 
+
+ align:start position:0%
+a higher price
+so it's in fact you know it's hard to
+
+ align:start position:0%
+so it's in fact you know it's hard to
+ 
+
+ align:start position:0%
+so it's in fact you know it's hard to
+say here what's optimal versus not it
+
+ align:start position:0%
+say here what's optimal versus not it
+ 
+
+ align:start position:0%
+say here what's optimal versus not it
+could be that overall people are like
+
+ align:start position:0%
+could be that overall people are like
+ 
+
+ align:start position:0%
+could be that overall people are like
+uh you know it's actually a good thing
+
+ align:start position:0%
+uh you know it's actually a good thing
+ 
+
+ align:start position:0%
+uh you know it's actually a good thing
+to do that depends a lot on essentially
+
+ align:start position:0%
+to do that depends a lot on essentially
+ 
+
+ align:start position:0%
+to do that depends a lot on essentially
+like your opportunity costs of
+
+ align:start position:0%
+like your opportunity costs of
+ 
+
+ align:start position:0%
+like your opportunity costs of
+of money in terms of like or you know
+
+ align:start position:0%
+of money in terms of like or you know
+ 
+
+ align:start position:0%
+of money in terms of like or you know
+your how
+
+ align:start position:0%
+your how
+ 
+
+ align:start position:0%
+your how
+costly is it for you to keep the the
+
+ align:start position:0%
+costly is it for you to keep the the
+ 
+
+ align:start position:0%
+costly is it for you to keep the the
+house on the market for a while
+
+ align:start position:0%
+house on the market for a while
+ 
+
+ align:start position:0%
+house on the market for a while
+but essentially um uh people have a
+
+ align:start position:0%
+but essentially um uh people have a
+ 
+
+ align:start position:0%
+but essentially um uh people have a
+lower hazard rate of sales that's to say
+
+ align:start position:0%
+lower hazard rate of sales that's to say
+ 
+
+ align:start position:0%
+lower hazard rate of sales that's to say
+it just takes them a lot longer to sell
+
+ align:start position:0%
+it just takes them a lot longer to sell
+ 
+
+ align:start position:0%
+it just takes them a lot longer to sell
+the house
+
+ align:start position:0%
+the house
+ 
+
+ align:start position:0%
+the house
+that tends to be very costly to do so
+
+ align:start position:0%
+that tends to be very costly to do so
+ 
+
+ align:start position:0%
+that tends to be very costly to do so
+but you know if you you know just
+
+ align:start position:0%
+but you know if you you know just
+ 
+
+ align:start position:0%
+but you know if you you know just
+otherwise would have your money in the
+
+ align:start position:0%
+otherwise would have your money in the
+ 
+
+ align:start position:0%
+otherwise would have your money in the
+bank and you have another place to stay
+
+ align:start position:0%
+bank and you have another place to stay
+ 
+
+ align:start position:0%
+bank and you have another place to stay
+and you don't really care
+
+ align:start position:0%
+and you don't really care
+ 
+
+ align:start position:0%
+and you don't really care
+maybe then that's fine uh but we surely
+
+ align:start position:0%
+maybe then that's fine uh but we surely
+ 
+
+ align:start position:0%
+maybe then that's fine uh but we surely
+have like real effects in terms of like
+
+ align:start position:0%
+have like real effects in terms of like
+ 
+
+ align:start position:0%
+have like real effects in terms of like
+uh people list their houses as high at
+
+ align:start position:0%
+uh people list their houses as high at
+ 
+
+ align:start position:0%
+uh people list their houses as high at
+higher prices people
+
+ align:start position:0%
+higher prices people
+ 
+
+ align:start position:0%
+higher prices people
+sell them at somewhat higher prices and
+
+ align:start position:0%
+sell them at somewhat higher prices and
+ 
+
+ align:start position:0%
+sell them at somewhat higher prices and
+people also keep them longer
+
+ align:start position:0%
+people also keep them longer
+ 
+
+ align:start position:0%
+people also keep them longer
+on the market okay yeah
+
+ align:start position:0%
+on the market okay yeah
+ 
+
+ align:start position:0%
+on the market okay yeah
+is this the same analysis if it's gains
+
+ align:start position:0%
+is this the same analysis if it's gains
+ 
+
+ align:start position:0%
+is this the same analysis if it's gains
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+value of the house
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so essentially what we're doing is we're
+
+ align:start position:0%
+so essentially what we're doing is we're
+ 
+
+ align:start position:0%
+so essentially what we're doing is we're
+implicitly comparing losses versus gains
+
+ align:start position:0%
+implicitly comparing losses versus gains
+ 
+
+ align:start position:0%
+implicitly comparing losses versus gains
+right so so that gains
+
+ align:start position:0%
+right so so that gains
+ 
+
+ align:start position:0%
+right so so that gains
+the gains here would be in the actual
+
+ align:start position:0%
+the gains here would be in the actual
+ 
+
+ align:start position:0%
+the gains here would be in the actual
+market value
+
+ align:start position:0%
+market value
+ 
+
+ align:start position:0%
+market value
+already as it is so it's
+
+ align:start position:0%
+already as it is so it's
+ 
+
+ align:start position:0%
+already as it is so it's
+so but essentially what you implicitly
+
+ align:start position:0%
+so but essentially what you implicitly
+ 
+
+ align:start position:0%
+so but essentially what you implicitly
+do is you create when comparing
+
+ align:start position:0%
+do is you create when comparing
+ 
+
+ align:start position:0%
+do is you create when comparing
+implicitly this is what i was saying
+
+ align:start position:0%
+implicitly this is what i was saying
+ 
+
+ align:start position:0%
+implicitly this is what i was saying
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+when you look at this picture implicitly
+
+ align:start position:0%
+when you look at this picture implicitly
+ 
+
+ align:start position:0%
+when you look at this picture implicitly
+what we're doing is we look at people
+
+ align:start position:0%
+what we're doing is we look at people
+ 
+
+ align:start position:0%
+what we're doing is we look at people
+who are
+
+ align:start position:0%
+who are
+ 
+
+ align:start position:0%
+who are
+um losing money compared to people who
+
+ align:start position:0%
+um losing money compared to people who
+ 
+
+ align:start position:0%
+um losing money compared to people who
+are gaining money
+
+ align:start position:0%
+are gaining money
+ 
+
+ align:start position:0%
+are gaining money
+and explicitly implicitly asking like is
+
+ align:start position:0%
+and explicitly implicitly asking like is
+ 
+
+ align:start position:0%
+and explicitly implicitly asking like is
+the increase in the gain sort of
+
+ align:start position:0%
+the increase in the gain sort of
+ 
+
+ align:start position:0%
+the increase in the gain sort of
+predictive of that
+
+ align:start position:0%
+predictive of that
+ 
+
+ align:start position:0%
+predictive of that
+sorry the the increase in the loss is a
+
+ align:start position:0%
+sorry the the increase in the loss is a
+ 
+
+ align:start position:0%
+sorry the the increase in the loss is a
+predictive of like your
+
+ align:start position:0%
+predictive of like your
+ 
+
+ align:start position:0%
+predictive of like your
+uh listing price now it's hard to do
+
+ align:start position:0%
+uh listing price now it's hard to do
+ 
+
+ align:start position:0%
+uh listing price now it's hard to do
+this at the same time
+
+ align:start position:0%
+this at the same time
+ 
+
+ align:start position:0%
+this at the same time
+for for gains because essentially an
+
+ align:start position:0%
+for for gains because essentially an
+ 
+
+ align:start position:0%
+for for gains because essentially an
+increase in the market
+
+ align:start position:0%
+increase in the market
+ 
+
+ align:start position:0%
+increase in the market
+price overall is this like that sort of
+
+ align:start position:0%
+price overall is this like that sort of
+ 
+
+ align:start position:0%
+price overall is this like that sort of
+culinaire
+
+ align:start position:0%
+culinaire
+ 
+
+ align:start position:0%
+culinaire
+in short essentially that's hard to
+
+ align:start position:0%
+in short essentially that's hard to
+ 
+
+ align:start position:0%
+in short essentially that's hard to
+separate you could do the same analysis
+
+ align:start position:0%
+separate you could do the same analysis
+ 
+
+ align:start position:0%
+separate you could do the same analysis
+and you wouldn't find that for the gains
+
+ align:start position:0%
+and you wouldn't find that for the gains
+ 
+
+ align:start position:0%
+and you wouldn't find that for the gains
+in part because
+
+ align:start position:0%
+in part because
+ 
+
+ align:start position:0%
+in part because
+essentially explicitly what we're doing
+
+ align:start position:0%
+essentially explicitly what we're doing
+ 
+
+ align:start position:0%
+essentially explicitly what we're doing
+is increasing losses to gains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh okay so then there's another
+
+ align:start position:0%
+okay uh okay so then there's another
+ 
+
+ align:start position:0%
+okay uh okay so then there's another
+piece of evidence that sort of tells us
+
+ align:start position:0%
+piece of evidence that sort of tells us
+ 
+
+ align:start position:0%
+piece of evidence that sort of tells us
+perhaps this is not optimal if you look
+
+ align:start position:0%
+perhaps this is not optimal if you look
+ 
+
+ align:start position:0%
+perhaps this is not optimal if you look
+at people who are
+
+ align:start position:0%
+at people who are
+ 
+
+ align:start position:0%
+at people who are
+owner occupied compared to investors so
+
+ align:start position:0%
+owner occupied compared to investors so
+ 
+
+ align:start position:0%
+owner occupied compared to investors so
+they're people who essentially invest in
+
+ align:start position:0%
+they're people who essentially invest in
+ 
+
+ align:start position:0%
+they're people who essentially invest in
+houses and they sell houses and they
+
+ align:start position:0%
+houses and they sell houses and they
+ 
+
+ align:start position:0%
+houses and they sell houses and they
+sell lots of houses over time
+
+ align:start position:0%
+sell lots of houses over time
+ 
+
+ align:start position:0%
+sell lots of houses over time
+those people have much lower uh
+
+ align:start position:0%
+those people have much lower uh
+ 
+
+ align:start position:0%
+those people have much lower uh
+endowment effects if you want for houses
+
+ align:start position:0%
+endowment effects if you want for houses
+ 
+
+ align:start position:0%
+endowment effects if you want for houses
+so they exhibit this behavior a lot less
+
+ align:start position:0%
+so they exhibit this behavior a lot less
+ 
+
+ align:start position:0%
+so they exhibit this behavior a lot less
+but people who live in that house who
+
+ align:start position:0%
+but people who live in that house who
+ 
+
+ align:start position:0%
+but people who live in that house who
+bought that house for them it's mostly
+
+ align:start position:0%
+bought that house for them it's mostly
+ 
+
+ align:start position:0%
+bought that house for them it's mostly
+like the only house they live in it's
+
+ align:start position:0%
+like the only house they live in it's
+ 
+
+ align:start position:0%
+like the only house they live in it's
+the main purchase that they have
+
+ align:start position:0%
+the main purchase that they have
+ 
+
+ align:start position:0%
+the main purchase that they have
+for them it's essentially their house
+
+ align:start position:0%
+for them it's essentially their house
+ 
+
+ align:start position:0%
+for them it's essentially their house
+for which they don't want to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a losses for them these effects are
+
+ align:start position:0%
+a losses for them these effects are
+ 
+
+ align:start position:0%
+a losses for them these effects are
+twice as large compared to the
+
+ align:start position:0%
+twice as large compared to the
+ 
+
+ align:start position:0%
+twice as large compared to the
+investors and that's perhaps some
+
+ align:start position:0%
+investors and that's perhaps some
+ 
+
+ align:start position:0%
+investors and that's perhaps some
+evidence that uh this is not optimal
+
+ align:start position:0%
+evidence that uh this is not optimal
+ 
+
+ align:start position:0%
+evidence that uh this is not optimal
+behavior in a sense of the
+
+ align:start position:0%
+behavior in a sense of the
+ 
+
+ align:start position:0%
+behavior in a sense of the
+sort of the professional investors they
+
+ align:start position:0%
+sort of the professional investors they
+ 
+
+ align:start position:0%
+sort of the professional investors they
+presumably know pretty well
+
+ align:start position:0%
+presumably know pretty well
+ 
+
+ align:start position:0%
+presumably know pretty well
+uh how to price their houses so if they
+
+ align:start position:0%
+uh how to price their houses so if they
+ 
+
+ align:start position:0%
+uh how to price their houses so if they
+do this behavior less
+
+ align:start position:0%
+do this behavior less
+ 
+
+ align:start position:0%
+do this behavior less
+uh presumably that's that's a sign that
+
+ align:start position:0%
+uh presumably that's that's a sign that
+ 
+
+ align:start position:0%
+uh presumably that's that's a sign that
+that there's some form of a mistake here
+
+ align:start position:0%
+that there's some form of a mistake here
+ 
+
+ align:start position:0%
+that there's some form of a mistake here
+um going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second there's some evidence in john
+
+ align:start position:0%
+second there's some evidence in john
+ 
+
+ align:start position:0%
+second there's some evidence in john
+list has some work on this
+
+ align:start position:0%
+list has some work on this
+ 
+
+ align:start position:0%
+list has some work on this
+overall is to say that experience can
+
+ align:start position:0%
+overall is to say that experience can
+ 
+
+ align:start position:0%
+overall is to say that experience can
+mitigate reference dependent
+
+ align:start position:0%
+mitigate reference dependent
+ 
+
+ align:start position:0%
+mitigate reference dependent
+effects essentially if you do a lot of
+
+ align:start position:0%
+effects essentially if you do a lot of
+ 
+
+ align:start position:0%
+effects essentially if you do a lot of
+trading if you sell a lot of houses and
+
+ align:start position:0%
+trading if you sell a lot of houses and
+ 
+
+ align:start position:0%
+trading if you sell a lot of houses and
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+then you might still feel losses of
+
+ align:start position:0%
+then you might still feel losses of
+ 
+
+ align:start position:0%
+then you might still feel losses of
+losses and gains
+
+ align:start position:0%
+losses and gains
+ 
+
+ align:start position:0%
+losses and gains
+but you might sort of have a lot more
+
+ align:start position:0%
+but you might sort of have a lot more
+ 
+
+ align:start position:0%
+but you might sort of have a lot more
+experience with this you kind of know
+
+ align:start position:0%
+experience with this you kind of know
+ 
+
+ align:start position:0%
+experience with this you kind of know
+that this is happening sometimes
+
+ align:start position:0%
+that this is happening sometimes
+ 
+
+ align:start position:0%
+that this is happening sometimes
+and you might be less prone to these
+
+ align:start position:0%
+and you might be less prone to these
+ 
+
+ align:start position:0%
+and you might be less prone to these
+types of effects because you kind of
+
+ align:start position:0%
+types of effects because you kind of
+ 
+
+ align:start position:0%
+types of effects because you kind of
+know that you shouldn't be doing
+
+ align:start position:0%
+know that you shouldn't be doing
+ 
+
+ align:start position:0%
+know that you shouldn't be doing
+this you shouldn't sort of have your
+
+ align:start position:0%
+this you shouldn't sort of have your
+ 
+
+ align:start position:0%
+this you shouldn't sort of have your
+feelings of losses and gains
+
+ align:start position:0%
+feelings of losses and gains
+ 
+
+ align:start position:0%
+feelings of losses and gains
+get in the way of making profits so
+
+ align:start position:0%
+get in the way of making profits so
+ 
+
+ align:start position:0%
+get in the way of making profits so
+there's some people who would argue that
+
+ align:start position:0%
+there's some people who would argue that
+ 
+
+ align:start position:0%
+there's some people who would argue that
+this is very much consistent with like
+
+ align:start position:0%
+this is very much consistent with like
+ 
+
+ align:start position:0%
+this is very much consistent with like
+markets over time or exposures to
+
+ align:start position:0%
+markets over time or exposures to
+ 
+
+ align:start position:0%
+markets over time or exposures to
+markets and several predictions
+
+ align:start position:0%
+markets and several predictions
+ 
+
+ align:start position:0%
+markets and several predictions
+experience
+
+ align:start position:0%
+experience
+ 
+
+ align:start position:0%
+experience
+makes some of these effects go away and
+
+ align:start position:0%
+makes some of these effects go away and
+ 
+
+ align:start position:0%
+makes some of these effects go away and
+john list has some
+
+ align:start position:0%
+john list has some
+ 
+
+ align:start position:0%
+john list has some
+separate evidence on this on traders of
+
+ align:start position:0%
+separate evidence on this on traders of
+ 
+
+ align:start position:0%
+separate evidence on this on traders of
+cards and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now next we're going to talk a
+
+ align:start position:0%
+okay so now next we're going to talk a
+ 
+
+ align:start position:0%
+okay so now next we're going to talk a
+little bit about finance and stocks
+
+ align:start position:0%
+little bit about finance and stocks
+ 
+
+ align:start position:0%
+little bit about finance and stocks
+so interestingly yeah sorry on the
+
+ align:start position:0%
+so interestingly yeah sorry on the
+ 
+
+ align:start position:0%
+so interestingly yeah sorry on the
+previous um study why is this a
+
+ align:start position:0%
+previous um study why is this a
+ 
+
+ align:start position:0%
+previous um study why is this a
+reference dependence
+
+ align:start position:0%
+reference dependence
+ 
+
+ align:start position:0%
+reference dependence
+on information um owner and i
+
+ align:start position:0%
+on information um owner and i
+ 
+
+ align:start position:0%
+on information um owner and i
+think that my house is worth this amount
+
+ align:start position:0%
+think that my house is worth this amount
+ 
+
+ align:start position:0%
+think that my house is worth this amount
+and i'm just
+
+ align:start position:0%
+and i'm just
+ 
+
+ align:start position:0%
+and i'm just
+really anchored to believing that that's
+
+ align:start position:0%
+really anchored to believing that that's
+ 
+
+ align:start position:0%
+really anchored to believing that that's
+the problem
+
+ align:start position:0%
+the problem
+ 
+
+ align:start position:0%
+the problem
+right so one thing you could say is like
+
+ align:start position:0%
+right so one thing you could say is like
+ 
+
+ align:start position:0%
+right so one thing you could say is like
+that uh so what you always have to make
+
+ align:start position:0%
+that uh so what you always have to make
+ 
+
+ align:start position:0%
+that uh so what you always have to make
+the argument is like people who are
+
+ align:start position:0%
+the argument is like people who are
+ 
+
+ align:start position:0%
+the argument is like people who are
+losses compared to who are at gains so
+
+ align:start position:0%
+losses compared to who are at gains so
+ 
+
+ align:start position:0%
+losses compared to who are at gains so
+you look at your
+
+ align:start position:0%
+you look at your
+ 
+
+ align:start position:0%
+you look at your
+investor a and b they might have like
+
+ align:start position:0%
+investor a and b they might have like
+ 
+
+ align:start position:0%
+investor a and b they might have like
+additional information
+
+ align:start position:0%
+additional information
+ 
+
+ align:start position:0%
+additional information
+on uh how much the house is worth so it
+
+ align:start position:0%
+on uh how much the house is worth so it
+ 
+
+ align:start position:0%
+on uh how much the house is worth so it
+could be for example that seller a
+
+ align:start position:0%
+could be for example that seller a
+ 
+
+ align:start position:0%
+could be for example that seller a
+knows a lot about this house it's like
+
+ align:start position:0%
+knows a lot about this house it's like
+ 
+
+ align:start position:0%
+knows a lot about this house it's like
+very beautiful and so much light and
+
+ align:start position:0%
+very beautiful and so much light and
+ 
+
+ align:start position:0%
+very beautiful and so much light and
+this and that
+
+ align:start position:0%
+this and that
+ 
+
+ align:start position:0%
+this and that
+um and therefore they paid a lot
+
+ align:start position:0%
+um and therefore they paid a lot
+ 
+
+ align:start position:0%
+um and therefore they paid a lot
+therefore they have private information
+
+ align:start position:0%
+therefore they have private information
+ 
+
+ align:start position:0%
+therefore they have private information
+that it's worth a lot
+
+ align:start position:0%
+that it's worth a lot
+ 
+
+ align:start position:0%
+that it's worth a lot
+therefore they listed at a really high
+
+ align:start position:0%
+therefore they listed at a really high
+ 
+
+ align:start position:0%
+therefore they listed at a really high
+price so there's some specification here
+
+ align:start position:0%
+price so there's some specification here
+ 
+
+ align:start position:0%
+price so there's some specification here
+that look at this
+
+ align:start position:0%
+that look at this
+ 
+
+ align:start position:0%
+that look at this
+what you see is this is like columns two
+
+ align:start position:0%
+what you see is this is like columns two
+ 
+
+ align:start position:0%
+what you see is this is like columns two
+four and six
+
+ align:start position:0%
+four and six
+ 
+
+ align:start position:0%
+four and six
+which is uh the residual from the last
+
+ align:start position:0%
+which is uh the residual from the last
+ 
+
+ align:start position:0%
+which is uh the residual from the last
+sales price
+
+ align:start position:0%
+sales price
+ 
+
+ align:start position:0%
+sales price
+what is that that's essentially the
+
+ align:start position:0%
+what is that that's essentially the
+ 
+
+ align:start position:0%
+what is that that's essentially the
+difference between at the
+
+ align:start position:0%
+difference between at the
+ 
+
+ align:start position:0%
+difference between at the
+time when previously the house was sold
+
+ align:start position:0%
+time when previously the house was sold
+ 
+
+ align:start position:0%
+time when previously the house was sold
+what was the prediction of the market
+
+ align:start position:0%
+what was the prediction of the market
+ 
+
+ align:start position:0%
+what was the prediction of the market
+price then and how much was it sold so
+
+ align:start position:0%
+price then and how much was it sold so
+ 
+
+ align:start position:0%
+price then and how much was it sold so
+it's kind of like how much did you
+
+ align:start position:0%
+it's kind of like how much did you
+ 
+
+ align:start position:0%
+it's kind of like how much did you
+over uh uh how much did you overpay if
+
+ align:start position:0%
+over uh uh how much did you overpay if
+ 
+
+ align:start position:0%
+over uh uh how much did you overpay if
+you want relative to what we expected at
+
+ align:start position:0%
+you want relative to what we expected at
+ 
+
+ align:start position:0%
+you want relative to what we expected at
+the time
+
+ align:start position:0%
+the time
+ 
+
+ align:start position:0%
+the time
+presumably that's reflective again using
+
+ align:start position:0%
+presumably that's reflective again using
+ 
+
+ align:start position:0%
+presumably that's reflective again using
+the same prediction method
+
+ align:start position:0%
+the same prediction method
+ 
+
+ align:start position:0%
+the same prediction method
+so if you thought you know it's really
+
+ align:start position:0%
+so if you thought you know it's really
+ 
+
+ align:start position:0%
+so if you thought you know it's really
+beautiful and lots of windows and this
+
+ align:start position:0%
+beautiful and lots of windows and this
+ 
+
+ align:start position:0%
+beautiful and lots of windows and this
+and that lots of light and
+
+ align:start position:0%
+and that lots of light and
+ 
+
+ align:start position:0%
+and that lots of light and
+really quiet and so on if you overpaid
+
+ align:start position:0%
+really quiet and so on if you overpaid
+ 
+
+ align:start position:0%
+really quiet and so on if you overpaid
+at the time
+
+ align:start position:0%
+at the time
+ 
+
+ align:start position:0%
+at the time
+that should then sort of pre predictive
+
+ align:start position:0%
+that should then sort of pre predictive
+ 
+
+ align:start position:0%
+that should then sort of pre predictive
+of the listing price
+
+ align:start position:0%
+of the listing price
+ 
+
+ align:start position:0%
+of the listing price
+and sort of controlling for that then
+
+ align:start position:0%
+and sort of controlling for that then
+ 
+
+ align:start position:0%
+and sort of controlling for that then
+should make this go away
+
+ align:start position:0%
+should make this go away
+ 
+
+ align:start position:0%
+should make this go away
+what you see however is this is um
+
+ align:start position:0%
+what you see however is this is um
+ 
+
+ align:start position:0%
+what you see however is this is um
+there's some of that perhaps going on if
+
+ align:start position:0%
+there's some of that perhaps going on if
+ 
+
+ align:start position:0%
+there's some of that perhaps going on if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+compare for example columns one and two
+
+ align:start position:0%
+compare for example columns one and two
+ 
+
+ align:start position:0%
+compare for example columns one and two
+you see that the effects goes down a
+
+ align:start position:0%
+you see that the effects goes down a
+ 
+
+ align:start position:0%
+you see that the effects goes down a
+little bit but it's still there quite a
+
+ align:start position:0%
+little bit but it's still there quite a
+ 
+
+ align:start position:0%
+little bit but it's still there quite a
+bit what's this is why i was saying like
+
+ align:start position:0%
+bit what's this is why i was saying like
+ 
+
+ align:start position:0%
+bit what's this is why i was saying like
+25 to 35 percent
+
+ align:start position:0%
+25 to 35 percent
+ 
+
+ align:start position:0%
+25 to 35 percent
+uh that is exactly right that's a big
+
+ align:start position:0%
+uh that is exactly right that's a big
+ 
+
+ align:start position:0%
+uh that is exactly right that's a big
+concern and there's a bunch of sort of
+
+ align:start position:0%
+concern and there's a bunch of sort of
+ 
+
+ align:start position:0%
+concern and there's a bunch of sort of
+robustness et cetera checks in this
+
+ align:start position:0%
+robustness et cetera checks in this
+ 
+
+ align:start position:0%
+robustness et cetera checks in this
+specific study
+
+ align:start position:0%
+specific study
+ 
+
+ align:start position:0%
+specific study
+but that's exactly right there could be
+
+ align:start position:0%
+but that's exactly right there could be
+ 
+
+ align:start position:0%
+but that's exactly right there could be
+sort of unobservable information that
+
+ align:start position:0%
+sort of unobservable information that
+ 
+
+ align:start position:0%
+sort of unobservable information that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh owner might have about the house that
+
+ align:start position:0%
+uh owner might have about the house that
+ 
+
+ align:start position:0%
+uh owner might have about the house that
+is not in zillow or in any sort of
+
+ align:start position:0%
+is not in zillow or in any sort of
+ 
+
+ align:start position:0%
+is not in zillow or in any sort of
+return etc
+
+ align:start position:0%
+return etc
+ 
+
+ align:start position:0%
+return etc
+predictions that's available for the
+
+ align:start position:0%
+predictions that's available for the
+ 
+
+ align:start position:0%
+predictions that's available for the
+public that's a great question but i
+
+ align:start position:0%
+public that's a great question but i
+ 
+
+ align:start position:0%
+public that's a great question but i
+think it's
+
+ align:start position:0%
+think it's
+ 
+
+ align:start position:0%
+think it's
+uh to the extent that that takes care of
+
+ align:start position:0%
+uh to the extent that that takes care of
+ 
+
+ align:start position:0%
+uh to the extent that that takes care of
+it it's sort of uh the authors have
+
+ align:start position:0%
+it it's sort of uh the authors have
+ 
+
+ align:start position:0%
+it it's sort of uh the authors have
+thought about that uh yes um on the
+
+ align:start position:0%
+thought about that uh yes um on the
+ 
+
+ align:start position:0%
+thought about that uh yes um on the
+following slide
+
+ align:start position:0%
+following slide
+ 
+
+ align:start position:0%
+following slide
+when you talk about the differences
+
+ align:start position:0%
+when you talk about the differences
+ 
+
+ align:start position:0%
+when you talk about the differences
+it's how do you control for like the
+
+ align:start position:0%
+it's how do you control for like the
+ 
+
+ align:start position:0%
+it's how do you control for like the
+selection bias about the people that
+
+ align:start position:0%
+selection bias about the people that
+ 
+
+ align:start position:0%
+selection bias about the people that
+may be the ones repeatedly selling
+
+ align:start position:0%
+may be the ones repeatedly selling
+ 
+
+ align:start position:0%
+may be the ones repeatedly selling
+houses
+
+ align:start position:0%
+houses
+ 
+
+ align:start position:0%
+houses
+exhibit this last and therefore like
+
+ align:start position:0%
+exhibit this last and therefore like
+ 
+
+ align:start position:0%
+exhibit this last and therefore like
+stay in the market
+
+ align:start position:0%
+stay in the market
+ 
+
+ align:start position:0%
+stay in the market
+versus a change in those individuals
+
+ align:start position:0%
+versus a change in those individuals
+ 
+
+ align:start position:0%
+versus a change in those individuals
+behavior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's a great question so the
+
+ align:start position:0%
+right that's a great question so the
+ 
+
+ align:start position:0%
+right that's a great question so the
+question you're asking is essentially to
+
+ align:start position:0%
+question you're asking is essentially to
+ 
+
+ align:start position:0%
+question you're asking is essentially to
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+and that's in fact a great um sort of a
+
+ align:start position:0%
+and that's in fact a great um sort of a
+ 
+
+ align:start position:0%
+and that's in fact a great um sort of a
+segue into like behavioral finance which
+
+ align:start position:0%
+segue into like behavioral finance which
+ 
+
+ align:start position:0%
+segue into like behavioral finance which
+is to say suppose there's some people
+
+ align:start position:0%
+is to say suppose there's some people
+ 
+
+ align:start position:0%
+is to say suppose there's some people
+who are really sophisticated
+
+ align:start position:0%
+who are really sophisticated
+ 
+
+ align:start position:0%
+who are really sophisticated
+they don't have certain uh behavioral
+
+ align:start position:0%
+they don't have certain uh behavioral
+ 
+
+ align:start position:0%
+they don't have certain uh behavioral
+biases maybe they're not philosophers
+
+ align:start position:0%
+biases maybe they're not philosophers
+ 
+
+ align:start position:0%
+biases maybe they're not philosophers
+that makes you like a better investor
+
+ align:start position:0%
+that makes you like a better investor
+ 
+
+ align:start position:0%
+that makes you like a better investor
+say and therefore you stay in the market
+
+ align:start position:0%
+say and therefore you stay in the market
+ 
+
+ align:start position:0%
+say and therefore you stay in the market
+overall i think from this observation
+
+ align:start position:0%
+overall i think from this observation
+ 
+
+ align:start position:0%
+overall i think from this observation
+that i have here i cannot tell you is it
+
+ align:start position:0%
+that i have here i cannot tell you is it
+ 
+
+ align:start position:0%
+that i have here i cannot tell you is it
+like select is it just
+
+ align:start position:0%
+like select is it just
+ 
+
+ align:start position:0%
+like select is it just
+is it just that people um
+
+ align:start position:0%
+is it just that people um
+ 
+
+ align:start position:0%
+is it just that people um
+is it experience or is it selection so
+
+ align:start position:0%
+is it experience or is it selection so
+ 
+
+ align:start position:0%
+is it experience or is it selection so
+the question kind of is
+
+ align:start position:0%
+the question kind of is
+ 
+
+ align:start position:0%
+the question kind of is
+when people are investors
+
+ align:start position:0%
+when people are investors
+ 
+
+ align:start position:0%
+when people are investors
+do they do the effects of reference
+
+ align:start position:0%
+do they do the effects of reference
+ 
+
+ align:start position:0%
+do they do the effects of reference
+dependence of gains and losses go over
+
+ align:start position:0%
+dependence of gains and losses go over
+ 
+
+ align:start position:0%
+dependence of gains and losses go over
+go away over time essentially like maybe
+
+ align:start position:0%
+go away over time essentially like maybe
+ 
+
+ align:start position:0%
+go away over time essentially like maybe
+the first second third time i feel like
+
+ align:start position:0%
+the first second third time i feel like
+ 
+
+ align:start position:0%
+the first second third time i feel like
+really a loss in terms of making a
+
+ align:start position:0%
+really a loss in terms of making a
+ 
+
+ align:start position:0%
+really a loss in terms of making a
+bad investment but in number house
+
+ align:start position:0%
+bad investment but in number house
+ 
+
+ align:start position:0%
+bad investment but in number house
+number 20 i'm just like that's like as
+
+ align:start position:0%
+number 20 i'm just like that's like as
+ 
+
+ align:start position:0%
+number 20 i'm just like that's like as
+usual and i shouldn't
+
+ align:start position:0%
+usual and i shouldn't
+ 
+
+ align:start position:0%
+usual and i shouldn't
+really care very much is it that this
+
+ align:start position:0%
+really care very much is it that this
+ 
+
+ align:start position:0%
+really care very much is it that this
+goes away or is it that like the people
+
+ align:start position:0%
+goes away or is it that like the people
+ 
+
+ align:start position:0%
+goes away or is it that like the people
+who are particularly lost a verse and
+
+ align:start position:0%
+who are particularly lost a verse and
+ 
+
+ align:start position:0%
+who are particularly lost a verse and
+sort of essentially
+
+ align:start position:0%
+sort of essentially
+ 
+
+ align:start position:0%
+sort of essentially
+uh engage in this type of behavior in
+
+ align:start position:0%
+uh engage in this type of behavior in
+ 
+
+ align:start position:0%
+uh engage in this type of behavior in
+terms of like uh
+
+ align:start position:0%
+terms of like uh
+ 
+
+ align:start position:0%
+terms of like uh
+over uh listing too high of a price um
+
+ align:start position:0%
+over uh listing too high of a price um
+ 
+
+ align:start position:0%
+over uh listing too high of a price um
+for losses
+
+ align:start position:0%
+for losses
+ 
+
+ align:start position:0%
+for losses
+these are sort of like that investor in
+
+ align:start position:0%
+these are sort of like that investor in
+ 
+
+ align:start position:0%
+these are sort of like that investor in
+the housing markets and they sort of
+
+ align:start position:0%
+the housing markets and they sort of
+ 
+
+ align:start position:0%
+the housing markets and they sort of
+are essentially driven out of the market
+
+ align:start position:0%
+are essentially driven out of the market
+ 
+
+ align:start position:0%
+are essentially driven out of the market
+so that specific setting um i don't
+
+ align:start position:0%
+so that specific setting um i don't
+ 
+
+ align:start position:0%
+so that specific setting um i don't
+think we can necessarily
+
+ align:start position:0%
+think we can necessarily
+ 
+
+ align:start position:0%
+think we can necessarily
+account for that i think in the uh
+
+ align:start position:0%
+account for that i think in the uh
+ 
+
+ align:start position:0%
+account for that i think in the uh
+studies by john list it's very much
+
+ align:start position:0%
+studies by john list it's very much
+ 
+
+ align:start position:0%
+studies by john list it's very much
+people argue it's about
+
+ align:start position:0%
+people argue it's about
+ 
+
+ align:start position:0%
+people argue it's about
+experience but again there could also
+
+ align:start position:0%
+experience but again there could also
+ 
+
+ align:start position:0%
+experience but again there could also
+some part could also be a
+
+ align:start position:0%
+some part could also be a
+ 
+
+ align:start position:0%
+some part could also be a
+selection i think so now in the
+
+ align:start position:0%
+selection i think so now in the
+ 
+
+ align:start position:0%
+selection i think so now in the
+so i think in some sense either way
+
+ align:start position:0%
+so i think in some sense either way
+ 
+
+ align:start position:0%
+so i think in some sense either way
+um uh uh i think the the evidence that
+
+ align:start position:0%
+um uh uh i think the the evidence that
+ 
+
+ align:start position:0%
+um uh uh i think the the evidence that
+the investors are doing this behavior
+
+ align:start position:0%
+the investors are doing this behavior
+ 
+
+ align:start position:0%
+the investors are doing this behavior
+last sort of tells us something about
+
+ align:start position:0%
+last sort of tells us something about
+ 
+
+ align:start position:0%
+last sort of tells us something about
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this is probably not at least
+
+ align:start position:0%
+this is probably not at least
+ 
+
+ align:start position:0%
+this is probably not at least
+financially optimal
+
+ align:start position:0%
+financially optimal
+ 
+
+ align:start position:0%
+financially optimal
+for you to engage in this type of
+
+ align:start position:0%
+for you to engage in this type of
+ 
+
+ align:start position:0%
+for you to engage in this type of
+behavior it might be privately optimal
+
+ align:start position:0%
+behavior it might be privately optimal
+ 
+
+ align:start position:0%
+behavior it might be privately optimal
+in some sense if you really feel bad at
+
+ align:start position:0%
+in some sense if you really feel bad at
+ 
+
+ align:start position:0%
+in some sense if you really feel bad at
+like selling your house at a loss you
+
+ align:start position:0%
+like selling your house at a loss you
+ 
+
+ align:start position:0%
+like selling your house at a loss you
+should probably
+
+ align:start position:0%
+should probably
+ 
+
+ align:start position:0%
+should probably
+list it at a higher price because that
+
+ align:start position:0%
+list it at a higher price because that
+ 
+
+ align:start position:0%
+list it at a higher price because that
+sort of limits you your losses
+
+ align:start position:0%
+sort of limits you your losses
+ 
+
+ align:start position:0%
+sort of limits you your losses
+that's just what the utility function
+
+ align:start position:0%
+that's just what the utility function
+ 
+
+ align:start position:0%
+that's just what the utility function
+looks like it's not necessarily a
+
+ align:start position:0%
+looks like it's not necessarily a
+ 
+
+ align:start position:0%
+looks like it's not necessarily a
+and the sub-optimal in the sense of like
+
+ align:start position:0%
+and the sub-optimal in the sense of like
+ 
+
+ align:start position:0%
+and the sub-optimal in the sense of like
+uh how you feel afterwards
+
+ align:start position:0%
+uh how you feel afterwards
+ 
+
+ align:start position:0%
+uh how you feel afterwards
+it might be sub-optimal in terms of like
+
+ align:start position:0%
+it might be sub-optimal in terms of like
+ 
+
+ align:start position:0%
+it might be sub-optimal in terms of like
+how much money you make or how much
+
+ align:start position:0%
+how much money you make or how much
+ 
+
+ align:start position:0%
+how much money you make or how much
+money you have eventually
+
+ align:start position:0%
+money you have eventually
+ 
+
+ align:start position:0%
+money you have eventually
+uh on how much you pay for keeping your
+
+ align:start position:0%
+uh on how much you pay for keeping your
+ 
+
+ align:start position:0%
+uh on how much you pay for keeping your
+house on the market and so on
+
+ align:start position:0%
+house on the market and so on
+ 
+
+ align:start position:0%
+house on the market and so on
+for an extended period of time um okay
+
+ align:start position:0%
+for an extended period of time um okay
+ 
+
+ align:start position:0%
+for an extended period of time um okay
+so does that answer your question no
+
+ align:start position:0%
+so does that answer your question no
+ 
+
+ align:start position:0%
+so does that answer your question no
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+so um so behavioral finance is an
+
+ align:start position:0%
+so um so behavioral finance is an
+ 
+
+ align:start position:0%
+so um so behavioral finance is an
+interesting field because
+
+ align:start position:0%
+interesting field because
+ 
+
+ align:start position:0%
+interesting field because
+for quite a while economists thought
+
+ align:start position:0%
+for quite a while economists thought
+ 
+
+ align:start position:0%
+for quite a while economists thought
+that sort of neoclassical assumptions
+
+ align:start position:0%
+that sort of neoclassical assumptions
+ 
+
+ align:start position:0%
+that sort of neoclassical assumptions
+are in fact most likely to hold in
+
+ align:start position:0%
+are in fact most likely to hold in
+ 
+
+ align:start position:0%
+are in fact most likely to hold in
+financial markets and why is that
+
+ align:start position:0%
+financial markets and why is that
+ 
+
+ align:start position:0%
+financial markets and why is that
+why do we think what and some of this
+
+ align:start position:0%
+why do we think what and some of this
+ 
+
+ align:start position:0%
+why do we think what and some of this
+already i mentioned but
+
+ align:start position:0%
+already i mentioned but
+ 
+
+ align:start position:0%
+already i mentioned but
+why are financial markets
+
+ align:start position:0%
+why are financial markets
+ 
+
+ align:start position:0%
+why are financial markets
+particular why might i think that
+
+ align:start position:0%
+particular why might i think that
+ 
+
+ align:start position:0%
+particular why might i think that
+financial markets are particularly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+efficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes well you might think that financial
+
+ align:start position:0%
+yes well you might think that financial
+ 
+
+ align:start position:0%
+yes well you might think that financial
+markets are very competitive
+
+ align:start position:0%
+markets are very competitive
+ 
+
+ align:start position:0%
+markets are very competitive
+and so it's actually the ones who can
+
+ align:start position:0%
+and so it's actually the ones who can
+ 
+
+ align:start position:0%
+and so it's actually the ones who can
+get rid of their behavioral biases that
+
+ align:start position:0%
+get rid of their behavioral biases that
+ 
+
+ align:start position:0%
+get rid of their behavioral biases that
+benefit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly so it's very much like sort of
+
+ align:start position:0%
+exactly so it's very much like sort of
+ 
+
+ align:start position:0%
+exactly so it's very much like sort of
+the chicago
+
+ align:start position:0%
+the chicago
+ 
+
+ align:start position:0%
+the chicago
+economics assumption is to say so uh
+
+ align:start position:0%
+economics assumption is to say so uh
+ 
+
+ align:start position:0%
+economics assumption is to say so uh
+financial markets are extremely
+
+ align:start position:0%
+financial markets are extremely
+ 
+
+ align:start position:0%
+financial markets are extremely
+competitive if now i'm an investor
+
+ align:start position:0%
+competitive if now i'm an investor
+ 
+
+ align:start position:0%
+competitive if now i'm an investor
+who has various behavioral biases
+
+ align:start position:0%
+who has various behavioral biases
+ 
+
+ align:start position:0%
+who has various behavioral biases
+presumably i'm going to lose some money
+
+ align:start position:0%
+presumably i'm going to lose some money
+ 
+
+ align:start position:0%
+presumably i'm going to lose some money
+one way or the other
+
+ align:start position:0%
+one way or the other
+ 
+
+ align:start position:0%
+one way or the other
+well if markets are really competitive
+
+ align:start position:0%
+well if markets are really competitive
+ 
+
+ align:start position:0%
+well if markets are really competitive
+in the long run i cannot stay in this
+
+ align:start position:0%
+in the long run i cannot stay in this
+ 
+
+ align:start position:0%
+in the long run i cannot stay in this
+market without sort of being
+
+ align:start position:0%
+market without sort of being
+ 
+
+ align:start position:0%
+market without sort of being
+a driven out so essentially the market
+
+ align:start position:0%
+a driven out so essentially the market
+ 
+
+ align:start position:0%
+a driven out so essentially the market
+favor sort of
+
+ align:start position:0%
+favor sort of
+ 
+
+ align:start position:0%
+favor sort of
+results oriented rational and selfish
+
+ align:start position:0%
+results oriented rational and selfish
+ 
+
+ align:start position:0%
+results oriented rational and selfish
+behavior so people are not rational and
+
+ align:start position:0%
+behavior so people are not rational and
+ 
+
+ align:start position:0%
+behavior so people are not rational and
+so on and so forth will be eliminated
+
+ align:start position:0%
+so on and so forth will be eliminated
+ 
+
+ align:start position:0%
+so on and so forth will be eliminated
+from the market
+
+ align:start position:0%
+from the market
+ 
+
+ align:start position:0%
+from the market
+eventually there's two parts to that
+
+ align:start position:0%
+eventually there's two parts to that
+ 
+
+ align:start position:0%
+eventually there's two parts to that
+that's true like across firms that's to
+
+ align:start position:0%
+that's true like across firms that's to
+ 
+
+ align:start position:0%
+that's true like across firms that's to
+say like you know there's some firms
+
+ align:start position:0%
+say like you know there's some firms
+ 
+
+ align:start position:0%
+say like you know there's some firms
+that are better than others
+
+ align:start position:0%
+that are better than others
+ 
+
+ align:start position:0%
+that are better than others
+but also within the firm if i'm an
+
+ align:start position:0%
+but also within the firm if i'm an
+ 
+
+ align:start position:0%
+but also within the firm if i'm an
+investor and i'm sort of like um
+
+ align:start position:0%
+investor and i'm sort of like um
+ 
+
+ align:start position:0%
+investor and i'm sort of like um
+advising clients and the like and i'm
+
+ align:start position:0%
+advising clients and the like and i'm
+ 
+
+ align:start position:0%
+advising clients and the like and i'm
+sort of not very good at this and like
+
+ align:start position:0%
+sort of not very good at this and like
+ 
+
+ align:start position:0%
+sort of not very good at this and like
+essentially i have certain payable
+
+ align:start position:0%
+essentially i have certain payable
+ 
+
+ align:start position:0%
+essentially i have certain payable
+biases that are not optimal in terms of
+
+ align:start position:0%
+biases that are not optimal in terms of
+ 
+
+ align:start position:0%
+biases that are not optimal in terms of
+like making
+
+ align:start position:0%
+like making
+ 
+
+ align:start position:0%
+like making
+money for people presumably i will not
+
+ align:start position:0%
+money for people presumably i will not
+ 
+
+ align:start position:0%
+money for people presumably i will not
+be promoted presumably i will be driven
+
+ align:start position:0%
+be promoted presumably i will be driven
+ 
+
+ align:start position:0%
+be promoted presumably i will be driven
+out of force fired from the
+
+ align:start position:0%
+out of force fired from the
+ 
+
+ align:start position:0%
+out of force fired from the
+the company um eventually so
+
+ align:start position:0%
+the company um eventually so
+ 
+
+ align:start position:0%
+the company um eventually so
+surprisingly in fact
+
+ align:start position:0%
+surprisingly in fact
+ 
+
+ align:start position:0%
+surprisingly in fact
+finance became one of the most
+
+ align:start position:0%
+finance became one of the most
+ 
+
+ align:start position:0%
+finance became one of the most
+influential and most fruitful
+
+ align:start position:0%
+influential and most fruitful
+ 
+
+ align:start position:0%
+influential and most fruitful
+applications of be able
+
+ align:start position:0%
+applications of be able
+ 
+
+ align:start position:0%
+applications of be able
+of the psychology and economics so
+
+ align:start position:0%
+of the psychology and economics so
+ 
+
+ align:start position:0%
+of the psychology and economics so
+behavioral economics there's lots and
+
+ align:start position:0%
+behavioral economics there's lots and
+ 
+
+ align:start position:0%
+behavioral economics there's lots and
+lots of work in behavioral finance
+
+ align:start position:0%
+lots of work in behavioral finance
+ 
+
+ align:start position:0%
+lots of work in behavioral finance
+the reason being perhaps not necessarily
+
+ align:start position:0%
+the reason being perhaps not necessarily
+ 
+
+ align:start position:0%
+the reason being perhaps not necessarily
+because people are um so some people are
+
+ align:start position:0%
+because people are um so some people are
+ 
+
+ align:start position:0%
+because people are um so some people are
+presumably driven out of the market but
+
+ align:start position:0%
+presumably driven out of the market but
+ 
+
+ align:start position:0%
+presumably driven out of the market but
+surely not everyone
+
+ align:start position:0%
+surely not everyone
+ 
+
+ align:start position:0%
+surely not everyone
+but in particular because there's like
+
+ align:start position:0%
+but in particular because there's like
+ 
+
+ align:start position:0%
+but in particular because there's like
+great data in finance like there's lots
+
+ align:start position:0%
+great data in finance like there's lots
+ 
+
+ align:start position:0%
+great data in finance like there's lots
+and lots of daily data in terms of like
+
+ align:start position:0%
+and lots of daily data in terms of like
+ 
+
+ align:start position:0%
+and lots of daily data in terms of like
+things that you should be doing compared
+
+ align:start position:0%
+things that you should be doing compared
+ 
+
+ align:start position:0%
+things that you should be doing compared
+to like what models would say
+
+ align:start position:0%
+to like what models would say
+ 
+
+ align:start position:0%
+to like what models would say
+so it's a really great way of like being
+
+ align:start position:0%
+so it's a really great way of like being
+ 
+
+ align:start position:0%
+so it's a really great way of like being
+able to test models or test essentially
+
+ align:start position:0%
+able to test models or test essentially
+ 
+
+ align:start position:0%
+able to test models or test essentially
+predictions of the neoclassical model or
+
+ align:start position:0%
+predictions of the neoclassical model or
+ 
+
+ align:start position:0%
+predictions of the neoclassical model or
+behavioral theories and so on
+
+ align:start position:0%
+behavioral theories and so on
+ 
+
+ align:start position:0%
+behavioral theories and so on
+so that's why behavioral finance has
+
+ align:start position:0%
+so that's why behavioral finance has
+ 
+
+ align:start position:0%
+so that's why behavioral finance has
+been very influential
+
+ align:start position:0%
+been very influential
+ 
+
+ align:start position:0%
+been very influential
+because there's so much data available
+
+ align:start position:0%
+because there's so much data available
+ 
+
+ align:start position:0%
+because there's so much data available
+for people to in fact
+
+ align:start position:0%
+for people to in fact
+ 
+
+ align:start position:0%
+for people to in fact
+test theories and then you know why is
+
+ align:start position:0%
+test theories and then you know why is
+ 
+
+ align:start position:0%
+test theories and then you know why is
+it that people are not entirely driven
+
+ align:start position:0%
+it that people are not entirely driven
+ 
+
+ align:start position:0%
+it that people are not entirely driven
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+i think often the case is that even if
+
+ align:start position:0%
+i think often the case is that even if
+ 
+
+ align:start position:0%
+i think often the case is that even if
+you're right for example even if you
+
+ align:start position:0%
+you're right for example even if you
+ 
+
+ align:start position:0%
+you're right for example even if you
+write that you can
+
+ align:start position:0%
+write that you can
+ 
+
+ align:start position:0%
+write that you can
+predict and if you watch some like um
+
+ align:start position:0%
+predict and if you watch some like um
+ 
+
+ align:start position:0%
+predict and if you watch some like um
+movies on the financial crisis and so on
+
+ align:start position:0%
+movies on the financial crisis and so on
+ 
+
+ align:start position:0%
+movies on the financial crisis and so on
+even if you're
+
+ align:start position:0%
+even if you're
+ 
+
+ align:start position:0%
+even if you're
+right about like in the long run the
+
+ align:start position:0%
+right about like in the long run the
+ 
+
+ align:start position:0%
+right about like in the long run the
+market is going to tank well actually
+
+ align:start position:0%
+market is going to tank well actually
+ 
+
+ align:start position:0%
+market is going to tank well actually
+it's going to take you a lot of money
+
+ align:start position:0%
+it's going to take you a lot of money
+ 
+
+ align:start position:0%
+it's going to take you a lot of money
+and then you know often you know if
+
+ align:start position:0%
+and then you know often you know if
+ 
+
+ align:start position:0%
+and then you know often you know if
+everybody is wrong
+
+ align:start position:0%
+everybody is wrong
+ 
+
+ align:start position:0%
+everybody is wrong
+prices will go up for quite a while so
+
+ align:start position:0%
+prices will go up for quite a while so
+ 
+
+ align:start position:0%
+prices will go up for quite a while so
+it's not actually clear that in the
+
+ align:start position:0%
+it's not actually clear that in the
+ 
+
+ align:start position:0%
+it's not actually clear that in the
+at least in the short medium run we'll
+
+ align:start position:0%
+at least in the short medium run we'll
+ 
+
+ align:start position:0%
+at least in the short medium run we'll
+be driven out of the market um
+
+ align:start position:0%
+be driven out of the market um
+ 
+
+ align:start position:0%
+be driven out of the market um
+uh uh quickly but that's sort of a
+
+ align:start position:0%
+uh uh quickly but that's sort of a
+ 
+
+ align:start position:0%
+uh uh quickly but that's sort of a
+separate topic
+
+ align:start position:0%
+separate topic
+ 
+
+ align:start position:0%
+separate topic
+okay so now um one uh a reason why or
+
+ align:start position:0%
+okay so now um one uh a reason why or
+ 
+
+ align:start position:0%
+okay so now um one uh a reason why or
+one way in which reference dependent
+
+ align:start position:0%
+one way in which reference dependent
+ 
+
+ align:start position:0%
+one way in which reference dependent
+behavior might be important in finance
+
+ align:start position:0%
+behavior might be important in finance
+ 
+
+ align:start position:0%
+behavior might be important in finance
+is uh people might be differentially
+
+ align:start position:0%
+is uh people might be differentially
+ 
+
+ align:start position:0%
+is uh people might be differentially
+likely to sell winners and hold on to
+
+ align:start position:0%
+likely to sell winners and hold on to
+ 
+
+ align:start position:0%
+likely to sell winners and hold on to
+losers
+
+ align:start position:0%
+losers
+ 
+
+ align:start position:0%
+losers
+uh financial stocks that was mentioned
+
+ align:start position:0%
+uh financial stocks that was mentioned
+ 
+
+ align:start position:0%
+uh financial stocks that was mentioned
+last time as well
+
+ align:start position:0%
+last time as well
+ 
+
+ align:start position:0%
+last time as well
+so what terry odin did in 1997 is like
+
+ align:start position:0%
+so what terry odin did in 1997 is like
+ 
+
+ align:start position:0%
+so what terry odin did in 1997 is like
+he had in fact
+
+ align:start position:0%
+he had in fact
+ 
+
+ align:start position:0%
+he had in fact
+a brokerage accounts from a national
+
+ align:start position:0%
+a brokerage accounts from a national
+ 
+
+ align:start position:0%
+a brokerage accounts from a national
+weight uh a brokerage house
+
+ align:start position:0%
+weight uh a brokerage house
+ 
+
+ align:start position:0%
+weight uh a brokerage house
+which had all trades and prices for i
+
+ align:start position:0%
+which had all trades and prices for i
+ 
+
+ align:start position:0%
+which had all trades and prices for i
+guess 87 to 93.
+
+ align:start position:0%
+guess 87 to 93.
+ 
+
+ align:start position:0%
+guess 87 to 93.
+in some sense a little bit like
+
+ align:start position:0%
+in some sense a little bit like
+ 
+
+ align:start position:0%
+in some sense a little bit like
+old-fashioned a sense of like you
+
+ align:start position:0%
+old-fashioned a sense of like you
+ 
+
+ align:start position:0%
+old-fashioned a sense of like you
+shouldn't be like in
+
+ align:start position:0%
+shouldn't be like in
+ 
+
+ align:start position:0%
+shouldn't be like in
+individual trading and so on you should
+
+ align:start position:0%
+individual trading and so on you should
+ 
+
+ align:start position:0%
+individual trading and so on you should
+just hold the stock market or the s p
+
+ align:start position:0%
+just hold the stock market or the s p
+ 
+
+ align:start position:0%
+just hold the stock market or the s p
+500 or some index funds and so on
+
+ align:start position:0%
+500 or some index funds and so on
+ 
+
+ align:start position:0%
+500 or some index funds and so on
+here these are people have like hold
+
+ align:start position:0%
+here these are people have like hold
+ 
+
+ align:start position:0%
+here these are people have like hold
+individual stocks and sell and buy them
+
+ align:start position:0%
+individual stocks and sell and buy them
+ 
+
+ align:start position:0%
+individual stocks and sell and buy them
+uh one by one and so during each trading
+
+ align:start position:0%
+uh one by one and so during each trading
+ 
+
+ align:start position:0%
+uh one by one and so during each trading
+day then what our dean can do is he can
+
+ align:start position:0%
+day then what our dean can do is he can
+ 
+
+ align:start position:0%
+day then what our dean can do is he can
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+evaluate each stock in the portfolio and
+
+ align:start position:0%
+evaluate each stock in the portfolio and
+ 
+
+ align:start position:0%
+evaluate each stock in the portfolio and
+look at this as a loss relative to a
+
+ align:start position:0%
+look at this as a loss relative to a
+ 
+
+ align:start position:0%
+look at this as a loss relative to a
+purchase
+
+ align:start position:0%
+purchase
+ 
+
+ align:start position:0%
+purchase
+uh relative to the purchase price so you
+
+ align:start position:0%
+uh relative to the purchase price so you
+ 
+
+ align:start position:0%
+uh relative to the purchase price so you
+can look at essentially
+
+ align:start position:0%
+can look at essentially
+ 
+
+ align:start position:0%
+can look at essentially
+the portfolio and say there's losers and
+
+ align:start position:0%
+the portfolio and say there's losers and
+ 
+
+ align:start position:0%
+the portfolio and say there's losers and
+winners
+
+ align:start position:0%
+winners
+ 
+
+ align:start position:0%
+winners
+he only has like data on trading day so
+
+ align:start position:0%
+he only has like data on trading day so
+ 
+
+ align:start position:0%
+he only has like data on trading day so
+you can look at like you know
+
+ align:start position:0%
+you can look at like you know
+ 
+
+ align:start position:0%
+you can look at like you know
+other losers and uh winners when they're
+
+ align:start position:0%
+other losers and uh winners when they're
+ 
+
+ align:start position:0%
+other losers and uh winners when they're
+being sold
+
+ align:start position:0%
+being sold
+ 
+
+ align:start position:0%
+being sold
+and um he can look at the net realized
+
+ align:start position:0%
+and um he can look at the net realized
+ 
+
+ align:start position:0%
+and um he can look at the net realized
+uh gains and realized losses
+
+ align:start position:0%
+uh gains and realized losses
+ 
+
+ align:start position:0%
+uh gains and realized losses
+so if you sell a stock and it's like
+
+ align:start position:0%
+so if you sell a stock and it's like
+ 
+
+ align:start position:0%
+so if you sell a stock and it's like
+essentially above the purchase price he
+
+ align:start position:0%
+essentially above the purchase price he
+ 
+
+ align:start position:0%
+essentially above the purchase price he
+calls it the realized um
+
+ align:start position:0%
+calls it the realized um
+ 
+
+ align:start position:0%
+calls it the realized um
+uh again loss and if it's um sorry if
+
+ align:start position:0%
+uh again loss and if it's um sorry if
+ 
+
+ align:start position:0%
+uh again loss and if it's um sorry if
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+if it's a losing stock it's old it's a
+
+ align:start position:0%
+if it's a losing stock it's old it's a
+ 
+
+ align:start position:0%
+if it's a losing stock it's old it's a
+realized loss it's below the purchase
+
+ align:start position:0%
+realized loss it's below the purchase
+ 
+
+ align:start position:0%
+realized loss it's below the purchase
+price
+
+ align:start position:0%
+price
+ 
+
+ align:start position:0%
+price
+if it's above the purchase price it's
+
+ align:start position:0%
+if it's above the purchase price it's
+ 
+
+ align:start position:0%
+if it's above the purchase price it's
+going to be a realized gain
+
+ align:start position:0%
+going to be a realized gain
+ 
+
+ align:start position:0%
+going to be a realized gain
+now one thing you could do is like
+
+ align:start position:0%
+now one thing you could do is like
+ 
+
+ align:start position:0%
+now one thing you could do is like
+compare the number of realized losses to
+
+ align:start position:0%
+compare the number of realized losses to
+ 
+
+ align:start position:0%
+compare the number of realized losses to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+number of realized gains does that work
+
+ align:start position:0%
+number of realized gains does that work
+ 
+
+ align:start position:0%
+number of realized gains does that work
+or is that reference dependence or what
+
+ align:start position:0%
+or is that reference dependence or what
+ 
+
+ align:start position:0%
+or is that reference dependence or what
+do we what do we learn from that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so i could look at like the
+
+ align:start position:0%
+right so i could look at like the
+ 
+
+ align:start position:0%
+right so i could look at like the
+realized gains and the number of
+
+ align:start position:0%
+realized gains and the number of
+ 
+
+ align:start position:0%
+realized gains and the number of
+realized gains and the number of
+
+ align:start position:0%
+realized gains and the number of
+ 
+
+ align:start position:0%
+realized gains and the number of
+realized losses
+
+ align:start position:0%
+realized losses
+ 
+
+ align:start position:0%
+realized losses
+but what's the problem with that i think
+
+ align:start position:0%
+but what's the problem with that i think
+ 
+
+ align:start position:0%
+but what's the problem with that i think
+that's exactly right but like what's the
+
+ align:start position:0%
+that's exactly right but like what's the
+ 
+
+ align:start position:0%
+that's exactly right but like what's the
+underlying what's the problem with this
+
+ align:start position:0%
+underlying what's the problem with this
+ 
+
+ align:start position:0%
+underlying what's the problem with this
+approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like how does this depend on the stock
+
+ align:start position:0%
+like how does this depend on the stock
+ 
+
+ align:start position:0%
+like how does this depend on the stock
+market going up and down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so that's a separate issue like you
+
+ align:start position:0%
+yeah so that's a separate issue like you
+ 
+
+ align:start position:0%
+yeah so that's a separate issue like you
+could look at the magnitudes
+
+ align:start position:0%
+could look at the magnitudes
+ 
+
+ align:start position:0%
+could look at the magnitudes
+themselves and you look at sort of like
+
+ align:start position:0%
+themselves and you look at sort of like
+ 
+
+ align:start position:0%
+themselves and you look at sort of like
+depending on where you are
+
+ align:start position:0%
+depending on where you are
+ 
+
+ align:start position:0%
+depending on where you are
+how does that matter but what about just
+
+ align:start position:0%
+how does that matter but what about just
+ 
+
+ align:start position:0%
+how does that matter but what about just
+a number of gains and losses
+
+ align:start position:0%
+a number of gains and losses
+ 
+
+ align:start position:0%
+a number of gains and losses
+like what if the stock market goes up a
+
+ align:start position:0%
+like what if the stock market goes up a
+ 
+
+ align:start position:0%
+like what if the stock market goes up a
+lot what are people going to
+
+ align:start position:0%
+lot what are people going to
+ 
+
+ align:start position:0%
+lot what are people going to
+sell or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so he does have that i think that
+
+ align:start position:0%
+right so he does have that i think that
+ 
+
+ align:start position:0%
+right so he does have that i think that
+i'm asking for something very
+
+ align:start position:0%
+i'm asking for something very
+ 
+
+ align:start position:0%
+i'm asking for something very
+basic which is if the stock market goes
+
+ align:start position:0%
+basic which is if the stock market goes
+ 
+
+ align:start position:0%
+basic which is if the stock market goes
+up a lot you'll have lots of winners so
+
+ align:start position:0%
+up a lot you'll have lots of winners so
+ 
+
+ align:start position:0%
+up a lot you'll have lots of winners so
+you're going to realize lots of
+
+ align:start position:0%
+you're going to realize lots of
+ 
+
+ align:start position:0%
+you're going to realize lots of
+if you just sell randomly stocks gains
+
+ align:start position:0%
+if you just sell randomly stocks gains
+ 
+
+ align:start position:0%
+if you just sell randomly stocks gains
+and losses and you just don't care
+
+ align:start position:0%
+and losses and you just don't care
+ 
+
+ align:start position:0%
+and losses and you just don't care
+you'll have much more realized gains um
+
+ align:start position:0%
+you'll have much more realized gains um
+ 
+
+ align:start position:0%
+you'll have much more realized gains um
+compared to realized losses just because
+
+ align:start position:0%
+compared to realized losses just because
+ 
+
+ align:start position:0%
+compared to realized losses just because
+your stock market went up a lot
+
+ align:start position:0%
+your stock market went up a lot
+ 
+
+ align:start position:0%
+your stock market went up a lot
+similarly if the stock market went down
+
+ align:start position:0%
+similarly if the stock market went down
+ 
+
+ align:start position:0%
+similarly if the stock market went down
+you will find that people have way more
+
+ align:start position:0%
+you will find that people have way more
+ 
+
+ align:start position:0%
+you will find that people have way more
+realized losses compared to realized
+
+ align:start position:0%
+realized losses compared to realized
+ 
+
+ align:start position:0%
+realized losses compared to realized
+gains and it looked like i'm really
+
+ align:start position:0%
+gains and it looked like i'm really
+ 
+
+ align:start position:0%
+gains and it looked like i'm really
+trying to sell the losers but it's not
+
+ align:start position:0%
+trying to sell the losers but it's not
+ 
+
+ align:start position:0%
+trying to sell the losers but it's not
+i'm actually selling to losers you just
+
+ align:start position:0%
+i'm actually selling to losers you just
+ 
+
+ align:start position:0%
+i'm actually selling to losers you just
+have a lot more
+
+ align:start position:0%
+have a lot more
+ 
+
+ align:start position:0%
+have a lot more
+losers that's all i was asking i think
+
+ align:start position:0%
+losers that's all i was asking i think
+ 
+
+ align:start position:0%
+losers that's all i was asking i think
+he has actually the information about
+
+ align:start position:0%
+he has actually the information about
+ 
+
+ align:start position:0%
+he has actually the information about
+the purchase prices
+
+ align:start position:0%
+the purchase prices
+ 
+
+ align:start position:0%
+the purchase prices
+so what he then does is something very
+
+ align:start position:0%
+so what he then does is something very
+ 
+
+ align:start position:0%
+so what he then does is something very
+simple it just looks at people's
+
+ align:start position:0%
+simple it just looks at people's
+ 
+
+ align:start position:0%
+simple it just looks at people's
+portfolios and says like how many losing
+
+ align:start position:0%
+portfolios and says like how many losing
+ 
+
+ align:start position:0%
+portfolios and says like how many losing
+stocks do you have
+
+ align:start position:0%
+stocks do you have
+ 
+
+ align:start position:0%
+stocks do you have
+what's your propensity to sell the
+
+ align:start position:0%
+what's your propensity to sell the
+ 
+
+ align:start position:0%
+what's your propensity to sell the
+losing stocks which is what he calls the
+
+ align:start position:0%
+losing stocks which is what he calls the
+ 
+
+ align:start position:0%
+losing stocks which is what he calls the
+plr
+
+ align:start position:0%
+plr
+ 
+
+ align:start position:0%
+plr
+the propensity proportion of losers
+
+ align:start position:0%
+the propensity proportion of losers
+ 
+
+ align:start position:0%
+the propensity proportion of losers
+realized the same he does for the pgr
+
+ align:start position:0%
+realized the same he does for the pgr
+ 
+
+ align:start position:0%
+realized the same he does for the pgr
+which is the poor proportion of gains
+
+ align:start position:0%
+which is the poor proportion of gains
+ 
+
+ align:start position:0%
+which is the poor proportion of gains
+realize
+
+ align:start position:0%
+realize
+ 
+
+ align:start position:0%
+realize
+so it looks at each person when they
+
+ align:start position:0%
+so it looks at each person when they
+ 
+
+ align:start position:0%
+so it looks at each person when they
+sell something they look at like how
+
+ align:start position:0%
+sell something they look at like how
+ 
+
+ align:start position:0%
+sell something they look at like how
+many losing stocks you have how many
+
+ align:start position:0%
+many losing stocks you have how many
+ 
+
+ align:start position:0%
+many losing stocks you have how many
+winning stocks you have
+
+ align:start position:0%
+winning stocks you have
+ 
+
+ align:start position:0%
+winning stocks you have
+and then you look at like what's the
+
+ align:start position:0%
+and then you look at like what's the
+ 
+
+ align:start position:0%
+and then you look at like what's the
+probability of you selling
+
+ align:start position:0%
+probability of you selling
+ 
+
+ align:start position:0%
+probability of you selling
+any of those depending on the winners or
+
+ align:start position:0%
+any of those depending on the winners or
+ 
+
+ align:start position:0%
+any of those depending on the winners or
+losers
+
+ align:start position:0%
+losers
+ 
+
+ align:start position:0%
+losers
+so what the main finding then here is
+
+ align:start position:0%
+so what the main finding then here is
+ 
+
+ align:start position:0%
+so what the main finding then here is
+that the pgr the proportion of
+
+ align:start position:0%
+that the pgr the proportion of
+ 
+
+ align:start position:0%
+that the pgr the proportion of
+gains realized is larger than the plr
+
+ align:start position:0%
+gains realized is larger than the plr
+ 
+
+ align:start position:0%
+gains realized is larger than the plr
+that's to say that's called what they
+
+ align:start position:0%
+that's to say that's called what they
+ 
+
+ align:start position:0%
+that's to say that's called what they
+call like the disposition effect
+
+ align:start position:0%
+call like the disposition effect
+ 
+
+ align:start position:0%
+call like the disposition effect
+which is the tendency to sell winners
+
+ align:start position:0%
+which is the tendency to sell winners
+ 
+
+ align:start position:0%
+which is the tendency to sell winners
+and hold on to losers
+
+ align:start position:0%
+and hold on to losers
+ 
+
+ align:start position:0%
+and hold on to losers
+does that make sense okay and so why do
+
+ align:start position:0%
+does that make sense okay and so why do
+ 
+
+ align:start position:0%
+does that make sense okay and so why do
+we care about that or why is this
+
+ align:start position:0%
+we care about that or why is this
+ 
+
+ align:start position:0%
+we care about that or why is this
+actually bad is this it's necessarily
+
+ align:start position:0%
+actually bad is this it's necessarily
+ 
+
+ align:start position:0%
+actually bad is this it's necessarily
+like sub-optimal behavior
+
+ align:start position:0%
+like sub-optimal behavior
+ 
+
+ align:start position:0%
+like sub-optimal behavior
+why do we care
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there probably shouldn't be an overall
+
+ align:start position:0%
+there probably shouldn't be an overall
+ 
+
+ align:start position:0%
+there probably shouldn't be an overall
+bias towards
+
+ align:start position:0%
+bias towards
+ 
+
+ align:start position:0%
+bias towards
+like selling like users and that
+
+ align:start position:0%
+like selling like users and that
+ 
+
+ align:start position:0%
+like selling like users and that
+probably isn't like an overall
+
+ align:start position:0%
+probably isn't like an overall
+ 
+
+ align:start position:0%
+probably isn't like an overall
+like effective strategy right so it
+
+ align:start position:0%
+like effective strategy right so it
+ 
+
+ align:start position:0%
+like effective strategy right so it
+depends on essentially how well the
+
+ align:start position:0%
+depends on essentially how well the
+ 
+
+ align:start position:0%
+depends on essentially how well the
+winners and the losers gonna do
+
+ align:start position:0%
+winners and the losers gonna do
+ 
+
+ align:start position:0%
+winners and the losers gonna do
+it turns out so in principle you would
+
+ align:start position:0%
+it turns out so in principle you would
+ 
+
+ align:start position:0%
+it turns out so in principle you would
+say well winners and losers should have
+
+ align:start position:0%
+say well winners and losers should have
+ 
+
+ align:start position:0%
+say well winners and losers should have
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+expected return regardless of their
+
+ align:start position:0%
+expected return regardless of their
+ 
+
+ align:start position:0%
+expected return regardless of their
+winners and losers in the past that's
+
+ align:start position:0%
+winners and losers in the past that's
+ 
+
+ align:start position:0%
+winners and losers in the past that's
+essentially the efficient market
+
+ align:start position:0%
+essentially the efficient market
+ 
+
+ align:start position:0%
+essentially the efficient market
+hypothesis just to say
+
+ align:start position:0%
+hypothesis just to say
+ 
+
+ align:start position:0%
+hypothesis just to say
+past uh price changes should just not be
+
+ align:start position:0%
+past uh price changes should just not be
+ 
+
+ align:start position:0%
+past uh price changes should just not be
+predictive of like future
+
+ align:start position:0%
+predictive of like future
+ 
+
+ align:start position:0%
+predictive of like future
+uh uh momentum or price changes overall
+
+ align:start position:0%
+uh uh momentum or price changes overall
+ 
+
+ align:start position:0%
+uh uh momentum or price changes overall
+because the current price should have
+
+ align:start position:0%
+because the current price should have
+ 
+
+ align:start position:0%
+because the current price should have
+incorporated essentially all information
+
+ align:start position:0%
+incorporated essentially all information
+ 
+
+ align:start position:0%
+incorporated essentially all information
+that's available at this point in time
+
+ align:start position:0%
+that's available at this point in time
+ 
+
+ align:start position:0%
+that's available at this point in time
+so to that degree it shouldn't matter
+
+ align:start position:0%
+so to that degree it shouldn't matter
+ 
+
+ align:start position:0%
+so to that degree it shouldn't matter
+actually what you sell you could just
+
+ align:start position:0%
+actually what you sell you could just
+ 
+
+ align:start position:0%
+actually what you sell you could just
+randomly sell stuff
+
+ align:start position:0%
+randomly sell stuff
+ 
+
+ align:start position:0%
+randomly sell stuff
+now you should not sell a lot usually
+
+ align:start position:0%
+now you should not sell a lot usually
+ 
+
+ align:start position:0%
+now you should not sell a lot usually
+there's commissions involved in these
+
+ align:start position:0%
+there's commissions involved in these
+ 
+
+ align:start position:0%
+there's commissions involved in these
+trades so like essentially you shouldn't
+
+ align:start position:0%
+trades so like essentially you shouldn't
+ 
+
+ align:start position:0%
+trades so like essentially you shouldn't
+sell anything that's essentially leading
+
+ align:start position:0%
+sell anything that's essentially leading
+ 
+
+ align:start position:0%
+sell anything that's essentially leading
+to over trading
+
+ align:start position:0%
+to over trading
+ 
+
+ align:start position:0%
+to over trading
+uh odin has another paper that shows
+
+ align:start position:0%
+uh odin has another paper that shows
+ 
+
+ align:start position:0%
+uh odin has another paper that shows
+essentially in particular men tend to be
+
+ align:start position:0%
+essentially in particular men tend to be
+ 
+
+ align:start position:0%
+essentially in particular men tend to be
+overconfident and and how good they are
+
+ align:start position:0%
+overconfident and and how good they are
+ 
+
+ align:start position:0%
+overconfident and and how good they are
+trading and they tend to over trade and
+
+ align:start position:0%
+trading and they tend to over trade and
+ 
+
+ align:start position:0%
+trading and they tend to over trade and
+that's really costly
+
+ align:start position:0%
+that's really costly
+ 
+
+ align:start position:0%
+that's really costly
+it turns out that like in their specific
+
+ align:start position:0%
+it turns out that like in their specific
+ 
+
+ align:start position:0%
+it turns out that like in their specific
+period
+
+ align:start position:0%
+period
+ 
+
+ align:start position:0%
+period
+um in fact there's momentum and that
+
+ align:start position:0%
+um in fact there's momentum and that
+ 
+
+ align:start position:0%
+um in fact there's momentum and that
+used to be the case
+
+ align:start position:0%
+used to be the case
+ 
+
+ align:start position:0%
+used to be the case
+uh quite a bit in that period of time
+
+ align:start position:0%
+uh quite a bit in that period of time
+ 
+
+ align:start position:0%
+uh quite a bit in that period of time
+which essentially is to do the winners
+
+ align:start position:0%
+which essentially is to do the winners
+ 
+
+ align:start position:0%
+which essentially is to do the winners
+actually doing better than the losers by
+
+ align:start position:0%
+actually doing better than the losers by
+ 
+
+ align:start position:0%
+actually doing better than the losers by
+quite a bit more big margin
+
+ align:start position:0%
+quite a bit more big margin
+ 
+
+ align:start position:0%
+quite a bit more big margin
+that is to say you should have actually
+
+ align:start position:0%
+that is to say you should have actually
+ 
+
+ align:start position:0%
+that is to say you should have actually
+did exactly done the opposite if
+
+ align:start position:0%
+did exactly done the opposite if
+ 
+
+ align:start position:0%
+did exactly done the opposite if
+anything you should have sold the losers
+
+ align:start position:0%
+anything you should have sold the losers
+ 
+
+ align:start position:0%
+anything you should have sold the losers
+and keep on keep the winners because
+
+ align:start position:0%
+and keep on keep the winners because
+ 
+
+ align:start position:0%
+and keep on keep the winners because
+they are
+
+ align:start position:0%
+they are
+ 
+
+ align:start position:0%
+they are
+in fact making more money in the short
+
+ align:start position:0%
+in fact making more money in the short
+ 
+
+ align:start position:0%
+in fact making more money in the short
+and medium run in that period
+
+ align:start position:0%
+and medium run in that period
+ 
+
+ align:start position:0%
+and medium run in that period
+okay um there's also the the investors
+
+ align:start position:0%
+okay um there's also the the investors
+ 
+
+ align:start position:0%
+okay um there's also the the investors
+sell more losers and winners in december
+
+ align:start position:0%
+sell more losers and winners in december
+ 
+
+ align:start position:0%
+sell more losers and winners in december
+um this is what you see here
+
+ align:start position:0%
+um this is what you see here
+ 
+
+ align:start position:0%
+um this is what you see here
+why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes exactly this is for tax reasons so
+
+ align:start position:0%
+yes exactly this is for tax reasons so
+ 
+
+ align:start position:0%
+yes exactly this is for tax reasons so
+that's actually happens to the
+
+ align:start position:0%
+that's actually happens to the
+ 
+
+ align:start position:0%
+that's actually happens to the
+shin portable i was in the economic
+
+ align:start position:0%
+shin portable i was in the economic
+ 
+
+ align:start position:0%
+shin portable i was in the economic
+support and actually if you paper in
+
+ align:start position:0%
+support and actually if you paper in
+ 
+
+ align:start position:0%
+support and actually if you paper in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so there you can essentially realize
+
+ align:start position:0%
+so there you can essentially realize
+ 
+
+ align:start position:0%
+so there you can essentially realize
+losses and that that
+
+ align:start position:0%
+losses and that that
+ 
+
+ align:start position:0%
+losses and that that
+reduces your taxes overall um
+
+ align:start position:0%
+reduces your taxes overall um
+ 
+
+ align:start position:0%
+reduces your taxes overall um
+exactly but overall essentially what's
+
+ align:start position:0%
+exactly but overall essentially what's
+ 
+
+ align:start position:0%
+exactly but overall essentially what's
+happening is that people do seem to
+
+ align:start position:0%
+happening is that people do seem to
+ 
+
+ align:start position:0%
+happening is that people do seem to
+engage in this behavior
+
+ align:start position:0%
+engage in this behavior
+ 
+
+ align:start position:0%
+engage in this behavior
+um in a pretty striking fashion they
+
+ align:start position:0%
+um in a pretty striking fashion they
+ 
+
+ align:start position:0%
+um in a pretty striking fashion they
+seem to be losing um
+
+ align:start position:0%
+seem to be losing um
+ 
+
+ align:start position:0%
+seem to be losing um
+quite a bit of money from that
+
+ align:start position:0%
+quite a bit of money from that
+ 
+
+ align:start position:0%
+quite a bit of money from that
+okay let me mention uh at least the
+
+ align:start position:0%
+okay let me mention uh at least the
+ 
+
+ align:start position:0%
+okay let me mention uh at least the
+marathon running and perhaps the golf
+
+ align:start position:0%
+marathon running and perhaps the golf
+ 
+
+ align:start position:0%
+marathon running and perhaps the golf
+example and then we're going to move
+
+ align:start position:0%
+example and then we're going to move
+ 
+
+ align:start position:0%
+example and then we're going to move
+towards like
+
+ align:start position:0%
+towards like
+ 
+
+ align:start position:0%
+towards like
+uh prices and firms how do firms react
+
+ align:start position:0%
+uh prices and firms how do firms react
+ 
+
+ align:start position:0%
+uh prices and firms how do firms react
+to these biases
+
+ align:start position:0%
+to these biases
+ 
+
+ align:start position:0%
+to these biases
+but what i'm trying to do here is
+
+ align:start position:0%
+but what i'm trying to do here is
+ 
+
+ align:start position:0%
+but what i'm trying to do here is
+essentially show you a bunch of
+
+ align:start position:0%
+essentially show you a bunch of
+ 
+
+ align:start position:0%
+essentially show you a bunch of
+different settings and essentially if
+
+ align:start position:0%
+different settings and essentially if
+ 
+
+ align:start position:0%
+different settings and essentially if
+you look at different settings in the
+
+ align:start position:0%
+you look at different settings in the
+ 
+
+ align:start position:0%
+you look at different settings in the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+there's lots and lots of different
+
+ align:start position:0%
+there's lots and lots of different
+ 
+
+ align:start position:0%
+there's lots and lots of different
+settings where reference dependence
+
+ align:start position:0%
+settings where reference dependence
+ 
+
+ align:start position:0%
+settings where reference dependence
+seems to matter one way or the other
+
+ align:start position:0%
+seems to matter one way or the other
+ 
+
+ align:start position:0%
+seems to matter one way or the other
+seems to be important in shaping
+
+ align:start position:0%
+seems to be important in shaping
+ 
+
+ align:start position:0%
+seems to be important in shaping
+people's behavior
+
+ align:start position:0%
+people's behavior
+ 
+
+ align:start position:0%
+people's behavior
+so um this is a very nice paper about
+
+ align:start position:0%
+so um this is a very nice paper about
+ 
+
+ align:start position:0%
+so um this is a very nice paper about
+marathon running
+
+ align:start position:0%
+marathon running
+ 
+
+ align:start position:0%
+marathon running
+finishing times these are many many
+
+ align:start position:0%
+finishing times these are many many
+ 
+
+ align:start position:0%
+finishing times these are many many
+marathons they have lots of data on
+
+ align:start position:0%
+marathons they have lots of data on
+ 
+
+ align:start position:0%
+marathons they have lots of data on
+finishing times for people
+
+ align:start position:0%
+finishing times for people
+ 
+
+ align:start position:0%
+finishing times for people
+so the lot of large numbers would
+
+ align:start position:0%
+so the lot of large numbers would
+ 
+
+ align:start position:0%
+so the lot of large numbers would
+predict that if you look at essentially
+
+ align:start position:0%
+predict that if you look at essentially
+ 
+
+ align:start position:0%
+predict that if you look at essentially
+people's finishing times
+
+ align:start position:0%
+people's finishing times
+ 
+
+ align:start position:0%
+people's finishing times
+if people have different talents and so
+
+ align:start position:0%
+if people have different talents and so
+ 
+
+ align:start position:0%
+if people have different talents and so
+on and so forth the finishing times
+
+ align:start position:0%
+on and so forth the finishing times
+ 
+
+ align:start position:0%
+on and so forth the finishing times
+should look something like this
+
+ align:start position:0%
+should look something like this
+ 
+
+ align:start position:0%
+should look something like this
+okay there's some people are faster some
+
+ align:start position:0%
+okay there's some people are faster some
+ 
+
+ align:start position:0%
+okay there's some people are faster some
+people are slower but overall there
+
+ align:start position:0%
+people are slower but overall there
+ 
+
+ align:start position:0%
+people are slower but overall there
+should be some
+
+ align:start position:0%
+should be some
+ 
+
+ align:start position:0%
+should be some
+um uh smooth distribution that
+
+ align:start position:0%
+um uh smooth distribution that
+ 
+
+ align:start position:0%
+um uh smooth distribution that
+essentially is like log normal or
+
+ align:start position:0%
+essentially is like log normal or
+ 
+
+ align:start position:0%
+essentially is like log normal or
+whatever you want it to be but
+
+ align:start position:0%
+whatever you want it to be but
+ 
+
+ align:start position:0%
+whatever you want it to be but
+essentially it should look something
+
+ align:start position:0%
+essentially it should look something
+ 
+
+ align:start position:0%
+essentially it should look something
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+so my why might it not look like this or
+
+ align:start position:0%
+so my why might it not look like this or
+ 
+
+ align:start position:0%
+so my why might it not look like this or
+what's what what might people do instead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes they may say i'll be 4 30 and then
+
+ align:start position:0%
+yes they may say i'll be 4 30 and then
+ 
+
+ align:start position:0%
+yes they may say i'll be 4 30 and then
+you might see bunching
+
+ align:start position:0%
+you might see bunching
+ 
+
+ align:start position:0%
+you might see bunching
+at certain points like four hours four
+
+ align:start position:0%
+at certain points like four hours four
+ 
+
+ align:start position:0%
+at certain points like four hours four
+thirty five hours five thursday
+
+ align:start position:0%
+thirty five hours five thursday
+ 
+
+ align:start position:0%
+thirty five hours five thursday
+right so exactly as you say it might be
+
+ align:start position:0%
+right so exactly as you say it might be
+ 
+
+ align:start position:0%
+right so exactly as you say it might be
+that people have reference points
+
+ align:start position:0%
+that people have reference points
+ 
+
+ align:start position:0%
+that people have reference points
+not in terms of like status quo here and
+
+ align:start position:0%
+not in terms of like status quo here and
+ 
+
+ align:start position:0%
+not in terms of like status quo here and
+the like reference points might be goals
+
+ align:start position:0%
+the like reference points might be goals
+ 
+
+ align:start position:0%
+the like reference points might be goals
+or aspirations you might say i really
+
+ align:start position:0%
+or aspirations you might say i really
+ 
+
+ align:start position:0%
+or aspirations you might say i really
+want to run the marathon in four hours
+
+ align:start position:0%
+want to run the marathon in four hours
+ 
+
+ align:start position:0%
+want to run the marathon in four hours
+or for 30 or
+
+ align:start position:0%
+or for 30 or
+ 
+
+ align:start position:0%
+or for 30 or
+five hours if you want and then um what
+
+ align:start position:0%
+five hours if you want and then um what
+ 
+
+ align:start position:0%
+five hours if you want and then um what
+the marathon times actually look like is
+
+ align:start position:0%
+the marathon times actually look like is
+ 
+
+ align:start position:0%
+the marathon times actually look like is
+something like this
+
+ align:start position:0%
+something like this
+ 
+
+ align:start position:0%
+something like this
+and in particular it seems like people
+
+ align:start position:0%
+and in particular it seems like people
+ 
+
+ align:start position:0%
+and in particular it seems like people
+have lots of goals of reaching something
+
+ align:start position:0%
+have lots of goals of reaching something
+ 
+
+ align:start position:0%
+have lots of goals of reaching something
+like um and
+
+ align:start position:0%
+like um and
+ 
+
+ align:start position:0%
+like um and
+you know as you if you look at this
+
+ align:start position:0%
+you know as you if you look at this
+ 
+
+ align:start position:0%
+you know as you if you look at this
+distribution what you see is exactly as
+
+ align:start position:0%
+distribution what you see is exactly as
+ 
+
+ align:start position:0%
+distribution what you see is exactly as
+you predict
+
+ align:start position:0%
+you predict
+ 
+
+ align:start position:0%
+you predict
+um uh if you look at the half hour or
+
+ align:start position:0%
+um uh if you look at the half hour or
+ 
+
+ align:start position:0%
+um uh if you look at the half hour or
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+even the quarter hour sort of points
+
+ align:start position:0%
+even the quarter hour sort of points
+ 
+
+ align:start position:0%
+even the quarter hour sort of points
+there's essentially bunching from below
+
+ align:start position:0%
+there's essentially bunching from below
+ 
+
+ align:start position:0%
+there's essentially bunching from below
+so essentially people seem to be
+
+ align:start position:0%
+so essentially people seem to be
+ 
+
+ align:start position:0%
+so essentially people seem to be
+if they're like at pace or finish at
+
+ align:start position:0%
+if they're like at pace or finish at
+ 
+
+ align:start position:0%
+if they're like at pace or finish at
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+hours in one minute they try to sort of
+
+ align:start position:0%
+hours in one minute they try to sort of
+ 
+
+ align:start position:0%
+hours in one minute they try to sort of
+speed up and just make it to like three
+
+ align:start position:0%
+speed up and just make it to like three
+ 
+
+ align:start position:0%
+speed up and just make it to like three
+um 59 and so
+
+ align:start position:0%
+um 59 and so
+ 
+
+ align:start position:0%
+um 59 and so
+you even so you see a bunch of bunching
+
+ align:start position:0%
+you even so you see a bunch of bunching
+ 
+
+ align:start position:0%
+you even so you see a bunch of bunching
+um at the half hour slots
+
+ align:start position:0%
+um at the half hour slots
+ 
+
+ align:start position:0%
+um at the half hour slots
+you see actually much less at like six
+
+ align:start position:0%
+you see actually much less at like six
+ 
+
+ align:start position:0%
+you see actually much less at like six
+hours and 30 minutes or something seemed
+
+ align:start position:0%
+hours and 30 minutes or something seemed
+ 
+
+ align:start position:0%
+hours and 30 minutes or something seemed
+to like few people have actually goals
+
+ align:start position:0%
+to like few people have actually goals
+ 
+
+ align:start position:0%
+to like few people have actually goals
+once you've
+
+ align:start position:0%
+once you've
+ 
+
+ align:start position:0%
+once you've
+like run the marathon in six hours and
+
+ align:start position:0%
+like run the marathon in six hours and
+ 
+
+ align:start position:0%
+like run the marathon in six hours and
+30 minutes which is probably what i
+
+ align:start position:0%
+30 minutes which is probably what i
+ 
+
+ align:start position:0%
+30 minutes which is probably what i
+would do
+
+ align:start position:0%
+would do
+ 
+
+ align:start position:0%
+would do
+you know it doesn't really matter
+
+ align:start position:0%
+you know it doesn't really matter
+ 
+
+ align:start position:0%
+you know it doesn't really matter
+whether you like 6 31 or 6 29
+
+ align:start position:0%
+whether you like 6 31 or 6 29
+ 
+
+ align:start position:0%
+whether you like 6 31 or 6 29
+uh but there's very ambitious people who
+
+ align:start position:0%
+uh but there's very ambitious people who
+ 
+
+ align:start position:0%
+uh but there's very ambitious people who
+want to like finish in like 4 30
+
+ align:start position:0%
+want to like finish in like 4 30
+ 
+
+ align:start position:0%
+want to like finish in like 4 30
+4 hours or 3 30 and the like and there's
+
+ align:start position:0%
+4 hours or 3 30 and the like and there's
+ 
+
+ align:start position:0%
+4 hours or 3 30 and the like and there's
+a bunch of um
+
+ align:start position:0%
+a bunch of um
+ 
+
+ align:start position:0%
+a bunch of um
+bunching from below there so you see the
+
+ align:start position:0%
+bunching from below there so you see the
+ 
+
+ align:start position:0%
+bunching from below there so you see the
+same for like
+
+ align:start position:0%
+same for like
+ 
+
+ align:start position:0%
+same for like
+a quarter hour times a little bit less
+
+ align:start position:0%
+a quarter hour times a little bit less
+ 
+
+ align:start position:0%
+a quarter hour times a little bit less
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+um and sort of that's consistent with
+
+ align:start position:0%
+um and sort of that's consistent with
+ 
+
+ align:start position:0%
+um and sort of that's consistent with
+the reference point here being like
+
+ align:start position:0%
+the reference point here being like
+ 
+
+ align:start position:0%
+the reference point here being like
+a goal and aspiration you want to reach
+
+ align:start position:0%
+a goal and aspiration you want to reach
+ 
+
+ align:start position:0%
+a goal and aspiration you want to reach
+four minutes you want to brag to your
+
+ align:start position:0%
+four minutes you want to brag to your
+ 
+
+ align:start position:0%
+four minutes you want to brag to your
+friends and so on and it's not so great
+
+ align:start position:0%
+friends and so on and it's not so great
+ 
+
+ align:start position:0%
+friends and so on and it's not so great
+if you do that and say i
+
+ align:start position:0%
+if you do that and say i
+ 
+
+ align:start position:0%
+if you do that and say i
+finished in four hours in one minute as
+
+ align:start position:0%
+finished in four hours in one minute as
+ 
+
+ align:start position:0%
+finished in four hours in one minute as
+opposed to if you say i finish below
+
+ align:start position:0%
+opposed to if you say i finish below
+ 
+
+ align:start position:0%
+opposed to if you say i finish below
+four hours now when you look at the
+
+ align:start position:0%
+four hours now when you look at the
+ 
+
+ align:start position:0%
+four hours now when you look at the
+effort at the
+
+ align:start position:0%
+effort at the
+ 
+
+ align:start position:0%
+effort at the
+end of the race what is it what would
+
+ align:start position:0%
+end of the race what is it what would
+ 
+
+ align:start position:0%
+end of the race what is it what would
+you expect so what we have here on the
+
+ align:start position:0%
+you expect so what we have here on the
+ 
+
+ align:start position:0%
+you expect so what we have here on the
+x-axis
+
+ align:start position:0%
+x-axis
+ 
+
+ align:start position:0%
+x-axis
+is people these are like the uh 40
+
+ align:start position:0%
+is people these are like the uh 40
+ 
+
+ align:start position:0%
+is people these are like the uh 40
+kilometer pace these are like in 30
+
+ align:start position:0%
+kilometer pace these are like in 30
+ 
+
+ align:start position:0%
+kilometer pace these are like in 30
+second increments this is kind of like
+
+ align:start position:0%
+second increments this is kind of like
+ 
+
+ align:start position:0%
+second increments this is kind of like
+during the so the marathon is 40 um
+
+ align:start position:0%
+during the so the marathon is 40 um
+ 
+
+ align:start position:0%
+during the so the marathon is 40 um
+uh uh 42.195 kilometers
+
+ align:start position:0%
+uh uh 42.195 kilometers
+ 
+
+ align:start position:0%
+uh uh 42.195 kilometers
+um so what i'm showing you here is like
+
+ align:start position:0%
+um so what i'm showing you here is like
+ 
+
+ align:start position:0%
+um so what i'm showing you here is like
+essentially people the 40 kilometer pace
+
+ align:start position:0%
+essentially people the 40 kilometer pace
+ 
+
+ align:start position:0%
+essentially people the 40 kilometer pace
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+are ranked by the 40 are distributed by
+
+ align:start position:0%
+are ranked by the 40 are distributed by
+ 
+
+ align:start position:0%
+are ranked by the 40 are distributed by
+the 40 kilometer pace
+
+ align:start position:0%
+the 40 kilometer pace
+ 
+
+ align:start position:0%
+the 40 kilometer pace
+uh the first 40 kilometers now what you
+
+ align:start position:0%
+uh the first 40 kilometers now what you
+ 
+
+ align:start position:0%
+uh the first 40 kilometers now what you
+would you expect for people so there's
+
+ align:start position:0%
+would you expect for people so there's
+ 
+
+ align:start position:0%
+would you expect for people so there's
+some people who
+
+ align:start position:0%
+some people who
+ 
+
+ align:start position:0%
+some people who
+like were at pace for like to reach um
+
+ align:start position:0%
+like were at pace for like to reach um
+ 
+
+ align:start position:0%
+like were at pace for like to reach um
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and some people at pace to reach four or
+
+ align:start position:0%
+and some people at pace to reach four or
+ 
+
+ align:start position:0%
+and some people at pace to reach four or
+five and so on what is it that you would
+
+ align:start position:0%
+five and so on what is it that you would
+ 
+
+ align:start position:0%
+five and so on what is it that you would
+expect people to do when you look at
+
+ align:start position:0%
+expect people to do when you look at
+ 
+
+ align:start position:0%
+expect people to do when you look at
+like how fast people run
+
+ align:start position:0%
+like how fast people run
+ 
+
+ align:start position:0%
+like how fast people run
+uh towards the end the last two
+
+ align:start position:0%
+uh towards the end the last two
+ 
+
+ align:start position:0%
+uh towards the end the last two
+kilometers of the race
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly and this is what you see so low
+
+ align:start position:0%
+exactly and this is what you see so low
+ 
+
+ align:start position:0%
+exactly and this is what you see so low
+means like you're running fast
+
+ align:start position:0%
+means like you're running fast
+ 
+
+ align:start position:0%
+means like you're running fast
+so this is like uh minutes per kilometer
+
+ align:start position:0%
+so this is like uh minutes per kilometer
+ 
+
+ align:start position:0%
+so this is like uh minutes per kilometer
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+or relative minutes per kilometers so
+
+ align:start position:0%
+or relative minutes per kilometers so
+ 
+
+ align:start position:0%
+or relative minutes per kilometers so
+what you should expect is like people
+
+ align:start position:0%
+what you should expect is like people
+ 
+
+ align:start position:0%
+what you should expect is like people
+who are
+
+ align:start position:0%
+who are
+ 
+
+ align:start position:0%
+who are
+just below the goal or people who are
+
+ align:start position:0%
+just below the goal or people who are
+ 
+
+ align:start position:0%
+just below the goal or people who are
+essentially just above the goal in fact
+
+ align:start position:0%
+essentially just above the goal in fact
+ 
+
+ align:start position:0%
+essentially just above the goal in fact
+these are the people who speed up okay
+
+ align:start position:0%
+these are the people who speed up okay
+ 
+
+ align:start position:0%
+these are the people who speed up okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um and this is exactly what you sort of
+
+ align:start position:0%
+um and this is exactly what you sort of
+ 
+
+ align:start position:0%
+um and this is exactly what you sort of
+see is the people who are
+
+ align:start position:0%
+see is the people who are
+ 
+
+ align:start position:0%
+see is the people who are
+just below the four or four minute mark
+
+ align:start position:0%
+just below the four or four minute mark
+ 
+
+ align:start position:0%
+just below the four or four minute mark
+or some people who are like just above
+
+ align:start position:0%
+or some people who are like just above
+ 
+
+ align:start position:0%
+or some people who are like just above
+they speed up to just make it uh to that
+
+ align:start position:0%
+they speed up to just make it uh to that
+ 
+
+ align:start position:0%
+they speed up to just make it uh to that
+goal and sort of um
+
+ align:start position:0%
+goal and sort of um
+ 
+
+ align:start position:0%
+goal and sort of um
+allen and i'll have like a sort of
+
+ align:start position:0%
+allen and i'll have like a sort of
+ 
+
+ align:start position:0%
+allen and i'll have like a sort of
+analysis of this essentially what they
+
+ align:start position:0%
+analysis of this essentially what they
+ 
+
+ align:start position:0%
+analysis of this essentially what they
+find is that
+
+ align:start position:0%
+find is that
+ 
+
+ align:start position:0%
+find is that
+um everybody gets sort of slower towards
+
+ align:start position:0%
+um everybody gets sort of slower towards
+ 
+
+ align:start position:0%
+um everybody gets sort of slower towards
+the end of the race but if you're sort
+
+ align:start position:0%
+the end of the race but if you're sort
+ 
+
+ align:start position:0%
+the end of the race but if you're sort
+of in reach of of reaching the goal by
+
+ align:start position:0%
+of in reach of of reaching the goal by
+ 
+
+ align:start position:0%
+of in reach of of reaching the goal by
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+for uh the reaching the time of four
+
+ align:start position:0%
+for uh the reaching the time of four
+ 
+
+ align:start position:0%
+for uh the reaching the time of four
+hours you're gonna
+
+ align:start position:0%
+hours you're gonna
+ 
+
+ align:start position:0%
+hours you're gonna
+uh slow down less so speed up a bit to
+
+ align:start position:0%
+uh slow down less so speed up a bit to
+ 
+
+ align:start position:0%
+uh slow down less so speed up a bit to
+just reach that
+
+ align:start position:0%
+just reach that
+ 
+
+ align:start position:0%
+just reach that
+uh a specific goal okay
+
+ align:start position:0%
+uh a specific goal okay
+ 
+
+ align:start position:0%
+uh a specific goal okay
+uh let me show you one more thing of
+
+ align:start position:0%
+uh let me show you one more thing of
+ 
+
+ align:start position:0%
+uh let me show you one more thing of
+sports which is like a
+
+ align:start position:0%
+sports which is like a
+ 
+
+ align:start position:0%
+sports which is like a
+a golf so how does golf work in case you
+
+ align:start position:0%
+a golf so how does golf work in case you
+ 
+
+ align:start position:0%
+a golf so how does golf work in case you
+don't know um
+
+ align:start position:0%
+don't know um
+ 
+
+ align:start position:0%
+don't know um
+you you hit a ball um with a club from a
+
+ align:start position:0%
+you you hit a ball um with a club from a
+ 
+
+ align:start position:0%
+you you hit a ball um with a club from a
+tee into like a hole
+
+ align:start position:0%
+tee into like a hole
+ 
+
+ align:start position:0%
+tee into like a hole
+um the way this works is um there's
+
+ align:start position:0%
+um the way this works is um there's
+ 
+
+ align:start position:0%
+um the way this works is um there's
+usually uh four rounds of 18 holes
+
+ align:start position:0%
+usually uh four rounds of 18 holes
+ 
+
+ align:start position:0%
+usually uh four rounds of 18 holes
+um this is there's very convex
+
+ align:start position:0%
+um this is there's very convex
+ 
+
+ align:start position:0%
+um this is there's very convex
+incentives
+
+ align:start position:0%
+incentives
+ 
+
+ align:start position:0%
+incentives
+in the golf tournaments so you get a
+
+ align:start position:0%
+in the golf tournaments so you get a
+ 
+
+ align:start position:0%
+in the golf tournaments so you get a
+bunch of money if you win if you're sort
+
+ align:start position:0%
+bunch of money if you win if you're sort
+ 
+
+ align:start position:0%
+bunch of money if you win if you're sort
+of at the top
+
+ align:start position:0%
+of at the top
+ 
+
+ align:start position:0%
+of at the top
+for an average performance essentially
+
+ align:start position:0%
+for an average performance essentially
+ 
+
+ align:start position:0%
+for an average performance essentially
+you don't make that much money i mean
+
+ align:start position:0%
+you don't make that much money i mean
+ 
+
+ align:start position:0%
+you don't make that much money i mean
+you make
+
+ align:start position:0%
+you make
+ 
+
+ align:start position:0%
+you make
+good money but you know the the the
+
+ align:start position:0%
+good money but you know the the the
+ 
+
+ align:start position:0%
+good money but you know the the the
+prize the money is really in terms of
+
+ align:start position:0%
+prize the money is really in terms of
+ 
+
+ align:start position:0%
+prize the money is really in terms of
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+uh when you do really well so now what
+
+ align:start position:0%
+uh when you do really well so now what
+ 
+
+ align:start position:0%
+uh when you do really well so now what
+is par
+
+ align:start position:0%
+is par
+ 
+
+ align:start position:0%
+is par
+par is like how many um strokes how many
+
+ align:start position:0%
+par is like how many um strokes how many
+ 
+
+ align:start position:0%
+par is like how many um strokes how many
+shots do you need to
+
+ align:start position:0%
+shots do you need to
+ 
+
+ align:start position:0%
+shots do you need to
+um how many shots a very good golfer
+
+ align:start position:0%
+um how many shots a very good golfer
+ 
+
+ align:start position:0%
+um how many shots a very good golfer
+should require to complete a given
+
+ align:start position:0%
+should require to complete a given
+ 
+
+ align:start position:0%
+should require to complete a given
+a hole so um so par is usually four
+
+ align:start position:0%
+a hole so um so par is usually four
+ 
+
+ align:start position:0%
+a hole so um so par is usually four
+three four or five um shots uh and then
+
+ align:start position:0%
+three four or five um shots uh and then
+ 
+
+ align:start position:0%
+three four or five um shots uh and then
+eagle is like two below par
+
+ align:start position:0%
+eagle is like two below par
+ 
+
+ align:start position:0%
+eagle is like two below par
+so if like you have a par four hole if
+
+ align:start position:0%
+so if like you have a par four hole if
+ 
+
+ align:start position:0%
+so if like you have a par four hole if
+you do two shots that's an eagle
+
+ align:start position:0%
+you do two shots that's an eagle
+ 
+
+ align:start position:0%
+you do two shots that's an eagle
+if you do three shots in that case that
+
+ align:start position:0%
+if you do three shots in that case that
+ 
+
+ align:start position:0%
+if you do three shots in that case that
+would be a birdie four would be par
+
+ align:start position:0%
+would be a birdie four would be par
+ 
+
+ align:start position:0%
+would be a birdie four would be par
+borgie would be one above par and double
+
+ align:start position:0%
+borgie would be one above par and double
+ 
+
+ align:start position:0%
+borgie would be one above par and double
+bogey would be
+
+ align:start position:0%
+bogey would be
+ 
+
+ align:start position:0%
+bogey would be
+uh two above par okay so knowing all
+
+ align:start position:0%
+uh two above par okay so knowing all
+ 
+
+ align:start position:0%
+uh two above par okay so knowing all
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and so what ends at the what matters for
+
+ align:start position:0%
+and so what ends at the what matters for
+ 
+
+ align:start position:0%
+and so what ends at the what matters for
+golf at the end of a tournament is like
+
+ align:start position:0%
+golf at the end of a tournament is like
+ 
+
+ align:start position:0%
+golf at the end of a tournament is like
+how many shots do you make in total so
+
+ align:start position:0%
+how many shots do you make in total so
+ 
+
+ align:start position:0%
+how many shots do you make in total so
+how can we now look at reference
+
+ align:start position:0%
+how can we now look at reference
+ 
+
+ align:start position:0%
+how can we now look at reference
+dependent preferences here
+
+ align:start position:0%
+dependent preferences here
+ 
+
+ align:start position:0%
+dependent preferences here
+in this setting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes the reference is the par now suppose
+
+ align:start position:0%
+yes the reference is the par now suppose
+ 
+
+ align:start position:0%
+yes the reference is the par now suppose
+you are
+
+ align:start position:0%
+you are
+ 
+
+ align:start position:0%
+you are
+putting which is at the end you know on
+
+ align:start position:0%
+putting which is at the end you know on
+ 
+
+ align:start position:0%
+putting which is at the end you know on
+the green uh what are you going to do
+
+ align:start position:0%
+the green uh what are you going to do
+ 
+
+ align:start position:0%
+the green uh what are you going to do
+what kinds of behaviors do you expect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um well it depends so if you are
+
+ align:start position:0%
+yes um well it depends so if you are
+ 
+
+ align:start position:0%
+yes um well it depends so if you are
+under par
+
+ align:start position:0%
+under par
+ 
+
+ align:start position:0%
+under par
+then you might try like you're shooting
+
+ align:start position:0%
+then you might try like you're shooting
+ 
+
+ align:start position:0%
+then you might try like you're shooting
+for birdie or you're shooting for a car
+
+ align:start position:0%
+for birdie or you're shooting for a car
+ 
+
+ align:start position:0%
+for birdie or you're shooting for a car
+and it's a long cut
+
+ align:start position:0%
+and it's a long cut
+ 
+
+ align:start position:0%
+and it's a long cut
+you might try to make sure that you get
+
+ align:start position:0%
+you might try to make sure that you get
+ 
+
+ align:start position:0%
+you might try to make sure that you get
+into the hole whereas if you're already
+
+ align:start position:0%
+into the hole whereas if you're already
+ 
+
+ align:start position:0%
+into the hole whereas if you're already
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+over par or double over car you might
+
+ align:start position:0%
+over par or double over car you might
+ 
+
+ align:start position:0%
+over par or double over car you might
+try to play a little safer to make sure
+
+ align:start position:0%
+try to play a little safer to make sure
+ 
+
+ align:start position:0%
+try to play a little safer to make sure
+you're not
+
+ align:start position:0%
+you're not
+ 
+
+ align:start position:0%
+you're not
+way over it right so some of this is
+
+ align:start position:0%
+way over it right so some of this is
+ 
+
+ align:start position:0%
+way over it right so some of this is
+about like risk preference is how
+
+ align:start position:0%
+about like risk preference is how
+ 
+
+ align:start position:0%
+about like risk preference is how
+risky your shots are you can another way
+
+ align:start position:0%
+risky your shots are you can another way
+ 
+
+ align:start position:0%
+risky your shots are you can another way
+to think about this is kind of like how
+
+ align:start position:0%
+to think about this is kind of like how
+ 
+
+ align:start position:0%
+to think about this is kind of like how
+much effort do you put in your shot in
+
+ align:start position:0%
+much effort do you put in your shot in
+ 
+
+ align:start position:0%
+much effort do you put in your shot in
+some sense you to the extent that like
+
+ align:start position:0%
+some sense you to the extent that like
+ 
+
+ align:start position:0%
+some sense you to the extent that like
+you can put in
+
+ align:start position:0%
+you can put in
+ 
+
+ align:start position:0%
+you can put in
+you can sort of allocate attention or
+
+ align:start position:0%
+you can sort of allocate attention or
+ 
+
+ align:start position:0%
+you can sort of allocate attention or
+really focus an effort
+
+ align:start position:0%
+really focus an effort
+ 
+
+ align:start position:0%
+really focus an effort
+maybe that's sort of limited over the
+
+ align:start position:0%
+maybe that's sort of limited over the
+ 
+
+ align:start position:0%
+maybe that's sort of limited over the
+course of like 18 holes and four
+
+ align:start position:0%
+course of like 18 holes and four
+ 
+
+ align:start position:0%
+course of like 18 holes and four
+uh uh four rounds uh of each of those
+
+ align:start position:0%
+uh uh four rounds uh of each of those
+ 
+
+ align:start position:0%
+uh uh four rounds uh of each of those
+you know you might sort of put in might
+
+ align:start position:0%
+you know you might sort of put in might
+ 
+
+ align:start position:0%
+you know you might sort of put in might
+try particularly hard to do well on
+
+ align:start position:0%
+try particularly hard to do well on
+ 
+
+ align:start position:0%
+try particularly hard to do well on
+shots that make you
+
+ align:start position:0%
+shots that make you
+ 
+
+ align:start position:0%
+shots that make you
+reach par compared to shots that might
+
+ align:start position:0%
+reach par compared to shots that might
+ 
+
+ align:start position:0%
+reach par compared to shots that might
+get you like a birdie or
+
+ align:start position:0%
+get you like a birdie or
+ 
+
+ align:start position:0%
+get you like a birdie or
+or even better and so this is exactly as
+
+ align:start position:0%
+or even better and so this is exactly as
+ 
+
+ align:start position:0%
+or even better and so this is exactly as
+you say
+
+ align:start position:0%
+you say
+ 
+
+ align:start position:0%
+you say
+the fairly obvious reference point for
+
+ align:start position:0%
+the fairly obvious reference point for
+ 
+
+ align:start position:0%
+the fairly obvious reference point for
+each hole in golf is reached par
+
+ align:start position:0%
+each hole in golf is reached par
+ 
+
+ align:start position:0%
+each hole in golf is reached par
+importantly it doesn't matter um uh
+
+ align:start position:0%
+importantly it doesn't matter um uh
+ 
+
+ align:start position:0%
+importantly it doesn't matter um uh
+whether you have birdie
+
+ align:start position:0%
+whether you have birdie
+ 
+
+ align:start position:0%
+whether you have birdie
+par and bogie versus par par and par
+
+ align:start position:0%
+par and bogie versus par par and par
+ 
+
+ align:start position:0%
+par and bogie versus par par and par
+essentially that gives you exactly the
+
+ align:start position:0%
+essentially that gives you exactly the
+ 
+
+ align:start position:0%
+essentially that gives you exactly the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+amount of shots overall but um
+
+ align:start position:0%
+amount of shots overall but um
+ 
+
+ align:start position:0%
+amount of shots overall but um
+not what pope and schweitzer ask is the
+
+ align:start position:0%
+not what pope and schweitzer ask is the
+ 
+
+ align:start position:0%
+not what pope and schweitzer ask is the
+question like
+
+ align:start position:0%
+question like
+ 
+
+ align:start position:0%
+question like
+putters um more likely to to make their
+
+ align:start position:0%
+putters um more likely to to make their
+ 
+
+ align:start position:0%
+putters um more likely to to make their
+par
+
+ align:start position:0%
+par
+ 
+
+ align:start position:0%
+par
+uh than their birdie parts right so
+
+ align:start position:0%
+uh than their birdie parts right so
+ 
+
+ align:start position:0%
+uh than their birdie parts right so
+essentially uh depending on like
+
+ align:start position:0%
+essentially uh depending on like
+ 
+
+ align:start position:0%
+essentially uh depending on like
+are you at possibility at losing or like
+
+ align:start position:0%
+are you at possibility at losing or like
+ 
+
+ align:start position:0%
+are you at possibility at losing or like
+at gaining uh
+
+ align:start position:0%
+at gaining uh
+ 
+
+ align:start position:0%
+at gaining uh
+to you essentially if you're worried
+
+ align:start position:0%
+to you essentially if you're worried
+ 
+
+ align:start position:0%
+to you essentially if you're worried
+about like losing par
+
+ align:start position:0%
+about like losing par
+ 
+
+ align:start position:0%
+about like losing par
+are you gonna behave differently
+
+ align:start position:0%
+are you gonna behave differently
+ 
+
+ align:start position:0%
+are you gonna behave differently
+compared to like when you can make a
+
+ align:start position:0%
+compared to like when you can make a
+ 
+
+ align:start position:0%
+compared to like when you can make a
+birdie which is in the game domain
+
+ align:start position:0%
+birdie which is in the game domain
+ 
+
+ align:start position:0%
+birdie which is in the game domain
+potentially
+
+ align:start position:0%
+potentially
+ 
+
+ align:start position:0%
+potentially
+the same you could say about bogeys
+
+ align:start position:0%
+the same you could say about bogeys
+ 
+
+ align:start position:0%
+the same you could say about bogeys
+where like you're already in the loss of
+
+ align:start position:0%
+where like you're already in the loss of
+ 
+
+ align:start position:0%
+where like you're already in the loss of
+men because you're already doing
+
+ align:start position:0%
+men because you're already doing
+ 
+
+ align:start position:0%
+men because you're already doing
+terribly and you're
+
+ align:start position:0%
+terribly and you're
+ 
+
+ align:start position:0%
+terribly and you're
+trying to avoid like a double um vogue
+
+ align:start position:0%
+trying to avoid like a double um vogue
+ 
+
+ align:start position:0%
+trying to avoid like a double um vogue
+so now what they find essentially is
+
+ align:start position:0%
+so now what they find essentially is
+ 
+
+ align:start position:0%
+so now what they find essentially is
+their power puts a much more
+
+ align:start position:0%
+their power puts a much more
+ 
+
+ align:start position:0%
+their power puts a much more
+likely uh to be made there's like two
+
+ align:start position:0%
+likely uh to be made there's like two
+ 
+
+ align:start position:0%
+likely uh to be made there's like two
+three percentage points more likely to
+
+ align:start position:0%
+three percentage points more likely to
+ 
+
+ align:start position:0%
+three percentage points more likely to
+be made compared to equivalent birdie
+
+ align:start position:0%
+be made compared to equivalent birdie
+ 
+
+ align:start position:0%
+be made compared to equivalent birdie
+puts
+
+ align:start position:0%
+puts
+ 
+
+ align:start position:0%
+puts
+the authors rule out a bunch of
+
+ align:start position:0%
+the authors rule out a bunch of
+ 
+
+ align:start position:0%
+the authors rule out a bunch of
+different explanations it doesn't have
+
+ align:start position:0%
+different explanations it doesn't have
+ 
+
+ align:start position:0%
+different explanations it doesn't have
+to do with like heterogeneity
+
+ align:start position:0%
+to do with like heterogeneity
+ 
+
+ align:start position:0%
+to do with like heterogeneity
+player ability they even have sort of
+
+ align:start position:0%
+player ability they even have sort of
+ 
+
+ align:start position:0%
+player ability they even have sort of
+like gps information of exactly where
+
+ align:start position:0%
+like gps information of exactly where
+ 
+
+ align:start position:0%
+like gps information of exactly where
+the ball is compared to the whole and
+
+ align:start position:0%
+the ball is compared to the whole and
+ 
+
+ align:start position:0%
+the ball is compared to the whole and
+they do all sorts of comparison of how
+
+ align:start position:0%
+they do all sorts of comparison of how
+ 
+
+ align:start position:0%
+they do all sorts of comparison of how
+hard the shot is
+
+ align:start position:0%
+hard the shot is
+ 
+
+ align:start position:0%
+hard the shot is
+they don't think it has to do with
+
+ align:start position:0%
+they don't think it has to do with
+ 
+
+ align:start position:0%
+they don't think it has to do with
+learning from earlier puts and it seems
+
+ align:start position:0%
+learning from earlier puts and it seems
+ 
+
+ align:start position:0%
+learning from earlier puts and it seems
+to also not have to do with like whole
+
+ align:start position:0%
+to also not have to do with like whole
+ 
+
+ align:start position:0%
+to also not have to do with like whole
+specific preferences some holes are
+
+ align:start position:0%
+specific preferences some holes are
+ 
+
+ align:start position:0%
+specific preferences some holes are
+really hard and some poles are really
+
+ align:start position:0%
+really hard and some poles are really
+ 
+
+ align:start position:0%
+really hard and some poles are really
+simple and easy and so on so it doesn't
+
+ align:start position:0%
+simple and easy and so on so it doesn't
+ 
+
+ align:start position:0%
+simple and easy and so on so it doesn't
+seem to be uh
+
+ align:start position:0%
+seem to be uh
+ 
+
+ align:start position:0%
+seem to be uh
+to do with any of that so again that's
+
+ align:start position:0%
+to do with any of that so again that's
+ 
+
+ align:start position:0%
+to do with any of that so again that's
+sort of another
+
+ align:start position:0%
+sort of another
+ 
+
+ align:start position:0%
+sort of another
+instance of like reference dependent
+
+ align:start position:0%
+instance of like reference dependent
+ 
+
+ align:start position:0%
+instance of like reference dependent
+that seems to be in quite a few
+
+ align:start position:0%
+that seems to be in quite a few
+ 
+
+ align:start position:0%
+that seems to be in quite a few
+settings let me sort of skip the deal
+
+ align:start position:0%
+settings let me sort of skip the deal
+ 
+
+ align:start position:0%
+settings let me sort of skip the deal
+and no deal tv show which we can
+
+ align:start position:0%
+and no deal tv show which we can
+ 
+
+ align:start position:0%
+and no deal tv show which we can
+do briefly in recitation and talk a
+
+ align:start position:0%
+do briefly in recitation and talk a
+ 
+
+ align:start position:0%
+do briefly in recitation and talk a
+little bit about prices
+
+ align:start position:0%
+little bit about prices
+ 
+
+ align:start position:0%
+little bit about prices
+and firms
+
+ align:start position:0%
+and firms
+ 
+
+ align:start position:0%
+and firms
+so one fact is that we see in the world
+
+ align:start position:0%
+so one fact is that we see in the world
+ 
+
+ align:start position:0%
+so one fact is that we see in the world
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+demand often responds more strongly to
+
+ align:start position:0%
+demand often responds more strongly to
+ 
+
+ align:start position:0%
+demand often responds more strongly to
+price increases than to price decreases
+
+ align:start position:0%
+price increases than to price decreases
+ 
+
+ align:start position:0%
+price increases than to price decreases
+of frequently purchased items and we we
+
+ align:start position:0%
+of frequently purchased items and we we
+ 
+
+ align:start position:0%
+of frequently purchased items and we we
+already discussed that last time is to
+
+ align:start position:0%
+already discussed that last time is to
+ 
+
+ align:start position:0%
+already discussed that last time is to
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+um so usually people have a reference
+
+ align:start position:0%
+um so usually people have a reference
+ 
+
+ align:start position:0%
+um so usually people have a reference
+point in terms of like either the price
+
+ align:start position:0%
+point in terms of like either the price
+ 
+
+ align:start position:0%
+point in terms of like either the price
+they pay or the expenditures on certain
+
+ align:start position:0%
+they pay or the expenditures on certain
+ 
+
+ align:start position:0%
+they pay or the expenditures on certain
+items
+
+ align:start position:0%
+items
+ 
+
+ align:start position:0%
+items
+so now something becomes more expensive
+
+ align:start position:0%
+so now something becomes more expensive
+ 
+
+ align:start position:0%
+so now something becomes more expensive
+what they tend to do is they essentially
+
+ align:start position:0%
+what they tend to do is they essentially
+ 
+
+ align:start position:0%
+what they tend to do is they essentially
+reduce how much they
+
+ align:start position:0%
+reduce how much they
+ 
+
+ align:start position:0%
+reduce how much they
+for example gasoline or the like they
+
+ align:start position:0%
+for example gasoline or the like they
+ 
+
+ align:start position:0%
+for example gasoline or the like they
+tend to then sort of just reduce
+
+ align:start position:0%
+tend to then sort of just reduce
+ 
+
+ align:start position:0%
+tend to then sort of just reduce
+uh uh their expenditures because they
+
+ align:start position:0%
+uh uh their expenditures because they
+ 
+
+ align:start position:0%
+uh uh their expenditures because they
+have like a budget for
+
+ align:start position:0%
+have like a budget for
+ 
+
+ align:start position:0%
+have like a budget for
+say gasoline or certain items and so
+
+ align:start position:0%
+say gasoline or certain items and so
+ 
+
+ align:start position:0%
+say gasoline or certain items and so
+what they tend to do is then the
+
+ align:start position:0%
+what they tend to do is then the
+ 
+
+ align:start position:0%
+what they tend to do is then the
+reference point is either the past price
+
+ align:start position:0%
+reference point is either the past price
+ 
+
+ align:start position:0%
+reference point is either the past price
+or the past expenditures
+
+ align:start position:0%
+or the past expenditures
+ 
+
+ align:start position:0%
+or the past expenditures
+and uh uh people tend to sort of be lost
+
+ align:start position:0%
+and uh uh people tend to sort of be lost
+ 
+
+ align:start position:0%
+and uh uh people tend to sort of be lost
+a verse than over
+
+ align:start position:0%
+a verse than over
+ 
+
+ align:start position:0%
+a verse than over
+uh other certain um their uh
+
+ align:start position:0%
+uh other certain um their uh
+ 
+
+ align:start position:0%
+uh other certain um their uh
+expenditures
+
+ align:start position:0%
+expenditures
+ 
+
+ align:start position:0%
+expenditures
+over the specific uh uh domain
+
+ align:start position:0%
+over the specific uh uh domain
+ 
+
+ align:start position:0%
+over the specific uh uh domain
+now that then leads to so if a firm
+
+ align:start position:0%
+now that then leads to so if a firm
+ 
+
+ align:start position:0%
+now that then leads to so if a firm
+knows this so essentially if you know
+
+ align:start position:0%
+knows this so essentially if you know
+ 
+
+ align:start position:0%
+knows this so essentially if you know
+that essentially people react a lot
+
+ align:start position:0%
+that essentially people react a lot
+ 
+
+ align:start position:0%
+that essentially people react a lot
+to price increases um
+
+ align:start position:0%
+to price increases um
+ 
+
+ align:start position:0%
+to price increases um
+compared to price decreases um that
+
+ align:start position:0%
+compared to price decreases um that
+ 
+
+ align:start position:0%
+compared to price decreases um that
+leads to sticky prices essentially so
+
+ align:start position:0%
+leads to sticky prices essentially so
+ 
+
+ align:start position:0%
+leads to sticky prices essentially so
+raising your price above like a pass
+
+ align:start position:0%
+raising your price above like a pass
+ 
+
+ align:start position:0%
+raising your price above like a pass
+price is very costly
+
+ align:start position:0%
+price is very costly
+ 
+
+ align:start position:0%
+price is very costly
+because you lose a lot of customers from
+
+ align:start position:0%
+because you lose a lot of customers from
+ 
+
+ align:start position:0%
+because you lose a lot of customers from
+doing that so now
+
+ align:start position:0%
+doing that so now
+ 
+
+ align:start position:0%
+doing that so now
+lowering your price below the pass price
+
+ align:start position:0%
+lowering your price below the pass price
+ 
+
+ align:start position:0%
+lowering your price below the pass price
+won't actually do very much essentially
+
+ align:start position:0%
+won't actually do very much essentially
+ 
+
+ align:start position:0%
+won't actually do very much essentially
+you're not going to
+
+ align:start position:0%
+you're not going to
+ 
+
+ align:start position:0%
+you're not going to
+generate a lot more extra demand plus
+
+ align:start position:0%
+generate a lot more extra demand plus
+ 
+
+ align:start position:0%
+generate a lot more extra demand plus
+raising the price in the future is
+
+ align:start position:0%
+raising the price in the future is
+ 
+
+ align:start position:0%
+raising the price in the future is
+costly you know essentially once you
+
+ align:start position:0%
+costly you know essentially once you
+ 
+
+ align:start position:0%
+costly you know essentially once you
+lower the price it's hard to get up
+
+ align:start position:0%
+lower the price it's hard to get up
+ 
+
+ align:start position:0%
+lower the price it's hard to get up
+anymore so
+
+ align:start position:0%
+anymore so
+ 
+
+ align:start position:0%
+anymore so
+uh for like these frequently purchased
+
+ align:start position:0%
+uh for like these frequently purchased
+ 
+
+ align:start position:0%
+uh for like these frequently purchased
+items you see a lot of price stickiness
+
+ align:start position:0%
+items you see a lot of price stickiness
+ 
+
+ align:start position:0%
+items you see a lot of price stickiness
+and price equalization
+
+ align:start position:0%
+and price equalization
+ 
+
+ align:start position:0%
+and price equalization
+um across markets across time and
+
+ align:start position:0%
+um across markets across time and
+ 
+
+ align:start position:0%
+um across markets across time and
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+now that's sort of one thing about like
+
+ align:start position:0%
+now that's sort of one thing about like
+ 
+
+ align:start position:0%
+now that's sort of one thing about like
+prices in the world that you would see
+
+ align:start position:0%
+prices in the world that you would see
+ 
+
+ align:start position:0%
+prices in the world that you would see
+but more generally i want to sort of ask
+
+ align:start position:0%
+but more generally i want to sort of ask
+ 
+
+ align:start position:0%
+but more generally i want to sort of ask
+the question in the last few minutes
+
+ align:start position:0%
+the question in the last few minutes
+ 
+
+ align:start position:0%
+the question in the last few minutes
+about like
+
+ align:start position:0%
+about like
+ 
+
+ align:start position:0%
+about like
+if you were a company um suppose you did
+
+ align:start position:0%
+if you were a company um suppose you did
+ 
+
+ align:start position:0%
+if you were a company um suppose you did
+an internship somewhere in the summer
+
+ align:start position:0%
+an internship somewhere in the summer
+ 
+
+ align:start position:0%
+an internship somewhere in the summer
+they told you
+
+ align:start position:0%
+they told you
+ 
+
+ align:start position:0%
+they told you
+um uh you know you you took behavioral
+
+ align:start position:0%
+um uh you know you you took behavioral
+ 
+
+ align:start position:0%
+um uh you know you you took behavioral
+economics uh
+
+ align:start position:0%
+economics uh
+ 
+
+ align:start position:0%
+economics uh
+uh hopefully you learned something but
+
+ align:start position:0%
+uh hopefully you learned something but
+ 
+
+ align:start position:0%
+uh hopefully you learned something but
+like what can we learn about
+
+ align:start position:0%
+like what can we learn about
+ 
+
+ align:start position:0%
+like what can we learn about
+um uh about like the firm policies and
+
+ align:start position:0%
+um uh about like the firm policies and
+ 
+
+ align:start position:0%
+um uh about like the firm policies and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+on now that you know about loss aversion
+
+ align:start position:0%
+on now that you know about loss aversion
+ 
+
+ align:start position:0%
+on now that you know about loss aversion
+what would you tell them they should do
+
+ align:start position:0%
+what would you tell them they should do
+ 
+
+ align:start position:0%
+what would you tell them they should do
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes having a really high price and then
+
+ align:start position:0%
+yes having a really high price and then
+ 
+
+ align:start position:0%
+yes having a really high price and then
+people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that was previously it was
+
+ align:start position:0%
+right so that was previously it was
+ 
+
+ align:start position:0%
+right so that was previously it was
+mentioned is to say you could sort of in
+
+ align:start position:0%
+mentioned is to say you could sort of in
+ 
+
+ align:start position:0%
+mentioned is to say you could sort of in
+particular when you introduce
+
+ align:start position:0%
+particular when you introduce
+ 
+
+ align:start position:0%
+particular when you introduce
+um a price a new product and so on you
+
+ align:start position:0%
+um a price a new product and so on you
+ 
+
+ align:start position:0%
+um a price a new product and so on you
+might want to start at a high price and
+
+ align:start position:0%
+might want to start at a high price and
+ 
+
+ align:start position:0%
+might want to start at a high price and
+then sort of like lowering them and
+
+ align:start position:0%
+then sort of like lowering them and
+ 
+
+ align:start position:0%
+then sort of like lowering them and
+people really like having deals and they
+
+ align:start position:0%
+people really like having deals and they
+ 
+
+ align:start position:0%
+people really like having deals and they
+feel
+
+ align:start position:0%
+feel
+ 
+
+ align:start position:0%
+feel
+good about it notice that that doesn't
+
+ align:start position:0%
+good about it notice that that doesn't
+ 
+
+ align:start position:0%
+good about it notice that that doesn't
+work so well for like
+
+ align:start position:0%
+work so well for like
+ 
+
+ align:start position:0%
+work so well for like
+products that you already have and so on
+
+ align:start position:0%
+products that you already have and so on
+ 
+
+ align:start position:0%
+products that you already have and so on
+because then essentially once you start
+
+ align:start position:0%
+because then essentially once you start
+ 
+
+ align:start position:0%
+because then essentially once you start
+with a high price people get really
+
+ align:start position:0%
+with a high price people get really
+ 
+
+ align:start position:0%
+with a high price people get really
+upset and they
+
+ align:start position:0%
+upset and they
+ 
+
+ align:start position:0%
+upset and they
+you will lose the customers but once you
+
+ align:start position:0%
+you will lose the customers but once you
+ 
+
+ align:start position:0%
+you will lose the customers but once you
+introduce like a new product
+
+ align:start position:0%
+introduce like a new product
+ 
+
+ align:start position:0%
+introduce like a new product
+be it like an iphone or be it like some
+
+ align:start position:0%
+be it like an iphone or be it like some
+ 
+
+ align:start position:0%
+be it like an iphone or be it like some
+whatever new uh
+
+ align:start position:0%
+whatever new uh
+ 
+
+ align:start position:0%
+whatever new uh
+uh computer or whatever it makes a lot
+
+ align:start position:0%
+uh computer or whatever it makes a lot
+ 
+
+ align:start position:0%
+uh computer or whatever it makes a lot
+of sense to start with a really high
+
+ align:start position:0%
+of sense to start with a really high
+ 
+
+ align:start position:0%
+of sense to start with a really high
+price that sort of sets the reference
+
+ align:start position:0%
+price that sort of sets the reference
+ 
+
+ align:start position:0%
+price that sort of sets the reference
+point and then people sort of feel like
+
+ align:start position:0%
+point and then people sort of feel like
+ 
+
+ align:start position:0%
+point and then people sort of feel like
+they go deal get good deals um overall
+
+ align:start position:0%
+they go deal get good deals um overall
+ 
+
+ align:start position:0%
+they go deal get good deals um overall
+what else could you do yes
+
+ align:start position:0%
+what else could you do yes
+ 
+
+ align:start position:0%
+what else could you do yes
+you could offer any single glory
+
+ align:start position:0%
+you could offer any single glory
+ 
+
+ align:start position:0%
+you could offer any single glory
+temporary discounts
+
+ align:start position:0%
+temporary discounts
+ 
+
+ align:start position:0%
+temporary discounts
+the way you keep your reference point
+
+ align:start position:0%
+the way you keep your reference point
+ 
+
+ align:start position:0%
+the way you keep your reference point
+the original price and your
+
+ align:start position:0%
+the original price and your
+ 
+
+ align:start position:0%
+the original price and your
+property for our list
+
+ align:start position:0%
+property for our list
+ 
+
+ align:start position:0%
+property for our list
+exactly that's what a lot of companies
+
+ align:start position:0%
+exactly that's what a lot of companies
+ 
+
+ align:start position:0%
+exactly that's what a lot of companies
+tend to do they tend to do essentially
+
+ align:start position:0%
+tend to do they tend to do essentially
+ 
+
+ align:start position:0%
+tend to do they tend to do essentially
+these like special occasions
+
+ align:start position:0%
+these like special occasions
+ 
+
+ align:start position:0%
+these like special occasions
+we had like black friday and the like
+
+ align:start position:0%
+we had like black friday and the like
+ 
+
+ align:start position:0%
+we had like black friday and the like
+it's not like exactly as you say it's
+
+ align:start position:0%
+it's not like exactly as you say it's
+ 
+
+ align:start position:0%
+it's not like exactly as you say it's
+temporary it's not like a thing that
+
+ align:start position:0%
+temporary it's not like a thing that
+ 
+
+ align:start position:0%
+temporary it's not like a thing that
+prices are uh
+
+ align:start position:0%
+prices are uh
+ 
+
+ align:start position:0%
+prices are uh
+uh permanently lower it's a just right
+
+ align:start position:0%
+uh permanently lower it's a just right
+ 
+
+ align:start position:0%
+uh permanently lower it's a just right
+now you get this like great deal and
+
+ align:start position:0%
+now you get this like great deal and
+ 
+
+ align:start position:0%
+now you get this like great deal and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+things go back to normal and somehow you
+
+ align:start position:0%
+things go back to normal and somehow you
+ 
+
+ align:start position:0%
+things go back to normal and somehow you
+have to hope that people don't sort of
+
+ align:start position:0%
+have to hope that people don't sort of
+ 
+
+ align:start position:0%
+have to hope that people don't sort of
+adjust the reference point uh towards
+
+ align:start position:0%
+adjust the reference point uh towards
+ 
+
+ align:start position:0%
+adjust the reference point uh towards
+the temporarily lowered
+
+ align:start position:0%
+the temporarily lowered
+ 
+
+ align:start position:0%
+the temporarily lowered
+um price what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than yes yes
+
+ align:start position:0%
+than yes yes
+ 
+
+ align:start position:0%
+than yes yes
+so if you shop online you might have
+
+ align:start position:0%
+so if you shop online you might have
+ 
+
+ align:start position:0%
+so if you shop online you might have
+wondered lots of companies have this
+
+ align:start position:0%
+wondered lots of companies have this
+ 
+
+ align:start position:0%
+wondered lots of companies have this
+thing i'm like oh you can order whatever
+
+ align:start position:0%
+thing i'm like oh you can order whatever
+ 
+
+ align:start position:0%
+thing i'm like oh you can order whatever
+you want you're like essentially it's
+
+ align:start position:0%
+you want you're like essentially it's
+ 
+
+ align:start position:0%
+you want you're like essentially it's
+like free returns and you kind of wonder
+
+ align:start position:0%
+like free returns and you kind of wonder
+ 
+
+ align:start position:0%
+like free returns and you kind of wonder
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that seems like a bad deal from the
+
+ align:start position:0%
+that seems like a bad deal from the
+ 
+
+ align:start position:0%
+that seems like a bad deal from the
+company's perspective because people buy
+
+ align:start position:0%
+company's perspective because people buy
+ 
+
+ align:start position:0%
+company's perspective because people buy
+a lot of stuff and send it back
+
+ align:start position:0%
+a lot of stuff and send it back
+ 
+
+ align:start position:0%
+a lot of stuff and send it back
+the hope is exactly as they say it might
+
+ align:start position:0%
+the hope is exactly as they say it might
+ 
+
+ align:start position:0%
+the hope is exactly as they say it might
+be just in part people like to
+
+ align:start position:0%
+be just in part people like to
+ 
+
+ align:start position:0%
+be just in part people like to
+experiment and they like some stuff and
+
+ align:start position:0%
+experiment and they like some stuff and
+ 
+
+ align:start position:0%
+experiment and they like some stuff and
+not others and that's worth doing it
+
+ align:start position:0%
+not others and that's worth doing it
+ 
+
+ align:start position:0%
+not others and that's worth doing it
+but the hope in particular is to say
+
+ align:start position:0%
+but the hope in particular is to say
+ 
+
+ align:start position:0%
+but the hope in particular is to say
+well i want you to try it out for a
+
+ align:start position:0%
+well i want you to try it out for a
+ 
+
+ align:start position:0%
+well i want you to try it out for a
+while you get used to it
+
+ align:start position:0%
+while you get used to it
+ 
+
+ align:start position:0%
+while you get used to it
+then the endowment effect kicks in you
+
+ align:start position:0%
+then the endowment effect kicks in you
+ 
+
+ align:start position:0%
+then the endowment effect kicks in you
+value it more he essentially becomes
+
+ align:start position:0%
+value it more he essentially becomes
+ 
+
+ align:start position:0%
+value it more he essentially becomes
+yours
+
+ align:start position:0%
+yours
+ 
+
+ align:start position:0%
+yours
+and uh then essentially you become lost
+
+ align:start position:0%
+and uh then essentially you become lost
+ 
+
+ align:start position:0%
+and uh then essentially you become lost
+of hers
+
+ align:start position:0%
+of hers
+ 
+
+ align:start position:0%
+of hers
+towards that by the way i should have
+
+ align:start position:0%
+towards that by the way i should have
+ 
+
+ align:start position:0%
+towards that by the way i should have
+mentioned uh this is really
+
+ align:start position:0%
+mentioned uh this is really
+ 
+
+ align:start position:0%
+mentioned uh this is really
+a fascinating book by chaldini who's
+
+ align:start position:0%
+a fascinating book by chaldini who's
+ 
+
+ align:start position:0%
+a fascinating book by chaldini who's
+uh talking about the psychology of
+
+ align:start position:0%
+uh talking about the psychology of
+ 
+
+ align:start position:0%
+uh talking about the psychology of
+persuasion he spent a lot of time with
+
+ align:start position:0%
+persuasion he spent a lot of time with
+ 
+
+ align:start position:0%
+persuasion he spent a lot of time with
+like sales people and particular sort of
+
+ align:start position:0%
+like sales people and particular sort of
+ 
+
+ align:start position:0%
+like sales people and particular sort of
+car sales people and so on trying to
+
+ align:start position:0%
+car sales people and so on trying to
+ 
+
+ align:start position:0%
+car sales people and so on trying to
+learn of what are they actually doing in
+
+ align:start position:0%
+learn of what are they actually doing in
+ 
+
+ align:start position:0%
+learn of what are they actually doing in
+markets
+
+ align:start position:0%
+markets
+ 
+
+ align:start position:0%
+markets
+and he has these like amazing stories of
+
+ align:start position:0%
+and he has these like amazing stories of
+ 
+
+ align:start position:0%
+and he has these like amazing stories of
+like sales people what's all sorts of
+
+ align:start position:0%
+like sales people what's all sorts of
+ 
+
+ align:start position:0%
+like sales people what's all sorts of
+tricks they they use
+
+ align:start position:0%
+tricks they they use
+ 
+
+ align:start position:0%
+tricks they they use
+it's psychologically extremely rich and
+
+ align:start position:0%
+it's psychologically extremely rich and
+ 
+
+ align:start position:0%
+it's psychologically extremely rich and
+interesting in terms of just trying to
+
+ align:start position:0%
+interesting in terms of just trying to
+ 
+
+ align:start position:0%
+interesting in terms of just trying to
+understand what people do
+
+ align:start position:0%
+understand what people do
+ 
+
+ align:start position:0%
+understand what people do
+and that ranges from things like you
+
+ align:start position:0%
+and that ranges from things like you
+ 
+
+ align:start position:0%
+and that ranges from things like you
+know once you um
+
+ align:start position:0%
+know once you um
+ 
+
+ align:start position:0%
+know once you um
+uh purchase a car they let you like test
+
+ align:start position:0%
+uh purchase a car they let you like test
+ 
+
+ align:start position:0%
+uh purchase a car they let you like test
+drive in the car and you sit in it and
+
+ align:start position:0%
+drive in the car and you sit in it and
+ 
+
+ align:start position:0%
+drive in the car and you sit in it and
+it feels like yours and then
+
+ align:start position:0%
+it feels like yours and then
+ 
+
+ align:start position:0%
+it feels like yours and then
+you know or when you try to buy a house
+
+ align:start position:0%
+you know or when you try to buy a house
+ 
+
+ align:start position:0%
+you know or when you try to buy a house
+you know then people would say like oh
+
+ align:start position:0%
+you know then people would say like oh
+ 
+
+ align:start position:0%
+you know then people would say like oh
+you know this will be your living room
+
+ align:start position:0%
+you know this will be your living room
+ 
+
+ align:start position:0%
+you know this will be your living room
+and this is where your baby is going to
+
+ align:start position:0%
+and this is where your baby is going to
+ 
+
+ align:start position:0%
+and this is where your baby is going to
+sleep and like
+
+ align:start position:0%
+sleep and like
+ 
+
+ align:start position:0%
+sleep and like
+you know there's lots of sort of ways in
+
+ align:start position:0%
+you know there's lots of sort of ways in
+ 
+
+ align:start position:0%
+you know there's lots of sort of ways in
+which people make sort of something feel
+
+ align:start position:0%
+which people make sort of something feel
+ 
+
+ align:start position:0%
+which people make sort of something feel
+yours and really try to sort of get the
+
+ align:start position:0%
+yours and really try to sort of get the
+ 
+
+ align:start position:0%
+yours and really try to sort of get the
+endowment effect um
+
+ align:start position:0%
+endowment effect um
+ 
+
+ align:start position:0%
+endowment effect um
+uh to kick in if you were to work in an
+
+ align:start position:0%
+uh to kick in if you were to work in an
+ 
+
+ align:start position:0%
+uh to kick in if you were to work in an
+insurance firm what would you do like
+
+ align:start position:0%
+insurance firm what would you do like
+ 
+
+ align:start position:0%
+insurance firm what would you do like
+somebody who offers insurance in one way
+
+ align:start position:0%
+somebody who offers insurance in one way
+ 
+
+ align:start position:0%
+somebody who offers insurance in one way
+or the other
+
+ align:start position:0%
+or the other
+ 
+
+ align:start position:0%
+or the other
+or products that offer insurance in some
+
+ align:start position:0%
+or products that offer insurance in some
+ 
+
+ align:start position:0%
+or products that offer insurance in some
+ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes we talked about this a little bit in
+
+ align:start position:0%
+yes we talked about this a little bit in
+ 
+
+ align:start position:0%
+yes we talked about this a little bit in
+the previous class
+
+ align:start position:0%
+the previous class
+ 
+
+ align:start position:0%
+the previous class
+but uh this is why i think companies
+
+ align:start position:0%
+but uh this is why i think companies
+ 
+
+ align:start position:0%
+but uh this is why i think companies
+will sell things like apple care or
+
+ align:start position:0%
+will sell things like apple care or
+ 
+
+ align:start position:0%
+will sell things like apple care or
+operational warranties because they can
+
+ align:start position:0%
+operational warranties because they can
+ 
+
+ align:start position:0%
+operational warranties because they can
+they know they'll make money off of it
+
+ align:start position:0%
+they know they'll make money off of it
+ 
+
+ align:start position:0%
+they know they'll make money off of it
+because people tend to overinsure
+
+ align:start position:0%
+because people tend to overinsure
+ 
+
+ align:start position:0%
+because people tend to overinsure
+exactly there's lots of different
+
+ align:start position:0%
+exactly there's lots of different
+ 
+
+ align:start position:0%
+exactly there's lots of different
+products where there's extended
+
+ align:start position:0%
+products where there's extended
+ 
+
+ align:start position:0%
+products where there's extended
+warranties and all sorts of like things
+
+ align:start position:0%
+warranties and all sorts of like things
+ 
+
+ align:start position:0%
+warranties and all sorts of like things
+like apple care etc
+
+ align:start position:0%
+like apple care etc
+ 
+
+ align:start position:0%
+like apple care etc
+where people are like very risk-averse
+
+ align:start position:0%
+where people are like very risk-averse
+ 
+
+ align:start position:0%
+where people are like very risk-averse
+what it looks like presumably loss of
+
+ align:start position:0%
+what it looks like presumably loss of
+ 
+
+ align:start position:0%
+what it looks like presumably loss of
+errors
+
+ align:start position:0%
+errors
+ 
+
+ align:start position:0%
+errors
+um where in fact you know they actually
+
+ align:start position:0%
+um where in fact you know they actually
+ 
+
+ align:start position:0%
+um where in fact you know they actually
+the claim rate tends to be very low
+
+ align:start position:0%
+the claim rate tends to be very low
+ 
+
+ align:start position:0%
+the claim rate tends to be very low
+so you can make a lot of money with this
+
+ align:start position:0%
+so you can make a lot of money with this
+ 
+
+ align:start position:0%
+so you can make a lot of money with this
+by saying like yes i'm going to exchange
+
+ align:start position:0%
+by saying like yes i'm going to exchange
+ 
+
+ align:start position:0%
+by saying like yes i'm going to exchange
+it in this and that
+
+ align:start position:0%
+it in this and that
+ 
+
+ align:start position:0%
+it in this and that
+because essentially it doesn't happen
+
+ align:start position:0%
+because essentially it doesn't happen
+ 
+
+ align:start position:0%
+because essentially it doesn't happen
+that often at the end of the day
+
+ align:start position:0%
+that often at the end of the day
+ 
+
+ align:start position:0%
+that often at the end of the day
+even if there's like moral hazard or
+
+ align:start position:0%
+even if there's like moral hazard or
+ 
+
+ align:start position:0%
+even if there's like moral hazard or
+other issues so people not treating
+
+ align:start position:0%
+other issues so people not treating
+ 
+
+ align:start position:0%
+other issues so people not treating
+their stuff that well once they have
+
+ align:start position:0%
+their stuff that well once they have
+ 
+
+ align:start position:0%
+their stuff that well once they have
+insurance what about wage setting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like when you when you set your your
+
+ align:start position:0%
+like when you when you set your your
+ 
+
+ align:start position:0%
+like when you when you set your your
+employees wages
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah could that be linked to mass
+
+ align:start position:0%
+yeah could that be linked to mass
+ 
+
+ align:start position:0%
+yeah could that be linked to mass
+unemployment in recessions because
+
+ align:start position:0%
+unemployment in recessions because
+ 
+
+ align:start position:0%
+unemployment in recessions because
+you know that if you lower the wage then
+
+ align:start position:0%
+you know that if you lower the wage then
+ 
+
+ align:start position:0%
+you know that if you lower the wage then
+morale will go down a lot
+
+ align:start position:0%
+morale will go down a lot
+ 
+
+ align:start position:0%
+morale will go down a lot
+and you could actually decide just to
+
+ align:start position:0%
+and you could actually decide just to
+ 
+
+ align:start position:0%
+and you could actually decide just to
+kick them out
+
+ align:start position:0%
+kick them out
+ 
+
+ align:start position:0%
+kick them out
+right so exactly so there is um
+
+ align:start position:0%
+right so exactly so there is um
+ 
+
+ align:start position:0%
+right so exactly so there is um
+there is um a large uh literature
+
+ align:start position:0%
+there is um a large uh literature
+ 
+
+ align:start position:0%
+there is um a large uh literature
+on uh wage stickiness um
+
+ align:start position:0%
+on uh wage stickiness um
+ 
+
+ align:start position:0%
+on uh wage stickiness um
+essentially exactly as you say
+
+ align:start position:0%
+essentially exactly as you say
+ 
+
+ align:start position:0%
+essentially exactly as you say
+where people are extremely reluctant to
+
+ align:start position:0%
+where people are extremely reluctant to
+ 
+
+ align:start position:0%
+where people are extremely reluctant to
+lower wages
+
+ align:start position:0%
+lower wages
+ 
+
+ align:start position:0%
+lower wages
+companies are very reluctant to lower
+
+ align:start position:0%
+companies are very reluctant to lower
+ 
+
+ align:start position:0%
+companies are very reluctant to lower
+wages because essentially workers are
+
+ align:start position:0%
+wages because essentially workers are
+ 
+
+ align:start position:0%
+wages because essentially workers are
+really unhappy
+
+ align:start position:0%
+really unhappy
+ 
+
+ align:start position:0%
+really unhappy
+so once you and these are like often
+
+ align:start position:0%
+so once you and these are like often
+ 
+
+ align:start position:0%
+so once you and these are like often
+nominal wages or real wages it doesn't
+
+ align:start position:0%
+nominal wages or real wages it doesn't
+ 
+
+ align:start position:0%
+nominal wages or real wages it doesn't
+really matter that much but usually it's
+
+ align:start position:0%
+really matter that much but usually it's
+ 
+
+ align:start position:0%
+really matter that much but usually it's
+nominal wages
+
+ align:start position:0%
+nominal wages
+ 
+
+ align:start position:0%
+nominal wages
+people really really dislike nominal
+
+ align:start position:0%
+people really really dislike nominal
+ 
+
+ align:start position:0%
+people really really dislike nominal
+wage
+
+ align:start position:0%
+wage
+ 
+
+ align:start position:0%
+wage
+reductions and so now in some times when
+
+ align:start position:0%
+reductions and so now in some times when
+ 
+
+ align:start position:0%
+reductions and so now in some times when
+uh companies would actually need to
+
+ align:start position:0%
+uh companies would actually need to
+ 
+
+ align:start position:0%
+uh companies would actually need to
+lower wages
+
+ align:start position:0%
+lower wages
+ 
+
+ align:start position:0%
+lower wages
+and sort of to be able to keep workers
+
+ align:start position:0%
+and sort of to be able to keep workers
+ 
+
+ align:start position:0%
+and sort of to be able to keep workers
+not to make losses
+
+ align:start position:0%
+not to make losses
+ 
+
+ align:start position:0%
+not to make losses
+companies might rather sort of fire some
+
+ align:start position:0%
+companies might rather sort of fire some
+ 
+
+ align:start position:0%
+companies might rather sort of fire some
+workers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rather than sort of lowering the wages
+
+ align:start position:0%
+rather than sort of lowering the wages
+ 
+
+ align:start position:0%
+rather than sort of lowering the wages
+for everybody because essentially
+
+ align:start position:0%
+for everybody because essentially
+ 
+
+ align:start position:0%
+for everybody because essentially
+the remaining workers once you lower
+
+ align:start position:0%
+the remaining workers once you lower
+ 
+
+ align:start position:0%
+the remaining workers once you lower
+wages for everybody everybody would be
+
+ align:start position:0%
+wages for everybody everybody would be
+ 
+
+ align:start position:0%
+wages for everybody everybody would be
+unhappy if you just
+
+ align:start position:0%
+unhappy if you just
+ 
+
+ align:start position:0%
+unhappy if you just
+fire one worker everybody else will be
+
+ align:start position:0%
+fire one worker everybody else will be
+ 
+
+ align:start position:0%
+fire one worker everybody else will be
+less unhappy than about their wage
+
+ align:start position:0%
+less unhappy than about their wage
+ 
+
+ align:start position:0%
+less unhappy than about their wage
+reductions similarly
+
+ align:start position:0%
+reductions similarly
+ 
+
+ align:start position:0%
+reductions similarly
+firms are reluctant to hire people at
+
+ align:start position:0%
+firms are reluctant to hire people at
+ 
+
+ align:start position:0%
+firms are reluctant to hire people at
+lower wages if there's other people who
+
+ align:start position:0%
+lower wages if there's other people who
+ 
+
+ align:start position:0%
+lower wages if there's other people who
+make higher wages because people really
+
+ align:start position:0%
+make higher wages because people really
+ 
+
+ align:start position:0%
+make higher wages because people really
+dislike wage dispersion
+
+ align:start position:0%
+dislike wage dispersion
+ 
+
+ align:start position:0%
+dislike wage dispersion
+so essentially overall you want to to
+
+ align:start position:0%
+so essentially overall you want to to
+ 
+
+ align:start position:0%
+so essentially overall you want to to
+avoid wage cuts as much as possible
+
+ align:start position:0%
+avoid wage cuts as much as possible
+ 
+
+ align:start position:0%
+avoid wage cuts as much as possible
+and that leads to essentially then the
+
+ align:start position:0%
+and that leads to essentially then the
+ 
+
+ align:start position:0%
+and that leads to essentially then the
+macroeconomic inefficiencies and people
+
+ align:start position:0%
+macroeconomic inefficiencies and people
+ 
+
+ align:start position:0%
+macroeconomic inefficiencies and people
+have argued in particular it leads to
+
+ align:start position:0%
+have argued in particular it leads to
+ 
+
+ align:start position:0%
+have argued in particular it leads to
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+unemployment because essentially uh
+
+ align:start position:0%
+unemployment because essentially uh
+ 
+
+ align:start position:0%
+unemployment because essentially uh
+wages are not going down as much as they
+
+ align:start position:0%
+wages are not going down as much as they
+ 
+
+ align:start position:0%
+wages are not going down as much as they
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+in recessions and that's bad for firms
+
+ align:start position:0%
+in recessions and that's bad for firms
+ 
+
+ align:start position:0%
+in recessions and that's bad for firms
+and therefore they hire fewer workers to
+
+ align:start position:0%
+and therefore they hire fewer workers to
+ 
+
+ align:start position:0%
+and therefore they hire fewer workers to
+retain fewer workers overall
+
+ align:start position:0%
+retain fewer workers overall
+ 
+
+ align:start position:0%
+retain fewer workers overall
+i think i mentioned we mentioned all of
+
+ align:start position:0%
+i think i mentioned we mentioned all of
+ 
+
+ align:start position:0%
+i think i mentioned we mentioned all of
+those uh uh kind of things
+
+ align:start position:0%
+those uh uh kind of things
+ 
+
+ align:start position:0%
+those uh uh kind of things
+so now um another thing that sort of
+
+ align:start position:0%
+so now um another thing that sort of
+ 
+
+ align:start position:0%
+so now um another thing that sort of
+that's sort of like what firms are doing
+
+ align:start position:0%
+that's sort of like what firms are doing
+ 
+
+ align:start position:0%
+that's sort of like what firms are doing
+now another thing you might think about
+
+ align:start position:0%
+now another thing you might think about
+ 
+
+ align:start position:0%
+now another thing you might think about
+is like what are you going to actually
+
+ align:start position:0%
+is like what are you going to actually
+ 
+
+ align:start position:0%
+is like what are you going to actually
+do in your real lives
+
+ align:start position:0%
+do in your real lives
+ 
+
+ align:start position:0%
+do in your real lives
+um i think there's many different things
+
+ align:start position:0%
+um i think there's many different things
+ 
+
+ align:start position:0%
+um i think there's many different things
+that you can actually think about is
+
+ align:start position:0%
+that you can actually think about is
+ 
+
+ align:start position:0%
+that you can actually think about is
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+the framing of situations for example
+
+ align:start position:0%
+the framing of situations for example
+ 
+
+ align:start position:0%
+the framing of situations for example
+can make a big difference if you
+
+ align:start position:0%
+can make a big difference if you
+ 
+
+ align:start position:0%
+can make a big difference if you
+present something to your friends
+
+ align:start position:0%
+present something to your friends
+ 
+
+ align:start position:0%
+present something to your friends
+different options whether you whether
+
+ align:start position:0%
+different options whether you whether
+ 
+
+ align:start position:0%
+different options whether you whether
+you present that as like gains or losses
+
+ align:start position:0%
+you present that as like gains or losses
+ 
+
+ align:start position:0%
+you present that as like gains or losses
+makes a big difference potentially
+
+ align:start position:0%
+makes a big difference potentially
+ 
+
+ align:start position:0%
+makes a big difference potentially
+managing people's expectations is really
+
+ align:start position:0%
+managing people's expectations is really
+ 
+
+ align:start position:0%
+managing people's expectations is really
+important if there's like
+
+ align:start position:0%
+important if there's like
+ 
+
+ align:start position:0%
+important if there's like
+some big goal that they could reach or
+
+ align:start position:0%
+some big goal that they could reach or
+ 
+
+ align:start position:0%
+some big goal that they could reach or
+some lower goal they could they could
+
+ align:start position:0%
+some lower goal they could they could
+ 
+
+ align:start position:0%
+some lower goal they could they could
+reach if you sort of oversell the high
+
+ align:start position:0%
+reach if you sort of oversell the high
+ 
+
+ align:start position:0%
+reach if you sort of oversell the high
+chance of like
+
+ align:start position:0%
+chance of like
+ 
+
+ align:start position:0%
+chance of like
+reaching some big goal they might reach
+
+ align:start position:0%
+reaching some big goal they might reach
+ 
+
+ align:start position:0%
+reaching some big goal they might reach
+the other goal that's actually pretty
+
+ align:start position:0%
+the other goal that's actually pretty
+ 
+
+ align:start position:0%
+the other goal that's actually pretty
+good might
+
+ align:start position:0%
+good might
+ 
+
+ align:start position:0%
+good might
+feel like really disappointed about that
+
+ align:start position:0%
+feel like really disappointed about that
+ 
+
+ align:start position:0%
+feel like really disappointed about that
+be it in job search or the like
+
+ align:start position:0%
+be it in job search or the like
+ 
+
+ align:start position:0%
+be it in job search or the like
+so managing people's expectations
+
+ align:start position:0%
+so managing people's expectations
+ 
+
+ align:start position:0%
+so managing people's expectations
+including your own expectations
+
+ align:start position:0%
+including your own expectations
+ 
+
+ align:start position:0%
+including your own expectations
+seems really important there's something
+
+ align:start position:0%
+seems really important there's something
+ 
+
+ align:start position:0%
+seems really important there's something
+about aggregating losses and gains which
+
+ align:start position:0%
+about aggregating losses and gains which
+ 
+
+ align:start position:0%
+about aggregating losses and gains which
+essentially is to say
+
+ align:start position:0%
+essentially is to say
+ 
+
+ align:start position:0%
+essentially is to say
+since people seem to be um uh
+
+ align:start position:0%
+since people seem to be um uh
+ 
+
+ align:start position:0%
+since people seem to be um uh
+uh risk averse over gains and um so
+
+ align:start position:0%
+uh risk averse over gains and um so
+ 
+
+ align:start position:0%
+uh risk averse over gains and um so
+since the value function is concave
+
+ align:start position:0%
+since the value function is concave
+ 
+
+ align:start position:0%
+since the value function is concave
+over gains and convex over losses um
+
+ align:start position:0%
+over gains and convex over losses um
+ 
+
+ align:start position:0%
+over gains and convex over losses um
+what you should do is potentially as
+
+ align:start position:0%
+what you should do is potentially as
+ 
+
+ align:start position:0%
+what you should do is potentially as
+like be really careful about like
+
+ align:start position:0%
+like be really careful about like
+ 
+
+ align:start position:0%
+like be really careful about like
+when you give people uh a positive or
+
+ align:start position:0%
+when you give people uh a positive or
+ 
+
+ align:start position:0%
+when you give people uh a positive or
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+um feedback or like bonuses and so on uh
+
+ align:start position:0%
+um feedback or like bonuses and so on uh
+ 
+
+ align:start position:0%
+um feedback or like bonuses and so on uh
+you might want to sort of be
+
+ align:start position:0%
+you might want to sort of be
+ 
+
+ align:start position:0%
+you might want to sort of be
+be careful like uh whether you uh
+
+ align:start position:0%
+be careful like uh whether you uh
+ 
+
+ align:start position:0%
+be careful like uh whether you uh
+aggregate the losses or
+
+ align:start position:0%
+aggregate the losses or
+ 
+
+ align:start position:0%
+aggregate the losses or
+so aggregating losses makes sense
+
+ align:start position:0%
+so aggregating losses makes sense
+ 
+
+ align:start position:0%
+so aggregating losses makes sense
+because it's essentially it's like um
+
+ align:start position:0%
+because it's essentially it's like um
+ 
+
+ align:start position:0%
+because it's essentially it's like um
+convex in the lost domain as opposed to
+
+ align:start position:0%
+convex in the lost domain as opposed to
+ 
+
+ align:start position:0%
+convex in the lost domain as opposed to
+like you want to give small increments
+
+ align:start position:0%
+like you want to give small increments
+ 
+
+ align:start position:0%
+like you want to give small increments
+of gains
+
+ align:start position:0%
+of gains
+ 
+
+ align:start position:0%
+of gains
+um overall now one thing that i do want
+
+ align:start position:0%
+um overall now one thing that i do want
+ 
+
+ align:start position:0%
+um overall now one thing that i do want
+to mention is like you want to be kind
+
+ align:start position:0%
+to mention is like you want to be kind
+ 
+
+ align:start position:0%
+to mention is like you want to be kind
+of very careful with last framed
+
+ align:start position:0%
+of very careful with last framed
+ 
+
+ align:start position:0%
+of very careful with last framed
+incentives
+
+ align:start position:0%
+incentives
+ 
+
+ align:start position:0%
+incentives
+there's a company who is trying to do
+
+ align:start position:0%
+there's a company who is trying to do
+ 
+
+ align:start position:0%
+there's a company who is trying to do
+this um uh and
+
+ align:start position:0%
+this um uh and
+ 
+
+ align:start position:0%
+this um uh and
+trying to give essentially these are
+
+ align:start position:0%
+trying to give essentially these are
+ 
+
+ align:start position:0%
+trying to give essentially these are
+like car manufacturers were trying to
+
+ align:start position:0%
+like car manufacturers were trying to
+ 
+
+ align:start position:0%
+like car manufacturers were trying to
+give essentially their car dealers
+
+ align:start position:0%
+give essentially their car dealers
+ 
+
+ align:start position:0%
+give essentially their car dealers
+incentives
+
+ align:start position:0%
+incentives
+ 
+
+ align:start position:0%
+incentives
+um sort of uh targets
+
+ align:start position:0%
+um sort of uh targets
+ 
+
+ align:start position:0%
+um sort of uh targets
+in their um for their sales of of their
+
+ align:start position:0%
+in their um for their sales of of their
+ 
+
+ align:start position:0%
+in their um for their sales of of their
+their cars what essentially happened at
+
+ align:start position:0%
+their cars what essentially happened at
+ 
+
+ align:start position:0%
+their cars what essentially happened at
+the end of the day is like there was a
+
+ align:start position:0%
+the end of the day is like there was a
+ 
+
+ align:start position:0%
+the end of the day is like there was a
+bunch of um
+
+ align:start position:0%
+bunch of um
+ 
+
+ align:start position:0%
+bunch of um
+multitasking is like the company or the
+
+ align:start position:0%
+multitasking is like the company or the
+ 
+
+ align:start position:0%
+multitasking is like the company or the
+car sales people were essentially
+
+ align:start position:0%
+car sales people were essentially
+ 
+
+ align:start position:0%
+car sales people were essentially
+selling certain cars but they're not
+
+ align:start position:0%
+selling certain cars but they're not
+ 
+
+ align:start position:0%
+selling certain cars but they're not
+others and we're essentially
+
+ align:start position:0%
+others and we're essentially
+ 
+
+ align:start position:0%
+others and we're essentially
+multitasking and then sort of
+
+ align:start position:0%
+multitasking and then sort of
+ 
+
+ align:start position:0%
+multitasking and then sort of
+reverting uh sort of reallocating
+
+ align:start position:0%
+reverting uh sort of reallocating
+ 
+
+ align:start position:0%
+reverting uh sort of reallocating
+efforts to one thing versus the other
+
+ align:start position:0%
+efforts to one thing versus the other
+ 
+
+ align:start position:0%
+efforts to one thing versus the other
+which then seemed like a really good
+
+ align:start position:0%
+which then seemed like a really good
+ 
+
+ align:start position:0%
+which then seemed like a really good
+idea there was a recent evaluation that
+
+ align:start position:0%
+idea there was a recent evaluation that
+ 
+
+ align:start position:0%
+idea there was a recent evaluation that
+sort of showed that
+
+ align:start position:0%
+sort of showed that
+ 
+
+ align:start position:0%
+sort of showed that
+um that was actually pretty bad idea and
+
+ align:start position:0%
+um that was actually pretty bad idea and
+ 
+
+ align:start position:0%
+um that was actually pretty bad idea and
+the company would have lost a lot of
+
+ align:start position:0%
+the company would have lost a lot of
+ 
+
+ align:start position:0%
+the company would have lost a lot of
+money overall
+
+ align:start position:0%
+money overall
+ 
+
+ align:start position:0%
+money overall
+if this had been uh scaled we're gonna
+
+ align:start position:0%
+if this had been uh scaled we're gonna
+ 
+
+ align:start position:0%
+if this had been uh scaled we're gonna
+have this the the dlr no deal and the
+
+ align:start position:0%
+have this the the dlr no deal and the
+ 
+
+ align:start position:0%
+have this the the dlr no deal and the
+specific paper and recitation to tell
+
+ align:start position:0%
+specific paper and recitation to tell
+ 
+
+ align:start position:0%
+specific paper and recitation to tell
+you in more detail
+
+ align:start position:0%
+you in more detail
+ 
+
+ align:start position:0%
+you in more detail
+because i want to move towards social
+
+ align:start position:0%
+because i want to move towards social
+ 
+
+ align:start position:0%
+because i want to move towards social
+preferences next time
+
+ align:start position:0%
+preferences next time
+ 
+
+ align:start position:0%
+preferences next time
+uh so as i said next time we talk about
+
+ align:start position:0%
+uh so as i said next time we talk about
+ 
+
+ align:start position:0%
+uh so as i said next time we talk about
+social preferences bring your laptop and
+
+ align:start position:0%
+social preferences bring your laptop and
+ 
+
+ align:start position:0%
+social preferences bring your laptop and
+i'll send you further instructions
+
+ align:start position:0%
+i'll send you further instructions
+ 
+
+ align:start position:0%
+i'll send you further instructions
+thank you
\ No newline at end of file
diff --git a/SI_GKdFQmds.txt b/SI_GKdFQmds.txt
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index 0000000000000000000000000000000000000000..e429f25f84953b3f1363203c330c8dc5265f1421
--- /dev/null
+++ b/SI_GKdFQmds.txt
@@ -0,0 +1,4081 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Mike Acton today
+who has done a lot of
+
+programming on cell and also
+done a lot of game
+
+development.
+
+He came from California just
+like this today and
+
+[OBSCURED].
+
+MIKE ACTON: Yeah, it's
+really cool.
+
+I'll tell you.
+
+PROFESSOR: He's going to talk
+about what it's really like to
+
+use cell and PS3 and what it's
+like to program games.
+
+So I think it's going
+to be a fun lecture.
+
+MIKE ACTON: All right, so
+anyway, I'm the Engine
+
+Director at Insomniac Games.
+
+I've only recently taken that
+position, previously I was
+
+working on PS3 technology at
+Highmoon studios, which is
+
+with vin studios.
+
+And I've worked at Sony.
+
+I've worked for Titus, and
+Bluesky Studios in San Diego.
+
+And I've been doing game
+development, 11, 12 years.
+
+Before that I was working
+in simulation.
+
+So, the PlayStation 3 is
+a really fun platform.
+
+And I know you guys have been
+working on cell development.
+
+Working with the PS3
+under Linux.
+
+Working as developers for the
+PS3 is definitely a different
+
+environment from that.
+
+I think I'm going to concentrate
+more on the
+
+high-level aspects of how you
+design a game for the cell.
+
+And how the cell would impact
+the design, and what are the
+
+elements of the game.
+
+Just stuff that you probably
+haven't had as part of this
+
+course that you might
+find interesting.
+
+And you can feel free to
+interrupt me at any time with
+
+questions or whatever
+you'd like.
+
+So just, I wanted to go over,
+briefly, some of the different
+
+types of game development and
+what the trade-offs for each
+
+one of them are.
+
+Casual games, console games,
+PC games, blah, blah, blah.
+
+Casual games, basically, are the
+small, simple games that
+
+you would download on
+the PC, or you would
+
+see on Yahoo or whatever.
+
+And those generally don't have
+really strict performance
+
+requirements.
+
+Where a console game, we have
+this particular advantage of
+
+knowing the hardware and the
+hardware doesn't change for an
+
+entire cycle.
+
+So for five, six years, we have
+
+exactly the same hardware.
+
+And that's definitely an
+advantage from a performance
+
+point anyway.
+
+In this case, it's
+PlayStation 3.
+
+As far as develpment priorities,
+development
+
+priorities for a console game--
+and especially a PS3
+
+game-- development would be
+completely different than you
+
+might find on another
+kind of application.
+
+We don't really consider the
+code itself important at all.
+
+The real value is in
+the programmers.
+
+The real value is in
+the experience,
+
+and is in those skills.
+
+Code is disposable.
+
+After six years, when we start
+a new platform we pretty much
+
+have to rewrite it anyway, so
+there's not much point in
+
+trying to plan for a long
+life span of code.
+
+Especially when you have
+optimized code written in
+
+assembly for a particular
+platform.
+
+And to that end, the data is
+way more significant to the
+
+performance than the
+code, anyway.
+
+And the data is specific
+to a particular game.
+
+Or specific to a particular
+type of game.
+
+And certainly specific to
+a studios pipeline.
+
+And it's the design of the data
+where you really want to
+
+spend your time concentrating,
+especially for the PS3.
+
+Ease of programming-- whether
+or not it's easier to do
+
+parallelism is not a major
+concern at all.
+
+If it's hard, so what?
+
+You do it.
+
+That's it.
+
+Portability, runs on PlayStation
+3, doesn't run
+
+anywhere else.
+
+That's a non-concern.
+
+And everything is about
+performance.
+
+Everything we do.
+
+A vast majority of our code is
+either hand up from IC, or
+
+assembly, very little
+high level code.
+
+Some of our gameplay programmers
+will write C plus
+
+plus for the high level logic,
+but as a general, most of the
+
+code that's running most the
+time is definitely optimized.
+
+Yeah?
+
+AUDIENCE: If programming is a
+non-priority, does that mean
+
+to say that if you're developing
+more than one
+
+product or game, they don't
+share any common
+
+infrastructure or need?
+
+MIKE ACTION: No, that's
+not necessarily true.
+
+If we have games that share
+similar needs, they can
+
+definitely share similar code.
+
+I mean, the point I'm trying to
+make is, let's say in order
+
+to make something fast it
+has to be complicated.
+
+So be it, it's complicated.
+
+Whether or not it's easy to use
+for another programmer is
+
+not a major concern.
+
+AUDIENCE: So you wish
+it was easier?
+
+MIKE ACTION: No.
+
+I don't care.
+
+That's my point.
+
+AUDIENCE: Well, it's not as
+important as performance, but
+
+if someone came to you with a
+high performance tool, you
+
+would like to use it?
+
+MIKE ACTION: I doubt
+they could.
+
+The highest performance tool
+that exists is the brains of
+
+the programmers on our team.
+
+You can not create--
+
+it's theoretically impossible.
+
+You can not out perform people
+who are customizing for the
+
+data, for the context
+for the game.
+
+It is not even remotely
+theoretically possible.
+
+AUDIENCE: That didn't come out
+in assembly programming for
+
+general purpose but we'll
+take this offline?
+
+And there was a day when that
+was also true for general
+
+preferred cleary at the time,
+but it's no longer true.
+
+MIKE ACTION: It is
+absolutely--
+
+AUDIENCE: So the average person
+prefers to go on --
+
+take it offline.
+
+MIKE ACTION: Average person.
+
+We're not the average people.
+
+We're game programmers.
+
+Yeah?
+
+AUDIENCE: So does cost
+ever become an issue?
+
+I mean--
+
+MIKE ACTION: Absolutely, cost
+does become an issue.
+
+At a certain pont, something
+is so difficult that you
+
+either have to throw up
+your hands or you
+
+can't finish in time.
+
+AUDIENCE: Do you ever
+hit that point?
+
+MIKE ACTION: Or you figure out
+a new way of doing it.
+
+Or do a little bit less.
+
+I mean we do have to prioritize
+
+what you want to do.
+
+At the end of the day you can't
+do everything you want
+
+to do, and you have another
+game you need to ship
+
+eventually, anyway.
+
+So, a lot of times you do
+end up tabling things.
+
+And say, look we can get 50%
+more performance out of this,
+
+but we're going to have to table
+that for now and scale
+
+back on the content.
+
+And that's why you have six
+years of development.
+
+You know, maybe in the next
+cycle, in the next game,
+
+you'll be able to squeeze
+out a little bit more.
+
+And the next one you squeeze
+out a little bit more.
+
+That's sort of this continuous
+development, and continuous
+
+optimization over the course
+of a platform.
+
+And sometimes, yeah, I mean
+occasionally you just say
+
+yeah, we can't do it or
+whatever, it doesn't work.
+
+I mean, that's part and parcel
+of development in general.
+
+Some ideas just don't pan out.
+
+But--
+
+AUDIENCE: Have you ever come
+into a situation where
+
+programming conflicts just
+kills a project?
+
+Like Microsoft had had a few
+times, like they couldn't put
+
+out [OBSCURED].
+
+Couldn't release for--
+
+MIKE ACTION: Sure, there's
+plenty of studios where the
+
+programming complexity has
+killed the studio, or killed
+
+the project.
+
+But I find it hard to believe--
+or it's very
+
+rarely-- because it's complexity
+that has to do
+
+specifically with
+optimization.
+
+That complexity usually has
+to do with unnecessary
+
+complexity.
+
+Complexity that doesn't
+achieve anything.
+
+Organization for the sake
+of organization.
+
+So you have these sort of over
+designed C plus plus
+
+hierarchies just for the sake
+of over organizing things.
+
+That's what will generally
+kill a project.
+
+But in performance, the
+complexity tends to come from
+
+the rule set-- what you need
+to do to set it up.
+
+But the code tends to be smaller
+when it's faster.
+
+You tend to be doing one
+thing and doing one
+
+thing really well.
+
+So it doesn't tend to
+get out of hand.
+
+I mean, it occasionally
+happens but, yeah?
+
+AUDIENCE: So in terms of the
+overall cost, how big is this
+
+programming versus the
+other aspect of
+
+coming up with the game?
+
+Like the game design,
+the graphics--
+
+AUDIENCE: So, for example,
+do you have--
+
+MIKE ACTION: OK, development
+team?
+
+So--
+
+AUDIENCE: So how many
+programmers, how many
+
+artists, how many--
+
+PROFESSOR: Maybe, let's-- so
+for example, like, now it's
+
+like, what, $20 million
+to deliver a PS3 game?
+
+MIKE ACTION: Between $10
+and $20 million, yeah.
+
+PROFESSOR: So let's
+develop [OBSCURED]
+
+MIKE ACTION: So artists
+are by far the most--
+
+the largest group
+of developers.
+
+So you have animators and shade
+artists, and textual
+
+artists, and modelers,
+and enviromental
+
+artists, and lighters.
+
+And so they'll often outnumber
+programmers 2:1.
+
+Which is completely different
+than-- certainly very
+
+different from PlayStation and
+the gap is much larger than it
+
+was on PlayStation 2.
+
+With programmers you tend to
+have a fairly even split or
+
+you tend to have a divide
+between the high level game
+
+play programmers and the low
+level engine programmers.
+
+And you will tend to have more
+game play programmers than
+
+engine programmers, although
+most-- the majority of the CPU
+
+time is spent in the
+engine code.
+
+And that partially comes down
+to education and experience.
+
+In order to get high performance
+code you need to
+
+have that experience.
+
+You need to know how
+to optimize.
+
+You need to understand
+the machine.
+
+You need to understand the
+architecture and you need to
+
+understand the data.
+
+And there's only so many people
+that can do that on any
+
+particular team.
+
+AUDIENCE: Code size wise, How
+is the code size divided
+
+between game playing and
+AI, special effects?
+
+MIKE ACTION: Just like,
+the amount of code?
+
+AUDIENCE: Yeah, it should
+be small I guess.
+
+MIKE ACTION: Yeah, I mean,
+it's hard to say.
+
+I mean, because it depends
+on how many
+
+features you're using.
+
+And, you know sort of the scope
+of the engine is how
+
+much is being used for a
+particular game, especially if
+
+you're targeting multiple
+games within a studio.
+
+But quite often-- interestingly
+enough-- the
+
+game play code actually
+overwhelms the engine code in
+
+terms of size and that is back
+to basically what I was saying
+
+that the engine code tends to do
+one thing really well or a
+
+series of things really well.
+
+AUDIENCE: Game play code
+also C plus plus?
+
+MIKE ACTON: These days it's
+much more likely that game
+
+play code is C plus plus in
+the high level and kills
+
+performance and doesn't think
+about things like cache.
+
+That's actually part of the
+problem with PlayStation 3
+
+development.
+
+It was part of the challenge
+that we've had with
+
+PlayStation 3 development.
+
+Is in the past, certainly with
+PlayStation 2 and definitely
+
+on any previous console, this
+divide between game play and
+
+engine worked very well.
+
+The game play programmers could
+just call a function and
+
+it did its fat thing really fast
+and it came back and they
+
+continue this, but in a serial
+program on one process that
+
+model works very well.
+
+But now when the high level
+design can destroy performance
+
+but through the simplest
+decision, like for example, in
+
+collision detection if the logic
+assumes that the result
+
+is immediately available there's
+virtually no way of
+
+making that fast. So the
+high-level design has to
+
+conform to the hardware.
+
+That's sort of a challenge
+now, is introducing those
+
+concepts to the high-level
+programmer who haven't
+
+traditionally had
+to deal with it.
+
+Does that answer that question
+as far as the split?
+
+AUDIENCE: You said 2:1, right?
+
+MIKE ACTON: Approximately 2:1,
+artist to programmers.
+
+It varies studio to studio and
+team to team, so it's hard to
+
+say in the industry
+as a whole.
+
+So back basically to the
+point of the code
+
+isn't really important.
+
+The code itself doesn't
+have a lot of value.
+
+There are fundamental things
+that affect how you would
+
+design it in the first place.
+
+The type of game, the kind of
+engine that would run a racing
+
+game is completely different
+than the kind of engine that
+
+would run a first
+person shooter.
+
+The needs are different, the
+optimizations are totally
+
+different, the data is totally
+different, so you wouldn't try
+
+to reuse code from
+one to the other.
+
+It just either wouldn't
+work or would work
+
+really, really poorly.
+
+The framerate--
+
+having a target of 30 frames per
+second is a much different
+
+problem than having a target
+of 60 frames per second.
+
+And in the NCSC territories
+those are pretty much your
+
+only two choices- 30 frames or
+60, which means everything has
+
+to be done in 16 and
+2/3 milliseconds.
+
+That's it, that's
+what you have--
+
+432 milliseconds.
+
+Of course, back to schedule
+and cost, how much?
+
+You know, do you have a two year
+cycle, one year cycle,
+
+how much can you get done?
+
+The kind of hardware.
+
+So taking for example, an engine
+from PlayStation 2 and
+
+trying to move it to PlayStation
+3 is sort of a
+
+lost cause.
+
+The kind of optimizations that
+you would do, the kind of
+
+parallelization you would do
+is so completely different,
+
+although there was
+parallelization in PlayStation
+
+2, the choices would have been
+completely different.
+
+The loss from trying to port it
+is much, much greater than
+
+the cost of just
+doing it again.
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: I don't know that
+there's an average.
+
+I mean, if you wanted to just
+like homogenize the industry,
+
+it's probably 18 months.
+
+The compiler actually makes a
+huge, significant difference
+
+in how you design your code.
+
+If you're working with GCC and
+you have programmers who have
+
+been working with GCC for 15
+years abd who understand the
+
+intricacies and issues involved
+in GCC, the kind of
+
+code you would write would be
+completely different than if
+
+you were using XLC for
+example, on the cell.
+
+There are studios--
+
+Insomniac doesn't, but there are
+other studios who do cross
+
+platform design.
+
+So for example, write
+Playstation 3 games and Xbox
+
+360 games and/or PC titles.
+
+At the moment, probably the
+easiest approach for that is
+
+to target the PlayStation 3.
+
+So you have these sort of SPU
+friendly chunks of processing
+
+SPU chunks, friendly chunks of
+data and move those onto
+
+homogenous parallel
+processors.
+
+It's not the perfect solution,
+but virtually all cross
+
+platform titles are not looking
+for the perfect
+
+solution anyway because they
+cannot fully optimize for any
+
+particular platform.
+
+I wanted to go through--
+
+these are a basic list of some
+of the major modules that a
+
+game is made out of.
+
+I'll go through some of these
+and explain how designing on
+
+the cell impacts the system.
+
+I'm not going to bother
+reading them.
+
+I assume you all can read.
+
+So yeah, I'm going to go over
+the major system, a few of the
+
+major systems and then we're
+going to drive a little bit
+
+into a specific system, in this
+case an animation system.
+
+And just talk it through,
+basically you see how each of
+
+these steps are affected by
+the hardware that we're
+
+running on it.
+
+So just to start with when
+you're designing a structure,
+
+any structure, anywhere--
+
+the initial structure is
+affected by the kind of
+
+hardware that you're running.
+
+And in this particular case on
+the SPU and there are other
+
+processors where this is equally
+true, but in this
+
+conventional structure where
+you say structure class or
+
+whatever and you have
+domain-constrained structures
+
+are of surprisingly
+little use.
+
+In general, the data is either
+compressed or is in a stram or
+
+is in blocks.
+
+It's sort of based on type,
+which means that there's no
+
+fixed size struct that you
+could define anyway.
+
+So as a general rule, the
+structure of the data is
+
+defined within the
+code as opposed
+
+to in a struct somewhere.
+
+And that's really to get the
+performance from the data, you
+
+group things of similar type
+together rather than for
+
+example, on SPU, having flags
+that say this is of type A and
+
+this is of type B. Any flag
+implies a branch, which is--
+
+I'm sure you all know at this
+point-- is really poor
+
+performing on SPU.
+
+So basically, pull flags out,
+resort everything and then
+
+move things in streams. And all
+of these types are going
+
+to be of varying sizes.
+
+In which case there's very
+little point to define those
+
+structures in the first place
+because you can't change them.
+
+And the fact that you're
+accessing data
+
+in quadwords anyway.
+
+You're always either loading and
+storing in quadwords, not
+
+on scalars, so having scalar
+fields in a structure is sort
+
+of pointless.
+
+So again, only SPU generally
+speaking
+
+structures are of much use.
+
+When you go to define structures
+in general you need
+
+to consider things like the
+cache, the TLB, how that's
+
+going to affect you're reading
+out of the structure or
+
+writing to the structure.
+
+More to the point of you cannot
+just assume that if
+
+you've written some data
+definition that you can port
+
+it to another platform.
+
+It's very easy to be poorly, a
+
+performing platform to platform.
+
+In this case, when we design
+structures you have to
+
+consider the fundamental
+units of the cell.
+
+The cache line is a fundamental
+unit of the cell.
+
+Basically, you want to define
+things in terms of
+
+128 bytes of wide.
+
+What can you fit in there
+because you read one you read
+
+them all, so you want to pack
+as much as possible into 128
+
+bytes and just deal with that
+as a fundamental unit.
+
+16 bytes, of course, you're
+doing load and stores through
+
+quadword load and store.
+
+So you don't want to have little
+scalar bits in there
+
+that you're shuffling around.
+
+Just deal with it
+as a quadword.
+
+And don't deal with anything
+smaller than that.
+
+So basically the minimum working
+sizes, in practice,
+
+would be 4 by 128 bits wide
+and you can split that up
+
+regularly however you want.
+
+So to that point I think--
+
+here's an example--
+
+I want to talk about
+a vector class.
+
+Vector class js usually the
+first thing a programmer will
+
+jump onto when they might want
+to make something for games.
+
+But in real life, it's probably
+the most useless
+
+thing you could ever write.
+
+It doesn't actually
+do anything.
+
+We have these, we know the
+instruction set, it's already
+
+in quadwords.
+
+We know the loads and stores,
+we've already designed your
+
+data so it fits properly.
+
+This doesn't give us anything.
+
+And it potentially makes
+things worse.
+
+Allowing component access to a
+quadword, especially on the
+
+PPU is ridiculously bad.
+
+In practice, if you allow
+component access, high-level
+
+programs will use component
+access.
+
+So if you have a vector class
+that says get x, get y,
+
+whatever, somebody somewhere
+is going to use it, which
+
+means the performance of the
+whole thing just drops and
+
+it's impossible to optimize.
+
+So as a general rule, you pick
+your fundamental unit.
+
+In this case, the 4 by 128 bit
+unit that I was talking about
+
+and you don't define anything
+smaller than that.
+
+Everything is packed into
+a unit about that size.
+
+And yes, in practice there'll
+be some wasted space at the
+
+beginning or end of streams of
+data, groups of data, but it
+
+doesn't make much difference.
+
+You're going to have that wasted
+space if you are--
+
+you're going to have much more
+than that in wasted space if
+
+you're using dynamic memory,
+for example, which
+
+when I get to it--
+
+I don't recommend
+you use either.
+
+So some things to consider when
+you're doing this sort of
+
+math transformation anyway is,
+are you going to do floats,
+
+double, fixed point?
+
+I mean, doubles write out.
+
+There's no point.
+
+Regardless of the speed on the
+SPU of a double, there's no
+
+value in it for games.
+
+We have known data, so if we
+need to we can renormalize a
+
+group of around a point and
+get into the range of a
+
+floating point.
+
+It's a nonissue.
+
+So there's no reason to waste
+the space in a double at all,
+
+unless it was actually faster,
+which it isn't.
+
+So we don't use it.
+
+Sort of the only real
+problematic thing with the SPU
+
+floating point is its format
+and not supporting
+
+denormalized numbers becomes
+problematic, but again, you
+
+can work around it by
+renormalizing your numbers
+
+within a known range so that it
+won't to get to the point
+
+where it needs to
+denormalize--
+
+at least for the work that
+you're actually doing.
+
+Yeah?
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: Every program will
+write its own vector class.
+
+And I'm saying that that's
+a useless exercise.
+
+Don't bother doing it.
+
+Don't use anybody
+else's either.
+
+If you're writing
+for the cell--
+
+if you're writing in C you
+have the SI intrinsics.
+
+They're already in quadwords,
+you can do everything you want
+
+to do and you're not restricted
+by this sort of
+
+concept of what a vector is.
+
+If you want to deal with,
+especially on the SPU where
+
+you can freely deal with them
+as integers or floats or
+
+whatever seamlessly without
+cost, there's plenty that you
+
+can do with the floating
+point number if you
+
+treat it as an integer.
+
+And when on either AltiVec or
+the SPU where you can do that
+
+without cost there's
+a huge advantage to
+
+just doing it straight.
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: Well, I'm saying
+write it in assembly.
+
+But if you have to, use
+the intrinsics.
+
+But certainly don't write
+a vector class.
+
+So memory management.
+
+Static allocations always
+prefer the dynamic.
+
+Basically, general purpose
+dynamic memory allocation,
+
+malloc free, whatever has just
+absolutely no place in games.
+
+We don't have enough unknowns
+for that to be valuable.
+
+We can group our data
+by specific types.
+
+We know basic ranges
+of those types.
+
+The vast majority of the data
+is known in advance, it's
+
+actually burned onto the disk.
+
+We can actually analyze that.
+
+So most of our allocations
+tend to
+
+calculate it in advance.
+
+So you load the level and
+oftentimes you just load
+
+memory in off the disc
+into memory and
+
+then fix up the pointers.
+
+For things that change during
+the runtime, just simple
+
+hierarchical allocators, block
+allocators where you have
+
+fixed sizes is always the
+easiest and best way to go.
+
+These are known types
+of known sizes.
+
+The key to that is to organize
+your data so that's actually a
+
+workable solution.
+
+So you don't have these sort of
+classes or structures that
+
+are dynamically sized.
+
+That you group them in terms
+of things that are similar.
+
+Physics data here and AI data
+is separately here in a
+
+separate array.
+
+And that way those sort of
+chunks of data are similarly
+
+sized and can be block
+allocated without any
+
+fragmentation issues at all.
+
+Eventually you'll probably want
+to design an allocator.
+
+Things to consider are
+the page sizes.
+
+That's critically important, you
+want to work within a page
+
+as much as you possibly can.
+
+So you want to group things,
+not necessarily the same
+
+things, but the things that
+will be read together or
+
+written together within
+the same page.
+
+So you want to have a concept of
+the actual page up through
+
+the system.
+
+Probably the most common mistake
+I see in a block
+
+allocator, so somebody says--
+
+everybody knows what I mean
+by block allocator?
+
+Yeah?
+
+OK.
+
+So the most common mistake I see
+people make is that they
+
+do least recently used.
+
+They just grab the most least
+recently used block and use
+
+that when summoning a request.
+That's actually pretty much
+
+the worst thing you can possibly
+do because that's the
+
+most likely thing
+to be called.
+
+That's the most likely thing to
+be out of cache, both out
+
+of L1 and L2.
+
+Just the easiest thing you can
+do to change that is just use
+
+most recently used.
+
+Just go up the other way.
+
+I mean, there are much more
+complicated systems you can
+
+use, but just that one small
+change where you're much more
+
+likely to get warm data is going
+to give you a big boost.
+
+And again, like I said, use
+hierarchies of allocations
+
+instead of these sort of static
+block allocations.
+
+Instead of trying to have one
+general purpose super mega
+
+allocator that does
+everything.
+
+And again, if it's well planned,
+fragmentation is a
+
+non-issue, it's impossible.
+
+Cache line, oh, and probably
+another important concept to
+
+keep in mind as you're writing
+your allocator is the transfer
+
+block size of the SPU.
+
+If you have a 16K block and the
+system is aware of fixing
+
+K blocks then there are plenty
+of cases where you don't have
+
+to keep track of-- in the
+system-- the size of things.
+
+It's just how many blocks, how
+many SPU blocks do you have?
+
+Or what percentage of
+SPU blocks you have?
+
+And that will help you can sort
+of compress down your
+
+memory requirements when you're
+referring to blocks and
+
+memory streams and memory.
+
+AUDIENCE: About the memory
+management for data here, you
+
+also write overlay managers
+for code for the user?
+
+MIKE ACTON: Well, it basically
+amounts to the same thing.
+
+I mean, the code is just data,
+you just load it in and fix up
+
+the pointers and you're done.
+
+AUDIENCE: I was just wondering
+whether IBM gives you
+
+embedding --
+
+MIKE ACTON: We don't
+usse any of the IBM
+
+systems at all for games.
+
+I know IBM has an overlay
+manager as part of the SDK.
+
+AUDIENCE: Well, not really.
+
+It's --
+
+MIKE ACTON: Well, they have some
+overlay support, right?
+
+That's not something
+we would ever use.
+
+And in general, I mean, I
+guess that's probably an
+
+interesting question of how--
+
+AUDIENCE: So it's
+all ground up?
+
+MIKE ACTON: What's that?
+
+AUDIENCE: All your development
+is ground up?
+
+MIKE ACTON: Yeah, for
+the most part.
+
+For us, that's definitely
+true.
+
+There are studios that,
+especially cross platform
+
+studios that will take
+middleware development and
+
+just sort of use it
+on a high-level.
+
+But especially when you're
+starting a first generation
+
+platform game, there's virtually
+nothing there to use
+
+because the hardware hasn't been
+around long enough for
+
+anybody else to write
+anything either.
+
+So if you need it, you
+write it yourself.
+
+Plus that's just sort of the
+general theme of game
+
+development.
+
+It's custom to your situation,
+to your data.
+
+And anything that's general
+purpose enough to sell as
+
+middleware is probably not going
+to be fast enough to run
+
+a triple A title.
+
+Not always true, but
+as a general
+
+rule, it's pretty valid.
+
+OK, so-- wait, so how'd
+I get here?
+
+All right, this is next.
+
+So here's another example
+of how the cell
+
+might affect design.
+
+So you're writing a collision
+detection system.
+
+It's obvious that you cannot or
+should not expect immediate
+
+results from a collision
+detection system, otherwise
+
+you're going to be sitting and
+syncing all the time for one
+
+result and performance just goes
+out the window, you may
+
+as well just have a
+serial program.
+
+So you want to group results,
+you want to group queries and
+
+you want potentially, for those
+queries to be deferred
+
+so that you can store them, you
+can just DMA them out and
+
+then whatever process needed
+then we'll come back and grab
+
+them later.
+
+So conceptually that's the
+design you want to build into
+
+a collision detection system,
+which then in turn affects the
+
+high-level design.
+
+So AI, scripts, any game code
+that might have previously
+
+depended on a result being
+immediately available, as in
+
+they have characters that shoot
+rays around the room to
+
+decide what they're going to
+do next or bullets that are
+
+flying through the air or
+whatever, can no longer make
+
+that assumption.
+
+So they have to be able to group
+up their queries and
+
+look them up later and
+have other work
+
+to do in the meantime.
+
+So this is a perfect example
+of how you cannot take old
+
+code and move it to the PS3.
+
+Because old code, serial code
+would have definitely assumed
+
+that the results were
+immediately available because
+
+honestly, that was the
+fastest way to do it.
+
+So on a separate issue, we have
+SPU decomposition for the
+
+geometry look up.
+
+So from a high-level you have
+your entire scene in the level
+
+of the world or whatever and you
+have the set of queries in
+
+the case of static--
+did I collide with
+
+anything in the world?
+
+Or you have a RAID that, where
+does this RAID collide with
+
+something in the world?
+
+And so you have this problem of
+you have this large sort of
+
+memory database in main RAM
+and you have the smallest
+
+spew, which obviously cannot
+read in the whole database,
+
+analyze it, and spit
+out the result.
+
+It has to go back and forth
+to main RAM in order
+
+to build its result.
+
+So the question is how do you
+decompose the memory in the
+
+first place to make
+that at least
+
+somewhat reasonably efficient?
+
+The first sort of instinct I
+think, based on history is
+
+sort of the traditional scene
+graph structures like BSP tree
+
+or off tree or something
+like that.
+
+Particularly, on the SPU because
+if TLB misses that
+
+becomes really expensive, really
+quickly when you're
+
+basically hitting random
+memory on every
+
+single node on the tree.
+
+So what you want to do is you
+want to make that hierarchy as
+
+flat as you possibly can.
+
+If the leafs have to be bigger
+that's fine because it turns
+
+out it's much, much cheaper to
+stream in a bigger group of--
+
+as much data as you can fit into
+the SPU and run through
+
+it and make your decisions and
+spit it back out than it is to
+
+traverse the hierarchy.
+
+So basically, the depth of your
+hierarchy in your scene
+
+database is completely
+determined by how much data
+
+you can fit into the
+SPU by the maximum
+
+size of the leaf node.
+
+The rest of the dep is only
+because you don't have any
+
+other choice.
+
+You know, And basically the same
+thing goes with dynamic
+
+geometry as you have geometry
+moving around in the scene,
+
+characters moving around
+in the scene--
+
+they basically need to update
+themselves into their own
+
+database, into their
+own leaves and
+
+they'll do this in groups.
+
+And then when you query, you
+basically want it to query as
+
+many of those as possible,
+as you can
+
+possibly fit in at once.
+
+So you could have sort of a
+broad faced collision first,
+
+where you have all of the groups
+of characters that are
+
+potentially maximum
+in this leaf, so
+
+bound and box or whatever.
+
+So even though you could in
+theory, in principle narrow
+
+that down even more, the cost
+for that, the cost for the
+
+potential memory miss for that
+is so high that you just want
+
+to do a linear search through
+as many as you
+
+possibly can on SPU.
+
+Does that make sense?
+
+Procedural graphics--
+
+so although we have a GPU on
+the PlayStation 3, it does
+
+turn out that the SPU
+is a lot better at
+
+doing a lot of things.
+
+Things basically where
+you create
+
+geometry for RSX to render.
+
+So particle system, dynamic
+particle systems. Especially
+
+where their systems have to
+interact with the world in
+
+some way, which will be much
+more expensive on the GPU.
+
+Sort of a dynamic systems
+like cloth.
+
+Fonts is actually really
+interesting because typically
+
+you'll just see bitmap
+fonts in which
+
+case are just textures.
+
+But if you have a very complex
+user interface then just the
+
+size of the bitmap becomes
+extreme and if you compressed
+
+them they look terrible,
+especially fonts.
+
+Fonts need to look perfect.
+
+So if you do do procedural
+fonts, for example, two type
+
+fonts, the cost of rendering
+a font actually gets
+
+significant.
+
+And in this case, the SPU is
+actually a great use for
+
+rendering a procedural font.
+
+Rendering textures
+is basically the
+
+same case as font.
+
+Procedural textures like if you
+do noise-based clouds or
+
+something like that.
+
+And parametric geometry, it's
+like nurbs or subdivision
+
+services or something like
+that, is a perfect
+
+case for the SPU.
+
+Is there a question?
+
+Geometry database, OK.
+
+First thing scene graphs
+are worthless.
+
+Yeah?
+
+AUDIENCE: So of those sort of
+differnet conceptualized
+
+paths, are you literally
+swapping code in and out of
+
+the SPUs with the data
+many times per frame?
+
+Or is it more of a static---
+
+MIKE ACTON: OK, that's an
+excellent question.
+
+It totally depends.
+
+I mean, in general through a
+game or through, at least a
+
+particular area of a game the
+SPU set up is stable.
+
+So if we decide you're going to
+have this SPU dedicated to
+
+physics for example, it is very
+likely that that SPU is
+
+stable and it's going to be
+dedicated physics, at least
+
+for some period of time through
+the level or through
+
+the zone or wherever it is.
+
+Sometimes through
+an entire game.
+
+So there are going to be
+elements of that where it's
+
+sort of a well balanced
+problem.
+
+There's basically no way you're
+going to get waste.
+
+It's always going to be full,
+it's always going to be busy.
+
+Collision detection and physics
+are the two things
+
+that you'll never have
+enough CPU to do.
+
+You can always use more
+and more CPU.
+
+And basically, the rest can
+be dynamically scheduled.
+
+And the question of how to
+schedule it, is actually an
+
+interesting problem.
+
+It's my opinion that sort of
+looking for the universal
+
+scheduler that solves all
+problems and magically makes
+
+everything work is a
+total lost cause.
+
+You have more than enough data
+to work with and in your game
+
+to decide how to schedule your
+SPUs basically, manually.
+
+And it's just not that
+complicated.
+
+We have six SPUs.
+
+How to schedule six SPUs is just
+not that complicated a
+
+problem, you could write it
+down on a piece of paper.
+
+OK, so scene graphs are almost
+always, universally a complete
+
+waste time.
+
+They store way too much data
+for no apparent reason.
+
+Store your databases
+independently based on what
+
+you're actually doing with
+them, optimize your data
+
+separately because you're
+accessing it separately.
+
+The only thing that should be
+linking your sort of domain
+
+object is a key that says all
+right, we'll exist in this
+
+database and the database
+and this database.
+
+But to have this sort of giant
+structure that keeps all of
+
+the data for each element in the
+scene is about the poorest
+
+performing you can imagine for
+both cache and TLB and SPU
+
+because you can't fit it in
+individual node on the SPU.
+
+I think I covered that.
+
+Here's an interesting example,
+so what you want to do is if
+
+you have the table of queries
+that you have-- bunch of
+
+people over the course of a
+frame say I want to know if I
+
+collided with something.
+
+And then if you basically make
+a pre-sort pass on that and
+
+basically, spatially sort these
+guys together, so let's
+
+say you have however many
+you can fit in a SPU.
+
+So you have four of these
+queries together.
+
+Although they might be a little
+further apart then you
+
+would hope, you could basically
+create a baling box
+
+through a single query on the
+database that's the sum of all
+
+of them and then as I said,
+now you have a linear list
+
+that you can just stream through
+for all of them.
+
+So even though it's doing more
+work for any individual one,
+
+the overhead is reduced so
+significantly that the end
+
+result is that it's
+significantly faster.
+
+And that's also what I mean by
+multiple simultaneous lookups.
+
+Basically you want to group
+queries together, but make
+
+sure that there's some
+advantage to that.
+
+By spatially pre-sorting them
+there is an advantage to that
+
+because it's more likely
+that they will have
+
+overlap in your queries.
+
+So game logic.
+
+Stuff that the cell would
+affect in game logic.
+
+State machines are
+a good example.
+
+If you defer your logic lines
+and defer your results, SPUs
+
+are amazingly perfect for
+defining state machines.
+
+If you expect your logic lines
+to be immediately available
+
+across the entire system, SPU
+is absolutely horrid.
+
+So if you basically write
+buffers into your state
+
+machines or your logic machines
+then each SPU can be
+
+cranking on multiple state
+machines at once where all the
+
+input and all the output lines
+are assumed to be deferred and
+
+it's just an extremely
+straightforward process.
+
+Scripting, so scripting
+things like--
+
+I don't know, lewis script
+or C script or
+
+something like that.
+
+I mean, obviously the first
+thing to look at is the size
+
+of the interpreter.
+
+Will it fit into an
+SPU to begin with?
+
+Another option to consider is,
+can it be converted into SPU
+
+code, either offline
+or dynamically?
+
+Because you'll find that most
+off the shelf scripting
+
+languages are scalar,
+
+sequential scripting languages.
+
+So all of a P code within the
+scripting language itself
+
+basically defines
+scalar access.
+
+So not only are you switching
+on every byte to every two
+
+bytes or whatever, so it's sort
+of poorly performing code
+
+from an SPU point of view, but
+it's also poorly performing
+
+code from a memory
+point of view.
+
+So I guess the question is
+whether or not you can
+
+optimize the script itself and
+turn turn it into SPU code
+
+that you can then dynamically
+load or come up with a new
+
+script that's just much more
+friendly for the SPUs.
+
+Another option if you have to
+use a single, sort of scalar
+
+scripting language like lua or
+C script or whatever, if you
+
+can run multiple streams
+simultaneously so that while
+
+you're doing these sort of
+individual offline memory
+
+lookups and reads and writes to
+main memory, that once one
+
+blocks you can start moving
+on another one.
+
+As long as there's no
+dependencies between these two
+
+scripts we should be able
+to stream them both
+
+simultaneously.
+
+Motion control actually turns
+out to be a critical problem
+
+in games in general that's
+often overlooked.
+
+It's who controls the
+motion in the game.
+
+Is is the AI?
+
+So is it the controller in
+the case of the player?
+
+I say, push forward, so
+the guy moves forward.
+
+Is that really what
+controls it?
+
+Or is it the physics?
+
+So all the AI does is say, I
+want to move forward, tells
+
+the physic system I want to move
+forward and the physics
+
+tries to follow it.
+
+Or is it the animation?
+
+That you have the animators
+actually put translation in
+
+the animation, so is that
+translation the thing that's
+
+actually driving the motion and
+everything else is trying
+
+to follow it?
+
+Turns out to be a surprisingly
+difficult problem to solve and
+
+every studio ends up with
+their own solution.
+
+I forget what point I was
+making on how the cell
+
+affected that decision.
+
+But--
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: I think the point,
+probably that I was trying to
+
+make is that because you want
+everything to be deferred
+
+anyway, then the order does
+become a clearer sort of
+
+winner in that order.
+
+Where you want the immediate
+feedback from the controls,
+
+the control leads the way.
+
+You have the physics, which then
+follows, perhaps, even a
+
+frame behind that to say how
+that new position is impacted
+
+by the physical reality
+of the world.
+
+And then potentially a frame
+behind that or half a frame
+
+behind that you have the
+animation system, which in
+
+that case would just be
+basically, a visual
+
+representation of what's
+going on rather
+
+than leading anything.
+
+It's basically an icon for
+what's happening in the
+
+physics and the AI.
+
+The limitations of your system
+are that it has to be deferred
+
+and that it has to be
+done in groups.
+
+Basically, some of these sort of
+really difficult decisions
+
+have only one or two
+obvious answers.
+
+All right, well I wanted to dig
+into animation a little
+
+bit, so does anybody have any
+questions on anything?
+
+Any of the sort of the
+high-level stuff that I've
+
+covered up to this point?
+
+Yeah?
+
+AUDIENCE: So does the need for
+deferral and breaking into
+
+groups and staging, does this
+need break the desire for the
+
+higher-level programmers to
+abstract what's going on at
+
+the data engine level?
+
+Or is that not quite
+the issue?
+
+MIKE ACTON: Well, let's
+say we get a game
+
+play programmer, right?
+
+Fresh out of school, he's
+taught in school, C
+
+plus plus in school.
+
+Taught to decompose the world
+into sort of the main classes
+
+and that they all communicate
+through each other maybe
+
+through messaging.
+
+All right, well the first thing
+we tell him is that all
+
+that is complete crap.
+
+None of that will actually
+work in practice.
+
+So in some sense, yes, there is
+a sort of tendency for them
+
+to want this interface, this
+sort of clean abstraction, but
+
+abstraction doesn't
+have any value.
+
+It doesn't make the game faster,
+it doesn't make the
+
+game cheaper.
+
+It doesn't make--
+
+AUDIENCE: [OBSCURED]
+
+PROFESSOR: There's a
+bit of a religious.
+
+Let's move on.
+
+He has a lot of other
+interesting things to say.
+
+And we can get to
+that question--
+
+AUDIENCE: It sounds like
+there's two completely
+
+different communities involved
+in the development.
+
+There's the engine developers
+and there's the higher-level--
+
+MIKE ACTON: That's a fair
+enough assessment.
+
+There are different
+communities.
+
+There is a community of the game
+play programmers and the
+
+community of engine
+programmers.
+
+And they have different
+priorities and they have
+
+different experiences.
+
+So yeah, in that way there
+is a division.
+
+PROFESSOR: I will
+let you go on.
+
+You said you had a lot
+of interesting
+
+information to cover.
+
+MIKE ACTON: OK.
+
+AUDIENCE: I can bitch
+about that.
+
+Don't worry.
+
+MIKE ACTON: So just to get into
+animation a little bit.
+
+Let's start with trying to
+build a simple animation
+
+system and see what problems
+come creep up as we're trying
+
+to implement it on the cell.
+
+So in the simplest case we
+have a set of animation
+
+channels defined for
+a character, which
+
+is made up of joints.
+
+We're just talking about sort
+of a simple hierarchical
+
+transformation here.
+
+And some of those channels
+are related.
+
+So in the case of rotation plus
+translation plus scale
+
+equals any individual joint.
+
+So the first thing, typically
+that you'll have to answer is
+
+whether or not you want to do
+euler or quaternion rotation.
+
+Now the tendency I guess,
+especially for new programmers
+
+is to go with quaternion.
+
+They're taught that gimbal
+lock is a sort of
+
+insurmountable problem that
+only quaternion solves.
+
+That's just simply not true.
+
+I mean, gimbal lock
+is completely
+
+manageable in practice.
+
+When you're trying to rotate
+on three axes and two axes
+
+rotate 90 degrees apart and
+the third axis can't be
+
+resolved or 180 degrees apart.
+
+So you can't resolve one
+of the axes, right?
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: Yeah, it's where
+it's impossible to resolve one
+
+of the axes and that's
+the nature of
+
+euler sort of rotation.
+
+But sort of a quaternion
+rotation completely solves
+
+that mathematical problem, it's
+always resolvable and
+
+it's not very messy at all.
+
+I mean, from a sort of C
+programmers perspective, it
+
+looks clean, the math's clean,
+everything's clean about it.
+
+Unfortunately, it doesn't
+compress very well at all.
+
+Where if you used euler
+rotation, which basically just
+
+means that the individual
+rotation for every axis.
+
+So x rotation, y rotation,
+z rotation.
+
+That's much, much more
+compressible because each one
+
+of those axes can be
+individually compressed.
+
+It's very unlikely that you're
+always rotating all three
+
+axes, all the time, especially
+in a human character.
+
+It's much more likely that only
+one axis is rotating on
+
+any one given time and
+so that makes it--
+
+just without any change,
+without any additional
+
+compression-- it tends to make
+it about 1/3 of the size.
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: The animation
+data.
+
+So you have this frame of
+animation, which is all these
+
+animation channels, right?
+
+And then over time you have
+these different frames of
+
+animation, right?
+
+If you store-- for every joint,
+for every rotation you
+
+store a quaternion over time,
+it's hard to compress across
+
+time because you're basically,
+essentially rotating all three
+
+axes, all the time.
+
+Well, with--
+
+yeah?
+
+All right.
+
+So let's say, of course, the
+next step is how do we store
+
+the actual rotation itself?
+
+Do we store it in cloth, double,
+half precision, fixed
+
+point precision?
+
+Probably the national tendency
+at this point would be to
+
+store it in a floating point
+number, but if you look at the
+
+actual range of rotation, which
+is extremely limited on
+
+a character, on any particular
+joint there are very few
+
+joints that would even
+rotate 180 degrees.
+
+So a floating point
+is overkill, by a
+
+large margin on rotation--
+
+for the range.
+
+For the precision, however
+it's fairly good.
+
+Especially if you're doing very
+small rotations over a
+
+long period of time.
+
+So probably a more balanced
+approach would be to go with a
+
+16 bit floating point from a
+half format where you keep
+
+most of the precision, but
+you reduce the range
+
+significantly.
+
+There's also the potential for
+going with an 8 bit floating
+
+point format depending
+on the kind of
+
+animation that you're doing.
+
+And I'll probably have this on
+another slide, but it really
+
+depends on how close--
+
+how compressible a joint is
+depends on how close to the
+
+root it is.
+
+The further away from the root
+the less it matters.
+
+So the joint at your fingertip,
+you can compress a
+
+whole lot more because it
+doesn't matter as much, it's
+
+not going to affect
+anything else.
+
+Where a joint at the actual
+root, the smallest change in
+
+motion will affect the entire
+system in animation and will
+
+make it virtually impossible for
+you to line up animations
+
+with each other, so that that
+particular joint needs to be
+
+nearly perfect.
+
+And how do you store rotation?
+
+Do you store them in degrees,
+radians, or normalized?
+
+I have seen people store
+them in degrees.
+
+I don't understand why you
+would ever do that.
+
+It's just adding math
+to the problem.
+
+Radians is perfectly fine if
+you're using off the shelf
+
+trigonometric functions-
+tan, sine whatever.
+
+But typically, if you're going
+to optimize those functions
+
+yourself anyway, it's going to
+be much more effective go with
+
+a normalized rotational value.
+
+So basically between
+zero and 1.
+
+Makes it a lot easier to do
+tricks based on the circle.
+
+Basically you can just take the
+fractional value and just
+
+deal with that.
+
+So normalized rotation is
+generally the way to go and
+
+normalizing a half precision is
+probably the even bet for
+
+how you would store.
+
+So looking at what we need to
+fit into an SPU if we're going
+
+to running to an end machine.
+
+Yeah?
+
+AUDIENCE: You talked a lot about
+compressing because of
+
+the way it's impacting data,
+what's the key driver of that?
+
+MIKE ACTON: The SPU has
+very little space.
+
+AUDIENCE: OK, so it's just
+the amount of space.
+
+MIKE ACTON: Yeah, well OK.
+
+There's two factors really,
+in all honesty.
+
+So starting with the SPU.
+
+That you have to be able
+to work through
+
+this data on the SPU.
+
+But you also have the
+DMA transfer itself.
+
+The SPU can actually calculate
+really, really fast, right?
+
+I mean, that's the
+whole point.
+
+So if you can transfer less
+data, burn through it a little
+
+bit to expand it, it's
+actually a huge win.
+
+And on top of that we have a
+big, big game and only 256
+
+megs of main ram.
+
+And the amount of geometry that
+people require from a
+
+current generation game or
+next generation game has
+
+scaled up way more than the
+amount of memory we've been
+
+given, so we've only been given
+eight times as much
+
+memory as we had in the
+previous generation.
+
+People expect significantly more
+than eight times as much
+
+geometry on the screen and
+where do we store that?
+
+We have the Blu-Ray, we can't
+be streaming everything off
+
+the disc all the time, which
+is to another point.
+
+You have 40 gigs of data
+on your disc, but
+
+only 256 megs of RAM.
+
+So there's this sort of a
+series of compression,
+
+decompression to keep
+everything--
+
+basically, think of RAM
+as your L3 cache.
+
+So we look at what we want
+to store on an SPU.
+
+Basically, the goal of this is
+we want to get an entire
+
+animation for a particular
+skeleton on an SPU so that we
+
+can transform the skeleton
+and output the
+
+resulting joint data.
+
+So let's look at how big
+that would have to be.
+
+So first we start with the basic
+nine channels per joint.
+
+That's not assuming and again,
+you'd probably have additional
+
+channels, like foot step
+channels and sound channels
+
+and other sort of animation
+channels to help
+
+actually make a game.
+
+In this case, we just want
+to animate the character.
+
+So we have rotation times 3,
+translations times 3, and
+
+scales times 3.
+
+So the first thing to drop and
+this will cover, this will
+
+reduce your data by 70%, is
+all the uniform channels.
+
+So any data that doesn't
+actually change across the
+
+entire length of
+the animation.
+
+It may not be zero, but it could
+be just one thing, one
+
+value that doesn't
+change across
+
+length of the animation.
+
+So you pull all the uniform
+channels out.
+
+And most things that's going to
+be scale, for example, most
+
+joints don't scale.
+
+Although occasionally they do.
+
+And translation, in a human our
+joints don't translate.
+
+However, when you actually
+animate a character in order
+
+to get particular effects, in
+order to make it look more
+
+human you do end up needing
+to translate joints.
+
+So we can reduce, but in order
+to that we need to build a
+
+map, basically, a table of
+these uniform channels.
+
+So now we know this table of
+uniform channels has to be
+
+stored in the SPU along with
+now the remaining actual
+
+animation data.
+
+Of course, multiplied by
+the number of joints.
+
+So now we have what
+is essentially
+
+raw animation data.
+
+So for the sake of argument,
+let's say the animation data
+
+has been baked out by
+Maya or whatever
+
+at 30 frames a second.
+
+We've pulled out the uniform
+data, so now for the joints
+
+that do move we have these
+curves over time of the entire
+
+length of the animation.
+
+The problem is if that animation
+is 10 seconds long,
+
+it's now way too big to fit in
+the SPU by a large margin.
+
+So how do we sort of compress
+it down so that it
+
+actually will fit?
+
+Again, just first of all, the
+easiest thing to do to start
+
+with is just do simple curve
+fitting to get rid of the
+
+things that don't need to be
+there that you can easily
+
+calculate out.
+
+And again, the closer that you
+are to the root, the tighter
+
+that fits need to be.
+
+Conversely, the further away you
+are from the root, you can
+
+loosen up the restrictions a
+little bit and have a little
+
+bit looser fit on the
+curve and compress
+
+a little bit more.
+
+So if you're doing a curve
+fitting with the simple
+
+spline, basically you have to
+store your time values in the
+
+places that were calculated.
+
+Part of the problem is now you
+have sort of these individual
+
+scalars with time can be
+randomly spread throughout the
+
+entire animation.
+
+So any point where there's
+basically a knot in the curve,
+
+there's a time value.
+
+And none of these knots are
+going to line up with each
+
+other in any of these
+animation channels.
+
+So in principle, if you wanted
+to code this you would have to
+
+basically say, what is time
+right now and loop through
+
+each of these scalar values,
+find out where time is,
+
+calculate the postition
+on the curve and then
+
+spit out the result.
+
+So one, you still have to have
+the unlimited length of data
+
+and two, you're looping through
+scalar values on the
+
+SPU, which is really
+actually, horrible.
+
+So we want to find a way
+to solve that problem.
+
+Probably the most trivial
+solution is
+
+just do spline segemnts.
+
+You lose some compressibility,
+but it solves the problem.
+
+Basically you split up the
+spline into say, sections of
+
+16 knots and you just do that.
+
+And in order to do that you just
+need a table, you need to
+
+add a table that says what the
+range of time are in each of
+
+those groups of 16 knots
+for every channel.
+
+So when you're going to
+transform the animation, first
+
+you load this table in, you say,
+what's my time right now
+
+at time, t?
+
+You go and say which blocks,
+which segments of the spline
+
+you need to load in for each
+channel, you load those in.
+
+So now you have basically one
+section of the spline, which
+
+is too big probably for the
+current t, but it covers what
+
+t you're actually in.
+
+So one block of spline for
+every single channel.
+
+So the advantage of this, now
+that the spline is sorted into
+
+sections is that rather than
+having all the spline data
+
+stored, sort of linearly, you
+can now reorder the blocks so
+
+that the spline data from
+different channels is actually
+
+tiled next to each other.
+
+So that when you actually go
+to do a load it's much more
+
+likely because you know you're
+going to be requesting all
+
+these channel at once and all
+on the same time, t, you can
+
+find a more or less, optimal
+ordering that will allow more
+
+of these group things to be
+grouped in the same cache or
+
+at least the same page.
+
+And the advantage of course
+again, is now the length of
+
+animation makes absolutely
+no difference at all.
+
+The disadvantage is its less
+compressible because you can
+
+only basically compress this one
+section of the curve, but
+
+a huge advantage is it solves
+the scalar loop problem.
+
+So now you can take four of
+these scalar values all with a
+
+fixed known number of knots in
+it and just loop through all
+
+of the knots.
+
+In principle you could search
+through and find a minimum
+
+number of knots to look through
+for each one of the
+
+scalars, but in practice it's
+much faster just to loop
+
+through all four simultaneously
+for all 16
+
+knots and just throw away the
+results that are invalid as
+
+you're going through it.
+
+That way you can use the
+SPU instruction set.
+
+You can load quadwords, store
+quadwords, and do everything
+
+in the minimum single
+loop, which you
+
+can completely unroll.
+
+Does anybody have the time?
+
+PROFESSOR: It's [OBSCURED]
+
+MIKE ACTON: So I'm OK.
+
+PROFESSOR: [OBSCURED]
+
+MIKE ACTON: Yeah?
+
+AUDIENCE: In
+
+context do you make like
+rendering the animation or it
+
+seems like there would be a blow
+to whatever you're doing
+
+on the SPUs.
+
+MIKE ACTON: Basically the SPUs
+are taking this channel
+
+animation data and baking it
+out into-- well, in the
+
+easiest case baking
+it out into a 4 by
+
+4 matrix per joint.
+
+AUDIENCE: So the output
+time's much bigger
+
+than the input time?
+
+I mean, you're compressing
+the input by animation?
+
+MIKE ACTON: No, the output size
+is significant, but it's
+
+much smaller.
+
+PROFESSOR: [OBSCURED]
+
+AUDIENCE: So the animation
+data it's [OBSCURED]
+
+[INTERPOSING VOICES]
+
+MIKE ACTON: No.
+
+I was just outputting the
+joint information.
+
+PROFESSOR: [OBSCURED]
+
+MIKE ACTON: Independently we
+have this skimming problem.
+
+Independently there's
+a rendering problem.
+
+This is just baking animation.
+
+This is purely animation
+channel problem.
+
+PROFESSOR: [OBSCURED]
+
+MIKE ACTON: OK, I'm just going
+to skip through this because
+
+this could take a long
+time to talk about.
+
+Basically, what I wanted to say
+here was let's take the
+
+next step with animation,
+let's add
+
+some dynamic support.
+
+The easiest thing to do is just
+create a second uniform
+
+data table that you then
+blend with the first
+
+one and that one.
+
+In principle, is basically all
+of the channels and then now a
+
+game play programmer can go and
+
+individually set any of those.
+
+So they can tweak the head or
+tweak the elbow or whatever.
+
+And that's definitely
+compressible because it's very
+
+unlikely thet're going to be
+moving all the joints at once.
+
+You can create a secondary map
+that says, this is the number
+
+of joints that are dynamic, this
+is how they map to the
+
+uniform values.
+
+But then once you add any kind
+of dynamic support, you have
+
+now complicated the problem
+significantly.
+
+Because now in reality, what
+you need are constraints.
+
+You need to be able to have a
+limit to how high the head can
+
+move because what's going to
+happen is although you could
+
+just say the head could only
+move so much, if that movement
+
+is algorithmic, so let's
+say follow a
+
+character or whatever--
+
+it is going to go outside
+of reasonable
+
+constraints really quickly.
+
+So it's much cleaner and simpler
+to support that on the
+
+engine side, so basically define
+constraints for the
+
+joints and then let the
+high-level code point
+
+wherever they want.
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: Yeah.
+
+Yeah, you can have max change
+over time so it only can move
+
+so fast. The max range of
+motion, the max acceleration
+
+is actually a much harder
+problem because it implies
+
+that you need to store the
+change over time, which we're
+
+not actually storing.
+
+Which would probably blow
+our memory on the SPU.
+
+So as far as impacting
+animation, I would immediately
+
+throw out max acceleration if an
+animator were to come to me
+
+and say, this is a feature
+that I wanted.
+
+I would say, it's unlikely
+because it's unlikely we can
+
+fit it on the SPU.
+
+Whereas, on the PC, it might
+be a different story.
+
+And blending information,
+how you blend
+
+these things together.
+
+What's that?
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: OK.
+
+So as far as mixing, there's
+plenty of additional problems
+
+in mixing animation.
+
+Phase matching, so for example,
+you have a running
+
+and a walk.
+
+Basically all that means is if
+you were going to blend from a
+
+run to a walk you kind of want
+to blend in basically the
+
+essentially same leg position.
+
+Because if you just blend from
+the middle of an animation to
+
+the beginning of the animation,
+it's unlikely the
+
+legs are going to match and for
+the transition time you're
+
+going to see the scissoring
+of the legs.
+
+Which you see that in plenty
+of games, but especially in
+
+next generation, especially
+as characters look more
+
+complicated they are expected
+to act more complicated.
+
+Transitions handling either
+programmatic transitions
+
+between animations, so we have
+an animation that's standing
+
+and animation that's crouching
+and with constraints, move
+
+them down; or artist
+driven animated
+
+transitions and/or both.
+
+Translation matching
+is actually
+
+an interesting problem.
+
+So you have an animation that's
+running and you have an
+
+animation that's walking.
+
+They both translate obviously,
+at different speeds,
+
+nonlinearly and you want to
+slowly run down into a walk,
+
+but you have to match these sort
+of nonlinear translations
+
+as his feet are stepping
+onto the ground.
+
+Turns out to be a really
+difficult problem to get
+
+perfectly right, especially if
+you have eye key on the feet
+
+where he's walking on the ground
+or maybe walking uphill
+
+or downhill and the translation
+is being affected
+
+by the world.
+
+In a lot of cases you'll see
+people pretty much just ignore
+
+this problem.
+
+But it is something to consider
+going forward and
+
+this is something that we would
+consider how to solve,
+
+regardless of whether or
+not we could get it in.
+
+As far as actually rendering
+the geometry goes, you now
+
+have your sort of matrices
+of joints and you have--
+
+let's say you want to send those
+to the GPU along with
+
+the geometry to skin
+and render.
+
+Now the question is, do
+you single or double
+
+buffer those joints?
+
+Because right now basically, the
+GPU can be reading these
+
+joints in parallel
+to when you're
+
+actually outputting them.
+
+So the traditional approach or
+the easiest approach is just
+
+to double buffer the joints.
+
+So just output into a different
+buffer that the R6
+
+is reading from.
+
+It's one frame or half a frame
+behind, doesn't much matter.
+
+But it also doubles now the
+space of your joints.
+
+One advantage that games have
+is that a frame is a well
+
+defined element in the games.
+
+We know what needs to happen
+across the course of a frame.
+
+So these characters need to be
+rendered, the collisions of
+
+this background needs
+to happen, physics
+
+need to happen here.
+
+So you can within a frame, set
+it up so that the update from
+
+the SPUs and the read from the
+GPU can never overlap.
+
+Even without any kind of
+synchronization or lock, it
+
+can be a well known fact that
+it's impossible for these two
+
+things because there's actually
+something in the
+
+middle happening that has its
+own synchronization primitive.
+
+That will allow you to do single
+buffering of the data.
+
+But it does require
+more organization.
+
+Especially if you're doing it
+on more than just one case.
+
+So you have all these things
+that you want single buffered,
+
+so you need to organize them
+within the frames so they're
+
+never updating and reading
+at the same time.
+
+So I'll make this the last
+point I'll make.
+
+Optimization, one of the things
+that you'll hear, save
+
+optimization till the end.
+
+My point here being is if you
+save optimization till the
+
+end, you don't know how to
+do it because you haven't
+
+actually practiced it.
+
+If you haven't practiced it
+you don't know what to do.
+
+So it will take much longer.
+
+You should always be optimizing
+in order to
+
+understand, when it actually
+counts, what to do.
+
+And the fact that real
+optimization does impact the
+
+design all the way up.
+
+Optimization of the hardware
+impacts how an engine is
+
+designed to be fast does impact
+the data, it impacts
+
+how game play needs to be
+written, high-level code needs
+
+to be called.
+
+So if you save optimization till
+last, what you're doing
+
+is completely limiting what
+you can optimize.
+
+And the idea that it's the root
+of all evil certainly
+
+didn't come from a game
+developer, I have to say.
+
+Anyway, that's it.
+
+I hope that was helpful.
+
+PROFESSOR: Any questions?
+
+I think it's very interesting
+because there is a lot of
+
+things you learn at MIT.
+
+Forget everything you learned
+so I think there's a very
+
+interesting perspective in there
+and for some of us it's
+
+kind of hard to even digest a
+little bit, but Question?
+
+AUDIENCE: Call of Duty 3 came
+out on the Xbox and on the
+
+PS3, is Call of Duty 3 on the
+PS3 just running on the GPU
+
+then or is it--
+
+MIKE ACTON: No, it's very
+likely using the SPUs.
+
+I mean, I don't know.
+
+I haven't looked at the source
+code, but I suspect that it's
+
+using the SPUs.
+
+How efficiently it's
+using them is an
+
+entirely different question.
+
+But it's easy to take the most
+trivial things right, say you
+
+do hot spot analysis on your
+sequential code and say, OK,
+
+well I can grab this section of
+thing and put it on the SPU
+
+right and just the heaviest
+hitters and
+
+put them on the SPU.
+
+That's pretty easy to do.
+
+It's taking it to the next level
+though, and to really
+
+have sort of the next
+gen of game--
+
+now there's nowhere
+to go from there.
+
+There's nowhere to go from that
+analysis, you've already
+
+sort of hit the limit of what
+you can do with that.
+
+It has to be redesigned.
+
+So I don't know what they're
+doing honestly and certainly
+
+I'm being recorded so--
+
+yeah?
+
+AUDIENCE: You guys have shipped
+a game, on the PS3?
+
+MIKE ACTON: Yeah, it
+was on action list.
+
+AUDIENCE: OK, so that was
+more like the [OBSCURED]
+
+games and whatever You seem to
+talk a lot about all these
+
+things you've had to redo.
+
+What else is there--
+
+games look better as a console
+was built on, what else is
+
+there that you guys plan on
+changing as far as working
+
+with the cell processor,
+or do you think
+
+you've got it all ready?
+
+MIKE ACTON: Oh, no.
+
+There's plenty of work.
+
+There's plenty more
+to be optimized.
+
+It's down to cost in scheduling
+those things.
+
+I mean, we have a team of
+people who now really
+
+understand the platform and
+whereas a lot of what went
+
+into previous titles was mixed
+with learning curve.
+
+So there's definitely a
+potential for going back and
+
+improving things and making
+things better.
+
+That's what a cycle of game
+development is all about.
+
+I mean, games at the end of the
+lifetime of PlayStation 3
+
+will look significantly better
+than release titles.
+
+That's the way it always is.
+
+AUDIENCE: The head of Sony
+computer and gaming said that
+
+PS3 pretty soon would
+be customizable.
+
+You're be able to get different
+
+amounts of RAM and whatnot.
+
+MIKE ACTON: Well, I think in
+that case he was talking
+
+specifically about a PS3 based,
+like Tivo kind of weird
+
+media thing, which has nothing
+to do with us.
+
+AUDIENCE: [OBSCURED]
+
+MIKE ACTON: We're not stuck.
+
+That's what we have. I mean,
+I don't see it as stuck.
+
+I would much rather have the--
+
+I mean, that's what console
+development is about, really.
+
+We have a machine, we have a set
+of limitations of it and
+
+we can push that machine over
+the lifetime of the platform.
+
+If it changes out from under us,
+it becomes PC development.
+
+AUDIENCE: Are you allowed
+to use the
+
+seven SPUs or are you--
+
+[OBSCURED]
+
+PROFESSOR: [OBSCURED]
+
+MIKE ACTON: I don't know how
+much I can answer this just
+
+from NDA point-of-view.
+
+But let's say hypothetically,
+there magically became more
+
+SPUs on the PS3, right?
+
+Probably nothing would happen.
+
+The game has to be optimized
+for the minimum case, so
+
+nothing would change.
+
+Anything else?
+
+Yeah?
+
+AUDIENCE: So what's the
+development life cycle like
+
+for the engine part
+of the game.
+
+And I don't assume you start by
+prototyping in higher-level
+
+mechanisms. Then you'll
+completely miss the design for
+
+performance aspects of it.
+
+How do you build up from
+empty [OBSCURED]
+
+MIKE ACTON: No, you don't
+start with an empty.
+
+That's the perspective
+difference.
+
+You don't start with code,
+code's not important.
+
+Start with the data.
+
+You sit down with an artist
+and they say, what
+
+do you want to do?
+
+And then you look at the data.
+
+What does that data look like?
+
+What does this animation
+data look like?
+
+PROFESSOR: Data size matters.
+
+[OBSCURED]
+
+MIKE ACTON: Right.
+
+We have to figure out how
+to make it smaller.
+
+But it all starts
+with the data.
+
+It all starts with that concept
+of what do we want to
+
+see on the screen?
+
+What do we even want to
+hear on the speakers?
+
+What kind of effects
+do we want.
+
+And actually look at that from
+the perspective of the content
+
+creator and what they're
+generating and what we can do
+
+with that data.
+
+Because game development is just
+this black box between
+
+the artists and the screen.
+
+We're providing a transformation
+engine that
+
+takes the vision of the
+designers and the artists and
+
+just transforming it and
+spitting it on to screen.
+
+So where you really need
+to start is with the
+
+source of the data.
+
+AUDIENCE: You've been doing game
+developoment for 11 years
+
+now is what you said.
+
+Have you had a favorite
+platform
+
+and a nightmare platform?
+
+MIKE ACTON: I've been pretty
+much with the PlayStation
+
+platform since there was a
+PlayStation platform and I
+
+don't know, it's hard to get
+perspective because you're
+
+getting it and you always really
+love plarform you're
+
+working on.
+
+So it's hard.
+
+I mean, it's hard to
+get perspective.
+
+In the program where I am today
+is not the same program
+
+where I was 10 years ago.
+
+Personally, right now my
+favorite plarform is PS3.
+
+PROFESSOR: So when put it in
+perspective, there are already
+
+some platforms that on the first
+time round, [COUGHING],
+
+it's like cost of development.
+
+So one platform that as time
+goes we have [OBSCURED]
+
+MIKE ACTON: Well, like with the
+PS3, some of the things
+
+that I like about the PS3, which
+is sort of a different
+
+question are the fact that the
+cell is much more public than
+
+any other platform
+has ever been.
+
+With IBM's documentation, with
+Toshiba's support and Sony
+
+support, I've never had a
+platform where I can get up on
+
+a website and actually talk
+about it outside of NDA.
+
+And that for me is an
+amazing change.
+
+Where I can go and talk to other
+people-- exactly like
+
+this group here- that have
+used the same exact
+
+platform I've used.
+
+That's never been able
+to happen before.
+
+Even on PS2, for quite a long
+part of the lifespan, even
+
+though there was a Linux
+eventually on the PS2,
+
+virtually everything was covered
+by NDA because there
+
+was no independent release
+of information.
+
+So that's one of the great
+things about PS3 is the public
+
+availability of cell.
+
+PROFESSOR: Thank you very much
+for coming all the way from
+
+California and giving
+us some insight.
\ No newline at end of file
diff --git a/Sygq1e0xWnM.txt b/Sygq1e0xWnM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e1e0dd7fc0a4a462578eef0eb8aae6377abd40c8
--- /dev/null
+++ b/Sygq1e0xWnM.txt
@@ -0,0 +1,3211 @@
+-- shortest paths.
+This is the finale.
+
+Hopefully it was worth waiting
+for.
+
+Remind you there's a quiz
+coming up soon,
+
+you should be studying for it.
+There's no problem set due at
+
+the same time as the quiz
+because you should be studying
+
+now.
+It's a take-home exam.
+
+It's required that you come to
+class on Monday.
+
+Of course, you'll all come,
+but everyone watching at home
+
+should also come next Monday to
+get the quiz.
+
+It's the required lecture.
+So, we need a bit of a recap in
+
+the trilogy so far.
+So, the last two lectures,
+
+the last two episodes,
+or about single source shortest
+
+paths.
+So, we wanted to find the
+
+shortest path from a source
+vertex to every other vertex.
+
+And, we saw a few algorithms
+for this.
+
+Here's some recap.
+We saw in the unweighted case,
+
+that was sort of the easiest
+where all the edge weights were
+
+one.
+Then we could use breadth first
+
+search.
+And this costs what we call
+
+linear time in the graph world,
+the number of vertices plus the
+
+number of edges.
+The next simplest case,
+
+perhaps, is nonnegative edge
+weights.
+
+And in that case,
+what algorithm do we use?
+
+Dijkstra, all right,
+everyone's awake.
+
+Several answers at once,
+great.
+
+So this takes almost linear
+time if you use a good heap
+
+structure, so,
+V log V plus E.
+
+And, in the general case,
+general weights,
+
+we would use Bellman-Ford which
+you saw.
+
+And that costs VE,
+good, OK, which is quite a bit
+
+worse.
+This is ignoring log factors.
+
+Dijkstra is basically linear
+time, Bellman-Ford you're
+
+quadratic if you have a
+connected graph.
+
+So, in the sparse case,
+when E is order V,
+
+this is about linear.
+This is about quadratic.
+
+In the dense case,
+when E is about V^2,
+
+this is quadratic,
+and this is cubic.
+
+So, Dijkstra and Bellman-Ford
+are separated by about an order
+
+of V factor, which is pretty
+bad.
+
+OK, but that's the best we know
+how to do for single source
+
+shortest paths,
+negative edge weights,
+
+Bellman-Ford is the best.
+We also saw in recitation the
+
+case of a DAG.
+And there, what do you do?
+
+Topological sort,
+yeah.
+
+So, you can do a topological
+sort to get an ordering on the
+
+vertices.
+That you run Bellman-Ford,
+
+one round.
+This is one way to think of
+
+what's going on.
+You run Bellman-Ford in the
+
+order given by the topological
+sort, which is once,
+
+and you get a linear time
+algorithm.
+
+So, DAG is another case where
+we know how to do well even with
+
+weights.
+Unweighted, we can also do
+
+linear time.
+But most of the time,
+
+though, will be,
+so you should keep these in
+
+mind in the quiz.
+When you get a shortest path
+
+problem, or what you end up
+determining is the shortest path
+
+problem, think about what's the
+best algorithm you can use in
+
+that case?
+OK, so that's single source
+
+shortest paths.
+And so, in our evolution of the
+
+Death Star, initially it was
+just nonnegative edge weights.
+
+Then we got negative edge
+weights.
+
+Today, the Death Star
+challenges us with all pair
+
+shortest paths,
+where we want to know the
+
+shortest path weight between
+every pair of vertices.
+
+OK, so let's get some quick
+results.
+
+What could we do with this
+case?
+
+So, for example,
+suppose I have an unweighted
+
+graph.
+Any suggestions of how I should
+
+compute all pair shortest paths?
+Between every pair of vertices,
+
+I want to know the shortest
+path weight.
+
+BFS, a couple more words?
+Yeah?
+
+Right, BFS V times.
+OK, I'll say V times BFS,
+
+OK?
+So, the running time would be
+
+V^2 plus V times E,
+yeah, which is assuming your
+
+graph is connected,
+V times E.
+
+OK, good.
+That's probably about the best
+
+algorithm we know for unweighted
+graphs.
+
+So, a lot of these are going to
+sort of be the obvious answer.
+
+You take your single source
+algorithm, you run it V times.
+
+That's the best you can do,
+OK, or the best we know how to
+
+do.
+This is not so bad.
+
+This is like one iteration of
+Bellman-Ford,
+
+for comparison.
+We definitely need at least,
+
+like, V^2 time,
+because the size of the output
+
+is V^2, shortest path weight we
+have to compute.
+
+So, this is not perfect,
+but pretty good.
+
+And we are not going to improve
+on that.
+
+So, nonnegative edge weights:
+the natural thing to do is to
+
+run Dijkstra V times,
+OK, no big surprise.
+
+And the running time of that
+is, well, V times E again,
+
+plus V^2, log V,
+which is also not too bad.
+
+I mean, it's basically the same
+as running BFS.
+
+And then, there's the log
+factor.
+
+If you ignore the log factor,
+this is the dominant term.
+
+And, I mean,
+this had an [added?] V^2 as
+
+well.
+So, these are both pretty good.
+
+I mean, this is kind of neat.
+Essentially,
+
+the time it takes to run one
+Bellman-Ford plus a log factor,
+
+you can compute all pair
+shortest paths if you have
+
+nonnegative edge weights.
+So, I mean, comparing all pairs
+
+to signal source,
+this seems a lot better,
+
+except we can only handle
+nonnegative edge weights.
+
+OK, so now let's think about
+the general case.
+
+Well, this is the focus of
+today, and here's where we can
+
+actually make an improvement.
+So the obvious thing is V times
+
+Bellman-Ford,
+which would cost V^2 times E.
+
+And that's pretty pitiful,
+and we're going to try to
+
+improve that to something closer
+to that nonnegative edge weight
+
+bound.
+So it turns out,
+
+here, we can actually make an
+improvement whereas in these
+
+special cases,
+we really can't do much better.
+
+OK, I don't have a good
+intuition why,
+
+but it's the case.
+So, we'll cover something like
+
+three algorithms today for this
+problem.
+
+The last one will be the best,
+but along the way we'll see
+
+some nice connections between
+shortest paths and dynamic
+
+programming, which we haven't
+really seen yet.
+
+We've seen shortest path,
+and applying greedy algorithms
+
+to it, but today will actually
+do dynamic programming.
+
+The intuition is that with all
+pair shortest paths,
+
+there's more potential
+subproblem reuse.
+
+We've got to compute the
+shortest path from x to y for
+
+all x and y.
+Maybe we can reuse those
+
+shortest paths in computing
+other shortest paths.
+
+OK, there's a bit more
+reusability, let's say.
+
+OK, let me quickly define all
+pair shortest paths formally,
+
+because we're going to change
+our notation slightly.
+
+It's because we care about all
+pairs.
+
+So, as usual,
+the input is directed graph,
+
+so, vertices and edges.
+We're going to say that the
+
+vertices are labeled one to n
+for convenience because with all
+
+pairs, we're going to think of
+things more as an n by n matrix
+
+instead of edges in some sense
+because it doesn't help to think
+
+any more in terms of adjacency
+lists.
+
+And, you have edge weights as
+usual.
+
+This is what makes it
+interesting.
+
+Some of them are going to be
+negative.
+
+So, w maps to every real
+number, and the target output is
+
+a shortest path matrix.
+So, this is now an n by n
+
+matrix.
+So, n is just the number of
+
+vertices of shortest path
+weights.
+
+So, delta of i,
+j is the shortest path weight
+
+from i to j for all pairs of
+vertices.
+
+So this, you could represent as
+an n by n matrix in particular.
+
+OK, so now let's start doing
+algorithms.
+
+So, we have this very simple
+algorithm, V times Bellman-Ford,
+
+V^2 times E,
+and just for comparison's sake,
+
+I'm going to say,
+let me rewrite that,
+
+V times Bellman-Ford gives us
+this running time of V^2 E,
+
+and I'm going to think about
+the case where,
+
+let's just say the graph is
+dense, meeting that the number
+
+of edges is quadratic,
+and the number of vertices.
+
+So in that case,
+this will take V^4 time,
+
+which is pretty slow.
+We'd like to do better.
+
+So, first goal would just be to
+beat V^4, V hypercubed,
+
+I guess.
+OK, and we are going to use
+
+dynamic programming to do that.
+Or at least that's what the
+
+motivation will come from.
+It will take us a while before
+
+we can even beat V^4,
+which is maybe a bit pathetic,
+
+but it takes some clever
+insights, let's say.
+
+OK, so I'm going to introduce a
+bit more notation for this
+
+graph.
+So, I'm going to think about
+
+the weighted adjacency matrix.
+So, I don't think we've really
+
+seen this in lecture before,
+although I think it's in the
+
+appendix.
+What that means,
+
+so normally adjacency matrix is
+like one if there's an edge,
+
+and zero if there isn't.
+And this is in a digraph,
+
+so you have to be a little bit
+careful.
+
+Here, these values,
+the entries in the matrix,
+
+are going to be the weights of
+the edges.
+
+OK, this is this if ij is an
+edge.
+
+So, if ij is an edge in the
+graph, and it's going to be
+
+infinity if there is no edge.
+OK, in terms of shortest paths,
+
+this is a more useful way to
+represent the graph.
+
+All right, and so this includes
+everything that we need from
+
+here.
+And now we just have to think
+
+about it as a matrix.
+Matrices will be a useful tool
+
+in a little while.
+OK, so now I'm going to define
+
+some sub problems.
+And, there's different ways
+
+that you could define what's
+going on in the shortest paths
+
+problem.
+OK, the natural thing is I want
+
+to go from vertex i to vertex j.
+What's the shortest path?
+
+OK, we need to refine the sub
+problems a little but more than
+
+that.
+Not surprising.
+
+And if you think about my
+analogy to Bellman-Ford,
+
+what Bellman-Ford does is it
+tries to build longer and longer
+
+shortest paths.
+But here, length is in terms of
+
+the number of edges.
+So, first, it builds shortest
+
+paths of length one.
+We've proven the first round it
+
+does that.
+The second round,
+
+it provides all shortest paths
+of length two,
+
+of count two,
+and so on.
+
+We'd like to do that sort of
+analogously, and try to reuse
+
+things a little bit more.
+So, I'm going to say d_ij^(m)
+
+is the weight of the shortest
+path from i to j with some
+
+restriction involving m.
+So: shortest path from i to j
+
+using at most m edges.
+OK, for example,
+
+if m is zero,
+then we don't have to really
+
+think very hard to find all
+shortest paths of length zero.
+
+OK, they use zero edges,
+I should say.
+
+So, Bellman-Ford sort of tells
+us how to go from m to m plus
+
+one.
+So, let's just figure that out.
+
+So one thing we know from the
+Bellman-Ford analysis is if we
+
+look at d_ij^(m-1),
+we know that in some sense the
+
+longest shortest path of
+relevance, unless you have
+
+negative weight cycle,
+the longest shortest path of
+
+relevance is when m equals n
+minus one because that's the
+
+longest simple path you can
+have.
+
+So, this should be a shortest
+path weight from i to j,
+
+and it would be no matter what
+larger value you put in the
+
+superscript.
+This should be delta of i comma
+
+j if there's no negative weight
+cycles.
+
+OK, so this feels good for
+dynamic programming.
+
+This will give us the answer if
+we can compute this for all m.
+
+Then we'll have the shortest
+path weights in particular.
+
+We need a way to detect
+negative weight cycles,
+
+but let's not worry about that
+too much for now.
+
+There are negative weights,
+but let's just assume for now
+
+there's no negative weight
+cycles.
+
+OK, and we get a recursion
+recurrence.
+
+And the base case is when m
+equals zero.
+
+This is pretty easy.
+They have the same vertices,
+
+the weight of zero,
+and otherwise it's infinity.
+
+OK, and then the actual
+recursion is for m.
+
+OK, if I got this right,
+this is a pretty easy,
+
+intuitive recursion for
+d_ij^(m) is a min of smaller
+
+things in terms of n minus one.
+I'll just show the picture,
+
+and then the proof of that
+claim should be obvious.
+
+So, this is proof by picture.
+So, we have on the one hand,
+
+I over here,
+and j over here.
+
+We want to know the shortest
+path from i to j.
+
+And, we want to use,
+at most, m edges.
+
+So, the idea is,
+well, you could use m minus one
+
+edges to get somewhere.
+So this is, at most,
+
+m minus one edges,
+some other place,
+
+and we'll call it k.
+So this is a candidate for k.
+
+And then you could take the
+edge directly from k to j.
+
+So, this costs A_k^j,
+and this costs DIK m minus one.
+
+OK, and that's a candidate path
+of length that uses,
+
+at most, m edges from I to j.
+And this is essentially just
+
+considering all of them.
+OK, so there's sort of many
+
+paths we are considering.
+All of these are candidate
+
+values of k.
+We are taking them in over all
+
+k as intermediate nodes,
+whatever.
+
+So there they are.
+We take the best such path.
+
+That should encompass all
+shortest paths.
+
+And this is essentially sort of
+what Bellman-Ford is doing,
+
+although not exactly.
+We also sort of want to think
+
+about, well, what if I just go
+directly with,
+
+say, m minus one edges?
+What if there is no edge here
+
+that I want to use,
+in some sense?
+
+Well, we always think about
+there being, and the way the A's
+
+are defined, there's always this
+zero weight edge to yourself.
+
+So, you could just take a path
+that's shorter,
+
+go from d i to j,
+and j is a particular value of
+
+k that we might consider,
+and then take a zero weight
+
+edge at the end from A and jj.
+OK, so this really encompasses
+
+everything.
+So that's a pretty trivial
+
+claim.
+OK, now once we have such a
+
+recursion, we get a dynamic
+program.
+
+I mean, there,
+this is it in some sense.
+
+It's written recursively.
+You can write a bottom up.
+
+And I would like to write it
+bottom up it little bit because
+
+while it doesn't look like it,
+this is a relaxation.
+
+This is yet another relaxation
+algorithm.
+
+So, I'll give you,
+so, this is sort of the
+
+algorithm.
+This is not a very interesting
+
+algorithm.
+So, you don't have to write it
+
+all down if you don't feel like
+it.
+
+It's probably not even in the
+book.
+
+This is just an intermediate
+step.
+
+So, we loop over all m.
+That's sort of the outermost
+
+thing to do.
+I want to build longer and
+
+longer paths,
+and this vaguely corresponds to
+
+Bellman-Ford,
+although it's actually worse
+
+than Bellman-Ford.
+But hey, what the heck?
+
+It's a stepping stone.
+OK, then for all i and j,
+
+and then we want to compute
+this min.
+
+So, we'll just loop over all k,
+and relax.
+
+And, here's where we're
+actually computing the min.
+
+And, it's a relaxation,
+is the point.
+
+This is our good friend,
+the relaxation step,
+
+relaxing edge.
+Well, it's not,
+
+yeah.
+I guess we're relaxing edge kj,
+
+or something,
+except we don't have the same
+
+clear notion.
+I mean, it's a particular thing
+
+that we're relaxing.
+It's not just a single edge
+
+because we don't have a single
+source anymore.
+
+It's now relative to source I,
+we are relaxing the edge kj,
+
+something like that.
+But this is clearly a
+
+relaxation.
+We are just making the triangle
+
+inequality true if it wasn't
+before.
+
+The tribal inequality has got
+to hold between all pairs.
+
+And that's just implementing
+this min, right?
+
+You're taking d ij.
+You take the min of what it was
+
+before in some sense.
+That was one of the
+
+possibilities we considered when
+we looked at the zero weight
+
+edge.
+We say, well,
+
+or you could go from i to some
+k in some way that we knew how
+
+to before, and then add on the
+edge, and check whether that's
+
+better if it's better,
+set our current estimate to
+
+that.
+And, you do this for all k.
+
+In particular,
+you might actually compute
+
+something smaller than this min
+because I didn't put
+
+superscripts up here.
+But that's just making paths
+
+even better.
+OK, so you have to argue that
+
+relaxation is always a good
+thing to do.
+
+So, by not putting
+superscripts,
+
+maybe I do some more
+relaxation, but more relaxation
+
+never hurts us.
+You can still argue correctness
+
+using this claim.
+So, it's not quite the direct
+
+implementation,
+but there you go,
+
+dynamic programming algorithm.
+The main reason I'll write it
+
+down: so you see that it's a
+relaxation, and you see the
+
+running time is n^4,
+OK, which is certainly no
+
+better than Bellman-Ford.
+Bellman-Ford was n^4 even in
+
+the dense case,
+and it's a little better in the
+
+sparse case.
+So: not doing so great.
+
+But it's a start.
+OK, it gets our dynamic
+
+programming minds thinking.
+And, we'll get a better dynamic
+
+program in a moment.
+But first, there's actually
+
+something useful we can do with
+this formulation,
+
+and I guess I'll ask,
+but I'll be really impressed if
+
+anyone can see.
+Does this formula look like
+
+anything else that you've seen
+in any context,
+
+mathematical or algorithmic?
+Have you seen that recurrence
+
+anywhere else?
+OK, not exactly as stated,
+
+but similar.
+I'm sure if you thought about
+
+it for awhile,
+you could come up with it.
+
+Any answers?
+I didn't think you would be
+
+very intuitive,
+but the answer is matrix
+
+multiplication.
+And it may now be obvious to
+
+you, or it may not.
+You have to think with the
+
+right quirky mind.
+Then it's obvious that it's
+
+matrix multiplication.
+Remember, matrix
+
+multiplication,
+we have A, B,
+
+and C.
+They're all n by n matrices.
+
+And, we want to compute C
+equals A times B.
+
+And what that meant was,
+well, c_ij was a sum over all k
+
+of a_ik times b_kj.
+All right, that was our
+
+definition of matrix
+multiplication.
+
+And that formula looks kind of
+like this one.
+
+I mean, notice the subscripts:
+ik and kj.
+
+Now, the operators are a little
+different.
+
+Here, we're multiplying the
+inside things and adding them
+
+all together.
+There, we're adding the inside
+
+things and taking them in.
+But other than that,
+
+it's the same.
+OK, weird, but here we go.
+
+So, the connection to shortest
+paths is you replace these
+
+operators.
+So, let's take matrix
+
+multiplication and replace,
+what should I do first,
+
+plus this thing with min.
+So, why not just change the
+
+operators, replace dot with
+plus?
+
+This is just a different
+algebra to work in,
+
+where plus actually means min,
+and dot actually means plus.
+
+So, you have to check that
+things sort of work out in that
+
+context, but if we do that,
+then we get that c_ij is the
+
+min overall k of a_ik plus,
+a bit messy here,
+
+b_kj.
+And that looks like what we
+
+actually want to compute,
+here, for one value of m,
+
+you have to sort of do this m
+times.
+
+But this conceptually is
+d_ij^(m), and this is
+
+d_ik^(m-1).
+So, this is looking like a
+
+matrix product,
+which is kind of cool.
+
+So, if we sort of plug in this
+claim, then, and think about
+
+things as matrices,
+the recurrence gives us,
+
+and I'll just write this now at
+matrix form, that d^(m) is d^(m)
+
+minus one, funny product,
+A.
+
+All right, so these are the
+weights.
+
+These were the weighted
+adjacency matrix.
+
+This was the previous d value.
+This is the new d value.
+
+So, I'll just rewrite that in
+matrix form with capital
+
+letters.
+OK, I have the circle up things
+
+that are using this funny
+algebra, so, in particular,
+
+circled product.
+OK, so that's kind of nifty.
+
+We know something about
+computing matrix
+
+multiplications.
+We can do it in n^3 time.
+
+If we were a bit fancier,
+maybe we could do it in
+
+sub-cubic time.
+So, we could try to sort of use
+
+this connection.
+And, well, think about what we
+
+are computing here.
+We are saying,
+
+well, d to the m is the
+previous one times A.
+
+So, what is d^(m)?
+Is that some other algebraic
+
+notion that we know?
+Yeah, it's the exponent.
+
+We're taking A,
+and we want to raise it to the
+
+power, m, with this funny notion
+of product.
+
+So, in other words,
+d to the m is really just A to
+
+the m in a funny way.
+So, I'll circle it,
+
+OK?
+So, that sounds good.
+
+We also know how to compute
+powers of things relatively
+
+quickly, if you remember how.
+OK, for this notion,
+
+this power notion,
+to make sense,
+
+I should say what A to the zero
+means.
+
+And so, I need some kind of
+identity matrix.
+
+And for here,
+the identity matrix is this
+
+one, if I get it right.
+So, it has zeros along the
+
+diagonal, and infinities
+everywhere else.
+
+OK, that sort of just to match
+this definition.
+
+d_ij zero should be zeros on
+the diagonals and infinity
+
+everywhere else.
+But you can check this is
+
+actually an identity.
+If you multiply it with this
+
+funny multiplication against any
+other matrix,
+
+you get the matrix back.
+Nothing changes.
+
+This really is a valid identity
+matrix.
+
+And, I should mention that for
+A to the m to make sense,
+
+you really knew that your
+product operation is
+
+associative.
+So, actually A to the m circled
+
+makes sense because circled
+multiplication is associative,
+
+and you can check that;
+not hard because,
+
+I mean, min is associative,
+and addition is associative,
+
+and all sorts of good stuff.
+And, you have some kind of
+
+distributivity property.
+And, this is,
+
+in turn, because the real
+numbers with,
+
+and get the right order here,
+with min as your addition
+
+operation, and plus as your
+multiplication operation is a
+
+closed semi-ring.
+So, if ever you want to know
+
+when powers make sense,
+this is a good rule.
+
+If you have a closed semi-ring,
+then matrix products on that
+
+semi-ring will give you an
+associative operator,
+
+and then, good,
+you can take products.
+
+OK, that's just some formalism.
+So now, we have some intuition.
+
+The question is,
+what's the right.
+
+Algorithm?
+There are many possible
+
+answers, some of which are
+right, some of which are not.
+
+So, we have this connection to
+matrix products,
+
+and we have a connection to
+matrix powers.
+
+And, we have algorithms for
+both.
+
+The question is,
+what should we do?
+
+So, all we need to do now is to
+compute A to the funny power,
+
+n minus one.
+n minus one is when we get
+
+shortest paths,
+assuming we have no negative
+
+weight cycles.
+In fact, we could compute a
+
+larger power than n minus one.
+Once you get beyond n minus
+
+one, multipling by A doesn't
+change you anymore.
+
+So, how should we do it?
+OK, you're not giving any smart
+
+answers.
+I'll give the stupid answer.
+
+You could say,
+well, I take A.
+
+I multiply it by A.
+Then I multiply it by A,
+
+and I multiply it by A,
+and I use normal,
+
+boring matrix to
+multiplication.
+
+So, I do, like,
+n minus two,
+
+standard matrix multiplies.
+So, standard multiply costs,
+
+like, n^3.
+And I'm doing n of them.
+
+So, this gives me an n^4
+algorithm, and compute all the
+
+shortest pathways in n^4.
+Woohoo!
+
+OK, no improvement.
+So, how can I do better?
+
+Right, natural thing to try
+which sadly does not work,
+
+is to use the sub cubic matrix
+multiply algorithm.
+
+We will, in some sense,
+get there in a moment with a
+
+somewhat simpler problem.
+But, it's actually not known
+
+how to compute shortest paths
+using fast matrix multiplication
+
+like Strassen's system
+algorithm.
+
+But, good suggestion.
+OK, you have to think about why
+
+it doesn't work,
+and I'll tell you.
+
+It's not obvious,
+so it's a perfectly reasonable
+
+suggestion.
+But in this context it doesn't
+
+quite work.
+It will come up in a few
+
+moments.
+The problem is,
+
+Strassen requires the notion of
+subtraction.
+
+And here, addition is min.
+And, there's no inverse to min.
+
+Once you take the arguments,
+you can't sort of undo a min.
+
+OK, so there's no notion of
+subtraction, so it's not known
+
+how to pull that off,
+sadly.
+
+So, what other tricks do we
+have up our sleeve?
+
+Yeah?
+Divide and conquer,
+
+log n powering,
+yeah, repeated squaring.
+
+That works.
+Good, we had a fancy way.
+
+If you had a number n,
+you sort of looked at the
+
+binary number representation of
+n, and you either squared the
+
+number or squared it and added
+another factor of A.
+
+Here, we don't even have to be
+smart about it.
+
+OK, we can just compute,
+we really only have to think
+
+about powers of two.
+What we want to know,
+
+and I'm going to need a bigger
+font here because there's
+
+multiple levels of subscripts,
+A to the circled power,
+
+two to the ceiling of log n.
+Actually, n minus one would be
+
+enough.
+But there you go.
+
+You can write n if you didn't
+leave yourself enough space like
+
+me, n the ceiling,
+n the circle.
+
+This just means the next power
+of two after n minus one,
+
+two to the ceiling log.
+So, we don't have to go
+
+directly to n minus one.
+We can go further because
+
+anything farther than n minus
+one is still just the shortest
+
+pathways.
+If you look at the definition,
+
+and you know that your paths
+are simple, which is true if you
+
+have no negative weight cycles,
+then fine, just go farther.
+
+Why not?
+And so, to compute this,
+
+we just do ceiling of log n
+minus one products,
+
+just take A squared,
+and then take the result and
+
+square it; take the result and
+square it.
+
+So, this is order log n
+squares.
+
+And, we don't know how to use
+Strassen, but we can use the
+
+boring, standard multiply of
+n^3, and that gives us n^3 log n
+
+running time,
+OK, which finally is something
+
+that beats Bellman-Ford in the
+dense case.
+
+OK, in the dense case,
+Bellman-Ford was n^4.
+
+Here we get n^3 log n,
+finally something better.
+
+In the sparse case,
+it's about the same,
+
+maybe a little worse.
+E is order V.
+
+Then we're going to get,
+like, V3 for Bellman-Ford.
+
+Here, we get n^3 log n.
+OK, after log factors,
+
+this is an improvement some of
+the time.
+
+OK, it's about the same the
+other times.
+
+Another nifty thing that you
+get for free out of this,
+
+is you can detect negative
+weight cycles.
+
+So, here's a bit of a puzzle.
+How would I detect,
+
+after I compute this product,
+A to the power to ceiling log n
+
+minus one, how would I know if I
+found a negative weight cycle?
+
+What would that mean it this
+matrix of all their shortest
+
+paths of, at most,
+a certain length?
+
+If I found a cycle,
+what would have to be in that
+
+matrix?
+Yeah?
+
+Right, so I could,
+for example,
+
+take this thing,
+multiply it by A,
+
+see if the matrix changed at
+all.
+
+Right, that works fine.
+That's what we do in
+
+Bellman-Ford.
+It's an even simpler thing.
+
+It's already there.
+You don't have to multiply.
+
+But that's the same running
+time.
+
+That's a good answer.
+The diagonal would have a
+
+negative value,
+yeah.
+
+So, this is just a cute thing.
+Both approaches would work,
+
+can detect a negative weight
+cycle just by looking at the
+
+diagonal of the matrix.
+You just look for a negative
+
+value in the diagonal.
+OK.
+
+So, that's algorithm one,
+let's say.
+
+I mean, we've seen several that
+are all bad, but I'll call this
+
+number one.
+OK, we'll see two more.
+
+This is the only one that will,
+well, I shouldn't say that.
+
+Fine, there we go.
+So, this is one dynamic program
+
+that wasn't so helpful,
+except it showed us a
+
+connection to matrix
+multiplication,
+
+which is interesting.
+We'll see why it's useful a
+
+little bit more.
+But, it bled to this nasty four
+
+nested loops.
+And, using this trick,
+
+we got down to n^3 log n.
+Let's try, just for n^3.
+
+OK, just get rid of that log.
+It's annoying.
+
+It makes you a little bit worse
+than Bellman-Ford,
+
+and the sparse case.
+So, let's just erase one of
+
+these nested loops.
+OK, I want to do that.
+
+OK, obviously that algorithm
+doesn't work because it's for
+
+first decay, and it's not
+defined, but,
+
+you know, I've got enough
+variables.
+
+Why don't I just define k to
+the m?
+
+OK, it turns out that works.
+I'll do it from scratch,
+
+but why not?
+I don't know if that's how
+
+Floyd and Warshall came up with
+their algorithm,
+
+but here you go.
+Here's Floyd-Warshall.
+
+The idea is to define the
+subproblems a little bit more
+
+cleverly so that to compute one
+of these values,
+
+you don't have to take the min
+of n things.
+
+I just want to take the min of
+two things.
+
+If I could do that,
+and I still only have n^3
+
+subproblems, then I would have
+n^3 time.
+
+So, all right,
+the running time of dynamic
+
+program is number of subproblems
+times the time to compute the
+
+recurrence for one subproblem.
+So, here's linear times n^3,
+
+and we want n^3 times constant.
+That would be good.
+
+So that's Floyd-Warshall.
+So, here's the way we're going
+
+to redefine c_ij.
+Or I guess, there it was called
+
+d_ij.
+Good, so we're going to define
+
+something new.
+So, c_ij superscript k is now
+
+going to be the weight of the
+shortest path from I to j as
+
+before.
+Notice I used the superscript k
+
+instead of m because I want k
+and m to be the same thing.
+
+Deep.
+OK, now, here's the new
+
+constraint.
+I want all intermediate
+
+vertices along the path,
+meeting all vertices except for
+
+I and j at the beginning and the
+end to have a small label.
+
+So, they should be in the set
+from one up to k.
+
+And this is where we are really
+using that our vertices are
+
+labeled one up to m.
+So, I'm going to say,
+
+well, first think about the
+shortest paths that don't use
+
+any other vertices.
+That's when k is zero.
+
+Then think about all the
+shortest paths that maybe they
+
+use vertex one.
+And then think about the
+
+shortest paths that maybe use
+vertex one or vertex two.
+
+Why not?
+You could define it in this
+
+way.
+It turns out,
+
+then when you increase k,
+you only have to think about
+
+one new vertex.
+Here, we had to take min over
+
+all k.
+Now we know which k to look at.
+
+OK, maybe that made sense.
+Maybe it's not quite obvious
+
+yet.
+But I'm going to redo this
+
+claim, redo a recurrence.
+So, maybe first I should say
+
+some obvious things.
+So, if I want delta of ij of
+
+the shortest pathway,
+well, just take all the
+
+vertices.
+So, take c_ij superscript n.
+
+That's everything.
+And this even works,
+
+this is true even if you have a
+negative weight cycle.
+
+Although, again,
+we're going to sort of ignore
+
+negative weight cycles as long
+as we can detect them.
+
+And, another simple case is if
+you have, well,
+
+c_ij to zero.
+Let me put that in the claim to
+
+be a little bit more consistent
+here.
+
+So, here's the new claim.
+If we want to compute c_ij
+
+superscript zero,
+what is it?
+
+Superscript zero means I really
+shouldn't use any intermediate
+
+vertices.
+So, this has a very simple
+
+answer, a three letter answer.
+So, it's not zero.
+
+It's four letters.
+What's that?
+
+Nil.
+No, not working yet.
+
+It has some subscripts,
+too.
+
+So, the definition would be,
+what's the shortest path weight
+
+from I to j when you're not
+allowed to use any intermediate
+
+vertices?
+Sorry?
+
+So, yeah, it has a very simple
+name.
+
+That's the tricky part.
+All right, so if i equals j,
+
+[LAUGHTER] you're clever,
+right, open bracket i equals j
+
+means one, well,
+OK.
+
+It sort of works,
+but it's not quite right.
+
+In fact, I want infinity if i
+does not equal j.
+
+And I want to zero if i equals
+j, a_ij, good.
+
+I think it's a_ij.
+It should be,
+
+right?
+Maybe I'm wrong.
+
+Right, a_ij.
+So it's essentially not what I
+
+said.
+That's the point.
+
+If i does not equal j,
+you still have to think about a
+
+single edge connecting i to j,
+right?
+
+OK, so that's a bit of a
+subtlety.
+
+This is only intermediate
+vertices, so you could still go
+
+from i to j via a single edge.
+That will cost a_ij.
+
+If there is an edge:
+infinity.
+
+If there isn't one:
+that is a_ij.
+
+So, OK, that gets us started.
+And then, we want a recurrence.
+
+And, the recurrence is,
+well, maybe you get away with
+
+all the vertices that you had
+before.
+
+So, if you want to know paths
+that you had before,
+
+so if you want to know paths
+that use one up to k,
+
+maybe I just use one up to k
+minus one.
+
+You could try that.
+Or, you could try using k.
+
+So, either you use k or you
+don't.
+
+If you don't,
+it's got to be this.
+
+If you do, then you've got to
+go to k.
+
+So why not go to k at the end?
+So, you go from I to k using
+
+the previous vertices.
+Obviously, you don't want to
+
+repeat k in there.
+And then, you go from k to j
+
+somehow using vertices that are
+not k.
+
+This should be pretty
+intuitive.
+
+Again, I can draw a picture.
+So, either you never go to k,
+
+and that's this wiggly line.
+You go from i to j using things
+
+only one up to k minus one.
+In other words,
+
+here we have to use one up to
+k.
+
+So, this just means don't use
+k.
+
+So, that's this thing.
+Or, you use k somewhere in the
+
+middle there.
+OK, it's got to be one of the
+
+two.
+And in this case,
+
+you go from i to k using only
+smaller vertices,
+
+because you don't want to
+repeat k.
+
+And here, you go from k to j
+using only smaller labeled
+
+vertices.
+So, every path is one of the
+
+two.
+So, we take the shortest of
+
+these two subproblems.
+That's the answer.
+
+So, now we have a min of two
+things.
+
+It takes constant time to
+compute.
+
+So, we get a cubic algorithm.
+So, let me write it down.
+
+So, this is the Floyd-Warshall
+algorithm.
+
+I'll write the name again.
+You give it a matrix A.
+
+That's all it really needs to
+know.
+
+It codes everything.
+You copy C to A.
+
+That's the warm up.
+Right at time zero,
+
+C equals A.
+And then you just have these
+
+three loops for every value of
+k, for every value of i,
+
+and for every value of j.
+You compute that min.
+
+And if you think about it a
+little bit, that min is a
+
+relaxation.
+Surprise, surprise.
+
+So, that is the Floyd-Warshall
+algorithm.
+
+And, the running time is
+clearly n^3, three nested loops,
+
+constant time inside.
+So, we're finally getting
+
+something that is never worse
+than Bellman-Ford.
+
+In the sparse case,
+it's the same.
+
+And anything denser,
+the number of edges is super
+
+linear.
+This is strictly better than
+
+Bellman-Ford.
+And, it's better than
+
+everything we've seen so far for
+all pair, shortest paths.
+
+And, this handles negative
+weights; very simple algorithm,
+
+even simpler than the one
+before.
+
+It's just relaxation within
+three loops.
+
+What more could you ask for?
+And we need to check that this
+
+is indeed what min we're
+computing here,
+
+except that the superscripts
+are omitted.
+
+That's, again,
+a bit of hand waving a bit.
+
+It's OK to omit subscripts
+because that can only mean that
+
+you're doing more relaxation
+techniques should be.
+
+Doing more relaxations can
+never hurt you.
+
+In particular,
+we do all the ones that we have
+
+to.
+Therefore, we find the shortest
+
+path weights.
+And, again, here,
+
+we're assuming that there is no
+negative weight cycles.
+
+It shouldn't be hard to find
+them, but you have to think
+
+about that a little bit.
+OK, you could run another round
+
+of Bellman-Ford,
+see if it relaxes in a new
+
+edges again.
+For example,
+
+I think there's no nifty trick
+for that version.
+
+And, we're going to cover,
+that's our second algorithm for
+
+all pairs shortest paths.
+Before we go up to the third
+
+algorithm, which is going to be
+the cleverest of them all,
+
+the one Ring to rule them all,
+to switch trilogies,
+
+we're going to take a little
+bit of a diversion,
+
+side story, whatever,
+and talk about transitive
+
+closure briefly.
+This is just a good thing to
+
+know about.
+And, it relates to the
+
+algorithms we've seen so far.
+So, here's a transitive closure
+
+problem.
+I give you a directed graph,
+
+and for all pair vertices,
+i and j, I want to compute this
+
+number.
+It's one if there's a path from
+
+i to j.
+From i to j,
+
+OK, and then zero otherwise.
+OK, this is sort of like a
+
+boring adjacency matrix with no
+weights, except it's about paths
+
+instead of being about edges.
+OK, so how can I compute this?
+
+That's very simple.
+How should I compute this?
+
+This gives me a graph in some
+sense.
+
+This is adjacency matrix of a
+new graph called the transitive
+
+closure of my input graph.
+So, breadth first search,
+
+yeah, good.
+So, all I need to do is find
+
+shortest paths,
+and if the weights come out
+
+infinity, then there's no path.
+If it's less than infinity,
+
+that there's a path.
+And so here,
+
+so you are saying maybe I don't
+care about the weights,
+
+so I can run breadth first
+search n times,
+
+and that will work indeed.
+So, if we do B times B of S,
+
+so it's maybe weird that I'm
+covering here in the middle,
+
+but it's just an interlude.
+So, we have,
+
+then, something like V times E.
+OK, you can run any of these
+
+algorithms.
+You could take Floyd-Warshall
+
+for example.
+Why not?
+
+OK, then it would just be V^ I
+mean, you could run in any of
+
+these algorithms with weights of
+one or zero, and just check
+
+whether the values are infinity
+or not.
+
+So, I mean, t_ij equals zero,
+if and only if the shortest
+
+path weight from i to j is
+infinity.
+
+So, just solve this.
+This is an easier problem than
+
+shortest paths.
+It is, in fact,
+
+strictly easier in a certain
+sense, because what's going on
+
+with transitive closure,
+and I just want to mention this
+
+out of interest because
+transitive closure is a useful
+
+thing to know about.
+Essentially,
+
+what we are doing,
+let me get this right,
+
+is using a different set of
+operators.
+
+We're using or and and,
+a logical or and and instead of
+
+min and plus,
+OK, because we want to know,
+
+if you think about a
+relaxation, in some sense,
+
+maybe I should think about it
+in terms of this min.
+
+So, if I want to know,
+is there a pathway from I to j
+
+that uses vertices labeled one
+through k in the middle?
+
+Well, either there is a path
+that doesn't use the vertex k,
+
+or there is a path that uses k,
+and then it would have to look
+
+like that.
+OK, so there would have to be a
+
+path here, and there would have
+to be a path there.
+
+So, the min and plus get
+replaced with or and and.
+
+And if you remember,
+this used to be plus,
+
+and this used to be product in
+the matrix world.
+
+So, plus is now like or.
+And, multiply is now like and,
+
+which sounds very good,
+right?
+
+Plus does feel like or,
+and multiply does feel like and
+
+if you live in a zero-one world.
+So, in fact,
+
+this is not quite the field Z
+mod two, but this is a good,
+
+nice, field to work in.
+This is the Boolean world.
+
+So, I'll just write Boole.
+Good old Boole knows all about
+
+this.
+It's like his master's thesis,
+
+I think, talking about Boolean
+algebra.
+
+And, this actually means that
+you can use fast matrix
+
+multiply.
+You can use Strassen's
+
+algorithm, and the fancier
+algorithms, and you can compute
+
+the transitive closure in
+subcubic time.
+
+So, this is sub cubic if the
+edges are sparse.
+
+But, it's cubic in the worst
+case if there are lots of edges.
+
+This is cubic.
+You can actually do better
+
+using Strassen.
+So, I'll just say you can do
+
+it.
+No details here.
+
+I think it should be,
+so in fact, there is a theorem.
+
+This is probably not in the
+textbook, but there's a theorem
+
+that says transitive closure is
+just as hard as matrix multiply.
+
+OK, they are equivalent.
+Their running times are the
+
+same.
+We don't know how long it takes
+
+to do a matrix multiply over a
+field.
+
+It's somewhere between n^2 and
+n^2.3.
+
+But, whatever the answer is:
+same for transitive closure.
+
+OK, there's the interlude.
+And that's where we actually
+
+get to use Strassen and friends.
+Remember, Strassen was n to the
+
+log base two of seven algorithm.
+Remember that,
+
+especially on the final.
+Those are things you should
+
+have at the tip of your tongue.
+OK, the last algorithm we're
+
+going to cover is really going
+to build on what we saw last
+
+time: Johnson's algorithm.
+And, I've lost some of the
+
+running times here.
+But, when we had unweighted
+
+graphs, we could do all pairs
+really fast, just as fast as a
+
+single source Bellman-Ford.
+That's kind of nifty.
+
+We don't know how to improve
+Bellman-Ford in the single
+
+source case.
+So, we can't really help to get
+
+anything better than V times E.
+And, if you remember running V
+
+times Dijkstra,
+V times Dijkstra was about the
+
+same.
+So, just put this in the recall
+
+bubble here: V times Dijkstra
+would give us V times E plus V^2
+
+log V.
+And, if you ignore that log
+
+factor, this is just VE.
+OK, so this was really good.
+
+Dijkstra was great.
+And this was for nonnegative
+
+edge weights.
+So, with negative edge weights,
+
+somehow we'd like to get the
+same running time.
+
+Now, how might I get the same
+running time?
+
+Well, it would be really nice
+if I could use Dijkstra.
+
+Of course, Dijkstra doesn't
+work with negative weights.
+
+So what could I do?
+What would I hope to do?
+
+What could I hope to?
+Suppose I want,
+
+in the middle of the algorithm,
+it says run Dijkstra n times.
+
+Then, what should I do to
+prepare for that?
+
+Make all the weights positive,
+or nonnegative.
+
+Why not, right?
+We're being wishful thinking.
+
+That's what we'll do.
+So, this is called graph
+
+re-weighting.
+And, what's cool is we actually
+
+already know how to do it.
+We just don't know that we know
+
+how to do it.
+But I know that we know that we
+
+know how to do it.
+You don't yet know that we know
+
+that I know that we know how to
+do it.
+
+So, it turns out you can
+re-weight the vertices.
+
+So, at the end of the last
+class someone asked me,
+
+can you just,
+like, add the same weight to
+
+all the edges?
+That doesn't work.
+
+Not quite, because different
+paths have different numbers of
+
+edges.
+What we are going to do is add
+
+a particular weight to each
+vertex.
+
+What does that mean?
+Well, because we really only
+
+have weights on the edges,
+here's what well do.
+
+We'll re-weight each edge,
+so, (u,v), let's say,
+
+going to go back into graph
+speak instead of matrix speak,
+
+(u,v) instead of I and j,
+and we'll call this modified
+
+weight w_h.
+h is our function.
+
+It gives us a number for every
+vertex.
+
+And, it's just going to be the
+old weight of that edge plus the
+
+weight of the start vertex minus
+the weight of the terminating
+
+vertex.
+I'm sure these have good names.
+
+One of these is the head,
+and the other is the tail,
+
+but I can never remember which.
+OK, so we've directed edge
+
+(u,v).
+Just add one of them;
+
+subtract the other.
+And, it's a directed edge,
+
+so that's a consistent
+definition.
+
+OK, so that's called
+re-weighting.
+
+Now, this is actually a
+theorem.
+
+If you do this,
+then, let's say,
+
+for any vertices,
+u and v in the graph,
+
+for any two vertices,
+all paths from u to v have the
+
+same weight as they did before,
+well, not quite.
+
+They have the same
+re-weighting.
+
+So, if you look at all the
+different paths and you say,
+
+well, what's the difference
+between vh, well,
+
+sorry, let's say delta,
+which is the old shortest
+
+paths, and deltas of h,
+which is the shortest path
+
+weights according to this new
+weight function,
+
+then that difference is the
+same.
+
+So, we'll say that all these
+paths are re-weighted by the
+
+same amounts.
+OK, this is actually a
+
+statement about all paths,
+not just shortest paths.
+
+There we go.
+OK, to how many people is this
+
+obvious already?
+A few, yeah,
+
+it is.
+And what's the one word?
+
+OK, it's maybe not that
+obvious.
+
+All right, shout out the word
+when you figure it out.
+
+Meanwhile, I'll write out this
+rather verbose proof.
+
+There's a one word proof,
+still waiting.
+
+So, let's just take one of
+these paths that starts at u and
+
+ends at v.
+Take any path.
+
+We're just going to see what
+its new weight is relative to
+
+its old weight.
+And so, let's just write out
+
+w_h of the path,
+which we define in the usual
+
+way as the sum over all edges of
+the new weight of the edge from
+
+v_i to v_i plus one.
+Do you have the word?
+
+No?
+Tough puzzle then,
+
+OK.
+So that's the definition of the
+
+weight of a path.
+And, then we know this thing is
+
+just w of v_i,
+v_i plus one.
+
+I'll get it right,
+plus the weight of the first
+
+vertex, plus,
+sorry, the re-weighting of v_i
+
+minus the re-weighting of v_i
+plus one.
+
+This is all in parentheses
+that's summed over I.
+
+Now I need the magic word.
+Telescopes, good.
+
+Now this is obvious:
+each of these telescopes with
+
+an extra previous,
+except the very beginning and
+
+the very end.
+So, this is the sum of these
+
+weights of edges,
+but then outside the sum,
+
+we have plus h of v_1,
+and minus h of v_k.
+
+OK, those guys don't quite
+cancel.
+
+We're not looking at a cycle,
+just a path.
+
+And, this thing is just w of
+the path, as this is the normal
+
+weight of the path.
+And so the change,
+
+the difference between w_h of P
+and w of P is this thing,
+
+which is just h of u minus h of
+v.
+
+And, the point is that's the
+same as long as you fix the
+
+endpoints, u and v,
+of the shortest path,
+
+you're changing this path
+weight by the same thing for all
+
+paths.
+This is for any path from u to
+
+v, and that proves the theorem.
+So, the one word here was
+
+telescopes.
+These change in weights
+
+telescope over any path.
+Therefore, if we want to find
+
+shortest paths,
+you just find the shortest
+
+paths in this re-weighted
+version, and then you just
+
+change it by this one amount.
+You subtract off this amount
+
+instead of adding it.
+That will give you the shortest
+
+path weight in the original
+weights.
+
+OK, so this is a tool.
+We now know how to change
+
+weights in the graph.
+But what we really want is to
+
+change weights in the graph so
+that the weights all come out
+
+nonnegative.
+OK, how do we do that?
+
+Why in the world would there be
+a function, h,
+
+that makes all the edge weights
+nonnegative?
+
+It doesn't make sense.
+It turns out we already know.
+
+So, I should write down this
+consequence.
+
+Let me get this in the right
+order.
+
+So in particular,
+the shortest path changes by
+
+this amount.
+And if you want to know this
+
+value, you just move the stuff
+to the other side.
+
+So, we compute deltas of h,
+then we can compute delta.
+
+That's the consequence here.
+How many people here pronounce
+
+this word corollary?
+OK, and how many people
+
+pronounce it corollary?
+Yeah, we are alone.
+
+Usually get at least one other
+student, and they're usually
+
+Canadian or British or
+something.
+
+I think that the accent.
+So, I always avoid pronouncing
+
+his word unless I really think,
+it's corollary,
+
+and get it right.
+I at least say Z not Zed.
+
+OK, here we go.
+So, what we want to do is find
+
+one of these functions.
+I mean, let's just write down
+
+what we could hope to have.
+We want to find a re-weighted
+
+function, h, the signs of weight
+to each vertex such that w_h of
+
+(u,v) is nonnegative.
+That would be great for all
+
+edges, all (u,v) in E.
+OK, then we could run Dijkstra.
+
+We could run Dijkstra,
+get the delta h's,
+
+and then just undo the
+re-weighting,
+
+and get what we want.
+And, that is Johnson's
+
+algorithm.
+The claim is that this is
+
+always possible.
+OK, why should it always be
+
+possible?
+Well, let's look at this
+
+constraint.
+w_h of (u,v) is that.
+
+So, it's w of (u,v) plus h of u
+minus h of V should be
+
+nonnegative.
+Let me rewrite this a little
+
+bit.
+I'm going to put these guys
+
+over here.
+That would be the right thing,
+
+h of v minus h of u is less
+than or equal to w of (u,v).
+
+Does that look familiar?
+Did I get it right?
+
+It should be right.
+Anyone seen that inequality
+
+before?
+Yeah, yes, correct answer.
+
+OK, where?
+In a previous lecture?
+
+In the previous lecture.
+What is this called if I
+
+replace h with x?
+Charles knows.
+
+Good, anyone else remember all
+the way back to episode two?
+
+I know there was a weekend.
+What's this operator called?
+
+Not subtraction but,
+I think I heard it,
+
+oh man.
+All right, I'll tell you.
+
+It's a difference constraint,
+all right?
+
+This is the difference
+operator.
+
+OK, it's our good friend
+difference constraints.
+
+So, this is what we want to
+satisfy.
+
+We have a system of difference
+constraints.
+
+h of V minus h of u should be,
+we want to find these.
+
+These are our unknowns.
+Subject to these constraints,
+
+we are given the w's.
+Now, we know in these
+
+difference constraints are
+satisfiable.
+
+Can someone tell me when these
+constraints are satisfiable?
+
+We know exactly when for any
+set of difference constraints.
+
+You've got to remember the
+math.
+
+Terminology,
+I can understand.
+
+It's hard to remember words
+unless you're a linguist,
+
+perhaps.
+So, when is the system of
+
+different constraints
+satisfiable?
+
+All right, you should
+definitely, very good.
+
+[LAUGHTER] Yes,
+very good.
+
+Someone brought their lecture
+notes: when the constraint graph
+
+has no negative weight cycles.
+Good, thank you.
+
+Now, what is the constraint
+graph?
+
+OK, this has a one letter
+answer more or less.
+
+I'll accept the one letter
+answer.
+
+What?
+A?
+
+A: close.
+G.
+
+Yeah, I mean,
+same thing.
+
+Yeah, so the constraint graph
+is essentially G.
+
+Actually, it is G.
+The constraint graph is G,
+
+good.
+And, we prove this by adding a
+
+new source for text,
+and connecting that to
+
+everyone.
+But that's sort of beside the
+
+point.
+That was in order to actually
+
+satisfy them.
+But this is our
+
+characterization.
+So, if we assume that there are
+
+no negative weight cycles in our
+graph, which we've been doing
+
+all the time,
+then we know that this thing is
+
+satisfiable.
+Therefore, there is an
+
+assignment of this h's.
+There is a re-weighting that
+
+makes all the weights
+nonnegative.
+
+Then we can run Dijkstra.
+OK, we're done.
+
+Isn't that cool?
+And how do we satisfy these
+
+constraints?
+We know how to do that with one
+
+run of Bellman-Ford,
+which costs order VE,
+
+which is less than V times
+Dijkstra.
+
+So, that's it,
+write down the details
+
+somewhere.
+
+So, this is Johnson's
+algorithm.
+
+This is the fanciest of them
+all.
+
+It will be our fastest,
+all pairs shortest path
+
+algorithm.
+So, the claim is,
+
+we can find a function,
+h, from V to R such that the
+
+modified weight of every edge is
+nonnegative for every edge,
+
+(u,v), in our graph.
+And, we do that using
+
+Bellman-Ford to solve the
+difference constraints.
+
+These are exactly the different
+constraints that we were born to
+
+solve that we learned to solve
+last time.
+
+The graphs here are
+corresponding exactly if you
+
+look back at the definition.
+Or, Bellman-Ford will tell us
+
+that there is a negative weight
+cycle.
+
+OK, great, so it's not that we
+really have to assume that there
+
+is no negative weight cycle.
+We'll get to know.
+
+And if your fancy,
+you can actually figure out the
+
+minus infinities from this.
+But, at this point,
+
+I just want to think about the
+case where there is no negative
+
+weight cycle.
+But if there is,
+
+we can find out that it exists,
+and that just tell the user.
+
+OK, then we'd stop.
+Otherwise, there is no negative
+
+weight cycle.
+Therefore, there is an
+
+assignment that gives is
+nonnegative edge weights.
+
+So, we just use it.
+We use it to run Dijkstra.
+
+So, step two is,
+oh, I should say the running
+
+time of all this is V times E.
+So, we're just running
+
+Bellman-Ford on exactly the
+input graph.
+
+Plus, we add a source,
+if you recall,
+
+to solve a set of difference
+constraints.
+
+You add a source vertex,
+S, connected to everyone at
+
+weight zero, run Bellman-Ford
+from there because we don't have
+
+a source here.
+We just have a graph.
+
+We want to know all pairs.
+So, this, you can use to find
+
+whether there is a negative
+weight cycle anywhere.
+
+Or, we get this magic
+assignment.
+
+So now, w_h is nonnegative,
+so we can run Dijkstra on w_h.
+
+We'll say, using w_h,
+so you compute w_h.
+
+That takes linear time.
+And, we run Dijkstra for each
+
+possible source.
+I'll write this out explicitly.
+
+We've had this in our minds
+several times.
+
+But, when we said n times
+Dijkstra over n times BFS,
+
+here it is.
+We want to compute delta sub h
+
+now, of (u,v) for all V,
+and we do this separately for
+
+all u.
+And so, the running time here
+
+is VE plus V^2 log V.
+This is just V times the
+
+running time of Dijkstra,
+which is E plus V log V.
+
+OK, it happens that this term
+is the same as this one,
+
+which is nice,
+because that means step one
+
+costs us nothing asymptotically.
+OK, and then,
+
+last step is,
+well, now we know delta h.
+
+We just need to compute delta.
+So, for each pair of vertices,
+
+we'll call it (u,v),
+we just compute what the
+
+original weights would be,
+so what delta (u,v) is.
+
+And we can do that using this
+corollary.
+
+It's just delta sub h of (u,v)
+minus h of u plus h of v.
+
+I got the signs right.
+Yeah, so this takes V^2 time,
+
+also dwarfed by the running
+time of Dijkstra.
+
+So, the overall running time of
+Johnson's algorithm is just the
+
+running time of step two,
+running Dijkstra n times --
+
+-- which is pretty cool.
+When it comes to single source
+
+shortest paths,
+Bellman-Ford is the best thing
+
+for general weights.
+Dijkstra is the best thing for
+
+nonnegative weights.
+But for all pair shortest
+
+paths, we can skirt the whole
+negative weight issue by using
+
+this magic we saw from
+Bellman-Ford.
+
+But now, running Dijkstra n
+times, which is still the best
+
+thing we know how to do,
+pretty much,
+
+for the all pairs nonnegative
+weights, now we can do it for
+
+general weights too,
+which is a pretty nice
+
+combination of all the
+techniques we've seen.
+
+In the trilogy,
+and along the way,
+
+we saw lots of dynamic
+programming, which is always
+
+good practice.
+Any questions?
+
+This is the last new content
+lecture before the quiz.
+
+On Wednesday it will be quiz
+review, if I recall correctly.
+
+And then it's Thanksgiving,
+so there's no recitation.
+
+And then the quiz starts on
+Monday.
+
+So, study up.
+See you then.
\ No newline at end of file
diff --git a/Tl_p5pgBsyM.txt b/Tl_p5pgBsyM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9a552740c1377cf66492e5e9c239a14680eb459c
--- /dev/null
+++ b/Tl_p5pgBsyM.txt
@@ -0,0 +1,9960 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu this week's problem is from
+
+ align:start position:0%
+ocw.mit.edu this week's problem is from
+ 
+
+ align:start position:0%
+ocw.mit.edu this week's problem is from
+the 2008 uh quiz one on search is
+
+ align:start position:0%
+the 2008 uh quiz one on search is
+ 
+
+ align:start position:0%
+the 2008 uh quiz one on search is
+motivated by the search of evil Overlord
+
+ align:start position:0%
+motivated by the search of evil Overlord
+ 
+
+ align:start position:0%
+motivated by the search of evil Overlord
+Mark Vader who is shopping for a new
+
+ align:start position:0%
+Mark Vader who is shopping for a new
+ 
+
+ align:start position:0%
+Mark Vader who is shopping for a new
+evil stronghold he starts from his
+
+ align:start position:0%
+evil stronghold he starts from his
+ 
+
+ align:start position:0%
+evil stronghold he starts from his
+current stronghold which is s the depth
+
+ align:start position:0%
+current stronghold which is s the depth
+ 
+
+ align:start position:0%
+current stronghold which is s the depth
+first search Star now the depth first
+
+ align:start position:0%
+first search Star now the depth first
+ 
+
+ align:start position:0%
+first search Star now the depth first
+search Star has the following qualities
+
+ align:start position:0%
+search Star has the following qualities
+ 
+
+ align:start position:0%
+search Star has the following qualities
+it has a small thermal exhaust pipe
+
+ align:start position:0%
+it has a small thermal exhaust pipe
+ 
+
+ align:start position:0%
+it has a small thermal exhaust pipe
+weakness it has the quality of that's no
+
+ align:start position:0%
+weakness it has the quality of that's no
+ 
+
+ align:start position:0%
+weakness it has the quality of that's no
+moon but it does not have a race of
+
+ align:start position:0%
+moon but it does not have a race of
+ 
+
+ align:start position:0%
+moon but it does not have a race of
+enslaved minions or a secret Escape
+
+ align:start position:0%
+enslaved minions or a secret Escape
+ 
+
+ align:start position:0%
+enslaved minions or a secret Escape
+Route or sharks with laser
+
+ align:start position:0%
+Route or sharks with laser
+ 
+
+ align:start position:0%
+Route or sharks with laser
+beams now when I originally wrote this
+
+ align:start position:0%
+beams now when I originally wrote this
+ 
+
+ align:start position:0%
+beams now when I originally wrote this
+problem in 2008 there was another
+
+ align:start position:0%
+problem in 2008 there was another
+ 
+
+ align:start position:0%
+problem in 2008 there was another
+quality that was very important that was
+
+ align:start position:0%
+quality that was very important that was
+ 
+
+ align:start position:0%
+quality that was very important that was
+a giant laser and it did have that
+
+ align:start position:0%
+a giant laser and it did have that
+ 
+
+ align:start position:0%
+a giant laser and it did have that
+property as did Dr Evil's W base but
+
+ align:start position:0%
+property as did Dr Evil's W base but
+ 
+
+ align:start position:0%
+property as did Dr Evil's W base but
+that was removed to make it easier to
+
+ align:start position:0%
+that was removed to make it easier to
+ 
+
+ align:start position:0%
+that was removed to make it easier to
+solve so we're going to solve it without
+
+ align:start position:0%
+solve so we're going to solve it without
+ 
+
+ align:start position:0%
+solve so we're going to solve it without
+the without the giant laser that we can
+
+ align:start position:0%
+the without the giant laser that we can
+ 
+
+ align:start position:0%
+the without the giant laser that we can
+just have the sharks with blazer beams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Mark Vader has gone to akar's
+
+ align:start position:0%
+so Mark Vader has gone to akar's
+ 
+
+ align:start position:0%
+so Mark Vader has gone to akar's
+Emporium of uh new evil strongholds
+
+ align:start position:0%
+Emporium of uh new evil strongholds
+ 
+
+ align:start position:0%
+Emporium of uh new evil strongholds
+which are listed on the left and he's
+
+ align:start position:0%
+which are listed on the left and he's
+ 
+
+ align:start position:0%
+which are listed on the left and he's
+trying to figure out the best way to um
+
+ align:start position:0%
+trying to figure out the best way to um
+ 
+
+ align:start position:0%
+trying to figure out the best way to um
+get from his current stronghold to his
+
+ align:start position:0%
+get from his current stronghold to his
+ 
+
+ align:start position:0%
+get from his current stronghold to his
+goal stronghold the 603 Fortress which
+
+ align:start position:0%
+goal stronghold the 603 Fortress which
+ 
+
+ align:start position:0%
+goal stronghold the 603 Fortress which
+has the aborable qualities of no small
+
+ align:start position:0%
+has the aborable qualities of no small
+ 
+
+ align:start position:0%
+has the aborable qualities of no small
+thermal exhaust pipe weakness and it
+
+ align:start position:0%
+thermal exhaust pipe weakness and it
+ 
+
+ align:start position:0%
+thermal exhaust pipe weakness and it
+still has that's no moon it has a race
+
+ align:start position:0%
+still has that's no moon it has a race
+ 
+
+ align:start position:0%
+still has that's no moon it has a race
+of enslaved minions and a secret Escape
+
+ align:start position:0%
+of enslaved minions and a secret Escape
+ 
+
+ align:start position:0%
+of enslaved minions and a secret Escape
+Route and sharks with blazer beams which
+
+ align:start position:0%
+Route and sharks with blazer beams which
+ 
+
+ align:start position:0%
+Route and sharks with blazer beams which
+so it's got everything you would want
+
+ align:start position:0%
+so it's got everything you would want
+ 
+
+ align:start position:0%
+so it's got everything you would want
+and no weakness however he can only uh
+
+ align:start position:0%
+and no weakness however he can only uh
+ 
+
+ align:start position:0%
+and no weakness however he can only uh
+move between fortresses that have
+
+ align:start position:0%
+move between fortresses that have
+ 
+
+ align:start position:0%
+move between fortresses that have
+exactly one
+
+ align:start position:0%
+exactly one
+ 
+
+ align:start position:0%
+exactly one
+difference fortunately Mark remembers
+
+ align:start position:0%
+difference fortunately Mark remembers
+ 
+
+ align:start position:0%
+difference fortunately Mark remembers
+how to perform the search techniques he
+
+ align:start position:0%
+how to perform the search techniques he
+ 
+
+ align:start position:0%
+how to perform the search techniques he
+learned in 6034 from his mentor Emperor
+
+ align:start position:0%
+learned in 6034 from his mentor Emperor
+ 
+
+ align:start position:0%
+learned in 6034 from his mentor Emperor
+Patrick teen so we've got several
+
+ align:start position:0%
+Patrick teen so we've got several
+ 
+
+ align:start position:0%
+Patrick teen so we've got several
+fortresses here we've got the dep for
+
+ align:start position:0%
+fortresses here we've got the dep for
+ 
+
+ align:start position:0%
+fortresses here we've got the dep for
+search Star we've also um got sh
+
+ align:start position:0%
+search Star we've also um got sh
+ 
+
+ align:start position:0%
+search Star we've also um got sh
+ghoul which has um the the quality is
+
+ align:start position:0%
+ghoul which has um the the quality is
+ 
+
+ align:start position:0%
+ghoul which has um the the quality is
+basically of that's no moon and none of
+
+ align:start position:0%
+basically of that's no moon and none of
+ 
+
+ align:start position:0%
+basically of that's no moon and none of
+the other qualities DOL gor here has got
+
+ align:start position:0%
+the other qualities DOL gor here has got
+ 
+
+ align:start position:0%
+the other qualities DOL gor here has got
+the uh exhaust pipe weakness somehow
+
+ align:start position:0%
+the uh exhaust pipe weakness somehow
+ 
+
+ align:start position:0%
+the uh exhaust pipe weakness somehow
+despite being saon stronghold uh it's
+
+ align:start position:0%
+despite being saon stronghold uh it's
+ 
+
+ align:start position:0%
+despite being saon stronghold uh it's
+not a moon and it has those enslaved
+
+ align:start position:0%
+not a moon and it has those enslaved
+ 
+
+ align:start position:0%
+not a moon and it has those enslaved
+minions I guess the Orcs are enslaved
+
+ align:start position:0%
+minions I guess the Orcs are enslaved
+ 
+
+ align:start position:0%
+minions I guess the Orcs are enslaved
+Moon raker here uh only has exhaust pipe
+
+ align:start position:0%
+Moon raker here uh only has exhaust pipe
+ 
+
+ align:start position:0%
+Moon raker here uh only has exhaust pipe
+weakness so it's it's not very good but
+
+ align:start position:0%
+weakness so it's it's not very good but
+ 
+
+ align:start position:0%
+weakness so it's it's not very good but
+James Bond didn't need to deal with
+
+ align:start position:0%
+James Bond didn't need to deal with
+ 
+
+ align:start position:0%
+James Bond didn't need to deal with
+stuff uh Zeal Underwater Palace has
+
+ align:start position:0%
+stuff uh Zeal Underwater Palace has
+ 
+
+ align:start position:0%
+stuff uh Zeal Underwater Palace has
+that's no moon and a secret Escape Route
+
+ align:start position:0%
+that's no moon and a secret Escape Route
+ 
+
+ align:start position:0%
+that's no moon and a secret Escape Route
+zeris is lunar core has an exhaust pipe
+
+ align:start position:0%
+zeris is lunar core has an exhaust pipe
+ 
+
+ align:start position:0%
+zeris is lunar core has an exhaust pipe
+weakness and a race of enslaved minions
+
+ align:start position:0%
+weakness and a race of enslaved minions
+ 
+
+ align:start position:0%
+weakness and a race of enslaved minions
+Whalers of the moon rde has the exhaust
+
+ align:start position:0%
+Whalers of the moon rde has the exhaust
+ 
+
+ align:start position:0%
+Whalers of the moon rde has the exhaust
+pipe weakness race of enslaved minions
+
+ align:start position:0%
+pipe weakness race of enslaved minions
+ 
+
+ align:start position:0%
+pipe weakness race of enslaved minions
+and sharks with laser beams 603 Fortress
+
+ align:start position:0%
+and sharks with laser beams 603 Fortress
+ 
+
+ align:start position:0%
+and sharks with laser beams 603 Fortress
+we've already been over at Atlantis has
+
+ align:start position:0%
+we've already been over at Atlantis has
+ 
+
+ align:start position:0%
+we've already been over at Atlantis has
+all qualities except for a secret Escape
+
+ align:start position:0%
+all qualities except for a secret Escape
+ 
+
+ align:start position:0%
+all qualities except for a secret Escape
+Route Wily Wonka's factory has some of
+
+ align:start position:0%
+Route Wily Wonka's factory has some of
+ 
+
+ align:start position:0%
+Route Wily Wonka's factory has some of
+everything it is after all Willy Wonka's
+
+ align:start position:0%
+everything it is after all Willy Wonka's
+ 
+
+ align:start position:0%
+everything it is after all Willy Wonka's
+factory highlight the race of enslaved
+
+ align:start position:0%
+factory highlight the race of enslaved
+ 
+
+ align:start position:0%
+factory highlight the race of enslaved
+minions the Oompa loomas and Dr Evil's
+
+ align:start position:0%
+minions the Oompa loomas and Dr Evil's
+ 
+
+ align:start position:0%
+minions the Oompa loomas and Dr Evil's
+moon base is only missing that's no moon
+
+ align:start position:0%
+moon base is only missing that's no moon
+ 
+
+ align:start position:0%
+moon base is only missing that's no moon
+because it is a moon because it's a moon
+
+ align:start position:0%
+because it is a moon because it's a moon
+ 
+
+ align:start position:0%
+because it is a moon because it's a moon
+base
+
+ align:start position:0%
+base
+ 
+
+ align:start position:0%
+base
+so if you got all the references that
+
+ align:start position:0%
+so if you got all the references that
+ 
+
+ align:start position:0%
+so if you got all the references that
+were used to make those fortresses I'm
+
+ align:start position:0%
+were used to make those fortresses I'm
+ 
+
+ align:start position:0%
+were used to make those fortresses I'm
+sorry there's nothing I can do for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+OHS now Mark being a clever evil
+
+ align:start position:0%
+OHS now Mark being a clever evil
+ 
+
+ align:start position:0%
+OHS now Mark being a clever evil
+Overlord realizes that he can grp
+
+ align:start position:0%
+Overlord realizes that he can grp
+ 
+
+ align:start position:0%
+Overlord realizes that he can grp
+produce a graph of the exploration
+
+ align:start position:0%
+produce a graph of the exploration
+ 
+
+ align:start position:0%
+produce a graph of the exploration
+choices with edges joining strongholds
+
+ align:start position:0%
+choices with edges joining strongholds
+ 
+
+ align:start position:0%
+choices with edges joining strongholds
+that differ by just one feature so
+
+ align:start position:0%
+that differ by just one feature so
+ 
+
+ align:start position:0%
+that differ by just one feature so
+although there's a graph here as Patrick
+
+ align:start position:0%
+although there's a graph here as Patrick
+ 
+
+ align:start position:0%
+although there's a graph here as Patrick
+often says and you'll get to hear again
+
+ align:start position:0%
+often says and you'll get to hear again
+ 
+
+ align:start position:0%
+often says and you'll get to hear again
+right now search is about choice not
+
+ align:start position:0%
+right now search is about choice not
+ 
+
+ align:start position:0%
+right now search is about choice not
+just about Maps so we're not moving
+
+ align:start position:0%
+just about Maps so we're not moving
+ 
+
+ align:start position:0%
+just about Maps so we're not moving
+around anywhere in the real world but we
+
+ align:start position:0%
+around anywhere in the real world but we
+ 
+
+ align:start position:0%
+around anywhere in the real world but we
+certainly are going to move around this
+
+ align:start position:0%
+certainly are going to move around this
+ 
+
+ align:start position:0%
+certainly are going to move around this
+graph to pick between these many
+
+ align:start position:0%
+graph to pick between these many
+ 
+
+ align:start position:0%
+graph to pick between these many
+stronghold choices how can we decide
+
+ align:start position:0%
+stronghold choices how can we decide
+ 
+
+ align:start position:0%
+stronghold choices how can we decide
+where to travel while we're about to
+
+ align:start position:0%
+where to travel while we're about to
+ 
+
+ align:start position:0%
+where to travel while we're about to
+find out so we've got this lovely graph
+
+ align:start position:0%
+find out so we've got this lovely graph
+ 
+
+ align:start position:0%
+find out so we've got this lovely graph
+right here and now we're going to get to
+
+ align:start position:0%
+right here and now we're going to get to
+ 
+
+ align:start position:0%
+right here and now we're going to get to
+do depth ver search on the
+
+ align:start position:0%
+do depth ver search on the
+ 
+
+ align:start position:0%
+do depth ver search on the
+graph now there's a lot of ways to do
+
+ align:start position:0%
+graph now there's a lot of ways to do
+ 
+
+ align:start position:0%
+graph now there's a lot of ways to do
+search and you've seen Patrick do it you
+
+ align:start position:0%
+search and you've seen Patrick do it you
+ 
+
+ align:start position:0%
+search and you've seen Patrick do it you
+may have seen some people do it in
+
+ align:start position:0%
+may have seen some people do it in
+ 
+
+ align:start position:0%
+may have seen some people do it in
+recitation and I'm going to offer you
+
+ align:start position:0%
+recitation and I'm going to offer you
+ 
+
+ align:start position:0%
+recitation and I'm going to offer you
+guys a unique opportunity to see me do
+
+ align:start position:0%
+guys a unique opportunity to see me do
+ 
+
+ align:start position:0%
+guys a unique opportunity to see me do
+search in one of several ways or
+
+ align:start position:0%
+search in one of several ways or
+ 
+
+ align:start position:0%
+search in one of several ways or
+possibly more I have the tried and true
+
+ align:start position:0%
+possibly more I have the tried and true
+ 
+
+ align:start position:0%
+possibly more I have the tried and true
+method you have the cue or agenda or
+
+ align:start position:0%
+method you have the cue or agenda or
+ 
+
+ align:start position:0%
+method you have the cue or agenda or
+whatever you want to call it you keep
+
+ align:start position:0%
+whatever you want to call it you keep
+ 
+
+ align:start position:0%
+whatever you want to call it you keep
+track of it at every level you make damn
+
+ align:start position:0%
+track of it at every level you make damn
+ 
+
+ align:start position:0%
+track of it at every level you make damn
+sure that everything you're doing is
+
+ align:start position:0%
+sure that everything you're doing is
+ 
+
+ align:start position:0%
+sure that everything you're doing is
+right it takes a long time and you got
+
+ align:start position:0%
+right it takes a long time and you got
+ 
+
+ align:start position:0%
+right it takes a long time and you got
+the answer right or there's one where
+
+ align:start position:0%
+the answer right or there's one where
+ 
+
+ align:start position:0%
+the answer right or there's one where
+you only work with the gold tree and you
+
+ align:start position:0%
+you only work with the gold tree and you
+ 
+
+ align:start position:0%
+you only work with the gold tree and you
+draw it really fast and you might make a
+
+ align:start position:0%
+draw it really fast and you might make a
+ 
+
+ align:start position:0%
+draw it really fast and you might make a
+mistake but it's going to solve it more
+
+ align:start position:0%
+mistake but it's going to solve it more
+ 
+
+ align:start position:0%
+mistake but it's going to solve it more
+quickly so who would rather see the
+
+ align:start position:0%
+quickly so who would rather see the
+ 
+
+ align:start position:0%
+quickly so who would rather see the
+reliable but slower approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who'd rather see the faster but less
+
+ align:start position:0%
+who'd rather see the faster but less
+ 
+
+ align:start position:0%
+who'd rather see the faster but less
+reliable approach all right mon Carlo
+
+ align:start position:0%
+reliable approach all right mon Carlo
+ 
+
+ align:start position:0%
+reliable approach all right mon Carlo
+people here rather than Las Vegas if you
+
+ align:start position:0%
+people here rather than Las Vegas if you
+ 
+
+ align:start position:0%
+people here rather than Las Vegas if you
+don't know what that is you'll learn it
+
+ align:start position:0%
+don't know what that is you'll learn it
+ 
+
+ align:start position:0%
+don't know what that is you'll learn it
+in algorithm's class all right then
+
+ align:start position:0%
+in algorithm's class all right then
+ 
+
+ align:start position:0%
+in algorithm's class all right then
+there's a third approach that I probably
+
+ align:start position:0%
+there's a third approach that I probably
+ 
+
+ align:start position:0%
+there's a third approach that I probably
+won't show you unless there's
+
+ align:start position:0%
+won't show you unless there's
+ 
+
+ align:start position:0%
+won't show you unless there's
+overwhelming favor for it that is the
+
+ align:start position:0%
+overwhelming favor for it that is the
+ 
+
+ align:start position:0%
+overwhelming favor for it that is the
+approach that is manically fast and will
+
+ align:start position:0%
+approach that is manically fast and will
+ 
+
+ align:start position:0%
+approach that is manically fast and will
+solve depth search in no time at all but
+
+ align:start position:0%
+solve depth search in no time at all but
+ 
+
+ align:start position:0%
+solve depth search in no time at all but
+is very likely to make
+
+ align:start position:0%
+is very likely to make
+ 
+
+ align:start position:0%
+is very likely to make
+mistakes uh that is the approach that I
+
+ align:start position:0%
+mistakes uh that is the approach that I
+ 
+
+ align:start position:0%
+mistakes uh that is the approach that I
+use when solving depth for search and
+
+ align:start position:0%
+use when solving depth for search and
+ 
+
+ align:start position:0%
+use when solving depth for search and
+I've used it enough times that I don't
+
+ align:start position:0%
+I've used it enough times that I don't
+ 
+
+ align:start position:0%
+I've used it enough times that I don't
+make mistakes that often but even I
+
+ align:start position:0%
+make mistakes that often but even I
+ 
+
+ align:start position:0%
+make mistakes that often but even I
+still do so does anyone want to see that
+
+ align:start position:0%
+still do so does anyone want to see that
+ 
+
+ align:start position:0%
+still do so does anyone want to see that
+one okay not that many people well it
+
+ align:start position:0%
+one okay not that many people well it
+ 
+
+ align:start position:0%
+one okay not that many people well it
+doesn't take much time but I'm just
+
+ align:start position:0%
+doesn't take much time but I'm just
+ 
+
+ align:start position:0%
+doesn't take much time but I'm just
+afraid if I show it to you that you'll
+
+ align:start position:0%
+afraid if I show it to you that you'll
+ 
+
+ align:start position:0%
+afraid if I show it to you that you'll
+be like oh that's the only way to do it
+
+ align:start position:0%
+be like oh that's the only way to do it
+ 
+
+ align:start position:0%
+be like oh that's the only way to do it
+so we'll say that for later if we have
+
+ align:start position:0%
+so we'll say that for later if we have
+ 
+
+ align:start position:0%
+so we'll say that for later if we have
+more time it essentially if people are
+
+ align:start position:0%
+more time it essentially if people are
+ 
+
+ align:start position:0%
+more time it essentially if people are
+interested involves just using your
+
+ align:start position:0%
+interested involves just using your
+ 
+
+ align:start position:0%
+interested involves just using your
+chalk or finger to trace through the
+
+ align:start position:0%
+chalk or finger to trace through the
+ 
+
+ align:start position:0%
+chalk or finger to trace through the
+tree really fast and figure out what
+
+ align:start position:0%
+tree really fast and figure out what
+ 
+
+ align:start position:0%
+tree really fast and figure out what
+it's doing
+
+ align:start position:0%
+it's doing
+ 
+
+ align:start position:0%
+it's doing
+by drawing little tiny lines it it is
+
+ align:start position:0%
+by drawing little tiny lines it it is
+ 
+
+ align:start position:0%
+by drawing little tiny lines it it is
+very fast but it's not very accurate and
+
+ align:start position:0%
+very fast but it's not very accurate and
+ 
+
+ align:start position:0%
+very fast but it's not very accurate and
+and you have shown basically no work if
+
+ align:start position:0%
+and you have shown basically no work if
+ 
+
+ align:start position:0%
+and you have shown basically no work if
+you get it wrong so shame on you
+
+ align:start position:0%
+you get it wrong so shame on you
+ 
+
+ align:start position:0%
+you get it wrong so shame on you
+okay well let's do the somewhat faster
+
+ align:start position:0%
+okay well let's do the somewhat faster
+ 
+
+ align:start position:0%
+okay well let's do the somewhat faster
+way we don't draw out the entire agenda
+
+ align:start position:0%
+way we don't draw out the entire agenda
+ 
+
+ align:start position:0%
+way we don't draw out the entire agenda
+and then people who were the almost
+
+ align:start position:0%
+and then people who were the almost
+ 
+
+ align:start position:0%
+and then people who were the almost
+nobody who raised their hand for that
+
+ align:start position:0%
+nobody who raised their hand for that
+ 
+
+ align:start position:0%
+nobody who raised their hand for that
+way can um check it out in tutorial um
+
+ align:start position:0%
+way can um check it out in tutorial um
+ 
+
+ align:start position:0%
+way can um check it out in tutorial um
+the way that you do it using the agenda
+
+ align:start position:0%
+the way that you do it using the agenda
+ 
+
+ align:start position:0%
+the way that you do it using the agenda
+so let's do it using the goal tree it's
+
+ align:start position:0%
+so let's do it using the goal tree it's
+ 
+
+ align:start position:0%
+so let's do it using the goal tree it's
+so it's a bit faster that way so we're
+
+ align:start position:0%
+so it's a bit faster that way so we're
+ 
+
+ align:start position:0%
+so it's a bit faster that way so we're
+going to search starting at s the start
+
+ align:start position:0%
+going to search starting at s the start
+ 
+
+ align:start position:0%
+going to search starting at s the start
+node and going to G the goal node that's
+
+ align:start position:0%
+node and going to G the goal node that's
+ 
+
+ align:start position:0%
+node and going to G the goal node that's
+a standard notation but make sure that
+
+ align:start position:0%
+a standard notation but make sure that
+ 
+
+ align:start position:0%
+a standard notation but make sure that
+when you're taking the test you check to
+
+ align:start position:0%
+when you're taking the test you check to
+ 
+
+ align:start position:0%
+when you're taking the test you check to
+make sure where the start Noe is where
+
+ align:start position:0%
+make sure where the start Noe is where
+ 
+
+ align:start position:0%
+make sure where the start Noe is where
+the goal Noe is it's pretty pretty much
+
+ align:start position:0%
+the goal Noe is it's pretty pretty much
+ 
+
+ align:start position:0%
+the goal Noe is it's pretty pretty much
+a a an move to have a g node
+
+ align:start position:0%
+a a an move to have a g node
+ 
+
+ align:start position:0%
+a a an move to have a g node
+that isn't the goal node but sometimes
+
+ align:start position:0%
+that isn't the goal node but sometimes
+ 
+
+ align:start position:0%
+that isn't the goal node but sometimes
+there won't be an S node that's a pretty
+
+ align:start position:0%
+there won't be an S node that's a pretty
+ 
+
+ align:start position:0%
+there won't be an S node that's a pretty
+good clue that something else is the
+
+ align:start position:0%
+good clue that something else is the
+ 
+
+ align:start position:0%
+good clue that something else is the
+start node now there's a few little
+
+ align:start position:0%
+start node now there's a few little
+ 
+
+ align:start position:0%
+start node now there's a few little
+white star ideas that we have or silver
+
+ align:start position:0%
+white star ideas that we have or silver
+ 
+
+ align:start position:0%
+white star ideas that we have or silver
+star ideas for search one is
+
+ align:start position:0%
+star ideas for search one is
+ 
+
+ align:start position:0%
+star ideas for search one is
+lexicography what is lexicography who
+
+ align:start position:0%
+lexicography what is lexicography who
+ 
+
+ align:start position:0%
+lexicography what is lexicography who
+cares well the most famous lexicographer
+
+ align:start position:0%
+cares well the most famous lexicographer
+ 
+
+ align:start position:0%
+cares well the most famous lexicographer
+I know of is Samuel Johnson who wrote a
+
+ align:start position:0%
+I know of is Samuel Johnson who wrote a
+ 
+
+ align:start position:0%
+I know of is Samuel Johnson who wrote a
+really famous dictionary and the only
+
+ align:start position:0%
+really famous dictionary and the only
+ 
+
+ align:start position:0%
+really famous dictionary and the only
+reason we care about it in this class is
+
+ align:start position:0%
+reason we care about it in this class is
+ 
+
+ align:start position:0%
+reason we care about it in this class is
+because you'll always see the
+
+ align:start position:0%
+because you'll always see the
+ 
+
+ align:start position:0%
+because you'll always see the
+instructions break ties and
+
+ align:start position:0%
+instructions break ties and
+ 
+
+ align:start position:0%
+instructions break ties and
+lexicographic Order and then you might
+
+ align:start position:0%
+lexicographic Order and then you might
+ 
+
+ align:start position:0%
+lexicographic Order and then you might
+be like wow that's really rather a wordy
+
+ align:start position:0%
+be like wow that's really rather a wordy
+ 
+
+ align:start position:0%
+be like wow that's really rather a wordy
+word uh or a cesop pelian word or
+
+ align:start position:0%
+word uh or a cesop pelian word or
+ 
+
+ align:start position:0%
+word uh or a cesop pelian word or
+whatever really long word you want to
+
+ align:start position:0%
+whatever really long word you want to
+ 
+
+ align:start position:0%
+whatever really long word you want to
+use to describe the word lexicographic
+
+ align:start position:0%
+use to describe the word lexicographic
+ 
+
+ align:start position:0%
+use to describe the word lexicographic
+what the heck does it mean basically it
+
+ align:start position:0%
+what the heck does it mean basically it
+ 
+
+ align:start position:0%
+what the heck does it mean basically it
+means alphabetical
+
+ align:start position:0%
+means alphabetical
+ 
+
+ align:start position:0%
+means alphabetical
+order like you would do in a
+
+ align:start position:0%
+order like you would do in a
+ 
+
+ align:start position:0%
+order like you would do in a
+dictionary so for instance
+
+ align:start position:0%
+dictionary so for instance
+ 
+
+ align:start position:0%
+dictionary so for instance
+in alphabetical order a comes from
+
+ align:start position:0%
+in alphabetical order a comes from
+ 
+
+ align:start position:0%
+in alphabetical order a comes from
+before B so you would go to a before B
+
+ align:start position:0%
+before B so you would go to a before B
+ 
+
+ align:start position:0%
+before B so you would go to a before B
+now even beyond that point there's
+
+ align:start position:0%
+now even beyond that point there's
+ 
+
+ align:start position:0%
+now even beyond that point there's
+several ways to do lexicographic
+
+ align:start position:0%
+several ways to do lexicographic
+ 
+
+ align:start position:0%
+several ways to do lexicographic
+tiebreak and it's not always consistent
+
+ align:start position:0%
+tiebreak and it's not always consistent
+ 
+
+ align:start position:0%
+tiebreak and it's not always consistent
+between algorithms how you would do
+
+ align:start position:0%
+between algorithms how you would do
+ 
+
+ align:start position:0%
+between algorithms how you would do
+lexic graphic tiebreak in the most
+
+ align:start position:0%
+lexic graphic tiebreak in the most
+ 
+
+ align:start position:0%
+lexic graphic tiebreak in the most
+recent time that Patrick was kind of
+
+ align:start position:0%
+recent time that Patrick was kind of
+ 
+
+ align:start position:0%
+recent time that Patrick was kind of
+randomly talking to the staff he made it
+
+ align:start position:0%
+randomly talking to the staff he made it
+ 
+
+ align:start position:0%
+randomly talking to the staff he made it
+clear that the way he would like us to
+
+ align:start position:0%
+clear that the way he would like us to
+ 
+
+ align:start position:0%
+clear that the way he would like us to
+do it and therefore the way we' like you
+
+ align:start position:0%
+do it and therefore the way we' like you
+ 
+
+ align:start position:0%
+do it and therefore the way we' like you
+to do it is to tiebreak based on the
+
+ align:start position:0%
+to do it is to tiebreak based on the
+ 
+
+ align:start position:0%
+to do it is to tiebreak based on the
+very latest nodes at the end so you
+
+ align:start position:0%
+very latest nodes at the end so you
+ 
+
+ align:start position:0%
+very latest nodes at the end so you
+might say that's not really lexical
+
+ align:start position:0%
+might say that's not really lexical
+ 
+
+ align:start position:0%
+might say that's not really lexical
+graphic wouldn't sa come before s GA in
+
+ align:start position:0%
+graphic wouldn't sa come before s GA in
+ 
+
+ align:start position:0%
+graphic wouldn't sa come before s GA in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+dictionary
+
+ align:start position:0%
+dictionary
+ 
+
+ align:start position:0%
+dictionary
+um and my answer my my answer to you is
+
+ align:start position:0%
+um and my answer my my answer to you is
+ 
+
+ align:start position:0%
+um and my answer my my answer to you is
+yes it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would yes yes it definitely
+
+ align:start position:0%
+would yes yes it definitely
+ 
+
+ align:start position:0%
+would yes yes it definitely
+would however
+
+ align:start position:0%
+would however
+ 
+
+ align:start position:0%
+would however
+um that is um that that is apparently
+
+ align:start position:0%
+um that is um that that is apparently
+ 
+
+ align:start position:0%
+um that is um that that is apparently
+what we're doing according to the last
+
+ align:start position:0%
+what we're doing according to the last
+ 
+
+ align:start position:0%
+what we're doing according to the last
+thing that Patrick said and we will keep
+
+ align:start position:0%
+thing that Patrick said and we will keep
+ 
+
+ align:start position:0%
+thing that Patrick said and we will keep
+you updated if um he decides to go back
+
+ align:start position:0%
+you updated if um he decides to go back
+ 
+
+ align:start position:0%
+you updated if um he decides to go back
+to dictionary order
+
+ align:start position:0%
+to dictionary order
+ 
+
+ align:start position:0%
+to dictionary order
+so um that's lexicographic lexicography
+
+ align:start position:0%
+so um that's lexicographic lexicography
+ 
+
+ align:start position:0%
+so um that's lexicographic lexicography
+you might be wondering what the picture
+
+ align:start position:0%
+you might be wondering what the picture
+ 
+
+ align:start position:0%
+you might be wondering what the picture
+here is well this is our friend the Ora
+
+ align:start position:0%
+here is well this is our friend the Ora
+ 
+
+ align:start position:0%
+here is well this is our friend the Ora
+Boris long has it been a symbol in
+
+ align:start position:0%
+Boris long has it been a symbol in
+ 
+
+ align:start position:0%
+Boris long has it been a symbol in
+alchemy of infinity eternity or maybe
+
+ align:start position:0%
+alchemy of infinity eternity or maybe
+ 
+
+ align:start position:0%
+alchemy of infinity eternity or maybe
+you know a um sort of infinite energy
+
+ align:start position:0%
+you know a um sort of infinite energy
+ 
+
+ align:start position:0%
+you know a um sort of infinite energy
+engine turning iron into gold but today
+
+ align:start position:0%
+engine turning iron into gold but today
+ 
+
+ align:start position:0%
+engine turning iron into gold but today
+unfortunately the orar is endangered
+
+ align:start position:0%
+unfortunately the orar is endangered
+ 
+
+ align:start position:0%
+unfortunately the orar is endangered
+species because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no biting your own tail in
+
+ align:start position:0%
+no biting your own tail in
+ 
+
+ align:start position:0%
+no biting your own tail in
+6034 a lot of people mess up from this
+
+ align:start position:0%
+6034 a lot of people mess up from this
+ 
+
+ align:start position:0%
+6034 a lot of people mess up from this
+it's an honest mistake I mean we've
+
+ align:start position:0%
+it's an honest mistake I mean we've
+ 
+
+ align:start position:0%
+it's an honest mistake I mean we've
+gotten some emails from staff members
+
+ align:start position:0%
+gotten some emails from staff members
+ 
+
+ align:start position:0%
+gotten some emails from staff members
+who um couldn't solve one of the
+
+ align:start position:0%
+who um couldn't solve one of the
+ 
+
+ align:start position:0%
+who um couldn't solve one of the
+problems because they forgot about this
+
+ align:start position:0%
+problems because they forgot about this
+ 
+
+ align:start position:0%
+problems because they forgot about this
+so it's okay if you forget but try your
+
+ align:start position:0%
+so it's okay if you forget but try your
+ 
+
+ align:start position:0%
+so it's okay if you forget but try your
+best to remember nobody in your own tell
+
+ align:start position:0%
+best to remember nobody in your own tell
+ 
+
+ align:start position:0%
+best to remember nobody in your own tell
+is the only smart thing our system does
+
+ align:start position:0%
+is the only smart thing our system does
+ 
+
+ align:start position:0%
+is the only smart thing our system does
+you'll remember last week when we were
+
+ align:start position:0%
+you'll remember last week when we were
+ 
+
+ align:start position:0%
+you'll remember last week when we were
+talking about rules and we were saying
+
+ align:start position:0%
+talking about rules and we were saying
+ 
+
+ align:start position:0%
+talking about rules and we were saying
+that the rule system is not a smart
+
+ align:start position:0%
+that the rule system is not a smart
+ 
+
+ align:start position:0%
+that the rule system is not a smart
+creature it doesn't know that there's
+
+ align:start position:0%
+creature it doesn't know that there's
+ 
+
+ align:start position:0%
+creature it doesn't know that there's
+diff there's difference between or sorry
+
+ align:start position:0%
+diff there's difference between or sorry
+ 
+
+ align:start position:0%
+diff there's difference between or sorry
+it doesn't know that not poly is dead
+
+ align:start position:0%
+it doesn't know that not poly is dead
+ 
+
+ align:start position:0%
+it doesn't know that not poly is dead
+should be the same as poly is not dead
+
+ align:start position:0%
+should be the same as poly is not dead
+ 
+
+ align:start position:0%
+should be the same as poly is not dead
+or something like that it's too dumb to
+
+ align:start position:0%
+or something like that it's too dumb to
+ 
+
+ align:start position:0%
+or something like that it's too dumb to
+figure that out well this system is also
+
+ align:start position:0%
+figure that out well this system is also
+ 
+
+ align:start position:0%
+figure that out well this system is also
+dumb but one thing it knows is that
+
+ align:start position:0%
+dumb but one thing it knows is that
+ 
+
+ align:start position:0%
+dumb but one thing it knows is that
+Patrick really hates if the same node
+
+ align:start position:0%
+Patrick really hates if the same node
+ 
+
+ align:start position:0%
+Patrick really hates if the same node
+appears twice within the same path and
+
+ align:start position:0%
+appears twice within the same path and
+ 
+
+ align:start position:0%
+appears twice within the same path and
+it will destroy that immediately before
+
+ align:start position:0%
+it will destroy that immediately before
+ 
+
+ align:start position:0%
+it will destroy that immediately before
+even adding it to the que it's gone it's
+
+ align:start position:0%
+even adding it to the que it's gone it's
+ 
+
+ align:start position:0%
+even adding it to the que it's gone it's
+not considered it's out of there so very
+
+ align:start position:0%
+not considered it's out of there so very
+ 
+
+ align:start position:0%
+not considered it's out of there so very
+important sad or Bor no biting your own
+
+ align:start position:0%
+important sad or Bor no biting your own
+ 
+
+ align:start position:0%
+important sad or Bor no biting your own
+tail all right so now that I've gotten
+
+ align:start position:0%
+tail all right so now that I've gotten
+ 
+
+ align:start position:0%
+tail all right so now that I've gotten
+through that let's actually solve the
+
+ align:start position:0%
+through that let's actually solve the
+ 
+
+ align:start position:0%
+through that let's actually solve the
+problem with some depth first search how
+
+ align:start position:0%
+problem with some depth first search how
+ 
+
+ align:start position:0%
+problem with some depth first search how
+will we do that while we're not going to
+
+ align:start position:0%
+will we do that while we're not going to
+ 
+
+ align:start position:0%
+will we do that while we're not going to
+use the Q at popular demand we're going
+
+ align:start position:0%
+use the Q at popular demand we're going
+ 
+
+ align:start position:0%
+use the Q at popular demand we're going
+to use a gold tree so we'll start at
+
+ align:start position:0%
+to use a gold tree so we'll start at
+ 
+
+ align:start position:0%
+to use a gold tree so we'll start at
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+s what do our choices at node
+
+ align:start position:0%
+s what do our choices at node
+ 
+
+ align:start position:0%
+s what do our choices at node
+s well I'm going to force you guys to
+
+ align:start position:0%
+s well I'm going to force you guys to
+ 
+
+ align:start position:0%
+s well I'm going to force you guys to
+help so it won't be quite as fast but it
+
+ align:start position:0%
+help so it won't be quite as fast but it
+ 
+
+ align:start position:0%
+help so it won't be quite as fast but it
+will be fun so what are choice at node
+
+ align:start position:0%
+will be fun so what are choice at node
+ 
+
+ align:start position:0%
+will be fun so what are choice at node
+s you not behind you me yes um A or B
+
+ align:start position:0%
+s you not behind you me yes um A or B
+ 
+
+ align:start position:0%
+s you not behind you me yes um A or B
+not quite and this is something I like
+
+ align:start position:0%
+not quite and this is something I like
+ 
+
+ align:start position:0%
+not quite and this is something I like
+about this problem you got most of them
+
+ align:start position:0%
+about this problem you got most of them
+ 
+
+ align:start position:0%
+about this problem you got most of them
+do you see that there might be another
+
+ align:start position:0%
+do you see that there might be another
+ 
+
+ align:start position:0%
+do you see that there might be another
+Choice everyone yes see this is a big
+
+ align:start position:0%
+Choice everyone yes see this is a big
+ 
+
+ align:start position:0%
+Choice everyone yes see this is a big
+problem that has happened on a few
+
+ align:start position:0%
+problem that has happened on a few
+ 
+
+ align:start position:0%
+problem that has happened on a few
+different quiz problems where there's a
+
+ align:start position:0%
+different quiz problems where there's a
+ 
+
+ align:start position:0%
+different quiz problems where there's a
+tree that you could where there's a sort
+
+ align:start position:0%
+tree that you could where there's a sort
+ 
+
+ align:start position:0%
+tree that you could where there's a sort
+of a grid that looks like a tree or
+
+ align:start position:0%
+of a grid that looks like a tree or
+ 
+
+ align:start position:0%
+of a grid that looks like a tree or
+graph that looks like a tree where
+
+ align:start position:0%
+graph that looks like a tree where
+ 
+
+ align:start position:0%
+graph that looks like a tree where
+people um aren't as willing to go up as
+
+ align:start position:0%
+people um aren't as willing to go up as
+ 
+
+ align:start position:0%
+people um aren't as willing to go up as
+they are to go down you can see it on
+
+ align:start position:0%
+they are to go down you can see it on
+ 
+
+ align:start position:0%
+they are to go down you can see it on
+some of the other past P problems too
+
+ align:start position:0%
+some of the other past P problems too
+ 
+
+ align:start position:0%
+some of the other past P problems too
+make sure that you check the
+
+ align:start position:0%
+make sure that you check the
+ 
+
+ align:start position:0%
+make sure that you check the
+connectivity and also note that unless
+
+ align:start position:0%
+connectivity and also note that unless
+ 
+
+ align:start position:0%
+connectivity and also note that unless
+otherwise specified and I don't think
+
+ align:start position:0%
+otherwise specified and I don't think
+ 
+
+ align:start position:0%
+otherwise specified and I don't think
+we've really done this much
+
+ align:start position:0%
+we've really done this much
+ 
+
+ align:start position:0%
+we've really done this much
+the little um connecting edges in our
+
+ align:start position:0%
+the little um connecting edges in our
+ 
+
+ align:start position:0%
+the little um connecting edges in our
+graphs are bir directional you'll see a
+
+ align:start position:0%
+graphs are bir directional you'll see a
+ 
+
+ align:start position:0%
+graphs are bir directional you'll see a
+big arrow and probably instructions
+
+ align:start position:0%
+big arrow and probably instructions
+ 
+
+ align:start position:0%
+big arrow and probably instructions
+written at least eight font sizes is
+
+ align:start position:0%
+written at least eight font sizes is
+ 
+
+ align:start position:0%
+written at least eight font sizes is
+higher than all the rest of them and
+
+ align:start position:0%
+higher than all the rest of them and
+ 
+
+ align:start position:0%
+higher than all the rest of them and
+bold if um if we're going to do
+
+ align:start position:0%
+bold if um if we're going to do
+ 
+
+ align:start position:0%
+bold if um if we're going to do
+something different for this quiz it
+
+ align:start position:0%
+something different for this quiz it
+ 
+
+ align:start position:0%
+something different for this quiz it
+happens that they do it sometimes while
+
+ align:start position:0%
+happens that they do it sometimes while
+ 
+
+ align:start position:0%
+happens that they do it sometimes while
+I was just say mega reation we never do
+
+ align:start position:0%
+I was just say mega reation we never do
+ 
+
+ align:start position:0%
+I was just say mega reation we never do
+this and then on the quiz they do it but
+
+ align:start position:0%
+this and then on the quiz they do it but
+ 
+
+ align:start position:0%
+this and then on the quiz they do it but
+it will be in giant letters which also
+
+ align:start position:0%
+it will be in giant letters which also
+ 
+
+ align:start position:0%
+it will be in giant letters which also
+leads me to another SilverStar idea that
+
+ align:start position:0%
+leads me to another SilverStar idea that
+ 
+
+ align:start position:0%
+leads me to another SilverStar idea that
+I forgot to tell you guys last week so I
+
+ align:start position:0%
+I forgot to tell you guys last week so I
+ 
+
+ align:start position:0%
+I forgot to tell you guys last week so I
+hope people didn't ditch out on me like
+
+ align:start position:0%
+hope people didn't ditch out on me like
+ 
+
+ align:start position:0%
+hope people didn't ditch out on me like
+oh Mark's boring we won't come next week
+
+ align:start position:0%
+oh Mark's boring we won't come next week
+ 
+
+ align:start position:0%
+oh Mark's boring we won't come next week
+and then missed this one because it just
+
+ align:start position:0%
+and then missed this one because it just
+ 
+
+ align:start position:0%
+and then missed this one because it just
+came to my mind that is read the
+
+ align:start position:0%
+came to my mind that is read the
+ 
+
+ align:start position:0%
+came to my mind that is read the
+instructions is a very important thing
+
+ align:start position:0%
+instructions is a very important thing
+ 
+
+ align:start position:0%
+instructions is a very important thing
+for the quizzes and uh Patrick will in a
+
+ align:start position:0%
+for the quizzes and uh Patrick will in a
+ 
+
+ align:start position:0%
+for the quizzes and uh Patrick will in a
+later lecture tell you guys ask why five
+
+ align:start position:0%
+later lecture tell you guys ask why five
+ 
+
+ align:start position:0%
+later lecture tell you guys ask why five
+times and he'll explain why that's a
+
+ align:start position:0%
+times and he'll explain why that's a
+ 
+
+ align:start position:0%
+times and he'll explain why that's a
+gold star idea my parallel to this is
+
+ align:start position:0%
+gold star idea my parallel to this is
+ 
+
+ align:start position:0%
+gold star idea my parallel to this is
+read the instructions five times maybe
+
+ align:start position:0%
+read the instructions five times maybe
+ 
+
+ align:start position:0%
+read the instructions five times maybe
+not five maybe three or four but at
+
+ align:start position:0%
+not five maybe three or four but at
+ 
+
+ align:start position:0%
+not five maybe three or four but at
+least three read the instructions read
+
+ align:start position:0%
+least three read the instructions read
+ 
+
+ align:start position:0%
+least three read the instructions read
+them again then read them a third time
+
+ align:start position:0%
+them again then read them a third time
+ 
+
+ align:start position:0%
+them again then read them a third time
+only paying attention to whatever is
+
+ align:start position:0%
+only paying attention to whatever is
+ 
+
+ align:start position:0%
+only paying attention to whatever is
+bold and eight sizes larger than all the
+
+ align:start position:0%
+bold and eight sizes larger than all the
+ 
+
+ align:start position:0%
+bold and eight sizes larger than all the
+other ones because there's going to be
+
+ align:start position:0%
+other ones because there's going to be
+ 
+
+ align:start position:0%
+other ones because there's going to be
+something there that's that size and
+
+ align:start position:0%
+something there that's that size and
+ 
+
+ align:start position:0%
+something there that's that size and
+it's going to be the one that thing that
+
+ align:start position:0%
+it's going to be the one that thing that
+ 
+
+ align:start position:0%
+it's going to be the one that thing that
+everyone misses so make sure you're not
+
+ align:start position:0%
+everyone misses so make sure you're not
+ 
+
+ align:start position:0%
+everyone misses so make sure you're not
+everyone and you read the instructions a
+
+ align:start position:0%
+everyone and you read the instructions a
+ 
+
+ align:start position:0%
+everyone and you read the instructions a
+lot of times but anyway so yeah we've
+
+ align:start position:0%
+lot of times but anyway so yeah we've
+ 
+
+ align:start position:0%
+lot of times but anyway so yeah we've
+got it right s goes to a b and
+
+ align:start position:0%
+got it right s goes to a b and
+ 
+
+ align:start position:0%
+got it right s goes to a b and
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+okay we're looking at a B and C as
+
+ align:start position:0%
+okay we're looking at a B and C as
+ 
+
+ align:start position:0%
+okay we're looking at a B and C as
+possibilities everyone let help we make
+
+ align:start position:0%
+possibilities everyone let help we make
+ 
+
+ align:start position:0%
+possibilities everyone let help we make
+the Le graphic tie bre where do we go a
+
+ align:start position:0%
+the Le graphic tie bre where do we go a
+ 
+
+ align:start position:0%
+the Le graphic tie bre where do we go a
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+right all right actually you know what
+
+ align:start position:0%
+right all right actually you know what
+ 
+
+ align:start position:0%
+right all right actually you know what
+I'll call on you guys for I'll call you
+
+ align:start position:0%
+I'll call on you guys for I'll call you
+ 
+
+ align:start position:0%
+I'll call on you guys for I'll call you
+guys for other ones but depth for
+
+ align:start position:0%
+guys for other ones but depth for
+ 
+
+ align:start position:0%
+guys for other ones but depth for
+service is pretty simple we can have
+
+ align:start position:0%
+service is pretty simple we can have
+ 
+
+ align:start position:0%
+service is pretty simple we can have
+everyone do it together a everyone a
+
+ align:start position:0%
+everyone do it together a everyone a
+ 
+
+ align:start position:0%
+everyone do it together a everyone a
+only leads to that's right why doesn't
+
+ align:start position:0%
+only leads to that's right why doesn't
+ 
+
+ align:start position:0%
+only leads to that's right why doesn't
+lead to S as
+
+ align:start position:0%
+lead to S as
+ 
+
+ align:start position:0%
+lead to S as
+well no biting your own tail everyone's
+
+ align:start position:0%
+well no biting your own tail everyone's
+ 
+
+ align:start position:0%
+well no biting your own tail everyone's
+right good job everyone all right s
+
+ align:start position:0%
+right good job everyone all right s
+ 
+
+ align:start position:0%
+right good job everyone all right s
+leads to a s leads to these three you go
+
+ align:start position:0%
+leads to a s leads to these three you go
+ 
+
+ align:start position:0%
+leads to a s leads to these three you go
+to a go to D oh dead
+
+ align:start position:0%
+to a go to D oh dead
+ 
+
+ align:start position:0%
+to a go to D oh dead
+and backtrack okay when we backtrack we
+
+ align:start position:0%
+and backtrack okay when we backtrack we
+ 
+
+ align:start position:0%
+and backtrack okay when we backtrack we
+had backtrack up to a there's no other
+
+ align:start position:0%
+had backtrack up to a there's no other
+ 
+
+ align:start position:0%
+had backtrack up to a there's no other
+children we backtrack up to S where we
+
+ align:start position:0%
+children we backtrack up to S where we
+ 
+
+ align:start position:0%
+children we backtrack up to S where we
+go now B it's the next one
+
+ align:start position:0%
+go now B it's the next one
+ 
+
+ align:start position:0%
+go now B it's the next one
+alphabetically all right B can't go to S
+
+ align:start position:0%
+alphabetically all right B can't go to S
+ 
+
+ align:start position:0%
+alphabetically all right B can't go to S
+so it only goes to yes one more at H we
+
+ align:start position:0%
+so it only goes to yes one more at H we
+ 
+
+ align:start position:0%
+so it only goes to yes one more at H we
+can go
+
+ align:start position:0%
+can go
+ 
+
+ align:start position:0%
+can go
+to f or i that's right you guys get it
+
+ align:start position:0%
+to f or i that's right you guys get it
+ 
+
+ align:start position:0%
+to f or i that's right you guys get it
+this dep for search is easy all right so
+
+ align:start position:0%
+this dep for search is easy all right so
+ 
+
+ align:start position:0%
+this dep for search is easy all right so
+but we
+
+ align:start position:0%
+but we
+ 
+
+ align:start position:0%
+but we
+choose F that's right when we F we can
+
+ align:start position:0%
+choose F that's right when we F we can
+ 
+
+ align:start position:0%
+choose F that's right when we F we can
+go to
+
+ align:start position:0%
+go to
+ 
+
+ align:start position:0%
+go to
+to e and J that's right we'll choose E
+
+ align:start position:0%
+to e and J that's right we'll choose E
+ 
+
+ align:start position:0%
+to e and J that's right we'll choose E
+when we're at e we can go
+
+ align:start position:0%
+when we're at e we can go
+ 
+
+ align:start position:0%
+when we're at e we can go
+to we uh we we can go to C it's not on
+
+ align:start position:0%
+to we uh we we can go to C it's not on
+ 
+
+ align:start position:0%
+to we uh we we can go to C it's not on
+this particular path people are correct
+
+ align:start position:0%
+this particular path people are correct
+ 
+
+ align:start position:0%
+this particular path people are correct
+when they say C when we go to C we can
+
+ align:start position:0%
+when they say C when we go to C we can
+ 
+
+ align:start position:0%
+when they say C when we go to C we can
+go to nowhere we're dead backtrack we
+
+ align:start position:0%
+go to nowhere we're dead backtrack we
+ 
+
+ align:start position:0%
+go to nowhere we're dead backtrack we
+backtrack uh we we can't do anything e
+
+ align:start position:0%
+backtrack uh we we can't do anything e
+ 
+
+ align:start position:0%
+backtrack uh we we can't do anything e
+we go to F now I forgot to tell you guys
+
+ align:start position:0%
+we go to F now I forgot to tell you guys
+ 
+
+ align:start position:0%
+we go to F now I forgot to tell you guys
+but this is an important note someone's
+
+ align:start position:0%
+but this is an important note someone's
+ 
+
+ align:start position:0%
+but this is an important note someone's
+going to get this wrong it's going to be
+
+ align:start position:0%
+going to get this wrong it's going to be
+ 
+
+ align:start position:0%
+going to get this wrong it's going to be
+one of you look around you all through
+
+ align:start position:0%
+one of you look around you all through
+ 
+
+ align:start position:0%
+one of you look around you all through
+the room at least one of you is going to
+
+ align:start position:0%
+the room at least one of you is going to
+ 
+
+ align:start position:0%
+the room at least one of you is going to
+do this so now I'm going to tell you not
+
+ align:start position:0%
+do this so now I'm going to tell you not
+ 
+
+ align:start position:0%
+do this so now I'm going to tell you not
+to do this and then hopefully that will
+
+ align:start position:0%
+to do this and then hopefully that will
+ 
+
+ align:start position:0%
+to do this and then hopefully that will
+still be true but for fewer people when
+
+ align:start position:0%
+still be true but for fewer people when
+ 
+
+ align:start position:0%
+still be true but for fewer people when
+I went to D and then I backtracked and I
+
+ align:start position:0%
+I went to D and then I backtracked and I
+ 
+
+ align:start position:0%
+I went to D and then I backtracked and I
+went to ask how many times did I
+
+ align:start position:0%
+went to ask how many times did I
+ 
+
+ align:start position:0%
+went to ask how many times did I
+backtrack
+
+ align:start position:0%
+backtrack
+ 
+
+ align:start position:0%
+backtrack
+once I backtracked once this would have
+
+ align:start position:0%
+once I backtracked once this would have
+ 
+
+ align:start position:0%
+once I backtracked once this would have
+been more obvious if we were doing the
+
+ align:start position:0%
+been more obvious if we were doing the
+ 
+
+ align:start position:0%
+been more obvious if we were doing the
+really slow boring agenda way with or Q
+
+ align:start position:0%
+really slow boring agenda way with or Q
+ 
+
+ align:start position:0%
+really slow boring agenda way with or Q
+way um because when we got to
+
+ align:start position:0%
+way um because when we got to
+ 
+
+ align:start position:0%
+way um because when we got to
+sad and we expanded it and there was
+
+ align:start position:0%
+sad and we expanded it and there was
+ 
+
+ align:start position:0%
+sad and we expanded it and there was
+nothing left we throw it off the top of
+
+ align:start position:0%
+nothing left we throw it off the top of
+ 
+
+ align:start position:0%
+nothing left we throw it off the top of
+the queue and go to the next thing on
+
+ align:start position:0%
+the queue and go to the next thing on
+ 
+
+ align:start position:0%
+the queue and go to the next thing on
+the Queue and it turns out the next
+
+ align:start position:0%
+the Queue and it turns out the next
+ 
+
+ align:start position:0%
+the Queue and it turns out the next
+thing on the que is SB that step was
+
+ align:start position:0%
+thing on the que is SB that step was
+ 
+
+ align:start position:0%
+thing on the que is SB that step was
+only taken once it since we're using the
+
+ align:start position:0%
+only taken once it since we're using the
+ 
+
+ align:start position:0%
+only taken once it since we're using the
+gold tree which is faster it looked like
+
+ align:start position:0%
+gold tree which is faster it looked like
+ 
+
+ align:start position:0%
+gold tree which is faster it looked like
+we did two but we didn't and if you use
+
+ align:start position:0%
+we did two but we didn't and if you use
+ 
+
+ align:start position:0%
+we did two but we didn't and if you use
+the que you'll see that because it'll go
+
+ align:start position:0%
+the que you'll see that because it'll go
+ 
+
+ align:start position:0%
+the que you'll see that because it'll go
+s and then we expend that sbsc okay we
+
+ align:start position:0%
+s and then we expend that sbsc okay we
+ 
+
+ align:start position:0%
+s and then we expend that sbsc okay we
+spend sa sad sbsc we spend s it's dead
+
+ align:start position:0%
+spend sa sad sbsc we spend s it's dead
+ 
+
+ align:start position:0%
+spend sa sad sbsc we spend s it's dead
+sbsc one back track we're back at spe so
+
+ align:start position:0%
+sbsc one back track we're back at spe so
+ 
+
+ align:start position:0%
+sbsc one back track we're back at spe so
+so far we've done two not four see I
+
+ align:start position:0%
+so far we've done two not four see I
+ 
+
+ align:start position:0%
+so far we've done two not four see I
+mean it's pretty intuitive to say that
+
+ align:start position:0%
+mean it's pretty intuitive to say that
+ 
+
+ align:start position:0%
+mean it's pretty intuitive to say that
+you did two there it turns out you
+
+ align:start position:0%
+you did two there it turns out you
+ 
+
+ align:start position:0%
+you did two there it turns out you
+didn't because of the algorith the
+
+ align:start position:0%
+didn't because of the algorith the
+ 
+
+ align:start position:0%
+didn't because of the algorith the
+algorithm that's backing what lets us do
+
+ align:start position:0%
+algorithm that's backing what lets us do
+ 
+
+ align:start position:0%
+algorithm that's backing what lets us do
+this gold tree search so make uh try to
+
+ align:start position:0%
+this gold tree search so make uh try to
+ 
+
+ align:start position:0%
+this gold tree search so make uh try to
+make sure you're not the one who says
+
+ align:start position:0%
+make sure you're not the one who says
+ 
+
+ align:start position:0%
+make sure you're not the one who says
+two well and we and I on the other hand
+
+ align:start position:0%
+two well and we and I on the other hand
+ 
+
+ align:start position:0%
+two well and we and I on the other hand
+we'll try to make sure that we don't
+
+ align:start position:0%
+we'll try to make sure that we don't
+ 
+
+ align:start position:0%
+we'll try to make sure that we don't
+take off too many points if you do
+
+ align:start position:0%
+take off too many points if you do
+ 
+
+ align:start position:0%
+take off too many points if you do
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how much it
+
+ align:start position:0%
+how much it
+ 
+
+ align:start position:0%
+how much it
+chains any backtracking is just
+
+ align:start position:0%
+chains any backtracking is just
+ 
+
+ align:start position:0%
+chains any backtracking is just
+considered once is always going to be
+
+ align:start position:0%
+considered once is always going to be
+ 
+
+ align:start position:0%
+considered once is always going to be
+considered one
+
+ align:start position:0%
+considered one
+ 
+
+ align:start position:0%
+considered one
+step it's possible to backstrap two
+
+ align:start position:0%
+step it's possible to backstrap two
+ 
+
+ align:start position:0%
+step it's possible to backstrap two
+times in a row like if s if B didn't go
+
+ align:start position:0%
+times in a row like if s if B didn't go
+ 
+
+ align:start position:0%
+times in a row like if s if B didn't go
+to anything instead of going to H then
+
+ align:start position:0%
+to anything instead of going to H then
+ 
+
+ align:start position:0%
+to anything instead of going to H then
+we might backtrack twice before we got
+
+ align:start position:0%
+we might backtrack twice before we got
+ 
+
+ align:start position:0%
+we might backtrack twice before we got
+to SC generally anytime you draw a
+
+ align:start position:0%
+to SC generally anytime you draw a
+ 
+
+ align:start position:0%
+to SC generally anytime you draw a
+swizzle if you're like me and you draw a
+
+ align:start position:0%
+swizzle if you're like me and you draw a
+ 
+
+ align:start position:0%
+swizzle if you're like me and you draw a
+swizzle I suggest the Swizzles they're
+
+ align:start position:0%
+swizzle I suggest the Swizzles they're
+ 
+
+ align:start position:0%
+swizzle I suggest the Swizzles they're
+very nice little things but if anytime
+
+ align:start position:0%
+very nice little things but if anytime
+ 
+
+ align:start position:0%
+very nice little things but if anytime
+you draw a swizzle on your graph you've
+
+ align:start position:0%
+you draw a swizzle on your graph you've
+ 
+
+ align:start position:0%
+you draw a swizzle on your graph you've
+backtracked once you could even write BT
+
+ align:start position:0%
+backtracked once you could even write BT
+ 
+
+ align:start position:0%
+backtracked once you could even write BT
+next to the Swizzle and go back and
+
+ align:start position:0%
+next to the Swizzle and go back and
+ 
+
+ align:start position:0%
+next to the Swizzle and go back and
+count those or even just count the
+
+ align:start position:0%
+count those or even just count the
+ 
+
+ align:start position:0%
+count those or even just count the
+Swizzles at the end you've got it you
+
+ align:start position:0%
+Swizzles at the end you've got it you
+ 
+
+ align:start position:0%
+Swizzles at the end you've got it you
+got the answer because they often ask
+
+ align:start position:0%
+got the answer because they often ask
+ 
+
+ align:start position:0%
+got the answer because they often ask
+how many times have you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+backtracked all right so good questions
+
+ align:start position:0%
+backtracked all right so good questions
+ 
+
+ align:start position:0%
+backtracked all right so good questions
+everyone so anyway we backtrack from C
+
+ align:start position:0%
+everyone so anyway we backtrack from C
+ 
+
+ align:start position:0%
+everyone so anyway we backtrack from C
+nothing e we got back we we at F so we
+
+ align:start position:0%
+nothing e we got back we we at F so we
+ 
+
+ align:start position:0%
+nothing e we got back we we at F so we
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+sbhf we go to J it's the only choice at
+
+ align:start position:0%
+sbhf we go to J it's the only choice at
+ 
+
+ align:start position:0%
+sbhf we go to J it's the only choice at
+J we can only go to and at I we can only
+
+ align:start position:0%
+J we can only go to and at I we can only
+ 
+
+ align:start position:0%
+J we can only go to and at I we can only
+go to and we win it's not an optimal
+
+ align:start position:0%
+go to and we win it's not an optimal
+ 
+
+ align:start position:0%
+go to and we win it's not an optimal
+search so as soon as we see anything
+
+ align:start position:0%
+search so as soon as we see anything
+ 
+
+ align:start position:0%
+search so as soon as we see anything
+with the G on the Q boom
+
+ align:start position:0%
+with the G on the Q boom
+ 
+
+ align:start position:0%
+with the G on the Q boom
+winner all right and we're done we did
+
+ align:start position:0%
+winner all right and we're done we did
+ 
+
+ align:start position:0%
+winner all right and we're done we did
+it that wasn't too bad for those of you
+
+ align:start position:0%
+it that wasn't too bad for those of you
+ 
+
+ align:start position:0%
+it that wasn't too bad for those of you
+who are vaguely interested in seeing how
+
+ align:start position:0%
+who are vaguely interested in seeing how
+ 
+
+ align:start position:0%
+who are vaguely interested in seeing how
+I would do it um the really super fast
+
+ align:start position:0%
+I would do it um the really super fast
+ 
+
+ align:start position:0%
+I would do it um the really super fast
+way it goes something like this all
+
+ align:start position:0%
+way it goes something like this all
+ 
+
+ align:start position:0%
+way it goes something like this all
+right ABC a comes first only D
+
+ align:start position:0%
+right ABC a comes first only D
+ 
+
+ align:start position:0%
+right ABC a comes first only D
+backtrack all right B comes first h f
+
+ align:start position:0%
+backtrack all right B comes first h f
+ 
+
+ align:start position:0%
+backtrack all right B comes first h f
+comes first e c nothing backtrack
+
+ align:start position:0%
+comes first e c nothing backtrack
+ 
+
+ align:start position:0%
+comes first e c nothing backtrack
+uh we came that way j i
+
+ align:start position:0%
+uh we came that way j i
+ 
+
+ align:start position:0%
+uh we came that way j i
+g so that's the really fast way to do
+
+ align:start position:0%
+g so that's the really fast way to do
+ 
+
+ align:start position:0%
+g so that's the really fast way to do
+depth resarch don't do that kids we
+
+ align:start position:0%
+depth resarch don't do that kids we
+ 
+
+ align:start position:0%
+depth resarch don't do that kids we
+don't like uh well maybe you can if you
+
+ align:start position:0%
+don't like uh well maybe you can if you
+ 
+
+ align:start position:0%
+don't like uh well maybe you can if you
+get it right we're not going to take off
+
+ align:start position:0%
+get it right we're not going to take off
+ 
+
+ align:start position:0%
+get it right we're not going to take off
+we're not going to take off points
+
+ align:start position:0%
+we're not going to take off points
+ 
+
+ align:start position:0%
+we're not going to take off points
+usually generally when we say draw the
+
+ align:start position:0%
+usually generally when we say draw the
+ 
+
+ align:start position:0%
+usually generally when we say draw the
+gold tree below it's to assign partial
+
+ align:start position:0%
+gold tree below it's to assign partial
+ 
+
+ align:start position:0%
+gold tree below it's to assign partial
+credit however we are pretty strict
+
+ align:start position:0%
+credit however we are pretty strict
+ 
+
+ align:start position:0%
+credit however we are pretty strict
+about that if anything is wrong except
+
+ align:start position:0%
+about that if anything is wrong except
+ 
+
+ align:start position:0%
+about that if anything is wrong except
+for maybe like okay you write everything
+
+ align:start position:0%
+for maybe like okay you write everything
+ 
+
+ align:start position:0%
+for maybe like okay you write everything
+exactly right and forget G at the end if
+
+ align:start position:0%
+exactly right and forget G at the end if
+ 
+
+ align:start position:0%
+exactly right and forget G at the end if
+anything that's not completely
+
+ align:start position:0%
+anything that's not completely
+ 
+
+ align:start position:0%
+anything that's not completely
+understandable is wrong you will
+
+ align:start position:0%
+understandable is wrong you will
+ 
+
+ align:start position:0%
+understandable is wrong you will
+probably lose all of the points and it
+
+ align:start position:0%
+probably lose all of the points and it
+ 
+
+ align:start position:0%
+probably lose all of the points and it
+will be a lot of points if you don't
+
+ align:start position:0%
+will be a lot of points if you don't
+ 
+
+ align:start position:0%
+will be a lot of points if you don't
+draw the gold tree so may I will
+
+ align:start position:0%
+draw the gold tree so may I will
+ 
+
+ align:start position:0%
+draw the gold tree so may I will
+emphasize drawing the gold tree is a
+
+ align:start position:0%
+emphasize drawing the gold tree is a
+ 
+
+ align:start position:0%
+emphasize drawing the gold tree is a
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+idea all right so now let's do a breath
+
+ align:start position:0%
+idea all right so now let's do a breath
+ 
+
+ align:start position:0%
+idea all right so now let's do a breath
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+search before we do the breath res
+
+ align:start position:0%
+search before we do the breath res
+ 
+
+ align:start position:0%
+search before we do the breath res
+search on this on this tree I will tell
+
+ align:start position:0%
+search on this on this tree I will tell
+ 
+
+ align:start position:0%
+search on this on this tree I will tell
+you guys that there is also a fast way
+
+ align:start position:0%
+you guys that there is also a fast way
+ 
+
+ align:start position:0%
+you guys that there is also a fast way
+to do the breath first search Which is
+
+ align:start position:0%
+to do the breath first search Which is
+ 
+
+ align:start position:0%
+to do the breath first search Which is
+less risky and it really depends on how
+
+ align:start position:0%
+less risky and it really depends on how
+ 
+
+ align:start position:0%
+less risky and it really depends on how
+nice they are about what they ask for in
+
+ align:start position:0%
+nice they are about what they ask for in
+ 
+
+ align:start position:0%
+nice they are about what they ask for in
+this case the breath first search
+
+ align:start position:0%
+this case the breath first search
+ 
+
+ align:start position:0%
+this case the breath first search
+question asks what path does Mark find
+
+ align:start position:0%
+question asks what path does Mark find
+ 
+
+ align:start position:0%
+question asks what path does Mark find
+using breath first search rather than
+
+ align:start position:0%
+using breath first search rather than
+ 
+
+ align:start position:0%
+using breath first search rather than
+saying what nodes does he expand in
+
+ align:start position:0%
+saying what nodes does he expand in
+ 
+
+ align:start position:0%
+saying what nodes does he expand in
+order or anything like that that is
+
+ align:start position:0%
+order or anything like that that is
+ 
+
+ align:start position:0%
+order or anything like that that is
+important if that question is asked you
+
+ align:start position:0%
+important if that question is asked you
+ 
+
+ align:start position:0%
+important if that question is asked you
+there is a trick that will let you solve
+
+ align:start position:0%
+there is a trick that will let you solve
+ 
+
+ align:start position:0%
+there is a trick that will let you solve
+it very very quickly in fact faster than
+
+ align:start position:0%
+it very very quickly in fact faster than
+ 
+
+ align:start position:0%
+it very very quickly in fact faster than
+dep first search you can solve it by
+
+ align:start position:0%
+dep first search you can solve it by
+ 
+
+ align:start position:0%
+dep first search you can solve it by
+inspection at about 30 seconds does
+
+ align:start position:0%
+inspection at about 30 seconds does
+ 
+
+ align:start position:0%
+inspection at about 30 seconds does
+anyone know what the answer is what path
+
+ align:start position:0%
+anyone know what the answer is what path
+ 
+
+ align:start position:0%
+anyone know what the answer is what path
+did you
+
+ align:start position:0%
+did you
+ 
+
+ align:start position:0%
+did you
+find that's correct so the answer is
+
+ align:start position:0%
+find that's correct so the answer is
+ 
+
+ align:start position:0%
+find that's correct so the answer is
+on this graph the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isbh that's the answer you would have
+
+ align:start position:0%
+isbh that's the answer you would have
+ 
+
+ align:start position:0%
+isbh that's the answer you would have
+your five
+
+ align:start position:0%
+your five
+ 
+
+ align:start position:0%
+your five
+points did people see that it doesn't
+
+ align:start position:0%
+points did people see that it doesn't
+ 
+
+ align:start position:0%
+points did people see that it doesn't
+always work so we're going to actually
+
+ align:start position:0%
+always work so we're going to actually
+ 
+
+ align:start position:0%
+always work so we're going to actually
+solve it but does everyone see that
+
+ align:start position:0%
+solve it but does everyone see that
+ 
+
+ align:start position:0%
+solve it but does everyone see that
+sometimes you can get away with not
+
+ align:start position:0%
+sometimes you can get away with not
+ 
+
+ align:start position:0%
+sometimes you can get away with not
+doing it because breath for search is
+
+ align:start position:0%
+doing it because breath for search is
+ 
+
+ align:start position:0%
+doing it because breath for search is
+guaranteed to give you the path as we
+
+ align:start position:0%
+guaranteed to give you the path as we
+ 
+
+ align:start position:0%
+guaranteed to give you the path as we
+heard correctly with the least number of
+
+ align:start position:0%
+heard correctly with the least number of
+ 
+
+ align:start position:0%
+heard correctly with the least number of
+jumps and if there more than one that
+
+ align:start position:0%
+jumps and if there more than one that
+ 
+
+ align:start position:0%
+jumps and if there more than one that
+tie with the least number of jumps you
+
+ align:start position:0%
+tie with the least number of jumps you
+ 
+
+ align:start position:0%
+tie with the least number of jumps you
+can just lexor graphically figure it out
+
+ align:start position:0%
+can just lexor graphically figure it out
+ 
+
+ align:start position:0%
+can just lexor graphically figure it out
+in this case with actual dictionary
+
+ align:start position:0%
+in this case with actual dictionary
+ 
+
+ align:start position:0%
+in this case with actual dictionary
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+but um sbig is the only one Let's do an
+
+ align:start position:0%
+but um sbig is the only one Let's do an
+ 
+
+ align:start position:0%
+but um sbig is the only one Let's do an
+actual breath first search though so we
+
+ align:start position:0%
+actual breath first search though so we
+ 
+
+ align:start position:0%
+actual breath first search though so we
+can feel better about
+
+ align:start position:0%
+can feel better about
+ 
+
+ align:start position:0%
+can feel better about
+ourselves okay
+
+ align:start position:0%
+ourselves okay
+ 
+
+ align:start position:0%
+ourselves okay
+so you've got S and S goes to as we saw
+
+ align:start position:0%
+so you've got S and S goes to as we saw
+ 
+
+ align:start position:0%
+so you've got S and S goes to as we saw
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+ABC maybe that doesn't have to go quite
+
+ align:start position:0%
+ABC maybe that doesn't have to go quite
+ 
+
+ align:start position:0%
+ABC maybe that doesn't have to go quite
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+high all right as we saw before s goes
+
+ align:start position:0%
+high all right as we saw before s goes
+ 
+
+ align:start position:0%
+high all right as we saw before s goes
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+ABC and you already told me that a goes
+
+ align:start position:0%
+ABC and you already told me that a goes
+ 
+
+ align:start position:0%
+ABC and you already told me that a goes
+to D and you told me that b goes to h
+
+ align:start position:0%
+to D and you told me that b goes to h
+ 
+
+ align:start position:0%
+to D and you told me that b goes to h
+but what does C Go
+
+ align:start position:0%
+but what does C Go
+ 
+
+ align:start position:0%
+but what does C Go
+to e that's right as you can see we're
+
+ align:start position:0%
+to e that's right as you can see we're
+ 
+
+ align:start position:0%
+to e that's right as you can see we're
+expanding it level by level left to
+
+ align:start position:0%
+expanding it level by level left to
+ 
+
+ align:start position:0%
+expanding it level by level left to
+right all right so
+
+ align:start position:0%
+right all right so
+ 
+
+ align:start position:0%
+right all right so
+sad where does sad go
+
+ align:start position:0%
+sad where does sad go
+ 
+
+ align:start position:0%
+sad where does sad go
+to sad goes to Nowhere it's dead sbh now
+
+ align:start position:0%
+to sad goes to Nowhere it's dead sbh now
+ 
+
+ align:start position:0%
+to sad goes to Nowhere it's dead sbh now
+wait you might say wait a minute Patrick
+
+ align:start position:0%
+wait you might say wait a minute Patrick
+ 
+
+ align:start position:0%
+wait you might say wait a minute Patrick
+said that we're using this weird
+
+ align:start position:0%
+said that we're using this weird
+ 
+
+ align:start position:0%
+said that we're using this weird
+dictionary order where E is at the end
+
+ align:start position:0%
+dictionary order where E is at the end
+ 
+
+ align:start position:0%
+dictionary order where E is at the end
+it comes before H that's our tiebreak
+
+ align:start position:0%
+it comes before H that's our tiebreak
+ 
+
+ align:start position:0%
+it comes before H that's our tiebreak
+order but it turns out that breath for
+
+ align:start position:0%
+order but it turns out that breath for
+ 
+
+ align:start position:0%
+order but it turns out that breath for
+search and depth for search don't sort
+
+ align:start position:0%
+search and depth for search don't sort
+ 
+
+ align:start position:0%
+search and depth for search don't sort
+in any way the um it's very important
+
+ align:start position:0%
+in any way the um it's very important
+ 
+
+ align:start position:0%
+in any way the um it's very important
+they don't sort the paths that are
+
+ align:start position:0%
+they don't sort the paths that are
+ 
+
+ align:start position:0%
+they don't sort the paths that are
+currently on the Queue so you're going
+
+ align:start position:0%
+currently on the Queue so you're going
+ 
+
+ align:start position:0%
+currently on the Queue so you're going
+to just go left to right left to right
+
+ align:start position:0%
+to just go left to right left to right
+ 
+
+ align:start position:0%
+to just go left to right left to right
+left to right and only at each node are
+
+ align:start position:0%
+left to right and only at each node are
+ 
+
+ align:start position:0%
+left to right and only at each node are
+you going to break ties in Lex's graphic
+
+ align:start position:0%
+you going to break ties in Lex's graphic
+ 
+
+ align:start position:0%
+you going to break ties in Lex's graphic
+order all right so sbh H goes to as we
+
+ align:start position:0%
+order all right so sbh H goes to as we
+ 
+
+ align:start position:0%
+order all right so sbh H goes to as we
+already know fni
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I E we think we already know but we
+
+ align:start position:0%
+I E we think we already know but we
+ 
+
+ align:start position:0%
+I E we think we already know but we
+don't quite because this is e coming
+
+ align:start position:0%
+don't quite because this is e coming
+ 
+
+ align:start position:0%
+don't quite because this is e coming
+from the other direction e this time
+
+ align:start position:0%
+from the other direction e this time
+ 
+
+ align:start position:0%
+from the other direction e this time
+goes to F that's right well actually you
+
+ align:start position:0%
+goes to F that's right well actually you
+ 
+
+ align:start position:0%
+goes to F that's right well actually you
+guys do already know it all right great
+
+ align:start position:0%
+guys do already know it all right great
+ 
+
+ align:start position:0%
+guys do already know it all right great
+now we come over here HF goes to as we
+
+ align:start position:0%
+now we come over here HF goes to as we
+ 
+
+ align:start position:0%
+now we come over here HF goes to as we
+already know e and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+j i goes to as we don't already know hi
+
+ align:start position:0%
+j i goes to as we don't already know hi
+ 
+
+ align:start position:0%
+j i goes to as we don't already know hi
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+to G and J that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and as it turns out by an
+
+ align:start position:0%
+right and as it turns out by an
+ 
+
+ align:start position:0%
+right and as it turns out by an
+implementation detail we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done question does it not expand EV at
+
+ align:start position:0%
+done question does it not expand EV at
+ 
+
+ align:start position:0%
+done question does it not expand EV at
+all now this is an implementation detail
+
+ align:start position:0%
+all now this is an implementation detail
+ 
+
+ align:start position:0%
+all now this is an implementation detail
+it's perfectly sane and reasonable to
+
+ align:start position:0%
+it's perfectly sane and reasonable to
+ 
+
+ align:start position:0%
+it's perfectly sane and reasonable to
+make a dep to breath first search that
+
+ align:start position:0%
+make a dep to breath first search that
+ 
+
+ align:start position:0%
+make a dep to breath first search that
+likes to finish its entire level that
+
+ align:start position:0%
+likes to finish its entire level that
+ 
+
+ align:start position:0%
+likes to finish its entire level that
+it's working on however in our
+
+ align:start position:0%
+it's working on however in our
+ 
+
+ align:start position:0%
+it's working on however in our
+implementation and we would have seen
+
+ align:start position:0%
+implementation and we would have seen
+ 
+
+ align:start position:0%
+implementation and we would have seen
+this if we had been pedantic and drawn
+
+ align:start position:0%
+this if we had been pedantic and drawn
+ 
+
+ align:start position:0%
+this if we had been pedantic and drawn
+out the entire queue it's another reason
+
+ align:start position:0%
+out the entire queue it's another reason
+ 
+
+ align:start position:0%
+out the entire queue it's another reason
+why drawing out the entire queue is as I
+
+ align:start position:0%
+why drawing out the entire queue is as I
+ 
+
+ align:start position:0%
+why drawing out the entire queue is as I
+said more reliable um in our
+
+ align:start position:0%
+said more reliable um in our
+ 
+
+ align:start position:0%
+said more reliable um in our
+implementation since it's not an optimal
+
+ align:start position:0%
+implementation since it's not an optimal
+ 
+
+ align:start position:0%
+implementation since it's not an optimal
+search as moment anywhere on the que you
+
+ align:start position:0%
+search as moment anywhere on the que you
+ 
+
+ align:start position:0%
+search as moment anywhere on the que you
+add something with a g at the end you
+
+ align:start position:0%
+add something with a g at the end you
+ 
+
+ align:start position:0%
+add something with a g at the end you
+finish and because of the fact that the
+
+ align:start position:0%
+finish and because of the fact that the
+ 
+
+ align:start position:0%
+finish and because of the fact that the
+way breath ver search does it's Mojo is
+
+ align:start position:0%
+way breath ver search does it's Mojo is
+ 
+
+ align:start position:0%
+way breath ver search does it's Mojo is
+that it adds everything to the end of
+
+ align:start position:0%
+that it adds everything to the end of
+ 
+
+ align:start position:0%
+that it adds everything to the end of
+the que that's how it does it level by
+
+ align:start position:0%
+the que that's how it does it level by
+ 
+
+ align:start position:0%
+the que that's how it does it level by
+level right it adds it to the end of the
+
+ align:start position:0%
+level right it adds it to the end of the
+ 
+
+ align:start position:0%
+level right it adds it to the end of the
+Q instead of the front well then you
+
+ align:start position:0%
+Q instead of the front well then you
+ 
+
+ align:start position:0%
+Q instead of the front well then you
+you'll add it to the end of the Q and
+
+ align:start position:0%
+you'll add it to the end of the Q and
+ 
+
+ align:start position:0%
+you'll add it to the end of the Q and
+then you will have it on the Q with a G
+
+ align:start position:0%
+then you will have it on the Q with a G
+ 
+
+ align:start position:0%
+then you will have it on the Q with a G
+so you won't have to do s
+
+ align:start position:0%
+so you won't have to do s
+ 
+
+ align:start position:0%
+so you won't have to do s
+CF uh another question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that's a good question so uh the
+
+ align:start position:0%
+um that's a good question so uh the
+ 
+
+ align:start position:0%
+um that's a good question so uh the
+question was so for the breath for
+
+ align:start position:0%
+question was so for the breath for
+ 
+
+ align:start position:0%
+question was so for the breath for
+search there was no backtracking d d
+
+ align:start position:0%
+search there was no backtracking d d
+ 
+
+ align:start position:0%
+search there was no backtracking d d
+died why didn't we backtrack or
+
+ align:start position:0%
+died why didn't we backtrack or
+ 
+
+ align:start position:0%
+died why didn't we backtrack or
+something the answer to that one is bre
+
+ align:start position:0%
+something the answer to that one is bre
+ 
+
+ align:start position:0%
+something the answer to that one is bre
+for breath first search backtracking
+
+ align:start position:0%
+for breath first search backtracking
+ 
+
+ align:start position:0%
+for breath first search backtracking
+doesn't really it isn't really a thing
+
+ align:start position:0%
+doesn't really it isn't really a thing
+ 
+
+ align:start position:0%
+doesn't really it isn't really a thing
+like it is for depth first search why
+
+ align:start position:0%
+like it is for depth first search why
+ 
+
+ align:start position:0%
+like it is for depth first search why
+well because breath first search we're
+
+ align:start position:0%
+well because breath first search we're
+ 
+
+ align:start position:0%
+well because breath first search we're
+sending our infinite monkeys down every
+
+ align:start position:0%
+sending our infinite monkeys down every
+ 
+
+ align:start position:0%
+sending our infinite monkeys down every
+path um in depth research we're really
+
+ align:start position:0%
+path um in depth research we're really
+ 
+
+ align:start position:0%
+path um in depth research we're really
+focused in N we're like we want to get
+
+ align:start position:0%
+focused in N we're like we want to get
+ 
+
+ align:start position:0%
+focused in N we're like we want to get
+there we want to get there ooh this way
+
+ align:start position:0%
+there we want to get there ooh this way
+ 
+
+ align:start position:0%
+there we want to get there ooh this way
+this way this way this way and we might
+
+ align:start position:0%
+this way this way this way and we might
+ 
+
+ align:start position:0%
+this way this way this way and we might
+have gone the wrong way and then we hit
+
+ align:start position:0%
+have gone the wrong way and then we hit
+ 
+
+ align:start position:0%
+have gone the wrong way and then we hit
+a dead end we're like oh crap and we go
+
+ align:start position:0%
+a dead end we're like oh crap and we go
+ 
+
+ align:start position:0%
+a dead end we're like oh crap and we go
+backwards but for for breath resarch
+
+ align:start position:0%
+backwards but for for breath resarch
+ 
+
+ align:start position:0%
+backwards but for for breath resarch
+we're we really are like an evil
+
+ align:start position:0%
+we're we really are like an evil
+ 
+
+ align:start position:0%
+we're we really are like an evil
+Overlord and you know we're like Mark
+
+ align:start position:0%
+Overlord and you know we're like Mark
+ 
+
+ align:start position:0%
+Overlord and you know we're like Mark
+Vader saying like Stormtroopers go every
+
+ align:start position:0%
+Vader saying like Stormtroopers go every
+ 
+
+ align:start position:0%
+Vader saying like Stormtroopers go every
+direction and then from there go every
+
+ align:start position:0%
+direction and then from there go every
+ 
+
+ align:start position:0%
+direction and then from there go every
+other direction and so even though yes
+
+ align:start position:0%
+other direction and so even though yes
+ 
+
+ align:start position:0%
+other direction and so even though yes
+when we got to D some of the
+
+ align:start position:0%
+when we got to D some of the
+ 
+
+ align:start position:0%
+when we got to D some of the
+Stormtroopers hit a dead end and
+
+ align:start position:0%
+Stormtroopers hit a dead end and
+ 
+
+ align:start position:0%
+Stormtroopers hit a dead end and
+probably like it was reflective and they
+
+ align:start position:0%
+probably like it was reflective and they
+ 
+
+ align:start position:0%
+probably like it was reflective and they
+shot it and hit themselves or something
+
+ align:start position:0%
+shot it and hit themselves or something
+ 
+
+ align:start position:0%
+shot it and hit themselves or something
+like that meanwhile the Stormtroopers be
+
+ align:start position:0%
+like that meanwhile the Stormtroopers be
+ 
+
+ align:start position:0%
+like that meanwhile the Stormtroopers be
+sent to B andc are still fine so we
+
+ align:start position:0%
+sent to B andc are still fine so we
+ 
+
+ align:start position:0%
+sent to B andc are still fine so we
+don't need to backtrack troops down yeah
+
+ align:start position:0%
+don't need to backtrack troops down yeah
+ 
+
+ align:start position:0%
+don't need to backtrack troops down yeah
+there are other troops going down the
+
+ align:start position:0%
+there are other troops going down the
+ 
+
+ align:start position:0%
+there are other troops going down the
+tree in every direction whereas in the
+
+ align:start position:0%
+tree in every direction whereas in the
+ 
+
+ align:start position:0%
+tree in every direction whereas in the
+def for search we only sent we're like
+
+ align:start position:0%
+def for search we only sent we're like
+ 
+
+ align:start position:0%
+def for search we only sent we're like
+there are definitely no Droids on this
+
+ align:start position:0%
+there are definitely no Droids on this
+ 
+
+ align:start position:0%
+there are definitely no Droids on this
+Escape pod send everyone this straight
+
+ align:start position:0%
+Escape pod send everyone this straight
+ 
+
+ align:start position:0%
+Escape pod send everyone this straight
+Direction and we only sent them to a and
+
+ align:start position:0%
+Direction and we only sent them to a and
+ 
+
+ align:start position:0%
+Direction and we only sent them to a and
+d and then so we had to back track
+
+ align:start position:0%
+d and then so we had to back track
+ 
+
+ align:start position:0%
+d and then so we had to back track
+because we hit a dead end does that make
+
+ align:start position:0%
+because we hit a dead end does that make
+ 
+
+ align:start position:0%
+because we hit a dead end does that make
+sense another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question so the question is in this uh
+
+ align:start position:0%
+question so the question is in this uh
+ 
+
+ align:start position:0%
+question so the question is in this uh
+breath res search did LAX graphic order
+
+ align:start position:0%
+breath res search did LAX graphic order
+ 
+
+ align:start position:0%
+breath res search did LAX graphic order
+ever come into play the answer is yes in
+
+ align:start position:0%
+ever come into play the answer is yes in
+ 
+
+ align:start position:0%
+ever come into play the answer is yes in
+a very subtle and sneaky way which is um
+
+ align:start position:0%
+a very subtle and sneaky way which is um
+ 
+
+ align:start position:0%
+a very subtle and sneaky way which is um
+I wrote E before J F before I and G
+
+ align:start position:0%
+I wrote E before J F before I and G
+ 
+
+ align:start position:0%
+I wrote E before J F before I and G
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+J if I was not using lexographic order
+
+ align:start position:0%
+J if I was not using lexographic order
+ 
+
+ align:start position:0%
+J if I was not using lexographic order
+it might have been reasonable to write
+
+ align:start position:0%
+it might have been reasonable to write
+ 
+
+ align:start position:0%
+it might have been reasonable to write
+for instance when I was expending I to
+
+ align:start position:0%
+for instance when I was expending I to
+ 
+
+ align:start position:0%
+for instance when I was expending I to
+write J before G because J was higher up
+
+ align:start position:0%
+write J before G because J was higher up
+ 
+
+ align:start position:0%
+write J before G because J was higher up
+on the tree or something like that but
+
+ align:start position:0%
+on the tree or something like that but
+ 
+
+ align:start position:0%
+on the tree or something like that but
+the only way it came into play is that I
+
+ align:start position:0%
+the only way it came into play is that I
+ 
+
+ align:start position:0%
+the only way it came into play is that I
+wrote them left to right in alphabetic
+
+ align:start position:0%
+wrote them left to right in alphabetic
+ 
+
+ align:start position:0%
+wrote them left to right in alphabetic
+order every time and I wrote
+
+ align:start position:0%
+order every time and I wrote
+ 
+
+ align:start position:0%
+order every time and I wrote
+ABC another question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I we have visited F again and we would
+
+ align:start position:0%
+I we have visited F again and we would
+ 
+
+ align:start position:0%
+I we have visited F again and we would
+have visited F again that's correct the
+
+ align:start position:0%
+have visited F again that's correct the
+ 
+
+ align:start position:0%
+have visited F again that's correct the
+question is f is listed twice so if we
+
+ align:start position:0%
+question is f is listed twice so if we
+ 
+
+ align:start position:0%
+question is f is listed twice so if we
+hadn't reached the goal node let's say
+
+ align:start position:0%
+hadn't reached the goal node let's say
+ 
+
+ align:start position:0%
+hadn't reached the goal node let's say
+that down there after I is z and after Z
+
+ align:start position:0%
+that down there after I is z and after Z
+ 
+
+ align:start position:0%
+that down there after I is z and after Z
+is the goal node then would we have
+
+ align:start position:0%
+is the goal node then would we have
+ 
+
+ align:start position:0%
+is the goal node then would we have
+visited F again the answer is yes as I
+
+ align:start position:0%
+visited F again the answer is yes as I
+ 
+
+ align:start position:0%
+visited F again the answer is yes as I
+said this is the approach that throws
+
+ align:start position:0%
+said this is the approach that throws
+ 
+
+ align:start position:0%
+said this is the approach that throws
+your troops every possible way so
+
+ align:start position:0%
+your troops every possible way so
+ 
+
+ align:start position:0%
+your troops every possible way so
+there's Storm Troopers going from E to F
+
+ align:start position:0%
+there's Storm Troopers going from E to F
+ 
+
+ align:start position:0%
+there's Storm Troopers going from E to F
+and there's Storm Troopers going from H
+
+ align:start position:0%
+and there's Storm Troopers going from H
+ 
+
+ align:start position:0%
+and there's Storm Troopers going from H
+to F and they're going everywhere now
+
+ align:start position:0%
+to F and they're going everywhere now
+ 
+
+ align:start position:0%
+to F and they're going everywhere now
+there is a way to cut down on this you
+
+ align:start position:0%
+there is a way to cut down on this you
+ 
+
+ align:start position:0%
+there is a way to cut down on this you
+could do breath first search with an
+
+ align:start position:0%
+could do breath first search with an
+ 
+
+ align:start position:0%
+could do breath first search with an
+extended list
+
+ align:start position:0%
+extended list
+ 
+
+ align:start position:0%
+extended list
+if you did do Brett first search with an
+
+ align:start position:0%
+if you did do Brett first search with an
+ 
+
+ align:start position:0%
+if you did do Brett first search with an
+extended list that would be sort of
+
+ align:start position:0%
+extended list that would be sort of
+ 
+
+ align:start position:0%
+extended list that would be sort of
+equivalent to after as soon as you
+
+ align:start position:0%
+equivalent to after as soon as you
+ 
+
+ align:start position:0%
+equivalent to after as soon as you
+expand one node you know as soon as
+
+ align:start position:0%
+expand one node you know as soon as
+ 
+
+ align:start position:0%
+expand one node you know as soon as
+storm you send Storm Troopers out of I
+
+ align:start position:0%
+storm you send Storm Troopers out of I
+ 
+
+ align:start position:0%
+storm you send Storm Troopers out of I
+to look at g& J one of them stays at I
+
+ align:start position:0%
+to look at g& J one of them stays at I
+ 
+
+ align:start position:0%
+to look at g& J one of them stays at I
+and if any other Storm Troopers come to
+
+ align:start position:0%
+and if any other Storm Troopers come to
+ 
+
+ align:start position:0%
+and if any other Storm Troopers come to
+I and they're like oh we want to see
+
+ align:start position:0%
+I and they're like oh we want to see
+ 
+
+ align:start position:0%
+I and they're like oh we want to see
+what's past ey he's like no no no we've
+
+ align:start position:0%
+what's past ey he's like no no no we've
+ 
+
+ align:start position:0%
+what's past ey he's like no no no we've
+already sent troops past ey we've got
+
+ align:start position:0%
+already sent troops past ey we've got
+ 
+
+ align:start position:0%
+already sent troops past ey we've got
+this go back home you're it's it's it's
+
+ align:start position:0%
+this go back home you're it's it's it's
+ 
+
+ align:start position:0%
+this go back home you're it's it's it's
+okay there are no Rebels here but it
+
+ align:start position:0%
+okay there are no Rebels here but it
+ 
+
+ align:start position:0%
+okay there are no Rebels here but it
+might be Han Solo dressed up as a
+
+ align:start position:0%
+might be Han Solo dressed up as a
+ 
+
+ align:start position:0%
+might be Han Solo dressed up as a
+stormtrooper as we'll see in the next
+
+ align:start position:0%
+stormtrooper as we'll see in the next
+ 
+
+ align:start position:0%
+stormtrooper as we'll see in the next
+problem um where our extended list
+
+ align:start position:0%
+problem um where our extended list
+ 
+
+ align:start position:0%
+problem um where our extended list
+screws us up
+
+ align:start position:0%
+screws us up
+ 
+
+ align:start position:0%
+screws us up
+um but for this problem um you see what
+
+ align:start position:0%
+um but for this problem um you see what
+ 
+
+ align:start position:0%
+um but for this problem um you see what
+I mean with an extended list we could
+
+ align:start position:0%
+I mean with an extended list we could
+ 
+
+ align:start position:0%
+I mean with an extended list we could
+avoid this because the extended list
+
+ align:start position:0%
+avoid this because the extended list
+ 
+
+ align:start position:0%
+avoid this because the extended list
+basically says once I've expanded and
+
+ align:start position:0%
+basically says once I've expanded and
+ 
+
+ align:start position:0%
+basically says once I've expanded and
+search past here don't do it again but
+
+ align:start position:0%
+search past here don't do it again but
+ 
+
+ align:start position:0%
+search past here don't do it again but
+if you don't have one yeah you'll do F
+
+ align:start position:0%
+if you don't have one yeah you'll do F
+ 
+
+ align:start position:0%
+if you don't have one yeah you'll do F
+twice in fact didn't we do something
+
+ align:start position:0%
+twice in fact didn't we do something
+ 
+
+ align:start position:0%
+twice in fact didn't we do something
+twice here oh it turns out we didn't but
+
+ align:start position:0%
+twice here oh it turns out we didn't but
+ 
+
+ align:start position:0%
+twice here oh it turns out we didn't but
+we we easily could have we almost did E
+
+ align:start position:0%
+we we easily could have we almost did E
+ 
+
+ align:start position:0%
+we we easily could have we almost did E
+twice we almost did uh we almost did F
+
+ align:start position:0%
+twice we almost did uh we almost did F
+ 
+
+ align:start position:0%
+twice we almost did uh we almost did F
+twice it turns out we didn't but we
+
+ align:start position:0%
+twice it turns out we didn't but we
+ 
+
+ align:start position:0%
+twice it turns out we didn't but we
+could have another question we assume
+
+ align:start position:0%
+could have another question we assume
+ 
+
+ align:start position:0%
+could have another question we assume
+that for the impementation of the that
+
+ align:start position:0%
+that for the impementation of the that
+ 
+
+ align:start position:0%
+that for the impementation of the that
+when you
+
+ align:start position:0%
+when you
+ 
+
+ align:start position:0%
+when you
+expand G and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+addan J so stop that's a very good
+
+ align:start position:0%
+addan J so stop that's a very good
+ 
+
+ align:start position:0%
+addan J so stop that's a very good
+question that provokes a minor change
+
+ align:start position:0%
+question that provokes a minor change
+ 
+
+ align:start position:0%
+question that provokes a minor change
+the question is when you expand
+
+ align:start position:0%
+the question is when you expand
+ 
+
+ align:start position:0%
+the question is when you expand
+sbhi is sbig added before sbhi J because
+
+ align:start position:0%
+sbhi is sbig added before sbhi J because
+ 
+
+ align:start position:0%
+sbhi is sbig added before sbhi J because
+of lexographic ordering or they both add
+
+ align:start position:0%
+of lexographic ordering or they both add
+ 
+
+ align:start position:0%
+of lexographic ordering or they both add
+at the same time the answer is
+
+ align:start position:0%
+at the same time the answer is
+ 
+
+ align:start position:0%
+at the same time the answer is
+simultaneous when you do the expansion
+
+ align:start position:0%
+simultaneous when you do the expansion
+ 
+
+ align:start position:0%
+simultaneous when you do the expansion
+you instantly receive a say a list maybe
+
+ align:start position:0%
+you instantly receive a say a list maybe
+ 
+
+ align:start position:0%
+you instantly receive a say a list maybe
+or whatever data structure you like
+
+ align:start position:0%
+or whatever data structure you like
+ 
+
+ align:start position:0%
+or whatever data structure you like
+containing all of the children and they
+
+ align:start position:0%
+containing all of the children and they
+ 
+
+ align:start position:0%
+containing all of the children and they
+all go get appended to the Queue at once
+
+ align:start position:0%
+all go get appended to the Queue at once
+ 
+
+ align:start position:0%
+all go get appended to the Queue at once
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+order so um you will receive all of them
+
+ align:start position:0%
+order so um you will receive all of them
+ 
+
+ align:start position:0%
+order so um you will receive all of them
+like I suppose you could create some
+
+ align:start position:0%
+like I suppose you could create some
+ 
+
+ align:start position:0%
+like I suppose you could create some
+kind of search problem where you have
+
+ align:start position:0%
+kind of search problem where you have
+ 
+
+ align:start position:0%
+kind of search problem where you have
+like an adversary node like a wus or
+
+ align:start position:0%
+like an adversary node like a wus or
+ 
+
+ align:start position:0%
+like an adversary node like a wus or
+you're hunting a wus and if you you
+
+ align:start position:0%
+you're hunting a wus and if you you
+ 
+
+ align:start position:0%
+you're hunting a wus and if you you
+don't want to add the exact wus to your
+
+ align:start position:0%
+don't want to add the exact wus to your
+ 
+
+ align:start position:0%
+don't want to add the exact wus to your
+search tree or you lose you only want to
+
+ align:start position:0%
+search tree or you lose you only want to
+ 
+
+ align:start position:0%
+search tree or you lose you only want to
+add the one next to the wus I don't know
+
+ align:start position:0%
+add the one next to the wus I don't know
+ 
+
+ align:start position:0%
+add the one next to the wus I don't know
+I'm making this up and unfortunately you
+
+ align:start position:0%
+I'm making this up and unfortunately you
+ 
+
+ align:start position:0%
+I'm making this up and unfortunately you
+would have to add all the you have to
+
+ align:start position:0%
+would have to add all the you have to
+ 
+
+ align:start position:0%
+would have to add all the you have to
+add all the children at once you uh our
+
+ align:start position:0%
+add all the children at once you uh our
+ 
+
+ align:start position:0%
+add all the children at once you uh our
+current algorithm does not add uh one at
+
+ align:start position:0%
+current algorithm does not add uh one at
+ 
+
+ align:start position:0%
+current algorithm does not add uh one at
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+time all right so we've done a breath
+
+ align:start position:0%
+time all right so we've done a breath
+ 
+
+ align:start position:0%
+time all right so we've done a breath
+for a search great now we're going to do
+
+ align:start position:0%
+for a search great now we're going to do
+ 
+
+ align:start position:0%
+for a search great now we're going to do
+some optimal
+
+ align:start position:0%
+some optimal
+ 
+
+ align:start position:0%
+some optimal
+search that is going to require me to
+
+ align:start position:0%
+search that is going to require me to
+ 
+
+ align:start position:0%
+search that is going to require me to
+draw a slightly different graph I will
+
+ align:start position:0%
+draw a slightly different graph I will
+ 
+
+ align:start position:0%
+draw a slightly different graph I will
+draw it on what is left of the bottom
+
+ align:start position:0%
+draw it on what is left of the bottom
+ 
+
+ align:start position:0%
+draw it on what is left of the bottom
+here and then we'll solve it on on what
+
+ align:start position:0%
+here and then we'll solve it on on what
+ 
+
+ align:start position:0%
+here and then we'll solve it on on what
+is left of the bottom here so all right
+
+ align:start position:0%
+is left of the bottom here so all right
+ 
+
+ align:start position:0%
+is left of the bottom here so all right
+Mark has his new stronghold and he wants
+
+ align:start position:0%
+Mark has his new stronghold and he wants
+ 
+
+ align:start position:0%
+Mark has his new stronghold and he wants
+to invade parallel
+
+ align:start position:0%
+to invade parallel
+ 
+
+ align:start position:0%
+to invade parallel
+universes now he's going to he's
+
+ align:start position:0%
+universes now he's going to he's
+ 
+
+ align:start position:0%
+universes now he's going to he's
+programmed his evil supercomputer to
+
+ align:start position:0%
+programmed his evil supercomputer to
+ 
+
+ align:start position:0%
+programmed his evil supercomputer to
+find the shortest path of jumps from his
+
+ align:start position:0%
+find the shortest path of jumps from his
+ 
+
+ align:start position:0%
+find the shortest path of jumps from his
+starting Universe to the goal Universe G
+
+ align:start position:0%
+starting Universe to the goal Universe G
+ 
+
+ align:start position:0%
+starting Universe to the goal Universe G
+he's
+
+ align:start position:0%
+he's
+ 
+
+ align:start position:0%
+he's
+also it takes a certain amount of energy
+
+ align:start position:0%
+also it takes a certain amount of energy
+ 
+
+ align:start position:0%
+also it takes a certain amount of energy
+to move from Universe to Universe based
+
+ align:start position:0%
+to move from Universe to Universe based
+ 
+
+ align:start position:0%
+to move from Universe to Universe based
+on the differing factors between those
+
+ align:start position:0%
+on the differing factors between those
+ 
+
+ align:start position:0%
+on the differing factors between those
+universes like maybe in one
+
+ align:start position:0%
+universes like maybe in one
+ 
+
+ align:start position:0%
+universes like maybe in one
+Universe a butterfly didn't flap its
+
+ align:start position:0%
+Universe a butterfly didn't flap its
+ 
+
+ align:start position:0%
+Universe a butterfly didn't flap its
+wings in China whereas in the other
+
+ align:start position:0%
+wings in China whereas in the other
+ 
+
+ align:start position:0%
+wings in China whereas in the other
+Universe there's a sentient reptiles
+
+ align:start position:0%
+Universe there's a sentient reptiles
+ 
+
+ align:start position:0%
+Universe there's a sentient reptiles
+rule the Earth um and so he has Mark
+
+ align:start position:0%
+rule the Earth um and so he has Mark
+ 
+
+ align:start position:0%
+rule the Earth um and so he has Mark
+supercomputer has tried to create a
+
+ align:start position:0%
+supercomputer has tried to create a
+ 
+
+ align:start position:0%
+supercomputer has tried to create a
+heris value that determines how
+
+ align:start position:0%
+heris value that determines how
+ 
+
+ align:start position:0%
+heris value that determines how
+different the universes are to guess
+
+ align:start position:0%
+different the universes are to guess
+ 
+
+ align:start position:0%
+different the universes are to guess
+sort of how much energy it's going to
+
+ align:start position:0%
+sort of how much energy it's going to
+ 
+
+ align:start position:0%
+sort of how much energy it's going to
+take to get from his start Universe s to
+
+ align:start position:0%
+take to get from his start Universe s to
+ 
+
+ align:start position:0%
+take to get from his start Universe s to
+his goal Universe G given that he's at a
+
+ align:start position:0%
+his goal Universe G given that he's at a
+ 
+
+ align:start position:0%
+his goal Universe G given that he's at a
+he's he currently his armies are at a
+
+ align:start position:0%
+he's he currently his armies are at a
+ 
+
+ align:start position:0%
+he's he currently his armies are at a
+particular Universe in other words okay
+
+ align:start position:0%
+particular Universe in other words okay
+ 
+
+ align:start position:0%
+particular Universe in other words okay
+it's not a ukian search but damn it
+
+ align:start position:0%
+it's not a ukian search but damn it
+ 
+
+ align:start position:0%
+it's not a ukian search but damn it
+we're going to have a heris distance to
+
+ align:start position:0%
+we're going to have a heris distance to
+ 
+
+ align:start position:0%
+we're going to have a heris distance to
+the goal and we're going to have a graph
+
+ align:start position:0%
+the goal and we're going to have a graph
+ 
+
+ align:start position:0%
+the goal and we're going to have a graph
+with distances so let's see what it
+
+ align:start position:0%
+with distances so let's see what it
+ 
+
+ align:start position:0%
+with distances so let's see what it
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+like all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and down here is
+
+ align:start position:0%
+and down here is
+ 
+
+ align:start position:0%
+and down here is
+G so this otherwise I'm assuming heart
+
+ align:start position:0%
+G so this otherwise I'm assuming heart
+ 
+
+ align:start position:0%
+G so this otherwise I'm assuming heart
+shape hides an evil Invasion Force so
+
+ align:start position:0%
+shape hides an evil Invasion Force so
+ 
+
+ align:start position:0%
+shape hides an evil Invasion Force so
+um let's see the distance here is 100
+
+ align:start position:0%
+um let's see the distance here is 100
+ 
+
+ align:start position:0%
+um let's see the distance here is 100
+the distance here is three four the
+
+ align:start position:0%
+the distance here is three four the
+ 
+
+ align:start position:0%
+the distance here is three four the
+distance here is four distance here is
+
+ align:start position:0%
+distance here is four distance here is
+ 
+
+ align:start position:0%
+distance here is four distance here is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+50 14
+
+ align:start position:0%
+50 14
+ 
+
+ align:start position:0%
+50 14
+4 16
+
+ align:start position:0%
+4 16
+ 
+
+ align:start position:0%
+4 16
+16 oh sorry these are
+
+ align:start position:0%
+16 oh sorry these are
+ 
+
+ align:start position:0%
+16 oh sorry these are
+connected
+
+ align:start position:0%
+connected
+ 
+
+ align:start position:0%
+connected
+30 and
+
+ align:start position:0%
+30 and
+ 
+
+ align:start position:0%
+30 and
+10 theistic values are zero at the start
+
+ align:start position:0%
+10 theistic values are zero at the start
+ 
+
+ align:start position:0%
+10 theistic values are zero at the start
+node 50 at
+
+ align:start position:0%
+node 50 at
+ 
+
+ align:start position:0%
+node 50 at
+B 60 at
+
+ align:start position:0%
+B 60 at
+ 
+
+ align:start position:0%
+B 60 at
+a 55 at
+
+ align:start position:0%
+a 55 at
+ 
+
+ align:start position:0%
+a 55 at
+C 50 at d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+56 at
+
+ align:start position:0%
+56 at
+ 
+
+ align:start position:0%
+56 at
+e 50 at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F zero at G because it's the goal
+
+ align:start position:0%
+F zero at G because it's the goal
+ 
+
+ align:start position:0%
+F zero at G because it's the goal
+mode 39 at H I'll draw the little H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smaller and zero at
+
+ align:start position:0%
+smaller and zero at
+ 
+
+ align:start position:0%
+smaller and zero at
+I well after all I goes right to G it
+
+ align:start position:0%
+I well after all I goes right to G it
+ 
+
+ align:start position:0%
+I well after all I goes right to G it
+can be zero it'll be great Okay so
+
+ align:start position:0%
+can be zero it'll be great Okay so
+ 
+
+ align:start position:0%
+can be zero it'll be great Okay so
+now this time Mark is trying to conserve
+
+ align:start position:0%
+now this time Mark is trying to conserve
+ 
+
+ align:start position:0%
+now this time Mark is trying to conserve
+the energy of his parallel universe
+
+ align:start position:0%
+the energy of his parallel universe
+ 
+
+ align:start position:0%
+the energy of his parallel universe
+jumper that understandably takes a lot
+
+ align:start position:0%
+jumper that understandably takes a lot
+ 
+
+ align:start position:0%
+jumper that understandably takes a lot
+of energy so he needs to find he needs
+
+ align:start position:0%
+of energy so he needs to find he needs
+ 
+
+ align:start position:0%
+of energy so he needs to find he needs
+to program in the shortest number of
+
+ align:start position:0%
+to program in the shortest number of
+ 
+
+ align:start position:0%
+to program in the shortest number of
+universe jumps that will get him to the
+
+ align:start position:0%
+universe jumps that will get him to the
+ 
+
+ align:start position:0%
+universe jumps that will get him to the
+goal he he's not interest and he doesn't
+
+ align:start position:0%
+goal he he's not interest and he doesn't
+ 
+
+ align:start position:0%
+goal he he's not interest and he doesn't
+mean the least number of jumps he means
+
+ align:start position:0%
+mean the least number of jumps he means
+ 
+
+ align:start position:0%
+mean the least number of jumps he means
+the least amount of energy on these
+
+ align:start position:0%
+the least amount of energy on these
+ 
+
+ align:start position:0%
+the least amount of energy on these
+edges he's not interested in conquering
+
+ align:start position:0%
+edges he's not interested in conquering
+ 
+
+ align:start position:0%
+edges he's not interested in conquering
+in getting to this new world and not
+
+ align:start position:0%
+in getting to this new world and not
+ 
+
+ align:start position:0%
+in getting to this new world and not
+having enough energy left to blast the
+
+ align:start position:0%
+having enough energy left to blast the
+ 
+
+ align:start position:0%
+having enough energy left to blast the
+crap out of it so we need to find the
+
+ align:start position:0%
+crap out of it so we need to find the
+ 
+
+ align:start position:0%
+crap out of it so we need to find the
+shortest path so first Mark programs a
+
+ align:start position:0%
+shortest path so first Mark programs a
+ 
+
+ align:start position:0%
+shortest path so first Mark programs a
+simple br in Bound search he adds in an
+
+ align:start position:0%
+simple br in Bound search he adds in an
+ 
+
+ align:start position:0%
+simple br in Bound search he adds in an
+extended list to his branch and bound
+
+ align:start position:0%
+extended list to his branch and bound
+ 
+
+ align:start position:0%
+extended list to his branch and bound
+just to make it a little bit faster as
+
+ align:start position:0%
+just to make it a little bit faster as
+ 
+
+ align:start position:0%
+just to make it a little bit faster as
+usual he breaks ties of equal length in
+
+ align:start position:0%
+usual he breaks ties of equal length in
+ 
+
+ align:start position:0%
+usual he breaks ties of equal length in
+lexographic order so let's list the
+
+ align:start position:0%
+lexographic order so let's list the
+ 
+
+ align:start position:0%
+lexographic order so let's list the
+nodes that Mark's computer adds to the
+
+ align:start position:0%
+nodes that Mark's computer adds to the
+ 
+
+ align:start position:0%
+nodes that Mark's computer adds to the
+extended list in
+
+ align:start position:0%
+extended list in
+ 
+
+ align:start position:0%
+extended list in
+order distances are shown next to the
+
+ align:start position:0%
+order distances are shown next to the
+ 
+
+ align:start position:0%
+order distances are shown next to the
+edges ignore the number in parentheses
+
+ align:start position:0%
+edges ignore the number in parentheses
+ 
+
+ align:start position:0%
+edges ignore the number in parentheses
+for now they are heris and we're not
+
+ align:start position:0%
+for now they are heris and we're not
+ 
+
+ align:start position:0%
+for now they are heris and we're not
+using them so that brings me to another
+
+ align:start position:0%
+using them so that brings me to another
+ 
+
+ align:start position:0%
+using them so that brings me to another
+point that I'd like to drive home before
+
+ align:start position:0%
+point that I'd like to drive home before
+ 
+
+ align:start position:0%
+point that I'd like to drive home before
+we go for the home stretch and solve
+
+ align:start position:0%
+we go for the home stretch and solve
+ 
+
+ align:start position:0%
+we go for the home stretch and solve
+these problems
+
+ align:start position:0%
+these problems
+ 
+
+ align:start position:0%
+these problems
+what the heck is the difference between
+
+ align:start position:0%
+what the heck is the difference between
+ 
+
+ align:start position:0%
+what the heck is the difference between
+branch and bound and a star okay I like
+
+ align:start position:0%
+branch and bound and a star okay I like
+ 
+
+ align:start position:0%
+branch and bound and a star okay I like
+to liken it to the following I probably
+
+ align:start position:0%
+to liken it to the following I probably
+ 
+
+ align:start position:0%
+to liken it to the following I probably
+should have I'll make this a SilverStar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea okay the SilverStar idea is pizza
+
+ align:start position:0%
+idea okay the SilverStar idea is pizza
+ 
+
+ align:start position:0%
+idea okay the SilverStar idea is pizza
+it doesn't really look like pizza but
+
+ align:start position:0%
+it doesn't really look like pizza but
+ 
+
+ align:start position:0%
+it doesn't really look like pizza but
+that's a SilverStar idea Branch inbound
+
+ align:start position:0%
+that's a SilverStar idea Branch inbound
+ 
+
+ align:start position:0%
+that's a SilverStar idea Branch inbound
+is a cheese pizza it's simple if you
+
+ align:start position:0%
+is a cheese pizza it's simple if you
+ 
+
+ align:start position:0%
+is a cheese pizza it's simple if you
+order it for a large group event of
+
+ align:start position:0%
+order it for a large group event of
+ 
+
+ align:start position:0%
+order it for a large group event of
+college students they will eat it and
+
+ align:start position:0%
+college students they will eat it and
+ 
+
+ align:start position:0%
+college students they will eat it and
+think things will be
+
+ align:start position:0%
+think things will be
+ 
+
+ align:start position:0%
+think things will be
+okay now a star search is some kind of
+
+ align:start position:0%
+okay now a star search is some kind of
+ 
+
+ align:start position:0%
+okay now a star search is some kind of
+meat lovers of supreme pizza maybe a
+
+ align:start position:0%
+meat lovers of supreme pizza maybe a
+ 
+
+ align:start position:0%
+meat lovers of supreme pizza maybe a
+meat lovers Pizza it's got all these
+
+ align:start position:0%
+meat lovers Pizza it's got all these
+ 
+
+ align:start position:0%
+meat lovers Pizza it's got all these
+extra toppings a lot of people are
+
+ align:start position:0%
+extra toppings a lot of people are
+ 
+
+ align:start position:0%
+extra toppings a lot of people are
+really going to like it it might be
+
+ align:start position:0%
+really going to like it it might be
+ 
+
+ align:start position:0%
+really going to like it it might be
+better but then you've got a vegetarian
+
+ align:start position:0%
+better but then you've got a vegetarian
+ 
+
+ align:start position:0%
+better but then you've got a vegetarian
+and everything's screwed
+
+ align:start position:0%
+and everything's screwed
+ 
+
+ align:start position:0%
+and everything's screwed
+up so basically branch and a star is
+
+ align:start position:0%
+up so basically branch and a star is
+ 
+
+ align:start position:0%
+up so basically branch and a star is
+just branch and bound with some extra
+
+ align:start position:0%
+just branch and bound with some extra
+ 
+
+ align:start position:0%
+just branch and bound with some extra
+toppings added on in this case one of
+
+ align:start position:0%
+toppings added on in this case one of
+ 
+
+ align:start position:0%
+toppings added on in this case one of
+the Toppings is an extended list uh
+
+ align:start position:0%
+the Toppings is an extended list uh
+ 
+
+ align:start position:0%
+the Toppings is an extended list uh
+extended list which uh we'll see keeps
+
+ align:start position:0%
+extended list which uh we'll see keeps
+ 
+
+ align:start position:0%
+extended list which uh we'll see keeps
+track of where we where we've passed
+
+ align:start position:0%
+track of where we where we've passed
+ 
+
+ align:start position:0%
+track of where we where we've passed
+through and already expended out and it
+
+ align:start position:0%
+through and already expended out and it
+ 
+
+ align:start position:0%
+through and already expended out and it
+never goes back the other topping that
+
+ align:start position:0%
+never goes back the other topping that
+ 
+
+ align:start position:0%
+never goes back the other topping that
+we were going to add is a heuristic
+
+ align:start position:0%
+we were going to add is a heuristic
+ 
+
+ align:start position:0%
+we were going to add is a heuristic
+heuristic tells us about how far we
+
+ align:start position:0%
+heuristic tells us about how far we
+ 
+
+ align:start position:0%
+heuristic tells us about how far we
+think we have left until we're at the
+
+ align:start position:0%
+think we have left until we're at the
+ 
+
+ align:start position:0%
+think we have left until we're at the
+end so we don't go through really short
+
+ align:start position:0%
+end so we don't go through really short
+ 
+
+ align:start position:0%
+end so we don't go through really short
+paths that go completely in the wrong
+
+ align:start position:0%
+paths that go completely in the wrong
+ 
+
+ align:start position:0%
+paths that go completely in the wrong
+direction all right between the two of
+
+ align:start position:0%
+direction all right between the two of
+ 
+
+ align:start position:0%
+direction all right between the two of
+those we get our supreme pizza but
+
+ align:start position:0%
+those we get our supreme pizza but
+ 
+
+ align:start position:0%
+those we get our supreme pizza but
+sometimes as we'll see they they sort of
+
+ align:start position:0%
+sometimes as we'll see they they sort of
+ 
+
+ align:start position:0%
+sometimes as we'll see they they sort of
+mess each other up so you know one of
+
+ align:start position:0%
+mess each other up so you know one of
+ 
+
+ align:start position:0%
+mess each other up so you know one of
+the topics just doesn't go well with the
+
+ align:start position:0%
+the topics just doesn't go well with the
+ 
+
+ align:start position:0%
+the topics just doesn't go well with the
+other one maybe a lot someone does like
+
+ align:start position:0%
+other one maybe a lot someone does like
+ 
+
+ align:start position:0%
+other one maybe a lot someone does like
+Hawaiian they think that the the ham
+
+ align:start position:0%
+Hawaiian they think that the the ham
+ 
+
+ align:start position:0%
+Hawaiian they think that the the ham
+doesn't go well with the pineapple
+
+ align:start position:0%
+doesn't go well with the pineapple
+ 
+
+ align:start position:0%
+doesn't go well with the pineapple
+anyway so let's do a branch inbound that
+
+ align:start position:0%
+anyway so let's do a branch inbound that
+ 
+
+ align:start position:0%
+anyway so let's do a branch inbound that
+just has an extended list maybe we've
+
+ align:start position:0%
+just has an extended list maybe we've
+ 
+
+ align:start position:0%
+just has an extended list maybe we've
+got some green peppers on this pizza
+
+ align:start position:0%
+got some green peppers on this pizza
+ 
+
+ align:start position:0%
+got some green peppers on this pizza
+this is going to be
+
+ align:start position:0%
+this is going to be
+ 
+
+ align:start position:0%
+this is going to be
+safe um all right so we're going to list
+
+ align:start position:0%
+safe um all right so we're going to list
+ 
+
+ align:start position:0%
+safe um all right so we're going to list
+the noesy as the extended list and the
+
+ align:start position:0%
+the noesy as the extended list and the
+ 
+
+ align:start position:0%
+the noesy as the extended list and the
+way we're going to do that is well you
+
+ align:start position:0%
+way we're going to do that is well you
+ 
+
+ align:start position:0%
+way we're going to do that is well you
+guys said you like gold tree more than Q
+
+ align:start position:0%
+guys said you like gold tree more than Q
+ 
+
+ align:start position:0%
+guys said you like gold tree more than Q
+so let's do it with a gold tree so we've
+
+ align:start position:0%
+so let's do it with a gold tree so we've
+ 
+
+ align:start position:0%
+so let's do it with a gold tree so we've
+got s and as we already know s goes
+
+ align:start position:0%
+got s and as we already know s goes
+ 
+
+ align:start position:0%
+got s and as we already know s goes
+well s is the only
+
+ align:start position:0%
+well s is the only
+ 
+
+ align:start position:0%
+well s is the only
+path our current length at s is zero
+
+ align:start position:0%
+path our current length at s is zero
+ 
+
+ align:start position:0%
+path our current length at s is zero
+that's the lowest of all of our lengths
+
+ align:start position:0%
+that's the lowest of all of our lengths
+ 
+
+ align:start position:0%
+that's the lowest of all of our lengths
+on the tree because it's the only length
+
+ align:start position:0%
+on the tree because it's the only length
+ 
+
+ align:start position:0%
+on the tree because it's the only length
+so we go to a b and
+
+ align:start position:0%
+so we go to a b and
+ 
+
+ align:start position:0%
+so we go to a b and
+c okay so what is everyone um it may be
+
+ align:start position:0%
+c okay so what is everyone um it may be
+ 
+
+ align:start position:0%
+c okay so what is everyone um it may be
+hard to see so the length of sa is
+
+ align:start position:0%
+hard to see so the length of sa is
+ 
+
+ align:start position:0%
+hard to see so the length of sa is
+100 the length of SB
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+H oh you're right it's a different tree
+
+ align:start position:0%
+H oh you're right it's a different tree
+ 
+
+ align:start position:0%
+H oh you're right it's a different tree
+I was doing ab and C from the other tree
+
+ align:start position:0%
+I was doing ab and C from the other tree
+ 
+
+ align:start position:0%
+I was doing ab and C from the other tree
+thank you friends for correcting my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foolishness the length of SB is three it
+
+ align:start position:0%
+foolishness the length of SB is three it
+ 
+
+ align:start position:0%
+foolishness the length of SB is three it
+is a different tree I was trying to save
+
+ align:start position:0%
+is a different tree I was trying to save
+ 
+
+ align:start position:0%
+is a different tree I was trying to save
+work that wound up creating more because
+
+ align:start position:0%
+work that wound up creating more because
+ 
+
+ align:start position:0%
+work that wound up creating more because
+someone's going to be confused by this
+
+ align:start position:0%
+someone's going to be confused by this
+ 
+
+ align:start position:0%
+someone's going to be confused by this
+so the length of a e and f are 1034 and
+
+ align:start position:0%
+so the length of a e and f are 1034 and
+ 
+
+ align:start position:0%
+so the length of a e and f are 1034 and
+14 which which one do we choose lexor
+
+ align:start position:0%
+14 which which one do we choose lexor
+ 
+
+ align:start position:0%
+14 which which one do we choose lexor
+graphically it's a we choose that one
+
+ align:start position:0%
+graphically it's a we choose that one
+ 
+
+ align:start position:0%
+graphically it's a we choose that one
+right f is going to be 14 that's a one
+
+ align:start position:0%
+right f is going to be 14 that's a one
+ 
+
+ align:start position:0%
+right f is going to be 14 that's a one
+sorry we oh it's
+
+ align:start position:0%
+sorry we oh it's
+ 
+
+ align:start position:0%
+sorry we oh it's
+four I wrote this problem I should know
+
+ align:start position:0%
+four I wrote this problem I should know
+ 
+
+ align:start position:0%
+four I wrote this problem I should know
+it you're right f f is four my apologies
+
+ align:start position:0%
+it you're right f f is four my apologies
+ 
+
+ align:start position:0%
+it you're right f f is four my apologies
+is once more that's what I get all right
+
+ align:start position:0%
+is once more that's what I get all right
+ 
+
+ align:start position:0%
+is once more that's what I get all right
+I'm going to send over here from now on
+
+ align:start position:0%
+I'm going to send over here from now on
+ 
+
+ align:start position:0%
+I'm going to send over here from now on
+when I write over
+
+ align:start position:0%
+when I write over
+ 
+
+ align:start position:0%
+when I write over
+there okay um so which one of these are
+
+ align:start position:0%
+there okay um so which one of these are
+ 
+
+ align:start position:0%
+there okay um so which one of these are
+we going to choose even with the four
+
+ align:start position:0%
+we going to choose even with the four
+ 
+
+ align:start position:0%
+we going to choose even with the four
+we're going to choose B that's right Le
+
+ align:start position:0%
+we're going to choose B that's right Le
+ 
+
+ align:start position:0%
+we're going to choose B that's right Le
+the graphic be damned it's only for ties
+
+ align:start position:0%
+the graphic be damned it's only for ties
+ 
+
+ align:start position:0%
+the graphic be damned it's only for ties
+we want the shortest path our special
+
+ align:start position:0%
+we want the shortest path our special
+ 
+
+ align:start position:0%
+we want the shortest path our special
+thing with brench and bound is we take
+
+ align:start position:0%
+thing with brench and bound is we take
+ 
+
+ align:start position:0%
+thing with brench and bound is we take
+the currently shortest path whatever it
+
+ align:start position:0%
+the currently shortest path whatever it
+ 
+
+ align:start position:0%
+the currently shortest path whatever it
+is great so we spend B fortunately and
+
+ align:start position:0%
+is great so we spend B fortunately and
+ 
+
+ align:start position:0%
+is great so we spend B fortunately and
+I'm pretty sure I've got this correct
+
+ align:start position:0%
+I'm pretty sure I've got this correct
+ 
+
+ align:start position:0%
+I'm pretty sure I've got this correct
+this time oh wait I've got an even
+
+ align:start position:0%
+this time oh wait I've got an even
+ 
+
+ align:start position:0%
+this time oh wait I've got an even
+better idea I'll just take this little
+
+ align:start position:0%
+better idea I'll just take this little
+ 
+
+ align:start position:0%
+better idea I'll just take this little
+hand sheet with me and then I don't have
+
+ align:start position:0%
+hand sheet with me and then I don't have
+ 
+
+ align:start position:0%
+hand sheet with me and then I don't have
+to look at that at all okay so once we
+
+ align:start position:0%
+to look at that at all okay so once we
+ 
+
+ align:start position:0%
+to look at that at all okay so once we
+expand b b goes to
+
+ align:start position:0%
+expand b b goes to
+ 
+
+ align:start position:0%
+expand b b goes to
+D our path length from B to D is four so
+
+ align:start position:0%
+D our path length from B to D is four so
+ 
+
+ align:start position:0%
+D our path length from B to D is four so
+what will we write next to Little D here
+
+ align:start position:0%
+what will we write next to Little D here
+ 
+
+ align:start position:0%
+what will we write next to Little D here
+seven that's right we add them all
+
+ align:start position:0%
+seven that's right we add them all
+ 
+
+ align:start position:0%
+seven that's right we add them all
+together I'm going to ask you guys again
+
+ align:start position:0%
+together I'm going to ask you guys again
+ 
+
+ align:start position:0%
+together I'm going to ask you guys again
+the next time we do this with theistic
+
+ align:start position:0%
+the next time we do this with theistic
+ 
+
+ align:start position:0%
+the next time we do this with theistic
+which is going to be the next part of
+
+ align:start position:0%
+which is going to be the next part of
+ 
+
+ align:start position:0%
+which is going to be the next part of
+the problem and someone's going to give
+
+ align:start position:0%
+the problem and someone's going to give
+ 
+
+ align:start position:0%
+the problem and someone's going to give
+me the wrong answer next time so stay
+
+ align:start position:0%
+me the wrong answer next time so stay
+ 
+
+ align:start position:0%
+me the wrong answer next time so stay
+tuned for that all right so we've got
+
+ align:start position:0%
+tuned for that all right so we've got
+ 
+
+ align:start position:0%
+tuned for that all right so we've got
+SPD we've got all of these where do we
+
+ align:start position:0%
+SPD we've got all of these where do we
+ 
+
+ align:start position:0%
+SPD we've got all of these where do we
+go next F that's right because currently
+
+ align:start position:0%
+go next F that's right because currently
+ 
+
+ align:start position:0%
+go next F that's right because currently
+four is the shortest because you guys
+
+ align:start position:0%
+four is the shortest because you guys
+ 
+
+ align:start position:0%
+four is the shortest because you guys
+corrected me correctly so SF four is the
+
+ align:start position:0%
+corrected me correctly so SF four is the
+ 
+
+ align:start position:0%
+corrected me correctly so SF four is the
+shortest F only goes to h and what do we
+
+ align:start position:0%
+shortest F only goes to h and what do we
+ 
+
+ align:start position:0%
+shortest F only goes to h and what do we
+write next to the h
+
+ align:start position:0%
+write next to the h
+ 
+
+ align:start position:0%
+write next to the h
+20 that's
+
+ align:start position:0%
+20 that's
+ 
+
+ align:start position:0%
+20 that's
+right 16 + 4 20 all right where's our
+
+ align:start position:0%
+right 16 + 4 20 all right where's our
+ 
+
+ align:start position:0%
+right 16 + 4 20 all right where's our
+current shortest it's the D SBD all
+
+ align:start position:0%
+current shortest it's the D SBD all
+ 
+
+ align:start position:0%
+current shortest it's the D SBD all
+right so SBD D only goes to I and we've
+
+ align:start position:0%
+right so SBD D only goes to I and we've
+ 
+
+ align:start position:0%
+right so SBD D only goes to I and we've
+got a 57 oh I want to get wait a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute 57 I think wait a minute I want
+
+ align:start position:0%
+minute 57 I think wait a minute I want
+ 
+
+ align:start position:0%
+minute 57 I think wait a minute I want
+to get this problem right so we better
+
+ align:start position:0%
+to get this problem right so we better
+ 
+
+ align:start position:0%
+to get this problem right so we better
+actually write the extended list better
+
+ align:start position:0%
+actually write the extended list better
+ 
+
+ align:start position:0%
+actually write the extended list better
+at we because that's the only thing
+
+ align:start position:0%
+at we because that's the only thing
+ 
+
+ align:start position:0%
+at we because that's the only thing
+they're asking us for so first first we
+
+ align:start position:0%
+they're asking us for so first first we
+ 
+
+ align:start position:0%
+they're asking us for so first first we
+extended s then we extended
+
+ align:start position:0%
+extended s then we extended
+ 
+
+ align:start position:0%
+extended s then we extended
+B then we extended
+
+ align:start position:0%
+B then we extended
+ 
+
+ align:start position:0%
+B then we extended
+F then we extended
+
+ align:start position:0%
+F then we extended
+ 
+
+ align:start position:0%
+F then we extended
+D all right so far so good and I have
+
+ align:start position:0%
+D all right so far so good and I have
+ 
+
+ align:start position:0%
+D all right so far so good and I have
+the answer key so I know we're doing it
+
+ align:start position:0%
+the answer key so I know we're doing it
+ 
+
+ align:start position:0%
+the answer key so I know we're doing it
+right okay what are we doing next e
+
+ align:start position:0%
+right okay what are we doing next e
+ 
+
+ align:start position:0%
+right okay what are we doing next e
+that's right so we extend e e goes to
+
+ align:start position:0%
+that's right so we extend e e goes to
+ 
+
+ align:start position:0%
+that's right so we extend e e goes to
+h and when e goes to eight we've got a
+
+ align:start position:0%
+h and when e goes to eight we've got a
+ 
+
+ align:start position:0%
+h and when e goes to eight we've got a
+length of 30 all right who's our winner
+
+ align:start position:0%
+length of 30 all right who's our winner
+ 
+
+ align:start position:0%
+length of 30 all right who's our winner
+now which H sfh that's right sfh is
+
+ align:start position:0%
+now which H sfh that's right sfh is
+ 
+
+ align:start position:0%
+now which H sfh that's right sfh is
+length 20 oh yeah of course I should
+
+ align:start position:0%
+length 20 oh yeah of course I should
+ 
+
+ align:start position:0%
+length 20 oh yeah of course I should
+write an e in here I always forget to do
+
+ align:start position:0%
+write an e in here I always forget to do
+ 
+
+ align:start position:0%
+write an e in here I always forget to do
+that sfh is length 20 so we'll extend H
+
+ align:start position:0%
+that sfh is length 20 so we'll extend H
+ 
+
+ align:start position:0%
+that sfh is length 20 so we'll extend H
+and I'm going to write it here
+
+ align:start position:0%
+and I'm going to write it here
+ 
+
+ align:start position:0%
+and I'm going to write it here
+preemptively all right when we extend H
+
+ align:start position:0%
+preemptively all right when we extend H
+ 
+
+ align:start position:0%
+preemptively all right when we extend H
+over here H only goes to I with length
+
+ align:start position:0%
+over here H only goes to I with length
+ 
+
+ align:start position:0%
+over here H only goes to I with length
+50 great what's the next
+
+ align:start position:0%
+50 great what's the next
+ 
+
+ align:start position:0%
+50 great what's the next
+shortest the next shortest is the other
+
+ align:start position:0%
+shortest the next shortest is the other
+ 
+
+ align:start position:0%
+shortest the next shortest is the other
+H however will we expand it you guess
+
+ align:start position:0%
+H however will we expand it you guess
+ 
+
+ align:start position:0%
+H however will we expand it you guess
+that because I asked that question in
+
+ align:start position:0%
+that because I asked that question in
+ 
+
+ align:start position:0%
+that because I asked that question in
+that way you knew the answer was no why
+
+ align:start position:0%
+that way you knew the answer was no why
+ 
+
+ align:start position:0%
+that way you knew the answer was no why
+don't we expand
+
+ align:start position:0%
+don't we expand
+ 
+
+ align:start position:0%
+don't we expand
+it it's already on the extended list
+
+ align:start position:0%
+it it's already on the extended list
+ 
+
+ align:start position:0%
+it it's already on the extended list
+that's right so since it's already on
+
+ align:start position:0%
+that's right so since it's already on
+ 
+
+ align:start position:0%
+that's right so since it's already on
+the expended extended list this one dies
+
+ align:start position:0%
+the expended extended list this one dies
+ 
+
+ align:start position:0%
+the expended extended list this one dies
+a horrible death I like writing an X
+
+ align:start position:0%
+a horrible death I like writing an X
+ 
+
+ align:start position:0%
+a horrible death I like writing an X
+through it instead of writing a swizzle
+
+ align:start position:0%
+through it instead of writing a swizzle
+ 
+
+ align:start position:0%
+through it instead of writing a swizzle
+at the bottom you can do whatever you
+
+ align:start position:0%
+at the bottom you can do whatever you
+ 
+
+ align:start position:0%
+at the bottom you can do whatever you
+want all right it's gone it's not a
+
+ align:start position:0%
+want all right it's gone it's not a
+ 
+
+ align:start position:0%
+want all right it's gone it's not a
+choice what's the next best
+
+ align:start position:0%
+choice what's the next best
+ 
+
+ align:start position:0%
+choice what's the next best
+one sfhi that's right Ro goes to G and
+
+ align:start position:0%
+one sfhi that's right Ro goes to G and
+ 
+
+ align:start position:0%
+one sfhi that's right Ro goes to G and
+the length is 60 and we've extended I
+
+ align:start position:0%
+the length is 60 and we've extended I
+ 
+
+ align:start position:0%
+the length is 60 and we've extended I
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so question is are we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done the people who say no I like you
+
+ align:start position:0%
+done the people who say no I like you
+ 
+
+ align:start position:0%
+done the people who say no I like you
+you're smart you realize that just
+
+ align:start position:0%
+you're smart you realize that just
+ 
+
+ align:start position:0%
+you're smart you realize that just
+because the G is on there that we can't
+
+ align:start position:0%
+because the G is on there that we can't
+ 
+
+ align:start position:0%
+because the G is on there that we can't
+end how are the people who said yes
+
+ align:start position:0%
+end how are the people who said yes
+ 
+
+ align:start position:0%
+end how are the people who said yes
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+either oblivious or really really smart
+
+ align:start position:0%
+either oblivious or really really smart
+ 
+
+ align:start position:0%
+either oblivious or really really smart
+and I'm going to choose to assume you're
+
+ align:start position:0%
+and I'm going to choose to assume you're
+ 
+
+ align:start position:0%
+and I'm going to choose to assume you're
+all really really smart because the
+
+ align:start position:0%
+all really really smart because the
+ 
+
+ align:start position:0%
+all really really smart because the
+really really smart people said okay yes
+
+ align:start position:0%
+really really smart people said okay yes
+ 
+
+ align:start position:0%
+really really smart people said okay yes
+we're not quite done just because we
+
+ align:start position:0%
+we're not quite done just because we
+ 
+
+ align:start position:0%
+we're not quite done just because we
+added a g we still have to check to make
+
+ align:start position:0%
+added a g we still have to check to make
+ 
+
+ align:start position:0%
+added a g we still have to check to make
+sure there are no length of shorter path
+
+ align:start position:0%
+sure there are no length of shorter path
+ 
+
+ align:start position:0%
+sure there are no length of shorter path
+but look the only one with the shorter
+
+ align:start position:0%
+but look the only one with the shorter
+ 
+
+ align:start position:0%
+but look the only one with the shorter
+path is I which is already on the
+
+ align:start position:0%
+path is I which is already on the
+ 
+
+ align:start position:0%
+path is I which is already on the
+extended list so actually we are done
+
+ align:start position:0%
+extended list so actually we are done
+ 
+
+ align:start position:0%
+extended list so actually we are done
+double Trend we've got it so these are
+
+ align:start position:0%
+double Trend we've got it so these are
+ 
+
+ align:start position:0%
+double Trend we've got it so these are
+the paths we extended in order and our
+
+ align:start position:0%
+the paths we extended in order and our
+ 
+
+ align:start position:0%
+the paths we extended in order and our
+final path is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everyone that's right sfh G I claim that
+
+ align:start position:0%
+everyone that's right sfh G I claim that
+ 
+
+ align:start position:0%
+everyone that's right sfh G I claim that
+is the correct path however Mark is
+
+ align:start position:0%
+is the correct path however Mark is
+ 
+
+ align:start position:0%
+is the correct path however Mark is
+frustrated by branch and bound speed I
+
+ align:start position:0%
+frustrated by branch and bound speed I
+ 
+
+ align:start position:0%
+frustrated by branch and bound speed I
+don't know I wasn't that frustrated
+
+ align:start position:0%
+don't know I wasn't that frustrated
+ 
+
+ align:start position:0%
+don't know I wasn't that frustrated
+seemed pretty good but Mark is
+
+ align:start position:0%
+seemed pretty good but Mark is
+ 
+
+ align:start position:0%
+seemed pretty good but Mark is
+frustrated by brench and brown speed so
+
+ align:start position:0%
+frustrated by brench and brown speed so
+ 
+
+ align:start position:0%
+frustrated by brench and brown speed so
+he reprograms his computer to use a star
+
+ align:start position:0%
+he reprograms his computer to use a star
+ 
+
+ align:start position:0%
+he reprograms his computer to use a star
+Mark counts the number of Subspace
+
+ align:start position:0%
+Mark counts the number of Subspace
+ 
+
+ align:start position:0%
+Mark counts the number of Subspace
+anomalies between each Universe in the
+
+ align:start position:0%
+anomalies between each Universe in the
+ 
+
+ align:start position:0%
+anomalies between each Universe in the
+goal and uses this count as theistic for
+
+ align:start position:0%
+goal and uses this count as theistic for
+ 
+
+ align:start position:0%
+goal and uses this count as theistic for
+a star these numbers are in parentheses
+
+ align:start position:0%
+a star these numbers are in parentheses
+ 
+
+ align:start position:0%
+a star these numbers are in parentheses
+hopefully you can read
+
+ align:start position:0%
+hopefully you can read
+ 
+
+ align:start position:0%
+hopefully you can read
+them yes oh we've got a question right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here ah that a very good question and
+
+ align:start position:0%
+here ah that a very good question and
+ 
+
+ align:start position:0%
+here ah that a very good question and
+the answer is very simple answer you
+
+ align:start position:0%
+the answer is very simple answer you
+ 
+
+ align:start position:0%
+the answer is very simple answer you
+guys tra me no but I should have been
+
+ align:start position:0%
+guys tra me no but I should have been
+ 
+
+ align:start position:0%
+guys tra me no but I should have been
+able to figure it out it does go to CN
+
+ align:start position:0%
+able to figure it out it does go to CN
+ 
+
+ align:start position:0%
+able to figure it out it does go to CN
+D the correct tree which you wouldn't we
+
+ align:start position:0%
+D the correct tree which you wouldn't we
+ 
+
+ align:start position:0%
+D the correct tree which you wouldn't we
+wouldn't have lost points for having the
+
+ align:start position:0%
+wouldn't have lost points for having the
+ 
+
+ align:start position:0%
+wouldn't have lost points for having the
+incorrect tree here we did get the
+
+ align:start position:0%
+incorrect tree here we did get the
+ 
+
+ align:start position:0%
+incorrect tree here we did get the
+correct answer yes the the reason why is
+
+ align:start position:0%
+correct answer yes the the reason why is
+ 
+
+ align:start position:0%
+correct answer yes the the reason why is
+that same reason that very first time I
+
+ align:start position:0%
+that same reason that very first time I
+ 
+
+ align:start position:0%
+that same reason that very first time I
+asked someone something he didn't
+
+ align:start position:0%
+asked someone something he didn't
+ 
+
+ align:start position:0%
+asked someone something he didn't
+remember the C it's easy to forget to go
+
+ align:start position:0%
+remember the C it's easy to forget to go
+ 
+
+ align:start position:0%
+remember the C it's easy to forget to go
+up the tree it does actually have a c
+
+ align:start position:0%
+up the tree it does actually have a c
+ 
+
+ align:start position:0%
+up the tree it does actually have a c
+and d however they are horrendous paths
+
+ align:start position:0%
+and d however they are horrendous paths
+ 
+
+ align:start position:0%
+and d however they are horrendous paths
+they are 100 and 100
+
+ align:start position:0%
+they are 100 and 100
+ 
+
+ align:start position:0%
+they are 100 and 100
+on their on their path length and so it
+
+ align:start position:0%
+on their on their path length and so it
+ 
+
+ align:start position:0%
+on their on their path length and so it
+doesn't matter but you were correct
+
+ align:start position:0%
+doesn't matter but you were correct
+ 
+
+ align:start position:0%
+doesn't matter but you were correct
+official answer we had up there is
+
+ align:start position:0%
+official answer we had up there is
+ 
+
+ align:start position:0%
+official answer we had up there is
+wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+add good question well the question is
+
+ align:start position:0%
+add good question well the question is
+ 
+
+ align:start position:0%
+add good question well the question is
+would the D get added to the children
+
+ align:start position:0%
+would the D get added to the children
+ 
+
+ align:start position:0%
+would the D get added to the children
+after all it's already in the extended
+
+ align:start position:0%
+after all it's already in the extended
+ 
+
+ align:start position:0%
+after all it's already in the extended
+list the answer is we search for and
+
+ align:start position:0%
+list the answer is we search for and
+ 
+
+ align:start position:0%
+list the answer is we search for and
+remove and kill all of the attempts to
+
+ align:start position:0%
+remove and kill all of the attempts to
+ 
+
+ align:start position:0%
+remove and kill all of the attempts to
+extend something that's already on the
+
+ align:start position:0%
+extend something that's already on the
+ 
+
+ align:start position:0%
+extend something that's already on the
+expended list at the time we try to
+
+ align:start position:0%
+expended list at the time we try to
+ 
+
+ align:start position:0%
+expended list at the time we try to
+expand it the time we try to expand it
+
+ align:start position:0%
+expand it the time we try to expand it
+ 
+
+ align:start position:0%
+expand it the time we try to expand it
+is only when it's on the front of the
+
+ align:start position:0%
+is only when it's on the front of the
+ 
+
+ align:start position:0%
+is only when it's on the front of the
+que because it's the currently shortest
+
+ align:start position:0%
+que because it's the currently shortest
+ 
+
+ align:start position:0%
+que because it's the currently shortest
+path so that means they get added it's
+
+ align:start position:0%
+path so that means they get added it's
+ 
+
+ align:start position:0%
+path so that means they get added it's
+just that when it comes time to expand
+
+ align:start position:0%
+just that when it comes time to expand
+ 
+
+ align:start position:0%
+just that when it comes time to expand
+it it will get crossed off no matter
+
+ align:start position:0%
+it it will get crossed off no matter
+ 
+
+ align:start position:0%
+it it will get crossed off no matter
+what turns out it escaped execution
+
+ align:start position:0%
+what turns out it escaped execution
+ 
+
+ align:start position:0%
+what turns out it escaped execution
+because of the fact that we never
+
+ align:start position:0%
+because of the fact that we never
+ 
+
+ align:start position:0%
+because of the fact that we never
+expanded
+
+ align:start position:0%
+expanded
+ 
+
+ align:start position:0%
+expanded
+it so H should go to e as well is the
+
+ align:start position:0%
+it so H should go to e as well is the
+ 
+
+ align:start position:0%
+it so H should go to e as well is the
+question the answer is yes H should go
+
+ align:start position:0%
+question the answer is yes H should go
+ 
+
+ align:start position:0%
+question the answer is yes H should go
+to e as
+
+ align:start position:0%
+to e as
+ 
+
+ align:start position:0%
+to e as
+well a lot slipped past me this time H
+
+ align:start position:0%
+well a lot slipped past me this time H
+ 
+
+ align:start position:0%
+well a lot slipped past me this time H
+should go to e as well with a length of
+
+ align:start position:0%
+should go to e as well with a length of
+ 
+
+ align:start position:0%
+should go to e as well with a length of
+36 and it dies there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one will actually be checked so it
+
+ align:start position:0%
+this one will actually be checked so it
+ 
+
+ align:start position:0%
+this one will actually be checked so it
+actually does make a difference if we
+
+ align:start position:0%
+actually does make a difference if we
+ 
+
+ align:start position:0%
+actually does make a difference if we
+ask how many times was a node um
+
+ align:start position:0%
+ask how many times was a node um
+ 
+
+ align:start position:0%
+ask how many times was a node um
+executed due to not going on the extend
+
+ align:start position:0%
+executed due to not going on the extend
+ 
+
+ align:start position:0%
+executed due to not going on the extend
+due to already being on the extended
+
+ align:start position:0%
+due to already being on the extended
+ 
+
+ align:start position:0%
+due to already being on the extended
+list very good very good notice it
+
+ align:start position:0%
+list very good very good notice it
+ 
+
+ align:start position:0%
+list very good very good notice it
+should be on there we'll get it right
+
+ align:start position:0%
+should be on there we'll get it right
+ 
+
+ align:start position:0%
+should be on there we'll get it right
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+time all right everyone so I'm working
+
+ align:start position:0%
+time all right everyone so I'm working
+ 
+
+ align:start position:0%
+time all right everyone so I'm working
+together with you I made the mistake to
+
+ align:start position:0%
+together with you I made the mistake to
+ 
+
+ align:start position:0%
+together with you I made the mistake to
+easy one to make it can it can mess you
+
+ align:start position:0%
+easy one to make it can it can mess you
+ 
+
+ align:start position:0%
+easy one to make it can it can mess you
+up it didn't this time we're going to
+
+ align:start position:0%
+up it didn't this time we're going to
+ 
+
+ align:start position:0%
+up it didn't this time we're going to
+get it up question
+
+ align:start position:0%
+get it up question
+ 
+
+ align:start position:0%
+get it up question
+if G's the
+
+ align:start position:0%
+if G's the
+ 
+
+ align:start position:0%
+if G's the
+goal get G in
+
+ align:start position:0%
+goal get G in
+ 
+
+ align:start position:0%
+goal get G in
+youres and know the number shorter than
+
+ align:start position:0%
+youres and know the number shorter than
+ 
+
+ align:start position:0%
+youres and know the number shorter than
+anything else do you have to actually
+
+ align:start position:0%
+anything else do you have to actually
+ 
+
+ align:start position:0%
+anything else do you have to actually
+extend it g so the question is do you
+
+ align:start position:0%
+extend it g so the question is do you
+ 
+
+ align:start position:0%
+extend it g so the question is do you
+exist do you actually extend G do you
+
+ align:start position:0%
+exist do you actually extend G do you
+ 
+
+ align:start position:0%
+exist do you actually extend G do you
+should should we even put G in the
+
+ align:start position:0%
+should should we even put G in the
+ 
+
+ align:start position:0%
+should should we even put G in the
+extended list the answer is the answer
+
+ align:start position:0%
+extended list the answer is the answer
+ 
+
+ align:start position:0%
+extended list the answer is the answer
+to that question is it is a matter of
+
+ align:start position:0%
+to that question is it is a matter of
+ 
+
+ align:start position:0%
+to that question is it is a matter of
+taste and in the questions where we in
+
+ align:start position:0%
+taste and in the questions where we in
+ 
+
+ align:start position:0%
+taste and in the questions where we in
+my opinion rather foolishly ask how many
+
+ align:start position:0%
+my opinion rather foolishly ask how many
+ 
+
+ align:start position:0%
+my opinion rather foolishly ask how many
+nodes were extended rather than asking
+
+ align:start position:0%
+nodes were extended rather than asking
+ 
+
+ align:start position:0%
+nodes were extended rather than asking
+you to write them out we generally
+
+ align:start position:0%
+you to write them out we generally
+ 
+
+ align:start position:0%
+you to write them out we generally
+accept the answer where you didn't
+
+ align:start position:0%
+accept the answer where you didn't
+ 
+
+ align:start position:0%
+accept the answer where you didn't
+extend or where you did extend G it's an
+
+ align:start position:0%
+extend or where you did extend G it's an
+ 
+
+ align:start position:0%
+extend or where you did extend G it's an
+implementation detail you can either
+
+ align:start position:0%
+implementation detail you can either
+ 
+
+ align:start position:0%
+implementation detail you can either
+have a fail safe that as soon as it sees
+
+ align:start position:0%
+have a fail safe that as soon as it sees
+ 
+
+ align:start position:0%
+have a fail safe that as soon as it sees
+g at the beginning of the list says
+
+ align:start position:0%
+g at the beginning of the list says
+ 
+
+ align:start position:0%
+g at the beginning of the list says
+we're out we're not going to extend
+
+ align:start position:0%
+we're out we're not going to extend
+ 
+
+ align:start position:0%
+we're out we're not going to extend
+we're done we win or fail safe that when
+
+ align:start position:0%
+we're done we win or fail safe that when
+ 
+
+ align:start position:0%
+we're done we win or fail safe that when
+you're about to extend something and you
+
+ align:start position:0%
+you're about to extend something and you
+ 
+
+ align:start position:0%
+you're about to extend something and you
+do go into the extension process and it
+
+ align:start position:0%
+do go into the extension process and it
+ 
+
+ align:start position:0%
+do go into the extension process and it
+sees that it ends in g that it wins so
+
+ align:start position:0%
+sees that it ends in g that it wins so
+ 
+
+ align:start position:0%
+sees that it ends in g that it wins so
+it is a matter of taste if you kind of
+
+ align:start position:0%
+it is a matter of taste if you kind of
+ 
+
+ align:start position:0%
+it is a matter of taste if you kind of
+like to watch your your little guy doing
+
+ align:start position:0%
+like to watch your your little guy doing
+ 
+
+ align:start position:0%
+like to watch your your little guy doing
+the search wi and have an S and a g you
+
+ align:start position:0%
+the search wi and have an S and a g you
+ 
+
+ align:start position:0%
+the search wi and have an S and a g you
+can put it on if you don't you canot put
+
+ align:start position:0%
+can put it on if you don't you canot put
+ 
+
+ align:start position:0%
+can put it on if you don't you canot put
+it on we won't take off points for
+
+ align:start position:0%
+it on we won't take off points for
+ 
+
+ align:start position:0%
+it on we won't take off points for
+whether or not it has a g at the end
+
+ align:start position:0%
+whether or not it has a g at the end
+ 
+
+ align:start position:0%
+whether or not it has a g at the end
+because clearly if you did all the other
+
+ align:start position:0%
+because clearly if you did all the other
+ 
+
+ align:start position:0%
+because clearly if you did all the other
+crazy stuff correct well you could have
+
+ align:start position:0%
+crazy stuff correct well you could have
+ 
+
+ align:start position:0%
+crazy stuff correct well you could have
+written in a g if you wanted to I think
+
+ align:start position:0%
+written in a g if you wanted to I think
+ 
+
+ align:start position:0%
+written in a g if you wanted to I think
+unless like there's someone who
+
+ align:start position:0%
+unless like there's someone who
+ 
+
+ align:start position:0%
+unless like there's someone who
+missolves the problem right at the end
+
+ align:start position:0%
+missolves the problem right at the end
+ 
+
+ align:start position:0%
+missolves the problem right at the end
+is like oh who cares about G oh no it's
+
+ align:start position:0%
+is like oh who cares about G oh no it's
+ 
+
+ align:start position:0%
+is like oh who cares about G oh no it's
+stuck it's a dead end we lose but that
+
+ align:start position:0%
+stuck it's a dead end we lose but that
+ 
+
+ align:start position:0%
+stuck it's a dead end we lose but that
+would be probably pretty rare all right
+
+ align:start position:0%
+would be probably pretty rare all right
+ 
+
+ align:start position:0%
+would be probably pretty rare all right
+so let's solve the um the AAR so I'm not
+
+ align:start position:0%
+so let's solve the um the AAR so I'm not
+ 
+
+ align:start position:0%
+so let's solve the um the AAR so I'm not
+going to make the same mistake twice we
+
+ align:start position:0%
+going to make the same mistake twice we
+ 
+
+ align:start position:0%
+going to make the same mistake twice we
+go from s to a b e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and S by the way had a value of zero all
+
+ align:start position:0%
+and S by the way had a value of zero all
+ 
+
+ align:start position:0%
+and S by the way had a value of zero all
+right what is the value at
+
+ align:start position:0%
+right what is the value at
+ 
+
+ align:start position:0%
+right what is the value at
+a well I think it's
+
+ align:start position:0%
+a well I think it's
+ 
+
+ align:start position:0%
+a well I think it's
+160 the question is how do we calculate
+
+ align:start position:0%
+160 the question is how do we calculate
+ 
+
+ align:start position:0%
+160 the question is how do we calculate
+this well it's the path that we traveled
+
+ align:start position:0%
+this well it's the path that we traveled
+ 
+
+ align:start position:0%
+this well it's the path that we traveled
+so far plus theistic value at the at the
+
+ align:start position:0%
+so far plus theistic value at the at the
+ 
+
+ align:start position:0%
+so far plus theistic value at the at the
+final
+
+ align:start position:0%
+final
+ 
+
+ align:start position:0%
+final
+node by way this is why someone's going
+
+ align:start position:0%
+node by way this is why someone's going
+ 
+
+ align:start position:0%
+node by way this is why someone's going
+to give me the wrong answer at BD but
+
+ align:start position:0%
+to give me the wrong answer at BD but
+ 
+
+ align:start position:0%
+to give me the wrong answer at BD but
+let's see so we have 160 here okay so SB
+
+ align:start position:0%
+let's see so we have 160 here okay so SB
+ 
+
+ align:start position:0%
+let's see so we have 160 here okay so SB
+we've got a uh what is theistic value
+
+ align:start position:0%
+we've got a uh what is theistic value
+ 
+
+ align:start position:0%
+we've got a uh what is theistic value
+here we've got three for the path and 50
+
+ align:start position:0%
+here we've got three for the path and 50
+ 
+
+ align:start position:0%
+here we've got three for the path and 50
+for the theistic so it's
+
+ align:start position:0%
+for the theistic so it's
+ 
+
+ align:start position:0%
+for the theistic so it's
+53 all right SE what have we got here
+
+ align:start position:0%
+53 all right SE what have we got here
+ 
+
+ align:start position:0%
+53 all right SE what have we got here
+we've got 14 for the path 56 for the
+
+ align:start position:0%
+we've got 14 for the path 56 for the
+ 
+
+ align:start position:0%
+we've got 14 for the path 56 for the
+heris so it's
+
+ align:start position:0%
+heris so it's
+ 
+
+ align:start position:0%
+heris so it's
+70 all right SF we've got four for the
+
+ align:start position:0%
+70 all right SF we've got four for the
+ 
+
+ align:start position:0%
+70 all right SF we've got four for the
+path 50 for the herti
+
+ align:start position:0%
+path 50 for the herti
+ 
+
+ align:start position:0%
+path 50 for the herti
+54 okay who's our winner it's B again
+
+ align:start position:0%
+54 okay who's our winner it's B again
+ 
+
+ align:start position:0%
+54 okay who's our winner it's B again
+barely but it is the winner extended
+
+ align:start position:0%
+barely but it is the winner extended
+ 
+
+ align:start position:0%
+barely but it is the winner extended
+list up here SB all right b as we saw
+
+ align:start position:0%
+list up here SB all right b as we saw
+ 
+
+ align:start position:0%
+list up here SB all right b as we saw
+goes only to
+
+ align:start position:0%
+goes only to
+ 
+
+ align:start position:0%
+goes only to
+D what is the what is the value that I
+
+ align:start position:0%
+D what is the what is the value that I
+ 
+
+ align:start position:0%
+D what is the what is the value that I
+should write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay I am happy I heard all the
+
+ align:start position:0%
+here okay I am happy I heard all the
+ 
+
+ align:start position:0%
+here okay I am happy I heard all the
+things that I expected to hear I heard
+
+ align:start position:0%
+things that I expected to hear I heard
+ 
+
+ align:start position:0%
+things that I expected to hear I heard
+the correct answer which is uh 57 I also
+
+ align:start position:0%
+the correct answer which is uh 57 I also
+ 
+
+ align:start position:0%
+the correct answer which is uh 57 I also
+heard someone say
+
+ align:start position:0%
+heard someone say
+ 
+
+ align:start position:0%
+heard someone say
+107 so why is it 57 and not
+
+ align:start position:0%
+107 so why is it 57 and not
+ 
+
+ align:start position:0%
+107 so why is it 57 and not
+107 someone does it this way every time
+
+ align:start position:0%
+107 someone does it this way every time
+ 
+
+ align:start position:0%
+107 someone does it this way every time
+do not add up all the heres of law in
+
+ align:start position:0%
+do not add up all the heres of law in
+ 
+
+ align:start position:0%
+do not add up all the heres of law in
+the way I'll try to explain to why you
+
+ align:start position:0%
+the way I'll try to explain to why you
+ 
+
+ align:start position:0%
+the way I'll try to explain to why you
+never want to do that theistic value at
+
+ align:start position:0%
+never want to do that theistic value at
+ 
+
+ align:start position:0%
+never want to do that theistic value at
+any given node
+
+ align:start position:0%
+any given node
+ 
+
+ align:start position:0%
+any given node
+says given that I'm here how much work
+
+ align:start position:0%
+says given that I'm here how much work
+ 
+
+ align:start position:0%
+says given that I'm here how much work
+do I think I have left to get to the end
+
+ align:start position:0%
+do I think I have left to get to the end
+ 
+
+ align:start position:0%
+do I think I have left to get to the end
+all right it's sort of like let's guess
+
+ align:start position:0%
+all right it's sort of like let's guess
+ 
+
+ align:start position:0%
+all right it's sort of like let's guess
+the last few nodes in the path that we
+
+ align:start position:0%
+the last few nodes in the path that we
+ 
+
+ align:start position:0%
+the last few nodes in the path that we
+haven't done out yet so you can see why
+
+ align:start position:0%
+haven't done out yet so you can see why
+ 
+
+ align:start position:0%
+haven't done out yet so you can see why
+it would be bad to add that every add
+
+ align:start position:0%
+it would be bad to add that every add
+ 
+
+ align:start position:0%
+it would be bad to add that every add
+that for every node in your list because
+
+ align:start position:0%
+that for every node in your list because
+ 
+
+ align:start position:0%
+that for every node in your list because
+then you're at you're double counting
+
+ align:start position:0%
+then you're at you're double counting
+ 
+
+ align:start position:0%
+then you're at you're double counting
+all the last nodes so add the path so
+
+ align:start position:0%
+all the last nodes so add the path so
+ 
+
+ align:start position:0%
+all the last nodes so add the path so
+far to the very finalistic that's 3 plus
+
+ align:start position:0%
+far to the very finalistic that's 3 plus
+ 
+
+ align:start position:0%
+far to the very finalistic that's 3 plus
+4 plus the 50 that's with D is 57 so our
+
+ align:start position:0%
+4 plus the 50 that's with D is 57 so our
+ 
+
+ align:start position:0%
+4 plus the 50 that's with D is 57 so our
+current winner then
+
+ align:start position:0%
+current winner then
+ 
+
+ align:start position:0%
+current winner then
+is 54 with f just same as last time F
+
+ align:start position:0%
+is 54 with f just same as last time F
+ 
+
+ align:start position:0%
+is 54 with f just same as last time F
+goes to
+
+ align:start position:0%
+goes to
+ 
+
+ align:start position:0%
+goes to
+h and what's our total value at
+
+ align:start position:0%
+h and what's our total value at
+ 
+
+ align:start position:0%
+h and what's our total value at
+H 20 plus that's a 39
+
+ align:start position:0%
+H 20 plus that's a 39
+ 
+
+ align:start position:0%
+H 20 plus that's a 39
+59 so who wins now D with
+
+ align:start position:0%
+59 so who wins now D with
+ 
+
+ align:start position:0%
+59 so who wins now D with
+57 but uh we extended F yes good all
+
+ align:start position:0%
+57 but uh we extended F yes good all
+ 
+
+ align:start position:0%
+57 but uh we extended F yes good all
+right so D with 57 all right so d was
+
+ align:start position:0%
+right so D with 57 all right so d was
+ 
+
+ align:start position:0%
+right so D with 57 all right so d was
+not one of the ones that I tricked
+
+ align:start position:0%
+not one of the ones that I tricked
+ 
+
+ align:start position:0%
+not one of the ones that I tricked
+myself with d only goes to
+
+ align:start position:0%
+myself with d only goes to
+ 
+
+ align:start position:0%
+myself with d only goes to
+I what's our value at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I think our value is 57 because I has
+
+ align:start position:0%
+I I think our value is 57 because I has
+ 
+
+ align:start position:0%
+I I think our value is 57 because I has
+a hero stick of
+
+ align:start position:0%
+a hero stick of
+ 
+
+ align:start position:0%
+a hero stick of
+zero yes I has a hero stick of zero our
+
+ align:start position:0%
+zero yes I has a hero stick of zero our
+ 
+
+ align:start position:0%
+zero yes I has a hero stick of zero our
+value at I is
+
+ align:start position:0%
+value at I is
+ 
+
+ align:start position:0%
+value at I is
+57 okay and I extended D who's the
+
+ align:start position:0%
+57 okay and I extended D who's the
+ 
+
+ align:start position:0%
+57 okay and I extended D who's the
+winner now I okay so I is the winner
+
+ align:start position:0%
+winner now I okay so I is the winner
+ 
+
+ align:start position:0%
+winner now I okay so I is the winner
+with i as a winner we extend I I goes to
+
+ align:start position:0%
+with i as a winner we extend I I goes to
+ 
+
+ align:start position:0%
+with i as a winner we extend I I goes to
+c d haha good call whoever back there
+
+ align:start position:0%
+c d haha good call whoever back there
+ 
+
+ align:start position:0%
+c d haha good call whoever back there
+figured out my secret error before CD
+
+ align:start position:0%
+figured out my secret error before CD
+ 
+
+ align:start position:0%
+figured out my secret error before CD
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+g c h and
+
+ align:start position:0%
+g c h and
+ 
+
+ align:start position:0%
+g c h and
+G oh you're right we already went to D
+
+ align:start position:0%
+G oh you're right we already went to D
+ 
+
+ align:start position:0%
+G oh you're right we already went to D
+aha c h and G you're
+
+ align:start position:0%
+aha c h and G you're
+ 
+
+ align:start position:0%
+aha c h and G you're
+correct everyone see that CH H and G
+
+ align:start position:0%
+correct everyone see that CH H and G
+ 
+
+ align:start position:0%
+correct everyone see that CH H and G
+absolutely right I goes to CH H and G so
+
+ align:start position:0%
+absolutely right I goes to CH H and G so
+ 
+
+ align:start position:0%
+absolutely right I goes to CH H and G so
+the path to see h& G is is a is a hard
+
+ align:start position:0%
+the path to see h& G is is a is a hard
+ 
+
+ align:start position:0%
+the path to see h& G is is a is a hard
+path um we've got to see we got what did
+
+ align:start position:0%
+path um we've got to see we got what did
+ 
+
+ align:start position:0%
+path um we've got to see we got what did
+we have 57 + 50 is
+
+ align:start position:0%
+we have 57 + 50 is
+ 
+
+ align:start position:0%
+we have 57 + 50 is
+127 oh and by way c g and H we've got to
+
+ align:start position:0%
+127 oh and by way c g and H we've got to
+ 
+
+ align:start position:0%
+127 oh and by way c g and H we've got to
+do it in L graphic order so 127 to C to
+
+ align:start position:0%
+do it in L graphic order so 127 to C to
+ 
+
+ align:start position:0%
+do it in L graphic order so 127 to C to
+G we have
+
+ align:start position:0%
+G we have
+ 
+
+ align:start position:0%
+G we have
+67 and to H we
+
+ align:start position:0%
+67 and to H we
+ 
+
+ align:start position:0%
+67 and to H we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+87 okay so who wins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now H H with 59 that's right
+
+ align:start position:0%
+now H H with 59 that's right
+ 
+
+ align:start position:0%
+now H H with 59 that's right
+H with 59 and as we already know because
+
+ align:start position:0%
+H with 59 and as we already know because
+ 
+
+ align:start position:0%
+H with 59 and as we already know because
+it was the winner last time H with 59
+
+ align:start position:0%
+it was the winner last time H with 59
+ 
+
+ align:start position:0%
+it was the winner last time H with 59
+goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I which has I believe um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50 well it still gets added remember
+
+ align:start position:0%
+50 well it still gets added remember
+ 
+
+ align:start position:0%
+50 well it still gets added remember
+we're only going to kill it when it gets
+
+ align:start position:0%
+we're only going to kill it when it gets
+ 
+
+ align:start position:0%
+we're only going to kill it when it gets
+extended so who's the shortest so you a
+
+ align:start position:0%
+extended so who's the shortest so you a
+ 
+
+ align:start position:0%
+extended so who's the shortest so you a
+step ahead whoever asked me the question
+
+ align:start position:0%
+step ahead whoever asked me the question
+ 
+
+ align:start position:0%
+step ahead whoever asked me the question
+who's the shortest H also goes to e h
+
+ align:start position:0%
+who's the shortest H also goes to e h
+ 
+
+ align:start position:0%
+who's the shortest H also goes to e h
+also goes to E absolutely right all
+
+ align:start position:0%
+also goes to E absolutely right all
+ 
+
+ align:start position:0%
+also goes to E absolutely right all
+right H also goes to E I was getting
+
+ align:start position:0%
+right H also goes to E I was getting
+ 
+
+ align:start position:0%
+right H also goes to E I was getting
+ahead of myself here H also goes to e
+
+ align:start position:0%
+ahead of myself here H also goes to e
+ 
+
+ align:start position:0%
+ahead of myself here H also goes to e
+with a length of extra 16 so we've got a
+
+ align:start position:0%
+with a length of extra 16 so we've got a
+ 
+
+ align:start position:0%
+with a length of extra 16 so we've got a
+20 + 16 is 36 + 56 is
+
+ align:start position:0%
+20 + 16 is 36 + 56 is
+ 
+
+ align:start position:0%
+20 + 16 is 36 + 56 is
+92 all right that's
+
+ align:start position:0%
+92 all right that's
+ 
+
+ align:start position:0%
+92 all right that's
+good so who's the
+
+ align:start position:0%
+good so who's the
+ 
+
+ align:start position:0%
+good so who's the
+shortest I is the shortest do we extend
+
+ align:start position:0%
+shortest I is the shortest do we extend
+ 
+
+ align:start position:0%
+shortest I is the shortest do we extend
+it no it's on the extended
+
+ align:start position:0%
+it no it's on the extended
+ 
+
+ align:start position:0%
+it no it's on the extended
+list all right who's the shortest
+
+ align:start position:0%
+list all right who's the shortest
+ 
+
+ align:start position:0%
+list all right who's the shortest
+now it's hard to read but the shortest
+
+ align:start position:0%
+now it's hard to read but the shortest
+ 
+
+ align:start position:0%
+now it's hard to read but the shortest
+is this 67 on the G so we're done we win
+
+ align:start position:0%
+is this 67 on the G so we're done we win
+ 
+
+ align:start position:0%
+is this 67 on the G so we're done we win
+our path is SBD i g yay for a star gets
+
+ align:start position:0%
+our path is SBD i g yay for a star gets
+ 
+
+ align:start position:0%
+our path is SBD i g yay for a star gets
+the right answer right
+
+ align:start position:0%
+the right answer right
+ 
+
+ align:start position:0%
+the right answer right
+no ah unfortunately not so what happened
+
+ align:start position:0%
+no ah unfortunately not so what happened
+ 
+
+ align:start position:0%
+no ah unfortunately not so what happened
+here why did we not get the right answer
+
+ align:start position:0%
+here why did we not get the right answer
+ 
+
+ align:start position:0%
+here why did we not get the right answer
+be as specific as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible what are people saying about
+
+ align:start position:0%
+possible what are people saying about
+ 
+
+ align:start position:0%
+possible what are people saying about
+heris
+
+ align:start position:0%
+heris
+ 
+
+ align:start position:0%
+heris
+sixs all right people are saying
+
+ align:start position:0%
+sixs all right people are saying
+ 
+
+ align:start position:0%
+sixs all right people are saying
+theistic must be consistent that is both
+
+ align:start position:0%
+theistic must be consistent that is both
+ 
+
+ align:start position:0%
+theistic must be consistent that is both
+correct and specific spefic so I applaud
+
+ align:start position:0%
+correct and specific spefic so I applaud
+ 
+
+ align:start position:0%
+correct and specific spefic so I applaud
+you too easy to say theistic was UN
+
+ align:start position:0%
+you too easy to say theistic was UN
+ 
+
+ align:start position:0%
+you too easy to say theistic was UN
+admissible it actually was completely
+
+ align:start position:0%
+admissible it actually was completely
+ 
+
+ align:start position:0%
+admissible it actually was completely
+admissible everywhere so that leads us
+
+ align:start position:0%
+admissible everywhere so that leads us
+ 
+
+ align:start position:0%
+admissible everywhere so that leads us
+into our very last point for the day
+
+ align:start position:0%
+into our very last point for the day
+ 
+
+ align:start position:0%
+into our very last point for the day
+what the hell are these juristic
+
+ align:start position:0%
+what the hell are these juristic
+ 
+
+ align:start position:0%
+what the hell are these juristic
+consistency and admissibility things and
+
+ align:start position:0%
+consistency and admissibility things and
+ 
+
+ align:start position:0%
+consistency and admissibility things and
+why do I care well the reason why you
+
+ align:start position:0%
+why do I care well the reason why you
+ 
+
+ align:start position:0%
+why do I care well the reason why you
+care is manyfold one of which is that
+
+ align:start position:0%
+care is manyfold one of which is that
+ 
+
+ align:start position:0%
+care is manyfold one of which is that
+it's almost guaranteed to be on the quiz
+
+ align:start position:0%
+it's almost guaranteed to be on the quiz
+ 
+
+ align:start position:0%
+it's almost guaranteed to be on the quiz
+but what are they admissibility is a
+
+ align:start position:0%
+but what are they admissibility is a
+ 
+
+ align:start position:0%
+but what are they admissibility is a
+check at every point to make sure your
+
+ align:start position:0%
+check at every point to make sure your
+ 
+
+ align:start position:0%
+check at every point to make sure your
+ceris at that point which is supposed to
+
+ align:start position:0%
+ceris at that point which is supposed to
+ 
+
+ align:start position:0%
+ceris at that point which is supposed to
+be an estimate of how much work you have
+
+ align:start position:0%
+be an estimate of how much work you have
+ 
+
+ align:start position:0%
+be an estimate of how much work you have
+left to do is always an under estimate
+
+ align:start position:0%
+left to do is always an under estimate
+ 
+
+ align:start position:0%
+left to do is always an under estimate
+or an accurate estimate it can never be
+
+ align:start position:0%
+or an accurate estimate it can never be
+ 
+
+ align:start position:0%
+or an accurate estimate it can never be
+an overestimate why not well as Patrick
+
+ align:start position:0%
+an overestimate why not well as Patrick
+ 
+
+ align:start position:0%
+an overestimate why not well as Patrick
+showed you with his mostly correct
+
+ align:start position:0%
+showed you with his mostly correct
+ 
+
+ align:start position:0%
+showed you with his mostly correct
+example on in lecture if it's an
+
+ align:start position:0%
+example on in lecture if it's an
+ 
+
+ align:start position:0%
+example on in lecture if it's an
+overestimate it's never going to expand
+
+ align:start position:0%
+overestimate it's never going to expand
+ 
+
+ align:start position:0%
+overestimate it's never going to expand
+that node because it's going to think
+
+ align:start position:0%
+that node because it's going to think
+ 
+
+ align:start position:0%
+that node because it's going to think
+you know if you write 1 million as a
+
+ align:start position:0%
+you know if you write 1 million as a
+ 
+
+ align:start position:0%
+you know if you write 1 million as a
+heuristic it's going to think it needs
+
+ align:start position:0%
+heuristic it's going to think it needs
+ 
+
+ align:start position:0%
+heuristic it's going to think it needs
+to do 1 million after it's done going
+
+ align:start position:0%
+to do 1 million after it's done going
+ 
+
+ align:start position:0%
+to do 1 million after it's done going
+that way it's not going to want to go
+
+ align:start position:0%
+that way it's not going to want to go
+ 
+
+ align:start position:0%
+that way it's not going to want to go
+that way all right so it's always got to
+
+ align:start position:0%
+that way all right so it's always got to
+ 
+
+ align:start position:0%
+that way all right so it's always got to
+be an underestimate or an equal estimate
+
+ align:start position:0%
+be an underestimate or an equal estimate
+ 
+
+ align:start position:0%
+be an underestimate or an equal estimate
+but let's say that you as at the quiz
+
+ align:start position:0%
+but let's say that you as at the quiz
+ 
+
+ align:start position:0%
+but let's say that you as at the quiz
+and you forget Mark told me this you
+
+ align:start position:0%
+and you forget Mark told me this you
+ 
+
+ align:start position:0%
+and you forget Mark told me this you
+didn't bring any notes you're just
+
+ align:start position:0%
+didn't bring any notes you're just
+ 
+
+ align:start position:0%
+didn't bring any notes you're just
+having a brain free oh know is it
+
+ align:start position:0%
+having a brain free oh know is it
+ 
+
+ align:start position:0%
+having a brain free oh know is it
+supposed to be an overestimate or an
+
+ align:start position:0%
+supposed to be an overestimate or an
+ 
+
+ align:start position:0%
+supposed to be an overestimate or an
+under estimate I can't remember which
+
+ align:start position:0%
+under estimate I can't remember which
+ 
+
+ align:start position:0%
+under estimate I can't remember which
+one how can I figure it out how can I
+
+ align:start position:0%
+one how can I figure it out how can I
+ 
+
+ align:start position:0%
+one how can I figure it out how can I
+figure it out I propose you the
+
+ align:start position:0%
+figure it out I propose you the
+ 
+
+ align:start position:0%
+figure it out I propose you the
+following calm soothing Mantra Sutra
+
+ align:start position:0%
+following calm soothing Mantra Sutra
+ 
+
+ align:start position:0%
+following calm soothing Mantra Sutra
+that will help protect you think to
+
+ align:start position:0%
+that will help protect you think to
+ 
+
+ align:start position:0%
+that will help protect you think to
+yourself of the following question does
+
+ align:start position:0%
+yourself of the following question does
+ 
+
+ align:start position:0%
+yourself of the following question does
+we know that a star sometimes messes up
+
+ align:start position:0%
+we know that a star sometimes messes up
+ 
+
+ align:start position:0%
+we know that a star sometimes messes up
+with the heuristic does branch and bound
+
+ align:start position:0%
+with the heuristic does branch and bound
+ 
+
+ align:start position:0%
+with the heuristic does branch and bound
+always get it right yes what heuristic
+
+ align:start position:0%
+always get it right yes what heuristic
+ 
+
+ align:start position:0%
+always get it right yes what heuristic
+values does branch and bound add
+
+ align:start position:0%
+values does branch and bound add
+ 
+
+ align:start position:0%
+values does branch and bound add
+everywhere zero right it has no heris
+
+ align:start position:0%
+everywhere zero right it has no heris
+ 
+
+ align:start position:0%
+everywhere zero right it has no heris
+get essentially add zero is zero an
+
+ align:start position:0%
+get essentially add zero is zero an
+ 
+
+ align:start position:0%
+get essentially add zero is zero an
+overestimate or underestimate an
+
+ align:start position:0%
+overestimate or underestimate an
+ 
+
+ align:start position:0%
+overestimate or underestimate an
+underestimate therefore since branch and
+
+ align:start position:0%
+underestimate therefore since branch and
+ 
+
+ align:start position:0%
+underestimate therefore since branch and
+bound always works the one you're
+
+ align:start position:0%
+bound always works the one you're
+ 
+
+ align:start position:0%
+bound always works the one you're
+looking for is underestimate I know from
+
+ align:start position:0%
+looking for is underestimate I know from
+ 
+
+ align:start position:0%
+looking for is underestimate I know from
+when I was taking the class I always had
+
+ align:start position:0%
+when I was taking the class I always had
+ 
+
+ align:start position:0%
+when I was taking the class I always had
+a moment where I had to spend like two
+
+ align:start position:0%
+a moment where I had to spend like two
+ 
+
+ align:start position:0%
+a moment where I had to spend like two
+minutes convincing myself okay I'm going
+
+ align:start position:0%
+minutes convincing myself okay I'm going
+ 
+
+ align:start position:0%
+minutes convincing myself okay I'm going
+for underestimate not overestimate this
+
+ align:start position:0%
+for underestimate not overestimate this
+ 
+
+ align:start position:0%
+for underestimate not overestimate this
+will help it will take fewer than two
+
+ align:start position:0%
+will help it will take fewer than two
+ 
+
+ align:start position:0%
+will help it will take fewer than two
+minutes to do that so what is
+
+ align:start position:0%
+minutes to do that so what is
+ 
+
+ align:start position:0%
+minutes to do that so what is
+consistency consistency is a Little Bit
+
+ align:start position:0%
+consistency consistency is a Little Bit
+ 
+
+ align:start position:0%
+consistency consistency is a Little Bit
+Stronger of a claim when you claim that
+
+ align:start position:0%
+Stronger of a claim when you claim that
+ 
+
+ align:start position:0%
+Stronger of a claim when you claim that
+a graph is consistent what you're saying
+
+ align:start position:0%
+a graph is consistent what you're saying
+ 
+
+ align:start position:0%
+a graph is consistent what you're saying
+is between any two nodes or to do it
+
+ align:start position:0%
+is between any two nodes or to do it
+ 
+
+ align:start position:0%
+is between any two nodes or to do it
+more simply between any two adjacent
+
+ align:start position:0%
+more simply between any two adjacent
+ 
+
+ align:start position:0%
+more simply between any two adjacent
+nodes the distance between the
+
+ align:start position:0%
+nodes the distance between the
+ 
+
+ align:start position:0%
+nodes the distance between the
+heuristics is less than the distance
+
+ align:start position:0%
+heuristics is less than the distance
+ 
+
+ align:start position:0%
+heuristics is less than the distance
+between the nodes in other words it's
+
+ align:start position:0%
+between the nodes in other words it's
+ 
+
+ align:start position:0%
+between the nodes in other words it's
+sort of like admissibility is this sort
+
+ align:start position:0%
+sort of like admissibility is this sort
+ 
+
+ align:start position:0%
+sort of like admissibility is this sort
+of like consistency between every node
+
+ align:start position:0%
+of like consistency between every node
+ 
+
+ align:start position:0%
+of like consistency between every node
+and G whereas consistency is consistency
+
+ align:start position:0%
+and G whereas consistency is consistency
+ 
+
+ align:start position:0%
+and G whereas consistency is consistency
+between every node in every other node
+
+ align:start position:0%
+between every node in every other node
+ 
+
+ align:start position:0%
+between every node in every other node
+all right consistency is a stronger
+
+ align:start position:0%
+all right consistency is a stronger
+ 
+
+ align:start position:0%
+all right consistency is a stronger
+claim any graph that's consistent is
+
+ align:start position:0%
+claim any graph that's consistent is
+ 
+
+ align:start position:0%
+claim any graph that's consistent is
+always admissible any graph that is
+
+ align:start position:0%
+always admissible any graph that is
+ 
+
+ align:start position:0%
+always admissible any graph that is
+inadmissible is always inconsistent
+
+ align:start position:0%
+inadmissible is always inconsistent
+ 
+
+ align:start position:0%
+inadmissible is always inconsistent
+that's the Contra positive
+
+ align:start position:0%
+that's the Contra positive
+ 
+
+ align:start position:0%
+that's the Contra positive
+L equal to is still okay equal to is
+
+ align:start position:0%
+L equal to is still okay equal to is
+ 
+
+ align:start position:0%
+L equal to is still okay equal to is
+always okay that's great it's a perfect
+
+ align:start position:0%
+always okay that's great it's a perfect
+ 
+
+ align:start position:0%
+always okay that's great it's a perfect
+estimate but never greater now if a
+
+ align:start position:0%
+estimate but never greater now if a
+ 
+
+ align:start position:0%
+estimate but never greater now if a
+graph is inconsistent will you lose will
+
+ align:start position:0%
+graph is inconsistent will you lose will
+ 
+
+ align:start position:0%
+graph is inconsistent will you lose will
+you lose why is it called admissible
+
+ align:start position:0%
+you lose why is it called admissible
+ 
+
+ align:start position:0%
+you lose why is it called admissible
+then if you can if if if it's sometimes
+
+ align:start position:0%
+then if you can if if if it's sometimes
+ 
+
+ align:start position:0%
+then if you can if if if it's sometimes
+not admissible the answer is why do why
+
+ align:start position:0%
+not admissible the answer is why do why
+ 
+
+ align:start position:0%
+not admissible the answer is why do why
+do we lose the answer is the extended
+
+ align:start position:0%
+do we lose the answer is the extended
+ 
+
+ align:start position:0%
+do we lose the answer is the extended
+list and you see that here if a graph is
+
+ align:start position:0%
+list and you see that here if a graph is
+ 
+
+ align:start position:0%
+list and you see that here if a graph is
+admissible you will always get the right
+
+ align:start position:0%
+admissible you will always get the right
+ 
+
+ align:start position:0%
+admissible you will always get the right
+answer and uh you'll always get the
+
+ align:start position:0%
+answer and uh you'll always get the
+ 
+
+ align:start position:0%
+answer and uh you'll always get the
+right answer unless you use an extended
+
+ align:start position:0%
+right answer unless you use an extended
+ 
+
+ align:start position:0%
+right answer unless you use an extended
+list because you're checking for from
+
+ align:start position:0%
+list because you're checking for from
+ 
+
+ align:start position:0%
+list because you're checking for from
+every node to the goal node and you're
+
+ align:start position:0%
+every node to the goal node and you're
+ 
+
+ align:start position:0%
+every node to the goal node and you're
+sure that your estimates are right but
+
+ align:start position:0%
+sure that your estimates are right but
+ 
+
+ align:start position:0%
+sure that your estimates are right but
+if estimates within nodes aren't correct
+
+ align:start position:0%
+if estimates within nodes aren't correct
+ 
+
+ align:start position:0%
+if estimates within nodes aren't correct
+you might go through them out of order
+
+ align:start position:0%
+you might go through them out of order
+ 
+
+ align:start position:0%
+you might go through them out of order
+and that violates your assumption that
+
+ align:start position:0%
+and that violates your assumption that
+ 
+
+ align:start position:0%
+and that violates your assumption that
+you made when you decide to use the
+
+ align:start position:0%
+you made when you decide to use the
+ 
+
+ align:start position:0%
+you made when you decide to use the
+extended list that you would always go
+
+ align:start position:0%
+extended list that you would always go
+ 
+
+ align:start position:0%
+extended list that you would always go
+through the sort of the subgraphs in
+
+ align:start position:0%
+through the sort of the subgraphs in
+ 
+
+ align:start position:0%
+through the sort of the subgraphs in
+order this graph is very expertly
+
+ align:start position:0%
+order this graph is very expertly
+ 
+
+ align:start position:0%
+order this graph is very expertly
+crafted to do that to you because I
+
+ align:start position:0%
+crafted to do that to you because I
+ 
+
+ align:start position:0%
+crafted to do that to you because I
+might as well be sort of a bottleneck
+
+ align:start position:0%
+might as well be sort of a bottleneck
+ 
+
+ align:start position:0%
+might as well be sort of a bottleneck
+goal node and I has an inconsistency
+
+ align:start position:0%
+goal node and I has an inconsistency
+ 
+
+ align:start position:0%
+goal node and I has an inconsistency
+there's a few other inconsistencies in
+
+ align:start position:0%
+there's a few other inconsistencies in
+ 
+
+ align:start position:0%
+there's a few other inconsistencies in
+this graph but they don't do anything to
+
+ align:start position:0%
+this graph but they don't do anything to
+ 
+
+ align:start position:0%
+this graph but they don't do anything to
+you in fact even eiss abilities
+
+ align:start position:0%
+you in fact even eiss abilities
+ 
+
+ align:start position:0%
+you in fact even eiss abilities
+sometimes don't mess you up so you can't
+
+ align:start position:0%
+sometimes don't mess you up so you can't
+ 
+
+ align:start position:0%
+sometimes don't mess you up so you can't
+just say blindly it's in admissible so
+
+ align:start position:0%
+just say blindly it's in admissible so
+ 
+
+ align:start position:0%
+just say blindly it's in admissible so
+it will never work it might work it
+
+ align:start position:0%
+it will never work it might work it
+ 
+
+ align:start position:0%
+it will never work it might work it
+turns out the only inconsistency that
+
+ align:start position:0%
+turns out the only inconsistency that
+ 
+
+ align:start position:0%
+turns out the only inconsistency that
+matters here is not the inconsistency
+
+ align:start position:0%
+matters here is not the inconsistency
+ 
+
+ align:start position:0%
+matters here is not the inconsistency
+between say s and and f that doesn't
+
+ align:start position:0%
+between say s and and f that doesn't
+ 
+
+ align:start position:0%
+between say s and and f that doesn't
+turn out to matter it's the
+
+ align:start position:0%
+turn out to matter it's the
+ 
+
+ align:start position:0%
+turn out to matter it's the
+inconsistency between um some of these
+
+ align:start position:0%
+inconsistency between um some of these
+ 
+
+ align:start position:0%
+inconsistency between um some of these
+nodes including I and H specifically
+
+ align:start position:0%
+nodes including I and H specifically
+ 
+
+ align:start position:0%
+nodes including I and H specifically
+so have a good weekend come in on Monday
+
+ align:start position:0%
+so have a good weekend come in on Monday
+ 
+
+ align:start position:0%
+so have a good weekend come in on Monday
+and Tuesday the tutorial ask about the Q
+
+ align:start position:0%
+and Tuesday the tutorial ask about the Q
+ 
+
+ align:start position:0%
+and Tuesday the tutorial ask about the Q
+method or or other methods ask about
+
+ align:start position:0%
+method or or other methods ask about
+ 
+
+ align:start position:0%
+method or or other methods ask about
+anything that's ningling in your brain
+
+ align:start position:0%
+anything that's ningling in your brain
+ 
+
+ align:start position:0%
+anything that's ningling in your brain
+but hopefully you guys have got this
+
+ align:start position:0%
+but hopefully you guys have got this
+ 
+
+ align:start position:0%
+but hopefully you guys have got this
+you're going to do fine
\ No newline at end of file
diff --git a/TnS8kI_KuJc.txt b/TnS8kI_KuJc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c171e1731f9862ec9ecc36f4e119befa044fa2bf
--- /dev/null
+++ b/TnS8kI_KuJc.txt
@@ -0,0 +1,6747 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's start with with a simple but
+
+ align:start position:0%
+so let's start with with a simple but
+ 
+
+ align:start position:0%
+so let's start with with a simple but
+quite illustrative example so suppose
+
+ align:start position:0%
+quite illustrative example so suppose
+ 
+
+ align:start position:0%
+quite illustrative example so suppose
+you're a bookie and what bookie does he
+
+ align:start position:0%
+you're a bookie and what bookie does he
+ 
+
+ align:start position:0%
+you're a bookie and what bookie does he
+accept bet on on on the horses sets the
+
+ align:start position:0%
+accept bet on on on the horses sets the
+ 
+
+ align:start position:0%
+accept bet on on on the horses sets the
+odds and then pays money back
+
+ align:start position:0%
+odds and then pays money back
+ 
+
+ align:start position:0%
+odds and then pays money back
+probably collects a fee somewhere in
+
+ align:start position:0%
+probably collects a fee somewhere in
+ 
+
+ align:start position:0%
+probably collects a fee somewhere in
+between so suppose it is a good bookie
+
+ align:start position:0%
+between so suppose it is a good bookie
+ 
+
+ align:start position:0%
+between so suppose it is a good bookie
+and he knows quite well the horses and
+
+ align:start position:0%
+and he knows quite well the horses and
+ 
+
+ align:start position:0%
+and he knows quite well the horses and
+there are two horses one horse has he
+
+ align:start position:0%
+there are two horses one horse has he
+ 
+
+ align:start position:0%
+there are two horses one horse has he
+knows that for sure one horse has twenty
+
+ align:start position:0%
+knows that for sure one horse has twenty
+ 
+
+ align:start position:0%
+knows that for sure one horse has twenty
+percent chance of winning in another
+
+ align:start position:0%
+percent chance of winning in another
+ 
+
+ align:start position:0%
+percent chance of winning in another
+horses eighty percent chance of winning
+
+ align:start position:0%
+horses eighty percent chance of winning
+ 
+
+ align:start position:0%
+horses eighty percent chance of winning
+obviously general public doesn't have
+
+ align:start position:0%
+obviously general public doesn't have
+ 
+
+ align:start position:0%
+obviously general public doesn't have
+all these information so they place a
+
+ align:start position:0%
+all these information so they place a
+ 
+
+ align:start position:0%
+all these information so they place a
+bet slightly differently and at the end
+
+ align:start position:0%
+bet slightly differently and at the end
+ 
+
+ align:start position:0%
+bet slightly differently and at the end
+there is ten thousand bet on one horse
+
+ align:start position:0%
+there is ten thousand bet on one horse
+ 
+
+ align:start position:0%
+there is ten thousand bet on one horse
+and fifty thousand bet on the another
+
+ align:start position:0%
+and fifty thousand bet on the another
+ 
+
+ align:start position:0%
+and fifty thousand bet on the another
+horse
+
+ align:start position:0%
+horse
+ 
+
+ align:start position:0%
+horse
+well bookie is sure that he possesses
+
+ align:start position:0%
+well bookie is sure that he possesses
+ 
+
+ align:start position:0%
+well bookie is sure that he possesses
+good information so he suppose he sets
+
+ align:start position:0%
+good information so he suppose he sets
+ 
+
+ align:start position:0%
+good information so he suppose he sets
+the odds according to the real real-life
+
+ align:start position:0%
+the odds according to the real real-life
+ 
+
+ align:start position:0%
+the odds according to the real real-life
+probabilities so he says at four to one
+
+ align:start position:0%
+probabilities so he says at four to one
+ 
+
+ align:start position:0%
+probabilities so he says at four to one
+what would be possible outcomes of the
+
+ align:start position:0%
+what would be possible outcomes of the
+ 
+
+ align:start position:0%
+what would be possible outcomes of the
+race for him monetary so suppose the
+
+ align:start position:0%
+race for him monetary so suppose the
+ 
+
+ align:start position:0%
+race for him monetary so suppose the
+first horse wins then what happens he he
+
+ align:start position:0%
+first horse wins then what happens he he
+ 
+
+ align:start position:0%
+first horse wins then what happens he he
+has to pay back ten thousand then four
+
+ align:start position:0%
+has to pay back ten thousand then four
+ 
+
+ align:start position:0%
+has to pay back ten thousand then four
+times more so he pays out fifty thousand
+
+ align:start position:0%
+times more so he pays out fifty thousand
+ 
+
+ align:start position:0%
+times more so he pays out fifty thousand
+and he received 60 right so he can keep
+
+ align:start position:0%
+and he received 60 right so he can keep
+ 
+
+ align:start position:0%
+and he received 60 right so he can keep
+ten thousand out of it okay so what
+
+ align:start position:0%
+ten thousand out of it okay so what
+ 
+
+ align:start position:0%
+ten thousand out of it okay so what
+happens is there are the other more
+
+ align:start position:0%
+happens is there are the other more
+ 
+
+ align:start position:0%
+happens is there are the other more
+probable horse wins
+
+ align:start position:0%
+probable horse wins
+ 
+
+ align:start position:0%
+probable horse wins
+well he'll you have to pay back the
+
+ align:start position:0%
+well he'll you have to pay back the
+ 
+
+ align:start position:0%
+well he'll you have to pay back the
+fifty thousand and one quarter of it
+
+ align:start position:0%
+fifty thousand and one quarter of it
+ 
+
+ align:start position:0%
+fifty thousand and one quarter of it
+which is twelve and twelve twenty five
+
+ align:start position:0%
+which is twelve and twelve twenty five
+ 
+
+ align:start position:0%
+which is twelve and twelve twenty five
+so at the end he'll pay sixty two and a
+
+ align:start position:0%
+so at the end he'll pay sixty two and a
+ 
+
+ align:start position:0%
+so at the end he'll pay sixty two and a
+half thousand while he collected 67
+
+ align:start position:0%
+half thousand while he collected 67
+ 
+
+ align:start position:0%
+half thousand while he collected 67
+right so he will in this situation he'll
+
+ align:start position:0%
+right so he will in this situation he'll
+ 
+
+ align:start position:0%
+right so he will in this situation he'll
+lose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$2,500 well all in all he expects to
+
+ align:start position:0%
+$2,500 well all in all he expects to
+ 
+
+ align:start position:0%
+$2,500 well all in all he expects to
+make nothing so he probably could
+
+ align:start position:0%
+make nothing so he probably could
+ 
+
+ align:start position:0%
+make nothing so he probably could
+collect enough fees to cover his
+
+ align:start position:0%
+collect enough fees to cover his
+ 
+
+ align:start position:0%
+collect enough fees to cover his
+potential loss but there is certainly a
+
+ align:start position:0%
+potential loss but there is certainly a
+ 
+
+ align:start position:0%
+potential loss but there is certainly a
+very variable
+
+ align:start position:0%
+very variable
+ 
+
+ align:start position:0%
+very variable
+in outcomes he can win a lot he can lose
+
+ align:start position:0%
+in outcomes he can win a lot he can lose
+ 
+
+ align:start position:0%
+in outcomes he can win a lot he can lose
+some now
+
+ align:start position:0%
+some now
+ 
+
+ align:start position:0%
+some now
+what if he forgets about his knowledge
+
+ align:start position:0%
+what if he forgets about his knowledge
+ 
+
+ align:start position:0%
+what if he forgets about his knowledge
+about the real real life probabilities
+
+ align:start position:0%
+about the real real life probabilities
+ 
+
+ align:start position:0%
+about the real real life probabilities
+of horses winning or losing and instead
+
+ align:start position:0%
+of horses winning or losing and instead
+ 
+
+ align:start position:0%
+of horses winning or losing and instead
+set the bet according to to the amount
+
+ align:start position:0%
+set the bet according to to the amount
+ 
+
+ align:start position:0%
+set the bet according to to the amount
+which were already bet according to the
+
+ align:start position:0%
+which were already bet according to the
+ 
+
+ align:start position:0%
+which were already bet according to the
+market effectively so what if he sets
+
+ align:start position:0%
+market effectively so what if he sets
+ 
+
+ align:start position:0%
+market effectively so what if he sets
+the better the odds five to one
+
+ align:start position:0%
+the better the odds five to one
+ 
+
+ align:start position:0%
+the better the odds five to one
+according to the bets placed well in
+
+ align:start position:0%
+according to the bets placed well in
+ 
+
+ align:start position:0%
+according to the bets placed well in
+this situation is the first horse wins
+
+ align:start position:0%
+this situation is the first horse wins
+ 
+
+ align:start position:0%
+this situation is the first horse wins
+he pays back ten plus five times ten so
+
+ align:start position:0%
+he pays back ten plus five times ten so
+ 
+
+ align:start position:0%
+he pays back ten plus five times ten so
+sixty he is zero and if the second horse
+
+ align:start position:0%
+sixty he is zero and if the second horse
+ 
+
+ align:start position:0%
+sixty he is zero and if the second horse
+wins he pays back fifty plus one-fifth
+
+ align:start position:0%
+wins he pays back fifty plus one-fifth
+ 
+
+ align:start position:0%
+wins he pays back fifty plus one-fifth
+of fifty plus another ten again 60 so no
+
+ align:start position:0%
+of fifty plus another ten again 60 so no
+ 
+
+ align:start position:0%
+of fifty plus another ten again 60 so no
+matter which were horse wins he will get
+
+ align:start position:0%
+matter which were horse wins he will get
+ 
+
+ align:start position:0%
+matter which were horse wins he will get
+zero with hunger potential and if he
+
+ align:start position:0%
+zero with hunger potential and if he
+ 
+
+ align:start position:0%
+zero with hunger potential and if he
+collects collects some fee on top of it
+
+ align:start position:0%
+collects collects some fee on top of it
+ 
+
+ align:start position:0%
+collects collects some fee on top of it
+he will make a riskless profit and
+
+ align:start position:0%
+he will make a riskless profit and
+ 
+
+ align:start position:0%
+he will make a riskless profit and
+that's how actually bookies are
+
+ align:start position:0%
+that's how actually bookies are
+ 
+
+ align:start position:0%
+that's how actually bookies are
+operating so it's a simple example but
+
+ align:start position:0%
+operating so it's a simple example but
+ 
+
+ align:start position:0%
+operating so it's a simple example but
+it gives us a first idea how risk
+
+ align:start position:0%
+it gives us a first idea how risk
+ 
+
+ align:start position:0%
+it gives us a first idea how risk
+neutral framework and risk-neutral
+
+ align:start position:0%
+neutral framework and risk-neutral
+ 
+
+ align:start position:0%
+neutral framework and risk-neutral
+pricing when works so we are here not in
+
+ align:start position:0%
+pricing when works so we are here not in
+ 
+
+ align:start position:0%
+pricing when works so we are here not in
+the business of making bets on horses
+
+ align:start position:0%
+the business of making bets on horses
+ 
+
+ align:start position:0%
+the business of making bets on horses
+we're actually in the business of
+
+ align:start position:0%
+we're actually in the business of
+ 
+
+ align:start position:0%
+we're actually in the business of
+pricing derivatives so we will talk
+
+ align:start position:0%
+pricing derivatives so we will talk
+ 
+
+ align:start position:0%
+pricing derivatives so we will talk
+about the simplest possible derivatives
+
+ align:start position:0%
+about the simplest possible derivatives
+ 
+
+ align:start position:0%
+about the simplest possible derivatives
+mostly derivatives on stocks but there
+
+ align:start position:0%
+mostly derivatives on stocks but there
+ 
+
+ align:start position:0%
+mostly derivatives on stocks but there
+there are more complicated derivatives
+
+ align:start position:0%
+there are more complicated derivatives
+ 
+
+ align:start position:0%
+there are more complicated derivatives
+which underline for which could be
+
+ align:start position:0%
+which underline for which could be
+ 
+
+ align:start position:0%
+which underline for which could be
+interest rates bond swaps commodities
+
+ align:start position:0%
+interest rates bond swaps commodities
+ 
+
+ align:start position:0%
+interest rates bond swaps commodities
+whatever so derivative contract is some
+
+ align:start position:0%
+whatever so derivative contract is some
+ 
+
+ align:start position:0%
+whatever so derivative contract is some
+in general a general speaking a formal
+
+ align:start position:0%
+in general a general speaking a formal
+ 
+
+ align:start position:0%
+in general a general speaking a formal
+payout connected to underline usually
+
+ align:start position:0%
+payout connected to underline usually
+ 
+
+ align:start position:0%
+payout connected to underline usually
+the underlying is a liquid instrument
+
+ align:start position:0%
+the underlying is a liquid instrument
+ 
+
+ align:start position:0%
+the underlying is a liquid instrument
+which is traded traded on exchanges and
+
+ align:start position:0%
+which is traded traded on exchanges and
+ 
+
+ align:start position:0%
+which is traded traded on exchanges and
+derivative may be traded on exchanges
+
+ align:start position:0%
+derivative may be traded on exchanges
+ 
+
+ align:start position:0%
+derivative may be traded on exchanges
+actually quite a few equity options are
+
+ align:start position:0%
+actually quite a few equity options are
+ 
+
+ align:start position:0%
+actually quite a few equity options are
+trade exchanges but in general they're
+
+ align:start position:0%
+trade exchanges but in general they're
+ 
+
+ align:start position:0%
+trade exchanges but in general they're
+over-the-counter over-the-counter
+
+ align:start position:0%
+over-the-counter over-the-counter
+ 
+
+ align:start position:0%
+over-the-counter over-the-counter
+contracts where two counterparties just
+
+ align:start position:0%
+contracts where two counterparties just
+ 
+
+ align:start position:0%
+contracts where two counterparties just
+agree on some kind of payout
+
+ align:start position:0%
+agree on some kind of payout
+ 
+
+ align:start position:0%
+agree on some kind of payout
+one of the simpler derivatives is is a
+
+ align:start position:0%
+one of the simpler derivatives is is a
+ 
+
+ align:start position:0%
+one of the simpler derivatives is is a
+forward contract so what is a forward
+
+ align:start position:0%
+forward contract so what is a forward
+ 
+
+ align:start position:0%
+forward contract so what is a forward
+contract for a contract is a contract
+
+ align:start position:0%
+contract for a contract is a contract
+ 
+
+ align:start position:0%
+contract for a contract is a contract
+where one party agrees to buy an asset
+
+ align:start position:0%
+where one party agrees to buy an asset
+ 
+
+ align:start position:0%
+where one party agrees to buy an asset
+from another party for a price which is
+
+ align:start position:0%
+from another party for a price which is
+ 
+
+ align:start position:0%
+from another party for a price which is
+agreed today usually the this contract
+
+ align:start position:0%
+agreed today usually the this contract
+ 
+
+ align:start position:0%
+agreed today usually the this contract
+has this forward price is is set in such
+
+ align:start position:0%
+has this forward price is is set in such
+ 
+
+ align:start position:0%
+has this forward price is is set in such
+a way that right now no money changes
+
+ align:start position:0%
+a way that right now no money changes
+ 
+
+ align:start position:0%
+a way that right now no money changes
+hands right so and here here is an
+
+ align:start position:0%
+hands right so and here here is an
+ 
+
+ align:start position:0%
+hands right so and here here is an
+example well suppose there is a stock
+
+ align:start position:0%
+example well suppose there is a stock
+ 
+
+ align:start position:0%
+example well suppose there is a stock
+which right now is priced at 80 and this
+
+ align:start position:0%
+which right now is priced at 80 and this
+ 
+
+ align:start position:0%
+which right now is priced at 80 and this
+is the forward for two years so somebody
+
+ align:start position:0%
+is the forward for two years so somebody
+ 
+
+ align:start position:0%
+is the forward for two years so somebody
+agrees to buy this stock in two years
+
+ align:start position:0%
+agrees to buy this stock in two years
+ 
+
+ align:start position:0%
+agrees to buy this stock in two years
+for this price and not surprisingly I
+
+ align:start position:0%
+for this price and not surprisingly I
+ 
+
+ align:start position:0%
+for this price and not surprisingly I
+somehow set this price such that
+
+ align:start position:0%
+somehow set this price such that
+ 
+
+ align:start position:0%
+somehow set this price such that
+currently the value the value of the
+
+ align:start position:0%
+currently the value the value of the
+ 
+
+ align:start position:0%
+currently the value the value of the
+contract is zero and we'll see how I'll
+
+ align:start position:0%
+contract is zero and we'll see how I'll
+ 
+
+ align:start position:0%
+contract is zero and we'll see how I'll
+come up with a price so this blue line
+
+ align:start position:0%
+come up with a price so this blue line
+ 
+
+ align:start position:0%
+come up with a price so this blue line
+is actually payout what will happen at
+
+ align:start position:0%
+is actually payout what will happen at
+ 
+
+ align:start position:0%
+is actually payout what will happen at
+the end right the the payout depending
+
+ align:start position:0%
+the end right the the payout depending
+ 
+
+ align:start position:0%
+the end right the the payout depending
+the graph of F at time T to
+
+ align:start position:0%
+the graph of F at time T to
+ 
+
+ align:start position:0%
+the graph of F at time T to
+determination time or expiry how it
+
+ align:start position:0%
+determination time or expiry how it
+ 
+
+ align:start position:0%
+determination time or expiry how it
+depends on the stock price right so
+
+ align:start position:0%
+depends on the stock price right so
+ 
+
+ align:start position:0%
+depends on the stock price right so
+obviously the payout is s minus K where
+
+ align:start position:0%
+obviously the payout is s minus K where
+ 
+
+ align:start position:0%
+obviously the payout is s minus K where
+as as as as the stock price so it's a
+
+ align:start position:0%
+as as as as the stock price so it's a
+ 
+
+ align:start position:0%
+as as as as the stock price so it's a
+linear function it turns out that the
+
+ align:start position:0%
+linear function it turns out that the
+ 
+
+ align:start position:0%
+linear function it turns out that the
+current price is also really no function
+
+ align:start position:0%
+current price is also really no function
+ 
+
+ align:start position:0%
+current price is also really no function
+but slightly shifted and we'll see how
+
+ align:start position:0%
+but slightly shifted and we'll see how
+ 
+
+ align:start position:0%
+but slightly shifted and we'll see how
+how come it slightly shifted and how
+
+ align:start position:0%
+how come it slightly shifted and how
+ 
+
+ align:start position:0%
+how come it slightly shifted and how
+much it should be shifted and K is
+
+ align:start position:0%
+much it should be shifted and K is
+ 
+
+ align:start position:0%
+much it should be shifted and K is
+usually referred as a strike price
+
+ align:start position:0%
+usually referred as a strike price
+ 
+
+ align:start position:0%
+usually referred as a strike price
+another slightly more complicated
+
+ align:start position:0%
+another slightly more complicated
+ 
+
+ align:start position:0%
+another slightly more complicated
+contract is called
+
+ align:start position:0%
+contract is called
+ 
+
+ align:start position:0%
+contract is called
+a call option so if previously the
+
+ align:start position:0%
+a call option so if previously the
+ 
+
+ align:start position:0%
+a call option so if previously the
+forward is is is an obligation to buy
+
+ align:start position:0%
+forward is is is an obligation to buy
+ 
+
+ align:start position:0%
+forward is is is an obligation to buy
+the asset for for an agreed price call
+
+ align:start position:0%
+the asset for for an agreed price call
+ 
+
+ align:start position:0%
+the asset for for an agreed price call
+option is actually an option to buy to
+
+ align:start position:0%
+option is actually an option to buy to
+ 
+
+ align:start position:0%
+option is actually an option to buy to
+buy an asset at the agreed price today
+
+ align:start position:0%
+buy an asset at the agreed price today
+ 
+
+ align:start position:0%
+buy an asset at the agreed price today
+you can view it a call option can be
+
+ align:start position:0%
+you can view it a call option can be
+ 
+
+ align:start position:0%
+you can view it a call option can be
+viewed as kind of insurance that the
+
+ align:start position:0%
+viewed as kind of insurance that the
+ 
+
+ align:start position:0%
+viewed as kind of insurance that the
+against the asset going down basically
+
+ align:start position:0%
+against the asset going down basically
+ 
+
+ align:start position:0%
+against the asset going down basically
+the payout is always pose
+
+ align:start position:0%
+the payout is always pose
+ 
+
+ align:start position:0%
+the payout is always pose
+you can never lose money on the forward
+
+ align:start position:0%
+you can never lose money on the forward
+ 
+
+ align:start position:0%
+you can never lose money on the forward
+you can lose money you agree on the
+
+ align:start position:0%
+you can lose money you agree on the
+ 
+
+ align:start position:0%
+you can lose money you agree on the
+price see the asset ends up being lower
+
+ align:start position:0%
+price see the asset ends up being lower
+ 
+
+ align:start position:0%
+price see the asset ends up being lower
+than this price but you still have to
+
+ align:start position:0%
+than this price but you still have to
+ 
+
+ align:start position:0%
+than this price but you still have to
+buy it right here if if the asset ends
+
+ align:start position:0%
+buy it right here if if the asset ends
+ 
+
+ align:start position:0%
+buy it right here if if the asset ends
+up at expiry below strike price or out
+
+ align:start position:0%
+up at expiry below strike price or out
+ 
+
+ align:start position:0%
+up at expiry below strike price or out
+of the money then the payout will be
+
+ align:start position:0%
+of the money then the payout will be
+ 
+
+ align:start position:0%
+of the money then the payout will be
+zero if on the other hand it it ends up
+
+ align:start position:0%
+zero if on the other hand it it ends up
+ 
+
+ align:start position:0%
+zero if on the other hand it it ends up
+being above a strike price or it is
+
+ align:start position:0%
+being above a strike price or it is
+ 
+
+ align:start position:0%
+being above a strike price or it is
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+the option is in the money then your the
+
+ align:start position:0%
+the option is in the money then your the
+ 
+
+ align:start position:0%
+the option is in the money then your the
+payout will be s minus K as before so in
+
+ align:start position:0%
+payout will be s minus K as before so in
+ 
+
+ align:start position:0%
+payout will be s minus K as before so in
+mathematical terms the the payout is
+
+ align:start position:0%
+mathematical terms the the payout is
+ 
+
+ align:start position:0%
+mathematical terms the the payout is
+maximum of s minus K and zero right and
+
+ align:start position:0%
+maximum of s minus K and zero right and
+ 
+
+ align:start position:0%
+maximum of s minus K and zero right and
+that's what happens at time of at expiry
+
+ align:start position:0%
+that's what happens at time of at expiry
+ 
+
+ align:start position:0%
+that's what happens at time of at expiry
+time this blue line so what is the price
+
+ align:start position:0%
+time this blue line so what is the price
+ 
+
+ align:start position:0%
+time this blue line so what is the price
+of this option now well obviously it it
+
+ align:start position:0%
+of this option now well obviously it it
+ 
+
+ align:start position:0%
+of this option now well obviously it it
+should be slightly both because even if
+
+ align:start position:0%
+should be slightly both because even if
+ 
+
+ align:start position:0%
+should be slightly both because even if
+the if even if now the the asset is
+
+ align:start position:0%
+the if even if now the the asset is
+ 
+
+ align:start position:0%
+the if even if now the the asset is
+slightly out of the money below strike
+
+ align:start position:0%
+slightly out of the money below strike
+ 
+
+ align:start position:0%
+slightly out of the money below strike
+price there is some volatility to it and
+
+ align:start position:0%
+price there is some volatility to it and
+ 
+
+ align:start position:0%
+price there is some volatility to it and
+there is a probability that we will
+
+ align:start position:0%
+there is a probability that we will
+ 
+
+ align:start position:0%
+there is a probability that we will
+still end up in the money at expiry so
+
+ align:start position:0%
+still end up in the money at expiry so
+ 
+
+ align:start position:0%
+still end up in the money at expiry so
+you you would be willing you should be
+
+ align:start position:0%
+you you would be willing you should be
+ 
+
+ align:start position:0%
+you you would be willing you should be
+willing to pay something for this
+
+ align:start position:0%
+willing to pay something for this
+ 
+
+ align:start position:0%
+willing to pay something for this
+obviously if it's way out of the money
+
+ align:start position:0%
+obviously if it's way out of the money
+ 
+
+ align:start position:0%
+obviously if it's way out of the money
+it should be zero right on the other
+
+ align:start position:0%
+it should be zero right on the other
+ 
+
+ align:start position:0%
+it should be zero right on the other
+hand if it's way in the money in fact it
+
+ align:start position:0%
+hand if it's way in the money in fact it
+ 
+
+ align:start position:0%
+hand if it's way in the money in fact it
+should be just as forward and in fact it
+
+ align:start position:0%
+should be just as forward and in fact it
+ 
+
+ align:start position:0%
+should be just as forward and in fact it
+is we will we'll see because if they
+
+ align:start position:0%
+is we will we'll see because if they
+ 
+
+ align:start position:0%
+is we will we'll see because if they
+were the probability for the for the
+
+ align:start position:0%
+were the probability for the for the
+ 
+
+ align:start position:0%
+were the probability for the for the
+asset going back to the strike price and
+
+ align:start position:0%
+asset going back to the strike price and
+ 
+
+ align:start position:0%
+asset going back to the strike price and
+below will be low and that the black
+
+ align:start position:0%
+below will be low and that the black
+ 
+
+ align:start position:0%
+below will be low and that the black
+Scholes equation is black Scholes
+
+ align:start position:0%
+Scholes equation is black Scholes
+ 
+
+ align:start position:0%
+Scholes equation is black Scholes
+formula is exactly the solution for this
+
+ align:start position:0%
+formula is exactly the solution for this
+ 
+
+ align:start position:0%
+formula is exactly the solution for this
+correct line which we'll see in a second
+
+ align:start position:0%
+correct line which we'll see in a second
+ 
+
+ align:start position:0%
+correct line which we'll see in a second
+another simple contract which is kind of
+
+ align:start position:0%
+another simple contract which is kind of
+ 
+
+ align:start position:0%
+another simple contract which is kind of
+dual to call option is a put option so
+
+ align:start position:0%
+dual to call option is a put option so
+ 
+
+ align:start position:0%
+dual to call option is a put option so
+put option on the contrary is a bet on
+
+ align:start position:0%
+put option on the contrary is a bet on
+ 
+
+ align:start position:0%
+put option on the contrary is a bet on
+on the asset going down rather than up
+
+ align:start position:0%
+on the asset going down rather than up
+ 
+
+ align:start position:0%
+on the asset going down rather than up
+right so the payout is maximum of K
+
+ align:start position:0%
+right so the payout is maximum of K
+ 
+
+ align:start position:0%
+right so the payout is maximum of K
+minus s and 0 so it's it's kind of
+
+ align:start position:0%
+minus s and 0 so it's it's kind of
+ 
+
+ align:start position:0%
+minus s and 0 so it's it's kind of
+reversed also a ramp function at the at
+
+ align:start position:0%
+reversed also a ramp function at the at
+ 
+
+ align:start position:0%
+reversed also a ramp function at the at
+maturity
+
+ align:start position:0%
+maturity
+ 
+
+ align:start position:0%
+maturity
+and here here is the current price again
+
+ align:start position:0%
+and here here is the current price again
+ 
+
+ align:start position:0%
+and here here is the current price again
+even if it's in the money if it's way in
+
+ align:start position:0%
+even if it's in the money if it's way in
+ 
+
+ align:start position:0%
+even if it's in the money if it's way in
+the money you expect it to be to be zero
+
+ align:start position:0%
+the money you expect it to be to be zero
+ 
+
+ align:start position:0%
+the money you expect it to be to be zero
+if it's way in the money we expect it to
+
+ align:start position:0%
+if it's way in the money we expect it to
+ 
+
+ align:start position:0%
+if it's way in the money we expect it to
+be slightly below below forward just
+
+ align:start position:0%
+be slightly below below forward just
+ 
+
+ align:start position:0%
+be slightly below below forward just
+because of discounting okay so and here
+
+ align:start position:0%
+because of discounting okay so and here
+ 
+
+ align:start position:0%
+because of discounting okay so and here
+here are a few three main points which
+
+ align:start position:0%
+here are a few three main points which
+ 
+
+ align:start position:0%
+here are a few three main points which
+we which will try to fall through the
+
+ align:start position:0%
+we which will try to fall through the
+ 
+
+ align:start position:0%
+we which will try to fall through the
+class so first of all what we'll see
+
+ align:start position:0%
+class so first of all what we'll see
+ 
+
+ align:start position:0%
+class so first of all what we'll see
+that if we we have current price of the
+
+ align:start position:0%
+that if we we have current price of the
+ 
+
+ align:start position:0%
+that if we we have current price of the
+underlying and some assumptions on the
+
+ align:start position:0%
+underlying and some assumptions on the
+ 
+
+ align:start position:0%
+underlying and some assumptions on the
+on how the the market or the the
+
+ align:start position:0%
+on how the the market or the the
+ 
+
+ align:start position:0%
+on how the the market or the the
+underlying behaves there is actually no
+
+ align:start position:0%
+underlying behaves there is actually no
+ 
+
+ align:start position:0%
+underlying behaves there is actually no
+uncertainty in the price of the option
+
+ align:start position:0%
+uncertainty in the price of the option
+ 
+
+ align:start position:0%
+uncertainty in the price of the option
+obviously if we if we fix the payout
+
+ align:start position:0%
+obviously if we if we fix the payout
+ 
+
+ align:start position:0%
+obviously if we if we fix the payout
+right so somehow there is no uncertainty
+
+ align:start position:0%
+right so somehow there is no uncertainty
+ 
+
+ align:start position:0%
+right so somehow there is no uncertainty
+it's completely deterministic once once
+
+ align:start position:0%
+it's completely deterministic once once
+ 
+
+ align:start position:0%
+it's completely deterministic once once
+we have once we know the price of
+
+ align:start position:0%
+we have once we know the price of
+ 
+
+ align:start position:0%
+we have once we know the price of
+underline the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interesting fact which we'll find out
+
+ align:start position:0%
+interesting fact which we'll find out
+ 
+
+ align:start position:0%
+interesting fact which we'll find out
+it's actually risk neutrality meaning
+
+ align:start position:0%
+it's actually risk neutrality meaning
+ 
+
+ align:start position:0%
+it's actually risk neutrality meaning
+that in fact the price of the option has
+
+ align:start position:0%
+that in fact the price of the option has
+ 
+
+ align:start position:0%
+that in fact the price of the option has
+nothing to do with the with the risk
+
+ align:start position:0%
+nothing to do with the with the risk
+ 
+
+ align:start position:0%
+nothing to do with the with the risk
+preferences of market participants or or
+
+ align:start position:0%
+preferences of market participants or or
+ 
+
+ align:start position:0%
+preferences of market participants or or
+or counterparties it's actually only
+
+ align:start position:0%
+or counterparties it's actually only
+ 
+
+ align:start position:0%
+or counterparties it's actually only
+depends on the dynamics of the stock
+
+ align:start position:0%
+depends on the dynamics of the stock
+ 
+
+ align:start position:0%
+depends on the dynamics of the stock
+only depends on volatility of the stock
+
+ align:start position:0%
+only depends on volatility of the stock
+ 
+
+ align:start position:0%
+only depends on volatility of the stock
+and finally the most important idea of
+
+ align:start position:0%
+and finally the most important idea of
+ 
+
+ align:start position:0%
+and finally the most important idea of
+this class that mathematical apparatus
+
+ align:start position:0%
+this class that mathematical apparatus
+ 
+
+ align:start position:0%
+this class that mathematical apparatus
+allows you to to figure out how much
+
+ align:start position:0%
+allows you to to figure out how much
+ 
+
+ align:start position:0%
+allows you to to figure out how much
+this deterministic option price is now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's consider a very simple example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very simple market to period so suppose
+
+ align:start position:0%
+very simple market to period so suppose
+ 
+
+ align:start position:0%
+very simple market to period so suppose
+our time is discrete and we are one step
+
+ align:start position:0%
+our time is discrete and we are one step
+ 
+
+ align:start position:0%
+our time is discrete and we are one step
+before the maturity so right now our
+
+ align:start position:0%
+before the maturity so right now our
+ 
+
+ align:start position:0%
+before the maturity so right now our
+stock has price as zero and there is
+
+ align:start position:0%
+stock has price as zero and there is
+ 
+
+ align:start position:0%
+stock has price as zero and there is
+some derivative F zero
+
+ align:start position:0%
+some derivative F zero
+ 
+
+ align:start position:0%
+some derivative F zero
+with some payout we will consider a few
+
+ align:start position:0%
+with some payout we will consider a few
+ 
+
+ align:start position:0%
+with some payout we will consider a few
+of those right also will add to the mix
+
+ align:start position:0%
+of those right also will add to the mix
+ 
+
+ align:start position:0%
+of those right also will add to the mix
+some a bit of cash right risk with cash
+
+ align:start position:0%
+some a bit of cash right risk with cash
+ 
+
+ align:start position:0%
+some a bit of cash right risk with cash
+this some amount of risk with cash be
+
+ align:start position:0%
+this some amount of risk with cash be
+ 
+
+ align:start position:0%
+this some amount of risk with cash be
+zero and risk less meaning that it grows
+
+ align:start position:0%
+zero and risk less meaning that it grows
+ 
+
+ align:start position:0%
+zero and risk less meaning that it grows
+exponentially with some interest rate R
+
+ align:start position:0%
+exponentially with some interest rate R
+ 
+
+ align:start position:0%
+exponentially with some interest rate R
+and there is no uncertainty it's
+
+ align:start position:0%
+and there is no uncertainty it's
+ 
+
+ align:start position:0%
+and there is no uncertainty it's
+completely if you have now busy row we
+
+ align:start position:0%
+completely if you have now busy row we
+ 
+
+ align:start position:0%
+completely if you have now busy row we
+know then in time DT our B 0 will be 0
+
+ align:start position:0%
+know then in time DT our B 0 will be 0
+ 
+
+ align:start position:0%
+know then in time DT our B 0 will be 0
+will will will grow exponentially it
+
+ align:start position:0%
+will will will grow exponentially it
+ 
+
+ align:start position:0%
+will will will grow exponentially it
+will become B e to the RT so a bond
+
+ align:start position:0%
+will become B e to the RT so a bond
+ 
+
+ align:start position:0%
+will become B e to the RT so a bond
+basically zero coupon one a money market
+
+ align:start position:0%
+basically zero coupon one a money market
+ 
+
+ align:start position:0%
+basically zero coupon one a money market
+account rather is its if you go to
+
+ align:start position:0%
+account rather is its if you go to
+ 
+
+ align:start position:0%
+account rather is its if you go to
+Cambridge Savings Bank put $1 in today
+
+ align:start position:0%
+Cambridge Savings Bank put $1 in today
+ 
+
+ align:start position:0%
+Cambridge Savings Bank put $1 in today
+then in a year you'll get $1 and
+
+ align:start position:0%
+then in a year you'll get $1 and
+ 
+
+ align:start position:0%
+then in a year you'll get $1 and
+basically nothing because interest rates
+
+ align:start position:0%
+basically nothing because interest rates
+ 
+
+ align:start position:0%
+basically nothing because interest rates
+are zero so in in time DT we will assume
+
+ align:start position:0%
+are zero so in in time DT we will assume
+ 
+
+ align:start position:0%
+are zero so in in time DT we will assume
+with some probability P our market can
+
+ align:start position:0%
+with some probability P our market can
+ 
+
+ align:start position:0%
+with some probability P our market can
+go to the state where stock becomes s1
+
+ align:start position:0%
+go to the state where stock becomes s1
+ 
+
+ align:start position:0%
+go to the state where stock becomes s1
+the price of stock becomes s1 our bond
+
+ align:start position:0%
+the price of stock becomes s1 our bond
+ 
+
+ align:start position:0%
+the price of stock becomes s1 our bond
+grows exponentially not no uncertainty
+
+ align:start position:0%
+grows exponentially not no uncertainty
+ 
+
+ align:start position:0%
+grows exponentially not no uncertainty
+and our derivative becomes f1 or with
+
+ align:start position:0%
+and our derivative becomes f1 or with
+ 
+
+ align:start position:0%
+and our derivative becomes f1 or with
+probability 1 minus P only two states so
+
+ align:start position:0%
+probability 1 minus P only two states so
+ 
+
+ align:start position:0%
+probability 1 minus P only two states so
+our stock becomes s2 bond stays the same
+
+ align:start position:0%
+our stock becomes s2 bond stays the same
+ 
+
+ align:start position:0%
+our stock becomes s2 bond stays the same
+and the the derivative is some f2 so
+
+ align:start position:0%
+and the the derivative is some f2 so
+ 
+
+ align:start position:0%
+and the the derivative is some f2 so
+let's start with with our simple
+
+ align:start position:0%
+let's start with with our simple
+ 
+
+ align:start position:0%
+let's start with with our simple
+contract the forward contract so one can
+
+ align:start position:0%
+contract the forward contract so one can
+ 
+
+ align:start position:0%
+contract the forward contract so one can
+naively approach this problem trying to
+
+ align:start position:0%
+naively approach this problem trying to
+ 
+
+ align:start position:0%
+naively approach this problem trying to
+get the price of of the derivative using
+
+ align:start position:0%
+get the price of of the derivative using
+ 
+
+ align:start position:0%
+get the price of of the derivative using
+the real-world probabilities P and minus
+
+ align:start position:0%
+the real-world probabilities P and minus
+ 
+
+ align:start position:0%
+the real-world probabilities P and minus
+P 1 minus P right so we know that the
+
+ align:start position:0%
+P 1 minus P right so we know that the
+ 
+
+ align:start position:0%
+P 1 minus P right so we know that the
+payout is s minus K that's that's given
+
+ align:start position:0%
+payout is s minus K that's that's given
+ 
+
+ align:start position:0%
+payout is s minus K that's that's given
+so one would say that if we we know we
+
+ align:start position:0%
+so one would say that if we we know we
+ 
+
+ align:start position:0%
+so one would say that if we we know we
+are one step before the payout so let's
+
+ align:start position:0%
+are one step before the payout so let's
+ 
+
+ align:start position:0%
+are one step before the payout so let's
+just compute expected value of the
+
+ align:start position:0%
+just compute expected value of the
+ 
+
+ align:start position:0%
+just compute expected value of the
+payout using real real-world
+
+ align:start position:0%
+payout using real real-world
+ 
+
+ align:start position:0%
+payout using real real-world
+probabilities get this this value and
+
+ align:start position:0%
+probabilities get this this value and
+ 
+
+ align:start position:0%
+probabilities get this this value and
+actually what we are looking here is to
+
+ align:start position:0%
+actually what we are looking here is to
+ 
+
+ align:start position:0%
+actually what we are looking here is to
+set K such that the price now at time
+
+ align:start position:0%
+set K such that the price now at time
+ 
+
+ align:start position:0%
+set K such that the price now at time
+and T is zero that's usual convention so
+
+ align:start position:0%
+and T is zero that's usual convention so
+ 
+
+ align:start position:0%
+and T is zero that's usual convention so
+will then set cake to do this to this
+
+ align:start position:0%
+will then set cake to do this to this
+ 
+
+ align:start position:0%
+will then set cake to do this to this
+probability to do this to this number
+
+ align:start position:0%
+probability to do this to this number
+ 
+
+ align:start position:0%
+probability to do this to this number
+which depends on real-world probability
+
+ align:start position:0%
+which depends on real-world probability
+ 
+
+ align:start position:0%
+which depends on real-world probability
+and obviously depends on the stock price
+
+ align:start position:0%
+and obviously depends on the stock price
+ 
+
+ align:start position:0%
+and obviously depends on the stock price
+at expiry so but obviously we don't know
+
+ align:start position:0%
+at expiry so but obviously we don't know
+ 
+
+ align:start position:0%
+at expiry so but obviously we don't know
+real-world probabilities we can guess we
+
+ align:start position:0%
+real-world probabilities we can guess we
+ 
+
+ align:start position:0%
+real-world probabilities we can guess we
+can say audits the stock is as likely to
+
+ align:start position:0%
+can say audits the stock is as likely to
+ 
+
+ align:start position:0%
+can say audits the stock is as likely to
+go up then then down then then it's just
+
+ align:start position:0%
+go up then then down then then it's just
+ 
+
+ align:start position:0%
+go up then then down then then it's just
+an average of n n stock prices or
+
+ align:start position:0%
+an average of n n stock prices or
+ 
+
+ align:start position:0%
+an average of n n stock prices or
+something else but it's all hand wavy
+
+ align:start position:0%
+something else but it's all hand wavy
+ 
+
+ align:start position:0%
+something else but it's all hand wavy
+and actually we never will be red
+
+ align:start position:0%
+and actually we never will be red
+ 
+
+ align:start position:0%
+and actually we never will be red
+instead of doing this we're kind of
+
+ align:start position:0%
+instead of doing this we're kind of
+ 
+
+ align:start position:0%
+instead of doing this we're kind of
+following bookie example let's try to do
+
+ align:start position:0%
+following bookie example let's try to do
+ 
+
+ align:start position:0%
+following bookie example let's try to do
+something else let's think a little bit
+
+ align:start position:0%
+something else let's think a little bit
+ 
+
+ align:start position:0%
+something else let's think a little bit
+so we have a stock which is trading it
+
+ align:start position:0%
+so we have a stock which is trading it
+ 
+
+ align:start position:0%
+so we have a stock which is trading it
+at market now for the price as zero how
+
+ align:start position:0%
+at market now for the price as zero how
+ 
+
+ align:start position:0%
+at market now for the price as zero how
+about we go to the bank and borrow as
+
+ align:start position:0%
+about we go to the bank and borrow as
+ 
+
+ align:start position:0%
+about we go to the bank and borrow as
+zero dollars right now and immediately
+
+ align:start position:0%
+zero dollars right now and immediately
+ 
+
+ align:start position:0%
+zero dollars right now and immediately
+go to the market and buy the stock so
+
+ align:start position:0%
+go to the market and buy the stock so
+ 
+
+ align:start position:0%
+go to the market and buy the stock so
+right now we are not net zero we
+
+ align:start position:0%
+right now we are not net zero we
+ 
+
+ align:start position:0%
+right now we are not net zero we
+borrowed as zero we paid it immediately
+
+ align:start position:0%
+borrowed as zero we paid it immediately
+ 
+
+ align:start position:0%
+borrowed as zero we paid it immediately
+to buy the stock so we have stock at
+
+ align:start position:0%
+to buy the stock so we have stock at
+ 
+
+ align:start position:0%
+to buy the stock so we have stock at
+hand then we'll wait for one period and
+
+ align:start position:0%
+hand then we'll wait for one period and
+ 
+
+ align:start position:0%
+hand then we'll wait for one period and
+and at the same time sorry we are we
+
+ align:start position:0%
+and at the same time sorry we are we
+ 
+
+ align:start position:0%
+and at the same time sorry we are we
+short we enter on the short side of the
+
+ align:start position:0%
+short we enter on the short side of the
+ 
+
+ align:start position:0%
+short we enter on the short side of the
+forward contract so we agree to sell the
+
+ align:start position:0%
+forward contract so we agree to sell the
+ 
+
+ align:start position:0%
+forward contract so we agree to sell the
+stock for for some price k zero so in DT
+
+ align:start position:0%
+stock for for some price k zero so in DT
+ 
+
+ align:start position:0%
+stock for for some price k zero so in DT
+in one period of time the the contrary
+
+ align:start position:0%
+in one period of time the the contrary
+ 
+
+ align:start position:0%
+in one period of time the the contrary
+expires we already have stock so we just
+
+ align:start position:0%
+expires we already have stock so we just
+ 
+
+ align:start position:0%
+expires we already have stock so we just
+go and exchange it for k 0 k zero
+
+ align:start position:0%
+go and exchange it for k 0 k zero
+ 
+
+ align:start position:0%
+go and exchange it for k 0 k zero
+dollars right but we at the same time we
+
+ align:start position:0%
+dollars right but we at the same time we
+ 
+
+ align:start position:0%
+dollars right but we at the same time we
+need to repay our loan which now have
+
+ align:start position:0%
+need to repay our loan which now have
+ 
+
+ align:start position:0%
+need to repay our loan which now have
+become as zero times e to the R DT this
+
+ align:start position:0%
+become as zero times e to the R DT this
+ 
+
+ align:start position:0%
+become as zero times e to the R DT this
+is deterministic right we borrowed a
+
+ align:start position:0%
+is deterministic right we borrowed a
+ 
+
+ align:start position:0%
+is deterministic right we borrowed a
+zero in time DT it became s times e to
+
+ align:start position:0%
+zero in time DT it became s times e to
+ 
+
+ align:start position:0%
+zero in time DT it became s times e to
+the R DT so what what's our net then
+
+ align:start position:0%
+the R DT so what what's our net then
+ 
+
+ align:start position:0%
+the R DT so what what's our net then
+that is K 0 minus s to the S
+
+ align:start position:0%
+that is K 0 minus s to the S
+ 
+
+ align:start position:0%
+that is K 0 minus s to the S
+times e R DT so suppose K 0 is greater
+
+ align:start position:0%
+times e R DT so suppose K 0 is greater
+ 
+
+ align:start position:0%
+times e R DT so suppose K 0 is greater
+than than this value then we made
+
+ align:start position:0%
+than than this value then we made
+ 
+
+ align:start position:0%
+than than this value then we made
+riskless profit that there is no risk in
+
+ align:start position:0%
+riskless profit that there is no risk in
+ 
+
+ align:start position:0%
+riskless profit that there is no risk in
+the in this in the strategy which we
+
+ align:start position:0%
+the in this in the strategy which we
+ 
+
+ align:start position:0%
+the in this in the strategy which we
+which we proposed so this is good but
+
+ align:start position:0%
+which we proposed so this is good but
+ 
+
+ align:start position:0%
+which we proposed so this is good but
+why wouldn't everybody do it all day
+
+ align:start position:0%
+why wouldn't everybody do it all day
+ 
+
+ align:start position:0%
+why wouldn't everybody do it all day
+long on the other hand if K 0 is less
+
+ align:start position:0%
+long on the other hand if K 0 is less
+ 
+
+ align:start position:0%
+long on the other hand if K 0 is less
+than s 0 that's that's that's a loss for
+
+ align:start position:0%
+than s 0 that's that's that's a loss for
+ 
+
+ align:start position:0%
+than s 0 that's that's that's a loss for
+sure and if anybody thinks as we did and
+
+ align:start position:0%
+sure and if anybody thinks as we did and
+ 
+
+ align:start position:0%
+sure and if anybody thinks as we did and
+we assume that everybody can do it and
+
+ align:start position:0%
+we assume that everybody can do it and
+ 
+
+ align:start position:0%
+we assume that everybody can do it and
+nobody would would want to enter it
+
+ align:start position:0%
+nobody would would want to enter it
+ 
+
+ align:start position:0%
+nobody would would want to enter it
+which means that in order for for our
+
+ align:start position:0%
+which means that in order for for our
+ 
+
+ align:start position:0%
+which means that in order for for our
+forward to pry it to be price 0 now the
+
+ align:start position:0%
+forward to pry it to be price 0 now the
+ 
+
+ align:start position:0%
+forward to pry it to be price 0 now the
+price the strike price has to be equal
+
+ align:start position:0%
+price the strike price has to be equal
+ 
+
+ align:start position:0%
+price the strike price has to be equal
+to 2 to this amount and there is no
+
+ align:start position:0%
+to 2 to this amount and there is no
+ 
+
+ align:start position:0%
+to 2 to this amount and there is no
+uncertainty about it so let's stop and
+
+ align:start position:0%
+uncertainty about it so let's stop and
+ 
+
+ align:start position:0%
+uncertainty about it so let's stop and
+think a little bit
+
+ align:start position:0%
+think a little bit
+ 
+
+ align:start position:0%
+think a little bit
+well actually just just to see just to
+
+ align:start position:0%
+well actually just just to see just to
+ 
+
+ align:start position:0%
+well actually just just to see just to
+see how it works and that's that's
+
+ align:start position:0%
+see how it works and that's that's
+ 
+
+ align:start position:0%
+see how it works and that's that's
+exactly why why why I set this this gate
+
+ align:start position:0%
+exactly why why why I set this this gate
+ 
+
+ align:start position:0%
+exactly why why why I set this this gate
+to this number so by the way who can
+
+ align:start position:0%
+to this number so by the way who can
+ 
+
+ align:start position:0%
+to this number so by the way who can
+tell me what which interest rate does it
+
+ align:start position:0%
+tell me what which interest rate does it
+ 
+
+ align:start position:0%
+tell me what which interest rate does it
+doesn't imply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if our strike is our stock prices 80 our
+
+ align:start position:0%
+if our strike is our stock prices 80 our
+ 
+
+ align:start position:0%
+if our strike is our stock prices 80 our
+strike is eighty eight point four to one
+
+ align:start position:0%
+strike is eighty eight point four to one
+ 
+
+ align:start position:0%
+strike is eighty eight point four to one
+and and the expires in two years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximately two point five so in two
+
+ align:start position:0%
+approximately two point five so in two
+ 
+
+ align:start position:0%
+approximately two point five so in two
+years it will be five percent so roughly
+
+ align:start position:0%
+years it will be five percent so roughly
+ 
+
+ align:start position:0%
+years it will be five percent so roughly
+speaking without compounding it should
+
+ align:start position:0%
+speaking without compounding it should
+ 
+
+ align:start position:0%
+speaking without compounding it should
+be five percent of eighty plus five
+
+ align:start position:0%
+be five percent of eighty plus five
+ 
+
+ align:start position:0%
+be five percent of eighty plus five
+percent it would be eighty four so ten
+
+ align:start position:0%
+percent it would be eighty four so ten
+ 
+
+ align:start position:0%
+percent it would be eighty four so ten
+percent for two years so the interest
+
+ align:start position:0%
+percent for two years so the interest
+ 
+
+ align:start position:0%
+percent for two years so the interest
+rate is five five percent yet so yet
+
+ align:start position:0%
+rate is five five percent yet so yet
+ 
+
+ align:start position:0%
+rate is five five percent yet so yet
+it's actually exactly five with least
+
+ align:start position:0%
+it's actually exactly five with least
+ 
+
+ align:start position:0%
+it's actually exactly five with least
+compatible exponential component yeah
+
+ align:start position:0%
+compatible exponential component yeah
+ 
+
+ align:start position:0%
+compatible exponential component yeah
+well so good world probably five years
+
+ align:start position:0%
+well so good world probably five years
+ 
+
+ align:start position:0%
+well so good world probably five years
+ago that's how it would work the two
+
+ align:start position:0%
+ago that's how it would work the two
+ 
+
+ align:start position:0%
+ago that's how it would work the two
+years interest rates now the last time I
+
+ align:start position:0%
+years interest rates now the last time I
+ 
+
+ align:start position:0%
+years interest rates now the last time I
+checked was I think 30 bits we can check
+
+ align:start position:0%
+checked was I think 30 bits we can check
+ 
+
+ align:start position:0%
+checked was I think 30 bits we can check
+where where is the bond is trading now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+give me a sec
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep 32 and a half basis points 1 11.6
+
+ align:start position:0%
+yep 32 and a half basis points 1 11.6
+ 
+
+ align:start position:0%
+yep 32 and a half basis points 1 11.6
+basis points up since the morning quite
+
+ align:start position:0%
+basis points up since the morning quite
+ 
+
+ align:start position:0%
+basis points up since the morning quite
+a bit by the way so yeah so right now
+
+ align:start position:0%
+a bit by the way so yeah so right now
+ 
+
+ align:start position:0%
+a bit by the way so yeah so right now
+interest rates are basically zero so
+
+ align:start position:0%
+interest rates are basically zero so
+ 
+
+ align:start position:0%
+interest rates are basically zero so
+these two these two lines would be very
+
+ align:start position:0%
+these two these two lines would be very
+ 
+
+ align:start position:0%
+these two these two lines would be very
+close right now in for two years in any
+
+ align:start position:0%
+close right now in for two years in any
+ 
+
+ align:start position:0%
+close right now in for two years in any
+case so coming back to our to our
+
+ align:start position:0%
+case so coming back to our to our
+ 
+
+ align:start position:0%
+case so coming back to our to our
+example so what's what's important here
+
+ align:start position:0%
+example so what's what's important here
+ 
+
+ align:start position:0%
+example so what's what's important here
+how did we arrive to to to the stripe
+
+ align:start position:0%
+how did we arrive to to to the stripe
+ 
+
+ align:start position:0%
+how did we arrive to to to the stripe
+resort to this price of the forward
+
+ align:start position:0%
+resort to this price of the forward
+ 
+
+ align:start position:0%
+resort to this price of the forward
+contract we in fact tried
+
+ align:start position:0%
+contract we in fact tried
+ 
+
+ align:start position:0%
+contract we in fact tried
+we took some some amount of stock in
+
+ align:start position:0%
+we took some some amount of stock in
+ 
+
+ align:start position:0%
+we took some some amount of stock in
+this particular case it will be the
+
+ align:start position:0%
+this particular case it will be the
+ 
+
+ align:start position:0%
+this particular case it will be the
+words the whole price of stock
+
+ align:start position:0%
+words the whole price of stock
+ 
+
+ align:start position:0%
+words the whole price of stock
+we took some amount of cash and by
+
+ align:start position:0%
+we took some amount of cash and by
+ 
+
+ align:start position:0%
+we took some amount of cash and by
+combining these two pieces we somehow
+
+ align:start position:0%
+combining these two pieces we somehow
+ 
+
+ align:start position:0%
+combining these two pieces we somehow
+replicated the final payoff right and
+
+ align:start position:0%
+replicated the final payoff right and
+ 
+
+ align:start position:0%
+replicated the final payoff right and
+that's the general idea of risk-neutral
+
+ align:start position:0%
+that's the general idea of risk-neutral
+ 
+
+ align:start position:0%
+that's the general idea of risk-neutral
+pricing pricing and replicating
+
+ align:start position:0%
+pricing pricing and replicating
+ 
+
+ align:start position:0%
+pricing pricing and replicating
+portfolio what we will try to do in the
+
+ align:start position:0%
+portfolio what we will try to do in the
+ 
+
+ align:start position:0%
+portfolio what we will try to do in the
+rest of the class is for take a payoff
+
+ align:start position:0%
+rest of the class is for take a payoff
+ 
+
+ align:start position:0%
+rest of the class is for take a payoff
+and try to find a replicating portfolio
+
+ align:start position:0%
+and try to find a replicating portfolio
+ 
+
+ align:start position:0%
+and try to find a replicating portfolio
+may be more complicated maybe than a
+
+ align:start position:0%
+may be more complicated maybe than a
+ 
+
+ align:start position:0%
+may be more complicated maybe than a
+dynamic dynamic such that at the end
+
+ align:start position:0%
+dynamic dynamic such that at the end
+ 
+
+ align:start position:0%
+dynamic dynamic such that at the end
+this replicating portfolio will be
+
+ align:start position:0%
+this replicating portfolio will be
+ 
+
+ align:start position:0%
+this replicating portfolio will be
+exactly our payoff right and what would
+
+ align:start position:0%
+exactly our payoff right and what would
+ 
+
+ align:start position:0%
+exactly our payoff right and what would
+it mean obviously it would mean that the
+
+ align:start position:0%
+it mean obviously it would mean that the
+ 
+
+ align:start position:0%
+it mean obviously it would mean that the
+current the the current price of the
+
+ align:start position:0%
+current the the current price of the
+ 
+
+ align:start position:0%
+current the the current price of the
+derivative should be the price of our
+
+ align:start position:0%
+derivative should be the price of our
+ 
+
+ align:start position:0%
+derivative should be the price of our
+replicating portfolio right now right
+
+ align:start position:0%
+replicating portfolio right now right
+ 
+
+ align:start position:0%
+replicating portfolio right now right
+and that's how the the risk-neutral
+
+ align:start position:0%
+and that's how the the risk-neutral
+ 
+
+ align:start position:0%
+and that's how the the risk-neutral
+pricing works so we are still in this
+
+ align:start position:0%
+pricing works so we are still in this
+ 
+
+ align:start position:0%
+pricing works so we are still in this
+simple situation but we will try to
+
+ align:start position:0%
+simple situation but we will try to
+ 
+
+ align:start position:0%
+simple situation but we will try to
+price a general pay payoff f1 a general
+
+ align:start position:0%
+price a general pay payoff f1 a general
+ 
+
+ align:start position:0%
+price a general pay payoff f1 a general
+payoff F right and here I how how it
+
+ align:start position:0%
+payoff F right and here I how how it
+ 
+
+ align:start position:0%
+payoff F right and here I how how it
+goes so we still will try to form our
+
+ align:start position:0%
+goes so we still will try to form our
+ 
+
+ align:start position:0%
+goes so we still will try to form our
+replicating portfolio out of the bond of
+
+ align:start position:0%
+replicating portfolio out of the bond of
+ 
+
+ align:start position:0%
+replicating portfolio out of the bond of
+some amount of bond and some amount of
+
+ align:start position:0%
+some amount of bond and some amount of
+ 
+
+ align:start position:0%
+some amount of bond and some amount of
+stock and we will say that will we will
+
+ align:start position:0%
+stock and we will say that will we will
+ 
+
+ align:start position:0%
+stock and we will say that will we will
+need a s1 and B of the bond right and we
+
+ align:start position:0%
+need a s1 and B of the bond right and we
+ 
+
+ align:start position:0%
+need a s1 and B of the bond right and we
+try to we'll try to find a and B
+
+ align:start position:0%
+try to we'll try to find a and B
+ 
+
+ align:start position:0%
+try to we'll try to find a and B
+that no matter what the real-world
+
+ align:start position:0%
+that no matter what the real-world
+ 
+
+ align:start position:0%
+that no matter what the real-world
+probability is we at maturity at one
+
+ align:start position:0%
+probability is we at maturity at one
+ 
+
+ align:start position:0%
+probability is we at maturity at one
+step maturity will replicate our payoff
+
+ align:start position:0%
+step maturity will replicate our payoff
+ 
+
+ align:start position:0%
+step maturity will replicate our payoff
+exactly unfortunately in this particular
+
+ align:start position:0%
+exactly unfortunately in this particular
+ 
+
+ align:start position:0%
+exactly unfortunately in this particular
+case that's very doable is just two
+
+ align:start position:0%
+case that's very doable is just two
+ 
+
+ align:start position:0%
+case that's very doable is just two
+equations with two variables we should
+
+ align:start position:0%
+equations with two variables we should
+ 
+
+ align:start position:0%
+equations with two variables we should
+be able to do it and we can solve it and
+
+ align:start position:0%
+be able to do it and we can solve it and
+ 
+
+ align:start position:0%
+be able to do it and we can solve it and
+find this a and B then we'll substitute
+
+ align:start position:0%
+find this a and B then we'll substitute
+ 
+
+ align:start position:0%
+find this a and B then we'll substitute
+them in this formula right take the
+
+ align:start position:0%
+them in this formula right take the
+ 
+
+ align:start position:0%
+them in this formula right take the
+current price of the stock which we know
+
+ align:start position:0%
+current price of the stock which we know
+ 
+
+ align:start position:0%
+current price of the stock which we know
+and and some cash and find the current
+
+ align:start position:0%
+and and some cash and find the current
+ 
+
+ align:start position:0%
+and and some cash and find the current
+price current price of the derivative
+
+ align:start position:0%
+price current price of the derivative
+ 
+
+ align:start position:0%
+price current price of the derivative
+right and this work this should work for
+
+ align:start position:0%
+right and this work this should work for
+ 
+
+ align:start position:0%
+right and this work this should work for
+any derivatives it doesn't matter is it
+
+ align:start position:0%
+any derivatives it doesn't matter is it
+ 
+
+ align:start position:0%
+any derivatives it doesn't matter is it
+forward call put or some complicated
+
+ align:start position:0%
+forward call put or some complicated
+ 
+
+ align:start position:0%
+forward call put or some complicated
+complicated option as long as it's
+
+ align:start position:0%
+complicated option as long as it's
+ 
+
+ align:start position:0%
+complicated option as long as it's
+deterministic at expiry an interesting
+
+ align:start position:0%
+deterministic at expiry an interesting
+ 
+
+ align:start position:0%
+deterministic at expiry an interesting
+way to look at it is to rewrite this
+
+ align:start position:0%
+way to look at it is to rewrite this
+ 
+
+ align:start position:0%
+way to look at it is to rewrite this
+formula slightly in such a way which
+
+ align:start position:0%
+formula slightly in such a way which
+ 
+
+ align:start position:0%
+formula slightly in such a way which
+does remind us taking a an expected
+
+ align:start position:0%
+does remind us taking a an expected
+ 
+
+ align:start position:0%
+does remind us taking a an expected
+value may be discounting it because this
+
+ align:start position:0%
+value may be discounting it because this
+ 
+
+ align:start position:0%
+value may be discounting it because this
+is expected value sometime in the future
+
+ align:start position:0%
+is expected value sometime in the future
+ 
+
+ align:start position:0%
+is expected value sometime in the future
+but this probability and it is a
+
+ align:start position:0%
+but this probability and it is a
+ 
+
+ align:start position:0%
+but this probability and it is a
+probability because this number Q here
+
+ align:start position:0%
+probability because this number Q here
+ 
+
+ align:start position:0%
+probability because this number Q here
+is between 0 and 1 but this probability
+
+ align:start position:0%
+is between 0 and 1 but this probability
+ 
+
+ align:start position:0%
+is between 0 and 1 but this probability
+has little to do with with real real
+
+ align:start position:0%
+has little to do with with real real
+ 
+
+ align:start position:0%
+has little to do with with real real
+real world right in fact it's something
+
+ align:start position:0%
+real world right in fact it's something
+ 
+
+ align:start position:0%
+real world right in fact it's something
+different but such probabilities exists
+
+ align:start position:0%
+different but such probabilities exists
+ 
+
+ align:start position:0%
+different but such probabilities exists
+and it's called the measure where our
+
+ align:start position:0%
+and it's called the measure where our
+ 
+
+ align:start position:0%
+and it's called the measure where our
+stock behaves like this is called a
+
+ align:start position:0%
+stock behaves like this is called a
+ 
+
+ align:start position:0%
+stock behaves like this is called a
+risk-neutral measure or martingale mere
+
+ align:start position:0%
+risk-neutral measure or martingale mere
+ 
+
+ align:start position:0%
+risk-neutral measure or martingale mere
+measure and in these measures will see
+
+ align:start position:0%
+measure and in these measures will see
+ 
+
+ align:start position:0%
+measure and in these measures will see
+the the value of all the derivative will
+
+ align:start position:0%
+the the value of all the derivative will
+ 
+
+ align:start position:0%
+the the value of all the derivative will
+be just expected value of our appeal and
+
+ align:start position:0%
+be just expected value of our appeal and
+ 
+
+ align:start position:0%
+be just expected value of our appeal and
+that's yeah that's what what I'm trying
+
+ align:start position:0%
+that's yeah that's what what I'm trying
+ 
+
+ align:start position:0%
+that's yeah that's what what I'm trying
+to say here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so now let's get into continuous
+
+ align:start position:0%
+now so now let's get into continuous
+ 
+
+ align:start position:0%
+now so now let's get into continuous
+world right in continuous world we will
+
+ align:start position:0%
+world right in continuous world we will
+ 
+
+ align:start position:0%
+world right in continuous world we will
+need some assumptions on the dynamics of
+
+ align:start position:0%
+need some assumptions on the dynamics of
+ 
+
+ align:start position:0%
+need some assumptions on the dynamics of
+our stock underline and let's make an
+
+ align:start position:0%
+our stock underline and let's make an
+ 
+
+ align:start position:0%
+our stock underline and let's make an
+assumption that it is law it it is log
+
+ align:start position:0%
+assumption that it is law it it is log
+ 
+
+ align:start position:0%
+assumption that it is law it it is log
+normal what it what does it mean that
+
+ align:start position:0%
+normal what it what does it mean that
+ 
+
+ align:start position:0%
+normal what it what does it mean that
+it's look more normal it means that the
+
+ align:start position:0%
+it's look more normal it means that the
+ 
+
+ align:start position:0%
+it's look more normal it means that the
+proportional change of the stock over
+
+ align:start position:0%
+proportional change of the stock over
+ 
+
+ align:start position:0%
+proportional change of the stock over
+infants infinitely small amount of time
+
+ align:start position:0%
+infants infinitely small amount of time
+ 
+
+ align:start position:0%
+infants infinitely small amount of time
+DT has some drift mu and some stochastic
+
+ align:start position:0%
+DT has some drift mu and some stochastic
+ 
+
+ align:start position:0%
+DT has some drift mu and some stochastic
+component which is just Brownian motion
+
+ align:start position:0%
+component which is just Brownian motion
+ 
+
+ align:start position:0%
+component which is just Brownian motion
+right so this DW is distributed normally
+
+ align:start position:0%
+right so this DW is distributed normally
+ 
+
+ align:start position:0%
+right so this DW is distributed normally
+with mean zero and start the deviation
+
+ align:start position:0%
+with mean zero and start the deviation
+ 
+
+ align:start position:0%
+with mean zero and start the deviation
+which is actually square root of DT
+
+ align:start position:0%
+which is actually square root of DT
+ 
+
+ align:start position:0%
+which is actually square root of DT
+that's how broadly emotion works and
+
+ align:start position:0%
+that's how broadly emotion works and
+ 
+
+ align:start position:0%
+that's how broadly emotion works and
+that's extremely important that the
+
+ align:start position:0%
+that's extremely important that the
+ 
+
+ align:start position:0%
+that's extremely important that the
+standard deviation of going Brownian
+
+ align:start position:0%
+standard deviation of going Brownian
+ 
+
+ align:start position:0%
+standard deviation of going Brownian
+motion is square root of delta T and
+
+ align:start position:0%
+motion is square root of delta T and
+ 
+
+ align:start position:0%
+motion is square root of delta T and
+that's how it works so and again we will
+
+ align:start position:0%
+that's how it works so and again we will
+ 
+
+ align:start position:0%
+that's how it works so and again we will
+use this idea of replicating portfolio
+
+ align:start position:0%
+use this idea of replicating portfolio
+ 
+
+ align:start position:0%
+use this idea of replicating portfolio
+what would it mean in this in this case
+
+ align:start position:0%
+what would it mean in this in this case
+ 
+
+ align:start position:0%
+what would it mean in this in this case
+well we will we would like to find such
+
+ align:start position:0%
+well we will we would like to find such
+ 
+
+ align:start position:0%
+well we will we would like to find such
+coefficients a and B on this infinitely
+
+ align:start position:0%
+coefficients a and B on this infinitely
+ 
+
+ align:start position:0%
+coefficients a and B on this infinitely
+small period of time DT such that by
+
+ align:start position:0%
+small period of time DT such that by
+ 
+
+ align:start position:0%
+small period of time DT such that by
+combining small changes in stock with
+
+ align:start position:0%
+combining small changes in stock with
+ 
+
+ align:start position:0%
+combining small changes in stock with
+coefficient a and small changes in in
+
+ align:start position:0%
+coefficient a and small changes in in
+ 
+
+ align:start position:0%
+coefficient a and small changes in in
+bond with with coefficient B will
+
+ align:start position:0%
+bond with with coefficient B will
+ 
+
+ align:start position:0%
+bond with with coefficient B will
+exactly replicate the change in the
+
+ align:start position:0%
+exactly replicate the change in the
+ 
+
+ align:start position:0%
+exactly replicate the change in the
+derivative in the payout of derivative
+
+ align:start position:0%
+derivative in the payout of derivative
+ 
+
+ align:start position:0%
+derivative in the payout of derivative
+in indeed not PL in the derivative in
+
+ align:start position:0%
+in indeed not PL in the derivative in
+ 
+
+ align:start position:0%
+in indeed not PL in the derivative in
+the change of the derivative over this
+
+ align:start position:0%
+the change of the derivative over this
+ 
+
+ align:start position:0%
+the change of the derivative over this
+infinitely small time T well to do this
+
+ align:start position:0%
+infinitely small time T well to do this
+ 
+
+ align:start position:0%
+infinitely small time T well to do this
+we will need to use it as formula did
+
+ align:start position:0%
+we will need to use it as formula did
+ 
+
+ align:start position:0%
+we will need to use it as formula did
+you talk about either already ok cool
+
+ align:start position:0%
+you talk about either already ok cool
+ 
+
+ align:start position:0%
+you talk about either already ok cool
+that's great
+
+ align:start position:0%
+that's great
+ 
+
+ align:start position:0%
+that's great
+so just to remind you that it is formula
+
+ align:start position:0%
+so just to remind you that it is formula
+ 
+
+ align:start position:0%
+so just to remind you that it is formula
+is nothing more than the Taylor rule
+
+ align:start position:0%
+is nothing more than the Taylor rule
+ 
+
+ align:start position:0%
+is nothing more than the Taylor rule
+the first approximation up to DT but
+
+ align:start position:0%
+the first approximation up to DT but
+ 
+
+ align:start position:0%
+the first approximation up to DT but
+because of of the standard deviation of
+
+ align:start position:0%
+because of of the standard deviation of
+ 
+
+ align:start position:0%
+because of of the standard deviation of
+the Brownian motion being on on the
+
+ align:start position:0%
+the Brownian motion being on on the
+ 
+
+ align:start position:0%
+the Brownian motion being on on the
+scale of square root of T we will need
+
+ align:start position:0%
+scale of square root of T we will need
+ 
+
+ align:start position:0%
+scale of square root of T we will need
+one more term right so one one term is
+
+ align:start position:0%
+one more term right so one one term is
+ 
+
+ align:start position:0%
+one more term right so one one term is
+DF DT by DT another is DF by D as well
+
+ align:start position:0%
+DF DT by DT another is DF by D as well
+ 
+
+ align:start position:0%
+DF DT by DT another is DF by D as well
+yes but and the square of GS now is is
+
+ align:start position:0%
+yes but and the square of GS now is is
+ 
+
+ align:start position:0%
+yes but and the square of GS now is is
+actually of order of magnitude of DT so
+
+ align:start position:0%
+actually of order of magnitude of DT so
+ 
+
+ align:start position:0%
+actually of order of magnitude of DT so
+we'll need a quadratic term there all
+
+ align:start position:0%
+we'll need a quadratic term there all
+ 
+
+ align:start position:0%
+we'll need a quadratic term there all
+right so if this is our DF so what we'll
+
+ align:start position:0%
+right so if this is our DF so what we'll
+ 
+
+ align:start position:0%
+right so if this is our DF so what we'll
+do we'll differentiate we will just
+
+ align:start position:0%
+do we'll differentiate we will just
+ 
+
+ align:start position:0%
+do we'll differentiate we will just
+substitute it here right we'll
+
+ align:start position:0%
+substitute it here right we'll
+ 
+
+ align:start position:0%
+substitute it here right we'll
+substitute it here we'll substitute DF
+
+ align:start position:0%
+substitute it here we'll substitute DF
+ 
+
+ align:start position:0%
+substitute it here we'll substitute DF
+taken from it as our D s each which is
+
+ align:start position:0%
+taken from it as our D s each which is
+ 
+
+ align:start position:0%
+taken from it as our D s each which is
+like this N and G B and D B is let's not
+
+ align:start position:0%
+like this N and G B and D B is let's not
+ 
+
+ align:start position:0%
+like this N and G B and D B is let's not
+forget that DB that B is deterministic
+
+ align:start position:0%
+forget that DB that B is deterministic
+ 
+
+ align:start position:0%
+forget that DB that B is deterministic
+right there is nothing uncertain about
+
+ align:start position:0%
+right there is nothing uncertain about
+ 
+
+ align:start position:0%
+right there is nothing uncertain about
+it so DB is actual RB DT right because
+
+ align:start position:0%
+it so DB is actual RB DT right because
+ 
+
+ align:start position:0%
+it so DB is actual RB DT right because
+our B grows exponentially with interest
+
+ align:start position:0%
+our B grows exponentially with interest
+ 
+
+ align:start position:0%
+our B grows exponentially with interest
+rate R so we substitute everything into
+
+ align:start position:0%
+rate R so we substitute everything into
+ 
+
+ align:start position:0%
+rate R so we substitute everything into
+the formula above this is just our DF
+
+ align:start position:0%
+the formula above this is just our DF
+ 
+
+ align:start position:0%
+the formula above this is just our DF
+with D as expanded and everything and
+
+ align:start position:0%
+with D as expanded and everything and
+ 
+
+ align:start position:0%
+with D as expanded and everything and
+then we start compare comparing the
+
+ align:start position:0%
+then we start compare comparing the
+ 
+
+ align:start position:0%
+then we start compare comparing the
+terms one immediate thing to notice that
+
+ align:start position:0%
+terms one immediate thing to notice that
+ 
+
+ align:start position:0%
+terms one immediate thing to notice that
+a has to be equal to G of D F for over D
+
+ align:start position:0%
+a has to be equal to G of D F for over D
+ 
+
+ align:start position:0%
+a has to be equal to G of D F for over D
+s for this for this to hold right and if
+
+ align:start position:0%
+s for this for this to hold right and if
+ 
+
+ align:start position:0%
+s for this for this to hold right and if
+we compare the the terms you know DT
+
+ align:start position:0%
+we compare the the terms you know DT
+ 
+
+ align:start position:0%
+we compare the the terms you know DT
+will get this expression here but that's
+
+ align:start position:0%
+will get this expression here but that's
+ 
+
+ align:start position:0%
+will get this expression here but that's
+actually even more the most important
+
+ align:start position:0%
+actually even more the most important
+ 
+
+ align:start position:0%
+actually even more the most important
+part then we'll we'll go and use the our
+
+ align:start position:0%
+part then we'll we'll go and use the our
+ 
+
+ align:start position:0%
+part then we'll we'll go and use the our
+knowledge that that some part of our
+
+ align:start position:0%
+knowledge that that some part of our
+ 
+
+ align:start position:0%
+knowledge that that some part of our
+equation is deterministic and basically
+
+ align:start position:0%
+equation is deterministic and basically
+ 
+
+ align:start position:0%
+equation is deterministic and basically
+take F and a s on one side and leave the
+
+ align:start position:0%
+take F and a s on one side and leave the
+ 
+
+ align:start position:0%
+take F and a s on one side and leave the
+deterministic part on the other side
+
+ align:start position:0%
+deterministic part on the other side
+ 
+
+ align:start position:0%
+deterministic part on the other side
+differentiate differentiate it once once
+
+ align:start position:0%
+differentiate differentiate it once once
+ 
+
+ align:start position:0%
+differentiate differentiate it once once
+again and left left side will be just RB
+
+ align:start position:0%
+again and left left side will be just RB
+ 
+
+ align:start position:0%
+again and left left side will be just RB
+DT and if we substitute once again d DF
+
+ align:start position:0%
+DT and if we substitute once again d DF
+ 
+
+ align:start position:0%
+DT and if we substitute once again d DF
+and don't forget that what we learned is
+
+ align:start position:0%
+and don't forget that what we learned is
+ 
+
+ align:start position:0%
+and don't forget that what we learned is
+that a is equal to DF by D s then we
+
+ align:start position:0%
+that a is equal to DF by D s then we
+ 
+
+ align:start position:0%
+that a is equal to DF by D s then we
+collect all the terms and arrive to this
+
+ align:start position:0%
+collect all the terms and arrive to this
+ 
+
+ align:start position:0%
+collect all the terms and arrive to this
+to this partial differential equation
+
+ align:start position:0%
+to this partial differential equation
+ 
+
+ align:start position:0%
+to this partial differential equation
+which which connects which basically is
+
+ align:start position:0%
+which which connects which basically is
+ 
+
+ align:start position:0%
+which which connects which basically is
+a partial differential equation for the
+
+ align:start position:0%
+a partial differential equation for the
+ 
+
+ align:start position:0%
+a partial differential equation for the
+current price of a derivative of any
+
+ align:start position:0%
+current price of a derivative of any
+ 
+
+ align:start position:0%
+current price of a derivative of any
+derivative and how it if we solve it
+
+ align:start position:0%
+derivative and how it if we solve it
+ 
+
+ align:start position:0%
+derivative and how it if we solve it
+then way we should should be able to to
+
+ align:start position:0%
+then way we should should be able to to
+ 
+
+ align:start position:0%
+then way we should should be able to to
+know the price of the order derivative
+
+ align:start position:0%
+know the price of the order derivative
+ 
+
+ align:start position:0%
+know the price of the order derivative
+so now how do we solve this this partial
+
+ align:start position:0%
+so now how do we solve this this partial
+ 
+
+ align:start position:0%
+so now how do we solve this this partial
+differential equation well yeah so a few
+
+ align:start position:0%
+differential equation well yeah so a few
+ 
+
+ align:start position:0%
+differential equation well yeah so a few
+observations about about this equation
+
+ align:start position:0%
+observations about about this equation
+ 
+
+ align:start position:0%
+observations about about this equation
+well the the first observation is that
+
+ align:start position:0%
+well the the first observation is that
+ 
+
+ align:start position:0%
+well the the first observation is that
+any tradable derivative we made no
+
+ align:start position:0%
+any tradable derivative we made no
+ 
+
+ align:start position:0%
+any tradable derivative we made no
+assumptions about the payoff so so any
+
+ align:start position:0%
+assumptions about the payoff so so any
+ 
+
+ align:start position:0%
+assumptions about the payoff so so any
+tradable derivative is any payoff should
+
+ align:start position:0%
+tradable derivative is any payoff should
+ 
+
+ align:start position:0%
+tradable derivative is any payoff should
+satisfy this equation the other
+
+ align:start position:0%
+satisfy this equation the other
+ 
+
+ align:start position:0%
+satisfy this equation the other
+observation is as we expected there is
+
+ align:start position:0%
+observation is as we expected there is
+ 
+
+ align:start position:0%
+observation is as we expected there is
+no dependency on real-world drift or any
+
+ align:start position:0%
+no dependency on real-world drift or any
+ 
+
+ align:start position:0%
+no dependency on real-world drift or any
+any probabilities of going up or down
+
+ align:start position:0%
+any probabilities of going up or down
+ 
+
+ align:start position:0%
+any probabilities of going up or down
+the only dependence dependence is on the
+
+ align:start position:0%
+the only dependence dependence is on the
+ 
+
+ align:start position:0%
+the only dependence dependence is on the
+volatility of the stock right not only
+
+ align:start position:0%
+volatility of the stock right not only
+ 
+
+ align:start position:0%
+volatility of the stock right not only
+we we found the value of the derivative
+
+ align:start position:0%
+we we found the value of the derivative
+ 
+
+ align:start position:0%
+we we found the value of the derivative
+so most importantly we actually we're
+
+ align:start position:0%
+so most importantly we actually we're
+ 
+
+ align:start position:0%
+so most importantly we actually we're
+able to come up with with a hedging
+
+ align:start position:0%
+able to come up with with a hedging
+ 
+
+ align:start position:0%
+able to come up with with a hedging
+strategy and what does it mean we came
+
+ align:start position:0%
+strategy and what does it mean we came
+ 
+
+ align:start position:0%
+strategy and what does it mean we came
+up with a hedging strategy
+
+ align:start position:0%
+up with a hedging strategy
+ 
+
+ align:start position:0%
+up with a hedging strategy
+well we found coefficients for any time
+
+ align:start position:0%
+well we found coefficients for any time
+ 
+
+ align:start position:0%
+well we found coefficients for any time
+we found the coefficients a and B such
+
+ align:start position:0%
+we found the coefficients a and B such
+ 
+
+ align:start position:0%
+we found the coefficients a and B such
+that we have a replicating portfolio so
+
+ align:start position:0%
+that we have a replicating portfolio so
+ 
+
+ align:start position:0%
+that we have a replicating portfolio so
+instead what we could do at any point of
+
+ align:start position:0%
+instead what we could do at any point of
+ 
+
+ align:start position:0%
+instead what we could do at any point of
+time we can hold the derivative the
+
+ align:start position:0%
+time we can hold the derivative the
+ 
+
+ align:start position:0%
+time we can hold the derivative the
+short a show derivative and long the
+
+ align:start position:0%
+short a show derivative and long the
+ 
+
+ align:start position:0%
+short a show derivative and long the
+portfolio of stock itself and some cash
+
+ align:start position:0%
+portfolio of stock itself and some cash
+ 
+
+ align:start position:0%
+portfolio of stock itself and some cash
+and we know how much it should be
+
+ align:start position:0%
+and we know how much it should be
+ 
+
+ align:start position:0%
+and we know how much it should be
+here it's more complicated we have to
+
+ align:start position:0%
+here it's more complicated we have to
+ 
+
+ align:start position:0%
+here it's more complicated we have to
+dynamically change these numbers as time
+
+ align:start position:0%
+dynamically change these numbers as time
+ 
+
+ align:start position:0%
+dynamically change these numbers as time
+develops every time DT we will have to
+
+ align:start position:0%
+develops every time DT we will have to
+ 
+
+ align:start position:0%
+develops every time DT we will have to
+rebound but both both parts will
+
+ align:start position:0%
+rebound but both both parts will
+ 
+
+ align:start position:0%
+rebound but both both parts will
+replicate each other perfectly
+
+ align:start position:0%
+replicate each other perfectly
+ 
+
+ align:start position:0%
+replicate each other perfectly
+it's like in a bookies example we can go
+
+ align:start position:0%
+it's like in a bookies example we can go
+ 
+
+ align:start position:0%
+it's like in a bookies example we can go
+go to a two counterparty I agree into
+
+ align:start position:0%
+go to a two counterparty I agree into
+ 
+
+ align:start position:0%
+go to a two counterparty I agree into
+four for some derivative contract
+
+ align:start position:0%
+four for some derivative contract
+ 
+
+ align:start position:0%
+four for some derivative contract
+probably with some fee and then we will
+
+ align:start position:0%
+probably with some fee and then we will
+ 
+
+ align:start position:0%
+probably with some fee and then we will
+go to exchange and buy the stock and and
+
+ align:start position:0%
+go to exchange and buy the stock and and
+ 
+
+ align:start position:0%
+go to exchange and buy the stock and and
+we will get just cash from the bank and
+
+ align:start position:0%
+we will get just cash from the bank and
+ 
+
+ align:start position:0%
+we will get just cash from the bank and
+we'll maintain this at some amount of
+
+ align:start position:0%
+we'll maintain this at some amount of
+ 
+
+ align:start position:0%
+we'll maintain this at some amount of
+talk and some amount of cash and we will
+
+ align:start position:0%
+talk and some amount of cash and we will
+ 
+
+ align:start position:0%
+talk and some amount of cash and we will
+be sure that we are we are hedged there
+
+ align:start position:0%
+be sure that we are we are hedged there
+ 
+
+ align:start position:0%
+be sure that we are we are hedged there
+is no risk in in this color combination
+
+ align:start position:0%
+is no risk in in this color combination
+ 
+
+ align:start position:0%
+is no risk in in this color combination
+of the derivative and in our hedge so we
+
+ align:start position:0%
+of the derivative and in our hedge so we
+ 
+
+ align:start position:0%
+of the derivative and in our hedge so we
+will just collect the fee on the
+
+ align:start position:0%
+will just collect the fee on the
+ 
+
+ align:start position:0%
+will just collect the fee on the
+transaction so that's that's what
+
+ align:start position:0%
+transaction so that's that's what
+ 
+
+ align:start position:0%
+transaction so that's that's what
+actually how the business is working we
+
+ align:start position:0%
+actually how the business is working we
+ 
+
+ align:start position:0%
+actually how the business is working we
+traders are trading and hedging their
+
+ align:start position:0%
+traders are trading and hedging their
+ 
+
+ align:start position:0%
+traders are trading and hedging their
+positions immediately I mean they do
+
+ align:start position:0%
+positions immediately I mean they do
+ 
+
+ align:start position:0%
+positions immediately I mean they do
+take some market risks but you want to
+
+ align:start position:0%
+take some market risks but you want to
+ 
+
+ align:start position:0%
+take some market risks but you want to
+take very very little and very
+
+ align:start position:0%
+take very very little and very
+ 
+
+ align:start position:0%
+take very very little and very
+directional or very specific market risk
+
+ align:start position:0%
+directional or very specific market risk
+ 
+
+ align:start position:0%
+directional or very specific market risk
+and not not everything so so the the our
+
+ align:start position:0%
+and not not everything so so the the our
+ 
+
+ align:start position:0%
+and not not everything so so the the our
+strategy allows us to have a hedging
+
+ align:start position:0%
+strategy allows us to have a hedging
+ 
+
+ align:start position:0%
+strategy allows us to have a hedging
+portfolio at the same time hedging
+
+ align:start position:0%
+portfolio at the same time hedging
+ 
+
+ align:start position:0%
+portfolio at the same time hedging
+strategy another more mathematical but
+
+ align:start position:0%
+strategy another more mathematical but
+ 
+
+ align:start position:0%
+strategy another more mathematical but
+practical consequence is that actually
+
+ align:start position:0%
+practical consequence is that actually
+ 
+
+ align:start position:0%
+practical consequence is that actually
+by certain not very easy change of
+
+ align:start position:0%
+by certain not very easy change of
+ 
+
+ align:start position:0%
+by certain not very easy change of
+variables we can take the black Scholes
+
+ align:start position:0%
+variables we can take the black Scholes
+ 
+
+ align:start position:0%
+variables we can take the black Scholes
+equation and put it back to heat
+
+ align:start position:0%
+equation and put it back to heat
+ 
+
+ align:start position:0%
+equation and put it back to heat
+equation actually it's I suggest it as
+
+ align:start position:0%
+equation actually it's I suggest it as
+ 
+
+ align:start position:0%
+equation actually it's I suggest it as
+one of the topics for the final paper
+
+ align:start position:0%
+one of the topics for the final paper
+ 
+
+ align:start position:0%
+one of the topics for the final paper
+for you to do it or check it out in the
+
+ align:start position:0%
+for you to do it or check it out in the
+ 
+
+ align:start position:0%
+for you to do it or check it out in the
+books and go and understand it but the
+
+ align:start position:0%
+books and go and understand it but the
+ 
+
+ align:start position:0%
+books and go and understand it but the
+good part of it that heat equation is
+
+ align:start position:0%
+good part of it that heat equation is
+ 
+
+ align:start position:0%
+good part of it that heat equation is
+well known and well well understood
+
+ align:start position:0%
+well known and well well understood
+ 
+
+ align:start position:0%
+well known and well well understood
+there there are many many ways to solve
+
+ align:start position:0%
+there there are many many ways to solve
+ 
+
+ align:start position:0%
+there there are many many ways to solve
+it numerically for for simple payouts or
+
+ align:start position:0%
+it numerically for for simple payouts or
+ 
+
+ align:start position:0%
+it numerically for for simple payouts or
+for calls and puts we don't have to do
+
+ align:start position:0%
+for calls and puts we don't have to do
+ 
+
+ align:start position:0%
+for calls and puts we don't have to do
+it numerically but if the payout payoffs
+
+ align:start position:0%
+it numerically but if the payout payoffs
+ 
+
+ align:start position:0%
+it numerically but if the payout payoffs
+are more complicated or the the dynamics
+
+ align:start position:0%
+are more complicated or the the dynamics
+ 
+
+ align:start position:0%
+are more complicated or the the dynamics
+is is different then numerical methods
+
+ align:start position:0%
+is is different then numerical methods
+ 
+
+ align:start position:0%
+is is different then numerical methods
+will be needed for
+
+ align:start position:0%
+will be needed for
+ 
+
+ align:start position:0%
+will be needed for
+so again to solve this equation we'll
+
+ align:start position:0%
+so again to solve this equation we'll
+ 
+
+ align:start position:0%
+so again to solve this equation we'll
+need as for any partial differential
+
+ align:start position:0%
+need as for any partial differential
+ 
+
+ align:start position:0%
+need as for any partial differential
+equation we'll need some boundary and
+
+ align:start position:0%
+equation we'll need some boundary and
+ 
+
+ align:start position:0%
+equation we'll need some boundary and
+initial conditions and these come from
+
+ align:start position:0%
+initial conditions and these come from
+ 
+
+ align:start position:0%
+initial conditions and these come from
+our final payout fro of the option right
+
+ align:start position:0%
+our final payout fro of the option right
+ 
+
+ align:start position:0%
+our final payout fro of the option right
+which we know we know what what happens
+
+ align:start position:0%
+which we know we know what what happens
+ 
+
+ align:start position:0%
+which we know we know what what happens
+at expiry and some boundary conditions
+
+ align:start position:0%
+at expiry and some boundary conditions
+ 
+
+ align:start position:0%
+at expiry and some boundary conditions
+for for call and put the final payout is
+
+ align:start position:0%
+for for call and put the final payout is
+ 
+
+ align:start position:0%
+for for call and put the final payout is
+we know right
+
+ align:start position:0%
+we know right
+ 
+
+ align:start position:0%
+we know right
+so at time T and the boundary conditions
+
+ align:start position:0%
+so at time T and the boundary conditions
+ 
+
+ align:start position:0%
+so at time T and the boundary conditions
+which describe we discussed we can
+
+ align:start position:0%
+which describe we discussed we can
+ 
+
+ align:start position:0%
+which describe we discussed we can
+observe them graphically so basically
+
+ align:start position:0%
+observe them graphically so basically
+ 
+
+ align:start position:0%
+observe them graphically so basically
+for call as we said at current time T
+
+ align:start position:0%
+for call as we said at current time T
+ 
+
+ align:start position:0%
+for call as we said at current time T
+and boundary 0 it should be 0 the price
+
+ align:start position:0%
+and boundary 0 it should be 0 the price
+ 
+
+ align:start position:0%
+and boundary 0 it should be 0 the price
+should be 0 and at at infinity it should
+
+ align:start position:0%
+should be 0 and at at infinity it should
+ 
+
+ align:start position:0%
+should be 0 and at at infinity it should
+be actually the forward price so it
+
+ align:start position:0%
+be actually the forward price so it
+ 
+
+ align:start position:0%
+be actually the forward price so it
+should be just discounted discounted
+
+ align:start position:0%
+should be just discounted discounted
+ 
+
+ align:start position:0%
+should be just discounted discounted
+discounted s minus K discounted payout
+
+ align:start position:0%
+discounted s minus K discounted payout
+ 
+
+ align:start position:0%
+discounted s minus K discounted payout
+rate and similarly fought for put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so given this these conditions and we we
+
+ align:start position:0%
+so given this these conditions and we we
+ 
+
+ align:start position:0%
+so given this these conditions and we we
+we can solve the equation and as I said
+
+ align:start position:0%
+we can solve the equation and as I said
+ 
+
+ align:start position:0%
+we can solve the equation and as I said
+for for : put and for simple dynamics or
+
+ align:start position:0%
+for for : put and for simple dynamics or
+ 
+
+ align:start position:0%
+for for : put and for simple dynamics or
+Blackshaw dynamic log normal dynamics
+
+ align:start position:0%
+Blackshaw dynamic log normal dynamics
+ 
+
+ align:start position:0%
+Blackshaw dynamic log normal dynamics
+actually these this equations can be
+
+ align:start position:0%
+actually these this equations can be
+ 
+
+ align:start position:0%
+actually these this equations can be
+solved exactly exactly
+
+ align:start position:0%
+solved exactly exactly
+ 
+
+ align:start position:0%
+solved exactly exactly
+meaning up to up to disturb the normal
+
+ align:start position:0%
+meaning up to up to disturb the normal
+ 
+
+ align:start position:0%
+meaning up to up to disturb the normal
+normal distribution which still has to
+
+ align:start position:0%
+normal distribution which still has to
+ 
+
+ align:start position:0%
+normal distribution which still has to
+be computed numerically obviously but
+
+ align:start position:0%
+be computed numerically obviously but
+ 
+
+ align:start position:0%
+be computed numerically obviously but
+here as a formulas they do kind of look
+
+ align:start position:0%
+here as a formulas they do kind of look
+ 
+
+ align:start position:0%
+here as a formulas they do kind of look
+a little bit and we'll see well about it
+
+ align:start position:0%
+a little bit and we'll see well about it
+ 
+
+ align:start position:0%
+a little bit and we'll see well about it
+that there is some kind of expected
+
+ align:start position:0%
+that there is some kind of expected
+ 
+
+ align:start position:0%
+that there is some kind of expected
+value blowing on right one probability
+
+ align:start position:0%
+value blowing on right one probability
+ 
+
+ align:start position:0%
+value blowing on right one probability
+times time times another but these are
+
+ align:start position:0%
+times time times another but these are
+ 
+
+ align:start position:0%
+times time times another but these are
+the formulas and that's how I drew the
+
+ align:start position:0%
+the formulas and that's how I drew the
+ 
+
+ align:start position:0%
+the formulas and that's how I drew the
+lines on the graphs and as I said in
+
+ align:start position:0%
+lines on the graphs and as I said in
+ 
+
+ align:start position:0%
+lines on the graphs and as I said in
+fact the whole world instead of solving
+
+ align:start position:0%
+fact the whole world instead of solving
+ 
+
+ align:start position:0%
+fact the whole world instead of solving
+the whole the whole partial differential
+
+ align:start position:0%
+the whole the whole partial differential
+ 
+
+ align:start position:0%
+the whole the whole partial differential
+equation we can approach it from a risk
+
+ align:start position:0%
+equation we can approach it from a risk
+ 
+
+ align:start position:0%
+equation we can approach it from a risk
+neutral risk neutral position and say
+
+ align:start position:0%
+neutral risk neutral position and say
+ 
+
+ align:start position:0%
+neutral risk neutral position and say
+that in fact the price of our derivative
+
+ align:start position:0%
+that in fact the price of our derivative
+ 
+
+ align:start position:0%
+that in fact the price of our derivative
+now is just as expected value of out pay
+
+ align:start position:0%
+now is just as expected value of out pay
+ 
+
+ align:start position:0%
+now is just as expected value of out pay
+or payout discounted probably from from
+
+ align:start position:0%
+or payout discounted probably from from
+ 
+
+ align:start position:0%
+or payout discounted probably from from
+the from the maturity but not in real
+
+ align:start position:0%
+the from the maturity but not in real
+ 
+
+ align:start position:0%
+the from the maturity but not in real
+time a real-world matter but in some
+
+ align:start position:0%
+time a real-world matter but in some
+ 
+
+ align:start position:0%
+time a real-world matter but in some
+specific risk-neutral measure and how
+
+ align:start position:0%
+specific risk-neutral measure and how
+ 
+
+ align:start position:0%
+specific risk-neutral measure and how
+how do you find this risk-neutral
+
+ align:start position:0%
+how do you find this risk-neutral
+ 
+
+ align:start position:0%
+how do you find this risk-neutral
+measure well the risk-neutral measure is
+
+ align:start position:0%
+measure well the risk-neutral measure is
+ 
+
+ align:start position:0%
+measure well the risk-neutral measure is
+such that the drift of our stock is
+
+ align:start position:0%
+such that the drift of our stock is
+ 
+
+ align:start position:0%
+such that the drift of our stock is
+actually interest rate its riskless
+
+ align:start position:0%
+actually interest rate its riskless
+ 
+
+ align:start position:0%
+actually interest rate its riskless
+that's exactly how how we saw we saw it
+
+ align:start position:0%
+that's exactly how how we saw we saw it
+ 
+
+ align:start position:0%
+that's exactly how how we saw we saw it
+we saw it in our binary example right so
+
+ align:start position:0%
+we saw it in our binary example right so
+ 
+
+ align:start position:0%
+we saw it in our binary example right so
+even in our binary example the our
+
+ align:start position:0%
+even in our binary example the our
+ 
+
+ align:start position:0%
+even in our binary example the our
+expected value of our stock under
+
+ align:start position:0%
+expected value of our stock under
+ 
+
+ align:start position:0%
+expected value of our stock under
+risk-neutral measure meaning
+
+ align:start position:0%
+risk-neutral measure meaning
+ 
+
+ align:start position:0%
+risk-neutral measure meaning
+using the risk-neutral probability was
+
+ align:start position:0%
+using the risk-neutral probability was
+ 
+
+ align:start position:0%
+using the risk-neutral probability was
+was drifting with this interest rate are
+
+ align:start position:0%
+was drifting with this interest rate are
+ 
+
+ align:start position:0%
+was drifting with this interest rate are
+so that the same happens in in
+
+ align:start position:0%
+so that the same happens in in
+ 
+
+ align:start position:0%
+so that the same happens in in
+continuous case and that's another good
+
+ align:start position:0%
+continuous case and that's another good
+ 
+
+ align:start position:0%
+continuous case and that's another good
+exercise and I would accept it as a
+
+ align:start position:0%
+exercise and I would accept it as a
+ 
+
+ align:start position:0%
+exercise and I would accept it as a
+final paper is computing black Scholes
+
+ align:start position:0%
+final paper is computing black Scholes
+ 
+
+ align:start position:0%
+final paper is computing black Scholes
+black Scholes driving the black Scholes
+
+ align:start position:0%
+black Scholes driving the black Scholes
+ 
+
+ align:start position:0%
+black Scholes driving the black Scholes
+formula just by discount by taking
+
+ align:start position:0%
+formula just by discount by taking
+ 
+
+ align:start position:0%
+formula just by discount by taking
+expected value of the Colin put payout
+
+ align:start position:0%
+expected value of the Colin put payout
+ 
+
+ align:start position:0%
+expected value of the Colin put payout
+with is the distribution log normal
+
+ align:start position:0%
+with is the distribution log normal
+ 
+
+ align:start position:0%
+with is the distribution log normal
+distribution terminal distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright so for more complicated payoffs
+
+ align:start position:0%
+alright so for more complicated payoffs
+ 
+
+ align:start position:0%
+alright so for more complicated payoffs
+the the the life becomes more
+
+ align:start position:0%
+the the the life becomes more
+ 
+
+ align:start position:0%
+the the the life becomes more
+complicated and some finite differences
+
+ align:start position:0%
+complicated and some finite differences
+ 
+
+ align:start position:0%
+complicated and some finite differences
+should be used for more complicated
+
+ align:start position:0%
+should be used for more complicated
+ 
+
+ align:start position:0%
+should be used for more complicated
+payoffs or American payoffs or past the
+
+ align:start position:0%
+payoffs or American payoffs or past the
+ 
+
+ align:start position:0%
+payoffs or American payoffs or past the
+penalty of three methods or Monte colors
+
+ align:start position:0%
+penalty of three methods or Monte colors
+ 
+
+ align:start position:0%
+penalty of three methods or Monte colors
+in simulations and that's what was
+
+ align:start position:0%
+in simulations and that's what was
+ 
+
+ align:start position:0%
+in simulations and that's what was
+happening in real life yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now since we have actually a point of
+
+ align:start position:0%
+now since we have actually a point of
+ 
+
+ align:start position:0%
+now since we have actually a point of
+time I I would like to give an example
+
+ align:start position:0%
+time I I would like to give an example
+ 
+
+ align:start position:0%
+time I I would like to give an example
+of how replicating idea of replicating
+
+ align:start position:0%
+of how replicating idea of replicating
+ 
+
+ align:start position:0%
+of how replicating idea of replicating
+portfolio works I give a couple of more
+
+ align:start position:0%
+portfolio works I give a couple of more
+ 
+
+ align:start position:0%
+portfolio works I give a couple of more
+examples so so okay here is a Bloomberg
+
+ align:start position:0%
+examples so so okay here is a Bloomberg
+ 
+
+ align:start position:0%
+examples so so okay here is a Bloomberg
+screen for foreign options call options
+
+ align:start position:0%
+screen for foreign options call options
+ 
+
+ align:start position:0%
+screen for foreign options call options
+on IBM stock it's actually was taking a
+
+ align:start position:0%
+on IBM stock it's actually was taking a
+ 
+
+ align:start position:0%
+on IBM stock it's actually was taking a
+while ago a few years ago but for add so
+
+ align:start position:0%
+while ago a few years ago but for add so
+ 
+
+ align:start position:0%
+while ago a few years ago but for add so
+here are different strikes for a call
+
+ align:start position:0%
+here are different strikes for a call
+ 
+
+ align:start position:0%
+here are different strikes for a call
+option the the current price of the
+
+ align:start position:0%
+option the the current price of the
+ 
+
+ align:start position:0%
+option the the current price of the
+stock is 81 point point 14 and here are
+
+ align:start position:0%
+stock is 81 point point 14 and here are
+ 
+
+ align:start position:0%
+stock is 81 point point 14 and here are
+the strikes of of the call so obviously
+
+ align:start position:0%
+the strikes of of the call so obviously
+ 
+
+ align:start position:0%
+the strikes of of the call so obviously
+if if the option is if the option is way
+
+ align:start position:0%
+if if the option is if the option is way
+ 
+
+ align:start position:0%
+if if the option is if the option is way
+out of the money meaning the strike is
+
+ align:start position:0%
+out of the money meaning the strike is
+ 
+
+ align:start position:0%
+out of the money meaning the strike is
+very high compared to to the stock price
+
+ align:start position:0%
+very high compared to to the stock price
+ 
+
+ align:start position:0%
+very high compared to to the stock price
+they the value of the option is 0 if
+
+ align:start position:0%
+they the value of the option is 0 if
+ 
+
+ align:start position:0%
+they the value of the option is 0 if
+it's way in the money in fact it is just
+
+ align:start position:0%
+it's way in the money in fact it is just
+ 
+
+ align:start position:0%
+it's way in the money in fact it is just
+s minus K so s meaning of being 81 and
+
+ align:start position:0%
+s minus K so s meaning of being 81 and
+ 
+
+ align:start position:0%
+s minus K so s meaning of being 81 and
+say the strike being 55 so it's 26 right
+
+ align:start position:0%
+say the strike being 55 so it's 26 right
+ 
+
+ align:start position:0%
+say the strike being 55 so it's 26 right
+there is some difference but actually
+
+ align:start position:0%
+there is some difference but actually
+ 
+
+ align:start position:0%
+there is some difference but actually
+here it's it's a bit small because the
+
+ align:start position:0%
+here it's it's a bit small because the
+ 
+
+ align:start position:0%
+here it's it's a bit small because the
+difference should be judge discounting
+
+ align:start position:0%
+difference should be judge discounting
+ 
+
+ align:start position:0%
+difference should be judge discounting
+as we know right but it's pretty short
+
+ align:start position:0%
+as we know right but it's pretty short
+ 
+
+ align:start position:0%
+as we know right but it's pretty short
+dated options the options they they're
+
+ align:start position:0%
+dated options the options they they're
+ 
+
+ align:start position:0%
+dated options the options they they're
+probably a month a month long so there
+
+ align:start position:0%
+probably a month a month long so there
+ 
+
+ align:start position:0%
+probably a month a month long so there
+is not much discounting so it becomes
+
+ align:start position:0%
+is not much discounting so it becomes
+ 
+
+ align:start position:0%
+is not much discounting so it becomes
+pretty pal it's similar here right so I
+
+ align:start position:0%
+pretty pal it's similar here right so I
+ 
+
+ align:start position:0%
+pretty pal it's similar here right so I
+mean this changes by five these changes
+
+ align:start position:0%
+mean this changes by five these changes
+ 
+
+ align:start position:0%
+mean this changes by five these changes
+by five it's pretty linear but it
+
+ align:start position:0%
+by five it's pretty linear but it
+ 
+
+ align:start position:0%
+by five it's pretty linear but it
+becomes nonlinear around the money
+
+ align:start position:0%
+becomes nonlinear around the money
+ 
+
+ align:start position:0%
+becomes nonlinear around the money
+around current stock price right so we
+
+ align:start position:0%
+around current stock price right so we
+ 
+
+ align:start position:0%
+around current stock price right so we
+do observe this this behavior but to
+
+ align:start position:0%
+do observe this this behavior but to
+ 
+
+ align:start position:0%
+do observe this this behavior but to
+tell the truth here if you were to I
+
+ align:start position:0%
+tell the truth here if you were to I
+ 
+
+ align:start position:0%
+tell the truth here if you were to I
+didn't put the implied volatilities here
+
+ align:start position:0%
+didn't put the implied volatilities here
+ 
+
+ align:start position:0%
+didn't put the implied volatilities here
+but that's actually you would observe
+
+ align:start position:0%
+but that's actually you would observe
+ 
+
+ align:start position:0%
+but that's actually you would observe
+that the world is not black Scholes
+
+ align:start position:0%
+that the world is not black Scholes
+ 
+
+ align:start position:0%
+that the world is not black Scholes
+meaning that what's the assumption of
+
+ align:start position:0%
+meaning that what's the assumption of
+ 
+
+ align:start position:0%
+meaning that what's the assumption of
+black Scholes the assumption of black
+
+ align:start position:0%
+black Scholes the assumption of black
+ 
+
+ align:start position:0%
+black Scholes the assumption of black
+Scholes is that every option for for any
+
+ align:start position:0%
+Scholes is that every option for for any
+ 
+
+ align:start position:0%
+Scholes is that every option for for any
+strike on a given stock and I give an
+
+ align:start position:0%
+strike on a given stock and I give an
+ 
+
+ align:start position:0%
+strike on a given stock and I give an
+expiry would have the same volatility
+
+ align:start position:0%
+expiry would have the same volatility
+ 
+
+ align:start position:0%
+expiry would have the same volatility
+right so if we went through the size of
+
+ align:start position:0%
+right so if we went through the size of
+ 
+
+ align:start position:0%
+right so if we went through the size of
+implying the volatility according to
+
+ align:start position:0%
+implying the volatility according to
+ 
+
+ align:start position:0%
+implying the volatility according to
+black Scholes formula from from the
+
+ align:start position:0%
+black Scholes formula from from the
+ 
+
+ align:start position:0%
+black Scholes formula from from the
+option price which is traded on the
+
+ align:start position:0%
+option price which is traded on the
+ 
+
+ align:start position:0%
+option price which is traded on the
+market and an current price we would
+
+ align:start position:0%
+market and an current price we would
+ 
+
+ align:start position:0%
+market and an current price we would
+find out that actually the the
+
+ align:start position:0%
+find out that actually the the
+ 
+
+ align:start position:0%
+find out that actually the the
+volatility is not is not constant with
+
+ align:start position:0%
+volatility is not is not constant with
+ 
+
+ align:start position:0%
+volatility is not is not constant with
+strike well it's actually skewed well
+
+ align:start position:0%
+strike well it's actually skewed well
+ 
+
+ align:start position:0%
+strike well it's actually skewed well
+actually it's it is smile we would find
+
+ align:start position:0%
+actually it's it is smile we would find
+ 
+
+ align:start position:0%
+actually it's it is smile we would find
+something like this which means that
+
+ align:start position:0%
+something like this which means that
+ 
+
+ align:start position:0%
+something like this which means that
+black hole theory is not perfectly good
+
+ align:start position:0%
+black hole theory is not perfectly good
+ 
+
+ align:start position:0%
+black hole theory is not perfectly good
+right so something more complicated is
+
+ align:start position:0%
+right so something more complicated is
+ 
+
+ align:start position:0%
+right so something more complicated is
+should be done but in some cases we even
+
+ align:start position:0%
+should be done but in some cases we even
+ 
+
+ align:start position:0%
+should be done but in some cases we even
+don't need to do something more
+
+ align:start position:0%
+don't need to do something more
+ 
+
+ align:start position:0%
+don't need to do something more
+complicated one example being so-called
+
+ align:start position:0%
+complicated one example being so-called
+ 
+
+ align:start position:0%
+complicated one example being so-called
+put-call parity right so let's see
+
+ align:start position:0%
+put-call parity right so let's see
+ 
+
+ align:start position:0%
+put-call parity right so let's see
+suppose we look at the screen so we know
+
+ align:start position:0%
+suppose we look at the screen so we know
+ 
+
+ align:start position:0%
+suppose we look at the screen so we know
+all prices for all Co options for all
+
+ align:start position:0%
+all prices for all Co options for all
+ 
+
+ align:start position:0%
+all prices for all Co options for all
+strikes well probably some granularity
+
+ align:start position:0%
+strikes well probably some granularity
+ 
+
+ align:start position:0%
+strikes well probably some granularity
+but we know those but instead of pricing
+
+ align:start position:0%
+but we know those but instead of pricing
+ 
+
+ align:start position:0%
+but we know those but instead of pricing
+a code we need to price a put somehow we
+
+ align:start position:0%
+a code we need to price a put somehow we
+ 
+
+ align:start position:0%
+a code we need to price a put somehow we
+don't know how I am except our stock
+
+ align:start position:0%
+don't know how I am except our stock
+ 
+
+ align:start position:0%
+don't know how I am except our stock
+looks like so we have strong suspicions
+
+ align:start position:0%
+looks like so we have strong suspicions
+ 
+
+ align:start position:0%
+looks like so we have strong suspicions
+it's not exactly log normal so there is
+
+ align:start position:0%
+it's not exactly log normal so there is
+ 
+
+ align:start position:0%
+it's not exactly log normal so there is
+some volatility smile it's not
+
+ align:start position:0%
+some volatility smile it's not
+ 
+
+ align:start position:0%
+some volatility smile it's not
+constantly the world is slightly not
+
+ align:start position:0%
+constantly the world is slightly not
+ 
+
+ align:start position:0%
+constantly the world is slightly not
+black Scholes
+
+ align:start position:0%
+black Scholes
+ 
+
+ align:start position:0%
+black Scholes
+so how how do we price put well let's
+
+ align:start position:0%
+so how how do we price put well let's
+ 
+
+ align:start position:0%
+so how how do we price put well let's
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will stare long enough at the payouts of
+
+ align:start position:0%
+will stare long enough at the payouts of
+ 
+
+ align:start position:0%
+will stare long enough at the payouts of
+the : put so what's the payout of of a
+
+ align:start position:0%
+the : put so what's the payout of of a
+ 
+
+ align:start position:0%
+the : put so what's the payout of of a
+call with some strike it looks like this
+
+ align:start position:0%
+call with some strike it looks like this
+ 
+
+ align:start position:0%
+call with some strike it looks like this
+right the payout of the put with the
+
+ align:start position:0%
+right the payout of the put with the
+ 
+
+ align:start position:0%
+right the payout of the put with the
+same strike would look like this so what
+
+ align:start position:0%
+same strike would look like this so what
+ 
+
+ align:start position:0%
+same strike would look like this so what
+if we take we buy a call and sell a put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this would go like this right
+
+ align:start position:0%
+so this would go like this right
+ 
+
+ align:start position:0%
+so this would go like this right
+straight line looks very much like
+
+ align:start position:0%
+straight line looks very much like
+ 
+
+ align:start position:0%
+straight line looks very much like
+forward right so if we actually subtract
+
+ align:start position:0%
+forward right so if we actually subtract
+ 
+
+ align:start position:0%
+forward right so if we actually subtract
+a stock from here move it from here then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it should be yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+- Kay yeah I think I think I do go to
+
+ align:start position:0%
+- Kay yeah I think I think I do go to
+ 
+
+ align:start position:0%
+- Kay yeah I think I think I do go to
+science correct right and and this is
+
+ align:start position:0%
+science correct right and and this is
+ 
+
+ align:start position:0%
+science correct right and and this is
+just a number right and that's what
+
+ align:start position:0%
+just a number right and that's what
+ 
+
+ align:start position:0%
+just a number right and that's what
+happens at payout so if we take this
+
+ align:start position:0%
+happens at payout so if we take this
+ 
+
+ align:start position:0%
+happens at payout so if we take this
+portfolio if we action now by call
+
+ align:start position:0%
+portfolio if we action now by call
+ 
+
+ align:start position:0%
+portfolio if we action now by call
+seller put and sell stock we know that
+
+ align:start position:0%
+seller put and sell stock we know that
+ 
+
+ align:start position:0%
+seller put and sell stock we know that
+at the end we'll for sure get the K in
+
+ align:start position:0%
+at the end we'll for sure get the K in
+ 
+
+ align:start position:0%
+at the end we'll for sure get the K in
+money right so which means that now so
+
+ align:start position:0%
+money right so which means that now so
+ 
+
+ align:start position:0%
+money right so which means that now so
+this this is at time T so right now it
+
+ align:start position:0%
+this this is at time T so right now it
+ 
+
+ align:start position:0%
+this this is at time T so right now it
+looks to me that if we do write this and
+
+ align:start position:0%
+looks to me that if we do write this and
+ 
+
+ align:start position:0%
+looks to me that if we do write this and
+that's just the current price of the
+
+ align:start position:0%
+that's just the current price of the
+ 
+
+ align:start position:0%
+that's just the current price of the
+stock this should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right we just need to discount this
+
+ align:start position:0%
+right we just need to discount this
+ 
+
+ align:start position:0%
+right we just need to discount this
+price to two now this amount of cash
+
+ align:start position:0%
+price to two now this amount of cash
+ 
+
+ align:start position:0%
+price to two now this amount of cash
+which means that our put at any time T
+
+ align:start position:0%
+which means that our put at any time T
+ 
+
+ align:start position:0%
+which means that our put at any time T
+is stock minus K right so if we know all
+
+ align:start position:0%
+is stock minus K right so if we know all
+ 
+
+ align:start position:0%
+is stock minus K right so if we know all
+the prices for any strike k if you know
+
+ align:start position:0%
+the prices for any strike k if you know
+ 
+
+ align:start position:0%
+the prices for any strike k if you know
+if we know price of a call we don't need
+
+ align:start position:0%
+if we know price of a call we don't need
+ 
+
+ align:start position:0%
+if we know price of a call we don't need
+any black Scholes or or anything we can
+
+ align:start position:0%
+any black Scholes or or anything we can
+ 
+
+ align:start position:0%
+any black Scholes or or anything we can
+immediately tell everybody how how much
+
+ align:start position:0%
+immediately tell everybody how how much
+ 
+
+ align:start position:0%
+immediately tell everybody how how much
+is either put right so this this
+
+ align:start position:0%
+is either put right so this this
+ 
+
+ align:start position:0%
+is either put right so this this
+relationship is actually called Co put
+
+ align:start position:0%
+relationship is actually called Co put
+ 
+
+ align:start position:0%
+relationship is actually called Co put
+parity and that's again that's that's a
+
+ align:start position:0%
+parity and that's again that's that's a
+ 
+
+ align:start position:0%
+parity and that's again that's that's a
+replicating portfolio it's a
+
+ align:start position:0%
+replicating portfolio it's a
+ 
+
+ align:start position:0%
+replicating portfolio it's a
+simplification possible it's static
+
+ align:start position:0%
+simplification possible it's static
+ 
+
+ align:start position:0%
+simplification possible it's static
+meaning that we fix it now and we don't
+
+ align:start position:0%
+meaning that we fix it now and we don't
+ 
+
+ align:start position:0%
+meaning that we fix it now and we don't
+change it till the till expire so it's
+
+ align:start position:0%
+change it till the till expire so it's
+ 
+
+ align:start position:0%
+change it till the till expire so it's
+it's quite good this way
+
+ align:start position:0%
+it's quite good this way
+ 
+
+ align:start position:0%
+it's quite good this way
+but that's that's how it works
+
+ align:start position:0%
+but that's that's how it works
+ 
+
+ align:start position:0%
+but that's that's how it works
+another example so for this I have
+
+ align:start position:0%
+another example so for this I have
+ 
+
+ align:start position:0%
+another example so for this I have
+actually a picture so again we have the
+
+ align:start position:0%
+actually a picture so again we have the
+ 
+
+ align:start position:0%
+actually a picture so again we have the
+same situation we have prices of cold
+
+ align:start position:0%
+same situation we have prices of cold
+ 
+
+ align:start position:0%
+same situation we have prices of cold
+but instead of pricing a call we want to
+
+ align:start position:0%
+but instead of pricing a call we want to
+ 
+
+ align:start position:0%
+but instead of pricing a call we want to
+price digital so what is digital digital
+
+ align:start position:0%
+price digital so what is digital digital
+ 
+
+ align:start position:0%
+price digital so what is digital digital
+is such a weird contract which payout is
+
+ align:start position:0%
+is such a weird contract which payout is
+ 
+
+ align:start position:0%
+is such a weird contract which payout is
+just step function basically it's a bet
+
+ align:start position:0%
+just step function basically it's a bet
+ 
+
+ align:start position:0%
+just step function basically it's a bet
+on on a stock to to finish above strike
+
+ align:start position:0%
+on on a stock to to finish above strike
+ 
+
+ align:start position:0%
+on on a stock to to finish above strike
+price K right if if at expiry the stock
+
+ align:start position:0%
+price K right if if at expiry the stock
+ 
+
+ align:start position:0%
+price K right if if at expiry the stock
+is above K you get one you get one
+
+ align:start position:0%
+is above K you get one you get one
+ 
+
+ align:start position:0%
+is above K you get one you get one
+dollar if it's below you get nothing
+
+ align:start position:0%
+dollar if it's below you get nothing
+ 
+
+ align:start position:0%
+dollar if it's below you get nothing
+zero right so so such an interesting
+
+ align:start position:0%
+zero right so so such an interesting
+ 
+
+ align:start position:0%
+zero right so so such an interesting
+contract the question is can we price it
+
+ align:start position:0%
+contract the question is can we price it
+ 
+
+ align:start position:0%
+contract the question is can we price it
+given that we know the the practice of
+
+ align:start position:0%
+given that we know the the practice of
+ 
+
+ align:start position:0%
+given that we know the the practice of
+calls so an I suggest we we use the idea
+
+ align:start position:0%
+calls so an I suggest we we use the idea
+ 
+
+ align:start position:0%
+calls so an I suggest we we use the idea
+of replicating portfolio any ideas
+
+ align:start position:0%
+of replicating portfolio any ideas
+ 
+
+ align:start position:0%
+of replicating portfolio any ideas
+how to do it it's my typical typical
+
+ align:start position:0%
+how to do it it's my typical typical
+ 
+
+ align:start position:0%
+how to do it it's my typical typical
+interview question we'll just pretend
+
+ align:start position:0%
+interview question we'll just pretend
+ 
+
+ align:start position:0%
+interview question we'll just pretend
+that your interview yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the culprit yeah you're absolutely good
+
+ align:start position:0%
+the culprit yeah you're absolutely good
+ 
+
+ align:start position:0%
+the culprit yeah you're absolutely good
+you're you got enough yeah so here here
+
+ align:start position:0%
+you're you got enough yeah so here here
+ 
+
+ align:start position:0%
+you're you got enough yeah so here here
+here how it goes so this is a a strike a
+
+ align:start position:0%
+here how it goes so this is a a strike a
+ 
+
+ align:start position:0%
+here how it goes so this is a a strike a
+right so let's let's buy well buy a call
+
+ align:start position:0%
+right so let's let's buy well buy a call
+ 
+
+ align:start position:0%
+right so let's let's buy well buy a call
+with strike K minus 1/2 and sell a call
+
+ align:start position:0%
+with strike K minus 1/2 and sell a call
+ 
+
+ align:start position:0%
+with strike K minus 1/2 and sell a call
+with with strike K plus 1/2 right that's
+
+ align:start position:0%
+with with strike K plus 1/2 right that's
+ 
+
+ align:start position:0%
+with with strike K plus 1/2 right that's
+we just sold so how the if we combine
+
+ align:start position:0%
+we just sold so how the if we combine
+ 
+
+ align:start position:0%
+we just sold so how the if we combine
+these two well actually if it if this is
+
+ align:start position:0%
+these two well actually if it if this is
+ 
+
+ align:start position:0%
+these two well actually if it if this is
+one yeah this is one it should look
+
+ align:start position:0%
+one yeah this is one it should look
+ 
+
+ align:start position:0%
+one yeah this is one it should look
+something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so how will it look like so obviously
+
+ align:start position:0%
+so how will it look like so obviously
+ 
+
+ align:start position:0%
+so how will it look like so obviously
+here it's zero right then it will be
+
+ align:start position:0%
+here it's zero right then it will be
+ 
+
+ align:start position:0%
+here it's zero right then it will be
+like this right and after that it will
+
+ align:start position:0%
+like this right and after that it will
+ 
+
+ align:start position:0%
+like this right and after that it will
+be what it will be constantly and
+
+ align:start position:0%
+be what it will be constantly and
+ 
+
+ align:start position:0%
+be what it will be constantly and
+because this is key minus 1/2 and this
+
+ align:start position:0%
+because this is key minus 1/2 and this
+ 
+
+ align:start position:0%
+because this is key minus 1/2 and this
+is K plus 1/2 it will be exactly 1 right
+
+ align:start position:0%
+is K plus 1/2 it will be exactly 1 right
+ 
+
+ align:start position:0%
+is K plus 1/2 it will be exactly 1 right
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so our way payout at the end will be
+
+ align:start position:0%
+so our way payout at the end will be
+ 
+
+ align:start position:0%
+so our way payout at the end will be
+like this so it's good but there is
+
+ align:start position:0%
+like this so it's good but there is
+ 
+
+ align:start position:0%
+like this so it's good but there is
+quite a bit of slope here so how can we
+
+ align:start position:0%
+quite a bit of slope here so how can we
+ 
+
+ align:start position:0%
+quite a bit of slope here so how can we
+do better than this well if we sell it
+
+ align:start position:0%
+do better than this well if we sell it
+ 
+
+ align:start position:0%
+do better than this well if we sell it
+at K minus by that K minus 1/4 and and
+
+ align:start position:0%
+at K minus by that K minus 1/4 and and
+ 
+
+ align:start position:0%
+at K minus by that K minus 1/4 and and
+sell that at K of plus 1/4 and combine
+
+ align:start position:0%
+sell that at K of plus 1/4 and combine
+ 
+
+ align:start position:0%
+sell that at K of plus 1/4 and combine
+just combine those it will be exactly
+
+ align:start position:0%
+just combine those it will be exactly
+ 
+
+ align:start position:0%
+just combine those it will be exactly
+the same but the the level will be 1/2
+
+ align:start position:0%
+the same but the the level will be 1/2
+ 
+
+ align:start position:0%
+the same but the the level will be 1/2
+so we need to buy to buy two of those in
+
+ align:start position:0%
+so we need to buy to buy two of those in
+ 
+
+ align:start position:0%
+so we need to buy to buy two of those in
+to sell two of those right well we might
+
+ align:start position:0%
+to sell two of those right well we might
+ 
+
+ align:start position:0%
+to sell two of those right well we might
+as well go k minus epsilon and K plus
+
+ align:start position:0%
+as well go k minus epsilon and K plus
+ 
+
+ align:start position:0%
+as well go k minus epsilon and K plus
+epsilon so it will be cold price at
+
+ align:start position:0%
+epsilon so it will be cold price at
+ 
+
+ align:start position:0%
+epsilon so it will be cold price at
+strike K minus epsilon minus call price
+
+ align:start position:0%
+strike K minus epsilon minus call price
+ 
+
+ align:start position:0%
+strike K minus epsilon minus call price
+at K plus epsilon divided by two epsilon
+
+ align:start position:0%
+at K plus epsilon divided by two epsilon
+ 
+
+ align:start position:0%
+at K plus epsilon divided by two epsilon
+right this this to epsilon Confucian
+
+ align:start position:0%
+right this this to epsilon Confucian
+ 
+
+ align:start position:0%
+right this this to epsilon Confucian
+needed to rescale back it they were
+
+ align:start position:0%
+needed to rescale back it they were
+ 
+
+ align:start position:0%
+needed to rescale back it they were
+scared back to 2 1 right so in fact if
+
+ align:start position:0%
+scared back to 2 1 right so in fact if
+ 
+
+ align:start position:0%
+scared back to 2 1 right so in fact if
+we go small apps and we need a lot of
+
+ align:start position:0%
+we go small apps and we need a lot of
+ 
+
+ align:start position:0%
+we go small apps and we need a lot of
+box right well and that's how how that
+
+ align:start position:0%
+box right well and that's how how that
+ 
+
+ align:start position:0%
+box right well and that's how how that
+that's that's the approximation of our
+
+ align:start position:0%
+that's that's the approximation of our
+ 
+
+ align:start position:0%
+that's that's the approximation of our
+digital price and that's actually how
+
+ align:start position:0%
+digital price and that's actually how
+ 
+
+ align:start position:0%
+digital price and that's actually how
+how people on the market do do price and
+
+ align:start position:0%
+how people on the market do do price and
+ 
+
+ align:start position:0%
+how people on the market do do price and
+catch the most importantly the the
+
+ align:start position:0%
+catch the most importantly the the
+ 
+
+ align:start position:0%
+catch the most importantly the the
+digital contracts because because Cole
+
+ align:start position:0%
+digital contracts because because Cole
+ 
+
+ align:start position:0%
+digital contracts because because Cole
+Cole contracts are liquid and they are
+
+ align:start position:0%
+Cole contracts are liquid and they are
+ 
+
+ align:start position:0%
+Cole contracts are liquid and they are
+traded on exchanges while digital's are
+
+ align:start position:0%
+traded on exchanges while digital's are
+ 
+
+ align:start position:0%
+traded on exchanges while digital's are
+way less liquid so somebody would go
+
+ align:start position:0%
+way less liquid so somebody would go
+ 
+
+ align:start position:0%
+way less liquid so somebody would go
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+to counterparty enter into digital &
+
+ align:start position:0%
+to counterparty enter into digital &
+ 
+
+ align:start position:0%
+to counterparty enter into digital &
+Hedges on the exchange this to cause
+
+ align:start position:0%
+Hedges on the exchange this to cause
+ 
+
+ align:start position:0%
+Hedges on the exchange this to cause
+physical spread but now tell me is it
+
+ align:start position:0%
+physical spread but now tell me is it
+ 
+
+ align:start position:0%
+physical spread but now tell me is it
+surprising that I mean how well what
+
+ align:start position:0%
+surprising that I mean how well what
+ 
+
+ align:start position:0%
+surprising that I mean how well what
+does it remind you yeah so it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative of the co price by with
+
+ align:start position:0%
+derivative of the co price by with
+ 
+
+ align:start position:0%
+derivative of the co price by with
+respect to to strike right is it is it
+
+ align:start position:0%
+respect to to strike right is it is it
+ 
+
+ align:start position:0%
+respect to to strike right is it is it
+surprising how did our Co price look
+
+ align:start position:0%
+surprising how did our Co price look
+ 
+
+ align:start position:0%
+surprising how did our Co price look
+like it's a ramp right if we take a
+
+ align:start position:0%
+like it's a ramp right if we take a
+ 
+
+ align:start position:0%
+like it's a ramp right if we take a
+derivative of this what what what vulgar
+
+ align:start position:0%
+derivative of this what what what vulgar
+ 
+
+ align:start position:0%
+derivative of this what what what vulgar
+yeah so it's just so in fact if we do
+
+ align:start position:0%
+yeah so it's just so in fact if we do
+ 
+
+ align:start position:0%
+yeah so it's just so in fact if we do
+something even more weird with this I
+
+ align:start position:0%
+something even more weird with this I
+ 
+
+ align:start position:0%
+something even more weird with this I
+don't know take a square or or something
+
+ align:start position:0%
+don't know take a square or or something
+ 
+
+ align:start position:0%
+don't know take a square or or something
+something else the same will apply right
+
+ align:start position:0%
+something else the same will apply right
+ 
+
+ align:start position:0%
+something else the same will apply right
+so it's not surprising at all all right
+
+ align:start position:0%
+so it's not surprising at all all right
+ 
+
+ align:start position:0%
+so it's not surprising at all all right
+so that's that's basically how how the
+
+ align:start position:0%
+so that's that's basically how how the
+ 
+
+ align:start position:0%
+so that's that's basically how how the
+duplicate this idea of replicating
+
+ align:start position:0%
+duplicate this idea of replicating
+ 
+
+ align:start position:0%
+duplicate this idea of replicating
+portfolios is is it extremely powerful
+
+ align:start position:0%
+portfolios is is it extremely powerful
+ 
+
+ align:start position:0%
+portfolios is is it extremely powerful
+and in fact that's that's what happens
+
+ align:start position:0%
+and in fact that's that's what happens
+ 
+
+ align:start position:0%
+and in fact that's that's what happens
+in in real life in real life you have
+
+ align:start position:0%
+in in real life in real life you have
+ 
+
+ align:start position:0%
+in in real life in real life you have
+some complicated derivative which you
+
+ align:start position:0%
+some complicated derivative which you
+ 
+
+ align:start position:0%
+some complicated derivative which you
+need to hedge and how to hedge you finds
+
+ align:start position:0%
+need to hedge and how to hedge you finds
+ 
+
+ align:start position:0%
+need to hedge and how to hedge you finds
+something else which replicate the to
+
+ align:start position:0%
+something else which replicate the to
+ 
+
+ align:start position:0%
+something else which replicate the to
+certain extent replicates your payoff
+
+ align:start position:0%
+certain extent replicates your payoff
+ 
+
+ align:start position:0%
+certain extent replicates your payoff
+that's what you'll try to do and that
+
+ align:start position:0%
+that's what you'll try to do and that
+ 
+
+ align:start position:0%
+that's what you'll try to do and that
+this will be your hedge portfolio
+
+ align:start position:0%
+this will be your hedge portfolio
+ 
+
+ align:start position:0%
+this will be your hedge portfolio
+usually it's dynamic so you you'll have
+
+ align:start position:0%
+usually it's dynamic so you you'll have
+ 
+
+ align:start position:0%
+usually it's dynamic so you you'll have
+to rebound and that's how you you
+
+ align:start position:0%
+to rebound and that's how you you
+ 
+
+ align:start position:0%
+to rebound and that's how you you
+basically reduce the risks
\ No newline at end of file
diff --git a/V0z_f7qxLcY.txt b/V0z_f7qxLcY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1b60c6aae86865d6a9561103e57f03526d450377
--- /dev/null
+++ b/V0z_f7qxLcY.txt
@@ -0,0 +1,2165 @@
+All right.
+Good morning all.
+
+Today we embark on another new
+chapter in what we do.
+
+And the topic is going to be --
+
+We will talk about this thing
+called an Operational Amplifier.
+
+Before I get into the lecture,
+I want to point out a couple of
+
+things.
+One is that you are going to
+
+hear about two big words in
+today's lecture.
+
+Two big and incredibly
+important words.
+
+And I want to mention those
+words to you right now so that
+
+when I come to them in lecture
+you can say OK,
+
+I better pay really close
+attention, these are important
+
+words.
+All right.
+
+One of them is abstraction.
+The second one is feedback.
+
+Two incredibly important
+concepts.
+
+Abstraction,
+you have been seeing a couple
+
+times during this course,
+once in the beginning where we
+
+abstracted out Maxwell's
+equations by focusing on a
+
+smaller playground and simply
+using KVL, KCL in place of those
+
+equations.
+A big abstraction.
+
+It turns out that almost all of
+EECS is based upon abstractions
+
+at various levels.
+In the first lecture,
+
+I also showed you the layer
+upon layer of abstraction that
+
+we built to be able to build
+interesting systems.
+
+The second big thing is
+feedback.
+
+And I am going to relate this
+to anti-lock breaks in cars.
+
+And so, you can wait and see
+how we do that.
+
+It's an incredibly important
+concept.
+
+Before we dive into the
+amplifier abstraction,
+
+let me first talk about
+something that you know.
+
+Start with something that you
+know and then lead up into the
+
+operational amplifier and its
+circuits.
+
+You know about the MOSFET
+amplifier.
+
+The MOSFET amplifier that you
+know about looked like this.
+
+It was based on a MOSFET.
+
+There was a VS supply.
+There was a vI input,
+
+a vO output and,
+as I said, a VS supply.
+
+So, this was a MOSFET circuit
+that you've seen before.
+
+One way of viewing this is that
+this circuit has three major
+
+ports.
+This here is the input port
+
+with voltage vI.
+This here, between the drain
+
+terminal and the ground,
+is the output port.
+
+I take the output between the
+drain terminal and ground.
+
+And, finally,
+we have a third port,
+
+which is this one.
+It is called the power port.
+
+I apply VS between this
+terminal here and the ground
+
+terminal.
+And that gives us the power
+
+port.
+This device here was a three
+
+port device.
+Input port or control port,
+
+output port and a power port.
+And so we looked at the circuit
+
+and did a whole bunch of
+analyses of it.
+
+Then what I can do at this
+point, now that you've seen
+
+this, it's often times
+interesting to think about
+
+abstracting this out into some
+kind of a building block.
+
+Much like in software,
+you write a procedure and you
+
+abstract out the internal
+details of the procedure in the
+
+procedure declaration and in the
+call that you make.
+
+In the same way,
+we can take this little device
+
+here and abstract that out into
+the following abstraction.
+
+We could abstract that out as a
+device that looks like this.
+
+I have my input port,
+I have my output port and I
+
+have my power port.
+So, I can apply VS here.
+
+Notice that I've taken these
+six terminals here,
+
+one, two, three,
+four, five and six,
+
+and put a box around it.
+And just exposed the terminals
+
+to you.
+And I need to tell you a little
+
+bit more about the internal
+properties, but suffice it to
+
+say that you can begin working
+with this little block.
+
+An even simpler version of this
+for many applications might just
+
+look like this,
+vI and vO where there is a
+
+ground that is shared among them
+that is implicit in this
+
+picture.
+And vI and vO can simply be the
+
+node voltages at these nodes.
+This is a progressively more
+
+abstract representation of this
+amplifier.
+
+What we can do is,
+provided we know,
+
+we can abstract out the
+relevant properties of this
+
+block and expose them outside.
+And the relevant properties
+
+might well be that,
+let's say here the properties
+
+may be that I in is always zero.
+I can also express to you the
+
+gain of this amplifier.
+I may also be able to tell you
+
+the Thevenin equivalent for the
+output.
+
+There are some properties that
+I can give you that will let you
+
+use this building block
+abstractly.
+
+Today, what we will do is
+introduce a powerful abstraction
+
+of a type of amplifier.
+This is called the operational
+
+amplifier or "op amp" for short.
+What I am going to do is give
+
+you a slightly more involved
+building block than the one I
+
+have shown you there.
+But suffice it to say that the
+
+idea is going to be the same.
+This building block looks like
+
+this.
+This building block has an
+
+input port.
+This building block also has a
+
+port in which to connect power
+or the power port.
+
+And the way I am going to
+connect power,
+
+I am going to connect a plus VS
+supply here.
+
+That is going to be my ground
+node.
+
+And I am going to connect a
+minus VS supply to this node
+
+here.
+So, these voltages are both VS.
+
+I want to apply a plus VS here
+and a negative VS out here.
+
+And I am going to take the
+output between the ground node
+
+and the output node of the
+operational amplifier and call
+
+that a vO.
+This is the output port.
+
+So, input port and output port
+and a power port.
+
+Think of this as a pattern
+where I have an input port
+
+across which I connect the
+input.
+
+I have a power port across
+which I connect a plus VS,
+
+minus VS supply,
+and then I take the output
+
+terminal and take a ground
+terminal, which is defined by
+
+external components of my
+circuitry, and use this as my
+
+reference node.
+Remember ground is just a
+
+reference node.
+I am going to use this as a
+
+reference node.
+These two are equal in
+
+magnitude.
+And take this as my output.
+
+And when I do something like
+this, I can build an even
+
+simpler, so this is an abstract
+differential input amplifier.
+
+In other words,
+this amplifier is going to
+
+amplify whatever I apply at the
+input.
+
+A slightly more abstract
+representation of this looks
+
+like this.
+vOUT and plus/minus vIN.
+
+This is a slightly more
+abstract representation where,
+
+remember, we are going to draw
+this again and again,
+
+maybe at least 38 or 39 times
+in this course.
+
+And, remember,
+each time you draw it,
+
+remember that there is an
+implicit power port,
+
+a plus/minus supply that is
+connected which we don't show.
+
+And I remember when I first
+learned about it a long time ago
+
+there was a confusion in me
+initially.
+
+How does this work?
+Where is the power coming from?
+
+Just remember that power comes
+from a plus/minus supply,
+
+and we just don't show that in
+this abstraction.
+
+Now, the details,
+a lot of details are in Chapter
+
+16 of your course notes.
+That's the reading for that.
+
+The other thing is that there
+are some other key properties of
+
+this amplifier.
+And let me discuss those very
+
+quickly.
+First of all,
+
+I can draw a circuit model for
+the amplifier.
+
+Make some room for myself here.
+And this is a circuit model for
+
+what we call the ideal
+operational amplifier.
+
+And the circuit model is going
+to look like this.
+
+This is an abstract device.
+And, in terms of analyzing how
+
+this behaves in a circuit,
+I am going to show you this
+
+abstract circuit that looks as
+follows.
+
+Some input v is applied at
+these two terminals here.
+
+And this terminal is called my
+v plus terminal and this is
+
+called my v minus terminal,
+so this corresponds to these
+
+two terminals.
+I am telling you that the
+
+current going in is going to be
+zero, so i plus is going to be
+
+zero and i minus is going to be
+zero.
+
+i plus is the current in here
+and i minus is the current into
+
+the v minus terminal,
+and both these currents are
+
+going to be zero in this device
+here.
+
+The output is going to look
+like this.
+
+Let me just call it vOUT to be
+consistent with this here.
+
+And taken with ground as my
+reference.
+
+The output is simply Av.
+In other words,
+
+what I am doing is I am going
+to model this as a device that
+
+has a dependent source at its
+output.
+
+And the dependent source here
+is a voltage controlled voltage
+
+source.
+It is a dependent source,
+
+it is a voltage controlled
+voltage source such that the
+
+output voltage is A times the
+voltage v across its input.
+
+This is actually very simple.
+Think of these three terminals
+
+I have shown you here.
+I applied input across these.
+
+And the output is going to be A
+times whatever I applied.
+
+And A is going to tend towards
+infinity.
+
+A is going to be huge.
+And specific values for A might
+
+be a hundred thousand or a
+million or things of that sort.
+
+Huge A in this abstract
+amplifier.
+
+In addition to that,
+the other properties are that
+
+it is going to have infinite
+input resistance.
+
+That means looking in this
+looks like an open circuit.
+
+The fact that this is open here
+implies the infinite input
+
+resistance across this port.
+What about the output here?
+
+Remember, this is a voltage
+source.
+
+And we have a zero output
+resistance, which means that no
+
+matter how the load affects
+this, as I apply a load this is
+
+going to behave like an ideal
+voltage source and keep holding
+
+the voltage constant based on
+whatever the function I
+
+establish here.
+And A is virtually infinite.
+
+Let me pause there for a few
+seconds and just dwell on this
+
+so you just understand what the
+basic device is.
+
+Following this basic
+definition, I am just going to
+
+build a whole bunch of fun
+little circuits.
+
+The analysis will be pretty
+straightforward,
+
+but this is a big conceptual
+leap here where there is some
+
+circuitry inside.
+Containing resistors,
+
+MOSFETs, a whole bunch of stuff
+in there.
+
+I am not telling you what is
+inside it.
+
+Much like I could build an
+abstract amplifier,
+
+I could put an abstract box
+around the amplifier you saw
+
+earlier, I want to put a box
+around some circuitry.
+
+I am not telling you what the
+circuitry is.
+
+And, if you are curious,
+you should look at page 581 of
+
+your course notes.
+There is an example solved.
+
+The example is for a
+differential amplifier.
+
+This is the small signal
+analysis chapter.
+
+That differential amplifier
+that's solved in that example is
+
+usually the first stage in an
+operational amplifier circuit.
+
+That differential amplifier is
+the first stage at the input.
+
+And that differential
+amplifier, as the name implies,
+
+amplifies not a single voltage
+but amplifies a differential
+
+voltage.
+Note that this guy amplifies
+
+the voltage difference between
+these two terminals.
+
+That's v here.
+And v is simply the same as v
+
+plus minus v minus.
+It's the node voltage here
+
+minus the node voltage here.
+That is what's amplified.
+
+It amplifies a difference.
+Therefore, it is called a
+
+difference amplifier or a
+differential amplifier.
+
+And so that input stage is what
+is inside the op amp.
+
+It's got a bunch of other
+circuitry like level shifters
+
+and so on.
+And at the output it has got a
+
+buffer.
+At at the output it has
+
+something that is reminiscent of
+the source follower circuit that
+
+you learned about in
+recitations, solved an example
+
+in the course notes and in your
+homework as well.
+
+And you solved a variant of the
+source follower on your quiz as
+
+well in problem two.
+So, a circuit that looks like
+
+that appears at the output.
+Remember, for the source
+
+follower, the resistance looking
+in from the output was very,
+
+very small.
+You have seen some of the
+
+pieces that go inside the
+amplifier, but we will deal with
+
+this as a building block and
+simply represent it using this
+
+abstract little circuit.
+To dwell on this a little
+
+longer, this little device here
+is the workhorse of the analog
+
+industry.
+Much like your primitive gate
+
+abstraction, your inverter and
+NAND gate and so on,
+
+much as your primitive inverter
+or NAND gate was from the
+
+foundations of the digital
+industry.
+
+Remember we learned how to
+build this little abstract
+
+device called a NAND gate or an
+inverter?
+
+We noticed that those form the
+foundations of very complicated
+
+microprocessors.
+Those were the building blocks
+
+of the digital industry.
+In the same way,
+
+this little beast here is the
+building block of the analog
+
+industry.
+Just to give you an analogy
+
+from software,
+think of this abstract little
+
+device as a library routine from
+a library of functions when you
+
+program in C++ or whatever.
+Can someone give me an example
+
+of an incredibly popular routine
+that we use all the time that
+
+may be called the workhorse of
+the software industry?
+
+Pardon?
+An abstraction,
+
+an abstract procedure.
+One example might be something
+
+like a printf.
+Printf is an abstract name for
+
+a procedure that goes and does
+something for you.
+
+It is amazing how we take the
+lowly printf for granted.
+
+I stick my printf into my
+program, it includes the
+
+standard IO library and it goes
+and prints a value.
+
+You won't believe how
+complicated the printf is.
+
+As you go into learning more
+advanced software subjects,
+
+implementing the printf is a
+nightmare.
+
+It is horrendously complicated.
+Just imagine.
+
+You give it a string and it has
+to go and print that on your
+
+terminal or on your Windows
+system or whatever.
+
+Think of the complicated steps
+it has to go through.
+
+But, as far as you're
+concerned, it's simple.
+
+Just print out something and
+you're done.
+
+The same way.
+Think of this as the printf of
+
+the analog business.
+It is really simple,
+
+and the analysis is going to be
+incredibly simple,
+
+it will be mind-bogglingly
+simple, but inside it,
+
+heavens forbid if you look
+inside it.
+
+Tell you what,
+go into to S-T-D-I-O dot in one
+
+of the library routines and just
+pore through printf.
+
+The world's worst horrendous
+macros are in there.
+
+I mean it is just nasty.
+The same way inside the op amp,
+
+it is nasty.
+You don't want to go there.
+
+Much like in your C programming
+in your classes,
+
+you were able to use printf
+without fully knowing how it was
+
+implemented.
+Probably some MIT god or some
+
+key graduate implemented it,
+but once it was implemented you
+
+just used it based on simple
+abstract rules as to how it
+
+behaved.
+You didn't have to know what
+
+was inside it to use it.
+The same way with the
+
+operational amplifier.
+So, just think of printf when
+
+you see this and just imagine
+how simple it is going to be to
+
+use it.
+You may think that I spend way
+
+too much time,
+ten minutes dwelling on this
+
+abstract concept,
+but I like to dwell on things
+
+that I think are incredibly
+important.
+
+The concept of abstraction is
+very important.
+
+And it's not just in software.
+The concept of abstraction
+
+pervades all of EECS.
+And if I were to give you a
+
+project to say go and ask every
+professor what is the one word
+
+that you think best describes
+all of EECS?
+
+Just pick one word.
+Go ask every single professor
+
+you know.
+What is a single word?
+
+If you were to characterize all
+of EECS with just one word,
+
+what might that word be?
+In my mind, it is the A word,
+
+abstraction.
+It is all over.
+
+If you do a grep on all the
+words used by all your
+
+professors in your four years
+here, I promise you the first
+
+one will be know.
+And the second one will be
+
+abstraction.
+Check it out.
+
+See if what I am saying is true
+or not.
+
+It is all over the place.
+In 6.001, how many times do you
+
+think the word abstraction was
+used in 6.001?
+
+It's all over the map.
+It's the A word all over.
+
+Imagine your shock when you see
+it being used in 002 because the
+
+same concept applies.
+We build more complicated
+
+systems by abstracting out the
+details of lesser objects,
+
+and then using those to build
+the more complicated systems.
+
+Abstraction is a very powerful
+mechanism of dealing with
+
+complexity.
+Next step is how do I go about
+
+using the op amp?
+Let me show you how it looks on
+
+a scope.
+What I am going to do is apply
+
+input to the op amp,
+I am going to look at the
+
+output, place the resistor RL to
+ground and look at the output.
+
+And here I am going to apply a
+plus VS and out here a minus VS.
+
+Again, remember that a plus VS
+simply looks like this and a
+
+minus VS simply looks like this.
+It's just an inverted VS
+
+applied here so I get a minus VS
+at this input.
+
+First of all,
+what I would like to do is as I
+
+change vIN, I am going to plot
+for you how vOUT looks.
+
+vIN and this is vO.
+I am going to plot vIN in terms
+
+of microvolts and vO in volts.
+vIN is going to have a very
+
+very small, the scale is going
+to be in microvolts because
+
+remember the gain of this is
+huge.
+
+It's on the order of ten to the
+sixth.
+
+It's huge.
+Small changes in vIN are going
+
+to cause massive changes in vO.
+I have a very fine scale on the
+
+X axis.
+What is going to happen if I
+
+somehow magically make vIN
+exactly zero?
+
+If I short these two terminals,
+if this was a completely ideal
+
+op amp, which it never is,
+if it's a completely ideal op
+
+amp, then my output should be
+zero.
+
+As I increase my vIN the output
+should be A times vIN.
+
+For some small value of vIN,
+small v, let's say one
+
+microvolt, the output should be
+one volt.
+
+A is a constant so this would
+look like a straight line.
+
+And let's say my supply
+voltages are 12 volts minus 12
+
+volts, if this were an ideal
+amplifier and I didn't have to
+
+worry about the supply,
+this would just go on extending
+
+forever.
+But I have a plus 12 volt
+
+supply and a minus 12 volt
+supply.
+
+My output cannot go past those
+limits.
+
+And so, therefore,
+my output kind of flattens out
+
+at these two points.
+And it is called hitting the
+
+rails.
+Output goes up and you hear a
+
+thunk sound and you hit the
+rails.
+
+When you play with op amps in
+your next lab,
+
+if you listen really,
+really carefully you may hear
+
+it.
+So, this saturates out.
+
+Not surprisingly,
+this region where the output
+
+saturates at the supply is
+called the saturation region.
+
+Remember, don't confuse it
+with-- It's not the same as your
+
+saturation in the MOSFET.
+It is a totally different
+
+thing.
+It is just happenstance that we
+
+call this saturation.
+And if you would like to think
+
+about it, you can think of it as
+the thunk region.
+
+That's probably more
+appropriate to distinguish it
+
+from the saturation region in
+the MOSFET.
+
+And, not surprisingly,
+this one is called the active
+
+region.
+And it is in this region that
+
+we use the op amp.
+Here it has hit the rails and
+
+is kind of dangling out there.
+It's not much use to us.
+
+It's in this active region that
+we use it because this is where
+
+the gain is seen.
+Now, it turns out that this is
+
+a very high gain device.
+It is very skittish.
+
+This gain is kind of a really
+funny thing.
+
+It's dependent on a bunch of
+factors.
+
+This could be temperature
+dependent.
+
+This gain here and this curve
+is just completely skittish.
+
+It could depend on temperature.
+It could depend on time of day.
+
+It could depend on what
+medication this amplifier is on.
+
+It could depend on its mood
+swings.
+
+Who knows what?
+This is kind of unstable.
+
+And A in particular is highly
+unstable.
+
+It is going to be big,
+that's for sure,
+
+but it could be ten to the six,
+on a rainy day it might be two
+
+times ten to the six.
+If it feeling sleepy it may be
+
+point five times ten to the
+sixth.
+
+It is big but I cannot rely on
+it.
+
+Let me show you an example.
+I want to show you this curve
+
+for this MOSFET,
+apply an input and plotting the
+
+output.
+What I will do is take a look
+
+at this curve.
+Then what I am going to do is
+
+use a heat gun to heat the op
+amp and you are going to see
+
+this vary all over the map.
+If you still remember last
+
+week, some of you may remember
+that from some place in a
+
+similar situation where the gm
+for the MOSFETs you were given
+
+was also dependent on
+temperature and stuff like that.
+
+It is a very common occurrence.
+And that is certainly the case
+
+for the MOSFET.
+
+Let's apply input.
+Let's do this.
+
+This is vIN versus vOUT for the
+amplifier.
+
+Notice that this is plus 12
+volts, this is minus 12 volts.
+
+It is about two volts per
+division.
+
+This axis here is in
+microvolts, I believe.
+
+For a very small change,
+for a few tens of microvolts,
+
+I have an incredibly high gain.
+Notice that this has an
+
+incredibly high gain here.
+The gain is the slope of this
+
+line, almost a vertical line.
+What I am going to do next,
+
+is to have some fun,
+is I am going to heat the op
+
+amp.
+To show you that A is kind of
+
+really skittish and also the
+fact that it doesn't quite hit
+
+zero, it does all kinds of weird
+things, I am going to heat the
+
+op amp.
+And then let's take a look at
+
+how that curve fluctuates.
+
+What you saw there was that the
+op amp began to behave really
+
+weirdly as I heated it.
+Instead of doing this it
+
+sometimes did this really
+weirdly, like getting an offset
+
+from the center and so on.
+And it does a bunch of other
+
+weird things,
+but we won't go into those
+
+details.
+It's not relevant for this
+
+course.
+But the point is that the gain
+
+and the offset at the input are
+dependent on temperature.
+
+And we look for ways to make it
+less dependent on temperature.
+
+As the next step,
+what I would like to do is
+
+build a circuit.
+This is model equivalent of
+
+your Hello World program.
+We are going to use the printf
+
+and build a small program on the
+printf.
+
+You don't have to worry about
+how printf is implemented,
+
+just that we can build very
+highly interesting circuits with
+
+this horrendously complicated
+function based on a simple
+
+abstraction of the device.
+The circuit that we will build
+
+is called a noninverting
+amplifier.
+
+From now on,
+I am not going to show you the
+
+plus/minus VS.
+I am not going to show the
+
+power port, but it is in there.
+It's hidden under the
+
+abstraction layer.
+This is my op amp.
+
+And I am going to build the
+following circuit.
+
+This is my v plus and this is
+my v minus.
+
+What I am going to do is for
+the v plus I shall apply a vIN.
+
+Let me talk a little bit about
+ground as well.
+
+Ground is commonly taken as the
+point at which I connect my VS
+
+and minus VS supply.
+It is kind of at the midpoint.
+
+And if VS and minus VS are very
+carefully tuned then the output
+
+is also going to be at that same
+ground reference when the input
+
+is zero.
+So, the ground is defined as
+
+the point at which I connect my
+plus/minus VS supplies.
+
+I apply my vIN out here.
+Then what I am going to do,
+
+here is my output vO.
+I am going to have a resistive
+
+divider to ground here and label
+these R1 and R2.
+
+And what I am going to do here
+is feed this back to the input,
+
+to the v minus input.
+I am going to sample the
+
+voltage here and feed that into
+here.
+
+So, this is my abstract model
+and this is my Hello World
+
+program.
+What we are going to do is
+
+simply analyze how this little
+program behaves.
+
+So, my equivalent circuit
+model.
+
+The way to analyze these is
+after one or two of these
+
+examples, you will be able to
+directly analyze this just by
+
+looking at it,
+by inspection.
+
+But, much as we did for the
+other pieces,
+
+let me grunge through drawing
+the equivalent circuit and
+
+grinding through the analysis,
+and then show you the much
+
+simpler way of doing it.
+And even here,
+
+even with this grinding
+analysis, it is going to be
+
+pretty simple in any case.
+So, I will replace the op amp
+
+with its equivalent circuit
+model.
+
+Its equivalent circuit was v
+plus, v minus.
+
+So, that was the equivalent
+circuit model of the operational
+
+amplifier, just this piece.
+I draw that for you.
+
+Then what I am going to do is I
+connect my v in here.
+
+And, remember,
+I have an R1,
+
+R2 resistive divider here.
+And this one gets connected to
+
+this terminal there.
+I also know that i plus is
+
+zero.
+I also know that i minus is
+
+zero.
+All I've done is simply
+
+replaced the amplifier with its
+equivalent circuit.
+
+Let's go ahead and analyze that
+circuit now.
+
+Let's go ahead and analyze that
+circuit.
+
+And it's going to be pretty
+simple, actually.
+
+What I am going to show you is
+the hard way of doing it.
+
+I will show you a much easier
+way, but the hard way itself is
+
+pathetically easy.
+What I want to do is find vO in
+
+terms of vIN.
+And there will be a bunch of
+
+other factors thrown in,
+including things like R1 and
+
+R2, A and stuff like that.
+Let's go and analyze it.
+
+vO, let's look at that circuit.
+By the way, let me take 30
+
+seconds and make a little speech
+at this point.
+
+When you see circuits like
+this, and I saw this happen in
+
+quiz two as well,
+for some reason,
+
+when you see a new kind of
+circuit, don't completely go
+
+berserk or freeze or whatever.
+There is just no reason to.
+
+You know the node method.
+The node method is the
+
+workhorse of our business.
+When in doubt apply the node
+
+method.
+It will simply work.
+
+Don't freeze.
+Don't think oh,
+
+man, I need to apply a pattern
+that I know already.
+
+I must have seen this
+somewhere.
+
+When in doubt boom,
+apply the node method.
+
+This circuit here,
+all I have here is one unknown
+
+node voltage.
+I know the voltage of v plus,
+
+I need to compute the voltage
+vO.
+
+There are two unknowns,
+vO is an unknown and the
+
+voltage here at v minus is
+another unknown.
+
+This is a very simple circuit
+involving a dependent voltage
+
+controlled voltage source,
+and you need to find out vO and
+
+v minus using the node method.
+Just apply it.
+
+It's simple.
+Don't freeze.
+
+Just look at it and say I can
+do it and apply the node method.
+
+It will simply work.
+So, let's do that.
+
+What I can do here is vO is A
+times v plus minus v minus.
+
+This is actually really simple.
+And then, if I take v plus
+
+here, I know v plus is simply
+vIN so I will just make that
+
+substitution right away.
+So, v plus is simply vIN.
+
+What is v minus?
+v minus here is vO --
+
+What is v plus?
+I'm sorry, v minus.
+
+v minus is simply the voltage
+that is between R1 and R2.
+
+Notice that no current flows in
+to the v minus node.
+
+There is no current flowing in.
+Voltage at v minus is simply
+
+the voltage given by the
+resistive divider,
+
+which is vO times R2 divided by
+R1 plus R2.
+
+Stare at that for another
+second.
+
+The voltage at this node here
+is simply given by the resistive
+
+divider.
+Because no current is flowing
+
+in this direction.
+And no current flows in because
+
+I am telling you there is no
+current there based on my
+
+abstraction.
+I am telling you i minus is
+
+zero.
+That voltage is simply the
+
+voltage at this resistive
+divider.
+
+And so I can simplify it
+further and write this as vO.
+
+So I get, there is a one here.
+And I move this thing over to
+
+this side so I get one plus A
+times R2 divided by R1 plus R2.
+
+And that is equal to AvIN.
+And simplifying it some more,
+
+I get vO is AvIN divided by one
+plus AR2 divided by R1 plus R2.
+
+Notice how simple this is,
+and this is the hard method.
+
+All I have done is analyze the
+circuit using the basic circuit
+
+analysis principle that you
+learned the first week of the
+
+course, and I have the output
+for you.
+
+I just noted very carefully
+what the relationships were
+
+between the various elements in
+the abstraction.
+
+Notice here that I am told that
+A is extremely large.
+
+A is on the order of ten to the
+six and so on.
+
+And suppose it is the case
+that, let me write that down
+
+again.
+vO is AvIN, one plus AR2,
+
+R2.
+Suppose R1 and R2 are more or
+
+less comparable and A is ten to
+the six, it's a huge number,
+
+so this whole number is much,
+much greater than one.
+
+If it is much huger than one,
+what I can do is I can then
+
+write this as follows.
+I can say that this is more or
+
+less equal to AvIN divided by
+AR2 divided by R1 plus R2.
+
+I am ignoring the one here.
+As soon as I do that,
+
+notice I can cancel out A and I
+get vO to be approximately equal
+
+to vIN times R1 plus R2 divided
+by R2.
+
+Notice now that when the gain
+is very large the output is a
+
+function of the input multiplied
+by some number.
+
+The beauty of this thing here
+is that when A is very large,
+
+or this expression is very
+large, A cancels out and there
+
+is no A in this relationship.
+This means that even though the
+
+basic amplifier was very
+skittish, the output here
+
+relates to the input based on
+components that I have control
+
+over.
+These are soldiers in my army.
+
+I control them.
+So, to give you a sense of some
+
+numbers here,
+suppose A was ten to the six.
+
+And I choose R1 to be 9R.
+And R to be some R.
+
+Then vO is ten to the sixth vIN
+divided by one plus ten to the
+
+six R divided by 9R plus R.
+So, that is ten to the six vIN
+
+divided by one plus ten to the
+six divided by ten.
+
+All right.
+If I ignore the one here,
+
+the ten to the six and ten to
+the six cancel out,
+
+this ends up giving me 10vIN.
+So, I get a really nice
+
+amplifier whose output is simply
+ten times the input and
+
+determined solely by some
+resistor values.
+
+Let me show you another quick
+demo this time and show you the
+
+amplifier again,
+but with resistors connected
+
+like that.
+And then I show you that I want
+
+to heat the amplifier to the
+wazoo, the op amp to the wazoo,
+
+but vO is going to be
+absolutely rock solid.
+
+Let's try that out.
+
+This time around,
+this is the transfer function,
+
+the vO versus vIN.
+And notice that this time
+
+around I have similar scales on
+the X and Y axes,
+
+and this has a slope of 10.
+This is the point where the
+
+amplifier saturates at plus 12
+volts, and this is minus 12
+
+volts, and this point here is a
+zero.
+
+So, this is vIN,
+vOUT, plus 12,
+
+minus 12 and this slope is 10.
+What I am going to do now is
+
+heat the op amp to the wazoo and
+this ain't going to change
+
+because it's my external
+resistors that control it
+
+independent of the value of A,
+provided A continues to be very
+
+large.
+I am just articulating the
+
+vOUT, vIN curve.
+And let me start heating the op
+
+amp.
+
+Notice that it's pretty stable.
+It doesn't change because it is
+
+independent of the amplifier
+values.
+
+What I have done now is by
+connecting these resistors in
+
+this way, I have a nice
+amplifier with a gain of ten.
+
+The question you may ask
+yourselves is why?
+
+There is this little sucker in
+there that wants to shoot things
+
+up by ten to the sixth.
+Wants to knock things off the
+
+one rail or the negative rail.
+Why is it that it's behaving
+
+like a docile lamb here and
+giving us a nice little factor
+
+of ten gain no matter what I do
+to it?
+
+Why is it doing that?
+What is the intuition behind
+
+it?
+I will draw something on the
+
+board, but for the next ten
+seconds I want you think about
+
+it.
+See if you can come up with
+
+some insight as to why is it
+doing that.
+
+Why is it exactly ten?
+Why isn't the ten to the sixth
+
+kind of killing me somehow?
+Why am I getting exactly ten no
+
+matter what happens?
+See if you can come up with
+
+some intuition and then I will
+show you how it works.
+
+I will redraw the circuit in
+the meantime.
+
+Let me see if I can give you
+some intuition.
+
+This is my circuit,
+and let's say this is R and
+
+this is R.
+As an example,
+
+let's assume that the input is
+5 volts, vIN is 5 volts.
+
+If R and R are equal,
+what should the output be?
+
+It's R and R,
+so it's R1 plus R2 divided by
+
+R2, right?
+It's 2R divided by R,
+
+so it has a gain of two.
+My amplifier has a gain of two
+
+because R1 plus R2 divided by
+R2, which is my gain,
+
+is R plus R divided by R equals
+two.
+
+So, this will be 10 volts.
+If that is 10 volts this is
+
+going to be 5 volts,
+correct?
+
+This R and R,
+voltage divider,
+
+this is five,
+so I get 5 volts here.
+
+This is v plus.
+This is v minus.
+
+I get R and R,
+5 volts here,
+
+that's how the circuit looks.
+Now let's understand what is
+
+going on.
+And listen very carefully.
+
+This is going to be a key
+insight that I hope you will
+
+carry with you for the rest of
+your lives.
+
+This is really,
+really key.
+
+What you are going to see is,
+I think, the third big ah-ha
+
+moment in 6.002.
+Like small signal analysis,
+
+like the frequency domain stuff
+we saw, I think this is the
+
+third big one in the next 30 or
+40 seconds, things that are
+
+completely either not
+necessarily intuitive but are
+
+just spectacular in terms of
+what they can do for you.
+
+Let's see.
+Let's suppose that because I am
+
+heating it, let's suppose that A
+suddenly tends to increase.
+
+It wants to increase because I
+have heated it.
+
+A is saying I want to get out
+this mold here and starts to
+
+break through its shackles here.
+Let's say, as a Gedanken
+
+experiment, that it tries to
+shoot up this to 12 volts.
+
+It tries to push it up higher.
+This is just a Gedanken
+
+experiment.
+The up arrow says that the
+
+increase in A is trying to push
+up vO momentarily.
+
+Let's see what happens.
+It is trying to push up vO
+
+momentarily, so let's say this
+goes to 12 hypothetically.
+
+If that goes to 12,
+what should this volt node go
+
+to?
+Six, exactly.
+
+This goes to 6 volts.
+If that goes to six,
+
+what does v minus go to?
+6 volts again.
+
+So, v minus goes to 6 volts.
+Now at the input I have 5 volts
+
+at v plus and 6 volts at v
+minus, so where should the
+
+output go?
+The output should go down
+
+because the voltage of the
+negative terminal is higher.
+
+And so the output is A times v
+plus minus v minus.
+
+And because this has gone down,
+this has gone up here it is
+
+going to try to pull the output
+down.
+
+That is going to pull the
+output down let's say to 9 volts
+
+or something.
+Cachunk, there is a big battle
+
+going on here.
+A has gone up,
+
+it has boosted it up to 12,
+but the moment that goes to 12,
+
+this goes to 6,
+this goes to 6,
+
+and the op amp output has to go
+down to 9 volts now because this
+
+input is higher here.
+If this goes to 9,
+
+this goes to 4.5.
+If that goes to 4.5,
+
+this goes to 4.5.
+What happens now?
+
+If this goes to 4.5,
+what happens?
+
+It wants to go back up.
+Can't it make up its mind?
+
+This guy wants to go back up
+now because v plus is higher
+
+than v minus.
+What am I seeing here?
+
+This whole circuit here behaves
+like my little son,
+
+my 9-year-old.
+If say do this,
+
+he wants to do the exact
+opposite.
+
+So, there is a trick in how you
+make them do things for you.
+
+Look at this.
+Because of this arrangement of
+
+the circuit when A tries to push
+the output up,
+
+the rest of the circuit tries
+to pull it back down to where it
+
+used to be.
+If the circuit tries not to
+
+follow the true path,
+the rest of the circuit tries
+
+to whack it into shape so it
+follows a true path.
+
+And what's happening is
+because, in this arrangement,
+
+I have fed back a portion of
+the output to the negative
+
+input.
+I have fed back some of the
+
+output to the negative input.
+And by providing this feedback
+
+of a portion of the output to
+the negative input,
+
+I have arranged it in a way
+that I have something called
+
+negative feedback.
+What negative feedback does is
+
+that if this wanted to go wild
+and crazy, the circuit provides
+
+it with some negative feedback
+like you just saw.
+
+Feedback, a big word.
+If you take a poll of all the
+
+EECS faculty,
+I suspect that feedback would
+
+rank at least as the ninth or
+tenth most important word in the
+
+EECS.
+If abstract is number one,
+
+I think this would rank like a
+nine or a ten or something.
+
+So, that's the reason why it
+worked.
+
+In the last couple of minutes,
+let me give you some insight,
+
+based on something that you
+know, on how feedback works.
+
+This is a road here.
+Let's look at anti lock breaks.
+
+This is my tire.
+And let's say I have a set of
+
+disk brakes here.
+As the car is moving forward,
+
+if I apply the brakes the tire
+stops rolling,
+
+but if I apply the breaks too
+hard it can lock up the tire and
+
+the whole car can skid.
+The way anti lock breaks work
+
+is as follows.
+There is a controller that sits
+
+here.
+And there is a little person
+
+looking at the wheel and seeing
+is it turning.
+
+So, this is a feedback.
+And it is saying is it turning?
+
+Yes.
+Or, is it not turning?
+
+No.
+All this person watching the
+
+tire is doing is saying is it
+turning or is it not turning.
+
+That is it.
+That is a negative feedback.
+
+And so, if it is no and if it
+is yes.
+
+If it is yes then what this
+does is it applies the brakes
+
+even more strongly.
+It is turning so I can apply
+
+more brakes.
+But if it says oops,
+
+it stopped turning,
+what it does is it simply
+
+releases, the controller
+releases the brakes.
+
+And when the controller
+releases the brakes this one
+
+tends to loosen up a little bit
+and the tire starts turning
+
+again.
+So, this way you are constantly
+
+keeping the tire in its region
+of critical friction so that it
+
+is constantly moving.
+And static friction applies to
+
+how hard you can brake and it
+doesn't start skidding.
+
+In fact, if you take your car
+out, and I don't say you do
+
+this.
+Let's say go onto the Charles
+
+River in the dead of winter and
+you drive on the lake and you
+
+slam your anti lock brakes on,
+on an icy patch,
+
+you will notice that there is a
+constant sound that looks like
+
+something is vibrating in there.
+That is exactly what is
+
+happening.
+Oops, the tire is locked.
+
+Release the brakes.
+The wheel is turning.
+
+Jam the brakes on.
+That is exactly what is
+
+happening.
+The same way as out there,
+
+you notice that oops,
+the output is going up,
+
+pull it down,
+oops, it's going down,
+
+pull it up.
+So, there is constant negative
+
+feedback that is keeping the
+output stable.
+
+A very important concept.
+And I will ask your recitation
+
+instructors to cover the very
+simple method that is on page 9.
\ No newline at end of file
diff --git a/V3Wg_jrMSQY.txt b/V3Wg_jrMSQY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2984973d250fe00486006a00172f1f0203223d61
--- /dev/null
+++ b/V3Wg_jrMSQY.txt
@@ -0,0 +1,12240 @@
+align:start position:0%
+ 
+so let's continue with our discussion of
+
+ align:start position:0%
+so let's continue with our discussion of
+ 
+
+ align:start position:0%
+so let's continue with our discussion of
+the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me recall that
+
+ align:start position:0%
+let me recall that
+ 
+
+ align:start position:0%
+let me recall that
+the derivative of a function if it
+
+ align:start position:0%
+the derivative of a function if it
+ 
+
+ align:start position:0%
+the derivative of a function if it
+exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we denote by f prime of c this is
+
+ align:start position:0%
+which we denote by f prime of c this is
+ 
+
+ align:start position:0%
+which we denote by f prime of c this is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+limit as x goes to c of f of x minus f
+
+ align:start position:0%
+limit as x goes to c of f of x minus f
+ 
+
+ align:start position:0%
+limit as x goes to c of f of x minus f
+of c
+
+ align:start position:0%
+of c
+ 
+
+ align:start position:0%
+of c
+over x minus
+
+ align:start position:0%
+over x minus
+ 
+
+ align:start position:0%
+over x minus
+c okay
+
+ align:start position:0%
+c okay
+ 
+
+ align:start position:0%
+c okay
+last time
+
+ align:start position:0%
+last time
+ 
+
+ align:start position:0%
+last time
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+looked at the relationship between
+
+ align:start position:0%
+looked at the relationship between
+ 
+
+ align:start position:0%
+looked at the relationship between
+continuity
+
+ align:start position:0%
+continuity
+ 
+
+ align:start position:0%
+continuity
+and differentiability
+
+ align:start position:0%
+and differentiability
+ 
+
+ align:start position:0%
+and differentiability
+and showed that differentiability
+
+ align:start position:0%
+and showed that differentiability
+ 
+
+ align:start position:0%
+and showed that differentiability
+implies continuity
+
+ align:start position:0%
+implies continuity
+ 
+
+ align:start position:0%
+implies continuity
+but that having a derivative is quite a
+
+ align:start position:0%
+but that having a derivative is quite a
+ 
+
+ align:start position:0%
+but that having a derivative is quite a
+miraculous
+
+ align:start position:0%
+miraculous
+ 
+
+ align:start position:0%
+miraculous
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+because there are continuous functions
+
+ align:start position:0%
+because there are continuous functions
+ 
+
+ align:start position:0%
+because there are continuous functions
+which we actually constructed
+
+ align:start position:0%
+which we actually constructed
+ 
+
+ align:start position:0%
+which we actually constructed
+we constructed a continuous function you
+
+ align:start position:0%
+we constructed a continuous function you
+ 
+
+ align:start position:0%
+we constructed a continuous function you
+can generalize that example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we constructed a continuous function
+
+ align:start position:0%
+so we constructed a continuous function
+ 
+
+ align:start position:0%
+so we constructed a continuous function
+that has
+
+ align:start position:0%
+that has
+ 
+
+ align:start position:0%
+that has
+that is differentiable nowhere so
+
+ align:start position:0%
+that is differentiable nowhere so
+ 
+
+ align:start position:0%
+that is differentiable nowhere so
+in fact
+
+ align:start position:0%
+in fact
+ 
+
+ align:start position:0%
+in fact
+you know differentiability is a much
+
+ align:start position:0%
+you know differentiability is a much
+ 
+
+ align:start position:0%
+you know differentiability is a much
+stronger
+
+ align:start position:0%
+stronger
+ 
+
+ align:start position:0%
+stronger
+condition than continuity and it's it's
+
+ align:start position:0%
+condition than continuity and it's it's
+ 
+
+ align:start position:0%
+condition than continuity and it's it's
+something of a miracle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know just as a side note if you go
+
+ align:start position:0%
+you know just as a side note if you go
+ 
+
+ align:start position:0%
+you know just as a side note if you go
+on to study complex analysis
+
+ align:start position:0%
+on to study complex analysis
+ 
+
+ align:start position:0%
+on to study complex analysis
+which are functions of a complex
+
+ align:start position:0%
+which are functions of a complex
+ 
+
+ align:start position:0%
+which are functions of a complex
+variable rather than a real variable you
+
+ align:start position:0%
+variable rather than a real variable you
+ 
+
+ align:start position:0%
+variable rather than a real variable you
+also have the notion of a derivative
+
+ align:start position:0%
+also have the notion of a derivative
+ 
+
+ align:start position:0%
+also have the notion of a derivative
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then the derivative is much more
+
+ align:start position:0%
+then the derivative is much more
+ 
+
+ align:start position:0%
+then the derivative is much more
+miraculous um
+
+ align:start position:0%
+miraculous um
+ 
+
+ align:start position:0%
+miraculous um
+uh than it is here in in the setting of
+
+ align:start position:0%
+uh than it is here in in the setting of
+ 
+
+ align:start position:0%
+uh than it is here in in the setting of
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+but the whole point is the derivative is
+
+ align:start position:0%
+but the whole point is the derivative is
+ 
+
+ align:start position:0%
+but the whole point is the derivative is
+something of a miracle
+
+ align:start position:0%
+something of a miracle
+ 
+
+ align:start position:0%
+something of a miracle
+so today the goal is to
+
+ align:start position:0%
+so today the goal is to
+ 
+
+ align:start position:0%
+so today the goal is to
+prove some properties about the
+
+ align:start position:0%
+prove some properties about the
+ 
+
+ align:start position:0%
+prove some properties about the
+derivatives you know
+
+ align:start position:0%
+derivatives you know
+ 
+
+ align:start position:0%
+derivatives you know
+most of these you know
+
+ align:start position:0%
+most of these you know
+ 
+
+ align:start position:0%
+most of these you know
+maybe you didn't cover the proofs of
+
+ align:start position:0%
+maybe you didn't cover the proofs of
+ 
+
+ align:start position:0%
+maybe you didn't cover the proofs of
+them in calculus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the ultimate goal of proving
+
+ align:start position:0%
+with the ultimate goal of proving
+ 
+
+ align:start position:0%
+with the ultimate goal of proving
+the mean value theorem which is
+
+ align:start position:0%
+the mean value theorem which is
+ 
+
+ align:start position:0%
+the mean value theorem which is
+to me kind of
+
+ align:start position:0%
+to me kind of
+ 
+
+ align:start position:0%
+to me kind of
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+the most underappreciated but most
+
+ align:start position:0%
+the most underappreciated but most
+ 
+
+ align:start position:0%
+the most underappreciated but most
+important um
+
+ align:start position:0%
+important um
+ 
+
+ align:start position:0%
+important um
+result in calculus
+
+ align:start position:0%
+result in calculus
+ 
+
+ align:start position:0%
+result in calculus
+now you
+
+ align:start position:0%
+now you
+ 
+
+ align:start position:0%
+now you
+could argue that probably the hero of
+
+ align:start position:0%
+could argue that probably the hero of
+ 
+
+ align:start position:0%
+could argue that probably the hero of
+the story of calculus is the fundamental
+
+ align:start position:0%
+the story of calculus is the fundamental
+ 
+
+ align:start position:0%
+the story of calculus is the fundamental
+theorem of calculus which connects
+
+ align:start position:0%
+theorem of calculus which connects
+ 
+
+ align:start position:0%
+theorem of calculus which connects
+integration which will cover next after
+
+ align:start position:0%
+integration which will cover next after
+ 
+
+ align:start position:0%
+integration which will cover next after
+differentiation
+
+ align:start position:0%
+differentiation
+ 
+
+ align:start position:0%
+differentiation
+which so the fundamental theorem of
+
+ align:start position:0%
+which so the fundamental theorem of
+ 
+
+ align:start position:0%
+which so the fundamental theorem of
+calculus connects integration and
+
+ align:start position:0%
+calculus connects integration and
+ 
+
+ align:start position:0%
+calculus connects integration and
+differentiation
+
+ align:start position:0%
+differentiation
+ 
+
+ align:start position:0%
+differentiation
+so that really is but
+
+ align:start position:0%
+so that really is but
+ 
+
+ align:start position:0%
+so that really is but
+and that is really the hero of calculus
+
+ align:start position:0%
+and that is really the hero of calculus
+ 
+
+ align:start position:0%
+and that is really the hero of calculus
+gets used more
+
+ align:start position:0%
+gets used more
+ 
+
+ align:start position:0%
+gets used more
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+to prove that
+
+ align:start position:0%
+to prove that
+ 
+
+ align:start position:0%
+to prove that
+you use the mean value theorem
+
+ align:start position:0%
+you use the mean value theorem
+ 
+
+ align:start position:0%
+you use the mean value theorem
+so you know
+
+ align:start position:0%
+so you know
+ 
+
+ align:start position:0%
+so you know
+if the fundamental theorem of calculus
+
+ align:start position:0%
+if the fundamental theorem of calculus
+ 
+
+ align:start position:0%
+if the fundamental theorem of calculus
+was batman
+
+ align:start position:0%
+was batman
+ 
+
+ align:start position:0%
+was batman
+i would say the mean value theorem is
+
+ align:start position:0%
+i would say the mean value theorem is
+ 
+
+ align:start position:0%
+i would say the mean value theorem is
+something like alfred
+
+ align:start position:0%
+something like alfred
+ 
+
+ align:start position:0%
+something like alfred
+you know he's he's really the reason why
+
+ align:start position:0%
+you know he's he's really the reason why
+ 
+
+ align:start position:0%
+you know he's he's really the reason why
+batman gets to be who he is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+all right enough analogies for now let's
+
+ align:start position:0%
+all right enough analogies for now let's
+ 
+
+ align:start position:0%
+all right enough analogies for now let's
+go back to proving some
+
+ align:start position:0%
+go back to proving some
+ 
+
+ align:start position:0%
+go back to proving some
+properties of the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+first let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some basic
+
+ align:start position:0%
+some basic
+ 
+
+ align:start position:0%
+some basic
+the basic linearity and
+
+ align:start position:0%
+the basic linearity and
+ 
+
+ align:start position:0%
+the basic linearity and
+rules for the derivative so
+
+ align:start position:0%
+rules for the derivative so
+ 
+
+ align:start position:0%
+rules for the derivative so
+let f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go from i to r i is always some interval
+
+ align:start position:0%
+go from i to r i is always some interval
+ 
+
+ align:start position:0%
+go from i to r i is always some interval
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+if f
+
+ align:start position:0%
+if f
+ 
+
+ align:start position:0%
+if f
+so i have two functions f and g from i
+
+ align:start position:0%
+so i have two functions f and g from i
+ 
+
+ align:start position:0%
+so i have two functions f and g from i
+to r c is a point in i
+
+ align:start position:0%
+to r c is a point in i
+ 
+
+ align:start position:0%
+to r c is a point in i
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and the conclusion is if f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable at
+
+ align:start position:0%
+differentiable at
+ 
+
+ align:start position:0%
+differentiable at
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have several
+
+ align:start position:0%
+we have several
+ 
+
+ align:start position:0%
+we have several
+rules that we can apply the first is
+
+ align:start position:0%
+rules that we can apply the first is
+ 
+
+ align:start position:0%
+rules that we can apply the first is
+basically the linearity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the derivative that
+
+ align:start position:0%
+of the derivative that
+ 
+
+ align:start position:0%
+of the derivative that
+for all alpha
+
+ align:start position:0%
+for all alpha
+ 
+
+ align:start position:0%
+for all alpha
+and r
+
+ align:start position:0%
+and r
+ 
+
+ align:start position:0%
+and r
+function alpha f
+
+ align:start position:0%
+function alpha f
+ 
+
+ align:start position:0%
+function alpha f
+plus g which now goes from
+
+ align:start position:0%
+plus g which now goes from
+ 
+
+ align:start position:0%
+plus g which now goes from
+i to r
+
+ align:start position:0%
+i to r
+ 
+
+ align:start position:0%
+i to r
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is differentiable at c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the derivative of the function alpha f
+
+ align:start position:0%
+the derivative of the function alpha f
+ 
+
+ align:start position:0%
+the derivative of the function alpha f
+plus g
+
+ align:start position:0%
+plus g
+ 
+
+ align:start position:0%
+plus g
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+alpha times f prime of c plus g prime of
+
+ align:start position:0%
+alpha times f prime of c plus g prime of
+ 
+
+ align:start position:0%
+alpha times f prime of c plus g prime of
+c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think okay starting right a little
+
+ align:start position:0%
+i think okay starting right a little
+ 
+
+ align:start position:0%
+i think okay starting right a little
+slanted here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplication rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the function f times g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is differentiable
+
+ align:start position:0%
+is differentiable
+ 
+
+ align:start position:0%
+is differentiable
+at c and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the derivative of the product is not the
+
+ align:start position:0%
+the derivative of the product is not the
+ 
+
+ align:start position:0%
+the derivative of the product is not the
+product of the derivatives but
+
+ align:start position:0%
+product of the derivatives but
+ 
+
+ align:start position:0%
+product of the derivatives but
+prime of c g of c
+
+ align:start position:0%
+prime of c g of c
+ 
+
+ align:start position:0%
+prime of c g of c
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+f of c g prime of c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a
+
+ align:start position:0%
+so that's a
+ 
+
+ align:start position:0%
+so that's a
+multiplication rule and then we also
+
+ align:start position:0%
+multiplication rule and then we also
+ 
+
+ align:start position:0%
+multiplication rule and then we also
+also have the quotient rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know just like when you need to
+
+ align:start position:0%
+you know just like when you need to
+ 
+
+ align:start position:0%
+you know just like when you need to
+divide by something you need to assume
+
+ align:start position:0%
+divide by something you need to assume
+ 
+
+ align:start position:0%
+divide by something you need to assume
+that you're never dividing by zero
+
+ align:start position:0%
+that you're never dividing by zero
+ 
+
+ align:start position:0%
+that you're never dividing by zero
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+g of x does not equal 0.
+
+ align:start position:0%
+g of x does not equal 0.
+ 
+
+ align:start position:0%
+g of x does not equal 0.
+for all x and i
+
+ align:start position:0%
+for all x and i
+ 
+
+ align:start position:0%
+for all x and i
+then the function
+
+ align:start position:0%
+then the function
+ 
+
+ align:start position:0%
+then the function
+f over g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is differentiable
+
+ align:start position:0%
+is differentiable
+ 
+
+ align:start position:0%
+is differentiable
+at c
+
+ align:start position:0%
+at c
+ 
+
+ align:start position:0%
+at c
+and the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the derivative of the top
+
+ align:start position:0%
+is the derivative of the top
+ 
+
+ align:start position:0%
+is the derivative of the top
+times the bottom minus
+
+ align:start position:0%
+times the bottom minus
+ 
+
+ align:start position:0%
+times the bottom minus
+the top times the derivative of the
+
+ align:start position:0%
+the top times the derivative of the
+ 
+
+ align:start position:0%
+the top times the derivative of the
+bottom
+
+ align:start position:0%
+bottom
+ 
+
+ align:start position:0%
+bottom
+over the bottom square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not prime g of c square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so i'll prove one and two uh three
+
+ align:start position:0%
+um so i'll prove one and two uh three
+ 
+
+ align:start position:0%
+um so i'll prove one and two uh three
+we'll leave as an exercise
+
+ align:start position:0%
+we'll leave as an exercise
+ 
+
+ align:start position:0%
+we'll leave as an exercise
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so uh for one we just compute
+
+ align:start position:0%
+all right so uh for one we just compute
+ 
+
+ align:start position:0%
+all right so uh for one we just compute
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the limit as
+
+ align:start position:0%
+the limit as
+ 
+
+ align:start position:0%
+the limit as
+x goes to c of alpha f plus g
+
+ align:start position:0%
+x goes to c of alpha f plus g
+ 
+
+ align:start position:0%
+x goes to c of alpha f plus g
+of x minus alpha f
+
+ align:start position:0%
+of x minus alpha f
+ 
+
+ align:start position:0%
+of x minus alpha f
+plus g
+
+ align:start position:0%
+plus g
+ 
+
+ align:start position:0%
+plus g
+of c
+
+ align:start position:0%
+of c
+ 
+
+ align:start position:0%
+of c
+over x minus c
+
+ align:start position:0%
+over x minus c
+ 
+
+ align:start position:0%
+over x minus c
+this is just by definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alpha times f of x plus g of x minus
+
+ align:start position:0%
+alpha times f of x plus g of x minus
+ 
+
+ align:start position:0%
+alpha times f of x plus g of x minus
+alpha times f of c plus g of c and so
+
+ align:start position:0%
+alpha times f of c plus g of c and so
+ 
+
+ align:start position:0%
+alpha times f of c plus g of c and so
+this equals the limit
+
+ align:start position:0%
+this equals the limit
+ 
+
+ align:start position:0%
+this equals the limit
+as x goes to c and just uh collecting
+
+ align:start position:0%
+as x goes to c and just uh collecting
+ 
+
+ align:start position:0%
+as x goes to c and just uh collecting
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+alpha times
+
+ align:start position:0%
+alpha times
+ 
+
+ align:start position:0%
+alpha times
+f of x minus f of c
+
+ align:start position:0%
+f of x minus f of c
+ 
+
+ align:start position:0%
+f of x minus f of c
+times x minus
+
+ align:start position:0%
+times x minus
+ 
+
+ align:start position:0%
+times x minus
+c plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g of x minus g of c
+
+ align:start position:0%
+g of x minus g of c
+ 
+
+ align:start position:0%
+g of x minus g of c
+over x minus c
+
+ align:start position:0%
+over x minus c
+ 
+
+ align:start position:0%
+over x minus c
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of these limits exist so this is
+
+ align:start position:0%
+all of these limits exist so this is
+ 
+
+ align:start position:0%
+all of these limits exist so this is
+just a fixed number the limit as x goes
+
+ align:start position:0%
+just a fixed number the limit as x goes
+ 
+
+ align:start position:0%
+just a fixed number the limit as x goes
+to c of this
+
+ align:start position:0%
+to c of this
+ 
+
+ align:start position:0%
+to c of this
+exists and this exists so by what we
+
+ align:start position:0%
+exists and this exists so by what we
+ 
+
+ align:start position:0%
+exists and this exists so by what we
+know about limits
+
+ align:start position:0%
+know about limits
+ 
+
+ align:start position:0%
+know about limits
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+namely that the
+
+ align:start position:0%
+namely that the
+ 
+
+ align:start position:0%
+namely that the
+limit of the sum is the sum of the
+
+ align:start position:0%
+limit of the sum is the sum of the
+ 
+
+ align:start position:0%
+limit of the sum is the sum of the
+limits and then scalars just pull out of
+
+ align:start position:0%
+limits and then scalars just pull out of
+ 
+
+ align:start position:0%
+limits and then scalars just pull out of
+the limit this is equal to
+
+ align:start position:0%
+the limit this is equal to
+ 
+
+ align:start position:0%
+the limit this is equal to
+alpha times f prime of c
+
+ align:start position:0%
+alpha times f prime of c
+ 
+
+ align:start position:0%
+alpha times f prime of c
+plus g prime of c
+
+ align:start position:0%
+plus g prime of c
+ 
+
+ align:start position:0%
+plus g prime of c
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's the proof of the first one
+
+ align:start position:0%
+so that's the proof of the first one
+ 
+
+ align:start position:0%
+so that's the proof of the first one
+for the proof of the second one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll use the fact that uh
+
+ align:start position:0%
+we'll use the fact that uh
+ 
+
+ align:start position:0%
+we'll use the fact that uh
+a function which is con
+
+ align:start position:0%
+a function which is con
+ 
+
+ align:start position:0%
+a function which is con
+differentiable at a point is also
+
+ align:start position:0%
+differentiable at a point is also
+ 
+
+ align:start position:0%
+differentiable at a point is also
+continuous at a point
+
+ align:start position:0%
+continuous at a point
+ 
+
+ align:start position:0%
+continuous at a point
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+since g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is differentiable let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+continuous at c
+
+ align:start position:0%
+continuous at c
+ 
+
+ align:start position:0%
+continuous at c
+ie
+
+ align:start position:0%
+ie
+ 
+
+ align:start position:0%
+ie
+limit as x goes to c
+
+ align:start position:0%
+limit as x goes to c
+ 
+
+ align:start position:0%
+limit as x goes to c
+of g of x
+
+ align:start position:0%
+of g of x
+ 
+
+ align:start position:0%
+of g of x
+equals g of c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we compute the limit as x goes to c
+
+ align:start position:0%
+now we compute the limit as x goes to c
+ 
+
+ align:start position:0%
+now we compute the limit as x goes to c
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+f times g of x minus f of c
+
+ align:start position:0%
+f times g of x minus f of c
+ 
+
+ align:start position:0%
+f times g of x minus f of c
+times g of c
+
+ align:start position:0%
+times g of c
+ 
+
+ align:start position:0%
+times g of c
+over x minus c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what i'm going to do is add and
+
+ align:start position:0%
+now what i'm going to do is add and
+ 
+
+ align:start position:0%
+now what i'm going to do is add and
+subtract
+
+ align:start position:0%
+subtract
+ 
+
+ align:start position:0%
+subtract
+f of c times g of x
+
+ align:start position:0%
+f of c times g of x
+ 
+
+ align:start position:0%
+f of c times g of x
+so this i can write as the limit as x
+
+ align:start position:0%
+so this i can write as the limit as x
+ 
+
+ align:start position:0%
+so this i can write as the limit as x
+goes to c
+
+ align:start position:0%
+goes to c
+ 
+
+ align:start position:0%
+goes to c
+of f of x
+
+ align:start position:0%
+of f of x
+ 
+
+ align:start position:0%
+of f of x
+minus f of c
+
+ align:start position:0%
+minus f of c
+ 
+
+ align:start position:0%
+minus f of c
+over x minus c times
+
+ align:start position:0%
+over x minus c times
+ 
+
+ align:start position:0%
+over x minus c times
+g of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of c
+
+ align:start position:0%
+f of c
+ 
+
+ align:start position:0%
+f of c
+times g of x minus g of c
+
+ align:start position:0%
+times g of x minus g of c
+ 
+
+ align:start position:0%
+times g of x minus g of c
+over x minus c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+again so this limit as x goes to c
+
+ align:start position:0%
+again so this limit as x goes to c
+ 
+
+ align:start position:0%
+again so this limit as x goes to c
+exists this is just the derivative of f
+
+ align:start position:0%
+exists this is just the derivative of f
+ 
+
+ align:start position:0%
+exists this is just the derivative of f
+at c
+
+ align:start position:0%
+at c
+ 
+
+ align:start position:0%
+at c
+and we noted that since g is
+
+ align:start position:0%
+and we noted that since g is
+ 
+
+ align:start position:0%
+and we noted that since g is
+differentiable at c g is also continuous
+
+ align:start position:0%
+differentiable at c g is also continuous
+ 
+
+ align:start position:0%
+differentiable at c g is also continuous
+at c meaning the limit as x goes to c of
+
+ align:start position:0%
+at c meaning the limit as x goes to c of
+ 
+
+ align:start position:0%
+at c meaning the limit as x goes to c of
+g of x equals g of c
+
+ align:start position:0%
+g of x equals g of c
+ 
+
+ align:start position:0%
+g of x equals g of c
+this is just a constant f c this goes to
+
+ align:start position:0%
+this is just a constant f c this goes to
+ 
+
+ align:start position:0%
+this is just a constant f c this goes to
+g prime of c so
+
+ align:start position:0%
+g prime of c so
+ 
+
+ align:start position:0%
+g prime of c so
+all these limits exist and therefore we
+
+ align:start position:0%
+all these limits exist and therefore we
+ 
+
+ align:start position:0%
+all these limits exist and therefore we
+get that this is equal to f prime of c
+
+ align:start position:0%
+get that this is equal to f prime of c
+ 
+
+ align:start position:0%
+get that this is equal to f prime of c
+times g of c
+
+ align:start position:0%
+times g of c
+ 
+
+ align:start position:0%
+times g of c
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+f of c
+
+ align:start position:0%
+f of c
+ 
+
+ align:start position:0%
+f of c
+g prime of c and three i'll leave as an
+
+ align:start position:0%
+g prime of c and three i'll leave as an
+ 
+
+ align:start position:0%
+g prime of c and three i'll leave as an
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+again you know you'll you'll write out
+
+ align:start position:0%
+again you know you'll you'll write out
+ 
+
+ align:start position:0%
+again you know you'll you'll write out
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll add and subtract something uh to
+
+ align:start position:0%
+you'll add and subtract something uh to
+ 
+
+ align:start position:0%
+you'll add and subtract something uh to
+f of x over g of x minus f of c over g
+
+ align:start position:0%
+f of x over g of x minus f of c over g
+ 
+
+ align:start position:0%
+f of x over g of x minus f of c over g
+of c and use the fact that we have
+
+ align:start position:0%
+of c and use the fact that we have
+ 
+
+ align:start position:0%
+of c and use the fact that we have
+continuity that differentiability at a
+
+ align:start position:0%
+continuity that differentiability at a
+ 
+
+ align:start position:0%
+continuity that differentiability at a
+point implies continuity and just
+
+ align:start position:0%
+point implies continuity and just
+ 
+
+ align:start position:0%
+point implies continuity and just
+evaluate the limit so i'm going to stop
+
+ align:start position:0%
+evaluate the limit so i'm going to stop
+ 
+
+ align:start position:0%
+evaluate the limit so i'm going to stop
+with these two rules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know why i called it the
+
+ align:start position:0%
+i don't know why i called it the
+ 
+
+ align:start position:0%
+i don't know why i called it the
+multiplication rule it's called the
+
+ align:start position:0%
+multiplication rule it's called the
+ 
+
+ align:start position:0%
+multiplication rule it's called the
+product rule
+
+ align:start position:0%
+product rule
+ 
+
+ align:start position:0%
+product rule
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+multiplication and product the same
+
+ align:start position:0%
+multiplication and product the same
+ 
+
+ align:start position:0%
+multiplication and product the same
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we also have the chain rule which
+
+ align:start position:0%
+but we also have the chain rule which
+ 
+
+ align:start position:0%
+but we also have the chain rule which
+requires
+
+ align:start position:0%
+requires
+ 
+
+ align:start position:0%
+requires
+a little more care to prove
+
+ align:start position:0%
+a little more care to prove
+ 
+
+ align:start position:0%
+a little more care to prove
+um than of what we've done so far for
+
+ align:start position:0%
+um than of what we've done so far for
+ 
+
+ align:start position:0%
+um than of what we've done so far for
+these rules
+
+ align:start position:0%
+these rules
+ 
+
+ align:start position:0%
+these rules
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose i have two intervals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then i have a function g going from
+
+ align:start position:0%
+and then i have a function g going from
+ 
+
+ align:start position:0%
+and then i have a function g going from
+i 1 to i 2
+
+ align:start position:0%
+i 1 to i 2
+ 
+
+ align:start position:0%
+i 1 to i 2
+f going from i 2
+
+ align:start position:0%
+f going from i 2
+ 
+
+ align:start position:0%
+f going from i 2
+to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and suppose
+
+ align:start position:0%
+and suppose
+ 
+
+ align:start position:0%
+and suppose
+g is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable at c
+
+ align:start position:0%
+differentiable at c
+ 
+
+ align:start position:0%
+differentiable at c
+and f
+
+ align:start position:0%
+and f
+ 
+
+ align:start position:0%
+and f
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable at gfc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which now goes from i 1 to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is differentiable
+
+ align:start position:0%
+this is differentiable
+ 
+
+ align:start position:0%
+this is differentiable
+at c
+
+ align:start position:0%
+at c
+ 
+
+ align:start position:0%
+at c
+and the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f prime of g of c
+
+ align:start position:0%
+f prime of g of c
+ 
+
+ align:start position:0%
+f prime of g of c
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+g prime of c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basic uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+what's kind of the basic idea
+
+ align:start position:0%
+what's kind of the basic idea
+ 
+
+ align:start position:0%
+what's kind of the basic idea
+again so this is basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea is that
+
+ align:start position:0%
+idea is that
+ 
+
+ align:start position:0%
+idea is that
+we write
+
+ align:start position:0%
+we write
+ 
+
+ align:start position:0%
+we write
+the difference quotient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g of x minus f of
+
+ align:start position:0%
+g of x minus f of
+ 
+
+ align:start position:0%
+g of x minus f of
+g of c over x minus c
+
+ align:start position:0%
+g of c over x minus c
+ 
+
+ align:start position:0%
+g of c over x minus c
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+f of g of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+g
+
+ align:start position:0%
+g
+ 
+
+ align:start position:0%
+g
+f at
+
+ align:start position:0%
+f at
+ 
+
+ align:start position:0%
+f at
+g of c
+
+ align:start position:0%
+g of c
+ 
+
+ align:start position:0%
+g of c
+times over g of x minus g of c
+
+ align:start position:0%
+times over g of x minus g of c
+ 
+
+ align:start position:0%
+times over g of x minus g of c
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+g of x
+
+ align:start position:0%
+g of x
+ 
+
+ align:start position:0%
+g of x
+over g of c times x minus c
+
+ align:start position:0%
+over g of c times x minus c
+ 
+
+ align:start position:0%
+over g of c times x minus c
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um you know let x go to z c and then
+
+ align:start position:0%
+um you know let x go to z c and then
+ 
+
+ align:start position:0%
+um you know let x go to z c and then
+we'll pick up the derivative of g here
+
+ align:start position:0%
+we'll pick up the derivative of g here
+ 
+
+ align:start position:0%
+we'll pick up the derivative of g here
+at c and right here
+
+ align:start position:0%
+at c and right here
+ 
+
+ align:start position:0%
+at c and right here
+uh this is f of something converging to
+
+ align:start position:0%
+uh this is f of something converging to
+ 
+
+ align:start position:0%
+uh this is f of something converging to
+g of c
+
+ align:start position:0%
+g of c
+ 
+
+ align:start position:0%
+g of c
+and so this should be like f prime of g
+
+ align:start position:0%
+and so this should be like f prime of g
+ 
+
+ align:start position:0%
+and so this should be like f prime of g
+is c but the only problem with
+
+ align:start position:0%
+is c but the only problem with
+ 
+
+ align:start position:0%
+is c but the only problem with
+really writing this down is that there
+
+ align:start position:0%
+really writing this down is that there
+ 
+
+ align:start position:0%
+really writing this down is that there
+could be points where
+
+ align:start position:0%
+could be points where
+ 
+
+ align:start position:0%
+could be points where
+g of x equals g of c and then i'm
+
+ align:start position:0%
+g of x equals g of c and then i'm
+ 
+
+ align:start position:0%
+g of x equals g of c and then i'm
+dividing by zero that's not allowed okay
+
+ align:start position:0%
+dividing by zero that's not allowed okay
+ 
+
+ align:start position:0%
+dividing by zero that's not allowed okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+writing this expression is meaningless
+
+ align:start position:0%
+writing this expression is meaningless
+ 
+
+ align:start position:0%
+writing this expression is meaningless
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but we're gonna do something like this
+
+ align:start position:0%
+but we're gonna do something like this
+ 
+
+ align:start position:0%
+but we're gonna do something like this
+in spirit
+
+ align:start position:0%
+in spirit
+ 
+
+ align:start position:0%
+in spirit
+okay where at least when g of x does not
+
+ align:start position:0%
+okay where at least when g of x does not
+ 
+
+ align:start position:0%
+okay where at least when g of x does not
+equal g of c
+
+ align:start position:0%
+equal g of c
+ 
+
+ align:start position:0%
+equal g of c
+this thing kind of equals this thing
+
+ align:start position:0%
+this thing kind of equals this thing
+ 
+
+ align:start position:0%
+this thing kind of equals this thing
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's uh um
+
+ align:start position:0%
+that's uh um
+ 
+
+ align:start position:0%
+that's uh um
+that's kind of the the basic idea
+
+ align:start position:0%
+that's kind of the the basic idea
+ 
+
+ align:start position:0%
+that's kind of the the basic idea
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to implement the strategy
+
+ align:start position:0%
+so to implement the strategy
+ 
+
+ align:start position:0%
+so to implement the strategy
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let's introduce uh
+
+ align:start position:0%
+um let's introduce uh
+ 
+
+ align:start position:0%
+um let's introduce uh
+some notation and a few auxiliary
+
+ align:start position:0%
+some notation and a few auxiliary
+ 
+
+ align:start position:0%
+some notation and a few auxiliary
+functions so first off
+
+ align:start position:0%
+functions so first off
+ 
+
+ align:start position:0%
+functions so first off
+the function we're interested in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+taking the derivative f of g let me call
+
+ align:start position:0%
+taking the derivative f of g let me call
+ 
+
+ align:start position:0%
+taking the derivative f of g let me call
+that h of x because i don't have to keep
+
+ align:start position:0%
+that h of x because i don't have to keep
+ 
+
+ align:start position:0%
+that h of x because i don't have to keep
+writing uh
+
+ align:start position:0%
+writing uh
+ 
+
+ align:start position:0%
+writing uh
+f of g of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call d this will be the point g of
+
+ align:start position:0%
+let's call d this will be the point g of
+ 
+
+ align:start position:0%
+let's call d this will be the point g of
+c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then that
+
+ align:start position:0%
+then that
+ 
+
+ align:start position:0%
+then that
+h prime of c
+
+ align:start position:0%
+h prime of c
+ 
+
+ align:start position:0%
+h prime of c
+exists and it's equal to
+
+ align:start position:0%
+exists and it's equal to
+ 
+
+ align:start position:0%
+exists and it's equal to
+f prime of d times g prime of c
+
+ align:start position:0%
+f prime of d times g prime of c
+ 
+
+ align:start position:0%
+f prime of d times g prime of c
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+just in this notation i've set up
+
+ align:start position:0%
+just in this notation i've set up
+ 
+
+ align:start position:0%
+just in this notation i've set up
+okay so now let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define some auxiliary functions u of y
+
+ align:start position:0%
+define some auxiliary functions u of y
+ 
+
+ align:start position:0%
+define some auxiliary functions u of y
+this is going to be essentially the
+
+ align:start position:0%
+this is going to be essentially the
+ 
+
+ align:start position:0%
+this is going to be essentially the
+difference quotient
+
+ align:start position:0%
+difference quotient
+ 
+
+ align:start position:0%
+difference quotient
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+except at
+
+ align:start position:0%
+except at
+ 
+
+ align:start position:0%
+except at
+a certain point so this is f of y
+
+ align:start position:0%
+a certain point so this is f of y
+ 
+
+ align:start position:0%
+a certain point so this is f of y
+minus f of d
+
+ align:start position:0%
+minus f of d
+ 
+
+ align:start position:0%
+minus f of d
+over y minus d
+
+ align:start position:0%
+over y minus d
+ 
+
+ align:start position:0%
+over y minus d
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+y does not equal d so that this is
+
+ align:start position:0%
+y does not equal d so that this is
+ 
+
+ align:start position:0%
+y does not equal d so that this is
+meaningful
+
+ align:start position:0%
+meaningful
+ 
+
+ align:start position:0%
+meaningful
+and then f prime of d
+
+ align:start position:0%
+and then f prime of d
+ 
+
+ align:start position:0%
+and then f prime of d
+when y
+
+ align:start position:0%
+when y
+ 
+
+ align:start position:0%
+when y
+equals d
+
+ align:start position:0%
+equals d
+ 
+
+ align:start position:0%
+equals d
+and then v of x
+
+ align:start position:0%
+and then v of x
+ 
+
+ align:start position:0%
+and then v of x
+so this is going to be this is going to
+
+ align:start position:0%
+so this is going to be this is going to
+ 
+
+ align:start position:0%
+so this is going to be this is going to
+kind of play the role of you know that
+
+ align:start position:0%
+kind of play the role of you know that
+ 
+
+ align:start position:0%
+kind of play the role of you know that
+first expression i wrote up there f of g
+
+ align:start position:0%
+first expression i wrote up there f of g
+ 
+
+ align:start position:0%
+first expression i wrote up there f of g
+of x minus f of g of c
+
+ align:start position:0%
+of x minus f of g of c
+ 
+
+ align:start position:0%
+of x minus f of g of c
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um and then v of x this will be
+
+ align:start position:0%
+um and then v of x this will be
+ 
+
+ align:start position:0%
+um and then v of x this will be
+g of x minus g of c
+
+ align:start position:0%
+g of x minus g of c
+ 
+
+ align:start position:0%
+g of x minus g of c
+x minus c when
+
+ align:start position:0%
+x minus c when
+ 
+
+ align:start position:0%
+x minus c when
+x does not equal c
+
+ align:start position:0%
+x does not equal c
+ 
+
+ align:start position:0%
+x does not equal c
+and g prime of c
+
+ align:start position:0%
+and g prime of c
+ 
+
+ align:start position:0%
+and g prime of c
+when x equals c
+
+ align:start position:0%
+when x equals c
+ 
+
+ align:start position:0%
+when x equals c
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+essentially what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do we what do we have here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if i look at f of y
+
+ align:start position:0%
+then if i look at f of y
+ 
+
+ align:start position:0%
+then if i look at f of y
+minus f of d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equal to u of y
+
+ align:start position:0%
+this is equal to u of y
+ 
+
+ align:start position:0%
+this is equal to u of y
+times y minus d always right
+
+ align:start position:0%
+times y minus d always right
+ 
+
+ align:start position:0%
+times y minus d always right
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+if y does not equal d
+
+ align:start position:0%
+if y does not equal d
+ 
+
+ align:start position:0%
+if y does not equal d
+then i divide over and i get u of y
+
+ align:start position:0%
+then i divide over and i get u of y
+ 
+
+ align:start position:0%
+then i divide over and i get u of y
+then i get f of y minus f of d on the
+
+ align:start position:0%
+then i get f of y minus f of d on the
+ 
+
+ align:start position:0%
+then i get f of y minus f of d on the
+left hand side over y minus d and that's
+
+ align:start position:0%
+left hand side over y minus d and that's
+ 
+
+ align:start position:0%
+left hand side over y minus d and that's
+equal to u of y by definition and then
+
+ align:start position:0%
+equal to u of y by definition and then
+ 
+
+ align:start position:0%
+equal to u of y by definition and then
+when y equals d i get 0 here and i get 0
+
+ align:start position:0%
+when y equals d i get 0 here and i get 0
+ 
+
+ align:start position:0%
+when y equals d i get 0 here and i get 0
+over here so that's that's clear
+
+ align:start position:0%
+over here so that's that's clear
+ 
+
+ align:start position:0%
+over here so that's that's clear
+and also
+
+ align:start position:0%
+and also
+ 
+
+ align:start position:0%
+and also
+the same here g of x minus g of c equals
+
+ align:start position:0%
+the same here g of x minus g of c equals
+ 
+
+ align:start position:0%
+the same here g of x minus g of c equals
+v of x minus something times x minus c
+
+ align:start position:0%
+v of x minus something times x minus c
+ 
+
+ align:start position:0%
+v of x minus something times x minus c
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we have these two um
+
+ align:start position:0%
+all right so we have these two um
+ 
+
+ align:start position:0%
+all right so we have these two um
+expressions
+
+ align:start position:0%
+expressions
+ 
+
+ align:start position:0%
+expressions
+and one more thing i want to note is
+
+ align:start position:0%
+and one more thing i want to note is
+ 
+
+ align:start position:0%
+and one more thing i want to note is
+that u and v are continuous at y equals
+
+ align:start position:0%
+that u and v are continuous at y equals
+ 
+
+ align:start position:0%
+that u and v are continuous at y equals
+d and x equals c um
+
+ align:start position:0%
+d and x equals c um
+ 
+
+ align:start position:0%
+d and x equals c um
+respectively
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so note that
+
+ align:start position:0%
+so note that
+ 
+
+ align:start position:0%
+so note that
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v of y
+
+ align:start position:0%
+v of y
+ 
+
+ align:start position:0%
+v of y
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous at
+
+ align:start position:0%
+continuous at
+ 
+
+ align:start position:0%
+continuous at
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+and v of
+
+ align:start position:0%
+and v of
+ 
+
+ align:start position:0%
+and v of
+x is
+
+ align:start position:0%
+x is
+ 
+
+ align:start position:0%
+x is
+continuous at c
+
+ align:start position:0%
+continuous at c
+ 
+
+ align:start position:0%
+continuous at c
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's look at the proof of that we just
+
+ align:start position:0%
+let's look at the proof of that we just
+ 
+
+ align:start position:0%
+let's look at the proof of that we just
+need to show that the limit as y
+
+ align:start position:0%
+need to show that the limit as y
+ 
+
+ align:start position:0%
+need to show that the limit as y
+goes to d of v of y equals v of d so
+
+ align:start position:0%
+goes to d of v of y equals v of d so
+ 
+
+ align:start position:0%
+goes to d of v of y equals v of d so
+compute the limit as y goes to d
+
+ align:start position:0%
+compute the limit as y goes to d
+ 
+
+ align:start position:0%
+compute the limit as y goes to d
+of v of y
+
+ align:start position:0%
+of v of y
+ 
+
+ align:start position:0%
+of v of y
+now when we look at limits remember
+
+ align:start position:0%
+now when we look at limits remember
+ 
+
+ align:start position:0%
+now when we look at limits remember
+we never
+
+ align:start position:0%
+we never
+ 
+
+ align:start position:0%
+we never
+we're not allowed to put y equals d
+
+ align:start position:0%
+we're not allowed to put y equals d
+ 
+
+ align:start position:0%
+we're not allowed to put y equals d
+in the expression for this limit okay
+
+ align:start position:0%
+in the expression for this limit okay
+ 
+
+ align:start position:0%
+in the expression for this limit okay
+we're always looking at points y close
+
+ align:start position:0%
+we're always looking at points y close
+ 
+
+ align:start position:0%
+we're always looking at points y close
+to d but not equal to d is what i'm what
+
+ align:start position:0%
+to d but not equal to d is what i'm what
+ 
+
+ align:start position:0%
+to d but not equal to d is what i'm what
+i'm saying and so therefore when y is
+
+ align:start position:0%
+i'm saying and so therefore when y is
+ 
+
+ align:start position:0%
+i'm saying and so therefore when y is
+near d
+
+ align:start position:0%
+near d
+ 
+
+ align:start position:0%
+near d
+and not equal to d v of y is given by
+
+ align:start position:0%
+and not equal to d v of y is given by
+ 
+
+ align:start position:0%
+and not equal to d v of y is given by
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i should this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should have written u here sorry u
+
+ align:start position:0%
+should have written u here sorry u
+ 
+
+ align:start position:0%
+should have written u here sorry u
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we're looking at y near d
+
+ align:start position:0%
+we're looking at y near d
+ 
+
+ align:start position:0%
+we're looking at y near d
+but not equal to d and therefore it's
+
+ align:start position:0%
+but not equal to d and therefore it's
+ 
+
+ align:start position:0%
+but not equal to d and therefore it's
+given by this expression right so this
+
+ align:start position:0%
+given by this expression right so this
+ 
+
+ align:start position:0%
+given by this expression right so this
+is the limit as y goes to d
+
+ align:start position:0%
+is the limit as y goes to d
+ 
+
+ align:start position:0%
+is the limit as y goes to d
+of f of y minus f of d
+
+ align:start position:0%
+of f of y minus f of d
+ 
+
+ align:start position:0%
+of f of y minus f of d
+over y minus d
+
+ align:start position:0%
+over y minus d
+ 
+
+ align:start position:0%
+over y minus d
+and this is just the definition of the
+
+ align:start position:0%
+and this is just the definition of the
+ 
+
+ align:start position:0%
+and this is just the definition of the
+derivative of f at d
+
+ align:start position:0%
+derivative of f at d
+ 
+
+ align:start position:0%
+derivative of f at d
+so remember d is g of c so f is
+
+ align:start position:0%
+so remember d is g of c so f is
+ 
+
+ align:start position:0%
+so remember d is g of c so f is
+differentiable there and this is uh
+
+ align:start position:0%
+differentiable there and this is uh
+ 
+
+ align:start position:0%
+differentiable there and this is uh
+by definition u of d
+
+ align:start position:0%
+by definition u of d
+ 
+
+ align:start position:0%
+by definition u of d
+right so this function u is continuous
+
+ align:start position:0%
+right so this function u is continuous
+ 
+
+ align:start position:0%
+right so this function u is continuous
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+uh y equals d
+
+ align:start position:0%
+uh y equals d
+ 
+
+ align:start position:0%
+uh y equals d
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and similarly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the limit as x goes to c of u of x v of
+
+ align:start position:0%
+the limit as x goes to c of u of x v of
+ 
+
+ align:start position:0%
+the limit as x goes to c of u of x v of
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+equals v of c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g prime of c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we're going to combine um
+
+ align:start position:0%
+okay so now we're going to combine um
+ 
+
+ align:start position:0%
+okay so now we're going to combine um
+what i've written here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to finish the proof so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then h of x
+
+ align:start position:0%
+then h of x
+ 
+
+ align:start position:0%
+then h of x
+minus h of c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equal to f of g of x
+
+ align:start position:0%
+this is equal to f of g of x
+ 
+
+ align:start position:0%
+this is equal to f of g of x
+minus f of
+
+ align:start position:0%
+minus f of
+ 
+
+ align:start position:0%
+minus f of
+g of c
+
+ align:start position:0%
+g of c
+ 
+
+ align:start position:0%
+g of c
+and this is equal to uh
+
+ align:start position:0%
+and this is equal to uh
+ 
+
+ align:start position:0%
+and this is equal to uh
+u of g of x
+
+ align:start position:0%
+u of g of x
+ 
+
+ align:start position:0%
+u of g of x
+times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g of x minus g of c
+
+ align:start position:0%
+g of x minus g of c
+ 
+
+ align:start position:0%
+g of x minus g of c
+this is from this relation here
+
+ align:start position:0%
+this is from this relation here
+ 
+
+ align:start position:0%
+this is from this relation here
+so call this one star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one double star
+
+ align:start position:0%
+this one double star
+ 
+
+ align:start position:0%
+this one double star
+so this is by star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now i use uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second relation double star to write
+
+ align:start position:0%
+the second relation double star to write
+ 
+
+ align:start position:0%
+the second relation double star to write
+g of x minus g of c equals
+
+ align:start position:0%
+g of x minus g of c equals
+ 
+
+ align:start position:0%
+g of x minus g of c equals
+b of x times
+
+ align:start position:0%
+b of x times
+ 
+
+ align:start position:0%
+b of x times
+x minus c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the limit as x goes to c
+
+ align:start position:0%
+the limit as x goes to c
+ 
+
+ align:start position:0%
+the limit as x goes to c
+of um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h of x
+
+ align:start position:0%
+h of x
+ 
+
+ align:start position:0%
+h of x
+minus um
+
+ align:start position:0%
+minus um
+ 
+
+ align:start position:0%
+minus um
+h of c
+
+ align:start position:0%
+h of c
+ 
+
+ align:start position:0%
+h of c
+over x minus c this is equal to the
+
+ align:start position:0%
+over x minus c this is equal to the
+ 
+
+ align:start position:0%
+over x minus c this is equal to the
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+as x goes to c
+
+ align:start position:0%
+as x goes to c
+ 
+
+ align:start position:0%
+as x goes to c
+of u of g of x
+
+ align:start position:0%
+of u of g of x
+ 
+
+ align:start position:0%
+of u of g of x
+times v
+
+ align:start position:0%
+times v
+ 
+
+ align:start position:0%
+times v
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+u is continuous at g of c g is
+
+ align:start position:0%
+u is continuous at g of c g is
+ 
+
+ align:start position:0%
+u is continuous at g of c g is
+continuous at c
+
+ align:start position:0%
+continuous at c
+ 
+
+ align:start position:0%
+continuous at c
+and we prove that the composition of two
+
+ align:start position:0%
+and we prove that the composition of two
+ 
+
+ align:start position:0%
+and we prove that the composition of two
+continuous functions is continuous
+
+ align:start position:0%
+continuous functions is continuous
+ 
+
+ align:start position:0%
+continuous functions is continuous
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this equals
+
+ align:start position:0%
+this equals
+ 
+
+ align:start position:0%
+this equals
+u of g of c
+
+ align:start position:0%
+u of g of c
+ 
+
+ align:start position:0%
+u of g of c
+and v of x we've proven already that
+
+ align:start position:0%
+and v of x we've proven already that
+ 
+
+ align:start position:0%
+and v of x we've proven already that
+limit is v
+
+ align:start position:0%
+limit is v
+ 
+
+ align:start position:0%
+limit is v
+of c
+
+ align:start position:0%
+of c
+ 
+
+ align:start position:0%
+of c
+and u of g of c you know so this is d
+
+ align:start position:0%
+and u of g of c you know so this is d
+ 
+
+ align:start position:0%
+and u of g of c you know so this is d
+remember in in the notation we had
+
+ align:start position:0%
+remember in in the notation we had
+ 
+
+ align:start position:0%
+remember in in the notation we had
+earlier and therefore that equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f prime of g of c
+
+ align:start position:0%
+f prime of g of c
+ 
+
+ align:start position:0%
+f prime of g of c
+remember g of c was d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+g prime of
+
+ align:start position:0%
+g prime of
+ 
+
+ align:start position:0%
+g prime of
+c okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to go from this point to this point
+
+ align:start position:0%
+so to go from this point to this point
+ 
+
+ align:start position:0%
+so to go from this point to this point
+we use the fact that u is continuous at
+
+ align:start position:0%
+we use the fact that u is continuous at
+ 
+
+ align:start position:0%
+we use the fact that u is continuous at
+c which we proved
+
+ align:start position:0%
+c which we proved
+ 
+
+ align:start position:0%
+c which we proved
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+u is continuous at g of c
+
+ align:start position:0%
+u is continuous at g of c
+ 
+
+ align:start position:0%
+u is continuous at g of c
+which we proved over there and that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g is continuous at c
+
+ align:start position:0%
+g is continuous at c
+ 
+
+ align:start position:0%
+g is continuous at c
+and therefore the composition of two
+
+ align:start position:0%
+and therefore the composition of two
+ 
+
+ align:start position:0%
+and therefore the composition of two
+continuous functions is continuous at
+
+ align:start position:0%
+continuous functions is continuous at
+ 
+
+ align:start position:0%
+continuous functions is continuous at
+that point to arrive at uh this guy
+
+ align:start position:0%
+that point to arrive at uh this guy
+ 
+
+ align:start position:0%
+that point to arrive at uh this guy
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but again the whole basic idea was to be
+
+ align:start position:0%
+but again the whole basic idea was to be
+ 
+
+ align:start position:0%
+but again the whole basic idea was to be
+able to write the difference quotient as
+
+ align:start position:0%
+able to write the difference quotient as
+ 
+
+ align:start position:0%
+able to write the difference quotient as
+kind of a product of
+
+ align:start position:0%
+kind of a product of
+ 
+
+ align:start position:0%
+kind of a product of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know what looks like the difference
+
+ align:start position:0%
+you know what looks like the difference
+ 
+
+ align:start position:0%
+you know what looks like the difference
+quotient of f
+
+ align:start position:0%
+quotient of f
+ 
+
+ align:start position:0%
+quotient of f
+times the difference quotient of g but
+
+ align:start position:0%
+times the difference quotient of g but
+ 
+
+ align:start position:0%
+times the difference quotient of g but
+you have to be careful because g of x
+
+ align:start position:0%
+you have to be careful because g of x
+ 
+
+ align:start position:0%
+you have to be careful because g of x
+could equal g of c
+
+ align:start position:0%
+could equal g of c
+ 
+
+ align:start position:0%
+could equal g of c
+in which case you're dividing by zero in
+
+ align:start position:0%
+in which case you're dividing by zero in
+ 
+
+ align:start position:0%
+in which case you're dividing by zero in
+this you know basic idea we had up there
+
+ align:start position:0%
+this you know basic idea we had up there
+ 
+
+ align:start position:0%
+this you know basic idea we had up there
+which is not allowed
+
+ align:start position:0%
+which is not allowed
+ 
+
+ align:start position:0%
+which is not allowed
+but you get around it by by
+
+ align:start position:0%
+but you get around it by by
+ 
+
+ align:start position:0%
+but you get around it by by
+you know using these uh
+
+ align:start position:0%
+you know using these uh
+ 
+
+ align:start position:0%
+you know using these uh
+functions which equal what you want
+
+ align:start position:0%
+functions which equal what you want
+ 
+
+ align:start position:0%
+functions which equal what you want
+as long as you're not dividing by zero
+
+ align:start position:0%
+as long as you're not dividing by zero
+ 
+
+ align:start position:0%
+as long as you're not dividing by zero
+basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that wraps it up for basic
+
+ align:start position:0%
+okay so that wraps it up for basic
+ 
+
+ align:start position:0%
+okay so that wraps it up for basic
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+of the derivative
+
+ align:start position:0%
+of the derivative
+ 
+
+ align:start position:0%
+of the derivative
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and now we're going to move on to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trying to prove the mean value theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the alfred of this
+
+ align:start position:0%
+the alfred of this
+ 
+
+ align:start position:0%
+the alfred of this
+batman tail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but first uh in order to prove this
+
+ align:start position:0%
+but first uh in order to prove this
+ 
+
+ align:start position:0%
+but first uh in order to prove this
+we'll need a result about um the
+
+ align:start position:0%
+we'll need a result about um the
+ 
+
+ align:start position:0%
+we'll need a result about um the
+derivative in relation to
+
+ align:start position:0%
+derivative in relation to
+ 
+
+ align:start position:0%
+derivative in relation to
+a certain relative minimum and relative
+
+ align:start position:0%
+a certain relative minimum and relative
+ 
+
+ align:start position:0%
+a certain relative minimum and relative
+maximum so let me first define what this
+
+ align:start position:0%
+maximum so let me first define what this
+ 
+
+ align:start position:0%
+maximum so let me first define what this
+means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let s be a subset of r
+
+ align:start position:0%
+let s be a subset of r
+ 
+
+ align:start position:0%
+let s be a subset of r
+f be a function from s to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we say f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relative max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at c
+
+ align:start position:0%
+at c
+ 
+
+ align:start position:0%
+at c
+in s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+there exists a delta positive
+
+ align:start position:0%
+there exists a delta positive
+ 
+
+ align:start position:0%
+there exists a delta positive
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+for all x and s
+
+ align:start position:0%
+for all x and s
+ 
+
+ align:start position:0%
+for all x and s
+x minus e is less than delta
+
+ align:start position:0%
+x minus e is less than delta
+ 
+
+ align:start position:0%
+x minus e is less than delta
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+f of x is less than or equal to f c
+
+ align:start position:0%
+f of x is less than or equal to f c
+ 
+
+ align:start position:0%
+f of x is less than or equal to f c
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the picture here and then
+
+ align:start position:0%
+so the picture here and then
+ 
+
+ align:start position:0%
+so the picture here and then
+let me um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state that there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analogous definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of relative min
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at c you just take this entire
+
+ align:start position:0%
+at c you just take this entire
+ 
+
+ align:start position:0%
+at c you just take this entire
+definition and flip the inequality
+
+ align:start position:0%
+definition and flip the inequality
+ 
+
+ align:start position:0%
+definition and flip the inequality
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's the definition for relative men
+
+ align:start position:0%
+that's the definition for relative men
+ 
+
+ align:start position:0%
+that's the definition for relative men
+so what this means pictorially so
+
+ align:start position:0%
+so what this means pictorially so
+ 
+
+ align:start position:0%
+so what this means pictorially so
+remember we had this notion of absolute
+
+ align:start position:0%
+remember we had this notion of absolute
+ 
+
+ align:start position:0%
+remember we had this notion of absolute
+min and absolute max an absolute max at
+
+ align:start position:0%
+min and absolute max an absolute max at
+ 
+
+ align:start position:0%
+min and absolute max an absolute max at
+a point c
+
+ align:start position:0%
+a point c
+ 
+
+ align:start position:0%
+a point c
+means every other point um at every
+
+ align:start position:0%
+means every other point um at every
+ 
+
+ align:start position:0%
+means every other point um at every
+other point in s
+
+ align:start position:0%
+other point in s
+ 
+
+ align:start position:0%
+other point in s
+f of x lies below f of c here we're just
+
+ align:start position:0%
+f of x lies below f of c here we're just
+ 
+
+ align:start position:0%
+f of x lies below f of c here we're just
+saying as long as you're close to
+
+ align:start position:0%
+saying as long as you're close to
+ 
+
+ align:start position:0%
+saying as long as you're close to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the point c
+
+ align:start position:0%
+the point c
+ 
+
+ align:start position:0%
+the point c
+then you lay below f c so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say our function looks something
+
+ align:start position:0%
+let's say our function looks something
+ 
+
+ align:start position:0%
+let's say our function looks something
+like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say we're at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so this would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolute max because the graph of the
+
+ align:start position:0%
+absolute max because the graph of the
+ 
+
+ align:start position:0%
+absolute max because the graph of the
+function sits below
+
+ align:start position:0%
+function sits below
+ 
+
+ align:start position:0%
+function sits below
+the value
+
+ align:start position:0%
+the value
+ 
+
+ align:start position:0%
+the value
+of the function at this point for all x
+
+ align:start position:0%
+of the function at this point for all x
+ 
+
+ align:start position:0%
+of the function at this point for all x
+in this uh interval a b okay and then
+
+ align:start position:0%
+in this uh interval a b okay and then
+ 
+
+ align:start position:0%
+in this uh interval a b okay and then
+here at this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we would have an absolute
+
+ align:start position:0%
+we would have an absolute
+ 
+
+ align:start position:0%
+we would have an absolute
+min right because
+
+ align:start position:0%
+min right because
+ 
+
+ align:start position:0%
+min right because
+the rest of
+
+ align:start position:0%
+the rest of
+ 
+
+ align:start position:0%
+the rest of
+because the graph of the function sits
+
+ align:start position:0%
+because the graph of the function sits
+ 
+
+ align:start position:0%
+because the graph of the function sits
+above that point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x in this interval but now if
+
+ align:start position:0%
+for all x in this interval but now if
+ 
+
+ align:start position:0%
+for all x in this interval but now if
+you if i go to this point
+
+ align:start position:0%
+you if i go to this point
+ 
+
+ align:start position:0%
+you if i go to this point
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this would be a relative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+max
+
+ align:start position:0%
+max
+ 
+
+ align:start position:0%
+max
+okay because why if i look at um
+
+ align:start position:0%
+okay because why if i look at um
+ 
+
+ align:start position:0%
+okay because why if i look at um
+you know an interval small interval
+
+ align:start position:0%
+you know an interval small interval
+ 
+
+ align:start position:0%
+you know an interval small interval
+around it
+
+ align:start position:0%
+around it
+ 
+
+ align:start position:0%
+around it
+and i look inside this interval there's
+
+ align:start position:0%
+and i look inside this interval there's
+ 
+
+ align:start position:0%
+and i look inside this interval there's
+too many dashed lines going on so i'm
+
+ align:start position:0%
+too many dashed lines going on so i'm
+ 
+
+ align:start position:0%
+too many dashed lines going on so i'm
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+erase this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i'm just going to do away with the
+
+ align:start position:0%
+yeah i'm just going to do away with the
+ 
+
+ align:start position:0%
+yeah i'm just going to do away with the
+dash
+
+ align:start position:0%
+dash
+ 
+
+ align:start position:0%
+dash
+if i zoom in on just this one piece of
+
+ align:start position:0%
+if i zoom in on just this one piece of
+ 
+
+ align:start position:0%
+if i zoom in on just this one piece of
+the graph then at this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the graph sits below this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inside this um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inside this little vertical strip okay
+
+ align:start position:0%
+inside this little vertical strip okay
+ 
+
+ align:start position:0%
+inside this little vertical strip okay
+so this guy would be a relative max and
+
+ align:start position:0%
+so this guy would be a relative max and
+ 
+
+ align:start position:0%
+so this guy would be a relative max and
+then similarly
+
+ align:start position:0%
+then similarly
+ 
+
+ align:start position:0%
+then similarly
+at this point here maybe it's uh let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really see what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph is
+
+ align:start position:0%
+graph is
+ 
+
+ align:start position:0%
+graph is
+should have brought different colors
+
+ align:start position:0%
+should have brought different colors
+ 
+
+ align:start position:0%
+should have brought different colors
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+at this point
+
+ align:start position:0%
+at this point
+ 
+
+ align:start position:0%
+at this point
+we have relative min
+
+ align:start position:0%
+we have relative min
+ 
+
+ align:start position:0%
+we have relative min
+right because nearby
+
+ align:start position:0%
+right because nearby
+ 
+
+ align:start position:0%
+right because nearby
+nearby points sit above the value of the
+
+ align:start position:0%
+nearby points sit above the value of the
+ 
+
+ align:start position:0%
+nearby points sit above the value of the
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+evaluated at this point okay so
+
+ align:start position:0%
+evaluated at this point okay so
+ 
+
+ align:start position:0%
+evaluated at this point okay so
+relative max means nearby points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f sits below that f f evaluated at that
+
+ align:start position:0%
+f sits below that f f evaluated at that
+ 
+
+ align:start position:0%
+f sits below that f f evaluated at that
+point and relative min is the other way
+
+ align:start position:0%
+point and relative min is the other way
+ 
+
+ align:start position:0%
+point and relative min is the other way
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i don't think we need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+belabor the point of what relative men
+
+ align:start position:0%
+belabor the point of what relative men
+ 
+
+ align:start position:0%
+belabor the point of what relative men
+relative maxes are i think that's pretty
+
+ align:start position:0%
+relative maxes are i think that's pretty
+ 
+
+ align:start position:0%
+relative maxes are i think that's pretty
+clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if f from a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a
+
+ align:start position:0%
+has a
+ 
+
+ align:start position:0%
+has a
+relative
+
+ align:start position:0%
+relative
+ 
+
+ align:start position:0%
+relative
+min or
+
+ align:start position:0%
+min or
+ 
+
+ align:start position:0%
+min or
+max
+
+ align:start position:0%
+max
+ 
+
+ align:start position:0%
+max
+at a point c
+
+ align:start position:0%
+at a point c
+ 
+
+ align:start position:0%
+at a point c
+strictly inside this closed interval in
+
+ align:start position:0%
+strictly inside this closed interval in
+ 
+
+ align:start position:0%
+strictly inside this closed interval in
+the open interval a b
+
+ align:start position:0%
+the open interval a b
+ 
+
+ align:start position:0%
+the open interval a b
+then and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable at c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f prime of c equals zero right and this
+
+ align:start position:0%
+f prime of c equals zero right and this
+ 
+
+ align:start position:0%
+f prime of c equals zero right and this
+is kind of clear from this picture
+
+ align:start position:0%
+is kind of clear from this picture
+ 
+
+ align:start position:0%
+is kind of clear from this picture
+although this kind of might look more
+
+ align:start position:0%
+although this kind of might look more
+ 
+
+ align:start position:0%
+although this kind of might look more
+like a sawtooth but it shouldn't that
+
+ align:start position:0%
+like a sawtooth but it shouldn't that
+ 
+
+ align:start position:0%
+like a sawtooth but it shouldn't that
+the tangent at this point is uh
+
+ align:start position:0%
+the tangent at this point is uh
+ 
+
+ align:start position:0%
+the tangent at this point is uh
+horizontal and the tangent at this point
+
+ align:start position:0%
+horizontal and the tangent at this point
+ 
+
+ align:start position:0%
+horizontal and the tangent at this point
+is horizontal which just
+
+ align:start position:0%
+is horizontal which just
+ 
+
+ align:start position:0%
+is horizontal which just
+is the expression that
+
+ align:start position:0%
+is the expression that
+ 
+
+ align:start position:0%
+is the expression that
+um was just expressing that f prime of c
+
+ align:start position:0%
+um was just expressing that f prime of c
+ 
+
+ align:start position:0%
+um was just expressing that f prime of c
+equals zero right so f prime of c is
+
+ align:start position:0%
+equals zero right so f prime of c is
+ 
+
+ align:start position:0%
+equals zero right so f prime of c is
+supposed to be the slope of the tangent
+
+ align:start position:0%
+supposed to be the slope of the tangent
+ 
+
+ align:start position:0%
+supposed to be the slope of the tangent
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea of the proof is
+
+ align:start position:0%
+so the idea of the proof is
+ 
+
+ align:start position:0%
+so the idea of the proof is
+and we'll do it for relative max
+
+ align:start position:0%
+and we'll do it for relative max
+ 
+
+ align:start position:0%
+and we'll do it for relative max
+relative min you get by taking minus f
+
+ align:start position:0%
+relative min you get by taking minus f
+ 
+
+ align:start position:0%
+relative min you get by taking minus f
+so we'll do it for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose f has a relative max at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c and a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm just going to draw a picture um
+
+ align:start position:0%
+so i'm just going to draw a picture um
+ 
+
+ align:start position:0%
+so i'm just going to draw a picture um
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+illustrate why this is the case so
+
+ align:start position:0%
+illustrate why this is the case so
+ 
+
+ align:start position:0%
+illustrate why this is the case so
+why what i'm about to say is the case so
+
+ align:start position:0%
+why what i'm about to say is the case so
+ 
+
+ align:start position:0%
+why what i'm about to say is the case so
+we have a b
+
+ align:start position:0%
+we have a b
+ 
+
+ align:start position:0%
+we have a b
+we have c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+delta positive
+
+ align:start position:0%
+delta positive
+ 
+
+ align:start position:0%
+delta positive
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+say delta 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+two things are true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x or c minus
+
+ align:start position:0%
+x or c minus
+ 
+
+ align:start position:0%
+x or c minus
+delta 1
+
+ align:start position:0%
+delta 1
+ 
+
+ align:start position:0%
+delta 1
+c plus delta 1 is contained in
+
+ align:start position:0%
+c plus delta 1 is contained in
+ 
+
+ align:start position:0%
+c plus delta 1 is contained in
+a b
+
+ align:start position:0%
+a b
+ 
+
+ align:start position:0%
+a b
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x and c minus delta one
+
+ align:start position:0%
+for all x and c minus delta one
+ 
+
+ align:start position:0%
+for all x and c minus delta one
+c plus delta one
+
+ align:start position:0%
+c plus delta one
+ 
+
+ align:start position:0%
+c plus delta one
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+f of x is less than or equal to f c
+
+ align:start position:0%
+f of x is less than or equal to f c
+ 
+
+ align:start position:0%
+f of x is less than or equal to f c
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+delta one is chosen as the minimum of uh
+
+ align:start position:0%
+delta one is chosen as the minimum of uh
+ 
+
+ align:start position:0%
+delta one is chosen as the minimum of uh
+so maybe let me not call it delta let me
+
+ align:start position:0%
+so maybe let me not call it delta let me
+ 
+
+ align:start position:0%
+so maybe let me not call it delta let me
+one let me just call it delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+first off you know that a b
+
+ align:start position:0%
+first off you know that a b
+ 
+
+ align:start position:0%
+first off you know that a b
+open interval this is a an open set
+
+ align:start position:0%
+open interval this is a an open set
+ 
+
+ align:start position:0%
+open interval this is a an open set
+which we've encountered in the
+
+ align:start position:0%
+which we've encountered in the
+ 
+
+ align:start position:0%
+which we've encountered in the
+assignments
+
+ align:start position:0%
+assignments
+ 
+
+ align:start position:0%
+assignments
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can find a delta
+
+ align:start position:0%
+you can find a delta
+ 
+
+ align:start position:0%
+you can find a delta
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta 0 say so that this interval
+
+ align:start position:0%
+delta 0 say so that this interval
+ 
+
+ align:start position:0%
+delta 0 say so that this interval
+centered at c is contained in a b
+
+ align:start position:0%
+centered at c is contained in a b
+ 
+
+ align:start position:0%
+centered at c is contained in a b
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now since
+
+ align:start position:0%
+now since
+ 
+
+ align:start position:0%
+now since
+f has a relative maximum at this point
+
+ align:start position:0%
+f has a relative maximum at this point
+ 
+
+ align:start position:0%
+f has a relative maximum at this point
+there exists another delta one say so
+
+ align:start position:0%
+there exists another delta one say so
+ 
+
+ align:start position:0%
+there exists another delta one say so
+that if
+
+ align:start position:0%
+that if
+ 
+
+ align:start position:0%
+that if
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm inside that interval
+
+ align:start position:0%
+i'm inside that interval
+ 
+
+ align:start position:0%
+i'm inside that interval
+then f of x is less than or equal to f c
+
+ align:start position:0%
+then f of x is less than or equal to f c
+ 
+
+ align:start position:0%
+then f of x is less than or equal to f c
+for all x in that interval
+
+ align:start position:0%
+for all x in that interval
+ 
+
+ align:start position:0%
+for all x in that interval
+okay and i choose delta to be the
+
+ align:start position:0%
+okay and i choose delta to be the
+ 
+
+ align:start position:0%
+okay and i choose delta to be the
+minimum of these two uh these two deltas
+
+ align:start position:0%
+minimum of these two uh these two deltas
+ 
+
+ align:start position:0%
+minimum of these two uh these two deltas
+and then i will have
+
+ align:start position:0%
+and then i will have
+ 
+
+ align:start position:0%
+and then i will have
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a chosen delta so that
+
+ align:start position:0%
+a chosen delta so that
+ 
+
+ align:start position:0%
+a chosen delta so that
+x that c minus delta c plus delta is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then delta 0 is chosen so that that
+
+ align:start position:0%
+and then delta 0 is chosen so that that
+ 
+
+ align:start position:0%
+and then delta 0 is chosen so that that
+is contained so i choose the minimum of
+
+ align:start position:0%
+is contained so i choose the minimum of
+ 
+
+ align:start position:0%
+is contained so i choose the minimum of
+these deltas and this is the delta i
+
+ align:start position:0%
+these deltas and this is the delta i
+ 
+
+ align:start position:0%
+these deltas and this is the delta i
+take for for this statement
+
+ align:start position:0%
+take for for this statement
+ 
+
+ align:start position:0%
+take for for this statement
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+now the way we get that the derivative
+
+ align:start position:0%
+now the way we get that the derivative
+ 
+
+ align:start position:0%
+now the way we get that the derivative
+is zero is we're going to approach uh c
+
+ align:start position:0%
+is zero is we're going to approach uh c
+ 
+
+ align:start position:0%
+is zero is we're going to approach uh c
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+above and
+
+ align:start position:0%
+above and
+ 
+
+ align:start position:0%
+above and
+from below
+
+ align:start position:0%
+from below
+ 
+
+ align:start position:0%
+from below
+and use the um
+
+ align:start position:0%
+and use the um
+ 
+
+ align:start position:0%
+and use the um
+the fact that we have a relative max to
+
+ align:start position:0%
+the fact that we have a relative max to
+ 
+
+ align:start position:0%
+the fact that we have a relative max to
+show that the derivative is both
+
+ align:start position:0%
+show that the derivative is both
+ 
+
+ align:start position:0%
+show that the derivative is both
+uh bigger than or equal to zero and less
+
+ align:start position:0%
+uh bigger than or equal to zero and less
+ 
+
+ align:start position:0%
+uh bigger than or equal to zero and less
+than or equal to zero all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let x in be um
+
+ align:start position:0%
+let x in be um
+ 
+
+ align:start position:0%
+let x in be um
+c minus
+
+ align:start position:0%
+c minus
+ 
+
+ align:start position:0%
+c minus
+um how did i write this
+
+ align:start position:0%
+um how did i write this
+ 
+
+ align:start position:0%
+um how did i write this
+delta over 2n which is
+
+ align:start position:0%
+delta over 2n which is
+ 
+
+ align:start position:0%
+delta over 2n which is
+in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interval c minus delta c
+
+ align:start position:0%
+interval c minus delta c
+ 
+
+ align:start position:0%
+interval c minus delta c
+for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then what do we know x in
+
+ align:start position:0%
+then what do we know x in
+ 
+
+ align:start position:0%
+then what do we know x in
+the limit as n goes to infinity of c
+
+ align:start position:0%
+the limit as n goes to infinity of c
+ 
+
+ align:start position:0%
+the limit as n goes to infinity of c
+minus delta over two
+
+ align:start position:0%
+minus delta over two
+ 
+
+ align:start position:0%
+minus delta over two
+n converges to
+
+ align:start position:0%
+n converges to
+ 
+
+ align:start position:0%
+n converges to
+c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+derivative at c
+
+ align:start position:0%
+derivative at c
+ 
+
+ align:start position:0%
+derivative at c
+is equal to the limit
+
+ align:start position:0%
+is equal to the limit
+ 
+
+ align:start position:0%
+is equal to the limit
+as n goes to infinity of
+
+ align:start position:0%
+as n goes to infinity of
+ 
+
+ align:start position:0%
+as n goes to infinity of
+f of x sub n minus f of c
+
+ align:start position:0%
+f of x sub n minus f of c
+ 
+
+ align:start position:0%
+f of x sub n minus f of c
+over x sub n minus c
+
+ align:start position:0%
+over x sub n minus c
+ 
+
+ align:start position:0%
+over x sub n minus c
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what do we note
+
+ align:start position:0%
+what do we note
+ 
+
+ align:start position:0%
+what do we note
+so x sub n is in this interval here
+
+ align:start position:0%
+so x sub n is in this interval here
+ 
+
+ align:start position:0%
+so x sub n is in this interval here
+which is contained in this interval here
+
+ align:start position:0%
+which is contained in this interval here
+ 
+
+ align:start position:0%
+which is contained in this interval here
+and therefore f of x sub n is always
+
+ align:start position:0%
+and therefore f of x sub n is always
+ 
+
+ align:start position:0%
+and therefore f of x sub n is always
+less than or equal to f of c
+
+ align:start position:0%
+less than or equal to f of c
+ 
+
+ align:start position:0%
+less than or equal to f of c
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what's on top is always less than or
+
+ align:start position:0%
+what's on top is always less than or
+ 
+
+ align:start position:0%
+what's on top is always less than or
+equal to zero
+
+ align:start position:0%
+equal to zero
+ 
+
+ align:start position:0%
+equal to zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now x sub n is always less than c
+
+ align:start position:0%
+now x sub n is always less than c
+ 
+
+ align:start position:0%
+now x sub n is always less than c
+so this thing on bottom is also less
+
+ align:start position:0%
+so this thing on bottom is also less
+ 
+
+ align:start position:0%
+so this thing on bottom is also less
+than zero
+
+ align:start position:0%
+than zero
+ 
+
+ align:start position:0%
+than zero
+and therefore something that's less than
+
+ align:start position:0%
+and therefore something that's less than
+ 
+
+ align:start position:0%
+and therefore something that's less than
+or equal to zero on top over something
+
+ align:start position:0%
+or equal to zero on top over something
+ 
+
+ align:start position:0%
+or equal to zero on top over something
+that's less than zero on bottom
+
+ align:start position:0%
+that's less than zero on bottom
+ 
+
+ align:start position:0%
+that's less than zero on bottom
+must be bigger than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's approaching c from the left if
+
+ align:start position:0%
+so that's approaching c from the left if
+ 
+
+ align:start position:0%
+so that's approaching c from the left if
+we approach c from the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta over 2 n which is contained in
+
+ align:start position:0%
+delta over 2 n which is contained in
+ 
+
+ align:start position:0%
+delta over 2 n which is contained in
+c c plus delta
+
+ align:start position:0%
+c c plus delta
+ 
+
+ align:start position:0%
+c c plus delta
+for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+x n converges to c
+
+ align:start position:0%
+x n converges to c
+ 
+
+ align:start position:0%
+x n converges to c
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if we look at f prime of c
+
+ align:start position:0%
+if we look at f prime of c
+ 
+
+ align:start position:0%
+if we look at f prime of c
+again this is equal to
+
+ align:start position:0%
+again this is equal to
+ 
+
+ align:start position:0%
+again this is equal to
+limit as n goes to infinity of f of
+
+ align:start position:0%
+limit as n goes to infinity of f of
+ 
+
+ align:start position:0%
+limit as n goes to infinity of f of
+y sub n minus f of c
+
+ align:start position:0%
+y sub n minus f of c
+ 
+
+ align:start position:0%
+y sub n minus f of c
+over y sub n minus c again
+
+ align:start position:0%
+over y sub n minus c again
+ 
+
+ align:start position:0%
+over y sub n minus c again
+uh f c is a relative maximum so this
+
+ align:start position:0%
+uh f c is a relative maximum so this
+ 
+
+ align:start position:0%
+uh f c is a relative maximum so this
+thing on top is still less than or equal
+
+ align:start position:0%
+thing on top is still less than or equal
+ 
+
+ align:start position:0%
+thing on top is still less than or equal
+to zero
+
+ align:start position:0%
+to zero
+ 
+
+ align:start position:0%
+to zero
+and the thing on bottom though is now
+
+ align:start position:0%
+and the thing on bottom though is now
+ 
+
+ align:start position:0%
+and the thing on bottom though is now
+since y sub n is bigger than c
+
+ align:start position:0%
+since y sub n is bigger than c
+ 
+
+ align:start position:0%
+since y sub n is bigger than c
+this is positive so something on top is
+
+ align:start position:0%
+this is positive so something on top is
+ 
+
+ align:start position:0%
+this is positive so something on top is
+negative something on top is positive so
+
+ align:start position:0%
+negative something on top is positive so
+ 
+
+ align:start position:0%
+negative something on top is positive so
+the limit must be negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we've just shown f prime of c is both
+
+ align:start position:0%
+so we've just shown f prime of c is both
+ 
+
+ align:start position:0%
+so we've just shown f prime of c is both
+bigger than or equal to zero and that
+
+ align:start position:0%
+bigger than or equal to zero and that
+ 
+
+ align:start position:0%
+bigger than or equal to zero and that
+it's also less than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore the derivative is zero
+
+ align:start position:0%
+and therefore the derivative is zero
+ 
+
+ align:start position:0%
+and therefore the derivative is zero
+at this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and again the proof for a relative
+
+ align:start position:0%
+and again the proof for a relative
+ 
+
+ align:start position:0%
+and again the proof for a relative
+minimum is is um
+
+ align:start position:0%
+minimum is is um
+ 
+
+ align:start position:0%
+minimum is is um
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very similar except um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+except that inequality flips signs
+
+ align:start position:0%
+except that inequality flips signs
+ 
+
+ align:start position:0%
+except that inequality flips signs
+and therefore you would get this is less
+
+ align:start position:0%
+and therefore you would get this is less
+ 
+
+ align:start position:0%
+and therefore you would get this is less
+than or equal to zero this one would be
+
+ align:start position:0%
+than or equal to zero this one would be
+ 
+
+ align:start position:0%
+than or equal to zero this one would be
+bigger than or equal to zero
+
+ align:start position:0%
+bigger than or equal to zero
+ 
+
+ align:start position:0%
+bigger than or equal to zero
+but you still get uh f prime of c is
+
+ align:start position:0%
+but you still get uh f prime of c is
+ 
+
+ align:start position:0%
+but you still get uh f prime of c is
+bounded between zero and zero
+
+ align:start position:0%
+bounded between zero and zero
+ 
+
+ align:start position:0%
+bounded between zero and zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+at a point
+
+ align:start position:0%
+at a point
+ 
+
+ align:start position:0%
+at a point
+where we have a relative minimum
+
+ align:start position:0%
+where we have a relative minimum
+ 
+
+ align:start position:0%
+where we have a relative minimum
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+strictly inside the interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the derivative must be zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the fact that it happens strictly
+
+ align:start position:0%
+and the fact that it happens strictly
+ 
+
+ align:start position:0%
+and the fact that it happens strictly
+inside the interval is important right
+
+ align:start position:0%
+inside the interval is important right
+ 
+
+ align:start position:0%
+inside the interval is important right
+this is not necessarily um
+
+ align:start position:0%
+this is not necessarily um
+ 
+
+ align:start position:0%
+this is not necessarily um
+true if the relative max or relative min
+
+ align:start position:0%
+true if the relative max or relative min
+ 
+
+ align:start position:0%
+true if the relative max or relative min
+happens at an endpoint right think of f
+
+ align:start position:0%
+happens at an endpoint right think of f
+ 
+
+ align:start position:0%
+happens at an endpoint right think of f
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+equals x on zero one right
+
+ align:start position:0%
+equals x on zero one right
+ 
+
+ align:start position:0%
+equals x on zero one right
+and it has a absolute minimum at zero
+
+ align:start position:0%
+and it has a absolute minimum at zero
+ 
+
+ align:start position:0%
+and it has a absolute minimum at zero
+absolute maximum at one and the
+
+ align:start position:0%
+absolute maximum at one and the
+ 
+
+ align:start position:0%
+absolute maximum at one and the
+derivative is one at both points
+
+ align:start position:0%
+derivative is one at both points
+ 
+
+ align:start position:0%
+derivative is one at both points
+not zero so this is only for relative
+
+ align:start position:0%
+not zero so this is only for relative
+ 
+
+ align:start position:0%
+not zero so this is only for relative
+min
+
+ align:start position:0%
+min
+ 
+
+ align:start position:0%
+min
+relative maxes that occur inside
+
+ align:start position:0%
+relative maxes that occur inside
+ 
+
+ align:start position:0%
+relative maxes that occur inside
+strictly inside the interval that the
+
+ align:start position:0%
+strictly inside the interval that the
+ 
+
+ align:start position:0%
+strictly inside the interval that the
+function's
+
+ align:start position:0%
+function's
+ 
+
+ align:start position:0%
+function's
+defined on and
+
+ align:start position:0%
+defined on and
+ 
+
+ align:start position:0%
+defined on and
+where it's differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have rolls theorem which is
+
+ align:start position:0%
+we have rolls theorem which is
+ 
+
+ align:start position:0%
+we have rolls theorem which is
+essentially the mean value theorem um
+
+ align:start position:0%
+essentially the mean value theorem um
+ 
+
+ align:start position:0%
+essentially the mean value theorem um
+rotated
+
+ align:start position:0%
+rotated
+ 
+
+ align:start position:0%
+rotated
+we'll get the mean value theorem from
+
+ align:start position:0%
+we'll get the mean value theorem from
+ 
+
+ align:start position:0%
+we'll get the mean value theorem from
+rolle's theorem and which states the
+
+ align:start position:0%
+rolle's theorem and which states the
+ 
+
+ align:start position:0%
+rolle's theorem and which states the
+following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f b from a b to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's continuous at every point in a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+every point inside of a b
+
+ align:start position:0%
+every point inside of a b
+ 
+
+ align:start position:0%
+every point inside of a b
+okay it could be differentiable at the
+
+ align:start position:0%
+okay it could be differentiable at the
+ 
+
+ align:start position:0%
+okay it could be differentiable at the
+end point so it's fine but it has to be
+
+ align:start position:0%
+end point so it's fine but it has to be
+ 
+
+ align:start position:0%
+end point so it's fine but it has to be
+differentiable
+
+ align:start position:0%
+differentiable
+ 
+
+ align:start position:0%
+differentiable
+on the open interval a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of f b a equals f of b equals 0.
+
+ align:start position:0%
+of f b a equals f of b equals 0.
+ 
+
+ align:start position:0%
+of f b a equals f of b equals 0.
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists a point c
+
+ align:start position:0%
+there exists a point c
+ 
+
+ align:start position:0%
+there exists a point c
+the open interval a b
+
+ align:start position:0%
+the open interval a b
+ 
+
+ align:start position:0%
+the open interval a b
+this is important
+
+ align:start position:0%
+this is important
+ 
+
+ align:start position:0%
+this is important
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+f prime of c equals 0.
+
+ align:start position:0%
+f prime of c equals 0.
+ 
+
+ align:start position:0%
+f prime of c equals 0.
+all right and what's the
+
+ align:start position:0%
+all right and what's the
+ 
+
+ align:start position:0%
+all right and what's the
+what's the picture that goes with this
+
+ align:start position:0%
+what's the picture that goes with this
+ 
+
+ align:start position:0%
+what's the picture that goes with this
+i'm sure you've seen it before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me draw a function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that looks kind of like sine or cosine
+
+ align:start position:0%
+that looks kind of like sine or cosine
+ 
+
+ align:start position:0%
+that looks kind of like sine or cosine
+but anyways
+
+ align:start position:0%
+but anyways
+ 
+
+ align:start position:0%
+but anyways
+function which is 0 here zero here then
+
+ align:start position:0%
+function which is 0 here zero here then
+ 
+
+ align:start position:0%
+function which is 0 here zero here then
+there has to exist a
+
+ align:start position:0%
+there has to exist a
+ 
+
+ align:start position:0%
+there has to exist a
+point where the tangent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is vertical
+
+ align:start position:0%
+is vertical
+ 
+
+ align:start position:0%
+is vertical
+in fact here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can occur at two different points all
+
+ align:start position:0%
+can occur at two different points all
+ 
+
+ align:start position:0%
+can occur at two different points all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but something that's already kind of
+
+ align:start position:0%
+but something that's already kind of
+ 
+
+ align:start position:0%
+but something that's already kind of
+giving the game away as far as how we'll
+
+ align:start position:0%
+giving the game away as far as how we'll
+ 
+
+ align:start position:0%
+giving the game away as far as how we'll
+prove this is
+
+ align:start position:0%
+prove this is
+ 
+
+ align:start position:0%
+prove this is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's look at where the function
+
+ align:start position:0%
+let's look at where the function
+ 
+
+ align:start position:0%
+let's look at where the function
+takes a maximum
+
+ align:start position:0%
+takes a maximum
+ 
+
+ align:start position:0%
+takes a maximum
+and a minimum okay
+
+ align:start position:0%
+and a minimum okay
+ 
+
+ align:start position:0%
+and a minimum okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know that that is the the heart of
+
+ align:start position:0%
+you know that that is the the heart of
+ 
+
+ align:start position:0%
+you know that that is the the heart of
+the proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and why can we why does it even have an
+
+ align:start position:0%
+and why can we why does it even have an
+ 
+
+ align:start position:0%
+and why can we why does it even have an
+absolute maximum or absolute minimum
+
+ align:start position:0%
+absolute maximum or absolute minimum
+ 
+
+ align:start position:0%
+absolute maximum or absolute minimum
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so i guess i didn't say this over there
+
+ align:start position:0%
+so i guess i didn't say this over there
+ 
+
+ align:start position:0%
+so i guess i didn't say this over there
+when i discussed relative min and
+
+ align:start position:0%
+when i discussed relative min and
+ 
+
+ align:start position:0%
+when i discussed relative min and
+relative max but an absolute maximum is
+
+ align:start position:0%
+relative max but an absolute maximum is
+ 
+
+ align:start position:0%
+relative max but an absolute maximum is
+also a relative maximum
+
+ align:start position:0%
+also a relative maximum
+ 
+
+ align:start position:0%
+also a relative maximum
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+absolute minimum is also a relative
+
+ align:start position:0%
+absolute minimum is also a relative
+ 
+
+ align:start position:0%
+absolute minimum is also a relative
+minimum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me make this this is kind of a late
+
+ align:start position:0%
+let me make this this is kind of a late
+ 
+
+ align:start position:0%
+let me make this this is kind of a late
+remark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolute max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is and
+
+ align:start position:0%
+is and
+ 
+
+ align:start position:0%
+is and
+is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relative max
+
+ align:start position:0%
+relative max
+ 
+
+ align:start position:0%
+relative max
+absolute men's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a relative mint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so um this picture's kind of
+
+ align:start position:0%
+all right so um this picture's kind of
+ 
+
+ align:start position:0%
+all right so um this picture's kind of
+giving the game away already uh let's
+
+ align:start position:0%
+giving the game away already uh let's
+ 
+
+ align:start position:0%
+giving the game away already uh let's
+look at where the function takes a max
+
+ align:start position:0%
+look at where the function takes a max
+ 
+
+ align:start position:0%
+look at where the function takes a max
+and a min
+
+ align:start position:0%
+and a min
+ 
+
+ align:start position:0%
+and a min
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+why can why does f take a max or a min
+
+ align:start position:0%
+why can why does f take a max or a min
+ 
+
+ align:start position:0%
+why can why does f take a max or a min
+it's because f is continuous on this
+
+ align:start position:0%
+it's because f is continuous on this
+ 
+
+ align:start position:0%
+it's because f is continuous on this
+closing bounded interval this is
+
+ align:start position:0%
+closing bounded interval this is
+ 
+
+ align:start position:0%
+closing bounded interval this is
+something we
+
+ align:start position:0%
+something we
+ 
+
+ align:start position:0%
+something we
+proved when we were discussing
+
+ align:start position:0%
+proved when we were discussing
+ 
+
+ align:start position:0%
+proved when we were discussing
+continuity the min max theorem
+
+ align:start position:0%
+continuity the min max theorem
+ 
+
+ align:start position:0%
+continuity the min max theorem
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's uh let's give the
+
+ align:start position:0%
+let's uh let's give the
+ 
+
+ align:start position:0%
+let's uh let's give the
+proof um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since f is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+achieves a
+
+ align:start position:0%
+achieves a
+ 
+
+ align:start position:0%
+achieves a
+relative
+
+ align:start position:0%
+relative
+ 
+
+ align:start position:0%
+relative
+max
+
+ align:start position:0%
+max
+ 
+
+ align:start position:0%
+max
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+some point c1
+
+ align:start position:0%
+some point c1
+ 
+
+ align:start position:0%
+some point c1
+and a b
+
+ align:start position:0%
+and a b
+ 
+
+ align:start position:0%
+and a b
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+relative min
+
+ align:start position:0%
+relative min
+ 
+
+ align:start position:0%
+relative min
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+c2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if there exists a x
+
+ align:start position:0%
+if there exists a x
+ 
+
+ align:start position:0%
+if there exists a x
+well so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if of f of c one is positive
+
+ align:start position:0%
+if of f of c one is positive
+ 
+
+ align:start position:0%
+if of f of c one is positive
+then what can you say
+
+ align:start position:0%
+then what can you say
+ 
+
+ align:start position:0%
+then what can you say
+well c1 cannot be one of the endpoints
+
+ align:start position:0%
+well c1 cannot be one of the endpoints
+ 
+
+ align:start position:0%
+well c1 cannot be one of the endpoints
+because at the endpoints
+
+ align:start position:0%
+because at the endpoints
+ 
+
+ align:start position:0%
+because at the endpoints
+f of a equals f of b equals zero right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies c one
+
+ align:start position:0%
+this implies c one
+ 
+
+ align:start position:0%
+this implies c one
+is in the open interval a b
+
+ align:start position:0%
+is in the open interval a b
+ 
+
+ align:start position:0%
+is in the open interval a b
+which implies by the previous theorem
+
+ align:start position:0%
+which implies by the previous theorem
+ 
+
+ align:start position:0%
+which implies by the previous theorem
+f prime of c1
+
+ align:start position:0%
+f prime of c1
+ 
+
+ align:start position:0%
+f prime of c1
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+so here you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c equals c1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i'm at the minimum now
+
+ align:start position:0%
+if i'm at the minimum now
+ 
+
+ align:start position:0%
+if i'm at the minimum now
+and this is less than zero
+
+ align:start position:0%
+and this is less than zero
+ 
+
+ align:start position:0%
+and this is less than zero
+then again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies that uh
+
+ align:start position:0%
+this implies that uh
+ 
+
+ align:start position:0%
+this implies that uh
+c2 is in the open interval a b
+
+ align:start position:0%
+c2 is in the open interval a b
+ 
+
+ align:start position:0%
+c2 is in the open interval a b
+which implies since uh
+
+ align:start position:0%
+which implies since uh
+ 
+
+ align:start position:0%
+which implies since uh
+f has a
+
+ align:start position:0%
+f has a
+ 
+
+ align:start position:0%
+f has a
+minimum at c two
+
+ align:start position:0%
+minimum at c two
+ 
+
+ align:start position:0%
+minimum at c two
+f prime of c two equals zero by the
+
+ align:start position:0%
+f prime of c two equals zero by the
+ 
+
+ align:start position:0%
+f prime of c two equals zero by the
+previous theorem and therefore we could
+
+ align:start position:0%
+previous theorem and therefore we could
+ 
+
+ align:start position:0%
+previous theorem and therefore we could
+take c equals c2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+now this is two cases f of c one
+
+ align:start position:0%
+now this is two cases f of c one
+ 
+
+ align:start position:0%
+now this is two cases f of c one
+if either f c one is positive or f c 2
+
+ align:start position:0%
+if either f c one is positive or f c 2
+ 
+
+ align:start position:0%
+if either f c one is positive or f c 2
+is less than 0 then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the result
+
+ align:start position:0%
+the result
+ 
+
+ align:start position:0%
+the result
+if f of
+
+ align:start position:0%
+if f of
+ 
+
+ align:start position:0%
+if f of
+c 1 is less than or equal to 0 is less
+
+ align:start position:0%
+c 1 is less than or equal to 0 is less
+ 
+
+ align:start position:0%
+c 1 is less than or equal to 0 is less
+than or equal to f c
+
+ align:start position:0%
+than or equal to f c
+ 
+
+ align:start position:0%
+than or equal to f c
+now remember
+
+ align:start position:0%
+now remember
+ 
+
+ align:start position:0%
+now remember
+f achieves a max at c1
+
+ align:start position:0%
+f achieves a max at c1
+ 
+
+ align:start position:0%
+f achieves a max at c1
+f achieves a min at c2
+
+ align:start position:0%
+f achieves a min at c2
+ 
+
+ align:start position:0%
+f achieves a min at c2
+and therefore this should always be less
+
+ align:start position:0%
+and therefore this should always be less
+ 
+
+ align:start position:0%
+and therefore this should always be less
+than or equal to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if uh the max and the min
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first off um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and make sure i'm getting my logic
+
+ align:start position:0%
+and make sure i'm getting my logic
+ 
+
+ align:start position:0%
+and make sure i'm getting my logic
+correct here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so rather than state it this way
+
+ align:start position:0%
+okay so rather than state it this way
+ 
+
+ align:start position:0%
+okay so rather than state it this way
+let's let's do it like uh
+
+ align:start position:0%
+let's let's do it like uh
+ 
+
+ align:start position:0%
+let's let's do it like uh
+let's let's
+
+ align:start position:0%
+let's let's
+ 
+
+ align:start position:0%
+let's let's
+do it like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in terms of the picture here
+
+ align:start position:0%
+so in terms of the picture here
+ 
+
+ align:start position:0%
+so in terms of the picture here
+this would be c1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c2 where we achieve a max and a min
+
+ align:start position:0%
+c2 where we achieve a max and a min
+ 
+
+ align:start position:0%
+c2 where we achieve a max and a min
+okay then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the final case that
+
+ align:start position:0%
+in the final case that
+ 
+
+ align:start position:0%
+in the final case that
+f of c1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then so this is the max
+
+ align:start position:0%
+then so this is the max
+ 
+
+ align:start position:0%
+then so this is the max
+0 is equal to
+
+ align:start position:0%
+0 is equal to
+ 
+
+ align:start position:0%
+0 is equal to
+f evaluated at a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let me go back to
+
+ align:start position:0%
+all right so let me go back to
+ 
+
+ align:start position:0%
+all right so let me go back to
+what i was going to say a minute ago so
+
+ align:start position:0%
+what i was going to say a minute ago so
+ 
+
+ align:start position:0%
+what i was going to say a minute ago so
+in the last case that
+
+ align:start position:0%
+in the last case that
+ 
+
+ align:start position:0%
+in the last case that
+f of c one is less than or equal to zero
+
+ align:start position:0%
+f of c one is less than or equal to zero
+ 
+
+ align:start position:0%
+f of c one is less than or equal to zero
+is less than f of c
+
+ align:start position:0%
+is less than f of c
+ 
+
+ align:start position:0%
+is less than f of c
+now remember this is
+
+ align:start position:0%
+now remember this is
+ 
+
+ align:start position:0%
+now remember this is
+the min
+
+ align:start position:0%
+the min
+ 
+
+ align:start position:0%
+the min
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+the max of f right
+
+ align:start position:0%
+the max of f right
+ 
+
+ align:start position:0%
+the max of f right
+so this should always sit
+
+ align:start position:0%
+so this should always sit
+ 
+
+ align:start position:0%
+so this should always sit
+above
+
+ align:start position:0%
+above
+ 
+
+ align:start position:0%
+above
+f of c2 so that implies
+
+ align:start position:0%
+f of c2 so that implies
+ 
+
+ align:start position:0%
+f of c2 so that implies
+that f of c1 equals
+
+ align:start position:0%
+that f of c1 equals
+ 
+
+ align:start position:0%
+that f of c1 equals
+f of c2
+
+ align:start position:0%
+f of c2
+ 
+
+ align:start position:0%
+f of c2
+and therefore the max and men equal each
+
+ align:start position:0%
+and therefore the max and men equal each
+ 
+
+ align:start position:0%
+and therefore the max and men equal each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x and a b
+
+ align:start position:0%
+for all x and a b
+ 
+
+ align:start position:0%
+for all x and a b
+since f of c one is uh
+
+ align:start position:0%
+since f of c one is uh
+ 
+
+ align:start position:0%
+since f of c one is uh
+uh the minimum
+
+ align:start position:0%
+uh the minimum
+ 
+
+ align:start position:0%
+uh the minimum
+or f of c two is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i started off with something here
+
+ align:start position:0%
+so i started off with something here
+ 
+
+ align:start position:0%
+so i started off with something here
+there and in between which implies
+
+ align:start position:0%
+there and in between which implies
+ 
+
+ align:start position:0%
+there and in between which implies
+for all x and a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of x equals f of c two
+
+ align:start position:0%
+f of x equals f of c two
+ 
+
+ align:start position:0%
+f of x equals f of c two
+so that means f is constant right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know what the derivative of a
+
+ align:start position:0%
+and we know what the derivative of a
+ 
+
+ align:start position:0%
+and we know what the derivative of a
+constant function is it's just 0.
+
+ align:start position:0%
+constant function is it's just 0.
+ 
+
+ align:start position:0%
+constant function is it's just 0.
+so we could take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say the midpoint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the end
+
+ align:start position:0%
+and that's the end
+ 
+
+ align:start position:0%
+and that's the end
+okay sorry so that i kind of fumbled
+
+ align:start position:0%
+okay sorry so that i kind of fumbled
+ 
+
+ align:start position:0%
+okay sorry so that i kind of fumbled
+through that uh
+
+ align:start position:0%
+through that uh
+ 
+
+ align:start position:0%
+through that uh
+for a minute but um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so for any function which is zero at uh
+
+ align:start position:0%
+so for any function which is zero at uh
+ 
+
+ align:start position:0%
+so for any function which is zero at uh
+um the endpoints there has to be a point
+
+ align:start position:0%
+um the endpoints there has to be a point
+ 
+
+ align:start position:0%
+um the endpoints there has to be a point
+in between where
+
+ align:start position:0%
+in between where
+ 
+
+ align:start position:0%
+in between where
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the function is
+
+ align:start position:0%
+the function is
+ 
+
+ align:start position:0%
+the function is
+the derivative of the function equals
+
+ align:start position:0%
+the derivative of the function equals
+ 
+
+ align:start position:0%
+the derivative of the function equals
+zero now
+
+ align:start position:0%
+zero now
+ 
+
+ align:start position:0%
+zero now
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+again we should come back to
+
+ align:start position:0%
+again we should come back to
+ 
+
+ align:start position:0%
+again we should come back to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know when we see a theorem we should
+
+ align:start position:0%
+you know when we see a theorem we should
+ 
+
+ align:start position:0%
+you know when we see a theorem we should
+kind of pick it apart a little bit to
+
+ align:start position:0%
+kind of pick it apart a little bit to
+ 
+
+ align:start position:0%
+kind of pick it apart a little bit to
+see what's necessary what's not
+
+ align:start position:0%
+see what's necessary what's not
+ 
+
+ align:start position:0%
+see what's necessary what's not
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+we had these two hypotheses coming in
+
+ align:start position:0%
+we had these two hypotheses coming in
+ 
+
+ align:start position:0%
+we had these two hypotheses coming in
+that the function is continuous and
+
+ align:start position:0%
+that the function is continuous and
+ 
+
+ align:start position:0%
+that the function is continuous and
+differentiable on this uh open interval
+
+ align:start position:0%
+differentiable on this uh open interval
+ 
+
+ align:start position:0%
+differentiable on this uh open interval
+a b
+
+ align:start position:0%
+a b
+ 
+
+ align:start position:0%
+a b
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+are these uh necessary so
+
+ align:start position:0%
+are these uh necessary so
+ 
+
+ align:start position:0%
+are these uh necessary so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for example let's say i have um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the function
+
+ align:start position:0%
+the function
+ 
+
+ align:start position:0%
+the function
+if i look at the function um
+
+ align:start position:0%
+if i look at the function um
+ 
+
+ align:start position:0%
+if i look at the function um
+1 minus the absolute value of x
+
+ align:start position:0%
+1 minus the absolute value of x
+ 
+
+ align:start position:0%
+1 minus the absolute value of x
+so at -1 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a continuous function on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus one one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and f of minus one equals f of one
+
+ align:start position:0%
+and f of minus one equals f of one
+ 
+
+ align:start position:0%
+and f of minus one equals f of one
+equals zero but there is no point where
+
+ align:start position:0%
+equals zero but there is no point where
+ 
+
+ align:start position:0%
+equals zero but there is no point where
+f prime of c equals 0. what hypothesis
+
+ align:start position:0%
+f prime of c equals 0. what hypothesis
+ 
+
+ align:start position:0%
+f prime of c equals 0. what hypothesis
+did i leave out for this function the
+
+ align:start position:0%
+did i leave out for this function the
+ 
+
+ align:start position:0%
+did i leave out for this function the
+fact that it's dif the hypothesis that
+
+ align:start position:0%
+fact that it's dif the hypothesis that
+ 
+
+ align:start position:0%
+fact that it's dif the hypothesis that
+it's differentiable at every point in
+
+ align:start position:0%
+it's differentiable at every point in
+ 
+
+ align:start position:0%
+it's differentiable at every point in
+between right this function's not
+
+ align:start position:0%
+between right this function's not
+ 
+
+ align:start position:0%
+between right this function's not
+differentiable uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but there's no point where the
+
+ align:start position:0%
+but there's no point where the
+ 
+
+ align:start position:0%
+but there's no point where the
+derivative equals zero right so this
+
+ align:start position:0%
+derivative equals zero right so this
+ 
+
+ align:start position:0%
+derivative equals zero right so this
+example um you know tells you that the
+
+ align:start position:0%
+example um you know tells you that the
+ 
+
+ align:start position:0%
+example um you know tells you that the
+hypothesis that the function is
+
+ align:start position:0%
+hypothesis that the function is
+ 
+
+ align:start position:0%
+hypothesis that the function is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you know differentiable on
+
+ align:start position:0%
+you know differentiable on
+ 
+
+ align:start position:0%
+you know differentiable on
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the interval minus one one or a b is
+
+ align:start position:0%
+the interval minus one one or a b is
+ 
+
+ align:start position:0%
+the interval minus one one or a b is
+necessary for the theorem to be true
+
+ align:start position:0%
+necessary for the theorem to be true
+ 
+
+ align:start position:0%
+necessary for the theorem to be true
+okay that's what i'm getting at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+you know the other hypothesis that the
+
+ align:start position:0%
+you know the other hypothesis that the
+ 
+
+ align:start position:0%
+you know the other hypothesis that the
+function is continuous on the closed
+
+ align:start position:0%
+function is continuous on the closed
+ 
+
+ align:start position:0%
+function is continuous on the closed
+interval
+
+ align:start position:0%
+interval
+ 
+
+ align:start position:0%
+interval
+is also necessary
+
+ align:start position:0%
+is also necessary
+ 
+
+ align:start position:0%
+is also necessary
+let's say i look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is this is pretty easy to come
+
+ align:start position:0%
+and this is this is pretty easy to come
+ 
+
+ align:start position:0%
+and this is this is pretty easy to come
+up with a counter example if i don't
+
+ align:start position:0%
+up with a counter example if i don't
+ 
+
+ align:start position:0%
+up with a counter example if i don't
+assume that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take the function which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the function that's x minus 1 for x not
+
+ align:start position:0%
+the function that's x minus 1 for x not
+ 
+
+ align:start position:0%
+the function that's x minus 1 for x not
+equal to -1 and 0
+
+ align:start position:0%
+equal to -1 and 0
+ 
+
+ align:start position:0%
+equal to -1 and 0
+for x equal to -1 so what does this
+
+ align:start position:0%
+for x equal to -1 so what does this
+ 
+
+ align:start position:0%
+for x equal to -1 so what does this
+function look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this function here
+
+ align:start position:0%
+so this function here
+ 
+
+ align:start position:0%
+so this function here
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable on
+
+ align:start position:0%
+differentiable on
+ 
+
+ align:start position:0%
+differentiable on
+minus 1 1
+
+ align:start position:0%
+minus 1 1
+ 
+
+ align:start position:0%
+minus 1 1
+f of minus 1 equals f of 1
+
+ align:start position:0%
+f of minus 1 equals f of 1
+ 
+
+ align:start position:0%
+f of minus 1 equals f of 1
+equals 0.
+
+ align:start position:0%
+equals 0.
+ 
+
+ align:start position:0%
+equals 0.
+but again there's no point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+n minus 1 1
+
+ align:start position:0%
+n minus 1 1
+ 
+
+ align:start position:0%
+n minus 1 1
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+f prime of c equals 0
+
+ align:start position:0%
+f prime of c equals 0
+ 
+
+ align:start position:0%
+f prime of c equals 0
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+because the derivative in between uh
+
+ align:start position:0%
+because the derivative in between uh
+ 
+
+ align:start position:0%
+because the derivative in between uh
+minus 1 1 is just 1.
+
+ align:start position:0%
+minus 1 1 is just 1.
+ 
+
+ align:start position:0%
+minus 1 1 is just 1.
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+both of these hypotheses
+
+ align:start position:0%
+both of these hypotheses
+ 
+
+ align:start position:0%
+both of these hypotheses
+that f is continuous on the closed
+
+ align:start position:0%
+that f is continuous on the closed
+ 
+
+ align:start position:0%
+that f is continuous on the closed
+interval and differentiable on the open
+
+ align:start position:0%
+interval and differentiable on the open
+ 
+
+ align:start position:0%
+interval and differentiable on the open
+interval
+
+ align:start position:0%
+interval
+ 
+
+ align:start position:0%
+interval
+are necessary for this theorem to be
+
+ align:start position:0%
+are necessary for this theorem to be
+ 
+
+ align:start position:0%
+are necessary for this theorem to be
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+if you drop either of those hypotheses
+
+ align:start position:0%
+if you drop either of those hypotheses
+ 
+
+ align:start position:0%
+if you drop either of those hypotheses
+then the theorem is false
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's rotate this picture
+
+ align:start position:0%
+all right so let's rotate this picture
+ 
+
+ align:start position:0%
+all right so let's rotate this picture
+here and arrive at the mean value
+
+ align:start position:0%
+here and arrive at the mean value
+ 
+
+ align:start position:0%
+here and arrive at the mean value
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+add f from a b to r
+
+ align:start position:0%
+add f from a b to r
+ 
+
+ align:start position:0%
+add f from a b to r
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+continuous so it's continuous on the
+
+ align:start position:0%
+continuous so it's continuous on the
+ 
+
+ align:start position:0%
+continuous so it's continuous on the
+closed interval a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable
+
+ align:start position:0%
+differentiable
+ 
+
+ align:start position:0%
+differentiable
+on a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists a c
+
+ align:start position:0%
+then there exists a c
+ 
+
+ align:start position:0%
+then there exists a c
+in the open interval a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f prime of c
+
+ align:start position:0%
+f prime of c
+ 
+
+ align:start position:0%
+f prime of c
+write it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of b minus f of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times b minus a
+
+ align:start position:0%
+times b minus a
+ 
+
+ align:start position:0%
+times b minus a
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so why do i refer to it as a kind of
+
+ align:start position:0%
+so why do i refer to it as a kind of
+ 
+
+ align:start position:0%
+so why do i refer to it as a kind of
+rotated picture of uh
+
+ align:start position:0%
+rotated picture of uh
+ 
+
+ align:start position:0%
+rotated picture of uh
+and shifted kind of version of rolle's
+
+ align:start position:0%
+and shifted kind of version of rolle's
+ 
+
+ align:start position:0%
+and shifted kind of version of rolle's
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a b
+
+ align:start position:0%
+so there's a b
+ 
+
+ align:start position:0%
+so there's a b
+there's uh
+
+ align:start position:0%
+there's uh
+ 
+
+ align:start position:0%
+there's uh
+f of a f b
+
+ align:start position:0%
+f of a f b
+ 
+
+ align:start position:0%
+f of a f b
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say that's uh how the function
+
+ align:start position:0%
+let's say that's uh how the function
+ 
+
+ align:start position:0%
+let's say that's uh how the function
+looks now
+
+ align:start position:0%
+looks now
+ 
+
+ align:start position:0%
+looks now
+the slope of the line
+
+ align:start position:0%
+the slope of the line
+ 
+
+ align:start position:0%
+the slope of the line
+connecting f of b to f of a is exactly f
+
+ align:start position:0%
+connecting f of b to f of a is exactly f
+ 
+
+ align:start position:0%
+connecting f of b to f of a is exactly f
+of b minus f of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the slope of that line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is f of b minus f of a
+
+ align:start position:0%
+is f of b minus f of a
+ 
+
+ align:start position:0%
+is f of b minus f of a
+and what we're stating is that there's a
+
+ align:start position:0%
+and what we're stating is that there's a
+ 
+
+ align:start position:0%
+and what we're stating is that there's a
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c so that the tangent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at that point is parallel to that line
+
+ align:start position:0%
+at that point is parallel to that line
+ 
+
+ align:start position:0%
+at that point is parallel to that line
+okay has the same slope as the line
+
+ align:start position:0%
+okay has the same slope as the line
+ 
+
+ align:start position:0%
+okay has the same slope as the line
+connecting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of b
+
+ align:start position:0%
+f of b
+ 
+
+ align:start position:0%
+f of b
+to f of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this stem really does reduce to rolls
+
+ align:start position:0%
+this stem really does reduce to rolls
+ 
+
+ align:start position:0%
+this stem really does reduce to rolls
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me define a function g from a b to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which satisfies the the hypotheses of
+
+ align:start position:0%
+which satisfies the the hypotheses of
+ 
+
+ align:start position:0%
+which satisfies the the hypotheses of
+rolle's theorem
+
+ align:start position:0%
+rolle's theorem
+ 
+
+ align:start position:0%
+rolle's theorem
+and will give us what we want basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so g of x
+
+ align:start position:0%
+so g of x
+ 
+
+ align:start position:0%
+so g of x
+equals f of x
+
+ align:start position:0%
+equals f of x
+ 
+
+ align:start position:0%
+equals f of x
+minus f of b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of b minus f of a
+
+ align:start position:0%
+f of b minus f of a
+ 
+
+ align:start position:0%
+f of b minus f of a
+over b minus a
+
+ align:start position:0%
+over b minus a
+ 
+
+ align:start position:0%
+over b minus a
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+b minus x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+basically what this function g does is
+
+ align:start position:0%
+basically what this function g does is
+ 
+
+ align:start position:0%
+basically what this function g does is
+it takes
+
+ align:start position:0%
+it takes
+ 
+
+ align:start position:0%
+it takes
+uh the function now
+
+ align:start position:0%
+uh the function now
+ 
+
+ align:start position:0%
+uh the function now
+and rotates it and shifts it down so
+
+ align:start position:0%
+and rotates it and shifts it down so
+ 
+
+ align:start position:0%
+and rotates it and shifts it down so
+that f
+
+ align:start position:0%
+that f
+ 
+
+ align:start position:0%
+that f
+kind of these two points then coincide
+
+ align:start position:0%
+kind of these two points then coincide
+ 
+
+ align:start position:0%
+kind of these two points then coincide
+and give you 0.
+
+ align:start position:0%
+and give you 0.
+ 
+
+ align:start position:0%
+and give you 0.
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+g
+
+ align:start position:0%
+g
+ 
+
+ align:start position:0%
+g
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+on the closed interval a b
+
+ align:start position:0%
+on the closed interval a b
+ 
+
+ align:start position:0%
+on the closed interval a b
+why because it's a sum of two continuous
+
+ align:start position:0%
+why because it's a sum of two continuous
+ 
+
+ align:start position:0%
+why because it's a sum of two continuous
+functions on a b f of x is continuous on
+
+ align:start position:0%
+functions on a b f of x is continuous on
+ 
+
+ align:start position:0%
+functions on a b f of x is continuous on
+a b on a b and this is just a constant
+
+ align:start position:0%
+a b on a b and this is just a constant
+ 
+
+ align:start position:0%
+a b on a b and this is just a constant
+that's just a constant this is a
+
+ align:start position:0%
+that's just a constant this is a
+ 
+
+ align:start position:0%
+that's just a constant this is a
+polynomial
+
+ align:start position:0%
+polynomial
+ 
+
+ align:start position:0%
+polynomial
+so g is continuous on bait on a b
+
+ align:start position:0%
+so g is continuous on bait on a b
+ 
+
+ align:start position:0%
+so g is continuous on bait on a b
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a b again because f is right f is
+
+ align:start position:0%
+a b again because f is right f is
+ 
+
+ align:start position:0%
+a b again because f is right f is
+differentiable on the open interval a b
+
+ align:start position:0%
+differentiable on the open interval a b
+ 
+
+ align:start position:0%
+differentiable on the open interval a b
+uh this part is differentiable
+
+ align:start position:0%
+uh this part is differentiable
+ 
+
+ align:start position:0%
+uh this part is differentiable
+everywhere so
+
+ align:start position:0%
+everywhere so
+ 
+
+ align:start position:0%
+everywhere so
+the sum of two differentiable functions
+
+ align:start position:0%
+the sum of two differentiable functions
+ 
+
+ align:start position:0%
+the sum of two differentiable functions
+is differentiable so g of x is
+
+ align:start position:0%
+is differentiable so g of x is
+ 
+
+ align:start position:0%
+is differentiable so g of x is
+differentiable on a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous on a b and differentiable on
+
+ align:start position:0%
+continuous on a b and differentiable on
+ 
+
+ align:start position:0%
+continuous on a b and differentiable on
+a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since i said we're going to use
+
+ align:start position:0%
+and since i said we're going to use
+ 
+
+ align:start position:0%
+and since i said we're going to use
+rolls theorem let's compute g of a this
+
+ align:start position:0%
+rolls theorem let's compute g of a this
+ 
+
+ align:start position:0%
+rolls theorem let's compute g of a this
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+f of a minus f of b
+
+ align:start position:0%
+f of a minus f of b
+ 
+
+ align:start position:0%
+f of a minus f of b
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+f of b minus f of a
+
+ align:start position:0%
+f of b minus f of a
+ 
+
+ align:start position:0%
+f of b minus f of a
+over b minus a
+
+ align:start position:0%
+over b minus a
+ 
+
+ align:start position:0%
+over b minus a
+times b minus a that cancels with that
+
+ align:start position:0%
+times b minus a that cancels with that
+ 
+
+ align:start position:0%
+times b minus a that cancels with that
+minus f of b cancels with f of b
+
+ align:start position:0%
+minus f of b cancels with f of b
+ 
+
+ align:start position:0%
+minus f of b cancels with f of b
+f of a cancels with minus f of a and we
+
+ align:start position:0%
+f of a cancels with minus f of a and we
+ 
+
+ align:start position:0%
+f of a cancels with minus f of a and we
+get 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then g of b
+
+ align:start position:0%
+then g of b
+ 
+
+ align:start position:0%
+then g of b
+this is even easier to see if i just
+
+ align:start position:0%
+this is even easier to see if i just
+ 
+
+ align:start position:0%
+this is even easier to see if i just
+stick this in this is f of b
+
+ align:start position:0%
+stick this in this is f of b
+ 
+
+ align:start position:0%
+stick this in this is f of b
+minus f of b
+
+ align:start position:0%
+minus f of b
+ 
+
+ align:start position:0%
+minus f of b
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+f of b
+
+ align:start position:0%
+f of b
+ 
+
+ align:start position:0%
+f of b
+minus f of a
+
+ align:start position:0%
+minus f of a
+ 
+
+ align:start position:0%
+minus f of a
+over b minus a b minus b
+
+ align:start position:0%
+over b minus a b minus b
+ 
+
+ align:start position:0%
+over b minus a b minus b
+and this also equals zero okay so g of a
+
+ align:start position:0%
+and this also equals zero okay so g of a
+ 
+
+ align:start position:0%
+and this also equals zero okay so g of a
+and g of b are zero it's the function is
+
+ align:start position:0%
+and g of b are zero it's the function is
+ 
+
+ align:start position:0%
+and g of b are zero it's the function is
+continuous on the closed interval it's
+
+ align:start position:0%
+continuous on the closed interval it's
+ 
+
+ align:start position:0%
+continuous on the closed interval it's
+differentiable on the open interval and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore by rolls theorem i think
+
+ align:start position:0%
+therefore by rolls theorem i think
+ 
+
+ align:start position:0%
+therefore by rolls theorem i think
+they're supposed to be some sort of
+
+ align:start position:0%
+they're supposed to be some sort of
+ 
+
+ align:start position:0%
+they're supposed to be some sort of
+accent over o but i can't
+
+ align:start position:0%
+accent over o but i can't
+ 
+
+ align:start position:0%
+accent over o but i can't
+i can't remember and i've forgotten it
+
+ align:start position:0%
+i can't remember and i've forgotten it
+ 
+
+ align:start position:0%
+i can't remember and i've forgotten it
+already um
+
+ align:start position:0%
+already um
+ 
+
+ align:start position:0%
+already um
+by roll's theorem there exists
+
+ align:start position:0%
+by roll's theorem there exists
+ 
+
+ align:start position:0%
+by roll's theorem there exists
+point c and a b
+
+ align:start position:0%
+point c and a b
+ 
+
+ align:start position:0%
+point c and a b
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+g prime of c which is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we take g and actually compute what the
+
+ align:start position:0%
+we take g and actually compute what the
+ 
+
+ align:start position:0%
+we take g and actually compute what the
+derivative is at
+
+ align:start position:0%
+derivative is at
+ 
+
+ align:start position:0%
+derivative is at
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+c is equal to f prime of c
+
+ align:start position:0%
+c is equal to f prime of c
+ 
+
+ align:start position:0%
+c is equal to f prime of c
+that's a constant derivative of that is
+
+ align:start position:0%
+that's a constant derivative of that is
+ 
+
+ align:start position:0%
+that's a constant derivative of that is
+0.
+
+ align:start position:0%
+0.
+ 
+
+ align:start position:0%
+0.
+this times this the derivative of x
+
+ align:start position:0%
+this times this the derivative of x
+ 
+
+ align:start position:0%
+this times this the derivative of x
+evaluated at c just gives me minus
+
+ align:start position:0%
+evaluated at c just gives me minus
+ 
+
+ align:start position:0%
+evaluated at c just gives me minus
+f of b minus f of a
+
+ align:start position:0%
+f of b minus f of a
+ 
+
+ align:start position:0%
+f of b minus f of a
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+b minus a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 is equal to f prime of f prime of c
+
+ align:start position:0%
+0 is equal to f prime of f prime of c
+ 
+
+ align:start position:0%
+0 is equal to f prime of f prime of c
+minus what we want we move that to the
+
+ align:start position:0%
+minus what we want we move that to the
+ 
+
+ align:start position:0%
+minus what we want we move that to the
+other side multiply through by b minus a
+
+ align:start position:0%
+other side multiply through by b minus a
+ 
+
+ align:start position:0%
+other side multiply through by b minus a
+and we're done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+very nice applications of the mean value
+
+ align:start position:0%
+very nice applications of the mean value
+ 
+
+ align:start position:0%
+very nice applications of the mean value
+theorem which i think you learned from
+
+ align:start position:0%
+theorem which i think you learned from
+ 
+
+ align:start position:0%
+theorem which i think you learned from
+calculus
+
+ align:start position:0%
+calculus
+ 
+
+ align:start position:0%
+calculus
+are the following
+
+ align:start position:0%
+are the following
+ 
+
+ align:start position:0%
+are the following
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let f from i to r b differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaning it's differentiable at every
+
+ align:start position:0%
+meaning it's differentiable at every
+ 
+
+ align:start position:0%
+meaning it's differentiable at every
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the interval i
+
+ align:start position:0%
+in the interval i
+ 
+
+ align:start position:0%
+in the interval i
+then we have two conclusions
+
+ align:start position:0%
+then we have two conclusions
+ 
+
+ align:start position:0%
+then we have two conclusions
+f is increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaning let me uh
+
+ align:start position:0%
+meaning let me uh
+ 
+
+ align:start position:0%
+meaning let me uh
+recall what that means for f to be
+
+ align:start position:0%
+recall what that means for f to be
+ 
+
+ align:start position:0%
+recall what that means for f to be
+increasing that means that if x is
+
+ align:start position:0%
+increasing that means that if x is
+ 
+
+ align:start position:0%
+increasing that means that if x is
+less than y
+
+ align:start position:0%
+less than y
+ 
+
+ align:start position:0%
+less than y
+this implies
+
+ align:start position:0%
+this implies
+ 
+
+ align:start position:0%
+this implies
+f of x is less than or equal to f of y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equivalent to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x and i
+
+ align:start position:0%
+for all x and i
+ 
+
+ align:start position:0%
+for all x and i
+f prime of x is bigger than or equal to
+
+ align:start position:0%
+f prime of x is bigger than or equal to
+ 
+
+ align:start position:0%
+f prime of x is bigger than or equal to
+zero so remember f is f prime is the
+
+ align:start position:0%
+zero so remember f is f prime is the
+ 
+
+ align:start position:0%
+zero so remember f is f prime is the
+rate of change if the rate of change is
+
+ align:start position:0%
+rate of change if the rate of change is
+ 
+
+ align:start position:0%
+rate of change if the rate of change is
+always non-negative then f has to be
+
+ align:start position:0%
+always non-negative then f has to be
+ 
+
+ align:start position:0%
+always non-negative then f has to be
+growing
+
+ align:start position:0%
+growing
+ 
+
+ align:start position:0%
+growing
+so this says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is decreasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaning x
+
+ align:start position:0%
+meaning x
+ 
+
+ align:start position:0%
+meaning x
+less than y implies
+
+ align:start position:0%
+less than y implies
+ 
+
+ align:start position:0%
+less than y implies
+f of x is bigger than or equal to f of y
+
+ align:start position:0%
+f of x is bigger than or equal to f of y
+ 
+
+ align:start position:0%
+f of x is bigger than or equal to f of y
+this is equivalent to
+
+ align:start position:0%
+this is equivalent to
+ 
+
+ align:start position:0%
+this is equivalent to
+since a function is increasing if and
+
+ align:start position:0%
+since a function is increasing if and
+ 
+
+ align:start position:0%
+since a function is increasing if and
+only if minus f is decreasing this
+
+ align:start position:0%
+only if minus f is decreasing this
+ 
+
+ align:start position:0%
+only if minus f is decreasing this
+inequality should flip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm going to do
+
+ align:start position:0%
+so i'm going to do
+ 
+
+ align:start position:0%
+so i'm going to do
+increasing decreasing follows from
+
+ align:start position:0%
+increasing decreasing follows from
+ 
+
+ align:start position:0%
+increasing decreasing follows from
+number one by taking minus f okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+how much time do i have okay i still
+
+ align:start position:0%
+how much time do i have okay i still
+ 
+
+ align:start position:0%
+how much time do i have okay i still
+have time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose first that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f prime of x is always non-negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let
+
+ align:start position:0%
+let
+ 
+
+ align:start position:0%
+let
+a b
+
+ align:start position:0%
+a b
+ 
+
+ align:start position:0%
+a b
+be in
+
+ align:start position:0%
+be in
+ 
+
+ align:start position:0%
+be in
+i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+excuse me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we now want to show f of a is less than
+
+ align:start position:0%
+we now want to show f of a is less than
+ 
+
+ align:start position:0%
+we now want to show f of a is less than
+or equal to f of b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then f
+
+ align:start position:0%
+then f
+ 
+
+ align:start position:0%
+then f
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+is continuous on this smaller interval a
+
+ align:start position:0%
+is continuous on this smaller interval a
+ 
+
+ align:start position:0%
+is continuous on this smaller interval a
+b why because f is differentiable at
+
+ align:start position:0%
+b why because f is differentiable at
+ 
+
+ align:start position:0%
+b why because f is differentiable at
+every point in i and therefore it is
+
+ align:start position:0%
+every point in i and therefore it is
+ 
+
+ align:start position:0%
+every point in i and therefore it is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+continuous at every point and i so in
+
+ align:start position:0%
+continuous at every point and i so in
+ 
+
+ align:start position:0%
+continuous at every point and i so in
+particular on this smaller interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on a b which implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists a c
+
+ align:start position:0%
+there exists a c
+ 
+
+ align:start position:0%
+there exists a c
+in a b
+
+ align:start position:0%
+in a b
+ 
+
+ align:start position:0%
+in a b
+so by the mean value theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that f of b
+
+ align:start position:0%
+such that f of b
+ 
+
+ align:start position:0%
+such that f of b
+minus f of a
+
+ align:start position:0%
+minus f of a
+ 
+
+ align:start position:0%
+minus f of a
+equals f prime of c
+
+ align:start position:0%
+equals f prime of c
+ 
+
+ align:start position:0%
+equals f prime of c
+times b minus a and now since the
+
+ align:start position:0%
+times b minus a and now since the
+ 
+
+ align:start position:0%
+times b minus a and now since the
+derivative is always non-negative and b
+
+ align:start position:0%
+derivative is always non-negative and b
+ 
+
+ align:start position:0%
+derivative is always non-negative and b
+minus a is positive this is bigger than
+
+ align:start position:0%
+minus a is positive this is bigger than
+ 
+
+ align:start position:0%
+minus a is positive this is bigger than
+or equal to zero
+
+ align:start position:0%
+or equal to zero
+ 
+
+ align:start position:0%
+or equal to zero
+i.e
+
+ align:start position:0%
+i.e
+ 
+
+ align:start position:0%
+i.e
+f of b minus f of a is bigger than or
+
+ align:start position:0%
+f of b minus f of a is bigger than or
+ 
+
+ align:start position:0%
+f of b minus f of a is bigger than or
+equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we've proven one direction we've
+
+ align:start position:0%
+so we've proven one direction we've
+ 
+
+ align:start position:0%
+so we've proven one direction we've
+proven that
+
+ align:start position:0%
+proven that
+ 
+
+ align:start position:0%
+proven that
+if you like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the function's derivative being
+
+ align:start position:0%
+the function's derivative being
+ 
+
+ align:start position:0%
+the function's derivative being
+non-negative implies that the function
+
+ align:start position:0%
+non-negative implies that the function
+ 
+
+ align:start position:0%
+non-negative implies that the function
+is increasing
+
+ align:start position:0%
+is increasing
+ 
+
+ align:start position:0%
+is increasing
+so now let's prove the opposite
+
+ align:start position:0%
+so now let's prove the opposite
+ 
+
+ align:start position:0%
+so now let's prove the opposite
+direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+suppose f is increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and c is an i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let x in be a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i
+
+ align:start position:0%
+and i
+ 
+
+ align:start position:0%
+and i
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+xn converges to c
+
+ align:start position:0%
+xn converges to c
+ 
+
+ align:start position:0%
+xn converges to c
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one of two things holds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and either
+
+ align:start position:0%
+and either
+ 
+
+ align:start position:0%
+and either
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all n x n is less than c or b
+
+ align:start position:0%
+for all n x n is less than c or b
+ 
+
+ align:start position:0%
+for all n x n is less than c or b
+for all n x n is bigger than c now we
+
+ align:start position:0%
+for all n x n is bigger than c now we
+ 
+
+ align:start position:0%
+for all n x n is bigger than c now we
+can always find such a sequence given a
+
+ align:start position:0%
+can always find such a sequence given a
+ 
+
+ align:start position:0%
+can always find such a sequence given a
+point c and the interval i so
+
+ align:start position:0%
+point c and the interval i so
+ 
+
+ align:start position:0%
+point c and the interval i so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know if we're
+
+ align:start position:0%
+you know if we're
+ 
+
+ align:start position:0%
+you know if we're
+if i
+
+ align:start position:0%
+if i
+ 
+
+ align:start position:0%
+if i
+so let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say it's a closed interval
+
+ align:start position:0%
+let's say it's a closed interval
+ 
+
+ align:start position:0%
+let's say it's a closed interval
+and c is in
+
+ align:start position:0%
+and c is in
+ 
+
+ align:start position:0%
+and c is in
+here then we can find a sequence x n
+
+ align:start position:0%
+here then we can find a sequence x n
+ 
+
+ align:start position:0%
+here then we can find a sequence x n
+converging to c
+
+ align:start position:0%
+converging to c
+ 
+
+ align:start position:0%
+converging to c
+you know approaching c from the left
+
+ align:start position:0%
+you know approaching c from the left
+ 
+
+ align:start position:0%
+you know approaching c from the left
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+if c is one of the endpoints then we can
+
+ align:start position:0%
+if c is one of the endpoints then we can
+ 
+
+ align:start position:0%
+if c is one of the endpoints then we can
+find a sequence from i approaching c
+
+ align:start position:0%
+find a sequence from i approaching c
+ 
+
+ align:start position:0%
+find a sequence from i approaching c
+from the right that's b
+
+ align:start position:0%
+from the right that's b
+ 
+
+ align:start position:0%
+from the right that's b
+right and the same thing if c is over
+
+ align:start position:0%
+right and the same thing if c is over
+ 
+
+ align:start position:0%
+right and the same thing if c is over
+here we can find a sequence approaching
+
+ align:start position:0%
+here we can find a sequence approaching
+ 
+
+ align:start position:0%
+here we can find a sequence approaching
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+strictly from the left
+
+ align:start position:0%
+strictly from the left
+ 
+
+ align:start position:0%
+strictly from the left
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so there always exists
+
+ align:start position:0%
+so there always exists
+ 
+
+ align:start position:0%
+so there always exists
+such a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i is an interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if the sequence satisfies uh case a
+
+ align:start position:0%
+if the sequence satisfies uh case a
+ 
+
+ align:start position:0%
+if the sequence satisfies uh case a
+and we look at f prime then uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get that f of
+
+ align:start position:0%
+we get that f of
+ 
+
+ align:start position:0%
+we get that f of
+x n is less than or equal to f of c
+
+ align:start position:0%
+x n is less than or equal to f of c
+ 
+
+ align:start position:0%
+x n is less than or equal to f of c
+for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me in fact write this a little
+
+ align:start position:0%
+and let me in fact write this a little
+ 
+
+ align:start position:0%
+and let me in fact write this a little
+bit differently
+
+ align:start position:0%
+bit differently
+ 
+
+ align:start position:0%
+bit differently
+since so here we're using that f is
+
+ align:start position:0%
+since so here we're using that f is
+ 
+
+ align:start position:0%
+since so here we're using that f is
+increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since f is increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies for all n
+
+ align:start position:0%
+which implies for all n
+ 
+
+ align:start position:0%
+which implies for all n
+f of x n minus f of
+
+ align:start position:0%
+f of x n minus f of
+ 
+
+ align:start position:0%
+f of x n minus f of
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+over x sub n
+
+ align:start position:0%
+over x sub n
+ 
+
+ align:start position:0%
+over x sub n
+minus c
+
+ align:start position:0%
+minus c
+ 
+
+ align:start position:0%
+minus c
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this thing on top is negative x n uh is
+
+ align:start position:0%
+this thing on top is negative x n uh is
+ 
+
+ align:start position:0%
+this thing on top is negative x n uh is
+less than c
+
+ align:start position:0%
+less than c
+ 
+
+ align:start position:0%
+less than c
+so this thing on the bottom is also
+
+ align:start position:0%
+so this thing on the bottom is also
+ 
+
+ align:start position:0%
+so this thing on the bottom is also
+negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore this thing is
+
+ align:start position:0%
+and therefore this thing is
+ 
+
+ align:start position:0%
+and therefore this thing is
+positive not negative i mean
+
+ align:start position:0%
+positive not negative i mean
+ 
+
+ align:start position:0%
+positive not negative i mean
+therefore the limit must also be
+
+ align:start position:0%
+therefore the limit must also be
+ 
+
+ align:start position:0%
+therefore the limit must also be
+non-negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that limit is just the derivative
+
+ align:start position:0%
+but that limit is just the derivative
+ 
+
+ align:start position:0%
+but that limit is just the derivative
+evaluated at c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and case b is kind of similar
+
+ align:start position:0%
+and case b is kind of similar
+ 
+
+ align:start position:0%
+and case b is kind of similar
+i mean not kind of it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in case b
+
+ align:start position:0%
+in case b
+ 
+
+ align:start position:0%
+in case b
+we get that
+
+ align:start position:0%
+we get that
+ 
+
+ align:start position:0%
+we get that
+for all n
+
+ align:start position:0%
+for all n
+ 
+
+ align:start position:0%
+for all n
+f of x n now since x ends to the right
+
+ align:start position:0%
+f of x n now since x ends to the right
+ 
+
+ align:start position:0%
+f of x n now since x ends to the right
+of c
+
+ align:start position:0%
+of c
+ 
+
+ align:start position:0%
+of c
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me write it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this minus f of c is bigger than or
+
+ align:start position:0%
+this minus f of c is bigger than or
+ 
+
+ align:start position:0%
+this minus f of c is bigger than or
+equal to 0
+
+ align:start position:0%
+equal to 0
+ 
+
+ align:start position:0%
+equal to 0
+which implies that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f prime of c which is the limit as n
+
+ align:start position:0%
+f prime of c which is the limit as n
+ 
+
+ align:start position:0%
+f prime of c which is the limit as n
+goes to infinity of f of
+
+ align:start position:0%
+goes to infinity of f of
+ 
+
+ align:start position:0%
+goes to infinity of f of
+x n minus
+
+ align:start position:0%
+x n minus
+ 
+
+ align:start position:0%
+x n minus
+f of c over x n minus c
+
+ align:start position:0%
+f of c over x n minus c
+ 
+
+ align:start position:0%
+f of c over x n minus c
+what's on top is non-negative and what's
+
+ align:start position:0%
+what's on top is non-negative and what's
+ 
+
+ align:start position:0%
+what's on top is non-negative and what's
+on bottom is non-negative because x n is
+
+ align:start position:0%
+on bottom is non-negative because x n is
+ 
+
+ align:start position:0%
+on bottom is non-negative because x n is
+bigger than c
+
+ align:start position:0%
+bigger than c
+ 
+
+ align:start position:0%
+bigger than c
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+bigger than zero bigger than zero
+
+ align:start position:0%
+bigger than zero bigger than zero
+ 
+
+ align:start position:0%
+bigger than zero bigger than zero
+bigger than 0.
+
+ align:start position:0%
+bigger than 0.
+ 
+
+ align:start position:0%
+bigger than 0.
+so in either k that's so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus in either case we get that f prime
+
+ align:start position:0%
+thus in either case we get that f prime
+ 
+
+ align:start position:0%
+thus in either case we get that f prime
+of c is bigger than or equal to 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and therefore we've proven that the
+
+ align:start position:0%
+and therefore we've proven that the
+ 
+
+ align:start position:0%
+and therefore we've proven that the
+derivative is always non-negative
+
+ align:start position:0%
+derivative is always non-negative
+ 
+
+ align:start position:0%
+derivative is always non-negative
+so that's uh
+
+ align:start position:0%
+so that's uh
+ 
+
+ align:start position:0%
+so that's uh
+one and two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreasing
+
+ align:start position:0%
+decreasing
+ 
+
+ align:start position:0%
+decreasing
+if and only if the function minus f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is increasing which by what we've done
+
+ align:start position:0%
+is increasing which by what we've done
+ 
+
+ align:start position:0%
+is increasing which by what we've done
+from part one
+
+ align:start position:0%
+from part one
+ 
+
+ align:start position:0%
+from part one
+is if and only if minus f prime of x
+
+ align:start position:0%
+is if and only if minus f prime of x
+ 
+
+ align:start position:0%
+is if and only if minus f prime of x
+is bigger than or equal to zero for all
+
+ align:start position:0%
+is bigger than or equal to zero for all
+ 
+
+ align:start position:0%
+is bigger than or equal to zero for all
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+and i
+
+ align:start position:0%
+and i
+ 
+
+ align:start position:0%
+and i
+and then multiplying through by minus
+
+ align:start position:0%
+and then multiplying through by minus
+ 
+
+ align:start position:0%
+and then multiplying through by minus
+by this
+
+ align:start position:0%
+by this
+ 
+
+ align:start position:0%
+by this
+minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gives me number two
+
+ align:start position:0%
+gives me number two
+ 
+
+ align:start position:0%
+gives me number two
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+let me make one last uh
+
+ align:start position:0%
+let me make one last uh
+ 
+
+ align:start position:0%
+let me make one last uh
+i know it's tabuta right on the back uh
+
+ align:start position:0%
+i know it's tabuta right on the back uh
+ 
+
+ align:start position:0%
+i know it's tabuta right on the back uh
+part but i'm gonna do it anyways
+
+ align:start position:0%
+part but i'm gonna do it anyways
+ 
+
+ align:start position:0%
+part but i'm gonna do it anyways
+we have the very simple theorem which
+
+ align:start position:0%
+we have the very simple theorem which
+ 
+
+ align:start position:0%
+we have the very simple theorem which
+now follow follows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let f from ida r
+
+ align:start position:0%
+let f from ida r
+ 
+
+ align:start position:0%
+let f from ida r
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is constant
+
+ align:start position:0%
+f is constant
+ 
+
+ align:start position:0%
+f is constant
+so f of
+
+ align:start position:0%
+so f of
+ 
+
+ align:start position:0%
+so f of
+x equals f of y for all x and y and i
+
+ align:start position:0%
+x equals f of y for all x and y and i
+ 
+
+ align:start position:0%
+x equals f of y for all x and y and i
+if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the derivative is identically zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is constant if and only if
+
+ align:start position:0%
+is constant if and only if
+ 
+
+ align:start position:0%
+is constant if and only if
+f is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and decreasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it satisfies the equality sign
+
+ align:start position:0%
+because it satisfies the equality sign
+ 
+
+ align:start position:0%
+because it satisfies the equality sign
+in both of those
+
+ align:start position:0%
+in both of those
+ 
+
+ align:start position:0%
+in both of those
+and by what we've done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now for all this means for all x and i
+
+ align:start position:0%
+now for all this means for all x and i
+ 
+
+ align:start position:0%
+now for all this means for all x and i
+f prime of x is bigger than or equal to
+
+ align:start position:0%
+f prime of x is bigger than or equal to
+ 
+
+ align:start position:0%
+f prime of x is bigger than or equal to
+zero and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's for the increasing part f prime
+
+ align:start position:0%
+that's for the increasing part f prime
+ 
+
+ align:start position:0%
+that's for the increasing part f prime
+of x is less than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f prime of x uh this is equivalent to f
+
+ align:start position:0%
+f prime of x uh this is equivalent to f
+ 
+
+ align:start position:0%
+f prime of x uh this is equivalent to f
+prime of x equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we'll stop there
\ No newline at end of file
diff --git a/VCOrx2jEKXk.txt b/VCOrx2jEKXk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9336a1ebfbd404af4788fb71c58cff7f37e597c4
--- /dev/null
+++ b/VCOrx2jEKXk.txt
@@ -0,0 +1,10571 @@
+align:start position:0%
+ 
+Okay. So remember that projection theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works differently over uh if you look in
+
+ align:start position:0%
+works differently over uh if you look in
+ 
+
+ align:start position:0%
+works differently over uh if you look in
+finite fields it works differently over
+
+ align:start position:0%
+finite fields it works differently over
+ 
+
+ align:start position:0%
+finite fields it works differently over
+a prime field or a notp prime field. And
+
+ align:start position:0%
+a prime field or a notp prime field. And
+ 
+
+ align:start position:0%
+a prime field or a notp prime field. And
+here was the key example.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, so we're going to do projection
+
+ align:start position:0%
+Um, so we're going to do projection
+ 
+
+ align:start position:0%
+Um, so we're going to do projection
+theory in FQ and Q is P ^2 and our set
+
+ align:start position:0%
+theory in FQ and Q is P ^2 and our set
+ 
+
+ align:start position:0%
+theory in FQ and Q is P ^2 and our set
+of points is going to be FP^2 which is a
+
+ align:start position:0%
+of points is going to be FP^2 which is a
+ 
+
+ align:start position:0%
+of points is going to be FP^2 which is a
+subset of FQ ^2 and our set of
+
+ align:start position:0%
+subset of FQ ^2 and our set of
+ 
+
+ align:start position:0%
+subset of FQ ^2 and our set of
+directions is going to be FP which is a
+
+ align:start position:0%
+directions is going to be FP which is a
+ 
+
+ align:start position:0%
+directions is going to be FP which is a
+subset of FQ. So remember that uh if
+
+ align:start position:0%
+subset of FQ. So remember that uh if
+ 
+
+ align:start position:0%
+subset of FQ. So remember that uh if
+theta is in fq then pi theta is going to
+
+ align:start position:0%
+theta is in fq then pi theta is going to
+ 
+
+ align:start position:0%
+theta is in fq then pi theta is going to
+be a projection a linear map from fq ^2
+
+ align:start position:0%
+be a projection a linear map from fq ^2
+ 
+
+ align:start position:0%
+be a projection a linear map from fq ^2
+to fq
+
+ align:start position:0%
+to fq
+ 
+
+ align:start position:0%
+to fq
+which is given by pi theta of x1 x2 is
+
+ align:start position:0%
+which is given by pi theta of x1 x2 is
+ 
+
+ align:start position:0%
+which is given by pi theta of x1 x2 is
+x1 + theta x2.
+
+ align:start position:0%
+x1 + theta x2.
+ 
+
+ align:start position:0%
+x1 + theta x2.
+So this is our set of directions
+
+ align:start position:0%
+So this is our set of directions
+ 
+
+ align:start position:0%
+So this is our set of directions
+and then s which is the maximum size of
+
+ align:start position:0%
+and then s which is the maximum size of
+ 
+
+ align:start position:0%
+and then s which is the maximum size of
+the projection of x over all these
+
+ align:start position:0%
+the projection of x over all these
+ 
+
+ align:start position:0%
+the projection of x over all these
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+um is uh is is p um because pi theta of
+
+ align:start position:0%
+um is uh is is p um because pi theta of
+ 
+
+ align:start position:0%
+um is uh is is p um because pi theta of
+x is just fp
+
+ align:start position:0%
+x is just fp
+ 
+
+ align:start position:0%
+x is just fp
+uh for theta and d.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So if you uh just write down the
+
+ align:start position:0%
+Okay. So if you uh just write down the
+ 
+
+ align:start position:0%
+Okay. So if you uh just write down the
+sizes of all the things in this
+
+ align:start position:0%
+sizes of all the things in this
+ 
+
+ align:start position:0%
+sizes of all the things in this
+important example, x is p ^2 which is q
+
+ align:start position:0%
+important example, x is p ^2 which is q
+ 
+
+ align:start position:0%
+important example, x is p ^2 which is q
+and s and d are p which is q to the
+
+ align:start position:0%
+and s and d are p which is q to the
+ 
+
+ align:start position:0%
+and s and d are p which is q to the
+half. So in in particular notice that
+
+ align:start position:0%
+half. So in in particular notice that
+ 
+
+ align:start position:0%
+half. So in in particular notice that
+the size of each projection is the
+
+ align:start position:0%
+the size of each projection is the
+ 
+
+ align:start position:0%
+the size of each projection is the
+square root of the size of the set.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um so
+
+ align:start position:0%
+Okay. Um so
+ 
+
+ align:start position:0%
+Okay. Um so
+so nothing like this is supposed to
+
+ align:start position:0%
+so nothing like this is supposed to
+ 
+
+ align:start position:0%
+so nothing like this is supposed to
+happen over FP and there's a hard open
+
+ align:start position:0%
+happen over FP and there's a hard open
+ 
+
+ align:start position:0%
+happen over FP and there's a hard open
+conjecture that um that gives bounds
+
+ align:start position:0%
+conjecture that um that gives bounds
+ 
+
+ align:start position:0%
+conjecture that um that gives bounds
+that are much stronger than this
+
+ align:start position:0%
+that are much stronger than this
+ 
+
+ align:start position:0%
+that are much stronger than this
+example. Um but the techniques that
+
+ align:start position:0%
+example. Um but the techniques that
+ 
+
+ align:start position:0%
+example. Um but the techniques that
+we've talked about for most of the class
+
+ align:start position:0%
+we've talked about for most of the class
+ 
+
+ align:start position:0%
+we've talked about for most of the class
+do not depend on the field. So the
+
+ align:start position:0%
+do not depend on the field. So the
+ 
+
+ align:start position:0%
+do not depend on the field. So the
+double counting does not distinguish
+
+ align:start position:0%
+double counting does not distinguish
+ 
+
+ align:start position:0%
+double counting does not distinguish
+prime fields from not prime fields and
+
+ align:start position:0%
+prime fields from not prime fields and
+ 
+
+ align:start position:0%
+prime fields from not prime fields and
+the 4A method does not distinguish prime
+
+ align:start position:0%
+the 4A method does not distinguish prime
+ 
+
+ align:start position:0%
+the 4A method does not distinguish prime
+fields from not prime fields.
+
+ align:start position:0%
+fields from not prime fields.
+ 
+
+ align:start position:0%
+fields from not prime fields.
+Um the summer ready trotder theorem
+
+ align:start position:0%
+Um the summer ready trotder theorem
+ 
+
+ align:start position:0%
+Um the summer ready trotder theorem
+proves that this numerology cannot
+
+ align:start position:0%
+proves that this numerology cannot
+ 
+
+ align:start position:0%
+proves that this numerology cannot
+happen for a set of points in R2. Um but
+
+ align:start position:0%
+happen for a set of points in R2. Um but
+ 
+
+ align:start position:0%
+happen for a set of points in R2. Um but
+the proof has the proof is very
+
+ align:start position:0%
+the proof has the proof is very
+ 
+
+ align:start position:0%
+the proof has the proof is very
+important but it has some limitations in
+
+ align:start position:0%
+important but it has some limitations in
+ 
+
+ align:start position:0%
+important but it has some limitations in
+how it could apply. It certainly won't
+
+ align:start position:0%
+how it could apply. It certainly won't
+ 
+
+ align:start position:0%
+how it could apply. It certainly won't
+apply over FP. Um and it also doesn't
+
+ align:start position:0%
+apply over FP. Um and it also doesn't
+ 
+
+ align:start position:0%
+apply over FP. Um and it also doesn't
+seem to help very much from the point of
+
+ align:start position:0%
+seem to help very much from the point of
+ 
+
+ align:start position:0%
+seem to help very much from the point of
+view of uh sets of balls in R2 with some
+
+ align:start position:0%
+view of uh sets of balls in R2 with some
+ 
+
+ align:start position:0%
+view of uh sets of balls in R2 with some
+kind of spacing condition. It depends
+
+ align:start position:0%
+kind of spacing condition. It depends
+ 
+
+ align:start position:0%
+kind of spacing condition. It depends
+what spacing condition but for the most
+
+ align:start position:0%
+what spacing condition but for the most
+ 
+
+ align:start position:0%
+what spacing condition but for the most
+interesting spacing condition it doesn't
+
+ align:start position:0%
+interesting spacing condition it doesn't
+ 
+
+ align:start position:0%
+interesting spacing condition it doesn't
+help very much.
+
+ align:start position:0%
+help very much.
+ 
+
+ align:start position:0%
+help very much.
+Okay. Nevertheless, we know that this
+
+ align:start position:0%
+Okay. Nevertheless, we know that this
+ 
+
+ align:start position:0%
+Okay. Nevertheless, we know that this
+cannot happen over finite fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the main theorem that we'll so this
+
+ align:start position:0%
+and the main theorem that we'll so this
+ 
+
+ align:start position:0%
+and the main theorem that we'll so this
+week we will prove a theorem that says
+
+ align:start position:0%
+week we will prove a theorem that says
+ 
+
+ align:start position:0%
+week we will prove a theorem that says
+that this cannot happen. So this is the
+
+ align:start position:0%
+that this cannot happen. So this is the
+ 
+
+ align:start position:0%
+that this cannot happen. So this is the
+theorem of Ban Kats and Tao.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So again cat's tow projection theorem.
+
+ align:start position:0%
+So again cat's tow projection theorem.
+ 
+
+ align:start position:0%
+So again cat's tow projection theorem.
+Okay it says the following thing. So if
+
+ align:start position:0%
+Okay it says the following thing. So if
+ 
+
+ align:start position:0%
+Okay it says the following thing. So if
+we have x in fp^2
+
+ align:start position:0%
+we have x in fp^2
+ 
+
+ align:start position:0%
+we have x in fp^2
+and let's say that the size of x is p to
+
+ align:start position:0%
+and let's say that the size of x is p to
+ 
+
+ align:start position:0%
+and let's say that the size of x is p to
+the s where s is uh somewhere between
+
+ align:start position:0%
+the s where s is uh somewhere between
+ 
+
+ align:start position:0%
+the s where s is uh somewhere between
+zero and two.
+
+ align:start position:0%
+zero and two.
+ 
+
+ align:start position:0%
+zero and two.
+Okay. And then we have a set of
+
+ align:start position:0%
+Okay. And then we have a set of
+ 
+
+ align:start position:0%
+Okay. And then we have a set of
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+in FP
+
+ align:start position:0%
+in FP
+ 
+
+ align:start position:0%
+in FP
+and the set of directions will be p to
+
+ align:start position:0%
+and the set of directions will be p to
+ 
+
+ align:start position:0%
+and the set of directions will be p to
+the t and t is uh bigger than zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So then if you look at the maximum
+
+ align:start position:0%
+Okay. So then if you look at the maximum
+ 
+
+ align:start position:0%
+Okay. So then if you look at the maximum
+size of a projection,
+
+ align:start position:0%
+size of a projection,
+ 
+
+ align:start position:0%
+size of a projection,
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+it's significantly bigger than half of
+
+ align:start position:0%
+it's significantly bigger than half of
+ 
+
+ align:start position:0%
+it's significantly bigger than half of
+the the square root of the of the size
+
+ align:start position:0%
+the the square root of the of the size
+ 
+
+ align:start position:0%
+the the square root of the of the size
+of of X. So this is bigger than P to the
+
+ align:start position:0%
+of of X. So this is bigger than P to the
+ 
+
+ align:start position:0%
+of of X. So this is bigger than P to the
+S over 2 plus epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where this epsilon only depends on S and
+
+ align:start position:0%
+where this epsilon only depends on S and
+ 
+
+ align:start position:0%
+where this epsilon only depends on S and
+T.
+
+ align:start position:0%
+T.
+ 
+
+ align:start position:0%
+T.
+It's bigger than zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um, so some remarks about the
+
+ align:start position:0%
+Okay. Um, so some remarks about the
+ 
+
+ align:start position:0%
+Okay. Um, so some remarks about the
+epsilon. It's it's an explicit function.
+
+ align:start position:0%
+epsilon. It's it's an explicit function.
+ 
+
+ align:start position:0%
+epsilon. It's it's an explicit function.
+I just don't write it down because it's
+
+ align:start position:0%
+I just don't write it down because it's
+ 
+
+ align:start position:0%
+I just don't write it down because it's
+a little bit messy. For example, it's
+
+ align:start position:0%
+a little bit messy. For example, it's
+ 
+
+ align:start position:0%
+a little bit messy. For example, it's
+continuous. It's not that hard to write
+
+ align:start position:0%
+continuous. It's not that hard to write
+ 
+
+ align:start position:0%
+continuous. It's not that hard to write
+it down, but it is also pretty small.
+
+ align:start position:0%
+it down, but it is also pretty small.
+ 
+
+ align:start position:0%
+it down, but it is also pretty small.
+Pretty disappointingly small.
+
+ align:start position:0%
+Pretty disappointingly small.
+ 
+
+ align:start position:0%
+Pretty disappointingly small.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+there's also something called Bans's
+
+ align:start position:0%
+there's also something called Bans's
+ 
+
+ align:start position:0%
+there's also something called Bans's
+projection theorem which is what publish
+
+ align:start position:0%
+projection theorem which is what publish
+ 
+
+ align:start position:0%
+projection theorem which is what publish
+MKin is going to talk about today which
+
+ align:start position:0%
+MKin is going to talk about today which
+ 
+
+ align:start position:0%
+MKin is going to talk about today which
+is the analog of this over the in the
+
+ align:start position:0%
+is the analog of this over the in the
+ 
+
+ align:start position:0%
+is the analog of this over the in the
+setting of the real of balls in R2.
+
+ align:start position:0%
+setting of the real of balls in R2.
+ 
+
+ align:start position:0%
+setting of the real of balls in R2.
+Um so there's an analog of this example
+
+ align:start position:0%
+Um so there's an analog of this example
+ 
+
+ align:start position:0%
+Um so there's an analog of this example
+using C2 instead of R2 and then BN's
+
+ align:start position:0%
+using C2 instead of R2 and then BN's
+ 
+
+ align:start position:0%
+using C2 instead of R2 and then BN's
+projection theorem is the analog of this
+
+ align:start position:0%
+projection theorem is the analog of this
+ 
+
+ align:start position:0%
+projection theorem is the analog of this
+theorem that rules out that example.
+
+ align:start position:0%
+theorem that rules out that example.
+ 
+
+ align:start position:0%
+theorem that rules out that example.
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is an analogous theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for balls and art.
+
+ align:start position:0%
+for balls and art.
+ 
+
+ align:start position:0%
+for balls and art.
+Okay. And these two theorems in spite of
+
+ align:start position:0%
+Okay. And these two theorems in spite of
+ 
+
+ align:start position:0%
+Okay. And these two theorems in spite of
+the fact that this epsilon is very small
+
+ align:start position:0%
+the fact that this epsilon is very small
+ 
+
+ align:start position:0%
+the fact that this epsilon is very small
+are very important sort of landmark
+
+ align:start position:0%
+are very important sort of landmark
+ 
+
+ align:start position:0%
+are very important sort of landmark
+results in the field of projection
+
+ align:start position:0%
+results in the field of projection
+ 
+
+ align:start position:0%
+results in the field of projection
+theory and they play a key role in many
+
+ align:start position:0%
+theory and they play a key role in many
+ 
+
+ align:start position:0%
+theory and they play a key role in many
+applications. Um uh this ban projection
+
+ align:start position:0%
+applications. Um uh this ban projection
+ 
+
+ align:start position:0%
+applications. Um uh this ban projection
+theorem it plays a key role in getting
+
+ align:start position:0%
+theorem it plays a key role in getting
+ 
+
+ align:start position:0%
+theorem it plays a key role in getting
+the sharp projection estimates in R2 the
+
+ align:start position:0%
+the sharp projection estimates in R2 the
+ 
+
+ align:start position:0%
+the sharp projection estimates in R2 the
+recent work uh that publish mkin and
+
+ align:start position:0%
+recent work uh that publish mkin and
+ 
+
+ align:start position:0%
+recent work uh that publish mkin and
+others were involved in. Um this banan
+
+ align:start position:0%
+others were involved in. Um this banan
+ 
+
+ align:start position:0%
+others were involved in. Um this banan
+projection theorem also plays an
+
+ align:start position:0%
+projection theorem also plays an
+ 
+
+ align:start position:0%
+projection theorem also plays an
+important role in the solution of the ka
+
+ align:start position:0%
+important role in the solution of the ka
+ 
+
+ align:start position:0%
+important role in the solution of the ka
+problem.
+
+ align:start position:0%
+problem.
+ 
+
+ align:start position:0%
+problem.
+Um and this finite field projection
+
+ align:start position:0%
+Um and this finite field projection
+ 
+
+ align:start position:0%
+Um and this finite field projection
+theorem as well as this one have some
+
+ align:start position:0%
+theorem as well as this one have some
+ 
+
+ align:start position:0%
+theorem as well as this one have some
+have a important role in some
+
+ align:start position:0%
+have a important role in some
+ 
+
+ align:start position:0%
+have a important role in some
+interesting applications about um how
+
+ align:start position:0%
+interesting applications about um how
+ 
+
+ align:start position:0%
+interesting applications about um how
+fast different processes mix. Like if
+
+ align:start position:0%
+fast different processes mix. Like if
+ 
+
+ align:start position:0%
+fast different processes mix. Like if
+you take some generators of a finite
+
+ align:start position:0%
+you take some generators of a finite
+ 
+
+ align:start position:0%
+you take some generators of a finite
+group like SL2 over FP
+
+ align:start position:0%
+group like SL2 over FP
+ 
+
+ align:start position:0%
+group like SL2 over FP
+um and then they make a random walk. How
+
+ align:start position:0%
+um and then they make a random walk. How
+ 
+
+ align:start position:0%
+um and then they make a random walk. How
+fast does this random walk become evenly
+
+ align:start position:0%
+fast does this random walk become evenly
+ 
+
+ align:start position:0%
+fast does this random walk become evenly
+distributed in SL2FP?
+
+ align:start position:0%
+distributed in SL2FP?
+ 
+
+ align:start position:0%
+distributed in SL2FP?
+This is an important ingredient in
+
+ align:start position:0%
+This is an important ingredient in
+ 
+
+ align:start position:0%
+This is an important ingredient in
+studying that.
+
+ align:start position:0%
+studying that.
+ 
+
+ align:start position:0%
+studying that.
+Okay. Um so okay. So in spite of the
+
+ align:start position:0%
+Okay. Um so okay. So in spite of the
+ 
+
+ align:start position:0%
+Okay. Um so okay. So in spite of the
+fact that the epsilon is small, these
+
+ align:start position:0%
+fact that the epsilon is small, these
+ 
+
+ align:start position:0%
+fact that the epsilon is small, these
+theorems are are very important and
+
+ align:start position:0%
+theorems are are very important and
+ 
+
+ align:start position:0%
+theorems are are very important and
+they're also qualitatively different
+
+ align:start position:0%
+they're also qualitatively different
+ 
+
+ align:start position:0%
+they're also qualitatively different
+from the other theorems because they're
+
+ align:start position:0%
+from the other theorems because they're
+ 
+
+ align:start position:0%
+from the other theorems because they're
+sensitive to what kind of field we're
+
+ align:start position:0%
+sensitive to what kind of field we're
+ 
+
+ align:start position:0%
+sensitive to what kind of field we're
+working. Yeah.
+
+ align:start position:0%
+working. Yeah.
+ 
+
+ align:start position:0%
+working. Yeah.
+>> What is the analog of P for ball or R2?
+
+ align:start position:0%
+>> What is the analog of P for ball or R2?
+ 
+
+ align:start position:0%
+>> What is the analog of P for ball or R2?
+>> The analog of P. So we would have uh the
+
+ align:start position:0%
+>> The analog of P. So we would have uh the
+ 
+
+ align:start position:0%
+>> The analog of P. So we would have uh the
+setting would be you'd have unit balls
+
+ align:start position:0%
+setting would be you'd have unit balls
+ 
+
+ align:start position:0%
+setting would be you'd have unit balls
+and a ball of radius r and r is the
+
+ align:start position:0%
+and a ball of radius r and r is the
+ 
+
+ align:start position:0%
+and a ball of radius r and r is the
+analog of p.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So all the sizes of things we would we
+
+ align:start position:0%
+So all the sizes of things we would we
+ 
+
+ align:start position:0%
+So all the sizes of things we would we
+could think of them as powers of r.
+
+ align:start position:0%
+could think of them as powers of r.
+ 
+
+ align:start position:0%
+could think of them as powers of r.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+>> Do the proofs use kind of similar
+
+ align:start position:0%
+>> Do the proofs use kind of similar
+ 
+
+ align:start position:0%
+>> Do the proofs use kind of similar
+arguments or they completely
+
+ align:start position:0%
+arguments or they completely
+ 
+
+ align:start position:0%
+arguments or they completely
+>> the question is do these two proofs use
+
+ align:start position:0%
+>> the question is do these two proofs use
+ 
+
+ align:start position:0%
+>> the question is do these two proofs use
+similar arguments or are they completely
+
+ align:start position:0%
+similar arguments or are they completely
+ 
+
+ align:start position:0%
+similar arguments or are they completely
+different? Um there are multiple proofs
+
+ align:start position:0%
+different? Um there are multiple proofs
+ 
+
+ align:start position:0%
+different? Um there are multiple proofs
+of this um but at least one of them is
+
+ align:start position:0%
+of this um but at least one of them is
+ 
+
+ align:start position:0%
+of this um but at least one of them is
+very similar to this with one sort of
+
+ align:start position:0%
+very similar to this with one sort of
+ 
+
+ align:start position:0%
+very similar to this with one sort of
+layer of additional ideas
+
+ align:start position:0%
+layer of additional ideas
+ 
+
+ align:start position:0%
+layer of additional ideas
+and so yeah so my plan is that we'll
+
+ align:start position:0%
+and so yeah so my plan is that we'll
+ 
+
+ align:start position:0%
+and so yeah so my plan is that we'll
+we'll do this and then we'll talk about
+
+ align:start position:0%
+we'll do this and then we'll talk about
+ 
+
+ align:start position:0%
+we'll do this and then we'll talk about
+the additional ideas to do this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay cool. Well so the key difference
+
+ align:start position:0%
+Okay cool. Well so the key difference
+ 
+
+ align:start position:0%
+Okay cool. Well so the key difference
+between FQ and FP is that FQ has a sub
+
+ align:start position:0%
+between FQ and FP is that FQ has a sub
+ 
+
+ align:start position:0%
+between FQ and FP is that FQ has a sub
+field and FP has no sub field. Now, it's
+
+ align:start position:0%
+field and FP has no sub field. Now, it's
+ 
+
+ align:start position:0%
+field and FP has no sub field. Now, it's
+elementary to check that FP has no
+
+ align:start position:0%
+elementary to check that FP has no
+ 
+
+ align:start position:0%
+elementary to check that FP has no
+subfield, but because we're proving some
+
+ align:start position:0%
+subfield, but because we're proving some
+ 
+
+ align:start position:0%
+subfield, but because we're proving some
+kind of quantitative estimates, we need
+
+ align:start position:0%
+kind of quantitative estimates, we need
+ 
+
+ align:start position:0%
+kind of quantitative estimates, we need
+some quantitative lema that that says
+
+ align:start position:0%
+some quantitative lema that that says
+ 
+
+ align:start position:0%
+some quantitative lema that that says
+that FP not only has no subfield, but it
+
+ align:start position:0%
+that FP not only has no subfield, but it
+ 
+
+ align:start position:0%
+that FP not only has no subfield, but it
+doesn't have anything that's kind of
+
+ align:start position:0%
+doesn't have anything that's kind of
+ 
+
+ align:start position:0%
+doesn't have anything that's kind of
+approximately a sub field. Um, so the
+
+ align:start position:0%
+approximately a sub field. Um, so the
+ 
+
+ align:start position:0%
+approximately a sub field. Um, so the
+main goal for today will be to uh to to
+
+ align:start position:0%
+main goal for today will be to uh to to
+ 
+
+ align:start position:0%
+main goal for today will be to uh to to
+prove to develop uh lambas like that.
+
+ align:start position:0%
+prove to develop uh lambas like that.
+ 
+
+ align:start position:0%
+prove to develop uh lambas like that.
+And let me show you. So, so here's the
+
+ align:start position:0%
+And let me show you. So, so here's the
+ 
+
+ align:start position:0%
+And let me show you. So, so here's the
+first version of a lema like that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level one. Actually, let me do I think
+
+ align:start position:0%
+level one. Actually, let me do I think
+ 
+
+ align:start position:0%
+level one. Actually, let me do I think
+we need a little notation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so suppose that A is a subset of
+
+ align:start position:0%
+Okay, so suppose that A is a subset of
+ 
+
+ align:start position:0%
+Okay, so suppose that A is a subset of
+FP.
+
+ align:start position:0%
+FP.
+ 
+
+ align:start position:0%
+FP.
+If I write a + a, then that means the
+
+ align:start position:0%
+If I write a + a, then that means the
+ 
+
+ align:start position:0%
+If I write a + a, then that means the
+set of all the sums a1 plus a2 where a1
+
+ align:start position:0%
+set of all the sums a1 plus a2 where a1
+ 
+
+ align:start position:0%
+set of all the sums a1 plus a2 where a1
+and a2 are a and we could write a * a.
+
+ align:start position:0%
+and a2 are a and we could write a * a.
+ 
+
+ align:start position:0%
+and a2 are a and we could write a * a.
+That's the set of all the products a1 *
+
+ align:start position:0%
+That's the set of all the products a1 *
+ 
+
+ align:start position:0%
+That's the set of all the products a1 *
+a2 a1 and a2 and a
+
+ align:start position:0%
+a2 a1 and a2 and a
+ 
+
+ align:start position:0%
+a2 a1 and a2 and a
+and so on. So there you can write a lot
+
+ align:start position:0%
+and so on. So there you can write a lot
+ 
+
+ align:start position:0%
+and so on. So there you can write a lot
+of similar things like this and um I
+
+ align:start position:0%
+of similar things like this and um I
+ 
+
+ align:start position:0%
+of similar things like this and um I
+think it'll be clear what they all mean
+
+ align:start position:0%
+think it'll be clear what they all mean
+ 
+
+ align:start position:0%
+think it'll be clear what they all mean
+but if it's not of course we we'll talk
+
+ align:start position:0%
+but if it's not of course we we'll talk
+ 
+
+ align:start position:0%
+but if it's not of course we we'll talk
+about it. Okay, so here's the lema. It's
+
+ align:start position:0%
+about it. Okay, so here's the lema. It's
+ 
+
+ align:start position:0%
+about it. Okay, so here's the lema. It's
+a quantitative lema that says that um
+
+ align:start position:0%
+a quantitative lema that says that um
+ 
+
+ align:start position:0%
+a quantitative lema that says that um
+that no subset behaves too much like a
+
+ align:start position:0%
+that no subset behaves too much like a
+ 
+
+ align:start position:0%
+that no subset behaves too much like a
+sub field.
+
+ align:start position:0%
+sub field.
+ 
+
+ align:start position:0%
+sub field.
+So it says if A is a subset of FP
+
+ align:start position:0%
+So it says if A is a subset of FP
+ 
+
+ align:start position:0%
+So it says if A is a subset of FP
+then either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one option is that A minus A over A
+
+ align:start position:0%
+one option is that A minus A over A
+ 
+
+ align:start position:0%
+one option is that A minus A over A
+minus A is all the death P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the second option
+
+ align:start position:0%
+and the second option
+ 
+
+ align:start position:0%
+and the second option
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+if you multiply try and add stuff in a
+
+ align:start position:0%
+if you multiply try and add stuff in a
+ 
+
+ align:start position:0%
+if you multiply try and add stuff in a
+and subtract stuff. A lot of times it
+
+ align:start position:0%
+and subtract stuff. A lot of times it
+ 
+
+ align:start position:0%
+and subtract stuff. A lot of times it
+will get bigger. 1 2 3 4 5 six. Six
+
+ align:start position:0%
+will get bigger. 1 2 3 4 5 six. Six
+ 
+
+ align:start position:0%
+will get bigger. 1 2 3 4 5 six. Six
+might be enough. I think it might be
+
+ align:start position:0%
+might be enough. I think it might be
+ 
+
+ align:start position:0%
+might be enough. I think it might be
+eight.
+
+ align:start position:0%
+eight.
+ 
+
+ align:start position:0%
+eight.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, one possibility is if you
+
+ align:start position:0%
+Okay. So, one possibility is if you
+ 
+
+ align:start position:0%
+Okay. So, one possibility is if you
+multiply, add and subtract elements of A
+
+ align:start position:0%
+multiply, add and subtract elements of A
+ 
+
+ align:start position:0%
+multiply, add and subtract elements of A
+lot of times, then you get a lot more
+
+ align:start position:0%
+lot of times, then you get a lot more
+ 
+
+ align:start position:0%
+lot of times, then you get a lot more
+stuff than just a. So this says A is not
+
+ align:start position:0%
+stuff than just a. So this says A is not
+ 
+
+ align:start position:0%
+stuff than just a. So this says A is not
+too close to a sub field. And the other
+
+ align:start position:0%
+too close to a sub field. And the other
+ 
+
+ align:start position:0%
+too close to a sub field. And the other
+options is if you do this you get all of
+
+ align:start position:0%
+options is if you do this you get all of
+ 
+
+ align:start position:0%
+options is if you do this you get all of
+FP.
+
+ align:start position:0%
+FP.
+ 
+
+ align:start position:0%
+FP.
+Now of course A could have been almost
+
+ align:start position:0%
+Now of course A could have been almost
+ 
+
+ align:start position:0%
+Now of course A could have been almost
+all of FP already. So then it is kind of
+
+ align:start position:0%
+all of FP already. So then it is kind of
+ 
+
+ align:start position:0%
+all of FP already. So then it is kind of
+almost a field. But if A was originally
+
+ align:start position:0%
+almost a field. But if A was originally
+ 
+
+ align:start position:0%
+almost a field. But if A was originally
+a lot smaller than FP then in this case
+
+ align:start position:0%
+a lot smaller than FP then in this case
+ 
+
+ align:start position:0%
+a lot smaller than FP then in this case
+this thing is a lot bigger than A.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So, here is the proof.
+
+ align:start position:0%
+So, here is the proof.
+ 
+
+ align:start position:0%
+So, here is the proof.
+Um, observation one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if uh c is not in a minus a over a
+
+ align:start position:0%
+So if uh c is not in a minus a over a
+ 
+
+ align:start position:0%
+So if uh c is not in a minus a over a
+minus a
+
+ align:start position:0%
+minus a
+ 
+
+ align:start position:0%
+minus a
+um then
+
+ align:start position:0%
+um then
+ 
+
+ align:start position:0%
+um then
+a + c a
+
+ align:start position:0%
+a + c a
+ 
+
+ align:start position:0%
+a + c a
+has size a squ.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Let me make sure it's clear what
+
+ align:start position:0%
+Okay. Let me make sure it's clear what
+ 
+
+ align:start position:0%
+Okay. Let me make sure it's clear what
+all the notation means. So if I write
+
+ align:start position:0%
+all the notation means. So if I write
+ 
+
+ align:start position:0%
+all the notation means. So if I write
+this thing, I have four copies of A. So
+
+ align:start position:0%
+this thing, I have four copies of A. So
+ 
+
+ align:start position:0%
+this thing, I have four copies of A. So
+you take A1, A2, A3, A4, any four guys
+
+ align:start position:0%
+you take A1, A2, A3, A4, any four guys
+ 
+
+ align:start position:0%
+you take A1, A2, A3, A4, any four guys
+in A and sort of plug them in for the
+
+ align:start position:0%
+in A and sort of plug them in for the
+ 
+
+ align:start position:0%
+in A and sort of plug them in for the
+capital A. All the things you can get.
+
+ align:start position:0%
+capital A. All the things you can get.
+ 
+
+ align:start position:0%
+capital A. All the things you can get.
+That's what this set is. And similarly
+
+ align:start position:0%
+That's what this set is. And similarly
+ 
+
+ align:start position:0%
+That's what this set is. And similarly
+over here the lowerase C is a particular
+
+ align:start position:0%
+over here the lowerase C is a particular
+ 
+
+ align:start position:0%
+over here the lowerase C is a particular
+element of FP and this means take any A1
+
+ align:start position:0%
+element of FP and this means take any A1
+ 
+
+ align:start position:0%
+element of FP and this means take any A1
+and A2 and and do this.
+
+ align:start position:0%
+and A2 and and do this.
+ 
+
+ align:start position:0%
+and A2 and and do this.
+Okay. Um so the proof of observation one
+
+ align:start position:0%
+Okay. Um so the proof of observation one
+ 
+
+ align:start position:0%
+Okay. Um so the proof of observation one
+is quite simple. So suppose that I have
+
+ align:start position:0%
+is quite simple. So suppose that I have
+ 
+
+ align:start position:0%
+is quite simple. So suppose that I have
+two different uh ele uh elements in here
+
+ align:start position:0%
+two different uh ele uh elements in here
+ 
+
+ align:start position:0%
+two different uh ele uh elements in here
+but that are equal to each other. So
+
+ align:start position:0%
+but that are equal to each other. So
+ 
+
+ align:start position:0%
+but that are equal to each other. So
+suppose a1 + c a2 is the same as a1
+
+ align:start position:0%
+suppose a1 + c a2 is the same as a1
+ 
+
+ align:start position:0%
+suppose a1 + c a2 is the same as a1
+prime plus c a2 prime.
+
+ align:start position:0%
+prime plus c a2 prime.
+ 
+
+ align:start position:0%
+prime plus c a2 prime.
+Well, if I do a little algebra, I can
+
+ align:start position:0%
+Well, if I do a little algebra, I can
+ 
+
+ align:start position:0%
+Well, if I do a little algebra, I can
+solve this for C. And I discover that C
+
+ align:start position:0%
+solve this for C. And I discover that C
+ 
+
+ align:start position:0%
+solve this for C. And I discover that C
+is um A1 prime minus A1
+
+ align:start position:0%
+is um A1 prime minus A1
+ 
+
+ align:start position:0%
+is um A1 prime minus A1
+/ A2 - A2 prime, which is in A minus A.
+
+ align:start position:0%
+/ A2 - A2 prime, which is in A minus A.
+ 
+
+ align:start position:0%
+/ A2 - A2 prime, which is in A minus A.
+So if C is not in A minus A, sorry,
+
+ align:start position:0%
+So if C is not in A minus A, sorry,
+ 
+
+ align:start position:0%
+So if C is not in A minus A, sorry,
+which is in A minus A over A minus A.
+
+ align:start position:0%
+which is in A minus A over A minus A.
+ 
+
+ align:start position:0%
+which is in A minus A over A minus A.
+So if C is not in here, then all of
+
+ align:start position:0%
+So if C is not in here, then all of
+ 
+
+ align:start position:0%
+So if C is not in here, then all of
+these different representations are
+
+ align:start position:0%
+these different representations are
+ 
+
+ align:start position:0%
+these different representations are
+actually different numbers. So the size
+
+ align:start position:0%
+actually different numbers. So the size
+ 
+
+ align:start position:0%
+actually different numbers. So the size
+of this set is A^ squ.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now if you want to be really
+
+ align:start position:0%
+Okay. Now if you want to be really
+ 
+
+ align:start position:0%
+Okay. Now if you want to be really
+careful, maybe we should worry about
+
+ align:start position:0%
+careful, maybe we should worry about
+ 
+
+ align:start position:0%
+careful, maybe we should worry about
+whether I have divided by zero. But if
+
+ align:start position:0%
+whether I have divided by zero. But if
+ 
+
+ align:start position:0%
+whether I have divided by zero. But if
+a2 is equal to a2 prime, then the only
+
+ align:start position:0%
+a2 is equal to a2 prime, then the only
+ 
+
+ align:start position:0%
+a2 is equal to a2 prime, then the only
+way that the top equation could be true
+
+ align:start position:0%
+way that the top equation could be true
+ 
+
+ align:start position:0%
+way that the top equation could be true
+is if also a1 is equal to a1 prime and
+
+ align:start position:0%
+is if also a1 is equal to a1 prime and
+ 
+
+ align:start position:0%
+is if also a1 is equal to a1 prime and
+then I just had the same thing. Okay.
+
+ align:start position:0%
+then I just had the same thing. Okay.
+ 
+
+ align:start position:0%
+then I just had the same thing. Okay.
+All right. Great.
+
+ align:start position:0%
+All right. Great.
+ 
+
+ align:start position:0%
+All right. Great.
+Okay. So,
+
+ align:start position:0%
+Okay. So,
+ 
+
+ align:start position:0%
+Okay. So,
+so if I can locate some C that is in um
+
+ align:start position:0%
+so if I can locate some C that is in um
+ 
+
+ align:start position:0%
+so if I can locate some C that is in um
+you know the ring of stuff I can make by
+
+ align:start position:0%
+you know the ring of stuff I can make by
+ 
+
+ align:start position:0%
+you know the ring of stuff I can make by
+adding and multip maybe the if I can add
+
+ align:start position:0%
+adding and multip maybe the if I can add
+ 
+
+ align:start position:0%
+adding and multip maybe the if I can add
+and subtract and multiply and divide a
+
+ align:start position:0%
+and subtract and multiply and divide a
+ 
+
+ align:start position:0%
+and subtract and multiply and divide a
+bunch of elements of A and I can locate
+
+ align:start position:0%
+bunch of elements of A and I can locate
+ 
+
+ align:start position:0%
+bunch of elements of A and I can locate
+some C which is not in here then I can
+
+ align:start position:0%
+some C which is not in here then I can
+ 
+
+ align:start position:0%
+some C which is not in here then I can
+use this observation and I can get some
+
+ align:start position:0%
+use this observation and I can get some
+ 
+
+ align:start position:0%
+use this observation and I can get some
+I can show that I can build out of A
+
+ align:start position:0%
+I can show that I can build out of A
+ 
+
+ align:start position:0%
+I can show that I can build out of A
+many different things.
+
+ align:start position:0%
+many different things.
+ 
+
+ align:start position:0%
+many different things.
+Okay, cool.
+
+ align:start position:0%
+Okay, cool.
+ 
+
+ align:start position:0%
+Okay, cool.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+now somewhere in our proof, we have to
+
+ align:start position:0%
+now somewhere in our proof, we have to
+ 
+
+ align:start position:0%
+now somewhere in our proof, we have to
+use that FP is a prime field.
+
+ align:start position:0%
+use that FP is a prime field.
+ 
+
+ align:start position:0%
+use that FP is a prime field.
+It wouldn't work in FQ and we haven't
+
+ align:start position:0%
+It wouldn't work in FQ and we haven't
+ 
+
+ align:start position:0%
+It wouldn't work in FQ and we haven't
+used it yet. Well, how are we going to
+
+ align:start position:0%
+used it yet. Well, how are we going to
+ 
+
+ align:start position:0%
+used it yet. Well, how are we going to
+use it? Well, let's just remember how we
+
+ align:start position:0%
+use it? Well, let's just remember how we
+ 
+
+ align:start position:0%
+use it? Well, let's just remember how we
+would prove that FP is a prime field.
+
+ align:start position:0%
+would prove that FP is a prime field.
+ 
+
+ align:start position:0%
+would prove that FP is a prime field.
+Um, sorry, how would we prove that FP
+
+ align:start position:0%
+Um, sorry, how would we prove that FP
+ 
+
+ align:start position:0%
+Um, sorry, how would we prove that FP
+has no sub fields? How are we going to
+
+ align:start position:0%
+has no sub fields? How are we going to
+ 
+
+ align:start position:0%
+has no sub fields? How are we going to
+prove? Well, um, if it had a sub field,
+
+ align:start position:0%
+prove? Well, um, if it had a sub field,
+ 
+
+ align:start position:0%
+prove? Well, um, if it had a sub field,
+it would have to contain one
+
+ align:start position:0%
+it would have to contain one
+ 
+
+ align:start position:0%
+it would have to contain one
+and then it would have to contain then
+
+ align:start position:0%
+and then it would have to contain then
+ 
+
+ align:start position:0%
+and then it would have to contain then
+it would be closed under addition. So,
+
+ align:start position:0%
+it would be closed under addition. So,
+ 
+
+ align:start position:0%
+it would be closed under addition. So,
+it would have to contain two and three
+
+ align:start position:0%
+it would have to contain two and three
+ 
+
+ align:start position:0%
+it would have to contain two and three
+and four and so on and then it would
+
+ align:start position:0%
+and four and so on and then it would
+ 
+
+ align:start position:0%
+and four and so on and then it would
+have to contain all of FP.
+
+ align:start position:0%
+have to contain all of FP.
+ 
+
+ align:start position:0%
+have to contain all of FP.
+Okay. Um,
+
+ align:start position:0%
+Okay. Um,
+ 
+
+ align:start position:0%
+Okay. Um,
+so we we're basically going to use that
+
+ align:start position:0%
+so we we're basically going to use that
+ 
+
+ align:start position:0%
+so we we're basically going to use that
+argument in observation two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So observation two if a minus a
+
+ align:start position:0%
+Okay. So observation two if a minus a
+ 
+
+ align:start position:0%
+Okay. So observation two if a minus a
+over a minus a is not everything
+
+ align:start position:0%
+over a minus a is not everything
+ 
+
+ align:start position:0%
+over a minus a is not everything
+um then there exists some b in a minus a
+
+ align:start position:0%
+um then there exists some b in a minus a
+ 
+
+ align:start position:0%
+um then there exists some b in a minus a
+over a minus a
+
+ align:start position:0%
+over a minus a
+ 
+
+ align:start position:0%
+over a minus a
+so that b + 1 is not in a minus a over a
+
+ align:start position:0%
+so that b + 1 is not in a minus a over a
+ 
+
+ align:start position:0%
+so that b + 1 is not in a minus a over a
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. Okay. So why is it um so so zero
+
+ align:start position:0%
+Right. Okay. So why is it um so so zero
+ 
+
+ align:start position:0%
+Right. Okay. So why is it um so so zero
+is an a minus a over a minus a. It's a
+
+ align:start position:0%
+is an a minus a over a minus a. It's a
+ 
+
+ align:start position:0%
+is an a minus a over a minus a. It's a
+proof of observation too.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero is in there because you could
+
+ align:start position:0%
+zero is in there because you could
+ 
+
+ align:start position:0%
+zero is in there because you could
+choose these to be the same and you can
+
+ align:start position:0%
+choose these to be the same and you can
+ 
+
+ align:start position:0%
+choose these to be the same and you can
+choose those to be different.
+
+ align:start position:0%
+choose those to be different.
+ 
+
+ align:start position:0%
+choose those to be different.
+Um okay if one is not
+
+ align:start position:0%
+Um okay if one is not
+ 
+
+ align:start position:0%
+Um okay if one is not
+uh yeah okay so then then we just if
+
+ align:start position:0%
+uh yeah okay so then then we just if
+ 
+
+ align:start position:0%
+uh yeah okay so then then we just if
+okay either everybody in FP is in A
+
+ align:start position:0%
+okay either everybody in FP is in A
+ 
+
+ align:start position:0%
+okay either everybody in FP is in A
+minus A minus A minus A or somebody's
+
+ align:start position:0%
+minus A minus A minus A or somebody's
+ 
+
+ align:start position:0%
+minus A minus A minus A or somebody's
+not and so then we take uh B + one is
+
+ align:start position:0%
+not and so then we take uh B + one is
+ 
+
+ align:start position:0%
+not and so then we take uh B + one is
+the smallest
+
+ align:start position:0%
+the smallest
+ 
+
+ align:start position:0%
+the smallest
+number which is not
+
+ align:start position:0%
+number which is not
+ 
+
+ align:start position:0%
+number which is not
+an A minus A over A minus A
+
+ align:start position:0%
+an A minus A over A minus A
+ 
+
+ align:start position:0%
+an A minus A over A minus A
+and there we go.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And the special thing that we're
+
+ align:start position:0%
+Okay. And the special thing that we're
+ 
+
+ align:start position:0%
+Okay. And the special thing that we're
+using about FP we've used that we have
+
+ align:start position:0%
+using about FP we've used that we have
+ 
+
+ align:start position:0%
+using about FP we've used that we have
+it's a prime field is just we're using
+
+ align:start position:0%
+it's a prime field is just we're using
+ 
+
+ align:start position:0%
+it's a prime field is just we're using
+that if you start at zero and you keep
+
+ align:start position:0%
+that if you start at zero and you keep
+ 
+
+ align:start position:0%
+that if you start at zero and you keep
+adding one you get all the elements.
+
+ align:start position:0%
+adding one you get all the elements.
+ 
+
+ align:start position:0%
+adding one you get all the elements.
+Okay. So that's the proof of observation
+
+ align:start position:0%
+Okay. So that's the proof of observation
+ 
+
+ align:start position:0%
+Okay. So that's the proof of observation
+too.
+
+ align:start position:0%
+too.
+ 
+
+ align:start position:0%
+too.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+and so now we are basically done. So now
+
+ align:start position:0%
+and so now we are basically done. So now
+ 
+
+ align:start position:0%
+and so now we are basically done. So now
+we have seen that if a minus a over a
+
+ align:start position:0%
+we have seen that if a minus a over a
+ 
+
+ align:start position:0%
+we have seen that if a minus a over a
+minus a is not fp
+
+ align:start position:0%
+minus a is not fp
+ 
+
+ align:start position:0%
+minus a is not fp
+then if you take a and you add this b +
+
+ align:start position:0%
+then if you take a and you add this b +
+ 
+
+ align:start position:0%
+then if you take a and you add this b +
+one. So b is an a minus a over a minus
+
+ align:start position:0%
+one. So b is an a minus a over a minus
+ 
+
+ align:start position:0%
+one. So b is an a minus a over a minus
+a. I'm going to add one to it. So b +
+
+ align:start position:0%
+a. I'm going to add one to it. So b +
+ 
+
+ align:start position:0%
+a. I'm going to add one to it. So b +
+one is in here. There is bigger than a
+
+ align:start position:0%
+one is in here. There is bigger than a
+ 
+
+ align:start position:0%
+one is in here. There is bigger than a
+square.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if I take six elements of a and I do
+
+ align:start position:0%
+So if I take six elements of a and I do
+ 
+
+ align:start position:0%
+So if I take six elements of a and I do
+this uh the number of different guys I
+
+ align:start position:0%
+this uh the number of different guys I
+ 
+
+ align:start position:0%
+this uh the number of different guys I
+will get is is really much bigger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then this doesn't look exactly
+
+ align:start position:0%
+okay and then this doesn't look exactly
+ 
+
+ align:start position:0%
+okay and then this doesn't look exactly
+like my two but I just like clear the
+
+ align:start position:0%
+like my two but I just like clear the
+ 
+
+ align:start position:0%
+like my two but I just like clear the
+denominator and expand things out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So when I clear the denominator, I'll
+
+ align:start position:0%
+So when I clear the denominator, I'll
+ 
+
+ align:start position:0%
+So when I clear the denominator, I'll
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+a * a minus a * a from this guy. Inside
+
+ align:start position:0%
+a * a minus a * a from this guy. Inside
+ 
+
+ align:start position:0%
+a * a minus a * a from this guy. Inside
+of here, I'll have a minus a plus a
+
+ align:start position:0%
+of here, I'll have a minus a plus a
+ 
+
+ align:start position:0%
+of here, I'll have a minus a plus a
+minus a all multiplied by a. Okay, I
+
+ align:start position:0%
+minus a all multiplied by a. Okay, I
+ 
+
+ align:start position:0%
+minus a all multiplied by a. Okay, I
+have a bunch of stuff.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So, I know so Nets Katz and I are old
+
+ align:start position:0%
+So, I know so Nets Katz and I are old
+ 
+
+ align:start position:0%
+So, I know so Nets Katz and I are old
+collaborators and I remember talking
+
+ align:start position:0%
+collaborators and I remember talking
+ 
+
+ align:start position:0%
+collaborators and I remember talking
+with him about this and and uh that
+
+ align:start position:0%
+with him about this and and uh that
+ 
+
+ align:start position:0%
+with him about this and and uh that
+it it took quite a while for them to
+
+ align:start position:0%
+it it took quite a while for them to
+ 
+
+ align:start position:0%
+it it took quite a while for them to
+figure out how to get started on this
+
+ align:start position:0%
+figure out how to get started on this
+ 
+
+ align:start position:0%
+figure out how to get started on this
+problem.
+
+ align:start position:0%
+problem.
+ 
+
+ align:start position:0%
+problem.
+Um okay, now looking back at this this
+
+ align:start position:0%
+Um okay, now looking back at this this
+ 
+
+ align:start position:0%
+Um okay, now looking back at this this
+this proof is really clean. this lema is
+
+ align:start position:0%
+this proof is really clean. this lema is
+ 
+
+ align:start position:0%
+this proof is really clean. this lema is
+perhaps not the the statement of the
+
+ align:start position:0%
+perhaps not the the statement of the
+ 
+
+ align:start position:0%
+perhaps not the the statement of the
+lema is perhaps not the nicest thing
+
+ align:start position:0%
+lema is perhaps not the nicest thing
+ 
+
+ align:start position:0%
+lema is perhaps not the nicest thing
+that you might like. Um and um
+
+ align:start position:0%
+that you might like. Um and um
+ 
+
+ align:start position:0%
+that you might like. Um and um
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are much there are kind of
+
+ align:start position:0%
+so there are much there are kind of
+ 
+
+ align:start position:0%
+so there are much there are kind of
+cleaner things like for example later
+
+ align:start position:0%
+cleaner things like for example later
+ 
+
+ align:start position:0%
+cleaner things like for example later
+today we'll show that you know just just
+
+ align:start position:0%
+today we'll show that you know just just
+ 
+
+ align:start position:0%
+today we'll show that you know just just
+this is significantly bigger than a
+
+ align:start position:0%
+this is significantly bigger than a
+ 
+
+ align:start position:0%
+this is significantly bigger than a
+um and and different variations.
+
+ align:start position:0%
+um and and different variations.
+ 
+
+ align:start position:0%
+um and and different variations.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so maybe we should mention we could ask
+
+ align:start position:0%
+so maybe we should mention we could ask
+ 
+
+ align:start position:0%
+so maybe we should mention we could ask
+some much simpler questions like we
+
+ align:start position:0%
+some much simpler questions like we
+ 
+
+ align:start position:0%
+some much simpler questions like we
+could just say um if you have a subset
+
+ align:start position:0%
+could just say um if you have a subset
+ 
+
+ align:start position:0%
+could just say um if you have a subset
+of FP called A, is it true that A plus A
+
+ align:start position:0%
+of FP called A, is it true that A plus A
+ 
+
+ align:start position:0%
+of FP called A, is it true that A plus A
+is always much bigger than A?
+
+ align:start position:0%
+is always much bigger than A?
+ 
+
+ align:start position:0%
+is always much bigger than A?
+That's true for most subsets, but it's
+
+ align:start position:0%
+That's true for most subsets, but it's
+ 
+
+ align:start position:0%
+That's true for most subsets, but it's
+not true for all of them. Um, but
+
+ align:start position:0%
+not true for all of them. Um, but
+ 
+
+ align:start position:0%
+not true for all of them. Um, but
+thinking about that much simpler
+
+ align:start position:0%
+thinking about that much simpler
+ 
+
+ align:start position:0%
+thinking about that much simpler
+question is actually uh so that that's
+
+ align:start position:0%
+question is actually uh so that that's
+ 
+
+ align:start position:0%
+question is actually uh so that that's
+like a a foundational question in in
+
+ align:start position:0%
+like a a foundational question in in
+ 
+
+ align:start position:0%
+like a a foundational question in in
+additive combinatorics to understand
+
+ align:start position:0%
+additive combinatorics to understand
+ 
+
+ align:start position:0%
+additive combinatorics to understand
+that um and and understanding that well
+
+ align:start position:0%
+that um and and understanding that well
+ 
+
+ align:start position:0%
+that um and and understanding that well
+feeds into being able to understand this
+
+ align:start position:0%
+feeds into being able to understand this
+ 
+
+ align:start position:0%
+feeds into being able to understand this
+this stuff better. Okay. So, let me pose
+
+ align:start position:0%
+this stuff better. Okay. So, let me pose
+ 
+
+ align:start position:0%
+this stuff better. Okay. So, let me pose
+this on the board and we'll start to
+
+ align:start position:0%
+this on the board and we'll start to
+ 
+
+ align:start position:0%
+this on the board and we'll start to
+talk about it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So my question for us is
+
+ align:start position:0%
+So my question for us is
+ 
+
+ align:start position:0%
+So my question for us is
+um when
+
+ align:start position:0%
+um when
+ 
+
+ align:start position:0%
+um when
+is a + a
+
+ align:start position:0%
+is a + a
+ 
+
+ align:start position:0%
+is a + a
+small?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here I have in mind that A is a
+
+ align:start position:0%
+So here I have in mind that A is a
+ 
+
+ align:start position:0%
+So here I have in mind that A is a
+subset of FP. Although we could have a
+
+ align:start position:0%
+subset of FP. Although we could have a
+ 
+
+ align:start position:0%
+subset of FP. Although we could have a
+very similar conversation if A was a
+
+ align:start position:0%
+very similar conversation if A was a
+ 
+
+ align:start position:0%
+very similar conversation if A was a
+subset of Z or A was a subset of R or
+
+ align:start position:0%
+subset of Z or A was a subset of R or
+ 
+
+ align:start position:0%
+subset of Z or A was a subset of R or
+dot dot dot.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Can anybody think of a subset if
+
+ align:start position:0%
+Okay. Can anybody think of a subset if
+ 
+
+ align:start position:0%
+Okay. Can anybody think of a subset if
+FP or A plus A is only a tiny bit bigger
+
+ align:start position:0%
+FP or A plus A is only a tiny bit bigger
+ 
+
+ align:start position:0%
+FP or A plus A is only a tiny bit bigger
+than A?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+>> is some set
+
+ align:start position:0%
+>> is some set
+ 
+
+ align:start position:0%
+>> is some set
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and that includes like numbers and then
+
+ align:start position:0%
+and that includes like numbers and then
+ 
+
+ align:start position:0%
+and that includes like numbers and then
+the negative values of those numbers in
+
+ align:start position:0%
+the negative values of those numbers in
+ 
+
+ align:start position:0%
+the negative values of those numbers in
+F like only one 2 -2 or something like
+
+ align:start position:0%
+F like only one 2 -2 or something like
+ 
+
+ align:start position:0%
+F like only one 2 -2 or something like
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+>> Yeah. Yeah. So the comment is maybe I
+
+ align:start position:0%
+>> Yeah. Yeah. So the comment is maybe I
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. So the comment is maybe I
+should have some numbers and negative of
+
+ align:start position:0%
+should have some numbers and negative of
+ 
+
+ align:start position:0%
+should have some numbers and negative of
+those numbers. Let me ask you a more
+
+ align:start position:0%
+those numbers. Let me ask you a more
+ 
+
+ align:start position:0%
+those numbers. Let me ask you a more
+precise question. So you have to choose
+
+ align:start position:0%
+precise question. So you have to choose
+ 
+
+ align:start position:0%
+precise question. So you have to choose
+L numbers in FP and you want to choose
+
+ align:start position:0%
+L numbers in FP and you want to choose
+ 
+
+ align:start position:0%
+L numbers in FP and you want to choose
+them to make A plus A as small as
+
+ align:start position:0%
+them to make A plus A as small as
+ 
+
+ align:start position:0%
+them to make A plus A as small as
+possible. Who would you choose?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+>> Yeah, you could choose an arithmetic
+
+ align:start position:0%
+>> Yeah, you could choose an arithmetic
+ 
+
+ align:start position:0%
+>> Yeah, you could choose an arithmetic
+progression.
+
+ align:start position:0%
+progression.
+ 
+
+ align:start position:0%
+progression.
+So example one.
+
+ align:start position:0%
+So example one.
+ 
+
+ align:start position:0%
+So example one.
+Um suppose A was just the numbers from
+
+ align:start position:0%
+Um suppose A was just the numbers from
+ 
+
+ align:start position:0%
+Um suppose A was just the numbers from
+one up to L.
+
+ align:start position:0%
+one up to L.
+ 
+
+ align:start position:0%
+one up to L.
+So a plus a will be the numbers from 2
+
+ align:start position:0%
+So a plus a will be the numbers from 2
+ 
+
+ align:start position:0%
+So a plus a will be the numbers from 2
+to 2 l. Uh so a + a is at most 2 * a.
+
+ align:start position:0%
+to 2 l. Uh so a + a is at most 2 * a.
+ 
+
+ align:start position:0%
+to 2 l. Uh so a + a is at most 2 * a.
+It's tiniest bit less than that but not
+
+ align:start position:0%
+It's tiniest bit less than that but not
+ 
+
+ align:start position:0%
+It's tiniest bit less than that but not
+very important for our discussion. And
+
+ align:start position:0%
+very important for our discussion. And
+ 
+
+ align:start position:0%
+very important for our discussion. And
+this is the small this is the the
+
+ align:start position:0%
+this is the small this is the the
+ 
+
+ align:start position:0%
+this is the small this is the the
+smallest that a plus a could possibly
+
+ align:start position:0%
+smallest that a plus a could possibly
+ 
+
+ align:start position:0%
+smallest that a plus a could possibly
+be.
+
+ align:start position:0%
+be.
+ 
+
+ align:start position:0%
+be.
+Okay. And it doesn't have to be one up
+
+ align:start position:0%
+Okay. And it doesn't have to be one up
+ 
+
+ align:start position:0%
+Okay. And it doesn't have to be one up
+to l. It would work just as well if it
+
+ align:start position:0%
+to l. It would work just as well if it
+ 
+
+ align:start position:0%
+to l. It would work just as well if it
+was an arithmetic progression. So
+
+ align:start position:0%
+was an arithmetic progression. So
+ 
+
+ align:start position:0%
+was an arithmetic progression. So
+example one prime
+
+ align:start position:0%
+example one prime
+ 
+
+ align:start position:0%
+example one prime
+our set A is little a + n d where n goes
+
+ align:start position:0%
+our set A is little a + n d where n goes
+ 
+
+ align:start position:0%
+our set A is little a + n d where n goes
+from one up to l.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and then if you think about it a
+
+ align:start position:0%
+Um and then if you think about it a
+ 
+
+ align:start position:0%
+Um and then if you think about it a
+little bit the size of the subset
+
+ align:start position:0%
+little bit the size of the subset
+ 
+
+ align:start position:0%
+little bit the size of the subset
+behaves just the same.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+there's another example that's a little
+
+ align:start position:0%
+there's another example that's a little
+ 
+
+ align:start position:0%
+there's another example that's a little
+bit more general than this. So this is
+
+ align:start position:0%
+bit more general than this. So this is
+ 
+
+ align:start position:0%
+bit more general than this. So this is
+an arithmetic progression where you have
+
+ align:start position:0%
+an arithmetic progression where you have
+ 
+
+ align:start position:0%
+an arithmetic progression where you have
+just one kind of difference.
+
+ align:start position:0%
+just one kind of difference.
+ 
+
+ align:start position:0%
+just one kind of difference.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+and you could have something uh
+
+ align:start position:0%
+and you could have something uh
+ 
+
+ align:start position:0%
+and you could have something uh
+uh so you should you could visualize it
+
+ align:start position:0%
+uh so you should you could visualize it
+ 
+
+ align:start position:0%
+uh so you should you could visualize it
+like this.
+
+ align:start position:0%
+like this.
+ 
+
+ align:start position:0%
+like this.
+And you could have a similar thing
+
+ align:start position:0%
+And you could have a similar thing
+ 
+
+ align:start position:0%
+And you could have a similar thing
+involving a two-dimensional grid or a
+
+ align:start position:0%
+involving a two-dimensional grid or a
+ 
+
+ align:start position:0%
+involving a two-dimensional grid or a
+higher dimensional grid.
+
+ align:start position:0%
+higher dimensional grid.
+ 
+
+ align:start position:0%
+higher dimensional grid.
+All right. So example two is that a is a
+
+ align:start position:0%
+All right. So example two is that a is a
+ 
+
+ align:start position:0%
+All right. So example two is that a is a
++ n1 d1 plus dot dot dot plus n r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where um n i goes from one up to l i.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what happens when you take a plus a?
+
+ align:start position:0%
+So what happens when you take a plus a?
+ 
+
+ align:start position:0%
+So what happens when you take a plus a?
+It is contained in two little a plus n1
+
+ align:start position:0%
+It is contained in two little a plus n1
+ 
+
+ align:start position:0%
+It is contained in two little a plus n1
+d1 plus dot dot dot plus nr
+
+ align:start position:0%
+d1 plus dot dot dot plus nr
+ 
+
+ align:start position:0%
+d1 plus dot dot dot plus nr
+where now the n i go in between two and
+
+ align:start position:0%
+where now the n i go in between two and
+ 
+
+ align:start position:0%
+where now the n i go in between two and
+2 li.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so we see from this and I well which
+
+ align:start position:0%
+And so we see from this and I well which
+ 
+
+ align:start position:0%
+And so we see from this and I well which
+so it which is contained in I could put
+
+ align:start position:0%
+so it which is contained in I could put
+ 
+
+ align:start position:0%
+so it which is contained in I could put
+a one um so it's contained in something
+
+ align:start position:0%
+a one um so it's contained in something
+ 
+
+ align:start position:0%
+a one um so it's contained in something
+that is 2 to the r * bigger. So we get a
+
+ align:start position:0%
+that is 2 to the r * bigger. So we get a
+ 
+
+ align:start position:0%
+that is 2 to the r * bigger. So we get a
++ a is bounded by 2 to the r * a.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this thing here is called a
+
+ align:start position:0%
+So this thing here is called a
+ 
+
+ align:start position:0%
+So this thing here is called a
+generalized arithmetic progression. It
+
+ align:start position:0%
+generalized arithmetic progression. It
+ 
+
+ align:start position:0%
+generalized arithmetic progression. It
+has a dimension little r and it has a
+
+ align:start position:0%
+has a dimension little r and it has a
+ 
+
+ align:start position:0%
+has a dimension little r and it has a
+volume or cardality which is
+
+ align:start position:0%
+volume or cardality which is
+ 
+
+ align:start position:0%
+volume or cardality which is
+L1 to LR.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+can anybody think of any others?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it is hard to think of other ones and
+
+ align:start position:0%
+So it is hard to think of other ones and
+ 
+
+ align:start position:0%
+So it is hard to think of other ones and
+in some sense and and depending on how
+
+ align:start position:0%
+in some sense and and depending on how
+ 
+
+ align:start position:0%
+in some sense and and depending on how
+we quantify it a little bit um these
+
+ align:start position:0%
+we quantify it a little bit um these
+ 
+
+ align:start position:0%
+we quantify it a little bit um these
+sets or maybe these sets and their close
+
+ align:start position:0%
+sets or maybe these sets and their close
+ 
+
+ align:start position:0%
+sets or maybe these sets and their close
+cousins appear to be the only sets that
+
+ align:start position:0%
+cousins appear to be the only sets that
+ 
+
+ align:start position:0%
+cousins appear to be the only sets that
+have a really small subset
+
+ align:start position:0%
+have a really small subset
+ 
+
+ align:start position:0%
+have a really small subset
+and um this was investigated by framan
+
+ align:start position:0%
+and um this was investigated by framan
+ 
+
+ align:start position:0%
+and um this was investigated by framan
+starting in the 60s and 70s and he
+
+ align:start position:0%
+starting in the 60s and 70s and he
+ 
+
+ align:start position:0%
+starting in the 60s and 70s and he
+proved a theorem to that effect called
+
+ align:start position:0%
+proved a theorem to that effect called
+ 
+
+ align:start position:0%
+proved a theorem to that effect called
+framan's theorem Um
+
+ align:start position:0%
+framan's theorem Um
+ 
+
+ align:start position:0%
+framan's theorem Um
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+uh and this was this is a a cornerstone
+
+ align:start position:0%
+uh and this was this is a a cornerstone
+ 
+
+ align:start position:0%
+uh and this was this is a a cornerstone
+of additive combinatorics.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um Framan's
+
+ align:start position:0%
+Um Framan's
+ 
+
+ align:start position:0%
+Um Framan's
+Framan's proof was was somewhat
+
+ align:start position:0%
+Framan's proof was was somewhat
+ 
+
+ align:start position:0%
+Framan's proof was was somewhat
+difficult to read and Rusa thought a lot
+
+ align:start position:0%
+difficult to read and Rusa thought a lot
+ 
+
+ align:start position:0%
+difficult to read and Rusa thought a lot
+about it and clarified it and so this is
+
+ align:start position:0%
+about it and clarified it and so this is
+ 
+
+ align:start position:0%
+about it and clarified it and so this is
+now called uh the Framan Rousa theory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So it says the following thing.
+
+ align:start position:0%
+Okay. So it says the following thing.
+ 
+
+ align:start position:0%
+Okay. So it says the following thing.
+Says that if a
+
+ align:start position:0%
+Says that if a
+ 
+
+ align:start position:0%
+Says that if a
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if a is in z the same thing would be
+
+ align:start position:0%
+so if a is in z the same thing would be
+ 
+
+ align:start position:0%
+so if a is in z the same thing would be
+true in z mod p and a + a is less than
+
+ align:start position:0%
+true in z mod p and a + a is less than
+ 
+
+ align:start position:0%
+true in z mod p and a + a is less than
+or equal to k a.
+
+ align:start position:0%
+or equal to k a.
+ 
+
+ align:start position:0%
+or equal to k a.
+Um then
+
+ align:start position:0%
+Um then
+ 
+
+ align:start position:0%
+Um then
+a is contained in a gap
+
+ align:start position:0%
+a is contained in a gap
+ 
+
+ align:start position:0%
+a is contained in a gap
+with dimension
+
+ align:start position:0%
+with dimension
+ 
+
+ align:start position:0%
+with dimension
+uh little r that only depends on k and
+
+ align:start position:0%
+uh little r that only depends on k and
+ 
+
+ align:start position:0%
+uh little r that only depends on k and
+volume at most uh v that only depends on
+
+ align:start position:0%
+volume at most uh v that only depends on
+ 
+
+ align:start position:0%
+volume at most uh v that only depends on
+k times the size of a.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it roughly says that if a plus a is
+
+ align:start position:0%
+So it roughly says that if a plus a is
+ 
+
+ align:start position:0%
+So it roughly says that if a plus a is
+small it is because a resembles example
+
+ align:start position:0%
+small it is because a resembles example
+ 
+
+ align:start position:0%
+small it is because a resembles example
+two which is a generalization of example
+
+ align:start position:0%
+two which is a generalization of example
+ 
+
+ align:start position:0%
+two which is a generalization of example
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+So in some sense these are the only sets
+
+ align:start position:0%
+So in some sense these are the only sets
+ 
+
+ align:start position:0%
+So in some sense these are the only sets
+that have a really small subset.
+
+ align:start position:0%
+that have a really small subset.
+ 
+
+ align:start position:0%
+that have a really small subset.
+Okay. So this is an important theorem in
+
+ align:start position:0%
+Okay. So this is an important theorem in
+ 
+
+ align:start position:0%
+Okay. So this is an important theorem in
+additive combinotaurics but there are
+
+ align:start position:0%
+additive combinotaurics but there are
+ 
+
+ align:start position:0%
+additive combinotaurics but there are
+two caveats about it. So one caveat is
+
+ align:start position:0%
+two caveats about it. So one caveat is
+ 
+
+ align:start position:0%
+two caveats about it. So one caveat is
+that it's a it's a pretty deep theorem.
+
+ align:start position:0%
+that it's a it's a pretty deep theorem.
+ 
+
+ align:start position:0%
+that it's a it's a pretty deep theorem.
+The proof is substantial
+
+ align:start position:0%
+The proof is substantial
+ 
+
+ align:start position:0%
+The proof is substantial
+and the other caveat is that the
+
+ align:start position:0%
+and the other caveat is that the
+ 
+
+ align:start position:0%
+and the other caveat is that the
+quantitative bounds are weak.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so in the original version
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r of k was quite large. So r of k was
+
+ align:start position:0%
+r of k was quite large. So r of k was
+ 
+
+ align:start position:0%
+r of k was quite large. So r of k was
+something like x of k to a power and v
+
+ align:start position:0%
+something like x of k to a power and v
+ 
+
+ align:start position:0%
+something like x of k to a power and v
+of k was even larger. It's like x of x
+
+ align:start position:0%
+of k was even larger. It's like x of x
+ 
+
+ align:start position:0%
+of k was even larger. It's like x of x
+of k to a power.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um now
+
+ align:start position:0%
+Okay. Um now
+ 
+
+ align:start position:0%
+Okay. Um now
+it is a trivial fact that any set A is
+
+ align:start position:0%
+it is a trivial fact that any set A is
+ 
+
+ align:start position:0%
+it is a trivial fact that any set A is
+contained in a generalized arithmetic
+
+ align:start position:0%
+contained in a generalized arithmetic
+ 
+
+ align:start position:0%
+contained in a generalized arithmetic
+progression of dimension equal to the
+
+ align:start position:0%
+progression of dimension equal to the
+ 
+
+ align:start position:0%
+progression of dimension equal to the
+size of A.
+
+ align:start position:0%
+size of A.
+ 
+
+ align:start position:0%
+size of A.
+So this is only interesting if R of K is
+
+ align:start position:0%
+So this is only interesting if R of K is
+ 
+
+ align:start position:0%
+So this is only interesting if R of K is
+smaller than the size of A.
+
+ align:start position:0%
+smaller than the size of A.
+ 
+
+ align:start position:0%
+smaller than the size of A.
+Um so this was only interesting
+
+ align:start position:0%
+Um so this was only interesting
+ 
+
+ align:start position:0%
+Um so this was only interesting
+only meaningful let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if k was quite small.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh there's a big in um goal in additive
+
+ align:start position:0%
+Uh there's a big in um goal in additive
+ 
+
+ align:start position:0%
+Uh there's a big in um goal in additive
+combinatorics to improve the
+
+ align:start position:0%
+combinatorics to improve the
+ 
+
+ align:start position:0%
+combinatorics to improve the
+quantitative bounds in framan's theorem
+
+ align:start position:0%
+quantitative bounds in framan's theorem
+ 
+
+ align:start position:0%
+quantitative bounds in framan's theorem
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+one benchmark is a conjecture called the
+
+ align:start position:0%
+one benchmark is a conjecture called the
+ 
+
+ align:start position:0%
+one benchmark is a conjecture called the
+polomial frame and roua conjecture which
+
+ align:start position:0%
+polomial frame and roua conjecture which
+ 
+
+ align:start position:0%
+polomial frame and roua conjecture which
+would say something meaningful even if k
+
+ align:start position:0%
+would say something meaningful even if k
+ 
+
+ align:start position:0%
+would say something meaningful even if k
+was a small power of a. So there's a
+
+ align:start position:0%
+was a small power of a. So there's a
+ 
+
+ align:start position:0%
+was a small power of a. So there's a
+conjecture that they would have a
+
+ align:start position:0%
+conjecture that they would have a
+ 
+
+ align:start position:0%
+conjecture that they would have a
+meaningful bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if k is a to the delta
+
+ align:start position:0%
+if k is a to the delta
+ 
+
+ align:start position:0%
+if k is a to the delta
+for some small but universal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta bigger than zero.
+
+ align:start position:0%
+delta bigger than zero.
+ 
+
+ align:start position:0%
+delta bigger than zero.
+Okay. And this is still an open
+
+ align:start position:0%
+Okay. And this is still an open
+ 
+
+ align:start position:0%
+Okay. And this is still an open
+conjecture. So it's out of range maybe
+
+ align:start position:0%
+conjecture. So it's out of range maybe
+ 
+
+ align:start position:0%
+conjecture. So it's out of range maybe
+only a little out of range of of uh
+
+ align:start position:0%
+only a little out of range of of uh
+ 
+
+ align:start position:0%
+only a little out of range of of uh
+current techniques. Um but if k was say
+
+ align:start position:0%
+current techniques. Um but if k was say
+ 
+
+ align:start position:0%
+current techniques. Um but if k was say
+I don't know a to the 0.1
+
+ align:start position:0%
+I don't know a to the 0.1
+ 
+
+ align:start position:0%
+I don't know a to the 0.1
+all this stuff about about framan's
+
+ align:start position:0%
+all this stuff about about framan's
+ 
+
+ align:start position:0%
+all this stuff about about framan's
+theorem uh we we are very far from being
+
+ align:start position:0%
+theorem uh we we are very far from being
+ 
+
+ align:start position:0%
+theorem uh we we are very far from being
+able to to deal with that.
+
+ align:start position:0%
+able to to deal with that.
+ 
+
+ align:start position:0%
+able to to deal with that.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+now if you look at framan's theorem what
+
+ align:start position:0%
+now if you look at framan's theorem what
+ 
+
+ align:start position:0%
+now if you look at framan's theorem what
+we're trying to do is to give a complete
+
+ align:start position:0%
+we're trying to do is to give a complete
+ 
+
+ align:start position:0%
+we're trying to do is to give a complete
+classification of all the sets A that do
+
+ align:start position:0%
+classification of all the sets A that do
+ 
+
+ align:start position:0%
+classification of all the sets A that do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and the complete classification is
+
+ align:start position:0%
+and the complete classification is
+ 
+
+ align:start position:0%
+and the complete classification is
+something we only understand if K is
+
+ align:start position:0%
+something we only understand if K is
+ 
+
+ align:start position:0%
+something we only understand if K is
+really really small.
+
+ align:start position:0%
+really really small.
+ 
+
+ align:start position:0%
+really really small.
+But you could also ask for something
+
+ align:start position:0%
+But you could also ask for something
+ 
+
+ align:start position:0%
+But you could also ask for something
+which is not as strong as a complete
+
+ align:start position:0%
+which is not as strong as a complete
+ 
+
+ align:start position:0%
+which is not as strong as a complete
+classification but just some kind of
+
+ align:start position:0%
+classification but just some kind of
+ 
+
+ align:start position:0%
+classification but just some kind of
+interesting information about sets A
+
+ align:start position:0%
+interesting information about sets A
+ 
+
+ align:start position:0%
+interesting information about sets A
+with small subset.
+
+ align:start position:0%
+with small subset.
+ 
+
+ align:start position:0%
+with small subset.
+Um okay
+
+ align:start position:0%
+Um okay
+ 
+
+ align:start position:0%
+Um okay
+so if you look at this example you'll
+
+ align:start position:0%
+so if you look at this example you'll
+ 
+
+ align:start position:0%
+so if you look at this example you'll
+notice that not only it has small subset
+
+ align:start position:0%
+notice that not only it has small subset
+ 
+
+ align:start position:0%
+notice that not only it has small subset
+but it has uh also small a bunch of
+
+ align:start position:0%
+but it has uh also small a bunch of
+ 
+
+ align:start position:0%
+but it has uh also small a bunch of
+other stuff like in these examples a
+
+ align:start position:0%
+other stuff like in these examples a
+ 
+
+ align:start position:0%
+other stuff like in these examples a
+plus a is small also a minus a is small
+
+ align:start position:0%
+plus a is small also a minus a is small
+ 
+
+ align:start position:0%
+plus a is small also a minus a is small
+also a plus a plus a is small
+
+ align:start position:0%
+also a plus a plus a is small
+ 
+
+ align:start position:0%
+also a plus a plus a is small
+um and and and those so those for those
+
+ align:start position:0%
+um and and and those so those for those
+ 
+
+ align:start position:0%
+um and and and those so those for those
+things we have much simpler proofs and
+
+ align:start position:0%
+things we have much simpler proofs and
+ 
+
+ align:start position:0%
+things we have much simpler proofs and
+the quantitative bound s are much better
+
+ align:start position:0%
+the quantitative bound s are much better
+ 
+
+ align:start position:0%
+the quantitative bound s are much better
+and they come from some lemmas that I
+
+ align:start position:0%
+and they come from some lemmas that I
+ 
+
+ align:start position:0%
+and they come from some lemmas that I
+think originally were designed as uh
+
+ align:start position:0%
+think originally were designed as uh
+ 
+
+ align:start position:0%
+think originally were designed as uh
+lemmas for this theorem but which have
+
+ align:start position:0%
+lemmas for this theorem but which have
+ 
+
+ align:start position:0%
+lemmas for this theorem but which have
+lots of independent applications.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this theorem we I don't plan to prove
+
+ align:start position:0%
+So this theorem we I don't plan to prove
+ 
+
+ align:start position:0%
+So this theorem we I don't plan to prove
+in the class but I wanted to mention it
+
+ align:start position:0%
+in the class but I wanted to mention it
+ 
+
+ align:start position:0%
+in the class but I wanted to mention it
+for historical context and and these
+
+ align:start position:0%
+for historical context and and these
+ 
+
+ align:start position:0%
+for historical context and and these
+lemmas are are really important and have
+
+ align:start position:0%
+lemmas are are really important and have
+ 
+
+ align:start position:0%
+lemmas are are really important and have
+reasonable short proofs and I think are
+
+ align:start position:0%
+reasonable short proofs and I think are
+ 
+
+ align:start position:0%
+reasonable short proofs and I think are
+worth for a wide range of people uh
+
+ align:start position:0%
+worth for a wide range of people uh
+ 
+
+ align:start position:0%
+worth for a wide range of people uh
+knowing about.
+
+ align:start position:0%
+knowing about.
+ 
+
+ align:start position:0%
+knowing about.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first of the lemas is called the
+
+ align:start position:0%
+so the first of the lemas is called the
+ 
+
+ align:start position:0%
+so the first of the lemas is called the
+rusa triangle inequality.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so it says if Z is an Aelian group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and A and B and C are subsets of Z,
+
+ align:start position:0%
+and A and B and C are subsets of Z,
+ 
+
+ align:start position:0%
+and A and B and C are subsets of Z,
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+size of A times the size of B minus C is
+
+ align:start position:0%
+size of A times the size of B minus C is
+ 
+
+ align:start position:0%
+size of A times the size of B minus C is
+bounded by the size of A minus B times
+
+ align:start position:0%
+bounded by the size of A minus B times
+ 
+
+ align:start position:0%
+bounded by the size of A minus B times
+the size of A minus C.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this might uh take a little
+
+ align:start position:0%
+Okay, so this might uh take a little
+ 
+
+ align:start position:0%
+Okay, so this might uh take a little
+digesting. Have all of these letters
+
+ align:start position:0%
+digesting. Have all of these letters
+ 
+
+ align:start position:0%
+digesting. Have all of these letters
+feels a little bit like alphabet soup.
+
+ align:start position:0%
+feels a little bit like alphabet soup.
+ 
+
+ align:start position:0%
+feels a little bit like alphabet soup.
+Um the fact that we have can put three
+
+ align:start position:0%
+Um the fact that we have can put three
+ 
+
+ align:start position:0%
+Um the fact that we have can put three
+different sets
+
+ align:start position:0%
+different sets
+ 
+
+ align:start position:0%
+different sets
+makes it a little harder to digest but
+
+ align:start position:0%
+makes it a little harder to digest but
+ 
+
+ align:start position:0%
+makes it a little harder to digest but
+it you know of course it makes it more
+
+ align:start position:0%
+it you know of course it makes it more
+ 
+
+ align:start position:0%
+it you know of course it makes it more
+flexible in general and by plugging in
+
+ align:start position:0%
+flexible in general and by plugging in
+ 
+
+ align:start position:0%
+flexible in general and by plugging in
+different choices for these three sets
+
+ align:start position:0%
+different choices for these three sets
+ 
+
+ align:start position:0%
+different choices for these three sets
+you can prove some simpler things. Let
+
+ align:start position:0%
+you can prove some simpler things. Let
+ 
+
+ align:start position:0%
+you can prove some simpler things. Let
+me illustrate this with an example.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+As a correlator of this we will see
+
+ align:start position:0%
+As a correlator of this we will see
+ 
+
+ align:start position:0%
+As a correlator of this we will see
+that if the if the sum set is small then
+
+ align:start position:0%
+that if the if the sum set is small then
+ 
+
+ align:start position:0%
+that if the if the sum set is small then
+the difference set is also small.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So correlary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if a + a is smaller than k * a
+
+ align:start position:0%
+if a + a is smaller than k * a
+ 
+
+ align:start position:0%
+if a + a is smaller than k * a
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+a minus a is smaller than k^ 2
+
+ align:start position:0%
+a minus a is smaller than k^ 2
+ 
+
+ align:start position:0%
+a minus a is smaller than k^ 2
+k^ 2 * a.
+
+ align:start position:0%
+k^ 2 * a.
+ 
+
+ align:start position:0%
+k^ 2 * a.
+So this lema is meaningful as long as k
+
+ align:start position:0%
+So this lema is meaningful as long as k
+ 
+
+ align:start position:0%
+So this lema is meaningful as long as k
+is slightly smaller than the square root
+
+ align:start position:0%
+is slightly smaller than the square root
+ 
+
+ align:start position:0%
+is slightly smaller than the square root
+of a.
+
+ align:start position:0%
+of a.
+ 
+
+ align:start position:0%
+of a.
+So in a in a much wider range than than
+
+ align:start position:0%
+So in a in a much wider range than than
+ 
+
+ align:start position:0%
+So in a in a much wider range than than
+the um uh frame and rusa theorem this is
+
+ align:start position:0%
+the um uh frame and rusa theorem this is
+ 
+
+ align:start position:0%
+the um uh frame and rusa theorem this is
+a meaningful statement.
+
+ align:start position:0%
+a meaningful statement.
+ 
+
+ align:start position:0%
+a meaningful statement.
+Okay. So proof um we're just going to
+
+ align:start position:0%
+Okay. So proof um we're just going to
+ 
+
+ align:start position:0%
+Okay. So proof um we're just going to
+use roua and I have to tell you who are
+
+ align:start position:0%
+use roua and I have to tell you who are
+ 
+
+ align:start position:0%
+use roua and I have to tell you who are
+a and b and c. So A will be A and then I
+
+ align:start position:0%
+a and b and c. So A will be A and then I
+ 
+
+ align:start position:0%
+a and b and c. So A will be A and then I
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah B and C are both negative A.
+
+ align:start position:0%
+yeah B and C are both negative A.
+ 
+
+ align:start position:0%
+yeah B and C are both negative A.
+Okay. So if you look at B minus C that's
+
+ align:start position:0%
+Okay. So if you look at B minus C that's
+ 
+
+ align:start position:0%
+Okay. So if you look at B minus C that's
+there's a lot of minus signs. This is a
+
+ align:start position:0%
+there's a lot of minus signs. This is a
+ 
+
+ align:start position:0%
+there's a lot of minus signs. This is a
+little bit silly looking.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+so that's just a minus a.
+
+ align:start position:0%
+so that's just a minus a.
+ 
+
+ align:start position:0%
+so that's just a minus a.
+Okay. And a minus b or a minus c.
+
+ align:start position:0%
+Okay. And a minus b or a minus c.
+ 
+
+ align:start position:0%
+Okay. And a minus b or a minus c.
+They're the same as each other because b
+
+ align:start position:0%
+They're the same as each other because b
+ 
+
+ align:start position:0%
+They're the same as each other because b
+is the same as c. That's a minus a. So
+
+ align:start position:0%
+is the same as c. That's a minus a. So
+ 
+
+ align:start position:0%
+is the same as c. That's a minus a. So
+that's a plus.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now if we just plug in ra it
+
+ align:start position:0%
+Okay. So now if we just plug in ra it
+ 
+
+ align:start position:0%
+Okay. So now if we just plug in ra it
+says a * this guy a minus a is less than
+
+ align:start position:0%
+says a * this guy a minus a is less than
+ 
+
+ align:start position:0%
+says a * this guy a minus a is less than
+this guy times this guy that's a + a 2.
+
+ align:start position:0%
+this guy times this guy that's a + a 2.
+ 
+
+ align:start position:0%
+this guy times this guy that's a + a 2.
+And by hypothesis that's smaller than k
+
+ align:start position:0%
+And by hypothesis that's smaller than k
+ 
+
+ align:start position:0%
+And by hypothesis that's smaller than k
+2 a 2.
+
+ align:start position:0%
+2 a 2.
+ 
+
+ align:start position:0%
+2 a 2.
+And if you cancel the factor of a that's
+
+ align:start position:0%
+And if you cancel the factor of a that's
+ 
+
+ align:start position:0%
+And if you cancel the factor of a that's
+it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And this has a a very simple proof
+
+ align:start position:0%
+Okay. And this has a a very simple proof
+ 
+
+ align:start position:0%
+Okay. And this has a a very simple proof
+that will fit on this board and which is
+
+ align:start position:0%
+that will fit on this board and which is
+ 
+
+ align:start position:0%
+that will fit on this board and which is
+already says something interesting and
+
+ align:start position:0%
+already says something interesting and
+ 
+
+ align:start position:0%
+already says something interesting and
+non-trivial about how sums and
+
+ align:start position:0%
+non-trivial about how sums and
+ 
+
+ align:start position:0%
+non-trivial about how sums and
+differences and stuff fit together. So
+
+ align:start position:0%
+differences and stuff fit together. So
+ 
+
+ align:start position:0%
+differences and stuff fit together. So
+here's the proof. uh we will construct
+
+ align:start position:0%
+here's the proof. uh we will construct
+ 
+
+ align:start position:0%
+here's the proof. uh we will construct
+a map fee that goes from a cross b minus
+
+ align:start position:0%
+a map fee that goes from a cross b minus
+ 
+
+ align:start position:0%
+a map fee that goes from a cross b minus
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+into a minus b cross a minus c which is
+
+ align:start position:0%
+into a minus b cross a minus c which is
+ 
+
+ align:start position:0%
+into a minus b cross a minus c which is
+injective.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is the cardality of this set and
+
+ align:start position:0%
+So this is the cardality of this set and
+ 
+
+ align:start position:0%
+So this is the cardality of this set and
+this is the cardality of that set. And
+
+ align:start position:0%
+this is the cardality of that set. And
+ 
+
+ align:start position:0%
+this is the cardality of that set. And
+the reason that that this set is bigger
+
+ align:start position:0%
+the reason that that this set is bigger
+ 
+
+ align:start position:0%
+the reason that that this set is bigger
+than that set is that we have an
+
+ align:start position:0%
+than that set is that we have an
+ 
+
+ align:start position:0%
+than that set is that we have an
+injection from one into the other.
+
+ align:start position:0%
+injection from one into the other.
+ 
+
+ align:start position:0%
+injection from one into the other.
+How does the injection work?
+
+ align:start position:0%
+How does the injection work?
+ 
+
+ align:start position:0%
+How does the injection work?
+For every D in B minus C, we can choose.
+
+ align:start position:0%
+For every D in B minus C, we can choose.
+ 
+
+ align:start position:0%
+For every D in B minus C, we can choose.
+So by definition, this D can be written
+
+ align:start position:0%
+So by definition, this D can be written
+ 
+
+ align:start position:0%
+So by definition, this D can be written
+as somebody in B minus somebody in C.
+
+ align:start position:0%
+as somebody in B minus somebody in C.
+ 
+
+ align:start position:0%
+as somebody in B minus somebody in C.
+Let's pick them. We choose B of D and B.
+
+ align:start position:0%
+Let's pick them. We choose B of D and B.
+ 
+
+ align:start position:0%
+Let's pick them. We choose B of D and B.
+C of D C so that D is B of D minus C of
+
+ align:start position:0%
+C of D C so that D is B of D minus C of
+ 
+
+ align:start position:0%
+C of D C so that D is B of D minus C of
+D.
+
+ align:start position:0%
+D.
+ 
+
+ align:start position:0%
+D.
+Okay. Now what's our map?
+
+ align:start position:0%
+Okay. Now what's our map?
+ 
+
+ align:start position:0%
+Okay. Now what's our map?
+V takes an A and a D. A lives here and D
+
+ align:start position:0%
+V takes an A and a D. A lives here and D
+ 
+
+ align:start position:0%
+V takes an A and a D. A lives here and D
+lives there. We need to output somebody
+
+ align:start position:0%
+lives there. We need to output somebody
+ 
+
+ align:start position:0%
+lives there. We need to output somebody
+in A minus B. So we take A minus B of D
+
+ align:start position:0%
+in A minus B. So we take A minus B of D
+ 
+
+ align:start position:0%
+in A minus B. So we take A minus B of D
+and then A minus C of D.
+
+ align:start position:0%
+and then A minus C of D.
+ 
+
+ align:start position:0%
+and then A minus C of D.
+So that is a map from here to here.
+
+ align:start position:0%
+So that is a map from here to here.
+ 
+
+ align:start position:0%
+So that is a map from here to here.
+Why is it injective?
+
+ align:start position:0%
+Why is it injective?
+ 
+
+ align:start position:0%
+Why is it injective?
+So to to check that it's injective.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we're going to suppose
+
+ align:start position:0%
+So we're going to suppose
+ 
+
+ align:start position:0%
+So we're going to suppose
+that v of a d is given to us. It's xy.
+
+ align:start position:0%
+that v of a d is given to us. It's xy.
+ 
+
+ align:start position:0%
+that v of a d is given to us. It's xy.
+And then we're going to find
+
+ align:start position:0%
+And then we're going to find
+ 
+
+ align:start position:0%
+And then we're going to find
+A and D from X and Y
+
+ align:start position:0%
+A and D from X and Y
+ 
+
+ align:start position:0%
+A and D from X and Y
+and from this choice.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the choice we made once and for all,
+
+ align:start position:0%
+So the choice we made once and for all,
+ 
+
+ align:start position:0%
+So the choice we made once and for all,
+we used it to build the map. And now we
+
+ align:start position:0%
+we used it to build the map. And now we
+ 
+
+ align:start position:0%
+we used it to build the map. And now we
+have to prove that there's only one A
+
+ align:start position:0%
+have to prove that there's only one A
+ 
+
+ align:start position:0%
+have to prove that there's only one A
+and D that give a certain X and Y here.
+
+ align:start position:0%
+and D that give a certain X and Y here.
+ 
+
+ align:start position:0%
+and D that give a certain X and Y here.
+Okay. So how do we recover them? Well,
+
+ align:start position:0%
+Okay. So how do we recover them? Well,
+ 
+
+ align:start position:0%
+Okay. So how do we recover them? Well,
+if you if this is X and this is Y, we
+
+ align:start position:0%
+if you if this is X and this is Y, we
+ 
+
+ align:start position:0%
+if you if this is X and this is Y, we
+see that Y - X is B of D minus C of D,
+
+ align:start position:0%
+see that Y - X is B of D minus C of D,
+ 
+
+ align:start position:0%
+see that Y - X is B of D minus C of D,
+which is D. So that's how we find D.
+
+ align:start position:0%
+which is D. So that's how we find D.
+ 
+
+ align:start position:0%
+which is D. So that's how we find D.
+And once we find D, it's easy to find we
+
+ align:start position:0%
+And once we find D, it's easy to find we
+ 
+
+ align:start position:0%
+And once we find D, it's easy to find we
+once we find D, then we know B of D and
+
+ align:start position:0%
+once we find D, then we know B of D and
+ 
+
+ align:start position:0%
+once we find D, then we know B of D and
+C of D. And now it's easy to find A. Um,
+
+ align:start position:0%
+C of D. And now it's easy to find A. Um,
+ 
+
+ align:start position:0%
+C of D. And now it's easy to find A. Um,
+so uh X uh minus X plus B of D is A.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's very short. It feels a teeny bit
+
+ align:start position:0%
+It's very short. It feels a teeny bit
+ 
+
+ align:start position:0%
+It's very short. It feels a teeny bit
+like a magic trick to me.
+
+ align:start position:0%
+like a magic trick to me.
+ 
+
+ align:start position:0%
+like a magic trick to me.
+But so on this board and this board we
+
+ align:start position:0%
+But so on this board and this board we
+ 
+
+ align:start position:0%
+But so on this board and this board we
+have seen that if the sum set is small
+
+ align:start position:0%
+have seen that if the sum set is small
+ 
+
+ align:start position:0%
+have seen that if the sum set is small
+then the difference set is also small.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+uh you
+
+ align:start position:0%
+uh you
+ 
+
+ align:start position:0%
+uh you
+like divide
+
+ align:start position:0%
+like divide
+ 
+
+ align:start position:0%
+like divide
+by *
+
+ align:start position:0%
+by *
+ 
+
+ align:start position:0%
+by *
+you get like something that looks
+
+ align:start position:0%
+you get like something that looks
+ 
+
+ align:start position:0%
+you get like something that looks
+exactly like a triangle
+
+ align:start position:0%
+exactly like a triangle
+ 
+
+ align:start position:0%
+exactly like a triangle
+way.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. Yeah. Okay. So the question is
+
+ align:start position:0%
+>> Yeah. Yeah. Okay. So the question is
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Okay. So the question is
+it's called Ruse's triangle inequality
+
+ align:start position:0%
+it's called Ruse's triangle inequality
+ 
+
+ align:start position:0%
+it's called Ruse's triangle inequality
+and it sort of looks like if we take the
+
+ align:start position:0%
+and it sort of looks like if we take the
+ 
+
+ align:start position:0%
+and it sort of looks like if we take the
+logarithm and play with this then
+
+ align:start position:0%
+logarithm and play with this then
+ 
+
+ align:start position:0%
+logarithm and play with this then
+something will look like the triangle
+
+ align:start position:0%
+something will look like the triangle
+ 
+
+ align:start position:0%
+something will look like the triangle
+inequality.
+
+ align:start position:0%
+inequality.
+ 
+
+ align:start position:0%
+inequality.
+Um and uh yeah so Russa did have that in
+
+ align:start position:0%
+Um and uh yeah so Russa did have that in
+ 
+
+ align:start position:0%
+Um and uh yeah so Russa did have that in
+mind when he named it that way. So he
+
+ align:start position:0%
+mind when he named it that way. So he
+ 
+
+ align:start position:0%
+mind when he named it that way. So he
+produced a pseudo distance between
+
+ align:start position:0%
+produced a pseudo distance between
+ 
+
+ align:start position:0%
+produced a pseudo distance between
+different sets say you know between A
+
+ align:start position:0%
+different sets say you know between A
+ 
+
+ align:start position:0%
+different sets say you know between A
+and B or B and C or whatever. And this
+
+ align:start position:0%
+and B or B and C or whatever. And this
+ 
+
+ align:start position:0%
+and B or B and C or whatever. And this
+um this translates into saying that the
+
+ align:start position:0%
+um this translates into saying that the
+ 
+
+ align:start position:0%
+um this translates into saying that the
+rud rou pseudo distance obeys the
+
+ align:start position:0%
+rud rou pseudo distance obeys the
+ 
+
+ align:start position:0%
+rud rou pseudo distance obeys the
+triangle inequality. The distance from B
+
+ align:start position:0%
+triangle inequality. The distance from B
+ 
+
+ align:start position:0%
+triangle inequality. The distance from B
+to C is bounded by the distance from A
+
+ align:start position:0%
+to C is bounded by the distance from A
+ 
+
+ align:start position:0%
+to C is bounded by the distance from A
+to B plus the different distance from
+
+ align:start position:0%
+to B plus the different distance from
+ 
+
+ align:start position:0%
+to B plus the different distance from
+from B to A plus the distance from A to
+
+ align:start position:0%
+from B to A plus the distance from A to
+ 
+
+ align:start position:0%
+from B to A plus the distance from A to
+C.
+
+ align:start position:0%
+C.
+ 
+
+ align:start position:0%
+C.
+Um I'm not sure whether that is helpful
+
+ align:start position:0%
+Um I'm not sure whether that is helpful
+ 
+
+ align:start position:0%
+Um I'm not sure whether that is helpful
+or or not. Um it's his pseudo distance
+
+ align:start position:0%
+or or not. Um it's his pseudo distance
+ 
+
+ align:start position:0%
+or or not. Um it's his pseudo distance
+is a little bit funny. Like it's not
+
+ align:start position:0%
+is a little bit funny. Like it's not
+ 
+
+ align:start position:0%
+is a little bit funny. Like it's not
+true that the distance from A to itself
+
+ align:start position:0%
+true that the distance from A to itself
+ 
+
+ align:start position:0%
+true that the distance from A to itself
+is zero. So it's not quite like
+
+ align:start position:0%
+is zero. So it's not quite like
+ 
+
+ align:start position:0%
+is zero. So it's not quite like
+distances that I'm used to. Um so that
+
+ align:start position:0%
+distances that I'm used to. Um so that
+ 
+
+ align:start position:0%
+distances that I'm used to. Um so that
+intuition I don't know may or may not be
+
+ align:start position:0%
+intuition I don't know may or may not be
+ 
+
+ align:start position:0%
+intuition I don't know may or may not be
+helpful.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um I guess we will see tomorrow that
+
+ align:start position:0%
+Um I guess we will see tomorrow that
+ 
+
+ align:start position:0%
+Um I guess we will see tomorrow that
+sometimes you use this many times like
+
+ align:start position:0%
+sometimes you use this many times like
+ 
+
+ align:start position:0%
+sometimes you use this many times like
+how you know how how would you use the
+
+ align:start position:0%
+how you know how how would you use the
+ 
+
+ align:start position:0%
+how you know how how would you use the
+triangle inequality? Well the distance
+
+ align:start position:0%
+triangle inequality? Well the distance
+ 
+
+ align:start position:0%
+triangle inequality? Well the distance
+from A to Z is bounded by the distance
+
+ align:start position:0%
+from A to Z is bounded by the distance
+ 
+
+ align:start position:0%
+from A to Z is bounded by the distance
+from A to B plus the distance from B to
+
+ align:start position:0%
+from A to B plus the distance from B to
+ 
+
+ align:start position:0%
+from A to B plus the distance from B to
+C plus the distance from C to D D D D D
+
+ align:start position:0%
+C plus the distance from C to D D D D D
+ 
+
+ align:start position:0%
+C plus the distance from C to D D D D D
+D D D D D D D D D D D D D D D D D D D D
+
+ align:start position:0%
+D D D D D D D D D D D D D D D D D D D D
+ 
+
+ align:start position:0%
+D D D D D D D D D D D D D D D D D D D D
+D D D D D D D D D D D D D D D D D D D D
+
+ align:start position:0%
+D D D D D D D D D D D D D D D D D D D D
+ 
+
+ align:start position:0%
+D D D D D D D D D D D D D D D D D D D D
+D D D D D D D D D D D D D D D D and
+
+ align:start position:0%
+D D D D D D D D D D D D D D D D and
+ 
+
+ align:start position:0%
+D D D D D D D D D D D D D D D D and
+maybe each of those things is easier to
+
+ align:start position:0%
+maybe each of those things is easier to
+ 
+
+ align:start position:0%
+maybe each of those things is easier to
+understand and by the triangle
+
+ align:start position:0%
+understand and by the triangle
+ 
+
+ align:start position:0%
+understand and by the triangle
+inequality, we can put them together. So
+
+ align:start position:0%
+inequality, we can put them together. So
+ 
+
+ align:start position:0%
+inequality, we can put them together. So
+you can use this inequality in that way.
+
+ align:start position:0%
+you can use this inequality in that way.
+ 
+
+ align:start position:0%
+you can use this inequality in that way.
+Um, and we'll see that tomorrow.
+
+ align:start position:0%
+Um, and we'll see that tomorrow.
+ 
+
+ align:start position:0%
+Um, and we'll see that tomorrow.
+Tomorrow, Thursday.
+
+ align:start position:0%
+Tomorrow, Thursday.
+ 
+
+ align:start position:0%
+Tomorrow, Thursday.
+Any other questions or comments?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Can I ask about the previous removing
+
+ align:start position:0%
+>> Can I ask about the previous removing
+ 
+
+ align:start position:0%
+>> Can I ask about the previous removing
+denominator?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Just not sure how that works out. Does
+
+ align:start position:0%
+Just not sure how that works out. Does
+ 
+
+ align:start position:0%
+Just not sure how that works out. Does
+it require something like this?
+
+ align:start position:0%
+it require something like this?
+ 
+
+ align:start position:0%
+it require something like this?
+Um the question is about the removing
+
+ align:start position:0%
+Um the question is about the removing
+ 
+
+ align:start position:0%
+Um the question is about the removing
+the denominator trick.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Um like when we had we had an a minus a
+
+ align:start position:0%
+>> Um like when we had we had an a minus a
+ 
+
+ align:start position:0%
+>> Um like when we had we had an a minus a
+in the denominator and we multiplied it
+
+ align:start position:0%
+in the denominator and we multiplied it
+ 
+
+ align:start position:0%
+in the denominator and we multiplied it
+out.
+
+ align:start position:0%
+out.
+ 
+
+ align:start position:0%
+out.
+>> So that that was just um
+
+ align:start position:0%
+>> So that that was just um
+ 
+
+ align:start position:0%
+>> So that that was just um
+algebra.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um it's not it's not something fancy
+
+ align:start position:0%
+Um it's not it's not something fancy
+ 
+
+ align:start position:0%
+Um it's not it's not something fancy
+like this.
+
+ align:start position:0%
+like this.
+ 
+
+ align:start position:0%
+like this.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+we'll u yeah let me bracket that we'll
+
+ align:start position:0%
+we'll u yeah let me bracket that we'll
+ 
+
+ align:start position:0%
+we'll u yeah let me bracket that we'll
+see a little later something else with
+
+ align:start position:0%
+see a little later something else with
+ 
+
+ align:start position:0%
+see a little later something else with
+removing denominators and and let's come
+
+ align:start position:0%
+removing denominators and and let's come
+ 
+
+ align:start position:0%
+removing denominators and and let's come
+back to it then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do do you think did I understand your
+
+ align:start position:0%
+do do you think did I understand your
+ 
+
+ align:start position:0%
+do do you think did I understand your
+question or
+
+ align:start position:0%
+question or
+ 
+
+ align:start position:0%
+question or
+>> yeah I'm just not sure how that how how
+
+ align:start position:0%
+>> yeah I'm just not sure how that how how
+ 
+
+ align:start position:0%
+>> yeah I'm just not sure how that how how
+that was actually
+
+ align:start position:0%
+that was actually
+ 
+
+ align:start position:0%
+that was actually
+>> I think you only need six instead of
+
+ align:start position:0%
+>> I think you only need six instead of
+ 
+
+ align:start position:0%
+>> I think you only need six instead of
+eight
+
+ align:start position:0%
+eight
+ 
+
+ align:start position:0%
+eight
+Yeah, let's check in about it at the end
+
+ align:start position:0%
+Yeah, let's check in about it at the end
+ 
+
+ align:start position:0%
+Yeah, let's check in about it at the end
+of class. Okay, the other important um
+
+ align:start position:0%
+of class. Okay, the other important um
+ 
+
+ align:start position:0%
+of class. Okay, the other important um
+lema from from this field that went into
+
+ align:start position:0%
+lema from from this field that went into
+ 
+
+ align:start position:0%
+lema from from this field that went into
+the proof of framan's theorem is called
+
+ align:start position:0%
+the proof of framan's theorem is called
+ 
+
+ align:start position:0%
+the proof of framan's theorem is called
+Plunka inequality.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Plunka inequality allows us to say
+
+ align:start position:0%
+Plunka inequality allows us to say
+ 
+
+ align:start position:0%
+Plunka inequality allows us to say
+things like if a plus a is small then a
+
+ align:start position:0%
+things like if a plus a is small then a
+ 
+
+ align:start position:0%
+things like if a plus a is small then a
+plus a plus a is small.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if A and B are subsets of Z in a
+
+ align:start position:0%
+So if A and B are subsets of Z in a
+ 
+
+ align:start position:0%
+So if A and B are subsets of Z in a
+billion group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and A + B is bounded by K * A
+
+ align:start position:0%
+um and A + B is bounded by K * A
+ 
+
+ align:start position:0%
+um and A + B is bounded by K * A
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um okay let me make a little notation.
+
+ align:start position:0%
+um okay let me make a little notation.
+ 
+
+ align:start position:0%
+um okay let me make a little notation.
+So sometimes we might want to talk about
+
+ align:start position:0%
+So sometimes we might want to talk about
+ 
+
+ align:start position:0%
+So sometimes we might want to talk about
+b + b many times
+
+ align:start position:0%
+b + b many times
+ 
+
+ align:start position:0%
+b + b many times
+um so let's say this is n times this is
+
+ align:start position:0%
+um so let's say this is n times this is
+ 
+
+ align:start position:0%
+um so let's say this is n times this is
+sometimes written as n * b um although I
+
+ align:start position:0%
+sometimes written as n * b um although I
+ 
+
+ align:start position:0%
+sometimes written as n * b um although I
+feel like that is slightly confusing um
+
+ align:start position:0%
+feel like that is slightly confusing um
+ 
+
+ align:start position:0%
+feel like that is slightly confusing um
+so I have decided to adopt this notation
+
+ align:start position:0%
+so I have decided to adopt this notation
+ 
+
+ align:start position:0%
+so I have decided to adopt this notation
+b like sum n times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I could take b + m * - b + n *
+
+ align:start position:0%
+okay so I could take b + m * - b + n *
+ 
+
+ align:start position:0%
+okay so I could take b + m * - b + n *
+and that's bounded by k to the m + n *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's do a few corlaries of this
+
+ align:start position:0%
+okay so let's do a few corlaries of this
+ 
+
+ align:start position:0%
+okay so let's do a few corlaries of this
+um so just by plugging in a equals b we
+
+ align:start position:0%
+um so just by plugging in a equals b we
+ 
+
+ align:start position:0%
+um so just by plugging in a equals b we
+see that if a + a is less than or equal
+
+ align:start position:0%
+see that if a + a is less than or equal
+ 
+
+ align:start position:0%
+see that if a + a is less than or equal
+to k a um then a minus a is less less
+
+ align:start position:0%
+to k a um then a minus a is less less
+ 
+
+ align:start position:0%
+to k a um then a minus a is less less
+than k^ 2 a. Uh that's actually the
+
+ align:start position:0%
+than k^ 2 a. Uh that's actually the
+ 
+
+ align:start position:0%
+than k^ 2 a. Uh that's actually the
+correlary we already proved. Um but also
+
+ align:start position:0%
+correlary we already proved. Um but also
+ 
+
+ align:start position:0%
+correlary we already proved. Um but also
+we could say a + a + a is bounded by k
+
+ align:start position:0%
+we could say a + a + a is bounded by k
+ 
+
+ align:start position:0%
+we could say a + a + a is bounded by k
+cubed a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh just plugging in a b and this is m is
+
+ align:start position:0%
+uh just plugging in a b and this is m is
+ 
+
+ align:start position:0%
+uh just plugging in a b and this is m is
+three and n is zero and you can see you
+
+ align:start position:0%
+three and n is zero and you can see you
+ 
+
+ align:start position:0%
+three and n is zero and you can see you
+can put higher powers here.
+
+ align:start position:0%
+can put higher powers here.
+ 
+
+ align:start position:0%
+can put higher powers here.
+Also another corlary we can get is we
+
+ align:start position:0%
+Also another corlary we can get is we
+ 
+
+ align:start position:0%
+Also another corlary we can get is we
+can switch the role of these guys in the
+
+ align:start position:0%
+can switch the role of these guys in the
+ 
+
+ align:start position:0%
+can switch the role of these guys in the
+first corlary. So we can say if a minus
+
+ align:start position:0%
+first corlary. So we can say if a minus
+ 
+
+ align:start position:0%
+first corlary. So we can say if a minus
+a is small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then a a plus a is also small.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+proof is that b is negative a. So this
+
+ align:start position:0%
+proof is that b is negative a. So this
+ 
+
+ align:start position:0%
+proof is that b is negative a. So this
+is a plus b and then this is basically b
+
+ align:start position:0%
+is a plus b and then this is basically b
+ 
+
+ align:start position:0%
+is a plus b and then this is basically b
+plus b.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um,
+
+ align:start position:0%
+Okay. Um,
+ 
+
+ align:start position:0%
+Okay. Um,
+we can also use this. So, we'll prove
+
+ align:start position:0%
+we can also use this. So, we'll prove
+ 
+
+ align:start position:0%
+we can also use this. So, we'll prove
+this. That'll be our last big goal of
+
+ align:start position:0%
+this. That'll be our last big goal of
+ 
+
+ align:start position:0%
+this. That'll be our last big goal of
+the class. Um but using
+
+ align:start position:0%
+the class. Um but using
+ 
+
+ align:start position:0%
+the class. Um but using
+so this rera inequality and plunic
+
+ align:start position:0%
+so this rera inequality and plunic
+ 
+
+ align:start position:0%
+so this rera inequality and plunic
+inequality have many many uses and one
+
+ align:start position:0%
+inequality have many many uses and one
+ 
+
+ align:start position:0%
+inequality have many many uses and one
+simple use is we can use it to sort of
+
+ align:start position:0%
+simple use is we can use it to sort of
+ 
+
+ align:start position:0%
+simple use is we can use it to sort of
+clean up and improve the statement of
+
+ align:start position:0%
+clean up and improve the statement of
+ 
+
+ align:start position:0%
+clean up and improve the statement of
+our lema that fp if that has no
+
+ align:start position:0%
+our lema that fp if that has no
+ 
+
+ align:start position:0%
+our lema that fp if that has no
+quantitative approximate sub fields. So
+
+ align:start position:0%
+quantitative approximate sub fields. So
+ 
+
+ align:start position:0%
+quantitative approximate sub fields. So
+let me recall what we proved so far and
+
+ align:start position:0%
+let me recall what we proved so far and
+ 
+
+ align:start position:0%
+let me recall what we proved so far and
+then we'll improve it a little bit.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so lma one was uh
+
+ align:start position:0%
+Um so lma one was uh
+ 
+
+ align:start position:0%
+Um so lma one was uh
+if a is in fp
+
+ align:start position:0%
+if a is in fp
+ 
+
+ align:start position:0%
+if a is in fp
+then either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a minus a over a minus a is all of fp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+uh a * a min - a * A.
+
+ align:start position:0%
+uh a * a min - a * A.
+ 
+
+ align:start position:0%
+uh a * a min - a * A.
+Okay. So now I can write this better. We
+
+ align:start position:0%
+Okay. So now I can write this better. We
+ 
+
+ align:start position:0%
+Okay. So now I can write this better. We
+have three or four of those
+
+ align:start position:0%
+have three or four of those
+ 
+
+ align:start position:0%
+have three or four of those
+minus three or four of those
+
+ align:start position:0%
+minus three or four of those
+ 
+
+ align:start position:0%
+minus three or four of those
+as it is.
+
+ align:start position:0%
+as it is.
+ 
+
+ align:start position:0%
+as it is.
+Okay. So we can improve this in a way
+
+ align:start position:0%
+Okay. So we can improve this in a way
+ 
+
+ align:start position:0%
+Okay. So we can improve this in a way
+that you don't need to have so many
+
+ align:start position:0%
+that you don't need to have so many
+ 
+
+ align:start position:0%
+that you don't need to have so many
+different expressions floating around.
+
+ align:start position:0%
+different expressions floating around.
+ 
+
+ align:start position:0%
+different expressions floating around.
+So we can say that if a is in fp
+
+ align:start position:0%
+So we can say that if a is in fp
+ 
+
+ align:start position:0%
+So we can say that if a is in fp
+and the size of a is p to the s where s
+
+ align:start position:0%
+and the size of a is p to the s where s
+ 
+
+ align:start position:0%
+and the size of a is p to the s where s
+is strictly less than one then the size
+
+ align:start position:0%
+is strictly less than one then the size
+ 
+
+ align:start position:0%
+is strictly less than one then the size
+of a * a minus a * a is at least p to
+
+ align:start position:0%
+of a * a minus a * a is at least p to
+ 
+
+ align:start position:0%
+of a * a minus a * a is at least p to
+the s plus epsilon of s.
+
+ align:start position:0%
+the s plus epsilon of s.
+ 
+
+ align:start position:0%
+the s plus epsilon of s.
+And here you could you could put either
+
+ align:start position:0%
+And here you could you could put either
+ 
+
+ align:start position:0%
+And here you could you could put either
+plus or minus.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this epsilon of s is bigger than
+
+ align:start position:0%
+And this epsilon of s is bigger than
+ 
+
+ align:start position:0%
+And this epsilon of s is bigger than
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+So again it's continuous it's explicit
+
+ align:start position:0%
+So again it's continuous it's explicit
+ 
+
+ align:start position:0%
+So again it's continuous it's explicit
+but it's a little bit messy and it's
+
+ align:start position:0%
+but it's a little bit messy and it's
+ 
+
+ align:start position:0%
+but it's a little bit messy and it's
+it's a little bit small.
+
+ align:start position:0%
+it's a little bit small.
+ 
+
+ align:start position:0%
+it's a little bit small.
+You take any subset which is
+
+ align:start position:0%
+You take any subset which is
+ 
+
+ align:start position:0%
+You take any subset which is
+significantly smaller than the whole
+
+ align:start position:0%
+significantly smaller than the whole
+ 
+
+ align:start position:0%
+significantly smaller than the whole
+field. If you do take a * a minus a * a
+
+ align:start position:0%
+field. If you do take a * a minus a * a
+ 
+
+ align:start position:0%
+field. If you do take a * a minus a * a
+it will be significantly bigger than you
+
+ align:start position:0%
+it will be significantly bigger than you
+ 
+
+ align:start position:0%
+it will be significantly bigger than you
+started with.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, you know, if you just took a minus
+
+ align:start position:0%
+So, you know, if you just took a minus
+ 
+
+ align:start position:0%
+So, you know, if you just took a minus
+a, that wouldn't be good enough because
+
+ align:start position:0%
+a, that wouldn't be good enough because
+ 
+
+ align:start position:0%
+a, that wouldn't be good enough because
+a could be an arithmetic progression. It
+
+ align:start position:0%
+a could be an arithmetic progression. It
+ 
+
+ align:start position:0%
+a could be an arithmetic progression. It
+might so that might have almost the same
+
+ align:start position:0%
+might so that might have almost the same
+ 
+
+ align:start position:0%
+might so that might have almost the same
+size as a. If you just took a time a
+
+ align:start position:0%
+size as a. If you just took a time a
+ 
+
+ align:start position:0%
+size as a. If you just took a time a
+that wouldn't be good enough because a
+
+ align:start position:0%
+that wouldn't be good enough because a
+ 
+
+ align:start position:0%
+that wouldn't be good enough because a
+could be a geometric progression. Two 2
+
+ align:start position:0%
+could be a geometric progression. Two 2
+ 
+
+ align:start position:0%
+could be a geometric progression. Two 2
+1 2 the 2 up to 2 to the l.
+
+ align:start position:0%
+1 2 the 2 up to 2 to the l.
+ 
+
+ align:start position:0%
+1 2 the 2 up to 2 to the l.
+Um, but if you take both sums and
+
+ align:start position:0%
+Um, but if you take both sums and
+ 
+
+ align:start position:0%
+Um, but if you take both sums and
+products, then you have to end up with
+
+ align:start position:0%
+products, then you have to end up with
+ 
+
+ align:start position:0%
+products, then you have to end up with
+significantly more stuff than you
+
+ align:start position:0%
+significantly more stuff than you
+ 
+
+ align:start position:0%
+significantly more stuff than you
+started with. Okay, so that's why this
+
+ align:start position:0%
+started with. Okay, so that's why this
+ 
+
+ align:start position:0%
+started with. Okay, so that's why this
+is called sum product theory. If you
+
+ align:start position:0%
+is called sum product theory. If you
+ 
+
+ align:start position:0%
+is called sum product theory. If you
+have both sums and products interacting
+
+ align:start position:0%
+have both sums and products interacting
+ 
+
+ align:start position:0%
+have both sums and products interacting
+with each other, then something happens.
+
+ align:start position:0%
+with each other, then something happens.
+ 
+
+ align:start position:0%
+with each other, then something happens.
+Okay, so uh proof
+
+ align:start position:0%
+Okay, so uh proof
+ 
+
+ align:start position:0%
+Okay, so uh proof
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so if
+
+ align:start position:0%
+okay so if
+ 
+
+ align:start position:0%
+okay so if
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so there there are two cases case
+
+ align:start position:0%
+okay so there there are two cases case
+ 
+
+ align:start position:0%
+okay so there there are two cases case
+one and case two but I'm actually going
+
+ align:start position:0%
+one and case two but I'm actually going
+ 
+
+ align:start position:0%
+one and case two but I'm actually going
+to do case two first.
+
+ align:start position:0%
+to do case two first.
+ 
+
+ align:start position:0%
+to do case two first.
+So case
+
+ align:start position:0%
+So case
+ 
+
+ align:start position:0%
+So case
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it could be that a * a is
+
+ align:start position:0%
+okay so it could be that a * a is
+ 
+
+ align:start position:0%
+okay so it could be that a * a is
+already much bigger than a then we just
+
+ align:start position:0%
+already much bigger than a then we just
+ 
+
+ align:start position:0%
+already much bigger than a then we just
+declare victory. So if
+
+ align:start position:0%
+declare victory. So if
+ 
+
+ align:start position:0%
+declare victory. So if
+a * a is bigger than a to the 1 + delta
+
+ align:start position:0%
+a * a is bigger than a to the 1 + delta
+ 
+
+ align:start position:0%
+a * a is bigger than a to the 1 + delta
+then we declare victory and here delta
+
+ align:start position:0%
+then we declare victory and here delta
+ 
+
+ align:start position:0%
+then we declare victory and here delta
+is going to be much smaller than epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+or maybe we could say okay otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otherwise
+
+ align:start position:0%
+otherwise
+ 
+
+ align:start position:0%
+otherwise
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh otherwise a * a is basically the same
+
+ align:start position:0%
+uh otherwise a * a is basically the same
+ 
+
+ align:start position:0%
+uh otherwise a * a is basically the same
+size as a.
+
+ align:start position:0%
+size as a.
+ 
+
+ align:start position:0%
+size as a.
+Okay. Now, if a * a um plus a * a is
+
+ align:start position:0%
+Okay. Now, if a * a um plus a * a is
+ 
+
+ align:start position:0%
+Okay. Now, if a * a um plus a * a is
+much bigger than a, then we declare
+
+ align:start position:0%
+much bigger than a, then we declare
+ 
+
+ align:start position:0%
+much bigger than a, then we declare
+victory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh where is I writing? Yeah, here. I
+
+ align:start position:0%
+Uh where is I writing? Yeah, here. I
+ 
+
+ align:start position:0%
+Uh where is I writing? Yeah, here. I
+guess let's just put this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we declare victory. Um otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we would have a * a + a * a is smaller
+
+ align:start position:0%
+we would have a * a + a * a is smaller
+ 
+
+ align:start position:0%
+we would have a * a + a * a is smaller
+than k a * a where k is like uh p to the
+
+ align:start position:0%
+than k a * a where k is like uh p to the
+ 
+
+ align:start position:0%
+than k a * a where k is like uh p to the
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+and then we can use plunker
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that would tell us that a * a to a
+
+ align:start position:0%
+and that would tell us that a * a to a
+ 
+
+ align:start position:0%
+and that would tell us that a * a to a
+big power
+
+ align:start position:0%
+big power
+ 
+
+ align:start position:0%
+big power
+minus a * a to another big power
+
+ align:start position:0%
+minus a * a to another big power
+ 
+
+ align:start position:0%
+minus a * a to another big power
+here. We could put
+
+ align:start position:0%
+here. We could put
+ 
+
+ align:start position:0%
+here. We could put
+four. Um that would be bounded by k to
+
+ align:start position:0%
+four. Um that would be bounded by k to
+ 
+
+ align:start position:0%
+four. Um that would be bounded by k to
+the eth a * a.
+
+ align:start position:0%
+the eth a * a.
+ 
+
+ align:start position:0%
+the eth a * a.
+Um and so that would be bounded by maybe
+
+ align:start position:0%
+Um and so that would be bounded by maybe
+ 
+
+ align:start position:0%
+Um and so that would be bounded by maybe
+um a * p to the tan epsilon or something
+
+ align:start position:0%
+um a * p to the tan epsilon or something
+ 
+
+ align:start position:0%
+um a * p to the tan epsilon or something
+like that. And this contradicts the fact
+
+ align:start position:0%
+like that. And this contradicts the fact
+ 
+
+ align:start position:0%
+like that. And this contradicts the fact
+that this we know this set is bigger.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And case one is similar but I
+
+ align:start position:0%
+Okay. And case one is similar but I
+ 
+
+ align:start position:0%
+Okay. And case one is similar but I
+think maybe I'll make that an exercise.
+
+ align:start position:0%
+think maybe I'll make that an exercise.
+ 
+
+ align:start position:0%
+think maybe I'll make that an exercise.
+You can just practice using pluna and
+
+ align:start position:0%
+You can just practice using pluna and
+ 
+
+ align:start position:0%
+You can just practice using pluna and
+rua things.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And I'm going to do one more
+
+ align:start position:0%
+Okay. And I'm going to do one more
+ 
+
+ align:start position:0%
+Okay. And I'm going to do one more
+correlary. Um so suppose you you know
+
+ align:start position:0%
+correlary. Um so suppose you you know
+ 
+
+ align:start position:0%
+correlary. Um so suppose you you know
+you start with the set A and you start
+
+ align:start position:0%
+you start with the set A and you start
+ 
+
+ align:start position:0%
+you start with the set A and you start
+multiplying and adding and subtracting
+
+ align:start position:0%
+multiplying and adding and subtracting
+ 
+
+ align:start position:0%
+multiplying and adding and subtracting
+and see what you get and we've proven
+
+ align:start position:0%
+and see what you get and we've proven
+ 
+
+ align:start position:0%
+and see what you get and we've proven
+that after you do after you do this
+
+ align:start position:0%
+that after you do after you do this
+ 
+
+ align:start position:0%
+that after you do after you do this
+operation it gets a bit bigger
+
+ align:start position:0%
+operation it gets a bit bigger
+ 
+
+ align:start position:0%
+operation it gets a bit bigger
+but suppose you don't just yeah
+
+ align:start position:0%
+but suppose you don't just yeah
+ 
+
+ align:start position:0%
+but suppose you don't just yeah
+>> one question about this so you said that
+
+ align:start position:0%
+>> one question about this so you said that
+ 
+
+ align:start position:0%
+>> one question about this so you said that
+kind of the idea is that if you have
+
+ align:start position:0%
+kind of the idea is that if you have
+ 
+
+ align:start position:0%
+kind of the idea is that if you have
+sort of arithmetic progression or
+
+ align:start position:0%
+sort of arithmetic progression or
+ 
+
+ align:start position:0%
+sort of arithmetic progression or
+geometric progression it can be small
+
+ align:start position:0%
+geometric progression it can be small
+ 
+
+ align:start position:0%
+geometric progression it can be small
+but with both it has to be large. Is it
+
+ align:start position:0%
+but with both it has to be large. Is it
+ 
+
+ align:start position:0%
+but with both it has to be large. Is it
+possible to prove that instead of the
+
+ align:start position:0%
+possible to prove that instead of the
+ 
+
+ align:start position:0%
+possible to prove that instead of the
+the difference of a * a and a * a you
+
+ align:start position:0%
+the difference of a * a and a * a you
+ 
+
+ align:start position:0%
+the difference of a * a and a * a you
+can just say a * a is large or a plus a
+
+ align:start position:0%
+can just say a * a is large or a plus a
+ 
+
+ align:start position:0%
+can just say a * a is large or a plus a
+is large.
+
+ align:start position:0%
+is large.
+ 
+
+ align:start position:0%
+is large.
+>> Okay. Yes. Great question. Okay. So the
+
+ align:start position:0%
+>> Okay. Yes. Great question. Okay. So the
+ 
+
+ align:start position:0%
+>> Okay. Yes. Great question. Okay. So the
+question is so so in the theme of lema 2
+
+ align:start position:0%
+question is so so in the theme of lema 2
+ 
+
+ align:start position:0%
+question is so so in the theme of lema 2
+is we tried to simplify as much as
+
+ align:start position:0%
+is we tried to simplify as much as
+ 
+
+ align:start position:0%
+is we tried to simplify as much as
+possible the expression that we put here
+
+ align:start position:0%
+possible the expression that we put here
+ 
+
+ align:start position:0%
+possible the expression that we put here
+and there is a suggestion um how to make
+
+ align:start position:0%
+and there is a suggestion um how to make
+ 
+
+ align:start position:0%
+and there is a suggestion um how to make
+it as simple as possible. Um, so let me
+
+ align:start position:0%
+it as simple as possible. Um, so let me
+ 
+
+ align:start position:0%
+it as simple as possible. Um, so let me
+I'm going to erase this proof and write
+
+ align:start position:0%
+I'm going to erase this proof and write
+ 
+
+ align:start position:0%
+I'm going to erase this proof and write
+that as a as a I'll write it as a
+
+ align:start position:0%
+that as a as a I'll write it as a
+ 
+
+ align:start position:0%
+that as a as a I'll write it as a
+theorem. It's a theorem.
+
+ align:start position:0%
+theorem. It's a theorem.
+ 
+
+ align:start position:0%
+theorem. It's a theorem.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+even better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is a theorem
+
+ align:start position:0%
+there is a theorem
+ 
+
+ align:start position:0%
+there is a theorem
+um ban cat's towel.
+
+ align:start position:0%
+um ban cat's towel.
+ 
+
+ align:start position:0%
+um ban cat's towel.
+So if a is subset of fp
+
+ align:start position:0%
+So if a is subset of fp
+ 
+
+ align:start position:0%
+So if a is subset of fp
+uh a equ= p to the s0 less than or equal
+
+ align:start position:0%
+uh a equ= p to the s0 less than or equal
+ 
+
+ align:start position:0%
+uh a equ= p to the s0 less than or equal
+to s less than 1 then
+
+ align:start position:0%
+to s less than 1 then
+ 
+
+ align:start position:0%
+to s less than 1 then
+you could take um the maximum
+
+ align:start position:0%
+you could take um the maximum
+ 
+
+ align:start position:0%
+you could take um the maximum
+of a + a and a * a
+
+ align:start position:0%
+of a + a and a * a
+ 
+
+ align:start position:0%
+of a + a and a * a
+and that is bigger than p to the s plus
+
+ align:start position:0%
+and that is bigger than p to the s plus
+ 
+
+ align:start position:0%
+and that is bigger than p to the s plus
+epsilon of s.
+
+ align:start position:0%
+epsilon of s.
+ 
+
+ align:start position:0%
+epsilon of s.
+So this is better than this
+
+ align:start position:0%
+So this is better than this
+ 
+
+ align:start position:0%
+So this is better than this
+qualitatively.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And actually the word sum product
+
+ align:start position:0%
+And actually the word sum product
+ 
+
+ align:start position:0%
+And actually the word sum product
+inequality it could refer to a lot of
+
+ align:start position:0%
+inequality it could refer to a lot of
+ 
+
+ align:start position:0%
+inequality it could refer to a lot of
+things but the the the inequality it
+
+ align:start position:0%
+things but the the the inequality it
+ 
+
+ align:start position:0%
+things but the the the inequality it
+most often refers to is this one. So
+
+ align:start position:0%
+most often refers to is this one. So
+ 
+
+ align:start position:0%
+most often refers to is this one. So
+either either the sums or the products
+
+ align:start position:0%
+either either the sums or the products
+ 
+
+ align:start position:0%
+either either the sums or the products
+grow. Yeah, that's right. Okay. So all
+
+ align:start position:0%
+grow. Yeah, that's right. Okay. So all
+ 
+
+ align:start position:0%
+grow. Yeah, that's right. Okay. So all
+the stuff we've seen are steps towards
+
+ align:start position:0%
+the stuff we've seen are steps towards
+ 
+
+ align:start position:0%
+the stuff we've seen are steps towards
+the proof of this theorem. But there is
+
+ align:start position:0%
+the proof of this theorem. But there is
+ 
+
+ align:start position:0%
+the proof of this theorem. But there is
+actually still some more ideas to get
+
+ align:start position:0%
+actually still some more ideas to get
+ 
+
+ align:start position:0%
+actually still some more ideas to get
+all the way down to here. And we may or
+
+ align:start position:0%
+all the way down to here. And we may or
+ 
+
+ align:start position:0%
+all the way down to here. And we may or
+may not end up doing it in the class.
+
+ align:start position:0%
+may not end up doing it in the class.
+ 
+
+ align:start position:0%
+may not end up doing it in the class.
+It's unclear to me if getting all the
+
+ align:start position:0%
+It's unclear to me if getting all the
+ 
+
+ align:start position:0%
+It's unclear to me if getting all the
+way down to there is actually uh
+
+ align:start position:0%
+way down to there is actually uh
+ 
+
+ align:start position:0%
+way down to there is actually uh
+important in in projection theory.
+
+ align:start position:0%
+important in in projection theory.
+ 
+
+ align:start position:0%
+important in in projection theory.
+Yeah. Cool.
+
+ align:start position:0%
+Yeah. Cool.
+ 
+
+ align:start position:0%
+Yeah. Cool.
+Okay. So, one goal you might have in in
+
+ align:start position:0%
+Okay. So, one goal you might have in in
+ 
+
+ align:start position:0%
+Okay. So, one goal you might have in in
+in simplifying and clarifying this story
+
+ align:start position:0%
+in simplifying and clarifying this story
+ 
+
+ align:start position:0%
+in simplifying and clarifying this story
+is to make this expression as simple as
+
+ align:start position:0%
+is to make this expression as simple as
+ 
+
+ align:start position:0%
+is to make this expression as simple as
+possible and get some gain. But another
+
+ align:start position:0%
+possible and get some gain. But another
+ 
+
+ align:start position:0%
+possible and get some gain. But another
+goal that you might have is to make this
+
+ align:start position:0%
+goal that you might have is to make this
+ 
+
+ align:start position:0%
+goal that you might have is to make this
+gain really large and perhaps this
+
+ align:start position:0%
+gain really large and perhaps this
+ 
+
+ align:start position:0%
+gain really large and perhaps this
+expression will be more complicated and
+
+ align:start position:0%
+expression will be more complicated and
+ 
+
+ align:start position:0%
+expression will be more complicated and
+you can also do that.
+
+ align:start position:0%
+you can also do that.
+ 
+
+ align:start position:0%
+you can also do that.
+So let me make some uh notation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's say poly k of a some sort of
+
+ align:start position:0%
+Let's say poly k of a some sort of
+ 
+
+ align:start position:0%
+Let's say poly k of a some sort of
+polomials of complexity k. So I take a
+
+ align:start position:0%
+polomials of complexity k. So I take a
+ 
+
+ align:start position:0%
+polomials of complexity k. So I take a
+to the k. So that's means I multiply
+
+ align:start position:0%
+to the k. So that's means I multiply
+ 
+
+ align:start position:0%
+to the k. So that's means I multiply
+uh k different elements of a together
+
+ align:start position:0%
+uh k different elements of a together
+ 
+
+ align:start position:0%
+uh k different elements of a together
+and then I add k things like that
+
+ align:start position:0%
+and then I add k things like that
+ 
+
+ align:start position:0%
+and then I add k things like that
+together and then maybe I also want some
+
+ align:start position:0%
+together and then maybe I also want some
+ 
+
+ align:start position:0%
+together and then maybe I also want some
+minuses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so a a to the k is a * a * a k *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these are polomials in A of
+
+ align:start position:0%
+okay so these are polomials in A of
+ 
+
+ align:start position:0%
+okay so these are polomials in A of
+complexity
+
+ align:start position:0%
+complexity
+ 
+
+ align:start position:0%
+complexity
+and uh another corlary which is at the
+
+ align:start position:0%
+and uh another corlary which is at the
+ 
+
+ align:start position:0%
+and uh another corlary which is at the
+same level follows easily from this one
+
+ align:start position:0%
+same level follows easily from this one
+ 
+
+ align:start position:0%
+same level follows easily from this one
+is that if we have zero less than s less
+
+ align:start position:0%
+is that if we have zero less than s less
+ 
+
+ align:start position:0%
+is that if we have zero less than s less
+than t less than one and a is in fp. So
+
+ align:start position:0%
+than t less than one and a is in fp. So
+ 
+
+ align:start position:0%
+than t less than one and a is in fp. So
+okay then there exists some k that only
+
+ align:start position:0%
+okay then there exists some k that only
+ 
+
+ align:start position:0%
+okay then there exists some k that only
+depends on s and t. So that for any set
+
+ align:start position:0%
+depends on s and t. So that for any set
+ 
+
+ align:start position:0%
+depends on s and t. So that for any set
+A in any FP where the size of A is P to
+
+ align:start position:0%
+A in any FP where the size of A is P to
+ 
+
+ align:start position:0%
+A in any FP where the size of A is P to
+the S, the size of poly K of A
+
+ align:start position:0%
+the S, the size of poly K of A
+ 
+
+ align:start position:0%
+the S, the size of poly K of A
+is at least P to the T.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And the proof of this is is easy.
+
+ align:start position:0%
+Okay. And the proof of this is is easy.
+ 
+
+ align:start position:0%
+Okay. And the proof of this is is easy.
+The proof is use lema too many times.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I start with the set A. A * A minus A
+
+ align:start position:0%
+So I start with the set A. A * A minus A
+ 
+
+ align:start position:0%
+So I start with the set A. A * A minus A
+* A is a bit bigger. Called this B. B *
+
+ align:start position:0%
+* A is a bit bigger. Called this B. B *
+ 
+
+ align:start position:0%
+* A is a bit bigger. Called this B. B *
+B minus B * B is even a bit bigger.
+
+ align:start position:0%
+B minus B * B is even a bit bigger.
+ 
+
+ align:start position:0%
+B minus B * B is even a bit bigger.
+And if you think about what B * B minus
+
+ align:start position:0%
+And if you think about what B * B minus
+ 
+
+ align:start position:0%
+And if you think about what B * B minus
+B * B means, it would fit in like
+
+ align:start position:0%
+B * B means, it would fit in like
+ 
+
+ align:start position:0%
+B * B means, it would fit in like
+probably four again.
+
+ align:start position:0%
+probably four again.
+ 
+
+ align:start position:0%
+probably four again.
+And you keep doing this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, cool.
+
+ align:start position:0%
+Okay, cool.
+ 
+
+ align:start position:0%
+Okay, cool.
+Cool.
+
+ align:start position:0%
+Cool.
+ 
+
+ align:start position:0%
+Cool.
+Um so these these lemas theorems and
+
+ align:start position:0%
+Um so these these lemas theorems and
+ 
+
+ align:start position:0%
+Um so these these lemas theorems and
+stuff they are important because um
+
+ align:start position:0%
+stuff they are important because um
+ 
+
+ align:start position:0%
+stuff they are important because um
+and plumac's inequality and ruse's
+
+ align:start position:0%
+and plumac's inequality and ruse's
+ 
+
+ align:start position:0%
+and plumac's inequality and ruse's
+inequality they are important
+
+ align:start position:0%
+inequality they are important
+ 
+
+ align:start position:0%
+inequality they are important
+um because um
+
+ align:start position:0%
+um because um
+ 
+
+ align:start position:0%
+um because um
+you so once we once we see so if we see
+
+ align:start position:0%
+you so once we once we see so if we see
+ 
+
+ align:start position:0%
+you so once we once we see so if we see
+something like a plus a is small that
+
+ align:start position:0%
+something like a plus a is small that
+ 
+
+ align:start position:0%
+something like a plus a is small that
+then that tells us that a has some
+
+ align:start position:0%
+then that tells us that a has some
+ 
+
+ align:start position:0%
+then that tells us that a has some
+structure and all these inequalities
+
+ align:start position:0%
+structure and all these inequalities
+ 
+
+ align:start position:0%
+structure and all these inequalities
+then imply that lots of other things are
+
+ align:start position:0%
+then imply that lots of other things are
+ 
+
+ align:start position:0%
+then imply that lots of other things are
+small. So it's sort of like a contagious
+
+ align:start position:0%
+small. So it's sort of like a contagious
+ 
+
+ align:start position:0%
+small. So it's sort of like a contagious
+structure like we start we input some
+
+ align:start position:0%
+structure like we start we input some
+ 
+
+ align:start position:0%
+structure like we start we input some
+structure but we find out more and more
+
+ align:start position:0%
+structure but we find out more and more
+ 
+
+ align:start position:0%
+structure but we find out more and more
+structure and that's a very useful tool
+
+ align:start position:0%
+structure and that's a very useful tool
+ 
+
+ align:start position:0%
+structure and that's a very useful tool
+and so lots of problems that we see in
+
+ align:start position:0%
+and so lots of problems that we see in
+ 
+
+ align:start position:0%
+and so lots of problems that we see in
+projection theory uh it seems to be
+
+ align:start position:0%
+projection theory uh it seems to be
+ 
+
+ align:start position:0%
+projection theory uh it seems to be
+helpful to try to phrase them in the
+
+ align:start position:0%
+helpful to try to phrase them in the
+ 
+
+ align:start position:0%
+helpful to try to phrase them in the
+form that some subset is small because
+
+ align:start position:0%
+form that some subset is small because
+ 
+
+ align:start position:0%
+form that some subset is small because
+then we can use Pluna's inequality and
+
+ align:start position:0%
+then we can use Pluna's inequality and
+ 
+
+ align:start position:0%
+then we can use Pluna's inequality and
+we can find out lots of other things.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So in the last part of the class
+
+ align:start position:0%
+Okay. So in the last part of the class
+ 
+
+ align:start position:0%
+Okay. So in the last part of the class
+we will prove this inequality. This is
+
+ align:start position:0%
+we will prove this inequality. This is
+ 
+
+ align:start position:0%
+we will prove this inequality. This is
+the trickiest thing that we will prove
+
+ align:start position:0%
+the trickiest thing that we will prove
+ 
+
+ align:start position:0%
+the trickiest thing that we will prove
+today.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So the original proof of the
+
+ align:start position:0%
+All right. So the original proof of the
+ 
+
+ align:start position:0%
+All right. So the original proof of the
+pluna inequality was somewhat difficult.
+
+ align:start position:0%
+pluna inequality was somewhat difficult.
+ 
+
+ align:start position:0%
+pluna inequality was somewhat difficult.
+Um and there was a short proof that was
+
+ align:start position:0%
+Um and there was a short proof that was
+ 
+
+ align:start position:0%
+Um and there was a short proof that was
+given by Jorgus Petritus
+
+ align:start position:0%
+given by Jorgus Petritus
+ 
+
+ align:start position:0%
+given by Jorgus Petritus
+um about 10 or 15 years ago which is the
+
+ align:start position:0%
+um about 10 or 15 years ago which is the
+ 
+
+ align:start position:0%
+um about 10 or 15 years ago which is the
+one that I'll that I'll show.
+
+ align:start position:0%
+one that I'll that I'll show.
+ 
+
+ align:start position:0%
+one that I'll that I'll show.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it's based on a key lema.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the key lema says that if a + b is at
+
+ align:start position:0%
+So the key lema says that if a + b is at
+ 
+
+ align:start position:0%
+So the key lema says that if a + b is at
+most k * a
+
+ align:start position:0%
+most k * a
+ 
+
+ align:start position:0%
+most k * a
+then there's a subset x contained in a
+
+ align:start position:0%
+then there's a subset x contained in a
+ 
+
+ align:start position:0%
+then there's a subset x contained in a
+so that for any set c
+
+ align:start position:0%
+so that for any set c
+ 
+
+ align:start position:0%
+so that for any set c
+x + c + b
+
+ align:start position:0%
+x + c + b
+ 
+
+ align:start position:0%
+x + c + b
+divided by x + c is also at most k.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So okay by the way this top inequality
+
+ align:start position:0%
+So okay by the way this top inequality
+ 
+
+ align:start position:0%
+So okay by the way this top inequality
+of course we can divide by a. The top
+
+ align:start position:0%
+of course we can divide by a. The top
+ 
+
+ align:start position:0%
+of course we can divide by a. The top
+inequality says a + b over a is bounded
+
+ align:start position:0%
+inequality says a + b over a is bounded
+ 
+
+ align:start position:0%
+inequality says a + b over a is bounded
+by k.
+
+ align:start position:0%
+by k.
+ 
+
+ align:start position:0%
+by k.
+The lema says that if this is true
+
+ align:start position:0%
+The lema says that if this is true
+ 
+
+ align:start position:0%
+The lema says that if this is true
+then it's so if it's true for the set a
+
+ align:start position:0%
+then it's so if it's true for the set a
+ 
+
+ align:start position:0%
+then it's so if it's true for the set a
+then it's also true for the set x plus c
+
+ align:start position:0%
+then it's also true for the set x plus c
+ 
+
+ align:start position:0%
+then it's also true for the set x plus c
+where x is carefully chosen. I'll
+
+ align:start position:0%
+where x is carefully chosen. I'll
+ 
+
+ align:start position:0%
+where x is carefully chosen. I'll
+explain in a bit how it's chosen but c
+
+ align:start position:0%
+explain in a bit how it's chosen but c
+ 
+
+ align:start position:0%
+explain in a bit how it's chosen but c
+is a totally arbitrary set. So there are
+
+ align:start position:0%
+is a totally arbitrary set. So there are
+ 
+
+ align:start position:0%
+is a totally arbitrary set. So there are
+many choices for C. So there are many
+
+ align:start position:0%
+many choices for C. So there are many
+ 
+
+ align:start position:0%
+many choices for C. So there are many
+different you know this this is many
+
+ align:start position:0%
+different you know this this is many
+ 
+
+ align:start position:0%
+different you know this this is many
+inequalities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Okay let me um tell you who X is
+
+ align:start position:0%
+right? Okay let me um tell you who X is
+ 
+
+ align:start position:0%
+right? Okay let me um tell you who X is
+which is an important idea in the proof.
+
+ align:start position:0%
+which is an important idea in the proof.
+ 
+
+ align:start position:0%
+which is an important idea in the proof.
+Um so first of all so x is a subset of a
+
+ align:start position:0%
+Um so first of all so x is a subset of a
+ 
+
+ align:start position:0%
+Um so first of all so x is a subset of a
+that we choose in order to minimize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minimize the ratio x + b / x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let me give an example that might
+
+ align:start position:0%
+So let me give an example that might
+ 
+
+ align:start position:0%
+So let me give an example that might
+help to motivate why you would want to
+
+ align:start position:0%
+help to motivate why you would want to
+ 
+
+ align:start position:0%
+help to motivate why you would want to
+look at this x.
+
+ align:start position:0%
+look at this x.
+ 
+
+ align:start position:0%
+look at this x.
+So suppose that a is the numbers from
+
+ align:start position:0%
+So suppose that a is the numbers from
+ 
+
+ align:start position:0%
+So suppose that a is the numbers from
+one up to 100
+
+ align:start position:0%
+one up to 100
+ 
+
+ align:start position:0%
+one up to 100
+which has a lot of additive structure
+
+ align:start position:0%
+which has a lot of additive structure
+ 
+
+ align:start position:0%
+which has a lot of additive structure
+together with some random number. So
+
+ align:start position:0%
+together with some random number. So
+ 
+
+ align:start position:0%
+together with some random number. So
+I've put a million
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and b is the numbers from one up to say
+
+ align:start position:0%
+and b is the numbers from one up to say
+ 
+
+ align:start position:0%
+and b is the numbers from one up to say
+50.
+
+ align:start position:0%
+50.
+ 
+
+ align:start position:0%
+50.
+Okay. So if you add A and B together,
+
+ align:start position:0%
+Okay. So if you add A and B together,
+ 
+
+ align:start position:0%
+Okay. So if you add A and B together,
+this stuff plus this stuff is quite
+
+ align:start position:0%
+this stuff plus this stuff is quite
+ 
+
+ align:start position:0%
+this stuff plus this stuff is quite
+small. There's a lot of structure there.
+
+ align:start position:0%
+small. There's a lot of structure there.
+ 
+
+ align:start position:0%
+small. There's a lot of structure there.
+Then there's this stuff plus this stuff
+
+ align:start position:0%
+Then there's this stuff plus this stuff
+ 
+
+ align:start position:0%
+Then there's this stuff plus this stuff
+that doesn't have any particular
+
+ align:start position:0%
+that doesn't have any particular
+ 
+
+ align:start position:0%
+that doesn't have any particular
+structure, but since there's only one
+
+ align:start position:0%
+structure, but since there's only one
+ 
+
+ align:start position:0%
+structure, but since there's only one
+stray element here, that's not so many
+
+ align:start position:0%
+stray element here, that's not so many
+ 
+
+ align:start position:0%
+stray element here, that's not so many
+of those either. So A plus B is pretty
+
+ align:start position:0%
+of those either. So A plus B is pretty
+ 
+
+ align:start position:0%
+of those either. So A plus B is pretty
+small.
+
+ align:start position:0%
+small.
+ 
+
+ align:start position:0%
+small.
+Now, who would X be?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is the subset of A which is chosen to
+
+ align:start position:0%
+X is the subset of A which is chosen to
+ 
+
+ align:start position:0%
+X is the subset of A which is chosen to
+minimize this ratio.
+
+ align:start position:0%
+minimize this ratio.
+ 
+
+ align:start position:0%
+minimize this ratio.
+and including this guy is not so
+
+ align:start position:0%
+and including this guy is not so
+ 
+
+ align:start position:0%
+and including this guy is not so
+helpful.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so x would actually be here just the
+
+ align:start position:0%
+Um so x would actually be here just the
+ 
+
+ align:start position:0%
+Um so x would actually be here just the
+numbers from one up to 100.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So I think perhaps that
+
+ align:start position:0%
+Okay. So I think perhaps that
+ 
+
+ align:start position:0%
+Okay. So I think perhaps that
+philosophically the point of doing this
+
+ align:start position:0%
+philosophically the point of doing this
+ 
+
+ align:start position:0%
+philosophically the point of doing this
+is identifying the part of A that really
+
+ align:start position:0%
+is identifying the part of A that really
+ 
+
+ align:start position:0%
+is identifying the part of A that really
+has the additive structure and throwing
+
+ align:start position:0%
+has the additive structure and throwing
+ 
+
+ align:start position:0%
+has the additive structure and throwing
+away possibly some parts of A that are
+
+ align:start position:0%
+away possibly some parts of A that are
+ 
+
+ align:start position:0%
+away possibly some parts of A that are
+not not that relevant.
+
+ align:start position:0%
+not not that relevant.
+ 
+
+ align:start position:0%
+not not that relevant.
+Okay. And then once you have found the
+
+ align:start position:0%
+Okay. And then once you have found the
+ 
+
+ align:start position:0%
+Okay. And then once you have found the
+heart of the matter here um then
+
+ align:start position:0%
+heart of the matter here um then
+ 
+
+ align:start position:0%
+heart of the matter here um then
+you can you can add anything else to it
+
+ align:start position:0%
+you can you can add anything else to it
+ 
+
+ align:start position:0%
+you can you can add anything else to it
+and you still have that amount of
+
+ align:start position:0%
+and you still have that amount of
+ 
+
+ align:start position:0%
+and you still have that amount of
+structure.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, let's give a name. Let's
+
+ align:start position:0%
+All right. So, let's give a name. Let's
+ 
+
+ align:start position:0%
+All right. So, let's give a name. Let's
+say that. So, that's who X is. And let's
+
+ align:start position:0%
+say that. So, that's who X is. And let's
+ 
+
+ align:start position:0%
+say that. So, that's who X is. And let's
+say x + b / x is k lower bar which is at
+
+ align:start position:0%
+say x + b / x is k lower bar which is at
+ 
+
+ align:start position:0%
+say x + b / x is k lower bar which is at
+most k.
+
+ align:start position:0%
+most k.
+ 
+
+ align:start position:0%
+most k.
+So a + b over a is at most k and x is
+
+ align:start position:0%
+So a + b over a is at most k and x is
+ 
+
+ align:start position:0%
+So a + b over a is at most k and x is
+allowed to be all of a but we might
+
+ align:start position:0%
+allowed to be all of a but we might
+ 
+
+ align:start position:0%
+allowed to be all of a but we might
+choose a smaller set if we can make this
+
+ align:start position:0%
+choose a smaller set if we can make this
+ 
+
+ align:start position:0%
+choose a smaller set if we can make this
+ratio even smaller. So k bar is less
+
+ align:start position:0%
+ratio even smaller. So k bar is less
+ 
+
+ align:start position:0%
+ratio even smaller. So k bar is less
+than or equal to k. Okay. And really the
+
+ align:start position:0%
+than or equal to k. Okay. And really the
+ 
+
+ align:start position:0%
+than or equal to k. Okay. And really the
+key claim
+
+ align:start position:0%
+key claim
+ 
+
+ align:start position:0%
+key claim
+is that x + c + b over x + c is at most
+
+ align:start position:0%
+is that x + c + b over x + c is at most
+ 
+
+ align:start position:0%
+is that x + c + b over x + c is at most
+k lower barc.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now we're going to prove the
+
+ align:start position:0%
+Okay. So now we're going to prove the
+ 
+
+ align:start position:0%
+Okay. So now we're going to prove the
+claim by induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we're going to prove the claim by
+
+ align:start position:0%
+So we're going to prove the claim by
+ 
+
+ align:start position:0%
+So we're going to prove the claim by
+induction
+
+ align:start position:0%
+induction
+ 
+
+ align:start position:0%
+induction
+on the cardality of C.
+
+ align:start position:0%
+on the cardality of C.
+ 
+
+ align:start position:0%
+on the cardality of C.
+And if the cardality of C is 1, then X +
+
+ align:start position:0%
+And if the cardality of C is 1, then X +
+ 
+
+ align:start position:0%
+And if the cardality of C is 1, then X +
+C + B is just X + B
+
+ align:start position:0%
+C + B is just X + B
+ 
+
+ align:start position:0%
+C + B is just X + B
+and X + C is just X. So if the cardality
+
+ align:start position:0%
+and X + C is just X. So if the cardality
+ 
+
+ align:start position:0%
+and X + C is just X. So if the cardality
+of C is one, I'm just shifting this set.
+
+ align:start position:0%
+of C is one, I'm just shifting this set.
+ 
+
+ align:start position:0%
+of C is one, I'm just shifting this set.
+and shifting that set doesn't change
+
+ align:start position:0%
+and shifting that set doesn't change
+ 
+
+ align:start position:0%
+and shifting that set doesn't change
+their cardalities.
+
+ align:start position:0%
+their cardalities.
+ 
+
+ align:start position:0%
+their cardalities.
+Okay. So now we can do the inductive
+
+ align:start position:0%
+Okay. So now we can do the inductive
+ 
+
+ align:start position:0%
+Okay. So now we can do the inductive
+step.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So let's say that C prime is
+
+ align:start position:0%
+All right. So let's say that C prime is
+ 
+
+ align:start position:0%
+All right. So let's say that C prime is
+C union one more guy. And by induction
+
+ align:start position:0%
+C union one more guy. And by induction
+ 
+
+ align:start position:0%
+C union one more guy. And by induction
+we know that it's true for C. So we know
+
+ align:start position:0%
+we know that it's true for C. So we know
+ 
+
+ align:start position:0%
+we know that it's true for C. So we know
+x + c + b is bounded by k lower bar x +
+
+ align:start position:0%
+x + c + b is bounded by k lower bar x +
+ 
+
+ align:start position:0%
+x + c + b is bounded by k lower bar x +
+c and we want to check for crop.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So the key character in this
+
+ align:start position:0%
+Okay. So the key character in this
+ 
+
+ align:start position:0%
+Okay. So the key character in this
+argument that Petrus came up with
+
+ align:start position:0%
+argument that Petrus came up with
+ 
+
+ align:start position:0%
+argument that Petrus came up with
+is a set y which is the set of x and x.
+
+ align:start position:0%
+is a set y which is the set of x and x.
+ 
+
+ align:start position:0%
+is a set y which is the set of x and x.
+So that x + little c + b is contained in
+
+ align:start position:0%
+So that x + little c + b is contained in
+ 
+
+ align:start position:0%
+So that x + little c + b is contained in
+big x plus big c plus b. Let's see how
+
+ align:start position:0%
+big x plus big c plus b. Let's see how
+ 
+
+ align:start position:0%
+big x plus big c plus b. Let's see how
+that naturally comes up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right.
+
+ align:start position:0%
+Right.
+ 
+
+ align:start position:0%
+Right.
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we we we're thinking about x plus c
+
+ align:start position:0%
+So we we we're thinking about x plus c
+ 
+
+ align:start position:0%
+So we we we're thinking about x plus c
+prime plus b. We want to see that it's
+
+ align:start position:0%
+prime plus b. We want to see that it's
+ 
+
+ align:start position:0%
+prime plus b. We want to see that it's
+not too big. And we're using induction.
+
+ align:start position:0%
+not too big. And we're using induction.
+ 
+
+ align:start position:0%
+not too big. And we're using induction.
+So we want to see how it changes when we
+
+ align:start position:0%
+So we want to see how it changes when we
+ 
+
+ align:start position:0%
+So we want to see how it changes when we
+added this one guy. So this is the
+
+ align:start position:0%
+added this one guy. So this is the
+ 
+
+ align:start position:0%
+added this one guy. So this is the
+previous guy x + c + b plus um
+
+ align:start position:0%
+previous guy x + c + b plus um
+ 
+
+ align:start position:0%
+previous guy x + c + b plus um
+the new ones.
+
+ align:start position:0%
+the new ones.
+ 
+
+ align:start position:0%
+the new ones.
+And I want them to be really new.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, here are some new elements that live
+
+ align:start position:0%
+So, here are some new elements that live
+ 
+
+ align:start position:0%
+So, here are some new elements that live
+here. And I'm going to take out any
+
+ align:start position:0%
+here. And I'm going to take out any
+ 
+
+ align:start position:0%
+here. And I'm going to take out any
+elements I've already counted,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sorry. Um,
+
+ align:start position:0%
+Sorry. Um,
+ 
+
+ align:start position:0%
+Sorry. Um,
+how, um, I don't quite understand the
+
+ align:start position:0%
+how, um, I don't quite understand the
+ 
+
+ align:start position:0%
+how, um, I don't quite understand the
+definition of y. How can x plus c plus b
+
+ align:start position:0%
+definition of y. How can x plus c plus b
+ 
+
+ align:start position:0%
+definition of y. How can x plus c plus b
+not be a subset of x plus c plus b?
+
+ align:start position:0%
+not be a subset of x plus c plus b?
+ 
+
+ align:start position:0%
+not be a subset of x plus c plus b?
+>> Right? So this uh so c prime is a
+
+ align:start position:0%
+>> Right? So this uh so c prime is a
+ 
+
+ align:start position:0%
+>> Right? So this uh so c prime is a
+previous set c union with some little c
+
+ align:start position:0%
+previous set c union with some little c
+ 
+
+ align:start position:0%
+previous set c union with some little c
+>> and little c is not in big c.
+
+ align:start position:0%
+>> and little c is not in big c.
+ 
+
+ align:start position:0%
+>> and little c is not in big c.
+>> Okay. Now I have to write all the little
+
+ align:start position:0%
+>> Okay. Now I have to write all the little
+ 
+
+ align:start position:0%
+>> Okay. Now I have to write all the little
+c's and big c's really carefully. But
+
+ align:start position:0%
+c's and big c's really carefully. But
+ 
+
+ align:start position:0%
+c's and big c's really carefully. But
+this is a little c and this is a big c.
+
+ align:start position:0%
+this is a little c and this is a big c.
+ 
+
+ align:start position:0%
+this is a little c and this is a big c.
+Cool. Okay. So this X is automatically
+
+ align:start position:0%
+Cool. Okay. So this X is automatically
+ 
+
+ align:start position:0%
+Cool. Okay. So this X is automatically
+in big X but in a failure of
+
+ align:start position:0%
+in big X but in a failure of
+ 
+
+ align:start position:0%
+in big X but in a failure of
+functorality of not of notation little C
+
+ align:start position:0%
+functorality of not of notation little C
+ 
+
+ align:start position:0%
+functorality of not of notation little C
+is not in big C.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now, one thing to note about this
+
+ align:start position:0%
+Okay. Now, one thing to note about this
+ 
+
+ align:start position:0%
+Okay. Now, one thing to note about this
+definition that helps to motivate it is
+
+ align:start position:0%
+definition that helps to motivate it is
+ 
+
+ align:start position:0%
+definition that helps to motivate it is
+that y + little c plus big b is
+
+ align:start position:0%
+that y + little c plus big b is
+ 
+
+ align:start position:0%
+that y + little c plus big b is
+contained in x plus big c plus big b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because for each element of y, little y
+
+ align:start position:0%
+because for each element of y, little y
+ 
+
+ align:start position:0%
+because for each element of y, little y
+plus little c plus big b is defined to
+
+ align:start position:0%
+plus little c plus big b is defined to
+ 
+
+ align:start position:0%
+plus little c plus big b is defined to
+be in here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is at most x + c + b plus
+
+ align:start position:0%
+So this is at most x + c + b plus
+ 
+
+ align:start position:0%
+So this is at most x + c + b plus
+x + c + b take away y + c + b.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All of these were already counted. So
+
+ align:start position:0%
+All of these were already counted. So
+ 
+
+ align:start position:0%
+All of these were already counted. So
+there are at most this many new guys.
+
+ align:start position:0%
+there are at most this many new guys.
+ 
+
+ align:start position:0%
+there are at most this many new guys.
+All right. And this is x + c + b + x + b
+
+ align:start position:0%
+All right. And this is x + c + b + x + b
+ 
+
+ align:start position:0%
+All right. And this is x + c + b + x + b
+- y + b because this is a subset of this
+
+ align:start position:0%
+- y + b because this is a subset of this
+ 
+
+ align:start position:0%
+- y + b because this is a subset of this
+and the plus c just translates things.
+
+ align:start position:0%
+and the plus c just translates things.
+ 
+
+ align:start position:0%
+and the plus c just translates things.
+So I have so this thing is that big and
+
+ align:start position:0%
+So I have so this thing is that big and
+ 
+
+ align:start position:0%
+So I have so this thing is that big and
+I remove from it this thing which is
+
+ align:start position:0%
+I remove from it this thing which is
+ 
+
+ align:start position:0%
+I remove from it this thing which is
+that big.
+
+ align:start position:0%
+that big.
+ 
+
+ align:start position:0%
+that big.
+So that's the upper bound for um the
+
+ align:start position:0%
+So that's the upper bound for um the
+ 
+
+ align:start position:0%
+So that's the upper bound for um the
+numerator.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+so I'm I'm trying to bound this thing
+
+ align:start position:0%
+so I'm I'm trying to bound this thing
+ 
+
+ align:start position:0%
+so I'm I'm trying to bound this thing
+with a C prime. I need I want to prove
+
+ align:start position:0%
+with a C prime. I need I want to prove
+ 
+
+ align:start position:0%
+with a C prime. I need I want to prove
+an upper bound. So I need an upper bound
+
+ align:start position:0%
+an upper bound. So I need an upper bound
+ 
+
+ align:start position:0%
+an upper bound. So I need an upper bound
+for the numerator and a lower bound for
+
+ align:start position:0%
+for the numerator and a lower bound for
+ 
+
+ align:start position:0%
+for the numerator and a lower bound for
+the denominator.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the denominator is x +
+
+ align:start position:0%
+so the denominator is x +
+ 
+
+ align:start position:0%
+so the denominator is x +
+uh c prime
+
+ align:start position:0%
+uh c prime
+ 
+
+ align:start position:0%
+uh c prime
+and so that's x + c plus um the the set
+
+ align:start position:0%
+and so that's x + c plus um the the set
+ 
+
+ align:start position:0%
+and so that's x + c plus um the the set
+how many x and x. So that little x plus
+
+ align:start position:0%
+how many x and x. So that little x plus
+ 
+
+ align:start position:0%
+how many x and x. So that little x plus
+little c is not contained in big x plus
+
+ align:start position:0%
+little c is not contained in big x plus
+ 
+
+ align:start position:0%
+little c is not contained in big x plus
+big c.
+
+ align:start position:0%
+big c.
+ 
+
+ align:start position:0%
+big c.
+So it's the guys I already had and then
+
+ align:start position:0%
+So it's the guys I already had and then
+ 
+
+ align:start position:0%
+So it's the guys I already had and then
+I have guys of the format little x plus
+
+ align:start position:0%
+I have guys of the format little x plus
+ 
+
+ align:start position:0%
+I have guys of the format little x plus
+little c. And I only want the new ones,
+
+ align:start position:0%
+little c. And I only want the new ones,
+ 
+
+ align:start position:0%
+little c. And I only want the new ones,
+the ones that aren't already counted.
+
+ align:start position:0%
+the ones that aren't already counted.
+ 
+
+ align:start position:0%
+the ones that aren't already counted.
+That's an equality. And I'm gonna write
+
+ align:start position:0%
+That's an equality. And I'm gonna write
+ 
+
+ align:start position:0%
+That's an equality. And I'm gonna write
+it as x + c plus x minus the x and x. So
+
+ align:start position:0%
+it as x + c plus x minus the x and x. So
+ 
+
+ align:start position:0%
+it as x + c plus x minus the x and x. So
+that x + c is an x plus c.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And now key observation is that
+
+ align:start position:0%
+Okay. And now key observation is that
+ 
+
+ align:start position:0%
+Okay. And now key observation is that
+these guys are all in y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is a subset of y.
+
+ align:start position:0%
+This is a subset of y.
+ 
+
+ align:start position:0%
+This is a subset of y.
+Right? Because if little x plus little c
+
+ align:start position:0%
+Right? Because if little x plus little c
+ 
+
+ align:start position:0%
+Right? Because if little x plus little c
+is in big x plus big c. Um so if little
+
+ align:start position:0%
+is in big x plus big c. Um so if little
+ 
+
+ align:start position:0%
+is in big x plus big c. Um so if little
+x plus little c is in big x plus big c
+
+ align:start position:0%
+x plus little c is in big x plus big c
+ 
+
+ align:start position:0%
+x plus little c is in big x plus big c
+then I can add b to both sides and this
+
+ align:start position:0%
+then I can add b to both sides and this
+ 
+
+ align:start position:0%
+then I can add b to both sides and this
+is in there.
+
+ align:start position:0%
+is in there.
+ 
+
+ align:start position:0%
+is in there.
+So those are all in y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is a subset of y. So the size of
+
+ align:start position:0%
+So this is a subset of y. So the size of
+ 
+
+ align:start position:0%
+So this is a subset of y. So the size of
+this guy is at most the size of y. And
+
+ align:start position:0%
+this guy is at most the size of y. And
+ 
+
+ align:start position:0%
+this guy is at most the size of y. And
+since I'm subtracting here, I can say
+
+ align:start position:0%
+since I'm subtracting here, I can say
+ 
+
+ align:start position:0%
+since I'm subtracting here, I can say
+this is at least x + c + x minus y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now we'll just put together
+
+ align:start position:0%
+So now we'll just put together
+ 
+
+ align:start position:0%
+So now we'll just put together
+everything that we know.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. We know that x + c + b over x + c
+
+ align:start position:0%
+Okay. We know that x + c + b over x + c
+ 
+
+ align:start position:0%
+Okay. We know that x + c + b over x + c
+is at most k bar. We know that by
+
+ align:start position:0%
+is at most k bar. We know that by
+ 
+
+ align:start position:0%
+is at most k bar. We know that by
+induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We know that x + b / x is equal to k
+
+ align:start position:0%
+We know that x + b / x is equal to k
+ 
+
+ align:start position:0%
+We know that x + b / x is equal to k
+bar. We know that by definition. That's
+
+ align:start position:0%
+bar. We know that by definition. That's
+ 
+
+ align:start position:0%
+bar. We know that by definition. That's
+just what k bar was.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we know that y + b over y is greater
+
+ align:start position:0%
+And we know that y + b over y is greater
+ 
+
+ align:start position:0%
+And we know that y + b over y is greater
+than or equal to k bar. That was the
+
+ align:start position:0%
+than or equal to k bar. That was the
+ 
+
+ align:start position:0%
+than or equal to k bar. That was the
+definition of x. x was chosen to
+
+ align:start position:0%
+definition of x. x was chosen to
+ 
+
+ align:start position:0%
+definition of x. x was chosen to
+minimize this ratio.
+
+ align:start position:0%
+minimize this ratio.
+ 
+
+ align:start position:0%
+minimize this ratio.
+Y might perhaps be equal to x, but
+
+ align:start position:0%
+Y might perhaps be equal to x, but
+ 
+
+ align:start position:0%
+Y might perhaps be equal to x, but
+that's that's okay anyway. But it's
+
+ align:start position:0%
+that's that's okay anyway. But it's
+ 
+
+ align:start position:0%
+that's that's okay anyway. But it's
+never going to be any smaller.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay? And so therefore by algebra by how
+
+ align:start position:0%
+Okay? And so therefore by algebra by how
+ 
+
+ align:start position:0%
+Okay? And so therefore by algebra by how
+fractions work x + c + b. Okay. So so
+
+ align:start position:0%
+fractions work x + c + b. Okay. So so
+ 
+
+ align:start position:0%
+fractions work x + c + b. Okay. So so
+now I can say I I want to say x + c
+
+ align:start position:0%
+now I can say I I want to say x + c
+ 
+
+ align:start position:0%
+now I can say I I want to say x + c
+prime + b over x + c prime. And I want
+
+ align:start position:0%
+prime + b over x + c prime. And I want
+ 
+
+ align:start position:0%
+prime + b over x + c prime. And I want
+an upper bound for that.
+
+ align:start position:0%
+an upper bound for that.
+ 
+
+ align:start position:0%
+an upper bound for that.
+Okay. So the numerator is bounded by 1.
+
+ align:start position:0%
+Okay. So the numerator is bounded by 1.
+ 
+
+ align:start position:0%
+Okay. So the numerator is bounded by 1.
+x + c + b + x + b
+
+ align:start position:0%
+x + c + b + x + b
+ 
+
+ align:start position:0%
+x + c + b + x + b
+minus y + b.
+
+ align:start position:0%
+minus y + b.
+ 
+
+ align:start position:0%
+minus y + b.
+And the denominator is lower bounded by
+
+ align:start position:0%
+And the denominator is lower bounded by
+ 
+
+ align:start position:0%
+And the denominator is lower bounded by
+part two and it's x + c + x - y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then because each of these ratios
+
+ align:start position:0%
+And then because each of these ratios
+ 
+
+ align:start position:0%
+And then because each of these ratios
+has the correct sign, this is at most k.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. So this is short. It is a little
+
+ align:start position:0%
+Yeah. So this is short. It is a little
+ 
+
+ align:start position:0%
+Yeah. So this is short. It is a little
+tricky and I must admit I don't quite
+
+ align:start position:0%
+tricky and I must admit I don't quite
+ 
+
+ align:start position:0%
+tricky and I must admit I don't quite
+understand how Petrus thought to do
+
+ align:start position:0%
+understand how Petrus thought to do
+ 
+
+ align:start position:0%
+understand how Petrus thought to do
+this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So from the key lama we can prove
+
+ align:start position:0%
+Okay. So from the key lama we can prove
+ 
+
+ align:start position:0%
+Okay. So from the key lama we can prove
+uh plunic's inequality
+
+ align:start position:0%
+uh plunic's inequality
+ 
+
+ align:start position:0%
+uh plunic's inequality
+and then see if anybody
+
+ align:start position:0%
+and then see if anybody
+ 
+
+ align:start position:0%
+and then see if anybody
+yeah if you have room you can turn turn
+
+ align:start position:0%
+yeah if you have room you can turn turn
+ 
+
+ align:start position:0%
+yeah if you have room you can turn turn
+over in your mind
+
+ align:start position:0%
+over in your mind
+ 
+
+ align:start position:0%
+over in your mind
+why did philosophically why did this
+
+ align:start position:0%
+why did philosophically why did this
+ 
+
+ align:start position:0%
+why did philosophically why did this
+work out so nicely. If anybody has
+
+ align:start position:0%
+work out so nicely. If anybody has
+ 
+
+ align:start position:0%
+work out so nicely. If anybody has
+thoughts about it I would be happy to
+
+ align:start position:0%
+thoughts about it I would be happy to
+ 
+
+ align:start position:0%
+thoughts about it I would be happy to
+hear.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, proof. Okay. So, say we're
+
+ align:start position:0%
+Okay. So, proof. Okay. So, say we're
+ 
+
+ align:start position:0%
+Okay. So, proof. Okay. So, say we're
+starting with this.
+
+ align:start position:0%
+starting with this.
+ 
+
+ align:start position:0%
+starting with this.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by the main the main we use our main
+
+ align:start position:0%
+so by the main the main we use our main
+ 
+
+ align:start position:0%
+so by the main the main we use our main
+lema.
+
+ align:start position:0%
+lema.
+ 
+
+ align:start position:0%
+lema.
+So it tells us that there exists some x
+
+ align:start position:0%
+So it tells us that there exists some x
+ 
+
+ align:start position:0%
+So it tells us that there exists some x
+and a and we have x + c + b at most k *
+
+ align:start position:0%
+and a and we have x + c + b at most k *
+ 
+
+ align:start position:0%
+and a and we have x + c + b at most k *
+x + c for any c.
+
+ align:start position:0%
+x + c for any c.
+ 
+
+ align:start position:0%
+x + c for any c.
+How might we use this?
+
+ align:start position:0%
+How might we use this?
+ 
+
+ align:start position:0%
+How might we use this?
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So okay, C could be empty. So we
+
+ align:start position:0%
+right. So okay, C could be empty. So we
+ 
+
+ align:start position:0%
+right. So okay, C could be empty. So we
+get X + B is at most K * X.
+
+ align:start position:0%
+get X + B is at most K * X.
+ 
+
+ align:start position:0%
+get X + B is at most K * X.
+C could be B. So we get X + B + B.
+
+ align:start position:0%
+C could be B. So we get X + B + B.
+ 
+
+ align:start position:0%
+C could be B. So we get X + B + B.
+That's at most K * X + B.
+
+ align:start position:0%
+That's at most K * X + B.
+ 
+
+ align:start position:0%
+That's at most K * X + B.
+And X plus B was at most K * X. So
+
+ align:start position:0%
+And X plus B was at most K * X. So
+ 
+
+ align:start position:0%
+And X plus B was at most K * X. So
+that's at most K 2 * X.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And you can see where this goes.
+
+ align:start position:0%
+Okay. And you can see where this goes.
+ 
+
+ align:start position:0%
+Okay. And you can see where this goes.
+So I'll do one more. you'll get the
+
+ align:start position:0%
+So I'll do one more. you'll get the
+ 
+
+ align:start position:0%
+So I'll do one more. you'll get the
+pattern. If I add one more b, that's at
+
+ align:start position:0%
+pattern. If I add one more b, that's at
+ 
+
+ align:start position:0%
+pattern. If I add one more b, that's at
+most k x plus b plus b. Plug in what I
+
+ align:start position:0%
+most k x plus b plus b. Plug in what I
+ 
+
+ align:start position:0%
+most k x plus b plus b. Plug in what I
+already know about this. That's at most
+
+ align:start position:0%
+already know about this. That's at most
+ 
+
+ align:start position:0%
+already know about this. That's at most
+k cub * x. All right. So if I add x + m
+
+ align:start position:0%
+k cub * x. All right. So if I add x + m
+ 
+
+ align:start position:0%
+k cub * x. All right. So if I add x + m
+copies of b, that will be at most k * x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And then uh
+
+ align:start position:0%
+And then uh
+ 
+
+ align:start position:0%
+And then uh
+we'll use the roua inequality. So this
+
+ align:start position:0%
+we'll use the roua inequality. So this
+ 
+
+ align:start position:0%
+we'll use the roua inequality. So this
+is already you know if um
+
+ align:start position:0%
+is already you know if um
+ 
+
+ align:start position:0%
+is already you know if um
+uh this is already pretty good thing uh
+
+ align:start position:0%
+uh this is already pretty good thing uh
+ 
+
+ align:start position:0%
+uh this is already pretty good thing uh
+like if a equals b here then I could say
+
+ align:start position:0%
+like if a equals b here then I could say
+ 
+
+ align:start position:0%
+like if a equals b here then I could say
+a to the m is bounded by k to the m * a
+
+ align:start position:0%
+a to the m is bounded by k to the m * a
+ 
+
+ align:start position:0%
+a to the m is bounded by k to the m * a
+right because a to the a to the m is
+
+ align:start position:0%
+right because a to the a to the m is
+ 
+
+ align:start position:0%
+right because a to the a to the m is
+obviously at least as big as x plus a to
+
+ align:start position:0%
+obviously at least as big as x plus a to
+ 
+
+ align:start position:0%
+obviously at least as big as x plus a to
+the m. So I get a the m is bounded by k
+
+ align:start position:0%
+the m. So I get a the m is bounded by k
+ 
+
+ align:start position:0%
+the m. So I get a the m is bounded by k
+the m * a. That's a typical correlary of
+
+ align:start position:0%
+the m * a. That's a typical correlary of
+ 
+
+ align:start position:0%
+the m * a. That's a typical correlary of
+Pluner.
+
+ align:start position:0%
+Pluner.
+ 
+
+ align:start position:0%
+Pluner.
+Anyway, to get the uh advertised finale,
+
+ align:start position:0%
+Anyway, to get the uh advertised finale,
+ 
+
+ align:start position:0%
+Anyway, to get the uh advertised finale,
+we use Ruse's inequality.
+
+ align:start position:0%
+we use Ruse's inequality.
+ 
+
+ align:start position:0%
+we use Ruse's inequality.
+Ruser was a times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there.
+
+ align:start position:0%
+there.
+ 
+
+ align:start position:0%
+there.
+So can plug in um
+
+ align:start position:0%
+So can plug in um
+ 
+
+ align:start position:0%
+So can plug in um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+I say so x * b + m - b + n is bounded by
+
+ align:start position:0%
+I say so x * b + m - b + n is bounded by
+ 
+
+ align:start position:0%
+I say so x * b + m - b + n is bounded by
+x + b + m
+
+ align:start position:0%
+x + b + m
+ 
+
+ align:start position:0%
+x + b + m
+x + b + n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+and then we plug in each of these and we
+
+ align:start position:0%
+and then we plug in each of these and we
+ 
+
+ align:start position:0%
+and then we plug in each of these and we
+get k to the m + n
+
+ align:start position:0%
+get k to the m + n
+ 
+
+ align:start position:0%
+get k to the m + n
+* x*
+
+ align:start position:0%
+* x*
+ 
+
+ align:start position:0%
+* x*
+x².
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, that's right. Okay. So then I uh
+
+ align:start position:0%
+Yeah, that's right. Okay. So then I uh
+ 
+
+ align:start position:0%
+Yeah, that's right. Okay. So then I uh
+get this by itself. So b + m - b + n is
+
+ align:start position:0%
+get this by itself. So b + m - b + n is
+ 
+
+ align:start position:0%
+get this by itself. So b + m - b + n is
+bounded by k m + n * x which is bounded
+
+ align:start position:0%
+bounded by k m + n * x which is bounded
+ 
+
+ align:start position:0%
+bounded by k m + n * x which is bounded
+by k the m + n * a because x is a subset
+
+ align:start position:0%
+by k the m + n * a because x is a subset
+ 
+
+ align:start position:0%
+by k the m + n * a because x is a subset
+of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this proof is short. It is a
+
+ align:start position:0%
+Okay, so this proof is short. It is a
+ 
+
+ align:start position:0%
+Okay, so this proof is short. It is a
+little tricky, but I think it is well
+
+ align:start position:0%
+little tricky, but I think it is well
+ 
+
+ align:start position:0%
+little tricky, but I think it is well
+worth spending some time with uh because
+
+ align:start position:0%
+worth spending some time with uh because
+ 
+
+ align:start position:0%
+worth spending some time with uh because
+this inequality is really quite
+
+ align:start position:0%
+this inequality is really quite
+ 
+
+ align:start position:0%
+this inequality is really quite
+important. I would say that it plays
+
+ align:start position:0%
+important. I would say that it plays
+ 
+
+ align:start position:0%
+important. I would say that it plays
+really a key role in all the later
+
+ align:start position:0%
+really a key role in all the later
+ 
+
+ align:start position:0%
+really a key role in all the later
+developments in projection theory and
+
+ align:start position:0%
+developments in projection theory and
+ 
+
+ align:start position:0%
+developments in projection theory and
+the solution to the CA problem in a lot
+
+ align:start position:0%
+the solution to the CA problem in a lot
+ 
+
+ align:start position:0%
+the solution to the CA problem in a lot
+of things.
+
+ align:start position:0%
+of things.
+ 
+
+ align:start position:0%
+of things.
+Um and uh so as we keep going, you know,
+
+ align:start position:0%
+Um and uh so as we keep going, you know,
+ 
+
+ align:start position:0%
+Um and uh so as we keep going, you know,
+tomorrow, Thursday, and so on, we'll
+
+ align:start position:0%
+tomorrow, Thursday, and so on, we'll
+ 
+
+ align:start position:0%
+tomorrow, Thursday, and so on, we'll
+reflect more about why this is useful
+
+ align:start position:0%
+reflect more about why this is useful
+ 
+
+ align:start position:0%
+reflect more about why this is useful
+and important. Um and um maybe I'll try
+
+ align:start position:0%
+and important. Um and um maybe I'll try
+ 
+
+ align:start position:0%
+and important. Um and um maybe I'll try
+to come up with some homework to try to
+
+ align:start position:0%
+to come up with some homework to try to
+ 
+
+ align:start position:0%
+to come up with some homework to try to
+reflect on on uh how this proof got put
+
+ align:start position:0%
+reflect on on uh how this proof got put
+ 
+
+ align:start position:0%
+reflect on on uh how this proof got put
+together.
\ No newline at end of file
diff --git a/VRMakiEeVJM.txt b/VRMakiEeVJM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a7fe1c54aa41b78172d4b25e720d20a95fb691ec
--- /dev/null
+++ b/VRMakiEeVJM.txt
@@ -0,0 +1,10028 @@
+align:start position:0%
+ 
+so we talked about Rhythm last time all
+
+ align:start position:0%
+so we talked about Rhythm last time all
+ 
+
+ align:start position:0%
+so we talked about Rhythm last time all
+right so the most important thing that
+
+ align:start position:0%
+right so the most important thing that
+ 
+
+ align:start position:0%
+right so the most important thing that
+you want to remember
+
+ align:start position:0%
+you want to remember
+ 
+
+ align:start position:0%
+you want to remember
+is what stressing the content words or
+
+ align:start position:0%
+is what stressing the content words or
+ 
+
+ align:start position:0%
+is what stressing the content words or
+function words content words you stress
+
+ align:start position:0%
+function words content words you stress
+ 
+
+ align:start position:0%
+function words content words you stress
+the content words right you stress the
+
+ align:start position:0%
+the content words right you stress the
+ 
+
+ align:start position:0%
+the content words right you stress the
+content words
+
+ align:start position:0%
+content words
+ 
+
+ align:start position:0%
+content words
+now what happens
+
+ align:start position:0%
+now what happens
+ 
+
+ align:start position:0%
+now what happens
+to what happens to the function words
+
+ align:start position:0%
+ 
+ 
+
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+then the vowels
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+
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+ 
+
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+
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+[Applause]
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+
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+
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+
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+
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+
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+together right d comes between two vows
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+together right d comes between two vows
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+
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+together right d comes between two vows
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+ 
+
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+sh okay sh should
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+ 
+
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+have so does that make sense there are
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+have so does that make sense there are
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+
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+
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+ align:start position:0%
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+ 
+
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+did okay should have could have would
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+did okay should have could have would
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+
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+
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+ 
+
+ align:start position:0%
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+money I could have gone had I had more
+
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+money I could have gone had I had more
+ 
+
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+money I could have gone had I had more
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+
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+money I would have gone had I had more
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+
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+money I would have gone had I had more
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+time and there are people who are glad
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+
+ align:start position:0%
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+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now let's go back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
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+
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+ align:start position:0%
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+ 
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+interesting oh
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+ 
+
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+go back to our course
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+ 
+
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+packet I you to do this
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+ 
+
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+right find the right mattress find the
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
+mattress okay compare your answers with
+ 
+
+ align:start position:0%
+mattress okay compare your answers with
+your NE compare your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answers page 71 page 71 in your course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+packet homework
+
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+packet homework
+ 
+
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+home home not class fork okay compare
+
+ align:start position:0%
+home home not class fork okay compare
+ 
+
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+home home not class fork okay compare
+your
+
+ align:start position:0%
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+ 
+
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+answers hmark people hmark you can
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+answers hmark people hmark you can
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+
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+answers hmark people hmark you can
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+
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+
+ align:start position:0%
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+with okay yeah compare your answers Jen
+
+ align:start position:0%
+with okay yeah compare your answers Jen
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+
+ align:start position:0%
+with okay yeah compare your answers Jen
+and youan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
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+ 
+
+ align:start position:0%
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+number
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+
+ align:start position:0%
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+one everyone number one here up here up
+
+ align:start position:0%
+one everyone number one here up here up
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+
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+one everyone number one here up here up
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+here up here number
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+
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+
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+
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+guys one more time try try to sleep or
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+
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+
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+three three syllables right three
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+three three syllables right three
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+
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+syllables what's okay what's the stress
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+syllables what's okay what's the stress
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+
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+ 
+
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+pattern content content so the answer is
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+e okay number two number two
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+
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+C C or D okay how many how many
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+syllables does this
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+
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+Pro to phone five syllables right five
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+ 
+
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+syllables
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+right you promise the phone everyone you
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+right you promise the phone everyone you
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+
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+ 
+
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+three okay tell
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+ 
+
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+what like to sleep
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+ 
+
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+10 minutes into class you want to go to
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+okay
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+
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+ 
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+this is this a
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+uh
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+
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+even because this occurs in across two
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+even because this occurs in across two
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+
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+
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+
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+
+ align:start position:0%
+it Ste on Ste on cuz there's a constant
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+
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+step okay
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+ align:start position:0%
+step okay
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+
+ align:start position:0%
+step okay
+oh now the uh
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+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I asked you to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right someone I need a volunteer to
+
+ align:start position:0%
+right someone I need a volunteer to
+ 
+
+ align:start position:0%
+right someone I need a volunteer to
+write the last
+
+ align:start position:0%
+write the last
+ 
+
+ align:start position:0%
+write the last
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh ftic symbols of the last
+
+ align:start position:0%
+uh ftic symbols of the last
+ 
+
+ align:start position:0%
+uh ftic symbols of the last
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
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+
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+
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+
+ align:start position:0%
+okay with the linking and everything
+ 
+
+ align:start position:0%
+okay with the linking and everything
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+
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+and I did this I did this for
+ 
+
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+and I did this I did this for
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+
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+you okay it's okay come up here and
+ 
+
+ align:start position:0%
+you okay it's okay come up here and
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+
+ align:start position:0%
+right I I forgot I'm confused so you
+ 
+
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+
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+
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
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+
+ align:start position:0%
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+
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+
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+
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+who wants to do this for us do did we do
+this no
+
+ align:start position:0%
+this no
+ 
+
+ align:start position:0%
+this no
+y I did that for you too I forgot so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+
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+okay very good my have been might have
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+
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+
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+
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+might have been might have been have
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+
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+
+ align:start position:0%
+might have been have this one
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+ align:start position:0%
+so
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+
+ align:start position:0%
+so
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+
+ align:start position:0%
+oh uh I think we want to break it like
+ 
+
+ align:start position:0%
+oh uh I think we want to break it like
+this cat Ain cat a cat Ain cat a bin
+
+ align:start position:0%
+this cat Ain cat a cat Ain cat a bin
+ 
+
+ align:start position:0%
+this cat Ain cat a cat Ain cat a bin
+okay so let's compare this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with how would you say
+
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+with how would you say
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+
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+
+ align:start position:0%
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+
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+becomes yes usually FL stop might be
+
+ align:start position:0%
+becomes yes usually FL stop might be
+ 
+
+ align:start position:0%
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+
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+
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+
+ align:start position:0%
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+
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+
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+that and here have just becomes a flat
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+
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+ma the minute you
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+
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+ 
+
+ align:start position:0%
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+ align:start position:0%
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+ 
+
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+
+ align:start position:0%
+might have been okay but here you don't
+ 
+
+ align:start position:0%
+might have been okay but here you don't
+you don't hear anything you say might be
+
+ align:start position:0%
+you don't hear anything you say might be
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+okay okay so let's do this
+
+ align:start position:0%
+okay okay so let's do this
+ 
+
+ align:start position:0%
+okay okay so let's do this
+together you can stomp along with me one
+
+ align:start position:0%
+together you can stomp along with me one
+ 
+
+ align:start position:0%
+together you can stomp along with me one
+two 3 everyone one two 3 one 2 three
+
+ align:start position:0%
+two 3 everyone one two 3 one 2 three
+ 
+
+ align:start position:0%
+two 3 everyone one two 3 one 2 three
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+ align:start position:0%
+chase CH mice the cats chased mice the
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+ align:start position:0%
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+
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+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
+chasing the mice the cats might have
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+
+ align:start position:0%
+chasing the mice the cats might have
+been chasing the mice the cat oh I
+
+ align:start position:0%
+been chasing the mice the cat oh I
+ 
+
+ align:start position:0%
+been chasing the mice the cat oh I
+messed up this the cats might have been
+
+ align:start position:0%
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+
+ align:start position:0%
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+this was a little difficult the cats
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+ 
+
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+might have been you have to stay might
+ 
+
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+
+ align:start position:0%
+have been to might have here the cats
+ 
+
+ align:start position:0%
+have been to might have here the cats
+have chased the cats have chased mice
+
+ align:start position:0%
+have chased the cats have chased mice
+ 
+
+ align:start position:0%
+have chased the cats have chased mice
+here what happened here the cats have
+
+ align:start position:0%
+here what happened here the cats have
+ 
+
+ align:start position:0%
+here what happened here the cats have
+chased chased over there you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could when I said it I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually now you could I released it I
+
+ align:start position:0%
+actually now you could I released it I
+ 
+
+ align:start position:0%
+actually now you could I released it I
+said chased mice chased mice I said
+
+ align:start position:0%
+said chased mice chased mice I said
+ 
+
+ align:start position:0%
+said chased mice chased mice I said
+chased mice chased mice cuz I was the
+
+ align:start position:0%
+chased mice chased mice cuz I was the
+ 
+
+ align:start position:0%
+chased mice chased mice cuz I was the
+rhythmic pattern chased mice chased mice
+
+ align:start position:0%
+rhythmic pattern chased mice chased mice
+ 
+
+ align:start position:0%
+rhythmic pattern chased mice chased mice
+it was kind of slow between chased and
+
+ align:start position:0%
+it was kind of slow between chased and
+ 
+
+ align:start position:0%
+it was kind of slow between chased and
+mice chased mice so I released the T but
+
+ align:start position:0%
+mice chased mice so I released the T but
+ 
+
+ align:start position:0%
+mice chased mice so I released the T but
+in real fast speech you might
+
+ align:start position:0%
+in real fast speech you might
+ 
+
+ align:start position:0%
+in real fast speech you might
+actually what happens to the T what can
+
+ align:start position:0%
+actually what happens to the T what can
+ 
+
+ align:start position:0%
+actually what happens to the T what can
+happen to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T huh drop it drop it what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because three syllables three consonants
+
+ align:start position:0%
+because three syllables three consonants
+ 
+
+ align:start position:0%
+because three syllables three consonants
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+
+ align:start position:0%
+1 two three three consonants you get rid
+ 
+
+ align:start position:0%
+1 two three three consonants you get rid
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+
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+
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as I asked him asked
+
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+
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+
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+him ask them okay ask them ask
+ 
+
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+them ask okay s
+
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+them ask okay s
+ 
+
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+
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+s as oh
+ 
+
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+
+ align:start position:0%
+oh here what we get rid of H
+ 
+
+ align:start position:0%
+oh here what we get rid of H
+automatically right we get and three
+
+ align:start position:0%
+automatically right we get and three
+ 
+
+ align:start position:0%
+automatically right we get and three
+consonants we get rid of the middle one
+
+ align:start position:0%
+consonants we get rid of the middle one
+ 
+
+ align:start position:0%
+consonants we get rid of the middle one
+okay ask them ask them ask them ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them but here you have to have Chase the
+
+ align:start position:0%
+them but here you have to have Chase the
+ 
+
+ align:start position:0%
+them but here you have to have Chase the
+chase the chase the M Chas the chase the
+
+ align:start position:0%
+chase the chase the M Chas the chase the
+ 
+
+ align:start position:0%
+chase the chase the M Chas the chase the
+chase the mice okay so this is this
+
+ align:start position:0%
+chase the mice okay so this is this
+ 
+
+ align:start position:0%
+chase the mice okay so this is this
+one's chase mice chase chase mice Chas
+
+ align:start position:0%
+one's chase mice chase chase mice Chas
+ 
+
+ align:start position:0%
+one's chase mice chase chase mice Chas
+chase the mice chase the mice chase the
+
+ align:start position:0%
+chase the mice chase the mice chase the
+ 
+
+ align:start position:0%
+chase the mice chase the mice chase the
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+
+ align:start position:0%
+mice chase the mice chase the mice chase
+ 
+
+ align:start position:0%
+mice chase the mice chase the mice chase
+the mice chase the mice Chase t Okay
+
+ align:start position:0%
+the mice chase the mice Chase t Okay
+ 
+
+ align:start position:0%
+the mice chase the mice Chase t Okay
+tast one more
+
+ align:start position:0%
+tast one more
+ 
+
+ align:start position:0%
+tast one more
+time 1 2 3 that's too fast one two three
+
+ align:start position:0%
+time 1 2 3 that's too fast one two three
+ 
+
+ align:start position:0%
+time 1 2 3 that's too fast one two three
+one two three cats chase mice cats chase
+
+ align:start position:0%
+one two three cats chase mice cats chase
+ 
+
+ align:start position:0%
+one two three cats chase mice cats chase
+mice the cats chase mice the cats chase
+
+ align:start position:0%
+mice the cats chase mice the cats chase
+ 
+
+ align:start position:0%
+mice the cats chase mice the cats chase
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+
+ align:start position:0%
+mice the cats have chased mice the cats
+ 
+
+ align:start position:0%
+mice the cats have chased mice the cats
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+
+ align:start position:0%
+have chased mice the cats have chased
+ 
+
+ align:start position:0%
+have chased mice the cats have chased
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+
+ align:start position:0%
+the mice the cats have chased the mice
+ 
+
+ align:start position:0%
+the mice the cats have chased the mice
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+
+ align:start position:0%
+the cats have been chasing the mice the
+ 
+
+ align:start position:0%
+the cats have been chasing the mice the
+cats been chasing the mice the cats
+
+ align:start position:0%
+cats been chasing the mice the cats
+ 
+
+ align:start position:0%
+cats been chasing the mice the cats
+might have been chasing the mice the
+
+ align:start position:0%
+might have been chasing the mice the
+ 
+
+ align:start position:0%
+might have been chasing the mice the
+cats might chasing theice yes we did it
+
+ align:start position:0%
+cats might chasing theice yes we did it
+ 
+
+ align:start position:0%
+cats might chasing theice yes we did it
+any questions about
+
+ align:start position:0%
+any questions about
+ 
+
+ align:start position:0%
+any questions about
+this reducing the vowels very important
+
+ align:start position:0%
+this reducing the vowels very important
+ 
+
+ align:start position:0%
+this reducing the vowels very important
+reducing the vows very important
+
+ align:start position:0%
+reducing the vows very important
+ 
+
+ align:start position:0%
+reducing the vows very important
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh how am I gonna one two one two
+
+ align:start position:0%
+uh how am I gonna one two one two
+ 
+
+ align:start position:0%
+uh how am I gonna one two one two
+we're going to okay one two one we're
+
+ align:start position:0%
+we're going to okay one two one we're
+ 
+
+ align:start position:0%
+we're going to okay one two one we're
+going to number off one two one two one
+
+ align:start position:0%
+going to number off one two one two one
+ 
+
+ align:start position:0%
+going to number off one two one two one
+two one two okay one two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay one so you're Partners one two
+
+ align:start position:0%
+one okay one so you're Partners one two
+ 
+
+ align:start position:0%
+one okay one so you're Partners one two
+one two you guys are Partners okay and I
+
+ align:start position:0%
+one two you guys are Partners okay and I
+ 
+
+ align:start position:0%
+one two you guys are Partners okay and I
+want you to pick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is this the right envelope yes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so each pair gets one sentence each pair
+
+ align:start position:0%
+so each pair gets one sentence each pair
+ 
+
+ align:start position:0%
+so each pair gets one sentence each pair
+gets one
+
+ align:start position:0%
+gets one
+ 
+
+ align:start position:0%
+gets one
+sentence no no no you got you guys got
+
+ align:start position:0%
+sentence no no no you got you guys got
+ 
+
+ align:start position:0%
+sentence no no no you got you guys got
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay each pair gets one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sentence each pair gets one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sentence okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay as a pair your task is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to come up with the correct rhythmic
+
+ align:start position:0%
+to come up with the correct rhythmic
+ 
+
+ align:start position:0%
+to come up with the correct rhythmic
+pattern okay
+
+ align:start position:0%
+pattern okay
+ 
+
+ align:start position:0%
+pattern okay
+like and I'm going to
+
+ align:start position:0%
+like and I'm going to
+ 
+
+ align:start position:0%
+like and I'm going to
+write the patterns on the board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it's the same task first thing
+
+ align:start position:0%
+okay so it's the same task first thing
+ 
+
+ align:start position:0%
+okay so it's the same task first thing
+you need to do is to figure out how many
+
+ align:start position:0%
+you need to do is to figure out how many
+ 
+
+ align:start position:0%
+you need to do is to figure out how many
+syllables your sentence has okay how
+
+ align:start position:0%
+syllables your sentence has okay how
+ 
+
+ align:start position:0%
+syllables your sentence has okay how
+many syllables count that and think
+
+ align:start position:0%
+many syllables count that and think
+ 
+
+ align:start position:0%
+many syllables count that and think
+about okay which ones are content Words
+
+ align:start position:0%
+about okay which ones are content Words
+ 
+
+ align:start position:0%
+about okay which ones are content Words
+which ones are function words and you're
+
+ align:start position:0%
+which ones are function words and you're
+ 
+
+ align:start position:0%
+which ones are function words and you're
+going to have stress on the content
+
+ align:start position:0%
+going to have stress on the content
+ 
+
+ align:start position:0%
+going to have stress on the content
+words right right and then you have to
+
+ align:start position:0%
+words right right and then you have to
+ 
+
+ align:start position:0%
+words right right and then you have to
+reduce function fun words reduce
+
+ align:start position:0%
+reduce function fun words reduce
+ 
+
+ align:start position:0%
+reduce function fun words reduce
+function words and do all the linking
+
+ align:start position:0%
+function words and do all the linking
+ 
+
+ align:start position:0%
+function words and do all the linking
+okay do all the
+
+ align:start position:0%
+okay do all the
+ 
+
+ align:start position:0%
+okay do all the
+linking and as a pair practice saying
+
+ align:start position:0%
+linking and as a pair practice saying
+ 
+
+ align:start position:0%
+linking and as a pair practice saying
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sentence
+
+ align:start position:0%
+sentence
+ 
+
+ align:start position:0%
+sentence
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+as as correctly as possible together
+
+ align:start position:0%
+as as correctly as possible together
+ 
+
+ align:start position:0%
+as as correctly as possible together
+okay and I'm going to ask uh both of you
+
+ align:start position:0%
+okay and I'm going to ask uh both of you
+ 
+
+ align:start position:0%
+okay and I'm going to ask uh both of you
+to say the sentence together at the same
+
+ align:start position:0%
+to say the sentence together at the same
+ 
+
+ align:start position:0%
+to say the sentence together at the same
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay your sentence should have at least
+
+ align:start position:0%
+okay your sentence should have at least
+ 
+
+ align:start position:0%
+okay your sentence should have at least
+should have one of these four patterns
+
+ align:start position:0%
+should have one of these four patterns
+ 
+
+ align:start position:0%
+should have one of these four patterns
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+what this is a reduced uh reduced
+
+ align:start position:0%
+what this is a reduced uh reduced
+ 
+
+ align:start position:0%
+what this is a reduced uh reduced
+syllable this is the stressed syllable
+
+ align:start position:0%
+syllable this is the stressed syllable
+ 
+
+ align:start position:0%
+syllable this is the stressed syllable
+okay and figure that out too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ready ready okay now everyone stand up
+
+ align:start position:0%
+ready ready okay now everyone stand up
+ 
+
+ align:start position:0%
+ready ready okay now everyone stand up
+up up and go to the board stand under
+
+ align:start position:0%
+up up and go to the board stand under
+ 
+
+ align:start position:0%
+up up and go to the board stand under
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number SC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah I I I forgot something I I
+
+ align:start position:0%
+okay yeah I I I forgot something I I
+ 
+
+ align:start position:0%
+okay yeah I I I forgot something I I
+forgot the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lines everyone ready did you did you
+
+ align:start position:0%
+lines everyone ready did you did you
+ 
+
+ align:start position:0%
+lines everyone ready did you did you
+practice see this sentence together okay
+
+ align:start position:0%
+practice see this sentence together okay
+ 
+
+ align:start position:0%
+practice see this sentence together okay
+remember the Rhythm linking get rid of
+
+ align:start position:0%
+remember the Rhythm linking get rid of
+ 
+
+ align:start position:0%
+remember the Rhythm linking get rid of
+certain sounds okay reduce the
+
+ align:start position:0%
+certain sounds okay reduce the
+ 
+
+ align:start position:0%
+certain sounds okay reduce the
+vowels ready okay we'll hear from the
+
+ align:start position:0%
+vowels ready okay we'll hear from the
+ 
+
+ align:start position:0%
+vowels ready okay we'll hear from the
+first group as loudly as
+
+ align:start position:0%
+first group as loudly as
+ 
+
+ align:start position:0%
+first group as loudly as
+possible he in
+
+ align:start position:0%
+possible he in
+ 
+
+ align:start position:0%
+possible he in
+Sp together at the same
+
+ align:start position:0%
+Sp together at the same
+ 
+
+ align:start position:0%
+Sp together at the same
+time one more time he Liv
+
+ align:start position:0%
+time one more time he Liv
+ 
+
+ align:start position:0%
+time one more time he Liv
+in okay everyone you have to pay
+
+ align:start position:0%
+in okay everyone you have to pay
+ 
+
+ align:start position:0%
+in okay everyone you have to pay
+attention is that is that good one more
+
+ align:start position:0%
+attention is that is that good one more
+ 
+
+ align:start position:0%
+attention is that is that good one more
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+he Liv
+
+ align:start position:0%
+he Liv
+ 
+
+ align:start position:0%
+he Liv
+in yes one more time he Liv and do we
+
+ align:start position:0%
+in yes one more time he Liv and do we
+ 
+
+ align:start position:0%
+in yes one more time he Liv and do we
+have the same do you have the do you
+
+ align:start position:0%
+have the same do you have the do you
+ 
+
+ align:start position:0%
+have the same do you have the do you
+have the correct rhythmic pattern he he
+
+ align:start position:0%
+have the correct rhythmic pattern he he
+ 
+
+ align:start position:0%
+have the correct rhythmic pattern he he
+lived in Spain he lived in Spain perfect
+
+ align:start position:0%
+lived in Spain he lived in Spain perfect
+ 
+
+ align:start position:0%
+lived in Spain he lived in Spain perfect
+very good very good thank
+
+ align:start position:0%
+very good very good thank
+ 
+
+ align:start position:0%
+very good very good thank
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+okay well and after you can you can
+
+ align:start position:0%
+okay well and after you can you can
+ 
+
+ align:start position:0%
+okay well and after you can you can
+write your sentence on the board now
+
+ align:start position:0%
+write your sentence on the board now
+ 
+
+ align:start position:0%
+write your sentence on the board now
+next everyone pay attention
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please she sat at home one more time she
+
+ align:start position:0%
+please she sat at home one more time she
+ 
+
+ align:start position:0%
+please she sat at home one more time she
+sat at home she sat at home she sat at
+
+ align:start position:0%
+sat at home she sat at home she sat at
+ 
+
+ align:start position:0%
+sat at home she sat at home she sat at
+home she's sad at home okay they have a
+
+ align:start position:0%
+home she's sad at home okay they have a
+ 
+
+ align:start position:0%
+home she's sad at home okay they have a
+flap there she's sad at home is that
+
+ align:start position:0%
+flap there she's sad at home is that
+ 
+
+ align:start position:0%
+flap there she's sad at home is that
+good sad at home she sad at home very
+
+ align:start position:0%
+good sad at home she sad at home very
+ 
+
+ align:start position:0%
+good sad at home she sad at home very
+good write your sentence in the board
+
+ align:start position:0%
+good write your sentence in the board
+ 
+
+ align:start position:0%
+good write your sentence in the board
+where your sent in the board and you can
+
+ align:start position:0%
+where your sent in the board and you can
+ 
+
+ align:start position:0%
+where your sent in the board and you can
+sit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay on three one two three they
+
+ align:start position:0%
+okay on three one two three they
+ 
+
+ align:start position:0%
+okay on three one two three they
+stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+listen pay attention
+
+ align:start position:0%
+listen pay attention
+ 
+
+ align:start position:0%
+listen pay attention
+please one two three they stop talk they
+
+ align:start position:0%
+please one two three they stop talk they
+ 
+
+ align:start position:0%
+please one two three they stop talk they
+stop talk stop to talk they
+
+ align:start position:0%
+stop talk stop to talk they
+ 
+
+ align:start position:0%
+stop talk stop to talk they
+stop okay two two is a syllable they
+
+ align:start position:0%
+stop okay two two is a syllable they
+ 
+
+ align:start position:0%
+stop okay two two is a syllable they
+stop to talk they stop to talk to to to
+
+ align:start position:0%
+stop to talk they stop to talk to to to
+ 
+
+ align:start position:0%
+stop to talk they stop to talk to to to
+has a vow to they stop to talk it sounds
+
+ align:start position:0%
+has a vow to they stop to talk it sounds
+ 
+
+ align:start position:0%
+has a vow to they stop to talk it sounds
+like you don't have a vow they sto to
+
+ align:start position:0%
+like you don't have a vow they sto to
+ 
+
+ align:start position:0%
+like you don't have a vow they sto to
+they sto to talk one more
+
+ align:start position:0%
+they sto to talk one more
+ 
+
+ align:start position:0%
+they sto to talk one more
+time they sto the talk one two three
+
+ align:start position:0%
+time they sto the talk one two three
+ 
+
+ align:start position:0%
+time they sto the talk one two three
+they sto the talk they sto to talk they
+
+ align:start position:0%
+they sto the talk they sto to talk they
+ 
+
+ align:start position:0%
+they sto the talk they sto to talk they
+stop to to to is a vow there's a vow
+
+ align:start position:0%
+stop to to to is a vow there's a vow
+ 
+
+ align:start position:0%
+stop to to to is a vow there's a vow
+there they stop to
+
+ align:start position:0%
+there they stop to
+ 
+
+ align:start position:0%
+there they stop to
+talk they stop the
+
+ align:start position:0%
+talk they stop the
+ 
+
+ align:start position:0%
+talk they stop the
+talk say to they sto the talk they sto
+
+ align:start position:0%
+talk say to they sto the talk they sto
+ 
+
+ align:start position:0%
+talk say to they sto the talk they sto
+to they stop stopped to they stopped to
+
+ align:start position:0%
+to they stop stopped to they stopped to
+ 
+
+ align:start position:0%
+to they stop stopped to they stopped to
+talk they stopped to talk they stopped
+
+ align:start position:0%
+talk they stopped to talk they stopped
+ 
+
+ align:start position:0%
+talk they stopped to talk they stopped
+to talk they stopped to
+
+ align:start position:0%
+to talk they stopped to
+ 
+
+ align:start position:0%
+to talk they stopped to
+talk they stopped to talk they stopped
+
+ align:start position:0%
+talk they stopped to talk they stopped
+ 
+
+ align:start position:0%
+talk they stopped to talk they stopped
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk they stopped to talk very good they
+
+ align:start position:0%
+talk they stopped to talk very good they
+ 
+
+ align:start position:0%
+talk they stopped to talk very good they
+stopped to talk okay write your sentence
+
+ align:start position:0%
+stopped to talk okay write your sentence
+ 
+
+ align:start position:0%
+stopped to talk okay write your sentence
+on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board one 2
+
+ align:start position:0%
+board one 2
+ 
+
+ align:start position:0%
+board one 2
+3 letter one 2 three she wrote a letter
+
+ align:start position:0%
+3 letter one 2 three she wrote a letter
+ 
+
+ align:start position:0%
+3 letter one 2 three she wrote a letter
+she wrote a slab is a little kind of she
+
+ align:start position:0%
+she wrote a slab is a little kind of she
+ 
+
+ align:start position:0%
+she wrote a slab is a little kind of she
+wrote a letter she wrote a letter she
+
+ align:start position:0%
+wrote a letter she wrote a letter she
+ 
+
+ align:start position:0%
+wrote a letter she wrote a letter she
+wrote a letter she wrote a
+
+ align:start position:0%
+wrote a letter she wrote a
+ 
+
+ align:start position:0%
+wrote a letter she wrote a
+letter
+
+ align:start position:0%
+letter
+ 
+
+ align:start position:0%
+letter
+letter this is very difficult because
+
+ align:start position:0%
+letter this is very difficult because
+ 
+
+ align:start position:0%
+letter this is very difficult because
+you have the L and R and the flap okay
+
+ align:start position:0%
+you have the L and R and the flap okay
+ 
+
+ align:start position:0%
+you have the L and R and the flap okay
+write your sentence on the board
+
+ align:start position:0%
+write your sentence on the board
+ 
+
+ align:start position:0%
+write your sentence on the board
+okay oh one two three ask question one
+
+ align:start position:0%
+okay oh one two three ask question one
+ 
+
+ align:start position:0%
+okay oh one two three ask question one
+two three ask
+
+ align:start position:0%
+two three ask
+ 
+
+ align:start position:0%
+two three ask
+question I don't I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't what 1 two
+
+ align:start position:0%
+don't what 1 two
+ 
+
+ align:start position:0%
+don't what 1 two
+three fish one okay together one two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three okay but please write your write
+
+ align:start position:0%
+three okay but please write your write
+ 
+
+ align:start position:0%
+three okay but please write your write
+your sentence on the board we'll work on
+
+ align:start position:0%
+your sentence on the board we'll work on
+ 
+
+ align:start position:0%
+your sentence on the board we'll work on
+that together write your sentence on the
+
+ align:start position:0%
+that together write your sentence on the
+ 
+
+ align:start position:0%
+that together write your sentence on the
+board and put a check mark next to
+
+ align:start position:0%
+board and put a check mark next to
+ 
+
+ align:start position:0%
+board and put a check mark next to
+it meaning not good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay one two 3 I see what do you
+
+ align:start position:0%
+okay one two 3 I see what do you
+ 
+
+ align:start position:0%
+okay one two 3 I see what do you
+mean one 2 three I see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no one more time one two three I see
+
+ align:start position:0%
+no one more time one two three I see
+ 
+
+ align:start position:0%
+no one more time one two three I see
+what you mean good what you what okay
+
+ align:start position:0%
+what you mean good what you what okay
+ 
+
+ align:start position:0%
+what you mean good what you what okay
+you have two options watch you you can
+
+ align:start position:0%
+you have two options watch you you can
+ 
+
+ align:start position:0%
+you have two options watch you you can
+you can you can palatalize it watch you
+
+ align:start position:0%
+you can you can palatalize it watch you
+ 
+
+ align:start position:0%
+you can you can palatalize it watch you
+or what you use a lot of stuff but you
+
+ align:start position:0%
+or what you use a lot of stuff but you
+ 
+
+ align:start position:0%
+or what you use a lot of stuff but you
+can't have a flap the first time you had
+
+ align:start position:0%
+can't have a flap the first time you had
+ 
+
+ align:start position:0%
+can't have a flap the first time you had
+a flap I see what you you had a flap
+
+ align:start position:0%
+a flap I see what you you had a flap
+ 
+
+ align:start position:0%
+a flap I see what you you had a flap
+right don't have a flap what you what
+
+ align:start position:0%
+right don't have a flap what you what
+ 
+
+ align:start position:0%
+right don't have a flap what you what
+you or what you one more time one two
+
+ align:start position:0%
+you or what you one more time one two
+ 
+
+ align:start position:0%
+you or what you one more time one two
+three I see what you mean very
+
+ align:start position:0%
+three I see what you mean very
+ 
+
+ align:start position:0%
+three I see what you mean very
+good I see what you mean where I see
+
+ align:start position:0%
+good I see what you mean where I see
+ 
+
+ align:start position:0%
+good I see what you mean where I see
+what you mean what you mean I think I
+
+ align:start position:0%
+what you mean what you mean I think I
+ 
+
+ align:start position:0%
+what you mean what you mean I think I
+mean I use a lot of stuff WR down on the
+
+ align:start position:0%
+mean I use a lot of stuff WR down on the
+ 
+
+ align:start position:0%
+mean I use a lot of stuff WR down on the
+board okay one two
+
+ align:start position:0%
+board okay one two
+ 
+
+ align:start position:0%
+board okay one two
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+SE one 2 3 we thought SE oh good
+
+ align:start position:0%
+SE one 2 3 we thought SE oh good
+ 
+
+ align:start position:0%
+SE one 2 3 we thought SE oh good
+one two
+
+ align:start position:0%
+one two
+ 
+
+ align:start position:0%
+one two
+three okay sick the Val sick it's the
+
+ align:start position:0%
+three okay sick the Val sick it's the
+ 
+
+ align:start position:0%
+three okay sick the Val sick it's the
+it's the last sick sick very good write
+
+ align:start position:0%
+it's the last sick sick very good write
+ 
+
+ align:start position:0%
+it's the last sick sick very good write
+your sentence in the board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next one two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three one 2 3
+
+ align:start position:0%
+three one 2 3
+ 
+
+ align:start position:0%
+three one 2 3
+start okay everyone
+
+ align:start position:0%
+start okay everyone
+ 
+
+ align:start position:0%
+start okay everyone
+listen one 2 3 he started the
+
+ align:start position:0%
+listen one 2 3 he started the
+ 
+
+ align:start position:0%
+listen one 2 3 he started the
+Le flat started started started he
+
+ align:start position:0%
+Le flat started started started he
+ 
+
+ align:start position:0%
+Le flat started started started he
+started to leave 1 2 3 started leave
+
+ align:start position:0%
+started to leave 1 2 3 started leave
+ 
+
+ align:start position:0%
+started to leave 1 2 3 started leave
+started started okay give me your
+
+ align:start position:0%
+started started okay give me your
+ 
+
+ align:start position:0%
+started started okay give me your
+sentence write your sentence on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board a sentence on the
+
+ align:start position:0%
+board a sentence on the
+ 
+
+ align:start position:0%
+board a sentence on the
+board put a check mark
+
+ align:start position:0%
+board put a check mark
+ 
+
+ align:start position:0%
+board put a check mark
+check mark next to it put a check mark
+
+ align:start position:0%
+check mark next to it put a check mark
+ 
+
+ align:start position:0%
+check mark next to it put a check mark
+here and you can sit down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay take your
+
+ align:start position:0%
+okay okay take your
+ 
+
+ align:start position:0%
+okay okay take your
+in one 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 one two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 one two 3 we have decided to live okay
+
+ align:start position:0%
+3 one two 3 we have decided to live okay
+ 
+
+ align:start position:0%
+3 one two 3 we have decided to live okay
+we decided to live good okay what in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+okay 1 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 1 2 3 they discuss prank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very ready
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's good the stress is
+
+ align:start position:0%
+that's good the stress is
+ 
+
+ align:start position:0%
+that's good the stress is
+here okay you want to do this
+
+ align:start position:0%
+here okay you want to do this
+ 
+
+ align:start position:0%
+here okay you want to do this
+again you ask the question okay that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question very okay one one more one
+
+ align:start position:0%
+question very okay one one more one
+ 
+
+ align:start position:0%
+question very okay one one more one
+time no no on three one 2 three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay one more time one 2 3
+
+ align:start position:0%
+okay one more time one 2 3
+ 
+
+ align:start position:0%
+okay one more time one 2 3
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together one 2 3 you ask the question
+
+ align:start position:0%
+together one 2 3 you ask the question
+ 
+
+ align:start position:0%
+together one 2 3 you ask the question
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+
+ align:start position:0%
+very good very good you can sit
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+ align:start position:0%
+down first time what they do not have
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+
+ align:start position:0%
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+you ask the the it's very important the
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+
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+
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+question you asked the question you as
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+
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+the question asked the asked the that's
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+
+ align:start position:0%
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+
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+difficult uh this
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+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one this is a flap okay flap but not a
+
+ align:start position:0%
+one this is a flap okay flap but not a
+ 
+
+ align:start position:0%
+one this is a flap okay flap but not a
+flap he started to leave he started to
+
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+flap he started to leave he started to
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+flap he started to leave he started to
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+
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+started started started started started
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+started started started started started
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+
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+started he started to leave started
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+started he started to leave started
+okay here we thought we thought
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+okay here we thought we thought
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+okay here we thought we thought
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+your you could again we thought we
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+thought you I I I use a GL stop we
+thought you sick we thought sick we
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+thought you sick we thought sick we
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+sick I see what you mean I see what you
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+mean I see what you mean I see what you
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+mean uh we decided to leave that was
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+mean uh we decided to leave that was
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+good oh this
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+one they disgusted as a friend they
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+ 
+Frank okay this
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+ 
+ 
+
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+ 
+one he lived in Spain lived in Spain he
+
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+okay they
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+okay they
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+
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+stop you're going to get rid of this one
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+
+ align:start position:0%
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+ 
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+th okay this becomes more like a
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+th okay this becomes more like a
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+th okay this becomes more like a
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+or they sto the talk no what you're
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+ align:start position:0%
+or they sto the talk no what you're
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+say say stop stop two two stop two stop
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+say say stop stop two two stop two stop
+to stop to stop to stop to talk stop to
+
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+to stop to stop to stop to talk stop to
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+
+ align:start position:0%
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+
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+they stop to talk they stop to
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+pleas yeah yeah you could think of it
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+pleas yeah yeah you could think of it
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+pleas yeah yeah you could think of it
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+
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+ align:start position:0%
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+
+ align:start position:0%
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+they I think they're different but I it
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+they I think they're different but I it
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+
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+I'm using a glot of stop here I they
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+I'm using a glot of stop here I they
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+
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+there might not be any difference they
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+stop to talk there are two t here two t
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+ align:start position:0%
+stop to talk there are two t here two t
+here right so get rid of one t stop to
+
+ align:start position:0%
+here right so get rid of one t stop to
+ 
+
+ align:start position:0%
+here right so get rid of one t stop to
+talk they stop to talk stop talk they
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+talk they stop to talk stop talk they
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+sto to
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+sto to
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+
+ align:start position:0%
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+flab okay
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+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ro becomes a flap she wrote a letter she
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+Ro becomes a flap she wrote a letter she
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+Ro becomes a flap she wrote a letter she
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+wrote a letter she wrote a letter she
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+wrote a letter she wrote a letter she
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+wrote a letter she wrote a letter she
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+wrote a letter she wrote a letter wrote
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+wrote a letter she wrote a letter wrote
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+
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+really
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+really
+tense she wrote a letter wrote a letter
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+tense she wrote a letter wrote a letter
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+
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+tense she wrote a letter wrote a letter
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+ align:start position:0%
+she wrote a letter she wrote a letter
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+
+ align:start position:0%
+she wrote a letter she wrote a letter
+okay any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+letter you explain why I can't apply
+
+ align:start position:0%
+letter you explain why I can't apply
+ 
+
+ align:start position:0%
+letter you explain why I can't apply
+flat between the Y and you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+why because this is a parallelization
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+why because this is a parallelization
+ 
+
+ align:start position:0%
+why because this is a parallelization
+this is a consonant sound U is a
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+this is a consonant sound U is a
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+
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+this is a consonant sound U is a
+consonant sound right whenever you have
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+consonant sound right whenever you have
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+
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+consonant sound right whenever you have
+t and Y together you becomes two right
+
+ align:start position:0%
+t and Y together you becomes two right
+ 
+
+ align:start position:0%
+t and Y together you becomes two right
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+palent or use a GL stop and why what you
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+ align:start position:0%
+palent or use a GL stop and why what you
+okay what do you what do you not good
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+okay what do you what do you not good
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+
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+okay what do you what do you not good
+what do you not
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+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+good
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+ align:start position:0%
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+ 
+
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+here so for inst
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+here so for inst
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+here so for inst
+what do you mean what do you mean what
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+what do you mean what do you mean what
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+what do you mean what do you mean what
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+
+ align:start position:0%
+do you mean yes then then T and D it
+becomes like what do you what do you
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+becomes like what do you what do you
+ 
+
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+becomes like what do you what do you
+like I said you say it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like do you do you okay so T and the
+
+ align:start position:0%
+like do you do you okay so T and the
+ 
+
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+like do you do you okay so T and the
+what's because this is so common we say
+
+ align:start position:0%
+what's because this is so common we say
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+
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+what's because this is so common we say
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+just uh put T and D together and say one
+
+ align:start position:0%
+just uh put T and D together and say one
+ 
+
+ align:start position:0%
+just uh put T and D together and say one
+flat what do you what what are you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions she said at home now again H
+
+ align:start position:0%
+questions she said at home now again H
+ 
+
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+questions she said at home now again H
+is a consonant right so she sat she sat
+
+ align:start position:0%
+is a consonant right so she sat she sat
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+
+ align:start position:0%
+is a consonant right so she sat she sat
+at home
+
+ align:start position:0%
+at home
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+
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+but she sad she sad at home she's sad at
+
+ align:start position:0%
+but she sad she sad at home she's sad at
+ 
+
+ align:start position:0%
+but she sad she sad at home she's sad at
+home I think this becomes a flap too
+
+ align:start position:0%
+home I think this becomes a flap too
+ 
+
+ align:start position:0%
+home I think this becomes a flap too
+actually she's sad at home she's sad at
+
+ align:start position:0%
+actually she's sad at home she's sad at
+ 
+
+ align:start position:0%
+actually she's sad at home she's sad at
+home she's sad at home she satad at
+
+ align:start position:0%
+home she's sad at home she satad at
+ 
+
+ align:start position:0%
+home she's sad at home she satad at
+homeed she sad to the
+
+ align:start position:0%
+homeed she sad to the
+ 
+
+ align:start position:0%
+homeed she sad to the
+but that that rule applies only to one
+
+ align:start position:0%
+but that that rule applies only to one
+ 
+
+ align:start position:0%
+but that that rule applies only to one
+one word not across two words not across
+
+ align:start position:0%
+one word not across two words not across
+ 
+
+ align:start position:0%
+one word not across two words not across
+to we had we had the same question last
+
+ align:start position:0%
+to we had we had the same question last
+ 
+
+ align:start position:0%
+to we had we had the same question last
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+right she sat at home she sat at home
+
+ align:start position:0%
+right she sat at home she sat at home
+ 
+
+ align:start position:0%
+right she sat at home she sat at home
+she sat at she sat she sat at home she
+
+ align:start position:0%
+she sat at she sat she sat at home she
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+
+ align:start position:0%
+she sat at she sat she sat at home she
+sat at she sat at home she sat at home
+
+ align:start position:0%
+sat at she sat at home she sat at home
+ 
+
+ align:start position:0%
+sat at she sat at home she sat at home
+she sat at home she sat at home yes to
+
+ align:start position:0%
+she sat at home she sat at home yes to
+ 
+
+ align:start position:0%
+she sat at home she sat at home yes to
+me becomes like a flap she sat at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+home okay did I did I collect all the
+
+ align:start position:0%
+home okay did I did I collect all the
+ 
+
+ align:start position:0%
+home okay did I did I collect all the
+sentences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back uh okay we just reviewed Rhythm any
+
+ align:start position:0%
+back uh okay we just reviewed Rhythm any
+ 
+
+ align:start position:0%
+back uh okay we just reviewed Rhythm any
+questions about Rhythm sentence stress
+
+ align:start position:0%
+questions about Rhythm sentence stress
+ 
+
+ align:start position:0%
+questions about Rhythm sentence stress
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+Rhythm okay now we're going to talk
+
+ align:start position:0%
+Rhythm okay now we're going to talk
+ 
+
+ align:start position:0%
+Rhythm okay now we're going to talk
+about unreal past conditional and after
+
+ align:start position:0%
+about unreal past conditional and after
+ 
+
+ align:start position:0%
+about unreal past conditional and after
+that we're going to talk we're going to
+
+ align:start position:0%
+that we're going to talk we're going to
+ 
+
+ align:start position:0%
+that we're going to talk we're going to
+start talking about prominence today um
+
+ align:start position:0%
+start talking about prominence today um
+ 
+
+ align:start position:0%
+start talking about prominence today um
+on Tuesday next week right Tuesday
+
+ align:start position:0%
+on Tuesday next week right Tuesday
+ 
+
+ align:start position:0%
+on Tuesday next week right Tuesday
+Tuesday after Tuesday we have a holiday
+
+ align:start position:0%
+Tuesday after Tuesday we have a holiday
+ 
+
+ align:start position:0%
+Tuesday after Tuesday we have a holiday
+on Thursday so after Tuesday I I get to
+
+ align:start position:0%
+on Thursday so after Tuesday I I get to
+ 
+
+ align:start position:0%
+on Thursday so after Tuesday I I get to
+say have a nice weekend after
+
+ align:start position:0%
+say have a nice weekend after
+ 
+
+ align:start position:0%
+say have a nice weekend after
+Tuesday now according to your schedule
+
+ align:start position:0%
+Tuesday now according to your schedule
+ 
+
+ align:start position:0%
+Tuesday now according to your schedule
+there should be an ADM quiz on Tuesday
+
+ align:start position:0%
+there should be an ADM quiz on Tuesday
+ 
+
+ align:start position:0%
+there should be an ADM quiz on Tuesday
+but no quiz on Tuesday we're going to
+
+ align:start position:0%
+but no quiz on Tuesday we're going to
+ 
+
+ align:start position:0%
+but no quiz on Tuesday we're going to
+have that uh the the following Tuesday
+
+ align:start position:0%
+have that uh the the following Tuesday
+ 
+
+ align:start position:0%
+have that uh the the following Tuesday
+okay uh but we will have our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+debate on Tuesday which means I want you
+
+ align:start position:0%
+debate on Tuesday which means I want you
+ 
+
+ align:start position:0%
+debate on Tuesday which means I want you
+to prepare for the debate uh so the two
+
+ align:start position:0%
+to prepare for the debate uh so the two
+ 
+
+ align:start position:0%
+to prepare for the debate uh so the two
+homework assignments for Tuesday is read
+
+ align:start position:0%
+homework assignments for Tuesday is read
+ 
+
+ align:start position:0%
+homework assignments for Tuesday is read
+uh big picture chapter 15 and prepare
+
+ align:start position:0%
+uh big picture chapter 15 and prepare
+ 
+
+ align:start position:0%
+uh big picture chapter 15 and prepare
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+
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+ 
+
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+
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+ align:start position:0%
+you can do it you can do it you can do
+it you can do it then then the listener
+
+ align:start position:0%
+it you can do it then then the listener
+ 
+
+ align:start position:0%
+it you can do it then then the listener
+gets really confused
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's turn to page
+
+ align:start position:0%
+okay let's turn to page
+ 
+
+ align:start position:0%
+okay let's turn to page
+90 page
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+90 okay so ABC the speaker
+
+ align:start position:0%
+90 okay so ABC the speaker
+ 
+
+ align:start position:0%
+90 okay so ABC the speaker
+used right I can swim I can you can hear
+
+ align:start position:0%
+used right I can swim I can you can hear
+ 
+
+ align:start position:0%
+used right I can swim I can you can hear
+the noise
+
+ align:start position:0%
+the noise
+ 
+
+ align:start position:0%
+the noise
+Shar can speak English speak English
+
+ align:start position:0%
+Shar can speak English speak English
+ 
+
+ align:start position:0%
+Shar can speak English speak English
+Okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+can no no they said she said can but d
+
+ align:start position:0%
+can no no they said she said can but d
+ 
+
+ align:start position:0%
+can no no they said she said can but d
+and e can you help me can can second one
+
+ align:start position:0%
+and e can you help me can can second one
+ 
+
+ align:start position:0%
+and e can you help me can can second one
+can you help me can you can you help me
+
+ align:start position:0%
+can you help me can you can you help me
+ 
+
+ align:start position:0%
+can you help me can you can you help me
+can you help me can you help me sounds
+
+ align:start position:0%
+can you help me can you help me sounds
+ 
+
+ align:start position:0%
+can you help me can you help me sounds
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+odd can you help me can you help can you
+
+ align:start position:0%
+odd can you help me can you help can you
+ 
+
+ align:start position:0%
+odd can you help me can you help can you
+help me where can we meet can we meet
+
+ align:start position:0%
+help me where can we meet can we meet
+ 
+
+ align:start position:0%
+help me where can we meet can we meet
+okay so in in a question you usually say
+
+ align:start position:0%
+okay so in in a question you usually say
+ 
+
+ align:start position:0%
+okay so in in a question you usually say
+can in a affirmative sentence usually we
+
+ align:start position:0%
+can in a affirmative sentence usually we
+ 
+
+ align:start position:0%
+can in a affirmative sentence usually we
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay okay
+
+ align:start position:0%
+Okay okay
+ 
+
+ align:start position:0%
+Okay okay
+so negative with if you have not you
+
+ align:start position:0%
+so negative with if you have not you
+ 
+
+ align:start position:0%
+so negative with if you have not you
+have to say can or can use a CL stop or
+
+ align:start position:0%
+have to say can or can use a CL stop or
+ 
+
+ align:start position:0%
+have to say can or can use a CL stop or
+can't or can all right and if it comes
+
+ align:start position:0%
+can't or can all right and if it comes
+ 
+
+ align:start position:0%
+can't or can all right and if it comes
+at the end of a word word you can't say
+
+ align:start position:0%
+at the end of a word word you can't say
+ 
+
+ align:start position:0%
+at the end of a word word you can't say
+could yes I can you have to say yes I
+
+ align:start position:0%
+could yes I can you have to say yes I
+ 
+
+ align:start position:0%
+could yes I can you have to say yes I
+can you can't say yes I could it sounds
+
+ align:start position:0%
+can you can't say yes I could it sounds
+ 
+
+ align:start position:0%
+can you can't say yes I could it sounds
+really funny okay do do you you know
+
+ align:start position:0%
+really funny okay do do you you know
+ 
+
+ align:start position:0%
+really funny okay do do you you know
+this movie Catch Me If You Can Catch Me
+
+ align:start position:0%
+this movie Catch Me If You Can Catch Me
+ 
+
+ align:start position:0%
+this movie Catch Me If You Can Catch Me
+If You Can okay you you say catch me she
+
+ align:start position:0%
+If You Can okay you you say catch me she
+ 
+
+ align:start position:0%
+If You Can okay you you say catch me she
+couldn't that's not good
+
+ align:start position:0%
+couldn't that's not good
+ 
+
+ align:start position:0%
+couldn't that's not good
+okay so what is difference number two
+
+ align:start position:0%
+okay so what is difference number two
+ 
+
+ align:start position:0%
+okay so what is difference number two
+and number three number two two
+
+ align:start position:0%
+and number three number two two
+ 
+
+ align:start position:0%
+and number three number two two
+negative and
+
+ align:start position:0%
+negative and
+ 
+
+ align:start position:0%
+negative and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+number two and number three yeah because
+
+ align:start position:0%
+number two and number three yeah because
+ 
+
+ align:start position:0%
+number two and number three yeah because
+the sound is
+
+ align:start position:0%
+the sound is
+ 
+
+ align:start position:0%
+the sound is
+SAR they are similar but not the same
+
+ align:start position:0%
+SAR they are similar but not the same
+ 
+
+ align:start position:0%
+SAR they are similar but not the same
+not the
+
+ align:start position:0%
+not the
+ 
+
+ align:start position:0%
+not the
+same it's yeah for me it's very hard to
+
+ align:start position:0%
+same it's yeah for me it's very hard to
+ 
+
+ align:start position:0%
+same it's yeah for me it's very hard to
+distinguish distinguish because there's
+
+ align:start position:0%
+distinguish distinguish because there's
+ 
+
+ align:start position:0%
+distinguish distinguish because there's
+a can't can't I can't that's the GL stop
+
+ align:start position:0%
+a can't can't I can't that's the GL stop
+ 
+
+ align:start position:0%
+a can't can't I can't that's the GL stop
+problem GL stop I can't do it I can't do
+
+ align:start position:0%
+problem GL stop I can't do it I can't do
+ 
+
+ align:start position:0%
+problem GL stop I can't do it I can't do
+it I can't there's a there's a SED stop
+
+ align:start position:0%
+it I can't there's a there's a SED stop
+ 
+
+ align:start position:0%
+it I can't there's a there's a SED stop
+here I can't do it I can't do it so how
+
+ align:start position:0%
+here I can't do it I can't do it so how
+ 
+
+ align:start position:0%
+here I can't do it I can't do it so how
+how can I understand the
+
+ align:start position:0%
+how can I understand the
+ 
+
+ align:start position:0%
+how can I understand the
+difference from
+
+ align:start position:0%
+difference from
+ 
+
+ align:start position:0%
+difference from
+the or how can you understand what
+
+ align:start position:0%
+the or how can you understand what
+ 
+
+ align:start position:0%
+the or how can you understand what
+difference difference in like in what
+
+ align:start position:0%
+difference difference in like in what
+ 
+
+ align:start position:0%
+difference difference in like in what
+example for example um number l or what
+
+ align:start position:0%
+example for example um number l or what
+ 
+
+ align:start position:0%
+example for example um number l or what
+what can we do what can we do and what
+
+ align:start position:0%
+what can we do what can we do and what
+ 
+
+ align:start position:0%
+what can we do what can we do and what
+can't we do okay so the difference will
+
+ align:start position:0%
+can't we do okay so the difference will
+ 
+
+ align:start position:0%
+can't we do okay so the difference will
+be what can we do what what can we do
+
+ align:start position:0%
+be what can we do what what can we do
+ 
+
+ align:start position:0%
+be what can we do what what can we do
+what can what can we do what
+
+ align:start position:0%
+what can what can we do what
+ 
+
+ align:start position:0%
+what can what can we do what
+what okay can't what have what can't
+
+ align:start position:0%
+what okay can't what have what can't
+ 
+
+ align:start position:0%
+what okay can't what have what can't
+what can't we do what can't we do can't
+
+ align:start position:0%
+what can't we do what can't we do can't
+ 
+
+ align:start position:0%
+what can't we do what can't we do can't
+there's a slight stop there stop there
+
+ align:start position:0%
+there's a slight stop there stop there
+ 
+
+ align:start position:0%
+there's a slight stop there stop there
+so it's actually yeah it's very similar
+
+ align:start position:0%
+so it's actually yeah it's very similar
+ 
+
+ align:start position:0%
+so it's actually yeah it's very similar
+but not not the same what can't we do
+
+ align:start position:0%
+but not not the same what can't we do
+ 
+
+ align:start position:0%
+but not not the same what can't we do
+can't can't what can't we do what can we
+
+ align:start position:0%
+can't can't what can't we do what can we
+ 
+
+ align:start position:0%
+can't can't what can't we do what can we
+do what can we do what can we do what
+
+ align:start position:0%
+do what can we do what can we do what
+ 
+
+ align:start position:0%
+do what can we do what can we do what
+can we do what can't we do what can't
+
+ align:start position:0%
+can we do what can't we do what can't
+ 
+
+ align:start position:0%
+can we do what can't we do what can't
+can't we do what can't we do what can't
+
+ align:start position:0%
+can't we do what can't we do what can't
+ 
+
+ align:start position:0%
+can't we do what can't we do what can't
+we do what can we do yeah sometimes and
+
+ align:start position:0%
+we do what can we do yeah sometimes and
+ 
+
+ align:start position:0%
+we do what can we do yeah sometimes and
+some times you you don't hear that so
+
+ align:start position:0%
+some times you you don't hear that so
+ 
+
+ align:start position:0%
+some times you you don't hear that so
+you ask what do you mean can or cannot
+
+ align:start position:0%
+you ask what do you mean can or cannot
+ 
+
+ align:start position:0%
+you ask what do you mean can or cannot
+okay you could you could ask him you
+
+ align:start position:0%
+okay you could you could ask him you
+ 
+
+ align:start position:0%
+okay you could you could ask him you
+could ask the speaker but it's very
+
+ align:start position:0%
+could ask the speaker but it's very
+ 
+
+ align:start position:0%
+could ask the speaker but it's very
+difficult what can't what can't we do
+
+ align:start position:0%
+difficult what can't what can't we do
+ 
+
+ align:start position:0%
+difficult what can't what can't we do
+they're not the same but similar what
+
+ align:start position:0%
+they're not the same but similar what
+ 
+
+ align:start position:0%
+they're not the same but similar what
+can't we do there's a stop what can't we
+
+ align:start position:0%
+can't we do there's a stop what can't we
+ 
+
+ align:start position:0%
+can't we do there's a stop what can't we
+can't we do okay lot of stop
+
+ align:start position:0%
+can't we do okay lot of stop
+ 
+
+ align:start position:0%
+can't we do okay lot of stop
+there about letter i m explain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why letter I and your question again
+
+ align:start position:0%
+why letter I and your question again
+ 
+
+ align:start position:0%
+why letter I and your question again
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is yeah and can't you do anything about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I don't know I don't there should be
+
+ align:start position:0%
+it I don't know I don't there should be
+ 
+
+ align:start position:0%
+it I don't know I don't there should be
+uh that's a very good question there
+
+ align:start position:0%
+uh that's a very good question there
+ 
+
+ align:start position:0%
+uh that's a very good question there
+should not be any stress here right
+
+ align:start position:0%
+should not be any stress here right
+ 
+
+ align:start position:0%
+should not be any stress here right
+because about is a
+
+ align:start position:0%
+because about is a
+ 
+
+ align:start position:0%
+because about is a
+preposition can do anything about
+
+ align:start position:0%
+preposition can do anything about
+ 
+
+ align:start position:0%
+preposition can do anything about
+it I would consider this a mistake
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no let me think about that but that's a
+
+ align:start position:0%
+no let me think about that but that's a
+ 
+
+ align:start position:0%
+no let me think about that but that's a
+very good question very good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+question what number what letter I I so
+
+ align:start position:0%
+question what number what letter I I so
+ 
+
+ align:start position:0%
+question what number what letter I I so
+you can do either can you or can you I
+
+ align:start position:0%
+you can do either can you or can you I
+ 
+
+ align:start position:0%
+you can do either can you or can you I
+me stress stress is can for example do
+
+ align:start position:0%
+me stress stress is can for example do
+ 
+
+ align:start position:0%
+me stress stress is can for example do
+you speak English or do you speak
+
+ align:start position:0%
+you speak English or do you speak
+ 
+
+ align:start position:0%
+you speak English or do you speak
+English no do you speak
+
+ align:start position:0%
+English no do you speak
+ 
+
+ align:start position:0%
+English no do you speak
+English not do you do you speak English
+
+ align:start position:0%
+English not do you do you speak English
+ 
+
+ align:start position:0%
+English not do you do you speak English
+the stress is English do you speak
+
+ align:start position:0%
+the stress is English do you speak
+ 
+
+ align:start position:0%
+the stress is English do you speak
+Engish so can't you can't you do
+
+ align:start position:0%
+Engish so can't you can't you do
+ 
+
+ align:start position:0%
+Engish so can't you can't you do
+anything about it can't you do anything
+
+ align:start position:0%
+anything about it can't you do anything
+ 
+
+ align:start position:0%
+anything about it can't you do anything
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+it yeah the stress marks they they're
+
+ align:start position:0%
+it yeah the stress marks they they're
+ 
+
+ align:start position:0%
+it yeah the stress marks they they're
+putting stress marks on every content
+
+ align:start position:0%
+putting stress marks on every content
+ 
+
+ align:start position:0%
+putting stress marks on every content
+words here every content word here we're
+
+ align:start position:0%
+words here every content word here we're
+ 
+
+ align:start position:0%
+words here every content word here we're
+not talking about intonation intonation
+
+ align:start position:0%
+not talking about intonation intonation
+ 
+
+ align:start position:0%
+not talking about intonation intonation
+is something that we're going to talk
+
+ align:start position:0%
+is something that we're going to talk
+ 
+
+ align:start position:0%
+is something that we're going to talk
+about after we talk about permanence
+
+ align:start position:0%
+about after we talk about permanence
+ 
+
+ align:start position:0%
+about after we talk about permanence
+okay or today I'll I I'll talk about uh
+
+ align:start position:0%
+okay or today I'll I I'll talk about uh
+ 
+
+ align:start position:0%
+okay or today I'll I I'll talk about uh
+intonation a little
+
+ align:start position:0%
+intonation a little
+ 
+
+ align:start position:0%
+intonation a little
+bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh maybe we
+
+ align:start position:0%
+uh maybe we
+ 
+
+ align:start position:0%
+uh maybe we
+should let's talk about prominence now
+
+ align:start position:0%
+should let's talk about prominence now
+ 
+
+ align:start position:0%
+should let's talk about prominence now
+okay since that question came up
+
+ align:start position:0%
+okay since that question came up
+ 
+
+ align:start position:0%
+okay since that question came up
+okay let's turn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to okay in your course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+packet this is course packet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page 74 74 page 74
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+now so Rhythm we talked
+
+ align:start position:0%
+now so Rhythm we talked
+ 
+
+ align:start position:0%
+now so Rhythm we talked
+about here when we talked about Rhythm
+
+ align:start position:0%
+about here when we talked about Rhythm
+ 
+
+ align:start position:0%
+about here when we talked about Rhythm
+uh we learned the fact that we need to
+
+ align:start position:0%
+uh we learned the fact that we need to
+ 
+
+ align:start position:0%
+uh we learned the fact that we need to
+stress the content
+
+ align:start position:0%
+stress the content
+ 
+
+ align:start position:0%
+stress the content
+words but no stress on function words
+
+ align:start position:0%
+words but no stress on function words
+ 
+
+ align:start position:0%
+words but no stress on function words
+right but if you put stress equal stress
+
+ align:start position:0%
+right but if you put stress equal stress
+ 
+
+ align:start position:0%
+right but if you put stress equal stress
+on all content words then it becomes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to and nobody speaks that way unless I
+
+ align:start position:0%
+to and nobody speaks that way unless I
+ 
+
+ align:start position:0%
+to and nobody speaks that way unless I
+mean we uh during the interview when you
+
+ align:start position:0%
+mean we uh during the interview when you
+ 
+
+ align:start position:0%
+mean we uh during the interview when you
+slow down when the person Robert seagull
+
+ align:start position:0%
+slow down when the person Robert seagull
+ 
+
+ align:start position:0%
+slow down when the person Robert seagull
+slow down a bruise A bruise or a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cut a bruise or a
+
+ align:start position:0%
+cut a bruise or a
+ 
+
+ align:start position:0%
+cut a bruise or a
+cut but in a fast regular speech nobody
+
+ align:start position:0%
+cut but in a fast regular speech nobody
+ 
+
+ align:start position:0%
+cut but in a fast regular speech nobody
+really speaks that way right so there is
+
+ align:start position:0%
+really speaks that way right so there is
+ 
+
+ align:start position:0%
+really speaks that way right so there is
+some stress on each content word but one
+
+ align:start position:0%
+some stress on each content word but one
+ 
+
+ align:start position:0%
+some stress on each content word but one
+word gets the most stress strongest
+
+ align:start position:0%
+word gets the most stress strongest
+ 
+
+ align:start position:0%
+word gets the most stress strongest
+stress and that element is called
+
+ align:start position:0%
+stress and that element is called
+ 
+
+ align:start position:0%
+stress and that element is called
+prominent element or prominence okay so
+
+ align:start position:0%
+prominent element or prominence okay so
+ 
+
+ align:start position:0%
+prominent element or prominence okay so
+that's one thing that we need to think
+
+ align:start position:0%
+that's one thing that we need to think
+ 
+
+ align:start position:0%
+that's one thing that we need to think
+about another
+
+ align:start position:0%
+about another
+ 
+
+ align:start position:0%
+about another
+thing is sometimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I the pronoun I is a Content word or a
+
+ align:start position:0%
+I the pronoun I is a Content word or a
+ 
+
+ align:start position:0%
+I the pronoun I is a Content word or a
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+word function it's a function word
+
+ align:start position:0%
+word function it's a function word
+ 
+
+ align:start position:0%
+word function it's a function word
+pronouns are function words okay read
+
+ align:start position:0%
+pronouns are function words okay read
+ 
+
+ align:start position:0%
+pronouns are function words okay read
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eyes italicize because there's more
+
+ align:start position:0%
+eyes italicize because there's more
+ 
+
+ align:start position:0%
+eyes italicize because there's more
+emphasis here why is it important for
+
+ align:start position:0%
+emphasis here why is it important for
+ 
+
+ align:start position:0%
+emphasis here why is it important for
+today's kids to learn algebra because I
+
+ align:start position:0%
+today's kids to learn algebra because I
+ 
+
+ align:start position:0%
+today's kids to learn algebra because I
+had to learn this junk in school and now
+
+ align:start position:0%
+had to learn this junk in school and now
+ 
+
+ align:start position:0%
+had to learn this junk in school and now
+it's your turn that's why because I had
+
+ align:start position:0%
+it's your turn that's why because I had
+ 
+
+ align:start position:0%
+it's your turn that's why because I had
+to turn I had this is funny okay good
+
+ align:start position:0%
+to turn I had this is funny okay good
+ 
+
+ align:start position:0%
+to turn I had this is funny okay good
+now finally I have one cartoon that's
+
+ align:start position:0%
+now finally I have one cartoon that's
+ 
+
+ align:start position:0%
+now finally I have one cartoon that's
+funny because I had to learn I I'm
+
+ align:start position:0%
+funny because I had to learn I I'm
+ 
+
+ align:start position:0%
+funny because I had to learn I I'm
+emphasizing I and the difference I had
+
+ align:start position:0%
+emphasizing I and the difference I had
+ 
+
+ align:start position:0%
+emphasizing I and the difference I had
+to learn it so you have to learn it too
+
+ align:start position:0%
+to learn it so you have to learn it too
+ 
+
+ align:start position:0%
+to learn it so you have to learn it too
+okay so now in in some situations you
+
+ align:start position:0%
+okay so now in in some situations you
+ 
+
+ align:start position:0%
+okay so now in in some situations you
+want to emphasize uh certain uh content
+
+ align:start position:0%
+want to emphasize uh certain uh content
+ 
+
+ align:start position:0%
+want to emphasize uh certain uh content
+words no no no no function words okay
+
+ align:start position:0%
+words no no no no function words okay
+ 
+
+ align:start position:0%
+words no no no no function words okay
+and if you switch the uh stress it
+
+ align:start position:0%
+and if you switch the uh stress it
+ 
+
+ align:start position:0%
+and if you switch the uh stress it
+changes the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaning so review you can read that
+
+ align:start position:0%
+meaning so review you can read that
+ 
+
+ align:start position:0%
+meaning so review you can read that
+one thing that we need to talk about
+
+ align:start position:0%
+one thing that we need to talk about
+ 
+
+ align:start position:0%
+one thing that we need to talk about
+before we start talking about prominence
+
+ align:start position:0%
+before we start talking about prominence
+ 
+
+ align:start position:0%
+before we start talking about prominence
+is thought groups or it's uh in your
+
+ align:start position:0%
+is thought groups or it's uh in your
+ 
+
+ align:start position:0%
+is thought groups or it's uh in your
+book it's called pause groups and some
+
+ align:start position:0%
+book it's called pause groups and some
+ 
+
+ align:start position:0%
+book it's called pause groups and some
+other some people call it ination
+
+ align:start position:0%
+other some people call it ination
+ 
+
+ align:start position:0%
+other some people call it ination
+groups these
+
+ align:start position:0%
+groups these
+ 
+
+ align:start position:0%
+groups these
+are you you pause after a thought group
+
+ align:start position:0%
+are you you pause after a thought group
+ 
+
+ align:start position:0%
+are you you pause after a thought group
+and the the the the the phrases are
+
+ align:start position:0%
+and the the the the the phrases are
+ 
+
+ align:start position:0%
+and the the the the the phrases are
+long if you speak fast right if you
+
+ align:start position:0%
+long if you speak fast right if you
+ 
+
+ align:start position:0%
+long if you speak fast right if you
+speak really slowly in a public speech
+
+ align:start position:0%
+speak really slowly in a public speech
+ 
+
+ align:start position:0%
+speak really slowly in a public speech
+then they are short right so that they
+
+ align:start position:0%
+then they are short right so that they
+ 
+
+ align:start position:0%
+then they are short right so that they
+actually differ the
+
+ align:start position:0%
+actually differ the
+ 
+
+ align:start position:0%
+actually differ the
+lengths and they're grammatically and
+
+ align:start position:0%
+lengths and they're grammatically and
+ 
+
+ align:start position:0%
+lengths and they're grammatically and
+semantically coherent they have to be
+
+ align:start position:0%
+semantically coherent they have to be
+ 
+
+ align:start position:0%
+semantically coherent they have to be
+some sort of phrases like if you have a
+
+ align:start position:0%
+some sort of phrases like if you have a
+ 
+
+ align:start position:0%
+some sort of phrases like if you have a
+very long subject the guy that I met
+
+ align:start position:0%
+very long subject the guy that I met
+ 
+
+ align:start position:0%
+very long subject the guy that I met
+yesterday then you would stop there
+
+ align:start position:0%
+yesterday then you would stop there
+ 
+
+ align:start position:0%
+yesterday then you would stop there
+because we have
+
+ align:start position:0%
+because we have
+ 
+
+ align:start position:0%
+because we have
+a actually goes to mit2 so you actually
+
+ align:start position:0%
+a actually goes to mit2 so you actually
+ 
+
+ align:start position:0%
+a actually goes to mit2 so you actually
+stop after the long subject okay so you
+
+ align:start position:0%
+stop after the long subject okay so you
+ 
+
+ align:start position:0%
+stop after the long subject okay so you
+can stop after long subject or stop
+
+ align:start position:0%
+can stop after long subject or stop
+ 
+
+ align:start position:0%
+can stop after long subject or stop
+after the whole sentence or a complete
+
+ align:start position:0%
+after the whole sentence or a complete
+ 
+
+ align:start position:0%
+after the whole sentence or a complete
+or one pral
+
+ align:start position:0%
+or one pral
+ 
+
+ align:start position:0%
+or one pral
+phrase are often set up by pauses but
+
+ align:start position:0%
+phrase are often set up by pauses but
+ 
+
+ align:start position:0%
+phrase are often set up by pauses but
+not all the time sometimes you
+
+ align:start position:0%
+not all the time sometimes you
+ 
+
+ align:start position:0%
+not all the time sometimes you
+completely pause sometimes you kind of
+
+ align:start position:0%
+completely pause sometimes you kind of
+ 
+
+ align:start position:0%
+completely pause sometimes you kind of
+slow down you lengthen the final
+
+ align:start position:0%
+slow down you lengthen the final
+ 
+
+ align:start position:0%
+slow down you lengthen the final
+syllable
+
+ align:start position:0%
+syllable
+ 
+
+ align:start position:0%
+syllable
+okay in each thought group there's one
+
+ align:start position:0%
+okay in each thought group there's one
+ 
+
+ align:start position:0%
+okay in each thought group there's one
+prominent element what does prominent
+
+ align:start position:0%
+prominent element what does prominent
+ 
+
+ align:start position:0%
+prominent element what does prominent
+element mean in each thought group every
+
+ align:start position:0%
+element mean in each thought group every
+ 
+
+ align:start position:0%
+element mean in each thought group every
+content word will get some sort of
+
+ align:start position:0%
+content word will get some sort of
+ 
+
+ align:start position:0%
+content word will get some sort of
+stress what does that mean the vales in
+
+ align:start position:0%
+stress what does that mean the vales in
+ 
+
+ align:start position:0%
+stress what does that mean the vales in
+those words are not going to be reduced
+
+ align:start position:0%
+those words are not going to be reduced
+ 
+
+ align:start position:0%
+those words are not going to be reduced
+that's what it means some sort of stress
+
+ align:start position:0%
+that's what it means some sort of stress
+ 
+
+ align:start position:0%
+that's what it means some sort of stress
+means the vales are not going to be
+
+ align:start position:0%
+means the vales are not going to be
+ 
+
+ align:start position:0%
+means the vales are not going to be
+reduced function words the vals are
+
+ align:start position:0%
+reduced function words the vals are
+ 
+
+ align:start position:0%
+reduced function words the vals are
+going to be reduced because no stress
+
+ align:start position:0%
+going to be reduced because no stress
+ 
+
+ align:start position:0%
+going to be reduced because no stress
+but there's one word that's going to get
+
+ align:start position:0%
+but there's one word that's going to get
+ 
+
+ align:start position:0%
+but there's one word that's going to get
+the most stress that's where you go up
+
+ align:start position:0%
+the most stress that's where you go up
+ 
+
+ align:start position:0%
+the most stress that's where you go up
+okay so in English the most common
+
+ align:start position:0%
+okay so in English the most common
+ 
+
+ align:start position:0%
+okay so in English the most common
+intonation pattern
+
+ align:start position:0%
+intonation pattern
+ 
+
+ align:start position:0%
+intonation pattern
+is okay you keep
+
+ align:start position:0%
+is okay you keep
+ 
+
+ align:start position:0%
+is okay you keep
+flat not
+
+ align:start position:0%
+flat not
+ 
+
+ align:start position:0%
+flat not
+uh very common mistake
+
+ align:start position:0%
+uh very common mistake
+ 
+
+ align:start position:0%
+uh very common mistake
+I like it I people do that all the
+
+ align:start position:0%
+I like it I people do that all the
+ 
+
+ align:start position:0%
+I like it I people do that all the
+time okay it has its own ination pattern
+
+ align:start position:0%
+time okay it has its own ination pattern
+ 
+
+ align:start position:0%
+time okay it has its own ination pattern
+and linking and blending blending occur
+
+ align:start position:0%
+and linking and blending blending occur
+ 
+
+ align:start position:0%
+and linking and blending blending occur
+within at this not across usually
+
+ align:start position:0%
+within at this not across usually
+ 
+
+ align:start position:0%
+within at this not across usually
+thought groups when you pause after a
+
+ align:start position:0%
+thought groups when you pause after a
+ 
+
+ align:start position:0%
+thought groups when you pause after a
+thought group you can't have linking but
+
+ align:start position:0%
+thought group you can't have linking but
+ 
+
+ align:start position:0%
+thought group you can't have linking but
+if you when you just slow down you can
+
+ align:start position:0%
+if you when you just slow down you can
+ 
+
+ align:start position:0%
+if you when you just slow down you can
+have linking okay if you just slow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down okay there there four four
+
+ align:start position:0%
+down okay there there four four
+ 
+
+ align:start position:0%
+down okay there there four four
+different four levels of s stress
+
+ align:start position:0%
+different four levels of s stress
+ 
+
+ align:start position:0%
+different four levels of s stress
+unstressed syllable right there's
+
+ align:start position:0%
+unstressed syllable right there's
+ 
+
+ align:start position:0%
+unstressed syllable right there's
+lightly stressed syllable all content
+
+ align:start position:0%
+lightly stressed syllable all content
+ 
+
+ align:start position:0%
+lightly stressed syllable all content
+Words which means no reduced vals number
+
+ align:start position:0%
+Words which means no reduced vals number
+ 
+
+ align:start position:0%
+Words which means no reduced vals number
+one unstress LEL reduced vals number
+
+ align:start position:0%
+one unstress LEL reduced vals number
+ 
+
+ align:start position:0%
+one unstress LEL reduced vals number
+two uh lightly stressed no reduced vals
+
+ align:start position:0%
+two uh lightly stressed no reduced vals
+ 
+
+ align:start position:0%
+two uh lightly stressed no reduced vals
+in strongly
+
+ align:start position:0%
+in strongly
+ 
+
+ align:start position:0%
+in strongly
+reduced strongly stressed that's the
+
+ align:start position:0%
+reduced strongly stressed that's the
+ 
+
+ align:start position:0%
+reduced strongly stressed that's the
+prominent element right and we have
+
+ align:start position:0%
+prominent element right and we have
+ 
+
+ align:start position:0%
+prominent element right and we have
+extra strong contrastive or lymphatic
+
+ align:start position:0%
+extra strong contrastive or lymphatic
+ 
+
+ align:start position:0%
+extra strong contrastive or lymphatic
+Str sometimes you're voice goes really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+high this sentence we have three words
+
+ align:start position:0%
+high this sentence we have three words
+ 
+
+ align:start position:0%
+high this sentence we have three words
+here I am listening
+
+ align:start position:0%
+here I am listening
+ 
+
+ align:start position:0%
+here I am listening
+if if I were to ask
+
+ align:start position:0%
+if if I were to ask
+ 
+
+ align:start position:0%
+if if I were to ask
+you uh what are you do like what are you
+
+ align:start position:0%
+you uh what are you do like what are you
+ 
+
+ align:start position:0%
+you uh what are you do like what are you
+doing are you
+
+ align:start position:0%
+doing are you
+ 
+
+ align:start position:0%
+doing are you
+listening what are you do are you
+
+ align:start position:0%
+listening what are you do are you
+ 
+
+ align:start position:0%
+listening what are you do are you
+listening yes yes I'm listening right
+
+ align:start position:0%
+listening yes yes I'm listening right
+ 
+
+ align:start position:0%
+listening yes yes I'm listening right
+what the stress would go where here yes
+
+ align:start position:0%
+what the stress would go where here yes
+ 
+
+ align:start position:0%
+what the stress would go where here yes
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+listening what are you doing are you
+
+ align:start position:0%
+listening what are you doing are you
+ 
+
+ align:start position:0%
+listening what are you doing are you
+listening yes I'm listening I'm
+
+ align:start position:0%
+listening yes I'm listening I'm
+ 
+
+ align:start position:0%
+listening yes I'm listening I'm
+listening I'm listening I'm listening
+
+ align:start position:0%
+listening I'm listening I'm listening
+ 
+
+ align:start position:0%
+listening I'm listening I'm listening
+right what are you doing what are you
+
+ align:start position:0%
+right what are you doing what are you
+ 
+
+ align:start position:0%
+right what are you doing what are you
+doing I'm listening I'm listening
+
+ align:start position:0%
+doing I'm listening I'm listening
+ 
+
+ align:start position:0%
+doing I'm listening I'm listening
+right if I
+
+ align:start position:0%
+right if I
+ 
+
+ align:start position:0%
+right if I
+said who's
+
+ align:start position:0%
+said who's
+ 
+
+ align:start position:0%
+said who's
+listening then you you you would
+
+ align:start position:0%
+listening then you you you would
+ 
+
+ align:start position:0%
+listening then you you you would
+say I'm listening I'm listening is
+
+ align:start position:0%
+say I'm listening I'm listening is
+ 
+
+ align:start position:0%
+say I'm listening I'm listening is
+anybody listening who's listening I'm
+
+ align:start position:0%
+anybody listening who's listening I'm
+ 
+
+ align:start position:0%
+anybody listening who's listening I'm
+listening right I'm
+
+ align:start position:0%
+listening right I'm
+ 
+
+ align:start position:0%
+listening right I'm
+listening so if you stress I'm listening
+
+ align:start position:0%
+listening so if you stress I'm listening
+ 
+
+ align:start position:0%
+listening so if you stress I'm listening
+then that's an answer
+
+ align:start position:0%
+then that's an answer
+ 
+
+ align:start position:0%
+then that's an answer
+to what's going on here you guys are
+
+ align:start position:0%
+to what's going on here you guys are
+ 
+
+ align:start position:0%
+to what's going on here you guys are
+having a party this is class time okay
+
+ align:start position:0%
+having a party this is class time okay
+ 
+
+ align:start position:0%
+having a party this is class time okay
+now if you say I'm
+
+ align:start position:0%
+now if you say I'm
+ 
+
+ align:start position:0%
+now if you say I'm
+listening that's an answer to a question
+
+ align:start position:0%
+listening that's an answer to a question
+ 
+
+ align:start position:0%
+listening that's an answer to a question
+like what are you doing what are you
+
+ align:start position:0%
+like what are you doing what are you
+ 
+
+ align:start position:0%
+like what are you doing what are you
+doing are you listening right but if you
+
+ align:start position:0%
+doing are you listening right but if you
+ 
+
+ align:start position:0%
+doing are you listening right but if you
+say I'm listening that's an answer to a
+
+ align:start position:0%
+say I'm listening that's an answer to a
+ 
+
+ align:start position:0%
+say I'm listening that's an answer to a
+question like who's listening so if you
+
+ align:start position:0%
+question like who's listening so if you
+ 
+
+ align:start position:0%
+question like who's listening so if you
+switch the stress it actually becomes a
+
+ align:start position:0%
+switch the stress it actually becomes a
+ 
+
+ align:start position:0%
+switch the stress it actually becomes a
+different different uh it has a
+
+ align:start position:0%
+different different uh it has a
+ 
+
+ align:start position:0%
+different different uh it has a
+different meaning when would you say can
+
+ align:start position:0%
+different meaning when would you say can
+ 
+
+ align:start position:0%
+different meaning when would you say can
+you stress the verb here the the beaver
+
+ align:start position:0%
+you stress the verb here the the beaver
+ 
+
+ align:start position:0%
+you stress the verb here the the beaver
+I am
+
+ align:start position:0%
+I am
+ 
+
+ align:start position:0%
+I am
+listening I am
+
+ align:start position:0%
+listening I am
+ 
+
+ align:start position:0%
+listening I am
+listening so when would you say that
+
+ align:start position:0%
+listening so when would you say that
+ 
+
+ align:start position:0%
+listening so when would you say that
+what would you say I am listening did
+
+ align:start position:0%
+what would you say I am listening did
+ 
+
+ align:start position:0%
+what would you say I am listening did
+you listen to the music
+
+ align:start position:0%
+you listen to the music
+ 
+
+ align:start position:0%
+you listen to the music
+did you listen to the
+
+ align:start position:0%
+did you listen to the
+ 
+
+ align:start position:0%
+did you listen to the
+music I amist to
+
+ align:start position:0%
+music I amist to
+ 
+
+ align:start position:0%
+music I amist to
+now uh
+
+ align:start position:0%
+now uh
+ 
+
+ align:start position:0%
+now uh
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+ATT ATT talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something yes I am listening I am
+
+ align:start position:0%
+something yes I am listening I am
+ 
+
+ align:start position:0%
+something yes I am listening I am
+listening oh okay so if someone says pay
+
+ align:start position:0%
+listening oh okay so if someone says pay
+ 
+
+ align:start position:0%
+listening oh okay so if someone says pay
+attention listen to me pay attention
+
+ align:start position:0%
+attention listen to me pay attention
+ 
+
+ align:start position:0%
+attention listen to me pay attention
+listen to me why aren't you listening
+
+ align:start position:0%
+listen to me why aren't you listening
+ 
+
+ align:start position:0%
+listen to me why aren't you listening
+uhhuh what I am listening I am that's
+
+ align:start position:0%
+uhhuh what I am listening I am that's
+ 
+
+ align:start position:0%
+uhhuh what I am listening I am that's
+here it's a contrastive extra
+
+ align:start position:0%
+here it's a contrastive extra
+ 
+
+ align:start position:0%
+here it's a contrastive extra
+strong uh pitch stress hey T what are
+
+ align:start position:0%
+strong uh pitch stress hey T what are
+ 
+
+ align:start position:0%
+strong uh pitch stress hey T what are
+you doing why are you talking to this is
+
+ align:start position:0%
+you doing why are you talking to this is
+ 
+
+ align:start position:0%
+you doing why are you talking to this is
+time pay attention I am listening very
+
+ align:start position:0%
+time pay attention I am listening very
+ 
+
+ align:start position:0%
+time pay attention I am listening very
+good what I am listening and she's lying
+
+ align:start position:0%
+good what I am listening and she's lying
+ 
+
+ align:start position:0%
+good what I am listening and she's lying
+what do you what do you mean you are not
+
+ align:start position:0%
+what do you what do you mean you are not
+ 
+
+ align:start position:0%
+what do you what do you mean you are not
+listening okay what I am listening after
+
+ align:start position:0%
+listening okay what I am listening after
+ 
+
+ align:start position:0%
+listening okay what I am listening after
+ref me I am listening I am L I am
+
+ align:start position:0%
+ref me I am listening I am L I am
+ 
+
+ align:start position:0%
+ref me I am listening I am L I am
+listening I am okay your voice is extra
+
+ align:start position:0%
+listening I am okay your voice is extra
+ 
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+mean weird why is it blue I mean blue
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+blue what was it thinking
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+blue okay uh let's hurry up now
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+uh the answer is high intermediate High
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+uh the answer is high intermediate High
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+uh the answer is high intermediate High
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+High
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+intermediate
+
+ align:start position:0%
+intermediate
+ 
+
+ align:start position:0%
+intermediate
+okay and it can it can occur across two
+
+ align:start position:0%
+okay and it can it can occur across two
+ 
+
+ align:start position:0%
+okay and it can it can occur across two
+speakers is this is this the low
+
+ align:start position:0%
+speakers is this is this the low
+ 
+
+ align:start position:0%
+speakers is this is this the low
+intermediate English class and no it's
+
+ align:start position:0%
+intermediate English class and no it's
+ 
+
+ align:start position:0%
+intermediate English class and no it's
+the high intermediate High intermediate
+
+ align:start position:0%
+the high intermediate High intermediate
+ 
+
+ align:start position:0%
+the high intermediate High intermediate
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+right okay Circle the words that receive
+
+ align:start position:0%
+right okay Circle the words that receive
+ 
+
+ align:start position:0%
+right okay Circle the words that receive
+the most
+
+ align:start position:0%
+the most
+ 
+
+ align:start position:0%
+the most
+stress this
+
+ align:start position:0%
+stress this
+ 
+
+ align:start position:0%
+stress this
+one how are you how are you how are you
+
+ align:start position:0%
+one how are you how are you how are you
+ 
+
+ align:start position:0%
+one how are you how are you how are you
+but nowadays people many people say how
+
+ align:start position:0%
+but nowadays people many people say how
+ 
+
+ align:start position:0%
+but nowadays people many people say how
+hey how are you how are you right people
+
+ align:start position:0%
+hey how are you how are you right people
+ 
+
+ align:start position:0%
+hey how are you how are you right people
+say how are you they do that but
+
+ align:start position:0%
+say how are you they do that but
+ 
+
+ align:start position:0%
+say how are you they do that but
+according to the book you have to say
+
+ align:start position:0%
+according to the book you have to say
+ 
+
+ align:start position:0%
+according to the book you have to say
+how are you how are you and pretty
+
+ align:start position:0%
+how are you how are you and pretty
+ 
+
+ align:start position:0%
+how are you how are you and pretty
+good then you say how are you how are
+
+ align:start position:0%
+good then you say how are you how are
+ 
+
+ align:start position:0%
+good then you say how are you how are
+you how are you how are you right how
+
+ align:start position:0%
+you how are you how are you right how
+ 
+
+ align:start position:0%
+you how are you how are you right how
+are you this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh uh what did you think of the
+
+ align:start position:0%
+okay uh uh what did you think of the
+ 
+
+ align:start position:0%
+okay uh uh what did you think of the
+movie what did you think of the movie
+
+ align:start position:0%
+movie what did you think of the movie
+ 
+
+ align:start position:0%
+movie what did you think of the movie
+what did you think of the movie so we
+
+ align:start position:0%
+what did you think of the movie so we
+ 
+
+ align:start position:0%
+what did you think of the movie so we
+say what here what did you what did you
+
+ align:start position:0%
+say what here what did you what did you
+ 
+
+ align:start position:0%
+say what here what did you what did you
+what did you think of the movie what did
+
+ align:start position:0%
+what did you think of the movie what did
+ 
+
+ align:start position:0%
+what did you think of the movie what did
+you think of the movie no get here of
+
+ align:start position:0%
+you think of the movie no get here of
+ 
+
+ align:start position:0%
+you think of the movie no get here of
+the whenever you have of the get rid of
+
+ align:start position:0%
+the whenever you have of the get rid of
+ 
+
+ align:start position:0%
+the whenever you have of the get rid of
+the V of the say of the especially in
+
+ align:start position:0%
+the V of the say of the especially in
+ 
+
+ align:start position:0%
+the V of the say of the especially in
+casual conversation what did you think
+
+ align:start position:0%
+casual conversation what did you think
+ 
+
+ align:start position:0%
+casual conversation what did you think
+of the think of the what did you think
+
+ align:start position:0%
+of the think of the what did you think
+ 
+
+ align:start position:0%
+of the think of the what did you think
+of the movie what you think of the movie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think the
+
+ align:start position:0%
+think the
+ 
+
+ align:start position:0%
+think the
+here it was really you could say it was
+
+ align:start position:0%
+here it was really you could say it was
+ 
+
+ align:start position:0%
+here it was really you could say it was
+really good or it was really if you want
+
+ align:start position:0%
+really good or it was really if you want
+ 
+
+ align:start position:0%
+really good or it was really if you want
+to emphasize really it was really good
+
+ align:start position:0%
+to emphasize really it was really good
+ 
+
+ align:start position:0%
+to emphasize really it was really good
+right it was really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good what did you think what did you
+
+ align:start position:0%
+good what did you think what did you
+ 
+
+ align:start position:0%
+good what did you think what did you
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+why you think what did you think what
+
+ align:start position:0%
+why you think what did you think what
+ 
+
+ align:start position:0%
+why you think what did you think what
+did you think okay so here you can
+
+ align:start position:0%
+did you think okay so here you can
+ 
+
+ align:start position:0%
+did you think okay so here you can
+emphasize these adverbs like uh man
+
+ align:start position:0%
+emphasize these adverbs like uh man
+ 
+
+ align:start position:0%
+emphasize these adverbs like uh man
+Isaiah's class is so boring I'm never
+
+ align:start position:0%
+Isaiah's class is so boring I'm never
+ 
+
+ align:start position:0%
+Isaiah's class is so boring I'm never
+taking Isaiah's class I'm never taking
+
+ align:start position:0%
+taking Isaiah's class I'm never taking
+ 
+
+ align:start position:0%
+taking Isaiah's class I'm never taking
+Isaiah's class or you could say I really
+
+ align:start position:0%
+Isaiah's class or you could say I really
+ 
+
+ align:start position:0%
+Isaiah's class or you could say I really
+like Isaiah's class right okay so let's
+
+ align:start position:0%
+like Isaiah's class right okay so let's
+ 
+
+ align:start position:0%
+like Isaiah's class right okay so let's
+practice something that you might say to
+
+ align:start position:0%
+practice something that you might say to
+ 
+
+ align:start position:0%
+practice something that you might say to
+your friends okay chances are you're
+
+ align:start position:0%
+your friends okay chances are you're
+ 
+
+ align:start position:0%
+your friends okay chances are you're
+going to say the ladder okay I really
+
+ align:start position:0%
+going to say the ladder okay I really
+ 
+
+ align:start position:0%
+going to say the ladder okay I really
+like Isaiah's
+
+ align:start position:0%
+like Isaiah's
+ 
+
+ align:start position:0%
+like Isaiah's
+class I really like IDE
+
+ align:start position:0%
+class I really like IDE
+ 
+
+ align:start position:0%
+class I really like IDE
+class okay here telephone rings and you
+
+ align:start position:0%
+class okay here telephone rings and you
+ 
+
+ align:start position:0%
+class okay here telephone rings and you
+say I'll get it I'll get it just I'll
+
+ align:start position:0%
+say I'll get it I'll get it just I'll
+ 
+
+ align:start position:0%
+say I'll get it I'll get it just I'll
+get it well I'll get it well I'll I'll
+
+ align:start position:0%
+get it well I'll get it well I'll I'll
+ 
+
+ align:start position:0%
+get it well I'll get it well I'll I'll
+get it I'll get
+
+ align:start position:0%
+get it I'll get
+ 
+
+ align:start position:0%
+get it I'll get
+it I'll get
+
+ align:start position:0%
+it I'll get
+ 
+
+ align:start position:0%
+it I'll get
+it uh I'll get it I'll get it I'll get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it no I'll you see I'll get it I'll get
+
+ align:start position:0%
+it no I'll you see I'll get it I'll get
+ 
+
+ align:start position:0%
+it no I'll you see I'll get it I'll get
+it right and no I'll get it no no I'll
+
+ align:start position:0%
+it right and no I'll get it no no I'll
+ 
+
+ align:start position:0%
+it right and no I'll get it no no I'll
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+you I'll get it
+
+ align:start position:0%
+you I'll get it
+ 
+
+ align:start position:0%
+you I'll get it
+right you go to you go to supermarket
+
+ align:start position:0%
+right you go to you go to supermarket
+ 
+
+ align:start position:0%
+right you go to you go to supermarket
+and the cashier uh Rings you up and you
+
+ align:start position:0%
+and the cashier uh Rings you up and you
+ 
+
+ align:start position:0%
+and the cashier uh Rings you up and you
+say oh she says thank you and you you go
+
+ align:start position:0%
+say oh she says thank you and you you go
+ 
+
+ align:start position:0%
+say oh she says thank you and you you go
+thank you thank you thank you thank you
+
+ align:start position:0%
+thank you thank you thank you thank you
+ 
+
+ align:start position:0%
+thank you thank you thank you thank you
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+huh say it
+
+ align:start position:0%
+huh say it
+ 
+
+ align:start position:0%
+huh say it
+again right she or he says you that
+
+ align:start position:0%
+again right she or he says you that
+ 
+
+ align:start position:0%
+again right she or he says you that
+happens to you some sometimes they say
+
+ align:start position:0%
+happens to you some sometimes they say
+ 
+
+ align:start position:0%
+happens to you some sometimes they say
+thank you yes then no no no no thank
+
+ align:start position:0%
+thank you yes then no no no no thank
+ 
+
+ align:start position:0%
+thank you yes then no no no no thank
+you okay you say thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+youo no no no thank you wor just thank
+
+ align:start position:0%
+youo no no no thank you wor just thank
+ 
+
+ align:start position:0%
+youo no no no thank you wor just thank
+you yeah yeah yeah so that's actually
+
+ align:start position:0%
+you yeah yeah yeah so that's actually
+ 
+
+ align:start position:0%
+you yeah yeah yeah so that's actually
+strange yes they they they should say
+
+ align:start position:0%
+strange yes they they they should say
+ 
+
+ align:start position:0%
+strange yes they they they should say
+thank you and then you say thank you
+
+ align:start position:0%
+thank you and then you say thank you
+ 
+
+ align:start position:0%
+thank you and then you say thank you
+thank you if say thank you oh no no no
+
+ align:start position:0%
+thank you if say thank you oh no no no
+ 
+
+ align:start position:0%
+thank you if say thank you oh no no no
+no no thank you you okay you could do
+
+ align:start position:0%
+no no thank you you okay you could do
+ 
+
+ align:start position:0%
+no no thank you you okay you could do
+that you could here this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one that was the movie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay you could say it was too long
+
+ align:start position:0%
+right okay you could say it was too long
+ 
+
+ align:start position:0%
+right okay you could say it was too long
+or it was too long you can say either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here was it a long
+
+ align:start position:0%
+here was it a long
+ 
+
+ align:start position:0%
+here was it a long
+drive you would go up on long because I
+
+ align:start position:0%
+drive you would go up on long because I
+ 
+
+ align:start position:0%
+drive you would go up on long because I
+guess uh what did you how did you get
+
+ align:start position:0%
+guess uh what did you how did you get
+ 
+
+ align:start position:0%
+guess uh what did you how did you get
+there I drove oh was it a long Drive
+
+ align:start position:0%
+there I drove oh was it a long Drive
+ 
+
+ align:start position:0%
+there I drove oh was it a long Drive
+drove is already old information so was
+
+ align:start position:0%
+drove is already old information so was
+ 
+
+ align:start position:0%
+drove is already old information so was
+it a long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drive it was too long this one you have
+
+ align:start position:0%
+drive it was too long this one you have
+ 
+
+ align:start position:0%
+drive it was too long this one you have
+to go up on two okay because long this
+
+ align:start position:0%
+to go up on two okay because long this
+ 
+
+ align:start position:0%
+to go up on two okay because long this
+is old
+
+ align:start position:0%
+is old
+ 
+
+ align:start position:0%
+is old
+information okay you want to put
+
+ align:start position:0%
+information okay you want to put
+ 
+
+ align:start position:0%
+information okay you want to put
+prominence on the U new information not
+
+ align:start position:0%
+prominence on the U new information not
+ 
+
+ align:start position:0%
+prominence on the U new information not
+old information so here you have to say
+
+ align:start position:0%
+old information so here you have to say
+ 
+
+ align:start position:0%
+old information so here you have to say
+it was too long but here you can it was
+
+ align:start position:0%
+it was too long but here you can it was
+ 
+
+ align:start position:0%
+it was too long but here you can it was
+too long how was the movie oh it was too
+
+ align:start position:0%
+too long how was the movie oh it was too
+ 
+
+ align:start position:0%
+too long how was the movie oh it was too
+long how was the movie it was was too
+
+ align:start position:0%
+long how was the movie it was was too
+ 
+
+ align:start position:0%
+long how was the movie it was was too
+long hey how was it a long drive yeah it
+
+ align:start position:0%
+long hey how was it a long drive yeah it
+ 
+
+ align:start position:0%
+long hey how was it a long drive yeah it
+was too
+
+ align:start position:0%
+was too
+ 
+
+ align:start position:0%
+was too
+long
+
+ align:start position:0%
+long
+ 
+
+ align:start position:0%
+long
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay uh we'll do this next Time Unreal
+
+ align:start position:0%
+okay uh we'll do this next Time Unreal
+ 
+
+ align:start position:0%
+okay uh we'll do this next Time Unreal
+past conditional
\ No newline at end of file
diff --git a/VUgN-YEklTU.txt b/VUgN-YEklTU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c53ca0066a23f43a7ff0ef21b7bca9998ffc1341
--- /dev/null
+++ b/VUgN-YEklTU.txt
@@ -0,0 +1,422 @@
+Hi.
+
+In this problem, we're going
+to look at random incidence
+
+under Erlang arrivals.
+
+First, let's parse
+what that means.
+
+In a Poisson process, remember,
+the time between
+
+arrivals, or the inter-arrival
+time, is distributed as an
+
+exponential random variable.
+
+And random incidence for a
+Poisson process refers to the
+
+somewhat surprising result
+that when you consider a
+
+specific time, say, T-star,
+then the length of the
+
+inter-arrival interval that
+contains that time T-star is
+
+not distributed as an
+exponential random variable.
+
+It's actually distributed as an
+Erlang random variable of
+
+order 2 or it's distributed as
+a sum of two exponential
+
+random variables.
+
+And the reason for
+that is that it
+
+comprises of two parts.
+
+One is the time since the last
+arrival until T-star, which is
+
+exponentially distributed, and
+the time from T-star until the
+
+next arrival, which is also
+exponentially distributed.
+
+So that brings us to a review
+of what Erlang random
+
+variables are.
+
+An Erlang random variable of
+order k is just the sum of k
+
+independent and identically
+distributed
+
+exponential random variables.
+
+So to be more specific, if Ti
+is an exponential random
+
+variable with parameter lambda,
+then if you take kiid
+
+copies of Ti and add them up,
+and call that Yk, then Yk is
+
+an Erlang random variable
+of order k.
+
+And one other fact is that the
+mean of Yk, the mean of an
+
+Erlang random variable of order
+k, is just k, the order,
+
+over lambda, which is the rate
+of the underlying exponential
+
+random variables.
+
+So as a consequence, if you have
+an Erlang random variable
+
+of order two and that random
+variable also has a mean of
+
+two over lambda, we can
+interpret that random variable
+
+as just being the sum of two
+exponential random variables.
+
+2 iid exponential random
+variables, T1 and T2, where
+
+each one takes exponential
+with the rate in lambda.
+
+OK, so in this problem now,
+we're dealing with the random
+
+incidence not under Poisson
+processes, but under something
+
+else, which we call here an
+Erlang process with Erlang
+
+arrival times.
+
+So to be more specific, what
+we're saying is that, instead
+
+of inter-arrival time being
+exponentially distributed, in
+
+this process, and inter-arrival
+time is actually
+
+distributed as an Erlang random
+variable of order 2
+
+with mean 2 over lambda.
+
+So to be explicit, this is no
+longer a Poisson process.
+
+It's some other process because
+the inter-arrival
+
+times are not exponential.
+
+So let's make use of this fact
+that we talked about earlier
+
+because now we know that the
+inter-arrival times of this
+
+Erlang process are
+Erlang order 2
+
+with mean 2 over lambda.
+
+But we know that that can just
+be re-interpreted as a sum of
+
+two simple exponentials, each
+with parameter lambda.
+
+So let's just draw another
+picture and imagine that for
+
+each of these arrivals, so say
+we have three sample arrivals
+
+in this Erlang process, we can
+fill in, kind of, the gaps
+
+between these with additional
+arrivals.
+
+And then think of each one of
+these times as all being
+
+exponential with parameter
+lambda.
+
+So this is a valid
+interpretation because when we
+
+connect these, these
+inter-arrival times correspond
+
+to the combination of two
+inter-arrival times, which we
+
+know we can split that into
+just two exponentials.
+
+So each one of these is an
+exponential random variable.
+
+And when you combine them, you
+get an Erlang order of 2.
+
+But the nice thing about this
+is that if we look at this
+
+diagram, it actually is just
+exactly a Poisson process with
+
+a rate lambda because
+now, what we're
+
+dealing with are exactly--
+
+the inter-arrival times
+are now exactly
+
+exponential random variables.
+
+And so this is in fact, now,
+just a simple Poisson process.
+
+And we can also just think of
+it as we take the Poisson
+
+process, and take every other
+arrival, say, all the
+
+even-numbered arrivals, and make
+those corresponds to be
+
+arrivals in the Erlang
+process.
+
+OK, so now let's think about
+some specific time T-star.
+
+We want to know what is the
+distribution of the length of
+
+this to be specific
+inter-arrival interval that
+
+T-star is in.
+
+Well, what we can do is take it
+down to the level of this
+
+Poisson process and look
+at it from there.
+
+Well, we do that because, for
+a Poisson process, we know
+
+about random incidence for
+Poisson processes.
+
+And we know how to deal with
+Poisson processes.
+
+So let's think about this now.
+
+Well, T-star is here.
+
+And what we know from random
+incidence for a Poisson
+
+processes is that the length of
+this inter-arrival interval
+
+for the Poisson process,
+we know that this is an
+
+exponential plus
+an exponential.
+
+So combined, this is
+Erlang order 2.
+
+ 
+
+But that only covers
+from here to here.
+
+And what we want is actually
+from here to there.
+
+Well now, we tack on an extra
+exponential because we know
+
+that the inter-arrival times--
+
+the time between this arrival
+and that arrival in the
+
+Poisson process is just
+another exponential.
+
+And now all of these are in
+[INAUDIBLE] time intervals.
+
+And they're all independent.
+
+And so the time of this
+inter-arrival interval in the
+
+Erlang process is just going
+to be the sum of three
+
+independent exponentials
+within the
+
+underlying Poisson process.
+
+And so to answer here is
+actually, it's going to be an
+
+Erlang of order 3.
+
+ 
+
+Now this is one possible
+scenario for
+
+how this might occur.
+
+Another scenario is actually
+that T-star is somewhere else.
+
+So let's draw this again.
+
+ 
+
+And suppose now, in this case,
+T-star landed between an even
+
+numbered arrival in the Poisson
+process and an odd
+
+numbered arrival.
+
+Now it could also arrive between
+an odd numbered and an
+
+even numbered arrival.
+
+So it could be that T-star
+is actually here.
+
+Well, but in this case, it's
+actually more or less the same
+
+thing because now what we want
+is the length of this entire
+
+inter-arrival interval, which,
+in the Poisson world, we can
+
+break it down into random
+incidence within this
+
+interval, this inter-arrival
+interval, which is two
+
+exponentials, or an Erlang of
+2, plus this interval, which
+
+is just a standard inter-arrival
+time, which is
+
+another exponential.
+
+So in this case as well, we
+have the sum of three
+
+independent exponential
+random variables.
+
+And so, in either case, we have
+that the inter-arrival
+
+time in the Erlang process
+is an Erlang of order 3.
+
+And so the final answer is, in
+fact, that the inter-arrival
+
+for random incidence under these
+Erlang-type arrivals is
+
+an Erlang of order 3.
+
+OK, so in this problem we looked
+at the random incidence
+
+under a different type of an
+arrival process, not Poisson,
+
+but with Erlang random
+variables.
+
+But we used the insight that
+Erlang really can be
+
+re-interpreted as the sum of
+independent and identically
+
+distributed exponential
+random variables.
+
+And exponential random variables
+can be viewed as one
+
+way of interpreting and viewing
+a Poisson process.
+
+And so by going through those
+steps, we were able to use
+
+what we know about random
+incidence under Poisson
+
+processes to help us solve
+this problem of random
+
+incidence its Erlang arrivals.
+
+So I hope that was helpful.
+
+And I'll see you next time.
\ No newline at end of file
diff --git a/Vyf-lQjk0rY.txt b/Vyf-lQjk0rY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3633350c1be420ccdb34f422fdfe738e90588a91
--- /dev/null
+++ b/Vyf-lQjk0rY.txt
@@ -0,0 +1,1740 @@
+PROFESSOR: All right, now for
+
+something completely different.
+
+Before beginning though,
+I would like to raise a
+
+procedural question.
+
+It was my intent that quiz
+number two, which is like a
+
+little more than a week away,
+was going to be part symmetry
+
+and part tensors.
+
+I don't want to have your
+fortunes based by weight of
+
+2:1 on symmetry theory as
+opposed to properties.
+
+What I would suggest, and you
+can express your opinion
+
+either way, is that we postpone
+quiz number two by
+
+maybe as much as 10 days, so
+that it can be half symmetry
+
+and half the introductory
+discussion of tensors.
+
+And if that does not create a
+conflict with some of your
+
+other classes, I would propose
+that as a suggestion.
+
+If not, we can just have on the
+quiz what we're going to
+
+cover of tensors in the
+next couple days and
+
+have the rest symmetry.
+
+So what I am suggesting is the
+quiz was scheduled for a week
+
+from November 8, which
+is a Tuesday.
+
+What I would suggest is putting
+that off to the 18th,
+
+and that will give us four
+extra lectures--
+
+six extra lectures-- on tensors
+and we can make the
+
+quiz 50-50.
+
+AUDIENCE: What does that do
+to quiz number three?
+
+PROFESSOR: Quiz number three
+is going to stay in place
+
+because it's right at
+the end of the term.
+
+AUDIENCE: What about the
+subject in three?
+
+PROFESSOR: It will
+be all tensors.
+
+It will be all tensors
+and properties.
+
+And the third quiz is set up
+for longer than you think.
+
+It's December 8, so it'll
+be about three weeks.
+
+AUDIENCE: So everything
+from here on?
+
+PROFESSOR: Yeah.
+
+Does that make sense?
+
+Or is somebody going to have a
+big, traumatic responsibility
+
+at that point?
+
+AUDIENCE: I don't know, but I
+think it would be probably be
+
+easiest for us not to
+have it three days
+
+before close of exams.
+
+PROFESSOR: OK, OK, that's
+what I wanted to hear.
+
+How about if we went just a
+little bit further then and
+
+did it not on the--
+
+when was the suggestion?
+
+The 18th.
+
+Let's say we did it on
+Tuesday the 15th?
+
+Does that conflict
+with anything?
+
+AUDIENCE: That's a little bit.
+
+AUDIENCE: We were doing
+it on the 18th.
+
+AUDIENCE: Is that Friday?
+
+[INTERPOSING VOICES]
+
+PROFESSOR: I'm sorry, 18th.
+
+I said it would be 17th.
+
+Excuse me.
+
+AUDIENCE: That definitely would
+be a little better.
+
+PROFESSOR: OK, let me allow you
+to think about that, and
+
+that would be pushing it back
+one week and maybe it'd be--
+
+we'll see how much material
+on tensors we cover.
+
+So let's table it for now but
+let's say, tentatively, let's
+
+consider seriously moving
+it to the 15th.
+
+OK?
+
+But you guys have final
+say if there's a
+
+preference that you have.
+
+OK let's talk about properties
+in first a general and rather
+
+philosophic way.
+
+When we discuss properties we
+very commonly lump together a
+
+set of behaviors which have
+some common phenomenology.
+
+So for example, we will talk
+about mechanical properties.
+
+And that's a basket in which we
+place many different sorts
+
+of behavior.
+
+We place things like fracture
+toughness, yield strength,
+
+elastic constants, a whole
+variety of things involving
+
+strength deformation
+and so on.
+
+Or another thing we very often
+lump together in a basket is
+
+something called electrical
+properties.
+
+And we talk about electrical
+conductivity, ionic
+
+conductivity, electronic
+conductivity.
+
+We talk about dielectric
+constants, we talk about
+
+permittivity and permeability,
+magnetic properties--
+
+a whole bunch of other classes
+of behavior, which have some
+
+sort of root or description in
+terms of electromagnetism.
+
+There are though a lot of
+strange aspects to properties.
+
+There are some properties that
+are determined for material
+
+which no longer exists
+when you're through
+
+determining the property.
+
+You have a sample you want
+to know what the
+
+yield strength is.
+
+So you put the gradually
+increasing load on it until
+
+finally, POP, it breaks.
+
+And now you know what the
+yield strength is for a
+
+material that no
+longer exists.
+
+Another example is an old one.
+
+Back before the days of X-ray
+diffraction when people would
+
+try to characterize material,
+anything that is very
+
+intensely colored usually looks
+black, and that's not a
+
+very definitive property.
+
+The color of something is a very
+prominent characteristic.
+
+So for mineralogists, in
+particular, anybody going out
+
+into the hills and wanting to be
+prepared to determine what
+
+a particular rock that they
+tripped over was had something
+
+on a rope around their neck
+called a streak plate.
+
+And what the streak plate
+was was a little
+
+rectangle of porcelain.
+
+And they would take this black
+mineral and rub it on this
+
+piece of porcelain and it
+would leave a mark--
+
+that was called the streak.
+
+And what this was was actually
+little bunch of fragments that
+
+rubbed off on to the porcelain
+because the porcelain was
+
+white and the fragments
+were very small.
+
+A black piece of rock could
+give you a streak that was
+
+brown or green or deep orange.
+
+And so you really were
+determining the color of the
+
+material when it was in a form
+finely divided enough that
+
+light could pass through it.
+
+So the streak test was a very
+important diagnostic for
+
+determining minerals.
+
+There are some properties
+that we refer to
+
+as structure sensitive.
+
+In the sense that
+their value--
+
+conductivity is a
+good example--
+
+the value of ionic conductivity
+depends on the
+
+impurities and point
+defects that are
+
+present in the material.
+
+So to say that the ionic
+conductivity of a certain
+
+material is such and such, you
+have to specify the purity and
+
+perfection of the material or
+the property's meaningless.
+
+There are some properties that
+are not even single-valued.
+
+And the best example there are
+dielectric or magnetic
+
+properties.
+
+If you plot the magnetization
+of a material, the magnetic
+
+moment per unit volume as a
+function of the applied
+
+magnetic field B, the material
+is initially non-magnetized.
+
+When you apply B, you get a
+magnetic moment per unit
+
+volume that eventually
+saturates.
+
+And then if you remove the
+magnetic field, the material
+
+keeps some of its
+magnetization.
+
+It doesn't go to zero when you
+reduce the field to zero.
+
+You have to reverse the field
+to get the property to go to
+
+zero and then magnetize it
+in another direction.
+
+And if you continue to cycle the
+magnetic field, you get a
+
+behavior like this.
+
+This is hysteresis, and this
+type of behavior is called
+
+generally hysteretic.
+
+Same thing would be a relation
+between the displacement
+
+vector and an applied
+electric field.
+
+But clearly you can have any
+value of the magnetization in
+
+this range.
+
+And if you relate the
+magnetization as a function of
+
+the applied field, you can
+get any value of the
+
+proportionality constant you
+like between a negative
+
+maximum and a positive maximum
+including zero.
+
+So there's a property that's
+not even single-valued.
+
+Depends on the past history
+of the sample.
+
+And then there are even more
+peculiar properties.
+
+There are properties
+that are--
+
+we call them composite
+properties and very often
+
+qualitative.
+
+What do they mean by a
+composite property.
+
+Let me give you one example--
+
+The property fuzzy.
+
+If I say fuzzy, you know
+exactly what I mean.
+
+It means something that has
+a diffuse reflectivity,
+
+something that has a surface
+texture that's yielding.
+
+It's not like rubbing
+a wire brush.
+
+It's soft and giving, a whole
+collection of different
+
+properties.
+
+But yet when I say fuzzy, you
+know exactly what I mean.
+
+Let me not be so facetious
+as talking
+
+about a fuzzy property.
+
+People such as ceramists or
+powder metallurgists very
+
+often will take a powder of a
+material and consolidate it by
+
+compacting it and heating it,
+very often subject to a
+
+compacting stress.
+
+And when you do that little
+necks grow between the
+
+particles and they
+hold together and
+
+the material is centric.
+
+So you refer to a property of
+a powder as being centerable
+
+or the centerability
+of a powder.
+
+You know exactly what somebody
+means by that.
+
+But what does it depend on?
+
+It depends on the surface
+energy, it depends on vapor
+
+pressure, depends on bulk
+diffusion coefficients.
+
+It depends on surface diffusion
+coefficients.
+
+And all of these things have to
+be just right to make the
+
+powder something that easily
+densifies upon heating in the
+
+application or not
+of pressure.
+
+So you know exactly what I mean
+by centerability, but it
+
+is a very complex property.
+
+And was one that really was not
+understood until probably
+
+the late 1950s.
+
+Until then, it was an art that
+was entirely empirical.
+
+And it was somebody here at
+MIT, a fellow named Robert
+
+Coble, who developed a theory
+of centering that was the
+
+first really workable theory
+that described densification
+
+by heating and compaction.
+
+OK, composite property that
+depends on many different
+
+individual properties
+of the material.
+
+OK, what we are going to examine
+here are equilibrium
+
+properties that can be
+rigorously defined and
+
+measurable.
+
+So we're going to leave out of
+the picture things like fuzzy
+
+and centerability.
+
+And let me give a very nice,
+obscure definition of what I
+
+mean by a property.
+
+And what I mean by a property,
+in terms of a formal
+
+statement, is the response of
+a material to a specific
+
+change in a given set
+of conditions.
+
+So the response of the material
+to a specific change
+
+in a set of conditions that
+relates independent properties
+
+and dependent properties for
+a particular process.
+
+So I'll state that again
+because I think
+
+it's terribly elegant.
+
+So a property is the response of
+the material to a specific
+
+change in a given set of
+conditions that relates
+
+independent and dependent
+quantities in
+
+a particular process.
+
+Now there are a lot of
+properties that have their
+
+roots solidly embedded
+in thermodynamics.
+
+So let me give you
+a few of those.
+
+What we'll talk about when
+we specify a property is
+
+something that we will refer
+to as a displacement.
+
+We'll talk about a generalized
+displacement in response to a
+
+generalized force.
+
+So some of the thermodynamic
+quantities that are related in
+
+this fashion--
+
+if we list some forces and some
+displacements, the thing
+
+that happens as a result of that
+stimulus that's applied
+
+to the material.
+
+Temperature can be regarded as
+a force that results in all
+
+sorts of processes
+as a result--
+
+thermal energy flow,
+thermal expansion,
+
+all sorts of things.
+
+But one of the things that will
+happen in response to a
+
+temperature change
+
+thermodynamically is an entropy.
+
+So you can view entropy as a
+generalized displacement
+
+resulting from the application
+of temperature as a
+
+generalized force.
+
+Another example is electric
+field and the thing that
+
+happens there, and
+electromagnetism, is the
+
+quantity, D, which
+is displacement.
+
+Still another example, stress,
+and the result of applying a
+
+stress, among other things,
+is a strain.
+
+What is special about these
+forces in this displacement is
+
+that their product is, in each
+of these cases, energy, the
+
+change in internal energy
+of the particular body.
+
+And when that is the case,
+these are said to be
+
+conjugate--
+
+a conjugate force and
+displacement.
+
+And there are other examples
+that one can come up .with.
+
+Now to talk about a specific
+set of properties.
+
+Very often, and this crept into
+the earlier discussion,
+
+very often the thing that we
+do to a material, as a
+
+generalized force,
+is a vector.
+
+So very often the thing that we
+do to the material, apply
+
+an electric field, apply a
+magnetic field, apply a
+
+temperature gradient, apply a
+tensile stress, it has the
+
+characteristics of a vector,
+magnitude and direction.
+
+And in many cases, the thing
+that happens as a generalized
+
+displacement, we may call
+this in general,
+
+q, is also a vector.
+
+An example is if we apply
+an electric field as a
+
+generalized force, one thing
+that might happen is a current
+
+flow, which is also a vector.
+
+And we are accustomed to
+writing, q, the generalized
+
+displacement, as a
+proportionality constant,
+
+sigma, which is in the case of
+electric field and current
+
+flow, the electrical
+conductivity.
+
+Let me call it, in general
+terms, proportionality
+
+constant, a, times the
+applied vector, p.
+
+Is this something we would
+like to stick with as a
+
+general relation?
+
+Well let me submit that writing
+an expression of this
+
+form makes an inherent
+assumption.
+
+Namely that this will be true
+for small, and we'll have to
+
+define for each property
+what we mean by a
+
+small, applied vector.
+
+Let me give you an example.
+
+If p were--
+
+the applied vector was electric
+field, and the
+
+resulting vector was current
+flow, and the relation between
+
+those is the conductivity--
+
+a relation of this sort says
+that if you double the field,
+
+you double the conductivity.
+
+You triple the field, you
+triple the conductivity.
+
+Obviously this can't go on
+indefinitely because all a
+
+sudden, POW, dielectric
+breakdown.
+
+The sample evaporates
+at the smoke.
+
+And again, you have the property
+of a material which
+
+no longer exists.
+
+So a lot of properties, we
+inherently assume that the
+
+applied vector is small in order
+to write something in an
+
+expression of this form.
+
+So for conductivity, dielectric
+breakdown is going
+
+to destroy the nice linear
+relation between current flow
+
+and electric field.
+
+That's not always the case.
+
+Let me give you an example
+of another property.
+
+And this is a property, magnetic
+susceptibility, which
+
+relates the magnetization, which
+is magnetic moment per
+
+unit volume, and relates that to
+an applied electric field--
+
+an applied magnetic field, H.
+And the proportionality
+
+constant, represented by a Greek
+chi, is the magnetic
+
+susceptibility.
+
+So let me give you a
+specific example.
+
+Suppose we have a chunk of glass
+and the glass contains a
+
+dilute concentration of iron.
+
+And iron carries a permanent
+magnetic moment.
+
+And the reason I want to make
+it a dilute concentration of
+
+iron is I don't want these
+magnetic moments close enough
+
+that they can interact
+with one another.
+
+I want this to, therefore,
+be a dilute system.
+
+So we have different
+iron atoms in this.
+
+Each iron atom has a
+magnetic moment.
+
+And then we put this in a
+magnetic field, H. And the
+
+magnetic field acts on each of
+these little magnetic moments
+
+just as though it were
+a compass needle.
+
+And so it will try to take each
+of these moments and drag
+
+it into coincidence with
+the magnetic field.
+
+But at a finite temperature,
+temperatures making these
+
+magnetic moments jiggle
+around, so at a finite
+
+temperature, the magnetic
+moments will just not simply
+
+zing into coincidence with
+the magnetic field.
+
+You'll have to increase
+the magnetic
+
+field to make it larger.
+
+When that happens, more and more
+of the magnetic moments
+
+will come into alignment.
+
+And if you put on a really
+strong magnetic field, then
+
+every single magnetic moment
+will be dragged into exact
+
+alignment with the magnetic
+field and
+
+the system has saturated.
+
+There's no way you could squeeze
+further magnetic
+
+moment per unit volume
+out of it.
+
+So again, you would expect, for
+this particular property,
+
+magnetic susceptibility of a
+material, if you plot it as a
+
+function of the applied
+magnetic field--
+
+linear maybe be at low
+applied fields--
+
+but eventually if you make the
+field strong enough, the
+
+system is going to saturate.
+
+And then again, no longer will
+the direction of the
+
+magnetization, and that magnetic
+moment, be parallel
+
+to H. But the property becomes
+nonlinear if the applied
+
+vector is strong enough.
+
+This is an example of a property
+where you would not
+
+go wrong at all by stating
+direct proportionality.
+
+For ordering to occur,
+temperature and applied field
+
+go hand in hand.
+
+Increased temperature tends
+to create more disorder.
+
+Increased magnetic field tends
+to align the moments.
+
+In the days when MIT had a
+national magnet laboratory,
+
+the magnet laboratory held the
+record for the strongest
+
+magnetic field ever produced
+artificially by man.
+
+And if you took that magnetic
+field and applied it to this
+
+system of dilute iron in a
+glass, you would have to lower
+
+the temperature of the sample
+to about 3 Kelvin before you
+
+would begin to see saturation.
+
+So even the strongest field that
+you could produce in a
+
+laboratory environment would
+not succeed in producing
+
+non-linearity until you cooled
+the sample down almost to
+
+absolute zero.
+
+So here would be a case where
+under any practical
+
+consideration whatsoever,
+assumption of strict
+
+proportionality would be
+right on the money.
+
+You'd be absolutely correct.
+
+But there's another assumption
+built into this statement.
+
+P, the generalized force, is
+a vector in the cases we're
+
+discussing now, and q
+is also a vector.
+
+So when we write an expression
+of this form you're making
+
+another assumption.
+
+And that is that the vector
+displacement that results is
+
+always exactly parallel to the
+vector that you apply.
+
+Do I make a big deal
+out of this?
+
+Isn't that always going
+to be the case?
+
+I mean whoever heard of taking
+a piece of metal and putting
+
+an electric field on it in this
+direction and having the
+
+current run off in
+this direction.
+
+It's absurd.
+
+Or maybe it isn't so absurd.
+
+So let's think of some of the
+atomistics of this process.
+
+Now, since I know I'm among
+friends, I will not hesitate
+
+to display my ignorance, total
+
+ignorance, of polymer chemistry.
+
+So suppose we had a
+piece of polymer.
+
+That's what a polymer
+molecule looks like.
+
+It's a more or less linear
+molecule, and so these might,
+
+in a very highly ordered
+polymer, be chains that lined
+
+up like this.
+
+And suppose we now put an
+electric field on this polymer
+
+and asked how the current
+will flow.
+
+Again, it would not be absurd
+to say that an electron
+
+sitting on this polymer chain
+in response to this field
+
+would be constrained only to
+flow in the direction of the
+
+chain and would find it rather
+difficult to hop from one
+
+chain to another.
+
+So maybe, just maybe, we could
+apply an electric field to a
+
+polymer and it would have a flow
+in this direction, that
+
+would be pointing in this
+direction, and the current
+
+flow, J, would be in
+that direction.
+
+So should we maybe rethink this
+idea of the direction of
+
+the generalized displacement
+being not parallel to the
+
+direction of the generalized
+force.
+
+OK, these are hypothetical
+examples.
+
+Let me now give you an example
+of a real property for a real
+
+material, for which the thing
+that happens, the vector that
+
+happens, is decidedly not
+parallel to the direction of
+
+the applied vector.
+
+OK, thermal conductivity is
+something that relates a heat
+
+flux, usually represented by the
+symbol K, and relates that
+
+to a temperature gradient,
+dt dx, which is a vector.
+
+The thing that gives rise to
+thermal conductivity can be
+
+either propagation of radiation
+as in propagation of
+
+light traveling through a
+transparent material.
+
+But the other mechanism for
+thermal conductivity is modes
+
+of lattice vibration.
+
+When a material is hot, the
+atoms are jiggling around and
+
+you can make the displacement
+of an individual atom be
+
+represented by a sum of waves
+moving in all different
+
+directions with a variety of
+wavelengths in a variety of
+
+amplitudes.
+
+Take all those waves, add them
+together at a particular time,
+
+and you get the displacement
+of the atom.
+
+Propagation of heat by this
+mechanism, by modes of thermal
+
+vibration, can be very, very
+anisotropic and probably the
+
+best example of this is--
+
+get a single crystal
+of graphite.
+
+And have the layers, the
+graphite sheets, which are
+
+hexagonal rings in which each
+carbon has three neighbors,
+
+and have the sheets be parallel
+to the surface of an
+
+extended two-dimensional slab.
+
+Now we can't do that.
+
+Single crystals of graphite
+don't occur
+
+in sizes like that.
+
+But what you can do is make a
+material called pyrolytic
+
+graphite that you make by having
+a reaction in the vapor
+
+phase and having the soot that's
+formed settle down onto
+
+a substrate.
+
+And what happens is you nucleate
+a graphite crystal in
+
+one orientation, and that grows
+preferentially with its
+
+layers parallel to the surface
+on which it's nucleated.
+
+And these nuclei occur
+at random.
+
+So you get a bunch of single
+crystals of graphite, which
+
+all have their layers, their
+three coordinated layers at
+
+parallel, but they
+are oriented at
+
+random about their c-axis.
+
+And that's a material that's
+very easy to prepare.
+
+And it's called pyrolytic
+graphite, and it has
+
+interesting applications
+and properties.
+
+OK, now I'm going to suggest an
+experiment to you and I'll
+
+caution you, please do
+not try this at home.
+
+Get yourself a piece of
+pyrolytic graphite.
+
+Put a Bunsen burner
+underneath it.
+
+Play the Bunsen burner on the
+bottom of the sheet of
+
+pyrolytic graphite.
+
+And to determine temperature,
+we'll take a ball of cotton
+
+and put it directly
+above the flame.
+
+And then take another ball of
+cotton and put it down at the
+
+end of the sheet.
+
+If you do that and bring up the
+Bunsen burner, this piece
+
+of cotton will sit there
+and sit there and sit
+
+there and sit there.
+
+And this piece of cotton will
+instantly burst into flame.
+
+So here's a case where dt dx,
+the thermal gradient, points
+
+in this direction.
+
+And the heat flow goes off in a
+direction at right angles to
+
+the temperature gradient,
+almost
+
+exactly at right angles.
+
+It turns out that the thermal
+conductivity in this
+
+direction, the value
+of K in the--
+
+I want to put crystallographic
+directions on this.
+
+But K parallel to the layers
+is equal to 10 to the third
+
+times K, perpendicular
+to the layers.
+
+So there's an anisotropy of the
+property that amounts to a
+
+factor of 1,000.
+
+Very dramatic.
+
+So what I'm leading up is that
+in a general relation between
+
+a generalized displacement, p,
+and a generalized force--
+
+I'm sorry, I'm using
+q-- p and q--
+
+we just can't simply put
+some constant in front.
+
+Because that assumes inherently
+that the direction
+
+of what happens, the vector
+that happens, is exactly
+
+parallel to the direction of
+the applied vector and that
+
+generally is not true.
+
+The difference may be small but
+it has to be taken into
+
+consideration.
+
+All right, let me now suggest
+a way of patching this up.
+
+What I'm going to
+do is assume--
+
+and it is an assumption--
+
+we're going to assume that each
+component of the vector
+
+that happens is given by--
+
+in fancy terms, the vector
+that results as the
+
+generalized displacement is
+given by a linear combination
+
+of every component of the
+vector that's applied.
+
+And that's what we've defined
+as the generalized force.
+
+So how would we express
+this analytically?
+
+I am going to use as my
+coordinate system, not x, y,
+
+and z as we usually do,
+I'm going to call
+
+it x1, x2, and x3.
+
+The reason is we'll see some
+unique properties of these
+
+indices that are very useful
+algebraically.
+
+So I'm going to now take my
+applied vector, p, and I'm
+
+going to assume that it has
+three components, p1, p2, and
+
+p3 along x1, x2, x3,
+respectively.
+
+My coordinate system, although I
+did not state it explicitly,
+
+is going to be a Cartesian
+coordinate system, not a
+
+crystallographic coordinate
+system.
+
+So what I'm proposing here is
+that we take each component of
+
+the resulting vector q--
+
+let's say q1--
+
+and we'll assume that that's
+given by a linear combination
+
+of all three components
+of the vector p.
+
+So it'll be some number times
+p1 plus some number times p2
+
+plus some number times p3.
+
+And those numbers in general
+will be different.
+
+So let's say I call the
+coefficient a, and now I'm
+
+going to define a convention
+that will stay with us.
+
+I'm going to define each of
+these coefficients, a, in
+
+terms of the index of the
+component of the generalized
+
+displacement which is being
+computed, and the coefficient
+
+modifies the component of the
+generalized force for that
+
+particular term.
+
+So I'm going to call this a11,
+where the 1 goes with this and
+
+the 1 goes with this.
+
+I'm going to call this a12, so
+that the 1 again says it's a
+
+contribution to q1.
+
+The 2 says that this
+term modifies p2. .
+
+And this similarly
+would be a13.
+
+For the term component of the
+generalized displacement, q2,
+
+I'll use the coefficients a21
+times p1 plus a22 times p2,
+
+plus 23 times p3.
+
+And q3 similarly will be a31
+times p1, plus a32 times p2
+
+plus a33 times p3.
+
+So I've got three simultaneous
+equations then, one for each
+
+component of the vector that
+results, the generalized
+
+displacement.
+
+So I can sum up this set of
+three equations by saying that
+
+the i-th component of q, where
+this is some particular
+
+component, q1, q2, or q3, is
+given by the sum over j from 1
+
+to 3 of aij times p sub j.
+
+So I've got ai1 times p1, ai2
+times p2 plus ai3 times p3.
+
+So this is in a nice, compact
+little nugget the expression
+
+that we are assuming will
+apply for all sorts of
+
+physical properties in which
+this is a vector
+
+and this is a vector--
+
+electrical conductivity,
+magnetic susceptibility,
+
+thermal conductivity,
+and so on.
+
+OK, this is a bad point to
+introduce something as hairy
+
+as what comes next.
+
+But I've got one minute left,
+and I think I can do it.
+
+I'm going to introduce something
+called the Einstein
+
+convention after old Albert
+Einstein himself.
+
+I'm sorry, but nobody
+said everything this
+
+term had to be easy.
+
+So let me introduce, if you're
+ready for it, the Einstein
+
+convention.
+
+Old Albert, I think, was just
+as lazy as anybody else.
+
+And he said it is going to be
+a bloody pain in the butt--
+
+I don't know if he put
+it exactly this way.
+
+It's going to be a pain in the
+butt to write this summation
+
+every time we want to combine
+three terms in a linear
+
+combination.
+
+So the Einstein convention is
+let us throw out the sigma and
+
+write this expression just
+as qi times aij p sub j.
+
+And whenever we see a subscript
+repeated, summation
+
+over repeated subscript
+is implied.
+
+OK so that's the Einstein
+convention.
+
+It will save us the trouble
+of writing in a lot
+
+of summation signs.
+
+But I would caution you that
+this convention, compact and
+
+convenient as it is, can define
+some polynomials that
+
+are nightmares.
+
+So let me give you one example
+of this, and this is actually
+
+a physical property.
+
+Let me say that Cijkl is given
+by ai capital I aj capital J
+
+ak capital K, al capital L times
+let's say D, capital I,
+
+capital J, capital K, capital
+L. That actually, believe it
+
+or not, means something
+physically and we're going to
+
+get to that in due course.
+
+But what this is, taking the
+Einstein convention into
+
+account, this is a quadruple
+summation over capital I,
+
+capital J, capital K, and
+capital L. These are very
+
+often referred to in this
+business as dummy indices,
+
+meaning that they don't really
+mean anything physically.
+
+They're just indices
+of summation.
+
+I would caution you that
+this is a term
+
+that does not permute.
+
+If I say those are dummy
+indices, it means one thing.
+
+If I say those are indices,
+dummy, it means something
+
+completely different, and
+you're apt to get
+
+a poke in the nose.
+
+OK so these are dummy indices.
+
+Now, what does this represent?
+
+I won't say what it represents
+physically, but this consists
+
+of terms in four variables
+times a coefficient.
+
+So there are five quantities
+in each term.
+
+If I sum over capital I, J, and
+K from 1 to 3, there are
+
+going to be 81 such terms,
+each with five
+
+elements in each term.
+
+So it's going to be on the order
+of 405 terms in this
+
+summation, and we've collapsed
+the whole thing down, 405
+
+terms in this nice summation.
+
+So it is a great facility for
+writing down expressions
+
+explicitly, but these terms can
+hide a terribly, terribly
+
+complex polynomial.
+
+All right, I think that's
+a good place to quit.
+
+It continues to amaze me,
+though, how some absolutely
+
+trivial convention, when first
+proposed by a great man, will
+
+carry that man's name no matter
+how stupid it is.
+
+So this is called the Einstein
+convention by everybody who
+
+works in this field.
+
+Another one, just briefly to
+finish up, when you discuss
+
+dislocations, you talk about a
+circuit of steps around the
+
+dislocation.
+
+That's called a Burgers
+circuit.
+
+And if you do the same circuit
+in a corresponding piece of
+
+material that doesn't have a
+dislocation, if this circuit
+
+closes, this circuit fails to
+close by something that's
+
+called the Burgers vector.
+
+Every book on dislocation theory
+says, Shockley called
+
+this good material.
+
+I'm sorry, Shockley called
+this good material, and
+
+Shockley called this
+bad material.
+
+Big deal--
+
+good material, bad material
+because it's got a
+
+dislocation in it.
+
+But that is identified with
+Shockley's name in every
+
+discussion of dislocation.
+
+I'm just jealous because nobody
+has ever said according
+
+to me, such and such is--
+
+all right, see you
+later in the week
+
+for more great things.
\ No newline at end of file
diff --git a/W5zVgQ4SbX8.txt b/W5zVgQ4SbX8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a4f4ae99287c6a9b8546bebf204b20ada5163d30
--- /dev/null
+++ b/W5zVgQ4SbX8.txt
@@ -0,0 +1,1171 @@
+align:start position:0%
+ 
+to predict the outcomes of the Supreme
+
+ align:start position:0%
+to predict the outcomes of the Supreme
+ 
+
+ align:start position:0%
+to predict the outcomes of the Supreme
+Court Martin used cases from 1994
+
+ align:start position:0%
+Court Martin used cases from 1994
+ 
+
+ align:start position:0%
+Court Martin used cases from 1994
+through 2001 he chose this period of
+
+ align:start position:0%
+through 2001 he chose this period of
+ 
+
+ align:start position:0%
+through 2001 he chose this period of
+time because the Supreme Court was
+
+ align:start position:0%
+time because the Supreme Court was
+ 
+
+ align:start position:0%
+time because the Supreme Court was
+composed of the same nine justices that
+
+ align:start position:0%
+composed of the same nine justices that
+ 
+
+ align:start position:0%
+composed of the same nine justices that
+were justices when he made his
+
+ align:start position:0%
+were justices when he made his
+ 
+
+ align:start position:0%
+were justices when he made his
+predictions in 2002 these nine justices
+
+ align:start position:0%
+predictions in 2002 these nine justices
+ 
+
+ align:start position:0%
+predictions in 2002 these nine justices
+were Breyer Ginsburg Kennedy O'Connor
+
+ align:start position:0%
+were Breyer Ginsburg Kennedy O'Connor
+ 
+
+ align:start position:0%
+were Breyer Ginsburg Kennedy O'Connor
+Rehnquist who was the Chief Justice
+
+ align:start position:0%
+Rehnquist who was the Chief Justice
+ 
+
+ align:start position:0%
+Rehnquist who was the Chief Justice
+Scalia Souter Stevens and Thomas this
+
+ align:start position:0%
+Scalia Souter Stevens and Thomas this
+ 
+
+ align:start position:0%
+Scalia Souter Stevens and Thomas this
+was a very rare dataset since as I
+
+ align:start position:0%
+was a very rare dataset since as I
+ 
+
+ align:start position:0%
+was a very rare dataset since as I
+mentioned earlier this was the longest
+
+ align:start position:0%
+mentioned earlier this was the longest
+ 
+
+ align:start position:0%
+mentioned earlier this was the longest
+period of time with the same set of
+
+ align:start position:0%
+period of time with the same set of
+ 
+
+ align:start position:0%
+period of time with the same set of
+justices in over a hundred and eighty
+
+ align:start position:0%
+justices in over a hundred and eighty
+ 
+
+ align:start position:0%
+justices in over a hundred and eighty
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+this allowed Martin to use a larger
+
+ align:start position:0%
+this allowed Martin to use a larger
+ 
+
+ align:start position:0%
+this allowed Martin to use a larger
+dataset that might have been available
+
+ align:start position:0%
+dataset that might have been available
+ 
+
+ align:start position:0%
+dataset that might have been available
+if he was doing this experiment at a
+
+ align:start position:0%
+if he was doing this experiment at a
+ 
+
+ align:start position:0%
+if he was doing this experiment at a
+different time in this lecture will
+
+ align:start position:0%
+different time in this lecture will
+ 
+
+ align:start position:0%
+different time in this lecture will
+focus on predicting justice Stevens
+
+ align:start position:0%
+focus on predicting justice Stevens
+ 
+
+ align:start position:0%
+focus on predicting justice Stevens
+decisions he is generally considered a
+
+ align:start position:0%
+decisions he is generally considered a
+ 
+
+ align:start position:0%
+decisions he is generally considered a
+justice who started out moderate but
+
+ align:start position:0%
+justice who started out moderate but
+ 
+
+ align:start position:0%
+justice who started out moderate but
+became more liberal during his time on
+
+ align:start position:0%
+became more liberal during his time on
+ 
+
+ align:start position:0%
+became more liberal during his time on
+the Supreme Court although he is a
+
+ align:start position:0%
+the Supreme Court although he is a
+ 
+
+ align:start position:0%
+the Supreme Court although he is a
+self-proclaimed conservative in this
+
+ align:start position:0%
+self-proclaimed conservative in this
+ 
+
+ align:start position:0%
+self-proclaimed conservative in this
+problem our dependent variable is
+
+ align:start position:0%
+problem our dependent variable is
+ 
+
+ align:start position:0%
+problem our dependent variable is
+whether or not justice Stevens voted to
+
+ align:start position:0%
+whether or not justice Stevens voted to
+ 
+
+ align:start position:0%
+whether or not justice Stevens voted to
+reverse the lower court decision this is
+
+ align:start position:0%
+reverse the lower court decision this is
+ 
+
+ align:start position:0%
+reverse the lower court decision this is
+a binary variable taking value one if
+
+ align:start position:0%
+a binary variable taking value one if
+ 
+
+ align:start position:0%
+a binary variable taking value one if
+justice Stevens decided to reverse or
+
+ align:start position:0%
+justice Stevens decided to reverse or
+ 
+
+ align:start position:0%
+justice Stevens decided to reverse or
+overturn the lower court decision and
+
+ align:start position:0%
+overturn the lower court decision and
+ 
+
+ align:start position:0%
+overturn the lower court decision and
+taking value zero if justice Stevens
+
+ align:start position:0%
+taking value zero if justice Stevens
+ 
+
+ align:start position:0%
+taking value zero if justice Stevens
+voted to affirm or maintain the lower
+
+ align:start position:0%
+voted to affirm or maintain the lower
+ 
+
+ align:start position:0%
+voted to affirm or maintain the lower
+court decision our independent variables
+
+ align:start position:0%
+court decision our independent variables
+ 
+
+ align:start position:0%
+court decision our independent variables
+are six different properties of the case
+
+ align:start position:0%
+are six different properties of the case
+ 
+
+ align:start position:0%
+are six different properties of the case
+the circuit court of origin or is the
+
+ align:start position:0%
+the circuit court of origin or is the
+ 
+
+ align:start position:0%
+the circuit court of origin or is the
+circuit or lower court where the case
+
+ align:start position:0%
+circuit or lower court where the case
+ 
+
+ align:start position:0%
+circuit or lower court where the case
+came from there are 13 different circuit
+
+ align:start position:0%
+came from there are 13 different circuit
+ 
+
+ align:start position:0%
+came from there are 13 different circuit
+courts in the United States the 1st
+
+ align:start position:0%
+courts in the United States the 1st
+ 
+
+ align:start position:0%
+courts in the United States the 1st
+through 11th and Washington DC courts
+
+ align:start position:0%
+through 11th and Washington DC courts
+ 
+
+ align:start position:0%
+through 11th and Washington DC courts
+are defined by region and the federal
+
+ align:start position:0%
+are defined by region and the federal
+ 
+
+ align:start position:0%
+are defined by region and the federal
+court is defined by the subject matter
+
+ align:start position:0%
+court is defined by the subject matter
+ 
+
+ align:start position:0%
+court is defined by the subject matter
+of the case the issue area of the case
+
+ align:start position:0%
+of the case the issue area of the case
+ 
+
+ align:start position:0%
+of the case the issue area of the case
+gives each case a category like Civil
+
+ align:start position:0%
+gives each case a category like Civil
+ 
+
+ align:start position:0%
+gives each case a category like Civil
+Rights or federal taxation the type of
+
+ align:start position:0%
+Rights or federal taxation the type of
+ 
+
+ align:start position:0%
+Rights or federal taxation the type of
+petitioner and type of respondent
+
+ align:start position:0%
+petitioner and type of respondent
+ 
+
+ align:start position:0%
+petitioner and type of respondent
+defined to parties in the case some
+
+ align:start position:0%
+defined to parties in the case some
+ 
+
+ align:start position:0%
+defined to parties in the case some
+examples are the
+
+ align:start position:0%
+examples are the
+ 
+
+ align:start position:0%
+examples are the
+United States an employer or an employee
+
+ align:start position:0%
+United States an employer or an employee
+ 
+
+ align:start position:0%
+United States an employer or an employee
+the ideological direction of the lower
+
+ align:start position:0%
+the ideological direction of the lower
+ 
+
+ align:start position:0%
+the ideological direction of the lower
+court decision describes whether the
+
+ align:start position:0%
+court decision describes whether the
+ 
+
+ align:start position:0%
+court decision describes whether the
+lower court made what was considered a
+
+ align:start position:0%
+lower court made what was considered a
+ 
+
+ align:start position:0%
+lower court made what was considered a
+liberal or a conservative decision the
+
+ align:start position:0%
+liberal or a conservative decision the
+ 
+
+ align:start position:0%
+liberal or a conservative decision the
+last variable indicates whether or not
+
+ align:start position:0%
+last variable indicates whether or not
+ 
+
+ align:start position:0%
+last variable indicates whether or not
+the petitioner argued that a law or
+
+ align:start position:0%
+the petitioner argued that a law or
+ 
+
+ align:start position:0%
+the petitioner argued that a law or
+practice was unconstitutional to collect
+
+ align:start position:0%
+practice was unconstitutional to collect
+ 
+
+ align:start position:0%
+practice was unconstitutional to collect
+this data Martin and his colleagues read
+
+ align:start position:0%
+this data Martin and his colleagues read
+ 
+
+ align:start position:0%
+this data Martin and his colleagues read
+through all of the cases and coded the
+
+ align:start position:0%
+through all of the cases and coded the
+ 
+
+ align:start position:0%
+through all of the cases and coded the
+information some of it like the circuit
+
+ align:start position:0%
+information some of it like the circuit
+ 
+
+ align:start position:0%
+information some of it like the circuit
+court is straightforward but other
+
+ align:start position:0%
+court is straightforward but other
+ 
+
+ align:start position:0%
+court is straightforward but other
+information required a judgment call
+
+ align:start position:0%
+information required a judgment call
+ 
+
+ align:start position:0%
+information required a judgment call
+like the ideological direction of the
+
+ align:start position:0%
+like the ideological direction of the
+ 
+
+ align:start position:0%
+like the ideological direction of the
+lower court now that we have our data
+
+ align:start position:0%
+lower court now that we have our data
+ 
+
+ align:start position:0%
+lower court now that we have our data
+and variables we are ready to predict
+
+ align:start position:0%
+and variables we are ready to predict
+ 
+
+ align:start position:0%
+and variables we are ready to predict
+the decisions of Justice Stevens we can
+
+ align:start position:0%
+the decisions of Justice Stevens we can
+ 
+
+ align:start position:0%
+the decisions of Justice Stevens we can
+use logistic regression and we get a
+
+ align:start position:0%
+use logistic regression and we get a
+ 
+
+ align:start position:0%
+use logistic regression and we get a
+model where some of the most significant
+
+ align:start position:0%
+model where some of the most significant
+ 
+
+ align:start position:0%
+model where some of the most significant
+variables are whether or not the case is
+
+ align:start position:0%
+variables are whether or not the case is
+ 
+
+ align:start position:0%
+variables are whether or not the case is
+from the Second Circuit Court with a
+
+ align:start position:0%
+from the Second Circuit Court with a
+ 
+
+ align:start position:0%
+from the Second Circuit Court with a
+coefficient of one point six six whether
+
+ align:start position:0%
+coefficient of one point six six whether
+ 
+
+ align:start position:0%
+coefficient of one point six six whether
+or not the case is from the Fourth
+
+ align:start position:0%
+or not the case is from the Fourth
+ 
+
+ align:start position:0%
+or not the case is from the Fourth
+Circuit Court with a coefficient of two
+
+ align:start position:0%
+Circuit Court with a coefficient of two
+ 
+
+ align:start position:0%
+Circuit Court with a coefficient of two
+point eight two and whether or not the
+
+ align:start position:0%
+point eight two and whether or not the
+ 
+
+ align:start position:0%
+point eight two and whether or not the
+lower court decision was liberal with a
+
+ align:start position:0%
+lower court decision was liberal with a
+ 
+
+ align:start position:0%
+lower court decision was liberal with a
+coefficient of negative one point two
+
+ align:start position:0%
+coefficient of negative one point two
+ 
+
+ align:start position:0%
+coefficient of negative one point two
+two well this tells us that the case
+
+ align:start position:0%
+two well this tells us that the case
+ 
+
+ align:start position:0%
+two well this tells us that the case
+being from the second or fourth circuit
+
+ align:start position:0%
+being from the second or fourth circuit
+ 
+
+ align:start position:0%
+being from the second or fourth circuit
+courts is predictive of justice Stevens
+
+ align:start position:0%
+courts is predictive of justice Stevens
+ 
+
+ align:start position:0%
+courts is predictive of justice Stevens
+reversing the case and the lower court
+
+ align:start position:0%
+reversing the case and the lower court
+ 
+
+ align:start position:0%
+reversing the case and the lower court
+decision being liberal is predictive of
+
+ align:start position:0%
+decision being liberal is predictive of
+ 
+
+ align:start position:0%
+decision being liberal is predictive of
+justice Stevens affirming the case it's
+
+ align:start position:0%
+justice Stevens affirming the case it's
+ 
+
+ align:start position:0%
+justice Stevens affirming the case it's
+difficult to understand which factors
+
+ align:start position:0%
+difficult to understand which factors
+ 
+
+ align:start position:0%
+difficult to understand which factors
+are more important due to things like
+
+ align:start position:0%
+are more important due to things like
+ 
+
+ align:start position:0%
+are more important due to things like
+the scales of the variables and the
+
+ align:start position:0%
+the scales of the variables and the
+ 
+
+ align:start position:0%
+the scales of the variables and the
+possibility of multicollinearity it's
+
+ align:start position:0%
+possibility of multicollinearity it's
+ 
+
+ align:start position:0%
+possibility of multicollinearity it's
+also difficult to quickly evaluate what
+
+ align:start position:0%
+also difficult to quickly evaluate what
+ 
+
+ align:start position:0%
+also difficult to quickly evaluate what
+the prediction would be for a new case
+
+ align:start position:0%
+the prediction would be for a new case
+ 
+
+ align:start position:0%
+the prediction would be for a new case
+so instead of logistic regression Martin
+
+ align:start position:0%
+so instead of logistic regression Martin
+ 
+
+ align:start position:0%
+so instead of logistic regression Martin
+and his colleagues used a method called
+
+ align:start position:0%
+and his colleagues used a method called
+ 
+
+ align:start position:0%
+and his colleagues used a method called
+classification and regression trees or
+
+ align:start position:0%
+classification and regression trees or
+ 
+
+ align:start position:0%
+classification and regression trees or
+cart this method builds what is called a
+
+ align:start position:0%
+cart this method builds what is called a
+ 
+
+ align:start position:0%
+cart this method builds what is called a
+tree by splitting on the values of the
+
+ align:start position:0%
+tree by splitting on the values of the
+ 
+
+ align:start position:0%
+tree by splitting on the values of the
+independent variables to predict the
+
+ align:start position:0%
+independent variables to predict the
+ 
+
+ align:start position:0%
+independent variables to predict the
+outcome for a new observation or case
+
+ align:start position:0%
+outcome for a new observation or case
+ 
+
+ align:start position:0%
+outcome for a new observation or case
+you can follow the splits in the tree
+
+ align:start position:0%
+you can follow the splits in the tree
+ 
+
+ align:start position:0%
+you can follow the splits in the tree
+and at the end you predict the most
+
+ align:start position:0%
+and at the end you predict the most
+ 
+
+ align:start position:0%
+and at the end you predict the most
+frequent outcome in the training set
+
+ align:start position:0%
+frequent outcome in the training set
+ 
+
+ align:start position:0%
+frequent outcome in the training set
+that followed the same path
+
+ align:start position:0%
+that followed the same path
+ 
+
+ align:start position:0%
+that followed the same path
+advantages of cart are that it does not
+
+ align:start position:0%
+advantages of cart are that it does not
+ 
+
+ align:start position:0%
+advantages of cart are that it does not
+assume a linear model like logistic
+
+ align:start position:0%
+assume a linear model like logistic
+ 
+
+ align:start position:0%
+assume a linear model like logistic
+regression or linear regression and it's
+
+ align:start position:0%
+regression or linear regression and it's
+ 
+
+ align:start position:0%
+regression or linear regression and it's
+a very interpretable model let's look at
+
+ align:start position:0%
+a very interpretable model let's look at
+ 
+
+ align:start position:0%
+a very interpretable model let's look at
+an example this plot shows sample data
+
+ align:start position:0%
+an example this plot shows sample data
+ 
+
+ align:start position:0%
+an example this plot shows sample data
+for two independent variables x and y
+
+ align:start position:0%
+for two independent variables x and y
+ 
+
+ align:start position:0%
+for two independent variables x and y
+and each data point is colored by the
+
+ align:start position:0%
+and each data point is colored by the
+ 
+
+ align:start position:0%
+and each data point is colored by the
+outcome variable red or gray cart tries
+
+ align:start position:0%
+outcome variable red or gray cart tries
+ 
+
+ align:start position:0%
+outcome variable red or gray cart tries
+to split this data into subsets so that
+
+ align:start position:0%
+to split this data into subsets so that
+ 
+
+ align:start position:0%
+to split this data into subsets so that
+each subset is as pure or homogeneous as
+
+ align:start position:0%
+each subset is as pure or homogeneous as
+ 
+
+ align:start position:0%
+each subset is as pure or homogeneous as
+possible the first three splits that
+
+ align:start position:0%
+possible the first three splits that
+ 
+
+ align:start position:0%
+possible the first three splits that
+cart would create are shown here then
+
+ align:start position:0%
+cart would create are shown here then
+ 
+
+ align:start position:0%
+cart would create are shown here then
+the standard prediction made by a cart
+
+ align:start position:0%
+the standard prediction made by a cart
+ 
+
+ align:start position:0%
+the standard prediction made by a cart
+model is just the majority in each
+
+ align:start position:0%
+model is just the majority in each
+ 
+
+ align:start position:0%
+model is just the majority in each
+subset if a new observation fell into
+
+ align:start position:0%
+subset if a new observation fell into
+ 
+
+ align:start position:0%
+subset if a new observation fell into
+one of these two subsets then we would
+
+ align:start position:0%
+one of these two subsets then we would
+ 
+
+ align:start position:0%
+one of these two subsets then we would
+predict red since the majority of the
+
+ align:start position:0%
+predict red since the majority of the
+ 
+
+ align:start position:0%
+predict red since the majority of the
+observations in those subsets are red
+
+ align:start position:0%
+observations in those subsets are red
+ 
+
+ align:start position:0%
+observations in those subsets are red
+however if a new observation fell into
+
+ align:start position:0%
+however if a new observation fell into
+ 
+
+ align:start position:0%
+however if a new observation fell into
+one of these two subsets we would
+
+ align:start position:0%
+one of these two subsets we would
+ 
+
+ align:start position:0%
+one of these two subsets we would
+predict gray since the majority of the
+
+ align:start position:0%
+predict gray since the majority of the
+ 
+
+ align:start position:0%
+predict gray since the majority of the
+observations in those two subsets are
+
+ align:start position:0%
+observations in those two subsets are
+ 
+
+ align:start position:0%
+observations in those two subsets are
+gray a cart model is represented by what
+
+ align:start position:0%
+gray a cart model is represented by what
+ 
+
+ align:start position:0%
+gray a cart model is represented by what
+we call a tree the tree for the splits
+
+ align:start position:0%
+we call a tree the tree for the splits
+ 
+
+ align:start position:0%
+we call a tree the tree for the splits
+we just generated is shown on the right
+
+ align:start position:0%
+we just generated is shown on the right
+ 
+
+ align:start position:0%
+we just generated is shown on the right
+the first split tests whether the
+
+ align:start position:0%
+the first split tests whether the
+ 
+
+ align:start position:0%
+the first split tests whether the
+variable X is less than 60 if yes the
+
+ align:start position:0%
+variable X is less than 60 if yes the
+ 
+
+ align:start position:0%
+variable X is less than 60 if yes the
+model says to predict red and if no the
+
+ align:start position:0%
+model says to predict red and if no the
+ 
+
+ align:start position:0%
+model says to predict red and if no the
+model moves on to the next split then
+
+ align:start position:0%
+model moves on to the next split then
+ 
+
+ align:start position:0%
+model moves on to the next split then
+the second split checks whether or not
+
+ align:start position:0%
+the second split checks whether or not
+ 
+
+ align:start position:0%
+the second split checks whether or not
+the variable Y is less than 20 if no the
+
+ align:start position:0%
+the variable Y is less than 20 if no the
+ 
+
+ align:start position:0%
+the variable Y is less than 20 if no the
+model says to predict gray but if yes
+
+ align:start position:0%
+model says to predict gray but if yes
+ 
+
+ align:start position:0%
+model says to predict gray but if yes
+the model moves on to the next split the
+
+ align:start position:0%
+the model moves on to the next split the
+ 
+
+ align:start position:0%
+the model moves on to the next split the
+third splay checks whether or not the
+
+ align:start position:0%
+third splay checks whether or not the
+ 
+
+ align:start position:0%
+third splay checks whether or not the
+variable X is less than 85 if yes then
+
+ align:start position:0%
+variable X is less than 85 if yes then
+ 
+
+ align:start position:0%
+variable X is less than 85 if yes then
+the model says to predict red and if no
+
+ align:start position:0%
+the model says to predict red and if no
+ 
+
+ align:start position:0%
+the model says to predict red and if no
+the model says to predict gray there are
+
+ align:start position:0%
+the model says to predict gray there are
+ 
+
+ align:start position:0%
+the model says to predict gray there are
+a couple things to keep in mind when
+
+ align:start position:0%
+a couple things to keep in mind when
+ 
+
+ align:start position:0%
+a couple things to keep in mind when
+reading trees in this tree and for the
+
+ align:start position:0%
+reading trees in this tree and for the
+ 
+
+ align:start position:0%
+reading trees in this tree and for the
+trees we'll generate in our a yes
+
+ align:start position:0%
+trees we'll generate in our a yes
+ 
+
+ align:start position:0%
+trees we'll generate in our a yes
+response is always to the left and a no
+
+ align:start position:0%
+response is always to the left and a no
+ 
+
+ align:start position:0%
+response is always to the left and a no
+response is always to the right also
+
+ align:start position:0%
+response is always to the right also
+ 
+
+ align:start position:0%
+response is always to the right also
+make sure you always start at the top of
+
+ align:start position:0%
+make sure you always start at the top of
+ 
+
+ align:start position:0%
+make sure you always start at the top of
+the tree the X less than 85 split
+
+ align:start position:0%
+the tree the X less than 85 split
+ 
+
+ align:start position:0%
+the tree the X less than 85 split
+only counts for observations for which X
+
+ align:start position:0%
+only counts for observations for which X
+ 
+
+ align:start position:0%
+only counts for observations for which X
+is greater than 60 and y is less than 20
+
+ align:start position:0%
+is greater than 60 and y is less than 20
+ 
+
+ align:start position:0%
+is greater than 60 and y is less than 20
+in the next video we'll discuss how cart
+
+ align:start position:0%
+in the next video we'll discuss how cart
+ 
+
+ align:start position:0%
+in the next video we'll discuss how cart
+decides how many splits to generate and
+
+ align:start position:0%
+decides how many splits to generate and
+ 
+
+ align:start position:0%
+decides how many splits to generate and
+how the final predictions are made
\ No newline at end of file
diff --git a/WFF2VR7syCE.txt b/WFF2VR7syCE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d6105b8edbe2defe911131e35ad472936273657a
--- /dev/null
+++ b/WFF2VR7syCE.txt
@@ -0,0 +1,13907 @@
+align:start position:0%
+ 
+okay so you remember in the last lecture
+
+ align:start position:0%
+okay so you remember in the last lecture
+ 
+
+ align:start position:0%
+okay so you remember in the last lecture
+we discussed a technique
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called and schen we were relying on the
+
+ align:start position:0%
+called and schen we were relying on the
+ 
+
+ align:start position:0%
+called and schen we were relying on the
+facts
+
+ align:start position:0%
+facts
+ 
+
+ align:start position:0%
+facts
+that plasma has refractive index
+
+ align:start position:0%
+that plasma has refractive index
+ 
+
+ align:start position:0%
+that plasma has refractive index
+gradients inside it uh which cause a
+
+ align:start position:0%
+gradients inside it uh which cause a
+ 
+
+ align:start position:0%
+gradients inside it uh which cause a
+deflection and that deflection angle of
+
+ align:start position:0%
+deflection and that deflection angle of
+ 
+
+ align:start position:0%
+deflection and that deflection angle of
+the uh Rays going through the plasma was
+
+ align:start position:0%
+the uh Rays going through the plasma was
+ 
+
+ align:start position:0%
+the uh Rays going through the plasma was
+going to be something like one over two
+
+ align:start position:0%
+going to be something like one over two
+ 
+
+ align:start position:0%
+going to be something like one over two
+times the critical density times the
+
+ align:start position:0%
+times the critical density times the
+ 
+
+ align:start position:0%
+times the critical density times the
+integral of the gradient of the electron
+
+ align:start position:0%
+integral of the gradient of the electron
+ 
+
+ align:start position:0%
+integral of the gradient of the electron
+density along the path of our probing B
+
+ align:start position:0%
+density along the path of our probing B
+ 
+
+ align:start position:0%
+density along the path of our probing B
+and what we did in schen is we filtered
+
+ align:start position:0%
+and what we did in schen is we filtered
+ 
+
+ align:start position:0%
+and what we did in schen is we filtered
+the Rays using a lens and a stop at the
+
+ align:start position:0%
+the Rays using a lens and a stop at the
+ 
+
+ align:start position:0%
+the Rays using a lens and a stop at the
+focal plane we're able to filter our
+
+ align:start position:0%
+focal plane we're able to filter our
+ 
+
+ align:start position:0%
+focal plane we're able to filter our
+Rays with certain angles we can let
+
+ align:start position:0%
+Rays with certain angles we can let
+ 
+
+ align:start position:0%
+Rays with certain angles we can let
+through undeflected Ray block undle
+
+ align:start position:0%
+through undeflected Ray block undle
+ 
+
+ align:start position:0%
+through undeflected Ray block undle
+Grays we could do it in isotropic
+
+ align:start position:0%
+Grays we could do it in isotropic
+ 
+
+ align:start position:0%
+Grays we could do it in isotropic
+fashion we could do it with a knife edge
+
+ align:start position:0%
+fashion we could do it with a knife edge
+ 
+
+ align:start position:0%
+fashion we could do it with a knife edge
+and this enabled us to image effectively
+
+ align:start position:0%
+and this enabled us to image effectively
+ 
+
+ align:start position:0%
+and this enabled us to image effectively
+the gradients in the electron density
+
+ align:start position:0%
+the gradients in the electron density
+ 
+
+ align:start position:0%
+the gradients in the electron density
+inside our plasma this is particularly
+
+ align:start position:0%
+inside our plasma this is particularly
+ 
+
+ align:start position:0%
+inside our plasma this is particularly
+useful if you got something with sharp
+
+ align:start position:0%
+useful if you got something with sharp
+ 
+
+ align:start position:0%
+useful if you got something with sharp
+density gradients such as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shs but when we were doing this we
+
+ align:start position:0%
+shs but when we were doing this we
+ 
+
+ align:start position:0%
+shs but when we were doing this we
+actually made a pretty big assumption
+
+ align:start position:0%
+actually made a pretty big assumption
+ 
+
+ align:start position:0%
+actually made a pretty big assumption
+that I kind of buried here we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assumed that we have know this placement
+
+ align:start position:0%
+assumed that we have know this placement
+ 
+
+ align:start position:0%
+assumed that we have know this placement
+of the ray that the Rays pick up some
+
+ align:start position:0%
+of the ray that the Rays pick up some
+ 
+
+ align:start position:0%
+of the ray that the Rays pick up some
+angle as they travel through our plasma
+
+ align:start position:0%
+angle as they travel through our plasma
+ 
+
+ align:start position:0%
+angle as they travel through our plasma
+so I'll draw a little plasma here we
+
+ align:start position:0%
+so I'll draw a little plasma here we
+ 
+
+ align:start position:0%
+so I'll draw a little plasma here we
+assume that the Rays picked up some sort
+
+ align:start position:0%
+assume that the Rays picked up some sort
+ 
+
+ align:start position:0%
+assume that the Rays picked up some sort
+of angle but they didn't themselves get
+
+ align:start position:0%
+of angle but they didn't themselves get
+ 
+
+ align:start position:0%
+of angle but they didn't themselves get
+displaced whereas for some realistic
+
+ align:start position:0%
+displaced whereas for some realistic
+ 
+
+ align:start position:0%
+displaced whereas for some realistic
+extended plasma they would be displaced
+
+ align:start position:0%
+extended plasma they would be displaced
+ 
+
+ align:start position:0%
+extended plasma they would be displaced
+inside the plasma as well as picking up
+
+ align:start position:0%
+inside the plasma as well as picking up
+ 
+
+ align:start position:0%
+inside the plasma as well as picking up
+some angle and so the Rays themselves
+
+ align:start position:0%
+some angle and so the Rays themselves
+ 
+
+ align:start position:0%
+some angle and so the Rays themselves
+would not only have an angle they would
+
+ align:start position:0%
+would not only have an angle they would
+ 
+
+ align:start position:0%
+would not only have an angle they would
+have some displacement and when we use
+
+ align:start position:0%
+have some displacement and when we use
+ 
+
+ align:start position:0%
+have some displacement and when we use
+our Imaging system with a lens the Rays
+
+ align:start position:0%
+our Imaging system with a lens the Rays
+ 
+
+ align:start position:0%
+our Imaging system with a lens the Rays
+should endend up somewhere else on our
+
+ align:start position:0%
+should endend up somewhere else on our
+ 
+
+ align:start position:0%
+should endend up somewhere else on our
+object plane not in the same place they
+
+ align:start position:0%
+object plane not in the same place they
+ 
+
+ align:start position:0%
+object plane not in the same place they
+started with buten we assume that there
+
+ align:start position:0%
+started with buten we assume that there
+ 
+
+ align:start position:0%
+started with buten we assume that there
+was no Ray
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+displacement and this was actually
+
+ align:start position:0%
+displacement and this was actually
+ 
+
+ align:start position:0%
+displacement and this was actually
+equivalent to US assuming that our
+
+ align:start position:0%
+equivalent to US assuming that our
+ 
+
+ align:start position:0%
+equivalent to US assuming that our
+object was very very thin so if instead
+
+ align:start position:0%
+object was very very thin so if instead
+ 
+
+ align:start position:0%
+object was very very thin so if instead
+of having this extended object like this
+
+ align:start position:0%
+of having this extended object like this
+ 
+
+ align:start position:0%
+of having this extended object like this
+we have an object that's incredibly thin
+
+ align:start position:0%
+we have an object that's incredibly thin
+ 
+
+ align:start position:0%
+we have an object that's incredibly thin
+like that and you have rays of light
+
+ align:start position:0%
+like that and you have rays of light
+ 
+
+ align:start position:0%
+like that and you have rays of light
+coming in but then just get
+
+ align:start position:0%
+coming in but then just get
+ 
+
+ align:start position:0%
+coming in but then just get
+instantaneously deflected like that this
+
+ align:start position:0%
+instantaneously deflected like that this
+ 
+
+ align:start position:0%
+instantaneously deflected like that this
+works out okay because there's no sort
+
+ align:start position:0%
+works out okay because there's no sort
+ 
+
+ align:start position:0%
+works out okay because there's no sort
+of uh path along inside the plasma for
+
+ align:start position:0%
+of uh path along inside the plasma for
+ 
+
+ align:start position:0%
+of uh path along inside the plasma for
+these Rays uh to become displaced
+
+ align:start position:0%
+these Rays uh to become displaced
+ 
+
+ align:start position:0%
+these Rays uh to become displaced
+whereas they are in an extended object
+
+ align:start position:0%
+whereas they are in an extended object
+ 
+
+ align:start position:0%
+whereas they are in an extended object
+so we made this assumption but we're now
+
+ align:start position:0%
+so we made this assumption but we're now
+ 
+
+ align:start position:0%
+so we made this assumption but we're now
+going to relax that and have a look at
+
+ align:start position:0%
+going to relax that and have a look at
+ 
+
+ align:start position:0%
+going to relax that and have a look at
+what happens when we do true shog graphy
+
+ align:start position:0%
+what happens when we do true shog graphy
+ 
+
+ align:start position:0%
+what happens when we do true shog graphy
+which is where we're interested not just
+
+ align:start position:0%
+which is where we're interested not just
+ 
+
+ align:start position:0%
+which is where we're interested not just
+in the angles of the Rays but their
+
+ align:start position:0%
+in the angles of the Rays but their
+ 
+
+ align:start position:0%
+in the angles of the Rays but their
+displacements as well so I'm going to
+
+ align:start position:0%
+displacements as well so I'm going to
+ 
+
+ align:start position:0%
+displacements as well so I'm going to
+try and draw slightly better version of
+
+ align:start position:0%
+try and draw slightly better version of
+ 
+
+ align:start position:0%
+try and draw slightly better version of
+this image hopefully with some nice
+
+ align:start position:0%
+this image hopefully with some nice
+ 
+
+ align:start position:0%
+this image hopefully with some nice
+straight lines let's see how it goes
+
+ align:start position:0%
+straight lines let's see how it goes
+ 
+
+ align:start position:0%
+straight lines let's see how it goes
+here's my plasma
+
+ align:start position:0%
+here's my plasma
+ 
+
+ align:start position:0%
+here's my plasma
+again I'm going to have a
+
+ align:start position:0%
+again I'm going to have a
+ 
+
+ align:start position:0%
+again I'm going to have a
+lens here I'm going to set up my lens
+
+ align:start position:0%
+lens here I'm going to set up my lens
+ 
+
+ align:start position:0%
+lens here I'm going to set up my lens
+such that it brings into
+
+ align:start position:0%
+such that it brings into
+ 
+
+ align:start position:0%
+such that it brings into
+Focus Rays from this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane onto some image plane back here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what I'm going to have is the
+
+ align:start position:0%
+and what I'm going to have is the
+ 
+
+ align:start position:0%
+and what I'm going to have is the
+undeflected Rays so imagine there was no
+
+ align:start position:0%
+undeflected Rays so imagine there was no
+ 
+
+ align:start position:0%
+undeflected Rays so imagine there was no
+plasma here the Rays would just go
+
+ align:start position:0%
+plasma here the Rays would just go
+ 
+
+ align:start position:0%
+plasma here the Rays would just go
+through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and they would all go through a
+
+ align:start position:0%
+here and they would all go through a
+ 
+
+ align:start position:0%
+here and they would all go through a
+focal point back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so this again looks like the setup
+
+ align:start position:0%
+here so this again looks like the setup
+ 
+
+ align:start position:0%
+here so this again looks like the setup
+we had for our schin but the difference
+
+ align:start position:0%
+we had for our schin but the difference
+ 
+
+ align:start position:0%
+we had for our schin but the difference
+is now if we consider the Rays being
+
+ align:start position:0%
+is now if we consider the Rays being
+ 
+
+ align:start position:0%
+is now if we consider the Rays being
+deflected inside the plasma they're
+
+ align:start position:0%
+deflected inside the plasma they're
+ 
+
+ align:start position:0%
+deflected inside the plasma they're
+going to pick up some sort of displac
+
+ align:start position:0%
+going to pick up some sort of displac
+ 
+
+ align:start position:0%
+going to pick up some sort of displac
+so for example this Ray is going to be
+
+ align:start position:0%
+so for example this Ray is going to be
+ 
+
+ align:start position:0%
+so for example this Ray is going to be
+displaced down like this this Ray maybe
+
+ align:start position:0%
+displaced down like this this Ray maybe
+ 
+
+ align:start position:0%
+displaced down like this this Ray maybe
+is also going to be displaced down with
+
+ align:start position:0%
+is also going to be displaced down with
+ 
+
+ align:start position:0%
+is also going to be displaced down with
+a little bit and this Ray is going to be
+
+ align:start position:0%
+a little bit and this Ray is going to be
+ 
+
+ align:start position:0%
+a little bit and this Ray is going to be
+this place upwards such that when they
+
+ align:start position:0%
+this place upwards such that when they
+ 
+
+ align:start position:0%
+this place upwards such that when they
+get to the object plane they now have
+
+ align:start position:0%
+get to the object plane they now have
+ 
+
+ align:start position:0%
+get to the object plane they now have
+some distance that they have been
+
+ align:start position:0%
+some distance that they have been
+ 
+
+ align:start position:0%
+some distance that they have been
+translated compared to the undeflected
+
+ align:start position:0%
+translated compared to the undeflected
+ 
+
+ align:start position:0%
+translated compared to the undeflected
+one and then all that a lens does is it
+
+ align:start position:0%
+one and then all that a lens does is it
+ 
+
+ align:start position:0%
+one and then all that a lens does is it
+puts light back on the image plane where
+
+ align:start position:0%
+puts light back on the image plane where
+ 
+
+ align:start position:0%
+puts light back on the image plane where
+it came from on the object plane with
+
+ align:start position:0%
+it came from on the object plane with
+ 
+
+ align:start position:0%
+it came from on the object plane with
+some inversion other things like that
+
+ align:start position:0%
+some inversion other things like that
+ 
+
+ align:start position:0%
+some inversion other things like that
+but that means because these Rays have
+
+ align:start position:0%
+but that means because these Rays have
+ 
+
+ align:start position:0%
+but that means because these Rays have
+actually been moved because the light
+
+ align:start position:0%
+actually been moved because the light
+ 
+
+ align:start position:0%
+actually been moved because the light
+has been moved around they're going to
+
+ align:start position:0%
+has been moved around they're going to
+ 
+
+ align:start position:0%
+has been moved around they're going to
+show up in different places on the image
+
+ align:start position:0%
+show up in different places on the image
+ 
+
+ align:start position:0%
+show up in different places on the image
+plane and this is why I really hope I
+
+ align:start position:0%
+plane and this is why I really hope I
+ 
+
+ align:start position:0%
+plane and this is why I really hope I
+can draw this properly because this is
+
+ align:start position:0%
+can draw this properly because this is
+ 
+
+ align:start position:0%
+can draw this properly because this is
+quite a complicated diagram so give me a
+
+ align:start position:0%
+quite a complicated diagram so give me a
+ 
+
+ align:start position:0%
+quite a complicated diagram so give me a
+moment to focus on
+
+ align:start position:0%
+moment to focus on
+ 
+
+ align:start position:0%
+moment to focus on
+it so let's start with this Ray here
+
+ align:start position:0%
+it so let's start with this Ray here
+ 
+
+ align:start position:0%
+it so let's start with this Ray here
+it's going to go down is going to go
+
+ align:start position:0%
+it's going to go down is going to go
+ 
+
+ align:start position:0%
+it's going to go down is going to go
+down below the focal point because it's
+
+ align:start position:0%
+down below the focal point because it's
+ 
+
+ align:start position:0%
+down below the focal point because it's
+been deflected downwards and so it's
+
+ align:start position:0%
+been deflected downwards and so it's
+ 
+
+ align:start position:0%
+been deflected downwards and so it's
+going to end
+
+ align:start position:0%
+going to end
+ 
+
+ align:start position:0%
+going to end
+up here so slightly above where the
+
+ align:start position:0%
+up here so slightly above where the
+ 
+
+ align:start position:0%
+up here so slightly above where the
+original Ray was going to go
+
+ align:start position:0%
+original Ray was going to go
+ 
+
+ align:start position:0%
+original Ray was going to go
+this Ray here is going to get deflected
+
+ align:start position:0%
+this Ray here is going to get deflected
+ 
+
+ align:start position:0%
+this Ray here is going to get deflected
+downwards and it's then the lens is
+
+ align:start position:0%
+downwards and it's then the lens is
+ 
+
+ align:start position:0%
+downwards and it's then the lens is
+going to push it up and it's also going
+
+ align:start position:0%
+going to push it up and it's also going
+ 
+
+ align:start position:0%
+going to push it up and it's also going
+to go
+
+ align:start position:0%
+to go
+ 
+
+ align:start position:0%
+to go
+below the focal point here as well but
+
+ align:start position:0%
+below the focal point here as well but
+ 
+
+ align:start position:0%
+below the focal point here as well but
+it's going to be deflected up from its
+
+ align:start position:0%
+it's going to be deflected up from its
+ 
+
+ align:start position:0%
+it's going to be deflected up from its
+original position and this one here is
+
+ align:start position:0%
+original position and this one here is
+ 
+
+ align:start position:0%
+original position and this one here is
+going to go
+
+ align:start position:0%
+going to go
+ 
+
+ align:start position:0%
+going to go
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+uh bend that one slightly oh no I didn't
+
+ align:start position:0%
+uh bend that one slightly oh no I didn't
+ 
+
+ align:start position:0%
+uh bend that one slightly oh no I didn't
+want it to goow I got it right the first
+
+ align:start position:0%
+want it to goow I got it right the first
+ 
+
+ align:start position:0%
+want it to goow I got it right the first
+time there we go and this one is
+
+ align:start position:0%
+time there we go and this one is
+ 
+
+ align:start position:0%
+time there we go and this one is
+deflected downwards because it was
+
+ align:start position:0%
+deflected downwards because it was
+ 
+
+ align:start position:0%
+deflected downwards because it was
+deflected up of the object here so what
+
+ align:start position:0%
+deflected up of the object here so what
+ 
+
+ align:start position:0%
+deflected up of the object here so what
+we are seeing is
+
+ align:start position:0%
+we are seeing is
+ 
+
+ align:start position:0%
+we are seeing is
+that this lens is now Imaging the light
+
+ align:start position:0%
+that this lens is now Imaging the light
+ 
+
+ align:start position:0%
+that this lens is now Imaging the light
+into slightly different places than we
+
+ align:start position:0%
+into slightly different places than we
+ 
+
+ align:start position:0%
+into slightly different places than we
+had before so we set a displacement of
+
+ align:start position:0%
+had before so we set a displacement of
+ 
+
+ align:start position:0%
+had before so we set a displacement of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rays and you might want to think about
+
+ align:start position:0%
+Rays and you might want to think about
+ 
+
+ align:start position:0%
+Rays and you might want to think about
+displacement as an
+
+ align:start position:0%
+displacement as an
+ 
+
+ align:start position:0%
+displacement as an
+intensity modulation because of course
+
+ align:start position:0%
+intensity modulation because of course
+ 
+
+ align:start position:0%
+intensity modulation because of course
+there aren't just three Rays there are a
+
+ align:start position:0%
+there aren't just three Rays there are a
+ 
+
+ align:start position:0%
+there aren't just three Rays there are a
+large number of rays and these all make
+
+ align:start position:0%
+large number of rays and these all make
+ 
+
+ align:start position:0%
+large number of rays and these all make
+up an image and so initially maybe you
+
+ align:start position:0%
+up an image and so initially maybe you
+ 
+
+ align:start position:0%
+up an image and so initially maybe you
+had a nice uniform pattern these yellow
+
+ align:start position:0%
+had a nice uniform pattern these yellow
+ 
+
+ align:start position:0%
+had a nice uniform pattern these yellow
+Rays would have made a nice uniform
+
+ align:start position:0%
+Rays would have made a nice uniform
+ 
+
+ align:start position:0%
+Rays would have made a nice uniform
+circular beam like this and now your
+
+ align:start position:0%
+circular beam like this and now your
+ 
+
+ align:start position:0%
+circular beam like this and now your
+blue-rays are going to be
+
+ align:start position:0%
+blue-rays are going to be
+ 
+
+ align:start position:0%
+blue-rays are going to be
+distorted and there's going to be
+
+ align:start position:0%
+distorted and there's going to be
+ 
+
+ align:start position:0%
+distorted and there's going to be
+regions of very bright intensity and
+
+ align:start position:0%
+regions of very bright intensity and
+ 
+
+ align:start position:0%
+regions of very bright intensity and
+regions of lesser intensity and regions
+
+ align:start position:0%
+regions of lesser intensity and regions
+ 
+
+ align:start position:0%
+regions of lesser intensity and regions
+that are about the same so we'll have
+
+ align:start position:0%
+that are about the same so we'll have
+ 
+
+ align:start position:0%
+that are about the same so we'll have
+all sorts of interesting features inside
+
+ align:start position:0%
+all sorts of interesting features inside
+ 
+
+ align:start position:0%
+all sorts of interesting features inside
+this one way to think about this
+
+ align:start position:0%
+this one way to think about this
+ 
+
+ align:start position:0%
+this one way to think about this
+imagine we took our beam and now we're
+
+ align:start position:0%
+imagine we took our beam and now we're
+ 
+
+ align:start position:0%
+imagine we took our beam and now we're
+looking at the laser beam it's coming
+
+ align:start position:0%
+looking at the laser beam it's coming
+ 
+
+ align:start position:0%
+looking at the laser beam it's coming
+directly towards us through the plasma
+
+ align:start position:0%
+directly towards us through the plasma
+ 
+
+ align:start position:0%
+directly towards us through the plasma
+imagine we arranged it so we have nine
+
+ align:start position:0%
+imagine we arranged it so we have nine
+ 
+
+ align:start position:0%
+imagine we arranged it so we have nine
+little dots maybe we've got nine little
+
+ align:start position:0%
+little dots maybe we've got nine little
+ 
+
+ align:start position:0%
+little dots maybe we've got nine little
+laser pointers pointing through our
+
+ align:start position:0%
+laser pointers pointing through our
+ 
+
+ align:start position:0%
+laser pointers pointing through our
+plasma like
+
+ align:start position:0%
+plasma like
+ 
+
+ align:start position:0%
+plasma like
+this now as these Rays come through the
+
+ align:start position:0%
+this now as these Rays come through the
+ 
+
+ align:start position:0%
+this now as these Rays come through the
+plasma and they're deflected onto our
+
+ align:start position:0%
+plasma and they're deflected onto our
+ 
+
+ align:start position:0%
+plasma and they're deflected onto our
+camera here we would end up with the
+
+ align:start position:0%
+camera here we would end up with the
+ 
+
+ align:start position:0%
+camera here we would end up with the
+dots in different places so we could
+
+ align:start position:0%
+dots in different places so we could
+ 
+
+ align:start position:0%
+dots in different places so we could
+have this one is moved up here this one
+
+ align:start position:0%
+have this one is moved up here this one
+ 
+
+ align:start position:0%
+have this one is moved up here this one
+is moved like this
+
+ align:start position:0%
+is moved like this
+ 
+
+ align:start position:0%
+is moved like this
+this one is moved like this and so on
+
+ align:start position:0%
+this one is moved like this and so on
+ 
+
+ align:start position:0%
+this one is moved like this and so on
+and you can just think there's a series
+
+ align:start position:0%
+and you can just think there's a series
+ 
+
+ align:start position:0%
+and you can just think there's a series
+of displacements for these dots and if
+
+ align:start position:0%
+of displacements for these dots and if
+ 
+
+ align:start position:0%
+of displacements for these dots and if
+you're able to measure all these
+
+ align:start position:0%
+you're able to measure all these
+ 
+
+ align:start position:0%
+you're able to measure all these
+displacements perhaps you could work out
+
+ align:start position:0%
+displacements perhaps you could work out
+ 
+
+ align:start position:0%
+displacements perhaps you could work out
+something about the plasma itself and
+
+ align:start position:0%
+something about the plasma itself and
+ 
+
+ align:start position:0%
+something about the plasma itself and
+we'll talk a little bit about more
+
+ align:start position:0%
+we'll talk a little bit about more
+ 
+
+ align:start position:0%
+we'll talk a little bit about more
+quantitative measurements doing this but
+
+ align:start position:0%
+quantitative measurements doing this but
+ 
+
+ align:start position:0%
+quantitative measurements doing this but
+this is just qualitatively the picture
+
+ align:start position:0%
+this is just qualitatively the picture
+ 
+
+ align:start position:0%
+this is just qualitatively the picture
+here another way to think about this if
+
+ align:start position:0%
+here another way to think about this if
+ 
+
+ align:start position:0%
+here another way to think about this if
+you prefer these are just different
+
+ align:start position:0%
+you prefer these are just different
+ 
+
+ align:start position:0%
+you prefer these are just different
+conceptual ways of trying to think about
+
+ align:start position:0%
+conceptual ways of trying to think about
+ 
+
+ align:start position:0%
+conceptual ways of trying to think about
+the same thing imagine we initially put
+
+ align:start position:0%
+the same thing imagine we initially put
+ 
+
+ align:start position:0%
+the same thing imagine we initially put
+through the sort of tic tac toe grid of
+
+ align:start position:0%
+through the sort of tic tac toe grid of
+ 
+
+ align:start position:0%
+through the sort of tic tac toe grid of
+light here we've sort of blocked it off
+
+ align:start position:0%
+light here we've sort of blocked it off
+ 
+
+ align:start position:0%
+light here we've sort of blocked it off
+so we've got two vertical lines two
+
+ align:start position:0%
+so we've got two vertical lines two
+ 
+
+ align:start position:0%
+so we've got two vertical lines two
+horizontal lines these lines as they go
+
+ align:start position:0%
+horizontal lines these lines as they go
+ 
+
+ align:start position:0%
+horizontal lines these lines as they go
+through the plasma the light will be
+
+ align:start position:0%
+through the plasma the light will be
+ 
+
+ align:start position:0%
+through the plasma the light will be
+deflected by different amounts so for
+
+ align:start position:0%
+deflected by different amounts so for
+ 
+
+ align:start position:0%
+deflected by different amounts so for
+example this line here could be
+
+ align:start position:0%
+example this line here could be
+ 
+
+ align:start position:0%
+example this line here could be
+deflected like this this one could be
+
+ align:start position:0%
+deflected like this this one could be
+ 
+
+ align:start position:0%
+deflected like this this one could be
+deflected like this and so you sort of
+
+ align:start position:0%
+deflected like this and so you sort of
+ 
+
+ align:start position:0%
+deflected like this and so you sort of
+see we have some sort of
+
+ align:start position:0%
+see we have some sort of
+ 
+
+ align:start position:0%
+see we have some sort of
+distortion to the grid that we're
+
+ align:start position:0%
+distortion to the grid that we're
+ 
+
+ align:start position:0%
+distortion to the grid that we're
+getting out of this and our initial grid
+
+ align:start position:0%
+getting out of this and our initial grid
+ 
+
+ align:start position:0%
+getting out of this and our initial grid
+will these nice straight parallel lines
+
+ align:start position:0%
+will these nice straight parallel lines
+ 
+
+ align:start position:0%
+will these nice straight parallel lines
+is now a distorted grid instead and
+
+ align:start position:0%
+is now a distorted grid instead and
+ 
+
+ align:start position:0%
+is now a distorted grid instead and
+that's very important because chidog
+
+ align:start position:0%
+that's very important because chidog
+ 
+
+ align:start position:0%
+that's very important because chidog
+graphy do not actually uce an image I've
+
+ align:start position:0%
+graphy do not actually uce an image I've
+ 
+
+ align:start position:0%
+graphy do not actually uce an image I've
+called this the image plane here but we
+
+ align:start position:0%
+called this the image plane here but we
+ 
+
+ align:start position:0%
+called this the image plane here but we
+don't actually get an image out because
+
+ align:start position:0%
+don't actually get an image out because
+ 
+
+ align:start position:0%
+don't actually get an image out because
+we have something which is significantly
+
+ align:start position:0%
+we have something which is significantly
+ 
+
+ align:start position:0%
+we have something which is significantly
+distorted and it no longer reserves the
+
+ align:start position:0%
+distorted and it no longer reserves the
+ 
+
+ align:start position:0%
+distorted and it no longer reserves the
+things that we like to preserve in
+
+ align:start position:0%
+things that we like to preserve in
+ 
+
+ align:start position:0%
+things that we like to preserve in
+images we take a picture with a camera
+
+ align:start position:0%
+images we take a picture with a camera
+ 
+
+ align:start position:0%
+images we take a picture with a camera
+we like straight lines to remain
+
+ align:start position:0%
+we like straight lines to remain
+ 
+
+ align:start position:0%
+we like straight lines to remain
+straight here the straight lines do not
+
+ align:start position:0%
+straight here the straight lines do not
+ 
+
+ align:start position:0%
+straight here the straight lines do not
+remain straight they don't remain
+
+ align:start position:0%
+remain straight they don't remain
+ 
+
+ align:start position:0%
+remain straight they don't remain
+parallel we don't preserve length
+
+ align:start position:0%
+parallel we don't preserve length
+ 
+
+ align:start position:0%
+parallel we don't preserve length
+anything like that but there's still
+
+ align:start position:0%
+anything like that but there's still
+ 
+
+ align:start position:0%
+anything like that but there's still
+clearly information stored inside these
+
+ align:start position:0%
+clearly information stored inside these
+ 
+
+ align:start position:0%
+clearly information stored inside these
+images pictures uh that corresponds to
+
+ align:start position:0%
+images pictures uh that corresponds to
+ 
+
+ align:start position:0%
+images pictures uh that corresponds to
+the density inside the plasma and we'll
+
+ align:start position:0%
+the density inside the plasma and we'll
+ 
+
+ align:start position:0%
+the density inside the plasma and we'll
+talk a little bit more about how to do
+
+ align:start position:0%
+talk a little bit more about how to do
+ 
+
+ align:start position:0%
+talk a little bit more about how to do
+this quantitatively so any questions on
+
+ align:start position:0%
+this quantitatively so any questions on
+ 
+
+ align:start position:0%
+this quantitatively so any questions on
+this yeah the plasma here is acting like
+
+ align:start position:0%
+this yeah the plasma here is acting like
+ 
+
+ align:start position:0%
+this yeah the plasma here is acting like
+a what we need the second lens for
+
+ align:start position:0%
+a what we need the second lens for
+ 
+
+ align:start position:0%
+a what we need the second lens for
+absolutely great question yeah
+
+ align:start position:0%
+absolutely great question yeah
+ 
+
+ align:start position:0%
+absolutely great question yeah
+so I put the second lens in here for a
+
+ align:start position:0%
+so I put the second lens in here for a
+ 
+
+ align:start position:0%
+so I put the second lens in here for a
+couple of reasons first of all I find it
+
+ align:start position:0%
+couple of reasons first of all I find it
+ 
+
+ align:start position:0%
+couple of reasons first of all I find it
+conceptually simpler because you can see
+
+ align:start position:0%
+conceptually simpler because you can see
+ 
+
+ align:start position:0%
+conceptually simpler because you can see
+the deflection angles at the focal point
+
+ align:start position:0%
+the deflection angles at the focal point
+ 
+
+ align:start position:0%
+the deflection angles at the focal point
+here because when I read off the
+
+ align:start position:0%
+here because when I read off the
+ 
+
+ align:start position:0%
+here because when I read off the
+position of the Rays at this focal plane
+
+ align:start position:0%
+position of the Rays at this focal plane
+ 
+
+ align:start position:0%
+position of the Rays at this focal plane
+I can tell whether they've been
+
+ align:start position:0%
+I can tell whether they've been
+ 
+
+ align:start position:0%
+I can tell whether they've been
+deflected up or down which is slightly
+
+ align:start position:0%
+deflected up or down which is slightly
+ 
+
+ align:start position:0%
+deflected up or down which is slightly
+harder to do here you could Absol
+
+ align:start position:0%
+harder to do here you could Absol
+ 
+
+ align:start position:0%
+harder to do here you could Absol
+absolutely put your detector right here
+
+ align:start position:0%
+absolutely put your detector right here
+ 
+
+ align:start position:0%
+absolutely put your detector right here
+okay so you could put a bit of film or
+
+ align:start position:0%
+okay so you could put a bit of film or
+ 
+
+ align:start position:0%
+okay so you could put a bit of film or
+something like here in practice you
+
+ align:start position:0%
+something like here in practice you
+ 
+
+ align:start position:0%
+something like here in practice you
+can't because it's right next to plasma
+
+ align:start position:0%
+can't because it's right next to plasma
+ 
+
+ align:start position:0%
+can't because it's right next to plasma
+so you need some sort of lens optic this
+
+ align:start position:0%
+so you need some sort of lens optic this
+ 
+
+ align:start position:0%
+so you need some sort of lens optic this
+technique actually looks a great deal
+
+ align:start position:0%
+technique actually looks a great deal
+ 
+
+ align:start position:0%
+technique actually looks a great deal
+like proton radiography which we'll talk
+
+ align:start position:0%
+like proton radiography which we'll talk
+ 
+
+ align:start position:0%
+like proton radiography which we'll talk
+about later on here in proton
+
+ align:start position:0%
+about later on here in proton
+ 
+
+ align:start position:0%
+about later on here in proton
+radiography you don't have any lenses
+
+ align:start position:0%
+radiography you don't have any lenses
+ 
+
+ align:start position:0%
+radiography you don't have any lenses
+you can't it's very difficult to make
+
+ align:start position:0%
+you can't it's very difficult to make
+ 
+
+ align:start position:0%
+you can't it's very difficult to make
+lenses for charge particles uh and so
+
+ align:start position:0%
+lenses for charge particles uh and so
+ 
+
+ align:start position:0%
+lenses for charge particles uh and so
+you do in fact put your bit of paper
+
+ align:start position:0%
+you do in fact put your bit of paper
+ 
+
+ align:start position:0%
+you do in fact put your bit of paper
+like your your film in this case very
+
+ align:start position:0%
+like your your film in this case very
+ 
+
+ align:start position:0%
+like your your film in this case very
+close to your plasma you might put a
+
+ align:start position:0%
+close to your plasma you might put a
+ 
+
+ align:start position:0%
+close to your plasma you might put a
+little bit further back and we'll talk
+
+ align:start position:0%
+little bit further back and we'll talk
+ 
+
+ align:start position:0%
+little bit further back and we'll talk
+in a moment about actually how important
+
+ align:start position:0%
+in a moment about actually how important
+ 
+
+ align:start position:0%
+in a moment about actually how important
+is your choice of exactly where you put
+
+ align:start position:0%
+is your choice of exactly where you put
+ 
+
+ align:start position:0%
+is your choice of exactly where you put
+your detector because I could put my
+
+ align:start position:0%
+your detector because I could put my
+ 
+
+ align:start position:0%
+your detector because I could put my
+detector here or here or here and I
+
+ align:start position:0%
+detector here or here or here and I
+ 
+
+ align:start position:0%
+detector here or here or here and I
+still get an image forming but the image
+
+ align:start position:0%
+still get an image forming but the image
+ 
+
+ align:start position:0%
+still get an image forming but the image
+will look different but yeah we do not
+
+ align:start position:0%
+will look different but yeah we do not
+ 
+
+ align:start position:0%
+will look different but yeah we do not
+need the lens Sol phography but in
+
+ align:start position:0%
+need the lens Sol phography but in
+ 
+
+ align:start position:0%
+need the lens Sol phography but in
+almost all realistic setups where we're
+
+ align:start position:0%
+almost all realistic setups where we're
+ 
+
+ align:start position:0%
+almost all realistic setups where we're
+using some probing beam through a plasma
+
+ align:start position:0%
+using some probing beam through a plasma
+ 
+
+ align:start position:0%
+using some probing beam through a plasma
+we're going to have a lens because it
+
+ align:start position:0%
+we're going to have a lens because it
+ 
+
+ align:start position:0%
+we're going to have a lens because it
+allows us to put our detector nice and
+
+ align:start position:0%
+allows us to put our detector nice and
+ 
+
+ align:start position:0%
+allows us to put our detector nice and
+far away and safe in the plasma yeah
+
+ align:start position:0%
+far away and safe in the plasma yeah
+ 
+
+ align:start position:0%
+far away and safe in the plasma yeah
+cool other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions anyone from Columbia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't see anyone so I'm going to keep
+
+ align:start position:0%
+I don't see anyone so I'm going to keep
+ 
+
+ align:start position:0%
+I don't see anyone so I'm going to keep
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+cool so let me raise this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side so as I just mentioned then we can
+
+ align:start position:0%
+side so as I just mentioned then we can
+ 
+
+ align:start position:0%
+side so as I just mentioned then we can
+actually change the shadow graphic image
+
+ align:start position:0%
+actually change the shadow graphic image
+ 
+
+ align:start position:0%
+actually change the shadow graphic image
+we get by moving the position of our
+
+ align:start position:0%
+we get by moving the position of our
+ 
+
+ align:start position:0%
+we get by moving the position of our
+object PL so that could be moving our
+
+ align:start position:0%
+object PL so that could be moving our
+ 
+
+ align:start position:0%
+object PL so that could be moving our
+detector if we've just placed a detector
+
+ align:start position:0%
+detector if we've just placed a detector
+ 
+
+ align:start position:0%
+detector if we've just placed a detector
+here or it could be by moving our lens
+
+ align:start position:0%
+here or it could be by moving our lens
+ 
+
+ align:start position:0%
+here or it could be by moving our lens
+because as we move the lens we change
+
+ align:start position:0%
+because as we move the lens we change
+ 
+
+ align:start position:0%
+because as we move the lens we change
+the place we're focusing on or we could
+
+ align:start position:0%
+the place we're focusing on or we could
+ 
+
+ align:start position:0%
+the place we're focusing on or we could
+move other anyway you get the idea
+
+ align:start position:0%
+move other anyway you get the idea
+ 
+
+ align:start position:0%
+move other anyway you get the idea
+there's lots of different ways of moving
+
+ align:start position:0%
+there's lots of different ways of moving
+ 
+
+ align:start position:0%
+there's lots of different ways of moving
+it some of a place so let's have a look
+
+ align:start position:0%
+it some of a place so let's have a look
+ 
+
+ align:start position:0%
+it some of a place so let's have a look
+here we've got again our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma and we've got our Rays coming
+
+ align:start position:0%
+plasma and we've got our Rays coming
+ 
+
+ align:start position:0%
+plasma and we've got our Rays coming
+through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it we got a ray that gets deflected
+
+ align:start position:0%
+it we got a ray that gets deflected
+ 
+
+ align:start position:0%
+it we got a ray that gets deflected
+downwards and array that gets deflected
+
+ align:start position:0%
+downwards and array that gets deflected
+ 
+
+ align:start position:0%
+downwards and array that gets deflected
+upwards and another one that gets
+
+ align:start position:0%
+upwards and another one that gets
+ 
+
+ align:start position:0%
+upwards and another one that gets
+deflected down like this I can draw some
+
+ align:start position:0%
+deflected down like this I can draw some
+ 
+
+ align:start position:0%
+deflected down like this I can draw some
+different planes in which we can put our
+
+ align:start position:0%
+different planes in which we can put our
+ 
+
+ align:start position:0%
+different planes in which we can put our
+detector let me just get them in the
+
+ align:start position:0%
+detector let me just get them in the
+ 
+
+ align:start position:0%
+detector let me just get them in the
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+places and maybe I can call these one
+
+ align:start position:0%
+places and maybe I can call these one
+ 
+
+ align:start position:0%
+places and maybe I can call these one
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+3 and four like that and so then we can
+
+ align:start position:0%
+3 and four like that and so then we can
+ 
+
+ align:start position:0%
+3 and four like that and so then we can
+have a look at what would we see for
+
+ align:start position:0%
+have a look at what would we see for
+ 
+
+ align:start position:0%
+have a look at what would we see for
+this very simple system where we've got
+
+ align:start position:0%
+this very simple system where we've got
+ 
+
+ align:start position:0%
+this very simple system where we've got
+some sort of focusing density gradients
+
+ align:start position:0%
+some sort of focusing density gradients
+ 
+
+ align:start position:0%
+some sort of focusing density gradients
+and some defocusing density gradient
+
+ align:start position:0%
+and some defocusing density gradient
+ 
+
+ align:start position:0%
+and some defocusing density gradient
+here so this could be a
+
+ align:start position:0%
+here so this could be a
+ 
+
+ align:start position:0%
+here so this could be a
+Maxima in the electron density and this
+
+ align:start position:0%
+Maxima in the electron density and this
+ 
+
+ align:start position:0%
+Maxima in the electron density and this
+would be a Minima here right so that we
+
+ align:start position:0%
+would be a Minima here right so that we
+ 
+
+ align:start position:0%
+would be a Minima here right so that we
+would get focusing focusing um so let's
+
+ align:start position:0%
+would get focusing focusing um so let's
+ 
+
+ align:start position:0%
+would get focusing focusing um so let's
+draw what those patterns would look like
+
+ align:start position:0%
+draw what those patterns would look like
+ 
+
+ align:start position:0%
+draw what those patterns would look like
+so if I
+
+ align:start position:0%
+so if I
+ 
+
+ align:start position:0%
+so if I
+have intensity like
+
+ align:start position:0%
+have intensity like
+ 
+
+ align:start position:0%
+have intensity like
+this and let's say that this is the
+
+ align:start position:0%
+this and let's say that this is the
+ 
+
+ align:start position:0%
+this and let's say that this is the
+y-coordinate that's I call this
+
+ align:start position:0%
+y-coordinate that's I call this
+ 
+
+ align:start position:0%
+y-coordinate that's I call this
+y here and I'll do the first one here
+
+ align:start position:0%
+y here and I'll do the first one here
+ 
+
+ align:start position:0%
+y here and I'll do the first one here
+we'll get something uh we're going to
+
+ align:start position:0%
+we'll get something uh we're going to
+ 
+
+ align:start position:0%
+we'll get something uh we're going to
+have a little bit of deficit of
+
+ align:start position:0%
+have a little bit of deficit of
+ 
+
+ align:start position:0%
+have a little bit of deficit of
+intensity round about here because the
+
+ align:start position:0%
+intensity round about here because the
+ 
+
+ align:start position:0%
+intensity round about here because the
+ray is being deflected away so if this
+
+ align:start position:0%
+ray is being deflected away so if this
+ 
+
+ align:start position:0%
+ray is being deflected away so if this
+is the background intensity of our
+
+ align:start position:0%
+is the background intensity of our
+ 
+
+ align:start position:0%
+is the background intensity of our
+probing being will have some sort of
+
+ align:start position:0%
+probing being will have some sort of
+ 
+
+ align:start position:0%
+probing being will have some sort of
+drop uh and then we'll have an increase
+
+ align:start position:0%
+drop uh and then we'll have an increase
+ 
+
+ align:start position:0%
+drop uh and then we'll have an increase
+because the light is being focused
+
+ align:start position:0%
+because the light is being focused
+ 
+
+ align:start position:0%
+because the light is being focused
+together in the middle here we'll have
+
+ align:start position:0%
+together in the middle here we'll have
+ 
+
+ align:start position:0%
+together in the middle here we'll have
+another deficit in this region and we'll
+
+ align:start position:0%
+another deficit in this region and we'll
+ 
+
+ align:start position:0%
+another deficit in this region and we'll
+have another little increase over there
+
+ align:start position:0%
+have another little increase over there
+ 
+
+ align:start position:0%
+have another little increase over there
+so we get some
+
+ align:start position:0%
+so we get some
+ 
+
+ align:start position:0%
+so we get some
+nice little modulation what it's looking
+
+ align:start position:0%
+nice little modulation what it's looking
+ 
+
+ align:start position:0%
+nice little modulation what it's looking
+like if we go to two we can see that the
+
+ align:start position:0%
+like if we go to two we can see that the
+ 
+
+ align:start position:0%
+like if we go to two we can see that the
+rays are now getting closer together and
+
+ align:start position:0%
+rays are now getting closer together and
+ 
+
+ align:start position:0%
+rays are now getting closer together and
+further apart so you'd expect for this
+
+ align:start position:0%
+further apart so you'd expect for this
+ 
+
+ align:start position:0%
+further apart so you'd expect for this
+pattern to be even more exaggerated
+
+ align:start position:0%
+pattern to be even more exaggerated
+ 
+
+ align:start position:0%
+pattern to be even more exaggerated
+maybe I should have drawn this less
+
+ align:start position:0%
+maybe I should have drawn this less
+ 
+
+ align:start position:0%
+maybe I should have drawn this less
+exaggerated to give myself more space
+
+ align:start position:0%
+exaggerated to give myself more space
+ 
+
+ align:start position:0%
+exaggerated to give myself more space
+but let's say it looks
+
+ align:start position:0%
+but let's say it looks
+ 
+
+ align:start position:0%
+but let's say it looks
+like like this and this is this is
+
+ align:start position:0%
+like like this and this is this is
+ 
+
+ align:start position:0%
+like like this and this is this is
+bigger if we get over to three now you
+
+ align:start position:0%
+bigger if we get over to three now you
+ 
+
+ align:start position:0%
+bigger if we get over to three now you
+see something interesting we actually
+
+ align:start position:0%
+see something interesting we actually
+ 
+
+ align:start position:0%
+see something interesting we actually
+have Rays crossing here so this means a
+
+ align:start position:0%
+have Rays crossing here so this means a
+ 
+
+ align:start position:0%
+have Rays crossing here so this means a
+lot of light is all piled into the same
+
+ align:start position:0%
+lot of light is all piled into the same
+ 
+
+ align:start position:0%
+lot of light is all piled into the same
+place so we're still going to have a
+
+ align:start position:0%
+place so we're still going to have a
+ 
+
+ align:start position:0%
+place so we're still going to have a
+little bit of defocusing but we're going
+
+ align:start position:0%
+little bit of defocusing but we're going
+ 
+
+ align:start position:0%
+little bit of defocusing but we're going
+to have a very sharp Spike here which
+
+ align:start position:0%
+to have a very sharp Spike here which
+ 
+
+ align:start position:0%
+to have a very sharp Spike here which
+goes off my page and then we don't
+
+ align:start position:0%
+goes off my page and then we don't
+ 
+
+ align:start position:0%
+goes off my page and then we don't
+really have so much precise focusing
+
+ align:start position:0%
+really have so much precise focusing
+ 
+
+ align:start position:0%
+really have so much precise focusing
+down here but maybe there's a little bit
+
+ align:start position:0%
+down here but maybe there's a little bit
+ 
+
+ align:start position:0%
+down here but maybe there's a little bit
+of light so like that and then the
+
+ align:start position:0%
+of light so like that and then the
+ 
+
+ align:start position:0%
+of light so like that and then the
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four we've got away from having this
+
+ align:start position:0%
+four we've got away from having this
+ 
+
+ align:start position:0%
+four we've got away from having this
+crossing here so we won't see it so
+
+ align:start position:0%
+crossing here so we won't see it so
+ 
+
+ align:start position:0%
+crossing here so we won't see it so
+strongly it's going to look a little bit
+
+ align:start position:0%
+strongly it's going to look a little bit
+ 
+
+ align:start position:0%
+strongly it's going to look a little bit
+more like this um so something maybe a
+
+ align:start position:0%
+more like this um so something maybe a
+ 
+
+ align:start position:0%
+more like this um so something maybe a
+little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that now one thing I haven't really
+
+ align:start position:0%
+like that now one thing I haven't really
+ 
+
+ align:start position:0%
+like that now one thing I haven't really
+exaggerated enough here is the fact that
+
+ align:start position:0%
+exaggerated enough here is the fact that
+ 
+
+ align:start position:0%
+exaggerated enough here is the fact that
+as these Rays move outwards the
+
+ align:start position:0%
+as these Rays move outwards the
+ 
+
+ align:start position:0%
+as these Rays move outwards the
+positions of these Maxima and Minima are
+
+ align:start position:0%
+positions of these Maxima and Minima are
+ 
+
+ align:start position:0%
+positions of these Maxima and Minima are
+changing so in reality maybe this one is
+
+ align:start position:0%
+changing so in reality maybe this one is
+ 
+
+ align:start position:0%
+changing so in reality maybe this one is
+a little bit closer in and then I'll
+
+ align:start position:0%
+a little bit closer in and then I'll
+ 
+
+ align:start position:0%
+a little bit closer in and then I'll
+make these one go further out so you can
+
+ align:start position:0%
+make these one go further out so you can
+ 
+
+ align:start position:0%
+make these one go further out so you can
+see that actually the
+
+ align:start position:0%
+see that actually the
+ 
+
+ align:start position:0%
+see that actually the
+position of where we get Peak intensity
+
+ align:start position:0%
+position of where we get Peak intensity
+ 
+
+ align:start position:0%
+position of where we get Peak intensity
+is going to change depending on how far
+
+ align:start position:0%
+is going to change depending on how far
+ 
+
+ align:start position:0%
+is going to change depending on how far
+away we are from the because the Rays
+
+ align:start position:0%
+away we are from the because the Rays
+ 
+
+ align:start position:0%
+away we are from the because the Rays
+have traveled and so their displacement
+
+ align:start position:0%
+have traveled and so their displacement
+ 
+
+ align:start position:0%
+have traveled and so their displacement
+has changed as
+
+ align:start position:0%
+has changed as
+ 
+
+ align:start position:0%
+has changed as
+well so there's a lot going on inside
+
+ align:start position:0%
+well so there's a lot going on inside
+ 
+
+ align:start position:0%
+well so there's a lot going on inside
+here you can see that there's a lot of
+
+ align:start position:0%
+here you can see that there's a lot of
+ 
+
+ align:start position:0%
+here you can see that there's a lot of
+richness and you can see that although
+
+ align:start position:0%
+richness and you can see that although
+ 
+
+ align:start position:0%
+richness and you can see that although
+we can identify why there are light and
+
+ align:start position:0%
+we can identify why there are light and
+ 
+
+ align:start position:0%
+we can identify why there are light and
+dark regions inside our image it's hard
+
+ align:start position:0%
+dark regions inside our image it's hard
+ 
+
+ align:start position:0%
+dark regions inside our image it's hard
+to map them directly back onto
+
+ align:start position:0%
+to map them directly back onto
+ 
+
+ align:start position:0%
+to map them directly back onto
+whatever's going on inside the plasma
+
+ align:start position:0%
+whatever's going on inside the plasma
+ 
+
+ align:start position:0%
+whatever's going on inside the plasma
+and again that's because as I said this
+
+ align:start position:0%
+and again that's because as I said this
+ 
+
+ align:start position:0%
+and again that's because as I said this
+is not an image you can tell it's not an
+
+ align:start position:0%
+is not an image you can tell it's not an
+ 
+
+ align:start position:0%
+is not an image you can tell it's not an
+image because if you move your detector
+
+ align:start position:0%
+image because if you move your detector
+ 
+
+ align:start position:0%
+image because if you move your detector
+or if you move where your
+
+ align:start position:0%
+or if you move where your
+ 
+
+ align:start position:0%
+or if you move where your
+the data you get a very different
+
+ align:start position:0%
+the data you get a very different
+ 
+
+ align:start position:0%
+the data you get a very different
+picture out here so although this Maxima
+
+ align:start position:0%
+picture out here so although this Maxima
+ 
+
+ align:start position:0%
+picture out here so although this Maxima
+here corresponds
+
+ align:start position:0%
+here corresponds
+ 
+
+ align:start position:0%
+here corresponds
+to this region of the plasma it shows up
+
+ align:start position:0%
+to this region of the plasma it shows up
+ 
+
+ align:start position:0%
+to this region of the plasma it shows up
+at different positions on your detector
+
+ align:start position:0%
+at different positions on your detector
+ 
+
+ align:start position:0%
+at different positions on your detector
+different places so you can't really say
+
+ align:start position:0%
+different places so you can't really say
+ 
+
+ align:start position:0%
+different places so you can't really say
+this is a direct image it is a bjective
+
+ align:start position:0%
+this is a direct image it is a bjective
+ 
+
+ align:start position:0%
+this is a direct image it is a bjective
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+means that at least
+
+ align:start position:0%
+means that at least
+ 
+
+ align:start position:0%
+means that at least
+for these smaller flections we have
+
+ align:start position:0%
+for these smaller flections we have
+ 
+
+ align:start position:0%
+for these smaller flections we have
+what's call a one for one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mapping that's only true for the small
+
+ align:start position:0%
+mapping that's only true for the small
+ 
+
+ align:start position:0%
+mapping that's only true for the small
+deflections one and two like that for
+
+ align:start position:0%
+deflections one and two like that for
+ 
+
+ align:start position:0%
+deflections one and two like that for
+these two slices here once we get to
+
+ align:start position:0%
+these two slices here once we get to
+ 
+
+ align:start position:0%
+these two slices here once we get to
+three and we have the Rays Crossing you
+
+ align:start position:0%
+three and we have the Rays Crossing you
+ 
+
+ align:start position:0%
+three and we have the Rays Crossing you
+can see that at this point light which
+
+ align:start position:0%
+can see that at this point light which
+ 
+
+ align:start position:0%
+can see that at this point light which
+is coming from these two regions now
+
+ align:start position:0%
+is coming from these two regions now
+ 
+
+ align:start position:0%
+is coming from these two regions now
+Maps into the same place on our image or
+
+ align:start position:0%
+Maps into the same place on our image or
+ 
+
+ align:start position:0%
+Maps into the same place on our image or
+on our uh on our detector and so we no
+
+ align:start position:0%
+on our uh on our detector and so we no
+ 
+
+ align:start position:0%
+on our uh on our detector and so we no
+longer have that one to one m and indeed
+
+ align:start position:0%
+longer have that one to one m and indeed
+ 
+
+ align:start position:0%
+longer have that one to one m and indeed
+after the Rays have crossed these two
+
+ align:start position:0%
+after the Rays have crossed these two
+ 
+
+ align:start position:0%
+after the Rays have crossed these two
+cross over and so it's very confusing
+
+ align:start position:0%
+cross over and so it's very confusing
+ 
+
+ align:start position:0%
+cross over and so it's very confusing
+looking at this and trying to work out
+
+ align:start position:0%
+looking at this and trying to work out
+ 
+
+ align:start position:0%
+looking at this and trying to work out
+where all the light has come from
+
+ align:start position:0%
+where all the light has come from
+ 
+
+ align:start position:0%
+where all the light has come from
+although we do have this oneto one map
+
+ align:start position:0%
+although we do have this oneto one map
+ 
+
+ align:start position:0%
+although we do have this oneto one map
+for one and two so you know in principle
+
+ align:start position:0%
+for one and two so you know in principle
+ 
+
+ align:start position:0%
+for one and two so you know in principle
+we can sort of work out where everything
+
+ align:start position:0%
+we can sort of work out where everything
+ 
+
+ align:start position:0%
+we can sort of work out where everything
+came from it doesn't have properties
+
+ align:start position:0%
+came from it doesn't have properties
+ 
+
+ align:start position:0%
+came from it doesn't have properties
+that we normally like to have from an
+
+ align:start position:0%
+that we normally like to have from an
+ 
+
+ align:start position:0%
+that we normally like to have from an
+image so for example parallel lines do
+
+ align:start position:0%
+image so for example parallel lines do
+ 
+
+ align:start position:0%
+image so for example parallel lines do
+not go
+
+ align:start position:0%
+not go
+ 
+
+ align:start position:0%
+not go
+to parallel lines from the object plane
+
+ align:start position:0%
+to parallel lines from the object plane
+ 
+
+ align:start position:0%
+to parallel lines from the object plane
+to the image plane as we sort of
+
+ align:start position:0%
+to the image plane as we sort of
+ 
+
+ align:start position:0%
+to the image plane as we sort of
+discussed over here and so you might
+
+ align:start position:0%
+discussed over here and so you might
+ 
+
+ align:start position:0%
+discussed over here and so you might
+want that in the normal Imaging
+
+ align:start position:0%
+want that in the normal Imaging
+ 
+
+ align:start position:0%
+want that in the normal Imaging
+diagnostic you want to take a picture of
+
+ align:start position:0%
+diagnostic you want to take a picture of
+ 
+
+ align:start position:0%
+diagnostic you want to take a picture of
+a square and it comes out looking like
+
+ align:start position:0%
+a square and it comes out looking like
+ 
+
+ align:start position:0%
+a square and it comes out looking like
+something spaghetti that's not really an
+
+ align:start position:0%
+something spaghetti that's not really an
+ 
+
+ align:start position:0%
+something spaghetti that's not really an
+image and also the length not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preserved things get even
+
+ align:start position:0%
+preserved things get even
+ 
+
+ align:start position:0%
+preserved things get even
+worse
+
+ align:start position:0%
+worse
+ 
+
+ align:start position:0%
+worse
+preserved things get even worse for um
+
+ align:start position:0%
+preserved things get even worse for um
+ 
+
+ align:start position:0%
+preserved things get even worse for um
+three and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four because now we don't even have this
+
+ align:start position:0%
+four because now we don't even have this
+ 
+
+ align:start position:0%
+four because now we don't even have this
+BCC property we end up in a regime which
+
+ align:start position:0%
+BCC property we end up in a regime which
+ 
+
+ align:start position:0%
+BCC property we end up in a regime which
+is called the coric regime which I'll
+
+ align:start position:0%
+is called the coric regime which I'll
+ 
+
+ align:start position:0%
+is called the coric regime which I'll
+talk more about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later course stics come up all the time
+
+ align:start position:0%
+later course stics come up all the time
+ 
+
+ align:start position:0%
+later course stics come up all the time
+in other fields that are sometimes
+
+ align:start position:0%
+in other fields that are sometimes
+ 
+
+ align:start position:0%
+in other fields that are sometimes
+called Optical catastrophes um and
+
+ align:start position:0%
+called Optical catastrophes um and
+ 
+
+ align:start position:0%
+called Optical catastrophes um and
+although they're very very pretty they
+
+ align:start position:0%
+although they're very very pretty they
+ 
+
+ align:start position:0%
+although they're very very pretty they
+do make analysis of this data very very
+
+ align:start position:0%
+do make analysis of this data very very
+ 
+
+ align:start position:0%
+do make analysis of this data very very
+difficult so what I'm trying to show
+
+ align:start position:0%
+difficult so what I'm trying to show
+ 
+
+ align:start position:0%
+difficult so what I'm trying to show
+here is something as simple as moving
+
+ align:start position:0%
+here is something as simple as moving
+ 
+
+ align:start position:0%
+here is something as simple as moving
+exactly where you make this measurement
+
+ align:start position:0%
+exactly where you make this measurement
+ 
+
+ align:start position:0%
+exactly where you make this measurement
+makes a big difference to the data that
+
+ align:start position:0%
+makes a big difference to the data that
+ 
+
+ align:start position:0%
+makes a big difference to the data that
+you have it turns out that the easiest
+
+ align:start position:0%
+you have it turns out that the easiest
+ 
+
+ align:start position:0%
+you have it turns out that the easiest
+place theoretically to analyze your data
+
+ align:start position:0%
+place theoretically to analyze your data
+ 
+
+ align:start position:0%
+place theoretically to analyze your data
+is nice and close to your plasma but the
+
+ align:start position:0%
+is nice and close to your plasma but the
+ 
+
+ align:start position:0%
+is nice and close to your plasma but the
+easiest place that actually make the
+
+ align:start position:0%
+easiest place that actually make the
+ 
+
+ align:start position:0%
+easiest place that actually make the
+measurement with decent signals and
+
+ align:start position:0%
+measurement with decent signals and
+ 
+
+ align:start position:0%
+measurement with decent signals and
+noise is somewhere around about three so
+
+ align:start position:0%
+noise is somewhere around about three so
+ 
+
+ align:start position:0%
+noise is somewhere around about three so
+you can't have it all um you can't end
+
+ align:start position:0%
+you can't have it all um you can't end
+ 
+
+ align:start position:0%
+you can't have it all um you can't end
+up in a regime where you have the
+
+ align:start position:0%
+up in a regime where you have the
+ 
+
+ align:start position:0%
+up in a regime where you have the
+absolute best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dat again this has all been very
+
+ align:start position:0%
+dat again this has all been very
+ 
+
+ align:start position:0%
+dat again this has all been very
+qualitative we're about to make it
+
+ align:start position:0%
+qualitative we're about to make it
+ 
+
+ align:start position:0%
+qualitative we're about to make it
+quantitative by showing at least in this
+
+ align:start position:0%
+quantitative by showing at least in this
+ 
+
+ align:start position:0%
+quantitative by showing at least in this
+small deflection regime uh what you can
+
+ align:start position:0%
+small deflection regime uh what you can
+ 
+
+ align:start position:0%
+small deflection regime uh what you can
+measure but does anyone have any
+
+ align:start position:0%
+measure but does anyone have any
+ 
+
+ align:start position:0%
+measure but does anyone have any
+questions on this General schema before
+
+ align:start position:0%
+questions on this General schema before
+ 
+
+ align:start position:0%
+questions on this General schema before
+we could go yeah are you saying that
+
+ align:start position:0%
+we could go yeah are you saying that
+ 
+
+ align:start position:0%
+we could go yeah are you saying that
+there's a bjective map between your
+
+ align:start position:0%
+there's a bjective map between your
+ 
+
+ align:start position:0%
+there's a bjective map between your
+measured intensity distribution and
+
+ align:start position:0%
+measured intensity distribution and
+ 
+
+ align:start position:0%
+measured intensity distribution and
+incident intensity distribution or
+
+ align:start position:0%
+incident intensity distribution or
+ 
+
+ align:start position:0%
+incident intensity distribution or
+between the measured intensity
+
+ align:start position:0%
+between the measured intensity
+ 
+
+ align:start position:0%
+between the measured intensity
+distribution and the plasma density
+
+ align:start position:0%
+distribution and the plasma density
+ 
+
+ align:start position:0%
+distribution and the plasma density
+profile really the former so between the
+
+ align:start position:0%
+profile really the former so between the
+ 
+
+ align:start position:0%
+profile really the former so between the
+incident laser the laser on this side
+
+ align:start position:0%
+incident laser the laser on this side
+ 
+
+ align:start position:0%
+incident laser the laser on this side
+and on this side but I would argue that
+
+ align:start position:0%
+and on this side but I would argue that
+ 
+
+ align:start position:0%
+and on this side but I would argue that
+if you have that you can then infer
+
+ align:start position:0%
+if you have that you can then infer
+ 
+
+ align:start position:0%
+if you have that you can then infer
+something about the plasma that you've
+
+ align:start position:0%
+something about the plasma that you've
+ 
+
+ align:start position:0%
+something about the plasma that you've
+gone through because you have some idea
+
+ align:start position:0%
+gone through because you have some idea
+ 
+
+ align:start position:0%
+gone through because you have some idea
+of if you're measuring here and you know
+
+ align:start position:0%
+of if you're measuring here and you know
+ 
+
+ align:start position:0%
+of if you're measuring here and you know
+it corresponds to here then you know
+
+ align:start position:0%
+it corresponds to here then you know
+ 
+
+ align:start position:0%
+it corresponds to here then you know
+that the cord that you took to the
+
+ align:start position:0%
+that the cord that you took to the
+ 
+
+ align:start position:0%
+that the cord that you took to the
+plasma was roughly that right so you
+
+ align:start position:0%
+plasma was roughly that right so you
+ 
+
+ align:start position:0%
+plasma was roughly that right so you
+have some idea of like what sort of
+
+ align:start position:0%
+have some idea of like what sort of
+ 
+
+ align:start position:0%
+have some idea of like what sort of
+plasma properties you were sensing or
+
+ align:start position:0%
+plasma properties you were sensing or
+ 
+
+ align:start position:0%
+plasma properties you were sensing or
+alternative way around you have some
+
+ align:start position:0%
+alternative way around you have some
+ 
+
+ align:start position:0%
+alternative way around you have some
+idea that if you ended up here that you
+
+ align:start position:0%
+idea that if you ended up here that you
+ 
+
+ align:start position:0%
+idea that if you ended up here that you
+must have gone through this bit of
+
+ align:start position:0%
+must have gone through this bit of
+ 
+
+ align:start position:0%
+must have gone through this bit of
+plasma and to get that displacement that
+
+ align:start position:0%
+plasma and to get that displacement that
+ 
+
+ align:start position:0%
+plasma and to get that displacement that
+bit of plasma must have had some Pro
+
+ align:start position:0%
+bit of plasma must have had some Pro
+ 
+
+ align:start position:0%
+bit of plasma must have had some Pro
+certain density gradients within it
+
+ align:start position:0%
+certain density gradients within it
+ 
+
+ align:start position:0%
+certain density gradients within it
+right like some sort of average density
+
+ align:start position:0%
+right like some sort of average density
+ 
+
+ align:start position:0%
+right like some sort of average density
+gradient yes exactly all this is all
+
+ align:start position:0%
+gradient yes exactly all this is all
+ 
+
+ align:start position:0%
+gradient yes exactly all this is all
+line integrated and we'll talk about
+
+ align:start position:0%
+line integrated and we'll talk about
+ 
+
+ align:start position:0%
+line integrated and we'll talk about
+that in moment when we we we'll make
+
+ align:start position:0%
+that in moment when we we we'll make
+ 
+
+ align:start position:0%
+that in moment when we we we'll make
+this displacement we will work out I
+
+ align:start position:0%
+this displacement we will work out I
+ 
+
+ align:start position:0%
+this displacement we will work out I
+guess it's a y is it it's a y axis we
+
+ align:start position:0%
+guess it's a y is it it's a y axis we
+ 
+
+ align:start position:0%
+guess it's a y is it it's a y axis we
+will work out what that displacement is
+
+ align:start position:0%
+will work out what that displacement is
+ 
+
+ align:start position:0%
+will work out what that displacement is
+in terms of the plasma parameters so
+
+ align:start position:0%
+in terms of the plasma parameters so
+ 
+
+ align:start position:0%
+in terms of the plasma parameters so
+we'll make that quenta but yeah this is
+
+ align:start position:0%
+we'll make that quenta but yeah this is
+ 
+
+ align:start position:0%
+we'll make that quenta but yeah this is
+this is kind of what I'm getting at is
+
+ align:start position:0%
+this is kind of what I'm getting at is
+ 
+
+ align:start position:0%
+this is kind of what I'm getting at is
+you have some idea of what you're
+
+ align:start position:0%
+you have some idea of what you're
+ 
+
+ align:start position:0%
+you have some idea of what you're
+actually measuring once you get into
+
+ align:start position:0%
+actually measuring once you get into
+ 
+
+ align:start position:0%
+actually measuring once you get into
+this costic regime you don't really know
+
+ align:start position:0%
+this costic regime you don't really know
+ 
+
+ align:start position:0%
+this costic regime you don't really know
+exactly where everything has come from
+
+ align:start position:0%
+exactly where everything has come from
+ 
+
+ align:start position:0%
+exactly where everything has come from
+anymore yeah sorry I saw that hand first
+
+ align:start position:0%
+anymore yeah sorry I saw that hand first
+ 
+
+ align:start position:0%
+anymore yeah sorry I saw that hand first
+um yeah is the intensity still
+
+ align:start position:0%
+um yeah is the intensity still
+ 
+
+ align:start position:0%
+um yeah is the intensity still
+proportional to the density gradient as
+
+ align:start position:0%
+proportional to the density gradient as
+ 
+
+ align:start position:0%
+proportional to the density gradient as
+it was previously or is it I'm sad that
+
+ align:start position:0%
+it was previously or is it I'm sad that
+ 
+
+ align:start position:0%
+it was previously or is it I'm sad that
+you took away from my previous lecture
+
+ align:start position:0%
+you took away from my previous lecture
+ 
+
+ align:start position:0%
+you took away from my previous lecture
+the in and the intensity proportional
+
+ align:start position:0%
+the in and the intensity proportional
+ 
+
+ align:start position:0%
+the in and the intensity proportional
+density gradient it almost never is in
+
+ align:start position:0%
+density gradient it almost never is in
+ 
+
+ align:start position:0%
+density gradient it almost never is in
+any realistic situation so that's not
+
+ align:start position:0%
+any realistic situation so that's not
+ 
+
+ align:start position:0%
+any realistic situation so that's not
+true and it's still not true here and we
+
+ align:start position:0%
+true and it's still not true here and we
+ 
+
+ align:start position:0%
+true and it's still not true here and we
+will derive that it's proportional to
+
+ align:start position:0%
+will derive that it's proportional to
+ 
+
+ align:start position:0%
+will derive that it's proportional to
+the second derivative of the density
+
+ align:start position:0%
+the second derivative of the density
+ 
+
+ align:start position:0%
+the second derivative of the density
+gradient and we'll also show that that
+
+ align:start position:0%
+gradient and we'll also show that that
+ 
+
+ align:start position:0%
+gradient and we'll also show that that
+is also not true in most reasonable
+
+ align:start position:0%
+is also not true in most reasonable
+ 
+
+ align:start position:0%
+is also not true in most reasonable
+cases so please take away from this that
+
+ align:start position:0%
+cases so please take away from this that
+ 
+
+ align:start position:0%
+cases so please take away from this that
+NE of these Diagnostics are easy to
+
+ align:start position:0%
+NE of these Diagnostics are easy to
+ 
+
+ align:start position:0%
+NE of these Diagnostics are easy to
+interpret but you will read in the
+
+ align:start position:0%
+interpret but you will read in the
+ 
+
+ align:start position:0%
+interpret but you will read in the
+textbooks or online that they're
+
+ align:start position:0%
+textbooks or online that they're
+ 
+
+ align:start position:0%
+textbooks or online that they're
+proportional to the first Der or the
+
+ align:start position:0%
+proportional to the first Der or the
+ 
+
+ align:start position:0%
+proportional to the first Der or the
+second derivative it's almost impossible
+
+ align:start position:0%
+second derivative it's almost impossible
+ 
+
+ align:start position:0%
+second derivative it's almost impossible
+to set your diagnostic such that that's
+
+ align:start position:0%
+to set your diagnostic such that that's
+ 
+
+ align:start position:0%
+to set your diagnostic such that that's
+actually true so
+
+ align:start position:0%
+actually true so
+ 
+
+ align:start position:0%
+actually true so
+cool so you say that if we are like two
+
+ align:start position:0%
+cool so you say that if we are like two
+ 
+
+ align:start position:0%
+cool so you say that if we are like two
+we can guess that it's coming from the
+
+ align:start position:0%
+we can guess that it's coming from the
+ 
+
+ align:start position:0%
+we can guess that it's coming from the
+first Ray but how can we say that why
+
+ align:start position:0%
+first Ray but how can we say that why
+ 
+
+ align:start position:0%
+first Ray but how can we say that why
+can't we say that it's like the lower
+
+ align:start position:0%
+can't we say that it's like the lower
+ 
+
+ align:start position:0%
+can't we say that it's like the lower
+Ray incredibly deflected up so how can
+
+ align:start position:0%
+Ray incredibly deflected up so how can
+ 
+
+ align:start position:0%
+Ray incredibly deflected up so how can
+we know where regime is yeah absolutely
+
+ align:start position:0%
+we know where regime is yeah absolutely
+ 
+
+ align:start position:0%
+we know where regime is yeah absolutely
+yeah so that's a great point so it is
+
+ align:start position:0%
+yeah so that's a great point so it is
+ 
+
+ align:start position:0%
+yeah so that's a great point so it is
+very hard to find the costic regime but
+
+ align:start position:0%
+very hard to find the costic regime but
+ 
+
+ align:start position:0%
+very hard to find the costic regime but
+the costic regime is defin by extreme
+
+ align:start position:0%
+the costic regime is defin by extreme
+ 
+
+ align:start position:0%
+the costic regime is defin by extreme
+intensity variations so if you see only
+
+ align:start position:0%
+intensity variations so if you see only
+ 
+
+ align:start position:0%
+intensity variations so if you see only
+small intensity variations you can't be
+
+ align:start position:0%
+small intensity variations you can't be
+ 
+
+ align:start position:0%
+small intensity variations you can't be
+in the cost
+
+ align:start position:0%
+in the cost
+ 
+
+ align:start position:0%
+in the cost
+regime you know theoretically this is a
+
+ align:start position:0%
+regime you know theoretically this is a
+ 
+
+ align:start position:0%
+regime you know theoretically this is a
+a spike to Infinity right fortunately
+
+ align:start position:0%
+a spike to Infinity right fortunately
+ 
+
+ align:start position:0%
+a spike to Infinity right fortunately
+the universe doesn't allow that to
+
+ align:start position:0%
+the universe doesn't allow that to
+ 
+
+ align:start position:0%
+the universe doesn't allow that to
+happen because your Optics aren't
+
+ align:start position:0%
+happen because your Optics aren't
+ 
+
+ align:start position:0%
+happen because your Optics aren't
+perfect and your detect isn't perfect
+
+ align:start position:0%
+perfect and your detect isn't perfect
+ 
+
+ align:start position:0%
+perfect and your detect isn't perfect
+but this is very very bright so you can
+
+ align:start position:0%
+but this is very very bright so you can
+ 
+
+ align:start position:0%
+but this is very very bright so you can
+tell by looking at an image if it's got
+
+ align:start position:0%
+tell by looking at an image if it's got
+ 
+
+ align:start position:0%
+tell by looking at an image if it's got
+no hugely bright regions you're not in
+
+ align:start position:0%
+no hugely bright regions you're not in
+ 
+
+ align:start position:0%
+no hugely bright regions you're not in
+this regime and then the your second
+
+ align:start position:0%
+this regime and then the your second
+ 
+
+ align:start position:0%
+this regime and then the your second
+question was yeah but still it could
+
+ align:start position:0%
+question was yeah but still it could
+ 
+
+ align:start position:0%
+question was yeah but still it could
+come from somewhere else you're right we
+
+ align:start position:0%
+come from somewhere else you're right we
+ 
+
+ align:start position:0%
+come from somewhere else you're right we
+when we talk about uh some of the
+
+ align:start position:0%
+when we talk about uh some of the
+ 
+
+ align:start position:0%
+when we talk about uh some of the
+advanced methods for I guess
+
+ align:start position:0%
+advanced methods for I guess
+ 
+
+ align:start position:0%
+advanced methods for I guess
+deconvolving or processing this data we
+
+ align:start position:0%
+deconvolving or processing this data we
+ 
+
+ align:start position:0%
+deconvolving or processing this data we
+will come across uh some long exciting
+
+ align:start position:0%
+will come across uh some long exciting
+ 
+
+ align:start position:0%
+will come across uh some long exciting
+sounding phrases like Optimal transport
+
+ align:start position:0%
+sounding phrases like Optimal transport
+ 
+
+ align:start position:0%
+sounding phrases like Optimal transport
+and poroid diagrams and there you're
+
+ align:start position:0%
+and poroid diagrams and there you're
+ 
+
+ align:start position:0%
+and poroid diagrams and there you're
+trying to like minimize how ridiculous
+
+ align:start position:0%
+trying to like minimize how ridiculous
+ 
+
+ align:start position:0%
+trying to like minimize how ridiculous
+your density distribution has to be to
+
+ align:start position:0%
+your density distribution has to be to
+ 
+
+ align:start position:0%
+your density distribution has to be to
+give you this result and so there are
+
+ align:start position:0%
+give you this result and so there are
+ 
+
+ align:start position:0%
+give you this result and so there are
+like very mathematically grounded ways
+
+ align:start position:0%
+like very mathematically grounded ways
+ 
+
+ align:start position:0%
+like very mathematically grounded ways
+of trying to put this back but you know
+
+ align:start position:0%
+of trying to put this back but you know
+ 
+
+ align:start position:0%
+of trying to put this back but you know
+if you're just staring at an image and
+
+ align:start position:0%
+if you're just staring at an image and
+ 
+
+ align:start position:0%
+if you're just staring at an image and
+it's got small intensity perturbations
+
+ align:start position:0%
+it's got small intensity perturbations
+ 
+
+ align:start position:0%
+it's got small intensity perturbations
+you're probably be like hey you know
+
+ align:start position:0%
+you're probably be like hey you know
+ 
+
+ align:start position:0%
+you're probably be like hey you know
+it's most likely to have come from up
+
+ align:start position:0%
+it's most likely to have come from up
+ 
+
+ align:start position:0%
+it's most likely to have come from up
+here it's unlikely it went whoop like
+
+ align:start position:0%
+here it's unlikely it went whoop like
+ 
+
+ align:start position:0%
+here it's unlikely it went whoop like
+that so if the we we image like way far
+
+ align:start position:0%
+that so if the we we image like way far
+ 
+
+ align:start position:0%
+that so if the we we image like way far
+to the right then it would start to look
+
+ align:start position:0%
+to the right then it would start to look
+ 
+
+ align:start position:0%
+to the right then it would start to look
+more reasonable right but then image
+
+ align:start position:0%
+more reasonable right but then image
+ 
+
+ align:start position:0%
+more reasonable right but then image
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+have yes what I haven't drawn this if I
+
+ align:start position:0%
+have yes what I haven't drawn this if I
+ 
+
+ align:start position:0%
+have yes what I haven't drawn this if I
+draw in more Rays there will actually be
+
+ align:start position:0%
+draw in more Rays there will actually be
+ 
+
+ align:start position:0%
+draw in more Rays there will actually be
+more oh can I do it easily here we'll
+
+ align:start position:0%
+more oh can I do it easily here we'll
+ 
+
+ align:start position:0%
+more oh can I do it easily here we'll
+find out that there are more cor sticks
+
+ align:start position:0%
+find out that there are more cor sticks
+ 
+
+ align:start position:0%
+find out that there are more cor sticks
+coming in later on so once you've gone
+
+ align:start position:0%
+coming in later on so once you've gone
+ 
+
+ align:start position:0%
+coming in later on so once you've gone
+past this point you will always have cor
+
+ align:start position:0%
+past this point you will always have cor
+ 
+
+ align:start position:0%
+past this point you will always have cor
+sticks in here I just I haven't drawn
+
+ align:start position:0%
+sticks in here I just I haven't drawn
+ 
+
+ align:start position:0%
+sticks in here I just I haven't drawn
+enough Rays to make that point really
+
+ align:start position:0%
+enough Rays to make that point really
+ 
+
+ align:start position:0%
+enough Rays to make that point really
+clearly but if you can imagine drawing
+
+ align:start position:0%
+clearly but if you can imagine drawing
+ 
+
+ align:start position:0%
+clearly but if you can imagine drawing
+more in you'll see that they will like
+
+ align:start position:0%
+more in you'll see that they will like
+ 
+
+ align:start position:0%
+more in you'll see that they will like
+maybe there's one that doesn't cross
+
+ align:start position:0%
+maybe there's one that doesn't cross
+ 
+
+ align:start position:0%
+maybe there's one that doesn't cross
+this one here and eventually that
+
+ align:start position:0%
+this one here and eventually that
+ 
+
+ align:start position:0%
+this one here and eventually that
+doesn't work CU it's not a straight line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um like that okay and then this one crop
+
+ align:start position:0%
+um like that okay and then this one crop
+ 
+
+ align:start position:0%
+um like that okay and then this one crop
+is scale we have a cross thing in that
+
+ align:start position:0%
+is scale we have a cross thing in that
+ 
+
+ align:start position:0%
+is scale we have a cross thing in that
+region so they eventually just start
+
+ align:start position:0%
+region so they eventually just start
+ 
+
+ align:start position:0%
+region so they eventually just start
+Crossing more and more and more they
+
+ align:start position:0%
+Crossing more and more and more they
+ 
+
+ align:start position:0%
+Crossing more and more and more they
+will eventually cross and and so I guess
+
+ align:start position:0%
+will eventually cross and and so I guess
+ 
+
+ align:start position:0%
+will eventually cross and and so I guess
+why it says there is always a point some
+
+ align:start position:0%
+why it says there is always a point some
+ 
+
+ align:start position:0%
+why it says there is always a point some
+uh place where you can put your detector
+
+ align:start position:0%
+uh place where you can put your detector
+ 
+
+ align:start position:0%
+uh place where you can put your detector
+back here where you will end up in the
+
+ align:start position:0%
+back here where you will end up in the
+ 
+
+ align:start position:0%
+back here where you will end up in the
+costic raion and there's indeed a
+
+ align:start position:0%
+costic raion and there's indeed a
+ 
+
+ align:start position:0%
+costic raion and there's indeed a
+dimensionist parameter that tells you
+
+ align:start position:0%
+dimensionist parameter that tells you
+ 
+
+ align:start position:0%
+dimensionist parameter that tells you
+whether you're in the CTIC regime or not
+
+ align:start position:0%
+whether you're in the CTIC regime or not
+ 
+
+ align:start position:0%
+whether you're in the CTIC regime or not
+and it's to do with the reflection angle
+
+ align:start position:0%
+and it's to do with the reflection angle
+ 
+
+ align:start position:0%
+and it's to do with the reflection angle
+and this distance actually cool any
+
+ align:start position:0%
+and this distance actually cool any
+ 
+
+ align:start position:0%
+and this distance actually cool any
+other questions anything from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Columbia okay so let's try and make this
+
+ align:start position:0%
+Columbia okay so let's try and make this
+ 
+
+ align:start position:0%
+Columbia okay so let's try and make this
+a bit quantitative because I can see
+
+ align:start position:0%
+a bit quantitative because I can see
+ 
+
+ align:start position:0%
+a bit quantitative because I can see
+that folks want to get some numbers into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this I think here I'm basically
+
+ align:start position:0%
+this I think here I'm basically
+ 
+
+ align:start position:0%
+this I think here I'm basically
+following hutchingson so if you need to
+
+ align:start position:0%
+following hutchingson so if you need to
+ 
+
+ align:start position:0%
+following hutchingson so if you need to
+look up the equations in more detail
+
+ align:start position:0%
+look up the equations in more detail
+ 
+
+ align:start position:0%
+look up the equations in more detail
+this is where you want to head we're
+
+ align:start position:0%
+this is where you want to head we're
+ 
+
+ align:start position:0%
+this is where you want to head we're
+going to be working in a regime
+
+ align:start position:0%
+going to be working in a regime
+ 
+
+ align:start position:0%
+going to be working in a regime
+with small angles so small values of
+
+ align:start position:0%
+with small angles so small values of
+ 
+
+ align:start position:0%
+with small angles so small values of
+theta and remember that Theta is going
+
+ align:start position:0%
+theta and remember that Theta is going
+ 
+
+ align:start position:0%
+theta and remember that Theta is going
+to be equal
+
+ align:start position:0%
+to be equal
+ 
+
+ align:start position:0%
+to be equal
+to I guess I put ddy here but I want to
+
+ align:start position:0%
+to I guess I put ddy here but I want to
+ 
+
+ align:start position:0%
+to I guess I put ddy here but I want to
+make this kind of two-dimensional so I'm
+
+ align:start position:0%
+make this kind of two-dimensional so I'm
+ 
+
+ align:start position:0%
+make this kind of two-dimensional so I'm
+just going to write gradient here and
+
+ align:start position:0%
+just going to write gradient here and
+ 
+
+ align:start position:0%
+just going to write gradient here and
+you can think of theta as a vector which
+
+ align:start position:0%
+you can think of theta as a vector which
+ 
+
+ align:start position:0%
+you can think of theta as a vector which
+contains you know the angle respect to
+
+ align:start position:0%
+contains you know the angle respect to
+ 
+
+ align:start position:0%
+contains you know the angle respect to
+the x- axis and the angle spectral Y
+
+ align:start position:0%
+the x- axis and the angle spectral Y
+ 
+
+ align:start position:0%
+the x- axis and the angle spectral Y
+axis here okay then this is the gradient
+
+ align:start position:0%
+axis here okay then this is the gradient
+ 
+
+ align:start position:0%
+axis here okay then this is the gradient
+of the line integration refractive index
+
+ align:start position:0%
+of the line integration refractive index
+ 
+
+ align:start position:0%
+of the line integration refractive index
+so I'm still going to work in refractive
+
+ align:start position:0%
+so I'm still going to work in refractive
+ 
+
+ align:start position:0%
+so I'm still going to work in refractive
+index here it's a little bit more
+
+ align:start position:0%
+index here it's a little bit more
+ 
+
+ align:start position:0%
+index here it's a little bit more
+Compact and also because this applies to
+
+ align:start position:0%
+Compact and also because this applies to
+ 
+
+ align:start position:0%
+Compact and also because this applies to
+any inhomogenous medium not just a
+
+ align:start position:0%
+any inhomogenous medium not just a
+ 
+
+ align:start position:0%
+any inhomogenous medium not just a
+plasma so you can use this for air and
+
+ align:start position:0%
+plasma so you can use this for air and
+ 
+
+ align:start position:0%
+plasma so you can use this for air and
+all things like that so we going to
+
+ align:start position:0%
+all things like that so we going to
+ 
+
+ align:start position:0%
+all things like that so we going to
+write it just in terms of N and at the
+
+ align:start position:0%
+write it just in terms of N and at the
+ 
+
+ align:start position:0%
+write it just in terms of N and at the
+end I'll turn this into plasma Den so
+
+ align:start position:0%
+end I'll turn this into plasma Den so
+ 
+
+ align:start position:0%
+end I'll turn this into plasma Den so
+you have final
+
+ align:start position:0%
+you have final
+ 
+
+ align:start position:0%
+you have final
+result so we're going to assume that
+
+ align:start position:0%
+result so we're going to assume that
+ 
+
+ align:start position:0%
+result so we're going to assume that
+we've got our rays of
+
+ align:start position:0%
+we've got our rays of
+ 
+
+ align:start position:0%
+we've got our rays of
+light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again incident like this onto
+
+ align:start position:0%
+again incident like this onto
+ 
+
+ align:start position:0%
+again incident like this onto
+some plane that we're going to
+
+ align:start position:0%
+some plane that we're going to
+ 
+
+ align:start position:0%
+some plane that we're going to
+call that has coordinates X and
+
+ align:start position:0%
+call that has coordinates X and
+ 
+
+ align:start position:0%
+call that has coordinates X and
+Y we're going to have some initial
+
+ align:start position:0%
+Y we're going to have some initial
+ 
+
+ align:start position:0%
+Y we're going to have some initial
+intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+profile that's incident on this plasma
+
+ align:start position:0%
+profile that's incident on this plasma
+ 
+
+ align:start position:0%
+profile that's incident on this plasma
+here so our plasma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rout just past the plane we're doing
+
+ align:start position:0%
+rout just past the plane we're doing
+ 
+
+ align:start position:0%
+rout just past the plane we're doing
+this and of course this could be
+
+ align:start position:0%
+this and of course this could be
+ 
+
+ align:start position:0%
+this and of course this could be
+something nice in uniform or it could be
+
+ align:start position:0%
+something nice in uniform or it could be
+ 
+
+ align:start position:0%
+something nice in uniform or it could be
+gaussian or it could be whatever want so
+
+ align:start position:0%
+gaussian or it could be whatever want so
+ 
+
+ align:start position:0%
+gaussian or it could be whatever want so
+whatever you can actually come up with
+
+ align:start position:0%
+whatever you can actually come up with
+ 
+
+ align:start position:0%
+whatever you can actually come up with
+um for your laser probate and our rays
+
+ align:start position:0%
+um for your laser probate and our rays
+ 
+
+ align:start position:0%
+um for your laser probate and our rays
+are going to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deflected by some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angle Thea like this and then you know
+
+ align:start position:0%
+angle Thea like this and then you know
+ 
+
+ align:start position:0%
+angle Thea like this and then you know
+we're going to
+
+ align:start position:0%
+we're going to
+ 
+
+ align:start position:0%
+we're going to
+have our detector and that's going to be
+
+ align:start position:0%
+have our detector and that's going to be
+ 
+
+ align:start position:0%
+have our detector and that's going to be
+in a primed coord system X Prime y Prime
+
+ align:start position:0%
+in a primed coord system X Prime y Prime
+ 
+
+ align:start position:0%
+in a primed coord system X Prime y Prime
+and of course if I don't want to put my
+
+ align:start position:0%
+and of course if I don't want to put my
+ 
+
+ align:start position:0%
+and of course if I don't want to put my
+detector just here I can always put a
+
+ align:start position:0%
+detector just here I can always put a
+ 
+
+ align:start position:0%
+detector just here I can always put a
+lens and then I can put my detector here
+
+ align:start position:0%
+lens and then I can put my detector here
+ 
+
+ align:start position:0%
+lens and then I can put my detector here
+and that would also have X Prime y Prime
+
+ align:start position:0%
+and that would also have X Prime y Prime
+ 
+
+ align:start position:0%
+and that would also have X Prime y Prime
+with maybe any magnification that the
+
+ align:start position:0%
+with maybe any magnification that the
+ 
+
+ align:start position:0%
+with maybe any magnification that the
+lens does but that's not really relevant
+
+ align:start position:0%
+lens does but that's not really relevant
+ 
+
+ align:start position:0%
+lens does but that's not really relevant
+for this that's just Optics so we're
+
+ align:start position:0%
+for this that's just Optics so we're
+ 
+
+ align:start position:0%
+for this that's just Optics so we're
+trying to work out how we get from the
+
+ align:start position:0%
+trying to work out how we get from the
+ 
+
+ align:start position:0%
+trying to work out how we get from the
+intensity I initial to the
+
+ align:start position:0%
+intensity I initial to the
+ 
+
+ align:start position:0%
+intensity I initial to the
+intensity what am I going to call it I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detector X Prime y
+
+ align:start position:0%
+detector X Prime y
+ 
+
+ align:start position:0%
+detector X Prime y
+like this okay so we can just stare at
+
+ align:start position:0%
+like this okay so we can just stare at
+ 
+
+ align:start position:0%
+like this okay so we can just stare at
+this and do some simple geometry we can
+
+ align:start position:0%
+this and do some simple geometry we can
+ 
+
+ align:start position:0%
+this and do some simple geometry we can
+say that if we're just talking about
+
+ align:start position:0%
+say that if we're just talking about
+ 
+
+ align:start position:0%
+say that if we're just talking about
+coordinates X Prime y Prime is going to
+
+ align:start position:0%
+coordinates X Prime y Prime is going to
+ 
+
+ align:start position:0%
+coordinates X Prime y Prime is going to
+equal wherever we started out X plus oh
+
+ align:start position:0%
+equal wherever we started out X plus oh
+ 
+
+ align:start position:0%
+equal wherever we started out X plus oh
+this is important we need a link
+
+ align:start position:0%
+this is important we need a link
+ 
+
+ align:start position:0%
+this is important we need a link
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+scale we're going to put our detector a
+
+ align:start position:0%
+scale we're going to put our detector a
+ 
+
+ align:start position:0%
+scale we're going to put our detector a
+distance L from the plasma here we're
+
+ align:start position:0%
+distance L from the plasma here we're
+ 
+
+ align:start position:0%
+distance L from the plasma here we're
+assuming the plasma is pretty thin still
+
+ align:start position:0%
+assuming the plasma is pretty thin still
+ 
+
+ align:start position:0%
+assuming the plasma is pretty thin still
+so this is going to be
+
+ align:start position:0%
+so this is going to be
+ 
+
+ align:start position:0%
+so this is going to be
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+DD
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X of the integral of n
+
+ align:start position:0%
+X of the integral of n
+ 
+
+ align:start position:0%
+X of the integral of n
+DL and the coordinate in y is going to
+
+ align:start position:0%
+DL and the coordinate in y is going to
+ 
+
+ align:start position:0%
+DL and the coordinate in y is going to
+be y plus L * d d y
+
+ align:start position:0%
+be y plus L * d d y
+ 
+
+ align:start position:0%
+be y plus L * d d y
+integral d
+
+ align:start position:0%
+integral d
+ 
+
+ align:start position:0%
+integral d
+l so again I said we're using a small
+
+ align:start position:0%
+l so again I said we're using a small
+ 
+
+ align:start position:0%
+l so again I said we're using a small
+angle approximation so we've taken the
+
+ align:start position:0%
+angle approximation so we've taken the
+ 
+
+ align:start position:0%
+angle approximation so we've taken the
+approximation that tan Theta is a sin
+
+ align:start position:0%
+approximation that tan Theta is a sin
+ 
+
+ align:start position:0%
+approximation that tan Theta is a sin
+Theta is
+
+ align:start position:0%
+Theta is
+ 
+
+ align:start position:0%
+Theta is
+approximately Theta so this is just a
+
+ align:start position:0%
+approximately Theta so this is just a
+ 
+
+ align:start position:0%
+approximately Theta so this is just a
+simple linear relationship here where
+
+ align:start position:0%
+simple linear relationship here where
+ 
+
+ align:start position:0%
+simple linear relationship here where
+this is L * the angle in X and this is L
+
+ align:start position:0%
+this is L * the angle in X and this is L
+ 
+
+ align:start position:0%
+this is L * the angle in X and this is L
+* the angle than
+
+ align:start position:0%
+* the angle than
+ 
+
+ align:start position:0%
+* the angle than
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+y and so we could write this more
+
+ align:start position:0%
+y and so we could write this more
+ 
+
+ align:start position:0%
+y and so we could write this more
+compact in sort of vector notation as
+
+ align:start position:0%
+compact in sort of vector notation as
+ 
+
+ align:start position:0%
+compact in sort of vector notation as
+some Vector X Prime is equal to some
+
+ align:start position:0%
+some Vector X Prime is equal to some
+ 
+
+ align:start position:0%
+some Vector X Prime is equal to some
+Vector X Plus X
+
+ align:start position:0%
+Vector X Plus X
+ 
+
+ align:start position:0%
+Vector X Plus X
+gradient operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on so this is just another
+
+ align:start position:0%
+on so this is just another
+ 
+
+ align:start position:0%
+on so this is just another
+representation of this okay now one
+
+ align:start position:0%
+representation of this okay now one
+ 
+
+ align:start position:0%
+representation of this okay now one
+thing that we need in order to make some
+
+ align:start position:0%
+thing that we need in order to make some
+ 
+
+ align:start position:0%
+thing that we need in order to make some
+progress here is we need to assume that
+
+ align:start position:0%
+progress here is we need to assume that
+ 
+
+ align:start position:0%
+progress here is we need to assume that
+the overall intensity so the integral of
+
+ align:start position:0%
+the overall intensity so the integral of
+ 
+
+ align:start position:0%
+the overall intensity so the integral of
+this over X and Y is equal to the
+
+ align:start position:0%
+this over X and Y is equal to the
+ 
+
+ align:start position:0%
+this over X and Y is equal to the
+integral of this over X and Y so we sort
+
+ align:start position:0%
+integral of this over X and Y so we sort
+ 
+
+ align:start position:0%
+integral of this over X and Y so we sort
+of conserving our intensity so we could
+
+ align:start position:0%
+of conserving our intensity so we could
+ 
+
+ align:start position:0%
+of conserving our intensity so we could
+write that down as I on the detector
+
+ align:start position:0%
+write that down as I on the detector
+ 
+
+ align:start position:0%
+write that down as I on the detector
+DX Prime d y Prime is equal to I instant
+
+ align:start position:0%
+DX Prime d y Prime is equal to I instant
+ 
+
+ align:start position:0%
+DX Prime d y Prime is equal to I instant
+DX Dy so we the plasma is not absorbing
+
+ align:start position:0%
+DX Dy so we the plasma is not absorbing
+ 
+
+ align:start position:0%
+DX Dy so we the plasma is not absorbing
+and I guess it's also not emitting any
+
+ align:start position:0%
+and I guess it's also not emitting any
+ 
+
+ align:start position:0%
+and I guess it's also not emitting any
+light in this way
+
+ align:start position:0%
+light in this way
+ 
+
+ align:start position:0%
+light in this way
+mation that's a pretty reasonable
+
+ align:start position:0%
+mation that's a pretty reasonable
+ 
+
+ align:start position:0%
+mation that's a pretty reasonable
+proc and then we can skip ahead and we
+
+ align:start position:0%
+proc and then we can skip ahead and we
+ 
+
+ align:start position:0%
+proc and then we can skip ahead and we
+can say that the light which is
+
+ align:start position:0%
+can say that the light which is
+ 
+
+ align:start position:0%
+can say that the light which is
+incident divided the intensity which is
+
+ align:start position:0%
+incident divided the intensity which is
+ 
+
+ align:start position:0%
+incident divided the intensity which is
+incident divided by the intensity our
+
+ align:start position:0%
+incident divided by the intensity our
+ 
+
+ align:start position:0%
+incident divided by the intensity our
+detector is going to be equal to 1
+
+ align:start position:0%
+detector is going to be equal to 1
+ 
+
+ align:start position:0%
+detector is going to be equal to 1
+plus gradient
+
+ align:start position:0%
+plus gradient
+ 
+
+ align:start position:0%
+plus gradient
+squared sorry one
+
+ align:start position:0%
+squared sorry one
+ 
+
+ align:start position:0%
+squared sorry one
+plus L * gradient squ of the integral of
+
+ align:start position:0%
+plus L * gradient squ of the integral of
+ 
+
+ align:start position:0%
+plus L * gradient squ of the integral of
+the refractive index along the path and
+
+ align:start position:0%
+the refractive index along the path and
+ 
+
+ align:start position:0%
+the refractive index along the path and
+if we work with relatively small
+
+ align:start position:0%
+if we work with relatively small
+ 
+
+ align:start position:0%
+if we work with relatively small
+value of this so if we assume that this
+
+ align:start position:0%
+value of this so if we assume that this
+ 
+
+ align:start position:0%
+value of this so if we assume that this
+is much much less than one we can
+
+ align:start position:0%
+is much much less than one we can
+ 
+
+ align:start position:0%
+is much much less than one we can
+rewrite this in terms of a change in
+
+ align:start position:0%
+rewrite this in terms of a change in
+ 
+
+ align:start position:0%
+rewrite this in terms of a change in
+intensity so this would be the change in
+
+ align:start position:0%
+intensity so this would be the change in
+ 
+
+ align:start position:0%
+intensity so this would be the change in
+intensity in our image Delta I
+
+ align:start position:0%
+intensity in our image Delta I
+ 
+
+ align:start position:0%
+intensity in our image Delta I
+normalized to our initial intensity and
+
+ align:start position:0%
+normalized to our initial intensity and
+ 
+
+ align:start position:0%
+normalized to our initial intensity and
+that is going to be equal to 1 minus L /
+
+ align:start position:0%
+that is going to be equal to 1 minus L /
+ 
+
+ align:start position:0%
+that is going to be equal to 1 minus L /
+2 critical
+
+ align:start position:0%
+2 critical
+ 
+
+ align:start position:0%
+2 critical
+density squ integral of NE DL where in
+
+ align:start position:0%
+density squ integral of NE DL where in
+ 
+
+ align:start position:0%
+density squ integral of NE DL where in
+this last step I substituted out the
+
+ align:start position:0%
+this last step I substituted out the
+ 
+
+ align:start position:0%
+this last step I substituted out the
+refractive index for the expression that
+
+ align:start position:0%
+refractive index for the expression that
+ 
+
+ align:start position:0%
+refractive index for the expression that
+we had for any much less than n critical
+
+ align:start position:0%
+we had for any much less than n critical
+ 
+
+ align:start position:0%
+we had for any much less than n critical
+so again we've made an assumption that
+
+ align:start position:0%
+so again we've made an assumption that
+ 
+
+ align:start position:0%
+so again we've made an assumption that
+we have small intensity variations we've
+
+ align:start position:0%
+we have small intensity variations we've
+ 
+
+ align:start position:0%
+we have small intensity variations we've
+also made the assumption that NE is much
+
+ align:start position:0%
+also made the assumption that NE is much
+ 
+
+ align:start position:0%
+also made the assumption that NE is much
+much less than n critical so we can use
+
+ align:start position:0%
+much less than n critical so we can use
+ 
+
+ align:start position:0%
+much less than n critical so we can use
+this nice linear formula for
+
+ align:start position:0%
+this nice linear formula for
+ 
+
+ align:start position:0%
+this nice linear formula for
+um the refractive index of the plasma
+
+ align:start position:0%
+um the refractive index of the plasma
+ 
+
+ align:start position:0%
+um the refractive index of the plasma
+this simplifies everything so this is
+
+ align:start position:0%
+this simplifies everything so this is
+ 
+
+ align:start position:0%
+this simplifies everything so this is
+kind of like our final nice result here
+
+ align:start position:0%
+kind of like our final nice result here
+ 
+
+ align:start position:0%
+kind of like our final nice result here
+so for very small intensity variations
+
+ align:start position:0%
+so for very small intensity variations
+ 
+
+ align:start position:0%
+so for very small intensity variations
+you do indeed get an intensity variation
+
+ align:start position:0%
+you do indeed get an intensity variation
+ 
+
+ align:start position:0%
+you do indeed get an intensity variation
+which is proportional to one minus
+
+ align:start position:0%
+which is proportional to one minus
+ 
+
+ align:start position:0%
+which is proportional to one minus
+radiant squ of your electron density so
+
+ align:start position:0%
+radiant squ of your electron density so
+ 
+
+ align:start position:0%
+radiant squ of your electron density so
+using this formula where do we expect to
+
+ align:start position:0%
+using this formula where do we expect to
+ 
+
+ align:start position:0%
+using this formula where do we expect to
+have bright regions in our plasma so
+
+ align:start position:0%
+have bright regions in our plasma so
+ 
+
+ align:start position:0%
+have bright regions in our plasma so
+where where or sorry where do we expect
+
+ align:start position:0%
+where where or sorry where do we expect
+ 
+
+ align:start position:0%
+where where or sorry where do we expect
+to have bright regions in our interam
+
+ align:start position:0%
+to have bright regions in our interam
+ 
+
+ align:start position:0%
+to have bright regions in our interam
+what do they correspond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to yeah anyone the bright regions would
+
+ align:start position:0%
+to yeah anyone the bright regions would
+ 
+
+ align:start position:0%
+to yeah anyone the bright regions would
+be places where the second term is
+
+ align:start position:0%
+be places where the second term is
+ 
+
+ align:start position:0%
+be places where the second term is
+small being small point of of the okay
+
+ align:start position:0%
+small being small point of of the okay
+ 
+
+ align:start position:0%
+small being small point of of the okay
+so only you where it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small like where it's negative and
+
+ align:start position:0%
+small like where it's negative and
+ 
+
+ align:start position:0%
+small like where it's negative and
+big like where it's negative and
+
+ align:start position:0%
+big like where it's negative and
+ 
+
+ align:start position:0%
+big like where it's negative and
+big right yeah exactly so the bright
+
+ align:start position:0%
+big right yeah exactly so the bright
+ 
+
+ align:start position:0%
+big right yeah exactly so the bright
+regions here are going to correspond to
+
+ align:start position:0%
+regions here are going to correspond to
+ 
+
+ align:start position:0%
+regions here are going to correspond to
+Minima in the
+
+ align:start position:0%
+Minima in the
+ 
+
+ align:start position:0%
+Minima in the
+density and the dark regions are kind
+
+ align:start position:0%
+density and the dark regions are kind
+ 
+
+ align:start position:0%
+density and the dark regions are kind
+kind of correspond to Ma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's because very roughly we think or
+
+ align:start position:0%
+that's because very roughly we think or
+ 
+
+ align:start position:0%
+that's because very roughly we think or
+when we think about what the plasma is
+
+ align:start position:0%
+when we think about what the plasma is
+ 
+
+ align:start position:0%
+when we think about what the plasma is
+doing we see that Minima in the electron
+
+ align:start position:0%
+doing we see that Minima in the electron
+ 
+
+ align:start position:0%
+doing we see that Minima in the electron
+density act as focusing lenses and
+
+ align:start position:0%
+density act as focusing lenses and
+ 
+
+ align:start position:0%
+density act as focusing lenses and
+Maxima act as diverging regions and so
+
+ align:start position:0%
+Maxima act as diverging regions and so
+ 
+
+ align:start position:0%
+Maxima act as diverging regions and so
+that's kind of what we saw around about
+
+ align:start position:0%
+that's kind of what we saw around about
+ 
+
+ align:start position:0%
+that's kind of what we saw around about
+here okay how did you get the um how did
+
+ align:start position:0%
+here okay how did you get the um how did
+ 
+
+ align:start position:0%
+here okay how did you get the um how did
+you get the I initial over idid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form okay yeah it's it's not it's not
+
+ align:start position:0%
+form okay yeah it's it's not it's not
+ 
+
+ align:start position:0%
+form okay yeah it's it's not it's not
+obvious but you can go to book and see
+
+ align:start position:0%
+obvious but you can go to book and see
+ 
+
+ align:start position:0%
+obvious but you can go to book and see
+if you can follow derivation there but
+
+ align:start position:0%
+if you can follow derivation there but
+ 
+
+ align:start position:0%
+if you can follow derivation there but
+yeah there's there's a little bit of
+
+ align:start position:0%
+yeah there's there's a little bit of
+ 
+
+ align:start position:0%
+yeah there's there's a little bit of
+magic to do that step there the thing
+
+ align:start position:0%
+magic to do that step there the thing
+ 
+
+ align:start position:0%
+magic to do that step there the thing
+that you want to recognize is we're
+
+ align:start position:0%
+that you want to recognize is we're
+ 
+
+ align:start position:0%
+that you want to recognize is we're
+doing something that looks like it's got
+
+ align:start position:0%
+doing something that looks like it's got
+ 
+
+ align:start position:0%
+doing something that looks like it's got
+a Jacobian or something like that
+
+ align:start position:0%
+a Jacobian or something like that
+ 
+
+ align:start position:0%
+a Jacobian or something like that
+involved there so it all uh eventually
+
+ align:start position:0%
+involved there so it all uh eventually
+ 
+
+ align:start position:0%
+involved there so it all uh eventually
+ends up working out there's also a paper
+
+ align:start position:0%
+ends up working out there's also a paper
+ 
+
+ align:start position:0%
+ends up working out there's also a paper
+by kland that I'll mention later that's
+
+ align:start position:0%
+by kland that I'll mention later that's
+ 
+
+ align:start position:0%
+by kland that I'll mention later that's
+really good for this stuff if you want
+
+ align:start position:0%
+really good for this stuff if you want
+ 
+
+ align:start position:0%
+really good for this stuff if you want
+to see an alternative derivation yeah
+
+ align:start position:0%
+to see an alternative derivation yeah
+ 
+
+ align:start position:0%
+to see an alternative derivation yeah
+wondering how do we what is theise meing
+
+ align:start position:0%
+wondering how do we what is theise meing
+ 
+
+ align:start position:0%
+wondering how do we what is theise meing
+of the gradient of a line in the graded
+
+ align:start position:0%
+of the gradient of a line in the graded
+ 
+
+ align:start position:0%
+of the gradient of a line in the graded
+quantity is it like we're changing a
+
+ align:start position:0%
+quantity is it like we're changing a
+ 
+
+ align:start position:0%
+quantity is it like we're changing a
+integration by infal amount what does
+
+ align:start position:0%
+integration by infal amount what does
+ 
+
+ align:start position:0%
+integration by infal amount what does
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+um I mean mathematically you can just
+
+ align:start position:0%
+um I mean mathematically you can just
+ 
+
+ align:start position:0%
+um I mean mathematically you can just
+work it out right there's nothing wrong
+
+ align:start position:0%
+work it out right there's nothing wrong
+ 
+
+ align:start position:0%
+work it out right there's nothing wrong
+with this because for example if we are
+
+ align:start position:0%
+with this because for example if we are
+ 
+
+ align:start position:0%
+with this because for example if we are
+doing any of X Y and Z integrated DZ
+
+ align:start position:0%
+doing any of X Y and Z integrated DZ
+ 
+
+ align:start position:0%
+doing any of X Y and Z integrated DZ
+like that then you can still
+
+ align:start position:0%
+like that then you can still
+ 
+
+ align:start position:0%
+like that then you can still
+take the derivative of this you just
+
+ align:start position:0%
+take the derivative of this you just
+ 
+
+ align:start position:0%
+take the derivative of this you just
+won't have any Z components anymore
+
+ align:start position:0%
+won't have any Z components anymore
+ 
+
+ align:start position:0%
+won't have any Z components anymore
+you'll just have components in X and Y
+
+ align:start position:0%
+you'll just have components in X and Y
+ 
+
+ align:start position:0%
+you'll just have components in X and Y
+um in reality When I See This written
+
+ align:start position:0%
+um in reality When I See This written
+ 
+
+ align:start position:0%
+um in reality When I See This written
+down I often see people and I do the
+
+ align:start position:0%
+down I often see people and I do the
+ 
+
+ align:start position:0%
+down I often see people and I do the
+same thing who sort of sneakily move
+
+ align:start position:0%
+same thing who sort of sneakily move
+ 
+
+ align:start position:0%
+same thing who sort of sneakily move
+this integration sign to here and then
+
+ align:start position:0%
+this integration sign to here and then
+ 
+
+ align:start position:0%
+this integration sign to here and then
+it makes a little bit more sense because
+
+ align:start position:0%
+it makes a little bit more sense because
+ 
+
+ align:start position:0%
+it makes a little bit more sense because
+you're actually looking for each step DL
+
+ align:start position:0%
+you're actually looking for each step DL
+ 
+
+ align:start position:0%
+you're actually looking for each step DL
+that the ray goes through the plasma you
+
+ align:start position:0%
+that the ray goes through the plasma you
+ 
+
+ align:start position:0%
+that the ray goes through the plasma you
+look at what the local density gradient
+
+ align:start position:0%
+look at what the local density gradient
+ 
+
+ align:start position:0%
+look at what the local density gradient
+is and I think these two things are
+
+ align:start position:0%
+is and I think these two things are
+ 
+
+ align:start position:0%
+is and I think these two things are
+different kind of obviously um but they
+
+ align:start position:0%
+different kind of obviously um but they
+ 
+
+ align:start position:0%
+different kind of obviously um but they
+are pretty close for thin plasmas and
+
+ align:start position:0%
+are pretty close for thin plasmas and
+ 
+
+ align:start position:0%
+are pretty close for thin plasmas and
+what most of the time people are doing
+
+ align:start position:0%
+what most of the time people are doing
+ 
+
+ align:start position:0%
+what most of the time people are doing
+is making approximations that the width
+
+ align:start position:0%
+is making approximations that the width
+ 
+
+ align:start position:0%
+is making approximations that the width
+of this plasma which might be a or
+
+ align:start position:0%
+of this plasma which might be a or
+ 
+
+ align:start position:0%
+of this plasma which might be a or
+something like that is much much less
+
+ align:start position:0%
+something like that is much much less
+ 
+
+ align:start position:0%
+something like that is much much less
+than L um so this is effectively
+
+ align:start position:0%
+than L um so this is effectively
+ 
+
+ align:start position:0%
+than L um so this is effectively
+assuming that the actual path that the
+
+ align:start position:0%
+assuming that the actual path that the
+ 
+
+ align:start position:0%
+assuming that the actual path that the
+ray takes through the plasma is
+
+ align:start position:0%
+ray takes through the plasma is
+ 
+
+ align:start position:0%
+ray takes through the plasma is
+unimportant we only just care about what
+
+ align:start position:0%
+unimportant we only just care about what
+ 
+
+ align:start position:0%
+unimportant we only just care about what
+path it takes through free space
+
+ align:start position:0%
+path it takes through free space
+ 
+
+ align:start position:0%
+path it takes through free space
+affluence which is be in the straight
+
+ align:start position:0%
+affluence which is be in the straight
+ 
+
+ align:start position:0%
+affluence which is be in the straight
+line if you don't have this condition
+
+ align:start position:0%
+line if you don't have this condition
+ 
+
+ align:start position:0%
+line if you don't have this condition
+you actually end up in the costic ra
+
+ align:start position:0%
+you actually end up in the costic ra
+ 
+
+ align:start position:0%
+you actually end up in the costic ra
+more easily and again I'll point you
+
+ align:start position:0%
+more easily and again I'll point you
+ 
+
+ align:start position:0%
+more easily and again I'll point you
+some references later which talk about
+
+ align:start position:0%
+some references later which talk about
+ 
+
+ align:start position:0%
+some references later which talk about
+this in a bit more detail for the for
+
+ align:start position:0%
+this in a bit more detail for the for
+ 
+
+ align:start position:0%
+this in a bit more detail for the for
+the in the case where the thickness of
+
+ align:start position:0%
+the in the case where the thickness of
+ 
+
+ align:start position:0%
+the in the case where the thickness of
+the plasma it is much less than the
+
+ align:start position:0%
+the plasma it is much less than the
+ 
+
+ align:start position:0%
+the plasma it is much less than the
+distance between the plasma and the
+
+ align:start position:0%
+distance between the plasma and the
+ 
+
+ align:start position:0%
+distance between the plasma and the
+detector it doesn't really matter which
+
+ align:start position:0%
+detector it doesn't really matter which
+ 
+
+ align:start position:0%
+detector it doesn't really matter which
+way around you do this
+
+ align:start position:0%
+way around you do this
+ 
+
+ align:start position:0%
+way around you do this
+operation yeah good question yeah seen
+
+ align:start position:0%
+operation yeah good question yeah seen
+ 
+
+ align:start position:0%
+operation yeah good question yeah seen
+the regime or sort of saying that the P
+
+ align:start position:0%
+the regime or sort of saying that the P
+ 
+
+ align:start position:0%
+the regime or sort of saying that the P
+probably doesn't matter isn't that just
+
+ align:start position:0%
+probably doesn't matter isn't that just
+ 
+
+ align:start position:0%
+probably doesn't matter isn't that just
+like the
+
+ align:start position:0%
+like the
+ 
+
+ align:start position:0%
+like the
+sh yeah and indeed this effect crops up
+
+ align:start position:0%
+sh yeah and indeed this effect crops up
+ 
+
+ align:start position:0%
+sh yeah and indeed this effect crops up
+in schen as well but in schen the bigger
+
+ align:start position:0%
+in schen as well but in schen the bigger
+ 
+
+ align:start position:0%
+in schen as well but in schen the bigger
+effect you get is by putting the stop
+
+ align:start position:0%
+effect you get is by putting the stop
+ 
+
+ align:start position:0%
+effect you get is by putting the stop
+and blocking out the Reds but you will
+
+ align:start position:0%
+and blocking out the Reds but you will
+ 
+
+ align:start position:0%
+and blocking out the Reds but you will
+have shog effects inside your schan
+
+ align:start position:0%
+have shog effects inside your schan
+ 
+
+ align:start position:0%
+have shog effects inside your schan
+Imaging system too okay so yeah I just
+
+ align:start position:0%
+Imaging system too okay so yeah I just
+ 
+
+ align:start position:0%
+Imaging system too okay so yeah I just
+introduced the schan first and now we
+
+ align:start position:0%
+introduced the schan first and now we
+ 
+
+ align:start position:0%
+introduced the schan first and now we
+have theography but these are both
+
+ align:start position:0%
+have theography but these are both
+ 
+
+ align:start position:0%
+have theography but these are both
+present here and they're also present in
+
+ align:start position:0%
+present here and they're also present in
+ 
+
+ align:start position:0%
+present here and they're also present in
+some inry we about but in each of these
+
+ align:start position:0%
+some inry we about but in each of these
+ 
+
+ align:start position:0%
+some inry we about but in each of these
+there's like something that causes the
+
+ align:start position:0%
+there's like something that causes the
+ 
+
+ align:start position:0%
+there's like something that causes the
+biggest intensity modulations thean is
+
+ align:start position:0%
+biggest intensity modulations thean is
+ 
+
+ align:start position:0%
+biggest intensity modulations thean is
+the schan stop clearly but here again
+
+ align:start position:0%
+the schan stop clearly but here again
+ 
+
+ align:start position:0%
+the schan stop clearly but here again
+we're only looking in this regim small
+
+ align:start position:0%
+we're only looking in this regim small
+ 
+
+ align:start position:0%
+we're only looking in this regim small
+intensity modulation for moment um but
+
+ align:start position:0%
+intensity modulation for moment um but
+ 
+
+ align:start position:0%
+intensity modulation for moment um but
+without the sh and stop this is the
+
+ align:start position:0%
+without the sh and stop this is the
+ 
+
+ align:start position:0%
+without the sh and stop this is the
+effect that shows up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our signal is proportional to thetion
+
+ align:start position:0%
+our signal is proportional to thetion
+ 
+
+ align:start position:0%
+our signal is proportional to thetion
+density and so why is it that maximum
+
+ align:start position:0%
+density and so why is it that maximum
+ 
+
+ align:start position:0%
+density and so why is it that maximum
+minimum of the signal correspond to
+
+ align:start position:0%
+minimum of the signal correspond to
+ 
+
+ align:start position:0%
+minimum of the signal correspond to
+maximum minimum of the density rather
+
+ align:start position:0%
+maximum minimum of the density rather
+ 
+
+ align:start position:0%
+maximum minimum of the density rather
+than Maxim minimum of the density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient yeah I see what you're saying I
+
+ align:start position:0%
+gradient yeah I see what you're saying I
+ 
+
+ align:start position:0%
+gradient yeah I see what you're saying I
+think it's because it's thean of the
+
+ align:start position:0%
+think it's because it's thean of the
+ 
+
+ align:start position:0%
+think it's because it's thean of the
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+in Asos
+
+ align:start position:0%
+in Asos
+ 
+
+ align:start position:0%
+in Asos
+to or like the integration over space
+
+ align:start position:0%
+to or like the integration over space
+ 
+
+ align:start position:0%
+to or like the integration over space
+brings you back a level yeah I'll I'll
+
+ align:start position:0%
+brings you back a level yeah I'll I'll
+ 
+
+ align:start position:0%
+brings you back a level yeah I'll I'll
+have a look at that and check I do see
+
+ align:start position:0%
+have a look at that and check I do see
+ 
+
+ align:start position:0%
+have a look at that and check I do see
+what you're saying I see what you're
+
+ align:start position:0%
+what you're saying I see what you're
+ 
+
+ align:start position:0%
+what you're saying I see what you're
+saying and I don't know what the
+
+ align:start position:0%
+saying and I don't know what the
+ 
+
+ align:start position:0%
+saying and I don't know what the
+resolution is right at the moment but
+
+ align:start position:0%
+resolution is right at the moment but
+ 
+
+ align:start position:0%
+resolution is right at the moment but
+yeah I'll have a look and see if I can
+
+ align:start position:0%
+yeah I'll have a look and see if I can
+ 
+
+ align:start position:0%
+yeah I'll have a look and see if I can
+work that out thank you cool so again
+
+ align:start position:0%
+work that out thank you cool so again
+ 
+
+ align:start position:0%
+work that out thank you cool so again
+this looks really nice because it looks
+
+ align:start position:0%
+this looks really nice because it looks
+ 
+
+ align:start position:0%
+this looks really nice because it looks
+like you can get out the second
+
+ align:start position:0%
+like you can get out the second
+ 
+
+ align:start position:0%
+like you can get out the second
+derivative of the density and then maybe
+
+ align:start position:0%
+derivative of the density and then maybe
+ 
+
+ align:start position:0%
+derivative of the density and then maybe
+you could like double integrate that and
+
+ align:start position:0%
+you could like double integrate that and
+ 
+
+ align:start position:0%
+you could like double integrate that and
+you could get out the actual line
+
+ align:start position:0%
+you could get out the actual line
+ 
+
+ align:start position:0%
+you could get out the actual line
+integrated electron density but in
+
+ align:start position:0%
+integrated electron density but in
+ 
+
+ align:start position:0%
+integrated electron density but in
+reality the assumptions we've had to
+
+ align:start position:0%
+reality the assumptions we've had to
+ 
+
+ align:start position:0%
+reality the assumptions we've had to
+make to get here mean this is really
+
+ align:start position:0%
+make to get here mean this is really
+ 
+
+ align:start position:0%
+make to get here mean this is really
+hard because the actual signal term we
+
+ align:start position:0%
+hard because the actual signal term we
+ 
+
+ align:start position:0%
+hard because the actual signal term we
+have assumed is much much smaller than
+
+ align:start position:0%
+have assumed is much much smaller than
+ 
+
+ align:start position:0%
+have assumed is much much smaller than
+one which means that it's really really
+
+ align:start position:0%
+one which means that it's really really
+ 
+
+ align:start position:0%
+one which means that it's really really
+hard to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure so for any realistic system with
+
+ align:start position:0%
+measure so for any realistic system with
+ 
+
+ align:start position:0%
+measure so for any realistic system with
+a realistic signal to noise we don't
+
+ align:start position:0%
+a realistic signal to noise we don't
+ 
+
+ align:start position:0%
+a realistic signal to noise we don't
+want to have this limitation we don't
+
+ align:start position:0%
+want to have this limitation we don't
+ 
+
+ align:start position:0%
+want to have this limitation we don't
+want to be working at position one or
+
+ align:start position:0%
+want to be working at position one or
+ 
+
+ align:start position:0%
+want to be working at position one or
+even position two we're actually get the
+
+ align:start position:0%
+even position two we're actually get the
+ 
+
+ align:start position:0%
+even position two we're actually get the
+best signal when we go to position three
+
+ align:start position:0%
+best signal when we go to position three
+ 
+
+ align:start position:0%
+best signal when we go to position three
+where all of this no longer applies and
+
+ align:start position:0%
+where all of this no longer applies and
+ 
+
+ align:start position:0%
+where all of this no longer applies and
+we can no longer get this nice result
+
+ align:start position:0%
+we can no longer get this nice result
+ 
+
+ align:start position:0%
+we can no longer get this nice result
+and this is what I'm saying where you
+
+ align:start position:0%
+and this is what I'm saying where you
+ 
+
+ align:start position:0%
+and this is what I'm saying where you
+will find people saying chog graphy is
+
+ align:start position:0%
+will find people saying chog graphy is
+ 
+
+ align:start position:0%
+will find people saying chog graphy is
+proportional to the second derivative of
+
+ align:start position:0%
+proportional to the second derivative of
+ 
+
+ align:start position:0%
+proportional to the second derivative of
+the electron density and that's sort of
+
+ align:start position:0%
+the electron density and that's sort of
+ 
+
+ align:start position:0%
+the electron density and that's sort of
+true but I've never seen anyone do it
+
+ align:start position:0%
+true but I've never seen anyone do it
+ 
+
+ align:start position:0%
+true but I've never seen anyone do it
+like it's not actually possible to do
+
+ align:start position:0%
+like it's not actually possible to do
+ 
+
+ align:start position:0%
+like it's not actually possible to do
+that measurement in a meaningful way you
+
+ align:start position:0%
+that measurement in a meaningful way you
+ 
+
+ align:start position:0%
+that measurement in a meaningful way you
+have to work in a regime where you can
+
+ align:start position:0%
+have to work in a regime where you can
+ 
+
+ align:start position:0%
+have to work in a regime where you can
+actually measure the modulation and I'll
+
+ align:start position:0%
+actually measure the modulation and I'll
+ 
+
+ align:start position:0%
+actually measure the modulation and I'll
+show you some example pictures of SCH an
+
+ align:start position:0%
+show you some example pictures of SCH an
+ 
+
+ align:start position:0%
+show you some example pictures of SCH an
+chonograph towards the end of this
+
+ align:start position:0%
+chonograph towards the end of this
+ 
+
+ align:start position:0%
+chonograph towards the end of this
+lecture so you get an idea of what it
+
+ align:start position:0%
+lecture so you get an idea of what it
+ 
+
+ align:start position:0%
+lecture so you get an idea of what it
+looks like inas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I think I kind of said a lot of
+
+ align:start position:0%
+okay I think I kind of said a lot of
+ 
+
+ align:start position:0%
+okay I think I kind of said a lot of
+this already if we end up in this regime
+
+ align:start position:0%
+this already if we end up in this regime
+ 
+
+ align:start position:0%
+this already if we end up in this regime
+here where we have these cor
+
+ align:start position:0%
+here where we have these cor
+ 
+
+ align:start position:0%
+here where we have these cor
+sticks we've clearly lost information we
+
+ align:start position:0%
+sticks we've clearly lost information we
+ 
+
+ align:start position:0%
+sticks we've clearly lost information we
+can no longer do this mapping here
+
+ align:start position:0%
+can no longer do this mapping here
+ 
+
+ align:start position:0%
+can no longer do this mapping here
+because it's no longer unique we've got
+
+ align:start position:0%
+because it's no longer unique we've got
+ 
+
+ align:start position:0%
+because it's no longer unique we've got
+raised Crossing so different bits of X
+
+ align:start position:0%
+raised Crossing so different bits of X
+ 
+
+ align:start position:0%
+raised Crossing so different bits of X
+Prime and Y Prime are mapping onto or
+
+ align:start position:0%
+Prime and Y Prime are mapping onto or
+ 
+
+ align:start position:0%
+Prime and Y Prime are mapping onto or
+one place in X Prime y Prime might map
+
+ align:start position:0%
+one place in X Prime y Prime might map
+ 
+
+ align:start position:0%
+one place in X Prime y Prime might map
+onto multiple X and Y and so we can't do
+
+ align:start position:0%
+onto multiple X and Y and so we can't do
+ 
+
+ align:start position:0%
+onto multiple X and Y and so we can't do
+this simple uh thing and it's kind of
+
+ align:start position:0%
+this simple uh thing and it's kind of
+ 
+
+ align:start position:0%
+this simple uh thing and it's kind of
+obvious actually that you'll be losing
+
+ align:start position:0%
+obvious actually that you'll be losing
+ 
+
+ align:start position:0%
+obvious actually that you'll be losing
+uh information and even a more advanced
+
+ align:start position:0%
+uh information and even a more advanced
+ 
+
+ align:start position:0%
+uh information and even a more advanced
+technique isn't going to be able to do
+
+ align:start position:0%
+technique isn't going to be able to do
+ 
+
+ align:start position:0%
+technique isn't going to be able to do
+the Reconstruction so I want to talk
+
+ align:start position:0%
+the Reconstruction so I want to talk
+ 
+
+ align:start position:0%
+the Reconstruction so I want to talk
+just now a little bit about some of
+
+ align:start position:0%
+just now a little bit about some of
+ 
+
+ align:start position:0%
+just now a little bit about some of
+these Advanced reconstruction techniques
+
+ align:start position:0%
+these Advanced reconstruction techniques
+ 
+
+ align:start position:0%
+these Advanced reconstruction techniques
+which go beyond this and then I'll show
+
+ align:start position:0%
+which go beyond this and then I'll show
+ 
+
+ align:start position:0%
+which go beyond this and then I'll show
+these examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first paper I've seen that really
+
+ align:start position:0%
+so the first paper I've seen that really
+ 
+
+ align:start position:0%
+so the first paper I've seen that really
+tackles this very nicely is
+
+ align:start position:0%
+tackles this very nicely is
+ 
+
+ align:start position:0%
+tackles this very nicely is
+candile in
+
+ align:start position:0%
+candile in
+ 
+
+ align:start position:0%
+candile in
+RSI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2012 so cand points out pretty quickly
+
+ align:start position:0%
+2012 so cand points out pretty quickly
+ 
+
+ align:start position:0%
+2012 so cand points out pretty quickly
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chirography has a direct equivalent to
+
+ align:start position:0%
+chirography has a direct equivalent to
+ 
+
+ align:start position:0%
+chirography has a direct equivalent to
+proton radiography so mathematically
+
+ align:start position:0%
+proton radiography so mathematically
+ 
+
+ align:start position:0%
+proton radiography so mathematically
+they both deal with the same quantities
+
+ align:start position:0%
+they both deal with the same quantities
+ 
+
+ align:start position:0%
+they both deal with the same quantities
+which is a sort of deflection potential
+
+ align:start position:0%
+which is a sort of deflection potential
+ 
+
+ align:start position:0%
+which is a sort of deflection potential
+in proton radiography this deflection
+
+ align:start position:0%
+in proton radiography this deflection
+ 
+
+ align:start position:0%
+in proton radiography this deflection
+potential is to do with electric and
+
+ align:start position:0%
+potential is to do with electric and
+ 
+
+ align:start position:0%
+potential is to do with electric and
+magnetic fields and we'll get on to
+
+ align:start position:0%
+magnetic fields and we'll get on to
+ 
+
+ align:start position:0%
+magnetic fields and we'll get on to
+proton radiography later and in shog
+
+ align:start position:0%
+proton radiography later and in shog
+ 
+
+ align:start position:0%
+proton radiography later and in shog
+graphy the deflection potential is to do
+
+ align:start position:0%
+graphy the deflection potential is to do
+ 
+
+ align:start position:0%
+graphy the deflection potential is to do
+with density radius but once you work in
+
+ align:start position:0%
+with density radius but once you work in
+ 
+
+ align:start position:0%
+with density radius but once you work in
+terms of this deflection potential and
+
+ align:start position:0%
+terms of this deflection potential and
+ 
+
+ align:start position:0%
+terms of this deflection potential and
+forget where it came from you get
+
+ align:start position:0%
+forget where it came from you get
+ 
+
+ align:start position:0%
+forget where it came from you get
+exactly the same results mathematically
+
+ align:start position:0%
+exactly the same results mathematically
+ 
+
+ align:start position:0%
+exactly the same results mathematically
+and he has this nice geometric
+
+ align:start position:0%
+and he has this nice geometric
+ 
+
+ align:start position:0%
+and he has this nice geometric
+approach and so if you found the
+
+ align:start position:0%
+approach and so if you found the
+ 
+
+ align:start position:0%
+approach and so if you found the
+derivation I just did not very very
+
+ align:start position:0%
+derivation I just did not very very
+ 
+
+ align:start position:0%
+derivation I just did not very very
+convincing you can go and have a look at
+
+ align:start position:0%
+convincing you can go and have a look at
+ 
+
+ align:start position:0%
+convincing you can go and have a look at
+this it's a little bit more rigorous and
+
+ align:start position:0%
+this it's a little bit more rigorous and
+ 
+
+ align:start position:0%
+this it's a little bit more rigorous and
+also he then extends it into the CTIC
+
+ align:start position:0%
+also he then extends it into the CTIC
+ 
+
+ align:start position:0%
+also he then extends it into the CTIC
+regime and Beyond and shows what you
+
+ align:start position:0%
+regime and Beyond and shows what you
+ 
+
+ align:start position:0%
+regime and Beyond and shows what you
+would expect to get from a plasma uh
+
+ align:start position:0%
+would expect to get from a plasma uh
+ 
+
+ align:start position:0%
+would expect to get from a plasma uh
+where you have Co stics so this is nice
+
+ align:start position:0%
+where you have Co stics so this is nice
+ 
+
+ align:start position:0%
+where you have Co stics so this is nice
+um but he still doesn't really tell you
+
+ align:start position:0%
+um but he still doesn't really tell you
+ 
+
+ align:start position:0%
+um but he still doesn't really tell you
+how to analyze it it's it's really
+
+ align:start position:0%
+how to analyze it it's it's really
+ 
+
+ align:start position:0%
+how to analyze it it's it's really
+talking about the problem where you go
+
+ align:start position:0%
+talking about the problem where you go
+ 
+
+ align:start position:0%
+talking about the problem where you go
+from knowing the density of the plasma
+
+ align:start position:0%
+from knowing the density of the plasma
+ 
+
+ align:start position:0%
+from knowing the density of the plasma
+to predicting what you're going to get
+
+ align:start position:0%
+to predicting what you're going to get
+ 
+
+ align:start position:0%
+to predicting what you're going to get
+out going the opposite direction to
+
+ align:start position:0%
+out going the opposite direction to
+ 
+
+ align:start position:0%
+out going the opposite direction to
+going from your intensity variations to
+
+ align:start position:0%
+going from your intensity variations to
+ 
+
+ align:start position:0%
+going from your intensity variations to
+the density uh isn't particularly well
+
+ align:start position:0%
+the density uh isn't particularly well
+ 
+
+ align:start position:0%
+the density uh isn't particularly well
+about so this is
+
+ align:start position:0%
+about so this is
+ 
+
+ align:start position:0%
+about so this is
+what some people call the forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem and the forward problem is going
+
+ align:start position:0%
+problem and the forward problem is going
+ 
+
+ align:start position:0%
+problem and the forward problem is going
+from NE of X Y and Z to intensity on
+
+ align:start position:0%
+from NE of X Y and Z to intensity on
+ 
+
+ align:start position:0%
+from NE of X Y and Z to intensity on
+your detector in X Prime and Y Prime
+
+ align:start position:0%
+your detector in X Prime and Y Prime
+ 
+
+ align:start position:0%
+your detector in X Prime and Y Prime
+useful but not exactly the
+
+ align:start position:0%
+useful but not exactly the
+ 
+
+ align:start position:0%
+useful but not exactly the
+solution so then in 2017 there were two
+
+ align:start position:0%
+solution so then in 2017 there were two
+ 
+
+ align:start position:0%
+solution so then in 2017 there were two
+almost competing papers that came out
+
+ align:start position:0%
+almost competing papers that came out
+ 
+
+ align:start position:0%
+almost competing papers that came out
+about this there was a paper by
+
+ align:start position:0%
+about this there was a paper by
+ 
+
+ align:start position:0%
+about this there was a paper by
+cassim asile in physical review e
+
+ align:start position:0%
+cassim asile in physical review e
+ 
+
+ align:start position:0%
+cassim asile in physical review e
+2017 what cassine did is he tried to
+
+ align:start position:0%
+2017 what cassine did is he tried to
+ 
+
+ align:start position:0%
+2017 what cassine did is he tried to
+reconstruct this deflection potential
+
+ align:start position:0%
+reconstruct this deflection potential
+ 
+
+ align:start position:0%
+reconstruct this deflection potential
+that cin would come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and he did this using uh a
+
+ align:start position:0%
+here and he did this using uh a
+ 
+
+ align:start position:0%
+here and he did this using uh a
+technique that was borrowed uh from some
+
+ align:start position:0%
+technique that was borrowed uh from some
+ 
+
+ align:start position:0%
+technique that was borrowed uh from some
+would say computer Graphics or at least
+
+ align:start position:0%
+would say computer Graphics or at least
+ 
+
+ align:start position:0%
+would say computer Graphics or at least
+some fields of Applied Mathematics uh
+
+ align:start position:0%
+some fields of Applied Mathematics uh
+ 
+
+ align:start position:0%
+some fields of Applied Mathematics uh
+which used a aoid diagram has anyone
+
+ align:start position:0%
+which used a aoid diagram has anyone
+ 
+
+ align:start position:0%
+which used a aoid diagram has anyone
+come across borono diagrams
+
+ align:start position:0%
+come across borono diagrams
+ 
+
+ align:start position:0%
+come across borono diagrams
+before huge in robotics sorry they're
+
+ align:start position:0%
+before huge in robotics sorry they're
+ 
+
+ align:start position:0%
+before huge in robotics sorry they're
+huge in robotics okay cool right so
+
+ align:start position:0%
+huge in robotics okay cool right so
+ 
+
+ align:start position:0%
+huge in robotics okay cool right so
+there's like they basically I think this
+
+ align:start position:0%
+there's like they basically I think this
+ 
+
+ align:start position:0%
+there's like they basically I think this
+worked well because they took some work
+
+ align:start position:0%
+worked well because they took some work
+ 
+
+ align:start position:0%
+worked well because they took some work
+that other people been doing in
+
+ align:start position:0%
+that other people been doing in
+ 
+
+ align:start position:0%
+that other people been doing in
+different F and applied it here so aoid
+
+ align:start position:0%
+different F and applied it here so aoid
+ 
+
+ align:start position:0%
+different F and applied it here so aoid
+diagram haha please don't shout me if I
+
+ align:start position:0%
+diagram haha please don't shout me if I
+ 
+
+ align:start position:0%
+diagram haha please don't shout me if I
+get this wrong is roughly if you have a
+
+ align:start position:0%
+get this wrong is roughly if you have a
+ 
+
+ align:start position:0%
+get this wrong is roughly if you have a
+series of points which are randomly
+
+ align:start position:0%
+series of points which are randomly
+ 
+
+ align:start position:0%
+series of points which are randomly
+distributed
+
+ align:start position:0%
+distributed
+ 
+
+ align:start position:0%
+distributed
+how do you draw quadrilaterals around
+
+ align:start position:0%
+how do you draw quadrilaterals around
+ 
+
+ align:start position:0%
+how do you draw quadrilaterals around
+them such that every Point inside the
+
+ align:start position:0%
+them such that every Point inside the
+ 
+
+ align:start position:0%
+them such that every Point inside the
+quadrilateral is closest to this point
+
+ align:start position:0%
+quadrilateral is closest to this point
+ 
+
+ align:start position:0%
+quadrilateral is closest to this point
+and not to any of the other points so
+
+ align:start position:0%
+and not to any of the other points so
+ 
+
+ align:start position:0%
+and not to any of the other points so
+it's a way of tiling up a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space and from this you can imagine
+
+ align:start position:0%
+space and from this you can imagine
+ 
+
+ align:start position:0%
+space and from this you can imagine
+these uh these tiles that youve produced
+
+ align:start position:0%
+these uh these tiles that youve produced
+ 
+
+ align:start position:0%
+these uh these tiles that youve produced
+in your um chog graphy can then be
+
+ align:start position:0%
+in your um chog graphy can then be
+ 
+
+ align:start position:0%
+in your um chog graphy can then be
+related back to a more uniform grid of
+
+ align:start position:0%
+related back to a more uniform grid of
+ 
+
+ align:start position:0%
+related back to a more uniform grid of
+tiles which all have the same shape and
+
+ align:start position:0%
+tiles which all have the same shape and
+ 
+
+ align:start position:0%
+tiles which all have the same shape and
+the same uh intensity which is your
+
+ align:start position:0%
+the same uh intensity which is your
+ 
+
+ align:start position:0%
+the same uh intensity which is your
+intensity beforehand and this is your
+
+ align:start position:0%
+intensity beforehand and this is your
+ 
+
+ align:start position:0%
+intensity beforehand and this is your
+intensity at the detector again this is
+
+ align:start position:0%
+intensity at the detector again this is
+ 
+
+ align:start position:0%
+intensity at the detector again this is
+just a very handwavy sketch of what they
+
+ align:start position:0%
+just a very handwavy sketch of what they
+ 
+
+ align:start position:0%
+just a very handwavy sketch of what they
+did they came up with an algorithm to do
+
+ align:start position:0%
+did they came up with an algorithm to do
+ 
+
+ align:start position:0%
+did they came up with an algorithm to do
+this and this enabled them to do the
+
+ align:start position:0%
+this and this enabled them to do the
+ 
+
+ align:start position:0%
+this and this enabled them to do the
+inverse problem which is intensity of
+
+ align:start position:0%
+inverse problem which is intensity of
+ 
+
+ align:start position:0%
+inverse problem which is intensity of
+our detector in X Prime y Prime going
+
+ align:start position:0%
+our detector in X Prime y Prime going
+ 
+
+ align:start position:0%
+our detector in X Prime y Prime going
+back towards density next y see and as
+
+ align:start position:0%
+back towards density next y see and as
+ 
+
+ align:start position:0%
+back towards density next y see and as
+you discussed before this is an illposed
+
+ align:start position:0%
+you discussed before this is an illposed
+ 
+
+ align:start position:0%
+you discussed before this is an illposed
+problem there are a large family of
+
+ align:start position:0%
+problem there are a large family of
+ 
+
+ align:start position:0%
+problem there are a large family of
+possible density structures that produce
+
+ align:start position:0%
+possible density structures that produce
+ 
+
+ align:start position:0%
+possible density structures that produce
+the same intensity but this roro diagram
+
+ align:start position:0%
+the same intensity but this roro diagram
+ 
+
+ align:start position:0%
+the same intensity but this roro diagram
+is making conservative assumptions about
+
+ align:start position:0%
+is making conservative assumptions about
+ 
+
+ align:start position:0%
+is making conservative assumptions about
+where light has come from in order to be
+
+ align:start position:0%
+where light has come from in order to be
+ 
+
+ align:start position:0%
+where light has come from in order to be
+able to put stuff
+
+ align:start position:0%
+able to put stuff
+ 
+
+ align:start position:0%
+able to put stuff
+back and almost exactly pling time
+
+ align:start position:0%
+back and almost exactly pling time
+ 
+
+ align:start position:0%
+back and almost exactly pling time
+but both groups are on yes so would this
+
+ align:start position:0%
+but both groups are on yes so would this
+ 
+
+ align:start position:0%
+but both groups are on yes so would this
+be applicable to shooting an array of
+
+ align:start position:0%
+be applicable to shooting an array of
+ 
+
+ align:start position:0%
+be applicable to shooting an array of
+blazers should G oh so no one does that
+
+ align:start position:0%
+blazers should G oh so no one does that
+ 
+
+ align:start position:0%
+blazers should G oh so no one does that
+but they should so they didn't proton
+
+ align:start position:0%
+but they should so they didn't proton
+ 
+
+ align:start position:0%
+but they should so they didn't proton
+radiography in the early days they
+
+ align:start position:0%
+radiography in the early days they
+ 
+
+ align:start position:0%
+radiography in the early days they
+actually had like little beamlets and
+
+ align:start position:0%
+actually had like little beamlets and
+ 
+
+ align:start position:0%
+actually had like little beamlets and
+then you can uniquely work out where
+
+ align:start position:0%
+then you can uniquely work out where
+ 
+
+ align:start position:0%
+then you can uniquely work out where
+each beamlet is deflected but of course
+
+ align:start position:0%
+each beamlet is deflected but of course
+ 
+
+ align:start position:0%
+each beamlet is deflected but of course
+you only get like n beamlets of points
+
+ align:start position:0%
+you only get like n beamlets of points
+ 
+
+ align:start position:0%
+you only get like n beamlets of points
+of data and it's like it doesn't look
+
+ align:start position:0%
+of data and it's like it doesn't look
+ 
+
+ align:start position:0%
+of data and it's like it doesn't look
+pretty you can't put in nature that sort
+
+ align:start position:0%
+pretty you can't put in nature that sort
+ 
+
+ align:start position:0%
+pretty you can't put in nature that sort
+of thing so people move very quickly
+
+ align:start position:0%
+of thing so people move very quickly
+ 
+
+ align:start position:0%
+of thing so people move very quickly
+away from that technique so now we have
+
+ align:start position:0%
+away from that technique so now we have
+ 
+
+ align:start position:0%
+away from that technique so now we have
+data that's impossible to analyze it's
+
+ align:start position:0%
+data that's impossible to analyze it's
+ 
+
+ align:start position:0%
+data that's impossible to analyze it's
+very beautiful whereas we used to have
+
+ align:start position:0%
+very beautiful whereas we used to have
+ 
+
+ align:start position:0%
+very beautiful whereas we used to have
+data that was entirely analyzable but
+
+ align:start position:0%
+data that was entirely analyzable but
+ 
+
+ align:start position:0%
+data that was entirely analyzable but
+not very beautiful so I have opinions
+
+ align:start position:0%
+not very beautiful so I have opinions
+ 
+
+ align:start position:0%
+not very beautiful so I have opinions
+this abely just a finite number of like
+
+ align:start position:0%
+this abely just a finite number of like
+ 
+
+ align:start position:0%
+this abely just a finite number of like
+r no I mean this this is entirely to do
+
+ align:start position:0%
+r no I mean this this is entirely to do
+ 
+
+ align:start position:0%
+r no I mean this this is entirely to do
+with um this is not to do with the
+
+ align:start position:0%
+with um this is not to do with the
+ 
+
+ align:start position:0%
+with um this is not to do with the
+finite number of R this is still to do
+
+ align:start position:0%
+finite number of R this is still to do
+ 
+
+ align:start position:0%
+finite number of R this is still to do
+with our nice like initially uniform
+
+ align:start position:0%
+with our nice like initially uniform
+ 
+
+ align:start position:0%
+with our nice like initially uniform
+beam it's just the way that we segment
+
+ align:start position:0%
+beam it's just the way that we segment
+ 
+
+ align:start position:0%
+beam it's just the way that we segment
+up the final image these dots don't
+
+ align:start position:0%
+up the final image these dots don't
+ 
+
+ align:start position:0%
+up the final image these dots don't
+really exist you actually in reality
+
+ align:start position:0%
+really exist you actually in reality
+ 
+
+ align:start position:0%
+really exist you actually in reality
+you're trying to
+
+ align:start position:0%
+you're trying to
+ 
+
+ align:start position:0%
+you're trying to
+find this is where I'm probably going to
+
+ align:start position:0%
+find this is where I'm probably going to
+ 
+
+ align:start position:0%
+find this is where I'm probably going to
+get it wrong you're trying to find
+
+ align:start position:0%
+get it wrong you're trying to find
+ 
+
+ align:start position:0%
+get it wrong you're trying to find
+Regions which contain the same intensity
+
+ align:start position:0%
+Regions which contain the same intensity
+ 
+
+ align:start position:0%
+Regions which contain the same intensity
+as one of these initial squares and
+
+ align:start position:0%
+as one of these initial squares and
+ 
+
+ align:start position:0%
+as one of these initial squares and
+you're trying to sort of tile them
+
+ align:start position:0%
+you're trying to sort of tile them
+ 
+
+ align:start position:0%
+you're trying to sort of tile them
+together in such a way that you don't
+
+ align:start position:0%
+together in such a way that you don't
+ 
+
+ align:start position:0%
+together in such a way that you don't
+have to have something that looks like a
+
+ align:start position:0%
+have to have something that looks like a
+ 
+
+ align:start position:0%
+have to have something that looks like a
+congressional district right
+
+ align:start position:0%
+congressional district right
+ 
+
+ align:start position:0%
+congressional district right
+where okay because that this is silly
+
+ align:start position:0%
+where okay because that this is silly
+ 
+
+ align:start position:0%
+where okay because that this is silly
+like that's unlikely to happen so we're
+
+ align:start position:0%
+like that's unlikely to happen so we're
+ 
+
+ align:start position:0%
+like that's unlikely to happen so we're
+trying to this is you know you could
+
+ align:start position:0%
+trying to this is you know you could
+ 
+
+ align:start position:0%
+trying to this is you know you could
+maybe use this algorithm to sort out a
+
+ align:start position:0%
+maybe use this algorithm to sort out a
+ 
+
+ align:start position:0%
+maybe use this algorithm to sort out a
+lot of problems in this
+
+ align:start position:0%
+lot of problems in this
+ 
+
+ align:start position:0%
+lot of problems in this
+anyway so at the same time bot uh was
+
+ align:start position:0%
+anyway so at the same time bot uh was
+ 
+
+ align:start position:0%
+anyway so at the same time bot uh was
+working on an algorithm that ended up
+
+ align:start position:0%
+working on an algorithm that ended up
+ 
+
+ align:start position:0%
+working on an algorithm that ended up
+doing the same thing and this is in jpp
+
+ align:start position:0%
+doing the same thing and this is in jpp
+ 
+
+ align:start position:0%
+doing the same thing and this is in jpp
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+2017 this paper is something like 120
+
+ align:start position:0%
+2017 this paper is something like 120
+ 
+
+ align:start position:0%
+2017 this paper is something like 120
+pages long very much helps to have your
+
+ align:start position:0%
+pages long very much helps to have your
+ 
+
+ align:start position:0%
+pages long very much helps to have your
+decent advisor be the Ed for and chief
+
+ align:start position:0%
+decent advisor be the Ed for and chief
+ 
+
+ align:start position:0%
+decent advisor be the Ed for and chief
+of jvp if you want publ paper L and they
+
+ align:start position:0%
+of jvp if you want publ paper L and they
+ 
+
+ align:start position:0%
+of jvp if you want publ paper L and they
+use a very interesting technique called
+
+ align:start position:0%
+use a very interesting technique called
+ 
+
+ align:start position:0%
+use a very interesting technique called
+the I'm probably G to say this WR and I
+
+ align:start position:0%
+the I'm probably G to say this WR and I
+ 
+
+ align:start position:0%
+the I'm probably G to say this WR and I
+certainly hand all the Accents in my
+
+ align:start position:0%
+certainly hand all the Accents in my
+ 
+
+ align:start position:0%
+certainly hand all the Accents in my
+notes Here M
+
+ align:start position:0%
+notes Here M
+ 
+
+ align:start position:0%
+notes Here M
+and optimal
+
+ align:start position:0%
+and optimal
+ 
+
+ align:start position:0%
+and optimal
+transport this optimal transport
+
+ align:start position:0%
+transport this optimal transport
+ 
+
+ align:start position:0%
+transport this optimal transport
+algorithm had actually won someone the
+
+ align:start position:0%
+algorithm had actually won someone the
+ 
+
+ align:start position:0%
+algorithm had actually won someone the
+fields medal only a few years before
+
+ align:start position:0%
+fields medal only a few years before
+ 
+
+ align:start position:0%
+fields medal only a few years before
+Cedric vanan wears his incredibly huge B
+
+ align:start position:0%
+Cedric vanan wears his incredibly huge B
+ 
+
+ align:start position:0%
+Cedric vanan wears his incredibly huge B
+ties and he has a wonderful book called
+
+ align:start position:0%
+ties and he has a wonderful book called
+ 
+
+ align:start position:0%
+ties and he has a wonderful book called
+The Life of the theorem where he
+
+ align:start position:0%
+The Life of the theorem where he
+ 
+
+ align:start position:0%
+The Life of the theorem where he
+discusses how gra cedri but so this
+
+ align:start position:0%
+discusses how gra cedri but so this
+ 
+
+ align:start position:0%
+discusses how gra cedri but so this
+algorithm was derived not at all to do
+
+ align:start position:0%
+algorithm was derived not at all to do
+ 
+
+ align:start position:0%
+algorithm was derived not at all to do
+with proton radiography but it is to do
+
+ align:start position:0%
+with proton radiography but it is to do
+ 
+
+ align:start position:0%
+with proton radiography but it is to do
+with how we how what is the most like
+
+ align:start position:0%
+with how we how what is the most like
+ 
+
+ align:start position:0%
+with how we how what is the most like
+conservative way to map one function
+
+ align:start position:0%
+conservative way to map one function
+ 
+
+ align:start position:0%
+conservative way to map one function
+into another function like this and once
+
+ align:start position:0%
+into another function like this and once
+ 
+
+ align:start position:0%
+into another function like this and once
+you derive that you can then put it back
+
+ align:start position:0%
+you derive that you can then put it back
+ 
+
+ align:start position:0%
+you derive that you can then put it back
+where you started with so this also
+
+ align:start position:0%
+where you started with so this also
+ 
+
+ align:start position:0%
+where you started with so this also
+enables you to do this same inverse
+
+ align:start position:0%
+enables you to do this same inverse
+ 
+
+ align:start position:0%
+enables you to do this same inverse
+problem like this and I'm not even gonna
+
+ align:start position:0%
+problem like this and I'm not even gonna
+ 
+
+ align:start position:0%
+problem like this and I'm not even gonna
+slightly go through my guess at what the
+
+ align:start position:0%
+slightly go through my guess at what the
+ 
+
+ align:start position:0%
+slightly go through my guess at what the
+mor amp equation does because I don't
+
+ align:start position:0%
+mor amp equation does because I don't
+ 
+
+ align:start position:0%
+mor amp equation does because I don't
+have um but it seems to work they give
+
+ align:start position:0%
+have um but it seems to work they give
+ 
+
+ align:start position:0%
+have um but it seems to work they give
+similar results turns out this is much
+
+ align:start position:0%
+similar results turns out this is much
+ 
+
+ align:start position:0%
+similar results turns out this is much
+faster I think most people
+
+ align:start position:0%
+faster I think most people
+ 
+
+ align:start position:0%
+faster I think most people
+use some version of this at the moment
+
+ align:start position:0%
+use some version of this at the moment
+ 
+
+ align:start position:0%
+use some version of this at the moment
+um but this one is maybe it easier to
+
+ align:start position:0%
+um but this one is maybe it easier to
+ 
+
+ align:start position:0%
+um but this one is maybe it easier to
+understand um so both of these give sort
+
+ align:start position:0%
+understand um so both of these give sort
+ 
+
+ align:start position:0%
+understand um so both of these give sort
+of similar results with slightly
+
+ align:start position:0%
+of similar results with slightly
+ 
+
+ align:start position:0%
+of similar results with slightly
+different techniques and I think in the
+
+ align:start position:0%
+different techniques and I think in the
+ 
+
+ align:start position:0%
+different techniques and I think in the
+end cassim wrote a code based on bot's
+
+ align:start position:0%
+end cassim wrote a code based on bot's
+ 
+
+ align:start position:0%
+end cassim wrote a code based on bot's
+paper that was faster than what bot had
+
+ align:start position:0%
+paper that was faster than what bot had
+ 
+
+ align:start position:0%
+paper that was faster than what bot had
+done so I think people have converged on
+
+ align:start position:0%
+done so I think people have converged on
+ 
+
+ align:start position:0%
+done so I think people have converged on
+using something to do with this and
+
+ align:start position:0%
+using something to do with this and
+ 
+
+ align:start position:0%
+using something to do with this and
+again these techniques were mostly uh
+
+ align:start position:0%
+again these techniques were mostly uh
+ 
+
+ align:start position:0%
+again these techniques were mostly uh
+invented for proton radiography but now
+
+ align:start position:0%
+invented for proton radiography but now
+ 
+
+ align:start position:0%
+invented for proton radiography but now
+uh as we said the mathematics is the
+
+ align:start position:0%
+uh as we said the mathematics is the
+ 
+
+ align:start position:0%
+uh as we said the mathematics is the
+same for phography I have not seen
+
+ align:start position:0%
+same for phography I have not seen
+ 
+
+ align:start position:0%
+same for phography I have not seen
+anyone use either technique to properly
+
+ align:start position:0%
+anyone use either technique to properly
+ 
+
+ align:start position:0%
+anyone use either technique to properly
+analyze phography should be possible yes
+
+ align:start position:0%
+analyze phography should be possible yes
+ 
+
+ align:start position:0%
+analyze phography should be possible yes
+how does this problem differ from more
+
+ align:start position:0%
+how does this problem differ from more
+ 
+
+ align:start position:0%
+how does this problem differ from more
+General tomography problems we encounter
+
+ align:start position:0%
+General tomography problems we encounter
+ 
+
+ align:start position:0%
+General tomography problems we encounter
+right like CT you know tomography when
+
+ align:start position:0%
+right like CT you know tomography when
+ 
+
+ align:start position:0%
+right like CT you know tomography when
+people do tomographic reconstru there's
+
+ align:start position:0%
+people do tomographic reconstru there's
+ 
+
+ align:start position:0%
+people do tomographic reconstru there's
+no tomography here we only have one line
+
+ align:start position:0%
+no tomography here we only have one line
+ 
+
+ align:start position:0%
+no tomography here we only have one line
+of s you can't do a tomographic
+
+ align:start position:0%
+of s you can't do a tomographic
+ 
+
+ align:start position:0%
+of s you can't do a tomographic
+reconstruction yeah I mean you can okay
+
+ align:start position:0%
+reconstruction yeah I mean you can okay
+ 
+
+ align:start position:0%
+reconstruction yeah I mean you can okay
+so now you can ask yourself if I have
+
+ align:start position:0%
+so now you can ask yourself if I have
+ 
+
+ align:start position:0%
+so now you can ask yourself if I have
+multiple lines of site can I do
+
+ align:start position:0%
+multiple lines of site can I do
+ 
+
+ align:start position:0%
+multiple lines of site can I do
+tomographic
+
+ align:start position:0%
+tomographic
+ 
+
+ align:start position:0%
+tomographic
+reconstruction which like yes obviously
+
+ align:start position:0%
+reconstruction which like yes obviously
+ 
+
+ align:start position:0%
+reconstruction which like yes obviously
+but it's also hard but you know it's
+
+ align:start position:0%
+but it's also hard but you know it's
+ 
+
+ align:start position:0%
+but it's also hard but you know it's
+might be possible but this is a single
+
+ align:start position:0%
+might be possible but this is a single
+ 
+
+ align:start position:0%
+might be possible but this is a single
+line of sight so we're not trying to ah
+
+ align:start position:0%
+line of sight so we're not trying to ah
+ 
+
+ align:start position:0%
+line of sight so we're not trying to ah
+thank you is the mistake I've been
+
+ align:start position:0%
+thank you is the mistake I've been
+ 
+
+ align:start position:0%
+thank you is the mistake I've been
+making we are not actually getting this
+
+ align:start position:0%
+making we are not actually getting this
+ 
+
+ align:start position:0%
+making we are not actually getting this
+out we are getting our best guess at
+
+ align:start position:0%
+out we are getting our best guess at
+ 
+
+ align:start position:0%
+out we are getting our best guess at
+this out right so this is not a full
+
+ align:start position:0%
+this out right so this is not a full
+ 
+
+ align:start position:0%
+this out right so this is not a full
+threedimensional
+
+ align:start position:0%
+threedimensional
+ 
+
+ align:start position:0%
+threedimensional
+reconstruction this is still a
+
+ align:start position:0%
+reconstruction this is still a
+ 
+
+ align:start position:0%
+reconstruction this is still a
+reconstruction of the line
+
+ align:start position:0%
+reconstruction of the line
+ 
+
+ align:start position:0%
+reconstruction of the line
+integrated uh electron it here so we
+
+ align:start position:0%
+integrated uh electron it here so we
+ 
+
+ align:start position:0%
+integrated uh electron it here so we
+yeah yeah that's a good point I forgot
+
+ align:start position:0%
+yeah yeah that's a good point I forgot
+ 
+
+ align:start position:0%
+yeah yeah that's a good point I forgot
+about that and so and it's sort of
+
+ align:start position:0%
+about that and so and it's sort of
+ 
+
+ align:start position:0%
+about that and so and it's sort of
+obvious that you should be able to do
+
+ align:start position:0%
+obvious that you should be able to do
+ 
+
+ align:start position:0%
+obvious that you should be able to do
+that but it's still there still can be
+
+ align:start position:0%
+that but it's still there still can be
+ 
+
+ align:start position:0%
+that but it's still there still can be
+multiple profiles that still produce the
+
+ align:start position:0%
+multiple profiles that still produce the
+ 
+
+ align:start position:0%
+multiple profiles that still produce the
+same intensity distribution so it's
+
+ align:start position:0%
+same intensity distribution so it's
+ 
+
+ align:start position:0%
+same intensity distribution so it's
+still not particularly well posed if you
+
+ align:start position:0%
+still not particularly well posed if you
+ 
+
+ align:start position:0%
+still not particularly well posed if you
+do have some cor sticks inside your
+
+ align:start position:0%
+do have some cor sticks inside your
+ 
+
+ align:start position:0%
+do have some cor sticks inside your
+detector image none of these work right
+
+ align:start position:0%
+detector image none of these work right
+ 
+
+ align:start position:0%
+detector image none of these work right
+so we no longer are able to do the
+
+ align:start position:0%
+so we no longer are able to do the
+ 
+
+ align:start position:0%
+so we no longer are able to do the
+Reconstruction you can actually have a
+
+ align:start position:0%
+Reconstruction you can actually have a
+ 
+
+ align:start position:0%
+Reconstruction you can actually have a
+go at doing the Reconstruction if you
+
+ align:start position:0%
+go at doing the Reconstruction if you
+ 
+
+ align:start position:0%
+go at doing the Reconstruction if you
+have some strong PRI so if you put you
+
+ align:start position:0%
+have some strong PRI so if you put you
+ 
+
+ align:start position:0%
+have some strong PRI so if you put you
+have some optimization algorithm that
+
+ align:start position:0%
+have some optimization algorithm that
+ 
+
+ align:start position:0%
+have some optimization algorithm that
+thinks like there's a shop here and that
+
+ align:start position:0%
+thinks like there's a shop here and that
+ 
+
+ align:start position:0%
+thinks like there's a shop here and that
+shop is going to cause cor sticks and I
+
+ align:start position:0%
+shop is going to cause cor sticks and I
+ 
+
+ align:start position:0%
+shop is going to cause cor sticks and I
+think the cor sticks will look like this
+
+ align:start position:0%
+think the cor sticks will look like this
+ 
+
+ align:start position:0%
+think the cor sticks will look like this
+you might be able to do it but of course
+
+ align:start position:0%
+you might be able to do it but of course
+ 
+
+ align:start position:0%
+you might be able to do it but of course
+you don't have Ro PRI the techniques are
+
+ align:start position:0%
+you don't have Ro PRI the techniques are
+ 
+
+ align:start position:0%
+you don't have Ro PRI the techniques are
+very line integrated as I just
+
+ align:start position:0%
+very line integrated as I just
+ 
+
+ align:start position:0%
+very line integrated as I just
+remembered and pointed out here so we're
+
+ align:start position:0%
+remembered and pointed out here so we're
+ 
+
+ align:start position:0%
+remembered and pointed out here so we're
+not getting the full 3d structure that's
+
+ align:start position:0%
+not getting the full 3d structure that's
+ 
+
+ align:start position:0%
+not getting the full 3d structure that's
+maybe a bit too much to ask from a
+
+ align:start position:0%
+maybe a bit too much to ask from a
+ 
+
+ align:start position:0%
+maybe a bit too much to ask from a
+diagnostic which is clearly integrated
+
+ align:start position:0%
+diagnostic which is clearly integrated
+ 
+
+ align:start position:0%
+diagnostic which is clearly integrated
+but it's still a limitation and then the
+
+ align:start position:0%
+but it's still a limitation and then the
+ 
+
+ align:start position:0%
+but it's still a limitation and then the
+final problem that uh in protal
+
+ align:start position:0%
+final problem that uh in protal
+ 
+
+ align:start position:0%
+final problem that uh in protal
+radiography is particularly profound is
+
+ align:start position:0%
+radiography is particularly profound is
+ 
+
+ align:start position:0%
+radiography is particularly profound is
+actually how
+
+ align:start position:0%
+actually how
+ 
+
+ align:start position:0%
+actually how
+reproducible this
+
+ align:start position:0%
+reproducible this
+ 
+
+ align:start position:0%
+reproducible this
+is how reproducible your initial reer
+
+ align:start position:0%
+is how reproducible your initial reer
+ 
+
+ align:start position:0%
+is how reproducible your initial reer
+I'm going to run out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space your initial intensity is because
+
+ align:start position:0%
+space your initial intensity is because
+ 
+
+ align:start position:0%
+space your initial intensity is because
+they before you do the experiment you
+
+ align:start position:0%
+they before you do the experiment you
+ 
+
+ align:start position:0%
+they before you do the experiment you
+find your La beam through the chamber
+
+ align:start position:0%
+find your La beam through the chamber
+ 
+
+ align:start position:0%
+find your La beam through the chamber
+and you measure that beam profile but
+
+ align:start position:0%
+and you measure that beam profile but
+ 
+
+ align:start position:0%
+and you measure that beam profile but
+then when you actually do the experiment
+
+ align:start position:0%
+then when you actually do the experiment
+ 
+
+ align:start position:0%
+then when you actually do the experiment
+that beam profile changes you know
+
+ align:start position:0%
+that beam profile changes you know
+ 
+
+ align:start position:0%
+that beam profile changes you know
+lasers are not completely stable the
+
+ align:start position:0%
+lasers are not completely stable the
+ 
+
+ align:start position:0%
+lasers are not completely stable the
+beam profile changes from time to time
+
+ align:start position:0%
+beam profile changes from time to time
+ 
+
+ align:start position:0%
+beam profile changes from time to time
+and so that means what you think you're
+
+ align:start position:0%
+and so that means what you think you're
+ 
+
+ align:start position:0%
+and so that means what you think you're
+mapping from here to here is actually
+
+ align:start position:0%
+mapping from here to here is actually
+ 
+
+ align:start position:0%
+mapping from here to here is actually
+slightly different and that's going to
+
+ align:start position:0%
+slightly different and that's going to
+ 
+
+ align:start position:0%
+slightly different and that's going to
+introduce Some Noise this is very um
+
+ align:start position:0%
+introduce Some Noise this is very um
+ 
+
+ align:start position:0%
+introduce Some Noise this is very um
+important for proton radiography where
+
+ align:start position:0%
+important for proton radiography where
+ 
+
+ align:start position:0%
+important for proton radiography where
+it's very hard to measure the beam for a
+
+ align:start position:0%
+it's very hard to measure the beam for a
+ 
+
+ align:start position:0%
+it's very hard to measure the beam for a
+laser chy setup you actually have more a
+
+ align:start position:0%
+laser chy setup you actually have more a
+ 
+
+ align:start position:0%
+laser chy setup you actually have more a
+chance you can put a beam split before
+
+ align:start position:0%
+chance you can put a beam split before
+ 
+
+ align:start position:0%
+chance you can put a beam split before
+the plasma and Sample the beam itself so
+
+ align:start position:0%
+the plasma and Sample the beam itself so
+ 
+
+ align:start position:0%
+the plasma and Sample the beam itself so
+you can actually simultaneously measure
+
+ align:start position:0%
+you can actually simultaneously measure
+ 
+
+ align:start position:0%
+you can actually simultaneously measure
+this Quant
+
+ align:start position:0%
+this Quant
+ 
+
+ align:start position:0%
+this Quant
+and this qu um so there's a lot of scope
+
+ align:start position:0%
+and this qu um so there's a lot of scope
+ 
+
+ align:start position:0%
+and this qu um so there's a lot of scope
+prod some really cool
+
+ align:start position:0%
+prod some really cool
+ 
+
+ align:start position:0%
+prod some really cool
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+questions yeah are obvious practical
+
+ align:start position:0%
+questions yeah are obvious practical
+ 
+
+ align:start position:0%
+questions yeah are obvious practical
+reasons why you wouldn't be
+
+ align:start position:0%
+reasons why you wouldn't be
+ 
+
+ align:start position:0%
+reasons why you wouldn't be
+measuring differences like I think it's
+
+ align:start position:0%
+measuring differences like I think it's
+ 
+
+ align:start position:0%
+measuring differences like I think it's
+a great idea no one's done it I want to
+
+ align:start position:0%
+a great idea no one's done it I want to
+ 
+
+ align:start position:0%
+a great idea no one's done it I want to
+do it yeah absolutely so it seems to me
+
+ align:start position:0%
+do it yeah absolutely so it seems to me
+ 
+
+ align:start position:0%
+do it yeah absolutely so it seems to me
+like if you have these images at
+
+ align:start position:0%
+like if you have these images at
+ 
+
+ align:start position:0%
+like if you have these images at
+different places you should be able to
+
+ align:start position:0%
+different places you should be able to
+ 
+
+ align:start position:0%
+different places you should be able to
+reconstruct the trajectories of the Rays
+
+ align:start position:0%
+reconstruct the trajectories of the Rays
+ 
+
+ align:start position:0%
+reconstruct the trajectories of the Rays
+and that would give you more information
+
+ align:start position:0%
+and that would give you more information
+ 
+
+ align:start position:0%
+and that would give you more information
+and in fact in some of the first
+
+ align:start position:0%
+and in fact in some of the first
+ 
+
+ align:start position:0%
+and in fact in some of the first
+radiography papers this is discussed
+
+ align:start position:0%
+radiography papers this is discussed
+ 
+
+ align:start position:0%
+radiography papers this is discussed
+from looking at like the position
+
+ align:start position:0%
+from looking at like the position
+ 
+
+ align:start position:0%
+from looking at like the position
+through multiple Stacks but I haven't
+
+ align:start position:0%
+through multiple Stacks but I haven't
+ 
+
+ align:start position:0%
+through multiple Stacks but I haven't
+seen it actually done practice kind of
+
+ align:start position:0%
+seen it actually done practice kind of
+ 
+
+ align:start position:0%
+seen it actually done practice kind of
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+it it's you
+
+ align:start position:0%
+it it's you
+ 
+
+ align:start position:0%
+it it's you
+know typically all your energy gets
+
+ align:start position:0%
+know typically all your energy gets
+ 
+
+ align:start position:0%
+know typically all your energy gets
+depit yeah so I think that's the problem
+
+ align:start position:0%
+depit yeah so I think that's the problem
+ 
+
+ align:start position:0%
+depit yeah so I think that's the problem
+but I I I like the idea like it's a cool
+
+ align:start position:0%
+but I I I like the idea like it's a cool
+ 
+
+ align:start position:0%
+but I I I like the idea like it's a cool
+like if it worked if people used this
+
+ align:start position:0%
+like if it worked if people used this
+ 
+
+ align:start position:0%
+like if it worked if people used this
+yeah so you can definitely do should be
+
+ align:start position:0%
+yeah so you can definitely do should be
+ 
+
+ align:start position:0%
+yeah so you can definitely do should be
+relatively straightforward yeah the
+
+ align:start position:0%
+relatively straightforward yeah the
+ 
+
+ align:start position:0%
+relatively straightforward yeah the
+other thing you can do is you could put
+
+ align:start position:0%
+other thing you can do is you could put
+ 
+
+ align:start position:0%
+other thing you can do is you could put
+multiple lasers different wavelengths
+
+ align:start position:0%
+multiple lasers different wavelengths
+ 
+
+ align:start position:0%
+multiple lasers different wavelengths
+through and they' be deflected by
+
+ align:start position:0%
+through and they' be deflected by
+ 
+
+ align:start position:0%
+through and they' be deflected by
+different angles and then you could use
+
+ align:start position:0%
+different angles and then you could use
+ 
+
+ align:start position:0%
+different angles and then you could use
+those different deflections like when
+
+ align:start position:0%
+those different deflections like when
+ 
+
+ align:start position:0%
+those different deflections like when
+you have your proton radiography and use
+
+ align:start position:0%
+you have your proton radiography and use
+ 
+
+ align:start position:0%
+you have your proton radiography and use
+different particle energies to determine
+
+ align:start position:0%
+different particle energies to determine
+ 
+
+ align:start position:0%
+different particle energies to determine
+between electric and magnetic fields uh
+
+ align:start position:0%
+between electric and magnetic fields uh
+ 
+
+ align:start position:0%
+between electric and magnetic fields uh
+here that we don't have uh electric and
+
+ align:start position:0%
+here that we don't have uh electric and
+ 
+
+ align:start position:0%
+here that we don't have uh electric and
+magnetic fields there's only one thing
+
+ align:start position:0%
+magnetic fields there's only one thing
+ 
+
+ align:start position:0%
+magnetic fields there's only one thing
+that can cause the deflection which is
+
+ align:start position:0%
+that can cause the deflection which is
+ 
+
+ align:start position:0%
+that can cause the deflection which is
+density gradients but those different
+
+ align:start position:0%
+density gradients but those different
+ 
+
+ align:start position:0%
+density gradients but those different
+colors will enable you to so you can
+
+ align:start position:0%
+colors will enable you to so you can
+ 
+
+ align:start position:0%
+colors will enable you to so you can
+imagine that one of your other Rays
+
+ align:start position:0%
+imagine that one of your other Rays
+ 
+
+ align:start position:0%
+imagine that one of your other Rays
+would get deflected less if it had a
+
+ align:start position:0%
+would get deflected less if it had a
+ 
+
+ align:start position:0%
+would get deflected less if it had a
+shorter wavelength and it would take a
+
+ align:start position:0%
+shorter wavelength and it would take a
+ 
+
+ align:start position:0%
+shorter wavelength and it would take a
+trajectory like that and by comparing
+
+ align:start position:0%
+trajectory like that and by comparing
+ 
+
+ align:start position:0%
+trajectory like that and by comparing
+where it ends up in one wavelength to
+
+ align:start position:0%
+where it ends up in one wavelength to
+ 
+
+ align:start position:0%
+where it ends up in one wavelength to
+where it ends up in the other like you
+
+ align:start position:0%
+where it ends up in the other like you
+ 
+
+ align:start position:0%
+where it ends up in the other like you
+should be able to actually precisely
+
+ align:start position:0%
+should be able to actually precisely
+ 
+
+ align:start position:0%
+should be able to actually precisely
+measure the angle made and therefore
+
+ align:start position:0%
+measure the angle made and therefore
+ 
+
+ align:start position:0%
+measure the angle made and therefore
+what I haven't seen anyone try that
+
+ align:start position:0%
+what I haven't seen anyone try that
+ 
+
+ align:start position:0%
+what I haven't seen anyone try that
+yet yeah when you're responding to J's
+
+ align:start position:0%
+yet yeah when you're responding to J's
+ 
+
+ align:start position:0%
+yet yeah when you're responding to J's
+question you mentioned that you know you
+
+ align:start position:0%
+question you mentioned that you know you
+ 
+
+ align:start position:0%
+question you mentioned that you know you
+only have one line of sight here but you
+
+ align:start position:0%
+only have one line of sight here but you
+ 
+
+ align:start position:0%
+only have one line of sight here but you
+know you're detector able to X and Y
+
+ align:start position:0%
+know you're detector able to X and Y
+ 
+
+ align:start position:0%
+know you're detector able to X and Y
+positions of
+
+ align:start position:0%
+positions of
+ 
+
+ align:start position:0%
+positions of
+your intensity you consider like each
+
+ align:start position:0%
+your intensity you consider like each
+ 
+
+ align:start position:0%
+your intensity you consider like each
+pixel as a different line of sight but
+
+ align:start position:0%
+pixel as a different line of sight but
+ 
+
+ align:start position:0%
+pixel as a different line of sight but
+it's only a cord through a certain bit
+
+ align:start position:0%
+it's only a cord through a certain bit
+ 
+
+ align:start position:0%
+it's only a cord through a certain bit
+of the plasma it's not a line of sight
+
+ align:start position:0%
+of the plasma it's not a line of sight
+ 
+
+ align:start position:0%
+of the plasma it's not a line of sight
+through the same bit of plasma when we
+
+ align:start position:0%
+through the same bit of plasma when we
+ 
+
+ align:start position:0%
+through the same bit of plasma when we
+do tomography you know you imagine
+
+ align:start position:0%
+do tomography you know you imagine
+ 
+
+ align:start position:0%
+do tomography you know you imagine
+you've got some cloud and you're looking
+
+ align:start position:0%
+you've got some cloud and you're looking
+ 
+
+ align:start position:0%
+you've got some cloud and you're looking
+through the same bit of plasma from
+
+ align:start position:0%
+through the same bit of plasma from
+ 
+
+ align:start position:0%
+through the same bit of plasma from
+multiple angles here you're looking at
+
+ align:start position:0%
+multiple angles here you're looking at
+ 
+
+ align:start position:0%
+multiple angles here you're looking at
+different bits of plasma so you can't
+
+ align:start position:0%
+different bits of plasma so you can't
+ 
+
+ align:start position:0%
+different bits of plasma so you can't
+tomographically reconstruct the density
+
+ align:start position:0%
+tomographically reconstruct the density
+ 
+
+ align:start position:0%
+tomographically reconstruct the density
+there because it's literally a different
+
+ align:start position:0%
+there because it's literally a different
+ 
+
+ align:start position:0%
+there because it's literally a different
+place in the
+
+ align:start position:0%
+place in the
+ 
+
+ align:start position:0%
+place in the
+plas um sure okay
+
+ align:start position:0%
+plas um sure okay
+ 
+
+ align:start position:0%
+plas um sure okay
+yes yeah um I would have expected like a
+
+ align:start position:0%
+yes yeah um I would have expected like a
+ 
+
+ align:start position:0%
+yes yeah um I would have expected like a
+smaller wave length to be deflected more
+
+ align:start position:0%
+smaller wave length to be deflected more
+ 
+
+ align:start position:0%
+smaller wave length to be deflected more
+because the length scale of the plasma
+
+ align:start position:0%
+because the length scale of the plasma
+ 
+
+ align:start position:0%
+because the length scale of the plasma
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+large we are doing geometric optics so
+
+ align:start position:0%
+large we are doing geometric optics so
+ 
+
+ align:start position:0%
+large we are doing geometric optics so
+we don't actually care about the
+
+ align:start position:0%
+we don't actually care about the
+ 
+
+ align:start position:0%
+we don't actually care about the
+wavelengths yeah so in in systems where
+
+ align:start position:0%
+wavelengths yeah so in in systems where
+ 
+
+ align:start position:0%
+wavelengths yeah so in in systems where
+you're not doing geometric optics where
+
+ align:start position:0%
+you're not doing geometric optics where
+ 
+
+ align:start position:0%
+you're not doing geometric optics where
+the wavelength is comparable to the size
+
+ align:start position:0%
+the wavelength is comparable to the size
+ 
+
+ align:start position:0%
+the wavelength is comparable to the size
+of the plasma that would be a defraction
+
+ align:start position:0%
+of the plasma that would be a defraction
+ 
+
+ align:start position:0%
+of the plasma that would be a defraction
+effect and that would be more important
+
+ align:start position:0%
+effect and that would be more important
+ 
+
+ align:start position:0%
+effect and that would be more important
+but we are actually doing geometric
+
+ align:start position:0%
+but we are actually doing geometric
+ 
+
+ align:start position:0%
+but we are actually doing geometric
+optics where that isn't important but
+
+ align:start position:0%
+optics where that isn't important but
+ 
+
+ align:start position:0%
+optics where that isn't important but
+you're right so all of the stuff I've
+
+ align:start position:0%
+you're right so all of the stuff I've
+ 
+
+ align:start position:0%
+you're right so all of the stuff I've
+been doing the reason I drawing straight
+
+ align:start position:0%
+been doing the reason I drawing straight
+ 
+
+ align:start position:0%
+been doing the reason I drawing straight
+lines everywhere is I'm doing geometric
+
+ align:start position:0%
+lines everywhere is I'm doing geometric
+ 
+
+ align:start position:0%
+lines everywhere is I'm doing geometric
+optics I'm doing Ray Optics so in that
+
+ align:start position:0%
+optics I'm doing Ray Optics so in that
+ 
+
+ align:start position:0%
+optics I'm doing Ray Optics so in that
+case it come the different deflection
+
+ align:start position:0%
+case it come the different deflection
+ 
+
+ align:start position:0%
+case it come the different deflection
+angle comes about it because for short
+
+ align:start position:0%
+angle comes about it because for short
+ 
+
+ align:start position:0%
+angle comes about it because for short
+the wavelengths the critical density is
+
+ align:start position:0%
+the wavelengths the critical density is
+ 
+
+ align:start position:0%
+the wavelengths the critical density is
+higher and so this quantity becomes
+
+ align:start position:0%
+higher and so this quantity becomes
+ 
+
+ align:start position:0%
+higher and so this quantity becomes
+store this is just a little bit of a
+
+ align:start position:0%
+store this is just a little bit of a
+ 
+
+ align:start position:0%
+store this is just a little bit of a
+light-hearted little picture show and we
+
+ align:start position:0%
+light-hearted little picture show and we
+ 
+
+ align:start position:0%
+light-hearted little picture show and we
+may finish off the lecture with this so
+
+ align:start position:0%
+may finish off the lecture with this so
+ 
+
+ align:start position:0%
+may finish off the lecture with this so
+we might get started on deometry
+
+ align:start position:0%
+we might get started on deometry
+ 
+
+ align:start position:0%
+we might get started on deometry
+depending on how I feel um but here are
+
+ align:start position:0%
+depending on how I feel um but here are
+ 
+
+ align:start position:0%
+depending on how I feel um but here are
+some nice pictures uh phography is
+
+ align:start position:0%
+some nice pictures uh phography is
+ 
+
+ align:start position:0%
+some nice pictures uh phography is
+absolutely everywhere you have already
+
+ align:start position:0%
+absolutely everywhere you have already
+ 
+
+ align:start position:0%
+absolutely everywhere you have already
+seen many Shadow graphs before uh if
+
+ align:start position:0%
+seen many Shadow graphs before uh if
+ 
+
+ align:start position:0%
+seen many Shadow graphs before uh if
+you've ever seen a mirage uh that is a
+
+ align:start position:0%
+you've ever seen a mirage uh that is a
+ 
+
+ align:start position:0%
+you've ever seen a mirage uh that is a
+shadow graph that is the natural
+
+ align:start position:0%
+shadow graph that is the natural
+ 
+
+ align:start position:0%
+shadow graph that is the natural
+focusing of Light by refracted index
+
+ align:start position:0%
+focusing of Light by refracted index
+ 
+
+ align:start position:0%
+focusing of Light by refracted index
+gradients in hot air right and you see
+
+ align:start position:0%
+gradients in hot air right and you see
+ 
+
+ align:start position:0%
+gradients in hot air right and you see
+that shimmering you see the fact that
+
+ align:start position:0%
+that shimmering you see the fact that
+ 
+
+ align:start position:0%
+that shimmering you see the fact that
+there appear to be mountains below where
+
+ align:start position:0%
+there appear to be mountains below where
+ 
+
+ align:start position:0%
+there appear to be mountains below where
+the mountains actually are that's
+
+ align:start position:0%
+the mountains actually are that's
+ 
+
+ align:start position:0%
+the mountains actually are that's
+because the Rays of Light have been Bent
+
+ align:start position:0%
+because the Rays of Light have been Bent
+ 
+
+ align:start position:0%
+because the Rays of Light have been Bent
+by the hot there back upwards into your
+
+ align:start position:0%
+by the hot there back upwards into your
+ 
+
+ align:start position:0%
+by the hot there back upwards into your
+ey so this is what I mean when I say
+
+ align:start position:0%
+ey so this is what I mean when I say
+ 
+
+ align:start position:0%
+ey so this is what I mean when I say
+that shogy is not an image whenever you
+
+ align:start position:0%
+that shogy is not an image whenever you
+ 
+
+ align:start position:0%
+that shogy is not an image whenever you
+take a shogy thing what you're really
+
+ align:start position:0%
+take a shogy thing what you're really
+ 
+
+ align:start position:0%
+take a shogy thing what you're really
+seeing is some sort of
+
+ align:start position:0%
+seeing is some sort of
+ 
+
+ align:start position:0%
+seeing is some sort of
+Mirage so the first person to ever we
+
+ align:start position:0%
+Mirage so the first person to ever we
+ 
+
+ align:start position:0%
+Mirage so the first person to ever we
+know study cograph was this guy John Pat
+
+ align:start position:0%
+know study cograph was this guy John Pat
+ 
+
+ align:start position:0%
+know study cograph was this guy John Pat
+Uh that's a portrait of him here is his
+
+ align:start position:0%
+Uh that's a portrait of him here is his
+ 
+
+ align:start position:0%
+Uh that's a portrait of him here is his
+shadow GS he actually Drew these by hand
+
+ align:start position:0%
+shadow GS he actually Drew these by hand
+ 
+
+ align:start position:0%
+shadow GS he actually Drew these by hand
+because he didn't have cameras back in
+
+ align:start position:0%
+because he didn't have cameras back in
+ 
+
+ align:start position:0%
+because he didn't have cameras back in
+the day this is the guy he's in 1793
+
+ align:start position:0%
+the day this is the guy he's in 1793
+ 
+
+ align:start position:0%
+the day this is the guy he's in 1793
+is's actually deeply unpleasant he was a
+
+ align:start position:0%
+is's actually deeply unpleasant he was a
+ 
+
+ align:start position:0%
+is's actually deeply unpleasant he was a
+jacobine he was responsible for deaths
+
+ align:start position:0%
+jacobine he was responsible for deaths
+ 
+
+ align:start position:0%
+jacobine he was responsible for deaths
+of hundreds of thousands of people in
+
+ align:start position:0%
+of hundreds of thousands of people in
+ 
+
+ align:start position:0%
+of hundreds of thousands of people in
+French Revolution and he was eventually
+
+ align:start position:0%
+French Revolution and he was eventually
+ 
+
+ align:start position:0%
+French Revolution and he was eventually
+murdered in the bathtub
+
+ align:start position:0%
+murdered in the bathtub
+ 
+
+ align:start position:0%
+murdered in the bathtub
+but before he was murdered he had a very
+
+ align:start position:0%
+but before he was murdered he had a very
+ 
+
+ align:start position:0%
+but before he was murdered he had a very
+famous guest he had a Prett famous guest
+
+ align:start position:0%
+famous guest he had a Prett famous guest
+ 
+
+ align:start position:0%
+famous guest he had a Prett famous guest
+who came and actually sat and he
+
+ align:start position:0%
+who came and actually sat and he
+ 
+
+ align:start position:0%
+who came and actually sat and he
+sketched the shadowgraphic effect of uh
+
+ align:start position:0%
+sketched the shadowgraphic effect of uh
+ 
+
+ align:start position:0%
+sketched the shadowgraphic effect of uh
+this uh the the effect of this guest's
+
+ align:start position:0%
+this uh the the effect of this guest's
+ 
+
+ align:start position:0%
+this uh the the effect of this guest's
+old head on on the air around so does
+
+ align:start position:0%
+old head on on the air around so does
+ 
+
+ align:start position:0%
+old head on on the air around so does
+anyone know who this is it is of course
+
+ align:start position:0%
+anyone know who this is it is of course
+ 
+
+ align:start position:0%
+anyone know who this is it is of course
+Ben Franklin so there we go who was made
+
+ align:start position:0%
+Ben Franklin so there we go who was made
+ 
+
+ align:start position:0%
+Ben Franklin so there we go who was made
+a habit of hanging around in France um
+
+ align:start position:0%
+a habit of hanging around in France um
+ 
+
+ align:start position:0%
+a habit of hanging around in France um
+um but these days we usually do things
+
+ align:start position:0%
+um but these days we usually do things
+ 
+
+ align:start position:0%
+um but these days we usually do things
+which are much more exciting than Ben
+
+ align:start position:0%
+which are much more exciting than Ben
+ 
+
+ align:start position:0%
+which are much more exciting than Ben
+Franklin's head so here are several
+
+ align:start position:0%
+Franklin's head so here are several
+ 
+
+ align:start position:0%
+Franklin's head so here are several
+different models uh these are models for
+
+ align:start position:0%
+different models uh these are models for
+ 
+
+ align:start position:0%
+different models uh these are models for
+the Gemini capsule um that was you know
+
+ align:start position:0%
+the Gemini capsule um that was you know
+ 
+
+ align:start position:0%
+the Gemini capsule um that was you know
+part of the American space program and
+
+ align:start position:0%
+part of the American space program and
+ 
+
+ align:start position:0%
+part of the American space program and
+they want to understand that the shop
+
+ align:start position:0%
+they want to understand that the shop
+ 
+
+ align:start position:0%
+they want to understand that the shop
+waves are around so you can see that
+
+ align:start position:0%
+waves are around so you can see that
+ 
+
+ align:start position:0%
+waves are around so you can see that
+this caption is coming from right to
+
+ align:start position:0%
+this caption is coming from right to
+ 
+
+ align:start position:0%
+this caption is coming from right to
+left it's got this blunt end here we
+
+ align:start position:0%
+left it's got this blunt end here we
+ 
+
+ align:start position:0%
+left it's got this blunt end here we
+have this very well defined bow shock
+
+ align:start position:0%
+have this very well defined bow shock
+ 
+
+ align:start position:0%
+have this very well defined bow shock
+structure here do we think that that's
+
+ align:start position:0%
+structure here do we think that that's
+ 
+
+ align:start position:0%
+structure here do we think that that's
+atic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a big intensity variation right
+
+ align:start position:0%
+it's a big intensity variation right
+ 
+
+ align:start position:0%
+it's a big intensity variation right
+it's extremely black here and it's very
+
+ align:start position:0%
+it's extremely black here and it's very
+ 
+
+ align:start position:0%
+it's extremely black here and it's very
+bright around the outside here behind it
+
+ align:start position:0%
+bright around the outside here behind it
+ 
+
+ align:start position:0%
+bright around the outside here behind it
+what do we have we got a set of shocks
+
+ align:start position:0%
+what do we have we got a set of shocks
+ 
+
+ align:start position:0%
+what do we have we got a set of shocks
+there a shock here there's another set
+
+ align:start position:0%
+there a shock here there's another set
+ 
+
+ align:start position:0%
+there a shock here there's another set
+of shocks coming off here and here which
+
+ align:start position:0%
+of shocks coming off here and here which
+ 
+
+ align:start position:0%
+of shocks coming off here and here which
+interact with the outer shocks and then
+
+ align:start position:0%
+interact with the outer shocks and then
+ 
+
+ align:start position:0%
+interact with the outer shocks and then
+we have this beautifully turbulent flow
+
+ align:start position:0%
+we have this beautifully turbulent flow
+ 
+
+ align:start position:0%
+we have this beautifully turbulent flow
+behind it right and the same thing here
+
+ align:start position:0%
+behind it right and the same thing here
+ 
+
+ align:start position:0%
+behind it right and the same thing here
+on this uh more hemispherical object and
+
+ align:start position:0%
+on this uh more hemispherical object and
+ 
+
+ align:start position:0%
+on this uh more hemispherical object and
+so I don't know how big these were but
+
+ align:start position:0%
+so I don't know how big these were but
+ 
+
+ align:start position:0%
+so I don't know how big these were but
+you can do this in a wind tunnel in this
+
+ align:start position:0%
+you can do this in a wind tunnel in this
+ 
+
+ align:start position:0%
+you can do this in a wind tunnel in this
+case it was probably not a wind tunnel
+
+ align:start position:0%
+case it was probably not a wind tunnel
+ 
+
+ align:start position:0%
+case it was probably not a wind tunnel
+but a static gas that they fired these
+
+ align:start position:0%
+but a static gas that they fired these
+ 
+
+ align:start position:0%
+but a static gas that they fired these
+through with a cannon and then they
+
+ align:start position:0%
+through with a cannon and then they
+ 
+
+ align:start position:0%
+through with a cannon and then they
+would have used some sort of bright
+
+ align:start position:0%
+would have used some sort of bright
+ 
+
+ align:start position:0%
+would have used some sort of bright
+light source probably not a laser in
+
+ align:start position:0%
+light source probably not a laser in
+ 
+
+ align:start position:0%
+light source probably not a laser in
+order to do
+
+ align:start position:0%
+order to do
+ 
+
+ align:start position:0%
+order to do
+this um also when you start looking the
+
+ align:start position:0%
+this um also when you start looking the
+ 
+
+ align:start position:0%
+this um also when you start looking the
+literature you get lots of beautiful
+
+ align:start position:0%
+literature you get lots of beautiful
+ 
+
+ align:start position:0%
+literature you get lots of beautiful
+pictures of bullets bullets are
+
+ align:start position:0%
+pictures of bullets bullets are
+ 
+
+ align:start position:0%
+pictures of bullets bullets are
+particularly good sources so um I
+
+ align:start position:0%
+particularly good sources so um I
+ 
+
+ align:start position:0%
+particularly good sources so um I
+believe in this picture the gun is just
+
+ align:start position:0%
+believe in this picture the gun is just
+ 
+
+ align:start position:0%
+believe in this picture the gun is just
+here and so you can see the cloud of uh
+
+ align:start position:0%
+here and so you can see the cloud of uh
+ 
+
+ align:start position:0%
+here and so you can see the cloud of uh
+exhaust Vapor coming out of the Gun
+
+ align:start position:0%
+exhaust Vapor coming out of the Gun
+ 
+
+ align:start position:0%
+exhaust Vapor coming out of the Gun
+Barrel you can see this is the sound
+
+ align:start position:0%
+Barrel you can see this is the sound
+ 
+
+ align:start position:0%
+Barrel you can see this is the sound
+wave of the the shot going off and then
+
+ align:start position:0%
+wave of the the shot going off and then
+ 
+
+ align:start position:0%
+wave of the the shot going off and then
+supersonically moving away from the gun
+
+ align:start position:0%
+supersonically moving away from the gun
+ 
+
+ align:start position:0%
+supersonically moving away from the gun
+is the bullet we can see the trail with
+
+ align:start position:0%
+is the bullet we can see the trail with
+ 
+
+ align:start position:0%
+is the bullet we can see the trail with
+the uh fine structure behind it and
+
+ align:start position:0%
+the uh fine structure behind it and
+ 
+
+ align:start position:0%
+the uh fine structure behind it and
+these very clearly defined shock waves
+
+ align:start position:0%
+these very clearly defined shock waves
+ 
+
+ align:start position:0%
+these very clearly defined shock waves
+here and again the shock waves have
+
+ align:start position:0%
+here and again the shock waves have
+ 
+
+ align:start position:0%
+here and again the shock waves have
+these light and dark regions
+
+ align:start position:0%
+these light and dark regions
+ 
+
+ align:start position:0%
+these light and dark regions
+corresponding to changes in the fact
+
+ align:start position:0%
+corresponding to changes in the fact
+ 
+
+ align:start position:0%
+corresponding to changes in the fact
+index and this is I think a zoom in of
+
+ align:start position:0%
+index and this is I think a zoom in of
+ 
+
+ align:start position:0%
+index and this is I think a zoom in of
+that photograph I can't be sure it looks
+
+ align:start position:0%
+that photograph I can't be sure it looks
+ 
+
+ align:start position:0%
+that photograph I can't be sure it looks
+like it is
+
+ align:start position:0%
+like it is
+ 
+
+ align:start position:0%
+like it is
+um of that so you can see you get an
+
+ align:start position:0%
+um of that so you can see you get an
+ 
+
+ align:start position:0%
+um of that so you can see you get an
+extraordinary amount of qualitative
+
+ align:start position:0%
+extraordinary amount of qualitative
+ 
+
+ align:start position:0%
+extraordinary amount of qualitative
+detail what you can measure from this
+
+ align:start position:0%
+detail what you can measure from this
+ 
+
+ align:start position:0%
+detail what you can measure from this
+straight away is the shock opening angle
+
+ align:start position:0%
+straight away is the shock opening angle
+ 
+
+ align:start position:0%
+straight away is the shock opening angle
+so you can measure the mark number
+
+ align:start position:0%
+so you can measure the mark number
+ 
+
+ align:start position:0%
+so you can measure the mark number
+what's going to be a lot more tricky
+
+ align:start position:0%
+what's going to be a lot more tricky
+ 
+
+ align:start position:0%
+what's going to be a lot more tricky
+look at these pictures is to work out
+
+ align:start position:0%
+look at these pictures is to work out
+ 
+
+ align:start position:0%
+look at these pictures is to work out
+what the density and temperature of the
+
+ align:start position:0%
+what the density and temperature of the
+ 
+
+ align:start position:0%
+what the density and temperature of the
+air is everywhere inside this picture
+
+ align:start position:0%
+air is everywhere inside this picture
+ 
+
+ align:start position:0%
+air is everywhere inside this picture
+that's not really going to be doable um
+
+ align:start position:0%
+that's not really going to be doable um
+ 
+
+ align:start position:0%
+that's not really going to be doable um
+because we're not in this small
+
+ align:start position:0%
+because we're not in this small
+ 
+
+ align:start position:0%
+because we're not in this small
+intensity variation regime we've
+
+ align:start position:0%
+intensity variation regime we've
+ 
+
+ align:start position:0%
+intensity variation regime we've
+deliberately gone into the regime where
+
+ align:start position:0%
+deliberately gone into the regime where
+ 
+
+ align:start position:0%
+deliberately gone into the regime where
+we get Co stics which means we also get
+
+ align:start position:0%
+we get Co stics which means we also get
+ 
+
+ align:start position:0%
+we get Co stics which means we also get
+strong intensity variation so we can
+
+ align:start position:0%
+strong intensity variation so we can
+ 
+
+ align:start position:0%
+strong intensity variation so we can
+actually measure if we were looking at
+
+ align:start position:0%
+actually measure if we were looking at
+ 
+
+ align:start position:0%
+actually measure if we were looking at
+on those small intensity variation
+
+ align:start position:0%
+on those small intensity variation
+ 
+
+ align:start position:0%
+on those small intensity variation
+shatter graphs it would be very boring
+
+ align:start position:0%
+shatter graphs it would be very boring
+ 
+
+ align:start position:0%
+shatter graphs it would be very boring
+it would mostly be gray we very very
+
+ align:start position:0%
+it would mostly be gray we very very
+ 
+
+ align:start position:0%
+it would mostly be gray we very very
+tiny modulations so yeah on the on
+
+ align:start position:0%
+tiny modulations so yeah on the on
+ 
+
+ align:start position:0%
+tiny modulations so yeah on the on
+figure B why are the light and do
+
+ align:start position:0%
+figure B why are the light and do
+ 
+
+ align:start position:0%
+figure B why are the light and do
+regions above and below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SWAT I'll put on on the problem
+
+ align:start position:0%
+SWAT I'll put on on the problem
+ 
+
+ align:start position:0%
+SWAT I'll put on on the problem
+set I don't know immediately uh why that
+
+ align:start position:0%
+set I don't know immediately uh why that
+ 
+
+ align:start position:0%
+set I don't know immediately uh why that
+is the thing is also to remember if you
+
+ align:start position:0%
+is the thing is also to remember if you
+ 
+
+ align:start position:0%
+is the thing is also to remember if you
+end up in a regime where you have cor
+
+ align:start position:0%
+end up in a regime where you have cor
+ 
+
+ align:start position:0%
+end up in a regime where you have cor
+sticks and you have strong deflections
+
+ align:start position:0%
+sticks and you have strong deflections
+ 
+
+ align:start position:0%
+sticks and you have strong deflections
+of your rays you may actually end up in
+
+ align:start position:0%
+of your rays you may actually end up in
+ 
+
+ align:start position:0%
+of your rays you may actually end up in
+a regime where the Rays don't go through
+
+ align:start position:0%
+a regime where the Rays don't go through
+ 
+
+ align:start position:0%
+a regime where the Rays don't go through
+your first Optics so they may be
+
+ align:start position:0%
+your first Optics so they may be
+ 
+
+ align:start position:0%
+your first Optics so they may be
+deflected out of the collection volume
+
+ align:start position:0%
+deflected out of the collection volume
+ 
+
+ align:start position:0%
+deflected out of the collection volume
+of your first optic and then they will
+
+ align:start position:0%
+of your first optic and then they will
+ 
+
+ align:start position:0%
+of your first optic and then they will
+just shut as dark regions so you can
+
+ align:start position:0%
+just shut as dark regions so you can
+ 
+
+ align:start position:0%
+just shut as dark regions so you can
+also have overlay theography effects
+
+ align:start position:0%
+also have overlay theography effects
+ 
+
+ align:start position:0%
+also have overlay theography effects
+what are effectively scharen type
+
+ align:start position:0%
+what are effectively scharen type
+ 
+
+ align:start position:0%
+what are effectively scharen type
+effects where we are rejecting Rays by
+
+ align:start position:0%
+effects where we are rejecting Rays by
+ 
+
+ align:start position:0%
+effects where we are rejecting Rays by
+their angle but that's just due to the
+
+ align:start position:0%
+their angle but that's just due to the
+ 
+
+ align:start position:0%
+their angle but that's just due to the
+physical SI of the Optics we use so I
+
+ align:start position:0%
+physical SI of the Optics we use so I
+ 
+
+ align:start position:0%
+physical SI of the Optics we use so I
+don't know if that's the case here but
+
+ align:start position:0%
+don't know if that's the case here but
+ 
+
+ align:start position:0%
+don't know if that's the case here but
+it does complicate the interpretation
+
+ align:start position:0%
+it does complicate the interpretation
+ 
+
+ align:start position:0%
+it does complicate the interpretation
+further yes in the previous pictures
+
+ align:start position:0%
+further yes in the previous pictures
+ 
+
+ align:start position:0%
+further yes in the previous pictures
+with the J capsules um there's like
+
+ align:start position:0%
+with the J capsules um there's like
+ 
+
+ align:start position:0%
+with the J capsules um there's like
+there's the effect of pressure waves
+
+ align:start position:0%
+there's the effect of pressure waves
+ 
+
+ align:start position:0%
+there's the effect of pressure waves
+shock waves and there's also like
+
+ align:start position:0%
+shock waves and there's also like
+ 
+
+ align:start position:0%
+shock waves and there's also like
+supposedly intense Heating that
+
+ align:start position:0%
+supposedly intense Heating that
+ 
+
+ align:start position:0%
+supposedly intense Heating that
+shouldn't be like on the
+
+ align:start position:0%
+shouldn't be like on the
+ 
+
+ align:start position:0%
+shouldn't be like on the
+surface and that's also going to change
+
+ align:start position:0%
+surface and that's also going to change
+ 
+
+ align:start position:0%
+surface and that's also going to change
+refra yes which effect of those like how
+
+ align:start position:0%
+refra yes which effect of those like how
+ 
+
+ align:start position:0%
+refra yes which effect of those like how
+could we distinguish it something it's
+
+ align:start position:0%
+could we distinguish it something it's
+ 
+
+ align:start position:0%
+could we distinguish it something it's
+like the termal refra index change or
+
+ align:start position:0%
+like the termal refra index change or
+ 
+
+ align:start position:0%
+like the termal refra index change or
+pressure in air in air yeah I think
+
+ align:start position:0%
+pressure in air in air yeah I think
+ 
+
+ align:start position:0%
+pressure in air in air yeah I think
+that's very difficult because they both
+
+ align:start position:0%
+that's very difficult because they both
+ 
+
+ align:start position:0%
+that's very difficult because they both
+are just the change in refractive index
+
+ align:start position:0%
+are just the change in refractive index
+ 
+
+ align:start position:0%
+are just the change in refractive index
+um yeah I don't think it's possible to
+
+ align:start position:0%
+um yeah I don't think it's possible to
+ 
+
+ align:start position:0%
+um yeah I don't think it's possible to
+tell the difference between those two
+
+ align:start position:0%
+tell the difference between those two
+ 
+
+ align:start position:0%
+tell the difference between those two
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um there's also some funky pictures in
+
+ align:start position:0%
+um there's also some funky pictures in
+ 
+
+ align:start position:0%
+um there's also some funky pictures in
+this book this looks pretty
+
+ align:start position:0%
+this book this looks pretty
+ 
+
+ align:start position:0%
+this book this looks pretty
+straightforward the bullets is actually
+
+ align:start position:0%
+straightforward the bullets is actually
+ 
+
+ align:start position:0%
+straightforward the bullets is actually
+flying
+
+ align:start position:0%
+flying
+ 
+
+ align:start position:0%
+flying
+backwards I don't know why they did that
+
+ align:start position:0%
+backwards I don't know why they did that
+ 
+
+ align:start position:0%
+backwards I don't know why they did that
+but there we go this is a great book by
+
+ align:start position:0%
+but there we go this is a great book by
+ 
+
+ align:start position:0%
+but there we go this is a great book by
+the way settled sh a shadowgraph
+
+ align:start position:0%
+the way settled sh a shadowgraph
+ 
+
+ align:start position:0%
+the way settled sh a shadowgraph
+techniques it's got wonderful pictures
+
+ align:start position:0%
+techniques it's got wonderful pictures
+ 
+
+ align:start position:0%
+techniques it's got wonderful pictures
+inside it if you want to know more about
+
+ align:start position:0%
+inside it if you want to know more about
+ 
+
+ align:start position:0%
+inside it if you want to know more about
+this it's in bibliography uh on the
+
+ align:start position:0%
+this it's in bibliography uh on the
+ 
+
+ align:start position:0%
+this it's in bibliography uh on the
+syllabus and it's a great read but I
+
+ align:start position:0%
+syllabus and it's a great read but I
+ 
+
+ align:start position:0%
+syllabus and it's a great read but I
+appreciate most people not going to be
+
+ align:start position:0%
+appreciate most people not going to be
+ 
+
+ align:start position:0%
+appreciate most people not going to be
+using chirography in schen but still
+
+ align:start position:0%
+using chirography in schen but still
+ 
+
+ align:start position:0%
+using chirography in schen but still
+good stuff
+
+ align:start position:0%
+good stuff
+ 
+
+ align:start position:0%
+good stuff
+um but you don't have to fire bullets at
+
+ align:start position:0%
+um but you don't have to fire bullets at
+ 
+
+ align:start position:0%
+um but you don't have to fire bullets at
+things this is actually a picture of the
+
+ align:start position:0%
+things this is actually a picture of the
+ 
+
+ align:start position:0%
+things this is actually a picture of the
+author of this book writing his book
+
+ align:start position:0%
+author of this book writing his book
+ 
+
+ align:start position:0%
+author of this book writing his book
+next speing unit there he is head not
+
+ align:start position:0%
+next speing unit there he is head not
+ 
+
+ align:start position:0%
+next speing unit there he is head not
+impressive as Frank that there's his
+
+ align:start position:0%
+impressive as Frank that there's his
+ 
+
+ align:start position:0%
+impressive as Frank that there's his
+computer as he types away and you can
+
+ align:start position:0%
+computer as he types away and you can
+ 
+
+ align:start position:0%
+computer as he types away and you can
+see that you can actually make these
+
+ align:start position:0%
+see that you can actually make these
+ 
+
+ align:start position:0%
+see that you can actually make these
+measurements um even in relatively
+
+ align:start position:0%
+measurements um even in relatively
+ 
+
+ align:start position:0%
+measurements um even in relatively
+benign condition and that's because
+
+ align:start position:0%
+benign condition and that's because
+ 
+
+ align:start position:0%
+benign condition and that's because
+again if we put our detector further and
+
+ align:start position:0%
+again if we put our detector further and
+ 
+
+ align:start position:0%
+again if we put our detector further and
+further back even small variations in
+
+ align:start position:0%
+further back even small variations in
+ 
+
+ align:start position:0%
+further back even small variations in
+the angle going through the refra medium
+
+ align:start position:0%
+the angle going through the refra medium
+ 
+
+ align:start position:0%
+the angle going through the refra medium
+are going to be mapped into large
+
+ align:start position:0%
+are going to be mapped into large
+ 
+
+ align:start position:0%
+are going to be mapped into large
+intensity variations so people use this
+
+ align:start position:0%
+intensity variations so people use this
+ 
+
+ align:start position:0%
+intensity variations so people use this
+technique to look for flows or air you
+
+ align:start position:0%
+technique to look for flows or air you
+ 
+
+ align:start position:0%
+technique to look for flows or air you
+can look for flows of air for all sorts
+
+ align:start position:0%
+can look for flows of air for all sorts
+ 
+
+ align:start position:0%
+can look for flows of air for all sorts
+of reasons a pretty benign reason would
+
+ align:start position:0%
+of reasons a pretty benign reason would
+ 
+
+ align:start position:0%
+of reasons a pretty benign reason would
+be in the H track industry if you want
+
+ align:start position:0%
+be in the H track industry if you want
+ 
+
+ align:start position:0%
+be in the H track industry if you want
+to see whether these things are working
+
+ align:start position:0%
+to see whether these things are working
+ 
+
+ align:start position:0%
+to see whether these things are working
+so there are applications for
+
+ align:start position:0%
+so there are applications for
+ 
+
+ align:start position:0%
+so there are applications for
+shadowgraphic techniques and Sh
+
+ align:start position:0%
+shadowgraphic techniques and Sh
+ 
+
+ align:start position:0%
+shadowgraphic techniques and Sh
+techniques just in very like benign
+
+ align:start position:0%
+techniques just in very like benign
+ 
+
+ align:start position:0%
+techniques just in very like benign
+conditions like
+
+ align:start position:0%
+conditions like
+ 
+
+ align:start position:0%
+conditions like
+this but we of course are interested in
+
+ align:start position:0%
+this but we of course are interested in
+ 
+
+ align:start position:0%
+this but we of course are interested in
+plasmas uh so we talked about this a
+
+ align:start position:0%
+plasmas uh so we talked about this a
+ 
+
+ align:start position:0%
+plasmas uh so we talked about this a
+little bit more on the last lecture but
+
+ align:start position:0%
+little bit more on the last lecture but
+ 
+
+ align:start position:0%
+little bit more on the last lecture but
+remember that we need a very bright
+
+ align:start position:0%
+remember that we need a very bright
+ 
+
+ align:start position:0%
+remember that we need a very bright
+light source to overcome the self
+
+ align:start position:0%
+light source to overcome the self
+ 
+
+ align:start position:0%
+light source to overcome the self
+emission from a plasma so that means we
+
+ align:start position:0%
+emission from a plasma so that means we
+ 
+
+ align:start position:0%
+emission from a plasma so that means we
+really have to go to a laser we just
+
+ align:start position:0%
+really have to go to a laser we just
+ 
+
+ align:start position:0%
+really have to go to a laser we just
+don't have any light sources that are
+
+ align:start position:0%
+don't have any light sources that are
+ 
+
+ align:start position:0%
+don't have any light sources that are
+great lasers are actually not ideal for
+
+ align:start position:0%
+great lasers are actually not ideal for
+ 
+
+ align:start position:0%
+great lasers are actually not ideal for
+any of these techniques you really want
+
+ align:start position:0%
+any of these techniques you really want
+ 
+
+ align:start position:0%
+any of these techniques you really want
+to have a nice large focal spot that
+
+ align:start position:0%
+to have a nice large focal spot that
+ 
+
+ align:start position:0%
+to have a nice large focal spot that
+turns out to be true for shog graphy as
+
+ align:start position:0%
+turns out to be true for shog graphy as
+ 
+
+ align:start position:0%
+turns out to be true for shog graphy as
+well but we didn't really go into why uh
+
+ align:start position:0%
+well but we didn't really go into why uh
+ 
+
+ align:start position:0%
+well but we didn't really go into why uh
+and so this small focal spot gives us
+
+ align:start position:0%
+and so this small focal spot gives us
+ 
+
+ align:start position:0%
+and so this small focal spot gives us
+quite limited dynamic range not to
+
+ align:start position:0%
+quite limited dynamic range not to
+ 
+
+ align:start position:0%
+quite limited dynamic range not to
+mention the fact that we are assuming in
+
+ align:start position:0%
+mention the fact that we are assuming in
+ 
+
+ align:start position:0%
+mention the fact that we are assuming in
+all of this that we don't have any
+
+ align:start position:0%
+all of this that we don't have any
+ 
+
+ align:start position:0%
+all of this that we don't have any
+coherence effects so we don't have
+
+ align:start position:0%
+coherence effects so we don't have
+ 
+
+ align:start position:0%
+coherence effects so we don't have
+interference and we'll talk a lot about
+
+ align:start position:0%
+interference and we'll talk a lot about
+ 
+
+ align:start position:0%
+interference and we'll talk a lot about
+interference in a little bit and so uh
+
+ align:start position:0%
+interference in a little bit and so uh
+ 
+
+ align:start position:0%
+interference in a little bit and so uh
+really we don't want to have that
+
+ align:start position:0%
+really we don't want to have that
+ 
+
+ align:start position:0%
+really we don't want to have that
+coherence when we're doing schin and
+
+ align:start position:0%
+coherence when we're doing schin and
+ 
+
+ align:start position:0%
+coherence when we're doing schin and
+shog graphy but if we've got a laser we
+
+ align:start position:0%
+shog graphy but if we've got a laser we
+ 
+
+ align:start position:0%
+shog graphy but if we've got a laser we
+tend to have coher appearance that we
+
+ align:start position:0%
+tend to have coher appearance that we
+ 
+
+ align:start position:0%
+tend to have coher appearance that we
+don't want so these are not great but
+
+ align:start position:0%
+don't want so these are not great but
+ 
+
+ align:start position:0%
+don't want so these are not great but
+you can still get some nice images out
+
+ align:start position:0%
+you can still get some nice images out
+ 
+
+ align:start position:0%
+you can still get some nice images out
+of it um here's a device called an X
+
+ align:start position:0%
+of it um here's a device called an X
+ 
+
+ align:start position:0%
+of it um here's a device called an X
+pinch um it consists of two wires that
+
+ align:start position:0%
+pinch um it consists of two wires that
+ 
+
+ align:start position:0%
+pinch um it consists of two wires that
+are crossed here this is only one
+
+ align:start position:0%
+are crossed here this is only one
+ 
+
+ align:start position:0%
+are crossed here this is only one
+millimeter across here so this is a
+
+ align:start position:0%
+millimeter across here so this is a
+ 
+
+ align:start position:0%
+millimeter across here so this is a
+pretty small object and these are X-ray
+
+ align:start position:0%
+pretty small object and these are X-ray
+ 
+
+ align:start position:0%
+pretty small object and these are X-ray
+gated x-ray images of the X pinch we put
+
+ align:start position:0%
+gated x-ray images of the X pinch we put
+ 
+
+ align:start position:0%
+gated x-ray images of the X pinch we put
+in this case 200 kiloamps through each
+
+ align:start position:0%
+in this case 200 kiloamps through each
+ 
+
+ align:start position:0%
+in this case 200 kiloamps through each
+wire and it forms a plasma here which
+
+ align:start position:0%
+wire and it forms a plasma here which
+ 
+
+ align:start position:0%
+wire and it forms a plasma here which
+pinches the fields here are maybe 100 or
+
+ align:start position:0%
+pinches the fields here are maybe 100 or
+ 
+
+ align:start position:0%
+pinches the fields here are maybe 100 or
+a thousand Tesla and it pinches the
+
+ align:start position:0%
+a thousand Tesla and it pinches the
+ 
+
+ align:start position:0%
+a thousand Tesla and it pinches the
+plasma inwards like this compressing it
+
+ align:start position:0%
+plasma inwards like this compressing it
+ 
+
+ align:start position:0%
+plasma inwards like this compressing it
+up so it becomes extremely hot and it
+
+ align:start position:0%
+up so it becomes extremely hot and it
+ 
+
+ align:start position:0%
+up so it becomes extremely hot and it
+emits a burst of x-rays which you can
+
+ align:start position:0%
+emits a burst of x-rays which you can
+ 
+
+ align:start position:0%
+emits a burst of x-rays which you can
+then use for Imaging things so when we
+
+ align:start position:0%
+then use for Imaging things so when we
+ 
+
+ align:start position:0%
+then use for Imaging things so when we
+get on to uh self mission Diagnostics
+
+ align:start position:0%
+get on to uh self mission Diagnostics
+ 
+
+ align:start position:0%
+get on to uh self mission Diagnostics
+xray Diagnostics we'll talk a little bit
+
+ align:start position:0%
+xray Diagnostics we'll talk a little bit
+ 
+
+ align:start position:0%
+xray Diagnostics we'll talk a little bit
+about this so these are the x-ray images
+
+ align:start position:0%
+about this so these are the x-ray images
+ 
+
+ align:start position:0%
+about this so these are the x-ray images
+but this rather beautiful schan image
+
+ align:start position:0%
+but this rather beautiful schan image
+ 
+
+ align:start position:0%
+but this rather beautiful schan image
+was captured of this x pinch uh in 2008
+
+ align:start position:0%
+was captured of this x pinch uh in 2008
+ 
+
+ align:start position:0%
+was captured of this x pinch uh in 2008
+here they used a dark field schan system
+
+ align:start position:0%
+here they used a dark field schan system
+ 
+
+ align:start position:0%
+here they used a dark field schan system
+is a circular stop you can tell that
+
+ align:start position:0%
+is a circular stop you can tell that
+ 
+
+ align:start position:0%
+is a circular stop you can tell that
+because it looks up down symmetric so
+
+ align:start position:0%
+because it looks up down symmetric so
+ 
+
+ align:start position:0%
+because it looks up down symmetric so
+we're not we don't have a nice stage
+
+ align:start position:0%
+we're not we don't have a nice stage
+ 
+
+ align:start position:0%
+we're not we don't have a nice stage
+where we have some distinction uh
+
+ align:start position:0%
+where we have some distinction uh
+ 
+
+ align:start position:0%
+where we have some distinction uh
+between the different directions and you
+
+ align:start position:0%
+between the different directions and you
+ 
+
+ align:start position:0%
+between the different directions and you
+can tell it dark field because outside
+
+ align:start position:0%
+can tell it dark field because outside
+ 
+
+ align:start position:0%
+can tell it dark field because outside
+where there is no plasma it's dark here
+
+ align:start position:0%
+where there is no plasma it's dark here
+ 
+
+ align:start position:0%
+where there is no plasma it's dark here
+if it was light field this region would
+
+ align:start position:0%
+if it was light field this region would
+ 
+
+ align:start position:0%
+if it was light field this region would
+be filled with laser light and we'd have
+
+ align:start position:0%
+be filled with laser light and we'd have
+ 
+
+ align:start position:0%
+be filled with laser light and we'd have
+Darkness whereever we have lightness
+
+ align:start position:0%
+Darkness whereever we have lightness
+ 
+
+ align:start position:0%
+Darkness whereever we have lightness
+here and you can see a beautiful amount
+
+ align:start position:0%
+here and you can see a beautiful amount
+ 
+
+ align:start position:0%
+here and you can see a beautiful amount
+of detail this projector isn't really
+
+ align:start position:0%
+of detail this projector isn't really
+ 
+
+ align:start position:0%
+of detail this projector isn't really
+doing it justice um you can see in the
+
+ align:start position:0%
+doing it justice um you can see in the
+ 
+
+ align:start position:0%
+doing it justice um you can see in the
+center here this is the pinching region
+
+ align:start position:0%
+center here this is the pinching region
+ 
+
+ align:start position:0%
+center here this is the pinching region
+it's far too dense for all of the laser
+
+ align:start position:0%
+it's far too dense for all of the laser
+ 
+
+ align:start position:0%
+it's far too dense for all of the laser
+light to make it through it's much above
+
+ align:start position:0%
+light to make it through it's much above
+ 
+
+ align:start position:0%
+light to make it through it's much above
+the critical density and so there's very
+
+ align:start position:0%
+the critical density and so there's very
+ 
+
+ align:start position:0%
+the critical density and so there's very
+strong refraction of the laser light
+
+ align:start position:0%
+strong refraction of the laser light
+ 
+
+ align:start position:0%
+strong refraction of the laser light
+outwards dark in the center there's Jets
+
+ align:start position:0%
+outwards dark in the center there's Jets
+ 
+
+ align:start position:0%
+outwards dark in the center there's Jets
+of plasma going up and down out of this
+
+ align:start position:0%
+of plasma going up and down out of this
+ 
+
+ align:start position:0%
+of plasma going up and down out of this
+compressed region and there's also
+
+ align:start position:0%
+compressed region and there's also
+ 
+
+ align:start position:0%
+compressed region and there's also
+oblation streams coming off each of the
+
+ align:start position:0%
+oblation streams coming off each of the
+ 
+
+ align:start position:0%
+oblation streams coming off each of the
+wires which have this beautiful
+
+ align:start position:0%
+wires which have this beautiful
+ 
+
+ align:start position:0%
+wires which have this beautiful
+modulated pattern which is actually due
+
+ align:start position:0%
+modulated pattern which is actually due
+ 
+
+ align:start position:0%
+modulated pattern which is actually due
+to a instability in The Wire abelation
+
+ align:start position:0%
+to a instability in The Wire abelation
+ 
+
+ align:start position:0%
+to a instability in The Wire abelation
+process so this is extremely rich
+
+ align:start position:0%
+process so this is extremely rich
+ 
+
+ align:start position:0%
+process so this is extremely rich
+there's a lot of information you can get
+
+ align:start position:0%
+there's a lot of information you can get
+ 
+
+ align:start position:0%
+there's a lot of information you can get
+out of this even though it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modated another thing that's been done
+
+ align:start position:0%
+modated another thing that's been done
+ 
+
+ align:start position:0%
+modated another thing that's been done
+is using schen Imaging to image shocks
+
+ align:start position:0%
+is using schen Imaging to image shocks
+ 
+
+ align:start position:0%
+is using schen Imaging to image shocks
+uh in uh what's initially a gas but
+
+ align:start position:0%
+uh in uh what's initially a gas but
+ 
+
+ align:start position:0%
+uh in uh what's initially a gas but
+quickly becomes a plas
+
+ align:start position:0%
+quickly becomes a plas
+ 
+
+ align:start position:0%
+quickly becomes a plas
+so what we had in these experiments was
+
+ align:start position:0%
+so what we had in these experiments was
+ 
+
+ align:start position:0%
+so what we had in these experiments was
+a metal liner this is only about 5 mm
+
+ align:start position:0%
+a metal liner this is only about 5 mm
+ 
+
+ align:start position:0%
+a metal liner this is only about 5 mm
+across and it's still pretty small and
+
+ align:start position:0%
+across and it's still pretty small and
+ 
+
+ align:start position:0%
+across and it's still pretty small and
+it was filled with a gas 8 MBS of argon
+
+ align:start position:0%
+it was filled with a gas 8 MBS of argon
+ 
+
+ align:start position:0%
+it was filled with a gas 8 MBS of argon
+15 Ms of nitrogen uh a current was put
+
+ align:start position:0%
+15 Ms of nitrogen uh a current was put
+ 
+
+ align:start position:0%
+15 Ms of nitrogen uh a current was put
+up through this metal cylinder again the
+
+ align:start position:0%
+up through this metal cylinder again the
+ 
+
+ align:start position:0%
+up through this metal cylinder again the
+cylinder is only about that tall and
+
+ align:start position:0%
+cylinder is only about that tall and
+ 
+
+ align:start position:0%
+cylinder is only about that tall and
+that wide and as it does so it heats the
+
+ align:start position:0%
+that wide and as it does so it heats the
+ 
+
+ align:start position:0%
+that wide and as it does so it heats the
+outside of the cylinder and launches a
+
+ align:start position:0%
+outside of the cylinder and launches a
+ 
+
+ align:start position:0%
+outside of the cylinder and launches a
+shock wave inwards and that shock wave
+
+ align:start position:0%
+shock wave inwards and that shock wave
+ 
+
+ align:start position:0%
+shock wave inwards and that shock wave
+couples the gas and it launches this
+
+ align:start position:0%
+couples the gas and it launches this
+ 
+
+ align:start position:0%
+couples the gas and it launches this
+first shock wave in and as the current
+
+ align:start position:0%
+first shock wave in and as the current
+ 
+
+ align:start position:0%
+first shock wave in and as the current
+continues to rise you actually get above
+
+ align:start position:0%
+continues to rise you actually get above
+ 
+
+ align:start position:0%
+continues to rise you actually get above
+the Melt point of the metal and that
+
+ align:start position:0%
+the Melt point of the metal and that
+ 
+
+ align:start position:0%
+the Melt point of the metal and that
+launches another shock wave due to
+
+ align:start position:0%
+launches another shock wave due to
+ 
+
+ align:start position:0%
+launches another shock wave due to
+material strength that starts coming in
+
+ align:start position:0%
+material strength that starts coming in
+ 
+
+ align:start position:0%
+material strength that starts coming in
+so we get these converging shock waves
+
+ align:start position:0%
+so we get these converging shock waves
+ 
+
+ align:start position:0%
+so we get these converging shock waves
+the beautiful thing here is that in
+
+ align:start position:0%
+the beautiful thing here is that in
+ 
+
+ align:start position:0%
+the beautiful thing here is that in
+argon we had a beautifully circular
+
+ align:start position:0%
+argon we had a beautifully circular
+ 
+
+ align:start position:0%
+argon we had a beautifully circular
+shock but in nitrogen for some reason we
+
+ align:start position:0%
+shock but in nitrogen for some reason we
+ 
+
+ align:start position:0%
+shock but in nitrogen for some reason we
+got like this hexagonal shape of shock
+
+ align:start position:0%
+got like this hexagonal shape of shock
+ 
+
+ align:start position:0%
+got like this hexagonal shape of shock
+which has never been explained
+
+ align:start position:0%
+which has never been explained
+ 
+
+ align:start position:0%
+which has never been explained
+absolutely bizarre there's no sixfold
+
+ align:start position:0%
+absolutely bizarre there's no sixfold
+ 
+
+ align:start position:0%
+absolutely bizarre there's no sixfold
+symmetry in this system it shouldn't
+
+ align:start position:0%
+symmetry in this system it shouldn't
+ 
+
+ align:start position:0%
+symmetry in this system it shouldn't
+have it so there's some instability
+
+ align:start position:0%
+have it so there's some instability
+ 
+
+ align:start position:0%
+have it so there's some instability
+which is giving it this uh really
+
+ align:start position:0%
+which is giving it this uh really
+ 
+
+ align:start position:0%
+which is giving it this uh really
+bizarre shape and again this was dark
+
+ align:start position:0%
+bizarre shape and again this was dark
+ 
+
+ align:start position:0%
+bizarre shape and again this was dark
+field with a circular stop that's a
+
+ align:start position:0%
+field with a circular stop that's a
+ 
+
+ align:start position:0%
+field with a circular stop that's a
+pretty standard configuration dark field
+
+ align:start position:0%
+pretty standard configuration dark field
+ 
+
+ align:start position:0%
+pretty standard configuration dark field
+is a bit more sensitive than light field
+
+ align:start position:0%
+is a bit more sensitive than light field
+ 
+
+ align:start position:0%
+is a bit more sensitive than light field
+because if you see any light at all you
+
+ align:start position:0%
+because if you see any light at all you
+ 
+
+ align:start position:0%
+because if you see any light at all you
+know that it's been deflected and that's
+
+ align:start position:0%
+know that it's been deflected and that's
+ 
+
+ align:start position:0%
+know that it's been deflected and that's
+really what you're looking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and then
+
+ align:start position:0%
+here and then
+ 
+
+ align:start position:0%
+here and then
+phography uh this is an image that I
+
+ align:start position:0%
+phography uh this is an image that I
+ 
+
+ align:start position:0%
+phography uh this is an image that I
+took of uh an imploding wire array so
+
+ align:start position:0%
+took of uh an imploding wire array so
+ 
+
+ align:start position:0%
+took of uh an imploding wire array so
+again this thing is only about 16
+
+ align:start position:0%
+again this thing is only about 16
+ 
+
+ align:start position:0%
+again this thing is only about 16
+millimeters tall 16 millim in diameter
+
+ align:start position:0%
+millimeters tall 16 millim in diameter
+ 
+
+ align:start position:0%
+millimeters tall 16 millim in diameter
+we've got eight carbon rods here current
+
+ align:start position:0%
+we've got eight carbon rods here current
+ 
+
+ align:start position:0%
+we've got eight carbon rods here current
+goes up through the rods the blades
+
+ align:start position:0%
+goes up through the rods the blades
+ 
+
+ align:start position:0%
+goes up through the rods the blades
+plasma of them jross B Force accelerates
+
+ align:start position:0%
+plasma of them jross B Force accelerates
+ 
+
+ align:start position:0%
+plasma of them jross B Force accelerates
+theas inwards and you get a z pinch
+
+ align:start position:0%
+theas inwards and you get a z pinch
+ 
+
+ align:start position:0%
+theas inwards and you get a z pinch
+column in the center here and looking
+
+ align:start position:0%
+column in the center here and looking
+ 
+
+ align:start position:0%
+column in the center here and looking
+from the side using a green laser beam
+
+ align:start position:0%
+from the side using a green laser beam
+ 
+
+ align:start position:0%
+from the side using a green laser beam
+uh we can see that we've got Shadows
+
+ align:start position:0%
+uh we can see that we've got Shadows
+ 
+
+ align:start position:0%
+uh we can see that we've got Shadows
+corresponding to the four wires so
+
+ align:start position:0%
+corresponding to the four wires so
+ 
+
+ align:start position:0%
+corresponding to the four wires so
+there's four wires on this side and
+
+ align:start position:0%
+there's four wires on this side and
+ 
+
+ align:start position:0%
+there's four wires on this side and
+they're blocking the four wires on the
+
+ align:start position:0%
+they're blocking the four wires on the
+ 
+
+ align:start position:0%
+they're blocking the four wires on the
+other side and you can see the column of
+
+ align:start position:0%
+other side and you can see the column of
+ 
+
+ align:start position:0%
+other side and you can see the column of
+plasma in the middle here and what you
+
+ align:start position:0%
+plasma in the middle here and what you
+ 
+
+ align:start position:0%
+plasma in the middle here and what you
+can see is there these very strong
+
+ align:start position:0%
+can see is there these very strong
+ 
+
+ align:start position:0%
+can see is there these very strong
+modulations to the intensity these are
+
+ align:start position:0%
+modulations to the intensity these are
+ 
+
+ align:start position:0%
+modulations to the intensity these are
+Co sticks okay we also see modulations
+
+ align:start position:0%
+Co sticks okay we also see modulations
+ 
+
+ align:start position:0%
+Co sticks okay we also see modulations
+to the flow as we saw in the exit and
+
+ align:start position:0%
+to the flow as we saw in the exit and
+ 
+
+ align:start position:0%
+to the flow as we saw in the exit and
+these Co sticks mean that this data
+
+ align:start position:0%
+these Co sticks mean that this data
+ 
+
+ align:start position:0%
+these Co sticks mean that this data
+while very pretty is pretty useless
+
+ align:start position:0%
+while very pretty is pretty useless
+ 
+
+ align:start position:0%
+while very pretty is pretty useless
+there's not much we can actually do with
+
+ align:start position:0%
+there's not much we can actually do with
+ 
+
+ align:start position:0%
+there's not much we can actually do with
+it because we can't do any decent
+
+ align:start position:0%
+it because we can't do any decent
+ 
+
+ align:start position:0%
+it because we can't do any decent
+analysis but it does tell us because the
+
+ align:start position:0%
+analysis but it does tell us because the
+ 
+
+ align:start position:0%
+analysis but it does tell us because the
+course six are on a large range of
+
+ align:start position:0%
+course six are on a large range of
+ 
+
+ align:start position:0%
+course six are on a large range of
+different spatial scales that we must
+
+ align:start position:0%
+different spatial scales that we must
+ 
+
+ align:start position:0%
+different spatial scales that we must
+have density pertubations inside the
+
+ align:start position:0%
+have density pertubations inside the
+ 
+
+ align:start position:0%
+have density pertubations inside the
+plasma and a lot of different spatial
+
+ align:start position:0%
+plasma and a lot of different spatial
+ 
+
+ align:start position:0%
+plasma and a lot of different spatial
+scales and so this means that plasma is
+
+ align:start position:0%
+scales and so this means that plasma is
+ 
+
+ align:start position:0%
+scales and so this means that plasma is
+likely to be to so this is a little
+
+ align:start position:0%
+likely to be to so this is a little
+ 
+
+ align:start position:0%
+likely to be to so this is a little
+turbulent Z pinch inside a boss P
+
+ align:start position:0%
+turbulent Z pinch inside a boss P
+ 
+
+ align:start position:0%
+turbulent Z pinch inside a boss P
+machine so is that it oh and you can
+
+ align:start position:0%
+machine so is that it oh and you can
+ 
+
+ align:start position:0%
+machine so is that it oh and you can
+also do some pretty good uh 3D mhd
+
+ align:start position:0%
+also do some pretty good uh 3D mhd
+ 
+
+ align:start position:0%
+also do some pretty good uh 3D mhd
+simulations of these things and then you
+
+ align:start position:0%
+simulations of these things and then you
+ 
+
+ align:start position:0%
+simulations of these things and then you
+can spend a lot of time doing multicolor
+
+ align:start position:0%
+can spend a lot of time doing multicolor
+ 
+
+ align:start position:0%
+can spend a lot of time doing multicolor
+R tracing tring Rays through them and
+
+ align:start position:0%
+R tracing tring Rays through them and
+ 
+
+ align:start position:0%
+R tracing tring Rays through them and
+seeing what the shadowy looks like I
+
+ align:start position:0%
+seeing what the shadowy looks like I
+ 
+
+ align:start position:0%
+seeing what the shadowy looks like I
+don't think this is a particularly bad
+
+ align:start position:0%
+don't think this is a particularly bad
+ 
+
+ align:start position:0%
+don't think this is a particularly bad
+match between what we saw from our
+
+ align:start position:0%
+match between what we saw from our
+ 
+
+ align:start position:0%
+match between what we saw from our
+simulations and what we saw our actual
+
+ align:start position:0%
+simulations and what we saw our actual
+ 
+
+ align:start position:0%
+simulations and what we saw our actual
+data here so it is possible to use
+
+ align:start position:0%
+data here so it is possible to use
+ 
+
+ align:start position:0%
+data here so it is possible to use
+computational tools uh to work out what
+
+ align:start position:0%
+computational tools uh to work out what
+ 
+
+ align:start position:0%
+computational tools uh to work out what
+we would predict so that's it that's all
+
+ align:start position:0%
+we would predict so that's it that's all
+ 
+
+ align:start position:0%
+we would predict so that's it that's all
+I've got on shogy and SCH any questions
+
+ align:start position:0%
+I've got on shogy and SCH any questions
+ 
+
+ align:start position:0%
+I've got on shogy and SCH any questions
+on that yeah even in case have Cs and no
+
+ align:start position:0%
+on that yeah even in case have Cs and no
+ 
+
+ align:start position:0%
+on that yeah even in case have Cs and no
+feeling get all the way back to initial
+
+ align:start position:0%
+feeling get all the way back to initial
+ 
+
+ align:start position:0%
+feeling get all the way back to initial
+distribution can you at least analyze it
+
+ align:start position:0%
+distribution can you at least analyze it
+ 
+
+ align:start position:0%
+distribution can you at least analyze it
+for like frequency distribution or
+
+ align:start position:0%
+for like frequency distribution or
+ 
+
+ align:start position:0%
+for like frequency distribution or
+something to get like oh I must have had
+
+ align:start position:0%
+something to get like oh I must have had
+ 
+
+ align:start position:0%
+something to get like oh I must have had
+this spatial scales my original plasma
+
+ align:start position:0%
+this spatial scales my original plasma
+ 
+
+ align:start position:0%
+this spatial scales my original plasma
+or something like yeah so it's very
+
+ align:start position:0%
+or something like yeah so it's very
+ 
+
+ align:start position:0%
+or something like yeah so it's very
+tempting when you have an image or when
+
+ align:start position:0%
+tempting when you have an image or when
+ 
+
+ align:start position:0%
+tempting when you have an image or when
+you have a a Time series bit of data to
+
+ align:start position:0%
+you have a a Time series bit of data to
+ 
+
+ align:start position:0%
+you have a a Time series bit of data to
+for transform it and like look for
+
+ align:start position:0%
+for transform it and like look for
+ 
+
+ align:start position:0%
+for transform it and like look for
+spectral content and in particular when
+
+ align:start position:0%
+spectral content and in particular when
+ 
+
+ align:start position:0%
+spectral content and in particular when
+we're talking about turbulence we might
+
+ align:start position:0%
+we're talking about turbulence we might
+ 
+
+ align:start position:0%
+we're talking about turbulence we might
+do that we might look for like power
+
+ align:start position:0%
+do that we might look for like power
+ 
+
+ align:start position:0%
+do that we might look for like power
+Spectra corresponding to some turbulent
+
+ align:start position:0%
+Spectra corresponding to some turbulent
+ 
+
+ align:start position:0%
+Spectra corresponding to some turbulent
+density fluctuation Spectrum so like
+
+ align:start position:0%
+density fluctuation Spectrum so like
+ 
+
+ align:start position:0%
+density fluctuation Spectrum so like
+Comm Off K to minus
+
+ align:start position:0%
+Comm Off K to minus
+ 
+
+ align:start position:0%
+Comm Off K to minus
+53 so I did this um I I did this and of
+
+ align:start position:0%
+53 so I did this um I I did this and of
+ 
+
+ align:start position:0%
+53 so I did this um I I did this and of
+course you get a really nice K to the
+
+ align:start position:0%
+course you get a really nice K to the
+ 
+
+ align:start position:0%
+course you get a really nice K to the
+minus 53s on this then I took the
+
+ align:start position:0%
+minus 53s on this then I took the
+ 
+
+ align:start position:0%
+minus 53s on this then I took the
+background image the one without the
+
+ align:start position:0%
+background image the one without the
+ 
+
+ align:start position:0%
+background image the one without the
+plasma and you also get Kus 5/3 and then
+
+ align:start position:0%
+plasma and you also get Kus 5/3 and then
+ 
+
+ align:start position:0%
+plasma and you also get Kus 5/3 and then
+I took a photograph of the experimental
+
+ align:start position:0%
+I took a photograph of the experimental
+ 
+
+ align:start position:0%
+I took a photograph of the experimental
+apparatus and for transform the
+
+ align:start position:0%
+apparatus and for transform the
+ 
+
+ align:start position:0%
+apparatus and for transform the
+photograph and you also get something
+
+ align:start position:0%
+photograph and you also get something
+ 
+
+ align:start position:0%
+photograph and you also get something
+like K to minus 53 the trouble is when
+
+ align:start position:0%
+like K to minus 53 the trouble is when
+ 
+
+ align:start position:0%
+like K to minus 53 the trouble is when
+you're doing foro transforms on images
+
+ align:start position:0%
+you're doing foro transforms on images
+ 
+
+ align:start position:0%
+you're doing foro transforms on images
+you've got to think how many pixels I've
+
+ align:start position:0%
+you've got to think how many pixels I've
+ 
+
+ align:start position:0%
+you've got to think how many pixels I've
+got you probably got like a thousand by
+
+ align:start position:0%
+got you probably got like a thousand by
+ 
+
+ align:start position:0%
+got you probably got like a thousand by
+a thousand pixels and so when you're
+
+ align:start position:0%
+a thousand pixels and so when you're
+ 
+
+ align:start position:0%
+a thousand pixels and so when you're
+doing your foro transform your dynamic
+
+ align:start position:0%
+doing your foro transform your dynamic
+ 
+
+ align:start position:0%
+doing your foro transform your dynamic
+range is only going to be about 10 plus
+
+ align:start position:0%
+range is only going to be about 10 plus
+ 
+
+ align:start position:0%
+range is only going to be about 10 plus
+three but at those large scales at the
+
+ align:start position:0%
+three but at those large scales at the
+ 
+
+ align:start position:0%
+three but at those large scales at the
+the the smallest K it's going to be like
+
+ align:start position:0%
+the the smallest K it's going to be like
+ 
+
+ align:start position:0%
+the the smallest K it's going to be like
+large scale structure so you wouldn't
+
+ align:start position:0%
+large scale structure so you wouldn't
+ 
+
+ align:start position:0%
+large scale structure so you wouldn't
+fit a power Spectrum there and at small
+
+ align:start position:0%
+fit a power Spectrum there and at small
+ 
+
+ align:start position:0%
+fit a power Spectrum there and at small
+scales it's going to be down at pixel
+
+ align:start position:0%
+scales it's going to be down at pixel
+ 
+
+ align:start position:0%
+scales it's going to be down at pixel
+noise so you wouldn't fit it there so
+
+ align:start position:0%
+noise so you wouldn't fit it there so
+ 
+
+ align:start position:0%
+noise so you wouldn't fit it there so
+actually you've only got maybe an order
+
+ align:start position:0%
+actually you've only got maybe an order
+ 
+
+ align:start position:0%
+actually you've only got maybe an order
+of magnitude and you can fit any
+
+ align:start position:0%
+of magnitude and you can fit any
+ 
+
+ align:start position:0%
+of magnitude and you can fit any
+straight line you want to a curve and
+
+ align:start position:0%
+straight line you want to a curve and
+ 
+
+ align:start position:0%
+straight line you want to a curve and
+claim that you've got Kus 5/3 or k to
+
+ align:start position:0%
+claim that you've got Kus 5/3 or k to
+ 
+
+ align:start position:0%
+claim that you've got Kus 5/3 or k to
+Theus three halves or whatever because
+
+ align:start position:0%
+Theus three halves or whatever because
+ 
+
+ align:start position:0%
+Theus three halves or whatever because
+when you do turbulence Theory they all
+
+ align:start position:0%
+when you do turbulence Theory they all
+ 
+
+ align:start position:0%
+when you do turbulence Theory they all
+turn out to be roughly the same so
+
+ align:start position:0%
+turn out to be roughly the same so
+ 
+
+ align:start position:0%
+turn out to be roughly the same so
+that's one reason it's really hard to
+
+ align:start position:0%
+that's one reason it's really hard to
+ 
+
+ align:start position:0%
+that's one reason it's really hard to
+just the for transform these the second
+
+ align:start position:0%
+just the for transform these the second
+ 
+
+ align:start position:0%
+just the for transform these the second
+reason is as we talked about before this
+
+ align:start position:0%
+reason is as we talked about before this
+ 
+
+ align:start position:0%
+reason is as we talked about before this
+is a mirage it's not an image so if I
+
+ align:start position:0%
+is a mirage it's not an image so if I
+ 
+
+ align:start position:0%
+is a mirage it's not an image so if I
+see a region like this black region here
+
+ align:start position:0%
+see a region like this black region here
+ 
+
+ align:start position:0%
+see a region like this black region here
+or another region maybe it's easier to
+
+ align:start position:0%
+or another region maybe it's easier to
+ 
+
+ align:start position:0%
+or another region maybe it's easier to
+point out on this one you know you see
+
+ align:start position:0%
+point out on this one you know you see
+ 
+
+ align:start position:0%
+point out on this one you know you see
+these sort of black voids here and you
+
+ align:start position:0%
+these sort of black voids here and you
+ 
+
+ align:start position:0%
+these sort of black voids here and you
+think okay I could just be like hey this
+
+ align:start position:0%
+think okay I could just be like hey this
+ 
+
+ align:start position:0%
+think okay I could just be like hey this
+is about 2 millimeters long this is one
+
+ align:start position:0%
+is about 2 millimeters long this is one
+ 
+
+ align:start position:0%
+is about 2 millimeters long this is one
+millimeter long make a histogram fit a
+
+ align:start position:0%
+millimeter long make a histogram fit a
+ 
+
+ align:start position:0%
+millimeter long make a histogram fit a
+power or something to it but these don't
+
+ align:start position:0%
+power or something to it but these don't
+ 
+
+ align:start position:0%
+power or something to it but these don't
+represent an object that is 2
+
+ align:start position:0%
+represent an object that is 2
+ 
+
+ align:start position:0%
+represent an object that is 2
+millimeters long they are a defocusing
+
+ align:start position:0%
+millimeters long they are a defocusing
+ 
+
+ align:start position:0%
+millimeters long they are a defocusing
+mechanism that could be a really tiny
+
+ align:start position:0%
+mechanism that could be a really tiny
+ 
+
+ align:start position:0%
+mechanism that could be a really tiny
+region of very high density that
+
+ align:start position:0%
+region of very high density that
+ 
+
+ align:start position:0%
+region of very high density that
+defocuses and then it's projected out
+
+ align:start position:0%
+defocuses and then it's projected out
+ 
+
+ align:start position:0%
+defocuses and then it's projected out
+into this larger region so we can't
+
+ align:start position:0%
+into this larger region so we can't
+ 
+
+ align:start position:0%
+into this larger region so we can't
+there's no spatial information properly
+
+ align:start position:0%
+there's no spatial information properly
+ 
+
+ align:start position:0%
+there's no spatial information properly
+left inside this image there's some
+
+ align:start position:0%
+left inside this image there's some
+ 
+
+ align:start position:0%
+left inside this image there's some
+spatial imation you know this this sort
+
+ align:start position:0%
+spatial imation you know this this sort
+ 
+
+ align:start position:0%
+spatial imation you know this this sort
+of structure here corresponds to this
+
+ align:start position:0%
+of structure here corresponds to this
+ 
+
+ align:start position:0%
+of structure here corresponds to this
+sort of structure and you think it's
+
+ align:start position:0%
+sort of structure and you think it's
+ 
+
+ align:start position:0%
+sort of structure and you think it's
+about 5 millimeters across it's probably
+
+ align:start position:0%
+about 5 millimeters across it's probably
+ 
+
+ align:start position:0%
+about 5 millimeters across it's probably
+slightly demagnified because it will
+
+ align:start position:0%
+slightly demagnified because it will
+ 
+
+ align:start position:0%
+slightly demagnified because it will
+actually make a a larger image um but
+
+ align:start position:0%
+actually make a a larger image um but
+ 
+
+ align:start position:0%
+actually make a a larger image um but
+each of these individual voids no longer
+
+ align:start position:0%
+each of these individual voids no longer
+ 
+
+ align:start position:0%
+each of these individual voids no longer
+has the same spatial size as the
+
+ align:start position:0%
+has the same spatial size as the
+ 
+
+ align:start position:0%
+has the same spatial size as the
+structure that produced it so it's very
+
+ align:start position:0%
+structure that produced it so it's very
+ 
+
+ align:start position:0%
+structure that produced it so it's very
+hard to infer things about
+
+ align:start position:0%
+hard to infer things about
+ 
+
+ align:start position:0%
+hard to infer things about
+terb but yeah it's a good
+
+ align:start position:0%
+terb but yeah it's a good
+ 
+
+ align:start position:0%
+terb but yeah it's a good
+question any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even though
+
+ align:start position:0%
+even though
+ 
+
+ align:start position:0%
+even though
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get so I don't think you can I mean when
+
+ align:start position:0%
+get so I don't think you can I mean when
+ 
+
+ align:start position:0%
+get so I don't think you can I mean when
+you run this algorithm on your data shog
+
+ align:start position:0%
+you run this algorithm on your data shog
+ 
+
+ align:start position:0%
+you run this algorithm on your data shog
+graphy or proton radiography one of
+
+ align:start position:0%
+graphy or proton radiography one of
+ 
+
+ align:start position:0%
+graphy or proton radiography one of
+these mamp optimal transer alth it will
+
+ align:start position:0%
+these mamp optimal transer alth it will
+ 
+
+ align:start position:0%
+these mamp optimal transer alth it will
+always give you an answer right so it
+
+ align:start position:0%
+always give you an answer right so it
+ 
+
+ align:start position:0%
+always give you an answer right so it
+returns it returns a solution right but
+
+ align:start position:0%
+returns it returns a solution right but
+ 
+
+ align:start position:0%
+returns it returns a solution right but
+we know that these uh reconstruction
+
+ align:start position:0%
+we know that these uh reconstruction
+ 
+
+ align:start position:0%
+we know that these uh reconstruction
+alems don't work when we have the coost
+
+ align:start position:0%
+alems don't work when we have the coost
+ 
+
+ align:start position:0%
+alems don't work when we have the coost
+stick regime and so that solution is is
+
+ align:start position:0%
+stick regime and so that solution is is
+ 
+
+ align:start position:0%
+stick regime and so that solution is is
+very suspect right like we don't believe
+
+ align:start position:0%
+very suspect right like we don't believe
+ 
+
+ align:start position:0%
+very suspect right like we don't believe
+we should trust it so I don't think
+
+ align:start position:0%
+we should trust it so I don't think
+ 
+
+ align:start position:0%
+we should trust it so I don't think
+there's anything you can use from that
+
+ align:start position:0%
+there's anything you can use from that
+ 
+
+ align:start position:0%
+there's anything you can use from that
+solution to help you reconstruct the
+
+ align:start position:0%
+solution to help you reconstruct the
+ 
+
+ align:start position:0%
+solution to help you reconstruct the
+actual thing I think at that point if
+
+ align:start position:0%
+actual thing I think at that point if
+ 
+
+ align:start position:0%
+actual thing I think at that point if
+you've got cor sticks your best bet is
+
+ align:start position:0%
+you've got cor sticks your best bet is
+ 
+
+ align:start position:0%
+you've got cor sticks your best bet is
+having some very strong priers as to the
+
+ align:start position:0%
+having some very strong priers as to the
+ 
+
+ align:start position:0%
+having some very strong priers as to the
+sort of plasma you think you've got and
+
+ align:start position:0%
+sort of plasma you think you've got and
+ 
+
+ align:start position:0%
+sort of plasma you think you've got and
+then pushing Monte Carlo Rays or protons
+
+ align:start position:0%
+then pushing Monte Carlo Rays or protons
+ 
+
+ align:start position:0%
+then pushing Monte Carlo Rays or protons
+through it doing the forward problem and
+
+ align:start position:0%
+through it doing the forward problem and
+ 
+
+ align:start position:0%
+through it doing the forward problem and
+adjusting the forward problem until it
+
+ align:start position:0%
+adjusting the forward problem until it
+ 
+
+ align:start position:0%
+adjusting the forward problem until it
+matches some of the features you see on
+
+ align:start position:0%
+matches some of the features you see on
+ 
+
+ align:start position:0%
+matches some of the features you see on
+your actual data I don't think you can
+
+ align:start position:0%
+your actual data I don't think you can
+ 
+
+ align:start position:0%
+your actual data I don't think you can
+do the inverse problem easly but there
+
+ align:start position:0%
+do the inverse problem easly but there
+ 
+
+ align:start position:0%
+do the inverse problem easly but there
+have been a few papers where people have
+
+ align:start position:0%
+have been a few papers where people have
+ 
+
+ align:start position:0%
+have been a few papers where people have
+tried to do this because we almost
+
+ align:start position:0%
+tried to do this because we almost
+ 
+
+ align:start position:0%
+tried to do this because we almost
+always end up in the costic regime so
+
+ align:start position:0%
+always end up in the costic regime so
+ 
+
+ align:start position:0%
+always end up in the costic regime so
+people have all this data and they want
+
+ align:start position:0%
+people have all this data and they want
+ 
+
+ align:start position:0%
+people have all this data and they want
+to use it like it's reasonable to try
+
+ align:start position:0%
+to use it like it's reasonable to try
+ 
+
+ align:start position:0%
+to use it like it's reasonable to try
+and do something with that data it's
+
+ align:start position:0%
+and do something with that data it's
+ 
+
+ align:start position:0%
+and do something with that data it's
+just very hard so
+
+ align:start position:0%
+just very hard so
+ 
+
+ align:start position:0%
+just very hard so
+yeah yeah so for this images of like the
+
+ align:start position:0%
+yeah yeah so for this images of like the
+ 
+
+ align:start position:0%
+yeah yeah so for this images of like the
+heads and like the room those are not
+
+ align:start position:0%
+heads and like the room those are not
+ 
+
+ align:start position:0%
+heads and like the room those are not
+super small scale effects so to see
+
+ align:start position:0%
+super small scale effects so to see
+ 
+
+ align:start position:0%
+super small scale effects so to see
+those you just push your Imaging surface
+
+ align:start position:0%
+those you just push your Imaging surface
+ 
+
+ align:start position:0%
+those you just push your Imaging surface
+really far away if you take a laser
+
+ align:start position:0%
+really far away if you take a laser
+ 
+
+ align:start position:0%
+really far away if you take a laser
+pointer uh and make it diverge by taking
+
+ align:start position:0%
+pointer uh and make it diverge by taking
+ 
+
+ align:start position:0%
+pointer uh and make it diverge by taking
+off the little lens at the front of it
+
+ align:start position:0%
+off the little lens at the front of it
+ 
+
+ align:start position:0%
+off the little lens at the front of it
+and you take a candle flame and you
+
+ align:start position:0%
+and you take a candle flame and you
+ 
+
+ align:start position:0%
+and you take a candle flame and you
+project it onto a wall you will see this
+
+ align:start position:0%
+project it onto a wall you will see this
+ 
+
+ align:start position:0%
+project it onto a wall you will see this
+like again you know you see Mires just
+
+ align:start position:0%
+like again you know you see Mires just
+ 
+
+ align:start position:0%
+like again you know you see Mires just
+using sunlight so yeah this not a hard
+
+ align:start position:0%
+using sunlight so yeah this not a hard
+ 
+
+ align:start position:0%
+using sunlight so yeah this not a hard
+thing to observe so if you see something
+
+ align:start position:0%
+thing to observe so if you see something
+ 
+
+ align:start position:0%
+thing to observe so if you see something
+with your naked eye it's either like a
+
+ align:start position:0%
+with your naked eye it's either like a
+ 
+
+ align:start position:0%
+with your naked eye it's either like a
+really small or something far away yes
+
+ align:start position:0%
+really small or something far away yes
+ 
+
+ align:start position:0%
+really small or something far away yes
+yes exactly and usually it's quite far
+
+ align:start position:0%
+yes exactly and usually it's quite far
+ 
+
+ align:start position:0%
+yes exactly and usually it's quite far
+away right I mean if we you can often
+
+ align:start position:0%
+away right I mean if we you can often
+ 
+
+ align:start position:0%
+away right I mean if we you can often
+see even the heat rising from like a
+
+ align:start position:0%
+see even the heat rising from like a
+ 
+
+ align:start position:0%
+see even the heat rising from like a
+vent or something like that but not when
+
+ align:start position:0%
+vent or something like that but not when
+ 
+
+ align:start position:0%
+vent or something like that but not when
+you're right up close to it give it a go
+
+ align:start position:0%
+you're right up close to it give it a go
+ 
+
+ align:start position:0%
+you're right up close to it give it a go
+next time you see something if it's
+
+ align:start position:0%
+next time you see something if it's
+ 
+
+ align:start position:0%
+next time you see something if it's
+sayfe put your eye right up next to it
+
+ align:start position:0%
+sayfe put your eye right up next to it
+ 
+
+ align:start position:0%
+sayfe put your eye right up next to it
+it disappears so
+
+ align:start position:0%
+it disappears so
+ 
+
+ align:start position:0%
+it disappears so
+yeah please don't
+
+ align:start position:0%
+yeah please don't
+ 
+
+ align:start position:0%
+yeah please don't
+anyway any other
+
+ align:start position:0%
+anyway any other
+ 
+
+ align:start position:0%
+anyway any other
+questions one more example like when you
+
+ align:start position:0%
+questions one more example like when you
+ 
+
+ align:start position:0%
+questions one more example like when you
+can see like this
+
+ align:start position:0%
+can see like this
+ 
+
+ align:start position:0%
+can see like this
+exact sitation is like if you have
+
+ align:start position:0%
+exact sitation is like if you have
+ 
+
+ align:start position:0%
+exact sitation is like if you have
+sunlight coming through a window and
+
+ align:start position:0%
+sunlight coming through a window and
+ 
+
+ align:start position:0%
+sunlight coming through a window and
+over like a yes on the
+
+ align:start position:0%
+over like a yes on the
+ 
+
+ align:start position:0%
+over like a yes on the
+yes yeah yeah exactly that's thing
+
+ align:start position:0%
+yes yeah yeah exactly that's thing
+ 
+
+ align:start position:0%
+yes yeah yeah exactly that's thing
+another place um the botom a swimming
+
+ align:start position:0%
+another place um the botom a swimming
+ 
+
+ align:start position:0%
+another place um the botom a swimming
+pool so when you have you know waves on
+
+ align:start position:0%
+pool so when you have you know waves on
+ 
+
+ align:start position:0%
+pool so when you have you know waves on
+the top surface of a swimming pool you
+
+ align:start position:0%
+the top surface of a swimming pool you
+ 
+
+ align:start position:0%
+the top surface of a swimming pool you
+get those bright lines on the bottom
+
+ align:start position:0%
+get those bright lines on the bottom
+ 
+
+ align:start position:0%
+get those bright lines on the bottom
+those are coost stics right so exactly
+
+ align:start position:0%
+those are coost stics right so exactly
+ 
+
+ align:start position:0%
+those are coost stics right so exactly
+the same sort of physics is produces
+
+ align:start position:0%
+the same sort of physics is produces
+ 
+
+ align:start position:0%
+the same sort of physics is produces
+these there is a beautiful book called
+
+ align:start position:0%
+these there is a beautiful book called
+ 
+
+ align:start position:0%
+these there is a beautiful book called
+The Natural focusing of Light which
+
+ align:start position:0%
+The Natural focusing of Light which
+ 
+
+ align:start position:0%
+The Natural focusing of Light which
+tries to analyze cotic but mostly does
+
+ align:start position:0%
+tries to analyze cotic but mostly does
+ 
+
+ align:start position:0%
+tries to analyze cotic but mostly does
+it in a way that I don't think it's
+
+ align:start position:0%
+it in a way that I don't think it's
+ 
+
+ align:start position:0%
+it in a way that I don't think it's
+practical it's theoretically beautiful
+
+ align:start position:0%
+practical it's theoretically beautiful
+ 
+
+ align:start position:0%
+practical it's theoretically beautiful
+um and one of the things that they point
+
+ align:start position:0%
+um and one of the things that they point
+ 
+
+ align:start position:0%
+um and one of the things that they point
+out about cors is where every time you
+
+ align:start position:0%
+out about cors is where every time you
+ 
+
+ align:start position:0%
+out about cors is where every time you
+get a bright region you get like a dark
+
+ align:start position:0%
+get a bright region you get like a dark
+ 
+
+ align:start position:0%
+get a bright region you get like a dark
+region on one side but not on the other
+
+ align:start position:0%
+region on one side but not on the other
+ 
+
+ align:start position:0%
+region on one side but not on the other
+side and that tells you like what
+
+ align:start position:0%
+side and that tells you like what
+ 
+
+ align:start position:0%
+side and that tells you like what
+direction the cor stick came from from
+
+ align:start position:0%
+direction the cor stick came from from
+ 
+
+ align:start position:0%
+direction the cor stick came from from
+and so you might be able to trace back a
+
+ align:start position:0%
+and so you might be able to trace back a
+ 
+
+ align:start position:0%
+and so you might be able to trace back a
+series of arrows around one of these cor
+
+ align:start position:0%
+series of arrows around one of these cor
+ 
+
+ align:start position:0%
+series of arrows around one of these cor
+sticks here and work out where the point
+
+ align:start position:0%
+sticks here and work out where the point
+ 
+
+ align:start position:0%
+sticks here and work out where the point
+was that the cor stick originated but
+
+ align:start position:0%
+was that the cor stick originated but
+ 
+
+ align:start position:0%
+was that the cor stick originated but
+it's very tricky to do the analysis of
+
+ align:start position:0%
+it's very tricky to do the analysis of
+ 
+
+ align:start position:0%
+it's very tricky to do the analysis of
+it but the point is the book is called
+
+ align:start position:0%
+it but the point is the book is called
+ 
+
+ align:start position:0%
+it but the point is the book is called
+the natural focusing of light so people
+
+ align:start position:0%
+the natural focusing of light so people
+ 
+
+ align:start position:0%
+the natural focusing of light so people
+refer to this field as natural focusing
+
+ align:start position:0%
+refer to this field as natural focusing
+ 
+
+ align:start position:0%
+refer to this field as natural focusing
+no one has tried to make a lens no one
+
+ align:start position:0%
+no one has tried to make a lens no one
+ 
+
+ align:start position:0%
+no one has tried to make a lens no one
+is trying to do any focusing our medium
+
+ align:start position:0%
+is trying to do any focusing our medium
+ 
+
+ align:start position:0%
+is trying to do any focusing our medium
+with its in homogeneous reflective index
+
+ align:start position:0%
+with its in homogeneous reflective index
+ 
+
+ align:start position:0%
+with its in homogeneous reflective index
+has just done it for us then we might
+
+ align:start position:0%
+has just done it for us then we might
+ 
+
+ align:start position:0%
+has just done it for us then we might
+try and work out what we can learn about
+
+ align:start position:0%
+try and work out what we can learn about
+ 
+
+ align:start position:0%
+try and work out what we can learn about
+the medium from looking at the light
+
+ align:start position:0%
+the medium from looking at the light
+ 
+
+ align:start position:0%
+the medium from looking at the light
+that's gone through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes one more thing to make sure I try
+
+ align:start position:0%
+yes one more thing to make sure I try
+ 
+
+ align:start position:0%
+yes one more thing to make sure I try
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+later so if you have an image like the
+
+ align:start position:0%
+later so if you have an image like the
+ 
+
+ align:start position:0%
+later so if you have an image like the
+one with the board for instance like
+
+ align:start position:0%
+one with the board for instance like
+ 
+
+ align:start position:0%
+one with the board for instance like
+there are some really clear to Sticks
+
+ align:start position:0%
+there are some really clear to Sticks
+ 
+
+ align:start position:0%
+there are some really clear to Sticks
+then and parts of the rest of the image
+
+ align:start position:0%
+then and parts of the rest of the image
+ 
+
+ align:start position:0%
+then and parts of the rest of the image
+look like they might be
+
+ align:start position:0%
+look like they might be
+ 
+
+ align:start position:0%
+look like they might be
+fine if you want to analyze the rest of
+
+ align:start position:0%
+fine if you want to analyze the rest of
+ 
+
+ align:start position:0%
+fine if you want to analyze the rest of
+your image is that oh yeah you can cut
+
+ align:start position:0%
+your image is that oh yeah you can cut
+ 
+
+ align:start position:0%
+your image is that oh yeah you can cut
+out the bit with the co sticks yeah yeah
+
+ align:start position:0%
+out the bit with the co sticks yeah yeah
+ 
+
+ align:start position:0%
+out the bit with the co sticks yeah yeah
+that's fine so I mean almost none of
+
+ align:start position:0%
+that's fine so I mean almost none of
+ 
+
+ align:start position:0%
+that's fine so I mean almost none of
+this image is actually suitable but like
+
+ align:start position:0%
+this image is actually suitable but like
+ 
+
+ align:start position:0%
+this image is actually suitable but like
+maybe this bit would be more because
+
+ align:start position:0%
+maybe this bit would be more because
+ 
+
+ align:start position:0%
+maybe this bit would be more because
+it's not small intensity variations you
+
+ align:start position:0%
+it's not small intensity variations you
+ 
+
+ align:start position:0%
+it's not small intensity variations you
+can see if you think about this gray as
+
+ align:start position:0%
+can see if you think about this gray as
+ 
+
+ align:start position:0%
+can see if you think about this gray as
+like .5 and you think about the white as
+
+ align:start position:0%
+like .5 and you think about the white as
+ 
+
+ align:start position:0%
+like .5 and you think about the white as
+one and the black as zero you can see
+
+ align:start position:0%
+one and the black as zero you can see
+ 
+
+ align:start position:0%
+one and the black as zero you can see
+that you're getting modulations on the
+
+ align:start position:0%
+that you're getting modulations on the
+ 
+
+ align:start position:0%
+that you're getting modulations on the
+order of 0.5 inside this image so it's
+
+ align:start position:0%
+order of 0.5 inside this image so it's
+ 
+
+ align:start position:0%
+order of 0.5 inside this image so it's
+clearly not in that small regime but
+
+ align:start position:0%
+clearly not in that small regime but
+ 
+
+ align:start position:0%
+clearly not in that small regime but
+it's not clear that these the coost
+
+ align:start position:0%
+it's not clear that these the coost
+ 
+
+ align:start position:0%
+it's not clear that these the coost
+stics so you may still be able to use
+
+ align:start position:0%
+stics so you may still be able to use
+ 
+
+ align:start position:0%
+stics so you may still be able to use
+one of the complicated mamp like style
+
+ align:start position:0%
+one of the complicated mamp like style
+ 
+
+ align:start position:0%
+one of the complicated mamp like style
+reconstruction techniques you just won't
+
+ align:start position:0%
+reconstruction techniques you just won't
+ 
+
+ align:start position:0%
+reconstruction techniques you just won't
+be able to use the nice formula that we
+
+ align:start position:0%
+be able to use the nice formula that we
+ 
+
+ align:start position:0%
+be able to use the nice formula that we
+wrote down analytically so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you've successfully timed me out I
+
+ align:start position:0%
+okay you've successfully timed me out I
+ 
+
+ align:start position:0%
+okay you've successfully timed me out I
+was going to start to go inry well done
+
+ align:start position:0%
+was going to start to go inry well done
+ 
+
+ align:start position:0%
+was going to start to go inry well done
+everyone so we'll leave it there and we
+
+ align:start position:0%
+everyone so we'll leave it there and we
+ 
+
+ align:start position:0%
+everyone so we'll leave it there and we
+will pick up on infmetry on uh Thursday
+
+ align:start position:0%
+will pick up on infmetry on uh Thursday
+ 
+
+ align:start position:0%
+will pick up on infmetry on uh Thursday
+so
\ No newline at end of file
diff --git a/WguhC64iAXI.txt b/WguhC64iAXI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..598d92f53ccde1cb896c4b20ac678a5344761e54
--- /dev/null
+++ b/WguhC64iAXI.txt
@@ -0,0 +1,1875 @@
+align:start position:0%
+ 
+the first project for the semester was
+
+ align:start position:0%
+the first project for the semester was
+ 
+
+ align:start position:0%
+the first project for the semester was
+designing a outside place in a Quarry
+
+ align:start position:0%
+designing a outside place in a Quarry
+ 
+
+ align:start position:0%
+designing a outside place in a Quarry
+North of Boston in
+
+ align:start position:0%
+North of Boston in
+ 
+
+ align:start position:0%
+North of Boston in
+Rockport we have gone to the Quarry and
+
+ align:start position:0%
+Rockport we have gone to the Quarry and
+ 
+
+ align:start position:0%
+Rockport we have gone to the Quarry and
+they were asked the students were asked
+
+ align:start position:0%
+they were asked the students were asked
+ 
+
+ align:start position:0%
+they were asked the students were asked
+to to find a place in the Quarry that
+
+ align:start position:0%
+to to find a place in the Quarry that
+ 
+
+ align:start position:0%
+to to find a place in the Quarry that
+they liked photograph it sketch it
+
+ align:start position:0%
+they liked photograph it sketch it
+ 
+
+ align:start position:0%
+they liked photograph it sketch it
+understand it bring it back to the
+
+ align:start position:0%
+understand it bring it back to the
+ 
+
+ align:start position:0%
+understand it bring it back to the
+studio and then design a
+
+ align:start position:0%
+studio and then design a
+ 
+
+ align:start position:0%
+studio and then design a
+classroom for themselves and
+
+ align:start position:0%
+classroom for themselves and
+ 
+
+ align:start position:0%
+classroom for themselves and
+me uh that was sheltered not
+
+ align:start position:0%
+me uh that was sheltered not
+ 
+
+ align:start position:0%
+me uh that was sheltered not
+enclosed but was the idea was making a
+
+ align:start position:0%
+enclosed but was the idea was making a
+ 
+
+ align:start position:0%
+enclosed but was the idea was making a
+place in the Quarry that was neither
+
+ align:start position:0%
+place in the Quarry that was neither
+ 
+
+ align:start position:0%
+place in the Quarry that was neither
+natural or was it to be appear to be
+
+ align:start position:0%
+natural or was it to be appear to be
+ 
+
+ align:start position:0%
+natural or was it to be appear to be
+built it was to fit into the context of
+
+ align:start position:0%
+built it was to fit into the context of
+ 
+
+ align:start position:0%
+built it was to fit into the context of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Quarry um they were welcome to use any
+
+ align:start position:0%
+Quarry um they were welcome to use any
+ 
+
+ align:start position:0%
+Quarry um they were welcome to use any
+materials that they thought would relate
+
+ align:start position:0%
+materials that they thought would relate
+ 
+
+ align:start position:0%
+materials that they thought would relate
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+Quarry when they came back from the
+
+ align:start position:0%
+Quarry when they came back from the
+ 
+
+ align:start position:0%
+Quarry when they came back from the
+Quarry I then asked them to do their
+
+ align:start position:0%
+Quarry I then asked them to do their
+ 
+
+ align:start position:0%
+Quarry I then asked them to do their
+first design and their first ideas of
+
+ align:start position:0%
+first design and their first ideas of
+ 
+
+ align:start position:0%
+first design and their first ideas of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Quarry so what you're about to see is
+
+ align:start position:0%
+Quarry so what you're about to see is
+ 
+
+ align:start position:0%
+Quarry so what you're about to see is
+the very first pinup of the semester of
+
+ align:start position:0%
+the very first pinup of the semester of
+ 
+
+ align:start position:0%
+the very first pinup of the semester of
+this very first project
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I um saw that um was the best
+
+ align:start position:0%
+so what I um saw that um was the best
+ 
+
+ align:start position:0%
+so what I um saw that um was the best
+about this night was um how nature is
+
+ align:start position:0%
+about this night was um how nature is
+ 
+
+ align:start position:0%
+about this night was um how nature is
+really um it it it's got a logic to it
+
+ align:start position:0%
+really um it it it's got a logic to it
+ 
+
+ align:start position:0%
+really um it it it's got a logic to it
+and every Gap and everything that that
+
+ align:start position:0%
+and every Gap and everything that that
+ 
+
+ align:start position:0%
+and every Gap and everything that that
+is there it's still been in some ways
+
+ align:start position:0%
+is there it's still been in some ways
+ 
+
+ align:start position:0%
+is there it's still been in some ways
+there's nothing lost there's nothing
+
+ align:start position:0%
+there's nothing lost there's nothing
+ 
+
+ align:start position:0%
+there's nothing lost there's nothing
+nothing wasted everything sort of
+
+ align:start position:0%
+nothing wasted everything sort of
+ 
+
+ align:start position:0%
+nothing wasted everything sort of
+belongs in that sort of net of things
+
+ align:start position:0%
+belongs in that sort of net of things
+ 
+
+ align:start position:0%
+belongs in that sort of net of things
+and um so when I I decided that my site
+
+ align:start position:0%
+and um so when I I decided that my site
+ 
+
+ align:start position:0%
+and um so when I I decided that my site
+would be right here where the seagull
+
+ align:start position:0%
+would be right here where the seagull
+ 
+
+ align:start position:0%
+would be right here where the seagull
+were um I figured that the seagull would
+
+ align:start position:0%
+were um I figured that the seagull would
+ 
+
+ align:start position:0%
+were um I figured that the seagull would
+know better than me what the best place
+
+ align:start position:0%
+know better than me what the best place
+ 
+
+ align:start position:0%
+know better than me what the best place
+was um since Nature has that logic um so
+
+ align:start position:0%
+was um since Nature has that logic um so
+ 
+
+ align:start position:0%
+was um since Nature has that logic um so
+the animals did too and
+
+ align:start position:0%
+the animals did too and
+ 
+
+ align:start position:0%
+the animals did too and
+um you know I realiz they lik about the
+
+ align:start position:0%
+um you know I realiz they lik about the
+ 
+
+ align:start position:0%
+um you know I realiz they lik about the
+site um but if you notice it's got a lot
+
+ align:start position:0%
+site um but if you notice it's got a lot
+ 
+
+ align:start position:0%
+site um but if you notice it's got a lot
+of um it's it basically is a cliff sort
+
+ align:start position:0%
+of um it's it basically is a cliff sort
+ 
+
+ align:start position:0%
+of um it's it basically is a cliff sort
+of cutout and what I'm trying to do is
+
+ align:start position:0%
+of cutout and what I'm trying to do is
+ 
+
+ align:start position:0%
+of cutout and what I'm trying to do is
+fill that space as nature does just have
+
+ align:start position:0%
+fill that space as nature does just have
+ 
+
+ align:start position:0%
+fill that space as nature does just have
+that space fill in um and and this is
+
+ align:start position:0%
+that space fill in um and and this is
+ 
+
+ align:start position:0%
+that space fill in um and and this is
+what the site looks like now um they're
+
+ align:start position:0%
+what the site looks like now um they're
+ 
+
+ align:start position:0%
+what the site looks like now um they're
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+seagull um and then this is what I'm
+
+ align:start position:0%
+seagull um and then this is what I'm
+ 
+
+ align:start position:0%
+seagull um and then this is what I'm
+hoping to do is to sort of feel that
+
+ align:start position:0%
+hoping to do is to sort of feel that
+ 
+
+ align:start position:0%
+hoping to do is to sort of feel that
+um to just make it look like how it used
+
+ align:start position:0%
+um to just make it look like how it used
+ 
+
+ align:start position:0%
+um to just make it look like how it used
+to be how I imag it been before when was
+
+ align:start position:0%
+to be how I imag it been before when was
+ 
+
+ align:start position:0%
+to be how I imag it been before when was
+already present
+
+ align:start position:0%
+already present
+ 
+
+ align:start position:0%
+already present
+inag um and I like the idea of just
+
+ align:start position:0%
+inag um and I like the idea of just
+ 
+
+ align:start position:0%
+inag um and I like the idea of just
+throwing those gaps um here it shows
+
+ align:start position:0%
+throwing those gaps um here it shows
+ 
+
+ align:start position:0%
+throwing those gaps um here it shows
+just how even it even the grass and the
+
+ align:start position:0%
+just how even it even the grass and the
+ 
+
+ align:start position:0%
+just how even it even the grass and the
+ground and the soil um evens out the all
+
+ align:start position:0%
+ground and the soil um evens out the all
+ 
+
+ align:start position:0%
+ground and the soil um evens out the all
+the Rocks even though the jacket um so
+
+ align:start position:0%
+the Rocks even though the jacket um so
+ 
+
+ align:start position:0%
+the Rocks even though the jacket um so
+evening things out here this night
+
+ align:start position:0%
+evening things out here this night
+ 
+
+ align:start position:0%
+evening things out here this night
+hoping that I'll just even that out in a
+
+ align:start position:0%
+hoping that I'll just even that out in a
+ 
+
+ align:start position:0%
+hoping that I'll just even that out in a
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+um also I while I was sitting there I
+
+ align:start position:0%
+um also I while I was sitting there I
+ 
+
+ align:start position:0%
+um also I while I was sitting there I
+was um as listen to the seagull and they
+
+ align:start position:0%
+was um as listen to the seagull and they
+ 
+
+ align:start position:0%
+was um as listen to the seagull and they
+were a little bit annoying at times but
+
+ align:start position:0%
+were a little bit annoying at times but
+ 
+
+ align:start position:0%
+were a little bit annoying at times but
+just the sound of the water splashing
+
+ align:start position:0%
+just the sound of the water splashing
+ 
+
+ align:start position:0%
+just the sound of the water splashing
+the sound of them
+
+ align:start position:0%
+the sound of them
+ 
+
+ align:start position:0%
+the sound of them
+um just flying around um the wind
+
+ align:start position:0%
+um just flying around um the wind
+ 
+
+ align:start position:0%
+um just flying around um the wind
+wrestling of all the plants and that was
+
+ align:start position:0%
+wrestling of all the plants and that was
+ 
+
+ align:start position:0%
+wrestling of all the plants and that was
+also part of the experience and um I'm
+
+ align:start position:0%
+also part of the experience and um I'm
+ 
+
+ align:start position:0%
+also part of the experience and um I'm
+hoping the co exist to with the sing I
+
+ align:start position:0%
+hoping the co exist to with the sing I
+ 
+
+ align:start position:0%
+hoping the co exist to with the sing I
+want to this is the site uh looking at
+
+ align:start position:0%
+want to this is the site uh looking at
+ 
+
+ align:start position:0%
+want to this is the site uh looking at
+it Southward
+
+ align:start position:0%
+it Southward
+ 
+
+ align:start position:0%
+it Southward
+um living here uh I saw this small sort
+
+ align:start position:0%
+um living here uh I saw this small sort
+ 
+
+ align:start position:0%
+um living here uh I saw this small sort
+of space here as a private area also in
+
+ align:start position:0%
+of space here as a private area also in
+ 
+
+ align:start position:0%
+of space here as a private area also in
+here as a private area and then this
+
+ align:start position:0%
+here as a private area and then this
+ 
+
+ align:start position:0%
+here as a private area and then this
+bigger space as place um I'm looking at
+
+ align:start position:0%
+bigger space as place um I'm looking at
+ 
+
+ align:start position:0%
+bigger space as place um I'm looking at
+the studio as more of a dynamic Place
+
+ align:start position:0%
+the studio as more of a dynamic Place
+ 
+
+ align:start position:0%
+the studio as more of a dynamic Place
+rather than all of us having our desks
+
+ align:start position:0%
+rather than all of us having our desks
+ 
+
+ align:start position:0%
+rather than all of us having our desks
+um this is my idea is adding a stone
+
+ align:start position:0%
+um this is my idea is adding a stone
+ 
+
+ align:start position:0%
+um this is my idea is adding a stone
+wall to the side so that it Blends and I
+
+ align:start position:0%
+wall to the side so that it Blends and I
+ 
+
+ align:start position:0%
+wall to the side so that it Blends and I
+I just I'm very literal about um I just
+
+ align:start position:0%
+I just I'm very literal about um I just
+ 
+
+ align:start position:0%
+I just I'm very literal about um I just
+imagine these trees just growing out of
+
+ align:start position:0%
+imagine these trees just growing out of
+ 
+
+ align:start position:0%
+imagine these trees just growing out of
+those gaps in the rocks and um making a
+
+ align:start position:0%
+those gaps in the rocks and um making a
+ 
+
+ align:start position:0%
+those gaps in the rocks and um making a
+canopy and intertwining in the top and
+
+ align:start position:0%
+canopy and intertwining in the top and
+ 
+
+ align:start position:0%
+canopy and intertwining in the top and
+um sort of like how when we entered the
+
+ align:start position:0%
+um sort of like how when we entered the
+ 
+
+ align:start position:0%
+um sort of like how when we entered the
+space there we came in this like T of
+
+ align:start position:0%
+space there we came in this like T of
+ 
+
+ align:start position:0%
+space there we came in this like T of
+just like canopy of plant um that's sort
+
+ align:start position:0%
+just like canopy of plant um that's sort
+ 
+
+ align:start position:0%
+just like canopy of plant um that's sort
+of what I want to do that that lip of of
+
+ align:start position:0%
+of what I want to do that that lip of of
+ 
+
+ align:start position:0%
+of what I want to do that that lip of of
+plants and people sitting around uh with
+
+ align:start position:0%
+plants and people sitting around uh with
+ 
+
+ align:start position:0%
+plants and people sitting around uh with
+their drawing boards on the LPS moving
+
+ align:start position:0%
+their drawing boards on the LPS moving
+ 
+
+ align:start position:0%
+their drawing boards on the LPS moving
+around going down here to look out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh here is my model
+
+ align:start position:0%
+um uh here is my model
+ 
+
+ align:start position:0%
+um uh here is my model
+um I was thinking of St on the side and
+
+ align:start position:0%
+um I was thinking of St on the side and
+ 
+
+ align:start position:0%
+um I was thinking of St on the side and
+then going all the way down um
+
+ align:start position:0%
+then going all the way down um
+ 
+
+ align:start position:0%
+then going all the way down um
+but add steps from one space the other
+
+ align:start position:0%
+but add steps from one space the other
+ 
+
+ align:start position:0%
+but add steps from one space the other
+but what did you just take away um these
+
+ align:start position:0%
+but what did you just take away um these
+ 
+
+ align:start position:0%
+but what did you just take away um these
+were the stats oh
+
+ align:start position:0%
+were the stats oh
+ 
+
+ align:start position:0%
+were the stats oh
+okay um well I could take out all the
+
+ align:start position:0%
+okay um well I could take out all the
+ 
+
+ align:start position:0%
+okay um well I could take out all the
+pieces and how you see the original but
+
+ align:start position:0%
+pieces and how you see the original but
+ 
+
+ align:start position:0%
+pieces and how you see the original but
+basically I added the stone walls um and
+
+ align:start position:0%
+basically I added the stone walls um and
+ 
+
+ align:start position:0%
+basically I added the stone walls um and
+I'm thinking I'm using I I I don't feel
+
+ align:start position:0%
+I'm thinking I'm using I I I don't feel
+ 
+
+ align:start position:0%
+I'm thinking I'm using I I I don't feel
+like I want to disturb the environment I
+
+ align:start position:0%
+like I want to disturb the environment I
+ 
+
+ align:start position:0%
+like I want to disturb the environment I
+feel like I want to use what's already
+
+ align:start position:0%
+feel like I want to use what's already
+ 
+
+ align:start position:0%
+feel like I want to use what's already
+there that sort of the the space is
+
+ align:start position:0%
+there that sort of the the space is
+ 
+
+ align:start position:0%
+there that sort of the the space is
+telling me this is useful you know use
+
+ align:start position:0%
+telling me this is useful you know use
+ 
+
+ align:start position:0%
+telling me this is useful you know use
+me as such this is a sitting a sitting
+
+ align:start position:0%
+me as such this is a sitting a sitting
+ 
+
+ align:start position:0%
+me as such this is a sitting a sitting
+area um that is a drawing board this is
+
+ align:start position:0%
+area um that is a drawing board this is
+ 
+
+ align:start position:0%
+area um that is a drawing board this is
+a drawing board um I I don't want I I
+
+ align:start position:0%
+a drawing board um I I don't want I I
+ 
+
+ align:start position:0%
+a drawing board um I I don't want I I
+feel like I can just work with what I
+
+ align:start position:0%
+feel like I can just work with what I
+ 
+
+ align:start position:0%
+feel like I can just work with what I
+have fill that space in um and and not
+
+ align:start position:0%
+have fill that space in um and and not
+ 
+
+ align:start position:0%
+have fill that space in um and and not
+disturb anyone none of the animals nor
+
+ align:start position:0%
+disturb anyone none of the animals nor
+ 
+
+ align:start position:0%
+disturb anyone none of the animals nor
+life can you just talk a little bit
+
+ align:start position:0%
+life can you just talk a little bit
+ 
+
+ align:start position:0%
+life can you just talk a little bit
+about that because it's quite different
+
+ align:start position:0%
+about that because it's quite different
+ 
+
+ align:start position:0%
+about that because it's quite different
+it looks quite different than your
+
+ align:start position:0%
+it looks quite different than your
+ 
+
+ align:start position:0%
+it looks quite different than your
+sketch okay well this is sort of the
+
+ align:start position:0%
+sketch okay well this is sort of the
+ 
+
+ align:start position:0%
+sketch okay well this is sort of the
+abstract version of the sketch um since
+
+ align:start position:0%
+abstract version of the sketch um since
+ 
+
+ align:start position:0%
+abstract version of the sketch um since
+the the spot that I picked is going to
+
+ align:start position:0%
+the the spot that I picked is going to
+ 
+
+ align:start position:0%
+the the spot that I picked is going to
+be very sunny um I wanted to take
+
+ align:start position:0%
+be very sunny um I wanted to take
+ 
+
+ align:start position:0%
+be very sunny um I wanted to take
+advantage of that so um I want something
+
+ align:start position:0%
+advantage of that so um I want something
+ 
+
+ align:start position:0%
+advantage of that so um I want something
+that that will be clear but also create
+
+ align:start position:0%
+that that will be clear but also create
+ 
+
+ align:start position:0%
+that that will be clear but also create
+some some Shadow some movement to um and
+
+ align:start position:0%
+some some Shadow some movement to um and
+ 
+
+ align:start position:0%
+some some Shadow some movement to um and
+in some ways I'm trying to use this as a
+
+ align:start position:0%
+in some ways I'm trying to use this as a
+ 
+
+ align:start position:0%
+in some ways I'm trying to use this as a
+tunnel um on this side and maybe on here
+
+ align:start position:0%
+tunnel um on this side and maybe on here
+ 
+
+ align:start position:0%
+tunnel um on this side and maybe on here
+S A curvature of the roof so that it
+
+ align:start position:0%
+S A curvature of the roof so that it
+ 
+
+ align:start position:0%
+S A curvature of the roof so that it
+trashs light in and BR into the space
+
+ align:start position:0%
+trashs light in and BR into the space
+ 
+
+ align:start position:0%
+trashs light in and BR into the space
+and it might bounce off from the top and
+
+ align:start position:0%
+and it might bounce off from the top and
+ 
+
+ align:start position:0%
+and it might bounce off from the top and
+go down um into the studio
+
+ align:start position:0%
+go down um into the studio
+ 
+
+ align:start position:0%
+go down um into the studio
+um but I just imagine it just growing
+
+ align:start position:0%
+um but I just imagine it just growing
+ 
+
+ align:start position:0%
+um but I just imagine it just growing
+out of the ground just covering it up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again it's a very very good start and
+
+ align:start position:0%
+again it's a very very good start and
+ 
+
+ align:start position:0%
+again it's a very very good start and
+then that gives me a license to negative
+
+ align:start position:0%
+then that gives me a license to negative
+ 
+
+ align:start position:0%
+then that gives me a license to negative
+now that I've done
+
+ align:start position:0%
+now that I've done
+ 
+
+ align:start position:0%
+now that I've done
+Sor um I'm really impressed also how
+
+ align:start position:0%
+Sor um I'm really impressed also how
+ 
+
+ align:start position:0%
+Sor um I'm really impressed also how
+quickly we have understood the Quarry
+
+ align:start position:0%
+quickly we have understood the Quarry
+ 
+
+ align:start position:0%
+quickly we have understood the Quarry
+and the subtleties of of the
+
+ align:start position:0%
+and the subtleties of of the
+ 
+
+ align:start position:0%
+and the subtleties of of the
+observations that you
+
+ align:start position:0%
+observations that you
+ 
+
+ align:start position:0%
+observations that you
+made uh I think the idea of coexisting
+
+ align:start position:0%
+made uh I think the idea of coexisting
+ 
+
+ align:start position:0%
+made uh I think the idea of coexisting
+with the Sea Calls is wonderful I don't
+
+ align:start position:0%
+with the Sea Calls is wonderful I don't
+ 
+
+ align:start position:0%
+with the Sea Calls is wonderful I don't
+know how you do that and if you can do
+
+ align:start position:0%
+know how you do that and if you can do
+ 
+
+ align:start position:0%
+know how you do that and if you can do
+that but I have to tell you a story I
+
+ align:start position:0%
+that but I have to tell you a story I
+ 
+
+ align:start position:0%
+that but I have to tell you a story I
+have a little summer house where I was
+
+ align:start position:0%
+have a little summer house where I was
+ 
+
+ align:start position:0%
+have a little summer house where I was
+which uh two uh young deer have decided
+
+ align:start position:0%
+which uh two uh young deer have decided
+ 
+
+ align:start position:0%
+which uh two uh young deer have decided
+as their house oh boy and uh they I was
+
+ align:start position:0%
+as their house oh boy and uh they I was
+ 
+
+ align:start position:0%
+as their house oh boy and uh they I was
+there and they were there and they were
+
+ align:start position:0%
+there and they were there and they were
+ 
+
+ align:start position:0%
+there and they were there and they were
+sort of wondering why why I was there CU
+
+ align:start position:0%
+sort of wondering why why I was there CU
+ 
+
+ align:start position:0%
+sort of wondering why why I was there CU
+I'm they're there more than I'm there
+
+ align:start position:0%
+I'm they're there more than I'm there
+ 
+
+ align:start position:0%
+I'm they're there more than I'm there
+and um we became friends over a couple
+
+ align:start position:0%
+and um we became friends over a couple
+ 
+
+ align:start position:0%
+and um we became friends over a couple
+days the two
+
+ align:start position:0%
+days the two
+ 
+
+ align:start position:0%
+days the two
+FS that SI dogs and you said the word
+
+ align:start position:0%
+FS that SI dogs and you said the word
+ 
+
+ align:start position:0%
+FS that SI dogs and you said the word
+and I said coexist I fig we could live
+
+ align:start position:0%
+and I said coexist I fig we could live
+ 
+
+ align:start position:0%
+and I said coexist I fig we could live
+together so the sensitivity towards the
+
+ align:start position:0%
+together so the sensitivity towards the
+ 
+
+ align:start position:0%
+together so the sensitivity towards the
+seagull which might have more problems
+
+ align:start position:0%
+seagull which might have more problems
+ 
+
+ align:start position:0%
+seagull which might have more problems
+than the deer I don't know in certain
+
+ align:start position:0%
+than the deer I don't know in certain
+ 
+
+ align:start position:0%
+than the deer I don't know in certain
+ways is wonderful and how you do that I
+
+ align:start position:0%
+ways is wonderful and how you do that I
+ 
+
+ align:start position:0%
+ways is wonderful and how you do that I
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+one is very interesting to me again from
+
+ align:start position:0%
+one is very interesting to me again from
+ 
+
+ align:start position:0%
+one is very interesting to me again from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+observation of the seall place I think
+
+ align:start position:0%
+observation of the seall place I think
+ 
+
+ align:start position:0%
+observation of the seall place I think
+you're right I think the sealls know
+
+ align:start position:0%
+you're right I think the sealls know
+ 
+
+ align:start position:0%
+you're right I think the sealls know
+something that they they know more than
+
+ align:start position:0%
+something that they they know more than
+ 
+
+ align:start position:0%
+something that they they know more than
+we know they've been around I don't know
+
+ align:start position:0%
+we know they've been around I don't know
+ 
+
+ align:start position:0%
+we know they've been around I don't know
+again how happy they're going to be
+
+ align:start position:0%
+again how happy they're going to be
+ 
+
+ align:start position:0%
+again how happy they're going to be
+about you moving in that's they'll let
+
+ align:start position:0%
+about you moving in that's they'll let
+ 
+
+ align:start position:0%
+about you moving in that's they'll let
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+think uh but I think it's a very good
+
+ align:start position:0%
+think uh but I think it's a very good
+ 
+
+ align:start position:0%
+think uh but I think it's a very good
+observation that this is a natural kind
+
+ align:start position:0%
+observation that this is a natural kind
+ 
+
+ align:start position:0%
+observation that this is a natural kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+some um the trans trans ation of that
+
+ align:start position:0%
+some um the trans trans ation of that
+ 
+
+ align:start position:0%
+some um the trans trans ation of that
+into what you say which is the case with
+
+ align:start position:0%
+into what you say which is the case with
+ 
+
+ align:start position:0%
+into what you say which is the case with
+all of us in the beginning as Architects
+
+ align:start position:0%
+all of us in the beginning as Architects
+ 
+
+ align:start position:0%
+all of us in the beginning as Architects
+and what we do is
+
+ align:start position:0%
+and what we do is
+ 
+
+ align:start position:0%
+and what we do is
+different um and that's our job that's
+
+ align:start position:0%
+different um and that's our job that's
+ 
+
+ align:start position:0%
+different um and that's our job that's
+what this is all about to try to get the
+
+ align:start position:0%
+what this is all about to try to get the
+ 
+
+ align:start position:0%
+what this is all about to try to get the
+head down to the body out to the hands
+
+ align:start position:0%
+head down to the body out to the hands
+ 
+
+ align:start position:0%
+head down to the body out to the hands
+and into this what it is we need and
+
+ align:start position:0%
+and into this what it is we need and
+ 
+
+ align:start position:0%
+and into this what it is we need and
+we're not going to get it right and I've
+
+ align:start position:0%
+we're not going to get it right and I've
+ 
+
+ align:start position:0%
+we're not going to get it right and I've
+been at it for a few years longer than
+
+ align:start position:0%
+been at it for a few years longer than
+ 
+
+ align:start position:0%
+been at it for a few years longer than
+you have and you'll see when I show you
+
+ align:start position:0%
+you have and you'll see when I show you
+ 
+
+ align:start position:0%
+you have and you'll see when I show you
+my own with I don't get it right either
+
+ align:start position:0%
+my own with I don't get it right either
+ 
+
+ align:start position:0%
+my own with I don't get it right either
+none of
+
+ align:start position:0%
+none of
+ 
+
+ align:start position:0%
+none of
+those I would like to challenge and
+
+ align:start position:0%
+those I would like to challenge and
+ 
+
+ align:start position:0%
+those I would like to challenge and
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+whether in this case the notion of this
+
+ align:start position:0%
+whether in this case the notion of this
+ 
+
+ align:start position:0%
+whether in this case the notion of this
+cover need to be as organic as what
+
+ align:start position:0%
+cover need to be as organic as what
+ 
+
+ align:start position:0%
+cover need to be as organic as what
+you're suggesting
+
+ align:start position:0%
+you're suggesting
+ 
+
+ align:start position:0%
+you're suggesting
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+because when I see if I if I when I saw
+
+ align:start position:0%
+because when I see if I if I when I saw
+ 
+
+ align:start position:0%
+because when I see if I if I when I saw
+this there is something already very
+
+ align:start position:0%
+this there is something already very
+ 
+
+ align:start position:0%
+this there is something already very
+elegant about the abstraction of this
+
+ align:start position:0%
+elegant about the abstraction of this
+ 
+
+ align:start position:0%
+elegant about the abstraction of this
+cover against the cord people see
+
+ align:start position:0%
+cover against the cord people see
+ 
+
+ align:start position:0%
+cover against the cord people see
+that um it's quite beautiful I was
+
+ align:start position:0%
+that um it's quite beautiful I was
+ 
+
+ align:start position:0%
+that um it's quite beautiful I was
+sitting over there looking at it and and
+
+ align:start position:0%
+sitting over there looking at it and and
+ 
+
+ align:start position:0%
+sitting over there looking at it and and
+the curved forms and the way that that
+
+ align:start position:0%
+the curved forms and the way that that
+ 
+
+ align:start position:0%
+the curved forms and the way that that
+you have started to address the solid is
+
+ align:start position:0%
+you have started to address the solid is
+ 
+
+ align:start position:0%
+you have started to address the solid is
+quite wonderful more wonderful in my
+
+ align:start position:0%
+quite wonderful more wonderful in my
+ 
+
+ align:start position:0%
+quite wonderful more wonderful in my
+mind than what's in your mind which is
+
+ align:start position:0%
+mind than what's in your mind which is
+ 
+
+ align:start position:0%
+mind than what's in your mind which is
+this and this is a takeoff I mean this
+
+ align:start position:0%
+this and this is a takeoff I mean this
+ 
+
+ align:start position:0%
+this and this is a takeoff I mean this
+is the beginning but whether would you
+
+ align:start position:0%
+is the beginning but whether would you
+ 
+
+ align:start position:0%
+is the beginning but whether would you
+correctly
+
+ align:start position:0%
+correctly
+ 
+
+ align:start position:0%
+correctly
+translate the architectural form and
+
+ align:start position:0%
+translate the architectural form and
+ 
+
+ align:start position:0%
+translate the architectural form and
+this great
+
+ align:start position:0%
+this great
+ 
+
+ align:start position:0%
+this great
+problem is not clear there could be
+
+ align:start position:0%
+problem is not clear there could be
+ 
+
+ align:start position:0%
+problem is not clear there could be
+another form as an example these could
+
+ align:start position:0%
+another form as an example these could
+ 
+
+ align:start position:0%
+another form as an example these could
+be even more uh
+
+ align:start position:0%
+be even more uh
+ 
+
+ align:start position:0%
+be even more uh
+Sals might move around flutter canvas
+
+ align:start position:0%
+Sals might move around flutter canvas
+ 
+
+ align:start position:0%
+Sals might move around flutter canvas
+different materials but it's very very
+
+ align:start position:0%
+different materials but it's very very
+ 
+
+ align:start position:0%
+different materials but it's very very
+powerful the form making of This related
+
+ align:start position:0%
+powerful the form making of This related
+ 
+
+ align:start position:0%
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+ align:start position:0%
+to the qualities of underneath I also
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+
+ align:start position:0%
+to the qualities of underneath I also
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+
+ align:start position:0%
+think in this one is very exciting that
+ 
+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+added to it but we've reinforced the
+
+ align:start position:0%
+added to it but we've reinforced the
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+
+ align:start position:0%
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+ align:start position:0%
+place so you are what I would say very
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+
+ align:start position:0%
+place so you are what I would say very
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+
+ align:start position:0%
+contexture you're taking what's there
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+
+ align:start position:0%
+contexture you're taking what's there
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+ align:start position:0%
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+
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+
+ align:start position:0%
+start but you're only halfway there in
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+
+ align:start position:0%
+start but you're only halfway there in
+terms of the architectural form but
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+ align:start position:0%
+terms of the architectural form but
+ 
+
+ align:start position:0%
+terms of the architectural form but
+you're a good halfway there in the sense
+
+ align:start position:0%
+you're a good halfway there in the sense
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+
+ align:start position:0%
+you're a good halfway there in the sense
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+ align:start position:0%
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+ align:start position:0%
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+to the C this to the sky I think this is
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+ align:start position:0%
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+
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+horrible
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+ align:start position:0%
+horrible
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+
+ align:start position:0%
+horrible
+agree you know like the fire es skap
+
+ align:start position:0%
+agree you know like the fire es skap
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+
+ align:start position:0%
+agree you know like the fire es skap
+coming down second means of eress which
+
+ align:start position:0%
+coming down second means of eress which
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+
+ align:start position:0%
+coming down second means of eress which
+is not what
+
+ align:start position:0%
+is not what
+ 
+
+ align:start position:0%
+is not what
+AR um this is a little bit better but
+
+ align:start position:0%
+AR um this is a little bit better but
+ 
+
+ align:start position:0%
+AR um this is a little bit better but
+still could be a little bit more subtle
+
+ align:start position:0%
+still could be a little bit more subtle
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+
+ align:start position:0%
+still could be a little bit more subtle
+uh I don't know where I'm talking you
+
+ align:start position:0%
+uh I don't know where I'm talking you
+ 
+
+ align:start position:0%
+uh I don't know where I'm talking you
+have me the other day here I don't want
+
+ align:start position:0%
+have me the other day here I don't want
+ 
+
+ align:start position:0%
+have me the other day here I don't want
+to be there thank you be some El so uh
+
+ align:start position:0%
+to be there thank you be some El so uh
+ 
+
+ align:start position:0%
+to be there thank you be some El so uh
+be careful about suggesting where the
+
+ align:start position:0%
+be careful about suggesting where the
+ 
+
+ align:start position:0%
+be careful about suggesting where the
+classroom is in terms of the
+
+ align:start position:0%
+classroom is in terms of the
+ 
+
+ align:start position:0%
+classroom is in terms of the
+direction because professors may not
+
+ align:start position:0%
+direction because professors may not
+ 
+
+ align:start position:0%
+direction because professors may not
+want to be where you want them to
+
+ align:start position:0%
+want to be where you want them to
+ 
+
+ align:start position:0%
+want to be where you want them to
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+be so but good start
\ No newline at end of file
diff --git a/Wi4W4PTzdhI.txt b/Wi4W4PTzdhI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a02398834cdfc06b85570dfb40c4827520d1de4d
--- /dev/null
+++ b/Wi4W4PTzdhI.txt
@@ -0,0 +1,843 @@
+align:start position:0%
+ 
+welcome to the launch of our course on
+
+ align:start position:0%
+welcome to the launch of our course on
+ 
+
+ align:start position:0%
+welcome to the launch of our course on
+shaping the future of work together over
+
+ align:start position:0%
+shaping the future of work together over
+ 
+
+ align:start position:0%
+shaping the future of work together over
+the next seven weeks we'll explore how
+
+ align:start position:0%
+the next seven weeks we'll explore how
+ 
+
+ align:start position:0%
+the next seven weeks we'll explore how
+to expand the number of good jobs career
+
+ align:start position:0%
+to expand the number of good jobs career
+ 
+
+ align:start position:0%
+to expand the number of good jobs career
+opportunities and workplaces that help
+
+ align:start position:0%
+opportunities and workplaces that help
+ 
+
+ align:start position:0%
+opportunities and workplaces that help
+us all realize our dreams our
+
+ align:start position:0%
+us all realize our dreams our
+ 
+
+ align:start position:0%
+us all realize our dreams our
+aspirations we have for work for our
+
+ align:start position:0%
+aspirations we have for work for our
+ 
+
+ align:start position:0%
+aspirations we have for work for our
+family lives and for building
+
+ align:start position:0%
+family lives and for building
+ 
+
+ align:start position:0%
+family lives and for building
+sustainable successful Enterprises and
+
+ align:start position:0%
+sustainable successful Enterprises and
+ 
+
+ align:start position:0%
+sustainable successful Enterprises and
+for our
+
+ align:start position:0%
+for our
+ 
+
+ align:start position:0%
+for our
+societies but before we talk about that
+
+ align:start position:0%
+societies but before we talk about that
+ 
+
+ align:start position:0%
+societies but before we talk about that
+let's talk about some of the
+
+ align:start position:0%
+let's talk about some of the
+ 
+
+ align:start position:0%
+let's talk about some of the
+difficulties we've experienced in the
+
+ align:start position:0%
+difficulties we've experienced in the
+ 
+
+ align:start position:0%
+difficulties we've experienced in the
+last week or so I want to begin with a
+
+ align:start position:0%
+last week or so I want to begin with a
+ 
+
+ align:start position:0%
+last week or so I want to begin with a
+statement of solidary for our colleagues
+
+ align:start position:0%
+statement of solidary for our colleagues
+ 
+
+ align:start position:0%
+statement of solidary for our colleagues
+in Europe and in Asia in light light of
+
+ align:start position:0%
+in Europe and in Asia in light light of
+ 
+
+ align:start position:0%
+in Europe and in Asia in light light of
+the terrible tragedies that have
+
+ align:start position:0%
+the terrible tragedies that have
+ 
+
+ align:start position:0%
+the terrible tragedies that have
+occurred in Brussels and in Pakistan
+
+ align:start position:0%
+occurred in Brussels and in Pakistan
+ 
+
+ align:start position:0%
+occurred in Brussels and in Pakistan
+today we are all sharing our concern
+
+ align:start position:0%
+today we are all sharing our concern
+ 
+
+ align:start position:0%
+today we are all sharing our concern
+that there have been over the past 18
+
+ align:start position:0%
+that there have been over the past 18
+ 
+
+ align:start position:0%
+that there have been over the past 18
+months 75 bombings in over 20 countries
+
+ align:start position:0%
+months 75 bombings in over 20 countries
+ 
+
+ align:start position:0%
+months 75 bombings in over 20 countries
+killing over 1300 people we think about
+
+ align:start position:0%
+killing over 1300 people we think about
+ 
+
+ align:start position:0%
+killing over 1300 people we think about
+the grief and the pain that so many
+
+ align:start position:0%
+the grief and the pain that so many
+ 
+
+ align:start position:0%
+the grief and the pain that so many
+nationalities and religions and people
+
+ align:start position:0%
+nationalities and religions and people
+ 
+
+ align:start position:0%
+nationalities and religions and people
+of different cultures all over the world
+
+ align:start position:0%
+of different cultures all over the world
+ 
+
+ align:start position:0%
+of different cultures all over the world
+have been experiencing and we are with
+
+ align:start position:0%
+have been experiencing and we are with
+ 
+
+ align:start position:0%
+have been experiencing and we are with
+them together my fellow cours team
+
+ align:start position:0%
+them together my fellow cours team
+ 
+
+ align:start position:0%
+them together my fellow cours team
+members here at MIT and I feel
+
+ align:start position:0%
+members here at MIT and I feel
+ 
+
+ align:start position:0%
+members here at MIT and I feel
+profoundly sad at yet more acts of
+
+ align:start position:0%
+profoundly sad at yet more acts of
+ 
+
+ align:start position:0%
+profoundly sad at yet more acts of
+violence we condemn them we we are
+
+ align:start position:0%
+violence we condemn them we we are
+ 
+
+ align:start position:0%
+violence we condemn them we we are
+committed to addressing the causes of
+
+ align:start position:0%
+committed to addressing the causes of
+ 
+
+ align:start position:0%
+committed to addressing the causes of
+violence in our societies and in our
+
+ align:start position:0%
+violence in our societies and in our
+ 
+
+ align:start position:0%
+violence in our societies and in our
+workplaces and to doing everything we
+
+ align:start position:0%
+workplaces and to doing everything we
+ 
+
+ align:start position:0%
+workplaces and to doing everything we
+can to help resolve these differences
+
+ align:start position:0%
+can to help resolve these differences
+ 
+
+ align:start position:0%
+can to help resolve these differences
+before they devolve into terrorism above
+
+ align:start position:0%
+before they devolve into terrorism above
+ 
+
+ align:start position:0%
+before they devolve into terrorism above
+all this course rests on the principle
+
+ align:start position:0%
+all this course rests on the principle
+ 
+
+ align:start position:0%
+all this course rests on the principle
+of respect for diversity in our world in
+
+ align:start position:0%
+of respect for diversity in our world in
+ 
+
+ align:start position:0%
+of respect for diversity in our world in
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+workplaces we had planned to show a bit
+
+ align:start position:0%
+workplaces we had planned to show a bit
+ 
+
+ align:start position:0%
+workplaces we had planned to show a bit
+later in the course a 20-minute video
+
+ align:start position:0%
+later in the course a 20-minute video
+ 
+
+ align:start position:0%
+later in the course a 20-minute video
+interview with Mary Row one of the
+
+ align:start position:0%
+interview with Mary Row one of the
+ 
+
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+interview with Mary Row one of the
+world's leaders in managing diversity
+
+ align:start position:0%
+world's leaders in managing diversity
+ 
+
+ align:start position:0%
+world's leaders in managing diversity
+and workplace conflicts Mary outlines
+
+ align:start position:0%
+and workplace conflicts Mary outlines
+ 
+
+ align:start position:0%
+and workplace conflicts Mary outlines
+the ways that we can address these
+
+ align:start position:0%
+the ways that we can address these
+ 
+
+ align:start position:0%
+the ways that we can address these
+tensions and the anger that they de they
+
+ align:start position:0%
+tensions and the anger that they de they
+ 
+
+ align:start position:0%
+tensions and the anger that they de they
+show in our society and that sometimes
+
+ align:start position:0%
+show in our society and that sometimes
+ 
+
+ align:start position:0%
+show in our society and that sometimes
+do spill over to our places of work but
+
+ align:start position:0%
+do spill over to our places of work but
+ 
+
+ align:start position:0%
+do spill over to our places of work but
+given the events in Europe and Asia and
+
+ align:start position:0%
+given the events in Europe and Asia and
+ 
+
+ align:start position:0%
+given the events in Europe and Asia and
+other parts of the world we'll post that
+
+ align:start position:0%
+other parts of the world we'll post that
+ 
+
+ align:start position:0%
+other parts of the world we'll post that
+interview this week so we can start
+
+ align:start position:0%
+interview this week so we can start
+ 
+
+ align:start position:0%
+interview this week so we can start
+discussing these issues now so we invite
+
+ align:start position:0%
+discussing these issues now so we invite
+ 
+
+ align:start position:0%
+discussing these issues now so we invite
+you to watch Mary's interview and use it
+
+ align:start position:0%
+you to watch Mary's interview and use it
+ 
+
+ align:start position:0%
+you to watch Mary's interview and use it
+uh in the discussion forum to comment on
+
+ align:start position:0%
+uh in the discussion forum to comment on
+ 
+
+ align:start position:0%
+uh in the discussion forum to comment on
+how issues of diversity inclusion and
+
+ align:start position:0%
+how issues of diversity inclusion and
+ 
+
+ align:start position:0%
+how issues of diversity inclusion and
+the management of inequities can be
+
+ align:start position:0%
+the management of inequities can be
+ 
+
+ align:start position:0%
+the management of inequities can be
+addressed in your workplace and in your
+
+ align:start position:0%
+addressed in your workplace and in your
+ 
+
+ align:start position:0%
+addressed in your workplace and in your
+job experiences we can design a better
+
+ align:start position:0%
+job experiences we can design a better
+ 
+
+ align:start position:0%
+job experiences we can design a better
+future as we help each other shape this
+
+ align:start position:0%
+future as we help each other shape this
+ 
+
+ align:start position:0%
+future as we help each other shape this
+aspect of our workplaces in a positive
+
+ align:start position:0%
+aspect of our workplaces in a positive
+ 
+
+ align:start position:0%
+aspect of our workplaces in a positive
+way I invite you also to get started by
+
+ align:start position:0%
+way I invite you also to get started by
+ 
+
+ align:start position:0%
+way I invite you also to get started by
+sampling the rich a array of other
+
+ align:start position:0%
+sampling the rich a array of other
+ 
+
+ align:start position:0%
+sampling the rich a array of other
+videos that we have posted this week we
+
+ align:start position:0%
+videos that we have posted this week we
+ 
+
+ align:start position:0%
+videos that we have posted this week we
+have welcoming comments from National
+
+ align:start position:0%
+have welcoming comments from National
+ 
+
+ align:start position:0%
+have welcoming comments from National
+and internationally res renowned leaders
+
+ align:start position:0%
+and internationally res renowned leaders
+ 
+
+ align:start position:0%
+and internationally res renowned leaders
+from all over the world the US Secretary
+
+ align:start position:0%
+from all over the world the US Secretary
+ 
+
+ align:start position:0%
+from all over the world the US Secretary
+of Labor Tom Perez the director general
+
+ align:start position:0%
+of Labor Tom Perez the director general
+ 
+
+ align:start position:0%
+of Labor Tom Perez the director general
+of the international labor organization
+
+ align:start position:0%
+of the international labor organization
+ 
+
+ align:start position:0%
+of the international labor organization
+guy Ryder the secretary treasurer of
+
+ align:start position:0%
+guy Ryder the secretary treasurer of
+ 
+
+ align:start position:0%
+guy Ryder the secretary treasurer of
+America's largest Union Federation Liz
+
+ align:start position:0%
+America's largest Union Federation Liz
+ 
+
+ align:start position:0%
+America's largest Union Federation Liz
+Schuler and our course teams Human
+
+ align:start position:0%
+Schuler and our course teams Human
+ 
+
+ align:start position:0%
+Schuler and our course teams Human
+Resource Management expert Lee Dyer we
+
+ align:start position:0%
+Resource Management expert Lee Dyer we
+ 
+
+ align:start position:0%
+Resource Management expert Lee Dyer we
+include this diversity of voices to show
+
+ align:start position:0%
+include this diversity of voices to show
+ 
+
+ align:start position:0%
+include this diversity of voices to show
+how all of these communities need to
+
+ align:start position:0%
+how all of these communities need to
+ 
+
+ align:start position:0%
+how all of these communities need to
+work together to shape the future of
+
+ align:start position:0%
+work together to shape the future of
+ 
+
+ align:start position:0%
+work together to shape the future of
+work for you and for all the parties
+
+ align:start position:0%
+work for you and for all the parties
+ 
+
+ align:start position:0%
+work for you and for all the parties
+that have a stake in it and don't miss
+
+ align:start position:0%
+that have a stake in it and don't miss
+ 
+
+ align:start position:0%
+that have a stake in it and don't miss
+our three minute animated video
+
+ align:start position:0%
+our three minute animated video
+ 
+
+ align:start position:0%
+our three minute animated video
+summarizing 3,000 years of the history
+
+ align:start position:0%
+summarizing 3,000 years of the history
+ 
+
+ align:start position:0%
+summarizing 3,000 years of the history
+of work I think you will enjoy it then
+
+ align:start position:0%
+of work I think you will enjoy it then
+ 
+
+ align:start position:0%
+of work I think you will enjoy it then
+we move on to other videos and readings
+
+ align:start position:0%
+we move on to other videos and readings
+ 
+
+ align:start position:0%
+we move on to other videos and readings
+that discuss the challenges and exciting
+
+ align:start position:0%
+that discuss the challenges and exciting
+ 
+
+ align:start position:0%
+that discuss the challenges and exciting
+opportunities Innovations occurring in
+
+ align:start position:0%
+opportunities Innovations occurring in
+ 
+
+ align:start position:0%
+opportunities Innovations occurring in
+our workplaces today these set the stage
+
+ align:start position:0%
+our workplaces today these set the stage
+ 
+
+ align:start position:0%
+our workplaces today these set the stage
+for a much much more in-depth
+
+ align:start position:0%
+for a much much more in-depth
+ 
+
+ align:start position:0%
+for a much much more in-depth
+conversation about these issues in the
+
+ align:start position:0%
+conversation about these issues in the
+ 
+
+ align:start position:0%
+conversation about these issues in the
+weeks
+
+ align:start position:0%
+weeks
+ 
+
+ align:start position:0%
+weeks
+ahead we also uh note in your discussion
+
+ align:start position:0%
+ahead we also uh note in your discussion
+ 
+
+ align:start position:0%
+ahead we also uh note in your discussion
+form that you already started that some
+
+ align:start position:0%
+form that you already started that some
+ 
+
+ align:start position:0%
+form that you already started that some
+of you are concerned about how the
+
+ align:start position:0%
+of you are concerned about how the
+ 
+
+ align:start position:0%
+of you are concerned about how the
+issues of jobs and the future of work
+
+ align:start position:0%
+issues of jobs and the future of work
+ 
+
+ align:start position:0%
+issues of jobs and the future of work
+are being discussed in the presidential
+
+ align:start position:0%
+are being discussed in the presidential
+ 
+
+ align:start position:0%
+are being discussed in the presidential
+campaign in the United States some of
+
+ align:start position:0%
+campaign in the United States some of
+ 
+
+ align:start position:0%
+campaign in the United States some of
+you have lamented that yes they talk
+
+ align:start position:0%
+you have lamented that yes they talk
+ 
+
+ align:start position:0%
+you have lamented that yes they talk
+about jobs but don't have a vision for
+
+ align:start position:0%
+about jobs but don't have a vision for
+ 
+
+ align:start position:0%
+about jobs but don't have a vision for
+the future of work well maybe it's our
+
+ align:start position:0%
+the future of work well maybe it's our
+ 
+
+ align:start position:0%
+the future of work well maybe it's our
+job to bring our voices into these
+
+ align:start position:0%
+job to bring our voices into these
+ 
+
+ align:start position:0%
+job to bring our voices into these
+conversations as we will try to do and
+
+ align:start position:0%
+conversations as we will try to do and
+ 
+
+ align:start position:0%
+conversations as we will try to do and
+really lay out a vision for what work
+
+ align:start position:0%
+really lay out a vision for what work
+ 
+
+ align:start position:0%
+really lay out a vision for what work
+could be what the real needs of workers
+
+ align:start position:0%
+could be what the real needs of workers
+ 
+
+ align:start position:0%
+could be what the real needs of workers
+are what the real needs of businesses
+
+ align:start position:0%
+are what the real needs of businesses
+ 
+
+ align:start position:0%
+are what the real needs of businesses
+are today so maybe we can add our voices
+
+ align:start position:0%
+are today so maybe we can add our voices
+ 
+
+ align:start position:0%
+are today so maybe we can add our voices
+to this discussion so welcome join us
+
+ align:start position:0%
+to this discussion so welcome join us
+ 
+
+ align:start position:0%
+to this discussion so welcome join us
+look forward to having you uh engage
+
+ align:start position:0%
+look forward to having you uh engage
+ 
+
+ align:start position:0%
+look forward to having you uh engage
+with us and helping to see if we can use
+
+ align:start position:0%
+with us and helping to see if we can use
+ 
+
+ align:start position:0%
+with us and helping to see if we can use
+our Collective efforts to shape the
+
+ align:start position:0%
+our Collective efforts to shape the
+ 
+
+ align:start position:0%
+our Collective efforts to shape the
+future of work
\ No newline at end of file
diff --git a/WiFahA1iAv4.txt b/WiFahA1iAv4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..69a4a98d8eb08099cd6a84afd009ebfc8f9a31e0
--- /dev/null
+++ b/WiFahA1iAv4.txt
@@ -0,0 +1,10459 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right um and I really
+
+ align:start position:0%
+ocw.mit.edu all right um and I really
+ 
+
+ align:start position:0%
+ocw.mit.edu all right um and I really
+wanted to show you my little Hook video
+
+ align:start position:0%
+wanted to show you my little Hook video
+ 
+
+ align:start position:0%
+wanted to show you my little Hook video
+and I downloaded it so I thought we'd
+
+ align:start position:0%
+and I downloaded it so I thought we'd
+ 
+
+ align:start position:0%
+and I downloaded it so I thought we'd
+start just by watching that and then
+
+ align:start position:0%
+start just by watching that and then
+ 
+
+ align:start position:0%
+start just by watching that and then
+I'll pick up um about modeling Foams
+
+ align:start position:0%
+I'll pick up um about modeling Foams
+ 
+
+ align:start position:0%
+I'll pick up um about modeling Foams
+okay so this takes like nine or 10
+
+ align:start position:0%
+okay so this takes like nine or 10
+ 
+
+ align:start position:0%
+okay so this takes like nine or 10
+minutes but um I just thought it was
+
+ align:start position:0%
+minutes but um I just thought it was
+ 
+
+ align:start position:0%
+minutes but um I just thought it was
+cute and I made it and I want you to see
+
+ align:start position:0%
+cute and I made it and I want you to see
+ 
+
+ align:start position:0%
+cute and I made it and I want you to see
+it so so let's do that to
+
+ align:start position:0%
+it so so let's do that to
+ 
+
+ align:start position:0%
+it so so let's do that to
+start we're here at the har University
+
+ align:start position:0%
+start we're here at the har University
+ 
+
+ align:start position:0%
+start we're here at the har University
+boty Library looking at a first edition
+
+ align:start position:0%
+boty Library looking at a first edition
+ 
+
+ align:start position:0%
+boty Library looking at a first edition
+of Robert Ho's micrographia published
+
+ align:start position:0%
+of Robert Ho's micrographia published
+ 
+
+ align:start position:0%
+of Robert Ho's micrographia published
+how do I get rid of the bar Craig oh
+
+ align:start position:0%
+how do I get rid of the bar Craig oh
+ 
+
+ align:start position:0%
+how do I get rid of the bar Craig oh
+there book to show the microscopic
+
+ align:start position:0%
+there book to show the microscopic
+ 
+
+ align:start position:0%
+there book to show the microscopic
+structure of materials and it has a
+
+ align:start position:0%
+structure of materials and it has a
+ 
+
+ align:start position:0%
+structure of materials and it has a
+number of remarkable drawings in it here
+
+ align:start position:0%
+number of remarkable drawings in it here
+ 
+
+ align:start position:0%
+number of remarkable drawings in it here
+we see drawings of silk these are two
+
+ align:start position:0%
+we see drawings of silk these are two
+ 
+
+ align:start position:0%
+we see drawings of silk these are two
+different silks on the top here we have
+
+ align:start position:0%
+different silks on the top here we have
+ 
+
+ align:start position:0%
+different silks on the top here we have
+a fine whed silk and in this more
+
+ align:start position:0%
+a fine whed silk and in this more
+ 
+
+ align:start position:0%
+a fine whed silk and in this more
+detailed drawing down here you can see
+
+ align:start position:0%
+detailed drawing down here you can see
+ 
+
+ align:start position:0%
+detailed drawing down here you can see
+the pattern of the weaving of the silk
+
+ align:start position:0%
+the pattern of the weaving of the silk
+ 
+
+ align:start position:0%
+the pattern of the weaving of the silk
+the bottom image here is a drawing of
+
+ align:start position:0%
+the bottom image here is a drawing of
+ 
+
+ align:start position:0%
+the bottom image here is a drawing of
+watered silk and over here there's
+
+ align:start position:0%
+watered silk and over here there's
+ 
+
+ align:start position:0%
+watered silk and over here there's
+another higher magnification image and
+
+ align:start position:0%
+another higher magnification image and
+ 
+
+ align:start position:0%
+another higher magnification image and
+you can see the pattern here is more
+
+ align:start position:0%
+you can see the pattern here is more
+ 
+
+ align:start position:0%
+you can see the pattern here is more
+sharply angled and it appears that this
+
+ align:start position:0%
+sharply angled and it appears that this
+ 
+
+ align:start position:0%
+sharply angled and it appears that this
+sharper angle here gives the different
+
+ align:start position:0%
+sharper angle here gives the different
+ 
+
+ align:start position:0%
+sharper angle here gives the different
+texture to the surface finish of the
+
+ align:start position:0%
+texture to the surface finish of the
+ 
+
+ align:start position:0%
+texture to the surface finish of the
+silk so here we see a drawing of charred
+
+ align:start position:0%
+silk so here we see a drawing of charred
+ 
+
+ align:start position:0%
+silk so here we see a drawing of charred
+wood and one of the things I find
+
+ align:start position:0%
+wood and one of the things I find
+ 
+
+ align:start position:0%
+wood and one of the things I find
+interesting about this drawing is how
+
+ align:start position:0%
+interesting about this drawing is how
+ 
+
+ align:start position:0%
+interesting about this drawing is how
+similar it is to Modern electron micr
+
+ align:start position:0%
+similar it is to Modern electron micr
+ 
+
+ align:start position:0%
+similar it is to Modern electron micr
+you see and in this drawing we can see
+
+ align:start position:0%
+you see and in this drawing we can see
+ 
+
+ align:start position:0%
+you see and in this drawing we can see
+two of the main features we see these
+
+ align:start position:0%
+two of the main features we see these
+ 
+
+ align:start position:0%
+two of the main features we see these
+small cells which are fibers that
+
+ align:start position:0%
+small cells which are fibers that
+ 
+
+ align:start position:0%
+small cells which are fibers that
+provide structural support to the tree
+
+ align:start position:0%
+provide structural support to the tree
+ 
+
+ align:start position:0%
+provide structural support to the tree
+and we see these larger cells here which
+
+ align:start position:0%
+and we see these larger cells here which
+ 
+
+ align:start position:0%
+and we see these larger cells here which
+are vessels which allow fluids to go up
+
+ align:start position:0%
+are vessels which allow fluids to go up
+ 
+
+ align:start position:0%
+are vessels which allow fluids to go up
+and down the tree and here we see a
+
+ align:start position:0%
+and down the tree and here we see a
+ 
+
+ align:start position:0%
+and down the tree and here we see a
+drawing of the surface of a rosemary
+
+ align:start position:0%
+drawing of the surface of a rosemary
+ 
+
+ align:start position:0%
+drawing of the surface of a rosemary
+leaf with an unexpected tiny little bars
+
+ align:start position:0%
+leaf with an unexpected tiny little bars
+ 
+
+ align:start position:0%
+leaf with an unexpected tiny little bars
+and this is something that you can only
+
+ align:start position:0%
+and this is something that you can only
+ 
+
+ align:start position:0%
+and this is something that you can only
+see with a microscope you wouldn't
+
+ align:start position:0%
+see with a microscope you wouldn't
+ 
+
+ align:start position:0%
+see with a microscope you wouldn't
+expect to see those if you just feel the
+
+ align:start position:0%
+expect to see those if you just feel the
+ 
+
+ align:start position:0%
+expect to see those if you just feel the
+surface of the Rosary so it's kind of
+
+ align:start position:0%
+surface of the Rosary so it's kind of
+ 
+
+ align:start position:0%
+surface of the Rosary so it's kind of
+interesting that with the microscope you
+
+ align:start position:0%
+interesting that with the microscope you
+ 
+
+ align:start position:0%
+interesting that with the microscope you
+can see these features that are
+
+ align:start position:0%
+can see these features that are
+ 
+
+ align:start position:0%
+can see these features that are
+invisible to the naked
+
+ align:start position:0%
+invisible to the naked
+ 
+
+ align:start position:0%
+invisible to the naked
+ey one of the main themes of Material
+
+ align:start position:0%
+ey one of the main themes of Material
+ 
+
+ align:start position:0%
+ey one of the main themes of Material
+Science is that the properties of
+
+ align:start position:0%
+Science is that the properties of
+ 
+
+ align:start position:0%
+Science is that the properties of
+materials are related to their structure
+
+ align:start position:0%
+materials are related to their structure
+ 
+
+ align:start position:0%
+materials are related to their structure
+and so being able to see the structure
+
+ align:start position:0%
+and so being able to see the structure
+ 
+
+ align:start position:0%
+and so being able to see the structure
+at a microscopic scale is very helpful
+
+ align:start position:0%
+at a microscopic scale is very helpful
+ 
+
+ align:start position:0%
+at a microscopic scale is very helpful
+and today we can even see the structure
+
+ align:start position:0%
+and today we can even see the structure
+ 
+
+ align:start position:0%
+and today we can even see the structure
+at the atomic scale Robert Hook
+
+ align:start position:0%
+at the atomic scale Robert Hook
+ 
+
+ align:start position:0%
+at the atomic scale Robert Hook
+understood this idea
+
+ align:start position:0%
+understood this idea
+ 
+
+ align:start position:0%
+understood this idea
+and in the description of the cork hook
+
+ align:start position:0%
+and in the description of the cork hook
+ 
+
+ align:start position:0%
+and in the description of the cork hook
+States I no sooner discerned these which
+
+ align:start position:0%
+States I no sooner discerned these which
+ 
+
+ align:start position:0%
+States I no sooner discerned these which
+were the first microscopical pores I
+
+ align:start position:0%
+were the first microscopical pores I
+ 
+
+ align:start position:0%
+were the first microscopical pores I
+ever saw but me thought that I had with
+
+ align:start position:0%
+ever saw but me thought that I had with
+ 
+
+ align:start position:0%
+ever saw but me thought that I had with
+the discovery of them perfectly hinted
+
+ align:start position:0%
+the discovery of them perfectly hinted
+ 
+
+ align:start position:0%
+the discovery of them perfectly hinted
+to me the true and intelligible reason
+
+ align:start position:0%
+to me the true and intelligible reason
+ 
+
+ align:start position:0%
+to me the true and intelligible reason
+for all of the phenomena of cork so what
+
+ align:start position:0%
+for all of the phenomena of cork so what
+ 
+
+ align:start position:0%
+for all of the phenomena of cork so what
+he's saying here is that by looking at
+
+ align:start position:0%
+he's saying here is that by looking at
+ 
+
+ align:start position:0%
+he's saying here is that by looking at
+the structure and looking at these cells
+
+ align:start position:0%
+the structure and looking at these cells
+ 
+
+ align:start position:0%
+the structure and looking at these cells
+here in the drawing he thinks he can
+
+ align:start position:0%
+here in the drawing he thinks he can
+ 
+
+ align:start position:0%
+here in the drawing he thinks he can
+understand the properties of cork or the
+
+ align:start position:0%
+understand the properties of cork or the
+ 
+
+ align:start position:0%
+understand the properties of cork or the
+phenomena of cork what was it about
+
+ align:start position:0%
+phenomena of cork what was it about
+ 
+
+ align:start position:0%
+phenomena of cork what was it about
+Robert Hook that allowed him to make
+
+ align:start position:0%
+Robert Hook that allowed him to make
+ 
+
+ align:start position:0%
+Robert Hook that allowed him to make
+this book why was it him and not
+
+ align:start position:0%
+this book why was it him and not
+ 
+
+ align:start position:0%
+this book why was it him and not
+somebody else well Robert Hook had kind
+
+ align:start position:0%
+somebody else well Robert Hook had kind
+ 
+
+ align:start position:0%
+somebody else well Robert Hook had kind
+of an interesting history he grew up on
+
+ align:start position:0%
+of an interesting history he grew up on
+ 
+
+ align:start position:0%
+of an interesting history he grew up on
+the aisle of white and as a boy he loved
+
+ align:start position:0%
+the aisle of white and as a boy he loved
+ 
+
+ align:start position:0%
+the aisle of white and as a boy he loved
+making drawings and he got quite skilled
+
+ align:start position:0%
+making drawings and he got quite skilled
+ 
+
+ align:start position:0%
+making drawings and he got quite skilled
+at making drawings the other thing was
+
+ align:start position:0%
+at making drawings the other thing was
+ 
+
+ align:start position:0%
+at making drawings the other thing was
+he loved making models of things he made
+
+ align:start position:0%
+he loved making models of things he made
+ 
+
+ align:start position:0%
+he loved making models of things he made
+models of ships he made a a wooden clock
+
+ align:start position:0%
+models of ships he made a a wooden clock
+ 
+
+ align:start position:0%
+models of ships he made a a wooden clock
+that was a working clock when he was a
+
+ align:start position:0%
+that was a working clock when he was a
+ 
+
+ align:start position:0%
+that was a working clock when he was a
+kid and as a teenager he moved to London
+
+ align:start position:0%
+kid and as a teenager he moved to London
+ 
+
+ align:start position:0%
+kid and as a teenager he moved to London
+and he became an apprentice to Sir Peter
+
+ align:start position:0%
+and he became an apprentice to Sir Peter
+ 
+
+ align:start position:0%
+and he became an apprentice to Sir Peter
+Lily who was a famous painter of the
+
+ align:start position:0%
+Lily who was a famous painter of the
+ 
+
+ align:start position:0%
+Lily who was a famous painter of the
+time so his drawing was good enough that
+
+ align:start position:0%
+time so his drawing was good enough that
+ 
+
+ align:start position:0%
+time so his drawing was good enough that
+he would be working with a very
+
+ align:start position:0%
+he would be working with a very
+ 
+
+ align:start position:0%
+he would be working with a very
+well-known painter after he did that he
+
+ align:start position:0%
+well-known painter after he did that he
+ 
+
+ align:start position:0%
+well-known painter after he did that he
+went to the Westminister school and he
+
+ align:start position:0%
+went to the Westminister school and he
+ 
+
+ align:start position:0%
+went to the Westminister school and he
+studied Classics he studied mathematics
+
+ align:start position:0%
+studied Classics he studied mathematics
+ 
+
+ align:start position:0%
+studied Classics he studied mathematics
+but he also learned to use a lathe and
+
+ align:start position:0%
+but he also learned to use a lathe and
+ 
+
+ align:start position:0%
+but he also learned to use a lathe and
+this was also very helpful in him making
+
+ align:start position:0%
+this was also very helpful in him making
+ 
+
+ align:start position:0%
+this was also very helpful in him making
+various sorts of
+
+ align:start position:0%
+various sorts of
+ 
+
+ align:start position:0%
+various sorts of
+apparatus and as a student at Oxford he
+
+ align:start position:0%
+apparatus and as a student at Oxford he
+ 
+
+ align:start position:0%
+apparatus and as a student at Oxford he
+worked in the lab of Robert Bole and his
+
+ align:start position:0%
+worked in the lab of Robert Bole and his
+ 
+
+ align:start position:0%
+worked in the lab of Robert Bole and his
+job in that lab was to develop
+
+ align:start position:0%
+job in that lab was to develop
+ 
+
+ align:start position:0%
+job in that lab was to develop
+scientific apparatus and he did things
+
+ align:start position:0%
+scientific apparatus and he did things
+ 
+
+ align:start position:0%
+scientific apparatus and he did things
+like he built pumps that allowed Robert
+
+ align:start position:0%
+like he built pumps that allowed Robert
+ 
+
+ align:start position:0%
+like he built pumps that allowed Robert
+Bole to do the experiments that led to
+
+ align:start position:0%
+Bole to do the experiments that led to
+ 
+
+ align:start position:0%
+Bole to do the experiments that led to
+Bo
+
+ align:start position:0%
+Bo
+ 
+
+ align:start position:0%
+Bo
+law when he returned to London after
+
+ align:start position:0%
+law when he returned to London after
+ 
+
+ align:start position:0%
+law when he returned to London after
+Oxford he became the curator of
+
+ align:start position:0%
+Oxford he became the curator of
+ 
+
+ align:start position:0%
+Oxford he became the curator of
+experiments at the Royal Society and one
+
+ align:start position:0%
+experiments at the Royal Society and one
+ 
+
+ align:start position:0%
+experiments at the Royal Society and one
+of the things he did was he got a
+
+ align:start position:0%
+of the things he did was he got a
+ 
+
+ align:start position:0%
+of the things he did was he got a
+microscope he improved that microscope
+
+ align:start position:0%
+microscope he improved that microscope
+ 
+
+ align:start position:0%
+microscope he improved that microscope
+increasing their magnification which was
+
+ align:start position:0%
+increasing their magnification which was
+ 
+
+ align:start position:0%
+increasing their magnification which was
+what allowed him to make the beautiful
+
+ align:start position:0%
+what allowed him to make the beautiful
+ 
+
+ align:start position:0%
+what allowed him to make the beautiful
+drawings that we see today and here in
+
+ align:start position:0%
+drawings that we see today and here in
+ 
+
+ align:start position:0%
+drawings that we see today and here in
+the preface of the book we see that he
+
+ align:start position:0%
+the preface of the book we see that he
+ 
+
+ align:start position:0%
+the preface of the book we see that he
+even made a drawing of his microscope so
+
+ align:start position:0%
+even made a drawing of his microscope so
+ 
+
+ align:start position:0%
+even made a drawing of his microscope so
+this thing down here this is Robert
+
+ align:start position:0%
+this thing down here this is Robert
+ 
+
+ align:start position:0%
+this thing down here this is Robert
+Hook's
+
+ align:start position:0%
+Hook's
+ 
+
+ align:start position:0%
+Hook's
+microscope the development of new
+
+ align:start position:0%
+microscope the development of new
+ 
+
+ align:start position:0%
+microscope the development of new
+microscopes with higher and higher
+
+ align:start position:0%
+microscopes with higher and higher
+ 
+
+ align:start position:0%
+microscopes with higher and higher
+magnifications continues to this day
+
+ align:start position:0%
+magnifications continues to this day
+ 
+
+ align:start position:0%
+magnifications continues to this day
+scanning electron microscopes were
+
+ align:start position:0%
+scanning electron microscopes were
+ 
+
+ align:start position:0%
+scanning electron microscopes were
+invented in the 1960s and today we have
+
+ align:start position:0%
+invented in the 1960s and today we have
+ 
+
+ align:start position:0%
+invented in the 1960s and today we have
+transmission electron microscopes and
+
+ align:start position:0%
+transmission electron microscopes and
+ 
+
+ align:start position:0%
+transmission electron microscopes and
+atomic Force microscopes with even
+
+ align:start position:0%
+atomic Force microscopes with even
+ 
+
+ align:start position:0%
+atomic Force microscopes with even
+higher magnifications at these higher
+
+ align:start position:0%
+higher magnifications at these higher
+ 
+
+ align:start position:0%
+higher magnifications at these higher
+magnifications we can see details that
+
+ align:start position:0%
+magnifications we can see details that
+ 
+
+ align:start position:0%
+magnifications we can see details that
+hook was unable to see because of the
+
+ align:start position:0%
+hook was unable to see because of the
+ 
+
+ align:start position:0%
+hook was unable to see because of the
+limitations of the microscope that he
+
+ align:start position:0%
+limitations of the microscope that he
+ 
+
+ align:start position:0%
+limitations of the microscope that he
+had the optical microscope but it's
+
+ align:start position:0%
+had the optical microscope but it's
+ 
+
+ align:start position:0%
+had the optical microscope but it's
+interesting to see today the images we
+
+ align:start position:0%
+interesting to see today the images we
+ 
+
+ align:start position:0%
+interesting to see today the images we
+see in a scanning electron microscope at
+
+ align:start position:0%
+see in a scanning electron microscope at
+ 
+
+ align:start position:0%
+see in a scanning electron microscope at
+a similar magnification to those that
+
+ align:start position:0%
+a similar magnification to those that
+ 
+
+ align:start position:0%
+a similar magnification to those that
+hook saw in his optical microscope and
+
+ align:start position:0%
+hook saw in his optical microscope and
+ 
+
+ align:start position:0%
+hook saw in his optical microscope and
+it's it's remarkable to see how many of
+
+ align:start position:0%
+it's it's remarkable to see how many of
+ 
+
+ align:start position:0%
+it's it's remarkable to see how many of
+the features that we see in these much
+
+ align:start position:0%
+the features that we see in these much
+ 
+
+ align:start position:0%
+the features that we see in these much
+more fancy microscopes that he was able
+
+ align:start position:0%
+more fancy microscopes that he was able
+ 
+
+ align:start position:0%
+more fancy microscopes that he was able
+to capture in his drawings with his
+
+ align:start position:0%
+to capture in his drawings with his
+ 
+
+ align:start position:0%
+to capture in his drawings with his
+simple Optical microscope okay so here
+
+ align:start position:0%
+simple Optical microscope okay so here
+ 
+
+ align:start position:0%
+simple Optical microscope okay so here
+we have a picture of cork we have hooks
+
+ align:start position:0%
+we have a picture of cork we have hooks
+ 
+
+ align:start position:0%
+we have a picture of cork we have hooks
+drawings showing two perpendicular
+
+ align:start position:0%
+drawings showing two perpendicular
+ 
+
+ align:start position:0%
+drawings showing two perpendicular
+planes we also have this nice little
+
+ align:start position:0%
+planes we also have this nice little
+ 
+
+ align:start position:0%
+planes we also have this nice little
+drawing of a cork Branch here cork is
+
+ align:start position:0%
+drawing of a cork Branch here cork is
+ 
+
+ align:start position:0%
+drawing of a cork Branch here cork is
+the Bark from the cork oak tree and in
+
+ align:start position:0%
+the Bark from the cork oak tree and in
+ 
+
+ align:start position:0%
+the Bark from the cork oak tree and in
+Hook's drawings of the micro structure
+
+ align:start position:0%
+Hook's drawings of the micro structure
+ 
+
+ align:start position:0%
+Hook's drawings of the micro structure
+we can see these cells here are roughly
+
+ align:start position:0%
+we can see these cells here are roughly
+ 
+
+ align:start position:0%
+we can see these cells here are roughly
+boxlike they're more or less rectangular
+
+ align:start position:0%
+boxlike they're more or less rectangular
+ 
+
+ align:start position:0%
+boxlike they're more or less rectangular
+and these cells look more or less
+
+ align:start position:0%
+and these cells look more or less
+ 
+
+ align:start position:0%
+and these cells look more or less
+circular so there's these two different
+
+ align:start position:0%
+circular so there's these two different
+ 
+
+ align:start position:0%
+circular so there's these two different
+perpendicular planes in the Cork and
+
+ align:start position:0%
+perpendicular planes in the Cork and
+ 
+
+ align:start position:0%
+perpendicular planes in the Cork and
+when we look at these scanning electron
+
+ align:start position:0%
+when we look at these scanning electron
+ 
+
+ align:start position:0%
+when we look at these scanning electron
+micrographs we can see a very similar
+
+ align:start position:0%
+micrographs we can see a very similar
+ 
+
+ align:start position:0%
+micrographs we can see a very similar
+structure there's some cells that are
+
+ align:start position:0%
+structure there's some cells that are
+ 
+
+ align:start position:0%
+structure there's some cells that are
+roughly box-like and others that are
+
+ align:start position:0%
+roughly box-like and others that are
+ 
+
+ align:start position:0%
+roughly box-like and others that are
+more or less hexagonal or roughly
+
+ align:start position:0%
+more or less hexagonal or roughly
+ 
+
+ align:start position:0%
+more or less hexagonal or roughly
+rounded one feature that hook was not
+
+ align:start position:0%
+rounded one feature that hook was not
+ 
+
+ align:start position:0%
+rounded one feature that hook was not
+able to see though that you do see on
+
+ align:start position:0%
+able to see though that you do see on
+ 
+
+ align:start position:0%
+able to see though that you do see on
+the scanning electron micrographs is the
+
+ align:start position:0%
+the scanning electron micrographs is the
+ 
+
+ align:start position:0%
+the scanning electron micrographs is the
+waviness in the cell walls and that was
+
+ align:start position:0%
+waviness in the cell walls and that was
+ 
+
+ align:start position:0%
+waviness in the cell walls and that was
+because the resolution of his microscope
+
+ align:start position:0%
+because the resolution of his microscope
+ 
+
+ align:start position:0%
+because the resolution of his microscope
+was insufficient to see that level of
+
+ align:start position:0%
+was insufficient to see that level of
+ 
+
+ align:start position:0%
+was insufficient to see that level of
+detail and here in this illustration on
+
+ align:start position:0%
+detail and here in this illustration on
+ 
+
+ align:start position:0%
+detail and here in this illustration on
+the bottom here is a drawing of sponge
+
+ align:start position:0%
+the bottom here is a drawing of sponge
+ 
+
+ align:start position:0%
+the bottom here is a drawing of sponge
+and when we look at the scanning
+
+ align:start position:0%
+and when we look at the scanning
+ 
+
+ align:start position:0%
+and when we look at the scanning
+electron micrograph we see that the
+
+ align:start position:0%
+electron micrograph we see that the
+ 
+
+ align:start position:0%
+electron micrograph we see that the
+structure is remarkably similar to what
+
+ align:start position:0%
+structure is remarkably similar to what
+ 
+
+ align:start position:0%
+structure is remarkably similar to what
+Hook is drawn so here we have Hook's
+
+ align:start position:0%
+Hook is drawn so here we have Hook's
+ 
+
+ align:start position:0%
+Hook is drawn so here we have Hook's
+drawing of feathers and we can see he's
+
+ align:start position:0%
+drawing of feathers and we can see he's
+ 
+
+ align:start position:0%
+drawing of feathers and we can see he's
+made several drawings at different
+
+ align:start position:0%
+made several drawings at different
+ 
+
+ align:start position:0%
+made several drawings at different
+length scales and if we look at this one
+
+ align:start position:0%
+length scales and if we look at this one
+ 
+
+ align:start position:0%
+length scales and if we look at this one
+here we see the barbule and you can see
+
+ align:start position:0%
+here we see the barbule and you can see
+ 
+
+ align:start position:0%
+here we see the barbule and you can see
+this little hooked regions there and
+
+ align:start position:0%
+this little hooked regions there and
+ 
+
+ align:start position:0%
+this little hooked regions there and
+those hooks lock into the little
+
+ align:start position:0%
+those hooks lock into the little
+ 
+
+ align:start position:0%
+those hooks lock into the little
+feathers over on this side over here of
+
+ align:start position:0%
+feathers over on this side over here of
+ 
+
+ align:start position:0%
+feathers over on this side over here of
+the adjacent barbule and in the higher
+
+ align:start position:0%
+the adjacent barbule and in the higher
+ 
+
+ align:start position:0%
+the adjacent barbule and in the higher
+magnification picture you can see on one
+
+ align:start position:0%
+magnification picture you can see on one
+ 
+
+ align:start position:0%
+magnification picture you can see on one
+barbule there's hooks on one side but
+
+ align:start position:0%
+barbule there's hooks on one side but
+ 
+
+ align:start position:0%
+barbule there's hooks on one side but
+not on the other and it's this hooking
+
+ align:start position:0%
+not on the other and it's this hooking
+ 
+
+ align:start position:0%
+not on the other and it's this hooking
+of the two sections together that allows
+
+ align:start position:0%
+of the two sections together that allows
+ 
+
+ align:start position:0%
+of the two sections together that allows
+the feathers to maintain a smooth
+
+ align:start position:0%
+the feathers to maintain a smooth
+ 
+
+ align:start position:0%
+the feathers to maintain a smooth
+surface for the wing when the bird is
+
+ align:start position:0%
+surface for the wing when the bird is
+ 
+
+ align:start position:0%
+surface for the wing when the bird is
+flying and you can see the same sort of
+
+ align:start position:0%
+flying and you can see the same sort of
+ 
+
+ align:start position:0%
+flying and you can see the same sort of
+thing when you look at the electron
+
+ align:start position:0%
+thing when you look at the electron
+ 
+
+ align:start position:0%
+thing when you look at the electron
+micrographs you can see the little hooks
+
+ align:start position:0%
+micrographs you can see the little hooks
+ 
+
+ align:start position:0%
+micrographs you can see the little hooks
+on one side of the barbules and you can
+
+ align:start position:0%
+on one side of the barbules and you can
+ 
+
+ align:start position:0%
+on one side of the barbules and you can
+see how they interconnect together with
+
+ align:start position:0%
+see how they interconnect together with
+ 
+
+ align:start position:0%
+see how they interconnect together with
+the next Barb one of the most reproduced
+
+ align:start position:0%
+the next Barb one of the most reproduced
+ 
+
+ align:start position:0%
+the next Barb one of the most reproduced
+images from Hook's book is that of the
+
+ align:start position:0%
+images from Hook's book is that of the
+ 
+
+ align:start position:0%
+images from Hook's book is that of the
+flea this image we see here and you can
+
+ align:start position:0%
+flea this image we see here and you can
+ 
+
+ align:start position:0%
+flea this image we see here and you can
+see why it's a gorgeous image and it
+
+ align:start position:0%
+see why it's a gorgeous image and it
+ 
+
+ align:start position:0%
+see why it's a gorgeous image and it
+shows details that people had never seen
+
+ align:start position:0%
+shows details that people had never seen
+ 
+
+ align:start position:0%
+shows details that people had never seen
+before people were amazed to see that
+
+ align:start position:0%
+before people were amazed to see that
+ 
+
+ align:start position:0%
+before people were amazed to see that
+the little flea that they might have
+
+ align:start position:0%
+the little flea that they might have
+ 
+
+ align:start position:0%
+the little flea that they might have
+found on their dog or something was
+
+ align:start position:0%
+found on their dog or something was
+ 
+
+ align:start position:0%
+found on their dog or something was
+actually made up of this you know
+
+ align:start position:0%
+actually made up of this you know
+ 
+
+ align:start position:0%
+actually made up of this you know
+compound body with all these little
+
+ align:start position:0%
+compound body with all these little
+ 
+
+ align:start position:0%
+compound body with all these little
+plates and little hairs here and you can
+
+ align:start position:0%
+plates and little hairs here and you can
+ 
+
+ align:start position:0%
+plates and little hairs here and you can
+see there little tiny claws on the legs
+
+ align:start position:0%
+see there little tiny claws on the legs
+ 
+
+ align:start position:0%
+see there little tiny claws on the legs
+and the legs have all these hairs nobody
+
+ align:start position:0%
+and the legs have all these hairs nobody
+ 
+
+ align:start position:0%
+and the legs have all these hairs nobody
+had any idea that this is what a flea
+
+ align:start position:0%
+had any idea that this is what a flea
+ 
+
+ align:start position:0%
+had any idea that this is what a flea
+actually looked like and so it it was an
+
+ align:start position:0%
+actually looked like and so it it was an
+ 
+
+ align:start position:0%
+actually looked like and so it it was an
+amazing drawing and it was something
+
+ align:start position:0%
+amazing drawing and it was something
+ 
+
+ align:start position:0%
+amazing drawing and it was something
+that people were just stunned by when
+
+ align:start position:0%
+that people were just stunned by when
+ 
+
+ align:start position:0%
+that people were just stunned by when
+when Hook's book came out and if we look
+
+ align:start position:0%
+when Hook's book came out and if we look
+ 
+
+ align:start position:0%
+when Hook's book came out and if we look
+at a modern electron micrograph we can
+
+ align:start position:0%
+at a modern electron micrograph we can
+ 
+
+ align:start position:0%
+at a modern electron micrograph we can
+see it's remarkably similar if we look
+
+ align:start position:0%
+see it's remarkably similar if we look
+ 
+
+ align:start position:0%
+see it's remarkably similar if we look
+at the same magnification so hook showed
+
+ align:start position:0%
+at the same magnification so hook showed
+ 
+
+ align:start position:0%
+at the same magnification so hook showed
+many of the same details showed some of
+
+ align:start position:0%
+many of the same details showed some of
+ 
+
+ align:start position:0%
+many of the same details showed some of
+the same hairs on the legs showed the
+
+ align:start position:0%
+the same hairs on the legs showed the
+ 
+
+ align:start position:0%
+the same hairs on the legs showed the
+same sorts of plates showed the claws at
+
+ align:start position:0%
+same sorts of plates showed the claws at
+ 
+
+ align:start position:0%
+same sorts of plates showed the claws at
+the ends of the legs and our modern
+
+ align:start position:0%
+the ends of the legs and our modern
+ 
+
+ align:start position:0%
+the ends of the legs and our modern
+image is probably from a different
+
+ align:start position:0%
+image is probably from a different
+ 
+
+ align:start position:0%
+image is probably from a different
+species of flea we don't know what
+
+ align:start position:0%
+species of flea we don't know what
+ 
+
+ align:start position:0%
+species of flea we don't know what
+species of flea that hook actually
+
+ align:start position:0%
+species of flea that hook actually
+ 
+
+ align:start position:0%
+species of flea that hook actually
+looked at but you can see there's a
+
+ align:start position:0%
+looked at but you can see there's a
+ 
+
+ align:start position:0%
+looked at but you can see there's a
+tremendous similarity between the two
+
+ align:start position:0%
+tremendous similarity between the two
+ 
+
+ align:start position:0%
+tremendous similarity between the two
+images and it's remarkable how many of
+
+ align:start position:0%
+images and it's remarkable how many of
+ 
+
+ align:start position:0%
+images and it's remarkable how many of
+the features that hook was able to
+
+ align:start position:0%
+the features that hook was able to
+ 
+
+ align:start position:0%
+the features that hook was able to
+capture in his drawing and here we have
+
+ align:start position:0%
+capture in his drawing and here we have
+ 
+
+ align:start position:0%
+capture in his drawing and here we have
+the compound eye of the fly and this
+
+ align:start position:0%
+the compound eye of the fly and this
+ 
+
+ align:start position:0%
+the compound eye of the fly and this
+again was astonishing to people in
+
+ align:start position:0%
+again was astonishing to people in
+ 
+
+ align:start position:0%
+again was astonishing to people in
+Hook's day and even today people look at
+
+ align:start position:0%
+Hook's day and even today people look at
+ 
+
+ align:start position:0%
+Hook's day and even today people look at
+this image and they're they're pretty
+
+ align:start position:0%
+this image and they're they're pretty
+ 
+
+ align:start position:0%
+this image and they're they're pretty
+amazed at the detail in this drawing and
+
+ align:start position:0%
+amazed at the detail in this drawing and
+ 
+
+ align:start position:0%
+amazed at the detail in this drawing and
+again we can compare this with a modern
+
+ align:start position:0%
+again we can compare this with a modern
+ 
+
+ align:start position:0%
+again we can compare this with a modern
+electron micrograph and again you can
+
+ align:start position:0%
+electron micrograph and again you can
+ 
+
+ align:start position:0%
+electron micrograph and again you can
+see the similarities between what hook
+
+ align:start position:0%
+see the similarities between what hook
+ 
+
+ align:start position:0%
+see the similarities between what hook
+saw and what we see in a modern scanning
+
+ align:start position:0%
+saw and what we see in a modern scanning
+ 
+
+ align:start position:0%
+saw and what we see in a modern scanning
+electron microscope at a similar
+
+ align:start position:0%
+electron microscope at a similar
+ 
+
+ align:start position:0%
+electron microscope at a similar
+magnification in the 1980s Atomic Force
+
+ align:start position:0%
+magnification in the 1980s Atomic Force
+ 
+
+ align:start position:0%
+magnification in the 1980s Atomic Force
+microscopes were invented which have a
+
+ align:start position:0%
+microscopes were invented which have a
+ 
+
+ align:start position:0%
+microscopes were invented which have a
+resolution down to tens of nanometers
+
+ align:start position:0%
+resolution down to tens of nanometers
+ 
+
+ align:start position:0%
+resolution down to tens of nanometers
+and today there's transmission electron
+
+ align:start position:0%
+and today there's transmission electron
+ 
+
+ align:start position:0%
+and today there's transmission electron
+microscopes which allow you to see the
+
+ align:start position:0%
+microscopes which allow you to see the
+ 
+
+ align:start position:0%
+microscopes which allow you to see the
+atomic structure so for instance in a
+
+ align:start position:0%
+atomic structure so for instance in a
+ 
+
+ align:start position:0%
+atomic structure so for instance in a
+crystal lattice you can see the
+
+ align:start position:0%
+crystal lattice you can see the
+ 
+
+ align:start position:0%
+crystal lattice you can see the
+individual atoms and the and the regular
+
+ align:start position:0%
+individual atoms and the and the regular
+ 
+
+ align:start position:0%
+individual atoms and the and the regular
+crystal
+
+ align:start position:0%
+crystal
+ 
+
+ align:start position:0%
+crystal
+structure today most experimental
+
+ align:start position:0%
+structure today most experimental
+ 
+
+ align:start position:0%
+structure today most experimental
+studies of materials include photographs
+
+ align:start position:0%
+studies of materials include photographs
+ 
+
+ align:start position:0%
+studies of materials include photographs
+of the microscopic structure structure
+
+ align:start position:0%
+of the microscopic structure structure
+ 
+
+ align:start position:0%
+of the microscopic structure structure
+of the material taken through some sort
+
+ align:start position:0%
+of the material taken through some sort
+ 
+
+ align:start position:0%
+of the material taken through some sort
+of microscope and the remarkable thing
+
+ align:start position:0%
+of microscope and the remarkable thing
+ 
+
+ align:start position:0%
+of microscope and the remarkable thing
+is that all of these studies really
+
+ align:start position:0%
+is that all of these studies really
+ 
+
+ align:start position:0%
+is that all of these studies really
+Trace back to this book here that we're
+
+ align:start position:0%
+Trace back to this book here that we're
+ 
+
+ align:start position:0%
+Trace back to this book here that we're
+looking at today to Robert Hook's
+
+ align:start position:0%
+looking at today to Robert Hook's
+ 
+
+ align:start position:0%
+looking at today to Robert Hook's
+micrographia there you have it so I just
+
+ align:start position:0%
+micrographia there you have it so I just
+ 
+
+ align:start position:0%
+micrographia there you have it so I just
+thought that was kind of cute you might
+
+ align:start position:0%
+thought that was kind of cute you might
+ 
+
+ align:start position:0%
+thought that was kind of cute you might
+enjoy that so so that was that all
+
+ align:start position:0%
+enjoy that so so that was that all
+ 
+
+ align:start position:0%
+enjoy that so so that was that all
+right oops let me get out of there yeah
+
+ align:start position:0%
+right oops let me get out of there yeah
+ 
+
+ align:start position:0%
+right oops let me get out of there yeah
+stop okay so let's go back to the Foams
+
+ align:start position:0%
+stop okay so let's go back to the Foams
+ 
+
+ align:start position:0%
+stop okay so let's go back to the Foams
+so I think last time we got us far as
+
+ align:start position:0%
+so I think last time we got us far as
+ 
+
+ align:start position:0%
+so I think last time we got us far as
+talking about the linear elastic
+
+ align:start position:0%
+talking about the linear elastic
+ 
+
+ align:start position:0%
+talking about the linear elastic
+behavior of Foams and modeling that uh
+
+ align:start position:0%
+behavior of Foams and modeling that uh
+ 
+
+ align:start position:0%
+behavior of Foams and modeling that uh
+but we didn't quite get to looking at
+
+ align:start position:0%
+but we didn't quite get to looking at
+ 
+
+ align:start position:0%
+but we didn't quite get to looking at
+the strength the compressive strength of
+
+ align:start position:0%
+the strength the compressive strength of
+ 
+
+ align:start position:0%
+the strength the compressive strength of
+the foam so I think we got as far as
+
+ align:start position:0%
+the foam so I think we got as far as
+ 
+
+ align:start position:0%
+the foam so I think we got as far as
+comparing the models with these
+
+ align:start position:0%
+comparing the models with these
+ 
+
+ align:start position:0%
+comparing the models with these
+equations here and these um plots of the
+
+ align:start position:0%
+equations here and these um plots of the
+ 
+
+ align:start position:0%
+equations here and these um plots of the
+data uh and what I wanted to pick up
+
+ align:start position:0%
+data uh and what I wanted to pick up
+ 
+
+ align:start position:0%
+data uh and what I wanted to pick up
+with today was looking at the
+
+ align:start position:0%
+with today was looking at the
+ 
+
+ align:start position:0%
+with today was looking at the
+compressive strength and we'll look at
+
+ align:start position:0%
+compressive strength and we'll look at
+ 
+
+ align:start position:0%
+compressive strength and we'll look at
+the fracture toughness as well uh in
+
+ align:start position:0%
+the fracture toughness as well uh in
+ 
+
+ align:start position:0%
+the fracture toughness as well uh in
+tension so we're going to start with
+
+ align:start position:0%
+tension so we're going to start with
+ 
+
+ align:start position:0%
+tension so we're going to start with
+nonlinear elasticity and the elastic
+
+ align:start position:0%
+nonlinear elasticity and the elastic
+ 
+
+ align:start position:0%
+nonlinear elasticity and the elastic
+collapse stress
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we have an open celled
+
+ align:start position:0%
+so if we have an open celled
+ 
+
+ align:start position:0%
+so if we have an open celled
+foam the uh derivation for the elastic
+
+ align:start position:0%
+foam the uh derivation for the elastic
+ 
+
+ align:start position:0%
+foam the uh derivation for the elastic
+collapse stress is really pretty
+
+ align:start position:0%
+collapse stress is really pretty
+ 
+
+ align:start position:0%
+collapse stress is really pretty
+straightforward we say we have the
+
+ align:start position:0%
+straightforward we say we have the
+ 
+
+ align:start position:0%
+straightforward we say we have the
+elastic collapse occurs when the cell
+
+ align:start position:0%
+elastic collapse occurs when the cell
+ 
+
+ align:start position:0%
+elastic collapse occurs when the cell
+walls Buckle so in this schematic here
+
+ align:start position:0%
+walls Buckle so in this schematic here
+ 
+
+ align:start position:0%
+walls Buckle so in this schematic here
+you can see the vertical cell walls have
+
+ align:start position:0%
+you can see the vertical cell walls have
+ 
+
+ align:start position:0%
+you can see the vertical cell walls have
+buckled and so there's going to be some
+
+ align:start position:0%
+buckled and so there's going to be some
+ 
+
+ align:start position:0%
+buckled and so there's going to be some
+Oiler load that that's related to that
+
+ align:start position:0%
+Oiler load that that's related to that
+ 
+
+ align:start position:0%
+Oiler load that that's related to that
+buckling and that's just the usual Oiler
+
+ align:start position:0%
+buckling and that's just the usual Oiler
+ 
+
+ align:start position:0%
+buckling and that's just the usual Oiler
+load n^2 the N constraint Factor pi^ 2 e
+
+ align:start position:0%
+load n^2 the N constraint Factor pi^ 2 e
+ 
+
+ align:start position:0%
+load n^2 the N constraint Factor pi^ 2 e
+this is going to be e of the solid I
+
+ align:start position:0%
+this is going to be e of the solid I
+ 
+
+ align:start position:0%
+this is going to be e of the solid I
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+l^2 the length of the member and then
+
+ align:start position:0%
+l^2 the length of the member and then
+ 
+
+ align:start position:0%
+l^2 the length of the member and then
+the stress that corresponds to that is
+
+ align:start position:0%
+the stress that corresponds to that is
+ 
+
+ align:start position:0%
+the stress that corresponds to that is
+just going to be proportional to that
+
+ align:start position:0%
+just going to be proportional to that
+ 
+
+ align:start position:0%
+just going to be proportional to that
+buckling load over the area of the cell
+
+ align:start position:0%
+buckling load over the area of the cell
+ 
+
+ align:start position:0%
+buckling load over the area of the cell
+which is just l^2 so just P critical
+
+ align:start position:0%
+which is just l^2 so just P critical
+ 
+
+ align:start position:0%
+which is just l^2 so just P critical
+over l^2 so that just goes as es s i is
+
+ align:start position:0%
+over l^2 so that just goes as es s i is
+ 
+
+ align:start position:0%
+over l^2 so that just goes as es s i is
+to go as T 4th because we have that
+
+ align:start position:0%
+to go as T 4th because we have that
+ 
+
+ align:start position:0%
+to go as T 4th because we have that
+square sectioned uh member and now this
+
+ align:start position:0%
+square sectioned uh member and now this
+ 
+
+ align:start position:0%
+square sectioned uh member and now this
+is going to be l^2 and that's an l^ S so
+
+ align:start position:0%
+is going to be l^2 and that's an l^ S so
+ 
+
+ align:start position:0%
+is going to be l^2 and that's an l^ S so
+that's L 4th and so if I combine all of
+
+ align:start position:0%
+that's L 4th and so if I combine all of
+ 
+
+ align:start position:0%
+that's L 4th and so if I combine all of
+that together I can say that the elastic
+
+ align:start position:0%
+that together I can say that the elastic
+ 
+
+ align:start position:0%
+that together I can say that the elastic
+buckling stress is going to be some
+
+ align:start position:0%
+buckling stress is going to be some
+ 
+
+ align:start position:0%
+buckling stress is going to be some
+constant and I think we're up to C4 now
+
+ align:start position:0%
+constant and I think we're up to C4 now
+ 
+
+ align:start position:0%
+constant and I think we're up to C4 now
+times the Young's modulus of the solid
+
+ align:start position:0%
+times the Young's modulus of the solid
+ 
+
+ align:start position:0%
+times the Young's modulus of the solid
+times the relative density of the foam
+
+ align:start position:0%
+times the relative density of the foam
+ 
+
+ align:start position:0%
+times the relative density of the foam
+squared okay so that's our
+
+ align:start position:0%
+squared okay so that's our
+ 
+
+ align:start position:0%
+squared okay so that's our
+equation for the elastic buckling stress
+
+ align:start position:0%
+equation for the elastic buckling stress
+ 
+
+ align:start position:0%
+equation for the elastic buckling stress
+and if you compare this with data you
+
+ align:start position:0%
+and if you compare this with data you
+ 
+
+ align:start position:0%
+and if you compare this with data you
+can make an estimate of what C4 is and
+
+ align:start position:0%
+can make an estimate of what C4 is and
+ 
+
+ align:start position:0%
+can make an estimate of what C4 is and
+we find that C4 is about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+05 and you can also say that 0.005
+
+ align:start position:0%
+05 and you can also say that 0.005
+ 
+
+ align:start position:0%
+05 and you can also say that 0.005
+really corresponds to The Strain at
+
+ align:start position:0%
+really corresponds to The Strain at
+ 
+
+ align:start position:0%
+really corresponds to The Strain at
+which the buckling occurs because the
+
+ align:start position:0%
+which the buckling occurs because the
+ 
+
+ align:start position:0%
+which the buckling occurs because the
+Young's modulus goes as the constants
+
+ align:start position:0%
+Young's modulus goes as the constants
+ 
+
+ align:start position:0%
+Young's modulus goes as the constants
+one * e s * the relative density squ so
+
+ align:start position:0%
+one * e s * the relative density squ so
+ 
+
+ align:start position:0%
+one * e s * the relative density squ so
+the strain is just going to be the
+
+ align:start position:0%
+the strain is just going to be the
+ 
+
+ align:start position:0%
+the strain is just going to be the
+stress over the modulus so that does
+
+ align:start position:0%
+stress over the modulus so that does
+ 
+
+ align:start position:0%
+stress over the modulus so that does
+correspond to the The
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Strain so that's saying that that
+
+ align:start position:0%
+Strain so that's saying that that
+ 
+
+ align:start position:0%
+Strain so that's saying that that
+buckling compressive stress occurs at a
+
+ align:start position:0%
+buckling compressive stress occurs at a
+ 
+
+ align:start position:0%
+buckling compressive stress occurs at a
+strain of about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+5% so that's open
+
+ align:start position:0%
+5% so that's open
+ 
+
+ align:start position:0%
+5% so that's open
+cells and then if we look at closed
+
+ align:start position:0%
+cells and then if we look at closed
+ 
+
+ align:start position:0%
+cells and then if we look at closed
+cells if you recall when we looked at
+
+ align:start position:0%
+cells if you recall when we looked at
+ 
+
+ align:start position:0%
+cells if you recall when we looked at
+the modui we looked at a couple of extra
+
+ align:start position:0%
+the modui we looked at a couple of extra
+ 
+
+ align:start position:0%
+the modui we looked at a couple of extra
+terms one was associated with face
+
+ align:start position:0%
+terms one was associated with face
+ 
+
+ align:start position:0%
+terms one was associated with face
+stretching for the modulus and the other
+
+ align:start position:0%
+stretching for the modulus and the other
+ 
+
+ align:start position:0%
+stretching for the modulus and the other
+was associated with the compression of
+
+ align:start position:0%
+was associated with the compression of
+ 
+
+ align:start position:0%
+was associated with the compression of
+the gas for the buckling the faces don't
+
+ align:start position:0%
+the gas for the buckling the faces don't
+ 
+
+ align:start position:0%
+the gas for the buckling the faces don't
+really contribute that much because
+
+ align:start position:0%
+really contribute that much because
+ 
+
+ align:start position:0%
+really contribute that much because
+typically the faces are very thin
+
+ align:start position:0%
+typically the faces are very thin
+ 
+
+ align:start position:0%
+typically the faces are very thin
+relative to the struts and because
+
+ align:start position:0%
+relative to the struts and because
+ 
+
+ align:start position:0%
+relative to the struts and because
+they're so thin they Buckle at a much
+
+ align:start position:0%
+they're so thin they Buckle at a much
+ 
+
+ align:start position:0%
+they're so thin they Buckle at a much
+lower load and they don't contribute too
+
+ align:start position:0%
+lower load and they don't contribute too
+ 
+
+ align:start position:0%
+lower load and they don't contribute too
+much so we're not going to worry about
+
+ align:start position:0%
+much so we're not going to worry about
+ 
+
+ align:start position:0%
+much so we're not going to worry about
+that contribution so I'm just going to
+
+ align:start position:0%
+that contribution so I'm just going to
+ 
+
+ align:start position:0%
+that contribution so I'm just going to
+say that the thickness of the face is
+
+ align:start position:0%
+say that the thickness of the face is
+ 
+
+ align:start position:0%
+say that the thickness of the face is
+often small
+
+ align:start position:0%
+often small
+ 
+
+ align:start position:0%
+often small
+compared to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges and that really is from the
+
+ align:start position:0%
+edges and that really is from the
+ 
+
+ align:start position:0%
+edges and that really is from the
+surface tension in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processing that draws material away from
+
+ align:start position:0%
+processing that draws material away from
+ 
+
+ align:start position:0%
+processing that draws material away from
+the face and into the edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there can be some contribution from the
+
+ align:start position:0%
+there can be some contribution from the
+ 
+
+ align:start position:0%
+there can be some contribution from the
+internal pressure so if the internal
+
+ align:start position:0%
+internal pressure so if the internal
+ 
+
+ align:start position:0%
+internal pressure so if the internal
+pressure is greater than atmospheric
+
+ align:start position:0%
+pressure is greater than atmospheric
+ 
+
+ align:start position:0%
+pressure is greater than atmospheric
+pressure then the cell walls are
+
+ align:start position:0%
+pressure then the cell walls are
+ 
+
+ align:start position:0%
+pressure then the cell walls are
+pre-tensioned and you'd have to account
+
+ align:start position:0%
+pre-tensioned and you'd have to account
+ 
+
+ align:start position:0%
+pre-tensioned and you'd have to account
+for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the buckling would have to overcome
+
+ align:start position:0%
+so the buckling would have to overcome
+ 
+
+ align:start position:0%
+so the buckling would have to overcome
+that pressure as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so then you would have the buckling
+
+ align:start position:0%
+well so then you would have the buckling
+ 
+
+ align:start position:0%
+well so then you would have the buckling
+stress would just be what we have up
+
+ align:start position:0%
+stress would just be what we have up
+ 
+
+ align:start position:0%
+stress would just be what we have up
+there C4 * es s * a relative density
+
+ align:start position:0%
+there C4 * es s * a relative density
+ 
+
+ align:start position:0%
+there C4 * es s * a relative density
+squared and then we just add on that
+
+ align:start position:0%
+squared and then we just add on that
+ 
+
+ align:start position:0%
+squared and then we just add on that
+factor P KN minus P
+
+ align:start position:0%
+factor P KN minus P
+ 
+
+ align:start position:0%
+factor P KN minus P
+atmospheric the thing that the gas tends
+
+ align:start position:0%
+atmospheric the thing that the gas tends
+ 
+
+ align:start position:0%
+atmospheric the thing that the gas tends
+to affect more than the buckling stress
+
+ align:start position:0%
+to affect more than the buckling stress
+ 
+
+ align:start position:0%
+to affect more than the buckling stress
+though is the post collapse Behavior so
+
+ align:start position:0%
+though is the post collapse Behavior so
+ 
+
+ align:start position:0%
+though is the post collapse Behavior so
+let me just show you a couple of things
+
+ align:start position:0%
+let me just show you a couple of things
+ 
+
+ align:start position:0%
+let me just show you a couple of things
+here so here's some data for the elastic
+
+ align:start position:0%
+here so here's some data for the elastic
+ 
+
+ align:start position:0%
+here so here's some data for the elastic
+collapse stress and you can see on the
+
+ align:start position:0%
+collapse stress and you can see on the
+ 
+
+ align:start position:0%
+collapse stress and you can see on the
+y- AIS we've got the stress normalized
+
+ align:start position:0%
+y- AIS we've got the stress normalized
+ 
+
+ align:start position:0%
+y- AIS we've got the stress normalized
+by the Young's modulus of the solid and
+
+ align:start position:0%
+by the Young's modulus of the solid and
+ 
+
+ align:start position:0%
+by the Young's modulus of the solid and
+on the xaxis we've got the relative
+
+ align:start position:0%
+on the xaxis we've got the relative
+ 
+
+ align:start position:0%
+on the xaxis we've got the relative
+density and that solid line there that
+
+ align:start position:0%
+density and that solid line there that
+ 
+
+ align:start position:0%
+density and that solid line there that
+sort of solid dark line is that equation
+
+ align:start position:0%
+sort of solid dark line is that equation
+ 
+
+ align:start position:0%
+sort of solid dark line is that equation
+there which is the same as this one up
+
+ align:start position:0%
+there which is the same as this one up
+ 
+
+ align:start position:0%
+there which is the same as this one up
+here and you can see the data lie fairly
+
+ align:start position:0%
+here and you can see the data lie fairly
+ 
+
+ align:start position:0%
+here and you can see the data lie fairly
+close to that uh but what's interesting
+
+ align:start position:0%
+close to that uh but what's interesting
+ 
+
+ align:start position:0%
+close to that uh but what's interesting
+is if you look at the Oops why is this
+
+ align:start position:0%
+is if you look at the Oops why is this
+ 
+
+ align:start position:0%
+is if you look at the Oops why is this
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+working
+
+ align:start position:0%
+working
+ 
+
+ align:start position:0%
+working
+okay maybe my batteries finally died
+
+ align:start position:0%
+okay maybe my batteries finally died
+ 
+
+ align:start position:0%
+okay maybe my batteries finally died
+here if we look at the the post collapse
+
+ align:start position:0%
+here if we look at the the post collapse
+ 
+
+ align:start position:0%
+here if we look at the the post collapse
+Behavior you can see if these are the
+
+ align:start position:0%
+Behavior you can see if these are the
+ 
+
+ align:start position:0%
+Behavior you can see if these are the
+stress strain
+
+ align:start position:0%
+stress strain
+ 
+
+ align:start position:0%
+stress strain
+curves uh they they don't they're not
+
+ align:start position:0%
+curves uh they they don't they're not
+ 
+
+ align:start position:0%
+curves uh they they don't they're not
+flat here they have some um rise to them
+
+ align:start position:0%
+flat here they have some um rise to them
+ 
+
+ align:start position:0%
+flat here they have some um rise to them
+and this is a closed cell foam and you
+
+ align:start position:0%
+and this is a closed cell foam and you
+ 
+
+ align:start position:0%
+and this is a closed cell foam and you
+can imagine as you're compressing the
+
+ align:start position:0%
+can imagine as you're compressing the
+ 
+
+ align:start position:0%
+can imagine as you're compressing the
+closed cell foam you're reducing the
+
+ align:start position:0%
+closed cell foam you're reducing the
+ 
+
+ align:start position:0%
+closed cell foam you're reducing the
+volume of the cell and as you're doing
+
+ align:start position:0%
+volume of the cell and as you're doing
+ 
+
+ align:start position:0%
+volume of the cell and as you're doing
+that you're increasing the pressure
+
+ align:start position:0%
+that you're increasing the pressure
+ 
+
+ align:start position:0%
+that you're increasing the pressure
+inside the cell from the gas and you can
+
+ align:start position:0%
+inside the cell from the gas and you can
+ 
+
+ align:start position:0%
+inside the cell from the gas and you can
+calculate what that is and I'll I'll do
+
+ align:start position:0%
+calculate what that is and I'll I'll do
+ 
+
+ align:start position:0%
+calculate what that is and I'll I'll do
+that in a second and if you subtract off
+
+ align:start position:0%
+that in a second and if you subtract off
+ 
+
+ align:start position:0%
+that in a second and if you subtract off
+that gas pressure contribution that
+
+ align:start position:0%
+that gas pressure contribution that
+ 
+
+ align:start position:0%
+that gas pressure contribution that
+works out to this line here then these
+
+ align:start position:0%
+works out to this line here then these
+ 
+
+ align:start position:0%
+works out to this line here then these
+lines will be more flat like this okay
+
+ align:start position:0%
+lines will be more flat like this okay
+ 
+
+ align:start position:0%
+lines will be more flat like this okay
+so and we already really pretty much
+
+ align:start position:0%
+so and we already really pretty much
+ 
+
+ align:start position:0%
+so and we already really pretty much
+worked out that gas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contribution so I'll just say for the
+
+ align:start position:0%
+contribution so I'll just say for the
+ 
+
+ align:start position:0%
+contribution so I'll just say for the
+Post collapse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Behavior Uh the stress Rises due to the
+
+ align:start position:0%
+Behavior Uh the stress Rises due to the
+ 
+
+ align:start position:0%
+Behavior Uh the stress Rises due to the
+gas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compression and that's as long as the
+
+ align:start position:0%
+compression and that's as long as the
+ 
+
+ align:start position:0%
+compression and that's as long as the
+faces don't rupt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you had aeric foam typically they
+
+ align:start position:0%
+so if you had aeric foam typically they
+ 
+
+ align:start position:0%
+so if you had aeric foam typically they
+don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rupture and what we had worked out
+
+ align:start position:0%
+rupture and what we had worked out
+ 
+
+ align:start position:0%
+rupture and what we had worked out
+before was that that pressure we called
+
+ align:start position:0%
+before was that that pressure we called
+ 
+
+ align:start position:0%
+before was that that pressure we called
+it P prime it was P KN minus P
+
+ align:start position:0%
+it P prime it was P KN minus P
+ 
+
+ align:start position:0%
+it P prime it was P KN minus P
+atmospheric that was equal to um P KN
+
+ align:start position:0%
+atmospheric that was equal to um P KN
+ 
+
+ align:start position:0%
+atmospheric that was equal to um P KN
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+oops time the amount of strain
+
+ align:start position:0%
+oops time the amount of strain
+ 
+
+ align:start position:0%
+oops time the amount of strain
+Epsilon Time 1 - 2 * the quon's ratio
+
+ align:start position:0%
+Epsilon Time 1 - 2 * the quon's ratio
+ 
+
+ align:start position:0%
+Epsilon Time 1 - 2 * the quon's ratio
+divided by 1 - Epsilon * 1 - 2
+
+ align:start position:0%
+divided by 1 - Epsilon * 1 - 2
+ 
+
+ align:start position:0%
+divided by 1 - Epsilon * 1 - 2
+muus the relative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density and once you get to the uh
+
+ align:start position:0%
+density and once you get to the uh
+ 
+
+ align:start position:0%
+density and once you get to the uh
+buckling stress then the pon ratio
+
+ align:start position:0%
+buckling stress then the pon ratio
+ 
+
+ align:start position:0%
+buckling stress then the pon ratio
+becomes zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you take a foam so I brought a
+
+ align:start position:0%
+so if you take a foam so I brought a
+ 
+
+ align:start position:0%
+so if you take a foam so I brought a
+little foam in so we can play around
+
+ align:start position:0%
+little foam in so we can play around
+ 
+
+ align:start position:0%
+little foam in so we can play around
+with this one so if you take a foam like
+
+ align:start position:0%
+with this one so if you take a foam like
+ 
+
+ align:start position:0%
+with this one so if you take a foam like
+this and you compress it once you've
+
+ align:start position:0%
+this and you compress it once you've
+ 
+
+ align:start position:0%
+this and you compress it once you've
+buckled it like this it's not getting
+
+ align:start position:0%
+buckled it like this it's not getting
+ 
+
+ align:start position:0%
+buckled it like this it's not getting
+any wider this way and part of the
+
+ align:start position:0%
+any wider this way and part of the
+ 
+
+ align:start position:0%
+any wider this way and part of the
+reason for that is you've got all these
+
+ align:start position:0%
+reason for that is you've got all these
+ 
+
+ align:start position:0%
+reason for that is you've got all these
+pores in here and the cells just
+
+ align:start position:0%
+pores in here and the cells just
+ 
+
+ align:start position:0%
+pores in here and the cells just
+collapse into the pores they don't you
+
+ align:start position:0%
+collapse into the pores they don't you
+ 
+
+ align:start position:0%
+collapse into the pores they don't you
+know they don't really need to move out
+
+ align:start position:0%
+know they don't really need to move out
+ 
+
+ align:start position:0%
+know they don't really need to move out
+sideways so you can smoos that yourself
+
+ align:start position:0%
+sideways so you can smoos that yourself
+ 
+
+ align:start position:0%
+sideways so you can smoos that yourself
+and try to convince yourself but the
+
+ align:start position:0%
+and try to convince yourself but the
+ 
+
+ align:start position:0%
+and try to convince yourself but the
+poson ratio is just zero yes Matt is
+
+ align:start position:0%
+poson ratio is just zero yes Matt is
+ 
+
+ align:start position:0%
+poson ratio is just zero yes Matt is
+there um are
+
+ align:start position:0%
+there um are
+ 
+
+ align:start position:0%
+there um are
+these uh I guess I would imagine stra
+
+ align:start position:0%
+these uh I guess I would imagine stra
+ 
+
+ align:start position:0%
+these uh I guess I would imagine stra
+rate comes into effect in the gas
+
+ align:start position:0%
+rate comes into effect in the gas
+ 
+
+ align:start position:0%
+rate comes into effect in the gas
+contribution yeah so so there was a
+
+ align:start position:0%
+contribution yeah so so there was a
+ 
+
+ align:start position:0%
+contribution yeah so so there was a
+strain rate effect with these things but
+
+ align:start position:0%
+strain rate effect with these things but
+ 
+
+ align:start position:0%
+strain rate effect with these things but
+I wasn't going to get into that here if
+
+ align:start position:0%
+I wasn't going to get into that here if
+ 
+
+ align:start position:0%
+I wasn't going to get into that here if
+you look in the book it's described in
+
+ align:start position:0%
+you look in the book it's described in
+ 
+
+ align:start position:0%
+you look in the book it's described in
+the book so there's I think there's two
+
+ align:start position:0%
+the book so there's I think there's two
+ 
+
+ align:start position:0%
+the book so there's I think there's two
+things one is that the solid itself can
+
+ align:start position:0%
+things one is that the solid itself can
+ 
+
+ align:start position:0%
+things one is that the solid itself can
+have a rate dependency and then there
+
+ align:start position:0%
+have a rate dependency and then there
+ 
+
+ align:start position:0%
+have a rate dependency and then there
+could be something
+
+ align:start position:0%
+could be something
+ 
+
+ align:start position:0%
+could be something
+connected yeah I mean I'm not going to
+
+ align:start position:0%
+connected yeah I mean I'm not going to
+ 
+
+ align:start position:0%
+connected yeah I mean I'm not going to
+go into that here but one one could look
+
+ align:start position:0%
+go into that here but one one could look
+ 
+
+ align:start position:0%
+go into that here but one one could look
+at that
+
+ align:start position:0%
+at that
+ 
+
+ align:start position:0%
+at that
+so okay so let me just write down one
+
+ align:start position:0%
+so okay so let me just write down one
+ 
+
+ align:start position:0%
+so okay so let me just write down one
+more thing here U because if we let new
+
+ align:start position:0%
+more thing here U because if we let new
+ 
+
+ align:start position:0%
+more thing here U because if we let new
+be zero then this thing here becomes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simpler so we could say the stress post
+
+ align:start position:0%
+simpler so we could say the stress post
+ 
+
+ align:start position:0%
+simpler so we could say the stress post
+collapse as a function of
+
+ align:start position:0%
+collapse as a function of
+ 
+
+ align:start position:0%
+collapse as a function of
+strain would be our buckling stress
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then plus this Factor
+
+ align:start position:0%
+and then plus this Factor
+ 
+
+ align:start position:0%
+and then plus this Factor
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops so that curve on the on the
+
+ align:start position:0%
+oops so that curve on the on the
+ 
+
+ align:start position:0%
+oops so that curve on the on the
+bottom over here if this is the stress
+
+ align:start position:0%
+bottom over here if this is the stress
+ 
+
+ align:start position:0%
+bottom over here if this is the stress
+strin curve this little dashed line here
+
+ align:start position:0%
+strin curve this little dashed line here
+ 
+
+ align:start position:0%
+strin curve this little dashed line here
+that's the gas contribution and that is
+
+ align:start position:0%
+that's the gas contribution and that is
+ 
+
+ align:start position:0%
+that's the gas contribution and that is
+this term here okay so you can kind of
+
+ align:start position:0%
+this term here okay so you can kind of
+ 
+
+ align:start position:0%
+this term here okay so you can kind of
+see how the shape of the curves reflects
+
+ align:start position:0%
+see how the shape of the curves reflects
+ 
+
+ align:start position:0%
+see how the shape of the curves reflects
+that gas contribution and when you
+
+ align:start position:0%
+that gas contribution and when you
+ 
+
+ align:start position:0%
+that gas contribution and when you
+subtract it out you get pretty much a
+
+ align:start position:0%
+subtract it out you get pretty much a
+ 
+
+ align:start position:0%
+subtract it out you get pretty much a
+horizontal Plateau over here
+
+ align:start position:0%
+horizontal Plateau over here
+ 
+
+ align:start position:0%
+horizontal Plateau over here
+okay are we
+
+ align:start position:0%
+okay are we
+ 
+
+ align:start position:0%
+okay are we
+happy
+
+ align:start position:0%
+happy
+ 
+
+ align:start position:0%
+happy
+yeah this is for the closed cell because
+
+ align:start position:0%
+yeah this is for the closed cell because
+ 
+
+ align:start position:0%
+yeah this is for the closed cell because
+the closed cell are the ones that are
+
+ align:start position:0%
+the closed cell are the ones that are
+ 
+
+ align:start position:0%
+the closed cell are the ones that are
+going to have the gas pressure right if
+
+ align:start position:0%
+going to have the gas pressure right if
+ 
+
+ align:start position:0%
+going to have the gas pressure right if
+it's open cells the gas can just move
+
+ align:start position:0%
+it's open cells the gas can just move
+ 
+
+ align:start position:0%
+it's open cells the gas can just move
+out of the
+
+ align:start position:0%
+out of the
+ 
+
+ align:start position:0%
+out of the
+cells oh oh sorry but that was sorry
+
+ align:start position:0%
+cells oh oh sorry but that was sorry
+ 
+
+ align:start position:0%
+cells oh oh sorry but that was sorry
+that was to show you that the plon ratio
+
+ align:start position:0%
+that was to show you that the plon ratio
+ 
+
+ align:start position:0%
+that was to show you that the plon ratio
+was zero and that's true for both of
+
+ align:start position:0%
+was zero and that's true for both of
+ 
+
+ align:start position:0%
+was zero and that's true for both of
+them yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then we can look at the plastic
+
+ align:start position:0%
+so then we can look at the plastic
+ 
+
+ align:start position:0%
+so then we can look at the plastic
+collapse stress say we had a a metal
+
+ align:start position:0%
+collapse stress say we had a a metal
+ 
+
+ align:start position:0%
+collapse stress say we had a a metal
+foam and we do a calculation a little
+
+ align:start position:0%
+foam and we do a calculation a little
+ 
+
+ align:start position:0%
+foam and we do a calculation a little
+bit like the one we did for the
+
+ align:start position:0%
+bit like the one we did for the
+ 
+
+ align:start position:0%
+bit like the one we did for the
+Honeycombs too so we say the failure
+
+ align:start position:0%
+Honeycombs too so we say the failure
+ 
+
+ align:start position:0%
+Honeycombs too so we say the failure
+occurs when the applied moment equals
+
+ align:start position:0%
+occurs when the applied moment equals
+ 
+
+ align:start position:0%
+occurs when the applied moment equals
+the plastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment and the applied moment is
+
+ align:start position:0%
+moment and the applied moment is
+ 
+
+ align:start position:0%
+moment and the applied moment is
+proportional to the applied stress times
+
+ align:start position:0%
+proportional to the applied stress times
+ 
+
+ align:start position:0%
+proportional to the applied stress times
+a length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubed so I'm going to call that applied
+
+ align:start position:0%
+cubed so I'm going to call that applied
+ 
+
+ align:start position:0%
+cubed so I'm going to call that applied
+stress our our strength Sigma star
+
+ align:start position:0%
+stress our our strength Sigma star
+ 
+
+ align:start position:0%
+stress our our strength Sigma star
+plastic times a length cubed so if you
+
+ align:start position:0%
+plastic times a length cubed so if you
+ 
+
+ align:start position:0%
+plastic times a length cubed so if you
+think of say the little schematic up
+
+ align:start position:0%
+think of say the little schematic up
+ 
+
+ align:start position:0%
+think of say the little schematic up
+here the force is going to go as stress
+
+ align:start position:0%
+here the force is going to go as stress
+ 
+
+ align:start position:0%
+here the force is going to go as stress
+times a length squared and the moment is
+
+ align:start position:0%
+times a length squared and the moment is
+ 
+
+ align:start position:0%
+times a length squared and the moment is
+going to be a force times a length so
+
+ align:start position:0%
+going to be a force times a length so
+ 
+
+ align:start position:0%
+going to be a force times a length so
+it's the force time the length cubed
+
+ align:start position:0%
+it's the force time the length cubed
+ 
+
+ align:start position:0%
+it's the force time the length cubed
+okay so rather sorry it's the stress
+
+ align:start position:0%
+okay so rather sorry it's the stress
+ 
+
+ align:start position:0%
+okay so rather sorry it's the stress
+times length cubed um and then the
+
+ align:start position:0%
+times length cubed um and then the
+ 
+
+ align:start position:0%
+times length cubed um and then the
+fracture rather the plastic moment
+
+ align:start position:0%
+fracture rather the plastic moment
+ 
+
+ align:start position:0%
+fracture rather the plastic moment
+goes as the yield
+
+ align:start position:0%
+goes as the yield
+ 
+
+ align:start position:0%
+goes as the yield
+strength times the thickness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubed and then if I just combine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those I get that the plastic collapse
+
+ align:start position:0%
+those I get that the plastic collapse
+ 
+
+ align:start position:0%
+those I get that the plastic collapse
+stress in compression is another
+
+ align:start position:0%
+stress in compression is another
+ 
+
+ align:start position:0%
+stress in compression is another
+constant I'm going to call it
+
+ align:start position:0%
+constant I'm going to call it
+ 
+
+ align:start position:0%
+constant I'm going to call it
+C5 times the yield
+
+ align:start position:0%
+C5 times the yield
+ 
+
+ align:start position:0%
+C5 times the yield
+strength times the relative
+
+ align:start position:0%
+strength times the relative
+ 
+
+ align:start position:0%
+strength times the relative
+density to the three halfes power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we look at data we find that this
+
+ align:start position:0%
+and if we look at data we find that this
+ 
+
+ align:start position:0%
+and if we look at data we find that this
+constant is about equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to3 and if I go to the next slide oops I
+
+ align:start position:0%
+to3 and if I go to the next slide oops I
+ 
+
+ align:start position:0%
+to3 and if I go to the next slide oops I
+missed one I think uh so here's a plot
+
+ align:start position:0%
+missed one I think uh so here's a plot
+ 
+
+ align:start position:0%
+missed one I think uh so here's a plot
+of the yield strength of the or the you
+
+ align:start position:0%
+of the yield strength of the or the you
+ 
+
+ align:start position:0%
+of the yield strength of the or the you
+know the plastic collapse strength of
+
+ align:start position:0%
+know the plastic collapse strength of
+ 
+
+ align:start position:0%
+know the plastic collapse strength of
+the foam divided by the yield strength
+
+ align:start position:0%
+the foam divided by the yield strength
+ 
+
+ align:start position:0%
+the foam divided by the yield strength
+of the solid plot us against the
+
+ align:start position:0%
+of the solid plot us against the
+ 
+
+ align:start position:0%
+of the solid plot us against the
+relative density and that dark bold line
+
+ align:start position:0%
+relative density and that dark bold line
+ 
+
+ align:start position:0%
+relative density and that dark bold line
+is this equation here and you can see
+
+ align:start position:0%
+is this equation here and you can see
+ 
+
+ align:start position:0%
+is this equation here and you can see
+the data like pretty well on that line
+
+ align:start position:0%
+the data like pretty well on that line
+ 
+
+ align:start position:0%
+the data like pretty well on that line
+there's one data set that's a little bit
+
+ align:start position:0%
+there's one data set that's a little bit
+ 
+
+ align:start position:0%
+there's one data set that's a little bit
+above the line but you can see the slope
+
+ align:start position:0%
+above the line but you can see the slope
+ 
+
+ align:start position:0%
+above the line but you can see the slope
+of that data set is still about three
+
+ align:start position:0%
+of that data set is still about three
+ 
+
+ align:start position:0%
+of that data set is still about three
+halves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the same as in the Honeycombs
+
+ align:start position:0%
+okay and the same as in the Honeycombs
+ 
+
+ align:start position:0%
+okay and the same as in the Honeycombs
+we could say that we could get elastic
+
+ align:start position:0%
+we could say that we could get elastic
+ 
+
+ align:start position:0%
+we could say that we could get elastic
+collapse before the plastic collapse if
+
+ align:start position:0%
+collapse before the plastic collapse if
+ 
+
+ align:start position:0%
+collapse before the plastic collapse if
+we were at a low density you can get the
+
+ align:start position:0%
+we were at a low density you can get the
+ 
+
+ align:start position:0%
+we were at a low density you can get the
+same thing in the Foams and you
+
+ align:start position:0%
+same thing in the Foams and you
+ 
+
+ align:start position:0%
+same thing in the Foams and you
+calculate out what the critical relative
+
+ align:start position:0%
+calculate out what the critical relative
+ 
+
+ align:start position:0%
+calculate out what the critical relative
+density is for that the same kind of way
+
+ align:start position:0%
+density is for that the same kind of way
+ 
+
+ align:start position:0%
+density is for that the same kind of way
+so we could say we can get elastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collapse precedes the plastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collapse if the elastic buckling stress
+
+ align:start position:0%
+collapse if the elastic buckling stress
+ 
+
+ align:start position:0%
+collapse if the elastic buckling stress
+is less than the plastic collapse
+
+ align:start position:0%
+is less than the plastic collapse
+ 
+
+ align:start position:0%
+is less than the plastic collapse
+stress so all we do is
+
+ align:start position:0%
+stress so all we do is
+ 
+
+ align:start position:0%
+stress so all we do is
+make those two things
+
+ align:start position:0%
+make those two things
+ 
+
+ align:start position:0%
+make those two things
+equal to figure out the critical
+
+ align:start position:0%
+equal to figure out the critical
+ 
+
+ align:start position:0%
+equal to figure out the critical
+relative density where you get the
+
+ align:start position:0%
+relative density where you get the
+ 
+
+ align:start position:0%
+relative density where you get the
+transition from one to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other so the relative density has to be
+
+ align:start position:0%
+other so the relative density has to be
+ 
+
+ align:start position:0%
+other so the relative density has to be
+less than 36 times the yield strength of
+
+ align:start position:0%
+less than 36 times the yield strength of
+ 
+
+ align:start position:0%
+less than 36 times the yield strength of
+the solid over the Young's modulus of
+
+ align:start position:0%
+the solid over the Young's modulus of
+ 
+
+ align:start position:0%
+the solid over the Young's modulus of
+the solid squared in order to get
+
+ align:start position:0%
+the solid squared in order to get
+ 
+
+ align:start position:0%
+the solid squared in order to get
+buckling before um
+
+ align:start position:0%
+buckling before um
+ 
+
+ align:start position:0%
+buckling before um
+yielding and let's see where can I put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so for rigid
+
+ align:start position:0%
+that so for rigid
+ 
+
+ align:start position:0%
+that so for rigid
+polymers that ratio of the strength of
+
+ align:start position:0%
+polymers that ratio of the strength of
+ 
+
+ align:start position:0%
+polymers that ratio of the strength of
+the solid over the modulus of the solid
+
+ align:start position:0%
+the solid over the modulus of the solid
+ 
+
+ align:start position:0%
+the solid over the modulus of the solid
+is about 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over3 and so the critical
+
+ align:start position:0%
+over3 and so the critical
+ 
+
+ align:start position:0%
+over3 and so the critical
+relative density for the transition is
+
+ align:start position:0%
+relative density for the transition is
+ 
+
+ align:start position:0%
+relative density for the transition is
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+004 so you'd have to have a pretty low
+
+ align:start position:0%
+004 so you'd have to have a pretty low
+ 
+
+ align:start position:0%
+004 so you'd have to have a pretty low
+density foam but it's possible and for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metals that
+
+ align:start position:0%
+metals that
+ 
+
+ align:start position:0%
+metals that
+ratio is about 1 in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th000 and then the critical transition
+
+ align:start position:0%
+th000 and then the critical transition
+ 
+
+ align:start position:0%
+th000 and then the critical transition
+density is less than 10us 5 so
+
+ align:start position:0%
+density is less than 10us 5 so
+ 
+
+ align:start position:0%
+density is less than 10us 5 so
+essentially it never happens for the
+
+ align:start position:0%
+essentially it never happens for the
+ 
+
+ align:start position:0%
+essentially it never happens for the
+metal foams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see go over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here then for the Clos cell Foams we
+
+ align:start position:0%
+here then for the Clos cell Foams we
+ 
+
+ align:start position:0%
+here then for the Clos cell Foams we
+could include the terms for face
+
+ align:start position:0%
+could include the terms for face
+ 
+
+ align:start position:0%
+could include the terms for face
+stretching and for the gas but in
+
+ align:start position:0%
+stretching and for the gas but in
+ 
+
+ align:start position:0%
+stretching and for the gas but in
+practice the faces don't really
+
+ align:start position:0%
+practice the faces don't really
+ 
+
+ align:start position:0%
+practice the faces don't really
+contribute very much and typically for
+
+ align:start position:0%
+contribute very much and typically for
+ 
+
+ align:start position:0%
+contribute very much and typically for
+Foams like say metal Foams or a rigid
+
+ align:start position:0%
+Foams like say metal Foams or a rigid
+ 
+
+ align:start position:0%
+Foams like say metal Foams or a rigid
+polymer that had a yield point the faces
+
+ align:start position:0%
+polymer that had a yield point the faces
+ 
+
+ align:start position:0%
+polymer that had a yield point the faces
+rupture and then if the faces rupture
+
+ align:start position:0%
+rupture and then if the faces rupture
+ 
+
+ align:start position:0%
+rupture and then if the faces rupture
+then you don't get the gas compression
+
+ align:start position:0%
+then you don't get the gas compression
+ 
+
+ align:start position:0%
+then you don't get the gas compression
+term either so I'll just write the full
+
+ align:start position:0%
+term either so I'll just write the full
+ 
+
+ align:start position:0%
+term either so I'll just write the full
+thing down but typically you don't need
+
+ align:start position:0%
+thing down but typically you don't need
+ 
+
+ align:start position:0%
+thing down but typically you don't need
+to use it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first term would be from the
+
+ align:start position:0%
+so the first term would be from the
+ 
+
+ align:start position:0%
+so the first term would be from the
+edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bending and the second term would be
+
+ align:start position:0%
+bending and the second term would be
+ 
+
+ align:start position:0%
+bending and the second term would be
+from the faces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stretching and this would be from the
+
+ align:start position:0%
+stretching and this would be from the
+ 
+
+ align:start position:0%
+stretching and this would be from the
+gas but in practice the first term is
+
+ align:start position:0%
+gas but in practice the first term is
+ 
+
+ align:start position:0%
+gas but in practice the first term is
+really the only one that's um
+
+ align:start position:0%
+really the only one that's um
+ 
+
+ align:start position:0%
+really the only one that's um
+significant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the for closed cell Foams this
+
+ align:start position:0%
+so the for closed cell Foams this
+ 
+
+ align:start position:0%
+so the for closed cell Foams this
+equation works pretty well too the same
+
+ align:start position:0%
+equation works pretty well too the same
+ 
+
+ align:start position:0%
+equation works pretty well too the same
+one is for the open cell foams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if we had a say a ceramic foam
+
+ align:start position:0%
+okay so if we had a say a ceramic foam
+ 
+
+ align:start position:0%
+okay so if we had a say a ceramic foam
+that was brittle it' be a brittle
+
+ align:start position:0%
+that was brittle it' be a brittle
+ 
+
+ align:start position:0%
+that was brittle it' be a brittle
+crushing strength and then we get
+
+ align:start position:0%
+crushing strength and then we get
+ 
+
+ align:start position:0%
+crushing strength and then we get
+failure when the applied moment m
+
+ align:start position:0%
+failure when the applied moment m
+ 
+
+ align:start position:0%
+failure when the applied moment m
+is equal to the fracture moment MF and
+
+ align:start position:0%
+is equal to the fracture moment MF and
+ 
+
+ align:start position:0%
+is equal to the fracture moment MF and
+this works very similar to the plastic
+
+ align:start position:0%
+this works very similar to the plastic
+ 
+
+ align:start position:0%
+this works very similar to the plastic
+yield
+
+ align:start position:0%
+yield
+ 
+
+ align:start position:0%
+yield
+strength uh so we find the applied
+
+ align:start position:0%
+strength uh so we find the applied
+ 
+
+ align:start position:0%
+strength uh so we find the applied
+moment goes as the global stress times
+
+ align:start position:0%
+moment goes as the global stress times
+ 
+
+ align:start position:0%
+moment goes as the global stress times
+the length cubed and the fracture moment
+
+ align:start position:0%
+the length cubed and the fracture moment
+ 
+
+ align:start position:0%
+the length cubed and the fracture moment
+goes as the cell wall strength times the
+
+ align:start position:0%
+goes as the cell wall strength times the
+ 
+
+ align:start position:0%
+goes as the cell wall strength times the
+length times the cell wall thickness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubed so the brittle crushing strength
+
+ align:start position:0%
+cubed so the brittle crushing strength
+ 
+
+ align:start position:0%
+cubed so the brittle crushing strength
+goes as another constant let's call let
+
+ align:start position:0%
+goes as another constant let's call let
+ 
+
+ align:start position:0%
+goes as another constant let's call let
+C6 times the wall
+
+ align:start position:0%
+C6 times the wall
+ 
+
+ align:start position:0%
+C6 times the wall
+strength times the relative density to
+
+ align:start position:0%
+strength times the relative density to
+ 
+
+ align:start position:0%
+strength times the relative density to
+the three Hales
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again and C6 is about equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to2 and typically ceramic Foams have
+
+ align:start position:0%
+to2 and typically ceramic Foams have
+ 
+
+ align:start position:0%
+to2 and typically ceramic Foams have
+open cells so I'm just going to leave it
+
+ align:start position:0%
+open cells so I'm just going to leave it
+ 
+
+ align:start position:0%
+open cells so I'm just going to leave it
+at the open cell um formula there so
+
+ align:start position:0%
+at the open cell um formula there so
+ 
+
+ align:start position:0%
+at the open cell um formula there so
+there's one last thing for the
+
+ align:start position:0%
+there's one last thing for the
+ 
+
+ align:start position:0%
+there's one last thing for the
+compressive behavior and that's the
+
+ align:start position:0%
+compressive behavior and that's the
+ 
+
+ align:start position:0%
+compressive behavior and that's the
+densification strain and we just have an
+
+ align:start position:0%
+densification strain and we just have an
+ 
+
+ align:start position:0%
+densification strain and we just have an
+empirical relationship for the
+
+ align:start position:0%
+empirical relationship for the
+ 
+
+ align:start position:0%
+empirical relationship for the
+densification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strain so if you compress the foam and
+
+ align:start position:0%
+strain so if you compress the foam and
+ 
+
+ align:start position:0%
+strain so if you compress the foam and
+you get to very large strains then the
+
+ align:start position:0%
+you get to very large strains then the
+ 
+
+ align:start position:0%
+you get to very large strains then the
+cell walls start to touch and the stress
+
+ align:start position:0%
+cell walls start to touch and the stress
+ 
+
+ align:start position:0%
+cell walls start to touch and the stress
+starts to rise steeply and there's some
+
+ align:start position:0%
+starts to rise steeply and there's some
+ 
+
+ align:start position:0%
+starts to rise steeply and there's some
+strain at which that occurs and we call
+
+ align:start position:0%
+strain at which that occurs and we call
+ 
+
+ align:start position:0%
+strain at which that occurs and we call
+that the densification strain and in the
+
+ align:start position:0%
+that the densification strain and in the
+ 
+
+ align:start position:0%
+that the densification strain and in the
+limit the modulus at that point would go
+
+ align:start position:0%
+limit the modulus at that point would go
+ 
+
+ align:start position:0%
+limit the modulus at that point would go
+to the modulus of the solid if you could
+
+ align:start position:0%
+to the modulus of the solid if you could
+ 
+
+ align:start position:0%
+to the modulus of the solid if you could
+completely squeeze all the pores out the
+
+ align:start position:0%
+completely squeeze all the pores out the
+ 
+
+ align:start position:0%
+completely squeeze all the pores out the
+stiffness of that uh would go to the
+
+ align:start position:0%
+stiffness of that uh would go to the
+ 
+
+ align:start position:0%
+stiffness of that uh would go to the
+modulus of the solid and you might
+
+ align:start position:0%
+modulus of the solid and you might
+ 
+
+ align:start position:0%
+modulus of the solid and you might
+expect that that densification strain is
+
+ align:start position:0%
+expect that that densification strain is
+ 
+
+ align:start position:0%
+expect that that densification strain is
+just one minus the relative density but
+
+ align:start position:0%
+just one minus the relative density but
+ 
+
+ align:start position:0%
+just one minus the relative density but
+it actually occurs at a slightly smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strain so a large compressive stress or
+
+ align:start position:0%
+strain so a large compressive stress or
+ 
+
+ align:start position:0%
+strain so a large compressive stress or
+strain I guess we could say the cell
+
+ align:start position:0%
+strain I guess we could say the cell
+ 
+
+ align:start position:0%
+strain I guess we could say the cell
+walls touch and we start to get this
+
+ align:start position:0%
+walls touch and we start to get this
+ 
+
+ align:start position:0%
+walls touch and we start to get this
+densification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the modulus and the limit would go to
+
+ align:start position:0%
+so the modulus and the limit would go to
+ 
+
+ align:start position:0%
+so the modulus and the limit would go to
+the modulus of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solid and you might expect that the
+
+ align:start position:0%
+solid and you might expect that the
+ 
+
+ align:start position:0%
+solid and you might expect that the
+densification strain was just equal to
+
+ align:start position:0%
+densification strain was just equal to
+ 
+
+ align:start position:0%
+densification strain was just equal to
+one minus the relative
+
+ align:start position:0%
+one minus the relative
+ 
+
+ align:start position:0%
+one minus the relative
+density but it occurs at a little bit
+
+ align:start position:0%
+density but it occurs at a little bit
+ 
+
+ align:start position:0%
+density but it occurs at a little bit
+less than that so empirically we find
+
+ align:start position:0%
+less than that so empirically we find
+ 
+
+ align:start position:0%
+less than that so empirically we find
+that it's just one -
+
+ align:start position:0%
+that it's just one -
+ 
+
+ align:start position:0%
+that it's just one -
+1.4 times the relative
+
+ align:start position:0%
+1.4 times the relative
+ 
+
+ align:start position:0%
+1.4 times the relative
+density okay okay and then I have this
+
+ align:start position:0%
+density okay okay and then I have this
+ 
+
+ align:start position:0%
+density okay okay and then I have this
+plot here which is really just fitting
+
+ align:start position:0%
+plot here which is really just fitting
+ 
+
+ align:start position:0%
+plot here which is really just fitting
+aligned to that data for the
+
+ align:start position:0%
+aligned to that data for the
+ 
+
+ align:start position:0%
+aligned to that data for the
+densification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strain so those equations describe the
+
+ align:start position:0%
+strain so those equations describe the
+ 
+
+ align:start position:0%
+strain so those equations describe the
+compressive stress or the compressive
+
+ align:start position:0%
+compressive stress or the compressive
+ 
+
+ align:start position:0%
+compressive stress or the compressive
+behavior of the foam so we've got the
+
+ align:start position:0%
+behavior of the foam so we've got the
+ 
+
+ align:start position:0%
+behavior of the foam so we've got the
+moduli we've got the three compressive
+
+ align:start position:0%
+moduli we've got the three compressive
+ 
+
+ align:start position:0%
+moduli we've got the three compressive
+uh strengths and we've got the
+
+ align:start position:0%
+uh strengths and we've got the
+ 
+
+ align:start position:0%
+uh strengths and we've got the
+densification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strain so what we're going to do later
+
+ align:start position:0%
+strain so what we're going to do later
+ 
+
+ align:start position:0%
+strain so what we're going to do later
+on in the course is we'll use those
+
+ align:start position:0%
+on in the course is we'll use those
+ 
+
+ align:start position:0%
+on in the course is we'll use those
+models to look at we can use Foams and
+
+ align:start position:0%
+models to look at we can use Foams and
+ 
+
+ align:start position:0%
+models to look at we can use Foams and
+things like sandwich panels and looking
+
+ align:start position:0%
+things like sandwich panels and looking
+ 
+
+ align:start position:0%
+things like sandwich panels and looking
+at energy absorption and we'll also look
+
+ align:start position:0%
+at energy absorption and we'll also look
+ 
+
+ align:start position:0%
+at energy absorption and we'll also look
+at these equations in terms of some
+
+ align:start position:0%
+at these equations in terms of some
+ 
+
+ align:start position:0%
+at these equations in terms of some
+biomedical materials looking at tricular
+
+ align:start position:0%
+biomedical materials looking at tricular
+ 
+
+ align:start position:0%
+biomedical materials looking at tricular
+bone and looking at tissue engineering
+
+ align:start position:0%
+bone and looking at tissue engineering
+ 
+
+ align:start position:0%
+bone and looking at tissue engineering
+scaffolds so there's one last property I
+
+ align:start position:0%
+scaffolds so there's one last property I
+ 
+
+ align:start position:0%
+scaffolds so there's one last property I
+wanted to go over and that's the
+
+ align:start position:0%
+wanted to go over and that's the
+ 
+
+ align:start position:0%
+wanted to go over and that's the
+fracture toughness so if we were pulling
+
+ align:start position:0%
+fracture toughness so if we were pulling
+ 
+
+ align:start position:0%
+fracture toughness so if we were pulling
+the foam in tension and we had a crack
+
+ align:start position:0%
+the foam in tension and we had a crack
+ 
+
+ align:start position:0%
+the foam in tension and we had a crack
+in the foam we'd want to know what the
+
+ align:start position:0%
+in the foam we'd want to know what the
+ 
+
+ align:start position:0%
+in the foam we'd want to know what the
+fracture toughness would be for a
+
+ align:start position:0%
+fracture toughness would be for a
+ 
+
+ align:start position:0%
+fracture toughness would be for a
+brittle foam and this follows the same
+
+ align:start position:0%
+brittle foam and this follows the same
+ 
+
+ align:start position:0%
+brittle foam and this follows the same
+sort of argument as we had for the
+
+ align:start position:0%
+sort of argument as we had for the
+ 
+
+ align:start position:0%
+sort of argument as we had for the
+honeycomb so all these equations really
+
+ align:start position:0%
+honeycomb so all these equations really
+ 
+
+ align:start position:0%
+honeycomb so all these equations really
+are just following the same kinds of
+
+ align:start position:0%
+are just following the same kinds of
+ 
+
+ align:start position:0%
+are just following the same kinds of
+arguments
+
+ align:start position:0%
+arguments
+ 
+
+ align:start position:0%
+arguments
+but you can kind of see how having the
+
+ align:start position:0%
+but you can kind of see how having the
+ 
+
+ align:start position:0%
+but you can kind of see how having the
+honeycomb calculations it it makes it
+
+ align:start position:0%
+honeycomb calculations it it makes it
+ 
+
+ align:start position:0%
+honeycomb calculations it it makes it
+easier to to do the foam
+
+ align:start position:0%
+easier to to do the foam
+ 
+
+ align:start position:0%
+easier to to do the foam
+ones so we'll do the fracture toughness
+
+ align:start position:0%
+ones so we'll do the fracture toughness
+ 
+
+ align:start position:0%
+ones so we'll do the fracture toughness
+calculation and then I wanted to talk a
+
+ align:start position:0%
+calculation and then I wanted to talk a
+ 
+
+ align:start position:0%
+calculation and then I wanted to talk a
+little bit about material selection and
+
+ align:start position:0%
+little bit about material selection and
+ 
+
+ align:start position:0%
+little bit about material selection and
+selection charts for Foams so that's
+
+ align:start position:0%
+selection charts for Foams so that's
+ 
+
+ align:start position:0%
+selection charts for Foams so that's
+less equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we're just going to look at
+
+ align:start position:0%
+okay and we're just going to look at
+ 
+
+ align:start position:0%
+okay and we're just going to look at
+open cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so imagine we have a crack of
+
+ align:start position:0%
+here so imagine we have a crack of
+ 
+
+ align:start position:0%
+here so imagine we have a crack of
+length 2 a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have some uh remote stress
+
+ align:start position:0%
+and we have some uh remote stress
+ 
+
+ align:start position:0%
+and we have some uh remote stress
+applied so a remote tensile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stress so I'm going to call that Sigma
+
+ align:start position:0%
+stress so I'm going to call that Sigma
+ 
+
+ align:start position:0%
+stress so I'm going to call that Sigma
+Infinity the far away stress and then we
+
+ align:start position:0%
+Infinity the far away stress and then we
+ 
+
+ align:start position:0%
+Infinity the far away stress and then we
+have a local stress on the cell
+
+ align:start position:0%
+have a local stress on the cell
+ 
+
+ align:start position:0%
+have a local stress on the cell
+walls I'm going to call that Sigma local
+
+ align:start position:0%
+walls I'm going to call that Sigma local
+ 
+
+ align:start position:0%
+walls I'm going to call that Sigma local
+so I have a little schematic that kind
+
+ align:start position:0%
+so I have a little schematic that kind
+ 
+
+ align:start position:0%
+so I have a little schematic that kind
+of shows what we're doing so we're
+
+ align:start position:0%
+of shows what we're doing so we're
+ 
+
+ align:start position:0%
+of shows what we're doing so we're
+pulling on it there's some crack the
+
+ align:start position:0%
+pulling on it there's some crack the
+ 
+
+ align:start position:0%
+pulling on it there's some crack the
+crack length is large compared to the
+
+ align:start position:0%
+crack length is large compared to the
+ 
+
+ align:start position:0%
+crack length is large compared to the
+cell size
+
+ align:start position:0%
+cell size
+ 
+
+ align:start position:0%
+cell size
+and we want to know what the fracture
+
+ align:start position:0%
+and we want to know what the fracture
+ 
+
+ align:start position:0%
+and we want to know what the fracture
+toughness is so we can say from fracture
+
+ align:start position:0%
+toughness is so we can say from fracture
+ 
+
+ align:start position:0%
+toughness is so we can say from fracture
+mechanics the local stress is going to
+
+ align:start position:0%
+mechanics the local stress is going to
+ 
+
+ align:start position:0%
+mechanics the local stress is going to
+equal to some constant time the far away
+
+ align:start position:0%
+equal to some constant time the far away
+ 
+
+ align:start position:0%
+equal to some constant time the far away
+stress time the < TK of Pi a over the <
+
+ align:start position:0%
+stress time the < TK of Pi a over the <
+ 
+
+ align:start position:0%
+stress time the < TK of Pi a over the <
+TK of 2i R and that's at a distance R
+
+ align:start position:0%
+TK of 2i R and that's at a distance R
+ 
+
+ align:start position:0%
+TK of 2i R and that's at a distance R
+from ahead of the crack tip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we look at our little schematic
+
+ align:start position:0%
+and if we look at our little schematic
+ 
+
+ align:start position:0%
+and if we look at our little schematic
+here we could say U it's hard to say
+
+ align:start position:0%
+here we could say U it's hard to say
+ 
+
+ align:start position:0%
+here we could say U it's hard to say
+exactly where the crack tip is but it
+
+ align:start position:0%
+exactly where the crack tip is but it
+ 
+
+ align:start position:0%
+exactly where the crack tip is but it
+would be somewhere in here and we'd say
+
+ align:start position:0%
+would be somewhere in here and we'd say
+ 
+
+ align:start position:0%
+would be somewhere in here and we'd say
+this next unbroken cell wall is a
+
+ align:start position:0%
+this next unbroken cell wall is a
+ 
+
+ align:start position:0%
+this next unbroken cell wall is a
+distance R ahead of the crack tip and
+
+ align:start position:0%
+distance R ahead of the crack tip and
+ 
+
+ align:start position:0%
+distance R ahead of the crack tip and
+that R is going to be related to L it's
+
+ align:start position:0%
+that R is going to be related to L it's
+ 
+
+ align:start position:0%
+that R is going to be related to L it's
+going to be some function of
+
+ align:start position:0%
+going to be some function of
+ 
+
+ align:start position:0%
+going to be some function of
+L so I can say the next unbroken wall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead of the crack
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tip at some distance R that's going to
+
+ align:start position:0%
+tip at some distance R that's going to
+ 
+
+ align:start position:0%
+tip at some distance R that's going to
+be related to
+
+ align:start position:0%
+be related to
+ 
+
+ align:start position:0%
+be related to
+L and that's subject to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+force which is going to be the local
+
+ align:start position:0%
+force which is going to be the local
+ 
+
+ align:start position:0%
+force which is going to be the local
+stress time l^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 okay so that force is going to go as
+
+ align:start position:0%
+2 okay so that force is going to go as
+ 
+
+ align:start position:0%
+2 okay so that force is going to go as
+the local stress times l^2 and the local
+
+ align:start position:0%
+the local stress times l^2 and the local
+ 
+
+ align:start position:0%
+the local stress times l^2 and the local
+stress I can substitute this thing here
+
+ align:start position:0%
+stress I can substitute this thing here
+ 
+
+ align:start position:0%
+stress I can substitute this thing here
+in that's going to be proportional to
+
+ align:start position:0%
+in that's going to be proportional to
+ 
+
+ align:start position:0%
+in that's going to be proportional to
+the far away stress and now I'm going to
+
+ align:start position:0%
+the far away stress and now I'm going to
+ 
+
+ align:start position:0%
+the far away stress and now I'm going to
+get rid of the
+
+ align:start position:0%
+get rid of the
+ 
+
+ align:start position:0%
+get rid of the
+pies and I'm going to substitute for R
+
+ align:start position:0%
+pies and I'm going to substitute for R
+ 
+
+ align:start position:0%
+pies and I'm going to substitute for R
+I'm going to put in L so it's going to
+
+ align:start position:0%
+I'm going to put in L so it's going to
+ 
+
+ align:start position:0%
+I'm going to put in L so it's going to
+be proportional to the far away stress
+
+ align:start position:0%
+be proportional to the far away stress
+ 
+
+ align:start position:0%
+be proportional to the far away stress
+time the root of a over L and times l s
+
+ align:start position:0%
+time the root of a over L and times l s
+ 
+
+ align:start position:0%
+time the root of a over L and times l s
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then we're we're going to say
+
+ align:start position:0%
+okay and then we're we're going to say
+ 
+
+ align:start position:0%
+okay and then we're we're going to say
+again the edges are going to fail when
+
+ align:start position:0%
+again the edges are going to fail when
+ 
+
+ align:start position:0%
+again the edges are going to fail when
+the applied moment equals the fracture
+
+ align:start position:0%
+the applied moment equals the fracture
+ 
+
+ align:start position:0%
+the applied moment equals the fracture
+moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the fracture moment is going to go
+
+ align:start position:0%
+and the fracture moment is going to go
+ 
+
+ align:start position:0%
+and the fracture moment is going to go
+as the modulus of rupture of the cell
+
+ align:start position:0%
+as the modulus of rupture of the cell
+ 
+
+ align:start position:0%
+as the modulus of rupture of the cell
+walls * T cubed and the applied moment
+
+ align:start position:0%
+walls * T cubed and the applied moment
+ 
+
+ align:start position:0%
+walls * T cubed and the applied moment
+is going to go as f * L and I've got F
+
+ align:start position:0%
+is going to go as f * L and I've got F
+ 
+
+ align:start position:0%
+is going to go as f * L and I've got F
+from up there so that goes as the far
+
+ align:start position:0%
+from up there so that goes as the far
+ 
+
+ align:start position:0%
+from up there so that goes as the far
+away stress Sigma infinite time the root
+
+ align:start position:0%
+away stress Sigma infinite time the root
+ 
+
+ align:start position:0%
+away stress Sigma infinite time the root
+of a over L and now I've got L Cub
+
+ align:start position:0%
+of a over L and now I've got L Cub
+ 
+
+ align:start position:0%
+of a over L and now I've got L Cub
+because there's an L squ there and
+
+ align:start position:0%
+because there's an L squ there and
+ 
+
+ align:start position:0%
+because there's an L squ there and
+there's an L down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and then if I just equate those
+
+ align:start position:0%
+here and then if I just equate those
+ 
+
+ align:start position:0%
+here and then if I just equate those
+then this is going to go as Sigma
+
+ align:start position:0%
+then this is going to go as Sigma
+ 
+
+ align:start position:0%
+then this is going to go as Sigma
+FS * T Cub like that so then I could say
+
+ align:start position:0%
+FS * T Cub like that so then I could say
+ 
+
+ align:start position:0%
+FS * T Cub like that so then I could say
+the fracture
+
+ align:start position:0%
+the fracture
+ 
+
+ align:start position:0%
+the fracture
+strength is equal to my far away stress
+
+ align:start position:0%
+strength is equal to my far away stress
+ 
+
+ align:start position:0%
+strength is equal to my far away stress
+that's going to go as my modulus of
+
+ align:start position:0%
+that's going to go as my modulus of
+ 
+
+ align:start position:0%
+that's going to go as my modulus of
+rupture time the root of L A * t
+
+ align:start position:0%
+rupture time the root of L A * t
+ 
+
+ align:start position:0%
+rupture time the root of L A * t
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+cubed and then my fracture toughness is
+
+ align:start position:0%
+cubed and then my fracture toughness is
+ 
+
+ align:start position:0%
+cubed and then my fracture toughness is
+going to be this tensile stress time the
+
+ align:start position:0%
+going to be this tensile stress time the
+ 
+
+ align:start position:0%
+going to be this tensile stress time the
+root of Pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so there's going to be some other
+
+ align:start position:0%
+a so there's going to be some other
+ 
+
+ align:start position:0%
+a so there's going to be some other
+constant here which I'm going to call
+
+ align:start position:0%
+constant here which I'm going to call
+ 
+
+ align:start position:0%
+constant here which I'm going to call
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+C8 I've got the modulus of rupture of
+
+ align:start position:0%
+C8 I've got the modulus of rupture of
+ 
+
+ align:start position:0%
+C8 I've got the modulus of rupture of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+solid I've got the square root of L and
+
+ align:start position:0%
+solid I've got the square root of L and
+ 
+
+ align:start position:0%
+solid I've got the square root of L and
+I'm just going to multiply by pi so it's
+
+ align:start position:0%
+I'm just going to multiply by pi so it's
+ 
+
+ align:start position:0%
+I'm just going to multiply by pi so it's
+like other fracture mechanics kinds of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations and then we multiply that
+
+ align:start position:0%
+equations and then we multiply that
+ 
+
+ align:start position:0%
+equations and then we multiply that
+times the relative density to the three
+
+ align:start position:0%
+times the relative density to the three
+ 
+
+ align:start position:0%
+times the relative density to the three
+Hales
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power and here if we look at
+
+ align:start position:0%
+power and here if we look at
+ 
+
+ align:start position:0%
+power and here if we look at
+data we find that that constant is about
+
+ align:start position:0%
+data we find that that constant is about
+ 
+
+ align:start position:0%
+data we find that that constant is about
+equal to 65
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's another one of these plots so
+
+ align:start position:0%
+and here's another one of these plots so
+ 
+
+ align:start position:0%
+and here's another one of these plots so
+here I've I've normalized the fracture
+
+ align:start position:0%
+here I've I've normalized the fracture
+ 
+
+ align:start position:0%
+here I've I've normalized the fracture
+toughness of the Foams by the modulus of
+
+ align:start position:0%
+toughness of the Foams by the modulus of
+ 
+
+ align:start position:0%
+toughness of the Foams by the modulus of
+rupture of the cell walls times the root
+
+ align:start position:0%
+rupture of the cell walls times the root
+ 
+
+ align:start position:0%
+rupture of the cell walls times the root
+of Pi l so I've taken the cell size into
+
+ align:start position:0%
+of Pi l so I've taken the cell size into
+ 
+
+ align:start position:0%
+of Pi l so I've taken the cell size into
+account here and I've plotted against
+
+ align:start position:0%
+account here and I've plotted against
+ 
+
+ align:start position:0%
+account here and I've plotted against
+the relative density and that equation
+
+ align:start position:0%
+the relative density and that equation
+ 
+
+ align:start position:0%
+the relative density and that equation
+there is the same as this equation I've
+
+ align:start position:0%
+there is the same as this equation I've
+ 
+
+ align:start position:0%
+there is the same as this equation I've
+got down on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board and this is the only one of the
+
+ align:start position:0%
+board and this is the only one of the
+ 
+
+ align:start position:0%
+board and this is the only one of the
+properties that we've looked at that
+
+ align:start position:0%
+properties that we've looked at that
+ 
+
+ align:start position:0%
+properties that we've looked at that
+depends on the cell size right there's a
+
+ align:start position:0%
+depends on the cell size right there's a
+ 
+
+ align:start position:0%
+depends on the cell size right there's a
+cell size dependence here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so I think that's all the
+
+ align:start position:0%
+all right so I think that's all the
+ 
+
+ align:start position:0%
+all right so I think that's all the
+modeling of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Foams are we
+
+ align:start position:0%
+Foams are we
+ 
+
+ align:start position:0%
+Foams are we
+good a lot of equations we're good okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Boop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I want to talk about how we might
+
+ align:start position:0%
+so I want to talk about how we might
+ 
+
+ align:start position:0%
+so I want to talk about how we might
+design Foams to improve their properties
+
+ align:start position:0%
+design Foams to improve their properties
+ 
+
+ align:start position:0%
+design Foams to improve their properties
+and then I wanted to talk about how we
+
+ align:start position:0%
+and then I wanted to talk about how we
+ 
+
+ align:start position:0%
+and then I wanted to talk about how we
+might select Foams for certain
+
+ align:start position:0%
+might select Foams for certain
+ 
+
+ align:start position:0%
+might select Foams for certain
+applications and look at Material
+
+ align:start position:0%
+applications and look at Material
+ 
+
+ align:start position:0%
+applications and look at Material
+selection charts so when we've been
+
+ align:start position:0%
+selection charts so when we've been
+ 
+
+ align:start position:0%
+selection charts so when we've been
+talking about the Foams especially the
+
+ align:start position:0%
+talking about the Foams especially the
+ 
+
+ align:start position:0%
+talking about the Foams especially the
+open cell foams we've been saying that
+
+ align:start position:0%
+open cell foams we've been saying that
+ 
+
+ align:start position:0%
+open cell foams we've been saying that
+their deformation is is largely by by
+
+ align:start position:0%
+their deformation is is largely by by
+ 
+
+ align:start position:0%
+their deformation is is largely by by
+bending of the cell edges and if we
+
+ align:start position:0%
+bending of the cell edges and if we
+ 
+
+ align:start position:0%
+bending of the cell edges and if we
+could do something to increase the
+
+ align:start position:0%
+could do something to increase the
+ 
+
+ align:start position:0%
+could do something to increase the
+stiffness of the edges or the strength
+
+ align:start position:0%
+stiffness of the edges or the strength
+ 
+
+ align:start position:0%
+stiffness of the edges or the strength
+of the edges then that would increase
+
+ align:start position:0%
+of the edges then that would increase
+ 
+
+ align:start position:0%
+of the edges then that would increase
+the overall properties of the foam and
+
+ align:start position:0%
+the overall properties of the foam and
+ 
+
+ align:start position:0%
+the overall properties of the foam and
+there's a couple of ways uh to think
+
+ align:start position:0%
+there's a couple of ways uh to think
+ 
+
+ align:start position:0%
+there's a couple of ways uh to think
+about doing that so the foam properties
+
+ align:start position:0%
+about doing that so the foam properties
+ 
+
+ align:start position:0%
+about doing that so the foam properties
+if if the foam is controlled by bending
+
+ align:start position:0%
+if if the foam is controlled by bending
+ 
+
+ align:start position:0%
+if if the foam is controlled by bending
+of the edges and the edges have some
+
+ align:start position:0%
+of the edges and the edges have some
+ 
+
+ align:start position:0%
+of the edges and the edges have some
+flexual rigidity EI if we could increase
+
+ align:start position:0%
+flexual rigidity EI if we could increase
+ 
+
+ align:start position:0%
+flexual rigidity EI if we could increase
+that EI of the edges we would increase
+
+ align:start position:0%
+that EI of the edges we would increase
+ 
+
+ align:start position:0%
+that EI of the edges we would increase
+the properties of the foam and one way
+
+ align:start position:0%
+the properties of the foam and one way
+ 
+
+ align:start position:0%
+the properties of the foam and one way
+to do that is by making the this the
+
+ align:start position:0%
+to do that is by making the this the
+ 
+
+ align:start position:0%
+to do that is by making the this the
+edges Hollow so if we had Hollow edges
+
+ align:start position:0%
+edges Hollow so if we had Hollow edges
+ 
+
+ align:start position:0%
+edges Hollow so if we had Hollow edges
+and you had a tube then that would
+
+ align:start position:0%
+and you had a tube then that would
+ 
+
+ align:start position:0%
+and you had a tube then that would
+increase the EI and I'll I'll we can
+
+ align:start position:0%
+increase the EI and I'll I'll we can
+ 
+
+ align:start position:0%
+increase the EI and I'll I'll we can
+work out sort of how much it's going to
+
+ align:start position:0%
+work out sort of how much it's going to
+ 
+
+ align:start position:0%
+work out sort of how much it's going to
+increase them and I have a little
+
+ align:start position:0%
+increase them and I have a little
+ 
+
+ align:start position:0%
+increase them and I have a little
+example here of ah wrong thing sorry I
+
+ align:start position:0%
+example here of ah wrong thing sorry I
+ 
+
+ align:start position:0%
+example here of ah wrong thing sorry I
+have a little example of a natural
+
+ align:start position:0%
+have a little example of a natural
+ 
+
+ align:start position:0%
+have a little example of a natural
+example of hollow foam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+struts so this is a a grass I don't know
+
+ align:start position:0%
+struts so this is a a grass I don't know
+ 
+
+ align:start position:0%
+struts so this is a a grass I don't know
+what kind of grass it is I just saw this
+
+ align:start position:0%
+what kind of grass it is I just saw this
+ 
+
+ align:start position:0%
+what kind of grass it is I just saw this
+grass and we picked some different
+
+ align:start position:0%
+grass and we picked some different
+ 
+
+ align:start position:0%
+grass and we picked some different
+grasses and we took some sem pictures
+
+ align:start position:0%
+grasses and we took some sem pictures
+ 
+
+ align:start position:0%
+grasses and we took some sem pictures
+and uh it has a really kind of common
+
+ align:start position:0%
+and uh it has a really kind of common
+ 
+
+ align:start position:0%
+and uh it has a really kind of common
+structure for a grass it's very common
+
+ align:start position:0%
+structure for a grass it's very common
+ 
+
+ align:start position:0%
+structure for a grass it's very common
+for grass stems to have sort of a solid
+
+ align:start position:0%
+for grass stems to have sort of a solid
+ 
+
+ align:start position:0%
+for grass stems to have sort of a solid
+uh outer part and then a foamlike inner
+
+ align:start position:0%
+uh outer part and then a foamlike inner
+ 
+
+ align:start position:0%
+uh outer part and then a foamlike inner
+part it's so common that botanists have
+
+ align:start position:0%
+part it's so common that botanists have
+ 
+
+ align:start position:0%
+part it's so common that botanists have
+a name for it they're called the Corine
+
+ align:start position:0%
+a name for it they're called the Corine
+ 
+
+ align:start position:0%
+a name for it they're called the Corine
+structure and if you take one of these
+
+ align:start position:0%
+structure and if you take one of these
+ 
+
+ align:start position:0%
+structure and if you take one of these
+um grass stems and you look at the sort
+
+ align:start position:0%
+um grass stems and you look at the sort
+ 
+
+ align:start position:0%
+um grass stems and you look at the sort
+of foamy bit in the middle and you uh do
+
+ align:start position:0%
+of foamy bit in the middle and you uh do
+ 
+
+ align:start position:0%
+of foamy bit in the middle and you uh do
+a you know sem picture of that you can
+
+ align:start position:0%
+a you know sem picture of that you can
+ 
+
+ align:start position:0%
+a you know sem picture of that you can
+see that the little cell walls are
+
+ align:start position:0%
+see that the little cell walls are
+ 
+
+ align:start position:0%
+see that the little cell walls are
+actually little Hollow tubes so if you
+
+ align:start position:0%
+actually little Hollow tubes so if you
+ 
+
+ align:start position:0%
+actually little Hollow tubes so if you
+know each one of these things is a
+
+ align:start position:0%
+know each one of these things is a
+ 
+
+ align:start position:0%
+know each one of these things is a
+little Hollow tube so what I wanted to
+
+ align:start position:0%
+little Hollow tube so what I wanted to
+ 
+
+ align:start position:0%
+little Hollow tube so what I wanted to
+do is work out how much the uh say
+
+ align:start position:0%
+do is work out how much the uh say
+ 
+
+ align:start position:0%
+do is work out how much the uh say
+modulus of the foam would increase if
+
+ align:start position:0%
+modulus of the foam would increase if
+ 
+
+ align:start position:0%
+modulus of the foam would increase if
+you could make all the edges into little
+
+ align:start position:0%
+you could make all the edges into little
+ 
+
+ align:start position:0%
+you could make all the edges into little
+hollow
+
+ align:start position:0%
+hollow
+ 
+
+ align:start position:0%
+hollow
+tubes so we're going to start by saying
+
+ align:start position:0%
+tubes so we're going to start by saying
+ 
+
+ align:start position:0%
+tubes so we're going to start by saying
+the foam behavior is dominated by cell
+
+ align:start position:0%
+the foam behavior is dominated by cell
+ 
+
+ align:start position:0%
+the foam behavior is dominated by cell
+bending C Edge bending
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the foam properties can be increased
+
+ align:start position:0%
+and the foam properties can be increased
+ 
+
+ align:start position:0%
+and the foam properties can be increased
+by increasing the EI of the cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wall so there's a couple ways we could
+
+ align:start position:0%
+wall so there's a couple ways we could
+ 
+
+ align:start position:0%
+wall so there's a couple ways we could
+do that so the first one is looking at
+
+ align:start position:0%
+do that so the first one is looking at
+ 
+
+ align:start position:0%
+do that so the first one is looking at
+hollow wall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so imagine I have a thin wall tube just
+
+ align:start position:0%
+so imagine I have a thin wall tube just
+ 
+
+ align:start position:0%
+so imagine I have a thin wall tube just
+a circular thin wall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tube there's my little wall there it has
+
+ align:start position:0%
+tube there's my little wall there it has
+ 
+
+ align:start position:0%
+tube there's my little wall there it has
+some radius little r and a wall
+
+ align:start position:0%
+some radius little r and a wall
+ 
+
+ align:start position:0%
+some radius little r and a wall
+thickness
+
+ align:start position:0%
+thickness
+ 
+
+ align:start position:0%
+thickness
+T and then imagine I have the same
+
+ align:start position:0%
+T and then imagine I have the same
+ 
+
+ align:start position:0%
+T and then imagine I have the same
+amount of mass but now I have a solid
+
+ align:start position:0%
+amount of mass but now I have a solid
+ 
+
+ align:start position:0%
+amount of mass but now I have a solid
+Circ cular
+
+ align:start position:0%
+Circ cular
+ 
+
+ align:start position:0%
+Circ cular
+section and I'm going to say the radius
+
+ align:start position:0%
+section and I'm going to say the radius
+ 
+
+ align:start position:0%
+section and I'm going to say the radius
+of that is Big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R okay so for our thin wall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tube the moment of inertia is pi R cubed
+
+ align:start position:0%
+tube the moment of inertia is pi R cubed
+ 
+
+ align:start position:0%
+tube the moment of inertia is pi R cubed
+times the thickness T if it's thin and
+
+ align:start position:0%
+times the thickness T if it's thin and
+ 
+
+ align:start position:0%
+times the thickness T if it's thin and
+for our solid circular section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I is going to be Pi Big R to 4th over
+
+ align:start position:0%
+I is going to be Pi Big R to 4th over
+ 
+
+ align:start position:0%
+I is going to be Pi Big R to 4th over
+4 and if I say I want to set this up so
+
+ align:start position:0%
+4 and if I say I want to set this up so
+ 
+
+ align:start position:0%
+4 and if I say I want to set this up so
+that the masses are equal then the areas
+
+ align:start position:0%
+that the masses are equal then the areas
+ 
+
+ align:start position:0%
+that the masses are equal then the areas
+of the cross-sections have to be equal
+
+ align:start position:0%
+of the cross-sections have to be equal
+ 
+
+ align:start position:0%
+of the cross-sections have to be equal
+say it's from the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material so the masses are going to be
+
+ align:start position:0%
+material so the masses are going to be
+ 
+
+ align:start position:0%
+material so the masses are going to be
+equal if P Pi Big R 2 is equal to 2 pi
+
+ align:start position:0%
+equal if P Pi Big R 2 is equal to 2 pi
+ 
+
+ align:start position:0%
+equal if P Pi Big R 2 is equal to 2 pi
+little r
+
+ align:start position:0%
+little r
+ 
+
+ align:start position:0%
+little r
+t so I'm going to solve here for R so
+
+ align:start position:0%
+t so I'm going to solve here for R so
+ 
+
+ align:start position:0%
+t so I'm going to solve here for R so
+the pi are going to cancel out so the
+
+ align:start position:0%
+the pi are going to cancel out so the
+ 
+
+ align:start position:0%
+the pi are going to cancel out so the
+masses are equal if Big R is equal to
+
+ align:start position:0%
+masses are equal if Big R is equal to
+ 
+
+ align:start position:0%
+masses are equal if Big R is equal to
+theare < TK of 2 * little r *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T and then what we're going to do is see
+
+ align:start position:0%
+T and then what we're going to do is see
+ 
+
+ align:start position:0%
+T and then what we're going to do is see
+how big is the moment of inertia of the
+
+ align:start position:0%
+how big is the moment of inertia of the
+ 
+
+ align:start position:0%
+how big is the moment of inertia of the
+tube relative to the solid so the tube
+
+ align:start position:0%
+tube relative to the solid so the tube
+ 
+
+ align:start position:0%
+tube relative to the solid so the tube
+was Pi little r Cub T and the solid was
+
+ align:start position:0%
+was Pi little r Cub T and the solid was
+ 
+
+ align:start position:0%
+was Pi little r Cub T and the solid was
+Pi Big R 4th / 4 and I'm going to get
+
+ align:start position:0%
+Pi Big R 4th / 4 and I'm going to get
+ 
+
+ align:start position:0%
+Pi Big R 4th / 4 and I'm going to get
+get rid of the Big R here I can get rid
+
+ align:start position:0%
+get rid of the Big R here I can get rid
+ 
+
+ align:start position:0%
+get rid of the Big R here I can get rid
+of the pies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there so R to the 4th is going to be 4
+
+ align:start position:0%
+there so R to the 4th is going to be 4
+ 
+
+ align:start position:0%
+there so R to the 4th is going to be 4
+r^ 2 t^
+
+ align:start position:0%
+r^ 2 t^
+ 
+
+ align:start position:0%
+r^ 2 t^
+2 so the fours are going to go and this
+
+ align:start position:0%
+2 so the fours are going to go and this
+ 
+
+ align:start position:0%
+2 so the fours are going to go and this
+boils down to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R/T so if I had a thin wall
+
+ align:start position:0%
+R/T so if I had a thin wall
+ 
+
+ align:start position:0%
+R/T so if I had a thin wall
+tube the moment of inertia is going to
+
+ align:start position:0%
+tube the moment of inertia is going to
+ 
+
+ align:start position:0%
+tube the moment of inertia is going to
+be r/ T bigger than if I had the same
+
+ align:start position:0%
+be r/ T bigger than if I had the same
+ 
+
+ align:start position:0%
+be r/ T bigger than if I had the same
+mass in a solid circular section
+
+ align:start position:0%
+mass in a solid circular section
+ 
+
+ align:start position:0%
+mass in a solid circular section
+so you can see for the little plant here
+
+ align:start position:0%
+so you can see for the little plant here
+ 
+
+ align:start position:0%
+so you can see for the little plant here
+by making a thin wall tube you're
+
+ align:start position:0%
+by making a thin wall tube you're
+ 
+
+ align:start position:0%
+by making a thin wall tube you're
+increasing the stiffness of the foam
+
+ align:start position:0%
+increasing the stiffness of the foam
+ 
+
+ align:start position:0%
+increasing the stiffness of the foam
+with the same amount of material okay
+
+ align:start position:0%
+with the same amount of material okay
+ 
+
+ align:start position:0%
+with the same amount of material okay
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+idea and you can do a similar kind of
+
+ align:start position:0%
+idea and you can do a similar kind of
+ 
+
+ align:start position:0%
+idea and you can do a similar kind of
+analysis for other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties so that's if we have hollow
+
+ align:start position:0%
+properties so that's if we have hollow
+ 
+
+ align:start position:0%
+properties so that's if we have hollow
+tubes so another option is we could have
+
+ align:start position:0%
+tubes so another option is we could have
+ 
+
+ align:start position:0%
+tubes so another option is we could have
+cell walls that are sandwich structures
+
+ align:start position:0%
+cell walls that are sandwich structures
+ 
+
+ align:start position:0%
+cell walls that are sandwich structures
+so imagine if the cell walls themselves
+
+ align:start position:0%
+so imagine if the cell walls themselves
+ 
+
+ align:start position:0%
+so imagine if the cell walls themselves
+were little tiny sandwich structures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you have a sandwich
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam what you have is two stiff strong
+
+ align:start position:0%
+beam what you have is two stiff strong
+ 
+
+ align:start position:0%
+beam what you have is two stiff strong
+faces that are separated by some sort of
+
+ align:start position:0%
+faces that are separated by some sort of
+ 
+
+ align:start position:0%
+faces that are separated by some sort of
+porous core like a honeycomb or a foam
+
+ align:start position:0%
+porous core like a honeycomb or a foam
+ 
+
+ align:start position:0%
+porous core like a honeycomb or a foam
+or bals of wood and the idea
+
+ align:start position:0%
+or bals of wood and the idea
+ 
+
+ align:start position:0%
+or bals of wood and the idea
+with the sandwich structure if I draw a
+
+ align:start position:0%
+with the sandwich structure if I draw a
+ 
+
+ align:start position:0%
+with the sandwich structure if I draw a
+little sort of sketch of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sandwich there's my faces so imagine
+
+ align:start position:0%
+sandwich there's my faces so imagine
+ 
+
+ align:start position:0%
+sandwich there's my faces so imagine
+those are solid so they might be
+
+ align:start position:0%
+those are solid so they might be
+ 
+
+ align:start position:0%
+those are solid so they might be
+aluminum sheets or they might be fiber
+
+ align:start position:0%
+aluminum sheets or they might be fiber
+ 
+
+ align:start position:0%
+aluminum sheets or they might be fiber
+reinforced Composites and then we have
+
+ align:start position:0%
+reinforced Composites and then we have
+ 
+
+ align:start position:0%
+reinforced Composites and then we have
+some sort of cellular thing
+
+ align:start position:0%
+some sort of cellular thing
+ 
+
+ align:start position:0%
+some sort of cellular thing
+here is the core and the idea is that's
+
+ align:start position:0%
+here is the core and the idea is that's
+ 
+
+ align:start position:0%
+here is the core and the idea is that's
+analogous to an I
+
+ align:start position:0%
+analogous to an I
+ 
+
+ align:start position:0%
+analogous to an I
+beam so in the sandwich beam we have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stiff strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+faces separated by a lightweight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+core so the core is typically a
+
+ align:start position:0%
+core so the core is typically a
+ 
+
+ align:start position:0%
+core so the core is typically a
+honeycomb or a
+
+ align:start position:0%
+honeycomb or a
+ 
+
+ align:start position:0%
+honeycomb or a
+foam or Bala
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wood and the idea is you increase the
+
+ align:start position:0%
+wood and the idea is you increase the
+ 
+
+ align:start position:0%
+wood and the idea is you increase the
+moment of inertia of the cross-section
+
+ align:start position:0%
+moment of inertia of the cross-section
+ 
+
+ align:start position:0%
+moment of inertia of the cross-section
+with little increase in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weight and if you think of an ibeam an
+
+ align:start position:0%
+weight and if you think of an ibeam an
+ 
+
+ align:start position:0%
+weight and if you think of an ibeam an
+ibeam has a large moment of inertia
+
+ align:start position:0%
+ibeam has a large moment of inertia
+ 
+
+ align:start position:0%
+ibeam has a large moment of inertia
+because you're separating the flanges by
+
+ align:start position:0%
+because you're separating the flanges by
+ 
+
+ align:start position:0%
+because you're separating the flanges by
+the web and the sandwich beam works in
+
+ align:start position:0%
+the web and the sandwich beam works in
+ 
+
+ align:start position:0%
+the web and the sandwich beam works in
+the same way you're separating the Faces
+
+ align:start position:0%
+the same way you're separating the Faces
+ 
+
+ align:start position:0%
+the same way you're separating the Faces
+by the core but the core doesn't weigh
+
+ align:start position:0%
+by the core but the core doesn't weigh
+ 
+
+ align:start position:0%
+by the core but the core doesn't weigh
+very much because it's a cellular
+
+ align:start position:0%
+very much because it's a cellular
+ 
+
+ align:start position:0%
+very much because it's a cellular
+thing so the faces of the sandwich are
+
+ align:start position:0%
+thing so the faces of the sandwich are
+ 
+
+ align:start position:0%
+thing so the faces of the sandwich are
+like the flanges in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ibeam and then the core is like the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+web okay so the idea is to make
+
+ align:start position:0%
+web okay so the idea is to make
+ 
+
+ align:start position:0%
+web okay so the idea is to make
+something called a micro sandwich foam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what you want to do is make the cell
+
+ align:start position:0%
+so what you want to do is make the cell
+ 
+
+ align:start position:0%
+so what you want to do is make the cell
+walls into sandwiches and one way to do
+
+ align:start position:0%
+walls into sandwiches and one way to do
+ 
+
+ align:start position:0%
+walls into sandwiches and one way to do
+that is to disperse a large volume
+
+ align:start position:0%
+that is to disperse a large volume
+ 
+
+ align:start position:0%
+that is to disperse a large volume
+fraction of thin walled spheres into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foam um and you have to get the geometry
+
+ align:start position:0%
+foam um and you have to get the geometry
+ 
+
+ align:start position:0%
+foam um and you have to get the geometry
+geometry right to make it work so let me
+
+ align:start position:0%
+geometry right to make it work so let me
+ 
+
+ align:start position:0%
+geometry right to make it work so let me
+draw a little kind of sketch here for
+
+ align:start position:0%
+draw a little kind of sketch here for
+ 
+
+ align:start position:0%
+draw a little kind of sketch here for
+how it
+
+ align:start position:0%
+how it
+ 
+
+ align:start position:0%
+how it
+works so here's our thin walled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spheres and then you're going to
+
+ align:start position:0%
+spheres and then you're going to
+ 
+
+ align:start position:0%
+spheres and then you're going to
+distribute those in a foam so here's
+
+ align:start position:0%
+distribute those in a foam so here's
+ 
+
+ align:start position:0%
+distribute those in a foam so here's
+another sphere over here spheres are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perfect let's say there was another one
+
+ align:start position:0%
+perfect let's say there was another one
+ 
+
+ align:start position:0%
+perfect let's say there was another one
+in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the idea is this stuff in here
+
+ align:start position:0%
+and then the idea is this stuff in here
+ 
+
+ align:start position:0%
+and then the idea is this stuff in here
+would be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foam so these guys are Hollow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spheres and say the Spheres have a
+
+ align:start position:0%
+spheres and say the Spheres have a
+ 
+
+ align:start position:0%
+spheres and say the Spheres have a
+diameter
+
+ align:start position:0%
+diameter
+ 
+
+ align:start position:0%
+diameter
+D and say they have a wall thickness
+
+ align:start position:0%
+D and say they have a wall thickness
+ 
+
+ align:start position:0%
+D and say they have a wall thickness
+here of T and say this the separation of
+
+ align:start position:0%
+here of T and say this the separation of
+ 
+
+ align:start position:0%
+here of T and say this the separation of
+the Spheres I'm going to call C
+
+ align:start position:0%
+the Spheres I'm going to call C
+ 
+
+ align:start position:0%
+the Spheres I'm going to call C
+if you can see that there and then the
+
+ align:start position:0%
+if you can see that there and then the
+ 
+
+ align:start position:0%
+if you can see that there and then the
+cell size of the
+
+ align:start position:0%
+cell size of the
+ 
+
+ align:start position:0%
+cell size of the
+foam I'm going to call Little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D so there's a bunch of parameters you
+
+ align:start position:0%
+D so there's a bunch of parameters you
+ 
+
+ align:start position:0%
+D so there's a bunch of parameters you
+have to kind of play with to get this to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work so you have to have thin walled
+
+ align:start position:0%
+work so you have to have thin walled
+ 
+
+ align:start position:0%
+work so you have to have thin walled
+spheres so that the faces are thin the
+
+ align:start position:0%
+spheres so that the faces are thin the
+ 
+
+ align:start position:0%
+spheres so that the faces are thin the
+sandwich panels work best when the faces
+
+ align:start position:0%
+sandwich panels work best when the faces
+ 
+
+ align:start position:0%
+sandwich panels work best when the faces
+are thin so you need the thickness of
+
+ align:start position:0%
+are thin so you need the thickness of
+ 
+
+ align:start position:0%
+are thin so you need the thickness of
+the sphere to be much less than D you
+
+ align:start position:0%
+the sphere to be much less than D you
+ 
+
+ align:start position:0%
+the sphere to be much less than D you
+you need the faces to be stiff relative
+
+ align:start position:0%
+you need the faces to be stiff relative
+ 
+
+ align:start position:0%
+you need the faces to be stiff relative
+to the foam so you need the modulus of
+
+ align:start position:0%
+to the foam so you need the modulus of
+ 
+
+ align:start position:0%
+to the foam so you need the modulus of
+the sphere material to be greater than
+
+ align:start position:0%
+the sphere material to be greater than
+ 
+
+ align:start position:0%
+the sphere material to be greater than
+the modulus of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foam and you need the volume fraction of
+
+ align:start position:0%
+foam and you need the volume fraction of
+ 
+
+ align:start position:0%
+foam and you need the volume fraction of
+the Spheres to be relatively High to get
+
+ align:start position:0%
+the Spheres to be relatively High to get
+ 
+
+ align:start position:0%
+the Spheres to be relatively High to get
+the Spheres close enough together for
+
+ align:start position:0%
+the Spheres close enough together for
+ 
+
+ align:start position:0%
+the Spheres close enough together for
+this to work so you want that volume
+
+ align:start position:0%
+this to work so you want that volume
+ 
+
+ align:start position:0%
+this to work so you want that volume
+fraction to be something like 50 to
+
+ align:start position:0%
+fraction to be something like 50 to
+ 
+
+ align:start position:0%
+fraction to be something like 50 to
+60% and for the foam you need to have
+
+ align:start position:0%
+60% and for the foam you need to have
+ 
+
+ align:start position:0%
+60% and for the foam you need to have
+the foam cell size less than the
+
+ align:start position:0%
+the foam cell size less than the
+ 
+
+ align:start position:0%
+the foam cell size less than the
+separation between the Spheres you need
+
+ align:start position:0%
+separation between the Spheres you need
+ 
+
+ align:start position:0%
+separation between the Spheres you need
+to have a number of you can't just have
+
+ align:start position:0%
+to have a number of you can't just have
+ 
+
+ align:start position:0%
+to have a number of you can't just have
+one pore in here it's not really like a
+
+ align:start position:0%
+one pore in here it's not really like a
+ 
+
+ align:start position:0%
+one pore in here it's not really like a
+foam you can't it won't behave like a
+
+ align:start position:0%
+foam you can't it won't behave like a
+ 
+
+ align:start position:0%
+foam you can't it won't behave like a
+foam as a Continuum so you need to have
+
+ align:start position:0%
+foam as a Continuum so you need to have
+ 
+
+ align:start position:0%
+foam as a Continuum so you need to have
+a number of different cell sizes in
+
+ align:start position:0%
+a number of different cell sizes in
+ 
+
+ align:start position:0%
+a number of different cell sizes in
+between each um between each sphere and
+
+ align:start position:0%
+between each um between each sphere and
+ 
+
+ align:start position:0%
+between each um between each sphere and
+so you need the cell size of the foam to
+
+ align:start position:0%
+so you need the cell size of the foam to
+ 
+
+ align:start position:0%
+so you need the cell size of the foam to
+be a lot less than the separation of the
+
+ align:start position:0%
+be a lot less than the separation of the
+ 
+
+ align:start position:0%
+be a lot less than the separation of the
+Spheres there C but if you can control
+
+ align:start position:0%
+Spheres there C but if you can control
+ 
+
+ align:start position:0%
+Spheres there C but if you can control
+this geometry you can get this sandwich
+
+ align:start position:0%
+this geometry you can get this sandwich
+ 
+
+ align:start position:0%
+this geometry you can get this sandwich
+effect and you can get uh improved
+
+ align:start position:0%
+effect and you can get uh improved
+ 
+
+ align:start position:0%
+effect and you can get uh improved
+Properties by doing that so there's ways
+
+ align:start position:0%
+Properties by doing that so there's ways
+ 
+
+ align:start position:0%
+Properties by doing that so there's ways
+you can play around with the structure
+
+ align:start position:0%
+you can play around with the structure
+ 
+
+ align:start position:0%
+you can play around with the structure
+of the Foams to improve their
+
+ align:start position:0%
+of the Foams to improve their
+ 
+
+ align:start position:0%
+of the Foams to improve their
+properties so that was one thing I
+
+ align:start position:0%
+properties so that was one thing I
+ 
+
+ align:start position:0%
+properties so that was one thing I
+wanted to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another way to improve the properties of
+
+ align:start position:0%
+another way to improve the properties of
+ 
+
+ align:start position:0%
+another way to improve the properties of
+a of a foam like material is to use one
+
+ align:start position:0%
+a of a foam like material is to use one
+ 
+
+ align:start position:0%
+a of a foam like material is to use one
+of those lattice materials so you know
+
+ align:start position:0%
+of those lattice materials so you know
+ 
+
+ align:start position:0%
+of those lattice materials so you know
+we've been talking about ways to improve
+
+ align:start position:0%
+we've been talking about ways to improve
+ 
+
+ align:start position:0%
+we've been talking about ways to improve
+the bending stiffness but if you could
+
+ align:start position:0%
+the bending stiffness but if you could
+ 
+
+ align:start position:0%
+the bending stiffness but if you could
+get rid of the bending all together and
+
+ align:start position:0%
+get rid of the bending all together and
+ 
+
+ align:start position:0%
+get rid of the bending all together and
+have axial deformation in the cell walls
+
+ align:start position:0%
+have axial deformation in the cell walls
+ 
+
+ align:start position:0%
+have axial deformation in the cell walls
+then it would be much stiffer and you
+
+ align:start position:0%
+then it would be much stiffer and you
+ 
+
+ align:start position:0%
+then it would be much stiffer and you
+can get axial deformation by having
+
+ align:start position:0%
+can get axial deformation by having
+ 
+
+ align:start position:0%
+can get axial deformation by having
+those uh 3D truss kind of materials so I
+
+ align:start position:0%
+those uh 3D truss kind of materials so I
+ 
+
+ align:start position:0%
+those uh 3D truss kind of materials so I
+just I think I have a picture of oops
+
+ align:start position:0%
+just I think I have a picture of oops
+ 
+
+ align:start position:0%
+just I think I have a picture of oops
+there we go so there's one of those 3D
+
+ align:start position:0%
+there we go so there's one of those 3D
+ 
+
+ align:start position:0%
+there we go so there's one of those 3D
+Trust materials so another alternative
+
+ align:start position:0%
+Trust materials so another alternative
+ 
+
+ align:start position:0%
+Trust materials so another alternative
+is to sort of get rid of the bending all
+
+ align:start position:0%
+is to sort of get rid of the bending all
+ 
+
+ align:start position:0%
+is to sort of get rid of the bending all
+together and to try to make a trust type
+
+ align:start position:0%
+together and to try to make a trust type
+ 
+
+ align:start position:0%
+together and to try to make a trust type
+material
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's various ways to make these I
+
+ align:start position:0%
+so there's various ways to make these I
+ 
+
+ align:start position:0%
+so there's various ways to make these I
+think we talked about a few of them
+
+ align:start position:0%
+think we talked about a few of them
+ 
+
+ align:start position:0%
+think we talked about a few of them
+earlier on and you can analyze them as
+
+ align:start position:0%
+earlier on and you can analyze them as
+ 
+
+ align:start position:0%
+earlier on and you can analyze them as
+as trust type structures and I can just
+
+ align:start position:0%
+as trust type structures and I can just
+ 
+
+ align:start position:0%
+as trust type structures and I can just
+run through a sort of little dimensional
+
+ align:start position:0%
+run through a sort of little dimensional
+ 
+
+ align:start position:0%
+run through a sort of little dimensional
+argument to get the modulus so the
+
+ align:start position:0%
+argument to get the modulus so the
+ 
+
+ align:start position:0%
+argument to get the modulus so the
+modulus is going to go as the stress
+
+ align:start position:0%
+modulus is going to go as the stress
+ 
+
+ align:start position:0%
+modulus is going to go as the stress
+over the strain the stress is going to
+
+ align:start position:0%
+over the strain the stress is going to
+ 
+
+ align:start position:0%
+over the strain the stress is going to
+go as a force over a length squared The
+
+ align:start position:0%
+go as a force over a length squared The
+ 
+
+ align:start position:0%
+go as a force over a length squared The
+Strain is going to go as a deformation
+
+ align:start position:0%
+Strain is going to go as a deformation
+ 
+
+ align:start position:0%
+Strain is going to go as a deformation
+over l so this is just like what we had
+
+ align:start position:0%
+over l so this is just like what we had
+ 
+
+ align:start position:0%
+over l so this is just like what we had
+before for the Foams but in this case
+
+ align:start position:0%
+before for the Foams but in this case
+ 
+
+ align:start position:0%
+before for the Foams but in this case
+the deformation is going to go as the
+
+ align:start position:0%
+the deformation is going to go as the
+ 
+
+ align:start position:0%
+the deformation is going to go as the
+force times the length over the area of
+
+ align:start position:0%
+force times the length over the area of
+ 
+
+ align:start position:0%
+force times the length over the area of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+cross-section uh divided by es
+
+ align:start position:0%
+cross-section uh divided by es
+ 
+
+ align:start position:0%
+cross-section uh divided by es
+s uh because we're pulling it or pushing
+
+ align:start position:0%
+s uh because we're pulling it or pushing
+ 
+
+ align:start position:0%
+s uh because we're pulling it or pushing
+it ax and so that goes as FL L over t^2
+
+ align:start position:0%
+it ax and so that goes as FL L over t^2
+ 
+
+ align:start position:0%
+it ax and so that goes as FL L over t^2
+es
+
+ align:start position:0%
+es
+ 
+
+ align:start position:0%
+es
+s and if I just put that back in the
+
+ align:start position:0%
+s and if I just put that back in the
+ 
+
+ align:start position:0%
+s and if I just put that back in the
+equation here for the modulus I get
+
+ align:start position:0%
+equation here for the modulus I get
+ 
+
+ align:start position:0%
+equation here for the modulus I get
+we've got F over L and then I've got
+
+ align:start position:0%
+we've got F over L and then I've got
+ 
+
+ align:start position:0%
+we've got F over L and then I've got
+Delta here so that's f l t^2
+
+ align:start position:0%
+Delta here so that's f l t^2
+ 
+
+ align:start position:0%
+Delta here so that's f l t^2
+DS and you just get the modulus goes
+
+ align:start position:0%
+DS and you just get the modulus goes
+ 
+
+ align:start position:0%
+DS and you just get the modulus goes
+as the modulus of the solid time T l^
+
+ align:start position:0%
+as the modulus of the solid time T l^
+ 
+
+ align:start position:0%
+as the modulus of the solid time T l^
+2 and that goes as the modulus of the
+
+ align:start position:0%
+2 and that goes as the modulus of the
+ 
+
+ align:start position:0%
+2 and that goes as the modulus of the
+solid
+
+ align:start position:0%
+solid
+ 
+
+ align:start position:0%
+solid
+times the relative density so for the
+
+ align:start position:0%
+times the relative density so for the
+ 
+
+ align:start position:0%
+times the relative density so for the
+open cell Foams the modulus went as the
+
+ align:start position:0%
+open cell Foams the modulus went as the
+ 
+
+ align:start position:0%
+open cell Foams the modulus went as the
+relative density squared so if it was
+
+ align:start position:0%
+relative density squared so if it was
+ 
+
+ align:start position:0%
+relative density squared so if it was
+10% solid the modulus would be 0.01 and
+
+ align:start position:0%
+10% solid the modulus would be 0.01 and
+ 
+
+ align:start position:0%
+10% solid the modulus would be 0.01 and
+this is saying if it's 10% solid the
+
+ align:start position:0%
+this is saying if it's 10% solid the
+ 
+
+ align:start position:0%
+this is saying if it's 10% solid the
+modulus is 0.1 so it's much bigger right
+
+ align:start position:0%
+modulus is 0.1 so it's much bigger right
+ 
+
+ align:start position:0%
+modulus is 0.1 so it's much bigger right
+so this is all sort of well and good uh
+
+ align:start position:0%
+so this is all sort of well and good uh
+ 
+
+ align:start position:0%
+so this is all sort of well and good uh
+the only difficulty is that uh in when
+
+ align:start position:0%
+the only difficulty is that uh in when
+ 
+
+ align:start position:0%
+the only difficulty is that uh in when
+you when you look at the modulus you can
+
+ align:start position:0%
+you when you look at the modulus you can
+ 
+
+ align:start position:0%
+you when you look at the modulus you can
+do reasonably well but when you look at
+
+ align:start position:0%
+do reasonably well but when you look at
+ 
+
+ align:start position:0%
+do reasonably well but when you look at
+the strength some of the members are
+
+ align:start position:0%
+the strength some of the members are
+ 
+
+ align:start position:0%
+the strength some of the members are
+going to be inevitably in compression
+
+ align:start position:0%
+going to be inevitably in compression
+ 
+
+ align:start position:0%
+going to be inevitably in compression
+when you have these trust materials some
+
+ align:start position:0%
+when you have these trust materials some
+ 
+
+ align:start position:0%
+when you have these trust materials some
+members are going to be in tension some
+
+ align:start position:0%
+members are going to be in tension some
+ 
+
+ align:start position:0%
+members are going to be in tension some
+members are going to be in compression
+
+ align:start position:0%
+members are going to be in compression
+ 
+
+ align:start position:0%
+members are going to be in compression
+and the compression members tend to
+
+ align:start position:0%
+and the compression members tend to
+ 
+
+ align:start position:0%
+and the compression members tend to
+buckle and once the compression members
+
+ align:start position:0%
+buckle and once the compression members
+ 
+
+ align:start position:0%
+buckle and once the compression members
+Buckle then you're back to the same kind
+
+ align:start position:0%
+Buckle then you're back to the same kind
+ 
+
+ align:start position:0%
+Buckle then you're back to the same kind
+of strength relationship that you have
+
+ align:start position:0%
+of strength relationship that you have
+ 
+
+ align:start position:0%
+of strength relationship that you have
+for the foam so that's um one of the
+
+ align:start position:0%
+for the foam so that's um one of the
+ 
+
+ align:start position:0%
+for the foam so that's um one of the
+difficulties of
+
+ align:start position:0%
+difficulties of
+ 
+
+ align:start position:0%
+difficulties of
+this so let me say that the
+
+ align:start position:0%
+this so let me say that the
+ 
+
+ align:start position:0%
+this so let me say that the
+strength so if the if it the strength
+
+ align:start position:0%
+strength so if the if it the strength
+ 
+
+ align:start position:0%
+strength so if the if it the strength
+failed if the strength was controlled by
+
+ align:start position:0%
+failed if the strength was controlled by
+ 
+
+ align:start position:0%
+failed if the strength was controlled by
+uni aial yield it would go linearly with
+
+ align:start position:0%
+uni aial yield it would go linearly with
+ 
+
+ align:start position:0%
+uni aial yield it would go linearly with
+relative density but if it goes as
+
+ align:start position:0%
+relative density but if it goes as
+ 
+
+ align:start position:0%
+relative density but if it goes as
+buckling it goes as the square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'll just say the compression members
+
+ align:start position:0%
+so I'll just say the compression members
+ 
+
+ align:start position:0%
+so I'll just say the compression members
+can can buckle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and say you had a
+
+ align:start position:0%
+and say you had a
+ 
+
+ align:start position:0%
+and say you had a
+metal um
+
+ align:start position:0%
+metal um
+ 
+
+ align:start position:0%
+metal um
+lattice then there's some interaction
+
+ align:start position:0%
+lattice then there's some interaction
+ 
+
+ align:start position:0%
+lattice then there's some interaction
+between the plastic Behavior and the
+
+ align:start position:0%
+between the plastic Behavior and the
+ 
+
+ align:start position:0%
+between the plastic Behavior and the
+buckling and you use What's called the
+
+ align:start position:0%
+buckling and you use What's called the
+ 
+
+ align:start position:0%
+buckling and you use What's called the
+tangent modulus instead of just the
+
+ align:start position:0%
+tangent modulus instead of just the
+ 
+
+ align:start position:0%
+tangent modulus instead of just the
+young modulus and the tangent meas
+
+ align:start position:0%
+young modulus and the tangent meas
+ 
+
+ align:start position:0%
+young modulus and the tangent meas
+modulus is lower and there's also what's
+
+ align:start position:0%
+modulus is lower and there's also what's
+ 
+
+ align:start position:0%
+modulus is lower and there's also what's
+called knockdown factors that can be
+
+ align:start position:0%
+called knockdown factors that can be
+ 
+
+ align:start position:0%
+called knockdown factors that can be
+large too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the knockdown Factor can be like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50% so that the measured strength can be
+
+ align:start position:0%
+50% so that the measured strength can be
+ 
+
+ align:start position:0%
+50% so that the measured strength can be
+half of what you thought it was going to
+
+ align:start position:0%
+half of what you thought it was going to
+ 
+
+ align:start position:0%
+half of what you thought it was going to
+be so oops this should be a squared over
+
+ align:start position:0%
+be so oops this should be a squared over
+ 
+
+ align:start position:0%
+be so oops this should be a squared over
+here Sor
+
+ align:start position:0%
+here Sor
+ 
+
+ align:start position:0%
+here Sor
+right so that even though the the
+
+ align:start position:0%
+right so that even though the the
+ 
+
+ align:start position:0%
+right so that even though the the
+stiffness of these 3D trusses can be
+
+ align:start position:0%
+stiffness of these 3D trusses can be
+ 
+
+ align:start position:0%
+stiffness of these 3D trusses can be
+quite good uh the strength often isn't
+
+ align:start position:0%
+quite good uh the strength often isn't
+ 
+
+ align:start position:0%
+quite good uh the strength often isn't
+quite as good as one might hope so so
+
+ align:start position:0%
+quite as good as one might hope so so
+ 
+
+ align:start position:0%
+quite as good as one might hope so so
+that's one of the issues with
+
+ align:start position:0%
+that's one of the issues with
+ 
+
+ align:start position:0%
+that's one of the issues with
+them all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so do you see the idea though with
+
+ align:start position:0%
+right so do you see the idea though with
+ 
+
+ align:start position:0%
+right so do you see the idea though with
+all these different um micro structures
+
+ align:start position:0%
+all these different um micro structures
+ 
+
+ align:start position:0%
+all these different um micro structures
+is that you can control the structure in
+
+ align:start position:0%
+is that you can control the structure in
+ 
+
+ align:start position:0%
+is that you can control the structure in
+a way to try to increase the bending
+
+ align:start position:0%
+a way to try to increase the bending
+ 
+
+ align:start position:0%
+a way to try to increase the bending
+stiffness or get rid of the bending
+
+ align:start position:0%
+stiffness or get rid of the bending
+ 
+
+ align:start position:0%
+stiffness or get rid of the bending
+stiffness and increase the axial
+
+ align:start position:0%
+stiffness and increase the axial
+ 
+
+ align:start position:0%
+stiffness and increase the axial
+stiffness so there's things you can do
+
+ align:start position:0%
+stiffness so there's things you can do
+ 
+
+ align:start position:0%
+stiffness so there's things you can do
+to play around with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and I wanted to talk a bit today
+
+ align:start position:0%
+okay and I wanted to talk a bit today
+ 
+
+ align:start position:0%
+okay and I wanted to talk a bit today
+about material selection charts for
+
+ align:start position:0%
+about material selection charts for
+ 
+
+ align:start position:0%
+about material selection charts for
+Foams so when we talked about Woods we
+
+ align:start position:0%
+Foams so when we talked about Woods we
+ 
+
+ align:start position:0%
+Foams so when we talked about Woods we
+started talking about this remember I
+
+ align:start position:0%
+started talking about this remember I
+ 
+
+ align:start position:0%
+started talking about this remember I
+derived a little performance index we
+
+ align:start position:0%
+derived a little performance index we
+ 
+
+ align:start position:0%
+derived a little performance index we
+said if we had a a material and we
+
+ align:start position:0%
+said if we had a a material and we
+ 
+
+ align:start position:0%
+said if we had a a material and we
+wanted to have a given stiffness and we
+
+ align:start position:0%
+wanted to have a given stiffness and we
+ 
+
+ align:start position:0%
+wanted to have a given stiffness and we
+wanted to minimize the mass we had that
+
+ align:start position:0%
+wanted to minimize the mass we had that
+ 
+
+ align:start position:0%
+wanted to minimize the mass we had that
+performance index that was e to the 1/2
+
+ align:start position:0%
+performance index that was e to the 1/2
+ 
+
+ align:start position:0%
+performance index that was e to the 1/2
+over row and we had a chart of modulus
+
+ align:start position:0%
+over row and we had a chart of modulus
+ 
+
+ align:start position:0%
+over row and we had a chart of modulus
+versus density and we saw that wood was
+
+ align:start position:0%
+versus density and we saw that wood was
+ 
+
+ align:start position:0%
+versus density and we saw that wood was
+really good you can do that for other
+
+ align:start position:0%
+really good you can do that for other
+ 
+
+ align:start position:0%
+really good you can do that for other
+sorts of properties not just modulus so
+
+ align:start position:0%
+sorts of properties not just modulus so
+ 
+
+ align:start position:0%
+sorts of properties not just modulus so
+you can you can make a a u depending on
+
+ align:start position:0%
+you can you can make a a u depending on
+ 
+
+ align:start position:0%
+you can you can make a a u depending on
+what the mechanical requirement is you
+
+ align:start position:0%
+what the mechanical requirement is you
+ 
+
+ align:start position:0%
+what the mechanical requirement is you
+can work out different performance
+
+ align:start position:0%
+can work out different performance
+ 
+
+ align:start position:0%
+can work out different performance
+indices so I wanted to go into that in a
+
+ align:start position:0%
+indices so I wanted to go into that in a
+ 
+
+ align:start position:0%
+indices so I wanted to go into that in a
+little bit more detail so so the
+
+ align:start position:0%
+little bit more detail so so the
+ 
+
+ align:start position:0%
+little bit more detail so so the
+question is how do we select the best
+
+ align:start position:0%
+question is how do we select the best
+ 
+
+ align:start position:0%
+question is how do we select the best
+material for some
+
+ align:start position:0%
+material for some
+ 
+
+ align:start position:0%
+material for some
+mechanical uh requirement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the wood section we looked at the
+
+ align:start position:0%
+so in the wood section we looked at the
+ 
+
+ align:start position:0%
+so in the wood section we looked at the
+minimum mass of a beam of a given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stiffness and we saw that the
+
+ align:start position:0%
+stiffness and we saw that the
+ 
+
+ align:start position:0%
+stiffness and we saw that the
+performance index was e to the2 over
+
+ align:start position:0%
+performance index was e to the2 over
+ 
+
+ align:start position:0%
+performance index was e to the2 over
+row so let me let me do another one of
+
+ align:start position:0%
+row so let me let me do another one of
+ 
+
+ align:start position:0%
+row so let me let me do another one of
+these little examples and then I'll show
+
+ align:start position:0%
+these little examples and then I'll show
+ 
+
+ align:start position:0%
+these little examples and then I'll show
+you some more of them so another example
+
+ align:start position:0%
+you some more of them so another example
+ 
+
+ align:start position:0%
+you some more of them so another example
+would be what material uh minimize the
+
+ align:start position:0%
+would be what material uh minimize the
+ 
+
+ align:start position:0%
+would be what material uh minimize the
+mass of of a beam of a given strength or
+
+ align:start position:0%
+mass of of a beam of a given strength or
+ 
+
+ align:start position:0%
+mass of of a beam of a given strength or
+given failure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+load so I'll call the failure load PF
+
+ align:start position:0%
+load so I'll call the failure load PF
+ 
+
+ align:start position:0%
+load so I'll call the failure load PF
+and we can say the maximum stress in the
+
+ align:start position:0%
+and we can say the maximum stress in the
+ 
+
+ align:start position:0%
+and we can say the maximum stress in the
+beam is going to be the moment in the
+
+ align:start position:0%
+beam is going to be the moment in the
+ 
+
+ align:start position:0%
+beam is going to be the moment in the
+beam times the distance from the neutral
+
+ align:start position:0%
+beam times the distance from the neutral
+ 
+
+ align:start position:0%
+beam times the distance from the neutral
+axis Y and divided by the moment of
+
+ align:start position:0%
+axis Y and divided by the moment of
+ 
+
+ align:start position:0%
+axis Y and divided by the moment of
+inertia so here m is the maximum moment
+
+ align:start position:0%
+inertia so here m is the maximum moment
+ 
+
+ align:start position:0%
+inertia so here m is the maximum moment
+in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam and Y is the maximum distance from
+
+ align:start position:0%
+beam and Y is the maximum distance from
+ 
+
+ align:start position:0%
+beam and Y is the maximum distance from
+the neutral axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I is the moment of inertia and I'm
+
+ align:start position:0%
+and I is the moment of inertia and I'm
+ 
+
+ align:start position:0%
+and I is the moment of inertia and I'm
+going to um say I goes as T 4th and I'm
+
+ align:start position:0%
+going to um say I goes as T 4th and I'm
+ 
+
+ align:start position:0%
+going to um say I goes as T 4th and I'm
+going to define a failure stress of the
+
+ align:start position:0%
+going to define a failure stress of the
+ 
+
+ align:start position:0%
+going to define a failure stress of the
+material Sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F so Sigma
+
+ align:start position:0%
+F so Sigma
+ 
+
+ align:start position:0%
+F so Sigma
+Max is going to go as my failure load
+
+ align:start position:0%
+Max is going to go as my failure load
+ 
+
+ align:start position:0%
+Max is going to go as my failure load
+times the length that would be the
+
+ align:start position:0%
+times the length that would be the
+ 
+
+ align:start position:0%
+times the length that would be the
+moment the distance from the neutral
+
+ align:start position:0%
+moment the distance from the neutral
+ 
+
+ align:start position:0%
+moment the distance from the neutral
+axis is going to go as T and the moment
+
+ align:start position:0%
+axis is going to go as T and the moment
+ 
+
+ align:start position:0%
+axis is going to go as T and the moment
+of inertia is going to go as T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4th and that's going to be the failure
+
+ align:start position:0%
+4th and that's going to be the failure
+ 
+
+ align:start position:0%
+4th and that's going to be the failure
+strength there so I can solve this for T
+
+ align:start position:0%
+strength there so I can solve this for T
+ 
+
+ align:start position:0%
+strength there so I can solve this for T
+and then I'm going to write the mass in
+
+ align:start position:0%
+and then I'm going to write the mass in
+ 
+
+ align:start position:0%
+and then I'm going to write the mass in
+terms of T and put that in there so here
+
+ align:start position:0%
+terms of T and put that in there so here
+ 
+
+ align:start position:0%
+terms of T and put that in there so here
+T goes
+
+ align:start position:0%
+T goes
+ 
+
+ align:start position:0%
+T goes
+as let's see p
+
+ align:start position:0%
+as let's see p
+ 
+
+ align:start position:0%
+as let's see p
+f Lo L / Sigma F and that's going to be
+
+ align:start position:0%
+f Lo L / Sigma F and that's going to be
+ 
+
+ align:start position:0%
+f Lo L / Sigma F and that's going to be
+to the 13
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power let's see I guess I could scoot
+
+ align:start position:0%
+power let's see I guess I could scoot
+ 
+
+ align:start position:0%
+power let's see I guess I could scoot
+over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we could say that the mass
+
+ align:start position:0%
+and we could say that the mass
+ 
+
+ align:start position:0%
+and we could say that the mass
+m goes as the density * T ^2 *
+
+ align:start position:0%
+m goes as the density * T ^2 *
+ 
+
+ align:start position:0%
+m goes as the density * T ^2 *
+l so the mass m is going to go as row *
+
+ align:start position:0%
+l so the mass m is going to go as row *
+ 
+
+ align:start position:0%
+l so the mass m is going to go as row *
+L * T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubed t^ squ
+
+ align:start position:0%
+cubed t^ squ
+ 
+
+ align:start position:0%
+cubed t^ squ
+rather so that whole thing goes to the
+
+ align:start position:0%
+rather so that whole thing goes to the
+ 
+
+ align:start position:0%
+rather so that whole thing goes to the
+2/3
+
+ align:start position:0%
+2/3
+ 
+
+ align:start position:0%
+2/3
+power so if we look at the material
+
+ align:start position:0%
+power so if we look at the material
+ 
+
+ align:start position:0%
+power so if we look at the material
+properties the Mass goes as the density
+
+ align:start position:0%
+properties the Mass goes as the density
+ 
+
+ align:start position:0%
+properties the Mass goes as the density
+time the failure
+
+ align:start position:0%
+time the failure
+ 
+
+ align:start position:0%
+time the failure
+stress raised to the 2/3 power so if we
+
+ align:start position:0%
+stress raised to the 2/3 power so if we
+ 
+
+ align:start position:0%
+stress raised to the 2/3 power so if we
+want to minimize the mass we want to
+
+ align:start position:0%
+want to minimize the mass we want to
+ 
+
+ align:start position:0%
+want to minimize the mass we want to
+minimize row over Sigma F to the 2/3 or
+
+ align:start position:0%
+minimize row over Sigma F to the 2/3 or
+ 
+
+ align:start position:0%
+minimize row over Sigma F to the 2/3 or
+we want to maximize Sigma F to the 2/3
+
+ align:start position:0%
+we want to maximize Sigma F to the 2/3
+ 
+
+ align:start position:0%
+we want to maximize Sigma F to the 2/3
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row so that's the performance index for
+
+ align:start position:0%
+row so that's the performance index for
+ 
+
+ align:start position:0%
+row so that's the performance index for
+that case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we can obtain these performance
+
+ align:start position:0%
+okay so we can obtain these performance
+ 
+
+ align:start position:0%
+okay so we can obtain these performance
+indices for different loading
+
+ align:start position:0%
+indices for different loading
+ 
+
+ align:start position:0%
+indices for different loading
+configurations and different mechanical
+
+ align:start position:0%
+configurations and different mechanical
+ 
+
+ align:start position:0%
+configurations and different mechanical
+requirements and I don't want to go
+
+ align:start position:0%
+requirements and I don't want to go
+ 
+
+ align:start position:0%
+requirements and I don't want to go
+through a whole lot of them but I'm
+
+ align:start position:0%
+through a whole lot of them but I'm
+ 
+
+ align:start position:0%
+through a whole lot of them but I'm
+going to put this up with the notes so
+
+ align:start position:0%
+going to put this up with the notes so
+ 
+
+ align:start position:0%
+going to put this up with the notes so
+this is from Mike Ashby's book on
+
+ align:start position:0%
+this is from Mike Ashby's book on
+ 
+
+ align:start position:0%
+this is from Mike Ashby's book on
+material selection and mechanical design
+
+ align:start position:0%
+material selection and mechanical design
+ 
+
+ align:start position:0%
+material selection and mechanical design
+and this is a whole series of these
+
+ align:start position:0%
+and this is a whole series of these
+ 
+
+ align:start position:0%
+and this is a whole series of these
+performance indices for different
+
+ align:start position:0%
+performance indices for different
+ 
+
+ align:start position:0%
+performance indices for different
+situations for things loaded in torsion
+
+ align:start position:0%
+situations for things loaded in torsion
+ 
+
+ align:start position:0%
+situations for things loaded in torsion
+for columns and buckling for panels and
+
+ align:start position:0%
+for columns and buckling for panels and
+ 
+
+ align:start position:0%
+for columns and buckling for panels and
+bending uh so these ones are all for
+
+ align:start position:0%
+bending uh so these ones are all for
+ 
+
+ align:start position:0%
+bending uh so these ones are all for
+stiffness and they're all involve a
+
+ align:start position:0%
+stiffness and they're all involve a
+ 
+
+ align:start position:0%
+stiffness and they're all involve a
+modulus raised to some power divided by
+
+ align:start position:0%
+modulus raised to some power divided by
+ 
+
+ align:start position:0%
+modulus raised to some power divided by
+a density so a tie in tension it's e
+
+ align:start position:0%
+a density so a tie in tension it's e
+ 
+
+ align:start position:0%
+a density so a tie in tension it's e
+over row uh the beam in bending is e to
+
+ align:start position:0%
+over row uh the beam in bending is e to
+ 
+
+ align:start position:0%
+over row uh the beam in bending is e to
+the one half over row a plate and
+
+ align:start position:0%
+the one half over row a plate and
+ 
+
+ align:start position:0%
+the one half over row a plate and
+bending is e to 1/3 over row so you
+
+ align:start position:0%
+bending is e to 1/3 over row so you
+ 
+
+ align:start position:0%
+bending is e to 1/3 over row so you
+don't need to memorize those but you can
+
+ align:start position:0%
+don't need to memorize those but you can
+ 
+
+ align:start position:0%
+don't need to memorize those but you can
+see you can derive these for different
+
+ align:start position:0%
+see you can derive these for different
+ 
+
+ align:start position:0%
+see you can derive these for different
+situations and here's another one for
+
+ align:start position:0%
+situations and here's another one for
+ 
+
+ align:start position:0%
+situations and here's another one for
+strength limited design so the shaft is
+
+ align:start position:0%
+strength limited design so the shaft is
+ 
+
+ align:start position:0%
+strength limited design so the shaft is
+uh you know depending on what the
+
+ align:start position:0%
+uh you know depending on what the
+ 
+
+ align:start position:0%
+uh you know depending on what the
+specifications are it's a strength
+
+ align:start position:0%
+specifications are it's a strength
+ 
+
+ align:start position:0%
+specifications are it's a strength
+raised to the 2/3 power over row the
+
+ align:start position:0%
+raised to the 2/3 power over row the
+ 
+
+ align:start position:0%
+raised to the 2/3 power over row the
+beam loaded and bending the top one
+
+ align:start position:0%
+beam loaded and bending the top one
+ 
+
+ align:start position:0%
+beam loaded and bending the top one
+there Sigma F to the the 2/3 over row
+
+ align:start position:0%
+there Sigma F to the the 2/3 over row
+ 
+
+ align:start position:0%
+there Sigma F to the the 2/3 over row
+that's what we just did so there's all
+
+ align:start position:0%
+that's what we just did so there's all
+ 
+
+ align:start position:0%
+that's what we just did so there's all
+these different kind of performance
+
+ align:start position:0%
+these different kind of performance
+ 
+
+ align:start position:0%
+these different kind of performance
+indices so depending on what your
+
+ align:start position:0%
+indices so depending on what your
+ 
+
+ align:start position:0%
+indices so depending on what your
+situation is you would pick one of these
+
+ align:start position:0%
+situation is you would pick one of these
+ 
+
+ align:start position:0%
+situation is you would pick one of these
+indices and then what you can do is use
+
+ align:start position:0%
+indices and then what you can do is use
+ 
+
+ align:start position:0%
+indices and then what you can do is use
+these material selection charts which
+
+ align:start position:0%
+these material selection charts which
+ 
+
+ align:start position:0%
+these material selection charts which
+plot one property against another on log
+
+ align:start position:0%
+plot one property against another on log
+ 
+
+ align:start position:0%
+plot one property against another on log
+log scales and because all of these
+
+ align:start position:0%
+log scales and because all of these
+ 
+
+ align:start position:0%
+log scales and because all of these
+performance indices involve a power they
+
+ align:start position:0%
+performance indices involve a power they
+ 
+
+ align:start position:0%
+performance indices involve a power they
+always end up being a straight line on
+
+ align:start position:0%
+always end up being a straight line on
+ 
+
+ align:start position:0%
+always end up being a straight line on
+your log log plot and here this one I
+
+ align:start position:0%
+your log log plot and here this one I
+ 
+
+ align:start position:0%
+your log log plot and here this one I
+think is the same as what I showed you
+
+ align:start position:0%
+think is the same as what I showed you
+ 
+
+ align:start position:0%
+think is the same as what I showed you
+for the for the wood this one's the
+
+ align:start position:0%
+for the for the wood this one's the
+ 
+
+ align:start position:0%
+for the for the wood this one's the
+modulus here plotted against
+
+ align:start position:0%
+modulus here plotted against
+ 
+
+ align:start position:0%
+modulus here plotted against
+so Foams are down here and there's you
+
+ align:start position:0%
+so Foams are down here and there's you
+ 
+
+ align:start position:0%
+so Foams are down here and there's you
+know other engineering materials are
+
+ align:start position:0%
+know other engineering materials are
+ 
+
+ align:start position:0%
+know other engineering materials are
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and these guidelines here are the
+
+ align:start position:0%
+here and these guidelines here are the
+ 
+
+ align:start position:0%
+here and these guidelines here are the
+different performance indices so this
+
+ align:start position:0%
+different performance indices so this
+ 
+
+ align:start position:0%
+different performance indices so this
+one's e over row this one's e to the 1/2
+
+ align:start position:0%
+one's e over row this one's e to the 1/2
+ 
+
+ align:start position:0%
+one's e over row this one's e to the 1/2
+over row this one's e to the 1/3 over
+
+ align:start position:0%
+over row this one's e to the 1/3 over
+ 
+
+ align:start position:0%
+over row this one's e to the 1/3 over
+row and for this case here is you move
+
+ align:start position:0%
+row and for this case here is you move
+ 
+
+ align:start position:0%
+row and for this case here is you move
+the lines up to the top leftand Corner
+
+ align:start position:0%
+the lines up to the top leftand Corner
+ 
+
+ align:start position:0%
+the lines up to the top leftand Corner
+E's getting bigger row is getting
+
+ align:start position:0%
+E's getting bigger row is getting
+ 
+
+ align:start position:0%
+E's getting bigger row is getting
+smaller and so the actual value of the
+
+ align:start position:0%
+smaller and so the actual value of the
+ 
+
+ align:start position:0%
+smaller and so the actual value of the
+performance index is getting bigger okay
+
+ align:start position:0%
+performance index is getting bigger okay
+ 
+
+ align:start position:0%
+performance index is getting bigger okay
+so you can use this to select the
+
+ align:start position:0%
+so you can use this to select the
+ 
+
+ align:start position:0%
+so you can use this to select the
+material so we've made these charts for
+
+ align:start position:0%
+material so we've made these charts for
+ 
+
+ align:start position:0%
+material so we've made these charts for
+Foams as well
+
+ align:start position:0%
+Foams as well
+ 
+
+ align:start position:0%
+Foams as well
+so here's a couple of charts for Foams
+
+ align:start position:0%
+so here's a couple of charts for Foams
+ 
+
+ align:start position:0%
+so here's a couple of charts for Foams
+and I think what I'm going to do is just
+
+ align:start position:0%
+and I think what I'm going to do is just
+ 
+
+ align:start position:0%
+and I think what I'm going to do is just
+go through them quickly and there aren't
+
+ align:start position:0%
+go through them quickly and there aren't
+ 
+
+ align:start position:0%
+go through them quickly and there aren't
+really that many notes I'll just put the
+
+ align:start position:0%
+really that many notes I'll just put the
+ 
+
+ align:start position:0%
+really that many notes I'll just put the
+notes on the website and you can I won't
+
+ align:start position:0%
+notes on the website and you can I won't
+ 
+
+ align:start position:0%
+notes on the website and you can I won't
+write all the notes down um and then we
+
+ align:start position:0%
+write all the notes down um and then we
+ 
+
+ align:start position:0%
+write all the notes down um and then we
+can finish this today um so this one
+
+ align:start position:0%
+can finish this today um so this one
+ 
+
+ align:start position:0%
+can finish this today um so this one
+here is the Young's modulus versus
+
+ align:start position:0%
+here is the Young's modulus versus
+ 
+
+ align:start position:0%
+here is the Young's modulus versus
+density and these are all sorts of
+
+ align:start position:0%
+density and these are all sorts of
+ 
+
+ align:start position:0%
+density and these are all sorts of
+different Foams so the low modulus ones
+
+ align:start position:0%
+different Foams so the low modulus ones
+ 
+
+ align:start position:0%
+different Foams so the low modulus ones
+tend to be flexible the higher modulus
+
+ align:start position:0%
+tend to be flexible the higher modulus
+ 
+
+ align:start position:0%
+tend to be flexible the higher modulus
+ones tend to be more rigid and you could
+
+ align:start position:0%
+ones tend to be more rigid and you could
+ 
+
+ align:start position:0%
+ones tend to be more rigid and you could
+use this to um select Foams if you
+
+ align:start position:0%
+use this to um select Foams if you
+ 
+
+ align:start position:0%
+use this to um select Foams if you
+wanted um you can also see what the
+
+ align:start position:0%
+wanted um you can also see what the
+ 
+
+ align:start position:0%
+wanted um you can also see what the
+range of values is so the values of the
+
+ align:start position:0%
+range of values is so the values of the
+ 
+
+ align:start position:0%
+range of values is so the values of the
+of the modulus here goes from uh a
+
+ align:start position:0%
+of the modulus here goes from uh a
+ 
+
+ align:start position:0%
+of the modulus here goes from uh a
+little less than 100 um because these
+
+ align:start position:0%
+little less than 100 um because these
+ 
+
+ align:start position:0%
+little less than 100 um because these
+this is two orders of magnitude here I
+
+ align:start position:0%
+this is two orders of magnitude here I
+ 
+
+ align:start position:0%
+this is two orders of magnitude here I
+think each one of these uh down to about
+
+ align:start position:0%
+think each one of these uh down to about
+ 
+
+ align:start position:0%
+think each one of these uh down to about
+10 Theus 4 a little less than that so
+
+ align:start position:0%
+10 Theus 4 a little less than that so
+ 
+
+ align:start position:0%
+10 Theus 4 a little less than that so
+there's a huge range there's almost a
+
+ align:start position:0%
+there's a huge range there's almost a
+ 
+
+ align:start position:0%
+there's a huge range there's almost a
+range of a factor of a million in those
+
+ align:start position:0%
+range of a factor of a million in those
+ 
+
+ align:start position:0%
+range of a factor of a million in those
+uh moduli and the same with the strength
+
+ align:start position:0%
+uh moduli and the same with the strength
+ 
+
+ align:start position:0%
+uh moduli and the same with the strength
+here the strengths go from uh 10us 3
+
+ align:start position:0%
+here the strengths go from uh 10us 3
+ 
+
+ align:start position:0%
+here the strengths go from uh 10us 3
+megapascals up to about maybe 30 megap
+
+ align:start position:0%
+megapascals up to about maybe 30 megap
+ 
+
+ align:start position:0%
+megapascals up to about maybe 30 megap
+pascals something like that and you can
+
+ align:start position:0%
+pascals something like that and you can
+ 
+
+ align:start position:0%
+pascals something like that and you can
+see for the modul and the strength
+
+ align:start position:0%
+see for the modul and the strength
+ 
+
+ align:start position:0%
+see for the modul and the strength
+things like the metal Foams are good the
+
+ align:start position:0%
+things like the metal Foams are good the
+ 
+
+ align:start position:0%
+things like the metal Foams are good the
+bals is good here's the BSA up here
+
+ align:start position:0%
+bals is good here's the BSA up here
+ 
+
+ align:start position:0%
+bals is good here's the BSA up here
+metal Foams up there so you can kind of
+
+ align:start position:0%
+metal Foams up there so you can kind of
+ 
+
+ align:start position:0%
+metal Foams up there so you can kind of
+see the range
+
+ align:start position:0%
+see the range
+ 
+
+ align:start position:0%
+see the range
+of the range of properties that you
+
+ align:start position:0%
+of the range of properties that you
+ 
+
+ align:start position:0%
+of the range of properties that you
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+get and then you can
+
+ align:start position:0%
+get and then you can
+ 
+
+ align:start position:0%
+get and then you can
+also I need to drink hang
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on you can also plot the specific
+
+ align:start position:0%
+on you can also plot the specific
+ 
+
+ align:start position:0%
+on you can also plot the specific
+properties so here's the compressive
+
+ align:start position:0%
+properties so here's the compressive
+ 
+
+ align:start position:0%
+properties so here's the compressive
+strength of divided by the density
+
+ align:start position:0%
+strength of divided by the density
+ 
+
+ align:start position:0%
+strength of divided by the density
+plotted against the Young's modulus
+
+ align:start position:0%
+plotted against the Young's modulus
+ 
+
+ align:start position:0%
+plotted against the Young's modulus
+divided by the density and here you want
+
+ align:start position:0%
+divided by the density and here you want
+ 
+
+ align:start position:0%
+divided by the density and here you want
+to be up at this end so you would have a
+
+ align:start position:0%
+to be up at this end so you would have a
+ 
+
+ align:start position:0%
+to be up at this end so you would have a
+high strength and a high stiffness so
+
+ align:start position:0%
+high strength and a high stiffness so
+ 
+
+ align:start position:0%
+high strength and a high stiffness so
+the Balsa and the metal Foams are good
+
+ align:start position:0%
+the Balsa and the metal Foams are good
+ 
+
+ align:start position:0%
+the Balsa and the metal Foams are good
+up here uh this next plot this is the
+
+ align:start position:0%
+up here uh this next plot this is the
+ 
+
+ align:start position:0%
+up here uh this next plot this is the
+compressive stress at 25% strain and
+
+ align:start position:0%
+compressive stress at 25% strain and
+ 
+
+ align:start position:0%
+compressive stress at 25% strain and
+this is the densification strain and if
+
+ align:start position:0%
+this is the densification strain and if
+ 
+
+ align:start position:0%
+this is the densification strain and if
+you think of
+
+ align:start position:0%
+you think of
+ 
+
+ align:start position:0%
+you think of
+having um you know your stress strain
+
+ align:start position:0%
+having um you know your stress strain
+ 
+
+ align:start position:0%
+having um you know your stress strain
+curve looks like
+
+ align:start position:0%
+curve looks like
+ 
+
+ align:start position:0%
+curve looks like
+this something like that so you could
+
+ align:start position:0%
+this something like that so you could
+ 
+
+ align:start position:0%
+this something like that so you could
+say that's
+
+ align:start position:0%
+say that's
+ 
+
+ align:start position:0%
+say that's
+a strain of 0.25 and that's the stress
+
+ align:start position:0%
+a strain of 0.25 and that's the stress
+ 
+
+ align:start position:0%
+a strain of 0.25 and that's the stress
+that corresponds to that so that stress
+
+ align:start position:0%
+that corresponds to that so that stress
+ 
+
+ align:start position:0%
+that corresponds to that so that stress
+times The densification Strain which is
+
+ align:start position:0%
+times The densification Strain which is
+ 
+
+ align:start position:0%
+times The densification Strain which is
+out here some place is an estimate of
+
+ align:start position:0%
+out here some place is an estimate of
+ 
+
+ align:start position:0%
+out here some place is an estimate of
+the energy underneath the stress strain
+
+ align:start position:0%
+the energy underneath the stress strain
+ 
+
+ align:start position:0%
+the energy underneath the stress strain
+curve so you can think of this right
+
+ align:start position:0%
+curve so you can think of this right
+ 
+
+ align:start position:0%
+curve so you can think of this right
+hand plot here those dashed lines these
+
+ align:start position:0%
+hand plot here those dashed lines these
+ 
+
+ align:start position:0%
+hand plot here those dashed lines these
+lines like this and this and this each
+
+ align:start position:0%
+lines like this and this and this each
+ 
+
+ align:start position:0%
+lines like this and this and this each
+one of those corresponds to how much
+
+ align:start position:0%
+one of those corresponds to how much
+ 
+
+ align:start position:0%
+one of those corresponds to how much
+energy you would absorb under the stress
+
+ align:start position:0%
+energy you would absorb under the stress
+ 
+
+ align:start position:0%
+energy you would absorb under the stress
+strain curve so here's uh you know
+
+ align:start position:0%
+strain curve so here's uh you know
+ 
+
+ align:start position:0%
+strain curve so here's uh you know
+points that lie on here would have an
+
+ align:start position:0%
+points that lie on here would have an
+ 
+
+ align:start position:0%
+points that lie on here would have an
+energy of 0.001 Mega per cubic meter and
+
+ align:start position:0%
+energy of 0.001 Mega per cubic meter and
+ 
+
+ align:start position:0%
+energy of 0.001 Mega per cubic meter and
+over here we're at 10 Jew per cubic
+
+ align:start position:0%
+over here we're at 10 Jew per cubic
+ 
+
+ align:start position:0%
+over here we're at 10 Jew per cubic
+meter so again the Bala and the metal
+
+ align:start position:0%
+meter so again the Bala and the metal
+ 
+
+ align:start position:0%
+meter so again the Bala and the metal
+Foams are are good over here so you can
+
+ align:start position:0%
+Foams are are good over here so you can
+ 
+
+ align:start position:0%
+Foams are are good over here so you can
+use these plots to try to identify Foams
+
+ align:start position:0%
+use these plots to try to identify Foams
+ 
+
+ align:start position:0%
+use these plots to try to identify Foams
+for particular
+
+ align:start position:0%
+for particular
+ 
+
+ align:start position:0%
+for particular
+applications and I think there's a
+
+ align:start position:0%
+applications and I think there's a
+ 
+
+ align:start position:0%
+applications and I think there's a
+couple more doesn't have to be
+
+ align:start position:0%
+couple more doesn't have to be
+ 
+
+ align:start position:0%
+couple more doesn't have to be
+mechanical properties here's thermal
+
+ align:start position:0%
+mechanical properties here's thermal
+ 
+
+ align:start position:0%
+mechanical properties here's thermal
+conductivity versus compressive strength
+
+ align:start position:0%
+conductivity versus compressive strength
+ 
+
+ align:start position:0%
+conductivity versus compressive strength
+so you could imagine if you wanted some
+
+ align:start position:0%
+so you could imagine if you wanted some
+ 
+
+ align:start position:0%
+so you could imagine if you wanted some
+insulation you want to have a certain
+
+ align:start position:0%
+insulation you want to have a certain
+ 
+
+ align:start position:0%
+insulation you want to have a certain
+thermal conductivity value you probably
+
+ align:start position:0%
+thermal conductivity value you probably
+ 
+
+ align:start position:0%
+thermal conductivity value you probably
+also need at least some minimal
+
+ align:start position:0%
+also need at least some minimal
+ 
+
+ align:start position:0%
+also need at least some minimal
+compressive strength uh you could also
+
+ align:start position:0%
+compressive strength uh you could also
+ 
+
+ align:start position:0%
+compressive strength uh you could also
+have something like a maximum service
+
+ align:start position:0%
+have something like a maximum service
+ 
+
+ align:start position:0%
+have something like a maximum service
+temperature that you know maybe the
+
+ align:start position:0%
+temperature that you know maybe the
+ 
+
+ align:start position:0%
+temperature that you know maybe the
+foam's going to melt at some temperature
+
+ align:start position:0%
+foam's going to melt at some temperature
+ 
+
+ align:start position:0%
+foam's going to melt at some temperature
+you can't go beyond that so uh so
+
+ align:start position:0%
+you can't go beyond that so uh so
+ 
+
+ align:start position:0%
+you can't go beyond that so uh so
+there's some property there and I think
+
+ align:start position:0%
+there's some property there and I think
+ 
+
+ align:start position:0%
+there's some property there and I think
+I think there's one more here um you can
+
+ align:start position:0%
+I think there's one more here um you can
+ 
+
+ align:start position:0%
+I think there's one more here um you can
+look at things like the density in terms
+
+ align:start position:0%
+look at things like the density in terms
+ 
+
+ align:start position:0%
+look at things like the density in terms
+of the buoyancy of the foam if you had
+
+ align:start position:0%
+of the buoyancy of the foam if you had
+ 
+
+ align:start position:0%
+of the buoyancy of the foam if you had
+some buoyancy application and you can
+
+ align:start position:0%
+some buoyancy application and you can
+ 
+
+ align:start position:0%
+some buoyancy application and you can
+look at cell size on this one here uh
+
+ align:start position:0%
+look at cell size on this one here uh
+ 
+
+ align:start position:0%
+look at cell size on this one here uh
+and cell size can be important for
+
+ align:start position:0%
+and cell size can be important for
+ 
+
+ align:start position:0%
+and cell size can be important for
+things like filtration and catalysis so
+
+ align:start position:0%
+things like filtration and catalysis so
+ 
+
+ align:start position:0%
+things like filtration and catalysis so
+the amount of surface area goes as one
+
+ align:start position:0%
+the amount of surface area goes as one
+ 
+
+ align:start position:0%
+the amount of surface area goes as one
+over the cell size the surface area per
+
+ align:start position:0%
+over the cell size the surface area per
+ 
+
+ align:start position:0%
+over the cell size the surface area per
+unit volume and so the cell size can be
+
+ align:start position:0%
+unit volume and so the cell size can be
+ 
+
+ align:start position:0%
+unit volume and so the cell size can be
+important for those sorts of
+
+ align:start position:0%
+important for those sorts of
+ 
+
+ align:start position:0%
+important for those sorts of
+applications so the idea is you can make
+
+ align:start position:0%
+applications so the idea is you can make
+ 
+
+ align:start position:0%
+applications so the idea is you can make
+these material selection charts for foam
+
+ align:start position:0%
+these material selection charts for foam
+ 
+
+ align:start position:0%
+these material selection charts for foam
+and you can put data on there and you
+
+ align:start position:0%
+and you can put data on there and you
+ 
+
+ align:start position:0%
+and you can put data on there and you
+can compare Foams and you can use these
+
+ align:start position:0%
+can compare Foams and you can use these
+ 
+
+ align:start position:0%
+can compare Foams and you can use these
+performance indices okay so I'm going to
+
+ align:start position:0%
+performance indices okay so I'm going to
+ 
+
+ align:start position:0%
+performance indices okay so I'm going to
+leave it at that there were there's a
+
+ align:start position:0%
+leave it at that there were there's a
+ 
+
+ align:start position:0%
+leave it at that there were there's a
+little bit more notes but I'll just put
+
+ align:start position:0%
+little bit more notes but I'll just put
+ 
+
+ align:start position:0%
+little bit more notes but I'll just put
+them on the website and you can you can
+
+ align:start position:0%
+them on the website and you can you can
+ 
+
+ align:start position:0%
+them on the website and you can you can
+get them from there okay so I think
+
+ align:start position:0%
+get them from there okay so I think
+ 
+
+ align:start position:0%
+get them from there okay so I think
+we're good for today
\ No newline at end of file
diff --git a/WtOJN2TCD6o.txt b/WtOJN2TCD6o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e32df320ad60161b575f540ee3af9a16664dd6e4
--- /dev/null
+++ b/WtOJN2TCD6o.txt
@@ -0,0 +1,13131 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so where were we
+
+ align:start position:0%
+ocw.mit.edu all right so where were we
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so where were we
+last time so we would had derived the
+
+ align:start position:0%
+last time so we would had derived the
+ 
+
+ align:start position:0%
+last time so we would had derived the
+fir on Lin which is at the top of the
+
+ align:start position:0%
+fir on Lin which is at the top of the
+ 
+
+ align:start position:0%
+fir on Lin which is at the top of the
+board and the really the only difference
+
+ align:start position:0%
+board and the really the only difference
+ 
+
+ align:start position:0%
+board and the really the only difference
+between this and what we talked about
+
+ align:start position:0%
+between this and what we talked about
+ 
+
+ align:start position:0%
+between this and what we talked about
+earlier is that we had performed the
+
+ align:start position:0%
+earlier is that we had performed the
+ 
+
+ align:start position:0%
+earlier is that we had performed the
+multiple expansion so we distinguished
+
+ align:start position:0%
+multiple expansion so we distinguished
+ 
+
+ align:start position:0%
+multiple expansion so we distinguished
+between cinear moment momenta that are
+
+ align:start position:0%
+between cinear moment momenta that are
+ 
+
+ align:start position:0%
+between cinear moment momenta that are
+scaling like a cinear momentum and
+
+ align:start position:0%
+scaling like a cinear momentum and
+ 
+
+ align:start position:0%
+scaling like a cinear momentum and
+momentum that are scaling like an Ultras
+
+ align:start position:0%
+momentum that are scaling like an Ultras
+ 
+
+ align:start position:0%
+momentum that are scaling like an Ultras
+soft and only the cinear pieces were
+
+ align:start position:0%
+soft and only the cinear pieces were
+ 
+
+ align:start position:0%
+soft and only the cinear pieces were
+showing up in here and same with the
+
+ align:start position:0%
+showing up in here and same with the
+ 
+
+ align:start position:0%
+showing up in here and same with the
+clinar gauge field it was only showing
+
+ align:start position:0%
+clinar gauge field it was only showing
+ 
+
+ align:start position:0%
+clinar gauge field it was only showing
+up in here whereas both were showing up
+
+ align:start position:0%
+up in here whereas both were showing up
+ 
+
+ align:start position:0%
+up in here whereas both were showing up
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+here there's only a single type of
+
+ align:start position:0%
+here there's only a single type of
+ 
+
+ align:start position:0%
+here there's only a single type of
+derivative here because ultr soft and
+
+ align:start position:0%
+derivative here because ultr soft and
+ 
+
+ align:start position:0%
+derivative here because ultr soft and
+cinear momentum are the same size in the
+
+ align:start position:0%
+cinear momentum are the same size in the
+ 
+
+ align:start position:0%
+cinear momentum are the same size in the
+N component but they're different in
+
+ align:start position:0%
+N component but they're different in
+ 
+
+ align:start position:0%
+N component but they're different in
+these other components so we had to we
+
+ align:start position:0%
+these other components so we had to we
+ 
+
+ align:start position:0%
+these other components so we had to we
+had these labels and this label operator
+
+ align:start position:0%
+had these labels and this label operator
+ 
+
+ align:start position:0%
+had these labels and this label operator
+that picked out the cinear momenta so we
+
+ align:start position:0%
+that picked out the cinear momenta so we
+ 
+
+ align:start position:0%
+that picked out the cinear momenta so we
+could Define cinear coant derivatives if
+
+ align:start position:0%
+could Define cinear coant derivatives if
+ 
+
+ align:start position:0%
+could Define cinear coant derivatives if
+you like with this subscript n whereas
+
+ align:start position:0%
+you like with this subscript n whereas
+ 
+
+ align:start position:0%
+you like with this subscript n whereas
+this D is kind of like a full derivative
+
+ align:start position:0%
+this D is kind of like a full derivative
+ 
+
+ align:start position:0%
+this D is kind of like a full derivative
+that involves both types of gauge field
+
+ align:start position:0%
+that involves both types of gauge field
+ 
+
+ align:start position:0%
+that involves both types of gauge field
+and then at the end of lecture it was
+
+ align:start position:0%
+and then at the end of lecture it was
+ 
+
+ align:start position:0%
+and then at the end of lecture it was
+kind of rush but I was talking about the
+
+ align:start position:0%
+kind of rush but I was talking about the
+ 
+
+ align:start position:0%
+kind of rush but I was talking about the
+colar gluon lrange and I said there's a
+
+ align:start position:0%
+colar gluon lrange and I said there's a
+ 
+
+ align:start position:0%
+colar gluon lrange and I said there's a
+set of replacement rules that we could
+
+ align:start position:0%
+set of replacement rules that we could
+ 
+
+ align:start position:0%
+set of replacement rules that we could
+make to effectively do the same thing
+
+ align:start position:0%
+make to effectively do the same thing
+ 
+
+ align:start position:0%
+make to effectively do the same thing
+that we did here and now I've just
+
+ align:start position:0%
+that we did here and now I've just
+ 
+
+ align:start position:0%
+that we did here and now I've just
+written out for you what that lran is
+
+ align:start position:0%
+written out for you what that lran is
+ 
+
+ align:start position:0%
+written out for you what that lran is
+with those replacement rules so curly D
+
+ align:start position:0%
+with those replacement rules so curly D
+ 
+
+ align:start position:0%
+with those replacement rules so curly D
+is is basically just taking all the
+
+ align:start position:0%
+is is basically just taking all the
+ 
+
+ align:start position:0%
+is is basically just taking all the
+derivatives and taking only the leading
+
+ align:start position:0%
+derivatives and taking only the leading
+ 
+
+ align:start position:0%
+derivatives and taking only the leading
+order pieces so we take the colinear
+
+ align:start position:0%
+order pieces so we take the colinear
+ 
+
+ align:start position:0%
+order pieces so we take the colinear
+pieces and the this component and this
+
+ align:start position:0%
+pieces and the this component and this
+ 
+
+ align:start position:0%
+pieces and the this component and this
+component we take the ultrasoft pieces
+
+ align:start position:0%
+component we take the ultrasoft pieces
+ 
+
+ align:start position:0%
+component we take the ultrasoft pieces
+in this component and then if you wrote
+
+ align:start position:0%
+in this component and then if you wrote
+ 
+
+ align:start position:0%
+in this component and then if you wrote
+the original lran as a commutator of two
+
+ align:start position:0%
+the original lran as a commutator of two
+ 
+
+ align:start position:0%
+the original lran as a commutator of two
+Co variant derivatives you just replace
+
+ align:start position:0%
+Co variant derivatives you just replace
+ 
+
+ align:start position:0%
+Co variant derivatives you just replace
+it by the leading order pieces and
+
+ align:start position:0%
+it by the leading order pieces and
+ 
+
+ align:start position:0%
+it by the leading order pieces and
+that's what the leading order action
+
+ align:start position:0%
+that's what the leading order action
+ 
+
+ align:start position:0%
+that's what the leading order action
+will be then we had to think about gauge
+
+ align:start position:0%
+will be then we had to think about gauge
+ 
+
+ align:start position:0%
+will be then we had to think about gauge
+fixing since this is the cinear gluon
+
+ align:start position:0%
+fixing since this is the cinear gluon
+ 
+
+ align:start position:0%
+fixing since this is the cinear gluon
+lran we should think about cinear gauge
+
+ align:start position:0%
+lran we should think about cinear gauge
+ 
+
+ align:start position:0%
+lran we should think about cinear gauge
+fixing this here is a general covariant
+
+ align:start position:0%
+fixing this here is a general covariant
+ 
+
+ align:start position:0%
+fixing this here is a general covariant
+gauge fixing the with parameter Tow and
+
+ align:start position:0%
+gauge fixing the with parameter Tow and
+ 
+
+ align:start position:0%
+gauge fixing the with parameter Tow and
+then there's a corresponding ghost term
+
+ align:start position:0%
+then there's a corresponding ghost term
+ 
+
+ align:start position:0%
+then there's a corresponding ghost term
+and in this lran the usual way it would
+
+ align:start position:0%
+and in this lran the usual way it would
+ 
+
+ align:start position:0%
+and in this lran the usual way it would
+look this would
+
+ align:start position:0%
+look this would
+ 
+
+ align:start position:0%
+look this would
+be I
+
+ align:start position:0%
+be I
+ 
+
+ align:start position:0%
+be I
+partial and then I said that because we
+
+ align:start position:0%
+partial and then I said that because we
+ 
+
+ align:start position:0%
+partial and then I said that because we
+don't want the colinear gauge fixing
+
+ align:start position:0%
+don't want the colinear gauge fixing
+ 
+
+ align:start position:0%
+don't want the colinear gauge fixing
+term to break ultrasoft gauge invariance
+
+ align:start position:0%
+term to break ultrasoft gauge invariance
+ 
+
+ align:start position:0%
+term to break ultrasoft gauge invariance
+we're going to turn that I partial into
+
+ align:start position:0%
+we're going to turn that I partial into
+ 
+
+ align:start position:0%
+we're going to turn that I partial into
+a variant derivative under under the
+
+ align:start position:0%
+a variant derivative under under the
+ 
+
+ align:start position:0%
+a variant derivative under under the
+under we're going to include this piece
+
+ align:start position:0%
+under we're going to include this piece
+ 
+
+ align:start position:0%
+under we're going to include this piece
+here with the N.A ultrasoft to make it
+
+ align:start position:0%
+here with the N.A ultrasoft to make it
+ 
+
+ align:start position:0%
+here with the N.A ultrasoft to make it
+colinear to make it ultrasoft gauge in
+
+ align:start position:0%
+colinear to make it ultrasoft gauge in
+ 
+
+ align:start position:0%
+colinear to make it ultrasoft gauge in
+variant at lowest order okay so that's
+
+ align:start position:0%
+variant at lowest order okay so that's
+ 
+
+ align:start position:0%
+variant at lowest order okay so that's
+really the only comp other than just
+
+ align:start position:0%
+really the only comp other than just
+ 
+
+ align:start position:0%
+really the only comp other than just
+doing the sort of most naive thing by
+
+ align:start position:0%
+doing the sort of most naive thing by
+ 
+
+ align:start position:0%
+doing the sort of most naive thing by
+just replacing derivatives by coant
+
+ align:start position:0%
+just replacing derivatives by coant
+ 
+
+ align:start position:0%
+just replacing derivatives by coant
+derivatives and you might think well
+
+ align:start position:0%
+derivatives and you might think well
+ 
+
+ align:start position:0%
+derivatives and you might think well
+I'll just keep this as a partial
+
+ align:start position:0%
+I'll just keep this as a partial
+ 
+
+ align:start position:0%
+I'll just keep this as a partial
+derivative since it's doing gauge fixing
+
+ align:start position:0%
+derivative since it's doing gauge fixing
+ 
+
+ align:start position:0%
+derivative since it's doing gauge fixing
+I don't need to make it covariant but we
+
+ align:start position:0%
+I don't need to make it covariant but we
+ 
+
+ align:start position:0%
+I don't need to make it covariant but we
+do want to make it coari under the
+
+ align:start position:0%
+do want to make it coari under the
+ 
+
+ align:start position:0%
+do want to make it coari under the
+ultrasofts and that's why I write this
+
+ align:start position:0%
+ultrasofts and that's why I write this
+ 
+
+ align:start position:0%
+ultrasofts and that's why I write this
+curly the Ultra
+
+ align:start position:0%
+curly the Ultra
+ 
+
+ align:start position:0%
+curly the Ultra
+Soft okay so that gives you the leading
+
+ align:start position:0%
+Soft okay so that gives you the leading
+ 
+
+ align:start position:0%
+Soft okay so that gives you the leading
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+lran once you put together this with
+
+ align:start position:0%
+lran once you put together this with
+ 
+
+ align:start position:0%
+lran once you put together this with
+what you want for the ultrasoft then you
+
+ align:start position:0%
+what you want for the ultrasoft then you
+ 
+
+ align:start position:0%
+what you want for the ultrasoft then you
+would have the full leading order lran
+
+ align:start position:0%
+would have the full leading order lran
+ 
+
+ align:start position:0%
+would have the full leading order lran
+and the ultrasoft part is actually very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simple so for the ultrasoft
+
+ align:start position:0%
+simple so for the ultrasoft
+ 
+
+ align:start position:0%
+simple so for the ultrasoft
+part we just take a a full qcd action
+
+ align:start position:0%
+part we just take a a full qcd action
+ 
+
+ align:start position:0%
+part we just take a a full qcd action
+for the ultrasoft field so this is just
+
+ align:start position:0%
+for the ultrasoft field so this is just
+ 
+
+ align:start position:0%
+for the ultrasoft field so this is just
+s ultrasoft or Q ultrasoft Bar
+
+ align:start position:0%
+s ultrasoft or Q ultrasoft Bar
+ 
+
+ align:start position:0%
+s ultrasoft or Q ultrasoft Bar
+id/ ultrasoft q ultrasoft and likewise
+
+ align:start position:0%
+id/ ultrasoft q ultrasoft and likewise
+ 
+
+ align:start position:0%
+id/ ultrasoft q ultrasoft and likewise
+for the for the gluon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+piece it's just
+
+ align:start position:0%
+piece it's just
+ 
+
+ align:start position:0%
+piece it's just
+qcd and we would do the gauge
+
+ align:start position:0%
+qcd and we would do the gauge
+ 
+
+ align:start position:0%
+qcd and we would do the gauge
+fixing without without thinking about uh
+
+ align:start position:0%
+fixing without without thinking about uh
+ 
+
+ align:start position:0%
+fixing without without thinking about uh
+any any complications like these ones
+
+ align:start position:0%
+any any complications like these ones
+ 
+
+ align:start position:0%
+any any complications like these ones
+and these are just involving ultrasoft
+
+ align:start position:0%
+and these are just involving ultrasoft
+ 
+
+ align:start position:0%
+and these are just involving ultrasoft
+Fields so just QC just ultrasoft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fields okay so the only place when you
+
+ align:start position:0%
+Fields okay so the only place when you
+ 
+
+ align:start position:0%
+Fields okay so the only place when you
+take everything here together the only
+
+ align:start position:0%
+take everything here together the only
+ 
+
+ align:start position:0%
+take everything here together the only
+place that the ultrasoft and cinear
+
+ align:start position:0%
+place that the ultrasoft and cinear
+ 
+
+ align:start position:0%
+place that the ultrasoft and cinear
+Fields talk to each other in the garage
+
+ align:start position:0%
+Fields talk to each other in the garage
+ 
+
+ align:start position:0%
+Fields talk to each other in the garage
+in is in this single component n.
+
+ align:start position:0%
+in is in this single component n.
+ 
+
+ align:start position:0%
+in is in this single component n.
+partial n. a ultrasoft and that comes
+
+ align:start position:0%
+partial n. a ultrasoft and that comes
+ 
+
+ align:start position:0%
+partial n. a ultrasoft and that comes
+about basically because
+
+ align:start position:0%
+about basically because
+ 
+
+ align:start position:0%
+about basically because
+of because of the power counting that
+
+ align:start position:0%
+of because of the power counting that
+ 
+
+ align:start position:0%
+of because of the power counting that
+this is really the only place that these
+
+ align:start position:0%
+this is really the only place that these
+ 
+
+ align:start position:0%
+this is really the only place that these
+two things can interact we'll talk about
+
+ align:start position:0%
+two things can interact we'll talk about
+ 
+
+ align:start position:0%
+two things can interact we'll talk about
+the implications of that later on
+
+ align:start position:0%
+the implications of that later on
+ 
+
+ align:start position:0%
+the implications of that later on
+on okay but that's the leading order ly
+
+ align:start position:0%
+on okay but that's the leading order ly
+ 
+
+ align:start position:0%
+on okay but that's the leading order ly
+so once you have this piece then this
+
+ align:start position:0%
+so once you have this piece then this
+ 
+
+ align:start position:0%
+so once you have this piece then this
+piece is pretty straightforward with
+
+ align:start position:0%
+piece is pretty straightforward with
+ 
+
+ align:start position:0%
+piece is pretty straightforward with
+this additional complication of worrying
+
+ align:start position:0%
+this additional complication of worrying
+ 
+
+ align:start position:0%
+this additional complication of worrying
+about what gauge symmetry means which
+
+ align:start position:0%
+about what gauge symmetry means which
+ 
+
+ align:start position:0%
+about what gauge symmetry means which
+we'll talk more about later but we had
+
+ align:start position:0%
+we'll talk more about later but we had
+ 
+
+ align:start position:0%
+we'll talk more about later but we had
+to be careful not to break it when we
+
+ align:start position:0%
+to be careful not to break it when we
+ 
+
+ align:start position:0%
+to be careful not to break it when we
+introduce this term because we want to
+
+ align:start position:0%
+introduce this term because we want to
+ 
+
+ align:start position:0%
+introduce this term because we want to
+in some sense have a gauge fixing both
+
+ align:start position:0%
+in some sense have a gauge fixing both
+ 
+
+ align:start position:0%
+in some sense have a gauge fixing both
+for the clinar Glon and a separate gauge
+
+ align:start position:0%
+for the clinar Glon and a separate gauge
+ 
+
+ align:start position:0%
+for the clinar Glon and a separate gauge
+fixing for the ultrasoft Glon and that's
+
+ align:start position:0%
+fixing for the ultrasoft Glon and that's
+ 
+
+ align:start position:0%
+fixing for the ultrasoft Glon and that's
+why we we wanted to do this and then
+
+ align:start position:0%
+why we we wanted to do this and then
+ 
+
+ align:start position:0%
+why we we wanted to do this and then
+this piece here is simple it's just qcd
+
+ align:start position:0%
+this piece here is simple it's just qcd
+ 
+
+ align:start position:0%
+this piece here is simple it's just qcd
+because it's
+
+ align:start position:0%
+because it's
+ 
+
+ align:start position:0%
+because it's
+if you like it's the lowest energy mode
+
+ align:start position:0%
+if you like it's the lowest energy mode
+ 
+
+ align:start position:0%
+if you like it's the lowest energy mode
+and it doesn't know about any of the
+
+ align:start position:0%
+and it doesn't know about any of the
+ 
+
+ align:start position:0%
+and it doesn't know about any of the
+complications that we had for the cinear
+
+ align:start position:0%
+complications that we had for the cinear
+ 
+
+ align:start position:0%
+complications that we had for the cinear
+modes okay so any questions about this
+
+ align:start position:0%
+modes okay so any questions about this
+ 
+
+ align:start position:0%
+modes okay so any questions about this
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far okay so everything that we did in
+
+ align:start position:0%
+far okay so everything that we did in
+ 
+
+ align:start position:0%
+far okay so everything that we did in
+deriving these actions is tree
+
+ align:start position:0%
+deriving these actions is tree
+ 
+
+ align:start position:0%
+deriving these actions is tree
+level all the steps that we did were
+
+ align:start position:0%
+level all the steps that we did were
+ 
+
+ align:start position:0%
+level all the steps that we did were
+tree level so you can ask if I start to
+
+ align:start position:0%
+tree level so you can ask if I start to
+ 
+
+ align:start position:0%
+tree level so you can ask if I start to
+do loops will there be some Wilson
+
+ align:start position:0%
+do loops will there be some Wilson
+ 
+
+ align:start position:0%
+do loops will there be some Wilson
+coefficient that shows up somewhere here
+
+ align:start position:0%
+coefficient that shows up somewhere here
+ 
+
+ align:start position:0%
+coefficient that shows up somewhere here
+will I generate some new operators that
+
+ align:start position:0%
+will I generate some new operators that
+ 
+
+ align:start position:0%
+will I generate some new operators that
+I don't don't see here those are are
+
+ align:start position:0%
+I don't don't see here those are are
+ 
+
+ align:start position:0%
+I don't don't see here those are are
+reasonable questions and that's what
+
+ align:start position:0%
+reasonable questions and that's what
+ 
+
+ align:start position:0%
+reasonable questions and that's what
+we're going to address
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next so to go further we'll use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetries and we're actually going to
+
+ align:start position:0%
+symmetries and we're actually going to
+ 
+
+ align:start position:0%
+symmetries and we're actually going to
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+three different symmetries gauge
+
+ align:start position:0%
+three different symmetries gauge
+ 
+
+ align:start position:0%
+three different symmetries gauge
+symmetry which I've been promising you
+
+ align:start position:0%
+symmetry which I've been promising you
+ 
+
+ align:start position:0%
+symmetry which I've been promising you
+for a
+
+ align:start position:0%
+for a
+ 
+
+ align:start position:0%
+for a
+while reparameterization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invariance and spin symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or I'll put a question mark by this last
+
+ align:start position:0%
+or I'll put a question mark by this last
+ 
+
+ align:start position:0%
+or I'll put a question mark by this last
+one because we need to answer the
+
+ align:start position:0%
+one because we need to answer the
+ 
+
+ align:start position:0%
+one because we need to answer the
+question whether there even is a spin
+
+ align:start position:0%
+question whether there even is a spin
+ 
+
+ align:start position:0%
+question whether there even is a spin
+symmetry these two here this number one
+
+ align:start position:0%
+symmetry these two here this number one
+ 
+
+ align:start position:0%
+symmetry these two here this number one
+and number two will turn out to
+
+ align:start position:0%
+and number two will turn out to
+ 
+
+ align:start position:0%
+and number two will turn out to
+be quite important number three is not
+
+ align:start position:0%
+be quite important number three is not
+ 
+
+ align:start position:0%
+be quite important number three is not
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important so reparameterization
+
+ align:start position:0%
+important so reparameterization
+ 
+
+ align:start position:0%
+important so reparameterization
+invariance here will be like
+
+ align:start position:0%
+invariance here will be like
+ 
+
+ align:start position:0%
+invariance here will be like
+reparameterization invariance in HQ
+
+ align:start position:0%
+reparameterization invariance in HQ
+ 
+
+ align:start position:0%
+reparameterization invariance in HQ
+except now it's different we've
+
+ align:start position:0%
+except now it's different we've
+ 
+
+ align:start position:0%
+except now it's different we've
+introduced parameters n and n Bar and
+
+ align:start position:0%
+introduced parameters n and n Bar and
+ 
+
+ align:start position:0%
+introduced parameters n and n Bar and
+we'll have to see what kind of
+
+ align:start position:0%
+we'll have to see what kind of
+ 
+
+ align:start position:0%
+we'll have to see what kind of
+symmetries we have with those with
+
+ align:start position:0%
+symmetries we have with those with
+ 
+
+ align:start position:0%
+symmetries we have with those with
+respect to that that choice of basis
+
+ align:start position:0%
+respect to that that choice of basis
+ 
+
+ align:start position:0%
+respect to that that choice of basis
+vectors that we made but it otherwise
+
+ align:start position:0%
+vectors that we made but it otherwise
+ 
+
+ align:start position:0%
+vectors that we made but it otherwise
+will be analogous to our discussion of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+HQ so let's actually first dispense with
+
+ align:start position:0%
+HQ so let's actually first dispense with
+ 
+
+ align:start position:0%
+HQ so let's actually first dispense with
+the one that in some sense is the least
+
+ align:start position:0%
+the one that in some sense is the least
+ 
+
+ align:start position:0%
+the one that in some sense is the least
+important is number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three so first let's revisit our
+
+ align:start position:0%
+three so first let's revisit our
+ 
+
+ align:start position:0%
+three so first let's revisit our
+Spinners a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I put together the information
+
+ align:start position:0%
+so if I put together the information
+ 
+
+ align:start position:0%
+so if I put together the information
+that we talked about when we derived the
+
+ align:start position:0%
+that we talked about when we derived the
+ 
+
+ align:start position:0%
+that we talked about when we derived the
+equation at the top of the board there
+
+ align:start position:0%
+equation at the top of the board there
+ 
+
+ align:start position:0%
+equation at the top of the board there
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+larian we worked out that at tree
+
+ align:start position:0%
+larian we worked out that at tree
+ 
+
+ align:start position:0%
+larian we worked out that at tree
+level we have this
+
+ align:start position:0%
+level we have this
+ 
+
+ align:start position:0%
+level we have this
+formula that relates the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+fields so from that formula if we just
+
+ align:start position:0%
+fields so from that formula if we just
+ 
+
+ align:start position:0%
+fields so from that formula if we just
+project onto the spinner pieces we can
+
+ align:start position:0%
+project onto the spinner pieces we can
+ 
+
+ align:start position:0%
+project onto the spinner pieces we can
+write down a formula that relates the
+
+ align:start position:0%
+write down a formula that relates the
+ 
+
+ align:start position:0%
+write down a formula that relates the
+Spinners so throwing away the the gauge
+
+ align:start position:0%
+Spinners so throwing away the the gauge
+ 
+
+ align:start position:0%
+Spinners so throwing away the the gauge
+fields we have in momentum space that U
+
+ align:start position:0%
+fields we have in momentum space that U
+ 
+
+ align:start position:0%
+fields we have in momentum space that U
+of P the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spinner would be related to whatever
+
+ align:start position:0%
+spinner would be related to whatever
+ 
+
+ align:start position:0%
+spinner would be related to whatever
+spinner we have for this CN field which
+
+ align:start position:0%
+spinner we have for this CN field which
+ 
+
+ align:start position:0%
+spinner we have for this CN field which
+I call Un by that
+
+ align:start position:0%
+I call Un by that
+ 
+
+ align:start position:0%
+I call Un by that
+formula and then if you take this
+
+ align:start position:0%
+formula and then if you take this
+ 
+
+ align:start position:0%
+formula and then if you take this
+formula you also see that if I hit it
+
+ align:start position:0%
+formula you also see that if I hit it
+ 
+
+ align:start position:0%
+formula you also see that if I hit it
+with a projector
+
+ align:start position:0%
+with a projector
+ 
+
+ align:start position:0%
+with a projector
+n/n bar SL
+
+ align:start position:0%
+n/n bar SL
+ 
+
+ align:start position:0%
+n/n bar SL
+over4 if I hit hit the U with a
+
+ align:start position:0%
+over4 if I hit hit the U with a
+ 
+
+ align:start position:0%
+over4 if I hit hit the U with a
+projector it's going to kill this piece
+
+ align:start position:0%
+projector it's going to kill this piece
+ 
+
+ align:start position:0%
+projector it's going to kill this piece
+because the n n slash and bar slash can
+
+ align:start position:0%
+because the n n slash and bar slash can
+ 
+
+ align:start position:0%
+because the n n slash and bar slash can
+be pushed through the P per slash and
+
+ align:start position:0%
+be pushed through the P per slash and
+ 
+
+ align:start position:0%
+be pushed through the P per slash and
+then n bar squar is zero so that kills
+
+ align:start position:0%
+then n bar squar is zero so that kills
+ 
+
+ align:start position:0%
+then n bar squar is zero so that kills
+that second piece so we also have this
+
+ align:start position:0%
+that second piece so we also have this
+ 
+
+ align:start position:0%
+that second piece so we also have this
+formula and then once you have this
+
+ align:start position:0%
+formula and then once you have this
+ 
+
+ align:start position:0%
+formula and then once you have this
+formula you
+
+ align:start position:0%
+formula you
+ 
+
+ align:start position:0%
+formula you
+have the formulas that we kind of wanted
+
+ align:start position:0%
+have the formulas that we kind of wanted
+ 
+
+ align:start position:0%
+have the formulas that we kind of wanted
+for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but this actually this spinner here
+
+ align:start position:0%
+okay but this actually this spinner here
+ 
+
+ align:start position:0%
+okay but this actually this spinner here
+this un is not exactly the same as the
+
+ align:start position:0%
+this un is not exactly the same as the
+ 
+
+ align:start position:0%
+this un is not exactly the same as the
+spinner that we talked about
+
+ align:start position:0%
+spinner that we talked about
+ 
+
+ align:start position:0%
+spinner that we talked about
+earlier uh so let me come back let me
+
+ align:start position:0%
+earlier uh so let me come back let me
+ 
+
+ align:start position:0%
+earlier uh so let me come back let me
+come to that in a
+
+ align:start position:0%
+come to that in a
+ 
+
+ align:start position:0%
+come to that in a
+minute so first thing you might consider
+
+ align:start position:0%
+minute so first thing you might consider
+ 
+
+ align:start position:0%
+minute so first thing you might consider
+is whether when I take this
+
+ align:start position:0%
+is whether when I take this
+ 
+
+ align:start position:0%
+is whether when I take this
+CN field and I take the lran up at the
+
+ align:start position:0%
+CN field and I take the lran up at the
+ 
+
+ align:start position:0%
+CN field and I take the lran up at the
+top of the board do I just get the
+
+ align:start position:0%
+top of the board do I just get the
+ 
+
+ align:start position:0%
+top of the board do I just get the
+clinar propagator that we talked about
+
+ align:start position:0%
+clinar propagator that we talked about
+ 
+
+ align:start position:0%
+clinar propagator that we talked about
+and indeed you do
+
+ align:start position:0%
+and indeed you do
+ 
+
+ align:start position:0%
+and indeed you do
+so if
+
+ align:start position:0%
+so if
+ 
+
+ align:start position:0%
+so if
+you if you consider it's kind of obvious
+
+ align:start position:0%
+you if you consider it's kind of obvious
+ 
+
+ align:start position:0%
+you if you consider it's kind of obvious
+for the momentum dependent parts and
+
+ align:start position:0%
+for the momentum dependent parts and
+ 
+
+ align:start position:0%
+for the momentum dependent parts and
+really you might only worry about the
+
+ align:start position:0%
+really you might only worry about the
+ 
+
+ align:start position:0%
+really you might only worry about the
+spin and so if you
+
+ align:start position:0%
+spin and so if you
+ 
+
+ align:start position:0%
+spin and so if you
+consider this formula and you consider
+
+ align:start position:0%
+consider this formula and you consider
+ 
+
+ align:start position:0%
+consider this formula and you consider
+the sum over
+
+ align:start position:0%
+the sum over
+ 
+
+ align:start position:0%
+the sum over
+spins of U Bar which is what's going to
+
+ align:start position:0%
+spins of U Bar which is what's going to
+ 
+
+ align:start position:0%
+spins of U Bar which is what's going to
+appear in the numerator of the
+
+ align:start position:0%
+appear in the numerator of the
+ 
+
+ align:start position:0%
+appear in the numerator of the
+propagator for the firon when you're
+
+ align:start position:0%
+propagator for the firon when you're
+ 
+
+ align:start position:0%
+propagator for the firon when you're
+deriving the firon propagator you get a
+
+ align:start position:0%
+deriving the firon propagator you get a
+ 
+
+ align:start position:0%
+deriving the firon propagator you get a
+sum over the physical
+
+ align:start position:0%
+sum over the physical
+ 
+
+ align:start position:0%
+sum over the physical
+spins then from this formula this is a
+
+ align:start position:0%
+spins then from this formula this is a
+ 
+
+ align:start position:0%
+spins then from this formula this is a
+projector
+
+ align:start position:0%
+projector
+ 
+
+ align:start position:0%
+projector
+on something you know how to do the spin
+
+ align:start position:0%
+on something you know how to do the spin
+ 
+
+ align:start position:0%
+on something you know how to do the spin
+sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for which is the full
+
+ align:start position:0%
+for which is the full
+ 
+
+ align:start position:0%
+for which is the full
+Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spinner and that spin sum is just P
+
+ align:start position:0%
+spinner and that spin sum is just P
+ 
+
+ align:start position:0%
+spinner and that spin sum is just P
+slash so this is like P slash sandwiched
+
+ align:start position:0%
+slash so this is like P slash sandwiched
+ 
+
+ align:start position:0%
+slash so this is like P slash sandwiched
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projectors and you can work out that
+
+ align:start position:0%
+projectors and you can work out that
+ 
+
+ align:start position:0%
+projectors and you can work out that
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+exactly the numerator that we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before after a little bit of dra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algebra so that part works as expected
+
+ align:start position:0%
+algebra so that part works as expected
+ 
+
+ align:start position:0%
+algebra so that part works as expected
+we if we take this lran and we work out
+
+ align:start position:0%
+we if we take this lran and we work out
+ 
+
+ align:start position:0%
+we if we take this lran and we work out
+what the propagator is we get exactly
+
+ align:start position:0%
+what the propagator is we get exactly
+ 
+
+ align:start position:0%
+what the propagator is we get exactly
+the propagator we got from expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so quantizing LC c0 gives us that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+propagator but the situation is not
+
+ align:start position:0%
+propagator but the situation is not
+ 
+
+ align:start position:0%
+propagator but the situation is not
+quite the same for the spinner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in some sense this is not this this
+
+ align:start position:0%
+and in some sense this is not this this
+ 
+
+ align:start position:0%
+and in some sense this is not this this
+point is not absolutely crucial but
+
+ align:start position:0%
+point is not absolutely crucial but
+ 
+
+ align:start position:0%
+point is not absolutely crucial but
+actually because I there's a little
+
+ align:start position:0%
+actually because I there's a little
+ 
+
+ align:start position:0%
+actually because I there's a little
+simplification I want to do in order to
+
+ align:start position:0%
+simplification I want to do in order to
+ 
+
+ align:start position:0%
+simplification I want to do in order to
+discuss the spin Symmetry and in order
+
+ align:start position:0%
+discuss the spin Symmetry and in order
+ 
+
+ align:start position:0%
+discuss the spin Symmetry and in order
+to do that this point it it it's
+
+ align:start position:0%
+to do that this point it it it's
+ 
+
+ align:start position:0%
+to do that this point it it it's
+important to understand this point so
+
+ align:start position:0%
+important to understand this point so
+ 
+
+ align:start position:0%
+important to understand this point so
+that I'm going through this in some
+
+ align:start position:0%
+that I'm going through this in some
+ 
+
+ align:start position:0%
+that I'm going through this in some
+sense because then it'll be very easy to
+
+ align:start position:0%
+sense because then it'll be very easy to
+ 
+
+ align:start position:0%
+sense because then it'll be very easy to
+discuss what spin symmetry we have in
+
+ align:start position:0%
+discuss what spin symmetry we have in
+ 
+
+ align:start position:0%
+discuss what spin symmetry we have in
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theory so this guy is actually not equal
+
+ align:start position:0%
+theory so this guy is actually not equal
+ 
+
+ align:start position:0%
+theory so this guy is actually not equal
+to our expanded
+
+ align:start position:0%
+to our expanded
+ 
+
+ align:start position:0%
+to our expanded
+spinner
+
+ align:start position:0%
+spinner
+ 
+
+ align:start position:0%
+spinner
+which putting in some
+
+ align:start position:0%
+which putting in some
+ 
+
+ align:start position:0%
+which putting in some
+normalization I could
+
+ align:start position:0%
+normalization I could
+ 
+
+ align:start position:0%
+normalization I could
+write like
+
+ align:start position:0%
+write like
+ 
+
+ align:start position:0%
+write like
+this which so this is what we got by
+
+ align:start position:0%
+this which so this is what we got by
+ 
+
+ align:start position:0%
+this which so this is what we got by
+expanding some thing like this which is
+
+ align:start position:0%
+expanding some thing like this which is
+ 
+
+ align:start position:0%
+expanding some thing like this which is
+very simple where this U was equal to 1
+
+ align:start position:0%
+very simple where this U was equal to 1
+ 
+
+ align:start position:0%
+very simple where this U was equal to 1
+0 or 01
+
+ align:start position:0%
+0 or 01
+ 
+
+ align:start position:0%
+0 or 01
+in the direct
+
+ align:start position:0%
+in the direct
+ 
+
+ align:start position:0%
+in the direct
+representation but that's actually not
+
+ align:start position:0%
+representation but that's actually not
+ 
+
+ align:start position:0%
+representation but that's actually not
+what we get if we just take the formula
+
+ align:start position:0%
+what we get if we just take the formula
+ 
+
+ align:start position:0%
+what we get if we just take the formula
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+here and use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so let's see what we do get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you use the formula up
+
+ align:start position:0%
+so if you use the formula up
+ 
+
+ align:start position:0%
+so if you use the formula up
+there and you have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following so here's the F Theory spinner
+
+ align:start position:0%
+following so here's the F Theory spinner
+ 
+
+ align:start position:0%
+following so here's the F Theory spinner
+with sort of a conventional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normalization this thing and this thing
+
+ align:start position:0%
+normalization this thing and this thing
+ 
+
+ align:start position:0%
+normalization this thing and this thing
+here is the
+
+ align:start position:0%
+here is the
+ 
+
+ align:start position:0%
+here is the
+projector okay
+
+ align:start position:0%
+projector okay
+ 
+
+ align:start position:0%
+projector okay
+so you could work out what that product
+
+ align:start position:0%
+so you could work out what that product
+ 
+
+ align:start position:0%
+so you could work out what that product
+is and it turns out that you can write
+
+ align:start position:0%
+is and it turns out that you can write
+ 
+
+ align:start position:0%
+is and it turns out that you can write
+it in the following way which
+
+ align:start position:0%
+it in the following way which
+ 
+
+ align:start position:0%
+it in the following way which
+is very closely related but not
+
+ align:start position:0%
+is very closely related but not
+ 
+
+ align:start position:0%
+is very closely related but not
+precisely the
+
+ align:start position:0%
+precisely the
+ 
+
+ align:start position:0%
+precisely the
+same as what we had
+
+ align:start position:0%
+same as what we had
+ 
+
+ align:start position:0%
+same as what we had
+before so you can write it in what looks
+
+ align:start position:0%
+before so you can write it in what looks
+ 
+
+ align:start position:0%
+before so you can write it in what looks
+like the same
+
+ align:start position:0%
+like the same
+ 
+
+ align:start position:0%
+like the same
+form as we have over here except this
+
+ align:start position:0%
+form as we have over here except this
+ 
+
+ align:start position:0%
+form as we have over here except this
+curly U curly capital
+
+ align:start position:0%
+curly U curly capital
+ 
+
+ align:start position:0%
+curly U curly capital
+u is a more complicated object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's just whatever I get by
+
+ align:start position:0%
+and it's just whatever I get by
+ 
+
+ align:start position:0%
+and it's just whatever I get by
+multiplying these two things out which
+
+ align:start position:0%
+multiplying these two things out which
+ 
+
+ align:start position:0%
+multiplying these two things out which
+turns out to be something I can write in
+
+ align:start position:0%
+turns out to be something I can write in
+ 
+
+ align:start position:0%
+turns out to be something I can write in
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form so it's some two compon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spinner but it's got momentum dependence
+
+ align:start position:0%
+spinner but it's got momentum dependence
+ 
+
+ align:start position:0%
+spinner but it's got momentum dependence
+unlike our simple one
+
+ align:start position:0%
+unlike our simple one
+ 
+
+ align:start position:0%
+unlike our simple one
+Z and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+01 but everything we said about un
+
+ align:start position:0%
+01 but everything we said about un
+ 
+
+ align:start position:0%
+01 but everything we said about un
+really depended only on the fact that it
+
+ align:start position:0%
+really depended only on the fact that it
+ 
+
+ align:start position:0%
+really depended only on the fact that it
+could have be written in this form in
+
+ align:start position:0%
+could have be written in this form in
+ 
+
+ align:start position:0%
+could have be written in this form in
+terms of some two component spinner the
+
+ align:start position:0%
+terms of some two component spinner the
+ 
+
+ align:start position:0%
+terms of some two component spinner the
+fact that n slash on it was Zero the
+
+ align:start position:0%
+fact that n slash on it was Zero the
+ 
+
+ align:start position:0%
+fact that n slash on it was Zero the
+fact that it had projection relation so
+
+ align:start position:0%
+fact that it had projection relation so
+ 
+
+ align:start position:0%
+fact that it had projection relation so
+these formulas here once you have once
+
+ align:start position:0%
+these formulas here once you have once
+ 
+
+ align:start position:0%
+these formulas here once you have once
+you have you know if you have a formula
+
+ align:start position:0%
+you have you know if you have a formula
+ 
+
+ align:start position:0%
+you have you know if you have a formula
+like is these formulas here are
+
+ align:start position:0%
+like is these formulas here are
+ 
+
+ align:start position:0%
+like is these formulas here are
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+okay so actually it would be true
+
+ align:start position:0%
+okay so actually it would be true
+ 
+
+ align:start position:0%
+okay so actually it would be true
+whatever spinner we have there so why
+
+ align:start position:0%
+whatever spinner we have there so why
+ 
+
+ align:start position:0%
+whatever spinner we have there so why
+should I why should I want this U
+
+ align:start position:0%
+should I why should I want this U
+ 
+
+ align:start position:0%
+should I why should I want this U
+twiddle spinner rather than the U the U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spinner that actually has to do with
+
+ align:start position:0%
+spinner that actually has to do with
+ 
+
+ align:start position:0%
+spinner that actually has to do with
+this reparameterization in variance so
+
+ align:start position:0%
+this reparameterization in variance so
+ 
+
+ align:start position:0%
+this reparameterization in variance so
+it'll
+
+ align:start position:0%
+it'll
+ 
+
+ align:start position:0%
+it'll
+become clear when we talk about
+
+ align:start position:0%
+become clear when we talk about
+ 
+
+ align:start position:0%
+become clear when we talk about
+that but these extra terms in
+
+ align:start position:0%
+that but these extra terms in
+ 
+
+ align:start position:0%
+that but these extra terms in
+u relative to those for the other guy
+
+ align:start position:0%
+u relative to those for the other guy
+ 
+
+ align:start position:0%
+u relative to those for the other guy
+the simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U actually inser the proper
+
+ align:start position:0%
+U actually inser the proper
+ 
+
+ align:start position:0%
+U actually inser the proper
+structure under
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reparametrizations and
+
+ align:start position:0%
+reparametrizations and
+ 
+
+ align:start position:0%
+reparametrizations and
+basically it'll come become clear at a
+
+ align:start position:0%
+basically it'll come become clear at a
+ 
+
+ align:start position:0%
+basically it'll come become clear at a
+moment but basically if we wanted to get
+
+ align:start position:0%
+moment but basically if we wanted to get
+ 
+
+ align:start position:0%
+moment but basically if we wanted to get
+this U spinner we should have a slightly
+
+ align:start position:0%
+this U spinner we should have a slightly
+ 
+
+ align:start position:0%
+this U spinner we should have a slightly
+different projector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which I'll call PN
+
+ align:start position:0%
+which I'll call PN
+ 
+
+ align:start position:0%
+which I'll call PN
+Prime and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's so we could have used a different
+
+ align:start position:0%
+it's so we could have used a different
+ 
+
+ align:start position:0%
+it's so we could have used a different
+projector which is this
+
+ align:start position:0%
+projector which is this
+ 
+
+ align:start position:0%
+projector which is this
+one and then we could have come up with
+
+ align:start position:0%
+one and then we could have come up with
+ 
+
+ align:start position:0%
+one and then we could have come up with
+a another projector which was the PN bar
+
+ align:start position:0%
+a another projector which was the PN bar
+ 
+
+ align:start position:0%
+a another projector which was the PN bar
+projector which would satisfy that the
+
+ align:start position:0%
+projector which would satisfy that the
+ 
+
+ align:start position:0%
+projector which would satisfy that the
+sum is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one if we wanted and this projector here
+
+ align:start position:0%
+one if we wanted and this projector here
+ 
+
+ align:start position:0%
+one if we wanted and this projector here
+when acting on the full Theory spinner
+
+ align:start position:0%
+when acting on the full Theory spinner
+ 
+
+ align:start position:0%
+when acting on the full Theory spinner
+would have the full Theory field would
+
+ align:start position:0%
+would have the full Theory field would
+ 
+
+ align:start position:0%
+would have the full Theory field would
+have given something that would have
+
+ align:start position:0%
+have given something that would have
+ 
+
+ align:start position:0%
+have given something that would have
+been proportional to this combination
+
+ align:start position:0%
+been proportional to this combination
+ 
+
+ align:start position:0%
+been proportional to this combination
+over here okay so you just have to
+
+ align:start position:0%
+over here okay so you just have to
+ 
+
+ align:start position:0%
+over here okay so you just have to
+believe me I don't want to go through
+
+ align:start position:0%
+believe me I don't want to go through
+ 
+
+ align:start position:0%
+believe me I don't want to go through
+the algebra or you can check it yourself
+
+ align:start position:0%
+the algebra or you can check it yourself
+ 
+
+ align:start position:0%
+the algebra or you can check it yourself
+but this projector here is not in
+
+ align:start position:0%
+but this projector here is not in
+ 
+
+ align:start position:0%
+but this projector here is not in
+invariant under that symmetry of
+
+ align:start position:0%
+invariant under that symmetry of
+ 
+
+ align:start position:0%
+invariant under that symmetry of
+reparameterization invariance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when we talk about RPI it'll be clear
+
+ align:start position:0%
+so when we talk about RPI it'll be clear
+ 
+
+ align:start position:0%
+so when we talk about RPI it'll be clear
+why we want a projector which is this
+
+ align:start position:0%
+why we want a projector which is this
+ 
+
+ align:start position:0%
+why we want a projector which is this
+projector and not the slightly different
+
+ align:start position:0%
+projector and not the slightly different
+ 
+
+ align:start position:0%
+projector and not the slightly different
+projector which is this extra has this
+
+ align:start position:0%
+projector which is this extra has this
+ 
+
+ align:start position:0%
+projector which is this extra has this
+extra in slash over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay but nevertheless the important
+
+ align:start position:0%
+two okay but nevertheless the important
+ 
+
+ align:start position:0%
+two okay but nevertheless the important
+point that I wanted to emphasize
+
+ align:start position:0%
+point that I wanted to emphasize
+ 
+
+ align:start position:0%
+point that I wanted to emphasize
+is really that we have this kind of way
+
+ align:start position:0%
+is really that we have this kind of way
+ 
+
+ align:start position:0%
+is really that we have this kind of way
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+decomposing the spinner the true spinner
+
+ align:start position:0%
+decomposing the spinner the true spinner
+ 
+
+ align:start position:0%
+decomposing the spinner the true spinner
+for our field CN in terms of a two
+
+ align:start position:0%
+for our field CN in terms of a two
+ 
+
+ align:start position:0%
+for our field CN in terms of a two
+component object you
+
+ align:start position:0%
+component object you
+ 
+
+ align:start position:0%
+component object you
+twiddle okay so this
+
+ align:start position:0%
+twiddle okay so this
+ 
+
+ align:start position:0%
+twiddle okay so this
+is we are able to do that and if you
+
+ align:start position:0%
+is we are able to do that and if you
+ 
+
+ align:start position:0%
+is we are able to do that and if you
+want to talk about spin symmetry of the
+
+ align:start position:0%
+want to talk about spin symmetry of the
+ 
+
+ align:start position:0%
+want to talk about spin symmetry of the
+theory it's easier if you use a two
+
+ align:start position:0%
+theory it's easier if you use a two
+ 
+
+ align:start position:0%
+theory it's easier if you use a two
+component notation so the reason that I
+
+ align:start position:0%
+component notation so the reason that I
+ 
+
+ align:start position:0%
+component notation so the reason that I
+wanted to go through this is really to
+
+ align:start position:0%
+wanted to go through this is really to
+ 
+
+ align:start position:0%
+wanted to go through this is really to
+have on the board this equation which I
+
+ align:start position:0%
+have on the board this equation which I
+ 
+
+ align:start position:0%
+have on the board this equation which I
+can then use to motivate writing down a
+
+ align:start position:0%
+can then use to motivate writing down a
+ 
+
+ align:start position:0%
+can then use to motivate writing down a
+two component version of CN
+
+ align:start position:0%
+two component version of CN
+ 
+
+ align:start position:0%
+two component version of CN
+once I have a two component version of
+
+ align:start position:0%
+once I have a two component version of
+ 
+
+ align:start position:0%
+once I have a two component version of
+then it's very easy to see what the spin
+
+ align:start position:0%
+then it's very easy to see what the spin
+ 
+
+ align:start position:0%
+then it's very easy to see what the spin
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is so let's write down this two
+
+ align:start position:0%
+is so let's write down this two
+ 
+
+ align:start position:0%
+is so let's write down this two
+component version of our cleaner cork
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lran you can do the same thing of course
+
+ align:start position:0%
+lran you can do the same thing of course
+ 
+
+ align:start position:0%
+lran you can do the same thing of course
+in hqt right down a two component
+
+ align:start position:0%
+in hqt right down a two component
+ 
+
+ align:start position:0%
+in hqt right down a two component
+version rather than a four component
+
+ align:start position:0%
+version rather than a four component
+ 
+
+ align:start position:0%
+version rather than a four component
+version if you have a four component
+
+ align:start position:0%
+version if you have a four component
+ 
+
+ align:start position:0%
+version if you have a four component
+version has this projection relation if
+
+ align:start position:0%
+version has this projection relation if
+ 
+
+ align:start position:0%
+version has this projection relation if
+you have the two component version the
+
+ align:start position:0%
+you have the two component version the
+ 
+
+ align:start position:0%
+you have the two component version the
+projection relation is built
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the reason to consider the four
+
+ align:start position:0%
+in the reason to consider the four
+ 
+
+ align:start position:0%
+in the reason to consider the four
+component version is if you want to
+
+ align:start position:0%
+component version is if you want to
+ 
+
+ align:start position:0%
+component version is if you want to
+couple four component this object to
+
+ align:start position:0%
+couple four component this object to
+ 
+
+ align:start position:0%
+couple four component this object to
+four component Fields like the ultrasoft
+
+ align:start position:0%
+four component Fields like the ultrasoft
+ 
+
+ align:start position:0%
+four component Fields like the ultrasoft
+field then it's of course a nice thing
+
+ align:start position:0%
+field then it's of course a nice thing
+ 
+
+ align:start position:0%
+field then it's of course a nice thing
+to have a four component
+
+ align:start position:0%
+to have a four component
+ 
+
+ align:start position:0%
+to have a four component
+version but some things are easier in
+
+ align:start position:0%
+version but some things are easier in
+ 
+
+ align:start position:0%
+version but some things are easier in
+two components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so take
+
+ align:start position:0%
+so take
+ 
+
+ align:start position:0%
+so take
+CN and write
+
+ align:start position:0%
+CN and write
+ 
+
+ align:start position:0%
+CN and write
+it as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follows with this F in is two components
+
+ align:start position:0%
+follows with this F in is two components
+ 
+
+ align:start position:0%
+follows with this F in is two components
+and I've set things up so the dimensions
+
+ align:start position:0%
+and I've set things up so the dimensions
+ 
+
+ align:start position:0%
+and I've set things up so the dimensions
+of CN are equal to the dimensions of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f okay so I can take that formula plug
+
+ align:start position:0%
+f okay so I can take that formula plug
+ 
+
+ align:start position:0%
+f okay so I can take that formula plug
+it into our lran
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I can using the direct
+
+ align:start position:0%
+and then I can using the direct
+ 
+
+ align:start position:0%
+and then I can using the direct
+representation for the gamma
+
+ align:start position:0%
+representation for the gamma
+ 
+
+ align:start position:0%
+representation for the gamma
+matrices write out a lran for
+
+ align:start position:0%
+matrices write out a lran for
+ 
+
+ align:start position:0%
+matrices write out a lran for
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F so that requires doing a bit of
+
+ align:start position:0%
+F so that requires doing a bit of
+ 
+
+ align:start position:0%
+F so that requires doing a bit of
+algebra which I
+
+ align:start position:0%
+algebra which I
+ 
+
+ align:start position:0%
+algebra which I
+will take you through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we get an equivalent LR in but
+
+ align:start position:0%
+and then we get an equivalent LR in but
+ 
+
+ align:start position:0%
+and then we get an equivalent LR in but
+in terms of this field and it looks as
+
+ align:start position:0%
+in terms of this field and it looks as
+ 
+
+ align:start position:0%
+in terms of this field and it looks as
+follows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it's almost independent of spin
+
+ align:start position:0%
+okay so it's almost independent of spin
+ 
+
+ align:start position:0%
+okay so it's almost independent of spin
+but not quite there's this Sigma 3
+
+ align:start position:0%
+but not quite there's this Sigma 3
+ 
+
+ align:start position:0%
+but not quite there's this Sigma 3
+sitting there if Sigma 3 wasn't there
+
+ align:start position:0%
+sitting there if Sigma 3 wasn't there
+ 
+
+ align:start position:0%
+sitting there if Sigma 3 wasn't there
+like hqt where you'd have an su2
+
+ align:start position:0%
+like hqt where you'd have an su2
+ 
+
+ align:start position:0%
+like hqt where you'd have an su2
+symmetry the fact that Sigma 3 is there
+
+ align:start position:0%
+symmetry the fact that Sigma 3 is there
+ 
+
+ align:start position:0%
+symmetry the fact that Sigma 3 is there
+means you don't have an su3 su2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Symmetry and really all you have is a U1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Symmetry and that U1 corresponds just to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+helicity so in four component
+
+ align:start position:0%
+helicity so in four component
+ 
+
+ align:start position:0%
+helicity so in four component
+notation that U1 would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following projecting the spin operator
+
+ align:start position:0%
+following projecting the spin operator
+ 
+
+ align:start position:0%
+following projecting the spin operator
+onto perpendicular indices anti-
+
+ align:start position:0%
+onto perpendicular indices anti-
+ 
+
+ align:start position:0%
+onto perpendicular indices anti-
+symmetric in both of them and in the two
+
+ align:start position:0%
+symmetric in both of them and in the two
+ 
+
+ align:start position:0%
+symmetric in both of them and in the two
+component that just becomes a
+
+ align:start position:0%
+component that just becomes a
+ 
+
+ align:start position:0%
+component that just becomes a
+sigma3 so obviously if we do an
+
+ align:start position:0%
+sigma3 so obviously if we do an
+ 
+
+ align:start position:0%
+sigma3 so obviously if we do an
+exponential rotation with respect to
+
+ align:start position:0%
+exponential rotation with respect to
+ 
+
+ align:start position:0%
+exponential rotation with respect to
+Sigma 3 Sigma 3 commutes with Sigma 3 so
+
+ align:start position:0%
+Sigma 3 Sigma 3 commutes with Sigma 3 so
+ 
+
+ align:start position:0%
+Sigma 3 Sigma 3 commutes with Sigma 3 so
+does the identity and so we could have a
+
+ align:start position:0%
+does the identity and so we could have a
+ 
+
+ align:start position:0%
+does the identity and so we could have a
+rotation of this guy by
+
+ align:start position:0%
+rotation of this guy by
+ 
+
+ align:start position:0%
+rotation of this guy by
+that and that's the only that's the only
+
+ align:start position:0%
+that and that's the only that's the only
+ 
+
+ align:start position:0%
+that and that's the only that's the only
+spin symmetry that you have is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solcity and and so because of the
+
+ align:start position:0%
+solcity and and so because of the
+ 
+
+ align:start position:0%
+solcity and and so because of the
+coordinates we're using this corresponds
+
+ align:start position:0%
+coordinates we're using this corresponds
+ 
+
+ align:start position:0%
+coordinates we're using this corresponds
+to the spin along the direction of
+
+ align:start position:0%
+to the spin along the direction of
+ 
+
+ align:start position:0%
+to the spin along the direction of
+motion which is the three direction if
+
+ align:start position:0%
+motion which is the three direction if
+ 
+
+ align:start position:0%
+motion which is the three direction if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+like which sometimes we denote by just
+
+ align:start position:0%
+like which sometimes we denote by just
+ 
+
+ align:start position:0%
+like which sometimes we denote by just
+saying it's along the direction n which
+
+ align:start position:0%
+saying it's along the direction n which
+ 
+
+ align:start position:0%
+saying it's along the direction n which
+is then more more independent of how we
+
+ align:start position:0%
+is then more more independent of how we
+ 
+
+ align:start position:0%
+is then more more independent of how we
+pick our
+
+ align:start position:0%
+pick our
+ 
+
+ align:start position:0%
+pick our
+axes so this is this symmetry here is
+
+ align:start position:0%
+axes so this is this symmetry here is
+ 
+
+ align:start position:0%
+axes so this is this symmetry here is
+actually related to what you would call
+
+ align:start position:0%
+actually related to what you would call
+ 
+
+ align:start position:0%
+actually related to what you would call
+the chirality in qcd so it's not
+
+ align:start position:0%
+the chirality in qcd so it's not
+ 
+
+ align:start position:0%
+the chirality in qcd so it's not
+really it's not really a new symmetry
+
+ align:start position:0%
+really it's not really a new symmetry
+ 
+
+ align:start position:0%
+really it's not really a new symmetry
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is just related to the chyo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation so if you look at Gamma 5 *
+
+ align:start position:0%
+rotation so if you look at Gamma 5 *
+ 
+
+ align:start position:0%
+rotation so if you look at Gamma 5 *
+C and Gamma 5 in our representation
+
+ align:start position:0%
+C and Gamma 5 in our representation
+ 
+
+ align:start position:0%
+C and Gamma 5 in our representation
+would be 0 1 1
+
+ align:start position:0%
+would be 0 1 1
+ 
+
+ align:start position:0%
+would be 0 1 1
+0 and then if I write it
+
+ align:start position:0%
+0 and then if I write it
+ 
+
+ align:start position:0%
+0 and then if I write it
+out terms of this two component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing then that is just giving me 1/ <
+
+ align:start position:0%
+thing then that is just giving me 1/ <
+ 
+
+ align:start position:0%
+thing then that is just giving me 1/ <
+tk2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's swapping up and
+
+ align:start position:0%
+and it's swapping up and
+ 
+
+ align:start position:0%
+and it's swapping up and
+down and so that just means that FN has
+
+ align:start position:0%
+down and so that just means that FN has
+ 
+
+ align:start position:0%
+down and so that just means that FN has
+gone to Sigma 3
+
+ align:start position:0%
+gone to Sigma 3
+ 
+
+ align:start position:0%
+gone to Sigma 3
+FN so multiplying by gamma 5 is actually
+
+ align:start position:0%
+FN so multiplying by gamma 5 is actually
+ 
+
+ align:start position:0%
+FN so multiplying by gamma 5 is actually
+the same as multiplying by Sigma 3 the
+
+ align:start position:0%
+the same as multiplying by Sigma 3 the
+ 
+
+ align:start position:0%
+the same as multiplying by Sigma 3 the
+two component notation okay so this SYM
+
+ align:start position:0%
+two component notation okay so this SYM
+ 
+
+ align:start position:0%
+two component notation okay so this SYM
+this is not really new Symmetry and
+
+ align:start position:0%
+this is not really new Symmetry and
+ 
+
+ align:start position:0%
+this is not really new Symmetry and
+actually all the usual things that you
+
+ align:start position:0%
+actually all the usual things that you
+ 
+
+ align:start position:0%
+actually all the usual things that you
+would say about kyl rotations in qcd
+
+ align:start position:0%
+would say about kyl rotations in qcd
+ 
+
+ align:start position:0%
+would say about kyl rotations in qcd
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+apply here too so kyl rotations of
+
+ align:start position:0%
+apply here too so kyl rotations of
+ 
+
+ align:start position:0%
+apply here too so kyl rotations of
+course are not exact col rotations are
+
+ align:start position:0%
+course are not exact col rotations are
+ 
+
+ align:start position:0%
+course are not exact col rotations are
+broken by masses col rotations are
+
+ align:start position:0%
+broken by masses col rotations are
+ 
+
+ align:start position:0%
+broken by masses col rotations are
+broken by non-perturbative
+
+ align:start position:0%
+broken by non-perturbative
+ 
+
+ align:start position:0%
+broken by non-perturbative
+effects there you can worry about
+
+ align:start position:0%
+effects there you can worry about
+ 
+
+ align:start position:0%
+effects there you can worry about
+anomalies they are useful in peration
+
+ align:start position:0%
+anomalies they are useful in peration
+ 
+
+ align:start position:0%
+anomalies they are useful in peration
+theory for quantifying operators and
+
+ align:start position:0%
+theory for quantifying operators and
+ 
+
+ align:start position:0%
+theory for quantifying operators and
+that remains true here but if the cinar
+
+ align:start position:0%
+that remains true here but if the cinar
+ 
+
+ align:start position:0%
+that remains true here but if the cinar
+fields were non-perturbative then you
+
+ align:start position:0%
+fields were non-perturbative then you
+ 
+
+ align:start position:0%
+fields were non-perturbative then you
+should worry about those other things as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay so spin symmetry there's not
+
+ align:start position:0%
+well okay so spin symmetry there's not
+ 
+
+ align:start position:0%
+well okay so spin symmetry there's not
+really any new anything new there to
+
+ align:start position:0%
+really any new anything new there to
+ 
+
+ align:start position:0%
+really any new anything new there to
+talk
+
+ align:start position:0%
+talk
+ 
+
+ align:start position:0%
+talk
+about but along the way we saw we could
+
+ align:start position:0%
+about but along the way we saw we could
+ 
+
+ align:start position:0%
+about but along the way we saw we could
+write in two component form which is
+
+ align:start position:0%
+write in two component form which is
+ 
+
+ align:start position:0%
+write in two component form which is
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+nice so let's talk about something
+
+ align:start position:0%
+nice so let's talk about something
+ 
+
+ align:start position:0%
+nice so let's talk about something
+that's more important which is gauge
+
+ align:start position:0%
+that's more important which is gauge
+ 
+
+ align:start position:0%
+that's more important which is gauge
+symmetry is there any questions about
+
+ align:start position:0%
+symmetry is there any questions about
+ 
+
+ align:start position:0%
+symmetry is there any questions about
+the spins before we talk about gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry so is they actually turned off
+
+ align:start position:0%
+symmetry so is they actually turned off
+ 
+
+ align:start position:0%
+symmetry so is they actually turned off
+integrating out the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is why you had the minus SL
+
+ align:start position:0%
+that is why you had the minus SL
+ 
+
+ align:start position:0%
+that is why you had the minus SL
+projectors and why you don't have the
+
+ align:start position:0%
+projectors and why you don't have the
+ 
+
+ align:start position:0%
+projectors and why you don't have the
+full
+
+ align:start position:0%
+full
+ 
+
+ align:start position:0%
+full
+su2 like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I looked at it once but it's hard for
+
+ align:start position:0%
+um I looked at it once but it's hard for
+ 
+
+ align:start position:0%
+um I looked at it once but it's hard for
+me to remember the answer I think not
+
+ align:start position:0%
+me to remember the answer I think not
+ 
+
+ align:start position:0%
+me to remember the answer I think not
+but I think if you do the other version
+
+ align:start position:0%
+but I think if you do the other version
+ 
+
+ align:start position:0%
+but I think if you do the other version
+then you just get something more
+
+ align:start position:0%
+then you just get something more
+ 
+
+ align:start position:0%
+then you just get something more
+complicated here but still breaks su2
+
+ align:start position:0%
+complicated here but still breaks su2
+ 
+
+ align:start position:0%
+complicated here but still breaks su2
+like it okay
+
+ align:start position:0%
+like it okay
+ 
+
+ align:start position:0%
+like it okay
+yeah I'm just looking
+
+ align:start position:0%
+yeah I'm just looking
+ 
+
+ align:start position:0%
+yeah I'm just looking
+yeah so they're two two disconnected
+
+ align:start position:0%
+yeah so they're two two disconnected
+ 
+
+ align:start position:0%
+yeah so they're two two disconnected
+fact that other the thing that you know
+
+ align:start position:0%
+fact that other the thing that you know
+ 
+
+ align:start position:0%
+fact that other the thing that you know
+that I wanted to motivate that I could
+
+ align:start position:0%
+that I wanted to motivate that I could
+ 
+
+ align:start position:0%
+that I wanted to motivate that I could
+use this formula and I wanted to be
+
+ align:start position:0%
+use this formula and I wanted to be
+ 
+
+ align:start position:0%
+use this formula and I wanted to be
+honest with you about where that came
+
+ align:start position:0%
+honest with you about where that came
+ 
+
+ align:start position:0%
+honest with you about where that came
+from and that's why I told you this
+
+ align:start position:0%
+from and that's why I told you this
+ 
+
+ align:start position:0%
+from and that's why I told you this
+other fact but once but I could have
+
+ align:start position:0%
+other fact but once but I could have
+ 
+
+ align:start position:0%
+other fact but once but I could have
+jumped right here and said remember and
+
+ align:start position:0%
+jumped right here and said remember and
+ 
+
+ align:start position:0%
+jumped right here and said remember and
+glossed over it and that would have been
+
+ align:start position:0%
+glossed over it and that would have been
+ 
+
+ align:start position:0%
+glossed over it and that would have been
+fine for this discussion so they're in
+
+ align:start position:0%
+fine for this discussion so they're in
+ 
+
+ align:start position:0%
+fine for this discussion so they're in
+some sense two disconnected things at
+
+ align:start position:0%
+some sense two disconnected things at
+ 
+
+ align:start position:0%
+some sense two disconnected things at
+least in my mind
+
+ align:start position:0%
+least in my mind
+ 
+
+ align:start position:0%
+least in my mind
+do you have some intuition for what
+
+ align:start position:0%
+do you have some intuition for what
+ 
+
+ align:start position:0%
+do you have some intuition for what
+Theta n bar
+
+ align:start position:0%
+Theta n bar
+ 
+
+ align:start position:0%
+Theta n bar
+is for Theta n Bar the
+
+ align:start position:0%
+is for Theta n Bar the
+ 
+
+ align:start position:0%
+is for Theta n Bar the
+thing oh the yeah I mean it's it's
+
+ align:start position:0%
+thing oh the yeah I mean it's it's
+ 
+
+ align:start position:0%
+thing oh the yeah I mean it's it's
+really just saying the my intuition for
+
+ align:start position:0%
+really just saying the my intuition for
+ 
+
+ align:start position:0%
+really just saying the my intuition for
+it is really just that when you're
+
+ align:start position:0%
+it is really just that when you're
+ 
+
+ align:start position:0%
+it is really just that when you're
+producing energetic particles you you
+
+ align:start position:0%
+producing energetic particles you you
+ 
+
+ align:start position:0%
+producing energetic particles you you
+know it's what we did at the beginning
+
+ align:start position:0%
+know it's what we did at the beginning
+ 
+
+ align:start position:0%
+know it's what we did at the beginning
+when you're intro when you're when
+
+ align:start position:0%
+when you're intro when you're when
+ 
+
+ align:start position:0%
+when you're intro when you're when
+you're producing energetic particles
+
+ align:start position:0%
+you're producing energetic particles
+ 
+
+ align:start position:0%
+you're producing energetic particles
+these are the spin components that you
+
+ align:start position:0%
+these are the spin components that you
+ 
+
+ align:start position:0%
+these are the spin components that you
+have at lowest order and that leads to
+
+ align:start position:0%
+have at lowest order and that leads to
+ 
+
+ align:start position:0%
+have at lowest order and that leads to
+if you like that the fact that you have
+
+ align:start position:0%
+if you like that the fact that you have
+ 
+
+ align:start position:0%
+if you like that the fact that you have
+this form and you have this projection
+
+ align:start position:0%
+this form and you have this projection
+ 
+
+ align:start position:0%
+this form and you have this projection
+relation is is kind of non-trivial even
+
+ align:start position:0%
+relation is is kind of non-trivial even
+ 
+
+ align:start position:0%
+relation is is kind of non-trivial even
+though you don't have a spin symmetry I
+
+ align:start position:0%
+though you don't have a spin symmetry I
+ 
+
+ align:start position:0%
+though you don't have a spin symmetry I
+mean there is something to it it's not
+
+ align:start position:0%
+mean there is something to it it's not
+ 
+
+ align:start position:0%
+mean there is something to it it's not
+it's not like a su2 symmetry that of the
+
+ align:start position:0%
+it's not like a su2 symmetry that of the
+ 
+
+ align:start position:0%
+it's not like a su2 symmetry that of the
+spin but it does for example when you go
+
+ align:start position:0%
+spin but it does for example when you go
+ 
+
+ align:start position:0%
+spin but it does for example when you go
+and look at form factors it does lead to
+
+ align:start position:0%
+and look at form factors it does lead to
+ 
+
+ align:start position:0%
+and look at form factors it does lead to
+non-trivial relations for those form
+
+ align:start position:0%
+non-trivial relations for those form
+ 
+
+ align:start position:0%
+non-trivial relations for those form
+factors so that I don't call it a
+
+ align:start position:0%
+factors so that I don't call it a
+ 
+
+ align:start position:0%
+factors so that I don't call it a
+symmetry I don't think of it as a
+
+ align:start position:0%
+symmetry I don't think of it as a
+ 
+
+ align:start position:0%
+symmetry I don't think of it as a
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+but because it's not a formal group
+
+ align:start position:0%
+but because it's not a formal group
+ 
+
+ align:start position:0%
+but because it's not a formal group
+theory state of larian but I think it's
+
+ align:start position:0%
+theory state of larian but I think it's
+ 
+
+ align:start position:0%
+theory state of larian but I think it's
+basically you know well okay let me not
+
+ align:start position:0%
+basically you know well okay let me not
+ 
+
+ align:start position:0%
+basically you know well okay let me not
+speculate any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+further caus some confusion in the
+
+ align:start position:0%
+further caus some confusion in the
+ 
+
+ align:start position:0%
+further caus some confusion in the
+literature actually as
+
+ align:start position:0%
+literature actually as
+ 
+
+ align:start position:0%
+literature actually as
+well all
+
+ align:start position:0%
+well all
+ 
+
+ align:start position:0%
+well all
+right so what about gauge
+
+ align:start position:0%
+right so what about gauge
+ 
+
+ align:start position:0%
+right so what about gauge
+symmetry so we're doing a nonan gauge
+
+ align:start position:0%
+symmetry so we're doing a nonan gauge
+ 
+
+ align:start position:0%
+symmetry so we're doing a nonan gauge
+Theory the gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transformation is something like this
+
+ align:start position:0%
+transformation is something like this
+ 
+
+ align:start position:0%
+transformation is something like this
+and in order to talk about gauge
+
+ align:start position:0%
+and in order to talk about gauge
+ 
+
+ align:start position:0%
+and in order to talk about gauge
+symmetry what we need to do is we need
+
+ align:start position:0%
+symmetry what we need to do is we need
+ 
+
+ align:start position:0%
+symmetry what we need to do is we need
+to talk about the gauge symmetries that
+
+ align:start position:0%
+to talk about the gauge symmetries that
+ 
+
+ align:start position:0%
+to talk about the gauge symmetries that
+are related to the two type of gluons
+
+ align:start position:0%
+are related to the two type of gluons
+ 
+
+ align:start position:0%
+are related to the two type of gluons
+that we have we have a cinear gluon we
+
+ align:start position:0%
+that we have we have a cinear gluon we
+ 
+
+ align:start position:0%
+that we have we have a cinear gluon we
+have an ultrasoft gluon you know that
+
+ align:start position:0%
+have an ultrasoft gluon you know that
+ 
+
+ align:start position:0%
+have an ultrasoft gluon you know that
+the field is acting like the connection
+
+ align:start position:0%
+the field is acting like the connection
+ 
+
+ align:start position:0%
+the field is acting like the connection
+for that gauge symmetry so there should
+
+ align:start position:0%
+for that gauge symmetry so there should
+ 
+
+ align:start position:0%
+for that gauge symmetry so there should
+be in some sense a gauge symmetry
+
+ align:start position:0%
+be in some sense a gauge symmetry
+ 
+
+ align:start position:0%
+be in some sense a gauge symmetry
+Associated to the ultrasoft gluon and a
+
+ align:start position:0%
+Associated to the ultrasoft gluon and a
+ 
+
+ align:start position:0%
+Associated to the ultrasoft gluon and a
+separate one Associated to the cinar
+
+ align:start position:0%
+separate one Associated to the cinar
+ 
+
+ align:start position:0%
+separate one Associated to the cinar
+gluon if the meaning of these things as
+
+ align:start position:0%
+gluon if the meaning of these things as
+ 
+
+ align:start position:0%
+gluon if the meaning of these things as
+gauge Fields is going to have any sense
+
+ align:start position:0%
+gauge Fields is going to have any sense
+ 
+
+ align:start position:0%
+gauge Fields is going to have any sense
+to it so rather than have just sort of
+
+ align:start position:0%
+to it so rather than have just sort of
+ 
+
+ align:start position:0%
+to it so rather than have just sort of
+this set of gauge transformation that we
+
+ align:start position:0%
+this set of gauge transformation that we
+ 
+
+ align:start position:0%
+this set of gauge transformation that we
+can make in qcd we should have some more
+
+ align:start position:0%
+can make in qcd we should have some more
+ 
+
+ align:start position:0%
+can make in qcd we should have some more
+complicated structure of gauge symmetry
+
+ align:start position:0%
+complicated structure of gauge symmetry
+ 
+
+ align:start position:0%
+complicated structure of gauge symmetry
+in the effective Theory because we have
+
+ align:start position:0%
+in the effective Theory because we have
+ 
+
+ align:start position:0%
+in the effective Theory because we have
+more complicated structure of gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fields so in order to talk about use
+
+ align:start position:0%
+Fields so in order to talk about use
+ 
+
+ align:start position:0%
+Fields so in order to talk about use
+we're going to want to divide them into
+
+ align:start position:0%
+we're going to want to divide them into
+ 
+
+ align:start position:0%
+we're going to want to divide them into
+camps and a useful thing to think about
+
+ align:start position:0%
+camps and a useful thing to think about
+ 
+
+ align:start position:0%
+camps and a useful thing to think about
+is that you want to have use that first
+
+ align:start position:0%
+is that you want to have use that first
+ 
+
+ align:start position:0%
+is that you want to have use that first
+of all leave you inside the effective
+
+ align:start position:0%
+of all leave you inside the effective
+ 
+
+ align:start position:0%
+of all leave you inside the effective
+Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and really what this means is that you
+
+ align:start position:0%
+and really what this means is that you
+ 
+
+ align:start position:0%
+and really what this means is that you
+want talking about gauge symmetry to
+
+ align:start position:0%
+want talking about gauge symmetry to
+ 
+
+ align:start position:0%
+want talking about gauge symmetry to
+commute with your discussion of talking
+
+ align:start position:0%
+commute with your discussion of talking
+ 
+
+ align:start position:0%
+commute with your discussion of talking
+about power
+
+ align:start position:0%
+about power
+ 
+
+ align:start position:0%
+about power
+counting so by way of example of
+
+ align:start position:0%
+counting so by way of example of
+ 
+
+ align:start position:0%
+counting so by way of example of
+this say you had a gauge transformation
+
+ align:start position:0%
+this say you had a gauge transformation
+ 
+
+ align:start position:0%
+this say you had a gauge transformation
+that it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large that had made a formula like that
+
+ align:start position:0%
+large that had made a formula like that
+ 
+
+ align:start position:0%
+large that had made a formula like that
+one that I partial on it was scaling
+
+ align:start position:0%
+one that I partial on it was scaling
+ 
+
+ align:start position:0%
+one that I partial on it was scaling
+like Q okay so this would be a very
+
+ align:start position:0%
+like Q okay so this would be a very
+ 
+
+ align:start position:0%
+like Q okay so this would be a very
+large momentum Associated to that space
+
+ align:start position:0%
+large momentum Associated to that space
+ 
+
+ align:start position:0%
+large momentum Associated to that space
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+dependence then if you talked about the
+
+ align:start position:0%
+dependence then if you talked about the
+ 
+
+ align:start position:0%
+dependence then if you talked about the
+gauge transformation which would
+
+ align:start position:0%
+gauge transformation which would
+ 
+
+ align:start position:0%
+gauge transformation which would
+be U * C even if this guy has colinear
+
+ align:start position:0%
+be U * C even if this guy has colinear
+ 
+
+ align:start position:0%
+be U * C even if this guy has colinear
+momentum scaling the new guy would not
+
+ align:start position:0%
+momentum scaling the new guy would not
+ 
+
+ align:start position:0%
+momentum scaling the new guy would not
+because of this fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if we want to talk about gauge
+
+ align:start position:0%
+okay so if we want to talk about gauge
+ 
+
+ align:start position:0%
+okay so if we want to talk about gauge
+symmetries we want to talk about
+
+ align:start position:0%
+symmetries we want to talk about
+ 
+
+ align:start position:0%
+symmetries we want to talk about
+symmetries that take us to the fields
+
+ align:start position:0%
+symmetries that take us to the fields
+ 
+
+ align:start position:0%
+symmetries that take us to the fields
+that we've already decided have a
+
+ align:start position:0%
+that we've already decided have a
+ 
+
+ align:start position:0%
+that we've already decided have a
+certain power counting and we don't want
+
+ align:start position:0%
+certain power counting and we don't want
+ 
+
+ align:start position:0%
+certain power counting and we don't want
+the gauge symmetry to mess that up so
+
+ align:start position:0%
+the gauge symmetry to mess that up so
+ 
+
+ align:start position:0%
+the gauge symmetry to mess that up so
+we're going to demand that that's
+
+ align:start position:0%
+we're going to demand that that's
+ 
+
+ align:start position:0%
+we're going to demand that that's
+true and then we can divide so given
+
+ align:start position:0%
+true and then we can divide so given
+ 
+
+ align:start position:0%
+true and then we can divide so given
+that we can think about dividing up the
+
+ align:start position:0%
+that we can think about dividing up the
+ 
+
+ align:start position:0%
+that we can think about dividing up the
+gauge symmetry into pieces into pieces
+
+ align:start position:0%
+gauge symmetry into pieces into pieces
+ 
+
+ align:start position:0%
+gauge symmetry into pieces into pieces
+that have different scaling in terms of
+
+ align:start position:0%
+that have different scaling in terms of
+ 
+
+ align:start position:0%
+that have different scaling in terms of
+how big the the transformation are how
+
+ align:start position:0%
+how big the the transformation are how
+ 
+
+ align:start position:0%
+how big the the transformation are how
+the how the coordinates are behaving
+
+ align:start position:0%
+the how the coordinates are behaving
+ 
+
+ align:start position:0%
+the how the coordinates are behaving
+and it's convenient to for this
+
+ align:start position:0%
+and it's convenient to for this
+ 
+
+ align:start position:0%
+and it's convenient to for this
+discussion divide them into three parts
+
+ align:start position:0%
+discussion divide them into three parts
+ 
+
+ align:start position:0%
+discussion divide them into three parts
+a global
+
+ align:start position:0%
+a global
+ 
+
+ align:start position:0%
+a global
+transformation where this guy is not
+
+ align:start position:0%
+transformation where this guy is not
+ 
+
+ align:start position:0%
+transformation where this guy is not
+space- time
+
+ align:start position:0%
+space- time
+ 
+
+ align:start position:0%
+space- time
+dependent a cinear
+
+ align:start position:0%
+dependent a cinear
+ 
+
+ align:start position:0%
+dependent a cinear
+transformation which I'll call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UC where I partial on
+
+ align:start position:0%
+UC where I partial on
+ 
+
+ align:start position:0%
+UC where I partial on
+U scales like a cinear momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ultrasoft U
+
+ align:start position:0%
+ultrasoft U
+ 
+
+ align:start position:0%
+ultrasoft U
+us where are the I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partial scales like an ultrasoft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum and basically what we want to
+
+ align:start position:0%
+momentum and basically what we want to
+ 
+
+ align:start position:0%
+momentum and basically what we want to
+do is we want to connect this gauge
+
+ align:start position:0%
+do is we want to connect this gauge
+ 
+
+ align:start position:0%
+do is we want to connect this gauge
+transformation to the gauge field for
+
+ align:start position:0%
+transformation to the gauge field for
+ 
+
+ align:start position:0%
+transformation to the gauge field for
+the cinear and this
+
+ align:start position:0%
+the cinear and this
+ 
+
+ align:start position:0%
+the cinear and this
+transformation to the gauge field for
+
+ align:start position:0%
+transformation to the gauge field for
+ 
+
+ align:start position:0%
+transformation to the gauge field for
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+softs
+
+ align:start position:0%
+softs
+ 
+
+ align:start position:0%
+softs
+okay so one complication that we have to
+
+ align:start position:0%
+okay so one complication that we have to
+ 
+
+ align:start position:0%
+okay so one complication that we have to
+deal with is this momentum labels that
+
+ align:start position:0%
+deal with is this momentum labels that
+ 
+
+ align:start position:0%
+deal with is this momentum labels that
+we were talking about because the way
+
+ align:start position:0%
+we were talking about because the way
+ 
+
+ align:start position:0%
+we were talking about because the way
+that we distinguish between these types
+
+ align:start position:0%
+that we distinguish between these types
+ 
+
+ align:start position:0%
+that we distinguish between these types
+of momenta and these types of momenta
+
+ align:start position:0%
+of momenta and these types of momenta
+ 
+
+ align:start position:0%
+of momenta and these types of momenta
+was dividing things into these labels
+
+ align:start position:0%
+was dividing things into these labels
+ 
+
+ align:start position:0%
+was dividing things into these labels
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+residuals gauge Transformations are
+
+ align:start position:0%
+residuals gauge Transformations are
+ 
+
+ align:start position:0%
+residuals gauge Transformations are
+something that's very nice in position
+
+ align:start position:0%
+something that's very nice in position
+ 
+
+ align:start position:0%
+something that's very nice in position
+space and not so nice in momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space and that's because gauge
+
+ align:start position:0%
+space and that's because gauge
+ 
+
+ align:start position:0%
+space and that's because gauge
+Transformations are local
+
+ align:start position:0%
+Transformations are local
+ 
+
+ align:start position:0%
+Transformations are local
+Transformations right and local it means
+
+ align:start position:0%
+Transformations right and local it means
+ 
+
+ align:start position:0%
+Transformations right and local it means
+local in X not in P so what is what what
+
+ align:start position:0%
+local in X not in P so what is what what
+ 
+
+ align:start position:0%
+local in X not in P so what is what what
+is simple multiplication in position
+
+ align:start position:0%
+is simple multiplication in position
+ 
+
+ align:start position:0%
+is simple multiplication in position
+space becomes convolutions in momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space so if you
+
+ align:start position:0%
+space so if you
+ 
+
+ align:start position:0%
+space so if you
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+go over to this kind of hybrid notation
+
+ align:start position:0%
+go over to this kind of hybrid notation
+ 
+
+ align:start position:0%
+go over to this kind of hybrid notation
+that we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+developed then you would have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following that this field if I do it
+
+ align:start position:0%
+following that this field if I do it
+ 
+
+ align:start position:0%
+following that this field if I do it
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goes into something like that where the
+
+ align:start position:0%
+goes into something like that where the
+ 
+
+ align:start position:0%
+goes into something like that where the
+way that you should think of what this
+
+ align:start position:0%
+way that you should think of what this
+ 
+
+ align:start position:0%
+way that you should think of what this
+sum over Q is is the is in the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way that if you have a transformation in
+
+ align:start position:0%
+way that if you have a transformation in
+ 
+
+ align:start position:0%
+way that if you have a transformation in
+position space that looks like
+
+ align:start position:0%
+position space that looks like
+ 
+
+ align:start position:0%
+position space that looks like
+that then in momentum
+
+ align:start position:0%
+that then in momentum
+ 
+
+ align:start position:0%
+that then in momentum
+space that simple product is convolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimension and you'd have that
+
+ align:start position:0%
+dimension and you'd have that
+ 
+
+ align:start position:0%
+dimension and you'd have that
+correspondence and so this kind of
+
+ align:start position:0%
+correspondence and so this kind of
+ 
+
+ align:start position:0%
+correspondence and so this kind of
+complication that we have here just
+
+ align:start position:0%
+complication that we have here just
+ 
+
+ align:start position:0%
+complication that we have here just
+corresponds to the complication that
+
+ align:start position:0%
+corresponds to the complication that
+ 
+
+ align:start position:0%
+corresponds to the complication that
+you'd have for any gauge symmetry that
+
+ align:start position:0%
+you'd have for any gauge symmetry that
+ 
+
+ align:start position:0%
+you'd have for any gauge symmetry that
+you want to write a momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space but we can be slick about this and
+
+ align:start position:0%
+space but we can be slick about this and
+ 
+
+ align:start position:0%
+space but we can be slick about this and
+introduce some notation and then
+
+ align:start position:0%
+introduce some notation and then
+ 
+
+ align:start position:0%
+introduce some notation and then
+dispense with it because it's really not
+
+ align:start position:0%
+dispense with it because it's really not
+ 
+
+ align:start position:0%
+dispense with it because it's really not
+a technical complication it's just an
+
+ align:start position:0%
+a technical complication it's just an
+ 
+
+ align:start position:0%
+a technical complication it's just an
+ational
+
+ align:start position:0%
+ational
+ 
+
+ align:start position:0%
+ational
+complication so let's do that in the
+
+ align:start position:0%
+complication so let's do that in the
+ 
+
+ align:start position:0%
+complication so let's do that in the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+way let's let UC
+
+ align:start position:0%
+way let's let UC
+ 
+
+ align:start position:0%
+way let's let UC
+see which is a
+
+ align:start position:0%
+see which is a
+ 
+
+ align:start position:0%
+see which is a
+matrix with two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indices be
+
+ align:start position:0%
+indices be
+ 
+
+ align:start position:0%
+indices be
+defined by this
+
+ align:start position:0%
+defined by this
+ 
+
+ align:start position:0%
+defined by this
+UC of PL minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ql so say Define a matrix
+
+ align:start position:0%
+ql so say Define a matrix
+ 
+
+ align:start position:0%
+ql so say Define a matrix
+then we can use a matrix notation for
+
+ align:start position:0%
+then we can use a matrix notation for
+ 
+
+ align:start position:0%
+then we can use a matrix notation for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+convolutions where we sum over repeated
+
+ align:start position:0%
+convolutions where we sum over repeated
+ 
+
+ align:start position:0%
+convolutions where we sum over repeated
+indices and that takes care of this
+
+ align:start position:0%
+indices and that takes care of this
+ 
+
+ align:start position:0%
+indices and that takes care of this
+notational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complication so the peak what what is
+
+ align:start position:0%
+complication so the peak what what is
+ 
+
+ align:start position:0%
+complication so the peak what what is
+meant by this is that the pl ql entry of
+
+ align:start position:0%
+meant by this is that the pl ql entry of
+ 
+
+ align:start position:0%
+meant by this is that the pl ql entry of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Matrix is a number and that number is
+
+ align:start position:0%
+Matrix is a number and that number is
+ 
+
+ align:start position:0%
+Matrix is a number and that number is
+given by this thing that we call
+
+ align:start position:0%
+given by this thing that we call
+ 
+
+ align:start position:0%
+given by this thing that we call
+UC PL minus ql
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then the formula up here could
+
+ align:start position:0%
+okay so then the formula up here could
+ 
+
+ align:start position:0%
+okay so then the formula up here could
+just be written turns that Matrix as a
+
+ align:start position:0%
+just be written turns that Matrix as a
+ 
+
+ align:start position:0%
+just be written turns that Matrix as a
+kind of matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplication okay so what are the
+
+ align:start position:0%
+multiplication okay so what are the
+ 
+
+ align:start position:0%
+multiplication okay so what are the
+Transformations if once we adopt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that let me write them down and then
+
+ align:start position:0%
+that let me write them down and then
+ 
+
+ align:start position:0%
+that let me write them down and then
+talk about them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so CN of X goes to U of X CN of X where
+
+ align:start position:0%
+so CN of X goes to U of X CN of X where
+ 
+
+ align:start position:0%
+so CN of X goes to U of X CN of X where
+you should understand this thing as a
+
+ align:start position:0%
+you should understand this thing as a
+ 
+
+ align:start position:0%
+you should understand this thing as a
+matrix that has two indices like
+
+ align:start position:0%
+matrix that has two indices like
+ 
+
+ align:start position:0%
+matrix that has two indices like
+this also depending on space
+
+ align:start position:0%
+this also depending on space
+ 
+
+ align:start position:0%
+this also depending on space
+time and I just dot over the repeated
+
+ align:start position:0%
+time and I just dot over the repeated
+ 
+
+ align:start position:0%
+time and I just dot over the repeated
+indices in this thing which is like a
+
+ align:start position:0%
+indices in this thing which is like a
+ 
+
+ align:start position:0%
+indices in this thing which is like a
+vector so this is like a
+
+ align:start position:0%
+vector so this is like a
+ 
+
+ align:start position:0%
+vector so this is like a
+matrix and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector that makes it look like it's the
+
+ align:start position:0%
+Vector that makes it look like it's the
+ 
+
+ align:start position:0%
+Vector that makes it look like it's the
+usual kind of notation which was the
+
+ align:start position:0%
+usual kind of notation which was the
+ 
+
+ align:start position:0%
+usual kind of notation which was the
+point introducing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation so for the colinear gaug guge
+
+ align:start position:0%
+notation so for the colinear gaug guge
+ 
+
+ align:start position:0%
+notation so for the colinear gaug guge
+field it's going to be basically that it
+
+ align:start position:0%
+field it's going to be basically that it
+ 
+
+ align:start position:0%
+field it's going to be basically that it
+as as we said over here that it's
+
+ align:start position:0%
+as as we said over here that it's
+ 
+
+ align:start position:0%
+as as we said over here that it's
+becomes the gauge field of that
+
+ align:start position:0%
+becomes the gauge field of that
+ 
+
+ align:start position:0%
+becomes the gauge field of that
+transformation and so that's what this
+
+ align:start position:0%
+transformation and so that's what this
+ 
+
+ align:start position:0%
+transformation and so that's what this
+would be that would be the standard
+
+ align:start position:0%
+would be that would be the standard
+ 
+
+ align:start position:0%
+would be that would be the standard
+gauge transformation and then there's
+
+ align:start position:0%
+gauge transformation and then there's
+ 
+
+ align:start position:0%
+gauge transformation and then there's
+one little complication here which is I
+
+ align:start position:0%
+one little complication here which is I
+ 
+
+ align:start position:0%
+one little complication here which is I
+wrote curly de ultrasoft the ultrasoft
+
+ align:start position:0%
+wrote curly de ultrasoft the ultrasoft
+ 
+
+ align:start position:0%
+wrote curly de ultrasoft the ultrasoft
+derivative the thing that has the N.A
+
+ align:start position:0%
+derivative the thing that has the N.A
+ 
+
+ align:start position:0%
+derivative the thing that has the N.A
+ultrasoft field in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so the reason that I wanted to do
+
+ align:start position:0%
+it so the reason that I wanted to do
+ 
+
+ align:start position:0%
+it so the reason that I wanted to do
+that is because I'm thinking here of the
+
+ align:start position:0%
+that is because I'm thinking here of the
+ 
+
+ align:start position:0%
+that is because I'm thinking here of the
+ultrasoft field when I'm thinking about
+
+ align:start position:0%
+ultrasoft field when I'm thinking about
+ 
+
+ align:start position:0%
+ultrasoft field when I'm thinking about
+cinear Fields I'm thinking of the
+
+ align:start position:0%
+cinear Fields I'm thinking of the
+ 
+
+ align:start position:0%
+cinear Fields I'm thinking of the
+ultrasoft field as a background field
+
+ align:start position:0%
+ultrasoft field as a background field
+ 
+
+ align:start position:0%
+ultrasoft field as a background field
+and if I was to do a background field
+
+ align:start position:0%
+and if I was to do a background field
+ 
+
+ align:start position:0%
+and if I was to do a background field
+gauge transformation then I would have a
+
+ align:start position:0%
+gauge transformation then I would have a
+ 
+
+ align:start position:0%
+gauge transformation then I would have a
+coant derivative here under the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+background so this n. a ultrasoft is
+
+ align:start position:0%
+background so this n. a ultrasoft is
+ 
+
+ align:start position:0%
+background so this n. a ultrasoft is
+like a background field to the cinear
+
+ align:start position:0%
+like a background field to the cinear
+ 
+
+ align:start position:0%
+like a background field to the cinear
+gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this if you want to make an analogy of
+
+ align:start position:0%
+this if you want to make an analogy of
+ 
+
+ align:start position:0%
+this if you want to make an analogy of
+what this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like it's like the quantum gauge
+
+ align:start position:0%
+like it's like the quantum gauge
+ 
+
+ align:start position:0%
+like it's like the quantum gauge
+transformation of a field that has a
+
+ align:start position:0%
+transformation of a field that has a
+ 
+
+ align:start position:0%
+transformation of a field that has a
+background
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you look up how background field
+
+ align:start position:0%
+so if you look up how background field
+ 
+
+ align:start position:0%
+so if you look up how background field
+gauge works and background field
+
+ align:start position:0%
+gauge works and background field
+ 
+
+ align:start position:0%
+gauge works and background field
+Transformations that's how you'd have
+
+ align:start position:0%
+Transformations that's how you'd have
+ 
+
+ align:start position:0%
+Transformations that's how you'd have
+the same thing you'd have something
+
+ align:start position:0%
+the same thing you'd have something
+ 
+
+ align:start position:0%
+the same thing you'd have something
+covariant under the background and
+
+ align:start position:0%
+covariant under the background and
+ 
+
+ align:start position:0%
+covariant under the background and
+that's what we're going to do here as
+
+ align:start position:0%
+that's what we're going to do here as
+ 
+
+ align:start position:0%
+that's what we're going to do here as
+well yep kind of Sil question so UC of X
+
+ align:start position:0%
+well yep kind of Sil question so UC of X
+ 
+
+ align:start position:0%
+well yep kind of Sil question so UC of X
+is a matrix mhm so what exactly UC p
+
+ align:start position:0%
+is a matrix mhm so what exactly UC p
+ 
+
+ align:start position:0%
+is a matrix mhm so what exactly UC p
+that should be right well no this is
+
+ align:start position:0%
+that should be right well no this is
+ 
+
+ align:start position:0%
+that should be right well no this is
+just a number so these have some this is
+
+ align:start position:0%
+just a number so these have some this is
+ 
+
+ align:start position:0%
+just a number so these have some this is
+just think of this as like you know this
+
+ align:start position:0%
+just think of this as like you know this
+ 
+
+ align:start position:0%
+just think of this as like you know this
+is some Vector this is some other Vector
+
+ align:start position:0%
+is some Vector this is some other Vector
+ 
+
+ align:start position:0%
+is some Vector this is some other Vector
+the difference of these is some label on
+
+ align:start position:0%
+the difference of these is some label on
+ 
+
+ align:start position:0%
+the difference of these is some label on
+this thing right and for each value of
+
+ align:start position:0%
+this thing right and for each value of
+ 
+
+ align:start position:0%
+this thing right and for each value of
+this I get a different number and know
+
+ align:start position:0%
+this I get a different number and know
+ 
+
+ align:start position:0%
+this I get a different number and know
+for each value of space time I get a
+
+ align:start position:0%
+for each value of space time I get a
+ 
+
+ align:start position:0%
+for each value of space time I get a
+different number but this thing is just
+
+ align:start position:0%
+different number but this thing is just
+ 
+
+ align:start position:0%
+different number but this thing is just
+a number and I'm saying think of it like
+
+ align:start position:0%
+a number and I'm saying think of it like
+ 
+
+ align:start position:0%
+a number and I'm saying think of it like
+a matrix in the sense of because we're
+
+ align:start position:0%
+a matrix in the sense of because we're
+ 
+
+ align:start position:0%
+a matrix in the sense of because we're
+thinking of these as
+
+ align:start position:0%
+thinking of these as
+ 
+
+ align:start position:0%
+thinking of these as
+discret but right UC has
+
+ align:start position:0%
+discret but right UC has
+ 
+
+ align:start position:0%
+discret but right UC has
+oh yeah yeah yeah that's another matrix
+
+ align:start position:0%
+oh yeah yeah yeah that's another matrix
+ 
+
+ align:start position:0%
+oh yeah yeah yeah that's another matrix
+it's an orthogonal matrix it's also a
+
+ align:start position:0%
+it's an orthogonal matrix it's also a
+ 
+
+ align:start position:0%
+it's an orthogonal matrix it's also a
+matrix in that space yeah yeah yeah so
+
+ align:start position:0%
+matrix in that space yeah yeah yeah so
+ 
+
+ align:start position:0%
+matrix in that space yeah yeah yeah so
+here it's a matrix I'm defining a matrix
+
+ align:start position:0%
+here it's a matrix I'm defining a matrix
+ 
+
+ align:start position:0%
+here it's a matrix I'm defining a matrix
+in a new space which is this momentum
+
+ align:start position:0%
+in a new space which is this momentum
+ 
+
+ align:start position:0%
+in a new space which is this momentum
+space and that's just really my way of
+
+ align:start position:0%
+space and that's just really my way of
+ 
+
+ align:start position:0%
+space and that's just really my way of
+making transformations in momentum space
+
+ align:start position:0%
+making transformations in momentum space
+ 
+
+ align:start position:0%
+making transformations in momentum space
+look like as simple as simple as they do
+
+ align:start position:0%
+look like as simple as simple as they do
+ 
+
+ align:start position:0%
+look like as simple as simple as they do
+in position Space by just having sort of
+
+ align:start position:0%
+in position Space by just having sort of
+ 
+
+ align:start position:0%
+in position Space by just having sort of
+a matrix notation for the
+
+ align:start position:0%
+a matrix notation for the
+ 
+
+ align:start position:0%
+a matrix notation for the
+convolutions so that number is
+
+ align:start position:0%
+convolutions so that number is
+ 
+
+ align:start position:0%
+convolutions so that number is
+essentially a matrix it's a matrix yeah
+
+ align:start position:0%
+essentially a matrix it's a matrix yeah
+ 
+
+ align:start position:0%
+essentially a matrix it's a matrix yeah
+in that space good point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about the ultrasoft
+
+ align:start position:0%
+what about the ultrasoft
+ 
+
+ align:start position:0%
+what about the ultrasoft
+fields well ultrasoft Fields shouldn't
+
+ align:start position:0%
+fields well ultrasoft Fields shouldn't
+ 
+
+ align:start position:0%
+fields well ultrasoft Fields shouldn't
+transform under colinear gauge
+
+ align:start position:0%
+transform under colinear gauge
+ 
+
+ align:start position:0%
+transform under colinear gauge
+Transformations because of the exactly
+
+ align:start position:0%
+Transformations because of the exactly
+ 
+
+ align:start position:0%
+Transformations because of the exactly
+the same logic that I gave you a minute
+
+ align:start position:0%
+the same logic that I gave you a minute
+ 
+
+ align:start position:0%
+the same logic that I gave you a minute
+ago about why I shouldn't be able to
+
+ align:start position:0%
+ago about why I shouldn't be able to
+ 
+
+ align:start position:0%
+ago about why I shouldn't be able to
+inject a hard momentum like this one
+
+ align:start position:0%
+inject a hard momentum like this one
+ 
+
+ align:start position:0%
+inject a hard momentum like this one
+into into the effective theory if I want
+
+ align:start position:0%
+into into the effective theory if I want
+ 
+
+ align:start position:0%
+into into the effective theory if I want
+my ultrasoft fields to remain Ultra
+
+ align:start position:0%
+my ultrasoft fields to remain Ultra
+ 
+
+ align:start position:0%
+my ultrasoft fields to remain Ultra
+Soft then I can't let them transform
+
+ align:start position:0%
+Soft then I can't let them transform
+ 
+
+ align:start position:0%
+Soft then I can't let them transform
+because that would spoil their power
+
+ align:start position:0%
+because that would spoil their power
+ 
+
+ align:start position:0%
+because that would spoil their power
+Counting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Q
+
+ align:start position:0%
+so Q
+ 
+
+ align:start position:0%
+so Q
+ultrasoft under this UC
+
+ align:start position:0%
+ultrasoft under this UC
+ 
+
+ align:start position:0%
+ultrasoft under this UC
+transformation just goes to Q ultr
+
+ align:start position:0%
+transformation just goes to Q ultr
+ 
+
+ align:start position:0%
+transformation just goes to Q ultr
+soft and a
+
+ align:start position:0%
+soft and a
+ 
+
+ align:start position:0%
+soft and a
+ultrasoft has to go to a
+
+ align:start position:0%
+ultrasoft has to go to a
+ 
+
+ align:start position:0%
+ultrasoft has to go to a
+ultrasoft so these things should not be
+
+ align:start position:0%
+ultrasoft so these things should not be
+ 
+
+ align:start position:0%
+ultrasoft so these things should not be
+touched by that transformation why can I
+
+ align:start position:0%
+touched by that transformation why can I
+ 
+
+ align:start position:0%
+touched by that transformation why can I
+mean make the ultt ultt and through well
+
+ align:start position:0%
+mean make the ultt ultt and through well
+ 
+
+ align:start position:0%
+mean make the ultt ultt and through well
+we don't want that you could think of
+
+ align:start position:0%
+we don't want that you could think of
+ 
+
+ align:start position:0%
+we don't want that you could think of
+trying to De develop effective Theory
+
+ align:start position:0%
+trying to De develop effective Theory
+ 
+
+ align:start position:0%
+trying to De develop effective Theory
+where they would mix right but whenever
+
+ align:start position:0%
+where they would mix right but whenever
+ 
+
+ align:start position:0%
+where they would mix right but whenever
+you have a lran that mixes two Fields
+
+ align:start position:0%
+you have a lran that mixes two Fields
+ 
+
+ align:start position:0%
+you have a lran that mixes two Fields
+the first thing you try to do is to
+
+ align:start position:0%
+the first thing you try to do is to
+ 
+
+ align:start position:0%
+the first thing you try to do is to
+force them not to mix so it's better you
+
+ align:start position:0%
+force them not to mix so it's better you
+ 
+
+ align:start position:0%
+force them not to mix so it's better you
+know yeah say I set the theory up so
+
+ align:start position:0%
+know yeah say I set the theory up so
+ 
+
+ align:start position:0%
+know yeah say I set the theory up so
+that they mixed the first thing I would
+
+ align:start position:0%
+that they mixed the first thing I would
+ 
+
+ align:start position:0%
+that they mixed the first thing I would
+try to do that lran is make field
+
+ align:start position:0%
+try to do that lran is make field
+ 
+
+ align:start position:0%
+try to do that lran is make field
+redefinitions to go to some set form of
+
+ align:start position:0%
+redefinitions to go to some set form of
+ 
+
+ align:start position:0%
+redefinitions to go to some set form of
+the lran that wouldn't mix okay so I
+
+ align:start position:0%
+the lran that wouldn't mix okay so I
+ 
+
+ align:start position:0%
+the lran that wouldn't mix okay so I
+prefer if you like to to develop you
+
+ align:start position:0%
+prefer if you like to to develop you
+ 
+
+ align:start position:0%
+prefer if you like to to develop you
+know the one that doesn't mix right from
+
+ align:start position:0%
+know the one that doesn't mix right from
+ 
+
+ align:start position:0%
+know the one that doesn't mix right from
+the start and you could view it that
+
+ align:start position:0%
+the start and you could view it that
+ 
+
+ align:start position:0%
+the start and you could view it that
+way so you know you could always think
+
+ align:start position:0%
+way so you know you could always think
+ 
+
+ align:start position:0%
+way so you know you could always think
+of I'm going to tell you likes two sets
+
+ align:start position:0%
+of I'm going to tell you likes two sets
+ 
+
+ align:start position:0%
+of I'm going to tell you likes two sets
+of Transformations you could always
+
+ align:start position:0%
+of Transformations you could always
+ 
+
+ align:start position:0%
+of Transformations you could always
+think of formulating linear combinations
+
+ align:start position:0%
+think of formulating linear combinations
+ 
+
+ align:start position:0%
+think of formulating linear combinations
+of those Transformations say these are
+
+ align:start position:0%
+of those Transformations say these are
+ 
+
+ align:start position:0%
+of those Transformations say these are
+the fundamental ones not the ones you
+
+ align:start position:0%
+the fundamental ones not the ones you
+ 
+
+ align:start position:0%
+the fundamental ones not the ones you
+wrote down but these other ones right
+
+ align:start position:0%
+wrote down but these other ones right
+ 
+
+ align:start position:0%
+wrote down but these other ones right
+and then you know by some manipulations
+
+ align:start position:0%
+and then you know by some manipulations
+ 
+
+ align:start position:0%
+and then you know by some manipulations
+one could go to the ones I'm talking
+
+ align:start position:0%
+one could go to the ones I'm talking
+ 
+
+ align:start position:0%
+one could go to the ones I'm talking
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so now the other set of
+
+ align:start position:0%
+right so now the other set of
+ 
+
+ align:start position:0%
+right so now the other set of
+Transformations that we
+
+ align:start position:0%
+Transformations that we
+ 
+
+ align:start position:0%
+Transformations that we
+want are these ultrasoft ones and for
+
+ align:start position:0%
+want are these ultrasoft ones and for
+ 
+
+ align:start position:0%
+want are these ultrasoft ones and for
+those for that type of trans
+
+ align:start position:0%
+those for that type of trans
+ 
+
+ align:start position:0%
+those for that type of trans
+transformation we don't have this same
+
+ align:start position:0%
+transformation we don't have this same
+ 
+
+ align:start position:0%
+transformation we don't have this same
+type of problem with the cinear we don't
+
+ align:start position:0%
+type of problem with the cinear we don't
+ 
+
+ align:start position:0%
+type of problem with the cinear we don't
+we can't say the cinear fields don't
+
+ align:start position:0%
+we can't say the cinear fields don't
+ 
+
+ align:start position:0%
+we can't say the cinear fields don't
+transform because that type of
+
+ align:start position:0%
+transform because that type of
+ 
+
+ align:start position:0%
+transform because that type of
+transformation it doesn't spoil the
+
+ align:start position:0%
+transformation it doesn't spoil the
+ 
+
+ align:start position:0%
+transformation it doesn't spoil the
+cinear field being cinear we can always
+
+ align:start position:0%
+cinear field being cinear we can always
+ 
+
+ align:start position:0%
+cinear field being cinear we can always
+add ultrasoft momentum to
+
+ align:start position:0%
+add ultrasoft momentum to
+ 
+
+ align:start position:0%
+add ultrasoft momentum to
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+it so these fields CN and a an will
+
+ align:start position:0%
+it so these fields CN and a an will
+ 
+
+ align:start position:0%
+it so these fields CN and a an will
+transform like background
+
+ align:start position:0%
+transform like background
+ 
+
+ align:start position:0%
+transform like background
+Fields sorry like Quantum fields in a
+
+ align:start position:0%
+Fields sorry like Quantum fields in a
+ 
+
+ align:start position:0%
+Fields sorry like Quantum fields in a
+background
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from the point of view of the CN
+
+ align:start position:0%
+so from the point of view of the CN
+ 
+
+ align:start position:0%
+so from the point of view of the CN
+fields which are the shorter distance
+
+ align:start position:0%
+fields which are the shorter distance
+ 
+
+ align:start position:0%
+fields which are the shorter distance
+Fields you can really think of like what
+
+ align:start position:0%
+Fields you can really think of like what
+ 
+
+ align:start position:0%
+Fields you can really think of like what
+we're doing here is exactly like what
+
+ align:start position:0%
+we're doing here is exactly like what
+ 
+
+ align:start position:0%
+we're doing here is exactly like what
+you would do if you had Quantum and
+
+ align:start position:0%
+you would do if you had Quantum and
+ 
+
+ align:start position:0%
+you would do if you had Quantum and
+background gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Transformations and the physics of
+
+ align:start position:0%
+Transformations and the physics of
+ 
+
+ align:start position:0%
+Transformations and the physics of
+thinking of the background is a longer
+
+ align:start position:0%
+thinking of the background is a longer
+ 
+
+ align:start position:0%
+thinking of the background is a longer
+wavelength mode is exactly the right way
+
+ align:start position:0%
+wavelength mode is exactly the right way
+ 
+
+ align:start position:0%
+wavelength mode is exactly the right way
+of thinking about how these fields which
+
+ align:start position:0%
+of thinking about how these fields which
+ 
+
+ align:start position:0%
+of thinking about how these fields which
+are shorter w length think about the
+
+ align:start position:0%
+are shorter w length think about the
+ 
+
+ align:start position:0%
+are shorter w length think about the
+ultrasoft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fields so what that means is that they
+
+ align:start position:0%
+fields so what that means is that they
+ 
+
+ align:start position:0%
+fields so what that means is that they
+transform like matter fields in the
+
+ align:start position:0%
+transform like matter fields in the
+ 
+
+ align:start position:0%
+transform like matter fields in the
+appropriate
+
+ align:start position:0%
+appropriate
+ 
+
+ align:start position:0%
+appropriate
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+representation okay so with that in hand
+
+ align:start position:0%
+representation okay so with that in hand
+ 
+
+ align:start position:0%
+representation okay so with that in hand
+then we can write down how things
+
+ align:start position:0%
+then we can write down how things
+ 
+
+ align:start position:0%
+then we can write down how things
+transform under the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ultrasofts a fion just transforms like
+
+ align:start position:0%
+ultrasofts a fion just transforms like
+ 
+
+ align:start position:0%
+ultrasofts a fion just transforms like
+that on the left and this unlike our
+
+ align:start position:0%
+that on the left and this unlike our
+ 
+
+ align:start position:0%
+that on the left and this unlike our
+notation over there this is one number
+
+ align:start position:0%
+notation over there this is one number
+ 
+
+ align:start position:0%
+notation over there this is one number
+for all entries in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vector this guy doesn't have any indices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is like transforming all
+
+ align:start position:0%
+okay so this is like transforming all
+ 
+
+ align:start position:0%
+okay so this is like transforming all
+the terms in the vector by the same
+
+ align:start position:0%
+the terms in the vector by the same
+ 
+
+ align:start position:0%
+the terms in the vector by the same
+overall Matrix overall color Matrix
+
+ align:start position:0%
+overall Matrix overall color Matrix
+ 
+
+ align:start position:0%
+overall Matrix overall color Matrix
+overall number in in the in the momentum
+
+ align:start position:0%
+overall number in in the in the momentum
+ 
+
+ align:start position:0%
+overall number in in the in the momentum
+Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space so this guy should transform like
+
+ align:start position:0%
+space so this guy should transform like
+ 
+
+ align:start position:0%
+space so this guy should transform like
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+adjoint and you can write the adjoint as
+
+ align:start position:0%
+adjoint and you can write the adjoint as
+ 
+
+ align:start position:0%
+adjoint and you can write the adjoint as
+a u each
+
+ align:start position:0%
+a u each
+ 
+
+ align:start position:0%
+a u each
+side so there's kind of two ways of
+
+ align:start position:0%
+side so there's kind of two ways of
+ 
+
+ align:start position:0%
+side so there's kind of two ways of
+writing the transformation here you
+
+ align:start position:0%
+writing the transformation here you
+ 
+
+ align:start position:0%
+writing the transformation here you
+could write it
+
+ align:start position:0%
+could write it
+ 
+
+ align:start position:0%
+could write it
+as like
+
+ align:start position:0%
+as like
+ 
+
+ align:start position:0%
+as like
+this if you wrote down an adjoint
+
+ align:start position:0%
+this if you wrote down an adjoint
+ 
+
+ align:start position:0%
+this if you wrote down an adjoint
+transformation then this guy would have
+
+ align:start position:0%
+transformation then this guy would have
+ 
+
+ align:start position:0%
+transformation then this guy would have
+two indices A and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B and you'd have a transformation like
+
+ align:start position:0%
+B and you'd have a transformation like
+ 
+
+ align:start position:0%
+B and you'd have a transformation like
+that where this is an ad in the ad joint
+
+ align:start position:0%
+that where this is an ad in the ad joint
+ 
+
+ align:start position:0%
+that where this is an ad in the ad joint
+but if you want to write it in terms of
+
+ align:start position:0%
+but if you want to write it in terms of
+ 
+
+ align:start position:0%
+but if you want to write it in terms of
+the U ultrasoft that's e to the it which
+
+ align:start position:0%
+the U ultrasoft that's e to the it which
+ 
+
+ align:start position:0%
+the U ultrasoft that's e to the it which
+is in the fund fundamental then you
+
+ align:start position:0%
+is in the fund fundamental then you
+ 
+
+ align:start position:0%
+is in the fund fundamental then you
+write it like this
+
+ align:start position:0%
+write it like this
+ 
+
+ align:start position:0%
+write it like this
+and those are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equivalent so why are they
+
+ align:start position:0%
+equivalent so why are they
+ 
+
+ align:start position:0%
+equivalent so why are they
+equivalent so they're equivalent because
+
+ align:start position:0%
+equivalent so they're equivalent because
+ 
+
+ align:start position:0%
+equivalent so they're equivalent because
+well okay maybe I'll tell you
+
+ align:start position:0%
+well okay maybe I'll tell you
+ 
+
+ align:start position:0%
+well okay maybe I'll tell you
+later yeah um I
+
+ align:start position:0%
+later yeah um I
+ 
+
+ align:start position:0%
+later yeah um I
+um I'm always confused about why
+
+ align:start position:0%
+um I'm always confused about why
+ 
+
+ align:start position:0%
+um I'm always confused about why
+n. is a background field um to a
+
+ align:start position:0%
+n. is a background field um to a
+ 
+
+ align:start position:0%
+n. is a background field um to a
+ultrasoft um it actually has the same
+
+ align:start position:0%
+ultrasoft um it actually has the same
+ 
+
+ align:start position:0%
+ultrasoft um it actually has the same
+size momentum so wavelength is the same
+
+ align:start position:0%
+size momentum so wavelength is the same
+ 
+
+ align:start position:0%
+size momentum so wavelength is the same
+size the wavelength is not the same size
+
+ align:start position:0%
+size the wavelength is not the same size
+ 
+
+ align:start position:0%
+size the wavelength is not the same size
+the component is the same the component
+
+ align:start position:0%
+the component is the same the component
+ 
+
+ align:start position:0%
+the component is the same the component
+power counting is the same size but the
+
+ align:start position:0%
+power counting is the same size but the
+ 
+
+ align:start position:0%
+power counting is the same size but the
+n. field carries momentum which have p^
+
+ align:start position:0%
+n. field carries momentum which have p^
+ 
+
+ align:start position:0%
+n. field carries momentum which have p^
+squ which is much larger right P squ do
+
+ align:start position:0%
+squ which is much larger right P squ do
+ 
+
+ align:start position:0%
+squ which is much larger right P squ do
+the wavelength so I'm talking about the
+
+ align:start position:0%
+the wavelength so I'm talking about the
+ 
+
+ align:start position:0%
+the wavelength so I'm talking about the
+wavelength which is related to that P
+
+ align:start position:0%
+wavelength which is related to that P
+ 
+
+ align:start position:0%
+wavelength which is related to that P
+squ so you think about the n.n field
+
+ align:start position:0%
+squ so you think about the n.n field
+ 
+
+ align:start position:0%
+squ so you think about the n.n field
+carries a large P minus momentum still
+
+ align:start position:0%
+carries a large P minus momentum still
+ 
+
+ align:start position:0%
+carries a large P minus momentum still
+right even though it has a
+
+ align:start position:0%
+right even though it has a
+ 
+
+ align:start position:0%
+right even though it has a
+small it it carries in order one p minus
+
+ align:start position:0%
+small it it carries in order one p minus
+ 
+
+ align:start position:0%
+small it it carries in order one p minus
+momentum so just if it's confusing think
+
+ align:start position:0%
+momentum so just if it's confusing think
+ 
+
+ align:start position:0%
+momentum so just if it's confusing think
+about just the P minus momentum the n.
+
+ align:start position:0%
+about just the P minus momentum the n.
+ 
+
+ align:start position:0%
+about just the P minus momentum the n.
+field right has P minus which is a water
+
+ align:start position:0%
+field right has P minus which is a water
+ 
+
+ align:start position:0%
+field right has P minus which is a water
+Lambda the
+
+ align:start position:0%
+Lambda the
+ 
+
+ align:start position:0%
+Lambda the
+zero so just let's think about
+
+ align:start position:0%
+zero so just let's think about
+ 
+
+ align:start position:0%
+zero so just let's think about
+wavelength with respect to P minus
+
+ align:start position:0%
+wavelength with respect to P minus
+ 
+
+ align:start position:0%
+wavelength with respect to P minus
+that's definitely true right whereas the
+
+ align:start position:0%
+that's definitely true right whereas the
+ 
+
+ align:start position:0%
+that's definitely true right whereas the
+N.A ultrasoft
+
+ align:start position:0%
+N.A ultrasoft
+ 
+
+ align:start position:0%
+N.A ultrasoft
+field carries P minus which is water
+
+ align:start position:0%
+field carries P minus which is water
+ 
+
+ align:start position:0%
+field carries P minus which is water
+Lambda squar so just just thinking about
+
+ align:start position:0%
+Lambda squar so just just thinking about
+ 
+
+ align:start position:0%
+Lambda squar so just just thinking about
+those two say
+
+ align:start position:0%
+those two say
+ 
+
+ align:start position:0%
+those two say
+the moment component thei yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah all right I have room here to
+
+ align:start position:0%
+yeah all right I have room here to
+ 
+
+ align:start position:0%
+yeah all right I have room here to
+squeeze final transformation so the the
+
+ align:start position:0%
+squeeze final transformation so the the
+ 
+
+ align:start position:0%
+squeeze final transformation so the the
+final Transformations are just what
+
+ align:start position:0%
+final Transformations are just what
+ 
+
+ align:start position:0%
+final Transformations are just what
+you'd expect that the ultrasoft fields
+
+ align:start position:0%
+you'd expect that the ultrasoft fields
+ 
+
+ align:start position:0%
+you'd expect that the ultrasoft fields
+transform as ultrasoft as regular gauge
+
+ align:start position:0%
+transform as ultrasoft as regular gauge
+ 
+
+ align:start position:0%
+transform as ultrasoft as regular gauge
+Fields so let me just squeeze that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so there's the regular
+
+ align:start position:0%
+all right so there's the regular
+ 
+
+ align:start position:0%
+all right so there's the regular
+Transformations that you'd have for a
+
+ align:start position:0%
+Transformations that you'd have for a
+ 
+
+ align:start position:0%
+Transformations that you'd have for a
+gauge
+
+ align:start position:0%
+gauge
+ 
+
+ align:start position:0%
+gauge
+field yeah so
+
+ align:start position:0%
+field yeah so
+ 
+
+ align:start position:0%
+field yeah so
+um I just want to clarify these two uh
+
+ align:start position:0%
+um I just want to clarify these two uh
+ 
+
+ align:start position:0%
+um I just want to clarify these two uh
+these two analogies to background
+
+ align:start position:0%
+these two analogies to background
+ 
+
+ align:start position:0%
+these two analogies to background
+transformation they are not disconnected
+
+ align:start position:0%
+transformation they are not disconnected
+ 
+
+ align:start position:0%
+transformation they are not disconnected
+right they're not disconnected in the
+
+ align:start position:0%
+right they're not disconnected in the
+ 
+
+ align:start position:0%
+right they're not disconnected in the
+sense that's right yeah so if you if you
+
+ align:start position:0%
+sense that's right yeah so if you if you
+ 
+
+ align:start position:0%
+sense that's right yeah so if you if you
+take the background field notation and
+
+ align:start position:0%
+take the background field notation and
+ 
+
+ align:start position:0%
+take the background field notation and
+you just really think about that then
+
+ align:start position:0%
+you just really think about that then
+ 
+
+ align:start position:0%
+you just really think about that then
+that's this is how you would transform
+
+ align:start position:0%
+that's this is how you would transform
+ 
+
+ align:start position:0%
+that's this is how you would transform
+the quantum field under the background
+
+ align:start position:0%
+the quantum field under the background
+ 
+
+ align:start position:0%
+the quantum field under the background
+gauge
+
+ align:start position:0%
+gauge
+ 
+
+ align:start position:0%
+gauge
+transformation and this is how you would
+
+ align:start position:0%
+transformation and this is how you would
+ 
+
+ align:start position:0%
+transformation and this is how you would
+transform the qu the quantum field under
+
+ align:start position:0%
+transform the qu the quantum field under
+ 
+
+ align:start position:0%
+transform the qu the quantum field under
+the quantum gaug transation yeah that's
+
+ align:start position:0%
+the quantum gaug transation yeah that's
+ 
+
+ align:start position:0%
+the quantum gaug transation yeah that's
+right yeah so even if you made this two
+
+ align:start position:0%
+right yeah so even if you made this two
+ 
+
+ align:start position:0%
+right yeah so even if you made this two
+separate guge transformation for they
+
+ align:start position:0%
+separate guge transformation for they
+ 
+
+ align:start position:0%
+separate guge transformation for they
+still have the same one numbers yeah
+
+ align:start position:0%
+still have the same one numbers yeah
+ 
+
+ align:start position:0%
+still have the same one numbers yeah
+that's right are they going to mix at
+
+ align:start position:0%
+that's right are they going to mix at
+ 
+
+ align:start position:0%
+that's right are they going to mix at
+some Loop level um we're going to make
+
+ align:start position:0%
+some Loop level um we're going to make
+ 
+
+ align:start position:0%
+some Loop level um we're going to make
+sure they don't
+
+ align:start position:0%
+sure they don't
+ 
+
+ align:start position:0%
+sure they don't
+okay yeah I mean in some sense we really
+
+ align:start position:0%
+okay yeah I mean in some sense we really
+ 
+
+ align:start position:0%
+okay yeah I mean in some sense we really
+want you know the picture is this one
+
+ align:start position:0%
+want you know the picture is this one
+ 
+
+ align:start position:0%
+want you know the picture is this one
+that we had
+
+ align:start position:0%
+that we had
+ 
+
+ align:start position:0%
+that we had
+earlier where we really want the cinear
+
+ align:start position:0%
+earlier where we really want the cinear
+ 
+
+ align:start position:0%
+earlier where we really want the cinear
+fields to live up
+
+ align:start position:0%
+fields to live up
+ 
+
+ align:start position:0%
+fields to live up
+here so we had these hyperbolas right we
+
+ align:start position:0%
+here so we had these hyperbolas right we
+ 
+
+ align:start position:0%
+here so we had these hyperbolas right we
+want this guy to live up here and this
+
+ align:start position:0%
+want this guy to live up here and this
+ 
+
+ align:start position:0%
+want this guy to live up here and this
+guy to live up down
+
+ align:start position:0%
+guy to live up down
+ 
+
+ align:start position:0%
+guy to live up down
+there in momentum space so this was P
+
+ align:start position:0%
+there in momentum space so this was P
+ 
+
+ align:start position:0%
+there in momentum space so this was P
+minus this is p+ so we want them to live
+
+ align:start position:0%
+minus this is p+ so we want them to live
+ 
+
+ align:start position:0%
+minus this is p+ so we want them to live
+in different places they have the same
+
+ align:start position:0%
+in different places they have the same
+ 
+
+ align:start position:0%
+in different places they have the same
+Quant quantum numbers except we want
+
+ align:start position:0%
+Quant quantum numbers except we want
+ 
+
+ align:start position:0%
+Quant quantum numbers except we want
+them in momentum space to live in
+
+ align:start position:0%
+them in momentum space to live in
+ 
+
+ align:start position:0%
+them in momentum space to live in
+different places and to describe
+
+ align:start position:0%
+different places and to describe
+ 
+
+ align:start position:0%
+different places and to describe
+different degrees of
+
+ align:start position:0%
+different degrees of
+ 
+
+ align:start position:0%
+different degrees of
+freedom right so everything that we did
+
+ align:start position:0%
+freedom right so everything that we did
+ 
+
+ align:start position:0%
+freedom right so everything that we did
+here is exactly related to this picture
+
+ align:start position:0%
+here is exactly related to this picture
+ 
+
+ align:start position:0%
+here is exactly related to this picture
+that we want to talk about this guy is
+
+ align:start position:0%
+that we want to talk about this guy is
+ 
+
+ align:start position:0%
+that we want to talk about this guy is
+having larger momentum talk about gauge
+
+ align:start position:0%
+having larger momentum talk about gauge
+ 
+
+ align:start position:0%
+having larger momentum talk about gauge
+Transformations that kind of Shuffle
+
+ align:start position:0%
+Transformations that kind of Shuffle
+ 
+
+ align:start position:0%
+Transformations that kind of Shuffle
+things around with components that have
+
+ align:start position:0%
+things around with components that have
+ 
+
+ align:start position:0%
+things around with components that have
+large momentum versus small momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right so we're going to hypothesize that
+
+ align:start position:0%
+right so we're going to hypothesize that
+ 
+
+ align:start position:0%
+right so we're going to hypothesize that
+these gauge Transformations are the
+
+ align:start position:0%
+these gauge Transformations are the
+ 
+
+ align:start position:0%
+these gauge Transformations are the
+fundamental symmetry of the effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory and I Tred to motivate fate them
+
+ align:start position:0%
+Theory and I Tred to motivate fate them
+ 
+
+ align:start position:0%
+Theory and I Tred to motivate fate them
+physically by this analogy with
+
+ align:start position:0%
+physically by this analogy with
+ 
+
+ align:start position:0%
+physically by this analogy with
+background field gauge and thinking
+
+ align:start position:0%
+background field gauge and thinking
+ 
+
+ align:start position:0%
+background field gauge and thinking
+about a longer wavelength mode with
+
+ align:start position:0%
+about a longer wavelength mode with
+ 
+
+ align:start position:0%
+about a longer wavelength mode with
+respect to a shorter wavelength mode
+
+ align:start position:0%
+respect to a shorter wavelength mode
+ 
+
+ align:start position:0%
+respect to a shorter wavelength mode
+which is in this picture exactly the
+
+ align:start position:0%
+which is in this picture exactly the
+ 
+
+ align:start position:0%
+which is in this picture exactly the
+fact that this hyperbola is higher than
+
+ align:start position:0%
+fact that this hyperbola is higher than
+ 
+
+ align:start position:0%
+fact that this hyperbola is higher than
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+one maybe the hyperbola should stay on
+
+ align:start position:0%
+one maybe the hyperbola should stay on
+ 
+
+ align:start position:0%
+one maybe the hyperbola should stay on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+board okay so the kind of multipole or
+
+ align:start position:0%
+board okay so the kind of multipole or
+ 
+
+ align:start position:0%
+board okay so the kind of multipole or
+the the multipole expansion that we did
+
+ align:start position:0%
+the the multipole expansion that we did
+ 
+
+ align:start position:0%
+the the multipole expansion that we did
+between these fields and the sort of
+
+ align:start position:0%
+between these fields and the sort of
+ 
+
+ align:start position:0%
+between these fields and the sort of
+thing that the statement that this is a
+
+ align:start position:0%
+thing that the statement that this is a
+ 
+
+ align:start position:0%
+thing that the statement that this is a
+longer wavelength
+
+ align:start position:0%
+longer wavelength
+ 
+
+ align:start position:0%
+longer wavelength
+mode is exactly the fact that there's a
+
+ align:start position:0%
+mode is exactly the fact that there's a
+ 
+
+ align:start position:0%
+mode is exactly the fact that there's a
+separation between these guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so we'll take these to be the
+
+ align:start position:0%
+so we'll take these to be the
+ 
+
+ align:start position:0%
+so we'll take these to be the
+fundamental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Transformations that do not get
+
+ align:start position:0%
+Transformations that do not get
+ 
+
+ align:start position:0%
+Transformations that do not get
+corrected by power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Corrections and I'm not claiming that
+
+ align:start position:0%
+Corrections and I'm not claiming that
+ 
+
+ align:start position:0%
+Corrections and I'm not claiming that
+that's necessarily unique way of getting
+
+ align:start position:0%
+that's necessarily unique way of getting
+ 
+
+ align:start position:0%
+that's necessarily unique way of getting
+to the effective Theory you could think
+
+ align:start position:0%
+to the effective Theory you could think
+ 
+
+ align:start position:0%
+to the effective Theory you could think
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+I there might be example in the
+
+ align:start position:0%
+I there might be example in the
+ 
+
+ align:start position:0%
+I there might be example in the
+literature where people were thinking of
+
+ align:start position:0%
+literature where people were thinking of
+ 
+
+ align:start position:0%
+literature where people were thinking of
+other gauge
+
+ align:start position:0%
+other gauge
+ 
+
+ align:start position:0%
+other gauge
+Transformations these are the ones that
+
+ align:start position:0%
+Transformations these are the ones that
+ 
+
+ align:start position:0%
+Transformations these are the ones that
+people talk about now but in the early
+
+ align:start position:0%
+people talk about now but in the early
+ 
+
+ align:start position:0%
+people talk about now but in the early
+days I think there's an example in the
+
+ align:start position:0%
+days I think there's an example in the
+ 
+
+ align:start position:0%
+days I think there's an example in the
+literature where people were thinking of
+
+ align:start position:0%
+literature where people were thinking of
+ 
+
+ align:start position:0%
+literature where people were thinking of
+other Transformations and you could
+
+ align:start position:0%
+other Transformations and you could
+ 
+
+ align:start position:0%
+other Transformations and you could
+prove that they could be connected to
+
+ align:start position:0%
+prove that they could be connected to
+ 
+
+ align:start position:0%
+prove that they could be connected to
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+ones um but we'll just take the the ones
+
+ align:start position:0%
+ones um but we'll just take the the ones
+ 
+
+ align:start position:0%
+ones um but we'll just take the the ones
+that are the most useful from the start
+
+ align:start position:0%
+that are the most useful from the start
+ 
+
+ align:start position:0%
+that are the most useful from the start
+and not worry about too much about what
+
+ align:start position:0%
+and not worry about too much about what
+ 
+
+ align:start position:0%
+and not worry about too much about what
+we could have done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so there's no mixing in the
+
+ align:start position:0%
+all right so there's no mixing in the
+ 
+
+ align:start position:0%
+all right so there's no mixing in the
+power counting and that's something that
+
+ align:start position:0%
+power counting and that's something that
+ 
+
+ align:start position:0%
+power counting and that's something that
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+like set up that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way if if there was a mixing if we
+
+ align:start position:0%
+way if if there was a mixing if we
+ 
+
+ align:start position:0%
+way if if there was a mixing if we
+connected things that were different
+
+ align:start position:0%
+connected things that were different
+ 
+
+ align:start position:0%
+connected things that were different
+sizes in Lambda then we would you know
+
+ align:start position:0%
+sizes in Lambda then we would you know
+ 
+
+ align:start position:0%
+sizes in Lambda then we would you know
+you could say well the power counting
+
+ align:start position:0%
+you could say well the power counting
+ 
+
+ align:start position:0%
+you could say well the power counting
+that the the gauge transformation
+
+ align:start position:0%
+that the the gauge transformation
+ 
+
+ align:start position:0%
+that the the gauge transformation
+induces power suppressed terms and you
+
+ align:start position:0%
+induces power suppressed terms and you
+ 
+
+ align:start position:0%
+induces power suppressed terms and you
+could end up with some situation where
+
+ align:start position:0%
+could end up with some situation where
+ 
+
+ align:start position:0%
+could end up with some situation where
+you're trying to connect things at
+
+ align:start position:0%
+you're trying to connect things at
+ 
+
+ align:start position:0%
+you're trying to connect things at
+different orders
+
+ align:start position:0%
+different orders
+ 
+
+ align:start position:0%
+different orders
+and we don't have that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and that's because if we want to
+
+ align:start position:0%
+here and that's because if we want to
+ 
+
+ align:start position:0%
+here and that's because if we want to
+think about this thing as a as a
+
+ align:start position:0%
+think about this thing as a as a
+ 
+
+ align:start position:0%
+think about this thing as a as a
+symmetry it should really be a symmetry
+
+ align:start position:0%
+symmetry it should really be a symmetry
+ 
+
+ align:start position:0%
+symmetry it should really be a symmetry
+of the leading order action that
+
+ align:start position:0%
+of the leading order action that
+ 
+
+ align:start position:0%
+of the leading order action that
+shouldn't require some other subleading
+
+ align:start position:0%
+shouldn't require some other subleading
+ 
+
+ align:start position:0%
+shouldn't require some other subleading
+terms uh necessarily to to compensate
+
+ align:start position:0%
+terms uh necessarily to to compensate
+ 
+
+ align:start position:0%
+terms uh necessarily to to compensate
+for it at least for a gauge symmetry
+
+ align:start position:0%
+for it at least for a gauge symmetry
+ 
+
+ align:start position:0%
+for it at least for a gauge symmetry
+like this that's we'd like to think that
+
+ align:start position:0%
+like this that's we'd like to think that
+ 
+
+ align:start position:0%
+like this that's we'd like to think that
+what the meaning of gauge symetry is and
+
+ align:start position:0%
+what the meaning of gauge symetry is and
+ 
+
+ align:start position:0%
+what the meaning of gauge symetry is and
+the redundancy encoded engage symmetry
+
+ align:start position:0%
+the redundancy encoded engage symmetry
+ 
+
+ align:start position:0%
+the redundancy encoded engage symmetry
+is all something that you're talking
+
+ align:start position:0%
+is all something that you're talking
+ 
+
+ align:start position:0%
+is all something that you're talking
+about at the order of the leading order
+
+ align:start position:0%
+about at the order of the leading order
+ 
+
+ align:start position:0%
+about at the order of the leading order
+action and you're not talking about
+
+ align:start position:0%
+action and you're not talking about
+ 
+
+ align:start position:0%
+action and you're not talking about
+redundancies and Fields that subleading
+
+ align:start position:0%
+redundancies and Fields that subleading
+ 
+
+ align:start position:0%
+redundancies and Fields that subleading
+order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Etc okay so let's do an example now that
+
+ align:start position:0%
+Etc okay so let's do an example now that
+ 
+
+ align:start position:0%
+Etc okay so let's do an example now that
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+this of sort of how it comes
+
+ align:start position:0%
+this of sort of how it comes
+ 
+
+ align:start position:0%
+this of sort of how it comes
+in and I want to come back to our
+
+ align:start position:0%
+in and I want to come back to our
+ 
+
+ align:start position:0%
+in and I want to come back to our
+example of our heavy Delight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current talk about gauge symmetry there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you just took the tree level result
+
+ align:start position:0%
+if you just took the tree level result
+ 
+
+ align:start position:0%
+if you just took the tree level result
+that we had in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case then we had something that just
+
+ align:start position:0%
+case then we had something that just
+ 
+
+ align:start position:0%
+case then we had something that just
+involved these two guys and this HV
+
+ align:start position:0%
+involved these two guys and this HV
+ 
+
+ align:start position:0%
+involved these two guys and this HV
+field was Ultra
+
+ align:start position:0%
+field was Ultra
+ 
+
+ align:start position:0%
+field was Ultra
+Soft this guy's
+
+ align:start position:0%
+Soft this guy's
+ 
+
+ align:start position:0%
+Soft this guy's
+cinear so if you did a UC transformation
+
+ align:start position:0%
+cinear so if you did a UC transformation
+ 
+
+ align:start position:0%
+cinear so if you did a UC transformation
+then under our rules what you'd
+
+ align:start position:0%
+then under our rules what you'd
+ 
+
+ align:start position:0%
+then under our rules what you'd
+find is that the the CN transforms and
+
+ align:start position:0%
+find is that the the CN transforms and
+ 
+
+ align:start position:0%
+find is that the the CN transforms and
+this guy doesn't the H doesn't so that
+
+ align:start position:0%
+this guy doesn't the H doesn't so that
+ 
+
+ align:start position:0%
+this guy doesn't the H doesn't so that
+would not be gaug in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variant but actually we saw that this
+
+ align:start position:0%
+variant but actually we saw that this
+ 
+
+ align:start position:0%
+variant but actually we saw that this
+also wasn't the the the lowest order
+
+ align:start position:0%
+also wasn't the the the lowest order
+ 
+
+ align:start position:0%
+also wasn't the the the lowest order
+current there was this additional thing
+
+ align:start position:0%
+current there was this additional thing
+ 
+
+ align:start position:0%
+current there was this additional thing
+the Wilson line that showed up and that
+
+ align:start position:0%
+the Wilson line that showed up and that
+ 
+
+ align:start position:0%
+the Wilson line that showed up and that
+Wilson line is going to fix this issue
+
+ align:start position:0%
+Wilson line is going to fix this issue
+ 
+
+ align:start position:0%
+Wilson line is going to fix this issue
+it's going to make it gaug
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invariant so we have to ask how the
+
+ align:start position:0%
+invariant so we have to ask how the
+ 
+
+ align:start position:0%
+invariant so we have to ask how the
+Wilson lines transform under G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetries and that Wilson line in
+
+ align:start position:0%
+symmetries and that Wilson line in
+ 
+
+ align:start position:0%
+symmetries and that Wilson line in
+position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space I called it something like
+
+ align:start position:0%
+space I called it something like
+ 
+
+ align:start position:0%
+space I called it something like
+this can't remember if I used a twiddle
+
+ align:start position:0%
+this can't remember if I used a twiddle
+ 
+
+ align:start position:0%
+this can't remember if I used a twiddle
+or a bar use a bar here for the position
+
+ align:start position:0%
+or a bar use a bar here for the position
+ 
+
+ align:start position:0%
+or a bar use a bar here for the position
+space Wilson
+
+ align:start position:0%
+space Wilson
+ 
+
+ align:start position:0%
+space Wilson
+line so in general in just a regular
+
+ align:start position:0%
+line so in general in just a regular
+ 
+
+ align:start position:0%
+line so in general in just a regular
+gauge Theory the Wilson line between two
+
+ align:start position:0%
+gauge Theory the Wilson line between two
+ 
+
+ align:start position:0%
+gauge Theory the Wilson line between two
+points transforms at the end points so
+
+ align:start position:0%
+points transforms at the end points so
+ 
+
+ align:start position:0%
+points transforms at the end points so
+you get U of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X then you get a UD Dagger of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y so if you like what we would say for
+
+ align:start position:0%
+Y so if you like what we would say for
+ 
+
+ align:start position:0%
+Y so if you like what we would say for
+this Wilson line is that we have a a u
+
+ align:start position:0%
+this Wilson line is that we have a a u
+ 
+
+ align:start position:0%
+this Wilson line is that we have a a u
+of X on one side and a u Dagger of minus
+
+ align:start position:0%
+of X on one side and a u Dagger of minus
+ 
+
+ align:start position:0%
+of X on one side and a u Dagger of minus
+infinity on the other side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus infinity is really long wavelength
+
+ align:start position:0%
+minus infinity is really long wavelength
+ 
+
+ align:start position:0%
+minus infinity is really long wavelength
+physics and so we have to worry a little
+
+ align:start position:0%
+physics and so we have to worry a little
+ 
+
+ align:start position:0%
+physics and so we have to worry a little
+bit about the the overlap between our
+
+ align:start position:0%
+bit about the the overlap between our
+ 
+
+ align:start position:0%
+bit about the the overlap between our
+different types of gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Transformations I divided them into
+
+ align:start position:0%
+Transformations I divided them into
+ 
+
+ align:start position:0%
+Transformations I divided them into
+three camps colinear ultrasoft and and
+
+ align:start position:0%
+three camps colinear ultrasoft and and
+ 
+
+ align:start position:0%
+three camps colinear ultrasoft and and
+the global so let me do the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to avoid some double counting with what
+
+ align:start position:0%
+to avoid some double counting with what
+ 
+
+ align:start position:0%
+to avoid some double counting with what
+I called UK Global let's just simply
+
+ align:start position:0%
+I called UK Global let's just simply
+ 
+
+ align:start position:0%
+I called UK Global let's just simply
+take Since U Global acts the same
+
+ align:start position:0%
+take Since U Global acts the same
+ 
+
+ align:start position:0%
+take Since U Global acts the same
+everywhere let's just simply take UC
+
+ align:start position:0%
+everywhere let's just simply take UC
+ 
+
+ align:start position:0%
+everywhere let's just simply take UC
+dagger at minus infinity to be
+
+ align:start position:0%
+dagger at minus infinity to be
+ 
+
+ align:start position:0%
+dagger at minus infinity to be
+one so this is at some particular
+
+ align:start position:0%
+one so this is at some particular
+ 
+
+ align:start position:0%
+one so this is at some particular
+SpaceTime point we take it to be one and
+
+ align:start position:0%
+SpaceTime point we take it to be one and
+ 
+
+ align:start position:0%
+SpaceTime point we take it to be one and
+that Since U Global will transform at
+
+ align:start position:0%
+that Since U Global will transform at
+ 
+
+ align:start position:0%
+that Since U Global will transform at
+that point we then know there's no
+
+ align:start position:0%
+that point we then know there's no
+ 
+
+ align:start position:0%
+that point we then know there's no
+overlap between UC and U global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that that's enough to ensure
+
+ align:start position:0%
+okay that that's enough to ensure
+ 
+
+ align:start position:0%
+okay that that's enough to ensure
+that so with
+
+ align:start position:0%
+that so with
+ 
+
+ align:start position:0%
+that so with
+that our guy under a cinear gauge
+
+ align:start position:0%
+that our guy under a cinear gauge
+ 
+
+ align:start position:0%
+that our guy under a cinear gauge
+transformation just transforms on one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side if you like what's happening is
+
+ align:start position:0%
+side if you like what's happening is
+ 
+
+ align:start position:0%
+side if you like what's happening is
+that the coordinate here corresponds to
+
+ align:start position:0%
+that the coordinate here corresponds to
+ 
+
+ align:start position:0%
+that the coordinate here corresponds to
+this very large
+
+ align:start position:0%
+this very large
+ 
+
+ align:start position:0%
+this very large
+momentum and we're stretching ourselves
+
+ align:start position:0%
+momentum and we're stretching ourselves
+ 
+
+ align:start position:0%
+momentum and we're stretching ourselves
+out to small to you know to longdistance
+
+ align:start position:0%
+out to small to you know to longdistance
+ 
+
+ align:start position:0%
+out to small to you know to longdistance
+physics which is corresponding to the
+
+ align:start position:0%
+physics which is corresponding to the
+ 
+
+ align:start position:0%
+physics which is corresponding to the
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+momentum so when I I think about
+
+ align:start position:0%
+momentum so when I I think about
+ 
+
+ align:start position:0%
+momentum so when I I think about
+Transformations that should be cinear I
+
+ align:start position:0%
+Transformations that should be cinear I
+ 
+
+ align:start position:0%
+Transformations that should be cinear I
+want them to be Associated to the X and
+
+ align:start position:0%
+want them to be Associated to the X and
+ 
+
+ align:start position:0%
+want them to be Associated to the X and
+I want to associate other types of
+
+ align:start position:0%
+I want to associate other types of
+ 
+
+ align:start position:0%
+I want to associate other types of
+transformations to what's going on in
+
+ align:start position:0%
+transformations to what's going on in
+ 
+
+ align:start position:0%
+transformations to what's going on in
+Infinity which is really A Spacetime of
+
+ align:start position:0%
+Infinity which is really A Spacetime of
+ 
+
+ align:start position:0%
+Infinity which is really A Spacetime of
+its own which is this ultrasoft space
+
+ align:start position:0%
+its own which is this ultrasoft space
+ 
+
+ align:start position:0%
+its own which is this ultrasoft space
+time that's sitting at sort of the
+
+ align:start position:0%
+time that's sitting at sort of the
+ 
+
+ align:start position:0%
+time that's sitting at sort of the
+cinear
+
+ align:start position:0%
+cinear
+ 
+
+ align:start position:0%
+cinear
+infinity so that's why I want actually
+
+ align:start position:0%
+infinity so that's why I want actually
+ 
+
+ align:start position:0%
+infinity so that's why I want actually
+it to look like
+
+ align:start position:0%
+it to look like
+ 
+
+ align:start position:0%
+it to look like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+lines just with thear fields or yeah
+
+ align:start position:0%
+lines just with thear fields or yeah
+ 
+
+ align:start position:0%
+lines just with thear fields or yeah
+okay yeah so this guy here was a path
+
+ align:start position:0%
+okay yeah so this guy here was a path
+ 
+
+ align:start position:0%
+okay yeah so this guy here was a path
+exponential and it just invol called the
+
+ align:start position:0%
+exponential and it just invol called the
+ 
+
+ align:start position:0%
+exponential and it just invol called the
+Nar
+
+ align:start position:0%
+Nar
+ 
+
+ align:start position:0%
+Nar
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+yeah so in momentum so that's what it
+
+ align:start position:0%
+yeah so in momentum so that's what it
+ 
+
+ align:start position:0%
+yeah so in momentum so that's what it
+was in position space and in momentum
+
+ align:start position:0%
+was in position space and in momentum
+ 
+
+ align:start position:0%
+was in position space and in momentum
+space we called it
+
+ align:start position:0%
+space we called it
+ 
+
+ align:start position:0%
+space we called it
+w and it you know was a sum over a bunch
+
+ align:start position:0%
+w and it you know was a sum over a bunch
+ 
+
+ align:start position:0%
+w and it you know was a sum over a bunch
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things I'm not going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we had this this
+
+ align:start position:0%
+we had this this
+ 
+
+ align:start position:0%
+we had this this
+formula let me not write it all out
+
+ align:start position:0%
+formula let me not write it all out
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again as a kind of short form for that
+
+ align:start position:0%
+again as a kind of short form for that
+ 
+
+ align:start position:0%
+again as a kind of short form for that
+formula we can write the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula which is given our notation that
+
+ align:start position:0%
+formula which is given our notation that
+ 
+
+ align:start position:0%
+formula which is given our notation that
+we've developed a useful
+
+ align:start position:0%
+we've developed a useful
+ 
+
+ align:start position:0%
+we've developed a useful
+wave thinking about it so if we formally
+
+ align:start position:0%
+wave thinking about it so if we formally
+ 
+
+ align:start position:0%
+wave thinking about it so if we formally
+expand out this
+
+ align:start position:0%
+expand out this
+ 
+
+ align:start position:0%
+expand out this
+exponential and we just just keep the
+
+ align:start position:0%
+exponential and we just just keep the
+ 
+
+ align:start position:0%
+exponential and we just just keep the
+order of that expansion where the P bar
+
+ align:start position:0%
+order of that expansion where the P bar
+ 
+
+ align:start position:0%
+order of that expansion where the P bar
+acts on all the fields to the right that
+
+ align:start position:0%
+acts on all the fields to the right that
+ 
+
+ align:start position:0%
+acts on all the fields to the right that
+will correctly reproduce this
+
+ align:start position:0%
+will correctly reproduce this
+ 
+
+ align:start position:0%
+will correctly reproduce this
+denominator the sum over perations is
+
+ align:start position:0%
+denominator the sum over perations is
+ 
+
+ align:start position:0%
+denominator the sum over perations is
+something that we still have to do there
+
+ align:start position:0%
+something that we still have to do there
+ 
+
+ align:start position:0%
+something that we still have to do there
+was a 1 over n factorial K factorial in
+
+ align:start position:0%
+was a 1 over n factorial K factorial in
+ 
+
+ align:start position:0%
+was a 1 over n factorial K factorial in
+here M factorial with this
+
+ align:start position:0%
+here M factorial with this
+ 
+
+ align:start position:0%
+here M factorial with this
+notation okay but this is like a little
+
+ align:start position:0%
+notation okay but this is like a little
+ 
+
+ align:start position:0%
+notation okay but this is like a little
+shorthand for that messy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+yeah to
+
+ align:start position:0%
+yeah to
+ 
+
+ align:start position:0%
+yeah to
+yeah how do you get
+
+ align:start position:0%
+yeah how do you get
+ 
+
+ align:start position:0%
+yeah how do you get
+thetion so yeah so that so that actually
+
+ align:start position:0%
+thetion so yeah so that so that actually
+ 
+
+ align:start position:0%
+thetion so yeah so that so that actually
+is related to the fact that when you
+
+ align:start position:0%
+is related to the fact that when you
+ 
+
+ align:start position:0%
+is related to the fact that when you
+look at the for the for this Wilson line
+
+ align:start position:0%
+look at the for the for this Wilson line
+ 
+
+ align:start position:0%
+look at the for the for this Wilson line
+with the iepsilon it's not it's not
+
+ align:start position:0%
+with the iepsilon it's not it's not
+ 
+
+ align:start position:0%
+with the iepsilon it's not it's not
+related to the gauge transformation
+
+ align:start position:0%
+related to the gauge transformation
+ 
+
+ align:start position:0%
+related to the gauge transformation
+Vanishing it want at Infinity but it's
+
+ align:start position:0%
+Vanishing it want at Infinity but it's
+ 
+
+ align:start position:0%
+Vanishing it want at Infinity but it's
+related to the fact that the path goes
+
+ align:start position:0%
+related to the fact that the path goes
+ 
+
+ align:start position:0%
+related to the fact that the path goes
+that way so that the when you do the 4E
+
+ align:start position:0%
+that way so that the when you do the 4E
+ 
+
+ align:start position:0%
+that way so that the when you do the 4E
+integral the fact that it goes from
+
+ align:start position:0%
+integral the fact that it goes from
+ 
+
+ align:start position:0%
+integral the fact that it goes from
+minus in Infinity to X will give the I
+
+ align:start position:0%
+minus in Infinity to X will give the I
+ 
+
+ align:start position:0%
+minus in Infinity to X will give the I
+zero okay but for these Wilson lines
+
+ align:start position:0%
+zero okay but for these Wilson lines
+ 
+
+ align:start position:0%
+zero okay but for these Wilson lines
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+if you think about what's happening at
+
+ align:start position:0%
+if you think about what's happening at
+ 
+
+ align:start position:0%
+if you think about what's happening at
+the place where the i z would actually
+
+ align:start position:0%
+the place where the i z would actually
+ 
+
+ align:start position:0%
+the place where the i z would actually
+matter that's exactly the zero
+
+ align:start position:0%
+matter that's exactly the zero
+ 
+
+ align:start position:0%
+matter that's exactly the zero
+bin so it's going to be a little more
+
+ align:start position:0%
+bin so it's going to be a little more
+ 
+
+ align:start position:0%
+bin so it's going to be a little more
+yeah so you don't really care
+
+ align:start position:0%
+yeah so you don't really care
+ 
+
+ align:start position:0%
+yeah so you don't really care
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I can only say that we'll explain
+
+ align:start position:0%
+yeah I can only say that we'll explain
+ 
+
+ align:start position:0%
+yeah I can only say that we'll explain
+what I just said to Il more when we come
+
+ align:start position:0%
+what I just said to Il more when we come
+ 
+
+ align:start position:0%
+what I just said to Il more when we come
+come to it later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on okay so this is this field here has
+
+ align:start position:0%
+on okay so this is this field here has
+ 
+
+ align:start position:0%
+on okay so this is this field here has
+it I I said it's a momentum
+
+ align:start position:0%
+it I I said it's a momentum
+ 
+
+ align:start position:0%
+it I I said it's a momentum
+space but then I wrote X so really what
+
+ align:start position:0%
+space but then I wrote X so really what
+ 
+
+ align:start position:0%
+space but then I wrote X so really what
+I mean by momentum space is momentum is
+
+ align:start position:0%
+I mean by momentum space is momentum is
+ 
+
+ align:start position:0%
+I mean by momentum space is momentum is
+in the label momentum space there's some
+
+ align:start position:0%
+in the label momentum space there's some
+ 
+
+ align:start position:0%
+in the label momentum space there's some
+guy and the labels are these these
+
+ align:start position:0%
+guy and the labels are these these
+ 
+
+ align:start position:0%
+guy and the labels are these these
+labels on the fields here right so
+
+ align:start position:0%
+labels on the fields here right so
+ 
+
+ align:start position:0%
+labels on the fields here right so
+there's still an X and that X
+
+ align:start position:0%
+there's still an X and that X
+ 
+
+ align:start position:0%
+there's still an X and that X
+corresponds to the residual coordinate
+
+ align:start position:0%
+corresponds to the residual coordinate
+ 
+
+ align:start position:0%
+corresponds to the residual coordinate
+that we were using to do the multiple
+
+ align:start position:0%
+that we were using to do the multiple
+ 
+
+ align:start position:0%
+that we were using to do the multiple
+expansion so this is in some sense this
+
+ align:start position:0%
+expansion so this is in some sense this
+ 
+
+ align:start position:0%
+expansion so this is in some sense this
+isn't simply the for transform of that
+
+ align:start position:0%
+isn't simply the for transform of that
+ 
+
+ align:start position:0%
+isn't simply the for transform of that
+because of that it still knows about
+
+ align:start position:0%
+because of that it still knows about
+ 
+
+ align:start position:0%
+because of that it still knows about
+this separation between the large
+
+ align:start position:0%
+this separation between the large
+ 
+
+ align:start position:0%
+this separation between the large
+momentum and the soft momentum
+
+ align:start position:0%
+momentum and the soft momentum
+ 
+
+ align:start position:0%
+momentum and the soft momentum
+from that multipole
+
+ align:start position:0%
+from that multipole
+ 
+
+ align:start position:0%
+from that multipole
+expansion so this dependence on X allows
+
+ align:start position:0%
+expansion so this dependence on X allows
+ 
+
+ align:start position:0%
+expansion so this dependence on X allows
+us to think about the multiple expansion
+
+ align:start position:0%
+us to think about the multiple expansion
+ 
+
+ align:start position:0%
+us to think about the multiple expansion
+on these Wilson
+
+ align:start position:0%
+on these Wilson
+ 
+
+ align:start position:0%
+on these Wilson
+lines encodes all the residual residual
+
+ align:start position:0%
+lines encodes all the residual residual
+ 
+
+ align:start position:0%
+lines encodes all the residual residual
+momenta and the fields in the Wilson
+
+ align:start position:0%
+momenta and the fields in the Wilson
+ 
+
+ align:start position:0%
+momenta and the fields in the Wilson
+line carry residual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momenta so we're just putting our
+
+ align:start position:0%
+momenta so we're just putting our
+ 
+
+ align:start position:0%
+momenta so we're just putting our
+notation to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and if you you really strictly want
+
+ align:start position:0%
+here and if you you really strictly want
+ 
+
+ align:start position:0%
+here and if you you really strictly want
+to connect to that formula up there and
+
+ align:start position:0%
+to connect to that formula up there and
+ 
+
+ align:start position:0%
+to connect to that formula up there and
+you would take the residual momentum to
+
+ align:start position:0%
+you would take the residual momentum to
+ 
+
+ align:start position:0%
+you would take the residual momentum to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+zero and
+
+ align:start position:0%
+zero and
+ 
+
+ align:start position:0%
+zero and
+then the 4
+
+ align:start position:0%
+then the 4
+ 
+
+ align:start position:0%
+then the 4
+transform with respect to just the large
+
+ align:start position:0%
+transform with respect to just the large
+ 
+
+ align:start position:0%
+transform with respect to just the large
+momentum PL
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus gives a
+
+ align:start position:0%
+minus gives a
+ 
+
+ align:start position:0%
+minus gives a
+line which is just depending on that one
+
+ align:start position:0%
+line which is just depending on that one
+ 
+
+ align:start position:0%
+line which is just depending on that one
+single coordinate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we just had a coordinate which is
+
+ align:start position:0%
+so if we just had a coordinate which is
+ 
+
+ align:start position:0%
+so if we just had a coordinate which is
+conjugate to the large momenta which is
+
+ align:start position:0%
+conjugate to the large momenta which is
+ 
+
+ align:start position:0%
+conjugate to the large momenta which is
+the thing that's showing up here or the
+
+ align:start position:0%
+the thing that's showing up here or the
+ 
+
+ align:start position:0%
+the thing that's showing up here or the
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+momenta then that you know that would be
+
+ align:start position:0%
+momenta then that you know that would be
+ 
+
+ align:start position:0%
+momenta then that you know that would be
+the analog of what we were talking about
+
+ align:start position:0%
+the analog of what we were talking about
+ 
+
+ align:start position:0%
+the analog of what we were talking about
+up here where in general this thing also
+
+ align:start position:0%
+up here where in general this thing also
+ 
+
+ align:start position:0%
+up here where in general this thing also
+has a dependence on the residual X which
+
+ align:start position:0%
+has a dependence on the residual X which
+ 
+
+ align:start position:0%
+has a dependence on the residual X which
+we'll make use of in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's think about so I told you how this
+
+ align:start position:0%
+let's think about so I told you how this
+ 
+
+ align:start position:0%
+let's think about so I told you how this
+Wilson line transforms under UC how does
+
+ align:start position:0%
+Wilson line transforms under UC how does
+ 
+
+ align:start position:0%
+Wilson line transforms under UC how does
+it transform under U
+
+ align:start position:0%
+it transform under U
+ 
+
+ align:start position:0%
+it transform under U
+ultrasoft so under
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UC again using this kind of Matrix type
+
+ align:start position:0%
+UC again using this kind of Matrix type
+ 
+
+ align:start position:0%
+UC again using this kind of Matrix type
+notation just UC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a matrix multiplication in
+
+ align:start position:0%
+so this is a matrix multiplication in
+ 
+
+ align:start position:0%
+so this is a matrix multiplication in
+momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space what about under a ultrasoft
+
+ align:start position:0%
+space what about under a ultrasoft
+ 
+
+ align:start position:0%
+space what about under a ultrasoft
+transformation well under an ultrasoft
+
+ align:start position:0%
+transformation well under an ultrasoft
+ 
+
+ align:start position:0%
+transformation well under an ultrasoft
+transformation this should be a derived
+
+ align:start position:0%
+transformation this should be a derived
+ 
+
+ align:start position:0%
+transformation this should be a derived
+in some sense under a cinear
+
+ align:start position:0%
+in some sense under a cinear
+ 
+
+ align:start position:0%
+in some sense under a cinear
+transformation it was a derived quantity
+
+ align:start position:0%
+transformation it was a derived quantity
+ 
+
+ align:start position:0%
+transformation it was a derived quantity
+because we knew how the gauge field
+
+ align:start position:0%
+because we knew how the gauge field
+ 
+
+ align:start position:0%
+because we knew how the gauge field
+transform the thing that gave us the
+
+ align:start position:0%
+transform the thing that gave us the
+ 
+
+ align:start position:0%
+transform the thing that gave us the
+transformation of the Wilson line is
+
+ align:start position:0%
+transformation of the Wilson line is
+ 
+
+ align:start position:0%
+transformation of the Wilson line is
+just the transformation of the gauge
+
+ align:start position:0%
+just the transformation of the gauge
+ 
+
+ align:start position:0%
+just the transformation of the gauge
+field okay okay so that's what led to
+
+ align:start position:0%
+field okay okay so that's what led to
+ 
+
+ align:start position:0%
+field okay okay so that's what led to
+that actual this form once we put in
+
+ align:start position:0%
+that actual this form once we put in
+ 
+
+ align:start position:0%
+that actual this form once we put in
+this fact so under the ultrasoft
+
+ align:start position:0%
+this fact so under the ultrasoft
+ 
+
+ align:start position:0%
+this fact so under the ultrasoft
+transformation we just take the
+
+ align:start position:0%
+transformation we just take the
+ 
+
+ align:start position:0%
+transformation we just take the
+transformation that we have for the
+
+ align:start position:0%
+transformation that we have for the
+ 
+
+ align:start position:0%
+transformation that we have for the
+ciner gauge field and then we derive how
+
+ align:start position:0%
+ciner gauge field and then we derive how
+ 
+
+ align:start position:0%
+ciner gauge field and then we derive how
+the ultrasoft GL how the ult how the
+
+ align:start position:0%
+the ultrasoft GL how the ult how the
+ 
+
+ align:start position:0%
+the ultrasoft GL how the ult how the
+Wilson line should transform under the
+
+ align:start position:0%
+Wilson line should transform under the
+ 
+
+ align:start position:0%
+Wilson line should transform under the
+ultrasoft gauge symmetry okay so how
+
+ align:start position:0%
+ultrasoft gauge symmetry okay so how
+ 
+
+ align:start position:0%
+ultrasoft gauge symmetry okay so how
+does this guy
+
+ align:start position:0%
+does this guy
+ 
+
+ align:start position:0%
+does this guy
+transform this guy transforms by putting
+
+ align:start position:0%
+transform this guy transforms by putting
+ 
+
+ align:start position:0%
+transform this guy transforms by putting
+u's on the left and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay that are at X
+
+ align:start position:0%
+right okay that are at X
+ 
+
+ align:start position:0%
+right okay that are at X
+but every field in this exponential has
+
+ align:start position:0%
+but every field in this exponential has
+ 
+
+ align:start position:0%
+but every field in this exponential has
+the same uu dagger multiply think about
+
+ align:start position:0%
+the same uu dagger multiply think about
+ 
+
+ align:start position:0%
+the same uu dagger multiply think about
+expanding that out all the uyu daggers
+
+ align:start position:0%
+expanding that out all the uyu daggers
+ 
+
+ align:start position:0%
+expanding that out all the uyu daggers
+that are next to each other cancel you
+
+ align:start position:0%
+that are next to each other cancel you
+ 
+
+ align:start position:0%
+that are next to each other cancel you
+just get an overall uu dagger that comes
+
+ align:start position:0%
+just get an overall uu dagger that comes
+ 
+
+ align:start position:0%
+just get an overall uu dagger that comes
+right outside the
+
+ align:start position:0%
+right outside the
+ 
+
+ align:start position:0%
+right outside the
+exponential so this
+
+ align:start position:0%
+exponential so this
+ 
+
+ align:start position:0%
+exponential so this
+guy so just transforming with U
+
+ align:start position:0%
+guy so just transforming with U
+ 
+
+ align:start position:0%
+guy so just transforming with U
+ultrasoft of X Wilson line back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again U ultrasoft diag of X and that's
+
+ align:start position:0%
+again U ultrasoft diag of X and that's
+ 
+
+ align:start position:0%
+again U ultrasoft diag of X and that's
+because this Wilson line with our
+
+ align:start position:0%
+because this Wilson line with our
+ 
+
+ align:start position:0%
+because this Wilson line with our
+notation is really a local thing with
+
+ align:start position:0%
+notation is really a local thing with
+ 
+
+ align:start position:0%
+notation is really a local thing with
+respect to the coordinate X all the
+
+ align:start position:0%
+respect to the coordinate X all the
+ 
+
+ align:start position:0%
+respect to the coordinate X all the
+fields sit at
+
+ align:start position:0%
+fields sit at
+ 
+
+ align:start position:0%
+fields sit at
+X okay so it just transforms like that
+
+ align:start position:0%
+X okay so it just transforms like that
+ 
+
+ align:start position:0%
+X okay so it just transforms like that
+because that's how the the gauge field
+
+ align:start position:0%
+because that's how the the gauge field
+ 
+
+ align:start position:0%
+because that's how the the gauge field
+inside it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transforms so in some sense both of
+
+ align:start position:0%
+transforms so in some sense both of
+ 
+
+ align:start position:0%
+transforms so in some sense both of
+these are derived from the
+
+ align:start position:0%
+these are derived from the
+ 
+
+ align:start position:0%
+these are derived from the
+transformation of a
+
+ align:start position:0%
+transformation of a
+ 
+
+ align:start position:0%
+transformation of a
+but it's easier to think about how
+
+ align:start position:0%
+but it's easier to think about how
+ 
+
+ align:start position:0%
+but it's easier to think about how
+Wilson line transforms and then think
+
+ align:start position:0%
+Wilson line transforms and then think
+ 
+
+ align:start position:0%
+Wilson line transforms and then think
+about how it should transform under
+
+ align:start position:0%
+about how it should transform under
+ 
+
+ align:start position:0%
+about how it should transform under
+cinear then just sort of go through the
+
+ align:start position:0%
+cinear then just sort of go through the
+ 
+
+ align:start position:0%
+cinear then just sort of go through the
+route and impose this
+
+ align:start position:0%
+route and impose this
+ 
+
+ align:start position:0%
+route and impose this
+condition okay so let's come back now to
+
+ align:start position:0%
+condition okay so let's come back now to
+ 
+
+ align:start position:0%
+condition okay so let's come back now to
+our our full current which was this that
+
+ align:start position:0%
+our our full current which was this that
+ 
+
+ align:start position:0%
+our our full current which was this that
+had the Wilson line in it and now if you
+
+ align:start position:0%
+had the Wilson line in it and now if you
+ 
+
+ align:start position:0%
+had the Wilson line in it and now if you
+ask how it transforms under UC you see
+
+ align:start position:0%
+ask how it transforms under UC you see
+ 
+
+ align:start position:0%
+ask how it transforms under UC you see
+what's going to
+
+ align:start position:0%
+what's going to
+ 
+
+ align:start position:0%
+what's going to
+happen you get UC
+
+ align:start position:0%
+happen you get UC
+ 
+
+ align:start position:0%
+happen you get UC
+dagger UC and the ultrasoft guy doesn't
+
+ align:start position:0%
+dagger UC and the ultrasoft guy doesn't
+ 
+
+ align:start position:0%
+dagger UC and the ultrasoft guy doesn't
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+and then these cancel so it's invariant
+
+ align:start position:0%
+and then these cancel so it's invariant
+ 
+
+ align:start position:0%
+and then these cancel so it's invariant
+under the Transformations that have
+
+ align:start position:0%
+under the Transformations that have
+ 
+
+ align:start position:0%
+under the Transformations that have
+momenta of order the ultrasoft have
+
+ align:start position:0%
+momenta of order the ultrasoft have
+ 
+
+ align:start position:0%
+momenta of order the ultrasoft have
+momenta of order the cinear scale
+
+ align:start position:0%
+momenta of order the cinear scale
+ 
+
+ align:start position:0%
+momenta of order the cinear scale
+there's two objects in this thing that
+
+ align:start position:0%
+there's two objects in this thing that
+ 
+
+ align:start position:0%
+there's two objects in this thing that
+have momenta that can be of that size
+
+ align:start position:0%
+have momenta that can be of that size
+ 
+
+ align:start position:0%
+have momenta that can be of that size
+the gluons they're in W in this cinear
+
+ align:start position:0%
+the gluons they're in W in this cinear
+ 
+
+ align:start position:0%
+the gluons they're in W in this cinear
+Quark field both of those things
+
+ align:start position:0%
+Quark field both of those things
+ 
+
+ align:start position:0%
+Quark field both of those things
+transform but that transformation
+
+ align:start position:0%
+transform but that transformation
+ 
+
+ align:start position:0%
+transform but that transformation
+cancels between the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things whoops that's important thank you
+
+ align:start position:0%
+things whoops that's important thank you
+ 
+
+ align:start position:0%
+things whoops that's important thank you
+and then under an ultrasoft
+
+ align:start position:0%
+and then under an ultrasoft
+ 
+
+ align:start position:0%
+and then under an ultrasoft
+transformation we can also transform
+
+ align:start position:0%
+transformation we can also transform
+ 
+
+ align:start position:0%
+transformation we can also transform
+this guy and then everybody's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transforming gamma of course is not got
+
+ align:start position:0%
+transforming gamma of course is not got
+ 
+
+ align:start position:0%
+transforming gamma of course is not got
+color
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indices and again it's gaug
+
+ align:start position:0%
+indices and again it's gaug
+ 
+
+ align:start position:0%
+indices and again it's gaug
+invariant okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+missed the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gamma gamma's not so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important all right so this current that
+
+ align:start position:0%
+important all right so this current that
+ 
+
+ align:start position:0%
+important all right so this current that
+we derived earlier is actually in varing
+
+ align:start position:0%
+we derived earlier is actually in varing
+ 
+
+ align:start position:0%
+we derived earlier is actually in varing
+under two different types of symmetries
+
+ align:start position:0%
+under two different types of symmetries
+ 
+
+ align:start position:0%
+under two different types of symmetries
+which are really momentum SP splitting
+
+ align:start position:0%
+which are really momentum SP splitting
+ 
+
+ align:start position:0%
+which are really momentum SP splitting
+of a standard gauge symmetry into pieces
+
+ align:start position:0%
+of a standard gauge symmetry into pieces
+ 
+
+ align:start position:0%
+of a standard gauge symmetry into pieces
+where we have a large momenta and pieces
+
+ align:start position:0%
+where we have a large momenta and pieces
+ 
+
+ align:start position:0%
+where we have a large momenta and pieces
+where we have these Ultra larger momenta
+
+ align:start position:0%
+where we have these Ultra larger momenta
+ 
+
+ align:start position:0%
+where we have these Ultra larger momenta
+cinear momenta and pieces where we have
+
+ align:start position:0%
+cinear momenta and pieces where we have
+ 
+
+ align:start position:0%
+cinear momenta and pieces where we have
+a smaller momenta this ultrasoft momenta
+
+ align:start position:0%
+a smaller momenta this ultrasoft momenta
+ 
+
+ align:start position:0%
+a smaller momenta this ultrasoft momenta
+but both of these types of momenta are
+
+ align:start position:0%
+but both of these types of momenta are
+ 
+
+ align:start position:0%
+but both of these types of momenta are
+momenta that we're allowing inside the
+
+ align:start position:0%
+momenta that we're allowing inside the
+ 
+
+ align:start position:0%
+momenta that we're allowing inside the
+effective the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah try to
+
+ align:start position:0%
+yeah try to
+ 
+
+ align:start position:0%
+yeah try to
+remember was
+
+ align:start position:0%
+remember was
+ 
+
+ align:start position:0%
+remember was
+for yeah yeah the the momentum of the
+
+ align:start position:0%
+for yeah yeah the the momentum of the
+ 
+
+ align:start position:0%
+for yeah yeah the the momentum of the
+ultrasoft the the the ultrasoft momentum
+
+ align:start position:0%
+ultrasoft the the the ultrasoft momentum
+ 
+
+ align:start position:0%
+ultrasoft the the the ultrasoft momentum
+of the cinear Quark you pulled out MV
+
+ align:start position:0%
+of the cinear Quark you pulled out MV
+ 
+
+ align:start position:0%
+of the cinear Quark you pulled out MV
+and then the remaining part was
+
+ align:start position:0%
+and then the remaining part was
+ 
+
+ align:start position:0%
+and then the remaining part was
+ultrasoft in the discussion for this
+
+ align:start position:0%
+ultrasoft in the discussion for this
+ 
+
+ align:start position:0%
+ultrasoft in the discussion for this
+particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so it's the Wilson line the moral
+
+ align:start position:0%
+right so it's the Wilson line the moral
+ 
+
+ align:start position:0%
+right so it's the Wilson line the moral
+of this is that what we were doing
+
+ align:start position:0%
+of this is that what we were doing
+ 
+
+ align:start position:0%
+of this is that what we were doing
+before where we're integrating out those
+
+ align:start position:0%
+before where we're integrating out those
+ 
+
+ align:start position:0%
+before where we're integrating out those
+cinear gluons is actually connected to
+
+ align:start position:0%
+cinear gluons is actually connected to
+ 
+
+ align:start position:0%
+cinear gluons is actually connected to
+gauge symmetry because without that
+
+ align:start position:0%
+gauge symmetry because without that
+ 
+
+ align:start position:0%
+gauge symmetry because without that
+Wilson line we wouldn't have a gauge a
+
+ align:start position:0%
+Wilson line we wouldn't have a gauge a
+ 
+
+ align:start position:0%
+Wilson line we wouldn't have a gauge a
+result that's invariant under the type
+
+ align:start position:0%
+result that's invariant under the type
+ 
+
+ align:start position:0%
+result that's invariant under the type
+of gauge simat we've been talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about so this Wilson line carries these
+
+ align:start position:0%
+about so this Wilson line carries these
+ 
+
+ align:start position:0%
+about so this Wilson line carries these
+n colinear
+
+ align:start position:0%
+n colinear
+ 
+
+ align:start position:0%
+n colinear
+gluons and those gluons would be the
+
+ align:start position:0%
+gluons and those gluons would be the
+ 
+
+ align:start position:0%
+gluons and those gluons would be the
+gluons that in the full Theory would
+
+ align:start position:0%
+gluons that in the full Theory would
+ 
+
+ align:start position:0%
+gluons that in the full Theory would
+give you a gauge symmetric result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they would
+
+ align:start position:0%
+they would
+ 
+
+ align:start position:0%
+they would
+combine they would be the attachments to
+
+ align:start position:0%
+combine they would be the attachments to
+ 
+
+ align:start position:0%
+combine they would be the attachments to
+the heavy quk that attach that combine
+
+ align:start position:0%
+the heavy quk that attach that combine
+ 
+
+ align:start position:0%
+the heavy quk that attach that combine
+with attachments to the light Quark to
+
+ align:start position:0%
+with attachments to the light Quark to
+ 
+
+ align:start position:0%
+with attachments to the light Quark to
+give you sort of a result that's
+
+ align:start position:0%
+give you sort of a result that's
+ 
+
+ align:start position:0%
+give you sort of a result that's
+invariant if you looked at w identities
+
+ align:start position:0%
+invariant if you looked at w identities
+ 
+
+ align:start position:0%
+invariant if you looked at w identities
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example but in the effective Theory
+
+ align:start position:0%
+example but in the effective Theory
+ 
+
+ align:start position:0%
+example but in the effective Theory
+these are just put into a Wilson line
+
+ align:start position:0%
+these are just put into a Wilson line
+ 
+
+ align:start position:0%
+these are just put into a Wilson line
+because that's the leading order way
+
+ align:start position:0%
+because that's the leading order way
+ 
+
+ align:start position:0%
+because that's the leading order way
+that they they can show up but still we
+
+ align:start position:0%
+that they they can show up but still we
+ 
+
+ align:start position:0%
+that they they can show up but still we
+have a gauge and variant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer so the Wilson line is really
+
+ align:start position:0%
+answer so the Wilson line is really
+ 
+
+ align:start position:0%
+answer so the Wilson line is really
+needed for the gauge
+
+ align:start position:0%
+needed for the gauge
+ 
+
+ align:start position:0%
+needed for the gauge
+Symmetry and finally the
+
+ align:start position:0%
+Symmetry and finally the
+ 
+
+ align:start position:0%
+Symmetry and finally the
+ultrasofts as kind of can be clear from
+
+ align:start position:0%
+ultrasofts as kind of can be clear from
+ 
+
+ align:start position:0%
+ultrasofts as kind of can be clear from
+the notation the ultrasofts can just as
+
+ align:start position:0%
+the notation the ultrasofts can just as
+ 
+
+ align:start position:0%
+the notation the ultrasofts can just as
+well include the global
+
+ align:start position:0%
+well include the global
+ 
+
+ align:start position:0%
+well include the global
+transformation if you
+
+ align:start position:0%
+transformation if you
+ 
+
+ align:start position:0%
+transformation if you
+like so we don't really need three we
+
+ align:start position:0%
+like so we don't really need three we
+ 
+
+ align:start position:0%
+like so we don't really need three we
+could put the global back with the
+
+ align:start position:0%
+could put the global back with the
+ 
+
+ align:start position:0%
+could put the global back with the
+ultrasofts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we just have
+
+ align:start position:0%
+then we just have
+ 
+
+ align:start position:0%
+then we just have
+two all right so that's our symmetry
+
+ align:start position:0%
+two all right so that's our symmetry
+ 
+
+ align:start position:0%
+two all right so that's our symmetry
+that's kind of an example of how it
+
+ align:start position:0%
+that's kind of an example of how it
+ 
+
+ align:start position:0%
+that's kind of an example of how it
+works now let's talk about covariant
+
+ align:start position:0%
+works now let's talk about covariant
+ 
+
+ align:start position:0%
+works now let's talk about covariant
+derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so gauge symmetry ties together regular
+
+ align:start position:0%
+so gauge symmetry ties together regular
+ 
+
+ align:start position:0%
+so gauge symmetry ties together regular
+derivatives with the gauge
+
+ align:start position:0%
+derivatives with the gauge
+ 
+
+ align:start position:0%
+derivatives with the gauge
+field and here what it ties together are
+
+ align:start position:0%
+field and here what it ties together are
+ 
+
+ align:start position:0%
+field and here what it ties together are
+the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things so because of the treatment of
+
+ align:start position:0%
+things so because of the treatment of
+ 
+
+ align:start position:0%
+things so because of the treatment of
+the a ultrasoft field as a background it
+
+ align:start position:0%
+the a ultrasoft field as a background it
+ 
+
+ align:start position:0%
+the a ultrasoft field as a background it
+actually ties together both of these
+
+ align:start position:0%
+actually ties together both of these
+ 
+
+ align:start position:0%
+actually ties together both of these
+things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then it kind of does what you expect
+
+ align:start position:0%
+and then it kind of does what you expect
+ 
+
+ align:start position:0%
+and then it kind of does what you expect
+in the cinear sector it ties together
+
+ align:start position:0%
+in the cinear sector it ties together
+ 
+
+ align:start position:0%
+in the cinear sector it ties together
+the derivative with the gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field and if you're acting on ultrasoft
+
+ align:start position:0%
+field and if you're acting on ultrasoft
+ 
+
+ align:start position:0%
+field and if you're acting on ultrasoft
+fields then there's an ultrasoft coant
+
+ align:start position:0%
+fields then there's an ultrasoft coant
+ 
+
+ align:start position:0%
+fields then there's an ultrasoft coant
+derivative which is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so now you can ask the question if
+
+ align:start position:0%
+that so now you can ask the question if
+ 
+
+ align:start position:0%
+that so now you can ask the question if
+I just had this gauge symmetry which is
+
+ align:start position:0%
+I just had this gauge symmetry which is
+ 
+
+ align:start position:0%
+I just had this gauge symmetry which is
+going to force me to use covariant
+
+ align:start position:0%
+going to force me to use covariant
+ 
+
+ align:start position:0%
+going to force me to use covariant
+derivativ which I was already kind of
+
+ align:start position:0%
+derivativ which I was already kind of
+ 
+
+ align:start position:0%
+derivativ which I was already kind of
+thinking ahead to when I wrote down the
+
+ align:start position:0%
+thinking ahead to when I wrote down the
+ 
+
+ align:start position:0%
+thinking ahead to when I wrote down the
+line earlier right we already wrote it
+
+ align:start position:0%
+line earlier right we already wrote it
+ 
+
+ align:start position:0%
+line earlier right we already wrote it
+in terms of these kind of objects so it
+
+ align:start position:0%
+in terms of these kind of objects so it
+ 
+
+ align:start position:0%
+in terms of these kind of objects so it
+seems like we're good to go so you can
+
+ align:start position:0%
+seems like we're good to go so you can
+ 
+
+ align:start position:0%
+seems like we're good to go so you can
+ask the question if I just have power
+
+ align:start position:0%
+ask the question if I just have power
+ 
+
+ align:start position:0%
+ask the question if I just have power
+counting the CN that I we we decided
+
+ align:start position:0%
+counting the CN that I we we decided
+ 
+
+ align:start position:0%
+counting the CN that I we we decided
+work on EOS and and gauge symmetry is
+
+ align:start position:0%
+work on EOS and and gauge symmetry is
+ 
+
+ align:start position:0%
+work on EOS and and gauge symmetry is
+that enough am I done do I have
+
+ align:start position:0%
+that enough am I done do I have
+ 
+
+ align:start position:0%
+that enough am I done do I have
+everything I need for the leading order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lran so power told us that we had this
+
+ align:start position:0%
+lran so power told us that we had this
+ 
+
+ align:start position:0%
+lran so power told us that we had this
+type of derivative and that we could
+
+ align:start position:0%
+type of derivative and that we could
+ 
+
+ align:start position:0%
+type of derivative and that we could
+have two of these per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivatives okay so those are the two
+
+ align:start position:0%
+derivatives okay so those are the two
+ 
+
+ align:start position:0%
+derivatives okay so those are the two
+type of terms we were getting and
+
+ align:start position:0%
+type of terms we were getting and
+ 
+
+ align:start position:0%
+type of terms we were getting and
+there's no other order Lambda
+
+ align:start position:0%
+there's no other order Lambda
+ 
+
+ align:start position:0%
+there's no other order Lambda
+operators or order Lambda squar other
+
+ align:start position:0%
+operators or order Lambda squar other
+ 
+
+ align:start position:0%
+operators or order Lambda squar other
+sorry there's no other order Lambda
+
+ align:start position:0%
+sorry there's no other order Lambda
+ 
+
+ align:start position:0%
+sorry there's no other order Lambda
+squared field
+
+ align:start position:0%
+squared field
+ 
+
+ align:start position:0%
+squared field
+structures that would be that would have
+
+ align:start position:0%
+structures that would be that would have
+ 
+
+ align:start position:0%
+structures that would be that would have
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+dimensions and
+
+ align:start position:0%
+dimensions and
+ 
+
+ align:start position:0%
+dimensions and
+that could do the job so these are the
+
+ align:start position:0%
+that could do the job so these are the
+ 
+
+ align:start position:0%
+that could do the job so these are the
+really the only two that we have to
+
+ align:start position:0%
+really the only two that we have to
+ 
+
+ align:start position:0%
+really the only two that we have to
+think about so you could try to think
+
+ align:start position:0%
+think about so you could try to think
+ 
+
+ align:start position:0%
+think about so you could try to think
+about you know maybe I can have
+
+ align:start position:0%
+about you know maybe I can have
+ 
+
+ align:start position:0%
+about you know maybe I can have
+something with some additional n bars
+
+ align:start position:0%
+something with some additional n bars
+ 
+
+ align:start position:0%
+something with some additional n bars
+floating
+
+ align:start position:0%
+floating
+ 
+
+ align:start position:0%
+floating
+around but really it boils down since
+
+ align:start position:0%
+around but really it boils down since
+ 
+
+ align:start position:0%
+around but really it boils down since
+you need to get a Lambda squar you need
+
+ align:start position:0%
+you need to get a Lambda squar you need
+ 
+
+ align:start position:0%
+you need to get a Lambda squar you need
+either two per
+
+ align:start position:0%
+either two per
+ 
+
+ align:start position:0%
+either two per
+derivatives the per deriv you need two
+
+ align:start position:0%
+derivatives the per deriv you need two
+ 
+
+ align:start position:0%
+derivatives the per deriv you need two
+of them because of the you still have a
+
+ align:start position:0%
+of them because of the you still have a
+ 
+
+ align:start position:0%
+of them because of the you still have a
+rotation symmetry around the direction
+
+ align:start position:0%
+rotation symmetry around the direction
+ 
+
+ align:start position:0%
+rotation symmetry around the direction
+of motion and you need to or you could
+
+ align:start position:0%
+of motion and you need to or you could
+ 
+
+ align:start position:0%
+of motion and you need to or you could
+have an
+
+ align:start position:0%
+have an
+ 
+
+ align:start position:0%
+have an
+N.D but there is is one operator that is
+
+ align:start position:0%
+N.D but there is is one operator that is
+ 
+
+ align:start position:0%
+N.D but there is is one operator that is
+not rolled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out by gauge symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alone and that isn't this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator when we wrote the
+
+ align:start position:0%
+operator when we wrote the
+ 
+
+ align:start position:0%
+operator when we wrote the
+operator we had d slash d slash but
+
+ align:start position:0%
+operator we had d slash d slash but
+ 
+
+ align:start position:0%
+operator we had d slash d slash but
+nothing stops me from doing something
+
+ align:start position:0%
+nothing stops me from doing something
+ 
+
+ align:start position:0%
+nothing stops me from doing something
+simpler in some way by just taking the D
+
+ align:start position:0%
+simpler in some way by just taking the D
+ 
+
+ align:start position:0%
+simpler in some way by just taking the D
+perss and Contracting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them like that that's a different
+
+ align:start position:0%
+them like that that's a different
+ 
+
+ align:start position:0%
+them like that that's a different
+operator and the d/d SL operator that we
+
+ align:start position:0%
+operator and the d/d SL operator that we
+ 
+
+ align:start position:0%
+operator and the d/d SL operator that we
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+before whoops only one of
+
+ align:start position:0%
+before whoops only one of
+ 
+
+ align:start position:0%
+before whoops only one of
+those okay so this operator is a
+
+ align:start position:0%
+those okay so this operator is a
+ 
+
+ align:start position:0%
+those okay so this operator is a
+different operator in a priority you
+
+ align:start position:0%
+different operator in a priority you
+ 
+
+ align:start position:0%
+different operator in a priority you
+could say well do Loop Corrections
+
+ align:start position:0%
+could say well do Loop Corrections
+ 
+
+ align:start position:0%
+could say well do Loop Corrections
+generate this operator which is
+
+ align:start position:0%
+generate this operator which is
+ 
+
+ align:start position:0%
+generate this operator which is
+different than the d/d SL
+
+ align:start position:0%
+different than the d/d SL
+ 
+
+ align:start position:0%
+different than the d/d SL
+operator the answer is no
+
+ align:start position:0%
+operator the answer is no
+ 
+
+ align:start position:0%
+operator the answer is no
+actually but so far what we've done it's
+
+ align:start position:0%
+actually but so far what we've done it's
+ 
+
+ align:start position:0%
+actually but so far what we've done it's
+not enough to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so we need actually this other
+
+ align:start position:0%
+that so we need actually this other
+ 
+
+ align:start position:0%
+that so we need actually this other
+symmetry that I alluded to the
+
+ align:start position:0%
+symmetry that I alluded to the
+ 
+
+ align:start position:0%
+symmetry that I alluded to the
+reparameterization
+
+ align:start position:0%
+reparameterization
+ 
+
+ align:start position:0%
+reparameterization
+invariance and that will actually rule
+
+ align:start position:0%
+invariance and that will actually rule
+ 
+
+ align:start position:0%
+invariance and that will actually rule
+out this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy so what's
+
+ align:start position:0%
+guy so what's
+ 
+
+ align:start position:0%
+guy so what's
+RPI well when we formulated this Theory
+
+ align:start position:0%
+RPI well when we formulated this Theory
+ 
+
+ align:start position:0%
+RPI well when we formulated this Theory
+we needed a direction for the cinear
+
+ align:start position:0%
+we needed a direction for the cinear
+ 
+
+ align:start position:0%
+we needed a direction for the cinear
+line for the cinear particles n and then
+
+ align:start position:0%
+line for the cinear particles n and then
+ 
+
+ align:start position:0%
+line for the cinear particles n and then
+we needed an auxiliary Vector n Bar and
+
+ align:start position:0%
+we needed an auxiliary Vector n Bar and
+ 
+
+ align:start position:0%
+we needed an auxiliary Vector n Bar and
+we formulated the whole setup in terms
+
+ align:start position:0%
+we formulated the whole setup in terms
+ 
+
+ align:start position:0%
+we formulated the whole setup in terms
+of this n and n bar but having vectors
+
+ align:start position:0%
+of this n and n bar but having vectors
+ 
+
+ align:start position:0%
+of this n and n bar but having vectors
+like that that we write down that breaks
+
+ align:start position:0%
+like that that we write down that breaks
+ 
+
+ align:start position:0%
+like that that we write down that breaks
+Loren in variance in the same way that
+
+ align:start position:0%
+Loren in variance in the same way that
+ 
+
+ align:start position:0%
+Loren in variance in the same way that
+specifying V mu in
+
+ align:start position:0%
+specifying V mu in
+ 
+
+ align:start position:0%
+specifying V mu in
+h2t breaks Loren inv
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variance so if you say that mu mu new is
+
+ align:start position:0%
+variance so if you say that mu mu new is
+ 
+
+ align:start position:0%
+variance so if you say that mu mu new is
+the set of Loren Transformations the
+
+ align:start position:0%
+the set of Loren Transformations the
+ 
+
+ align:start position:0%
+the set of Loren Transformations the
+usual six generators that are anti-
+
+ align:start position:0%
+usual six generators that are anti-
+ 
+
+ align:start position:0%
+usual six generators that are anti-
+symmetric then the ones that are broken
+
+ align:start position:0%
+symmetric then the ones that are broken
+ 
+
+ align:start position:0%
+symmetric then the ones that are broken
+are these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones and there's five of
+
+ align:start position:0%
+ones and there's five of
+ 
+
+ align:start position:0%
+ones and there's five of
+them and the one that's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broken is this
+
+ align:start position:0%
+broken is this
+ 
+
+ align:start position:0%
+broken is this
+one which corresponds to rotations about
+
+ align:start position:0%
+one which corresponds to rotations about
+ 
+
+ align:start position:0%
+one which corresponds to rotations about
+the three Axis or the axis specified by
+
+ align:start position:0%
+the three Axis or the axis specified by
+ 
+
+ align:start position:0%
+the three Axis or the axis specified by
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so those rotations would would act
+
+ align:start position:0%
+okay so those rotations would would act
+ 
+
+ align:start position:0%
+okay so those rotations would would act
+in sort of the components of these guys
+
+ align:start position:0%
+in sort of the components of these guys
+ 
+
+ align:start position:0%
+in sort of the components of these guys
+that are zero if you like so there's no
+
+ align:start position:0%
+that are zero if you like so there's no
+ 
+
+ align:start position:0%
+that are zero if you like so there's no
+issue there and these guys are the guys
+
+ align:start position:0%
+issue there and these guys are the guys
+ 
+
+ align:start position:0%
+issue there and these guys are the guys
+that are are connected to the pieces
+
+ align:start position:0%
+that are are connected to the pieces
+ 
+
+ align:start position:0%
+that are are connected to the pieces
+that were nonzero in
+
+ align:start position:0%
+that were nonzero in
+ 
+
+ align:start position:0%
+that were nonzero in
+general so there's going to be a larger
+
+ align:start position:0%
+general so there's going to be a larger
+ 
+
+ align:start position:0%
+general so there's going to be a larger
+because there's sort of five things here
+
+ align:start position:0%
+because there's sort of five things here
+ 
+
+ align:start position:0%
+because there's sort of five things here
+and because there's there's two vectors
+
+ align:start position:0%
+and because there's there's two vectors
+ 
+
+ align:start position:0%
+and because there's there's two vectors
+it's going to be a larger set of
+
+ align:start position:0%
+it's going to be a larger set of
+ 
+
+ align:start position:0%
+it's going to be a larger set of
+reparameterization symmetries than
+
+ align:start position:0%
+reparameterization symmetries than
+ 
+
+ align:start position:0%
+reparameterization symmetries than
+HQ and there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually first talk about just the n and
+
+ align:start position:0%
+actually first talk about just the n and
+ 
+
+ align:start position:0%
+actually first talk about just the n and
+n Bar themselves there's three types of
+
+ align:start position:0%
+n Bar themselves there's three types of
+ 
+
+ align:start position:0%
+n Bar themselves there's three types of
+reparametrization invariance that would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leave n^2 equal 0 and bar^ S equal 0 and
+
+ align:start position:0%
+leave n^2 equal 0 and bar^ S equal 0 and
+ 
+
+ align:start position:0%
+leave n^2 equal 0 and bar^ S equal 0 and
+n. n Bar = 2 and those were the formulas
+
+ align:start position:0%
+n. n Bar = 2 and those were the formulas
+ 
+
+ align:start position:0%
+n. n Bar = 2 and those were the formulas
+that we using over and over again really
+
+ align:start position:0%
+that we using over and over again really
+ 
+
+ align:start position:0%
+that we using over and over again really
+everything else was just
+
+ align:start position:0%
+everything else was just
+ 
+
+ align:start position:0%
+everything else was just
+convention
+
+ align:start position:0%
+convention
+ 
+
+ align:start position:0%
+convention
+okay so what are those three
+
+ align:start position:0%
+okay so what are those three
+ 
+
+ align:start position:0%
+okay so what are those three
+types well we could take n and we could
+
+ align:start position:0%
+types well we could take n and we could
+ 
+
+ align:start position:0%
+types well we could take n and we could
+change it by some amount in the per
+
+ align:start position:0%
+change it by some amount in the per
+ 
+
+ align:start position:0%
+change it by some amount in the per
+Direction and leave n Bar unchanged and
+
+ align:start position:0%
+Direction and leave n Bar unchanged and
+ 
+
+ align:start position:0%
+Direction and leave n Bar unchanged and
+since Nar do something per is zero that
+
+ align:start position:0%
+since Nar do something per is zero that
+ 
+
+ align:start position:0%
+since Nar do something per is zero that
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+a that would satisfy this or we could do
+
+ align:start position:0%
+a that would satisfy this or we could do
+ 
+
+ align:start position:0%
+a that would satisfy this or we could do
+the opposite that would be type
+
+ align:start position:0%
+the opposite that would be type
+ 
+
+ align:start position:0%
+the opposite that would be type
+two so it don't change n
+
+ align:start position:0%
+two so it don't change n
+ 
+
+ align:start position:0%
+two so it don't change n
+and change in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar and so this is two Transformations
+
+ align:start position:0%
+bar and so this is two Transformations
+ 
+
+ align:start position:0%
+bar and so this is two Transformations
+there's two things specified by this
+
+ align:start position:0%
+there's two things specified by this
+ 
+
+ align:start position:0%
+there's two things specified by this
+this per guy and two here and then
+
+ align:start position:0%
+this per guy and two here and then
+ 
+
+ align:start position:0%
+this per guy and two here and then
+there's one more which is called
+
+ align:start position:0%
+there's one more which is called
+ 
+
+ align:start position:0%
+there's one more which is called
+three and this
+
+ align:start position:0%
+three and this
+ 
+
+ align:start position:0%
+three and this
+one let me write like this it's a
+
+ align:start position:0%
+one let me write like this it's a
+ 
+
+ align:start position:0%
+one let me write like this it's a
+simultaneous transformation of these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guys where I just do a multip
+
+ align:start position:0%
+guys where I just do a multip
+ 
+
+ align:start position:0%
+guys where I just do a multip
+multiplicative Factor well
+
+ align:start position:0%
+multiplicative Factor well
+ 
+
+ align:start position:0%
+multiplicative Factor well
+multiplicative factor is not going to
+
+ align:start position:0%
+multiplicative factor is not going to
+ 
+
+ align:start position:0%
+multiplicative factor is not going to
+change the fact that's the square of
+
+ align:start position:0%
+change the fact that's the square of
+ 
+
+ align:start position:0%
+change the fact that's the square of
+something zero the place where they
+
+ align:start position:0%
+something zero the place where they
+ 
+
+ align:start position:0%
+something zero the place where they
+where the normalization comes in is this
+
+ align:start position:0%
+where the normalization comes in is this
+ 
+
+ align:start position:0%
+where the normalization comes in is this
+n.n bar and if I just rescale them both
+
+ align:start position:0%
+n.n bar and if I just rescale them both
+ 
+
+ align:start position:0%
+n.n bar and if I just rescale them both
+by an opposite amount then I remain that
+
+ align:start position:0%
+by an opposite amount then I remain that
+ 
+
+ align:start position:0%
+by an opposite amount then I remain that
+remains satisfied as
+
+ align:start position:0%
+remains satisfied as
+ 
+
+ align:start position:0%
+remains satisfied as
+well so I formulated this in terms of an
+
+ align:start position:0%
+well so I formulated this in terms of an
+ 
+
+ align:start position:0%
+well so I formulated this in terms of an
+INF I'm going to think about this as an
+
+ align:start position:0%
+INF I'm going to think about this as an
+ 
+
+ align:start position:0%
+INF I'm going to think about this as an
+infantes transformation for Delta per
+
+ align:start position:0%
+infantes transformation for Delta per
+ 
+
+ align:start position:0%
+infantes transformation for Delta per
+infantes for Epsilon per I could also
+
+ align:start position:0%
+infantes for Epsilon per I could also
+ 
+
+ align:start position:0%
+infantes for Epsilon per I could also
+expand this exponential and think of it
+
+ align:start position:0%
+expand this exponential and think of it
+ 
+
+ align:start position:0%
+expand this exponential and think of it
+as infal but it's even the finite ones
+
+ align:start position:0%
+as infal but it's even the finite ones
+ 
+
+ align:start position:0%
+as infal but it's even the finite ones
+easier so let's just think of the finite
+
+ align:start position:0%
+easier so let's just think of the finite
+ 
+
+ align:start position:0%
+easier so let's just think of the finite
+transformation in the last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one now this is an effective Theory so
+
+ align:start position:0%
+one now this is an effective Theory so
+ 
+
+ align:start position:0%
+one now this is an effective Theory so
+whenever we think about Transformations
+
+ align:start position:0%
+whenever we think about Transformations
+ 
+
+ align:start position:0%
+whenever we think about Transformations
+we should think about power counting we
+
+ align:start position:0%
+we should think about power counting we
+ 
+
+ align:start position:0%
+we should think about power counting we
+just did to spend a lot of time thinking
+
+ align:start position:0%
+just did to spend a lot of time thinking
+ 
+
+ align:start position:0%
+just did to spend a lot of time thinking
+about that for gauge Symmetry and we
+
+ align:start position:0%
+about that for gauge Symmetry and we
+ 
+
+ align:start position:0%
+about that for gauge Symmetry and we
+should think about power counting here
+
+ align:start position:0%
+should think about power counting here
+ 
+
+ align:start position:0%
+should think about power counting here
+too did you have a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what yeah so well just about to talk
+
+ align:start position:0%
+what yeah so well just about to talk
+ 
+
+ align:start position:0%
+what yeah so well just about to talk
+about how how big the ACT how big things
+
+ align:start position:0%
+about how how big the ACT how big things
+ 
+
+ align:start position:0%
+about how how big the ACT how big things
+can be so
+
+ align:start position:0%
+can be so
+ 
+
+ align:start position:0%
+can be so
+the power counting that's the right
+
+ align:start position:0%
+the power counting that's the right
+ 
+
+ align:start position:0%
+the power counting that's the right
+power counting for these guys so these
+
+ align:start position:0%
+power counting for these guys so these
+ 
+
+ align:start position:0%
+power counting for these guys so these
+things are infal or finite but they also
+
+ align:start position:0%
+things are infal or finite but they also
+ 
+
+ align:start position:0%
+things are infal or finite but they also
+have some counting in a different space
+
+ align:start position:0%
+have some counting in a different space
+ 
+
+ align:start position:0%
+have some counting in a different space
+which is the power counting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space and the right power counting for
+
+ align:start position:0%
+space and the right power counting for
+ 
+
+ align:start position:0%
+space and the right power counting for
+these guys is that is as follows so this
+
+ align:start position:0%
+these guys is that is as follows so this
+ 
+
+ align:start position:0%
+these guys is that is as follows so this
+means I can make arbitrarily large
+
+ align:start position:0%
+means I can make arbitrarily large
+ 
+
+ align:start position:0%
+means I can make arbitrarily large
+transformations in a power counting
+
+ align:start position:0%
+transformations in a power counting
+ 
+
+ align:start position:0%
+transformations in a power counting
+sense of type two and type three there's
+
+ align:start position:0%
+sense of type two and type three there's
+ 
+
+ align:start position:0%
+sense of type two and type three there's
+no constraint that's what this means so
+
+ align:start position:0%
+no constraint that's what this means so
+ 
+
+ align:start position:0%
+no constraint that's what this means so
+maybe that's easier to swallow this one
+
+ align:start position:0%
+maybe that's easier to swallow this one
+ 
+
+ align:start position:0%
+maybe that's easier to swallow this one
+there is a constraint and the reason
+
+ align:start position:0%
+there is a constraint and the reason
+ 
+
+ align:start position:0%
+there is a constraint and the reason
+that you can think of there being a
+
+ align:start position:0%
+that you can think of there being a
+ 
+
+ align:start position:0%
+that you can think of there being a
+constraint we can I can give you a
+
+ align:start position:0%
+constraint we can I can give you a
+ 
+
+ align:start position:0%
+constraint we can I can give you a
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+example and then you'll see how you
+
+ align:start position:0%
+example and then you'll see how you
+ 
+
+ align:start position:0%
+example and then you'll see how you
+would derive the other things as well so
+
+ align:start position:0%
+would derive the other things as well so
+ 
+
+ align:start position:0%
+would derive the other things as well so
+think of n.p if you transform n.p that
+
+ align:start position:0%
+think of n.p if you transform n.p that
+ 
+
+ align:start position:0%
+think of n.p if you transform n.p that
+becomes n do think of this as n mu P
+
+ align:start position:0%
+becomes n do think of this as n mu P
+ 
+
+ align:start position:0%
+becomes n do think of this as n mu P
+mu that becomes n n mu P mu plus Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p.p so this is order Lambda squ so this
+
+ align:start position:0%
+p.p so this is order Lambda squ so this
+ 
+
+ align:start position:0%
+p.p so this is order Lambda squ so this
+better be order Lambda squ but this
+
+ align:start position:0%
+better be order Lambda squ but this
+ 
+
+ align:start position:0%
+better be order Lambda squ but this
+momentum here is order Lambda so you
+
+ align:start position:0%
+momentum here is order Lambda so you
+ 
+
+ align:start position:0%
+momentum here is order Lambda so you
+need to have a power counting for the
+
+ align:start position:0%
+need to have a power counting for the
+ 
+
+ align:start position:0%
+need to have a power counting for the
+Delta per that makes it of order
+
+ align:start position:0%
+Delta per that makes it of order
+ 
+
+ align:start position:0%
+Delta per that makes it of order
+Lambda in order to keep the transform
+
+ align:start position:0%
+Lambda in order to keep the transform
+ 
+
+ align:start position:0%
+Lambda in order to keep the transform
+guy the same size as the guy you started
+
+ align:start position:0%
+guy the same size as the guy you started
+ 
+
+ align:start position:0%
+guy the same size as the guy you started
+with because I don't want to consider
+
+ align:start position:0%
+with because I don't want to consider
+ 
+
+ align:start position:0%
+with because I don't want to consider
+Transformations that would take me away
+
+ align:start position:0%
+Transformations that would take me away
+ 
+
+ align:start position:0%
+Transformations that would take me away
+from my power counting that would
+
+ align:start position:0%
+from my power counting that would
+ 
+
+ align:start position:0%
+from my power counting that would
+violate it so the imposing that this
+
+ align:start position:0%
+violate it so the imposing that this
+ 
+
+ align:start position:0%
+violate it so the imposing that this
+thing is a water Lambda
+
+ align:start position:0%
+thing is a water Lambda
+ 
+
+ align:start position:0%
+thing is a water Lambda
+squar says that this is true if you go
+
+ align:start position:0%
+squar says that this is true if you go
+ 
+
+ align:start position:0%
+squar says that this is true if you go
+through the same logic for The Other
+
+ align:start position:0%
+through the same logic for The Other
+ 
+
+ align:start position:0%
+through the same logic for The Other
+Guys well you know the Nar component was
+
+ align:start position:0%
+Guys well you know the Nar component was
+ 
+
+ align:start position:0%
+Guys well you know the Nar component was
+order Lambda 0er so you can make the
+
+ align:start position:0%
+order Lambda 0er so you can make the
+ 
+
+ align:start position:0%
+order Lambda 0er so you can make the
+Epsilon purple order Lambda 0o doesn't
+
+ align:start position:0%
+Epsilon purple order Lambda 0o doesn't
+ 
+
+ align:start position:0%
+Epsilon purple order Lambda 0o doesn't
+cost you anything because there's no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraint you're not making something
+
+ align:start position:0%
+constraint you're not making something
+ 
+
+ align:start position:0%
+constraint you're not making something
+that would mess up the power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+count all
+
+ align:start position:0%
+count all
+ 
+
+ align:start position:0%
+count all
+right so what does this correspond to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physically so type three is actually
+
+ align:start position:0%
+physically so type three is actually
+ 
+
+ align:start position:0%
+physically so type three is actually
+pretty simple simple type three is like
+
+ align:start position:0%
+pretty simple simple type three is like
+ 
+
+ align:start position:0%
+pretty simple simple type three is like
+a boost along if you think about our
+
+ align:start position:0%
+a boost along if you think about our
+ 
+
+ align:start position:0%
+a boost along if you think about our
+backtack vectors type 3 is like the
+
+ align:start position:0%
+backtack vectors type 3 is like the
+ 
+
+ align:start position:0%
+backtack vectors type 3 is like the
+analog of a boost but you're
+
+ align:start position:0%
+analog of a boost but you're
+ 
+
+ align:start position:0%
+analog of a boost but you're
+transforming it in the passive sense of
+
+ align:start position:0%
+transforming it in the passive sense of
+ 
+
+ align:start position:0%
+transforming it in the passive sense of
+transforming the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis and what the outcome is is very
+
+ align:start position:0%
+axis and what the outcome is is very
+ 
+
+ align:start position:0%
+axis and what the outcome is is very
+simple it just implies that any
+
+ align:start position:0%
+simple it just implies that any
+ 
+
+ align:start position:0%
+simple it just implies that any
+operator that has an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N must have a corresponding n Bar
+
+ align:start position:0%
+N must have a corresponding n Bar
+ 
+
+ align:start position:0%
+N must have a corresponding n Bar
+sitting next to
+
+ align:start position:0%
+sitting next to
+ 
+
+ align:start position:0%
+sitting next to
+it effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'll give you some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples so really if you have let's
+
+ align:start position:0%
+examples so really if you have let's
+ 
+
+ align:start position:0%
+examples so really if you have let's
+just say it this way if you have an Nar
+
+ align:start position:0%
+just say it this way if you have an Nar
+ 
+
+ align:start position:0%
+just say it this way if you have an Nar
+mu in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numerator then you either
+
+ align:start position:0%
+numerator then you either
+ 
+
+ align:start position:0%
+numerator then you either
+have a corresponding n in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numerator or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or you have an Nar in the
+
+ align:start position:0%
+or you have an Nar in the
+ 
+
+ align:start position:0%
+or you have an Nar in the
+denominator since we could have n bars
+
+ align:start position:0%
+denominator since we could have n bars
+ 
+
+ align:start position:0%
+denominator since we could have n bars
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+denominator that was showing up in some
+
+ align:start position:0%
+denominator that was showing up in some
+ 
+
+ align:start position:0%
+denominator that was showing up in some
+places those are the two possible ways
+
+ align:start position:0%
+places those are the two possible ways
+ 
+
+ align:start position:0%
+places those are the two possible ways
+of compensating for the transformation
+
+ align:start position:0%
+of compensating for the transformation
+ 
+
+ align:start position:0%
+of compensating for the transformation
+so it's just like a simple counting that
+
+ align:start position:0%
+so it's just like a simple counting that
+ 
+
+ align:start position:0%
+so it's just like a simple counting that
+you have so if you look at our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lc0 we had various terms one of them was
+
+ align:start position:0%
+lc0 we had various terms one of them was
+ 
+
+ align:start position:0%
+lc0 we had various terms one of them was
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+nar1 over
+
+ align:start position:0%
+nar1 over
+ 
+
+ align:start position:0%
+nar1 over
+I.D so here we have an Nar in both the
+
+ align:start position:0%
+I.D so here we have an Nar in both the
+ 
+
+ align:start position:0%
+I.D so here we have an Nar in both the
+numerator and the denominator and that
+
+ align:start position:0%
+numerator and the denominator and that
+ 
+
+ align:start position:0%
+numerator and the denominator and that
+compensates for the transformation and
+
+ align:start position:0%
+compensates for the transformation and
+ 
+
+ align:start position:0%
+compensates for the transformation and
+then in another term we had an
+
+ align:start position:0%
+then in another term we had an
+ 
+
+ align:start position:0%
+then in another term we had an
+n/
+
+ align:start position:0%
+n/
+ 
+
+ align:start position:0%
+n/
+N.D and then then that again is
+
+ align:start position:0%
+N.D and then then that again is
+ 
+
+ align:start position:0%
+N.D and then then that again is
+invariant to this type of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transformation what about type one and
+
+ align:start position:0%
+transformation what about type one and
+ 
+
+ align:start position:0%
+transformation what about type one and
+two so
+
+ align:start position:0%
+two so
+ 
+
+ align:start position:0%
+two so
+type one is the following so think about
+
+ align:start position:0%
+type one is the following so think about
+ 
+
+ align:start position:0%
+type one is the following so think about
+these guys as in this kind of language
+
+ align:start position:0%
+these guys as in this kind of language
+ 
+
+ align:start position:0%
+these guys as in this kind of language
+they would be back to
+
+ align:start position:0%
+they would be back to
+ 
+
+ align:start position:0%
+they would be back to
+back we're trying to describe the
+
+ align:start position:0%
+back we're trying to describe the
+ 
+
+ align:start position:0%
+back we're trying to describe the
+physics in this cone for the cinear
+
+ align:start position:0%
+physics in this cone for the cinear
+ 
+
+ align:start position:0%
+physics in this cone for the cinear
+particles and N was the vector that was
+
+ align:start position:0%
+particles and N was the vector that was
+ 
+
+ align:start position:0%
+particles and N was the vector that was
+pointing inside that
+
+ align:start position:0%
+pointing inside that
+ 
+
+ align:start position:0%
+pointing inside that
+cone what this is saying type one is
+
+ align:start position:0%
+cone what this is saying type one is
+ 
+
+ align:start position:0%
+cone what this is saying type one is
+that I can rotate that guy and as long
+
+ align:start position:0%
+that I can rotate that guy and as long
+ 
+
+ align:start position:0%
+that I can rotate that guy and as long
+as I'm not rotating it by too much IE
+
+ align:start position:0%
+as I'm not rotating it by too much IE
+ 
+
+ align:start position:0%
+as I'm not rotating it by too much IE
+I'm rotating it by a small amount of
+
+ align:start position:0%
+I'm rotating it by a small amount of
+ 
+
+ align:start position:0%
+I'm rotating it by a small amount of
+order Lambda which you can think of as
+
+ align:start position:0%
+order Lambda which you can think of as
+ 
+
+ align:start position:0%
+order Lambda which you can think of as
+staying inside the
+
+ align:start position:0%
+staying inside the
+ 
+
+ align:start position:0%
+staying inside the
+then I can describe everything equally
+
+ align:start position:0%
+then I can describe everything equally
+ 
+
+ align:start position:0%
+then I can describe everything equally
+well by some other Vector that lives in
+
+ align:start position:0%
+well by some other Vector that lives in
+ 
+
+ align:start position:0%
+well by some other Vector that lives in
+that cone and I can decompose the
+
+ align:start position:0%
+that cone and I can decompose the
+ 
+
+ align:start position:0%
+that cone and I can decompose the
+momento and the modes in terms of that
+
+ align:start position:0%
+momento and the modes in terms of that
+ 
+
+ align:start position:0%
+momento and the modes in terms of that
+Vector it will work equally
+
+ align:start position:0%
+Vector it will work equally
+ 
+
+ align:start position:0%
+Vector it will work equally
+well okay so that's what type
+
+ align:start position:0%
+well okay so that's what type
+ 
+
+ align:start position:0%
+well okay so that's what type
+one is physically doing and so you're
+
+ align:start position:0%
+one is physically doing and so you're
+ 
+
+ align:start position:0%
+one is physically doing and so you're
+not making a large transformation here
+
+ align:start position:0%
+not making a large transformation here
+ 
+
+ align:start position:0%
+not making a large transformation here
+because you want to still be inside the
+
+ align:start position:0%
+because you want to still be inside the
+ 
+
+ align:start position:0%
+because you want to still be inside the
+cone you still want something that's
+
+ align:start position:0%
+cone you still want something that's
+ 
+
+ align:start position:0%
+cone you still want something that's
+pointing in the colinear direction type
+
+ align:start position:0%
+pointing in the colinear direction type
+ 
+
+ align:start position:0%
+pointing in the colinear direction type
+two is related to the fact that this Nar
+
+ align:start position:0%
+two is related to the fact that this Nar
+ 
+
+ align:start position:0%
+two is related to the fact that this Nar
+Vector was just an auxiliary Vector that
+
+ align:start position:0%
+Vector was just an auxiliary Vector that
+ 
+
+ align:start position:0%
+Vector was just an auxiliary Vector that
+we used to decompose things we didn't
+
+ align:start position:0%
+we used to decompose things we didn't
+ 
+
+ align:start position:0%
+we used to decompose things we didn't
+really care about it it didn't have
+
+ align:start position:0%
+really care about it it didn't have
+ 
+
+ align:start position:0%
+really care about it it didn't have
+a a strong
+
+ align:start position:0%
+a a strong
+ 
+
+ align:start position:0%
+a a strong
+physical motivation it was just needed
+
+ align:start position:0%
+physical motivation it was just needed
+ 
+
+ align:start position:0%
+physical motivation it was just needed
+because we're using light cone
+
+ align:start position:0%
+because we're using light cone
+ 
+
+ align:start position:0%
+because we're using light cone
+coordinates so I can make a very large
+
+ align:start position:0%
+coordinates so I can make a very large
+ 
+
+ align:start position:0%
+coordinates so I can make a very large
+transformation of that
+
+ align:start position:0%
+transformation of that
+ 
+
+ align:start position:0%
+transformation of that
+guy so here's a large
+
+ align:start position:0%
+guy so here's a large
+ 
+
+ align:start position:0%
+guy so here's a large
+transformation and I can use some other
+
+ align:start position:0%
+transformation and I can use some other
+ 
+
+ align:start position:0%
+transformation and I can use some other
+guy and we gave you an example earlier
+
+ align:start position:0%
+guy and we gave you an example earlier
+ 
+
+ align:start position:0%
+guy and we gave you an example earlier
+which was 3221 as a possible value for
+
+ align:start position:0%
+which was 3221 as a possible value for
+ 
+
+ align:start position:0%
+which was 3221 as a possible value for
+the Nar and that's you know something
+
+ align:start position:0%
+the Nar and that's you know something
+ 
+
+ align:start position:0%
+the Nar and that's you know something
+that you could think of getting to by a
+
+ align:start position:0%
+that you could think of getting to by a
+ 
+
+ align:start position:0%
+that you could think of getting to by a
+finite type two reparameterization
+
+ align:start position:0%
+finite type two reparameterization
+ 
+
+ align:start position:0%
+finite type two reparameterization
+transformation okay so that's the kind
+
+ align:start position:0%
+transformation okay so that's the kind
+ 
+
+ align:start position:0%
+transformation okay so that's the kind
+of picture for what these
+
+ align:start position:0%
+of picture for what these
+ 
+
+ align:start position:0%
+of picture for what these
+Transformations are and we will finish
+
+ align:start position:0%
+Transformations are and we will finish
+ 
+
+ align:start position:0%
+Transformations are and we will finish
+up talking about them next time and
+
+ align:start position:0%
+up talking about them next time and
+ 
+
+ align:start position:0%
+up talking about them next time and
+we'll show that actually this additional
+
+ align:start position:0%
+we'll show that actually this additional
+ 
+
+ align:start position:0%
+we'll show that actually this additional
+term that we could write down in the
+
+ align:start position:0%
+term that we could write down in the
+ 
+
+ align:start position:0%
+term that we could write down in the
+lran is actually ruled out by
+
+ align:start position:0%
+lran is actually ruled out by
+ 
+
+ align:start position:0%
+lran is actually ruled out by
+reparameterization symmetries
\ No newline at end of file
diff --git a/X8DlaW83HJc.txt b/X8DlaW83HJc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b47a12afcbdd16898e94291c84887f49e371b0bb
--- /dev/null
+++ b/X8DlaW83HJc.txt
@@ -0,0 +1,2395 @@
+align:start position:0%
+ 
+what's the fuel consumption of a car say
+
+ align:start position:0%
+what's the fuel consumption of a car say
+ 
+
+ align:start position:0%
+what's the fuel consumption of a car say
+on the highway moving at highway speeds
+
+ align:start position:0%
+on the highway moving at highway speeds
+ 
+
+ align:start position:0%
+on the highway moving at highway speeds
+we can look it up but can we understand
+
+ align:start position:0%
+we can look it up but can we understand
+ 
+
+ align:start position:0%
+we can look it up but can we understand
+those numbers can we predict them from
+
+ align:start position:0%
+those numbers can we predict them from
+ 
+
+ align:start position:0%
+those numbers can we predict them from
+our knowledge of Science and Engineering
+
+ align:start position:0%
+our knowledge of Science and Engineering
+ 
+
+ align:start position:0%
+our knowledge of Science and Engineering
+that's what we're going to do in this
+
+ align:start position:0%
+that's what we're going to do in this
+ 
+
+ align:start position:0%
+that's what we're going to do in this
+video this video is part of the problem
+
+ align:start position:0%
+video this video is part of the problem
+ 
+
+ align:start position:0%
+video this video is part of the problem
+solving video
+
+ align:start position:0%
+solving video
+ 
+
+ align:start position:0%
+solving video
+series problem solving skills in
+
+ align:start position:0%
+series problem solving skills in
+ 
+
+ align:start position:0%
+series problem solving skills in
+combination with an understanding of the
+
+ align:start position:0%
+combination with an understanding of the
+ 
+
+ align:start position:0%
+combination with an understanding of the
+natural and human-made world are
+
+ align:start position:0%
+natural and human-made world are
+ 
+
+ align:start position:0%
+natural and human-made world are
+critical to the design and optim ization
+
+ align:start position:0%
+critical to the design and optim ization
+ 
+
+ align:start position:0%
+critical to the design and optim ization
+of systems and
+
+ align:start position:0%
+of systems and
+ 
+
+ align:start position:0%
+of systems and
+processes hi my name is sanjoy Mahajan
+
+ align:start position:0%
+processes hi my name is sanjoy Mahajan
+ 
+
+ align:start position:0%
+processes hi my name is sanjoy Mahajan
+and I'm a professor of applied science
+
+ align:start position:0%
+and I'm a professor of applied science
+ 
+
+ align:start position:0%
+and I'm a professor of applied science
+and engineering at Doan college and I
+
+ align:start position:0%
+and engineering at Doan college and I
+ 
+
+ align:start position:0%
+and engineering at Doan college and I
+excel at street fighting mathematics
+
+ align:start position:0%
+excel at street fighting mathematics
+ 
+
+ align:start position:0%
+excel at street fighting mathematics
+before watching this video you should be
+
+ align:start position:0%
+before watching this video you should be
+ 
+
+ align:start position:0%
+before watching this video you should be
+familiar with free body diagrams and
+
+ align:start position:0%
+familiar with free body diagrams and
+ 
+
+ align:start position:0%
+familiar with free body diagrams and
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+analysis after watching this video you
+
+ align:start position:0%
+analysis after watching this video you
+ 
+
+ align:start position:0%
+analysis after watching this video you
+will be able to model drag to predict
+
+ align:start position:0%
+will be able to model drag to predict
+ 
+
+ align:start position:0%
+will be able to model drag to predict
+terminal velocities and determine the
+
+ align:start position:0%
+terminal velocities and determine the
+ 
+
+ align:start position:0%
+terminal velocities and determine the
+fuel efficiency of a car
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fuel is consumed in fighting drag on the
+
+ align:start position:0%
+fuel is consumed in fighting drag on the
+ 
+
+ align:start position:0%
+fuel is consumed in fighting drag on the
+highway at least what's the force of
+
+ align:start position:0%
+highway at least what's the force of
+ 
+
+ align:start position:0%
+highway at least what's the force of
+drag on a car that's fluid mechanics we
+
+ align:start position:0%
+drag on a car that's fluid mechanics we
+ 
+
+ align:start position:0%
+drag on a car that's fluid mechanics we
+could try the hard way solving the
+
+ align:start position:0%
+could try the hard way solving the
+ 
+
+ align:start position:0%
+could try the hard way solving the
+navier Stokes equations of fluid
+
+ align:start position:0%
+navier Stokes equations of fluid
+ 
+
+ align:start position:0%
+navier Stokes equations of fluid
+mechanics now after 10 years of learning
+
+ align:start position:0%
+mechanics now after 10 years of learning
+ 
+
+ align:start position:0%
+mechanics now after 10 years of learning
+mathematics you'll discover that this is
+
+ align:start position:0%
+mathematics you'll discover that this is
+ 
+
+ align:start position:0%
+mathematics you'll discover that this is
+a really hard problem you can only Solve
+
+ align:start position:0%
+a really hard problem you can only Solve
+ 
+
+ align:start position:0%
+a really hard problem you can only Solve
+IT analytically in certain special cases
+
+ align:start position:0%
+IT analytically in certain special cases
+ 
+
+ align:start position:0%
+IT analytically in certain special cases
+like a sphere moving at really slow
+
+ align:start position:0%
+like a sphere moving at really slow
+ 
+
+ align:start position:0%
+like a sphere moving at really slow
+speeds and a car is not one of those
+
+ align:start position:0%
+speeds and a car is not one of those
+ 
+
+ align:start position:0%
+speeds and a car is not one of those
+special cases certainly not a car moving
+
+ align:start position:0%
+special cases certainly not a car moving
+ 
+
+ align:start position:0%
+special cases certainly not a car moving
+at any reasonable speed so we need
+
+ align:start position:0%
+at any reasonable speed so we need
+ 
+
+ align:start position:0%
+at any reasonable speed so we need
+another way by applying approximations
+
+ align:start position:0%
+another way by applying approximations
+ 
+
+ align:start position:0%
+another way by applying approximations
+artfully we're going to find the drag
+
+ align:start position:0%
+artfully we're going to find the drag
+ 
+
+ align:start position:0%
+artfully we're going to find the drag
+force and the fuel consumption of a car
+
+ align:start position:0%
+force and the fuel consumption of a car
+ 
+
+ align:start position:0%
+force and the fuel consumption of a car
+with a simple experiment and some
+
+ align:start position:0%
+with a simple experiment and some
+ 
+
+ align:start position:0%
+with a simple experiment and some
+scientific and Engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasoning first we need to model drag to
+
+ align:start position:0%
+reasoning first we need to model drag to
+ 
+
+ align:start position:0%
+reasoning first we need to model drag to
+do this we're going to figure out how
+
+ align:start position:0%
+do this we're going to figure out how
+ 
+
+ align:start position:0%
+do this we're going to figure out how
+the drag Force depends on the quantities
+
+ align:start position:0%
+the drag Force depends on the quantities
+ 
+
+ align:start position:0%
+the drag Force depends on the quantities
+that control it drag Force F depends on
+
+ align:start position:0%
+that control it drag Force F depends on
+ 
+
+ align:start position:0%
+that control it drag Force F depends on
+the density of the air to some power
+
+ align:start position:0%
+the density of the air to some power
+ 
+
+ align:start position:0%
+the density of the air to some power
+which we don't know yet times the speed
+
+ align:start position:0%
+which we don't know yet times the speed
+ 
+
+ align:start position:0%
+which we don't know yet times the speed
+of the car moving through the air to
+
+ align:start position:0%
+of the car moving through the air to
+ 
+
+ align:start position:0%
+of the car moving through the air to
+some power we don't know yet it depends
+
+ align:start position:0%
+some power we don't know yet it depends
+ 
+
+ align:start position:0%
+some power we don't know yet it depends
+on how big the car is which will
+
+ align:start position:0%
+on how big the car is which will
+ 
+
+ align:start position:0%
+on how big the car is which will
+represent by the area traditionally the
+
+ align:start position:0%
+represent by the area traditionally the
+ 
+
+ align:start position:0%
+represent by the area traditionally the
+cross-sectional area to some power and
+
+ align:start position:0%
+cross-sectional area to some power and
+ 
+
+ align:start position:0%
+cross-sectional area to some power and
+it also can depend on the viscosity here
+
+ align:start position:0%
+it also can depend on the viscosity here
+ 
+
+ align:start position:0%
+it also can depend on the viscosity here
+the kinematic viscosity of the air to
+
+ align:start position:0%
+the kinematic viscosity of the air to
+ 
+
+ align:start position:0%
+the kinematic viscosity of the air to
+some power and what those powers are we
+
+ align:start position:0%
+some power and what those powers are we
+ 
+
+ align:start position:0%
+some power and what those powers are we
+don't yet know to figure them out let's
+
+ align:start position:0%
+don't yet know to figure them out let's
+ 
+
+ align:start position:0%
+don't yet know to figure them out let's
+do an experiment for the experiment we
+
+ align:start position:0%
+do an experiment for the experiment we
+ 
+
+ align:start position:0%
+do an experiment for the experiment we
+make two cones first by making a large
+
+ align:start position:0%
+make two cones first by making a large
+ 
+
+ align:start position:0%
+make two cones first by making a large
+Circle and cutting out a quarter of it
+
+ align:start position:0%
+Circle and cutting out a quarter of it
+ 
+
+ align:start position:0%
+Circle and cutting out a quarter of it
+the large Circle has a radius of 7 cm
+
+ align:start position:0%
+the large Circle has a radius of 7 cm
+ 
+
+ align:start position:0%
+the large Circle has a radius of 7 cm
+and the small 3/4 Circle has half the
+
+ align:start position:0%
+and the small 3/4 Circle has half the
+ 
+
+ align:start position:0%
+and the small 3/4 Circle has half the
+radius cut them out and then tape this
+
+ align:start position:0%
+radius cut them out and then tape this
+ 
+
+ align:start position:0%
+radius cut them out and then tape this
+Edge to that edge and this Edge to that
+
+ align:start position:0%
+Edge to that edge and this Edge to that
+ 
+
+ align:start position:0%
+Edge to that edge and this Edge to that
+edge in order to make the two
+
+ align:start position:0%
+edge in order to make the two
+ 
+
+ align:start position:0%
+edge in order to make the two
+cones next we're going to rase them the
+
+ align:start position:0%
+cones next we're going to rase them the
+ 
+
+ align:start position:0%
+cones next we're going to rase them the
+big cone versus the small cone but first
+
+ align:start position:0%
+big cone versus the small cone but first
+ 
+
+ align:start position:0%
+big cone versus the small cone but first
+make a prediction the question is what
+
+ align:start position:0%
+make a prediction the question is what
+ 
+
+ align:start position:0%
+make a prediction the question is what
+is the ratio of fall speeds of the big
+
+ align:start position:0%
+is the ratio of fall speeds of the big
+ 
+
+ align:start position:0%
+is the ratio of fall speeds of the big
+cone and the small cone approximately is
+
+ align:start position:0%
+cone and the small cone approximately is
+ 
+
+ align:start position:0%
+cone and the small cone approximately is
+the big big cone roughly twice as fast
+
+ align:start position:0%
+the big big cone roughly twice as fast
+ 
+
+ align:start position:0%
+the big big cone roughly twice as fast
+is the small cone twice as fast or do
+
+ align:start position:0%
+is the small cone twice as fast or do
+ 
+
+ align:start position:0%
+is the small cone twice as fast or do
+they fall at roughly the same
+
+ align:start position:0%
+they fall at roughly the same
+ 
+
+ align:start position:0%
+they fall at roughly the same
+speed pause the video and make your best
+
+ align:start position:0%
+speed pause the video and make your best
+ 
+
+ align:start position:0%
+speed pause the video and make your best
+guess you may want to try the experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yourself the experimental result is that
+
+ align:start position:0%
+yourself the experimental result is that
+ 
+
+ align:start position:0%
+yourself the experimental result is that
+they both fall at roughly the same speed
+
+ align:start position:0%
+they both fall at roughly the same speed
+ 
+
+ align:start position:0%
+they both fall at roughly the same speed
+now what does that mean for the
+
+ align:start position:0%
+now what does that mean for the
+ 
+
+ align:start position:0%
+now what does that mean for the
+exponents in the drag Force to decide
+
+ align:start position:0%
+exponents in the drag Force to decide
+ 
+
+ align:start position:0%
+exponents in the drag Force to decide
+use a free body diagram here is a free
+
+ align:start position:0%
+use a free body diagram here is a free
+ 
+
+ align:start position:0%
+use a free body diagram here is a free
+body diagram of a cone as it falls what
+
+ align:start position:0%
+body diagram of a cone as it falls what
+ 
+
+ align:start position:0%
+body diagram of a cone as it falls what
+are the forces on the cone pause and
+
+ align:start position:0%
+are the forces on the cone pause and
+ 
+
+ align:start position:0%
+are the forces on the cone pause and
+fill in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram there is drag and gravity
+
+ align:start position:0%
+diagram there is drag and gravity
+ 
+
+ align:start position:0%
+diagram there is drag and gravity
+because the cones are falling at their
+
+ align:start position:0%
+because the cones are falling at their
+ 
+
+ align:start position:0%
+because the cones are falling at their
+terminal speed in other words at the
+
+ align:start position:0%
+terminal speed in other words at the
+ 
+
+ align:start position:0%
+terminal speed in other words at the
+constant velocity that they reach pretty
+
+ align:start position:0%
+constant velocity that they reach pretty
+ 
+
+ align:start position:0%
+constant velocity that they reach pretty
+quickly the drag must equal the force
+
+ align:start position:0%
+quickly the drag must equal the force
+ 
+
+ align:start position:0%
+quickly the drag must equal the force
+due to
+
+ align:start position:0%
+due to
+ 
+
+ align:start position:0%
+due to
+gravity so the drag force can easily be
+
+ align:start position:0%
+gravity so the drag force can easily be
+ 
+
+ align:start position:0%
+gravity so the drag force can easily be
+measured just by sticking the cones on a
+
+ align:start position:0%
+measured just by sticking the cones on a
+ 
+
+ align:start position:0%
+measured just by sticking the cones on a
+scale we don't actually have to stick
+
+ align:start position:0%
+scale we don't actually have to stick
+ 
+
+ align:start position:0%
+scale we don't actually have to stick
+the cones on a scale because we know
+
+ align:start position:0%
+the cones on a scale because we know
+ 
+
+ align:start position:0%
+the cones on a scale because we know
+what their relative weights are and
+
+ align:start position:0%
+what their relative weights are and
+ 
+
+ align:start position:0%
+what their relative weights are and
+that's what we're going to use to figure
+
+ align:start position:0%
+that's what we're going to use to figure
+ 
+
+ align:start position:0%
+that's what we're going to use to figure
+out one of the exponents knowing that
+
+ align:start position:0%
+out one of the exponents knowing that
+ 
+
+ align:start position:0%
+out one of the exponents knowing that
+the drag Force equals the force due to
+
+ align:start position:0%
+the drag Force equals the force due to
+ 
+
+ align:start position:0%
+the drag Force equals the force due to
+gravity let's compare the drag forces
+
+ align:start position:0%
+gravity let's compare the drag forces
+ 
+
+ align:start position:0%
+gravity let's compare the drag forces
+which are the factors on the right side
+
+ align:start position:0%
+which are the factors on the right side
+ 
+
+ align:start position:0%
+which are the factors on the right side
+of the small and large
+
+ align:start position:0%
+of the small and large
+ 
+
+ align:start position:0%
+of the small and large
+cones the large cone was made out of a
+
+ align:start position:0%
+cones the large cone was made out of a
+ 
+
+ align:start position:0%
+cones the large cone was made out of a
+paper circle with twice the radius so it
+
+ align:start position:0%
+paper circle with twice the radius so it
+ 
+
+ align:start position:0%
+paper circle with twice the radius so it
+has four times the area four time the
+
+ align:start position:0%
+has four times the area four time the
+ 
+
+ align:start position:0%
+has four times the area four time the
+mass and four times the force due to
+
+ align:start position:0%
+mass and four times the force due to
+ 
+
+ align:start position:0%
+mass and four times the force due to
+gravity therefore four times the drag
+
+ align:start position:0%
+gravity therefore four times the drag
+ 
+
+ align:start position:0%
+gravity therefore four times the drag
+Force now let's look at the causes one
+
+ align:start position:0%
+Force now let's look at the causes one
+ 
+
+ align:start position:0%
+Force now let's look at the causes one
+by one this density here is the density
+
+ align:start position:0%
+by one this density here is the density
+ 
+
+ align:start position:0%
+by one this density here is the density
+of the air and both cones feel the same
+
+ align:start position:0%
+of the air and both cones feel the same
+ 
+
+ align:start position:0%
+of the air and both cones feel the same
+air so there's no difference here so
+
+ align:start position:0%
+air so there's no difference here so
+ 
+
+ align:start position:0%
+air so there's no difference here so
+that's times one no matter the exponent
+
+ align:start position:0%
+that's times one no matter the exponent
+ 
+
+ align:start position:0%
+that's times one no matter the exponent
+now what about the speed the speeds were
+
+ align:start position:0%
+now what about the speed the speeds were
+ 
+
+ align:start position:0%
+now what about the speed the speeds were
+the same that was the result of our
+
+ align:start position:0%
+the same that was the result of our
+ 
+
+ align:start position:0%
+the same that was the result of our
+experiment so no matter what the
+
+ align:start position:0%
+experiment so no matter what the
+ 
+
+ align:start position:0%
+experiment so no matter what the
+exponent here the speed contributes to
+
+ align:start position:0%
+exponent here the speed contributes to
+ 
+
+ align:start position:0%
+exponent here the speed contributes to
+the effect by a factor of one in other
+
+ align:start position:0%
+the effect by a factor of one in other
+ 
+
+ align:start position:0%
+the effect by a factor of one in other
+words
+
+ align:start position:0%
+words
+ 
+
+ align:start position:0%
+words
+nothing now the area this is
+
+ align:start position:0%
+nothing now the area this is
+ 
+
+ align:start position:0%
+nothing now the area this is
+traditionally the cross-sectional area
+
+ align:start position:0%
+traditionally the cross-sectional area
+ 
+
+ align:start position:0%
+traditionally the cross-sectional area
+the big cone has four times the
+
+ align:start position:0%
+the big cone has four times the
+ 
+
+ align:start position:0%
+the big cone has four times the
+cross-sectional area of the small cone
+
+ align:start position:0%
+cross-sectional area of the small cone
+ 
+
+ align:start position:0%
+cross-sectional area of the small cone
+so this area factor is times four and
+
+ align:start position:0%
+so this area factor is times four and
+ 
+
+ align:start position:0%
+so this area factor is times four and
+raised to the unknown
+
+ align:start position:0%
+raised to the unknown
+ 
+
+ align:start position:0%
+raised to the unknown
+exponent and here the kinematic
+
+ align:start position:0%
+exponent and here the kinematic
+ 
+
+ align:start position:0%
+exponent and here the kinematic
+viscosity that's the kinematic viscosity
+
+ align:start position:0%
+viscosity that's the kinematic viscosity
+ 
+
+ align:start position:0%
+viscosity that's the kinematic viscosity
+of air both cones feel the same
+
+ align:start position:0%
+of air both cones feel the same
+ 
+
+ align:start position:0%
+of air both cones feel the same
+kinematic viscosity therefore that
+
+ align:start position:0%
+kinematic viscosity therefore that
+ 
+
+ align:start position:0%
+kinematic viscosity therefore that
+contributes a factor of one just like
+
+ align:start position:0%
+contributes a factor of one just like
+ 
+
+ align:start position:0%
+contributes a factor of one just like
+the density
+
+ align:start position:0%
+the density
+ 
+
+ align:start position:0%
+the density
+does so now we know what the question
+
+ align:start position:0%
+does so now we know what the question
+ 
+
+ align:start position:0%
+does so now we know what the question
+mark here has to be the question mark
+
+ align:start position:0%
+mark here has to be the question mark
+ 
+
+ align:start position:0%
+mark here has to be the question mark
+here must be one so that this four to
+
+ align:start position:0%
+here must be one so that this four to
+ 
+
+ align:start position:0%
+here must be one so that this four to
+the question mark is equal to this
+
+ align:start position:0%
+the question mark is equal to this
+ 
+
+ align:start position:0%
+the question mark is equal to this
+four and so does this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one now that we have found one exponent
+
+ align:start position:0%
+one now that we have found one exponent
+ 
+
+ align:start position:0%
+one now that we have found one exponent
+we can find the remaining three using
+
+ align:start position:0%
+we can find the remaining three using
+ 
+
+ align:start position:0%
+we can find the remaining three using
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+analysis we make sure that the exponents
+
+ align:start position:0%
+analysis we make sure that the exponents
+ 
+
+ align:start position:0%
+analysis we make sure that the exponents
+chosen on the right side produce
+
+ align:start position:0%
+chosen on the right side produce
+ 
+
+ align:start position:0%
+chosen on the right side produce
+dimensions of force which are the
+
+ align:start position:0%
+dimensions of force which are the
+ 
+
+ align:start position:0%
+dimensions of force which are the
+dimensions on the left side a force has
+
+ align:start position:0%
+dimensions on the left side a force has
+ 
+
+ align:start position:0%
+dimensions on the left side a force has
+dimensions of mass length per time
+
+ align:start position:0%
+dimensions of mass length per time
+ 
+
+ align:start position:0%
+dimensions of mass length per time
+squared that's mass times acceleration
+
+ align:start position:0%
+squared that's mass times acceleration
+ 
+
+ align:start position:0%
+squared that's mass times acceleration
+density has dimensions of mass per
+
+ align:start position:0%
+density has dimensions of mass per
+ 
+
+ align:start position:0%
+density has dimensions of mass per
+length cubed raised to this unknown
+
+ align:start position:0%
+length cubed raised to this unknown
+ 
+
+ align:start position:0%
+length cubed raised to this unknown
+exponent velocity has dimensions of
+
+ align:start position:0%
+exponent velocity has dimensions of
+ 
+
+ align:start position:0%
+exponent velocity has dimensions of
+length per time raised to this unknown
+
+ align:start position:0%
+length per time raised to this unknown
+ 
+
+ align:start position:0%
+length per time raised to this unknown
+exponent area has dimensions of length
+
+ align:start position:0%
+exponent area has dimensions of length
+ 
+
+ align:start position:0%
+exponent area has dimensions of length
+squared raised to the power one we've
+
+ align:start position:0%
+squared raised to the power one we've
+ 
+
+ align:start position:0%
+squared raised to the power one we've
+already figured that
+
+ align:start position:0%
+already figured that
+ 
+
+ align:start position:0%
+already figured that
+out and kinematic viscosity now that's
+
+ align:start position:0%
+out and kinematic viscosity now that's
+ 
+
+ align:start position:0%
+out and kinematic viscosity now that's
+the regular viscosity divided by the
+
+ align:start position:0%
+the regular viscosity divided by the
+ 
+
+ align:start position:0%
+the regular viscosity divided by the
+density it has dimensions of length
+
+ align:start position:0%
+density it has dimensions of length
+ 
+
+ align:start position:0%
+density it has dimensions of length
+squared per time raised to this unknown
+
+ align:start position:0%
+squared per time raised to this unknown
+ 
+
+ align:start position:0%
+squared per time raised to this unknown
+exponent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's solve for these unknown
+
+ align:start position:0%
+now let's solve for these unknown
+ 
+
+ align:start position:0%
+now let's solve for these unknown
+exponents one at a time looking first at
+
+ align:start position:0%
+exponents one at a time looking first at
+ 
+
+ align:start position:0%
+exponents one at a time looking first at
+the mass there is mass here and mass
+
+ align:start position:0%
+the mass there is mass here and mass
+ 
+
+ align:start position:0%
+the mass there is mass here and mass
+here on the left side but there is no
+
+ align:start position:0%
+here on the left side but there is no
+ 
+
+ align:start position:0%
+here on the left side but there is no
+other Mass so the only way to get the
+
+ align:start position:0%
+other Mass so the only way to get the
+ 
+
+ align:start position:0%
+other Mass so the only way to get the
+mass to work out is to make this
+
+ align:start position:0%
+mass to work out is to make this
+ 
+
+ align:start position:0%
+mass to work out is to make this
+exponent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one now what do we have left we have to
+
+ align:start position:0%
+one now what do we have left we have to
+ 
+
+ align:start position:0%
+one now what do we have left we have to
+make sure the lengths and times work out
+
+ align:start position:0%
+make sure the lengths and times work out
+ 
+
+ align:start position:0%
+make sure the lengths and times work out
+and we have two unknowns this exponent
+
+ align:start position:0%
+and we have two unknowns this exponent
+ 
+
+ align:start position:0%
+and we have two unknowns this exponent
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+exponent let's see how many more lengths
+
+ align:start position:0%
+exponent let's see how many more lengths
+ 
+
+ align:start position:0%
+exponent let's see how many more lengths
+we need given what we already have we
+
+ align:start position:0%
+we need given what we already have we
+ 
+
+ align:start position:0%
+we need given what we already have we
+have mass worked out we have two lengths
+
+ align:start position:0%
+have mass worked out we have two lengths
+ 
+
+ align:start position:0%
+have mass worked out we have two lengths
+here over three lengths so we have mass
+
+ align:start position:0%
+here over three lengths so we have mass
+ 
+
+ align:start position:0%
+here over three lengths so we have mass
+per length so we have length to the
+
+ align:start position:0%
+per length so we have length to the
+ 
+
+ align:start position:0%
+per length so we have length to the
+minus one so
+
+ align:start position:0%
+minus one so
+ 
+
+ align:start position:0%
+minus one so
+far and what about time well we have no
+
+ align:start position:0%
+far and what about time well we have no
+ 
+
+ align:start position:0%
+far and what about time well we have no
+times yet except in these question marks
+
+ align:start position:0%
+times yet except in these question marks
+ 
+
+ align:start position:0%
+times yet except in these question marks
+so we need to get two more times on the
+
+ align:start position:0%
+so we need to get two more times on the
+ 
+
+ align:start position:0%
+so we need to get two more times on the
+bottom two more lengths on the top so we
+
+ align:start position:0%
+bottom two more lengths on the top so we
+ 
+
+ align:start position:0%
+bottom two more lengths on the top so we
+need to multiply by length squar over
+
+ align:start position:0%
+need to multiply by length squar over
+ 
+
+ align:start position:0%
+need to multiply by length squar over
+time squar and the only way to do that
+
+ align:start position:0%
+time squar and the only way to do that
+ 
+
+ align:start position:0%
+time squar and the only way to do that
+is to make this exponent a two and this
+
+ align:start position:0%
+is to make this exponent a two and this
+ 
+
+ align:start position:0%
+is to make this exponent a two and this
+exponent here a
+
+ align:start position:0%
+exponent here a
+ 
+
+ align:start position:0%
+exponent here a
+zero you can pause the video and go
+
+ align:start position:0%
+zero you can pause the video and go
+ 
+
+ align:start position:0%
+zero you can pause the video and go
+ahead and try other combinations of
+
+ align:start position:0%
+ahead and try other combinations of
+ 
+
+ align:start position:0%
+ahead and try other combinations of
+exponents you'll find that none of them
+
+ align:start position:0%
+exponents you'll find that none of them
+ 
+
+ align:start position:0%
+exponents you'll find that none of them
+will get both length and time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct so now we have all the exponents
+
+ align:start position:0%
+correct so now we have all the exponents
+ 
+
+ align:start position:0%
+correct so now we have all the exponents
+we can actually enter that into our drag
+
+ align:start position:0%
+we can actually enter that into our drag
+ 
+
+ align:start position:0%
+we can actually enter that into our drag
+Force formula drag force is proportional
+
+ align:start position:0%
+Force formula drag force is proportional
+ 
+
+ align:start position:0%
+Force formula drag force is proportional
+to density to the first power to speed
+
+ align:start position:0%
+to density to the first power to speed
+ 
+
+ align:start position:0%
+to density to the first power to speed
+squared to area to the first Power which
+
+ align:start position:0%
+squared to area to the first Power which
+ 
+
+ align:start position:0%
+squared to area to the first Power which
+we got from our home EXP experiment and
+
+ align:start position:0%
+we got from our home EXP experiment and
+ 
+
+ align:start position:0%
+we got from our home EXP experiment and
+to viscosity here to the zeroth
+
+ align:start position:0%
+to viscosity here to the zeroth
+ 
+
+ align:start position:0%
+to viscosity here to the zeroth
+power now let's test our formula with a
+
+ align:start position:0%
+power now let's test our formula with a
+ 
+
+ align:start position:0%
+power now let's test our formula with a
+second demonstration and see if it
+
+ align:start position:0%
+second demonstration and see if it
+ 
+
+ align:start position:0%
+second demonstration and see if it
+predicts this new situation we're going
+
+ align:start position:0%
+predicts this new situation we're going
+ 
+
+ align:start position:0%
+predicts this new situation we're going
+to race four small cones stacked on top
+
+ align:start position:0%
+to race four small cones stacked on top
+ 
+
+ align:start position:0%
+to race four small cones stacked on top
+of each other 1 2 3 4 so we stack them
+
+ align:start position:0%
+of each other 1 2 3 4 so we stack them
+ 
+
+ align:start position:0%
+of each other 1 2 3 4 so we stack them
+to make one small cone that is four time
+
+ align:start position:0%
+to make one small cone that is four time
+ 
+
+ align:start position:0%
+to make one small cone that is four time
+the mass of the other small cone and
+
+ align:start position:0%
+the mass of the other small cone and
+ 
+
+ align:start position:0%
+the mass of the other small cone and
+then we're going to erase them but first
+
+ align:start position:0%
+then we're going to erase them but first
+ 
+
+ align:start position:0%
+then we're going to erase them but first
+what's the drag Force ratio between the
+
+ align:start position:0%
+what's the drag Force ratio between the
+ 
+
+ align:start position:0%
+what's the drag Force ratio between the
+four small cones stacked together and
+
+ align:start position:0%
+four small cones stacked together and
+ 
+
+ align:start position:0%
+four small cones stacked together and
+the single small cone pause the video
+
+ align:start position:0%
+the single small cone pause the video
+ 
+
+ align:start position:0%
+the single small cone pause the video
+and think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it the four cones weigh four times as
+
+ align:start position:0%
+it the four cones weigh four times as
+ 
+
+ align:start position:0%
+it the four cones weigh four times as
+much as one cone so that's times four on
+
+ align:start position:0%
+much as one cone so that's times four on
+ 
+
+ align:start position:0%
+much as one cone so that's times four on
+the left side what about the right side
+
+ align:start position:0%
+the left side what about the right side
+ 
+
+ align:start position:0%
+the left side what about the right side
+again both contestants feel the same air
+
+ align:start position:0%
+again both contestants feel the same air
+ 
+
+ align:start position:0%
+again both contestants feel the same air
+density the velocity ratio that's what
+
+ align:start position:0%
+density the velocity ratio that's what
+ 
+
+ align:start position:0%
+density the velocity ratio that's what
+we're trying to figure out and let's see
+
+ align:start position:0%
+we're trying to figure out and let's see
+ 
+
+ align:start position:0%
+we're trying to figure out and let's see
+what all the other pieces are the area
+
+ align:start position:0%
+what all the other pieces are the area
+ 
+
+ align:start position:0%
+what all the other pieces are the area
+well here in this case the stack of four
+
+ align:start position:0%
+well here in this case the stack of four
+ 
+
+ align:start position:0%
+well here in this case the stack of four
+has the same cross-sectional area as the
+
+ align:start position:0%
+has the same cross-sectional area as the
+ 
+
+ align:start position:0%
+has the same cross-sectional area as the
+one cone so that's just one and the
+
+ align:start position:0%
+one cone so that's just one and the
+ 
+
+ align:start position:0%
+one cone so that's just one and the
+viscosity doesn't B so this factor of
+
+ align:start position:0%
+viscosity doesn't B so this factor of
+ 
+
+ align:start position:0%
+viscosity doesn't B so this factor of
+four on the left side has to be produced
+
+ align:start position:0%
+four on the left side has to be produced
+ 
+
+ align:start position:0%
+four on the left side has to be produced
+by the v^ s in other words the V goes up
+
+ align:start position:0%
+by the v^ s in other words the V goes up
+ 
+
+ align:start position:0%
+by the v^ s in other words the V goes up
+by factor of two so that when it's
+
+ align:start position:0%
+by factor of two so that when it's
+ 
+
+ align:start position:0%
+by factor of two so that when it's
+squared you get a factor of four that
+
+ align:start position:0%
+squared you get a factor of four that
+ 
+
+ align:start position:0%
+squared you get a factor of four that
+means the correct answer should be 2:
+
+ align:start position:0%
+means the correct answer should be 2:
+ 
+
+ align:start position:0%
+means the correct answer should be 2:
+1 now let's test our prediction with a
+
+ align:start position:0%
+1 now let's test our prediction with a
+ 
+
+ align:start position:0%
+1 now let's test our prediction with a
+demonstration to check whether nature
+
+ align:start position:0%
+demonstration to check whether nature
+ 
+
+ align:start position:0%
+demonstration to check whether nature
+behaves as we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+predict it looks like our prediction was
+
+ align:start position:0%
+predict it looks like our prediction was
+ 
+
+ align:start position:0%
+predict it looks like our prediction was
+correct now we feel pretty confident
+
+ align:start position:0%
+correct now we feel pretty confident
+ 
+
+ align:start position:0%
+correct now we feel pretty confident
+that we can use this formula to try and
+
+ align:start position:0%
+that we can use this formula to try and
+ 
+
+ align:start position:0%
+that we can use this formula to try and
+F figure out the fuel consumption of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+car let's clean up our formula here just
+
+ align:start position:0%
+car let's clean up our formula here just
+ 
+
+ align:start position:0%
+car let's clean up our formula here just
+a bit and erase the viscosity since it
+
+ align:start position:0%
+a bit and erase the viscosity since it
+ 
+
+ align:start position:0%
+a bit and erase the viscosity since it
+comes in with a zero exponent so it
+
+ align:start position:0%
+comes in with a zero exponent so it
+ 
+
+ align:start position:0%
+comes in with a zero exponent so it
+doesn't matter and this is our drag
+
+ align:start position:0%
+doesn't matter and this is our drag
+ 
+
+ align:start position:0%
+doesn't matter and this is our drag
+formula which we're going to use to
+
+ align:start position:0%
+formula which we're going to use to
+ 
+
+ align:start position:0%
+formula which we're going to use to
+estimate the fuel consumption of a car
+
+ align:start position:0%
+estimate the fuel consumption of a car
+ 
+
+ align:start position:0%
+estimate the fuel consumption of a car
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+highway fuel efficiency is measured as a
+
+ align:start position:0%
+highway fuel efficiency is measured as a
+ 
+
+ align:start position:0%
+highway fuel efficiency is measured as a
+distance that the car travels on one
+
+ align:start position:0%
+distance that the car travels on one
+ 
+
+ align:start position:0%
+distance that the car travels on one
+gallon or liter of
+
+ align:start position:0%
+gallon or liter of
+ 
+
+ align:start position:0%
+gallon or liter of
+gasoline so it depends on how much
+
+ align:start position:0%
+gasoline so it depends on how much
+ 
+
+ align:start position:0%
+gasoline so it depends on how much
+energy you can get out of a gas G of
+
+ align:start position:0%
+energy you can get out of a gas G of
+ 
+
+ align:start position:0%
+energy you can get out of a gas G of
+gasoline divided by the drag Force which
+
+ align:start position:0%
+gasoline divided by the drag Force which
+ 
+
+ align:start position:0%
+gasoline divided by the drag Force which
+is the formula we've just
+
+ align:start position:0%
+is the formula we've just
+ 
+
+ align:start position:0%
+is the formula we've just
+found so let's put in some numbers
+
+ align:start position:0%
+found so let's put in some numbers
+ 
+
+ align:start position:0%
+found so let's put in some numbers
+what's the energy from a gallon of
+
+ align:start position:0%
+what's the energy from a gallon of
+ 
+
+ align:start position:0%
+what's the energy from a gallon of
+gasoline a gallon is roughly 4 lit and
+
+ align:start position:0%
+gasoline a gallon is roughly 4 lit and
+ 
+
+ align:start position:0%
+gasoline a gallon is roughly 4 lit and
+gasoline is roughly like water so there
+
+ align:start position:0%
+gasoline is roughly like water so there
+ 
+
+ align:start position:0%
+gasoline is roughly like water so there
+are th000 gr per
+
+ align:start position:0%
+are th000 gr per
+ 
+
+ align:start position:0%
+are th000 gr per
+liter how much energy do you get out of
+
+ align:start position:0%
+liter how much energy do you get out of
+ 
+
+ align:start position:0%
+liter how much energy do you get out of
+each gram of gasoline gasoline is like
+
+ align:start position:0%
+each gram of gasoline gasoline is like
+ 
+
+ align:start position:0%
+each gram of gasoline gasoline is like
+fat and from the side of a butter packet
+
+ align:start position:0%
+fat and from the side of a butter packet
+ 
+
+ align:start position:0%
+fat and from the side of a butter packet
+you can read that 100 kilo calories 10
+
+ align:start position:0%
+you can read that 100 kilo calories 10
+ 
+
+ align:start position:0%
+you can read that 100 kilo calories 10
+to the 2 2 kilo calories come from 11 G
+
+ align:start position:0%
+to the 2 2 kilo calories come from 11 G
+ 
+
+ align:start position:0%
+to the 2 2 kilo calories come from 11 G
+of butter but now we want to convert
+
+ align:start position:0%
+of butter but now we want to convert
+ 
+
+ align:start position:0%
+of butter but now we want to convert
+kilo calories to some reasonable metric
+
+ align:start position:0%
+kilo calories to some reasonable metric
+ 
+
+ align:start position:0%
+kilo calories to some reasonable metric
+unit so that's 4 Jew per
+
+ align:start position:0%
+unit so that's 4 Jew per
+ 
+
+ align:start position:0%
+unit so that's 4 Jew per
+calorie or 4 K per kilo
+
+ align:start position:0%
+calorie or 4 K per kilo
+ 
+
+ align:start position:0%
+calorie or 4 K per kilo
+calorie and that is all divided by the
+
+ align:start position:0%
+calorie and that is all divided by the
+ 
+
+ align:start position:0%
+calorie and that is all divided by the
+drag Force so let's put in those terms
+
+ align:start position:0%
+drag Force so let's put in those terms
+ 
+
+ align:start position:0%
+drag Force so let's put in those terms
+one by
+
+ align:start position:0%
+one by
+ 
+
+ align:start position:0%
+one by
+one first the density here 1 kilg per
+
+ align:start position:0%
+one first the density here 1 kilg per
+ 
+
+ align:start position:0%
+one first the density here 1 kilg per
+meter cubed is a density of air roughly
+
+ align:start position:0%
+meter cubed is a density of air roughly
+ 
+
+ align:start position:0%
+meter cubed is a density of air roughly
+now V for highway speeds say 100 km an
+
+ align:start position:0%
+now V for highway speeds say 100 km an
+ 
+
+ align:start position:0%
+now V for highway speeds say 100 km an
+hour 65 M hour that's roughly 30 m/s
+
+ align:start position:0%
+hour 65 M hour that's roughly 30 m/s
+ 
+
+ align:start position:0%
+hour 65 M hour that's roughly 30 m/s
+don't forget to square it and then the
+
+ align:start position:0%
+don't forget to square it and then the
+ 
+
+ align:start position:0%
+don't forget to square it and then the
+area of a car well it's about 2 m wide
+
+ align:start position:0%
+area of a car well it's about 2 m wide
+ 
+
+ align:start position:0%
+area of a car well it's about 2 m wide
+by 1.5 M high now we have to work out
+
+ align:start position:0%
+by 1.5 M high now we have to work out
+ 
+
+ align:start position:0%
+by 1.5 M high now we have to work out
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+numbers before you do that pause the
+
+ align:start position:0%
+numbers before you do that pause the
+ 
+
+ align:start position:0%
+numbers before you do that pause the
+video to check that the dimensions all
+
+ align:start position:0%
+video to check that the dimensions all
+ 
+
+ align:start position:0%
+video to check that the dimensions all
+cancel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appropriately you should have found that
+
+ align:start position:0%
+appropriately you should have found that
+ 
+
+ align:start position:0%
+appropriately you should have found that
+the result has of meters which is good
+
+ align:start position:0%
+the result has of meters which is good
+ 
+
+ align:start position:0%
+the result has of meters which is good
+but how
+
+ align:start position:0%
+but how
+ 
+
+ align:start position:0%
+but how
+many a quick numerical approximation
+
+ align:start position:0%
+many a quick numerical approximation
+ 
+
+ align:start position:0%
+many a quick numerical approximation
+will tell you that you get 50 km which
+
+ align:start position:0%
+will tell you that you get 50 km which
+ 
+
+ align:start position:0%
+will tell you that you get 50 km which
+is 30 m
+
+ align:start position:0%
+is 30 m
+ 
+
+ align:start position:0%
+is 30 m
+roughly the fuel efficiency of a car on
+
+ align:start position:0%
+roughly the fuel efficiency of a car on
+ 
+
+ align:start position:0%
+roughly the fuel efficiency of a car on
+the highway should be about 30 m per
+
+ align:start position:0%
+the highway should be about 30 m per
+ 
+
+ align:start position:0%
+the highway should be about 30 m per
+gallon or 50 km per
+
+ align:start position:0%
+gallon or 50 km per
+ 
+
+ align:start position:0%
+gallon or 50 km per
+gallon in the units used in the European
+
+ align:start position:0%
+gallon in the units used in the European
+ 
+
+ align:start position:0%
+gallon in the units used in the European
+Union that's 8 L per 100
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+km with our approximation methods we've
+
+ align:start position:0%
+km with our approximation methods we've
+ 
+
+ align:start position:0%
+km with our approximation methods we've
+come to pretty reasonable numbers for
+
+ align:start position:0%
+come to pretty reasonable numbers for
+ 
+
+ align:start position:0%
+come to pretty reasonable numbers for
+the fuel efficiency of a car without
+
+ align:start position:0%
+the fuel efficiency of a car without
+ 
+
+ align:start position:0%
+the fuel efficiency of a car without
+having to solve any of the complicated
+
+ align:start position:0%
+having to solve any of the complicated
+ 
+
+ align:start position:0%
+having to solve any of the complicated
+equations of fluid mechanics instead we
+
+ align:start position:0%
+equations of fluid mechanics instead we
+ 
+
+ align:start position:0%
+equations of fluid mechanics instead we
+used one simple home experiment dropping
+
+ align:start position:0%
+used one simple home experiment dropping
+ 
+
+ align:start position:0%
+used one simple home experiment dropping
+the cones and the powerful principle of
+
+ align:start position:0%
+the cones and the powerful principle of
+ 
+
+ align:start position:0%
+the cones and the powerful principle of
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+analysis from that we were able to find
+
+ align:start position:0%
+analysis from that we were able to find
+ 
+
+ align:start position:0%
+analysis from that we were able to find
+all the exponents here in the
+
+ align:start position:0%
+all the exponents here in the
+ 
+
+ align:start position:0%
+all the exponents here in the
+relationship between drag and density
+
+ align:start position:0%
+relationship between drag and density
+ 
+
+ align:start position:0%
+relationship between drag and density
+speed and cross-sectional
+
+ align:start position:0%
+speed and cross-sectional
+ 
+
+ align:start position:0%
+speed and cross-sectional
+area so the moral of this is that there
+
+ align:start position:0%
+area so the moral of this is that there
+ 
+
+ align:start position:0%
+area so the moral of this is that there
+is an art to
+
+ align:start position:0%
+is an art to
+ 
+
+ align:start position:0%
+is an art to
+approximations reasoning tools such as
+
+ align:start position:0%
+approximations reasoning tools such as
+ 
+
+ align:start position:0%
+approximations reasoning tools such as
+dimensional analysis give you an
+
+ align:start position:0%
+dimensional analysis give you an
+ 
+
+ align:start position:0%
+dimensional analysis give you an
+understanding of how systems behave
+
+ align:start position:0%
+understanding of how systems behave
+ 
+
+ align:start position:0%
+understanding of how systems behave
+without having to solve every single
+
+ align:start position:0%
+without having to solve every single
+ 
+
+ align:start position:0%
+without having to solve every single
+last bit of the detailed mathematics
+
+ align:start position:0%
+last bit of the detailed mathematics
+ 
+
+ align:start position:0%
+last bit of the detailed mathematics
+this understanding allows us to redesign
+
+ align:start position:0%
+this understanding allows us to redesign
+ 
+
+ align:start position:0%
+this understanding allows us to redesign
+the world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/XKYpKYspe1w.txt b/XKYpKYspe1w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..077399b446eb26f3cd04ab88793d2b3d128b20b8
--- /dev/null
+++ b/XKYpKYspe1w.txt
@@ -0,0 +1,1315 @@
+align:start position:0%
+ 
+we are going to spend the rest of this
+
+ align:start position:0%
+we are going to spend the rest of this
+ 
+
+ align:start position:0%
+we are going to spend the rest of this
+lecture by looking into an interesting
+
+ align:start position:0%
+lecture by looking into an interesting
+ 
+
+ align:start position:0%
+lecture by looking into an interesting
+subclass of Markov chains for which
+
+ align:start position:0%
+subclass of Markov chains for which
+ 
+
+ align:start position:0%
+subclass of Markov chains for which
+steady-state convergent exists the class
+
+ align:start position:0%
+steady-state convergent exists the class
+ 
+
+ align:start position:0%
+steady-state convergent exists the class
+of birth and death processes so what is
+
+ align:start position:0%
+of birth and death processes so what is
+ 
+
+ align:start position:0%
+of birth and death processes so what is
+a birth and death process
+
+ align:start position:0%
+a birth and death process
+ 
+
+ align:start position:0%
+a birth and death process
+it's a Markov chain was diagram looks
+
+ align:start position:0%
+it's a Markov chain was diagram looks
+ 
+
+ align:start position:0%
+it's a Markov chain was diagram looks
+like this the states of the Markov chain
+
+ align:start position:0%
+like this the states of the Markov chain
+ 
+
+ align:start position:0%
+like this the states of the Markov chain
+start from zero and go up to some finite
+
+ align:start position:0%
+start from zero and go up to some finite
+ 
+
+ align:start position:0%
+start from zero and go up to some finite
+integer number M and if you are at a
+
+ align:start position:0%
+integer number M and if you are at a
+ 
+
+ align:start position:0%
+integer number M and if you are at a
+typical state in the middle say I then
+
+ align:start position:0%
+typical state in the middle say I then
+ 
+
+ align:start position:0%
+typical state in the middle say I then
+next you will either go to the right or
+
+ align:start position:0%
+next you will either go to the right or
+ 
+
+ align:start position:0%
+next you will either go to the right or
+up by one unit or you will go to the
+
+ align:start position:0%
+up by one unit or you will go to the
+ 
+
+ align:start position:0%
+up by one unit or you will go to the
+left or down by one unit or you will
+
+ align:start position:0%
+left or down by one unit or you will
+ 
+
+ align:start position:0%
+left or down by one unit or you will
+stay where you are
+
+ align:start position:0%
+stay where you are
+ 
+
+ align:start position:0%
+stay where you are
+and this will happen with the following
+
+ align:start position:0%
+and this will happen with the following
+ 
+
+ align:start position:0%
+and this will happen with the following
+transition probabilities here P I I
+
+ align:start position:0%
+transition probabilities here P I I
+ 
+
+ align:start position:0%
+transition probabilities here P I I
+function of the state here Q I and this
+
+ align:start position:0%
+function of the state here Q I and this
+ 
+
+ align:start position:0%
+function of the state here Q I and this
+one the remaining one minus P I minus Q
+
+ align:start position:0%
+one the remaining one minus P I minus Q
+ 
+
+ align:start position:0%
+one the remaining one minus P I minus Q
+I so it's like keeping track of some
+
+ align:start position:0%
+I so it's like keeping track of some
+ 
+
+ align:start position:0%
+I so it's like keeping track of some
+animal population animals get born they
+
+ align:start position:0%
+animal population animals get born they
+ 
+
+ align:start position:0%
+animal population animals get born they
+die the assumption here is that at any
+
+ align:start position:0%
+die the assumption here is that at any
+ 
+
+ align:start position:0%
+die the assumption here is that at any
+point in time either one animal gets
+
+ align:start position:0%
+point in time either one animal gets
+ 
+
+ align:start position:0%
+point in time either one animal gets
+born or one dies or nothing happens
+
+ align:start position:0%
+born or one dies or nothing happens
+ 
+
+ align:start position:0%
+born or one dies or nothing happens
+there are no multiple deaths no births
+
+ align:start position:0%
+there are no multiple deaths no births
+ 
+
+ align:start position:0%
+there are no multiple deaths no births
+happening at the same time there are
+
+ align:start position:0%
+happening at the same time there are
+ 
+
+ align:start position:0%
+happening at the same time there are
+many practical applications where the
+
+ align:start position:0%
+many practical applications where the
+ 
+
+ align:start position:0%
+many practical applications where the
+structure provides a basic first level
+
+ align:start position:0%
+structure provides a basic first level
+ 
+
+ align:start position:0%
+structure provides a basic first level
+Moll an example of a chain of this kind
+
+ align:start position:0%
+Moll an example of a chain of this kind
+ 
+
+ align:start position:0%
+Moll an example of a chain of this kind
+was the supermarket counter example that
+
+ align:start position:0%
+was the supermarket counter example that
+ 
+
+ align:start position:0%
+was the supermarket counter example that
+we discussed before where the states
+
+ align:start position:0%
+we discussed before where the states
+ 
+
+ align:start position:0%
+we discussed before where the states
+represented the number of customers in
+
+ align:start position:0%
+represented the number of customers in
+ 
+
+ align:start position:0%
+represented the number of customers in
+the queue a customer arrives and the
+
+ align:start position:0%
+the queue a customer arrives and the
+ 
+
+ align:start position:0%
+the queue a customer arrives and the
+queue increases by one a customer leaves
+
+ align:start position:0%
+queue increases by one a customer leaves
+ 
+
+ align:start position:0%
+queue increases by one a customer leaves
+and the queue decreases by one or
+
+ align:start position:0%
+and the queue decreases by one or
+ 
+
+ align:start position:0%
+and the queue decreases by one or
+nothing happens and the queue stay as it
+
+ align:start position:0%
+nothing happens and the queue stay as it
+ 
+
+ align:start position:0%
+nothing happens and the queue stay as it
+is now in this supermarket example the
+
+ align:start position:0%
+is now in this supermarket example the
+ 
+
+ align:start position:0%
+is now in this supermarket example the
+peas and the queues were all taken to be
+
+ align:start position:0%
+peas and the queues were all taken to be
+ 
+
+ align:start position:0%
+peas and the queues were all taken to be
+the same across the states but we can
+
+ align:start position:0%
+the same across the states but we can
+ 
+
+ align:start position:0%
+the same across the states but we can
+generalize for example the departure
+
+ align:start position:0%
+generalize for example the departure
+ 
+
+ align:start position:0%
+generalize for example the departure
+rate Q could be different from state to
+
+ align:start position:0%
+rate Q could be different from state to
+ 
+
+ align:start position:0%
+rate Q could be different from state to
+state for example with lots of customers
+
+ align:start position:0%
+state for example with lots of customers
+ 
+
+ align:start position:0%
+state for example with lots of customers
+in the queue perhaps the clerk will work
+
+ align:start position:0%
+in the queue perhaps the clerk will work
+ 
+
+ align:start position:0%
+in the queue perhaps the clerk will work
+faster such a chain can also be used to
+
+ align:start position:0%
+faster such a chain can also be used to
+ 
+
+ align:start position:0%
+faster such a chain can also be used to
+model the spread of disease in
+
+ align:start position:0%
+model the spread of disease in
+ 
+
+ align:start position:0%
+model the spread of disease in
+population for example the states could
+
+ align:start position:0%
+population for example the states could
+ 
+
+ align:start position:0%
+population for example the states could
+represent the number of people in a
+
+ align:start position:0%
+represent the number of people in a
+ 
+
+ align:start position:0%
+represent the number of people in a
+given population that have the flu one
+
+ align:start position:0%
+given population that have the flu one
+ 
+
+ align:start position:0%
+given population that have the flu one
+more person gets the flu the count goes
+
+ align:start position:0%
+more person gets the flu the count goes
+ 
+
+ align:start position:0%
+more person gets the flu the count goes
+up one more person gets healed the count
+
+ align:start position:0%
+up one more person gets healed the count
+ 
+
+ align:start position:0%
+up one more person gets healed the count
+goes down these probabilities in such an
+
+ align:start position:0%
+goes down these probabilities in such an
+ 
+
+ align:start position:0%
+goes down these probabilities in such an
+epidemic Mao would certainly depend on
+
+ align:start position:0%
+epidemic Mao would certainly depend on
+ 
+
+ align:start position:0%
+epidemic Mao would certainly depend on
+the current state if lots of people
+
+ align:start position:0%
+the current state if lots of people
+ 
+
+ align:start position:0%
+the current state if lots of people
+already have the flu the priority that
+
+ align:start position:0%
+already have the flu the priority that
+ 
+
+ align:start position:0%
+already have the flu the priority that
+another person catches it would be
+
+ align:start position:0%
+another person catches it would be
+ 
+
+ align:start position:0%
+another person catches it would be
+pretty high but if no one has the flu
+
+ align:start position:0%
+pretty high but if no one has the flu
+ 
+
+ align:start position:0%
+pretty high but if no one has the flu
+then the priority that one gets a
+
+ align:start position:0%
+then the priority that one gets a
+ 
+
+ align:start position:0%
+then the priority that one gets a
+transition where someone catches the flu
+
+ align:start position:0%
+transition where someone catches the flu
+ 
+
+ align:start position:0%
+transition where someone catches the flu
+would be pretty small the rate at which
+
+ align:start position:0%
+would be pretty small the rate at which
+ 
+
+ align:start position:0%
+would be pretty small the rate at which
+new people get the disease definitely
+
+ align:start position:0%
+new people get the disease definitely
+ 
+
+ align:start position:0%
+new people get the disease definitely
+depends on how many people already have
+
+ align:start position:0%
+depends on how many people already have
+ 
+
+ align:start position:0%
+depends on how many people already have
+it and that motivates cases were those
+
+ align:start position:0%
+it and that motivates cases were those
+ 
+
+ align:start position:0%
+it and that motivates cases were those
+bees here depend on the state of the
+
+ align:start position:0%
+bees here depend on the state of the
+ 
+
+ align:start position:0%
+bees here depend on the state of the
+chain there are lots of other
+
+ align:start position:0%
+chain there are lots of other
+ 
+
+ align:start position:0%
+chain there are lots of other
+applications for which these special
+
+ align:start position:0%
+applications for which these special
+ 
+
+ align:start position:0%
+applications for which these special
+Markov chains are useful so how do we
+
+ align:start position:0%
+Markov chains are useful so how do we
+ 
+
+ align:start position:0%
+Markov chains are useful so how do we
+study them such a chain consists of a
+
+ align:start position:0%
+study them such a chain consists of a
+ 
+
+ align:start position:0%
+study them such a chain consists of a
+single a periodic recurrent class and so
+
+ align:start position:0%
+single a periodic recurrent class and so
+ 
+
+ align:start position:0%
+single a periodic recurrent class and so
+as a well-defined to the state behavior
+
+ align:start position:0%
+as a well-defined to the state behavior
+ 
+
+ align:start position:0%
+as a well-defined to the state behavior
+to calculate the steady-state
+
+ align:start position:0%
+to calculate the steady-state
+ 
+
+ align:start position:0%
+to calculate the steady-state
+probability PI of I of a state I you can
+
+ align:start position:0%
+probability PI of I of a state I you can
+ 
+
+ align:start position:0%
+probability PI of I of a state I you can
+write the system of M linear equations
+
+ align:start position:0%
+write the system of M linear equations
+ 
+
+ align:start position:0%
+write the system of M linear equations
+in the PI's that we had discussed before
+
+ align:start position:0%
+in the PI's that we had discussed before
+ 
+
+ align:start position:0%
+in the PI's that we had discussed before
+but this may be cumbersome and in fact
+
+ align:start position:0%
+but this may be cumbersome and in fact
+ 
+
+ align:start position:0%
+but this may be cumbersome and in fact
+more work than one actually needs to do
+
+ align:start position:0%
+more work than one actually needs to do
+ 
+
+ align:start position:0%
+more work than one actually needs to do
+there is a very clever shortcut that
+
+ align:start position:0%
+there is a very clever shortcut that
+ 
+
+ align:start position:0%
+there is a very clever shortcut that
+applies to birth and death processes and
+
+ align:start position:0%
+applies to birth and death processes and
+ 
+
+ align:start position:0%
+applies to birth and death processes and
+it's based on the frequency
+
+ align:start position:0%
+it's based on the frequency
+ 
+
+ align:start position:0%
+it's based on the frequency
+interpretation that we discussed in the
+
+ align:start position:0%
+interpretation that we discussed in the
+ 
+
+ align:start position:0%
+interpretation that we discussed in the
+recent clip to see this let's draw a
+
+ align:start position:0%
+recent clip to see this let's draw a
+ 
+
+ align:start position:0%
+recent clip to see this let's draw a
+line somewhere in the middle of this
+
+ align:start position:0%
+line somewhere in the middle of this
+ 
+
+ align:start position:0%
+line somewhere in the middle of this
+chain and focus on the transitions
+
+ align:start position:0%
+chain and focus on the transitions
+ 
+
+ align:start position:0%
+chain and focus on the transitions
+between this left part and this right
+
+ align:start position:0%
+between this left part and this right
+ 
+
+ align:start position:0%
+between this left part and this right
+part assume that the line cut through
+
+ align:start position:0%
+part assume that the line cut through
+ 
+
+ align:start position:0%
+part assume that the line cut through
+the middle of two adjacent states I and
+
+ align:start position:0%
+the middle of two adjacent states I and
+ 
+
+ align:start position:0%
+the middle of two adjacent states I and
+I plus one like here and so then you
+
+ align:start position:0%
+I plus one like here and so then you
+ 
+
+ align:start position:0%
+I plus one like here and so then you
+zoom here and this is the picture of
+
+ align:start position:0%
+zoom here and this is the picture of
+ 
+
+ align:start position:0%
+zoom here and this is the picture of
+what you have here so what is the chain
+
+ align:start position:0%
+what you have here so what is the chain
+ 
+
+ align:start position:0%
+what you have here so what is the chain
+going to do let's say it starts on the
+
+ align:start position:0%
+going to do let's say it starts on the
+ 
+
+ align:start position:0%
+going to do let's say it starts on the
+left it's going to move around and at
+
+ align:start position:0%
+left it's going to move around and at
+ 
+
+ align:start position:0%
+left it's going to move around and at
+some point it makes a transition to the
+
+ align:start position:0%
+some point it makes a transition to the
+ 
+
+ align:start position:0%
+some point it makes a transition to the
+other side going here and that is a
+
+ align:start position:0%
+other side going here and that is a
+ 
+
+ align:start position:0%
+other side going here and that is a
+transition
+
+ align:start position:0%
+transition
+ 
+
+ align:start position:0%
+transition
+i to i plus one and now once it's on the
+
+ align:start position:0%
+i to i plus one and now once it's on the
+ 
+
+ align:start position:0%
+i to i plus one and now once it's on the
+right side it's going to move around as
+
+ align:start position:0%
+right side it's going to move around as
+ 
+
+ align:start position:0%
+right side it's going to move around as
+well and then at one point it will come
+
+ align:start position:0%
+well and then at one point it will come
+ 
+
+ align:start position:0%
+well and then at one point it will come
+back to that part again and this is a
+
+ align:start position:0%
+back to that part again and this is a
+ 
+
+ align:start position:0%
+back to that part again and this is a
+transition from i plus 1 to i and so on
+
+ align:start position:0%
+transition from i plus 1 to i and so on
+ 
+
+ align:start position:0%
+transition from i plus 1 to i and so on
+and so forth now there is a certain
+
+ align:start position:0%
+and so forth now there is a certain
+ 
+
+ align:start position:0%
+and so forth now there is a certain
+balance that must be obeyed here the
+
+ align:start position:0%
+balance that must be obeyed here the
+ 
+
+ align:start position:0%
+balance that must be obeyed here the
+number of upward transitions through
+
+ align:start position:0%
+number of upward transitions through
+ 
+
+ align:start position:0%
+number of upward transitions through
+this line cannot be very different from
+
+ align:start position:0%
+this line cannot be very different from
+ 
+
+ align:start position:0%
+this line cannot be very different from
+the number of downward transition from
+
+ align:start position:0%
+the number of downward transition from
+ 
+
+ align:start position:0%
+the number of downward transition from
+this line because if we cross this way
+
+ align:start position:0%
+this line because if we cross this way
+ 
+
+ align:start position:0%
+this line because if we cross this way
+then in order to cross again this way
+
+ align:start position:0%
+then in order to cross again this way
+ 
+
+ align:start position:0%
+then in order to cross again this way
+you will have first to cross down the
+
+ align:start position:0%
+you will have first to cross down the
+ 
+
+ align:start position:0%
+you will have first to cross down the
+other way
+
+ align:start position:0%
+other way
+ 
+
+ align:start position:0%
+other way
+you cannot go up one other times here in
+
+ align:start position:0%
+you cannot go up one other times here in
+ 
+
+ align:start position:0%
+you cannot go up one other times here in
+that direction and go down here 50 times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have gone up one other times it
+
+ align:start position:0%
+if you have gone up one other times it
+ 
+
+ align:start position:0%
+if you have gone up one other times it
+means that you have gone down 99 100 or
+
+ align:start position:0%
+means that you have gone down 99 100 or
+ 
+
+ align:start position:0%
+means that you have gone down 99 100 or
+101 but nothing different from that so
+
+ align:start position:0%
+101 but nothing different from that so
+ 
+
+ align:start position:0%
+101 but nothing different from that so
+the long-term frequency with which
+
+ align:start position:0%
+the long-term frequency with which
+ 
+
+ align:start position:0%
+the long-term frequency with which
+transition of this kind occur has to be
+
+ align:start position:0%
+transition of this kind occur has to be
+ 
+
+ align:start position:0%
+transition of this kind occur has to be
+the same as the long-term frequency the
+
+ align:start position:0%
+the same as the long-term frequency the
+ 
+
+ align:start position:0%
+the same as the long-term frequency the
+transition of that kind occur or in this
+
+ align:start position:0%
+transition of that kind occur or in this
+ 
+
+ align:start position:0%
+transition of that kind occur or in this
+diagram the frequency of that kind has
+
+ align:start position:0%
+diagram the frequency of that kind has
+ 
+
+ align:start position:0%
+diagram the frequency of that kind has
+to be the same as the frequency of that
+
+ align:start position:0%
+to be the same as the frequency of that
+ 
+
+ align:start position:0%
+to be the same as the frequency of that
+kind so what are these frequencies we
+
+ align:start position:0%
+kind so what are these frequencies we
+ 
+
+ align:start position:0%
+kind so what are these frequencies we
+discussed that before the fraction of
+
+ align:start position:0%
+discussed that before the fraction of
+ 
+
+ align:start position:0%
+discussed that before the fraction of
+times at which transition of this kind
+
+ align:start position:0%
+times at which transition of this kind
+ 
+
+ align:start position:0%
+times at which transition of this kind
+are observed is the fraction of time
+
+ align:start position:0%
+are observed is the fraction of time
+ 
+
+ align:start position:0%
+are observed is the fraction of time
+that we happen to be at that state which
+
+ align:start position:0%
+that we happen to be at that state which
+ 
+
+ align:start position:0%
+that we happen to be at that state which
+is PI of I and out of the terms that we
+
+ align:start position:0%
+is PI of I and out of the terms that we
+ 
+
+ align:start position:0%
+is PI of I and out of the terms that we
+are in that state the fraction of time
+
+ align:start position:0%
+are in that state the fraction of time
+ 
+
+ align:start position:0%
+are in that state the fraction of time
+that transitions of that time happen is
+
+ align:start position:0%
+that transitions of that time happen is
+ 
+
+ align:start position:0%
+that transitions of that time happen is
+P of I so the overall frequency will be
+
+ align:start position:0%
+P of I so the overall frequency will be
+ 
+
+ align:start position:0%
+P of I so the overall frequency will be
+PI I times P of I and with the same
+
+ align:start position:0%
+PI I times P of I and with the same
+ 
+
+ align:start position:0%
+PI I times P of I and with the same
+argument this is the frequency with
+
+ align:start position:0%
+argument this is the frequency with
+ 
+
+ align:start position:0%
+argument this is the frequency with
+which transition of that kind our
+
+ align:start position:0%
+which transition of that kind our
+ 
+
+ align:start position:0%
+which transition of that kind our
+observed pie I plus 1 times Q I plus 1
+
+ align:start position:0%
+observed pie I plus 1 times Q I plus 1
+ 
+
+ align:start position:0%
+observed pie I plus 1 times Q I plus 1
+since these two frequencies are the same
+
+ align:start position:0%
+since these two frequencies are the same
+ 
+
+ align:start position:0%
+since these two frequencies are the same
+we get an equation that relates PI of I
+
+ align:start position:0%
+we get an equation that relates PI of I
+ 
+
+ align:start position:0%
+we get an equation that relates PI of I
+to PI of I plus one like this so this is
+
+ align:start position:0%
+to PI of I plus one like this so this is
+ 
+
+ align:start position:0%
+to PI of I plus one like this so this is
+the frequency that we observed here of
+
+ align:start position:0%
+the frequency that we observed here of
+ 
+
+ align:start position:0%
+the frequency that we observed here of
+this transition and these are the
+
+ align:start position:0%
+this transition and these are the
+ 
+
+ align:start position:0%
+this transition and these are the
+frequency of these transitions and they
+
+ align:start position:0%
+frequency of these transitions and they
+ 
+
+ align:start position:0%
+frequency of these transitions and they
+had to be equal this has a nice form
+
+ align:start position:0%
+had to be equal this has a nice form
+ 
+
+ align:start position:0%
+had to be equal this has a nice form
+because it gives us a recursion
+
+ align:start position:0%
+because it gives us a recursion
+ 
+
+ align:start position:0%
+because it gives us a recursion
+if we knew PI I you can calculate pi I
+
+ align:start position:0%
+if we knew PI I you can calculate pi I
+ 
+
+ align:start position:0%
+if we knew PI I you can calculate pi I
+plus 1 a search
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's a system of equations that's
+
+ align:start position:0%
+so it's a system of equations that's
+ 
+
+ align:start position:0%
+so it's a system of equations that's
+easier to solve than the original system
+
+ align:start position:0%
+easier to solve than the original system
+ 
+
+ align:start position:0%
+easier to solve than the original system
+of linear equations which represent it
+
+ align:start position:0%
+of linear equations which represent it
+ 
+
+ align:start position:0%
+of linear equations which represent it
+before for a general Markov chain but
+
+ align:start position:0%
+before for a general Markov chain but
+ 
+
+ align:start position:0%
+before for a general Markov chain but
+how do we get started
+
+ align:start position:0%
+how do we get started
+ 
+
+ align:start position:0%
+how do we get started
+if we knew PI of 0 then we can use it to
+
+ align:start position:0%
+if we knew PI of 0 then we can use it to
+ 
+
+ align:start position:0%
+if we knew PI of 0 then we can use it to
+find PI of 1 then from PI of 1 you can
+
+ align:start position:0%
+find PI of 1 then from PI of 1 you can
+ 
+
+ align:start position:0%
+find PI of 1 then from PI of 1 you can
+get PI of 2 by oh 3 etc but we don't
+
+ align:start position:0%
+get PI of 2 by oh 3 etc but we don't
+ 
+
+ align:start position:0%
+get PI of 2 by oh 3 etc but we don't
+know PI of 0 it's one more unknown it's
+
+ align:start position:0%
+know PI of 0 it's one more unknown it's
+ 
+
+ align:start position:0%
+know PI of 0 it's one more unknown it's
+an unknown and we need to actually use
+
+ align:start position:0%
+an unknown and we need to actually use
+ 
+
+ align:start position:0%
+an unknown and we need to actually use
+the extra normalization conditions that
+
+ align:start position:0%
+the extra normalization conditions that
+ 
+
+ align:start position:0%
+the extra normalization conditions that
+the Sun of all the P I PI J has to be
+
+ align:start position:0%
+the Sun of all the P I PI J has to be
+ 
+
+ align:start position:0%
+the Sun of all the P I PI J has to be
+equal to 1 and after we use that
+
+ align:start position:0%
+equal to 1 and after we use that
+ 
+
+ align:start position:0%
+equal to 1 and after we use that
+normalization condition then we can find
+
+ align:start position:0%
+normalization condition then we can find
+ 
+
+ align:start position:0%
+normalization condition then we can find
+all of the PI by first solving for PI of
+
+ align:start position:0%
+all of the PI by first solving for PI of
+ 
+
+ align:start position:0%
+all of the PI by first solving for PI of
+0 how this can be written PI 0 plus PI 1
+
+ align:start position:0%
+0 how this can be written PI 0 plus PI 1
+ 
+
+ align:start position:0%
+0 how this can be written PI 0 plus PI 1
+which is PI 0 times spiezio over Q 1
+
+ align:start position:0%
+which is PI 0 times spiezio over Q 1
+ 
+
+ align:start position:0%
+which is PI 0 times spiezio over Q 1
+plus PI of 2 which is PI of 1 times P 1
+
+ align:start position:0%
+plus PI of 2 which is PI of 1 times P 1
+ 
+
+ align:start position:0%
+plus PI of 2 which is PI of 1 times P 1
+over Q 2 PI of 0 times P 0 times P 1
+
+ align:start position:0%
+over Q 2 PI of 0 times P 0 times P 1
+ 
+
+ align:start position:0%
+over Q 2 PI of 0 times P 0 times P 1
+over q1 times q2 which is PI 2 plus etc
+
+ align:start position:0%
+over q1 times q2 which is PI 2 plus etc
+ 
+
+ align:start position:0%
+over q1 times q2 which is PI 2 plus etc
+equals 1 so this equation allows us to
+
+ align:start position:0%
+equals 1 so this equation allows us to
+ 
+
+ align:start position:0%
+equals 1 so this equation allows us to
+find PI of 0 and then we use this
+
+ align:start position:0%
+find PI of 0 and then we use this
+ 
+
+ align:start position:0%
+find PI of 0 and then we use this
+recursion to find PI of 1 PI of 2 pi 3
+
+ align:start position:0%
+recursion to find PI of 1 PI of 2 pi 3
+ 
+
+ align:start position:0%
+recursion to find PI of 1 PI of 2 pi 3
+etc
\ No newline at end of file
diff --git a/XSUjp-cDyeY.txt b/XSUjp-cDyeY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..647a60b3799b9b7a56fe66b9c14ca2f939ea07a4
--- /dev/null
+++ b/XSUjp-cDyeY.txt
@@ -0,0 +1,16347 @@
+align:start position:0%
+ 
+let's start with some announcements
+
+ align:start position:0%
+let's start with some announcements
+ 
+
+ align:start position:0%
+let's start with some announcements
+we've had three homework problems and
+
+ align:start position:0%
+we've had three homework problems and
+ 
+
+ align:start position:0%
+we've had three homework problems and
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+ready for the first
+
+ align:start position:0%
+ready for the first
+ 
+
+ align:start position:0%
+ready for the first
+take-home quiz
+
+ align:start position:0%
+take-home quiz
+ 
+
+ align:start position:0%
+take-home quiz
+and the rules again are that it'll count
+
+ align:start position:0%
+and the rules again are that it'll count
+ 
+
+ align:start position:0%
+and the rules again are that it'll count
+twice as much as the homework problem
+
+ align:start position:0%
+twice as much as the homework problem
+ 
+
+ align:start position:0%
+twice as much as the homework problem
+and there's no collaboration unlike
+
+ align:start position:0%
+and there's no collaboration unlike
+ 
+
+ align:start position:0%
+and there's no collaboration unlike
+homework problems
+
+ align:start position:0%
+homework problems
+ 
+
+ align:start position:0%
+homework problems
+so that's uh
+
+ align:start position:0%
+so that's uh
+ 
+
+ align:start position:0%
+so that's uh
+next week
+
+ align:start position:0%
+next week
+ 
+
+ align:start position:0%
+next week
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+those of you in 686
+
+ align:start position:0%
+those of you in 686
+ 
+
+ align:start position:0%
+those of you in 686
+there's a proposal due on the 22nd
+
+ align:start position:0%
+there's a proposal due on the 22nd
+ 
+
+ align:start position:0%
+there's a proposal due on the 22nd
+and that's meant to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+short
+
+ align:start position:0%
+short
+ 
+
+ align:start position:0%
+short
+and that's where you tell me uh what
+
+ align:start position:0%
+and that's where you tell me uh what
+ 
+
+ align:start position:0%
+and that's where you tell me uh what
+you'll be doing for the term project
+
+ align:start position:0%
+you'll be doing for the term project
+ 
+
+ align:start position:0%
+you'll be doing for the term project
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+the idea of the term project is to take
+
+ align:start position:0%
+the idea of the term project is to take
+ 
+
+ align:start position:0%
+the idea of the term project is to take
+some machine vision
+
+ align:start position:0%
+some machine vision
+ 
+
+ align:start position:0%
+some machine vision
+problem uh preferably something we
+
+ align:start position:0%
+problem uh preferably something we
+ 
+
+ align:start position:0%
+problem uh preferably something we
+discussed in class
+
+ align:start position:0%
+discussed in class
+ 
+
+ align:start position:0%
+discussed in class
+and implement it in some way
+
+ align:start position:0%
+and implement it in some way
+ 
+
+ align:start position:0%
+and implement it in some way
+and your choice it could be
+
+ align:start position:0%
+and your choice it could be
+ 
+
+ align:start position:0%
+and your choice it could be
+i don't know windows matlab
+
+ align:start position:0%
+i don't know windows matlab
+ 
+
+ align:start position:0%
+i don't know windows matlab
+android
+
+ align:start position:0%
+android
+ 
+
+ align:start position:0%
+android
+whatever
+
+ align:start position:0%
+whatever
+ 
+
+ align:start position:0%
+whatever
+it could also be something
+
+ align:start position:0%
+it could also be something
+ 
+
+ align:start position:0%
+it could also be something
+more theoretical it could be
+
+ align:start position:0%
+more theoretical it could be
+ 
+
+ align:start position:0%
+more theoretical it could be
+some mathematical solution to some
+
+ align:start position:0%
+some mathematical solution to some
+ 
+
+ align:start position:0%
+some mathematical solution to some
+machine vision problem most people opt
+
+ align:start position:0%
+machine vision problem most people opt
+ 
+
+ align:start position:0%
+machine vision problem most people opt
+to do some kind of implementation
+
+ align:start position:0%
+to do some kind of implementation
+ 
+
+ align:start position:0%
+to do some kind of implementation
+and it's very flexible i mean if you
+
+ align:start position:0%
+and it's very flexible i mean if you
+ 
+
+ align:start position:0%
+and it's very flexible i mean if you
+find that
+
+ align:start position:0%
+find that
+ 
+
+ align:start position:0%
+find that
+you can use opencv
+
+ align:start position:0%
+you can use opencv
+ 
+
+ align:start position:0%
+you can use opencv
+to implement part of what you want to do
+
+ align:start position:0%
+to implement part of what you want to do
+ 
+
+ align:start position:0%
+to implement part of what you want to do
+go ahead and do that but of course then
+
+ align:start position:0%
+go ahead and do that but of course then
+ 
+
+ align:start position:0%
+go ahead and do that but of course then
+your contribution has to be on top of
+
+ align:start position:0%
+your contribution has to be on top of
+ 
+
+ align:start position:0%
+your contribution has to be on top of
+that not just using opencv but
+
+ align:start position:0%
+that not just using opencv but
+ 
+
+ align:start position:0%
+that not just using opencv but
+doing something useful with it
+
+ align:start position:0%
+doing something useful with it
+ 
+
+ align:start position:0%
+doing something useful with it
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if you have problems coming up with
+
+ align:start position:0%
+if you have problems coming up with
+ 
+
+ align:start position:0%
+if you have problems coming up with
+ideas send me email
+
+ align:start position:0%
+ideas send me email
+ 
+
+ align:start position:0%
+ideas send me email
+what will happen with the proposal is
+
+ align:start position:0%
+what will happen with the proposal is
+ 
+
+ align:start position:0%
+what will happen with the proposal is
+i'll take a look at them and if i can
+
+ align:start position:0%
+i'll take a look at them and if i can
+ 
+
+ align:start position:0%
+i'll take a look at them and if i can
+point you to sources that might be
+
+ align:start position:0%
+point you to sources that might be
+ 
+
+ align:start position:0%
+point you to sources that might be
+helpful in implementing that project
+
+ align:start position:0%
+helpful in implementing that project
+ 
+
+ align:start position:0%
+helpful in implementing that project
+then then i will do so
+
+ align:start position:0%
+then then i will do so
+ 
+
+ align:start position:0%
+then then i will do so
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+just about to finish our discussion of
+
+ align:start position:0%
+just about to finish our discussion of
+ 
+
+ align:start position:0%
+just about to finish our discussion of
+how to extract stuff from image
+
+ align:start position:0%
+how to extract stuff from image
+ 
+
+ align:start position:0%
+how to extract stuff from image
+brightness
+
+ align:start position:0%
+brightness
+ 
+
+ align:start position:0%
+brightness
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in particular shape from shading
+
+ align:start position:0%
+in particular shape from shading
+ 
+
+ align:start position:0%
+in particular shape from shading
+and it's a little bit abstract a little
+
+ align:start position:0%
+and it's a little bit abstract a little
+ 
+
+ align:start position:0%
+and it's a little bit abstract a little
+bit mathematical and would soon have a
+
+ align:start position:0%
+bit mathematical and would soon have a
+ 
+
+ align:start position:0%
+bit mathematical and would soon have a
+big change of pace
+
+ align:start position:0%
+big change of pace
+ 
+
+ align:start position:0%
+big change of pace
+when we start talking about industrial
+
+ align:start position:0%
+when we start talking about industrial
+ 
+
+ align:start position:0%
+when we start talking about industrial
+machine vision
+
+ align:start position:0%
+machine vision
+ 
+
+ align:start position:0%
+machine vision
+and of course we can't cover everything
+
+ align:start position:0%
+and of course we can't cover everything
+ 
+
+ align:start position:0%
+and of course we can't cover everything
+and we'll take a different approach to
+
+ align:start position:0%
+and we'll take a different approach to
+ 
+
+ align:start position:0%
+and we'll take a different approach to
+covering it so rather than use published
+
+ align:start position:0%
+covering it so rather than use published
+ 
+
+ align:start position:0%
+covering it so rather than use published
+papers
+
+ align:start position:0%
+papers
+ 
+
+ align:start position:0%
+papers
+or textbooks
+
+ align:start position:0%
+or textbooks
+ 
+
+ align:start position:0%
+or textbooks
+we'll look at patents and part of the
+
+ align:start position:0%
+we'll look at patents and part of the
+ 
+
+ align:start position:0%
+we'll look at patents and part of the
+reason for that is that you know in our
+
+ align:start position:0%
+reason for that is that you know in our
+ 
+
+ align:start position:0%
+reason for that is that you know in our
+world you publish papers that's what you
+
+ align:start position:0%
+world you publish papers that's what you
+ 
+
+ align:start position:0%
+world you publish papers that's what you
+get credit for
+
+ align:start position:0%
+get credit for
+ 
+
+ align:start position:0%
+get credit for
+in their world you don't publish that's
+
+ align:start position:0%
+in their world you don't publish that's
+ 
+
+ align:start position:0%
+in their world you don't publish that's
+what you get credit for so
+
+ align:start position:0%
+what you get credit for so
+ 
+
+ align:start position:0%
+what you get credit for so
+when you do see what they're doing
+
+ align:start position:0%
+when you do see what they're doing
+ 
+
+ align:start position:0%
+when you do see what they're doing
+it's in the patents where they're trying
+
+ align:start position:0%
+it's in the patents where they're trying
+ 
+
+ align:start position:0%
+it's in the patents where they're trying
+to cover themselves
+
+ align:start position:0%
+to cover themselves
+ 
+
+ align:start position:0%
+to cover themselves
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+protect themselves from somebody else
+
+ align:start position:0%
+protect themselves from somebody else
+ 
+
+ align:start position:0%
+protect themselves from somebody else
+using that same idea so that'll be a big
+
+ align:start position:0%
+using that same idea so that'll be a big
+ 
+
+ align:start position:0%
+using that same idea so that'll be a big
+change of pace and in the process we'll
+
+ align:start position:0%
+change of pace and in the process we'll
+ 
+
+ align:start position:0%
+change of pace and in the process we'll
+learn a little bit about
+
+ align:start position:0%
+learn a little bit about
+ 
+
+ align:start position:0%
+learn a little bit about
+patents and patent language
+
+ align:start position:0%
+patents and patent language
+ 
+
+ align:start position:0%
+patents and patent language
+since you know that's a
+
+ align:start position:0%
+since you know that's a
+ 
+
+ align:start position:0%
+since you know that's a
+important topic if you're
+
+ align:start position:0%
+important topic if you're
+ 
+
+ align:start position:0%
+important topic if you're
+an entrepreneur
+
+ align:start position:0%
+an entrepreneur
+ 
+
+ align:start position:0%
+an entrepreneur
+involved in a startup or something of
+
+ align:start position:0%
+involved in a startup or something of
+ 
+
+ align:start position:0%
+involved in a startup or something of
+that sort so obviously that's going to
+
+ align:start position:0%
+that sort so obviously that's going to
+ 
+
+ align:start position:0%
+that sort so obviously that's going to
+be a little different from partial
+
+ align:start position:0%
+be a little different from partial
+ 
+
+ align:start position:0%
+be a little different from partial
+differential equations
+
+ align:start position:0%
+differential equations
+ 
+
+ align:start position:0%
+differential equations
+and some of you may be looking forward
+
+ align:start position:0%
+and some of you may be looking forward
+ 
+
+ align:start position:0%
+and some of you may be looking forward
+to that but but let's finish with the
+
+ align:start position:0%
+to that but but let's finish with the
+ 
+
+ align:start position:0%
+to that but but let's finish with the
+partial differential equations so where
+
+ align:start position:0%
+partial differential equations so where
+ 
+
+ align:start position:0%
+partial differential equations so where
+are we oh okay
+
+ align:start position:0%
+are we oh okay
+ 
+
+ align:start position:0%
+are we oh okay
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+for example you could implement time to
+
+ align:start position:0%
+for example you could implement time to
+ 
+
+ align:start position:0%
+for example you could implement time to
+contact on your android phone
+
+ align:start position:0%
+contact on your android phone
+ 
+
+ align:start position:0%
+contact on your android phone
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in that case
+
+ align:start position:0%
+in that case
+ 
+
+ align:start position:0%
+in that case
+you'd use android studio
+
+ align:start position:0%
+you'd use android studio
+ 
+
+ align:start position:0%
+you'd use android studio
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+i could supply you with a dummy project
+
+ align:start position:0%
+i could supply you with a dummy project
+ 
+
+ align:start position:0%
+i could supply you with a dummy project
+that's just a shell
+
+ align:start position:0%
+that's just a shell
+ 
+
+ align:start position:0%
+that's just a shell
+so that you don't have to uh write all
+
+ align:start position:0%
+so that you don't have to uh write all
+ 
+
+ align:start position:0%
+so that you don't have to uh write all
+of those files for android studio so
+
+ align:start position:0%
+of those files for android studio so
+ 
+
+ align:start position:0%
+of those files for android studio so
+that's an example um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could uh implement some of the
+
+ align:start position:0%
+you could uh implement some of the
+ 
+
+ align:start position:0%
+you could uh implement some of the
+subpixel
+
+ align:start position:0%
+subpixel
+ 
+
+ align:start position:0%
+subpixel
+methods that we'll talk about
+
+ align:start position:0%
+methods that we'll talk about
+ 
+
+ align:start position:0%
+methods that we'll talk about
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+edge detection
+
+ align:start position:0%
+edge detection
+ 
+
+ align:start position:0%
+edge detection
+and use
+
+ align:start position:0%
+and use
+ 
+
+ align:start position:0%
+and use
+whatever matlab
+
+ align:start position:0%
+whatever matlab
+ 
+
+ align:start position:0%
+whatever matlab
+whatever is convenient
+
+ align:start position:0%
+whatever is convenient
+ 
+
+ align:start position:0%
+whatever is convenient
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+that's an example project
+
+ align:start position:0%
+that's an example project
+ 
+
+ align:start position:0%
+that's an example project
+another example more theoretical would
+
+ align:start position:0%
+another example more theoretical would
+ 
+
+ align:start position:0%
+another example more theoretical would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+you know we've talked about
+
+ align:start position:0%
+you know we've talked about
+ 
+
+ align:start position:0%
+you know we've talked about
+shape from shading in the context of
+
+ align:start position:0%
+shape from shading in the context of
+ 
+
+ align:start position:0%
+shape from shading in the context of
+particular types of reflectance maps
+
+ align:start position:0%
+particular types of reflectance maps
+ 
+
+ align:start position:0%
+particular types of reflectance maps
+like hapki
+
+ align:start position:0%
+like hapki
+ 
+
+ align:start position:0%
+like hapki
+and you could implement you could work
+
+ align:start position:0%
+and you could implement you could work
+ 
+
+ align:start position:0%
+and you could implement you could work
+out the details for a different type of
+
+ align:start position:0%
+out the details for a different type of
+ 
+
+ align:start position:0%
+out the details for a different type of
+reflectance map there would be a more
+
+ align:start position:0%
+reflectance map there would be a more
+ 
+
+ align:start position:0%
+reflectance map there would be a more
+abstract mathematical project
+
+ align:start position:0%
+abstract mathematical project
+ 
+
+ align:start position:0%
+abstract mathematical project
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i think what i'll do is i'll pull
+
+ align:start position:0%
+i think what i'll do is i'll pull
+ 
+
+ align:start position:0%
+i think what i'll do is i'll pull
+together some of those and
+
+ align:start position:0%
+together some of those and
+ 
+
+ align:start position:0%
+together some of those and
+maybe say something about them on on the
+
+ align:start position:0%
+maybe say something about them on on the
+ 
+
+ align:start position:0%
+maybe say something about them on on the
+stella website
+
+ align:start position:0%
+stella website
+ 
+
+ align:start position:0%
+stella website
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh
+
+ align:start position:0%
+okay so uh
+ 
+
+ align:start position:0%
+okay so uh
+the first part of the term we were
+
+ align:start position:0%
+the first part of the term we were
+ 
+
+ align:start position:0%
+the first part of the term we were
+focusing mostly on
+
+ align:start position:0%
+focusing mostly on
+ 
+
+ align:start position:0%
+focusing mostly on
+image projection perspective projection
+
+ align:start position:0%
+image projection perspective projection
+ 
+
+ align:start position:0%
+image projection perspective projection
+equation and derivatives motion
+
+ align:start position:0%
+equation and derivatives motion
+ 
+
+ align:start position:0%
+equation and derivatives motion
+motion in the world motion in the image
+
+ align:start position:0%
+motion in the world motion in the image
+ 
+
+ align:start position:0%
+motion in the world motion in the image
+and then we switch to
+
+ align:start position:0%
+and then we switch to
+ 
+
+ align:start position:0%
+and then we switch to
+one one thing that we can do with image
+
+ align:start position:0%
+one one thing that we can do with image
+ 
+
+ align:start position:0%
+one one thing that we can do with image
+brightness measurements which is the
+
+ align:start position:0%
+brightness measurements which is the
+ 
+
+ align:start position:0%
+brightness measurements which is the
+other half of image formation
+
+ align:start position:0%
+other half of image formation
+ 
+
+ align:start position:0%
+other half of image formation
+and in particular
+
+ align:start position:0%
+and in particular
+ 
+
+ align:start position:0%
+and in particular
+we're looking at shape from shading
+
+ align:start position:0%
+we're looking at shape from shading
+ 
+
+ align:start position:0%
+we're looking at shape from shading
+and so far we've
+
+ align:start position:0%
+and so far we've
+ 
+
+ align:start position:0%
+and so far we've
+solved the problem for very particular
+
+ align:start position:0%
+solved the problem for very particular
+ 
+
+ align:start position:0%
+solved the problem for very particular
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+which is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hapka model of surface reflectance
+
+ align:start position:0%
+hapka model of surface reflectance
+ 
+
+ align:start position:0%
+hapka model of surface reflectance
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the core of all of it is
+
+ align:start position:0%
+at the core of all of it is
+ 
+
+ align:start position:0%
+at the core of all of it is
+the image irradiance equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which basically says the
+
+ align:start position:0%
+which basically says the
+ 
+
+ align:start position:0%
+which basically says the
+brightness at some point in the image
+
+ align:start position:0%
+brightness at some point in the image
+ 
+
+ align:start position:0%
+brightness at some point in the image
+is the reflectance map
+
+ align:start position:0%
+is the reflectance map
+ 
+
+ align:start position:0%
+is the reflectance map
+corresponding to that surface
+
+ align:start position:0%
+corresponding to that surface
+ 
+
+ align:start position:0%
+corresponding to that surface
+orientation so here we're focusing on
+
+ align:start position:0%
+orientation so here we're focusing on
+ 
+
+ align:start position:0%
+orientation so here we're focusing on
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dependence of brightness on surface
+
+ align:start position:0%
+dependence of brightness on surface
+ 
+
+ align:start position:0%
+dependence of brightness on surface
+orientation and as we mentioned it
+
+ align:start position:0%
+orientation and as we mentioned it
+ 
+
+ align:start position:0%
+orientation and as we mentioned it
+depends on illumination
+
+ align:start position:0%
+depends on illumination
+ 
+
+ align:start position:0%
+depends on illumination
+it depends on
+
+ align:start position:0%
+it depends on
+ 
+
+ align:start position:0%
+it depends on
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+material that's where the reflectance
+
+ align:start position:0%
+material that's where the reflectance
+ 
+
+ align:start position:0%
+material that's where the reflectance
+map comes into it
+
+ align:start position:0%
+map comes into it
+ 
+
+ align:start position:0%
+map comes into it
+and it depends on
+
+ align:start position:0%
+and it depends on
+ 
+
+ align:start position:0%
+and it depends on
+the geometry in particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in particular surface orientation and
+
+ align:start position:0%
+in particular surface orientation and
+ 
+
+ align:start position:0%
+in particular surface orientation and
+it's a local thing so that's sort of
+
+ align:start position:0%
+it's a local thing so that's sort of
+ 
+
+ align:start position:0%
+it's a local thing so that's sort of
+good it means that the brightness
+
+ align:start position:0%
+good it means that the brightness
+ 
+
+ align:start position:0%
+good it means that the brightness
+measurement at a particular point in the
+
+ align:start position:0%
+measurement at a particular point in the
+ 
+
+ align:start position:0%
+measurement at a particular point in the
+image typically depends on what's
+
+ align:start position:0%
+image typically depends on what's
+ 
+
+ align:start position:0%
+image typically depends on what's
+happening at the corresponding point on
+
+ align:start position:0%
+happening at the corresponding point on
+ 
+
+ align:start position:0%
+happening at the corresponding point on
+on the object
+
+ align:start position:0%
+on the object
+ 
+
+ align:start position:0%
+on the object
+and the reflectance map was our way of
+
+ align:start position:0%
+and the reflectance map was our way of
+ 
+
+ align:start position:0%
+and the reflectance map was our way of
+sort of summarizing
+
+ align:start position:0%
+sort of summarizing
+ 
+
+ align:start position:0%
+sort of summarizing
+uh the detailed reflecting properties
+
+ align:start position:0%
+uh the detailed reflecting properties
+ 
+
+ align:start position:0%
+uh the detailed reflecting properties
+which in turn atomically
+
+ align:start position:0%
+which in turn atomically
+ 
+
+ align:start position:0%
+which in turn atomically
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+reflected in the brdf
+
+ align:start position:0%
+reflected in the brdf
+ 
+
+ align:start position:0%
+reflected in the brdf
+so we had the
+
+ align:start position:0%
+so we had the
+ 
+
+ align:start position:0%
+so we had the
+bi-directional reflectance distribution
+
+ align:start position:0%
+bi-directional reflectance distribution
+ 
+
+ align:start position:0%
+bi-directional reflectance distribution
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+but we pretty much
+
+ align:start position:0%
+but we pretty much
+ 
+
+ align:start position:0%
+but we pretty much
+built up on that to where we have a
+
+ align:start position:0%
+built up on that to where we have a
+ 
+
+ align:start position:0%
+built up on that to where we have a
+somewhat easier to manage
+
+ align:start position:0%
+somewhat easier to manage
+ 
+
+ align:start position:0%
+somewhat easier to manage
+reflectance map so the brdf depends on
+
+ align:start position:0%
+reflectance map so the brdf depends on
+ 
+
+ align:start position:0%
+reflectance map so the brdf depends on
+four parameters the reflectance map only
+
+ align:start position:0%
+four parameters the reflectance map only
+ 
+
+ align:start position:0%
+four parameters the reflectance map only
+depends on two but it's it's derived
+
+ align:start position:0%
+depends on two but it's it's derived
+ 
+
+ align:start position:0%
+depends on two but it's it's derived
+it's built on top of the the brdf
+
+ align:start position:0%
+it's built on top of the the brdf
+ 
+
+ align:start position:0%
+it's built on top of the the brdf
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we looked at a particular case
+
+ align:start position:0%
+we looked at a particular case
+ 
+
+ align:start position:0%
+we looked at a particular case
+which is that of
+
+ align:start position:0%
+which is that of
+ 
+
+ align:start position:0%
+which is that of
+reflecting properties of the
+
+ align:start position:0%
+reflecting properties of the
+ 
+
+ align:start position:0%
+reflecting properties of the
+moon the mara of mario of the moon and
+
+ align:start position:0%
+moon the mara of mario of the moon and
+ 
+
+ align:start position:0%
+moon the mara of mario of the moon and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+rocky
+
+ align:start position:0%
+rocky
+ 
+
+ align:start position:0%
+rocky
+other rocky planets
+
+ align:start position:0%
+other rocky planets
+ 
+
+ align:start position:0%
+other rocky planets
+and in that case
+
+ align:start position:0%
+and in that case
+ 
+
+ align:start position:0%
+and in that case
+we found that we could solve this
+
+ align:start position:0%
+we found that we could solve this
+ 
+
+ align:start position:0%
+we found that we could solve this
+problem in a particular direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in in
+
+ align:start position:0%
+so in in
+ 
+
+ align:start position:0%
+so in in
+case of the moon
+
+ align:start position:0%
+case of the moon
+ 
+
+ align:start position:0%
+case of the moon
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if we take the ecliptic plane
+
+ align:start position:0%
+if we take the ecliptic plane
+ 
+
+ align:start position:0%
+if we take the ecliptic plane
+then that's the direction along which we
+
+ align:start position:0%
+then that's the direction along which we
+ 
+
+ align:start position:0%
+then that's the direction along which we
+can actually determine the surface
+
+ align:start position:0%
+can actually determine the surface
+ 
+
+ align:start position:0%
+can actually determine the surface
+orientation
+
+ align:start position:0%
+orientation
+ 
+
+ align:start position:0%
+orientation
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can integrate out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in certain direction and we can't
+
+ align:start position:0%
+in certain direction and we can't
+ 
+
+ align:start position:0%
+in certain direction and we can't
+integrate at all
+
+ align:start position:0%
+integrate at all
+ 
+
+ align:start position:0%
+integrate at all
+in the direction at right angles and i
+
+ align:start position:0%
+in the direction at right angles and i
+ 
+
+ align:start position:0%
+in the direction at right angles and i
+mean typically we'd be looking at some
+
+ align:start position:0%
+mean typically we'd be looking at some
+ 
+
+ align:start position:0%
+mean typically we'd be looking at some
+small patch
+
+ align:start position:0%
+small patch
+ 
+
+ align:start position:0%
+small patch
+but this gives us the idea of what
+
+ align:start position:0%
+but this gives us the idea of what
+ 
+
+ align:start position:0%
+but this gives us the idea of what
+directions we can perform this in and
+
+ align:start position:0%
+directions we can perform this in and
+ 
+
+ align:start position:0%
+directions we can perform this in and
+whatnot
+
+ align:start position:0%
+whatnot
+ 
+
+ align:start position:0%
+whatnot
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+what we ended up with is a set of
+
+ align:start position:0%
+what we ended up with is a set of
+ 
+
+ align:start position:0%
+what we ended up with is a set of
+equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+take us from point to point on the
+
+ align:start position:0%
+take us from point to point on the
+ 
+
+ align:start position:0%
+take us from point to point on the
+surface and first of all um
+
+ align:start position:0%
+surface and first of all um
+ 
+
+ align:start position:0%
+surface and first of all um
+x and y are varying in this way and i
+
+ align:start position:0%
+x and y are varying in this way and i
+ 
+
+ align:start position:0%
+x and y are varying in this way and i
+have to apologize i think maybe last
+
+ align:start position:0%
+have to apologize i think maybe last
+ 
+
+ align:start position:0%
+have to apologize i think maybe last
+time i ended up with i was reversed
+
+ align:start position:0%
+time i ended up with i was reversed
+ 
+
+ align:start position:0%
+time i ended up with i was reversed
+i had the first one being qs and ps
+
+ align:start position:0%
+i had the first one being qs and ps
+ 
+
+ align:start position:0%
+i had the first one being qs and ps
+and this corresponds to that angle of
+
+ align:start position:0%
+and this corresponds to that angle of
+ 
+
+ align:start position:0%
+and this corresponds to that angle of
+rotation where we rotated one coordinate
+
+ align:start position:0%
+rotation where we rotated one coordinate
+ 
+
+ align:start position:0%
+rotation where we rotated one coordinate
+system to the other
+
+ align:start position:0%
+system to the other
+ 
+
+ align:start position:0%
+system to the other
+and then what's uh
+
+ align:start position:0%
+and then what's uh
+ 
+
+ align:start position:0%
+and then what's uh
+the change in height
+
+ align:start position:0%
+the change in height
+ 
+
+ align:start position:0%
+the change in height
+uh well according to you know chain rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which sort of looks intimidating but
+
+ align:start position:0%
+which sort of looks intimidating but
+ 
+
+ align:start position:0%
+which sort of looks intimidating but
+it's just uh
+
+ align:start position:0%
+it's just uh
+ 
+
+ align:start position:0%
+it's just uh
+p times
+
+ align:start position:0%
+p times
+ 
+
+ align:start position:0%
+p times
+the derivative up here so we got um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just uh
+
+ align:start position:0%
+just uh
+ 
+
+ align:start position:0%
+just uh
+p times ps or ps plus
+
+ align:start position:0%
+p times ps or ps plus
+ 
+
+ align:start position:0%
+p times ps or ps plus
+qsq
+
+ align:start position:0%
+qsq
+ 
+
+ align:start position:0%
+qsq
+okay so this
+
+ align:start position:0%
+okay so this
+ 
+
+ align:start position:0%
+okay so this
+is the rule we can use to take a small
+
+ align:start position:0%
+is the rule we can use to take a small
+ 
+
+ align:start position:0%
+is the rule we can use to take a small
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+uh and we we take a small step
+
+ align:start position:0%
+uh and we we take a small step
+ 
+
+ align:start position:0%
+uh and we we take a small step
+in the image
+
+ align:start position:0%
+in the image
+ 
+
+ align:start position:0%
+in the image
+based on that and that corresponds to a
+
+ align:start position:0%
+based on that and that corresponds to a
+ 
+
+ align:start position:0%
+based on that and that corresponds to a
+small step in height
+
+ align:start position:0%
+small step in height
+ 
+
+ align:start position:0%
+small step in height
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+forgot to mention it here but
+
+ align:start position:0%
+forgot to mention it here but
+ 
+
+ align:start position:0%
+forgot to mention it here but
+we're now assuming orthographic
+
+ align:start position:0%
+we're now assuming orthographic
+ 
+
+ align:start position:0%
+we're now assuming orthographic
+projection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's sort of a point
+
+ align:start position:0%
+that's sort of a point
+ 
+
+ align:start position:0%
+that's sort of a point
+that's important which is that
+
+ align:start position:0%
+that's important which is that
+ 
+
+ align:start position:0%
+that's important which is that
+once we switch to dealing with
+
+ align:start position:0%
+once we switch to dealing with
+ 
+
+ align:start position:0%
+once we switch to dealing with
+brightness we switch to orthographic
+
+ align:start position:0%
+brightness we switch to orthographic
+ 
+
+ align:start position:0%
+brightness we switch to orthographic
+projection
+
+ align:start position:0%
+projection
+ 
+
+ align:start position:0%
+projection
+why well because it makes everything
+
+ align:start position:0%
+why well because it makes everything
+ 
+
+ align:start position:0%
+why well because it makes everything
+much easier all of this can be done with
+
+ align:start position:0%
+much easier all of this can be done with
+ 
+
+ align:start position:0%
+much easier all of this can be done with
+perspective projection and it originally
+
+ align:start position:0%
+perspective projection and it originally
+ 
+
+ align:start position:0%
+perspective projection and it originally
+was but the math gets messy
+
+ align:start position:0%
+was but the math gets messy
+ 
+
+ align:start position:0%
+was but the math gets messy
+and so uh the thing to remember is that
+
+ align:start position:0%
+and so uh the thing to remember is that
+ 
+
+ align:start position:0%
+and so uh the thing to remember is that
+you know pretending we have a
+
+ align:start position:0%
+you know pretending we have a
+ 
+
+ align:start position:0%
+you know pretending we have a
+telecentric lens we talked about
+
+ align:start position:0%
+telecentric lens we talked about
+ 
+
+ align:start position:0%
+telecentric lens we talked about
+telecentric lenses and uh using a
+
+ align:start position:0%
+telecentric lenses and uh using a
+ 
+
+ align:start position:0%
+telecentric lenses and uh using a
+orthographic projection is it
+
+ align:start position:0%
+orthographic projection is it
+ 
+
+ align:start position:0%
+orthographic projection is it
+corresponds to being very far away
+
+ align:start position:0%
+corresponds to being very far away
+ 
+
+ align:start position:0%
+corresponds to being very far away
+as we are when we're looking at the moon
+
+ align:start position:0%
+as we are when we're looking at the moon
+ 
+
+ align:start position:0%
+as we are when we're looking at the moon
+and the light source is very far away
+
+ align:start position:0%
+and the light source is very far away
+ 
+
+ align:start position:0%
+and the light source is very far away
+and we have a very small visual angle
+
+ align:start position:0%
+and we have a very small visual angle
+ 
+
+ align:start position:0%
+and we have a very small visual angle
+and it simplifies things it's just like
+
+ align:start position:0%
+and it simplifies things it's just like
+ 
+
+ align:start position:0%
+and it simplifies things it's just like
+lambertian you know
+
+ align:start position:0%
+lambertian you know
+ 
+
+ align:start position:0%
+lambertian you know
+it's not that these methods are
+
+ align:start position:0%
+it's not that these methods are
+ 
+
+ align:start position:0%
+it's not that these methods are
+restricted to lambertian well in fact
+
+ align:start position:0%
+restricted to lambertian well in fact
+ 
+
+ align:start position:0%
+restricted to lambertian well in fact
+we're talking about non-laboration here
+
+ align:start position:0%
+we're talking about non-laboration here
+ 
+
+ align:start position:0%
+we're talking about non-laboration here
+um it's just that uh you can do some
+
+ align:start position:0%
+um it's just that uh you can do some
+ 
+
+ align:start position:0%
+um it's just that uh you can do some
+interesting things if you make that uh
+
+ align:start position:0%
+interesting things if you make that uh
+ 
+
+ align:start position:0%
+interesting things if you make that uh
+assumption
+
+ align:start position:0%
+assumption
+ 
+
+ align:start position:0%
+assumption
+and then generalize from there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+that's the rule
+
+ align:start position:0%
+that's the rule
+ 
+
+ align:start position:0%
+that's the rule
+and basically we have three ordinary
+
+ align:start position:0%
+and basically we have three ordinary
+ 
+
+ align:start position:0%
+and basically we have three ordinary
+differential equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we're going to solve numerically
+
+ align:start position:0%
+that we're going to solve numerically
+ 
+
+ align:start position:0%
+that we're going to solve numerically
+and we don't need very sophisticated
+
+ align:start position:0%
+and we don't need very sophisticated
+ 
+
+ align:start position:0%
+and we don't need very sophisticated
+methods like you know eighth order range
+
+ align:start position:0%
+methods like you know eighth order range
+ 
+
+ align:start position:0%
+methods like you know eighth order range
+cutter or something we're just going to
+
+ align:start position:0%
+cutter or something we're just going to
+ 
+
+ align:start position:0%
+cutter or something we're just going to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+forward euler or in other words
+
+ align:start position:0%
+forward euler or in other words
+ 
+
+ align:start position:0%
+forward euler or in other words
+if you have the slope and you have a
+
+ align:start position:0%
+if you have the slope and you have a
+ 
+
+ align:start position:0%
+if you have the slope and you have a
+step size you just multiply the slope by
+
+ align:start position:0%
+step size you just multiply the slope by
+ 
+
+ align:start position:0%
+step size you just multiply the slope by
+the step size to see how much higher
+
+ align:start position:0%
+the step size to see how much higher
+ 
+
+ align:start position:0%
+the step size to see how much higher
+you've gone come so
+
+ align:start position:0%
+you've gone come so
+ 
+
+ align:start position:0%
+you've gone come so
+that that's the method we're going to
+
+ align:start position:0%
+that that's the method we're going to
+ 
+
+ align:start position:0%
+that that's the method we're going to
+use and of course it's not terribly
+
+ align:start position:0%
+use and of course it's not terribly
+ 
+
+ align:start position:0%
+use and of course it's not terribly
+accurate but
+
+ align:start position:0%
+accurate but
+ 
+
+ align:start position:0%
+accurate but
+if we make the steps small enough it's
+
+ align:start position:0%
+if we make the steps small enough it's
+ 
+
+ align:start position:0%
+if we make the steps small enough it's
+it's good enough
+
+ align:start position:0%
+it's good enough
+ 
+
+ align:start position:0%
+it's good enough
+and the measurements we're dealing with
+
+ align:start position:0%
+and the measurements we're dealing with
+ 
+
+ align:start position:0%
+and the measurements we're dealing with
+are themselves noisy so it doesn't make
+
+ align:start position:0%
+are themselves noisy so it doesn't make
+ 
+
+ align:start position:0%
+are themselves noisy so it doesn't make
+sense to you know apply a method that's
+
+ align:start position:0%
+sense to you know apply a method that's
+ 
+
+ align:start position:0%
+sense to you know apply a method that's
+good to
+
+ align:start position:0%
+good to
+ 
+
+ align:start position:0%
+good to
+12 decimal places when we start off with
+
+ align:start position:0%
+12 decimal places when we start off with
+ 
+
+ align:start position:0%
+12 decimal places when we start off with
+things based on image brightness
+
+ align:start position:0%
+things based on image brightness
+ 
+
+ align:start position:0%
+things based on image brightness
+measurements
+
+ align:start position:0%
+measurements
+ 
+
+ align:start position:0%
+measurements
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+how do we employ this well we need to
+
+ align:start position:0%
+how do we employ this well we need to
+ 
+
+ align:start position:0%
+how do we employ this well we need to
+tie it to brightness
+
+ align:start position:0%
+tie it to brightness
+ 
+
+ align:start position:0%
+tie it to brightness
+so somehow brightness has to feed into
+
+ align:start position:0%
+so somehow brightness has to feed into
+ 
+
+ align:start position:0%
+so somehow brightness has to feed into
+this this equation
+
+ align:start position:0%
+this this equation
+ 
+
+ align:start position:0%
+this this equation
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+for the hapka type surface we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have this kind of dependence or
+
+ align:start position:0%
+we have this kind of dependence or
+ 
+
+ align:start position:0%
+we have this kind of dependence or
+actually it was cosine
+
+ align:start position:0%
+actually it was cosine
+ 
+
+ align:start position:0%
+actually it was cosine
+theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in our
+
+ align:start position:0%
+in our
+ 
+
+ align:start position:0%
+in our
+arrangement for orthographic projection
+
+ align:start position:0%
+arrangement for orthographic projection
+ 
+
+ align:start position:0%
+arrangement for orthographic projection
+it's very convenient to have the viewer
+
+ align:start position:0%
+it's very convenient to have the viewer
+ 
+
+ align:start position:0%
+it's very convenient to have the viewer
+up along the z axis so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then we can plug in
+
+ align:start position:0%
+and then we can plug in
+ 
+
+ align:start position:0%
+and then we can plug in
+in terms of p and q
+
+ align:start position:0%
+in terms of p and q
+ 
+
+ align:start position:0%
+in terms of p and q
+so that's in terms of angles and in
+
+ align:start position:0%
+so that's in terms of angles and in
+ 
+
+ align:start position:0%
+so that's in terms of angles and in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+unit normals
+
+ align:start position:0%
+unit normals
+ 
+
+ align:start position:0%
+unit normals
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+we we would like to express it in terms
+
+ align:start position:0%
+we we would like to express it in terms
+ 
+
+ align:start position:0%
+we we would like to express it in terms
+of p and q
+
+ align:start position:0%
+of p and q
+ 
+
+ align:start position:0%
+of p and q
+and then you remember that n dot s came
+
+ align:start position:0%
+and then you remember that n dot s came
+ 
+
+ align:start position:0%
+and then you remember that n dot s came
+out to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's see we're going to take the
+
+ align:start position:0%
+and let's see we're going to take the
+ 
+
+ align:start position:0%
+and let's see we're going to take the
+square root of that
+
+ align:start position:0%
+square root of that
+ 
+
+ align:start position:0%
+square root of that
+and then we're going to divide it by
+
+ align:start position:0%
+and then we're going to divide it by
+ 
+
+ align:start position:0%
+and then we're going to divide it by
+n dot v or where v is the same as z so
+
+ align:start position:0%
+n dot v or where v is the same as z so
+ 
+
+ align:start position:0%
+n dot v or where v is the same as z so
+that's n dot z so that's one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that conveniently cancels out
+
+ align:start position:0%
+and that conveniently cancels out
+ 
+
+ align:start position:0%
+and that conveniently cancels out
+so so we're in the end up with that so
+
+ align:start position:0%
+so so we're in the end up with that so
+ 
+
+ align:start position:0%
+so so we're in the end up with that so
+this is our r of p and q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by the um our assumption here about
+
+ align:start position:0%
+and by the um our assumption here about
+ 
+
+ align:start position:0%
+and by the um our assumption here about
+the image of radiance equation that's e
+
+ align:start position:0%
+the image of radiance equation that's e
+ 
+
+ align:start position:0%
+the image of radiance equation that's e
+of x and y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can write
+
+ align:start position:0%
+so we can write
+ 
+
+ align:start position:0%
+so we can write
+e of x and y is this thing
+
+ align:start position:0%
+e of x and y is this thing
+ 
+
+ align:start position:0%
+e of x and y is this thing
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you can see the term we're looking for
+
+ align:start position:0%
+you can see the term we're looking for
+ 
+
+ align:start position:0%
+you can see the term we're looking for
+is right in here p s p plus q qsq
+
+ align:start position:0%
+is right in here p s p plus q qsq
+ 
+
+ align:start position:0%
+is right in here p s p plus q qsq
+so we need to square
+
+ align:start position:0%
+so we need to square
+ 
+
+ align:start position:0%
+so we need to square
+the whole thing get rid of the square
+
+ align:start position:0%
+the whole thing get rid of the square
+ 
+
+ align:start position:0%
+the whole thing get rid of the square
+root and then multiply through by rs and
+
+ align:start position:0%
+root and then multiply through by rs and
+ 
+
+ align:start position:0%
+root and then multiply through by rs and
+subtract the 1. so we end up with um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for this particular surface
+
+ align:start position:0%
+okay so for this particular surface
+ 
+
+ align:start position:0%
+okay so for this particular surface
+there's a direct relationship between
+
+ align:start position:0%
+there's a direct relationship between
+ 
+
+ align:start position:0%
+there's a direct relationship between
+the quantity we can measure uh e
+
+ align:start position:0%
+the quantity we can measure uh e
+ 
+
+ align:start position:0%
+the quantity we can measure uh e
+and the thing we need
+
+ align:start position:0%
+and the thing we need
+ 
+
+ align:start position:0%
+and the thing we need
+to continue the solution
+
+ align:start position:0%
+to continue the solution
+ 
+
+ align:start position:0%
+to continue the solution
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+we are what's r s well r s is just um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dependent on the source position it's a
+
+ align:start position:0%
+dependent on the source position it's a
+ 
+
+ align:start position:0%
+dependent on the source position it's a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+and it just avoids having to write that
+
+ align:start position:0%
+and it just avoids having to write that
+ 
+
+ align:start position:0%
+and it just avoids having to write that
+all the time
+
+ align:start position:0%
+all the time
+ 
+
+ align:start position:0%
+all the time
+so we just take the brightness we square
+
+ align:start position:0%
+so we just take the brightness we square
+ 
+
+ align:start position:0%
+so we just take the brightness we square
+it we multiply it by rs we subtract one
+
+ align:start position:0%
+it we multiply it by rs we subtract one
+ 
+
+ align:start position:0%
+it we multiply it by rs we subtract one
+and there's the derivative in the z
+
+ align:start position:0%
+and there's the derivative in the z
+ 
+
+ align:start position:0%
+and there's the derivative in the z
+direction and that's it we just march
+
+ align:start position:0%
+direction and that's it we just march
+ 
+
+ align:start position:0%
+direction and that's it we just march
+along
+
+ align:start position:0%
+along
+ 
+
+ align:start position:0%
+along
+you know from one point to the next
+
+ align:start position:0%
+you know from one point to the next
+ 
+
+ align:start position:0%
+you know from one point to the next
+adjusting
+
+ align:start position:0%
+adjusting
+ 
+
+ align:start position:0%
+adjusting
+x y and z as we go and at each point we
+
+ align:start position:0%
+x y and z as we go and at each point we
+ 
+
+ align:start position:0%
+x y and z as we go and at each point we
+do we know the surface orientation
+
+ align:start position:0%
+do we know the surface orientation
+ 
+
+ align:start position:0%
+do we know the surface orientation
+wells a bit of it
+
+ align:start position:0%
+wells a bit of it
+ 
+
+ align:start position:0%
+wells a bit of it
+we know the slope in in that direction i
+
+ align:start position:0%
+we know the slope in in that direction i
+ 
+
+ align:start position:0%
+we know the slope in in that direction i
+mean that's what we're exploiting
+
+ align:start position:0%
+mean that's what we're exploiting
+ 
+
+ align:start position:0%
+mean that's what we're exploiting
+but as we indicated we don't know
+
+ align:start position:0%
+but as we indicated we don't know
+ 
+
+ align:start position:0%
+but as we indicated we don't know
+anything about the slope in the other
+
+ align:start position:0%
+anything about the slope in the other
+ 
+
+ align:start position:0%
+anything about the slope in the other
+direction so so no we don't don't know
+
+ align:start position:0%
+direction so so no we don't don't know
+ 
+
+ align:start position:0%
+direction so so no we don't don't know
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+surface orientation
+
+ align:start position:0%
+surface orientation
+ 
+
+ align:start position:0%
+surface orientation
+based on this and we need something else
+
+ align:start position:0%
+based on this and we need something else
+ 
+
+ align:start position:0%
+based on this and we need something else
+to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+since each of these profiles is going to
+
+ align:start position:0%
+since each of these profiles is going to
+ 
+
+ align:start position:0%
+since each of these profiles is going to
+be independent
+
+ align:start position:0%
+be independent
+ 
+
+ align:start position:0%
+be independent
+to actually get z as a function of x and
+
+ align:start position:0%
+to actually get z as a function of x and
+ 
+
+ align:start position:0%
+to actually get z as a function of x and
+y in a real description of the surface
+
+ align:start position:0%
+y in a real description of the surface
+ 
+
+ align:start position:0%
+y in a real description of the surface
+we need to somehow have initial
+
+ align:start position:0%
+we need to somehow have initial
+ 
+
+ align:start position:0%
+we need to somehow have initial
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+for these differential equations
+
+ align:start position:0%
+for these differential equations
+ 
+
+ align:start position:0%
+for these differential equations
+so you know x and y
+
+ align:start position:0%
+so you know x and y
+ 
+
+ align:start position:0%
+so you know x and y
+well we pick some point in the image to
+
+ align:start position:0%
+well we pick some point in the image to
+ 
+
+ align:start position:0%
+well we pick some point in the image to
+start
+
+ align:start position:0%
+start
+ 
+
+ align:start position:0%
+start
+but what about z
+
+ align:start position:0%
+but what about z
+ 
+
+ align:start position:0%
+but what about z
+well under our assumption of
+
+ align:start position:0%
+well under our assumption of
+ 
+
+ align:start position:0%
+well under our assumption of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+image formation model
+
+ align:start position:0%
+image formation model
+ 
+
+ align:start position:0%
+image formation model
+there is no dependence on z the
+
+ align:start position:0%
+there is no dependence on z the
+ 
+
+ align:start position:0%
+there is no dependence on z the
+dependence is on the slope of z
+
+ align:start position:0%
+dependence is on the slope of z
+ 
+
+ align:start position:0%
+dependence is on the slope of z
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+actually if we moved
+
+ align:start position:0%
+actually if we moved
+ 
+
+ align:start position:0%
+actually if we moved
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+object in the z direction its image
+
+ align:start position:0%
+object in the z direction its image
+ 
+
+ align:start position:0%
+object in the z direction its image
+wouldn't change well under perspective
+
+ align:start position:0%
+wouldn't change well under perspective
+ 
+
+ align:start position:0%
+wouldn't change well under perspective
+projection it would change in size
+
+ align:start position:0%
+projection it would change in size
+ 
+
+ align:start position:0%
+projection it would change in size
+but we're not
+
+ align:start position:0%
+but we're not
+ 
+
+ align:start position:0%
+but we're not
+dealing with perspective projection
+
+ align:start position:0%
+dealing with perspective projection
+ 
+
+ align:start position:0%
+dealing with perspective projection
+we're dealing with orthographic
+
+ align:start position:0%
+we're dealing with orthographic
+ 
+
+ align:start position:0%
+we're dealing with orthographic
+projection
+
+ align:start position:0%
+projection
+ 
+
+ align:start position:0%
+projection
+and so its size doesn't change so so
+
+ align:start position:0%
+and so its size doesn't change so so
+ 
+
+ align:start position:0%
+and so its size doesn't change so so
+there's an ambiguity
+
+ align:start position:0%
+there's an ambiguity
+ 
+
+ align:start position:0%
+there's an ambiguity
+so for each of those
+
+ align:start position:0%
+so for each of those
+ 
+
+ align:start position:0%
+so for each of those
+uh curves that we're computing
+
+ align:start position:0%
+uh curves that we're computing
+ 
+
+ align:start position:0%
+uh curves that we're computing
+we need an initial condition so actually
+
+ align:start position:0%
+we need an initial condition so actually
+ 
+
+ align:start position:0%
+we need an initial condition so actually
+we need an initial curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so in 3d how do we do that well
+
+ align:start position:0%
+and so in 3d how do we do that well
+ 
+
+ align:start position:0%
+and so in 3d how do we do that well
+here's a way of
+
+ align:start position:0%
+here's a way of
+ 
+
+ align:start position:0%
+here's a way of
+defining a curve
+
+ align:start position:0%
+defining a curve
+ 
+
+ align:start position:0%
+defining a curve
+we have some parameter that varies along
+
+ align:start position:0%
+we have some parameter that varies along
+ 
+
+ align:start position:0%
+we have some parameter that varies along
+the curve could be arc length or some
+
+ align:start position:0%
+the curve could be arc length or some
+ 
+
+ align:start position:0%
+the curve could be arc length or some
+arbitrary parameter
+
+ align:start position:0%
+arbitrary parameter
+ 
+
+ align:start position:0%
+arbitrary parameter
+eta
+
+ align:start position:0%
+eta
+ 
+
+ align:start position:0%
+eta
+and for each eta we give a position in
+
+ align:start position:0%
+and for each eta we give a position in
+ 
+
+ align:start position:0%
+and for each eta we give a position in
+space x y and z
+
+ align:start position:0%
+space x y and z
+ 
+
+ align:start position:0%
+space x y and z
+and that's a curve and so that's our
+
+ align:start position:0%
+and that's a curve and so that's our
+ 
+
+ align:start position:0%
+and that's a curve and so that's our
+let's assume we have that initial curve
+
+ align:start position:0%
+let's assume we have that initial curve
+ 
+
+ align:start position:0%
+let's assume we have that initial curve
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+some sort of curve like this and then we
+
+ align:start position:0%
+some sort of curve like this and then we
+ 
+
+ align:start position:0%
+some sort of curve like this and then we
+can start at any point on that curve
+
+ align:start position:0%
+can start at any point on that curve
+ 
+
+ align:start position:0%
+can start at any point on that curve
+and integrate out those equations
+
+ align:start position:0%
+and integrate out those equations
+ 
+
+ align:start position:0%
+and integrate out those equations
+numerically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's our surface
+
+ align:start position:0%
+there's our surface
+ 
+
+ align:start position:0%
+there's our surface
+and as we mentioned
+
+ align:start position:0%
+and as we mentioned
+ 
+
+ align:start position:0%
+and as we mentioned
+we can actually go in both directions
+
+ align:start position:0%
+we can actually go in both directions
+ 
+
+ align:start position:0%
+we can actually go in both directions
+from the initial curve
+
+ align:start position:0%
+from the initial curve
+ 
+
+ align:start position:0%
+from the initial curve
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we end up with
+
+ align:start position:0%
+we end up with
+ 
+
+ align:start position:0%
+we end up with
+z of x y or actually z of
+
+ align:start position:0%
+z of x y or actually z of
+ 
+
+ align:start position:0%
+z of x y or actually z of
+eta and psi
+
+ align:start position:0%
+eta and psi
+ 
+
+ align:start position:0%
+eta and psi
+right because the way we've
+
+ align:start position:0%
+right because the way we've
+ 
+
+ align:start position:0%
+right because the way we've
+parameterized it is
+
+ align:start position:0%
+parameterized it is
+ 
+
+ align:start position:0%
+parameterized it is
+one parameter
+
+ align:start position:0%
+one parameter
+ 
+
+ align:start position:0%
+one parameter
+goes along the
+
+ align:start position:0%
+goes along the
+ 
+
+ align:start position:0%
+goes along the
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+the other parameter goes along the
+
+ align:start position:0%
+the other parameter goes along the
+ 
+
+ align:start position:0%
+the other parameter goes along the
+initial curve so
+
+ align:start position:0%
+initial curve so
+ 
+
+ align:start position:0%
+initial curve so
+so it's the surface in 3d and it takes
+
+ align:start position:0%
+so it's the surface in 3d and it takes
+ 
+
+ align:start position:0%
+so it's the surface in 3d and it takes
+two parameters to parameterize that so
+
+ align:start position:0%
+two parameters to parameterize that so
+ 
+
+ align:start position:0%
+two parameters to parameterize that so
+so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+straightforward i hope
+
+ align:start position:0%
+straightforward i hope
+ 
+
+ align:start position:0%
+straightforward i hope
+that in that particular case we
+
+ align:start position:0%
+that in that particular case we
+ 
+
+ align:start position:0%
+that in that particular case we
+have some very special properties one of
+
+ align:start position:0%
+have some very special properties one of
+ 
+
+ align:start position:0%
+have some very special properties one of
+them is that we can locally determine
+
+ align:start position:0%
+them is that we can locally determine
+ 
+
+ align:start position:0%
+them is that we can locally determine
+the slope in a particular direction and
+
+ align:start position:0%
+the slope in a particular direction and
+ 
+
+ align:start position:0%
+the slope in a particular direction and
+that means of course we can go in that
+
+ align:start position:0%
+that means of course we can go in that
+ 
+
+ align:start position:0%
+that means of course we can go in that
+direction and and build up a curve
+
+ align:start position:0%
+direction and and build up a curve
+ 
+
+ align:start position:0%
+direction and and build up a curve
+and that's
+
+ align:start position:0%
+and that's
+ 
+
+ align:start position:0%
+and that's
+not going to be true in the general case
+
+ align:start position:0%
+not going to be true in the general case
+ 
+
+ align:start position:0%
+not going to be true in the general case
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what do we do about
+
+ align:start position:0%
+what do we do about
+ 
+
+ align:start position:0%
+what do we do about
+about the general case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll still start off with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our image irradiance equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which says that the brightness at a
+
+ align:start position:0%
+which says that the brightness at a
+ 
+
+ align:start position:0%
+which says that the brightness at a
+particular point in the image
+
+ align:start position:0%
+particular point in the image
+ 
+
+ align:start position:0%
+particular point in the image
+is dependent on the surface orientation
+
+ align:start position:0%
+is dependent on the surface orientation
+ 
+
+ align:start position:0%
+is dependent on the surface orientation
+at the corresponding point point on the
+
+ align:start position:0%
+at the corresponding point point on the
+ 
+
+ align:start position:0%
+at the corresponding point point on the
+object and we'll sort of try and follow
+
+ align:start position:0%
+object and we'll sort of try and follow
+ 
+
+ align:start position:0%
+object and we'll sort of try and follow
+this model here so
+
+ align:start position:0%
+this model here so
+ 
+
+ align:start position:0%
+this model here so
+you know suppose we're at some
+
+ align:start position:0%
+you know suppose we're at some
+ 
+
+ align:start position:0%
+you know suppose we're at some
+particular point x y z
+
+ align:start position:0%
+particular point x y z
+ 
+
+ align:start position:0%
+particular point x y z
+and then we take a small step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in the image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's suppose the steps
+
+ align:start position:0%
+let's suppose the steps
+ 
+
+ align:start position:0%
+let's suppose the steps
+size is delta x delta y and
+
+ align:start position:0%
+size is delta x delta y and
+ 
+
+ align:start position:0%
+size is delta x delta y and
+for the moment we won't say which
+
+ align:start position:0%
+for the moment we won't say which
+ 
+
+ align:start position:0%
+for the moment we won't say which
+direction we're going we'll just
+
+ align:start position:0%
+direction we're going we'll just
+ 
+
+ align:start position:0%
+direction we're going we'll just
+leave that
+
+ align:start position:0%
+leave that
+ 
+
+ align:start position:0%
+leave that
+unknown
+
+ align:start position:0%
+unknown
+ 
+
+ align:start position:0%
+unknown
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+to construct the solution what we need
+
+ align:start position:0%
+to construct the solution what we need
+ 
+
+ align:start position:0%
+to construct the solution what we need
+to know is you know what's z how is z
+
+ align:start position:0%
+to know is you know what's z how is z
+ 
+
+ align:start position:0%
+to know is you know what's z how is z
+going to change
+
+ align:start position:0%
+going to change
+ 
+
+ align:start position:0%
+going to change
+and so of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we have that relationship the change
+
+ align:start position:0%
+um we have that relationship the change
+ 
+
+ align:start position:0%
+um we have that relationship the change
+in z is dz dx times delta x plus dz dy
+
+ align:start position:0%
+in z is dz dx times delta x plus dz dy
+ 
+
+ align:start position:0%
+in z is dz dx times delta x plus dz dy
+times delta y
+
+ align:start position:0%
+times delta y
+ 
+
+ align:start position:0%
+times delta y
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we can calculate the change in height
+
+ align:start position:0%
+we can calculate the change in height
+ 
+
+ align:start position:0%
+we can calculate the change in height
+if we know p and q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and suppose we know p and q then we're
+
+ align:start position:0%
+and suppose we know p and q then we're
+ 
+
+ align:start position:0%
+and suppose we know p and q then we're
+at a new point on the surface and we can
+
+ align:start position:0%
+at a new point on the surface and we can
+ 
+
+ align:start position:0%
+at a new point on the surface and we can
+repeat we
+
+ align:start position:0%
+repeat we
+ 
+
+ align:start position:0%
+repeat we
+take a small step in x and y and
+
+ align:start position:0%
+take a small step in x and y and
+ 
+
+ align:start position:0%
+take a small step in x and y and
+now over here we kept on going in in a
+
+ align:start position:0%
+now over here we kept on going in in a
+ 
+
+ align:start position:0%
+now over here we kept on going in in a
+certain direction that
+
+ align:start position:0%
+certain direction that
+ 
+
+ align:start position:0%
+certain direction that
+in this case we may need to
+
+ align:start position:0%
+in this case we may need to
+ 
+
+ align:start position:0%
+in this case we may need to
+choose a direction in some particular
+
+ align:start position:0%
+choose a direction in some particular
+ 
+
+ align:start position:0%
+choose a direction in some particular
+way but
+
+ align:start position:0%
+way but
+ 
+
+ align:start position:0%
+way but
+we need to know p and q
+
+ align:start position:0%
+we need to know p and q
+ 
+
+ align:start position:0%
+we need to know p and q
+okay well uh we can assume that we start
+
+ align:start position:0%
+okay well uh we can assume that we start
+ 
+
+ align:start position:0%
+okay well uh we can assume that we start
+off not only knowing x y and z but also
+
+ align:start position:0%
+off not only knowing x y and z but also
+ 
+
+ align:start position:0%
+off not only knowing x y and z but also
+the surface orientation
+
+ align:start position:0%
+the surface orientation
+ 
+
+ align:start position:0%
+the surface orientation
+so we could have
+
+ align:start position:0%
+so we could have
+ 
+
+ align:start position:0%
+so we could have
+you know x y and z and p and q
+
+ align:start position:0%
+you know x y and z and p and q
+ 
+
+ align:start position:0%
+you know x y and z and p and q
+but then how do we update every step we
+
+ align:start position:0%
+but then how do we update every step we
+ 
+
+ align:start position:0%
+but then how do we update every step we
+need to
+
+ align:start position:0%
+need to
+ 
+
+ align:start position:0%
+need to
+update p and q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here we have updates rules for x y
+
+ align:start position:0%
+so here we have updates rules for x y
+ 
+
+ align:start position:0%
+so here we have updates rules for x y
+and z for x and y you know we're the
+
+ align:start position:0%
+and z for x and y you know we're the
+ 
+
+ align:start position:0%
+and z for x and y you know we're the
+ones controlling the step
+
+ align:start position:0%
+ones controlling the step
+ 
+
+ align:start position:0%
+ones controlling the step
+and then z
+
+ align:start position:0%
+and then z
+ 
+
+ align:start position:0%
+and then z
+the change in z is given by this
+
+ align:start position:0%
+the change in z is given by this
+ 
+
+ align:start position:0%
+the change in z is given by this
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+so um well we can use the same chain
+
+ align:start position:0%
+so um well we can use the same chain
+ 
+
+ align:start position:0%
+so um well we can use the same chain
+rule trick we can say that delta p is p
+
+ align:start position:0%
+rule trick we can say that delta p is p
+ 
+
+ align:start position:0%
+rule trick we can say that delta p is p
+sub x delta x plus
+
+ align:start position:0%
+sub x delta x plus
+ 
+
+ align:start position:0%
+sub x delta x plus
+p sub y delta y
+
+ align:start position:0%
+p sub y delta y
+ 
+
+ align:start position:0%
+p sub y delta y
+and delta q is q sub x delta x plus
+
+ align:start position:0%
+and delta q is q sub x delta x plus
+ 
+
+ align:start position:0%
+and delta q is q sub x delta x plus
+q sub y delta y
+
+ align:start position:0%
+q sub y delta y
+ 
+
+ align:start position:0%
+q sub y delta y
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+we can update p and q as we go along so
+
+ align:start position:0%
+we can update p and q as we go along so
+ 
+
+ align:start position:0%
+we can update p and q as we go along so
+we're not only updating x y and z but
+
+ align:start position:0%
+we're not only updating x y and z but
+ 
+
+ align:start position:0%
+we're not only updating x y and z but
+we're also updating p and q so this is
+
+ align:start position:0%
+we're also updating p and q so this is
+ 
+
+ align:start position:0%
+we're also updating p and q so this is
+kind of interesting before we had a
+
+ align:start position:0%
+kind of interesting before we had a
+ 
+
+ align:start position:0%
+kind of interesting before we had a
+curve in space we were tracing out x y
+
+ align:start position:0%
+curve in space we were tracing out x y
+ 
+
+ align:start position:0%
+curve in space we were tracing out x y
+and z
+
+ align:start position:0%
+and z
+ 
+
+ align:start position:0%
+and z
+as we construct the solution now we've
+
+ align:start position:0%
+as we construct the solution now we've
+ 
+
+ align:start position:0%
+as we construct the solution now we've
+got more because at every point we know
+
+ align:start position:0%
+got more because at every point we know
+ 
+
+ align:start position:0%
+got more because at every point we know
+p and q
+
+ align:start position:0%
+p and q
+ 
+
+ align:start position:0%
+p and q
+which means we know the surface
+
+ align:start position:0%
+which means we know the surface
+ 
+
+ align:start position:0%
+which means we know the surface
+orientation
+
+ align:start position:0%
+orientation
+ 
+
+ align:start position:0%
+orientation
+so what we're really constructing now is
+
+ align:start position:0%
+so what we're really constructing now is
+ 
+
+ align:start position:0%
+so what we're really constructing now is
+a strip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well not
+
+ align:start position:0%
+well not
+ 
+
+ align:start position:0%
+well not
+not very elegant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is called a characteristic
+
+ align:start position:0%
+and this is called a characteristic
+ 
+
+ align:start position:0%
+and this is called a characteristic
+strip characteristic of that
+
+ align:start position:0%
+strip characteristic of that
+ 
+
+ align:start position:0%
+strip characteristic of that
+differential equation and
+
+ align:start position:0%
+differential equation and
+ 
+
+ align:start position:0%
+differential equation and
+that means that
+
+ align:start position:0%
+that means that
+ 
+
+ align:start position:0%
+that means that
+you know we're carrying a long surface
+
+ align:start position:0%
+you know we're carrying a long surface
+ 
+
+ align:start position:0%
+you know we're carrying a long surface
+orientation so if i wanted to i could
+
+ align:start position:0%
+orientation so if i wanted to i could
+ 
+
+ align:start position:0%
+orientation so if i wanted to i could
+erect
+
+ align:start position:0%
+erect
+ 
+
+ align:start position:0%
+erect
+surface normals as as i go along so
+
+ align:start position:0%
+surface normals as as i go along so
+ 
+
+ align:start position:0%
+surface normals as as i go along so
+that's obviously more information than
+
+ align:start position:0%
+that's obviously more information than
+ 
+
+ align:start position:0%
+that's obviously more information than
+just a curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's what we'll be doing we'll
+
+ align:start position:0%
+okay so that's what we'll be doing we'll
+ 
+
+ align:start position:0%
+okay so that's what we'll be doing we'll
+update not just x y and z but p and q
+
+ align:start position:0%
+update not just x y and z but p and q
+ 
+
+ align:start position:0%
+update not just x y and z but p and q
+which we didn't have to do over here
+
+ align:start position:0%
+which we didn't have to do over here
+ 
+
+ align:start position:0%
+which we didn't have to do over here
+because of the particular
+
+ align:start position:0%
+because of the particular
+ 
+
+ align:start position:0%
+because of the particular
+properties of of the hapka type model
+
+ align:start position:0%
+properties of of the hapka type model
+ 
+
+ align:start position:0%
+properties of of the hapka type model
+okay but
+
+ align:start position:0%
+okay but
+ 
+
+ align:start position:0%
+okay but
+how do we do this well in order to
+
+ align:start position:0%
+how do we do this well in order to
+ 
+
+ align:start position:0%
+how do we do this well in order to
+update we need to know p x p y
+
+ align:start position:0%
+update we need to know p x p y
+ 
+
+ align:start position:0%
+update we need to know p x p y
+q x and q y and
+
+ align:start position:0%
+q x and q y and
+ 
+
+ align:start position:0%
+q x and q y and
+we can write this another way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in matrix form so the two two linear
+
+ align:start position:0%
+in matrix form so the two two linear
+ 
+
+ align:start position:0%
+in matrix form so the two two linear
+equations two unknowns we can write it
+
+ align:start position:0%
+equations two unknowns we can write it
+ 
+
+ align:start position:0%
+equations two unknowns we can write it
+with a two by two matrix
+
+ align:start position:0%
+with a two by two matrix
+ 
+
+ align:start position:0%
+with a two by two matrix
+and so what are these are are s and t so
+
+ align:start position:0%
+and so what are these are are s and t so
+ 
+
+ align:start position:0%
+and so what are these are are s and t so
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+is p sub x which is really uh
+
+ align:start position:0%
+is p sub x which is really uh
+ 
+
+ align:start position:0%
+is p sub x which is really uh
+you know the second derivative of z
+
+ align:start position:0%
+you know the second derivative of z
+ 
+
+ align:start position:0%
+you know the second derivative of z
+s is p sub y
+
+ align:start position:0%
+s is p sub y
+ 
+
+ align:start position:0%
+s is p sub y
+which is q sub x which is this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+quantities we need in order to use this
+
+ align:start position:0%
+quantities we need in order to use this
+ 
+
+ align:start position:0%
+quantities we need in order to use this
+update rule are the second partial
+
+ align:start position:0%
+update rule are the second partial
+ 
+
+ align:start position:0%
+update rule are the second partial
+derivatives of
+
+ align:start position:0%
+derivatives of
+ 
+
+ align:start position:0%
+derivatives of
+height
+
+ align:start position:0%
+height
+ 
+
+ align:start position:0%
+height
+and those are interesting because they
+
+ align:start position:0%
+and those are interesting because they
+ 
+
+ align:start position:0%
+and those are interesting because they
+correspond to curvature so the first
+
+ align:start position:0%
+correspond to curvature so the first
+ 
+
+ align:start position:0%
+correspond to curvature so the first
+derivative have to do with surface
+
+ align:start position:0%
+derivative have to do with surface
+ 
+
+ align:start position:0%
+derivative have to do with surface
+orientation and the second derivatives
+
+ align:start position:0%
+orientation and the second derivatives
+ 
+
+ align:start position:0%
+orientation and the second derivatives
+have to do with how quickly the
+
+ align:start position:0%
+have to do with how quickly the
+ 
+
+ align:start position:0%
+have to do with how quickly the
+orientation is changing and that of
+
+ align:start position:0%
+orientation is changing and that of
+ 
+
+ align:start position:0%
+orientation is changing and that of
+course is curvature and for
+
+ align:start position:0%
+course is curvature and for
+ 
+
+ align:start position:0%
+course is curvature and for
+a 3d surface curvature is a little bit
+
+ align:start position:0%
+a 3d surface curvature is a little bit
+ 
+
+ align:start position:0%
+a 3d surface curvature is a little bit
+more complicated than it is for say a
+
+ align:start position:0%
+more complicated than it is for say a
+ 
+
+ align:start position:0%
+more complicated than it is for say a
+curve in the plane
+
+ align:start position:0%
+curve in the plane
+ 
+
+ align:start position:0%
+curve in the plane
+and you need
+
+ align:start position:0%
+and you need
+ 
+
+ align:start position:0%
+and you need
+three numbers to describe it so for a
+
+ align:start position:0%
+three numbers to describe it so for a
+ 
+
+ align:start position:0%
+three numbers to describe it so for a
+curve in the plane you can just give the
+
+ align:start position:0%
+curve in the plane you can just give the
+ 
+
+ align:start position:0%
+curve in the plane you can just give the
+radius of curvature
+
+ align:start position:0%
+radius of curvature
+ 
+
+ align:start position:0%
+radius of curvature
+or the inverse of that which is called
+
+ align:start position:0%
+or the inverse of that which is called
+ 
+
+ align:start position:0%
+or the inverse of that which is called
+curvature just one number but for 3d
+
+ align:start position:0%
+curvature just one number but for 3d
+ 
+
+ align:start position:0%
+curvature just one number but for 3d
+surface it's a little bit more
+
+ align:start position:0%
+surface it's a little bit more
+ 
+
+ align:start position:0%
+surface it's a little bit more
+complicated and you need this whole
+
+ align:start position:0%
+complicated and you need this whole
+ 
+
+ align:start position:0%
+complicated and you need this whole
+matrix of
+
+ align:start position:0%
+matrix of
+ 
+
+ align:start position:0%
+matrix of
+second order derivatives and it's called
+
+ align:start position:0%
+second order derivatives and it's called
+ 
+
+ align:start position:0%
+second order derivatives and it's called
+the hessian matrix
+
+ align:start position:0%
+the hessian matrix
+ 
+
+ align:start position:0%
+the hessian matrix
+and in here i assume that
+
+ align:start position:0%
+and in here i assume that
+ 
+
+ align:start position:0%
+and in here i assume that
+you know the order of differentiation
+
+ align:start position:0%
+you know the order of differentiation
+ 
+
+ align:start position:0%
+you know the order of differentiation
+doesn't matter that z of x y is z of y x
+
+ align:start position:0%
+doesn't matter that z of x y is z of y x
+ 
+
+ align:start position:0%
+doesn't matter that z of x y is z of y x
+and that will be true for some
+
+ align:start position:0%
+and that will be true for some
+ 
+
+ align:start position:0%
+and that will be true for some
+reasonable surface
+
+ align:start position:0%
+reasonable surface
+ 
+
+ align:start position:0%
+reasonable surface
+won't specify the exact conditions for
+
+ align:start position:0%
+won't specify the exact conditions for
+ 
+
+ align:start position:0%
+won't specify the exact conditions for
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and of course you can construct
+
+ align:start position:0%
+and of course you can construct
+ 
+
+ align:start position:0%
+and of course you can construct
+pathological things
+
+ align:start position:0%
+pathological things
+ 
+
+ align:start position:0%
+pathological things
+that don't satisfy that but
+
+ align:start position:0%
+that don't satisfy that but
+ 
+
+ align:start position:0%
+that don't satisfy that but
+you know those are mathematical
+
+ align:start position:0%
+you know those are mathematical
+ 
+
+ align:start position:0%
+you know those are mathematical
+curiosities rather than
+
+ align:start position:0%
+curiosities rather than
+ 
+
+ align:start position:0%
+curiosities rather than
+real surfaces that will
+
+ align:start position:0%
+real surfaces that will
+ 
+
+ align:start position:0%
+real surfaces that will
+meet in machine vision
+
+ align:start position:0%
+meet in machine vision
+ 
+
+ align:start position:0%
+meet in machine vision
+okay so that's the
+
+ align:start position:0%
+okay so that's the
+ 
+
+ align:start position:0%
+okay so that's the
+curvature matrix and so
+
+ align:start position:0%
+curvature matrix and so
+ 
+
+ align:start position:0%
+curvature matrix and so
+uh we if we know the steps and we know
+
+ align:start position:0%
+uh we if we know the steps and we know
+ 
+
+ align:start position:0%
+uh we if we know the steps and we know
+that matrix we can
+
+ align:start position:0%
+that matrix we can
+ 
+
+ align:start position:0%
+that matrix we can
+calculate the change in p and q
+
+ align:start position:0%
+calculate the change in p and q
+ 
+
+ align:start position:0%
+calculate the change in p and q
+and we can continue the solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that kind of means that we should
+
+ align:start position:0%
+well that kind of means that we should
+ 
+
+ align:start position:0%
+well that kind of means that we should
+add r s and t
+
+ align:start position:0%
+add r s and t
+ 
+
+ align:start position:0%
+add r s and t
+to our menagerie of variables so we're
+
+ align:start position:0%
+to our menagerie of variables so we're
+ 
+
+ align:start position:0%
+to our menagerie of variables so we're
+going to carry along x y and z
+
+ align:start position:0%
+going to carry along x y and z
+ 
+
+ align:start position:0%
+going to carry along x y and z
+p and q
+
+ align:start position:0%
+p and q
+ 
+
+ align:start position:0%
+p and q
+r s and t
+
+ align:start position:0%
+r s and t
+ 
+
+ align:start position:0%
+r s and t
+and yeah we can do that now how do we
+
+ align:start position:0%
+and yeah we can do that now how do we
+ 
+
+ align:start position:0%
+and yeah we can do that now how do we
+update our s and t
+
+ align:start position:0%
+update our s and t
+ 
+
+ align:start position:0%
+update our s and t
+second derivatives well we use the third
+
+ align:start position:0%
+second derivatives well we use the third
+ 
+
+ align:start position:0%
+second derivatives well we use the third
+derivatives
+
+ align:start position:0%
+derivatives
+ 
+
+ align:start position:0%
+derivatives
+so i think you can see where this is
+
+ align:start position:0%
+so i think you can see where this is
+ 
+
+ align:start position:0%
+so i think you can see where this is
+going this is kind of
+
+ align:start position:0%
+going this is kind of
+ 
+
+ align:start position:0%
+going this is kind of
+continuing ad nauseam using higher and
+
+ align:start position:0%
+continuing ad nauseam using higher and
+ 
+
+ align:start position:0%
+continuing ad nauseam using higher and
+higher higher order derivatives
+
+ align:start position:0%
+higher higher order derivatives
+ 
+
+ align:start position:0%
+higher higher order derivatives
+and so that's probably uh not going to
+
+ align:start position:0%
+and so that's probably uh not going to
+ 
+
+ align:start position:0%
+and so that's probably uh not going to
+work in fact
+
+ align:start position:0%
+work in fact
+ 
+
+ align:start position:0%
+work in fact
+we end up with more unknowns
+
+ align:start position:0%
+we end up with more unknowns
+ 
+
+ align:start position:0%
+we end up with more unknowns
+you know here we've got before we didn't
+
+ align:start position:0%
+you know here we've got before we didn't
+ 
+
+ align:start position:0%
+you know here we've got before we didn't
+know p and q
+
+ align:start position:0%
+know p and q
+ 
+
+ align:start position:0%
+know p and q
+two unknowns now we don't know r s and t
+
+ align:start position:0%
+two unknowns now we don't know r s and t
+ 
+
+ align:start position:0%
+two unknowns now we don't know r s and t
+three unknowns so it's it's not going in
+
+ align:start position:0%
+three unknowns so it's it's not going in
+ 
+
+ align:start position:0%
+three unknowns so it's it's not going in
+in a good direction
+
+ align:start position:0%
+in a good direction
+ 
+
+ align:start position:0%
+in a good direction
+but what's sort of neat is that
+
+ align:start position:0%
+but what's sort of neat is that
+ 
+
+ align:start position:0%
+but what's sort of neat is that
+we haven't yet even used our image
+
+ align:start position:0%
+we haven't yet even used our image
+ 
+
+ align:start position:0%
+we haven't yet even used our image
+irradiance equation
+
+ align:start position:0%
+irradiance equation
+ 
+
+ align:start position:0%
+irradiance equation
+you know we haven't looked at the image
+
+ align:start position:0%
+you know we haven't looked at the image
+ 
+
+ align:start position:0%
+you know we haven't looked at the image
+so far we're just playing with
+
+ align:start position:0%
+so far we're just playing with
+ 
+
+ align:start position:0%
+so far we're just playing with
+derivatives so that that's obviously
+
+ align:start position:0%
+derivatives so that that's obviously
+ 
+
+ align:start position:0%
+derivatives so that that's obviously
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a flaw in our reasoning here we're only
+
+ align:start position:0%
+a flaw in our reasoning here we're only
+ 
+
+ align:start position:0%
+a flaw in our reasoning here we're only
+looking at the derivatives of z we're
+
+ align:start position:0%
+looking at the derivatives of z we're
+ 
+
+ align:start position:0%
+looking at the derivatives of z we're
+not uh using image brightness
+
+ align:start position:0%
+not uh using image brightness
+ 
+
+ align:start position:0%
+not uh using image brightness
+measurements at all so that doesn't make
+
+ align:start position:0%
+measurements at all so that doesn't make
+ 
+
+ align:start position:0%
+measurements at all so that doesn't make
+any sense so let's see what we can do
+
+ align:start position:0%
+any sense so let's see what we can do
+ 
+
+ align:start position:0%
+any sense so let's see what we can do
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+image irradiance equation and in
+
+ align:start position:0%
+image irradiance equation and in
+ 
+
+ align:start position:0%
+image irradiance equation and in
+particular we're often interested in the
+
+ align:start position:0%
+particular we're often interested in the
+ 
+
+ align:start position:0%
+particular we're often interested in the
+brightness gradient so let's look at the
+
+ align:start position:0%
+brightness gradient so let's look at the
+ 
+
+ align:start position:0%
+brightness gradient so let's look at the
+brightness gradient
+
+ align:start position:0%
+brightness gradient
+ 
+
+ align:start position:0%
+brightness gradient
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+which way do i want to write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again by the chain rule
+
+ align:start position:0%
+again by the chain rule
+ 
+
+ align:start position:0%
+again by the chain rule
+uh well i get the derivative r r with
+
+ align:start position:0%
+uh well i get the derivative r r with
+ 
+
+ align:start position:0%
+uh well i get the derivative r r with
+respect to p
+
+ align:start position:0%
+respect to p
+ 
+
+ align:start position:0%
+respect to p
+times the dp dx
+
+ align:start position:0%
+times the dp dx
+ 
+
+ align:start position:0%
+times the dp dx
+plus r with respect to q times dq dx and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course these are the very
+
+ align:start position:0%
+and of course these are the very
+ 
+
+ align:start position:0%
+and of course these are the very
+quantities that we've run into over here
+
+ align:start position:0%
+quantities that we've run into over here
+ 
+
+ align:start position:0%
+quantities that we've run into over here
+so this is what we call r
+
+ align:start position:0%
+so this is what we call r
+ 
+
+ align:start position:0%
+so this is what we call r
+this is s
+
+ align:start position:0%
+this is s
+ 
+
+ align:start position:0%
+this is s
+that's s and that's t
+
+ align:start position:0%
+that's s and that's t
+ 
+
+ align:start position:0%
+that's s and that's t
+so that's sort of an interesting analogy
+
+ align:start position:0%
+so that's sort of an interesting analogy
+ 
+
+ align:start position:0%
+so that's sort of an interesting analogy
+with with this we can write this in
+
+ align:start position:0%
+with with this we can write this in
+ 
+
+ align:start position:0%
+with with this we can write this in
+matrix vector form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the same matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that matrix is important
+
+ align:start position:0%
+so that matrix is important
+ 
+
+ align:start position:0%
+so that matrix is important
+and it makes sense okay if you have a
+
+ align:start position:0%
+and it makes sense okay if you have a
+ 
+
+ align:start position:0%
+and it makes sense okay if you have a
+surface with constant surface
+
+ align:start position:0%
+surface with constant surface
+ 
+
+ align:start position:0%
+surface with constant surface
+orientation the image will be constant
+
+ align:start position:0%
+orientation the image will be constant
+ 
+
+ align:start position:0%
+orientation the image will be constant
+brightness in this model where
+
+ align:start position:0%
+brightness in this model where
+ 
+
+ align:start position:0%
+brightness in this model where
+brightness depends only on surface
+
+ align:start position:0%
+brightness depends only on surface
+ 
+
+ align:start position:0%
+brightness depends only on surface
+orientation
+
+ align:start position:0%
+orientation
+ 
+
+ align:start position:0%
+orientation
+if we are looking for gradient we're
+
+ align:start position:0%
+if we are looking for gradient we're
+ 
+
+ align:start position:0%
+if we are looking for gradient we're
+looking for changes in brightness and
+
+ align:start position:0%
+looking for changes in brightness and
+ 
+
+ align:start position:0%
+looking for changes in brightness and
+those are only going to happen if there
+
+ align:start position:0%
+those are only going to happen if there
+ 
+
+ align:start position:0%
+those are only going to happen if there
+changes in surface orientation changes
+
+ align:start position:0%
+changes in surface orientation changes
+ 
+
+ align:start position:0%
+changes in surface orientation changes
+in surface orientation correspond to
+
+ align:start position:0%
+in surface orientation correspond to
+ 
+
+ align:start position:0%
+in surface orientation correspond to
+curvature right so at one place i'm
+
+ align:start position:0%
+curvature right so at one place i'm
+ 
+
+ align:start position:0%
+curvature right so at one place i'm
+going downhill and then it's flat and
+
+ align:start position:0%
+going downhill and then it's flat and
+ 
+
+ align:start position:0%
+going downhill and then it's flat and
+then it's going uphill
+
+ align:start position:0%
+then it's going uphill
+ 
+
+ align:start position:0%
+then it's going uphill
+second derivative is non-zero
+
+ align:start position:0%
+second derivative is non-zero
+ 
+
+ align:start position:0%
+second derivative is non-zero
+so and exactly the second
+
+ align:start position:0%
+so and exactly the second
+ 
+
+ align:start position:0%
+so and exactly the second
+derivative matrix controls that that's
+
+ align:start position:0%
+derivative matrix controls that that's
+ 
+
+ align:start position:0%
+derivative matrix controls that that's
+the precise statement of how that all
+
+ align:start position:0%
+the precise statement of how that all
+ 
+
+ align:start position:0%
+the precise statement of how that all
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+if we look at these two
+
+ align:start position:0%
+if we look at these two
+ 
+
+ align:start position:0%
+if we look at these two
+things just a post
+
+ align:start position:0%
+things just a post
+ 
+
+ align:start position:0%
+things just a post
+you know there's that common matrix h
+
+ align:start position:0%
+you know there's that common matrix h
+ 
+
+ align:start position:0%
+you know there's that common matrix h
+now if we could somehow figure out what
+
+ align:start position:0%
+now if we could somehow figure out what
+ 
+
+ align:start position:0%
+now if we could somehow figure out what
+h was
+
+ align:start position:0%
+h was
+ 
+
+ align:start position:0%
+h was
+we could just plug it in here and we
+
+ align:start position:0%
+we could just plug it in here and we
+ 
+
+ align:start position:0%
+we could just plug it in here and we
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+golden we know you know we can
+
+ align:start position:0%
+golden we know you know we can
+ 
+
+ align:start position:0%
+golden we know you know we can
+implement this method because
+
+ align:start position:0%
+implement this method because
+ 
+
+ align:start position:0%
+implement this method because
+we take a small step in the image delta
+
+ align:start position:0%
+we take a small step in the image delta
+ 
+
+ align:start position:0%
+we take a small step in the image delta
+x delta y multiply by this matrix h and
+
+ align:start position:0%
+x delta y multiply by this matrix h and
+ 
+
+ align:start position:0%
+x delta y multiply by this matrix h and
+out comes the small change in p and q so
+
+ align:start position:0%
+out comes the small change in p and q so
+ 
+
+ align:start position:0%
+out comes the small change in p and q so
+we can have update rules for x y z and p
+
+ align:start position:0%
+we can have update rules for x y z and p
+ 
+
+ align:start position:0%
+we can have update rules for x y z and p
+and q and you know we're done
+
+ align:start position:0%
+and q and you know we're done
+ 
+
+ align:start position:0%
+and q and you know we're done
+so i guess the question is how do you
+
+ align:start position:0%
+so i guess the question is how do you
+ 
+
+ align:start position:0%
+so i guess the question is how do you
+solve this thing for for h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what have we got so so this we can
+
+ align:start position:0%
+so what have we got so so this we can
+ 
+
+ align:start position:0%
+so what have we got so so this we can
+get from the image
+
+ align:start position:0%
+get from the image
+ 
+
+ align:start position:0%
+get from the image
+the brightness gradient
+
+ align:start position:0%
+the brightness gradient
+ 
+
+ align:start position:0%
+the brightness gradient
+so that's available
+
+ align:start position:0%
+so that's available
+ 
+
+ align:start position:0%
+so that's available
+and then this we get from our
+
+ align:start position:0%
+and then this we get from our
+ 
+
+ align:start position:0%
+and then this we get from our
+reflectance model
+
+ align:start position:0%
+reflectance model
+ 
+
+ align:start position:0%
+reflectance model
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is from the reflectance map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you know assuming we know p and q and
+
+ align:start position:0%
+um you know assuming we know p and q and
+ 
+
+ align:start position:0%
+um you know assuming we know p and q and
+we said we're carrying along x y z p and
+
+ align:start position:0%
+we said we're carrying along x y z p and
+ 
+
+ align:start position:0%
+we said we're carrying along x y z p and
+q
+
+ align:start position:0%
+q
+ 
+
+ align:start position:0%
+q
+and so uh
+
+ align:start position:0%
+and so uh
+ 
+
+ align:start position:0%
+and so uh
+if we have a model of how the surface
+
+ align:start position:0%
+if we have a model of how the surface
+ 
+
+ align:start position:0%
+if we have a model of how the surface
+reflects light we can we have a
+
+ align:start position:0%
+reflects light we can we have a
+ 
+
+ align:start position:0%
+reflects light we can we have a
+reflectance map we can just take the
+
+ align:start position:0%
+reflectance map we can just take the
+ 
+
+ align:start position:0%
+reflectance map we can just take the
+gradient in the reflectance map which is
+
+ align:start position:0%
+gradient in the reflectance map which is
+ 
+
+ align:start position:0%
+gradient in the reflectance map which is
+r sub p r sub q so so we have this
+
+ align:start position:0%
+r sub p r sub q so so we have this
+ 
+
+ align:start position:0%
+r sub p r sub q so so we have this
+vector and we have that vector can we
+
+ align:start position:0%
+vector and we have that vector can we
+ 
+
+ align:start position:0%
+vector and we have that vector can we
+solve for h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know one of the things we use a
+
+ align:start position:0%
+so you know one of the things we use a
+ 
+
+ align:start position:0%
+so you know one of the things we use a
+lot is
+
+ align:start position:0%
+lot is
+ 
+
+ align:start position:0%
+lot is
+uh equation counting and constraint
+
+ align:start position:0%
+uh equation counting and constraint
+ 
+
+ align:start position:0%
+uh equation counting and constraint
+counting
+
+ align:start position:0%
+counting
+ 
+
+ align:start position:0%
+counting
+unknown counting
+
+ align:start position:0%
+unknown counting
+ 
+
+ align:start position:0%
+unknown counting
+so what do we got
+
+ align:start position:0%
+so what do we got
+ 
+
+ align:start position:0%
+so what do we got
+well these are two equations two linear
+
+ align:start position:0%
+well these are two equations two linear
+ 
+
+ align:start position:0%
+well these are two equations two linear
+equations so two equations how many
+
+ align:start position:0%
+equations so two equations how many
+ 
+
+ align:start position:0%
+equations so two equations how many
+unknowns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah three right we got r s and t
+
+ align:start position:0%
+ah three right we got r s and t
+ 
+
+ align:start position:0%
+ah three right we got r s and t
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+we can't do that
+
+ align:start position:0%
+we can't do that
+ 
+
+ align:start position:0%
+we can't do that
+that that's too bad we had a very good
+
+ align:start position:0%
+that that's too bad we had a very good
+ 
+
+ align:start position:0%
+that that's too bad we had a very good
+thing going there
+
+ align:start position:0%
+thing going there
+ 
+
+ align:start position:0%
+thing going there
+you know because here we we can get this
+
+ align:start position:0%
+you know because here we we can get this
+ 
+
+ align:start position:0%
+you know because here we we can get this
+from the image we can get that from the
+
+ align:start position:0%
+from the image we can get that from the
+ 
+
+ align:start position:0%
+from the image we can get that from the
+reflectance map and if we could solve
+
+ align:start position:0%
+reflectance map and if we could solve
+ 
+
+ align:start position:0%
+reflectance map and if we could solve
+for h we could plug it in here and we
+
+ align:start position:0%
+for h we could plug it in here and we
+ 
+
+ align:start position:0%
+for h we could plug it in here and we
+would uh we'd be we'd be done
+
+ align:start position:0%
+would uh we'd be we'd be done
+ 
+
+ align:start position:0%
+would uh we'd be we'd be done
+okay so here's the the whole trick of
+
+ align:start position:0%
+okay so here's the the whole trick of
+ 
+
+ align:start position:0%
+okay so here's the the whole trick of
+the method
+
+ align:start position:0%
+the method
+ 
+
+ align:start position:0%
+the method
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+because h appears in both of these
+
+ align:start position:0%
+because h appears in both of these
+ 
+
+ align:start position:0%
+because h appears in both of these
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+we can make some progress
+
+ align:start position:0%
+we can make some progress
+ 
+
+ align:start position:0%
+we can make some progress
+we won't be able to solve for h
+
+ align:start position:0%
+we won't be able to solve for h
+ 
+
+ align:start position:0%
+we won't be able to solve for h
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+that's not really our aim our aim is to
+
+ align:start position:0%
+that's not really our aim our aim is to
+ 
+
+ align:start position:0%
+that's not really our aim our aim is to
+get an increment p and q
+
+ align:start position:0%
+get an increment p and q
+ 
+
+ align:start position:0%
+get an increment p and q
+right the only reason we want h is
+
+ align:start position:0%
+right the only reason we want h is
+ 
+
+ align:start position:0%
+right the only reason we want h is
+because this is our formula for
+
+ align:start position:0%
+because this is our formula for
+ 
+
+ align:start position:0%
+because this is our formula for
+computing the change in p and q um
+
+ align:start position:0%
+computing the change in p and q um
+ 
+
+ align:start position:0%
+computing the change in p and q um
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+maybe we can't solve for h
+
+ align:start position:0%
+maybe we can't solve for h
+ 
+
+ align:start position:0%
+maybe we can't solve for h
+uh but maybe if we pick delta x delta y
+
+ align:start position:0%
+uh but maybe if we pick delta x delta y
+ 
+
+ align:start position:0%
+uh but maybe if we pick delta x delta y
+in a nice way
+
+ align:start position:0%
+in a nice way
+ 
+
+ align:start position:0%
+in a nice way
+we can use this formula right and so
+
+ align:start position:0%
+we can use this formula right and so
+ 
+
+ align:start position:0%
+we can use this formula right and so
+how would we pick it well we'd want to
+
+ align:start position:0%
+how would we pick it well we'd want to
+ 
+
+ align:start position:0%
+how would we pick it well we'd want to
+match you know pat and match these two
+
+ align:start position:0%
+match you know pat and match these two
+ 
+
+ align:start position:0%
+match you know pat and match these two
+things right
+
+ align:start position:0%
+things right
+ 
+
+ align:start position:0%
+things right
+so can you can you see what what's going
+
+ align:start position:0%
+so can you can you see what what's going
+ 
+
+ align:start position:0%
+so can you can you see what what's going
+to happen
+
+ align:start position:0%
+to happen
+ 
+
+ align:start position:0%
+to happen
+what's the direction that we're going to
+
+ align:start position:0%
+what's the direction that we're going to
+ 
+
+ align:start position:0%
+what's the direction that we're going to
+go what what del what delta x and delta
+
+ align:start position:0%
+go what what del what delta x and delta
+ 
+
+ align:start position:0%
+go what what del what delta x and delta
+y would you use
+
+ align:start position:0%
+y would you use
+ 
+
+ align:start position:0%
+y would you use
+so that we can actually compute delta p
+
+ align:start position:0%
+so that we can actually compute delta p
+ 
+
+ align:start position:0%
+so that we can actually compute delta p
+delta q using that formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+pattern match
+
+ align:start position:0%
+pattern match
+ 
+
+ align:start position:0%
+pattern match
+okay how about this
+
+ align:start position:0%
+okay how about this
+ 
+
+ align:start position:0%
+okay how about this
+equals that
+
+ align:start position:0%
+equals that
+ 
+
+ align:start position:0%
+equals that
+right so let's try
+
+ align:start position:0%
+right so let's try
+ 
+
+ align:start position:0%
+right so let's try
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just so we can control the step size
+
+ align:start position:0%
+and just so we can control the step size
+ 
+
+ align:start position:0%
+and just so we can control the step size
+let's do
+
+ align:start position:0%
+let's do
+ 
+
+ align:start position:0%
+let's do
+multiply it by some small quantity
+
+ align:start position:0%
+multiply it by some small quantity
+ 
+
+ align:start position:0%
+multiply it by some small quantity
+so so that's it i mean before um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we had a direction that we had to pick
+
+ align:start position:0%
+we had a direction that we had to pick
+ 
+
+ align:start position:0%
+we had a direction that we had to pick
+and remember we couldn't
+
+ align:start position:0%
+and remember we couldn't
+ 
+
+ align:start position:0%
+and remember we couldn't
+compute the profile in any other
+
+ align:start position:0%
+compute the profile in any other
+ 
+
+ align:start position:0%
+compute the profile in any other
+direction the direction was given but
+
+ align:start position:0%
+direction the direction was given but
+ 
+
+ align:start position:0%
+direction the direction was given but
+what was special about hakker was that
+
+ align:start position:0%
+what was special about hakker was that
+ 
+
+ align:start position:0%
+what was special about hakker was that
+that direction was the same everywhere
+
+ align:start position:0%
+that direction was the same everywhere
+ 
+
+ align:start position:0%
+that direction was the same everywhere
+so it was like built into the whole
+
+ align:start position:0%
+so it was like built into the whole
+ 
+
+ align:start position:0%
+so it was like built into the whole
+solution well now maybe the direction is
+
+ align:start position:0%
+solution well now maybe the direction is
+ 
+
+ align:start position:0%
+solution well now maybe the direction is
+going to change as we explore
+
+ align:start position:0%
+going to change as we explore
+ 
+
+ align:start position:0%
+going to change as we explore
+the surface
+
+ align:start position:0%
+the surface
+ 
+
+ align:start position:0%
+the surface
+okay so what happens if we try this well
+
+ align:start position:0%
+okay so what happens if we try this well
+ 
+
+ align:start position:0%
+okay so what happens if we try this well
+then we plug that into
+
+ align:start position:0%
+then we plug that into
+ 
+
+ align:start position:0%
+then we plug that into
+that equation and we get this and we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again there's a particular direction
+
+ align:start position:0%
+again there's a particular direction
+ 
+
+ align:start position:0%
+again there's a particular direction
+that we can make progress in and that's
+
+ align:start position:0%
+that we can make progress in and that's
+ 
+
+ align:start position:0%
+that we can make progress in and that's
+this direction
+
+ align:start position:0%
+this direction
+ 
+
+ align:start position:0%
+this direction
+and if we go in that direction we can
+
+ align:start position:0%
+and if we go in that direction we can
+ 
+
+ align:start position:0%
+and if we go in that direction we can
+figure out what how to change p and q
+
+ align:start position:0%
+figure out what how to change p and q
+ 
+
+ align:start position:0%
+figure out what how to change p and q
+and and that's it
+
+ align:start position:0%
+and and that's it
+ 
+
+ align:start position:0%
+and and that's it
+we're done
+
+ align:start position:0%
+we're done
+ 
+
+ align:start position:0%
+we're done
+so if we want to summarize all of this
+
+ align:start position:0%
+so if we want to summarize all of this
+ 
+
+ align:start position:0%
+so if we want to summarize all of this
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's just uh
+
+ align:start position:0%
+right that's just uh
+ 
+
+ align:start position:0%
+right that's just uh
+from here
+
+ align:start position:0%
+from here
+ 
+
+ align:start position:0%
+from here
+and then we've got let's leave out dz
+
+ align:start position:0%
+and then we've got let's leave out dz
+ 
+
+ align:start position:0%
+and then we've got let's leave out dz
+for the moment dpd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course we're interested in z so
+
+ align:start position:0%
+and of course we're interested in z so
+ 
+
+ align:start position:0%
+and of course we're interested in z so
+we need to write that one as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we've got is five uh ordinary
+
+ align:start position:0%
+so what we've got is five uh ordinary
+ 
+
+ align:start position:0%
+so what we've got is five uh ordinary
+differential equations and they're you
+
+ align:start position:0%
+differential equations and they're you
+ 
+
+ align:start position:0%
+differential equations and they're you
+know particularly simple the first order
+
+ align:start position:0%
+know particularly simple the first order
+ 
+
+ align:start position:0%
+know particularly simple the first order
+equations and
+
+ align:start position:0%
+equations and
+ 
+
+ align:start position:0%
+equations and
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we explore the surface along these
+
+ align:start position:0%
+we explore the surface along these
+ 
+
+ align:start position:0%
+we explore the surface along these
+curves and actually along these strips
+
+ align:start position:0%
+curves and actually along these strips
+ 
+
+ align:start position:0%
+curves and actually along these strips
+and those are the equations that
+
+ align:start position:0%
+and those are the equations that
+ 
+
+ align:start position:0%
+and those are the equations that
+generate
+
+ align:start position:0%
+generate
+ 
+
+ align:start position:0%
+generate
+that strip
+
+ align:start position:0%
+that strip
+ 
+
+ align:start position:0%
+that strip
+so it's very simple we as we go along we
+
+ align:start position:0%
+so it's very simple we as we go along we
+ 
+
+ align:start position:0%
+so it's very simple we as we go along we
+have the image brightness we look at the
+
+ align:start position:0%
+have the image brightness we look at the
+ 
+
+ align:start position:0%
+have the image brightness we look at the
+brightness gradient and that's going to
+
+ align:start position:0%
+brightness gradient and that's going to
+ 
+
+ align:start position:0%
+brightness gradient and that's going to
+tell us how to update p and q
+
+ align:start position:0%
+tell us how to update p and q
+ 
+
+ align:start position:0%
+tell us how to update p and q
+since we're carrying along p and q we
+
+ align:start position:0%
+since we're carrying along p and q we
+ 
+
+ align:start position:0%
+since we're carrying along p and q we
+know where we are in the reflectance map
+
+ align:start position:0%
+know where we are in the reflectance map
+ 
+
+ align:start position:0%
+know where we are in the reflectance map
+so we can compute
+
+ align:start position:0%
+so we can compute
+ 
+
+ align:start position:0%
+so we can compute
+r sub p r sub q that tells us
+
+ align:start position:0%
+r sub p r sub q that tells us
+ 
+
+ align:start position:0%
+r sub p r sub q that tells us
+the step to take the update in x and y
+
+ align:start position:0%
+the step to take the update in x and y
+ 
+
+ align:start position:0%
+the step to take the update in x and y
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+well there's also the this
+
+ align:start position:0%
+well there's also the this
+ 
+
+ align:start position:0%
+well there's also the this
+output rule so to speak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which tells us how much the height is
+
+ align:start position:0%
+which tells us how much the height is
+ 
+
+ align:start position:0%
+which tells us how much the height is
+changing and that's just you know
+
+ align:start position:0%
+changing and that's just you know
+ 
+
+ align:start position:0%
+changing and that's just you know
+based on p delta x plus q delta y
+
+ align:start position:0%
+based on p delta x plus q delta y
+ 
+
+ align:start position:0%
+based on p delta x plus q delta y
+same old formula we've used all along
+
+ align:start position:0%
+same old formula we've used all along
+ 
+
+ align:start position:0%
+same old formula we've used all along
+i i separate this equation from the rest
+
+ align:start position:0%
+i i separate this equation from the rest
+ 
+
+ align:start position:0%
+i i separate this equation from the rest
+because the others sort of have are a
+
+ align:start position:0%
+because the others sort of have are a
+ 
+
+ align:start position:0%
+because the others sort of have are a
+dynamic system that where the first two
+
+ align:start position:0%
+dynamic system that where the first two
+ 
+
+ align:start position:0%
+dynamic system that where the first two
+feed into the second two and the second
+
+ align:start position:0%
+feed into the second two and the second
+ 
+
+ align:start position:0%
+feed into the second two and the second
+two feed into the first two so you know
+
+ align:start position:0%
+two feed into the first two so you know
+ 
+
+ align:start position:0%
+two feed into the first two so you know
+if you're sort of thinking control
+
+ align:start position:0%
+if you're sort of thinking control
+ 
+
+ align:start position:0%
+if you're sort of thinking control
+theory and stability and stuff like that
+
+ align:start position:0%
+theory and stability and stuff like that
+ 
+
+ align:start position:0%
+theory and stability and stuff like that
+that's the interesting part that they're
+
+ align:start position:0%
+that's the interesting part that they're
+ 
+
+ align:start position:0%
+that's the interesting part that they're
+these two systems that are feeding uh
+
+ align:start position:0%
+these two systems that are feeding uh
+ 
+
+ align:start position:0%
+these two systems that are feeding uh
+into each other
+
+ align:start position:0%
+into each other
+ 
+
+ align:start position:0%
+into each other
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+it's kind of weird but what happens is
+
+ align:start position:0%
+it's kind of weird but what happens is
+ 
+
+ align:start position:0%
+it's kind of weird but what happens is
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the image space
+
+ align:start position:0%
+in the image space
+ 
+
+ align:start position:0%
+in the image space
+and the gradient space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have this
+
+ align:start position:0%
+we have this
+ 
+
+ align:start position:0%
+we have this
+way of going in uh gradient directions
+
+ align:start position:0%
+way of going in uh gradient directions
+ 
+
+ align:start position:0%
+way of going in uh gradient directions
+and so uh let's plot the isophotes in
+
+ align:start position:0%
+and so uh let's plot the isophotes in
+ 
+
+ align:start position:0%
+and so uh let's plot the isophotes in
+just some random isophotes in those two
+
+ align:start position:0%
+just some random isophotes in those two
+ 
+
+ align:start position:0%
+just some random isophotes in those two
+spaces
+
+ align:start position:0%
+spaces
+ 
+
+ align:start position:0%
+spaces
+so i don't know
+
+ align:start position:0%
+so i don't know
+ 
+
+ align:start position:0%
+so i don't know
+this one here could be
+
+ align:start position:0%
+this one here could be
+ 
+
+ align:start position:0%
+this one here could be
+sort of lamborghini and i don't know
+
+ align:start position:0%
+sort of lamborghini and i don't know
+ 
+
+ align:start position:0%
+sort of lamborghini and i don't know
+this is some
+
+ align:start position:0%
+this is some
+ 
+
+ align:start position:0%
+this is some
+whatever that is these are the isophotes
+
+ align:start position:0%
+whatever that is these are the isophotes
+ 
+
+ align:start position:0%
+whatever that is these are the isophotes
+in the image
+
+ align:start position:0%
+in the image
+ 
+
+ align:start position:0%
+in the image
+and what this is saying if we're at a
+
+ align:start position:0%
+and what this is saying if we're at a
+ 
+
+ align:start position:0%
+and what this is saying if we're at a
+particular point suppose we're here
+
+ align:start position:0%
+particular point suppose we're here
+ 
+
+ align:start position:0%
+particular point suppose we're here
+in x and y and we're also carrying along
+
+ align:start position:0%
+in x and y and we're also carrying along
+ 
+
+ align:start position:0%
+in x and y and we're also carrying along
+p and q so we also somewhere
+
+ align:start position:0%
+p and q so we also somewhere
+ 
+
+ align:start position:0%
+p and q so we also somewhere
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+let's suppose we're here
+
+ align:start position:0%
+let's suppose we're here
+ 
+
+ align:start position:0%
+let's suppose we're here
+then the step we take is based on the
+
+ align:start position:0%
+then the step we take is based on the
+ 
+
+ align:start position:0%
+then the step we take is based on the
+gradient which is perpendicular to the
+
+ align:start position:0%
+gradient which is perpendicular to the
+ 
+
+ align:start position:0%
+gradient which is perpendicular to the
+iso
+
+ align:start position:0%
+iso
+ 
+
+ align:start position:0%
+iso
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+and so the step we take here though
+
+ align:start position:0%
+and so the step we take here though
+ 
+
+ align:start position:0%
+and so the step we take here though
+weirdly is dependent on the gradient
+
+ align:start position:0%
+weirdly is dependent on the gradient
+ 
+
+ align:start position:0%
+weirdly is dependent on the gradient
+there so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the actual step we take
+
+ align:start position:0%
+so this is the actual step we take
+ 
+
+ align:start position:0%
+so this is the actual step we take
+and then the step we take in p and q
+
+ align:start position:0%
+and then the step we take in p and q
+ 
+
+ align:start position:0%
+and then the step we take in p and q
+is strangely dependent on the
+
+ align:start position:0%
+is strangely dependent on the
+ 
+
+ align:start position:0%
+is strangely dependent on the
+gradient there
+
+ align:start position:0%
+gradient there
+ 
+
+ align:start position:0%
+gradient there
+so we actually take a step in that
+
+ align:start position:0%
+so we actually take a step in that
+ 
+
+ align:start position:0%
+so we actually take a step in that
+direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's you know a little weird you're
+
+ align:start position:0%
+so it's you know a little weird you're
+ 
+
+ align:start position:0%
+so it's you know a little weird you're
+not going uphill you're not just doing
+
+ align:start position:0%
+not going uphill you're not just doing
+ 
+
+ align:start position:0%
+not going uphill you're not just doing
+gradient ascent or gradient descent
+
+ align:start position:0%
+gradient ascent or gradient descent
+ 
+
+ align:start position:0%
+gradient ascent or gradient descent
+but you're going in the gradient in in
+
+ align:start position:0%
+but you're going in the gradient in in
+ 
+
+ align:start position:0%
+but you're going in the gradient in in
+the other diagram anyway uh
+
+ align:start position:0%
+the other diagram anyway uh
+ 
+
+ align:start position:0%
+the other diagram anyway uh
+this makes it clear you know how to
+
+ align:start position:0%
+this makes it clear you know how to
+ 
+
+ align:start position:0%
+this makes it clear you know how to
+implement that you just have to have
+
+ align:start position:0%
+implement that you just have to have
+ 
+
+ align:start position:0%
+implement that you just have to have
+these two things
+
+ align:start position:0%
+these two things
+ 
+
+ align:start position:0%
+these two things
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+image
+
+ align:start position:0%
+image
+ 
+
+ align:start position:0%
+image
+e of x and y
+
+ align:start position:0%
+e of x and y
+ 
+
+ align:start position:0%
+e of x and y
+and the reflectance map r of p and q
+
+ align:start position:0%
+and the reflectance map r of p and q
+ 
+
+ align:start position:0%
+and the reflectance map r of p and q
+and once you're plonked down somewhere
+
+ align:start position:0%
+and once you're plonked down somewhere
+ 
+
+ align:start position:0%
+and once you're plonked down somewhere
+in there you just follow this rule
+
+ align:start position:0%
+in there you just follow this rule
+ 
+
+ align:start position:0%
+in there you just follow this rule
+and it'll trace out
+
+ align:start position:0%
+and it'll trace out
+ 
+
+ align:start position:0%
+and it'll trace out
+a curve in the image and indirectly
+
+ align:start position:0%
+a curve in the image and indirectly
+ 
+
+ align:start position:0%
+a curve in the image and indirectly
+it'll trace out a curve in 3d
+
+ align:start position:0%
+it'll trace out a curve in 3d
+ 
+
+ align:start position:0%
+it'll trace out a curve in 3d
+and actually it'll trace out a whole
+
+ align:start position:0%
+and actually it'll trace out a whole
+ 
+
+ align:start position:0%
+and actually it'll trace out a whole
+strip because all along we know the
+
+ align:start position:0%
+strip because all along we know the
+ 
+
+ align:start position:0%
+strip because all along we know the
+surface orientation
+
+ align:start position:0%
+surface orientation
+ 
+
+ align:start position:0%
+surface orientation
+and that's a little different from the
+
+ align:start position:0%
+and that's a little different from the
+ 
+
+ align:start position:0%
+and that's a little different from the
+hapka case
+
+ align:start position:0%
+hapka case
+ 
+
+ align:start position:0%
+hapka case
+where we don't know p and q as we go
+
+ align:start position:0%
+where we don't know p and q as we go
+ 
+
+ align:start position:0%
+where we don't know p and q as we go
+along we only know one component in a
+
+ align:start position:0%
+along we only know one component in a
+ 
+
+ align:start position:0%
+along we only know one component in a
+certain direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we've reduced
+
+ align:start position:0%
+we've reduced
+ 
+
+ align:start position:0%
+we've reduced
+our image irradiance equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to those
+
+ align:start position:0%
+to those
+ 
+
+ align:start position:0%
+to those
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+ordinary differential coupled ordinary
+
+ align:start position:0%
+ordinary differential coupled ordinary
+ 
+
+ align:start position:0%
+ordinary differential coupled ordinary
+differential equations and this is a
+
+ align:start position:0%
+differential equations and this is a
+ 
+
+ align:start position:0%
+differential equations and this is a
+partial differential equation
+
+ align:start position:0%
+partial differential equation
+ 
+
+ align:start position:0%
+partial differential equation
+why is that well because p is dz dx
+
+ align:start position:0%
+why is that well because p is dz dx
+ 
+
+ align:start position:0%
+why is that well because p is dz dx
+and q is dzby
+
+ align:start position:0%
+and q is dzby
+ 
+
+ align:start position:0%
+and q is dzby
+and we're just sort of making things
+
+ align:start position:0%
+and we're just sort of making things
+ 
+
+ align:start position:0%
+and we're just sort of making things
+look less intimidating by using these
+
+ align:start position:0%
+look less intimidating by using these
+ 
+
+ align:start position:0%
+look less intimidating by using these
+abbreviations p and q but this is really
+
+ align:start position:0%
+abbreviations p and q but this is really
+ 
+
+ align:start position:0%
+abbreviations p and q but this is really
+a first order non-linear partial
+
+ align:start position:0%
+a first order non-linear partial
+ 
+
+ align:start position:0%
+a first order non-linear partial
+differential equation and you know
+
+ align:start position:0%
+differential equation and you know
+ 
+
+ align:start position:0%
+differential equation and you know
+in physics you run into loads of partial
+
+ align:start position:0%
+in physics you run into loads of partial
+ 
+
+ align:start position:0%
+in physics you run into loads of partial
+differential equations
+
+ align:start position:0%
+differential equations
+ 
+
+ align:start position:0%
+differential equations
+but they're
+
+ align:start position:0%
+but they're
+ 
+
+ align:start position:0%
+but they're
+generally
+
+ align:start position:0%
+generally
+ 
+
+ align:start position:0%
+generally
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+second order those are the ones of
+
+ align:start position:0%
+second order those are the ones of
+ 
+
+ align:start position:0%
+second order those are the ones of
+interest you know heat flow
+
+ align:start position:0%
+interest you know heat flow
+ 
+
+ align:start position:0%
+interest you know heat flow
+wave propagation
+
+ align:start position:0%
+wave propagation
+ 
+
+ align:start position:0%
+wave propagation
+so they're typically second order and
+
+ align:start position:0%
+so they're typically second order and
+ 
+
+ align:start position:0%
+so they're typically second order and
+they're typically linear
+
+ align:start position:0%
+they're typically linear
+ 
+
+ align:start position:0%
+they're typically linear
+and here we've got something unusual we
+
+ align:start position:0%
+and here we've got something unusual we
+ 
+
+ align:start position:0%
+and here we've got something unusual we
+have first order which you think should
+
+ align:start position:0%
+have first order which you think should
+ 
+
+ align:start position:0%
+have first order which you think should
+be simpler
+
+ align:start position:0%
+be simpler
+ 
+
+ align:start position:0%
+be simpler
+and it's non-linear
+
+ align:start position:0%
+and it's non-linear
+ 
+
+ align:start position:0%
+and it's non-linear
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know
+
+ align:start position:0%
+so you know
+ 
+
+ align:start position:0%
+so you know
+if it wasn't for that i wouldn't have to
+
+ align:start position:0%
+if it wasn't for that i wouldn't have to
+ 
+
+ align:start position:0%
+if it wasn't for that i wouldn't have to
+explain all of this because you would
+
+ align:start position:0%
+explain all of this because you would
+ 
+
+ align:start position:0%
+explain all of this because you would
+have learned this in physics but physics
+
+ align:start position:0%
+have learned this in physics but physics
+ 
+
+ align:start position:0%
+have learned this in physics but physics
+does second order linear pdes and not
+
+ align:start position:0%
+does second order linear pdes and not
+ 
+
+ align:start position:0%
+does second order linear pdes and not
+first order non-linear pdes so
+
+ align:start position:0%
+first order non-linear pdes so
+ 
+
+ align:start position:0%
+first order non-linear pdes so
+we've just
+
+ align:start position:0%
+we've just
+ 
+
+ align:start position:0%
+we've just
+come up with a method for solving those
+
+ align:start position:0%
+come up with a method for solving those
+ 
+
+ align:start position:0%
+come up with a method for solving those
+and that that's what we need to do in
+
+ align:start position:0%
+and that that's what we need to do in
+ 
+
+ align:start position:0%
+and that that's what we need to do in
+shape from shading since the brightness
+
+ align:start position:0%
+shape from shading since the brightness
+ 
+
+ align:start position:0%
+shape from shading since the brightness
+depends on the first derivative so
+
+ align:start position:0%
+depends on the first derivative so
+ 
+
+ align:start position:0%
+depends on the first derivative so
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+now this is general for any r of p and q
+
+ align:start position:0%
+now this is general for any r of p and q
+ 
+
+ align:start position:0%
+now this is general for any r of p and q
+let's just take a look at it for some
+
+ align:start position:0%
+let's just take a look at it for some
+ 
+
+ align:start position:0%
+let's just take a look at it for some
+particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface properties that we've been
+
+ align:start position:0%
+surface properties that we've been
+ 
+
+ align:start position:0%
+surface properties that we've been
+studying so one of them of course is
+
+ align:start position:0%
+studying so one of them of course is
+ 
+
+ align:start position:0%
+studying so one of them of course is
+hapki and that's a special case we
+
+ align:start position:0%
+hapki and that's a special case we
+ 
+
+ align:start position:0%
+hapki and that's a special case we
+solved up there but let's just see how
+
+ align:start position:0%
+solved up there but let's just see how
+ 
+
+ align:start position:0%
+solved up there but let's just see how
+the general case reduces
+
+ align:start position:0%
+the general case reduces
+ 
+
+ align:start position:0%
+the general case reduces
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+we you assume this for the reflectance
+
+ align:start position:0%
+we you assume this for the reflectance
+ 
+
+ align:start position:0%
+we you assume this for the reflectance
+map
+
+ align:start position:0%
+map
+ 
+
+ align:start position:0%
+map
+okay so here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a reflectance map for for
+
+ align:start position:0%
+so that's a reflectance map for for
+ 
+
+ align:start position:0%
+so that's a reflectance map for for
+hopkins so what do we need we need r r
+
+ align:start position:0%
+hopkins so what do we need we need r r
+ 
+
+ align:start position:0%
+hopkins so what do we need we need r r
+sub p
+
+ align:start position:0%
+sub p
+ 
+
+ align:start position:0%
+sub p
+so we differentiate this with respect to
+
+ align:start position:0%
+so we differentiate this with respect to
+ 
+
+ align:start position:0%
+so we differentiate this with respect to
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+as square root so we're going to get a
+
+ align:start position:0%
+as square root so we're going to get a
+ 
+
+ align:start position:0%
+as square root so we're going to get a
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+divided by the square root let's take
+
+ align:start position:0%
+divided by the square root let's take
+ 
+
+ align:start position:0%
+divided by the square root let's take
+out the 1 over square root of r s first
+
+ align:start position:0%
+out the 1 over square root of r s first
+ 
+
+ align:start position:0%
+out the 1 over square root of r s first
+it's just a constant
+
+ align:start position:0%
+it's just a constant
+ 
+
+ align:start position:0%
+it's just a constant
+and then the rest is going to be 1 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because um we have something
+
+ align:start position:0%
+right because um we have something
+ 
+
+ align:start position:0%
+right because um we have something
+raised to the half power so you
+
+ align:start position:0%
+raised to the half power so you
+ 
+
+ align:start position:0%
+raised to the half power so you
+differentiate that you get a half times
+
+ align:start position:0%
+differentiate that you get a half times
+ 
+
+ align:start position:0%
+differentiate that you get a half times
+that thing to the minus half power
+
+ align:start position:0%
+that thing to the minus half power
+ 
+
+ align:start position:0%
+that thing to the minus half power
+and then we have to differentiate what's
+
+ align:start position:0%
+and then we have to differentiate what's
+ 
+
+ align:start position:0%
+and then we have to differentiate what's
+this term inside with respect to p and
+
+ align:start position:0%
+this term inside with respect to p and
+ 
+
+ align:start position:0%
+this term inside with respect to p and
+we get ps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course r sub q is very similar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the other one we need is p r
+
+ align:start position:0%
+and then the other one we need is p r
+ 
+
+ align:start position:0%
+and then the other one we need is p r
+sub p plus q r sub q
+
+ align:start position:0%
+sub p plus q r sub q
+ 
+
+ align:start position:0%
+sub p plus q r sub q
+and that's just going to be the same
+
+ align:start position:0%
+and that's just going to be the same
+ 
+
+ align:start position:0%
+and that's just going to be the same
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these three share this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplier
+
+ align:start position:0%
+multiplier
+ 
+
+ align:start position:0%
+multiplier
+and that multiplier as you mentioned
+
+ align:start position:0%
+and that multiplier as you mentioned
+ 
+
+ align:start position:0%
+and that multiplier as you mentioned
+last time it's it's really just
+
+ align:start position:0%
+last time it's it's really just
+ 
+
+ align:start position:0%
+last time it's it's really just
+controlling how fast
+
+ align:start position:0%
+controlling how fast
+ 
+
+ align:start position:0%
+controlling how fast
+you go along the curve as you solve it
+
+ align:start position:0%
+you go along the curve as you solve it
+ 
+
+ align:start position:0%
+you go along the curve as you solve it
+so you could
+
+ align:start position:0%
+so you could
+ 
+
+ align:start position:0%
+so you could
+change that and
+
+ align:start position:0%
+change that and
+ 
+
+ align:start position:0%
+change that and
+i mean it would change numerical
+
+ align:start position:0%
+i mean it would change numerical
+ 
+
+ align:start position:0%
+i mean it would change numerical
+stability and you know how accurate the
+
+ align:start position:0%
+stability and you know how accurate the
+ 
+
+ align:start position:0%
+stability and you know how accurate the
+solution is but in the infinitesimal
+
+ align:start position:0%
+solution is but in the infinitesimal
+ 
+
+ align:start position:0%
+solution is but in the infinitesimal
+case it wouldn't change the solution so
+
+ align:start position:0%
+case it wouldn't change the solution so
+ 
+
+ align:start position:0%
+case it wouldn't change the solution so
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+we could
+
+ align:start position:0%
+we could
+ 
+
+ align:start position:0%
+we could
+remove these three terms
+
+ align:start position:0%
+remove these three terms
+ 
+
+ align:start position:0%
+remove these three terms
+as long as we do it on all three
+
+ align:start position:0%
+as long as we do it on all three
+ 
+
+ align:start position:0%
+as long as we do it on all three
+equations and then we have rp is
+
+ align:start position:0%
+equations and then we have rp is
+ 
+
+ align:start position:0%
+equations and then we have rp is
+proportional to ps and rq is
+
+ align:start position:0%
+proportional to ps and rq is
+ 
+
+ align:start position:0%
+proportional to ps and rq is
+proportional to qs and so our update
+
+ align:start position:0%
+proportional to qs and so our update
+ 
+
+ align:start position:0%
+proportional to qs and so our update
+rules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know the update rule for x is just p
+
+ align:start position:0%
+you know the update rule for x is just p
+ 
+
+ align:start position:0%
+you know the update rule for x is just p
+s the update rule for y is q s and and
+
+ align:start position:0%
+s the update rule for y is q s and and
+ 
+
+ align:start position:0%
+s the update rule for y is q s and and
+that's what we had had up there so
+
+ align:start position:0%
+that's what we had had up there so
+ 
+
+ align:start position:0%
+that's what we had had up there so
+so the general case
+
+ align:start position:0%
+so the general case
+ 
+
+ align:start position:0%
+so the general case
+reduces down to
+
+ align:start position:0%
+reduces down to
+ 
+
+ align:start position:0%
+reduces down to
+this pretty easily particularly since i
+
+ align:start position:0%
+this pretty easily particularly since i
+ 
+
+ align:start position:0%
+this pretty easily particularly since i
+guess this is let's see r s e squared
+
+ align:start position:0%
+guess this is let's see r s e squared
+ 
+
+ align:start position:0%
+guess this is let's see r s e squared
+minus one
+
+ align:start position:0%
+minus one
+ 
+
+ align:start position:0%
+minus one
+as we showed
+
+ align:start position:0%
+as we showed
+ 
+
+ align:start position:0%
+as we showed
+up there somewhere
+
+ align:start position:0%
+up there somewhere
+ 
+
+ align:start position:0%
+up there somewhere
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+that's good the general case reduces
+
+ align:start position:0%
+that's good the general case reduces
+ 
+
+ align:start position:0%
+that's good the general case reduces
+correctly
+
+ align:start position:0%
+correctly
+ 
+
+ align:start position:0%
+correctly
+to that special case that
+
+ align:start position:0%
+to that special case that
+ 
+
+ align:start position:0%
+to that special case that
+we saw first
+
+ align:start position:0%
+we saw first
+ 
+
+ align:start position:0%
+we saw first
+um let's look at some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other case
+
+ align:start position:0%
+other case
+ 
+
+ align:start position:0%
+other case
+so we said that in the scanning electron
+
+ align:start position:0%
+so we said that in the scanning electron
+ 
+
+ align:start position:0%
+so we said that in the scanning electron
+microscope
+
+ align:start position:0%
+microscope
+ 
+
+ align:start position:0%
+microscope
+we had dependence of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slope uh right remember that
+
+ align:start position:0%
+slope uh right remember that
+ 
+
+ align:start position:0%
+slope uh right remember that
+you know unless you do something strange
+
+ align:start position:0%
+you know unless you do something strange
+ 
+
+ align:start position:0%
+you know unless you do something strange
+to your microscope it's rotationally
+
+ align:start position:0%
+to your microscope it's rotationally
+ 
+
+ align:start position:0%
+to your microscope it's rotationally
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+in imaging and so if you look at a
+
+ align:start position:0%
+in imaging and so if you look at a
+ 
+
+ align:start position:0%
+in imaging and so if you look at a
+reflectance map for that instrument
+
+ align:start position:0%
+reflectance map for that instrument
+ 
+
+ align:start position:0%
+reflectance map for that instrument
+the brightness is only dependent on the
+
+ align:start position:0%
+the brightness is only dependent on the
+ 
+
+ align:start position:0%
+the brightness is only dependent on the
+slope
+
+ align:start position:0%
+slope
+ 
+
+ align:start position:0%
+slope
+not the you know the magnitude of the
+
+ align:start position:0%
+not the you know the magnitude of the
+ 
+
+ align:start position:0%
+not the you know the magnitude of the
+gradient not the gradient direction so
+
+ align:start position:0%
+gradient not the gradient direction so
+ 
+
+ align:start position:0%
+gradient not the gradient direction so
+okay so uh you know what's f well that
+
+ align:start position:0%
+okay so uh you know what's f well that
+ 
+
+ align:start position:0%
+okay so uh you know what's f well that
+depends on the instrument uh and it and
+
+ align:start position:0%
+depends on the instrument uh and it and
+ 
+
+ align:start position:0%
+depends on the instrument uh and it and
+also the material of the object and so
+
+ align:start position:0%
+also the material of the object and so
+ 
+
+ align:start position:0%
+also the material of the object and so
+you need to calibrate that but let's
+
+ align:start position:0%
+you need to calibrate that but let's
+ 
+
+ align:start position:0%
+you need to calibrate that but let's
+leave it general let's just leave it as
+
+ align:start position:0%
+leave it general let's just leave it as
+ 
+
+ align:start position:0%
+leave it general let's just leave it as
+as f
+
+ align:start position:0%
+as f
+ 
+
+ align:start position:0%
+as f
+okay then to use this method we need r
+
+ align:start position:0%
+okay then to use this method we need r
+ 
+
+ align:start position:0%
+okay then to use this method we need r
+sub p r sub q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we differentiate with respect to p
+
+ align:start position:0%
+and we differentiate with respect to p
+ 
+
+ align:start position:0%
+and we differentiate with respect to p
+and we get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we differentiate with respect to q
+
+ align:start position:0%
+and we differentiate with respect to q
+ 
+
+ align:start position:0%
+and we differentiate with respect to q
+we get that and so this is going to tell
+
+ align:start position:0%
+we get that and so this is going to tell
+ 
+
+ align:start position:0%
+we get that and so this is going to tell
+us our update for
+
+ align:start position:0%
+us our update for
+ 
+
+ align:start position:0%
+us our update for
+x and this is going to tell us our
+
+ align:start position:0%
+x and this is going to tell us our
+ 
+
+ align:start position:0%
+x and this is going to tell us our
+update for y
+
+ align:start position:0%
+update for y
+ 
+
+ align:start position:0%
+update for y
+and we also need prp plus qrq
+
+ align:start position:0%
+and we also need prp plus qrq
+ 
+
+ align:start position:0%
+and we also need prp plus qrq
+which is going to be this constant times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is our update for
+
+ align:start position:0%
+and this is our update for
+ 
+
+ align:start position:0%
+and this is our update for
+the height
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can certainly apply this method to
+
+ align:start position:0%
+so we can certainly apply this method to
+ 
+
+ align:start position:0%
+so we can certainly apply this method to
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+scanning electron microscope images
+
+ align:start position:0%
+scanning electron microscope images
+ 
+
+ align:start position:0%
+scanning electron microscope images
+and again there's this constant
+
+ align:start position:0%
+and again there's this constant
+ 
+
+ align:start position:0%
+and again there's this constant
+multiplier here we'll talk about this
+
+ align:start position:0%
+multiplier here we'll talk about this
+ 
+
+ align:start position:0%
+multiplier here we'll talk about this
+some more
+
+ align:start position:0%
+some more
+ 
+
+ align:start position:0%
+some more
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+oh not the whole thing but that only
+
+ align:start position:0%
+oh not the whole thing but that only
+ 
+
+ align:start position:0%
+oh not the whole thing but that only
+affects how fast we move along the
+
+ align:start position:0%
+affects how fast we move along the
+ 
+
+ align:start position:0%
+affects how fast we move along the
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+so we could actually simplify things
+
+ align:start position:0%
+so we could actually simplify things
+ 
+
+ align:start position:0%
+so we could actually simplify things
+by you know
+
+ align:start position:0%
+by you know
+ 
+
+ align:start position:0%
+by you know
+getting rid of that
+
+ align:start position:0%
+getting rid of that
+ 
+
+ align:start position:0%
+getting rid of that
+and then the equations are very simple
+
+ align:start position:0%
+and then the equations are very simple
+ 
+
+ align:start position:0%
+and then the equations are very simple
+what is it telling us it's telling us
+
+ align:start position:0%
+what is it telling us it's telling us
+ 
+
+ align:start position:0%
+what is it telling us it's telling us
+that the direction we're going is the
+
+ align:start position:0%
+that the direction we're going is the
+ 
+
+ align:start position:0%
+that the direction we're going is the
+gradient
+
+ align:start position:0%
+gradient
+ 
+
+ align:start position:0%
+gradient
+we're going
+
+ align:start position:0%
+we're going
+ 
+
+ align:start position:0%
+we're going
+uphill
+
+ align:start position:0%
+uphill
+ 
+
+ align:start position:0%
+uphill
+so the gradient
+
+ align:start position:0%
+so the gradient
+ 
+
+ align:start position:0%
+so the gradient
+is the direction of steepest descent
+
+ align:start position:0%
+is the direction of steepest descent
+ 
+
+ align:start position:0%
+is the direction of steepest descent
+so if i'm standing on the mountain
+
+ align:start position:0%
+so if i'm standing on the mountain
+ 
+
+ align:start position:0%
+so if i'm standing on the mountain
+you know you know what the gradient is
+
+ align:start position:0%
+you know you know what the gradient is
+ 
+
+ align:start position:0%
+you know you know what the gradient is
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's where we're going or or downhill
+
+ align:start position:0%
+that's where we're going or or downhill
+ 
+
+ align:start position:0%
+that's where we're going or or downhill
+we can as we said we can reverse the
+
+ align:start position:0%
+we can as we said we can reverse the
+ 
+
+ align:start position:0%
+we can as we said we can reverse the
+direction we can make uh delta uh chi
+
+ align:start position:0%
+direction we can make uh delta uh chi
+ 
+
+ align:start position:0%
+direction we can make uh delta uh chi
+chi be negative and go in minus p minus
+
+ align:start position:0%
+chi be negative and go in minus p minus
+ 
+
+ align:start position:0%
+chi be negative and go in minus p minus
+q direction so it's very simple and then
+
+ align:start position:0%
+q direction so it's very simple and then
+ 
+
+ align:start position:0%
+q direction so it's very simple and then
+here's the
+
+ align:start position:0%
+here's the
+ 
+
+ align:start position:0%
+here's the
+rule that tells us how much we're
+
+ align:start position:0%
+rule that tells us how much we're
+ 
+
+ align:start position:0%
+rule that tells us how much we're
+updating z so
+
+ align:start position:0%
+updating z so
+ 
+
+ align:start position:0%
+updating z so
+so scanning electron microscope is a
+
+ align:start position:0%
+so scanning electron microscope is a
+ 
+
+ align:start position:0%
+so scanning electron microscope is a
+little bit simpler than you know
+
+ align:start position:0%
+little bit simpler than you know
+ 
+
+ align:start position:0%
+little bit simpler than you know
+lambertian
+
+ align:start position:0%
+lambertian
+ 
+
+ align:start position:0%
+lambertian
+but it
+
+ align:start position:0%
+but it
+ 
+
+ align:start position:0%
+but it
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+rather than solve this one
+
+ align:start position:0%
+rather than solve this one
+ 
+
+ align:start position:0%
+rather than solve this one
+separately
+
+ align:start position:0%
+separately
+ 
+
+ align:start position:0%
+separately
+after doing hapka we just went to the
+
+ align:start position:0%
+after doing hapka we just went to the
+ 
+
+ align:start position:0%
+after doing hapka we just went to the
+general case in general
+
+ align:start position:0%
+general case in general
+ 
+
+ align:start position:0%
+general case in general
+okay and you can do the same for
+
+ align:start position:0%
+okay and you can do the same for
+ 
+
+ align:start position:0%
+okay and you can do the same for
+lambertian unfortunately it gets messy
+
+ align:start position:0%
+lambertian unfortunately it gets messy
+ 
+
+ align:start position:0%
+lambertian unfortunately it gets messy
+because the lambertian has that square
+
+ align:start position:0%
+because the lambertian has that square
+ 
+
+ align:start position:0%
+because the lambertian has that square
+root and the 1 plus p squared plus q
+
+ align:start position:0%
+root and the 1 plus p squared plus q
+ 
+
+ align:start position:0%
+root and the 1 plus p squared plus q
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+but of course you can you can't do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so a couple of things the one to
+
+ align:start position:0%
+okay so a couple of things the one to
+ 
+
+ align:start position:0%
+okay so a couple of things the one to
+remember is that we're dealing with a
+
+ align:start position:0%
+remember is that we're dealing with a
+ 
+
+ align:start position:0%
+remember is that we're dealing with a
+solution that generates
+
+ align:start position:0%
+solution that generates
+ 
+
+ align:start position:0%
+solution that generates
+characteristic strips
+
+ align:start position:0%
+characteristic strips
+ 
+
+ align:start position:0%
+characteristic strips
+so we're not just exploring the surface
+
+ align:start position:0%
+so we're not just exploring the surface
+ 
+
+ align:start position:0%
+so we're not just exploring the surface
+along curves
+
+ align:start position:0%
+along curves
+ 
+
+ align:start position:0%
+along curves
+but along the curve we also know the
+
+ align:start position:0%
+but along the curve we also know the
+ 
+
+ align:start position:0%
+but along the curve we also know the
+surface orientation
+
+ align:start position:0%
+surface orientation
+ 
+
+ align:start position:0%
+surface orientation
+and then um
+
+ align:start position:0%
+and then um
+ 
+
+ align:start position:0%
+and then um
+another related concept is that of a
+
+ align:start position:0%
+another related concept is that of a
+ 
+
+ align:start position:0%
+another related concept is that of a
+base characteristic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the characteristic strip has x y
+
+ align:start position:0%
+okay so the characteristic strip has x y
+ 
+
+ align:start position:0%
+okay so the characteristic strip has x y
+z uh p and q along the strip
+
+ align:start position:0%
+z uh p and q along the strip
+ 
+
+ align:start position:0%
+z uh p and q along the strip
+and the base characteristic is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the projection into the image plane
+
+ align:start position:0%
+the projection into the image plane
+ 
+
+ align:start position:0%
+the projection into the image plane
+and to some extent that's of interest to
+
+ align:start position:0%
+and to some extent that's of interest to
+ 
+
+ align:start position:0%
+and to some extent that's of interest to
+us because
+
+ align:start position:0%
+us because
+ 
+
+ align:start position:0%
+us because
+uh you know that's what we have we have
+
+ align:start position:0%
+uh you know that's what we have we have
+ 
+
+ align:start position:0%
+uh you know that's what we have we have
+the image we're trying to explore it and
+
+ align:start position:0%
+the image we're trying to explore it and
+ 
+
+ align:start position:0%
+the image we're trying to explore it and
+uh for one thing we want to make sure
+
+ align:start position:0%
+uh for one thing we want to make sure
+ 
+
+ align:start position:0%
+uh for one thing we want to make sure
+that we sort of cover much of the image
+
+ align:start position:0%
+that we sort of cover much of the image
+ 
+
+ align:start position:0%
+that we sort of cover much of the image
+with these curves
+
+ align:start position:0%
+with these curves
+ 
+
+ align:start position:0%
+with these curves
+uh and of course the ultimate goal is
+
+ align:start position:0%
+uh and of course the ultimate goal is
+ 
+
+ align:start position:0%
+uh and of course the ultimate goal is
+the surface in 3d
+
+ align:start position:0%
+the surface in 3d
+ 
+
+ align:start position:0%
+the surface in 3d
+but we're also quite interested in in
+
+ align:start position:0%
+but we're also quite interested in in
+ 
+
+ align:start position:0%
+but we're also quite interested in in
+what happens in the image plane that
+
+ align:start position:0%
+what happens in the image plane that
+ 
+
+ align:start position:0%
+what happens in the image plane that
+we're actually covering uh covering that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+how what might this look like these bass
+
+ align:start position:0%
+how what might this look like these bass
+ 
+
+ align:start position:0%
+how what might this look like these bass
+characteristic
+
+ align:start position:0%
+characteristic
+ 
+
+ align:start position:0%
+characteristic
+so here's our image and uh
+
+ align:start position:0%
+so here's our image and uh
+ 
+
+ align:start position:0%
+so here's our image and uh
+for the moment we're assuming we have
+
+ align:start position:0%
+for the moment we're assuming we have
+ 
+
+ align:start position:0%
+for the moment we're assuming we have
+some sort of initial curve and then
+
+ align:start position:0%
+some sort of initial curve and then
+ 
+
+ align:start position:0%
+some sort of initial curve and then
+these uh
+
+ align:start position:0%
+these uh
+ 
+
+ align:start position:0%
+these uh
+base characteristics you know go
+
+ align:start position:0%
+base characteristics you know go
+ 
+
+ align:start position:0%
+base characteristics you know go
+out from there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and maybe the other direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+as i mentioned one reason you might be
+
+ align:start position:0%
+as i mentioned one reason you might be
+ 
+
+ align:start position:0%
+as i mentioned one reason you might be
+interested in these base characteristics
+
+ align:start position:0%
+interested in these base characteristics
+ 
+
+ align:start position:0%
+interested in these base characteristics
+is because
+
+ align:start position:0%
+is because
+ 
+
+ align:start position:0%
+is because
+you want to make sure that you're
+
+ align:start position:0%
+you want to make sure that you're
+ 
+
+ align:start position:0%
+you want to make sure that you're
+exploring as much as possible of the
+
+ align:start position:0%
+exploring as much as possible of the
+ 
+
+ align:start position:0%
+exploring as much as possible of the
+image
+
+ align:start position:0%
+image
+ 
+
+ align:start position:0%
+image
+and not leaving out some areas and also
+
+ align:start position:0%
+and not leaving out some areas and also
+ 
+
+ align:start position:0%
+and not leaving out some areas and also
+you might say well
+
+ align:start position:0%
+you might say well
+ 
+
+ align:start position:0%
+you might say well
+you know this is sort of no man's land
+
+ align:start position:0%
+you know this is sort of no man's land
+ 
+
+ align:start position:0%
+you know this is sort of no man's land
+i should really be interpolating another
+
+ align:start position:0%
+i should really be interpolating another
+ 
+
+ align:start position:0%
+i should really be interpolating another
+one in here
+
+ align:start position:0%
+one in here
+ 
+
+ align:start position:0%
+one in here
+and in some other areas
+
+ align:start position:0%
+and in some other areas
+ 
+
+ align:start position:0%
+and in some other areas
+conversely
+
+ align:start position:0%
+conversely
+ 
+
+ align:start position:0%
+conversely
+the base characteristics might get close
+
+ align:start position:0%
+the base characteristics might get close
+ 
+
+ align:start position:0%
+the base characteristics might get close
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+and you might say well that's
+
+ align:start position:0%
+and you might say well that's
+ 
+
+ align:start position:0%
+and you might say well that's
+unreasonable
+
+ align:start position:0%
+unreasonable
+ 
+
+ align:start position:0%
+unreasonable
+i should really have the same pretty
+
+ align:start position:0%
+i should really have the same pretty
+ 
+
+ align:start position:0%
+i should really have the same pretty
+much the same height there so just drop
+
+ align:start position:0%
+much the same height there so just drop
+ 
+
+ align:start position:0%
+much the same height there so just drop
+one of them or merge them take their
+
+ align:start position:0%
+one of them or merge them take their
+ 
+
+ align:start position:0%
+one of them or merge them take their
+average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in terms of
+
+ align:start position:0%
+so in terms of
+ 
+
+ align:start position:0%
+so in terms of
+you know implementing this
+
+ align:start position:0%
+you know implementing this
+ 
+
+ align:start position:0%
+you know implementing this
+you'd be looking at these base
+
+ align:start position:0%
+you'd be looking at these base
+ 
+
+ align:start position:0%
+you'd be looking at these base
+characteristics
+
+ align:start position:0%
+characteristics
+ 
+
+ align:start position:0%
+characteristics
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+interpolating and removing as required
+
+ align:start position:0%
+interpolating and removing as required
+ 
+
+ align:start position:0%
+interpolating and removing as required
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now another issue is
+
+ align:start position:0%
+now another issue is
+ 
+
+ align:start position:0%
+now another issue is
+you know it sounds very sequential which
+
+ align:start position:0%
+you know it sounds very sequential which
+ 
+
+ align:start position:0%
+you know it sounds very sequential which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+unpleasant from the point of view of
+
+ align:start position:0%
+unpleasant from the point of view of
+ 
+
+ align:start position:0%
+unpleasant from the point of view of
+implementation
+
+ align:start position:0%
+implementation
+ 
+
+ align:start position:0%
+implementation
+because it could take a long time to do
+
+ align:start position:0%
+because it could take a long time to do
+ 
+
+ align:start position:0%
+because it could take a long time to do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and also
+
+ align:start position:0%
+and also
+ 
+
+ align:start position:0%
+and also
+unpleasant from the point of view of
+
+ align:start position:0%
+unpleasant from the point of view of
+ 
+
+ align:start position:0%
+unpleasant from the point of view of
+biological interpretation
+
+ align:start position:0%
+biological interpretation
+ 
+
+ align:start position:0%
+biological interpretation
+but it turns out that the solutions
+
+ align:start position:0%
+but it turns out that the solutions
+ 
+
+ align:start position:0%
+but it turns out that the solutions
+along these curves are independent i
+
+ align:start position:0%
+along these curves are independent i
+ 
+
+ align:start position:0%
+along these curves are independent i
+mean each of them satisfies
+
+ align:start position:0%
+mean each of them satisfies
+ 
+
+ align:start position:0%
+mean each of them satisfies
+a set of differential equations and the
+
+ align:start position:0%
+a set of differential equations and the
+ 
+
+ align:start position:0%
+a set of differential equations and the
+only way they interact is that well they
+
+ align:start position:0%
+only way they interact is that well they
+ 
+
+ align:start position:0%
+only way they interact is that well they
+all sprout from the initial curve
+
+ align:start position:0%
+all sprout from the initial curve
+ 
+
+ align:start position:0%
+all sprout from the initial curve
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+actually you could have a process
+
+ align:start position:0%
+actually you could have a process
+ 
+
+ align:start position:0%
+actually you could have a process
+running along each of these curves so it
+
+ align:start position:0%
+running along each of these curves so it
+ 
+
+ align:start position:0%
+running along each of these curves so it
+is parallelizable
+
+ align:start position:0%
+is parallelizable
+ 
+
+ align:start position:0%
+is parallelizable
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that's actually kind of uh implied by
+
+ align:start position:0%
+that's actually kind of uh implied by
+ 
+
+ align:start position:0%
+that's actually kind of uh implied by
+what i said a minute ago because
+
+ align:start position:0%
+what i said a minute ago because
+ 
+
+ align:start position:0%
+what i said a minute ago because
+if you're going to interpolate new
+
+ align:start position:0%
+if you're going to interpolate new
+ 
+
+ align:start position:0%
+if you're going to interpolate new
+characteristics it's best that you do it
+
+ align:start position:0%
+characteristics it's best that you do it
+ 
+
+ align:start position:0%
+characteristics it's best that you do it
+as as you
+
+ align:start position:0%
+as as you
+ 
+
+ align:start position:0%
+as as you
+grow
+
+ align:start position:0%
+grow
+ 
+
+ align:start position:0%
+grow
+and say oh wait these two are getting
+
+ align:start position:0%
+and say oh wait these two are getting
+ 
+
+ align:start position:0%
+and say oh wait these two are getting
+too far apart so let me interpolate a
+
+ align:start position:0%
+too far apart so let me interpolate a
+ 
+
+ align:start position:0%
+too far apart so let me interpolate a
+new one there or if they get too close
+
+ align:start position:0%
+new one there or if they get too close
+ 
+
+ align:start position:0%
+new one there or if they get too close
+together let me merge them so
+
+ align:start position:0%
+together let me merge them so
+ 
+
+ align:start position:0%
+together let me merge them so
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+it's not full parallelism it's not like
+
+ align:start position:0%
+it's not full parallelism it's not like
+ 
+
+ align:start position:0%
+it's not full parallelism it's not like
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+do something at every pixel at the same
+
+ align:start position:0%
+do something at every pixel at the same
+ 
+
+ align:start position:0%
+do something at every pixel at the same
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+but it's a
+
+ align:start position:0%
+but it's a
+ 
+
+ align:start position:0%
+but it's a
+significant uh
+
+ align:start position:0%
+significant uh
+ 
+
+ align:start position:0%
+significant uh
+improvement over you know complete
+
+ align:start position:0%
+improvement over you know complete
+ 
+
+ align:start position:0%
+improvement over you know complete
+serial computation so
+
+ align:start position:0%
+serial computation so
+ 
+
+ align:start position:0%
+serial computation so
+so it's sort of like a
+
+ align:start position:0%
+so it's sort of like a
+ 
+
+ align:start position:0%
+so it's sort of like a
+a wave front that's
+
+ align:start position:0%
+a wave front that's
+ 
+
+ align:start position:0%
+a wave front that's
+propagating outward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we have some sort of initial
+
+ align:start position:0%
+so if we have some sort of initial
+ 
+
+ align:start position:0%
+so if we have some sort of initial
+conditions you can imagine that as the
+
+ align:start position:0%
+conditions you can imagine that as the
+ 
+
+ align:start position:0%
+conditions you can imagine that as the
+solutions progress
+
+ align:start position:0%
+solutions progress
+ 
+
+ align:start position:0%
+solutions progress
+we could keep them
+
+ align:start position:0%
+we could keep them
+ 
+
+ align:start position:0%
+we could keep them
+moving at more or less the same speed
+
+ align:start position:0%
+moving at more or less the same speed
+ 
+
+ align:start position:0%
+moving at more or less the same speed
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+look at neighboring ones in order to
+
+ align:start position:0%
+look at neighboring ones in order to
+ 
+
+ align:start position:0%
+look at neighboring ones in order to
+improve and interpolate and what have
+
+ align:start position:0%
+improve and interpolate and what have
+ 
+
+ align:start position:0%
+improve and interpolate and what have
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that means that they ought to move sort
+
+ align:start position:0%
+that means that they ought to move sort
+ 
+
+ align:start position:0%
+that means that they ought to move sort
+of at similar speeds so that gets us to
+
+ align:start position:0%
+of at similar speeds so that gets us to
+ 
+
+ align:start position:0%
+of at similar speeds so that gets us to
+this question of
+
+ align:start position:0%
+this question of
+ 
+
+ align:start position:0%
+this question of
+speed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i mean in terms of the numerical
+
+ align:start position:0%
+and i mean in terms of the numerical
+ 
+
+ align:start position:0%
+and i mean in terms of the numerical
+solution of these equations is just the
+
+ align:start position:0%
+solution of these equations is just the
+ 
+
+ align:start position:0%
+solution of these equations is just the
+step size you know what step size well
+
+ align:start position:0%
+step size you know what step size well
+ 
+
+ align:start position:0%
+step size you know what step size well
+clearly if the step size is a hundredth
+
+ align:start position:0%
+clearly if the step size is a hundredth
+ 
+
+ align:start position:0%
+clearly if the step size is a hundredth
+of a pixel
+
+ align:start position:0%
+of a pixel
+ 
+
+ align:start position:0%
+of a pixel
+that's overkill that's not going to work
+
+ align:start position:0%
+that's overkill that's not going to work
+ 
+
+ align:start position:0%
+that's overkill that's not going to work
+very well because the brightness doesn't
+
+ align:start position:0%
+very well because the brightness doesn't
+ 
+
+ align:start position:0%
+very well because the brightness doesn't
+change much in the hundredth of a pixel
+
+ align:start position:0%
+change much in the hundredth of a pixel
+ 
+
+ align:start position:0%
+change much in the hundredth of a pixel
+conversely if the step size is 100
+
+ align:start position:0%
+conversely if the step size is 100
+ 
+
+ align:start position:0%
+conversely if the step size is 100
+pixels that's probably completely wrong
+
+ align:start position:0%
+pixels that's probably completely wrong
+ 
+
+ align:start position:0%
+pixels that's probably completely wrong
+because you're missing all of the
+
+ align:start position:0%
+because you're missing all of the
+ 
+
+ align:start position:0%
+because you're missing all of the
+in-between brightness variations
+
+ align:start position:0%
+in-between brightness variations
+ 
+
+ align:start position:0%
+in-between brightness variations
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you'd like to have a reasonable step
+
+ align:start position:0%
+you'd like to have a reasonable step
+ 
+
+ align:start position:0%
+you'd like to have a reasonable step
+size and so let's look at
+
+ align:start position:0%
+size and so let's look at
+ 
+
+ align:start position:0%
+size and so let's look at
+what we can do in terms of controlling
+
+ align:start position:0%
+what we can do in terms of controlling
+ 
+
+ align:start position:0%
+what we can do in terms of controlling
+the step size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as i mentioned
+
+ align:start position:0%
+and as i mentioned
+ 
+
+ align:start position:0%
+and as i mentioned
+you know all we need to do really is
+
+ align:start position:0%
+you know all we need to do really is
+ 
+
+ align:start position:0%
+you know all we need to do really is
+multiply all of our equations by the
+
+ align:start position:0%
+multiply all of our equations by the
+ 
+
+ align:start position:0%
+multiply all of our equations by the
+same quantity and
+
+ align:start position:0%
+same quantity and
+ 
+
+ align:start position:0%
+same quantity and
+all it does is it changes the
+
+ align:start position:0%
+all it does is it changes the
+ 
+
+ align:start position:0%
+all it does is it changes the
+increment
+
+ align:start position:0%
+increment
+ 
+
+ align:start position:0%
+increment
+and so let's look at some simple cases
+
+ align:start position:0%
+and so let's look at some simple cases
+ 
+
+ align:start position:0%
+and so let's look at some simple cases
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+step size
+
+ align:start position:0%
+step size
+ 
+
+ align:start position:0%
+step size
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's interesting because that means
+
+ align:start position:0%
+so that's interesting because that means
+ 
+
+ align:start position:0%
+so that's interesting because that means
+that you're kind of stepping from
+
+ align:start position:0%
+that you're kind of stepping from
+ 
+
+ align:start position:0%
+that you're kind of stepping from
+contour to contour think of a contour
+
+ align:start position:0%
+contour to contour think of a contour
+ 
+
+ align:start position:0%
+contour to contour think of a contour
+map
+
+ align:start position:0%
+map
+ 
+
+ align:start position:0%
+map
+uh in if we implement that then these
+
+ align:start position:0%
+uh in if we implement that then these
+ 
+
+ align:start position:0%
+uh in if we implement that then these
+would be contours of constant height on
+
+ align:start position:0%
+would be contours of constant height on
+ 
+
+ align:start position:0%
+would be contours of constant height on
+the surface
+
+ align:start position:0%
+the surface
+ 
+
+ align:start position:0%
+the surface
+and what we're doing is
+
+ align:start position:0%
+and what we're doing is
+ 
+
+ align:start position:0%
+and what we're doing is
+all of these solutions as they grow
+
+ align:start position:0%
+all of these solutions as they grow
+ 
+
+ align:start position:0%
+all of these solutions as they grow
+are going from you know the contour at a
+
+ align:start position:0%
+are going from you know the contour at a
+ 
+
+ align:start position:0%
+are going from you know the contour at a
+thousand meters to the contour at 990
+
+ align:start position:0%
+thousand meters to the contour at 990
+ 
+
+ align:start position:0%
+thousand meters to the contour at 990
+meters to the contour at 980 meters and
+
+ align:start position:0%
+meters to the contour at 980 meters and
+ 
+
+ align:start position:0%
+meters to the contour at 980 meters and
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+and so that's a
+
+ align:start position:0%
+and so that's a
+ 
+
+ align:start position:0%
+and so that's a
+interesting and useful way of
+
+ align:start position:0%
+interesting and useful way of
+ 
+
+ align:start position:0%
+interesting and useful way of
+controlling the step size and what do we
+
+ align:start position:0%
+controlling the step size and what do we
+ 
+
+ align:start position:0%
+controlling the step size and what do we
+need to do that well we've got
+
+ align:start position:0%
+need to do that well we've got
+ 
+
+ align:start position:0%
+need to do that well we've got
+p r p plus q r q
+
+ align:start position:0%
+p r p plus q r q
+ 
+
+ align:start position:0%
+p r p plus q r q
+in the equation for z which just
+
+ align:start position:0%
+in the equation for z which just
+ 
+
+ align:start position:0%
+in the equation for z which just
+disappeared
+
+ align:start position:0%
+disappeared
+ 
+
+ align:start position:0%
+disappeared
+and so we just divide by that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh why is that well because then dz d
+
+ align:start position:0%
+uh why is that well because then dz d
+ 
+
+ align:start position:0%
+uh why is that well because then dz d
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+call it
+
+ align:start position:0%
+call it
+ 
+
+ align:start position:0%
+call it
+psi
+
+ align:start position:0%
+psi
+ 
+
+ align:start position:0%
+psi
+dash is one
+
+ align:start position:0%
+dash is one
+ 
+
+ align:start position:0%
+dash is one
+right so we had this equation over here
+
+ align:start position:0%
+right so we had this equation over here
+ 
+
+ align:start position:0%
+right so we had this equation over here
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+c d psi is
+
+ align:start position:0%
+c d psi is
+ 
+
+ align:start position:0%
+c d psi is
+p r p plus q r q
+
+ align:start position:0%
+p r p plus q r q
+ 
+
+ align:start position:0%
+p r p plus q r q
+now if we just divide by that then the
+
+ align:start position:0%
+now if we just divide by that then the
+ 
+
+ align:start position:0%
+now if we just divide by that then the
+rate of change is uh the derivative is
+
+ align:start position:0%
+rate of change is uh the derivative is
+ 
+
+ align:start position:0%
+rate of change is uh the derivative is
+one and that means that we have constant
+
+ align:start position:0%
+one and that means that we have constant
+ 
+
+ align:start position:0%
+one and that means that we have constant
+increments in the z direction of course
+
+ align:start position:0%
+increments in the z direction of course
+ 
+
+ align:start position:0%
+increments in the z direction of course
+we have to
+
+ align:start position:0%
+we have to
+ 
+
+ align:start position:0%
+we have to
+multiply or divide all of the other
+
+ align:start position:0%
+multiply or divide all of the other
+ 
+
+ align:start position:0%
+multiply or divide all of the other
+equations by the same factor so that's
+
+ align:start position:0%
+equations by the same factor so that's
+ 
+
+ align:start position:0%
+equations by the same factor so that's
+sort of an easy to visualize
+
+ align:start position:0%
+sort of an easy to visualize
+ 
+
+ align:start position:0%
+sort of an easy to visualize
+change that has potential benefits
+
+ align:start position:0%
+change that has potential benefits
+ 
+
+ align:start position:0%
+change that has potential benefits
+we just multiply all of the divide all
+
+ align:start position:0%
+we just multiply all of the divide all
+ 
+
+ align:start position:0%
+we just multiply all of the divide all
+of the equations by that and then we're
+
+ align:start position:0%
+of the equations by that and then we're
+ 
+
+ align:start position:0%
+of the equations by that and then we're
+stepping uh from contour to contour as
+
+ align:start position:0%
+stepping uh from contour to contour as
+ 
+
+ align:start position:0%
+stepping uh from contour to contour as
+we explore the surface
+
+ align:start position:0%
+we explore the surface
+ 
+
+ align:start position:0%
+we explore the surface
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that sort of makes it
+
+ align:start position:0%
+that sort of makes it
+ 
+
+ align:start position:0%
+that sort of makes it
+a little clearer how
+
+ align:start position:0%
+a little clearer how
+ 
+
+ align:start position:0%
+a little clearer how
+how we're exploring the surface
+
+ align:start position:0%
+how we're exploring the surface
+ 
+
+ align:start position:0%
+how we're exploring the surface
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we can
+
+ align:start position:0%
+but we can
+ 
+
+ align:start position:0%
+but we can
+pick something else
+
+ align:start position:0%
+pick something else
+ 
+
+ align:start position:0%
+pick something else
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+we were talking about
+
+ align:start position:0%
+we were talking about
+ 
+
+ align:start position:0%
+we were talking about
+steps in terms of pixels so
+
+ align:start position:0%
+steps in terms of pixels so
+ 
+
+ align:start position:0%
+steps in terms of pixels so
+secondly we can look at
+
+ align:start position:0%
+secondly we can look at
+ 
+
+ align:start position:0%
+secondly we can look at
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+step size in image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we want delta x squared plus delta y
+
+ align:start position:0%
+so we want delta x squared plus delta y
+ 
+
+ align:start position:0%
+so we want delta x squared plus delta y
+squared to be a constant and those are
+
+ align:start position:0%
+squared to be a constant and those are
+ 
+
+ align:start position:0%
+squared to be a constant and those are
+proportional to r p and r q
+
+ align:start position:0%
+proportional to r p and r q
+ 
+
+ align:start position:0%
+proportional to r p and r q
+so we divide by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i shouldn't have wiped out these
+
+ align:start position:0%
+i shouldn't have wiped out these
+ 
+
+ align:start position:0%
+i shouldn't have wiped out these
+equations yet because
+
+ align:start position:0%
+equations yet because
+ 
+
+ align:start position:0%
+equations yet because
+it's handy to
+
+ align:start position:0%
+it's handy to
+ 
+
+ align:start position:0%
+it's handy to
+have them
+
+ align:start position:0%
+have them
+ 
+
+ align:start position:0%
+have them
+at this point dxt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that assures that um the square root
+
+ align:start position:0%
+so that assures that um the square root
+ 
+
+ align:start position:0%
+so that assures that um the square root
+of delta x squared plus delta y squared
+
+ align:start position:0%
+of delta x squared plus delta y squared
+ 
+
+ align:start position:0%
+of delta x squared plus delta y squared
+is going to be constant if you like make
+
+ align:start position:0%
+is going to be constant if you like make
+ 
+
+ align:start position:0%
+is going to be constant if you like make
+it one
+
+ align:start position:0%
+it one
+ 
+
+ align:start position:0%
+it one
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's another way where instead
+
+ align:start position:0%
+okay so that's another way where instead
+ 
+
+ align:start position:0%
+okay so that's another way where instead
+of moving in constant increments in
+
+ align:start position:0%
+of moving in constant increments in
+ 
+
+ align:start position:0%
+of moving in constant increments in
+height
+
+ align:start position:0%
+height
+ 
+
+ align:start position:0%
+height
+uh the intervals in the image are uh
+
+ align:start position:0%
+uh the intervals in the image are uh
+ 
+
+ align:start position:0%
+uh the intervals in the image are uh
+fixed in size and and
+
+ align:start position:0%
+fixed in size and and
+ 
+
+ align:start position:0%
+fixed in size and and
+well a couple of issues with that one of
+
+ align:start position:0%
+well a couple of issues with that one of
+ 
+
+ align:start position:0%
+well a couple of issues with that one of
+them is
+
+ align:start position:0%
+them is
+ 
+
+ align:start position:0%
+them is
+that those
+
+ align:start position:0%
+that those
+ 
+
+ align:start position:0%
+that those
+curves
+
+ align:start position:0%
+curves
+ 
+
+ align:start position:0%
+curves
+may
+
+ align:start position:0%
+may
+ 
+
+ align:start position:0%
+may
+uh run at different rates so that one of
+
+ align:start position:0%
+uh run at different rates so that one of
+ 
+
+ align:start position:0%
+uh run at different rates so that one of
+the curves is sort of getting ahead of
+
+ align:start position:0%
+the curves is sort of getting ahead of
+ 
+
+ align:start position:0%
+the curves is sort of getting ahead of
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+because we're not tying them together in
+
+ align:start position:0%
+because we're not tying them together in
+ 
+
+ align:start position:0%
+because we're not tying them together in
+height or anything we're only tying them
+
+ align:start position:0%
+height or anything we're only tying them
+ 
+
+ align:start position:0%
+height or anything we're only tying them
+together in how far are we from where we
+
+ align:start position:0%
+together in how far are we from where we
+ 
+
+ align:start position:0%
+together in how far are we from where we
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+so that's a problem and then another
+
+ align:start position:0%
+so that's a problem and then another
+ 
+
+ align:start position:0%
+so that's a problem and then another
+problem is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we're going to divide by that because
+
+ align:start position:0%
+um we're going to divide by that because
+ 
+
+ align:start position:0%
+um we're going to divide by that because
+if that's zero then
+
+ align:start position:0%
+if that's zero then
+ 
+
+ align:start position:0%
+if that's zero then
+we're out to lunch so and i make a note
+
+ align:start position:0%
+we're out to lunch so and i make a note
+ 
+
+ align:start position:0%
+we're out to lunch so and i make a note
+of that now because we'll need that in a
+
+ align:start position:0%
+of that now because we'll need that in a
+ 
+
+ align:start position:0%
+of that now because we'll need that in a
+minute
+
+ align:start position:0%
+minute
+ 
+
+ align:start position:0%
+minute
+okay constant size steps in the image
+
+ align:start position:0%
+okay constant size steps in the image
+ 
+
+ align:start position:0%
+okay constant size steps in the image
+how about constant size steps in 3d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means we want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that to be one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so that means we need to divide by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by that quantity
+
+ align:start position:0%
+by that quantity
+ 
+
+ align:start position:0%
+by that quantity
+and so for that where's that come from
+
+ align:start position:0%
+and so for that where's that come from
+ 
+
+ align:start position:0%
+and so for that where's that come from
+uh that's that's this thing here so this
+
+ align:start position:0%
+uh that's that's this thing here so this
+ 
+
+ align:start position:0%
+uh that's that's this thing here so this
+gives us delta x this gives us delta y
+
+ align:start position:0%
+gives us delta x this gives us delta y
+ 
+
+ align:start position:0%
+gives us delta x this gives us delta y
+this gives us delta z
+
+ align:start position:0%
+this gives us delta z
+ 
+
+ align:start position:0%
+this gives us delta z
+and if we want
+
+ align:start position:0%
+and if we want
+ 
+
+ align:start position:0%
+and if we want
+the sum of the squares of those to be 1
+
+ align:start position:0%
+the sum of the squares of those to be 1
+ 
+
+ align:start position:0%
+the sum of the squares of those to be 1
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we divide by that and again this has the
+
+ align:start position:0%
+we divide by that and again this has the
+ 
+
+ align:start position:0%
+we divide by that and again this has the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem or special case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if rp and rq are zero then that is
+
+ align:start position:0%
+that if rp and rq are zero then that is
+ 
+
+ align:start position:0%
+that if rp and rq are zero then that is
+zero and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we step
+
+ align:start position:0%
+if we step
+ 
+
+ align:start position:0%
+if we step
+in isophodes in contours in the image of
+
+ align:start position:0%
+in isophodes in contours in the image of
+ 
+
+ align:start position:0%
+in isophodes in contours in the image of
+contrast of brightness so
+
+ align:start position:0%
+contrast of brightness so
+ 
+
+ align:start position:0%
+contrast of brightness so
+here we
+
+ align:start position:0%
+here we
+ 
+
+ align:start position:0%
+here we
+had contours on the surface
+
+ align:start position:0%
+had contours on the surface
+ 
+
+ align:start position:0%
+had contours on the surface
+z was the
+
+ align:start position:0%
+z was the
+ 
+
+ align:start position:0%
+z was the
+constant along each of those
+
+ align:start position:0%
+constant along each of those
+ 
+
+ align:start position:0%
+constant along each of those
+curves but it might be interesting to
+
+ align:start position:0%
+curves but it might be interesting to
+ 
+
+ align:start position:0%
+curves but it might be interesting to
+step in the image from one brightness
+
+ align:start position:0%
+step in the image from one brightness
+ 
+
+ align:start position:0%
+step in the image from one brightness
+level to another so
+
+ align:start position:0%
+level to another so
+ 
+
+ align:start position:0%
+level to another so
+um well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i won't go
+
+ align:start position:0%
+i won't go
+ 
+
+ align:start position:0%
+i won't go
+too much into detail of that but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we basically then have to divide by that
+
+ align:start position:0%
+we basically then have to divide by that
+ 
+
+ align:start position:0%
+we basically then have to divide by that
+quantity
+
+ align:start position:0%
+quantity
+ 
+
+ align:start position:0%
+quantity
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember the two gradients the one in
+
+ align:start position:0%
+remember the two gradients the one in
+ 
+
+ align:start position:0%
+remember the two gradients the one in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+in the image and the other one in the
+
+ align:start position:0%
+in the image and the other one in the
+ 
+
+ align:start position:0%
+in the image and the other one in the
+reflectance map well that's the dot
+
+ align:start position:0%
+reflectance map well that's the dot
+ 
+
+ align:start position:0%
+reflectance map well that's the dot
+product of those two but
+
+ align:start position:0%
+product of those two but
+ 
+
+ align:start position:0%
+product of those two but
+i don't know if that means anything but
+
+ align:start position:0%
+i don't know if that means anything but
+ 
+
+ align:start position:0%
+i don't know if that means anything but
+it's just
+
+ align:start position:0%
+it's just
+ 
+
+ align:start position:0%
+it's just
+interesting to note and we won't go into
+
+ align:start position:0%
+interesting to note and we won't go into
+ 
+
+ align:start position:0%
+interesting to note and we won't go into
+too much detail but obviously that's
+
+ align:start position:0%
+too much detail but obviously that's
+ 
+
+ align:start position:0%
+too much detail but obviously that's
+another interesting uh
+
+ align:start position:0%
+another interesting uh
+ 
+
+ align:start position:0%
+another interesting uh
+speed control
+
+ align:start position:0%
+speed control
+ 
+
+ align:start position:0%
+speed control
+in that we're moving from contour to
+
+ align:start position:0%
+in that we're moving from contour to
+ 
+
+ align:start position:0%
+in that we're moving from contour to
+contour in the image and you know one
+
+ align:start position:0%
+contour in the image and you know one
+ 
+
+ align:start position:0%
+contour in the image and you know one
+advantage of some of these is that they
+
+ align:start position:0%
+advantage of some of these is that they
+ 
+
+ align:start position:0%
+advantage of some of these is that they
+tend to make it easier to tie together
+
+ align:start position:0%
+tend to make it easier to tie together
+ 
+
+ align:start position:0%
+tend to make it easier to tie together
+neighboring solutions so in this case
+
+ align:start position:0%
+neighboring solutions so in this case
+ 
+
+ align:start position:0%
+neighboring solutions so in this case
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+curves these wave fronts would be just
+
+ align:start position:0%
+curves these wave fronts would be just
+ 
+
+ align:start position:0%
+curves these wave fronts would be just
+isophodes in the image plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and you know in terms of
+
+ align:start position:0%
+and you know in terms of
+ 
+
+ align:start position:0%
+and you know in terms of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+numerical analysis aspect of it
+
+ align:start position:0%
+numerical analysis aspect of it
+ 
+
+ align:start position:0%
+numerical analysis aspect of it
+again we're not doing any fancy methods
+
+ align:start position:0%
+again we're not doing any fancy methods
+ 
+
+ align:start position:0%
+again we're not doing any fancy methods
+for solving ordinary differential
+
+ align:start position:0%
+for solving ordinary differential
+ 
+
+ align:start position:0%
+for solving ordinary differential
+equation we're just saying you know if
+
+ align:start position:0%
+equation we're just saying you know if
+ 
+
+ align:start position:0%
+equation we're just saying you know if
+the slope is m and we take a step delta
+
+ align:start position:0%
+the slope is m and we take a step delta
+ 
+
+ align:start position:0%
+the slope is m and we take a step delta
+then the change is m times delta
+
+ align:start position:0%
+then the change is m times delta
+ 
+
+ align:start position:0%
+then the change is m times delta
+which is you know the lowest order
+
+ align:start position:0%
+which is you know the lowest order
+ 
+
+ align:start position:0%
+which is you know the lowest order
+crudest thing you can do
+
+ align:start position:0%
+crudest thing you can do
+ 
+
+ align:start position:0%
+crudest thing you can do
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+as i mentioned we don't really
+
+ align:start position:0%
+as i mentioned we don't really
+ 
+
+ align:start position:0%
+as i mentioned we don't really
+expect to get much better by using
+
+ align:start position:0%
+expect to get much better by using
+ 
+
+ align:start position:0%
+expect to get much better by using
+something very sophisticated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you may have heard that there's a
+
+ align:start position:0%
+you may have heard that there's a
+ 
+
+ align:start position:0%
+you may have heard that there's a
+result recently about three bodies so
+
+ align:start position:0%
+result recently about three bodies so
+ 
+
+ align:start position:0%
+result recently about three bodies so
+you all know that if you have two bodies
+
+ align:start position:0%
+you all know that if you have two bodies
+ 
+
+ align:start position:0%
+you all know that if you have two bodies
+then they orbit
+
+ align:start position:0%
+then they orbit
+ 
+
+ align:start position:0%
+then they orbit
+in elliptical fashion and the ellipses
+
+ align:start position:0%
+in elliptical fashion and the ellipses
+ 
+
+ align:start position:0%
+in elliptical fashion and the ellipses
+are stable and you know all that good
+
+ align:start position:0%
+are stable and you know all that good
+ 
+
+ align:start position:0%
+are stable and you know all that good
+stuff from
+
+ align:start position:0%
+stuff from
+ 
+
+ align:start position:0%
+stuff from
+starting from newton and kepler and
+
+ align:start position:0%
+starting from newton and kepler and
+ 
+
+ align:start position:0%
+starting from newton and kepler and
+copernicus and so on if you have three
+
+ align:start position:0%
+copernicus and so on if you have three
+ 
+
+ align:start position:0%
+copernicus and so on if you have three
+bodies
+
+ align:start position:0%
+bodies
+ 
+
+ align:start position:0%
+bodies
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+chaos ensues
+
+ align:start position:0%
+chaos ensues
+ 
+
+ align:start position:0%
+chaos ensues
+uh all sorts of things can happen and
+
+ align:start position:0%
+uh all sorts of things can happen and
+ 
+
+ align:start position:0%
+uh all sorts of things can happen and
+mostly the orbits are not periodic and
+
+ align:start position:0%
+mostly the orbits are not periodic and
+ 
+
+ align:start position:0%
+mostly the orbits are not periodic and
+so even if you want to know suppose you
+
+ align:start position:0%
+so even if you want to know suppose you
+ 
+
+ align:start position:0%
+so even if you want to know suppose you
+live in a world with three suns and
+
+ align:start position:0%
+live in a world with three suns and
+ 
+
+ align:start position:0%
+live in a world with three suns and
+they're orbiting each other then suppose
+
+ align:start position:0%
+they're orbiting each other then suppose
+ 
+
+ align:start position:0%
+they're orbiting each other then suppose
+you want to know whether
+
+ align:start position:0%
+you want to know whether
+ 
+
+ align:start position:0%
+you want to know whether
+at some point one of them will run into
+
+ align:start position:0%
+at some point one of them will run into
+ 
+
+ align:start position:0%
+at some point one of them will run into
+another and blow up your world um
+
+ align:start position:0%
+another and blow up your world um
+ 
+
+ align:start position:0%
+another and blow up your world um
+it's uh
+
+ align:start position:0%
+it's uh
+ 
+
+ align:start position:0%
+it's uh
+there's no periodicity so you can't use
+
+ align:start position:0%
+there's no periodicity so you can't use
+ 
+
+ align:start position:0%
+there's no periodicity so you can't use
+simple method anyway there's a wonderful
+
+ align:start position:0%
+simple method anyway there's a wonderful
+ 
+
+ align:start position:0%
+simple method anyway there's a wonderful
+science fiction book called the
+
+ align:start position:0%
+science fiction book called the
+ 
+
+ align:start position:0%
+science fiction book called the
+three-body problem
+
+ align:start position:0%
+three-body problem
+ 
+
+ align:start position:0%
+three-body problem
+where people live on in such a place
+
+ align:start position:0%
+where people live on in such a place
+ 
+
+ align:start position:0%
+where people live on in such a place
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+curiously just recently someone has
+
+ align:start position:0%
+curiously just recently someone has
+ 
+
+ align:start position:0%
+curiously just recently someone has
+actually put to good use one of these
+
+ align:start position:0%
+actually put to good use one of these
+ 
+
+ align:start position:0%
+actually put to good use one of these
+gigantic super computers so you know
+
+ align:start position:0%
+gigantic super computers so you know
+ 
+
+ align:start position:0%
+gigantic super computers so you know
+nations compete with each other in
+
+ align:start position:0%
+nations compete with each other in
+ 
+
+ align:start position:0%
+nations compete with each other in
+various stupid ways and one of them is
+
+ align:start position:0%
+various stupid ways and one of them is
+ 
+
+ align:start position:0%
+various stupid ways and one of them is
+you know i can build a bigger computer
+
+ align:start position:0%
+you know i can build a bigger computer
+ 
+
+ align:start position:0%
+you know i can build a bigger computer
+than you
+
+ align:start position:0%
+than you
+ 
+
+ align:start position:0%
+than you
+and so periodically you know the us has
+
+ align:start position:0%
+and so periodically you know the us has
+ 
+
+ align:start position:0%
+and so periodically you know the us has
+the biggest and then i don't know japan
+
+ align:start position:0%
+the biggest and then i don't know japan
+ 
+
+ align:start position:0%
+the biggest and then i don't know japan
+and then china so i i think at this
+
+ align:start position:0%
+and then china so i i think at this
+ 
+
+ align:start position:0%
+and then china so i i think at this
+point it might be china anyway a lot of
+
+ align:start position:0%
+point it might be china anyway a lot of
+ 
+
+ align:start position:0%
+point it might be china anyway a lot of
+times then you ask well okay they got
+
+ align:start position:0%
+times then you ask well okay they got
+ 
+
+ align:start position:0%
+times then you ask well okay they got
+this fantastic computer
+
+ align:start position:0%
+this fantastic computer
+ 
+
+ align:start position:0%
+this fantastic computer
+what are they getting out of it and well
+
+ align:start position:0%
+what are they getting out of it and well
+ 
+
+ align:start position:0%
+what are they getting out of it and well
+you can do some things you can do
+
+ align:start position:0%
+you can do some things you can do
+ 
+
+ align:start position:0%
+you can do some things you can do
+weather simulations better than anyone
+
+ align:start position:0%
+weather simulations better than anyone
+ 
+
+ align:start position:0%
+weather simulations better than anyone
+else you can
+
+ align:start position:0%
+else you can
+ 
+
+ align:start position:0%
+else you can
+you can solve some quantum equations of
+
+ align:start position:0%
+you can solve some quantum equations of
+ 
+
+ align:start position:0%
+you can solve some quantum equations of
+you know more than one particle uh on it
+
+ align:start position:0%
+you know more than one particle uh on it
+ 
+
+ align:start position:0%
+you know more than one particle uh on it
+well what he did this person
+
+ align:start position:0%
+well what he did this person
+ 
+
+ align:start position:0%
+well what he did this person
+was the three-body problem
+
+ align:start position:0%
+was the three-body problem
+ 
+
+ align:start position:0%
+was the three-body problem
+and so he was interested in finding
+
+ align:start position:0%
+and so he was interested in finding
+ 
+
+ align:start position:0%
+and so he was interested in finding
+periodic solutions and for a hundred
+
+ align:start position:0%
+periodic solutions and for a hundred
+ 
+
+ align:start position:0%
+periodic solutions and for a hundred
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+uh it's been known that there's some
+
+ align:start position:0%
+uh it's been known that there's some
+ 
+
+ align:start position:0%
+uh it's been known that there's some
+periodic solutions but they were very
+
+ align:start position:0%
+periodic solutions but they were very
+ 
+
+ align:start position:0%
+periodic solutions but they were very
+special you know things go in particular
+
+ align:start position:0%
+special you know things go in particular
+ 
+
+ align:start position:0%
+special you know things go in particular
+figure eight patterns and s asteroid uh
+
+ align:start position:0%
+figure eight patterns and s asteroid uh
+ 
+
+ align:start position:0%
+figure eight patterns and s asteroid uh
+orbits
+
+ align:start position:0%
+orbits
+ 
+
+ align:start position:0%
+orbits
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+but there's a very small number of these
+
+ align:start position:0%
+but there's a very small number of these
+ 
+
+ align:start position:0%
+but there's a very small number of these
+solutions known i forget what i don't
+
+ align:start position:0%
+solutions known i forget what i don't
+ 
+
+ align:start position:0%
+solutions known i forget what i don't
+know six or something well he used this
+
+ align:start position:0%
+know six or something well he used this
+ 
+
+ align:start position:0%
+know six or something well he used this
+supercomputer to find uh i don't know 68
+
+ align:start position:0%
+supercomputer to find uh i don't know 68
+ 
+
+ align:start position:0%
+supercomputer to find uh i don't know 68
+and you know it's amazing it's fantastic
+
+ align:start position:0%
+and you know it's amazing it's fantastic
+ 
+
+ align:start position:0%
+and you know it's amazing it's fantastic
+they're wonderful orbits
+
+ align:start position:0%
+they're wonderful orbits
+ 
+
+ align:start position:0%
+they're wonderful orbits
+and you might say well wait a minute uh
+
+ align:start position:0%
+and you might say well wait a minute uh
+ 
+
+ align:start position:0%
+and you might say well wait a minute uh
+this is really something that should be
+
+ align:start position:0%
+this is really something that should be
+ 
+
+ align:start position:0%
+this is really something that should be
+done analytically because
+
+ align:start position:0%
+done analytically because
+ 
+
+ align:start position:0%
+done analytically because
+you know you can do the numerical
+
+ align:start position:0%
+you know you can do the numerical
+ 
+
+ align:start position:0%
+you know you can do the numerical
+simulation but how do you know that it's
+
+ align:start position:0%
+simulation but how do you know that it's
+ 
+
+ align:start position:0%
+simulation but how do you know that it's
+really really periodic
+
+ align:start position:0%
+really really periodic
+ 
+
+ align:start position:0%
+really really periodic
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+having this supercomputer he is able to
+
+ align:start position:0%
+having this supercomputer he is able to
+ 
+
+ align:start position:0%
+having this supercomputer he is able to
+do things that mere mortals wouldn't
+
+ align:start position:0%
+do things that mere mortals wouldn't
+ 
+
+ align:start position:0%
+do things that mere mortals wouldn't
+normally do
+
+ align:start position:0%
+normally do
+ 
+
+ align:start position:0%
+normally do
+like you know approximate the taylor
+
+ align:start position:0%
+like you know approximate the taylor
+ 
+
+ align:start position:0%
+like you know approximate the taylor
+series to
+
+ align:start position:0%
+series to
+ 
+
+ align:start position:0%
+series to
+a thousand terms you know you'd usually
+
+ align:start position:0%
+a thousand terms you know you'd usually
+ 
+
+ align:start position:0%
+a thousand terms you know you'd usually
+stop at two or three
+
+ align:start position:0%
+stop at two or three
+ 
+
+ align:start position:0%
+stop at two or three
+and maybe if you on the computer you
+
+ align:start position:0%
+and maybe if you on the computer you
+ 
+
+ align:start position:0%
+and maybe if you on the computer you
+might do i don't know eight
+
+ align:start position:0%
+might do i don't know eight
+ 
+
+ align:start position:0%
+might do i don't know eight
+but he didn't stop at any particular
+
+ align:start position:0%
+but he didn't stop at any particular
+ 
+
+ align:start position:0%
+but he didn't stop at any particular
+point he simply kept on adding until he
+
+ align:start position:0%
+point he simply kept on adding until he
+ 
+
+ align:start position:0%
+point he simply kept on adding until he
+didn't need to go any further and the
+
+ align:start position:0%
+didn't need to go any further and the
+ 
+
+ align:start position:0%
+didn't need to go any further and the
+same with the calculations the uh you
+
+ align:start position:0%
+same with the calculations the uh you
+ 
+
+ align:start position:0%
+same with the calculations the uh you
+know eighth order range cutter that's a
+
+ align:start position:0%
+know eighth order range cutter that's a
+ 
+
+ align:start position:0%
+know eighth order range cutter that's a
+very sophisticated method for solving
+
+ align:start position:0%
+very sophisticated method for solving
+ 
+
+ align:start position:0%
+very sophisticated method for solving
+odes well he used thousand order
+
+ align:start position:0%
+odes well he used thousand order
+ 
+
+ align:start position:0%
+odes well he used thousand order
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh in the process
+
+ align:start position:0%
+uh in the process
+ 
+
+ align:start position:0%
+uh in the process
+he discovered uh these periodic orbits
+
+ align:start position:0%
+he discovered uh these periodic orbits
+ 
+
+ align:start position:0%
+he discovered uh these periodic orbits
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+where was it going with this well the
+
+ align:start position:0%
+where was it going with this well the
+ 
+
+ align:start position:0%
+where was it going with this well the
+point is that
+
+ align:start position:0%
+point is that
+ 
+
+ align:start position:0%
+point is that
+there are very sophisticated methods for
+
+ align:start position:0%
+there are very sophisticated methods for
+ 
+
+ align:start position:0%
+there are very sophisticated methods for
+numerically solving equations
+
+ align:start position:0%
+numerically solving equations
+ 
+
+ align:start position:0%
+numerically solving equations
+and if you're trying to say for example
+
+ align:start position:0%
+and if you're trying to say for example
+ 
+
+ align:start position:0%
+and if you're trying to say for example
+figure out how long our solar system is
+
+ align:start position:0%
+figure out how long our solar system is
+ 
+
+ align:start position:0%
+figure out how long our solar system is
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+you it's very difficult you need to use
+
+ align:start position:0%
+you it's very difficult you need to use
+ 
+
+ align:start position:0%
+you it's very difficult you need to use
+much more sophisticated methods than we
+
+ align:start position:0%
+much more sophisticated methods than we
+ 
+
+ align:start position:0%
+much more sophisticated methods than we
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know gerald sussman actually built a
+
+ align:start position:0%
+you know gerald sussman actually built a
+ 
+
+ align:start position:0%
+you know gerald sussman actually built a
+machine to do that
+
+ align:start position:0%
+machine to do that
+ 
+
+ align:start position:0%
+machine to do that
+but it's
+
+ align:start position:0%
+but it's
+ 
+
+ align:start position:0%
+but it's
+because it's chaotic you can't be sure
+
+ align:start position:0%
+because it's chaotic you can't be sure
+ 
+
+ align:start position:0%
+because it's chaotic you can't be sure
+but he can say that
+
+ align:start position:0%
+but he can say that
+ 
+
+ align:start position:0%
+but he can say that
+nothing bad is going to happen in the
+
+ align:start position:0%
+nothing bad is going to happen in the
+ 
+
+ align:start position:0%
+nothing bad is going to happen in the
+next 100 million years so you can rest
+
+ align:start position:0%
+next 100 million years so you can rest
+ 
+
+ align:start position:0%
+next 100 million years so you can rest
+assured that things will be fairly safe
+
+ align:start position:0%
+assured that things will be fairly safe
+ 
+
+ align:start position:0%
+assured that things will be fairly safe
+fortunately we have a case where we
+
+ align:start position:0%
+fortunately we have a case where we
+ 
+
+ align:start position:0%
+fortunately we have a case where we
+don't need to have anything like that
+
+ align:start position:0%
+don't need to have anything like that
+ 
+
+ align:start position:0%
+don't need to have anything like that
+kind of numerical precision
+
+ align:start position:0%
+kind of numerical precision
+ 
+
+ align:start position:0%
+kind of numerical precision
+okay um we do need an initial curve
+
+ align:start position:0%
+okay um we do need an initial curve
+ 
+
+ align:start position:0%
+okay um we do need an initial curve
+though so let's talk about which is a
+
+ align:start position:0%
+though so let's talk about which is a
+ 
+
+ align:start position:0%
+though so let's talk about which is a
+nuisance
+
+ align:start position:0%
+nuisance
+ 
+
+ align:start position:0%
+nuisance
+right because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know the whole point is to explore
+
+ align:start position:0%
+you know the whole point is to explore
+ 
+
+ align:start position:0%
+you know the whole point is to explore
+the surface using
+
+ align:start position:0%
+the surface using
+ 
+
+ align:start position:0%
+the surface using
+optical machine vision methods not
+
+ align:start position:0%
+optical machine vision methods not
+ 
+
+ align:start position:0%
+optical machine vision methods not
+not go there with a measuring tape and
+
+ align:start position:0%
+not go there with a measuring tape and
+ 
+
+ align:start position:0%
+not go there with a measuring tape and
+so having an initial curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is kind of not desirable i mean it's uh
+
+ align:start position:0%
+is kind of not desirable i mean it's uh
+ 
+
+ align:start position:0%
+is kind of not desirable i mean it's uh
+it's better than actually having to
+
+ align:start position:0%
+it's better than actually having to
+ 
+
+ align:start position:0%
+it's better than actually having to
+measure the whole surface because you're
+
+ align:start position:0%
+measure the whole surface because you're
+ 
+
+ align:start position:0%
+measure the whole surface because you're
+only measuring one curve on it and then
+
+ align:start position:0%
+only measuring one curve on it and then
+ 
+
+ align:start position:0%
+only measuring one curve on it and then
+the rest is filled in using the image
+
+ align:start position:0%
+the rest is filled in using the image
+ 
+
+ align:start position:0%
+the rest is filled in using the image
+but actually here we have an even worse
+
+ align:start position:0%
+but actually here we have an even worse
+ 
+
+ align:start position:0%
+but actually here we have an even worse
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is we're carrying along not just x
+
+ align:start position:0%
+which is we're carrying along not just x
+ 
+
+ align:start position:0%
+which is we're carrying along not just x
+y and z but we're carrying along
+
+ align:start position:0%
+y and z but we're carrying along
+ 
+
+ align:start position:0%
+y and z but we're carrying along
+orientation as well so
+
+ align:start position:0%
+orientation as well so
+ 
+
+ align:start position:0%
+orientation as well so
+we get these characteristic strips so
+
+ align:start position:0%
+we get these characteristic strips so
+ 
+
+ align:start position:0%
+we get these characteristic strips so
+shouldn't it also be an initial strip
+
+ align:start position:0%
+shouldn't it also be an initial strip
+ 
+
+ align:start position:0%
+shouldn't it also be an initial strip
+in other words you know we're not just
+
+ align:start position:0%
+in other words you know we're not just
+ 
+
+ align:start position:0%
+in other words you know we're not just
+going to be forced to supply
+
+ align:start position:0%
+going to be forced to supply
+ 
+
+ align:start position:0%
+going to be forced to supply
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+and z
+
+ align:start position:0%
+and z
+ 
+
+ align:start position:0%
+and z
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you know that makes it even worse that
+
+ align:start position:0%
+you know that makes it even worse that
+ 
+
+ align:start position:0%
+you know that makes it even worse that
+means you have to measure that curve and
+
+ align:start position:0%
+means you have to measure that curve and
+ 
+
+ align:start position:0%
+means you have to measure that curve and
+also at every point on the curve
+
+ align:start position:0%
+also at every point on the curve
+ 
+
+ align:start position:0%
+also at every point on the curve
+measure the orientation
+
+ align:start position:0%
+measure the orientation
+ 
+
+ align:start position:0%
+measure the orientation
+well fortunately
+
+ align:start position:0%
+well fortunately
+ 
+
+ align:start position:0%
+well fortunately
+that's not
+
+ align:start position:0%
+that's not
+ 
+
+ align:start position:0%
+that's not
+necessary
+
+ align:start position:0%
+necessary
+ 
+
+ align:start position:0%
+necessary
+and there are two reasons for that one
+
+ align:start position:0%
+and there are two reasons for that one
+ 
+
+ align:start position:0%
+and there are two reasons for that one
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+that on the initial curve
+
+ align:start position:0%
+that on the initial curve
+ 
+
+ align:start position:0%
+that on the initial curve
+we have the image irradiance equation
+
+ align:start position:0%
+we have the image irradiance equation
+ 
+
+ align:start position:0%
+we have the image irradiance equation
+so we have e of x y
+
+ align:start position:0%
+so we have e of x y
+ 
+
+ align:start position:0%
+so we have e of x y
+is r of pq
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or you know
+
+ align:start position:0%
+or you know
+ 
+
+ align:start position:0%
+or you know
+you you're on the curve you look in the
+
+ align:start position:0%
+you you're on the curve you look in the
+ 
+
+ align:start position:0%
+you you're on the curve you look in the
+image what's the brightness there
+
+ align:start position:0%
+image what's the brightness there
+ 
+
+ align:start position:0%
+image what's the brightness there
+doesn't tell you the orientation but it
+
+ align:start position:0%
+doesn't tell you the orientation but it
+ 
+
+ align:start position:0%
+doesn't tell you the orientation but it
+gives you one constraint on the
+
+ align:start position:0%
+gives you one constraint on the
+ 
+
+ align:start position:0%
+gives you one constraint on the
+orientation
+
+ align:start position:0%
+orientation
+ 
+
+ align:start position:0%
+orientation
+and if we look at our reflectance map
+
+ align:start position:0%
+and if we look at our reflectance map
+ 
+
+ align:start position:0%
+and if we look at our reflectance map
+then it means we're you know we're on
+
+ align:start position:0%
+then it means we're you know we're on
+ 
+
+ align:start position:0%
+then it means we're you know we're on
+some curve
+
+ align:start position:0%
+some curve
+ 
+
+ align:start position:0%
+some curve
+so we have one constraint
+
+ align:start position:0%
+so we have one constraint
+ 
+
+ align:start position:0%
+so we have one constraint
+so we
+
+ align:start position:0%
+so we
+ 
+
+ align:start position:0%
+so we
+it's not like it could be any p and q it
+
+ align:start position:0%
+it's not like it could be any p and q it
+ 
+
+ align:start position:0%
+it's not like it could be any p and q it
+has to be one of those but then the
+
+ align:start position:0%
+has to be one of those but then the
+ 
+
+ align:start position:0%
+has to be one of those but then the
+other thing is that
+
+ align:start position:0%
+other thing is that
+ 
+
+ align:start position:0%
+other thing is that
+we have this curve and we're told that
+
+ align:start position:0%
+we have this curve and we're told that
+ 
+
+ align:start position:0%
+we have this curve and we're told that
+that curve's actually in the surface
+
+ align:start position:0%
+that curve's actually in the surface
+ 
+
+ align:start position:0%
+that curve's actually in the surface
+so that means that if i differentiate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dz d theta should be
+
+ align:start position:0%
+dz d theta should be
+ 
+
+ align:start position:0%
+dz d theta should be
+p dx theta plus q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right by the chain rule of course p is
+
+ align:start position:0%
+right by the chain rule of course p is
+ 
+
+ align:start position:0%
+right by the chain rule of course p is
+dz dx
+
+ align:start position:0%
+dz dx
+ 
+
+ align:start position:0%
+dz dx
+and q is dz dy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since i'm since someone magically
+
+ align:start position:0%
+and since i'm since someone magically
+ 
+
+ align:start position:0%
+and since i'm since someone magically
+gave me this initial curve i can compute
+
+ align:start position:0%
+gave me this initial curve i can compute
+ 
+
+ align:start position:0%
+gave me this initial curve i can compute
+these derivatives dx data dydata
+
+ align:start position:0%
+these derivatives dx data dydata
+ 
+
+ align:start position:0%
+these derivatives dx data dydata
+decediator and
+
+ align:start position:0%
+decediator and
+ 
+
+ align:start position:0%
+decediator and
+amazingly this is a linear equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's my job my job is to
+
+ align:start position:0%
+so what's my job my job is to
+ 
+
+ align:start position:0%
+so what's my job my job is to
+recover the unknowns p and q
+
+ align:start position:0%
+recover the unknowns p and q
+ 
+
+ align:start position:0%
+recover the unknowns p and q
+and i have two equations two unknowns
+
+ align:start position:0%
+and i have two equations two unknowns
+ 
+
+ align:start position:0%
+and i have two equations two unknowns
+and so there we are
+
+ align:start position:0%
+and so there we are
+ 
+
+ align:start position:0%
+and so there we are
+i can solve
+
+ align:start position:0%
+i can solve
+ 
+
+ align:start position:0%
+i can solve
+for p and q
+
+ align:start position:0%
+for p and q
+ 
+
+ align:start position:0%
+for p and q
+well you might say
+
+ align:start position:0%
+well you might say
+ 
+
+ align:start position:0%
+well you might say
+this first equation is likely to be
+
+ align:start position:0%
+this first equation is likely to be
+ 
+
+ align:start position:0%
+this first equation is likely to be
+non-linear you know you look at
+
+ align:start position:0%
+non-linear you know you look at
+ 
+
+ align:start position:0%
+non-linear you know you look at
+lambertian equation
+
+ align:start position:0%
+lambertian equation
+ 
+
+ align:start position:0%
+lambertian equation
+but there's one linear equation
+
+ align:start position:0%
+but there's one linear equation
+ 
+
+ align:start position:0%
+but there's one linear equation
+so then by bazoot's theorem
+
+ align:start position:0%
+so then by bazoot's theorem
+ 
+
+ align:start position:0%
+so then by bazoot's theorem
+what matters is you know what order is
+
+ align:start position:0%
+what matters is you know what order is
+ 
+
+ align:start position:0%
+what matters is you know what order is
+this equation and if it's second order
+
+ align:start position:0%
+this equation and if it's second order
+ 
+
+ align:start position:0%
+this equation and if it's second order
+that means you might have as many as two
+
+ align:start position:0%
+that means you might have as many as two
+ 
+
+ align:start position:0%
+that means you might have as many as two
+solutions but two solutions is better
+
+ align:start position:0%
+solutions but two solutions is better
+ 
+
+ align:start position:0%
+solutions but two solutions is better
+than an infinite number of solutions so
+
+ align:start position:0%
+than an infinite number of solutions so
+ 
+
+ align:start position:0%
+than an infinite number of solutions so
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+in practice we don't really need
+
+ align:start position:0%
+in practice we don't really need
+ 
+
+ align:start position:0%
+in practice we don't really need
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+an initial strip we can get along with
+
+ align:start position:0%
+an initial strip we can get along with
+ 
+
+ align:start position:0%
+an initial strip we can get along with
+an initial curve because we can find the
+
+ align:start position:0%
+an initial curve because we can find the
+ 
+
+ align:start position:0%
+an initial curve because we can find the
+orientation using those two equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but we'd really like to get rid of
+
+ align:start position:0%
+okay but we'd really like to get rid of
+ 
+
+ align:start position:0%
+okay but we'd really like to get rid of
+this initial curve business it's really
+
+ align:start position:0%
+this initial curve business it's really
+ 
+
+ align:start position:0%
+this initial curve business it's really
+annoying
+
+ align:start position:0%
+annoying
+ 
+
+ align:start position:0%
+annoying
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+what do we do well we great
+
+ align:start position:0%
+what do we do well we great
+ 
+
+ align:start position:0%
+what do we do well we great
+if there were some special points
+
+ align:start position:0%
+if there were some special points
+ 
+
+ align:start position:0%
+if there were some special points
+on the object where we know the
+
+ align:start position:0%
+on the object where we know the
+ 
+
+ align:start position:0%
+on the object where we know the
+shape orientation you know something
+
+ align:start position:0%
+shape orientation you know something
+ 
+
+ align:start position:0%
+shape orientation you know something
+uh so
+
+ align:start position:0%
+uh so
+ 
+
+ align:start position:0%
+uh so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know so here's our prototypical
+
+ align:start position:0%
+you know so here's our prototypical
+ 
+
+ align:start position:0%
+you know so here's our prototypical
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+and that the image of this prototypical
+
+ align:start position:0%
+and that the image of this prototypical
+ 
+
+ align:start position:0%
+and that the image of this prototypical
+object and so you know question arises
+
+ align:start position:0%
+object and so you know question arises
+ 
+
+ align:start position:0%
+object and so you know question arises
+are there some
+
+ align:start position:0%
+are there some
+ 
+
+ align:start position:0%
+are there some
+so in most places we don't really know
+
+ align:start position:0%
+so in most places we don't really know
+ 
+
+ align:start position:0%
+so in most places we don't really know
+what the orientation is like we go here
+
+ align:start position:0%
+what the orientation is like we go here
+ 
+
+ align:start position:0%
+what the orientation is like we go here
+and we measure brightness
+
+ align:start position:0%
+and we measure brightness
+ 
+
+ align:start position:0%
+and we measure brightness
+e i don't know 23 and we go to the
+
+ align:start position:0%
+e i don't know 23 and we go to the
+ 
+
+ align:start position:0%
+e i don't know 23 and we go to the
+reflectance map and we get a contour
+
+ align:start position:0%
+reflectance map and we get a contour
+ 
+
+ align:start position:0%
+reflectance map and we get a contour
+there's a constraint but we don't know
+
+ align:start position:0%
+there's a constraint but we don't know
+ 
+
+ align:start position:0%
+there's a constraint but we don't know
+what the orientation is so are there any
+
+ align:start position:0%
+what the orientation is so are there any
+ 
+
+ align:start position:0%
+what the orientation is so are there any
+places here where you could tell me what
+
+ align:start position:0%
+places here where you could tell me what
+ 
+
+ align:start position:0%
+places here where you could tell me what
+the surface normal is
+
+ align:start position:0%
+the surface normal is
+ 
+
+ align:start position:0%
+the surface normal is
+the edge right so um
+
+ align:start position:0%
+the edge right so um
+ 
+
+ align:start position:0%
+the edge right so um
+the thing i draw here i guess the
+
+ align:start position:0%
+the thing i draw here i guess the
+ 
+
+ align:start position:0%
+the thing i draw here i guess the
+official word is occluding boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+the image version of it is called
+
+ align:start position:0%
+the image version of it is called
+ 
+
+ align:start position:0%
+the image version of it is called
+silhouette
+
+ align:start position:0%
+silhouette
+ 
+
+ align:start position:0%
+silhouette
+why well because that's where the object
+
+ align:start position:0%
+why well because that's where the object
+ 
+
+ align:start position:0%
+why well because that's where the object
+curls around and
+
+ align:start position:0%
+curls around and
+ 
+
+ align:start position:0%
+curls around and
+the part over here is visible and then
+
+ align:start position:0%
+the part over here is visible and then
+ 
+
+ align:start position:0%
+the part over here is visible and then
+the part where it curled around is not
+
+ align:start position:0%
+the part where it curled around is not
+ 
+
+ align:start position:0%
+the part where it curled around is not
+visible and the terminator that
+
+ align:start position:0%
+visible and the terminator that
+ 
+
+ align:start position:0%
+visible and the terminator that
+separates them
+
+ align:start position:0%
+separates them
+ 
+
+ align:start position:0%
+separates them
+i can draw
+
+ align:start position:0%
+i can draw
+ 
+
+ align:start position:0%
+i can draw
+a surface normal perpendicular
+
+ align:start position:0%
+a surface normal perpendicular
+ 
+
+ align:start position:0%
+a surface normal perpendicular
+to this curve and the
+
+ align:start position:0%
+to this curve and the
+ 
+
+ align:start position:0%
+to this curve and the
+surface normal at that point on the
+
+ align:start position:0%
+surface normal at that point on the
+ 
+
+ align:start position:0%
+surface normal at that point on the
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+parallel to that
+
+ align:start position:0%
+parallel to that
+ 
+
+ align:start position:0%
+parallel to that
+so what i'm saying is that
+
+ align:start position:0%
+so what i'm saying is that
+ 
+
+ align:start position:0%
+so what i'm saying is that
+if i go all along the occluding boundary
+
+ align:start position:0%
+if i go all along the occluding boundary
+ 
+
+ align:start position:0%
+if i go all along the occluding boundary
+i can construct a vector in the image
+
+ align:start position:0%
+i can construct a vector in the image
+ 
+
+ align:start position:0%
+i can construct a vector in the image
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+on the object the corresponding surface
+
+ align:start position:0%
+on the object the corresponding surface
+ 
+
+ align:start position:0%
+on the object the corresponding surface
+normal will be parallel to that
+
+ align:start position:0%
+normal will be parallel to that
+ 
+
+ align:start position:0%
+normal will be parallel to that
+so that's different from other places
+
+ align:start position:0%
+so that's different from other places
+ 
+
+ align:start position:0%
+so that's different from other places
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+you know i i don't have
+
+ align:start position:0%
+you know i i don't have
+ 
+
+ align:start position:0%
+you know i i don't have
+local information on surface orientation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and of course in perspective
+
+ align:start position:0%
+so and of course in perspective
+ 
+
+ align:start position:0%
+so and of course in perspective
+projection it's a little different but
+
+ align:start position:0%
+projection it's a little different but
+ 
+
+ align:start position:0%
+projection it's a little different but
+we're talking about orthographic
+
+ align:start position:0%
+we're talking about orthographic
+ 
+
+ align:start position:0%
+we're talking about orthographic
+projections so
+
+ align:start position:0%
+projections so
+ 
+
+ align:start position:0%
+projections so
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+i could perhaps use those as starting
+
+ align:start position:0%
+i could perhaps use those as starting
+ 
+
+ align:start position:0%
+i could perhaps use those as starting
+conditions i could you know start my
+
+ align:start position:0%
+conditions i could you know start my
+ 
+
+ align:start position:0%
+conditions i could you know start my
+solutions there
+
+ align:start position:0%
+solutions there
+ 
+
+ align:start position:0%
+solutions there
+well the problem is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the slope is infinite there right if you
+
+ align:start position:0%
+the slope is infinite there right if you
+ 
+
+ align:start position:0%
+the slope is infinite there right if you
+think about approaching that edge
+
+ align:start position:0%
+think about approaching that edge
+ 
+
+ align:start position:0%
+think about approaching that edge
+uh you fall off dz dz dx and dz ddy
+
+ align:start position:0%
+uh you fall off dz dz dx and dz ddy
+ 
+
+ align:start position:0%
+uh you fall off dz dz dx and dz ddy
+become infinite the slope is infinite so
+
+ align:start position:0%
+become infinite the slope is infinite so
+ 
+
+ align:start position:0%
+become infinite the slope is infinite so
+that's obviously going to be a problem
+
+ align:start position:0%
+that's obviously going to be a problem
+ 
+
+ align:start position:0%
+that's obviously going to be a problem
+if we try to somehow incorporate that in
+
+ align:start position:0%
+if we try to somehow incorporate that in
+ 
+
+ align:start position:0%
+if we try to somehow incorporate that in
+in an equation so
+
+ align:start position:0%
+in an equation so
+ 
+
+ align:start position:0%
+in an equation so
+what's interesting is that the ratio is
+
+ align:start position:0%
+what's interesting is that the ratio is
+ 
+
+ align:start position:0%
+what's interesting is that the ratio is
+is known
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because the ratio just defines
+
+ align:start position:0%
+right because the ratio just defines
+ 
+
+ align:start position:0%
+right because the ratio just defines
+this direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so it's a funny sort of thing where
+
+ align:start position:0%
+and so it's a funny sort of thing where
+ 
+
+ align:start position:0%
+and so it's a funny sort of thing where
+you know p and q are infinite whatever
+
+ align:start position:0%
+you know p and q are infinite whatever
+ 
+
+ align:start position:0%
+you know p and q are infinite whatever
+that means but we know their ratio but
+
+ align:start position:0%
+that means but we know their ratio but
+ 
+
+ align:start position:0%
+that means but we know their ratio but
+unfortunately it turns out that we can't
+
+ align:start position:0%
+unfortunately it turns out that we can't
+ 
+
+ align:start position:0%
+unfortunately it turns out that we can't
+use that
+
+ align:start position:0%
+use that
+ 
+
+ align:start position:0%
+use that
+you know we have these equations that
+
+ align:start position:0%
+you know we have these equations that
+ 
+
+ align:start position:0%
+you know we have these equations that
+tell us
+
+ align:start position:0%
+tell us
+ 
+
+ align:start position:0%
+tell us
+how p and q are changing as we take a
+
+ align:start position:0%
+how p and q are changing as we take a
+ 
+
+ align:start position:0%
+how p and q are changing as we take a
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+but if the slope is infinite
+
+ align:start position:0%
+but if the slope is infinite
+ 
+
+ align:start position:0%
+but if the slope is infinite
+then that that doesn't work so
+
+ align:start position:0%
+then that that doesn't work so
+ 
+
+ align:start position:0%
+then that that doesn't work so
+the occluding boundary tells us
+
+ align:start position:0%
+the occluding boundary tells us
+ 
+
+ align:start position:0%
+the occluding boundary tells us
+something but we can't start the
+
+ align:start position:0%
+something but we can't start the
+ 
+
+ align:start position:0%
+something but we can't start the
+solution there and we get back to using
+
+ align:start position:0%
+solution there and we get back to using
+ 
+
+ align:start position:0%
+solution there and we get back to using
+the occluding boundary
+
+ align:start position:0%
+the occluding boundary
+ 
+
+ align:start position:0%
+the occluding boundary
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's number one
+
+ align:start position:0%
+that's number one
+ 
+
+ align:start position:0%
+that's number one
+now number two
+
+ align:start position:0%
+now number two
+ 
+
+ align:start position:0%
+now number two
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we look at uh
+
+ align:start position:0%
+if we look at uh
+ 
+
+ align:start position:0%
+if we look at uh
+imagine the
+
+ align:start position:0%
+imagine the
+ 
+
+ align:start position:0%
+imagine the
+beach ball painted white and the sun is
+
+ align:start position:0%
+beach ball painted white and the sun is
+ 
+
+ align:start position:0%
+beach ball painted white and the sun is
+behind you and you're looking at it
+
+ align:start position:0%
+behind you and you're looking at it
+ 
+
+ align:start position:0%
+behind you and you're looking at it
+there'll be some spot on it that's
+
+ align:start position:0%
+there'll be some spot on it that's
+ 
+
+ align:start position:0%
+there'll be some spot on it that's
+brighter than any other spot
+
+ align:start position:0%
+brighter than any other spot
+ 
+
+ align:start position:0%
+brighter than any other spot
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+from your knowledge of ambition surfaces
+
+ align:start position:0%
+from your knowledge of ambition surfaces
+ 
+
+ align:start position:0%
+from your knowledge of ambition surfaces
+say right away what the surface
+
+ align:start position:0%
+say right away what the surface
+ 
+
+ align:start position:0%
+say right away what the surface
+orientation there is
+
+ align:start position:0%
+orientation there is
+ 
+
+ align:start position:0%
+orientation there is
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because it's
+
+ align:start position:0%
+right because it's
+ 
+
+ align:start position:0%
+right because it's
+brightness is
+
+ align:start position:0%
+brightness is
+ 
+
+ align:start position:0%
+brightness is
+you know cosine of the incident angle
+
+ align:start position:0%
+you know cosine of the incident angle
+ 
+
+ align:start position:0%
+you know cosine of the incident angle
+and the cosine doesn't get bigger than
+
+ align:start position:0%
+and the cosine doesn't get bigger than
+ 
+
+ align:start position:0%
+and the cosine doesn't get bigger than
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and it does so for zero angle so that's
+
+ align:start position:0%
+and it does so for zero angle so that's
+ 
+
+ align:start position:0%
+and it does so for zero angle so that's
+when the surface normal and the
+
+ align:start position:0%
+when the surface normal and the
+ 
+
+ align:start position:0%
+when the surface normal and the
+direction to the light source are the
+
+ align:start position:0%
+direction to the light source are the
+ 
+
+ align:start position:0%
+direction to the light source are the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's kind of a special thing
+
+ align:start position:0%
+so that's kind of a special thing
+ 
+
+ align:start position:0%
+so that's kind of a special thing
+and so unique i mean it doesn't happen
+
+ align:start position:0%
+and so unique i mean it doesn't happen
+ 
+
+ align:start position:0%
+and so unique i mean it doesn't happen
+anywhere else so let's see
+
+ align:start position:0%
+anywhere else so let's see
+ 
+
+ align:start position:0%
+anywhere else so let's see
+how to formalize this
+
+ align:start position:0%
+how to formalize this
+ 
+
+ align:start position:0%
+how to formalize this
+unique
+
+ align:start position:0%
+unique
+ 
+
+ align:start position:0%
+unique
+global
+
+ align:start position:0%
+global
+ 
+
+ align:start position:0%
+global
+isolated
+
+ align:start position:0%
+isolated
+ 
+
+ align:start position:0%
+isolated
+extremum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i go back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know for example inversion surface
+
+ align:start position:0%
+you know for example inversion surface
+ 
+
+ align:start position:0%
+you know for example inversion surface
+i have a reflectance map like this
+
+ align:start position:0%
+i have a reflectance map like this
+ 
+
+ align:start position:0%
+i have a reflectance map like this
+and here is my unique global isolated
+
+ align:start position:0%
+and here is my unique global isolated
+ 
+
+ align:start position:0%
+and here is my unique global isolated
+extremum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so most brightness measurements
+
+ align:start position:0%
+right so most brightness measurements
+ 
+
+ align:start position:0%
+right so most brightness measurements
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+don't tell me the orientation that you
+
+ align:start position:0%
+don't tell me the orientation that you
+ 
+
+ align:start position:0%
+don't tell me the orientation that you
+know if i measure this brightness well
+
+ align:start position:0%
+know if i measure this brightness well
+ 
+
+ align:start position:0%
+know if i measure this brightness well
+it could be any one of those
+
+ align:start position:0%
+it could be any one of those
+ 
+
+ align:start position:0%
+it could be any one of those
+if i measure this brightness it could be
+
+ align:start position:0%
+if i measure this brightness it could be
+ 
+
+ align:start position:0%
+if i measure this brightness it could be
+any one of those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if i measure that brightness
+
+ align:start position:0%
+but if i measure that brightness
+ 
+
+ align:start position:0%
+but if i measure that brightness
+i have i have the surface orientation so
+
+ align:start position:0%
+i have i have the surface orientation so
+ 
+
+ align:start position:0%
+i have i have the surface orientation so
+that's very special and these things are
+
+ align:start position:0%
+that's very special and these things are
+ 
+
+ align:start position:0%
+that's very special and these things are
+called stationary points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and why that well because
+
+ align:start position:0%
+and why that well because
+ 
+
+ align:start position:0%
+and why that well because
+places where the derivative is zero in
+
+ align:start position:0%
+places where the derivative is zero in
+ 
+
+ align:start position:0%
+places where the derivative is zero in
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reflectance map and we'll see there's
+
+ align:start position:0%
+reflectance map and we'll see there's
+ 
+
+ align:start position:0%
+reflectance map and we'll see there's
+another reason for calling them
+
+ align:start position:0%
+another reason for calling them
+ 
+
+ align:start position:0%
+another reason for calling them
+stationary points so maybe we can start
+
+ align:start position:0%
+stationary points so maybe we can start
+ 
+
+ align:start position:0%
+stationary points so maybe we can start
+the solution there
+
+ align:start position:0%
+the solution there
+ 
+
+ align:start position:0%
+the solution there
+and get rid of this problem about
+
+ align:start position:0%
+and get rid of this problem about
+ 
+
+ align:start position:0%
+and get rid of this problem about
+needing
+
+ align:start position:0%
+needing
+ 
+
+ align:start position:0%
+needing
+an initial curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+if it's an extremum
+
+ align:start position:0%
+if it's an extremum
+ 
+
+ align:start position:0%
+if it's an extremum
+that means that uh r sub p
+
+ align:start position:0%
+that means that uh r sub p
+ 
+
+ align:start position:0%
+that means that uh r sub p
+and r sub q are zero
+
+ align:start position:0%
+and r sub q are zero
+ 
+
+ align:start position:0%
+and r sub q are zero
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+if it's smooth and and uh
+
+ align:start position:0%
+if it's smooth and and uh
+ 
+
+ align:start position:0%
+if it's smooth and and uh
+an extreme
+
+ align:start position:0%
+an extreme
+ 
+
+ align:start position:0%
+an extreme
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+we could we could consider the case
+
+ align:start position:0%
+we could we could consider the case
+ 
+
+ align:start position:0%
+we could we could consider the case
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+we have some sort of
+
+ align:start position:0%
+we have some sort of
+ 
+
+ align:start position:0%
+we have some sort of
+non-differentiable
+
+ align:start position:0%
+non-differentiable
+ 
+
+ align:start position:0%
+non-differentiable
+r of p and q but
+
+ align:start position:0%
+r of p and q but
+ 
+
+ align:start position:0%
+r of p and q but
+let's let's not do that let's uh
+
+ align:start position:0%
+let's let's not do that let's uh
+ 
+
+ align:start position:0%
+let's let's not do that let's uh
+stay real
+
+ align:start position:0%
+stay real
+ 
+
+ align:start position:0%
+stay real
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+fine
+
+ align:start position:0%
+fine
+ 
+
+ align:start position:0%
+fine
+what's the problem with that well the
+
+ align:start position:0%
+what's the problem with that well the
+ 
+
+ align:start position:0%
+what's the problem with that well the
+problem with that is that
+
+ align:start position:0%
+problem with that is that
+ 
+
+ align:start position:0%
+problem with that is that
+our five differential equations
+
+ align:start position:0%
+our five differential equations
+ 
+
+ align:start position:0%
+our five differential equations
+included
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+at this particular point suppose i put
+
+ align:start position:0%
+at this particular point suppose i put
+ 
+
+ align:start position:0%
+at this particular point suppose i put
+my solution my solver down at that point
+
+ align:start position:0%
+my solution my solver down at that point
+ 
+
+ align:start position:0%
+my solution my solver down at that point
+in the image
+
+ align:start position:0%
+in the image
+ 
+
+ align:start position:0%
+in the image
+corresponding point in the image
+
+ align:start position:0%
+corresponding point in the image
+ 
+
+ align:start position:0%
+corresponding point in the image
+it's not going to go anywhere
+
+ align:start position:0%
+it's not going to go anywhere
+ 
+
+ align:start position:0%
+it's not going to go anywhere
+because you know
+
+ align:start position:0%
+because you know
+ 
+
+ align:start position:0%
+because you know
+r sub p and r sub q are zero
+
+ align:start position:0%
+r sub p and r sub q are zero
+ 
+
+ align:start position:0%
+r sub p and r sub q are zero
+and actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+if we
+
+ align:start position:0%
+if we
+ 
+
+ align:start position:0%
+if we
+consider the image itself so that's the
+
+ align:start position:0%
+consider the image itself so that's the
+ 
+
+ align:start position:0%
+consider the image itself so that's the
+reflectance map
+
+ align:start position:0%
+reflectance map
+ 
+
+ align:start position:0%
+reflectance map
+and here's the image itself
+
+ align:start position:0%
+and here's the image itself
+ 
+
+ align:start position:0%
+and here's the image itself
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+corresponding to that point in the
+
+ align:start position:0%
+corresponding to that point in the
+ 
+
+ align:start position:0%
+corresponding to that point in the
+reflectance map you know i suppose
+
+ align:start position:0%
+reflectance map you know i suppose
+ 
+
+ align:start position:0%
+reflectance map you know i suppose
+here's my beach ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know there's there's this point
+
+ align:start position:0%
+you know there's there's this point
+ 
+
+ align:start position:0%
+you know there's there's this point
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+well that's an extremum in the image and
+
+ align:start position:0%
+well that's an extremum in the image and
+ 
+
+ align:start position:0%
+well that's an extremum in the image and
+so here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the same argument if it's you know if
+
+ align:start position:0%
+by the same argument if it's you know if
+ 
+
+ align:start position:0%
+by the same argument if it's you know if
+e of x and y is smooth and uh it's
+
+ align:start position:0%
+e of x and y is smooth and uh it's
+ 
+
+ align:start position:0%
+e of x and y is smooth and uh it's
+that's supposed to be uh
+
+ align:start position:0%
+that's supposed to be uh
+ 
+
+ align:start position:0%
+that's supposed to be uh
+extremum then the derivatives there will
+
+ align:start position:0%
+extremum then the derivatives there will
+ 
+
+ align:start position:0%
+extremum then the derivatives there will
+be zero and so what does that mean well
+
+ align:start position:0%
+be zero and so what does that mean well
+ 
+
+ align:start position:0%
+be zero and so what does that mean well
+that means that uh dpd
+
+ align:start position:0%
+that means that uh dpd
+ 
+
+ align:start position:0%
+that means that uh dpd
+that these also don't change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and since z is dependent on those
+
+ align:start position:0%
+right and since z is dependent on those
+ 
+
+ align:start position:0%
+right and since z is dependent on those
+and nothing changes we're just stuck at
+
+ align:start position:0%
+and nothing changes we're just stuck at
+ 
+
+ align:start position:0%
+and nothing changes we're just stuck at
+that point i mean it would have been
+
+ align:start position:0%
+that point i mean it would have been
+ 
+
+ align:start position:0%
+that point i mean it would have been
+perhaps that well you're at that point
+
+ align:start position:0%
+perhaps that well you're at that point
+ 
+
+ align:start position:0%
+perhaps that well you're at that point
+but p and q change and after a while
+
+ align:start position:0%
+but p and q change and after a while
+ 
+
+ align:start position:0%
+but p and q change and after a while
+there'll be a change in x and y but no
+
+ align:start position:0%
+there'll be a change in x and y but no
+ 
+
+ align:start position:0%
+there'll be a change in x and y but no
+that doesn't work that way everything is
+
+ align:start position:0%
+that doesn't work that way everything is
+ 
+
+ align:start position:0%
+that doesn't work that way everything is
+is zero there
+
+ align:start position:0%
+is zero there
+ 
+
+ align:start position:0%
+is zero there
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+stationary points are
+
+ align:start position:0%
+stationary points are
+ 
+
+ align:start position:0%
+stationary points are
+very interesting because they give us
+
+ align:start position:0%
+very interesting because they give us
+ 
+
+ align:start position:0%
+very interesting because they give us
+local information about surface
+
+ align:start position:0%
+local information about surface
+ 
+
+ align:start position:0%
+local information about surface
+orientation but they don't sort of
+
+ align:start position:0%
+orientation but they don't sort of
+ 
+
+ align:start position:0%
+orientation but they don't sort of
+directly allow us to start start the
+
+ align:start position:0%
+directly allow us to start start the
+ 
+
+ align:start position:0%
+directly allow us to start start the
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+we can go on with this i said extremum
+
+ align:start position:0%
+we can go on with this i said extremum
+ 
+
+ align:start position:0%
+we can go on with this i said extremum
+rather than maximum
+
+ align:start position:0%
+rather than maximum
+ 
+
+ align:start position:0%
+rather than maximum
+because for lambertian it's a maximum
+
+ align:start position:0%
+because for lambertian it's a maximum
+ 
+
+ align:start position:0%
+because for lambertian it's a maximum
+but for the scanning electron microscope
+
+ align:start position:0%
+but for the scanning electron microscope
+ 
+
+ align:start position:0%
+but for the scanning electron microscope
+it's not it's it's a minimum right for
+
+ align:start position:0%
+it's not it's it's a minimum right for
+ 
+
+ align:start position:0%
+it's not it's it's a minimum right for
+the scanning electron microscope we had
+
+ align:start position:0%
+the scanning electron microscope we had
+ 
+
+ align:start position:0%
+the scanning electron microscope we had
+reflectance map that looked like this
+
+ align:start position:0%
+reflectance map that looked like this
+ 
+
+ align:start position:0%
+reflectance map that looked like this
+and this this was the magic point and
+
+ align:start position:0%
+and this this was the magic point and
+ 
+
+ align:start position:0%
+and this this was the magic point and
+there uh the brightness is minimum
+
+ align:start position:0%
+there uh the brightness is minimum
+ 
+
+ align:start position:0%
+there uh the brightness is minimum
+right remember the objects were the
+
+ align:start position:0%
+right remember the objects were the
+ 
+
+ align:start position:0%
+right remember the objects were the
+edges the occluding boundaries were
+
+ align:start position:0%
+edges the occluding boundaries were
+ 
+
+ align:start position:0%
+edges the occluding boundaries were
+bright in the image
+
+ align:start position:0%
+bright in the image
+ 
+
+ align:start position:0%
+bright in the image
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+part facing you was dark so in the case
+
+ align:start position:0%
+part facing you was dark so in the case
+ 
+
+ align:start position:0%
+part facing you was dark so in the case
+of a scanning electron microscope we do
+
+ align:start position:0%
+of a scanning electron microscope we do
+ 
+
+ align:start position:0%
+of a scanning electron microscope we do
+also have stationary points but they
+
+ align:start position:0%
+also have stationary points but they
+ 
+
+ align:start position:0%
+also have stationary points but they
+correspond to
+
+ align:start position:0%
+correspond to
+ 
+
+ align:start position:0%
+correspond to
+minima rather than maxima but anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what to do well
+
+ align:start position:0%
+so what to do well
+ 
+
+ align:start position:0%
+so what to do well
+if we can get away
+
+ align:start position:0%
+if we can get away
+ 
+
+ align:start position:0%
+if we can get away
+if we can get a little bit away from
+
+ align:start position:0%
+if we can get a little bit away from
+ 
+
+ align:start position:0%
+if we can get a little bit away from
+this point
+
+ align:start position:0%
+this point
+ 
+
+ align:start position:0%
+this point
+then those conditions aren't
+
+ align:start position:0%
+then those conditions aren't
+ 
+
+ align:start position:0%
+then those conditions aren't
+going to be true anymore and those
+
+ align:start position:0%
+going to be true anymore and those
+ 
+
+ align:start position:0%
+going to be true anymore and those
+quantities may be small but at least we
+
+ align:start position:0%
+quantities may be small but at least we
+ 
+
+ align:start position:0%
+quantities may be small but at least we
+can move and of course we can control
+
+ align:start position:0%
+can move and of course we can control
+ 
+
+ align:start position:0%
+can move and of course we can control
+the speed so suppose the quantities are
+
+ align:start position:0%
+the speed so suppose the quantities are
+ 
+
+ align:start position:0%
+the speed so suppose the quantities are
+small big deal we just multiply the step
+
+ align:start position:0%
+small big deal we just multiply the step
+ 
+
+ align:start position:0%
+small big deal we just multiply the step
+size so so as long as we can get away
+
+ align:start position:0%
+size so so as long as we can get away
+ 
+
+ align:start position:0%
+size so so as long as we can get away
+from that point but
+
+ align:start position:0%
+from that point but
+ 
+
+ align:start position:0%
+from that point but
+you know how do we get away so here's
+
+ align:start position:0%
+you know how do we get away so here's
+ 
+
+ align:start position:0%
+you know how do we get away so here's
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+stationary point and one thing we can
+
+ align:start position:0%
+stationary point and one thing we can
+ 
+
+ align:start position:0%
+stationary point and one thing we can
+think of doing is
+
+ align:start position:0%
+think of doing is
+ 
+
+ align:start position:0%
+think of doing is
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+constructing a
+
+ align:start position:0%
+constructing a
+ 
+
+ align:start position:0%
+constructing a
+approximation of the surface
+
+ align:start position:0%
+approximation of the surface
+ 
+
+ align:start position:0%
+approximation of the surface
+let's suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's the story we know
+
+ align:start position:0%
+okay so here's the story we know
+ 
+
+ align:start position:0%
+okay so here's the story we know
+uh we know the surface orientation there
+
+ align:start position:0%
+uh we know the surface orientation there
+ 
+
+ align:start position:0%
+uh we know the surface orientation there
+because it's one of those stationary
+
+ align:start position:0%
+because it's one of those stationary
+ 
+
+ align:start position:0%
+because it's one of those stationary
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+and now we want to get away from it a
+
+ align:start position:0%
+and now we want to get away from it a
+ 
+
+ align:start position:0%
+and now we want to get away from it a
+little bit so we can start the solution
+
+ align:start position:0%
+little bit so we can start the solution
+ 
+
+ align:start position:0%
+little bit so we can start the solution
+so the idea is we want to start the
+
+ align:start position:0%
+so the idea is we want to start the
+ 
+
+ align:start position:0%
+so the idea is we want to start the
+solution from from this curve
+
+ align:start position:0%
+solution from from this curve
+ 
+
+ align:start position:0%
+solution from from this curve
+so we know the orientation so we can
+
+ align:start position:0%
+so we know the orientation so we can
+ 
+
+ align:start position:0%
+so we know the orientation so we can
+construct a small plane
+
+ align:start position:0%
+construct a small plane
+ 
+
+ align:start position:0%
+construct a small plane
+and you know i don't know make a radius
+
+ align:start position:0%
+and you know i don't know make a radius
+ 
+
+ align:start position:0%
+and you know i don't know make a radius
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+start the solutions there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that gonna work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if it's a plane
+
+ align:start position:0%
+well if it's a plane
+ 
+
+ align:start position:0%
+well if it's a plane
+then all parts of it have the same
+
+ align:start position:0%
+then all parts of it have the same
+ 
+
+ align:start position:0%
+then all parts of it have the same
+orientation they all have the same
+
+ align:start position:0%
+orientation they all have the same
+ 
+
+ align:start position:0%
+orientation they all have the same
+brightness
+
+ align:start position:0%
+brightness
+ 
+
+ align:start position:0%
+brightness
+and we're just exactly the same problem
+
+ align:start position:0%
+and we're just exactly the same problem
+ 
+
+ align:start position:0%
+and we're just exactly the same problem
+out here than we were there
+
+ align:start position:0%
+out here than we were there
+ 
+
+ align:start position:0%
+out here than we were there
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+idea doesn't quite work
+
+ align:start position:0%
+idea doesn't quite work
+ 
+
+ align:start position:0%
+idea doesn't quite work
+so the answer is well let's have a
+
+ align:start position:0%
+so the answer is well let's have a
+ 
+
+ align:start position:0%
+so the answer is well let's have a
+curved surface so we still have that
+
+ align:start position:0%
+curved surface so we still have that
+ 
+
+ align:start position:0%
+curved surface so we still have that
+special point but now let's suppose that
+
+ align:start position:0%
+special point but now let's suppose that
+ 
+
+ align:start position:0%
+special point but now let's suppose that
+the surface is curved and we're going to
+
+ align:start position:0%
+the surface is curved and we're going to
+ 
+
+ align:start position:0%
+the surface is curved and we're going to
+construct
+
+ align:start position:0%
+construct
+ 
+
+ align:start position:0%
+construct
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+you know curved shape around that point
+
+ align:start position:0%
+you know curved shape around that point
+ 
+
+ align:start position:0%
+you know curved shape around that point
+and we'll start the solution from there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know this this sounds
+
+ align:start position:0%
+so you know this this sounds
+ 
+
+ align:start position:0%
+so you know this this sounds
+kind of um i don't know specialized
+
+ align:start position:0%
+kind of um i don't know specialized
+ 
+
+ align:start position:0%
+kind of um i don't know specialized
+weird um
+
+ align:start position:0%
+weird um
+ 
+
+ align:start position:0%
+weird um
+why these points and so on but actually
+
+ align:start position:0%
+why these points and so on but actually
+ 
+
+ align:start position:0%
+why these points and so on but actually
+these points are very important in human
+
+ align:start position:0%
+these points are very important in human
+ 
+
+ align:start position:0%
+these points are very important in human
+perception as well so you know you can
+
+ align:start position:0%
+perception as well so you know you can
+ 
+
+ align:start position:0%
+perception as well so you know you can
+do experiments where you
+
+ align:start position:0%
+do experiments where you
+ 
+
+ align:start position:0%
+do experiments where you
+show someone a picture of a vaz and i
+
+ align:start position:0%
+show someone a picture of a vaz and i
+ 
+
+ align:start position:0%
+show someone a picture of a vaz and i
+have a very good idea of what its shape
+
+ align:start position:0%
+have a very good idea of what its shape
+ 
+
+ align:start position:0%
+have a very good idea of what its shape
+is i mean not metrically accurate but
+
+ align:start position:0%
+is i mean not metrically accurate but
+ 
+
+ align:start position:0%
+is i mean not metrically accurate but
+generally pretty good
+
+ align:start position:0%
+generally pretty good
+ 
+
+ align:start position:0%
+generally pretty good
+and then you
+
+ align:start position:0%
+and then you
+ 
+
+ align:start position:0%
+and then you
+photoshop out the bright spot
+
+ align:start position:0%
+photoshop out the bright spot
+ 
+
+ align:start position:0%
+photoshop out the bright spot
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+they still have a shape in mind but it's
+
+ align:start position:0%
+they still have a shape in mind but it's
+ 
+
+ align:start position:0%
+they still have a shape in mind but it's
+changed and so actually
+
+ align:start position:0%
+changed and so actually
+ 
+
+ align:start position:0%
+changed and so actually
+it turns out that we use
+
+ align:start position:0%
+it turns out that we use
+ 
+
+ align:start position:0%
+it turns out that we use
+these stationary points as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another example is where you have
+
+ align:start position:0%
+another example is where you have
+ 
+
+ align:start position:0%
+another example is where you have
+cut out
+
+ align:start position:0%
+cut out
+ 
+
+ align:start position:0%
+cut out
+so you have some
+
+ align:start position:0%
+so you have some
+ 
+
+ align:start position:0%
+so you have some
+some blob in the world like like this
+
+ align:start position:0%
+some blob in the world like like this
+ 
+
+ align:start position:0%
+some blob in the world like like this
+but now you're showing someone a picture
+
+ align:start position:0%
+but now you're showing someone a picture
+ 
+
+ align:start position:0%
+but now you're showing someone a picture
+of only i don't know say that
+
+ align:start position:0%
+of only i don't know say that
+ 
+
+ align:start position:0%
+of only i don't know say that
+that doesn't include uh the bright point
+
+ align:start position:0%
+that doesn't include uh the bright point
+ 
+
+ align:start position:0%
+that doesn't include uh the bright point
+it turns out that this is much more
+
+ align:start position:0%
+it turns out that this is much more
+ 
+
+ align:start position:0%
+it turns out that this is much more
+ambiguous that
+
+ align:start position:0%
+ambiguous that
+ 
+
+ align:start position:0%
+ambiguous that
+then if you included that bright point
+
+ align:start position:0%
+then if you included that bright point
+ 
+
+ align:start position:0%
+then if you included that bright point
+so it's
+
+ align:start position:0%
+so it's
+ 
+
+ align:start position:0%
+so it's
+it's a real thing it's not just you know
+
+ align:start position:0%
+it's a real thing it's not just you know
+ 
+
+ align:start position:0%
+it's a real thing it's not just you know
+something that
+
+ align:start position:0%
+something that
+ 
+
+ align:start position:0%
+something that
+affects our particular method of
+
+ align:start position:0%
+affects our particular method of
+ 
+
+ align:start position:0%
+affects our particular method of
+solution it's uh important for there to
+
+ align:start position:0%
+solution it's uh important for there to
+ 
+
+ align:start position:0%
+solution it's uh important for there to
+be a unique solution
+
+ align:start position:0%
+be a unique solution
+ 
+
+ align:start position:0%
+be a unique solution
+or or a small number of solutions as
+
+ align:start position:0%
+or or a small number of solutions as
+ 
+
+ align:start position:0%
+or or a small number of solutions as
+opposed to an infinite number of
+
+ align:start position:0%
+opposed to an infinite number of
+ 
+
+ align:start position:0%
+opposed to an infinite number of
+solutions
+
+ align:start position:0%
+solutions
+ 
+
+ align:start position:0%
+solutions
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+this is going to be some sort of uh
+
+ align:start position:0%
+this is going to be some sort of uh
+ 
+
+ align:start position:0%
+this is going to be some sort of uh
+curved uh surface
+
+ align:start position:0%
+curved uh surface
+ 
+
+ align:start position:0%
+curved uh surface
+and we need to find out
+
+ align:start position:0%
+and we need to find out
+ 
+
+ align:start position:0%
+and we need to find out
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+its curvature is
+
+ align:start position:0%
+its curvature is
+ 
+
+ align:start position:0%
+its curvature is
+in order to construct it right and sort
+
+ align:start position:0%
+in order to construct it right and sort
+ 
+
+ align:start position:0%
+in order to construct it right and sort
+of like oh my god now we not only need
+
+ align:start position:0%
+of like oh my god now we not only need
+ 
+
+ align:start position:0%
+of like oh my god now we not only need
+to guess at the surface but we need to
+
+ align:start position:0%
+to guess at the surface but we need to
+ 
+
+ align:start position:0%
+to guess at the surface but we need to
+know the curvature of the surface
+
+ align:start position:0%
+know the curvature of the surface
+ 
+
+ align:start position:0%
+know the curvature of the surface
+but actually it turns out that's uh
+
+ align:start position:0%
+but actually it turns out that's uh
+ 
+
+ align:start position:0%
+but actually it turns out that's uh
+possible and so let's see um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see how that might work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we are going to
+
+ align:start position:0%
+we are going to
+ 
+
+ align:start position:0%
+we are going to
+have a small patch and i'm going to make
+
+ align:start position:0%
+have a small patch and i'm going to make
+ 
+
+ align:start position:0%
+have a small patch and i'm going to make
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as simple as it can be
+
+ align:start position:0%
+as simple as it can be
+ 
+
+ align:start position:0%
+as simple as it can be
+so we're going to assume first of all
+
+ align:start position:0%
+so we're going to assume first of all
+ 
+
+ align:start position:0%
+so we're going to assume first of all
+that we have an sem type of
+
+ align:start position:0%
+that we have an sem type of
+ 
+
+ align:start position:0%
+that we have an sem type of
+reflectance map just to make it really
+
+ align:start position:0%
+reflectance map just to make it really
+ 
+
+ align:start position:0%
+reflectance map just to make it really
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+and then let's suppose we have a surface
+
+ align:start position:0%
+and then let's suppose we have a surface
+ 
+
+ align:start position:0%
+and then let's suppose we have a surface
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this will have a
+
+ align:start position:0%
+this will have a
+ 
+
+ align:start position:0%
+this will have a
+stationary point at the origin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's see so you've got p is dz dx
+
+ align:start position:0%
+and let's see so you've got p is dz dx
+ 
+
+ align:start position:0%
+and let's see so you've got p is dz dx
+is 2x
+
+ align:start position:0%
+is 2x
+ 
+
+ align:start position:0%
+is 2x
+q is dz dy
+
+ align:start position:0%
+q is dz dy
+ 
+
+ align:start position:0%
+q is dz dy
+is 4
+
+ align:start position:0%
+is 4
+ 
+
+ align:start position:0%
+is 4
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+and then the reflectance map gives us p
+
+ align:start position:0%
+and then the reflectance map gives us p
+ 
+
+ align:start position:0%
+and then the reflectance map gives us p
+squared plus q squared is
+
+ align:start position:0%
+squared plus q squared is
+ 
+
+ align:start position:0%
+squared plus q squared is
+4x squared plus 16
+
+ align:start position:0%
+4x squared plus 16
+ 
+
+ align:start position:0%
+4x squared plus 16
+y squared
+
+ align:start position:0%
+y squared
+ 
+
+ align:start position:0%
+y squared
+and by the image irradiance equation
+
+ align:start position:0%
+and by the image irradiance equation
+ 
+
+ align:start position:0%
+and by the image irradiance equation
+that's actually
+
+ align:start position:0%
+that's actually
+ 
+
+ align:start position:0%
+that's actually
+the image
+
+ align:start position:0%
+the image
+ 
+
+ align:start position:0%
+the image
+okay and i'm going to take the gradient
+
+ align:start position:0%
+okay and i'm going to take the gradient
+ 
+
+ align:start position:0%
+okay and i'm going to take the gradient
+of the image
+
+ align:start position:0%
+of the image
+ 
+
+ align:start position:0%
+of the image
+will be 8 x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and not surprisingly the gradient is 0
+
+ align:start position:0%
+and not surprisingly the gradient is 0
+ 
+
+ align:start position:0%
+and not surprisingly the gradient is 0
+at the origin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that corresponds to it being an
+
+ align:start position:0%
+and that corresponds to it being an
+ 
+
+ align:start position:0%
+and that corresponds to it being an
+extreme so
+
+ align:start position:0%
+extreme so
+ 
+
+ align:start position:0%
+extreme so
+that just confirms that we have in fact
+
+ align:start position:0%
+that just confirms that we have in fact
+ 
+
+ align:start position:0%
+that just confirms that we have in fact
+set it up so that we have an extremum at
+
+ align:start position:0%
+set it up so that we have an extremum at
+ 
+
+ align:start position:0%
+set it up so that we have an extremum at
+the origin
+
+ align:start position:0%
+the origin
+ 
+
+ align:start position:0%
+the origin
+okay now can i use the gradient to
+
+ align:start position:0%
+okay now can i use the gradient to
+ 
+
+ align:start position:0%
+okay now can i use the gradient to
+estimate the shape local local shape
+
+ align:start position:0%
+estimate the shape local local shape
+ 
+
+ align:start position:0%
+estimate the shape local local shape
+well no because the gradient is zero
+
+ align:start position:0%
+well no because the gradient is zero
+ 
+
+ align:start position:0%
+well no because the gradient is zero
+right at the origin
+
+ align:start position:0%
+right at the origin
+ 
+
+ align:start position:0%
+right at the origin
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+let's take the second derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the plan is
+
+ align:start position:0%
+so the plan is
+ 
+
+ align:start position:0%
+so the plan is
+the gradient will be zero so that's
+
+ align:start position:0%
+the gradient will be zero so that's
+ 
+
+ align:start position:0%
+the gradient will be zero so that's
+useless brightness itself we've already
+
+ align:start position:0%
+useless brightness itself we've already
+ 
+
+ align:start position:0%
+useless brightness itself we've already
+used to determine that it's a stationary
+
+ align:start position:0%
+used to determine that it's a stationary
+ 
+
+ align:start position:0%
+used to determine that it's a stationary
+point but if we take the second partial
+
+ align:start position:0%
+point but if we take the second partial
+ 
+
+ align:start position:0%
+point but if we take the second partial
+derivatives of brightness
+
+ align:start position:0%
+derivatives of brightness
+ 
+
+ align:start position:0%
+derivatives of brightness
+we get some information about the shape
+
+ align:start position:0%
+we get some information about the shape
+ 
+
+ align:start position:0%
+we get some information about the shape
+and we're going to try and recover you
+
+ align:start position:0%
+and we're going to try and recover you
+ 
+
+ align:start position:0%
+and we're going to try and recover you
+know the x squared plus 2y squared from
+
+ align:start position:0%
+know the x squared plus 2y squared from
+ 
+
+ align:start position:0%
+know the x squared plus 2y squared from
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so it might say well how can i measure
+
+ align:start position:0%
+so it might say well how can i measure
+ 
+
+ align:start position:0%
+so it might say well how can i measure
+the second derivative well of course
+
+ align:start position:0%
+the second derivative well of course
+ 
+
+ align:start position:0%
+the second derivative well of course
+let's just apply the first derivative
+
+ align:start position:0%
+let's just apply the first derivative
+ 
+
+ align:start position:0%
+let's just apply the first derivative
+twice and we also already talked about
+
+ align:start position:0%
+twice and we also already talked about
+ 
+
+ align:start position:0%
+twice and we also already talked about
+uh convenient uh
+
+ align:start position:0%
+uh convenient uh
+ 
+
+ align:start position:0%
+uh convenient uh
+computational molecules for doing that
+
+ align:start position:0%
+computational molecules for doing that
+ 
+
+ align:start position:0%
+computational molecules for doing that
+so there's you know one for ex
+
+ align:start position:0%
+so there's you know one for ex
+ 
+
+ align:start position:0%
+so there's you know one for ex
+exxx
+
+ align:start position:0%
+exxx
+ 
+
+ align:start position:0%
+exxx
+so the plan will be
+
+ align:start position:0%
+so the plan will be
+ 
+
+ align:start position:0%
+so the plan will be
+uh we find the stationary points we
+
+ align:start position:0%
+uh we find the stationary points we
+ 
+
+ align:start position:0%
+uh we find the stationary points we
+estimate the local shape by looking at
+
+ align:start position:0%
+estimate the local shape by looking at
+ 
+
+ align:start position:0%
+estimate the local shape by looking at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+second not the gradient but the gradient
+
+ align:start position:0%
+second not the gradient but the gradient
+ 
+
+ align:start position:0%
+second not the gradient but the gradient
+of the gradient so to speak and
+
+ align:start position:0%
+of the gradient so to speak and
+ 
+
+ align:start position:0%
+of the gradient so to speak and
+construct a small cap of that shape
+
+ align:start position:0%
+construct a small cap of that shape
+ 
+
+ align:start position:0%
+construct a small cap of that shape
+around the stationary point and then
+
+ align:start position:0%
+around the stationary point and then
+ 
+
+ align:start position:0%
+around the stationary point and then
+start the solutions from there
+
+ align:start position:0%
+start the solutions from there
+ 
+
+ align:start position:0%
+start the solutions from there
+but that
+
+ align:start position:0%
+but that
+ 
+
+ align:start position:0%
+but that
+didn't quite get done with that so we'll
+
+ align:start position:0%
+didn't quite get done with that so we'll
+ 
+
+ align:start position:0%
+didn't quite get done with that so we'll
+finish that next time and then as i said
+
+ align:start position:0%
+finish that next time and then as i said
+ 
+
+ align:start position:0%
+finish that next time and then as i said
+then we'll
+
+ align:start position:0%
+then we'll
+ 
+
+ align:start position:0%
+then we'll
+have a real big change of pace and we
+
+ align:start position:0%
+have a real big change of pace and we
+ 
+
+ align:start position:0%
+have a real big change of pace and we
+start talking about some industrial
+
+ align:start position:0%
+start talking about some industrial
+ 
+
+ align:start position:0%
+start talking about some industrial
+machine vision methods
+
+ align:start position:0%
+machine vision methods
+ 
+
+ align:start position:0%
+machine vision methods
+and the patterns that
+
+ align:start position:0%
+and the patterns that
+ 
+
+ align:start position:0%
+and the patterns that
+describe them
\ No newline at end of file
diff --git a/Xa2jPbURTjQ.txt b/Xa2jPbURTjQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..617e97e538f9e92cd44ef55ca2081daaf5579c10
--- /dev/null
+++ b/Xa2jPbURTjQ.txt
@@ -0,0 +1,6379 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+so we're really moving along this review
+
+ align:start position:0%
+so we're really moving along this review
+ 
+
+ align:start position:0%
+so we're really moving along this review
+of highlights of linear algebra and
+
+ align:start position:0%
+of highlights of linear algebra and
+ 
+
+ align:start position:0%
+of highlights of linear algebra and
+today it's matrices Q they get that name
+
+ align:start position:0%
+today it's matrices Q they get that name
+ 
+
+ align:start position:0%
+today it's matrices Q they get that name
+there they have orthonormal columns so
+
+ align:start position:0%
+there they have orthonormal columns so
+ 
+
+ align:start position:0%
+there they have orthonormal columns so
+that's what one looks like and then the
+
+ align:start position:0%
+that's what one looks like and then the
+ 
+
+ align:start position:0%
+that's what one looks like and then the
+key fact orthonormal columns translates
+
+ align:start position:0%
+key fact orthonormal columns translates
+ 
+
+ align:start position:0%
+key fact orthonormal columns translates
+directly into that simple fact that you
+
+ align:start position:0%
+directly into that simple fact that you
+ 
+
+ align:start position:0%
+directly into that simple fact that you
+just keep remembering every time you see
+
+ align:start position:0%
+just keep remembering every time you see
+ 
+
+ align:start position:0%
+just keep remembering every time you see
+Q transpose Q you've got the identity
+
+ align:start position:0%
+Q transpose Q you've got the identity
+ 
+
+ align:start position:0%
+Q transpose Q you've got the identity
+matrix let's just see why so Q transpose
+
+ align:start position:0%
+matrix let's just see why so Q transpose
+ 
+
+ align:start position:0%
+matrix let's just see why so Q transpose
+would be I'll take those columns and
+
+ align:start position:0%
+would be I'll take those columns and
+ 
+
+ align:start position:0%
+would be I'll take those columns and
+make them into rows and then I multiply
+
+ align:start position:0%
+make them into rows and then I multiply
+ 
+
+ align:start position:0%
+make them into rows and then I multiply
+by Q with the columns and what do I get
+
+ align:start position:0%
+by Q with the columns and what do I get
+ 
+
+ align:start position:0%
+by Q with the columns and what do I get
+well hopefully I get the identity matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+why because oh yeah the normal part
+
+ align:start position:0%
+why because oh yeah the normal part
+ 
+
+ align:start position:0%
+why because oh yeah the normal part
+tells me that the lengths of each vector
+
+ align:start position:0%
+tells me that the lengths of each vector
+ 
+
+ align:start position:0%
+tells me that the lengths of each vector
+that's the length squared Q transpose Q
+
+ align:start position:0%
+that's the length squared Q transpose Q
+ 
+
+ align:start position:0%
+that's the length squared Q transpose Q
+the length squared is 1 so that gives me
+
+ align:start position:0%
+the length squared is 1 so that gives me
+ 
+
+ align:start position:0%
+the length squared is 1 so that gives me
+the 1 in the identity matrix along the
+
+ align:start position:0%
+the 1 in the identity matrix along the
+ 
+
+ align:start position:0%
+the 1 in the identity matrix along the
+diagonal and then Q transpose times a
+
+ align:start position:0%
+diagonal and then Q transpose times a
+ 
+
+ align:start position:0%
+diagonal and then Q transpose times a
+different Q is 0 that's the ortho part
+
+ align:start position:0%
+different Q is 0 that's the ortho part
+ 
+
+ align:start position:0%
+different Q is 0 that's the ortho part
+so that gives me the zeros so that's a
+
+ align:start position:0%
+so that gives me the zeros so that's a
+ 
+
+ align:start position:0%
+so that gives me the zeros so that's a
+simple identity but it translates from a
+
+ align:start position:0%
+simple identity but it translates from a
+ 
+
+ align:start position:0%
+simple identity but it translates from a
+lot of words into a simple expression
+
+ align:start position:0%
+lot of words into a simple expression
+ 
+
+ align:start position:0%
+lot of words into a simple expression
+now does that mean that in the other
+
+ align:start position:0%
+now does that mean that in the other
+ 
+
+ align:start position:0%
+now does that mean that in the other
+order Q Q transpose is that the identity
+
+ align:start position:0%
+order Q Q transpose is that the identity
+ 
+
+ align:start position:0%
+order Q Q transpose is that the identity
+that's so that's a question to think
+
+ align:start position:0%
+that's so that's a question to think
+ 
+
+ align:start position:0%
+that's so that's a question to think
+about is QQ transpose equal the identity
+
+ align:start position:0%
+about is QQ transpose equal the identity
+ 
+
+ align:start position:0%
+about is QQ transpose equal the identity
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+sometimes yes sometimes no easy to tell
+
+ align:start position:0%
+sometimes yes sometimes no easy to tell
+ 
+
+ align:start position:0%
+sometimes yes sometimes no easy to tell
+which the answer is yes yes when Q is
+
+ align:start position:0%
+which the answer is yes yes when Q is
+ 
+
+ align:start position:0%
+which the answer is yes yes when Q is
+square the answer is yes if Q is a
+
+ align:start position:0%
+square the answer is yes if Q is a
+ 
+
+ align:start position:0%
+square the answer is yes if Q is a
+square matrix a square matrix a this is
+
+ align:start position:0%
+square matrix a square matrix a this is
+ 
+
+ align:start position:0%
+square matrix a square matrix a this is
+saying that the square matrix Q has that
+
+ align:start position:0%
+saying that the square matrix Q has that
+ 
+
+ align:start position:0%
+saying that the square matrix Q has that
+inverse on its left but for square
+
+ align:start position:0%
+inverse on its left but for square
+ 
+
+ align:start position:0%
+inverse on its left but for square
+matrices a left inverse Q transpose is
+
+ align:start position:0%
+matrices a left inverse Q transpose is
+ 
+
+ align:start position:0%
+matrices a left inverse Q transpose is
+also a right inverse so for a square
+
+ align:start position:0%
+also a right inverse so for a square
+ 
+
+ align:start position:0%
+also a right inverse so for a square
+matrix if you have an inverse that works
+
+ align:start position:0%
+matrix if you have an inverse that works
+ 
+
+ align:start position:0%
+matrix if you have an inverse that works
+on one side it will work on the other
+
+ align:start position:0%
+on one side it will work on the other
+ 
+
+ align:start position:0%
+on one side it will work on the other
+side so the answer is yes in that case
+
+ align:start position:0%
+side so the answer is yes in that case
+ 
+
+ align:start position:0%
+side so the answer is yes in that case
+and then in that case that's the case
+
+ align:start position:0%
+and then in that case that's the case
+ 
+
+ align:start position:0%
+and then in that case that's the case
+when we call Q is well we really don't
+
+ align:start position:0%
+when we call Q is well we really don't
+ 
+
+ align:start position:0%
+when we call Q is well we really don't
+know what the right name would be but
+
+ align:start position:0%
+know what the right name would be but
+ 
+
+ align:start position:0%
+know what the right name would be but
+here's the name everybody uses an
+
+ align:start position:0%
+here's the name everybody uses an
+ 
+
+ align:start position:0%
+here's the name everybody uses an
+orthogonal matrix and that's that's only
+
+ align:start position:0%
+orthogonal matrix and that's that's only
+ 
+
+ align:start position:0%
+orthogonal matrix and that's that's only
+in their square case square here is an
+
+ align:start position:0%
+in their square case square here is an
+ 
+
+ align:start position:0%
+in their square case square here is an
+orthogonal matrix right right do you -
+
+ align:start position:0%
+orthogonal matrix right right do you -
+ 
+
+ align:start position:0%
+orthogonal matrix right right do you -
+do you want to just see an example of
+
+ align:start position:0%
+do you want to just see an example of
+ 
+
+ align:start position:0%
+do you want to just see an example of
+how that works and it will not so if Q
+
+ align:start position:0%
+how that works and it will not so if Q
+ 
+
+ align:start position:0%
+how that works and it will not so if Q
+is rectangular let's let me do a
+
+ align:start position:0%
+is rectangular let's let me do a
+ 
+
+ align:start position:0%
+is rectangular let's let me do a
+rectangular Q and square Q okay square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right good to see some orthogonal
+
+ align:start position:0%
+all right good to see some orthogonal
+ 
+
+ align:start position:0%
+all right good to see some orthogonal
+matrices because my message is that
+
+ align:start position:0%
+matrices because my message is that
+ 
+
+ align:start position:0%
+matrices because my message is that
+they're really important in all kinds of
+
+ align:start position:0%
+they're really important in all kinds of
+ 
+
+ align:start position:0%
+they're really important in all kinds of
+applications let's start two-by-two I
+
+ align:start position:0%
+applications let's start two-by-two I
+ 
+
+ align:start position:0%
+applications let's start two-by-two I
+can think of two different ways to get
+
+ align:start position:0%
+can think of two different ways to get
+ 
+
+ align:start position:0%
+can think of two different ways to get
+an orthogonal matrix that's a 2 by 2
+
+ align:start position:0%
+an orthogonal matrix that's a 2 by 2
+ 
+
+ align:start position:0%
+an orthogonal matrix that's a 2 by 2
+matrix and one of them you will know
+
+ align:start position:0%
+matrix and one of them you will know
+ 
+
+ align:start position:0%
+matrix and one of them you will know
+immediately cos theta sine theta so
+
+ align:start position:0%
+immediately cos theta sine theta so
+ 
+
+ align:start position:0%
+immediately cos theta sine theta so
+that's a unit vector it's normalized cos
+
+ align:start position:0%
+that's a unit vector it's normalized cos
+ 
+
+ align:start position:0%
+that's a unit vector it's normalized cos
+squared plus sine squared is 1 and this
+
+ align:start position:0%
+squared plus sine squared is 1 and this
+ 
+
+ align:start position:0%
+squared plus sine squared is 1 and this
+guy has to be orthogonal to it
+
+ align:start position:0%
+guy has to be orthogonal to it
+ 
+
+ align:start position:0%
+guy has to be orthogonal to it
+so I make that - sine theta and cos
+
+ align:start position:0%
+so I make that - sine theta and cos
+ 
+
+ align:start position:0%
+so I make that - sine theta and cos
+theta okay
+
+ align:start position:0%
+theta okay
+ 
+
+ align:start position:0%
+theta okay
+those are both links one they're
+
+ align:start position:0%
+those are both links one they're
+ 
+
+ align:start position:0%
+those are both links one they're
+orthogonal then this is my Q and the
+
+ align:start position:0%
+orthogonal then this is my Q and the
+ 
+
+ align:start position:0%
+orthogonal then this is my Q and the
+inverse of Q will be the transpose if I
+
+ align:start position:0%
+inverse of Q will be the transpose if I
+ 
+
+ align:start position:0%
+inverse of Q will be the transpose if I
+multiply the transpose would put the
+
+ align:start position:0%
+multiply the transpose would put the
+ 
+
+ align:start position:0%
+multiply the transpose would put the
+minus sign down here and would produce
+
+ align:start position:0%
+minus sign down here and would produce
+ 
+
+ align:start position:0%
+minus sign down here and would produce
+the inverse matrix and what is that
+
+ align:start position:0%
+the inverse matrix and what is that
+ 
+
+ align:start position:0%
+the inverse matrix and what is that
+particular matrix represent whoa why do
+
+ align:start position:0%
+particular matrix represent whoa why do
+ 
+
+ align:start position:0%
+particular matrix represent whoa why do
+geometrically why do we where do we see
+
+ align:start position:0%
+geometrically why do we where do we see
+ 
+
+ align:start position:0%
+geometrically why do we where do we see
+that matrix it's a rotation thank you
+
+ align:start position:0%
+that matrix it's a rotation thank you
+ 
+
+ align:start position:0%
+that matrix it's a rotation thank you
+it's a rotation of the whole plane by
+
+ align:start position:0%
+it's a rotation of the whole plane by
+ 
+
+ align:start position:0%
+it's a rotation of the whole plane by
+SATA
+
+ align:start position:0%
+SATA
+ 
+
+ align:start position:0%
+SATA
+yeah so so if I apply that to one zero
+
+ align:start position:0%
+yeah so so if I apply that to one zero
+ 
+
+ align:start position:0%
+yeah so so if I apply that to one zero
+for example I get the first column which
+
+ align:start position:0%
+for example I get the first column which
+ 
+
+ align:start position:0%
+for example I get the first column which
+is cos theta sine theta and that's just
+
+ align:start position:0%
+is cos theta sine theta and that's just
+ 
+
+ align:start position:0%
+is cos theta sine theta and that's just
+a rope let me draw a picture that vector
+
+ align:start position:0%
+a rope let me draw a picture that vector
+ 
+
+ align:start position:0%
+a rope let me draw a picture that vector
+1 0 has got rotated up - so there's the
+
+ align:start position:0%
+1 0 has got rotated up - so there's the
+ 
+
+ align:start position:0%
+1 0 has got rotated up - so there's the
+the 1 0 and there it got rotated through
+
+ align:start position:0%
+the 1 0 and there it got rotated through
+ 
+
+ align:start position:0%
+the 1 0 and there it got rotated through
+an angle theta and similarly 0 1 will
+
+ align:start position:0%
+an angle theta and similarly 0 1 will
+ 
+
+ align:start position:0%
+an angle theta and similarly 0 1 will
+get rotated through an angle theta 2
+
+ align:start position:0%
+get rotated through an angle theta 2
+ 
+
+ align:start position:0%
+get rotated through an angle theta 2
+there so the whole plane rotates oh that
+
+ align:start position:0%
+there so the whole plane rotates oh that
+ 
+
+ align:start position:0%
+there so the whole plane rotates oh that
+makes me remember a highly important
+
+ align:start position:0%
+makes me remember a highly important
+ 
+
+ align:start position:0%
+makes me remember a highly important
+very important property of Q it doesn't
+
+ align:start position:0%
+very important property of Q it doesn't
+ 
+
+ align:start position:0%
+very important property of Q it doesn't
+change length the length of any vector
+
+ align:start position:0%
+change length the length of any vector
+ 
+
+ align:start position:0%
+change length the length of any vector
+is the same after you rotate it the
+
+ align:start position:0%
+is the same after you rotate it the
+ 
+
+ align:start position:0%
+is the same after you rotate it the
+length of any vector is the same after
+
+ align:start position:0%
+length of any vector is the same after
+ 
+
+ align:start position:0%
+length of any vector is the same after
+you multiply by Q can I just do that
+
+ align:start position:0%
+you multiply by Q can I just do that
+ 
+
+ align:start position:0%
+you multiply by Q can I just do that
+I claim any X any vector X I want to
+
+ align:start position:0%
+I claim any X any vector X I want to
+ 
+
+ align:start position:0%
+I claim any X any vector X I want to
+look at the length of Q X and I claim
+
+ align:start position:0%
+look at the length of Q X and I claim
+ 
+
+ align:start position:0%
+look at the length of Q X and I claim
+that it has the same length as X
+
+ align:start position:0%
+that it has the same length as X
+ 
+
+ align:start position:0%
+that it has the same length as X
+actually that's the reason in
+
+ align:start position:0%
+actually that's the reason in
+ 
+
+ align:start position:0%
+actually that's the reason in
+computations that orthogonal matrix are
+
+ align:start position:0%
+computations that orthogonal matrix are
+ 
+
+ align:start position:0%
+computations that orthogonal matrix are
+so much loved because no overflow can
+
+ align:start position:0%
+so much loved because no overflow can
+ 
+
+ align:start position:0%
+so much loved because no overflow can
+happen with orthogonal matrices lengths
+
+ align:start position:0%
+happen with orthogonal matrices lengths
+ 
+
+ align:start position:0%
+happen with orthogonal matrices lengths
+don't change I can multiply by any
+
+ align:start position:0%
+don't change I can multiply by any
+ 
+
+ align:start position:0%
+don't change I can multiply by any
+number of orthogonal matrices and the
+
+ align:start position:0%
+number of orthogonal matrices and the
+ 
+
+ align:start position:0%
+number of orthogonal matrices and the
+lengths don't change can we just see why
+
+ align:start position:0%
+lengths don't change can we just see why
+ 
+
+ align:start position:0%
+lengths don't change can we just see why
+that's true how would you so what do we
+
+ align:start position:0%
+that's true how would you so what do we
+ 
+
+ align:start position:0%
+that's true how would you so what do we
+have to go on we
+
+ align:start position:0%
+have to go on we
+ 
+
+ align:start position:0%
+have to go on we
+what we have to go on is Q transpose Q
+
+ align:start position:0%
+what we have to go on is Q transpose Q
+ 
+
+ align:start position:0%
+what we have to go on is Q transpose Q
+equal I whenever we're gonna prove it's
+
+ align:start position:0%
+equal I whenever we're gonna prove it's
+ 
+
+ align:start position:0%
+equal I whenever we're gonna prove it's
+got to come out of that because that's
+
+ align:start position:0%
+got to come out of that because that's
+ 
+
+ align:start position:0%
+got to come out of that because that's
+all we know so how do I use that to get
+
+ align:start position:0%
+all we know so how do I use that to get
+ 
+
+ align:start position:0%
+all we know so how do I use that to get
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+well we haven't said a whole lot about
+
+ align:start position:0%
+well we haven't said a whole lot about
+ 
+
+ align:start position:0%
+well we haven't said a whole lot about
+lengths but you'll see it all now it'll
+
+ align:start position:0%
+lengths but you'll see it all now it'll
+ 
+
+ align:start position:0%
+lengths but you'll see it all now it'll
+be easier to prove that the squares are
+
+ align:start position:0%
+be easier to prove that the squares are
+ 
+
+ align:start position:0%
+be easier to prove that the squares are
+the same so what's the what's the matrix
+
+ align:start position:0%
+the same so what's the what's the matrix
+ 
+
+ align:start position:0%
+the same so what's the what's the matrix
+expression for the length squared what's
+
+ align:start position:0%
+expression for the length squared what's
+ 
+
+ align:start position:0%
+expression for the length squared what's
+what's the right-hand side of that
+
+ align:start position:0%
+what's the right-hand side of that
+ 
+
+ align:start position:0%
+what's the right-hand side of that
+equation X transpose X right X transpose
+
+ align:start position:0%
+equation X transpose X right X transpose
+ 
+
+ align:start position:0%
+equation X transpose X right X transpose
+X gives me the sum of the squares
+
+ align:start position:0%
+X gives me the sum of the squares
+ 
+
+ align:start position:0%
+X gives me the sum of the squares
+Pythagoras says that's the length
+
+ align:start position:0%
+Pythagoras says that's the length
+ 
+
+ align:start position:0%
+Pythagoras says that's the length
+squared so that right hand side is X
+
+ align:start position:0%
+squared so that right hand side is X
+ 
+
+ align:start position:0%
+squared so that right hand side is X
+transpose X what's the left side
+
+ align:start position:0%
+transpose X what's the left side
+ 
+
+ align:start position:0%
+transpose X what's the left side
+it's a length squared of this of QX so
+
+ align:start position:0%
+it's a length squared of this of QX so
+ 
+
+ align:start position:0%
+it's a length squared of this of QX so
+it must be the same as hue X transpose
+
+ align:start position:0%
+it must be the same as hue X transpose
+ 
+
+ align:start position:0%
+it must be the same as hue X transpose
+QX and the claim is that that equation
+
+ align:start position:0%
+QX and the claim is that that equation
+ 
+
+ align:start position:0%
+QX and the claim is that that equation
+holds and do you see it
+
+ align:start position:0%
+holds and do you see it
+ 
+
+ align:start position:0%
+holds and do you see it
+whereís so any property if from Q is
+
+ align:start position:0%
+whereís so any property if from Q is
+ 
+
+ align:start position:0%
+whereís so any property if from Q is
+going to has to just come out directly
+
+ align:start position:0%
+going to has to just come out directly
+ 
+
+ align:start position:0%
+going to has to just come out directly
+from that where is it here do I just
+
+ align:start position:0%
+from that where is it here do I just
+ 
+
+ align:start position:0%
+from that where is it here do I just
+like push away a little bit at that left
+
+ align:start position:0%
+like push away a little bit at that left
+ 
+
+ align:start position:0%
+like push away a little bit at that left
+hand side and see it
+
+ align:start position:0%
+hand side and see it
+ 
+
+ align:start position:0%
+hand side and see it
+QX transpose is the same as X transpose
+
+ align:start position:0%
+QX transpose is the same as X transpose
+ 
+
+ align:start position:0%
+QX transpose is the same as X transpose
+Q transpose and QX is QX and now I'm
+
+ align:start position:0%
+Q transpose and QX is QX and now I'm
+ 
+
+ align:start position:0%
+Q transpose and QX is QX and now I'm
+seeing well you might say wait a minute
+
+ align:start position:0%
+seeing well you might say wait a minute
+ 
+
+ align:start position:0%
+seeing well you might say wait a minute
+the parentheses were there and there but
+
+ align:start position:0%
+the parentheses were there and there but
+ 
+
+ align:start position:0%
+the parentheses were there and there but
+I say the most important law for matrix
+
+ align:start position:0%
+I say the most important law for matrix
+ 
+
+ align:start position:0%
+I say the most important law for matrix
+multiplication is you can move
+
+ align:start position:0%
+multiplication is you can move
+ 
+
+ align:start position:0%
+multiplication is you can move
+parentheses or throw them away let's
+
+ align:start position:0%
+parentheses or throw them away let's
+ 
+
+ align:start position:0%
+parentheses or throw them away let's
+roam away so in here I'm seeing Q
+
+ align:start position:0%
+roam away so in here I'm seeing Q
+ 
+
+ align:start position:0%
+roam away so in here I'm seeing Q
+transpose Q which is the identity so
+
+ align:start position:0%
+transpose Q which is the identity so
+ 
+
+ align:start position:0%
+transpose Q which is the identity so
+it's it's true yeah so that means that
+
+ align:start position:0%
+it's it's true yeah so that means that
+ 
+
+ align:start position:0%
+it's it's true yeah so that means that
+you're never underflow or overflow when
+
+ align:start position:0%
+you're never underflow or overflow when
+ 
+
+ align:start position:0%
+you're never underflow or overflow when
+you're multiplying by Q every numerical
+
+ align:start position:0%
+you're multiplying by Q every numerical
+ 
+
+ align:start position:0%
+you're multiplying by Q every numerical
+algorithm is written to use orthogonal
+
+ align:start position:0%
+algorithm is written to use orthogonal
+ 
+
+ align:start position:0%
+algorithm is written to use orthogonal
+matrices if wherever it can can okay and
+
+ align:start position:0%
+matrices if wherever it can can okay and
+ 
+
+ align:start position:0%
+matrices if wherever it can can okay and
+here's the first example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think maybe good for me to think of
+
+ align:start position:0%
+I think maybe good for me to think of
+ 
+
+ align:start position:0%
+I think maybe good for me to think of
+other examples or for us to think of
+
+ align:start position:0%
+other examples or for us to think of
+ 
+
+ align:start position:0%
+other examples or for us to think of
+other examples of orthogonal matrices so
+
+ align:start position:0%
+other examples of orthogonal matrices so
+ 
+
+ align:start position:0%
+other examples of orthogonal matrices so
+I'm using that word orthogonal matrix I
+
+ align:start position:0%
+I'm using that word orthogonal matrix I
+ 
+
+ align:start position:0%
+I'm using that word orthogonal matrix I
+should it really should we should really
+
+ align:start position:0%
+should it really should we should really
+ 
+
+ align:start position:0%
+should it really should we should really
+be saying orthonormal and I'm really
+
+ align:start position:0%
+be saying orthonormal and I'm really
+ 
+
+ align:start position:0%
+be saying orthonormal and I'm really
+thinking mostly of square ones so so the
+
+ align:start position:0%
+thinking mostly of square ones so so the
+ 
+
+ align:start position:0%
+thinking mostly of square ones so so the
+so in the square case when Q transpose
+
+ align:start position:0%
+so in the square case when Q transpose
+ 
+
+ align:start position:0%
+so in the square case when Q transpose
+is Q inverse of course that fact makes
+
+ align:start position:0%
+is Q inverse of course that fact makes
+ 
+
+ align:start position:0%
+is Q inverse of course that fact makes
+it easy to solve all equations that have
+
+ align:start position:0%
+it easy to solve all equations that have
+ 
+
+ align:start position:0%
+it easy to solve all equations that have
+Q as a coefficient matrix because you
+
+ align:start position:0%
+Q as a coefficient matrix because you
+ 
+
+ align:start position:0%
+Q as a coefficient matrix because you
+want the inverse and you just use the
+
+ align:start position:0%
+want the inverse and you just use the
+ 
+
+ align:start position:0%
+want the inverse and you just use the
+transpose okay let's just take a some
+
+ align:start position:0%
+transpose okay let's just take a some
+ 
+
+ align:start position:0%
+transpose okay let's just take a some
+minutes to think of examples of Q's if
+
+ align:start position:0%
+minutes to think of examples of Q's if
+ 
+
+ align:start position:0%
+minutes to think of examples of Q's if
+they're so important there have to be
+
+ align:start position:0%
+they're so important there have to be
+ 
+
+ align:start position:0%
+they're so important there have to be
+interesting examples and that was a
+
+ align:start position:0%
+interesting examples and that was a
+ 
+
+ align:start position:0%
+interesting examples and that was a
+first one now there's one more
+
+ align:start position:0%
+first one now there's one more
+ 
+
+ align:start position:0%
+first one now there's one more
+two-by-two example that I that you
+
+ align:start position:0%
+two-by-two example that I that you
+ 
+
+ align:start position:0%
+two-by-two example that I that you
+should know do you know what that would
+
+ align:start position:0%
+should know do you know what that would
+ 
+
+ align:start position:0%
+should know do you know what that would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+so another this will be example two and
+
+ align:start position:0%
+so another this will be example two and
+ 
+
+ align:start position:0%
+so another this will be example two and
+it's also going to be only two by two
+
+ align:start position:0%
+it's also going to be only two by two
+ 
+
+ align:start position:0%
+it's also going to be only two by two
+and real and what possibility have I got
+
+ align:start position:0%
+and real and what possibility have I got
+ 
+
+ align:start position:0%
+and real and what possibility have I got
+left here I'll use the same first column
+
+ align:start position:0%
+left here I'll use the same first column
+ 
+
+ align:start position:0%
+left here I'll use the same first column
+cos theta sine theta because that's more
+
+ align:start position:0%
+cos theta sine theta because that's more
+ 
+
+ align:start position:0%
+cos theta sine theta because that's more
+or less any any unit vector in two
+
+ align:start position:0%
+or less any any unit vector in two
+ 
+
+ align:start position:0%
+or less any any unit vector in two
+dimensions this has got that form so
+
+ align:start position:0%
+dimensions this has got that form so
+ 
+
+ align:start position:0%
+dimensions this has got that form so
+what do you propose for the second
+
+ align:start position:0%
+what do you propose for the second
+ 
+
+ align:start position:0%
+what do you propose for the second
+column
+
+ align:start position:0%
+column
+ 
+
+ align:start position:0%
+column
+yes yeah put the put the minus sign down
+
+ align:start position:0%
+yes yeah put the put the minus sign down
+ 
+
+ align:start position:0%
+yes yeah put the put the minus sign down
+here so you think does that make any
+
+ align:start position:0%
+here so you think does that make any
+ 
+
+ align:start position:0%
+here so you think does that make any
+difference so sine theta and minus cos
+
+ align:start position:0%
+difference so sine theta and minus cos
+ 
+
+ align:start position:0%
+difference so sine theta and minus cos
+theta I don't know if you've ever looked
+
+ align:start position:0%
+theta I don't know if you've ever looked
+ 
+
+ align:start position:0%
+theta I don't know if you've ever looked
+at that matrix you know we're trying to
+
+ align:start position:0%
+at that matrix you know we're trying to
+ 
+
+ align:start position:0%
+at that matrix you know we're trying to
+collect together a few matrices that are
+
+ align:start position:0%
+collect together a few matrices that are
+ 
+
+ align:start position:0%
+collect together a few matrices that are
+worth knowing are worth looking at okay
+
+ align:start position:0%
+worth knowing are worth looking at okay
+ 
+
+ align:start position:0%
+worth knowing are worth looking at okay
+now what kind of what's happened here
+
+ align:start position:0%
+now what kind of what's happened here
+ 
+
+ align:start position:0%
+now what kind of what's happened here
+you may say that was a trivial change
+
+ align:start position:0%
+you may say that was a trivial change
+ 
+
+ align:start position:0%
+you may say that was a trivial change
+which it kind of was but it's a
+
+ align:start position:0%
+which it kind of was but it's a
+ 
+
+ align:start position:0%
+which it kind of was but it's a
+different matrix now it's not a rotation
+
+ align:start position:0%
+different matrix now it's not a rotation
+ 
+
+ align:start position:0%
+different matrix now it's not a rotation
+anymore
+
+ align:start position:0%
+anymore
+ 
+
+ align:start position:0%
+anymore
+that's not a rote
+
+ align:start position:0%
+that's not a rote
+ 
+
+ align:start position:0%
+that's not a rote
+and yeah somehow now it's symmetric and
+
+ align:start position:0%
+and yeah somehow now it's symmetric and
+ 
+
+ align:start position:0%
+and yeah somehow now it's symmetric and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah what its eigenvectors must be
+
+ align:start position:0%
+yeah what its eigenvectors must be
+ 
+
+ align:start position:0%
+yeah what its eigenvectors must be
+something or other we'll get to those
+
+ align:start position:0%
+something or other we'll get to those
+ 
+
+ align:start position:0%
+something or other we'll get to those
+but what did what does that matrix do I
+
+ align:start position:0%
+but what did what does that matrix do I
+ 
+
+ align:start position:0%
+but what did what does that matrix do I
+don't know I don't know if you've seen
+
+ align:start position:0%
+don't know I don't know if you've seen
+ 
+
+ align:start position:0%
+don't know I don't know if you've seen
+it if you haven't it's not it doesn't
+
+ align:start position:0%
+it if you haven't it's not it doesn't
+ 
+
+ align:start position:0%
+it if you haven't it's not it doesn't
+jump out but it's a important case this
+
+ align:start position:0%
+jump out but it's a important case this
+ 
+
+ align:start position:0%
+jump out but it's a important case this
+is a reflection matrix notice that it's
+
+ align:start position:0%
+is a reflection matrix notice that it's
+ 
+
+ align:start position:0%
+is a reflection matrix notice that it's
+determined it is minus 1 you have minus
+
+ align:start position:0%
+determined it is minus 1 you have minus
+ 
+
+ align:start position:0%
+determined it is minus 1 you have minus
+cos squared theta minus sine squared
+
+ align:start position:0%
+cos squared theta minus sine squared
+ 
+
+ align:start position:0%
+cos squared theta minus sine squared
+theta it's determinate is minus 1
+
+ align:start position:0%
+theta it's determinate is minus 1
+ 
+
+ align:start position:0%
+theta it's determinate is minus 1
+there's some some some eigenvalue it
+
+ align:start position:0%
+there's some some some eigenvalue it
+ 
+
+ align:start position:0%
+there's some some some eigenvalue it
+coming up with that that's got a - yeah
+
+ align:start position:0%
+coming up with that that's got a - yeah
+ 
+
+ align:start position:0%
+coming up with that that's got a - yeah
+ok so what do I mean by a reflection
+
+ align:start position:0%
+ok so what do I mean by a reflection
+ 
+
+ align:start position:0%
+ok so what do I mean by a reflection
+matrix let me draw the plane and I think
+
+ align:start position:0%
+matrix let me draw the plane and I think
+ 
+
+ align:start position:0%
+matrix let me draw the plane and I think
+so so 1 0 let's follow it follow again 1
+
+ align:start position:0%
+so so 1 0 let's follow it follow again 1
+ 
+
+ align:start position:0%
+so so 1 0 let's follow it follow again 1
+0 where does that go
+
+ align:start position:0%
+0 where does that go
+ 
+
+ align:start position:0%
+0 where does that go
+that gives me the first column so as
+
+ align:start position:0%
+that gives me the first column so as
+ 
+
+ align:start position:0%
+that gives me the first column so as
+before it goes to cos theta sine theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when I say reflection let me put put
+
+ align:start position:0%
+and when I say reflection let me put put
+ 
+
+ align:start position:0%
+and when I say reflection let me put put
+the the mirror into the picture so you
+
+ align:start position:0%
+the the mirror into the picture so you
+ 
+
+ align:start position:0%
+the the mirror into the picture so you
+see what reflection it is the mirror is
+
+ align:start position:0%
+see what reflection it is the mirror is
+ 
+
+ align:start position:0%
+see what reflection it is the mirror is
+is along here at angle fate / - stayed
+
+ align:start position:0%
+is along here at angle fate / - stayed
+ 
+
+ align:start position:0%
+is along here at angle fate / - stayed
+over to live so sure enough 1 0 at angle
+
+ align:start position:0%
+over to live so sure enough 1 0 at angle
+ 
+
+ align:start position:0%
+over to live so sure enough 1 0 at angle
+0 got reflected into a unit vector at
+
+ align:start position:0%
+0 got reflected into a unit vector at
+ 
+
+ align:start position:0%
+0 got reflected into a unit vector at
+angle theta and halfway between was the
+
+ align:start position:0%
+angle theta and halfway between was the
+ 
+
+ align:start position:0%
+angle theta and halfway between was the
+saito virtu line that's that's not
+
+ align:start position:0%
+saito virtu line that's that's not
+ 
+
+ align:start position:0%
+saito virtu line that's that's not
+that's okay now what about the other guy
+
+ align:start position:0%
+that's okay now what about the other guy
+ 
+
+ align:start position:0%
+that's okay now what about the other guy
+0 1
+
+ align:start position:0%
+0 1
+ 
+
+ align:start position:0%
+0 1
+here's 0 1 ok I multiply that can I put
+
+ align:start position:0%
+here's 0 1 ok I multiply that can I put
+ 
+
+ align:start position:0%
+here's 0 1 ok I multiply that can I put
+the 0 1 up here so you just your eye
+
+ align:start position:0%
+the 0 1 up here so you just your eye
+ 
+
+ align:start position:0%
+the 0 1 up here so you just your eye
+does the multiplication where is the
+
+ align:start position:0%
+does the multiplication where is the
+ 
+
+ align:start position:0%
+does the multiplication where is the
+result of 0 1 what's the output from
+
+ align:start position:0%
+result of 0 1 what's the output from
+ 
+
+ align:start position:0%
+result of 0 1 what's the output from
+from cue applied to zero one sine theta
+
+ align:start position:0%
+from cue applied to zero one sine theta
+ 
+
+ align:start position:0%
+from cue applied to zero one sine theta
+minus cos theta right it's the it's the
+
+ align:start position:0%
+minus cos theta right it's the it's the
+ 
+
+ align:start position:0%
+minus cos theta right it's the it's the
+second column and so where is that
+
+ align:start position:0%
+second column and so where is that
+ 
+
+ align:start position:0%
+second column and so where is that
+well it's perpendicular to that guy
+
+ align:start position:0%
+well it's perpendicular to that guy
+ 
+
+ align:start position:0%
+well it's perpendicular to that guy
+that's right I know right that was the
+
+ align:start position:0%
+that's right I know right that was the
+ 
+
+ align:start position:0%
+that's right I know right that was the
+point that the two columns are
+
+ align:start position:0%
+point that the two columns are
+ 
+
+ align:start position:0%
+point that the two columns are
+perpendicular so it's so it must go down
+
+ align:start position:0%
+perpendicular so it's so it must go down
+ 
+
+ align:start position:0%
+perpendicular so it's so it must go down
+this way right sine theta cos theta and
+
+ align:start position:0%
+this way right sine theta cos theta and
+ 
+
+ align:start position:0%
+this way right sine theta cos theta and
+it doesn't change lengths all these
+
+ align:start position:0%
+it doesn't change lengths all these
+ 
+
+ align:start position:0%
+it doesn't change lengths all these
+facts that we just learned are key so
+
+ align:start position:0%
+facts that we just learned are key so
+ 
+
+ align:start position:0%
+facts that we just learned are key so
+there's there's zero one and it goes to
+
+ align:start position:0%
+there's there's zero one and it goes to
+ 
+
+ align:start position:0%
+there's there's zero one and it goes to
+this guy which is whatever that second
+
+ align:start position:0%
+this guy which is whatever that second
+ 
+
+ align:start position:0%
+this guy which is whatever that second
+column is sine theta minus cos theta and
+
+ align:start position:0%
+column is sine theta minus cos theta and
+ 
+
+ align:start position:0%
+column is sine theta minus cos theta and
+if you check that actually like plain
+
+ align:start position:0%
+if you check that actually like plain
+ 
+
+ align:start position:0%
+if you check that actually like plain
+geometry I believe never occurred to me
+
+ align:start position:0%
+geometry I believe never occurred to me
+ 
+
+ align:start position:0%
+geometry I believe never occurred to me
+before but I believe it that that this
+
+ align:start position:0%
+before but I believe it that that this
+ 
+
+ align:start position:0%
+before but I believe it that that this
+angle going down to there that that goes
+
+ align:start position:0%
+angle going down to there that that goes
+ 
+
+ align:start position:0%
+angle going down to there that that goes
+straight through and that the halfway
+
+ align:start position:0%
+straight through and that the halfway
+ 
+
+ align:start position:0%
+straight through and that the halfway
+one is that line yeah I think that
+
+ align:start position:0%
+one is that line yeah I think that
+ 
+
+ align:start position:0%
+one is that line yeah I think that
+picture is got it and I think it's in
+
+ align:start position:0%
+picture is got it and I think it's in
+ 
+
+ align:start position:0%
+picture is got it and I think it's in
+the note so that's a reflection matrix
+
+ align:start position:0%
+the note so that's a reflection matrix
+ 
+
+ align:start position:0%
+the note so that's a reflection matrix
+well that's a two-by-two reflection
+
+ align:start position:0%
+well that's a two-by-two reflection
+ 
+
+ align:start position:0%
+well that's a two-by-two reflection
+matrix would you like to see some other
+
+ align:start position:0%
+matrix would you like to see some other
+ 
+
+ align:start position:0%
+matrix would you like to see some other
+matrices like this one but but larger
+
+ align:start position:0%
+matrices like this one but but larger
+ 
+
+ align:start position:0%
+matrices like this one but but larger
+they're named after a guy named
+
+ align:start position:0%
+they're named after a guy named
+ 
+
+ align:start position:0%
+they're named after a guy named
+householder so these are householder
+
+ align:start position:0%
+householder so these are householder
+ 
+
+ align:start position:0%
+householder so these are householder
+reflections what am I doing here I'm
+
+ align:start position:0%
+reflections what am I doing here I'm
+ 
+
+ align:start position:0%
+reflections what am I doing here I'm
+collecting together some orthogonal
+
+ align:start position:0%
+collecting together some orthogonal
+ 
+
+ align:start position:0%
+collecting together some orthogonal
+matrices that are useful and important
+
+ align:start position:0%
+matrices that are useful and important
+ 
+
+ align:start position:0%
+matrices that are useful and important
+and householder found a whole bunch of
+
+ align:start position:0%
+and householder found a whole bunch of
+ 
+
+ align:start position:0%
+and householder found a whole bunch of
+them and and his algorithm is a much
+
+ align:start position:0%
+them and and his algorithm is a much
+ 
+
+ align:start position:0%
+them and and his algorithm is a much
+used part of numerical linear algebra so
+
+ align:start position:0%
+used part of numerical linear algebra so
+ 
+
+ align:start position:0%
+used part of numerical linear algebra so
+he started with a unit vector start with
+
+ align:start position:0%
+he started with a unit vector start with
+ 
+
+ align:start position:0%
+he started with a unit vector start with
+a unit vector
+
+ align:start position:0%
+a unit vector
+ 
+
+ align:start position:0%
+a unit vector
+you transpose u equal 1 so the length of
+
+ align:start position:0%
+you transpose u equal 1 so the length of
+ 
+
+ align:start position:0%
+you transpose u equal 1 so the length of
+the vector is 1 and then he created
+
+ align:start position:0%
+the vector is 1 and then he created
+ 
+
+ align:start position:0%
+the vector is 1 and then he created
+let's name it after him H he created
+
+ align:start position:0%
+let's name it after him H he created
+ 
+
+ align:start position:0%
+let's name it after him H he created
+this matrix the identity minus 2 uu
+
+ align:start position:0%
+this matrix the identity minus 2 uu
+ 
+
+ align:start position:0%
+this matrix the identity minus 2 uu
+transpose and I believe that that's a
+
+ align:start position:0%
+transpose and I believe that that's a
+ 
+
+ align:start position:0%
+transpose and I believe that that's a
+really useful matrix so it's just like I
+
+ align:start position:0%
+really useful matrix so it's just like I
+ 
+
+ align:start position:0%
+really useful matrix so it's just like I
+think this review is like going beyond
+
+ align:start position:0%
+think this review is like going beyond
+ 
+
+ align:start position:0%
+think this review is like going beyond
+1806 into what is what ones are really
+
+ align:start position:0%
+1806 into what is what ones are really
+ 
+
+ align:start position:0%
+1806 into what is what ones are really
+worth knowing that worth knowing
+
+ align:start position:0%
+worth knowing that worth knowing
+ 
+
+ align:start position:0%
+worth knowing that worth knowing
+individually ok could we just check what
+
+ align:start position:0%
+individually ok could we just check what
+ 
+
+ align:start position:0%
+individually ok could we just check what
+are the properties of house holders
+
+ align:start position:0%
+are the properties of house holders
+ 
+
+ align:start position:0%
+are the properties of house holders
+reflection of that I - to you you
+
+ align:start position:0%
+reflection of that I - to you you
+ 
+
+ align:start position:0%
+reflection of that I - to you you
+recognize here column times a row so
+
+ align:start position:0%
+recognize here column times a row so
+ 
+
+ align:start position:0%
+recognize here column times a row so
+that's a matrix and what kind of what
+
+ align:start position:0%
+that's a matrix and what kind of what
+ 
+
+ align:start position:0%
+that's a matrix and what kind of what
+could you tell me about that matrix u u
+
+ align:start position:0%
+could you tell me about that matrix u u
+ 
+
+ align:start position:0%
+could you tell me about that matrix u u
+transpose it's yeah so uh or what what
+
+ align:start position:0%
+transpose it's yeah so uh or what what
+ 
+
+ align:start position:0%
+transpose it's yeah so uh or what what
+can we say about about about H so I
+
+ align:start position:0%
+can we say about about about H so I
+ 
+
+ align:start position:0%
+can we say about about about H so I
+guess I'm believing that H is a
+
+ align:start position:0%
+guess I'm believing that H is a
+ 
+
+ align:start position:0%
+guess I'm believing that H is a
+orthogonal matrix otherwise it wouldn't
+
+ align:start position:0%
+orthogonal matrix otherwise it wouldn't
+ 
+
+ align:start position:0%
+orthogonal matrix otherwise it wouldn't
+be here today
+
+ align:start position:0%
+be here today
+ 
+
+ align:start position:0%
+be here today
+so I believe that and that not only is
+
+ align:start position:0%
+so I believe that and that not only is
+ 
+
+ align:start position:0%
+so I believe that and that not only is
+it orthogonal it is also have a look at
+
+ align:start position:0%
+it orthogonal it is also have a look at
+ 
+
+ align:start position:0%
+it orthogonal it is also have a look at
+it symmetric it's also symmetric the
+
+ align:start position:0%
+it symmetric it's also symmetric the
+ 
+
+ align:start position:0%
+it symmetric it's also symmetric the
+identity symmetric uu transpose is
+
+ align:start position:0%
+identity symmetric uu transpose is
+ 
+
+ align:start position:0%
+identity symmetric uu transpose is
+symmetric so that this is a family of
+
+ align:start position:0%
+symmetric so that this is a family of
+ 
+
+ align:start position:0%
+symmetric so that this is a family of
+symmetric orthogonal matrices and that
+
+ align:start position:0%
+symmetric orthogonal matrices and that
+ 
+
+ align:start position:0%
+symmetric orthogonal matrices and that
+was one of them that's a symmetric
+
+ align:start position:0%
+was one of them that's a symmetric
+ 
+
+ align:start position:0%
+was one of them that's a symmetric
+orthogonal matrix these matrices are
+
+ align:start position:0%
+orthogonal matrix these matrices are
+ 
+
+ align:start position:0%
+orthogonal matrix these matrices are
+really great to have you just like in in
+
+ align:start position:0%
+really great to have you just like in in
+ 
+
+ align:start position:0%
+really great to have you just like in in
+using linear algebra it's you just get a
+
+ align:start position:0%
+using linear algebra it's you just get a
+ 
+
+ align:start position:0%
+using linear algebra it's you just get a
+collection of useful matrices that you
+
+ align:start position:0%
+collection of useful matrices that you
+ 
+
+ align:start position:0%
+collection of useful matrices that you
+can call on and these are definitely one
+
+ align:start position:0%
+can call on and these are definitely one
+ 
+
+ align:start position:0%
+can call on and these are definitely one
+family well it's obviously symmetric
+
+ align:start position:0%
+family well it's obviously symmetric
+ 
+
+ align:start position:0%
+family well it's obviously symmetric
+shall we check that it's orthogonal so
+
+ align:start position:0%
+shall we check that it's orthogonal so
+ 
+
+ align:start position:0%
+shall we check that it's orthogonal so
+to check that it's orthogonal I just so
+
+ align:start position:0%
+to check that it's orthogonal I just so
+ 
+
+ align:start position:0%
+to check that it's orthogonal I just so
+I'm going to check that H transpose H is
+
+ align:start position:0%
+I'm going to check that H transpose H is
+ 
+
+ align:start position:0%
+I'm going to check that H transpose H is
+the identity can I just check that
+
+ align:start position:0%
+the identity can I just check that
+ 
+
+ align:start position:0%
+the identity can I just check that
+well H transpose is the same as H
+
+ align:start position:0%
+well H transpose is the same as H
+ 
+
+ align:start position:0%
+well H transpose is the same as H
+because it was symmetric so I'm gonna
+
+ align:start position:0%
+because it was symmetric so I'm gonna
+ 
+
+ align:start position:0%
+because it was symmetric so I'm gonna
+square this guy this is really H times H
+
+ align:start position:0%
+square this guy this is really H times H
+ 
+
+ align:start position:0%
+square this guy this is really H times H
+I'm squaring it and what do I get if I
+
+ align:start position:0%
+I'm squaring it and what do I get if I
+ 
+
+ align:start position:0%
+I'm squaring it and what do I get if I
+square so so I get I hope I get the
+
+ align:start position:0%
+square so so I get I hope I get the
+ 
+
+ align:start position:0%
+square so so I get I hope I get the
+identity but let's see it what do I get
+
+ align:start position:0%
+identity but let's see it what do I get
+ 
+
+ align:start position:0%
+identity but let's see it what do I get
+when I Square this get little multiply
+
+ align:start position:0%
+when I Square this get little multiply
+ 
+
+ align:start position:0%
+when I Square this get little multiply
+it out
+
+ align:start position:0%
+it out
+ 
+
+ align:start position:0%
+it out
+so I times I is I and then I get some
+
+ align:start position:0%
+so I times I is I and then I get some
+ 
+
+ align:start position:0%
+so I times I is I and then I get some
+number of uu transpose this how many do
+
+ align:start position:0%
+number of uu transpose this how many do
+ 
+
+ align:start position:0%
+number of uu transpose this how many do
+I get for that from that so I'm squaring
+
+ align:start position:0%
+I get for that from that so I'm squaring
+ 
+
+ align:start position:0%
+I get for that from that so I'm squaring
+this thing because H transpose H is the
+
+ align:start position:0%
+this thing because H transpose H is the
+ 
+
+ align:start position:0%
+this thing because H transpose H is the
+same as H times H so I'm squaring it so
+
+ align:start position:0%
+same as H times H so I'm squaring it so
+ 
+
+ align:start position:0%
+same as H times H so I'm squaring it so
+how many what do I put here for thanks
+
+ align:start position:0%
+how many what do I put here for thanks
+ 
+
+ align:start position:0%
+how many what do I put here for thanks
+and now I've got this guy squared with a
+
+ align:start position:0%
+and now I've got this guy squared with a
+ 
+
+ align:start position:0%
+and now I've got this guy squared with a
+plus so that's four uu transpose uu
+
+ align:start position:0%
+plus so that's four uu transpose uu
+ 
+
+ align:start position:0%
+plus so that's four uu transpose uu
+transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I'm totally realizing I've
+
+ align:start position:0%
+yeah I'm totally realizing I've
+ 
+
+ align:start position:0%
+yeah I'm totally realizing I've
+practiced for a lifetime doing these
+
+ align:start position:0%
+practiced for a lifetime doing these
+ 
+
+ align:start position:0%
+practiced for a lifetime doing these
+dinky little calculations but they are
+
+ align:start position:0%
+dinky little calculations but they are
+ 
+
+ align:start position:0%
+dinky little calculations but they are
+dinky and you'll get the hang of it
+
+ align:start position:0%
+dinky and you'll get the hang of it
+ 
+
+ align:start position:0%
+dinky and you'll get the hang of it
+quickly now what am i hoping out of that
+
+ align:start position:0%
+quickly now what am i hoping out of that
+ 
+
+ align:start position:0%
+quickly now what am i hoping out of that
+bottom line that it is I hope you to get
+
+ align:start position:0%
+bottom line that it is I hope you to get
+ 
+
+ align:start position:0%
+bottom line that it is I hope you to get
+I do we get I yes we're who sees how to
+
+ align:start position:0%
+I do we get I yes we're who sees how to
+ 
+
+ align:start position:0%
+I do we get I yes we're who sees how to
+get eye out of that thing yeah u
+
+ align:start position:0%
+get eye out of that thing yeah u
+ 
+
+ align:start position:0%
+get eye out of that thing yeah u
+transpose u in here is a number that was
+
+ align:start position:0%
+transpose u in here is a number that was
+ 
+
+ align:start position:0%
+transpose u in here is a number that was
+you that was column times row times
+
+ align:start position:0%
+you that was column times row times
+ 
+
+ align:start position:0%
+you that was column times row times
+column times row and I look at the in
+
+ align:start position:0%
+column times row and I look at the in
+ 
+
+ align:start position:0%
+column times row and I look at the in
+the middle here is Rho times column and
+
+ align:start position:0%
+the middle here is Rho times column and
+ 
+
+ align:start position:0%
+the middle here is Rho times column and
+that's the number one right because it's
+
+ align:start position:0%
+that's the number one right because it's
+ 
+
+ align:start position:0%
+that's the number one right because it's
+there so that's one and then I have
+
+ align:start position:0%
+there so that's one and then I have
+ 
+
+ align:start position:0%
+there so that's one and then I have
+minus four of that plus four of that
+
+ align:start position:0%
+minus four of that plus four of that
+ 
+
+ align:start position:0%
+minus four of that plus four of that
+they cancel each other and I get I so
+
+ align:start position:0%
+they cancel each other and I get I so
+ 
+
+ align:start position:0%
+they cancel each other and I get I so
+those are good matrices we'll we'll use
+
+ align:start position:0%
+those are good matrices we'll we'll use
+ 
+
+ align:start position:0%
+those are good matrices we'll we'll use
+them we'll use them actually they're
+
+ align:start position:0%
+them we'll use them actually they're
+ 
+
+ align:start position:0%
+them we'll use them actually they're
+better than gram-schmidt so we'll use
+
+ align:start position:0%
+better than gram-schmidt so we'll use
+ 
+
+ align:start position:0%
+better than gram-schmidt so we'll use
+them in in making things orthogonal
+
+ align:start position:0%
+them in in making things orthogonal
+ 
+
+ align:start position:0%
+them in in making things orthogonal
+so what what other orthogonal matrices
+
+ align:start position:0%
+so what what other orthogonal matrices
+ 
+
+ align:start position:0%
+so what what other orthogonal matrices
+let's create some you know creating
+
+ align:start position:0%
+let's create some you know creating
+ 
+
+ align:start position:0%
+let's create some you know creating
+Gordo orthogonal matrices is you know
+
+ align:start position:0%
+Gordo orthogonal matrices is you know
+ 
+
+ align:start position:0%
+Gordo orthogonal matrices is you know
+it's it pays off let's think so there's
+
+ align:start position:0%
+it's it pays off let's think so there's
+ 
+
+ align:start position:0%
+it's it pays off let's think so there's
+a family named after this French guy who
+
+ align:start position:0%
+a family named after this French guy who
+ 
+
+ align:start position:0%
+a family named after this French guy who
+lived to a hundred he was a real old
+
+ align:start position:0%
+lived to a hundred he was a real old
+ 
+
+ align:start position:0%
+lived to a hundred he was a real old
+timer
+
+ align:start position:0%
+timer
+ 
+
+ align:start position:0%
+timer
+well MIT had a faculty member in math
+
+ align:start position:0%
+well MIT had a faculty member in math
+ 
+
+ align:start position:0%
+well MIT had a faculty member in math
+when I came professor strike who lived
+
+ align:start position:0%
+when I came professor strike who lived
+ 
+
+ align:start position:0%
+when I came professor strike who lived
+to a hundred and six and I heard him
+
+ align:start position:0%
+to a hundred and six and I heard him
+ 
+
+ align:start position:0%
+to a hundred and six and I heard him
+give a lecture at Brown University at
+
+ align:start position:0%
+give a lecture at Brown University at
+ 
+
+ align:start position:0%
+give a lecture at Brown University at
+age 100 and it was like perfect you
+
+ align:start position:0%
+age 100 and it was like perfect you
+ 
+
+ align:start position:0%
+age 100 and it was like perfect you
+could not have done it better so he's my
+
+ align:start position:0%
+could not have done it better so he's my
+ 
+
+ align:start position:0%
+could not have done it better so he's my
+inspiration I'm keep going I only have
+
+ align:start position:0%
+inspiration I'm keep going I only have
+ 
+
+ align:start position:0%
+inspiration I'm keep going I only have
+like 10 more years to get there well
+
+ align:start position:0%
+like 10 more years to get there well
+ 
+
+ align:start position:0%
+like 10 more years to get there well
+it's too many anyway okay Adam re all
+
+ align:start position:0%
+it's too many anyway okay Adam re all
+ 
+
+ align:start position:0%
+it's too many anyway okay Adam re all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so Adam art he created well that's the
+
+ align:start position:0%
+so Adam art he created well that's the
+ 
+
+ align:start position:0%
+so Adam art he created well that's the
+simplest the smallest now the next guy
+
+ align:start position:0%
+simplest the smallest now the next guy
+ 
+
+ align:start position:0%
+simplest the smallest now the next guy
+is gonna be four by four I'm going to
+
+ align:start position:0%
+is gonna be four by four I'm going to
+ 
+
+ align:start position:0%
+is gonna be four by four I'm going to
+put that so where I see a one I'm gonna
+
+ align:start position:0%
+put that so where I see a one I'm gonna
+ 
+
+ align:start position:0%
+put that so where I see a one I'm gonna
+put Adam artis 1 1 1 minus 1 1 1 1 minus
+
+ align:start position:0%
+put Adam artis 1 1 1 minus 1 1 1 1 minus
+ 
+
+ align:start position:0%
+put Adam artis 1 1 1 minus 1 1 1 1 minus
+1 and then when I see a minus I'm gonna
+
+ align:start position:0%
+1 and then when I see a minus I'm gonna
+ 
+
+ align:start position:0%
+1 and then when I see a minus I'm gonna
+put it in with a minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you saw that picture it was a picture of
+
+ align:start position:0%
+you saw that picture it was a picture of
+ 
+
+ align:start position:0%
+you saw that picture it was a picture of
+H 2 H 2 h 2 and minus H 2 that's what
+
+ align:start position:0%
+H 2 H 2 h 2 and minus H 2 that's what
+ 
+
+ align:start position:0%
+H 2 H 2 h 2 and minus H 2 that's what
+I've got there and I believe those
+
+ align:start position:0%
+I've got there and I believe those
+ 
+
+ align:start position:0%
+I've got there and I believe those
+columns are orthogonal right now what
+
+ align:start position:0%
+columns are orthogonal right now what
+ 
+
+ align:start position:0%
+columns are orthogonal right now what
+could I do
+
+ align:start position:0%
+could I do
+ 
+
+ align:start position:0%
+could I do
+well it's not quite an orthogonal matrix
+
+ align:start position:0%
+well it's not quite an orthogonal matrix
+ 
+
+ align:start position:0%
+well it's not quite an orthogonal matrix
+what do I have to do to make this isn't
+
+ align:start position:0%
+what do I have to do to make this isn't
+ 
+
+ align:start position:0%
+what do I have to do to make this isn't
+quite an orthogonal matrix either what
+
+ align:start position:0%
+quite an orthogonal matrix either what
+ 
+
+ align:start position:0%
+quite an orthogonal matrix either what
+what do I do to make that an orthogonal
+
+ align:start position:0%
+what do I do to make that an orthogonal
+ 
+
+ align:start position:0%
+what do I do to make that an orthogonal
+matrix /
+
+ align:start position:0%
+matrix /
+ 
+
+ align:start position:0%
+matrix /
+square root of two I need I need unit
+
+ align:start position:0%
+square root of two I need I need unit
+ 
+
+ align:start position:0%
+square root of two I need I need unit
+vectors there and here those lengths are
+
+ align:start position:0%
+vectors there and here those lengths are
+ 
+
+ align:start position:0%
+vectors there and here those lengths are
+1 squared 1 squared 4 square root of 4
+
+ align:start position:0%
+1 squared 1 squared 4 square root of 4
+ 
+
+ align:start position:0%
+1 squared 1 squared 4 square root of 4
+is 2 so I better divided by the 2 there
+
+ align:start position:0%
+is 2 so I better divided by the 2 there
+ 
+
+ align:start position:0%
+is 2 so I better divided by the 2 there
+and now here I'm gonna here I'm up to
+
+ align:start position:0%
+and now here I'm gonna here I'm up to
+ 
+
+ align:start position:0%
+and now here I'm gonna here I'm up to
+yeah so that was that one don't tell me
+
+ align:start position:0%
+yeah so that was that one don't tell me
+ 
+
+ align:start position:0%
+yeah so that was that one don't tell me
+the next one up what's that going to be
+
+ align:start position:0%
+the next one up what's that going to be
+ 
+
+ align:start position:0%
+the next one up what's that going to be
+8 by 8 what's that so this is H 4 here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops 4 so tell me what I should do 4 8
+
+ align:start position:0%
+oops 4 so tell me what I should do 4 8
+ 
+
+ align:start position:0%
+oops 4 so tell me what I should do 4 8
+by 8 you'll think this is like simple
+
+ align:start position:0%
+by 8 you'll think this is like simple
+ 
+
+ align:start position:0%
+by 8 you'll think this is like simple
+but that's that's a good thing to say
+
+ align:start position:0%
+but that's that's a good thing to say
+ 
+
+ align:start position:0%
+but that's that's a good thing to say
+about it you know they're in encoding
+
+ align:start position:0%
+about it you know they're in encoding
+ 
+
+ align:start position:0%
+about it you know they're in encoding
+theory all sorts of places you want
+
+ align:start position:0%
+theory all sorts of places you want
+ 
+
+ align:start position:0%
+theory all sorts of places you want
+matrices of ones and minus ones
+
+ align:start position:0%
+matrices of ones and minus ones
+ 
+
+ align:start position:0%
+matrices of ones and minus ones
+ok what's H 8 I'm gonna build it out of
+
+ align:start position:0%
+ok what's H 8 I'm gonna build it out of
+ 
+
+ align:start position:0%
+ok what's H 8 I'm gonna build it out of
+H 4 so what am I gonna what's it going
+
+ align:start position:0%
+H 4 so what am I gonna what's it going
+ 
+
+ align:start position:0%
+H 4 so what am I gonna what's it going
+to be I'm gonna put an H for there what
+
+ align:start position:0%
+to be I'm gonna put an H for there what
+ 
+
+ align:start position:0%
+to be I'm gonna put an H for there what
+am I going to put here another H 4 and
+
+ align:start position:0%
+am I going to put here another H 4 and
+ 
+
+ align:start position:0%
+am I going to put here another H 4 and
+up here another H 4 and finally here
+
+ align:start position:0%
+up here another H 4 and finally here
+ 
+
+ align:start position:0%
+up here another H 4 and finally here
+minus H and I think I've got orthogonal
+
+ align:start position:0%
+minus H and I think I've got orthogonal
+ 
+
+ align:start position:0%
+minus H and I think I've got orthogonal
+columns again right because the the
+
+ align:start position:0%
+columns again right because the the
+ 
+
+ align:start position:0%
+columns again right because the the
+columns within these dot products with
+
+ align:start position:0%
+columns within these dot products with
+ 
+
+ align:start position:0%
+columns within these dot products with
+themselves give 0 and 0 the dot products
+
+ align:start position:0%
+themselves give 0 and 0 the dot products
+ 
+
+ align:start position:0%
+themselves give 0 and 0 the dot products
+from these columns and these columns
+
+ align:start position:0%
+from these columns and these columns
+ 
+
+ align:start position:0%
+from these columns and these columns
+obviously have the minus and the dot
+
+ align:start position:0%
+obviously have the minus and the dot
+ 
+
+ align:start position:0%
+obviously have the minus and the dot
+products in here or 0 from that and 0
+
+ align:start position:0%
+products in here or 0 from that and 0
+ 
+
+ align:start position:0%
+products in here or 0 from that and 0
+from that yeah it works and we could
+
+ align:start position:0%
+from that yeah it works and we could
+ 
+
+ align:start position:0%
+from that yeah it works and we could
+keep going to 16 and 32 and 64 but then
+
+ align:start position:0%
+keep going to 16 and 32 and 64 but then
+ 
+
+ align:start position:0%
+keep going to 16 and 32 and 64 but then
+up comes a question what about H 12 is
+
+ align:start position:0%
+up comes a question what about H 12 is
+ 
+
+ align:start position:0%
+up comes a question what about H 12 is
+there ones and minus ones matrix of size
+
+ align:start position:0%
+there ones and minus ones matrix of size
+ 
+
+ align:start position:0%
+there ones and minus ones matrix of size
+12 12 by 12 it
+
+ align:start position:0%
+12 12 by 12 it
+ 
+
+ align:start position:0%
+12 12 by 12 it
+it doesn't come directly from our little
+
+ align:start position:0%
+it doesn't come directly from our little
+ 
+
+ align:start position:0%
+it doesn't come directly from our little
+pattern which is doubling size every
+
+ align:start position:0%
+pattern which is doubling size every
+ 
+
+ align:start position:0%
+pattern which is doubling size every
+time but you could still hope and it
+
+ align:start position:0%
+time but you could still hope and it
+ 
+
+ align:start position:0%
+time but you could still hope and it
+works there is a I don't know what it is
+
+ align:start position:0%
+works there is a I don't know what it is
+ 
+
+ align:start position:0%
+works there is a I don't know what it is
+but there's a there's a matrix of ones
+
+ align:start position:0%
+but there's a there's a matrix of ones
+ 
+
+ align:start position:0%
+but there's a there's a matrix of ones
+and minus ones orthogonal twelve
+
+ align:start position:0%
+and minus ones orthogonal twelve
+ 
+
+ align:start position:0%
+and minus ones orthogonal twelve
+orthogonal columns so the answer is yes
+
+ align:start position:0%
+orthogonal columns so the answer is yes
+ 
+
+ align:start position:0%
+orthogonal columns so the answer is yes
+okay so we make an 1806 five conjecture
+
+ align:start position:0%
+okay so we make an 1806 five conjecture
+ 
+
+ align:start position:0%
+okay so we make an 1806 five conjecture
+every matrix every matrix size well not
+
+ align:start position:0%
+every matrix every matrix size well not
+ 
+
+ align:start position:0%
+every matrix every matrix size well not
+every matrix size because 3x3 is not
+
+ align:start position:0%
+every matrix size because 3x3 is not
+ 
+
+ align:start position:0%
+every matrix size because 3x3 is not
+going to work one by one is not going to
+
+ align:start position:0%
+going to work one by one is not going to
+ 
+
+ align:start position:0%
+going to work one by one is not going to
+work either but age twelve works
+
+ align:start position:0%
+work either but age twelve works
+ 
+
+ align:start position:0%
+work either but age twelve works
+h/h sixteen what's our conjecture we
+
+ align:start position:0%
+h/h sixteen what's our conjecture we
+ 
+
+ align:start position:0%
+h/h sixteen what's our conjecture we
+won't be the first conjecture --it that
+
+ align:start position:0%
+won't be the first conjecture --it that
+ 
+
+ align:start position:0%
+won't be the first conjecture --it that
+there is a ones and minus ones
+
+ align:start position:0%
+there is a ones and minus ones
+ 
+
+ align:start position:0%
+there is a ones and minus ones
+orthogonal matrix with orthogonal
+
+ align:start position:0%
+orthogonal matrix with orthogonal
+ 
+
+ align:start position:0%
+orthogonal matrix with orthogonal
+columns of every size n so always so so
+
+ align:start position:0%
+columns of every size n so always so so
+ 
+
+ align:start position:0%
+columns of every size n so always so so
+I'll start to conjecture always possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and which is the size of the matrix
+
+ align:start position:0%
+if and which is the size of the matrix
+ 
+
+ align:start position:0%
+if and which is the size of the matrix
+let's say what would you guess just take
+
+ align:start position:0%
+let's say what would you guess just take
+ 
+
+ align:start position:0%
+let's say what would you guess just take
+a shot you won't be asked for a proof
+
+ align:start position:0%
+a shot you won't be asked for a proof
+ 
+
+ align:start position:0%
+a shot you won't be asked for a proof
+because nobody has the proof even well
+
+ align:start position:0%
+because nobody has the proof even well
+ 
+
+ align:start position:0%
+because nobody has the proof even well
+you could hope for even you could look
+
+ align:start position:0%
+you could hope for even you could look
+ 
+
+ align:start position:0%
+you could hope for even you could look
+for try six I guess would be the first
+
+ align:start position:0%
+for try six I guess would be the first
+ 
+
+ align:start position:0%
+for try six I guess would be the first
+guy there and I don't think it's
+
+ align:start position:0%
+guy there and I don't think it's
+ 
+
+ align:start position:0%
+guy there and I don't think it's
+possible I think six is not possible so
+
+ align:start position:0%
+possible I think six is not possible so
+ 
+
+ align:start position:0%
+possible I think six is not possible so
+every even sizes is I think not gonna
+
+ align:start position:0%
+every even sizes is I think not gonna
+ 
+
+ align:start position:0%
+every even sizes is I think not gonna
+work but it's natural idea to try what's
+
+ align:start position:0%
+work but it's natural idea to try what's
+ 
+
+ align:start position:0%
+work but it's natural idea to try what's
+the next thought every multiple of four
+
+ align:start position:0%
+the next thought every multiple of four
+ 
+
+ align:start position:0%
+the next thought every multiple of four
+if n over four is a whole number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but nobody has a way a systematic way
+
+ align:start position:0%
+so but nobody has a way a systematic way
+ 
+
+ align:start position:0%
+so but nobody has a way a systematic way
+to create these things so like some of
+
+ align:start position:0%
+to create these things so like some of
+ 
+
+ align:start position:0%
+to create these things so like some of
+them are we're at this point we're down
+
+ align:start position:0%
+them are we're at this point we're down
+ 
+
+ align:start position:0%
+them are we're at this point we're down
+to doing it one at a time and we're up
+
+ align:start position:0%
+to doing it one at a time and we're up
+ 
+
+ align:start position:0%
+to doing it one at a time and we're up
+to 668 but we haven't got that one yet
+
+ align:start position:0%
+to 668 but we haven't got that one yet
+ 
+
+ align:start position:0%
+to 668 but we haven't got that one yet
+isn't that crazy so all this is coming
+
+ align:start position:0%
+isn't that crazy so all this is coming
+ 
+
+ align:start position:0%
+isn't that crazy so all this is coming
+from Wikipedia my source of my short
+
+ align:start position:0%
+from Wikipedia my source of my short
+ 
+
+ align:start position:0%
+from Wikipedia my source of my short
+mice my source of all its good in
+
+ align:start position:0%
+mice my source of all its good in
+ 
+
+ align:start position:0%
+mice my source of all its good in
+mathematics is there on Wikipedia anyway
+
+ align:start position:0%
+mathematics is there on Wikipedia anyway
+ 
+
+ align:start position:0%
+mathematics is there on Wikipedia anyway
+this is the conjecture conjecture means
+
+ align:start position:0%
+this is the conjecture conjecture means
+ 
+
+ align:start position:0%
+this is the conjecture conjecture means
+you don't have any damn idea of whether
+
+ align:start position:0%
+you don't have any damn idea of whether
+ 
+
+ align:start position:0%
+you don't have any damn idea of whether
+it's true or not that every is that
+
+ align:start position:0%
+it's true or not that every is that
+ 
+
+ align:start position:0%
+it's true or not that every is that
+divisible by four yeah I guess it would
+
+ align:start position:0%
+divisible by four yeah I guess it would
+ 
+
+ align:start position:0%
+divisible by four yeah I guess it would
+be right 600 certainly is and 68 yeah
+
+ align:start position:0%
+be right 600 certainly is and 68 yeah
+ 
+
+ align:start position:0%
+be right 600 certainly is and 68 yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I think that's the first one that's
+
+ align:start position:0%
+so I think that's the first one that's
+ 
+
+ align:start position:0%
+so I think that's the first one that's
+so anybody if if you find one of size
+
+ align:start position:0%
+so anybody if if you find one of size
+ 
+
+ align:start position:0%
+so anybody if if you find one of size
+six six you just skip the homework and
+
+ align:start position:0%
+six six you just skip the homework and
+ 
+
+ align:start position:0%
+six six you just skip the homework and
+tell us about that one but I don't think
+
+ align:start position:0%
+tell us about that one but I don't think
+ 
+
+ align:start position:0%
+tell us about that one but I don't think
+I'll assign them yeah I guess well yeah
+
+ align:start position:0%
+I'll assign them yeah I guess well yeah
+ 
+
+ align:start position:0%
+I'll assign them yeah I guess well yeah
+I must have searched for it online yeah
+
+ align:start position:0%
+I must have searched for it online yeah
+ 
+
+ align:start position:0%
+I must have searched for it online yeah
+anyway so those are the Adam are
+
+ align:start position:0%
+anyway so those are the Adam are
+ 
+
+ align:start position:0%
+anyway so those are the Adam are
+matrices now where else do I remember
+
+ align:start position:0%
+matrices now where else do I remember
+ 
+
+ align:start position:0%
+matrices now where else do I remember
+orthogonal matrices coming from well
+
+ align:start position:0%
+orthogonal matrices coming from well
+ 
+
+ align:start position:0%
+orthogonal matrices coming from well
+yeah really the biggest source of some
+
+ align:start position:0%
+yeah really the biggest source of some
+ 
+
+ align:start position:0%
+yeah really the biggest source of some
+what I'm looking for orthogonal matrices
+
+ align:start position:0%
+what I'm looking for orthogonal matrices
+ 
+
+ align:start position:0%
+what I'm looking for orthogonal matrices
+I'm looking for a basis of orthogonal
+
+ align:start position:0%
+I'm looking for a basis of orthogonal
+ 
+
+ align:start position:0%
+I'm looking for a basis of orthogonal
+vectors and we're in math am I going to
+
+ align:start position:0%
+vectors and we're in math am I going to
+ 
+
+ align:start position:0%
+vectors and we're in math am I going to
+find vectors that come out to be
+
+ align:start position:0%
+find vectors that come out to be
+ 
+
+ align:start position:0%
+find vectors that come out to be
+orthogonal we haven't seen that's the
+
+ align:start position:0%
+orthogonal we haven't seen that's the
+ 
+
+ align:start position:0%
+orthogonal we haven't seen that's the
+next section of the notes but maybe you
+
+ align:start position:0%
+next section of the notes but maybe you
+ 
+
+ align:start position:0%
+next section of the notes but maybe you
+were remembering where will we sort of
+
+ align:start position:0%
+were remembering where will we sort of
+ 
+
+ align:start position:0%
+were remembering where will we sort of
+like automatically show up with
+
+ align:start position:0%
+like automatically show up with
+ 
+
+ align:start position:0%
+like automatically show up with
+orthogonal vectors they could be the
+
+ align:start position:0%
+orthogonal vectors they could be the
+ 
+
+ align:start position:0%
+orthogonal vectors they could be the
+eigenvectors of symmetric matrix and
+
+ align:start position:0%
+eigenvectors of symmetric matrix and
+ 
+
+ align:start position:0%
+eigenvectors of symmetric matrix and
+that's where the most important ones
+
+ align:start position:0%
+that's where the most important ones
+ 
+
+ align:start position:0%
+that's where the most important ones
+come from oh I could tell you about
+
+ align:start position:0%
+come from oh I could tell you about
+ 
+
+ align:start position:0%
+come from oh I could tell you about
+wavelets though wavelets are more like
+
+ align:start position:0%
+wavelets though wavelets are more like
+ 
+
+ align:start position:0%
+wavelets though wavelets are more like
+this picture they're ones and minus ones
+
+ align:start position:0%
+this picture they're ones and minus ones
+ 
+
+ align:start position:0%
+this picture they're ones and minus ones
+or the simplest wavelets are ones
+
+ align:start position:0%
+or the simplest wavelets are ones
+ 
+
+ align:start position:0%
+or the simplest wavelets are ones
+- once can I cut it before I go on to
+
+ align:start position:0%
+- once can I cut it before I go on to
+ 
+
+ align:start position:0%
+- once can I cut it before I go on to
+the to the eigenvector business can I
+
+ align:start position:0%
+the to the eigenvector business can I
+ 
+
+ align:start position:0%
+the to the eigenvector business can I
+mention the wavelets matrices yeah these
+
+ align:start position:0%
+mention the wavelets matrices yeah these
+ 
+
+ align:start position:0%
+mention the wavelets matrices yeah these
+are these are really important simple
+
+ align:start position:0%
+are these are really important simple
+ 
+
+ align:start position:0%
+are these are really important simple
+and important constructions so wavelets
+
+ align:start position:0%
+and important constructions so wavelets
+ 
+
+ align:start position:0%
+and important constructions so wavelets
+let me yeah let me draw a picture of so
+
+ align:start position:0%
+let me yeah let me draw a picture of so
+ 
+
+ align:start position:0%
+let me yeah let me draw a picture of so
+so I'm going to come up with four-way
+
+ align:start position:0%
+so I'm going to come up with four-way
+ 
+
+ align:start position:0%
+so I'm going to come up with four-way
+I'll do the four by four case and and
+
+ align:start position:0%
+I'll do the four by four case and and
+ 
+
+ align:start position:0%
+I'll do the four by four case and and
+this is these these are the orthogonal
+
+ align:start position:0%
+this is these these are the orthogonal
+ 
+
+ align:start position:0%
+this is these these are the orthogonal
+guys and then the next one is up and
+
+ align:start position:0%
+guys and then the next one is up and
+ 
+
+ align:start position:0%
+guys and then the next one is up and
+down and 0 and the last one is 0 and up
+
+ align:start position:0%
+down and 0 and the last one is 0 and up
+ 
+
+ align:start position:0%
+down and 0 and the last one is 0 and up
+and down so that's that's for things but
+
+ align:start position:0%
+and down so that's that's for things but
+ 
+
+ align:start position:0%
+and down so that's that's for things but
+let me show you the matrix so I'll call
+
+ align:start position:0%
+let me show you the matrix so I'll call
+ 
+
+ align:start position:0%
+let me show you the matrix so I'll call
+it W for wavelets so that guy I'm
+
+ align:start position:0%
+it W for wavelets so that guy I'm
+ 
+
+ align:start position:0%
+it W for wavelets so that guy I'm
+thinking I was 1 1 1 1 this guy I'm
+
+ align:start position:0%
+thinking I was 1 1 1 1 this guy I'm
+ 
+
+ align:start position:0%
+thinking I was 1 1 1 1 this guy I'm
+thinking of as 1 1 minus 1 minus 1 it's
+
+ align:start position:0%
+thinking of as 1 1 minus 1 minus 1 it's
+ 
+
+ align:start position:0%
+thinking of as 1 1 minus 1 minus 1 it's
+looking sort of atom hard way but but
+
+ align:start position:0%
+looking sort of atom hard way but but
+ 
+
+ align:start position:0%
+looking sort of atom hard way but but
+there's a difference here this guy is 1
+
+ align:start position:0%
+there's a difference here this guy is 1
+ 
+
+ align:start position:0%
+there's a difference here this guy is 1
+minus 1 0 0 so the wavelets rescale
+
+ align:start position:0%
+minus 1 0 0 so the wavelets rescale
+ 
+
+ align:start position:0%
+minus 1 0 0 so the wavelets rescale
+that's that's the difference between
+
+ align:start position:0%
+that's that's the difference between
+ 
+
+ align:start position:0%
+that's that's the difference between
+atom arden wavelets wavelets are scaling
+
+ align:start position:0%
+atom arden wavelets wavelets are scaling
+ 
+
+ align:start position:0%
+atom arden wavelets wavelets are scaling
+self scaling and what's the last guy
+
+ align:start position:0%
+self scaling and what's the last guy
+ 
+
+ align:start position:0%
+self scaling and what's the last guy
+here what's the fourth column from that
+
+ align:start position:0%
+here what's the fourth column from that
+ 
+
+ align:start position:0%
+here what's the fourth column from that
+fourth wavelet 0 0 1 minus 1 yeah so har
+
+ align:start position:0%
+fourth wavelet 0 0 1 minus 1 yeah so har
+ 
+
+ align:start position:0%
+fourth wavelet 0 0 1 minus 1 yeah so har
+came up with that this is the haar
+
+ align:start position:0%
+came up with that this is the haar
+ 
+
+ align:start position:0%
+came up with that this is the haar
+wavelet which was many years before the
+
+ align:start position:0%
+wavelet which was many years before the
+ 
+
+ align:start position:0%
+wavelet which was many years before the
+word wavelets was invented he came up
+
+ align:start position:0%
+word wavelets was invented he came up
+ 
+
+ align:start position:0%
+word wavelets was invented he came up
+with this construction the horror horror
+
+ align:start position:0%
+with this construction the horror horror
+ 
+
+ align:start position:0%
+with this construction the horror horror
+the horror matrix there are functions so
+
+ align:start position:0%
+the horror matrix there are functions so
+ 
+
+ align:start position:0%
+the horror matrix there are functions so
+they're very simple functions but you
+
+ align:start position:0%
+they're very simple functions but you
+ 
+
+ align:start position:0%
+they're very simple functions but you
+know you can
+
+ align:start position:0%
+know you can
+ 
+
+ align:start position:0%
+know you can
+that makes them usable that's the fact
+
+ align:start position:0%
+that makes them usable that's the fact
+ 
+
+ align:start position:0%
+that makes them usable that's the fact
+that they're so simple now I don't know
+
+ align:start position:0%
+that they're so simple now I don't know
+ 
+
+ align:start position:0%
+that they're so simple now I don't know
+if we want
+
+ align:start position:0%
+if we want
+ 
+
+ align:start position:0%
+if we want
+see the pattern an eight-by-eight but
+
+ align:start position:0%
+see the pattern an eight-by-eight but
+ 
+
+ align:start position:0%
+see the pattern an eight-by-eight but
+let me start the 8x8 so you you'll know
+
+ align:start position:0%
+let me start the 8x8 so you you'll know
+ 
+
+ align:start position:0%
+let me start the 8x8 so you you'll know
+what wavelets are about you'll know what
+
+ align:start position:0%
+what wavelets are about you'll know what
+ 
+
+ align:start position:0%
+what wavelets are about you'll know what
+these horror wavelets are about anyway
+
+ align:start position:0%
+these horror wavelets are about anyway
+ 
+
+ align:start position:0%
+these horror wavelets are about anyway
+they're they're the ones that were that
+
+ align:start position:0%
+they're they're the ones that were that
+ 
+
+ align:start position:0%
+they're they're the ones that were that
+we're kind of easy to visualize so let's
+
+ align:start position:0%
+we're kind of easy to visualize so let's
+ 
+
+ align:start position:0%
+we're kind of easy to visualize so let's
+this is if that's w-4 let's let's just
+
+ align:start position:0%
+this is if that's w-4 let's let's just
+ 
+
+ align:start position:0%
+this is if that's w-4 let's let's just
+take a minute
+
+ align:start position:0%
+take a minute
+ 
+
+ align:start position:0%
+take a minute
+it won't take long for WH okay so the
+
+ align:start position:0%
+it won't take long for WH okay so the
+ 
+
+ align:start position:0%
+it won't take long for WH okay so the
+first column is going to be eight ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and what's the next column gonna be four
+
+ align:start position:0%
+and what's the next column gonna be four
+ 
+
+ align:start position:0%
+and what's the next column gonna be four
+ones and four minus ones like so so four
+
+ align:start position:0%
+ones and four minus ones like so so four
+ 
+
+ align:start position:0%
+ones and four minus ones like so so four
+ones and four minus ones
+
+ align:start position:0%
+ones and four minus ones
+ 
+
+ align:start position:0%
+ones and four minus ones
+okay and now the next color - ones - -
+
+ align:start position:0%
+okay and now the next color - ones - -
+ 
+
+ align:start position:0%
+okay and now the next color - ones - -
+ones and zeros right 1 1 minus 1 minus 1
+
+ align:start position:0%
+ones and zeros right 1 1 minus 1 minus 1
+ 
+
+ align:start position:0%
+ones and zeros right 1 1 minus 1 minus 1
+and 0 and the fourth will be zeros and
+
+ align:start position:0%
+and 0 and the fourth will be zeros and
+ 
+
+ align:start position:0%
+and 0 and the fourth will be zeros and
+two ones and two months we got half a
+
+ align:start position:0%
+two ones and two months we got half a
+ 
+
+ align:start position:0%
+two ones and two months we got half a
+matrix now now if we just tell me the
+
+ align:start position:0%
+matrix now now if we just tell me the
+ 
+
+ align:start position:0%
+matrix now now if we just tell me the
+fifth I'm what do you think what do I
+
+ align:start position:0%
+fifth I'm what do you think what do I
+ 
+
+ align:start position:0%
+fifth I'm what do you think what do I
+put in the fifth one so again it's gonna
+
+ align:start position:0%
+put in the fifth one so again it's gonna
+ 
+
+ align:start position:0%
+put in the fifth one so again it's gonna
+squeeze down and rescale and what's the
+
+ align:start position:0%
+squeeze down and rescale and what's the
+ 
+
+ align:start position:0%
+squeeze down and rescale and what's the
+fifth column up here that's gonna be
+
+ align:start position:0%
+fifth column up here that's gonna be
+ 
+
+ align:start position:0%
+fifth column up here that's gonna be
+ones and minus ones and zeros now so
+
+ align:start position:0%
+ones and minus ones and zeros now so
+ 
+
+ align:start position:0%
+ones and minus ones and zeros now so
+it's not at AMARG
+
+ align:start position:0%
+it's not at AMARG
+ 
+
+ align:start position:0%
+it's not at AMARG
+it's har and what should I put 1 1 how
+
+ align:start position:0%
+it's har and what should I put 1 1 how
+ 
+
+ align:start position:0%
+it's har and what should I put 1 1 how
+they start with 1 101 my yeah and then
+
+ align:start position:0%
+they start with 1 101 my yeah and then
+ 
+
+ align:start position:0%
+they start with 1 101 my yeah and then
+all those zeros oh yeah thanks perfect 1
+
+ align:start position:0%
+all those zeros oh yeah thanks perfect 1
+ 
+
+ align:start position:0%
+all those zeros oh yeah thanks perfect 1
+minus 1 and they're all zeros and then
+
+ align:start position:0%
+minus 1 and they're all zeros and then
+ 
+
+ align:start position:0%
+minus 1 and they're all zeros and then
+the next three column says we'll have
+
+ align:start position:0%
+the next three column says we'll have
+ 
+
+ align:start position:0%
+the next three column says we'll have
+the 1 minus 1 here and the 1 minus 1
+
+ align:start position:0%
+the 1 minus 1 here and the 1 minus 1
+ 
+
+ align:start position:0%
+the 1 minus 1 here and the 1 minus 1
+here and the 1 minus 1 here and I saw
+
+ align:start position:0%
+here and the 1 minus 1 here and I saw
+ 
+
+ align:start position:0%
+here and the 1 minus 1 here and I saw
+zeros yeah so you see the pattern it's
+
+ align:start position:0%
+zeros yeah so you see the pattern it's
+ 
+
+ align:start position:0%
+zeros yeah so you see the pattern it's
+scaling at every step
+
+ align:start position:0%
+scaling at every step
+ 
+
+ align:start position:0%
+scaling at every step
+and and the so that matrix has the
+
+ align:start position:0%
+and and the so that matrix has the
+ 
+
+ align:start position:0%
+and and the so that matrix has the
+advantage of being quite sparse sort of
+
+ align:start position:0%
+advantage of being quite sparse sort of
+ 
+
+ align:start position:0%
+advantage of being quite sparse sort of
+this this in my mind is a or but for
+
+ align:start position:0%
+this this in my mind is a or but for
+ 
+
+ align:start position:0%
+this this in my mind is a or but for
+ones that's involved with like taking
+
+ align:start position:0%
+ones that's involved with like taking
+ 
+
+ align:start position:0%
+ones that's involved with like taking
+the average then this guy is like taking
+
+ align:start position:0%
+the average then this guy is like taking
+ 
+
+ align:start position:0%
+the average then this guy is like taking
+the differences differences between
+
+ align:start position:0%
+the differences differences between
+ 
+
+ align:start position:0%
+the differences differences between
+those and those and then this is like
+
+ align:start position:0%
+those and those and then this is like
+ 
+
+ align:start position:0%
+those and those and then this is like
+taking the difference at a smaller scale
+
+ align:start position:0%
+taking the difference at a smaller scale
+ 
+
+ align:start position:0%
+taking the difference at a smaller scale
+I'm not also at a smaller scale so
+
+ align:start position:0%
+I'm not also at a smaller scale so
+ 
+
+ align:start position:0%
+I'm not also at a smaller scale so
+that's what we keep doing yeah yeah
+
+ align:start position:0%
+that's what we keep doing yeah yeah
+ 
+
+ align:start position:0%
+that's what we keep doing yeah yeah
+so that's wavelets it looks so simple
+
+ align:start position:0%
+so that's wavelets it looks so simple
+ 
+
+ align:start position:0%
+so that's wavelets it looks so simple
+right but at the just a one minute
+
+ align:start position:0%
+right but at the just a one minute
+ 
+
+ align:start position:0%
+right but at the just a one minute
+history of wavelet Sohar invented this
+
+ align:start position:0%
+history of wavelet Sohar invented this
+ 
+
+ align:start position:0%
+history of wavelet Sohar invented this
+in like 1910 I mean along forever but
+
+ align:start position:0%
+in like 1910 I mean along forever but
+ 
+
+ align:start position:0%
+in like 1910 I mean along forever but
+then you wanted wavelets that were a
+
+ align:start position:0%
+then you wanted wavelets that were a
+ 
+
+ align:start position:0%
+then you wanted wavelets that were a
+little better and not just ones and
+
+ align:start position:0%
+little better and not just ones and
+ 
+
+ align:start position:0%
+little better and not just ones and
+minus ones and zeros and it that took
+
+ align:start position:0%
+minus ones and zeros and it that took
+ 
+
+ align:start position:0%
+minus ones and zeros and it that took
+some some a lot of thinking a lot of
+
+ align:start position:0%
+some some a lot of thinking a lot of
+ 
+
+ align:start position:0%
+some some a lot of thinking a lot of
+people were searching for it and Ingrid
+
+ align:start position:0%
+people were searching for it and Ingrid
+ 
+
+ align:start position:0%
+people were searching for it and Ingrid
+dobashi
+
+ align:start position:0%
+dobashi
+ 
+
+ align:start position:0%
+dobashi
+so I'll just put her name became famous
+
+ align:start position:0%
+so I'll just put her name became famous
+ 
+
+ align:start position:0%
+so I'll just put her name became famous
+for finding them so in about 1988 she
+
+ align:start position:0%
+for finding them so in about 1988 she
+ 
+
+ align:start position:0%
+for finding them so in about 1988 she
+found a lot of families of wavelets and
+
+ align:start position:0%
+found a lot of families of wavelets and
+ 
+
+ align:start position:0%
+found a lot of families of wavelets and
+when I say wavelets she found a whole
+
+ align:start position:0%
+when I say wavelets she found a whole
+ 
+
+ align:start position:0%
+when I say wavelets she found a whole
+lot of orthogonal matrices that were
+
+ align:start position:0%
+lot of orthogonal matrices that were
+ 
+
+ align:start position:0%
+lot of orthogonal matrices that were
+that had good properties yep so that's
+
+ align:start position:0%
+that had good properties yep so that's
+ 
+
+ align:start position:0%
+that had good properties yep so that's
+that's the wave of a picture okay now to
+
+ align:start position:0%
+that's the wave of a picture okay now to
+ 
+
+ align:start position:0%
+that's the wave of a picture okay now to
+close today and to connect with the next
+
+ align:start position:0%
+close today and to connect with the next
+ 
+
+ align:start position:0%
+close today and to connect with the next
+lecture on eigenvalues eigenvectors
+
+ align:start position:0%
+lecture on eigenvalues eigenvectors
+ 
+
+ align:start position:0%
+lecture on eigenvalues eigenvectors
+positive definite matrices we're really
+
+ align:start position:0%
+positive definite matrices we're really
+ 
+
+ align:start position:0%
+positive definite matrices we're really
+getting to the heart of things here
+
+ align:start position:0%
+getting to the heart of things here
+ 
+
+ align:start position:0%
+getting to the heart of things here
+let me follow through on that idea
+
+ align:start position:0%
+let me follow through on that idea
+ 
+
+ align:start position:0%
+let me follow through on that idea
+so the eigenvectors of symmetric matrix
+
+ align:start position:0%
+so the eigenvectors of symmetric matrix
+ 
+
+ align:start position:0%
+so the eigenvectors of symmetric matrix
+but also of an orthogonal matrix are
+
+ align:start position:0%
+but also of an orthogonal matrix are
+ 
+
+ align:start position:0%
+but also of an orthogonal matrix are
+orthogonal and that is really where
+
+ align:start position:0%
+orthogonal and that is really where
+ 
+
+ align:start position:0%
+orthogonal and that is really where
+people where you can invent because you
+
+ align:start position:0%
+people where you can invent because you
+ 
+
+ align:start position:0%
+people where you can invent because you
+don't have to work hard you just find a
+
+ align:start position:0%
+don't have to work hard you just find a
+ 
+
+ align:start position:0%
+don't have to work hard you just find a
+symmetric matrix its eigenvectors are
+
+ align:start position:0%
+symmetric matrix its eigenvectors are
+ 
+
+ align:start position:0%
+symmetric matrix its eigenvectors are
+automatically orthogonal that doesn't
+
+ align:start position:0%
+automatically orthogonal that doesn't
+ 
+
+ align:start position:0%
+automatically orthogonal that doesn't
+mean they're great for for use but some
+
+ align:start position:0%
+mean they're great for for use but some
+ 
+
+ align:start position:0%
+mean they're great for for use but some
+of them are really important and that
+
+ align:start position:0%
+of them are really important and that
+ 
+
+ align:start position:0%
+of them are really important and that
+may be the most important of all is the
+
+ align:start position:0%
+may be the most important of all is the
+ 
+
+ align:start position:0%
+may be the most important of all is the
+fourier so you probably have seen
+
+ align:start position:0%
+fourier so you probably have seen
+ 
+
+ align:start position:0%
+fourier so you probably have seen
+Fourier series sines and cosines those
+
+ align:start position:0%
+Fourier series sines and cosines those
+ 
+
+ align:start position:0%
+Fourier series sines and cosines those
+guys are orthogonal functions but
+
+ align:start position:0%
+guys are orthogonal functions but
+ 
+
+ align:start position:0%
+guys are orthogonal functions but
+discrete Fourier series is what
+
+ align:start position:0%
+discrete Fourier series is what
+ 
+
+ align:start position:0%
+discrete Fourier series is what
+everybody computes and those are
+
+ align:start position:0%
+everybody computes and those are
+ 
+
+ align:start position:0%
+everybody computes and those are
+orthogonal vectors so the orthogonal
+
+ align:start position:0%
+orthogonal vectors so the orthogonal
+ 
+
+ align:start position:0%
+orthogonal vectors so the orthogonal
+vectors that go into the discrete
+
+ align:start position:0%
+vectors that go into the discrete
+ 
+
+ align:start position:0%
+vectors that go into the discrete
+Fourier transform and and then they're
+
+ align:start position:0%
+Fourier transform and and then they're
+ 
+
+ align:start position:0%
+Fourier transform and and then they're
+done at high speed by the fast Fourier
+
+ align:start position:0%
+done at high speed by the fast Fourier
+ 
+
+ align:start position:0%
+done at high speed by the fast Fourier
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+those are eigenvectors of q eigenvectors
+
+ align:start position:0%
+those are eigenvectors of q eigenvectors
+ 
+
+ align:start position:0%
+those are eigenvectors of q eigenvectors
+of the right q so let me just invent the
+
+ align:start position:0%
+of the right q so let me just invent the
+ 
+
+ align:start position:0%
+of the right q so let me just invent the
+right tell you the right q that get
+
+ align:start position:0%
+right tell you the right q that get
+ 
+
+ align:start position:0%
+right tell you the right q that get
+whose eigenvectors so so i here we go
+
+ align:start position:0%
+whose eigenvectors so so i here we go
+ 
+
+ align:start position:0%
+whose eigenvectors so so i here we go
+I can vectors of Q let me you will just
+
+ align:start position:0%
+I can vectors of Q let me you will just
+ 
+
+ align:start position:0%
+I can vectors of Q let me you will just
+be amazed by how simple this matrix is
+
+ align:start position:0%
+be amazed by how simple this matrix is
+ 
+
+ align:start position:0%
+be amazed by how simple this matrix is
+it's just that matrix it's a called a
+
+ align:start position:0%
+it's just that matrix it's a called a
+ 
+
+ align:start position:0%
+it's just that matrix it's a called a
+permutation matrix it just puts the
+
+ align:start position:0%
+permutation matrix it just puts the
+ 
+
+ align:start position:0%
+permutation matrix it just puts the
+those are the four eight for Fourier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discrete discrete let me put their word
+
+ align:start position:0%
+discrete discrete let me put their word
+ 
+
+ align:start position:0%
+discrete discrete let me put their word
+discrete up here transfer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I really meant to put discrete
+
+ align:start position:0%
+so I really meant to put discrete
+ 
+
+ align:start position:0%
+so I really meant to put discrete
+Fourier transform yeah
+
+ align:start position:0%
+Fourier transform yeah
+ 
+
+ align:start position:0%
+Fourier transform yeah
+the eigenvectors of that matrix first of
+
+ align:start position:0%
+the eigenvectors of that matrix first of
+ 
+
+ align:start position:0%
+the eigenvectors of that matrix first of
+all they are orthogonal and then second
+
+ align:start position:0%
+all they are orthogonal and then second
+ 
+
+ align:start position:0%
+all they are orthogonal and then second
+and more important they're they're
+
+ align:start position:0%
+and more important they're they're
+ 
+
+ align:start position:0%
+and more important they're they're
+tremendously useful they're the they're
+
+ align:start position:0%
+tremendously useful they're the they're
+ 
+
+ align:start position:0%
+tremendously useful they're the they're
+the heart of signal processing you know
+
+ align:start position:0%
+the heart of signal processing you know
+ 
+
+ align:start position:0%
+the heart of signal processing you know
+in in signal processing they just take
+
+ align:start position:0%
+in in signal processing they just take
+ 
+
+ align:start position:0%
+in in signal processing they just take
+the discrete Fourier transform of a
+
+ align:start position:0%
+the discrete Fourier transform of a
+ 
+
+ align:start position:0%
+the discrete Fourier transform of a
+vector before they even look at it I
+
+ align:start position:0%
+vector before they even look at it I
+ 
+
+ align:start position:0%
+vector before they even look at it I
+mean it's like that's the way to see it
+
+ align:start position:0%
+mean it's like that's the way to see it
+ 
+
+ align:start position:0%
+mean it's like that's the way to see it
+is split it into its frequencies and
+
+ align:start position:0%
+is split it into its frequencies and
+ 
+
+ align:start position:0%
+is split it into its frequencies and
+that's what the eigenvectors of this
+
+ align:start position:0%
+that's what the eigenvectors of this
+ 
+
+ align:start position:0%
+that's what the eigenvectors of this
+will do so we're going to see the
+
+ align:start position:0%
+will do so we're going to see the
+ 
+
+ align:start position:0%
+will do so we're going to see the
+discrete Fourier transform and but my
+
+ align:start position:0%
+discrete Fourier transform and but my
+ 
+
+ align:start position:0%
+discrete Fourier transform and but my
+point here is to know that they're
+
+ align:start position:0%
+point here is to know that they're
+ 
+
+ align:start position:0%
+point here is to know that they're
+orthogonal is just comes out of this
+
+ align:start position:0%
+orthogonal is just comes out of this
+ 
+
+ align:start position:0%
+orthogonal is just comes out of this
+fact that the eigenvectors are
+
+ align:start position:0%
+fact that the eigenvectors are
+ 
+
+ align:start position:0%
+fact that the eigenvectors are
+orthogonal for any Q and that is
+
+ align:start position:0%
+orthogonal for any Q and that is
+ 
+
+ align:start position:0%
+orthogonal for any Q and that is
+certainly a Q everybody can see that
+
+ align:start position:0%
+certainly a Q everybody can see that
+ 
+
+ align:start position:0%
+certainly a Q everybody can see that
+those columns are orthogonal the columns
+
+ align:start position:0%
+those columns are orthogonal the columns
+ 
+
+ align:start position:0%
+those columns are orthogonal the columns
+of a print that's a permutation matrix
+
+ align:start position:0%
+of a print that's a permutation matrix
+ 
+
+ align:start position:0%
+of a print that's a permutation matrix
+right it's a you've taken the columns of
+
+ align:start position:0%
+right it's a you've taken the columns of
+ 
+
+ align:start position:0%
+right it's a you've taken the columns of
+the identity which are totally
+
+ align:start position:0%
+the identity which are totally
+ 
+
+ align:start position:0%
+the identity which are totally
+orthogonal and you just put them in a
+
+ align:start position:0%
+orthogonal and you just put them in a
+ 
+
+ align:start position:0%
+orthogonal and you just put them in a
+different order so a permutation matrix
+
+ align:start position:0%
+different order so a permutation matrix
+ 
+
+ align:start position:0%
+different order so a permutation matrix
+is a reordering of the identity matrix
+
+ align:start position:0%
+is a reordering of the identity matrix
+ 
+
+ align:start position:0%
+is a reordering of the identity matrix
+it's got to be a q and therefore its
+
+ align:start position:0%
+it's got to be a q and therefore its
+ 
+
+ align:start position:0%
+it's got to be a q and therefore its
+eigenvectors are orthogonal and they're
+
+ align:start position:0%
+eigenvectors are orthogonal and they're
+ 
+
+ align:start position:0%
+eigenvectors are orthogonal and they're
+just the winners i mean that the the
+
+ align:start position:0%
+just the winners i mean that the the
+ 
+
+ align:start position:0%
+just the winners i mean that the the
+matrix of the fourier matrix with those
+
+ align:start position:0%
+matrix of the fourier matrix with those
+ 
+
+ align:start position:0%
+matrix of the fourier matrix with those
+four eigen vectors in it I'll show you
+
+ align:start position:0%
+four eigen vectors in it I'll show you
+ 
+
+ align:start position:0%
+four eigen vectors in it I'll show you
+now okay so this is really we're
+
+ align:start position:0%
+now okay so this is really we're
+ 
+
+ align:start position:0%
+now okay so this is really we're
+finishing today by leading into
+
+ align:start position:0%
+finishing today by leading into
+ 
+
+ align:start position:0%
+finishing today by leading into
+Wednesday
+
+ align:start position:0%
+Wednesday
+ 
+
+ align:start position:0%
+Wednesday
+I can vectors and eigen values and we
+
+ align:start position:0%
+I can vectors and eigen values and we
+ 
+
+ align:start position:0%
+I can vectors and eigen values and we
+happen to be doing eigen vectors and
+
+ align:start position:0%
+happen to be doing eigen vectors and
+ 
+
+ align:start position:0%
+happen to be doing eigen vectors and
+eigen values of a queue not today of an
+
+ align:start position:0%
+eigen values of a queue not today of an
+ 
+
+ align:start position:0%
+eigen values of a queue not today of an
+S well most of the time it's a symmetric
+
+ align:start position:0%
+S well most of the time it's a symmetric
+ 
+
+ align:start position:0%
+S well most of the time it's a symmetric
+matrix whose eigenvectors we take but
+
+ align:start position:0%
+matrix whose eigenvectors we take but
+ 
+
+ align:start position:0%
+matrix whose eigenvectors we take but
+here that happens to be a q can I show
+
+ align:start position:0%
+here that happens to be a q can I show
+ 
+
+ align:start position:0%
+here that happens to be a q can I show
+you the eigenvectors
+
+ align:start position:0%
+you the eigenvectors
+ 
+
+ align:start position:0%
+you the eigenvectors
+the four eigenvectors of that now oh the
+
+ align:start position:0%
+the four eigenvectors of that now oh the
+ 
+
+ align:start position:0%
+the four eigenvectors of that now oh the
+complex number I is going to come in you
+
+ align:start position:0%
+complex number I is going to come in you
+ 
+
+ align:start position:0%
+complex number I is going to come in you
+have to you have to let it in here yeah
+
+ align:start position:0%
+have to you have to let it in here yeah
+ 
+
+ align:start position:0%
+have to you have to let it in here yeah
+sorry ma if s if s is a real symmetric
+
+ align:start position:0%
+sorry ma if s if s is a real symmetric
+ 
+
+ align:start position:0%
+sorry ma if s if s is a real symmetric
+matrix its eigenvectors are real but if
+
+ align:start position:0%
+matrix its eigenvectors are real but if
+ 
+
+ align:start position:0%
+matrix its eigenvectors are real but if
+q is a orthogonal matrix its
+
+ align:start position:0%
+q is a orthogonal matrix its
+ 
+
+ align:start position:0%
+q is a orthogonal matrix its
+eigenvectors even though it's you know
+
+ align:start position:0%
+eigenvectors even though it's you know
+ 
+
+ align:start position:0%
+eigenvectors even though it's you know
+you couldn't ask for a more real matrix
+
+ align:start position:0%
+you couldn't ask for a more real matrix
+ 
+
+ align:start position:0%
+you couldn't ask for a more real matrix
+than that but its eigenvectors are at
+
+ align:start position:0%
+than that but its eigenvectors are at
+ 
+
+ align:start position:0%
+than that but its eigenvectors are at
+least yeah the one the good way are
+
+ align:start position:0%
+least yeah the one the good way are
+ 
+
+ align:start position:0%
+least yeah the one the good way are
+complex numbers so can I show you the
+
+ align:start position:0%
+complex numbers so can I show you the
+ 
+
+ align:start position:0%
+complex numbers so can I show you the
+eigenvectors of so again overall the
+
+ align:start position:0%
+eigenvectors of so again overall the
+ 
+
+ align:start position:0%
+eigenvectors of so again overall the
+point today is to see orthogonal
+
+ align:start position:0%
+point today is to see orthogonal
+ 
+
+ align:start position:0%
+point today is to see orthogonal
+matrices so I'll just repeat now while I
+
+ align:start position:0%
+matrices so I'll just repeat now while I
+ 
+
+ align:start position:0%
+matrices so I'll just repeat now while I
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+rotations here reflections wavelets the
+
+ align:start position:0%
+rotations here reflections wavelets the
+ 
+
+ align:start position:0%
+rotations here reflections wavelets the
+householder idea of reflections of big
+
+ align:start position:0%
+householder idea of reflections of big
+ 
+
+ align:start position:0%
+householder idea of reflections of big
+large matrices that have this form I
+
+ align:start position:0%
+large matrices that have this form I
+ 
+
+ align:start position:0%
+large matrices that have this form I
+minus 2 uu transpose orthogonal and now
+
+ align:start position:0%
+minus 2 uu transpose orthogonal and now
+ 
+
+ align:start position:0%
+minus 2 uu transpose orthogonal and now
+we're going to see the big guys the the
+
+ align:start position:0%
+we're going to see the big guys the the
+ 
+
+ align:start position:0%
+we're going to see the big guys the the
+eigenvectors of q right yes oh yeah we
+
+ align:start position:0%
+eigenvectors of q right yes oh yeah we
+ 
+
+ align:start position:0%
+eigenvectors of q right yes oh yeah we
+don't have orthonormal that's right we
+
+ align:start position:0%
+don't have orthonormal that's right we
+ 
+
+ align:start position:0%
+don't have orthonormal that's right we
+don't have orthonormal I better divide
+
+ align:start position:0%
+don't have orthonormal I better divide
+ 
+
+ align:start position:0%
+don't have orthonormal I better divide
+by square root of 8 right oh yeah so
+
+ align:start position:0%
+by square root of 8 right oh yeah so
+ 
+
+ align:start position:0%
+by square root of 8 right oh yeah so
+you're right sorry I thought I'd get
+
+ align:start position:0%
+you're right sorry I thought I'd get
+ 
+
+ align:start position:0%
+you're right sorry I thought I'd get
+away with that but I didn't yeah so
+
+ align:start position:0%
+away with that but I didn't yeah so
+ 
+
+ align:start position:0%
+away with that but I didn't yeah so
+these guys are screws of 8 so are these
+
+ align:start position:0%
+these guys are screws of 8 so are these
+ 
+
+ align:start position:0%
+these guys are screws of 8 so are these
+but these guys are fruits of 4 and these
+
+ align:start position:0%
+but these guys are fruits of 4 and these
+ 
+
+ align:start position:0%
+but these guys are fruits of 4 and these
+guys are screw to - thank you absolutely
+
+ align:start position:0%
+guys are screw to - thank you absolutely
+ 
+
+ align:start position:0%
+guys are screw to - thank you absolutely
+right absolutely yeah
+
+ align:start position:0%
+right absolutely yeah
+ 
+
+ align:start position:0%
+right absolutely yeah
+okay so what are the eigenvectors of a
+
+ align:start position:0%
+okay so what are the eigenvectors of a
+ 
+
+ align:start position:0%
+okay so what are the eigenvectors of a
+of a permutation this is going to be
+
+ align:start position:0%
+of a permutation this is going to be
+ 
+
+ align:start position:0%
+of a permutation this is going to be
+nice to see and I'll use the matrix F
+
+ align:start position:0%
+nice to see and I'll use the matrix F
+ 
+
+ align:start position:0%
+nice to see and I'll use the matrix F
+for the eigenvector matrix of that of
+
+ align:start position:0%
+for the eigenvector matrix of that of
+ 
+
+ align:start position:0%
+for the eigenvector matrix of that of
+that of that queue up there and F is for
+
+ align:start position:0%
+that of that queue up there and F is for
+ 
+
+ align:start position:0%
+that of that queue up there and F is for
+for you and it be the four by four for a
+
+ align:start position:0%
+for you and it be the four by four for a
+ 
+
+ align:start position:0%
+for you and it be the four by four for a
+matrix okay what are the eigenvectors of
+
+ align:start position:0%
+matrix okay what are the eigenvectors of
+ 
+
+ align:start position:0%
+matrix okay what are the eigenvectors of
+Q okay so Q is a permutation so like I'm
+
+ align:start position:0%
+Q okay so Q is a permutation so like I'm
+ 
+
+ align:start position:0%
+Q okay so Q is a permutation so like I'm
+gonna ask you for one eigenvector of
+
+ align:start position:0%
+gonna ask you for one eigenvector of
+ 
+
+ align:start position:0%
+gonna ask you for one eigenvector of
+every permutation matrix what what
+
+ align:start position:0%
+every permutation matrix what what
+ 
+
+ align:start position:0%
+every permutation matrix what what
+vector can you tell me that it actually
+
+ align:start position:0%
+vector can you tell me that it actually
+ 
+
+ align:start position:0%
+vector can you tell me that it actually
+the eigenvalue will be one what vector
+
+ align:start position:0%
+the eigenvalue will be one what vector
+ 
+
+ align:start position:0%
+the eigenvalue will be one what vector
+can you tell me where if i permute it I
+
+ align:start position:0%
+can you tell me where if i permute it I
+ 
+
+ align:start position:0%
+can you tell me where if i permute it I
+don't change it one one one one it's
+
+ align:start position:0%
+don't change it one one one one it's
+ 
+
+ align:start position:0%
+don't change it one one one one it's
+like it's everywhere here one one one
+
+ align:start position:0%
+like it's everywhere here one one one
+ 
+
+ align:start position:0%
+like it's everywhere here one one one
+one so that's the zero frequency Fourier
+
+ align:start position:0%
+one so that's the zero frequency Fourier
+ 
+
+ align:start position:0%
+one so that's the zero frequency Fourier
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+the constant vector all ones everybody
+
+ align:start position:0%
+the constant vector all ones everybody
+ 
+
+ align:start position:0%
+the constant vector all ones everybody
+sees that if I I multiply by Q it
+
+ align:start position:0%
+sees that if I I multiply by Q it
+ 
+
+ align:start position:0%
+sees that if I I multiply by Q it
+doesn't change okay now the next one
+
+ align:start position:0%
+doesn't change okay now the next one
+ 
+
+ align:start position:0%
+doesn't change okay now the next one
+I'll show you the for now the next one
+
+ align:start position:0%
+I'll show you the for now the next one
+ 
+
+ align:start position:0%
+I'll show you the for now the next one
+will be one I I squared and I cubed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of course I squared I don't know how
+
+ align:start position:0%
+of course I squared I don't know how
+ 
+
+ align:start position:0%
+of course I squared I don't know how
+many course 6j people are in this
+
+ align:start position:0%
+many course 6j people are in this
+ 
+
+ align:start position:0%
+many course 6j people are in this
+audience but this is a math building we
+
+ align:start position:0%
+audience but this is a math building we
+ 
+
+ align:start position:0%
+audience but this is a math building we
+pay for it it's to 190 and it's I in
+
+ align:start position:0%
+pay for it it's to 190 and it's I in
+ 
+
+ align:start position:0%
+pay for it it's to 190 and it's I in
+this room yeah
+
+ align:start position:0%
+this room yeah
+ 
+
+ align:start position:0%
+this room yeah
+so anyway I is the first letter in in
+
+ align:start position:0%
+so anyway I is the first letter in in
+ 
+
+ align:start position:0%
+so anyway I is the first letter in in
+what imaginary thank you the first
+
+ align:start position:0%
+what imaginary thank you the first
+ 
+
+ align:start position:0%
+what imaginary thank you the first
+letter in imaginary you can't say
+
+ align:start position:0%
+letter in imaginary you can't say
+ 
+
+ align:start position:0%
+letter in imaginary you can't say
+imaginary so so so that's it okay and
+
+ align:start position:0%
+imaginary so so so that's it okay and
+ 
+
+ align:start position:0%
+imaginary so so so that's it okay and
+then the next one is one I squared I
+
+ align:start position:0%
+then the next one is one I squared I
+ 
+
+ align:start position:0%
+then the next one is one I squared I
+fourth I six and the next one is one I
+
+ align:start position:0%
+fourth I six and the next one is one I
+ 
+
+ align:start position:0%
+fourth I six and the next one is one I
+cubed I six an i-9
+
+ align:start position:0%
+cubed I six an i-9
+ 
+
+ align:start position:0%
+cubed I six an i-9
+that's isn't that just beautiful and you
+
+ align:start position:0%
+that's isn't that just beautiful and you
+ 
+
+ align:start position:0%
+that's isn't that just beautiful and you
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+show that every one of those four
+
+ align:start position:0%
+show that every one of those four
+ 
+
+ align:start position:0%
+show that every one of those four
+columns if you multiply them by Q you
+
+ align:start position:0%
+columns if you multiply them by Q you
+ 
+
+ align:start position:0%
+columns if you multiply them by Q you
+would get the eigenvalues and you would
+
+ align:start position:0%
+would get the eigenvalues and you would
+ 
+
+ align:start position:0%
+would get the eigenvalues and you would
+see that it's an eigenvector and this is
+
+ align:start position:0%
+see that it's an eigenvector and this is
+ 
+
+ align:start position:0%
+see that it's an eigenvector and this is
+just sort of like a discrete fourier
+
+ align:start position:0%
+just sort of like a discrete fourier
+ 
+
+ align:start position:0%
+just sort of like a discrete fourier
+stuff and you know instead of e to the I
+
+ align:start position:0%
+stuff and you know instead of e to the I
+ 
+
+ align:start position:0%
+stuff and you know instead of e to the I
+II to the IX e to the 2i X e to the 3 IX
+
+ align:start position:0%
+II to the IX e to the 2i X e to the 3 IX
+ 
+
+ align:start position:0%
+II to the IX e to the 2i X e to the 3 IX
+and so on we just have vectors but I so
+
+ align:start position:0%
+and so on we just have vectors but I so
+ 
+
+ align:start position:0%
+and so on we just have vectors but I so
+those are the four eigenvectors of the
+
+ align:start position:0%
+those are the four eigenvectors of the
+ 
+
+ align:start position:0%
+those are the four eigenvectors of the
+of that of that permutation and those
+
+ align:start position:0%
+of that of that permutation and those
+ 
+
+ align:start position:0%
+of that of that permutation and those
+are orthogonal because I just check that
+
+ align:start position:0%
+are orthogonal because I just check that
+ 
+
+ align:start position:0%
+are orthogonal because I just check that
+how do you know that this first column
+
+ align:start position:0%
+how do you know that this first column
+ 
+
+ align:start position:0%
+how do you know that this first column
+in the second well I should really say
+
+ align:start position:0%
+in the second well I should really say
+ 
+
+ align:start position:0%
+in the second well I should really say
+0th column and first column if I'm if
+
+ align:start position:0%
+0th column and first column if I'm if
+ 
+
+ align:start position:0%
+0th column and first column if I'm if
+I'm talking frequencies do you see that
+
+ align:start position:0%
+I'm talking frequencies do you see that
+ 
+
+ align:start position:0%
+I'm talking frequencies do you see that
+that's orthogonal to that well Y is one
+
+ align:start position:0%
+that's orthogonal to that well Y is one
+ 
+
+ align:start position:0%
+that's orthogonal to that well Y is one
+plus I plus I squared plus I cube equal
+
+ align:start position:0%
+plus I plus I squared plus I cube equal
+ 
+
+ align:start position:0%
+plus I plus I squared plus I cube equal
+zero that's the dot product this is
+
+ align:start position:0%
+zero that's the dot product this is
+ 
+
+ align:start position:0%
+zero that's the dot product this is
+column 1 dot column 2 yeah yeah you're
+
+ align:start position:0%
+column 1 dot column 2 yeah yeah you're
+ 
+
+ align:start position:0%
+column 1 dot column 2 yeah yeah you're
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this happens to come out 0 is that right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that'll come out 0 but somebody
+
+ align:start position:0%
+that'll come out 0 but somebody
+ 
+
+ align:start position:0%
+that'll come out 0 but somebody
+mentioned that this isn't right this is
+
+ align:start position:0%
+mentioned that this isn't right this is
+ 
+
+ align:start position:0%
+mentioned that this isn't right this is
+I mean that it's true that that came out
+
+ align:start position:0%
+I mean that it's true that that came out
+ 
+
+ align:start position:0%
+I mean that it's true that that came out
+0 but when I have imaginary vector
+
+ align:start position:0%
+0 but when I have imaginary vector
+ 
+
+ align:start position:0%
+0 but when I have imaginary vector
+imaginary numbers so anywhere around
+
+ align:start position:0%
+imaginary numbers so anywhere around
+ 
+
+ align:start position:0%
+imaginary numbers so anywhere around
+this isn't the correct dot product to
+
+ align:start position:0%
+this isn't the correct dot product to
+ 
+
+ align:start position:0%
+this isn't the correct dot product to
+test orthogonal if I have imaginary
+
+ align:start position:0%
+test orthogonal if I have imaginary
+ 
+
+ align:start position:0%
+test orthogonal if I have imaginary
+complex vectors if I have complex
+
+ align:start position:0%
+complex vectors if I have complex
+ 
+
+ align:start position:0%
+complex vectors if I have complex
+numbers complex vectors I should test
+
+ align:start position:0%
+numbers complex vectors I should test
+ 
+
+ align:start position:0%
+numbers complex vectors I should test
+column 1 conjugate dotted with column 2
+
+ align:start position:0%
+column 1 conjugate dotted with column 2
+ 
+
+ align:start position:0%
+column 1 conjugate dotted with column 2
+column I conjugate well let me take
+
+ align:start position:0%
+column I conjugate well let me take
+ 
+
+ align:start position:0%
+column I conjugate well let me take
+column C what which one shall I take
+
+ align:start position:0%
+column C what which one shall I take
+ 
+
+ align:start position:0%
+column C what which one shall I take
+maybe that guy in that guy many of them
+
+ align:start position:0%
+maybe that guy in that guy many of them
+ 
+
+ align:start position:0%
+maybe that guy in that guy many of them
+you luck out here but but really I
+
+ align:start position:0%
+you luck out here but but really I
+ 
+
+ align:start position:0%
+you luck out here but but really I
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+taking their conjugate so so so these
+
+ align:start position:0%
+taking their conjugate so so so these
+ 
+
+ align:start position:0%
+taking their conjugate so so so these
+ones but the thing is the country the
+
+ align:start position:0%
+ones but the thing is the country the
+ 
+
+ align:start position:0%
+ones but the thing is the country the
+complex conjugate of one is one so that
+
+ align:start position:0%
+complex conjugate of one is one so that
+ 
+
+ align:start position:0%
+complex conjugate of one is one so that
+was that was okay but in general if I
+
+ align:start position:0%
+was that was okay but in general if I
+ 
+
+ align:start position:0%
+was that was okay but in general if I
+wanted to take column two dotted with
+
+ align:start position:0%
+wanted to take column two dotted with
+ 
+
+ align:start position:0%
+wanted to take column two dotted with
+column I don't know maybe four would be
+
+ align:start position:0%
+column I don't know maybe four would be
+ 
+
+ align:start position:0%
+column I don't know maybe four would be
+a little dodgy yeah look look what
+
+ align:start position:0%
+a little dodgy yeah look look what
+ 
+
+ align:start position:0%
+a little dodgy yeah look look what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+take that column and that column take
+
+ align:start position:0%
+take that column and that column take
+ 
+
+ align:start position:0%
+take that column and that column take
+their dot product do it the wrong way so
+
+ align:start position:0%
+their dot product do it the wrong way so
+ 
+
+ align:start position:0%
+their dot product do it the wrong way so
+what's the wrong way
+
+ align:start position:0%
+what's the wrong way
+ 
+
+ align:start position:0%
+what's the wrong way
+forget about the complex conjugate and
+
+ align:start position:0%
+forget about the complex conjugate and
+ 
+
+ align:start position:0%
+forget about the complex conjugate and
+just do it the usual way so one times
+
+ align:start position:0%
+just do it the usual way so one times
+ 
+
+ align:start position:0%
+just do it the usual way so one times
+one is one I times I cube is 1 I squared
+
+ align:start position:0%
+one is one I times I cube is 1 I squared
+ 
+
+ align:start position:0%
+one is one I times I cube is 1 I squared
+times I six is one I'm getting all ones
+
+ align:start position:0%
+times I six is one I'm getting all ones
+ 
+
+ align:start position:0%
+times I six is one I'm getting all ones
+I'm not getting a orthogonality there
+
+ align:start position:0%
+I'm not getting a orthogonality there
+ 
+
+ align:start position:0%
+I'm not getting a orthogonality there
+and that's because I forgot that I
+
+ align:start position:0%
+and that's because I forgot that I
+ 
+
+ align:start position:0%
+and that's because I forgot that I
+should take the complex conjugate well
+
+ align:start position:0%
+should take the complex conjugate well
+ 
+
+ align:start position:0%
+should take the complex conjugate well
+of these guys one I should take minus I
+
+ align:start position:0%
+of these guys one I should take minus I
+ 
+
+ align:start position:0%
+of these guys one I should take minus I
+minus I square minus i well that's real
+
+ align:start position:0%
+minus I square minus i well that's real
+ 
+
+ align:start position:0%
+minus I square minus i well that's real
+so it's okay - they're so so minus I
+
+ align:start position:0%
+so it's okay - they're so so minus I
+ 
+
+ align:start position:0%
+so it's okay - they're so so minus I
+squared is still minus one so now if I
+
+ align:start position:0%
+squared is still minus one so now if I
+ 
+
+ align:start position:0%
+squared is still minus one so now if I
+do it it comes out zero so so let me
+
+ align:start position:0%
+do it it comes out zero so so let me
+ 
+
+ align:start position:0%
+do it it comes out zero so so let me
+repeat again let me just make this
+
+ align:start position:0%
+repeat again let me just make this
+ 
+
+ align:start position:0%
+repeat again let me just make this
+statement if Q transpose Q is I and Q X
+
+ align:start position:0%
+statement if Q transpose Q is I and Q X
+ 
+
+ align:start position:0%
+statement if Q transpose Q is I and Q X
+is lambda X and Q Y is a different eigen
+
+ align:start position:0%
+is lambda X and Q Y is a different eigen
+ 
+
+ align:start position:0%
+is lambda X and Q Y is a different eigen
+value Y okay so I'm I'm setting up the
+
+ align:start position:0%
+value Y okay so I'm I'm setting up the
+ 
+
+ align:start position:0%
+value Y okay so I'm I'm setting up the
+main fact that in the last minute I'm
+
+ align:start position:0%
+main fact that in the last minute I'm
+ 
+
+ align:start position:0%
+main fact that in the last minute I'm
+just gonna write down so I have an
+
+ align:start position:0%
+just gonna write down so I have an
+ 
+
+ align:start position:0%
+just gonna write down so I have an
+orthogonal matrix I have an eigenvector
+
+ align:start position:0%
+orthogonal matrix I have an eigenvector
+ 
+
+ align:start position:0%
+orthogonal matrix I have an eigenvector
+with eigenvalue lambda I have another
+
+ align:start position:0%
+with eigenvalue lambda I have another
+ 
+
+ align:start position:0%
+with eigenvalue lambda I have another
+eigenvector with a different eigen value
+
+ align:start position:0%
+eigenvector with a different eigen value
+ 
+
+ align:start position:0%
+eigenvector with a different eigen value
+mu then the claim is that what is the
+
+ align:start position:0%
+mu then the claim is that what is the
+ 
+
+ align:start position:0%
+mu then the claim is that what is the
+claim about the eigenvectors so here's
+
+ align:start position:0%
+claim about the eigenvectors so here's
+ 
+
+ align:start position:0%
+claim about the eigenvectors so here's
+has one eigen this has an eigen value
+
+ align:start position:0%
+has one eigen this has an eigen value
+ 
+
+ align:start position:0%
+has one eigen this has an eigen value
+this has a different eigen value
+
+ align:start position:0%
+this has a different eigen value
+ 
+
+ align:start position:0%
+this has a different eigen value
+I need them to be different to really
+
+ align:start position:0%
+I need them to be different to really
+ 
+
+ align:start position:0%
+I need them to be different to really
+know that they're the XS and the Y's
+
+ align:start position:0%
+know that they're the XS and the Y's
+ 
+
+ align:start position:0%
+know that they're the XS and the Y's
+can't be the same so what is it that I
+
+ align:start position:0%
+can't be the same so what is it that I
+ 
+
+ align:start position:0%
+can't be the same so what is it that I
+want to show yes that X I have to
+
+ align:start position:0%
+want to show yes that X I have to
+ 
+
+ align:start position:0%
+want to show yes that X I have to
+remember to do that X transpose Y is 0
+
+ align:start position:0%
+remember to do that X transpose Y is 0
+ 
+
+ align:start position:0%
+remember to do that X transpose Y is 0
+that's orthogonality that's
+
+ align:start position:0%
+that's orthogonality that's
+ 
+
+ align:start position:0%
+that's orthogonality that's
+orthogonality for complex vectors I have
+
+ align:start position:0%
+orthogonality for complex vectors I have
+ 
+
+ align:start position:0%
+orthogonality for complex vectors I have
+to remember to take the to change every
+
+ align:start position:0%
+to remember to take the to change every
+ 
+
+ align:start position:0%
+to remember to take the to change every
+I to a minus I in one of the vectors and
+
+ align:start position:0%
+I to a minus I in one of the vectors and
+ 
+
+ align:start position:0%
+I to a minus I in one of the vectors and
+I can prove that fact by playing with
+
+ align:start position:0%
+I can prove that fact by playing with
+ 
+
+ align:start position:0%
+I can prove that fact by playing with
+these these by playing with starting
+
+ align:start position:0%
+these these by playing with starting
+ 
+
+ align:start position:0%
+these these by playing with starting
+from here I can get to that ok that's it
+
+ align:start position:0%
+from here I can get to that ok that's it
+ 
+
+ align:start position:0%
+from here I can get to that ok that's it
+we've done a lot today a lot of stuff
+
+ align:start position:0%
+we've done a lot today a lot of stuff
+ 
+
+ align:start position:0%
+we've done a lot today a lot of stuff
+about orthogonal matrices important ones
+
+ align:start position:0%
+about orthogonal matrices important ones
+ 
+
+ align:start position:0%
+about orthogonal matrices important ones
+and the sources of important ones I ghen
+
+ align:start position:0%
+and the sources of important ones I ghen
+ 
+
+ align:start position:0%
+and the sources of important ones I ghen
+vectors and so it'll be eigenvectors on
+
+ align:start position:0%
+vectors and so it'll be eigenvectors on
+ 
+
+ align:start position:0%
+vectors and so it'll be eigenvectors on
+Wednesday
\ No newline at end of file
diff --git a/Y6J8I056Ffw.txt b/Y6J8I056Ffw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1da7d6d93877beab7e26c2229489dff3bb012412
--- /dev/null
+++ b/Y6J8I056Ffw.txt
@@ -0,0 +1,251 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so the question was if you
+
+ align:start position:0%
+ocw.mit.edu so the question was if you
+ 
+
+ align:start position:0%
+ocw.mit.edu so the question was if you
+have this these two um these two lines
+
+ align:start position:0%
+have this these two um these two lines
+ 
+
+ align:start position:0%
+have this these two um these two lines
+right here which I'll just put them up
+
+ align:start position:0%
+right here which I'll just put them up
+ 
+
+ align:start position:0%
+right here which I'll just put them up
+here just so what's bigger type five
+
+ align:start position:0%
+here just so what's bigger type five
+ 
+
+ align:start position:0%
+here just so what's bigger type five
+print 3.0 minus1 what is going to be the
+
+ align:start position:0%
+print 3.0 minus1 what is going to be the
+ 
+
+ align:start position:0%
+print 3.0 minus1 what is going to be the
+output so if I run this in the editor so
+
+ align:start position:0%
+output so if I run this in the editor so
+ 
+
+ align:start position:0%
+output so if I run this in the editor so
+for these types of problems you can
+
+ align:start position:0%
+for these types of problems you can
+ 
+
+ align:start position:0%
+for these types of problems you can
+always check yourself and this comes
+
+ align:start position:0%
+always check yourself and this comes
+ 
+
+ align:start position:0%
+always check yourself and this comes
+back to if you're new to programming
+
+ align:start position:0%
+back to if you're new to programming
+ 
+
+ align:start position:0%
+back to if you're new to programming
+don't be afraid to try it out don't ask
+
+ align:start position:0%
+don't be afraid to try it out don't ask
+ 
+
+ align:start position:0%
+don't be afraid to try it out don't ask
+me don't ask your your neighbor just
+
+ align:start position:0%
+me don't ask your your neighbor just
+ 
+
+ align:start position:0%
+me don't ask your your neighbor just
+type it into the into the shell and hit
+
+ align:start position:0%
+type it into the into the shell and hit
+ 
+
+ align:start position:0%
+type it into the into the shell and hit
+run and and then you get to see what the
+
+ align:start position:0%
+run and and then you get to see what the
+ 
+
+ align:start position:0%
+run and and then you get to see what the
+answer is so the answer to this question
+
+ align:start position:0%
+answer is so the answer to this question
+ 
+
+ align:start position:0%
+answer is so the answer to this question
+is going to be 2.0 right and let's see
+
+ align:start position:0%
+is going to be 2.0 right and let's see
+ 
+
+ align:start position:0%
+is going to be 2.0 right and let's see
+are we right yeah great 75% of the
+
+ align:start position:0%
+are we right yeah great 75% of the
+ 
+
+ align:start position:0%
+are we right yeah great 75% of the
+people got it right
+
+ align:start position:0%
+people got it right
+ 
+
+ align:start position:0%
+people got it right
+perfect um so if you didn't get it right
+
+ align:start position:0%
+perfect um so if you didn't get it right
+ 
+
+ align:start position:0%
+perfect um so if you didn't get it right
+just to explain again the reason why
+
+ align:start position:0%
+just to explain again the reason why
+ 
+
+ align:start position:0%
+just to explain again the reason why
+this doesn't get printed out is because
+
+ align:start position:0%
+this doesn't get printed out is because
+ 
+
+ align:start position:0%
+this doesn't get printed out is because
+we never actually had a print statement
+
+ align:start position:0%
+we never actually had a print statement
+ 
+
+ align:start position:0%
+we never actually had a print statement
+okay so if you want to show something to
+
+ align:start position:0%
+okay so if you want to show something to
+ 
+
+ align:start position:0%
+okay so if you want to show something to
+the the console you need to use a print
+
+ align:start position:0%
+the the console you need to use a print
+ 
+
+ align:start position:0%
+the the console you need to use a print
+statement
\ No newline at end of file
diff --git a/YLp8RziRbpg.txt b/YLp8RziRbpg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6bd0b07a9fb39ae85043cea482dd41f0ce461ee0
--- /dev/null
+++ b/YLp8RziRbpg.txt
@@ -0,0 +1,8643 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today we launched into radioactive decay
+
+ align:start position:0%
+today we launched into radioactive decay
+ 
+
+ align:start position:0%
+today we launched into radioactive decay
+and so this is you know kind of what
+
+ align:start position:0%
+and so this is you know kind of what
+ 
+
+ align:start position:0%
+and so this is you know kind of what
+makes us us in this field right now that
+
+ align:start position:0%
+makes us us in this field right now that
+ 
+
+ align:start position:0%
+makes us us in this field right now that
+you've learned the general q equation
+
+ align:start position:0%
+you've learned the general q equation
+ 
+
+ align:start position:0%
+you've learned the general q equation
+we're going to look at some very simple
+
+ align:start position:0%
+we're going to look at some very simple
+ 
+
+ align:start position:0%
+we're going to look at some very simple
+specific cases and specifically all the
+
+ align:start position:0%
+specific cases and specifically all the
+ 
+
+ align:start position:0%
+specific cases and specifically all the
+different things that can come flying
+
+ align:start position:0%
+different things that can come flying
+ 
+
+ align:start position:0%
+different things that can come flying
+out of nuclei and the orbiting electrons
+
+ align:start position:0%
+out of nuclei and the orbiting electrons
+ 
+
+ align:start position:0%
+out of nuclei and the orbiting electrons
+around them first I'd like to try and
+
+ align:start position:0%
+around them first I'd like to try and
+ 
+
+ align:start position:0%
+around them first I'd like to try and
+develop a generalized decayed diagram
+
+ align:start position:0%
+develop a generalized decayed diagram
+ 
+
+ align:start position:0%
+develop a generalized decayed diagram
+what are all the different ways that
+
+ align:start position:0%
+what are all the different ways that
+ 
+
+ align:start position:0%
+what are all the different ways that
+nuclei can decay and I had written one
+
+ align:start position:0%
+nuclei can decay and I had written one
+ 
+
+ align:start position:0%
+nuclei can decay and I had written one
+of these up to show on the slides and my
+
+ align:start position:0%
+of these up to show on the slides and my
+ 
+
+ align:start position:0%
+of these up to show on the slides and my
+one-year-old son fixed it with a bunch
+
+ align:start position:0%
+one-year-old son fixed it with a bunch
+ 
+
+ align:start position:0%
+one-year-old son fixed it with a bunch
+of markers and crayons so I think we're
+
+ align:start position:0%
+of markers and crayons so I think we're
+ 
+
+ align:start position:0%
+of markers and crayons so I think we're
+gonna have to redo this from scratch so
+
+ align:start position:0%
+gonna have to redo this from scratch so
+ 
+
+ align:start position:0%
+gonna have to redo this from scratch so
+let's say you had a generalized unstable
+
+ align:start position:0%
+let's say you had a generalized unstable
+ 
+
+ align:start position:0%
+let's say you had a generalized unstable
+nucleus over here and we're gonna start
+
+ align:start position:0%
+nucleus over here and we're gonna start
+ 
+
+ align:start position:0%
+nucleus over here and we're gonna start
+drawing a generalize decay diagram
+
+ align:start position:0%
+drawing a generalize decay diagram
+ 
+
+ align:start position:0%
+drawing a generalize decay diagram
+you'll see decay diagrams well much like
+
+ align:start position:0%
+you'll see decay diagrams well much like
+ 
+
+ align:start position:0%
+you'll see decay diagrams well much like
+these I've already shown you a couple of
+
+ align:start position:0%
+these I've already shown you a couple of
+ 
+
+ align:start position:0%
+these I've already shown you a couple of
+these like these decay diagrams for
+
+ align:start position:0%
+these like these decay diagrams for
+ 
+
+ align:start position:0%
+these like these decay diagrams for
+uranium-235 as soon as I clone my screen
+
+ align:start position:0%
+uranium-235 as soon as I clone my screen
+ 
+
+ align:start position:0%
+uranium-235 as soon as I clone my screen
+so you can see it there are a couple of
+
+ align:start position:0%
+so you can see it there are a couple of
+ 
+
+ align:start position:0%
+so you can see it there are a couple of
+axes that aren't drawn on these decay
+
+ align:start position:0%
+axes that aren't drawn on these decay
+ 
+
+ align:start position:0%
+axes that aren't drawn on these decay
+diagrams that'll help you interpret them
+
+ align:start position:0%
+diagrams that'll help you interpret them
+ 
+
+ align:start position:0%
+diagrams that'll help you interpret them
+and the first one the imaginary y axis
+
+ align:start position:0%
+and the first one the imaginary y axis
+ 
+
+ align:start position:0%
+and the first one the imaginary y axis
+is an order of increasing energy and the
+
+ align:start position:0%
+is an order of increasing energy and the
+ 
+
+ align:start position:0%
+is an order of increasing energy and the
+second imaginary y axis is Z atomic
+
+ align:start position:0%
+second imaginary y axis is Z atomic
+ 
+
+ align:start position:0%
+second imaginary y axis is Z atomic
+number so this will help you determine
+
+ align:start position:0%
+number so this will help you determine
+ 
+
+ align:start position:0%
+number so this will help you determine
+how we read these and how to actually
+
+ align:start position:0%
+how we read these and how to actually
+ 
+
+ align:start position:0%
+how we read these and how to actually
+write them now what are some of the
+
+ align:start position:0%
+write them now what are some of the
+ 
+
+ align:start position:0%
+write them now what are some of the
+different ways you've heard of things
+
+ align:start position:0%
+different ways you've heard of things
+ 
+
+ align:start position:0%
+different ways you've heard of things
+that can radioactively decay or that you
+
+ align:start position:0%
+that can radioactively decay or that you
+ 
+
+ align:start position:0%
+that can radioactively decay or that you
+might have read from the reading this
+
+ align:start position:0%
+might have read from the reading this
+ 
+
+ align:start position:0%
+might have read from the reading this
+yellow mout alpha decay so in alpha
+
+ align:start position:0%
+yellow mout alpha decay so in alpha
+ 
+
+ align:start position:0%
+yellow mout alpha decay so in alpha
+decay what actually happens let's say
+
+ align:start position:0%
+decay what actually happens let's say
+ 
+
+ align:start position:0%
+decay what actually happens let's say
+that we had a parent nucleus with atomic
+
+ align:start position:0%
+that we had a parent nucleus with atomic
+ 
+
+ align:start position:0%
+that we had a parent nucleus with atomic
+number Z and mass number a what does it
+
+ align:start position:0%
+number Z and mass number a what does it
+ 
+
+ align:start position:0%
+number Z and mass number a what does it
+change into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone know what an alpha particle
+
+ align:start position:0%
+anyone know what an alpha particle
+ 
+
+ align:start position:0%
+anyone know what an alpha particle
+consists of yeah a helium nucleus so
+
+ align:start position:0%
+consists of yeah a helium nucleus so
+ 
+
+ align:start position:0%
+consists of yeah a helium nucleus so
+let's just say helium well this will be
+
+ align:start position:0%
+let's just say helium well this will be
+ 
+
+ align:start position:0%
+let's just say helium well this will be
+a 4 and a 2 and there's going to be some
+
+ align:start position:0%
+a 4 and a 2 and there's going to be some
+ 
+
+ align:start position:0%
+a 4 and a 2 and there's going to be some
+daughter nucleus we don't know what with
+
+ align:start position:0%
+daughter nucleus we don't know what with
+ 
+
+ align:start position:0%
+daughter nucleus we don't know what with
+Z minus 2 protons and a minus for total
+
+ align:start position:0%
+Z minus 2 protons and a minus for total
+ 
+
+ align:start position:0%
+Z minus 2 protons and a minus for total
+nucleons so if we were to describe alpha
+
+ align:start position:0%
+nucleons so if we were to describe alpha
+ 
+
+ align:start position:0%
+nucleons so if we were to describe alpha
+decay on a decay diagram where would we
+
+ align:start position:0%
+decay on a decay diagram where would we
+ 
+
+ align:start position:0%
+decay on a decay diagram where would we
+write the final state of this alpha
+
+ align:start position:0%
+write the final state of this alpha
+ 
+
+ align:start position:0%
+write the final state of this alpha
+decay new alpha decayed daughter nucleus
+
+ align:start position:0%
+decay new alpha decayed daughter nucleus
+ 
+
+ align:start position:0%
+decay new alpha decayed daughter nucleus
+to the left or to the right I know it's
+
+ align:start position:0%
+to the left or to the right I know it's
+ 
+
+ align:start position:0%
+to the left or to the right I know it's
+like 9 a.m. but someone just shout it
+
+ align:start position:0%
+like 9 a.m. but someone just shout it
+ 
+
+ align:start position:0%
+like 9 a.m. but someone just shout it
+out you'd have to raise your hand to the
+
+ align:start position:0%
+out you'd have to raise your hand to the
+ 
+
+ align:start position:0%
+out you'd have to raise your hand to the
+left yep something that's decreasing in
+
+ align:start position:0%
+left yep something that's decreasing in
+ 
+
+ align:start position:0%
+left yep something that's decreasing in
+Z and also decreasing in energy we would
+
+ align:start position:0%
+Z and also decreasing in energy we would
+ 
+
+ align:start position:0%
+Z and also decreasing in energy we would
+draw an alpha decay like this to the
+
+ align:start position:0%
+draw an alpha decay like this to the
+ 
+
+ align:start position:0%
+draw an alpha decay like this to the
+left so let's say this would be
+
+ align:start position:0%
+left so let's say this would be
+ 
+
+ align:start position:0%
+left so let's say this would be
+something more stable with a Z - to make
+
+ align:start position:0%
+something more stable with a Z - to make
+ 
+
+ align:start position:0%
+something more stable with a Z - to make
+that clear and then a minus 4 what are
+
+ align:start position:0%
+that clear and then a minus 4 what are
+ 
+
+ align:start position:0%
+that clear and then a minus 4 what are
+some other ways things can decay I heard
+
+ align:start position:0%
+some other ways things can decay I heard
+ 
+
+ align:start position:0%
+some other ways things can decay I heard
+a whisper beta decay so what happens in
+
+ align:start position:0%
+a whisper beta decay so what happens in
+ 
+
+ align:start position:0%
+a whisper beta decay so what happens in
+usually by beta decay we're referring to
+
+ align:start position:0%
+usually by beta decay we're referring to
+ 
+
+ align:start position:0%
+usually by beta decay we're referring to
+beta minus decay which would be the
+
+ align:start position:0%
+beta minus decay which would be the
+ 
+
+ align:start position:0%
+beta minus decay which would be the
+emission of an electron from the nucleus
+
+ align:start position:0%
+emission of an electron from the nucleus
+ 
+
+ align:start position:0%
+emission of an electron from the nucleus
+again the differ what's the difference
+
+ align:start position:0%
+again the differ what's the difference
+ 
+
+ align:start position:0%
+again the differ what's the difference
+what's the physical difference between a
+
+ align:start position:0%
+what's the physical difference between a
+ 
+
+ align:start position:0%
+what's the physical difference between a
+beta particle and an electron nothing
+
+ align:start position:0%
+beta particle and an electron nothing
+ 
+
+ align:start position:0%
+beta particle and an electron nothing
+what's the nomenclature difference the
+
+ align:start position:0%
+what's the nomenclature difference the
+ 
+
+ align:start position:0%
+what's the nomenclature difference the
+beta comes from the nucleus otherwise
+
+ align:start position:0%
+beta comes from the nucleus otherwise
+ 
+
+ align:start position:0%
+beta comes from the nucleus otherwise
+when they come out they're kind of
+
+ align:start position:0%
+when they come out they're kind of
+ 
+
+ align:start position:0%
+when they come out they're kind of
+indistinguishable so what happens in
+
+ align:start position:0%
+indistinguishable so what happens in
+ 
+
+ align:start position:0%
+indistinguishable so what happens in
+beta decay let's say we have the same
+
+ align:start position:0%
+beta decay let's say we have the same
+ 
+
+ align:start position:0%
+beta decay let's say we have the same
+parent nucleus starting with Z a we know
+
+ align:start position:0%
+parent nucleus starting with Z a we know
+ 
+
+ align:start position:0%
+parent nucleus starting with Z a we know
+it emits an electron with no mass and
+
+ align:start position:0%
+it emits an electron with no mass and
+ 
+
+ align:start position:0%
+it emits an electron with no mass and
+what else this is just a matter of
+
+ align:start position:0%
+what else this is just a matter of
+ 
+
+ align:start position:0%
+what else this is just a matter of
+conservation of things here yep
+
+ align:start position:0%
+conservation of things here yep
+ 
+
+ align:start position:0%
+conservation of things here yep
+there is an anti-neutrino which has
+
+ align:start position:0%
+there is an anti-neutrino which has
+ 
+
+ align:start position:0%
+there is an anti-neutrino which has
+pretty close to no mass and no charge
+
+ align:start position:0%
+pretty close to no mass and no charge
+ 
+
+ align:start position:0%
+pretty close to no mass and no charge
+and what about this daughter nucleus how
+
+ align:start position:0%
+and what about this daughter nucleus how
+ 
+
+ align:start position:0%
+and what about this daughter nucleus how
+many protons and total nucleons would it
+
+ align:start position:0%
+many protons and total nucleons would it
+ 
+
+ align:start position:0%
+many protons and total nucleons would it
+have yeah should have one more proton
+
+ align:start position:0%
+have yeah should have one more proton
+ 
+
+ align:start position:0%
+have yeah should have one more proton
+and how many more total nucleons the
+
+ align:start position:0%
+and how many more total nucleons the
+ 
+
+ align:start position:0%
+and how many more total nucleons the
+same yep like that and so how would we
+
+ align:start position:0%
+same yep like that and so how would we
+ 
+
+ align:start position:0%
+same yep like that and so how would we
+draw a beta decay on this generalized
+
+ align:start position:0%
+draw a beta decay on this generalized
+ 
+
+ align:start position:0%
+draw a beta decay on this generalized
+diagram to the left or to the right to
+
+ align:start position:0%
+diagram to the left or to the right to
+ 
+
+ align:start position:0%
+diagram to the left or to the right to
+the right it's increasing in Z I haven't
+
+ align:start position:0%
+the right it's increasing in Z I haven't
+ 
+
+ align:start position:0%
+the right it's increasing in Z I haven't
+defined any scale so let's just say
+
+ align:start position:0%
+defined any scale so let's just say
+ 
+
+ align:start position:0%
+defined any scale so let's just say
+that's a change of 0 that's 1 that's 2
+
+ align:start position:0%
+that's a change of 0 that's 1 that's 2
+ 
+
+ align:start position:0%
+that's a change of 0 that's 1 that's 2
+and that's plus 1 that's plus 2
+
+ align:start position:0%
+and that's plus 1 that's plus 2
+ 
+
+ align:start position:0%
+and that's plus 1 that's plus 2
+hopefully we won't get to today so a
+
+ align:start position:0%
+hopefully we won't get to today so a
+ 
+
+ align:start position:0%
+hopefully we won't get to today so a
+beta decay would proceed thusly so you'd
+
+ align:start position:0%
+beta decay would proceed thusly so you'd
+ 
+
+ align:start position:0%
+beta decay would proceed thusly so you'd
+have some other stable nucleus with Z
+
+ align:start position:0%
+have some other stable nucleus with Z
+ 
+
+ align:start position:0%
+have some other stable nucleus with Z
+plus 1 and mass number 8
+
+ align:start position:0%
+plus 1 and mass number 8
+ 
+
+ align:start position:0%
+plus 1 and mass number 8
+what are some other decays you might
+
+ align:start position:0%
+what are some other decays you might
+ 
+
+ align:start position:0%
+what are some other decays you might
+have heard of before electron capture so
+
+ align:start position:0%
+have heard of before electron capture so
+ 
+
+ align:start position:0%
+have heard of before electron capture so
+in electron capture what actually
+
+ align:start position:0%
+in electron capture what actually
+ 
+
+ align:start position:0%
+in electron capture what actually
+happens start with the same parent
+
+ align:start position:0%
+happens start with the same parent
+ 
+
+ align:start position:0%
+happens start with the same parent
+nucleus in this case the nucleus
+
+ align:start position:0%
+nucleus in this case the nucleus
+ 
+
+ align:start position:0%
+nucleus in this case the nucleus
+actually captures an electron from one
+
+ align:start position:0%
+actually captures an electron from one
+ 
+
+ align:start position:0%
+actually captures an electron from one
+of the inner orbitals and so that in
+
+ align:start position:0%
+of the inner orbitals and so that in
+ 
+
+ align:start position:0%
+of the inner orbitals and so that in
+effect like neutralizes a proton right
+
+ align:start position:0%
+effect like neutralizes a proton right
+ 
+
+ align:start position:0%
+effect like neutralizes a proton right
+in terms of charge so what do we end up
+
+ align:start position:0%
+in terms of charge so what do we end up
+ 
+
+ align:start position:0%
+in terms of charge so what do we end up
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so we'd have some daughter nucleus
+
+ align:start position:0%
+yep so we'd have some daughter nucleus
+ 
+
+ align:start position:0%
+yep so we'd have some daughter nucleus
+if it neutralizes a proton we'd have one
+
+ align:start position:0%
+if it neutralizes a proton we'd have one
+ 
+
+ align:start position:0%
+if it neutralizes a proton we'd have one
+fewer protons and then how many total
+
+ align:start position:0%
+fewer protons and then how many total
+ 
+
+ align:start position:0%
+fewer protons and then how many total
+nucleons the same yep there we go and so
+
+ align:start position:0%
+nucleons the same yep there we go and so
+ 
+
+ align:start position:0%
+nucleons the same yep there we go and so
+if we were to draw electron capture on
+
+ align:start position:0%
+if we were to draw electron capture on
+ 
+
+ align:start position:0%
+if we were to draw electron capture on
+this map we would have one fewer proton
+
+ align:start position:0%
+this map we would have one fewer proton
+ 
+
+ align:start position:0%
+this map we would have one fewer proton
+so we could have some sort of decay by
+
+ align:start position:0%
+so we could have some sort of decay by
+ 
+
+ align:start position:0%
+so we could have some sort of decay by
+electron capture anything else what
+
+ align:start position:0%
+electron capture anything else what
+ 
+
+ align:start position:0%
+electron capture anything else what
+other particles can be emitted from a
+
+ align:start position:0%
+other particles can be emitted from a
+ 
+
+ align:start position:0%
+other particles can be emitted from a
+nucleus yeah positrons so let's get this
+
+ align:start position:0%
+nucleus yeah positrons so let's get this
+ 
+
+ align:start position:0%
+nucleus yeah positrons so let's get this
+list going up yeah so if we start off
+
+ align:start position:0%
+list going up yeah so if we start off
+ 
+
+ align:start position:0%
+list going up yeah so if we start off
+with a parent Z and a we know we emit a
+
+ align:start position:0%
+with a parent Z and a we know we emit a
+ 
+
+ align:start position:0%
+with a parent Z and a we know we emit a
+positron which is the antimatter
+
+ align:start position:0%
+positron which is the antimatter
+ 
+
+ align:start position:0%
+positron which is the antimatter
+equivalent of an electron so same
+
+ align:start position:0%
+equivalent of an electron so same
+ 
+
+ align:start position:0%
+equivalent of an electron so same
+general characteristics except opposite
+
+ align:start position:0%
+general characteristics except opposite
+ 
+
+ align:start position:0%
+general characteristics except opposite
+charge in this case we'll give it a zero
+
+ align:start position:0%
+charge in this case we'll give it a zero
+ 
+
+ align:start position:0%
+charge in this case we'll give it a zero
+protons and zero neutrons and we end up
+
+ align:start position:0%
+protons and zero neutrons and we end up
+ 
+
+ align:start position:0%
+protons and zero neutrons and we end up
+with well the same daughter nucleus so
+
+ align:start position:0%
+with well the same daughter nucleus so
+ 
+
+ align:start position:0%
+with well the same daughter nucleus so
+we could say that this precedes by
+
+ align:start position:0%
+we could say that this precedes by
+ 
+
+ align:start position:0%
+we could say that this precedes by
+positron creation or electron capture
+
+ align:start position:0%
+positron creation or electron capture
+ 
+
+ align:start position:0%
+positron creation or electron capture
+it's the same process or the same ending
+
+ align:start position:0%
+it's the same process or the same ending
+ 
+
+ align:start position:0%
+it's the same process or the same ending
+state but can you have positrons in any
+
+ align:start position:0%
+state but can you have positrons in any
+ 
+
+ align:start position:0%
+state but can you have positrons in any
+possible decay we actually went over
+
+ align:start position:0%
+possible decay we actually went over
+ 
+
+ align:start position:0%
+possible decay we actually went over
+this once
+
+ align:start position:0%
+this once
+ 
+
+ align:start position:0%
+this once
+anyone remember yeah so you're saying
+
+ align:start position:0%
+anyone remember yeah so you're saying
+ 
+
+ align:start position:0%
+anyone remember yeah so you're saying
+your head no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll get back into that you're right so
+
+ align:start position:0%
+we'll get back into that you're right so
+ 
+
+ align:start position:0%
+we'll get back into that you're right so
+we'll put a little box around this
+
+ align:start position:0%
+we'll put a little box around this
+ 
+
+ align:start position:0%
+we'll put a little box around this
+because you have to have a certain
+
+ align:start position:0%
+because you have to have a certain
+ 
+
+ align:start position:0%
+because you have to have a certain
+amount of energy in order to create the
+
+ align:start position:0%
+amount of energy in order to create the
+ 
+
+ align:start position:0%
+amount of energy in order to create the
+positron and what else what about the
+
+ align:start position:0%
+positron and what else what about the
+ 
+
+ align:start position:0%
+positron and what else what about the
+the easiest one what else can be emitted
+
+ align:start position:0%
+the easiest one what else can be emitted
+ 
+
+ align:start position:0%
+the easiest one what else can be emitted
+from a nucleus I heard a couple things
+
+ align:start position:0%
+from a nucleus I heard a couple things
+ 
+
+ align:start position:0%
+from a nucleus I heard a couple things
+neutrons so certainly if you emit a
+
+ align:start position:0%
+neutrons so certainly if you emit a
+ 
+
+ align:start position:0%
+neutrons so certainly if you emit a
+neutron there are some very unstable
+
+ align:start position:0%
+neutron there are some very unstable
+ 
+
+ align:start position:0%
+neutron there are some very unstable
+nuclei like helium five which exists for
+
+ align:start position:0%
+nuclei like helium five which exists for
+ 
+
+ align:start position:0%
+nuclei like helium five which exists for
+what ten to the minus twenty six seconds
+
+ align:start position:0%
+what ten to the minus twenty six seconds
+ 
+
+ align:start position:0%
+what ten to the minus twenty six seconds
+or something that could have been a
+
+ align:start position:0%
+or something that could have been a
+ 
+
+ align:start position:0%
+or something that could have been a
+neutron if we start off with Z an a then
+
+ align:start position:0%
+neutron if we start off with Z an a then
+ 
+
+ align:start position:0%
+neutron if we start off with Z an a then
+we'll start off with a neutron and a
+
+ align:start position:0%
+we'll start off with a neutron and a
+ 
+
+ align:start position:0%
+we'll start off with a neutron and a
+daughter with the same Z and a minus one
+
+ align:start position:0%
+daughter with the same Z and a minus one
+ 
+
+ align:start position:0%
+daughter with the same Z and a minus one
+total so what would that look like on a
+
+ align:start position:0%
+total so what would that look like on a
+ 
+
+ align:start position:0%
+total so what would that look like on a
+decay chain you don't usually see this
+
+ align:start position:0%
+decay chain you don't usually see this
+ 
+
+ align:start position:0%
+decay chain you don't usually see this
+but we're draw it anyway it would go
+
+ align:start position:0%
+but we're draw it anyway it would go
+ 
+
+ align:start position:0%
+but we're draw it anyway it would go
+straight down right so it'll be some
+
+ align:start position:0%
+straight down right so it'll be some
+ 
+
+ align:start position:0%
+straight down right so it'll be some
+other nucleus so the same Z but an a
+
+ align:start position:0%
+other nucleus so the same Z but an a
+ 
+
+ align:start position:0%
+other nucleus so the same Z but an a
+minus one and it could decay by Neutron
+
+ align:start position:0%
+minus one and it could decay by Neutron
+ 
+
+ align:start position:0%
+minus one and it could decay by Neutron
+emission yeah that totally happens if
+
+ align:start position:0%
+emission yeah that totally happens if
+ 
+
+ align:start position:0%
+emission yeah that totally happens if
+you look at the very very right edge of
+
+ align:start position:0%
+you look at the very very right edge of
+ 
+
+ align:start position:0%
+you look at the very very right edge of
+the table of nuclides let's go back to
+
+ align:start position:0%
+the table of nuclides let's go back to
+ 
+
+ align:start position:0%
+the table of nuclides let's go back to
+the home page for that and look at the
+
+ align:start position:0%
+the home page for that and look at the
+ 
+
+ align:start position:0%
+the home page for that and look at the
+super Neutron rich like helium ten who's
+
+ align:start position:0%
+super Neutron rich like helium ten who's
+ 
+
+ align:start position:0%
+super Neutron rich like helium ten who's
+ever heard of this right doesn't even
+
+ align:start position:0%
+ever heard of this right doesn't even
+ 
+
+ align:start position:0%
+ever heard of this right doesn't even
+say let's say two neutrons so this is so
+
+ align:start position:0%
+say let's say two neutrons so this is so
+ 
+
+ align:start position:0%
+say let's say two neutrons so this is so
+unstable that it just immediately spits
+
+ align:start position:0%
+unstable that it just immediately spits
+ 
+
+ align:start position:0%
+unstable that it just immediately spits
+out two neutrons so yeah these things
+
+ align:start position:0%
+out two neutrons so yeah these things
+ 
+
+ align:start position:0%
+out two neutrons so yeah these things
+happen you won't tend to see this decay
+
+ align:start position:0%
+happen you won't tend to see this decay
+ 
+
+ align:start position:0%
+happen you won't tend to see this decay
+in textbooks because it only happens for
+
+ align:start position:0%
+in textbooks because it only happens for
+ 
+
+ align:start position:0%
+in textbooks because it only happens for
+exceptionally unstable nuclei but yeah
+
+ align:start position:0%
+exceptionally unstable nuclei but yeah
+ 
+
+ align:start position:0%
+exceptionally unstable nuclei but yeah
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+it does happen what else could happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember we've been talking about yeah
+
+ align:start position:0%
+remember we've been talking about yeah
+ 
+
+ align:start position:0%
+remember we've been talking about yeah
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+it could be gammas and so I'll make one
+
+ align:start position:0%
+it could be gammas and so I'll make one
+ 
+
+ align:start position:0%
+it could be gammas and so I'll make one
+little extra piece here for a gamma
+
+ align:start position:0%
+little extra piece here for a gamma
+ 
+
+ align:start position:0%
+little extra piece here for a gamma
+decay which is nothing more than a
+
+ align:start position:0%
+decay which is nothing more than a
+ 
+
+ align:start position:0%
+decay which is nothing more than a
+photon emitted from the nucleus we start
+
+ align:start position:0%
+photon emitted from the nucleus we start
+ 
+
+ align:start position:0%
+photon emitted from the nucleus we start
+off with a parent Z and a
+
+ align:start position:0%
+off with a parent Z and a
+ 
+
+ align:start position:0%
+off with a parent Z and a
+and this becomes well what should I even
+
+ align:start position:0%
+and this becomes well what should I even
+ 
+
+ align:start position:0%
+and this becomes well what should I even
+write daughter nucleus I see some people
+
+ align:start position:0%
+write daughter nucleus I see some people
+ 
+
+ align:start position:0%
+write daughter nucleus I see some people
+shaking their heads no why not yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so very close you have the same atom
+
+ align:start position:0%
+yep so very close you have the same atom
+ 
+
+ align:start position:0%
+yep so very close you have the same atom
+so let's say the same parent with the
+
+ align:start position:0%
+so let's say the same parent with the
+ 
+
+ align:start position:0%
+so let's say the same parent with the
+same number of protons same number of
+
+ align:start position:0%
+same number of protons same number of
+ 
+
+ align:start position:0%
+same number of protons same number of
+total nucleons and I'll just correct
+
+ align:start position:0%
+total nucleons and I'll just correct
+ 
+
+ align:start position:0%
+total nucleons and I'll just correct
+that to say one of its nuclei is at a
+
+ align:start position:0%
+that to say one of its nuclei is at a
+ 
+
+ align:start position:0%
+that to say one of its nuclei is at a
+lower energy state but otherwise
+
+ align:start position:0%
+lower energy state but otherwise
+ 
+
+ align:start position:0%
+lower energy state but otherwise
+everything is completely correct so why
+
+ align:start position:0%
+everything is completely correct so why
+ 
+
+ align:start position:0%
+everything is completely correct so why
+don't we put a little star here to say
+
+ align:start position:0%
+don't we put a little star here to say
+ 
+
+ align:start position:0%
+don't we put a little star here to say
+that that was at an excited state just
+
+ align:start position:0%
+that that was at an excited state just
+ 
+
+ align:start position:0%
+that that was at an excited state just
+like electrons can be promoted to outer
+
+ align:start position:0%
+like electrons can be promoted to outer
+ 
+
+ align:start position:0%
+like electrons can be promoted to outer
+shells pick up a little bit of energy so
+
+ align:start position:0%
+shells pick up a little bit of energy so
+ 
+
+ align:start position:0%
+shells pick up a little bit of energy so
+can nucleon so can protons and neutrons
+
+ align:start position:0%
+can nucleon so can protons and neutrons
+ 
+
+ align:start position:0%
+can nucleon so can protons and neutrons
+and this is so going to be a subject of
+
+ align:start position:0%
+and this is so going to be a subject of
+ 
+
+ align:start position:0%
+and this is so going to be a subject of
+well great discussion in 22:02
+
+ align:start position:0%
+well great discussion in 22:02
+ 
+
+ align:start position:0%
+well great discussion in 22:02
+for now all you have to know is that
+
+ align:start position:0%
+for now all you have to know is that
+ 
+
+ align:start position:0%
+for now all you have to know is that
+nucleons like electrons can occupy
+
+ align:start position:0%
+nucleons like electrons can occupy
+ 
+
+ align:start position:0%
+nucleons like electrons can occupy
+higher energy states and when they fall
+
+ align:start position:0%
+higher energy states and when they fall
+ 
+
+ align:start position:0%
+higher energy states and when they fall
+down to lower energy state they can
+
+ align:start position:0%
+down to lower energy state they can
+ 
+
+ align:start position:0%
+down to lower energy state they can
+release that energy in the form of a
+
+ align:start position:0%
+release that energy in the form of a
+ 
+
+ align:start position:0%
+release that energy in the form of a
+gamma ray so you could also have let's
+
+ align:start position:0%
+gamma ray so you could also have let's
+ 
+
+ align:start position:0%
+gamma ray so you could also have let's
+say squiggly line gamma decay to
+
+ align:start position:0%
+say squiggly line gamma decay to
+ 
+
+ align:start position:0%
+say squiggly line gamma decay to
+something stable and so this right here
+
+ align:start position:0%
+something stable and so this right here
+ 
+
+ align:start position:0%
+something stable and so this right here
+would be the generalized decay diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone ever heard of one isotope that
+
+ align:start position:0%
+anyone ever heard of one isotope that
+ 
+
+ align:start position:0%
+anyone ever heard of one isotope that
+undergoes all these possible decay
+
+ align:start position:0%
+undergoes all these possible decay
+ 
+
+ align:start position:0%
+undergoes all these possible decay
+mechanisms glad no one's saying anything
+
+ align:start position:0%
+mechanisms glad no one's saying anything
+ 
+
+ align:start position:0%
+mechanisms glad no one's saying anything
+because neither have I there's one that
+
+ align:start position:0%
+because neither have I there's one that
+ 
+
+ align:start position:0%
+because neither have I there's one that
+comes close actually if you look at no
+
+ align:start position:0%
+comes close actually if you look at no
+ 
+
+ align:start position:0%
+comes close actually if you look at no
+that's not this part I want to show you
+
+ align:start position:0%
+that's not this part I want to show you
+ 
+
+ align:start position:0%
+that's not this part I want to show you
+I want to show you the big one if you
+
+ align:start position:0%
+I want to show you the big one if you
+ 
+
+ align:start position:0%
+I want to show you the big one if you
+look at potassium-40 the nuclide we've
+
+ align:start position:0%
+look at potassium-40 the nuclide we've
+ 
+
+ align:start position:0%
+look at potassium-40 the nuclide we've
+probably talked about the most so far it
+
+ align:start position:0%
+probably talked about the most so far it
+ 
+
+ align:start position:0%
+probably talked about the most so far it
+covers most of the space of this
+
+ align:start position:0%
+covers most of the space of this
+ 
+
+ align:start position:0%
+covers most of the space of this
+generalized a.k diagram and there was a
+
+ align:start position:0%
+generalized a.k diagram and there was a
+ 
+
+ align:start position:0%
+generalized a.k diagram and there was a
+question that came through at least I
+
+ align:start position:0%
+question that came through at least I
+ 
+
+ align:start position:0%
+question that came through at least I
+think or non-anonymous email what is it
+
+ align:start position:0%
+think or non-anonymous email what is it
+ 
+
+ align:start position:0%
+think or non-anonymous email what is it
+that makes these even even versus
+
+ align:start position:0%
+that makes these even even versus
+ 
+
+ align:start position:0%
+that makes these even even versus
+odd-odd nuclei less or more stable
+
+ align:start position:0%
+odd-odd nuclei less or more stable
+ 
+
+ align:start position:0%
+odd-odd nuclei less or more stable
+anytime you have an odd odd nucleus both
+
+ align:start position:0%
+anytime you have an odd odd nucleus both
+ 
+
+ align:start position:0%
+anytime you have an odd odd nucleus both
+the number of protons the number of
+
+ align:start position:0%
+the number of protons the number of
+ 
+
+ align:start position:0%
+the number of protons the number of
+neutrons these nuclear shells are not
+
+ align:start position:0%
+neutrons these nuclear shells are not
+ 
+
+ align:start position:0%
+neutrons these nuclear shells are not
+fully occupied and they're not that
+
+ align:start position:0%
+fully occupied and they're not that
+ 
+
+ align:start position:0%
+fully occupied and they're not that
+stable compared to an even even nucleus
+
+ align:start position:0%
+stable compared to an even even nucleus
+ 
+
+ align:start position:0%
+stable compared to an even even nucleus
+that has an even number of Z and an even
+
+ align:start position:0%
+that has an even number of Z and an even
+ 
+
+ align:start position:0%
+that has an even number of Z and an even
+number of n just kind of like electrons
+
+ align:start position:0%
+number of n just kind of like electrons
+ 
+
+ align:start position:0%
+number of n just kind of like electrons
+these things tend to travel in pairs and
+
+ align:start position:0%
+these things tend to travel in pairs and
+ 
+
+ align:start position:0%
+these things tend to travel in pairs and
+not fully occupied energy levels will be
+
+ align:start position:0%
+not fully occupied energy levels will be
+ 
+
+ align:start position:0%
+not fully occupied energy levels will be
+less stable potassium-40 happens to be
+
+ align:start position:0%
+less stable potassium-40 happens to be
+ 
+
+ align:start position:0%
+less stable potassium-40 happens to be
+one of those odd-odd nuclei that is
+
+ align:start position:0%
+one of those odd-odd nuclei that is
+ 
+
+ align:start position:0%
+one of those odd-odd nuclei that is
+relatively unstable and it can go either
+
+ align:start position:0%
+relatively unstable and it can go either
+ 
+
+ align:start position:0%
+relatively unstable and it can go either
+way either you can lose a proton or you
+
+ align:start position:0%
+way either you can lose a proton or you
+ 
+
+ align:start position:0%
+way either you can lose a proton or you
+can gain a proton by competing
+
+ align:start position:0%
+can gain a proton by competing
+ 
+
+ align:start position:0%
+can gain a proton by competing
+mechanisms like positron or electron
+
+ align:start position:0%
+mechanisms like positron or electron
+ 
+
+ align:start position:0%
+mechanisms like positron or electron
+capture
+
+ align:start position:0%
+capture
+ 
+
+ align:start position:0%
+capture
+or beta emission so this one I like a
+
+ align:start position:0%
+or beta emission so this one I like a
+ 
+
+ align:start position:0%
+or beta emission so this one I like a
+lot because it gives you almost every
+
+ align:start position:0%
+lot because it gives you almost every
+ 
+
+ align:start position:0%
+lot because it gives you almost every
+possible decay with the exception of
+
+ align:start position:0%
+possible decay with the exception of
+ 
+
+ align:start position:0%
+possible decay with the exception of
+alpha decay and spontaneous Neutron
+
+ align:start position:0%
+alpha decay and spontaneous Neutron
+ 
+
+ align:start position:0%
+alpha decay and spontaneous Neutron
+emission it's not that unstable and you
+
+ align:start position:0%
+emission it's not that unstable and you
+ 
+
+ align:start position:0%
+emission it's not that unstable and you
+know only one really missing from here I
+
+ align:start position:0%
+know only one really missing from here I
+ 
+
+ align:start position:0%
+know only one really missing from here I
+found what I think is the simplest to K
+
+ align:start position:0%
+found what I think is the simplest to K
+ 
+
+ align:start position:0%
+found what I think is the simplest to K
+diagram ever just prozium 151 there's
+
+ align:start position:0%
+diagram ever just prozium 151 there's
+ 
+
+ align:start position:0%
+diagram ever just prozium 151 there's
+only one thing it can do is it can decay
+
+ align:start position:0%
+only one thing it can do is it can decay
+ 
+
+ align:start position:0%
+only one thing it can do is it can decay
+via alpha decay to its ground state I
+
+ align:start position:0%
+via alpha decay to its ground state I
+ 
+
+ align:start position:0%
+via alpha decay to its ground state I
+want to point out a few of the features
+
+ align:start position:0%
+want to point out a few of the features
+ 
+
+ align:start position:0%
+want to point out a few of the features
+of these decay diagrams so you know what
+
+ align:start position:0%
+of these decay diagrams so you know what
+ 
+
+ align:start position:0%
+of these decay diagrams so you know what
+to look for up here is the parent
+
+ align:start position:0%
+to look for up here is the parent
+ 
+
+ align:start position:0%
+to look for up here is the parent
+nucleus down there's the daughter
+
+ align:start position:0%
+nucleus down there's the daughter
+ 
+
+ align:start position:0%
+nucleus down there's the daughter
+nucleus and these energies are not
+
+ align:start position:0%
+nucleus and these energies are not
+ 
+
+ align:start position:0%
+nucleus and these energies are not
+absolute they're relative to the ground
+
+ align:start position:0%
+absolute they're relative to the ground
+ 
+
+ align:start position:0%
+absolute they're relative to the ground
+state of whatever the daughter nucleus
+
+ align:start position:0%
+state of whatever the daughter nucleus
+ 
+
+ align:start position:0%
+state of whatever the daughter nucleus
+is so this is a simple example who helps
+
+ align:start position:0%
+is so this is a simple example who helps
+ 
+
+ align:start position:0%
+is so this is a simple example who helps
+show you that Galilean 147 doesn't have
+
+ align:start position:0%
+show you that Galilean 147 doesn't have
+ 
+
+ align:start position:0%
+show you that Galilean 147 doesn't have
+a binding energy of zero this is
+
+ align:start position:0%
+a binding energy of zero this is
+ 
+
+ align:start position:0%
+a binding energy of zero this is
+relative to the ground state of Gadd 147
+
+ align:start position:0%
+relative to the ground state of Gadd 147
+ 
+
+ align:start position:0%
+relative to the ground state of Gadd 147
+and that will tell you that the Q value
+
+ align:start position:0%
+and that will tell you that the Q value
+ 
+
+ align:start position:0%
+and that will tell you that the Q value
+for this reaction is 4.1 796 MeV these
+
+ align:start position:0%
+for this reaction is 4.1 796 MeV these
+ 
+
+ align:start position:0%
+for this reaction is 4.1 796 MeV these
+things are usually listed in MeV unless
+
+ align:start position:0%
+things are usually listed in MeV unless
+ 
+
+ align:start position:0%
+things are usually listed in MeV unless
+said otherwise you also might notice a
+
+ align:start position:0%
+said otherwise you also might notice a
+ 
+
+ align:start position:0%
+said otherwise you also might notice a
+pattern that most alpha particles tend
+
+ align:start position:0%
+pattern that most alpha particles tend
+ 
+
+ align:start position:0%
+pattern that most alpha particles tend
+to come out around 4 MeV or larger the
+
+ align:start position:0%
+to come out around 4 MeV or larger the
+ 
+
+ align:start position:0%
+to come out around 4 MeV or larger the
+answer to y is going to be given in 2202
+
+ align:start position:0%
+answer to y is going to be given in 2202
+ 
+
+ align:start position:0%
+answer to y is going to be given in 2202
+yep these percentages tell you the
+
+ align:start position:0%
+yep these percentages tell you the
+ 
+
+ align:start position:0%
+yep these percentages tell you the
+probability that each decay will happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are usually measured because it
+
+ align:start position:0%
+these are usually measured because it
+ 
+
+ align:start position:0%
+these are usually measured because it
+can be let's say let's say things get
+
+ align:start position:0%
+can be let's say let's say things get
+ 
+
+ align:start position:0%
+can be let's say let's say things get
+quantum and difficult in terms of
+
+ align:start position:0%
+quantum and difficult in terms of
+ 
+
+ align:start position:0%
+quantum and difficult in terms of
+calculating these and our knowledge of
+
+ align:start position:0%
+calculating these and our knowledge of
+ 
+
+ align:start position:0%
+calculating these and our knowledge of
+wave functions of well higher and higher
+
+ align:start position:0%
+wave functions of well higher and higher
+ 
+
+ align:start position:0%
+wave functions of well higher and higher
+a or Z nuclei gets a little less time a
+
+ align:start position:0%
+a or Z nuclei gets a little less time a
+ 
+
+ align:start position:0%
+a or Z nuclei gets a little less time a
+little more tenuous so a lot of these
+
+ align:start position:0%
+little more tenuous so a lot of these
+ 
+
+ align:start position:0%
+little more tenuous so a lot of these
+would be measured you can look at the
+
+ align:start position:0%
+would be measured you can look at the
+ 
+
+ align:start position:0%
+would be measured you can look at the
+number of alpha particles of each energy
+
+ align:start position:0%
+number of alpha particles of each energy
+ 
+
+ align:start position:0%
+number of alpha particles of each energy
+that you observe and then you get the
+
+ align:start position:0%
+that you observe and then you get the
+ 
+
+ align:start position:0%
+that you observe and then you get the
+average probabilities for this one it's
+
+ align:start position:0%
+average probabilities for this one it's
+ 
+
+ align:start position:0%
+average probabilities for this one it's
+simple there's a hundred percent
+
+ align:start position:0%
+simple there's a hundred percent
+ 
+
+ align:start position:0%
+simple there's a hundred percent
+probability that this is the only thing
+
+ align:start position:0%
+probability that this is the only thing
+ 
+
+ align:start position:0%
+probability that this is the only thing
+that exists the other things to note the
+
+ align:start position:0%
+that exists the other things to note the
+ 
+
+ align:start position:0%
+that exists the other things to note the
+half-life will be given up here in this
+
+ align:start position:0%
+half-life will be given up here in this
+ 
+
+ align:start position:0%
+half-life will be given up here in this
+case at seventeen point nine minutes so
+
+ align:start position:0%
+case at seventeen point nine minutes so
+ 
+
+ align:start position:0%
+case at seventeen point nine minutes so
+relatively long half-life compared to
+
+ align:start position:0%
+relatively long half-life compared to
+ 
+
+ align:start position:0%
+relatively long half-life compared to
+helium five and we'll be going over what
+
+ align:start position:0%
+helium five and we'll be going over what
+ 
+
+ align:start position:0%
+helium five and we'll be going over what
+half-life is and what they are on Friday
+
+ align:start position:0%
+half-life is and what they are on Friday
+ 
+
+ align:start position:0%
+half-life is and what they are on Friday
+and then the last thing are the spin
+
+ align:start position:0%
+and then the last thing are the spin
+ 
+
+ align:start position:0%
+and then the last thing are the spin
+states of the initial and final nuclei
+
+ align:start position:0%
+states of the initial and final nuclei
+ 
+
+ align:start position:0%
+states of the initial and final nuclei
+which we will not cover in this class
+
+ align:start position:0%
+which we will not cover in this class
+ 
+
+ align:start position:0%
+which we will not cover in this class
+but you will cover in 22:02 so
+
+ align:start position:0%
+but you will cover in 22:02 so
+ 
+
+ align:start position:0%
+but you will cover in 22:02 so
+don't worry about those now but do know
+
+ align:start position:0%
+don't worry about those now but do know
+ 
+
+ align:start position:0%
+don't worry about those now but do know
+that when you need to go find the spin
+
+ align:start position:0%
+that when you need to go find the spin
+ 
+
+ align:start position:0%
+that when you need to go find the spin
+states of the initial and final nuclei
+
+ align:start position:0%
+states of the initial and final nuclei
+ 
+
+ align:start position:0%
+states of the initial and final nuclei
+to see if certain transitions are
+
+ align:start position:0%
+to see if certain transitions are
+ 
+
+ align:start position:0%
+to see if certain transitions are
+allowed this is where you're going to go
+
+ align:start position:0%
+allowed this is where you're going to go
+ 
+
+ align:start position:0%
+allowed this is where you're going to go
+any questions on what you see here on
+
+ align:start position:0%
+any questions on what you see here on
+ 
+
+ align:start position:0%
+any questions on what you see here on
+how to read these decay diagrams okay
+
+ align:start position:0%
+how to read these decay diagrams okay
+ 
+
+ align:start position:0%
+how to read these decay diagrams okay
+then let's move on to some the simplest
+
+ align:start position:0%
+then let's move on to some the simplest
+ 
+
+ align:start position:0%
+then let's move on to some the simplest
+of them which in the table can look the
+
+ align:start position:0%
+of them which in the table can look the
+ 
+
+ align:start position:0%
+of them which in the table can look the
+most complicated so here you can see
+
+ align:start position:0%
+most complicated so here you can see
+ 
+
+ align:start position:0%
+most complicated so here you can see
+that there's a whole bunch of different
+
+ align:start position:0%
+that there's a whole bunch of different
+ 
+
+ align:start position:0%
+that there's a whole bunch of different
+probabilities for different alpha decay
+
+ align:start position:0%
+probabilities for different alpha decay
+ 
+
+ align:start position:0%
+probabilities for different alpha decay
+nuclear this is one of those more
+
+ align:start position:0%
+nuclear this is one of those more
+ 
+
+ align:start position:0%
+nuclear this is one of those more
+complex examples where the easiest thing
+
+ align:start position:0%
+complex examples where the easiest thing
+ 
+
+ align:start position:0%
+complex examples where the easiest thing
+to do is just measure see how many
+
+ align:start position:0%
+to do is just measure see how many
+ 
+
+ align:start position:0%
+to do is just measure see how many
+alphas you get at each energy and this
+
+ align:start position:0%
+alphas you get at each energy and this
+ 
+
+ align:start position:0%
+alphas you get at each energy and this
+will give you the approximate
+
+ align:start position:0%
+will give you the approximate
+ 
+
+ align:start position:0%
+will give you the approximate
+probabilities that each decay happens
+
+ align:start position:0%
+probabilities that each decay happens
+ 
+
+ align:start position:0%
+probabilities that each decay happens
+and you'll notice here that the final
+
+ align:start position:0%
+and you'll notice here that the final
+ 
+
+ align:start position:0%
+and you'll notice here that the final
+energy states for each of these alphas
+
+ align:start position:0%
+energy states for each of these alphas
+ 
+
+ align:start position:0%
+energy states for each of these alphas
+is not necessarily zero this will tell
+
+ align:start position:0%
+is not necessarily zero this will tell
+ 
+
+ align:start position:0%
+is not necessarily zero this will tell
+you what they are relative to the ground
+
+ align:start position:0%
+you what they are relative to the ground
+ 
+
+ align:start position:0%
+you what they are relative to the ground
+state of in this case thorium 231 so you
+
+ align:start position:0%
+state of in this case thorium 231 so you
+ 
+
+ align:start position:0%
+state of in this case thorium 231 so you
+can emit an alpha from from any
+
+ align:start position:0%
+can emit an alpha from from any
+ 
+
+ align:start position:0%
+can emit an alpha from from any
+combination of nuclear shell levels
+
+ align:start position:0%
+combination of nuclear shell levels
+ 
+
+ align:start position:0%
+combination of nuclear shell levels
+inside this nucleus and you might end up
+
+ align:start position:0%
+inside this nucleus and you might end up
+ 
+
+ align:start position:0%
+inside this nucleus and you might end up
+with a new daughter nucleus whose
+
+ align:start position:0%
+with a new daughter nucleus whose
+ 
+
+ align:start position:0%
+with a new daughter nucleus whose
+protons or neutrons are in excited
+
+ align:start position:0%
+protons or neutrons are in excited
+ 
+
+ align:start position:0%
+protons or neutrons are in excited
+States and the way you remove those
+
+ align:start position:0%
+States and the way you remove those
+ 
+
+ align:start position:0%
+States and the way you remove those
+excited States is gamma decay like we
+
+ align:start position:0%
+excited States is gamma decay like we
+ 
+
+ align:start position:0%
+excited States is gamma decay like we
+talked about here so a lot of alpha
+
+ align:start position:0%
+talked about here so a lot of alpha
+ 
+
+ align:start position:0%
+talked about here so a lot of alpha
+decays are immediately followed by a
+
+ align:start position:0%
+decays are immediately followed by a
+ 
+
+ align:start position:0%
+decays are immediately followed by a
+chain of gamma decays or what we call I
+
+ align:start position:0%
+chain of gamma decays or what we call I
+ 
+
+ align:start position:0%
+chain of gamma decays or what we call I
+teased or isomeric transitions so you'll
+
+ align:start position:0%
+teased or isomeric transitions so you'll
+ 
+
+ align:start position:0%
+teased or isomeric transitions so you'll
+see a couple bits of notation for
+
+ align:start position:0%
+see a couple bits of notation for
+ 
+
+ align:start position:0%
+see a couple bits of notation for
+example you make here called gamma decay
+
+ align:start position:0%
+example you make here called gamma decay
+ 
+
+ align:start position:0%
+example you make here called gamma decay
+you may hear it called isomeric
+
+ align:start position:0%
+you may hear it called isomeric
+ 
+
+ align:start position:0%
+you may hear it called isomeric
+transition we'll try to give them all so
+
+ align:start position:0%
+transition we'll try to give them all so
+ 
+
+ align:start position:0%
+transition we'll try to give them all so
+that in the various readings you have
+
+ align:start position:0%
+that in the various readings you have
+ 
+
+ align:start position:0%
+that in the various readings you have
+you know what's what so notice here you
+
+ align:start position:0%
+you know what's what so notice here you
+ 
+
+ align:start position:0%
+you know what's what so notice here you
+can have with the probability still
+
+ align:start position:0%
+can have with the probability still
+ 
+
+ align:start position:0%
+can have with the probability still
+small that they didn't bother to draw it
+
+ align:start position:0%
+small that they didn't bother to draw it
+ 
+
+ align:start position:0%
+small that they didn't bother to draw it
+an alpha decay to 0.6 3 4 MeV and then
+
+ align:start position:0%
+an alpha decay to 0.6 3 4 MeV and then
+ 
+
+ align:start position:0%
+an alpha decay to 0.6 3 4 MeV and then
+any series of gammas from let's say from
+
+ align:start position:0%
+any series of gammas from let's say from
+ 
+
+ align:start position:0%
+any series of gammas from let's say from
+this state to that state and then from
+
+ align:start position:0%
+this state to that state and then from
+ 
+
+ align:start position:0%
+this state to that state and then from
+this state to one of those or one of
+
+ align:start position:0%
+this state to one of those or one of
+ 
+
+ align:start position:0%
+this state to one of those or one of
+those and then another one down there so
+
+ align:start position:0%
+those and then another one down there so
+ 
+
+ align:start position:0%
+those and then another one down there so
+an alpha decay may be followed by a
+
+ align:start position:0%
+an alpha decay may be followed by a
+ 
+
+ align:start position:0%
+an alpha decay may be followed by a
+whole bunch of gamma transitions or as
+
+ align:start position:0%
+whole bunch of gamma transitions or as
+ 
+
+ align:start position:0%
+whole bunch of gamma transitions or as
+few as none if you want to see what the
+
+ align:start position:0%
+few as none if you want to see what the
+ 
+
+ align:start position:0%
+few as none if you want to see what the
+Alpha energies are well let's head to
+
+ align:start position:0%
+Alpha energies are well let's head to
+ 
+
+ align:start position:0%
+Alpha energies are well let's head to
+the table of nuclides and look at
+
+ align:start position:0%
+the table of nuclides and look at
+ 
+
+ align:start position:0%
+the table of nuclides and look at
+uranium-235
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we look up u-235 you can see that
+
+ align:start position:0%
+so if we look up u-235 you can see that
+ 
+
+ align:start position:0%
+so if we look up u-235 you can see that
+at alpha decays to thorium 231 and I'll
+
+ align:start position:0%
+at alpha decays to thorium 231 and I'll
+ 
+
+ align:start position:0%
+at alpha decays to thorium 231 and I'll
+show you the part of the table that I
+
+ align:start position:0%
+show you the part of the table that I
+ 
+
+ align:start position:0%
+show you the part of the table that I
+didn't show you in the slides which is
+
+ align:start position:0%
+didn't show you in the slides which is
+ 
+
+ align:start position:0%
+didn't show you in the slides which is
+then you've got a table of alpha decay
+
+ align:start position:0%
+then you've got a table of alpha decay
+ 
+
+ align:start position:0%
+then you've got a table of alpha decay
+energies as well as relative intensities
+
+ align:start position:0%
+energies as well as relative intensities
+ 
+
+ align:start position:0%
+energies as well as relative intensities
+and what's called a hindrance this stuff
+
+ align:start position:0%
+and what's called a hindrance this stuff
+ 
+
+ align:start position:0%
+and what's called a hindrance this stuff
+right here comes from the fact that
+
+ align:start position:0%
+right here comes from the fact that
+ 
+
+ align:start position:0%
+right here comes from the fact that
+different alpha decay energies can
+
+ align:start position:0%
+different alpha decay energies can
+ 
+
+ align:start position:0%
+different alpha decay energies can
+happen with different probabilities at
+
+ align:start position:0%
+happen with different probabilities at
+ 
+
+ align:start position:0%
+happen with different probabilities at
+different times so the half-life of a
+
+ align:start position:0%
+different times so the half-life of a
+ 
+
+ align:start position:0%
+different times so the half-life of a
+particular alpha decay can be slightly
+
+ align:start position:0%
+particular alpha decay can be slightly
+ 
+
+ align:start position:0%
+particular alpha decay can be slightly
+different and this is another one of
+
+ align:start position:0%
+different and this is another one of
+ 
+
+ align:start position:0%
+different and this is another one of
+those really kooky things where certain
+
+ align:start position:0%
+those really kooky things where certain
+ 
+
+ align:start position:0%
+those really kooky things where certain
+energy alpha transitions will happen a
+
+ align:start position:0%
+energy alpha transitions will happen a
+ 
+
+ align:start position:0%
+energy alpha transitions will happen a
+little more often initially then finally
+
+ align:start position:0%
+little more often initially then finally
+ 
+
+ align:start position:0%
+little more often initially then finally
+but we don't have to worry about that
+
+ align:start position:0%
+but we don't have to worry about that
+ 
+
+ align:start position:0%
+but we don't have to worry about that
+yet I just want you to know that's why
+
+ align:start position:0%
+yet I just want you to know that's why
+ 
+
+ align:start position:0%
+yet I just want you to know that's why
+the hindrance is there and so you can
+
+ align:start position:0%
+the hindrance is there and so you can
+ 
+
+ align:start position:0%
+the hindrance is there and so you can
+look from this table what's the
+
+ align:start position:0%
+look from this table what's the
+ 
+
+ align:start position:0%
+look from this table what's the
+probability that each of these alphas
+
+ align:start position:0%
+probability that each of these alphas
+ 
+
+ align:start position:0%
+probability that each of these alphas
+will come out and there's going to be
+
+ align:start position:0%
+will come out and there's going to be
+ 
+
+ align:start position:0%
+will come out and there's going to be
+some uncertainty associated with these
+
+ align:start position:0%
+some uncertainty associated with these
+ 
+
+ align:start position:0%
+some uncertainty associated with these
+this is going to usually be some sort of
+
+ align:start position:0%
+this is going to usually be some sort of
+ 
+
+ align:start position:0%
+this is going to usually be some sort of
+measurement uncertainty then you might
+
+ align:start position:0%
+measurement uncertainty then you might
+ 
+
+ align:start position:0%
+measurement uncertainty then you might
+also ask why is it that the highest
+
+ align:start position:0%
+also ask why is it that the highest
+ 
+
+ align:start position:0%
+also ask why is it that the highest
+energy alpha ray is not the same energy
+
+ align:start position:0%
+energy alpha ray is not the same energy
+ 
+
+ align:start position:0%
+energy alpha ray is not the same energy
+as the Q value so for this
+
+ align:start position:0%
+as the Q value so for this
+ 
+
+ align:start position:0%
+as the Q value so for this
+it's a greatly simplified application of
+
+ align:start position:0%
+it's a greatly simplified application of
+ 
+
+ align:start position:0%
+it's a greatly simplified application of
+the Q equation that we learned last time
+
+ align:start position:0%
+the Q equation that we learned last time
+ 
+
+ align:start position:0%
+the Q equation that we learned last time
+so for here what are the two equations
+
+ align:start position:0%
+so for here what are the two equations
+ 
+
+ align:start position:0%
+so for here what are the two equations
+that we need to conserve if we have a
+
+ align:start position:0%
+that we need to conserve if we have a
+ 
+
+ align:start position:0%
+that we need to conserve if we have a
+system consisting of we have our initial
+
+ align:start position:0%
+system consisting of we have our initial
+ 
+
+ align:start position:0%
+system consisting of we have our initial
+nuclei going into our final nuclei and
+
+ align:start position:0%
+nuclei going into our final nuclei and
+ 
+
+ align:start position:0%
+nuclei going into our final nuclei and
+they go off in equal and opposite
+
+ align:start position:0%
+they go off in equal and opposite
+ 
+
+ align:start position:0%
+they go off in equal and opposite
+directions if it's alpha decay then we
+
+ align:start position:0%
+directions if it's alpha decay then we
+ 
+
+ align:start position:0%
+directions if it's alpha decay then we
+have no little initial nucleus we just
+
+ align:start position:0%
+have no little initial nucleus we just
+ 
+
+ align:start position:0%
+have no little initial nucleus we just
+had a large initial nucleus at last at
+
+ align:start position:0%
+had a large initial nucleus at last at
+ 
+
+ align:start position:0%
+had a large initial nucleus at last at
+rest and afterwards you've got a small
+
+ align:start position:0%
+rest and afterwards you've got a small
+ 
+
+ align:start position:0%
+rest and afterwards you've got a small
+final nucleus which we know is the alpha
+
+ align:start position:0%
+final nucleus which we know is the alpha
+ 
+
+ align:start position:0%
+final nucleus which we know is the alpha
+particle and a large final nucleus which
+
+ align:start position:0%
+particle and a large final nucleus which
+ 
+
+ align:start position:0%
+particle and a large final nucleus which
+we'll call the daughter product and
+
+ align:start position:0%
+we'll call the daughter product and
+ 
+
+ align:start position:0%
+we'll call the daughter product and
+let's say this is the parent it's a much
+
+ align:start position:0%
+let's say this is the parent it's a much
+ 
+
+ align:start position:0%
+let's say this is the parent it's a much
+much simpler system than the general one
+
+ align:start position:0%
+much simpler system than the general one
+ 
+
+ align:start position:0%
+much simpler system than the general one
+we analyzed last week so what are the
+
+ align:start position:0%
+we analyzed last week so what are the
+ 
+
+ align:start position:0%
+we analyzed last week so what are the
+equations that will use to conserve to
+
+ align:start position:0%
+equations that will use to conserve to
+ 
+
+ align:start position:0%
+equations that will use to conserve to
+find out what's the energy of this alpha
+
+ align:start position:0%
+find out what's the energy of this alpha
+ 
+
+ align:start position:0%
+find out what's the energy of this alpha
+particle anyone same three answers as
+
+ align:start position:0%
+particle anyone same three answers as
+ 
+
+ align:start position:0%
+particle anyone same three answers as
+always yep yep mass energy and momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm gonna lump these two together
+
+ align:start position:0%
+I'm gonna lump these two together
+ 
+
+ align:start position:0%
+I'm gonna lump these two together
+because they're kind of the same thing
+
+ align:start position:0%
+because they're kind of the same thing
+ 
+
+ align:start position:0%
+because they're kind of the same thing
+so let's just go with energy and
+
+ align:start position:0%
+so let's just go with energy and
+ 
+
+ align:start position:0%
+so let's just go with energy and
+momentum so what is the initial kinetic
+
+ align:start position:0%
+momentum so what is the initial kinetic
+ 
+
+ align:start position:0%
+momentum so what is the initial kinetic
+energy or let's say the initial kinetic
+
+ align:start position:0%
+energy or let's say the initial kinetic
+ 
+
+ align:start position:0%
+energy or let's say the initial kinetic
+energy of this parent nucleus we can
+
+ align:start position:0%
+energy of this parent nucleus we can
+ 
+
+ align:start position:0%
+energy of this parent nucleus we can
+assume to be zero
+
+ align:start position:0%
+assume to be zero
+ 
+
+ align:start position:0%
+assume to be zero
+what about the final kinetic energy of
+
+ align:start position:0%
+what about the final kinetic energy of
+ 
+
+ align:start position:0%
+what about the final kinetic energy of
+the system well there's only two
+
+ align:start position:0%
+the system well there's only two
+ 
+
+ align:start position:0%
+the system well there's only two
+particles there's going to be some
+
+ align:start position:0%
+particles there's going to be some
+ 
+
+ align:start position:0%
+particles there's going to be some
+kinetic energy of the alpha particle
+
+ align:start position:0%
+kinetic energy of the alpha particle
+ 
+
+ align:start position:0%
+kinetic energy of the alpha particle
+plus the recoiled kinetic energy because
+
+ align:start position:0%
+plus the recoiled kinetic energy because
+ 
+
+ align:start position:0%
+plus the recoiled kinetic energy because
+if the alpha goes in one direction the
+
+ align:start position:0%
+if the alpha goes in one direction the
+ 
+
+ align:start position:0%
+if the alpha goes in one direction the
+daughter nucleus has to go off in the
+
+ align:start position:0%
+daughter nucleus has to go off in the
+ 
+
+ align:start position:0%
+daughter nucleus has to go off in the
+other direction and the total energy
+
+ align:start position:0%
+other direction and the total energy
+ 
+
+ align:start position:0%
+other direction and the total energy
+comes out to Q this Q value you can get
+
+ align:start position:0%
+comes out to Q this Q value you can get
+ 
+
+ align:start position:0%
+comes out to Q this Q value you can get
+by conserving Nath's where we can say
+
+ align:start position:0%
+by conserving Nath's where we can say
+ 
+
+ align:start position:0%
+by conserving Nath's where we can say
+that the mass of the parent has to equal
+
+ align:start position:0%
+that the mass of the parent has to equal
+ 
+
+ align:start position:0%
+that the mass of the parent has to equal
+the mass of the Alpha plus the mass of
+
+ align:start position:0%
+the mass of the Alpha plus the mass of
+ 
+
+ align:start position:0%
+the mass of the Alpha plus the mass of
+the daughter plus Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's where we can get cute if we
+
+ align:start position:0%
+so that's where we can get cute if we
+ 
+
+ align:start position:0%
+so that's where we can get cute if we
+don't know it already luckily we know it
+
+ align:start position:0%
+don't know it already luckily we know it
+ 
+
+ align:start position:0%
+don't know it already luckily we know it
+already so there we've used mass there
+
+ align:start position:0%
+already so there we've used mass there
+ 
+
+ align:start position:0%
+already so there we've used mass there
+we've used energy and now what are the
+
+ align:start position:0%
+we've used energy and now what are the
+ 
+
+ align:start position:0%
+we've used energy and now what are the
+momentum of the initial and final states
+
+ align:start position:0%
+momentum of the initial and final states
+ 
+
+ align:start position:0%
+momentum of the initial and final states
+here anyone just shout it out what's the
+
+ align:start position:0%
+here anyone just shout it out what's the
+ 
+
+ align:start position:0%
+here anyone just shout it out what's the
+initial momentum of the parent nucleus
+
+ align:start position:0%
+initial momentum of the parent nucleus
+ 
+
+ align:start position:0%
+initial momentum of the parent nucleus
+zero equals what's the momentum of the
+
+ align:start position:0%
+zero equals what's the momentum of the
+ 
+
+ align:start position:0%
+zero equals what's the momentum of the
+Alpha and then remember that trick if we
+
+ align:start position:0%
+Alpha and then remember that trick if we
+ 
+
+ align:start position:0%
+Alpha and then remember that trick if we
+want to say p equals MV equals what more
+
+ align:start position:0%
+want to say p equals MV equals what more
+ 
+
+ align:start position:0%
+want to say p equals MV equals what more
+convenient form that contains the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+square root of 2m t so let's go with
+
+ align:start position:0%
+square root of 2m t so let's go with
+ 
+
+ align:start position:0%
+square root of 2m t so let's go with
+that so there'll be the square root of
+
+ align:start position:0%
+that so there'll be the square root of
+ 
+
+ align:start position:0%
+that so there'll be the square root of
+two mass of the Alpha kinetic energy of
+
+ align:start position:0%
+two mass of the Alpha kinetic energy of
+ 
+
+ align:start position:0%
+two mass of the Alpha kinetic energy of
+the Alpha minus the square root of two
+
+ align:start position:0%
+the Alpha minus the square root of two
+ 
+
+ align:start position:0%
+the Alpha minus the square root of two
+times the mass of the daughter times the
+
+ align:start position:0%
+times the mass of the daughter times the
+ 
+
+ align:start position:0%
+times the mass of the daughter times the
+kinetic energy of the daughter because
+
+ align:start position:0%
+kinetic energy of the daughter because
+ 
+
+ align:start position:0%
+kinetic energy of the daughter because
+these have to have equal and opposite
+
+ align:start position:0%
+these have to have equal and opposite
+ 
+
+ align:start position:0%
+these have to have equal and opposite
+momentum so all we have to do is move
+
+ align:start position:0%
+momentum so all we have to do is move
+ 
+
+ align:start position:0%
+momentum so all we have to do is move
+that one over here this makes that
+
+ align:start position:0%
+that one over here this makes that
+ 
+
+ align:start position:0%
+that one over here this makes that
+equation easy everything's got a square
+
+ align:start position:0%
+equation easy everything's got a square
+ 
+
+ align:start position:0%
+equation easy everything's got a square
+root of two we can square both sides and
+
+ align:start position:0%
+root of two we can square both sides and
+ 
+
+ align:start position:0%
+root of two we can square both sides and
+we end up with a pretty simple relation
+
+ align:start position:0%
+we end up with a pretty simple relation
+ 
+
+ align:start position:0%
+we end up with a pretty simple relation
+mass of the alpha times the kinetic
+
+ align:start position:0%
+mass of the alpha times the kinetic
+ 
+
+ align:start position:0%
+mass of the alpha times the kinetic
+energy of the Alpha is the mass of the
+
+ align:start position:0%
+energy of the Alpha is the mass of the
+ 
+
+ align:start position:0%
+energy of the Alpha is the mass of the
+daughter times the kinetic energy of the
+
+ align:start position:0%
+daughter times the kinetic energy of the
+ 
+
+ align:start position:0%
+daughter times the kinetic energy of the
+daughter we don't usually care about the
+
+ align:start position:0%
+daughter we don't usually care about the
+ 
+
+ align:start position:0%
+daughter we don't usually care about the
+kinetic energy of the recoil nucleus or
+
+ align:start position:0%
+kinetic energy of the recoil nucleus or
+ 
+
+ align:start position:0%
+kinetic energy of the recoil nucleus or
+the daughter because the range is so
+
+ align:start position:0%
+the daughter because the range is so
+ 
+
+ align:start position:0%
+the daughter because the range is so
+small that we usually don't get to
+
+ align:start position:0%
+small that we usually don't get to
+ 
+
+ align:start position:0%
+small that we usually don't get to
+measure it but we are trying to measure
+
+ align:start position:0%
+measure it but we are trying to measure
+ 
+
+ align:start position:0%
+measure it but we are trying to measure
+what are the actual alpha particle
+
+ align:start position:0%
+what are the actual alpha particle
+ 
+
+ align:start position:0%
+what are the actual alpha particle
+energies so that we can reconstruct oops
+
+ align:start position:0%
+energies so that we can reconstruct oops
+ 
+
+ align:start position:0%
+energies so that we can reconstruct oops
+this table down here so we can take our
+
+ align:start position:0%
+this table down here so we can take our
+ 
+
+ align:start position:0%
+this table down here so we can take our
+energy conservation equation and
+
+ align:start position:0%
+energy conservation equation and
+ 
+
+ align:start position:0%
+energy conservation equation and
+rearrange it to isolate TD the kinetic
+
+ align:start position:0%
+rearrange it to isolate TD the kinetic
+ 
+
+ align:start position:0%
+rearrange it to isolate TD the kinetic
+energy of the daughter and say TD equals
+
+ align:start position:0%
+energy of the daughter and say TD equals
+ 
+
+ align:start position:0%
+energy of the daughter and say TD equals
+Q minus T alpha substitute that in here
+
+ align:start position:0%
+Q minus T alpha substitute that in here
+ 
+
+ align:start position:0%
+Q minus T alpha substitute that in here
+and let's rewrite what we've got mass of
+
+ align:start position:0%
+and let's rewrite what we've got mass of
+ 
+
+ align:start position:0%
+and let's rewrite what we've got mass of
+the alpha T alpha equals mass of the
+
+ align:start position:0%
+the alpha T alpha equals mass of the
+ 
+
+ align:start position:0%
+the alpha T alpha equals mass of the
+daughter times
+
+ align:start position:0%
+daughter times
+ 
+
+ align:start position:0%
+daughter times
+Q minus T alpha if we multiply each term
+
+ align:start position:0%
+Q minus T alpha if we multiply each term
+ 
+
+ align:start position:0%
+Q minus T alpha if we multiply each term
+in here by M D we get M DQ minus M D T
+
+ align:start position:0%
+in here by M D we get M DQ minus M D T
+ 
+
+ align:start position:0%
+in here by M D we get M DQ minus M D T
+alpha then we can take all of the T
+
+ align:start position:0%
+alpha then we can take all of the T
+ 
+
+ align:start position:0%
+alpha then we can take all of the T
+alphas on one side so we'll just add T I
+
+ align:start position:0%
+alphas on one side so we'll just add T I
+ 
+
+ align:start position:0%
+alphas on one side so we'll just add T I
+add M DT alpha to each side so we have M
+
+ align:start position:0%
+add M DT alpha to each side so we have M
+ 
+
+ align:start position:0%
+add M DT alpha to each side so we have M
+alpha T alpha plus M DT alpha equals M
+
+ align:start position:0%
+alpha T alpha plus M DT alpha equals M
+ 
+
+ align:start position:0%
+alpha T alpha plus M DT alpha equals M
+DQ we can factor out the T alpha here
+
+ align:start position:0%
+DQ we can factor out the T alpha here
+ 
+
+ align:start position:0%
+DQ we can factor out the T alpha here
+and then we can divide each side by M
+
+ align:start position:0%
+and then we can divide each side by M
+ 
+
+ align:start position:0%
+and then we can divide each side by M
+alpha plus M daughter cancel out the MA
+
+ align:start position:0%
+alpha plus M daughter cancel out the MA
+ 
+
+ align:start position:0%
+alpha plus M daughter cancel out the MA
+plus M D and there we have the answer
+
+ align:start position:0%
+plus M D and there we have the answer
+ 
+
+ align:start position:0%
+plus M D and there we have the answer
+the kinetic energy alpha is just the Q
+
+ align:start position:0%
+the kinetic energy alpha is just the Q
+ 
+
+ align:start position:0%
+the kinetic energy alpha is just the Q
+value times the ratio of the daughter
+
+ align:start position:0%
+value times the ratio of the daughter
+ 
+
+ align:start position:0%
+value times the ratio of the daughter
+mass to the total mass this should look
+
+ align:start position:0%
+mass to the total mass this should look
+ 
+
+ align:start position:0%
+mass to the total mass this should look
+awfully familiar when we did this in the
+
+ align:start position:0%
+awfully familiar when we did this in the
+ 
+
+ align:start position:0%
+awfully familiar when we did this in the
+frame of Neutron elastic scattering or
+
+ align:start position:0%
+frame of Neutron elastic scattering or
+ 
+
+ align:start position:0%
+frame of Neutron elastic scattering or
+any other reaction we had the same
+
+ align:start position:0%
+any other reaction we had the same
+ 
+
+ align:start position:0%
+any other reaction we had the same
+equation with just different notation so
+
+ align:start position:0%
+equation with just different notation so
+ 
+
+ align:start position:0%
+equation with just different notation so
+do you guys recognize this firmware we
+
+ align:start position:0%
+do you guys recognize this firmware we
+ 
+
+ align:start position:0%
+do you guys recognize this firmware we
+had t3 equals Q times M 4 over m 3 plus
+
+ align:start position:0%
+had t3 equals Q times M 4 over m 3 plus
+ 
+
+ align:start position:0%
+had t3 equals Q times M 4 over m 3 plus
+M 4 it's the exact same result just
+
+ align:start position:0%
+M 4 it's the exact same result just
+ 
+
+ align:start position:0%
+M 4 it's the exact same result just
+different notation last time we did it
+
+ align:start position:0%
+different notation last time we did it
+ 
+
+ align:start position:0%
+different notation last time we did it
+in the most complex way possible this
+
+ align:start position:0%
+in the most complex way possible this
+ 
+
+ align:start position:0%
+in the most complex way possible this
+time we started off with the simplest
+
+ align:start position:0%
+time we started off with the simplest
+ 
+
+ align:start position:0%
+time we started off with the simplest
+possible equations for alpha decay in
+
+ align:start position:0%
+possible equations for alpha decay in
+ 
+
+ align:start position:0%
+possible equations for alpha decay in
+the end it's the same q equation we just
+
+ align:start position:0%
+the end it's the same q equation we just
+ 
+
+ align:start position:0%
+the end it's the same q equation we just
+didn't bother what all the other terms
+
+ align:start position:0%
+didn't bother what all the other terms
+ 
+
+ align:start position:0%
+didn't bother what all the other terms
+and angles and things that we don't need
+
+ align:start position:0%
+and angles and things that we don't need
+ 
+
+ align:start position:0%
+and angles and things that we don't need
+so is everyone clear where this came
+
+ align:start position:0%
+so is everyone clear where this came
+ 
+
+ align:start position:0%
+so is everyone clear where this came
+from cool and that's why you're never
+
+ align:start position:0%
+from cool and that's why you're never
+ 
+
+ align:start position:0%
+from cool and that's why you're never
+going to see an alpha particle that's
+
+ align:start position:0%
+going to see an alpha particle that's
+ 
+
+ align:start position:0%
+going to see an alpha particle that's
+got the same energy as the initial minus
+
+ align:start position:0%
+got the same energy as the initial minus
+ 
+
+ align:start position:0%
+got the same energy as the initial minus
+the final energy because the recoil
+
+ align:start position:0%
+the final energy because the recoil
+ 
+
+ align:start position:0%
+the final energy because the recoil
+nucleus or the daughter nucleus takes
+
+ align:start position:0%
+nucleus or the daughter nucleus takes
+ 
+
+ align:start position:0%
+nucleus or the daughter nucleus takes
+away some of that kinetic energy in
+
+ align:start position:0%
+away some of that kinetic energy in
+ 
+
+ align:start position:0%
+away some of that kinetic energy in
+order to conserve the momentum of the
+
+ align:start position:0%
+order to conserve the momentum of the
+ 
+
+ align:start position:0%
+order to conserve the momentum of the
+system that was initially at rest
+
+ align:start position:0%
+system that was initially at rest
+ 
+
+ align:start position:0%
+system that was initially at rest
+another way to say this for those who
+
+ align:start position:0%
+another way to say this for those who
+ 
+
+ align:start position:0%
+another way to say this for those who
+like center of mass coordinates is the
+
+ align:start position:0%
+like center of mass coordinates is the
+ 
+
+ align:start position:0%
+like center of mass coordinates is the
+center of mass of this system was
+
+ align:start position:0%
+center of mass of this system was
+ 
+
+ align:start position:0%
+center of mass of this system was
+the parent nucleus it was at rest the
+
+ align:start position:0%
+the parent nucleus it was at rest the
+ 
+
+ align:start position:0%
+the parent nucleus it was at rest the
+center of mass of the final system has
+
+ align:start position:0%
+center of mass of the final system has
+ 
+
+ align:start position:0%
+center of mass of the final system has
+to remain at rest to conserve momentum
+
+ align:start position:0%
+to remain at rest to conserve momentum
+ 
+
+ align:start position:0%
+to remain at rest to conserve momentum
+but again I won't go into much into
+
+ align:start position:0%
+but again I won't go into much into
+ 
+
+ align:start position:0%
+but again I won't go into much into
+center of mass because I find it a
+
+ align:start position:0%
+center of mass because I find it a
+ 
+
+ align:start position:0%
+center of mass because I find it a
+little unintuitive
+
+ align:start position:0%
+little unintuitive
+ 
+
+ align:start position:0%
+little unintuitive
+I'll stick with a laboratory frame of
+
+ align:start position:0%
+I'll stick with a laboratory frame of
+ 
+
+ align:start position:0%
+I'll stick with a laboratory frame of
+reference so any questions before I move
+
+ align:start position:0%
+reference so any questions before I move
+ 
+
+ align:start position:0%
+reference so any questions before I move
+on alpha I think is the simplest case of
+
+ align:start position:0%
+on alpha I think is the simplest case of
+ 
+
+ align:start position:0%
+on alpha I think is the simplest case of
+radioactive decay and think now you know
+
+ align:start position:0%
+radioactive decay and think now you know
+ 
+
+ align:start position:0%
+radioactive decay and think now you know
+all you need to know about it yes they
+
+ align:start position:0%
+all you need to know about it yes they
+ 
+
+ align:start position:0%
+all you need to know about it yes they
+were not not MA and MD but TA and TD
+
+ align:start position:0%
+were not not MA and MD but TA and TD
+ 
+
+ align:start position:0%
+were not not MA and MD but TA and TD
+would change yep so in this case for a
+
+ align:start position:0%
+would change yep so in this case for a
+ 
+
+ align:start position:0%
+would change yep so in this case for a
+different alpha decays they'll have
+
+ align:start position:0%
+different alpha decays they'll have
+ 
+
+ align:start position:0%
+different alpha decays they'll have
+different Q values so the Q value of
+
+ align:start position:0%
+different Q values so the Q value of
+ 
+
+ align:start position:0%
+different Q values so the Q value of
+let's say this top alpha decay is this
+
+ align:start position:0%
+let's say this top alpha decay is this
+ 
+
+ align:start position:0%
+let's say this top alpha decay is this
+energy here four point six seven six MeV
+
+ align:start position:0%
+energy here four point six seven six MeV
+ 
+
+ align:start position:0%
+energy here four point six seven six MeV
+minus 0.63 four so use a different Q and
+
+ align:start position:0%
+minus 0.63 four so use a different Q and
+ 
+
+ align:start position:0%
+minus 0.63 four so use a different Q and
+you'll get different TAS and T DS yep so
+
+ align:start position:0%
+you'll get different TAS and T DS yep so
+ 
+
+ align:start position:0%
+you'll get different TAS and T DS yep so
+don't worry you'll get chances to try
+
+ align:start position:0%
+don't worry you'll get chances to try
+ 
+
+ align:start position:0%
+don't worry you'll get chances to try
+out these calculations on the homework
+
+ align:start position:0%
+out these calculations on the homework
+ 
+
+ align:start position:0%
+out these calculations on the homework
+well I'll actually ask you to verify
+
+ align:start position:0%
+well I'll actually ask you to verify
+ 
+
+ align:start position:0%
+well I'll actually ask you to verify
+some of these you know calculate some of
+
+ align:start position:0%
+some of these you know calculate some of
+ 
+
+ align:start position:0%
+some of these you know calculate some of
+these from this equation make sure you
+
+ align:start position:0%
+these from this equation make sure you
+ 
+
+ align:start position:0%
+these from this equation make sure you
+get the same values as the table any
+
+ align:start position:0%
+get the same values as the table any
+ 
+
+ align:start position:0%
+get the same values as the table any
+other questions on alpha decay before
+
+ align:start position:0%
+other questions on alpha decay before
+ 
+
+ align:start position:0%
+other questions on alpha decay before
+moving on to beta we're just going an
+
+ align:start position:0%
+moving on to beta we're just going an
+ 
+
+ align:start position:0%
+moving on to beta we're just going an
+order of the Greek alphabet so beta
+
+ align:start position:0%
+order of the Greek alphabet so beta
+ 
+
+ align:start position:0%
+order of the Greek alphabet so beta
+decay is a kind of funny one you don't
+
+ align:start position:0%
+decay is a kind of funny one you don't
+ 
+
+ align:start position:0%
+decay is a kind of funny one you don't
+tend to get a beta particle out at the
+
+ align:start position:0%
+tend to get a beta particle out at the
+ 
+
+ align:start position:0%
+tend to get a beta particle out at the
+energy of this Q value you actually end
+
+ align:start position:0%
+energy of this Q value you actually end
+ 
+
+ align:start position:0%
+energy of this Q value you actually end
+up getting a spectrum and this measured
+
+ align:start position:0%
+up getting a spectrum and this measured
+ 
+
+ align:start position:0%
+up getting a spectrum and this measured
+spectrum of different beta kinetic
+
+ align:start position:0%
+spectrum of different beta kinetic
+ 
+
+ align:start position:0%
+spectrum of different beta kinetic
+energies is what led to the thoughts
+
+ align:start position:0%
+energies is what led to the thoughts
+ 
+
+ align:start position:0%
+energies is what led to the thoughts
+that there must be something else
+
+ align:start position:0%
+that there must be something else
+ 
+
+ align:start position:0%
+that there must be something else
+carrying away some of that extra mass of
+
+ align:start position:0%
+carrying away some of that extra mass of
+ 
+
+ align:start position:0%
+carrying away some of that extra mass of
+some of that extra energy I say that
+
+ align:start position:0%
+some of that extra energy I say that
+ 
+
+ align:start position:0%
+some of that extra energy I say that
+like it's the same thing because yeah it
+
+ align:start position:0%
+like it's the same thing because yeah it
+ 
+
+ align:start position:0%
+like it's the same thing because yeah it
+totally is and this is what led to the
+
+ align:start position:0%
+totally is and this is what led to the
+ 
+
+ align:start position:0%
+totally is and this is what led to the
+thinking that there's got to be some
+
+ align:start position:0%
+thinking that there's got to be some
+ 
+
+ align:start position:0%
+thinking that there's got to be some
+other very difficult to detect particle
+
+ align:start position:0%
+other very difficult to detect particle
+ 
+
+ align:start position:0%
+other very difficult to detect particle
+so the theorists here we're saying if we
+
+ align:start position:0%
+so the theorists here we're saying if we
+ 
+
+ align:start position:0%
+so the theorists here we're saying if we
+take we know the initial and final
+
+ align:start position:0%
+take we know the initial and final
+ 
+
+ align:start position:0%
+take we know the initial and final
+energies from beta decay and we know
+
+ align:start position:0%
+energies from beta decay and we know
+ 
+
+ align:start position:0%
+energies from beta decay and we know
+that we get a spectrum of different beta
+
+ align:start position:0%
+that we get a spectrum of different beta
+ 
+
+ align:start position:0%
+that we get a spectrum of different beta
+energies and the probability of finding
+
+ align:start position:0%
+energies and the probability of finding
+ 
+
+ align:start position:0%
+energies and the probability of finding
+a beta particle at energy Q drops to
+
+ align:start position:0%
+a beta particle at energy Q drops to
+ 
+
+ align:start position:0%
+a beta particle at energy Q drops to
+like zero you'll almost never see it
+
+ align:start position:0%
+like zero you'll almost never see it
+ 
+
+ align:start position:0%
+like zero you'll almost never see it
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+ought to be something else carrying away
+
+ align:start position:0%
+ought to be something else carrying away
+ 
+
+ align:start position:0%
+ought to be something else carrying away
+the energy so this idea of the neutrino
+
+ align:start position:0%
+the energy so this idea of the neutrino
+ 
+
+ align:start position:0%
+the energy so this idea of the neutrino
+or in this case the anti neutrino was
+
+ align:start position:0%
+or in this case the anti neutrino was
+ 
+
+ align:start position:0%
+or in this case the anti neutrino was
+proposed a long time before it was
+
+ align:start position:0%
+proposed a long time before it was
+ 
+
+ align:start position:0%
+proposed a long time before it was
+confirmed and finally we know why and
+
+ align:start position:0%
+confirmed and finally we know why and
+ 
+
+ align:start position:0%
+confirmed and finally we know why and
+one of the questions I want you to think
+
+ align:start position:0%
+one of the questions I want you to think
+ 
+
+ align:start position:0%
+one of the questions I want you to think
+about because it might be on an exam in
+
+ align:start position:0%
+about because it might be on an exam in
+ 
+
+ align:start position:0%
+about because it might be on an exam in
+exactly two weeks is if this is the
+
+ align:start position:0%
+exactly two weeks is if this is the
+ 
+
+ align:start position:0%
+exactly two weeks is if this is the
+relative number of electrons from beta
+
+ align:start position:0%
+relative number of electrons from beta
+ 
+
+ align:start position:0%
+relative number of electrons from beta
+decay as a function of energy what does
+
+ align:start position:0%
+decay as a function of energy what does
+ 
+
+ align:start position:0%
+decay as a function of energy what does
+the number of anti neutrinos versus
+
+ align:start position:0%
+the number of anti neutrinos versus
+ 
+
+ align:start position:0%
+the number of anti neutrinos versus
+energy look like in order to maintain
+
+ align:start position:0%
+energy look like in order to maintain
+ 
+
+ align:start position:0%
+energy look like in order to maintain
+conservation of energy so it's something
+
+ align:start position:0%
+conservation of energy so it's something
+ 
+
+ align:start position:0%
+conservation of energy so it's something
+I want you guys to think about but I'm
+
+ align:start position:0%
+I want you guys to think about but I'm
+ 
+
+ align:start position:0%
+I want you guys to think about but I'm
+not going to tell you what it is until
+
+ align:start position:0%
+not going to tell you what it is until
+ 
+
+ align:start position:0%
+not going to tell you what it is until
+the solutions for an exam in the
+
+ align:start position:0%
+the solutions for an exam in the
+ 
+
+ align:start position:0%
+the solutions for an exam in the
+meantime what another thing to note is
+
+ align:start position:0%
+meantime what another thing to note is
+ 
+
+ align:start position:0%
+meantime what another thing to note is
+that these beta decays can also be
+
+ align:start position:0%
+that these beta decays can also be
+ 
+
+ align:start position:0%
+that these beta decays can also be
+followed by any number of gamma
+
+ align:start position:0%
+followed by any number of gamma
+ 
+
+ align:start position:0%
+followed by any number of gamma
+transitions I've given you a simple one
+
+ align:start position:0%
+transitions I've given you a simple one
+ 
+
+ align:start position:0%
+transitions I've given you a simple one
+if you want to look up simple ones to
+
+ align:start position:0%
+if you want to look up simple ones to
+ 
+
+ align:start position:0%
+if you want to look up simple ones to
+test your knowledge go with the light
+
+ align:start position:0%
+test your knowledge go with the light
+ 
+
+ align:start position:0%
+test your knowledge go with the light
+elements they don't have that many
+
+ align:start position:0%
+elements they don't have that many
+ 
+
+ align:start position:0%
+elements they don't have that many
+nucleons and they won't have that many
+
+ align:start position:0%
+nucleons and they won't have that many
+ 
+
+ align:start position:0%
+nucleons and they won't have that many
+transitions for example if we pick a
+
+ align:start position:0%
+transitions for example if we pick a
+ 
+
+ align:start position:0%
+transitions for example if we pick a
+beta decay nucleus something simple
+
+ align:start position:0%
+beta decay nucleus something simple
+ 
+
+ align:start position:0%
+beta decay nucleus something simple
+let's go with lithium which typically
+
+ align:start position:0%
+let's go with lithium which typically
+ 
+
+ align:start position:0%
+let's go with lithium which typically
+has the stable isotopes are lithium six
+
+ align:start position:0%
+has the stable isotopes are lithium six
+ 
+
+ align:start position:0%
+has the stable isotopes are lithium six
+or lithium seven so do you think that
+
+ align:start position:0%
+or lithium seven so do you think that
+ 
+
+ align:start position:0%
+or lithium seven so do you think that
+higher or lower mass number lithium will
+
+ align:start position:0%
+higher or lower mass number lithium will
+ 
+
+ align:start position:0%
+higher or lower mass number lithium will
+tend to go by beta decay based on this
+
+ align:start position:0%
+tend to go by beta decay based on this
+ 
+
+ align:start position:0%
+tend to go by beta decay based on this
+generalized decay diagram it's what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lower lower proton number well we got to
+
+ align:start position:0%
+lower lower proton number well we got to
+ 
+
+ align:start position:0%
+lower lower proton number well we got to
+stick with no number of protons because
+
+ align:start position:0%
+stick with no number of protons because
+ 
+
+ align:start position:0%
+stick with no number of protons because
+we need to remain lithium so in other
+
+ align:start position:0%
+we need to remain lithium so in other
+ 
+
+ align:start position:0%
+we need to remain lithium so in other
+words do you expect lithium four and
+
+ align:start position:0%
+words do you expect lithium four and
+ 
+
+ align:start position:0%
+words do you expect lithium four and
+lithium five or lithium eight lithium
+
+ align:start position:0%
+lithium five or lithium eight lithium
+ 
+
+ align:start position:0%
+lithium five or lithium eight lithium
+nine to go by beta decay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the higher ones okay if you guys
+
+ align:start position:0%
+the higher ones okay if you guys
+ 
+
+ align:start position:0%
+the higher ones okay if you guys
+remember the math parabolas from a
+
+ align:start position:0%
+remember the math parabolas from a
+ 
+
+ align:start position:0%
+remember the math parabolas from a
+couple weeks ago we delineated where
+
+ align:start position:0%
+couple weeks ago we delineated where
+ 
+
+ align:start position:0%
+couple weeks ago we delineated where
+you'd expect beta decay in order to
+
+ align:start position:0%
+you'd expect beta decay in order to
+ 
+
+ align:start position:0%
+you'd expect beta decay in order to
+reduce the proton number and positron
+
+ align:start position:0%
+reduce the proton number and positron
+ 
+
+ align:start position:0%
+reduce the proton number and positron
+decay in order I'm sorry beta decay in
+
+ align:start position:0%
+decay in order I'm sorry beta decay in
+ 
+
+ align:start position:0%
+decay in order I'm sorry beta decay in
+order to increase the proton number so
+
+ align:start position:0%
+order to increase the proton number so
+ 
+
+ align:start position:0%
+order to increase the proton number so
+if you've got too many neutrons and not
+
+ align:start position:0%
+if you've got too many neutrons and not
+ 
+
+ align:start position:0%
+if you've got too many neutrons and not
+enough protons chances are beta decay
+
+ align:start position:0%
+enough protons chances are beta decay
+ 
+
+ align:start position:0%
+enough protons chances are beta decay
+will help equalize you out so that's a
+
+ align:start position:0%
+will help equalize you out so that's a
+ 
+
+ align:start position:0%
+will help equalize you out so that's a
+guess I haven't even tried this at home
+
+ align:start position:0%
+guess I haven't even tried this at home
+ 
+
+ align:start position:0%
+guess I haven't even tried this at home
+let's see let's see what happens with
+
+ align:start position:0%
+let's see let's see what happens with
+ 
+
+ align:start position:0%
+let's see let's see what happens with
+lithium eight oh look at that
+
+ align:start position:0%
+lithium eight oh look at that
+ 
+
+ align:start position:0%
+lithium eight oh look at that
+beta decay can also decay by beta plus
+
+ align:start position:0%
+beta decay can also decay by beta plus
+ 
+
+ align:start position:0%
+beta decay can also decay by beta plus
+two alpha which is another word for the
+
+ align:start position:0%
+two alpha which is another word for the
+ 
+
+ align:start position:0%
+two alpha which is another word for the
+nucleus just blows apart it's
+
+ align:start position:0%
+nucleus just blows apart it's
+ 
+
+ align:start position:0%
+nucleus just blows apart it's
+interesting too if you read Chadwicks
+
+ align:start position:0%
+interesting too if you read Chadwicks
+ 
+
+ align:start position:0%
+interesting too if you read Chadwicks
+paper again the way he described a
+
+ align:start position:0%
+paper again the way he described a
+ 
+
+ align:start position:0%
+paper again the way he described a
+beryllium nucleus is consisting of a
+
+ align:start position:0%
+beryllium nucleus is consisting of a
+ 
+
+ align:start position:0%
+beryllium nucleus is consisting of a
+neutron plus two alpha particles
+
+ align:start position:0%
+neutron plus two alpha particles
+ 
+
+ align:start position:0%
+neutron plus two alpha particles
+interesting huh
+
+ align:start position:0%
+interesting huh
+ 
+
+ align:start position:0%
+interesting huh
+lithium nine could decay by or let's say
+
+ align:start position:0%
+lithium nine could decay by or let's say
+ 
+
+ align:start position:0%
+lithium nine could decay by or let's say
+lithium eight what do we have beta plus
+
+ align:start position:0%
+lithium eight what do we have beta plus
+ 
+
+ align:start position:0%
+lithium eight what do we have beta plus
+2 alpha yeah so Chadwick described any
+
+ align:start position:0%
+2 alpha yeah so Chadwick described any
+ 
+
+ align:start position:0%
+2 alpha yeah so Chadwick described any
+nucleus as consisting of these
+
+ align:start position:0%
+nucleus as consisting of these
+ 
+
+ align:start position:0%
+nucleus as consisting of these
+elementary ish particles that you could
+
+ align:start position:0%
+elementary ish particles that you could
+ 
+
+ align:start position:0%
+elementary ish particles that you could
+measure and in this case you kind of see
+
+ align:start position:0%
+measure and in this case you kind of see
+ 
+
+ align:start position:0%
+measure and in this case you kind of see
+a physical example when this nucleus
+
+ align:start position:0%
+a physical example when this nucleus
+ 
+
+ align:start position:0%
+a physical example when this nucleus
+blows apart it just becomes two alphas
+
+ align:start position:0%
+blows apart it just becomes two alphas
+ 
+
+ align:start position:0%
+blows apart it just becomes two alphas
+and a beta interesting but let's look at
+
+ align:start position:0%
+and a beta interesting but let's look at
+ 
+
+ align:start position:0%
+and a beta interesting but let's look at
+the beta decay two beryllium eight
+
+ align:start position:0%
+the beta decay two beryllium eight
+ 
+
+ align:start position:0%
+the beta decay two beryllium eight
+pretty simple you may ask why can't you
+
+ align:start position:0%
+pretty simple you may ask why can't you
+ 
+
+ align:start position:0%
+pretty simple you may ask why can't you
+have beta decay for directly from the
+
+ align:start position:0%
+have beta decay for directly from the
+ 
+
+ align:start position:0%
+have beta decay for directly from the
+highest energy to the ground state
+
+ align:start position:0%
+highest energy to the ground state
+ 
+
+ align:start position:0%
+highest energy to the ground state
+energy that is a 2202 question that I'll
+
+ align:start position:0%
+energy that is a 2202 question that I'll
+ 
+
+ align:start position:0%
+energy that is a 2202 question that I'll
+mention there are allowed and
+
+ align:start position:0%
+mention there are allowed and
+ 
+
+ align:start position:0%
+mention there are allowed and
+unallowable in and energy states so if
+
+ align:start position:0%
+unallowable in and energy states so if
+ 
+
+ align:start position:0%
+unallowable in and energy states so if
+you're wondering why isn't every line
+
+ align:start position:0%
+you're wondering why isn't every line
+ 
+
+ align:start position:0%
+you're wondering why isn't every line
+drawn in the case of really complex
+
+ align:start position:0%
+drawn in the case of really complex
+ 
+
+ align:start position:0%
+drawn in the case of really complex
+nuclei there aren't enough pixels on the
+
+ align:start position:0%
+nuclei there aren't enough pixels on the
+ 
+
+ align:start position:0%
+nuclei there aren't enough pixels on the
+screen sometimes but for the simple
+
+ align:start position:0%
+screen sometimes but for the simple
+ 
+
+ align:start position:0%
+screen sometimes but for the simple
+nuclei there are actually rules of
+
+ align:start position:0%
+nuclei there are actually rules of
+ 
+
+ align:start position:0%
+nuclei there are actually rules of
+selection to decide when you can make
+
+ align:start position:0%
+selection to decide when you can make
+ 
+
+ align:start position:0%
+selection to decide when you can make
+this transition but a lot of beta decays
+
+ align:start position:0%
+this transition but a lot of beta decays
+ 
+
+ align:start position:0%
+this transition but a lot of beta decays
+will usually be something like a beta
+
+ align:start position:0%
+will usually be something like a beta
+ 
+
+ align:start position:0%
+will usually be something like a beta
+decay followed by a gamma so let's see a
+
+ align:start position:0%
+decay followed by a gamma so let's see a
+ 
+
+ align:start position:0%
+decay followed by a gamma so let's see a
+couple of well-known examples for
+
+ align:start position:0%
+couple of well-known examples for
+ 
+
+ align:start position:0%
+couple of well-known examples for
+example carbon-14 this is the basis
+
+ align:start position:0%
+example carbon-14 this is the basis
+ 
+
+ align:start position:0%
+example carbon-14 this is the basis
+behind carbon dating one of those rare
+
+ align:start position:0%
+behind carbon dating one of those rare
+ 
+
+ align:start position:0%
+behind carbon dating one of those rare
+instances when you have a beta decay
+
+ align:start position:0%
+instances when you have a beta decay
+ 
+
+ align:start position:0%
+instances when you have a beta decay
+directly to the ground state it's about
+
+ align:start position:0%
+directly to the ground state it's about
+ 
+
+ align:start position:0%
+directly to the ground state it's about
+as simple as it gets
+
+ align:start position:0%
+as simple as it gets
+ 
+
+ align:start position:0%
+as simple as it gets
+and because the half-life is 5730 years
+
+ align:start position:0%
+and because the half-life is 5730 years
+ 
+
+ align:start position:0%
+and because the half-life is 5730 years
+it's really useful for dating when did
+
+ align:start position:0%
+it's really useful for dating when did
+ 
+
+ align:start position:0%
+it's really useful for dating when did
+an organism or a piece of material die
+
+ align:start position:0%
+an organism or a piece of material die
+ 
+
+ align:start position:0%
+an organism or a piece of material die
+on the timescale of let's say 10
+
+ align:start position:0%
+on the timescale of let's say 10
+ 
+
+ align:start position:0%
+on the timescale of let's say 10
+to tens of thousands of years once
+
+ align:start position:0%
+to tens of thousands of years once
+ 
+
+ align:start position:0%
+to tens of thousands of years once
+you've gone past a few half-lives and
+
+ align:start position:0%
+you've gone past a few half-lives and
+ 
+
+ align:start position:0%
+you've gone past a few half-lives and
+there's very little carbon-14 left there
+
+ align:start position:0%
+there's very little carbon-14 left there
+ 
+
+ align:start position:0%
+there's very little carbon-14 left there
+aren't a lot of decays left and your
+
+ align:start position:0%
+aren't a lot of decays left and your
+ 
+
+ align:start position:0%
+aren't a lot of decays left and your
+counting statistics get crappy and it
+
+ align:start position:0%
+counting statistics get crappy and it
+ 
+
+ align:start position:0%
+counting statistics get crappy and it
+gets harder and harder to carbon-date
+
+ align:start position:0%
+gets harder and harder to carbon-date
+ 
+
+ align:start position:0%
+gets harder and harder to carbon-date
+things the basis behind this is that all
+
+ align:start position:0%
+things the basis behind this is that all
+ 
+
+ align:start position:0%
+things the basis behind this is that all
+living organisms that are in taking an
+
+ align:start position:0%
+living organisms that are in taking an
+ 
+
+ align:start position:0%
+living organisms that are in taking an
+exhaling carbon by some means remain an
+
+ align:start position:0%
+exhaling carbon by some means remain an
+ 
+
+ align:start position:0%
+exhaling carbon by some means remain an
+isotopic equilibrium with the carbon
+
+ align:start position:0%
+isotopic equilibrium with the carbon
+ 
+
+ align:start position:0%
+isotopic equilibrium with the carbon
+surrounding them and while most carbon
+
+ align:start position:0%
+surrounding them and while most carbon
+ 
+
+ align:start position:0%
+surrounding them and while most carbon
+is co2 and sand food and whatever is
+
+ align:start position:0%
+is co2 and sand food and whatever is
+ 
+
+ align:start position:0%
+is co2 and sand food and whatever is
+carbon-12 you're going to have a little
+
+ align:start position:0%
+carbon-12 you're going to have a little
+ 
+
+ align:start position:0%
+carbon-12 you're going to have a little
+bit of carbon-14 production from the
+
+ align:start position:0%
+bit of carbon-14 production from the
+ 
+
+ align:start position:0%
+bit of carbon-14 production from the
+upper atmosphere this is usually a
+
+ align:start position:0%
+upper atmosphere this is usually a
+ 
+
+ align:start position:0%
+upper atmosphere this is usually a
+cosmic ray phenomenon which we'll get
+
+ align:start position:0%
+cosmic ray phenomenon which we'll get
+ 
+
+ align:start position:0%
+cosmic ray phenomenon which we'll get
+into when we get into cosmic rays the
+
+ align:start position:0%
+into when we get into cosmic rays the
+ 
+
+ align:start position:0%
+into when we get into cosmic rays the
+moment you die you stop in taking carbon
+
+ align:start position:0%
+moment you die you stop in taking carbon
+ 
+
+ align:start position:0%
+moment you die you stop in taking carbon
+and the little bit of carbon-14 in the
+
+ align:start position:0%
+and the little bit of carbon-14 in the
+ 
+
+ align:start position:0%
+and the little bit of carbon-14 in the
+cloth and the food and your body
+
+ align:start position:0%
+cloth and the food and your body
+ 
+
+ align:start position:0%
+cloth and the food and your body
+whatever starts to decay naturally with
+
+ align:start position:0%
+whatever starts to decay naturally with
+ 
+
+ align:start position:0%
+whatever starts to decay naturally with
+a very regular decay curve and so this
+
+ align:start position:0%
+a very regular decay curve and so this
+ 
+
+ align:start position:0%
+a very regular decay curve and so this
+is the whole basis behind carbon dating
+
+ align:start position:0%
+is the whole basis behind carbon dating
+ 
+
+ align:start position:0%
+is the whole basis behind carbon dating
+and in the next pset you'll actually see
+
+ align:start position:0%
+and in the next pset you'll actually see
+ 
+
+ align:start position:0%
+and in the next pset you'll actually see
+how this was used to debunk the Shroud
+
+ align:start position:0%
+how this was used to debunk the Shroud
+ 
+
+ align:start position:0%
+how this was used to debunk the Shroud
+of Turin or the supposed burial cloth of
+
+ align:start position:0%
+of Turin or the supposed burial cloth of
+ 
+
+ align:start position:0%
+of Turin or the supposed burial cloth of
+Jesus of Nazareth because the carbon
+
+ align:start position:0%
+Jesus of Nazareth because the carbon
+ 
+
+ align:start position:0%
+Jesus of Nazareth because the carbon
+dating data just didn't check out as
+
+ align:start position:0%
+dating data just didn't check out as
+ 
+
+ align:start position:0%
+dating data just didn't check out as
+much as people really wanted to feel
+
+ align:start position:0%
+much as people really wanted to feel
+ 
+
+ align:start position:0%
+much as people really wanted to feel
+like we found it no science that's the
+
+ align:start position:0%
+like we found it no science that's the
+ 
+
+ align:start position:0%
+like we found it no science that's the
+answer no another well-known one we've
+
+ align:start position:0%
+answer no another well-known one we've
+ 
+
+ align:start position:0%
+answer no another well-known one we've
+talked about before is molybdenum-99
+
+ align:start position:0%
+talked about before is molybdenum-99
+ 
+
+ align:start position:0%
+talked about before is molybdenum-99
+decaying to technetium-99 metastable
+
+ align:start position:0%
+decaying to technetium-99 metastable
+ 
+
+ align:start position:0%
+decaying to technetium-99 metastable
+notice how here any number of beta
+
+ align:start position:0%
+notice how here any number of beta
+ 
+
+ align:start position:0%
+notice how here any number of beta
+decays and any cascade of very fast
+
+ align:start position:0%
+decays and any cascade of very fast
+ 
+
+ align:start position:0%
+decays and any cascade of very fast
+gamma transitions they almost all end
+
+ align:start position:0%
+gamma transitions they almost all end
+ 
+
+ align:start position:0%
+gamma transitions they almost all end
+right here at this state of about C
+
+ align:start position:0%
+right here at this state of about C
+ 
+
+ align:start position:0%
+right here at this state of about C
+there's two numbers written over each
+
+ align:start position:0%
+there's two numbers written over each
+ 
+
+ align:start position:0%
+there's two numbers written over each
+other but it's about a hundred and forty
+
+ align:start position:0%
+other but it's about a hundred and forty
+ 
+
+ align:start position:0%
+other but it's about a hundred and forty
+ke V or 0.14 MeV this transition from
+
+ align:start position:0%
+ke V or 0.14 MeV this transition from
+ 
+
+ align:start position:0%
+ke V or 0.14 MeV this transition from
+this state to the ground state is a slow
+
+ align:start position:0%
+this state to the ground state is a slow
+ 
+
+ align:start position:0%
+this state to the ground state is a slow
+transition so you can actually build up
+
+ align:start position:0%
+transition so you can actually build up
+ 
+
+ align:start position:0%
+transition so you can actually build up
+technetium-99 in what's called series
+
+ align:start position:0%
+technetium-99 in what's called series
+ 
+
+ align:start position:0%
+technetium-99 in what's called series
+decay which were going to cover on
+
+ align:start position:0%
+decay which were going to cover on
+ 
+
+ align:start position:0%
+decay which were going to cover on
+Friday and then you can use these 140 ke
+
+ align:start position:0%
+Friday and then you can use these 140 ke
+ 
+
+ align:start position:0%
+Friday and then you can use these 140 ke
+V gamma rays to do medical imaging so
+
+ align:start position:0%
+V gamma rays to do medical imaging so
+ 
+
+ align:start position:0%
+V gamma rays to do medical imaging so
+when you get a medical imaging procedure
+
+ align:start position:0%
+when you get a medical imaging procedure
+ 
+
+ align:start position:0%
+when you get a medical imaging procedure
+done chances are this is how it's done
+
+ align:start position:0%
+done chances are this is how it's done
+ 
+
+ align:start position:0%
+done chances are this is how it's done
+you get Molly 99 out of a reactor or an
+
+ align:start position:0%
+you get Molly 99 out of a reactor or an
+ 
+
+ align:start position:0%
+you get Molly 99 out of a reactor or an
+accelerator Technic a toda that
+
+ align:start position:0%
+accelerator Technic a toda that
+ 
+
+ align:start position:0%
+accelerator Technic a toda that
+chemically isolate the technetium-99
+
+ align:start position:0%
+chemically isolate the technetium-99
+ 
+
+ align:start position:0%
+chemically isolate the technetium-99
+metastable which lasts on the order of
+
+ align:start position:0%
+metastable which lasts on the order of
+ 
+
+ align:start position:0%
+metastable which lasts on the order of
+six days or so very quickly get it to
+
+ align:start position:0%
+six days or so very quickly get it to
+ 
+
+ align:start position:0%
+six days or so very quickly get it to
+someone inject it an image where do the
+
+ align:start position:0%
+someone inject it an image where do the
+ 
+
+ align:start position:0%
+someone inject it an image where do the
+gamma rays go
+
+ align:start position:0%
+gamma rays go
+ 
+
+ align:start position:0%
+gamma rays go
+or what are the gamma rays come from one
+
+ align:start position:0%
+or what are the gamma rays come from one
+ 
+
+ align:start position:0%
+or what are the gamma rays come from one
+last notable one is responsible for a
+
+ align:start position:0%
+last notable one is responsible for a
+ 
+
+ align:start position:0%
+last notable one is responsible for a
+lot of well problems when folks go urban
+
+ align:start position:0%
+lot of well problems when folks go urban
+ 
+
+ align:start position:0%
+lot of well problems when folks go urban
+exploring an old dentists offices
+
+ align:start position:0%
+exploring an old dentists offices
+ 
+
+ align:start position:0%
+exploring an old dentists offices
+nowadays they have electrostatic x-ray
+
+ align:start position:0%
+nowadays they have electrostatic x-ray
+ 
+
+ align:start position:0%
+nowadays they have electrostatic x-ray
+machines at dentists offices but back in
+
+ align:start position:0%
+machines at dentists offices but back in
+ 
+
+ align:start position:0%
+machines at dentists offices but back in
+the day you could get a little button of
+
+ align:start position:0%
+the day you could get a little button of
+ 
+
+ align:start position:0%
+the day you could get a little button of
+cobalt-60 which would emit two very
+
+ align:start position:0%
+cobalt-60 which would emit two very
+ 
+
+ align:start position:0%
+cobalt-60 which would emit two very
+characteristic gamma rays in addition to
+
+ align:start position:0%
+characteristic gamma rays in addition to
+ 
+
+ align:start position:0%
+characteristic gamma rays in addition to
+its beta decays so normally what happens
+
+ align:start position:0%
+its beta decays so normally what happens
+ 
+
+ align:start position:0%
+its beta decays so normally what happens
+is cobalt-60 decays quickly to an
+
+ align:start position:0%
+is cobalt-60 decays quickly to an
+ 
+
+ align:start position:0%
+is cobalt-60 decays quickly to an
+excited state and gives off two gamma
+
+ align:start position:0%
+excited state and gives off two gamma
+ 
+
+ align:start position:0%
+excited state and gives off two gamma
+rays an accession succession which would
+
+ align:start position:0%
+rays an accession succession which would
+ 
+
+ align:start position:0%
+rays an accession succession which would
+be used for imaging problem is that's a
+
+ align:start position:0%
+be used for imaging problem is that's a
+ 
+
+ align:start position:0%
+be used for imaging problem is that's a
+radioactive cobalt source and if you
+
+ align:start position:0%
+radioactive cobalt source and if you
+ 
+
+ align:start position:0%
+radioactive cobalt source and if you
+don't know what it is and you're like oh
+
+ align:start position:0%
+don't know what it is and you're like oh
+ 
+
+ align:start position:0%
+don't know what it is and you're like oh
+cool what's this blue thing I think I'll
+
+ align:start position:0%
+cool what's this blue thing I think I'll
+ 
+
+ align:start position:0%
+cool what's this blue thing I think I'll
+put it in my pocket and keep it that has
+
+ align:start position:0%
+put it in my pocket and keep it that has
+ 
+
+ align:start position:0%
+put it in my pocket and keep it that has
+been responsible for some injuries from
+
+ align:start position:0%
+been responsible for some injuries from
+ 
+
+ align:start position:0%
+been responsible for some injuries from
+some folks that didn't know any better
+
+ align:start position:0%
+some folks that didn't know any better
+ 
+
+ align:start position:0%
+some folks that didn't know any better
+then how do you detect the neutrinos we
+
+ align:start position:0%
+then how do you detect the neutrinos we
+ 
+
+ align:start position:0%
+then how do you detect the neutrinos we
+talked about the theoretical reason why
+
+ align:start position:0%
+talked about the theoretical reason why
+ 
+
+ align:start position:0%
+talked about the theoretical reason why
+they exist let's actually see how
+
+ align:start position:0%
+they exist let's actually see how
+ 
+
+ align:start position:0%
+they exist let's actually see how
+they're measured there's a hollowed-out
+
+ align:start position:0%
+they're measured there's a hollowed-out
+ 
+
+ align:start position:0%
+they're measured there's a hollowed-out
+salt mine of some sort called kamiokande
+
+ align:start position:0%
+salt mine of some sort called kamiokande
+ 
+
+ align:start position:0%
+salt mine of some sort called kamiokande
+in Japan it's a humongous Hall in the
+
+ align:start position:0%
+in Japan it's a humongous Hall in the
+ 
+
+ align:start position:0%
+in Japan it's a humongous Hall in the
+ground filled with water for a reason
+
+ align:start position:0%
+ground filled with water for a reason
+ 
+
+ align:start position:0%
+ground filled with water for a reason
+and lined with tens of thousands of
+
+ align:start position:0%
+and lined with tens of thousands of
+ 
+
+ align:start position:0%
+and lined with tens of thousands of
+highly sensitive photo tubes that can
+
+ align:start position:0%
+highly sensitive photo tubes that can
+ 
+
+ align:start position:0%
+highly sensitive photo tubes that can
+pick up tiny tiny amounts of light the
+
+ align:start position:0%
+pick up tiny tiny amounts of light the
+ 
+
+ align:start position:0%
+pick up tiny tiny amounts of light the
+reason for this is because neutrinos as
+
+ align:start position:0%
+reason for this is because neutrinos as
+ 
+
+ align:start position:0%
+reason for this is because neutrinos as
+you saw in problem set 1 are always
+
+ align:start position:0%
+you saw in problem set 1 are always
+ 
+
+ align:start position:0%
+you saw in problem set 1 are always
+traveling near the speed of light in a
+
+ align:start position:0%
+traveling near the speed of light in a
+ 
+
+ align:start position:0%
+traveling near the speed of light in a
+vacuum so if the speed of light in a
+
+ align:start position:0%
+vacuum so if the speed of light in a
+ 
+
+ align:start position:0%
+vacuum so if the speed of light in a
+vacuum let's call that one and the
+
+ align:start position:0%
+vacuum let's call that one and the
+ 
+
+ align:start position:0%
+vacuum let's call that one and the
+velocity of the neutrino wasn't it
+
+ align:start position:0%
+velocity of the neutrino wasn't it
+ 
+
+ align:start position:0%
+velocity of the neutrino wasn't it
+something like 0.999 C or something like
+
+ align:start position:0%
+something like 0.999 C or something like
+ 
+
+ align:start position:0%
+something like 0.999 C or something like
+that it was pretty high the speed of
+
+ align:start position:0%
+that it was pretty high the speed of
+ 
+
+ align:start position:0%
+that it was pretty high the speed of
+light and water is significantly less
+
+ align:start position:0%
+light and water is significantly less
+ 
+
+ align:start position:0%
+light and water is significantly less
+than the speed of light in a vacuum when
+
+ align:start position:0%
+than the speed of light in a vacuum when
+ 
+
+ align:start position:0%
+than the speed of light in a vacuum when
+you have a material or a particle that
+
+ align:start position:0%
+you have a material or a particle that
+ 
+
+ align:start position:0%
+you have a material or a particle that
+goes faster than the speed of light in
+
+ align:start position:0%
+goes faster than the speed of light in
+ 
+
+ align:start position:0%
+goes faster than the speed of light in
+the medium that it's traveling in then
+
+ align:start position:0%
+the medium that it's traveling in then
+ 
+
+ align:start position:0%
+the medium that it's traveling in then
+you can produce what's called Cherenkov
+
+ align:start position:0%
+you can produce what's called Cherenkov
+ 
+
+ align:start position:0%
+you can produce what's called Cherenkov
+radiation which I think I've mentioned
+
+ align:start position:0%
+radiation which I think I've mentioned
+ 
+
+ align:start position:0%
+radiation which I think I've mentioned
+once before it's kind of like a sonic
+
+ align:start position:0%
+once before it's kind of like a sonic
+ 
+
+ align:start position:0%
+once before it's kind of like a sonic
+boom in that you get a conical shock
+
+ align:start position:0%
+boom in that you get a conical shock
+ 
+
+ align:start position:0%
+boom in that you get a conical shock
+wave of energy radiated from that
+
+ align:start position:0%
+wave of energy radiated from that
+ 
+
+ align:start position:0%
+wave of energy radiated from that
+particle that tells you which direction
+
+ align:start position:0%
+particle that tells you which direction
+ 
+
+ align:start position:0%
+particle that tells you which direction
+it's coming from but instead of a sound
+
+ align:start position:0%
+it's coming from but instead of a sound
+ 
+
+ align:start position:0%
+it's coming from but instead of a sound
+wave you get light and this whole
+
+ align:start position:0%
+wave you get light and this whole
+ 
+
+ align:start position:0%
+wave you get light and this whole
+detector is designed to look at the
+
+ align:start position:0%
+detector is designed to look at the
+ 
+
+ align:start position:0%
+detector is designed to look at the
+ellipses of Cherenkov radiation released
+
+ align:start position:0%
+ellipses of Cherenkov radiation released
+ 
+
+ align:start position:0%
+ellipses of Cherenkov radiation released
+by neutrinos and antineutrinos so what
+
+ align:start position:0%
+by neutrinos and antineutrinos so what
+ 
+
+ align:start position:0%
+by neutrinos and antineutrinos so what
+happens is if a neutrino happens to
+
+ align:start position:0%
+happens is if a neutrino happens to
+ 
+
+ align:start position:0%
+happens is if a neutrino happens to
+interact with the water here it produces
+
+ align:start position:0%
+interact with the water here it produces
+ 
+
+ align:start position:0%
+interact with the water here it produces
+Cherenkov radiation lighting up a ring
+
+ align:start position:0%
+Cherenkov radiation lighting up a ring
+ 
+
+ align:start position:0%
+Cherenkov radiation lighting up a ring
+of these detectors so you can tell it's
+
+ align:start position:0%
+of these detectors so you can tell it's
+ 
+
+ align:start position:0%
+of these detectors so you can tell it's
+energy and you can tell where it came
+
+ align:start position:0%
+energy and you can tell where it came
+ 
+
+ align:start position:0%
+energy and you can tell where it came
+from so if you let's say cone correlate
+
+ align:start position:0%
+from so if you let's say cone correlate
+ 
+
+ align:start position:0%
+from so if you let's say cone correlate
+a supernova or some sort of crazy
+
+ align:start position:0%
+a supernova or some sort of crazy
+ 
+
+ align:start position:0%
+a supernova or some sort of crazy
+galactic whatever with a slight burst of
+
+ align:start position:0%
+galactic whatever with a slight burst of
+ 
+
+ align:start position:0%
+galactic whatever with a slight burst of
+neutrinos then you've got a pretty
+
+ align:start position:0%
+neutrinos then you've got a pretty
+ 
+
+ align:start position:0%
+neutrinos then you've got a pretty
+significant astronomical event it also
+
+ align:start position:0%
+significant astronomical event it also
+ 
+
+ align:start position:0%
+significant astronomical event it also
+led to my favorite BBC headline ever
+
+ align:start position:0%
+led to my favorite BBC headline ever
+ 
+
+ align:start position:0%
+led to my favorite BBC headline ever
+particle physics telescope explodes
+
+ align:start position:0%
+particle physics telescope explodes
+ 
+
+ align:start position:0%
+particle physics telescope explodes
+you'd see this on like fox news or
+
+ align:start position:0%
+you'd see this on like fox news or
+ 
+
+ align:start position:0%
+you'd see this on like fox news or
+something no this was the BBC what
+
+ align:start position:0%
+something no this was the BBC what
+ 
+
+ align:start position:0%
+something no this was the BBC what
+happened here is one of these 30,000 or
+
+ align:start position:0%
+happened here is one of these 30,000 or
+ 
+
+ align:start position:0%
+happened here is one of these 30,000 or
+so tubes was slightly defective couldn't
+
+ align:start position:0%
+so tubes was slightly defective couldn't
+ 
+
+ align:start position:0%
+so tubes was slightly defective couldn't
+hold the pressure and it burst and the
+
+ align:start position:0%
+hold the pressure and it burst and the
+ 
+
+ align:start position:0%
+hold the pressure and it burst and the
+resulting sound shockwave from one photo
+
+ align:start position:0%
+resulting sound shockwave from one photo
+ 
+
+ align:start position:0%
+resulting sound shockwave from one photo
+- bursting blew up about 11,000 of them
+
+ align:start position:0%
+- bursting blew up about 11,000 of them
+ 
+
+ align:start position:0%
+- bursting blew up about 11,000 of them
+so yeah the particle physics telescope
+
+ align:start position:0%
+so yeah the particle physics telescope
+ 
+
+ align:start position:0%
+so yeah the particle physics telescope
+kind of did explode they did rebuild it
+
+ align:start position:0%
+kind of did explode they did rebuild it
+ 
+
+ align:start position:0%
+kind of did explode they did rebuild it
+and it's still going it was an expensive
+
+ align:start position:0%
+and it's still going it was an expensive
+ 
+
+ align:start position:0%
+and it's still going it was an expensive
+repair cuz all eleven thousand three
+
+ align:start position:0%
+repair cuz all eleven thousand three
+ 
+
+ align:start position:0%
+repair cuz all eleven thousand three
+hundred something tubes had to be
+
+ align:start position:0%
+hundred something tubes had to be
+ 
+
+ align:start position:0%
+hundred something tubes had to be
+rebuilt and if you noticed there was a
+
+ align:start position:0%
+rebuilt and if you noticed there was a
+ 
+
+ align:start position:0%
+rebuilt and if you noticed there was a
+guy on a boat there how do you install
+
+ align:start position:0%
+guy on a boat there how do you install
+ 
+
+ align:start position:0%
+guy on a boat there how do you install
+them well you float on a boat quietly
+
+ align:start position:0%
+them well you float on a boat quietly
+ 
+
+ align:start position:0%
+them well you float on a boat quietly
+and put the photo tubes in and raise the
+
+ align:start position:0%
+and put the photo tubes in and raise the
+ 
+
+ align:start position:0%
+and put the photo tubes in and raise the
+water level and float to another part of
+
+ align:start position:0%
+water level and float to another part of
+ 
+
+ align:start position:0%
+water level and float to another part of
+the Tector quietly and continue
+
+ align:start position:0%
+the Tector quietly and continue
+ 
+
+ align:start position:0%
+the Tector quietly and continue
+installing the photo tubes until you're
+
+ align:start position:0%
+installing the photo tubes until you're
+ 
+
+ align:start position:0%
+installing the photo tubes until you're
+done yeah you don't ya don't sneeze so
+
+ align:start position:0%
+done yeah you don't ya don't sneeze so
+ 
+
+ align:start position:0%
+done yeah you don't ya don't sneeze so
+ya favorite BBC headline ever thanks
+
+ align:start position:0%
+ya favorite BBC headline ever thanks
+ 
+
+ align:start position:0%
+ya favorite BBC headline ever thanks
+again science for a positron decay okay
+
+ align:start position:0%
+again science for a positron decay okay
+ 
+
+ align:start position:0%
+again science for a positron decay okay
+we've got about 10 minutes left for
+
+ align:start position:0%
+we've got about 10 minutes left for
+ 
+
+ align:start position:0%
+we've got about 10 minutes left for
+positron decay this is the energy that
+
+ align:start position:0%
+positron decay this is the energy that
+ 
+
+ align:start position:0%
+positron decay this is the energy that
+you need in order to make a positron it
+
+ align:start position:0%
+you need in order to make a positron it
+ 
+
+ align:start position:0%
+you need in order to make a positron it
+is approximately exactly double the MER
+
+ align:start position:0%
+is approximately exactly double the MER
+ 
+
+ align:start position:0%
+is approximately exactly double the MER
+rest mass of an electron and the
+
+ align:start position:0%
+rest mass of an electron and the
+ 
+
+ align:start position:0%
+rest mass of an electron and the
+question usually comes up well a
+
+ align:start position:0%
+question usually comes up well a
+ 
+
+ align:start position:0%
+question usually comes up well a
+positron has a rest mass energy of 0.5 1
+
+ align:start position:0%
+positron has a rest mass energy of 0.5 1
+ 
+
+ align:start position:0%
+positron has a rest mass energy of 0.5 1
+1 MeV why do you need double that to
+
+ align:start position:0%
+1 MeV why do you need double that to
+ 
+
+ align:start position:0%
+1 MeV why do you need double that to
+make the positron because in order to
+
+ align:start position:0%
+make the positron because in order to
+ 
+
+ align:start position:0%
+make the positron because in order to
+conserve the charge of the system you
+
+ align:start position:0%
+conserve the charge of the system you
+ 
+
+ align:start position:0%
+conserve the charge of the system you
+have to shed an orbital electron so the
+
+ align:start position:0%
+have to shed an orbital electron so the
+ 
+
+ align:start position:0%
+have to shed an orbital electron so the
+system has got to be able to lose two
+
+ align:start position:0%
+system has got to be able to lose two
+ 
+
+ align:start position:0%
+system has got to be able to lose two
+electrons in the process of one
+
+ align:start position:0%
+electrons in the process of one
+ 
+
+ align:start position:0%
+electrons in the process of one
+positively charged and one negatively
+
+ align:start position:0%
+positively charged and one negatively
+ 
+
+ align:start position:0%
+positively charged and one negatively
+charged and so that's why the
+
+ align:start position:0%
+charged and so that's why the
+ 
+
+ align:start position:0%
+charged and so that's why the
+q for positron decay is just gonna be
+
+ align:start position:0%
+q for positron decay is just gonna be
+ 
+
+ align:start position:0%
+q for positron decay is just gonna be
+remember the symbols the excess mass
+
+ align:start position:0%
+remember the symbols the excess mass
+ 
+
+ align:start position:0%
+remember the symbols the excess mass
+here excess mass of the parent - SS mass
+
+ align:start position:0%
+here excess mass of the parent - SS mass
+ 
+
+ align:start position:0%
+here excess mass of the parent - SS mass
+of the daughter - two times the rest
+
+ align:start position:0%
+of the daughter - two times the rest
+ 
+
+ align:start position:0%
+of the daughter - two times the rest
+mass of the electrons squared to refresh
+
+ align:start position:0%
+mass of the electrons squared to refresh
+ 
+
+ align:start position:0%
+mass of the electrons squared to refresh
+your memories a bit find some empty
+
+ align:start position:0%
+your memories a bit find some empty
+ 
+
+ align:start position:0%
+your memories a bit find some empty
+space the excess mass is nothing more
+
+ align:start position:0%
+space the excess mass is nothing more
+ 
+
+ align:start position:0%
+space the excess mass is nothing more
+than the mass - the horrible
+
+ align:start position:0%
+than the mass - the horrible
+ 
+
+ align:start position:0%
+than the mass - the horrible
+approximation of the mass so the excess
+
+ align:start position:0%
+approximation of the mass so the excess
+ 
+
+ align:start position:0%
+approximation of the mass so the excess
+mass and the real mass are directly
+
+ align:start position:0%
+mass and the real mass are directly
+ 
+
+ align:start position:0%
+mass and the real mass are directly
+related and these are things that you
+
+ align:start position:0%
+related and these are things that you
+ 
+
+ align:start position:0%
+related and these are things that you
+can look up just to remind you guys that
+
+ align:start position:0%
+can look up just to remind you guys that
+ 
+
+ align:start position:0%
+can look up just to remind you guys that
+excess mass and mass and binding energy
+
+ align:start position:0%
+excess mass and mass and binding energy
+ 
+
+ align:start position:0%
+excess mass and mass and binding energy
+and kinetic energy are all related again
+
+ align:start position:0%
+and kinetic energy are all related again
+ 
+
+ align:start position:0%
+and kinetic energy are all related again
+by the Q equation it's probably the last
+
+ align:start position:0%
+by the Q equation it's probably the last
+ 
+
+ align:start position:0%
+by the Q equation it's probably the last
+time I'll say it cuz I think that's
+
+ align:start position:0%
+time I'll say it cuz I think that's
+ 
+
+ align:start position:0%
+time I'll say it cuz I think that's
+about a hundred by my count positrons
+
+ align:start position:0%
+about a hundred by my count positrons
+ 
+
+ align:start position:0%
+about a hundred by my count positrons
+can be used for some pretty awesome
+
+ align:start position:0%
+can be used for some pretty awesome
+ 
+
+ align:start position:0%
+can be used for some pretty awesome
+things and I will in the last five
+
+ align:start position:0%
+things and I will in the last five
+ 
+
+ align:start position:0%
+things and I will in the last five
+minutes of show I want to show you some
+
+ align:start position:0%
+minutes of show I want to show you some
+ 
+
+ align:start position:0%
+minutes of show I want to show you some
+work done by Professor Brian Werth at
+
+ align:start position:0%
+work done by Professor Brian Werth at
+ 
+
+ align:start position:0%
+work done by Professor Brian Werth at
+the University of Tennessee Knoxville on
+
+ align:start position:0%
+the University of Tennessee Knoxville on
+ 
+
+ align:start position:0%
+the University of Tennessee Knoxville on
+positron annihilation spectroscopy using
+
+ align:start position:0%
+positron annihilation spectroscopy using
+ 
+
+ align:start position:0%
+positron annihilation spectroscopy using
+antimatter to probe matter and find out
+
+ align:start position:0%
+antimatter to probe matter and find out
+ 
+
+ align:start position:0%
+antimatter to probe matter and find out
+what sort of defects exist and as a
+
+ align:start position:0%
+what sort of defects exist and as a
+ 
+
+ align:start position:0%
+what sort of defects exist and as a
+nuclear material scientist I'd be well
+
+ align:start position:0%
+nuclear material scientist I'd be well
+ 
+
+ align:start position:0%
+nuclear material scientist I'd be well
+terrible if I didn't inject a little bit
+
+ align:start position:0%
+terrible if I didn't inject a little bit
+ 
+
+ align:start position:0%
+terrible if I didn't inject a little bit
+of materials and how we use nuclear
+
+ align:start position:0%
+of materials and how we use nuclear
+ 
+
+ align:start position:0%
+of materials and how we use nuclear
+stuff in 2201 in order to probe that
+
+ align:start position:0%
+stuff in 2201 in order to probe that
+ 
+
+ align:start position:0%
+stuff in 2201 in order to probe that
+thing so the way that positron
+
+ align:start position:0%
+thing so the way that positron
+ 
+
+ align:start position:0%
+thing so the way that positron
+annihilation spectroscopy works is that
+
+ align:start position:0%
+annihilation spectroscopy works is that
+ 
+
+ align:start position:0%
+annihilation spectroscopy works is that
+well matters mostly empty space and in a
+
+ align:start position:0%
+well matters mostly empty space and in a
+ 
+
+ align:start position:0%
+well matters mostly empty space and in a
+in a regular crystal lattice where the
+
+ align:start position:0%
+in a regular crystal lattice where the
+ 
+
+ align:start position:0%
+in a regular crystal lattice where the
+atoms are arranged in a very regular
+
+ align:start position:0%
+atoms are arranged in a very regular
+ 
+
+ align:start position:0%
+atoms are arranged in a very regular
+array let's say these atoms have their
+
+ align:start position:0%
+array let's say these atoms have their
+ 
+
+ align:start position:0%
+array let's say these atoms have their
+orbital electrons the empty space
+
+ align:start position:0%
+orbital electrons the empty space
+ 
+
+ align:start position:0%
+orbital electrons the empty space
+between is also arranged in a very
+
+ align:start position:0%
+between is also arranged in a very
+ 
+
+ align:start position:0%
+between is also arranged in a very
+regular array and positrons annihilated
+
+ align:start position:0%
+regular array and positrons annihilated
+ 
+
+ align:start position:0%
+regular array and positrons annihilated
+electrons to produce well we'll find out
+
+ align:start position:0%
+electrons to produce well we'll find out
+ 
+
+ align:start position:0%
+electrons to produce well we'll find out
+in a second but we're in matter would
+
+ align:start position:0%
+in a second but we're in matter would
+ 
+
+ align:start position:0%
+in a second but we're in matter would
+they want to live or where were they
+
+ align:start position:0%
+they want to live or where were they
+ 
+
+ align:start position:0%
+they want to live or where were they
+last longer not near an atom but near
+
+ align:start position:0%
+last longer not near an atom but near
+ 
+
+ align:start position:0%
+last longer not near an atom but near
+the space in between so you can map out
+
+ align:start position:0%
+the space in between so you can map out
+ 
+
+ align:start position:0%
+the space in between so you can map out
+the empty spaces in matter in a regular
+
+ align:start position:0%
+the empty spaces in matter in a regular
+ 
+
+ align:start position:0%
+the empty spaces in matter in a regular
+crystal and calculate an average
+
+ align:start position:0%
+crystal and calculate an average
+ 
+
+ align:start position:0%
+crystal and calculate an average
+positron lifetime if you were to fire a
+
+ align:start position:0%
+positron lifetime if you were to fire a
+ 
+
+ align:start position:0%
+positron lifetime if you were to fire a
+positron into this matter how long would
+
+ align:start position:0%
+positron into this matter how long would
+ 
+
+ align:start position:0%
+positron into this matter how long would
+it sit and bounce around before
+
+ align:start position:0%
+it sit and bounce around before
+ 
+
+ align:start position:0%
+it sit and bounce around before
+colliding with an electron and releasing
+
+ align:start position:0%
+colliding with an electron and releasing
+ 
+
+ align:start position:0%
+colliding with an electron and releasing
+that extra rest mass energy it turns out
+
+ align:start position:0%
+that extra rest mass energy it turns out
+ 
+
+ align:start position:0%
+that extra rest mass energy it turns out
+if you have crystalline defects but
+
+ align:start position:0%
+if you have crystalline defects but
+ 
+
+ align:start position:0%
+if you have crystalline defects but
+positrons tend to last a little longer
+
+ align:start position:0%
+positrons tend to last a little longer
+ 
+
+ align:start position:0%
+positrons tend to last a little longer
+there's a little more empty space which
+
+ align:start position:0%
+there's a little more empty space which
+ 
+
+ align:start position:0%
+there's a little more empty space which
+is to say there are more places with a
+
+ align:start position:0%
+is to say there are more places with a
+ 
+
+ align:start position:0%
+is to say there are more places with a
+slightly less probability of finding an
+
+ align:start position:0%
+slightly less probability of finding an
+ 
+
+ align:start position:0%
+slightly less probability of finding an
+electron and so they last longer and you
+
+ align:start position:0%
+electron and so they last longer and you
+ 
+
+ align:start position:0%
+electron and so they last longer and you
+can measure the lifetime of positrons as
+
+ align:start position:0%
+can measure the lifetime of positrons as
+ 
+
+ align:start position:0%
+can measure the lifetime of positrons as
+they before they enter the material and
+
+ align:start position:0%
+they before they enter the material and
+ 
+
+ align:start position:0%
+they before they enter the material and
+then how long before they produce their
+
+ align:start position:0%
+then how long before they produce their
+ 
+
+ align:start position:0%
+then how long before they produce their
+characteristic destruction gamma rays so
+
+ align:start position:0%
+characteristic destruction gamma rays so
+ 
+
+ align:start position:0%
+characteristic destruction gamma rays so
+if you think about it you have a
+
+ align:start position:0%
+if you think about it you have a
+ 
+
+ align:start position:0%
+if you think about it you have a
+positron coming in with a rest mass 0.51
+
+ align:start position:0%
+positron coming in with a rest mass 0.51
+ 
+
+ align:start position:0%
+positron coming in with a rest mass 0.51
+one MeV and it collides with an electron
+
+ align:start position:0%
+one MeV and it collides with an electron
+ 
+
+ align:start position:0%
+one MeV and it collides with an electron
+from some orbital nucleus that has the
+
+ align:start position:0%
+from some orbital nucleus that has the
+ 
+
+ align:start position:0%
+from some orbital nucleus that has the
+same rest mass the positron and the
+
+ align:start position:0%
+same rest mass the positron and the
+ 
+
+ align:start position:0%
+same rest mass the positron and the
+electron annihilate sending off gamma
+
+ align:start position:0%
+electron annihilate sending off gamma
+ 
+
+ align:start position:0%
+electron annihilate sending off gamma
+rays in opposite directions where the
+
+ align:start position:0%
+rays in opposite directions where the
+ 
+
+ align:start position:0%
+rays in opposite directions where the
+energy of this gamma is the same thing
+
+ align:start position:0%
+energy of this gamma is the same thing
+ 
+
+ align:start position:0%
+energy of this gamma is the same thing
+point five one one MeV so you can tell
+
+ align:start position:0%
+point five one one MeV so you can tell
+ 
+
+ align:start position:0%
+point five one one MeV so you can tell
+when a positron was destroyed because
+
+ align:start position:0%
+when a positron was destroyed because
+ 
+
+ align:start position:0%
+when a positron was destroyed because
+you instantly get a half MeV gamma ray
+
+ align:start position:0%
+you instantly get a half MeV gamma ray
+ 
+
+ align:start position:0%
+you instantly get a half MeV gamma ray
+or actually you get two half MeV gamma
+
+ align:start position:0%
+or actually you get two half MeV gamma
+ 
+
+ align:start position:0%
+or actually you get two half MeV gamma
+rays then the question is how do you
+
+ align:start position:0%
+rays then the question is how do you
+ 
+
+ align:start position:0%
+rays then the question is how do you
+tell its lifetime let's go back to
+
+ align:start position:0%
+tell its lifetime let's go back to
+ 
+
+ align:start position:0%
+tell its lifetime let's go back to
+something that I didn't quite point out
+
+ align:start position:0%
+something that I didn't quite point out
+ 
+
+ align:start position:0%
+something that I didn't quite point out
+but I want to show you now is this
+
+ align:start position:0%
+but I want to show you now is this
+ 
+
+ align:start position:0%
+but I want to show you now is this
+positron decay is immediately followed
+
+ align:start position:0%
+positron decay is immediately followed
+ 
+
+ align:start position:0%
+positron decay is immediately followed
+by a one point two seven MeV gamma ray
+
+ align:start position:0%
+by a one point two seven MeV gamma ray
+ 
+
+ align:start position:0%
+by a one point two seven MeV gamma ray
+which is in pas or positron annihilation
+
+ align:start position:0%
+which is in pas or positron annihilation
+ 
+
+ align:start position:0%
+which is in pas or positron annihilation
+spectroscopy we call this the birth
+
+ align:start position:0%
+spectroscopy we call this the birth
+ 
+
+ align:start position:0%
+spectroscopy we call this the birth
+gamma ray this gamma ray is emitted the
+
+ align:start position:0%
+gamma ray this gamma ray is emitted the
+ 
+
+ align:start position:0%
+gamma ray this gamma ray is emitted the
+instant this nucleus is born and the
+
+ align:start position:0%
+instant this nucleus is born and the
+ 
+
+ align:start position:0%
+instant this nucleus is born and the
+positron takes a little bit of time to
+
+ align:start position:0%
+positron takes a little bit of time to
+ 
+
+ align:start position:0%
+positron takes a little bit of time to
+get destroyed
+
+ align:start position:0%
+get destroyed
+ 
+
+ align:start position:0%
+get destroyed
+so you actually look at the difference
+
+ align:start position:0%
+so you actually look at the difference
+ 
+
+ align:start position:0%
+so you actually look at the difference
+in time between sensing the 1.27 MeV
+
+ align:start position:0%
+in time between sensing the 1.27 MeV
+ 
+
+ align:start position:0%
+in time between sensing the 1.27 MeV
+gamma ray and the 0.5 one 1 MeV
+
+ align:start position:0%
+gamma ray and the 0.5 one 1 MeV
+ 
+
+ align:start position:0%
+gamma ray and the 0.5 one 1 MeV
+annihilation photons and that is
+
+ align:start position:0%
+annihilation photons and that is
+ 
+
+ align:start position:0%
+annihilation photons and that is
+measured in let's say hundreds of Pico
+
+ align:start position:0%
+measured in let's say hundreds of Pico
+ 
+
+ align:start position:0%
+measured in let's say hundreds of Pico
+seconds with resolution of around 5 Pico
+
+ align:start position:0%
+seconds with resolution of around 5 Pico
+ 
+
+ align:start position:0%
+seconds with resolution of around 5 Pico
+seconds and you can then tell from the
+
+ align:start position:0%
+seconds and you can then tell from the
+ 
+
+ align:start position:0%
+seconds and you can then tell from the
+lifetime at how many survived what sort
+
+ align:start position:0%
+lifetime at how many survived what sort
+ 
+
+ align:start position:0%
+lifetime at how many survived what sort
+of atomic defects might exist in the
+
+ align:start position:0%
+of atomic defects might exist in the
+ 
+
+ align:start position:0%
+of atomic defects might exist in the
+material so if you want to count the
+
+ align:start position:0%
+material so if you want to count the
+ 
+
+ align:start position:0%
+material so if you want to count the
+number of missing atoms or vacancies in
+
+ align:start position:0%
+number of missing atoms or vacancies in
+ 
+
+ align:start position:0%
+number of missing atoms or vacancies in
+a material which is extremely important
+
+ align:start position:0%
+a material which is extremely important
+ 
+
+ align:start position:0%
+a material which is extremely important
+to those of us in radiation damage you
+
+ align:start position:0%
+to those of us in radiation damage you
+ 
+
+ align:start position:0%
+to those of us in radiation damage you
+can do so with positron annihilation
+
+ align:start position:0%
+can do so with positron annihilation
+ 
+
+ align:start position:0%
+can do so with positron annihilation
+spectroscopy so I think I wanted to show
+
+ align:start position:0%
+spectroscopy so I think I wanted to show
+ 
+
+ align:start position:0%
+spectroscopy so I think I wanted to show
+you a little bit about how this works
+
+ align:start position:0%
+you a little bit about how this works
+ 
+
+ align:start position:0%
+you a little bit about how this works
+you start off by making a radioactive
+
+ align:start position:0%
+you start off by making a radioactive
+ 
+
+ align:start position:0%
+you start off by making a radioactive
+salt sandwich you take some sodium
+
+ align:start position:0%
+salt sandwich you take some sodium
+ 
+
+ align:start position:0%
+salt sandwich you take some sodium
+chloride specifically of the isotope
+
+ align:start position:0%
+chloride specifically of the isotope
+ 
+
+ align:start position:0%
+chloride specifically of the isotope
+sodium 22 which is giving off positrons
+
+ align:start position:0%
+sodium 22 which is giving off positrons
+ 
+
+ align:start position:0%
+sodium 22 which is giving off positrons
+all the time and you sandwich that
+
+ align:start position:0%
+all the time and you sandwich that
+ 
+
+ align:start position:0%
+all the time and you sandwich that
+radioactive jelly between the two slices
+
+ align:start position:0%
+radioactive jelly between the two slices
+ 
+
+ align:start position:0%
+radioactive jelly between the two slices
+of bread better known as your sample
+
+ align:start position:0%
+of bread better known as your sample
+ 
+
+ align:start position:0%
+of bread better known as your sample
+that way you catch every positron that
+
+ align:start position:0%
+that way you catch every positron that
+ 
+
+ align:start position:0%
+that way you catch every positron that
+gets out so you don't lose half of them
+
+ align:start position:0%
+gets out so you don't lose half of them
+ 
+
+ align:start position:0%
+gets out so you don't lose half of them
+to one side you've got two detectors on
+
+ align:start position:0%
+to one side you've got two detectors on
+ 
+
+ align:start position:0%
+to one side you've got two detectors on
+either side waiting so that that's
+
+ align:start position:0%
+either side waiting so that that's
+ 
+
+ align:start position:0%
+either side waiting so that that's
+there's some probability that the
+
+ align:start position:0%
+there's some probability that the
+ 
+
+ align:start position:0%
+there's some probability that the
+photons emitted are going to go in the
+
+ align:start position:0%
+photons emitted are going to go in the
+ 
+
+ align:start position:0%
+photons emitted are going to go in the
+direction of the detectors so you miss
+
+ align:start position:0%
+direction of the detectors so you miss
+ 
+
+ align:start position:0%
+direction of the detectors so you miss
+most of the signal but so what
+
+ align:start position:0%
+most of the signal but so what
+ 
+
+ align:start position:0%
+most of the signal but so what
+whenever you actually sense a 1.27 MeV
+
+ align:start position:0%
+whenever you actually sense a 1.27 MeV
+ 
+
+ align:start position:0%
+whenever you actually sense a 1.27 MeV
+gamma ray followed by to 511 K V's here
+
+ align:start position:0%
+gamma ray followed by to 511 K V's here
+ 
+
+ align:start position:0%
+gamma ray followed by to 511 K V's here
+then you know you've had a positron
+
+ align:start position:0%
+then you know you've had a positron
+ 
+
+ align:start position:0%
+then you know you've had a positron
+annihilation event and you can actually
+
+ align:start position:0%
+annihilation event and you can actually
+ 
+
+ align:start position:0%
+annihilation event and you can actually
+count the time between when those things
+
+ align:start position:0%
+count the time between when those things
+ 
+
+ align:start position:0%
+count the time between when those things
+happened and you can see the number of
+
+ align:start position:0%
+happened and you can see the number of
+ 
+
+ align:start position:0%
+happened and you can see the number of
+counts and get the average positron
+
+ align:start position:0%
+counts and get the average positron
+ 
+
+ align:start position:0%
+counts and get the average positron
+lifetime from finding out how many
+
+ align:start position:0%
+lifetime from finding out how many
+ 
+
+ align:start position:0%
+lifetime from finding out how many
+counts you get every five Pico seconds
+
+ align:start position:0%
+counts you get every five Pico seconds
+ 
+
+ align:start position:0%
+counts you get every five Pico seconds
+for example there's something to note
+
+ align:start position:0%
+for example there's something to note
+ 
+
+ align:start position:0%
+for example there's something to note
+about these counting spectra anybody
+
+ align:start position:0%
+about these counting spectra anybody
+ 
+
+ align:start position:0%
+about these counting spectra anybody
+know why they're so smooth up here and
+
+ align:start position:0%
+know why they're so smooth up here and
+ 
+
+ align:start position:0%
+know why they're so smooth up here and
+then they're so delineating down here
+
+ align:start position:0%
+then they're so delineating down here
+ 
+
+ align:start position:0%
+then they're so delineating down here
+anyone have an idea you're gonna see
+
+ align:start position:0%
+anyone have an idea you're gonna see
+ 
+
+ align:start position:0%
+anyone have an idea you're gonna see
+this a lot in 2209 when you actually
+
+ align:start position:0%
+this a lot in 2209 when you actually
+ 
+
+ align:start position:0%
+this a lot in 2209 when you actually
+count beta particles or alpha particles
+
+ align:start position:0%
+count beta particles or alpha particles
+ 
+
+ align:start position:0%
+count beta particles or alpha particles
+and you're counting statistics get a
+
+ align:start position:0%
+and you're counting statistics get a
+ 
+
+ align:start position:0%
+and you're counting statistics get a
+little crappier this is a log scale of
+
+ align:start position:0%
+little crappier this is a log scale of
+ 
+
+ align:start position:0%
+little crappier this is a log scale of
+counts or in this case counts per 5 Pico
+
+ align:start position:0%
+counts or in this case counts per 5 Pico
+ 
+
+ align:start position:0%
+counts or in this case counts per 5 Pico
+seconds 10 to the 0 is better known as 1
+
+ align:start position:0%
+seconds 10 to the 0 is better known as 1
+ 
+
+ align:start position:0%
+seconds 10 to the 0 is better known as 1
+so you're looking at one count or two or
+
+ align:start position:0%
+so you're looking at one count or two or
+ 
+
+ align:start position:0%
+so you're looking at one count or two or
+three you're looking at the discrete
+
+ align:start position:0%
+three you're looking at the discrete
+ 
+
+ align:start position:0%
+three you're looking at the discrete
+events you can't have one-and-a-half
+
+ align:start position:0%
+events you can't have one-and-a-half
+ 
+
+ align:start position:0%
+events you can't have one-and-a-half
+counts so you're gonna see this kind of
+
+ align:start position:0%
+counts so you're gonna see this kind of
+ 
+
+ align:start position:0%
+counts so you're gonna see this kind of
+thing quite a lot when you're trying to
+
+ align:start position:0%
+thing quite a lot when you're trying to
+ 
+
+ align:start position:0%
+thing quite a lot when you're trying to
+count very rare events and if you're
+
+ align:start position:0%
+count very rare events and if you're
+ 
+
+ align:start position:0%
+count very rare events and if you're
+down in that down in the weeds like this
+
+ align:start position:0%
+down in that down in the weeds like this
+ 
+
+ align:start position:0%
+down in that down in the weeds like this
+let's just say your statistics aren't
+
+ align:start position:0%
+let's just say your statistics aren't
+ 
+
+ align:start position:0%
+let's just say your statistics aren't
+that good but since this is a
+
+ align:start position:0%
+that good but since this is a
+ 
+
+ align:start position:0%
+that good but since this is a
+logarithmic scale 10 to the fourth is
+
+ align:start position:0%
+logarithmic scale 10 to the fourth is
+ 
+
+ align:start position:0%
+logarithmic scale 10 to the fourth is
+better known as 10,000 that's enough to
+
+ align:start position:0%
+better known as 10,000 that's enough to
+ 
+
+ align:start position:0%
+better known as 10,000 that's enough to
+get good statistics and fit a nice curve
+
+ align:start position:0%
+get good statistics and fit a nice curve
+ 
+
+ align:start position:0%
+get good statistics and fit a nice curve
+to this positron lifetime thing this is
+
+ align:start position:0%
+to this positron lifetime thing this is
+ 
+
+ align:start position:0%
+to this positron lifetime thing this is
+what one of them actually looks like and
+
+ align:start position:0%
+what one of them actually looks like and
+ 
+
+ align:start position:0%
+what one of them actually looks like and
+you can kind of tell right there's the
+
+ align:start position:0%
+you can kind of tell right there's the
+ 
+
+ align:start position:0%
+you can kind of tell right there's the
+big inside there is where all the
+
+ align:start position:0%
+big inside there is where all the
+ 
+
+ align:start position:0%
+big inside there is where all the
+positrons are coming out so that's
+
+ align:start position:0%
+positrons are coming out so that's
+ 
+
+ align:start position:0%
+positrons are coming out so that's
+probably lead shielding here's two
+
+ align:start position:0%
+probably lead shielding here's two
+ 
+
+ align:start position:0%
+probably lead shielding here's two
+detectors on either side and here's
+
+ align:start position:0%
+detectors on either side and here's
+ 
+
+ align:start position:0%
+detectors on either side and here's
+another detector to detect that
+
+ align:start position:0%
+another detector to detect that
+ 
+
+ align:start position:0%
+another detector to detect that
+1.27 mev birth gamma-ray so if you get
+
+ align:start position:0%
+1.27 mev birth gamma-ray so if you get
+ 
+
+ align:start position:0%
+1.27 mev birth gamma-ray so if you get
+those three events happening all in the
+
+ align:start position:0%
+those three events happening all in the
+ 
+
+ align:start position:0%
+those three events happening all in the
+right time you've got a positive event
+
+ align:start position:0%
+right time you've got a positive event
+ 
+
+ align:start position:0%
+right time you've got a positive event
+that you can count and last thing I'll
+
+ align:start position:0%
+that you can count and last thing I'll
+ 
+
+ align:start position:0%
+that you can count and last thing I'll
+mention is you can actually use this
+
+ align:start position:0%
+mention is you can actually use this
+ 
+
+ align:start position:0%
+mention is you can actually use this
+like I said to gut not just a number of
+
+ align:start position:0%
+like I said to gut not just a number of
+ 
+
+ align:start position:0%
+like I said to gut not just a number of
+vacancies but the number of different
+
+ align:start position:0%
+vacancies but the number of different
+ 
+
+ align:start position:0%
+vacancies but the number of different
+size defects you might have two or three
+
+ align:start position:0%
+size defects you might have two or three
+ 
+
+ align:start position:0%
+size defects you might have two or three
+missing atoms next to each other
+
+ align:start position:0%
+missing atoms next to each other
+ 
+
+ align:start position:0%
+missing atoms next to each other
+which will have different positron
+
+ align:start position:0%
+which will have different positron
+ 
+
+ align:start position:0%
+which will have different positron
+lifetimes and you can actually count the
+
+ align:start position:0%
+lifetimes and you can actually count the
+ 
+
+ align:start position:0%
+lifetimes and you can actually count the
+number of each of these to get the
+
+ align:start position:0%
+number of each of these to get the
+ 
+
+ align:start position:0%
+number of each of these to get the
+diameter or the size of these atomic
+
+ align:start position:0%
+diameter or the size of these atomic
+ 
+
+ align:start position:0%
+diameter or the size of these atomic
+defects and this is one of the ways of
+
+ align:start position:0%
+defects and this is one of the ways of
+ 
+
+ align:start position:0%
+defects and this is one of the ways of
+confirming our models of radiation
+
+ align:start position:0%
+confirming our models of radiation
+ 
+
+ align:start position:0%
+confirming our models of radiation
+damage which is like all I do that's
+
+ align:start position:0%
+damage which is like all I do that's
+ 
+
+ align:start position:0%
+damage which is like all I do that's
+half of our group if you want to read
+
+ align:start position:0%
+half of our group if you want to read
+ 
+
+ align:start position:0%
+half of our group if you want to read
+anything more about positron
+
+ align:start position:0%
+anything more about positron
+ 
+
+ align:start position:0%
+anything more about positron
+annihilation spectroscopy all the stuff
+
+ align:start position:0%
+annihilation spectroscopy all the stuff
+ 
+
+ align:start position:0%
+annihilation spectroscopy all the stuff
+in these slides were from these
+
+ align:start position:0%
+in these slides were from these
+ 
+
+ align:start position:0%
+in these slides were from these
+references which you can look up easily
+
+ align:start position:0%
+references which you can look up easily
+ 
+
+ align:start position:0%
+references which you can look up easily
+on the MIT libraries we have access to
+
+ align:start position:0%
+on the MIT libraries we have access to
+ 
+
+ align:start position:0%
+on the MIT libraries we have access to
+everything because that's MIT we just
+
+ align:start position:0%
+everything because that's MIT we just
+ 
+
+ align:start position:0%
+everything because that's MIT we just
+buy everything there is so I'd encourage
+
+ align:start position:0%
+buy everything there is so I'd encourage
+ 
+
+ align:start position:0%
+buy everything there is so I'd encourage
+you to look here if you want to see more
+
+ align:start position:0%
+you to look here if you want to see more
+ 
+
+ align:start position:0%
+you to look here if you want to see more
+details on how this works and why it
+
+ align:start position:0%
+details on how this works and why it
+ 
+
+ align:start position:0%
+details on how this works and why it
+works so because it's exactly ten of
+
+ align:start position:0%
+works so because it's exactly ten of
+ 
+
+ align:start position:0%
+works so because it's exactly ten of
+tenna
+
+ align:start position:0%
+tenna
+ 
+
+ align:start position:0%
+tenna
+or five of five of I want to open it up
+
+ align:start position:0%
+or five of five of I want to open it up
+ 
+
+ align:start position:0%
+or five of five of I want to open it up
+to any questions on alpha decay beta
+
+ align:start position:0%
+to any questions on alpha decay beta
+ 
+
+ align:start position:0%
+to any questions on alpha decay beta
+decay positron decay or the decay
+
+ align:start position:0%
+decay positron decay or the decay
+ 
+
+ align:start position:0%
+decay positron decay or the decay
+diagrams that we've developed today yes
+
+ align:start position:0%
+diagrams that we've developed today yes
+ 
+
+ align:start position:0%
+diagrams that we've developed today yes
+what is the most dangerous kind of decay
+
+ align:start position:0%
+what is the most dangerous kind of decay
+ 
+
+ align:start position:0%
+what is the most dangerous kind of decay
+to be exposed to so in this case you'd
+
+ align:start position:0%
+to be exposed to so in this case you'd
+ 
+
+ align:start position:0%
+to be exposed to so in this case you'd
+want to say the energy of the particle
+
+ align:start position:0%
+want to say the energy of the particle
+ 
+
+ align:start position:0%
+want to say the energy of the particle
+is held constant and the number of those
+
+ align:start position:0%
+is held constant and the number of those
+ 
+
+ align:start position:0%
+is held constant and the number of those
+particles is held constant and actually
+
+ align:start position:0%
+particles is held constant and actually
+ 
+
+ align:start position:0%
+particles is held constant and actually
+we're going to answer this question when
+
+ align:start position:0%
+we're going to answer this question when
+ 
+
+ align:start position:0%
+we're going to answer this question when
+we get to medical and biological effects
+
+ align:start position:0%
+we get to medical and biological effects
+ 
+
+ align:start position:0%
+we get to medical and biological effects
+but let's do a little flash board now
+
+ align:start position:0%
+but let's do a little flash board now
+ 
+
+ align:start position:0%
+but let's do a little flash board now
+let's assume if you want to see which
+
+ align:start position:0%
+let's assume if you want to see which
+ 
+
+ align:start position:0%
+let's assume if you want to see which
+one of these decays is most dangerous
+
+ align:start position:0%
+one of these decays is most dangerous
+ 
+
+ align:start position:0%
+one of these decays is most dangerous
+we'll have to say constant constant
+
+ align:start position:0%
+we'll have to say constant constant
+ 
+
+ align:start position:0%
+we'll have to say constant constant
+energy of decay constant activity and
+
+ align:start position:0%
+energy of decay constant activity and
+ 
+
+ align:start position:0%
+energy of decay constant activity and
+what else can we hold constant well
+
+ align:start position:0%
+what else can we hold constant well
+ 
+
+ align:start position:0%
+what else can we hold constant well
+constant you let's say the same number
+
+ align:start position:0%
+constant you let's say the same number
+ 
+
+ align:start position:0%
+constant you let's say the same number
+of particles end up hitting you that
+
+ align:start position:0%
+of particles end up hitting you that
+ 
+
+ align:start position:0%
+of particles end up hitting you that
+depends on whether they're inside or
+
+ align:start position:0%
+depends on whether they're inside or
+ 
+
+ align:start position:0%
+depends on whether they're inside or
+outside your body if you were to ingest
+
+ align:start position:0%
+outside your body if you were to ingest
+ 
+
+ align:start position:0%
+outside your body if you were to ingest
+material then alphas would be your worst
+
+ align:start position:0%
+material then alphas would be your worst
+ 
+
+ align:start position:0%
+material then alphas would be your worst
+because alpha particles are massive and
+
+ align:start position:0%
+because alpha particles are massive and
+ 
+
+ align:start position:0%
+because alpha particles are massive and
+charged nuclei which means they interact
+
+ align:start position:0%
+charged nuclei which means they interact
+ 
+
+ align:start position:0%
+charged nuclei which means they interact
+very strong
+
+ align:start position:0%
+very strong
+ 
+
+ align:start position:0%
+very strong
+with matter around them so if you ingest
+
+ align:start position:0%
+with matter around them so if you ingest
+ 
+
+ align:start position:0%
+with matter around them so if you ingest
+them and they end up incorporating into
+
+ align:start position:0%
+them and they end up incorporating into
+ 
+
+ align:start position:0%
+them and they end up incorporating into
+your cells where they can just get next
+
+ align:start position:0%
+your cells where they can just get next
+ 
+
+ align:start position:0%
+your cells where they can just get next
+to DNA they can just blast it apart
+
+ align:start position:0%
+to DNA they can just blast it apart
+ 
+
+ align:start position:0%
+to DNA they can just blast it apart
+however an alpha source of equal
+
+ align:start position:0%
+however an alpha source of equal
+ 
+
+ align:start position:0%
+however an alpha source of equal
+strength held in your hand would do
+
+ align:start position:0%
+strength held in your hand would do
+ 
+
+ align:start position:0%
+strength held in your hand would do
+nothing the dead skin cells are enough
+
+ align:start position:0%
+nothing the dead skin cells are enough
+ 
+
+ align:start position:0%
+nothing the dead skin cells are enough
+to stop alpha particles and we're gonna
+
+ align:start position:0%
+to stop alpha particles and we're gonna
+ 
+
+ align:start position:0%
+to stop alpha particles and we're gonna
+find out exactly why when we look at the
+
+ align:start position:0%
+find out exactly why when we look at the
+ 
+
+ align:start position:0%
+find out exactly why when we look at the
+range and stopping power of different
+
+ align:start position:0%
+range and stopping power of different
+ 
+
+ align:start position:0%
+range and stopping power of different
+particles and matter from the outside
+
+ align:start position:0%
+particles and matter from the outside
+ 
+
+ align:start position:0%
+particles and matter from the outside
+alphas won't really get through your
+
+ align:start position:0%
+alphas won't really get through your
+ 
+
+ align:start position:0%
+alphas won't really get through your
+skin betas might get through a little
+
+ align:start position:0%
+skin betas might get through a little
+ 
+
+ align:start position:0%
+skin betas might get through a little
+bit of your skin but not much gamma rays
+
+ align:start position:0%
+bit of your skin but not much gamma rays
+ 
+
+ align:start position:0%
+bit of your skin but not much gamma rays
+will mostly go right through you it's
+
+ align:start position:0%
+will mostly go right through you it's
+ 
+
+ align:start position:0%
+will mostly go right through you it's
+neutrons that are the real killers says
+
+ align:start position:0%
+neutrons that are the real killers says
+ 
+
+ align:start position:0%
+neutrons that are the real killers says
+neutrons are heavy but uncharged so they
+
+ align:start position:0%
+neutrons are heavy but uncharged so they
+ 
+
+ align:start position:0%
+neutrons are heavy but uncharged so they
+interact kind of strongly when they do
+
+ align:start position:0%
+interact kind of strongly when they do
+ 
+
+ align:start position:0%
+interact kind of strongly when they do
+hit they pack a wallop and they do a lot
+
+ align:start position:0%
+hit they pack a wallop and they do a lot
+ 
+
+ align:start position:0%
+hit they pack a wallop and they do a lot
+of damage and they're mean free path and
+
+ align:start position:0%
+of damage and they're mean free path and
+ 
+
+ align:start position:0%
+of damage and they're mean free path and
+you is on the order of 10 centimeters so
+
+ align:start position:0%
+you is on the order of 10 centimeters so
+ 
+
+ align:start position:0%
+you is on the order of 10 centimeters so
+a neutron source from the outside can do
+
+ align:start position:0%
+a neutron source from the outside can do
+ 
+
+ align:start position:0%
+a neutron source from the outside can do
+a lot of damage from the outside the
+
+ align:start position:0%
+a lot of damage from the outside the
+ 
+
+ align:start position:0%
+a lot of damage from the outside the
+alphas and the beta's would be stopped
+
+ align:start position:0%
+alphas and the beta's would be stopped
+ 
+
+ align:start position:0%
+alphas and the beta's would be stopped
+by your skin and clothes the gamma rays
+
+ align:start position:0%
+by your skin and clothes the gamma rays
+ 
+
+ align:start position:0%
+by your skin and clothes the gamma rays
+almost all of them will go right through
+
+ align:start position:0%
+almost all of them will go right through
+ 
+
+ align:start position:0%
+almost all of them will go right through
+you and you guys will actually have to
+
+ align:start position:0%
+you and you guys will actually have to
+ 
+
+ align:start position:0%
+you and you guys will actually have to
+do this calculation to find out how many
+
+ align:start position:0%
+do this calculation to find out how many
+ 
+
+ align:start position:0%
+do this calculation to find out how many
+gamma rays would you absorb from a gamma
+
+ align:start position:0%
+gamma rays would you absorb from a gamma
+ 
+
+ align:start position:0%
+gamma rays would you absorb from a gamma
+ray emission and how many go right
+
+ align:start position:0%
+ray emission and how many go right
+ 
+
+ align:start position:0%
+ray emission and how many go right
+through you the hint is most of them get
+
+ align:start position:0%
+through you the hint is most of them get
+ 
+
+ align:start position:0%
+through you the hint is most of them get
+out so there's a there's an exam
+
+ align:start position:0%
+out so there's a there's an exam
+ 
+
+ align:start position:0%
+out so there's a there's an exam
+question we used to ask in 2201 that I
+
+ align:start position:0%
+question we used to ask in 2201 that I
+ 
+
+ align:start position:0%
+question we used to ask in 2201 that I
+was asked during the first exam is
+
+ align:start position:0%
+was asked during the first exam is
+ 
+
+ align:start position:0%
+was asked during the first exam is
+you've got four cookies an alpha emitter
+
+ align:start position:0%
+you've got four cookies an alpha emitter
+ 
+
+ align:start position:0%
+you've got four cookies an alpha emitter
+a beta emitter a gamma emitter and a
+
+ align:start position:0%
+a beta emitter a gamma emitter and a
+ 
+
+ align:start position:0%
+a beta emitter a gamma emitter and a
+neutron emitter of constant energy and
+
+ align:start position:0%
+neutron emitter of constant energy and
+ 
+
+ align:start position:0%
+neutron emitter of constant energy and
+activity you must do one of the
+
+ align:start position:0%
+activity you must do one of the
+ 
+
+ align:start position:0%
+activity you must do one of the
+following you have to hold one in your
+
+ align:start position:0%
+following you have to hold one in your
+ 
+
+ align:start position:0%
+following you have to hold one in your
+hand at arm's length you have to put one
+
+ align:start position:0%
+hand at arm's length you have to put one
+ 
+
+ align:start position:0%
+hand at arm's length you have to put one
+in your pocket you have to eat one and
+
+ align:start position:0%
+in your pocket you have to eat one and
+ 
+
+ align:start position:0%
+in your pocket you have to eat one and
+you have to give one to a friend what do
+
+ align:start position:0%
+you have to give one to a friend what do
+ 
+
+ align:start position:0%
+you have to give one to a friend what do
+you do and why anyone have an idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pop quiz yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right I can tell this is the West
+
+ align:start position:0%
+that's right I can tell this is the West
+ 
+
+ align:start position:0%
+that's right I can tell this is the West
+because when I asked a group of
+
+ align:start position:0%
+because when I asked a group of
+ 
+
+ align:start position:0%
+because when I asked a group of
+Singaporean students the same question
+
+ align:start position:0%
+Singaporean students the same question
+ 
+
+ align:start position:0%
+Singaporean students the same question
+they would eat the neutron to save the
+
+ align:start position:0%
+they would eat the neutron to save the
+ 
+
+ align:start position:0%
+they would eat the neutron to save the
+friend because of Confucian ethics yeah
+
+ align:start position:0%
+friend because of Confucian ethics yeah
+ 
+
+ align:start position:0%
+friend because of Confucian ethics yeah
+I doesn't fly here your answer is
+
+ align:start position:0%
+I doesn't fly here your answer is
+ 
+
+ align:start position:0%
+I doesn't fly here your answer is
+correct because this is America what
+
+ align:start position:0%
+correct because this is America what
+ 
+
+ align:start position:0%
+correct because this is America what
+would you do with the other three eat
+
+ align:start position:0%
+would you do with the other three eat
+ 
+
+ align:start position:0%
+would you do with the other three eat
+the gamma because most of the gammas
+
+ align:start position:0%
+the gamma because most of the gammas
+ 
+
+ align:start position:0%
+the gamma because most of the gammas
+will just get to the friend right what
+
+ align:start position:0%
+will just get to the friend right what
+ 
+
+ align:start position:0%
+will just get to the friend right what
+about the Alpha and the beta yep hold
+
+ align:start position:0%
+about the Alpha and the beta yep hold
+ 
+
+ align:start position:0%
+about the Alpha and the beta yep hold
+the beta at arm's length because there's
+
+ align:start position:0%
+the beta at arm's length because there's
+ 
+
+ align:start position:0%
+the beta at arm's length because there's
+another aspect of shielding betas that
+
+ align:start position:0%
+another aspect of shielding betas that
+ 
+
+ align:start position:0%
+another aspect of shielding betas that
+we'll get into when betas stop in
+
+ align:start position:0%
+we'll get into when betas stop in
+ 
+
+ align:start position:0%
+we'll get into when betas stop in
+material they produce some low energy
+
+ align:start position:0%
+material they produce some low energy
+ 
+
+ align:start position:0%
+material they produce some low energy
+x-rays called bremsstrahlung so you'd
+
+ align:start position:0%
+x-rays called bremsstrahlung so you'd
+ 
+
+ align:start position:0%
+x-rays called bremsstrahlung so you'd
+want to get those far from you and the
+
+ align:start position:0%
+want to get those far from you and the
+ 
+
+ align:start position:0%
+want to get those far from you and the
+Alpha in your pocket we'll just be
+
+ align:start position:0%
+Alpha in your pocket we'll just be
+ 
+
+ align:start position:0%
+Alpha in your pocket we'll just be
+absorbed by the pocket yeah so that's
+
+ align:start position:0%
+absorbed by the pocket yeah so that's
+ 
+
+ align:start position:0%
+absorbed by the pocket yeah so that's
+the right question so you're not gonna
+
+ align:start position:0%
+the right question so you're not gonna
+ 
+
+ align:start position:0%
+the right question so you're not gonna
+see that on the exam but good news is
+
+ align:start position:0%
+see that on the exam but good news is
+ 
+
+ align:start position:0%
+see that on the exam but good news is
+you've pretty much got the right answer
+
+ align:start position:0%
+you've pretty much got the right answer
+ 
+
+ align:start position:0%
+you've pretty much got the right answer
+because this is America probably time
+
+ align:start position:0%
+because this is America probably time
+ 
+
+ align:start position:0%
+because this is America probably time
+for one more question if anyone has one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool if not then I want to remind you
+
+ align:start position:0%
+cool if not then I want to remind you
+ 
+
+ align:start position:0%
+cool if not then I want to remind you
+Amelia
+
+ align:start position:0%
+Amelia
+ 
+
+ align:start position:0%
+Amelia
+we'll see you on Thursday so do come to
+
+ align:start position:0%
+we'll see you on Thursday so do come to
+ 
+
+ align:start position:0%
+we'll see you on Thursday so do come to
+class Thursday I'm gonna change the
+
+ align:start position:0%
+class Thursday I'm gonna change the
+ 
+
+ align:start position:0%
+class Thursday I'm gonna change the
+syllabus to reflect that and we'll have
+
+ align:start position:0%
+syllabus to reflect that and we'll have
+ 
+
+ align:start position:0%
+syllabus to reflect that and we'll have
+two hours of class on Friday to get
+
+ align:start position:0%
+two hours of class on Friday to get
+ 
+
+ align:start position:0%
+two hours of class on Friday to get
+through decay and activity in half-life
+
+ align:start position:0%
+through decay and activity in half-life
+ 
+
+ align:start position:0%
+through decay and activity in half-life
+followed by an hour of recitation so I
+
+ align:start position:0%
+followed by an hour of recitation so I
+ 
+
+ align:start position:0%
+followed by an hour of recitation so I
+will see you guys Friday and we'll see
+
+ align:start position:0%
+will see you guys Friday and we'll see
+ 
+
+ align:start position:0%
+will see you guys Friday and we'll see
+what mood I'm in depending on how the
+
+ align:start position:0%
+what mood I'm in depending on how the
+ 
+
+ align:start position:0%
+what mood I'm in depending on how the
+nano caliber entry goes could be a fun
+
+ align:start position:0%
+nano caliber entry goes could be a fun
+ 
+
+ align:start position:0%
+nano caliber entry goes could be a fun
+measurement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/YWxY6mZwRSQ.txt b/YWxY6mZwRSQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8dcd943d4cd646e3b8f3c954a2caa05b13bd4dc4
--- /dev/null
+++ b/YWxY6mZwRSQ.txt
@@ -0,0 +1,2963 @@
+align:start position:0%
+ 
+two particles is interesting many cases
+
+ align:start position:0%
+two particles is interesting many cases
+ 
+
+ align:start position:0%
+two particles is interesting many cases
+but in order to see what really is
+
+ align:start position:0%
+but in order to see what really is
+ 
+
+ align:start position:0%
+but in order to see what really is
+happening and how much structure you
+
+ align:start position:0%
+happening and how much structure you
+ 
+
+ align:start position:0%
+happening and how much structure you
+have to go to more than two particles to
+
+ align:start position:0%
+have to go to more than two particles to
+ 
+
+ align:start position:0%
+have to go to more than two particles to
+party this is a little too special it's
+
+ align:start position:0%
+party this is a little too special it's
+ 
+
+ align:start position:0%
+party this is a little too special it's
+so we need to go beyond two particles
+
+ align:start position:0%
+so we need to go beyond two particles
+ 
+
+ align:start position:0%
+so we need to go beyond two particles
+and see what happens with this operator
+
+ align:start position:0%
+and see what happens with this operator
+ 
+
+ align:start position:0%
+and see what happens with this operator
+so I'll do that so we'll add more
+
+ align:start position:0%
+so I'll do that so we'll add more
+ 
+
+ align:start position:0%
+so I'll do that so we'll add more
+particles so let's do that so if you
+
+ align:start position:0%
+particles so let's do that so if you
+ 
+
+ align:start position:0%
+particles so let's do that so if you
+have n particles and particles capital n
+
+ align:start position:0%
+have n particles and particles capital n
+ 
+
+ align:start position:0%
+have n particles and particles capital n
+we can consider also permutations and
+
+ align:start position:0%
+we can consider also permutations and
+ 
+
+ align:start position:0%
+we can consider also permutations and
+how many permutations are you gonna have
+
+ align:start position:0%
+how many permutations are you gonna have
+ 
+
+ align:start position:0%
+how many permutations are you gonna have
+you're gonna have n factorial
+
+ align:start position:0%
+you're gonna have n factorial
+ 
+
+ align:start position:0%
+you're gonna have n factorial
+permutations in notation of Hilbert
+
+ align:start position:0%
+permutations in notation of Hilbert
+ 
+
+ align:start position:0%
+permutations in notation of Hilbert
+space n factorial permutations operators
+
+ align:start position:0%
+space n factorial permutations operators
+ 
+
+ align:start position:0%
+space n factorial permutations operators
+so why is n factorial because a
+
+ align:start position:0%
+so why is n factorial because a
+ 
+
+ align:start position:0%
+so why is n factorial because a
+permutation is a reordering of your n
+
+ align:start position:0%
+permutation is a reordering of your n
+ 
+
+ align:start position:0%
+permutation is a reordering of your n
+objects and therefore in order to define
+
+ align:start position:0%
+objects and therefore in order to define
+ 
+
+ align:start position:0%
+objects and therefore in order to define
+a reordering you must decide which
+
+ align:start position:0%
+a reordering you must decide which
+ 
+
+ align:start position:0%
+a reordering you must decide which
+object is going to be the new first you
+
+ align:start position:0%
+object is going to be the new first you
+ 
+
+ align:start position:0%
+object is going to be the new first you
+have your n objects there so you have n
+
+ align:start position:0%
+have your n objects there so you have n
+ 
+
+ align:start position:0%
+have your n objects there so you have n
+choices to pick a first and n minus 1
+
+ align:start position:0%
+choices to pick a first and n minus 1
+ 
+
+ align:start position:0%
+choices to pick a first and n minus 1
+choices to pick a second and minus 2 so
+
+ align:start position:0%
+choices to pick a second and minus 2 so
+ 
+
+ align:start position:0%
+choices to pick a second and minus 2 so
+n factorial is the number of
+
+ align:start position:0%
+n factorial is the number of
+ 
+
+ align:start position:0%
+n factorial is the number of
+permutations the permutations form a
+
+ align:start position:0%
+permutations the permutations form a
+ 
+
+ align:start position:0%
+permutations the permutations form a
+group so the permutations of n objects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form the symmetric group group s capital
+
+ align:start position:0%
+form the symmetric group group s capital
+ 
+
+ align:start position:0%
+form the symmetric group group s capital
+n with
+
+ align:start position:0%
+n with
+ 
+
+ align:start position:0%
+n with
+n-factorial elements just like you study
+
+ align:start position:0%
+n-factorial elements just like you study
+ 
+
+ align:start position:0%
+n-factorial elements just like you study
+the group su 2 of two-by-two unitary
+
+ align:start position:0%
+the group su 2 of two-by-two unitary
+ 
+
+ align:start position:0%
+the group su 2 of two-by-two unitary
+matrices or the group so3 of
+
+ align:start position:0%
+matrices or the group so3 of
+ 
+
+ align:start position:0%
+matrices or the group so3 of
+3-dimensional rotations in space the
+
+ align:start position:0%
+3-dimensional rotations in space the
+ 
+
+ align:start position:0%
+3-dimensional rotations in space the
+permutation group is a group that
+
+ align:start position:0%
+permutation group is a group that
+ 
+
+ align:start position:0%
+permutation group is a group that
+deserves a lot of study it's a finite
+
+ align:start position:0%
+deserves a lot of study it's a finite
+ 
+
+ align:start position:0%
+deserves a lot of study it's a finite
+discrete group is not a continuous group
+
+ align:start position:0%
+discrete group is not a continuous group
+ 
+
+ align:start position:0%
+discrete group is not a continuous group
+of transformations is discrete
+
+ align:start position:0%
+of transformations is discrete
+ 
+
+ align:start position:0%
+of transformations is discrete
+transformations and they do funny things
+
+ align:start position:0%
+transformations and they do funny things
+ 
+
+ align:start position:0%
+transformations and they do funny things
+so we need to understand this group so
+
+ align:start position:0%
+so we need to understand this group so
+ 
+
+ align:start position:0%
+so we need to understand this group so
+let's describe the notation of what is a
+
+ align:start position:0%
+let's describe the notation of what is a
+ 
+
+ align:start position:0%
+let's describe the notation of what is a
+permutation suppose you have n equal 4 4
+
+ align:start position:0%
+permutation suppose you have n equal 4 4
+ 
+
+ align:start position:0%
+permutation suppose you have n equal 4 4
+particles so a given state is
+
+ align:start position:0%
+particles so a given state is
+ 
+
+ align:start position:0%
+particles so a given state is
+represented by a b c d and you could say
+
+ align:start position:0%
+represented by a b c d and you could say
+ 
+
+ align:start position:0%
+represented by a b c d and you could say
+this is the first particle 2nd 3rd and
+
+ align:start position:0%
+this is the first particle 2nd 3rd and
+ 
+
+ align:start position:0%
+this is the first particle 2nd 3rd and
+4th and these are the states and now
+
+ align:start position:0%
+4th and these are the states and now
+ 
+
+ align:start position:0%
+4th and these are the states and now
+we're gonna write the perturbation the
+
+ align:start position:0%
+we're gonna write the perturbation the
+ 
+
+ align:start position:0%
+we're gonna write the perturbation the
+best thing I think is just doing example
+
+ align:start position:0%
+best thing I think is just doing example
+ 
+
+ align:start position:0%
+best thing I think is just doing example
+3 3 1 4 2 so a permutation now has
+
+ align:start position:0%
+3 3 1 4 2 so a permutation now has
+ 
+
+ align:start position:0%
+3 3 1 4 2 so a permutation now has
+capital n labels so for labels and this
+
+ align:start position:0%
+capital n labels so for labels and this
+ 
+
+ align:start position:0%
+capital n labels so for labels and this
+is a permutation acting on this state
+
+ align:start position:0%
+is a permutation acting on this state
+ 
+
+ align:start position:0%
+is a permutation acting on this state
+remember the to one permutation exchange
+
+ align:start position:0%
+remember the to one permutation exchange
+ 
+
+ align:start position:0%
+remember the to one permutation exchange
+the state in two was put in 1 the state
+
+ align:start position:0%
+the state in two was put in 1 the state
+ 
+
+ align:start position:0%
+the state in two was put in 1 the state
+in one was put in to here is the
+
+ align:start position:0%
+in one was put in to here is the
+ 
+
+ align:start position:0%
+in one was put in to here is the
+instruction so the instruction is put in
+
+ align:start position:0%
+instruction so the instruction is put in
+ 
+
+ align:start position:0%
+instruction so the instruction is put in
+position 1 the third state so here it
+
+ align:start position:0%
+position 1 the third state so here it
+ 
+
+ align:start position:0%
+position 1 the third state so here it
+says 3 so the third state goes into the
+
+ align:start position:0%
+says 3 so the third state goes into the
+ 
+
+ align:start position:0%
+says 3 so the third state goes into the
+first position so that's the first
+
+ align:start position:0%
+first position so that's the first
+ 
+
+ align:start position:0%
+first position so that's the first
+position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first date goes into the second
+
+ align:start position:0%
+the first date goes into the second
+ 
+
+ align:start position:0%
+the first date goes into the second
+position the fourth state goes into the
+
+ align:start position:0%
+position the fourth state goes into the
+ 
+
+ align:start position:0%
+position the fourth state goes into the
+third position the third in that's here
+
+ align:start position:0%
+third position the third in that's here
+ 
+
+ align:start position:0%
+third position the third in that's here
+so the third position is now occupied by
+
+ align:start position:0%
+so the third position is now occupied by
+ 
+
+ align:start position:0%
+so the third position is now occupied by
+the fourth state D and the second state
+
+ align:start position:0%
+the fourth state D and the second state
+ 
+
+ align:start position:0%
+the fourth state D and the second state
+goes into the fourth position so this is
+
+ align:start position:0%
+goes into the fourth position so this is
+ 
+
+ align:start position:0%
+goes into the fourth position so this is
+the way we are going to define
+
+ align:start position:0%
+the way we are going to define
+ 
+
+ align:start position:0%
+the way we are going to define
+perturbation permutations people define
+
+ align:start position:0%
+perturbation permutations people define
+ 
+
+ align:start position:0%
+perturbation permutations people define
+them in different ways and you have to
+
+ align:start position:0%
+them in different ways and you have to
+ 
+
+ align:start position:0%
+them in different ways and you have to
+be sure you know what it means but I'll
+
+ align:start position:0%
+be sure you know what it means but I'll
+ 
+
+ align:start position:0%
+be sure you know what it means but I'll
+write this this means put third object
+
+ align:start position:0%
+write this this means put third object
+ 
+
+ align:start position:0%
+write this this means put third object
+in first position here the second one
+
+ align:start position:0%
+in first position here the second one
+ 
+
+ align:start position:0%
+in first position here the second one
+let's write put first object in second
+
+ align:start position:0%
+let's write put first object in second
+ 
+
+ align:start position:0%
+let's write put first object in second
+position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's it's nice to have this notation
+
+ align:start position:0%
+so it's it's nice to have this notation
+ 
+
+ align:start position:0%
+so it's it's nice to have this notation
+because now you can understand how the
+
+ align:start position:0%
+because now you can understand how the
+ 
+
+ align:start position:0%
+because now you can understand how the
+group works a group of transformations
+
+ align:start position:0%
+group works a group of transformations
+ 
+
+ align:start position:0%
+group works a group of transformations
+this is a set of elements that can be
+
+ align:start position:0%
+this is a set of elements that can be
+ 
+
+ align:start position:0%
+this is a set of elements that can be
+multiplied there is an identity and
+
+ align:start position:0%
+multiplied there is an identity and
+ 
+
+ align:start position:0%
+multiplied there is an identity and
+things have inverses as well so
+
+ align:start position:0%
+things have inverses as well so
+ 
+
+ align:start position:0%
+things have inverses as well so
+permutations have inverses if you
+
+ align:start position:0%
+permutations have inverses if you
+ 
+
+ align:start position:0%
+permutations have inverses if you
+rearrange the objects in one way you can
+
+ align:start position:0%
+rearrange the objects in one way you can
+ 
+
+ align:start position:0%
+rearrange the objects in one way you can
+rearrange them back so for example what
+
+ align:start position:0%
+rearrange them back so for example what
+ 
+
+ align:start position:0%
+rearrange them back so for example what
+would be the inverse of this permutation
+
+ align:start position:0%
+would be the inverse of this permutation
+ 
+
+ align:start position:0%
+would be the inverse of this permutation
+I try to figure out what is the inverse
+
+ align:start position:0%
+I try to figure out what is the inverse
+ 
+
+ align:start position:0%
+I try to figure out what is the inverse
+inverse of P 3 1 4 2 so I look at this
+
+ align:start position:0%
+inverse of P 3 1 4 2 so I look at this
+ 
+
+ align:start position:0%
+inverse of P 3 1 4 2 so I look at this
+thing and I think of what is the
+
+ align:start position:0%
+thing and I think of what is the
+ 
+
+ align:start position:0%
+thing and I think of what is the
+instruction that I must put in order to
+
+ align:start position:0%
+instruction that I must put in order to
+ 
+
+ align:start position:0%
+instruction that I must put in order to
+rearrange back this series and I say
+
+ align:start position:0%
+rearrange back this series and I say
+ 
+
+ align:start position:0%
+rearrange back this series and I say
+well I must put the 2nd back in position
+
+ align:start position:0%
+well I must put the 2nd back in position
+ 
+
+ align:start position:0%
+well I must put the 2nd back in position
+1 so there should be a p2 here I should
+
+ align:start position:0%
+1 so there should be a p2 here I should
+ 
+
+ align:start position:0%
+1 so there should be a p2 here I should
+put the 4th in position 2 and then I
+
+ align:start position:0%
+put the 4th in position 2 and then I
+ 
+
+ align:start position:0%
+put the 4th in position 2 and then I
+should put the first in position 3 first
+
+ align:start position:0%
+should put the first in position 3 first
+ 
+
+ align:start position:0%
+should put the first in position 3 first
+in position 3 and I should put the 3rd
+
+ align:start position:0%
+in position 3 and I should put the 3rd
+ 
+
+ align:start position:0%
+in position 3 and I should put the 3rd
+in position 4 so I claim that is the
+
+ align:start position:0%
+in position 4 so I claim that is the
+ 
+
+ align:start position:0%
+in position 4 so I claim that is the
+inverse of this operator P 2 1 3 is the
+
+ align:start position:0%
+inverse of this operator P 2 1 3 is the
+ 
+
+ align:start position:0%
+inverse of this operator P 2 1 3 is the
+inverse of this is so you can check it
+
+ align:start position:0%
+inverse of this is so you can check it
+ 
+
+ align:start position:0%
+inverse of this is so you can check it
+again P 2 2
+
+ align:start position:0%
+again P 2 2
+ 
+
+ align:start position:0%
+again P 2 2
+for 1/3 times p3 1 for 2 you just do it
+
+ align:start position:0%
+for 1/3 times p3 1 for 2 you just do it
+ 
+
+ align:start position:0%
+for 1/3 times p3 1 for 2 you just do it
+on a b c b well the first one you
+
+ align:start position:0%
+on a b c b well the first one you
+ 
+
+ align:start position:0%
+on a b c b well the first one you
+already know is 2 for 1 3 is put the
+
+ align:start position:0%
+already know is 2 for 1 3 is put the
+ 
+
+ align:start position:0%
+already know is 2 for 1 3 is put the
+third in 1 put the first in to put the
+
+ align:start position:0%
+third in 1 put the first in to put the
+ 
+
+ align:start position:0%
+third in 1 put the first in to put the
+fourth in 3 and put the second in fourth
+
+ align:start position:0%
+fourth in 3 and put the second in fourth
+ 
+
+ align:start position:0%
+fourth in 3 and put the second in fourth
+B and then it says put the second first
+
+ align:start position:0%
+B and then it says put the second first
+ 
+
+ align:start position:0%
+B and then it says put the second first
+so that's an a put the fourth second B
+
+ align:start position:0%
+so that's an a put the fourth second B
+ 
+
+ align:start position:0%
+so that's an a put the fourth second B
+put the first third C and put the third
+
+ align:start position:0%
+put the first third C and put the third
+ 
+
+ align:start position:0%
+put the first third C and put the third
+fourth B so it's back to the original
+
+ align:start position:0%
+fourth B so it's back to the original
+ 
+
+ align:start position:0%
+fourth B so it's back to the original
+one so indeed it is the inverse so you
+
+ align:start position:0%
+one so indeed it is the inverse so you
+ 
+
+ align:start position:0%
+one so indeed it is the inverse so you
+can ride your permutations and play with
+
+ align:start position:0%
+can ride your permutations and play with
+ 
+
+ align:start position:0%
+can ride your permutations and play with
+them and figure out how to multiply any
+
+ align:start position:0%
+them and figure out how to multiply any
+ 
+
+ align:start position:0%
+them and figure out how to multiply any
+two permutations more generally we write
+
+ align:start position:0%
+two permutations more generally we write
+ 
+
+ align:start position:0%
+two permutations more generally we write
+the permutation as follows suppose you
+
+ align:start position:0%
+the permutation as follows suppose you
+ 
+
+ align:start position:0%
+the permutation as follows suppose you
+have more generally a permutation is
+
+ align:start position:0%
+have more generally a permutation is
+ 
+
+ align:start position:0%
+have more generally a permutation is
+written with some index alpha collective
+
+ align:start position:0%
+written with some index alpha collective
+ 
+
+ align:start position:0%
+written with some index alpha collective
+index alpha that says how the integers 1
+
+ align:start position:0%
+index alpha that says how the integers 1
+ 
+
+ align:start position:0%
+index alpha that says how the integers 1
+up to end our rearranged into alpha of 1
+
+ align:start position:0%
+up to end our rearranged into alpha of 1
+ 
+
+ align:start position:0%
+up to end our rearranged into alpha of 1
+alpha of 2 up to alpha of M so think of
+
+ align:start position:0%
+alpha of 2 up to alpha of M so think of
+ 
+
+ align:start position:0%
+alpha of 2 up to alpha of M so think of
+a permutation taking n integers and
+
+ align:start position:0%
+a permutation taking n integers and
+ 
+
+ align:start position:0%
+a permutation taking n integers and
+rearranging them so the first one the
+
+ align:start position:0%
+rearranging them so the first one the
+ 
+
+ align:start position:0%
+rearranging them so the first one the
+new first index is going to be alpha of
+
+ align:start position:0%
+new first index is going to be alpha of
+ 
+
+ align:start position:0%
+new first index is going to be alpha of
+1 out of 2 and alpha is a rule that
+
+ align:start position:0%
+1 out of 2 and alpha is a rule that
+ 
+
+ align:start position:0%
+1 out of 2 and alpha is a rule that
+takings takes the n integers from 1
+
+ align:start position:0%
+takings takes the n integers from 1
+ 
+
+ align:start position:0%
+takings takes the n integers from 1
+to end and reshuffle them so if you have
+
+ align:start position:0%
+to end and reshuffle them so if you have
+ 
+
+ align:start position:0%
+to end and reshuffle them so if you have
+a state so this is a simple thing
+
+ align:start position:0%
+a state so this is a simple thing
+ 
+
+ align:start position:0%
+a state so this is a simple thing
+because then if you have a P alpha this
+
+ align:start position:0%
+because then if you have a P alpha this
+ 
+
+ align:start position:0%
+because then if you have a P alpha this
+alpha means really P alpha 1 alpha 2 all
+
+ align:start position:0%
+alpha means really P alpha 1 alpha 2 all
+ 
+
+ align:start position:0%
+alpha means really P alpha 1 alpha 2 all
+these things be are for 1 or 2 or 3 or 4
+
+ align:start position:0%
+these things be are for 1 or 2 or 3 or 4
+ 
+
+ align:start position:0%
+these things be are for 1 or 2 or 3 or 4
+if those act on u 1 1 u 2 2 up to u and
+
+ align:start position:0%
+if those act on u 1 1 u 2 2 up to u and
+ 
+
+ align:start position:0%
+if those act on u 1 1 u 2 2 up to u and
+capital m and what does it give you well
+
+ align:start position:0%
+capital m and what does it give you well
+ 
+
+ align:start position:0%
+capital m and what does it give you well
+it says here that you should put the one
+
+ align:start position:0%
+it says here that you should put the one
+ 
+
+ align:start position:0%
+it says here that you should put the one
+that has alpha 1 here on the first
+
+ align:start position:0%
+that has alpha 1 here on the first
+ 
+
+ align:start position:0%
+that has alpha 1 here on the first
+position so you should put first the u
+
+ align:start position:0%
+position so you should put first the u
+ 
+
+ align:start position:0%
+position so you should put first the u
+alpha 1 and then you should put next the
+
+ align:start position:0%
+alpha 1 and then you should put next the
+ 
+
+ align:start position:0%
+alpha 1 and then you should put next the
+u alpha 2 and all the way up to the u
+
+ align:start position:0%
+u alpha 2 and all the way up to the u
+ 
+
+ align:start position:0%
+u alpha 2 and all the way up to the u
+alpha m that's in formulas the rule that
+
+ align:start position:0%
+alpha m that's in formulas the rule that
+ 
+
+ align:start position:0%
+alpha m that's in formulas the rule that
+I was giving you above it tells you how
+
+ align:start position:0%
+I was giving you above it tells you how
+ 
+
+ align:start position:0%
+I was giving you above it tells you how
+to move the state from one to the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see if alpha 1 was three it would
+
+ align:start position:0%
+you see if alpha 1 was three it would
+ 
+
+ align:start position:0%
+you see if alpha 1 was three it would
+correspond to take the state u3 and
+
+ align:start position:0%
+correspond to take the state u3 and
+ 
+
+ align:start position:0%
+correspond to take the state u3 and
+putting it first so it's like that
+
+ align:start position:0%
+putting it first so it's like that
+ 
+
+ align:start position:0%
+putting it first so it's like that
+so whatever alpha 1 is whatever number
+
+ align:start position:0%
+so whatever alpha 1 is whatever number
+ 
+
+ align:start position:0%
+so whatever alpha 1 is whatever number
+that state must be pulled into the first
+
+ align:start position:0%
+that state must be pulled into the first
+ 
+
+ align:start position:0%
+that state must be pulled into the first
+kit okay so let's just think a little
+
+ align:start position:0%
+kit okay so let's just think a little
+ 
+
+ align:start position:0%
+kit okay so let's just think a little
+about an example because if it starts
+
+ align:start position:0%
+about an example because if it starts
+ 
+
+ align:start position:0%
+about an example because if it starts
+getting out interesting so let's do
+
+ align:start position:0%
+getting out interesting so let's do
+ 
+
+ align:start position:0%
+getting out interesting so let's do
+three particles for for a little while
+
+ align:start position:0%
+three particles for for a little while
+ 
+
+ align:start position:0%
+three particles for for a little while
+just to see what it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so three particles and equal three so
+
+ align:start position:0%
+so three particles and equal three so
+ 
+
+ align:start position:0%
+so three particles and equal three so
+what are the permutation operators you
+
+ align:start position:0%
+what are the permutation operators you
+ 
+
+ align:start position:0%
+what are the permutation operators you
+would say P 1 2 3 is what put the first
+
+ align:start position:0%
+would say P 1 2 3 is what put the first
+ 
+
+ align:start position:0%
+would say P 1 2 3 is what put the first
+particle first the second particle
+
+ align:start position:0%
+particle first the second particle
+ 
+
+ align:start position:0%
+particle first the second particle
+second the third particle third doesn't
+
+ align:start position:0%
+second the third particle third doesn't
+ 
+
+ align:start position:0%
+second the third particle third doesn't
+do anything that is the identity so
+
+ align:start position:0%
+do anything that is the identity so
+ 
+
+ align:start position:0%
+do anything that is the identity so
+that's the identity element but then you
+
+ align:start position:0%
+that's the identity element but then you
+ 
+
+ align:start position:0%
+that's the identity element but then you
+could cycle them P 3 2 1 P 2 3 1 these
+
+ align:start position:0%
+could cycle them P 3 2 1 P 2 3 1 these
+ 
+
+ align:start position:0%
+could cycle them P 3 2 1 P 2 3 1 these
+are two more elements this should have
+
+ align:start position:0%
+are two more elements this should have
+ 
+
+ align:start position:0%
+are two more elements this should have
+six elements because it's 3 factorial
+
+ align:start position:0%
+six elements because it's 3 factorial
+ 
+
+ align:start position:0%
+six elements because it's 3 factorial
+and now you have the following 1 P 1 3 2
+
+ align:start position:0%
+and now you have the following 1 P 1 3 2
+ 
+
+ align:start position:0%
+and now you have the following 1 P 1 3 2
+for example that was not in the list you
+
+ align:start position:0%
+for example that was not in the list you
+ 
+
+ align:start position:0%
+for example that was not in the list you
+had the P 1 2 3 now you flip this to be
+
+ align:start position:0%
+had the P 1 2 3 now you flip this to be
+ 
+
+ align:start position:0%
+had the P 1 2 3 now you flip this to be
+1 3 2 if I cycle them P 3 2 1 and P 2 1
+
+ align:start position:0%
+1 3 2 if I cycle them P 3 2 1 and P 2 1
+ 
+
+ align:start position:0%
+1 3 2 if I cycle them P 3 2 1 and P 2 1
+3 these are it
+
+ align:start position:0%
+3 these are it
+ 
+
+ align:start position:0%
+3 these are it
+the middle 1 3 1 2
+
+ align:start position:0%
+the middle 1 3 1 2
+ 
+
+ align:start position:0%
+the middle 1 3 1 2
+yes I was supposed to be cycling them 3
+
+ align:start position:0%
+yes I was supposed to be cycling them 3
+ 
+
+ align:start position:0%
+yes I was supposed to be cycling them 3
+1 2 & 2 3 1 yes
+
+ align:start position:0%
+1 2 & 2 3 1 yes
+ 
+
+ align:start position:0%
+1 2 & 2 3 1 yes
+otherwise I would have repeated that
+
+ align:start position:0%
+otherwise I would have repeated that
+ 
+
+ align:start position:0%
+otherwise I would have repeated that
+good right okay so these are our
+
+ align:start position:0%
+good right okay so these are our
+ 
+
+ align:start position:0%
+good right okay so these are our
+operators and this ones are kind of
+
+ align:start position:0%
+operators and this ones are kind of
+ 
+
+ align:start position:0%
+operators and this ones are kind of
+funny there are simpler ones
+
+ align:start position:0%
+funny there are simpler ones
+ 
+
+ align:start position:0%
+funny there are simpler ones
+please look at them this operator says
+
+ align:start position:0%
+please look at them this operator says
+ 
+
+ align:start position:0%
+please look at them this operator says
+put the first particle in the first
+
+ align:start position:0%
+put the first particle in the first
+ 
+
+ align:start position:0%
+put the first particle in the first
+position so the first particle is left
+
+ align:start position:0%
+position so the first particle is left
+ 
+
+ align:start position:0%
+position so the first particle is left
+unchanged that the 3 & 2 are permuted
+
+ align:start position:0%
+unchanged that the 3 & 2 are permuted
+ 
+
+ align:start position:0%
+unchanged that the 3 & 2 are permuted
+so people sometimes write this they say
+
+ align:start position:0%
+so people sometimes write this they say
+ 
+
+ align:start position:0%
+so people sometimes write this they say
+this permutation operator is just as
+
+ align:start position:0%
+this permutation operator is just as
+ 
+
+ align:start position:0%
+this permutation operator is just as
+transposition 3 2 or 2 3
+
+ align:start position:0%
+transposition 3 2 or 2 3
+ 
+
+ align:start position:0%
+transposition 3 2 or 2 3
+these two are transposed and the first
+
+ align:start position:0%
+these two are transposed and the first
+ 
+
+ align:start position:0%
+these two are transposed and the first
+is left invariant so this can be written
+
+ align:start position:0%
+is left invariant so this can be written
+ 
+
+ align:start position:0%
+is left invariant so this can be written
+as a single transposition in this
+
+ align:start position:0%
+as a single transposition in this
+ 
+
+ align:start position:0%
+as a single transposition in this
+permutation operator a 2 is left
+
+ align:start position:0%
+permutation operator a 2 is left
+ 
+
+ align:start position:0%
+permutation operator a 2 is left
+invariant the second state is copied to
+
+ align:start position:0%
+invariant the second state is copied to
+ 
+
+ align:start position:0%
+invariant the second state is copied to
+the second position but the 1 & 3 are
+
+ align:start position:0%
+the second position but the 1 & 3 are
+ 
+
+ align:start position:0%
+the second position but the 1 & 3 are
+exchanged so this is a transposition of
+
+ align:start position:0%
+exchanged so this is a transposition of
+ 
+
+ align:start position:0%
+exchanged so this is a transposition of
+1 & 3 and in this last permutation
+
+ align:start position:0%
+1 & 3 and in this last permutation
+ 
+
+ align:start position:0%
+1 & 3 and in this last permutation
+operator the third state is left
+
+ align:start position:0%
+operator the third state is left
+ 
+
+ align:start position:0%
+operator the third state is left
+invariant on the third position never
+
+ align:start position:0%
+invariant on the third position never
+ 
+
+ align:start position:0%
+invariant on the third position never
+that as the second is put in first and
+
+ align:start position:0%
+that as the second is put in first and
+ 
+
+ align:start position:0%
+that as the second is put in first and
+the first is put in second so it's a 1 -
+
+ align:start position:0%
+the first is put in second so it's a 1 -
+ 
+
+ align:start position:0%
+the first is put in second so it's a 1 -
+transposition okay so the group has
+
+ align:start position:0%
+transposition okay so the group has
+ 
+
+ align:start position:0%
+transposition okay so the group has
+broken into things that are
+
+ align:start position:0%
+broken into things that are
+ 
+
+ align:start position:0%
+broken into things that are
+transpositions
+
+ align:start position:0%
+transpositions
+ 
+
+ align:start position:0%
+transpositions
+and slightly more complicated things now
+
+ align:start position:0%
+and slightly more complicated things now
+ 
+
+ align:start position:0%
+and slightly more complicated things now
+let's look at the transpositions so
+
+ align:start position:0%
+let's look at the transpositions so
+ 
+
+ align:start position:0%
+let's look at the transpositions so
+these are trans positions and positions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what about the transpositions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transpositions are like the permutation
+
+ align:start position:0%
+transpositions are like the permutation
+ 
+
+ align:start position:0%
+transpositions are like the permutation
+operators who were doing before of two
+
+ align:start position:0%
+operators who were doing before of two
+ 
+
+ align:start position:0%
+operators who were doing before of two
+particles you're just changing two
+
+ align:start position:0%
+particles you're just changing two
+ 
+
+ align:start position:0%
+particles you're just changing two
+particles you're leaving the other ones
+
+ align:start position:0%
+particles you're leaving the other ones
+ 
+
+ align:start position:0%
+particles you're leaving the other ones
+unchanged
+
+ align:start position:0%
+unchanged
+ 
+
+ align:start position:0%
+unchanged
+so these transpositions are hermitian
+
+ align:start position:0%
+so these transpositions are hermitian
+ 
+
+ align:start position:0%
+so these transpositions are hermitian
+and unitary positions are hermitian and
+
+ align:start position:0%
+and unitary positions are hermitian and
+ 
+
+ align:start position:0%
+and unitary positions are hermitian and
+unitary just like we had p21 before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here comes the first statement that
+
+ align:start position:0%
+now here comes the first statement that
+ 
+
+ align:start position:0%
+now here comes the first statement that
+is quite remarkable about this
+
+ align:start position:0%
+is quite remarkable about this
+ 
+
+ align:start position:0%
+is quite remarkable about this
+permutation group any permutation now a
+
+ align:start position:0%
+permutation group any permutation now a
+ 
+
+ align:start position:0%
+permutation group any permutation now a
+claim is the product of some
+
+ align:start position:0%
+claim is the product of some
+ 
+
+ align:start position:0%
+claim is the product of some
+transpositions you see if somebody gives
+
+ align:start position:0%
+transpositions you see if somebody gives
+ 
+
+ align:start position:0%
+transpositions you see if somebody gives
+you a permutation of n integers I think
+
+ align:start position:0%
+you a permutation of n integers I think
+ 
+
+ align:start position:0%
+you a permutation of n integers I think
+you're convinced that by changing two at
+
+ align:start position:0%
+you're convinced that by changing two at
+ 
+
+ align:start position:0%
+you're convinced that by changing two at
+a time you can reach that so that means
+
+ align:start position:0%
+a time you can reach that so that means
+ 
+
+ align:start position:0%
+a time you can reach that so that means
+that with transpositions
+
+ align:start position:0%
+that with transpositions
+ 
+
+ align:start position:0%
+that with transpositions
+you can reach every possible element so
+
+ align:start position:0%
+you can reach every possible element so
+ 
+
+ align:start position:0%
+you can reach every possible element so
+any this is very important any
+
+ align:start position:0%
+any this is very important any
+ 
+
+ align:start position:0%
+any this is very important any
+permutation is the product of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transpositions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that implies in a sense the main
+
+ align:start position:0%
+and that implies in a sense the main
+ 
+
+ align:start position:0%
+and that implies in a sense the main
+result that you want from operators in
+
+ align:start position:0%
+result that you want from operators in
+ 
+
+ align:start position:0%
+result that you want from operators in
+this Hilbert space since transpositions
+
+ align:start position:0%
+this Hilbert space since transpositions
+ 
+
+ align:start position:0%
+this Hilbert space since transpositions
+are unitary and any permutation is a
+
+ align:start position:0%
+are unitary and any permutation is a
+ 
+
+ align:start position:0%
+are unitary and any permutation is a
+product of transpositions
+
+ align:start position:0%
+product of transpositions
+ 
+
+ align:start position:0%
+product of transpositions
+any permutation is unitary
+
+ align:start position:0%
+any permutation is unitary
+ 
+
+ align:start position:0%
+any permutation is unitary
+so all permutations are unitary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not true that all permutations are
+
+ align:start position:0%
+it's not true that all permutations are
+ 
+
+ align:start position:0%
+it's not true that all permutations are
+hermitian you see when you have the
+
+ align:start position:0%
+hermitian you see when you have the
+ 
+
+ align:start position:0%
+hermitian you see when you have the
+product of hermitian operators the
+
+ align:start position:0%
+product of hermitian operators the
+ 
+
+ align:start position:0%
+product of hermitian operators the
+product of hermitian operators is not
+
+ align:start position:0%
+product of hermitian operators is not
+ 
+
+ align:start position:0%
+product of hermitian operators is not
+necessarily hermitian you've seen that
+
+ align:start position:0%
+necessarily hermitian you've seen that
+ 
+
+ align:start position:0%
+necessarily hermitian you've seen that
+if you have two operator hermitian the
+
+ align:start position:0%
+if you have two operator hermitian the
+ 
+
+ align:start position:0%
+if you have two operator hermitian the
+border changes and and the product is
+
+ align:start position:0%
+border changes and and the product is
+ 
+
+ align:start position:0%
+border changes and and the product is
+not hermitian X and P hermitian
+
+ align:start position:0%
+not hermitian X and P hermitian
+ 
+
+ align:start position:0%
+not hermitian X and P hermitian
+operators the product is not hermitian
+
+ align:start position:0%
+operators the product is not hermitian
+ 
+
+ align:start position:0%
+operators the product is not hermitian
+so all permutations are unitary but are
+
+ align:start position:0%
+so all permutations are unitary but are
+ 
+
+ align:start position:0%
+so all permutations are unitary but are
+not hermitian and the third concept that
+
+ align:start position:0%
+not hermitian and the third concept that
+ 
+
+ align:start position:0%
+not hermitian and the third concept that
+comes here Illustrated all in s3 is also
+
+ align:start position:0%
+comes here Illustrated all in s3 is also
+ 
+
+ align:start position:0%
+comes here Illustrated all in s3 is also
+a very fundamental concept we said that
+
+ align:start position:0%
+a very fundamental concept we said that
+ 
+
+ align:start position:0%
+a very fundamental concept we said that
+any permutation is a product of
+
+ align:start position:0%
+any permutation is a product of
+ 
+
+ align:start position:0%
+any permutation is a product of
+transpositions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's not a unique product of
+
+ align:start position:0%
+but it's not a unique product of
+ 
+
+ align:start position:0%
+but it's not a unique product of
+transposition in fact you could if you
+
+ align:start position:0%
+transposition in fact you could if you
+ 
+
+ align:start position:0%
+transposition in fact you could if you
+are given some order of objects and
+
+ align:start position:0%
+are given some order of objects and
+ 
+
+ align:start position:0%
+are given some order of objects and
+you're asked to rearrange them by
+
+ align:start position:0%
+you're asked to rearrange them by
+ 
+
+ align:start position:0%
+you're asked to rearrange them by
+transposition you may do them in
+
+ align:start position:0%
+transposition you may do them in
+ 
+
+ align:start position:0%
+transposition you may do them in
+different order so the product is not
+
+ align:start position:0%
+different order so the product is not
+ 
+
+ align:start position:0%
+different order so the product is not
+uniquely determined the product is in
+
+ align:start position:0%
+uniquely determined the product is in
+ 
+
+ align:start position:0%
+uniquely determined the product is in
+fact you could find somebody that does a
+
+ align:start position:0%
+fact you could find somebody that does a
+ 
+
+ align:start position:0%
+fact you could find somebody that does a
+permutation with some number of
+
+ align:start position:0%
+permutation with some number of
+ 
+
+ align:start position:0%
+permutation with some number of
+transpositions
+
+ align:start position:0%
+transpositions
+ 
+
+ align:start position:0%
+transpositions
+and another person with another set of
+
+ align:start position:0%
+and another person with another set of
+ 
+
+ align:start position:0%
+and another person with another set of
+transpositions but one thing that has to
+
+ align:start position:0%
+transpositions but one thing that has to
+ 
+
+ align:start position:0%
+transpositions but one thing that has to
+happen and it's always the same is that
+
+ align:start position:0%
+happen and it's always the same is that
+ 
+
+ align:start position:0%
+happen and it's always the same is that
+the number of transpositions
+
+ align:start position:0%
+the number of transpositions
+ 
+
+ align:start position:0%
+the number of transpositions
+is the same mod 2 that is if you find
+
+ align:start position:0%
+is the same mod 2 that is if you find
+ 
+
+ align:start position:0%
+is the same mod 2 that is if you find
+that to get a permutation you need an
+
+ align:start position:0%
+that to get a permutation you need an
+ 
+
+ align:start position:0%
+that to get a permutation you need an
+even number of transpositions everybody
+
+ align:start position:0%
+even number of transpositions everybody
+ 
+
+ align:start position:0%
+even number of transpositions everybody
+else will need also an even number of
+
+ align:start position:0%
+else will need also an even number of
+ 
+
+ align:start position:0%
+else will need also an even number of
+transpositions if you find an odd number
+
+ align:start position:0%
+transpositions if you find an odd number
+ 
+
+ align:start position:0%
+transpositions if you find an odd number
+of transpositions everybody will find an
+
+ align:start position:0%
+of transpositions everybody will find an
+ 
+
+ align:start position:0%
+of transpositions everybody will find an
+odd
+
+ align:start position:0%
+odd
+ 
+
+ align:start position:0%
+odd
+number of transpositions and that's kind
+
+ align:start position:0%
+number of transpositions and that's kind
+ 
+
+ align:start position:0%
+number of transpositions and that's kind
+of clear if you have if you've achieved
+
+ align:start position:0%
+of clear if you have if you've achieved
+ 
+
+ align:start position:0%
+of clear if you have if you've achieved
+the desired order by doing some number
+
+ align:start position:0%
+the desired order by doing some number
+ 
+
+ align:start position:0%
+the desired order by doing some number
+of trans positions you can add two more
+
+ align:start position:0%
+of trans positions you can add two more
+ 
+
+ align:start position:0%
+of trans positions you can add two more
+trans positions and not change anything
+
+ align:start position:0%
+trans positions and not change anything
+ 
+
+ align:start position:0%
+trans positions and not change anything
+you can flip two objects and flip them
+
+ align:start position:0%
+you can flip two objects and flip them
+ 
+
+ align:start position:0%
+you can flip two objects and flip them
+back so this is a pretty important
+
+ align:start position:0%
+back so this is a pretty important
+ 
+
+ align:start position:0%
+back so this is a pretty important
+result as well so it means that
+
+ align:start position:0%
+result as well so it means that
+ 
+
+ align:start position:0%
+result as well so it means that
+permutations are either even or are odd
+
+ align:start position:0%
+permutations are either even or are odd
+ 
+
+ align:start position:0%
+permutations are either even or are odd
+so permutations are even if built built
+
+ align:start position:0%
+so permutations are even if built built
+ 
+
+ align:start position:0%
+so permutations are even if built built
+built with an even number of trans
+
+ align:start position:0%
+built with an even number of trans
+ 
+
+ align:start position:0%
+built with an even number of trans
+positions and are or odd if built with
+
+ align:start position:0%
+positions and are or odd if built with
+ 
+
+ align:start position:0%
+positions and are or odd if built with
+an odd number of trans positions
+
+ align:start position:0%
+an odd number of trans positions
+ 
+
+ align:start position:0%
+an odd number of trans positions
+so two kinds of permutations even
+
+ align:start position:0%
+so two kinds of permutations even
+ 
+
+ align:start position:0%
+so two kinds of permutations even
+permutations or odd permutations so all
+
+ align:start position:0%
+permutations or odd permutations so all
+ 
+
+ align:start position:0%
+permutations or odd permutations so all
+these things we've kind of seen with the
+
+ align:start position:0%
+these things we've kind of seen with the
+ 
+
+ align:start position:0%
+these things we've kind of seen with the
+this permutation group there's one more
+
+ align:start position:0%
+this permutation group there's one more
+ 
+
+ align:start position:0%
+this permutation group there's one more
+thing that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+necessary to note something that may
+
+ align:start position:0%
+necessary to note something that may
+ 
+
+ align:start position:0%
+necessary to note something that may
+have seemed the coincidence there in
+
+ align:start position:0%
+have seemed the coincidence there in
+ 
+
+ align:start position:0%
+have seemed the coincidence there in
+fact the three on the right are trans
+
+ align:start position:0%
+fact the three on the right are trans
+ 
+
+ align:start position:0%
+fact the three on the right are trans
+positions and they're a single trans
+
+ align:start position:0%
+positions and they're a single trans
+ 
+
+ align:start position:0%
+positions and they're a single trans
+position each so each one of those on
+
+ align:start position:0%
+position each so each one of those on
+ 
+
+ align:start position:0%
+position each so each one of those on
+the right is
+
+ align:start position:0%
+the right is
+ 
+
+ align:start position:0%
+ 
+an odd permutation it's built with one
+
+ align:start position:0%
+an odd permutation it's built with one
+ 
+
+ align:start position:0%
+an odd permutation it's built with one
+transposition on the other hand the
+
+ align:start position:0%
+transposition on the other hand the
+ 
+
+ align:start position:0%
+transposition on the other hand the
+other ones are even transpositions the
+
+ align:start position:0%
+other ones are even transpositions the
+ 
+
+ align:start position:0%
+other ones are even transpositions the
+first three they the first one is built
+
+ align:start position:0%
+first three they the first one is built
+ 
+
+ align:start position:0%
+first three they the first one is built
+with zero trans positions but the others
+
+ align:start position:0%
+with zero trans positions but the others
+ 
+
+ align:start position:0%
+with zero trans positions but the others
+are built with two trans positions it's
+
+ align:start position:0%
+are built with two trans positions it's
+ 
+
+ align:start position:0%
+are built with two trans positions it's
+something you could just see in detail
+
+ align:start position:0%
+something you could just see in detail
+ 
+
+ align:start position:0%
+something you could just see in detail
+in fact I would say it's worth doing the
+
+ align:start position:0%
+in fact I would say it's worth doing the
+ 
+
+ align:start position:0%
+in fact I would say it's worth doing the
+table of multiplication of this group
+
+ align:start position:0%
+table of multiplication of this group
+ 
+
+ align:start position:0%
+table of multiplication of this group
+but that coincidence is in fact true in
+
+ align:start position:0%
+but that coincidence is in fact true in
+ 
+
+ align:start position:0%
+but that coincidence is in fact true in
+any in SM in the group SM the number of
+
+ align:start position:0%
+any in SM in the group SM the number of
+ 
+
+ align:start position:0%
+any in SM in the group SM the number of
+even permutations is equal to the number
+
+ align:start position:0%
+even permutations is equal to the number
+ 
+
+ align:start position:0%
+even permutations is equal to the number
+of odd permutations some pretty nice
+
+ align:start position:0%
+of odd permutations some pretty nice
+ 
+
+ align:start position:0%
+of odd permutations some pretty nice
+result there's equal numbers of even and
+
+ align:start position:0%
+result there's equal numbers of even and
+ 
+
+ align:start position:0%
+result there's equal numbers of even and
+not permutations in any permutation
+
+ align:start position:0%
+not permutations in any permutation
+ 
+
+ align:start position:0%
+not permutations in any permutation
+group actually it's surprisingly simple
+
+ align:start position:0%
+group actually it's surprisingly simple
+ 
+
+ align:start position:0%
+group actually it's surprisingly simple
+to show that you think of the even
+
+ align:start position:0%
+to show that you think of the even
+ 
+
+ align:start position:0%
+to show that you think of the even
+permutations here here are the even
+
+ align:start position:0%
+permutations here here are the even
+ 
+
+ align:start position:0%
+permutations here here are the even
+permutations and here are the odds
+
+ align:start position:0%
+permutations and here are the odds
+ 
+
+ align:start position:0%
+permutations and here are the odds
+permutations and you can easily show
+
+ align:start position:0%
+permutations and you can easily show
+ 
+
+ align:start position:0%
+permutations and you can easily show
+that there's equal number on this one so
+
+ align:start position:0%
+that there's equal number on this one so
+ 
+
+ align:start position:0%
+that there's equal number on this one so
+let's do it one way is to take the
+
+ align:start position:0%
+let's do it one way is to take the
+ 
+
+ align:start position:0%
+let's do it one way is to take the
+permutation element so suppose you have
+
+ align:start position:0%
+permutation element so suppose you have
+ 
+
+ align:start position:0%
+permutation element so suppose you have
+a permutation how should I call it
+
+ align:start position:0%
+a permutation how should I call it
+ 
+
+ align:start position:0%
+a permutation how should I call it
+p21 you leave everything the same but
+
+ align:start position:0%
+p21 you leave everything the same but
+ 
+
+ align:start position:0%
+p21 you leave everything the same but
+you have p21 that permutes of
+
+ align:start position:0%
+you have p21 that permutes of
+ 
+
+ align:start position:0%
+you have p21 that permutes of
+second and first labels since it's an n
+
+ align:start position:0%
+second and first labels since it's an n
+ 
+
+ align:start position:0%
+second and first labels since it's an n
+group the rest are left in variance of 3
+
+ align:start position:0%
+group the rest are left in variance of 3
+ 
+
+ align:start position:0%
+group the rest are left in variance of 3
+4 5 6 7 8 9 10 and you say this maps any
+
+ align:start position:0%
+4 5 6 7 8 9 10 and you say this maps any
+ 
+
+ align:start position:0%
+4 5 6 7 8 9 10 and you say this maps any
+permutation here into a permutation
+
+ align:start position:0%
+permutation here into a permutation
+ 
+
+ align:start position:0%
+permutation here into a permutation
+there why because if you have an even
+
+ align:start position:0%
+there why because if you have an even
+ 
+
+ align:start position:0%
+there why because if you have an even
+permutation here any element here has an
+
+ align:start position:0%
+permutation here any element here has an
+ 
+
+ align:start position:0%
+permutation here any element here has an
+even number of transmutations of
+
+ align:start position:0%
+even number of transmutations of
+ 
+
+ align:start position:0%
+even number of transmutations of
+transpositions so this is another
+
+ align:start position:0%
+transpositions so this is another
+ 
+
+ align:start position:0%
+transpositions so this is another
+transposition it transposes 2 and 1 so
+
+ align:start position:0%
+transposition it transposes 2 and 1 so
+ 
+
+ align:start position:0%
+transposition it transposes 2 and 1 so
+when you multiply an element here by p21
+
+ align:start position:0%
+when you multiply an element here by p21
+ 
+
+ align:start position:0%
+when you multiply an element here by p21
+if it has an even number of
+
+ align:start position:0%
+if it has an even number of
+ 
+
+ align:start position:0%
+if it has an even number of
+transpositions now it has an odd one so
+
+ align:start position:0%
+transpositions now it has an odd one so
+ 
+
+ align:start position:0%
+transpositions now it has an odd one so
+it must land somewhere here so any this
+
+ align:start position:0%
+it must land somewhere here so any this
+ 
+
+ align:start position:0%
+it must land somewhere here so any this
+ptoo 1 maps the even the even
+
+ align:start position:0%
+ptoo 1 maps the even the even
+ 
+
+ align:start position:0%
+ptoo 1 maps the even the even
+permutations to the odd permutations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moreover it maps them well in what's
+
+ align:start position:0%
+moreover it maps them well in what's
+ 
+
+ align:start position:0%
+moreover it maps them well in what's
+called one-to-one fashion if you have
+
+ align:start position:0%
+called one-to-one fashion if you have
+ 
+
+ align:start position:0%
+called one-to-one fashion if you have
+two permutations here that are different
+
+ align:start position:0%
+two permutations here that are different
+ 
+
+ align:start position:0%
+two permutations here that are different
+it will map to two permutations here
+
+ align:start position:0%
+it will map to two permutations here
+ 
+
+ align:start position:0%
+it will map to two permutations here
+that are different
+
+ align:start position:0%
+that are different
+ 
+
+ align:start position:0%
+that are different
+why because suppose you have here P I
+
+ align:start position:0%
+why because suppose you have here P I
+ 
+
+ align:start position:0%
+why because suppose you have here P I
+and PJ two permutations one is mapped to
+
+ align:start position:0%
+and PJ two permutations one is mapped to
+ 
+
+ align:start position:0%
+and PJ two permutations one is mapped to
+p2 one P I and the other is mapped to p2
+
+ align:start position:0%
+p2 one P I and the other is mapped to p2
+ 
+
+ align:start position:0%
+p2 one P I and the other is mapped to p2
+one PJ but if P I and PJ are different
+
+ align:start position:0%
+one PJ but if P I and PJ are different
+ 
+
+ align:start position:0%
+one PJ but if P I and PJ are different
+to permutations here i and j p i and pj
+
+ align:start position:0%
+to permutations here i and j p i and pj
+ 
+
+ align:start position:0%
+to permutations here i and j p i and pj
+and if they are different then it
+
+ align:start position:0%
+and if they are different then it
+ 
+
+ align:start position:0%
+and if they are different then it
+follows that these two are different as
+
+ align:start position:0%
+follows that these two are different as
+ 
+
+ align:start position:0%
+follows that these two are different as
+well after you multiply them by p21 why
+
+ align:start position:0%
+well after you multiply them by p21 why
+ 
+
+ align:start position:0%
+well after you multiply them by p21 why
+because if they were equal p21 has an
+
+ align:start position:0%
+because if they were equal p21 has an
+ 
+
+ align:start position:0%
+because if they were equal p21 has an
+inverse is itself p21 so you could
+
+ align:start position:0%
+inverse is itself p21 so you could
+ 
+
+ align:start position:0%
+inverse is itself p21 so you could
+multiply them in and then you would show
+
+ align:start position:0%
+multiply them in and then you would show
+ 
+
+ align:start position:0%
+multiply them in and then you would show
+that p is equal to pj and that can't
+
+ align:start position:0%
+that p is equal to pj and that can't
+ 
+
+ align:start position:0%
+that p is equal to pj and that can't
+happen so two different elements here
+
+ align:start position:0%
+happen so two different elements here
+ 
+
+ align:start position:0%
+happen so two different elements here
+will go to two different elements there
+
+ align:start position:0%
+will go to two different elements there
+ 
+
+ align:start position:0%
+will go to two different elements there
+so if you think of your all your
+
+ align:start position:0%
+so if you think of your all your
+ 
+
+ align:start position:0%
+so if you think of your all your
+elements here go if you have 20 elements
+
+ align:start position:0%
+elements here go if you have 20 elements
+ 
+
+ align:start position:0%
+elements here go if you have 20 elements
+here they go to 20 elements here the
+
+ align:start position:0%
+here they go to 20 elements here the
+ 
+
+ align:start position:0%
+here they go to 20 elements here the
+only thing that can happen is that some
+
+ align:start position:0%
+only thing that can happen is that some
+ 
+
+ align:start position:0%
+only thing that can happen is that some
+elements are not reached here that would
+
+ align:start position:0%
+elements are not reached here that would
+ 
+
+ align:start position:0%
+elements are not reached here that would
+mean that these two sets are not the
+
+ align:start position:0%
+mean that these two sets are not the
+ 
+
+ align:start position:0%
+mean that these two sets are not the
+same so you need to show that this map
+
+ align:start position:0%
+same so you need to show that this map
+ 
+
+ align:start position:0%
+same so you need to show that this map
+reaches everybody so this shows it's a
+
+ align:start position:0%
+reaches everybody so this shows it's a
+ 
+
+ align:start position:0%
+reaches everybody so this shows it's a
+one to one to one map and in fact it's
+
+ align:start position:0%
+one to one to one map and in fact it's
+ 
+
+ align:start position:0%
+one to one to one map and in fact it's
+kind of a joke but in a way to think of
+
+ align:start position:0%
+kind of a joke but in a way to think of
+ 
+
+ align:start position:0%
+kind of a joke but in a way to think of
+this one to one really means to to two
+
+ align:start position:0%
+this one to one really means to to two
+ 
+
+ align:start position:0%
+this one to one really means to to two
+in the sense that two things go to two
+
+ align:start position:0%
+in the sense that two things go to two
+ 
+
+ align:start position:0%
+in the sense that two things go to two
+things so it's kind of a funny name
+
+ align:start position:0%
+things so it's kind of a funny name
+ 
+
+ align:start position:0%
+things so it's kind of a funny name
+one to one so the other thing is that
+
+ align:start position:0%
+one to one so the other thing is that
+ 
+
+ align:start position:0%
+one to one so the other thing is that
+you need to show that everybody reaches
+
+ align:start position:0%
+you need to show that everybody reaches
+ 
+
+ align:start position:0%
+you need to show that everybody reaches
+so the map is
+
+ align:start position:0%
+so the map is
+ 
+
+ align:start position:0%
+so the map is
+cause surjective everybody reaches so
+
+ align:start position:0%
+cause surjective everybody reaches so
+ 
+
+ align:start position:0%
+cause surjective everybody reaches so
+it's clear that everybody reaches
+
+ align:start position:0%
+it's clear that everybody reaches
+ 
+
+ align:start position:0%
+it's clear that everybody reaches
+because if you have a P K in here
+
+ align:start position:0%
+because if you have a P K in here
+ 
+
+ align:start position:0%
+because if you have a P K in here
+permutation P K this P K can be written
+
+ align:start position:0%
+permutation P K this P K can be written
+ 
+
+ align:start position:0%
+permutation P K this P K can be written
+as P - 1 times P - 1 x PK plus P - 1
+
+ align:start position:0%
+as P - 1 times P - 1 x PK plus P - 1
+ 
+
+ align:start position:0%
+as P - 1 times P - 1 x PK plus P - 1
+times P - 1 is 1 and this B K since this
+
+ align:start position:0%
+times P - 1 is 1 and this B K since this
+ 
+
+ align:start position:0%
+times P - 1 is 1 and this B K since this
+was an odd permutation this is an even 1
+
+ align:start position:0%
+was an odd permutation this is an even 1
+ 
+
+ align:start position:0%
+was an odd permutation this is an even 1
+and then you've shown that PK is
+
+ align:start position:0%
+and then you've shown that PK is
+ 
+
+ align:start position:0%
+and then you've shown that PK is
+obtained by acting with P - 1 on some
+
+ align:start position:0%
+obtained by acting with P - 1 on some
+ 
+
+ align:start position:0%
+obtained by acting with P - 1 on some
+even permutation so you reach so the map
+
+ align:start position:0%
+even permutation so you reach so the map
+ 
+
+ align:start position:0%
+even permutation so you reach so the map
+is surjective directive and therefore
+
+ align:start position:0%
+is surjective directive and therefore
+ 
+
+ align:start position:0%
+is surjective directive and therefore
+these two things are the same they're
+
+ align:start position:0%
+these two things are the same they're
+ 
+
+ align:start position:0%
+these two things are the same they're
+identical numbers of even and odd
+
+ align:start position:0%
+identical numbers of even and odd
+ 
+
+ align:start position:0%
+identical numbers of even and odd
+permutations a very nice fact about
+
+ align:start position:0%
+permutations a very nice fact about
+ 
+
+ align:start position:0%
+permutations a very nice fact about
+these groups
\ No newline at end of file
diff --git a/YiqIkSHSmyc.txt b/YiqIkSHSmyc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..caa13ac6cd1b5ee06538d54bc9ca9b7db6486055
--- /dev/null
+++ b/YiqIkSHSmyc.txt
@@ -0,0 +1,6794 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shall we start let me just say this is a
+
+ align:start position:0%
+shall we start let me just say this is a
+ 
+
+ align:start position:0%
+shall we start let me just say this is a
+great adventure for me to be here all on
+
+ align:start position:0%
+great adventure for me to be here all on
+ 
+
+ align:start position:0%
+great adventure for me to be here all on
+my own teaching a course that involves
+
+ align:start position:0%
+my own teaching a course that involves
+ 
+
+ align:start position:0%
+my own teaching a course that involves
+learning from data so it's exciting
+
+ align:start position:0%
+learning from data so it's exciting
+ 
+
+ align:start position:0%
+learning from data so it's exciting
+subject and a lot of linear algebra goes
+
+ align:start position:0%
+subject and a lot of linear algebra goes
+ 
+
+ align:start position:0%
+subject and a lot of linear algebra goes
+into it so it's sort of a second course
+
+ align:start position:0%
+into it so it's sort of a second course
+ 
+
+ align:start position:0%
+into it so it's sort of a second course
+in linear algebra can I just
+
+ align:start position:0%
+in linear algebra can I just
+ 
+
+ align:start position:0%
+in linear algebra can I just
+you'll know what so there is a stellar
+
+ align:start position:0%
+you'll know what so there is a stellar
+ 
+
+ align:start position:0%
+you'll know what so there is a stellar
+site established and that will be the
+
+ align:start position:0%
+site established and that will be the
+ 
+
+ align:start position:0%
+site established and that will be the
+basic thing that we use this is a public
+
+ align:start position:0%
+basic thing that we use this is a public
+ 
+
+ align:start position:0%
+basic thing that we use this is a public
+site method mit.edu
+
+ align:start position:0%
+site method mit.edu
+ 
+
+ align:start position:0%
+site method mit.edu
+learning from data and so a book is
+
+ align:start position:0%
+learning from data and so a book is
+ 
+
+ align:start position:0%
+learning from data and so a book is
+coming pretty quickly as we speak or
+
+ align:start position:0%
+coming pretty quickly as we speak or
+ 
+
+ align:start position:0%
+coming pretty quickly as we speak or
+after we speak and that site has the
+
+ align:start position:0%
+after we speak and that site has the
+ 
+
+ align:start position:0%
+after we speak and that site has the
+table of contents of the book which
+
+ align:start position:0%
+table of contents of the book which
+ 
+
+ align:start position:0%
+table of contents of the book which
+would give you an idea of what could be
+
+ align:start position:0%
+would give you an idea of what could be
+ 
+
+ align:start position:0%
+would give you an idea of what could be
+in the course and I and I printed out a
+
+ align:start position:0%
+in the course and I and I printed out a
+ 
+
+ align:start position:0%
+in the course and I and I printed out a
+copy for everybody just of that one page
+
+ align:start position:0%
+copy for everybody just of that one page
+ 
+
+ align:start position:0%
+copy for everybody just of that one page
+that's probably the final first and last
+
+ align:start position:0%
+that's probably the final first and last
+ 
+
+ align:start position:0%
+that's probably the final first and last
+handout maybe with with the table of
+
+ align:start position:0%
+handout maybe with with the table of
+ 
+
+ align:start position:0%
+handout maybe with with the table of
+contents which you'll see there and also
+
+ align:start position:0%
+contents which you'll see there and also
+ 
+
+ align:start position:0%
+contents which you'll see there and also
+you'll see there the first two sections
+
+ align:start position:0%
+you'll see there the first two sections
+ 
+
+ align:start position:0%
+you'll see there the first two sections
+of the book which is what I'll talk
+
+ align:start position:0%
+of the book which is what I'll talk
+ 
+
+ align:start position:0%
+of the book which is what I'll talk
+about today and and on a little bit in
+
+ align:start position:0%
+about today and and on a little bit in
+ 
+
+ align:start position:0%
+about today and and on a little bit in
+to Friday so that's that's linear
+
+ align:start position:0%
+to Friday so that's that's linear
+ 
+
+ align:start position:0%
+to Friday so that's that's linear
+algebra of course because the course
+
+ align:start position:0%
+algebra of course because the course
+ 
+
+ align:start position:0%
+algebra of course because the course
+sort of begins with linear algebra
+
+ align:start position:0%
+sort of begins with linear algebra
+ 
+
+ align:start position:0%
+sort of begins with linear algebra
+actually things that you would know from
+
+ align:start position:0%
+actually things that you would know from
+ 
+
+ align:start position:0%
+actually things that you would know from
+1806 but you but this is a way to say
+
+ align:start position:0%
+1806 but you but this is a way to say
+ 
+
+ align:start position:0%
+1806 but you but this is a way to say
+this is really important stuff so that's
+
+ align:start position:0%
+this is really important stuff so that's
+ 
+
+ align:start position:0%
+this is really important stuff so that's
+what I'll do today I'd like to do some
+
+ align:start position:0%
+what I'll do today I'd like to do some
+ 
+
+ align:start position:0%
+what I'll do today I'd like to do some
+start on the linear algebra today
+
+ align:start position:0%
+start on the linear algebra today
+ 
+
+ align:start position:0%
+start on the linear algebra today
+and here's the great facts about the
+
+ align:start position:0%
+and here's the great facts about the
+ 
+
+ align:start position:0%
+and here's the great facts about the
+course at least we knew there were so we
+
+ align:start position:0%
+course at least we knew there were so we
+ 
+
+ align:start position:0%
+course at least we knew there were so we
+taught it last year several of us
+
+ align:start position:0%
+taught it last year several of us
+ 
+
+ align:start position:0%
+taught it last year several of us
+together and we knew there wouldn't be a
+
+ align:start position:0%
+together and we knew there wouldn't be a
+ 
+
+ align:start position:0%
+together and we knew there wouldn't be a
+final exam but we imagined there might
+
+ align:start position:0%
+final exam but we imagined there might
+ 
+
+ align:start position:0%
+final exam but we imagined there might
+be quizzes along the way but then we
+
+ align:start position:0%
+be quizzes along the way but then we
+ 
+
+ align:start position:0%
+be quizzes along the way but then we
+couldn't think of anything to put on the
+
+ align:start position:0%
+couldn't think of anything to put on the
+ 
+
+ align:start position:0%
+couldn't think of anything to put on the
+quizzes so we canceled those but you do
+
+ align:start position:0%
+quizzes so we canceled those but you do
+ 
+
+ align:start position:0%
+quizzes so we canceled those but you do
+learn a lot nevertheless and so I guess
+
+ align:start position:0%
+learn a lot nevertheless and so I guess
+ 
+
+ align:start position:0%
+learn a lot nevertheless and so I guess
+we base the grades on the homeworks so
+
+ align:start position:0%
+we base the grades on the homeworks so
+ 
+
+ align:start position:0%
+we base the grades on the homeworks so
+the homeworks will be partly linear
+
+ align:start position:0%
+the homeworks will be partly linear
+ 
+
+ align:start position:0%
+the homeworks will be partly linear
+algebra questions and partly online you
+
+ align:start position:0%
+algebra questions and partly online you
+ 
+
+ align:start position:0%
+algebra questions and partly online you
+know like recognizing handwriting
+
+ align:start position:0%
+know like recognizing handwriting
+ 
+
+ align:start position:0%
+know like recognizing handwriting
+stitching images together many other
+
+ align:start position:0%
+stitching images together many other
+ 
+
+ align:start position:0%
+stitching images together many other
+things and I'll talk about those as we
+
+ align:start position:0%
+things and I'll talk about those as we
+ 
+
+ align:start position:0%
+things and I'll talk about those as we
+go right good yeah
+
+ align:start position:0%
+go right good yeah
+ 
+
+ align:start position:0%
+go right good yeah
+so this that's the general picture and
+
+ align:start position:0%
+so this that's the general picture and
+ 
+
+ align:start position:0%
+so this that's the general picture and
+I'll say more about it today and I could
+
+ align:start position:0%
+I'll say more about it today and I could
+ 
+
+ align:start position:0%
+I'll say more about it today and I could
+answer any question about it so we're
+
+ align:start position:0%
+answer any question about it so we're
+ 
+
+ align:start position:0%
+answer any question about it so we're
+getting videotaped so if anybody's
+
+ align:start position:0%
+getting videotaped so if anybody's
+ 
+
+ align:start position:0%
+getting videotaped so if anybody's
+bashful sit at the far back but it'll be
+
+ align:start position:0%
+bashful sit at the far back but it'll be
+ 
+
+ align:start position:0%
+bashful sit at the far back but it'll be
+fun yeah you may know the videos for
+
+ align:start position:0%
+fun yeah you may know the videos for
+ 
+
+ align:start position:0%
+fun yeah you may know the videos for
+1806 so this is like the next step 1806
+
+ align:start position:0%
+1806 so this is like the next step 1806
+ 
+
+ align:start position:0%
+1806 so this is like the next step 1806
+five that's pretty exciting for me so
+
+ align:start position:0%
+five that's pretty exciting for me so
+ 
+
+ align:start position:0%
+five that's pretty exciting for me so
+any question or shall I do a little math
+
+ align:start position:0%
+any question or shall I do a little math
+ 
+
+ align:start position:0%
+any question or shall I do a little math
+why not and then and then I'll say a
+
+ align:start position:0%
+why not and then and then I'll say a
+ 
+
+ align:start position:0%
+why not and then and then I'll say a
+little more about the course just so you
+
+ align:start position:0%
+little more about the course just so you
+ 
+
+ align:start position:0%
+little more about the course just so you
+have an idea of what what's ahead yeah
+
+ align:start position:0%
+have an idea of what what's ahead yeah
+ 
+
+ align:start position:0%
+have an idea of what what's ahead yeah
+and it looks like this room is exactly
+
+ align:start position:0%
+and it looks like this room is exactly
+ 
+
+ align:start position:0%
+and it looks like this room is exactly
+the right size to me so I'm pleased okay
+
+ align:start position:0%
+the right size to me so I'm pleased okay
+ 
+
+ align:start position:0%
+the right size to me so I'm pleased okay
+so so what's the deal in linear algebra
+
+ align:start position:0%
+so so what's the deal in linear algebra
+ 
+
+ align:start position:0%
+so so what's the deal in linear algebra
+let me I'll start forgive me if I start
+
+ align:start position:0%
+let me I'll start forgive me if I start
+ 
+
+ align:start position:0%
+let me I'll start forgive me if I start
+with what I do the very first day in
+
+ align:start position:0%
+with what I do the very first day in
+ 
+
+ align:start position:0%
+with what I do the very first day in
+1806 which is multiply a matrix by a
+
+ align:start position:0%
+1806 which is multiply a matrix by a
+ 
+
+ align:start position:0%
+1806 which is multiply a matrix by a
+vector and then I'll graduate to
+
+ align:start position:0%
+vector and then I'll graduate to
+ 
+
+ align:start position:0%
+vector and then I'll graduate to
+multiplying a matrix by a May
+
+ align:start position:0%
+multiplying a matrix by a May
+ 
+
+ align:start position:0%
+multiplying a matrix by a May
+tricks so that and you will say I know
+
+ align:start position:0%
+tricks so that and you will say I know
+ 
+
+ align:start position:0%
+tricks so that and you will say I know
+that stuff but do you know it the right
+
+ align:start position:0%
+that stuff but do you know it the right
+ 
+
+ align:start position:0%
+that stuff but do you know it the right
+way do you think of the multiplication
+
+ align:start position:0%
+way do you think of the multiplication
+ 
+
+ align:start position:0%
+way do you think of the multiplication
+the right way so let me tell you what I
+
+ align:start position:0%
+the right way so let me tell you what I
+ 
+
+ align:start position:0%
+the right way so let me tell you what I
+believe to be the right way so let me
+
+ align:start position:0%
+believe to be the right way so let me
+ 
+
+ align:start position:0%
+believe to be the right way so let me
+take a matrix say two three five one one
+
+ align:start position:0%
+take a matrix say two three five one one
+ 
+
+ align:start position:0%
+take a matrix say two three five one one
+seven and three four twelve okay and
+
+ align:start position:0%
+seven and three four twelve okay and
+ 
+
+ align:start position:0%
+seven and three four twelve okay and
+I'll always call matrices a okay so
+
+ align:start position:0%
+I'll always call matrices a okay so
+ 
+
+ align:start position:0%
+I'll always call matrices a okay so
+first step is just a times X a times a
+
+ align:start position:0%
+first step is just a times X a times a
+ 
+
+ align:start position:0%
+first step is just a times X a times a
+vector so I multiply a a by let's say x1
+
+ align:start position:0%
+vector so I multiply a a by let's say x1
+ 
+
+ align:start position:0%
+vector so I multiply a a by let's say x1
+x2 x3 and how do I look at that answer
+
+ align:start position:0%
+x2 x3 and how do I look at that answer
+ 
+
+ align:start position:0%
+x2 x3 and how do I look at that answer
+so the choice is think of the rows of
+
+ align:start position:0%
+so the choice is think of the rows of
+ 
+
+ align:start position:0%
+so the choice is think of the rows of
+the matrix or think of the columns and
+
+ align:start position:0%
+the matrix or think of the columns and
+ 
+
+ align:start position:0%
+the matrix or think of the columns and
+if you think of the rows which is the
+
+ align:start position:0%
+if you think of the rows which is the
+ 
+
+ align:start position:0%
+if you think of the rows which is the
+standard way to multiply you would take
+
+ align:start position:0%
+standard way to multiply you would take
+ 
+
+ align:start position:0%
+standard way to multiply you would take
+the dot product so the first way is the
+
+ align:start position:0%
+the dot product so the first way is the
+ 
+
+ align:start position:0%
+the dot product so the first way is the
+first way is dot product of Row Row
+
+ align:start position:0%
+first way is dot product of Row Row
+ 
+
+ align:start position:0%
+first way is dot product of Row Row
+dotted with X right 2 X 1 plus X 2 plus
+
+ align:start position:0%
+dotted with X right 2 X 1 plus X 2 plus
+ 
+
+ align:start position:0%
+dotted with X right 2 X 1 plus X 2 plus
+3 X 3 it gives you the answer a
+
+ align:start position:0%
+3 X 3 it gives you the answer a
+ 
+
+ align:start position:0%
+3 X 3 it gives you the answer a
+component at a time that's the low level
+
+ align:start position:0%
+component at a time that's the low level
+ 
+
+ align:start position:0%
+component at a time that's the low level
+way the good way to see it is vector
+
+ align:start position:0%
+way the good way to see it is vector
+ 
+
+ align:start position:0%
+way the good way to see it is vector
+wise see this as X 1 multiplies that
+
+ align:start position:0%
+wise see this as X 1 multiplies that
+ 
+
+ align:start position:0%
+wise see this as X 1 multiplies that
+first column X 2 times the second column
+
+ align:start position:0%
+first column X 2 times the second column
+ 
+
+ align:start position:0%
+first column X 2 times the second column
+1 1 7 and X 3 times the third column 3 4
+
+ align:start position:0%
+1 1 7 and X 3 times the third column 3 4
+ 
+
+ align:start position:0%
+1 1 7 and X 3 times the third column 3 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so it's a combination of vectors
+
+ align:start position:0%
+good so it's a combination of vectors
+ 
+
+ align:start position:0%
+good so it's a combination of vectors
+and of course it produces a vector and
+
+ align:start position:0%
+and of course it produces a vector and
+ 
+
+ align:start position:0%
+and of course it produces a vector and
+here we have a three by three matrix and
+
+ align:start position:0%
+here we have a three by three matrix and
+ 
+
+ align:start position:0%
+here we have a three by three matrix and
+our vectors are in r3 and most vectors
+
+ align:start position:0%
+our vectors are in r3 and most vectors
+ 
+
+ align:start position:0%
+our vectors are in r3 and most vectors
+will be in r3 or RN for this course so
+
+ align:start position:0%
+will be in r3 or RN for this course so
+ 
+
+ align:start position:0%
+will be in r3 or RN for this course so
+that's the right answer and of course
+
+ align:start position:0%
+that's the right answer and of course
+ 
+
+ align:start position:0%
+that's the right answer and of course
+the first component is 2 X 1 + 1 X 2 + 3
+
+ align:start position:0%
+the first component is 2 X 1 + 1 X 2 + 3
+ 
+
+ align:start position:0%
+the first component is 2 X 1 + 1 X 2 + 3
+X 3 the same 2 1 3 the same dot product
+
+ align:start position:0%
+X 3 the same 2 1 3 the same dot product
+ 
+
+ align:start position:0%
+X 3 the same 2 1 3 the same dot product
+comes out right but you see it like sort
+
+ align:start position:0%
+comes out right but you see it like sort
+ 
+
+ align:start position:0%
+comes out right but you see it like sort
+of all at once instead of piecemeal so
+
+ align:start position:0%
+of all at once instead of piecemeal so
+ 
+
+ align:start position:0%
+of all at once instead of piecemeal so
+that's you know part of the course I
+
+ align:start position:0%
+that's you know part of the course I
+ 
+
+ align:start position:0%
+that's you know part of the course I
+guess part of what I hope to get across
+
+ align:start position:0%
+guess part of what I hope to get across
+ 
+
+ align:start position:0%
+guess part of what I hope to get across
+is thinking of a matrix of a matrix as a
+
+ align:start position:0%
+is thinking of a matrix of a matrix as a
+ 
+
+ align:start position:0%
+is thinking of a matrix of a matrix as a
+whole thing not just a bunch of 9 or or
+
+ align:start position:0%
+whole thing not just a bunch of 9 or or
+ 
+
+ align:start position:0%
+whole thing not just a bunch of 9 or or
+M times n numbers but thinking of it as
+
+ align:start position:0%
+M times n numbers but thinking of it as
+ 
+
+ align:start position:0%
+M times n numbers but thinking of it as
+a as a thing a matrix multiplies a
+
+ align:start position:0%
+a as a thing a matrix multiplies a
+ 
+
+ align:start position:0%
+a as a thing a matrix multiplies a
+vector to give another vector yeah think
+
+ align:start position:0%
+vector to give another vector yeah think
+ 
+
+ align:start position:0%
+vector to give another vector yeah think
+so that when I say ax that you
+
+ align:start position:0%
+so that when I say ax that you
+ 
+
+ align:start position:0%
+so that when I say ax that you
+immediately think that you immediately
+
+ align:start position:0%
+immediately think that you immediately
+ 
+
+ align:start position:0%
+immediately think that you immediately
+think okay ax has a clear meaning it's a
+
+ align:start position:0%
+think okay ax has a clear meaning it's a
+ 
+
+ align:start position:0%
+think okay ax has a clear meaning it's a
+combination of the columns of a so now
+
+ align:start position:0%
+combination of the columns of a so now
+ 
+
+ align:start position:0%
+combination of the columns of a so now
+let me take that next step and the next
+
+ align:start position:0%
+let me take that next step and the next
+ 
+
+ align:start position:0%
+let me take that next step and the next
+step is think about all combinations of
+
+ align:start position:0%
+step is think about all combinations of
+ 
+
+ align:start position:0%
+step is think about all combinations of
+the columns of a we take the matrix a
+
+ align:start position:0%
+the columns of a we take the matrix a
+ 
+
+ align:start position:0%
+the columns of a we take the matrix a
+and we take all X's and we imagine all
+
+ align:start position:0%
+and we take all X's and we imagine all
+ 
+
+ align:start position:0%
+and we take all X's and we imagine all
+the outputs and what I want to ask you
+
+ align:start position:0%
+the outputs and what I want to ask you
+ 
+
+ align:start position:0%
+the outputs and what I want to ask you
+is what does that look like if I just
+
+ align:start position:0%
+is what does that look like if I just
+ 
+
+ align:start position:0%
+is what does that look like if I just
+take 1 X 1 vector X I get a vector
+
+ align:start position:0%
+take 1 X 1 vector X I get a vector
+ 
+
+ align:start position:0%
+take 1 X 1 vector X I get a vector
+output takes a vector to a vector but
+
+ align:start position:0%
+output takes a vector to a vector but
+ 
+
+ align:start position:0%
+output takes a vector to a vector but
+now I take all X's the hole all of
+
+ align:start position:0%
+now I take all X's the hole all of
+ 
+
+ align:start position:0%
+now I take all X's the hole all of
+vectors X in or in 3d and I get all
+
+ align:start position:0%
+vectors X in or in 3d and I get all
+ 
+
+ align:start position:0%
+vectors X in or in 3d and I get all
+these answers and I think of them all
+
+ align:start position:0%
+these answers and I think of them all
+ 
+
+ align:start position:0%
+these answers and I think of them all
+together and so I've got a bunch of
+
+ align:start position:0%
+together and so I've got a bunch of
+ 
+
+ align:start position:0%
+together and so I've got a bunch of
+vectors infinitely many vectors actually
+
+ align:start position:0%
+vectors infinitely many vectors actually
+ 
+
+ align:start position:0%
+vectors infinitely many vectors actually
+and the question is what if I plot those
+
+ align:start position:0%
+and the question is what if I plot those
+ 
+
+ align:start position:0%
+and the question is what if I plot those
+infinitely many vectors what do I have
+
+ align:start position:0%
+infinitely many vectors what do I have
+ 
+
+ align:start position:0%
+infinitely many vectors what do I have
+and the beauty of linear algebra is that
+
+ align:start position:0%
+and the beauty of linear algebra is that
+ 
+
+ align:start position:0%
+and the beauty of linear algebra is that
+questions like this
+
+ align:start position:0%
+questions like this
+ 
+
+ align:start position:0%
+questions like this
+you can answer them and they you
+
+ align:start position:0%
+you can answer them and they you
+ 
+
+ align:start position:0%
+you can answer them and they you
+intuitively see it you certainly see it
+
+ align:start position:0%
+intuitively see it you certainly see it
+ 
+
+ align:start position:0%
+intuitively see it you certainly see it
+in 3d and you kind of have the right and
+
+ align:start position:0%
+in 3d and you kind of have the right and
+ 
+
+ align:start position:0%
+in 3d and you kind of have the right and
+the right idea in ten dimensions even
+
+ align:start position:0%
+the right idea in ten dimensions even
+ 
+
+ align:start position:0%
+the right idea in ten dimensions even
+though most of us don't see too well in
+
+ align:start position:0%
+though most of us don't see too well in
+ 
+
+ align:start position:0%
+though most of us don't see too well in
+10 D in our 10 but here we got three
+
+ align:start position:0%
+10 D in our 10 but here we got three
+ 
+
+ align:start position:0%
+10 D in our 10 but here we got three
+okay so so do you see what I'm saying
+
+ align:start position:0%
+okay so so do you see what I'm saying
+ 
+
+ align:start position:0%
+okay so so do you see what I'm saying
+I'm taking all X's so now so all a X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gives us a big bunch of vectors and that
+
+ align:start position:0%
+gives us a big bunch of vectors and that
+ 
+
+ align:start position:0%
+gives us a big bunch of vectors and that
+collection of vectors is called the
+
+ align:start position:0%
+collection of vectors is called the
+ 
+
+ align:start position:0%
+collection of vectors is called the
+column space of a it's a space in other
+
+ align:start position:0%
+column space of a it's a space in other
+ 
+
+ align:start position:0%
+column space of a it's a space in other
+words that that's the keyword there the
+
+ align:start position:0%
+words that that's the keyword there the
+ 
+
+ align:start position:0%
+words that that's the keyword there the
+column space of a and I'll just write it
+
+ align:start position:0%
+column space of a and I'll just write it
+ 
+
+ align:start position:0%
+column space of a and I'll just write it
+as C of a when I need a letters for it
+
+ align:start position:0%
+as C of a when I need a letters for it
+ 
+
+ align:start position:0%
+as C of a when I need a letters for it
+okay so I'm going to ask you what does
+
+ align:start position:0%
+okay so I'm going to ask you what does
+ 
+
+ align:start position:0%
+okay so I'm going to ask you what does
+this column space look like and that
+
+ align:start position:0%
+this column space look like and that
+ 
+
+ align:start position:0%
+this column space look like and that
+depends on the matrix sometimes the
+
+ align:start position:0%
+depends on the matrix sometimes the
+ 
+
+ align:start position:0%
+depends on the matrix sometimes the
+column space would be the whole of r3
+
+ align:start position:0%
+column space would be the whole of r3
+ 
+
+ align:start position:0%
+column space would be the whole of r3
+sometimes it's a smaller set in r3 or
+
+ align:start position:0%
+sometimes it's a smaller set in r3 or
+ 
+
+ align:start position:0%
+sometimes it's a smaller set in r3 or
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+do you know what it is in this case do I
+
+ align:start position:0%
+do you know what it is in this case do I
+ 
+
+ align:start position:0%
+do you know what it is in this case do I
+get do I get all of 3d out of these guys
+
+ align:start position:0%
+get do I get all of 3d out of these guys
+ 
+
+ align:start position:0%
+get do I get all of 3d out of these guys
+by choosing all X 1 and X 2 and X 3 it
+
+ align:start position:0%
+by choosing all X 1 and X 2 and X 3 it
+ 
+
+ align:start position:0%
+by choosing all X 1 and X 2 and X 3 it
+seemed like if it was a random matrix
+
+ align:start position:0%
+seemed like if it was a random matrix
+ 
+
+ align:start position:0%
+seemed like if it was a random matrix
+the answer would be surely yes if the
+
+ align:start position:0%
+the answer would be surely yes if the
+ 
+
+ align:start position:0%
+the answer would be surely yes if the
+random 3x3 matrix is its column space is
+
+ align:start position:0%
+random 3x3 matrix is its column space is
+ 
+
+ align:start position:0%
+random 3x3 matrix is its column space is
+going to be all of our three its columns
+
+ align:start position:0%
+going to be all of our three its columns
+ 
+
+ align:start position:0%
+going to be all of our three its columns
+are going to be independent its rows are
+
+ align:start position:0%
+are going to be independent its rows are
+ 
+
+ align:start position:0%
+are going to be independent its rows are
+going to be independent it's going to be
+
+ align:start position:0%
+going to be independent it's going to be
+ 
+
+ align:start position:0%
+going to be independent it's going to be
+invertible it's going to be great but is
+
+ align:start position:0%
+invertible it's going to be great but is
+ 
+
+ align:start position:0%
+invertible it's going to be great but is
+this matrix what's up with that matrix
+
+ align:start position:0%
+this matrix what's up with that matrix
+ 
+
+ align:start position:0%
+this matrix what's up with that matrix
+no it's not right
+
+ align:start position:0%
+no it's not right
+ 
+
+ align:start position:0%
+no it's not right
+so what do I get instead of all of our
+
+ align:start position:0%
+so what do I get instead of all of our
+ 
+
+ align:start position:0%
+so what do I get instead of all of our
+three I get a plane yeah if you get that
+
+ align:start position:0%
+three I get a plane yeah if you get that
+ 
+
+ align:start position:0%
+three I get a plane yeah if you get that
+in sight so by taking all X's
+
+ align:start position:0%
+in sight so by taking all X's
+ 
+
+ align:start position:0%
+in sight so by taking all X's
+everybody's with me all X's here so so
+
+ align:start position:0%
+everybody's with me all X's here so so
+ 
+
+ align:start position:0%
+everybody's with me all X's here so so
+that means that like it fills in
+
+ align:start position:0%
+that means that like it fills in
+ 
+
+ align:start position:0%
+that means that like it fills in
+whatever and well because it's linear
+
+ align:start position:0%
+whatever and well because it's linear
+ 
+
+ align:start position:0%
+whatever and well because it's linear
+algebra it's gonna be likely all of our
+
+ align:start position:0%
+algebra it's gonna be likely all of our
+ 
+
+ align:start position:0%
+algebra it's gonna be likely all of our
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+or a plane or even a line what let me
+
+ align:start position:0%
+or a plane or even a line what let me
+ 
+
+ align:start position:0%
+or a plane or even a line what let me
+just bat over here for a moment
+
+ align:start position:0%
+just bat over here for a moment
+ 
+
+ align:start position:0%
+just bat over here for a moment
+give me a matrix which would whose
+
+ align:start position:0%
+give me a matrix which would whose
+ 
+
+ align:start position:0%
+give me a matrix which would whose
+column space would only be a line all
+
+ align:start position:0%
+column space would only be a line all
+ 
+
+ align:start position:0%
+column space would only be a line all
+one's okay wow that's a let me liven it
+
+ align:start position:0%
+one's okay wow that's a let me liven it
+ 
+
+ align:start position:0%
+one's okay wow that's a let me liven it
+up a little three three three eight
+
+ align:start position:0%
+up a little three three three eight
+ 
+
+ align:start position:0%
+up a little three three three eight
+eight eight I think okay so I think that
+
+ align:start position:0%
+eight eight I think okay so I think that
+ 
+
+ align:start position:0%
+eight eight I think okay so I think that
+the combinations of those columns are
+
+ align:start position:0%
+the combinations of those columns are
+ 
+
+ align:start position:0%
+the combinations of those columns are
+all on the same line look that says that
+
+ align:start position:0%
+all on the same line look that says that
+ 
+
+ align:start position:0%
+all on the same line look that says that
+the column space is just a line and I
+
+ align:start position:0%
+the column space is just a line and I
+ 
+
+ align:start position:0%
+the column space is just a line and I
+would say then that the matrix so a
+
+ align:start position:0%
+would say then that the matrix so a
+ 
+
+ align:start position:0%
+would say then that the matrix so a
+column space of this a is a line another
+
+ align:start position:0%
+column space of this a is a line another
+ 
+
+ align:start position:0%
+column space of this a is a line another
+way I could say this is that the rank of
+
+ align:start position:0%
+way I could say this is that the rank of
+ 
+
+ align:start position:0%
+way I could say this is that the rank of
+the matrix is one the rank is sort of
+
+ align:start position:0%
+the matrix is one the rank is sort of
+ 
+
+ align:start position:0%
+the matrix is one the rank is sort of
+the dimension of the column space well
+
+ align:start position:0%
+the dimension of the column space well
+ 
+
+ align:start position:0%
+the dimension of the column space well
+not sort of that's what it is the rank
+
+ align:start position:0%
+not sort of that's what it is the rank
+ 
+
+ align:start position:0%
+not sort of that's what it is the rank
+is the dimension of the column see
+
+ align:start position:0%
+is the dimension of the column see
+ 
+
+ align:start position:0%
+is the dimension of the column see
+everybody sees that you get a line
+
+ align:start position:0%
+everybody sees that you get a line
+ 
+
+ align:start position:0%
+everybody sees that you get a line
+because any combination x1 of that plus
+
+ align:start position:0%
+because any combination x1 of that plus
+ 
+
+ align:start position:0%
+because any combination x1 of that plus
+x2 of that plus x3 of that is is going
+
+ align:start position:0%
+x2 of that plus x3 of that is is going
+ 
+
+ align:start position:0%
+x2 of that plus x3 of that is is going
+to go in in along that line here's the
+
+ align:start position:0%
+to go in in along that line here's the
+ 
+
+ align:start position:0%
+to go in in along that line here's the
+first column here's the second column
+
+ align:start position:0%
+first column here's the second column
+ 
+
+ align:start position:0%
+first column here's the second column
+they're all on a line so I'll never get
+
+ align:start position:0%
+they're all on a line so I'll never get
+ 
+
+ align:start position:0%
+they're all on a line so I'll never get
+off that line if I allow all X's I'll
+
+ align:start position:0%
+off that line if I allow all X's I'll
+ 
+
+ align:start position:0%
+off that line if I allow all X's I'll
+get the whole line
+
+ align:start position:0%
+get the whole line
+ 
+
+ align:start position:0%
+get the whole line
+now here you said not a line right what
+
+ align:start position:0%
+now here you said not a line right what
+ 
+
+ align:start position:0%
+now here you said not a line right what
+was what was the column space for this
+
+ align:start position:0%
+was what was the column space for this
+ 
+
+ align:start position:0%
+was what was the column space for this
+guy plain now why isn't it all of our
+
+ align:start position:0%
+guy plain now why isn't it all of our
+ 
+
+ align:start position:0%
+guy plain now why isn't it all of our
+three what what is what do you see that
+
+ align:start position:0%
+three what what is what do you see that
+ 
+
+ align:start position:0%
+three what what is what do you see that
+special there because it is special
+
+ align:start position:0%
+special there because it is special
+ 
+
+ align:start position:0%
+special there because it is special
+that's making the column space sort of
+
+ align:start position:0%
+that's making the column space sort of
+ 
+
+ align:start position:0%
+that's making the column space sort of
+special a plane instead of the whole
+
+ align:start position:0%
+special a plane instead of the whole
+ 
+
+ align:start position:0%
+special a plane instead of the whole
+thing yeah what's up with these three
+
+ align:start position:0%
+thing yeah what's up with these three
+ 
+
+ align:start position:0%
+thing yeah what's up with these three
+columns the third column is the sum of
+
+ align:start position:0%
+columns the third column is the sum of
+ 
+
+ align:start position:0%
+columns the third column is the sum of
+these two so the first column is fine to
+
+ align:start position:0%
+these two so the first column is fine to
+ 
+
+ align:start position:0%
+these two so the first column is fine to
+3/5 second column is in a different
+
+ align:start position:0%
+3/5 second column is in a different
+ 
+
+ align:start position:0%
+3/5 second column is in a different
+direction and when I take combinations
+
+ align:start position:0%
+direction and when I take combinations
+ 
+
+ align:start position:0%
+direction and when I take combinations
+of the first two columns what will I get
+
+ align:start position:0%
+of the first two columns what will I get
+ 
+
+ align:start position:0%
+of the first two columns what will I get
+sorry to keep asking your questions but
+
+ align:start position:0%
+sorry to keep asking your questions but
+ 
+
+ align:start position:0%
+sorry to keep asking your questions but
+that's that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway that's what I always do so so so
+
+ align:start position:0%
+anyway that's what I always do so so so
+ 
+
+ align:start position:0%
+anyway that's what I always do so so so
+the fur the combinations of those first
+
+ align:start position:0%
+the fur the combinations of those first
+ 
+
+ align:start position:0%
+the fur the combinations of those first
+two columns are a plane because they're
+
+ align:start position:0%
+two columns are a plane because they're
+ 
+
+ align:start position:0%
+two columns are a plane because they're
+in different everybody kind of sees that
+
+ align:start position:0%
+in different everybody kind of sees that
+ 
+
+ align:start position:0%
+in different everybody kind of sees that
+picture we've got one column one going
+
+ align:start position:0%
+picture we've got one column one going
+ 
+
+ align:start position:0%
+picture we've got one column one going
+that way and call them to go in that way
+
+ align:start position:0%
+that way and call them to go in that way
+ 
+
+ align:start position:0%
+that way and call them to go in that way
+and then if I take any multiple of
+
+ align:start position:0%
+and then if I take any multiple of
+ 
+
+ align:start position:0%
+and then if I take any multiple of
+column one I've got a whole line any
+
+ align:start position:0%
+column one I've got a whole line any
+ 
+
+ align:start position:0%
+column one I've got a whole line any
+multiple of column two and then when I
+
+ align:start position:0%
+multiple of column two and then when I
+ 
+
+ align:start position:0%
+multiple of column two and then when I
+put the two together it fills in the
+
+ align:start position:0%
+put the two together it fills in the
+ 
+
+ align:start position:0%
+put the two together it fills in the
+fills in the plane yeah yeah our ear
+
+ align:start position:0%
+fills in the plane yeah yeah our ear
+ 
+
+ align:start position:0%
+fills in the plane yeah yeah our ear
+intuition says that's right so this is a
+
+ align:start position:0%
+intuition says that's right so this is a
+ 
+
+ align:start position:0%
+intuition says that's right so this is a
+matrix of rank what's the rank of this
+
+ align:start position:0%
+matrix of rank what's the rank of this
+ 
+
+ align:start position:0%
+matrix of rank what's the rank of this
+matrix two because it's got two
+
+ align:start position:0%
+matrix two because it's got two
+ 
+
+ align:start position:0%
+matrix two because it's got two
+independent columns but the third column
+
+ align:start position:0%
+independent columns but the third column
+ 
+
+ align:start position:0%
+independent columns but the third column
+is dependent the third column is a
+
+ align:start position:0%
+is dependent the third column is a
+ 
+
+ align:start position:0%
+is dependent the third column is a
+combination of the others so this is
+
+ align:start position:0%
+combination of the others so this is
+ 
+
+ align:start position:0%
+combination of the others so this is
+matrices like this are really the
+
+ align:start position:0%
+matrices like this are really the
+ 
+
+ align:start position:0%
+matrices like this are really the
+building blocks of linear algebra
+
+ align:start position:0%
+building blocks of linear algebra
+ 
+
+ align:start position:0%
+building blocks of linear algebra
+they're the building blocks of data
+
+ align:start position:0%
+they're the building blocks of data
+ 
+
+ align:start position:0%
+they're the building blocks of data
+science they're rank one matrices and
+
+ align:start position:0%
+science they're rank one matrices and
+ 
+
+ align:start position:0%
+science they're rank one matrices and
+let me show you a special way to think
+
+ align:start position:0%
+let me show you a special way to think
+ 
+
+ align:start position:0%
+let me show you a special way to think
+write those rank one matrices I think of
+
+ align:start position:0%
+write those rank one matrices I think of
+ 
+
+ align:start position:0%
+write those rank one matrices I think of
+this matrix as column vector 1 1 1 times
+
+ align:start position:0%
+this matrix as column vector 1 1 1 times
+ 
+
+ align:start position:0%
+this matrix as column vector 1 1 1 times
+the row vector 1 3 8 so it's a column
+
+ align:start position:0%
+the row vector 1 3 8 so it's a column
+ 
+
+ align:start position:0%
+the row vector 1 3 8 so it's a column
+times a row that's a rank one matrix do
+
+ align:start position:0%
+times a row that's a rank one matrix do
+ 
+
+ align:start position:0%
+times a row that's a rank one matrix do
+you see that it's a that's a true
+
+ align:start position:0%
+you see that it's a that's a true
+ 
+
+ align:start position:0%
+you see that it's a that's a true
+multiplication there it looks a little
+
+ align:start position:0%
+multiplication there it looks a little
+ 
+
+ align:start position:0%
+multiplication there it looks a little
+weird but it's a three by one matrix
+
+ align:start position:0%
+weird but it's a three by one matrix
+ 
+
+ align:start position:0%
+weird but it's a three by one matrix
+times a 1 by 3 matrix these numbers have
+
+ align:start position:0%
+times a 1 by 3 matrix these numbers have
+ 
+
+ align:start position:0%
+times a 1 by 3 matrix these numbers have
+to be the same and then the output is 3
+
+ align:start position:0%
+to be the same and then the output is 3
+ 
+
+ align:start position:0%
+to be the same and then the output is 3
+by 3 and it's that and you see that it
+
+ align:start position:0%
+by 3 and it's that and you see that it
+ 
+
+ align:start position:0%
+by 3 and it's that and you see that it
+factors so I'm going to move on to that
+
+ align:start position:0%
+factors so I'm going to move on to that
+ 
+
+ align:start position:0%
+factors so I'm going to move on to that
+idea the next idea coming up will be
+
+ align:start position:0%
+idea the next idea coming up will be
+ 
+
+ align:start position:0%
+idea the next idea coming up will be
+that that we we can see well that's
+
+ align:start position:0%
+that that we we can see well that's
+ 
+
+ align:start position:0%
+that that we we can see well that's
+coming that we're going to see matrices
+
+ align:start position:0%
+coming that we're going to see matrices
+ 
+
+ align:start position:0%
+coming that we're going to see matrices
+in with two factors okay let me let me
+
+ align:start position:0%
+in with two factors okay let me let me
+ 
+
+ align:start position:0%
+in with two factors okay let me let me
+move to that but but they're back for
+
+ align:start position:0%
+move to that but but they're back for
+ 
+
+ align:start position:0%
+move to that but but they're back for
+this original matrix
+
+ align:start position:0%
+this original matrix
+ 
+
+ align:start position:0%
+this original matrix
+okay so what's with this the column
+
+ align:start position:0%
+okay so what's with this the column
+ 
+
+ align:start position:0%
+okay so what's with this the column
+space is a plane so if I think about now
+
+ align:start position:0%
+space is a plane so if I think about now
+ 
+
+ align:start position:0%
+space is a plane so if I think about now
+the key idea of independent columns how
+
+ align:start position:0%
+the key idea of independent columns how
+ 
+
+ align:start position:0%
+the key idea of independent columns how
+many independent columns have I got here
+
+ align:start position:0%
+many independent columns have I got here
+ 
+
+ align:start position:0%
+many independent columns have I got here
+to correct to the third column if I want
+
+ align:start position:0%
+to correct to the third column if I want
+ 
+
+ align:start position:0%
+to correct to the third column if I want
+to especially pick on that one so I
+
+ align:start position:0%
+to especially pick on that one so I
+ 
+
+ align:start position:0%
+to especially pick on that one so I
+often go left to right so I'll say the
+
+ align:start position:0%
+often go left to right so I'll say the
+ 
+
+ align:start position:0%
+often go left to right so I'll say the
+first guy's good second guy's good the
+
+ align:start position:0%
+first guy's good second guy's good the
+ 
+
+ align:start position:0%
+first guy's good second guy's good the
+third guy not is not independent of the
+
+ align:start position:0%
+third guy not is not independent of the
+ 
+
+ align:start position:0%
+third guy not is not independent of the
+others so I just have two independent
+
+ align:start position:0%
+others so I just have two independent
+ 
+
+ align:start position:0%
+others so I just have two independent
+columns and those are those two columns
+
+ align:start position:0%
+columns and those are those two columns
+ 
+
+ align:start position:0%
+columns and those are those two columns
+would be a basis for the column space so
+
+ align:start position:0%
+would be a basis for the column space so
+ 
+
+ align:start position:0%
+would be a basis for the column space so
+that's the like the critical idea of
+
+ align:start position:0%
+that's the like the critical idea of
+ 
+
+ align:start position:0%
+that's the like the critical idea of
+linear algebra that's what you compute
+
+ align:start position:0%
+linear algebra that's what you compute
+ 
+
+ align:start position:0%
+linear algebra that's what you compute
+with you find a basis and and every
+
+ align:start position:0%
+with you find a basis and and every
+ 
+
+ align:start position:0%
+with you find a basis and and every
+thing in the column space is a
+
+ align:start position:0%
+thing in the column space is a
+ 
+
+ align:start position:0%
+thing in the column space is a
+combination of these including that is
+
+ align:start position:0%
+combination of these including that is
+ 
+
+ align:start position:0%
+combination of these including that is
+also that's already a combination of
+
+ align:start position:0%
+also that's already a combination of
+ 
+
+ align:start position:0%
+also that's already a combination of
+those but everything else in the column
+
+ align:start position:0%
+those but everything else in the column
+ 
+
+ align:start position:0%
+those but everything else in the column
+space is a combination of those two so
+
+ align:start position:0%
+space is a combination of those two so
+ 
+
+ align:start position:0%
+space is a combination of those two so
+so there a basis for it okay so you have
+
+ align:start position:0%
+so there a basis for it okay so you have
+ 
+
+ align:start position:0%
+so there a basis for it okay so you have
+the idea of a times X you have the idea
+
+ align:start position:0%
+the idea of a times X you have the idea
+ 
+
+ align:start position:0%
+the idea of a times X you have the idea
+of column space of a which allows all XS
+
+ align:start position:0%
+of column space of a which allows all XS
+ 
+
+ align:start position:0%
+of column space of a which allows all XS
+then now we're moving into the idea of
+
+ align:start position:0%
+then now we're moving into the idea of
+ 
+
+ align:start position:0%
+then now we're moving into the idea of
+independent columns and the number of
+
+ align:start position:0%
+independent columns and the number of
+ 
+
+ align:start position:0%
+independent columns and the number of
+independent columns is is the rank so
+
+ align:start position:0%
+independent columns is is the rank so
+ 
+
+ align:start position:0%
+independent columns is is the rank so
+the rank shall I write that somewhere
+
+ align:start position:0%
+the rank shall I write that somewhere
+ 
+
+ align:start position:0%
+the rank shall I write that somewhere
+maybe here the rank is the number of
+
+ align:start position:0%
+maybe here the rank is the number of
+ 
+
+ align:start position:0%
+maybe here the rank is the number of
+independent columns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and right now what do I mean by
+
+ align:start position:0%
+and right now what do I mean by
+ 
+
+ align:start position:0%
+and right now what do I mean by
+independent columns well let's just see
+
+ align:start position:0%
+independent columns well let's just see
+ 
+
+ align:start position:0%
+independent columns well let's just see
+what that means by by using it are we
+
+ align:start position:0%
+what that means by by using it are we
+ 
+
+ align:start position:0%
+what that means by by using it are we
+good I'm I know I'm reviewing here but
+
+ align:start position:0%
+good I'm I know I'm reviewing here but
+ 
+
+ align:start position:0%
+good I'm I know I'm reviewing here but
+allow me for this first class and part
+
+ align:start position:0%
+allow me for this first class and part
+ 
+
+ align:start position:0%
+allow me for this first class and part
+of next time also to review but you'll
+
+ align:start position:0%
+of next time also to review but you'll
+ 
+
+ align:start position:0%
+of next time also to review but you'll
+see something new fact why don't we see
+
+ align:start position:0%
+see something new fact why don't we see
+ 
+
+ align:start position:0%
+see something new fact why don't we see
+something new right away let me follow
+
+ align:start position:0%
+something new right away let me follow
+ 
+
+ align:start position:0%
+something new right away let me follow
+up on the idea of Independence in a
+
+ align:start position:0%
+up on the idea of Independence in a
+ 
+
+ align:start position:0%
+up on the idea of Independence in a
+systematic way so here's my matrix a can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I write that again two three five one
+
+ align:start position:0%
+I write that again two three five one
+ 
+
+ align:start position:0%
+I write that again two three five one
+one seven and this guy was the sum of
+
+ align:start position:0%
+one seven and this guy was the sum of
+ 
+
+ align:start position:0%
+one seven and this guy was the sum of
+those okay so that's my matrix a ok so
+
+ align:start position:0%
+those okay so that's my matrix a ok so
+ 
+
+ align:start position:0%
+those okay so that's my matrix a ok so
+let's start from scratch and find a
+
+ align:start position:0%
+let's start from scratch and find a
+ 
+
+ align:start position:0%
+let's start from scratch and find a
+basis for the column space in in the
+
+ align:start position:0%
+basis for the column space in in the
+ 
+
+ align:start position:0%
+basis for the column space in in the
+most natural way so I'm going to take a
+
+ align:start position:0%
+most natural way so I'm going to take a
+ 
+
+ align:start position:0%
+most natural way so I'm going to take a
+basis I'm going to what's a basis a
+
+ align:start position:0%
+basis I'm going to what's a basis a
+ 
+
+ align:start position:0%
+basis I'm going to what's a basis a
+basis is independent columns so all
+
+ align:start position:0%
+basis is independent columns so all
+ 
+
+ align:start position:0%
+basis is independent columns so all
+three together would not be a basis but
+
+ align:start position:0%
+three together would not be a basis but
+ 
+
+ align:start position:0%
+three together would not be a basis but
+there have to be not just independent
+
+ align:start position:0%
+there have to be not just independent
+ 
+
+ align:start position:0%
+there have to be not just independent
+but but they have to fill the space
+
+ align:start position:0%
+but but they have to fill the space
+ 
+
+ align:start position:0%
+but but they have to fill the space
+their combinations have to fill the
+
+ align:start position:0%
+their combinations have to fill the
+ 
+
+ align:start position:0%
+their combinations have to fill the
+space so so two three five can let's say
+
+ align:start position:0%
+space so so two three five can let's say
+ 
+
+ align:start position:0%
+space so so two three five can let's say
+I want to create a basis I'll call the
+
+ align:start position:0%
+I want to create a basis I'll call the
+ 
+
+ align:start position:0%
+I want to create a basis I'll call the
+matrix C column a basis for the column
+
+ align:start position:0%
+matrix C column a basis for the column
+ 
+
+ align:start position:0%
+matrix C column a basis for the column
+space so here's a natural way to do it I
+
+ align:start position:0%
+space so here's a natural way to do it I
+ 
+
+ align:start position:0%
+space so here's a natural way to do it I
+look at the first column it's not zeros
+
+ align:start position:0%
+look at the first column it's not zeros
+ 
+
+ align:start position:0%
+look at the first column it's not zeros
+if it was all zeros I wouldn't want that
+
+ align:start position:0%
+if it was all zeros I wouldn't want that
+ 
+
+ align:start position:0%
+if it was all zeros I wouldn't want that
+in a basis but it's not so I put it in
+
+ align:start position:0%
+in a basis but it's not so I put it in
+ 
+
+ align:start position:0%
+in a basis but it's not so I put it in
+so that's the first vector in my basis
+
+ align:start position:0%
+so that's the first vector in my basis
+ 
+
+ align:start position:0%
+so that's the first vector in my basis
+then I go on to the second column if
+
+ align:start position:0%
+then I go on to the second column if
+ 
+
+ align:start position:0%
+then I go on to the second column if
+that column was four six ten what would
+
+ align:start position:0%
+that column was four six ten what would
+ 
+
+ align:start position:0%
+that column was four six ten what would
+I do if that second column was four six
+
+ align:start position:0%
+I do if that second column was four six
+ 
+
+ align:start position:0%
+I do if that second column was four six
+ten would I put it in the basis no but
+
+ align:start position:0%
+ten would I put it in the basis no but
+ 
+
+ align:start position:0%
+ten would I put it in the basis no but
+one one seven is okay right one one
+
+ align:start position:0%
+one one seven is okay right one one
+ 
+
+ align:start position:0%
+one one seven is okay right one one
+seven is
+
+ align:start position:0%
+seven is
+ 
+
+ align:start position:0%
+seven is
+different direction it's not a
+
+ align:start position:0%
+different direction it's not a
+ 
+
+ align:start position:0%
+different direction it's not a
+combination of what we've already got so
+
+ align:start position:0%
+combination of what we've already got so
+ 
+
+ align:start position:0%
+combination of what we've already got so
+I say okay that adds something new put
+
+ align:start position:0%
+I say okay that adds something new put
+ 
+
+ align:start position:0%
+I say okay that adds something new put
+it in then I move on to the third column
+
+ align:start position:0%
+it in then I move on to the third column
+ 
+
+ align:start position:0%
+it in then I move on to the third column
+do I put that into a basis you know the
+
+ align:start position:0%
+do I put that into a basis you know the
+ 
+
+ align:start position:0%
+do I put that into a basis you know the
+answer by now no because I'm looking to
+
+ align:start position:0%
+answer by now no because I'm looking to
+ 
+
+ align:start position:0%
+answer by now no because I'm looking to
+see is it a combination of these guys
+
+ align:start position:0%
+see is it a combination of these guys
+ 
+
+ align:start position:0%
+see is it a combination of these guys
+and it is it's one of that plus one of
+
+ align:start position:0%
+and it is it's one of that plus one of
+ 
+
+ align:start position:0%
+and it is it's one of that plus one of
+that so it's not independent so I've
+
+ align:start position:0%
+that so it's not independent so I've
+ 
+
+ align:start position:0%
+that so it's not independent so I've
+I've finished now I've got a matrix C
+
+ align:start position:0%
+I've finished now I've got a matrix C
+ 
+
+ align:start position:0%
+I've finished now I've got a matrix C
+which was like taken directly from a and
+
+ align:start position:0%
+which was like taken directly from a and
+ 
+
+ align:start position:0%
+which was like taken directly from a and
+I kept only independent columns and I
+
+ align:start position:0%
+I kept only independent columns and I
+ 
+
+ align:start position:0%
+I kept only independent columns and I
+worked from left to right and I can see
+
+ align:start position:0%
+worked from left to right and I can see
+ 
+
+ align:start position:0%
+worked from left to right and I can see
+that right away now that the rank is to
+
+ align:start position:0%
+that right away now that the rank is to
+ 
+
+ align:start position:0%
+that right away now that the rank is to
+the column rank I should say the column
+
+ align:start position:0%
+the column rank I should say the column
+ 
+
+ align:start position:0%
+the column rank I should say the column
+rank a number of independent columns is
+
+ align:start position:0%
+rank a number of independent columns is
+ 
+
+ align:start position:0%
+rank a number of independent columns is
+too good now comes a key step I'm gonna
+
+ align:start position:0%
+too good now comes a key step I'm gonna
+ 
+
+ align:start position:0%
+too good now comes a key step I'm gonna
+produce a third matrix R which is going
+
+ align:start position:0%
+produce a third matrix R which is going
+ 
+
+ align:start position:0%
+produce a third matrix R which is going
+to tell me how to get these columns from
+
+ align:start position:0%
+to tell me how to get these columns from
+ 
+
+ align:start position:0%
+to tell me how to get these columns from
+these columns and its shape is going to
+
+ align:start position:0%
+these columns and its shape is going to
+ 
+
+ align:start position:0%
+these columns and its shape is going to
+be well its shape I don't have any
+
+ align:start position:0%
+be well its shape I don't have any
+ 
+
+ align:start position:0%
+be well its shape I don't have any
+choice this is 3 by 2 so R has to be to
+
+ align:start position:0%
+choice this is 3 by 2 so R has to be to
+ 
+
+ align:start position:0%
+choice this is 3 by 2 so R has to be to
+buy something so so so I'm like so I
+
+ align:start position:0%
+buy something so so so I'm like so I
+ 
+
+ align:start position:0%
+buy something so so so I'm like so I
+guess it has to be 2 by 3 because I want
+
+ align:start position:0%
+guess it has to be 2 by 3 because I want
+ 
+
+ align:start position:0%
+guess it has to be 2 by 3 because I want
+to come out this way 2 by 3 what am I
+
+ align:start position:0%
+to come out this way 2 by 3 what am I
+ 
+
+ align:start position:0%
+to come out this way 2 by 3 what am I
+gonna do here I'm just going to put in
+
+ align:start position:0%
+gonna do here I'm just going to put in
+ 
+
+ align:start position:0%
+gonna do here I'm just going to put in
+the numbers are that make this correct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a first matrix factorization
+
+ align:start position:0%
+so this is a first matrix factorization
+ 
+
+ align:start position:0%
+so this is a first matrix factorization
+it's not well it is a famous one
+
+ align:start position:0%
+it's not well it is a famous one
+ 
+
+ align:start position:0%
+it's not well it is a famous one
+actually when we see it we'll recognize
+
+ align:start position:0%
+actually when we see it we'll recognize
+ 
+
+ align:start position:0%
+actually when we see it we'll recognize
+what it is it's but it's famous in
+
+ align:start position:0%
+what it is it's but it's famous in
+ 
+
+ align:start position:0%
+what it is it's but it's famous in
+teaching the near algebra but now
+
+ align:start position:0%
+teaching the near algebra but now
+ 
+
+ align:start position:0%
+teaching the near algebra but now
+actually see times are columns times
+
+ align:start position:0%
+actually see times are columns times
+ 
+
+ align:start position:0%
+actually see times are columns times
+rows has become very very important in
+
+ align:start position:0%
+rows has become very very important in
+ 
+
+ align:start position:0%
+rows has become very very important in
+large scale numerical linear algebra
+
+ align:start position:0%
+large scale numerical linear algebra
+ 
+
+ align:start position:0%
+large scale numerical linear algebra
+yeah so let's figure out what goes into
+
+ align:start position:0%
+yeah so let's figure out what goes into
+ 
+
+ align:start position:0%
+yeah so let's figure out what goes into
+our okay so what's going in what am I
+
+ align:start position:0%
+our okay so what's going in what am I
+ 
+
+ align:start position:0%
+our okay so what's going in what am I
+thinking here I'm putting in our that
+
+ align:start position:0%
+thinking here I'm putting in our that
+ 
+
+ align:start position:0%
+thinking here I'm putting in our that
+tel so every one of these columns is a
+
+ align:start position:0%
+tel so every one of these columns is a
+ 
+
+ align:start position:0%
+tel so every one of these columns is a
+combination of these that's the whole
+
+ align:start position:0%
+combination of these that's the whole
+ 
+
+ align:start position:0%
+combination of these that's the whole
+point and I'm just going to put in the
+
+ align:start position:0%
+point and I'm just going to put in the
+ 
+
+ align:start position:0%
+point and I'm just going to put in the
+numbers that you need so what goes in
+
+ align:start position:0%
+numbers that you need so what goes in
+ 
+
+ align:start position:0%
+numbers that you need so what goes in
+the first column of our what goes in the
+
+ align:start position:0%
+the first column of our what goes in the
+ 
+
+ align:start position:0%
+the first column of our what goes in the
+first column of our so I want to look
+
+ align:start position:0%
+first column of our so I want to look
+ 
+
+ align:start position:0%
+first column of our so I want to look
+what combination of that column and that
+
+ align:start position:0%
+what combination of that column and that
+ 
+
+ align:start position:0%
+what combination of that column and that
+column gives me this one yeah one zero
+
+ align:start position:0%
+column gives me this one yeah one zero
+ 
+
+ align:start position:0%
+column gives me this one yeah one zero
+one zero because you remember how we
+
+ align:start position:0%
+one zero because you remember how we
+ 
+
+ align:start position:0%
+one zero because you remember how we
+multiply a matrix by a vector when I
+
+ align:start position:0%
+multiply a matrix by a vector when I
+ 
+
+ align:start position:0%
+multiply a matrix by a vector when I
+multiply that matrix by that vector I
+
+ align:start position:0%
+multiply that matrix by that vector I
+ 
+
+ align:start position:0%
+multiply that matrix by that vector I
+take one of this plus zero of that I see
+
+ align:start position:0%
+take one of this plus zero of that I see
+ 
+
+ align:start position:0%
+take one of this plus zero of that I see
+it vector wise and of course I get it
+
+ align:start position:0%
+it vector wise and of course I get it
+ 
+
+ align:start position:0%
+it vector wise and of course I get it
+right and what about the second column
+
+ align:start position:0%
+right and what about the second column
+ 
+
+ align:start position:0%
+right and what about the second column
+of R so the second column should be the
+
+ align:start position:0%
+of R so the second column should be the
+ 
+
+ align:start position:0%
+of R so the second column should be the
+combination that produces the second
+
+ align:start position:0%
+combination that produces the second
+ 
+
+ align:start position:0%
+combination that produces the second
+column of a correctly what will that be
+
+ align:start position:0%
+column of a correctly what will that be
+ 
+
+ align:start position:0%
+column of a correctly what will that be
+zero one thanks and finally the third
+
+ align:start position:0%
+zero one thanks and finally the third
+ 
+
+ align:start position:0%
+zero one thanks and finally the third
+column one one yes right because one of
+
+ align:start position:0%
+column one one yes right because one of
+ 
+
+ align:start position:0%
+column one one yes right because one of
+this plus one of this produces the third
+
+ align:start position:0%
+this plus one of this produces the third
+ 
+
+ align:start position:0%
+this plus one of this produces the third
+column so so all I did was put in the
+
+ align:start position:0%
+column so so all I did was put in the
+ 
+
+ align:start position:0%
+column so so all I did was put in the
+right numbers there really right and
+
+ align:start position:0%
+right numbers there really right and
+ 
+
+ align:start position:0%
+right numbers there really right and
+this is correct now a SC times R and so
+
+ align:start position:0%
+this is correct now a SC times R and so
+ 
+
+ align:start position:0%
+this is correct now a SC times R and so
+that's this is like what I've done here
+
+ align:start position:0%
+that's this is like what I've done here
+ 
+
+ align:start position:0%
+that's this is like what I've done here
+is like the first two pages of section
+
+ align:start position:0%
+is like the first two pages of section
+ 
+
+ align:start position:0%
+is like the first two pages of section
+1.1 in these notes so 1.1 and actually
+
+ align:start position:0%
+1.1 in these notes so 1.1 and actually
+ 
+
+ align:start position:0%
+1.1 in these notes so 1.1 and actually
+so I tell you literally what happened
+
+ align:start position:0%
+so I tell you literally what happened
+ 
+
+ align:start position:0%
+so I tell you literally what happened
+earlier this year I wish this I wrote I
+
+ align:start position:0%
+earlier this year I wish this I wrote I
+ 
+
+ align:start position:0%
+earlier this year I wish this I wrote I
+wrote this down with a different example
+
+ align:start position:0%
+wrote this down with a different example
+ 
+
+ align:start position:0%
+wrote this down with a different example
+and then I realized something that that
+
+ align:start position:0%
+and then I realized something that that
+ 
+
+ align:start position:0%
+and then I realized something that that
+sitting here in front of me was the
+
+ align:start position:0%
+sitting here in front of me was the
+ 
+
+ align:start position:0%
+sitting here in front of me was the
+first great theorem in linear algebra
+
+ align:start position:0%
+first great theorem in linear algebra
+ 
+
+ align:start position:0%
+first great theorem in linear algebra
+the fact that the column rank equals the
+
+ align:start position:0%
+the fact that the column rank equals the
+ 
+
+ align:start position:0%
+the fact that the column rank equals the
+row rank the fact that if I have a
+
+ align:start position:0%
+row rank the fact that if I have a
+ 
+
+ align:start position:0%
+row rank the fact that if I have a
+matrix where that column plus that
+
+ align:start position:0%
+matrix where that column plus that
+ 
+
+ align:start position:0%
+matrix where that column plus that
+column gives that one oh so what am I
+
+ align:start position:0%
+column gives that one oh so what am I
+ 
+
+ align:start position:0%
+column gives that one oh so what am I
+going to say here I'm getting nervous
+
+ align:start position:0%
+going to say here I'm getting nervous
+ 
+
+ align:start position:0%
+going to say here I'm getting nervous
+about it I believe that a combination of
+
+ align:start position:0%
+about it I believe that a combination of
+ 
+
+ align:start position:0%
+about it I believe that a combination of
+the rows gives 0 do you believe that I
+
+ align:start position:0%
+the rows gives 0 do you believe that I
+ 
+
+ align:start position:0%
+the rows gives 0 do you believe that I
+mean you got to believe it this is like
+
+ align:start position:0%
+mean you got to believe it this is like
+ 
+
+ align:start position:0%
+mean you got to believe it this is like
+a linear algebra the matrix is not
+
+ align:start position:0%
+a linear algebra the matrix is not
+ 
+
+ align:start position:0%
+a linear algebra the matrix is not
+invertible it's square but the columns
+
+ align:start position:0%
+invertible it's square but the columns
+ 
+
+ align:start position:0%
+invertible it's square but the columns
+are dependent so the rows have to be
+
+ align:start position:0%
+are dependent so the rows have to be
+ 
+
+ align:start position:0%
+are dependent so the rows have to be
+dependent and I don't exactly see I
+
+ align:start position:0%
+dependent and I don't exactly see I
+ 
+
+ align:start position:0%
+dependent and I don't exactly see I
+there's some combination of that row and
+
+ align:start position:0%
+there's some combination of that row and
+ 
+
+ align:start position:0%
+there's some combination of that row and
+that row that gives that one and when I
+
+ align:start position:0%
+that row that gives that one and when I
+ 
+
+ align:start position:0%
+that row that gives that one and when I
+of course when I looked at the first
+
+ align:start position:0%
+of course when I looked at the first
+ 
+
+ align:start position:0%
+of course when I looked at the first
+column I thought ok it's going to be
+
+ align:start position:0%
+column I thought ok it's going to be
+ 
+
+ align:start position:0%
+column I thought ok it's going to be
+it's going to be too easy one of that
+
+ align:start position:0%
+it's going to be too easy one of that
+ 
+
+ align:start position:0%
+it's going to be too easy one of that
+and one of that gives that but then my I
+
+ align:start position:0%
+and one of that gives that but then my I
+ 
+
+ align:start position:0%
+and one of that gives that but then my I
+went over to the second column and I
+
+ align:start position:0%
+went over to the second column and I
+ 
+
+ align:start position:0%
+went over to the second column and I
+realize it's not easy at all so you're
+
+ align:start position:0%
+realize it's not easy at all so you're
+ 
+
+ align:start position:0%
+realize it's not easy at all so you're
+entitled to pull out a your phone and
+
+ align:start position:0%
+entitled to pull out a your phone and
+ 
+
+ align:start position:0%
+entitled to pull out a your phone and
+figure this out but there is some damn
+
+ align:start position:0%
+figure this out but there is some damn
+ 
+
+ align:start position:0%
+figure this out but there is some damn
+combination of those of those two rows
+
+ align:start position:0%
+combination of those of those two rows
+ 
+
+ align:start position:0%
+combination of those of those two rows
+it gives the third row it's otherwise
+
+ align:start position:0%
+it gives the third row it's otherwise
+ 
+
+ align:start position:0%
+it gives the third row it's otherwise
+like the course is over we stop but well
+
+ align:start position:0%
+like the course is over we stop but well
+ 
+
+ align:start position:0%
+like the course is over we stop but well
+maybe we're gonna find it or somehow
+
+ align:start position:0%
+maybe we're gonna find it or somehow
+ 
+
+ align:start position:0%
+maybe we're gonna find it or somehow
+yeah yeah so so that's this is the
+
+ align:start position:0%
+yeah yeah so so that's this is the
+ 
+
+ align:start position:0%
+yeah yeah so so that's this is the
+theorem so I so I have to tell you I
+
+ align:start position:0%
+theorem so I so I have to tell you I
+ 
+
+ align:start position:0%
+theorem so I so I have to tell you I
+mean you know I was like really pleased
+
+ align:start position:0%
+mean you know I was like really pleased
+ 
+
+ align:start position:0%
+mean you know I was like really pleased
+so the first two pages got two more
+
+ align:start position:0%
+so the first two pages got two more
+ 
+
+ align:start position:0%
+so the first two pages got two more
+pages to follow up on that idea that
+
+ align:start position:0%
+pages to follow up on that idea that
+ 
+
+ align:start position:0%
+pages to follow up on that idea that
+here we were seeing something that I
+
+ align:start position:0%
+here we were seeing something that I
+ 
+
+ align:start position:0%
+here we were seeing something that I
+sort of proved in 1806 but not you know
+
+ align:start position:0%
+sort of proved in 1806 but not you know
+ 
+
+ align:start position:0%
+sort of proved in 1806 but not you know
+not in the first lecture that's for sure
+
+ align:start position:0%
+not in the first lecture that's for sure
+ 
+
+ align:start position:0%
+not in the first lecture that's for sure
+and I'm not not maybe so clearly but now
+
+ align:start position:0%
+and I'm not not maybe so clearly but now
+ 
+
+ align:start position:0%
+and I'm not not maybe so clearly but now
+I can I try to prove it
+
+ align:start position:0%
+I can I try to prove it
+ 
+
+ align:start position:0%
+I can I try to prove it
+so and so here's the there won't be a
+
+ align:start position:0%
+so and so here's the there won't be a
+ 
+
+ align:start position:0%
+so and so here's the there won't be a
+lot of proofs in this class but this is
+
+ align:start position:0%
+lot of proofs in this class but this is
+ 
+
+ align:start position:0%
+lot of proofs in this class but this is
+such an important fact a equals CR is
+
+ align:start position:0%
+such an important fact a equals CR is
+ 
+
+ align:start position:0%
+such an important fact a equals CR is
+important factorization and and out of
+
+ align:start position:0%
+important factorization and and out of
+ 
+
+ align:start position:0%
+important factorization and and out of
+it we can connect them so what am I
+
+ align:start position:0%
+it we can connect them so what am I
+ 
+
+ align:start position:0%
+it we can connect them so what am I
+saying I'm saying that all that that
+
+ align:start position:0%
+saying I'm saying that all that that
+ 
+
+ align:start position:0%
+saying I'm saying that all that that
+that the row so what's the row rank yeah
+
+ align:start position:0%
+that the row so what's the row rank yeah
+ 
+
+ align:start position:0%
+that the row so what's the row rank yeah
+I could go back up here what's the row
+
+ align:start position:0%
+I could go back up here what's the row
+ 
+
+ align:start position:0%
+I could go back up here what's the row
+rank what's the row space so the row
+
+ align:start position:0%
+rank what's the row space so the row
+ 
+
+ align:start position:0%
+rank what's the row space so the row
+rank is going to be the definite the
+
+ align:start position:0%
+rank is going to be the definite the
+ 
+
+ align:start position:0%
+rank is going to be the definite the
+dimension of that space so so I look at
+
+ align:start position:0%
+dimension of that space so so I look at
+ 
+
+ align:start position:0%
+dimension of that space so so I look at
+my matrix a what's the row space of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm gonna look at its rows now maybe
+
+ align:start position:0%
+I'm gonna look at its rows now maybe
+ 
+
+ align:start position:0%
+I'm gonna look at its rows now maybe
+just so we don't get a whole new letters
+
+ align:start position:0%
+just so we don't get a whole new letters
+ 
+
+ align:start position:0%
+just so we don't get a whole new letters
+for the row space there I'm for me the
+
+ align:start position:0%
+for the row space there I'm for me the
+ 
+
+ align:start position:0%
+for the row space there I'm for me the
+row space of a of a matrix so so first
+
+ align:start position:0%
+row space of a of a matrix so so first
+ 
+
+ align:start position:0%
+row space of a of a matrix so so first
+of all tell me in words what it is
+
+ align:start position:0%
+of all tell me in words what it is
+ 
+
+ align:start position:0%
+of all tell me in words what it is
+what's the row space of the matrix all
+
+ align:start position:0%
+what's the row space of the matrix all
+ 
+
+ align:start position:0%
+what's the row space of the matrix all
+combinations of the rows all
+
+ align:start position:0%
+combinations of the rows all
+ 
+
+ align:start position:0%
+combinations of the rows all
+combinations of the rows that's the
+
+ align:start position:0%
+combinations of the rows that's the
+ 
+
+ align:start position:0%
+combinations of the rows that's the
+space so I would take all combinations
+
+ align:start position:0%
+space so I would take all combinations
+ 
+
+ align:start position:0%
+space so I would take all combinations
+of those rows to get combinations of the
+
+ align:start position:0%
+of those rows to get combinations of the
+ 
+
+ align:start position:0%
+of those rows to get combinations of the
+rows I well two ways I can get
+
+ align:start position:0%
+rows I well two ways I can get
+ 
+
+ align:start position:0%
+rows I well two ways I can get
+combinations of the rows and the way
+
+ align:start position:0%
+combinations of the rows and the way
+ 
+
+ align:start position:0%
+combinations of the rows and the way
+I'll do it is
+
+ align:start position:0%
+I'll do it is
+ 
+
+ align:start position:0%
+I'll do it is
+I'll just transpose the matrix so those
+
+ align:start position:0%
+I'll just transpose the matrix so those
+ 
+
+ align:start position:0%
+I'll just transpose the matrix so those
+rows become columns and then I'm back to
+
+ align:start position:0%
+rows become columns and then I'm back to
+ 
+
+ align:start position:0%
+rows become columns and then I'm back to
+what I did so the row space of a is the
+
+ align:start position:0%
+what I did so the row space of a is the
+ 
+
+ align:start position:0%
+what I did so the row space of a is the
+column space of a transpose and and this
+
+ align:start position:0%
+column space of a transpose and and this
+ 
+
+ align:start position:0%
+column space of a transpose and and this
+has the advantage that we don't
+
+ align:start position:0%
+has the advantage that we don't
+ 
+
+ align:start position:0%
+has the advantage that we don't
+introduce a new letter so it's it'll be
+
+ align:start position:0%
+introduce a new letter so it's it'll be
+ 
+
+ align:start position:0%
+introduce a new letter so it's it'll be
+the column space of a transpose so we
+
+ align:start position:0%
+the column space of a transpose so we
+ 
+
+ align:start position:0%
+the column space of a transpose so we
+don't introduce a new letter we keep the
+
+ align:start position:0%
+don't introduce a new letter we keep the
+ 
+
+ align:start position:0%
+don't introduce a new letter we keep the
+convention that vectors are column
+
+ align:start position:0%
+convention that vectors are column
+ 
+
+ align:start position:0%
+convention that vectors are column
+vectors which would be the MATLAB and
+
+ align:start position:0%
+vectors which would be the MATLAB and
+ 
+
+ align:start position:0%
+vectors which would be the MATLAB and
+and Julia and Python convention so is
+
+ align:start position:0%
+and Julia and Python convention so is
+ 
+
+ align:start position:0%
+and Julia and Python convention so is
+that okay
+
+ align:start position:0%
+that okay
+ 
+
+ align:start position:0%
+that okay
+the row space is the combination of
+
+ align:start position:0%
+the row space is the combination of
+ 
+
+ align:start position:0%
+the row space is the combination of
+these rows but I'll flip i'll make them
+
+ align:start position:0%
+these rows but I'll flip i'll make them
+ 
+
+ align:start position:0%
+these rows but I'll flip i'll make them
+stand up 2 1 3 2 2 B column vectors so
+
+ align:start position:0%
+stand up 2 1 3 2 2 B column vectors so
+ 
+
+ align:start position:0%
+stand up 2 1 3 2 2 B column vectors so
+it's a totally different space and
+
+ align:start position:0%
+it's a totally different space and
+ 
+
+ align:start position:0%
+it's a totally different space and
+actually in my I happen to take a 3 by 3
+
+ align:start position:0%
+actually in my I happen to take a 3 by 3
+ 
+
+ align:start position:0%
+actually in my I happen to take a 3 by 3
+example so that the column space is part
+
+ align:start position:0%
+example so that the column space is part
+ 
+
+ align:start position:0%
+example so that the column space is part
+of our three and the row space is also
+
+ align:start position:0%
+of our three and the row space is also
+ 
+
+ align:start position:0%
+of our three and the row space is also
+part of our three because my matrix is
+
+ align:start position:0%
+part of our three because my matrix is
+ 
+
+ align:start position:0%
+part of our three because my matrix is
+three by three a better example I mean
+
+ align:start position:0%
+three by three a better example I mean
+ 
+
+ align:start position:0%
+three by three a better example I mean
+and the whole point of data data doesn't
+
+ align:start position:0%
+and the whole point of data data doesn't
+ 
+
+ align:start position:0%
+and the whole point of data data doesn't
+come in square matrices fortunately for
+
+ align:start position:0%
+come in square matrices fortunately for
+ 
+
+ align:start position:0%
+come in square matrices fortunately for
+us data very very often comes in
+
+ align:start position:0%
+us data very very often comes in
+ 
+
+ align:start position:0%
+us data very very often comes in
+matrices but the to the columns might be
+
+ align:start position:0%
+matrices but the to the columns might be
+ 
+
+ align:start position:0%
+matrices but the to the columns might be
+sampled might be patients and the rows
+
+ align:start position:0%
+sampled might be patients and the rows
+ 
+
+ align:start position:0%
+sampled might be patients and the rows
+might be diseases or something I mean
+
+ align:start position:0%
+might be diseases or something I mean
+ 
+
+ align:start position:0%
+might be diseases or something I mean
+they're they're different spaces so
+
+ align:start position:0%
+they're they're different spaces so
+ 
+
+ align:start position:0%
+they're they're different spaces so
+matrices are not likely to be square but
+
+ align:start position:0%
+matrices are not likely to be square but
+ 
+
+ align:start position:0%
+matrices are not likely to be square but
+anyway we're good here okay okay so the
+
+ align:start position:0%
+anyway we're good here okay okay so the
+ 
+
+ align:start position:0%
+anyway we're good here okay okay so the
+row space
+
+ align:start position:0%
+row space
+ 
+
+ align:start position:0%
+row space
+now now can I come back to the proof
+
+ align:start position:0%
+now now can I come back to the proof
+ 
+
+ align:start position:0%
+now now can I come back to the proof
+because we what I want to say is that
+
+ align:start position:0%
+because we what I want to say is that
+ 
+
+ align:start position:0%
+because we what I want to say is that
+the proof of this fundamental fact is
+
+ align:start position:0%
+the proof of this fundamental fact is
+ 
+
+ align:start position:0%
+the proof of this fundamental fact is
+staring at us but we don't quite see it
+
+ align:start position:0%
+staring at us but we don't quite see it
+ 
+
+ align:start position:0%
+staring at us but we don't quite see it
+yet and I want to see it so I claim that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these rows are a basis for the row space
+
+ align:start position:0%
+these rows are a basis for the row space
+ 
+
+ align:start position:0%
+these rows are a basis for the row space
+and we already saw that these columns
+
+ align:start position:0%
+and we already saw that these columns
+ 
+
+ align:start position:0%
+and we already saw that these columns
+our basis for the column space and two
+
+ align:start position:0%
+our basis for the column space and two
+ 
+
+ align:start position:0%
+our basis for the column space and two
+equals two right two vectors here or a
+
+ align:start position:0%
+equals two right two vectors here or a
+ 
+
+ align:start position:0%
+equals two right two vectors here or a
+basis for the column space now if I can
+
+ align:start position:0%
+basis for the column space now if I can
+ 
+
+ align:start position:0%
+basis for the column space now if I can
+see why this shows me that these two
+
+ align:start position:0%
+see why this shows me that these two
+ 
+
+ align:start position:0%
+see why this shows me that these two
+vectors are a basis for the row space
+
+ align:start position:0%
+vectors are a basis for the row space
+ 
+
+ align:start position:0%
+vectors are a basis for the row space
+then then I have my example is right
+
+ align:start position:0%
+then then I have my example is right
+ 
+
+ align:start position:0%
+then then I have my example is right
+both both of these will give to the
+
+ align:start position:0%
+both both of these will give to the
+ 
+
+ align:start position:0%
+both both of these will give to the
+column rank is to two columns the row
+
+ align:start position:0%
+column rank is to two columns the row
+ 
+
+ align:start position:0%
+column rank is to two columns the row
+rank is to two rows so
+
+ align:start position:0%
+rank is to two rows so
+ 
+
+ align:start position:0%
+rank is to two rows so
+I have to explain why I believe that
+
+ align:start position:0%
+I have to explain why I believe that
+ 
+
+ align:start position:0%
+I have to explain why I believe that
+these two rows are a basis for the row
+
+ align:start position:0%
+these two rows are a basis for the row
+ 
+
+ align:start position:0%
+these two rows are a basis for the row
+space right with me I have to prove to
+
+ align:start position:0%
+space right with me I have to prove to
+ 
+
+ align:start position:0%
+space right with me I have to prove to
+see why first are there so when I say
+
+ align:start position:0%
+see why first are there so when I say
+ 
+
+ align:start position:0%
+see why first are there so when I say
+basis what do I have to check basis is
+
+ align:start position:0%
+basis what do I have to check basis is
+ 
+
+ align:start position:0%
+basis what do I have to check basis is
+is just is the critical idea it I have
+
+ align:start position:0%
+is just is the critical idea it I have
+ 
+
+ align:start position:0%
+is just is the critical idea it I have
+to check that they're independent so I
+
+ align:start position:0%
+to check that they're independent so I
+ 
+
+ align:start position:0%
+to check that they're independent so I
+haven't got too many vectors I've got
+
+ align:start position:0%
+haven't got too many vectors I've got
+ 
+
+ align:start position:0%
+haven't got too many vectors I've got
+any extra vectors in there and I also
+
+ align:start position:0%
+any extra vectors in there and I also
+ 
+
+ align:start position:0%
+any extra vectors in there and I also
+have to check that their combinations
+
+ align:start position:0%
+have to check that their combinations
+ 
+
+ align:start position:0%
+have to check that their combinations
+produce all the rows should I say that
+
+ align:start position:0%
+produce all the rows should I say that
+ 
+
+ align:start position:0%
+produce all the rows should I say that
+again that's because that's what I'm
+
+ align:start position:0%
+again that's because that's what I'm
+ 
+
+ align:start position:0%
+again that's because that's what I'm
+going to check I'm gonna check that
+
+ align:start position:0%
+going to check I'm gonna check that
+ 
+
+ align:start position:0%
+going to check I'm gonna check that
+those guys are independent well you can
+
+ align:start position:0%
+those guys are independent well you can
+ 
+
+ align:start position:0%
+those guys are independent well you can
+see that they're independent and I'm
+
+ align:start position:0%
+see that they're independent and I'm
+ 
+
+ align:start position:0%
+see that they're independent and I'm
+going to check that the that their
+
+ align:start position:0%
+going to check that the that their
+ 
+
+ align:start position:0%
+going to check that the that their
+combinations produce all three of these
+
+ align:start position:0%
+combinations produce all three of these
+ 
+
+ align:start position:0%
+combinations produce all three of these
+rows if we didn't create those numbers
+
+ align:start position:0%
+rows if we didn't create those numbers
+ 
+
+ align:start position:0%
+rows if we didn't create those numbers
+for this purpose but what I'm saying is
+
+ align:start position:0%
+for this purpose but what I'm saying is
+ 
+
+ align:start position:0%
+for this purpose but what I'm saying is
+they work so I claim that this is a
+
+ align:start position:0%
+they work so I claim that this is a
+ 
+
+ align:start position:0%
+they work so I claim that this is a
+basis because what what combination of
+
+ align:start position:0%
+basis because what what combination of
+ 
+
+ align:start position:0%
+basis because what what combination of
+those two rows would produce this this
+
+ align:start position:0%
+those two rows would produce this this
+ 
+
+ align:start position:0%
+those two rows would produce this this
+first row yeah let me just ask you that
+
+ align:start position:0%
+first row yeah let me just ask you that
+ 
+
+ align:start position:0%
+first row yeah let me just ask you that
+what combination what numbers should I
+
+ align:start position:0%
+what combination what numbers should I
+ 
+
+ align:start position:0%
+what combination what numbers should I
+multiply these two rows by to get the
+
+ align:start position:0%
+multiply these two rows by to get the
+ 
+
+ align:start position:0%
+multiply these two rows by to get the
+first row of any two and one and where
+
+ align:start position:0%
+first row of any two and one and where
+ 
+
+ align:start position:0%
+first row of any two and one and where
+do you find two and one
+
+ align:start position:0%
+do you find two and one
+ 
+
+ align:start position:0%
+do you find two and one
+it's sitting there in see what I'm and
+
+ align:start position:0%
+it's sitting there in see what I'm and
+ 
+
+ align:start position:0%
+it's sitting there in see what I'm and
+will it work again does three of this
+
+ align:start position:0%
+will it work again does three of this
+ 
+
+ align:start position:0%
+will it work again does three of this
+plus one of that give three one four yes
+
+ align:start position:0%
+plus one of that give three one four yes
+ 
+
+ align:start position:0%
+plus one of that give three one four yes
+so far so good
+
+ align:start position:0%
+so far so good
+ 
+
+ align:start position:0%
+so far so good
+does five of this and seven of that see
+
+ align:start position:0%
+does five of this and seven of that see
+ 
+
+ align:start position:0%
+does five of this and seven of that see
+I'm multiplying I guess I'm doing matrix
+
+ align:start position:0%
+I'm multiplying I guess I'm doing matrix
+ 
+
+ align:start position:0%
+I'm multiplying I guess I'm doing matrix
+multiplication a sort of backward wait
+
+ align:start position:0%
+multiplication a sort of backward wait
+ 
+
+ align:start position:0%
+multiplication a sort of backward wait
+or a different different way I'm taking
+
+ align:start position:0%
+or a different different way I'm taking
+ 
+
+ align:start position:0%
+or a different different way I'm taking
+combinations of the rows of the second
+
+ align:start position:0%
+combinations of the rows of the second
+ 
+
+ align:start position:0%
+combinations of the rows of the second
+guy that's another way that one
+
+ align:start position:0%
+guy that's another way that one
+ 
+
+ align:start position:0%
+guy that's another way that one
+careful thing about matrix
+
+ align:start position:0%
+careful thing about matrix
+ 
+
+ align:start position:0%
+careful thing about matrix
+multiplication is you can do it a lot of
+
+ align:start position:0%
+multiplication is you can do it a lot of
+ 
+
+ align:start position:0%
+multiplication is you can do it a lot of
+ways it comes out the same every way and
+
+ align:start position:0%
+ways it comes out the same every way and
+ 
+
+ align:start position:0%
+ways it comes out the same every way and
+each way tells you something so 5 of
+
+ align:start position:0%
+each way tells you something so 5 of
+ 
+
+ align:start position:0%
+each way tells you something so 5 of
+that row plus 7 of that row sure enough
+
+ align:start position:0%
+that row plus 7 of that row sure enough
+ 
+
+ align:start position:0%
+that row plus 7 of that row sure enough
+is here do you see that that is not like
+
+ align:start position:0%
+is here do you see that that is not like
+ 
+
+ align:start position:0%
+is here do you see that that is not like
+accident that that the proof is really
+
+ align:start position:0%
+accident that that the proof is really
+ 
+
+ align:start position:0%
+accident that that the proof is really
+to look at this multiplication C times
+
+ align:start position:0%
+to look at this multiplication C times
+ 
+
+ align:start position:0%
+to look at this multiplication C times
+are two ways look at it first as
+
+ align:start position:0%
+are two ways look at it first as
+ 
+
+ align:start position:0%
+are two ways look at it first as
+combinations of columns of C to give the
+
+ align:start position:0%
+combinations of columns of C to give the
+ 
+
+ align:start position:0%
+combinations of columns of C to give the
+columns look at it second to get as
+
+ align:start position:0%
+columns look at it second to get as
+ 
+
+ align:start position:0%
+columns look at it second to get as
+combinations of the rows of R and that
+
+ align:start position:0%
+combinations of the rows of R and that
+ 
+
+ align:start position:0%
+combinations of the rows of R and that
+produces the rows so that factorization
+
+ align:start position:0%
+produces the rows so that factorization
+ 
+
+ align:start position:0%
+produces the rows so that factorization
+a equals C R was what's the key idea and
+
+ align:start position:0%
+a equals C R was what's the key idea and
+ 
+
+ align:start position:0%
+a equals C R was what's the key idea and
+actually this R that we've come up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a name
+
+ align:start position:0%
+has a name
+ 
+
+ align:start position:0%
+has a name
+anybody remember enough 1806 here's a
+
+ align:start position:0%
+anybody remember enough 1806 here's a
+ 
+
+ align:start position:0%
+anybody remember enough 1806 here's a
+like have you all taken 1806 I'm no I
+
+ align:start position:0%
+like have you all taken 1806 I'm no I
+ 
+
+ align:start position:0%
+like have you all taken 1806 I'm no I
+see us how many have let's yes okay good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a while 1806 was taught in a very
+
+ align:start position:0%
+for a while 1806 was taught in a very
+ 
+
+ align:start position:0%
+for a while 1806 was taught in a very
+abstract way I said what's going on but
+
+ align:start position:0%
+abstract way I said what's going on but
+ 
+
+ align:start position:0%
+abstract way I said what's going on but
+anyway so if you took it that semester
+
+ align:start position:0%
+anyway so if you took it that semester
+ 
+
+ align:start position:0%
+anyway so if you took it that semester
+you maybe never heard of the column
+
+ align:start position:0%
+you maybe never heard of the column
+ 
+
+ align:start position:0%
+you maybe never heard of the column
+space I'm not sure or by a different
+
+ align:start position:0%
+space I'm not sure or by a different
+ 
+
+ align:start position:0%
+space I'm not sure or by a different
+name it has another name
+
+ align:start position:0%
+name it has another name
+ 
+
+ align:start position:0%
+name it has another name
+what's its other name the column space
+
+ align:start position:0%
+what's its other name the column space
+ 
+
+ align:start position:0%
+what's its other name the column space
+of a matrix range I think it's the range
+
+ align:start position:0%
+of a matrix range I think it's the range
+ 
+
+ align:start position:0%
+of a matrix range I think it's the range
+yeah right right yep yep and of course
+
+ align:start position:0%
+yeah right right yep yep and of course
+ 
+
+ align:start position:0%
+yeah right right yep yep and of course
+it's all this is fundamental in
+
+ align:start position:0%
+it's all this is fundamental in
+ 
+
+ align:start position:0%
+it's all this is fundamental in
+mathematics so of course it everything
+
+ align:start position:0%
+mathematics so of course it everything
+ 
+
+ align:start position:0%
+mathematics so of course it everything
+here is is has different languages and
+
+ align:start position:0%
+here is is has different languages and
+ 
+
+ align:start position:0%
+here is is has different languages and
+different emphasis but you see what the
+
+ align:start position:0%
+different emphasis but you see what the
+ 
+
+ align:start position:0%
+different emphasis but you see what the
+emphasis is here okay so you see the
+
+ align:start position:0%
+emphasis is here okay so you see the
+ 
+
+ align:start position:0%
+emphasis is here okay so you see the
+proof that a equals C R is just reveals
+
+ align:start position:0%
+proof that a equals C R is just reveals
+ 
+
+ align:start position:0%
+proof that a equals C R is just reveals
+everything so it's a first idea of a
+
+ align:start position:0%
+everything so it's a first idea of a
+ 
+
+ align:start position:0%
+everything so it's a first idea of a
+factorization of a matrix
+
+ align:start position:0%
+factorization of a matrix
+ 
+
+ align:start position:0%
+factorization of a matrix
+and and we've multiplied see times are
+
+ align:start position:0%
+and and we've multiplied see times are
+ 
+
+ align:start position:0%
+and and we've multiplied see times are
+now I could just say cuz so that's
+
+ align:start position:0%
+now I could just say cuz so that's
+ 
+
+ align:start position:0%
+now I could just say cuz so that's
+really you've seen the now the main
+
+ align:start position:0%
+really you've seen the now the main
+ 
+
+ align:start position:0%
+really you've seen the now the main
+point of section 1.1 of the notes to
+
+ align:start position:0%
+point of section 1.1 of the notes to
+ 
+
+ align:start position:0%
+point of section 1.1 of the notes to
+come up with that factorization and that
+
+ align:start position:0%
+come up with that factorization and that
+ 
+
+ align:start position:0%
+come up with that factorization and that
+conclusion and and and you see why C has
+
+ align:start position:0%
+conclusion and and and you see why C has
+ 
+
+ align:start position:0%
+conclusion and and and you see why C has
+the same number of the number of columns
+
+ align:start position:0%
+the same number of the number of columns
+ 
+
+ align:start position:0%
+the same number of the number of columns
+of C will the number of rows of our and
+
+ align:start position:0%
+of C will the number of rows of our and
+ 
+
+ align:start position:0%
+of C will the number of rows of our and
+those are the column rank and the row
+
+ align:start position:0%
+those are the column rank and the row
+ 
+
+ align:start position:0%
+those are the column rank and the row
+rank yeah it's just pretty neat and here
+
+ align:start position:0%
+rank yeah it's just pretty neat and here
+ 
+
+ align:start position:0%
+rank yeah it's just pretty neat and here
+was the special case where those column
+
+ align:start position:0%
+was the special case where those column
+ 
+
+ align:start position:0%
+was the special case where those column
+space the column space is all multiples
+
+ align:start position:0%
+space the column space is all multiples
+ 
+
+ align:start position:0%
+space the column space is all multiples
+of you it's a line through you the row
+
+ align:start position:0%
+of you it's a line through you the row
+ 
+
+ align:start position:0%
+of you it's a line through you the row
+space is all multiples of V it's a line
+
+ align:start position:0%
+space is all multiples of V it's a line
+ 
+
+ align:start position:0%
+space is all multiples of V it's a line
+through V and that's the basic building
+
+ align:start position:0%
+through V and that's the basic building
+ 
+
+ align:start position:0%
+through V and that's the basic building
+block yeah can I just say another little
+
+ align:start position:0%
+block yeah can I just say another little
+ 
+
+ align:start position:0%
+block yeah can I just say another little
+word before I push on beyond CR that
+
+ align:start position:0%
+word before I push on beyond CR that
+ 
+
+ align:start position:0%
+word before I push on beyond CR that
+that this has become if you have a giant
+
+ align:start position:0%
+that this has become if you have a giant
+ 
+
+ align:start position:0%
+that this has become if you have a giant
+matrix like size 10 to the fifth that's
+
+ align:start position:0%
+matrix like size 10 to the fifth that's
+ 
+
+ align:start position:0%
+matrix like size 10 to the fifth that's
+that you know you can't put that into
+
+ align:start position:0%
+that you know you can't put that into
+ 
+
+ align:start position:0%
+that you know you can't put that into
+fast memory you it's it's it's a mess
+
+ align:start position:0%
+fast memory you it's it's it's a mess
+ 
+
+ align:start position:0%
+fast memory you it's it's it's a mess
+how do you deal with a matrix of size 10
+
+ align:start position:0%
+how do you deal with a matrix of size 10
+ 
+
+ align:start position:0%
+how do you deal with a matrix of size 10
+to the fifth when you cannot deal with
+
+ align:start position:0%
+to the fifth when you cannot deal with
+ 
+
+ align:start position:0%
+to the fifth when you cannot deal with
+all the entries that that's just not
+
+ align:start position:0%
+all the entries that that's just not
+ 
+
+ align:start position:0%
+all the entries that that's just not
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+will you sample it so later in the
+
+ align:start position:0%
+will you sample it so later in the
+ 
+
+ align:start position:0%
+will you sample it so later in the
+course we'll be doing random sampling of
+
+ align:start position:0%
+course we'll be doing random sampling of
+ 
+
+ align:start position:0%
+course we'll be doing random sampling of
+a matrix so how could your sample a
+
+ align:start position:0%
+a matrix so how could your sample a
+ 
+
+ align:start position:0%
+a matrix so how could your sample a
+matrix so you have a matrix of course
+
+ align:start position:0%
+matrix so you have a matrix of course
+ 
+
+ align:start position:0%
+matrix so you have a matrix of course
+you're not looking at it because but
+
+ align:start position:0%
+you're not looking at it because but
+ 
+
+ align:start position:0%
+you're not looking at it because but
+it's and you want to get some typical
+
+ align:start position:0%
+it's and you want to get some typical
+ 
+
+ align:start position:0%
+it's and you want to get some typical
+columns okay here's the natural idea you
+
+ align:start position:0%
+columns okay here's the natural idea you
+ 
+
+ align:start position:0%
+columns okay here's the natural idea you
+just look at any x x when you take let X
+
+ align:start position:0%
+just look at any x x when you take let X
+ 
+
+ align:start position:0%
+just look at any x x when you take let X
+be a random vector random vector R and R
+
+ align:start position:0%
+be a random vector random vector R and R
+ 
+
+ align:start position:0%
+be a random vector random vector R and R
+and of so it's got M rows and one column
+
+ align:start position:0%
+and of so it's got M rows and one column
+ 
+
+ align:start position:0%
+and of so it's got M rows and one column
+it's a vector and what can I say about
+
+ align:start position:0%
+it's a vector and what can I say about
+ 
+
+ align:start position:0%
+it's a vector and what can I say about
+ax
+
+ align:start position:0%
+ax
+ 
+
+ align:start position:0%
+ax
+it's in what spaces it in column space
+
+ align:start position:0%
+it's in what spaces it in column space
+ 
+
+ align:start position:0%
+it's in what spaces it in column space
+thanks that was the first idea in this
+
+ align:start position:0%
+thanks that was the first idea in this
+ 
+
+ align:start position:0%
+thanks that was the first idea in this
+in this lecture ax is in the column
+
+ align:start position:0%
+in this lecture ax is in the column
+ 
+
+ align:start position:0%
+in this lecture ax is in the column
+space so if you want a random vector in
+
+ align:start position:0%
+space so if you want a random vector in
+ 
+
+ align:start position:0%
+space so if you want a random vector in
+the column space I wouldn't suggest it
+
+ align:start position:0%
+the column space I wouldn't suggest it
+ 
+
+ align:start position:0%
+the column space I wouldn't suggest it
+just randomly pick one of the columns
+
+ align:start position:0%
+just randomly pick one of the columns
+ 
+
+ align:start position:0%
+just randomly pick one of the columns
+better to take a mixture of columns by
+
+ align:start position:0%
+better to take a mixture of columns by
+ 
+
+ align:start position:0%
+better to take a mixture of columns by
+taking a random vector X and looking at
+
+ align:start position:0%
+taking a random vector X and looking at
+ 
+
+ align:start position:0%
+taking a random vector X and looking at
+looking at ax and if you wanted a
+
+ align:start position:0%
+looking at ax and if you wanted a
+ 
+
+ align:start position:0%
+looking at ax and if you wanted a
+hundred random vectors you take a
+
+ align:start position:0%
+hundred random vectors you take a
+ 
+
+ align:start position:0%
+hundred random vectors you take a
+hundred random X's and that would give
+
+ align:start position:0%
+hundred random X's and that would give
+ 
+
+ align:start position:0%
+hundred random X's and that would give
+you a pretty good idea in many cases of
+
+ align:start position:0%
+you a pretty good idea in many cases of
+ 
+
+ align:start position:0%
+you a pretty good idea in many cases of
+what what the column space looks like
+
+ align:start position:0%
+what what the column space looks like
+ 
+
+ align:start position:0%
+what what the column space looks like
+that would be enough to work with often
+
+ align:start position:0%
+that would be enough to work with often
+ 
+
+ align:start position:0%
+that would be enough to work with often
+yeah okay okay can I just throw in
+
+ align:start position:0%
+yeah okay okay can I just throw in
+ 
+
+ align:start position:0%
+yeah okay okay can I just throw in
+another question so so ax is in the
+
+ align:start position:0%
+another question so so ax is in the
+ 
+
+ align:start position:0%
+another question so so ax is in the
+column space of a let me just ask you
+
+ align:start position:0%
+column space of a let me just ask you
+ 
+
+ align:start position:0%
+column space of a let me just ask you
+this question is is ABC X is that in the
+
+ align:start position:0%
+this question is is ABC X is that in the
+ 
+
+ align:start position:0%
+this question is is ABC X is that in the
+column space of a suppose I have
+
+ align:start position:0%
+column space of a suppose I have
+ 
+
+ align:start position:0%
+column space of a suppose I have
+matrices a B and C and a vector X and I
+
+ align:start position:0%
+matrices a B and C and a vector X and I
+ 
+
+ align:start position:0%
+matrices a B and C and a vector X and I
+take their product does that give me
+
+ align:start position:0%
+take their product does that give me
+ 
+
+ align:start position:0%
+take their product does that give me
+something in the column space of a yes
+
+ align:start position:0%
+something in the column space of a yes
+ 
+
+ align:start position:0%
+something in the column space of a yes
+good for you why how do you know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's a time something right putting
+
+ align:start position:0%
+yeah it's a time something right putting
+ 
+
+ align:start position:0%
+yeah it's a time something right putting
+parentheses in the right place is the
+
+ align:start position:0%
+parentheses in the right place is the
+ 
+
+ align:start position:0%
+parentheses in the right place is the
+key to linear algebra and they're okay
+
+ align:start position:0%
+key to linear algebra and they're okay
+ 
+
+ align:start position:0%
+key to linear algebra and they're okay
+it's a question just occurred to me and
+
+ align:start position:0%
+it's a question just occurred to me and
+ 
+
+ align:start position:0%
+it's a question just occurred to me and
+I thought well I wonder if you'd do it
+
+ align:start position:0%
+I thought well I wonder if you'd do it
+ 
+
+ align:start position:0%
+I thought well I wonder if you'd do it
+okay so we have still time to multiply
+
+ align:start position:0%
+okay so we have still time to multiply
+ 
+
+ align:start position:0%
+okay so we have still time to multiply
+matrices oh I was going to say about C
+
+ align:start position:0%
+matrices oh I was going to say about C
+ 
+
+ align:start position:0%
+matrices oh I was going to say about C
+and R so these are real columns from a
+
+ align:start position:0%
+and R so these are real columns from a
+ 
+
+ align:start position:0%
+and R so these are real columns from a
+but R is the rows are not taken directly
+
+ align:start position:0%
+but R is the rows are not taken directly
+ 
+
+ align:start position:0%
+but R is the rows are not taken directly
+from the rows of a actually there's a
+
+ align:start position:0%
+from the rows of a actually there's a
+ 
+
+ align:start position:0%
+from the rows of a actually there's a
+name for this it's called the row
+
+ align:start position:0%
+name for this it's called the row
+ 
+
+ align:start position:0%
+name for this it's called the row
+reduced echelon form of the matrix and
+
+ align:start position:0%
+reduced echelon form of the matrix and
+ 
+
+ align:start position:0%
+reduced echelon form of the matrix and
+it's a big goal in in 1806 it has the
+
+ align:start position:0%
+it's a big goal in in 1806 it has the
+ 
+
+ align:start position:0%
+it's a big goal in in 1806 it has the
+identity there and then the other
+
+ align:start position:0%
+identity there and then the other
+ 
+
+ align:start position:0%
+identity there and then the other
+columns are tell you the right
+
+ align:start position:0%
+columns are tell you the right
+ 
+
+ align:start position:0%
+columns are tell you the right
+combinations yep yep another big
+
+ align:start position:0%
+combinations yep yep another big
+ 
+
+ align:start position:0%
+combinations yep yep another big
+factorization would be to take columns
+
+ align:start position:0%
+factorization would be to take columns
+ 
+
+ align:start position:0%
+factorization would be to take columns
+from from a so this is another so I'll
+
+ align:start position:0%
+from from a so this is another so I'll
+ 
+
+ align:start position:0%
+from from a so this is another so I'll
+put maybe or and we won't be doing this
+
+ align:start position:0%
+put maybe or and we won't be doing this
+ 
+
+ align:start position:0%
+put maybe or and we won't be doing this
+for a month
+
+ align:start position:0%
+for a month
+ 
+
+ align:start position:0%
+for a month
+we could start take columns of columns
+
+ align:start position:0%
+we could start take columns of columns
+ 
+
+ align:start position:0%
+we could start take columns of columns
+of a and put them in to see if they were
+
+ align:start position:0%
+of a and put them in to see if they were
+ 
+
+ align:start position:0%
+of a and put them in to see if they were
+independent and suppose I took rows of a
+
+ align:start position:0%
+independent and suppose I took rows of a
+ 
+
+ align:start position:0%
+independent and suppose I took rows of a
+now I'm going to take literally rows of
+
+ align:start position:0%
+now I'm going to take literally rows of
+ 
+
+ align:start position:0%
+now I'm going to take literally rows of
+a and put them into or well so I call it
+
+ align:start position:0%
+a and put them into or well so I call it
+ 
+
+ align:start position:0%
+a and put them into or well so I call it
+our twiddle or something cuz it'll be a
+
+ align:start position:0%
+our twiddle or something cuz it'll be a
+ 
+
+ align:start position:0%
+our twiddle or something cuz it'll be a
+different R I'm gonna use actually not
+
+ align:start position:0%
+different R I'm gonna use actually not
+ 
+
+ align:start position:0%
+different R I'm gonna use actually not
+I'm not going to use those rows but I'm
+
+ align:start position:0%
+I'm not going to use those rows but I'm
+ 
+
+ align:start position:0%
+I'm not going to use those rows but I'm
+gonna take two actual rows of a then
+
+ align:start position:0%
+gonna take two actual rows of a then
+ 
+
+ align:start position:0%
+gonna take two actual rows of a then
+what so that's important factorization
+
+ align:start position:0%
+what so that's important factorization
+ 
+
+ align:start position:0%
+what so that's important factorization
+but it's not correct I wouldn't if I
+
+ align:start position:0%
+but it's not correct I wouldn't if I
+ 
+
+ align:start position:0%
+but it's not correct I wouldn't if I
+took two other rows of our it wouldn't
+
+ align:start position:0%
+took two other rows of our it wouldn't
+ 
+
+ align:start position:0%
+took two other rows of our it wouldn't
+work so you have to put in the middle
+
+ align:start position:0%
+work so you have to put in the middle
+ 
+
+ align:start position:0%
+work so you have to put in the middle
+some two-by-two matrix you that makes it
+
+ align:start position:0%
+some two-by-two matrix you that makes it
+ 
+
+ align:start position:0%
+some two-by-two matrix you that makes it
+correct just you'll see on the in the in
+
+ align:start position:0%
+correct just you'll see on the in the in
+ 
+
+ align:start position:0%
+correct just you'll see on the in the in
+that section 1.1 that I got excited and
+
+ align:start position:0%
+that section 1.1 that I got excited and
+ 
+
+ align:start position:0%
+that section 1.1 that I got excited and
+wrote a page about seeing you are yep
+
+ align:start position:0%
+wrote a page about seeing you are yep
+ 
+
+ align:start position:0%
+wrote a page about seeing you are yep
+solid just mention that okay so now I'm
+
+ align:start position:0%
+solid just mention that okay so now I'm
+ 
+
+ align:start position:0%
+solid just mention that okay so now I'm
+ready oh I wanted to say something about
+
+ align:start position:0%
+ready oh I wanted to say something about
+ 
+
+ align:start position:0%
+ready oh I wanted to say something about
+the course decided thing about mass but
+
+ align:start position:0%
+the course decided thing about mass but
+ 
+
+ align:start position:0%
+the course decided thing about mass but
+there is this course so what's up so
+
+ align:start position:0%
+there is this course so what's up so
+ 
+
+ align:start position:0%
+there is this course so what's up so
+there be linear algebra problems but but
+
+ align:start position:0%
+there be linear algebra problems but but
+ 
+
+ align:start position:0%
+there be linear algebra problems but but
+what makes this course special is the
+
+ align:start position:0%
+what makes this course special is the
+ 
+
+ align:start position:0%
+what makes this course special is the
+other homeworks which are online and you
+
+ align:start position:0%
+other homeworks which are online and you
+ 
+
+ align:start position:0%
+other homeworks which are online and you
+would use let's see in principle you
+
+ align:start position:0%
+would use let's see in principle you
+ 
+
+ align:start position:0%
+would use let's see in principle you
+could use any of the languages
+
+ align:start position:0%
+could use any of the languages
+ 
+
+ align:start position:0%
+could use any of the languages
+MATLAB Python which has become the
+
+ align:start position:0%
+MATLAB Python which has become the
+ 
+
+ align:start position:0%
+MATLAB Python which has become the
+biggest most used for deep learning or
+
+ align:start position:0%
+biggest most used for deep learning or
+ 
+
+ align:start position:0%
+biggest most used for deep learning or
+Julia which is the hot
+
+ align:start position:0%
+Julia which is the hot
+ 
+
+ align:start position:0%
+Julia which is the hot
+new language and so last semester the
+
+ align:start position:0%
+new language and so last semester the
+ 
+
+ align:start position:0%
+new language and so last semester the
+problems oh so what happened last year
+
+ align:start position:0%
+problems oh so what happened last year
+ 
+
+ align:start position:0%
+problems oh so what happened last year
+well everything in this course is ode to
+
+ align:start position:0%
+well everything in this course is ode to
+ 
+
+ align:start position:0%
+well everything in this course is ode to
+a professor who visited from University
+
+ align:start position:0%
+a professor who visited from University
+ 
+
+ align:start position:0%
+a professor who visited from University
+of Michigan professor rah-rahs Rao
+
+ align:start position:0%
+of Michigan professor rah-rahs Rao
+ 
+
+ align:start position:0%
+of Michigan professor rah-rahs Rao
+who taught gave most of the lectures a
+
+ align:start position:0%
+who taught gave most of the lectures a
+ 
+
+ align:start position:0%
+who taught gave most of the lectures a
+year ago brought these homework problems
+
+ align:start position:0%
+year ago brought these homework problems
+ 
+
+ align:start position:0%
+year ago brought these homework problems
+online homework problems so that people
+
+ align:start position:0%
+online homework problems so that people
+ 
+
+ align:start position:0%
+online homework problems so that people
+brought laptops to class and we did
+
+ align:start position:0%
+brought laptops to class and we did
+ 
+
+ align:start position:0%
+brought laptops to class and we did
+things in class and so he had had and
+
+ align:start position:0%
+things in class and so he had had and
+ 
+
+ align:start position:0%
+things in class and so he had had and
+has very successful course in EE in
+
+ align:start position:0%
+has very successful course in EE in
+ 
+
+ align:start position:0%
+has very successful course in EE in
+Michigan and but he was a PhD from here
+
+ align:start position:0%
+Michigan and but he was a PhD from here
+ 
+
+ align:start position:0%
+Michigan and but he was a PhD from here
+and he came back on a sabbatical and he
+
+ align:start position:0%
+and he came back on a sabbatical and he
+ 
+
+ align:start position:0%
+and he came back on a sabbatical and he
+created this got us started and we
+
+ align:start position:0%
+created this got us started and we
+ 
+
+ align:start position:0%
+created this got us started and we
+really owe a lot to him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also professor Adelman was involved with
+
+ align:start position:0%
+also professor Adelman was involved with
+ 
+
+ align:start position:0%
+also professor Adelman was involved with
+this course and you may be know that he
+
+ align:start position:0%
+this course and you may be know that he
+ 
+
+ align:start position:0%
+this course and you may be know that he
+created julia how many like know what
+
+ align:start position:0%
+created julia how many like know what
+ 
+
+ align:start position:0%
+created julia how many like know what
+julia is Oh wonderful
+
+ align:start position:0%
+julia is Oh wonderful
+ 
+
+ align:start position:0%
+julia is Oh wonderful
+that will make his day he tells me every
+
+ align:start position:0%
+that will make his day he tells me every
+ 
+
+ align:start position:0%
+that will make his day he tells me every
+time I see him Julia's good and I tell
+
+ align:start position:0%
+time I see him Julia's good and I tell
+ 
+
+ align:start position:0%
+time I see him Julia's good and I tell
+him I believe it ok anyway and it's
+
+ align:start position:0%
+him I believe it ok anyway and it's
+ 
+
+ align:start position:0%
+him I believe it ok anyway and it's
+become the professor Johnson in 1806 has
+
+ align:start position:0%
+become the professor Johnson in 1806 has
+ 
+
+ align:start position:0%
+become the professor Johnson in 1806 has
+used Julia and every semester Stephen
+
+ align:start position:0%
+used Julia and every semester Stephen
+ 
+
+ align:start position:0%
+used Julia and every semester Stephen
+Johnson gives in the first week a
+
+ align:start position:0%
+Johnson gives in the first week a
+ 
+
+ align:start position:0%
+Johnson gives in the first week a
+tutorial on Julia and so he's that's
+
+ align:start position:0%
+tutorial on Julia and so he's that's
+ 
+
+ align:start position:0%
+tutorial on Julia and so he's that's
+arranged and I promised to tell you
+
+ align:start position:0%
+arranged and I promised to tell you
+ 
+
+ align:start position:0%
+arranged and I promised to tell you
+where where when that is so I think if
+
+ align:start position:0%
+where where when that is so I think if
+ 
+
+ align:start position:0%
+where where when that is so I think if
+you don't know anything about Julia try
+
+ align:start position:0%
+you don't know anything about Julia try
+ 
+
+ align:start position:0%
+you don't know anything about Julia try
+to go it's in Stata it's on Friday at
+
+ align:start position:0%
+to go it's in Stata it's on Friday at
+ 
+
+ align:start position:0%
+to go it's in Stata it's on Friday at
+5:00 5:00 to 7:00 so Julia from
+
+ align:start position:0%
+5:00 5:00 to 7:00 so Julia from
+ 
+
+ align:start position:0%
+5:00 5:00 to 7:00 so Julia from
+professor Johnson
+
+ align:start position:0%
+professor Johnson
+ 
+
+ align:start position:0%
+professor Johnson
+so he's done this multiple times he's
+
+ align:start position:0%
+so he's done this multiple times he's
+ 
+
+ align:start position:0%
+so he's done this multiple times he's
+good at it
+
+ align:start position:0%
+good at it
+ 
+
+ align:start position:0%
+good at it
+so that's McQueen Oh yet what I I guess
+
+ align:start position:0%
+so that's McQueen Oh yet what I I guess
+ 
+
+ align:start position:0%
+so that's McQueen Oh yet what I I guess
+I'm hoping that you'll have an option to
+
+ align:start position:0%
+I'm hoping that you'll have an option to
+ 
+
+ align:start position:0%
+I'm hoping that you'll have an option to
+use all any of the three languages but
+
+ align:start position:0%
+use all any of the three languages but
+ 
+
+ align:start position:0%
+use all any of the three languages but
+the the the online thing that we give
+
+ align:start position:0%
+the the the online thing that we give
+ 
+
+ align:start position:0%
+the the the online thing that we give
+you was created in Julia so professor
+
+ align:start position:0%
+you was created in Julia so professor
+ 
+
+ align:start position:0%
+you was created in Julia so professor
+Rao had to learn Julia last spring and
+
+ align:start position:0%
+Rao had to learn Julia last spring and
+ 
+
+ align:start position:0%
+Rao had to learn Julia last spring and
+though their class did too and there was
+
+ align:start position:0%
+though their class did too and there was
+ 
+
+ align:start position:0%
+though their class did too and there was
+a certain amount of bitching about it
+
+ align:start position:0%
+a certain amount of bitching about it
+ 
+
+ align:start position:0%
+a certain amount of bitching about it
+but I think with maybe one exception who
+
+ align:start position:0%
+but I think with maybe one exception who
+ 
+
+ align:start position:0%
+but I think with maybe one exception who
+still got an A we everybody was kind of
+
+ align:start position:0%
+still got an A we everybody was kind of
+ 
+
+ align:start position:0%
+still got an A we everybody was kind of
+okay and was glad to learn Julia and
+
+ align:start position:0%
+okay and was glad to learn Julia and
+ 
+
+ align:start position:0%
+okay and was glad to learn Julia and
+professor Rao now uses Julia entirely
+
+ align:start position:0%
+professor Rao now uses Julia entirely
+ 
+
+ align:start position:0%
+professor Rao now uses Julia entirely
+like so he's creating a new on-ramp with
+
+ align:start position:0%
+like so he's creating a new on-ramp with
+ 
+
+ align:start position:0%
+like so he's creating a new on-ramp with
+Julia
+
+ align:start position:0%
+Julia
+ 
+
+ align:start position:0%
+Julia
+MATLAB by the way has just issued an
+
+ align:start position:0%
+MATLAB by the way has just issued an
+ 
+
+ align:start position:0%
+MATLAB by the way has just issued an
+on-ramp to deep learning that I'll tell
+
+ align:start position:0%
+on-ramp to deep learning that I'll tell
+ 
+
+ align:start position:0%
+on-ramp to deep learning that I'll tell
+you about and probably get a MATLAB
+
+ align:start position:0%
+you about and probably get a MATLAB
+ 
+
+ align:start position:0%
+you about and probably get a MATLAB
+somebody from math works to to say
+
+ align:start position:0%
+somebody from math works to to say
+ 
+
+ align:start position:0%
+somebody from math works to to say
+something about it yeah so that's what's
+
+ align:start position:0%
+something about it yeah so that's what's
+ 
+
+ align:start position:0%
+something about it yeah so that's what's
+coming that we don't quite know exactly
+
+ align:start position:0%
+coming that we don't quite know exactly
+ 
+
+ align:start position:0%
+coming that we don't quite know exactly
+how we'll organize those homeworks would
+
+ align:start position:0%
+how we'll organize those homeworks would
+ 
+
+ align:start position:0%
+how we'll organize those homeworks would
+just take the first one and see see what
+
+ align:start position:0%
+just take the first one and see see what
+ 
+
+ align:start position:0%
+just take the first one and see see what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+so I'll certainly say more about
+
+ align:start position:0%
+so I'll certainly say more about
+ 
+
+ align:start position:0%
+so I'll certainly say more about
+homeworks when when the maybe even
+
+ align:start position:0%
+homeworks when when the maybe even
+ 
+
+ align:start position:0%
+homeworks when when the maybe even
+Friday but are there other questions
+
+ align:start position:0%
+Friday but are there other questions
+ 
+
+ align:start position:0%
+Friday but are there other questions
+that I should answer so because some
+
+ align:start position:0%
+that I should answer so because some
+ 
+
+ align:start position:0%
+that I should answer so because some
+people will be thinking okay am I going
+
+ align:start position:0%
+people will be thinking okay am I going
+ 
+
+ align:start position:0%
+people will be thinking okay am I going
+to do this or am I gonna sit in six oh
+
+ align:start position:0%
+to do this or am I gonna sit in six oh
+ 
+
+ align:start position:0%
+to do this or am I gonna sit in six oh
+three six or some other course in deep
+
+ align:start position:0%
+three six or some other course in deep
+ 
+
+ align:start position:0%
+three six or some other course in deep
+learning anything on your mind and you
+
+ align:start position:0%
+learning anything on your mind and you
+ 
+
+ align:start position:0%
+learning anything on your mind and you
+can email me so we will have a stellar
+
+ align:start position:0%
+can email me so we will have a stellar
+ 
+
+ align:start position:0%
+can email me so we will have a stellar
+site and you'll see all the the TAS are
+
+ align:start position:0%
+site and you'll see all the the TAS are
+ 
+
+ align:start position:0%
+site and you'll see all the the TAS are
+still to be named but the wonderful
+
+ align:start position:0%
+still to be named but the wonderful
+ 
+
+ align:start position:0%
+still to be named but the wonderful
+thing is that undergraduates who took
+
+ align:start position:0%
+thing is that undergraduates who took
+ 
+
+ align:start position:0%
+thing is that undergraduates who took
+this course last year are volunteering
+
+ align:start position:0%
+this course last year are volunteering
+ 
+
+ align:start position:0%
+this course last year are volunteering
+to be graders for you guys so they will
+
+ align:start position:0%
+to be graders for you guys so they will
+ 
+
+ align:start position:0%
+to be graders for you guys so they will
+know what those online homeworks were
+
+ align:start position:0%
+know what those online homeworks were
+ 
+
+ align:start position:0%
+know what those online homeworks were
+about it okay so that's what's it's a
+
+ align:start position:0%
+about it okay so that's what's it's a
+ 
+
+ align:start position:0%
+about it okay so that's what's it's a
+sort of first word about what's coming
+
+ align:start position:0%
+sort of first word about what's coming
+ 
+
+ align:start position:0%
+sort of first word about what's coming
+about about the language okay
+
+ align:start position:0%
+about about the language okay
+ 
+
+ align:start position:0%
+about about the language okay
+I'm gonna finish by a very important
+
+ align:start position:0%
+I'm gonna finish by a very important
+ 
+
+ align:start position:0%
+I'm gonna finish by a very important
+topic multiplying a times B oh look
+
+ align:start position:0%
+topic multiplying a times B oh look
+ 
+
+ align:start position:0%
+topic multiplying a times B oh look
+cleaning board so I know I want multiply
+
+ align:start position:0%
+cleaning board so I know I want multiply
+ 
+
+ align:start position:0%
+cleaning board so I know I want multiply
+multiply a matrix by a vector
+
+ align:start position:0%
+multiply a matrix by a vector
+ 
+
+ align:start position:0%
+multiply a matrix by a vector
+okay everybody knows how to do it you
+
+ align:start position:0%
+okay everybody knows how to do it you
+ 
+
+ align:start position:0%
+okay everybody knows how to do it you
+take a row of a so you take a row of a
+
+ align:start position:0%
+take a row of a so you take a row of a
+ 
+
+ align:start position:0%
+take a row of a so you take a row of a
+and you take a column of B and you take
+
+ align:start position:0%
+and you take a column of B and you take
+ 
+
+ align:start position:0%
+and you take a column of B and you take
+that dot product so you get dot product
+
+ align:start position:0%
+that dot product so you get dot product
+ 
+
+ align:start position:0%
+that dot product so you get dot product
+row row got column row dot that's again
+
+ align:start position:0%
+row row got column row dot that's again
+ 
+
+ align:start position:0%
+row row got column row dot that's again
+low level like okay for beginners but we
+
+ align:start position:0%
+low level like okay for beginners but we
+ 
+
+ align:start position:0%
+low level like okay for beginners but we
+want to see that matrix multiplication a
+
+ align:start position:0%
+want to see that matrix multiplication a
+ 
+
+ align:start position:0%
+want to see that matrix multiplication a
+B in a deeper way and the deeper way is
+
+ align:start position:0%
+B in a deeper way and the deeper way is
+ 
+
+ align:start position:0%
+B in a deeper way and the deeper way is
+columns times rows columns of a rows of
+
+ align:start position:0%
+columns times rows columns of a rows of
+ 
+
+ align:start position:0%
+columns times rows columns of a rows of
+B columns times rows well we had a
+
+ align:start position:0%
+B columns times rows well we had a
+ 
+
+ align:start position:0%
+B columns times rows well we had a
+column times a row right that was this
+
+ align:start position:0%
+column times a row right that was this
+ 
+
+ align:start position:0%
+column times a row right that was this
+rank one example we had our column times
+
+ align:start position:0%
+rank one example we had our column times
+ 
+
+ align:start position:0%
+rank one example we had our column times
+a row and it produced a matrix and
+
+ align:start position:0%
+a row and it produced a matrix and
+ 
+
+ align:start position:0%
+a row and it produced a matrix and
+that's what it looks like and it's rank
+
+ align:start position:0%
+that's what it looks like and it's rank
+ 
+
+ align:start position:0%
+that's what it looks like and it's rank
+was one so those are what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have a good so it's a combination of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's very like ax I'm really just
+
+ align:start position:0%
+it's very like ax I'm really just
+ 
+
+ align:start position:0%
+it's very like ax I'm really just
+extending the ax idea to a B so so this
+
+ align:start position:0%
+extending the ax idea to a B so so this
+ 
+
+ align:start position:0%
+extending the ax idea to a B so so this
+this is the old way a new way is columns
+
+ align:start position:0%
+this is the old way a new way is columns
+ 
+
+ align:start position:0%
+this is the old way a new way is columns
+so there's column K it will multiply
+
+ align:start position:0%
+so there's column K it will multiply
+ 
+
+ align:start position:0%
+so there's column K it will multiply
+sure enough it multiplies r okay
+
+ align:start position:0%
+sure enough it multiplies r okay
+ 
+
+ align:start position:0%
+sure enough it multiplies r okay
+everybody sees that it will happen that
+
+ align:start position:0%
+everybody sees that it will happen that
+ 
+
+ align:start position:0%
+everybody sees that it will happen that
+way if you do it the old way when you do
+
+ align:start position:0%
+way if you do it the old way when you do
+ 
+
+ align:start position:0%
+way if you do it the old way when you do
+a dot product of something here
+
+ align:start position:0%
+a dot product of something here
+ 
+
+ align:start position:0%
+a dot product of something here
+something here you're doing these
+
+ align:start position:0%
+something here you're doing these
+ 
+
+ align:start position:0%
+something here you're doing these
+multiplications and when you hit column
+
+ align:start position:0%
+multiplications and when you hit column
+ 
+
+ align:start position:0%
+multiplications and when you hit column
+K here you hit row K there so so these
+
+ align:start position:0%
+K here you hit row K there so so these
+ 
+
+ align:start position:0%
+K here you hit row K there so so these
+are connected so so I get things like
+
+ align:start position:0%
+are connected so so I get things like
+ 
+
+ align:start position:0%
+are connected so so I get things like
+column K of a times R okay of B and I
+
+ align:start position:0%
+column K of a times R okay of B and I
+ 
+
+ align:start position:0%
+column K of a times R okay of B and I
+don't know what notation to you so I
+
+ align:start position:0%
+don't know what notation to you so I
+ 
+
+ align:start position:0%
+don't know what notation to you so I
+just wrote them wrote the words okay
+
+ align:start position:0%
+just wrote them wrote the words okay
+ 
+
+ align:start position:0%
+just wrote them wrote the words okay
+but now that's one piece of the of the
+
+ align:start position:0%
+but now that's one piece of the of the
+ 
+
+ align:start position:0%
+but now that's one piece of the of the
+fun of the final answer a B that's a
+
+ align:start position:0%
+fun of the final answer a B that's a
+ 
+
+ align:start position:0%
+fun of the final answer a B that's a
+rank one piece that's a like a building
+
+ align:start position:0%
+rank one piece that's a like a building
+ 
+
+ align:start position:0%
+rank one piece that's a like a building
+block so I add from k equal 1 tom 1
+
+ align:start position:0%
+block so I add from k equal 1 tom 1
+ 
+
+ align:start position:0%
+block so I add from k equal 1 tom 1
+times Row one column one of a times Row
+
+ align:start position:0%
+times Row one column one of a times Row
+ 
+
+ align:start position:0%
+times Row one column one of a times Row
+one of B plus da plus column K plus and
+
+ align:start position:0%
+one of B plus da plus column K plus and
+ 
+
+ align:start position:0%
+one of B plus da plus column K plus and
+of course I stop it column in of a times
+
+ align:start position:0%
+of course I stop it column in of a times
+ 
+
+ align:start position:0%
+of course I stop it column in of a times
+row in so it's a sum of outer products
+
+ align:start position:0%
+row in so it's a sum of outer products
+ 
+
+ align:start position:0%
+row in so it's a sum of outer products
+some of so everybody sees a sum because
+
+ align:start position:0%
+some of so everybody sees a sum because
+ 
+
+ align:start position:0%
+some of so everybody sees a sum because
+I I have column 1 times Row 1 column K
+
+ align:start position:0%
+I I have column 1 times Row 1 column K
+ 
+
+ align:start position:0%
+I I have column 1 times Row 1 column K
+times R ok call them n times row in and
+
+ align:start position:0%
+times R ok call them n times row in and
+ 
+
+ align:start position:0%
+times R ok call them n times row in and
+then I add those pieces it's just the
+
+ align:start position:0%
+then I add those pieces it's just the
+ 
+
+ align:start position:0%
+then I add those pieces it's just the
+generalization of a X 2 matrix B there
+
+ align:start position:0%
+generalization of a X 2 matrix B there
+ 
+
+ align:start position:0%
+generalization of a X 2 matrix B there
+so it's the sum of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m'kay rogue of a Roque of B and maybe we
+
+ align:start position:0%
+m'kay rogue of a Roque of B and maybe we
+ 
+
+ align:start position:0%
+m'kay rogue of a Roque of B and maybe we
+should we check that that gives us the
+
+ align:start position:0%
+should we check that that gives us the
+ 
+
+ align:start position:0%
+should we check that that gives us the
+right answer or maybe I won't do that
+
+ align:start position:0%
+right answer or maybe I won't do that
+ 
+
+ align:start position:0%
+right answer or maybe I won't do that
+here but it it's it's all we're doing is
+
+ align:start position:0%
+here but it it's it's all we're doing is
+ 
+
+ align:start position:0%
+here but it it's it's all we're doing is
+the same multiplications in a different
+
+ align:start position:0%
+the same multiplications in a different
+ 
+
+ align:start position:0%
+the same multiplications in a different
+order actually let's just quit with one
+
+ align:start position:0%
+order actually let's just quit with one
+ 
+
+ align:start position:0%
+order actually let's just quit with one
+minute we can figure out how many
+
+ align:start position:0%
+minute we can figure out how many
+ 
+
+ align:start position:0%
+minute we can figure out how many
+multiplications are there how many
+
+ align:start position:0%
+multiplications are there how many
+ 
+
+ align:start position:0%
+multiplications are there how many
+multiplications to do a M by n matrix a
+
+ align:start position:0%
+multiplications to do a M by n matrix a
+ 
+
+ align:start position:0%
+multiplications to do a M by n matrix a
+time's the end by P matrix B so that's a
+
+ align:start position:0%
+time's the end by P matrix B so that's a
+ 
+
+ align:start position:0%
+time's the end by P matrix B so that's a
+times B how many individual numbers
+
+ align:start position:0%
+times B how many individual numbers
+ 
+
+ align:start position:0%
+times B how many individual numbers
+because this is determine the cost of it
+
+ align:start position:0%
+because this is determine the cost of it
+ 
+
+ align:start position:0%
+because this is determine the cost of it
+how many numbers would we need well
+
+ align:start position:0%
+how many numbers would we need well
+ 
+
+ align:start position:0%
+how many numbers would we need well
+suppose we do it the old way by in inner
+
+ align:start position:0%
+suppose we do it the old way by in inner
+ 
+
+ align:start position:0%
+suppose we do it the old way by in inner
+product row x column so how many how
+
+ align:start position:0%
+product row x column so how many how
+ 
+
+ align:start position:0%
+product row x column so how many how
+many multiplications to do a row times I
+
+ align:start position:0%
+many multiplications to do a row times I
+ 
+
+ align:start position:0%
+many multiplications to do a row times I
+call them and get one entry in the
+
+ align:start position:0%
+call them and get one entry in the
+ 
+
+ align:start position:0%
+call them and get one entry in the
+answer n right the row has length in the
+
+ align:start position:0%
+answer n right the row has length in the
+ 
+
+ align:start position:0%
+answer n right the row has length in the
+column has length in n multiplications
+
+ align:start position:0%
+column has length in n multiplications
+ 
+
+ align:start position:0%
+column has length in n multiplications
+so that's N and now how many of those do
+
+ align:start position:0%
+so that's N and now how many of those do
+ 
+
+ align:start position:0%
+so that's N and now how many of those do
+I have to do MP because what's the size
+
+ align:start position:0%
+I have to do MP because what's the size
+ 
+
+ align:start position:0%
+I have to do MP because what's the size
+of this answer the size of this answer
+
+ align:start position:0%
+of this answer the size of this answer
+ 
+
+ align:start position:0%
+of this answer the size of this answer
+is n by P okay so if I do they do it in
+
+ align:start position:0%
+is n by P okay so if I do they do it in
+ 
+
+ align:start position:0%
+is n by P okay so if I do they do it in
+that old order like n multiplications to
+
+ align:start position:0%
+that old order like n multiplications to
+ 
+
+ align:start position:0%
+that old order like n multiplications to
+do a dot product and I've got this many
+
+ align:start position:0%
+do a dot product and I've got this many
+ 
+
+ align:start position:0%
+do a dot product and I've got this many
+dot products in the answer so I've got M
+
+ align:start position:0%
+dot products in the answer so I've got M
+ 
+
+ align:start position:0%
+dot products in the answer so I've got M
+and P multiple multiplies now suppose I
+
+ align:start position:0%
+and P multiple multiplies now suppose I
+ 
+
+ align:start position:0%
+and P multiple multiplies now suppose I
+do it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many multiplications to do one of
+
+ align:start position:0%
+how many multiplications to do one of
+ 
+
+ align:start position:0%
+how many multiplications to do one of
+those guys to multiply a column by a row
+
+ align:start position:0%
+those guys to multiply a column by a row
+ 
+
+ align:start position:0%
+those guys to multiply a column by a row
+to multiply a column by a row this this
+
+ align:start position:0%
+to multiply a column by a row this this
+ 
+
+ align:start position:0%
+to multiply a column by a row this this
+is an M by one and this is a 1 by P one
+
+ align:start position:0%
+is an M by one and this is a 1 by P one
+ 
+
+ align:start position:0%
+is an M by one and this is a 1 by P one
+column one row
+
+ align:start position:0%
+column one row
+ 
+
+ align:start position:0%
+column one row
+how many multiplications for that guy in
+
+ align:start position:0%
+how many multiplications for that guy in
+ 
+
+ align:start position:0%
+how many multiplications for that guy in
+P and how many of those ranked ones do I
+
+ align:start position:0%
+P and how many of those ranked ones do I
+ 
+
+ align:start position:0%
+P and how many of those ranked ones do I
+have to do you got it it's MP times in
+
+ align:start position:0%
+have to do you got it it's MP times in
+ 
+
+ align:start position:0%
+have to do you got it it's MP times in
+now it's the other way was was n times
+
+ align:start position:0%
+now it's the other way was was n times
+ 
+
+ align:start position:0%
+now it's the other way was was n times
+MP so it gives the same answer MN p
+
+ align:start position:0%
+MP so it gives the same answer MN p
+ 
+
+ align:start position:0%
+MP so it gives the same answer MN p
+mostly in fact they're exactly the same
+
+ align:start position:0%
+mostly in fact they're exactly the same
+ 
+
+ align:start position:0%
+mostly in fact they're exactly the same
+multiplications just a different order
+
+ align:start position:0%
+multiplications just a different order
+ 
+
+ align:start position:0%
+multiplications just a different order
+okay we're at 155 thanks for coming
+
+ align:start position:0%
+okay we're at 155 thanks for coming
+ 
+
+ align:start position:0%
+okay we're at 155 thanks for coming
+today I'll talk more about the class and
+
+ align:start position:0%
+today I'll talk more about the class and
+ 
+
+ align:start position:0%
+today I'll talk more about the class and
+about linear algebra on Friday thank you
\ No newline at end of file
diff --git a/ZBlHexE8m6A.txt b/ZBlHexE8m6A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2c481974f0fdedaa601fa6cc902dd774c21b7dbd
--- /dev/null
+++ b/ZBlHexE8m6A.txt
@@ -0,0 +1,1107 @@
+align:start position:0%
+ 
+let's review what we've done this week
+
+ align:start position:0%
+let's review what we've done this week
+ 
+
+ align:start position:0%
+let's review what we've done this week
+we've seen that the work done by a force
+
+ align:start position:0%
+we've seen that the work done by a force
+ 
+
+ align:start position:0%
+we've seen that the work done by a force
+along a trajectory from point A to point
+
+ align:start position:0%
+along a trajectory from point A to point
+ 
+
+ align:start position:0%
+along a trajectory from point A to point
+B can be written as the integral of the
+
+ align:start position:0%
+B can be written as the integral of the
+ 
+
+ align:start position:0%
+B can be written as the integral of the
+dot product of that force with the
+
+ align:start position:0%
+dot product of that force with the
+ 
+
+ align:start position:0%
+dot product of that force with the
+displacement going from point A to point
+
+ align:start position:0%
+displacement going from point A to point
+ 
+
+ align:start position:0%
+displacement going from point A to point
+B well we note that this integral in
+
+ align:start position:0%
+B well we note that this integral in
+ 
+
+ align:start position:0%
+B well we note that this integral in
+general must be evaluated over the
+
+ align:start position:0%
+general must be evaluated over the
+ 
+
+ align:start position:0%
+general must be evaluated over the
+particular path taken from point A to
+
+ align:start position:0%
+particular path taken from point A to
+ 
+
+ align:start position:0%
+particular path taken from point A to
+point B this is called a line integral
+
+ align:start position:0%
+point B this is called a line integral
+ 
+
+ align:start position:0%
+point B this is called a line integral
+or a path integral and again I want to
+
+ align:start position:0%
+or a path integral and again I want to
+ 
+
+ align:start position:0%
+or a path integral and again I want to
+emphasize the value of this integral
+
+ align:start position:0%
+emphasize the value of this integral
+ 
+
+ align:start position:0%
+emphasize the value of this integral
+depends in general on the path taken
+
+ align:start position:0%
+depends in general on the path taken
+ 
+
+ align:start position:0%
+depends in general on the path taken
+from point A to point B and you can
+
+ align:start position:0%
+from point A to point B and you can
+ 
+
+ align:start position:0%
+from point A to point B and you can
+understand that if you consider the fact
+
+ align:start position:0%
+understand that if you consider the fact
+ 
+
+ align:start position:0%
+understand that if you consider the fact
+that in general the force is a function
+
+ align:start position:0%
+that in general the force is a function
+ 
+
+ align:start position:0%
+that in general the force is a function
+of position and so if you go along
+
+ align:start position:0%
+of position and so if you go along
+ 
+
+ align:start position:0%
+of position and so if you go along
+different paths the dot product of the
+
+ align:start position:0%
+different paths the dot product of the
+ 
+
+ align:start position:0%
+different paths the dot product of the
+force with a particular path may be
+
+ align:start position:0%
+force with a particular path may be
+ 
+
+ align:start position:0%
+force with a particular path may be
+different even though you're going
+
+ align:start position:0%
+different even though you're going
+ 
+
+ align:start position:0%
+different even though you're going
+between the same end points now the
+
+ align:start position:0%
+between the same end points now the
+ 
+
+ align:start position:0%
+between the same end points now the
+reason that the work is a useful concept
+
+ align:start position:0%
+reason that the work is a useful concept
+ 
+
+ align:start position:0%
+reason that the work is a useful concept
+is that it allows us to understand how
+
+ align:start position:0%
+is that it allows us to understand how
+ 
+
+ align:start position:0%
+is that it allows us to understand how
+the kinetic energy of an object so the
+
+ align:start position:0%
+the kinetic energy of an object so the
+ 
+
+ align:start position:0%
+the kinetic energy of an object so the
+kinetic energy is one-half MV squared
+
+ align:start position:0%
+kinetic energy is one-half MV squared
+ 
+
+ align:start position:0%
+kinetic energy is one-half MV squared
+the work allows us to understand how the
+
+ align:start position:0%
+the work allows us to understand how the
+ 
+
+ align:start position:0%
+the work allows us to understand how the
+kinetic energy evolves under the action
+
+ align:start position:0%
+kinetic energy evolves under the action
+ 
+
+ align:start position:0%
+kinetic energy evolves under the action
+of the force and we see that through
+
+ align:start position:0%
+of the force and we see that through
+ 
+
+ align:start position:0%
+of the force and we see that through
+what's called the work kinetic energy
+
+ align:start position:0%
+what's called the work kinetic energy
+ 
+
+ align:start position:0%
+what's called the work kinetic energy
+theorem which states that the work done
+
+ align:start position:0%
+theorem which states that the work done
+ 
+
+ align:start position:0%
+theorem which states that the work done
+so again the integral of F dot d s from
+
+ align:start position:0%
+so again the integral of F dot d s from
+ 
+
+ align:start position:0%
+so again the integral of F dot d s from
+point A to point B evaluated along the
+
+ align:start position:0%
+point A to point B evaluated along the
+ 
+
+ align:start position:0%
+point A to point B evaluated along the
+specific path is equal to the change in
+
+ align:start position:0%
+specific path is equal to the change in
+ 
+
+ align:start position:0%
+specific path is equal to the change in
+the kinetic energy so that's one-half
+
+ align:start position:0%
+the kinetic energy so that's one-half
+ 
+
+ align:start position:0%
+the kinetic energy so that's one-half
+and the B squared since B is the final
+
+ align:start position:0%
+and the B squared since B is the final
+ 
+
+ align:start position:0%
+and the B squared since B is the final
+point minus one-half M VA squared where
+
+ align:start position:0%
+point minus one-half M VA squared where
+ 
+
+ align:start position:0%
+point minus one-half M VA squared where
+a is the initial point and this is equal
+
+ align:start position:0%
+a is the initial point and this is equal
+ 
+
+ align:start position:0%
+a is the initial point and this is equal
+to the change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the kinetic energy and we derived
+
+ align:start position:0%
+in the kinetic energy and we derived
+ 
+
+ align:start position:0%
+in the kinetic energy and we derived
+this theorem from Newton's second law F
+
+ align:start position:0%
+this theorem from Newton's second law F
+ 
+
+ align:start position:0%
+this theorem from Newton's second law F
+equals MA so this is essentially just a
+
+ align:start position:0%
+equals MA so this is essentially just a
+ 
+
+ align:start position:0%
+equals MA so this is essentially just a
+restatement of Newton's second law now
+
+ align:start position:0%
+restatement of Newton's second law now
+ 
+
+ align:start position:0%
+restatement of Newton's second law now
+two things to note about the work and
+
+ align:start position:0%
+two things to note about the work and
+ 
+
+ align:start position:0%
+two things to note about the work and
+this work integral the first is that the
+
+ align:start position:0%
+this work integral the first is that the
+ 
+
+ align:start position:0%
+this work integral the first is that the
+work integral when evaluated can it just
+
+ align:start position:0%
+work integral when evaluated can it just
+ 
+
+ align:start position:0%
+work integral when evaluated can it just
+gives a number right because the dot
+
+ align:start position:0%
+gives a number right because the dot
+ 
+
+ align:start position:0%
+gives a number right because the dot
+product is a scalar and that number can
+
+ align:start position:0%
+product is a scalar and that number can
+ 
+
+ align:start position:0%
+product is a scalar and that number can
+be either positive or negative or even
+
+ align:start position:0%
+be either positive or negative or even
+ 
+
+ align:start position:0%
+be either positive or negative or even
+zero depending upon whether the velocity
+
+ align:start position:0%
+zero depending upon whether the velocity
+ 
+
+ align:start position:0%
+zero depending upon whether the velocity
+increases decreases or stays the same
+
+ align:start position:0%
+increases decreases or stays the same
+ 
+
+ align:start position:0%
+increases decreases or stays the same
+under the action of the force as you go
+
+ align:start position:0%
+under the action of the force as you go
+ 
+
+ align:start position:0%
+under the action of the force as you go
+from point A to point B the second point
+
+ align:start position:0%
+from point A to point B the second point
+ 
+
+ align:start position:0%
+from point A to point B the second point
+to emphasize is that again this integral
+
+ align:start position:0%
+to emphasize is that again this integral
+ 
+
+ align:start position:0%
+to emphasize is that again this integral
+in general must be evaluated along the
+
+ align:start position:0%
+in general must be evaluated along the
+ 
+
+ align:start position:0%
+in general must be evaluated along the
+specific path taken from point A to
+
+ align:start position:0%
+specific path taken from point A to
+ 
+
+ align:start position:0%
+specific path taken from point A to
+point B which means that in order to
+
+ align:start position:0%
+point B which means that in order to
+ 
+
+ align:start position:0%
+point B which means that in order to
+evaluate the integral we need to know
+
+ align:start position:0%
+evaluate the integral we need to know
+ 
+
+ align:start position:0%
+evaluate the integral we need to know
+what that path is now if we have a
+
+ align:start position:0%
+what that path is now if we have a
+ 
+
+ align:start position:0%
+what that path is now if we have a
+situation where we don't know in advance
+
+ align:start position:0%
+situation where we don't know in advance
+ 
+
+ align:start position:0%
+situation where we don't know in advance
+what the path is then we can't evaluate
+
+ align:start position:0%
+what the path is then we can't evaluate
+ 
+
+ align:start position:0%
+what the path is then we can't evaluate
+the integral so in a way it might seem
+
+ align:start position:0%
+the integral so in a way it might seem
+ 
+
+ align:start position:0%
+the integral so in a way it might seem
+like a not very useful concept that we
+
+ align:start position:0%
+like a not very useful concept that we
+ 
+
+ align:start position:0%
+like a not very useful concept that we
+haven't really made progress because we
+
+ align:start position:0%
+haven't really made progress because we
+ 
+
+ align:start position:0%
+haven't really made progress because we
+need to know the answer about what the
+
+ align:start position:0%
+need to know the answer about what the
+ 
+
+ align:start position:0%
+need to know the answer about what the
+trajectory is before we can calculate
+
+ align:start position:0%
+trajectory is before we can calculate
+ 
+
+ align:start position:0%
+trajectory is before we can calculate
+the work done and it's not clear why
+
+ align:start position:0%
+the work done and it's not clear why
+ 
+
+ align:start position:0%
+the work done and it's not clear why
+that's useful however what I want to
+
+ align:start position:0%
+that's useful however what I want to
+ 
+
+ align:start position:0%
+that's useful however what I want to
+point out is that there are two special
+
+ align:start position:0%
+point out is that there are two special
+ 
+
+ align:start position:0%
+point out is that there are two special
+cases that are particularly useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first special case is that of
+
+ align:start position:0%
+the first special case is that of
+ 
+
+ align:start position:0%
+the first special case is that of
+constrained motion sometimes we know in
+
+ align:start position:0%
+constrained motion sometimes we know in
+ 
+
+ align:start position:0%
+constrained motion sometimes we know in
+advance sometimes we know in advance
+
+ align:start position:0%
+advance sometimes we know in advance
+ 
+
+ align:start position:0%
+advance sometimes we know in advance
+what the path is going to be because
+
+ align:start position:0%
+what the path is going to be because
+ 
+
+ align:start position:0%
+what the path is going to be because
+it's because the motion is constrained
+
+ align:start position:0%
+it's because the motion is constrained
+ 
+
+ align:start position:0%
+it's because the motion is constrained
+we know that it's going to be moving
+
+ align:start position:0%
+we know that it's going to be moving
+ 
+
+ align:start position:0%
+we know that it's going to be moving
+along the other going to be moving along
+
+ align:start position:0%
+along the other going to be moving along
+ 
+
+ align:start position:0%
+along the other going to be moving along
+a circular path or along some particular
+
+ align:start position:0%
+a circular path or along some particular
+ 
+
+ align:start position:0%
+a circular path or along some particular
+track of some particular shape and as
+
+ align:start position:0%
+track of some particular shape and as
+ 
+
+ align:start position:0%
+track of some particular shape and as
+long as we can describe that trajectory
+
+ align:start position:0%
+long as we can describe that trajectory
+ 
+
+ align:start position:0%
+long as we can describe that trajectory
+we can evaluate our work integral along
+
+ align:start position:0%
+we can evaluate our work integral along
+ 
+
+ align:start position:0%
+we can evaluate our work integral along
+that trajectory so that's a case where
+
+ align:start position:0%
+that trajectory so that's a case where
+ 
+
+ align:start position:0%
+that trajectory so that's a case where
+even though the work is a path dependent
+
+ align:start position:0%
+even though the work is a path dependent
+ 
+
+ align:start position:0%
+even though the work is a path dependent
+integral we know the path and so we can
+
+ align:start position:0%
+integral we know the path and so we can
+ 
+
+ align:start position:0%
+integral we know the path and so we can
+evaluate the integral the second special
+
+ align:start position:0%
+evaluate the integral the second special
+ 
+
+ align:start position:0%
+evaluate the integral the second special
+case we've seen is that there is a
+
+ align:start position:0%
+case we've seen is that there is a
+ 
+
+ align:start position:0%
+case we've seen is that there is a
+special class of forces called
+
+ align:start position:0%
+special class of forces called
+ 
+
+ align:start position:0%
+special class of forces called
+conservative forces and conservative
+
+ align:start position:0%
+conservative forces and conservative
+ 
+
+ align:start position:0%
+conservative forces and conservative
+forces have the property that the work
+
+ align:start position:0%
+forces have the property that the work
+ 
+
+ align:start position:0%
+forces have the property that the work
+integral is independent of the path so
+
+ align:start position:0%
+integral is independent of the path so
+ 
+
+ align:start position:0%
+integral is independent of the path so
+for a work integral all that Matt sorry
+
+ align:start position:0%
+for a work integral all that Matt sorry
+ 
+
+ align:start position:0%
+for a work integral all that Matt sorry
+for for a conservative force the work
+
+ align:start position:0%
+for for a conservative force the work
+ 
+
+ align:start position:0%
+for for a conservative force the work
+integral only depends upon the endpoints
+
+ align:start position:0%
+integral only depends upon the endpoints
+ 
+
+ align:start position:0%
+integral only depends upon the endpoints
+a and B and not upon the path you take
+
+ align:start position:0%
+a and B and not upon the path you take
+ 
+
+ align:start position:0%
+a and B and not upon the path you take
+to get from A to B so for any path
+
+ align:start position:0%
+to get from A to B so for any path
+ 
+
+ align:start position:0%
+to get from A to B so for any path
+you'll always get the same value of the
+
+ align:start position:0%
+you'll always get the same value of the
+ 
+
+ align:start position:0%
+you'll always get the same value of the
+work integral if the force is
+
+ align:start position:0%
+work integral if the force is
+ 
+
+ align:start position:0%
+work integral if the force is
+conservative and so those are the two
+
+ align:start position:0%
+conservative and so those are the two
+ 
+
+ align:start position:0%
+conservative and so those are the two
+cases in which we can usefully apply
+
+ align:start position:0%
+cases in which we can usefully apply
+ 
+
+ align:start position:0%
+cases in which we can usefully apply
+work and the work-energy theorem now in
+
+ align:start position:0%
+work and the work-energy theorem now in
+ 
+
+ align:start position:0%
+work and the work-energy theorem now in
+general one might have a combination of
+
+ align:start position:0%
+general one might have a combination of
+ 
+
+ align:start position:0%
+general one might have a combination of
+conservative and non-conservative forces
+
+ align:start position:0%
+conservative and non-conservative forces
+ 
+
+ align:start position:0%
+conservative and non-conservative forces
+acting on a system and in that case we
+
+ align:start position:0%
+acting on a system and in that case we
+ 
+
+ align:start position:0%
+acting on a system and in that case we
+can actually write the work as
+
+ align:start position:0%
+can actually write the work as
+ 
+
+ align:start position:0%
+can actually write the work as
+consisting of two separate terms the
+
+ align:start position:0%
+consisting of two separate terms the
+ 
+
+ align:start position:0%
+consisting of two separate terms the
+work done by conservative forces what
+
+ align:start position:0%
+work done by conservative forces what
+ 
+
+ align:start position:0%
+work done by conservative forces what
+I'll write is w sze plus the work done
+
+ align:start position:0%
+I'll write is w sze plus the work done
+ 
+
+ align:start position:0%
+I'll write is w sze plus the work done
+by the non-conservative forces WNC and
+
+ align:start position:0%
+by the non-conservative forces WNC and
+ 
+
+ align:start position:0%
+by the non-conservative forces WNC and
+so the conservative work is just the
+
+ align:start position:0%
+so the conservative work is just the
+ 
+
+ align:start position:0%
+so the conservative work is just the
+work integral evaluated for the
+
+ align:start position:0%
+work integral evaluated for the
+ 
+
+ align:start position:0%
+work integral evaluated for the
+conservative forces
+
+ align:start position:0%
+conservative forces
+ 
+
+ align:start position:0%
+conservative forces
+so f c for conservative force dot d s
+
+ align:start position:0%
+so f c for conservative force dot d s
+ 
+
+ align:start position:0%
+so f c for conservative force dot d s
+going from a to b and because this force
+
+ align:start position:0%
+going from a to b and because this force
+ 
+
+ align:start position:0%
+going from a to b and because this force
+is conservative
+
+ align:start position:0%
+is conservative
+ 
+
+ align:start position:0%
+is conservative
+this integral is path independent let me
+
+ align:start position:0%
+this integral is path independent let me
+ 
+
+ align:start position:0%
+this integral is path independent let me
+emphasize that here this is a path
+
+ align:start position:0%
+emphasize that here this is a path
+ 
+
+ align:start position:0%
+emphasize that here this is a path
+independent integral it's not a line
+
+ align:start position:0%
+independent integral it's not a line
+ 
+
+ align:start position:0%
+independent integral it's not a line
+integral it only depends upon the
+
+ align:start position:0%
+integral it only depends upon the
+ 
+
+ align:start position:0%
+integral it only depends upon the
+endpoints because the force is
+
+ align:start position:0%
+endpoints because the force is
+ 
+
+ align:start position:0%
+endpoints because the force is
+conservative the second term is the non
+
+ align:start position:0%
+conservative the second term is the non
+ 
+
+ align:start position:0%
+conservative the second term is the non
+conservative work and that is the work
+
+ align:start position:0%
+conservative work and that is the work
+ 
+
+ align:start position:0%
+conservative work and that is the work
+done by the non-conservative force F sub
+
+ align:start position:0%
+done by the non-conservative force F sub
+ 
+
+ align:start position:0%
+done by the non-conservative force F sub
+n C dotted with D s between the same
+
+ align:start position:0%
+n C dotted with D s between the same
+ 
+
+ align:start position:0%
+n C dotted with D s between the same
+endpoints a and B but this integral does
+
+ align:start position:0%
+endpoints a and B but this integral does
+ 
+
+ align:start position:0%
+endpoints a and B but this integral does
+depend upon the specific path the path
+
+ align:start position:0%
+depend upon the specific path the path
+ 
+
+ align:start position:0%
+depend upon the specific path the path
+matters for this term because there the
+
+ align:start position:0%
+matters for this term because there the
+ 
+
+ align:start position:0%
+matters for this term because there the
+force is non conservative so in general
+
+ align:start position:0%
+force is non conservative so in general
+ 
+
+ align:start position:0%
+force is non conservative so in general
+you can compute the work by separating
+
+ align:start position:0%
+you can compute the work by separating
+ 
+
+ align:start position:0%
+you can compute the work by separating
+out the conservative force and the non
+
+ align:start position:0%
+out the conservative force and the non
+ 
+
+ align:start position:0%
+out the conservative force and the non
+conservative force acting on the system
+
+ align:start position:0%
+conservative force acting on the system
+ 
+
+ align:start position:0%
+conservative force acting on the system
+if both are acting if the force is only
+
+ align:start position:0%
+if both are acting if the force is only
+ 
+
+ align:start position:0%
+if both are acting if the force is only
+conservative then you only have to worry
+
+ align:start position:0%
+conservative then you only have to worry
+ 
+
+ align:start position:0%
+conservative then you only have to worry
+about the path independent integral
+
+ align:start position:0%
+about the path independent integral
+ 
+
+ align:start position:0%
+about the path independent integral
+which in general is much simpler to
+
+ align:start position:0%
+which in general is much simpler to
+ 
+
+ align:start position:0%
+which in general is much simpler to
+evaluate if the force is non
+
+ align:start position:0%
+evaluate if the force is non
+ 
+
+ align:start position:0%
+evaluate if the force is non
+conservative then you need to specify
+
+ align:start position:0%
+conservative then you need to specify
+ 
+
+ align:start position:0%
+conservative then you need to specify
+the path in order to evaluate the
+
+ align:start position:0%
+the path in order to evaluate the
+ 
+
+ align:start position:0%
+the path in order to evaluate the
+integral again a path dependent integral
+
+ align:start position:0%
+integral again a path dependent integral
+ 
+
+ align:start position:0%
+integral again a path dependent integral
+is often called a path integral or a
+
+ align:start position:0%
+is often called a path integral or a
+ 
+
+ align:start position:0%
+is often called a path integral or a
+line integral
\ No newline at end of file
diff --git a/ZTNip78TUvA.txt b/ZTNip78TUvA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..87f9a915e329f041607be3c5f1cb74ace1f11bf9
--- /dev/null
+++ b/ZTNip78TUvA.txt
@@ -0,0 +1,3054 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocs.mit.edu.
+
+PROFESSOR: Today we
+have plenty to do.
+
+We really begin
+in all generality
+
+the addition of
+angular momentum.
+
+But we will do it in the set
+up of a physical problem.
+
+The problem of
+computing the spin
+
+orbit interactions of
+electrons with the nucleus.
+
+So this is a rather interesting
+and complicated interaction.
+
+So we'll spend a
+little time telling you
+
+about the physics
+of this interaction.
+
+And then once the
+physics is clear,
+
+it will become
+more obvious why we
+
+have to do these mathematical
+contortions of adding angular
+
+momentum in order to solve
+this physical problem.
+
+So it's a sophisticated problem
+that requires several steps.
+
+The first step is
+something that is
+
+a result in perturbation theory.
+
+Feynman Hellman Theorem
+of perturbation theory.
+
+And that's where we begin.
+
+So it's called Feynman
+Hellman Theorem.
+
+It's a very simple result.
+
+Theorem.
+
+And we'll need it in
+order to understand
+
+how a small perturbation
+to the Hamiltonian
+
+changes the energy spectrum.
+
+So we have H of lambda be a
+Hamiltonian with a parameter
+
+in lambda.
+
+Lambda.
+
+And psi n of lambda
+being normalized energy
+
+eigenstate with
+energy, En of lambda.
+
+So that's the whole
+assumption of the theorem.
+
+We have a Hamiltonian.
+
+It depends on some parameter
+that we're going to vary.
+
+And suppose we consider now an
+eigenstate of this Hamiltonian
+
+that depends on lambda,
+so the eigenstate also
+
+depends on lambda.
+
+And it has an
+energy, En of lambda.
+
+So the purpose of
+this theorem is
+
+to relate these
+various quantities.
+
+And the claim is that
+the rate of change
+
+of the energy with
+respect to lambda
+
+can be computed pretty much by
+evaluating the rate of change
+
+of the Hamiltonian on
+the relevant states.
+
+So that's the claim.
+
+And it's a pretty nice result.
+
+It's useful in
+many circumstances.
+
+And for us will be a way to
+discuss a little perturbation
+
+theory.
+
+Perturbation theory is the
+subject of 806 in all details.
+
+And it's a very
+sophisticated subject.
+
+Even today we were going
+to be finding that it's not
+
+all that easy to carry it out.
+
+So how does this begin?
+
+Well, proof.
+
+You begin by saying
+that En of lambda
+
+is the energy eigenstate,
+is nothing else
+
+but psi n of lambda.
+
+H of lambda.
+
+Psi n of lambda.
+
+And the reason is, of
+course, that H and psi n
+
+is En of lambda times
+psi n of lambda.
+
+And this is a number goes out.
+
+And the inner product
+of this things
+
+is 1, because the
+state is normalized.
+
+So this is a good
+starting point.
+
+And the funny thing that you see
+already is that, in some sense,
+
+you just get the
+middle term when
+
+you take the derivative
+with respect to lambda.
+
+You don't get anything
+from these two.
+
+And it's simple in fact.
+
+So let me just do it.
+
+V, En, V lambda
+would be the term
+
+that Feynman and Hellman gave.
+
+V, H, V lambda, psi n of lambda.
+
+Plus one term in which we
+differentiate this one.
+
+V, d lambda of the
+state psi n of lambda.
+
+Times H of lambda,
+psi n of lambda.
+
+Plus the other term in which
+you differentiate the ket.
+
+So psi n of lambda, H of lambda,
+d, d lambda of psi n of lambda.
+
+And the reason these
+terms are going to vanish
+
+is that you can now act
+with H again on psi n.
+
+H is supposed to be Hermitian,
+so it can act on the left.
+
+And therefore, these two
+terms give you En of lambda,
+
+times d d lambda of psi n of
+lambda-- psi n of lambda--
+
+plus the other term, which
+would be psi n of lambda,
+
+the bra times the
+derivative of the ket.
+
+But this is nothing
+else than the derivative
+
+of the inner product.
+
+In the inner product
+to differentiate--
+
+the inner product
+differentiates the bra,
+
+it differentiates the ket.
+
+And do it.
+
+And this thing is equal to
+1, because it's normalized.
+
+So this is 0.
+
+End of proof.
+
+These two terms vanish.
+
+And the result holds.
+
+Yes?
+
+AUDIENCE: How do you
+know it stays normalized
+
+when you vary lambda?
+
+PROFESSOR: It's an assumption.
+
+The state is normalized
+for all values of n.
+
+So if you have a state
+that you've constructed,
+
+that is normalized, you
+can have this result.
+
+So it's an assumption.
+
+You have to keep the
+state normalized.
+
+Now this is a baby version
+of perturbation theory.
+
+It's a result I think that
+Feynman did as an undergrad.
+
+And as you can see,
+it's very simple.
+
+Calling it a theorem
+is a little too much.
+
+But still, the fact
+is that it's useful.
+
+And so we'll just
+go ahead and use it.
+
+Now I want to rewrite
+it in another way.
+
+So, suppose you have
+a Hamiltonian, H,
+
+which has a term
+H0, plus lambda, H1.
+
+So, the parameter lambda, H of
+lambda, is given in this way.
+
+And that's a
+reasonable H of lambda.
+
+Sometimes, this could be
+written as H0 plus something
+
+that we will call the
+change in the Hamiltonian.
+
+And we usually think
+of it as a small thing.
+
+So what do we have
+from this theorem?
+
+From this here we would
+have the d, En, d lambda
+
+is equal to psi n of
+lambda, H1, psi n of lambda.
+
+Now, we can be
+particularly interested
+
+in the evaluation of this
+thing at lambda equals 0.
+
+So what is d En of lambda?
+
+d lambda at lambda equals
+0 would be psi n at zero,
+
+H1, psi n at 0.
+
+And therefore, you would say
+that the En of lambda energies
+
+would be the energies
+at 0, plus lambda, d En
+
+of lambda, d lambda
+at lambda equals 0,
+
+plus order lambda squared.
+
+I'm doing just the
+Taylor expansion
+
+of En's of lambda
+from lambda equals 0.
+
+So this thing tells you that
+En of lambda is equal En of 0,
+
+plus-- this derivative you can
+write it as psi n, lambda, H1,
+
+psi n, all at 0.
+
+Like that.
+
+Plus order lambda squared.
+
+So in this step, I just use the
+evaluation that we did here.
+
+I substituted that
+and put the lambda in.
+
+So that I recognize now that En
+of lambda is equal to En of 0,
+
+plus psi n of 0-- and I can
+write this as delta H-- psi
+
+n of 0, plus order
+delta H squared.
+
+It's nice to write it this
+way, because you appreciate
+
+more the power of the theorem.
+
+The theorem here doesn't assume
+which value of lambda you have.
+
+And you have to have
+normalized eigenstates.
+
+And you wonder what is
+it helping you with,
+
+if finding the states for every
+value of lambda is complicated.
+
+Well, it certainly
+helps you to figure out
+
+how the energy of the state
+varies by a simple calculation.
+
+Suppose you know the states
+of the simple Hamiltonian.
+
+Those are the psi's, n, 0.
+
+So if you have the
+psi n 0 over here,
+
+you can do the following step.
+
+If you want to figure out
+how it's energy has varied,
+
+use this formula in which
+you compute the expectation
+
+value of the change in the
+Hamiltonian on that state.
+
+And that is the first correction
+to the energy of the state.
+
+So you have this state.
+
+You compute the
+expectation value
+
+of the extra piece
+in the Hamiltonian.
+
+And that's the
+correction to the energy.
+
+It's a little more
+complicated of course
+
+to compute the
+correction to the state.
+
+But that's a subject
+of perturbation theory.
+
+And that's not what we
+care about right now.
+
+So the reason we're doing this
+is because actually whatever
+
+we're going to have
+with spin orbit coupling
+
+represents an addition
+to the hydrogen
+
+Hamiltonian of a new term.
+
+Therefore, you want to know what
+happens to the energy levels.
+
+And the best thing
+to think about them
+
+is to-- if you know the
+energy levels of this one,
+
+well, a formula of
+this type can let
+
+you know what happens
+to the energy levels
+
+after the perturbation.
+
+There will be an
+extra complication
+
+in that the energy levels
+that we're going to deal with
+
+are going to be degenerate.
+
+But let's wait for that
+complication until it appears.
+
+So any questions?
+
+Yes?
+
+AUDIENCE: So I would
+imagine that this
+
+would work just
+as well for time.
+
+Because time [INAUDIBLE] a
+parameter in quantum mechanics.
+
+So [INAUDIBLE]
+
+PROFESSOR: Time dependent
+perturbation theory
+
+is a bit more complicated.
+
+I'd rather not get into it now.
+
+So let's leave it here, in
+which we don't have time.
+
+And the Schrodinger
+equation is something
+
+like H psi equal [INAUDIBLE]
+psi, that's all we care.
+
+And leave it for that moment.
+
+Other questions?
+
+OK.
+
+So let's proceed with
+addition of angular momentum.
+
+So first, let me give you
+the fundamental result
+
+of addition of angular momentum.
+
+It's a little abstract,
+but it's what we really
+
+mean by addition of
+angular momentum.
+
+Of angular momentum.
+
+And the main result
+is the following.
+
+Suppose you have a set
+of operators, J, i,
+
+1, that have the algebra
+of angular momentum.
+
+Of angular momentum.
+
+Which is to say
+Ji1, JJ1, is equal
+
+i, h bar, epsilon iJK, JK1.
+
+And this algebra is realized
+on some state space.
+
+On some vector space, V1.
+
+And suppose you have
+another operator,
+
+J-- set of operators actually.
+
+Ji2, which have the algebra
+of angular momentum.
+
+I will not write that.
+
+On some V2.
+
+OK.
+
+Angular momentum,
+some sets of states.
+
+Angular momentum on some
+other set of states.
+
+Here comes the thing.
+
+There is a new angular
+momentum, which
+
+is the sum Ji defined
+as Ji1, added with Ji2.
+
+Now, soon enough you will
+just write Ji1, plus Ji2.
+
+But let me be a little
+more careful now.
+
+This sum is Ji1,
+plus 1, tensor Ji2.
+
+So i is the same index.
+
+But here, we're
+having this operator
+
+that we're being defined
+that we call it the sum.
+
+Now how do you sum two operators
+that act in different spaces?
+
+Well, the only thing
+that you can actually do
+
+is sum them in the
+tensor product.
+
+So the claim is that this is an
+angular momentum in V1 tensor
+
+V2.
+
+That is an operator.
+
+You see, you have to sum them.
+
+So you have to create a
+space where both can act,
+
+and you can sum them.
+
+You cannot sum a thing, an
+operator that acts on one
+
+vector space to an operator that
+acts on another vector space.
+
+You have to create one
+vector space where both act.
+
+And then you can define
+the sum of the operators.
+
+Sum of operators
+is a simple thing.
+
+So you form the tensor product.
+
+In here, this
+operator gets upgraded
+
+in this way, in which in the
+tensor product it has a 1
+
+for the second input.
+
+This one gets
+upgrade to this way.
+
+And this is the sum.
+
+So this is a claim--
+this is a definition.
+
+And this is a claim.
+
+So this has to be proven.
+
+So let me prove it.
+
+Ji, JJ.
+
+I compute this commutator.
+
+So I don't have to
+do the following.
+
+I have to do Ji1, tensor
+1, plus 1 tensor Ji2.
+
+And then the JJ would be JJ1,
+tensor 1, plus 1, tensor JJ2.
+
+Have to compute this commutator.
+
+Now, an important
+fact about this
+
+result that I'm not
+trying to generalize,
+
+if you had put a minus
+here, it wouldn't work out.
+
+If you would have put a 2
+here, it wouldn't work out.
+
+If you would have put a 1/2
+here, it won't work out.
+
+This is pretty much
+the only way you
+
+can have two angular momenta,
+and create a third angular
+
+momentum.
+
+So look at this.
+
+It looks like we're going
+to have to work hard,
+
+but that's not true.
+
+Consider this commutator.
+
+The commutator of this
+term with this term.
+
+That's 0 actually.
+
+Because if you multiply them
+in this order, this times that,
+
+you get Ji1 times Ji2,
+because the ones do nothing.
+
+You multiply them in
+the reverse order,
+
+you get again, Ji1 times Ji2.
+
+This is to say that the
+operators that originally lived
+
+in the different
+vector spaces commute.
+
+Yes?
+
+AUDIENCE: Since the cross
+terms between those two
+
+are 0-- like you just said,
+the cross terms are 0.
+
+And if you put a minus sign
+in there, it will cancel.
+
+But when you do
+the multiplications
+
+with the second ones, why can't
+you put a minus sign in there?
+
+[INAUDIBLE]
+
+PROFESSOR: In the whole thing?
+
+In this definition,
+a minus sign?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: Well, here
+if I put a minus--
+
+it's like I'm going to
+prove that this works.
+
+So if-- I'm going to
+get an angular momentum.
+
+If I put a minus sign
+to angular momentum,
+
+I ruin the algebra here.
+
+I put a minus minus, it cancels.
+
+But then I get a
+minus sign here.
+
+So I cannot really
+even change a sign.
+
+So any way, these are operators
+acting on different spaces.
+
+They commute.
+
+It's clear they commute.
+
+You just multiply
+them, and see that.
+
+These one's commute as well.
+
+The only ones that don't
+commute are this with this.
+
+And that with that.
+
+So let me just write them.
+
+Ji1, tensor 1,
+with JJ1, tensor 1.
+
+Plus this one, 1 tensor
+Ji2, 1 tensor JJ2.
+
+OK, next step is to
+realize that actually
+
+the 1 is a spectator here.
+
+Therefore, this
+commutator is nothing
+
+but the commutator Ji1
+with JJ1, tensor 1.
+
+You can do it.
+
+If you prefer to
+write it, write it.
+
+This product is Ji
+times JJ, tensor 1.
+
+And the other product
+is JJ, Ji, tensor 1.
+
+So the tensor 1 factors out.
+
+Here the tensor 1
+also factors out.
+
+And you get an honest
+commutator, Ji2, JJ2.
+
+So one last step.
+
+This is i, h bar, epsilon, iJK.
+
+I'll put a big parentheses.
+
+JK1, tensor 1,
+for the first one.
+
+Because J1 forms an
+angular momentum algebra.
+
+And here, 1 tensor JK2.
+
+And this thing is i,
+h bar, epsilon, iJK.
+
+The total angular
+momentum, K. And you've
+
+shown the algebra works out.
+
+Now most people after
+a little practice,
+
+they just say, oh, Ji is
+J1 plus J2, J1 plus J2.
+
+J1 and J2 don't commute.
+
+J2 and J1-- I'm sorry.
+
+J1 and J2 commute.
+
+J2 and J1 commute.
+
+Therefore you get
+this 2, like that.
+
+And this gives you--
+J1 and J1 gives you J1.
+
+J2 and J2 gives you J2,
+so the sum works out.
+
+So most people after
+a little practice
+
+just don't put all
+these tensor things.
+
+But at the beginning it's
+nice to just make sure
+
+that you understand what
+these tensor things do.
+
+All right.
+
+So that's our main
+theorem-- that you
+
+start with one angular
+momentum on a state space.
+
+Another angular momentum that
+has nothing to do perhaps
+
+with the first on
+another vector space.
+
+And on the tensor product you
+have another angular momentum,
+
+which is the sum.
+
+All right.
+
+So now, we do spin
+orbit coupling
+
+to try to apply these ideas.
+
+So for spin orbit coupling, we
+will consider the hydrogen atom
+
+coupling.
+
+And the new term in the
+Hamiltonian, mu dot B.
+
+The kind of term that we've
+done so much in this semester.
+
+We've looked over magnetic ones.
+
+So which magnetic
+moment at which B?
+
+There was no B in
+the hydrogen atom.
+
+Well, there's no
+B to begin with.
+
+But here is one where you can
+think there is a B. First,
+
+this will be the
+electron dipole moment.
+
+Magnetic dipole moment.
+
+So we have a formula for it.
+
+The formula for it is the mu of
+the electron is minus E over m,
+
+times the spin of the electron.
+
+And I actually will use a
+little different formula
+
+that is valued in
+Gaussian units.
+
+ge over mC, S, in
+Gaussian units.
+
+And g is the g factor of
+the electron, which is 2.
+
+I'm sorry.
+
+There's a 2 here.
+
+OK.
+
+So look what I've written.
+
+I don't want to distract
+you with this too much.
+
+But you know that the magnetic
+dipole of the electron
+
+is given by this quantity.
+
+Now, you could put a
+2 up, and a 2 down.
+
+And that's why people
+actually classically
+
+there seems to be a 2 down.
+
+But there's a 2 up, because
+it's an effect of the electron.
+
+And you have this formula.
+
+The only thing I've
+added in that formula
+
+is a factor of C that is
+because of Gaussian units.
+
+And it allows you to estimate
+terms a little more easily.
+
+So that's the mu
+of the electron.
+
+But the electron apparently
+would feel no magnetic field.
+
+You didn't put an
+external magnetic field.
+
+Except that here
+you go in this way
+
+of thinking-- you think
+suppose you are the electron.
+
+You see a proton, which is
+a nucleus going around you.
+
+And a proton going around you
+is a current going around you.
+
+It generates a magnetic field.
+
+And therefore, you
+see a magnetic field
+
+created by the proton
+going around you.
+
+So there is a magnetic field.
+
+And there's a magnetic
+field experienced
+
+by the electron--
+felt by electron.
+
+So you can think of
+this, the electron.
+
+Here is the proton
+with the plus charge,
+
+and here's the electron.
+
+And the electron is
+going around the proton.
+
+Now, from the viewpoint
+of the electron,
+
+the proton is going around him.
+
+So here is the proton.
+
+Here is the electron
+going like that.
+
+From the viewpoint
+of the electron,
+
+the proton is going like this.
+
+Also, from the viewpoint
+of the electron,
+
+the proton would be
+going in this direction
+
+and creating a
+magnetic field up.
+
+And the magnetic field
+up corresponds actually
+
+to the idea that the angular
+momentum of the electron
+
+is also up-- L of the
+electron is also up.
+
+So the whole point
+of this thing is
+
+that somehow this magnetic field
+is proportional to the angular
+
+momentum.
+
+And then, L will come here.
+
+And here, you have
+S. So you have
+
+L dot S. That's the
+fine structure coupling.
+
+Now let me do a little
+of this so that we just
+
+get a bit more feeling,
+although it's unfortunately
+
+a somewhat frustrating exercise.
+
+So let me tell you
+what's going on.
+
+So consider the electron.
+
+At some point, look at
+it and draw a plane.
+
+So the electron-- let's
+assume it's going down.
+
+Here is the proton.
+
+It's going around in circles.
+
+So here, it's going down.
+
+The electron is going down.
+
+Electron, its velocity of
+the electron is going down.
+
+The proton is over here.
+
+And the electron is
+going around like that.
+
+The proton would produce an
+electric field of this form.
+
+Now, in relativity, the
+electric and magnetic fields
+
+seen by different
+observers are different.
+
+So there is this electric
+field that we see.
+
+We sit here, and we
+see in our rest frame
+
+this proton creates
+an electric field.
+
+And then, from the
+viewpoint of the electron,
+
+the electron is moving.
+
+And there is an electric field.
+
+But whenever you are moving
+inside an electric field,
+
+you also see a magnetic field
+generated by the motion,
+
+by relativistic effects.
+
+The magnetic field
+that you see is roughly
+
+given to first order in
+relativity by V cross E over c.
+
+So V cross E, VE
+V cross E over c
+
+up-- change sign
+because of this.
+
+And the magnetic
+field consistently,
+
+as we would expect,
+goes in this direction.
+
+So it's consistent
+with the picture
+
+that we developed that if you
+were the electron, the proton,
+
+would be going around
+in circles like that
+
+and the magnetic
+field would be up.
+
+Now here I can change the sign
+by doing E cross V over c.
+
+So this is the magnetic
+field seen by the electron.
+
+OK, so we need a little more
+work on that magnetic field
+
+by calculating the
+electric field.
+
+Now, what is the electric field?
+
+Well, the scalar potential
+for the hydrogen atom,
+
+we write it as minus
+e squared over r.
+
+It's actually not quite
+the scalar potential.
+
+But it is the potential energy.
+
+It has one factor of e more than
+what the scalar potential is.
+
+Remember, the scalar
+potential in electromagnetism
+
+is charge divided by r.
+
+So it has one factor of e more.
+
+What is the derivative
+of this potential?
+
+With respect to r, it's
+e squared over r squared.
+
+So the electric field goes
+like e over r squared.
+
+So the electric field is
+equal to dV dr divided by e.
+
+That's the magnitude
+of the electric field.
+
+And its direction is radial from
+the viewpoint of the proton.
+
+The electric field is here.
+
+So this can be written
+as r vector divided by r.
+
+Therefore, the magnetic field
+will-- [INAUDIBLE] this.
+
+The magnetic field
+now can be calculated.
+
+And we'll see what
+we claimed was
+
+the relation with
+angular momentum.
+
+Because B prime
+is now E cross V.
+
+So you have 1 over
+ec 1 over r dV dr.
+
+I've taken care of this.
+
+And now I just have
+r cross V. Well,
+
+r cross V is your angular
+momentum if you had p here.
+
+So we borrow a factor of
+the mass of the electron,
+
+ecm 1 over r dV dr
+L, L of the electron.
+
+p equals mv.
+
+So we have a nice formula
+for B. And then, we
+
+can go and calculate delta
+H. Delta H would then
+
+be minus mu dot B. And that
+would be ge over 2mc spin
+
+dot L-- mu was given here--
+S dot L 1 over r dV dr.
+
+And that is the split
+spin orbit interaction.
+
+Now, the downside
+of this derivation
+
+is that it has a
+relativistic error.
+
+There's a phenomenon
+called Thomas precession
+
+that affects this result.
+
+We didn't waste our time.
+
+The true result is that you
+must subtract from this g 1.
+
+So g must really be
+replaced by g minus 1.
+
+Since g is approximately
+2 for the electron,
+
+the true result is
+really 1/2 of this thing.
+
+So this should not
+be in parentheses,
+
+but true result is this.
+
+And the mistake that is done
+in calculating this spin orbit
+
+coupling is that this
+spin orbit coupling
+
+affects precession rates.
+
+All these interactions
+of magnetic dipoles
+
+with magnetic fields
+affect precession rates.
+
+And you have to be a
+little more careful here
+
+that the system where you've
+worked, the electron rest frame
+
+is not quite an inertial system.
+
+Because it's doing
+circular motion.
+
+So there's an extra correction
+that has to be done.
+
+Thomas precession or Thomas
+correction it's called.
+
+And it would be a
+detour of about one hour
+
+in special relativity
+to do it right.
+
+So Griffiths doesn't do it.
+
+I don't think Shankar does it.
+
+Pretty much graduate
+books do it.
+
+So we will not try to do better.
+
+I mentioned that
+fact that this really
+
+should be reduced to
+one half of its value.
+
+And it's an interesting
+system to analyze.
+
+So Thomas precession is
+that relativistic correction
+
+to precession rates when the
+object that is precessing
+
+is in an accelerated frame.
+
+And any rotating
+frame is accelerated.
+
+So this result needs correction.
+
+OK, but let's take this result
+as it is-- instead of g,
+
+g minus 1.
+
+Let's not worry
+too much about it.
+
+And let's just estimate
+how big this effect is.
+
+It's the last thing I want
+to do as a way of motivating
+
+this subject.
+
+So delta H is this.
+
+Let's estimate it.
+
+Now for estimates, a couple of
+things are useful to remember,
+
+that Bohr radius is h
+squared over me squared.
+
+We did that last time.
+
+And there's this constant
+that is very useful,
+
+the fine structure constant,
+which is e squared over hc.
+
+And it's about 1 over 137.
+
+And it helps you estimate
+all kinds of things.
+
+Because it's a rather
+complicated number to evaluate,
+
+you need all kinds of
+units and things like that.
+
+So the charge of the electron
+divided by hc being 1 over 137
+
+is quite nice.
+
+So let's estimate
+delta H. Well, g
+
+we won't worry-- 2,
+1, doesn't matter.
+
+e mc-- so far, that
+is kind of simple.
+
+Then we have S dot L. Well,
+how do I estimate S dot L?
+
+I don't do too much.
+
+S spin is multiples of h bar.
+
+L for an atomic state will be
+1, 2, 3, so multiples of h bar.
+
+So h bar squared,
+that's it for S dot L.
+
+1 over r is 1 over r.
+
+dV dr is e squared
+over r squared.
+
+And that's it.
+
+But here, instead of r, I
+should put the typical length
+
+of the hydrogen
+atom, which is a0.
+
+So what do I get?
+
+I'm sorry, I made
+a mistake here.
+
+AUDIENCE: Yeah, it's up there.
+
+PROFESSOR: Oh, I
+made a mistake here
+
+in that I didn't put
+this factor, 1 over ecm.
+
+So the e cancels.
+
+And this is the result
+here-- g over 2m
+
+squared c squared S dot L 1 over
+r dV dr. So let me start again.
+
+1 over m squared c squared h
+bar squared 1 over r dV dr--
+
+that much I got right.
+
+So this is roughly
+1 over [INAUDIBLE]
+
+of the electron
+squared c squared e
+
+squared over a0 cubed
+h squared-- still quite
+
+messy, but not that terrible.
+
+So in order to get an
+idea of how big this is,
+
+the ground state energy
+of the hydrogen atom
+
+was e squared over 2a0.
+
+So let's divide delta H over
+the ground state energy.
+
+And that's how much?
+
+Well, we have all this
+quantity, 1 over m
+
+squared c squared e
+squared a0 cubed h squared.
+
+And now, we must divide by
+e squared over a0 like this.
+
+Well, the e squareds cancel.
+
+And we get h squared over m
+squared c squared a0 squared.
+
+You need to know what a0 is.
+
+Let's just boil it down
+to the simplest thing,
+
+so h squared m
+squared c squared.
+
+a0 squared would be h to
+the fourth m squared e
+
+to the fourth.
+
+So this is actually e
+to the fourth over h
+
+squared c squared, or e squared
+over hc squared, which is alpha
+
+squared.
+
+Whew-- lots of work to
+get something very nice.
+
+The ratio of the spin orbit
+coupling to the ground state
+
+energy is 1 over alpha squared.
+
+It's alpha squared, which
+is 1 over 137 squared.
+
+So it's a pretty small thing.
+
+It's about 1 over 19,000.
+
+So when this is called fine
+structure of the hydrogen atom,
+
+it means that it's in
+the level in your page
+
+that you use a few inches
+to plot the 13.6 electron
+
+volts-- well, you're talking
+about 20,000 times smaller,
+
+something that you don't see.
+
+But of course, it's a
+pretty important thing.
+
+So all in all, in the
+conventions of-- this
+
+is done in Gaussian units.
+
+In SI units, which is
+what Griffiths uses,
+
+delta H is e squared over
+8 pi epsilon 0 1 over m
+
+squared c squared r cubed S
+dot L. That's for reference.
+
+This is Griffiths.
+
+But this is correct as well.
+
+This is the correct value.
+
+This is the correct
+value already taking
+
+into account the
+relativistic correction.
+
+So here, you're supposed
+to let g go to g minus 1.
+
+So you can put the 1 there,
+and it's pretty accurate.
+
+All right, so what is
+the physics question
+
+we want to answer with
+this spin orbit coupling?
+
+So here it comes.
+
+You have the hydrogen
+atom spectrum.
+
+And that spectrum you know.
+
+At L equals 0, you
+have one state here.
+
+Then, that's n
+equals 1, n equals 2.
+
+You have one state here and
+one state here at L equals 1.
+
+Then n equals 3, they start
+getting very close together.
+
+n equals 4 is like that.
+
+Let's consider if you want
+to have spin orbit coupling,
+
+we must have angular momentum.
+
+And that's L. And therefore,
+let's consider this state here.
+
+l equals 1, n equals 1--
+n equals 2, I'm sorry.
+
+What happens to those
+states, is the question.
+
+First, how many states
+do you have there
+
+and how should
+you think of them?
+
+Well actually, we know that
+an l equals 1 corresponds
+
+to three states.
+
+So you'd have lm
+with l equals 1.
+
+And then m can be
+1, 0, or minus 1.
+
+So you have three states.
+
+But there's not
+really three states.
+
+Because the electron
+can have spin.
+
+So here it is, a tensor product
+that appears in your face
+
+because there is
+more than angular
+
+momentum to the electron.
+
+There's spin.
+
+And it's a totally different
+vector space, the same particle
+
+but another vector
+space, the spin space.
+
+So here, you have the possible
+spins of the electron.
+
+So that's another
+angular momentum.
+
+And well, you could have the
+plus/minus states, for example.
+
+So you have three states
+here and two states here.
+
+So this is really six
+states, so six states
+
+whose fate we would
+like to understand
+
+due to this spin orbit coupling.
+
+So to use the language
+of angular momentum,
+
+instead of writing
+plus/minus, you
+
+could write Smz, if you will--
+ms I will call, spin of s.
+
+You have here spin of 1/2
+and states 1/2 or minus 1/2.
+
+This is the up.
+
+When the z component of the spin
+that we always call m-- m now
+
+corresponds to the z
+component of angular momentum.
+
+So in general, even
+for spin, we use m.
+
+And we have that our two
+spin states of the electron
+
+are spin 1/2 particle with
+plus spin in the z direction,
+
+spin 1/2 particle with minus
+spin in the z direction.
+
+We usually never
+put this 1/2 here.
+
+But now you have here
+really three states--
+
+1, 1, 1, 0, 1, minus 1,
+the first telling you
+
+about the total
+angular momentum.
+
+Here, the total spin is 1/2.
+
+But it happens to be
+either up or down.
+
+Here, the total
+angular momentum is 1.
+
+But it happens to be plus
+1, 0, or minus 1 here.
+
+So these are our six states.
+
+You can combine this with this,
+this with that, this with this,
+
+this with that.
+
+You make all the products.
+
+And these are the six
+states of the hydrogen
+
+atom at this level.
+
+And we wish to know
+what happens to them.
+
+Now, this correction is small.
+
+So it fits our understanding
+of the perturbation theory
+
+of Feynman-Hellman
+in which we try
+
+to find the corrections
+to these things.
+
+Our difficulty now is a
+little serious, however.
+
+It's the fact that
+Feynman-Hellman
+
+assumed that you had a state.
+
+And it was an eigenstate of
+the corrected Hamiltonian
+
+as you moved along.
+
+And then, you could compute
+how its energy changes.
+
+Here, unfortunately, we have a
+much more difficult situation.
+
+These six states that
+I'm not listing yet,
+
+but I will list very soon,
+are not obviously eigenstates
+
+of delta H. In fact, they are
+not eigenstates of delta H.
+
+They're degenerate states,
+six degenerate states,
+
+that are not eigenstates
+of delta H. Therefore,
+
+I cannot use the Feynman-Hellman
+theorem until I find what are
+
+the combinations that
+are eigenstates of this
+
+perturbation.
+
+So we are a little
+bit in trouble.
+
+Because we have a perturbation
+for which these product
+
+states-- we call them uncoupled
+bases-- are not eigenstates.
+
+Now, we've written this
+operator a little naively.
+
+What does this operator
+really mean, S dot L?
+
+In our tensor products,
+it means S1 tensor L1.
+
+Actually, I'll use
+L dot S. I'll always
+
+put the L information first and
+the S information afterward.
+
+So L dot S is clearly
+an operator that
+
+must be thought to act
+on the tensor product.
+
+Because both have to act.
+
+S has to act and L has to act.
+
+So it only lives in
+the tensor product.
+
+So what does it mean?
+
+It means this-- S2 L2 plus S3
+L3, or sum over i Si tensor Li.
+
+So this is the kind of thing
+that you need to understand--
+
+how do you find for this
+operator's eigenstates here?
+
+So that is our difficulty.
+
+And that's what
+we have to solve.
+
+We're going to solve it
+in the next half hour.
+
+So it's a complicated operator,
+L dot S. But on the other hand,
+
+we have to use our ideas
+that we've learned already
+
+about summing angular momenta.
+
+What if I define
+J to be L plus S,
+
+which really means L
+tensor 1 plus 1 tensor S?
+
+So this is what I really
+mean by this operator.
+
+J, as we've demonstrated,
+will be an angular momentum,
+
+because this satisfies the
+algebra of angular momentum
+
+and this satisfies the
+algebra of angular momentum.
+
+So this thing satisfies the
+algebra of angular momentum.
+
+And why do we look at that term?
+
+Because of the following reason.
+
+We can square it-- JiJi.
+
+Now we would have to
+square this thing.
+
+How do you square this thing?
+
+Well, there's two ways.
+
+Naively-- L squared
+plus L squared plus 2L
+
+dot S-- basically correct.
+
+But you can do it a
+little more slowly.
+
+If you square this term,
+you get L squared tensor 1.
+
+If you square this term,
+you get 1 tensor S squared.
+
+But when you do
+the mixed products,
+
+you just must take the
+i's here and the i's here
+
+and multiply them.
+
+So actually, you do get two i's,
+the sum over i Li tensor Si.
+
+This is sum over i.
+
+This is J squared.
+
+So basically, what I'm saying
+is that J squared naively
+
+is L squared plus S squared
+plus our interaction
+
+2L dot S defined property.
+
+So L dot S is equal to 1/2
+of J squared minus L squared
+
+minus S squared.
+
+And that tells you all kinds of
+interesting things about L dot
+
+S.
+
+Basically, we can trade
+L dot S for J squared,
+
+L squared, and S squared.
+
+L squared is very
+simple, and S squared
+
+is extremely simple as well.
+
+Remember, L squared
+commutes with any Li.
+
+So L squared with
+any Li is equal to 0.
+
+S squared with any
+Si is equal to 0.
+
+And Li's and Si's commute.
+
+They live in different worlds.
+
+So L squared and Si's commute.
+
+S squareds and Li's commute.
+
+These things are
+pretty nice and simple.
+
+So let's think now
+of our Hamiltonian
+
+and what is happening to it.
+
+Whenever we had
+the hydrogen atom,
+
+we had a set of commuting
+observables H, L squared,
+
+and Lz.
+
+It's a complete set of
+commuting observables.
+
+Now, in the hydrogen
+atom, you could add to it
+
+S squared and Sz.
+
+We didn't talk about
+spin at the beginning,
+
+because we just considered
+a particle going
+
+around the hydrogen atom.
+
+But if you have spin, the
+hydrogen atom Hamiltonian,
+
+the original one, doesn't
+involve spin in any way.
+
+So certainly, Hamiltonian
+commutes with spin,
+
+with spin z.
+
+L and S don't talk, so
+this is the complete set
+
+of commuting observables.
+
+But what happens to this list?
+
+This is our problem for
+H0, the hydrogen atom,
+
+plus delta H that
+has the S dot L.
+
+Well, what are complete set
+of commuting observables?
+
+This is a very
+important question.
+
+Because this is
+what tells you how
+
+you're going to try to
+organize the spectrum.
+
+So we could have H,
+the total, H total.
+
+And what else?
+
+Well, can I still
+have L squared here?
+
+Can I include L squared and say
+it commutes with the total H?
+
+A little worrisome,
+but actually,
+
+you know that L squared commutes
+with the original Hamiltonian.
+
+Now, the question is
+whether L squared commutes
+
+with this extra piece.
+
+Well, but L squared
+commutes with any Li.
+
+And it doesn't even talk
+to S. So L squared is safe.
+
+L squared we can keep.
+
+OK, S squared-- can
+we keep S squared?
+
+Well, S squared was here.
+
+So it commuted with the
+Hamiltonian, and that was good.
+
+S squared commutes with any
+Si, and it doesn't talk to L.
+
+So S squared can stay.
+
+But that's not good enough.
+
+We won't be able to solve
+the problem with this still.
+
+We need more.
+
+How about Lz?
+
+It was here, so
+let's try our luck.
+
+Any opinions on Lz--
+can we keep it or not?
+
+Yes.
+
+AUDIENCE: I don't think so.
+
+Because in the J term, we
+have Lx's and Ly's, which
+
+don't commute with Lz.
+
+PROFESSOR: Right,
+it can't be kept.
+
+Here, this term has SxLx
+plus SyLy plus SzLz.
+
+And Lz doesn't
+commute with this one.
+
+So no, you can't
+keep Lz-- no good.
+
+On the other hand, let's
+think about J squared.
+
+J squared is here.
+
+And J squared commutes with
+L squared and with S squared.
+
+J squared, therefore, is--
+well, let me say it this way.
+
+Here is L dot S, which
+is our extra interaction.
+
+Here we have this thing.
+
+I would like to say
+on behalf of J squared
+
+that we can include
+it here, J squared,
+
+because J squared is
+really pretty much the same
+
+as L dot S up to this L
+squared and S squared.
+
+But J squared commutes with
+L squared and S squared.
+
+I should probably
+write it there.
+
+J squared commutes
+with L squared.
+
+And J squared communicates with
+S squared that we have here.
+
+And moreover, we have over
+here that J squared therefore
+
+will commute, or it's
+pretty much the same,
+
+as L dot S. J squared
+with L dot S would
+
+be J squared times
+this thing, which is 0.
+
+So J squared commutes
+with this term.
+
+And it commutes with
+the Hamiltonian,
+
+your original
+hydrogen Hamiltonian.
+
+So J squared can be added here.
+
+J square is a good
+operator to have.
+
+And now we can get one more
+kind of free from here.
+
+It's Jz.
+
+Z
+
+Because Jz commutes
+with J squared.
+
+Jz commutes with these things.
+
+And Jz, which is a symmetry
+of the original Hamiltonian,
+
+also commutes with our new
+interaction, the L dot S,
+
+which is proportional
+to J squared.
+
+So you have to go
+through this yourselves
+
+probably even a little
+more slowly than I've gone.
+
+Just check that
+everything that I'm
+
+saying about whatever
+commutes commutes.
+
+So for example, when I say
+that J squared commutes
+
+with L dot S, it's
+because I can put
+
+instead of L dot S all of this.
+
+And go slowly through this.
+
+So this is actually the complete
+set of committing observables.
+
+And it's basically
+saying to us, try
+
+to diagonalize this thing
+with total angular momentum.
+
+So it's about time
+to really do it.
+
+We haven't done it yet.
+
+But now the part that
+we have to do now,
+
+it's kind of a nice exercise.
+
+And it's fun.
+
+Now, there's one problem
+in the homework set
+
+that sort of uses
+this kind of thing.
+
+And I will suggest there to
+Will and Aram that tomorrow,
+
+they spend some time discussing
+it and helping you with it.
+
+The last problem
+in the homework set
+
+would've been better if you
+had a little more time for it
+
+and you had more time to
+digest what I'm doing today.
+
+But nevertheless,
+go to recitation,
+
+learn more about the problem.
+
+It will not be all
+that difficult.
+
+OK, so we're trying
+now to finally form
+
+another basis of states.
+
+We had these six states.
+
+And we're going to
+try to organize them
+
+in a better way-- as eigenstates
+of the total angular momentum L
+
+plus S. So I'm going to
+write them here in this way.
+
+Here is one of the
+states of this L equals
+
+1 electron, the 1, 1
+coupled to the 1/2, 1/2.
+
+Here are two more states- 1, 0,
+1/2, 1/2, 1, 1, 1/2, minus 1/2,
+
+so the 1, 0 with the top,
+the 1, 1 with the bottom.
+
+Here are two more
+states-- 1, 0 with 1/2,
+
+minus 1/2 and 1,
+minus 1 with 1/2, 1/2.
+
+And here is the last state--
+1, minus 1 with 1/2, minus 1.
+
+These are our six states.
+
+And I've organized them
+in a nice way actually.
+
+I've organized
+them in such a way
+
+that you can read what is
+the value of Jz over h bar.
+
+Remember, Jz is 1
+over h bar Lz plus Sz.
+
+So what is it?
+
+These are, I claim,
+eigenstates of Jz.
+
+Why?
+
+Because let's act on them.
+
+Suppose I act with
+Jz on this state.
+
+The Lz comes here and says, 1.
+
+The Sz comes here and says, 1/2.
+
+So the sum of them give you
+Jz over h bar equal to 3/2.
+
+And that's why I organized
+these states in such a way
+
+that these second things add up
+to the same value-- 0 and 1/2,
+
+1 and minus 1/2.
+
+So if you act with
+Jz on this state,
+
+it's an eigenstate with Jz.
+
+Here, 0 contribution, here 1/2.
+
+So this is with plus 1/2.
+
+Here, you have 0 and minus 1/2,
+minus 1, and that is minus 1/2.
+
+And here you have minus 3/2.
+
+OK, questions.
+
+We've written the states.
+
+And I'm evaluating the total z
+component of angular momentum.
+
+And these two states
+are like that.
+
+So what does our theorem
+guarantee for us?
+
+Our theorem guarantees that we
+have-- in this tensor product,
+
+there is an algebra of angular
+momentum of the Jz operators.
+
+And the states have to
+fall into representations
+
+of those operators.
+
+So you must have angular
+momentum multiplets.
+
+So at this moment,
+you can figure out
+
+what angular momentum you're
+going to get for the result.
+
+Here we obtained a
+maximum Jz of 3/2.
+
+So we must get a J
+equals 3/2 multiplet.
+
+Because a J equaling
+3/2 multiplets
+
+has Jz 3/2, 1/2,
+minus 1/2, and 0.
+
+So actually, this state must be
+the top state of the multiplet.
+
+This state must be the bottom
+state of the multiplet.
+
+I don't know which one is the
+middle state of the multiplet
+
+and which one is here.
+
+But we have four states
+here, four states.
+
+So one linear combination
+of these two states
+
+must be, then, that Jz equals
+1/2 state of the multiplet.
+
+And one inner combination
+of these two states
+
+must be that Jz equals minus
+1/2 state of the multiplet.
+
+Which one is it?
+
+I don't know.
+
+But we can figure it out.
+
+We'll figure it out in a second.
+
+Once you get this
+J 3/2 multiplet,
+
+there will be one linear
+combination here left over
+
+and one linear combination
+here left over.
+
+Those are two state, one with
+Jz plus 1/2 and one with Jz
+
+equals minus 1/2.
+
+So you also get a J
+equals 1/2 multiplet.
+
+So the whole tensor
+product of six
+
+states-- it was the
+tensor product of a spin 1
+
+with a spin 1/2.
+
+So we write it like this.
+
+The tensor product of a
+spin 1 with a spin 1/2
+
+will give you a total
+spin 3/2 plus total spin
+
+1/2-- funny formula.
+
+Here is the tensor
+product, the tensor
+
+product of these three
+states with these two states.
+
+This can be written as 3
+times 2 is equal to 4 plus 2
+
+in terms of number of states.
+
+The tensor product of
+this spin 1 and spin 1/2
+
+gives you a spin 3/2
+multiplet with four states
+
+and a spin 1/2 multiplet
+with two states.
+
+So how do you calculate what
+are the states themselves?
+
+So the states themselves
+are the following.
+
+All right, here I have them.
+
+I claim that the J
+equals 3/2 states,
+
+m equals 3/2 states, the
+top state of that multiplet
+
+can only be the state here,
+the 1, 1 tensor 1/2, 1/2.
+
+And there's no way any other
+state can be put on the right.
+
+Because there's no other
+state with total z component
+
+of angular momentum equals 3/2.
+
+So that must be the state.
+
+Similarly, the J
+equals 3/2, m equals
+
+minus 3/2 state must be the
+bottom one-- 1, minus 1, 1/2,
+
+minus 1/2.
+
+The one that we
+wish to figure out
+
+is the next state here, which is
+the J equals 3/2, m equals 1/2.
+
+It's a linear
+combination of these two.
+
+But which one?
+
+That is kind of the last
+thing we want to do.
+
+Because it will pretty much
+solve the rest of the problem.
+
+So how do we solve for this?
+
+Well, we had this
+basic relation that we
+
+know how to lower or raise
+states of angular momentum--
+
+m times m plus/minus 1 J--
+I should have written it
+
+J plus/minus Jm equals
+h bar square root.
+
+More space for everybody
+to see this-- J times
+
+J plus 1 minus m
+times m plus/minus 1.
+
+Close the square
+root-- Jm plus/minus 1.
+
+So what I should try to
+do is lower this state,
+
+try to find this state
+by acting with J minus.
+
+So let me try to
+lower the state, so
+
+J minus on this state, on
+J equals 3/2, m equals 3/2.
+
+I can go to that formula and
+write it as h bar square root.
+
+J is 3/2, so 3/2 times
+5/2 minus m, which is 3/2,
+
+times m minus 1, 1/2.
+
+We're doing the minus--
+times the state 3/2, 1/2.
+
+So the state we want is here.
+
+And it's obtained by
+doing J minus on that.
+
+But we want the number here.
+
+So that's why I did
+all these square roots.
+
+And that just gives h bar
+square root of 3, 3/2, 1/2.
+
+Well, that still doesn't
+calculate it for me.
+
+But it comes very close.
+
+So you have it there.
+
+Now I want to do this but
+using the right hand side.
+
+So look at the right hand side.
+
+We want to do J minus, but
+on 1, 1 tensor 1/2, 1/2.
+
+So I applied J minus
+to the left hand side.
+
+Now we have to apply J minus
+to the right hand side.
+
+But J minus is L minus plus S
+minus on 1, 1 tensor 1/2, 1/2.
+
+When this acts, it
+acts on the first.
+
+So you get L minus on
+1, 1 tensor 1/2, 1/2.
+
+And in the second term,
+you get plus 1, 1 tensor S
+
+minus on 1/2, 1/2.
+
+Now, what is L minus on 1, 1?
+
+You can use the same formula.
+
+It's 1, 1.
+
+And it's an angular momentum.
+
+So it just goes on and
+gives you h bar square
+
+root of 1 times 2
+minus 1 times 0.
+
+1, 0-- it lowers
+it-- times 1/2, 1/2.
+
+Let me go here-- plus 1, 1.
+
+And what is S minus on this?
+
+Use the formula
+with J equals 1/2.
+
+So this is h bar square root of
+1/2 times 3/2 minus 1/2 times
+
+minus 1/2 times 1/2 minus 1/2.
+
+Whew-- well not too difficult.
+
+But this gives you h over square
+root of 2, 1, 0 tensor 1/2,
+
+1/2 plus just h bar.
+
+This whole thing is 1-- 1,
+1 tensor 1/2, minus 1/2.
+
+OK, stop a second to
+see what's happened.
+
+We had this equality.
+
+And we acted with J minus.
+
+Acting on the left,
+it gives us a number
+
+times the state we want.
+
+Acting on the
+right, we got this.
+
+So actually, equating this
+to that, or left hand side
+
+to right hand side, we finally
+found the state 3/2, 1/2.
+
+So the state 3/2,
+1/2 is as follows.
+
+3/2, 1/2 is-- you must
+divide by that square root.
+
+So you get the square
+root of 3 down.
+
+The h bars cancel.
+
+So here it is, a very nice
+little formula-- 2 over 3,
+
+1, 0 tensor 1/2, 1/2 plus
+1 over square root of 3,
+
+1, 1 tensor 1/2, minus 1/2.
+
+So we have the top
+state of the multiplet.
+
+We have the next state
+of the multiplet.
+
+We have-- I'm sorry, the
+top state of the multiplet
+
+was this.
+
+You have the bottom
+state of the multiplet,
+
+the middle state
+of the multiplet.
+
+What you're missing is the
+bottom and the middle term.
+
+And this one can be
+obtained in many ways.
+
+One way would be to
+raise this state.
+
+The minus 3/2 could
+be raised by one unit
+
+and do exactly the same thing.
+
+Well, the result is square root
+of 2 over 3, 1, 0 tensor 1/2,
+
+minus 1/2 plus 1 over
+square root of 3.
+
+That square root of 2
+doesn't look right to me now.
+
+I must have copied it wrong.
+
+It's 1 over square root of
+3-- 1 over square root of 3,
+
+1, minus 1 tensor 1/2, 1/2.
+
+So you've built that
+whole multiplet.
+
+And this state, as we said,
+was a linear combination
+
+of the two possible states.
+
+This 3 minus 1/2 was
+a linear combination
+
+of these two possible states.
+
+So the other states
+that are left over,
+
+the other linear
+combinations, form
+
+the J equals 1/2 multiplet.
+
+So basically, every state must
+be orthogonal to each other.
+
+So the other state, the 1/2, 1/2
+and the 1/2, minus 1/2 of the J
+
+equals 1/2 multiplet must
+be this orthogonal to this.
+
+And this must be
+orthogonal to that.
+
+So those formulas are easily
+found by orthogonality.
+
+So I'll conclude by
+writing them-- minus 1
+
+over square root of
+3, 1, 0, 1/2, 1/2
+
+plus the square root of 2
+over 3, 1, 1, 1/2, minus 1/2.
+
+And here, you get 1 over
+square root of 3, 1, 0, 1/2,
+
+minus 1/2 minus 2 over
+square root of 3, 1, minus 1
+
+tensor 1/2, 1/2.
+
+So lots of terms, a little
+hard to read-- I apologize.
+
+Now, the punchline here is
+that you've found these states.
+
+And the claim is
+that these are states
+
+in which L dot S is diagonal.
+
+And it's kind of obvious
+that that should be the case.
+
+Because what was L dot S?
+
+So one last formula--
+L dot S equals
+
+1/2 of J squared minus L
+squared minus S squared.
+
+Now, in terms of
+eigenvalues, this
+
+is 1/2 h squared J times
+J plus 1 minus L times L
+
+plus 1 minus S times S plus 1.
+
+Now, all the states
+that we built
+
+have definite
+values of J squared,
+
+definite values of S squared.
+
+Because L was 1.
+
+And S is 1/2.
+
+So here you go h squared over 2
+J times J plus 1 minus 1 times
+
+2 is 2 minus 1/2
+times 3/2 is 3/4.
+
+And that's the whole story.
+
+The whole story in a sense
+has been summarized by this.
+
+We have four states
+with J equals 3/2
+
+and two states
+with J equals 1/2.
+
+So these six states
+that you have here--
+
+split because of
+this interaction
+
+into four states that have
+J equal to 3/2 and two
+
+states that have J equal to 1/2.
+
+And you plug the numbers here.
+
+And that gives you the
+amount of splitting.
+
+So actually, this height
+that this goes up here
+
+is h squared over 2.
+
+And this is minus h
+squared by the time you
+
+put the numbers J, 3/2, and 1/2.
+
+So all our work was because
+the Hamiltonian at the end
+
+was simple in J squared.
+
+And therefore, we
+needed J multiplets.
+
+J multiplets are the addition
+of angular momentum multiplets.
+
+In a sense, we don't have
+to construct these things
+
+if you don't want to calculate
+very explicit details.
+
+Once you have that,
+you have everything.
+
+This product of angular
+momentum 1, angular momentum 1/2
+
+gave you total
+angular momentum 3/2
+
+and 1/2-- four
+states, two states.
+
+So four states split one way,
+two states split the other way,
+
+and that's the end of the story.
+
+So more of this in recitation
+and more of this all
+
+of next week.
+
+We'll see you then.
\ No newline at end of file
diff --git a/ZyDUHHfPBZI.txt b/ZyDUHHfPBZI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..87dc5f141cbfaf82c2d0ce5a13bddc67a92f724a
--- /dev/null
+++ b/ZyDUHHfPBZI.txt
@@ -0,0 +1,7835 @@
+align:start position:0%
+ 
+all right this is what we were talking
+
+ align:start position:0%
+all right this is what we were talking
+ 
+
+ align:start position:0%
+all right this is what we were talking
+about last time and we're going to
+
+ align:start position:0%
+about last time and we're going to
+ 
+
+ align:start position:0%
+about last time and we're going to
+continue today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the recurring goals that people trying
+
+ align:start position:0%
+the recurring goals that people trying
+ 
+
+ align:start position:0%
+the recurring goals that people trying
+to relate brain and behavior have
+
+ align:start position:0%
+to relate brain and behavior have
+ 
+
+ align:start position:0%
+to relate brain and behavior have
+pursued
+
+ align:start position:0%
+pursued
+ 
+
+ align:start position:0%
+pursued
+we talked last time mainly about the
+
+ align:start position:0%
+we talked last time mainly about the
+ 
+
+ align:start position:0%
+we talked last time mainly about the
+first one specific neural circuits which
+
+ align:start position:0%
+first one specific neural circuits which
+ 
+
+ align:start position:0%
+first one specific neural circuits which
+underlie behavior
+
+ align:start position:0%
+underlie behavior
+ 
+
+ align:start position:0%
+underlie behavior
+another prime example was
+
+ align:start position:0%
+another prime example was
+ 
+
+ align:start position:0%
+another prime example was
+the concept and discovery of the reflex
+
+ align:start position:0%
+the concept and discovery of the reflex
+ 
+
+ align:start position:0%
+the concept and discovery of the reflex
+arc
+
+ align:start position:0%
+arc
+ 
+
+ align:start position:0%
+arc
+which led to the
+
+ align:start position:0%
+which led to the
+ 
+
+ align:start position:0%
+which led to the
+philosophy of life called reflexology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mentioned that many even the discovery
+
+ align:start position:0%
+i mentioned that many even the discovery
+ 
+
+ align:start position:0%
+i mentioned that many even the discovery
+of reflexes was probably inspired by
+
+ align:start position:0%
+of reflexes was probably inspired by
+ 
+
+ align:start position:0%
+of reflexes was probably inspired by
+human machines
+
+ align:start position:0%
+human machines
+ 
+
+ align:start position:0%
+human machines
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+theory in this field has been influenced
+
+ align:start position:0%
+theory in this field has been influenced
+ 
+
+ align:start position:0%
+theory in this field has been influenced
+by machines for a long time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example when homeostatic governors
+
+ align:start position:0%
+for example when homeostatic governors
+ 
+
+ align:start position:0%
+for example when homeostatic governors
+were developed
+
+ align:start position:0%
+were developed
+ 
+
+ align:start position:0%
+were developed
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it seemed like machines were showing
+
+ align:start position:0%
+it seemed like machines were showing
+ 
+
+ align:start position:0%
+it seemed like machines were showing
+purpose of behavior and that actually
+
+ align:start position:0%
+purpose of behavior and that actually
+ 
+
+ align:start position:0%
+purpose of behavior and that actually
+was a big surprise to many people at
+
+ align:start position:0%
+was a big surprise to many people at
+ 
+
+ align:start position:0%
+was a big surprise to many people at
+that time
+
+ align:start position:0%
+that time
+ 
+
+ align:start position:0%
+that time
+they didn't think a machine could
+
+ align:start position:0%
+they didn't think a machine could
+ 
+
+ align:start position:0%
+they didn't think a machine could
+possibly show purpose and behavior but
+
+ align:start position:0%
+possibly show purpose and behavior but
+ 
+
+ align:start position:0%
+possibly show purpose and behavior but
+of course
+
+ align:start position:0%
+of course
+ 
+
+ align:start position:0%
+of course
+homeostatic governors and servo
+
+ align:start position:0%
+homeostatic governors and servo
+ 
+
+ align:start position:0%
+homeostatic governors and servo
+mechanisms
+
+ align:start position:0%
+mechanisms
+ 
+
+ align:start position:0%
+mechanisms
+and homing devices
+
+ align:start position:0%
+and homing devices
+ 
+
+ align:start position:0%
+and homing devices
+which you're all very familiar with
+
+ align:start position:0%
+which you're all very familiar with
+ 
+
+ align:start position:0%
+which you're all very familiar with
+because you grew up with them but it
+
+ align:start position:0%
+because you grew up with them but it
+ 
+
+ align:start position:0%
+because you grew up with them but it
+wasn't always so obvious to people that
+
+ align:start position:0%
+wasn't always so obvious to people that
+ 
+
+ align:start position:0%
+wasn't always so obvious to people that
+these machines could show purposive
+
+ align:start position:0%
+these machines could show purposive
+ 
+
+ align:start position:0%
+these machines could show purposive
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+homeostatic governors are still a model
+
+ align:start position:0%
+homeostatic governors are still a model
+ 
+
+ align:start position:0%
+homeostatic governors are still a model
+for homeostatic control of visceral
+
+ align:start position:0%
+for homeostatic control of visceral
+ 
+
+ align:start position:0%
+for homeostatic control of visceral
+states physiologists
+
+ align:start position:0%
+states physiologists
+ 
+
+ align:start position:0%
+states physiologists
+now of course the major machine that
+
+ align:start position:0%
+now of course the major machine that
+ 
+
+ align:start position:0%
+now of course the major machine that
+serves as an inspiration to models
+
+ align:start position:0%
+serves as an inspiration to models
+ 
+
+ align:start position:0%
+serves as an inspiration to models
+the computer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll see that as we
+
+ align:start position:0%
+you'll see that as we
+ 
+
+ align:start position:0%
+you'll see that as we
+come to some simple models for
+
+ align:start position:0%
+come to some simple models for
+ 
+
+ align:start position:0%
+come to some simple models for
+explaining behavior in this class
+
+ align:start position:0%
+explaining behavior in this class
+ 
+
+ align:start position:0%
+explaining behavior in this class
+flow diagrams information flow diagrams
+
+ align:start position:0%
+flow diagrams information flow diagrams
+ 
+
+ align:start position:0%
+flow diagrams information flow diagrams
+are similar to what engineers use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now i mentioned descartes and
+
+ align:start position:0%
+okay now i mentioned descartes and
+ 
+
+ align:start position:0%
+okay now i mentioned descartes and
+showed his picture
+
+ align:start position:0%
+showed his picture
+ 
+
+ align:start position:0%
+showed his picture
+i didn't read anything from him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i won't read you the whole quote but the
+
+ align:start position:0%
+i won't read you the whole quote but the
+ 
+
+ align:start position:0%
+i won't read you the whole quote but the
+he talks about these as
+
+ align:start position:0%
+he talks about these as
+ 
+
+ align:start position:0%
+he talks about these as
+little filaments in tubes connected to
+
+ align:start position:0%
+little filaments in tubes connected to
+ 
+
+ align:start position:0%
+little filaments in tubes connected to
+tubes
+
+ align:start position:0%
+tubes
+ 
+
+ align:start position:0%
+tubes
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he ends with an analogy after he
+
+ align:start position:0%
+he ends with an analogy after he
+ 
+
+ align:start position:0%
+he ends with an analogy after he
+describes the circuit which as you know
+
+ align:start position:0%
+describes the circuit which as you know
+ 
+
+ align:start position:0%
+describes the circuit which as you know
+wasn't completely accurate anatomically
+
+ align:start position:0%
+wasn't completely accurate anatomically
+ 
+
+ align:start position:0%
+wasn't completely accurate anatomically
+but his concept of the reflex was
+
+ align:start position:0%
+but his concept of the reflex was
+ 
+
+ align:start position:0%
+but his concept of the reflex was
+accurate
+
+ align:start position:0%
+accurate
+ 
+
+ align:start position:0%
+accurate
+he said
+
+ align:start position:0%
+he said
+ 
+
+ align:start position:0%
+he said
+this happens just as by pulling one end
+
+ align:start position:0%
+this happens just as by pulling one end
+ 
+
+ align:start position:0%
+this happens just as by pulling one end
+of the cord
+
+ align:start position:0%
+of the cord
+ 
+
+ align:start position:0%
+of the cord
+one of the ends of the cord you cause a
+
+ align:start position:0%
+one of the ends of the cord you cause a
+ 
+
+ align:start position:0%
+one of the ends of the cord you cause a
+bell attached to the other end to ring
+
+ align:start position:0%
+bell attached to the other end to ring
+ 
+
+ align:start position:0%
+bell attached to the other end to ring
+at the same time
+
+ align:start position:0%
+at the same time
+ 
+
+ align:start position:0%
+at the same time
+so that's the basic idea of a reflex a
+
+ align:start position:0%
+so that's the basic idea of a reflex a
+ 
+
+ align:start position:0%
+so that's the basic idea of a reflex a
+simple stimulus leads in inevitably to a
+
+ align:start position:0%
+simple stimulus leads in inevitably to a
+ 
+
+ align:start position:0%
+simple stimulus leads in inevitably to a
+certain response and it's a fixed
+
+ align:start position:0%
+certain response and it's a fixed
+ 
+
+ align:start position:0%
+certain response and it's a fixed
+relationship
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it didn't say anything about the anatomy
+
+ align:start position:0%
+it didn't say anything about the anatomy
+ 
+
+ align:start position:0%
+it didn't say anything about the anatomy
+and the beginnings of understanding the
+
+ align:start position:0%
+and the beginnings of understanding the
+ 
+
+ align:start position:0%
+and the beginnings of understanding the
+anatomy of reflex was the discovery of
+
+ align:start position:0%
+anatomy of reflex was the discovery of
+ 
+
+ align:start position:0%
+anatomy of reflex was the discovery of
+the law of roots
+
+ align:start position:0%
+the law of roots
+ 
+
+ align:start position:0%
+the law of roots
+somebody asked me at the end of the
+
+ align:start position:0%
+somebody asked me at the end of the
+ 
+
+ align:start position:0%
+somebody asked me at the end of the
+class what exactly is the law of roots
+
+ align:start position:0%
+class what exactly is the law of roots
+ 
+
+ align:start position:0%
+class what exactly is the law of roots
+how can you remember that
+
+ align:start position:0%
+how can you remember that
+ 
+
+ align:start position:0%
+how can you remember that
+every spinal nerve as it approaches the
+
+ align:start position:0%
+every spinal nerve as it approaches the
+ 
+
+ align:start position:0%
+every spinal nerve as it approaches the
+cord separates into two major divisions
+
+ align:start position:0%
+cord separates into two major divisions
+ 
+
+ align:start position:0%
+cord separates into two major divisions
+one entering the cord dorsally
+
+ align:start position:0%
+one entering the cord dorsally
+ 
+
+ align:start position:0%
+one entering the cord dorsally
+and the other ventrally
+
+ align:start position:0%
+and the other ventrally
+ 
+
+ align:start position:0%
+and the other ventrally
+okay the dorsal root
+
+ align:start position:0%
+okay the dorsal root
+ 
+
+ align:start position:0%
+okay the dorsal root
+is sensory the ventral root is motor
+
+ align:start position:0%
+is sensory the ventral root is motor
+ 
+
+ align:start position:0%
+is sensory the ventral root is motor
+input dorsally output ventrally how can
+
+ align:start position:0%
+input dorsally output ventrally how can
+ 
+
+ align:start position:0%
+input dorsally output ventrally how can
+you remember that think of a pain in the
+
+ align:start position:0%
+you remember that think of a pain in the
+ 
+
+ align:start position:0%
+you remember that think of a pain in the
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+the pain is towards the back this is
+
+ align:start position:0%
+the pain is towards the back this is
+ 
+
+ align:start position:0%
+the pain is towards the back this is
+dorsal okay this is ventral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pain in the back summarizes what the law
+
+ align:start position:0%
+pain in the back summarizes what the law
+ 
+
+ align:start position:0%
+pain in the back summarizes what the law
+of roots is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these were the people that
+
+ align:start position:0%
+and these were the people that
+ 
+
+ align:start position:0%
+and these were the people that
+first discovered it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then i talked a little bit about
+
+ align:start position:0%
+then i talked a little bit about
+ 
+
+ align:start position:0%
+then i talked a little bit about
+reflexology and how it originated with
+
+ align:start position:0%
+reflexology and how it originated with
+ 
+
+ align:start position:0%
+reflexology and how it originated with
+people reading the writings of sechinoff
+
+ align:start position:0%
+people reading the writings of sechinoff
+ 
+
+ align:start position:0%
+people reading the writings of sechinoff
+ivan sechenov
+
+ align:start position:0%
+ivan sechenov
+ 
+
+ align:start position:0%
+ivan sechenov
+in russia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now before that let me describe them a
+
+ align:start position:0%
+now before that let me describe them a
+ 
+
+ align:start position:0%
+now before that let me describe them a
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+what was
+
+ align:start position:0%
+what was
+ 
+
+ align:start position:0%
+what was
+what did i say that
+
+ align:start position:0%
+what did i say that
+ 
+
+ align:start position:0%
+what did i say that
+llama tree's concept of the uniqueness
+
+ align:start position:0%
+llama tree's concept of the uniqueness
+ 
+
+ align:start position:0%
+llama tree's concept of the uniqueness
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the human laws
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right differ from other animals simply
+
+ align:start position:0%
+right differ from other animals simply
+ 
+
+ align:start position:0%
+right differ from other animals simply
+in the complexity of the reflexes
+
+ align:start position:0%
+in the complexity of the reflexes
+ 
+
+ align:start position:0%
+in the complexity of the reflexes
+underlying his behavior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he's well known for a phrase
+
+ align:start position:0%
+he's well known for a phrase
+ 
+
+ align:start position:0%
+he's well known for a phrase
+that is in the following quote
+
+ align:start position:0%
+that is in the following quote
+ 
+
+ align:start position:0%
+that is in the following quote
+let me just read you
+
+ align:start position:0%
+let me just read you
+ 
+
+ align:start position:0%
+let me just read you
+one sentence from a tree translated of
+
+ align:start position:0%
+one sentence from a tree translated of
+ 
+
+ align:start position:0%
+one sentence from a tree translated of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+since all the faculties of the soul
+
+ align:start position:0%
+since all the faculties of the soul
+ 
+
+ align:start position:0%
+since all the faculties of the soul
+depend with such a degree on the proper
+
+ align:start position:0%
+depend with such a degree on the proper
+ 
+
+ align:start position:0%
+depend with such a degree on the proper
+organization of the brain
+
+ align:start position:0%
+organization of the brain
+ 
+
+ align:start position:0%
+organization of the brain
+and of the whole body
+
+ align:start position:0%
+and of the whole body
+ 
+
+ align:start position:0%
+and of the whole body
+that apparently they are but this
+
+ align:start position:0%
+that apparently they are but this
+ 
+
+ align:start position:0%
+that apparently they are but this
+organization itself the soul is clearly
+
+ align:start position:0%
+organization itself the soul is clearly
+ 
+
+ align:start position:0%
+organization itself the soul is clearly
+an enlightened machine
+
+ align:start position:0%
+an enlightened machine
+ 
+
+ align:start position:0%
+an enlightened machine
+and that phrase the enlightened machine
+
+ align:start position:0%
+and that phrase the enlightened machine
+ 
+
+ align:start position:0%
+and that phrase the enlightened machine
+has been repeated many times even in
+
+ align:start position:0%
+has been repeated many times even in
+ 
+
+ align:start position:0%
+has been repeated many times even in
+modern
+
+ align:start position:0%
+modern
+ 
+
+ align:start position:0%
+modern
+neuroscience
+
+ align:start position:0%
+neuroscience
+ 
+
+ align:start position:0%
+neuroscience
+he can he continued by saying the soul
+
+ align:start position:0%
+he can he continued by saying the soul
+ 
+
+ align:start position:0%
+he can he continued by saying the soul
+is therefore but an empty word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't agree with that but that is the
+
+ align:start position:0%
+i don't agree with that but that is the
+ 
+
+ align:start position:0%
+i don't agree with that but that is the
+view of some people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will say a little more about that in a
+
+ align:start position:0%
+will say a little more about that in a
+ 
+
+ align:start position:0%
+will say a little more about that in a
+minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how did pavlov change that whole picture
+
+ align:start position:0%
+how did pavlov change that whole picture
+ 
+
+ align:start position:0%
+how did pavlov change that whole picture
+and bring
+
+ align:start position:0%
+and bring
+ 
+
+ align:start position:0%
+and bring
+make the influence of reflexology
+
+ align:start position:0%
+make the influence of reflexology
+ 
+
+ align:start position:0%
+make the influence of reflexology
+much more marked in america especially
+
+ align:start position:0%
+much more marked in america especially
+ 
+
+ align:start position:0%
+much more marked in america especially
+the american educational system which
+
+ align:start position:0%
+the american educational system which
+ 
+
+ align:start position:0%
+the american educational system which
+was based on the the idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasticity changeability of the reflexes
+
+ align:start position:0%
+plasticity changeability of the reflexes
+ 
+
+ align:start position:0%
+plasticity changeability of the reflexes
+that is the stimulus response model was
+
+ align:start position:0%
+that is the stimulus response model was
+ 
+
+ align:start position:0%
+that is the stimulus response model was
+accepted
+
+ align:start position:0%
+accepted
+ 
+
+ align:start position:0%
+accepted
+often we think of the stimulus response
+
+ align:start position:0%
+often we think of the stimulus response
+ 
+
+ align:start position:0%
+often we think of the stimulus response
+model is sort of a generalization of the
+
+ align:start position:0%
+model is sort of a generalization of the
+ 
+
+ align:start position:0%
+model is sort of a generalization of the
+reflex idea
+
+ align:start position:0%
+reflex idea
+ 
+
+ align:start position:0%
+reflex idea
+that all behavior can be explained by
+
+ align:start position:0%
+that all behavior can be explained by
+ 
+
+ align:start position:0%
+that all behavior can be explained by
+stimuli leading to responses
+
+ align:start position:0%
+stimuli leading to responses
+ 
+
+ align:start position:0%
+stimuli leading to responses
+but the idea that they could be plastic
+
+ align:start position:0%
+but the idea that they could be plastic
+ 
+
+ align:start position:0%
+but the idea that they could be plastic
+but in other words learning could occur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+became very important in educational
+
+ align:start position:0%
+became very important in educational
+ 
+
+ align:start position:0%
+became very important in educational
+theory in america where it was believed
+
+ align:start position:0%
+theory in america where it was believed
+ 
+
+ align:start position:0%
+theory in america where it was believed
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay animals have instincts but people
+
+ align:start position:0%
+okay animals have instincts but people
+ 
+
+ align:start position:0%
+okay animals have instincts but people
+are plastic
+
+ align:start position:0%
+are plastic
+ 
+
+ align:start position:0%
+are plastic
+and everything can be changed by
+
+ align:start position:0%
+and everything can be changed by
+ 
+
+ align:start position:0%
+and everything can be changed by
+learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not actually
+
+ align:start position:0%
+it's not actually
+ 
+
+ align:start position:0%
+it's not actually
+completely true most things are
+
+ align:start position:0%
+completely true most things are
+ 
+
+ align:start position:0%
+completely true most things are
+is a large instinctive component
+
+ align:start position:0%
+is a large instinctive component
+ 
+
+ align:start position:0%
+is a large instinctive component
+and some of those aspects of the
+
+ align:start position:0%
+and some of those aspects of the
+ 
+
+ align:start position:0%
+and some of those aspects of the
+instincts are not very changeable but in
+
+ align:start position:0%
+instincts are not very changeable but in
+ 
+
+ align:start position:0%
+instincts are not very changeable but in
+fact most behaviors there's some
+
+ align:start position:0%
+fact most behaviors there's some
+ 
+
+ align:start position:0%
+fact most behaviors there's some
+influence of experience as well as of
+
+ align:start position:0%
+influence of experience as well as of
+ 
+
+ align:start position:0%
+influence of experience as well as of
+built-in connections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mentioned makai
+
+ align:start position:0%
+i mentioned makai
+ 
+
+ align:start position:0%
+i mentioned makai
+and i posted his reading one one paper
+
+ align:start position:0%
+and i posted his reading one one paper
+ 
+
+ align:start position:0%
+and i posted his reading one one paper
+by him on the web
+
+ align:start position:0%
+by him on the web
+ 
+
+ align:start position:0%
+by him on the web
+who argued that a strict determinism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinism he could accept but then he
+
+ align:start position:0%
+determinism he could accept but then he
+ 
+
+ align:start position:0%
+determinism he could accept but then he
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+in the strict sense
+
+ align:start position:0%
+in the strict sense
+ 
+
+ align:start position:0%
+in the strict sense
+it's logically impossible because
+
+ align:start position:0%
+it's logically impossible because
+ 
+
+ align:start position:0%
+it's logically impossible because
+it doesn't allow you to say a person is
+
+ align:start position:0%
+it doesn't allow you to say a person is
+ 
+
+ align:start position:0%
+it doesn't allow you to say a person is
+responsible for his actions and so i'm
+
+ align:start position:0%
+responsible for his actions and so i'm
+ 
+
+ align:start position:0%
+responsible for his actions and so i'm
+asking you some questions about that
+
+ align:start position:0%
+asking you some questions about that
+ 
+
+ align:start position:0%
+asking you some questions about that
+here that i've added
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does this mean that some things are not
+
+ align:start position:0%
+does this mean that some things are not
+ 
+
+ align:start position:0%
+does this mean that some things are not
+determined by awful cause effect
+
+ align:start position:0%
+determined by awful cause effect
+ 
+
+ align:start position:0%
+determined by awful cause effect
+relationships no that's not what he
+
+ align:start position:0%
+relationships no that's not what he
+ 
+
+ align:start position:0%
+relationships no that's not what he
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well then why should a person be held
+
+ align:start position:0%
+well then why should a person be held
+ 
+
+ align:start position:0%
+well then why should a person be held
+responsible for something that
+
+ align:start position:0%
+responsible for something that
+ 
+
+ align:start position:0%
+responsible for something that
+necessarily had to occur once the
+
+ align:start position:0%
+necessarily had to occur once the
+ 
+
+ align:start position:0%
+necessarily had to occur once the
+conditions were there once the stage was
+
+ align:start position:0%
+conditions were there once the stage was
+ 
+
+ align:start position:0%
+conditions were there once the stage was
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+this is a question in forensic
+
+ align:start position:0%
+this is a question in forensic
+ 
+
+ align:start position:0%
+this is a question in forensic
+psychiatry
+
+ align:start position:0%
+psychiatry
+ 
+
+ align:start position:0%
+psychiatry
+it's why psychiatrists
+
+ align:start position:0%
+it's why psychiatrists
+ 
+
+ align:start position:0%
+it's why psychiatrists
+are asked to come in the courtroom
+
+ align:start position:0%
+are asked to come in the courtroom
+ 
+
+ align:start position:0%
+are asked to come in the courtroom
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+testify that someone was
+
+ align:start position:0%
+testify that someone was
+ 
+
+ align:start position:0%
+testify that someone was
+too crazy to be responsible for his
+
+ align:start position:0%
+too crazy to be responsible for his
+ 
+
+ align:start position:0%
+too crazy to be responsible for his
+actions
+
+ align:start position:0%
+actions
+ 
+
+ align:start position:0%
+actions
+or some other
+
+ align:start position:0%
+or some other
+ 
+
+ align:start position:0%
+or some other
+problem he had some other problem
+
+ align:start position:0%
+problem he had some other problem
+ 
+
+ align:start position:0%
+problem he had some other problem
+but i would argue that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if everything is determined then the
+
+ align:start position:0%
+if everything is determined then the
+ 
+
+ align:start position:0%
+if everything is determined then the
+culpability and the punishments are also
+
+ align:start position:0%
+culpability and the punishments are also
+ 
+
+ align:start position:0%
+culpability and the punishments are also
+determined
+
+ align:start position:0%
+determined
+ 
+
+ align:start position:0%
+determined
+and they also must necessarily occur by
+
+ align:start position:0%
+and they also must necessarily occur by
+ 
+
+ align:start position:0%
+and they also must necessarily occur by
+the same kind of deterministic laws
+
+ align:start position:0%
+the same kind of deterministic laws
+ 
+
+ align:start position:0%
+the same kind of deterministic laws
+so you can't have part of one
+
+ align:start position:0%
+so you can't have part of one
+ 
+
+ align:start position:0%
+so you can't have part of one
+you see
+
+ align:start position:0%
+you see
+ 
+
+ align:start position:0%
+you see
+without the other so
+
+ align:start position:0%
+without the other so
+ 
+
+ align:start position:0%
+without the other so
+i like makai's argument
+
+ align:start position:0%
+i like makai's argument
+ 
+
+ align:start position:0%
+i like makai's argument
+even though some people
+
+ align:start position:0%
+even though some people
+ 
+
+ align:start position:0%
+even though some people
+don't i think it helps us it points out
+
+ align:start position:0%
+don't i think it helps us it points out
+ 
+
+ align:start position:0%
+don't i think it helps us it points out
+a logical conundrum that we are always
+
+ align:start position:0%
+a logical conundrum that we are always
+ 
+
+ align:start position:0%
+a logical conundrum that we are always
+faced with in this field
+
+ align:start position:0%
+faced with in this field
+ 
+
+ align:start position:0%
+faced with in this field
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why did people move to a different kind
+
+ align:start position:0%
+why did people move to a different kind
+ 
+
+ align:start position:0%
+why did people move to a different kind
+of goal giving up the idea of specific
+
+ align:start position:0%
+of goal giving up the idea of specific
+ 
+
+ align:start position:0%
+of goal giving up the idea of specific
+neural circuits underlying behavior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's because they thought the first goal
+
+ align:start position:0%
+it's because they thought the first goal
+ 
+
+ align:start position:0%
+it's because they thought the first goal
+was a pipe dream it was impossible
+
+ align:start position:0%
+was a pipe dream it was impossible
+ 
+
+ align:start position:0%
+was a pipe dream it was impossible
+how could we ever trace these
+
+ align:start position:0%
+how could we ever trace these
+ 
+
+ align:start position:0%
+how could we ever trace these
+connections between
+
+ align:start position:0%
+connections between
+ 
+
+ align:start position:0%
+connections between
+the input and the output stimulus and
+
+ align:start position:0%
+the input and the output stimulus and
+ 
+
+ align:start position:0%
+the input and the output stimulus and
+response
+
+ align:start position:0%
+response
+ 
+
+ align:start position:0%
+response
+in the human brain where there's 10
+
+ align:start position:0%
+in the human brain where there's 10
+ 
+
+ align:start position:0%
+in the human brain where there's 10
+billion
+
+ align:start position:0%
+billion
+ 
+
+ align:start position:0%
+billion
+nerve cells at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's actually many more than that it
+
+ align:start position:0%
+there's actually many more than that it
+ 
+
+ align:start position:0%
+there's actually many more than that it
+was once that was the number always
+
+ align:start position:0%
+was once that was the number always
+ 
+
+ align:start position:0%
+was once that was the number always
+given then they discovered there were
+
+ align:start position:0%
+given then they discovered there were
+ 
+
+ align:start position:0%
+given then they discovered there were
+more than that just in the cerebellum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that says
+
+ align:start position:0%
+and that says
+ 
+
+ align:start position:0%
+and that says
+the number of connections is much much
+
+ align:start position:0%
+the number of connections is much much
+ 
+
+ align:start position:0%
+the number of connections is much much
+greater
+
+ align:start position:0%
+greater
+ 
+
+ align:start position:0%
+greater
+one study was done some years ago with
+
+ align:start position:0%
+one study was done some years ago with
+ 
+
+ align:start position:0%
+one study was done some years ago with
+the electron microscope looking at the
+
+ align:start position:0%
+the electron microscope looking at the
+ 
+
+ align:start position:0%
+the electron microscope looking at the
+monkey neocortex
+
+ align:start position:0%
+monkey neocortex
+ 
+
+ align:start position:0%
+monkey neocortex
+it should say motor cortex
+
+ align:start position:0%
+it should say motor cortex
+ 
+
+ align:start position:0%
+it should say motor cortex
+in the monkey motor cortex where it was
+
+ align:start position:0%
+in the monkey motor cortex where it was
+ 
+
+ align:start position:0%
+in the monkey motor cortex where it was
+found we'll mention motor cortex in a
+
+ align:start position:0%
+found we'll mention motor cortex in a
+ 
+
+ align:start position:0%
+found we'll mention motor cortex in a
+few minutes
+
+ align:start position:0%
+few minutes
+ 
+
+ align:start position:0%
+few minutes
+it was found that on the average one
+
+ align:start position:0%
+it was found that on the average one
+ 
+
+ align:start position:0%
+it was found that on the average one
+neuron had 60 000 inputs that is 60 000
+
+ align:start position:0%
+neuron had 60 000 inputs that is 60 000
+ 
+
+ align:start position:0%
+neuron had 60 000 inputs that is 60 000
+synapses on its surfaces
+
+ align:start position:0%
+synapses on its surfaces
+ 
+
+ align:start position:0%
+synapses on its surfaces
+in the monkey visual cortex it was four
+
+ align:start position:0%
+in the monkey visual cortex it was four
+ 
+
+ align:start position:0%
+in the monkey visual cortex it was four
+thousand
+
+ align:start position:0%
+thousand
+ 
+
+ align:start position:0%
+thousand
+but if you take
+
+ align:start position:0%
+but if you take
+ 
+
+ align:start position:0%
+but if you take
+those are probably the extremes in the
+
+ align:start position:0%
+those are probably the extremes in the
+ 
+
+ align:start position:0%
+those are probably the extremes in the
+neocortex but it gives you an idea
+
+ align:start position:0%
+neocortex but it gives you an idea
+ 
+
+ align:start position:0%
+neocortex but it gives you an idea
+enormous numbers and connections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the task of specifying circuitry
+
+ align:start position:0%
+the task of specifying circuitry
+ 
+
+ align:start position:0%
+the task of specifying circuitry
+is pretty formidable even in the spinal
+
+ align:start position:0%
+is pretty formidable even in the spinal
+ 
+
+ align:start position:0%
+is pretty formidable even in the spinal
+cord
+
+ align:start position:0%
+cord
+ 
+
+ align:start position:0%
+cord
+but their reflex ideas can explain many
+
+ align:start position:0%
+but their reflex ideas can explain many
+ 
+
+ align:start position:0%
+but their reflex ideas can explain many
+reactions and that's been known since
+
+ align:start position:0%
+reactions and that's been known since
+ 
+
+ align:start position:0%
+reactions and that's been known since
+the detailed studies of
+
+ align:start position:0%
+the detailed studies of
+ 
+
+ align:start position:0%
+the detailed studies of
+charles scott sherrington around the
+
+ align:start position:0%
+charles scott sherrington around the
+ 
+
+ align:start position:0%
+charles scott sherrington around the
+turn of the
+
+ align:start position:0%
+turn of the
+ 
+
+ align:start position:0%
+turn of the
+previous century 1900
+
+ align:start position:0%
+previous century 1900
+ 
+
+ align:start position:0%
+previous century 1900
+the man that coined the term synapse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what else can we do if it's so
+
+ align:start position:0%
+so what else can we do if it's so
+ 
+
+ align:start position:0%
+so what else can we do if it's so
+difficult to trace connections
+
+ align:start position:0%
+difficult to trace connections
+ 
+
+ align:start position:0%
+difficult to trace connections
+from s to r
+
+ align:start position:0%
+from s to r
+ 
+
+ align:start position:0%
+from s to r
+connections that underlie behavior well
+
+ align:start position:0%
+connections that underlie behavior well
+ 
+
+ align:start position:0%
+connections that underlie behavior well
+many people have simply pursued a very
+
+ align:start position:0%
+many people have simply pursued a very
+ 
+
+ align:start position:0%
+many people have simply pursued a very
+different kind of goal localizing
+
+ align:start position:0%
+different kind of goal localizing
+ 
+
+ align:start position:0%
+different kind of goal localizing
+function in specific parts of the
+
+ align:start position:0%
+function in specific parts of the
+ 
+
+ align:start position:0%
+function in specific parts of the
+central nervous system brain and spinal
+
+ align:start position:0%
+central nervous system brain and spinal
+ 
+
+ align:start position:0%
+central nervous system brain and spinal
+cord
+
+ align:start position:0%
+cord
+ 
+
+ align:start position:0%
+cord
+without necessarily any
+
+ align:start position:0%
+without necessarily any
+ 
+
+ align:start position:0%
+without necessarily any
+specification of circuitry within
+
+ align:start position:0%
+specification of circuitry within
+ 
+
+ align:start position:0%
+specification of circuitry within
+a functional subdivision or even be
+
+ align:start position:0%
+a functional subdivision or even be
+ 
+
+ align:start position:0%
+a functional subdivision or even be
+sometimes not even between them
+
+ align:start position:0%
+sometimes not even between them
+ 
+
+ align:start position:0%
+sometimes not even between them
+although the modern
+
+ align:start position:0%
+although the modern
+ 
+
+ align:start position:0%
+although the modern
+synthesis often tries to at least
+
+ align:start position:0%
+synthesis often tries to at least
+ 
+
+ align:start position:0%
+synthesis often tries to at least
+specify connections between the major
+
+ align:start position:0%
+specify connections between the major
+ 
+
+ align:start position:0%
+specify connections between the major
+functional divisions of the brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this kind of goal
+
+ align:start position:0%
+this kind of goal
+ 
+
+ align:start position:0%
+this kind of goal
+started out with simple arguments about
+
+ align:start position:0%
+started out with simple arguments about
+ 
+
+ align:start position:0%
+started out with simple arguments about
+where the seed of the soul was
+
+ align:start position:0%
+where the seed of the soul was
+ 
+
+ align:start position:0%
+where the seed of the soul was
+but then
+
+ align:start position:0%
+but then
+ 
+
+ align:start position:0%
+but then
+we'll see how localization
+
+ align:start position:0%
+we'll see how localization
+ 
+
+ align:start position:0%
+we'll see how localization
+took on a very different form and
+
+ align:start position:0%
+took on a very different form and
+ 
+
+ align:start position:0%
+took on a very different form and
+detailed mosaic maps the brain were
+
+ align:start position:0%
+detailed mosaic maps the brain were
+ 
+
+ align:start position:0%
+detailed mosaic maps the brain were
+developed
+
+ align:start position:0%
+developed
+ 
+
+ align:start position:0%
+developed
+but there was an opposing type of idea
+
+ align:start position:0%
+but there was an opposing type of idea
+ 
+
+ align:start position:0%
+but there was an opposing type of idea
+that we'll cover also i don't know if
+
+ align:start position:0%
+that we'll cover also i don't know if
+ 
+
+ align:start position:0%
+that we'll cover also i don't know if
+we'll get to it today we call it it's
+
+ align:start position:0%
+we'll get to it today we call it it's
+ 
+
+ align:start position:0%
+we'll get to it today we call it it's
+sometimes called anti-localization
+
+ align:start position:0%
+sometimes called anti-localization
+ 
+
+ align:start position:0%
+sometimes called anti-localization
+because they didn't believe that you
+
+ align:start position:0%
+because they didn't believe that you
+ 
+
+ align:start position:0%
+because they didn't believe that you
+could localize functions so easily in
+
+ align:start position:0%
+could localize functions so easily in
+ 
+
+ align:start position:0%
+could localize functions so easily in
+different parts of the brain but they
+
+ align:start position:0%
+different parts of the brain but they
+ 
+
+ align:start position:0%
+different parts of the brain but they
+did have a kind of general localization
+
+ align:start position:0%
+did have a kind of general localization
+ 
+
+ align:start position:0%
+did have a kind of general localization
+and i'll explain what that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the seed of the
+
+ align:start position:0%
+the seed of the
+ 
+
+ align:start position:0%
+the seed of the
+soul is exemplified by a quote from
+
+ align:start position:0%
+soul is exemplified by a quote from
+ 
+
+ align:start position:0%
+soul is exemplified by a quote from
+shakespeare and the merchant of venice
+
+ align:start position:0%
+shakespeare and the merchant of venice
+ 
+
+ align:start position:0%
+shakespeare and the merchant of venice
+who asked tell me where is fancy bread
+
+ align:start position:0%
+who asked tell me where is fancy bread
+ 
+
+ align:start position:0%
+who asked tell me where is fancy bread
+in the heart or in the head
+
+ align:start position:0%
+in the heart or in the head
+ 
+
+ align:start position:0%
+in the heart or in the head
+but the ideal as well
+
+ align:start position:0%
+but the ideal as well
+ 
+
+ align:start position:0%
+but the ideal as well
+is it in the brain or is it in the heart
+
+ align:start position:0%
+is it in the brain or is it in the heart
+ 
+
+ align:start position:0%
+is it in the brain or is it in the heart
+that we have feeling or that we have
+
+ align:start position:0%
+that we have feeling or that we have
+ 
+
+ align:start position:0%
+that we have feeling or that we have
+imagination or whatever it wasn't always
+
+ align:start position:0%
+imagination or whatever it wasn't always
+ 
+
+ align:start position:0%
+imagination or whatever it wasn't always
+so clear to people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+although there were many
+
+ align:start position:0%
+although there were many
+ 
+
+ align:start position:0%
+although there were many
+many people that correctly assumed it
+
+ align:start position:0%
+many people that correctly assumed it
+ 
+
+ align:start position:0%
+many people that correctly assumed it
+was in something in the head
+
+ align:start position:0%
+was in something in the head
+ 
+
+ align:start position:0%
+was in something in the head
+in many different cultures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there were many arguments because we
+
+ align:start position:0%
+but there were many arguments because we
+ 
+
+ align:start position:0%
+but there were many arguments because we
+seem to feel
+
+ align:start position:0%
+seem to feel
+ 
+
+ align:start position:0%
+seem to feel
+feelings in particular
+
+ align:start position:0%
+feelings in particular
+ 
+
+ align:start position:0%
+feelings in particular
+not here but here or throughout our body
+
+ align:start position:0%
+not here but here or throughout our body
+ 
+
+ align:start position:0%
+not here but here or throughout our body
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a picture from leonardo leonardo
+
+ align:start position:0%
+this is a picture from leonardo leonardo
+ 
+
+ align:start position:0%
+this is a picture from leonardo leonardo
+da vinci
+
+ align:start position:0%
+da vinci
+ 
+
+ align:start position:0%
+da vinci
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+has this picture an outline of the brain
+
+ align:start position:0%
+has this picture an outline of the brain
+ 
+
+ align:start position:0%
+has this picture an outline of the brain
+very large but he's stressing the
+
+ align:start position:0%
+very large but he's stressing the
+ 
+
+ align:start position:0%
+very large but he's stressing the
+ventricles
+
+ align:start position:0%
+ventricles
+ 
+
+ align:start position:0%
+ventricles
+the ventricles are the fluid filled
+
+ align:start position:0%
+the ventricles are the fluid filled
+ 
+
+ align:start position:0%
+the ventricles are the fluid filled
+cavities
+
+ align:start position:0%
+cavities
+ 
+
+ align:start position:0%
+cavities
+in the central center part of the brain
+
+ align:start position:0%
+in the central center part of the brain
+ 
+
+ align:start position:0%
+in the central center part of the brain
+and spinal cord
+
+ align:start position:0%
+and spinal cord
+ 
+
+ align:start position:0%
+and spinal cord
+and to many people
+
+ align:start position:0%
+and to many people
+ 
+
+ align:start position:0%
+and to many people
+it seemed appropriate that they didn't
+
+ align:start position:0%
+it seemed appropriate that they didn't
+ 
+
+ align:start position:0%
+it seemed appropriate that they didn't
+know they were filled with fluid they
+
+ align:start position:0%
+know they were filled with fluid they
+ 
+
+ align:start position:0%
+know they were filled with fluid they
+thought like they might be filled with a
+
+ align:start position:0%
+thought like they might be filled with a
+ 
+
+ align:start position:0%
+thought like they might be filled with a
+kind of gas and they thought that was
+
+ align:start position:0%
+kind of gas and they thought that was
+ 
+
+ align:start position:0%
+kind of gas and they thought that was
+very appropriate for the soul
+
+ align:start position:0%
+very appropriate for the soul
+ 
+
+ align:start position:0%
+very appropriate for the soul
+you see it wasn't
+
+ align:start position:0%
+you see it wasn't
+ 
+
+ align:start position:0%
+you see it wasn't
+didn't seem so physical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in fact descartes was influenced by that
+
+ align:start position:0%
+in fact descartes was influenced by that
+ 
+
+ align:start position:0%
+in fact descartes was influenced by that
+kind of idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the idea of localizing functions and
+
+ align:start position:0%
+the idea of localizing functions and
+ 
+
+ align:start position:0%
+the idea of localizing functions and
+specifically in different parts of the
+
+ align:start position:0%
+specifically in different parts of the
+ 
+
+ align:start position:0%
+specifically in different parts of the
+brain really got its first strong
+
+ align:start position:0%
+brain really got its first strong
+ 
+
+ align:start position:0%
+brain really got its first strong
+impetus from
+
+ align:start position:0%
+impetus from
+ 
+
+ align:start position:0%
+impetus from
+what we now would call a false science
+
+ align:start position:0%
+what we now would call a false science
+ 
+
+ align:start position:0%
+what we now would call a false science
+the science called phrenology
+
+ align:start position:0%
+the science called phrenology
+ 
+
+ align:start position:0%
+the science called phrenology
+prince joseph gaul was a neuroanatomist
+
+ align:start position:0%
+prince joseph gaul was a neuroanatomist
+ 
+
+ align:start position:0%
+prince joseph gaul was a neuroanatomist
+well let's say an anatomist he wasn't
+
+ align:start position:0%
+well let's say an anatomist he wasn't
+ 
+
+ align:start position:0%
+well let's say an anatomist he wasn't
+really a neuroanatomist but he's known
+
+ align:start position:0%
+really a neuroanatomist but he's known
+ 
+
+ align:start position:0%
+really a neuroanatomist but he's known
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+being the first one to separate gray and
+
+ align:start position:0%
+being the first one to separate gray and
+ 
+
+ align:start position:0%
+being the first one to separate gray and
+white matter
+
+ align:start position:0%
+white matter
+ 
+
+ align:start position:0%
+white matter
+in his dissections of the brain
+
+ align:start position:0%
+in his dissections of the brain
+ 
+
+ align:start position:0%
+in his dissections of the brain
+and a follower of his in america
+
+ align:start position:0%
+and a follower of his in america
+ 
+
+ align:start position:0%
+and a follower of his in america
+spurtzheim helped to popularize
+
+ align:start position:0%
+spurtzheim helped to popularize
+ 
+
+ align:start position:0%
+spurtzheim helped to popularize
+the ideas
+
+ align:start position:0%
+the ideas
+ 
+
+ align:start position:0%
+the ideas
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the shape of the skull somehow
+
+ align:start position:0%
+the shape of the skull somehow
+ 
+
+ align:start position:0%
+the shape of the skull somehow
+represents character because it
+
+ align:start position:0%
+represents character because it
+ 
+
+ align:start position:0%
+represents character because it
+corresponds to different parts the
+
+ align:start position:0%
+corresponds to different parts the
+ 
+
+ align:start position:0%
+corresponds to different parts the
+underlying brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's one of their maps this became
+
+ align:start position:0%
+and here's one of their maps this became
+ 
+
+ align:start position:0%
+and here's one of their maps this became
+very popular
+
+ align:start position:0%
+very popular
+ 
+
+ align:start position:0%
+very popular
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not just in the 19th century but it
+
+ align:start position:0%
+not just in the 19th century but it
+ 
+
+ align:start position:0%
+not just in the 19th century but it
+continued into the 20th century and
+
+ align:start position:0%
+continued into the 20th century and
+ 
+
+ align:start position:0%
+continued into the 20th century and
+you'll find books of phrenology
+
+ align:start position:0%
+you'll find books of phrenology
+ 
+
+ align:start position:0%
+you'll find books of phrenology
+on some of your parents or grandparents
+
+ align:start position:0%
+on some of your parents or grandparents
+ 
+
+ align:start position:0%
+on some of your parents or grandparents
+shelves
+
+ align:start position:0%
+shelves
+ 
+
+ align:start position:0%
+shelves
+and they also sold these little models
+
+ align:start position:0%
+and they also sold these little models
+ 
+
+ align:start position:0%
+and they also sold these little models
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that look something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the skull divided up they what they
+
+ align:start position:0%
+with the skull divided up they what they
+ 
+
+ align:start position:0%
+with the skull divided up they what they
+claimed was that simply by feeling the
+
+ align:start position:0%
+claimed was that simply by feeling the
+ 
+
+ align:start position:0%
+claimed was that simply by feeling the
+prominences and the bumps on your skull
+
+ align:start position:0%
+prominences and the bumps on your skull
+ 
+
+ align:start position:0%
+prominences and the bumps on your skull
+you could say something about character
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what on earth was that based on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is another one of the pictures
+
+ align:start position:0%
+this is another one of the pictures
+ 
+
+ align:start position:0%
+this is another one of the pictures
+where they're depicting the various
+
+ align:start position:0%
+where they're depicting the various
+ 
+
+ align:start position:0%
+where they're depicting the various
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this graphical format
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well they made certain assumptions
+
+ align:start position:0%
+well they made certain assumptions
+ 
+
+ align:start position:0%
+well they made certain assumptions
+and we don't argue with all of those
+
+ align:start position:0%
+and we don't argue with all of those
+ 
+
+ align:start position:0%
+and we don't argue with all of those
+assumptions now
+
+ align:start position:0%
+assumptions now
+ 
+
+ align:start position:0%
+assumptions now
+they said the brain is the sole organ of
+
+ align:start position:0%
+they said the brain is the sole organ of
+ 
+
+ align:start position:0%
+they said the brain is the sole organ of
+the mind it's not in the heart it's not
+
+ align:start position:0%
+the mind it's not in the heart it's not
+ 
+
+ align:start position:0%
+the mind it's not in the heart it's not
+elsewhere it's all in the brain
+
+ align:start position:0%
+elsewhere it's all in the brain
+ 
+
+ align:start position:0%
+elsewhere it's all in the brain
+and we don't argue with that now for the
+
+ align:start position:0%
+and we don't argue with that now for the
+ 
+
+ align:start position:0%
+and we don't argue with that now for the
+most part
+
+ align:start position:0%
+most part
+ 
+
+ align:start position:0%
+most part
+they also argued that basic character
+
+ align:start position:0%
+they also argued that basic character
+ 
+
+ align:start position:0%
+they also argued that basic character
+traits were innate
+
+ align:start position:0%
+traits were innate
+ 
+
+ align:start position:0%
+traits were innate
+something we're born with
+
+ align:start position:0%
+something we're born with
+ 
+
+ align:start position:0%
+something we're born with
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+there's a large degree of truth to that
+
+ align:start position:0%
+there's a large degree of truth to that
+ 
+
+ align:start position:0%
+there's a large degree of truth to that
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+we may be shaped by experience but in
+
+ align:start position:0%
+we may be shaped by experience but in
+ 
+
+ align:start position:0%
+we may be shaped by experience but in
+fact
+
+ align:start position:0%
+fact
+ 
+
+ align:start position:0%
+fact
+basic character traits are built-in
+
+ align:start position:0%
+basic character traits are built-in
+ 
+
+ align:start position:0%
+basic character traits are built-in
+they're genetic
+
+ align:start position:0%
+they're genetic
+ 
+
+ align:start position:0%
+they're genetic
+because the brain structure the basic
+
+ align:start position:0%
+because the brain structure the basic
+ 
+
+ align:start position:0%
+because the brain structure the basic
+structure of the brain is inherited
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the third assumption was the differences
+
+ align:start position:0%
+the third assumption was the differences
+ 
+
+ align:start position:0%
+the third assumption was the differences
+in characters and ability imply
+
+ align:start position:0%
+in characters and ability imply
+ 
+
+ align:start position:0%
+in characters and ability imply
+differences in structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just going that far
+
+ align:start position:0%
+and just going that far
+ 
+
+ align:start position:0%
+and just going that far
+i think many people would in
+
+ align:start position:0%
+i think many people would in
+ 
+
+ align:start position:0%
+i think many people would in
+neuroscience would still agree with that
+
+ align:start position:0%
+neuroscience would still agree with that
+ 
+
+ align:start position:0%
+neuroscience would still agree with that
+but then they said that that was
+
+ align:start position:0%
+but then they said that that was
+ 
+
+ align:start position:0%
+but then they said that that was
+manifest mainly as differences in size
+
+ align:start position:0%
+manifest mainly as differences in size
+ 
+
+ align:start position:0%
+manifest mainly as differences in size
+well there are a number of examples
+
+ align:start position:0%
+well there are a number of examples
+ 
+
+ align:start position:0%
+well there are a number of examples
+where functional differences are
+
+ align:start position:0%
+where functional differences are
+ 
+
+ align:start position:0%
+where functional differences are
+correlated with differences in size
+
+ align:start position:0%
+correlated with differences in size
+ 
+
+ align:start position:0%
+correlated with differences in size
+and i talk about a few of those later in
+
+ align:start position:0%
+and i talk about a few of those later in
+ 
+
+ align:start position:0%
+and i talk about a few of those later in
+the class and in the second term also
+
+ align:start position:0%
+the class and in the second term also
+ 
+
+ align:start position:0%
+the class and in the second term also
+but there are so many exceptions to that
+
+ align:start position:0%
+but there are so many exceptions to that
+ 
+
+ align:start position:0%
+but there are so many exceptions to that
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+the final
+
+ align:start position:0%
+the final
+ 
+
+ align:start position:0%
+the final
+assumption and this is the one
+
+ align:start position:0%
+assumption and this is the one
+ 
+
+ align:start position:0%
+assumption and this is the one
+that was the most wrong that shaped the
+
+ align:start position:0%
+that was the most wrong that shaped the
+ 
+
+ align:start position:0%
+that was the most wrong that shaped the
+shape the brains correlated with the
+
+ align:start position:0%
+shape the brains correlated with the
+ 
+
+ align:start position:0%
+shape the brains correlated with the
+shape of the skull but wait a minute i
+
+ align:start position:0%
+shape of the skull but wait a minute i
+ 
+
+ align:start position:0%
+shape of the skull but wait a minute i
+mean our brain is shaped pretty much
+
+ align:start position:0%
+mean our brain is shaped pretty much
+ 
+
+ align:start position:0%
+mean our brain is shaped pretty much
+like our skull
+
+ align:start position:0%
+like our skull
+ 
+
+ align:start position:0%
+like our skull
+but what about details
+
+ align:start position:0%
+but what about details
+ 
+
+ align:start position:0%
+but what about details
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+we're very thick skulled species
+
+ align:start position:0%
+we're very thick skulled species
+ 
+
+ align:start position:0%
+we're very thick skulled species
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we can't tell too much about details of
+
+ align:start position:0%
+we can't tell too much about details of
+ 
+
+ align:start position:0%
+we can't tell too much about details of
+shape
+
+ align:start position:0%
+shape
+ 
+
+ align:start position:0%
+shape
+by looking in the outside of the brain
+
+ align:start position:0%
+by looking in the outside of the brain
+ 
+
+ align:start position:0%
+by looking in the outside of the brain
+if we look at the inside of the outside
+
+ align:start position:0%
+if we look at the inside of the outside
+ 
+
+ align:start position:0%
+if we look at the inside of the outside
+of the skull but if we look at the
+
+ align:start position:0%
+of the skull but if we look at the
+ 
+
+ align:start position:0%
+of the skull but if we look at the
+inside of the skull
+
+ align:start position:0%
+inside of the skull
+ 
+
+ align:start position:0%
+inside of the skull
+and people in anthropology use that of
+
+ align:start position:0%
+and people in anthropology use that of
+ 
+
+ align:start position:0%
+and people in anthropology use that of
+this method of making what they call an
+
+ align:start position:0%
+this method of making what they call an
+ 
+
+ align:start position:0%
+this method of making what they call an
+endocranial cast
+
+ align:start position:0%
+endocranial cast
+ 
+
+ align:start position:0%
+endocranial cast
+the cast made from the inside of a skull
+
+ align:start position:0%
+the cast made from the inside of a skull
+ 
+
+ align:start position:0%
+the cast made from the inside of a skull
+you can actually see quite a bit about
+
+ align:start position:0%
+you can actually see quite a bit about
+ 
+
+ align:start position:0%
+you can actually see quite a bit about
+major features of the external surface
+
+ align:start position:0%
+major features of the external surface
+ 
+
+ align:start position:0%
+major features of the external surface
+of the brain we can tell where certain
+
+ align:start position:0%
+of the brain we can tell where certain
+ 
+
+ align:start position:0%
+of the brain we can tell where certain
+major vessels were located major
+
+ align:start position:0%
+major vessels were located major
+ 
+
+ align:start position:0%
+major vessels were located major
+fissures in
+
+ align:start position:0%
+fissures in
+ 
+
+ align:start position:0%
+fissures in
+people who have not existed for many
+
+ align:start position:0%
+people who have not existed for many
+ 
+
+ align:start position:0%
+people who have not existed for many
+thousands of years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+so their assumptions were
+
+ align:start position:0%
+so their assumptions were
+ 
+
+ align:start position:0%
+so their assumptions were
+true or partially true
+
+ align:start position:0%
+true or partially true
+ 
+
+ align:start position:0%
+true or partially true
+but their methods
+
+ align:start position:0%
+but their methods
+ 
+
+ align:start position:0%
+but their methods
+were not what we would call scientific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they practiced what i suppose you could
+
+ align:start position:0%
+they practiced what i suppose you could
+ 
+
+ align:start position:0%
+they practiced what i suppose you could
+call newspaper science
+
+ align:start position:0%
+call newspaper science
+ 
+
+ align:start position:0%
+call newspaper science
+they collected anecdotes and then used
+
+ align:start position:0%
+they collected anecdotes and then used
+ 
+
+ align:start position:0%
+they collected anecdotes and then used
+it to argue immediately for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the generality of the phenomenon
+
+ align:start position:0%
+the generality of the phenomenon
+ 
+
+ align:start position:0%
+the generality of the phenomenon
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+you would read in their book about
+
+ align:start position:0%
+you would read in their book about
+ 
+
+ align:start position:0%
+you would read in their book about
+a student who is
+
+ align:start position:0%
+a student who is
+ 
+
+ align:start position:0%
+a student who is
+discovered to be torturing animals and
+
+ align:start position:0%
+discovered to be torturing animals and
+ 
+
+ align:start position:0%
+discovered to be torturing animals and
+he was found to have
+
+ align:start position:0%
+he was found to have
+ 
+
+ align:start position:0%
+he was found to have
+you know to have prominence above his
+
+ align:start position:0%
+you know to have prominence above his
+ 
+
+ align:start position:0%
+you know to have prominence above his
+ears so they concluded that that area
+
+ align:start position:0%
+ears so they concluded that that area
+ 
+
+ align:start position:0%
+ears so they concluded that that area
+if it's prominent corresponds to
+
+ align:start position:0%
+if it's prominent corresponds to
+ 
+
+ align:start position:0%
+if it's prominent corresponds to
+that character trait
+
+ align:start position:0%
+that character trait
+ 
+
+ align:start position:0%
+that character trait
+that's an anecdote and of course there's
+
+ align:start position:0%
+that's an anecdote and of course there's
+ 
+
+ align:start position:0%
+that's an anecdote and of course there's
+nothing general about it they didn't do
+
+ align:start position:0%
+nothing general about it they didn't do
+ 
+
+ align:start position:0%
+nothing general about it they didn't do
+the statistics you would need i'm not
+
+ align:start position:0%
+the statistics you would need i'm not
+ 
+
+ align:start position:0%
+the statistics you would need i'm not
+saying that there might not be some
+
+ align:start position:0%
+saying that there might not be some
+ 
+
+ align:start position:0%
+saying that there might not be some
+correlates that could be found like that
+
+ align:start position:0%
+correlates that could be found like that
+ 
+
+ align:start position:0%
+correlates that could be found like that
+and there are people that still pursue
+
+ align:start position:0%
+and there are people that still pursue
+ 
+
+ align:start position:0%
+and there are people that still pursue
+that kind of thing
+
+ align:start position:0%
+that kind of thing
+ 
+
+ align:start position:0%
+that kind of thing
+but their methods were simply anecdotal
+
+ align:start position:0%
+but their methods were simply anecdotal
+ 
+
+ align:start position:0%
+but their methods were simply anecdotal
+and can't be dependent on
+
+ align:start position:0%
+and can't be dependent on
+ 
+
+ align:start position:0%
+and can't be dependent on
+so why do we talk about it then
+
+ align:start position:0%
+so why do we talk about it then
+ 
+
+ align:start position:0%
+so why do we talk about it then
+it was very important in the history of
+
+ align:start position:0%
+it was very important in the history of
+ 
+
+ align:start position:0%
+it was very important in the history of
+the field because it drew attention to
+
+ align:start position:0%
+the field because it drew attention to
+ 
+
+ align:start position:0%
+the field because it drew attention to
+brain behavior relationships
+
+ align:start position:0%
+brain behavior relationships
+ 
+
+ align:start position:0%
+brain behavior relationships
+and it
+
+ align:start position:0%
+and it
+ 
+
+ align:start position:0%
+and it
+it made successors
+
+ align:start position:0%
+it made successors
+ 
+
+ align:start position:0%
+it made successors
+who talked about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more believable data
+
+ align:start position:0%
+more believable data
+ 
+
+ align:start position:0%
+more believable data
+correlating structure and function it
+
+ align:start position:0%
+correlating structure and function it
+ 
+
+ align:start position:0%
+correlating structure and function it
+made them seem more made them
+
+ align:start position:0%
+made them seem more made them
+ 
+
+ align:start position:0%
+made them seem more made them
+conservative and made it easier to
+
+ align:start position:0%
+conservative and made it easier to
+ 
+
+ align:start position:0%
+conservative and made it easier to
+believe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it was a popular thing that called
+
+ align:start position:0%
+so it was a popular thing that called
+ 
+
+ align:start position:0%
+so it was a popular thing that called
+attention
+
+ align:start position:0%
+attention
+ 
+
+ align:start position:0%
+attention
+to brain behavior relationships and lynn
+
+ align:start position:0%
+to brain behavior relationships and lynn
+ 
+
+ align:start position:0%
+to brain behavior relationships and lynn
+made it easier for what followed
+
+ align:start position:0%
+made it easier for what followed
+ 
+
+ align:start position:0%
+made it easier for what followed
+let's talk about some of the later
+
+ align:start position:0%
+let's talk about some of the later
+ 
+
+ align:start position:0%
+let's talk about some of the later
+discoveries beginning with the speech
+
+ align:start position:0%
+discoveries beginning with the speech
+ 
+
+ align:start position:0%
+discoveries beginning with the speech
+areas paul broca
+
+ align:start position:0%
+areas paul broca
+ 
+
+ align:start position:0%
+areas paul broca
+in 1861 published cases and i'm not
+
+ align:start position:0%
+in 1861 published cases and i'm not
+ 
+
+ align:start position:0%
+in 1861 published cases and i'm not
+showing his cases
+
+ align:start position:0%
+showing his cases
+ 
+
+ align:start position:0%
+showing his cases
+but what broca said was
+
+ align:start position:0%
+but what broca said was
+ 
+
+ align:start position:0%
+but what broca said was
+he had certain he was a neurologist he
+
+ align:start position:0%
+he had certain he was a neurologist he
+ 
+
+ align:start position:0%
+he had certain he was a neurologist he
+said i had certain patients that
+
+ align:start position:0%
+said i had certain patients that
+ 
+
+ align:start position:0%
+said i had certain patients that
+could not speak after suffering brain
+
+ align:start position:0%
+could not speak after suffering brain
+ 
+
+ align:start position:0%
+could not speak after suffering brain
+damage
+
+ align:start position:0%
+damage
+ 
+
+ align:start position:0%
+damage
+okay they had strokes
+
+ align:start position:0%
+okay they had strokes
+ 
+
+ align:start position:0%
+okay they had strokes
+and they were rendered
+
+ align:start position:0%
+and they were rendered
+ 
+
+ align:start position:0%
+and they were rendered
+speechless they couldn't get any words
+
+ align:start position:0%
+speechless they couldn't get any words
+ 
+
+ align:start position:0%
+speechless they couldn't get any words
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+and yet they seemed to be able to
+
+ align:start position:0%
+and yet they seemed to be able to
+ 
+
+ align:start position:0%
+and yet they seemed to be able to
+understand speech
+
+ align:start position:0%
+understand speech
+ 
+
+ align:start position:0%
+understand speech
+but they couldn't speak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he found that there was some consistency
+
+ align:start position:0%
+he found that there was some consistency
+ 
+
+ align:start position:0%
+he found that there was some consistency
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the more than one patient that he looked
+
+ align:start position:0%
+the more than one patient that he looked
+ 
+
+ align:start position:0%
+the more than one patient that he looked
+at they had damage in the left
+
+ align:start position:0%
+at they had damage in the left
+ 
+
+ align:start position:0%
+at they had damage in the left
+hemisphere
+
+ align:start position:0%
+hemisphere
+ 
+
+ align:start position:0%
+hemisphere
+in the frontal lobe in the ventral part
+
+ align:start position:0%
+in the frontal lobe in the ventral part
+ 
+
+ align:start position:0%
+in the frontal lobe in the ventral part
+and you can see here in these more
+
+ align:start position:0%
+and you can see here in these more
+ 
+
+ align:start position:0%
+and you can see here in these more
+recently done
+
+ align:start position:0%
+recently done
+ 
+
+ align:start position:0%
+recently done
+these are about well i don't know 20
+
+ align:start position:0%
+these are about well i don't know 20
+ 
+
+ align:start position:0%
+these are about well i don't know 20
+years old now
+
+ align:start position:0%
+years old now
+ 
+
+ align:start position:0%
+years old now
+when functional imaging first began
+
+ align:start position:0%
+when functional imaging first began
+ 
+
+ align:start position:0%
+when functional imaging first began
+to become popular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+marcus directly was one of the universe
+
+ align:start position:0%
+marcus directly was one of the universe
+ 
+
+ align:start position:0%
+marcus directly was one of the universe
+universe st louis university
+
+ align:start position:0%
+universe st louis university
+ 
+
+ align:start position:0%
+universe st louis university
+was one of the people that pioneered in
+
+ align:start position:0%
+was one of the people that pioneered in
+ 
+
+ align:start position:0%
+was one of the people that pioneered in
+this area
+
+ align:start position:0%
+this area
+ 
+
+ align:start position:0%
+this area
+he noted that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when a person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spoke
+
+ align:start position:0%
+spoke
+ 
+
+ align:start position:0%
+spoke
+and here he had them generating verbs
+
+ align:start position:0%
+and here he had them generating verbs
+ 
+
+ align:start position:0%
+and here he had them generating verbs
+this area became more showed more
+
+ align:start position:0%
+this area became more showed more
+ 
+
+ align:start position:0%
+this area became more showed more
+tissue oxygenation or blood flow
+
+ align:start position:0%
+tissue oxygenation or blood flow
+ 
+
+ align:start position:0%
+tissue oxygenation or blood flow
+different methods for imaging
+
+ align:start position:0%
+different methods for imaging
+ 
+
+ align:start position:0%
+different methods for imaging
+based on one of those two things
+
+ align:start position:0%
+based on one of those two things
+ 
+
+ align:start position:0%
+based on one of those two things
+the imaging people will say it's
+
+ align:start position:0%
+the imaging people will say it's
+ 
+
+ align:start position:0%
+the imaging people will say it's
+activated this area in the frontal lobe
+
+ align:start position:0%
+activated this area in the frontal lobe
+ 
+
+ align:start position:0%
+activated this area in the frontal lobe
+on the left side the lower part of the
+
+ align:start position:0%
+on the left side the lower part of the
+ 
+
+ align:start position:0%
+on the left side the lower part of the
+left side
+
+ align:start position:0%
+left side
+ 
+
+ align:start position:0%
+left side
+well that was the area where boca found
+
+ align:start position:0%
+well that was the area where boca found
+ 
+
+ align:start position:0%
+well that was the area where boca found
+the damage to be centered there was
+
+ align:start position:0%
+the damage to be centered there was
+ 
+
+ align:start position:0%
+the damage to be centered there was
+variability in patient patient but there
+
+ align:start position:0%
+variability in patient patient but there
+ 
+
+ align:start position:0%
+variability in patient patient but there
+was some
+
+ align:start position:0%
+was some
+ 
+
+ align:start position:0%
+was some
+that was the area that was consistently
+
+ align:start position:0%
+that was the area that was consistently
+ 
+
+ align:start position:0%
+that was the area that was consistently
+damaged in the people with
+
+ align:start position:0%
+damaged in the people with
+ 
+
+ align:start position:0%
+damaged in the people with
+aphasia that's the word for the lack of
+
+ align:start position:0%
+aphasia that's the word for the lack of
+ 
+
+ align:start position:0%
+aphasia that's the word for the lack of
+speech after brain damage
+
+ align:start position:0%
+speech after brain damage
+ 
+
+ align:start position:0%
+speech after brain damage
+aphasia or dysphagia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see that other aspects of
+
+ align:start position:0%
+you can see that other aspects of
+ 
+
+ align:start position:0%
+you can see that other aspects of
+language were differently localized
+
+ align:start position:0%
+language were differently localized
+ 
+
+ align:start position:0%
+language were differently localized
+hearing
+
+ align:start position:0%
+hearing
+ 
+
+ align:start position:0%
+hearing
+verbs
+
+ align:start position:0%
+verbs
+ 
+
+ align:start position:0%
+verbs
+activated
+
+ align:start position:0%
+activated
+ 
+
+ align:start position:0%
+activated
+an area there that we know to be
+
+ align:start position:0%
+an area there that we know to be
+ 
+
+ align:start position:0%
+an area there that we know to be
+auditory in function
+
+ align:start position:0%
+auditory in function
+ 
+
+ align:start position:0%
+auditory in function
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think this one stopped working there
+
+ align:start position:0%
+i think this one stopped working there
+ 
+
+ align:start position:0%
+i think this one stopped working there
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it's not going to work
+
+ align:start position:0%
+okay so it's not going to work
+ 
+
+ align:start position:0%
+okay so it's not going to work
+just seeing the words not hearing them
+
+ align:start position:0%
+just seeing the words not hearing them
+ 
+
+ align:start position:0%
+just seeing the words not hearing them
+in the upper right there activated an
+
+ align:start position:0%
+in the upper right there activated an
+ 
+
+ align:start position:0%
+in the upper right there activated an
+area we now know to be concerned with
+
+ align:start position:0%
+area we now know to be concerned with
+ 
+
+ align:start position:0%
+area we now know to be concerned with
+vision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and reading
+
+ align:start position:0%
+and reading
+ 
+
+ align:start position:0%
+and reading
+of course involves not only seeing the
+
+ align:start position:0%
+of course involves not only seeing the
+ 
+
+ align:start position:0%
+of course involves not only seeing the
+words but
+
+ align:start position:0%
+words but
+ 
+
+ align:start position:0%
+words but
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+uttering them speaking them
+
+ align:start position:0%
+uttering them speaking them
+ 
+
+ align:start position:0%
+uttering them speaking them
+and that activated sensory motor cortex
+
+ align:start position:0%
+and that activated sensory motor cortex
+ 
+
+ align:start position:0%
+and that activated sensory motor cortex
+now you say well if he's seeing the
+
+ align:start position:0%
+now you say well if he's seeing the
+ 
+
+ align:start position:0%
+now you say well if he's seeing the
+words why isn't it activating the visual
+
+ align:start position:0%
+words why isn't it activating the visual
+ 
+
+ align:start position:0%
+words why isn't it activating the visual
+system also is in the upper right there
+
+ align:start position:0%
+system also is in the upper right there
+ 
+
+ align:start position:0%
+system also is in the upper right there
+and that points out something that's
+
+ align:start position:0%
+and that points out something that's
+ 
+
+ align:start position:0%
+and that points out something that's
+very important about these imaging that
+
+ align:start position:0%
+very important about these imaging that
+ 
+
+ align:start position:0%
+very important about these imaging that
+they're always using thresholding
+
+ align:start position:0%
+they're always using thresholding
+ 
+
+ align:start position:0%
+they're always using thresholding
+techniques okay so the engineers and the
+
+ align:start position:0%
+techniques okay so the engineers and the
+ 
+
+ align:start position:0%
+techniques okay so the engineers and the
+mathematicians
+
+ align:start position:0%
+mathematicians
+ 
+
+ align:start position:0%
+mathematicians
+are in between the data
+
+ align:start position:0%
+are in between the data
+ 
+
+ align:start position:0%
+are in between the data
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the people that are getting the data and
+
+ align:start position:0%
+the people that are getting the data and
+ 
+
+ align:start position:0%
+the people that are getting the data and
+interpreting it
+
+ align:start position:0%
+interpreting it
+ 
+
+ align:start position:0%
+interpreting it
+okay and they have to choose a cut off
+
+ align:start position:0%
+okay and they have to choose a cut off
+ 
+
+ align:start position:0%
+okay and they have to choose a cut off
+so all it means is the
+
+ align:start position:0%
+so all it means is the
+ 
+
+ align:start position:0%
+so all it means is the
+area with the greatest tissue
+
+ align:start position:0%
+area with the greatest tissue
+ 
+
+ align:start position:0%
+area with the greatest tissue
+oxygenation or the greatest blood blood
+
+ align:start position:0%
+oxygenation or the greatest blood blood
+ 
+
+ align:start position:0%
+oxygenation or the greatest blood blood
+flow
+
+ align:start position:0%
+flow
+ 
+
+ align:start position:0%
+flow
+or sometimes it's even a temperature
+
+ align:start position:0%
+or sometimes it's even a temperature
+ 
+
+ align:start position:0%
+or sometimes it's even a temperature
+change they're looking at
+
+ align:start position:0%
+change they're looking at
+ 
+
+ align:start position:0%
+change they're looking at
+that's what they're showing
+
+ align:start position:0%
+that's what they're showing
+ 
+
+ align:start position:0%
+that's what they're showing
+okay so you're not seeing all the data
+
+ align:start position:0%
+okay so you're not seeing all the data
+ 
+
+ align:start position:0%
+okay so you're not seeing all the data
+in these imaging pictures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that method
+
+ align:start position:0%
+and that method
+ 
+
+ align:start position:0%
+and that method
+often is not discussed adequately and
+
+ align:start position:0%
+often is not discussed adequately and
+ 
+
+ align:start position:0%
+often is not discussed adequately and
+there's not enough variety in my view of
+
+ align:start position:0%
+there's not enough variety in my view of
+ 
+
+ align:start position:0%
+there's not enough variety in my view of
+the methods being used
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk about another discovery that
+
+ align:start position:0%
+let's talk about another discovery that
+ 
+
+ align:start position:0%
+let's talk about another discovery that
+came not that long afterwards
+
+ align:start position:0%
+came not that long afterwards
+ 
+
+ align:start position:0%
+came not that long afterwards
+the discovery of the motor cortex
+
+ align:start position:0%
+the discovery of the motor cortex
+ 
+
+ align:start position:0%
+the discovery of the motor cortex
+fridge and hidsick were two german
+
+ align:start position:0%
+fridge and hidsick were two german
+ 
+
+ align:start position:0%
+fridge and hidsick were two german
+physiologists
+
+ align:start position:0%
+physiologists
+ 
+
+ align:start position:0%
+physiologists
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+did studies of dogs initially using
+
+ align:start position:0%
+did studies of dogs initially using
+ 
+
+ align:start position:0%
+did studies of dogs initially using
+what at that time was fairly new
+
+ align:start position:0%
+what at that time was fairly new
+ 
+
+ align:start position:0%
+what at that time was fairly new
+newly
+
+ align:start position:0%
+newly
+ 
+
+ align:start position:0%
+newly
+developing methods for studying the
+
+ align:start position:0%
+developing methods for studying the
+ 
+
+ align:start position:0%
+developing methods for studying the
+brain electrical stimulation
+
+ align:start position:0%
+brain electrical stimulation
+ 
+
+ align:start position:0%
+brain electrical stimulation
+and they systematically studied
+
+ align:start position:0%
+and they systematically studied
+ 
+
+ align:start position:0%
+and they systematically studied
+the exposed surface of dog brains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trying to put out of our minds for the
+
+ align:start position:0%
+trying to put out of our minds for the
+ 
+
+ align:start position:0%
+trying to put out of our minds for the
+moment that they
+
+ align:start position:0%
+moment that they
+ 
+
+ align:start position:0%
+moment that they
+didn't have anesthetics at that time
+
+ align:start position:0%
+didn't have anesthetics at that time
+ 
+
+ align:start position:0%
+didn't have anesthetics at that time
+they found that they could get movements
+
+ align:start position:0%
+they found that they could get movements
+ 
+
+ align:start position:0%
+they found that they could get movements
+from many different parts of the brain
+
+ align:start position:0%
+from many different parts of the brain
+ 
+
+ align:start position:0%
+from many different parts of the brain
+but there was one region
+
+ align:start position:0%
+but there was one region
+ 
+
+ align:start position:0%
+but there was one region
+where they could get the movement at the
+
+ align:start position:0%
+where they could get the movement at the
+ 
+
+ align:start position:0%
+where they could get the movement at the
+lowest thresholds
+
+ align:start position:0%
+lowest thresholds
+ 
+
+ align:start position:0%
+lowest thresholds
+the least amount of current and they
+
+ align:start position:0%
+the least amount of current and they
+ 
+
+ align:start position:0%
+the least amount of current and they
+call that the motor cortex
+
+ align:start position:0%
+call that the motor cortex
+ 
+
+ align:start position:0%
+call that the motor cortex
+and they found that when they stimulated
+
+ align:start position:0%
+and they found that when they stimulated
+ 
+
+ align:start position:0%
+and they found that when they stimulated
+different parts of the strip of tissue
+
+ align:start position:0%
+different parts of the strip of tissue
+ 
+
+ align:start position:0%
+different parts of the strip of tissue
+different parts of the body moved and it
+
+ align:start position:0%
+different parts of the body moved and it
+ 
+
+ align:start position:0%
+different parts of the body moved and it
+was very systematic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the area they were talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is called in this picture of the human
+
+ align:start position:0%
+is called in this picture of the human
+ 
+
+ align:start position:0%
+is called in this picture of the human
+brain primary motor cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the strip of cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right in front of the central fissure
+
+ align:start position:0%
+right in front of the central fissure
+ 
+
+ align:start position:0%
+right in front of the central fissure
+okay other parts that are called
+
+ align:start position:0%
+okay other parts that are called
+ 
+
+ align:start position:0%
+okay other parts that are called
+pre-motor
+
+ align:start position:0%
+pre-motor
+ 
+
+ align:start position:0%
+pre-motor
+where you also get movements but they're
+
+ align:start position:0%
+where you also get movements but they're
+ 
+
+ align:start position:0%
+where you also get movements but they're
+a little involving larger parts of the
+
+ align:start position:0%
+a little involving larger parts of the
+ 
+
+ align:start position:0%
+a little involving larger parts of the
+body more organized movements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that the topography of that
+
+ align:start position:0%
+and that the topography of that
+ 
+
+ align:start position:0%
+and that the topography of that
+system is expressed in this kind of
+
+ align:start position:0%
+system is expressed in this kind of
+ 
+
+ align:start position:0%
+system is expressed in this kind of
+there's many different versions of that
+
+ align:start position:0%
+there's many different versions of that
+ 
+
+ align:start position:0%
+there's many different versions of that
+this is one for the motor cortex
+
+ align:start position:0%
+this is one for the motor cortex
+ 
+
+ align:start position:0%
+this is one for the motor cortex
+the term homunculus means little man
+
+ align:start position:0%
+the term homunculus means little man
+ 
+
+ align:start position:0%
+the term homunculus means little man
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is the little man in the head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there you see the map
+
+ align:start position:0%
+so there you see the map
+ 
+
+ align:start position:0%
+so there you see the map
+of movements
+
+ align:start position:0%
+of movements
+ 
+
+ align:start position:0%
+of movements
+laid out in a
+
+ align:start position:0%
+laid out in a
+ 
+
+ align:start position:0%
+laid out in a
+more or less frontal section of the
+
+ align:start position:0%
+more or less frontal section of the
+ 
+
+ align:start position:0%
+more or less frontal section of the
+human brain that goes through
+
+ align:start position:0%
+human brain that goes through
+ 
+
+ align:start position:0%
+human brain that goes through
+cuts through that precentral gyrus in
+
+ align:start position:0%
+cuts through that precentral gyrus in
+ 
+
+ align:start position:0%
+cuts through that precentral gyrus in
+front of that the central fissure in the
+
+ align:start position:0%
+front of that the central fissure in the
+ 
+
+ align:start position:0%
+front of that the central fissure in the
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+and they're simply depicting
+
+ align:start position:0%
+and they're simply depicting
+ 
+
+ align:start position:0%
+and they're simply depicting
+both with words and then with pictures
+
+ align:start position:0%
+both with words and then with pictures
+ 
+
+ align:start position:0%
+both with words and then with pictures
+how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different parts of the body are will
+
+ align:start position:0%
+different parts of the body are will
+ 
+
+ align:start position:0%
+different parts of the body are will
+move when you stimulate different parts
+
+ align:start position:0%
+move when you stimulate different parts
+ 
+
+ align:start position:0%
+move when you stimulate different parts
+and you find a much greater
+
+ align:start position:0%
+and you find a much greater
+ 
+
+ align:start position:0%
+and you find a much greater
+representation much more tissue
+
+ align:start position:0%
+representation much more tissue
+ 
+
+ align:start position:0%
+representation much more tissue
+representing say the hands
+
+ align:start position:0%
+representing say the hands
+ 
+
+ align:start position:0%
+representing say the hands
+the lips and the tongue
+
+ align:start position:0%
+the lips and the tongue
+ 
+
+ align:start position:0%
+the lips and the tongue
+than other parts of the body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice in the motor cortex
+
+ align:start position:0%
+notice in the motor cortex
+ 
+
+ align:start position:0%
+notice in the motor cortex
+some things don't appear to be
+
+ align:start position:0%
+some things don't appear to be
+ 
+
+ align:start position:0%
+some things don't appear to be
+represented at all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is another
+
+ align:start position:0%
+this is another
+ 
+
+ align:start position:0%
+this is another
+a picture of the area
+
+ align:start position:0%
+a picture of the area
+ 
+
+ align:start position:0%
+a picture of the area
+the gyrus just behind the motor cortex
+
+ align:start position:0%
+the gyrus just behind the motor cortex
+ 
+
+ align:start position:0%
+the gyrus just behind the motor cortex
+which responds to sensory input now that
+
+ align:start position:0%
+which responds to sensory input now that
+ 
+
+ align:start position:0%
+which responds to sensory input now that
+was discovered later if you stimulate
+
+ align:start position:0%
+was discovered later if you stimulate
+ 
+
+ align:start position:0%
+was discovered later if you stimulate
+the surface of different parts of the
+
+ align:start position:0%
+the surface of different parts of the
+ 
+
+ align:start position:0%
+the surface of different parts of the
+body you will activate
+
+ align:start position:0%
+body you will activate
+ 
+
+ align:start position:0%
+body you will activate
+certain areas much more than others in
+
+ align:start position:0%
+certain areas much more than others in
+ 
+
+ align:start position:0%
+certain areas much more than others in
+the brain
+
+ align:start position:0%
+the brain
+ 
+
+ align:start position:0%
+the brain
+and you'll see that it pretty much
+
+ align:start position:0%
+and you'll see that it pretty much
+ 
+
+ align:start position:0%
+and you'll see that it pretty much
+matches the motor cortex right in front
+
+ align:start position:0%
+matches the motor cortex right in front
+ 
+
+ align:start position:0%
+matches the motor cortex right in front
+of it again much larger
+
+ align:start position:0%
+of it again much larger
+ 
+
+ align:start position:0%
+of it again much larger
+area representing lips
+
+ align:start position:0%
+area representing lips
+ 
+
+ align:start position:0%
+area representing lips
+and face and fingers and hands
+
+ align:start position:0%
+and face and fingers and hands
+ 
+
+ align:start position:0%
+and face and fingers and hands
+than other parts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you always find the face
+
+ align:start position:0%
+and you always find the face
+ 
+
+ align:start position:0%
+and you always find the face
+tongue
+
+ align:start position:0%
+tongue
+ 
+
+ align:start position:0%
+tongue
+and throat
+
+ align:start position:0%
+and throat
+ 
+
+ align:start position:0%
+and throat
+located more ventrally as you go up on
+
+ align:start position:0%
+located more ventrally as you go up on
+ 
+
+ align:start position:0%
+located more ventrally as you go up on
+top
+
+ align:start position:0%
+top
+ 
+
+ align:start position:0%
+top
+you find
+
+ align:start position:0%
+you find
+ 
+
+ align:start position:0%
+you find
+first the hands
+
+ align:start position:0%
+first the hands
+ 
+
+ align:start position:0%
+first the hands
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+more parts of the body and the feet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's another way they represent it
+
+ align:start position:0%
+there's another way they represent it
+ 
+
+ align:start position:0%
+there's another way they represent it
+you get all varieties of these pictures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is another common way to show the
+
+ align:start position:0%
+this is another common way to show the
+ 
+
+ align:start position:0%
+this is another common way to show the
+homunculus to emphasize the
+
+ align:start position:0%
+homunculus to emphasize the
+ 
+
+ align:start position:0%
+homunculus to emphasize the
+distortions
+
+ align:start position:0%
+distortions
+ 
+
+ align:start position:0%
+distortions
+now remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you actually look at the tissue
+
+ align:start position:0%
+if you actually look at the tissue
+ 
+
+ align:start position:0%
+if you actually look at the tissue
+you're not
+
+ align:start position:0%
+you're not
+ 
+
+ align:start position:0%
+you're not
+seeing anything like that this is just a
+
+ align:start position:0%
+seeing anything like that this is just a
+ 
+
+ align:start position:0%
+seeing anything like that this is just a
+way to represent it
+
+ align:start position:0%
+way to represent it
+ 
+
+ align:start position:0%
+way to represent it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+way to represent
+
+ align:start position:0%
+way to represent
+ 
+
+ align:start position:0%
+way to represent
+something when we're talking about
+
+ align:start position:0%
+something when we're talking about
+ 
+
+ align:start position:0%
+something when we're talking about
+sensory cortex we call the relative
+
+ align:start position:0%
+sensory cortex we call the relative
+ 
+
+ align:start position:0%
+sensory cortex we call the relative
+magnification
+
+ align:start position:0%
+magnification
+ 
+
+ align:start position:0%
+magnification
+of the sensory surfaces
+
+ align:start position:0%
+of the sensory surfaces
+ 
+
+ align:start position:0%
+of the sensory surfaces
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but there's a corresponding concept for
+
+ align:start position:0%
+but there's a corresponding concept for
+ 
+
+ align:start position:0%
+but there's a corresponding concept for
+the motor
+
+ align:start position:0%
+the motor
+ 
+
+ align:start position:0%
+the motor
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's more there's a greater area of
+
+ align:start position:0%
+there's more there's a greater area of
+ 
+
+ align:start position:0%
+there's more there's a greater area of
+cortex representing
+
+ align:start position:0%
+cortex representing
+ 
+
+ align:start position:0%
+cortex representing
+a square centimeter of your the skin on
+
+ align:start position:0%
+a square centimeter of your the skin on
+ 
+
+ align:start position:0%
+a square centimeter of your the skin on
+your finger than there is the skin on
+
+ align:start position:0%
+your finger than there is the skin on
+ 
+
+ align:start position:0%
+your finger than there is the skin on
+your back
+
+ align:start position:0%
+your back
+ 
+
+ align:start position:0%
+your back
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not if it's sensory area
+
+ align:start position:0%
+not if it's sensory area
+ 
+
+ align:start position:0%
+not if it's sensory area
+it means for the motor cortex that you
+
+ align:start position:0%
+it means for the motor cortex that you
+ 
+
+ align:start position:0%
+it means for the motor cortex that you
+will get a response
+
+ align:start position:0%
+will get a response
+ 
+
+ align:start position:0%
+will get a response
+say of the finger over a bigger area of
+
+ align:start position:0%
+say of the finger over a bigger area of
+ 
+
+ align:start position:0%
+say of the finger over a bigger area of
+cortex then you will get say the twitch
+
+ align:start position:0%
+cortex then you will get say the twitch
+ 
+
+ align:start position:0%
+cortex then you will get say the twitch
+of a muscle in your back
+
+ align:start position:0%
+of a muscle in your back
+ 
+
+ align:start position:0%
+of a muscle in your back
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+shortly after the motor cortex had been
+
+ align:start position:0%
+shortly after the motor cortex had been
+ 
+
+ align:start position:0%
+shortly after the motor cortex had been
+mapped by fritz and hitzig
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a german anatomist named bets
+
+ align:start position:0%
+a german anatomist named bets
+ 
+
+ align:start position:0%
+a german anatomist named bets
+was doing separate independent studies
+
+ align:start position:0%
+was doing separate independent studies
+ 
+
+ align:start position:0%
+was doing separate independent studies
+and he noticed a very large
+
+ align:start position:0%
+and he noticed a very large
+ 
+
+ align:start position:0%
+and he noticed a very large
+neuron
+
+ align:start position:0%
+neuron
+ 
+
+ align:start position:0%
+neuron
+was consistently located in one part of
+
+ align:start position:0%
+was consistently located in one part of
+ 
+
+ align:start position:0%
+was consistently located in one part of
+the cortex and it turns out that that
+
+ align:start position:0%
+the cortex and it turns out that that
+ 
+
+ align:start position:0%
+the cortex and it turns out that that
+cortex where this very large pyramidal
+
+ align:start position:0%
+cortex where this very large pyramidal
+ 
+
+ align:start position:0%
+cortex where this very large pyramidal
+cell was located in the fifth layer of
+
+ align:start position:0%
+cell was located in the fifth layer of
+ 
+
+ align:start position:0%
+cell was located in the fifth layer of
+the cortex
+
+ align:start position:0%
+the cortex
+ 
+
+ align:start position:0%
+the cortex
+was what was in the motor cortex
+
+ align:start position:0%
+was what was in the motor cortex
+ 
+
+ align:start position:0%
+was what was in the motor cortex
+and that's remained true uh
+
+ align:start position:0%
+and that's remained true uh
+ 
+
+ align:start position:0%
+and that's remained true uh
+ever since that time it was never
+
+ align:start position:0%
+ever since that time it was never
+ 
+
+ align:start position:0%
+ever since that time it was never
+it's it was a finding that was very real
+
+ align:start position:0%
+it's it was a finding that was very real
+ 
+
+ align:start position:0%
+it's it was a finding that was very real
+and we always find these largest
+
+ align:start position:0%
+and we always find these largest
+ 
+
+ align:start position:0%
+and we always find these largest
+pyramidal cells the largest cells in the
+
+ align:start position:0%
+pyramidal cells the largest cells in the
+ 
+
+ align:start position:0%
+pyramidal cells the largest cells in the
+neocortex
+
+ align:start position:0%
+neocortex
+ 
+
+ align:start position:0%
+neocortex
+located in the
+
+ align:start position:0%
+located in the
+ 
+
+ align:start position:0%
+located in the
+precentral gyrus the motor cortex
+
+ align:start position:0%
+precentral gyrus the motor cortex
+ 
+
+ align:start position:0%
+precentral gyrus the motor cortex
+okay we find them there in rats we find
+
+ align:start position:0%
+okay we find them there in rats we find
+ 
+
+ align:start position:0%
+okay we find them there in rats we find
+them there in dogs we find them there in
+
+ align:start position:0%
+them there in dogs we find them there in
+ 
+
+ align:start position:0%
+them there in dogs we find them there in
+humans
+
+ align:start position:0%
+humans
+ 
+
+ align:start position:0%
+humans
+okay there was a question over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good question does the does the
+
+ align:start position:0%
+very good question does the does the
+ 
+
+ align:start position:0%
+very good question does the does the
+size correspond to sensitivity well
+
+ align:start position:0%
+size correspond to sensitivity well
+ 
+
+ align:start position:0%
+size correspond to sensitivity well
+in fact there's a very good correlation
+
+ align:start position:0%
+in fact there's a very good correlation
+ 
+
+ align:start position:0%
+in fact there's a very good correlation
+between sensory acuity and the area of
+
+ align:start position:0%
+between sensory acuity and the area of
+ 
+
+ align:start position:0%
+between sensory acuity and the area of
+cortex
+
+ align:start position:0%
+cortex
+ 
+
+ align:start position:0%
+cortex
+concerned with that part of the body
+
+ align:start position:0%
+concerned with that part of the body
+ 
+
+ align:start position:0%
+concerned with that part of the body
+okay now how do you measure sensory
+
+ align:start position:0%
+okay now how do you measure sensory
+ 
+
+ align:start position:0%
+okay now how do you measure sensory
+acuity
+
+ align:start position:0%
+acuity
+ 
+
+ align:start position:0%
+acuity
+well one
+
+ align:start position:0%
+well one
+ 
+
+ align:start position:0%
+well one
+method would be what's called two-point
+
+ align:start position:0%
+method would be what's called two-point
+ 
+
+ align:start position:0%
+method would be what's called two-point
+discrimination you take you know two
+
+ align:start position:0%
+discrimination you take you know two
+ 
+
+ align:start position:0%
+discrimination you take you know two
+little needles
+
+ align:start position:0%
+little needles
+ 
+
+ align:start position:0%
+little needles
+and you
+
+ align:start position:0%
+and you
+ 
+
+ align:start position:0%
+and you
+if you put them very close together and
+
+ align:start position:0%
+if you put them very close together and
+ 
+
+ align:start position:0%
+if you put them very close together and
+touch the back of my hand
+
+ align:start position:0%
+touch the back of my hand
+ 
+
+ align:start position:0%
+touch the back of my hand
+they will i won't be able to tell that
+
+ align:start position:0%
+they will i won't be able to tell that
+ 
+
+ align:start position:0%
+they will i won't be able to tell that
+there's two but if you make them further
+
+ align:start position:0%
+there's two but if you make them further
+ 
+
+ align:start position:0%
+there's two but if you make them further
+and further apart
+
+ align:start position:0%
+and further apart
+ 
+
+ align:start position:0%
+and further apart
+you know you'll reach a point where i'll
+
+ align:start position:0%
+you know you'll reach a point where i'll
+ 
+
+ align:start position:0%
+you know you'll reach a point where i'll
+say there's two of them
+
+ align:start position:0%
+say there's two of them
+ 
+
+ align:start position:0%
+say there's two of them
+that's two-point discrimination it's a
+
+ align:start position:0%
+that's two-point discrimination it's a
+ 
+
+ align:start position:0%
+that's two-point discrimination it's a
+measure of acuity
+
+ align:start position:0%
+measure of acuity
+ 
+
+ align:start position:0%
+measure of acuity
+well your you will be able to tell
+
+ align:start position:0%
+well your you will be able to tell
+ 
+
+ align:start position:0%
+well your you will be able to tell
+there's two and those two needles are
+
+ align:start position:0%
+there's two and those two needles are
+ 
+
+ align:start position:0%
+there's two and those two needles are
+much closer to each other on the tip of
+
+ align:start position:0%
+much closer to each other on the tip of
+ 
+
+ align:start position:0%
+much closer to each other on the tip of
+your finger
+
+ align:start position:0%
+your finger
+ 
+
+ align:start position:0%
+your finger
+than the back of your hand
+
+ align:start position:0%
+than the back of your hand
+ 
+
+ align:start position:0%
+than the back of your hand
+and either of those will you'll have
+
+ align:start position:0%
+and either of those will you'll have
+ 
+
+ align:start position:0%
+and either of those will you'll have
+much higher acuity than say on the thigh
+
+ align:start position:0%
+much higher acuity than say on the thigh
+ 
+
+ align:start position:0%
+much higher acuity than say on the thigh
+on the back
+
+ align:start position:0%
+on the back
+ 
+
+ align:start position:0%
+on the back
+and that we use that method as a measure
+
+ align:start position:0%
+and that we use that method as a measure
+ 
+
+ align:start position:0%
+and that we use that method as a measure
+of acuity and the correspondence to the
+
+ align:start position:0%
+of acuity and the correspondence to the
+ 
+
+ align:start position:0%
+of acuity and the correspondence to the
+homunculus
+
+ align:start position:0%
+homunculus
+ 
+
+ align:start position:0%
+homunculus
+is very good
+
+ align:start position:0%
+is very good
+ 
+
+ align:start position:0%
+is very good
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does the tissue look different
+
+ align:start position:0%
+does the tissue look different
+ 
+
+ align:start position:0%
+does the tissue look different
+no it basically looks the same
+
+ align:start position:0%
+no it basically looks the same
+ 
+
+ align:start position:0%
+no it basically looks the same
+uh throughout but
+
+ align:start position:0%
+uh throughout but
+ 
+
+ align:start position:0%
+uh throughout but
+it's very interesting question because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the relative growth of brain does affect
+
+ align:start position:0%
+the relative growth of brain does affect
+ 
+
+ align:start position:0%
+the relative growth of brain does affect
+the shape of the gyri the way it folds
+
+ align:start position:0%
+the shape of the gyri the way it folds
+ 
+
+ align:start position:0%
+the shape of the gyri the way it folds
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in animals that have developed large
+
+ align:start position:0%
+in animals that have developed large
+ 
+
+ align:start position:0%
+in animals that have developed large
+representation of certain parts of their
+
+ align:start position:0%
+representation of certain parts of their
+ 
+
+ align:start position:0%
+representation of certain parts of their
+body sometimes they develop separate
+
+ align:start position:0%
+body sometimes they develop separate
+ 
+
+ align:start position:0%
+body sometimes they develop separate
+gyry for each part like the raccoon's
+
+ align:start position:0%
+gyry for each part like the raccoon's
+ 
+
+ align:start position:0%
+gyry for each part like the raccoon's
+hand their separate diary for each
+
+ align:start position:0%
+hand their separate diary for each
+ 
+
+ align:start position:0%
+hand their separate diary for each
+finger he also has a large magnification
+
+ align:start position:0%
+finger he also has a large magnification
+ 
+
+ align:start position:0%
+finger he also has a large magnification
+of the representation of his fingers
+
+ align:start position:0%
+of the representation of his fingers
+ 
+
+ align:start position:0%
+of the representation of his fingers
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's very good question okay why are
+
+ align:start position:0%
+that's very good question okay why are
+ 
+
+ align:start position:0%
+that's very good question okay why are
+the genitals so small in the picture
+
+ align:start position:0%
+the genitals so small in the picture
+ 
+
+ align:start position:0%
+the genitals so small in the picture
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+in fact our two-point discrimination
+
+ align:start position:0%
+in fact our two-point discrimination
+ 
+
+ align:start position:0%
+in fact our two-point discrimination
+the the same kind of sensory ability we
+
+ align:start position:0%
+the the same kind of sensory ability we
+ 
+
+ align:start position:0%
+the the same kind of sensory ability we
+measure in fingers or hands
+
+ align:start position:0%
+measure in fingers or hands
+ 
+
+ align:start position:0%
+measure in fingers or hands
+are not that good
+
+ align:start position:0%
+are not that good
+ 
+
+ align:start position:0%
+are not that good
+genitals
+
+ align:start position:0%
+genitals
+ 
+
+ align:start position:0%
+genitals
+but they're very sensitive because
+
+ align:start position:0%
+but they're very sensitive because
+ 
+
+ align:start position:0%
+but they're very sensitive because
+there's another representation
+
+ align:start position:0%
+there's another representation
+ 
+
+ align:start position:0%
+there's another representation
+for these areas in what in an area more
+
+ align:start position:0%
+for these areas in what in an area more
+ 
+
+ align:start position:0%
+for these areas in what in an area more
+concerned with emotion and motivation
+
+ align:start position:0%
+concerned with emotion and motivation
+ 
+
+ align:start position:0%
+concerned with emotion and motivation
+limbic system okay
+
+ align:start position:0%
+limbic system okay
+ 
+
+ align:start position:0%
+limbic system okay
+that's separate from these sensory areas
+
+ align:start position:0%
+that's separate from these sensory areas
+ 
+
+ align:start position:0%
+that's separate from these sensory areas
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+thank you for giving me an opportunity
+
+ align:start position:0%
+thank you for giving me an opportunity
+ 
+
+ align:start position:0%
+thank you for giving me an opportunity
+to introduce the limbic system so early
+
+ align:start position:0%
+to introduce the limbic system so early
+ 
+
+ align:start position:0%
+to introduce the limbic system so early
+in the class yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say that again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are some differences between males
+
+ align:start position:0%
+there are some differences between males
+ 
+
+ align:start position:0%
+there are some differences between males
+and females but not in these kinds of
+
+ align:start position:0%
+and females but not in these kinds of
+ 
+
+ align:start position:0%
+and females but not in these kinds of
+things except the real the size of
+
+ align:start position:0%
+things except the real the size of
+ 
+
+ align:start position:0%
+things except the real the size of
+the brain tends to correspond to body
+
+ align:start position:0%
+the brain tends to correspond to body
+ 
+
+ align:start position:0%
+the brain tends to correspond to body
+weight there's a very good correlation
+
+ align:start position:0%
+weight there's a very good correlation
+ 
+
+ align:start position:0%
+weight there's a very good correlation
+so male brains tend to be a little
+
+ align:start position:0%
+so male brains tend to be a little
+ 
+
+ align:start position:0%
+so male brains tend to be a little
+bigger but only because of the
+
+ align:start position:0%
+bigger but only because of the
+ 
+
+ align:start position:0%
+bigger but only because of the
+correlation with body size and body
+
+ align:start position:0%
+correlation with body size and body
+ 
+
+ align:start position:0%
+correlation with body size and body
+weight and size
+
+ align:start position:0%
+weight and size
+ 
+
+ align:start position:0%
+weight and size
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there are some other sex differences in
+
+ align:start position:0%
+there are some other sex differences in
+ 
+
+ align:start position:0%
+there are some other sex differences in
+the brain
+
+ align:start position:0%
+the brain
+ 
+
+ align:start position:0%
+the brain
+that i talk about more of the second
+
+ align:start position:0%
+that i talk about more of the second
+ 
+
+ align:start position:0%
+that i talk about more of the second
+term but we will you will read a little
+
+ align:start position:0%
+term but we will you will read a little
+ 
+
+ align:start position:0%
+term but we will you will read a little
+bit about that
+
+ align:start position:0%
+bit about that
+ 
+
+ align:start position:0%
+bit about that
+later in the class
+
+ align:start position:0%
+later in the class
+ 
+
+ align:start position:0%
+later in the class
+these are all very good questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay one more
+
+ align:start position:0%
+okay one more
+ 
+
+ align:start position:0%
+okay one more
+of the early localization is carl
+
+ align:start position:0%
+of the early localization is carl
+ 
+
+ align:start position:0%
+of the early localization is carl
+wernicke who was the most modern of
+
+ align:start position:0%
+wernicke who was the most modern of
+ 
+
+ align:start position:0%
+wernicke who was the most modern of
+these people in the way he thought about
+
+ align:start position:0%
+these people in the way he thought about
+ 
+
+ align:start position:0%
+these people in the way he thought about
+brain function
+
+ align:start position:0%
+brain function
+ 
+
+ align:start position:0%
+brain function
+wernicke
+
+ align:start position:0%
+wernicke
+ 
+
+ align:start position:0%
+wernicke
+whose
+
+ align:start position:0%
+whose
+ 
+
+ align:start position:0%
+whose
+theory was taken up again
+
+ align:start position:0%
+theory was taken up again
+ 
+
+ align:start position:0%
+theory was taken up again
+in the last century
+
+ align:start position:0%
+in the last century
+ 
+
+ align:start position:0%
+in the last century
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+norman geschwind so we now call this the
+
+ align:start position:0%
+norman geschwind so we now call this the
+ 
+
+ align:start position:0%
+norman geschwind so we now call this the
+wernicke geshwant connections model of
+
+ align:start position:0%
+wernicke geshwant connections model of
+ 
+
+ align:start position:0%
+wernicke geshwant connections model of
+speech
+
+ align:start position:0%
+speech
+ 
+
+ align:start position:0%
+speech
+yeshuan was really the founder of the
+
+ align:start position:0%
+yeshuan was really the founder of the
+ 
+
+ align:start position:0%
+yeshuan was really the founder of the
+boston behavioral neurologist school
+
+ align:start position:0%
+boston behavioral neurologist school
+ 
+
+ align:start position:0%
+boston behavioral neurologist school
+and his students still are very
+
+ align:start position:0%
+and his students still are very
+ 
+
+ align:start position:0%
+and his students still are very
+prominent in behavioral neurology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he used to teach with me here at mit i'm
+
+ align:start position:0%
+he used to teach with me here at mit i'm
+ 
+
+ align:start position:0%
+he used to teach with me here at mit i'm
+proud to say
+
+ align:start position:0%
+proud to say
+ 
+
+ align:start position:0%
+proud to say
+but he died a number of years ago
+
+ align:start position:0%
+but he died a number of years ago
+ 
+
+ align:start position:0%
+but he died a number of years ago
+okay so here is broca's area
+
+ align:start position:0%
+okay so here is broca's area
+ 
+
+ align:start position:0%
+okay so here is broca's area
+that we know is concerned with speech
+
+ align:start position:0%
+that we know is concerned with speech
+ 
+
+ align:start position:0%
+that we know is concerned with speech
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+here's the auditory
+
+ align:start position:0%
+here's the auditory
+ 
+
+ align:start position:0%
+here's the auditory
+area shown in purple there
+
+ align:start position:0%
+area shown in purple there
+ 
+
+ align:start position:0%
+area shown in purple there
+here's visual cortex here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wernicke discovered that there was an
+
+ align:start position:0%
+wernicke discovered that there was an
+ 
+
+ align:start position:0%
+wernicke discovered that there was an
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+in the posterior dorsal temporal region
+
+ align:start position:0%
+in the posterior dorsal temporal region
+ 
+
+ align:start position:0%
+in the posterior dorsal temporal region
+of the brain of the left hemisphere in
+
+ align:start position:0%
+of the brain of the left hemisphere in
+ 
+
+ align:start position:0%
+of the brain of the left hemisphere in
+most people that when damaged cause a
+
+ align:start position:0%
+most people that when damaged cause a
+ 
+
+ align:start position:0%
+most people that when damaged cause a
+different kind of disturbance
+
+ align:start position:0%
+different kind of disturbance
+ 
+
+ align:start position:0%
+different kind of disturbance
+of language
+
+ align:start position:0%
+of language
+ 
+
+ align:start position:0%
+of language
+they could still talk
+
+ align:start position:0%
+they could still talk
+ 
+
+ align:start position:0%
+they could still talk
+but they didn't understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nor could they read
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we call that arie wernicke's area
+
+ align:start position:0%
+we call that arie wernicke's area
+ 
+
+ align:start position:0%
+we call that arie wernicke's area
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+wernicke
+
+ align:start position:0%
+wernicke
+ 
+
+ align:start position:0%
+wernicke
+showed
+
+ align:start position:0%
+showed
+ 
+
+ align:start position:0%
+showed
+a a kind of connectionist model of
+
+ align:start position:0%
+a a kind of connectionist model of
+ 
+
+ align:start position:0%
+a a kind of connectionist model of
+speech that is still held to by many
+
+ align:start position:0%
+speech that is still held to by many
+ 
+
+ align:start position:0%
+speech that is still held to by many
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+although there are arguments about it
+
+ align:start position:0%
+although there are arguments about it
+ 
+
+ align:start position:0%
+although there are arguments about it
+so when you hear a word and you hear the
+
+ align:start position:0%
+so when you hear a word and you hear the
+ 
+
+ align:start position:0%
+so when you hear a word and you hear the
+word and then speak it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the input comes into the auditory area
+
+ align:start position:0%
+the input comes into the auditory area
+ 
+
+ align:start position:0%
+the input comes into the auditory area
+of cortex now it comes into subcortical
+
+ align:start position:0%
+of cortex now it comes into subcortical
+ 
+
+ align:start position:0%
+of cortex now it comes into subcortical
+areas first but it does reach the cortex
+
+ align:start position:0%
+areas first but it does reach the cortex
+ 
+
+ align:start position:0%
+areas first but it does reach the cortex
+first in this region
+
+ align:start position:0%
+first in this region
+ 
+
+ align:start position:0%
+first in this region
+the upper part of the temporal lobe
+
+ align:start position:0%
+the upper part of the temporal lobe
+ 
+
+ align:start position:0%
+the upper part of the temporal lobe
+the information he said passes from
+
+ align:start position:0%
+the information he said passes from
+ 
+
+ align:start position:0%
+the information he said passes from
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+to wernicke's area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not necessarily with a single synapse it
+
+ align:start position:0%
+not necessarily with a single synapse it
+ 
+
+ align:start position:0%
+not necessarily with a single synapse it
+might take a couple
+
+ align:start position:0%
+might take a couple
+ 
+
+ align:start position:0%
+might take a couple
+okay and the information then to
+
+ align:start position:0%
+okay and the information then to
+ 
+
+ align:start position:0%
+okay and the information then to
+actually speak the word has to go from
+
+ align:start position:0%
+actually speak the word has to go from
+ 
+
+ align:start position:0%
+actually speak the word has to go from
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+through long accents that go to broca's
+
+ align:start position:0%
+through long accents that go to broca's
+ 
+
+ align:start position:0%
+through long accents that go to broca's
+area and then to the motor cortex
+
+ align:start position:0%
+area and then to the motor cortex
+ 
+
+ align:start position:0%
+area and then to the motor cortex
+that model is and then he said for
+
+ align:start position:0%
+that model is and then he said for
+ 
+
+ align:start position:0%
+that model is and then he said for
+reading
+
+ align:start position:0%
+reading
+ 
+
+ align:start position:0%
+reading
+if you have a written word you see it
+
+ align:start position:0%
+if you have a written word you see it
+ 
+
+ align:start position:0%
+if you have a written word you see it
+and speak the word the information comes
+
+ align:start position:0%
+and speak the word the information comes
+ 
+
+ align:start position:0%
+and speak the word the information comes
+into the visual cortex and has to go
+
+ align:start position:0%
+into the visual cortex and has to go
+ 
+
+ align:start position:0%
+into the visual cortex and has to go
+from there
+
+ align:start position:0%
+from there
+ 
+
+ align:start position:0%
+from there
+to an association area which connects to
+
+ align:start position:0%
+to an association area which connects to
+ 
+
+ align:start position:0%
+to an association area which connects to
+wernicke's area
+
+ align:start position:0%
+wernicke's area
+ 
+
+ align:start position:0%
+wernicke's area
+and then again the rest of it's the same
+
+ align:start position:0%
+and then again the rest of it's the same
+ 
+
+ align:start position:0%
+and then again the rest of it's the same
+goes to broca's area and then to the
+
+ align:start position:0%
+goes to broca's area and then to the
+ 
+
+ align:start position:0%
+goes to broca's area and then to the
+motor cortex okay
+
+ align:start position:0%
+motor cortex okay
+ 
+
+ align:start position:0%
+motor cortex okay
+now that model has been supported
+
+ align:start position:0%
+now that model has been supported
+ 
+
+ align:start position:0%
+now that model has been supported
+by a number of lesion studies including
+
+ align:start position:0%
+by a number of lesion studies including
+ 
+
+ align:start position:0%
+by a number of lesion studies including
+studies where people have suffered a
+
+ align:start position:0%
+studies where people have suffered a
+ 
+
+ align:start position:0%
+studies where people have suffered a
+disconnection of one of those pathways
+
+ align:start position:0%
+disconnection of one of those pathways
+ 
+
+ align:start position:0%
+disconnection of one of those pathways
+so for example if people
+
+ align:start position:0%
+so for example if people
+ 
+
+ align:start position:0%
+so for example if people
+lose the connections between the posture
+
+ align:start position:0%
+lose the connections between the posture
+ 
+
+ align:start position:0%
+lose the connections between the posture
+temporal region and the frontal cortex
+
+ align:start position:0%
+temporal region and the frontal cortex
+ 
+
+ align:start position:0%
+temporal region and the frontal cortex
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+brain damage that sever is what we call
+
+ align:start position:0%
+brain damage that sever is what we call
+ 
+
+ align:start position:0%
+brain damage that sever is what we call
+the arcuate fasciculus
+
+ align:start position:0%
+the arcuate fasciculus
+ 
+
+ align:start position:0%
+the arcuate fasciculus
+they can understand speech and they can
+
+ align:start position:0%
+they can understand speech and they can
+ 
+
+ align:start position:0%
+they can understand speech and they can
+speak but when they speak
+
+ align:start position:0%
+speak but when they speak
+ 
+
+ align:start position:0%
+speak but when they speak
+they speak sort of a word salad
+
+ align:start position:0%
+they speak sort of a word salad
+ 
+
+ align:start position:0%
+they speak sort of a word salad
+it doesn't make sense because they don't
+
+ align:start position:0%
+it doesn't make sense because they don't
+ 
+
+ align:start position:0%
+it doesn't make sense because they don't
+have the normal connection between the
+
+ align:start position:0%
+have the normal connection between the
+ 
+
+ align:start position:0%
+have the normal connection between the
+areas comprehension and the area needed
+
+ align:start position:0%
+areas comprehension and the area needed
+ 
+
+ align:start position:0%
+areas comprehension and the area needed
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+producing the utterance utterances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now these people use different words for
+
+ align:start position:0%
+now these people use different words for
+ 
+
+ align:start position:0%
+now these people use different words for
+talking about these than we do
+
+ align:start position:0%
+talking about these than we do
+ 
+
+ align:start position:0%
+talking about these than we do
+especially bronco he talked about this
+
+ align:start position:0%
+especially bronco he talked about this
+ 
+
+ align:start position:0%
+especially bronco he talked about this
+area being sort of a depot of
+
+ align:start position:0%
+area being sort of a depot of
+ 
+
+ align:start position:0%
+area being sort of a depot of
+representations for
+
+ align:start position:0%
+representations for
+ 
+
+ align:start position:0%
+representations for
+speech articulation
+
+ align:start position:0%
+speech articulation
+ 
+
+ align:start position:0%
+speech articulation
+but what happened afterwards was very
+
+ align:start position:0%
+but what happened afterwards was very
+ 
+
+ align:start position:0%
+but what happened afterwards was very
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+now a neurologist every time they had a
+
+ align:start position:0%
+now a neurologist every time they had a
+ 
+
+ align:start position:0%
+now a neurologist every time they had a
+patient
+
+ align:start position:0%
+patient
+ 
+
+ align:start position:0%
+patient
+with a specific brain damage that could
+
+ align:start position:0%
+with a specific brain damage that could
+ 
+
+ align:start position:0%
+with a specific brain damage that could
+be localized they tried to specify the
+
+ align:start position:0%
+be localized they tried to specify the
+ 
+
+ align:start position:0%
+be localized they tried to specify the
+function that was disturbed and these
+
+ align:start position:0%
+function that was disturbed and these
+ 
+
+ align:start position:0%
+function that was disturbed and these
+maps of
+
+ align:start position:0%
+maps of
+ 
+
+ align:start position:0%
+maps of
+functional maps of the brain got more
+
+ align:start position:0%
+functional maps of the brain got more
+ 
+
+ align:start position:0%
+functional maps of the brain got more
+and more elaborate this is a little
+
+ align:start position:0%
+and more elaborate this is a little
+ 
+
+ align:start position:0%
+and more elaborate this is a little
+yellow because i took it out of a
+
+ align:start position:0%
+yellow because i took it out of a
+ 
+
+ align:start position:0%
+yellow because i took it out of a
+book of alexander luria a russian
+
+ align:start position:0%
+book of alexander luria a russian
+ 
+
+ align:start position:0%
+book of alexander luria a russian
+neuropsychologist
+
+ align:start position:0%
+neuropsychologist
+ 
+
+ align:start position:0%
+neuropsychologist
+is the only place i could find this map
+
+ align:start position:0%
+is the only place i could find this map
+ 
+
+ align:start position:0%
+is the only place i could find this map
+it shows many many different details and
+
+ align:start position:0%
+it shows many many different details and
+ 
+
+ align:start position:0%
+it shows many many different details and
+the details
+
+ align:start position:0%
+the details
+ 
+
+ align:start position:0%
+the details
+the functions are sometimes do
+
+ align:start position:0%
+the functions are sometimes do
+ 
+
+ align:start position:0%
+the functions are sometimes do
+correspond to physiological functions
+
+ align:start position:0%
+correspond to physiological functions
+ 
+
+ align:start position:0%
+correspond to physiological functions
+and sometimes they're more psychological
+
+ align:start position:0%
+and sometimes they're more psychological
+ 
+
+ align:start position:0%
+and sometimes they're more psychological
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+and that sometimes raised some
+
+ align:start position:0%
+and that sometimes raised some
+ 
+
+ align:start position:0%
+and that sometimes raised some
+difficulties but what the maps did is
+
+ align:start position:0%
+difficulties but what the maps did is
+ 
+
+ align:start position:0%
+difficulties but what the maps did is
+simply summarize neurological findings
+
+ align:start position:0%
+simply summarize neurological findings
+ 
+
+ align:start position:0%
+simply summarize neurological findings
+so if you knew that
+
+ align:start position:0%
+so if you knew that
+ 
+
+ align:start position:0%
+so if you knew that
+if you look at this map then you'll know
+
+ align:start position:0%
+if you look at this map then you'll know
+ 
+
+ align:start position:0%
+if you look at this map then you'll know
+that okay somebody that suffered the
+
+ align:start position:0%
+that okay somebody that suffered the
+ 
+
+ align:start position:0%
+that okay somebody that suffered the
+damage in that area
+
+ align:start position:0%
+damage in that area
+ 
+
+ align:start position:0%
+damage in that area
+had that
+
+ align:start position:0%
+had that
+ 
+
+ align:start position:0%
+had that
+disturbance of that function one problem
+
+ align:start position:0%
+disturbance of that function one problem
+ 
+
+ align:start position:0%
+disturbance of that function one problem
+is is that lesions are often not very
+
+ align:start position:0%
+is is that lesions are often not very
+ 
+
+ align:start position:0%
+is is that lesions are often not very
+precisely localized they could easily
+
+ align:start position:0%
+precisely localized they could easily
+ 
+
+ align:start position:0%
+precisely localized they could easily
+make mistakes and sometimes the lesions
+
+ align:start position:0%
+make mistakes and sometimes the lesions
+ 
+
+ align:start position:0%
+make mistakes and sometimes the lesions
+would disturb connections between areas
+
+ align:start position:0%
+would disturb connections between areas
+ 
+
+ align:start position:0%
+would disturb connections between areas
+and not just the
+
+ align:start position:0%
+and not just the
+ 
+
+ align:start position:0%
+and not just the
+the cells in that region
+
+ align:start position:0%
+the cells in that region
+ 
+
+ align:start position:0%
+the cells in that region
+and by the time the first textbook in
+
+ align:start position:0%
+and by the time the first textbook in
+ 
+
+ align:start position:0%
+and by the time the first textbook in
+physiological psychology came out
+
+ align:start position:0%
+physiological psychology came out
+ 
+
+ align:start position:0%
+physiological psychology came out
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+word that was used for the field that
+
+ align:start position:0%
+word that was used for the field that
+ 
+
+ align:start position:0%
+word that was used for the field that
+now we just call neuroscience or
+
+ align:start position:0%
+now we just call neuroscience or
+ 
+
+ align:start position:0%
+now we just call neuroscience or
+behavioral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neuroscience was a book by morgan and
+
+ align:start position:0%
+neuroscience was a book by morgan and
+ 
+
+ align:start position:0%
+neuroscience was a book by morgan and
+stellar it came out in 1950 their maps
+
+ align:start position:0%
+stellar it came out in 1950 their maps
+ 
+
+ align:start position:0%
+stellar it came out in 1950 their maps
+were much much simpler than the kleist
+
+ align:start position:0%
+were much much simpler than the kleist
+ 
+
+ align:start position:0%
+were much much simpler than the kleist
+map so just between 1935 and 1950 there
+
+ align:start position:0%
+map so just between 1935 and 1950 there
+ 
+
+ align:start position:0%
+map so just between 1935 and 1950 there
+was this regress people became more
+
+ align:start position:0%
+was this regress people became more
+ 
+
+ align:start position:0%
+was this regress people became more
+critical
+
+ align:start position:0%
+critical
+ 
+
+ align:start position:0%
+critical
+and weren't so willing to accept
+
+ align:start position:0%
+and weren't so willing to accept
+ 
+
+ align:start position:0%
+and weren't so willing to accept
+these localizations
+
+ align:start position:0%
+these localizations
+ 
+
+ align:start position:0%
+these localizations
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+by that time many contradictions had
+
+ align:start position:0%
+by that time many contradictions had
+ 
+
+ align:start position:0%
+by that time many contradictions had
+appeared in the literature so morgan and
+
+ align:start position:0%
+appeared in the literature so morgan and
+ 
+
+ align:start position:0%
+appeared in the literature so morgan and
+stella weren't they felt that if you
+
+ align:start position:0%
+stella weren't they felt that if you
+ 
+
+ align:start position:0%
+stella weren't they felt that if you
+didn't do precise experiments with many
+
+ align:start position:0%
+didn't do precise experiments with many
+ 
+
+ align:start position:0%
+didn't do precise experiments with many
+cases especially if it were backed up by
+
+ align:start position:0%
+cases especially if it were backed up by
+ 
+
+ align:start position:0%
+cases especially if it were backed up by
+animal studies you couldn't really
+
+ align:start position:0%
+animal studies you couldn't really
+ 
+
+ align:start position:0%
+animal studies you couldn't really
+believe it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now next time we're going to deal
+
+ align:start position:0%
+okay now next time we're going to deal
+ 
+
+ align:start position:0%
+okay now next time we're going to deal
+with this issue
+
+ align:start position:0%
+with this issue
+ 
+
+ align:start position:0%
+with this issue
+how can you carve up the soul like this
+
+ align:start position:0%
+how can you carve up the soul like this
+ 
+
+ align:start position:0%
+how can you carve up the soul like this
+aren't we unified beings
+
+ align:start position:0%
+aren't we unified beings
+ 
+
+ align:start position:0%
+aren't we unified beings
+are we really just this
+
+ align:start position:0%
+are we really just this
+ 
+
+ align:start position:0%
+are we really just this
+but a collection of functions
+
+ align:start position:0%
+but a collection of functions
+ 
+
+ align:start position:0%
+but a collection of functions
+represented in different parts of the
+
+ align:start position:0%
+represented in different parts of the
+ 
+
+ align:start position:0%
+represented in different parts of the
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+read this
+
+ align:start position:0%
+read this
+ 
+
+ align:start position:0%
+read this
+bring your notes to class next time and
+
+ align:start position:0%
+bring your notes to class next time and
+ 
+
+ align:start position:0%
+bring your notes to class next time and
+we'll continue with the discussion then
\ No newline at end of file
diff --git a/_0LtZx6epcg.txt b/_0LtZx6epcg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b0999e4ead62bdd8cd68b6d875f88aa90d2f909b
--- /dev/null
+++ b/_0LtZx6epcg.txt
@@ -0,0 +1,827 @@
+align:start position:0%
+ 
+skin effect describes the tendency for
+
+ align:start position:0%
+skin effect describes the tendency for
+ 
+
+ align:start position:0%
+skin effect describes the tendency for
+highfrequency currents to be near
+
+ align:start position:0%
+highfrequency currents to be near
+ 
+
+ align:start position:0%
+highfrequency currents to be near
+surfaces of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conductors here's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiment the section where essentially
+
+ align:start position:0%
+experiment the section where essentially
+ 
+
+ align:start position:0%
+experiment the section where essentially
+onedimensional magnetic diffusion occurs
+
+ align:start position:0%
+onedimensional magnetic diffusion occurs
+ 
+
+ align:start position:0%
+onedimensional magnetic diffusion occurs
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here by making the conductor long in the
+
+ align:start position:0%
+here by making the conductor long in the
+ 
+
+ align:start position:0%
+here by making the conductor long in the
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+direction we provide enough length for
+
+ align:start position:0%
+direction we provide enough length for
+ 
+
+ align:start position:0%
+direction we provide enough length for
+the current distribution to become
+
+ align:start position:0%
+the current distribution to become
+ 
+
+ align:start position:0%
+the current distribution to become
+primarily dependent on X over the middle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross-section to avoid an influence of
+
+ align:start position:0%
+cross-section to avoid an influence of
+ 
+
+ align:start position:0%
+cross-section to avoid an influence of
+the magnetic core on the field
+
+ align:start position:0%
+the magnetic core on the field
+ 
+
+ align:start position:0%
+the magnetic core on the field
+distribution here at the
+
+ align:start position:0%
+distribution here at the
+ 
+
+ align:start position:0%
+distribution here at the
+center we've placed it to one end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this transverse probe can be inserted so
+
+ align:start position:0%
+this transverse probe can be inserted so
+ 
+
+ align:start position:0%
+this transverse probe can be inserted so
+that it samples the vertical magnetic
+
+ align:start position:0%
+that it samples the vertical magnetic
+ 
+
+ align:start position:0%
+that it samples the vertical magnetic
+field intensity over the span of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conductor the field component normal to
+
+ align:start position:0%
+conductor the field component normal to
+ 
+
+ align:start position:0%
+conductor the field component normal to
+the flat phase is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measured the slit is little more than
+
+ align:start position:0%
+measured the slit is little more than
+ 
+
+ align:start position:0%
+measured the slit is little more than
+large enough enough for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probe the top Trace is the current in
+
+ align:start position:0%
+probe the top Trace is the current in
+ 
+
+ align:start position:0%
+probe the top Trace is the current in
+the primary of the Transformer the
+
+ align:start position:0%
+the primary of the Transformer the
+ 
+
+ align:start position:0%
+the primary of the Transformer the
+driving
+
+ align:start position:0%
+driving
+ 
+
+ align:start position:0%
+driving
+current the bottom Trace is the probe
+
+ align:start position:0%
+current the bottom Trace is the probe
+ 
+
+ align:start position:0%
+current the bottom Trace is the probe
+signal the magnetic flux
+
+ align:start position:0%
+signal the magnetic flux
+ 
+
+ align:start position:0%
+signal the magnetic flux
+density as we pull the probe
+
+ align:start position:0%
+density as we pull the probe
+ 
+
+ align:start position:0%
+density as we pull the probe
+out we see the field distribution with x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the frequency is 60
+
+ align:start position:0%
+the frequency is 60
+ 
+
+ align:start position:0%
+the frequency is 60
+hertz here we're at 3 cm half the slab
+
+ align:start position:0%
+hertz here we're at 3 cm half the slab
+ 
+
+ align:start position:0%
+hertz here we're at 3 cm half the slab
+thickness it appears that the Decay is
+
+ align:start position:0%
+thickness it appears that the Decay is
+ 
+
+ align:start position:0%
+thickness it appears that the Decay is
+somewhat more rapid than
+
+ align:start position:0%
+somewhat more rapid than
+ 
+
+ align:start position:0%
+somewhat more rapid than
+linear so it looks like the skin depth
+
+ align:start position:0%
+linear so it looks like the skin depth
+ 
+
+ align:start position:0%
+linear so it looks like the skin depth
+at 60 HZ is less than the thickness of
+
+ align:start position:0%
+at 60 HZ is less than the thickness of
+ 
+
+ align:start position:0%
+at 60 HZ is less than the thickness of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aluminum here's a prediction of the
+
+ align:start position:0%
+aluminum here's a prediction of the
+ 
+
+ align:start position:0%
+aluminum here's a prediction of the
+field Decay with distance from the left
+
+ align:start position:0%
+field Decay with distance from the left
+ 
+
+ align:start position:0%
+field Decay with distance from the left
+edge of the conductor
+
+ align:start position:0%
+edge of the conductor
+ 
+
+ align:start position:0%
+edge of the conductor
+this curve is for 60
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hertz in going from 0 to 1 cm here on
+
+ align:start position:0%
+hertz in going from 0 to 1 cm here on
+ 
+
+ align:start position:0%
+hertz in going from 0 to 1 cm here on
+the 60 Herz curve we should see the
+
+ align:start position:0%
+the 60 Herz curve we should see the
+ 
+
+ align:start position:0%
+the 60 Herz curve we should see the
+field Decay by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+40% what we measure decays to about 50%
+
+ align:start position:0%
+40% what we measure decays to about 50%
+ 
+
+ align:start position:0%
+40% what we measure decays to about 50%
+of its original value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value remember the skin depth is
+
+ align:start position:0%
+value remember the skin depth is
+ 
+
+ align:start position:0%
+value remember the skin depth is
+inversely proportional to the square
+
+ align:start position:0%
+inversely proportional to the square
+ 
+
+ align:start position:0%
+inversely proportional to the square
+root of the
+
+ align:start position:0%
+root of the
+ 
+
+ align:start position:0%
+root of the
+frequency so if we increase the
+
+ align:start position:0%
+frequency so if we increase the
+ 
+
+ align:start position:0%
+frequency so if we increase the
+frequency to 240 Herz four times the
+
+ align:start position:0%
+frequency to 240 Herz four times the
+ 
+
+ align:start position:0%
+frequency to 240 Herz four times the
+frequency the skin depth is half as much
+
+ align:start position:0%
+frequency the skin depth is half as much
+ 
+
+ align:start position:0%
+frequency the skin depth is half as much
+and the Decay should be more rapid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the Decay at 60
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+HZ here we're at 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cm here we're at 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cm now we raise the frequency to 240
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Herz this is the Decay at 240
+
+ align:start position:0%
+Herz this is the Decay at 240
+ 
+
+ align:start position:0%
+Herz this is the Decay at 240
+hertz 1
+
+ align:start position:0%
+hertz 1
+ 
+
+ align:start position:0%
+hertz 1
+cm 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cm the Decay at 1 cm and 240 HZ plots
+
+ align:start position:0%
+cm the Decay at 1 cm and 240 HZ plots
+ 
+
+ align:start position:0%
+cm the Decay at 1 cm and 240 HZ plots
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this these are additional data
+
+ align:start position:0%
+this these are additional data
+ 
+
+ align:start position:0%
+this these are additional data
+points here's the measured Decay at 2 40
+
+ align:start position:0%
+points here's the measured Decay at 2 40
+ 
+
+ align:start position:0%
+points here's the measured Decay at 2 40
+HZ here at 60
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+HZ the discrepancy is probably due to
+
+ align:start position:0%
+HZ the discrepancy is probably due to
+ 
+
+ align:start position:0%
+HZ the discrepancy is probably due to
+the finite length of the aluminum in the
+
+ align:start position:0%
+the finite length of the aluminum in the
+ 
+
+ align:start position:0%
+the finite length of the aluminum in the
+direction of current
+
+ align:start position:0%
+direction of current
+ 
+
+ align:start position:0%
+direction of current
+circulation our one-dimensional Theory
+
+ align:start position:0%
+circulation our one-dimensional Theory
+ 
+
+ align:start position:0%
+circulation our one-dimensional Theory
+strictly applies only where the currents
+
+ align:start position:0%
+strictly applies only where the currents
+ 
+
+ align:start position:0%
+strictly applies only where the currents
+have had sufficient development length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when the skin depth is short compared to
+
+ align:start position:0%
+when the skin depth is short compared to
+ 
+
+ align:start position:0%
+when the skin depth is short compared to
+the conductor thickness the current
+
+ align:start position:0%
+the conductor thickness the current
+ 
+
+ align:start position:0%
+the conductor thickness the current
+distribution takes the form of a
+
+ align:start position:0%
+distribution takes the form of a
+ 
+
+ align:start position:0%
+distribution takes the form of a
+wave we've been observing the decay of
+
+ align:start position:0%
+wave we've been observing the decay of
+ 
+
+ align:start position:0%
+wave we've been observing the decay of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+wave there's also a phase shift with X
+
+ align:start position:0%
+wave there's also a phase shift with X
+ 
+
+ align:start position:0%
+wave there's also a phase shift with X
+caused by the propagation of this
+
+ align:start position:0%
+caused by the propagation of this
+ 
+
+ align:start position:0%
+caused by the propagation of this
+diffusion wave into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conductor by looking at the probe signal
+
+ align:start position:0%
+conductor by looking at the probe signal
+ 
+
+ align:start position:0%
+conductor by looking at the probe signal
+on an oscilloscope we can see this phase
+
+ align:start position:0%
+on an oscilloscope we can see this phase
+ 
+
+ align:start position:0%
+on an oscilloscope we can see this phase
+shift as the probe is
+
+ align:start position:0%
+shift as the probe is
+ 
+
+ align:start position:0%
+shift as the probe is
+withdrawn the top Trace is the exitation
+
+ align:start position:0%
+withdrawn the top Trace is the exitation
+ 
+
+ align:start position:0%
+withdrawn the top Trace is the exitation
+current the bottom one probe current
+
+ align:start position:0%
+current the bottom one probe current
+ 
+
+ align:start position:0%
+current the bottom one probe current
+sync to the exitation
+
+ align:start position:0%
+sync to the exitation
+ 
+
+ align:start position:0%
+sync to the exitation
+current the frequency is 240 Herz so as
+
+ align:start position:0%
+current the frequency is 240 Herz so as
+ 
+
+ align:start position:0%
+current the frequency is 240 Herz so as
+the probe is withdrawn the field decays
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rapidly to see the phase shift
+
+ align:start position:0%
+rapidly to see the phase shift
+ 
+
+ align:start position:0%
+rapidly to see the phase shift
+associated with the propagation let's
+
+ align:start position:0%
+associated with the propagation let's
+ 
+
+ align:start position:0%
+associated with the propagation let's
+put the probe signal on top of the
+
+ align:start position:0%
+put the probe signal on top of the
+ 
+
+ align:start position:0%
+put the probe signal on top of the
+driving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signal watch the position of a peak in
+
+ align:start position:0%
+signal watch the position of a peak in
+ 
+
+ align:start position:0%
+signal watch the position of a peak in
+the probe signal relative to that of the
+
+ align:start position:0%
+the probe signal relative to that of the
+ 
+
+ align:start position:0%
+the probe signal relative to that of the
+driving current as the probe is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+withdrawn as the probe is pulled into
+
+ align:start position:0%
+withdrawn as the probe is pulled into
+ 
+
+ align:start position:0%
+withdrawn as the probe is pulled into
+the conductor it measures a field that
+
+ align:start position:0%
+the conductor it measures a field that
+ 
+
+ align:start position:0%
+the conductor it measures a field that
+is increasingly delayed in phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the magnitude of the magnetic diffusion
+
+ align:start position:0%
+the magnitude of the magnetic diffusion
+ 
+
+ align:start position:0%
+the magnitude of the magnetic diffusion
+wave decays exponentially into the
+
+ align:start position:0%
+wave decays exponentially into the
+ 
+
+ align:start position:0%
+wave decays exponentially into the
+conductor with a Decay length that is
+
+ align:start position:0%
+conductor with a Decay length that is
+ 
+
+ align:start position:0%
+conductor with a Decay length that is
+the skin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depth the phase shift shows that the
+
+ align:start position:0%
+depth the phase shift shows that the
+ 
+
+ align:start position:0%
+depth the phase shift shows that the
+wave has phases that propagate into the
+
+ align:start position:0%
+wave has phases that propagate into the
+ 
+
+ align:start position:0%
+wave has phases that propagate into the
+conductor for
\ No newline at end of file
diff --git a/_CdoRiNSrqI.txt b/_CdoRiNSrqI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..67263acc897d50f6ea0d76f9bcf33f4a853a2155
--- /dev/null
+++ b/_CdoRiNSrqI.txt
@@ -0,0 +1,7563 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu today I'm going to tell you
+
+ align:start position:0%
+ocw.mit.edu today I'm going to tell you
+ 
+
+ align:start position:0%
+ocw.mit.edu today I'm going to tell you
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flux of uh vector bu through a curve
+
+ align:start position:0%
+flux of uh vector bu through a curve
+ 
+
+ align:start position:0%
+flux of uh vector bu through a curve
+so you know in case you've seen flux in
+
+ align:start position:0%
+so you know in case you've seen flux in
+ 
+
+ align:start position:0%
+so you know in case you've seen flux in
+physics probably you've seen flux in
+
+ align:start position:0%
+physics probably you've seen flux in
+ 
+
+ align:start position:0%
+physics probably you've seen flux in
+space and we're going to come to that in
+
+ align:start position:0%
+space and we're going to come to that in
+ 
+
+ align:start position:0%
+space and we're going to come to that in
+a couple of weeks but for now we still
+
+ align:start position:0%
+a couple of weeks but for now we still
+ 
+
+ align:start position:0%
+a couple of weeks but for now we still
+doing everything in the plane so you
+
+ align:start position:0%
+doing everything in the plane so you
+ 
+
+ align:start position:0%
+doing everything in the plane so you
+know bear with me if you've seen a more
+
+ align:start position:0%
+know bear with me if you've seen a more
+ 
+
+ align:start position:0%
+know bear with me if you've seen a more
+complicated version of flux we're going
+
+ align:start position:0%
+complicated version of flux we're going
+ 
+
+ align:start position:0%
+complicated version of flux we're going
+to do the easy one
+
+ align:start position:0%
+to do the easy one
+ 
+
+ align:start position:0%
+to do the easy one
+first uh so what is flux well flux it's
+
+ align:start position:0%
+first uh so what is flux well flux it's
+ 
+
+ align:start position:0%
+first uh so what is flux well flux it's
+actually another kind of line ingal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say that I have a plain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve and a vector fied in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane then the
+
+ align:start position:0%
+plane then the
+ 
+
+ align:start position:0%
+plane then the
+flux of
+
+ align:start position:0%
+flux of
+ 
+
+ align:start position:0%
+flux of
+f across a curve
+
+ align:start position:0%
+f across a curve
+ 
+
+ align:start position:0%
+f across a curve
+C is by definition it's a line integral
+
+ align:start position:0%
+C is by definition it's a line integral
+ 
+
+ align:start position:0%
+C is by definition it's a line integral
+but I will use I will use notation f. n
+
+ align:start position:0%
+but I will use I will use notation f. n
+ 
+
+ align:start position:0%
+but I will use I will use notation f. n
+DS so I have to explain to you what it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means but let me first box that because
+
+ align:start position:0%
+means but let me first box that because
+ 
+
+ align:start position:0%
+means but let me first box that because
+that's the important formula to remember
+
+ align:start position:0%
+that's the important formula to remember
+ 
+
+ align:start position:0%
+that's the important formula to remember
+that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition so what does that
+
+ align:start position:0%
+definition so what does that
+ 
+
+ align:start position:0%
+definition so what does that
+mean so first I mean I have mostly I
+
+ align:start position:0%
+mean so first I mean I have mostly I
+ 
+
+ align:start position:0%
+mean so first I mean I have mostly I
+have to tell you what is this little n
+
+ align:start position:0%
+have to tell you what is this little n
+ 
+
+ align:start position:0%
+have to tell you what is this little n
+so n the notation suggests you know it's
+
+ align:start position:0%
+so n the notation suggests you know it's
+ 
+
+ align:start position:0%
+so n the notation suggests you know it's
+a normal Vector so what does what does
+
+ align:start position:0%
+a normal Vector so what does what does
+ 
+
+ align:start position:0%
+a normal Vector so what does what does
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean so I have a curve in the
+
+ align:start position:0%
+mean so I have a curve in the
+ 
+
+ align:start position:0%
+mean so I have a curve in the
+plane and I have a vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field let's see my Vector field will be
+
+ align:start position:0%
+field let's see my Vector field will be
+ 
+
+ align:start position:0%
+field let's see my Vector field will be
+yellow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today and I will want to integrate along
+
+ align:start position:0%
+today and I will want to integrate along
+ 
+
+ align:start position:0%
+today and I will want to integrate along
+the Curve
+
+ align:start position:0%
+the Curve
+ 
+
+ align:start position:0%
+the Curve
+the dot product of f with the normal
+
+ align:start position:0%
+the dot product of f with the normal
+ 
+
+ align:start position:0%
+the dot product of f with the normal
+Vector to the curve the unit normal
+
+ align:start position:0%
+Vector to the curve the unit normal
+ 
+
+ align:start position:0%
+Vector to the curve the unit normal
+Vector to the curve so that means a
+
+ align:start position:0%
+Vector to the curve so that means a
+ 
+
+ align:start position:0%
+Vector to the curve so that means a
+vector that's at every point of the
+
+ align:start position:0%
+vector that's at every point of the
+ 
+
+ align:start position:0%
+vector that's at every point of the
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+perpendicular to the curve and of length
+
+ align:start position:0%
+perpendicular to the curve and of length
+ 
+
+ align:start position:0%
+perpendicular to the curve and of length
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so n
+
+ align:start position:0%
+so n
+ 
+
+ align:start position:0%
+so n
+everywhere will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be the unit
+
+ align:start position:0%
+be the unit
+ 
+
+ align:start position:0%
+be the unit
+normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector to the curve
+
+ align:start position:0%
+Vector to the curve
+ 
+
+ align:start position:0%
+Vector to the curve
+C pointing 90°
+
+ align:start position:0%
+C pointing 90°
+ 
+
+ align:start position:0%
+C pointing 90°
+clockwise from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T so what does that mean that means you
+
+ align:start position:0%
+T so what does that mean that means you
+ 
+
+ align:start position:0%
+T so what does that mean that means you
+know I have two normal vectors one
+
+ align:start position:0%
+know I have two normal vectors one
+ 
+
+ align:start position:0%
+know I have two normal vectors one
+that's pointing this way one that's
+
+ align:start position:0%
+that's pointing this way one that's
+ 
+
+ align:start position:0%
+that's pointing this way one that's
+pointing that way I have to choose a
+
+ align:start position:0%
+pointing that way I have to choose a
+ 
+
+ align:start position:0%
+pointing that way I have to choose a
+convention and the convention is that
+
+ align:start position:0%
+convention and the convention is that
+ 
+
+ align:start position:0%
+convention and the convention is that
+the normal Vector that I take goes to
+
+ align:start position:0%
+the normal Vector that I take goes to
+ 
+
+ align:start position:0%
+the normal Vector that I take goes to
+the right of the Curve as I'm traveling
+
+ align:start position:0%
+the right of the Curve as I'm traveling
+ 
+
+ align:start position:0%
+the right of the Curve as I'm traveling
+along the curve so see imagine that
+
+ align:start position:0%
+along the curve so see imagine that
+ 
+
+ align:start position:0%
+along the curve so see imagine that
+you're walking along this curve then you
+
+ align:start position:0%
+you're walking along this curve then you
+ 
+
+ align:start position:0%
+you're walking along this curve then you
+look to your right that's that
+
+ align:start position:0%
+look to your right that's that
+ 
+
+ align:start position:0%
+look to your right that's that
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+okay so what we will do is we'll just at
+
+ align:start position:0%
+okay so what we will do is we'll just at
+ 
+
+ align:start position:0%
+okay so what we will do is we'll just at
+every point along the curve we'll do the
+
+ align:start position:0%
+every point along the curve we'll do the
+ 
+
+ align:start position:0%
+every point along the curve we'll do the
+dot product between the vector field and
+
+ align:start position:0%
+dot product between the vector field and
+ 
+
+ align:start position:0%
+dot product between the vector field and
+the normal vector and we sum that along
+
+ align:start position:0%
+the normal vector and we sum that along
+ 
+
+ align:start position:0%
+the normal vector and we sum that along
+the various pieces of the
+
+ align:start position:0%
+the various pieces of the
+ 
+
+ align:start position:0%
+the various pieces of the
+curve so what this notation
+
+ align:start position:0%
+curve so what this notation
+ 
+
+ align:start position:0%
+curve so what this notation
+means is that if we actually break C
+
+ align:start position:0%
+means is that if we actually break C
+ 
+
+ align:start position:0%
+means is that if we actually break C
+into small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pieces of length Delta
+
+ align:start position:0%
+pieces of length Delta
+ 
+
+ align:start position:0%
+pieces of length Delta
+s then the
+
+ align:start position:0%
+s then the
+ 
+
+ align:start position:0%
+s then the
+flux will be the
+
+ align:start position:0%
+flux will be the
+ 
+
+ align:start position:0%
+flux will be the
+limit as the pieces become smaller and
+
+ align:start position:0%
+limit as the pieces become smaller and
+ 
+
+ align:start position:0%
+limit as the pieces become smaller and
+smaller of the sum of f.n Delta s where
+
+ align:start position:0%
+smaller of the sum of f.n Delta s where
+ 
+
+ align:start position:0%
+smaller of the sum of f.n Delta s where
+you know so I take each small piece of
+
+ align:start position:0%
+you know so I take each small piece of
+ 
+
+ align:start position:0%
+you know so I take each small piece of
+my curve I do the dot product between F
+
+ align:start position:0%
+my curve I do the dot product between F
+ 
+
+ align:start position:0%
+my curve I do the dot product between F
+and N and I multiply by the length of
+
+ align:start position:0%
+and N and I multiply by the length of
+ 
+
+ align:start position:0%
+and N and I multiply by the length of
+the piece and then I add these together
+
+ align:start position:0%
+the piece and then I add these together
+ 
+
+ align:start position:0%
+the piece and then I add these together
+that's what the line integral means of
+
+ align:start position:0%
+that's what the line integral means of
+ 
+
+ align:start position:0%
+that's what the line integral means of
+course that's again not how I will
+
+ align:start position:0%
+course that's again not how I will
+ 
+
+ align:start position:0%
+course that's again not how I will
+compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so just to compare this with work see
+
+ align:start position:0%
+it so just to compare this with work see
+ 
+
+ align:start position:0%
+it so just to compare this with work see
+conceptually it's similar to the line
+
+ align:start position:0%
+conceptually it's similar to the line
+ 
+
+ align:start position:0%
+conceptually it's similar to the line
+integral we did for work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+except well the line integral for work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work is the line inte of
+
+ align:start position:0%
+work is the line inte of
+ 
+
+ align:start position:0%
+work is the line inte of
+f.d which is also the line integral of f
+
+ align:start position:0%
+f.d which is also the line integral of f
+ 
+
+ align:start position:0%
+f.d which is also the line integral of f
+do TDS that's how we formulated it that
+
+ align:start position:0%
+do TDS that's how we formulated it that
+ 
+
+ align:start position:0%
+do TDS that's how we formulated it that
+means you know we take our curve and we
+
+ align:start position:0%
+means you know we take our curve and we
+ 
+
+ align:start position:0%
+means you know we take our curve and we
+figure out at each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point how big the tangent
+
+ align:start position:0%
+point how big the tangent
+ 
+
+ align:start position:0%
+point how big the tangent
+component I guess I should probably take
+
+ align:start position:0%
+component I guess I should probably take
+ 
+
+ align:start position:0%
+component I guess I should probably take
+the same Vector field as before so let's
+
+ align:start position:0%
+the same Vector field as before so let's
+ 
+
+ align:start position:0%
+the same Vector field as before so let's
+see my field was pointing mik that
+
+ align:start position:0%
+see my field was pointing mik that
+ 
+
+ align:start position:0%
+see my field was pointing mik that
+way so what I do at any point is I
+
+ align:start position:0%
+way so what I do at any point is I
+ 
+
+ align:start position:0%
+way so what I do at any point is I
+project F to the tangent Direction and I
+
+ align:start position:0%
+project F to the tangent Direction and I
+ 
+
+ align:start position:0%
+project F to the tangent Direction and I
+figure out how much f is going along my
+
+ align:start position:0%
+figure out how much f is going along my
+ 
+
+ align:start position:0%
+figure out how much f is going along my
+curve and then I sum these things
+
+ align:start position:0%
+curve and then I sum these things
+ 
+
+ align:start position:0%
+curve and then I sum these things
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+so you know I'm actually
+
+ align:start position:0%
+so you know I'm actually
+ 
+
+ align:start position:0%
+so you know I'm actually
+summing oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the tangential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+component of my field
+
+ align:start position:0%
+component of my field
+ 
+
+ align:start position:0%
+component of my field
+F okay
+
+ align:start position:0%
+F okay
+ 
+
+ align:start position:0%
+F okay
+so roughly speaking the work measures
+
+ align:start position:0%
+so roughly speaking the work measures
+ 
+
+ align:start position:0%
+so roughly speaking the work measures
+you know when I move along my curve how
+
+ align:start position:0%
+you know when I move along my curve how
+ 
+
+ align:start position:0%
+you know when I move along my curve how
+much I'm going with or against
+
+ align:start position:0%
+much I'm going with or against
+ 
+
+ align:start position:0%
+much I'm going with or against
+F flux on the other hand measures when I
+
+ align:start position:0%
+F flux on the other hand measures when I
+ 
+
+ align:start position:0%
+F flux on the other hand measures when I
+go along the curve roughly how much the
+
+ align:start position:0%
+go along the curve roughly how much the
+ 
+
+ align:start position:0%
+go along the curve roughly how much the
+field is going across the curve counting
+
+ align:start position:0%
+field is going across the curve counting
+ 
+
+ align:start position:0%
+field is going across the curve counting
+positively what goes to the right
+
+ align:start position:0%
+positively what goes to the right
+ 
+
+ align:start position:0%
+positively what goes to the right
+negatively what goes to the left okay so
+
+ align:start position:0%
+negatively what goes to the left okay so
+ 
+
+ align:start position:0%
+negatively what goes to the left okay so
+flux is integral of f. n
+
+ align:start position:0%
+flux is integral of f. n
+ 
+
+ align:start position:0%
+flux is integral of f. n
+DS and that one corresponds
+
+ align:start position:0%
+DS and that one corresponds
+ 
+
+ align:start position:0%
+DS and that one corresponds
+to summing the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normal component of a vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field okay but apart from that
+
+ align:start position:0%
+field okay but apart from that
+ 
+
+ align:start position:0%
+field okay but apart from that
+conceptually it's the same kind of thing
+
+ align:start position:0%
+conceptually it's the same kind of thing
+ 
+
+ align:start position:0%
+conceptually it's the same kind of thing
+just the physical interpretations will
+
+ align:start position:0%
+just the physical interpretations will
+ 
+
+ align:start position:0%
+just the physical interpretations will
+be very different but for a
+
+ align:start position:0%
+be very different but for a
+ 
+
+ align:start position:0%
+be very different but for a
+mathematician these are two line
+
+ align:start position:0%
+mathematician these are two line
+ 
+
+ align:start position:0%
+mathematician these are two line
+integrals that you set up compute pretty
+
+ align:start position:0%
+integrals that you set up compute pretty
+ 
+
+ align:start position:0%
+integrals that you set up compute pretty
+much in the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's see I should probably tell you
+
+ align:start position:0%
+so let's see I should probably tell you
+ 
+
+ align:start position:0%
+so let's see I should probably tell you
+what it means you know why do we make
+
+ align:start position:0%
+what it means you know why do we make
+ 
+
+ align:start position:0%
+what it means you know why do we make
+this definition what does it correspond
+
+ align:start position:0%
+this definition what does it correspond
+ 
+
+ align:start position:0%
+this definition what does it correspond
+to so the interpretation for work made a
+
+ align:start position:0%
+to so the interpretation for work made a
+ 
+
+ align:start position:0%
+to so the interpretation for work made a
+lot of sense when f was representing a
+
+ align:start position:0%
+lot of sense when f was representing a
+ 
+
+ align:start position:0%
+lot of sense when f was representing a
+force then the L integral was actually
+
+ align:start position:0%
+force then the L integral was actually
+ 
+
+ align:start position:0%
+force then the L integral was actually
+the work done by the force the
+
+ align:start position:0%
+the work done by the force the
+ 
+
+ align:start position:0%
+the work done by the force the
+interpretation for flux makes more sense
+
+ align:start position:0%
+interpretation for flux makes more sense
+ 
+
+ align:start position:0%
+interpretation for flux makes more sense
+if you think of f as a velocity field
+
+ align:start position:0%
+if you think of f as a velocity field
+ 
+
+ align:start position:0%
+if you think of f as a velocity field
+okay so what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interpretation let's say that
+
+ align:start position:0%
+interpretation let's say that
+ 
+
+ align:start position:0%
+interpretation let's say that
+f for f a velocity field so that means
+
+ align:start position:0%
+f for f a velocity field so that means
+ 
+
+ align:start position:0%
+f for f a velocity field so that means
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+I'm thinking of some fluid that's moving
+
+ align:start position:0%
+I'm thinking of some fluid that's moving
+ 
+
+ align:start position:0%
+I'm thinking of some fluid that's moving
+maybe water or something and it's moving
+
+ align:start position:0%
+maybe water or something and it's moving
+ 
+
+ align:start position:0%
+maybe water or something and it's moving
+at a certain speed and my Vector field
+
+ align:start position:0%
+at a certain speed and my Vector field
+ 
+
+ align:start position:0%
+at a certain speed and my Vector field
+represents how things are moving at
+
+ align:start position:0%
+represents how things are moving at
+ 
+
+ align:start position:0%
+represents how things are moving at
+every point of the
+
+ align:start position:0%
+every point of the
+ 
+
+ align:start position:0%
+every point of the
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+so I claim that flux
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measures how much fluid passes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through through a curve C per unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so if you imagine that you know
+
+ align:start position:0%
+time so if you imagine that you know
+ 
+
+ align:start position:0%
+time so if you imagine that you know
+maybe you have a river and you're
+
+ align:start position:0%
+maybe you have a river and you're
+ 
+
+ align:start position:0%
+maybe you have a river and you're
+somehow building a dam here but you know
+
+ align:start position:0%
+somehow building a dam here but you know
+ 
+
+ align:start position:0%
+somehow building a dam here but you know
+a dam with holes in it so that the water
+
+ align:start position:0%
+a dam with holes in it so that the water
+ 
+
+ align:start position:0%
+a dam with holes in it so that the water
+still passes through then this measures
+
+ align:start position:0%
+still passes through then this measures
+ 
+
+ align:start position:0%
+still passes through then this measures
+how much water passes through your
+
+ align:start position:0%
+how much water passes through your
+ 
+
+ align:start position:0%
+how much water passes through your
+membrane per unit
+
+ align:start position:0%
+membrane per unit
+ 
+
+ align:start position:0%
+membrane per unit
+time okay let's try to figure out why
+
+ align:start position:0%
+time okay let's try to figure out why
+ 
+
+ align:start position:0%
+time okay let's try to figure out why
+this is true you know why does this make
+
+ align:start position:0%
+this is true you know why does this make
+ 
+
+ align:start position:0%
+this is true you know why does this make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+so let's look at what happens on a small
+
+ align:start position:0%
+so let's look at what happens on a small
+ 
+
+ align:start position:0%
+so let's look at what happens on a small
+portion of our curve
+
+ align:start position:0%
+portion of our curve
+ 
+
+ align:start position:0%
+portion of our curve
+C so I'm zooming in on make of C sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to guess I need to zoom further
+
+ align:start position:0%
+to guess I need to zoom further
+ 
+
+ align:start position:0%
+to guess I need to zoom further
+okay so you know that's a little piece
+
+ align:start position:0%
+okay so you know that's a little piece
+ 
+
+ align:start position:0%
+okay so you know that's a little piece
+of my curve of length Delta s and
+
+ align:start position:0%
+of my curve of length Delta s and
+ 
+
+ align:start position:0%
+of my curve of length Delta s and
+there's a fluid flow so on my picture
+
+ align:start position:0%
+there's a fluid flow so on my picture
+ 
+
+ align:start position:0%
+there's a fluid flow so on my picture
+things are flowing to the
+
+ align:start position:0%
+things are flowing to the
+ 
+
+ align:start position:0%
+things are flowing to the
+right so here I'm drawing a constant
+
+ align:start position:0%
+right so here I'm drawing a constant
+ 
+
+ align:start position:0%
+right so here I'm drawing a constant
+Vector field because you know if you
+
+ align:start position:0%
+Vector field because you know if you
+ 
+
+ align:start position:0%
+Vector field because you know if you
+zoom in enough then your vectors will
+
+ align:start position:0%
+zoom in enough then your vectors will
+ 
+
+ align:start position:0%
+zoom in enough then your vectors will
+pretty much be the same
+
+ align:start position:0%
+pretty much be the same
+ 
+
+ align:start position:0%
+pretty much be the same
+everywhere right if you you know enlarge
+
+ align:start position:0%
+everywhere right if you you know enlarge
+ 
+
+ align:start position:0%
+everywhere right if you you know enlarge
+the picture enough then things will be
+
+ align:start position:0%
+the picture enough then things will be
+ 
+
+ align:start position:0%
+the picture enough then things will be
+pretty much a uniform flow so now how
+
+ align:start position:0%
+pretty much a uniform flow so now how
+ 
+
+ align:start position:0%
+pretty much a uniform flow so now how
+much stuff goes through this little
+
+ align:start position:0%
+much stuff goes through this little
+ 
+
+ align:start position:0%
+much stuff goes through this little
+piece of curve per unit time well what
+
+ align:start position:0%
+piece of curve per unit time well what
+ 
+
+ align:start position:0%
+piece of curve per unit time well what
+happens over time the fluid is moving
+
+ align:start position:0%
+happens over time the fluid is moving
+ 
+
+ align:start position:0%
+happens over time the fluid is moving
+while my curve is staying in the same
+
+ align:start position:0%
+while my curve is staying in the same
+ 
+
+ align:start position:0%
+while my curve is staying in the same
+place so corresponds to something like
+
+ align:start position:0%
+place so corresponds to something like
+ 
+
+ align:start position:0%
+place so corresponds to something like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I claim that what goes through C in
+
+ align:start position:0%
+so I claim that what goes through C in
+ 
+
+ align:start position:0%
+so I claim that what goes through C in
+unit time is actually going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be is actually going to be a
+
+ align:start position:0%
+be is actually going to be a
+ 
+
+ align:start position:0%
+be is actually going to be a
+parallelogram okay so here's a better
+
+ align:start position:0%
+parallelogram okay so here's a better
+ 
+
+ align:start position:0%
+parallelogram okay so here's a better
+picture I claim that what we'll be going
+
+ align:start position:0%
+picture I claim that what we'll be going
+ 
+
+ align:start position:0%
+picture I claim that what we'll be going
+through C is this shaded parallelogram
+
+ align:start position:0%
+through C is this shaded parallelogram
+ 
+
+ align:start position:0%
+through C is this shaded parallelogram
+to the left of C well let's see if I
+
+ align:start position:0%
+to the left of C well let's see if I
+ 
+
+ align:start position:0%
+to the left of C well let's see if I
+move for unit time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it
+
+ align:start position:0%
+okay it
+ 
+
+ align:start position:0%
+okay it
+works okay so that's the stuff that goes
+
+ align:start position:0%
+works okay so that's the stuff that goes
+ 
+
+ align:start position:0%
+works okay so that's the stuff that goes
+through my curve in a unit time for a
+
+ align:start position:0%
+through my curve in a unit time for a
+ 
+
+ align:start position:0%
+through my curve in a unit time for a
+small portion of curve and of course I
+
+ align:start position:0%
+small portion of curve and of course I
+ 
+
+ align:start position:0%
+small portion of curve and of course I
+would need to add all of these together
+
+ align:start position:0%
+would need to add all of these together
+ 
+
+ align:start position:0%
+would need to add all of these together
+to get the entire curve so let's try to
+
+ align:start position:0%
+to get the entire curve so let's try to
+ 
+
+ align:start position:0%
+to get the entire curve so let's try to
+understand how big is this
+
+ align:start position:0%
+understand how big is this
+ 
+
+ align:start position:0%
+understand how big is this
+parallelogram so you know to know how
+
+ align:start position:0%
+parallelogram so you know to know how
+ 
+
+ align:start position:0%
+parallelogram so you know to know how
+big this parogram is I would like to use
+
+ align:start position:0%
+big this parogram is I would like to use
+ 
+
+ align:start position:0%
+big this parogram is I would like to use
+base time height or something like that
+
+ align:start position:0%
+base time height or something like that
+ 
+
+ align:start position:0%
+base time height or something like that
+and maybe I want to actually flip my
+
+ align:start position:0%
+and maybe I want to actually flip my
+ 
+
+ align:start position:0%
+and maybe I want to actually flip my
+picture so that the base and the height
+
+ align:start position:0%
+picture so that the base and the height
+ 
+
+ align:start position:0%
+picture so that the base and the height
+make more sense to me so let me actually
+
+ align:start position:0%
+make more sense to me so let me actually
+ 
+
+ align:start position:0%
+make more sense to me so let me actually
+turn it to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay and in case you have trouble
+
+ align:start position:0%
+this okay and in case you have trouble
+ 
+
+ align:start position:0%
+this okay and in case you have trouble
+reading the rotated picture let me redo
+
+ align:start position:0%
+reading the rotated picture let me redo
+ 
+
+ align:start position:0%
+reading the rotated picture let me redo
+it on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what passes
+
+ align:start position:0%
+so what passes
+ 
+
+ align:start position:0%
+so what passes
+through a
+
+ align:start position:0%
+through a
+ 
+
+ align:start position:0%
+through a
+portion of C in unit time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time is the contents of a parallelogram
+
+ align:start position:0%
+time is the contents of a parallelogram
+ 
+
+ align:start position:0%
+time is the contents of a parallelogram
+whose base is on C so it has length
+
+ align:start position:0%
+whose base is on C so it has length
+ 
+
+ align:start position:0%
+whose base is on C so it has length
+Delta s okay that's that's a piece
+
+ align:start position:0%
+Delta s okay that's that's a piece
+ 
+
+ align:start position:0%
+Delta s okay that's that's a piece
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+and the other
+
+ align:start position:0%
+and the other
+ 
+
+ align:start position:0%
+and the other
+side is going to
+
+ align:start position:0%
+side is going to
+ 
+
+ align:start position:0%
+side is going to
+be given by my velocity Vector f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and to find the height of this thing I
+
+ align:start position:0%
+and to find the height of this thing I
+ 
+
+ align:start position:0%
+and to find the height of this thing I
+need to know well what is actually the
+
+ align:start position:0%
+need to know well what is actually the
+ 
+
+ align:start position:0%
+need to know well what is actually the
+normal component of this
+
+ align:start position:0%
+normal component of this
+ 
+
+ align:start position:0%
+normal component of this
+Vector right so if I call n the the unit
+
+ align:start position:0%
+Vector right so if I call n the the unit
+ 
+
+ align:start position:0%
+Vector right so if I call n the the unit
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+Vector to the curve then the area
+
+ align:start position:0%
+Vector to the curve then the area
+ 
+
+ align:start position:0%
+Vector to the curve then the area
+is base time
+
+ align:start position:0%
+is base time
+ 
+
+ align:start position:0%
+is base time
+height is just so the base is Delta s
+
+ align:start position:0%
+height is just so the base is Delta s
+ 
+
+ align:start position:0%
+height is just so the base is Delta s
+and the height is the normal component
+
+ align:start position:0%
+and the height is the normal component
+ 
+
+ align:start position:0%
+and the height is the normal component
+of f so it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f.n and so you see that when you sum
+
+ align:start position:0%
+f.n and so you see that when you sum
+ 
+
+ align:start position:0%
+f.n and so you see that when you sum
+these things together you get what I
+
+ align:start position:0%
+these things together you get what I
+ 
+
+ align:start position:0%
+these things together you get what I
+said you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flux now if you're worried about the
+
+ align:start position:0%
+flux now if you're worried about the
+ 
+
+ align:start position:0%
+flux now if you're worried about the
+fact that actually you know if your unit
+
+ align:start position:0%
+fact that actually you know if your unit
+ 
+
+ align:start position:0%
+fact that actually you know if your unit
+time is too long then of course things
+
+ align:start position:0%
+time is too long then of course things
+ 
+
+ align:start position:0%
+time is too long then of course things
+might start changing you know as the
+
+ align:start position:0%
+might start changing you know as the
+ 
+
+ align:start position:0%
+might start changing you know as the
+fluid flows I mean it might so you have
+
+ align:start position:0%
+fluid flows I mean it might so you have
+ 
+
+ align:start position:0%
+fluid flows I mean it might so you have
+to take a Time unit and a length unit
+
+ align:start position:0%
+to take a Time unit and a length unit
+ 
+
+ align:start position:0%
+to take a Time unit and a length unit
+that are sufficiently small so that
+
+ align:start position:0%
+that are sufficiently small so that
+ 
+
+ align:start position:0%
+that are sufficiently small so that
+really this approximation where C is a
+
+ align:start position:0%
+really this approximation where C is a
+ 
+
+ align:start position:0%
+really this approximation where C is a
+straight line and the flow is at
+
+ align:start position:0%
+straight line and the flow is at
+ 
+
+ align:start position:0%
+straight line and the flow is at
+constant speed are valid so you know you
+
+ align:start position:0%
+constant speed are valid so you know you
+ 
+
+ align:start position:0%
+constant speed are valid so you know you
+want to take maybe a segment here that's
+
+ align:start position:0%
+want to take maybe a segment here that's
+ 
+
+ align:start position:0%
+want to take maybe a segment here that's
+like a few micrometers and you know the
+
+ align:start position:0%
+like a few micrometers and you know the
+ 
+
+ align:start position:0%
+like a few micrometers and you know the
+time unit might be a few NS or whatever
+
+ align:start position:0%
+time unit might be a few NS or whatever
+ 
+
+ align:start position:0%
+time unit might be a few NS or whatever
+and then it's a good
+
+ align:start position:0%
+and then it's a good
+ 
+
+ align:start position:0%
+and then it's a good
+approximation um so what I mean by per
+
+ align:start position:0%
+approximation um so what I mean by per
+ 
+
+ align:start position:0%
+approximation um so what I mean by per
+unit time actually it's V you
+
+ align:start position:0%
+unit time actually it's V you
+ 
+
+ align:start position:0%
+unit time actually it's V you
+know well yeah actually that works but
+
+ align:start position:0%
+know well yeah actually that works but
+ 
+
+ align:start position:0%
+know well yeah actually that works but
+you know you want to think of a really
+
+ align:start position:0%
+you know you want to think of a really
+ 
+
+ align:start position:0%
+you know you want to think of a really
+really small time and then the amount of
+
+ align:start position:0%
+really small time and then the amount of
+ 
+
+ align:start position:0%
+really small time and then the amount of
+matter that passes in that really really
+
+ align:start position:0%
+matter that passes in that really really
+ 
+
+ align:start position:0%
+matter that passes in that really really
+small time
+
+ align:start position:0%
+small time
+ 
+
+ align:start position:0%
+small time
+is the flux times the amount of
+
+ align:start position:0%
+is the flux times the amount of
+ 
+
+ align:start position:0%
+is the flux times the amount of
+time okay um let's be a tiny bit more
+
+ align:start position:0%
+time okay um let's be a tiny bit more
+ 
+
+ align:start position:0%
+time okay um let's be a tiny bit more
+careful when I'm saying it's the amount
+
+ align:start position:0%
+careful when I'm saying it's the amount
+ 
+
+ align:start position:0%
+careful when I'm saying it's the amount
+of stuff that passes through C well it
+
+ align:start position:0%
+of stuff that passes through C well it
+ 
+
+ align:start position:0%
+of stuff that passes through C well it
+depends actually on whether n is going
+
+ align:start position:0%
+depends actually on whether n is going
+ 
+
+ align:start position:0%
+depends actually on whether n is going
+this way or the or the opposite way so
+
+ align:start position:0%
+this way or the or the opposite way so
+ 
+
+ align:start position:0%
+this way or the or the opposite way so
+actually you know what's implicit in
+
+ align:start position:0%
+actually you know what's implicit in
+ 
+
+ align:start position:0%
+actually you know what's implicit in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+explanation is that I'm counting
+
+ align:start position:0%
+explanation is that I'm counting
+ 
+
+ align:start position:0%
+explanation is that I'm counting
+positively all the stuff that flows
+
+ align:start position:0%
+positively all the stuff that flows
+ 
+
+ align:start position:0%
+positively all the stuff that flows
+across C in the direction of N and
+
+ align:start position:0%
+across C in the direction of N and
+ 
+
+ align:start position:0%
+across C in the direction of N and
+negatively What flows in the opposite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction okay so what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flows to the right of C
+
+ align:start position:0%
+flows to the right of C
+ 
+
+ align:start position:0%
+flows to the right of C
+towards well across
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C from left to right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is counted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positively while What flows right to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left is counted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negatively okay so in fact it's the net
+
+ align:start position:0%
+negatively okay so in fact it's the net
+ 
+
+ align:start position:0%
+negatively okay so in fact it's the net
+flow through C per unit time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions about the definition
+
+ align:start position:0%
+okay any questions about the definition
+ 
+
+ align:start position:0%
+okay any questions about the definition
+or the
+
+ align:start position:0%
+or the
+ 
+
+ align:start position:0%
+or the
+interpretation or things like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes how do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry ah well you can have both not in
+
+ align:start position:0%
+sorry ah well you can have both not in
+ 
+
+ align:start position:0%
+sorry ah well you can have both not in
+the same small segment but you know it
+
+ align:start position:0%
+the same small segment but you know it
+ 
+
+ align:start position:0%
+the same small segment but you know it
+could be that well imagine that you know
+
+ align:start position:0%
+could be that well imagine that you know
+ 
+
+ align:start position:0%
+could be that well imagine that you know
+my Vector field you know here suddenly
+
+ align:start position:0%
+my Vector field you know here suddenly
+ 
+
+ align:start position:0%
+my Vector field you know here suddenly
+you know goes in the opposite direction
+
+ align:start position:0%
+you know goes in the opposite direction
+ 
+
+ align:start position:0%
+you know goes in the opposite direction
+then this part of the curve while things
+
+ align:start position:0%
+then this part of the curve while things
+ 
+
+ align:start position:0%
+then this part of the curve while things
+are flowing to the left so this part of
+
+ align:start position:0%
+are flowing to the left so this part of
+ 
+
+ align:start position:0%
+are flowing to the left so this part of
+the curve contributes negatively to flux
+
+ align:start position:0%
+the curve contributes negatively to flux
+ 
+
+ align:start position:0%
+the curve contributes negatively to flux
+and here you know maybe a field is
+
+ align:start position:0%
+and here you know maybe a field is
+ 
+
+ align:start position:0%
+and here you know maybe a field is
+tangent so the normal component becomes
+
+ align:start position:0%
+tangent so the normal component becomes
+ 
+
+ align:start position:0%
+tangent so the normal component becomes
+zero and then it becomes positive and
+
+ align:start position:0%
+zero and then it becomes positive and
+ 
+
+ align:start position:0%
+zero and then it becomes positive and
+this part of the curve contributes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positively you know for example you know
+
+ align:start position:0%
+positively you know for example you know
+ 
+
+ align:start position:0%
+positively you know for example you know
+if you imagine that you have a round
+
+ align:start position:0%
+if you imagine that you have a round
+ 
+
+ align:start position:0%
+if you imagine that you have a round
+tank in which the fluid is rotating and
+
+ align:start position:0%
+tank in which the fluid is rotating and
+ 
+
+ align:start position:0%
+tank in which the fluid is rotating and
+you put your Dam you know just on a
+
+ align:start position:0%
+you put your Dam you know just on a
+ 
+
+ align:start position:0%
+you put your Dam you know just on a
+diameter across then things are going
+
+ align:start position:0%
+diameter across then things are going
+ 
+
+ align:start position:0%
+diameter across then things are going
+one way on one side the have way on the
+
+ align:start position:0%
+one way on one side the have way on the
+ 
+
+ align:start position:0%
+one way on one side the have way on the
+other side and actually it just evens
+
+ align:start position:0%
+other side and actually it just evens
+ 
+
+ align:start position:0%
+other side and actually it just evens
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+um yeah so we don't have complete
+
+ align:start position:0%
+um yeah so we don't have complete
+ 
+
+ align:start position:0%
+um yeah so we don't have complete
+information it's just the total net
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flux okay so if there's no other
+
+ align:start position:0%
+flux okay so if there's no other
+ 
+
+ align:start position:0%
+flux okay so if there's no other
+questions then I guess we'll need to
+
+ align:start position:0%
+questions then I guess we'll need to
+ 
+
+ align:start position:0%
+questions then I guess we'll need to
+figure out how to compute this guy and
+
+ align:start position:0%
+figure out how to compute this guy and
+ 
+
+ align:start position:0%
+figure out how to compute this guy and
+you know how to actually do this line
+
+ align:start position:0%
+you know how to actually do this line
+ 
+
+ align:start position:0%
+you know how to actually do this line
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so well let's start with a couple of
+
+ align:start position:0%
+so well let's start with a couple of
+ 
+
+ align:start position:0%
+so well let's start with a couple of
+easy examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's say that
+
+ align:start position:0%
+okay so let's say that
+ 
+
+ align:start position:0%
+okay so let's say that
+c is a
+
+ align:start position:0%
+c is a
+ 
+
+ align:start position:0%
+c is a
+circle of radius
+
+ align:start position:0%
+circle of radius
+ 
+
+ align:start position:0%
+circle of radius
+a centered at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+origin going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+counterclockwise and let's say that our
+
+ align:start position:0%
+counterclockwise and let's say that our
+ 
+
+ align:start position:0%
+counterclockwise and let's say that our
+Vector field
+
+ align:start position:0%
+Vector field
+ 
+
+ align:start position:0%
+Vector field
+is x i + y
+
+ align:start position:0%
+is x i + y
+ 
+
+ align:start position:0%
+is x i + y
+j so what does that look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so remember x i + y j is a vector
+
+ align:start position:0%
+like so remember x i + y j is a vector
+ 
+
+ align:start position:0%
+like so remember x i + y j is a vector
+field that's pointing radially away from
+
+ align:start position:0%
+field that's pointing radially away from
+ 
+
+ align:start position:0%
+field that's pointing radially away from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+origin right because at every point it's
+
+ align:start position:0%
+origin right because at every point it's
+ 
+
+ align:start position:0%
+origin right because at every point it's
+equal to the vector from the origin to
+
+ align:start position:0%
+equal to the vector from the origin to
+ 
+
+ align:start position:0%
+equal to the vector from the origin to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+point so now if we
+
+ align:start position:0%
+point so now if we
+ 
+
+ align:start position:0%
+point so now if we
+have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circle and let's say we're going
+
+ align:start position:0%
+circle and let's say we're going
+ 
+
+ align:start position:0%
+circle and let's say we're going
+counterclock
+
+ align:start position:0%
+counterclock
+ 
+
+ align:start position:0%
+counterclock
+so I have a nicer picture so let me do
+
+ align:start position:0%
+so I have a nicer picture so let me do
+ 
+
+ align:start position:0%
+so I have a nicer picture so let me do
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so
+
+ align:start position:0%
+here okay so
+ 
+
+ align:start position:0%
+here okay so
+that's my curve and my Vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+and well so the normal Vector C when you
+
+ align:start position:0%
+and well so the normal Vector C when you
+ 
+
+ align:start position:0%
+and well so the normal Vector C when you
+go counterclockwise on a closed curve
+
+ align:start position:0%
+go counterclockwise on a closed curve
+ 
+
+ align:start position:0%
+go counterclockwise on a closed curve
+this convention that the normal vector
+
+ align:start position:0%
+this convention that the normal vector
+ 
+
+ align:start position:0%
+this convention that the normal vector
+points to the right of a curve makes it
+
+ align:start position:0%
+points to the right of a curve makes it
+ 
+
+ align:start position:0%
+points to the right of a curve makes it
+point out so the usual convention when
+
+ align:start position:0%
+point out so the usual convention when
+ 
+
+ align:start position:0%
+point out so the usual convention when
+you take flux through a closed curve is
+
+ align:start position:0%
+you take flux through a closed curve is
+ 
+
+ align:start position:0%
+you take flux through a closed curve is
+that you're counting the flux going out
+
+ align:start position:0%
+that you're counting the flux going out
+ 
+
+ align:start position:0%
+that you're counting the flux going out
+of the region enclosed by the
+
+ align:start position:0%
+of the region enclosed by the
+ 
+
+ align:start position:0%
+of the region enclosed by the
+curve and of course if you went
+
+ align:start position:0%
+curve and of course if you went
+ 
+
+ align:start position:0%
+curve and of course if you went
+clockwise it would be the other way
+
+ align:start position:0%
+clockwise it would be the other way
+ 
+
+ align:start position:0%
+clockwise it would be the other way
+around you choose to do it the way you
+
+ align:start position:0%
+around you choose to do it the way you
+ 
+
+ align:start position:0%
+around you choose to do it the way you
+want but the usual the most common one
+
+ align:start position:0%
+want but the usual the most common one
+ 
+
+ align:start position:0%
+want but the usual the most common one
+is to count flux going out of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region so
+
+ align:start position:0%
+region so
+ 
+
+ align:start position:0%
+region so
+let's see what happens well if I'm
+
+ align:start position:0%
+let's see what happens well if I'm
+ 
+
+ align:start position:0%
+let's see what happens well if I'm
+anywhere on my
+
+ align:start position:0%
+anywhere on my
+ 
+
+ align:start position:0%
+anywhere on my
+circle see the normal Vector is sticking
+
+ align:start position:0%
+circle see the normal Vector is sticking
+ 
+
+ align:start position:0%
+circle see the normal Vector is sticking
+straight out of a circle right that's a
+
+ align:start position:0%
+straight out of a circle right that's a
+ 
+
+ align:start position:0%
+straight out of a circle right that's a
+property of a circle that the radial
+
+ align:start position:0%
+property of a circle that the radial
+ 
+
+ align:start position:0%
+property of a circle that the radial
+direction is perpendicular to the circle
+
+ align:start position:0%
+direction is perpendicular to the circle
+ 
+
+ align:start position:0%
+direction is perpendicular to the circle
+so actually let me complete a withit
+
+ align:start position:0%
+so actually let me complete a withit
+ 
+
+ align:start position:0%
+so actually let me complete a withit
+this picture if I take a point on the
+
+ align:start position:0%
+this picture if I take a point on the
+ 
+
+ align:start position:0%
+this picture if I take a point on the
+circle I have my normal
+
+ align:start position:0%
+circle I have my normal
+ 
+
+ align:start position:0%
+circle I have my normal
+Vector that's pointing straight out so
+
+ align:start position:0%
+Vector that's pointing straight out so
+ 
+
+ align:start position:0%
+Vector that's pointing straight out so
+it's parallel to f
+
+ align:start position:0%
+it's parallel to f
+ 
+
+ align:start position:0%
+it's parallel to f
+okay so along
+
+ align:start position:0%
+okay so along
+ 
+
+ align:start position:0%
+okay so along
+c we know that f is parallel to n so
+
+ align:start position:0%
+c we know that f is parallel to n so
+ 
+
+ align:start position:0%
+c we know that f is parallel to n so
+f.n will be equal to the length the
+
+ align:start position:0%
+f.n will be equal to the length the
+ 
+
+ align:start position:0%
+f.n will be equal to the length the
+magnitude of f times well the magnitude
+
+ align:start position:0%
+magnitude of f times well the magnitude
+ 
+
+ align:start position:0%
+magnitude of f times well the magnitude
+of n but that's one let me put it anyway
+
+ align:start position:0%
+of n but that's one let me put it anyway
+ 
+
+ align:start position:0%
+of n but that's one let me put it anyway
+but that's a unit normal
+
+ align:start position:0%
+but that's a unit normal
+ 
+
+ align:start position:0%
+but that's a unit normal
+Vector now What's the magnitude of this
+
+ align:start position:0%
+Vector now What's the magnitude of this
+ 
+
+ align:start position:0%
+Vector now What's the magnitude of this
+Vector field if I'm at a point x y well
+
+ align:start position:0%
+Vector field if I'm at a point x y well
+ 
+
+ align:start position:0%
+Vector field if I'm at a point x y well
+it's Square OT of x + y^2 that's the
+
+ align:start position:0%
+it's Square OT of x + y^2 that's the
+ 
+
+ align:start position:0%
+it's Square OT of x + y^2 that's the
+same as the distance from the origin
+
+ align:start position:0%
+same as the distance from the origin
+ 
+
+ align:start position:0%
+same as the distance from the origin
+okay so if this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance if this radius is a then the
+
+ align:start position:0%
+distance if this radius is a then the
+ 
+
+ align:start position:0%
+distance if this radius is a then the
+magnitude of f will just be
+
+ align:start position:0%
+magnitude of f will just be
+ 
+
+ align:start position:0%
+magnitude of f will just be
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+right so in
+
+ align:start position:0%
+right so in
+ 
+
+ align:start position:0%
+right so in
+fact f.n is constant always equal to a
+
+ align:start position:0%
+fact f.n is constant always equal to a
+ 
+
+ align:start position:0%
+fact f.n is constant always equal to a
+so the line integral will be pretty easy
+
+ align:start position:0%
+so the line integral will be pretty easy
+ 
+
+ align:start position:0%
+so the line integral will be pretty easy
+because all I have to
+
+ align:start position:0%
+because all I have to
+ 
+
+ align:start position:0%
+because all I have to
+do is the integral
+
+ align:start position:0%
+do is the integral
+ 
+
+ align:start position:0%
+do is the integral
+of f. n DS becomes the integral of a DS
+
+ align:start position:0%
+of f. n DS becomes the integral of a DS
+ 
+
+ align:start position:0%
+of f. n DS becomes the integral of a DS
+a is a constant so I can take it out and
+
+ align:start position:0%
+a is a constant so I can take it out and
+ 
+
+ align:start position:0%
+a is a constant so I can take it out and
+integral DS is just the length of
+
+ align:start position:0%
+integral DS is just the length of
+ 
+
+ align:start position:0%
+integral DS is just the length of
+C which is 2 pi a so I will get 2 pi a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 okay and that is positive as we
+
+ align:start position:0%
+2 okay and that is positive as we
+ 
+
+ align:start position:0%
+2 okay and that is positive as we
+expected because stuff is Flowing out of
+
+ align:start position:0%
+expected because stuff is Flowing out of
+ 
+
+ align:start position:0%
+expected because stuff is Flowing out of
+a circle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay just out of curiosity let's say
+
+ align:start position:0%
+no okay just out of curiosity let's say
+ 
+
+ align:start position:0%
+no okay just out of curiosity let's say
+that we had taken our other favorite
+
+ align:start position:0%
+that we had taken our other favorite
+ 
+
+ align:start position:0%
+that we had taken our other favorite
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+field so let's say that we had the same
+
+ align:start position:0%
+field so let's say that we had the same
+ 
+
+ align:start position:0%
+field so let's say that we had the same
+C but
+
+ align:start position:0%
+C but
+ 
+
+ align:start position:0%
+C but
+now the vector field negative y comma X
+
+ align:start position:0%
+now the vector field negative y comma X
+ 
+
+ align:start position:0%
+now the vector field negative y comma X
+so remember that one
+
+ align:start position:0%
+so remember that one
+ 
+
+ align:start position:0%
+so remember that one
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+counterclockwise around the
+
+ align:start position:0%
+counterclockwise around the
+ 
+
+ align:start position:0%
+counterclockwise around the
+origin
+
+ align:start position:0%
+origin
+ 
+
+ align:start position:0%
+origin
+okay so if you remember what we did
+
+ align:start position:0%
+okay so if you remember what we did
+ 
+
+ align:start position:0%
+okay so if you remember what we did
+several times Well along the circle that
+
+ align:start position:0%
+several times Well along the circle that
+ 
+
+ align:start position:0%
+several times Well along the circle that
+Vector field now is tangent to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circle so if it's tangent to the circle
+
+ align:start position:0%
+circle so if it's tangent to the circle
+ 
+
+ align:start position:0%
+circle so if it's tangent to the circle
+it doesn't have any normal component the
+
+ align:start position:0%
+it doesn't have any normal component the
+ 
+
+ align:start position:0%
+it doesn't have any normal component the
+normal component is
+
+ align:start position:0%
+normal component is
+ 
+
+ align:start position:0%
+normal component is
+zero right things are not flowing into
+
+ align:start position:0%
+zero right things are not flowing into
+ 
+
+ align:start position:0%
+zero right things are not flowing into
+the circle or out of it they're just
+
+ align:start position:0%
+the circle or out of it they're just
+ 
+
+ align:start position:0%
+the circle or out of it they're just
+flowing along the circle around and
+
+ align:start position:0%
+flowing along the circle around and
+ 
+
+ align:start position:0%
+flowing along the circle around and
+around so the flux will be
+
+ align:start position:0%
+around so the flux will be
+ 
+
+ align:start position:0%
+around so the flux will be
+zero okay F now is tangent to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C so
+
+ align:start position:0%
+C so
+ 
+
+ align:start position:0%
+C so
+f.n is zero and therefore the flux will
+
+ align:start position:0%
+f.n is zero and therefore the flux will
+ 
+
+ align:start position:0%
+f.n is zero and therefore the flux will
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero okay so these are examples where
+
+ align:start position:0%
+zero okay so these are examples where
+ 
+
+ align:start position:0%
+zero okay so these are examples where
+you can compute things
+
+ align:start position:0%
+you can compute things
+ 
+
+ align:start position:0%
+you can compute things
+geometrically and I would say generally
+
+ align:start position:0%
+geometrically and I would say generally
+ 
+
+ align:start position:0%
+geometrically and I would say generally
+speaking
+
+ align:start position:0%
+speaking
+ 
+
+ align:start position:0%
+speaking
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+flux you you know well if it's a very
+
+ align:start position:0%
+flux you you know well if it's a very
+ 
+
+ align:start position:0%
+flux you you know well if it's a very
+complicated field then you can't but if
+
+ align:start position:0%
+complicated field then you can't but if
+ 
+
+ align:start position:0%
+complicated field then you can't but if
+a field is fairly simple you should be
+
+ align:start position:0%
+a field is fairly simple you should be
+ 
+
+ align:start position:0%
+a field is fairly simple you should be
+able to get some general feeling for
+
+ align:start position:0%
+able to get some general feeling for
+ 
+
+ align:start position:0%
+able to get some general feeling for
+whether your answer at least should be
+
+ align:start position:0%
+whether your answer at least should be
+ 
+
+ align:start position:0%
+whether your answer at least should be
+positive negative or zero just by
+
+ align:start position:0%
+positive negative or zero just by
+ 
+
+ align:start position:0%
+positive negative or zero just by
+thinking about which way is my flow
+
+ align:start position:0%
+thinking about which way is my flow
+ 
+
+ align:start position:0%
+thinking about which way is my flow
+going is it going across the curve one
+
+ align:start position:0%
+going is it going across the curve one
+ 
+
+ align:start position:0%
+going is it going across the curve one
+way or the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way okay still no questions about these
+
+ align:start position:0%
+way okay still no questions about these
+ 
+
+ align:start position:0%
+way okay still no questions about these
+examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay so next thing we need to know is
+
+ align:start position:0%
+no okay so next thing we need to know is
+ 
+
+ align:start position:0%
+no okay so next thing we need to know is
+how we actually compute these things you
+
+ align:start position:0%
+how we actually compute these things you
+ 
+
+ align:start position:0%
+how we actually compute these things you
+know because yeah here it works pretty
+
+ align:start position:0%
+know because yeah here it works pretty
+ 
+
+ align:start position:0%
+know because yeah here it works pretty
+well but what if you don't have a simple
+
+ align:start position:0%
+well but what if you don't have a simple
+ 
+
+ align:start position:0%
+well but what if you don't have a simple
+geometric interpretation what if I give
+
+ align:start position:0%
+geometric interpretation what if I give
+ 
+
+ align:start position:0%
+geometric interpretation what if I give
+you a really complicated
+
+ align:start position:0%
+you a really complicated
+ 
+
+ align:start position:0%
+you a really complicated
+curve and you know then you have trouble
+
+ align:start position:0%
+curve and you know then you have trouble
+ 
+
+ align:start position:0%
+curve and you know then you have trouble
+finding the normal Vector it's going to
+
+ align:start position:0%
+finding the normal Vector it's going to
+ 
+
+ align:start position:0%
+finding the normal Vector it's going to
+be annoying to set up things this way so
+
+ align:start position:0%
+be annoying to set up things this way so
+ 
+
+ align:start position:0%
+be annoying to set up things this way so
+actually there's a better way to do it
+
+ align:start position:0%
+actually there's a better way to do it
+ 
+
+ align:start position:0%
+actually there's a better way to do it
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+coordinates just as you know when we do
+
+ align:start position:0%
+coordinates just as you know when we do
+ 
+
+ align:start position:0%
+coordinates just as you know when we do
+work when we compute this line integral
+
+ align:start position:0%
+work when we compute this line integral
+ 
+
+ align:start position:0%
+work when we compute this line integral
+usually we don't do it geometrically
+
+ align:start position:0%
+usually we don't do it geometrically
+ 
+
+ align:start position:0%
+usually we don't do it geometrically
+like this most of the time we just
+
+ align:start position:0%
+like this most of the time we just
+ 
+
+ align:start position:0%
+like this most of the time we just
+integrate MDX plus n Dy in
+
+ align:start position:0%
+integrate MDX plus n Dy in
+ 
+
+ align:start position:0%
+integrate MDX plus n Dy in
+coordinates so there's a similar way to
+
+ align:start position:0%
+coordinates so there's a similar way to
+ 
+
+ align:start position:0%
+coordinates so there's a similar way to
+do it because it's again a line integral
+
+ align:start position:0%
+do it because it's again a line integral
+ 
+
+ align:start position:0%
+do it because it's again a line integral
+so it should work the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so let's try to figure that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how do we do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculation in
+
+ align:start position:0%
+calculation in
+ 
+
+ align:start position:0%
+calculation in
+coordinates or I should say maybe using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components so you know that's General
+
+ align:start position:0%
+components so you know that's General
+ 
+
+ align:start position:0%
+components so you know that's General
+method of calculation when we don't have
+
+ align:start position:0%
+method of calculation when we don't have
+ 
+
+ align:start position:0%
+method of calculation when we don't have
+something geometric to do so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember when we were doing things for
+
+ align:start position:0%
+remember when we were doing things for
+ 
+
+ align:start position:0%
+remember when we were doing things for
+work we said this Vector Dr or if you
+
+ align:start position:0%
+work we said this Vector Dr or if you
+ 
+
+ align:start position:0%
+work we said this Vector Dr or if you
+prefer
+
+ align:start position:0%
+prefer
+ 
+
+ align:start position:0%
+prefer
+TDS we said just becomes symbolically DX
+
+ align:start position:0%
+TDS we said just becomes symbolically DX
+ 
+
+ align:start position:0%
+TDS we said just becomes symbolically DX
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+Dy so that you know when you do the line
+
+ align:start position:0%
+Dy so that you know when you do the line
+ 
+
+ align:start position:0%
+Dy so that you know when you do the line
+integral of f. Dr you get line integral
+
+ align:start position:0%
+integral of f. Dr you get line integral
+ 
+
+ align:start position:0%
+integral of f. Dr you get line integral
+of MD X Plus n
+
+ align:start position:0%
+of MD X Plus n
+ 
+
+ align:start position:0%
+of MD X Plus n
+Dy so now let's think for a second about
+
+ align:start position:0%
+Dy so now let's think for a second about
+ 
+
+ align:start position:0%
+Dy so now let's think for a second about
+how we would Express n
+
+ align:start position:0%
+how we would Express n
+ 
+
+ align:start position:0%
+how we would Express n
+DS well what is NDS compared to
+
+ align:start position:0%
+DS well what is NDS compared to
+ 
+
+ align:start position:0%
+DS well what is NDS compared to
+TDs well n is just T rotated by 90 Dees
+
+ align:start position:0%
+TDs well n is just T rotated by 90 Dees
+ 
+
+ align:start position:0%
+TDs well n is just T rotated by 90 Dees
+so NDS is TDS rotated by 90° you know
+
+ align:start position:0%
+so NDS is TDS rotated by 90° you know
+ 
+
+ align:start position:0%
+so NDS is TDS rotated by 90° you know
+that might sound a little bit outrageous
+
+ align:start position:0%
+that might sound a little bit outrageous
+ 
+
+ align:start position:0%
+that might sound a little bit outrageous
+because you know these are really
+
+ align:start position:0%
+because you know these are really
+ 
+
+ align:start position:0%
+because you know these are really
+symbolic notations but it
+
+ align:start position:0%
+symbolic notations but it
+ 
+
+ align:start position:0%
+symbolic notations but it
+works so probably I'm not going to spend
+
+ align:start position:0%
+works so probably I'm not going to spend
+ 
+
+ align:start position:0%
+works so probably I'm not going to spend
+too much time trying to convince you
+
+ align:start position:0%
+too much time trying to convince you
+ 
+
+ align:start position:0%
+too much time trying to convince you
+carefully but
+
+ align:start position:0%
+carefully but
+ 
+
+ align:start position:0%
+carefully but
+really if you go back to you know where
+
+ align:start position:0%
+really if you go back to you know where
+ 
+
+ align:start position:0%
+really if you go back to you know where
+we wrote this and how we try to justify
+
+ align:start position:0%
+we wrote this and how we try to justify
+ 
+
+ align:start position:0%
+we wrote this and how we try to justify
+this and you work your way through it
+
+ align:start position:0%
+this and you work your way through it
+ 
+
+ align:start position:0%
+this and you work your way through it
+you will see that NDS can be analyzed
+
+ align:start position:0%
+you will see that NDS can be analyzed
+ 
+
+ align:start position:0%
+you will see that NDS can be analyzed
+the same way
+
+ align:start position:0%
+the same way
+ 
+
+ align:start position:0%
+the same way
+so n is
+
+ align:start position:0%
+so n is
+ 
+
+ align:start position:0%
+so n is
+T rotated 90°
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clockwise so that tells us that
+
+ align:start position:0%
+clockwise so that tells us that
+ 
+
+ align:start position:0%
+clockwise so that tells us that
+NDS is so how do we rotate a vector by
+
+ align:start position:0%
+NDS is so how do we rotate a vector by
+ 
+
+ align:start position:0%
+NDS is so how do we rotate a vector by
+90° well we swap the two components and
+
+ align:start position:0%
+90° well we swap the two components and
+ 
+
+ align:start position:0%
+90° well we swap the two components and
+we put a minus sign so swap them you
+
+ align:start position:0%
+we put a minus sign so swap them you
+ 
+
+ align:start position:0%
+we put a minus sign so swap them you
+have Dy and DX and you have to be
+
+ align:start position:0%
+have Dy and DX and you have to be
+ 
+
+ align:start position:0%
+have Dy and DX and you have to be
+careful where to put the minus sign well
+
+ align:start position:0%
+careful where to put the minus sign well
+ 
+
+ align:start position:0%
+careful where to put the minus sign well
+it's if you're doing it clockwise it's
+
+ align:start position:0%
+it's if you're doing it clockwise it's
+ 
+
+ align:start position:0%
+it's if you're doing it clockwise it's
+in front of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX well actually let me just convince
+
+ align:start position:0%
+DX well actually let me just convince
+ 
+
+ align:start position:0%
+DX well actually let me just convince
+you quickly by you know let's say we
+
+ align:start position:0%
+you quickly by you know let's say we
+ 
+
+ align:start position:0%
+you quickly by you know let's say we
+have a small piece of
+
+ align:start position:0%
+have a small piece of
+ 
+
+ align:start position:0%
+have a small piece of
+C so if we do T Delta s okay T Delta s
+
+ align:start position:0%
+C so if we do T Delta s okay T Delta s
+ 
+
+ align:start position:0%
+C so if we do T Delta s okay T Delta s
+that's also Vector Dr if you Delta R
+
+ align:start position:0%
+that's also Vector Dr if you Delta R
+ 
+
+ align:start position:0%
+that's also Vector Dr if you Delta R
+sorry that's going to be just you know
+
+ align:start position:0%
+sorry that's going to be just you know
+ 
+
+ align:start position:0%
+sorry that's going to be just you know
+the vector that goes along the
+
+ align:start position:0%
+the vector that goes along the
+ 
+
+ align:start position:0%
+the vector that goes along the
+curve it's given by this so its
+
+ align:start position:0%
+curve it's given by this so its
+ 
+
+ align:start position:0%
+curve it's given by this so its
+components will be indeed the change in
+
+ align:start position:0%
+components will be indeed the change in
+ 
+
+ align:start position:0%
+components will be indeed the change in
+X Delta X and the change in y Delta y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now if I want to get n Delta
+
+ align:start position:0%
+and now if I want to get n Delta
+ 
+
+ align:start position:0%
+and now if I want to get n Delta
+s well I claim now it's perfectly valid
+
+ align:start position:0%
+s well I claim now it's perfectly valid
+ 
+
+ align:start position:0%
+s well I claim now it's perfectly valid
+and rigorous to just rotate that by 90°
+
+ align:start position:0%
+and rigorous to just rotate that by 90°
+ 
+
+ align:start position:0%
+and rigorous to just rotate that by 90°
+so I lost my red
+
+ align:start position:0%
+so I lost my red
+ 
+
+ align:start position:0%
+so I lost my red
+choke here it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is so if I want to rotate this by 90
+
+ align:start position:0%
+is so if I want to rotate this by 90
+ 
+
+ align:start position:0%
+is so if I want to rotate this by 90
+degrees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clockwise then the X component will
+
+ align:start position:0%
+clockwise then the X component will
+ 
+
+ align:start position:0%
+clockwise then the X component will
+become the same as the old y
+
+ align:start position:0%
+become the same as the old y
+ 
+
+ align:start position:0%
+become the same as the old y
+component and the Y component will be
+
+ align:start position:0%
+component and the Y component will be
+ 
+
+ align:start position:0%
+component and the Y component will be
+minus Delta X and then you take the
+
+ align:start position:0%
+minus Delta X and then you take the
+ 
+
+ align:start position:0%
+minus Delta X and then you take the
+limit when the segment becomes shorter
+
+ align:start position:0%
+limit when the segment becomes shorter
+ 
+
+ align:start position:0%
+limit when the segment becomes shorter
+and shorter and that's how you can
+
+ align:start position:0%
+and shorter and that's how you can
+ 
+
+ align:start position:0%
+and shorter and that's how you can
+justify
+
+ align:start position:0%
+justify
+ 
+
+ align:start position:0%
+justify
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay so that's the key to Computing
+
+ align:start position:0%
+okay so that's the key to Computing
+ 
+
+ align:start position:0%
+okay so that's the key to Computing
+things in practice it means actually you
+
+ align:start position:0%
+things in practice it means actually you
+ 
+
+ align:start position:0%
+things in practice it means actually you
+already know how to compute line
+
+ align:start position:0%
+already know how to compute line
+ 
+
+ align:start position:0%
+already know how to compute line
+integrals for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flux let me just
+
+ align:start position:0%
+flux let me just
+ 
+
+ align:start position:0%
+flux let me just
+write it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explicitly so let's say that our Vector
+
+ align:start position:0%
+explicitly so let's say that our Vector
+ 
+
+ align:start position:0%
+explicitly so let's say that our Vector
+field has two components so let me just
+
+ align:start position:0%
+field has two components so let me just
+ 
+
+ align:start position:0%
+field has two components so let me just
+confuse you a little bit and not call
+
+ align:start position:0%
+confuse you a little bit and not call
+ 
+
+ align:start position:0%
+confuse you a little bit and not call
+them M and N for this time just to
+
+ align:start position:0%
+them M and N for this time just to
+ 
+
+ align:start position:0%
+them M and N for this time just to
+stress out you know just to stress the
+
+ align:start position:0%
+stress out you know just to stress the
+ 
+
+ align:start position:0%
+stress out you know just to stress the
+fact that we doing a different line
+
+ align:start position:0%
+fact that we doing a different line
+ 
+
+ align:start position:0%
+fact that we doing a different line
+integral so let me call them p and Q for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now then the line
+
+ align:start position:0%
+now then the line
+ 
+
+ align:start position:0%
+now then the line
+integral of f. n
+
+ align:start position:0%
+integral of f. n
+ 
+
+ align:start position:0%
+integral of f. n
+DS will be the line integral of well
+
+ align:start position:0%
+DS will be the line integral of well
+ 
+
+ align:start position:0%
+DS will be the line integral of well
+PQ
+
+ align:start position:0%
+PQ
+ 
+
+ align:start position:0%
+PQ
+product uh where is it
+
+ align:start position:0%
+product uh where is it
+ 
+
+ align:start position:0%
+product uh where is it
+Dy netive
+
+ align:start position:0%
+Dy netive
+ 
+
+ align:start position:0%
+Dy netive
+DX so that will be the integral of
+
+ align:start position:0%
+DX so that will be the integral of
+ 
+
+ align:start position:0%
+DX so that will be the integral of
+qdx plus P well I'm running out of space
+
+ align:start position:0%
+qdx plus P well I'm running out of space
+ 
+
+ align:start position:0%
+qdx plus P well I'm running out of space
+here it's integral along c of Q DX Plus
+
+ align:start position:0%
+here it's integral along c of Q DX Plus
+ 
+
+ align:start position:0%
+here it's integral along c of Q DX Plus
+pdy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and from that point onwards you
+
+ align:start position:0%
+okay and from that point onwards you
+ 
+
+ align:start position:0%
+okay and from that point onwards you
+just do it the usual way namely you you
+
+ align:start position:0%
+just do it the usual way namely you you
+ 
+
+ align:start position:0%
+just do it the usual way namely you you
+know remember here you have two
+
+ align:start position:0%
+know remember here you have two
+ 
+
+ align:start position:0%
+know remember here you have two
+variables X and Y but you're integrating
+
+ align:start position:0%
+variables X and Y but you're integrating
+ 
+
+ align:start position:0%
+variables X and Y but you're integrating
+along a curve so if you're integrating
+
+ align:start position:0%
+along a curve so if you're integrating
+ 
+
+ align:start position:0%
+along a curve so if you're integrating
+along a curve X and Y are related they
+
+ align:start position:0%
+along a curve X and Y are related they
+ 
+
+ align:start position:0%
+along a curve X and Y are related they
+depend on each other or maybe on some
+
+ align:start position:0%
+depend on each other or maybe on some
+ 
+
+ align:start position:0%
+depend on each other or maybe on some
+other parameter like T or Theta or
+
+ align:start position:0%
+other parameter like T or Theta or
+ 
+
+ align:start position:0%
+other parameter like T or Theta or
+whatever so you express everything in
+
+ align:start position:0%
+whatever so you express everything in
+ 
+
+ align:start position:0%
+whatever so you express everything in
+terms of a single variable and then you
+
+ align:start position:0%
+terms of a single variable and then you
+ 
+
+ align:start position:0%
+terms of a single variable and then you
+do a usual single integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I see a lot of confused faces so
+
+ align:start position:0%
+that I see a lot of confused faces so
+ 
+
+ align:start position:0%
+that I see a lot of confused faces so
+maybe I shouldn't have called my
+
+ align:start position:0%
+maybe I shouldn't have called my
+ 
+
+ align:start position:0%
+maybe I shouldn't have called my
+components p and Q so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prefer okay so if you if you you know if
+
+ align:start position:0%
+prefer okay so if you if you you know if
+ 
+
+ align:start position:0%
+prefer okay so if you if you you know if
+you're really sentimentally attached to
+
+ align:start position:0%
+you're really sentimentally attached to
+ 
+
+ align:start position:0%
+you're really sentimentally attached to
+M and N
+
+ align:start position:0%
+M and N
+ 
+
+ align:start position:0%
+M and N
+then this new line
+
+ align:start position:0%
+then this new line
+ 
+
+ align:start position:0%
+then this new line
+integral becomes the integral of minus n
+
+ align:start position:0%
+integral becomes the integral of minus n
+ 
+
+ align:start position:0%
+integral becomes the integral of minus n
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mdy okay so you know if a problem tells
+
+ align:start position:0%
+mdy okay so you know if a problem tells
+ 
+
+ align:start position:0%
+mdy okay so you know if a problem tells
+you compute flux instead of saying
+
+ align:start position:0%
+you compute flux instead of saying
+ 
+
+ align:start position:0%
+you compute flux instead of saying
+compute work the only thing you change
+
+ align:start position:0%
+compute work the only thing you change
+ 
+
+ align:start position:0%
+compute work the only thing you change
+is instead of doing MDX plus n d y you
+
+ align:start position:0%
+is instead of doing MDX plus n d y you
+ 
+
+ align:start position:0%
+is instead of doing MDX plus n d y you
+do minus ndx plus
+
+ align:start position:0%
+do minus ndx plus
+ 
+
+ align:start position:0%
+do minus ndx plus
+mdy and I'm sorry to say I don't have
+
+ align:start position:0%
+mdy and I'm sorry to say I don't have
+ 
+
+ align:start position:0%
+mdy and I'm sorry to say I don't have
+any good way of helping you remember
+
+ align:start position:0%
+any good way of helping you remember
+ 
+
+ align:start position:0%
+any good way of helping you remember
+which one of the two gets the minus sign
+
+ align:start position:0%
+which one of the two gets the minus sign
+ 
+
+ align:start position:0%
+which one of the two gets the minus sign
+so you know you just have to remember
+
+ align:start position:0%
+so you know you just have to remember
+ 
+
+ align:start position:0%
+so you know you just have to remember
+this formula by heart that's the only
+
+ align:start position:0%
+this formula by heart that's the only
+ 
+
+ align:start position:0%
+this formula by heart that's the only
+way I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know well I mean can try to you know go
+
+ align:start position:0%
+know well I mean can try to you know go
+ 
+
+ align:start position:0%
+know well I mean can try to you know go
+through this argument again but it's I
+
+ align:start position:0%
+through this argument again but it's I
+ 
+
+ align:start position:0%
+through this argument again but it's I
+mean it's really best if you just
+
+ align:start position:0%
+mean it's really best if you just
+ 
+
+ align:start position:0%
+mean it's really best if you just
+remember that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+okay so I'm not going to do an example
+
+ align:start position:0%
+okay so I'm not going to do an example
+ 
+
+ align:start position:0%
+okay so I'm not going to do an example
+because we already know how to do line
+
+ align:start position:0%
+because we already know how to do line
+ 
+
+ align:start position:0%
+because we already know how to do line
+integrals okay but hopefully you will
+
+ align:start position:0%
+integrals okay but hopefully you will
+ 
+
+ align:start position:0%
+integrals okay but hopefully you will
+get to see one at least in recitation on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Monday okay so that's all pretty good
+
+ align:start position:0%
+Monday okay so that's all pretty good
+ 
+
+ align:start position:0%
+Monday okay so that's all pretty good
+let me tell you now what if I have to
+
+ align:start position:0%
+let me tell you now what if I have to
+ 
+
+ align:start position:0%
+let me tell you now what if I have to
+compute flux along a closed curve and I
+
+ align:start position:0%
+compute flux along a closed curve and I
+ 
+
+ align:start position:0%
+compute flux along a closed curve and I
+don't want to compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so well remember in the case of work we
+
+ align:start position:0%
+so well remember in the case of work we
+ 
+
+ align:start position:0%
+so well remember in the case of work we
+had grein theorum we saw yesterday grein
+
+ align:start position:0%
+had grein theorum we saw yesterday grein
+ 
+
+ align:start position:0%
+had grein theorum we saw yesterday grein
+theorum Let's us replace a line integral
+
+ align:start position:0%
+theorum Let's us replace a line integral
+ 
+
+ align:start position:0%
+theorum Let's us replace a line integral
+along a closed curve by a double
+
+ align:start position:0%
+along a closed curve by a double
+ 
+
+ align:start position:0%
+along a closed curve by a double
+integral well here it's the same we have
+
+ align:start position:0%
+integral well here it's the same we have
+ 
+
+ align:start position:0%
+integral well here it's the same we have
+a line integral along a curve we should
+
+ align:start position:0%
+a line integral along a curve we should
+ 
+
+ align:start position:0%
+a line integral along a curve we should
+be able if it's a closed curve we should
+
+ align:start position:0%
+be able if it's a closed curve we should
+ 
+
+ align:start position:0%
+be able if it's a closed curve we should
+be able to replace it by a double
+
+ align:start position:0%
+be able to replace it by a double
+ 
+
+ align:start position:0%
+be able to replace it by a double
+integral so there is a vers of green
+
+ align:start position:0%
+integral so there is a vers of green
+ 
+
+ align:start position:0%
+integral so there is a vers of green
+theorem for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flux and you'll see it's not more scary
+
+ align:start position:0%
+flux and you'll see it's not more scary
+ 
+
+ align:start position:0%
+flux and you'll see it's not more scary
+than the other one
+
+ align:start position:0%
+than the other one
+ 
+
+ align:start position:0%
+than the other one
+it's perhaps less scary or perhaps just
+
+ align:start position:0%
+it's perhaps less scary or perhaps just
+ 
+
+ align:start position:0%
+it's perhaps less scary or perhaps just
+as scary or just as not scary depending
+
+ align:start position:0%
+as scary or just as not scary depending
+ 
+
+ align:start position:0%
+as scary or just as not scary depending
+on how you feel about it but
+
+ align:start position:0%
+on how you feel about it but
+ 
+
+ align:start position:0%
+on how you feel about it but
+it's it works pretty much the same
+
+ align:start position:0%
+it's it works pretty much the same
+ 
+
+ align:start position:0%
+it's it works pretty much the same
+way okay so what does green spor for
+
+ align:start position:0%
+way okay so what does green spor for
+ 
+
+ align:start position:0%
+way okay so what does green spor for
+C so it says if C is a curve that
+
+ align:start position:0%
+C so it says if C is a curve that
+ 
+
+ align:start position:0%
+C so it says if C is a curve that
+encloses or region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+counterclockwise and if I have a vector
+
+ align:start position:0%
+counterclockwise and if I have a vector
+ 
+
+ align:start position:0%
+counterclockwise and if I have a vector
+field that's defined everywhere not just
+
+ align:start position:0%
+field that's defined everywhere not just
+ 
+
+ align:start position:0%
+field that's defined everywhere not just
+on C but also inside so also on r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defined well and differentiable and so
+
+ align:start position:0%
+defined well and differentiable and so
+ 
+
+ align:start position:0%
+defined well and differentiable and so
+on in R well maybe I should give names
+
+ align:start position:0%
+on in R well maybe I should give names
+ 
+
+ align:start position:0%
+on in R well maybe I should give names
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+components so if you'll forgive me for a
+
+ align:start position:0%
+components so if you'll forgive me for a
+ 
+
+ align:start position:0%
+components so if you'll forgive me for a
+second I will still use p and Q for now
+
+ align:start position:0%
+second I will still use p and Q for now
+ 
+
+ align:start position:0%
+second I will still use p and Q for now
+you'll see why
+
+ align:start position:0%
+you'll see why
+ 
+
+ align:start position:0%
+you'll see why
+um is defined and differentiable in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R then I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually replace the line integral for
+
+ align:start position:0%
+actually replace the line integral for
+ 
+
+ align:start position:0%
+actually replace the line integral for
+flux by a double integral over R of some
+
+ align:start position:0%
+flux by a double integral over R of some
+ 
+
+ align:start position:0%
+flux by a double integral over R of some
+function and that function is called the
+
+ align:start position:0%
+function and that function is called the
+ 
+
+ align:start position:0%
+function and that function is called the
+Divergence of
+
+ align:start position:0%
+Divergence of
+ 
+
+ align:start position:0%
+Divergence of
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+da okay
+
+ align:start position:0%
+da okay
+ 
+
+ align:start position:0%
+da okay
+so this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Divergence of f
+
+ align:start position:0%
+Divergence of f
+ 
+
+ align:start position:0%
+Divergence of f
+and I have to Define for you what this
+
+ align:start position:0%
+and I have to Define for you what this
+ 
+
+ align:start position:0%
+and I have to Define for you what this
+guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is so the Divergence of a vector field
+
+ align:start position:0%
+is so the Divergence of a vector field
+ 
+
+ align:start position:0%
+is so the Divergence of a vector field
+with components p and Q is just P subx
+
+ align:start position:0%
+with components p and Q is just P subx
+ 
+
+ align:start position:0%
+with components p and Q is just P subx
+plus Q sub
+
+ align:start position:0%
+plus Q sub
+ 
+
+ align:start position:0%
+plus Q sub
+y so this one is actually easier to
+
+ align:start position:0%
+y so this one is actually easier to
+ 
+
+ align:start position:0%
+y so this one is actually easier to
+remember than Cur right because you just
+
+ align:start position:0%
+remember than Cur right because you just
+ 
+
+ align:start position:0%
+remember than Cur right because you just
+take the X component take it special
+
+ align:start position:0%
+take the X component take it special
+ 
+
+ align:start position:0%
+take the X component take it special
+with respect to X take the Y component
+
+ align:start position:0%
+with respect to X take the Y component
+ 
+
+ align:start position:0%
+with respect to X take the Y component
+take it special respect to Y and add
+
+ align:start position:0%
+take it special respect to Y and add
+ 
+
+ align:start position:0%
+take it special respect to Y and add
+them together no signs no switching
+
+ align:start position:0%
+them together no signs no switching
+ 
+
+ align:start position:0%
+them together no signs no switching
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+around this one is pretty
+
+ align:start position:0%
+around this one is pretty
+ 
+
+ align:start position:0%
+around this one is pretty
+straightforward okay so the picture
+
+ align:start position:0%
+straightforward okay so the picture
+ 
+
+ align:start position:0%
+straightforward okay so the picture
+again is if I have my curve C going
+
+ align:start position:0%
+again is if I have my curve C going
+ 
+
+ align:start position:0%
+again is if I have my curve C going
+counterclockwise around the Orion
+
+ align:start position:0%
+counterclockwise around the Orion
+ 
+
+ align:start position:0%
+counterclockwise around the Orion
+R and I want to find the flux of some
+
+ align:start position:0%
+R and I want to find the flux of some
+ 
+
+ align:start position:0%
+R and I want to find the flux of some
+Vector field
+
+ align:start position:0%
+Vector field
+ 
+
+ align:start position:0%
+Vector field
+F that you know is everywhere in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so maybe some parts of C will contribute
+
+ align:start position:0%
+so maybe some parts of C will contribute
+ 
+
+ align:start position:0%
+so maybe some parts of C will contribute
+positively some parts will contribute
+
+ align:start position:0%
+positively some parts will contribute
+ 
+
+ align:start position:0%
+positively some parts will contribute
+negatively way just to reiterate what I
+
+ align:start position:0%
+negatively way just to reiterate what I
+ 
+
+ align:start position:0%
+negatively way just to reiterate what I
+said positively here means because we
+
+ align:start position:0%
+said positively here means because we
+ 
+
+ align:start position:0%
+said positively here means because we
+going counterclockwise the normal Vector
+
+ align:start position:0%
+going counterclockwise the normal Vector
+ 
+
+ align:start position:0%
+going counterclockwise the normal Vector
+points out of the
+
+ align:start position:0%
+points out of the
+ 
+
+ align:start position:0%
+points out of the
+region okay so this guy here is the
+
+ align:start position:0%
+region okay so this guy here is the
+ 
+
+ align:start position:0%
+region okay so this guy here is the
+flux
+
+ align:start position:0%
+flux
+ 
+
+ align:start position:0%
+flux
+out of R through C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the formula any questions
+
+ align:start position:0%
+okay so that's the formula any questions
+ 
+
+ align:start position:0%
+okay so that's the formula any questions
+about what the statement says or how to
+
+ align:start position:0%
+about what the statement says or how to
+ 
+
+ align:start position:0%
+about what the statement says or how to
+use it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concretely
+
+ align:start position:0%
+concretely
+ 
+
+ align:start position:0%
+concretely
+no okay so it's pretty similar to Green
+
+ align:start position:0%
+no okay so it's pretty similar to Green
+ 
+
+ align:start position:0%
+no okay so it's pretty similar to Green
+theorem for work so actually I should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say so maybe I should see this is green
+
+ align:start position:0%
+say so maybe I should see this is green
+ 
+
+ align:start position:0%
+say so maybe I should see this is green
+this is called Green
+
+ align:start position:0%
+this is called Green
+ 
+
+ align:start position:0%
+this is called Green
+sporum in normal form also so not that
+
+ align:start position:0%
+sporum in normal form also so not that
+ 
+
+ align:start position:0%
+sporum in normal form also so not that
+the other one is abnormal but just that
+
+ align:start position:0%
+the other one is abnormal but just that
+ 
+
+ align:start position:0%
+the other one is abnormal but just that
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+know the old
+
+ align:start position:0%
+know the old
+ 
+
+ align:start position:0%
+know the old
+one for work was you could say in
+
+ align:start position:0%
+one for work was you could say in
+ 
+
+ align:start position:0%
+one for work was you could say in
+tangential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form that just means well green theorem
+
+ align:start position:0%
+form that just means well green theorem
+ 
+
+ align:start position:0%
+form that just means well green theorem
+as seen yesterday was for the line
+
+ align:start position:0%
+as seen yesterday was for the line
+ 
+
+ align:start position:0%
+as seen yesterday was for the line
+integral F.T DS integrating the tangent
+
+ align:start position:0%
+integral F.T DS integrating the tangent
+ 
+
+ align:start position:0%
+integral F.T DS integrating the tangent
+component of T of f
+
+ align:start position:0%
+component of T of f
+ 
+
+ align:start position:0%
+component of T of f
+sorry um the one today is for
+
+ align:start position:0%
+sorry um the one today is for
+ 
+
+ align:start position:0%
+sorry um the one today is for
+integrating the normal component of
+
+ align:start position:0%
+integrating the normal component of
+ 
+
+ align:start position:0%
+integrating the normal component of
+f okay let's prove this
+
+ align:start position:0%
+f okay let's prove this
+ 
+
+ align:start position:0%
+f okay let's prove this
+so good news it's much easier to prove
+
+ align:start position:0%
+so good news it's much easier to prove
+ 
+
+ align:start position:0%
+so good news it's much easier to prove
+than the one we did yesterday because
+
+ align:start position:0%
+than the one we did yesterday because
+ 
+
+ align:start position:0%
+than the one we did yesterday because
+we're just going to show that it's the
+
+ align:start position:0%
+we're just going to show that it's the
+ 
+
+ align:start position:0%
+we're just going to show that it's the
+same thing just using different
+
+ align:start position:0%
+same thing just using different
+ 
+
+ align:start position:0%
+same thing just using different
+notations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so how do I prove
+
+ align:start position:0%
+okay so how do I prove
+ 
+
+ align:start position:0%
+okay so how do I prove
+it well maybe actually it would help if
+
+ align:start position:0%
+it well maybe actually it would help if
+ 
+
+ align:start position:0%
+it well maybe actually it would help if
+first before proving it I actually
+
+ align:start position:0%
+first before proving it I actually
+ 
+
+ align:start position:0%
+first before proving it I actually
+rewrite what it means in
+
+ align:start position:0%
+rewrite what it means in
+ 
+
+ align:start position:0%
+rewrite what it means in
+components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we said the line integral of f.
+
+ align:start position:0%
+okay so we said the line integral of f.
+ 
+
+ align:start position:0%
+okay so we said the line integral of f.
+n DS is actually the line integral
+
+ align:start position:0%
+n DS is actually the line integral
+ 
+
+ align:start position:0%
+n DS is actually the line integral
+of Q DX plus P
+
+ align:start position:0%
+of Q DX plus P
+ 
+
+ align:start position:0%
+of Q DX plus P
+Dy right and we want to show that this
+
+ align:start position:0%
+Dy right and we want to show that this
+ 
+
+ align:start position:0%
+Dy right and we want to show that this
+is equal to the double integral of p
+
+ align:start position:0%
+is equal to the double integral of p
+ 
+
+ align:start position:0%
+is equal to the double integral of p
+subx plus Q sub y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+da so this looks a lot like you know
+
+ align:start position:0%
+da so this looks a lot like you know
+ 
+
+ align:start position:0%
+da so this looks a lot like you know
+this is really one of the features of
+
+ align:start position:0%
+this is really one of the features of
+ 
+
+ align:start position:0%
+this is really one of the features of
+green theorum no matter which form it's
+
+ align:start position:0%
+green theorum no matter which form it's
+ 
+
+ align:start position:0%
+green theorum no matter which form it's
+in it relates a line integral to a
+
+ align:start position:0%
+in it relates a line integral to a
+ 
+
+ align:start position:0%
+in it relates a line integral to a
+double
+
+ align:start position:0%
+double
+ 
+
+ align:start position:0%
+double
+integral so let's just try to see if we
+
+ align:start position:0%
+integral so let's just try to see if we
+ 
+
+ align:start position:0%
+integral so let's just try to see if we
+can reduce it to the one we had
+
+ align:start position:0%
+can reduce it to the one we had
+ 
+
+ align:start position:0%
+can reduce it to the one we had
+yesterday
+
+ align:start position:0%
+yesterday
+ 
+
+ align:start position:0%
+yesterday
+so you know let me
+
+ align:start position:0%
+so you know let me
+ 
+
+ align:start position:0%
+so you know let me
+forget what these things mean physically
+
+ align:start position:0%
+forget what these things mean physically
+ 
+
+ align:start position:0%
+forget what these things mean physically
+and just focus on the math on the math
+
+ align:start position:0%
+and just focus on the math on the math
+ 
+
+ align:start position:0%
+and just focus on the math on the math
+it's a line integral of something DX
+
+ align:start position:0%
+it's a line integral of something DX
+ 
+
+ align:start position:0%
+it's a line integral of something DX
+Plus something Dy so let's call this guy
+
+ align:start position:0%
+Plus something Dy so let's call this guy
+ 
+
+ align:start position:0%
+Plus something Dy so let's call this guy
+M and let's call this guy
+
+ align:start position:0%
+M and let's call this guy
+ 
+
+ align:start position:0%
+M and let's call this guy
+n okay so let m = q and N equal
+
+ align:start position:0%
+n okay so let m = q and N equal
+ 
+
+ align:start position:0%
+n okay so let m = q and N equal
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+then I know well this guy here
+
+ align:start position:0%
+then I know well this guy here
+ 
+
+ align:start position:0%
+then I know well this guy here
+becomes integral of M DX plus n
+
+ align:start position:0%
+becomes integral of M DX plus n
+ 
+
+ align:start position:0%
+becomes integral of M DX plus n
+Dy and I know from
+
+ align:start position:0%
+Dy and I know from
+ 
+
+ align:start position:0%
+Dy and I know from
+yesterday what this is equal to namely
+
+ align:start position:0%
+yesterday what this is equal to namely
+ 
+
+ align:start position:0%
+yesterday what this is equal to namely
+using the tangential form of green
+
+ align:start position:0%
+using the tangential form of green
+ 
+
+ align:start position:0%
+using the tangential form of green
+theoren for work this is the double
+
+ align:start position:0%
+theoren for work this is the double
+ 
+
+ align:start position:0%
+theoren for work this is the double
+integral of Cur of this guy so that's NX
+
+ align:start position:0%
+integral of Cur of this guy so that's NX
+ 
+
+ align:start position:0%
+integral of Cur of this guy so that's NX
+minus n y
+
+ align:start position:0%
+minus n y
+ 
+
+ align:start position:0%
+minus n y
+da but now let's think about what this
+
+ align:start position:0%
+da but now let's think about what this
+ 
+
+ align:start position:0%
+da but now let's think about what this
+is in terms of M and N well we
+
+ align:start position:0%
+is in terms of M and N well we
+ 
+
+ align:start position:0%
+is in terms of M and N well we
+said that m is negative Q so this is
+
+ align:start position:0%
+said that m is negative Q so this is
+ 
+
+ align:start position:0%
+said that m is negative Q so this is
+negative m
+
+ align:start position:0%
+negative m
+ 
+
+ align:start position:0%
+negative m
+y and we say p is the same as n so this
+
+ align:start position:0%
+y and we say p is the same as n so this
+ 
+
+ align:start position:0%
+y and we say p is the same as n so this
+is n
+
+ align:start position:0%
+is n
+ 
+
+ align:start position:0%
+is n
+x so C just by renaming the
+
+ align:start position:0%
+x so C just by renaming the
+ 
+
+ align:start position:0%
+x so C just by renaming the
+components I go from one form to the
+
+ align:start position:0%
+components I go from one form to the
+ 
+
+ align:start position:0%
+components I go from one form to the
+other one so it's really the same
+
+ align:start position:0%
+other one so it's really the same
+ 
+
+ align:start position:0%
+other one so it's really the same
+theorem that's why it's also called
+
+ align:start position:0%
+theorem that's why it's also called
+ 
+
+ align:start position:0%
+theorem that's why it's also called
+Green theorem but the way we think about
+
+ align:start position:0%
+Green theorem but the way we think about
+ 
+
+ align:start position:0%
+Green theorem but the way we think about
+it when we use it is different because
+
+ align:start position:0%
+it when we use it is different because
+ 
+
+ align:start position:0%
+it when we use it is different because
+one of them computes the work done by a
+
+ align:start position:0%
+one of them computes the work done by a
+ 
+
+ align:start position:0%
+one of them computes the work done by a
+force along a closed curve the other one
+
+ align:start position:0%
+force along a closed curve the other one
+ 
+
+ align:start position:0%
+force along a closed curve the other one
+computes the flux maybe of a velocity
+
+ align:start position:0%
+computes the flux maybe of a velocity
+ 
+
+ align:start position:0%
+computes the flux maybe of a velocity
+field out of a closed region out of out
+
+ align:start position:0%
+field out of a closed region out of out
+ 
+
+ align:start position:0%
+field out of a closed region out of out
+of a region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions yes so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we yeah that's correct so if you're
+
+ align:start position:0%
+we yeah that's correct so if you're
+ 
+
+ align:start position:0%
+we yeah that's correct so if you're
+trying to compute you know a line
+
+ align:start position:0%
+trying to compute you know a line
+ 
+
+ align:start position:0%
+trying to compute you know a line
+integral for flux you see it just
+
+ align:start position:0%
+integral for flux you see it just
+ 
+
+ align:start position:0%
+integral for flux you see it just
+becomes wait where did I put it so the
+
+ align:start position:0%
+becomes wait where did I put it so the
+ 
+
+ align:start position:0%
+becomes wait where did I put it so the
+line integral for flux just becomes this
+
+ align:start position:0%
+line integral for flux just becomes this
+ 
+
+ align:start position:0%
+line integral for flux just becomes this
+and once you're here you know how to
+
+ align:start position:0%
+and once you're here you know how to
+ 
+
+ align:start position:0%
+and once you're here you know how to
+compute that kind of
+
+ align:start position:0%
+compute that kind of
+ 
+
+ align:start position:0%
+compute that kind of
+thing um you know the double integral
+
+ align:start position:0%
+thing um you know the double integral
+ 
+
+ align:start position:0%
+thing um you know the double integral
+side there's no even there's not even
+
+ align:start position:0%
+side there's no even there's not even
+ 
+
+ align:start position:0%
+side there's no even there's not even
+any kind of renaming to do you know how
+
+ align:start position:0%
+any kind of renaming to do you know how
+ 
+
+ align:start position:0%
+any kind of renaming to do you know how
+to compute a double integral of a
+
+ align:start position:0%
+to compute a double integral of a
+ 
+
+ align:start position:0%
+to compute a double integral of a
+function and this is just a particular
+
+ align:start position:0%
+function and this is just a particular
+ 
+
+ align:start position:0%
+function and this is just a particular
+kind of function that you get out of a
+
+ align:start position:0%
+kind of function that you get out of a
+ 
+
+ align:start position:0%
+kind of function that you get out of a
+vector field but it's any fun you know
+
+ align:start position:0%
+vector field but it's any fun you know
+ 
+
+ align:start position:0%
+vector field but it's any fun you know
+it's like any function the way you would
+
+ align:start position:0%
+it's like any function the way you would
+ 
+
+ align:start position:0%
+it's like any function the way you would
+evaluate these double integrals is just
+
+ align:start position:0%
+evaluate these double integrals is just
+ 
+
+ align:start position:0%
+evaluate these double integrals is just
+the usual way you have a function of X
+
+ align:start position:0%
+the usual way you have a function of X
+ 
+
+ align:start position:0%
+the usual way you have a function of X
+and Y you have a region and you set up
+
+ align:start position:0%
+and Y you have a region and you set up
+ 
+
+ align:start position:0%
+and Y you have a region and you set up
+the bounds for the iterated
+
+ align:start position:0%
+the bounds for the iterated
+ 
+
+ align:start position:0%
+the bounds for the iterated
+integral quiet please there's a lot of
+
+ align:start position:0%
+integral quiet please there's a lot of
+ 
+
+ align:start position:0%
+integral quiet please there's a lot of
+people talking
+
+ align:start position:0%
+people talking
+ 
+
+ align:start position:0%
+people talking
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+okay so the way you would evaluate the
+
+ align:start position:0%
+okay so the way you would evaluate the
+ 
+
+ align:start position:0%
+okay so the way you would evaluate the
+double integrals is really the usual Way
+
+ align:start position:0%
+double integrals is really the usual Way
+ 
+
+ align:start position:0%
+double integrals is really the usual Way
+by slicing the region and setting up the
+
+ align:start position:0%
+by slicing the region and setting up the
+ 
+
+ align:start position:0%
+by slicing the region and setting up the
+bounds for iterated integrals in you
+
+ align:start position:0%
+bounds for iterated integrals in you
+ 
+
+ align:start position:0%
+bounds for iterated integrals in you
+know DX Dy or dydx or maybe Rd Rd Theta
+
+ align:start position:0%
+know DX Dy or dydx or maybe Rd Rd Theta
+ 
+
+ align:start position:0%
+know DX Dy or dydx or maybe Rd Rd Theta
+or whatever you
+
+ align:start position:0%
+or whatever you
+ 
+
+ align:start position:0%
+or whatever you
+want um so in fact in terms of computing
+
+ align:start position:0%
+want um so in fact in terms of computing
+ 
+
+ align:start position:0%
+want um so in fact in terms of computing
+integrals we just have two sets of
+
+ align:start position:0%
+integrals we just have two sets of
+ 
+
+ align:start position:0%
+integrals we just have two sets of
+skills one is setting up evaluating
+
+ align:start position:0%
+skills one is setting up evaluating
+ 
+
+ align:start position:0%
+skills one is setting up evaluating
+double integrals the other one is
+
+ align:start position:0%
+double integrals the other one is
+ 
+
+ align:start position:0%
+double integrals the other one is
+setting up evaluating line integrals and
+
+ align:start position:0%
+setting up evaluating line integrals and
+ 
+
+ align:start position:0%
+setting up evaluating line integrals and
+whether these line integrals or double
+
+ align:start position:0%
+whether these line integrals or double
+ 
+
+ align:start position:0%
+whether these line integrals or double
+integrals are representing a work a flux
+
+ align:start position:0%
+integrals are representing a work a flux
+ 
+
+ align:start position:0%
+integrals are representing a work a flux
+integral of a curl whatever the way that
+
+ align:start position:0%
+integral of a curl whatever the way that
+ 
+
+ align:start position:0%
+integral of a curl whatever the way that
+we actually compute them is the
+
+ align:start position:0%
+we actually compute them is the
+ 
+
+ align:start position:0%
+we actually compute them is the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+okay okay let's do an
+
+ align:start position:0%
+okay okay let's do an
+ 
+
+ align:start position:0%
+okay okay let's do an
+example oh by the way no so first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry so this renaming here see that's
+
+ align:start position:0%
+sorry so this renaming here see that's
+ 
+
+ align:start position:0%
+sorry so this renaming here see that's
+why actually I called my components p
+
+ align:start position:0%
+why actually I called my components p
+ 
+
+ align:start position:0%
+why actually I called my components p
+and Q because the argument would have
+
+ align:start position:0%
+and Q because the argument would have
+ 
+
+ align:start position:0%
+and Q because the argument would have
+gotten very messy if I had told you oh
+
+ align:start position:0%
+gotten very messy if I had told you oh
+ 
+
+ align:start position:0%
+gotten very messy if I had told you oh
+well now I call m n and I call n minus M
+
+ align:start position:0%
+well now I call m n and I call n minus M
+ 
+
+ align:start position:0%
+well now I call m n and I call n minus M
+and so on uh but now that we're done you
+
+ align:start position:0%
+and so on uh but now that we're done you
+ 
+
+ align:start position:0%
+and so on uh but now that we're done you
+now that we're full with this if you
+
+ align:start position:0%
+now that we're full with this if you
+ 
+
+ align:start position:0%
+now that we're full with this if you
+still like m&n
+
+ align:start position:0%
+still like m&n
+ 
+
+ align:start position:0%
+still like m&n
+better you know then what this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+says then the form you know the
+
+ align:start position:0%
+says then the form you know the
+ 
+
+ align:start position:0%
+says then the form you know the
+formulation of green theorem in this
+
+ align:start position:0%
+formulation of green theorem in this
+ 
+
+ align:start position:0%
+formulation of green theorem in this
+language is just integral of minus n DX
+
+ align:start position:0%
+language is just integral of minus n DX
+ 
+
+ align:start position:0%
+language is just integral of minus n DX
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+mdy is double integral over R of MX plus
+
+ align:start position:0%
+mdy is double integral over R of MX plus
+ 
+
+ align:start position:0%
+mdy is double integral over R of MX plus
+NY
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+da
+
+ align:start position:0%
+da
+ 
+
+ align:start position:0%
+da
+okay okay so now let's do an example
+
+ align:start position:0%
+okay okay so now let's do an example
+ 
+
+ align:start position:0%
+okay okay so now let's do an example
+let's look at this picture again you
+
+ align:start position:0%
+let's look at this picture again you
+ 
+
+ align:start position:0%
+let's look at this picture again you
+know the Flux Of x i + y j out of a
+
+ align:start position:0%
+know the Flux Of x i + y j out of a
+ 
+
+ align:start position:0%
+know the Flux Of x i + y j out of a
+circle of radius
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so we did the calculation directly
+
+ align:start position:0%
+a so we did the calculation directly
+ 
+
+ align:start position:0%
+a so we did the calculation directly
+using geometry and it wasn't all that
+
+ align:start position:0%
+using geometry and it wasn't all that
+ 
+
+ align:start position:0%
+using geometry and it wasn't all that
+bad but let's see what green does for us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so example let's take the same
+
+ align:start position:0%
+here okay so example let's take the same
+ 
+
+ align:start position:0%
+here okay so example let's take the same
+example as last time um so x i + y j
+
+ align:start position:0%
+example as last time um so x i + y j
+ 
+
+ align:start position:0%
+example as last time um so x i + y j
+through C the
+
+ align:start position:0%
+through C the
+ 
+
+ align:start position:0%
+through C the
+circle of radius a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+counterclockwise okay so how do we do
+
+ align:start position:0%
+counterclockwise okay so how do we do
+ 
+
+ align:start position:0%
+counterclockwise okay so how do we do
+how do we set up grein theorum well
+
+ align:start position:0%
+how do we set up grein theorum well
+ 
+
+ align:start position:0%
+how do we set up grein theorum well
+let's first figure
+
+ align:start position:0%
+let's first figure
+ 
+
+ align:start position:0%
+let's first figure
+out the Divergence of
+
+ align:start position:0%
+out the Divergence of
+ 
+
+ align:start position:0%
+out the Divergence of
+f that's you
+
+ align:start position:0%
+f that's you
+ 
+
+ align:start position:0%
+f that's you
+so so the Divergence of this field I
+
+ align:start position:0%
+so so the Divergence of this field I
+ 
+
+ align:start position:0%
+so so the Divergence of this field I
+take the X component which is X and I
+
+ align:start position:0%
+take the X component which is X and I
+ 
+
+ align:start position:0%
+take the X component which is X and I
+take it special respect to X and then I
+
+ align:start position:0%
+take it special respect to X and then I
+ 
+
+ align:start position:0%
+take it special respect to X and then I
+do the same with the Y
+
+ align:start position:0%
+do the same with the Y
+ 
+
+ align:start position:0%
+do the same with the Y
+component and I will get 1 + 1 equals 2
+
+ align:start position:0%
+component and I will get 1 + 1 equals 2
+ 
+
+ align:start position:0%
+component and I will get 1 + 1 equals 2
+okay so the diverence of this field is
+
+ align:start position:0%
+okay so the diverence of this field is
+ 
+
+ align:start position:0%
+okay so the diverence of this field is
+two now green theorem tells us that the
+
+ align:start position:0%
+two now green theorem tells us that the
+ 
+
+ align:start position:0%
+two now green theorem tells us that the
+flux out of this region is going to be
+
+ align:start position:0%
+flux out of this region is going to be
+ 
+
+ align:start position:0%
+flux out of this region is going to be
+the double
+
+ align:start position:0%
+the double
+ 
+
+ align:start position:0%
+the double
+integral of 2 Da
+
+ align:start position:0%
+integral of 2 Da
+ 
+
+ align:start position:0%
+integral of 2 Da
+where what is r now well R is the region
+
+ align:start position:0%
+where what is r now well R is the region
+ 
+
+ align:start position:0%
+where what is r now well R is the region
+enclosed by C so if C is the circle R is
+
+ align:start position:0%
+enclosed by C so if C is the circle R is
+ 
+
+ align:start position:0%
+enclosed by C so if C is the circle R is
+the dis of radius
+
+ align:start position:0%
+the dis of radius
+ 
+
+ align:start position:0%
+the dis of radius
+a so of course we can compute it but we
+
+ align:start position:0%
+a so of course we can compute it but we
+ 
+
+ align:start position:0%
+a so of course we can compute it but we
+don't have to because double integral of
+
+ align:start position:0%
+don't have to because double integral of
+ 
+
+ align:start position:0%
+don't have to because double integral of
+2 Da is just twice the double integral
+
+ align:start position:0%
+2 Da is just twice the double integral
+ 
+
+ align:start position:0%
+2 Da is just twice the double integral
+of Da so it's twice the
+
+ align:start position:0%
+of Da so it's twice the
+ 
+
+ align:start position:0%
+of Da so it's twice the
+area of R and we know the area of a
+
+ align:start position:0%
+area of R and we know the area of a
+ 
+
+ align:start position:0%
+area of R and we know the area of a
+circle of radius a that's Pi a s so
+
+ align:start position:0%
+circle of radius a that's Pi a s so
+ 
+
+ align:start position:0%
+circle of radius a that's Pi a s so
+that's 2 pi a s
+
+ align:start position:0%
+that's 2 pi a s
+ 
+
+ align:start position:0%
+that's 2 pi a s
+here that's the same answer that we got
+
+ align:start position:0%
+here that's the same answer that we got
+ 
+
+ align:start position:0%
+here that's the same answer that we got
+directly which is good
+
+ align:start position:0%
+directly which is good
+ 
+
+ align:start position:0%
+directly which is good
+news so now we can even do better let's
+
+ align:start position:0%
+news so now we can even do better let's
+ 
+
+ align:start position:0%
+news so now we can even do better let's
+say that my circle is not at the origin
+
+ align:start position:0%
+say that my circle is not at the origin
+ 
+
+ align:start position:0%
+say that my circle is not at the origin
+you know let's say that it's out
+
+ align:start position:0%
+you know let's say that it's out
+ 
+
+ align:start position:0%
+you know let's say that it's out
+here well then it becomes harder to
+
+ align:start position:0%
+here well then it becomes harder to
+ 
+
+ align:start position:0%
+here well then it becomes harder to
+calculate the flux directly you know and
+
+ align:start position:0%
+calculate the flux directly you know and
+ 
+
+ align:start position:0%
+calculate the flux directly you know and
+it's harder even to guess exactly what
+
+ align:start position:0%
+it's harder even to guess exactly what
+ 
+
+ align:start position:0%
+it's harder even to guess exactly what
+will happen because on this side here
+
+ align:start position:0%
+will happen because on this side here
+ 
+
+ align:start position:0%
+will happen because on this side here
+well the vector field will go into the
+
+ align:start position:0%
+well the vector field will go into the
+ 
+
+ align:start position:0%
+well the vector field will go into the
+region so the contribution to flux will
+
+ align:start position:0%
+region so the contribution to flux will
+ 
+
+ align:start position:0%
+region so the contribution to flux will
+be negative here
+
+ align:start position:0%
+be negative here
+ 
+
+ align:start position:0%
+be negative here
+well here it will be positive because
+
+ align:start position:0%
+well here it will be positive because
+ 
+
+ align:start position:0%
+well here it will be positive because
+it's going out of the region so there's
+
+ align:start position:0%
+it's going out of the region so there's
+ 
+
+ align:start position:0%
+it's going out of the region so there's
+positive there's negative terms well it
+
+ align:start position:0%
+positive there's negative terms well it
+ 
+
+ align:start position:0%
+positive there's negative terms well it
+looks like positive should win because
+
+ align:start position:0%
+looks like positive should win because
+ 
+
+ align:start position:0%
+looks like positive should win because
+here the vector field is much larger
+
+ align:start position:0%
+here the vector field is much larger
+ 
+
+ align:start position:0%
+here the vector field is much larger
+than over
+
+ align:start position:0%
+than over
+ 
+
+ align:start position:0%
+than over
+there um but you know
+
+ align:start position:0%
+there um but you know
+ 
+
+ align:start position:0%
+there um but you know
+Computing short of computing it we won't
+
+ align:start position:0%
+Computing short of computing it we won't
+ 
+
+ align:start position:0%
+Computing short of computing it we won't
+actually know what it is so if you want
+
+ align:start position:0%
+actually know what it is so if you want
+ 
+
+ align:start position:0%
+actually know what it is so if you want
+to do it by direct calculation then you
+
+ align:start position:0%
+to do it by direct calculation then you
+ 
+
+ align:start position:0%
+to do it by direct calculation then you
+have to parameterize this circle and
+
+ align:start position:0%
+have to parameterize this circle and
+ 
+
+ align:start position:0%
+have to parameterize this circle and
+figure out you know what the line
+
+ align:start position:0%
+figure out you know what the line
+ 
+
+ align:start position:0%
+figure out you know what the line
+integral will be but if you use green
+
+ align:start position:0%
+integral will be but if you use green
+ 
+
+ align:start position:0%
+integral will be but if you use green
+theorem well we never used the fact it's
+
+ align:start position:0%
+theorem well we never used the fact it's
+ 
+
+ align:start position:0%
+theorem well we never used the fact it's
+the circle of radius a at the
+
+ align:start position:0%
+the circle of radius a at the
+ 
+
+ align:start position:0%
+the circle of radius a at the
+origin right it's true actually for any
+
+ align:start position:0%
+origin right it's true actually for any
+ 
+
+ align:start position:0%
+origin right it's true actually for any
+closed curve that the flux out of it is
+
+ align:start position:0%
+closed curve that the flux out of it is
+ 
+
+ align:start position:0%
+closed curve that the flux out of it is
+going to be twice the area of the region
+
+ align:start position:0%
+going to be twice the area of the region
+ 
+
+ align:start position:0%
+going to be twice the area of the region
+inside so it will still be 2 pi a s even
+
+ align:start position:0%
+inside so it will still be 2 pi a s even
+ 
+
+ align:start position:0%
+inside so it will still be 2 pi a s even
+if my circle is anywhere else in the
+
+ align:start position:0%
+if my circle is anywhere else in the
+ 
+
+ align:start position:0%
+if my circle is anywhere else in the
+plane so you know if I had asked you the
+
+ align:start position:0%
+plane so you know if I had asked you the
+ 
+
+ align:start position:0%
+plane so you know if I had asked you the
+TR question where do you want to place
+
+ align:start position:0%
+TR question where do you want to place
+ 
+
+ align:start position:0%
+TR question where do you want to place
+this circle so that the flux is the
+
+ align:start position:0%
+this circle so that the flux is the
+ 
+
+ align:start position:0%
+this circle so that the flux is the
+largest well the answer is actually it
+
+ align:start position:0%
+largest well the answer is actually it
+ 
+
+ align:start position:0%
+largest well the answer is actually it
+doesn't
+
+ align:start position:0%
+doesn't
+ 
+
+ align:start position:0%
+doesn't
+matter okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+let's just finish quickly by answering a
+
+ align:start position:0%
+let's just finish quickly by answering a
+ 
+
+ align:start position:0%
+let's just finish quickly by answering a
+question that some of you I'm sure must
+
+ align:start position:0%
+question that some of you I'm sure must
+ 
+
+ align:start position:0%
+question that some of you I'm sure must
+have which is what does Divergence mean
+
+ align:start position:0%
+have which is what does Divergence mean
+ 
+
+ align:start position:0%
+have which is what does Divergence mean
+what does it measure right I mean we say
+
+ align:start position:0%
+what does it measure right I mean we say
+ 
+
+ align:start position:0%
+what does it measure right I mean we say
+it for curl curl measures how much
+
+ align:start position:0%
+it for curl curl measures how much
+ 
+
+ align:start position:0%
+it for curl curl measures how much
+things are rotating somehow so what does
+
+ align:start position:0%
+things are rotating somehow so what does
+ 
+
+ align:start position:0%
+things are rotating somehow so what does
+the Divergence
+
+ align:start position:0%
+the Divergence
+ 
+
+ align:start position:0%
+the Divergence
+mean well the answer is Divergence mean
+
+ align:start position:0%
+mean well the answer is Divergence mean
+ 
+
+ align:start position:0%
+mean well the answer is Divergence mean
+Divergence measures how much things are
+
+ align:start position:0%
+Divergence measures how much things are
+ 
+
+ align:start position:0%
+Divergence measures how much things are
+diverging okay
+
+ align:start position:0%
+diverging okay
+ 
+
+ align:start position:0%
+diverging okay
+that's uh let's be
+
+ align:start position:0%
+that's uh let's be
+ 
+
+ align:start position:0%
+that's uh let's be
+more explicit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so interpretation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Divergence actually you can think of it
+
+ align:start position:0%
+Divergence actually you can think of it
+ 
+
+ align:start position:0%
+Divergence actually you can think of it
+you know imagine that so what do I want
+
+ align:start position:0%
+you know imagine that so what do I want
+ 
+
+ align:start position:0%
+you know imagine that so what do I want
+to say first so if you take a vector
+
+ align:start position:0%
+to say first so if you take a vector
+ 
+
+ align:start position:0%
+to say first so if you take a vector
+field that just like maybe you know
+
+ align:start position:0%
+field that just like maybe you know
+ 
+
+ align:start position:0%
+field that just like maybe you know
+that's a constant Vector field where
+
+ align:start position:0%
+that's a constant Vector field where
+ 
+
+ align:start position:0%
+that's a constant Vector field where
+everything just translates then there's
+
+ align:start position:0%
+everything just translates then there's
+ 
+
+ align:start position:0%
+everything just translates then there's
+no Divergence involved because the
+
+ align:start position:0%
+no Divergence involved because the
+ 
+
+ align:start position:0%
+no Divergence involved because the
+derivatives will be zero if you take the
+
+ align:start position:0%
+derivatives will be zero if you take the
+ 
+
+ align:start position:0%
+derivatives will be zero if you take the
+guy that rotates things around you'll
+
+ align:start position:0%
+guy that rotates things around you'll
+ 
+
+ align:start position:0%
+guy that rotates things around you'll
+also compute and find zero for
+
+ align:start position:0%
+also compute and find zero for
+ 
+
+ align:start position:0%
+also compute and find zero for
+Divergence so this is not sensitive to
+
+ align:start position:0%
+Divergence so this is not sensitive to
+ 
+
+ align:start position:0%
+Divergence so this is not sensitive to
+translation motions where everything
+
+ align:start position:0%
+translation motions where everything
+ 
+
+ align:start position:0%
+translation motions where everything
+moves together or to rotation motions
+
+ align:start position:0%
+moves together or to rotation motions
+ 
+
+ align:start position:0%
+moves together or to rotation motions
+but instead it's sensitive to expanding
+
+ align:start position:0%
+but instead it's sensitive to expanding
+ 
+
+ align:start position:0%
+but instead it's sensitive to expanding
+motions so possible answer is that it
+
+ align:start position:0%
+motions so possible answer is that it
+ 
+
+ align:start position:0%
+motions so possible answer is that it
+measures how much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+flow is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expanding areas okay so if you you know
+
+ align:start position:0%
+expanding areas okay so if you you know
+ 
+
+ align:start position:0%
+expanding areas okay so if you you know
+if you imagine this flow that we have
+
+ align:start position:0%
+if you imagine this flow that we have
+ 
+
+ align:start position:0%
+if you imagine this flow that we have
+here on that picture things are moving
+
+ align:start position:0%
+here on that picture things are moving
+ 
+
+ align:start position:0%
+here on that picture things are moving
+away from the origin and they you know
+
+ align:start position:0%
+away from the origin and they you know
+ 
+
+ align:start position:0%
+away from the origin and they you know
+fill out the plane if you imagine this
+
+ align:start position:0%
+fill out the plane if you imagine this
+ 
+
+ align:start position:0%
+fill out the plane if you imagine this
+fluid flowing out there it's occupying
+
+ align:start position:0%
+fluid flowing out there it's occupying
+ 
+
+ align:start position:0%
+fluid flowing out there it's occupying
+more and more
+
+ align:start position:0%
+more and more
+ 
+
+ align:start position:0%
+more and more
+space and so that's what it means to
+
+ align:start position:0%
+space and so that's what it means to
+ 
+
+ align:start position:0%
+space and so that's what it means to
+have positive Divergence if you took the
+
+ align:start position:0%
+have positive Divergence if you took the
+ 
+
+ align:start position:0%
+have positive Divergence if you took the
+opposite Vector field that contracts
+
+ align:start position:0%
+opposite Vector field that contracts
+ 
+
+ align:start position:0%
+opposite Vector field that contracts
+everything to the
+
+ align:start position:0%
+everything to the
+ 
+
+ align:start position:0%
+everything to the
+origin that would have negative
+
+ align:start position:0%
+origin that would have negative
+ 
+
+ align:start position:0%
+origin that would have negative
+diverence so that's a good way to think
+
+ align:start position:0%
+diverence so that's a good way to think
+ 
+
+ align:start position:0%
+diverence so that's a good way to think
+about it if you're thinking of a gas
+
+ align:start position:0%
+about it if you're thinking of a gas
+ 
+
+ align:start position:0%
+about it if you're thinking of a gas
+maybe that can expand to fill out more
+
+ align:start position:0%
+maybe that can expand to fill out more
+ 
+
+ align:start position:0%
+maybe that can expand to fill out more
+volume if you're thinking of water well
+
+ align:start position:0%
+volume if you're thinking of water well
+ 
+
+ align:start position:0%
+volume if you're thinking of water well
+water doesn't really shrink or expand so
+
+ align:start position:0%
+water doesn't really shrink or expand so
+ 
+
+ align:start position:0%
+water doesn't really shrink or expand so
+the fact that it's taking more and more
+
+ align:start position:0%
+the fact that it's taking more and more
+ 
+
+ align:start position:0%
+the fact that it's taking more and more
+space actually means that there's more
+
+ align:start position:0%
+space actually means that there's more
+ 
+
+ align:start position:0%
+space actually means that there's more
+and more water so the other way to think
+
+ align:start position:0%
+and more water so the other way to think
+ 
+
+ align:start position:0%
+and more water so the other way to think
+about it is Divergence is the source
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate so it's the amount of fluid that's
+
+ align:start position:0%
+rate so it's the amount of fluid that's
+ 
+
+ align:start position:0%
+rate so it's the amount of fluid that's
+being inserted into the system that's
+
+ align:start position:0%
+being inserted into the system that's
+ 
+
+ align:start position:0%
+being inserted into the system that's
+being pumped into the system per unit
+
+ align:start position:0%
+being pumped into the system per unit
+ 
+
+ align:start position:0%
+being pumped into the system per unit
+time per unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area per unit time and per unit area so
+
+ align:start position:0%
+area per unit time and per unit area so
+ 
+
+ align:start position:0%
+area per unit time and per unit area so
+what div f equals 2 here means is that
+
+ align:start position:0%
+what div f equals 2 here means is that
+ 
+
+ align:start position:0%
+what div f equals 2 here means is that
+here you have actually matter being
+
+ align:start position:0%
+here you have actually matter being
+ 
+
+ align:start position:0%
+here you have actually matter being
+created or being pumped into the system
+
+ align:start position:0%
+created or being pumped into the system
+ 
+
+ align:start position:0%
+created or being pumped into the system
+so that you know you have more and more
+
+ align:start position:0%
+so that you know you have more and more
+ 
+
+ align:start position:0%
+so that you know you have more and more
+water filling more and more space as it
+
+ align:start position:0%
+water filling more and more space as it
+ 
+
+ align:start position:0%
+water filling more and more space as it
+flows but actually diverence is not too
+
+ align:start position:0%
+flows but actually diverence is not too
+ 
+
+ align:start position:0%
+flows but actually diverence is not too
+just at the origin it's two everywhere
+
+ align:start position:0%
+just at the origin it's two everywhere
+ 
+
+ align:start position:0%
+just at the origin it's two everywhere
+so in fact to have this you need to have
+
+ align:start position:0%
+so in fact to have this you need to have
+ 
+
+ align:start position:0%
+so in fact to have this you need to have
+a system of pumps that actually is
+
+ align:start position:0%
+a system of pumps that actually is
+ 
+
+ align:start position:0%
+a system of pumps that actually is
+inserting water absolutely everywhere
+
+ align:start position:0%
+inserting water absolutely everywhere
+ 
+
+ align:start position:0%
+inserting water absolutely everywhere
+uniformly that's the only way to do this
+
+ align:start position:0%
+uniformly that's the only way to do this
+ 
+
+ align:start position:0%
+uniformly that's the only way to do this
+I mean if you imagine that you just have
+
+ align:start position:0%
+I mean if you imagine that you just have
+ 
+
+ align:start position:0%
+I mean if you imagine that you just have
+one you know spring at the origin then
+
+ align:start position:0%
+one you know spring at the origin then
+ 
+
+ align:start position:0%
+one you know spring at the origin then
+sure water will flow out but as you go
+
+ align:start position:0%
+sure water will flow out but as you go
+ 
+
+ align:start position:0%
+sure water will flow out but as you go
+further and further away it will do so
+
+ align:start position:0%
+further and further away it will do so
+ 
+
+ align:start position:0%
+further and further away it will do so
+more and more slowly while here it's
+
+ align:start position:0%
+more and more slowly while here it's
+ 
+
+ align:start position:0%
+more and more slowly while here it's
+flowing away faster and faster and that
+
+ align:start position:0%
+flowing away faster and faster and that
+ 
+
+ align:start position:0%
+flowing away faster and faster and that
+means you know everywhere actually
+
+ align:start position:0%
+means you know everywhere actually
+ 
+
+ align:start position:0%
+means you know everywhere actually
+you're still pumping more water into
+
+ align:start position:0%
+you're still pumping more water into
+ 
+
+ align:start position:0%
+you're still pumping more water into
+it um so that's what Divergence measures
\ No newline at end of file
diff --git a/_bTZbn7M2Hc.txt b/_bTZbn7M2Hc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b02ce9b05b41f2d25115b4d468867acfd9da71d5
--- /dev/null
+++ b/_bTZbn7M2Hc.txt
@@ -0,0 +1,1394 @@
+align:start position:0%
+ 
+all right so let's get now the state and
+
+ align:start position:0%
+all right so let's get now the state and
+ 
+
+ align:start position:0%
+all right so let's get now the state and
+one so I want to make a general remark
+
+ align:start position:0%
+one so I want to make a general remark
+ 
+
+ align:start position:0%
+one so I want to make a general remark
+you have an equation like this and we
+
+ align:start position:0%
+you have an equation like this and we
+ 
+
+ align:start position:0%
+you have an equation like this and we
+want to solve it it's a vector equation
+
+ align:start position:0%
+want to solve it it's a vector equation
+ 
+
+ align:start position:0%
+want to solve it it's a vector equation
+operator and a vector equal number and a
+
+ align:start position:0%
+operator and a vector equal number and a
+ 
+
+ align:start position:0%
+operator and a vector equal number and a
+vector am or operator and a vector to
+
+ align:start position:0%
+vector am or operator and a vector to
+ 
+
+ align:start position:0%
+vector am or operator and a vector to
+make sure you have solved it when you
+
+ align:start position:0%
+make sure you have solved it when you
+ 
+
+ align:start position:0%
+make sure you have solved it when you
+have a vector equation you must make
+
+ align:start position:0%
+have a vector equation you must make
+ 
+
+ align:start position:0%
+have a vector equation you must make
+sure that every component you can write
+
+ align:start position:0%
+sure that every component you can write
+ 
+
+ align:start position:0%
+sure that every component you can write
+a vector in equation in the firm vector
+
+ align:start position:0%
+a vector in equation in the firm vector
+ 
+
+ align:start position:0%
+a vector in equation in the firm vector
+equals zero and then you must make sure
+
+ align:start position:0%
+equals zero and then you must make sure
+ 
+
+ align:start position:0%
+equals zero and then you must make sure
+that every component of the vector is
+
+ align:start position:0%
+that every component of the vector is
+ 
+
+ align:start position:0%
+that every component of the vector is
+zero what we did here is we found what
+
+ align:start position:0%
+zero what we did here is we found what
+ 
+
+ align:start position:0%
+zero what we did here is we found what
+happens when I look at the component
+
+ align:start position:0%
+happens when I look at the component
+ 
+
+ align:start position:0%
+happens when I look at the component
+along and zero and I figure out that
+
+ align:start position:0%
+along and zero and I figure out that
+ 
+
+ align:start position:0%
+along and zero and I figure out that
+whoops this equation when I look at the
+
+ align:start position:0%
+whoops this equation when I look at the
+ 
+
+ align:start position:0%
+whoops this equation when I look at the
+component along and zero tells me what
+
+ align:start position:0%
+component along and zero tells me what
+ 
+
+ align:start position:0%
+component along and zero tells me what
+the energy is so the rest of the
+
+ align:start position:0%
+the energy is so the rest of the
+ 
+
+ align:start position:0%
+the energy is so the rest of the
+information of this equation arises when
+
+ align:start position:0%
+information of this equation arises when
+ 
+
+ align:start position:0%
+information of this equation arises when
+I look at it along the components on the
+
+ align:start position:0%
+I look at it along the components on the
+ 
+
+ align:start position:0%
+I look at it along the components on the
+other states not in zero but the K
+
+ align:start position:0%
+other states not in zero but the K
+ 
+
+ align:start position:0%
+other states not in zero but the K
+states that we introduced from the
+
+ align:start position:0%
+states that we introduced from the
+ 
+
+ align:start position:0%
+states that we introduced from the
+beginning the KZ rows that run with from
+
+ align:start position:0%
+beginning the KZ rows that run with from
+ 
+
+ align:start position:0%
+beginning the KZ rows that run with from
+1 to infinity so what we're gonna do is
+
+ align:start position:0%
+1 to infinity so what we're gonna do is
+ 
+
+ align:start position:0%
+1 to infinity so what we're gonna do is
+take that original this second equation
+
+ align:start position:0%
+take that original this second equation
+ 
+
+ align:start position:0%
+take that original this second equation
+and form K 0 H 0 minus e + 0 + 1 is
+
+ align:start position:0%
+and form K 0 H 0 minus e + 0 + 1 is
+ 
+
+ align:start position:0%
+and form K 0 H 0 minus e + 0 + 1 is
+equal to K 0 e n1 minus Delta H + 0 so I
+
+ align:start position:0%
+equal to K 0 e n1 minus Delta H + 0 so I
+ 
+
+ align:start position:0%
+equal to K 0 e n1 minus Delta H + 0 so I
+now took the same equation and I put an
+
+ align:start position:0%
+now took the same equation and I put an
+ 
+
+ align:start position:0%
+now took the same equation and I put an
+inner product with K 0 and I say look K
+
+ align:start position:0%
+inner product with K 0 and I say look K
+ 
+
+ align:start position:0%
+inner product with K 0 and I say look K
+will be different from n because when we
+
+ align:start position:0%
+will be different from n because when we
+ 
+
+ align:start position:0%
+will be different from n because when we
+put k equal to n that already we've done
+
+ align:start position:0%
+put k equal to n that already we've done
+ 
+
+ align:start position:0%
+put k equal to n that already we've done
+and we've learned all about it and in
+
+ align:start position:0%
+and we've learned all about it and in
+ 
+
+ align:start position:0%
+and we've learned all about it and in
+fact and one didn't appear the state
+
+ align:start position:0%
+fact and one didn't appear the state
+ 
+
+ align:start position:0%
+fact and one didn't appear the state
+that we wanted didn't appear at all so
+
+ align:start position:0%
+that we wanted didn't appear at all so
+ 
+
+ align:start position:0%
+that we wanted didn't appear at all so
+now we do this with arbitrary K and we
+
+ align:start position:0%
+now we do this with arbitrary K and we
+ 
+
+ align:start position:0%
+now we do this with arbitrary K and we
+need to figure out what this gives so so
+
+ align:start position:0%
+need to figure out what this gives so so
+ 
+
+ align:start position:0%
+need to figure out what this gives so so
+you have to look at these things and try
+
+ align:start position:0%
+you have to look at these things and try
+ 
+
+ align:start position:0%
+you have to look at these things and try
+to remember a little the definitions
+
+ align:start position:0%
+to remember a little the definitions
+ 
+
+ align:start position:0%
+to remember a little the definitions
+we've put so H 0 we know what it gives
+
+ align:start position:0%
+we've put so H 0 we know what it gives
+ 
+
+ align:start position:0%
+we've put so H 0 we know what it gives
+them K 0 it gives you a number the
+
+ align:start position:0%
+them K 0 it gives you a number the
+ 
+
+ align:start position:0%
+them K 0 it gives you a number the
+energy of that state so this is another
+
+ align:start position:0%
+energy of that state so this is another
+ 
+
+ align:start position:0%
+energy of that state so this is another
+number so that's great this simplifies
+
+ align:start position:0%
+number so that's great this simplifies
+ 
+
+ align:start position:0%
+number so that's great this simplifies
+this to e K 0 minus e and 0 times the
+
+ align:start position:0%
+this to e K 0 minus e and 0 times the
+ 
+
+ align:start position:0%
+this to e K 0 minus e and 0 times the
+overlap of K is 0 with N 1 that's the
+
+ align:start position:0%
+overlap of K is 0 with N 1 that's the
+ 
+
+ align:start position:0%
+overlap of K is 0 with N 1 that's the
+left-hand side how about the right-hand
+
+ align:start position:0%
+left-hand side how about the right-hand
+ 
+
+ align:start position:0%
+left-hand side how about the right-hand
+side all right let's see what this is
+
+ align:start position:0%
+side all right let's see what this is
+ 
+
+ align:start position:0%
+side all right let's see what this is
+first term the Ian 1 is a number so I
+
+ align:start position:0%
+first term the Ian 1 is a number so I
+ 
+
+ align:start position:0%
+first term the Ian 1 is a number so I
+must ask myself is what happens when K 0
+
+ align:start position:0%
+must ask myself is what happens when K 0
+ 
+
+ align:start position:0%
+must ask myself is what happens when K 0
+meets n 0 well those are our original or
+
+ align:start position:0%
+meets n 0 well those are our original or
+ 
+
+ align:start position:0%
+meets n 0 well those are our original or
+third normal States and we said that K
+
+ align:start position:0%
+third normal States and we said that K
+ 
+
+ align:start position:0%
+third normal States and we said that K
+is different from n so this term is 0
+
+ align:start position:0%
+is different from n so this term is 0
+ 
+
+ align:start position:0%
+is different from n so this term is 0
+with the en 1 this is a number and these
+
+ align:start position:0%
+with the en 1 this is a number and these
+ 
+
+ align:start position:0%
+with the en 1 this is a number and these
+two states are orthogonal so this term
+
+ align:start position:0%
+two states are orthogonal so this term
+ 
+
+ align:start position:0%
+two states are orthogonal so this term
+gives you a 0 not because this number is
+
+ align:start position:0%
+gives you a 0 not because this number is
+ 
+
+ align:start position:0%
+gives you a 0 not because this number is
+0 but because the overlap is 0 and I get
+
+ align:start position:0%
+0 but because the overlap is 0 and I get
+ 
+
+ align:start position:0%
+0 but because the overlap is 0 and I get
+here minus K 0 Delta H and 0 and it's a
+
+ align:start position:0%
+here minus K 0 Delta H and 0 and it's a
+ 
+
+ align:start position:0%
+here minus K 0 Delta H and 0 and it's a
+good notation to call this to save
+
+ align:start position:0%
+good notation to call this to save
+ 
+
+ align:start position:0%
+good notation to call this to save
+writing Delta H K and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a good name for it it's the matrix
+
+ align:start position:0%
+it's a good name for it it's the matrix
+ 
+
+ align:start position:0%
+it's a good name for it it's the matrix
+k KN 'the element of the matrix Delta H
+
+ align:start position:0%
+k KN 'the element of the matrix Delta H
+ 
+
+ align:start position:0%
+k KN 'the element of the matrix Delta H
+and this is a number so I can solve k 0
+
+ align:start position:0%
+and this is a number so I can solve k 0
+ 
+
+ align:start position:0%
+and this is a number so I can solve k 0
+and 1 is equal to minus Delta H K and /
+
+ align:start position:0%
+and 1 is equal to minus Delta H K and /
+ 
+
+ align:start position:0%
+and 1 is equal to minus Delta H K and /
+EK 0 minus e n 0 and this is true for
+
+ align:start position:0%
+EK 0 minus e n 0 and this is true for
+ 
+
+ align:start position:0%
+EK 0 minus e n 0 and this is true for
+every k different from n and here we
+
+ align:start position:0%
+every k different from n and here we
+ 
+
+ align:start position:0%
+every k different from n and here we
+find for the first time our energy
+
+ align:start position:0%
+find for the first time our energy
+ 
+
+ align:start position:0%
+find for the first time our energy
+denominators these energy denominators
+
+ align:start position:0%
+denominators these energy denominators
+ 
+
+ align:start position:0%
+denominators these energy denominators
+are the things that are gonna make life
+
+ align:start position:0%
+are the things that are gonna make life
+ 
+
+ align:start position:0%
+are the things that are gonna make life
+interesting and difficult and it answers
+
+ align:start position:0%
+interesting and difficult and it answers
+ 
+
+ align:start position:0%
+interesting and difficult and it answers
+the question already that if you had the
+
+ align:start position:0%
+the question already that if you had the
+ 
+
+ align:start position:0%
+the question already that if you had the
+generate states there would be some K
+
+ align:start position:0%
+generate states there would be some K
+ 
+
+ align:start position:0%
+generate states there would be some K
+states that have the same energy as this
+
+ align:start position:0%
+states that have the same energy as this
+ 
+
+ align:start position:0%
+states that have the same energy as this
+one and this blows up and this is
+
+ align:start position:0%
+one and this blows up and this is
+ 
+
+ align:start position:0%
+one and this blows up and this is
+unsolvable for this component so you
+
+ align:start position:0%
+unsolvable for this component so you
+ 
+
+ align:start position:0%
+unsolvable for this component so you
+start getting difficult ease if you have
+
+ align:start position:0%
+start getting difficult ease if you have
+ 
+
+ align:start position:0%
+start getting difficult ease if you have
+degeneracies as long as every K state
+
+ align:start position:0%
+degeneracies as long as every K state
+ 
+
+ align:start position:0%
+degeneracies as long as every K state
+all the other states of the spectrum
+
+ align:start position:0%
+all the other states of the spectrum
+ 
+
+ align:start position:0%
+all the other states of the spectrum
+have different energy from en never mind
+
+ align:start position:0%
+have different energy from en never mind
+ 
+
+ align:start position:0%
+have different energy from en never mind
+if the other states are degenerate
+
+ align:start position:0%
+if the other states are degenerate
+ 
+
+ align:start position:0%
+if the other states are degenerate
+they're not degenerate with a state you
+
+ align:start position:0%
+they're not degenerate with a state you
+ 
+
+ align:start position:0%
+they're not degenerate with a state you
+care you care just about one state now
+
+ align:start position:0%
+care you care just about one state now
+ 
+
+ align:start position:0%
+care you care just about one state now
+the nth state and if that's non
+
+ align:start position:0%
+the nth state and if that's non
+ 
+
+ align:start position:0%
+the nth state and if that's non
+degenerate all these denominators are
+
+ align:start position:0%
+degenerate all these denominators are
+ 
+
+ align:start position:0%
+degenerate all these denominators are
+non zero and you're okay so here is the
+
+ align:start position:0%
+non zero and you're okay so here is the
+ 
+
+ align:start position:0%
+non zero and you're okay so here is the
+solution for this thing now I can write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the expressions
+
+ align:start position:0%
+the expressions
+ 
+
+ align:start position:0%
+the expressions
+for the state and the energy so let me
+
+ align:start position:0%
+for the state and the energy so let me
+ 
+
+ align:start position:0%
+for the state and the energy so let me
+do it so I have this n1 like that you
+
+ align:start position:0%
+do it so I have this n1 like that you
+ 
+
+ align:start position:0%
+do it so I have this n1 like that you
+can say the following let me do this
+
+ align:start position:0%
+can say the following let me do this
+ 
+
+ align:start position:0%
+can say the following let me do this
+very deliberately first and one is equal
+
+ align:start position:0%
+very deliberately first and one is equal
+ 
+
+ align:start position:0%
+very deliberately first and one is equal
+to the sum over all K of K naught K
+
+ align:start position:0%
+to the sum over all K of K naught K
+ 
+
+ align:start position:0%
+to the sum over all K of K naught K
+naught and 1 this is the resolution of
+
+ align:start position:0%
+naught and 1 this is the resolution of
+ 
+
+ align:start position:0%
+naught and 1 this is the resolution of
+the identity formula that's the unit
+
+ align:start position:0%
+the identity formula that's the unit
+ 
+
+ align:start position:0%
+the identity formula that's the unit
+operator you can always do that and now
+
+ align:start position:0%
+operator you can always do that and now
+ 
+
+ align:start position:0%
+operator you can always do that and now
+you know that the state N 1 is
+
+ align:start position:0%
+you know that the state N 1 is
+ 
+
+ align:start position:0%
+you know that the state N 1 is
+orthogonal to n 0 so this becomes the
+
+ align:start position:0%
+orthogonal to n 0 so this becomes the
+ 
+
+ align:start position:0%
+orthogonal to n 0 so this becomes the
+sum over K different from n because for
+
+ align:start position:0%
+sum over K different from n because for
+ 
+
+ align:start position:0%
+sum over K different from n because for
+k equal to n these are orthogonal of K
+
+ align:start position:0%
+k equal to n these are orthogonal of K
+ 
+
+ align:start position:0%
+k equal to n these are orthogonal of K
+naught K naught and 1 and that's what we
+
+ align:start position:0%
+naught K naught and 1 and that's what we
+ 
+
+ align:start position:0%
+naught K naught and 1 and that's what we
+calculated here so so what did we get
+
+ align:start position:0%
+calculated here so so what did we get
+ 
+
+ align:start position:0%
+calculated here so so what did we get
+there for the state and 1 I can
+
+ align:start position:0%
+there for the state and 1 I can
+ 
+
+ align:start position:0%
+there for the state and 1 I can
+substitute what we had there it's the
+
+ align:start position:0%
+substitute what we had there it's the
+ 
+
+ align:start position:0%
+substitute what we had there it's the
+sum from k different from n of K naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta H and K over e K naught minus E
+
+ align:start position:0%
+Delta H and K over e K naught minus E
+ 
+
+ align:start position:0%
+Delta H and K over e K naught minus E
+and not that's N 1 I should have a minus
+
+ align:start position:0%
+and not that's N 1 I should have a minus
+ 
+
+ align:start position:0%
+and not that's N 1 I should have a minus
+sign the minus sign is there at state N
+
+ align:start position:0%
+sign the minus sign is there at state N
+ 
+
+ align:start position:0%
+sign the minus sign is there at state N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the state and one is gets it is a
+
+ align:start position:0%
+so the state and one is gets it is a
+ 
+
+ align:start position:0%
+so the state and one is gets it is a
+complicated correction it gets a little
+
+ align:start position:0%
+complicated correction it gets a little
+ 
+
+ align:start position:0%
+complicated correction it gets a little
+component from every other state of the
+
+ align:start position:0%
+component from every other state of the
+ 
+
+ align:start position:0%
+component from every other state of the
+spectrum and the coefficient depends on
+
+ align:start position:0%
+spectrum and the coefficient depends on
+ 
+
+ align:start position:0%
+spectrum and the coefficient depends on
+the matrix element of your state with
+
+ align:start position:0%
+the matrix element of your state with
+ 
+
+ align:start position:0%
+the matrix element of your state with
+the state you're contributing with so
+
+ align:start position:0%
+the state you're contributing with so
+ 
+
+ align:start position:0%
+the state you're contributing with so
+you have the state n here and all the
+
+ align:start position:0%
+you have the state n here and all the
+ 
+
+ align:start position:0%
+you have the state n here and all the
+other states here the amount of this
+
+ align:start position:0%
+other states here the amount of this
+ 
+
+ align:start position:0%
+other states here the amount of this
+state K that enters into the correction
+
+ align:start position:0%
+state K that enters into the correction
+ 
+
+ align:start position:0%
+state K that enters into the correction
+is proportional to the matrix element
+
+ align:start position:0%
+is proportional to the matrix element
+ 
+
+ align:start position:0%
+is proportional to the matrix element
+between m and K if the matrix element is
+
+ align:start position:0%
+between m and K if the matrix element is
+ 
+
+ align:start position:0%
+between m and K if the matrix element is
+zero that state does not contribute here
+
+ align:start position:0%
+zero that state does not contribute here
+ 
+
+ align:start position:0%
+zero that state does not contribute here
+and then there is the energy denominator
+
+ align:start position:0%
+and then there is the energy denominator
+ 
+
+ align:start position:0%
+and then there is the energy denominator
+as well so we're getting to the end of
+
+ align:start position:0%
+as well so we're getting to the end of
+ 
+
+ align:start position:0%
+as well so we're getting to the end of
+this calculation there's one more thing
+
+ align:start position:0%
+this calculation there's one more thing
+ 
+
+ align:start position:0%
+this calculation there's one more thing
+one can do which is to find and so I'm
+
+ align:start position:0%
+one can do which is to find and so I'm
+ 
+
+ align:start position:0%
+one can do which is to find and so I'm
+starting to wrap up this but still an
+
+ align:start position:0%
+starting to wrap up this but still an
+ 
+
+ align:start position:0%
+starting to wrap up this but still an
+important step what we have to do I'll
+
+ align:start position:0%
+important step what we have to do I'll
+ 
+
+ align:start position:0%
+important step what we have to do I'll
+get the second order energy correction
+
+ align:start position:0%
+get the second order energy correction
+ 
+
+ align:start position:0%
+get the second order energy correction
+what is our second order energy
+
+ align:start position:0%
+what is our second order energy
+ 
+
+ align:start position:0%
+what is our second order energy
+correction our second order energy
+
+ align:start position:0%
+correction our second order energy
+ 
+
+ align:start position:0%
+correction our second order energy
+correction can be found from the formula
+
+ align:start position:0%
+correction can be found from the formula
+ 
+
+ align:start position:0%
+correction can be found from the formula
+on that blackboard e + 2 we already
+
+ align:start position:0%
+on that blackboard e + 2 we already
+ 
+
+ align:start position:0%
+on that blackboard e + 2 we already
+found the first order energy correction
+
+ align:start position:0%
+found the first order energy correction
+ 
+
+ align:start position:0%
+found the first order energy correction
+which I happen to have erased it right
+
+ align:start position:0%
+which I happen to have erased it right
+ 
+
+ align:start position:0%
+which I happen to have erased it right
+now it was there en 2 is obtained by
+
+ align:start position:0%
+now it was there en 2 is obtained by
+ 
+
+ align:start position:0%
+now it was there en 2 is obtained by
+doing n 0 Delta H times N 1 which we
+
+ align:start position:0%
+doing n 0 Delta H times N 1 which we
+ 
+
+ align:start position:0%
+doing n 0 Delta H times N 1 which we
+already know so I must do n 0 Delta H on
+
+ align:start position:0%
+already know so I must do n 0 Delta H on
+ 
+
+ align:start position:0%
+already know so I must do n 0 Delta H on
+that so look what you get you get minus
+
+ align:start position:0%
+that so look what you get you get minus
+ 
+
+ align:start position:0%
+that so look what you get you get minus
+the sum over K different from n think of
+
+ align:start position:0%
+the sum over K different from n think of
+ 
+
+ align:start position:0%
+the sum over K different from n think of
+booting the N 0 and the Delta H they're
+
+ align:start position:0%
+booting the N 0 and the Delta H they're
+ 
+
+ align:start position:0%
+booting the N 0 and the Delta H they're
+all together it's a bra so far it's a
+
+ align:start position:0%
+all together it's a bra so far it's a
+ 
+
+ align:start position:0%
+all together it's a bra so far it's a
+Delta H and 0 it should go into N 1 but
+
+ align:start position:0%
+Delta H and 0 it should go into N 1 but
+ 
+
+ align:start position:0%
+Delta H and 0 it should go into N 1 but
+the only state in and 1 is K 0 so here
+
+ align:start position:0%
+the only state in and 1 is K 0 so here
+ 
+
+ align:start position:0%
+the only state in and 1 is K 0 so here
+half k0 and then we have delta h MK / EK
+
+ align:start position:0%
+half k0 and then we have delta h MK / EK
+ 
+
+ align:start position:0%
+half k0 and then we have delta h MK / EK
+0 minus e and 0 okay a little bit of
+
+ align:start position:0%
+0 minus e and 0 okay a little bit of
+ 
+
+ align:start position:0%
+0 minus e and 0 okay a little bit of
+work so what is this this is another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix element this is the matrix I'm
+
+ align:start position:0%
+matrix element this is the matrix I'm
+ 
+
+ align:start position:0%
+matrix element this is the matrix I'm
+sorry here do I have a mistake yes I
+
+ align:start position:0%
+sorry here do I have a mistake yes I
+ 
+
+ align:start position:0%
+sorry here do I have a mistake yes I
+have KNI I copied it wrong it's K and
+
+ align:start position:0%
+have KNI I copied it wrong it's K and
+ 
+
+ align:start position:0%
+have KNI I copied it wrong it's K and
+yes yes so here I have Delta 8mk but
+
+ align:start position:0%
+yes yes so here I have Delta 8mk but
+ 
+
+ align:start position:0%
+yes yes so here I have Delta 8mk but
+Delta H and K is this
+
+ align:start position:0%
+Delta H and K is this
+ 
+
+ align:start position:0%
+Delta H and K is this
+if you complex conjugate if you complex
+
+ align:start position:0%
+if you complex conjugate if you complex
+ 
+
+ align:start position:0%
+if you complex conjugate if you complex
+on the Delta 8k and complex conjugate is
+
+ align:start position:0%
+on the Delta 8k and complex conjugate is
+ 
+
+ align:start position:0%
+on the Delta 8k and complex conjugate is
+K Delta H and complex conjugate which
+
+ align:start position:0%
+K Delta H and complex conjugate which
+ 
+
+ align:start position:0%
+K Delta H and complex conjugate which
+changes the order and Delta H which is
+
+ align:start position:0%
+changes the order and Delta H which is
+ 
+
+ align:start position:0%
+changes the order and Delta H which is
+hermitian K and that's Delta H and K so
+
+ align:start position:0%
+hermitian K and that's Delta H and K so
+ 
+
+ align:start position:0%
+hermitian K and that's Delta H and K so
+Delta H NK is equal to Delta H K and
+
+ align:start position:0%
+Delta H NK is equal to Delta H K and
+ 
+
+ align:start position:0%
+Delta H NK is equal to Delta H K and
+star and therefore the second order
+
+ align:start position:0%
+star and therefore the second order
+ 
+
+ align:start position:0%
+star and therefore the second order
+energy correction has a nice formula e
+
+ align:start position:0%
+energy correction has a nice formula e
+ 
+
+ align:start position:0%
+energy correction has a nice formula e
+n2 is equal to minus the sum over K
+
+ align:start position:0%
+n2 is equal to minus the sum over K
+ 
+
+ align:start position:0%
+n2 is equal to minus the sum over K
+different from n Delta H and K which is
+
+ align:start position:0%
+different from n Delta H and K which is
+ 
+
+ align:start position:0%
+different from n Delta H and K which is
+the star of that times this one so you
+
+ align:start position:0%
+the star of that times this one so you
+ 
+
+ align:start position:0%
+the star of that times this one so you
+get Delta H and K absolute value squared
+
+ align:start position:0%
+get Delta H and K absolute value squared
+ 
+
+ align:start position:0%
+get Delta H and K absolute value squared
+divided by e m EK n equals zero minus E
+
+ align:start position:0%
+divided by e m EK n equals zero minus E
+ 
+
+ align:start position:0%
+divided by e m EK n equals zero minus E
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've done a lot of work with written
+
+ align:start position:0%
+so we've done a lot of work with written
+ 
+
+ align:start position:0%
+so we've done a lot of work with written
+the perturbation here is an answer so
+
+ align:start position:0%
+the perturbation here is an answer so
+ 
+
+ align:start position:0%
+the perturbation here is an answer so
+far we have n of lambda equal n 0 plus
+
+ align:start position:0%
+far we have n of lambda equal n 0 plus
+ 
+
+ align:start position:0%
+far we have n of lambda equal n 0 plus
+lambda N 1 and 1 has been calculated
+
+ align:start position:0%
+lambda N 1 and 1 has been calculated
+ 
+
+ align:start position:0%
+lambda N 1 and 1 has been calculated
+energies a and 0 plus lambda e in one
+
+ align:start position:0%
+energies a and 0 plus lambda e in one
+ 
+
+ align:start position:0%
+energies a and 0 plus lambda e in one
+that was calculated what was just Delta
+
+ align:start position:0%
+that was calculated what was just Delta
+ 
+
+ align:start position:0%
+that was calculated what was just Delta
+H in this state plus lambda squared e n2
+
+ align:start position:0%
+H in this state plus lambda squared e n2
+ 
+
+ align:start position:0%
+H in this state plus lambda squared e n2
+which we have calculated so this is as
+
+ align:start position:0%
+which we have calculated so this is as
+ 
+
+ align:start position:0%
+which we have calculated so this is as
+far as we will do for non degenerate
+
+ align:start position:0%
+far as we will do for non degenerate
+ 
+
+ align:start position:0%
+far as we will do for non degenerate
+perturbation theory but we have found
+
+ align:start position:0%
+perturbation theory but we have found
+ 
+
+ align:start position:0%
+perturbation theory but we have found
+rather interesting formulas and we're
+
+ align:start position:0%
+rather interesting formulas and we're
+ 
+
+ align:start position:0%
+rather interesting formulas and we're
+going to spend half of next lecture
+
+ align:start position:0%
+going to spend half of next lecture
+ 
+
+ align:start position:0%
+going to spend half of next lecture
+trying to understand them better
\ No newline at end of file
diff --git a/_fWt9yHslDo.txt b/_fWt9yHslDo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..541c24914e45bf1b8385a6a60326238343002e5d
--- /dev/null
+++ b/_fWt9yHslDo.txt
@@ -0,0 +1,4571 @@
+align:start position:0%
+ 
+so to start out I just wanted to mention
+
+ align:start position:0%
+so to start out I just wanted to mention
+ 
+
+ align:start position:0%
+so to start out I just wanted to mention
+we talk a lot about dogma
+
+ align:start position:0%
+we talk a lot about dogma
+ 
+
+ align:start position:0%
+we talk a lot about dogma
+in the lab so we talked about dogma
+
+ align:start position:0%
+in the lab so we talked about dogma
+ 
+
+ align:start position:0%
+in the lab so we talked about dogma
+right there's the central dogma which is
+
+ align:start position:0%
+right there's the central dogma which is
+ 
+
+ align:start position:0%
+right there's the central dogma which is
+DNA information flows from DNA to RNA to
+
+ align:start position:0%
+DNA information flows from DNA to RNA to
+ 
+
+ align:start position:0%
+DNA information flows from DNA to RNA to
+protein I'm gonna describe another dogma
+
+ align:start position:0%
+protein I'm gonna describe another dogma
+ 
+
+ align:start position:0%
+protein I'm gonna describe another dogma
+if you will which is that life starts as
+
+ align:start position:0%
+if you will which is that life starts as
+ 
+
+ align:start position:0%
+if you will which is that life starts as
+sort of a fertilized egg so you're get a
+
+ align:start position:0%
+sort of a fertilized egg so you're get a
+ 
+
+ align:start position:0%
+sort of a fertilized egg so you're get a
+fertilized egg and this fertilized egg
+
+ align:start position:0%
+fertilized egg and this fertilized egg
+ 
+
+ align:start position:0%
+fertilized egg and this fertilized egg
+which you see in the video up here
+
+ align:start position:0%
+which you see in the video up here
+ 
+
+ align:start position:0%
+which you see in the video up here
+undergoes development and as part of
+
+ align:start position:0%
+undergoes development and as part of
+ 
+
+ align:start position:0%
+undergoes development and as part of
+that development there is what is known
+
+ align:start position:0%
+that development there is what is known
+ 
+
+ align:start position:0%
+that development there is what is known
+as differentiation where cells acquire
+
+ align:start position:0%
+as differentiation where cells acquire
+ 
+
+ align:start position:0%
+as differentiation where cells acquire
+more specialized cell types so there's
+
+ align:start position:0%
+more specialized cell types so there's
+ 
+
+ align:start position:0%
+more specialized cell types so there's
+development and differentiation and this
+
+ align:start position:0%
+development and differentiation and this
+ 
+
+ align:start position:0%
+development and differentiation and this
+results in adult cell types that are
+
+ align:start position:0%
+results in adult cell types that are
+ 
+
+ align:start position:0%
+results in adult cell types that are
+known as differentiated so that results
+
+ align:start position:0%
+known as differentiated so that results
+ 
+
+ align:start position:0%
+known as differentiated so that results
+in differentiated / adult cell types
+
+ align:start position:0%
+in differentiated / adult cell types
+ 
+
+ align:start position:0%
+in differentiated / adult cell types
+with specialized functions and you see
+
+ align:start position:0%
+with specialized functions and you see
+ 
+
+ align:start position:0%
+with specialized functions and you see
+just a few of them up on the slide above
+
+ align:start position:0%
+just a few of them up on the slide above
+ 
+
+ align:start position:0%
+just a few of them up on the slide above
+there are in fact thousands of different
+
+ align:start position:0%
+there are in fact thousands of different
+ 
+
+ align:start position:0%
+there are in fact thousands of different
+sort of cell types that humans have but
+
+ align:start position:0%
+sort of cell types that humans have but
+ 
+
+ align:start position:0%
+sort of cell types that humans have but
+the dogma at least up until fairly
+
+ align:start position:0%
+the dogma at least up until fairly
+ 
+
+ align:start position:0%
+the dogma at least up until fairly
+recently in the past couple decades or
+
+ align:start position:0%
+recently in the past couple decades or
+ 
+
+ align:start position:0%
+recently in the past couple decades or
+so or at least before 1960 1950s is that
+
+ align:start position:0%
+so or at least before 1960 1950s is that
+ 
+
+ align:start position:0%
+so or at least before 1960 1950s is that
+this is unidirectional that you
+
+ align:start position:0%
+this is unidirectional that you
+ 
+
+ align:start position:0%
+this is unidirectional that you
+basically the development goes in one
+
+ align:start position:0%
+basically the development goes in one
+ 
+
+ align:start position:0%
+basically the development goes in one
+direction where you go from the
+
+ align:start position:0%
+direction where you go from the
+ 
+
+ align:start position:0%
+direction where you go from the
+fertilized egg to the differentiated
+
+ align:start position:0%
+fertilized egg to the differentiated
+ 
+
+ align:start position:0%
+fertilized egg to the differentiated
+adult cell types and so this state down
+
+ align:start position:0%
+adult cell types and so this state down
+ 
+
+ align:start position:0%
+adult cell types and so this state down
+here the differentiated adult cell types
+
+ align:start position:0%
+here the differentiated adult cell types
+ 
+
+ align:start position:0%
+here the differentiated adult cell types
+are fairly stable right
+
+ align:start position:0%
+are fairly stable right
+ 
+
+ align:start position:0%
+are fairly stable right
+I mean if you look at your neighbor you
+
+ align:start position:0%
+I mean if you look at your neighbor you
+ 
+
+ align:start position:0%
+I mean if you look at your neighbor you
+see they don't have muscle growing on
+
+ align:start position:0%
+see they don't have muscle growing on
+ 
+
+ align:start position:0%
+see they don't have muscle growing on
+the outside of their bodies right their
+
+ align:start position:0%
+the outside of their bodies right their
+ 
+
+ align:start position:0%
+the outside of their bodies right their
+skin cells taste skin cells and that is
+
+ align:start position:0%
+skin cells taste skin cells and that is
+ 
+
+ align:start position:0%
+skin cells taste skin cells and that is
+a relatively stable state okay now last
+
+ align:start position:0%
+a relatively stable state okay now last
+ 
+
+ align:start position:0%
+a relatively stable state okay now last
+week you learned about sort of a
+
+ align:start position:0%
+week you learned about sort of a
+ 
+
+ align:start position:0%
+week you learned about sort of a
+contradiction to the central dogma which
+
+ align:start position:0%
+contradiction to the central dogma which
+ 
+
+ align:start position:0%
+contradiction to the central dogma which
+is the behavior of retroviruses which
+
+ align:start position:0%
+is the behavior of retroviruses which
+ 
+
+ align:start position:0%
+is the behavior of retroviruses which
+which have reverse transcriptase which
+
+ align:start position:0%
+which have reverse transcriptase which
+ 
+
+ align:start position:0%
+which have reverse transcriptase which
+can sort of go backwards up this pathway
+
+ align:start position:0%
+can sort of go backwards up this pathway
+ 
+
+ align:start position:0%
+can sort of go backwards up this pathway
+where you can get DNA from RNA okay and
+
+ align:start position:0%
+where you can get DNA from RNA okay and
+ 
+
+ align:start position:0%
+where you can get DNA from RNA okay and
+today we're going to talk about how you
+
+ align:start position:0%
+today we're going to talk about how you
+ 
+
+ align:start position:0%
+today we're going to talk about how you
+can sort of overcome sort of this
+
+ align:start position:0%
+can sort of overcome sort of this
+ 
+
+ align:start position:0%
+can sort of overcome sort of this
+uni-directional path here and this is
+
+ align:start position:0%
+uni-directional path here and this is
+ 
+
+ align:start position:0%
+uni-directional path here and this is
+going to be what we will call
+
+ align:start position:0%
+going to be what we will call
+ 
+
+ align:start position:0%
+going to be what we will call
+reprogramming but first I want to talk
+
+ align:start position:0%
+reprogramming but first I want to talk
+ 
+
+ align:start position:0%
+reprogramming but first I want to talk
+about this differentiation process
+
+ align:start position:0%
+about this differentiation process
+ 
+
+ align:start position:0%
+about this differentiation process
+because it's important for us to
+
+ align:start position:0%
+because it's important for us to
+ 
+
+ align:start position:0%
+because it's important for us to
+understand this before we get into the
+
+ align:start position:0%
+understand this before we get into the
+ 
+
+ align:start position:0%
+understand this before we get into the
+reprogramming event and so the
+
+ align:start position:0%
+reprogramming event and so the
+ 
+
+ align:start position:0%
+reprogramming event and so the
+fertilized egg is capable of producing
+
+ align:start position:0%
+fertilized egg is capable of producing
+ 
+
+ align:start position:0%
+fertilized egg is capable of producing
+all of these different cell types okay
+
+ align:start position:0%
+all of these different cell types okay
+ 
+
+ align:start position:0%
+all of these different cell types okay
+so the fertilized egg will be known as
+
+ align:start position:0%
+so the fertilized egg will be known as
+ 
+
+ align:start position:0%
+so the fertilized egg will be known as
+totipotent meeting and has the potential
+
+ align:start position:0%
+totipotent meeting and has the potential
+ 
+
+ align:start position:0%
+totipotent meeting and has the potential
+to form all cell types and in over
+
+ align:start position:0%
+to form all cell types and in over
+ 
+
+ align:start position:0%
+to form all cell types and in over
+development this potency goes down such
+
+ align:start position:0%
+development this potency goes down such
+ 
+
+ align:start position:0%
+development this potency goes down such
+that when cells differentiate into their
+
+ align:start position:0%
+that when cells differentiate into their
+ 
+
+ align:start position:0%
+that when cells differentiate into their
+final adult form there's a much more
+
+ align:start position:0%
+final adult form there's a much more
+ 
+
+ align:start position:0%
+final adult form there's a much more
+limited repertoire of cell types that
+
+ align:start position:0%
+limited repertoire of cell types that
+ 
+
+ align:start position:0%
+limited repertoire of cell types that
+the cell can go into and one way of
+
+ align:start position:0%
+the cell can go into and one way of
+ 
+
+ align:start position:0%
+the cell can go into and one way of
+thinking about this is that if you think
+
+ align:start position:0%
+thinking about this is that if you think
+ 
+
+ align:start position:0%
+thinking about this is that if you think
+of this marble run here right the
+
+ align:start position:0%
+of this marble run here right the
+ 
+
+ align:start position:0%
+of this marble run here right the
+totipotent state is right at the top
+
+ align:start position:0%
+totipotent state is right at the top
+ 
+
+ align:start position:0%
+totipotent state is right at the top
+here right if I put a marble on the top
+
+ align:start position:0%
+here right if I put a marble on the top
+ 
+
+ align:start position:0%
+here right if I put a marble on the top
+here it has the potential of going into
+
+ align:start position:0%
+here it has the potential of going into
+ 
+
+ align:start position:0%
+here it has the potential of going into
+any of these three sort of different
+
+ align:start position:0%
+any of these three sort of different
+ 
+
+ align:start position:0%
+any of these three sort of different
+fates okay so this is the toady
+
+ align:start position:0%
+fates okay so this is the toady
+ 
+
+ align:start position:0%
+fates okay so this is the toady
+and state up at the top and you'll see
+
+ align:start position:0%
+and state up at the top and you'll see
+ 
+
+ align:start position:0%
+and state up at the top and you'll see
+these marbles will be able to go into
+
+ align:start position:0%
+these marbles will be able to go into
+ 
+
+ align:start position:0%
+these marbles will be able to go into
+any of these three different states here
+
+ align:start position:0%
+any of these three different states here
+ 
+
+ align:start position:0%
+any of these three different states here
+okay but you see how that marble went
+
+ align:start position:0%
+okay but you see how that marble went
+ 
+
+ align:start position:0%
+okay but you see how that marble went
+down on this path some marbles go down
+
+ align:start position:0%
+down on this path some marbles go down
+ 
+
+ align:start position:0%
+down on this path some marbles go down
+in this path and so you can think of
+
+ align:start position:0%
+in this path and so you can think of
+ 
+
+ align:start position:0%
+in this path and so you can think of
+cells going through development is sort
+
+ align:start position:0%
+cells going through development is sort
+ 
+
+ align:start position:0%
+cells going through development is sort
+of getting funneled into these distinct
+
+ align:start position:0%
+of getting funneled into these distinct
+ 
+
+ align:start position:0%
+of getting funneled into these distinct
+paths in in this case it's kind of
+
+ align:start position:0%
+paths in in this case it's kind of
+ 
+
+ align:start position:0%
+paths in in this case it's kind of
+random but in development it relies on
+
+ align:start position:0%
+random but in development it relies on
+ 
+
+ align:start position:0%
+random but in development it relies on
+signaling between cells and interaction
+
+ align:start position:0%
+signaling between cells and interaction
+ 
+
+ align:start position:0%
+signaling between cells and interaction
+between cells and the multicellular
+
+ align:start position:0%
+between cells and the multicellular
+ 
+
+ align:start position:0%
+between cells and the multicellular
+organism okay okay so as an example I
+
+ align:start position:0%
+organism okay okay so as an example I
+ 
+
+ align:start position:0%
+organism okay okay so as an example I
+want to tell you about early mammalian
+
+ align:start position:0%
+want to tell you about early mammalian
+ 
+
+ align:start position:0%
+want to tell you about early mammalian
+development in the differentiation of
+
+ align:start position:0%
+development in the differentiation of
+ 
+
+ align:start position:0%
+development in the differentiation of
+cell types in the early mammalian embryo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we start with an oocyte it's the
+
+ align:start position:0%
+okay so we start with an oocyte it's the
+ 
+
+ align:start position:0%
+okay so we start with an oocyte it's the
+female gamete and the male gamete the
+
+ align:start position:0%
+female gamete and the male gamete the
+ 
+
+ align:start position:0%
+female gamete and the male gamete the
+sperm so these can come together to form
+
+ align:start position:0%
+sperm so these can come together to form
+ 
+
+ align:start position:0%
+sperm so these can come together to form
+the zygote if I draw a little circle in
+
+ align:start position:0%
+the zygote if I draw a little circle in
+ 
+
+ align:start position:0%
+the zygote if I draw a little circle in
+the middle it's a nucleus okay in this
+
+ align:start position:0%
+the middle it's a nucleus okay in this
+ 
+
+ align:start position:0%
+the middle it's a nucleus okay in this
+is I goat is totipotent and the embryo
+
+ align:start position:0%
+is I goat is totipotent and the embryo
+ 
+
+ align:start position:0%
+is I goat is totipotent and the embryo
+undergoes cleavage divisions which I'll
+
+ align:start position:0%
+undergoes cleavage divisions which I'll
+ 
+
+ align:start position:0%
+undergoes cleavage divisions which I'll
+show here you see how that zygote
+
+ align:start position:0%
+show here you see how that zygote
+ 
+
+ align:start position:0%
+show here you see how that zygote
+divided into two cells now it's going to
+
+ align:start position:0%
+divided into two cells now it's going to
+ 
+
+ align:start position:0%
+divided into two cells now it's going to
+divide into four and it'll keep dividing
+
+ align:start position:0%
+divide into four and it'll keep dividing
+ 
+
+ align:start position:0%
+divide into four and it'll keep dividing
+until it's 16 probably so you get
+
+ align:start position:0%
+until it's 16 probably so you get
+ 
+
+ align:start position:0%
+until it's 16 probably so you get
+cleavage divisions that generate more
+
+ align:start position:0%
+cleavage divisions that generate more
+ 
+
+ align:start position:0%
+cleavage divisions that generate more
+than one cell you start with a single
+
+ align:start position:0%
+than one cell you start with a single
+ 
+
+ align:start position:0%
+than one cell you start with a single
+cell the cleavage divisions give you
+
+ align:start position:0%
+cell the cleavage divisions give you
+ 
+
+ align:start position:0%
+cell the cleavage divisions give you
+more than one cell and what you see up
+
+ align:start position:0%
+more than one cell and what you see up
+ 
+
+ align:start position:0%
+more than one cell and what you see up
+here now is a stage known as the blast
+
+ align:start position:0%
+here now is a stage known as the blast
+ 
+
+ align:start position:0%
+here now is a stage known as the blast
+of blastocyst or the blastula you can
+
+ align:start position:0%
+of blastocyst or the blastula you can
+ 
+
+ align:start position:0%
+of blastocyst or the blastula you can
+see there's a hollow sort of inner
+
+ align:start position:0%
+see there's a hollow sort of inner
+ 
+
+ align:start position:0%
+see there's a hollow sort of inner
+fluid-filled area here and you see their
+
+ align:start position:0%
+fluid-filled area here and you see their
+ 
+
+ align:start position:0%
+fluid-filled area here and you see their
+cells around
+
+ align:start position:0%
+cells around
+ 
+
+ align:start position:0%
+cells around
+that fluid-filled cavity and there's a
+
+ align:start position:0%
+that fluid-filled cavity and there's a
+ 
+
+ align:start position:0%
+that fluid-filled cavity and there's a
+thickening on one side of the embryo
+
+ align:start position:0%
+thickening on one side of the embryo
+ 
+
+ align:start position:0%
+thickening on one side of the embryo
+okay so I'm gonna draw that out here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry mine is a little flat up here
+
+ align:start position:0%
+sorry mine is a little flat up here
+ 
+
+ align:start position:0%
+sorry mine is a little flat up here
+should be perfectly spherical okay and
+
+ align:start position:0%
+should be perfectly spherical okay and
+ 
+
+ align:start position:0%
+should be perfectly spherical okay and
+there there's this thickening on one
+
+ align:start position:0%
+there there's this thickening on one
+ 
+
+ align:start position:0%
+there there's this thickening on one
+side of the blastula which is a bunch of
+
+ align:start position:0%
+side of the blastula which is a bunch of
+ 
+
+ align:start position:0%
+side of the blastula which is a bunch of
+cells that are kind of interior and on
+
+ align:start position:0%
+cells that are kind of interior and on
+ 
+
+ align:start position:0%
+cells that are kind of interior and on
+the inside of the embryo
+
+ align:start position:0%
+the inside of the embryo
+ 
+
+ align:start position:0%
+the inside of the embryo
+okay these cells on the interior are
+
+ align:start position:0%
+okay these cells on the interior are
+ 
+
+ align:start position:0%
+okay these cells on the interior are
+known as the inner cell mass and these
+
+ align:start position:0%
+known as the inner cell mass and these
+ 
+
+ align:start position:0%
+known as the inner cell mass and these
+cells are now restricted in what they
+
+ align:start position:0%
+cells are now restricted in what they
+ 
+
+ align:start position:0%
+cells are now restricted in what they
+can become
+
+ align:start position:0%
+can become
+ 
+
+ align:start position:0%
+can become
+these cells will become the embryo
+
+ align:start position:0%
+these cells will become the embryo
+ 
+
+ align:start position:0%
+these cells will become the embryo
+proper okay so they'll become the cell
+
+ align:start position:0%
+proper okay so they'll become the cell
+ 
+
+ align:start position:0%
+proper okay so they'll become the cell
+types that'll be a part of the fetus
+
+ align:start position:0%
+types that'll be a part of the fetus
+ 
+
+ align:start position:0%
+types that'll be a part of the fetus
+this these cells on the outside are
+
+ align:start position:0%
+this these cells on the outside are
+ 
+
+ align:start position:0%
+this these cells on the outside are
+known as the trophoblast cells and these
+
+ align:start position:0%
+known as the trophoblast cells and these
+ 
+
+ align:start position:0%
+known as the trophoblast cells and these
+are these cells will form part of the
+
+ align:start position:0%
+are these cells will form part of the
+ 
+
+ align:start position:0%
+are these cells will form part of the
+placenta the embryonic portion of the
+
+ align:start position:0%
+placenta the embryonic portion of the
+ 
+
+ align:start position:0%
+placenta the embryonic portion of the
+placenta so they form part of the
+
+ align:start position:0%
+placenta so they form part of the
+ 
+
+ align:start position:0%
+placenta so they form part of the
+placenta and they're important for this
+
+ align:start position:0%
+placenta and they're important for this
+ 
+
+ align:start position:0%
+placenta and they're important for this
+embryo being able to implant into the
+
+ align:start position:0%
+embryo being able to implant into the
+ 
+
+ align:start position:0%
+embryo being able to implant into the
+uterine wall okay so if we think about
+
+ align:start position:0%
+uterine wall okay so if we think about
+ 
+
+ align:start position:0%
+uterine wall okay so if we think about
+this is the first example of
+
+ align:start position:0%
+this is the first example of
+ 
+
+ align:start position:0%
+this is the first example of
+differentiation in the early mammalian
+
+ align:start position:0%
+differentiation in the early mammalian
+ 
+
+ align:start position:0%
+differentiation in the early mammalian
+embryo B as you can see based on what I
+
+ align:start position:0%
+embryo B as you can see based on what I
+ 
+
+ align:start position:0%
+embryo B as you can see based on what I
+said here
+
+ align:start position:0%
+said here
+ 
+
+ align:start position:0%
+said here
+these cells are becoming restricted and
+
+ align:start position:0%
+these cells are becoming restricted and
+ 
+
+ align:start position:0%
+these cells are becoming restricted and
+what they can become okay so this is
+
+ align:start position:0%
+what they can become okay so this is
+ 
+
+ align:start position:0%
+what they can become okay so this is
+kind of like the first branch point in
+
+ align:start position:0%
+kind of like the first branch point in
+ 
+
+ align:start position:0%
+kind of like the first branch point in
+differentiation so we get some more sort
+
+ align:start position:0%
+differentiation so we get some more sort
+ 
+
+ align:start position:0%
+differentiation so we get some more sort
+of marbles going down here alright so
+
+ align:start position:0%
+of marbles going down here alright so
+ 
+
+ align:start position:0%
+of marbles going down here alright so
+this would be the sort of stage right
+
+ align:start position:0%
+this would be the sort of stage right
+ 
+
+ align:start position:0%
+this would be the sort of stage right
+before the blastula before
+
+ align:start position:0%
+before the blastula before
+ 
+
+ align:start position:0%
+before the blastula before
+differentiation and you can see these
+
+ align:start position:0%
+differentiation and you can see these
+ 
+
+ align:start position:0%
+differentiation and you can see these
+marbles when I let them they will have
+
+ align:start position:0%
+marbles when I let them they will have
+ 
+
+ align:start position:0%
+marbles when I let them they will have
+it they will either go this way and
+
+ align:start position:0%
+it they will either go this way and
+ 
+
+ align:start position:0%
+it they will either go this way and
+become one fate or they'll go the other
+
+ align:start position:0%
+become one fate or they'll go the other
+ 
+
+ align:start position:0%
+become one fate or they'll go the other
+way and be sort of direct
+
+ align:start position:0%
+way and be sort of direct
+ 
+
+ align:start position:0%
+way and be sort of direct
+down on another sort of potential fates
+
+ align:start position:0%
+down on another sort of potential fates
+ 
+
+ align:start position:0%
+down on another sort of potential fates
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+there we go so this is the first sort of
+
+ align:start position:0%
+there we go so this is the first sort of
+ 
+
+ align:start position:0%
+there we go so this is the first sort of
+branch point if you will in fake
+
+ align:start position:0%
+branch point if you will in fake
+ 
+
+ align:start position:0%
+branch point if you will in fake
+determination for the mammalian embryo
+
+ align:start position:0%
+determination for the mammalian embryo
+ 
+
+ align:start position:0%
+determination for the mammalian embryo
+and so this branch point here right is
+
+ align:start position:0%
+and so this branch point here right is
+ 
+
+ align:start position:0%
+and so this branch point here right is
+different from this because once the
+
+ align:start position:0%
+different from this because once the
+ 
+
+ align:start position:0%
+different from this because once the
+marble goes one way or the other it's
+
+ align:start position:0%
+marble goes one way or the other it's
+ 
+
+ align:start position:0%
+marble goes one way or the other it's
+restricted in what fate it can become
+
+ align:start position:0%
+restricted in what fate it can become
+ 
+
+ align:start position:0%
+restricted in what fate it can become
+okay so this is the so this these cells
+
+ align:start position:0%
+okay so this is the so this these cells
+ 
+
+ align:start position:0%
+okay so this is the so this these cells
+here are not totipotent because they
+
+ align:start position:0%
+here are not totipotent because they
+ 
+
+ align:start position:0%
+here are not totipotent because they
+can't form the trophoblast they can't
+
+ align:start position:0%
+can't form the trophoblast they can't
+ 
+
+ align:start position:0%
+can't form the trophoblast they can't
+form the part of the placenta needed by
+
+ align:start position:0%
+form the part of the placenta needed by
+ 
+
+ align:start position:0%
+form the part of the placenta needed by
+the embryo but they do form the embryo
+
+ align:start position:0%
+the embryo but they do form the embryo
+ 
+
+ align:start position:0%
+the embryo but they do form the embryo
+proper so they are still capable of many
+
+ align:start position:0%
+proper so they are still capable of many
+ 
+
+ align:start position:0%
+proper so they are still capable of many
+faiths and so these cells are known as
+
+ align:start position:0%
+faiths and so these cells are known as
+ 
+
+ align:start position:0%
+faiths and so these cells are known as
+pluripotent which means capable of many
+
+ align:start position:0%
+pluripotent which means capable of many
+ 
+
+ align:start position:0%
+pluripotent which means capable of many
+things okay and so a type of cell type
+
+ align:start position:0%
+things okay and so a type of cell type
+ 
+
+ align:start position:0%
+things okay and so a type of cell type
+which I'm sure you've heard about is
+
+ align:start position:0%
+which I'm sure you've heard about is
+ 
+
+ align:start position:0%
+which I'm sure you've heard about is
+called embryonic stem cells or ES cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these ES cells are derived from the
+
+ align:start position:0%
+these ES cells are derived from the
+ 
+
+ align:start position:0%
+these ES cells are derived from the
+inner cell mass okay so these would be
+
+ align:start position:0%
+inner cell mass okay so these would be
+ 
+
+ align:start position:0%
+inner cell mass okay so these would be
+if they were taken out of the blastula
+
+ align:start position:0%
+if they were taken out of the blastula
+ 
+
+ align:start position:0%
+if they were taken out of the blastula
+sorry this is called the blastula if
+
+ align:start position:0%
+sorry this is called the blastula if
+ 
+
+ align:start position:0%
+sorry this is called the blastula if
+they're are taken from the blastula
+
+ align:start position:0%
+they're are taken from the blastula
+ 
+
+ align:start position:0%
+they're are taken from the blastula
+and cultured in vitro that these would
+
+ align:start position:0%
+and cultured in vitro that these would
+ 
+
+ align:start position:0%
+and cultured in vitro that these would
+be sort of embryonic stem cells that can
+
+ align:start position:0%
+be sort of embryonic stem cells that can
+ 
+
+ align:start position:0%
+be sort of embryonic stem cells that can
+be propagated okay so and they form the
+
+ align:start position:0%
+be propagated okay so and they form the
+ 
+
+ align:start position:0%
+be propagated okay so and they form the
+embryo proper right so these are
+
+ align:start position:0%
+embryo proper right so these are
+ 
+
+ align:start position:0%
+embryo proper right so these are
+pluripotent stem cells that can
+
+ align:start position:0%
+pluripotent stem cells that can
+ 
+
+ align:start position:0%
+pluripotent stem cells that can
+basically they are still capable of
+
+ align:start position:0%
+basically they are still capable of
+ 
+
+ align:start position:0%
+basically they are still capable of
+forming sort of any of the cell types in
+
+ align:start position:0%
+forming sort of any of the cell types in
+ 
+
+ align:start position:0%
+forming sort of any of the cell types in
+the embryo capable of forming
+
+ align:start position:0%
+the embryo capable of forming
+ 
+
+ align:start position:0%
+the embryo capable of forming
+embryonic cell types
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now let's look at the next slide so
+
+ align:start position:0%
+okay now let's look at the next slide so
+ 
+
+ align:start position:0%
+okay now let's look at the next slide so
+this this branch point right this first
+
+ align:start position:0%
+this this branch point right this first
+ 
+
+ align:start position:0%
+this this branch point right this first
+branch point sort of in development is
+
+ align:start position:0%
+branch point sort of in development is
+ 
+
+ align:start position:0%
+branch point sort of in development is
+associated with changes in gene
+
+ align:start position:0%
+associated with changes in gene
+ 
+
+ align:start position:0%
+associated with changes in gene
+expression okay so there are changes in
+
+ align:start position:0%
+expression okay so there are changes in
+ 
+
+ align:start position:0%
+expression okay so there are changes in
+gene expression and you're seeing one up
+
+ align:start position:0%
+gene expression and you're seeing one up
+ 
+
+ align:start position:0%
+gene expression and you're seeing one up
+on the slide above the slide above is a
+
+ align:start position:0%
+on the slide above the slide above is a
+ 
+
+ align:start position:0%
+on the slide above the slide above is a
+fixed blastula and all of the nuclei and
+
+ align:start position:0%
+fixed blastula and all of the nuclei and
+ 
+
+ align:start position:0%
+fixed blastula and all of the nuclei and
+the blastula are stained with green but
+
+ align:start position:0%
+the blastula are stained with green but
+ 
+
+ align:start position:0%
+the blastula are stained with green but
+there's one gene that's stained in red
+
+ align:start position:0%
+there's one gene that's stained in red
+ 
+
+ align:start position:0%
+there's one gene that's stained in red
+that's called act four and this is a
+
+ align:start position:0%
+that's called act four and this is a
+ 
+
+ align:start position:0%
+that's called act four and this is a
+transcription factor that marks sort of
+
+ align:start position:0%
+transcription factor that marks sort of
+ 
+
+ align:start position:0%
+transcription factor that marks sort of
+pluripotency and you can see how it's
+
+ align:start position:0%
+pluripotency and you can see how it's
+ 
+
+ align:start position:0%
+pluripotency and you can see how it's
+expressed specifically in these cells of
+
+ align:start position:0%
+expressed specifically in these cells of
+ 
+
+ align:start position:0%
+expressed specifically in these cells of
+the inner cell mass which are the what
+
+ align:start position:0%
+the inner cell mass which are the what
+ 
+
+ align:start position:0%
+the inner cell mass which are the what
+the embryonic stem cells are derived
+
+ align:start position:0%
+the embryonic stem cells are derived
+ 
+
+ align:start position:0%
+the embryonic stem cells are derived
+from okay so they're clearly changes in
+
+ align:start position:0%
+from okay so they're clearly changes in
+ 
+
+ align:start position:0%
+from okay so they're clearly changes in
+gene expression and one question you
+
+ align:start position:0%
+gene expression and one question you
+ 
+
+ align:start position:0%
+gene expression and one question you
+might have is whether or not these cells
+
+ align:start position:0%
+might have is whether or not these cells
+ 
+
+ align:start position:0%
+might have is whether or not these cells
+that that are going to form the embryo
+
+ align:start position:0%
+that that are going to form the embryo
+ 
+
+ align:start position:0%
+that that are going to form the embryo
+proper whether they have lost
+
+ align:start position:0%
+proper whether they have lost
+ 
+
+ align:start position:0%
+proper whether they have lost
+information such that they're unable to
+
+ align:start position:0%
+information such that they're unable to
+ 
+
+ align:start position:0%
+information such that they're unable to
+form the part of the placenta okay and
+
+ align:start position:0%
+form the part of the placenta okay and
+ 
+
+ align:start position:0%
+form the part of the placenta okay and
+you can also ask this for an adult cell
+
+ align:start position:0%
+you can also ask this for an adult cell
+ 
+
+ align:start position:0%
+you can also ask this for an adult cell
+right has an adult cell in your body
+
+ align:start position:0%
+right has an adult cell in your body
+ 
+
+ align:start position:0%
+right has an adult cell in your body
+hasn't lost gene content such that it's
+
+ align:start position:0%
+hasn't lost gene content such that it's
+ 
+
+ align:start position:0%
+hasn't lost gene content such that it's
+unable to make an entire organism okay
+
+ align:start position:0%
+unable to make an entire organism okay
+ 
+
+ align:start position:0%
+unable to make an entire organism okay
+I'm gonna tell you the answer I want you
+
+ align:start position:0%
+I'm gonna tell you the answer I want you
+ 
+
+ align:start position:0%
+I'm gonna tell you the answer I want you
+to think about what experiment would
+
+ align:start position:0%
+to think about what experiment would
+ 
+
+ align:start position:0%
+to think about what experiment would
+allow you to sort of determine the
+
+ align:start position:0%
+allow you to sort of determine the
+ 
+
+ align:start position:0%
+allow you to sort of determine the
+answer but I'm gonna tell you the answer
+
+ align:start position:0%
+answer but I'm gonna tell you the answer
+ 
+
+ align:start position:0%
+answer but I'm gonna tell you the answer
+is that there is not a loss of gene
+
+ align:start position:0%
+is that there is not a loss of gene
+ 
+
+ align:start position:0%
+is that there is not a loss of gene
+content but this differentiation process
+
+ align:start position:0%
+content but this differentiation process
+ 
+
+ align:start position:0%
+content but this differentiation process
+is due to changes in gene expression for
+
+ align:start position:0%
+is due to changes in gene expression for
+ 
+
+ align:start position:0%
+is due to changes in gene expression for
+the vast majority of our cell types okay
+
+ align:start position:0%
+the vast majority of our cell types okay
+ 
+
+ align:start position:0%
+the vast majority of our cell types okay
+so let's say you wanted to determine
+
+ align:start position:0%
+so let's say you wanted to determine
+ 
+
+ align:start position:0%
+so let's say you wanted to determine
+whether or not a differentiated cell had
+
+ align:start position:0%
+whether or not a differentiated cell had
+ 
+
+ align:start position:0%
+whether or not a differentiated cell had
+lost some sort of capability to
+
+ align:start position:0%
+lost some sort of capability to
+ 
+
+ align:start position:0%
+lost some sort of capability to
+regenerate an entire organism what might
+
+ align:start position:0%
+regenerate an entire organism what might
+ 
+
+ align:start position:0%
+regenerate an entire organism what might
+be some type of experiment you could do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+to see it alright great so Brett had two
+
+ align:start position:0%
+to see it alright great so Brett had two
+ 
+
+ align:start position:0%
+to see it alright great so Brett had two
+really good points I think the first is
+
+ align:start position:0%
+really good points I think the first is
+ 
+
+ align:start position:0%
+really good points I think the first is
+to try to sort of reproduce conditions
+
+ align:start position:0%
+to try to sort of reproduce conditions
+ 
+
+ align:start position:0%
+to try to sort of reproduce conditions
+of pluripotency or you could even try to
+
+ align:start position:0%
+of pluripotency or you could even try to
+ 
+
+ align:start position:0%
+of pluripotency or you could even try to
+reproduce conditions of totipotency
+
+ align:start position:0%
+reproduce conditions of totipotency
+ 
+
+ align:start position:0%
+reproduce conditions of totipotency
+right in which case you'd want to sort
+
+ align:start position:0%
+right in which case you'd want to sort
+ 
+
+ align:start position:0%
+right in which case you'd want to sort
+of like take the genetic material of the
+
+ align:start position:0%
+of like take the genetic material of the
+ 
+
+ align:start position:0%
+of like take the genetic material of the
+somatic cell and sort of put it back in
+
+ align:start position:0%
+somatic cell and sort of put it back in
+ 
+
+ align:start position:0%
+somatic cell and sort of put it back in
+this situation where its present sort of
+
+ align:start position:0%
+this situation where its present sort of
+ 
+
+ align:start position:0%
+this situation where its present sort of
+in the cytoplasm of a zygote okay and
+
+ align:start position:0%
+in the cytoplasm of a zygote okay and
+ 
+
+ align:start position:0%
+in the cytoplasm of a zygote okay and
+the other point that Brett's made is to
+
+ align:start position:0%
+the other point that Brett's made is to
+ 
+
+ align:start position:0%
+the other point that Brett's made is to
+try to maybe like express something that
+
+ align:start position:0%
+try to maybe like express something that
+ 
+
+ align:start position:0%
+try to maybe like express something that
+would induce this type of pluripotent
+
+ align:start position:0%
+would induce this type of pluripotent
+ 
+
+ align:start position:0%
+would induce this type of pluripotent
+state if we knew exactly what the genes
+
+ align:start position:0%
+state if we knew exactly what the genes
+ 
+
+ align:start position:0%
+state if we knew exactly what the genes
+were that sort of like create this
+
+ align:start position:0%
+were that sort of like create this
+ 
+
+ align:start position:0%
+were that sort of like create this
+pluripotent state maybe we could just
+
+ align:start position:0%
+pluripotent state maybe we could just
+ 
+
+ align:start position:0%
+pluripotent state maybe we could just
+Express those genes and regenerate sort
+
+ align:start position:0%
+Express those genes and regenerate sort
+ 
+
+ align:start position:0%
+Express those genes and regenerate sort
+of a cell that sort of moves from like
+
+ align:start position:0%
+of a cell that sort of moves from like
+ 
+
+ align:start position:0%
+of a cell that sort of moves from like
+way down here all the way up to the top
+
+ align:start position:0%
+way down here all the way up to the top
+ 
+
+ align:start position:0%
+way down here all the way up to the top
+again okay and actually what Brett
+
+ align:start position:0%
+again okay and actually what Brett
+ 
+
+ align:start position:0%
+again okay and actually what Brett
+suggested were the two experiments that
+
+ align:start position:0%
+suggested were the two experiments that
+ 
+
+ align:start position:0%
+suggested were the two experiments that
+won these two folks the Nobel Prize in
+
+ align:start position:0%
+won these two folks the Nobel Prize in
+ 
+
+ align:start position:0%
+won these two folks the Nobel Prize in
+2012 so in 2012 the Nobel Prize was
+
+ align:start position:0%
+2012 so in 2012 the Nobel Prize was
+ 
+
+ align:start position:0%
+2012 so in 2012 the Nobel Prize was
+awarded jointly to Sir John Gurdon right
+
+ align:start position:0%
+awarded jointly to Sir John Gurdon right
+ 
+
+ align:start position:0%
+awarded jointly to Sir John Gurdon right
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+who incidentally has the best hair of
+
+ align:start position:0%
+who incidentally has the best hair of
+ 
+
+ align:start position:0%
+who incidentally has the best hair of
+all Nobel laureates and also Shinya
+
+ align:start position:0%
+all Nobel laureates and also Shinya
+ 
+
+ align:start position:0%
+all Nobel laureates and also Shinya
+Yamanaka okay and so these two folks
+
+ align:start position:0%
+Yamanaka okay and so these two folks
+ 
+
+ align:start position:0%
+Yamanaka okay and so these two folks
+were awarded the Nobel Prize for being
+
+ align:start position:0%
+were awarded the Nobel Prize for being
+ 
+
+ align:start position:0%
+were awarded the Nobel Prize for being
+able to show that mature differentiated
+
+ align:start position:0%
+able to show that mature differentiated
+ 
+
+ align:start position:0%
+able to show that mature differentiated
+cells can be reprogrammed to be to
+
+ align:start position:0%
+cells can be reprogrammed to be to
+ 
+
+ align:start position:0%
+cells can be reprogrammed to be to
+become pluripotent again okay which
+
+ align:start position:0%
+become pluripotent again okay which
+ 
+
+ align:start position:0%
+become pluripotent again okay which
+basically gives us the conclusion that
+
+ align:start position:0%
+basically gives us the conclusion that
+ 
+
+ align:start position:0%
+basically gives us the conclusion that
+there's not a loss of gene content
+
+ align:start position:0%
+there's not a loss of gene content
+ 
+
+ align:start position:0%
+there's not a loss of gene content
+during the differentiation process and
+
+ align:start position:0%
+during the differentiation process and
+ 
+
+ align:start position:0%
+during the differentiation process and
+the work from Yamanaka showed us
+
+ align:start position:0%
+the work from Yamanaka showed us
+ 
+
+ align:start position:0%
+the work from Yamanaka showed us
+of all genes whose expression is
+
+ align:start position:0%
+of all genes whose expression is
+ 
+
+ align:start position:0%
+of all genes whose expression is
+critical to induce this type of
+
+ align:start position:0%
+critical to induce this type of
+ 
+
+ align:start position:0%
+critical to induce this type of
+reprogramming okay and their work
+
+ align:start position:0%
+reprogramming okay and their work
+ 
+
+ align:start position:0%
+reprogramming okay and their work
+spanned from frogs so John Gurdon worked
+
+ align:start position:0%
+spanned from frogs so John Gurdon worked
+ 
+
+ align:start position:0%
+spanned from frogs so John Gurdon worked
+on development of frogs specifically
+
+ align:start position:0%
+on development of frogs specifically
+ 
+
+ align:start position:0%
+on development of frogs specifically
+xenakis Lavis which you've seen before
+
+ align:start position:0%
+xenakis Lavis which you've seen before
+ 
+
+ align:start position:0%
+xenakis Lavis which you've seen before
+Shinya Yamanaka is work involved mice
+
+ align:start position:0%
+Shinya Yamanaka is work involved mice
+ 
+
+ align:start position:0%
+Shinya Yamanaka is work involved mice
+and also human cell lines okay so I'm
+
+ align:start position:0%
+and also human cell lines okay so I'm
+ 
+
+ align:start position:0%
+and also human cell lines okay so I'm
+going to tell you about their
+
+ align:start position:0%
+going to tell you about their
+ 
+
+ align:start position:0%
+going to tell you about their
+experiments and how this sort of
+
+ align:start position:0%
+experiments and how this sort of
+ 
+
+ align:start position:0%
+experiments and how this sort of
+demonstrated this conclusion here and
+
+ align:start position:0%
+demonstrated this conclusion here and
+ 
+
+ align:start position:0%
+demonstrated this conclusion here and
+the first thing I want to show you is an
+
+ align:start position:0%
+the first thing I want to show you is an
+ 
+
+ align:start position:0%
+the first thing I want to show you is an
+experiment which is very simple
+
+ align:start position:0%
+experiment which is very simple
+ 
+
+ align:start position:0%
+experiment which is very simple
+conceptually technically it's very
+
+ align:start position:0%
+conceptually technically it's very
+ 
+
+ align:start position:0%
+conceptually technically it's very
+complicated which is if you are able to
+
+ align:start position:0%
+complicated which is if you are able to
+ 
+
+ align:start position:0%
+complicated which is if you are able to
+take a nucleus from an adult cell that's
+
+ align:start position:0%
+take a nucleus from an adult cell that's
+ 
+
+ align:start position:0%
+take a nucleus from an adult cell that's
+differentiated could you get it to
+
+ align:start position:0%
+differentiated could you get it to
+ 
+
+ align:start position:0%
+differentiated could you get it to
+change by introducing it back into the
+
+ align:start position:0%
+change by introducing it back into the
+ 
+
+ align:start position:0%
+change by introducing it back into the
+egg cell or a zygote cell okay so this
+
+ align:start position:0%
+egg cell or a zygote cell okay so this
+ 
+
+ align:start position:0%
+egg cell or a zygote cell okay so this
+experiment involves having an oocyte but
+
+ align:start position:0%
+experiment involves having an oocyte but
+ 
+
+ align:start position:0%
+experiment involves having an oocyte but
+in this case an oocyte where the nucleus
+
+ align:start position:0%
+in this case an oocyte where the nucleus
+ 
+
+ align:start position:0%
+in this case an oocyte where the nucleus
+has been removed okay so you're taking
+
+ align:start position:0%
+has been removed okay so you're taking
+ 
+
+ align:start position:0%
+has been removed okay so you're taking
+enucleated
+
+ align:start position:0%
+enucleated
+ 
+
+ align:start position:0%
+enucleated
+a site and you want to know if the
+
+ align:start position:0%
+a site and you want to know if the
+ 
+
+ align:start position:0%
+a site and you want to know if the
+cytoplasm of this Oh site is somehow
+
+ align:start position:0%
+cytoplasm of this Oh site is somehow
+ 
+
+ align:start position:0%
+cytoplasm of this Oh site is somehow
+special that would allow it to reprogram
+
+ align:start position:0%
+special that would allow it to reprogram
+ 
+
+ align:start position:0%
+special that would allow it to reprogram
+the nucleus of a differentiated cell and
+
+ align:start position:0%
+the nucleus of a differentiated cell and
+ 
+
+ align:start position:0%
+the nucleus of a differentiated cell and
+so you could suck up the nucleus of a
+
+ align:start position:0%
+so you could suck up the nucleus of a
+ 
+
+ align:start position:0%
+so you could suck up the nucleus of a
+differentiated cell so somatic cells
+
+ align:start position:0%
+differentiated cell so somatic cells
+ 
+
+ align:start position:0%
+differentiated cell so somatic cells
+another way to say differentiated the
+
+ align:start position:0%
+another way to say differentiated the
+ 
+
+ align:start position:0%
+another way to say differentiated the
+somatic cell nucleus and the experiment
+
+ align:start position:0%
+somatic cell nucleus and the experiment
+ 
+
+ align:start position:0%
+somatic cell nucleus and the experiment
+conceptually then is to just take this
+
+ align:start position:0%
+conceptually then is to just take this
+ 
+
+ align:start position:0%
+conceptually then is to just take this
+somatic cell nucleus that you've sucked
+
+ align:start position:0%
+somatic cell nucleus that you've sucked
+ 
+
+ align:start position:0%
+somatic cell nucleus that you've sucked
+up and inject it into an oocyte without
+
+ align:start position:0%
+up and inject it into an oocyte without
+ 
+
+ align:start position:0%
+up and inject it into an oocyte without
+a nucleus and see if the cytoplasm of
+
+ align:start position:0%
+a nucleus and see if the cytoplasm of
+ 
+
+ align:start position:0%
+a nucleus and see if the cytoplasm of
+this Oh site is somehow able to sort of
+
+ align:start position:0%
+this Oh site is somehow able to sort of
+ 
+
+ align:start position:0%
+this Oh site is somehow able to sort of
+change the properties of the nucleus
+
+ align:start position:0%
+change the properties of the nucleus
+ 
+
+ align:start position:0%
+change the properties of the nucleus
+such that it now is in an
+
+ align:start position:0%
+such that it now is in an
+ 
+
+ align:start position:0%
+such that it now is in an
+undifferentiated state so you generate a
+
+ align:start position:0%
+undifferentiated state so you generate a
+ 
+
+ align:start position:0%
+undifferentiated state so you generate a
+site now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the somatic cell nucleus and the
+
+ align:start position:0%
+with the somatic cell nucleus and the
+ 
+
+ align:start position:0%
+with the somatic cell nucleus and the
+question is whether this somatic cell
+
+ align:start position:0%
+question is whether this somatic cell
+ 
+
+ align:start position:0%
+question is whether this somatic cell
+nucleus is capable of generating the
+
+ align:start position:0%
+nucleus is capable of generating the
+ 
+
+ align:start position:0%
+nucleus is capable of generating the
+diversity of cell types that are
+
+ align:start position:0%
+diversity of cell types that are
+ 
+
+ align:start position:0%
+diversity of cell types that are
+normally present in an organism so you
+
+ align:start position:0%
+normally present in an organism so you
+ 
+
+ align:start position:0%
+normally present in an organism so you
+could then let this go and develop you
+
+ align:start position:0%
+could then let this go and develop you
+ 
+
+ align:start position:0%
+could then let this go and develop you
+can let it develop into a blast do
+
+ align:start position:0%
+can let it develop into a blast do
+ 
+
+ align:start position:0%
+can let it develop into a blast do
+blastula which I'm drawing here so you
+
+ align:start position:0%
+blastula which I'm drawing here so you
+ 
+
+ align:start position:0%
+blastula which I'm drawing here so you
+could generate a blastula and this will
+
+ align:start position:0%
+could generate a blastula and this will
+ 
+
+ align:start position:0%
+could generate a blastula and this will
+be a way to get embryonic stem cells
+
+ align:start position:0%
+be a way to get embryonic stem cells
+ 
+
+ align:start position:0%
+be a way to get embryonic stem cells
+derived from sort of this type of
+
+ align:start position:0%
+derived from sort of this type of
+ 
+
+ align:start position:0%
+derived from sort of this type of
+nucleus but you can also let it grow
+
+ align:start position:0%
+nucleus but you can also let it grow
+ 
+
+ align:start position:0%
+nucleus but you can also let it grow
+into an entire organism but this
+
+ align:start position:0%
+into an entire organism but this
+ 
+
+ align:start position:0%
+into an entire organism but this
+organism would be genetically identical
+
+ align:start position:0%
+organism would be genetically identical
+ 
+
+ align:start position:0%
+organism would be genetically identical
+to whatever organism donated this
+
+ align:start position:0%
+to whatever organism donated this
+ 
+
+ align:start position:0%
+to whatever organism donated this
+nucleus okay so because you're
+
+ align:start position:0%
+nucleus okay so because you're
+ 
+
+ align:start position:0%
+nucleus okay so because you're
+duplicating an organism that is known as
+
+ align:start position:0%
+duplicating an organism that is known as
+ 
+
+ align:start position:0%
+duplicating an organism that is known as
+reproductive cloning
+
+ align:start position:0%
+reproductive cloning
+ 
+
+ align:start position:0%
+reproductive cloning
+this is reproductive cloning if you go
+
+ align:start position:0%
+this is reproductive cloning if you go
+ 
+
+ align:start position:0%
+this is reproductive cloning if you go
+all the way to the organism I'll show
+
+ align:start position:0%
+all the way to the organism I'll show
+ 
+
+ align:start position:0%
+all the way to the organism I'll show
+you just a little video on the nuclear
+
+ align:start position:0%
+you just a little video on the nuclear
+ 
+
+ align:start position:0%
+you just a little video on the nuclear
+transfer you see now that this drilling
+
+ align:start position:0%
+transfer you see now that this drilling
+ 
+
+ align:start position:0%
+transfer you see now that this drilling
+pipette is going to suck it drill a
+
+ align:start position:0%
+pipette is going to suck it drill a
+ 
+
+ align:start position:0%
+pipette is going to suck it drill a
+little hole into the membrane you can
+
+ align:start position:0%
+little hole into the membrane you can
+ 
+
+ align:start position:0%
+little hole into the membrane you can
+maybe see a little bit of the hole right
+
+ align:start position:0%
+maybe see a little bit of the hole right
+ 
+
+ align:start position:0%
+maybe see a little bit of the hole right
+here at the next part it's talking about
+
+ align:start position:0%
+here at the next part it's talking about
+ 
+
+ align:start position:0%
+here at the next part it's talking about
+this pipette here you can see a bit of
+
+ align:start position:0%
+this pipette here you can see a bit of
+ 
+
+ align:start position:0%
+this pipette here you can see a bit of
+the hole and now the pipette is gonna go
+
+ align:start position:0%
+the hole and now the pipette is gonna go
+ 
+
+ align:start position:0%
+the hole and now the pipette is gonna go
+in and remove the nucleus and if you
+
+ align:start position:0%
+in and remove the nucleus and if you
+ 
+
+ align:start position:0%
+in and remove the nucleus and if you
+look carefully in the pipette you'll see
+
+ align:start position:0%
+look carefully in the pipette you'll see
+ 
+
+ align:start position:0%
+look carefully in the pipette you'll see
+a line in the nucleus which are all the
+
+ align:start position:0%
+a line in the nucleus which are all the
+ 
+
+ align:start position:0%
+a line in the nucleus which are all the
+chromosomes lined up so their nucleus is
+
+ align:start position:0%
+chromosomes lined up so their nucleus is
+ 
+
+ align:start position:0%
+chromosomes lined up so their nucleus is
+going to be squirted out now because we
+
+ align:start position:0%
+going to be squirted out now because we
+ 
+
+ align:start position:0%
+going to be squirted out now because we
+don't need it anymore
+
+ align:start position:0%
+don't need it anymore
+ 
+
+ align:start position:0%
+don't need it anymore
+and there we have an enucleated egg now
+
+ align:start position:0%
+and there we have an enucleated egg now
+ 
+
+ align:start position:0%
+and there we have an enucleated egg now
+the next step is to take a set of eggs
+
+ align:start position:0%
+the next step is to take a set of eggs
+ 
+
+ align:start position:0%
+the next step is to take a set of eggs
+like that and I'll show you - and then
+
+ align:start position:0%
+like that and I'll show you - and then
+ 
+
+ align:start position:0%
+like that and I'll show you - and then
+transfer into them and nucleus from
+
+ align:start position:0%
+transfer into them and nucleus from
+ 
+
+ align:start position:0%
+transfer into them and nucleus from
+another kind of cell a fully
+
+ align:start position:0%
+another kind of cell a fully
+ 
+
+ align:start position:0%
+another kind of cell a fully
+differentiated cymatics
+
+ align:start position:0%
+differentiated cymatics
+ 
+
+ align:start position:0%
+differentiated cymatics
+so here the enucleated egg is set on the
+
+ align:start position:0%
+so here the enucleated egg is set on the
+ 
+
+ align:start position:0%
+so here the enucleated egg is set on the
+side then it's held by this holding
+
+ align:start position:0%
+side then it's held by this holding
+ 
+
+ align:start position:0%
+side then it's held by this holding
+pipette on the Left there's drilling the
+
+ align:start position:0%
+pipette on the Left there's drilling the
+ 
+
+ align:start position:0%
+pipette on the Left there's drilling the
+little hole in the membrane here we go
+
+ align:start position:0%
+little hole in the membrane here we go
+ 
+
+ align:start position:0%
+little hole in the membrane here we go
+in here comes the nucleus from the rice
+
+ align:start position:0%
+in here comes the nucleus from the rice
+ 
+
+ align:start position:0%
+in here comes the nucleus from the rice
+these pipettes are operated with a piezo
+
+ align:start position:0%
+these pipettes are operated with a piezo
+ 
+
+ align:start position:0%
+these pipettes are operated with a piezo
+electric device so you can't see it here
+
+ align:start position:0%
+electric device so you can't see it here
+ 
+
+ align:start position:0%
+electric device so you can't see it here
+but it's like a little jackhammer going
+
+ align:start position:0%
+but it's like a little jackhammer going
+ 
+
+ align:start position:0%
+but it's like a little jackhammer going
+very quickly like woody the woodpecker
+
+ align:start position:0%
+very quickly like woody the woodpecker
+ 
+
+ align:start position:0%
+very quickly like woody the woodpecker
+getting in there - I don't know if I
+
+ align:start position:0%
+getting in there - I don't know if I
+ 
+
+ align:start position:0%
+getting in there - I don't know if I
+would have used woody the woodpecker as
+
+ align:start position:0%
+would have used woody the woodpecker as
+ 
+
+ align:start position:0%
+would have used woody the woodpecker as
+an analogy but that's basically the idea
+
+ align:start position:0%
+an analogy but that's basically the idea
+ 
+
+ align:start position:0%
+an analogy but that's basically the idea
+okay so you can take a nucleus from a
+
+ align:start position:0%
+okay so you can take a nucleus from a
+ 
+
+ align:start position:0%
+okay so you can take a nucleus from a
+somatic cell and Transplant it if you
+
+ align:start position:0%
+somatic cell and Transplant it if you
+ 
+
+ align:start position:0%
+somatic cell and Transplant it if you
+will into an oocyte and then determine
+
+ align:start position:0%
+will into an oocyte and then determine
+ 
+
+ align:start position:0%
+will into an oocyte and then determine
+whether you can get either a blastula or
+
+ align:start position:0%
+whether you can get either a blastula or
+ 
+
+ align:start position:0%
+whether you can get either a blastula or
+an entire organism from that
+
+ align:start position:0%
+an entire organism from that
+ 
+
+ align:start position:0%
+an entire organism from that
+differentiated cells nucleus so this is
+
+ align:start position:0%
+differentiated cells nucleus so this is
+ 
+
+ align:start position:0%
+differentiated cells nucleus so this is
+one result from Sir John Gurdon and what
+
+ align:start position:0%
+one result from Sir John Gurdon and what
+ 
+
+ align:start position:0%
+one result from Sir John Gurdon and what
+the experiment was in this case was to
+
+ align:start position:0%
+the experiment was in this case was to
+ 
+
+ align:start position:0%
+the experiment was in this case was to
+take a sites or eggs from this wild-type
+
+ align:start position:0%
+take a sites or eggs from this wild-type
+ 
+
+ align:start position:0%
+take a sites or eggs from this wild-type
+lavis frog and a transplant nuclei from
+
+ align:start position:0%
+lavis frog and a transplant nuclei from
+ 
+
+ align:start position:0%
+lavis frog and a transplant nuclei from
+donor frogs that are ID by albino so you
+
+ align:start position:0%
+donor frogs that are ID by albino so you
+ 
+
+ align:start position:0%
+donor frogs that are ID by albino so you
+can see this is an elegant experiment in
+
+ align:start position:0%
+can see this is an elegant experiment in
+ 
+
+ align:start position:0%
+can see this is an elegant experiment in
+that you can sort of track the origin of
+
+ align:start position:0%
+that you can sort of track the origin of
+ 
+
+ align:start position:0%
+that you can sort of track the origin of
+the nucleus because it's genetically
+
+ align:start position:0%
+the nucleus because it's genetically
+ 
+
+ align:start position:0%
+the nucleus because it's genetically
+marked with this albino sort of
+
+ align:start position:0%
+marked with this albino sort of
+ 
+
+ align:start position:0%
+marked with this albino sort of
+phenotype so that you're getting a
+
+ align:start position:0%
+phenotype so that you're getting a
+ 
+
+ align:start position:0%
+phenotype so that you're getting a
+nuclei from you're getting some nuclei
+
+ align:start position:0%
+nuclei from you're getting some nuclei
+ 
+
+ align:start position:0%
+nuclei from you're getting some nuclei
+from albino tadpoles so these are
+
+ align:start position:0%
+from albino tadpoles so these are
+ 
+
+ align:start position:0%
+from albino tadpoles so these are
+differentiated cell nuclei and they're
+
+ align:start position:0%
+differentiated cell nuclei and they're
+ 
+
+ align:start position:0%
+differentiated cell nuclei and they're
+transplanted into wild-type donor eggs
+
+ align:start position:0%
+transplanted into wild-type donor eggs
+ 
+
+ align:start position:0%
+transplanted into wild-type donor eggs
+right so normally the wild-type frog
+
+ align:start position:0%
+right so normally the wild-type frog
+ 
+
+ align:start position:0%
+right so normally the wild-type frog
+would reproduce frogs that look like it
+
+ align:start position:0%
+would reproduce frogs that look like it
+ 
+
+ align:start position:0%
+would reproduce frogs that look like it
+that are non albino but in this
+
+ align:start position:0%
+that are non albino but in this
+ 
+
+ align:start position:0%
+that are non albino but in this
+experiment our Gurdon and his lab were
+
+ align:start position:0%
+experiment our Gurdon and his lab were
+ 
+
+ align:start position:0%
+experiment our Gurdon and his lab were
+able to get frogs that were albino okay
+
+ align:start position:0%
+able to get frogs that were albino okay
+ 
+
+ align:start position:0%
+able to get frogs that were albino okay
+so these would be sort of clones of
+
+ align:start position:0%
+so these would be sort of clones of
+ 
+
+ align:start position:0%
+so these would be sort of clones of
+whatever albino tadpoles they got the
+
+ align:start position:0%
+whatever albino tadpoles they got the
+ 
+
+ align:start position:0%
+whatever albino tadpoles they got the
+nuclei from okay so you see in this case
+
+ align:start position:0%
+nuclei from okay so you see in this case
+ 
+
+ align:start position:0%
+nuclei from okay so you see in this case
+it's the origin
+
+ align:start position:0%
+it's the origin
+ 
+
+ align:start position:0%
+it's the origin
+the nucleus that is determining sort of
+
+ align:start position:0%
+the nucleus that is determining sort of
+ 
+
+ align:start position:0%
+the nucleus that is determining sort of
+the the phenotype of these frogs so that
+
+ align:start position:0%
+the the phenotype of these frogs so that
+ 
+
+ align:start position:0%
+the the phenotype of these frogs so that
+allowed them to show that the nucleus is
+
+ align:start position:0%
+allowed them to show that the nucleus is
+ 
+
+ align:start position:0%
+allowed them to show that the nucleus is
+getting reprogrammed from this albino
+
+ align:start position:0%
+getting reprogrammed from this albino
+ 
+
+ align:start position:0%
+getting reprogrammed from this albino
+tadpole and is able to still generate
+
+ align:start position:0%
+tadpole and is able to still generate
+ 
+
+ align:start position:0%
+tadpole and is able to still generate
+all of the cell types present in a
+
+ align:start position:0%
+all of the cell types present in a
+ 
+
+ align:start position:0%
+all of the cell types present in a
+normal organism yes Brett yes yeah yeah
+
+ align:start position:0%
+normal organism yes Brett yes yeah yeah
+ 
+
+ align:start position:0%
+normal organism yes Brett yes yeah yeah
+so yeah and actually it was taking
+
+ align:start position:0%
+so yeah and actually it was taking
+ 
+
+ align:start position:0%
+so yeah and actually it was taking
+unfertilized eggs which is the biggest
+
+ align:start position:0%
+unfertilized eggs which is the biggest
+ 
+
+ align:start position:0%
+unfertilized eggs which is the biggest
+trick i think people had tried to do
+
+ align:start position:0%
+trick i think people had tried to do
+ 
+
+ align:start position:0%
+trick i think people had tried to do
+this in frogs before and it failed
+
+ align:start position:0%
+this in frogs before and it failed
+ 
+
+ align:start position:0%
+this in frogs before and it failed
+because they were using fertilized eggs
+
+ align:start position:0%
+because they were using fertilized eggs
+ 
+
+ align:start position:0%
+because they were using fertilized eggs
+and there's something about sort of the
+
+ align:start position:0%
+and there's something about sort of the
+ 
+
+ align:start position:0%
+and there's something about sort of the
+the state the oocyte development that
+
+ align:start position:0%
+the state the oocyte development that
+ 
+
+ align:start position:0%
+the state the oocyte development that
+makes it better at reprogramming the
+
+ align:start position:0%
+makes it better at reprogramming the
+ 
+
+ align:start position:0%
+makes it better at reprogramming the
+nucleus okay so that's with frogs so
+
+ align:start position:0%
+nucleus okay so that's with frogs so
+ 
+
+ align:start position:0%
+nucleus okay so that's with frogs so
+that that experiment was actually done
+
+ align:start position:0%
+that that experiment was actually done
+ 
+
+ align:start position:0%
+that that experiment was actually done
+in the late nineteen fifties published
+
+ align:start position:0%
+in the late nineteen fifties published
+ 
+
+ align:start position:0%
+in the late nineteen fifties published
+in the early 1960s and so it took
+
+ align:start position:0%
+in the early 1960s and so it took
+ 
+
+ align:start position:0%
+in the early 1960s and so it took
+another forty years or so for the first
+
+ align:start position:0%
+another forty years or so for the first
+ 
+
+ align:start position:0%
+another forty years or so for the first
+mammal to be cloned and you guys
+
+ align:start position:0%
+mammal to be cloned and you guys
+ 
+
+ align:start position:0%
+mammal to be cloned and you guys
+probably weren't even born yet but for
+
+ align:start position:0%
+probably weren't even born yet but for
+ 
+
+ align:start position:0%
+probably weren't even born yet but for
+those of us who are older we remember
+
+ align:start position:0%
+those of us who are older we remember
+ 
+
+ align:start position:0%
+those of us who are older we remember
+this because there was a big brouhaha
+
+ align:start position:0%
+this because there was a big brouhaha
+ 
+
+ align:start position:0%
+this because there was a big brouhaha
+over Dolly the sheep which was the first
+
+ align:start position:0%
+over Dolly the sheep which was the first
+ 
+
+ align:start position:0%
+over Dolly the sheep which was the first
+cloned mammal
+
+ align:start position:0%
+cloned mammal
+ 
+
+ align:start position:0%
+cloned mammal
+I believe that's Dolly there so this is
+
+ align:start position:0%
+I believe that's Dolly there so this is
+ 
+
+ align:start position:0%
+I believe that's Dolly there so this is
+I'm not sure which one is Dolly that
+
+ align:start position:0%
+I'm not sure which one is Dolly that
+ 
+
+ align:start position:0%
+I'm not sure which one is Dolly that
+they're both the same type of sheep so
+
+ align:start position:0%
+they're both the same type of sheep so
+ 
+
+ align:start position:0%
+they're both the same type of sheep so
+this was done by ian wilmut and his
+
+ align:start position:0%
+this was done by ian wilmut and his
+ 
+
+ align:start position:0%
+this was done by ian wilmut and his
+group one thing i want to point out
+
+ align:start position:0%
+group one thing i want to point out
+ 
+
+ align:start position:0%
+group one thing i want to point out
+about this is it's incredibly
+
+ align:start position:0%
+about this is it's incredibly
+ 
+
+ align:start position:0%
+about this is it's incredibly
+inefficient okay if you look over here
+
+ align:start position:0%
+inefficient okay if you look over here
+ 
+
+ align:start position:0%
+inefficient okay if you look over here
+right this dolly resulted from for over
+
+ align:start position:0%
+right this dolly resulted from for over
+ 
+
+ align:start position:0%
+right this dolly resulted from for over
+400 sites having this sort of nuclear
+
+ align:start position:0%
+400 sites having this sort of nuclear
+ 
+
+ align:start position:0%
+400 sites having this sort of nuclear
+transplant take place okay so it's not a
+
+ align:start position:0%
+transplant take place okay so it's not a
+ 
+
+ align:start position:0%
+transplant take place okay so it's not a
+very efficient process and so that lack
+
+ align:start position:0%
+very efficient process and so that lack
+ 
+
+ align:start position:0%
+very efficient process and so that lack
+of efficiency is due to the fact that
+
+ align:start position:0%
+of efficiency is due to the fact that
+ 
+
+ align:start position:0%
+of efficiency is due to the fact that
+the nucleus is resisting getting
+
+ align:start position:0%
+the nucleus is resisting getting
+ 
+
+ align:start position:0%
+the nucleus is resisting getting
+reprogrammed okay
+
+ align:start position:0%
+reprogrammed okay
+ 
+
+ align:start position:0%
+reprogrammed okay
+this is a graph from one of John Gurdon
+
+ align:start position:0%
+this is a graph from one of John Gurdon
+ 
+
+ align:start position:0%
+this is a graph from one of John Gurdon
+z' sort of he wrote a review article on
+
+ align:start position:0%
+z' sort of he wrote a review article on
+ 
+
+ align:start position:0%
+z' sort of he wrote a review article on
+sort of reprogramming after he won the
+
+ align:start position:0%
+sort of reprogramming after he won the
+ 
+
+ align:start position:0%
+sort of reprogramming after he won the
+Nobel Prize this is from that and what's
+
+ align:start position:0%
+Nobel Prize this is from that and what's
+ 
+
+ align:start position:0%
+Nobel Prize this is from that and what's
+plotted is sort of the the frequency in
+
+ align:start position:0%
+plotted is sort of the the frequency in
+ 
+
+ align:start position:0%
+plotted is sort of the the frequency in
+which transfers results in sort of a
+
+ align:start position:0%
+which transfers results in sort of a
+ 
+
+ align:start position:0%
+which transfers results in sort of a
+differentiated organism and what's on
+
+ align:start position:0%
+differentiated organism and what's on
+ 
+
+ align:start position:0%
+differentiated organism and what's on
+the x-axis is the stage of the cell
+
+ align:start position:0%
+the x-axis is the stage of the cell
+ 
+
+ align:start position:0%
+the x-axis is the stage of the cell
+that's used to transplant okay and so
+
+ align:start position:0%
+that's used to transplant okay and so
+ 
+
+ align:start position:0%
+that's used to transplant okay and so
+what you see is that over the course of
+
+ align:start position:0%
+what you see is that over the course of
+ 
+
+ align:start position:0%
+what you see is that over the course of
+differentiation it gets harder and
+
+ align:start position:0%
+differentiation it gets harder and
+ 
+
+ align:start position:0%
+differentiation it gets harder and
+harder for the nucleus to get
+
+ align:start position:0%
+harder for the nucleus to get
+ 
+
+ align:start position:0%
+harder for the nucleus to get
+reprogrammed to create a sort of all the
+
+ align:start position:0%
+reprogrammed to create a sort of all the
+ 
+
+ align:start position:0%
+reprogrammed to create a sort of all the
+cell types that are normally present in
+
+ align:start position:0%
+cell types that are normally present in
+ 
+
+ align:start position:0%
+cell types that are normally present in
+an adult animal
+
+ align:start position:0%
+an adult animal
+ 
+
+ align:start position:0%
+an adult animal
+okay so nuclei do become more restricted
+
+ align:start position:0%
+okay so nuclei do become more restricted
+ 
+
+ align:start position:0%
+okay so nuclei do become more restricted
+in their ability to be reprogrammed over
+
+ align:start position:0%
+in their ability to be reprogrammed over
+ 
+
+ align:start position:0%
+in their ability to be reprogrammed over
+development but the fact that any of
+
+ align:start position:0%
+development but the fact that any of
+ 
+
+ align:start position:0%
+development but the fact that any of
+them are able to be reprogrammed
+
+ align:start position:0%
+them are able to be reprogrammed
+ 
+
+ align:start position:0%
+them are able to be reprogrammed
+suggests that when they're we that
+
+ align:start position:0%
+suggests that when they're we that
+ 
+
+ align:start position:0%
+suggests that when they're we that
+during differentiation there's not a
+
+ align:start position:0%
+during differentiation there's not a
+ 
+
+ align:start position:0%
+during differentiation there's not a
+loss of gene content okay and John
+
+ align:start position:0%
+loss of gene content okay and John
+ 
+
+ align:start position:0%
+loss of gene content okay and John
+Gurdon has done a lot to characterize
+
+ align:start position:0%
+Gurdon has done a lot to characterize
+ 
+
+ align:start position:0%
+Gurdon has done a lot to characterize
+sort of the changes in the nucleus that
+
+ align:start position:0%
+sort of the changes in the nucleus that
+ 
+
+ align:start position:0%
+sort of the changes in the nucleus that
+happened during differentiation which
+
+ align:start position:0%
+happened during differentiation which
+ 
+
+ align:start position:0%
+happened during differentiation which
+sort of resist this reprogramming by the
+
+ align:start position:0%
+sort of resist this reprogramming by the
+ 
+
+ align:start position:0%
+sort of resist this reprogramming by the
+no site cytoplasm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright so mechanistically what's
+
+ align:start position:0%
+alright so mechanistically what's
+ 
+
+ align:start position:0%
+alright so mechanistically what's
+happening well one big one of the people
+
+ align:start position:0%
+happening well one big one of the people
+ 
+
+ align:start position:0%
+happening well one big one of the people
+who really showed what's going on there
+
+ align:start position:0%
+who really showed what's going on there
+ 
+
+ align:start position:0%
+who really showed what's going on there
+is Shinya Yamanaka and what his work
+
+ align:start position:0%
+is Shinya Yamanaka and what his work
+ 
+
+ align:start position:0%
+is Shinya Yamanaka and what his work
+shows is that you can take just a few
+
+ align:start position:0%
+shows is that you can take just a few
+ 
+
+ align:start position:0%
+shows is that you can take just a few
+genes it turns out is four and you can
+
+ align:start position:0%
+genes it turns out is four and you can
+ 
+
+ align:start position:0%
+genes it turns out is four and you can
+induce reprogramming by just expressing
+
+ align:start position:0%
+induce reprogramming by just expressing
+ 
+
+ align:start position:0%
+induce reprogramming by just expressing
+these four genes in an adult
+
+ align:start position:0%
+these four genes in an adult
+ 
+
+ align:start position:0%
+these four genes in an adult
+differentiated cell okay so in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case you have a differentiated
+
+ align:start position:0%
+in this case you have a differentiated
+ 
+
+ align:start position:0%
+in this case you have a differentiated
+cell and what T initially used were
+
+ align:start position:0%
+cell and what T initially used were
+ 
+
+ align:start position:0%
+cell and what T initially used were
+fibroblasts which are a type of
+
+ align:start position:0%
+fibroblasts which are a type of
+ 
+
+ align:start position:0%
+fibroblasts which are a type of
+differentiated cell and what Yamanaka
+
+ align:start position:0%
+differentiated cell and what Yamanaka
+ 
+
+ align:start position:0%
+differentiated cell and what Yamanaka
+showed is that you can express four
+
+ align:start position:0%
+showed is that you can express four
+ 
+
+ align:start position:0%
+showed is that you can express four
+transcription factors one of them being
+
+ align:start position:0%
+transcription factors one of them being
+ 
+
+ align:start position:0%
+transcription factors one of them being
+this factor here acht 4 which is
+
+ align:start position:0%
+this factor here acht 4 which is
+ 
+
+ align:start position:0%
+this factor here acht 4 which is
+expressed in the inner cell mass and was
+
+ align:start position:0%
+expressed in the inner cell mass and was
+ 
+
+ align:start position:0%
+expressed in the inner cell mass and was
+shown to be involved involved in sort of
+
+ align:start position:0%
+shown to be involved involved in sort of
+ 
+
+ align:start position:0%
+shown to be involved involved in sort of
+maintaining pluripotency of these inner
+
+ align:start position:0%
+maintaining pluripotency of these inner
+ 
+
+ align:start position:0%
+maintaining pluripotency of these inner
+mass inner cell mass cells so you could
+
+ align:start position:0%
+mass inner cell mass cells so you could
+ 
+
+ align:start position:0%
+mass inner cell mass cells so you could
+take out 4 plus another transcription
+
+ align:start position:0%
+take out 4 plus another transcription
+ 
+
+ align:start position:0%
+take out 4 plus another transcription
+factor which is important for
+
+ align:start position:0%
+factor which is important for
+ 
+
+ align:start position:0%
+factor which is important for
+pluripotency plus 2 others and scénic
+
+ align:start position:0%
+pluripotency plus 2 others and scénic
+ 
+
+ align:start position:0%
+pluripotency plus 2 others and scénic
+these are the 4 so these are all
+
+ align:start position:0%
+these are the 4 so these are all
+ 
+
+ align:start position:0%
+these are the 4 so these are all
+transcription factors and what they
+
+ align:start position:0%
+transcription factors and what they
+ 
+
+ align:start position:0%
+transcription factors and what they
+found is if you express these four
+
+ align:start position:0%
+found is if you express these four
+ 
+
+ align:start position:0%
+found is if you express these four
+transcription factors in a
+
+ align:start position:0%
+transcription factors in a
+ 
+
+ align:start position:0%
+transcription factors in a
+differentiated cell you could get it
+
+ align:start position:0%
+differentiated cell you could get it
+ 
+
+ align:start position:0%
+differentiated cell you could get it
+revert to revert to a more pluripotent
+
+ align:start position:0%
+revert to revert to a more pluripotent
+ 
+
+ align:start position:0%
+revert to revert to a more pluripotent
+state ok so this results in what is
+
+ align:start position:0%
+state ok so this results in what is
+ 
+
+ align:start position:0%
+state ok so this results in what is
+known as induced pluripotent stem cells
+
+ align:start position:0%
+known as induced pluripotent stem cells
+ 
+
+ align:start position:0%
+known as induced pluripotent stem cells
+or iPS cells for short okay and then
+
+ align:start position:0%
+or iPS cells for short okay and then
+ 
+
+ align:start position:0%
+or iPS cells for short okay and then
+like embryonic stem cells all right here
+
+ align:start position:0%
+like embryonic stem cells all right here
+ 
+
+ align:start position:0%
+like embryonic stem cells all right here
+these cells can give rise to different
+
+ align:start position:0%
+these cells can give rise to different
+ 
+
+ align:start position:0%
+these cells can give rise to different
+cell types okay and so one of the goals
+
+ align:start position:0%
+cell types okay and so one of the goals
+ 
+
+ align:start position:0%
+cell types okay and so one of the goals
+of this field of developmental biology
+
+ align:start position:0%
+of this field of developmental biology
+ 
+
+ align:start position:0%
+of this field of developmental biology
+and and cell reprogramming is to use
+
+ align:start position:0%
+and and cell reprogramming is to use
+ 
+
+ align:start position:0%
+and and cell reprogramming is to use
+this technology to replace cells that
+
+ align:start position:0%
+this technology to replace cells that
+ 
+
+ align:start position:0%
+this technology to replace cells that
+are lost in patients so this is known as
+
+ align:start position:0%
+are lost in patients so this is known as
+ 
+
+ align:start position:0%
+are lost in patients so this is known as
+regenerative medicine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the idea of regenerator the theory
+
+ align:start position:0%
+and the idea of regenerator the theory
+ 
+
+ align:start position:0%
+and the idea of regenerator the theory
+of regenerative medicine is to take ES
+
+ align:start position:0%
+of regenerative medicine is to take ES
+ 
+
+ align:start position:0%
+of regenerative medicine is to take ES
+cells or induced pluripotent stem cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from patients and to be able to culture
+
+ align:start position:0%
+from patients and to be able to culture
+ 
+
+ align:start position:0%
+from patients and to be able to culture
+them in vitro so culture in vitro and
+
+ align:start position:0%
+them in vitro so culture in vitro and
+ 
+
+ align:start position:0%
+them in vitro so culture in vitro and
+then to be able to direct these cultured
+
+ align:start position:0%
+then to be able to direct these cultured
+ 
+
+ align:start position:0%
+then to be able to direct these cultured
+cells into different cell fates in order
+
+ align:start position:0%
+cells into different cell fates in order
+ 
+
+ align:start position:0%
+cells into different cell fates in order
+to use these cells possibly to
+
+ align:start position:0%
+to use these cells possibly to
+ 
+
+ align:start position:0%
+to use these cells possibly to
+transplant them back into an individual
+
+ align:start position:0%
+transplant them back into an individual
+ 
+
+ align:start position:0%
+transplant them back into an individual
+where maybe these cell types are dying
+
+ align:start position:0%
+where maybe these cell types are dying
+ 
+
+ align:start position:0%
+where maybe these cell types are dying
+okay so you could then differentiate
+
+ align:start position:0%
+okay so you could then differentiate
+ 
+
+ align:start position:0%
+okay so you could then differentiate
+these cells using certain biochemical
+
+ align:start position:0%
+these cells using certain biochemical
+ 
+
+ align:start position:0%
+these cells using certain biochemical
+signals that you can add to the media in
+
+ align:start position:0%
+signals that you can add to the media in
+ 
+
+ align:start position:0%
+signals that you can add to the media in
+order to create different cell types
+
+ align:start position:0%
+order to create different cell types
+ 
+
+ align:start position:0%
+order to create different cell types
+like neurons muscle babies skin okay one
+
+ align:start position:0%
+like neurons muscle babies skin okay one
+ 
+
+ align:start position:0%
+like neurons muscle babies skin okay one
+example of this was shown by Shinya
+
+ align:start position:0%
+example of this was shown by Shinya
+ 
+
+ align:start position:0%
+example of this was shown by Shinya
+Yamanaka where what they did was to take
+
+ align:start position:0%
+Yamanaka where what they did was to take
+ 
+
+ align:start position:0%
+Yamanaka where what they did was to take
+human human fibroblast cells put them
+
+ align:start position:0%
+human human fibroblast cells put them
+ 
+
+ align:start position:0%
+human human fibroblast cells put them
+back in the pluripotent state by
+
+ align:start position:0%
+back in the pluripotent state by
+ 
+
+ align:start position:0%
+back in the pluripotent state by
+expressing those four factors and then
+
+ align:start position:0%
+expressing those four factors and then
+ 
+
+ align:start position:0%
+expressing those four factors and then
+get these cells to differentiate into
+
+ align:start position:0%
+get these cells to differentiate into
+ 
+
+ align:start position:0%
+get these cells to differentiate into
+cardio cardiac tissue so cardiac cells
+
+ align:start position:0%
+cardio cardiac tissue so cardiac cells
+ 
+
+ align:start position:0%
+cardio cardiac tissue so cardiac cells
+here's a movie so these are from from
+
+ align:start position:0%
+here's a movie so these are from from
+ 
+
+ align:start position:0%
+here's a movie so these are from from
+adult fibroblast cells but now you can
+
+ align:start position:0%
+adult fibroblast cells but now you can
+ 
+
+ align:start position:0%
+adult fibroblast cells but now you can
+see they're beating like sort of like a
+
+ align:start position:0%
+see they're beating like sort of like a
+ 
+
+ align:start position:0%
+see they're beating like sort of like a
+cardiac tissue would okay so these were
+
+ align:start position:0%
+cardiac tissue would okay so these were
+ 
+
+ align:start position:0%
+cardiac tissue would okay so these were
+made into IPS stem cells cultured in
+
+ align:start position:0%
+made into IPS stem cells cultured in
+ 
+
+ align:start position:0%
+made into IPS stem cells cultured in
+vitro and then directed into a cardiac
+
+ align:start position:0%
+vitro and then directed into a cardiac
+ 
+
+ align:start position:0%
+vitro and then directed into a cardiac
+muscle fate okay so the goal would then
+
+ align:start position:0%
+muscle fate okay so the goal would then
+ 
+
+ align:start position:0%
+muscle fate okay so the goal would then
+to be used these
+
+ align:start position:0%
+to be used these
+ 
+
+ align:start position:0%
+to be used these
+and to transplant them back into back
+
+ align:start position:0%
+and to transplant them back into back
+ 
+
+ align:start position:0%
+and to transplant them back into back
+into a patient such that if a patient
+
+ align:start position:0%
+into a patient such that if a patient
+ 
+
+ align:start position:0%
+into a patient such that if a patient
+had let's say a neurodegenerative
+
+ align:start position:0%
+had let's say a neurodegenerative
+ 
+
+ align:start position:0%
+had let's say a neurodegenerative
+disease and was lacking a certain type
+
+ align:start position:0%
+disease and was lacking a certain type
+ 
+
+ align:start position:0%
+disease and was lacking a certain type
+of neuron you could then take cells
+
+ align:start position:0%
+of neuron you could then take cells
+ 
+
+ align:start position:0%
+of neuron you could then take cells
+start them on the path to neuronal
+
+ align:start position:0%
+start them on the path to neuronal
+ 
+
+ align:start position:0%
+start them on the path to neuronal
+development and then Transplant them
+
+ align:start position:0%
+development and then Transplant them
+ 
+
+ align:start position:0%
+development and then Transplant them
+back into that patient and if these
+
+ align:start position:0%
+back into that patient and if these
+ 
+
+ align:start position:0%
+back into that patient and if these
+cells are derived from the DNA of that
+
+ align:start position:0%
+cells are derived from the DNA of that
+ 
+
+ align:start position:0%
+cells are derived from the DNA of that
+patient then there won't be transplant
+
+ align:start position:0%
+patient then there won't be transplant
+ 
+
+ align:start position:0%
+patient then there won't be transplant
+rejection because what regulates
+
+ align:start position:0%
+rejection because what regulates
+ 
+
+ align:start position:0%
+rejection because what regulates
+transplant rejection is the major
+
+ align:start position:0%
+transplant rejection is the major
+ 
+
+ align:start position:0%
+transplant rejection is the major
+histocompatibility a complex locus and
+
+ align:start position:0%
+histocompatibility a complex locus and
+ 
+
+ align:start position:0%
+histocompatibility a complex locus and
+it's polymorphic but if you're taking a
+
+ align:start position:0%
+it's polymorphic but if you're taking a
+ 
+
+ align:start position:0%
+it's polymorphic but if you're taking a
+nucleus from the patient and then
+
+ align:start position:0%
+nucleus from the patient and then
+ 
+
+ align:start position:0%
+nucleus from the patient and then
+causing the cells to differentiate in
+
+ align:start position:0%
+causing the cells to differentiate in
+ 
+
+ align:start position:0%
+causing the cells to differentiate in
+vitro you're taking the exact same
+
+ align:start position:0%
+vitro you're taking the exact same
+ 
+
+ align:start position:0%
+vitro you're taking the exact same
+you're taking clonal cells and putting
+
+ align:start position:0%
+you're taking clonal cells and putting
+ 
+
+ align:start position:0%
+you're taking clonal cells and putting
+them back in the same patient such that
+
+ align:start position:0%
+them back in the same patient such that
+ 
+
+ align:start position:0%
+them back in the same patient such that
+they won't be rejected
+
+ align:start position:0%
+they won't be rejected
+ 
+
+ align:start position:0%
+they won't be rejected
+ideally all right now we want to try
+
+ align:start position:0%
+ideally all right now we want to try
+ 
+
+ align:start position:0%
+ideally all right now we want to try
+something with the remainder of our time
+
+ align:start position:0%
+something with the remainder of our time
+ 
+
+ align:start position:0%
+something with the remainder of our time
+I want a group all right everyone on
+
+ align:start position:0%
+I want a group all right everyone on
+ 
+
+ align:start position:0%
+I want a group all right everyone on
+this side of the room over I want you
+
+ align:start position:0%
+this side of the room over I want you
+ 
+
+ align:start position:0%
+this side of the room over I want you
+over here and everyone on this side of
+
+ align:start position:0%
+over here and everyone on this side of
+ 
+
+ align:start position:0%
+over here and everyone on this side of
+the room I want you on this side over
+
+ align:start position:0%
+the room I want you on this side over
+ 
+
+ align:start position:0%
+the room I want you on this side over
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+maybe maybe you guys could go over here
+
+ align:start position:0%
+maybe maybe you guys could go over here
+ 
+
+ align:start position:0%
+maybe maybe you guys could go over here
+so that we're more balanced we're gonna
+
+ align:start position:0%
+so that we're more balanced we're gonna
+ 
+
+ align:start position:0%
+so that we're more balanced we're gonna
+have a little debate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can sit down it's okay be in a
+
+ align:start position:0%
+you can sit down it's okay be in a
+ 
+
+ align:start position:0%
+you can sit down it's okay be in a
+position to talk to each other I want
+
+ align:start position:0%
+position to talk to each other I want
+ 
+
+ align:start position:0%
+position to talk to each other I want
+you guys talking to each other that's
+
+ align:start position:0%
+you guys talking to each other that's
+ 
+
+ align:start position:0%
+you guys talking to each other that's
+that's that was the goal of putting you
+
+ align:start position:0%
+that's that was the goal of putting you
+ 
+
+ align:start position:0%
+that's that was the goal of putting you
+close together okay okay so in the past
+
+ align:start position:0%
+close together okay okay so in the past
+ 
+
+ align:start position:0%
+close together okay okay so in the past
+couple weeks there has been a little bit
+
+ align:start position:0%
+couple weeks there has been a little bit
+ 
+
+ align:start position:0%
+couple weeks there has been a little bit
+of a stir because researcher there's a
+
+ align:start position:0%
+of a stir because researcher there's a
+ 
+
+ align:start position:0%
+of a stir because researcher there's a
+researcher in China who has claimed to
+
+ align:start position:0%
+researcher in China who has claimed to
+ 
+
+ align:start position:0%
+researcher in China who has claimed to
+have made the first Jean edited baby
+
+ align:start position:0%
+have made the first Jean edited baby
+ 
+
+ align:start position:0%
+have made the first Jean edited baby
+perhaps you have heard of this you
+
+ align:start position:0%
+perhaps you have heard of this you
+ 
+
+ align:start position:0%
+perhaps you have heard of this you
+probably have because it's been all over
+
+ align:start position:0%
+probably have because it's been all over
+ 
+
+ align:start position:0%
+probably have because it's been all over
+the news so I want you guys let's see I
+
+ align:start position:0%
+the news so I want you guys let's see I
+ 
+
+ align:start position:0%
+the news so I want you guys let's see I
+want us to debate whether we should
+
+ align:start position:0%
+want us to debate whether we should
+ 
+
+ align:start position:0%
+want us to debate whether we should
+whether sort of what are the advantages
+
+ align:start position:0%
+whether sort of what are the advantages
+ 
+
+ align:start position:0%
+whether sort of what are the advantages
+or disadvantages of gene editing or
+
+ align:start position:0%
+or disadvantages of gene editing or
+ 
+
+ align:start position:0%
+or disadvantages of gene editing or
+human cloning you could talk about both
+
+ align:start position:0%
+human cloning you could talk about both
+ 
+
+ align:start position:0%
+human cloning you could talk about both
+and then I want you guys to be able to
+
+ align:start position:0%
+and then I want you guys to be able to
+ 
+
+ align:start position:0%
+and then I want you guys to be able to
+kind of like present them to me I'll
+
+ align:start position:0%
+kind of like present them to me I'll
+ 
+
+ align:start position:0%
+kind of like present them to me I'll
+write them down and we'll have a
+
+ align:start position:0%
+write them down and we'll have a
+ 
+
+ align:start position:0%
+write them down and we'll have a
+discussion about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+near this discussion sort of outside
+
+ align:start position:0%
+near this discussion sort of outside
+ 
+
+ align:start position:0%
+near this discussion sort of outside
+class I think it's really interesting
+
+ align:start position:0%
+class I think it's really interesting
+ 
+
+ align:start position:0%
+class I think it's really interesting
+and it's going to be something that
+
+ align:start position:0%
+and it's going to be something that
+ 
+
+ align:start position:0%
+and it's going to be something that
+you're gonna hear a lot about in the
+
+ align:start position:0%
+you're gonna hear a lot about in the
+ 
+
+ align:start position:0%
+you're gonna hear a lot about in the
+coming year as I'm sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/aeQA5d3gZTI.txt b/aeQA5d3gZTI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0ce6298ecbb626a4ae44a772273c357ee9e36761
--- /dev/null
+++ b/aeQA5d3gZTI.txt
@@ -0,0 +1,1339 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+segment we're going to look at the chain
+
+ align:start position:0%
+segment we're going to look at the chain
+ 
+
+ align:start position:0%
+segment we're going to look at the chain
+Rule and specifically we're going to
+
+ align:start position:0%
+Rule and specifically we're going to
+ 
+
+ align:start position:0%
+Rule and specifically we're going to
+answer a question that I've placed on
+
+ align:start position:0%
+answer a question that I've placed on
+ 
+
+ align:start position:0%
+answer a question that I've placed on
+the board I want you to find two values
+
+ align:start position:0%
+the board I want you to find two values
+ 
+
+ align:start position:0%
+the board I want you to find two values
+for Theta so that DD Theta of the
+
+ align:start position:0%
+for Theta so that DD Theta of the
+ 
+
+ align:start position:0%
+for Theta so that DD Theta of the
+function cosine 2 Theta 4th equals z at
+
+ align:start position:0%
+function cosine 2 Theta 4th equals z at
+ 
+
+ align:start position:0%
+function cosine 2 Theta 4th equals z at
+this point I should also point out a few
+
+ align:start position:0%
+this point I should also point out a few
+ 
+
+ align:start position:0%
+this point I should also point out a few
+things one Theta is is a variable in
+
+ align:start position:0%
+things one Theta is is a variable in
+ 
+
+ align:start position:0%
+things one Theta is is a variable in
+this case and if you haven't seen it
+
+ align:start position:0%
+this case and if you haven't seen it
+ 
+
+ align:start position:0%
+this case and if you haven't seen it
+before frequently we use it when we're
+
+ align:start position:0%
+before frequently we use it when we're
+ 
+
+ align:start position:0%
+before frequently we use it when we're
+dealing with trigonometric functions
+
+ align:start position:0%
+dealing with trigonometric functions
+ 
+
+ align:start position:0%
+dealing with trigonometric functions
+Theta often represents the variable
+
+ align:start position:0%
+Theta often represents the variable
+ 
+
+ align:start position:0%
+Theta often represents the variable
+that's that measures angle so if you
+
+ align:start position:0%
+that's that measures angle so if you
+ 
+
+ align:start position:0%
+that's that measures angle so if you
+haven't seen Theta before this is what
+
+ align:start position:0%
+haven't seen Theta before this is what
+ 
+
+ align:start position:0%
+haven't seen Theta before this is what
+it looks like that's how you say it and
+
+ align:start position:0%
+it looks like that's how you say it and
+ 
+
+ align:start position:0%
+it looks like that's how you say it and
+I'm actually doing the same things we've
+
+ align:start position:0%
+I'm actually doing the same things we've
+ 
+
+ align:start position:0%
+I'm actually doing the same things we've
+done before I'm taking the derivative
+
+ align:start position:0%
+done before I'm taking the derivative
+ 
+
+ align:start position:0%
+done before I'm taking the derivative
+with respect to the variable Theta of a
+
+ align:start position:0%
+with respect to the variable Theta of a
+ 
+
+ align:start position:0%
+with respect to the variable Theta of a
+function of theta the other thing I want
+
+ align:start position:0%
+function of theta the other thing I want
+ 
+
+ align:start position:0%
+function of theta the other thing I want
+to point out which I think we know
+
+ align:start position:0%
+to point out which I think we know
+ 
+
+ align:start position:0%
+to point out which I think we know
+already but just to be sure is that this
+
+ align:start position:0%
+already but just to be sure is that this
+ 
+
+ align:start position:0%
+already but just to be sure is that this
+squar here cosine squ Theta to 4
+
+ align:start position:0%
+squar here cosine squ Theta to 4
+ 
+
+ align:start position:0%
+squar here cosine squ Theta to 4
+means I'm taking cosine OFA 4 and I'm
+
+ align:start position:0%
+means I'm taking cosine OFA 4 and I'm
+ 
+
+ align:start position:0%
+means I'm taking cosine OFA 4 and I'm
+actually squaring it so with that
+
+ align:start position:0%
+actually squaring it so with that
+ 
+
+ align:start position:0%
+actually squaring it so with that
+knowledge I would like us to use the
+
+ align:start position:0%
+knowledge I would like us to use the
+ 
+
+ align:start position:0%
+knowledge I would like us to use the
+chain rule to find two values for Theta
+
+ align:start position:0%
+chain rule to find two values for Theta
+ 
+
+ align:start position:0%
+chain rule to find two values for Theta
+where this derivative is equal to zero
+
+ align:start position:0%
+where this derivative is equal to zero
+ 
+
+ align:start position:0%
+where this derivative is equal to zero
+so I'll give you a moment to to take a
+
+ align:start position:0%
+so I'll give you a moment to to take a
+ 
+
+ align:start position:0%
+so I'll give you a moment to to take a
+stab at finding the derivative uh
+
+ align:start position:0%
+stab at finding the derivative uh
+ 
+
+ align:start position:0%
+stab at finding the derivative uh
+setting it equal to zero and finding
+
+ align:start position:0%
+setting it equal to zero and finding
+ 
+
+ align:start position:0%
+setting it equal to zero and finding
+some values for Theta uh that make this
+
+ align:start position:0%
+some values for Theta uh that make this
+ 
+
+ align:start position:0%
+some values for Theta uh that make this
+that make this equation this uh the
+
+ align:start position:0%
+that make this equation this uh the
+ 
+
+ align:start position:0%
+that make this equation this uh the
+derivative equals zero and um and we'll
+
+ align:start position:0%
+derivative equals zero and um and we'll
+ 
+
+ align:start position:0%
+derivative equals zero and um and we'll
+come back and then I'll work it out as
+
+ align:start position:0%
+come back and then I'll work it out as
+ 
+
+ align:start position:0%
+come back and then I'll work it out as
+well okay so the first thing we
+
+ align:start position:0%
+well okay so the first thing we
+ 
+
+ align:start position:0%
+well okay so the first thing we
+obviously need to do is be able to take
+
+ align:start position:0%
+obviously need to do is be able to take
+ 
+
+ align:start position:0%
+obviously need to do is be able to take
+the derivative of this function on the
+
+ align:start position:0%
+the derivative of this function on the
+ 
+
+ align:start position:0%
+the derivative of this function on the
+left hand side and I should say it's a
+
+ align:start position:0%
+left hand side and I should say it's a
+ 
+
+ align:start position:0%
+left hand side and I should say it's a
+little more complicated than than an
+
+ align:start position:0%
+little more complicated than than an
+ 
+
+ align:start position:0%
+little more complicated than than an
+example you saw in the lecture because
+
+ align:start position:0%
+example you saw in the lecture because
+ 
+
+ align:start position:0%
+example you saw in the lecture because
+in the lecture you were given an example
+
+ align:start position:0%
+in the lecture you were given an example
+ 
+
+ align:start position:0%
+in the lecture you were given an example
+with just two functions so I want to
+
+ align:start position:0%
+with just two functions so I want to
+ 
+
+ align:start position:0%
+with just two functions so I want to
+write it a little differently just to
+
+ align:start position:0%
+write it a little differently just to
+ 
+
+ align:start position:0%
+write it a little differently just to
+show very obviously what the three
+
+ align:start position:0%
+show very obviously what the three
+ 
+
+ align:start position:0%
+show very obviously what the three
+functions are we're composing so this
+
+ align:start position:0%
+functions are we're composing so this
+ 
+
+ align:start position:0%
+functions are we're composing so this
+function I can rewrite it as cosine of
+
+ align:start position:0%
+function I can rewrite it as cosine of
+ 
+
+ align:start position:0%
+function I can rewrite it as cosine of
+theta to the
+
+ align:start position:0%
+theta to the
+ 
+
+ align:start position:0%
+theta to the
+4th does that look like a four there we
+
+ align:start position:0%
+4th does that look like a four there we
+ 
+
+ align:start position:0%
+4th does that look like a four there we
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+go and then I square that whole thing
+
+ align:start position:0%
+go and then I square that whole thing
+ 
+
+ align:start position:0%
+go and then I square that whole thing
+that's really what the function is okay
+
+ align:start position:0%
+that's really what the function is okay
+ 
+
+ align:start position:0%
+that's really what the function is okay
+so we can see what is the outermost
+
+ align:start position:0%
+so we can see what is the outermost
+ 
+
+ align:start position:0%
+so we can see what is the outermost
+function here the outermost function is
+
+ align:start position:0%
+function here the outermost function is
+ 
+
+ align:start position:0%
+function here the outermost function is
+actually the quantity of something
+
+ align:start position:0%
+actually the quantity of something
+ 
+
+ align:start position:0%
+actually the quantity of something
+squared so the outermost function is x s
+
+ align:start position:0%
+squared so the outermost function is x s
+ 
+
+ align:start position:0%
+squared so the outermost function is x s
+what's the next function in in this
+
+ align:start position:0%
+what's the next function in in this
+ 
+
+ align:start position:0%
+what's the next function in in this
+composition the next function in is the
+
+ align:start position:0%
+composition the next function in is the
+ 
+
+ align:start position:0%
+composition the next function in is the
+cosine function and then the last
+
+ align:start position:0%
+cosine function and then the last
+ 
+
+ align:start position:0%
+cosine function and then the last
+function in is the function taking
+
+ align:start position:0%
+function in is the function taking
+ 
+
+ align:start position:0%
+function in is the function taking
+something raising it to the fourth so
+
+ align:start position:0%
+something raising it to the fourth so
+ 
+
+ align:start position:0%
+something raising it to the fourth so
+it's it's very you understand sort of
+
+ align:start position:0%
+it's it's very you understand sort of
+ 
+
+ align:start position:0%
+it's it's very you understand sort of
+the composition which is the outermost
+
+ align:start position:0%
+the composition which is the outermost
+ 
+
+ align:start position:0%
+the composition which is the outermost
+function which is the innermost function
+
+ align:start position:0%
+function which is the innermost function
+ 
+
+ align:start position:0%
+function which is the innermost function
+um in order to do this this chain Rule
+
+ align:start position:0%
+um in order to do this this chain Rule
+ 
+
+ align:start position:0%
+um in order to do this this chain Rule
+now as you saw in recitation um you were
+
+ align:start position:0%
+now as you saw in recitation um you were
+ 
+
+ align:start position:0%
+now as you saw in recitation um you were
+given the example uh do y you had Y is a
+
+ align:start position:0%
+given the example uh do y you had Y is a
+ 
+
+ align:start position:0%
+given the example uh do y you had Y is a
+function of T sorry not in recitation in
+
+ align:start position:0%
+function of T sorry not in recitation in
+ 
+
+ align:start position:0%
+function of T sorry not in recitation in
+the lecture you were given um you were
+
+ align:start position:0%
+the lecture you were given um you were
+ 
+
+ align:start position:0%
+the lecture you were given um you were
+given y as a function of t or a function
+
+ align:start position:0%
+given y as a function of t or a function
+ 
+
+ align:start position:0%
+given y as a function of t or a function
+of X and then you had to put one other
+
+ align:start position:0%
+of X and then you had to put one other
+ 
+
+ align:start position:0%
+of X and then you had to put one other
+variable in the middle here we're going
+
+ align:start position:0%
+variable in the middle here we're going
+ 
+
+ align:start position:0%
+variable in the middle here we're going
+to have a composition of three functions
+
+ align:start position:0%
+to have a composition of three functions
+ 
+
+ align:start position:0%
+to have a composition of three functions
+so we need to have two other things sort
+
+ align:start position:0%
+so we need to have two other things sort
+ 
+
+ align:start position:0%
+so we need to have two other things sort
+of in the middle so let's let's write
+
+ align:start position:0%
+of in the middle so let's let's write
+ 
+
+ align:start position:0%
+of in the middle so let's let's write
+this out first the outermost function we
+
+ align:start position:0%
+this out first the outermost function we
+ 
+
+ align:start position:0%
+this out first the outermost function we
+we'll call the whole thing y so Y is
+
+ align:start position:0%
+we'll call the whole thing y so Y is
+ 
+
+ align:start position:0%
+we'll call the whole thing y so Y is
+equal to X2 is the outermost function so
+
+ align:start position:0%
+equal to X2 is the outermost function so
+ 
+
+ align:start position:0%
+equal to X2 is the outermost function so
+then this whole thing is X now so then
+
+ align:start position:0%
+then this whole thing is X now so then
+ 
+
+ align:start position:0%
+then this whole thing is X now so then
+we'll write X is equal to cosine of
+
+ align:start position:0%
+we'll write X is equal to cosine of
+ 
+
+ align:start position:0%
+we'll write X is equal to cosine of
+w okay and then
+
+ align:start position:0%
+w okay and then
+ 
+
+ align:start position:0%
+w okay and then
+W is equal to Theta to the 4th okay
+
+ align:start position:0%
+W is equal to Theta to the 4th okay
+ 
+
+ align:start position:0%
+W is equal to Theta to the 4th okay
+again this is this this is what you saw
+
+ align:start position:0%
+again this is this this is what you saw
+ 
+
+ align:start position:0%
+again this is this this is what you saw
+before um in the lecture so you write
+
+ align:start position:0%
+before um in the lecture so you write
+ 
+
+ align:start position:0%
+before um in the lecture so you write
+the outermost function and then that
+
+ align:start position:0%
+the outermost function and then that
+ 
+
+ align:start position:0%
+the outermost function and then that
+function is a function of cosine of
+
+ align:start position:0%
+function is a function of cosine of
+ 
+
+ align:start position:0%
+function is a function of cosine of
+another one cosine of w and W is a
+
+ align:start position:0%
+another one cosine of w and W is a
+ 
+
+ align:start position:0%
+another one cosine of w and W is a
+function of theta the 4 so if I put all
+
+ align:start position:0%
+function of theta the 4 so if I put all
+ 
+
+ align:start position:0%
+function of theta the 4 so if I put all
+these back together I have Theta to the
+
+ align:start position:0%
+these back together I have Theta to the
+ 
+
+ align:start position:0%
+these back together I have Theta to the
+4th in here and then I square that and I
+
+ align:start position:0%
+4th in here and then I square that and I
+ 
+
+ align:start position:0%
+4th in here and then I square that and I
+come back to the to the function I
+
+ align:start position:0%
+come back to the to the function I
+ 
+
+ align:start position:0%
+come back to the to the function I
+wanted now we know from the lecture what
+
+ align:start position:0%
+wanted now we know from the lecture what
+ 
+
+ align:start position:0%
+wanted now we know from the lecture what
+we need to do to find essentially Dy D
+
+ align:start position:0%
+we need to do to find essentially Dy D
+ 
+
+ align:start position:0%
+we need to do to find essentially Dy D
+Theta that's what we're looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for okay so Dy D Theta you'll see you
+
+ align:start position:0%
+for okay so Dy D Theta you'll see you
+ 
+
+ align:start position:0%
+for okay so Dy D Theta you'll see you
+remember from the lecture it should be
+
+ align:start position:0%
+remember from the lecture it should be
+ 
+
+ align:start position:0%
+remember from the lecture it should be
+Dy DX time DX
+
+ align:start position:0%
+Dy DX time DX
+ 
+
+ align:start position:0%
+Dy DX time DX
+DW time
+
+ align:start position:0%
+DW time
+ 
+
+ align:start position:0%
+DW time
+DW D
+
+ align:start position:0%
+DW D
+ 
+
+ align:start position:0%
+DW D
+Theta okay so it's slightly more
+
+ align:start position:0%
+Theta okay so it's slightly more
+ 
+
+ align:start position:0%
+Theta okay so it's slightly more
+complicated than we saw before because
+
+ align:start position:0%
+complicated than we saw before because
+ 
+
+ align:start position:0%
+complicated than we saw before because
+there's one more term okay so now let's
+
+ align:start position:0%
+there's one more term okay so now let's
+ 
+
+ align:start position:0%
+there's one more term okay so now let's
+work out what these are well dydx is
+
+ align:start position:0%
+work out what these are well dydx is
+ 
+
+ align:start position:0%
+work out what these are well dydx is
+fairly straightforward dydx is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2X and then DX DW well what's the
+
+ align:start position:0%
+2X and then DX DW well what's the
+ 
+
+ align:start position:0%
+2X and then DX DW well what's the
+derivative of the cosine function the
+
+ align:start position:0%
+derivative of the cosine function the
+ 
+
+ align:start position:0%
+derivative of the cosine function the
+derivative of cosine is negative sign so
+
+ align:start position:0%
+derivative of cosine is negative sign so
+ 
+
+ align:start position:0%
+derivative of cosine is negative sign so
+this is times negative s of
+
+ align:start position:0%
+this is times negative s of
+ 
+
+ align:start position:0%
+this is times negative s of
+w times and what's DW D Theta so w is
+
+ align:start position:0%
+w times and what's DW D Theta so w is
+ 
+
+ align:start position:0%
+w times and what's DW D Theta so w is
+the function Theta to the 4th so DW D
+
+ align:start position:0%
+the function Theta to the 4th so DW D
+ 
+
+ align:start position:0%
+the function Theta to the 4th so DW D
+Theta is 4 Theta to the thir now when
+
+ align:start position:0%
+Theta is 4 Theta to the thir now when
+ 
+
+ align:start position:0%
+Theta is 4 Theta to the thir now when
+you look at this you should
+
+ align:start position:0%
+you look at this you should
+ 
+
+ align:start position:0%
+you look at this you should
+remember X we sort of inserted into the
+
+ align:start position:0%
+remember X we sort of inserted into the
+ 
+
+ align:start position:0%
+remember X we sort of inserted into the
+problem to make the problem easier and W
+
+ align:start position:0%
+problem to make the problem easier and W
+ 
+
+ align:start position:0%
+problem to make the problem easier and W
+we inserted into the problem to make the
+
+ align:start position:0%
+we inserted into the problem to make the
+ 
+
+ align:start position:0%
+we inserted into the problem to make the
+problem easier for us to follow so we
+
+ align:start position:0%
+problem easier for us to follow so we
+ 
+
+ align:start position:0%
+problem easier for us to follow so we
+don't want all these x's and W's we want
+
+ align:start position:0%
+don't want all these x's and W's we want
+ 
+
+ align:start position:0%
+don't want all these x's and W's we want
+everything in terms of in terms of theta
+
+ align:start position:0%
+everything in terms of in terms of theta
+ 
+
+ align:start position:0%
+everything in terms of in terms of theta
+right but what is w Well w is Theta to
+
+ align:start position:0%
+right but what is w Well w is Theta to
+ 
+
+ align:start position:0%
+right but what is w Well w is Theta to
+the 4th so I can replace that by Theta
+
+ align:start position:0%
+the 4th so I can replace that by Theta
+ 
+
+ align:start position:0%
+the 4th so I can replace that by Theta
+to the 4th and what is X x is cosine W
+
+ align:start position:0%
+to the 4th and what is X x is cosine W
+ 
+
+ align:start position:0%
+to the 4th and what is X x is cosine W
+but W is Theta to the 4th so X is
+
+ align:start position:0%
+but W is Theta to the 4th so X is
+ 
+
+ align:start position:0%
+but W is Theta to the 4th so X is
+actually cosine of theta to 4th okay so
+
+ align:start position:0%
+actually cosine of theta to 4th okay so
+ 
+
+ align:start position:0%
+actually cosine of theta to 4th okay so
+I get 2 cosine of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 Time s w again iset 4th of theta to
+
+ align:start position:0%
+4 Time s w again iset 4th of theta to
+ 
+
+ align:start position:0%
+4 Time s w again iset 4th of theta to
+4th Time 4 Theta to the 3 and let's make
+
+ align:start position:0%
+4th Time 4 Theta to the 3 and let's make
+ 
+
+ align:start position:0%
+4th Time 4 Theta to the 3 and let's make
+this nicer I'll bring the coefficient
+
+ align:start position:0%
+this nicer I'll bring the coefficient
+ 
+
+ align:start position:0%
+this nicer I'll bring the coefficient
+and the Theta to the 3 in front and this
+
+ align:start position:0%
+and the Theta to the 3 in front and this
+ 
+
+ align:start position:0%
+and the Theta to the 3 in front and this
+minus sign in front I get -8 Theta to
+
+ align:start position:0%
+minus sign in front I get -8 Theta to
+ 
+
+ align:start position:0%
+minus sign in front I get -8 Theta to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+3 cosine of theta to
+
+ align:start position:0%
+3 cosine of theta to
+ 
+
+ align:start position:0%
+3 cosine of theta to
+4th s of theta to 4th
+
+ align:start position:0%
+4th s of theta to 4th
+ 
+
+ align:start position:0%
+4th s of theta to 4th
+okay and then the problem asked to find
+
+ align:start position:0%
+okay and then the problem asked to find
+ 
+
+ align:start position:0%
+okay and then the problem asked to find
+where the derivative is equal to zero
+
+ align:start position:0%
+where the derivative is equal to zero
+ 
+
+ align:start position:0%
+where the derivative is equal to zero
+find two values now why did I ask you to
+
+ align:start position:0%
+find two values now why did I ask you to
+ 
+
+ align:start position:0%
+find two values now why did I ask you to
+find two values because one is very easy
+
+ align:start position:0%
+find two values because one is very easy
+ 
+
+ align:start position:0%
+find two values because one is very easy
+if this thing is set equal to zero one
+
+ align:start position:0%
+if this thing is set equal to zero one
+ 
+
+ align:start position:0%
+if this thing is set equal to zero one
+value should stand out right away for
+
+ align:start position:0%
+value should stand out right away for
+ 
+
+ align:start position:0%
+value should stand out right away for
+Theta that makes uh makes this this
+
+ align:start position:0%
+Theta that makes uh makes this this
+ 
+
+ align:start position:0%
+Theta that makes uh makes this this
+product Zer and that is theta equals z
+
+ align:start position:0%
+product Zer and that is theta equals z
+ 
+
+ align:start position:0%
+product Zer and that is theta equals z
+so theta equals z is our EAS easiest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer okay so if you didn't do that
+
+ align:start position:0%
+answer okay so if you didn't do that
+ 
+
+ align:start position:0%
+answer okay so if you didn't do that
+then you wanted the more challenging you
+
+ align:start position:0%
+then you wanted the more challenging you
+ 
+
+ align:start position:0%
+then you wanted the more challenging you
+could have done it done the other things
+
+ align:start position:0%
+could have done it done the other things
+ 
+
+ align:start position:0%
+could have done it done the other things
+also so what about cosine Theta 4th if
+
+ align:start position:0%
+also so what about cosine Theta 4th if
+ 
+
+ align:start position:0%
+also so what about cosine Theta 4th if
+we want a product of three things to be
+
+ align:start position:0%
+we want a product of three things to be
+ 
+
+ align:start position:0%
+we want a product of three things to be
+zero then at least one of them has to be
+
+ align:start position:0%
+zero then at least one of them has to be
+ 
+
+ align:start position:0%
+zero then at least one of them has to be
+zero so I could have set cosine Theta to
+
+ align:start position:0%
+zero so I could have set cosine Theta to
+ 
+
+ align:start position:0%
+zero so I could have set cosine Theta to
+4th equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and for what values of of an angle
+
+ align:start position:0%
+zero and for what values of of an angle
+ 
+
+ align:start position:0%
+zero and for what values of of an angle
+I should just say for what values of
+
+ align:start position:0%
+I should just say for what values of
+ 
+
+ align:start position:0%
+I should just say for what values of
+theta to 4th is this going to be zero
+
+ align:start position:0%
+theta to 4th is this going to be zero
+ 
+
+ align:start position:0%
+theta to 4th is this going to be zero
+well this means that Theta the 4
+
+ align:start position:0%
+well this means that Theta the 4
+ 
+
+ align:start position:0%
+well this means that Theta the 4
+4 is equal
+
+ align:start position:0%
+4 is equal
+ 
+
+ align:start position:0%
+4 is equal
+to either maybe pi/ 2 or you could add
+
+ align:start position:0%
+to either maybe pi/ 2 or you could add
+ 
+
+ align:start position:0%
+to either maybe pi/ 2 or you could add
+another Pi okay so we could say Pi well
+
+ align:start position:0%
+another Pi okay so we could say Pi well
+ 
+
+ align:start position:0%
+another Pi okay so we could say Pi well
+let's let's just say that's one example
+
+ align:start position:0%
+let's let's just say that's one example
+ 
+
+ align:start position:0%
+let's let's just say that's one example
+Theta to 4 equals pi over 2 would work
+
+ align:start position:0%
+Theta to 4 equals pi over 2 would work
+ 
+
+ align:start position:0%
+Theta to 4 equals pi over 2 would work
+right because cosine of pi/ 2 is equal
+
+ align:start position:0%
+right because cosine of pi/ 2 is equal
+ 
+
+ align:start position:0%
+right because cosine of pi/ 2 is equal
+to zero okay and so then we could have
+
+ align:start position:0%
+to zero okay and so then we could have
+ 
+
+ align:start position:0%
+to zero okay and so then we could have
+said Theta is equal to pi over
+
+ align:start position:0%
+said Theta is equal to pi over
+ 
+
+ align:start position:0%
+said Theta is equal to pi over
+2 to the
+
+ align:start position:0%
+2 to the
+ 
+
+ align:start position:0%
+2 to the
+1/4 okay that's another that's another
+
+ align:start position:0%
+1/4 okay that's another that's another
+ 
+
+ align:start position:0%
+1/4 okay that's another that's another
+example there we could have also done um
+
+ align:start position:0%
+example there we could have also done um
+ 
+
+ align:start position:0%
+example there we could have also done um
+we could have added pi to this and
+
+ align:start position:0%
+we could have added pi to this and
+ 
+
+ align:start position:0%
+we could have added pi to this and
+gotten another answer but I only asked
+
+ align:start position:0%
+gotten another answer but I only asked
+ 
+
+ align:start position:0%
+gotten another answer but I only asked
+for two so I guess that I'm allowed to
+
+ align:start position:0%
+for two so I guess that I'm allowed to
+ 
+
+ align:start position:0%
+for two so I guess that I'm allowed to
+stop there
\ No newline at end of file
diff --git a/ajXDBKIJsJ8.txt b/ajXDBKIJsJ8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..70573b2e3ef1eb1fc4229ff6c58881c7021c3337
--- /dev/null
+++ b/ajXDBKIJsJ8.txt
@@ -0,0 +1,3189 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: All right.
+
+Can everyone hear me?
+
+So I guess it's 2:35, and we
+might as well get started.
+
+So the calendar, I think, still
+says that we have a
+
+guest lecture today but sorry to
+disappoint you, there is no
+
+guest lecture.
+
+Instead we have a quiz for
+you on Thursday, which is
+
+so much more fun.
+
+Not really.
+
+But I do realize that everybody
+has a lot to do,
+
+even just for this class.
+
+You guys have your final
+project and so on.
+
+So hopefully this
+will be helpful.
+
+It won't take the entire 1 and
+1/2 hours, I don't think.
+
+And the remaining time will be
+up in office hours, answering
+
+questions about stuff.
+
+So the first thing is I decided
+to run some stats that
+
+we haven't run before
+for this class.
+
+These are your Project 42
+4.2 final submissions.
+
+And in the red are your beta
+submission run times.
+
+And in the blue are your
+corresponding final
+
+submission run times.
+
+I thought it was just
+interesting to see some groups
+
+did massive improvements, while
+others didn't really
+
+change their programs much.
+
+And just to give you an idea,
+a 90% for your performance
+
+grade is indicated by that
+green line and below.
+
+So the majority of the class
+did really well.
+
+All right.
+
+So the thing that everybody's
+concerned about.
+
+So Quiz 2 will be in lecture
+on Thursday.
+
+It'll be an 80 minute quiz,
+similar in format to the
+
+previous one.
+
+And you guys once again are
+allowed a one-page handwritten
+
+crib sheet.
+
+And it covers everything that
+has been done since Quiz 1.
+
+It's not designed to be
+cumulative, but unfortunately
+
+due to the nature of the class,
+there's going to be
+
+some things from the previous
+part of the class that you
+
+would need to know or it would
+be helpful to know.
+
+Unlike last time, we didn't
+post a practice quiz on
+
+Stellar, because it turns out
+that the material and the
+
+order of the material gets
+shuffled around quite a bit
+
+every year.
+
+And we have different focuses.
+
+So posting a practice quiz would
+actually be pretty mean,
+
+because it would cause
+you guys to study the
+
+wrong things instead.
+
+Instead I try to extract the
+most useful things from our
+
+discussions of what the quiz
+is going to be this time.
+
+So hopefully all this
+information is helpful.
+
+Feel free to interrupt
+me at any
+
+time if you have questions.
+
+So the first part, I would
+roughly call analyzing and
+
+possibly writing parallel
+programs.
+
+And to start off, is everybody
+familiar with what one of
+
+these graphs represents?
+
+So you have work and then
+each circle is a
+
+unit amount of work.
+
+And then the graph shows the
+dependencies of the things.
+
+So just to start off with a
+really simple question, what
+
+is the total amount of
+work represented?
+
+AUDIENCE: [LAUGHTER]
+
+PROFESSOR: Uh oh.
+
+I heard 17, which is not what I
+got when I counted this last
+
+night at 2:00.
+
+AUDIENCE: 26.
+
+AUDIENCE: 24.
+
+PROFESSOR: I like 24.
+
+AUDIENCE: [LAUGHTER]
+
+PROFESSOR: And I'm going to
+assume it's 24, and not
+
+embarrass myself by trying
+to count it.
+
+Now what is the span?
+
+AUDIENCE: 8.
+
+AUDIENCE: 8.
+
+AUDIENCE: 8.
+
+PROFESSOR: 8 sounds right.
+
+So the longest path-- there's
+actually a couple different
+
+paths that end up being 8, but
+I think 8's the right answer.
+
+So then parallelism?
+
+AUDIENCE: 3.
+
+PROFESSOR: Cool.
+
+All right.
+
+So now that we're done with
+that, how about a little bit
+
+of background on caches.
+
+So when you run programs in
+parallel, it causes some more
+
+interesting things to happen in
+cache that did not happen
+
+with serial execution.
+
+One of those things
+is true sharing--
+
+cache misses-- which are
+caused when multiple
+
+processors, like multiple
+threads, are trying to operate
+
+on the same piece of
+data in memory.
+
+So as a result, your cache would
+be forced to synchronize
+
+that cache line and
+move it across--
+
+copy it from the freshest
+processor to the other ones
+
+every time that it's
+requested.
+
+And you end up with a lot
+of overhead generated by
+
+continually doing
+these copies.
+
+So ideally you don't
+want to do this.
+
+But it's a lot easier
+said than done.
+
+False sharing is a little bit
+trickier because it's not
+
+immediately apparent from
+looking at your program that
+
+you're having multiple
+threads do the--
+
+operate on the same data.
+
+Instead with false sharing, you
+have multiple processors
+
+that want to operate on
+different locations in memory.
+
+But due to the way that your
+computer's cache is organized,
+
+they just happen to be in
+the same cache line.
+
+As a result, you end up with
+the same memory, the same
+
+overhead, that you would
+see with true sharing.
+
+But when you look at the code
+itself, you don't think that
+
+you're doing anything that
+involves multiple threads
+
+operating on the same data.
+
+And so with that, here's
+a piece of code.
+
+And my question is this true
+sharing or false sharing?
+
+Let's take a vote.
+
+How many people think
+it's true sharing?
+
+Nobody.
+
+Well, how many people think
+it's false sharing?
+
+Come on.
+
+You have to vote one
+way or another.
+
+Let's try this again.
+
+True sharing?
+
+False sharing?
+
+That's better.
+
+All right, so it is indeed
+false sharing.
+
+And can someone propose
+a solution to fix it?
+
+Yes?
+
+AUDIENCE: Separate A
+and B, and put them
+
+in different shelves.
+
+PROFESSOR: Would that
+be sufficient?
+
+Putting them in different
+trucks?
+
+AUDIENCE: Then, padding
+the trucks.
+
+PROFESSOR: Yeah.
+
+Maybe with a little
+bit of padding,
+
+depending on your system.
+
+But sure, I'll accept that.
+
+But on the quiz, you might be
+asked to propose solutions to
+
+problems that you find.
+
+And hopefully those
+will be easier.
+
+Now on to a more fun topic--
+
+synchronization.
+
+Yes?
+
+AUDIENCE: I have a question
+on sharing.
+
+So if two programs only access
+data, does that still count ?
+
+PROFESSOR: If you only access
+the data and nothing in the
+
+cache line is being modified,
+then you're safe, because
+
+every processor can
+independently read from their
+
+own copy of that.
+
+AUDIENCE: So that
+doesn't count.
+
+PROFESSOR: That doesn't
+count, correct.
+
+But the problem is if your cache
+line is 64 kilobytes,
+
+and any thread on any processor
+changes one piece of
+
+data inside that cache,
+then everybody
+
+has to pull new copies.
+
+So the classic example to
+demonstrate synchronization
+
+correctness is the dining
+philosophers problem, where
+
+you have n--
+
+I believe five in this case--
+
+philosophers, and
+five chopsticks.
+
+And each philosopher
+has to eat.
+
+So they use mutexes to--
+
+well, generally you need--
+
+each philosopher's code would be
+pick up two chopsticks and
+
+then eat and then put down
+their two chopsticks.
+
+It's somewhat of a contrived
+example, but it actually comes
+
+up in a lot of cases.
+
+And one of the cases where it
+comes up is in the system that
+
+I use to grade your
+unit tests.
+
+So I got impatient about
+running 200 or so
+
+unit test in series.
+
+And since I had about 200 cores
+altogether on the cloud
+
+machines, I figured, why not
+do them in parallel?
+
+But the problem is I need to
+run-- if I have students A and
+
+B, I need to run student A's
+test against student B's
+
+implementation.
+
+So the rough way that I did that
+was I grabbed a lock on
+
+student A's repository, grabbed
+a lock on student B's
+
+repository, and then
+modified--
+
+swapped in their test files, did
+all my testing, and then
+
+returned the files to the
+original conditions, and then
+
+let go of the locks.
+
+Unfortunately, when you do that,
+you run into much of the
+
+same problem as the dining
+philosophers problems.
+
+So the naive strategy is for
+each philosopher, you grab a
+
+lock on your left chopstick.
+
+You grab a lock on your right
+one, with respect to you.
+
+And then you eat and then you
+unlock them in the same order.
+
+So this has a bug.
+
+Can anyone point
+out what it is?
+
+AUDIENCE: You want to unlock
+in a certain order.
+
+PROFESSOR: Actually, it doesn't
+matter which order you
+
+unlock in in in this case.
+
+So bad things happen if
+everybody starts at
+
+the exact same time.
+
+So everybody grabs their left
+chopstick. there's five
+
+people, five chopsticks,
+so that works fine.
+
+Now everybody wants to
+grab their right one,
+
+but it's not there.
+
+Because the person to the right
+already grabbed it as
+
+their left.
+
+So they wait forever for the
+right chopstick to appear and
+
+it never does.
+
+So the situation is
+called a deadlock.
+
+And it's obvious to spot,
+because all of your threads
+
+are going to be stuck doing
+absolutely nothing.
+
+Your CPU is not doing
+anything.
+
+And you're just sitting there.
+
+So a very common work-around
+that people like for this is
+
+to use what's called
+a try lock pattern.
+
+So what you do is you grab a
+lock on one of them, like,
+
+say, your left one.
+
+And then for the right one,
+instead of directly going and
+
+trying to grab the
+lock, you ask--
+
+you basically do--
+
+if the thing is unlocked,
+grab it.
+
+Otherwise, don't grab it.
+
+So it's a non-blocking
+approach to
+
+trying to get a lock.
+
+So it either succeeds and
+you have the lock, or
+
+it instantly fails.
+
+And if it fails, then you switch
+the order of which--
+
+you put down the chopstick that
+you grabbed, and then you
+
+try the next one.
+
+Maybe you wait a little
+bit before then.
+
+This is more or less than what
+I did for your beta test, for
+
+your unit test tester.
+
+When it fails to--
+
+if first grabs one student's
+directory's locks.
+
+And then it tries to grab
+the second one.
+
+If that fails, then it puts down
+both locks, and then it
+
+waits a little bit, and
+then it tries again.
+
+So what's the problem
+with this approach?
+
+Yes?
+
+AUDIENCE: It can
+still hold up.
+
+PROFESSOR: What's that?
+
+AUDIENCE: It can keep waiting
+and grabbing, and sometimes it
+
+will contend.
+
+PROFESSOR: Yeah, pretty much,
+the same problem happens.
+
+Only now you have the case where
+everybody grabs their
+
+left, and now the right
+one's gone.
+
+So they put down
+their left one.
+
+And then they all go to
+grab the right one.
+
+Now they have the right
+one, and now they
+
+want the left one.
+
+But the left one not there.
+
+So in theory, they can end
+up doing this for a
+
+very, very long time.
+
+But in practice what happens
+is because of scheduling
+
+overhead, and the phase of the
+moon and whatever else affects
+
+computing, you'll end up after
+a while, this become distinct
+
+from this pattern and eventually
+all the locks go
+
+through, and you're OK.
+
+But in the meantime, you spent a
+lot of time spinning, trying
+
+to grab locks.
+
+And so this situation is
+called a livelock.
+
+And it's a lot more
+annoying than a
+
+deadlock because it happens--
+
+it tends to be less
+reproducible.
+
+And it's harder to diagnose,
+because if you're looking at
+
+top or your favorite CPU
+monitor, you see that the
+
+program seems to be
+making progress.
+
+Maybe some of them actually get
+the lock and go through.
+
+But the rest of them don't.
+
+So it's hard to argue
+whether or not
+
+there's correctness issue.
+
+Now there's various classes
+of solutions to the dining
+
+philosophers problem, but you
+guys can go look that up.
+
+I'm not going to go over them.
+
+So another issue with
+synchronization is suppose you
+
+have two threads.
+
+Let's say this is a Mars Rover,
+and it's on Mars.
+
+And the two things that the
+programmer wanted to do are
+
+send back its debugging log, so
+that the nerdier people at
+
+NASA, I suppose, can read
+them over, or whatever
+
+they do with logs.
+
+And the high priority, what
+everybody actually wants, is
+
+for the Rover to send
+back pictures.
+
+Now both of these things require
+access to the radio
+
+that's supposed to transfer
+something.
+
+And only one thing can
+transmit at time.
+
+Otherwise, the transmission
+is garbled.
+
+So a reasonable approach might
+be to just lock the radio in
+
+each thread before you transmit,
+and then unlock
+
+after you transmit.
+
+So what could be a potential
+issue with this?
+
+AUDIENCE: One might
+get all the time.
+
+PROFESSOR: Let's say, the
+scheduler interrupts every 10
+
+milliseconds, and then 1 out of
+the 10 times, it allows 10
+
+logs to run.
+
+And then 9 out of the 10 times,
+it will allow some
+
+pictures to run.
+
+So everybody gets
+time scheduled.
+
+So I guess the easiest way to
+illustrate this is what
+
+happens if it's currently
+running said logs, and it
+
+grabs this lock.
+
+And then while it's
+transmitting, let's say on the
+
+second megabyte, the scheduler
+says your time is up.
+
+And then it swaps in this
+program, and it tries to run.
+
+So now when this program runs,
+it tries to lock the radio,
+
+but the radio's already
+locked.
+
+And the one that locked
+the radio is
+
+the send locks thread.
+
+And so it could sit there and
+spin for a while waiting for
+
+the lock to be available.
+
+But that's not going
+to happen.
+
+Because the guy that's holding
+the lock is a bug.
+
+So in general, this is called
+starvation, where in the
+
+process of having a shared
+resource, you end up unfairly
+
+depriving someone else of
+a resource when you're
+
+not truly using it.
+
+Well, I guess that's not the--
+
+I guess you are using it, but
+you're using it for longer
+
+than is fair for you.
+
+Like in the scheduler you wanted
+90% to one process and
+
+10% to the other, but in reality
+you end up with a
+
+completely different
+set of priorities.
+
+And this inversion of priorities
+is commonly called
+
+priority inversion.
+
+Does that make sense?
+
+Cool.
+
+So on a completely
+different topic.
+
+So Cilk hyperobjects
+were covered
+
+extensively in lecture.
+
+You guys had a problem set on
+it, although it was not
+
+received very warmly from
+what I see in the
+
+problems sets write ups.
+
+But I think all of the basic
+material for what a Cilk
+
+hyperobjects is and what it
+does can be found in the
+
+lecture material.
+
+But more interesting, let's
+explore what you can do with
+
+hyperobjects that aren't
+in the documentation.
+
+So I'm going to define
+a piece of code here.
+
+And it's C++ or Cilk++ code.
+
+And the first part of it
+defines a very simple
+
+structure called a point.
+
+And it has three members.
+
+Or actually it has two members,
+x and y, and it has
+
+three methods for setting the
+values of x and y and also
+
+getting the values of x and y.
+
+Question?
+
+No?
+
+OK.
+
+And then there's also a
+hyperpoint class which
+
+contains some extra Cilk junk.
+
+And it also implements the
+same three methods.
+
+Set, get x, and get y.
+
+And if you look at the monoid
+that it contains the point
+
+monoid it implements a
+reduce function that
+
+just doesn't do anything.
+
+And for the public methods, the
+setters and getters, they
+
+grab the point represented by
+the local view to the reducer
+
+that it contains.
+
+And it calls the method that
+you called on that point.
+
+So the question is what
+does this thing do,
+
+the hyperpoint object?
+
+Anybody have any wild guesses
+at this point?
+
+That's a no.
+
+So OK.
+
+Let's try using this code.
+
+So to put the example
+into perspective.
+
+Suppose I have this artificially
+contrived
+
+function that takes an array of
+100 points, and it tries to
+
+do an in place reversal
+of its elements.
+
+So one way that it can
+do that is you have a
+
+global temporary point.
+
+And you, at every step of the
+iteration, first you step
+
+through half of the list.
+
+And then at every step of the
+iteration, you copy the ith
+
+element into the temporary
+variable.
+
+And then you set the ith from
+the other end to the--
+
+you swap the two.
+
+And then you--
+
+yeah, so if it is a
+three-variable swap, I guess
+
+is the simplest way
+of explaining it.
+
+It's a swap using a using
+a temporary variable.
+
+Anyone not get what that code
+does, despite my attempts to
+
+confuse you?
+
+So as far as this space
+complexity of this procedure,
+
+really what it needs at minimum
+is enough memory to
+
+store the temporary point, and
+then one register to use to
+
+put in the temporary values.
+
+You can think of a solution that
+uses only one register to
+
+update values within your
+point structure.
+
+And so let's suppose I want
+to do this in parallel.
+
+And so what I do is I call it
+parallel reverse, and I
+
+replace for with Cilk for.
+
+So am I done?
+
+What's wrong with my code?
+
+AUDIENCE: Race.
+
+PROFESSOR: Yes.
+
+Well first it takes that much--
+it takes the same
+
+amount of space.
+
+But there is a data race on
+temp, because multiple threads
+
+could be updating temp.
+
+So now what I do is I replace
+my point with a hyperpoint.
+
+So now what does the
+hyperpoint do?
+
+So within each iteration of the
+Cilk for loop, so if that
+
+iteration has been-- if the
+work of that iteration has
+
+been stolen or spawned off.
+
+Then the hyperobject, because
+it has a reducer within it,
+
+it'll get a new local
+view which is a new
+
+point object to use.
+
+And if it's not still in that
+it continues running in the
+
+same thread, then it actually
+just continues using the local
+
+view that was previously
+instantiated.
+
+So no matter what Cilk does
+in the background, you're
+
+guaranteed to not have any data
+races on temp, because
+
+whenever you spawn off a new
+thread, the hyperobject will
+
+instantiate a new temp object
+for you to use.
+
+And this is an example of what's
+called thread local
+
+storage, so like a temporary
+storage space for each thread.
+
+Any questions?
+
+Cool.
+
+So on the quiz, you might be
+asked about various abusing of
+
+various other novel hyperobjects
+that don't do the
+
+typical thing, which
+is take a left and
+
+right and reduce them.
+
+They might do something
+a little bit quirky.
+
+And you might be asked to
+explain what they do.
+
+AUDIENCE: Maybe?
+
+PROFESSOR: Yes?
+
+Maybe.
+
+Maybe.
+
+AUDIENCE: But this is purely for
+illustrating that you can
+
+do such a thing with
+hyperobjects.
+
+Because you can always create
+a temporary variable there.
+
+PROFESSOR: But suppose point
+was a much larger object.
+
+Sure, this is a contrived
+example.
+
+But yes.
+
+Anyone?
+
+Everyone gets this?
+
+So, in that case, why would that
+problem be more efficient
+
+than creating a new copy of
+it, say another point?
+
+PROFESSOR: Because if you think
+about the case where
+
+this code runs on a single
+processor with no work
+
+stealing, this version does the
+exact same thing as the
+
+single threaded version.
+
+No extra objects are
+being created.
+
+And if you're running on however
+many processors and
+
+Cilk decides what to do in the
+background as far as how many
+
+threads to allocate for you, and
+your code doesn't have to
+
+know anything about that.
+
+AUDIENCE: What's the
+monoid again?
+
+PROFESSOR: The monoid is the
+associative operator that has
+
+an identity and a reduce
+operation and some other
+
+things that I forgot.
+
+Any more questions?
+
+Cool.
+
+So switching gears, and this
+time I actually have a
+
+placeholder slide for it, next
+part is more about like the
+
+types of things that you might
+have learned from doing or
+
+experience you might
+have gained
+
+from doing your projects.
+
+And it primarily pertains to lab
+oriented, like in practice
+
+hands on things, as opposed
+to theoretical concepts.
+
+So just as a fun warm up,
+everybody has hopefully at
+
+this point used some
+STL data structure.
+
+Vectors should definitely
+look familiar.
+
+So let's compare some operations
+on these three.
+
+Because, as far as the API
+is concerned, both list--
+
+all three of them support
+almost the same set of
+
+functions, as far as Insert,
+at pushback, pop front.
+
+All those operations are
+supported by these things.
+
+So it's kind of--
+
+You might ask why would you
+use one over the other?
+
+Well, it turns out that they
+have slightly different
+
+performance characteristics
+that are useful in noting.
+
+So anyone want to compare and
+contrast like what data
+
+structure a list corresponds
+to compared to a vector?
+
+So which one would be
+like a linked list?
+
+List, yep.
+
+And then vector obviously is a
+dynamically growing array.
+
+And a deque--
+
+how many people have
+used the deque?
+
+Cool.
+
+One.
+
+How many people know what
+deque does even if they
+
+haven't used it?
+
+Three?
+
+Four?
+
+OK.
+
+So a deque is actually
+implemented similar to a
+
+vector, but it's dynamically
+growing on both ends.
+
+OK, so let's start with
+filling in the
+
+table for the list.
+
+So inserting and removing
+at the end of a list.
+
+Constant time?
+
+Linear time?
+
+How many people say
+constant time?
+
+Linear?
+
+Half and half, wow.
+
+Don't rely on your neighbor
+during the test.
+
+So it's actually
+constant time.
+
+If you think about appending to
+the end of a linked list,
+
+it's just a matter of couple
+pointer operations.
+
+How about inserting and
+removing at the front?
+
+Constant?
+
+Cool.
+
+Linear?
+
+OK.
+
+I'll stop picking
+on people now.
+
+So next is inserting and
+removing an arbitrary offset.
+
+So what I mean by that is you
+have an iterator to a
+
+particular point inside
+the list.
+
+Now I say insert this element
+five or n elements away from
+
+that iterator.
+
+How long does that
+operation take?
+
+How many people say
+constant time?
+
+Three people.
+
+How many people say some
+sort of linear time?
+
+I agree with you guys.
+
+It is indeed a linear
+time thing,
+
+because you have to traverse--
+
+you have to actually fall the
+next pointers to the location
+
+or the previous pointers
+to the location
+
+that you want to insert.
+
+So although list might appear
+to support randomish axis,
+
+like you can add numbers to
+the iterator, it doesn't
+
+actually support that operation
+efficiently in the
+
+background.
+
+Now the next one is also
+kind of tricky.
+
+Checking the size.
+
+Like checking how many elements
+are calling the dot
+
+size method of a
+standard list.
+
+How many people think
+that's constant?
+
+Cool.
+
+About four or five.
+
+How many people think
+that's linear?
+
+One.
+
+How many people think it's
+possible to have a linked list
+
+data structure that's forced
+constant time?
+
+There we go.
+
+Well, unfortunately, the STL
+only requires you to have a
+
+big O of n time for this.
+
+In fact, I peeked inside the
+code for glibc the lib
+
+standard C++ that is used
+on the cloud machines.
+
+And in fact, what they do is
+they actually walk through
+
+everything from start to
+end, and they count up
+
+the number of times.
+
+So in fact, it is a linear time
+operation, although I'm
+
+sure somewhere out in the
+world, there exists a C
+
+library, C++ library that does
+linear time, or constant time,
+
+size look ups.
+
+So you might want to be careful
+about that one.
+
+On a different note, there's
+actually a dot empty method
+
+for checking whether or not a
+list is empty, and for any
+
+type of STL collection
+that is guaranteed
+
+to be constant time.
+
+So if you just want to know
+whether something's empty,
+
+don't use dot size equals 0.
+
+What about reversing a
+linked list in place?
+
+Linear?
+
+More than linear?
+
+It's not a technical term, and
+Charles is probably going to
+
+hurt me now.
+
+Linear?
+
+Yes.
+
+Linear.
+
+What about in place sorting
+of a linked list?
+
+How many people think
+it's N log(N)?
+
+One or two daring souls.
+
+Three daring souls.
+
+A well informed daring soul.
+
+How many people think it's
+more than N log(N)?
+
+One.
+
+OK.
+
+So actually it is N log(N).
+
+And that's actually not
+specified by the specs.
+
+But it happens to be.
+
+And it turns out that there is
+a variant merge sort that
+
+works on link list
+that is N log(N).
+
+I didn't know that,
+but anyway.
+
+So how about let's fill this
+in for the vector.
+
+Inserting and removing an
+element at the end--
+
+constant time?
+
+Linear time?
+
+Nobody says linear time.
+
+So it's amortized constant
+time, I guess.
+
+I'll just call it
+constant time.
+
+What about inserting
+or removing at
+
+the front of a vector--
+
+constant time?
+
+Linear time?
+
+Come on, guys.
+
+I'm getting like three hands for
+linear time and zero for
+
+constant time.
+
+I guess that's reasonable.
+
+So it does, in fact,
+insert one element.
+
+It puts the element in and then
+it grows the vector in.
+
+It copies everything in.
+
+So don't insert at the front,
+don't insert or remove at the
+
+front of a vector.
+
+It's a very bad idea if
+you do that a lot.
+
+What about inserting or removing
+at an arbitrary
+
+location inside a vector?
+
+Well, that one's fairly obvious
+to be some sort of
+
+linear time too, because it
+has to shift all of the
+
+elements after it.
+
+Checking the size
+of the vector?
+
+Some people are getting
+pessimistic about the STL.
+
+That's my personal opinion,
+but I won't
+
+transfer that onto you.
+
+So it turns out that for a
+vector, yes, it is constant
+
+time to check the size.
+
+So that's OK.
+
+In place reversal,
+linear time.
+
+And sorting is N log(N),
+which is not
+
+surprising by any means.
+
+So a deque?
+
+Inserting or removing
+at the end--
+
+constant?
+
+Sure, constant.
+
+And inserting or removing
+at the front?
+
+Cool.
+
+Constant.
+
+So that's the primary
+difference between
+
+a deque and a vector.
+
+And for everything else, it
+behaves exactly like a vector.
+
+Does that makes sense?
+
+Yes.
+
+AUDIENCE: So is list like
+a doubly linked list?
+
+PROFESSOR: A standard list is in
+fact a doubly linked list.
+
+So it supports both forward
+and reverse traversal.
+
+There's a standard S list, which
+is a singly linked list,
+
+and it only supports
+forward traversal.
+
+Any other questions?
+
+Moving on to a slightly
+different topic, can anyone
+
+point out what is bad
+about this code?
+
+And I mean from a performance
+standpoint.
+
+AUDIENCE: It's O of n.
+
+PROFESSOR: All right.
+
+Someone said it,
+so it's O of n.
+
+So the vector that's passed in
+here is passed in by value,
+
+which means whenever you call
+this function, it'll actually
+
+make a brand new copy
+of the vector and
+
+copy all of the elements.
+
+So it's linear time with respect
+to the number of
+
+elements in the vector.
+
+PROFESSOR: So how
+do you fix that?
+
+AUDIENCE: You can pass
+in a pointer.
+
+PROFESSOR: So there's
+two ways.
+
+So on the left is the original
+code, and on the right are two
+
+different ways to pass in just
+a pointer to the same thing.
+
+So you can do a reference
+pass, which is the first
+
+version above.
+
+And then you can use a dot
+to access the methods.
+
+Or you can pass in by pointer
+which everyone is already
+
+familiar with.
+
+And that's where you
+have to use arrows
+
+to access the elements.
+
+And then you also have to change
+the way that you call
+
+the function.
+
+So oftentimes if you just catch
+something in code, like
+
+say the final project where
+something is passed by value,
+
+where it should be passed by
+reference, oftentimes the
+
+easiest way to modify the code
+is to just change it to use a
+
+reference rather
+than a pointer.
+
+So the next thing that I want
+to cover is a question type
+
+that will be on the final,
+will be on the quiz.
+
+And I'll give some examples
+of problems of this form.
+
+But most importantly, I want
+everybody to be familiar with
+
+the form of the question, the
+rules involving the question,
+
+so nobody accidentally loses
+points for not reading the
+
+instructions, which nobody
+seems to do on quizzes.
+
+So you are given two versions
+of the same function written
+
+in C or C++.
+
+And you are to assume
+that your compiler--
+
+well, the compiler, as far as
+like what the CPU is executing
+
+is a literal interpretation
+of the code you
+
+see before and after.
+
+By this point, everybody is
+probably familiar with some of
+
+the simple tricks a compiler
+does, like if you say int x
+
+equals 1 plus 1 there is no
+circumstance in which the
+
+compiler actually puts two 1s in
+two different registers and
+
+tells it to add it and
+then put it in x.
+
+So you are assuming that your
+compiler is doing a literal
+
+translation.
+
+And then you are asked to
+determine three properties
+
+about the optimization,
+so going from the
+
+before to the after.
+
+So the first thing is
+whether or not the
+
+optimization is legal.
+
+And when we define legal, we
+mean that the optimized
+
+version always has the same--
+
+preserves the same behavior
+as the other version.
+
+It should be relatively simple
+to infer from the code
+
+snippets that we give you, what
+the intended purpose of a
+
+function is.
+
+And you are to determine whether
+or not the optimized
+
+version acts like the
+unoptimized version, as far as
+
+the correctness of the result.
+
+Second, you are asked to
+determine whether or not this
+
+optimized version is faster
+than the previous version.
+
+And by faster, we mean faster
+in most conceivable cases.
+
+It's a short answer question so
+you might want to explain
+
+what you mean.
+
+But we do expect a yes
+or no answer to
+
+start off the question.
+
+And it should be pretty
+clear whether the
+
+answer is yes or no.
+
+And then finally, I'm sure by
+this point everybody knows
+
+that when you compile with gcc
+-02 or -03, the compiler does
+
+a lot of things for you.
+
+So there's oftentimes no point
+in writing certain
+
+optimizations by hand, when
+you know when you hit the
+
+compile button, the compiler's
+going to do it in the
+
+background anyway.
+
+So this question asks whether
+or not you can reasonably
+
+assume that the optimizing
+compilers, like the ones that
+
+you're using for your projects,
+would do this
+
+optimization for you or should
+you take the effort to
+
+actually do this optimization
+by hand.
+
+And then, legalese, if the
+optimization is illegal, let's
+
+not answer whether or not it's
+faster or automatic.
+
+And if the optimization actually
+makes things slower,
+
+then let's not answer whether
+the compiler does it for you.
+
+Some of us have more cynical
+views of the
+
+compiler than others.
+
+So we'll just disregard that.
+
+Any question on the rules?
+
+AUDIENCE: How are we supposed
+to know what types of things
+
+the compiler's going to do,
+can we just read the
+
+documentation?
+
+PROFESSOR: So there was a
+lecture that Samaan gave
+
+called What Compilers
+Can and Cannot Do.
+
+AUDIENCE: So it's just stuff
+from that lecture?
+
+PROFESSOR: I would say most
+of it is that lecture.
+
+And then other things-- we might
+throw in a thing or two
+
+that you guys hopefully
+learn from.
+
+So throughout the term, we've
+been misguiding you on those
+
+walk through P-sets, suggesting
+you to do things
+
+that actually don't help.
+
+And you guys have gotten
+pretty pissed at
+
+us about that probably.
+
+But there was a method
+to the madness.
+
+I mean, there was something to
+be learned from that, whether
+
+or not we actually
+meant to do it.
+
+So hopefully some level of
+intuition would answer it, and
+
+you would get the bulk of the
+points for just understanding
+
+the points raised
+in the lecture.
+
+Any other questions
+about the rules?
+
+All right.
+
+So I have a couple of examples
+of these types of questions.
+
+So the first one is this.
+
+So it should be fairly obvious
+what the code does.
+
+It takes your input, and it
+wants to mod it by 256.
+
+So first question is this
+a legal optimization?
+
+How many people say yes?
+
+A lot of people.
+
+Anybody say no?
+
+Reed almost scared me
+for a moment there.
+
+He had his hand up.
+
+So yes, it is indeed legal.
+
+And it's a standard bit hack
+for doing a modulo
+
+by a power of two.
+
+AUDIENCE: What if it's 257?
+
+PROFESSOR: I was fortunate
+enough to make it a uint64.
+
+So next question is given that
+it's legal, is it faster to do
+
+the and instead of the mod?
+
+How many people say yes?
+
+How many people say no?
+
+So a majority of the
+class says yes, and
+
+some people say no.
+
+So what would be a reason why
+you think it's not faster?
+
+AUDIENCE: Well, I didn't say
+it's not faster faster.
+
+It's probably the same time,
+because I assume the
+
+instruction for modding is not
+actually dividing by it.
+
+PROFESSOR: So for the other
+people who said no, how many
+
+people agree with that
+line of reasoning?
+
+All right.
+
+Seems like everybody.
+
+So unfortunately,
+it is faster.
+
+And it turns out, I compiled
+down both of these pieces of
+
+code under-- well, actually,
+the compiler--
+
+but anyway, I'll get
+to that next.
+
+Not giving away any answers.
+
+But so I executed the assembly
+instructions corresponding to
+
+both of these operations.
+
+And it does turn out that the
+compiler, the CPU, when you
+
+ask it to take the mod of an
+arbitrary number, usually it's
+
+an instruction called div mod.
+
+And what that does is that it
+does a divided by b, and it
+
+puts the dividend in one
+register and it puts the
+
+modulo in another register.
+
+And we do that for, let's say,
+2 to the 63rd modulo 256,
+
+because it actually goes through
+all the clock cycles
+
+for doing that division
+process.
+
+And then it dumps out the
+modulo at the end.
+
+So yes, this actually does
+tend to be a lot faster.
+
+Now next question is will the
+compiler do this for you?
+
+How many people say yes?
+
+Most of the class.
+
+Anybody say no?
+
+Good.
+
+We all trust the compiler
+to some extent.
+
+So yeah, it turns out that gcc,
+starting from 01, will do
+
+this for you.
+
+Any questions?
+
+All right.
+
+Next question.
+
+So you have a list.
+
+And you pushed in.
+
+You pushed at the end.
+
+It's 42, twice.
+
+And then you returned the result
+of popping the front
+
+element and then popping the
+back element, subtracted.
+
+So first of all, is this
+a legal operation?
+
+Let me give everybody
+a chance to think.
+
+AUDIENCE: Legal optimization
+as opposed to an operation.
+
+PROFESSOR: Yeah.
+
+How many people vote yes,
+this is going legal?
+
+Roughly half the class.
+
+How many people say no,
+this is not legal?
+
+Two people.
+
+OK, so why would it
+not be legal?
+
+You can't do that.
+
+Yes?
+
+AUDIENCE: There happens to be
+wastefulness on some problems.
+
+PROFESSOR: Well, that could
+certainly happen.
+
+But for the purpose of
+these problems--
+
+see this is why I'm bringing up
+these problems-- so for the
+
+purpose of these problems,
+assume there's no man behind
+
+the curtain doing things.
+
+For any given problem, you
+could say that's someone
+
+attaching a debugger to your
+program and changing the
+
+memory between instructions.
+
+So let's just assume
+that's happening.
+
+AUDIENCE: Also, who's
+local, right?
+
+PROFESSOR: Yeah.
+
+Yea, Foo is actually local,
+so if anybody else's doing
+
+anything to it, they're
+a very bad person.
+
+So fine.
+
+It's a legal optimization.
+
+Now.
+
+is it faster?
+
+How many people think that
+returning zero is slower than
+
+pushing two things up?
+
+AUDIENCE: [LAUGHTER]
+
+AUDIENCE: Depends upon
+how big zero is.
+
+PROFESSOR: That's true.
+
+So OK, so yes, obviously,
+it's faster to just
+
+directly return zero.
+
+And finally, is this an
+automatic optimization?
+
+How many people say yes?
+
+Cool.
+
+Nobody said yes.
+
+How many people say no?
+
+People who say yes, if you
+could work for compiler
+
+companies, I would appreciate
+that a lot.
+
+So unfortunately, the compiler
+does not make--
+
+cannot reason through how an
+STL list works, and realize
+
+that what you're doing
+is an no op.
+
+It turns out that for a related
+set of questions, like
+
+have any of your mentors said
+anything to-- so my mentor
+
+said this to me last year.
+
+And I was pretty interested
+when I tried it out.
+
+Have you ever used a for loop to
+set everything in an array
+
+to equals 0?
+
+Most people seem to
+have done that.
+
+Who has used the memset or heard
+of the memset set API
+
+call before?
+
+A good portion of the class.
+
+OK, so some people.
+
+So a little bit of
+background then.
+
+Mem set instruction takes in an
+array or a pointer rather,
+
+and a constant, and the
+size of the array.
+
+And it sets that many elements
+of the array to that constant.
+
+So it turns out that depending
+on the machine that you're
+
+using, there is more efficient
+and less efficient ways of
+
+setting all the elements
+of an array to 0.
+
+And functions like mem set are
+actually are several pages
+
+long of hand optimized assembly
+to be optimal for
+
+your architecture.
+
+So it's always tempting to take
+a for loop that iterates
+
+through an array, setting
+everything to 0, and changing
+
+it to a single mem
+set instruction.
+
+And it turns out that for both
+gcc and icc, Intel C compiler,
+
+when you compile at sufficient
+optimization level, the
+
+compiler actually does
+this for you.
+
+It actually looks through
+the arrays.
+
+It actually realizes that you're
+setting all the members
+
+in the array to a constant, and
+it does that optimization
+
+for you by replacing it
+with a memset call.
+
+So just as a general question,
+why could it be advantageous
+
+for you to write the four loop
+as is, and have the compiler
+
+do the optimization for you?
+
+AUDIENCE: Because you later
+might add code in the loop.
+
+PROFESSOR: True.
+
+Any other reasons?
+
+PROFESSOR: I didn't
+hear question.
+
+PROFESSOR: You might want to
+add code that changes the
+
+behavior inside the loop.
+
+AUDIENCE: It's much more
+readable to have a for loop
+
+and you just read it, and I get
+that's what he's doing.
+
+PROFESSOR: Yes, indeed.
+
+Looking over some of your code
+submissions, it seems to be a
+
+non-trivial task of figuring out
+the size of something when
+
+you call malloc or memset.
+
+And actually, it sometimes is
+a non-trivial operation to
+
+figure out how big something
+is in bytes, especially for
+
+structs and things like that.
+
+So it actually is easier to
+let the compiler do the
+
+optimization for you, and you
+don't make any embarrassing
+
+mistakes in the process.
+
+So next question.
+
+So here you have a
+helper function.
+
+And in the after version,
+seems to do the
+
+same thing, does it?
+
+So who thinks this is a
+legal optimization?
+
+Half the class.
+
+Anyone think it's illegal?
+
+So yeah, it is legal.
+
+The only thing that I've done
+is that I've copy pasted
+
+basically the function body
+in the bottom example.
+
+And it's relatively easy to
+prove that or infer that the
+
+two do the same thing.
+
+So is it faster?
+
+How many people say yes?
+
+How many people say no?
+
+One person said no.
+
+Why is it not faster?
+
+AUDIENCE: I mean, I've said
+that it is the same speed,
+
+because so the only thing that
+would make it slower would be
+
+the-- you need to actually
+do like a compass switch.
+
+Because you need to call that
+function every time.
+
+But I think it could provide
+the concept for you-- like
+
+basically, it's a
+static function.
+
+It would inline it even though
+you don't have to declare it.
+
+PROFESSOR: OK.
+
+So if you recall the rules for
+the question, so basically we
+
+want you to interpret the
+code, as is, like a very
+
+literal interpretation as in--
+
+the point was raised that for
+this function call, what you
+
+actually want to do is assume
+that the compiler is setting
+
+up a function called by putting
+the arguments in the
+
+right register and jumping
+to the address of
+
+that function above.
+
+So for the case of this-- for
+the matter-- for the purpose
+
+of this question, yes, it's
+much faster to just do a
+
+multiply compared to setting up
+a call stack and tearing it
+
+down after the function
+is done.
+
+Now the next question is is this
+automatic, which was more
+
+or less answered.
+
+And that's yes.
+
+So at a sufficient optimization
+level which is
+
+-03 or -02 with dash f inline
+functions, the compiler will
+
+actually use a heuristic that it
+has for determining whether
+
+or not a function is a good
+candidate for inlining.
+
+And for good candidates, it'll
+do the inlining for you.
+
+Now the specific
+heuristics vary
+
+from compiler to compiler.
+
+But for this specific problem
+that we gave you, it's a prime
+
+candidate for inlining, because
+it's declared as
+
+static, which means it's
+local to this C file.
+
+And it does a very simple
+task, a one-liner, so it
+
+almost certainly will
+be inline for you.
+
+Any questions?
+
+Cool.
+
+So this one.
+
+Question?
+
+AUDIENCE: I don't get it.
+
+Could you explain again?
+
+I know I've asked this
+before, like what's
+
+static, the static function?
+
+And it's different
+than in Java?
+
+PROFESSOR: OK.
+
+So the question was what's a
+static function in C. And so
+
+in C, a static function means
+when you declare a function as
+
+static, it means that the
+function is local to the
+
+current file that you're work--
+the current module, the
+
+dot-o file, which is almost
+always your dot-c file.
+
+So like the function only exists
+within this dot-c file.
+
+A function in another
+dot-c file
+
+cannot call this function.
+
+So it basically allows the
+compiler to assume that
+
+there's no external effects on
+this function that are not
+
+within this file.
+
+Remember the compiler compiles
+object files one by one, and
+
+then the linker is the one that
+brings it all together.
+
+AUDIENCE: So the important thing
+is that it knows that it
+
+can just delete helper after
+it's gotten rid of it.
+
+PROFESSOR: Right, right.
+
+That's another good point.
+
+So in this case, after inlining,
+the compiler
+
+actually won't bother to put in
+the function helper inside
+
+the actual object file.
+
+So you save on my code space.
+
+Because the compiler knows
+that nowhere else this
+
+function can be called.
+
+AUDIENCE: What about
+static in C++?
+
+PROFESSOR: Static in C++ when
+used inside a class means that
+
+the function is a static
+member function.
+
+So it's a function that's tied
+to the class itself, rather
+
+than an object, and instance
+of the class.
+
+AUDIENCE: Just like Java.
+
+PROFESSOR: Just like Java.
+
+More questions?
+
+Cool.
+
+So back to this code.
+
+First of all, is anyone not
+familiar with the syntax or
+
+wants the syntax explained?
+
+OK, cool.
+
+So first question,
+is it legal?
+
+How may people say yes?
+
+Half the class.
+
+How many people say no.
+
+Roughly half the class.
+
+Well, I and the people grading
+the quiz will side with the
+
+people who say no, because down
+here when you're doing--
+
+this is the correct version
+of the XOR swap.
+
+I'm not trying to trick
+anyone there.
+
+But it turns out--
+
+well, I'd rather not assume
+that t, the arbitrary type
+
+name, has an operator XOR
+defined for it that has all
+
+the properties that you need
+in order for it to do this.
+
+Like the simplest example is
+if I pass in a double, this
+
+would not work.
+
+Double does not have an operator
+XOR defined for it.
+
+Some people look upset.
+
+AUDIENCE: [LAUGHTER]
+
+PROFESSOR: A list too
+would not have an
+
+XOR defined for it.
+
+Anyone disagree with me?
+
+That's not a challenge.
+
+So yeah, some of these questions
+require you to do a
+
+little bit of reasoning, like
+reasonable reasoning, as far
+
+as what to assume for the
+purposes of the question.
+
+So watch out for that.
+
+So in this case, it's not legal,
+so you don't have to
+
+answer the next two questions.
+
+So OK.
+
+So let's fix this.
+
+And by fix it, I mean
+not use templates.
+
+So now we're just operating
+on ints.
+
+And ints do have the proper
+operator XOR that has all the
+
+good properties that you want.
+
+Yes?
+
+AUDIENCE: What's the and
+notation of the variable.
+
+PROFESSOR: It's a reference.
+
+So it's a reference to it.
+
+Because you need references,
+because you actually want to
+
+swap the two items that
+are being called in.
+
+Right?
+
+AUDIENCE: Can you use
+like pointeres?
+
+PROFESSOR: Yes, so you can also
+use a pointer for it.
+
+Pointers and references, C
+will treat this use of
+
+references the same way as
+if you use pointers.
+
+So references are
+syntactic sugar.
+
+And what it basically allows you
+to do is write code that
+
+looks like you're operating on
+standard intervals, standard
+
+integers, but in fact that it's
+a pointer to the value
+
+that the name of the variable
+that's passed in here.
+
+Otherwise this code would be
+riddled with a bunch of stars.
+
+Now is this legal?
+
+How many people say yes?
+
+Most of the class.
+
+How many people say no?
+
+One person.
+
+Yes?
+
+AUDIENCE: If A and B are
+the same variable,
+
+you set it to zero.
+
+PROFESSOR: Yes, exactly.
+
+The XOR law has a nasty side
+effect where you want to make
+
+sure that A and B are not
+the same variable.
+
+Not they don't contain the
+same-- they can contain the
+
+same value in different
+variables, but they can't be
+
+the same variable or the
+same register or
+
+the same memory location.
+
+Otherwise, when you do A equals
+Ax or B, that's 0.
+
+And now both A and
+B point to 0.
+
+And there's nothing you can do
+to get your old value back.
+
+AUDIENCE: Can you check
+for equivalence of
+
+recordkeeping in C++.
+
+PROFESSOR: Indeed, you can.
+
+If you take the address of the
+reference, it gives you the
+
+address of the original value.
+
+So this would be the proper
+way, I guess, of
+
+doing an XOR swap.
+
+So now that we've gotten over
+all the trick questions, is
+
+this actually faster?
+
+How many people say yes?
+
+One, two, three, four.
+
+How many people say no?
+
+Cool.
+
+Most of the class.
+
+So this is another example
+of a gray area question.
+
+So in this class, we primarily
+talk about the cloud machines,
+
+as far as the performance
+analysis that we've done.
+
+So on the cloud machines, and
+this was mentioned in
+
+Charles's bit hacks lecture
+which was, well, the second
+
+lecture in the course.
+
+This trick is not faster
+on the cloud machines.
+
+Because what you end up doing
+is you create a lot of
+
+dependencies between these
+operands, so that the pipeline
+
+must execute these one
+by one serially.
+
+So you introduce a lot
+of delays by that.
+
+And plus now that we actually
+want you to write a correct
+
+program, you have to
+do this check, and
+
+that's an extra branch.
+
+And finally these XORs have to
+be done by the ALU, and up to
+
+five execution ports.
+
+Only three of them are ALUs.
+
+The other two can do memory
+operations just fine.
+
+So it turns out that for a
+combination of these reasons,
+
+this version indeed with the
+temporary register actually
+
+does run faster.
+
+Any questions?
+
+Yes.
+
+AUDIENCE: For branches, we
+assume advanced features, like
+
+it will preload the exceptions
+and only invalidates the thing
+
+when certain branches fail.
+
+PROFESSOR: Sure, you can assume
+cool properties about
+
+the chip, such as speculative
+execution,
+
+prefetching, and so on.
+
+But the problem is those tricks
+are fine when you're
+
+doing things sparsely as in
+you're sometimes doing work
+
+and other times not
+doing work.
+
+But like speculative execution,
+like when you
+
+execute both sides of a branch,
+you're using more or
+
+less double your execution
+or resources.
+
+And if you have all processors
+running some intense piece of
+
+code that's doing swapping,
+you don't have any extra
+
+resources to dedicate towards
+running code that
+
+might not be useful.
+
+Any other questions?
+
+Cool.
+
+So finally, I got tired
+of making slides.
+
+Well, actually that's
+not true.
+
+It's more I'd rather concentrate
+the slides on
+
+things that I think are more
+useful than other things, as
+
+far as per preparation
+for your quiz.
+
+All your time is valuable.
+
+And so there's other topics
+that are fair game for the
+
+quiz, because they've been
+mentioned in lectures up to
+
+this point.
+
+But I haven't prepared
+any slides on them.
+
+And the fractal trees were
+covered by the guest lecture
+
+by Bradley.
+
+And the slides are up.
+
+I suggest familiarizing yourself
+with the basic
+
+workings of how the data
+structure that
+
+he described works.
+
+And lock free data structures
+were covered on your take home
+
+P set, and also in a lecture.
+
+So be prepared to
+answer potential
+
+questions about that.
+
+And then finally the mechanism
+behind the Cilk runtime, the
+
+work stealing scheduler, how
+it's implemented on the Linux
+
+side, and also the basics of
+what a Cilk hyperobject is,
+
+what a Cilk hyperobject
+has to have.
+
+Advantages and disadvantages
+of using them and so on.
+
+Yes.
+
+AUDIENCE: Are the grades
+for the P-set out?
+
+PROFESSOR: No, they
+are not out yet.
+
+AUDIENCE: Are there solutions
+for the P-set?
+
+PROFESSOR: Not yet.
+
+But I believe we have something
+
+prepared for that, right?
+
+Somewhat?
+
+Yeah, it's somewhat prepared.
+
+If you have any questions about
+like questions on the
+
+pset that you want answer to,
+feel free to stop by office
+
+hours or email us and
+we can help you.
+
+Yeah, apologies for not
+getting that P set
+
+back to you in time.
+
+Any other questions relating
+to the quiz.
+
+It's really all the material
+I have as far as reviewing.
+
+Yes?
+
+AUDIENCE: Are you going to
+put these slides up?
+
+AUDIENCE: Yeah, I'll
+put these slides up
+
+right after the lecture.
+
+So as far as a general notes,
+I guess you guys turned in
+
+your finals yesterday, and you
+guys have a design report that
+
+you also turned in.
+
+Your POSSE members should have
+contacted you by now, as far
+
+as scheduling a design
+review session.
+
+Since this project is actually
+due on next Thursday, it might
+
+be a good idea to get this done
+by the end of the week.
+
+Otherwise, the design
+review won't be
+
+a very useful process.
+
+AUDIENCE: There are a couple of
+students without a mentor
+
+right now here.
+
+We are fixing that.
+
+PROFESSOR: Right.
+
+There's a couple of students
+caught in limbo right now.
+
+Sorry about that.
+
+PROFESSOR: If you were--
+previously dropped on Stellar,
+
+send us an email.
+
+If you haven't been to drop
+through this course, there are
+
+no longer drops allowed.
+
+Yeah,
+
+AUDIENCE: So it's your
+responsibility.
+
+I'm going to put
+on my mean hat.
+
+It's your responsibility to
+schedule a meeting with your
+
+POSSE member, and make sure
+that it happens by
+
+the end of the week.
+
+And if it doesn't look like
+it's going to happen, or
+
+you're having difficulties
+getting in touch with your
+
+mentor, or you don't have one
+yet, please drop us an email
+
+or come by office hours and
+make sure that we know.
+
+All right.
+
+That's it.
\ No newline at end of file
diff --git a/bEF_PpP6eCM.txt b/bEF_PpP6eCM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9b43b437e9043e1c008d0786bb037c46faf337d5
--- /dev/null
+++ b/bEF_PpP6eCM.txt
@@ -0,0 +1,1835 @@
+align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+given that you have a valuation model
+
+ align:start position:0%
+given that you have a valuation model
+ 
+
+ align:start position:0%
+given that you have a valuation model
+given that you have uncertainties
+
+ align:start position:0%
+given that you have uncertainties
+ 
+
+ align:start position:0%
+given that you have uncertainties
+you can see what the outcome the
+
+ align:start position:0%
+you can see what the outcome the
+ 
+
+ align:start position:0%
+you can see what the outcome the
+performance of your system is
+
+ align:start position:0%
+performance of your system is
+ 
+
+ align:start position:0%
+performance of your system is
+when there's no flexibility simply
+
+ align:start position:0%
+when there's no flexibility simply
+ 
+
+ align:start position:0%
+when there's no flexibility simply
+saying okay if we build this plant
+
+ align:start position:0%
+saying okay if we build this plant
+ 
+
+ align:start position:0%
+saying okay if we build this plant
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then see what the revenues are
+
+ align:start position:0%
+then see what the revenues are
+ 
+
+ align:start position:0%
+then see what the revenues are
+we can think about well our production
+
+ align:start position:0%
+we can think about well our production
+ 
+
+ align:start position:0%
+we can think about well our production
+may go up and down because of mechanical
+
+ align:start position:0%
+may go up and down because of mechanical
+ 
+
+ align:start position:0%
+may go up and down because of mechanical
+problems or whatever the demand may go
+
+ align:start position:0%
+problems or whatever the demand may go
+ 
+
+ align:start position:0%
+problems or whatever the demand may go
+up and down
+
+ align:start position:0%
+up and down
+ 
+
+ align:start position:0%
+up and down
+depending upon competition or whatever
+
+ align:start position:0%
+depending upon competition or whatever
+ 
+
+ align:start position:0%
+depending upon competition or whatever
+and all together we may have the
+
+ align:start position:0%
+and all together we may have the
+ 
+
+ align:start position:0%
+and all together we may have the
+following results in terms of benefits
+
+ align:start position:0%
+following results in terms of benefits
+ 
+
+ align:start position:0%
+following results in terms of benefits
+and costs
+
+ align:start position:0%
+and costs
+ 
+
+ align:start position:0%
+and costs
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you will to do this you generate a
+
+ align:start position:0%
+you will to do this you generate a
+ 
+
+ align:start position:0%
+you will to do this you generate a
+dynamic scenario and apply it to the
+
+ align:start position:0%
+dynamic scenario and apply it to the
+ 
+
+ align:start position:0%
+dynamic scenario and apply it to the
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+period by period that is the demand
+
+ align:start position:0%
+period by period that is the demand
+ 
+
+ align:start position:0%
+period by period that is the demand
+starts at one level goes up goes up goes
+
+ align:start position:0%
+starts at one level goes up goes up goes
+ 
+
+ align:start position:0%
+starts at one level goes up goes up goes
+down up down whatever and you do that
+
+ align:start position:0%
+down up down whatever and you do that
+ 
+
+ align:start position:0%
+down up down whatever and you do that
+for all the different demand
+
+ align:start position:0%
+for all the different demand
+ 
+
+ align:start position:0%
+for all the different demand
+possibilities that you simulate and then
+
+ align:start position:0%
+possibilities that you simulate and then
+ 
+
+ align:start position:0%
+possibilities that you simulate and then
+you can think about that would also
+
+ align:start position:0%
+you can think about that would also
+ 
+
+ align:start position:0%
+you can think about that would also
+happen in terms of production
+
+ align:start position:0%
+happen in terms of production
+ 
+
+ align:start position:0%
+happen in terms of production
+possibilities
+
+ align:start position:0%
+possibilities
+ 
+
+ align:start position:0%
+possibilities
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for each of those scenarios
+
+ align:start position:0%
+for each of those scenarios
+ 
+
+ align:start position:0%
+for each of those scenarios
+combination of the variables you'll get
+
+ align:start position:0%
+combination of the variables you'll get
+ 
+
+ align:start position:0%
+combination of the variables you'll get
+a performance measure for example the
+
+ align:start position:0%
+a performance measure for example the
+ 
+
+ align:start position:0%
+a performance measure for example the
+net present value for that
+
+ align:start position:0%
+net present value for that
+ 
+
+ align:start position:0%
+net present value for that
+you go through the simulation we'll go
+
+ align:start position:0%
+you go through the simulation we'll go
+ 
+
+ align:start position:0%
+you go through the simulation we'll go
+through this process
+
+ align:start position:0%
+through this process
+ 
+
+ align:start position:0%
+through this process
+2 000 examples is a standard number so a
+
+ align:start position:0%
+2 000 examples is a standard number so a
+ 
+
+ align:start position:0%
+2 000 examples is a standard number so a
+lot of people use there's a way of
+
+ align:start position:0%
+lot of people use there's a way of
+ 
+
+ align:start position:0%
+lot of people use there's a way of
+saying of determining whether you think
+
+ align:start position:0%
+saying of determining whether you think
+ 
+
+ align:start position:0%
+saying of determining whether you think
+2 000 is better than 1 000 or better
+
+ align:start position:0%
+2 000 is better than 1 000 or better
+ 
+
+ align:start position:0%
+2 000 is better than 1 000 or better
+than 10 000 or what's the right balance
+
+ align:start position:0%
+than 10 000 or what's the right balance
+ 
+
+ align:start position:0%
+than 10 000 or what's the right balance
+we won't get into that for the moment
+
+ align:start position:0%
+we won't get into that for the moment
+ 
+
+ align:start position:0%
+we won't get into that for the moment
+but what i'm saying is
+
+ align:start position:0%
+but what i'm saying is
+ 
+
+ align:start position:0%
+but what i'm saying is
+that doing 2000 is a
+
+ align:start position:0%
+that doing 2000 is a
+ 
+
+ align:start position:0%
+that doing 2000 is a
+reasonable first order approximation at
+
+ align:start position:0%
+reasonable first order approximation at
+ 
+
+ align:start position:0%
+reasonable first order approximation at
+least
+
+ align:start position:0%
+least
+ 
+
+ align:start position:0%
+least
+so that you have 2 000
+
+ align:start position:0%
+so that you have 2 000
+ 
+
+ align:start position:0%
+so that you have 2 000
+measures of performance such as the
+
+ align:start position:0%
+measures of performance such as the
+ 
+
+ align:start position:0%
+measures of performance such as the
+present value
+
+ align:start position:0%
+present value
+ 
+
+ align:start position:0%
+present value
+and you can calculate the averages
+
+ align:start position:0%
+and you can calculate the averages
+ 
+
+ align:start position:0%
+and you can calculate the averages
+the in particular the e and b the
+
+ align:start position:0%
+the in particular the e and b the
+ 
+
+ align:start position:0%
+the in particular the e and b the
+expected
+
+ align:start position:0%
+expected
+ 
+
+ align:start position:0%
+expected
+the average and you could then think
+
+ align:start position:0%
+the average and you could then think
+ 
+
+ align:start position:0%
+the average and you could then think
+about what the extremes are and so on
+
+ align:start position:0%
+about what the extremes are and so on
+ 
+
+ align:start position:0%
+about what the extremes are and so on
+you can plot the distribution so that's
+
+ align:start position:0%
+you can plot the distribution so that's
+ 
+
+ align:start position:0%
+you can plot the distribution so that's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the basic result of a simulation
+
+ align:start position:0%
+the basic result of a simulation
+ 
+
+ align:start position:0%
+the basic result of a simulation
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+it's important to recognize
+
+ align:start position:0%
+it's important to recognize
+ 
+
+ align:start position:0%
+it's important to recognize
+the nature of the product from the
+
+ align:start position:0%
+the nature of the product from the
+ 
+
+ align:start position:0%
+the nature of the product from the
+simulation analysis
+
+ align:start position:0%
+simulation analysis
+ 
+
+ align:start position:0%
+simulation analysis
+a traditional discount cash flow
+
+ align:start position:0%
+a traditional discount cash flow
+ 
+
+ align:start position:0%
+a traditional discount cash flow
+spreadsheet analysis
+
+ align:start position:0%
+spreadsheet analysis
+ 
+
+ align:start position:0%
+spreadsheet analysis
+for the use for net present value is
+
+ align:start position:0%
+for the use for net present value is
+ 
+
+ align:start position:0%
+for the use for net present value is
+numbers in and numbers out
+
+ align:start position:0%
+numbers in and numbers out
+ 
+
+ align:start position:0%
+numbers in and numbers out
+you use your best estimate for
+
+ align:start position:0%
+you use your best estimate for
+ 
+
+ align:start position:0%
+you use your best estimate for
+investment cost production sales etc
+
+ align:start position:0%
+investment cost production sales etc
+ 
+
+ align:start position:0%
+investment cost production sales etc
+you put the numbers in you run the
+
+ align:start position:0%
+you put the numbers in you run the
+ 
+
+ align:start position:0%
+you put the numbers in you run the
+machine you get a number the net present
+
+ align:start position:0%
+machine you get a number the net present
+ 
+
+ align:start position:0%
+machine you get a number the net present
+value is such they're turning on
+
+ align:start position:0%
+value is such they're turning on
+ 
+
+ align:start position:0%
+value is such they're turning on
+investment it's such
+
+ align:start position:0%
+investment it's such
+ 
+
+ align:start position:0%
+investment it's such
+in a simulation and uncertainty analysis
+
+ align:start position:0%
+in a simulation and uncertainty analysis
+ 
+
+ align:start position:0%
+in a simulation and uncertainty analysis
+you don't put a number in you put in a
+
+ align:start position:0%
+you don't put a number in you put in a
+ 
+
+ align:start position:0%
+you don't put a number in you put in a
+shape and a distribution
+
+ align:start position:0%
+shape and a distribution
+ 
+
+ align:start position:0%
+shape and a distribution
+and you get a distribution out
+
+ align:start position:0%
+and you get a distribution out
+ 
+
+ align:start position:0%
+and you get a distribution out
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the target curve is a generic name to
+
+ align:start position:0%
+the target curve is a generic name to
+ 
+
+ align:start position:0%
+the target curve is a generic name to
+describe what that distribution is
+
+ align:start position:0%
+describe what that distribution is
+ 
+
+ align:start position:0%
+describe what that distribution is
+typically it's either of two shapes
+
+ align:start position:0%
+typically it's either of two shapes
+ 
+
+ align:start position:0%
+typically it's either of two shapes
+one is the one i personally prefer but
+
+ align:start position:0%
+one is the one i personally prefer but
+ 
+
+ align:start position:0%
+one is the one i personally prefer but
+it's a matter of choice
+
+ align:start position:0%
+it's a matter of choice
+ 
+
+ align:start position:0%
+it's a matter of choice
+uh is a cumulative distribution
+
+ align:start position:0%
+uh is a cumulative distribution
+ 
+
+ align:start position:0%
+uh is a cumulative distribution
+it shows from
+
+ align:start position:0%
+it shows from
+ 
+
+ align:start position:0%
+it shows from
+there may be some chances things are
+
+ align:start position:0%
+there may be some chances things are
+ 
+
+ align:start position:0%
+there may be some chances things are
+really bad
+
+ align:start position:0%
+really bad
+ 
+
+ align:start position:0%
+really bad
+more chances of things are better and
+
+ align:start position:0%
+more chances of things are better and
+ 
+
+ align:start position:0%
+more chances of things are better and
+etc it goes on up a cumulative
+
+ align:start position:0%
+etc it goes on up a cumulative
+ 
+
+ align:start position:0%
+etc it goes on up a cumulative
+distribution to
+
+ align:start position:0%
+distribution to
+ 
+
+ align:start position:0%
+distribution to
+uh there's nothing that's not likely to
+
+ align:start position:0%
+uh there's nothing that's not likely to
+ 
+
+ align:start position:0%
+uh there's nothing that's not likely to
+be any better than a particular maxim
+
+ align:start position:0%
+be any better than a particular maxim
+ 
+
+ align:start position:0%
+be any better than a particular maxim
+and but you could also show it as a
+
+ align:start position:0%
+and but you could also show it as a
+ 
+
+ align:start position:0%
+and but you could also show it as a
+distribution sort of think of it as a
+
+ align:start position:0%
+distribution sort of think of it as a
+ 
+
+ align:start position:0%
+distribution sort of think of it as a
+normal shape or something
+
+ align:start position:0%
+normal shape or something
+ 
+
+ align:start position:0%
+normal shape or something
+it could be or it could be bimodal but
+
+ align:start position:0%
+it could be or it could be bimodal but
+ 
+
+ align:start position:0%
+it could be or it could be bimodal but
+the shape of a frequency or the
+
+ align:start position:0%
+the shape of a frequency or the
+ 
+
+ align:start position:0%
+the shape of a frequency or the
+cumulative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um how do you create the target curve or
+
+ align:start position:0%
+um how do you create the target curve or
+ 
+
+ align:start position:0%
+um how do you create the target curve or
+how does the process create the target
+
+ align:start position:0%
+how does the process create the target
+ 
+
+ align:start position:0%
+how does the process create the target
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the simulation produces many trials
+
+ align:start position:0%
+so the simulation produces many trials
+ 
+
+ align:start position:0%
+so the simulation produces many trials
+now the probability of each scenario
+
+ align:start position:0%
+now the probability of each scenario
+ 
+
+ align:start position:0%
+now the probability of each scenario
+when you've done the simulation
+
+ align:start position:0%
+when you've done the simulation
+ 
+
+ align:start position:0%
+when you've done the simulation
+correctly the way it should be done
+
+ align:start position:0%
+correctly the way it should be done
+ 
+
+ align:start position:0%
+correctly the way it should be done
+is that each one is equally probable why
+
+ align:start position:0%
+is that each one is equally probable why
+ 
+
+ align:start position:0%
+is that each one is equally probable why
+because you sampled from the underlying
+
+ align:start position:0%
+because you sampled from the underlying
+ 
+
+ align:start position:0%
+because you sampled from the underlying
+distribution according to their
+
+ align:start position:0%
+distribution according to their
+ 
+
+ align:start position:0%
+distribution according to their
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+high value was four times more probable
+
+ align:start position:0%
+high value was four times more probable
+ 
+
+ align:start position:0%
+high value was four times more probable
+than the low value you sampled the high
+
+ align:start position:0%
+than the low value you sampled the high
+ 
+
+ align:start position:0%
+than the low value you sampled the high
+value four times and the low value one
+
+ align:start position:0%
+value four times and the low value one
+ 
+
+ align:start position:0%
+value four times and the low value one
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+you've sampled it from the uh
+
+ align:start position:0%
+you've sampled it from the uh
+ 
+
+ align:start position:0%
+you've sampled it from the uh
+according to the distribution so the
+
+ align:start position:0%
+according to the distribution so the
+ 
+
+ align:start position:0%
+according to the distribution so the
+consequence is that each of your 2000 or
+
+ align:start position:0%
+consequence is that each of your 2000 or
+ 
+
+ align:start position:0%
+consequence is that each of your 2000 or
+however many
+
+ align:start position:0%
+however many
+ 
+
+ align:start position:0%
+however many
+simulations have the same probability
+
+ align:start position:0%
+simulations have the same probability
+ 
+
+ align:start position:0%
+simulations have the same probability
+given that giving you 2000 results the
+
+ align:start position:0%
+given that giving you 2000 results the
+ 
+
+ align:start position:0%
+given that giving you 2000 results the
+way that
+
+ align:start position:0%
+way that
+ 
+
+ align:start position:0%
+way that
+it proceeded mechanically is to bend the
+
+ align:start position:0%
+it proceeded mechanically is to bend the
+ 
+
+ align:start position:0%
+it proceeded mechanically is to bend the
+results but as you look at outcome
+
+ align:start position:0%
+results but as you look at outcome
+ 
+
+ align:start position:0%
+results but as you look at outcome
+ranges the first one percent two percent
+
+ align:start position:0%
+ranges the first one percent two percent
+ 
+
+ align:start position:0%
+ranges the first one percent two percent
+three you know maybe a hundred times 100
+
+ align:start position:0%
+three you know maybe a hundred times 100
+ 
+
+ align:start position:0%
+three you know maybe a hundred times 100
+bins
+
+ align:start position:0%
+bins
+ 
+
+ align:start position:0%
+bins
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that there so the number of samples in
+
+ align:start position:0%
+that there so the number of samples in
+ 
+
+ align:start position:0%
+that there so the number of samples in
+each bin is that frequency and that
+
+ align:start position:0%
+each bin is that frequency and that
+ 
+
+ align:start position:0%
+each bin is that frequency and that
+creates a histogram if you want or if
+
+ align:start position:0%
+creates a histogram if you want or if
+ 
+
+ align:start position:0%
+creates a histogram if you want or if
+it's if you have enough ones
+
+ align:start position:0%
+it's if you have enough ones
+ 
+
+ align:start position:0%
+it's if you have enough ones
+it is no longer a bar chart but it's a
+
+ align:start position:0%
+it is no longer a bar chart but it's a
+ 
+
+ align:start position:0%
+it is no longer a bar chart but it's a
+and that can easily be
+
+ align:start position:0%
+and that can easily be
+ 
+
+ align:start position:0%
+and that can easily be
+calculated into a cumulative
+
+ align:start position:0%
+calculated into a cumulative
+ 
+
+ align:start position:0%
+calculated into a cumulative
+distribution so this entire process is
+
+ align:start position:0%
+distribution so this entire process is
+ 
+
+ align:start position:0%
+distribution so this entire process is
+easily automated and the garage case
+
+ align:start position:0%
+easily automated and the garage case
+ 
+
+ align:start position:0%
+easily automated and the garage case
+template which is a very
+
+ align:start position:0%
+template which is a very
+ 
+
+ align:start position:0%
+template which is a very
+trivial um spreadsheet but it does that
+
+ align:start position:0%
+trivial um spreadsheet but it does that
+ 
+
+ align:start position:0%
+trivial um spreadsheet but it does that
+for you so if you wanted to do it
+
+ align:start position:0%
+for you so if you wanted to do it
+ 
+
+ align:start position:0%
+for you so if you wanted to do it
+yourself you can do it but it's not
+
+ align:start position:0%
+yourself you can do it but it's not
+ 
+
+ align:start position:0%
+yourself you can do it but it's not
+particularly unnecessary it's all done
+
+ align:start position:0%
+particularly unnecessary it's all done
+ 
+
+ align:start position:0%
+particularly unnecessary it's all done
+for you for your projects if you're
+
+ align:start position:0%
+for you for your projects if you're
+ 
+
+ align:start position:0%
+for you for your projects if you're
+using it or
+
+ align:start position:0%
+using it or
+ 
+
+ align:start position:0%
+using it or
+after class or
+
+ align:start position:0%
+after class or
+ 
+
+ align:start position:0%
+after class or
+later times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here is an example for of it that
+
+ align:start position:0%
+so here is an example for of it that
+ 
+
+ align:start position:0%
+so here is an example for of it that
+there's a
+
+ align:start position:0%
+there's a
+ 
+
+ align:start position:0%
+there's a
+all these uh individual bins have been
+
+ align:start position:0%
+all these uh individual bins have been
+ 
+
+ align:start position:0%
+all these uh individual bins have been
+put together and here is the
+
+ align:start position:0%
+put together and here is the
+ 
+
+ align:start position:0%
+put together and here is the
+on their probability of each and here is
+
+ align:start position:0%
+on their probability of each and here is
+ 
+
+ align:start position:0%
+on their probability of each and here is
+the cumulative distribution the target
+
+ align:start position:0%
+the cumulative distribution the target
+ 
+
+ align:start position:0%
+the cumulative distribution the target
+curve a target curve
+
+ align:start position:0%
+curve a target curve
+ 
+
+ align:start position:0%
+curve a target curve
+um by the way just to make it clear here
+
+ align:start position:0%
+um by the way just to make it clear here
+ 
+
+ align:start position:0%
+um by the way just to make it clear here
+so this is the
+
+ align:start position:0%
+so this is the
+ 
+
+ align:start position:0%
+so this is the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+going from 0 to a hundred percent so
+
+ align:start position:0%
+going from 0 to a hundred percent so
+ 
+
+ align:start position:0%
+going from 0 to a hundred percent so
+there's nothing worse than this
+
+ align:start position:0%
+there's nothing worse than this
+ 
+
+ align:start position:0%
+there's nothing worse than this
+particular number in your distribution
+
+ align:start position:0%
+particular number in your distribution
+ 
+
+ align:start position:0%
+particular number in your distribution
+that's the lowest one this is the
+
+ align:start position:0%
+that's the lowest one this is the
+ 
+
+ align:start position:0%
+that's the lowest one this is the
+highest 100
+
+ align:start position:0%
+highest 100
+ 
+
+ align:start position:0%
+highest 100
+and this one for example here is
+
+ align:start position:0%
+and this one for example here is
+ 
+
+ align:start position:0%
+and this one for example here is
+that at the zero level for some reason
+
+ align:start position:0%
+that at the zero level for some reason
+ 
+
+ align:start position:0%
+that at the zero level for some reason
+uh it's 50
+
+ align:start position:0%
+uh it's 50
+ 
+
+ align:start position:0%
+uh it's 50
+but it doesn't have to be that way but
+
+ align:start position:0%
+but it doesn't have to be that way but
+ 
+
+ align:start position:0%
+but it doesn't have to be that way but
+uh it is in this in this particular case
+
+ align:start position:0%
+uh it is in this in this particular case
+ 
+
+ align:start position:0%
+uh it is in this in this particular case
+so this is an example of a cumulative
+
+ align:start position:0%
+so this is an example of a cumulative
+ 
+
+ align:start position:0%
+so this is an example of a cumulative
+distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the interesting aspect is how do you
+
+ align:start position:0%
+now the interesting aspect is how do you
+ 
+
+ align:start position:0%
+now the interesting aspect is how do you
+look at flexibility
+
+ align:start position:0%
+look at flexibility
+ 
+
+ align:start position:0%
+look at flexibility
+so the first question is of course well
+
+ align:start position:0%
+so the first question is of course well
+ 
+
+ align:start position:0%
+so the first question is of course well
+what flexibility what are we talking
+
+ align:start position:0%
+what flexibility what are we talking
+ 
+
+ align:start position:0%
+what flexibility what are we talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+and the answer to that in general is the
+
+ align:start position:0%
+and the answer to that in general is the
+ 
+
+ align:start position:0%
+and the answer to that in general is the
+flexibility
+
+ align:start position:0%
+flexibility
+ 
+
+ align:start position:0%
+flexibility
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+has the most impact regarding the
+
+ align:start position:0%
+has the most impact regarding the
+ 
+
+ align:start position:0%
+has the most impact regarding the
+uncertainties and how if you had a
+
+ align:start position:0%
+uncertainties and how if you had a
+ 
+
+ align:start position:0%
+uncertainties and how if you had a
+really bad case uh what would you do
+
+ align:start position:0%
+really bad case uh what would you do
+ 
+
+ align:start position:0%
+really bad case uh what would you do
+about it and what kind of flexibility
+
+ align:start position:0%
+about it and what kind of flexibility
+ 
+
+ align:start position:0%
+about it and what kind of flexibility
+would help you in the would be most
+
+ align:start position:0%
+would help you in the would be most
+ 
+
+ align:start position:0%
+would help you in the would be most
+impactful
+
+ align:start position:0%
+impactful
+ 
+
+ align:start position:0%
+impactful
+in the case of the garage case
+
+ align:start position:0%
+in the case of the garage case
+ 
+
+ align:start position:0%
+in the case of the garage case
+the uncertainty is in the demand so what
+
+ align:start position:0%
+the uncertainty is in the demand so what
+ 
+
+ align:start position:0%
+the uncertainty is in the demand so what
+kind of flexibility is the capacity meat
+
+ align:start position:0%
+kind of flexibility is the capacity meat
+ 
+
+ align:start position:0%
+kind of flexibility is the capacity meat
+to demand so it's the number of levels
+
+ align:start position:0%
+to demand so it's the number of levels
+ 
+
+ align:start position:0%
+to demand so it's the number of levels
+in the garage
+
+ align:start position:0%
+in the garage
+ 
+
+ align:start position:0%
+in the garage
+in a particular case you'd have to think
+
+ align:start position:0%
+in a particular case you'd have to think
+ 
+
+ align:start position:0%
+in a particular case you'd have to think
+about that for your problem of what kind
+
+ align:start position:0%
+about that for your problem of what kind
+ 
+
+ align:start position:0%
+about that for your problem of what kind
+of flexibility might be most impactful
+
+ align:start position:0%
+of flexibility might be most impactful
+ 
+
+ align:start position:0%
+of flexibility might be most impactful
+and for those of you who are doing
+
+ align:start position:0%
+and for those of you who are doing
+ 
+
+ align:start position:0%
+and for those of you who are doing
+projects we'll look at that uh in detail
+
+ align:start position:0%
+projects we'll look at that uh in detail
+ 
+
+ align:start position:0%
+projects we'll look at that uh in detail
+that is one of the questions that you'll
+
+ align:start position:0%
+that is one of the questions that you'll
+ 
+
+ align:start position:0%
+that is one of the questions that you'll
+want to wrestle with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+then the thing is okay i have this
+
+ align:start position:0%
+then the thing is okay i have this
+ 
+
+ align:start position:0%
+then the thing is okay i have this
+flexibility for example of building an
+
+ align:start position:0%
+flexibility for example of building an
+ 
+
+ align:start position:0%
+flexibility for example of building an
+extra floor on my garage
+
+ align:start position:0%
+extra floor on my garage
+ 
+
+ align:start position:0%
+extra floor on my garage
+when should i exercise it should i do it
+
+ align:start position:0%
+when should i exercise it should i do it
+ 
+
+ align:start position:0%
+when should i exercise it should i do it
+right away should i do an anticipation
+
+ align:start position:0%
+right away should i do an anticipation
+ 
+
+ align:start position:0%
+right away should i do an anticipation
+of future demand should i wait until
+
+ align:start position:0%
+of future demand should i wait until
+ 
+
+ align:start position:0%
+of future demand should i wait until
+demand is there
+
+ align:start position:0%
+demand is there
+ 
+
+ align:start position:0%
+demand is there
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in simulation we can't do this we don't
+
+ align:start position:0%
+in simulation we can't do this we don't
+ 
+
+ align:start position:0%
+in simulation we can't do this we don't
+have a way of calculating when's the
+
+ align:start position:0%
+have a way of calculating when's the
+ 
+
+ align:start position:0%
+have a way of calculating when's the
+optimal time
+
+ align:start position:0%
+optimal time
+ 
+
+ align:start position:0%
+optimal time
+there are some methods for dealing with
+
+ align:start position:0%
+there are some methods for dealing with
+ 
+
+ align:start position:0%
+there are some methods for dealing with
+that such as dynamic programming
+
+ align:start position:0%
+that such as dynamic programming
+ 
+
+ align:start position:0%
+that such as dynamic programming
+but it implies dynamic programming
+
+ align:start position:0%
+but it implies dynamic programming
+ 
+
+ align:start position:0%
+but it implies dynamic programming
+implies there's nothing you can do about
+
+ align:start position:0%
+implies there's nothing you can do about
+ 
+
+ align:start position:0%
+implies there's nothing you can do about
+it to affect future aspects this is the
+
+ align:start position:0%
+it to affect future aspects this is the
+ 
+
+ align:start position:0%
+it to affect future aspects this is the
+so-called path independence function and
+
+ align:start position:0%
+so-called path independence function and
+ 
+
+ align:start position:0%
+so-called path independence function and
+the whole point of having flexibility is
+
+ align:start position:0%
+the whole point of having flexibility is
+ 
+
+ align:start position:0%
+the whole point of having flexibility is
+precisely that you can do things so that
+
+ align:start position:0%
+precisely that you can do things so that
+ 
+
+ align:start position:0%
+precisely that you can do things so that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+powerful method
+
+ align:start position:0%
+powerful method
+ 
+
+ align:start position:0%
+powerful method
+does not work for for us so
+
+ align:start position:0%
+does not work for for us so
+ 
+
+ align:start position:0%
+does not work for for us so
+and there's so many paths i mean if we
+
+ align:start position:0%
+and there's so many paths i mean if we
+ 
+
+ align:start position:0%
+and there's so many paths i mean if we
+think about 2 000 samples of what may
+
+ align:start position:0%
+think about 2 000 samples of what may
+ 
+
+ align:start position:0%
+think about 2 000 samples of what may
+happen that's only 2 000 samples of what
+
+ align:start position:0%
+happen that's only 2 000 samples of what
+ 
+
+ align:start position:0%
+happen that's only 2 000 samples of what
+may be a million possibility of past as
+
+ align:start position:0%
+may be a million possibility of past as
+ 
+
+ align:start position:0%
+may be a million possibility of past as
+a combination of the different
+
+ align:start position:0%
+a combination of the different
+ 
+
+ align:start position:0%
+a combination of the different
+probabilities at different times uh
+
+ align:start position:0%
+probabilities at different times uh
+ 
+
+ align:start position:0%
+probabilities at different times uh
+of prices and quantities and so forth
+
+ align:start position:0%
+of prices and quantities and so forth
+ 
+
+ align:start position:0%
+of prices and quantities and so forth
+it's much too large to be searched
+
+ align:start position:0%
+it's much too large to be searched
+ 
+
+ align:start position:0%
+it's much too large to be searched
+so the procedure is to define
+
+ align:start position:0%
+so the procedure is to define
+ 
+
+ align:start position:0%
+so the procedure is to define
+what we know as decision rules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/d4skxu7MpFI.txt b/d4skxu7MpFI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3bbd9d9d7e7db240afc743cde5fa149bc15ec7fc
--- /dev/null
+++ b/d4skxu7MpFI.txt
@@ -0,0 +1,1971 @@
+align:start position:0%
+ 
+we were faced last time with the
+
+ align:start position:0%
+we were faced last time with the
+ 
+
+ align:start position:0%
+we were faced last time with the
+question of interpretation of the
+
+ align:start position:0%
+question of interpretation of the
+ 
+
+ align:start position:0%
+question of interpretation of the
+shrenger wavefunction and so to recap or
+
+ align:start position:0%
+shrenger wavefunction and so to recap or
+ 
+
+ align:start position:0%
+shrenger wavefunction and so to recap or
+the main ideas that were looking at we
+
+ align:start position:0%
+the main ideas that were looking at we
+ 
+
+ align:start position:0%
+the main ideas that were looking at we
+derived the Schrodinger equation
+
+ align:start position:0%
+derived the Schrodinger equation
+ 
+
+ align:start position:0%
+derived the Schrodinger equation
+basically derived it from simple ideas
+
+ align:start position:0%
+basically derived it from simple ideas
+ 
+
+ align:start position:0%
+basically derived it from simple ideas
+having operators energy operator
+
+ align:start position:0%
+having operators energy operator
+ 
+
+ align:start position:0%
+having operators energy operator
+momentum operator and exploring how the
+
+ align:start position:0%
+momentum operator and exploring how the
+ 
+
+ align:start position:0%
+momentum operator and exploring how the
+de Broglie wavelength associated to a
+
+ align:start position:0%
+de Broglie wavelength associated to a
+ 
+
+ align:start position:0%
+de Broglie wavelength associated to a
+particle would be a wave that would
+
+ align:start position:0%
+particle would be a wave that would
+ 
+
+ align:start position:0%
+particle would be a wave that would
+solve the equation and the equation was
+
+ align:start position:0%
+solve the equation and the equation was
+ 
+
+ align:start position:0%
+solve the equation and the equation was
+the Schrodinger equation a free shown in
+
+ align:start position:0%
+the Schrodinger equation a free shown in
+ 
+
+ align:start position:0%
+the Schrodinger equation a free shown in
+the equation and then we added a
+
+ align:start position:0%
+the equation and then we added a
+ 
+
+ align:start position:0%
+the equation and then we added a
+potential to make it interacting and
+
+ align:start position:0%
+potential to make it interacting and
+ 
+
+ align:start position:0%
+potential to make it interacting and
+that way we motivated the Schrodinger
+
+ align:start position:0%
+that way we motivated the Schrodinger
+ 
+
+ align:start position:0%
+that way we motivated the Schrodinger
+equation and took this form side effects
+
+ align:start position:0%
+equation and took this form side effects
+ 
+
+ align:start position:0%
+equation and took this form side effects
+on T and this is the dynamical equation
+
+ align:start position:0%
+on T and this is the dynamical equation
+ 
+
+ align:start position:0%
+on T and this is the dynamical equation
+that governs the wave function but the
+
+ align:start position:0%
+that governs the wave function but the
+ 
+
+ align:start position:0%
+that governs the wave function but the
+interpretation that we had for the wave
+
+ align:start position:0%
+interpretation that we had for the wave
+ 
+
+ align:start position:0%
+interpretation that we had for the wave
+function we discuss what Bourne said was
+
+ align:start position:0%
+function we discuss what Bourne said was
+ 
+
+ align:start position:0%
+function we discuss what Bourne said was
+that it's related to probabilities and
+
+ align:start position:0%
+that it's related to probabilities and
+ 
+
+ align:start position:0%
+that it's related to probabilities and
+size squared multiplied by a little DX
+
+ align:start position:0%
+size squared multiplied by a little DX
+ 
+
+ align:start position:0%
+size squared multiplied by a little DX
+would give you the probability to find
+
+ align:start position:0%
+would give you the probability to find
+ 
+
+ align:start position:0%
+would give you the probability to find
+the particle in that little DX at some
+
+ align:start position:0%
+the particle in that little DX at some
+ 
+
+ align:start position:0%
+the particle in that little DX at some
+particular time so sine of X and T
+
+ align:start position:0%
+particular time so sine of X and T
+ 
+
+ align:start position:0%
+particular time so sine of X and T
+squared DX
+
+ align:start position:0%
+squared DX
+ 
+
+ align:start position:0%
+squared DX
+would be the probability to find the
+
+ align:start position:0%
+would be the probability to find the
+ 
+
+ align:start position:0%
+would be the probability to find the
+particle at that interval DX around X
+
+ align:start position:0%
+particle at that interval DX around X
+ 
+
+ align:start position:0%
+particle at that interval DX around X
+and if you're describing the physics of
+
+ align:start position:0%
+and if you're describing the physics of
+ 
+
+ align:start position:0%
+and if you're describing the physics of
+your Schrodinger equation is that the
+
+ align:start position:0%
+your Schrodinger equation is that the
+ 
+
+ align:start position:0%
+your Schrodinger equation is that the
+single particle which is the case here
+
+ align:start position:0%
+single particle which is the case here
+ 
+
+ align:start position:0%
+single particle which is the case here
+one coordinate the coordinate of the
+
+ align:start position:0%
+one coordinate the coordinate of the
+ 
+
+ align:start position:0%
+one coordinate the coordinate of the
+particle this integral if you integrate
+
+ align:start position:0%
+particle this integral if you integrate
+ 
+
+ align:start position:0%
+particle this integral if you integrate
+this all over us
+
+ align:start position:0%
+this all over us
+ 
+
+ align:start position:0%
+this all over us
+must be one for the probability to make
+
+ align:start position:0%
+must be one for the probability to make
+ 
+
+ align:start position:0%
+must be one for the probability to make
+sense so the total probability of
+
+ align:start position:0%
+sense so the total probability of
+ 
+
+ align:start position:0%
+sense so the total probability of
+finding the particle must be 1 must be
+
+ align:start position:0%
+finding the particle must be 1 must be
+ 
+
+ align:start position:0%
+finding the particle must be 1 must be
+somewhere if it's in one part or another
+
+ align:start position:0%
+somewhere if it's in one part or another
+ 
+
+ align:start position:0%
+somewhere if it's in one part or another
+part or another part is probabilities
+
+ align:start position:0%
+part or another part is probabilities
+ 
+
+ align:start position:0%
+part or another part is probabilities
+for this to be a probability
+
+ align:start position:0%
+for this to be a probability
+ 
+
+ align:start position:0%
+for this to be a probability
+distribution has to be well normalized
+
+ align:start position:0%
+distribution has to be well normalized
+ 
+
+ align:start position:0%
+distribution has to be well normalized
+which means 1 and we said that this
+
+ align:start position:0%
+which means 1 and we said that this
+ 
+
+ align:start position:0%
+which means 1 and we said that this
+equation was interesting but somewhat
+
+ align:start position:0%
+equation was interesting but somewhat
+ 
+
+ align:start position:0%
+equation was interesting but somewhat
+worrisome because if the normalization
+
+ align:start position:0%
+worrisome because if the normalization
+ 
+
+ align:start position:0%
+worrisome because if the normalization
+of the wave function satisfies if this
+
+ align:start position:0%
+of the wave function satisfies if this
+ 
+
+ align:start position:0%
+of the wave function satisfies if this
+holds for a T equal T naught then the
+
+ align:start position:0%
+holds for a T equal T naught then the
+ 
+
+ align:start position:0%
+holds for a T equal T naught then the
+Schrodinger equation if you know the
+
+ align:start position:0%
+Schrodinger equation if you know the
+ 
+
+ align:start position:0%
+Schrodinger equation if you know the
+wave function all over space for T equal
+
+ align:start position:0%
+wave function all over space for T equal
+ 
+
+ align:start position:0%
+wave function all over space for T equal
+to naught which is what you would need
+
+ align:start position:0%
+to naught which is what you would need
+ 
+
+ align:start position:0%
+to naught which is what you would need
+to know in order to check that this is
+
+ align:start position:0%
+to know in order to check that this is
+ 
+
+ align:start position:0%
+to know in order to check that this is
+working at time equal T naught you take
+
+ align:start position:0%
+working at time equal T naught you take
+ 
+
+ align:start position:0%
+working at time equal T naught you take
+the sy of X and T naught integrate it
+
+ align:start position:0%
+the sy of X and T naught integrate it
+ 
+
+ align:start position:0%
+the sy of X and T naught integrate it
+but if you know sy of X and T naught for
+
+ align:start position:0%
+but if you know sy of X and T naught for
+ 
+
+ align:start position:0%
+but if you know sy of X and T naught for
+all X then the Schrodinger equation
+
+ align:start position:0%
+all X then the Schrodinger equation
+ 
+
+ align:start position:0%
+all X then the Schrodinger equation
+tells you what the wave function is at a
+
+ align:start position:0%
+tells you what the wave function is at a
+ 
+
+ align:start position:0%
+tells you what the wave function is at a
+later time because it gives you the time
+
+ align:start position:0%
+later time because it gives you the time
+ 
+
+ align:start position:0%
+later time because it gives you the time
+derivative of the wave function in terms
+
+ align:start position:0%
+derivative of the wave function in terms
+ 
+
+ align:start position:0%
+derivative of the wave function in terms
+of beta about the wave function all over
+
+ align:start position:0%
+of beta about the wave function all over
+ 
+
+ align:start position:0%
+of beta about the wave function all over
+space so automatically the Schrodinger
+
+ align:start position:0%
+space so automatically the Schrodinger
+ 
+
+ align:start position:0%
+space so automatically the Schrodinger
+equation must make it true that this
+
+ align:start position:0%
+equation must make it true that this
+ 
+
+ align:start position:0%
+equation must make it true that this
+will hold at later times you cannot
+
+ align:start position:0%
+will hold at later times you cannot
+ 
+
+ align:start position:0%
+will hold at later times you cannot
+force the wave function to satisfy this
+
+ align:start position:0%
+force the wave function to satisfy this
+ 
+
+ align:start position:0%
+force the wave function to satisfy this
+at all times you can force it maybe to
+
+ align:start position:0%
+at all times you can force it maybe to
+ 
+
+ align:start position:0%
+at all times you can force it maybe to
+satisfy it at one time but once it
+
+ align:start position:0%
+satisfy it at one time but once it
+ 
+
+ align:start position:0%
+satisfy it at one time but once it
+satisfies it at this time then it will
+
+ align:start position:0%
+satisfies it at this time then it will
+ 
+
+ align:start position:0%
+satisfies it at this time then it will
+evolve and it better be that at every
+
+ align:start position:0%
+evolve and it better be that at every
+ 
+
+ align:start position:0%
+evolve and it better be that at every
+time later it still satisfies this
+
+ align:start position:0%
+time later it still satisfies this
+ 
+
+ align:start position:0%
+time later it still satisfies this
+equation so this is a very
+
+ align:start position:0%
+equation so this is a very
+ 
+
+ align:start position:0%
+equation so this is a very
+important constraint so we'll basically
+
+ align:start position:0%
+important constraint so we'll basically
+ 
+
+ align:start position:0%
+important constraint so we'll basically
+develop this throughout the lecture
+
+ align:start position:0%
+develop this throughout the lecture
+ 
+
+ align:start position:0%
+develop this throughout the lecture
+today we're going to make a big point of
+
+ align:start position:0%
+today we're going to make a big point of
+ 
+
+ align:start position:0%
+today we're going to make a big point of
+this trying to explain why the
+
+ align:start position:0%
+this trying to explain why the
+ 
+
+ align:start position:0%
+this trying to explain why the
+conditions that we're going to impose on
+
+ align:start position:0%
+conditions that we're going to impose on
+ 
+
+ align:start position:0%
+conditions that we're going to impose on
+the wavefunction are necessary what it
+
+ align:start position:0%
+the wavefunction are necessary what it
+ 
+
+ align:start position:0%
+the wavefunction are necessary what it
+teaches you about the Hamiltonian will
+
+ align:start position:0%
+teaches you about the Hamiltonian will
+ 
+
+ align:start position:0%
+teaches you about the Hamiltonian will
+teach you that it's a hermitian operator
+
+ align:start position:0%
+teach you that it's a hermitian operator
+ 
+
+ align:start position:0%
+teach you that it's a hermitian operator
+what do you learn about probability you
+
+ align:start position:0%
+what do you learn about probability you
+ 
+
+ align:start position:0%
+what do you learn about probability you
+will learn that there's a probability
+
+ align:start position:0%
+will learn that there's a probability
+ 
+
+ align:start position:0%
+will learn that there's a probability
+current and all kinds of things is will
+
+ align:start position:0%
+current and all kinds of things is will
+ 
+
+ align:start position:0%
+current and all kinds of things is will
+come out of taking seriously the
+
+ align:start position:0%
+come out of taking seriously the
+ 
+
+ align:start position:0%
+come out of taking seriously the
+interpretation of it as probability the
+
+ align:start position:0%
+interpretation of it as probability the
+ 
+
+ align:start position:0%
+interpretation of it as probability the
+main point being that we can be sure it
+
+ align:start position:0%
+main point being that we can be sure it
+ 
+
+ align:start position:0%
+main point being that we can be sure it
+behaves as a probability at one time but
+
+ align:start position:0%
+behaves as a probability at one time but
+ 
+
+ align:start position:0%
+behaves as a probability at one time but
+then for later times to behave as a
+
+ align:start position:0%
+then for later times to behave as a
+ 
+
+ align:start position:0%
+then for later times to behave as a
+probability the Schrodinger equation
+
+ align:start position:0%
+probability the Schrodinger equation
+ 
+
+ align:start position:0%
+probability the Schrodinger equation
+must help must somehow be part of the
+
+ align:start position:0%
+must help must somehow be part of the
+ 
+
+ align:start position:0%
+must help must somehow be part of the
+reason this works out so that's what
+
+ align:start position:0%
+reason this works out so that's what
+ 
+
+ align:start position:0%
+reason this works out so that's what
+we're going to try to do now when we
+
+ align:start position:0%
+we're going to try to do now when we
+ 
+
+ align:start position:0%
+we're going to try to do now when we
+write an equation like this and more
+
+ align:start position:0%
+write an equation like this and more
+ 
+
+ align:start position:0%
+write an equation like this and more
+explicitly this means integral of size
+
+ align:start position:0%
+explicitly this means integral of size
+ 
+
+ align:start position:0%
+explicitly this means integral of size
+star of X and T Phi of X and T the X
+
+ align:start position:0%
+star of X and T Phi of X and T the X
+ 
+
+ align:start position:0%
+star of X and T Phi of X and T the X
+equal one you can imagine that not all
+
+ align:start position:0%
+equal one you can imagine that not all
+ 
+
+ align:start position:0%
+equal one you can imagine that not all
+kind of wave functions will satisfy it
+
+ align:start position:0%
+kind of wave functions will satisfy it
+ 
+
+ align:start position:0%
+kind of wave functions will satisfy it
+in particular any wave function for
+
+ align:start position:0%
+in particular any wave function for
+ 
+
+ align:start position:0%
+in particular any wave function for
+example that at infinity approaches a
+
+ align:start position:0%
+example that at infinity approaches a
+ 
+
+ align:start position:0%
+example that at infinity approaches a
+constant will never satisfy this because
+
+ align:start position:0%
+constant will never satisfy this because
+ 
+
+ align:start position:0%
+constant will never satisfy this because
+if at infinity you approach a constant
+
+ align:start position:0%
+if at infinity you approach a constant
+ 
+
+ align:start position:0%
+if at infinity you approach a constant
+then the integral is going to be
+
+ align:start position:0%
+then the integral is going to be
+ 
+
+ align:start position:0%
+then the integral is going to be
+infinite and it's just not gonna work
+
+ align:start position:0%
+infinite and it's just not gonna work
+ 
+
+ align:start position:0%
+infinite and it's just not gonna work
+out so you cannot the wave function
+
+ align:start position:0%
+out so you cannot the wave function
+ 
+
+ align:start position:0%
+out so you cannot the wave function
+cannot approach a finite number a finite
+
+ align:start position:0%
+cannot approach a finite number a finite
+ 
+
+ align:start position:0%
+cannot approach a finite number a finite
+constant as X goes to infinity so in
+
+ align:start position:0%
+constant as X goes to infinity so in
+ 
+
+ align:start position:0%
+constant as X goes to infinity so in
+order for this to hold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order to warranty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this can even hold can conceivably hold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hold will require a bit of boundary
+
+ align:start position:0%
+hold will require a bit of boundary
+ 
+
+ align:start position:0%
+hold will require a bit of boundary
+conditions and will say that the limit
+
+ align:start position:0%
+conditions and will say that the limit
+ 
+
+ align:start position:0%
+conditions and will say that the limit
+as X goes to infinity or minus infinity
+
+ align:start position:0%
+as X goes to infinity or minus infinity
+ 
+
+ align:start position:0%
+as X goes to infinity or minus infinity
+plus minus infinity of sigh of X and T
+
+ align:start position:0%
+plus minus infinity of sigh of X and T
+ 
+
+ align:start position:0%
+plus minus infinity of sigh of X and T
+will be equal to zero it better be true
+
+ align:start position:0%
+will be equal to zero it better be true
+ 
+
+ align:start position:0%
+will be equal to zero it better be true
+and we'll ask a little more now you
+
+ align:start position:0%
+and we'll ask a little more now you
+ 
+
+ align:start position:0%
+and we'll ask a little more now you
+could say look certainly the limit of
+
+ align:start position:0%
+could say look certainly the limit of
+ 
+
+ align:start position:0%
+could say look certainly the limit of
+this function could not be a number
+
+ align:start position:0%
+this function could not be a number
+ 
+
+ align:start position:0%
+this function could not be a number
+because if it would be a nonzero number
+
+ align:start position:0%
+because if it would be a nonzero number
+ 
+
+ align:start position:0%
+because if it would be a nonzero number
+the integral will diverge but maybe
+
+ align:start position:0%
+the integral will diverge but maybe
+ 
+
+ align:start position:0%
+the integral will diverge but maybe
+there's no limit the wave function is so
+
+ align:start position:0%
+there's no limit the wave function is so
+ 
+
+ align:start position:0%
+there's no limit the wave function is so
+crazy that it can be integrated but
+
+ align:start position:0%
+crazy that it can be integrated but
+ 
+
+ align:start position:0%
+crazy that it can be integrated but
+suddenly it has a little spike and it
+
+ align:start position:0%
+suddenly it has a little spike and it
+ 
+
+ align:start position:0%
+suddenly it has a little spike and it
+just doesn't have a normal limit that
+
+ align:start position:0%
+just doesn't have a normal limit that
+ 
+
+ align:start position:0%
+just doesn't have a normal limit that
+could conceivably be the case
+
+ align:start position:0%
+could conceivably be the case
+ 
+
+ align:start position:0%
+could conceivably be the case
+nevertheless it doesn't seem to happen
+
+ align:start position:0%
+nevertheless it doesn't seem to happen
+ 
+
+ align:start position:0%
+nevertheless it doesn't seem to happen
+in any example that is of relevance so
+
+ align:start position:0%
+in any example that is of relevance so
+ 
+
+ align:start position:0%
+in any example that is of relevance so
+we will assume that the situations are
+
+ align:start position:0%
+we will assume that the situations are
+ 
+
+ align:start position:0%
+we will assume that the situations are
+not that crazy that this happens so
+
+ align:start position:0%
+not that crazy that this happens so
+ 
+
+ align:start position:0%
+not that crazy that this happens so
+we'll take wave functions that
+
+ align:start position:0%
+we'll take wave functions that
+ 
+
+ align:start position:0%
+we'll take wave functions that
+necessarily go to zero at infinity and
+
+ align:start position:0%
+necessarily go to zero at infinity and
+ 
+
+ align:start position:0%
+necessarily go to zero at infinity and
+that certainly is good it's a it's you
+
+ align:start position:0%
+that certainly is good it's a it's you
+ 
+
+ align:start position:0%
+that certainly is good it's a it's you
+cannot prove it's a necessary condition
+
+ align:start position:0%
+cannot prove it's a necessary condition
+ 
+
+ align:start position:0%
+cannot prove it's a necessary condition
+but if it holds it simplifies many many
+
+ align:start position:0%
+but if it holds it simplifies many many
+ 
+
+ align:start position:0%
+but if it holds it simplifies many many
+things and essentially if the wave
+
+ align:start position:0%
+things and essentially if the wave
+ 
+
+ align:start position:0%
+things and essentially if the wave
+function is good enough to have a limit
+
+ align:start position:0%
+function is good enough to have a limit
+ 
+
+ align:start position:0%
+function is good enough to have a limit
+then the limit must be zero the other
+
+ align:start position:0%
+then the limit must be zero the other
+ 
+
+ align:start position:0%
+then the limit must be zero the other
+thing that we will want is that
+
+ align:start position:0%
+thing that we will want is that
+ 
+
+ align:start position:0%
+thing that we will want is that
+sigh the X the limit as X goes to plus
+
+ align:start position:0%
+sigh the X the limit as X goes to plus
+ 
+
+ align:start position:0%
+sigh the X the limit as X goes to plus
+minus infinity is bounded that is yes
+
+ align:start position:0%
+minus infinity is bounded that is yes
+ 
+
+ align:start position:0%
+minus infinity is bounded that is yes
+the limit may exist and it may be a
+
+ align:start position:0%
+the limit may exist and it may be a
+ 
+
+ align:start position:0%
+the limit may exist and it may be a
+number but is not infinite and in every
+
+ align:start position:0%
+number but is not infinite and in every
+ 
+
+ align:start position:0%
+number but is not infinite and in every
+example that I know in front when this
+
+ align:start position:0%
+example that I know in front when this
+ 
+
+ align:start position:0%
+example that I know in front when this
+goes to zero this goes to zero as well
+
+ align:start position:0%
+goes to zero this goes to zero as well
+ 
+
+ align:start position:0%
+goes to zero this goes to zero as well
+but this is basically all you will ever
+
+ align:start position:0%
+but this is basically all you will ever
+ 
+
+ align:start position:0%
+but this is basically all you will ever
+need in order to make sense of the wave
+
+ align:start position:0%
+need in order to make sense of the wave
+ 
+
+ align:start position:0%
+need in order to make sense of the wave
+functions and their integrals that we're
+
+ align:start position:0%
+functions and their integrals that we're
+ 
+
+ align:start position:0%
+functions and their integrals that we're
+going to be doing now you shouldn't be
+
+ align:start position:0%
+going to be doing now you shouldn't be
+ 
+
+ align:start position:0%
+going to be doing now you shouldn't be
+too surprised that you need to say
+
+ align:start position:0%
+too surprised that you need to say
+ 
+
+ align:start position:0%
+too surprised that you need to say
+something about this wave function in
+
+ align:start position:0%
+something about this wave function in
+ 
+
+ align:start position:0%
+something about this wave function in
+the analysis that will follow because
+
+ align:start position:0%
+the analysis that will follow because
+ 
+
+ align:start position:0%
+the analysis that will follow because
+the derivative you have the wave
+
+ align:start position:0%
+the derivative you have the wave
+ 
+
+ align:start position:0%
+the derivative you have the wave
+function its derivative because
+
+ align:start position:0%
+function its derivative because
+ 
+
+ align:start position:0%
+function its derivative because
+certainly there are two derivatives here
+
+ align:start position:0%
+certainly there are two derivatives here
+ 
+
+ align:start position:0%
+certainly there are two derivatives here
+so it's when we manipulate this
+
+ align:start position:0%
+so it's when we manipulate this
+ 
+
+ align:start position:0%
+so it's when we manipulate this
+quantities inside an integrals you will
+
+ align:start position:0%
+quantities inside an integrals you will
+ 
+
+ align:start position:0%
+quantities inside an integrals you will
+see very soon single derivatives will
+
+ align:start position:0%
+see very soon single derivatives will
+ 
+
+ align:start position:0%
+see very soon single derivatives will
+show up and we will have to control them
+
+ align:start position:0%
+show up and we will have to control them
+ 
+
+ align:start position:0%
+show up and we will have to control them
+so so the only thing that I'm saying is
+
+ align:start position:0%
+so so the only thing that I'm saying is
+ 
+
+ align:start position:0%
+so so the only thing that I'm saying is
+that when you see a wave function that
+
+ align:start position:0%
+that when you see a wave function that
+ 
+
+ align:start position:0%
+that when you see a wave function that
+satisfies this property you know that
+
+ align:start position:0%
+satisfies this property you know that
+ 
+
+ align:start position:0%
+satisfies this property you know that
+unless the function is extremely crazy
+
+ align:start position:0%
+unless the function is extremely crazy
+ 
+
+ align:start position:0%
+unless the function is extremely crazy
+it's a function that goes to zero at
+
+ align:start position:0%
+it's a function that goes to zero at
+ 
+
+ align:start position:0%
+it's a function that goes to zero at
+plus minus infinity and it's derivative
+
+ align:start position:0%
+plus minus infinity and it's derivative
+ 
+
+ align:start position:0%
+plus minus infinity and it's derivative
+presumably also goes to zero but it will
+
+ align:start position:0%
+presumably also goes to zero but it will
+ 
+
+ align:start position:0%
+presumably also goes to zero but it will
+be enough to say that it maybe goes to a
+
+ align:start position:0%
+be enough to say that it maybe goes to a
+ 
+
+ align:start position:0%
+be enough to say that it maybe goes to a
+number now there is another possibility
+
+ align:start position:0%
+number now there is another possibility
+ 
+
+ align:start position:0%
+number now there is another possibility
+I think for confusion here with things
+
+ align:start position:0%
+I think for confusion here with things
+ 
+
+ align:start position:0%
+I think for confusion here with things
+that we've been saying before we've said
+
+ align:start position:0%
+that we've been saying before we've said
+ 
+
+ align:start position:0%
+that we've been saying before we've said
+before that the physics of a wave
+
+ align:start position:0%
+before that the physics of a wave
+ 
+
+ align:start position:0%
+before that the physics of a wave
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+is not altered by multiplying the
+
+ align:start position:0%
+is not altered by multiplying the
+ 
+
+ align:start position:0%
+is not altered by multiplying the
+wavefunction by a number we said that
+
+ align:start position:0%
+wavefunction by a number we said that
+ 
+
+ align:start position:0%
+wavefunction by a number we said that
+psy added oops I is the same state size
+
+ align:start position:0%
+psy added oops I is the same state size
+ 
+
+ align:start position:0%
+psy added oops I is the same state size
+the same state at square root of tube
+
+ align:start position:0%
+the same state at square root of tube
+ 
+
+ align:start position:0%
+the same state at square root of tube
+sigh all this is the same physics but
+
+ align:start position:0%
+sigh all this is the same physics but
+ 
+
+ align:start position:0%
+sigh all this is the same physics but
+here it looks a little surprising if you
+
+ align:start position:0%
+here it looks a little surprising if you
+ 
+
+ align:start position:0%
+here it looks a little surprising if you
+wish because if I have a pie and I got
+
+ align:start position:0%
+wish because if I have a pie and I got
+ 
+
+ align:start position:0%
+wish because if I have a pie and I got
+this already working out if I multiply
+
+ align:start position:0%
+this already working out if I multiply
+ 
+
+ align:start position:0%
+this already working out if I multiply
+psi by square root of two it will not
+
+ align:start position:0%
+psi by square root of two it will not
+ 
+
+ align:start position:0%
+psi by square root of two it will not
+hold so there seems to be a little maybe
+
+ align:start position:0%
+hold so there seems to be a little maybe
+ 
+
+ align:start position:0%
+hold so there seems to be a little maybe
+something with the words that we've been
+
+ align:start position:0%
+something with the words that we've been
+ 
+
+ align:start position:0%
+something with the words that we've been
+using it's not exactly right and I want
+
+ align:start position:0%
+using it's not exactly right and I want
+ 
+
+ align:start position:0%
+using it's not exactly right and I want
+to make sure there's no room for
+
+ align:start position:0%
+to make sure there's no room for
+ 
+
+ align:start position:0%
+to make sure there's no room for
+confusion here and it's it's the
+
+ align:start position:0%
+confusion here and it's it's the
+ 
+
+ align:start position:0%
+confusion here and it's it's the
+following fact here this wavefunction
+
+ align:start position:0%
+following fact here this wavefunction
+ 
+
+ align:start position:0%
+following fact here this wavefunction
+has been normalized so there's two kinds
+
+ align:start position:0%
+has been normalized so there's two kinds
+ 
+
+ align:start position:0%
+has been normalized so there's two kinds
+of wave functions that you can have we
+
+ align:start position:0%
+of wave functions that you can have we
+ 
+
+ align:start position:0%
+of wave functions that you can have we
+functions that can be normalized and we
+
+ align:start position:0%
+functions that can be normalized and we
+ 
+
+ align:start position:0%
+functions that can be normalized and we
+functions cannot be normal I suppose
+
+ align:start position:0%
+functions cannot be normal I suppose
+ 
+
+ align:start position:0%
+functions cannot be normal I suppose
+somebody comes to you and gives you up
+
+ align:start position:0%
+somebody comes to you and gives you up
+ 
+
+ align:start position:0%
+somebody comes to you and gives you up
+size of X and T or let's assume we give
+
+ align:start position:0%
+size of X and T or let's assume we give
+ 
+
+ align:start position:0%
+size of X and T or let's assume we give
+subside an output X and T no problem now
+
+ align:start position:0%
+subside an output X and T no problem now
+ 
+
+ align:start position:0%
+subside an output X and T no problem now
+suppose you go and start doing this
+
+ align:start position:0%
+suppose you go and start doing this
+ 
+
+ align:start position:0%
+suppose you go and start doing this
+integral integral of Phi squared DX and
+
+ align:start position:0%
+integral integral of Phi squared DX and
+ 
+
+ align:start position:0%
+integral integral of Phi squared DX and
+then you find that it's not equal to 1
+
+ align:start position:0%
+then you find that it's not equal to 1
+ 
+
+ align:start position:0%
+then you find that it's not equal to 1
+but is equal to some value n which is
+
+ align:start position:0%
+but is equal to some value n which is
+ 
+
+ align:start position:0%
+but is equal to some value n which is
+different from woman maybe if this
+
+ align:start position:0%
+different from woman maybe if this
+ 
+
+ align:start position:0%
+different from woman maybe if this
+happens we say that psy is normalizable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which means it can be normalized and
+
+ align:start position:0%
+which means it can be normalized and
+ 
+
+ align:start position:0%
+which means it can be normalized and
+using this idea that changing the value
+
+ align:start position:0%
+using this idea that changing the value
+ 
+
+ align:start position:0%
+using this idea that changing the value
+the coefficient of the function doesn't
+
+ align:start position:0%
+the coefficient of the function doesn't
+ 
+
+ align:start position:0%
+the coefficient of the function doesn't
+change it too much we simply say use
+
+ align:start position:0%
+change it too much we simply say use
+ 
+
+ align:start position:0%
+change it too much we simply say use
+instead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops I prime which is equal to psi over
+
+ align:start position:0%
+oops I prime which is equal to psi over
+ 
+
+ align:start position:0%
+oops I prime which is equal to psi over
+square root of N and look what the nice
+
+ align:start position:0%
+square root of N and look what the nice
+ 
+
+ align:start position:0%
+square root of N and look what the nice
+property this side Prime has if you
+
+ align:start position:0%
+property this side Prime has if you
+ 
+
+ align:start position:0%
+property this side Prime has if you
+integrate sie prime squared it would be
+
+ align:start position:0%
+integrate sie prime squared it would be
+ 
+
+ align:start position:0%
+integrate sie prime squared it would be
+equal because you have side prime here
+
+ align:start position:0%
+equal because you have side prime here
+ 
+
+ align:start position:0%
+equal because you have side prime here
+squared would be equal to the integral
+
+ align:start position:0%
+squared would be equal to the integral
+ 
+
+ align:start position:0%
+squared would be equal to the integral
+of size squared divided by the number n
+
+ align:start position:0%
+of size squared divided by the number n
+ 
+
+ align:start position:0%
+of size squared divided by the number n
+because it's two of them DX and that's
+
+ align:start position:0%
+because it's two of them DX and that's
+ 
+
+ align:start position:0%
+because it's two of them DX and that's
+the number goes out and you have the
+
+ align:start position:0%
+the number goes out and you have the
+ 
+
+ align:start position:0%
+the number goes out and you have the
+integral of size squared DX
+
+ align:start position:0%
+integral of size squared DX
+ 
+
+ align:start position:0%
+integral of size squared DX
+but that integral was exactly in so
+
+ align:start position:0%
+but that integral was exactly in so
+ 
+
+ align:start position:0%
+but that integral was exactly in so
+that's one so if your wave function has
+
+ align:start position:0%
+that's one so if your wave function has
+ 
+
+ align:start position:0%
+that's one so if your wave function has
+a finite integral in this sense a number
+
+ align:start position:0%
+a finite integral in this sense a number
+ 
+
+ align:start position:0%
+a finite integral in this sense a number
+that is less than infinity then sigh can
+
+ align:start position:0%
+that is less than infinity then sigh can
+ 
+
+ align:start position:0%
+that is less than infinity then sigh can
+be normalized and if you're gonna work
+
+ align:start position:0%
+be normalized and if you're gonna work
+ 
+
+ align:start position:0%
+be normalized and if you're gonna work
+with probabilities you should use
+
+ align:start position:0%
+with probabilities you should use
+ 
+
+ align:start position:0%
+with probabilities you should use
+instead this wave function which is the
+
+ align:start position:0%
+instead this wave function which is the
+ 
+
+ align:start position:0%
+instead this wave function which is the
+original wave function divided by a
+
+ align:start position:0%
+original wave function divided by a
+ 
+
+ align:start position:0%
+original wave function divided by a
+number so the idea is that in some sense
+
+ align:start position:0%
+number so the idea is that in some sense
+ 
+
+ align:start position:0%
+number so the idea is that in some sense
+you can be lay all of this and you can
+
+ align:start position:0%
+you can be lay all of this and you can
+ 
+
+ align:start position:0%
+you can be lay all of this and you can
+always work with wave functions that
+
+ align:start position:0%
+always work with wave functions that
+ 
+
+ align:start position:0%
+always work with wave functions that
+our normalizable but only when you're
+
+ align:start position:0%
+our normalizable but only when you're
+ 
+
+ align:start position:0%
+our normalizable but only when you're
+going to calculate your probabilities
+
+ align:start position:0%
+going to calculate your probabilities
+ 
+
+ align:start position:0%
+going to calculate your probabilities
+you can take the trouble to actually
+
+ align:start position:0%
+you can take the trouble to actually
+ 
+
+ align:start position:0%
+you can take the trouble to actually
+normalize them and those are the ones
+
+ align:start position:0%
+normalize them and those are the ones
+ 
+
+ align:start position:0%
+normalize them and those are the ones
+you use in this formulas so so the idea
+
+ align:start position:0%
+you use in this formulas so so the idea
+ 
+
+ align:start position:0%
+you use in this formulas so so the idea
+remains that we work flexibly with wave
+
+ align:start position:0%
+remains that we work flexibly with wave
+ 
+
+ align:start position:0%
+remains that we work flexibly with wave
+functions and multiply them by numbers
+
+ align:start position:0%
+functions and multiply them by numbers
+ 
+
+ align:start position:0%
+functions and multiply them by numbers
+and nothing changes as long as you
+
+ align:start position:0%
+and nothing changes as long as you
+ 
+
+ align:start position:0%
+and nothing changes as long as you
+realize that you cannot change the fact
+
+ align:start position:0%
+realize that you cannot change the fact
+ 
+
+ align:start position:0%
+realize that you cannot change the fact
+that the wave function is normalizable
+
+ align:start position:0%
+that the wave function is normalizable
+ 
+
+ align:start position:0%
+that the wave function is normalizable
+by multiplying it by any finite number
+
+ align:start position:0%
+by multiplying it by any finite number
+ 
+
+ align:start position:0%
+by multiplying it by any finite number
+it will still be normalizable and if
+
+ align:start position:0%
+it will still be normalizable and if
+ 
+
+ align:start position:0%
+it will still be normalizable and if
+it's normalizable it's equivalent to a
+
+ align:start position:0%
+it's normalizable it's equivalent to a
+ 
+
+ align:start position:0%
+it's normalizable it's equivalent to a
+normalized wave function so those two
+
+ align:start position:0%
+normalized wave function so those two
+ 
+
+ align:start position:0%
+normalized wave function so those two
+words sound very similar but they're a
+
+ align:start position:0%
+words sound very similar but they're a
+ 
+
+ align:start position:0%
+words sound very similar but they're a
+little different
+
+ align:start position:0%
+little different
+ 
+
+ align:start position:0%
+little different
+one is normalizable which means it has
+
+ align:start position:0%
+one is normalizable which means it has
+ 
+
+ align:start position:0%
+one is normalizable which means it has
+into a sigh squared
+
+ align:start position:0%
+into a sigh squared
+ 
+
+ align:start position:0%
+into a sigh squared
+finite and normalize is one that already
+
+ align:start position:0%
+finite and normalize is one that already
+ 
+
+ align:start position:0%
+finite and normalize is one that already
+has been adjusted to do this and can be
+
+ align:start position:0%
+has been adjusted to do this and can be
+ 
+
+ align:start position:0%
+has been adjusted to do this and can be
+used to define a probability
+
+ align:start position:0%
+used to define a probability
+ 
+
+ align:start position:0%
+used to define a probability
+distribution okay so that's in a way of
+
+ align:start position:0%
+distribution okay so that's in a way of
+ 
+
+ align:start position:0%
+distribution okay so that's in a way of
+introduction to the problem that we have
+
+ align:start position:0%
+introduction to the problem that we have
+ 
+
+ align:start position:0%
+introduction to the problem that we have
+to do our serious problem is indeed
+
+ align:start position:0%
+to do our serious problem is indeed
+ 
+
+ align:start position:0%
+to do our serious problem is indeed
+justifying that the time evolution
+
+ align:start position:0%
+justifying that the time evolution
+ 
+
+ align:start position:0%
+justifying that the time evolution
+doesn't mess up the normalization and
+
+ align:start position:0%
+doesn't mess up the normalization and
+ 
+
+ align:start position:0%
+doesn't mess up the normalization and
+how does it do that
\ No newline at end of file
diff --git a/dCw-x9ZOljY.txt b/dCw-x9ZOljY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..14de998cf4f94f7c4993f145ec5fd1428d263750
--- /dev/null
+++ b/dCw-x9ZOljY.txt
@@ -0,0 +1,11667 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the founding of Ghent a little bit about
+
+ align:start position:0%
+the founding of Ghent a little bit about
+ 
+
+ align:start position:0%
+the founding of Ghent a little bit about
+the old Herbert Boyer ms4 1936 he was a
+
+ align:start position:0%
+the old Herbert Boyer ms4 1936 he was a
+ 
+
+ align:start position:0%
+the old Herbert Boyer ms4 1936 he was a
+biochemist from Pennsylvania in Orgeon
+
+ align:start position:0%
+biochemist from Pennsylvania in Orgeon
+ 
+
+ align:start position:0%
+biochemist from Pennsylvania in Orgeon
+Pennsylvania and then worked at the
+
+ align:start position:0%
+Pennsylvania and then worked at the
+ 
+
+ align:start position:0%
+Pennsylvania and then worked at the
+University of California in San
+
+ align:start position:0%
+University of California in San
+ 
+
+ align:start position:0%
+University of California in San
+Francisco and he's sort of considered
+
+ align:start position:0%
+Francisco and he's sort of considered
+ 
+
+ align:start position:0%
+Francisco and he's sort of considered
+one of the first pioneers in the field
+
+ align:start position:0%
+one of the first pioneers in the field
+ 
+
+ align:start position:0%
+one of the first pioneers in the field
+of molecular genetics and they also have
+
+ align:start position:0%
+of molecular genetics and they also have
+ 
+
+ align:start position:0%
+of molecular genetics and they also have
+Roberts Wednesday who was born in 1947
+
+ align:start position:0%
+Roberts Wednesday who was born in 1947
+ 
+
+ align:start position:0%
+Roberts Wednesday who was born in 1947
+and died 1999 he was from Brooklyn went
+
+ align:start position:0%
+and died 1999 he was from Brooklyn went
+ 
+
+ align:start position:0%
+and died 1999 he was from Brooklyn went
+to MIT and then eventually got into
+
+ align:start position:0%
+to MIT and then eventually got into
+ 
+
+ align:start position:0%
+to MIT and then eventually got into
+venture capital and he was instrumental
+
+ align:start position:0%
+venture capital and he was instrumental
+ 
+
+ align:start position:0%
+venture capital and he was instrumental
+in finding that finding denatech and
+
+ align:start position:0%
+in finding that finding denatech and
+ 
+
+ align:start position:0%
+in finding that finding denatech and
+kind of developing the financing
+
+ align:start position:0%
+kind of developing the financing
+ 
+
+ align:start position:0%
+kind of developing the financing
+structure for that
+
+ align:start position:0%
+structure for that
+ 
+
+ align:start position:0%
+structure for that
+so he's enlisted some other players that
+
+ align:start position:0%
+so he's enlisted some other players that
+ 
+
+ align:start position:0%
+so he's enlisted some other players that
+were involved they kind of came in
+
+ align:start position:0%
+were involved they kind of came in
+ 
+
+ align:start position:0%
+were involved they kind of came in
+through out the process of various
+
+ align:start position:0%
+through out the process of various
+ 
+
+ align:start position:0%
+through out the process of various
+talents that were recruited both
+
+ align:start position:0%
+talents that were recruited both
+ 
+
+ align:start position:0%
+talents that were recruited both
+nationally and internationally
+
+ align:start position:0%
+nationally and internationally
+ 
+
+ align:start position:0%
+nationally and internationally
+Boyer worked with Arthur Riggs and he
+
+ align:start position:0%
+Boyer worked with Arthur Riggs and he
+ 
+
+ align:start position:0%
+Boyer worked with Arthur Riggs and he
+took it Akua from the Beckman Research
+
+ align:start position:0%
+took it Akua from the Beckman Research
+ 
+
+ align:start position:0%
+took it Akua from the Beckman Research
+Institute and the group had become the
+
+ align:start position:0%
+Institute and the group had become the
+ 
+
+ align:start position:0%
+Institute and the group had become the
+first to successfully express a human
+
+ align:start position:0%
+first to successfully express a human
+ 
+
+ align:start position:0%
+first to successfully express a human
+gene in bacteria when they produced when
+
+ align:start position:0%
+gene in bacteria when they produced when
+ 
+
+ align:start position:0%
+gene in bacteria when they produced when
+they produce somatostatin in 1977 and
+
+ align:start position:0%
+they produce somatostatin in 1977 and
+ 
+
+ align:start position:0%
+they produce somatostatin in 1977 and
+then David god--all and Dennis quite as
+
+ align:start position:0%
+then David god--all and Dennis quite as
+ 
+
+ align:start position:0%
+then David god--all and Dennis quite as
+well were brought on later on in 1978 I
+
+ align:start position:0%
+well were brought on later on in 1978 I
+ 
+
+ align:start position:0%
+well were brought on later on in 1978 I
+believe yeah and they were they went on
+
+ align:start position:0%
+believe yeah and they were they went on
+ 
+
+ align:start position:0%
+believe yeah and they were they went on
+to be instrumental figures in the
+
+ align:start position:0%
+to be instrumental figures in the
+ 
+
+ align:start position:0%
+to be instrumental figures in the
+company as well so I'll go into a little
+
+ align:start position:0%
+company as well so I'll go into a little
+ 
+
+ align:start position:0%
+company as well so I'll go into a little
+bit about what they what they
+
+ align:start position:0%
+bit about what they what they
+ 
+
+ align:start position:0%
+bit about what they what they
+accomplished just sort of the early
+
+ align:start position:0%
+accomplished just sort of the early
+ 
+
+ align:start position:0%
+accomplished just sort of the early
+history of the company there really were
+
+ align:start position:0%
+history of the company there really were
+ 
+
+ align:start position:0%
+history of the company there really were
+the first kind of kick-started the
+
+ align:start position:0%
+the first kind of kick-started the
+ 
+
+ align:start position:0%
+the first kind of kick-started the
+American biotech industry and you know
+
+ align:start position:0%
+American biotech industry and you know
+ 
+
+ align:start position:0%
+American biotech industry and you know
+it all started when the two of them kind
+
+ align:start position:0%
+it all started when the two of them kind
+ 
+
+ align:start position:0%
+it all started when the two of them kind
+of met Bob Bob Blair and Swanson met
+
+ align:start position:0%
+of met Bob Bob Blair and Swanson met
+ 
+
+ align:start position:0%
+of met Bob Bob Blair and Swanson met
+over beer and they've done $500 to
+
+ align:start position:0%
+over beer and they've done $500 to
+ 
+
+ align:start position:0%
+over beer and they've done $500 to
+stretch his pharmaceutical company that
+
+ align:start position:0%
+stretch his pharmaceutical company that
+ 
+
+ align:start position:0%
+stretch his pharmaceutical company that
+would explore proteins a bacterial
+
+ align:start position:0%
+would explore proteins a bacterial
+ 
+
+ align:start position:0%
+would explore proteins a bacterial
+engineer
+
+ align:start position:0%
+engineer
+ 
+
+ align:start position:0%
+engineer
+and the first targeted human the first
+
+ align:start position:0%
+and the first targeted human the first
+ 
+
+ align:start position:0%
+and the first targeted human the first
+targeted human insulin because you know
+
+ align:start position:0%
+targeted human insulin because you know
+ 
+
+ align:start position:0%
+targeted human insulin because you know
+that was kind of a competitive area at
+
+ align:start position:0%
+that was kind of a competitive area at
+ 
+
+ align:start position:0%
+that was kind of a competitive area at
+the time and there was a lot of demand
+
+ align:start position:0%
+the time and there was a lot of demand
+ 
+
+ align:start position:0%
+the time and there was a lot of demand
+for treatments but there was a worry
+
+ align:start position:0%
+for treatments but there was a worry
+ 
+
+ align:start position:0%
+for treatments but there was a worry
+that there wasn't enough and people have
+
+ align:start position:0%
+that there wasn't enough and people have
+ 
+
+ align:start position:0%
+that there wasn't enough and people have
+animal until inter meet those rising
+
+ align:start position:0%
+animal until inter meet those rising
+ 
+
+ align:start position:0%
+animal until inter meet those rising
+demand so they've kind of decided
+
+ align:start position:0%
+demand so they've kind of decided
+ 
+
+ align:start position:0%
+demand so they've kind of decided
+working to make synthetic insulin up to
+
+ align:start position:0%
+working to make synthetic insulin up to
+ 
+
+ align:start position:0%
+working to make synthetic insulin up to
+scratch and be competitive with what was
+
+ align:start position:0%
+scratch and be competitive with what was
+ 
+
+ align:start position:0%
+scratch and be competitive with what was
+previously used and they targeted
+
+ align:start position:0%
+previously used and they targeted
+ 
+
+ align:start position:0%
+previously used and they targeted
+meeting the requirements of Eli Lilly
+
+ align:start position:0%
+meeting the requirements of Eli Lilly
+ 
+
+ align:start position:0%
+meeting the requirements of Eli Lilly
+who they could have wanted to get his
+
+ align:start position:0%
+who they could have wanted to get his
+ 
+
+ align:start position:0%
+who they could have wanted to get his
+business to be they targeted his
+
+ align:start position:0%
+business to be they targeted his
+ 
+
+ align:start position:0%
+business to be they targeted his
+requirements they could get his business
+
+ align:start position:0%
+requirements they could get his business
+ 
+
+ align:start position:0%
+requirements they could get his business
+eventually and get the company going
+
+ align:start position:0%
+eventually and get the company going
+ 
+
+ align:start position:0%
+eventually and get the company going
+so getting money and was kind of a tough
+
+ align:start position:0%
+so getting money and was kind of a tough
+ 
+
+ align:start position:0%
+so getting money and was kind of a tough
+process for the you know throughout the
+
+ align:start position:0%
+process for the you know throughout the
+ 
+
+ align:start position:0%
+process for the you know throughout the
+entire time they both some really staked
+
+ align:start position:0%
+entire time they both some really staked
+ 
+
+ align:start position:0%
+entire time they both some really staked
+a lot of their career on this endeavor
+
+ align:start position:0%
+a lot of their career on this endeavor
+ 
+
+ align:start position:0%
+a lot of their career on this endeavor
+and Swanson
+
+ align:start position:0%
+and Swanson
+ 
+
+ align:start position:0%
+and Swanson
+at the time was very young and went
+
+ align:start position:0%
+at the time was very young and went
+ 
+
+ align:start position:0%
+at the time was very young and went
+through many periods of unemployment as
+
+ align:start position:0%
+through many periods of unemployment as
+ 
+
+ align:start position:0%
+through many periods of unemployment as
+he was trying to you know get the money
+
+ align:start position:0%
+he was trying to you know get the money
+ 
+
+ align:start position:0%
+he was trying to you know get the money
+for financing this man-boy continuing
+
+ align:start position:0%
+for financing this man-boy continuing
+ 
+
+ align:start position:0%
+for financing this man-boy continuing
+his his day job teaching so eventually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the they branded to many obstacles
+
+ align:start position:0%
+so the they branded to many obstacles
+ 
+
+ align:start position:0%
+so the they branded to many obstacles
+financially but they also at the time
+
+ align:start position:0%
+financially but they also at the time
+ 
+
+ align:start position:0%
+financially but they also at the time
+when they decided to bank target humans
+
+ align:start position:0%
+when they decided to bank target humans
+ 
+
+ align:start position:0%
+when they decided to bank target humans
+in the first place that kind of
+
+ align:start position:0%
+in the first place that kind of
+ 
+
+ align:start position:0%
+in the first place that kind of
+kick-started a nationwide race to do
+
+ align:start position:0%
+kick-started a nationwide race to do
+ 
+
+ align:start position:0%
+kick-started a nationwide race to do
+this and so there was a group at Harvard
+
+ align:start position:0%
+this and so there was a group at Harvard
+ 
+
+ align:start position:0%
+this and so there was a group at Harvard
+and another group at some another
+
+ align:start position:0%
+and another group at some another
+ 
+
+ align:start position:0%
+and another group at some another
+university in California blanking on the
+
+ align:start position:0%
+university in California blanking on the
+ 
+
+ align:start position:0%
+university in California blanking on the
+name but yeah they it was a they're
+
+ align:start position:0%
+name but yeah they it was a they're
+ 
+
+ align:start position:0%
+name but yeah they it was a they're
+particularly formidable rivals and they
+
+ align:start position:0%
+particularly formidable rivals and they
+ 
+
+ align:start position:0%
+particularly formidable rivals and they
+had those other two groups were kind of
+
+ align:start position:0%
+had those other two groups were kind of
+ 
+
+ align:start position:0%
+had those other two groups were kind of
+entrenched in academia and they had all
+
+ align:start position:0%
+entrenched in academia and they had all
+ 
+
+ align:start position:0%
+entrenched in academia and they had all
+the resources that you brought them
+
+ align:start position:0%
+the resources that you brought them
+ 
+
+ align:start position:0%
+the resources that you brought them
+whereas Boyer influence and were
+
+ align:start position:0%
+whereas Boyer influence and were
+ 
+
+ align:start position:0%
+whereas Boyer influence and were
+relatively resource poor but they had
+
+ align:start position:0%
+relatively resource poor but they had
+ 
+
+ align:start position:0%
+relatively resource poor but they had
+one advantage that he was working for I
+
+ align:start position:0%
+one advantage that he was working for I
+ 
+
+ align:start position:0%
+one advantage that he was working for I
+was working with synthetic DNA which
+
+ align:start position:0%
+was working with synthetic DNA which
+ 
+
+ align:start position:0%
+was working with synthetic DNA which
+would allow him to get around
+
+ align:start position:0%
+would allow him to get around
+ 
+
+ align:start position:0%
+would allow him to get around
+regulations at the NIH put on natural
+
+ align:start position:0%
+regulations at the NIH put on natural
+ 
+
+ align:start position:0%
+regulations at the NIH put on natural
+DNA during this process so they faced a
+
+ align:start position:0%
+DNA during this process so they faced a
+ 
+
+ align:start position:0%
+DNA during this process so they faced a
+lot of other obstacles and but they
+
+ align:start position:0%
+lot of other obstacles and but they
+ 
+
+ align:start position:0%
+lot of other obstacles and but they
+still had advantages other teams still
+
+ align:start position:0%
+still had advantages other teams still
+ 
+
+ align:start position:0%
+still had advantages other teams still
+advantages of scale and sales ability
+
+ align:start position:0%
+advantages of scale and sales ability
+ 
+
+ align:start position:0%
+advantages of scale and sales ability
+Swanson goal was to make Genentech a
+
+ align:start position:0%
+Swanson goal was to make Genentech a
+ 
+
+ align:start position:0%
+Swanson goal was to make Genentech a
+fully integrated pharmaceutical company
+
+ align:start position:0%
+fully integrated pharmaceutical company
+ 
+
+ align:start position:0%
+fully integrated pharmaceutical company
+and they wanted the eventual goal is to
+
+ align:start position:0%
+and they wanted the eventual goal is to
+ 
+
+ align:start position:0%
+and they wanted the eventual goal is to
+be able to produce and sell a wide range
+
+ align:start position:0%
+be able to produce and sell a wide range
+ 
+
+ align:start position:0%
+be able to produce and sell a wide range
+of drugs
+
+ align:start position:0%
+of drugs
+ 
+
+ align:start position:0%
+of drugs
+and they believe that if they were the
+
+ align:start position:0%
+and they believe that if they were the
+ 
+
+ align:start position:0%
+and they believe that if they were the
+first to make the issue and that we will
+
+ align:start position:0%
+first to make the issue and that we will
+ 
+
+ align:start position:0%
+first to make the issue and that we will
+that would give them the lift up in the
+
+ align:start position:0%
+that would give them the lift up in the
+ 
+
+ align:start position:0%
+that would give them the lift up in the
+industry that they needed so Swanson
+
+ align:start position:0%
+industry that they needed so Swanson
+ 
+
+ align:start position:0%
+industry that they needed so Swanson
+wanted a hiring spree and recruited
+
+ align:start position:0%
+wanted a hiring spree and recruited
+ 
+
+ align:start position:0%
+wanted a hiring spree and recruited
+talent they were able to evoke open up
+
+ align:start position:0%
+talent they were able to evoke open up
+ 
+
+ align:start position:0%
+talent they were able to evoke open up
+their own lab eventually he was able to
+
+ align:start position:0%
+their own lab eventually he was able to
+ 
+
+ align:start position:0%
+their own lab eventually he was able to
+get a hundred K from various sources for
+
+ align:start position:0%
+get a hundred K from various sources for
+ 
+
+ align:start position:0%
+get a hundred K from various sources for
+that initial push so eventually by
+
+ align:start position:0%
+that initial push so eventually by
+ 
+
+ align:start position:0%
+that initial push so eventually by
+August of 1978 we were able to make the
+
+ align:start position:0%
+August of 1978 we were able to make the
+ 
+
+ align:start position:0%
+August of 1978 we were able to make the
+first 20 nanograms of these and they
+
+ align:start position:0%
+first 20 nanograms of these and they
+ 
+
+ align:start position:0%
+first 20 nanograms of these and they
+immediately contacted UI Lilly and
+
+ align:start position:0%
+immediately contacted UI Lilly and
+ 
+
+ align:start position:0%
+immediately contacted UI Lilly and
+sponson kind of went against Convention
+
+ align:start position:0%
+sponson kind of went against Convention
+ 
+
+ align:start position:0%
+sponson kind of went against Convention
+and how does this huge televised press
+
+ align:start position:0%
+and how does this huge televised press
+ 
+
+ align:start position:0%
+and how does this huge televised press
+conference where he announced that the
+
+ align:start position:0%
+conference where he announced that the
+ 
+
+ align:start position:0%
+conference where he announced that the
+achieve what they wanted to achieve and
+
+ align:start position:0%
+achieve what they wanted to achieve and
+ 
+
+ align:start position:0%
+achieve what they wanted to achieve and
+that kind of do it he attended and quit
+
+ align:start position:0%
+that kind of do it he attended and quit
+ 
+
+ align:start position:0%
+that kind of do it he attended and quit
+Genentech really put it on the map and
+
+ align:start position:0%
+Genentech really put it on the map and
+ 
+
+ align:start position:0%
+Genentech really put it on the map and
+in the public eye and eventually you
+
+ align:start position:0%
+in the public eye and eventually you
+ 
+
+ align:start position:0%
+in the public eye and eventually you
+know Eli ladies company came forward
+
+ align:start position:0%
+know Eli ladies company came forward
+ 
+
+ align:start position:0%
+know Eli ladies company came forward
+with ten million dollars for genetic and
+
+ align:start position:0%
+with ten million dollars for genetic and
+ 
+
+ align:start position:0%
+with ten million dollars for genetic and
+they were eventually able to pass track
+
+ align:start position:0%
+they were eventually able to pass track
+ 
+
+ align:start position:0%
+they were eventually able to pass track
+it for industrial production and in 1980
+
+ align:start position:0%
+it for industrial production and in 1980
+ 
+
+ align:start position:0%
+it for industrial production and in 1980
+they had their IPO it was one of the
+
+ align:start position:0%
+they had their IPO it was one of the
+ 
+
+ align:start position:0%
+they had their IPO it was one of the
+most protected IPOs seen from this
+
+ align:start position:0%
+most protected IPOs seen from this
+ 
+
+ align:start position:0%
+most protected IPOs seen from this
+industry and they were eventually able
+
+ align:start position:0%
+industry and they were eventually able
+ 
+
+ align:start position:0%
+industry and they were eventually able
+to in 1985 they were able to release a
+
+ align:start position:0%
+to in 1985 they were able to release a
+ 
+
+ align:start position:0%
+to in 1985 they were able to release a
+second drug and these are some of the
+
+ align:start position:0%
+second drug and these are some of the
+ 
+
+ align:start position:0%
+second drug and these are some of the
+early products
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so going on to the types of
+
+ align:start position:0%
+yeah so going on to the types of
+ 
+
+ align:start position:0%
+yeah so going on to the types of
+qualities of great groups that we've
+
+ align:start position:0%
+qualities of great groups that we've
+ 
+
+ align:start position:0%
+qualities of great groups that we've
+been talking about so I think one of the
+
+ align:start position:0%
+been talking about so I think one of the
+ 
+
+ align:start position:0%
+been talking about so I think one of the
+main things was Swanson's leadership so
+
+ align:start position:0%
+main things was Swanson's leadership so
+ 
+
+ align:start position:0%
+main things was Swanson's leadership so
+the article mentioned that he had a very
+
+ align:start position:0%
+the article mentioned that he had a very
+ 
+
+ align:start position:0%
+the article mentioned that he had a very
+down-to-earth style and was the look
+
+ align:start position:0%
+down-to-earth style and was the look
+ 
+
+ align:start position:0%
+down-to-earth style and was the look
+that connected with everyone who was
+
+ align:start position:0%
+that connected with everyone who was
+ 
+
+ align:start position:0%
+that connected with everyone who was
+involved as well as a great generosity
+
+ align:start position:0%
+involved as well as a great generosity
+ 
+
+ align:start position:0%
+involved as well as a great generosity
+towards everybody and so he was he
+
+ align:start position:0%
+towards everybody and so he was he
+ 
+
+ align:start position:0%
+towards everybody and so he was he
+offered basically everyone from the top
+
+ align:start position:0%
+offered basically everyone from the top
+ 
+
+ align:start position:0%
+offered basically everyone from the top
+scientists to the custodians a share of
+
+ align:start position:0%
+scientists to the custodians a share of
+ 
+
+ align:start position:0%
+scientists to the custodians a share of
+a company at one point and you had a
+
+ align:start position:0%
+a company at one point and you had a
+ 
+
+ align:start position:0%
+a company at one point and you had a
+really great effective recruitment of
+
+ align:start position:0%
+really great effective recruitment of
+ 
+
+ align:start position:0%
+really great effective recruitment of
+talent he was able to see where they
+
+ align:start position:0%
+talent he was able to see where they
+ 
+
+ align:start position:0%
+talent he was able to see where they
+needed people and had that good for that
+
+ align:start position:0%
+needed people and had that good for that
+ 
+
+ align:start position:0%
+needed people and had that good for that
+those positions another really important
+
+ align:start position:0%
+those positions another really important
+ 
+
+ align:start position:0%
+those positions another really important
+one for an element is that there was a
+
+ align:start position:0%
+one for an element is that there was a
+ 
+
+ align:start position:0%
+one for an element is that there was a
+real conviction of cause so Boyer
+
+ align:start position:0%
+real conviction of cause so Boyer
+ 
+
+ align:start position:0%
+real conviction of cause so Boyer
+initially wanted to get into
+
+ align:start position:0%
+initially wanted to get into
+ 
+
+ align:start position:0%
+initially wanted to get into
+commercialization because he felt that
+
+ align:start position:0%
+commercialization because he felt that
+ 
+
+ align:start position:0%
+commercialization because he felt that
+university research and
+
+ align:start position:0%
+university research and
+ 
+
+ align:start position:0%
+university research and
+government-funded research wouldn't
+
+ align:start position:0%
+government-funded research wouldn't
+ 
+
+ align:start position:0%
+government-funded research wouldn't
+allow him to see the real benefits
+
+ align:start position:0%
+allow him to see the real benefits
+ 
+
+ align:start position:0%
+allow him to see the real benefits
+practical benefits of this work so it's
+
+ align:start position:0%
+practical benefits of this work so it's
+ 
+
+ align:start position:0%
+practical benefits of this work so it's
+kind of a really altruistic goal of his
+
+ align:start position:0%
+kind of a really altruistic goal of his
+ 
+
+ align:start position:0%
+kind of a really altruistic goal of his
+and that mission kind of carried them
+
+ align:start position:0%
+and that mission kind of carried them
+ 
+
+ align:start position:0%
+and that mission kind of carried them
+out okay I think throughout this process
+
+ align:start position:0%
+out okay I think throughout this process
+ 
+
+ align:start position:0%
+out okay I think throughout this process
+that they were going to be making
+
+ align:start position:0%
+that they were going to be making
+ 
+
+ align:start position:0%
+that they were going to be making
+something that would better people's
+
+ align:start position:0%
+something that would better people's
+ 
+
+ align:start position:0%
+something that would better people's
+lives save lives another important
+
+ align:start position:0%
+lives save lives another important
+ 
+
+ align:start position:0%
+lives save lives another important
+element is that they were working
+
+ align:start position:0%
+element is that they were working
+ 
+
+ align:start position:0%
+element is that they were working
+against a common enemy so it wasn't
+
+ align:start position:0%
+against a common enemy so it wasn't
+ 
+
+ align:start position:0%
+against a common enemy so it wasn't
+exactly an enemy but they were there
+
+ align:start position:0%
+exactly an enemy but they were there
+ 
+
+ align:start position:0%
+exactly an enemy but they were there
+were those other teams that they were
+
+ align:start position:0%
+were those other teams that they were
+ 
+
+ align:start position:0%
+were those other teams that they were
+working against and that competition
+
+ align:start position:0%
+working against and that competition
+ 
+
+ align:start position:0%
+working against and that competition
+really filled them and going along with
+
+ align:start position:0%
+really filled them and going along with
+ 
+
+ align:start position:0%
+really filled them and going along with
+that they were kind of like the
+
+ align:start position:0%
+that they were kind of like the
+ 
+
+ align:start position:0%
+that they were kind of like the
+underdogs and the young company that
+
+ align:start position:0%
+underdogs and the young company that
+ 
+
+ align:start position:0%
+underdogs and the young company that
+didn't have the resources and didn't
+
+ align:start position:0%
+didn't have the resources and didn't
+ 
+
+ align:start position:0%
+didn't have the resources and didn't
+have the funding so that really was
+
+ align:start position:0%
+have the funding so that really was
+ 
+
+ align:start position:0%
+have the funding so that really was
+another motivating factor as well yeah
+
+ align:start position:0%
+another motivating factor as well yeah
+ 
+
+ align:start position:0%
+another motivating factor as well yeah
+another one is optimism and a degree of
+
+ align:start position:0%
+another one is optimism and a degree of
+ 
+
+ align:start position:0%
+another one is optimism and a degree of
+naivete so that kind of came in to play
+
+ align:start position:0%
+naivete so that kind of came in to play
+ 
+
+ align:start position:0%
+naivete so that kind of came in to play
+when they first made insulin but Eli
+
+ align:start position:0%
+when they first made insulin but Eli
+ 
+
+ align:start position:0%
+when they first made insulin but Eli
+Lilly said that they needed had put
+
+ align:start position:0%
+Lilly said that they needed had put
+ 
+
+ align:start position:0%
+Lilly said that they needed had put
+really strict timeline on them for
+
+ align:start position:0%
+really strict timeline on them for
+ 
+
+ align:start position:0%
+really strict timeline on them for
+developing it for industrial production
+
+ align:start position:0%
+developing it for industrial production
+ 
+
+ align:start position:0%
+developing it for industrial production
+and most people would have said that
+
+ align:start position:0%
+and most people would have said that
+ 
+
+ align:start position:0%
+and most people would have said that
+that was impossible and that they
+
+ align:start position:0%
+that was impossible and that they
+ 
+
+ align:start position:0%
+that was impossible and that they
+couldn't do that in that timeframe but
+
+ align:start position:0%
+couldn't do that in that timeframe but
+ 
+
+ align:start position:0%
+couldn't do that in that timeframe but
+they were none the wiser and kind of
+
+ align:start position:0%
+they were none the wiser and kind of
+ 
+
+ align:start position:0%
+they were none the wiser and kind of
+went for it anyways and
+
+ align:start position:0%
+went for it anyways and
+ 
+
+ align:start position:0%
+went for it anyways and
+it end up working out working out for
+
+ align:start position:0%
+it end up working out working out for
+ 
+
+ align:start position:0%
+it end up working out working out for
+them another thing is that the people
+
+ align:start position:0%
+them another thing is that the people
+ 
+
+ align:start position:0%
+them another thing is that the people
+were not interchangeable so like I said
+
+ align:start position:0%
+were not interchangeable so like I said
+ 
+
+ align:start position:0%
+were not interchangeable so like I said
+before they read there were that list of
+
+ align:start position:0%
+before they read there were that list of
+ 
+
+ align:start position:0%
+before they read there were that list of
+places that I showed you were very
+
+ align:start position:0%
+places that I showed you were very
+ 
+
+ align:start position:0%
+places that I showed you were very
+instrumental and they weren't specific
+
+ align:start position:0%
+instrumental and they weren't specific
+ 
+
+ align:start position:0%
+instrumental and they weren't specific
+expertise that they brought to the
+
+ align:start position:0%
+expertise that they brought to the
+ 
+
+ align:start position:0%
+expertise that they brought to the
+project also but there was there was
+
+ align:start position:0%
+project also but there was there was
+ 
+
+ align:start position:0%
+project also but there was there was
+relative freedom for a lot of the
+
+ align:start position:0%
+relative freedom for a lot of the
+ 
+
+ align:start position:0%
+relative freedom for a lot of the
+scientists involved in denatech so one
+
+ align:start position:0%
+scientists involved in denatech so one
+ 
+
+ align:start position:0%
+scientists involved in denatech so one
+of the things that Swanson did to get
+
+ align:start position:0%
+of the things that Swanson did to get
+ 
+
+ align:start position:0%
+of the things that Swanson did to get
+people on board especially David Coto
+
+ align:start position:0%
+people on board especially David Coto
+ 
+
+ align:start position:0%
+people on board especially David Coto
+he said that they could still have the
+
+ align:start position:0%
+he said that they could still have the
+ 
+
+ align:start position:0%
+he said that they could still have the
+freedom to publish under their own name
+
+ align:start position:0%
+freedom to publish under their own name
+ 
+
+ align:start position:0%
+freedom to publish under their own name
+even though they were contracted to
+
+ align:start position:0%
+even though they were contracted to
+ 
+
+ align:start position:0%
+even though they were contracted to
+genitive so that was a real incentive
+
+ align:start position:0%
+genitive so that was a real incentive
+ 
+
+ align:start position:0%
+genitive so that was a real incentive
+for people to join them and lastly there
+
+ align:start position:0%
+for people to join them and lastly there
+ 
+
+ align:start position:0%
+for people to join them and lastly there
+was a really casual environment in the
+
+ align:start position:0%
+was a really casual environment in the
+ 
+
+ align:start position:0%
+was a really casual environment in the
+office teacher attire and you know there
+
+ align:start position:0%
+office teacher attire and you know there
+ 
+
+ align:start position:0%
+office teacher attire and you know there
+wasn't any you know strict rules or a
+
+ align:start position:0%
+wasn't any you know strict rules or a
+ 
+
+ align:start position:0%
+wasn't any you know strict rules or a
+sense of top-down management so um some
+
+ align:start position:0%
+sense of top-down management so um some
+ 
+
+ align:start position:0%
+sense of top-down management so um some
+other dynamics that I think they're
+
+ align:start position:0%
+other dynamics that I think they're
+ 
+
+ align:start position:0%
+other dynamics that I think they're
+important this was an interesting case
+
+ align:start position:0%
+important this was an interesting case
+ 
+
+ align:start position:0%
+important this was an interesting case
+of a great group because it came at a
+
+ align:start position:0%
+of a great group because it came at a
+ 
+
+ align:start position:0%
+of a great group because it came at a
+time when there was kind of a changing
+
+ align:start position:0%
+time when there was kind of a changing
+ 
+
+ align:start position:0%
+time when there was kind of a changing
+relationship between science and
+
+ align:start position:0%
+relationship between science and
+ 
+
+ align:start position:0%
+relationship between science and
+business and academia and the commercial
+
+ align:start position:0%
+business and academia and the commercial
+ 
+
+ align:start position:0%
+business and academia and the commercial
+sector and Boyer's journey was pretty
+
+ align:start position:0%
+sector and Boyer's journey was pretty
+ 
+
+ align:start position:0%
+sector and Boyer's journey was pretty
+interesting he started out firmly in
+
+ align:start position:0%
+interesting he started out firmly in
+ 
+
+ align:start position:0%
+interesting he started out firmly in
+academia but he chose to look beyond
+
+ align:start position:0%
+academia but he chose to look beyond
+ 
+
+ align:start position:0%
+academia but he chose to look beyond
+that his words like I said it with his
+
+ align:start position:0%
+that his words like I said it with his
+ 
+
+ align:start position:0%
+that his words like I said it with his
+words at the initial meeting with
+
+ align:start position:0%
+words at the initial meeting with
+ 
+
+ align:start position:0%
+words at the initial meeting with
+Swanson about wanting to see the real
+
+ align:start position:0%
+Swanson about wanting to see the real
+ 
+
+ align:start position:0%
+Swanson about wanting to see the real
+practical benefits of his work kind of
+
+ align:start position:0%
+practical benefits of his work kind of
+ 
+
+ align:start position:0%
+practical benefits of his work kind of
+carry them carried the whole team
+
+ align:start position:0%
+carry them carried the whole team
+ 
+
+ align:start position:0%
+carry them carried the whole team
+throughout but you know the flip side of
+
+ align:start position:0%
+throughout but you know the flip side of
+ 
+
+ align:start position:0%
+throughout but you know the flip side of
+that was that in the early history of
+
+ align:start position:0%
+that was that in the early history of
+ 
+
+ align:start position:0%
+that was that in the early history of
+Genentech he was a target for academic
+
+ align:start position:0%
+Genentech he was a target for academic
+ 
+
+ align:start position:0%
+Genentech he was a target for academic
+scientists who dismissed the idea that
+
+ align:start position:0%
+scientists who dismissed the idea that
+ 
+
+ align:start position:0%
+scientists who dismissed the idea that
+parking signs would ever be able to
+
+ align:start position:0%
+parking signs would ever be able to
+ 
+
+ align:start position:0%
+parking signs would ever be able to
+achieve the kind of things that they
+
+ align:start position:0%
+achieve the kind of things that they
+ 
+
+ align:start position:0%
+achieve the kind of things that they
+would be able to achieve and his move to
+
+ align:start position:0%
+would be able to achieve and his move to
+ 
+
+ align:start position:0%
+would be able to achieve and his move to
+commercialization really drew the
+
+ align:start position:0%
+commercialization really drew the
+ 
+
+ align:start position:0%
+commercialization really drew the
+animosity of academia because he was one
+
+ align:start position:0%
+animosity of academia because he was one
+ 
+
+ align:start position:0%
+animosity of academia because he was one
+of the first of many scientists at the
+
+ align:start position:0%
+of the first of many scientists at the
+ 
+
+ align:start position:0%
+of the first of many scientists at the
+frontier of molecular biology who were
+
+ align:start position:0%
+frontier of molecular biology who were
+ 
+
+ align:start position:0%
+frontier of molecular biology who were
+who sought to capitalize on the
+
+ align:start position:0%
+who sought to capitalize on the
+ 
+
+ align:start position:0%
+who sought to capitalize on the
+commercial opportunities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of Swanson's and boys to some
+
+ align:start position:0%
+and one of Swanson's and boys to some
+ 
+
+ align:start position:0%
+and one of Swanson's and boys to some
+extent strength was their ability to
+
+ align:start position:0%
+extent strength was their ability to
+ 
+
+ align:start position:0%
+extent strength was their ability to
+recognize the exact moment in in the in
+
+ align:start position:0%
+recognize the exact moment in in the in
+ 
+
+ align:start position:0%
+recognize the exact moment in in the in
+basic research in molecular
+
+ align:start position:0%
+basic research in molecular
+ 
+
+ align:start position:0%
+basic research in molecular
+biotechnology that was most beneficial
+
+ align:start position:0%
+biotechnology that was most beneficial
+ 
+
+ align:start position:0%
+biotechnology that was most beneficial
+to open up to it to open it up to a
+
+ align:start position:0%
+to open up to it to open it up to a
+ 
+
+ align:start position:0%
+to open up to it to open it up to a
+commercial endeavor so they were able to
+
+ align:start position:0%
+commercial endeavor so they were able to
+ 
+
+ align:start position:0%
+commercial endeavor so they were able to
+combine an extensive knowledge of the
+
+ align:start position:0%
+combine an extensive knowledge of the
+ 
+
+ align:start position:0%
+combine an extensive knowledge of the
+science moment they were trying to do
+
+ align:start position:0%
+science moment they were trying to do
+ 
+
+ align:start position:0%
+science moment they were trying to do
+and also the business acumen needed to
+
+ align:start position:0%
+and also the business acumen needed to
+ 
+
+ align:start position:0%
+and also the business acumen needed to
+move it forward and this really set them
+
+ align:start position:0%
+move it forward and this really set them
+ 
+
+ align:start position:0%
+move it forward and this really set them
+apart from other big drunk drug
+
+ align:start position:0%
+apart from other big drunk drug
+ 
+
+ align:start position:0%
+apart from other big drunk drug
+companies at the time and I think
+
+ align:start position:0%
+companies at the time and I think
+ 
+
+ align:start position:0%
+companies at the time and I think
+ultimately contributed to their great
+
+ align:start position:0%
+ultimately contributed to their great
+ 
+
+ align:start position:0%
+ultimately contributed to their great
+success as well yeah so this is a quote
+
+ align:start position:0%
+success as well yeah so this is a quote
+ 
+
+ align:start position:0%
+success as well yeah so this is a quote
+about Swanson who was really kind of one
+
+ align:start position:0%
+about Swanson who was really kind of one
+ 
+
+ align:start position:0%
+about Swanson who was really kind of one
+of the first figures who was able to
+
+ align:start position:0%
+of the first figures who was able to
+ 
+
+ align:start position:0%
+of the first figures who was able to
+really bridge that the partnership
+
+ align:start position:0%
+really bridge that the partnership
+ 
+
+ align:start position:0%
+really bridge that the partnership
+between science and business so in a way
+
+ align:start position:0%
+between science and business so in a way
+ 
+
+ align:start position:0%
+between science and business so in a way
+you can kind of think of him as like an
+
+ align:start position:0%
+you can kind of think of him as like an
+ 
+
+ align:start position:0%
+you can kind of think of him as like an
+advocate before the scientists that he
+
+ align:start position:0%
+advocate before the scientists that he
+ 
+
+ align:start position:0%
+advocate before the scientists that he
+was representing and people like Jenna
+
+ align:start position:0%
+was representing and people like Jenna
+ 
+
+ align:start position:0%
+was representing and people like Jenna
+fact who were looking to really advance
+
+ align:start position:0%
+fact who were looking to really advance
+ 
+
+ align:start position:0%
+fact who were looking to really advance
+in this field that was quite new so I
+
+ align:start position:0%
+in this field that was quite new so I
+ 
+
+ align:start position:0%
+in this field that was quite new so I
+guess one of going into sort of
+
+ align:start position:0%
+guess one of going into sort of
+ 
+
+ align:start position:0%
+guess one of going into sort of
+discussion questions one of my main
+
+ align:start position:0%
+discussion questions one of my main
+ 
+
+ align:start position:0%
+discussion questions one of my main
+questions was did the relative newness
+
+ align:start position:0%
+questions was did the relative newness
+ 
+
+ align:start position:0%
+questions was did the relative newness
+of this field in this industry really
+
+ align:start position:0%
+of this field in this industry really
+ 
+
+ align:start position:0%
+of this field in this industry really
+help them I mean did that offer their
+
+ align:start position:0%
+help them I mean did that offer their
+ 
+
+ align:start position:0%
+help them I mean did that offer their
+opportunities to Swanson to worry that
+
+ align:start position:0%
+opportunities to Swanson to worry that
+ 
+
+ align:start position:0%
+opportunities to Swanson to worry that
+maybe more established industry or field
+
+ align:start position:0%
+maybe more established industry or field
+ 
+
+ align:start position:0%
+maybe more established industry or field
+would not have did that allow so I'm
+
+ align:start position:0%
+would not have did that allow so I'm
+ 
+
+ align:start position:0%
+would not have did that allow so I'm
+gonna put that on hold for just a second
+
+ align:start position:0%
+gonna put that on hold for just a second
+ 
+
+ align:start position:0%
+gonna put that on hold for just a second
+because through a couple of kind of
+
+ align:start position:0%
+because through a couple of kind of
+ 
+
+ align:start position:0%
+because through a couple of kind of
+framing points out but that's I think
+
+ align:start position:0%
+framing points out but that's I think
+ 
+
+ align:start position:0%
+framing points out but that's I think
+that's a key question and I'll lead up
+
+ align:start position:0%
+that's a key question and I'll lead up
+ 
+
+ align:start position:0%
+that's a key question and I'll lead up
+to that to them this is the first
+
+ align:start position:0%
+to that to them this is the first
+ 
+
+ align:start position:0%
+to that to them this is the first
+biotech right this creates the model and
+
+ align:start position:0%
+biotech right this creates the model and
+ 
+
+ align:start position:0%
+biotech right this creates the model and
+you know as you point out this
+
+ align:start position:0%
+you know as you point out this
+ 
+
+ align:start position:0%
+you know as you point out this
+combination of Boyer and Swanson is a
+
+ align:start position:0%
+combination of Boyer and Swanson is a
+ 
+
+ align:start position:0%
+combination of Boyer and Swanson is a
+fascinating combination because they are
+
+ align:start position:0%
+fascinating combination because they are
+ 
+
+ align:start position:0%
+fascinating combination because they are
+as you put it able to kind of bridge
+
+ align:start position:0%
+as you put it able to kind of bridge
+ 
+
+ align:start position:0%
+as you put it able to kind of bridge
+this divide between business and science
+
+ align:start position:0%
+this divide between business and science
+ 
+
+ align:start position:0%
+this divide between business and science
+and that is the inherent you know
+
+ align:start position:0%
+and that is the inherent you know
+ 
+
+ align:start position:0%
+and that is the inherent you know
+brilliance of the biotech model and
+
+ align:start position:0%
+brilliance of the biotech model and
+ 
+
+ align:start position:0%
+brilliance of the biotech model and
+these folks really figure out how to do
+
+ align:start position:0%
+these folks really figure out how to do
+ 
+
+ align:start position:0%
+these folks really figure out how to do
+it and genatech to this day is an
+
+ align:start position:0%
+it and genatech to this day is an
+ 
+
+ align:start position:0%
+it and genatech to this day is an
+extremely successful company so it has
+
+ align:start position:0%
+extremely successful company so it has
+ 
+
+ align:start position:0%
+extremely successful company so it has
+been able to keep on that innovation
+
+ align:start position:0%
+been able to keep on that innovation
+ 
+
+ align:start position:0%
+been able to keep on that innovation
+pathway which means to the culture that
+
+ align:start position:0%
+pathway which means to the culture that
+ 
+
+ align:start position:0%
+pathway which means to the culture that
+they set up here has been able to keep
+
+ align:start position:0%
+they set up here has been able to keep
+ 
+
+ align:start position:0%
+they set up here has been able to keep
+you know innovation occurring on a kind
+
+ align:start position:0%
+you know innovation occurring on a kind
+ 
+
+ align:start position:0%
+you know innovation occurring on a kind
+of ongoing basis and some of the points
+
+ align:start position:0%
+of ongoing basis and some of the points
+ 
+
+ align:start position:0%
+of ongoing basis and some of the points
+you made sand them just to emphasize
+
+ align:start position:0%
+you made sand them just to emphasize
+ 
+
+ align:start position:0%
+you made sand them just to emphasize
+some of the points you made the fact
+
+ align:start position:0%
+some of the points you made the fact
+ 
+
+ align:start position:0%
+some of the points you made the fact
+that Boyer and Swanson allowed their
+
+ align:start position:0%
+that Boyer and Swanson allowed their
+ 
+
+ align:start position:0%
+that Boyer and Swanson allowed their
+researchers to do their own publishing
+
+ align:start position:0%
+researchers to do their own publishing
+ 
+
+ align:start position:0%
+researchers to do their own publishing
+right that they didn't treat what they
+
+ align:start position:0%
+right that they didn't treat what they
+ 
+
+ align:start position:0%
+right that they didn't treat what they
+were working on is a complete trade
+
+ align:start position:0%
+were working on is a complete trade
+ 
+
+ align:start position:0%
+were working on is a complete trade
+secret that was a huge enabler in
+
+ align:start position:0%
+secret that was a huge enabler in
+ 
+
+ align:start position:0%
+secret that was a huge enabler in
+enabling the academic community to kind
+
+ align:start position:0%
+enabling the academic community to kind
+ 
+
+ align:start position:0%
+enabling the academic community to kind
+of enter into these biotech so in other
+
+ align:start position:0%
+of enter into these biotech so in other
+ 
+
+ align:start position:0%
+of enter into these biotech so in other
+words their academic role was going to
+
+ align:start position:0%
+words their academic role was going to
+ 
+
+ align:start position:0%
+words their academic role was going to
+be respected their role as researchers
+
+ align:start position:0%
+be respected their role as researchers
+ 
+
+ align:start position:0%
+be respected their role as researchers
+and scientists and contributing to
+
+ align:start position:0%
+and scientists and contributing to
+ 
+
+ align:start position:0%
+and scientists and contributing to
+general knowledge was going to have
+
+ align:start position:0%
+general knowledge was going to have
+ 
+
+ align:start position:0%
+general knowledge was going to have
+respect it here and that created a rule
+
+ align:start position:0%
+respect it here and that created a rule
+ 
+
+ align:start position:0%
+respect it here and that created a rule
+in this biotech that you know prevails
+
+ align:start position:0%
+in this biotech that you know prevails
+ 
+
+ align:start position:0%
+in this biotech that you know prevails
+this to this day and yet it very much
+
+ align:start position:0%
+this to this day and yet it very much
+ 
+
+ align:start position:0%
+this to this day and yet it very much
+influenced the kind of model but the
+
+ align:start position:0%
+influenced the kind of model but the
+ 
+
+ align:start position:0%
+influenced the kind of model but the
+ability so in the biotech model and
+
+ align:start position:0%
+ability so in the biotech model and
+ 
+
+ align:start position:0%
+ability so in the biotech model and
+Swenson and Swanson and and and Boyer
+
+ align:start position:0%
+Swenson and Swanson and and and Boyer
+ 
+
+ align:start position:0%
+Swenson and Swanson and and and Boyer
+pioneer this they create this revolving
+
+ align:start position:0%
+pioneer this they create this revolving
+ 
+
+ align:start position:0%
+pioneer this they create this revolving
+door capability so in other words
+
+ align:start position:0%
+door capability so in other words
+ 
+
+ align:start position:0%
+door capability so in other words
+scientists at universities now in the
+
+ align:start position:0%
+scientists at universities now in the
+ 
+
+ align:start position:0%
+scientists at universities now in the
+United States that work in in life
+
+ align:start position:0%
+United States that work in in life
+ 
+
+ align:start position:0%
+United States that work in in life
+science areas and related areas are able
+
+ align:start position:0%
+science areas and related areas are able
+ 
+
+ align:start position:0%
+science areas and related areas are able
+to have careers whether in the Academy
+
+ align:start position:0%
+to have careers whether in the Academy
+ 
+
+ align:start position:0%
+to have careers whether in the Academy
+they moved to a biotech you know as a
+
+ align:start position:0%
+they moved to a biotech you know as a
+ 
+
+ align:start position:0%
+they moved to a biotech you know as a
+scientist for a period of time they can
+
+ align:start position:0%
+scientist for a period of time they can
+ 
+
+ align:start position:0%
+scientist for a period of time they can
+move back to the Academy right taking
+
+ align:start position:0%
+move back to the Academy right taking
+ 
+
+ align:start position:0%
+move back to the Academy right taking
+their advances with them in other words
+
+ align:start position:0%
+their advances with them in other words
+ 
+
+ align:start position:0%
+their advances with them in other words
+they can move between these sectors so
+
+ align:start position:0%
+they can move between these sectors so
+ 
+
+ align:start position:0%
+they can move between these sectors so
+there was in European science and
+
+ align:start position:0%
+there was in European science and
+ 
+
+ align:start position:0%
+there was in European science and
+historical Upstairs Downstairs treatment
+
+ align:start position:0%
+historical Upstairs Downstairs treatment
+ 
+
+ align:start position:0%
+historical Upstairs Downstairs treatment
+right the academic scientists thought
+
+ align:start position:0%
+right the academic scientists thought
+ 
+
+ align:start position:0%
+right the academic scientists thought
+they were in curiosity-driven basic
+
+ align:start position:0%
+they were in curiosity-driven basic
+ 
+
+ align:start position:0%
+they were in curiosity-driven basic
+research and should have nothing to do
+
+ align:start position:0%
+research and should have nothing to do
+ 
+
+ align:start position:0%
+research and should have nothing to do
+with the kind of ugliness and kind of
+
+ align:start position:0%
+with the kind of ugliness and kind of
+ 
+
+ align:start position:0%
+with the kind of ugliness and kind of
+downstairs of commercialization of
+
+ align:start position:0%
+downstairs of commercialization of
+ 
+
+ align:start position:0%
+downstairs of commercialization of
+products and that these worlds ought to
+
+ align:start position:0%
+products and that these worlds ought to
+ 
+
+ align:start position:0%
+products and that these worlds ought to
+be kept separate and biotech is the
+
+ align:start position:0%
+be kept separate and biotech is the
+ 
+
+ align:start position:0%
+be kept separate and biotech is the
+first really serious attempt in the in
+
+ align:start position:0%
+first really serious attempt in the in
+ 
+
+ align:start position:0%
+first really serious attempt in the in
+the Academy in America to kind of bridge
+
+ align:start position:0%
+the Academy in America to kind of bridge
+ 
+
+ align:start position:0%
+the Academy in America to kind of bridge
+these worlds effectively and they do
+
+ align:start position:0%
+these worlds effectively and they do
+ 
+
+ align:start position:0%
+these worlds effectively and they do
+brilliantly and part of it is as you
+
+ align:start position:0%
+brilliantly and part of it is as you
+ 
+
+ align:start position:0%
+brilliantly and part of it is as you
+point out you know Swanson is a
+
+ align:start position:0%
+point out you know Swanson is a
+ 
+
+ align:start position:0%
+point out you know Swanson is a
+chemistry major at MIT so he is not
+
+ align:start position:0%
+chemistry major at MIT so he is not
+ 
+
+ align:start position:0%
+chemistry major at MIT so he is not
+afraid of science just as you suggest
+
+ align:start position:0%
+afraid of science just as you suggest
+ 
+
+ align:start position:0%
+afraid of science just as you suggest
+that he understands what it is he has he
+
+ align:start position:0%
+that he understands what it is he has he
+ 
+
+ align:start position:0%
+that he understands what it is he has he
+has the ability to be in the room
+
+ align:start position:0%
+has the ability to be in the room
+ 
+
+ align:start position:0%
+has the ability to be in the room
+with these academic scientists and be in
+
+ align:start position:0%
+with these academic scientists and be in
+ 
+
+ align:start position:0%
+with these academic scientists and be in
+the game but he also comes to this with
+
+ align:start position:0%
+the game but he also comes to this with
+ 
+
+ align:start position:0%
+the game but he also comes to this with
+early venture capital experience so he
+
+ align:start position:0%
+early venture capital experience so he
+ 
+
+ align:start position:0%
+early venture capital experience so he
+first goes to work on Sand Hill Road you
+
+ align:start position:0%
+first goes to work on Sand Hill Road you
+ 
+
+ align:start position:0%
+first goes to work on Sand Hill Road you
+know out outside outside in silicon
+
+ align:start position:0%
+know out outside outside in silicon
+ 
+
+ align:start position:0%
+know out outside outside in silicon
+valley outside Stanford and they're only
+
+ align:start position:0%
+valley outside Stanford and they're only
+ 
+
+ align:start position:0%
+valley outside Stanford and they're only
+in Reston to doing IT they have no idea
+
+ align:start position:0%
+in Reston to doing IT they have no idea
+ 
+
+ align:start position:0%
+in Reston to doing IT they have no idea
+about this biotech stuff so he has to
+
+ align:start position:0%
+about this biotech stuff so he has to
+ 
+
+ align:start position:0%
+about this biotech stuff so he has to
+leave this major event early venture
+
+ align:start position:0%
+leave this major event early venture
+ 
+
+ align:start position:0%
+leave this major event early venture
+capital for him that he's with and
+
+ align:start position:0%
+capital for him that he's with and
+ 
+
+ align:start position:0%
+capital for him that he's with and
+essentially starve you know eat hot dogs
+
+ align:start position:0%
+essentially starve you know eat hot dogs
+ 
+
+ align:start position:0%
+essentially starve you know eat hot dogs
+for months at a time as he tries to
+
+ align:start position:0%
+for months at a time as he tries to
+ 
+
+ align:start position:0%
+for months at a time as he tries to
+figure out how is he going to work in
+
+ align:start position:0%
+figure out how is he going to work in
+ 
+
+ align:start position:0%
+figure out how is he going to work in
+this biotech area and famously he as
+
+ align:start position:0%
+this biotech area and famously he as
+ 
+
+ align:start position:0%
+this biotech area and famously he as
+Sonam suggested famously he starts cold
+
+ align:start position:0%
+Sonam suggested famously he starts cold
+ 
+
+ align:start position:0%
+Sonam suggested famously he starts cold
+calling he has this idea that
+
+ align:start position:0%
+calling he has this idea that
+ 
+
+ align:start position:0%
+calling he has this idea that
+bioengineering is going to be this
+
+ align:start position:0%
+bioengineering is going to be this
+ 
+
+ align:start position:0%
+bioengineering is going to be this
+incredibly creative new field he's aware
+
+ align:start position:0%
+incredibly creative new field he's aware
+ 
+
+ align:start position:0%
+incredibly creative new field he's aware
+of it from his own training so he starts
+
+ align:start position:0%
+of it from his own training so he starts
+ 
+
+ align:start position:0%
+of it from his own training so he starts
+cold calling scientists that are working
+
+ align:start position:0%
+cold calling scientists that are working
+ 
+
+ align:start position:0%
+cold calling scientists that are working
+in this bioengineering field he only has
+
+ align:start position:0%
+in this bioengineering field he only has
+ 
+
+ align:start position:0%
+in this bioengineering field he only has
+to get to the bees right to Boyer and
+
+ align:start position:0%
+to get to the bees right to Boyer and
+ 
+
+ align:start position:0%
+to get to the bees right to Boyer and
+then they have this famous meeting at
+
+ align:start position:0%
+then they have this famous meeting at
+ 
+
+ align:start position:0%
+then they have this famous meeting at
+Churchill's pub where they actually so
+
+ align:start position:0%
+Churchill's pub where they actually so
+ 
+
+ align:start position:0%
+Churchill's pub where they actually so
+much hit it off exactly as Sonam
+
+ align:start position:0%
+much hit it off exactly as Sonam
+ 
+
+ align:start position:0%
+much hit it off exactly as Sonam
+described Boyer is concerned that if he
+
+ align:start position:0%
+described Boyer is concerned that if he
+ 
+
+ align:start position:0%
+described Boyer is concerned that if he
+just stays in the Academy nothing he
+
+ align:start position:0%
+just stays in the Academy nothing he
+ 
+
+ align:start position:0%
+just stays in the Academy nothing he
+works on is ever gonna get out right and
+
+ align:start position:0%
+works on is ever gonna get out right and
+ 
+
+ align:start position:0%
+works on is ever gonna get out right and
+he wants to get his stuff out he truly
+
+ align:start position:0%
+he wants to get his stuff out he truly
+ 
+
+ align:start position:0%
+he wants to get his stuff out he truly
+believes this this is not like this he
+
+ align:start position:0%
+believes this this is not like this he
+ 
+
+ align:start position:0%
+believes this this is not like this he
+is not out to get rich here he is really
+
+ align:start position:0%
+is not out to get rich here he is really
+ 
+
+ align:start position:0%
+is not out to get rich here he is really
+out to get to save people and get the
+
+ align:start position:0%
+out to get to save people and get the
+ 
+
+ align:start position:0%
+out to get to save people and get the
+technology out the door so in there's a
+
+ align:start position:0%
+technology out the door so in there's a
+ 
+
+ align:start position:0%
+technology out the door so in there's a
+statue in front of Genentech to this day
+
+ align:start position:0%
+statue in front of Genentech to this day
+ 
+
+ align:start position:0%
+statue in front of Genentech to this day
+that pictures Boyer and Swanson sitting
+
+ align:start position:0%
+that pictures Boyer and Swanson sitting
+ 
+
+ align:start position:0%
+that pictures Boyer and Swanson sitting
+at the bar each pointing the hundred
+
+ align:start position:0%
+at the bar each pointing the hundred
+ 
+
+ align:start position:0%
+at the bar each pointing the hundred
+dollars down on the table as they toast
+
+ align:start position:0%
+dollars down on the table as they toast
+ 
+
+ align:start position:0%
+dollars down on the table as they toast
+each other with beers that that's what
+
+ align:start position:0%
+each other with beers that that's what
+ 
+
+ align:start position:0%
+each other with beers that that's what
+you see when you drive in and see the
+
+ align:start position:0%
+you see when you drive in and see the
+ 
+
+ align:start position:0%
+you see when you drive in and see the
+company headquarters and genatech and
+
+ align:start position:0%
+company headquarters and genatech and
+ 
+
+ align:start position:0%
+company headquarters and genatech and
+that's symbolic think of what's
+
+ align:start position:0%
+that's symbolic think of what's
+ 
+
+ align:start position:0%
+that's symbolic think of what's
+happening here
+
+ align:start position:0%
+happening here
+ 
+
+ align:start position:0%
+happening here
+these folks figure out how to make a
+
+ align:start position:0%
+these folks figure out how to make a
+ 
+
+ align:start position:0%
+these folks figure out how to make a
+really workable marriage between
+
+ align:start position:0%
+really workable marriage between
+ 
+
+ align:start position:0%
+really workable marriage between
+business and science that's you know
+
+ align:start position:0%
+business and science that's you know
+ 
+
+ align:start position:0%
+business and science that's you know
+remarkably productive on both sides of
+
+ align:start position:0%
+remarkably productive on both sides of
+ 
+
+ align:start position:0%
+remarkably productive on both sides of
+the world Boyer is totally ostracized
+
+ align:start position:0%
+the world Boyer is totally ostracized
+ 
+
+ align:start position:0%
+the world Boyer is totally ostracized
+for doing this right
+
+ align:start position:0%
+for doing this right
+ 
+
+ align:start position:0%
+for doing this right
+he faces tremendous recrimination at
+
+ align:start position:0%
+he faces tremendous recrimination at
+ 
+
+ align:start position:0%
+he faces tremendous recrimination at
+UCSF
+
+ align:start position:0%
+UCSF
+ 
+
+ align:start position:0%
+UCSF
+for having gone this commercial roof and
+
+ align:start position:0%
+for having gone this commercial roof and
+ 
+
+ align:start position:0%
+for having gone this commercial roof and
+it's only when they come up with these
+
+ align:start position:0%
+it's only when they come up with these
+ 
+
+ align:start position:0%
+it's only when they come up with these
+stunning successes that the scientific
+
+ align:start position:0%
+stunning successes that the scientific
+ 
+
+ align:start position:0%
+stunning successes that the scientific
+community really has to rethink the kind
+
+ align:start position:0%
+community really has to rethink the kind
+ 
+
+ align:start position:0%
+community really has to rethink the kind
+of way that it went after him so this
+
+ align:start position:0%
+of way that it went after him so this
+ 
+
+ align:start position:0%
+of way that it went after him so this
+was not easy for either of these players
+
+ align:start position:0%
+was not easy for either of these players
+ 
+
+ align:start position:0%
+was not easy for either of these players
+but it's really it's a fascinating
+
+ align:start position:0%
+but it's really it's a fascinating
+ 
+
+ align:start position:0%
+but it's really it's a fascinating
+moment and our way creates a culture
+
+ align:start position:0%
+moment and our way creates a culture
+ 
+
+ align:start position:0%
+moment and our way creates a culture
+that to this day kind of still dominates
+
+ align:start position:0%
+that to this day kind of still dominates
+ 
+
+ align:start position:0%
+that to this day kind of still dominates
+that whole sector that's a fair summary
+
+ align:start position:0%
+that whole sector that's a fair summary
+ 
+
+ align:start position:0%
+that whole sector that's a fair summary
+now let's come back to your great
+
+ align:start position:0%
+now let's come back to your great
+ 
+
+ align:start position:0%
+now let's come back to your great
+question why don't you just pose it
+
+ align:start position:0%
+question why don't you just pose it
+ 
+
+ align:start position:0%
+question why don't you just pose it
+again quickly cinnamon wondering what's
+
+ align:start position:0%
+again quickly cinnamon wondering what's
+ 
+
+ align:start position:0%
+again quickly cinnamon wondering what's
+there you had mentioned the ability to
+
+ align:start position:0%
+there you had mentioned the ability to
+ 
+
+ align:start position:0%
+there you had mentioned the ability to
+publish under their own name was there
+
+ align:start position:0%
+publish under their own name was there
+ 
+
+ align:start position:0%
+publish under their own name was there
+anything else that might have spurred
+
+ align:start position:0%
+anything else that might have spurred
+ 
+
+ align:start position:0%
+anything else that might have spurred
+their success or that might have spurred
+
+ align:start position:0%
+their success or that might have spurred
+ 
+
+ align:start position:0%
+their success or that might have spurred
+the success of this marriage as you put
+
+ align:start position:0%
+the success of this marriage as you put
+ 
+
+ align:start position:0%
+the success of this marriage as you put
+it between I could even have business
+
+ align:start position:0%
+it between I could even have business
+ 
+
+ align:start position:0%
+it between I could even have business
+well that's recruitment tool in other
+
+ align:start position:0%
+well that's recruitment tool in other
+ 
+
+ align:start position:0%
+well that's recruitment tool in other
+words if you leave academic research you
+
+ align:start position:0%
+words if you leave academic research you
+ 
+
+ align:start position:0%
+words if you leave academic research you
+know University labs and come to work
+
+ align:start position:0%
+know University labs and come to work
+ 
+
+ align:start position:0%
+know University labs and come to work
+for Genentech you don't have to abandon
+
+ align:start position:0%
+for Genentech you don't have to abandon
+ 
+
+ align:start position:0%
+for Genentech you don't have to abandon
+your academic career you can still keep
+
+ align:start position:0%
+your academic career you can still keep
+ 
+
+ align:start position:0%
+your academic career you can still keep
+doing your research work and building
+
+ align:start position:0%
+doing your research work and building
+ 
+
+ align:start position:0%
+doing your research work and building
+your research reputation while you're
+
+ align:start position:0%
+your research reputation while you're
+ 
+
+ align:start position:0%
+your research reputation while you're
+working at a company and that's what
+
+ align:start position:0%
+working at a company and that's what
+ 
+
+ align:start position:0%
+working at a company and that's what
+that enabled so what enabled academic
+
+ align:start position:0%
+that enabled so what enabled academic
+ 
+
+ align:start position:0%
+that enabled so what enabled academic
+researchers to feel that they weren't
+
+ align:start position:0%
+researchers to feel that they weren't
+ 
+
+ align:start position:0%
+researchers to feel that they weren't
+leaving the universe that they had that
+
+ align:start position:0%
+leaving the universe that they had that
+ 
+
+ align:start position:0%
+leaving the universe that they had that
+had nurtured them they could continue
+
+ align:start position:0%
+had nurtured them they could continue
+ 
+
+ align:start position:0%
+had nurtured them they could continue
+doing terrific academic work as well as
+
+ align:start position:0%
+doing terrific academic work as well as
+ 
+
+ align:start position:0%
+doing terrific academic work as well as
+practical work in this kind of company
+
+ align:start position:0%
+practical work in this kind of company
+ 
+
+ align:start position:0%
+practical work in this kind of company
+setting and that was very reassuring and
+
+ align:start position:0%
+setting and that was very reassuring and
+ 
+
+ align:start position:0%
+setting and that was very reassuring and
+it was a great it was a great it broke
+
+ align:start position:0%
+it was a great it was a great it broke
+ 
+
+ align:start position:0%
+it was a great it was a great it broke
+down a whole divide between the worlds
+
+ align:start position:0%
+down a whole divide between the worlds
+ 
+
+ align:start position:0%
+down a whole divide between the worlds
+because previously in in pharmaceutical
+
+ align:start position:0%
+because previously in in pharmaceutical
+ 
+
+ align:start position:0%
+because previously in in pharmaceutical
+companies everything was secret right
+
+ align:start position:0%
+companies everything was secret right
+ 
+
+ align:start position:0%
+companies everything was secret right
+everything was treated as a trade secret
+
+ align:start position:0%
+everything was treated as a trade secret
+ 
+
+ align:start position:0%
+everything was treated as a trade secret
+so there was no outside discussion
+
+ align:start position:0%
+so there was no outside discussion
+ 
+
+ align:start position:0%
+so there was no outside discussion
+allowed until patents occurred this
+
+ align:start position:0%
+allowed until patents occurred this
+ 
+
+ align:start position:0%
+allowed until patents occurred this
+really changed that culture but soon I
+
+ align:start position:0%
+really changed that culture but soon I
+ 
+
+ align:start position:0%
+really changed that culture but soon I
+restate your question because it was a
+
+ align:start position:0%
+restate your question because it was a
+ 
+
+ align:start position:0%
+restate your question because it was a
+very good one let's go back to it yeah
+
+ align:start position:0%
+very good one let's go back to it yeah
+ 
+
+ align:start position:0%
+very good one let's go back to it yeah
+so my question was do you think that the
+
+ align:start position:0%
+so my question was do you think that the
+ 
+
+ align:start position:0%
+so my question was do you think that the
+the fact that the skill and the field
+
+ align:start position:0%
+the fact that the skill and the field
+ 
+
+ align:start position:0%
+the fact that the skill and the field
+this field was so new and so starting
+
+ align:start position:0%
+this field was so new and so starting
+ 
+
+ align:start position:0%
+this field was so new and so starting
+you know very few years before that we
+
+ align:start position:0%
+you know very few years before that we
+ 
+
+ align:start position:0%
+you know very few years before that we
+help them or afforded them certain
+
+ align:start position:0%
+help them or afforded them certain
+ 
+
+ align:start position:0%
+help them or afforded them certain
+opportunities that they might not have
+
+ align:start position:0%
+opportunities that they might not have
+ 
+
+ align:start position:0%
+opportunities that they might not have
+been able to have any more establish
+
+ align:start position:0%
+been able to have any more establish
+ 
+
+ align:start position:0%
+been able to have any more establish
+entrenched the older industry absolutely
+
+ align:start position:0%
+entrenched the older industry absolutely
+ 
+
+ align:start position:0%
+entrenched the older industry absolutely
+because there was a previous
+
+ align:start position:0%
+because there was a previous
+ 
+
+ align:start position:0%
+because there was a previous
+infrastructure there was no
+
+ align:start position:0%
+infrastructure there was no
+ 
+
+ align:start position:0%
+infrastructure there was no
+establishment to fight that was just the
+
+ align:start position:0%
+establishment to fight that was just the
+ 
+
+ align:start position:0%
+establishment to fight that was just the
+scientific challenge and then trying to
+
+ align:start position:0%
+scientific challenge and then trying to
+ 
+
+ align:start position:0%
+scientific challenge and then trying to
+commercialize it of course I mean there
+
+ align:start position:0%
+commercialize it of course I mean there
+ 
+
+ align:start position:0%
+commercialize it of course I mean there
+were other there were other companies
+
+ align:start position:0%
+were other there were other companies
+ 
+
+ align:start position:0%
+were other there were other companies
+that were trying to do these things but
+
+ align:start position:0%
+that were trying to do these things but
+ 
+
+ align:start position:0%
+that were trying to do these things but
+because it wasn't as established its I'm
+
+ align:start position:0%
+because it wasn't as established its I'm
+ 
+
+ align:start position:0%
+because it wasn't as established its I'm
+no coal or the railroad industries and
+
+ align:start position:0%
+no coal or the railroad industries and
+ 
+
+ align:start position:0%
+no coal or the railroad industries and
+like that it it's I think it certainly
+
+ align:start position:0%
+like that it it's I think it certainly
+ 
+
+ align:start position:0%
+like that it it's I think it certainly
+made things a lot easier
+
+ align:start position:0%
+made things a lot easier
+ 
+
+ align:start position:0%
+made things a lot easier
+the market was a lot more fluid and they
+
+ align:start position:0%
+the market was a lot more fluid and they
+ 
+
+ align:start position:0%
+the market was a lot more fluid and they
+had a lot more areas to expand into I
+
+ align:start position:0%
+had a lot more areas to expand into I
+ 
+
+ align:start position:0%
+had a lot more areas to expand into I
+think not only that sorry there is also
+
+ align:start position:0%
+think not only that sorry there is also
+ 
+
+ align:start position:0%
+think not only that sorry there is also
+a lot more room for error especially as
+
+ align:start position:0%
+a lot more room for error especially as
+ 
+
+ align:start position:0%
+a lot more room for error especially as
+they're getting started initially
+
+ align:start position:0%
+they're getting started initially
+ 
+
+ align:start position:0%
+they're getting started initially
+they're able to like experiment they
+
+ align:start position:0%
+they're able to like experiment they
+ 
+
+ align:start position:0%
+they're able to like experiment they
+more leeway in the way they can mark it
+
+ align:start position:0%
+more leeway in the way they can mark it
+ 
+
+ align:start position:0%
+more leeway in the way they can mark it
+and present their product because there
+
+ align:start position:0%
+and present their product because there
+ 
+
+ align:start position:0%
+and present their product because there
+is no established market doesn't mean if
+
+ align:start position:0%
+is no established market doesn't mean if
+ 
+
+ align:start position:0%
+is no established market doesn't mean if
+someone could share maybe what they
+
+ align:start position:0%
+someone could share maybe what they
+ 
+
+ align:start position:0%
+someone could share maybe what they
+thought the regulatory challenges that
+
+ align:start position:0%
+thought the regulatory challenges that
+ 
+
+ align:start position:0%
+thought the regulatory challenges that
+they didn't face were I think it was
+
+ align:start position:0%
+they didn't face were I think it was
+ 
+
+ align:start position:0%
+they didn't face were I think it was
+mentioned that they pretty much use the
+
+ align:start position:0%
+mentioned that they pretty much use the
+ 
+
+ align:start position:0%
+mentioned that they pretty much use the
+ability to use synthetic DNA in order to
+
+ align:start position:0%
+ability to use synthetic DNA in order to
+ 
+
+ align:start position:0%
+ability to use synthetic DNA in order to
+get over a lot of regulations also is
+
+ align:start position:0%
+get over a lot of regulations also is
+ 
+
+ align:start position:0%
+get over a lot of regulations also is
+relatively early nowadays it's a lot
+
+ align:start position:0%
+relatively early nowadays it's a lot
+ 
+
+ align:start position:0%
+relatively early nowadays it's a lot
+harder I didn't like the price point to
+
+ align:start position:0%
+harder I didn't like the price point to
+ 
+
+ align:start position:0%
+harder I didn't like the price point to
+make a drug it's over a billion back
+
+ align:start position:0%
+make a drug it's over a billion back
+ 
+
+ align:start position:0%
+make a drug it's over a billion back
+then I really don't know what it was so
+
+ align:start position:0%
+then I really don't know what it was so
+ 
+
+ align:start position:0%
+then I really don't know what it was so
+really was a great opportunity also
+
+ align:start position:0%
+really was a great opportunity also
+ 
+
+ align:start position:0%
+really was a great opportunity also
+their investors were kleiner perkins
+
+ align:start position:0%
+their investors were kleiner perkins
+ 
+
+ align:start position:0%
+their investors were kleiner perkins
+also one of those purchases attended
+
+ align:start position:0%
+also one of those purchases attended
+ 
+
+ align:start position:0%
+also one of those purchases attended
+swanson had originally worked for
+
+ align:start position:0%
+swanson had originally worked for
+ 
+
+ align:start position:0%
+swanson had originally worked for
+had to leave because they didn't want to
+
+ align:start position:0%
+had to leave because they didn't want to
+ 
+
+ align:start position:0%
+had to leave because they didn't want to
+do biotech but he went back to them with
+
+ align:start position:0%
+do biotech but he went back to them with
+ 
+
+ align:start position:0%
+do biotech but he went back to them with
+this advance and they you know gave him
+
+ align:start position:0%
+this advance and they you know gave him
+ 
+
+ align:start position:0%
+this advance and they you know gave him
+some money but the investors were
+
+ align:start position:0%
+some money but the investors were
+ 
+
+ align:start position:0%
+some money but the investors were
+adequate and what about Chris do you
+
+ align:start position:0%
+adequate and what about Chris do you
+ 
+
+ align:start position:0%
+adequate and what about Chris do you
+have any thoughts on the regulatory
+
+ align:start position:0%
+have any thoughts on the regulatory
+ 
+
+ align:start position:0%
+have any thoughts on the regulatory
+challenge yeah so definitely using
+
+ align:start position:0%
+challenge yeah so definitely using
+ 
+
+ align:start position:0%
+challenge yeah so definitely using
+synthetic kinds of molecules in an
+
+ align:start position:0%
+synthetic kinds of molecules in an
+ 
+
+ align:start position:0%
+synthetic kinds of molecules in an
+approach definitely helps because you
+
+ align:start position:0%
+approach definitely helps because you
+ 
+
+ align:start position:0%
+approach definitely helps because you
+can surpass that whole and clinical
+
+ align:start position:0%
+can surpass that whole and clinical
+ 
+
+ align:start position:0%
+can surpass that whole and clinical
+challenge which not only is like hard to
+
+ align:start position:0%
+challenge which not only is like hard to
+ 
+
+ align:start position:0%
+challenge which not only is like hard to
+pass but it also takes a long time right
+
+ align:start position:0%
+pass but it also takes a long time right
+ 
+
+ align:start position:0%
+pass but it also takes a long time right
+especially they were mentioning there's
+
+ align:start position:0%
+especially they were mentioning there's
+ 
+
+ align:start position:0%
+especially they were mentioning there's
+a real time crunch a lot of groups were
+
+ align:start position:0%
+a real time crunch a lot of groups were
+ 
+
+ align:start position:0%
+a real time crunch a lot of groups were
+doing this that's kind of approaching
+
+ align:start position:0%
+doing this that's kind of approaching
+ 
+
+ align:start position:0%
+doing this that's kind of approaching
+research in this field they really had
+
+ align:start position:0%
+research in this field they really had
+ 
+
+ align:start position:0%
+research in this field they really had
+to be the first ones out there so they
+
+ align:start position:0%
+to be the first ones out there so they
+ 
+
+ align:start position:0%
+to be the first ones out there so they
+could establish themselves as leader and
+
+ align:start position:0%
+could establish themselves as leader and
+ 
+
+ align:start position:0%
+could establish themselves as leader and
+the real innovators and kind of this new
+
+ align:start position:0%
+the real innovators and kind of this new
+ 
+
+ align:start position:0%
+the real innovators and kind of this new
+biotech field so I think their approach
+
+ align:start position:0%
+biotech field so I think their approach
+ 
+
+ align:start position:0%
+biotech field so I think their approach
+is smart right I mean this is a moment
+
+ align:start position:0%
+is smart right I mean this is a moment
+ 
+
+ align:start position:0%
+is smart right I mean this is a moment
+where there's a deep concern that comes
+
+ align:start position:0%
+where there's a deep concern that comes
+ 
+
+ align:start position:0%
+where there's a deep concern that comes
+up from the public but also in the
+
+ align:start position:0%
+up from the public but also in the
+ 
+
+ align:start position:0%
+up from the public but also in the
+academic community itself about the
+
+ align:start position:0%
+academic community itself about the
+ 
+
+ align:start position:0%
+academic community itself about the
+implications of this genetic engineering
+
+ align:start position:0%
+implications of this genetic engineering
+ 
+
+ align:start position:0%
+implications of this genetic engineering
+right I mean that's what Genentech
+
+ align:start position:0%
+right I mean that's what Genentech
+ 
+
+ align:start position:0%
+right I mean that's what Genentech
+stands for genetic engineering right
+
+ align:start position:0%
+stands for genetic engineering right
+ 
+
+ align:start position:0%
+stands for genetic engineering right
+that's what they're all about and
+
+ align:start position:0%
+that's what they're all about and
+ 
+
+ align:start position:0%
+that's what they're all about and
+there's a major effort to put this whole
+
+ align:start position:0%
+there's a major effort to put this whole
+ 
+
+ align:start position:0%
+there's a major effort to put this whole
+movement on pause right and there is an
+
+ align:start position:0%
+movement on pause right and there is an
+ 
+
+ align:start position:0%
+movement on pause right and there is an
+outcry in the City Council that that in
+
+ align:start position:0%
+outcry in the City Council that that in
+ 
+
+ align:start position:0%
+outcry in the City Council that that in
+Cambridge here you know a wild hearing
+
+ align:start position:0%
+Cambridge here you know a wild hearing
+ 
+
+ align:start position:0%
+Cambridge here you know a wild hearing
+by the City Council trying to shut down
+
+ align:start position:0%
+by the City Council trying to shut down
+ 
+
+ align:start position:0%
+by the City Council trying to shut down
+related research at Harvard and MIT
+
+ align:start position:0%
+related research at Harvard and MIT
+ 
+
+ align:start position:0%
+related research at Harvard and MIT
+because they're very worried about the
+
+ align:start position:0%
+because they're very worried about the
+ 
+
+ align:start position:0%
+because they're very worried about the
+implications of what's going to be
+
+ align:start position:0%
+implications of what's going to be
+ 
+
+ align:start position:0%
+implications of what's going to be
+happening here so then there's an effort
+
+ align:start position:0%
+happening here so then there's an effort
+ 
+
+ align:start position:0%
+happening here so then there's an effort
+by the scientific community in this
+
+ align:start position:0%
+by the scientific community in this
+ 
+
+ align:start position:0%
+by the scientific community in this
+famous conference called simmilar out in
+
+ align:start position:0%
+famous conference called simmilar out in
+ 
+
+ align:start position:0%
+famous conference called simmilar out in
+California where the whole community
+
+ align:start position:0%
+California where the whole community
+ 
+
+ align:start position:0%
+California where the whole community
+comes together there and kind of really
+
+ align:start position:0%
+comes together there and kind of really
+ 
+
+ align:start position:0%
+comes together there and kind of really
+begins to work through the ethics but
+
+ align:start position:0%
+begins to work through the ethics but
+ 
+
+ align:start position:0%
+begins to work through the ethics but
+their principal competitor Wally Gilbert
+
+ align:start position:0%
+their principal competitor Wally Gilbert
+ 
+
+ align:start position:0%
+their principal competitor Wally Gilbert
+at Harvard is forced because of this
+
+ align:start position:0%
+at Harvard is forced because of this
+ 
+
+ align:start position:0%
+at Harvard is forced because of this
+limit on genetic engineering the ability
+
+ align:start position:0%
+limit on genetic engineering the ability
+ 
+
+ align:start position:0%
+limit on genetic engineering the ability
+to use genetic DNA he has to go to
+
+ align:start position:0%
+to use genetic DNA he has to go to
+ 
+
+ align:start position:0%
+to use genetic DNA he has to go to
+England where they're still allowing
+
+ align:start position:0%
+England where they're still allowing
+ 
+
+ align:start position:0%
+England where they're still allowing
+that research and enlist the whole group
+
+ align:start position:0%
+that research and enlist the whole group
+ 
+
+ align:start position:0%
+that research and enlist the whole group
+of British scientists done to take his
+
+ align:start position:0%
+of British scientists done to take his
+ 
+
+ align:start position:0%
+of British scientists done to take his
+research but Swanson and Bohr get around
+
+ align:start position:0%
+research but Swanson and Bohr get around
+ 
+
+ align:start position:0%
+research but Swanson and Bohr get around
+that by using synthetic DNA and they
+
+ align:start position:0%
+that by using synthetic DNA and they
+ 
+
+ align:start position:0%
+that by using synthetic DNA and they
+avoid the whole outcry so it's a very
+
+ align:start position:0%
+avoid the whole outcry so it's a very
+ 
+
+ align:start position:0%
+avoid the whole outcry so it's a very
+interesting development it's slowed down
+
+ align:start position:0%
+interesting development it's slowed down
+ 
+
+ align:start position:0%
+interesting development it's slowed down
+they're competitors you know pretty
+
+ align:start position:0%
+they're competitors you know pretty
+ 
+
+ align:start position:0%
+they're competitors you know pretty
+considerably and Wally Gilbert was a
+
+ align:start position:0%
+considerably and Wally Gilbert was a
+ 
+
+ align:start position:0%
+considerably and Wally Gilbert was a
+great talent to be up against I mean a
+
+ align:start position:0%
+great talent to be up against I mean a
+ 
+
+ align:start position:0%
+great talent to be up against I mean a
+famous scientific leader and researcher
+
+ align:start position:0%
+famous scientific leader and researcher
+ 
+
+ align:start position:0%
+famous scientific leader and researcher
+I didn't do this reading or know that
+
+ align:start position:0%
+I didn't do this reading or know that
+ 
+
+ align:start position:0%
+I didn't do this reading or know that
+much about the genetic backgrounds at
+
+ align:start position:0%
+much about the genetic backgrounds at
+ 
+
+ align:start position:0%
+much about the genetic backgrounds at
+all but where the pharmaceutical
+
+ align:start position:0%
+all but where the pharmaceutical
+ 
+
+ align:start position:0%
+all but where the pharmaceutical
+companies at all their competitors are
+
+ align:start position:0%
+companies at all their competitors are
+ 
+
+ align:start position:0%
+companies at all their competitors are
+they very much so focused on just
+
+ align:start position:0%
+they very much so focused on just
+ 
+
+ align:start position:0%
+they very much so focused on just
+chemical stuff right I think boy I
+
+ align:start position:0%
+chemical stuff right I think boy I
+ 
+
+ align:start position:0%
+chemical stuff right I think boy I
+really came you saw that drawing with
+
+ align:start position:0%
+really came you saw that drawing with
+ 
+
+ align:start position:0%
+really came you saw that drawing with
+the pseudo that's a bacterial plasmid
+
+ align:start position:0%
+the pseudo that's a bacterial plasmid
+ 
+
+ align:start position:0%
+the pseudo that's a bacterial plasmid
+what's go back to this and then that
+
+ align:start position:0%
+what's go back to this and then that
+ 
+
+ align:start position:0%
+what's go back to this and then that
+original insert your synthetic gene into
+
+ align:start position:0%
+original insert your synthetic gene into
+ 
+
+ align:start position:0%
+original insert your synthetic gene into
+it loose that ya rectangle like he
+
+ align:start position:0%
+it loose that ya rectangle like he
+ 
+
+ align:start position:0%
+it loose that ya rectangle like he
+basically came up with that wasn't exist
+
+ align:start position:0%
+basically came up with that wasn't exist
+ 
+
+ align:start position:0%
+basically came up with that wasn't exist
+before and now it's used every day and
+
+ align:start position:0%
+before and now it's used every day and
+ 
+
+ align:start position:0%
+before and now it's used every day and
+almost everything like of the biology
+
+ align:start position:0%
+almost everything like of the biology
+ 
+
+ align:start position:0%
+almost everything like of the biology
+lab yeah so I don't think that the
+
+ align:start position:0%
+lab yeah so I don't think that the
+ 
+
+ align:start position:0%
+lab yeah so I don't think that the
+pharmaceuticals wrong to this okay yeah
+
+ align:start position:0%
+pharmaceuticals wrong to this okay yeah
+ 
+
+ align:start position:0%
+pharmaceuticals wrong to this okay yeah
+looking at that you can try and guess
+
+ align:start position:0%
+looking at that you can try and guess
+ 
+
+ align:start position:0%
+looking at that you can try and guess
+which one went to the Sloan School Boyer
+
+ align:start position:0%
+which one went to the Sloan School Boyer
+ 
+
+ align:start position:0%
+which one went to the Sloan School Boyer
+almost never looked that good let me do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and masters right how about another good
+
+ align:start position:0%
+and masters right how about another good
+ 
+
+ align:start position:0%
+and masters right how about another good
+question cement so something that of
+
+ align:start position:0%
+question cement so something that of
+ 
+
+ align:start position:0%
+question cement so something that of
+some of you who had read this kind of
+
+ align:start position:0%
+some of you who had read this kind of
+ 
+
+ align:start position:0%
+some of you who had read this kind of
+raised and I was curious about as well
+
+ align:start position:0%
+raised and I was curious about as well
+ 
+
+ align:start position:0%
+raised and I was curious about as well
+it was so the initial years because it
+
+ align:start position:0%
+it was so the initial years because it
+ 
+
+ align:start position:0%
+it was so the initial years because it
+was so new and because they were doing
+
+ align:start position:0%
+was so new and because they were doing
+ 
+
+ align:start position:0%
+was so new and because they were doing
+something that hadn't been done before
+
+ align:start position:0%
+something that hadn't been done before
+ 
+
+ align:start position:0%
+something that hadn't been done before
+there was an increased amount of
+
+ align:start position:0%
+there was an increased amount of
+ 
+
+ align:start position:0%
+there was an increased amount of
+risk-taking that was needed and you know
+
+ align:start position:0%
+risk-taking that was needed and you know
+ 
+
+ align:start position:0%
+risk-taking that was needed and you know
+they both really staked their careers on
+
+ align:start position:0%
+they both really staked their careers on
+ 
+
+ align:start position:0%
+they both really staked their careers on
+it especially Swanson who ended up
+
+ align:start position:0%
+it especially Swanson who ended up
+ 
+
+ align:start position:0%
+it especially Swanson who ended up
+having to check himself at the hospital
+
+ align:start position:0%
+having to check himself at the hospital
+ 
+
+ align:start position:0%
+having to check himself at the hospital
+when they had sat back so I wonder if
+
+ align:start position:0%
+when they had sat back so I wonder if
+ 
+
+ align:start position:0%
+when they had sat back so I wonder if
+there's kind of a way to encourage more
+
+ align:start position:0%
+there's kind of a way to encourage more
+ 
+
+ align:start position:0%
+there's kind of a way to encourage more
+sustainable risk-taking in people who
+
+ align:start position:0%
+sustainable risk-taking in people who
+ 
+
+ align:start position:0%
+sustainable risk-taking in people who
+have the visions like Swanson and people
+
+ align:start position:0%
+have the visions like Swanson and people
+ 
+
+ align:start position:0%
+have the visions like Swanson and people
+who you know people who are we were
+
+ align:start position:0%
+who you know people who are we were
+ 
+
+ align:start position:0%
+who you know people who are we were
+starting up endeavors like this there
+
+ align:start position:0%
+starting up endeavors like this there
+ 
+
+ align:start position:0%
+starting up endeavors like this there
+was a way to make that they are
+
+ align:start position:0%
+was a way to make that they are
+ 
+
+ align:start position:0%
+was a way to make that they are
+incentive to artists advice to take
+
+ align:start position:0%
+incentive to artists advice to take
+ 
+
+ align:start position:0%
+incentive to artists advice to take
+these risks that are necessary to
+
+ align:start position:0%
+these risks that are necessary to
+ 
+
+ align:start position:0%
+these risks that are necessary to
+further their careers but also maybe not
+
+ align:start position:0%
+further their careers but also maybe not
+ 
+
+ align:start position:0%
+further their careers but also maybe not
+to the point that's what's a good when
+
+ align:start position:0%
+to the point that's what's a good when
+ 
+
+ align:start position:0%
+to the point that's what's a good when
+I've led three innovation groups where I
+
+ align:start position:0%
+I've led three innovation groups where I
+ 
+
+ align:start position:0%
+I've led three innovation groups where I
+teach certain people not just students
+
+ align:start position:0%
+teach certain people not just students
+ 
+
+ align:start position:0%
+teach certain people not just students
+for people the engineering design cycle
+
+ align:start position:0%
+for people the engineering design cycle
+ 
+
+ align:start position:0%
+for people the engineering design cycle
+and I think one of my big takeaway is
+
+ align:start position:0%
+and I think one of my big takeaway is
+ 
+
+ align:start position:0%
+and I think one of my big takeaway is
+you know having taught students as young
+
+ align:start position:0%
+you know having taught students as young
+ 
+
+ align:start position:0%
+you know having taught students as young
+as five years old to you know
+
+ align:start position:0%
+as five years old to you know
+ 
+
+ align:start position:0%
+as five years old to you know
+individuals is all missing and their
+
+ align:start position:0%
+individuals is all missing and their
+ 
+
+ align:start position:0%
+individuals is all missing and their
+50th eighteen sixties is that there
+
+ align:start position:0%
+50th eighteen sixties is that there
+ 
+
+ align:start position:0%
+50th eighteen sixties is that there
+really needs to be a sense of safety and
+
+ align:start position:0%
+really needs to be a sense of safety and
+ 
+
+ align:start position:0%
+really needs to be a sense of safety and
+security which is something that was
+
+ align:start position:0%
+security which is something that was
+ 
+
+ align:start position:0%
+security which is something that was
+brought up I think is a Biederman
+
+ align:start position:0%
+brought up I think is a Biederman
+ 
+
+ align:start position:0%
+brought up I think is a Biederman
+reading which is I think one of the
+
+ align:start position:0%
+reading which is I think one of the
+ 
+
+ align:start position:0%
+reading which is I think one of the
+reasons why there's that sort of a big
+
+ align:start position:0%
+reasons why there's that sort of a big
+ 
+
+ align:start position:0%
+reasons why there's that sort of a big
+paradigm of founding a company out of
+
+ align:start position:0%
+paradigm of founding a company out of
+ 
+
+ align:start position:0%
+paradigm of founding a company out of
+your dorm room because there's something
+
+ align:start position:0%
+your dorm room because there's something
+ 
+
+ align:start position:0%
+your dorm room because there's something
+that's implied there which is that you
+
+ align:start position:0%
+that's implied there which is that you
+ 
+
+ align:start position:0%
+that's implied there which is that you
+have a place to live and then if you you
+
+ align:start position:0%
+have a place to live and then if you you
+ 
+
+ align:start position:0%
+have a place to live and then if you you
+know attend an institution where you
+
+ align:start position:0%
+know attend an institution where you
+ 
+
+ align:start position:0%
+know attend an institution where you
+have a dorm you also have access to food
+
+ align:start position:0%
+have a dorm you also have access to food
+ 
+
+ align:start position:0%
+have a dorm you also have access to food
+and you're also not super concerned
+
+ align:start position:0%
+and you're also not super concerned
+ 
+
+ align:start position:0%
+and you're also not super concerned
+about getting a paycheck and so I think
+
+ align:start position:0%
+about getting a paycheck and so I think
+ 
+
+ align:start position:0%
+about getting a paycheck and so I think
+that sense of security sort of both
+
+ align:start position:0%
+that sense of security sort of both
+ 
+
+ align:start position:0%
+that sense of security sort of both
+mentally to sort of take a step back and
+
+ align:start position:0%
+mentally to sort of take a step back and
+ 
+
+ align:start position:0%
+mentally to sort of take a step back and
+explore your dreams is really important
+
+ align:start position:0%
+explore your dreams is really important
+ 
+
+ align:start position:0%
+explore your dreams is really important
+in to the sense of stability
+
+ align:start position:0%
+in to the sense of stability
+ 
+
+ align:start position:0%
+in to the sense of stability
+like literally access to shelter access
+
+ align:start position:0%
+like literally access to shelter access
+ 
+
+ align:start position:0%
+like literally access to shelter access
+to food access to health care becomes
+
+ align:start position:0%
+to food access to health care becomes
+ 
+
+ align:start position:0%
+to food access to health care becomes
+really important so in those
+
+ align:start position:0%
+really important so in those
+ 
+
+ align:start position:0%
+really important so in those
+circumstances I feel like universities
+
+ align:start position:0%
+circumstances I feel like universities
+ 
+
+ align:start position:0%
+circumstances I feel like universities
+not just maybe their undergraduate
+
+ align:start position:0%
+not just maybe their undergraduate
+ 
+
+ align:start position:0%
+not just maybe their undergraduate
+programs but maybe universities
+
+ align:start position:0%
+programs but maybe universities
+ 
+
+ align:start position:0%
+programs but maybe universities
+generally provide really interesting
+
+ align:start position:0%
+generally provide really interesting
+ 
+
+ align:start position:0%
+generally provide really interesting
+opportunities to innovate for these
+
+ align:start position:0%
+opportunities to innovate for these
+ 
+
+ align:start position:0%
+opportunities to innovate for these
+kinds of you know very disruptive
+
+ align:start position:0%
+kinds of you know very disruptive
+ 
+
+ align:start position:0%
+kinds of you know very disruptive
+innovations because they do provide that
+
+ align:start position:0%
+innovations because they do provide that
+ 
+
+ align:start position:0%
+innovations because they do provide that
+sort of holistic support to an
+
+ align:start position:0%
+sort of holistic support to an
+ 
+
+ align:start position:0%
+sort of holistic support to an
+individual but that's still a theory
+
+ align:start position:0%
+individual but that's still a theory
+ 
+
+ align:start position:0%
+individual but that's still a theory
+that I'm working under and you know sort
+
+ align:start position:0%
+that I'm working under and you know sort
+ 
+
+ align:start position:0%
+that I'm working under and you know sort
+of hope to continue exploring over maybe
+
+ align:start position:0%
+of hope to continue exploring over maybe
+ 
+
+ align:start position:0%
+of hope to continue exploring over maybe
+master's thesis or a PhD but I think the
+
+ align:start position:0%
+master's thesis or a PhD but I think the
+ 
+
+ align:start position:0%
+master's thesis or a PhD but I think the
+other really big point about mental
+
+ align:start position:0%
+other really big point about mental
+ 
+
+ align:start position:0%
+other really big point about mental
+health is something that was also
+
+ align:start position:0%
+health is something that was also
+ 
+
+ align:start position:0%
+health is something that was also
+addressed in the Biederman reading and
+
+ align:start position:0%
+addressed in the Biederman reading and
+ 
+
+ align:start position:0%
+addressed in the Biederman reading and
+he goes back to that sense of safety and
+
+ align:start position:0%
+he goes back to that sense of safety and
+ 
+
+ align:start position:0%
+he goes back to that sense of safety and
+security that a lot of times individuals
+
+ align:start position:0%
+security that a lot of times individuals
+ 
+
+ align:start position:0%
+security that a lot of times individuals
+who don't feel comfortable in their sort
+
+ align:start position:0%
+who don't feel comfortable in their sort
+ 
+
+ align:start position:0%
+who don't feel comfortable in their sort
+of organic or natural ecosystem feel
+
+ align:start position:0%
+of organic or natural ecosystem feel
+ 
+
+ align:start position:0%
+of organic or natural ecosystem feel
+more stressed and thus that prevents
+
+ align:start position:0%
+more stressed and thus that prevents
+ 
+
+ align:start position:0%
+more stressed and thus that prevents
+them from being productive and so I
+
+ align:start position:0%
+them from being productive and so I
+ 
+
+ align:start position:0%
+them from being productive and so I
+think about that in the context of the
+
+ align:start position:0%
+think about that in the context of the
+ 
+
+ align:start position:0%
+think about that in the context of the
+current political situation and the ways
+
+ align:start position:0%
+current political situation and the ways
+ 
+
+ align:start position:0%
+current political situation and the ways
+in which maybe some people who might be
+
+ align:start position:0%
+in which maybe some people who might be
+ 
+
+ align:start position:0%
+in which maybe some people who might be
+interested in innovating or pursuing
+
+ align:start position:0%
+interested in innovating or pursuing
+ 
+
+ align:start position:0%
+interested in innovating or pursuing
+innovative projects may not be able to
+
+ align:start position:0%
+innovative projects may not be able to
+ 
+
+ align:start position:0%
+innovative projects may not be able to
+do so effectively because of the ways in
+
+ align:start position:0%
+do so effectively because of the ways in
+ 
+
+ align:start position:0%
+do so effectively because of the ways in
+which the political situation is you
+
+ align:start position:0%
+which the political situation is you
+ 
+
+ align:start position:0%
+which the political situation is you
+know literally motivating stress in
+
+ align:start position:0%
+know literally motivating stress in
+ 
+
+ align:start position:0%
+know literally motivating stress in
+their lives and is preventing them from
+
+ align:start position:0%
+their lives and is preventing them from
+ 
+
+ align:start position:0%
+their lives and is preventing them from
+innovating so those are some thoughts I
+
+ align:start position:0%
+innovating so those are some thoughts I
+ 
+
+ align:start position:0%
+innovating so those are some thoughts I
+have a lot of them you should share
+
+ align:start position:0%
+have a lot of them you should share
+ 
+
+ align:start position:0%
+have a lot of them you should share
+those to this aspect of having stress
+
+ align:start position:0%
+those to this aspect of having stress
+ 
+
+ align:start position:0%
+those to this aspect of having stress
+like a necessary stress is important
+
+ align:start position:0%
+like a necessary stress is important
+ 
+
+ align:start position:0%
+like a necessary stress is important
+like I think with the Manhattan Project
+
+ align:start position:0%
+like I think with the Manhattan Project
+ 
+
+ align:start position:0%
+like I think with the Manhattan Project
+like there's no safety and security and
+
+ align:start position:0%
+like there's no safety and security and
+ 
+
+ align:start position:0%
+like there's no safety and security and
+measurements are gonna give the
+
+ align:start position:0%
+measurements are gonna give the
+ 
+
+ align:start position:0%
+measurements are gonna give the
+conference and I mean I couldn't think
+
+ align:start position:0%
+conference and I mean I couldn't think
+ 
+
+ align:start position:0%
+conference and I mean I couldn't think
+of a better impetus that you know this
+
+ align:start position:0%
+of a better impetus that you know this
+ 
+
+ align:start position:0%
+of a better impetus that you know this
+has to work for I don't have a house to
+
+ align:start position:0%
+has to work for I don't have a house to
+ 
+
+ align:start position:0%
+has to work for I don't have a house to
+live in or if we D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's actually not what they had to
+
+ align:start position:0%
+that's actually not what they had to
+ 
+
+ align:start position:0%
+that's actually not what they had to
+deal with it all I mean like they might
+
+ align:start position:0%
+deal with it all I mean like they might
+ 
+
+ align:start position:0%
+deal with it all I mean like they might
+say like yeah oh we don't have any flies
+
+ align:start position:0%
+say like yeah oh we don't have any flies
+ 
+
+ align:start position:0%
+say like yeah oh we don't have any flies
+but so I kind of agree but I mean
+
+ align:start position:0%
+but so I kind of agree but I mean
+ 
+
+ align:start position:0%
+but so I kind of agree but I mean
+Oppenheimer didn't mention in that paper
+
+ align:start position:0%
+Oppenheimer didn't mention in that paper
+ 
+
+ align:start position:0%
+Oppenheimer didn't mention in that paper
+like he went six months and he didn't
+
+ align:start position:0%
+like he went six months and he didn't
+ 
+
+ align:start position:0%
+like he went six months and he didn't
+even realize he had a pro paycheck yet
+
+ align:start position:0%
+even realize he had a pro paycheck yet
+ 
+
+ align:start position:0%
+even realize he had a pro paycheck yet
+he hadn't received one and I saw that
+
+ align:start position:0%
+he hadn't received one and I saw that
+ 
+
+ align:start position:0%
+he hadn't received one and I saw that
+and I just thought that was such
+
+ align:start position:0%
+and I just thought that was such
+ 
+
+ align:start position:0%
+and I just thought that was such
+privilege so the fact that someone could
+
+ align:start position:0%
+privilege so the fact that someone could
+ 
+
+ align:start position:0%
+privilege so the fact that someone could
+have that that sense of okay well if
+
+ align:start position:0%
+have that that sense of okay well if
+ 
+
+ align:start position:0%
+have that that sense of okay well if
+this ignoring the implications of
+
+ align:start position:0%
+this ignoring the implications of
+ 
+
+ align:start position:0%
+this ignoring the implications of
+obviously failing on this project
+
+ align:start position:0%
+obviously failing on this project
+ 
+
+ align:start position:0%
+obviously failing on this project
+outside of the Manhattan Project any
+
+ align:start position:0%
+outside of the Manhattan Project any
+ 
+
+ align:start position:0%
+outside of the Manhattan Project any
+other technological pursuit I think that
+
+ align:start position:0%
+other technological pursuit I think that
+ 
+
+ align:start position:0%
+other technological pursuit I think that
+definitely helps with Korea think more
+
+ align:start position:0%
+definitely helps with Korea think more
+ 
+
+ align:start position:0%
+definitely helps with Korea think more
+creatively when you have to think about
+
+ align:start position:0%
+creatively when you have to think about
+ 
+
+ align:start position:0%
+creatively when you have to think about
+oh how am I gonna pay for my car or how
+
+ align:start position:0%
+oh how am I gonna pay for my car or how
+ 
+
+ align:start position:0%
+oh how am I gonna pay for my car or how
+am I gonna get to work or whatever so
+
+ align:start position:0%
+am I gonna get to work or whatever so
+ 
+
+ align:start position:0%
+am I gonna get to work or whatever so
+one of the important rules I think here
+
+ align:start position:0%
+one of the important rules I think here
+ 
+
+ align:start position:0%
+one of the important rules I think here
+is that the group needs to be on a
+
+ align:start position:0%
+is that the group needs to be on a
+ 
+
+ align:start position:0%
+is that the group needs to be on a
+protected island and the point you're
+
+ align:start position:0%
+protected island and the point you're
+ 
+
+ align:start position:0%
+protected island and the point you're
+adding stuff I think is a significant
+
+ align:start position:0%
+adding stuff I think is a significant
+ 
+
+ align:start position:0%
+adding stuff I think is a significant
+one it needs to feel secure in itself
+
+ align:start position:0%
+one it needs to feel secure in itself
+ 
+
+ align:start position:0%
+one it needs to feel secure in itself
+right people have to be comfortable in
+
+ align:start position:0%
+right people have to be comfortable in
+ 
+
+ align:start position:0%
+right people have to be comfortable in
+this group to be willing to be creative
+
+ align:start position:0%
+this group to be willing to be creative
+ 
+
+ align:start position:0%
+this group to be willing to be creative
+together and contribute to each other I
+
+ align:start position:0%
+together and contribute to each other I
+ 
+
+ align:start position:0%
+together and contribute to each other I
+think that's an important perception
+
+ align:start position:0%
+think that's an important perception
+ 
+
+ align:start position:0%
+think that's an important perception
+here that probably applies to a lot of
+
+ align:start position:0%
+here that probably applies to a lot of
+ 
+
+ align:start position:0%
+here that probably applies to a lot of
+these groups but why having too little
+
+ align:start position:0%
+these groups but why having too little
+ 
+
+ align:start position:0%
+these groups but why having too little
+means so much you don't have your full
+
+ align:start position:0%
+means so much you don't have your full
+ 
+
+ align:start position:0%
+means so much you don't have your full
+band widths if you're worried about what
+
+ align:start position:0%
+band widths if you're worried about what
+ 
+
+ align:start position:0%
+band widths if you're worried about what
+you don't have and what you need to work
+
+ align:start position:0%
+you don't have and what you need to work
+ 
+
+ align:start position:0%
+you don't have and what you need to work
+on so and that's front up for you to do
+
+ align:start position:0%
+on so and that's front up for you to do
+ 
+
+ align:start position:0%
+on so and that's front up for you to do
+so then did this group have that sense
+
+ align:start position:0%
+so then did this group have that sense
+ 
+
+ align:start position:0%
+so then did this group have that sense
+of security from what I read here they
+
+ align:start position:0%
+of security from what I read here they
+ 
+
+ align:start position:0%
+of security from what I read here they
+definitely did I mean a lot of them were
+
+ align:start position:0%
+definitely did I mean a lot of them were
+ 
+
+ align:start position:0%
+definitely did I mean a lot of them were
+and you don't see in this picture the
+
+ align:start position:0%
+and you don't see in this picture the
+ 
+
+ align:start position:0%
+and you don't see in this picture the
+whole team it is a whole team that's
+
+ align:start position:0%
+whole team it is a whole team that's
+ 
+
+ align:start position:0%
+whole team it is a whole team that's
+very collaborative with these with this
+
+ align:start position:0%
+very collaborative with these with this
+ 
+
+ align:start position:0%
+very collaborative with these with this
+duo yeah and I think that that was an
+
+ align:start position:0%
+duo yeah and I think that that was an
+ 
+
+ align:start position:0%
+duo yeah and I think that that was an
+interesting point about I did kind of
+
+ align:start position:0%
+interesting point about I did kind of
+ 
+
+ align:start position:0%
+interesting point about I did kind of
+get a sense that like class 10 came into
+
+ align:start position:0%
+get a sense that like class 10 came into
+ 
+
+ align:start position:0%
+get a sense that like class 10 came into
+this in a way that you know really
+
+ align:start position:0%
+this in a way that you know really
+ 
+
+ align:start position:0%
+this in a way that you know really
+benefited you know Boyer had this he
+
+ align:start position:0%
+benefited you know Boyer had this he
+ 
+
+ align:start position:0%
+benefited you know Boyer had this he
+went into a commercial I think because
+
+ align:start position:0%
+went into a commercial I think because
+ 
+
+ align:start position:0%
+went into a commercial I think because
+he had an altruistic vision or just
+
+ align:start position:0%
+he had an altruistic vision or just
+ 
+
+ align:start position:0%
+he had an altruistic vision or just
+interesting but he also you know he had
+
+ align:start position:0%
+interesting but he also you know he had
+ 
+
+ align:start position:0%
+interesting but he also you know he had
+that ability to not have to worry about
+
+ align:start position:0%
+that ability to not have to worry about
+ 
+
+ align:start position:0%
+that ability to not have to worry about
+making money and things like that so I
+
+ align:start position:0%
+making money and things like that so I
+ 
+
+ align:start position:0%
+making money and things like that so I
+think that's a really interesting point
+
+ align:start position:0%
+think that's a really interesting point
+ 
+
+ align:start position:0%
+think that's a really interesting point
+that you all raised and yeah we were
+
+ align:start position:0%
+that you all raised and yeah we were
+ 
+
+ align:start position:0%
+that you all raised and yeah we were
+saying about how people who feel like
+
+ align:start position:0%
+saying about how people who feel like
+ 
+
+ align:start position:0%
+saying about how people who feel like
+they are actively under threat or to
+
+ align:start position:0%
+they are actively under threat or to
+ 
+
+ align:start position:0%
+they are actively under threat or to
+actively don't have you know the basic
+
+ align:start position:0%
+actively don't have you know the basic
+ 
+
+ align:start position:0%
+actively don't have you know the basic
+necessity necessity is taken care of
+
+ align:start position:0%
+necessity necessity is taken care of
+ 
+
+ align:start position:0%
+necessity necessity is taken care of
+would not be able to function maybe the
+
+ align:start position:0%
+would not be able to function maybe the
+ 
+
+ align:start position:0%
+would not be able to function maybe the
+way that you make those innovations in
+
+ align:start position:0%
+way that you make those innovations in
+ 
+
+ align:start position:0%
+way that you make those innovations in
+right during an island then I was
+
+ align:start position:0%
+right during an island then I was
+ 
+
+ align:start position:0%
+right during an island then I was
+starving book by Paul Corning you did he
+
+ align:start position:0%
+starving book by Paul Corning you did he
+ 
+
+ align:start position:0%
+starving book by Paul Corning you did he
+was a neuroscientist who was a resident
+
+ align:start position:0%
+was a neuroscientist who was a resident
+ 
+
+ align:start position:0%
+was a neuroscientist who was a resident
+I believe at Stanford you're a surgeon
+
+ align:start position:0%
+I believe at Stanford you're a surgeon
+ 
+
+ align:start position:0%
+I believe at Stanford you're a surgeon
+oh he was a medical resident at Stanford
+
+ align:start position:0%
+oh he was a medical resident at Stanford
+ 
+
+ align:start position:0%
+oh he was a medical resident at Stanford
+who's just about to complete his new
+
+ align:start position:0%
+who's just about to complete his new
+ 
+
+ align:start position:0%
+who's just about to complete his new
+science residency and he was diagnosed
+
+ align:start position:0%
+science residency and he was diagnosed
+ 
+
+ align:start position:0%
+science residency and he was diagnosed
+with brain cancer and he ended up
+
+ align:start position:0%
+with brain cancer and he ended up
+ 
+
+ align:start position:0%
+with brain cancer and he ended up
+passing away just shy of you know
+
+ align:start position:0%
+passing away just shy of you know
+ 
+
+ align:start position:0%
+passing away just shy of you know
+completing his residency but there is a
+
+ align:start position:0%
+completing his residency but there is a
+ 
+
+ align:start position:0%
+completing his residency but there is a
+really incredible portion in his memoir
+
+ align:start position:0%
+really incredible portion in his memoir
+ 
+
+ align:start position:0%
+really incredible portion in his memoir
+where he talks about what he had to do
+
+ align:start position:0%
+where he talks about what he had to do
+ 
+
+ align:start position:0%
+where he talks about what he had to do
+in order to be able to achieve what he
+
+ align:start position:0%
+in order to be able to achieve what he
+ 
+
+ align:start position:0%
+in order to be able to achieve what he
+did which is essentially after going to
+
+ align:start position:0%
+did which is essentially after going to
+ 
+
+ align:start position:0%
+did which is essentially after going to
+Stanford undergrad he spent a year
+
+ align:start position:0%
+Stanford undergrad he spent a year
+ 
+
+ align:start position:0%
+Stanford undergrad he spent a year
+essentially being homeless living in an
+
+ align:start position:0%
+essentially being homeless living in an
+ 
+
+ align:start position:0%
+essentially being homeless living in an
+abandoned home and taking classes at
+
+ align:start position:0%
+abandoned home and taking classes at
+ 
+
+ align:start position:0%
+abandoned home and taking classes at
+Stanford while studying for the MCAT and
+
+ align:start position:0%
+Stanford while studying for the MCAT and
+ 
+
+ align:start position:0%
+Stanford while studying for the MCAT and
+I think there's a really other reason I
+
+ align:start position:0%
+I think there's a really other reason I
+ 
+
+ align:start position:0%
+I think there's a really other reason I
+recommend everyone read this book if
+
+ align:start position:0%
+recommend everyone read this book if
+ 
+
+ align:start position:0%
+recommend everyone read this book if
+they're interested in becoming
+
+ align:start position:0%
+they're interested in becoming
+ 
+
+ align:start position:0%
+they're interested in becoming
+innovators or entrepreneurs or you know
+
+ align:start position:0%
+innovators or entrepreneurs or you know
+ 
+
+ align:start position:0%
+innovators or entrepreneurs or you know
+people who change the world is that he
+
+ align:start position:0%
+people who change the world is that he
+ 
+
+ align:start position:0%
+people who change the world is that he
+elicits a really great point about not
+
+ align:start position:0%
+elicits a really great point about not
+ 
+
+ align:start position:0%
+elicits a really great point about not
+necessarily just couldn't go up the male
+
+ align:start position:0%
+necessarily just couldn't go up the male
+ 
+
+ align:start position:0%
+necessarily just couldn't go up the male
+privilege but just privilege generally
+
+ align:start position:0%
+privilege but just privilege generally
+ 
+
+ align:start position:0%
+privilege but just privilege generally
+because he was able to sort of an opt
+
+ align:start position:0%
+because he was able to sort of an opt
+ 
+
+ align:start position:0%
+because he was able to sort of an opt
+out of being alive and utilize whatever
+
+ align:start position:0%
+out of being alive and utilize whatever
+ 
+
+ align:start position:0%
+out of being alive and utilize whatever
+money his parents were sending him or
+
+ align:start position:0%
+money his parents were sending him or
+ 
+
+ align:start position:0%
+money his parents were sending him or
+whatever money he had saved job in order
+
+ align:start position:0%
+whatever money he had saved job in order
+ 
+
+ align:start position:0%
+whatever money he had saved job in order
+to take these classes in order to study
+
+ align:start position:0%
+to take these classes in order to study
+ 
+
+ align:start position:0%
+to take these classes in order to study
+for the MCAT and and go on you know to
+
+ align:start position:0%
+for the MCAT and and go on you know to
+ 
+
+ align:start position:0%
+for the MCAT and and go on you know to
+do incredible work in medical school
+
+ align:start position:0%
+do incredible work in medical school
+ 
+
+ align:start position:0%
+do incredible work in medical school
+women in residency and I feel like
+
+ align:start position:0%
+women in residency and I feel like
+ 
+
+ align:start position:0%
+women in residency and I feel like
+that's a sort of close as you get and
+
+ align:start position:0%
+that's a sort of close as you get and
+ 
+
+ align:start position:0%
+that's a sort of close as you get and
+the clearest sort of articulation of the
+
+ align:start position:0%
+the clearest sort of articulation of the
+ 
+
+ align:start position:0%
+the clearest sort of articulation of the
+process of giving up your whole life in
+
+ align:start position:0%
+process of giving up your whole life in
+ 
+
+ align:start position:0%
+process of giving up your whole life in
+order to pursue this big dream that you
+
+ align:start position:0%
+order to pursue this big dream that you
+ 
+
+ align:start position:0%
+order to pursue this big dream that you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+and so Paul clinic's book I think is a
+
+ align:start position:0%
+and so Paul clinic's book I think is a
+ 
+
+ align:start position:0%
+and so Paul clinic's book I think is a
+really really great study not just of a
+
+ align:start position:0%
+really really great study not just of a
+ 
+
+ align:start position:0%
+really really great study not just of a
+great group of a great individual and a
+
+ align:start position:0%
+great group of a great individual and a
+ 
+
+ align:start position:0%
+great group of a great individual and a
+person who's sort of a risk-taker and
+
+ align:start position:0%
+person who's sort of a risk-taker and
+ 
+
+ align:start position:0%
+person who's sort of a risk-taker and
+willing to give up their life for their
+
+ align:start position:0%
+willing to give up their life for their
+ 
+
+ align:start position:0%
+willing to give up their life for their
+work and then ultimately obviously you
+
+ align:start position:0%
+work and then ultimately obviously you
+ 
+
+ align:start position:0%
+work and then ultimately obviously you
+know the conclusion of it is you know
+
+ align:start position:0%
+know the conclusion of it is you know
+ 
+
+ align:start position:0%
+know the conclusion of it is you know
+quite rude
+
+ align:start position:0%
+quite rude
+ 
+
+ align:start position:0%
+quite rude
+near any markets there but these folks
+
+ align:start position:0%
+near any markets there but these folks
+ 
+
+ align:start position:0%
+near any markets there but these folks
+are giving up you know a tremendous
+
+ align:start position:0%
+are giving up you know a tremendous
+ 
+
+ align:start position:0%
+are giving up you know a tremendous
+amount to pursue a dream only linking of
+
+ align:start position:0%
+amount to pursue a dream only linking of
+ 
+
+ align:start position:0%
+amount to pursue a dream only linking of
+the winners right I would say that
+
+ align:start position:0%
+the winners right I would say that
+ 
+
+ align:start position:0%
+the winners right I would say that
+pretty much every biotech entrepreneur
+
+ align:start position:0%
+pretty much every biotech entrepreneur
+ 
+
+ align:start position:0%
+pretty much every biotech entrepreneur
+ends up with all servers of high blood
+
+ align:start position:0%
+ends up with all servers of high blood
+ 
+
+ align:start position:0%
+ends up with all servers of high blood
+pressure that's just they do she only
+
+ align:start position:0%
+pressure that's just they do she only
+ 
+
+ align:start position:0%
+pressure that's just they do she only
+said biotech with the biotech side but I
+
+ align:start position:0%
+said biotech with the biotech side but I
+ 
+
+ align:start position:0%
+said biotech with the biotech side but I
+think that because these I think that's
+
+ align:start position:0%
+think that because these I think that's
+ 
+
+ align:start position:0%
+think that because these I think that's
+also a characteristic of the great group
+
+ align:start position:0%
+also a characteristic of the great group
+ 
+
+ align:start position:0%
+also a characteristic of the great group
+leaders that they're able to take risks
+
+ align:start position:0%
+leaders that they're able to take risks
+ 
+
+ align:start position:0%
+leaders that they're able to take risks
+and get ulcers so that the rest of their
+
+ align:start position:0%
+and get ulcers so that the rest of their
+ 
+
+ align:start position:0%
+and get ulcers so that the rest of their
+team can feel the insulation and as
+
+ align:start position:0%
+team can feel the insulation and as
+ 
+
+ align:start position:0%
+team can feel the insulation and as
+though they have the opportunity for
+
+ align:start position:0%
+though they have the opportunity for
+ 
+
+ align:start position:0%
+though they have the opportunity for
+success resources and security so I
+
+ align:start position:0%
+success resources and security so I
+ 
+
+ align:start position:0%
+success resources and security so I
+think that's an aspect of this yeah
+
+ align:start position:0%
+think that's an aspect of this yeah
+ 
+
+ align:start position:0%
+think that's an aspect of this yeah
+there are some others of quote in the
+
+ align:start position:0%
+there are some others of quote in the
+ 
+
+ align:start position:0%
+there are some others of quote in the
+paper that was the scientist at
+
+ align:start position:0%
+paper that was the scientist at
+ 
+
+ align:start position:0%
+paper that was the scientist at
+Genentech had a new boss other than this
+
+ align:start position:0%
+Genentech had a new boss other than this
+ 
+
+ align:start position:0%
+Genentech had a new boss other than this
+one thens nervous vigilance so that
+
+ align:start position:0%
+one thens nervous vigilance so that
+ 
+
+ align:start position:0%
+one thens nervous vigilance so that
+really like that's a great line so yeah
+
+ align:start position:0%
+really like that's a great line so yeah
+ 
+
+ align:start position:0%
+really like that's a great line so yeah
+it's good
+
+ align:start position:0%
+it's good
+ 
+
+ align:start position:0%
+it's good
+all right let's do Venter Lily so I'm
+
+ align:start position:0%
+all right let's do Venter Lily so I'm
+ 
+
+ align:start position:0%
+all right let's do Venter Lily so I'm
+going over the craig venter great group
+
+ align:start position:0%
+going over the craig venter great group
+ 
+
+ align:start position:0%
+going over the craig venter great group
+today a few of you have heard of him
+
+ align:start position:0%
+today a few of you have heard of him
+ 
+
+ align:start position:0%
+today a few of you have heard of him
+most have not the leader of the great
+
+ align:start position:0%
+most have not the leader of the great
+ 
+
+ align:start position:0%
+most have not the leader of the great
+group of course was craig Venter and
+
+ align:start position:0%
+group of course was craig Venter and
+ 
+
+ align:start position:0%
+group of course was craig Venter and
+just going through some of the venison
+
+ align:start position:0%
+just going through some of the venison
+ 
+
+ align:start position:0%
+just going through some of the venison
+Biederman necessities of great Brutus or
+
+ align:start position:0%
+Biederman necessities of great Brutus or
+ 
+
+ align:start position:0%
+Biederman necessities of great Brutus or
+greatness in a group his mission from
+
+ align:start position:0%
+greatness in a group his mission from
+ 
+
+ align:start position:0%
+greatness in a group his mission from
+God was to sequence and decode the human
+
+ align:start position:0%
+God was to sequence and decode the human
+ 
+
+ align:start position:0%
+God was to sequence and decode the human
+genome so check we have a mission from
+
+ align:start position:0%
+genome so check we have a mission from
+ 
+
+ align:start position:0%
+genome so check we have a mission from
+God the island in this particular case
+
+ align:start position:0%
+God the island in this particular case
+ 
+
+ align:start position:0%
+God the island in this particular case
+study while they were decoding
+
+ align:start position:0%
+study while they were decoding
+ 
+
+ align:start position:0%
+study while they were decoding
+sequencing and decoding human genome
+
+ align:start position:0%
+sequencing and decoding human genome
+ 
+
+ align:start position:0%
+sequencing and decoding human genome
+their island was Solera which was a
+
+ align:start position:0%
+their island was Solera which was a
+ 
+
+ align:start position:0%
+their island was Solera which was a
+biotech that was it's complicated I'm
+
+ align:start position:0%
+biotech that was it's complicated I'm
+ 
+
+ align:start position:0%
+biotech that was it's complicated I'm
+gonna try to keep it as simple as
+
+ align:start position:0%
+gonna try to keep it as simple as
+ 
+
+ align:start position:0%
+gonna try to keep it as simple as
+possible for the purposes of this
+
+ align:start position:0%
+possible for the purposes of this
+ 
+
+ align:start position:0%
+possible for the purposes of this
+presentation
+
+ align:start position:0%
+presentation
+ 
+
+ align:start position:0%
+presentation
+just know that craig Venter had like
+
+ align:start position:0%
+just know that craig Venter had like
+ 
+
+ align:start position:0%
+just know that craig Venter had like
+many many for profits and non for
+
+ align:start position:0%
+many many for profits and non for
+ 
+
+ align:start position:0%
+many many for profits and non for
+profits institutions all running at the
+
+ align:start position:0%
+profits institutions all running at the
+ 
+
+ align:start position:0%
+profits institutions all running at the
+same time he has net he has
+
+ align:start position:0%
+same time he has net he has
+ 
+
+ align:start position:0%
+same time he has net he has
+now more than used to so I'm just really
+
+ align:start position:0%
+now more than used to so I'm just really
+ 
+
+ align:start position:0%
+now more than used to so I'm just really
+gonna talk about Solera for the purposes
+
+ align:start position:0%
+gonna talk about Solera for the purposes
+ 
+
+ align:start position:0%
+gonna talk about Solera for the purposes
+of this presentation and then the
+
+ align:start position:0%
+of this presentation and then the
+ 
+
+ align:start position:0%
+of this presentation and then the
+mainland he has connections with the
+
+ align:start position:0%
+mainland he has connections with the
+ 
+
+ align:start position:0%
+mainland he has connections with the
+public there's a lot of publicity going
+
+ align:start position:0%
+public there's a lot of publicity going
+ 
+
+ align:start position:0%
+public there's a lot of publicity going
+on for at this time over the Human
+
+ align:start position:0%
+on for at this time over the Human
+ 
+
+ align:start position:0%
+on for at this time over the Human
+Genome Project so that's sort of their
+
+ align:start position:0%
+Genome Project so that's sort of their
+ 
+
+ align:start position:0%
+Genome Project so that's sort of their
+their highway to the the public or the
+
+ align:start position:0%
+their highway to the the public or the
+ 
+
+ align:start position:0%
+their highway to the the public or the
+mainland
+
+ align:start position:0%
+mainland
+ 
+
+ align:start position:0%
+mainland
+annie has contacts still at the NIH and
+
+ align:start position:0%
+annie has contacts still at the NIH and
+ 
+
+ align:start position:0%
+annie has contacts still at the NIH and
+adversaries at the NIH as well and they
+
+ align:start position:0%
+adversaries at the NIH as well and they
+ 
+
+ align:start position:0%
+adversaries at the NIH as well and they
+are indeed the underdog Craig Venters
+
+ align:start position:0%
+are indeed the underdog Craig Venters
+ 
+
+ align:start position:0%
+are indeed the underdog Craig Venters
+great group defect from the NIH and
+
+ align:start position:0%
+great group defect from the NIH and
+ 
+
+ align:start position:0%
+great group defect from the NIH and
+they're up against funding from the US
+
+ align:start position:0%
+they're up against funding from the US
+ 
+
+ align:start position:0%
+they're up against funding from the US
+government and actually international
+
+ align:start position:0%
+government and actually international
+ 
+
+ align:start position:0%
+government and actually international
+collaboration especially with the
+
+ align:start position:0%
+collaboration especially with the
+ 
+
+ align:start position:0%
+collaboration especially with the
+British government and the anyway I
+
+ align:start position:0%
+British government and the anyway I
+ 
+
+ align:start position:0%
+British government and the anyway I
+think it's actually wants and rather
+
+ align:start position:0%
+think it's actually wants and rather
+ 
+
+ align:start position:0%
+think it's actually wants and rather
+than Crick right oh yeah yeah yeah sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no Branson's Kirk had nothing to do with
+
+ align:start position:0%
+no Branson's Kirk had nothing to do with
+ 
+
+ align:start position:0%
+no Branson's Kirk had nothing to do with
+this it was a lot and Watson was heading
+
+ align:start position:0%
+this it was a lot and Watson was heading
+ 
+
+ align:start position:0%
+this it was a lot and Watson was heading
+the genome project at NIH at the time
+
+ align:start position:0%
+the genome project at NIH at the time
+ 
+
+ align:start position:0%
+the genome project at NIH at the time
+yeah yeah drives men to rev it so an
+
+ align:start position:0%
+yeah yeah drives men to rev it so an
+ 
+
+ align:start position:0%
+yeah yeah drives men to rev it so an
+inventor and and Watson begin as a very
+
+ align:start position:0%
+inventor and and Watson begin as a very
+ 
+
+ align:start position:0%
+inventor and and Watson begin as a very
+powerful duo and ventur'd thinks that
+
+ align:start position:0%
+powerful duo and ventur'd thinks that
+ 
+
+ align:start position:0%
+powerful duo and ventur'd thinks that
+the genome needs to be sequenced in a
+
+ align:start position:0%
+the genome needs to be sequenced in a
+ 
+
+ align:start position:0%
+the genome needs to be sequenced in a
+slightly different way and Watson is not
+
+ align:start position:0%
+slightly different way and Watson is not
+ 
+
+ align:start position:0%
+slightly different way and Watson is not
+okay with that because so much money and
+
+ align:start position:0%
+okay with that because so much money and
+ 
+
+ align:start position:0%
+okay with that because so much money and
+so much effort has been put into it the
+
+ align:start position:0%
+so much effort has been put into it the
+ 
+
+ align:start position:0%
+so much effort has been put into it the
+sort of outdated way and he completely
+
+ align:start position:0%
+sort of outdated way and he completely
+ 
+
+ align:start position:0%
+sort of outdated way and he completely
+undermines mentor in front of US
+
+ align:start position:0%
+undermines mentor in front of US
+ 
+
+ align:start position:0%
+undermines mentor in front of US
+Congress etcetera I'll get into that a
+
+ align:start position:0%
+Congress etcetera I'll get into that a
+ 
+
+ align:start position:0%
+Congress etcetera I'll get into that a
+little more but yeah basically the enemy
+
+ align:start position:0%
+little more but yeah basically the enemy
+ 
+
+ align:start position:0%
+little more but yeah basically the enemy
+is anyone who pisses off Venter which
+
+ align:start position:0%
+is anyone who pisses off Venter which
+ 
+
+ align:start position:0%
+is anyone who pisses off Venter which
+turns out to be quite a lot of people
+
+ align:start position:0%
+turns out to be quite a lot of people
+ 
+
+ align:start position:0%
+turns out to be quite a lot of people
+over here she's Venter Craig mentor I
+
+ align:start position:0%
+over here she's Venter Craig mentor I
+ 
+
+ align:start position:0%
+over here she's Venter Craig mentor I
+think is one of them more one of the
+
+ align:start position:0%
+think is one of them more one of the
+ 
+
+ align:start position:0%
+think is one of them more one of the
+most controversial scientists in biotech
+
+ align:start position:0%
+most controversial scientists in biotech
+ 
+
+ align:start position:0%
+most controversial scientists in biotech
+in our time
+
+ align:start position:0%
+in our time
+ 
+
+ align:start position:0%
+in our time
+he's a very little bit of a hothead
+
+ align:start position:0%
+he's a very little bit of a hothead
+ 
+
+ align:start position:0%
+he's a very little bit of a hothead
+and he people in science either love him
+
+ align:start position:0%
+and he people in science either love him
+ 
+
+ align:start position:0%
+and he people in science either love him
+or hate him so a little bit of
+
+ align:start position:0%
+or hate him so a little bit of
+ 
+
+ align:start position:0%
+or hate him so a little bit of
+background his early life he's sort of
+
+ align:start position:0%
+background his early life he's sort of
+ 
+
+ align:start position:0%
+background his early life he's sort of
+he was reminiscent for me of Thomas
+
+ align:start position:0%
+he was reminiscent for me of Thomas
+ 
+
+ align:start position:0%
+he was reminiscent for me of Thomas
+Edison he has some severe learning
+
+ align:start position:0%
+Edison he has some severe learning
+ 
+
+ align:start position:0%
+Edison he has some severe learning
+issues almost flunked out of high school
+
+ align:start position:0%
+issues almost flunked out of high school
+ 
+
+ align:start position:0%
+issues almost flunked out of high school
+does not go to college he ends up a
+
+ align:start position:0%
+does not go to college he ends up a
+ 
+
+ align:start position:0%
+does not go to college he ends up a
+surfer bum in Southern California on
+
+ align:start position:0%
+surfer bum in Southern California on
+ 
+
+ align:start position:0%
+surfer bum in Southern California on
+Redondo Beach I want to add one fact not
+
+ align:start position:0%
+Redondo Beach I want to add one fact not
+ 
+
+ align:start position:0%
+Redondo Beach I want to add one fact not
+just one parent but both his parents
+
+ align:start position:0%
+just one parent but both his parents
+ 
+
+ align:start position:0%
+just one parent but both his parents
+were Marine sergeants yeah you can only
+
+ align:start position:0%
+were Marine sergeants yeah you can only
+ 
+
+ align:start position:0%
+were Marine sergeants yeah you can only
+imagine what that does to you from this
+
+ align:start position:0%
+imagine what that does to you from this
+ 
+
+ align:start position:0%
+imagine what that does to you from this
+militant household and besides that as
+
+ align:start position:0%
+militant household and besides that as
+ 
+
+ align:start position:0%
+militant household and besides that as
+soon as he's I think used like 17 when
+
+ align:start position:0%
+soon as he's I think used like 17 when
+ 
+
+ align:start position:0%
+soon as he's I think used like 17 when
+he graduates from high school he decides
+
+ align:start position:0%
+he graduates from high school he decides
+ 
+
+ align:start position:0%
+he graduates from high school he decides
+I'm getting out of here I'm gonna live
+
+ align:start position:0%
+I'm getting out of here I'm gonna live
+ 
+
+ align:start position:0%
+I'm getting out of here I'm gonna live
+in Redondo Beach in a surf shack and
+
+ align:start position:0%
+in Redondo Beach in a surf shack and
+ 
+
+ align:start position:0%
+in Redondo Beach in a surf shack and
+grow my hair out long and wear cut-offs
+
+ align:start position:0%
+grow my hair out long and wear cut-offs
+ 
+
+ align:start position:0%
+grow my hair out long and wear cut-offs
+so that was his I think rebellion
+
+ align:start position:0%
+so that was his I think rebellion
+ 
+
+ align:start position:0%
+so that was his I think rebellion
+against his parents this is during the
+
+ align:start position:0%
+against his parents this is during the
+ 
+
+ align:start position:0%
+against his parents this is during the
+time of Vietnam vinter realizes he comes
+
+ align:start position:0%
+time of Vietnam vinter realizes he comes
+ 
+
+ align:start position:0%
+time of Vietnam vinter realizes he comes
+from a military family first of all so I
+
+ align:start position:0%
+from a military family first of all so I
+ 
+
+ align:start position:0%
+from a military family first of all so I
+think he has a somewhat a sense of duty
+
+ align:start position:0%
+think he has a somewhat a sense of duty
+ 
+
+ align:start position:0%
+think he has a somewhat a sense of duty
+but he also realizes that he's probably
+
+ align:start position:0%
+but he also realizes that he's probably
+ 
+
+ align:start position:0%
+but he also realizes that he's probably
+going to get drafted and it's better for
+
+ align:start position:0%
+going to get drafted and it's better for
+ 
+
+ align:start position:0%
+going to get drafted and it's better for
+him if he joins the Navy voluntarily
+
+ align:start position:0%
+him if he joins the Navy voluntarily
+ 
+
+ align:start position:0%
+him if he joins the Navy voluntarily
+he's actually an extremely good
+
+ align:start position:0%
+he's actually an extremely good
+ 
+
+ align:start position:0%
+he's actually an extremely good
+competitive swimmer possibly Olympic
+
+ align:start position:0%
+competitive swimmer possibly Olympic
+ 
+
+ align:start position:0%
+competitive swimmer possibly Olympic
+quality so he joins the Navy thinking
+
+ align:start position:0%
+quality so he joins the Navy thinking
+ 
+
+ align:start position:0%
+quality so he joins the Navy thinking
+that he's going to be on the swim team
+
+ align:start position:0%
+that he's going to be on the swim team
+ 
+
+ align:start position:0%
+that he's going to be on the swim team
+and that actually is the active duty and
+
+ align:start position:0%
+and that actually is the active duty and
+ 
+
+ align:start position:0%
+and that actually is the active duty and
+this turns out to be couldn't be farther
+
+ align:start position:0%
+this turns out to be couldn't be farther
+ 
+
+ align:start position:0%
+this turns out to be couldn't be farther
+from the truth
+
+ align:start position:0%
+from the truth
+ 
+
+ align:start position:0%
+from the truth
+we Vietnam ramps up and he is trained as
+
+ align:start position:0%
+we Vietnam ramps up and he is trained as
+ 
+
+ align:start position:0%
+we Vietnam ramps up and he is trained as
+an EMT and deployed to Da Nang and he
+
+ align:start position:0%
+an EMT and deployed to Da Nang and he
+ 
+
+ align:start position:0%
+an EMT and deployed to Da Nang and he
+actually has two active deployments in
+
+ align:start position:0%
+actually has two active deployments in
+ 
+
+ align:start position:0%
+actually has two active deployments in
+Vietnam these see some things that I
+
+ align:start position:0%
+Vietnam these see some things that I
+ 
+
+ align:start position:0%
+Vietnam these see some things that I
+think changed his life forever in the
+
+ align:start position:0%
+think changed his life forever in the
+ 
+
+ align:start position:0%
+think changed his life forever in the
+interview he talks about how he's the
+
+ align:start position:0%
+interview he talks about how he's the
+ 
+
+ align:start position:0%
+interview he talks about how he's the
+person he is because of his time in
+
+ align:start position:0%
+person he is because of his time in
+ 
+
+ align:start position:0%
+person he is because of his time in
+Vietnam he survives and attends
+
+ align:start position:0%
+Vietnam he survives and attends
+ 
+
+ align:start position:0%
+Vietnam he survives and attends
+Community College in California
+
+ align:start position:0%
+Community College in California
+ 
+
+ align:start position:0%
+Community College in California
+transfers to UCSD which is the
+
+ align:start position:0%
+transfers to UCSD which is the
+ 
+
+ align:start position:0%
+transfers to UCSD which is the
+University of California San Diego gets
+
+ align:start position:0%
+University of California San Diego gets
+ 
+
+ align:start position:0%
+University of California San Diego gets
+a BS and then a PhD there I think he
+
+ align:start position:0%
+a BS and then a PhD there I think he
+ 
+
+ align:start position:0%
+a BS and then a PhD there I think he
+completed his PhD in three years the
+
+ align:start position:0%
+completed his PhD in three years the
+ 
+
+ align:start position:0%
+completed his PhD in three years the
+fastest at that time it was the fastest
+
+ align:start position:0%
+fastest at that time it was the fastest
+ 
+
+ align:start position:0%
+fastest at that time it was the fastest
+biochem PhD in in UCSD history he goes
+
+ align:start position:0%
+biochem PhD in in UCSD history he goes
+ 
+
+ align:start position:0%
+biochem PhD in in UCSD history he goes
+immediately to a faculty position at
+
+ align:start position:0%
+immediately to a faculty position at
+ 
+
+ align:start position:0%
+immediately to a faculty position at
+Buffalo and the
+
+ align:start position:0%
+Buffalo and the
+ 
+
+ align:start position:0%
+Buffalo and the
+or interesting transition for him
+
+ align:start position:0%
+or interesting transition for him
+ 
+
+ align:start position:0%
+or interesting transition for him
+yeah there's that's part of the the
+
+ align:start position:0%
+yeah there's that's part of the the
+ 
+
+ align:start position:0%
+yeah there's that's part of the the
+interview he talks about how he's this
+
+ align:start position:0%
+interview he talks about how he's this
+ 
+
+ align:start position:0%
+interview he talks about how he's this
+Californian with long hair and then goes
+
+ align:start position:0%
+Californian with long hair and then goes
+ 
+
+ align:start position:0%
+Californian with long hair and then goes
+to goes to puffle oh where he begins to
+
+ align:start position:0%
+to goes to puffle oh where he begins to
+ 
+
+ align:start position:0%
+to goes to puffle oh where he begins to
+make people angry actually so he starts
+
+ align:start position:0%
+make people angry actually so he starts
+ 
+
+ align:start position:0%
+make people angry actually so he starts
+young his fat so he marries his PhD
+
+ align:start position:0%
+young his fat so he marries his PhD
+ 
+
+ align:start position:0%
+young his fat so he marries his PhD
+student Claire Fraser he's very clear
+
+ align:start position:0%
+student Claire Fraser he's very clear
+ 
+
+ align:start position:0%
+student Claire Fraser he's very clear
+that they get married after she
+
+ align:start position:0%
+that they get married after she
+ 
+
+ align:start position:0%
+that they get married after she
+graduates so there's nothing wrong with
+
+ align:start position:0%
+graduates so there's nothing wrong with
+ 
+
+ align:start position:0%
+graduates so there's nothing wrong with
+that at all and in 1984 he leaves
+
+ align:start position:0%
+that at all and in 1984 he leaves
+ 
+
+ align:start position:0%
+that at all and in 1984 he leaves
+Buffalo pretty much so that she can
+
+ align:start position:0%
+Buffalo pretty much so that she can
+ 
+
+ align:start position:0%
+Buffalo pretty much so that she can
+start her prove herself as her own
+
+ align:start position:0%
+start her prove herself as her own
+ 
+
+ align:start position:0%
+start her prove herself as her own
+scientist at the end age and I think
+
+ align:start position:0%
+scientist at the end age and I think
+ 
+
+ align:start position:0%
+scientist at the end age and I think
+this is where the the great group really
+
+ align:start position:0%
+this is where the the great group really
+ 
+
+ align:start position:0%
+this is where the the great group really
+starts to coalesce and starts to deform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the sequence of events at the NIF so
+
+ align:start position:0%
+so the sequence of events at the NIF so
+ 
+
+ align:start position:0%
+so the sequence of events at the NIF so
+while at the NIH Venter is traditionally
+
+ align:start position:0%
+while at the NIH Venter is traditionally
+ 
+
+ align:start position:0%
+while at the NIH Venter is traditionally
+trained as a neuroscientist working in
+
+ align:start position:0%
+trained as a neuroscientist working in
+ 
+
+ align:start position:0%
+trained as a neuroscientist working in
+receptors so is Claire Fraser they have
+
+ align:start position:0%
+receptors so is Claire Fraser they have
+ 
+
+ align:start position:0%
+receptors so is Claire Fraser they have
+separate left labs at the NIH but
+
+ align:start position:0%
+separate left labs at the NIH but
+ 
+
+ align:start position:0%
+separate left labs at the NIH but
+something that Venter gets really
+
+ align:start position:0%
+something that Venter gets really
+ 
+
+ align:start position:0%
+something that Venter gets really
+interested in is molecular biology he
+
+ align:start position:0%
+interested in is molecular biology he
+ 
+
+ align:start position:0%
+interested in is molecular biology he
+sees that it's this field that's going
+
+ align:start position:0%
+sees that it's this field that's going
+ 
+
+ align:start position:0%
+sees that it's this field that's going
+to explode is extremely important and
+
+ align:start position:0%
+to explode is extremely important and
+ 
+
+ align:start position:0%
+to explode is extremely important and
+it's basically our path to future
+
+ align:start position:0%
+it's basically our path to future
+ 
+
+ align:start position:0%
+it's basically our path to future
+medicine so he starts to try to get
+
+ align:start position:0%
+medicine so he starts to try to get
+ 
+
+ align:start position:0%
+medicine so he starts to try to get
+funding to do molecular biology
+
+ align:start position:0%
+funding to do molecular biology
+ 
+
+ align:start position:0%
+funding to do molecular biology
+experiments and get into this field by
+
+ align:start position:0%
+experiments and get into this field by
+ 
+
+ align:start position:0%
+experiments and get into this field by
+the machines necessary and he's totally
+
+ align:start position:0%
+the machines necessary and he's totally
+ 
+
+ align:start position:0%
+the machines necessary and he's totally
+stoned all that the NIH she's basically
+
+ align:start position:0%
+stoned all that the NIH she's basically
+ 
+
+ align:start position:0%
+stoned all that the NIH she's basically
+told no you're a neuroscientist you
+
+ align:start position:0%
+told no you're a neuroscientist you
+ 
+
+ align:start position:0%
+told no you're a neuroscientist you
+can't work in this other stovepipe at
+
+ align:start position:0%
+can't work in this other stovepipe at
+ 
+
+ align:start position:0%
+can't work in this other stovepipe at
+the NIH that's just not done it won't
+
+ align:start position:0%
+the NIH that's just not done it won't
+ 
+
+ align:start position:0%
+the NIH that's just not done it won't
+work so he becomes increasingly and
+
+ align:start position:0%
+work so he becomes increasingly and
+ 
+
+ align:start position:0%
+work so he becomes increasingly and
+increasingly frustrated with the with
+
+ align:start position:0%
+increasingly frustrated with the with
+ 
+
+ align:start position:0%
+increasingly frustrated with the with
+the bureaucracy basically and he says
+
+ align:start position:0%
+the bureaucracy basically and he says
+ 
+
+ align:start position:0%
+the bureaucracy basically and he says
+that he looks around and he sees people
+
+ align:start position:0%
+that he looks around and he sees people
+ 
+
+ align:start position:0%
+that he looks around and he sees people
+who are lifers at the NIH who just go
+
+ align:start position:0%
+who are lifers at the NIH who just go
+ 
+
+ align:start position:0%
+who are lifers at the NIH who just go
+through the motions of being a scientist
+
+ align:start position:0%
+through the motions of being a scientist
+ 
+
+ align:start position:0%
+through the motions of being a scientist
+who couldn't really compete in the
+
+ align:start position:0%
+who couldn't really compete in the
+ 
+
+ align:start position:0%
+who couldn't really compete in the
+academic or the outside world so
+
+ align:start position:0%
+academic or the outside world so
+ 
+
+ align:start position:0%
+academic or the outside world so
+he does something a little maverick he
+
+ align:start position:0%
+he does something a little maverick he
+ 
+
+ align:start position:0%
+he does something a little maverick he
+creates this he he's reading about and
+
+ align:start position:0%
+creates this he he's reading about and
+ 
+
+ align:start position:0%
+creates this he he's reading about and
+hearing about the Human Genome Project
+
+ align:start position:0%
+hearing about the Human Genome Project
+ 
+
+ align:start position:0%
+hearing about the Human Genome Project
+because it's a big initiative at NIH and
+
+ align:start position:0%
+because it's a big initiative at NIH and
+ 
+
+ align:start position:0%
+because it's a big initiative at NIH and
+he decides well if they're not going to
+
+ align:start position:0%
+he decides well if they're not going to
+ 
+
+ align:start position:0%
+he decides well if they're not going to
+let me get into molecular biology and
+
+ align:start position:0%
+let me get into molecular biology and
+ 
+
+ align:start position:0%
+let me get into molecular biology and
+and sequencing the human genome then I'm
+
+ align:start position:0%
+and sequencing the human genome then I'm
+ 
+
+ align:start position:0%
+and sequencing the human genome then I'm
+going to sneak in by basically
+
+ align:start position:0%
+going to sneak in by basically
+ 
+
+ align:start position:0%
+going to sneak in by basically
+sequencing a gene involved in in in
+
+ align:start position:0%
+sequencing a gene involved in in in
+ 
+
+ align:start position:0%
+sequencing a gene involved in in in
+neurobiology so he does that and he
+
+ align:start position:0%
+neurobiology so he does that and he
+ 
+
+ align:start position:0%
+neurobiology so he does that and he
+invents this thing called est I'm not
+
+ align:start position:0%
+invents this thing called est I'm not
+ 
+
+ align:start position:0%
+invents this thing called est I'm not
+gonna get into it honestly it's such an
+
+ align:start position:0%
+gonna get into it honestly it's such an
+ 
+
+ align:start position:0%
+gonna get into it honestly it's such an
+outdated thing that I didn't even learn
+
+ align:start position:0%
+outdated thing that I didn't even learn
+ 
+
+ align:start position:0%
+outdated thing that I didn't even learn
+about it during my during my studies and
+
+ align:start position:0%
+about it during my during my studies and
+ 
+
+ align:start position:0%
+about it during my during my studies and
+then Watson and vendor have met so
+
+ align:start position:0%
+then Watson and vendor have met so
+ 
+
+ align:start position:0%
+then Watson and vendor have met so
+Watson is running the UNAM Human Genome
+
+ align:start position:0%
+Watson is running the UNAM Human Genome
+ 
+
+ align:start position:0%
+Watson is running the UNAM Human Genome
+Project at NIH right Venter comes up he
+
+ align:start position:0%
+Project at NIH right Venter comes up he
+ 
+
+ align:start position:0%
+Project at NIH right Venter comes up he
+has the sequence at this gene he he's
+
+ align:start position:0%
+has the sequence at this gene he he's
+ 
+
+ align:start position:0%
+has the sequence at this gene he he's
+made some pretty cool breakthroughs and
+
+ align:start position:0%
+made some pretty cool breakthroughs and
+ 
+
+ align:start position:0%
+made some pretty cool breakthroughs and
+goes in and meets with Watson and Watson
+
+ align:start position:0%
+goes in and meets with Watson and Watson
+ 
+
+ align:start position:0%
+goes in and meets with Watson and Watson
+gets excited about it at first but then
+
+ align:start position:0%
+gets excited about it at first but then
+ 
+
+ align:start position:0%
+gets excited about it at first but then
+craig venter goes off and kind of
+
+ align:start position:0%
+craig venter goes off and kind of
+ 
+
+ align:start position:0%
+craig venter goes off and kind of
+procures a machine sort of behind
+
+ align:start position:0%
+procures a machine sort of behind
+ 
+
+ align:start position:0%
+procures a machine sort of behind
+Watson's back because what Watson thinks
+
+ align:start position:0%
+Watson's back because what Watson thinks
+ 
+
+ align:start position:0%
+Watson's back because what Watson thinks
+and makes Watson really mad so he
+
+ align:start position:0%
+and makes Watson really mad so he
+ 
+
+ align:start position:0%
+and makes Watson really mad so he
+totally undermines and vilifies Venter
+
+ align:start position:0%
+totally undermines and vilifies Venter
+ 
+
+ align:start position:0%
+totally undermines and vilifies Venter
+in front of Congress and the US public
+
+ align:start position:0%
+in front of Congress and the US public
+ 
+
+ align:start position:0%
+in front of Congress and the US public
+because this is a huge this is a huge
+
+ align:start position:0%
+because this is a huge this is a huge
+ 
+
+ align:start position:0%
+because this is a huge this is a huge
+initiative this is like people are
+
+ align:start position:0%
+initiative this is like people are
+ 
+
+ align:start position:0%
+initiative this is like people are
+talking about it the dinner table it's a
+
+ align:start position:0%
+talking about it the dinner table it's a
+ 
+
+ align:start position:0%
+talking about it the dinner table it's a
+big deal back in the mid 1990s I would
+
+ align:start position:0%
+big deal back in the mid 1990s I would
+ 
+
+ align:start position:0%
+big deal back in the mid 1990s I would
+say so
+
+ align:start position:0%
+say so
+ 
+
+ align:start position:0%
+say so
+Watson basically doesn't like to wait
+
+ align:start position:0%
+Watson basically doesn't like to wait
+ 
+
+ align:start position:0%
+Watson basically doesn't like to wait
+Craig's doing things so let me just add
+
+ align:start position:0%
+Craig's doing things so let me just add
+ 
+
+ align:start position:0%
+Craig's doing things so let me just add
+one quick detail lilies so there's an
+
+ align:start position:0%
+one quick detail lilies so there's an
+ 
+
+ align:start position:0%
+one quick detail lilies so there's an
+issue here on what gets patented on a
+
+ align:start position:0%
+issue here on what gets patented on a
+ 
+
+ align:start position:0%
+issue here on what gets patented on a
+project like the human genome can you
+
+ align:start position:0%
+project like the human genome can you
+ 
+
+ align:start position:0%
+project like the human genome can you
+patent the genome right so this this
+
+ align:start position:0%
+patent the genome right so this this
+ 
+
+ align:start position:0%
+patent the genome right so this this
+whole issue is coming up the general
+
+ align:start position:0%
+whole issue is coming up the general
+ 
+
+ align:start position:0%
+whole issue is coming up the general
+counsel at NIH advises Venter that yes
+
+ align:start position:0%
+counsel at NIH advises Venter that yes
+ 
+
+ align:start position:0%
+counsel at NIH advises Venter that yes
+we are going to be able to patent a lot
+
+ align:start position:0%
+we are going to be able to patent a lot
+ 
+
+ align:start position:0%
+we are going to be able to patent a lot
+of this emerging genetics fields so
+
+ align:start position:0%
+of this emerging genetics fields so
+ 
+
+ align:start position:0%
+of this emerging genetics fields so
+let's protect he's a researcher for NIH
+
+ align:start position:0%
+let's protect he's a researcher for NIH
+ 
+
+ align:start position:0%
+let's protect he's a researcher for NIH
+so he's intramural researcher at NIH
+
+ align:start position:0%
+so he's intramural researcher at NIH
+ 
+
+ align:start position:0%
+so he's intramural researcher at NIH
+let's protect NIH by filing a lot
+
+ align:start position:0%
+let's protect NIH by filing a lot
+ 
+
+ align:start position:0%
+let's protect NIH by filing a lot
+the patents ourselves and the
+
+ align:start position:0%
+the patents ourselves and the
+ 
+
+ align:start position:0%
+the patents ourselves and the
+confrontation with Congress is where
+
+ align:start position:0%
+confrontation with Congress is where
+ 
+
+ align:start position:0%
+confrontation with Congress is where
+Watson attacks Venter for patenting you
+
+ align:start position:0%
+Watson attacks Venter for patenting you
+ 
+
+ align:start position:0%
+Watson attacks Venter for patenting you
+know genome technologies in other words
+
+ align:start position:0%
+know genome technologies in other words
+ 
+
+ align:start position:0%
+know genome technologies in other words
+it's not going to be available to the
+
+ align:start position:0%
+it's not going to be available to the
+ 
+
+ align:start position:0%
+it's not going to be available to the
+scientific world it's not going to be
+
+ align:start position:0%
+scientific world it's not going to be
+ 
+
+ align:start position:0%
+scientific world it's not going to be
+open based it's not going to be in the
+
+ align:start position:0%
+open based it's not going to be in the
+ 
+
+ align:start position:0%
+open based it's not going to be in the
+comments even though Venter had receipt
+
+ align:start position:0%
+comments even though Venter had receipt
+ 
+
+ align:start position:0%
+comments even though Venter had receipt
+we had been told by the General
+
+ align:start position:0%
+we had been told by the General
+ 
+
+ align:start position:0%
+we had been told by the General
+Counsel's office in NIH that that's what
+
+ align:start position:0%
+Counsel's office in NIH that that's what
+ 
+
+ align:start position:0%
+Counsel's office in NIH that that's what
+he had to do so that leads to this
+
+ align:start position:0%
+he had to do so that leads to this
+ 
+
+ align:start position:0%
+he had to do so that leads to this
+explosion of anger by Venter is that a
+
+ align:start position:0%
+explosion of anger by Venter is that a
+ 
+
+ align:start position:0%
+explosion of anger by Venter is that a
+fair summary definitely yeah from
+
+ align:start position:0%
+fair summary definitely yeah from
+ 
+
+ align:start position:0%
+fair summary definitely yeah from
+venture side of the story he says I
+
+ align:start position:0%
+venture side of the story he says I
+ 
+
+ align:start position:0%
+venture side of the story he says I
+didn't necessarily want to patent these
+
+ align:start position:0%
+didn't necessarily want to patent these
+ 
+
+ align:start position:0%
+didn't necessarily want to patent these
+genes the NIH advised me to it was their
+
+ align:start position:0%
+genes the NIH advised me to it was their
+ 
+
+ align:start position:0%
+genes the NIH advised me to it was their
+initiative and Watson used it as a way
+
+ align:start position:0%
+initiative and Watson used it as a way
+ 
+
+ align:start position:0%
+initiative and Watson used it as a way
+to undermine me in front of the American
+
+ align:start position:0%
+to undermine me in front of the American
+ 
+
+ align:start position:0%
+to undermine me in front of the American
+public because he didn't want me to use
+
+ align:start position:0%
+public because he didn't want me to use
+ 
+
+ align:start position:0%
+public because he didn't want me to use
+my technology that I had come up with so
+
+ align:start position:0%
+my technology that I had come up with so
+ 
+
+ align:start position:0%
+my technology that I had come up with so
+that's the sort of the back story Venter
+
+ align:start position:0%
+that's the sort of the back story Venter
+ 
+
+ align:start position:0%
+that's the sort of the back story Venter
+is insanely angry and he and his wife
+
+ align:start position:0%
+is insanely angry and he and his wife
+ 
+
+ align:start position:0%
+is insanely angry and he and his wife
+defect from the NIH and form Solera with
+
+ align:start position:0%
+defect from the NIH and form Solera with
+ 
+
+ align:start position:0%
+defect from the NIH and form Solera with
+the help of venture capitalists who
+
+ align:start position:0%
+the help of venture capitalists who
+ 
+
+ align:start position:0%
+the help of venture capitalists who
+later also anger Venter and that
+
+ align:start position:0%
+later also anger Venter and that
+ 
+
+ align:start position:0%
+later also anger Venter and that
+explodes and they take with them 12 men
+
+ align:start position:0%
+explodes and they take with them 12 men
+ 
+
+ align:start position:0%
+explodes and they take with them 12 men
+of their lab members from the NIH so the
+
+ align:start position:0%
+of their lab members from the NIH so the
+ 
+
+ align:start position:0%
+of their lab members from the NIH so the
+team and I think that craig Venter
+
+ align:start position:0%
+team and I think that craig Venter
+ 
+
+ align:start position:0%
+team and I think that craig Venter
+really exemplifies a great great group
+
+ align:start position:0%
+really exemplifies a great great group
+ 
+
+ align:start position:0%
+really exemplifies a great great group
+leader in that he seems able to identify
+
+ align:start position:0%
+leader in that he seems able to identify
+ 
+
+ align:start position:0%
+leader in that he seems able to identify
+talent and others so they start out with
+
+ align:start position:0%
+talent and others so they start out with
+ 
+
+ align:start position:0%
+talent and others so they start out with
+the 12 from NIH they have their island
+
+ align:start position:0%
+the 12 from NIH they have their island
+ 
+
+ align:start position:0%
+the 12 from NIH they have their island
+of Solera and the team that they start
+
+ align:start position:0%
+of Solera and the team that they start
+ 
+
+ align:start position:0%
+of Solera and the team that they start
+to form this is not including like the
+
+ align:start position:0%
+to form this is not including like the
+ 
+
+ align:start position:0%
+to form this is not including like the
+board of directors and such which also
+
+ align:start position:0%
+board of directors and such which also
+ 
+
+ align:start position:0%
+board of directors and such which also
+seem to be pretty amazing people but
+
+ align:start position:0%
+seem to be pretty amazing people but
+ 
+
+ align:start position:0%
+seem to be pretty amazing people but
+they recruit Hamiltons actually I think
+
+ align:start position:0%
+they recruit Hamiltons actually I think
+ 
+
+ align:start position:0%
+they recruit Hamiltons actually I think
+well Hamilton Smith comes on to the
+
+ align:start position:0%
+well Hamilton Smith comes on to the
+ 
+
+ align:start position:0%
+well Hamilton Smith comes on to the
+scene and he's their premier molecular
+
+ align:start position:0%
+scene and he's their premier molecular
+ 
+
+ align:start position:0%
+scene and he's their premier molecular
+biologist and he's a Nobel Prize well
+
+ align:start position:0%
+biologist and he's a Nobel Prize well
+ 
+
+ align:start position:0%
+biologist and he's a Nobel Prize well
+did he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prior yeah yeah so I don't think any of
+
+ align:start position:0%
+prior yeah yeah so I don't think any of
+ 
+
+ align:start position:0%
+prior yeah yeah so I don't think any of
+this is actually a question I'm going to
+
+ align:start position:0%
+this is actually a question I'm going to
+ 
+
+ align:start position:0%
+this is actually a question I'm going to
+pose to the class at the end of my
+
+ align:start position:0%
+pose to the class at the end of my
+ 
+
+ align:start position:0%
+pose to the class at the end of my
+presentation I don't think anyone in
+
+ align:start position:0%
+presentation I don't think anyone in
+ 
+
+ align:start position:0%
+presentation I don't think anyone in
+this great group has one of the Nobel
+
+ align:start position:0%
+this great group has one of the Nobel
+ 
+
+ align:start position:0%
+this great group has one of the Nobel
+Prize except
+
+ align:start position:0%
+Prize except
+ 
+
+ align:start position:0%
+Prize except
+for this previously ham Smith wrote so
+
+ align:start position:0%
+for this previously ham Smith wrote so
+ 
+
+ align:start position:0%
+for this previously ham Smith wrote so
+Marshall Peterson is this computer geek
+
+ align:start position:0%
+Marshall Peterson is this computer geek
+ 
+
+ align:start position:0%
+Marshall Peterson is this computer geek
+because not only is Hamilton Smith
+
+ align:start position:0%
+because not only is Hamilton Smith
+ 
+
+ align:start position:0%
+because not only is Hamilton Smith
+literally coming up with the sequencing
+
+ align:start position:0%
+literally coming up with the sequencing
+ 
+
+ align:start position:0%
+literally coming up with the sequencing
+technology to do this this is a this is
+
+ align:start position:0%
+technology to do this this is a this is
+ 
+
+ align:start position:0%
+technology to do this this is a this is
+like 30 billion base pairs of DNA the
+
+ align:start position:0%
+like 30 billion base pairs of DNA the
+ 
+
+ align:start position:0%
+like 30 billion base pairs of DNA the
+most anyone has sequenced at this point
+
+ align:start position:0%
+most anyone has sequenced at this point
+ 
+
+ align:start position:0%
+most anyone has sequenced at this point
+is like C elegans or like a worm like
+
+ align:start position:0%
+is like C elegans or like a worm like
+ 
+
+ align:start position:0%
+is like C elegans or like a worm like
+tiny tiny genome this is a huge deal
+
+ align:start position:0%
+tiny tiny genome this is a huge deal
+ 
+
+ align:start position:0%
+tiny tiny genome this is a huge deal
+they have to come up with new sequencing
+
+ align:start position:0%
+they have to come up with new sequencing
+ 
+
+ align:start position:0%
+they have to come up with new sequencing
+technologies new ways to decode the
+
+ align:start position:0%
+technologies new ways to decode the
+ 
+
+ align:start position:0%
+technologies new ways to decode the
+sequence and new computing so they
+
+ align:start position:0%
+sequence and new computing so they
+ 
+
+ align:start position:0%
+sequence and new computing so they
+literally build the third largest
+
+ align:start position:0%
+literally build the third largest
+ 
+
+ align:start position:0%
+literally build the third largest
+computer on the planet I think the do-e
+
+ align:start position:0%
+computer on the planet I think the do-e
+ 
+
+ align:start position:0%
+computer on the planet I think the do-e
+has a larger computer and there's
+
+ align:start position:0%
+has a larger computer and there's
+ 
+
+ align:start position:0%
+has a larger computer and there's
+someone somewhere else in the world and
+
+ align:start position:0%
+someone somewhere else in the world and
+ 
+
+ align:start position:0%
+someone somewhere else in the world and
+they build this massive computing
+
+ align:start position:0%
+they build this massive computing
+ 
+
+ align:start position:0%
+they build this massive computing
+facility and then bring on gene Myers as
+
+ align:start position:0%
+facility and then bring on gene Myers as
+ 
+
+ align:start position:0%
+facility and then bring on gene Myers as
+this coder who's coming up with the
+
+ align:start position:0%
+this coder who's coming up with the
+ 
+
+ align:start position:0%
+this coder who's coming up with the
+algorithms to try to piece together all
+
+ align:start position:0%
+algorithms to try to piece together all
+ 
+
+ align:start position:0%
+algorithms to try to piece together all
+these little pieces of DNA and build up
+
+ align:start position:0%
+these little pieces of DNA and build up
+ 
+
+ align:start position:0%
+these little pieces of DNA and build up
+30 billion base sequence so in the
+
+ align:start position:0%
+30 billion base sequence so in the
+ 
+
+ align:start position:0%
+30 billion base sequence so in the
+meantime the public sector academia the
+
+ align:start position:0%
+meantime the public sector academia the
+ 
+
+ align:start position:0%
+meantime the public sector academia the
+NIH are becoming increasingly angry with
+
+ align:start position:0%
+NIH are becoming increasingly angry with
+ 
+
+ align:start position:0%
+NIH are becoming increasingly angry with
+craig Venter saying that he's he's
+
+ align:start position:0%
+craig Venter saying that he's he's
+ 
+
+ align:start position:0%
+craig Venter saying that he's he's
+defecting to the private sector and he's
+
+ align:start position:0%
+defecting to the private sector and he's
+ 
+
+ align:start position:0%
+defecting to the private sector and he's
+going after the human genome for profit
+
+ align:start position:0%
+going after the human genome for profit
+ 
+
+ align:start position:0%
+going after the human genome for profit
+Craig is saying I don't I'm not in this
+
+ align:start position:0%
+Craig is saying I don't I'm not in this
+ 
+
+ align:start position:0%
+Craig is saying I don't I'm not in this
+for profit I'm in this because we need a
+
+ align:start position:0%
+for profit I'm in this because we need a
+ 
+
+ align:start position:0%
+for profit I'm in this because we need a
+human genome so that we can promote
+
+ align:start position:0%
+human genome so that we can promote
+ 
+
+ align:start position:0%
+human genome so that we can promote
+human you know molecular biology based
+
+ align:start position:0%
+human you know molecular biology based
+ 
+
+ align:start position:0%
+human you know molecular biology based
+medicine in the meantime he sequences
+
+ align:start position:0%
+medicine in the meantime he sequences
+ 
+
+ align:start position:0%
+medicine in the meantime he sequences
+the drosophila genome and gives it its
+
+ align:start position:0%
+the drosophila genome and gives it its
+ 
+
+ align:start position:0%
+the drosophila genome and gives it its
+publishes it in science gets rich Laurie
+
+ align:start position:0%
+publishes it in science gets rich Laurie
+ 
+
+ align:start position:0%
+publishes it in science gets rich Laurie
+yeah the fruit fly genome which people
+
+ align:start position:0%
+yeah the fruit fly genome which people
+ 
+
+ align:start position:0%
+yeah the fruit fly genome which people
+have been trying to figure out what
+
+ align:start position:0%
+have been trying to figure out what
+ 
+
+ align:start position:0%
+have been trying to figure out what
+genes and fruit fly do for decades and
+
+ align:start position:0%
+genes and fruit fly do for decades and
+ 
+
+ align:start position:0%
+genes and fruit fly do for decades and
+decades and decades and so there's this
+
+ align:start position:0%
+decades and decades and so there's this
+ 
+
+ align:start position:0%
+decades and decades and so there's this
+really cool part in the interview where
+
+ align:start position:0%
+really cool part in the interview where
+ 
+
+ align:start position:0%
+really cool part in the interview where
+he talks about this community of fruit
+
+ align:start position:0%
+he talks about this community of fruit
+ 
+
+ align:start position:0%
+he talks about this community of fruit
+fly researchers who I think are kind of
+
+ align:start position:0%
+fly researchers who I think are kind of
+ 
+
+ align:start position:0%
+fly researchers who I think are kind of
+like the physics community they're
+
+ align:start position:0%
+like the physics community they're
+ 
+
+ align:start position:0%
+like the physics community they're
+pretty close-knit they have their
+
+ align:start position:0%
+pretty close-knit they have their
+ 
+
+ align:start position:0%
+pretty close-knit they have their
+conferences and they they write try to
+
+ align:start position:0%
+conferences and they they write try to
+ 
+
+ align:start position:0%
+conferences and they they write try to
+get together and and decode the fruit
+
+ align:start position:0%
+get together and and decode the fruit
+ 
+
+ align:start position:0%
+get together and and decode the fruit
+fly which they don't have the bases or
+
+ align:start position:0%
+fly which they don't have the bases or
+ 
+
+ align:start position:0%
+fly which they don't have the bases or
+the knowledge to do that yes they're
+
+ align:start position:0%
+the knowledge to do that yes they're
+ 
+
+ align:start position:0%
+the knowledge to do that yes they're
+doing it like gene by gene
+
+ align:start position:0%
+doing it like gene by gene
+ 
+
+ align:start position:0%
+doing it like gene by gene
+by Jeanne over many years and Craig
+
+ align:start position:0%
+by Jeanne over many years and Craig
+ 
+
+ align:start position:0%
+by Jeanne over many years and Craig
+decodes the the fruit fly genome and
+
+ align:start position:0%
+decodes the the fruit fly genome and
+ 
+
+ align:start position:0%
+decodes the the fruit fly genome and
+says come to Solara I have all of the
+
+ align:start position:0%
+says come to Solara I have all of the
+ 
+
+ align:start position:0%
+says come to Solara I have all of the
+information that you've been looking for
+
+ align:start position:0%
+information that you've been looking for
+ 
+
+ align:start position:0%
+information that you've been looking for
+for the past few decades and you can
+
+ align:start position:0%
+for the past few decades and you can
+ 
+
+ align:start position:0%
+for the past few decades and you can
+have it it's here so a couple says um
+
+ align:start position:0%
+have it it's here so a couple says um
+ 
+
+ align:start position:0%
+have it it's here so a couple says um
+maybe on the order of a hundred or so
+
+ align:start position:0%
+maybe on the order of a hundred or so
+ 
+
+ align:start position:0%
+maybe on the order of a hundred or so
+fruit fly researchers come and they're
+
+ align:start position:0%
+fruit fly researchers come and they're
+ 
+
+ align:start position:0%
+fruit fly researchers come and they're
+just like kids in a candy shop they stay
+
+ align:start position:0%
+just like kids in a candy shop they stay
+ 
+
+ align:start position:0%
+just like kids in a candy shop they stay
+up all hours of the night and like
+
+ align:start position:0%
+up all hours of the night and like
+ 
+
+ align:start position:0%
+up all hours of the night and like
+making these breakthroughs that they've
+
+ align:start position:0%
+making these breakthroughs that they've
+ 
+
+ align:start position:0%
+making these breakthroughs that they've
+been that they've been looking for for
+
+ align:start position:0%
+been that they've been looking for for
+ 
+
+ align:start position:0%
+been that they've been looking for for
+decades so that's pretty fun pretty cool
+
+ align:start position:0%
+decades so that's pretty fun pretty cool
+ 
+
+ align:start position:0%
+decades so that's pretty fun pretty cool
+so fruit flying sequenced NIH you would
+
+ align:start position:0%
+so fruit flying sequenced NIH you would
+ 
+
+ align:start position:0%
+so fruit flying sequenced NIH you would
+probably know more about the the
+
+ align:start position:0%
+probably know more about the the
+ 
+
+ align:start position:0%
+probably know more about the the
+interplay between Francis Collins and
+
+ align:start position:0%
+interplay between Francis Collins and
+ 
+
+ align:start position:0%
+interplay between Francis Collins and
+vinter because that I don't I'm not it's
+
+ align:start position:0%
+vinter because that I don't I'm not it's
+ 
+
+ align:start position:0%
+vinter because that I don't I'm not it's
+a little fuzzy for me I can never figure
+
+ align:start position:0%
+a little fuzzy for me I can never figure
+ 
+
+ align:start position:0%
+a little fuzzy for me I can never figure
+out if they're working together or
+
+ align:start position:0%
+out if they're working together or
+ 
+
+ align:start position:0%
+out if they're working together or
+against each other but eventually what
+
+ align:start position:0%
+against each other but eventually what
+ 
+
+ align:start position:0%
+against each other but eventually what
+happens in 2001 the NIH and the public
+
+ align:start position:0%
+happens in 2001 the NIH and the public
+ 
+
+ align:start position:0%
+happens in 2001 the NIH and the public
+like academia so people from different
+
+ align:start position:0%
+like academia so people from different
+ 
+
+ align:start position:0%
+like academia so people from different
+universities come together and publish
+
+ align:start position:0%
+universities come together and publish
+ 
+
+ align:start position:0%
+universities come together and publish
+the human genome in the journal Nature
+
+ align:start position:0%
+the human genome in the journal Nature
+ 
+
+ align:start position:0%
+the human genome in the journal Nature
+and it's like two days later salera
+
+ align:start position:0%
+and it's like two days later salera
+ 
+
+ align:start position:0%
+and it's like two days later salera
+announces same day oh it is the same day
+
+ align:start position:0%
+announces same day oh it is the same day
+ 
+
+ align:start position:0%
+announces same day oh it is the same day
+comes out in science so this is yes so
+
+ align:start position:0%
+comes out in science so this is yes so
+ 
+
+ align:start position:0%
+comes out in science so this is yes so
+there had to be I mean it's a
+
+ align:start position:0%
+there had to be I mean it's a
+ 
+
+ align:start position:0%
+there had to be I mean it's a
+fascinating story right and there's rich
+
+ align:start position:0%
+fascinating story right and there's rich
+ 
+
+ align:start position:0%
+fascinating story right and there's rich
+MIT history which MIT was on the side of
+
+ align:start position:0%
+MIT history which MIT was on the side of
+ 
+
+ align:start position:0%
+MIT history which MIT was on the side of
+NIH to see you know so Venter through
+
+ align:start position:0%
+NIH to see you know so Venter through
+ 
+
+ align:start position:0%
+NIH to see you know so Venter through
+you know a research model that was
+
+ align:start position:0%
+you know a research model that was
+ 
+
+ align:start position:0%
+you know a research model that was
+extremely focused on getting this
+
+ align:start position:0%
+extremely focused on getting this
+ 
+
+ align:start position:0%
+extremely focused on getting this
+project done right everything was to be
+
+ align:start position:0%
+project done right everything was to be
+ 
+
+ align:start position:0%
+project done right everything was to be
+organized for the project NIH is on a
+
+ align:start position:0%
+organized for the project NIH is on a
+ 
+
+ align:start position:0%
+organized for the project NIH is on a
+research model that could be described
+
+ align:start position:0%
+research model that could be described
+ 
+
+ align:start position:0%
+research model that could be described
+as let's let a thousand flowers bloom
+
+ align:start position:0%
+as let's let a thousand flowers bloom
+ 
+
+ align:start position:0%
+as let's let a thousand flowers bloom
+we'll have a lot of ro1 researchers out
+
+ align:start position:0%
+we'll have a lot of ro1 researchers out
+ 
+
+ align:start position:0%
+we'll have a lot of ro1 researchers out
+there you know eventually that will turn
+
+ align:start position:0%
+there you know eventually that will turn
+ 
+
+ align:start position:0%
+there you know eventually that will turn
+into the Human Genome Project someone
+
+ align:start position:0%
+into the Human Genome Project someone
+ 
+
+ align:start position:0%
+into the Human Genome Project someone
+made the analogy to that research model
+
+ align:start position:0%
+made the analogy to that research model
+ 
+
+ align:start position:0%
+made the analogy to that research model
+as okay if you put a whole lot of
+
+ align:start position:0%
+as okay if you put a whole lot of
+ 
+
+ align:start position:0%
+as okay if you put a whole lot of
+monkeys into a room and give them
+
+ align:start position:0%
+monkeys into a room and give them
+ 
+
+ align:start position:0%
+monkeys into a room and give them
+typewriters eventually we'll get
+
+ align:start position:0%
+typewriters eventually we'll get
+ 
+
+ align:start position:0%
+typewriters eventually we'll get
+Shakespeare right it's obviously exact
+
+ align:start position:0%
+Shakespeare right it's obviously exact
+ 
+
+ align:start position:0%
+Shakespeare right it's obviously exact
+exaggeration here but
+
+ align:start position:0%
+exaggeration here but
+ 
+
+ align:start position:0%
+exaggeration here but
+Venter with his very focused research
+
+ align:start position:0%
+Venter with his very focused research
+ 
+
+ align:start position:0%
+Venter with his very focused research
+project than these computer scientists
+
+ align:start position:0%
+project than these computer scientists
+ 
+
+ align:start position:0%
+project than these computer scientists
+and Venter himself becomes a master of
+
+ align:start position:0%
+and Venter himself becomes a master of
+ 
+
+ align:start position:0%
+and Venter himself becomes a master of
+the computers that he's working on
+
+ align:start position:0%
+the computers that he's working on
+ 
+
+ align:start position:0%
+the computers that he's working on
+building and est technology is from that
+
+ align:start position:0%
+building and est technology is from that
+ 
+
+ align:start position:0%
+building and est technology is from that
+versus a much more decentralized
+
+ align:start position:0%
+versus a much more decentralized
+ 
+
+ align:start position:0%
+versus a much more decentralized
+research operation so slowly Inayat
+
+ align:start position:0%
+research operation so slowly Inayat
+ 
+
+ align:start position:0%
+research operation so slowly Inayat
+relies it's gonna lose the race unless
+
+ align:start position:0%
+relies it's gonna lose the race unless
+ 
+
+ align:start position:0%
+relies it's gonna lose the race unless
+against its act together so they begin
+
+ align:start position:0%
+against its act together so they begin
+ 
+
+ align:start position:0%
+against its act together so they begin
+to focus on you know getting rid of the
+
+ align:start position:0%
+to focus on you know getting rid of the
+ 
+
+ align:start position:0%
+to focus on you know getting rid of the
+thousand flowers let's get down to a
+
+ align:start position:0%
+thousand flowers let's get down to a
+ 
+
+ align:start position:0%
+thousand flowers let's get down to a
+small number of focused research centers
+
+ align:start position:0%
+small number of focused research centers
+ 
+
+ align:start position:0%
+small number of focused research centers
+and it's you know it's a race really
+
+ align:start position:0%
+and it's you know it's a race really
+ 
+
+ align:start position:0%
+and it's you know it's a race really
+between who's the broad institute and
+
+ align:start position:0%
+between who's the broad institute and
+ 
+
+ align:start position:0%
+between who's the broad institute and
+head what's his name
+
+ align:start position:0%
+head what's his name
+ 
+
+ align:start position:0%
+head what's his name
+you know how can I forget Eric Lander
+
+ align:start position:0%
+you know how can I forget Eric Lander
+ 
+
+ align:start position:0%
+you know how can I forget Eric Lander
+yeah of course sorry excuse me
+
+ align:start position:0%
+yeah of course sorry excuse me
+ 
+
+ align:start position:0%
+yeah of course sorry excuse me
+so Eric Erickson mathematician he's not
+
+ align:start position:0%
+so Eric Erickson mathematician he's not
+ 
+
+ align:start position:0%
+so Eric Erickson mathematician he's not
+a life scientist right and he becomes
+
+ align:start position:0%
+a life scientist right and he becomes
+ 
+
+ align:start position:0%
+a life scientist right and he becomes
+the leader of the human Human Genome
+
+ align:start position:0%
+the leader of the human Human Genome
+ 
+
+ align:start position:0%
+the leader of the human Human Genome
+Project for NIH Collins is heading it
+
+ align:start position:0%
+Project for NIH Collins is heading it
+ 
+
+ align:start position:0%
+Project for NIH Collins is heading it
+but Eric is the one who's carrying out
+
+ align:start position:0%
+but Eric is the one who's carrying out
+ 
+
+ align:start position:0%
+but Eric is the one who's carrying out
+the computational parts of it right and
+
+ align:start position:0%
+the computational parts of it right and
+ 
+
+ align:start position:0%
+the computational parts of it right and
+they do it in cooperation with the
+
+ align:start position:0%
+they do it in cooperation with the
+ 
+
+ align:start position:0%
+they do it in cooperation with the
+Department of Energy super computer labs
+
+ align:start position:0%
+Department of Energy super computer labs
+ 
+
+ align:start position:0%
+Department of Energy super computer labs
+because they need their own
+
+ align:start position:0%
+because they need their own
+ 
+
+ align:start position:0%
+because they need their own
+supercomputing capability ventures built
+
+ align:start position:0%
+supercomputing capability ventures built
+ 
+
+ align:start position:0%
+supercomputing capability ventures built
+is NIH uses do e so this race is ongoing
+
+ align:start position:0%
+is NIH uses do e so this race is ongoing
+ 
+
+ align:start position:0%
+is NIH uses do e so this race is ongoing
+the NIH crowd is attacking Venter
+
+ align:start position:0%
+the NIH crowd is attacking Venter
+ 
+
+ align:start position:0%
+the NIH crowd is attacking Venter
+constantly for essentially trying to
+
+ align:start position:0%
+constantly for essentially trying to
+ 
+
+ align:start position:0%
+constantly for essentially trying to
+profit from patenting the genome that's
+
+ align:start position:0%
+profit from patenting the genome that's
+ 
+
+ align:start position:0%
+profit from patenting the genome that's
+the complaint that he's gonna take this
+
+ align:start position:0%
+the complaint that he's gonna take this
+ 
+
+ align:start position:0%
+the complaint that he's gonna take this
+critical scientific advance few critical
+
+ align:start position:0%
+critical scientific advance few critical
+ 
+
+ align:start position:0%
+critical scientific advance few critical
+to the future of medicine and take it
+
+ align:start position:0%
+to the future of medicine and take it
+ 
+
+ align:start position:0%
+to the future of medicine and take it
+out of circulation and access to science
+
+ align:start position:0%
+out of circulation and access to science
+ 
+
+ align:start position:0%
+out of circulation and access to science
+and patent it and prevent anybody from
+
+ align:start position:0%
+and patent it and prevent anybody from
+ 
+
+ align:start position:0%
+and patent it and prevent anybody from
+using it that's the case being made
+
+ align:start position:0%
+using it that's the case being made
+ 
+
+ align:start position:0%
+using it that's the case being made
+against him it's pretty far in reality
+
+ align:start position:0%
+against him it's pretty far in reality
+ 
+
+ align:start position:0%
+against him it's pretty far in reality
+from what the truth is but that's the
+
+ align:start position:0%
+from what the truth is but that's the
+ 
+
+ align:start position:0%
+from what the truth is but that's the
+case being made and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Eric and the NIH team are gradually they
+
+ align:start position:0%
+Eric and the NIH team are gradually they
+ 
+
+ align:start position:0%
+Eric and the NIH team are gradually they
+are using some Avengers technology the
+
+ align:start position:0%
+are using some Avengers technology the
+ 
+
+ align:start position:0%
+are using some Avengers technology the
+originating certainly many of their own
+
+ align:start position:0%
+originating certainly many of their own
+ 
+
+ align:start position:0%
+originating certainly many of their own
+they're within range so at that point a
+
+ align:start position:0%
+they're within range so at that point a
+ 
+
+ align:start position:0%
+they're within range so at that point a
+negotiated truth is arranged so that
+
+ align:start position:0%
+negotiated truth is arranged so that
+ 
+
+ align:start position:0%
+negotiated truth is arranged so that
+nobody gets embarrassed here right and
+
+ align:start position:0%
+nobody gets embarrassed here right and
+ 
+
+ align:start position:0%
+nobody gets embarrassed here right and
+the real worry was that NIH would lose
+
+ align:start position:0%
+the real worry was that NIH would lose
+ 
+
+ align:start position:0%
+the real worry was that NIH would lose
+the race right so eventually Venter has
+
+ align:start position:0%
+the race right so eventually Venter has
+ 
+
+ align:start position:0%
+the race right so eventually Venter has
+prevailed on to declare a tie and each
+
+ align:start position:0%
+prevailed on to declare a tie and each
+ 
+
+ align:start position:0%
+prevailed on to declare a tie and each
+side will publish in the two major
+
+ align:start position:0%
+side will publish in the two major
+ 
+
+ align:start position:0%
+side will publish in the two major
+scientific publications their version of
+
+ align:start position:0%
+scientific publications their version of
+ 
+
+ align:start position:0%
+scientific publications their version of
+the genome and that's in fact what
+
+ align:start position:0%
+the genome and that's in fact what
+ 
+
+ align:start position:0%
+the genome and that's in fact what
+occurs it's go ahead one is that in this
+
+ align:start position:0%
+occurs it's go ahead one is that in this
+ 
+
+ align:start position:0%
+occurs it's go ahead one is that in this
+interview Venter says that he finds out
+
+ align:start position:0%
+interview Venter says that he finds out
+ 
+
+ align:start position:0%
+interview Venter says that he finds out
+that Francis Collins the head of the NIH
+
+ align:start position:0%
+that Francis Collins the head of the NIH
+ 
+
+ align:start position:0%
+that Francis Collins the head of the NIH
+has not has budgeted less than half of
+
+ align:start position:0%
+has not has budgeted less than half of
+ 
+
+ align:start position:0%
+has not has budgeted less than half of
+what it's going to take at their current
+
+ align:start position:0%
+what it's going to take at their current
+ 
+
+ align:start position:0%
+what it's going to take at their current
+rate to complete the human genome so in
+
+ align:start position:0%
+rate to complete the human genome so in
+ 
+
+ align:start position:0%
+rate to complete the human genome so in
+his mind Collins has no intention of
+
+ align:start position:0%
+his mind Collins has no intention of
+ 
+
+ align:start position:0%
+his mind Collins has no intention of
+really completing it and they can't as
+
+ align:start position:0%
+really completing it and they can't as
+ 
+
+ align:start position:0%
+really completing it and they can't as
+the way things stood the other point I
+
+ align:start position:0%
+the way things stood the other point I
+ 
+
+ align:start position:0%
+the way things stood the other point I
+wanted to make is that the niña like
+
+ align:start position:0%
+wanted to make is that the niña like
+ 
+
+ align:start position:0%
+wanted to make is that the niña like
+Venters enemies and adversaries keep on
+
+ align:start position:0%
+Venters enemies and adversaries keep on
+ 
+
+ align:start position:0%
+Venters enemies and adversaries keep on
+barding him and the public by saying
+
+ align:start position:0%
+barding him and the public by saying
+ 
+
+ align:start position:0%
+barding him and the public by saying
+he's gonna profit off the human genome
+
+ align:start position:0%
+he's gonna profit off the human genome
+ 
+
+ align:start position:0%
+he's gonna profit off the human genome
+and there is a little there's actually a
+
+ align:start position:0%
+and there is a little there's actually a
+ 
+
+ align:start position:0%
+and there is a little there's actually a
+lot of friction between
+
+ align:start position:0%
+lot of friction between
+ 
+
+ align:start position:0%
+lot of friction between
+vinter and has been sure capitalists
+
+ align:start position:0%
+vinter and has been sure capitalists
+ 
+
+ align:start position:0%
+vinter and has been sure capitalists
+because he wants to publish publish
+
+ align:start position:0%
+because he wants to publish publish
+ 
+
+ align:start position:0%
+because he wants to publish publish
+publish publish the findings that
+
+ align:start position:0%
+publish publish the findings that
+ 
+
+ align:start position:0%
+publish publish the findings that
+they're making so that other people can
+
+ align:start position:0%
+they're making so that other people can
+ 
+
+ align:start position:0%
+they're making so that other people can
+utilize them and the venture capitalists
+
+ align:start position:0%
+utilize them and the venture capitalists
+ 
+
+ align:start position:0%
+utilize them and the venture capitalists
+keep saying no we don't want you can't
+
+ align:start position:0%
+keep saying no we don't want you can't
+ 
+
+ align:start position:0%
+keep saying no we don't want you can't
+do that you can't do that it's private
+
+ align:start position:0%
+do that you can't do that it's private
+ 
+
+ align:start position:0%
+do that you can't do that it's private
+we we want to patent etc so there's that
+
+ align:start position:0%
+we we want to patent etc so there's that
+ 
+
+ align:start position:0%
+we we want to patent etc so there's that
+friction going on so yes eventually
+
+ align:start position:0%
+friction going on so yes eventually
+ 
+
+ align:start position:0%
+friction going on so yes eventually
+published at the same time salera
+
+ align:start position:0%
+published at the same time salera
+ 
+
+ align:start position:0%
+published at the same time salera
+actually Venter is both quits and is
+
+ align:start position:0%
+actually Venter is both quits and is
+ 
+
+ align:start position:0%
+actually Venter is both quits and is
+fired from Solera
+
+ align:start position:0%
+fired from Solera
+ 
+
+ align:start position:0%
+fired from Solera
+at the same time inventors mind he was
+
+ align:start position:0%
+at the same time inventors mind he was
+ 
+
+ align:start position:0%
+at the same time inventors mind he was
+about to quit anyway
+
+ align:start position:0%
+about to quit anyway
+ 
+
+ align:start position:0%
+about to quit anyway
+but yeah he was basically asked to leave
+
+ align:start position:0%
+but yeah he was basically asked to leave
+ 
+
+ align:start position:0%
+but yeah he was basically asked to leave
+on a Monday morning yeah yeah there are
+
+ align:start position:0%
+on a Monday morning yeah yeah there are
+ 
+
+ align:start position:0%
+on a Monday morning yeah yeah there are
+a lot of parallels but Martine he's
+
+ align:start position:0%
+a lot of parallels but Martine he's
+ 
+
+ align:start position:0%
+a lot of parallels but Martine he's
+different right he creates this group
+
+ align:start position:0%
+different right he creates this group
+ 
+
+ align:start position:0%
+different right he creates this group
+originally at his NIH lab it's basically
+
+ align:start position:0%
+originally at his NIH lab it's basically
+ 
+
+ align:start position:0%
+originally at his NIH lab it's basically
+still with him right right this is not
+
+ align:start position:0%
+still with him right right this is not
+ 
+
+ align:start position:0%
+still with him right right this is not
+Joe
+
+ align:start position:0%
+Joe
+ 
+
+ align:start position:0%
+Joe
+abrasiveness right and screaming this is
+
+ align:start position:0%
+abrasiveness right and screaming this is
+ 
+
+ align:start position:0%
+abrasiveness right and screaming this is
+somebody who is really he's a pretty
+
+ align:start position:0%
+somebody who is really he's a pretty
+ 
+
+ align:start position:0%
+somebody who is really he's a pretty
+charismatic figure I've spent a little
+
+ align:start position:0%
+charismatic figure I've spent a little
+ 
+
+ align:start position:0%
+charismatic figure I've spent a little
+time with him and you know he is able to
+
+ align:start position:0%
+time with him and you know he is able to
+ 
+
+ align:start position:0%
+time with him and you know he is able to
+keep over absolutely remarkable team
+
+ align:start position:0%
+keep over absolutely remarkable team
+ 
+
+ align:start position:0%
+keep over absolutely remarkable team
+together for a remarkably long period of
+
+ align:start position:0%
+together for a remarkably long period of
+ 
+
+ align:start position:0%
+together for a remarkably long period of
+time so it's a different personal
+
+ align:start position:0%
+time so it's a different personal
+ 
+
+ align:start position:0%
+time so it's a different personal
+atmosphere a different kind of
+
+ align:start position:0%
+atmosphere a different kind of
+ 
+
+ align:start position:0%
+atmosphere a different kind of
+leadership style but you know remember
+
+ align:start position:0%
+leadership style but you know remember
+ 
+
+ align:start position:0%
+leadership style but you know remember
+what it must have been like I mean he
+
+ align:start position:0%
+what it must have been like I mean he
+ 
+
+ align:start position:0%
+what it must have been like I mean he
+comes back from you know the Vietnam War
+
+ align:start position:0%
+comes back from you know the Vietnam War
+ 
+
+ align:start position:0%
+comes back from you know the Vietnam War
+full of you know Navy and Marine Corps
+
+ align:start position:0%
+full of you know Navy and Marine Corps
+ 
+
+ align:start position:0%
+full of you know Navy and Marine Corps
+tattoos right he's you know a veteran of
+
+ align:start position:0%
+tattoos right he's you know a veteran of
+ 
+
+ align:start position:0%
+tattoos right he's you know a veteran of
+this you know ghastly war and he's been
+
+ align:start position:0%
+this you know ghastly war and he's been
+ 
+
+ align:start position:0%
+this you know ghastly war and he's been
+he's seen some of the worst outcomes
+
+ align:start position:0%
+he's seen some of the worst outcomes
+ 
+
+ align:start position:0%
+he's seen some of the worst outcomes
+running a whole hospital wing virtually
+
+ align:start position:0%
+running a whole hospital wing virtually
+ 
+
+ align:start position:0%
+running a whole hospital wing virtually
+on his own and Danang and sees two men
+
+ align:start position:0%
+on his own and Danang and sees two men
+ 
+
+ align:start position:0%
+on his own and Danang and sees two men
+you know death and loss of life and
+
+ align:start position:0%
+you know death and loss of life and
+ 
+
+ align:start position:0%
+you know death and loss of life and
+trying to save life firsthand in a very
+
+ align:start position:0%
+trying to save life firsthand in a very
+ 
+
+ align:start position:0%
+trying to save life firsthand in a very
+personal kind of way he's completely
+
+ align:start position:0%
+personal kind of way he's completely
+ 
+
+ align:start position:0%
+personal kind of way he's completely
+different than the kind of culture of
+
+ align:start position:0%
+different than the kind of culture of
+ 
+
+ align:start position:0%
+different than the kind of culture of
+NIH you know he's up from a
+
+ align:start position:0%
+NIH you know he's up from a
+ 
+
+ align:start position:0%
+NIH you know he's up from a
+working-class military family and it's
+
+ align:start position:0%
+working-class military family and it's
+ 
+
+ align:start position:0%
+working-class military family and it's
+just a different world that he's been
+
+ align:start position:0%
+just a different world that he's been
+ 
+
+ align:start position:0%
+just a different world that he's been
+exposed to and he doesn't get along with
+
+ align:start position:0%
+exposed to and he doesn't get along with
+ 
+
+ align:start position:0%
+exposed to and he doesn't get along with
+this kind of you know established
+
+ align:start position:0%
+this kind of you know established
+ 
+
+ align:start position:0%
+this kind of you know established
+liberal community of scientists and NIH
+
+ align:start position:0%
+liberal community of scientists and NIH
+ 
+
+ align:start position:0%
+liberal community of scientists and NIH
+so that's part of what's going on here I
+
+ align:start position:0%
+so that's part of what's going on here I
+ 
+
+ align:start position:0%
+so that's part of what's going on here I
+think Willie it just he's just a really
+
+ align:start position:0%
+think Willie it just he's just a really
+ 
+
+ align:start position:0%
+think Willie it just he's just a really
+different character pushing him at the
+
+ align:start position:0%
+different character pushing him at the
+ 
+
+ align:start position:0%
+different character pushing him at the
+NIH is and through that throughout the
+
+ align:start position:0%
+NIH is and through that throughout the
+ 
+
+ align:start position:0%
+NIH is and through that throughout the
+human genome project is decode the human
+
+ align:start position:0%
+human genome project is decode the human
+ 
+
+ align:start position:0%
+human genome project is decode the human
+genome so we don't see the situation or
+
+ align:start position:0%
+genome so we don't see the situation or
+ 
+
+ align:start position:0%
+genome so we don't see the situation or
+the things that he saw in the hospital
+
+ align:start position:0%
+the things that he saw in the hospital
+ 
+
+ align:start position:0%
+the things that he saw in the hospital
+at done it doesn't he thinks that modern
+
+ align:start position:0%
+at done it doesn't he thinks that modern
+ 
+
+ align:start position:0%
+at done it doesn't he thinks that modern
+medicine should eradicate those sorts of
+
+ align:start position:0%
+medicine should eradicate those sorts of
+ 
+
+ align:start position:0%
+medicine should eradicate those sorts of
+injuries and really his vision is
+
+ align:start position:0%
+injuries and really his vision is
+ 
+
+ align:start position:0%
+injuries and really his vision is
+synthetic biology we regrow we grow
+
+ align:start position:0%
+synthetic biology we regrow we grow
+ 
+
+ align:start position:0%
+synthetic biology we regrow we grow
+everything synthetically we grow human
+
+ align:start position:0%
+everything synthetically we grow human
+ 
+
+ align:start position:0%
+everything synthetically we grow human
+limbs become you know he's very
+
+ align:start position:0%
+limbs become you know he's very
+ 
+
+ align:start position:0%
+limbs become you know he's very
+forward-thinking as far as the medical
+
+ align:start position:0%
+forward-thinking as far as the medical
+ 
+
+ align:start position:0%
+forward-thinking as far as the medical
+uses of knowing genetics I just question
+
+ align:start position:0%
+uses of knowing genetics I just question
+ 
+
+ align:start position:0%
+uses of knowing genetics I just question
+like so what exactly were they trying to
+
+ align:start position:0%
+like so what exactly were they trying to
+ 
+
+ align:start position:0%
+like so what exactly were they trying to
+kind underside
+
+ align:start position:0%
+kind underside
+ 
+
+ align:start position:0%
+kind underside
+lots of things so I think that one worry
+
+ align:start position:0%
+lots of things so I think that one worry
+ 
+
+ align:start position:0%
+lots of things so I think that one worry
+was that his invention his Craig's
+
+ align:start position:0%
+was that his invention his Craig's
+ 
+
+ align:start position:0%
+was that his invention his Craig's
+method of est would be patented itself
+
+ align:start position:0%
+method of est would be patented itself
+ 
+
+ align:start position:0%
+method of est would be patented itself
+and it's an extremely it was for well
+
+ align:start position:0%
+and it's an extremely it was for well
+ 
+
+ align:start position:0%
+and it's an extremely it was for well
+some areas of biology still use it not
+
+ align:start position:0%
+some areas of biology still use it not
+ 
+
+ align:start position:0%
+some areas of biology still use it not
+my particular field but a lot of areas
+
+ align:start position:0%
+my particular field but a lot of areas
+ 
+
+ align:start position:0%
+my particular field but a lot of areas
+in biology still use it and if it were
+
+ align:start position:0%
+in biology still use it and if it were
+ 
+
+ align:start position:0%
+in biology still use it and if it were
+that they wouldn't be able to obviously
+
+ align:start position:0%
+that they wouldn't be able to obviously
+ 
+
+ align:start position:0%
+that they wouldn't be able to obviously
+so it's an it's widely applicable its
+
+ align:start position:0%
+so it's an it's widely applicable its
+ 
+
+ align:start position:0%
+so it's an it's widely applicable its
+technique and there was there was
+
+ align:start position:0%
+technique and there was there was
+ 
+
+ align:start position:0%
+technique and there was there was
+worried that he would try to patent EST
+
+ align:start position:0%
+worried that he would try to patent EST
+ 
+
+ align:start position:0%
+worried that he would try to patent EST
+or there might have I think there was a
+
+ align:start position:0%
+or there might have I think there was a
+ 
+
+ align:start position:0%
+or there might have I think there was a
+patent in and the NIH pulled it or
+
+ align:start position:0%
+patent in and the NIH pulled it or
+ 
+
+ align:start position:0%
+patent in and the NIH pulled it or
+something like that with so much
+
+ align:start position:0%
+something like that with so much
+ 
+
+ align:start position:0%
+something like that with so much
+negative press there were a couple of
+
+ align:start position:0%
+negative press there were a couple of
+ 
+
+ align:start position:0%
+negative press there were a couple of
+other things up for patent maybe but I
+
+ align:start position:0%
+other things up for patent maybe but I
+ 
+
+ align:start position:0%
+other things up for patent maybe but I
+don't know the specifics why don't we
+
+ align:start position:0%
+don't know the specifics why don't we
+ 
+
+ align:start position:0%
+don't know the specifics why don't we
+get into some questions okay oh yeah so
+
+ align:start position:0%
+get into some questions okay oh yeah so
+ 
+
+ align:start position:0%
+get into some questions okay oh yeah so
+what does he do
+
+ align:start position:0%
+what does he do
+ 
+
+ align:start position:0%
+what does he do
+so Solera goes boom with the dot-com
+
+ align:start position:0%
+so Solera goes boom with the dot-com
+ 
+
+ align:start position:0%
+so Solera goes boom with the dot-com
+bubbles like worth fifteen billion
+
+ align:start position:0%
+bubbles like worth fifteen billion
+ 
+
+ align:start position:0%
+bubbles like worth fifteen billion
+dollars in an inflating the stock goes
+
+ align:start position:0%
+dollars in an inflating the stock goes
+ 
+
+ align:start position:0%
+dollars in an inflating the stock goes
+from five hundred bucks to six dollars
+
+ align:start position:0%
+from five hundred bucks to six dollars
+ 
+
+ align:start position:0%
+from five hundred bucks to six dollars
+at that point Craig had already left one
+
+ align:start position:0%
+at that point Craig had already left one
+ 
+
+ align:start position:0%
+at that point Craig had already left one
+of the reasons that the stock dropped so
+
+ align:start position:0%
+of the reasons that the stock dropped so
+ 
+
+ align:start position:0%
+of the reasons that the stock dropped so
+drastically was because people found out
+
+ align:start position:0%
+drastically was because people found out
+ 
+
+ align:start position:0%
+drastically was because people found out
+that Craig left so now well not now but
+
+ align:start position:0%
+that Craig left so now well not now but
+ 
+
+ align:start position:0%
+that Craig left so now well not now but
+then he decides well I'm gonna do my own
+
+ align:start position:0%
+then he decides well I'm gonna do my own
+ 
+
+ align:start position:0%
+then he decides well I'm gonna do my own
+science and I'm gonna sequence the
+
+ align:start position:0%
+science and I'm gonna sequence the
+ 
+
+ align:start position:0%
+science and I'm gonna sequence the
+entire ocean I'm done with the human
+
+ align:start position:0%
+entire ocean I'm done with the human
+ 
+
+ align:start position:0%
+entire ocean I'm done with the human
+genome now I'm gonna go to the ocean so
+
+ align:start position:0%
+genome now I'm gonna go to the ocean so
+ 
+
+ align:start position:0%
+genome now I'm gonna go to the ocean so
+he gets on this 100-foot yacht the
+
+ align:start position:0%
+he gets on this 100-foot yacht the
+ 
+
+ align:start position:0%
+he gets on this 100-foot yacht the
+sorcerer or two and a couple of people I
+
+ align:start position:0%
+sorcerer or two and a couple of people I
+ 
+
+ align:start position:0%
+sorcerer or two and a couple of people I
+talk with a with a woman who's a
+
+ align:start position:0%
+talk with a with a woman who's a
+ 
+
+ align:start position:0%
+talk with a with a woman who's a
+professor at USC who was on some of the
+
+ align:start position:0%
+professor at USC who was on some of the
+ 
+
+ align:start position:0%
+professor at USC who was on some of the
+sorcerer legs of the journey and then
+
+ align:start position:0%
+sorcerer legs of the journey and then
+ 
+
+ align:start position:0%
+sorcerer legs of the journey and then
+her husband John Heidelberg is on he was
+
+ align:start position:0%
+her husband John Heidelberg is on he was
+ 
+
+ align:start position:0%
+her husband John Heidelberg is on he was
+on my thesis committee so he's the third
+
+ align:start position:0%
+on my thesis committee so he's the third
+ 
+
+ align:start position:0%
+on my thesis committee so he's the third
+author on this paper and they have lots
+
+ align:start position:0%
+author on this paper and they have lots
+ 
+
+ align:start position:0%
+author on this paper and they have lots
+of fun craig stories as well and one of
+
+ align:start position:0%
+of fun craig stories as well and one of
+ 
+
+ align:start position:0%
+of fun craig stories as well and one of
+the i think one of the themes throughout
+
+ align:start position:0%
+the i think one of the themes throughout
+ 
+
+ align:start position:0%
+the i think one of the themes throughout
+the great groups is that there are a lot
+
+ align:start position:0%
+the great groups is that there are a lot
+ 
+
+ align:start position:0%
+the great groups is that there are a lot
+of partiers like if they're not doing
+
+ align:start position:0%
+of partiers like if they're not doing
+ 
+
+ align:start position:0%
+of partiers like if they're not doing
+really crazy good science they're
+
+ align:start position:0%
+really crazy good science they're
+ 
+
+ align:start position:0%
+really crazy good science they're
+partying hey doc and they just have a
+
+ align:start position:0%
+partying hey doc and they just have a
+ 
+
+ align:start position:0%
+partying hey doc and they just have a
+huge party so then he finishes sailing
+
+ align:start position:0%
+huge party so then he finishes sailing
+ 
+
+ align:start position:0%
+huge party so then he finishes sailing
+around the world a couple of times in
+
+ align:start position:0%
+around the world a couple of times in
+ 
+
+ align:start position:0%
+around the world a couple of times in
+sequencing all the bacteria in the ocean
+
+ align:start position:0%
+sequencing all the bacteria in the ocean
+ 
+
+ align:start position:0%
+sequencing all the bacteria in the ocean
+and sets up the JCB i which is located
+
+ align:start position:0%
+and sets up the JCB i which is located
+ 
+
+ align:start position:0%
+and sets up the JCB i which is located
+in la jolla right next to his alma mater
+
+ align:start position:0%
+in la jolla right next to his alma mater
+ 
+
+ align:start position:0%
+in la jolla right next to his alma mater
+UCSD
+
+ align:start position:0%
+UCSD
+ 
+
+ align:start position:0%
+UCSD
+that's a picture Craig from a few years
+
+ align:start position:0%
+that's a picture Craig from a few years
+ 
+
+ align:start position:0%
+that's a picture Craig from a few years
+ago so to conclude a few Joyce quotes
+
+ align:start position:0%
+ago so to conclude a few Joyce quotes
+ 
+
+ align:start position:0%
+ago so to conclude a few Joyce quotes
+from Craig I've gotten some pretty nice
+
+ align:start position:0%
+from Craig I've gotten some pretty nice
+ 
+
+ align:start position:0%
+from Craig I've gotten some pretty nice
+awards and I'm having trouble finding
+
+ align:start position:0%
+awards and I'm having trouble finding
+ 
+
+ align:start position:0%
+awards and I'm having trouble finding
+places to put them all and then one
+
+ align:start position:0%
+places to put them all and then one
+ 
+
+ align:start position:0%
+places to put them all and then one
+that's more pertinent to this class is
+
+ align:start position:0%
+that's more pertinent to this class is
+ 
+
+ align:start position:0%
+that's more pertinent to this class is
+the environment has fallen to the
+
+ align:start position:0%
+the environment has fallen to the
+ 
+
+ align:start position:0%
+the environment has fallen to the
+wayside in politics
+
+ align:start position:0%
+wayside in politics
+ 
+
+ align:start position:0%
+wayside in politics
+lastly oh I wanted to go over Venters
+
+ align:start position:0%
+lastly oh I wanted to go over Venters
+ 
+
+ align:start position:0%
+lastly oh I wanted to go over Venters
+thoughts on innovation but that's not
+
+ align:start position:0%
+thoughts on innovation but that's not
+ 
+
+ align:start position:0%
+thoughts on innovation but that's not
+we're getting quotes on time so that's
+
+ align:start position:0%
+we're getting quotes on time so that's
+ 
+
+ align:start position:0%
+we're getting quotes on time so that's
+not really necessary these are better
+
+ align:start position:0%
+not really necessary these are better
+ 
+
+ align:start position:0%
+not really necessary these are better
+how about some questions okay
+
+ align:start position:0%
+how about some questions okay
+ 
+
+ align:start position:0%
+how about some questions okay
+um so show up I wanted to see in the
+
+ align:start position:0%
+um so show up I wanted to see in the
+ 
+
+ align:start position:0%
+um so show up I wanted to see in the
+class by show of hands who thinks that
+
+ align:start position:0%
+class by show of hands who thinks that
+ 
+
+ align:start position:0%
+class by show of hands who thinks that
+Venter or maybe a couple of people
+
+ align:start position:0%
+Venter or maybe a couple of people
+ 
+
+ align:start position:0%
+Venter or maybe a couple of people
+within his group I mean they decoded the
+
+ align:start position:0%
+within his group I mean they decoded the
+ 
+
+ align:start position:0%
+within his group I mean they decoded the
+human genome which was just the amount
+
+ align:start position:0%
+human genome which was just the amount
+ 
+
+ align:start position:0%
+human genome which was just the amount
+of new technologies that they came up
+
+ align:start position:0%
+of new technologies that they came up
+ 
+
+ align:start position:0%
+of new technologies that they came up
+with both in computing and molecular
+
+ align:start position:0%
+with both in computing and molecular
+ 
+
+ align:start position:0%
+with both in computing and molecular
+biology in order to do that are
+
+ align:start position:0%
+biology in order to do that are
+ 
+
+ align:start position:0%
+biology in order to do that are
+astounding so who in here would say like
+
+ align:start position:0%
+astounding so who in here would say like
+ 
+
+ align:start position:0%
+astounding so who in here would say like
+he should be a Nobel Prize winner for
+
+ align:start position:0%
+he should be a Nobel Prize winner for
+ 
+
+ align:start position:0%
+he should be a Nobel Prize winner for
+people in his group
+
+ align:start position:0%
+people in his group
+ 
+
+ align:start position:0%
+people in his group
+I'm sure there's got to be some other
+
+ align:start position:0%
+I'm sure there's got to be some other
+ 
+
+ align:start position:0%
+I'm sure there's got to be some other
+equivalent biology centered award
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's like a watson-crick award and he
+
+ align:start position:0%
+there's like a watson-crick award and he
+ 
+
+ align:start position:0%
+there's like a watson-crick award and he
+wins what we started oh other stuff was
+
+ align:start position:0%
+wins what we started oh other stuff was
+ 
+
+ align:start position:0%
+wins what we started oh other stuff was
+based off of shrinkers what his life
+
+ align:start position:0%
+based off of shrinkers what his life
+ 
+
+ align:start position:0%
+based off of shrinkers what his life
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question where do they call it decoding
+
+ align:start position:0%
+question where do they call it decoding
+ 
+
+ align:start position:0%
+question where do they call it decoding
+and not encoding the human genome mmm I
+
+ align:start position:0%
+and not encoding the human genome mmm I
+ 
+
+ align:start position:0%
+and not encoding the human genome mmm I
+think it would be called decoding
+
+ align:start position:0%
+think it would be called decoding
+ 
+
+ align:start position:0%
+think it would be called decoding
+because what this looks like when you
+
+ align:start position:0%
+because what this looks like when you
+ 
+
+ align:start position:0%
+because what this looks like when you
+actually read the basis is fluorescent
+
+ align:start position:0%
+actually read the basis is fluorescent
+ 
+
+ align:start position:0%
+actually read the basis is fluorescent
+dye so you have to read you have to
+
+ align:start position:0%
+dye so you have to read you have to
+ 
+
+ align:start position:0%
+dye so you have to read you have to
+decode the fluorescent signature in
+
+ align:start position:0%
+decode the fluorescent signature in
+ 
+
+ align:start position:0%
+decode the fluorescent signature in
+order to get the base pairs so it's not
+
+ align:start position:0%
+order to get the base pairs so it's not
+ 
+
+ align:start position:0%
+order to get the base pairs so it's not
+about it's about we're so evaluating the
+
+ align:start position:0%
+about it's about we're so evaluating the
+ 
+
+ align:start position:0%
+about it's about we're so evaluating the
+results than it is about sort of
+
+ align:start position:0%
+results than it is about sort of
+ 
+
+ align:start position:0%
+results than it is about sort of
+expressing the results yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one thing about this effort here at me
+
+ align:start position:0%
+one thing about this effort here at me
+ 
+
+ align:start position:0%
+one thing about this effort here at me
+you have to get a sense of how
+
+ align:start position:0%
+you have to get a sense of how
+ 
+
+ align:start position:0%
+you have to get a sense of how
+transformational this seemed in the
+
+ align:start position:0%
+transformational this seemed in the
+ 
+
+ align:start position:0%
+transformational this seemed in the
+nineteen nineties it was really quite
+
+ align:start position:0%
+nineteen nineties it was really quite
+ 
+
+ align:start position:0%
+nineteen nineties it was really quite
+amazing but this was one of the great
+
+ align:start position:0%
+amazing but this was one of the great
+ 
+
+ align:start position:0%
+amazing but this was one of the great
+scientific competitions of all time
+
+ align:start position:0%
+scientific competitions of all time
+ 
+
+ align:start position:0%
+scientific competitions of all time
+right this incredible race to do that to
+
+ align:start position:0%
+right this incredible race to do that to
+ 
+
+ align:start position:0%
+right this incredible race to do that to
+decode the genome and this is being you
+
+ align:start position:0%
+decode the genome and this is being you
+ 
+
+ align:start position:0%
+decode the genome and this is being you
+know this is a major news story right
+
+ align:start position:0%
+know this is a major news story right
+ 
+
+ align:start position:0%
+know this is a major news story right
+and Francis Collins has a Harley
+
+ align:start position:0%
+and Francis Collins has a Harley
+ 
+
+ align:start position:0%
+and Francis Collins has a Harley
+motorcycle and sings on a blues band and
+
+ align:start position:0%
+motorcycle and sings on a blues band and
+ 
+
+ align:start position:0%
+motorcycle and sings on a blues band and
+you know he has his own you know fast he
+
+ align:start position:0%
+you know he has his own you know fast he
+ 
+
+ align:start position:0%
+you know he has his own you know fast he
+still rides his motorcycle into work in
+
+ align:start position:0%
+still rides his motorcycle into work in
+ 
+
+ align:start position:0%
+still rides his motorcycle into work in
+nih Venter is a yachtsman who buys these
+
+ align:start position:0%
+nih Venter is a yachtsman who buys these
+ 
+
+ align:start position:0%
+nih Venter is a yachtsman who buys these
+wild incredibly dangerous you know
+
+ align:start position:0%
+wild incredibly dangerous you know
+ 
+
+ align:start position:0%
+wild incredibly dangerous you know
+sailboats and loves that the kind of
+
+ align:start position:0%
+sailboats and loves that the kind of
+ 
+
+ align:start position:0%
+sailboats and loves that the kind of
+wild adventure of you know being you
+
+ align:start position:0%
+wild adventure of you know being you
+ 
+
+ align:start position:0%
+wild adventure of you know being you
+know tempestuous sea close to the wind
+
+ align:start position:0%
+know tempestuous sea close to the wind
+ 
+
+ align:start position:0%
+know tempestuous sea close to the wind
+and near capsized danger with these you
+
+ align:start position:0%
+and near capsized danger with these you
+ 
+
+ align:start position:0%
+and near capsized danger with these you
+know monsters sailboats so both of them
+
+ align:start position:0%
+know monsters sailboats so both of them
+ 
+
+ align:start position:0%
+know monsters sailboats so both of them
+have their kind of wild side here
+
+ align:start position:0%
+have their kind of wild side here
+ 
+
+ align:start position:0%
+have their kind of wild side here
+there's no question about it but this
+
+ align:start position:0%
+there's no question about it but this
+ 
+
+ align:start position:0%
+there's no question about it but this
+competition captures the public
+
+ align:start position:0%
+competition captures the public
+ 
+
+ align:start position:0%
+competition captures the public
+imagination and it's a very important
+
+ align:start position:0%
+imagination and it's a very important
+ 
+
+ align:start position:0%
+imagination and it's a very important
+race because the race forces incredible
+
+ align:start position:0%
+race because the race forces incredible
+ 
+
+ align:start position:0%
+race because the race forces incredible
+speed in the project so what had I
+
+ align:start position:0%
+speed in the project so what had I
+ 
+
+ align:start position:0%
+speed in the project so what had I
+probably been originally viewed as a 40
+
+ align:start position:0%
+probably been originally viewed as a 40
+ 
+
+ align:start position:0%
+probably been originally viewed as a 40
+year project gets you know knocked down
+
+ align:start position:0%
+year project gets you know knocked down
+ 
+
+ align:start position:0%
+year project gets you know knocked down
+to well less than a decade by the time
+
+ align:start position:0%
+to well less than a decade by the time
+ 
+
+ align:start position:0%
+to well less than a decade by the time
+these characters you know kind of
+
+ align:start position:0%
+these characters you know kind of
+ 
+
+ align:start position:0%
+these characters you know kind of
+complete the race and agree to a truce
+
+ align:start position:0%
+complete the race and agree to a truce
+ 
+
+ align:start position:0%
+complete the race and agree to a truce
+by publishing on the same day and in
+
+ align:start position:0%
+by publishing on the same day and in
+ 
+
+ align:start position:0%
+by publishing on the same day and in
+turn I was working on in the Senate you
+
+ align:start position:0%
+turn I was working on in the Senate you
+ 
+
+ align:start position:0%
+turn I was working on in the Senate you
+know while this is all going on and you
+
+ align:start position:0%
+know while this is all going on and you
+ 
+
+ align:start position:0%
+know while this is all going on and you
+know the public is getting a sense gee
+
+ align:start position:0%
+know the public is getting a sense gee
+ 
+
+ align:start position:0%
+know the public is getting a sense gee
+we really are getting fairly close to
+
+ align:start position:0%
+we really are getting fairly close to
+ 
+
+ align:start position:0%
+we really are getting fairly close to
+this one obviously fundamental answers
+
+ align:start position:0%
+this one obviously fundamental answers
+ 
+
+ align:start position:0%
+this one obviously fundamental answers
+here and when two US senators senator
+
+ align:start position:0%
+here and when two US senators senator
+ 
+
+ align:start position:0%
+here and when two US senators senator
+Specter and Senator Harkin from
+
+ align:start position:0%
+Specter and Senator Harkin from
+ 
+
+ align:start position:0%
+Specter and Senator Harkin from
+Pennsylvania in Iowa respectively were
+
+ align:start position:0%
+Pennsylvania in Iowa respectively were
+ 
+
+ align:start position:0%
+Pennsylvania in Iowa respectively were
+cheran ranking on the Appropriations
+
+ align:start position:0%
+cheran ranking on the Appropriations
+ 
+
+ align:start position:0%
+cheran ranking on the Appropriations
+Subcommittee that handles NIH they
+
+ align:start position:0%
+Subcommittee that handles NIH they
+ 
+
+ align:start position:0%
+Subcommittee that handles NIH they
+actually there's a in the Clinton years
+
+ align:start position:0%
+actually there's a in the Clinton years
+ 
+
+ align:start position:0%
+actually there's a in the Clinton years
+because the IT revolution is creating a
+
+ align:start position:0%
+because the IT revolution is creating a
+ 
+
+ align:start position:0%
+because the IT revolution is creating a
+lot of extra tax revenue we're balancing
+
+ align:start position:0%
+lot of extra tax revenue we're balancing
+ 
+
+ align:start position:0%
+lot of extra tax revenue we're balancing
+the budget so there's revenue on one of
+
+ align:start position:0%
+the budget so there's revenue on one of
+ 
+
+ align:start position:0%
+the budget so there's revenue on one of
+those rare moments there's revenue in
+
+ align:start position:0%
+those rare moments there's revenue in
+ 
+
+ align:start position:0%
+those rare moments there's revenue in
+the federal government
+
+ align:start position:0%
+the federal government
+ 
+
+ align:start position:0%
+the federal government
+Spectre and heart can go down and take
+
+ align:start position:0%
+Spectre and heart can go down and take
+ 
+
+ align:start position:0%
+Spectre and heart can go down and take
+the revenue and that's what doubles NIH
+
+ align:start position:0%
+the revenue and that's what doubles NIH
+ 
+
+ align:start position:0%
+the revenue and that's what doubles NIH
+and nobody says they're wrong because of
+
+ align:start position:0%
+and nobody says they're wrong because of
+ 
+
+ align:start position:0%
+and nobody says they're wrong because of
+the excitement that this race to get to
+
+ align:start position:0%
+the excitement that this race to get to
+ 
+
+ align:start position:0%
+the excitement that this race to get to
+the genome is created and what it's what
+
+ align:start position:0%
+the genome is created and what it's what
+ 
+
+ align:start position:0%
+the genome is created and what it's what
+its scientific possibilities are so sure
+
+ align:start position:0%
+its scientific possibilities are so sure
+ 
+
+ align:start position:0%
+its scientific possibilities are so sure
+there's a whole political effort to
+
+ align:start position:0%
+there's a whole political effort to
+ 
+
+ align:start position:0%
+there's a whole political effort to
+radically increase NIH funding but the
+
+ align:start position:0%
+radically increase NIH funding but the
+ 
+
+ align:start position:0%
+radically increase NIH funding but the
+enabler here is the public excitement
+
+ align:start position:0%
+enabler here is the public excitement
+ 
+
+ align:start position:0%
+enabler here is the public excitement
+around the genome race and what its
+
+ align:start position:0%
+around the genome race and what its
+ 
+
+ align:start position:0%
+around the genome race and what its
+possibilities might be to accomplish so
+
+ align:start position:0%
+possibilities might be to accomplish so
+ 
+
+ align:start position:0%
+possibilities might be to accomplish so
+this has enduring kind of lasting
+
+ align:start position:0%
+this has enduring kind of lasting
+ 
+
+ align:start position:0%
+this has enduring kind of lasting
+effects that spill over in many kind of
+
+ align:start position:0%
+effects that spill over in many kind of
+ 
+
+ align:start position:0%
+effects that spill over in many kind of
+ways into the into the life science
+
+ align:start position:0%
+ways into the into the life science
+ 
+
+ align:start position:0%
+ways into the into the life science
+arena next question now but you want to
+
+ align:start position:0%
+arena next question now but you want to
+ 
+
+ align:start position:0%
+arena next question now but you want to
+pose a couple of questions and one then
+
+ align:start position:0%
+pose a couple of questions and one then
+ 
+
+ align:start position:0%
+pose a couple of questions and one then
+we'll wrap things up yeah one of the
+
+ align:start position:0%
+we'll wrap things up yeah one of the
+ 
+
+ align:start position:0%
+we'll wrap things up yeah one of the
+things I was thinking about while
+
+ align:start position:0%
+things I was thinking about while
+ 
+
+ align:start position:0%
+things I was thinking about while
+reading this and the other readings in
+
+ align:start position:0%
+reading this and the other readings in
+ 
+
+ align:start position:0%
+reading this and the other readings in
+the class is that Venter seems to form
+
+ align:start position:0%
+the class is that Venter seems to form
+ 
+
+ align:start position:0%
+the class is that Venter seems to form
+and dissolve and reform multiple great
+
+ align:start position:0%
+and dissolve and reform multiple great
+ 
+
+ align:start position:0%
+and dissolve and reform multiple great
+groups throughout his lifetime like from
+
+ align:start position:0%
+groups throughout his lifetime like from
+ 
+
+ align:start position:0%
+groups throughout his lifetime like from
+the 80s to present day and in thinking
+
+ align:start position:0%
+the 80s to present day and in thinking
+ 
+
+ align:start position:0%
+the 80s to present day and in thinking
+about other great lilies only changing
+
+ align:start position:0%
+about other great lilies only changing
+ 
+
+ align:start position:0%
+about other great lilies only changing
+the formal structure the team really
+
+ align:start position:0%
+the formal structure the team really
+ 
+
+ align:start position:0%
+the formal structure the team really
+follows him from one organizational
+
+ align:start position:0%
+follows him from one organizational
+ 
+
+ align:start position:0%
+follows him from one organizational
+model to another
+
+ align:start position:0%
+model to another
+ 
+
+ align:start position:0%
+model to another
+that's true anyway so do we think that
+
+ align:start position:0%
+that's true anyway so do we think that
+ 
+
+ align:start position:0%
+that's true anyway so do we think that
+most great group leaders have a great
+
+ align:start position:0%
+most great group leaders have a great
+ 
+
+ align:start position:0%
+most great group leaders have a great
+one great group and then that's their
+
+ align:start position:0%
+one great group and then that's their
+ 
+
+ align:start position:0%
+one great group and then that's their
+like their opus they don't go on and
+
+ align:start position:0%
+like their opus they don't go on and
+ 
+
+ align:start position:0%
+like their opus they don't go on and
+they have one mission like Apple because
+
+ align:start position:0%
+they have one mission like Apple because
+ 
+
+ align:start position:0%
+they have one mission like Apple because
+there is the Mac team so that's a
+
+ align:start position:0%
+there is the Mac team so that's a
+ 
+
+ align:start position:0%
+there is the Mac team so that's a
+certain product so if it's a once
+
+ align:start position:0%
+certain product so if it's a once
+ 
+
+ align:start position:0%
+certain product so if it's a once
+particular problem you have a group and
+
+ align:start position:0%
+particular problem you have a group and
+ 
+
+ align:start position:0%
+particular problem you have a group and
+then you can choose to take a belief
+
+ align:start position:0%
+then you can choose to take a belief
+ 
+
+ align:start position:0%
+then you can choose to take a belief
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+the Apple is remarkable for its ability
+
+ align:start position:0%
+the Apple is remarkable for its ability
+ 
+
+ align:start position:0%
+the Apple is remarkable for its ability
+to go from one major technology launch
+
+ align:start position:0%
+to go from one major technology launch
+ 
+
+ align:start position:0%
+to go from one major technology launch
+to another in sequence it's really very
+
+ align:start position:0%
+to another in sequence it's really very
+ 
+
+ align:start position:0%
+to another in sequence it's really very
+hard and very difficult and
+
+ align:start position:0%
+hard and very difficult and
+ 
+
+ align:start position:0%
+hard and very difficult and
+interestingly it hasn't happened since
+
+ align:start position:0%
+interestingly it hasn't happened since
+ 
+
+ align:start position:0%
+interestingly it hasn't happened since
+Jobs type that we know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the hybrid apples kind of sorry to die
+
+ align:start position:0%
+the hybrid apples kind of sorry to die
+ 
+
+ align:start position:0%
+the hybrid apples kind of sorry to die
+down there's there's a model industry I
+
+ align:start position:0%
+down there's there's a model industry I
+ 
+
+ align:start position:0%
+down there's there's a model industry I
+mean how does a big company innovate
+
+ align:start position:0%
+mean how does a big company innovate
+ 
+
+ align:start position:0%
+mean how does a big company innovate
+it's a terribly difficult problem right
+
+ align:start position:0%
+it's a terribly difficult problem right
+ 
+
+ align:start position:0%
+it's a terribly difficult problem right
+there this suits the other bureaucracy
+
+ align:start position:0%
+there this suits the other bureaucracy
+ 
+
+ align:start position:0%
+there this suits the other bureaucracy
+Lockheed is kind of noted as the
+
+ align:start position:0%
+Lockheed is kind of noted as the
+ 
+
+ align:start position:0%
+Lockheed is kind of noted as the
+experimenter here they they set up
+
+ align:start position:0%
+experimenter here they they set up
+ 
+
+ align:start position:0%
+experimenter here they they set up
+something called the skunk works as a
+
+ align:start position:0%
+something called the skunk works as a
+ 
+
+ align:start position:0%
+something called the skunk works as a
+completely side separate organization on
+
+ align:start position:0%
+completely side separate organization on
+ 
+
+ align:start position:0%
+completely side separate organization on
+a protected island with a bridge back to
+
+ align:start position:0%
+a protected island with a bridge back to
+ 
+
+ align:start position:0%
+a protected island with a bridge back to
+the Lockheed management and they do
+
+ align:start position:0%
+the Lockheed management and they do
+ 
+
+ align:start position:0%
+the Lockheed management and they do
+remarkable advances in in Aeronautics
+
+ align:start position:0%
+remarkable advances in in Aeronautics
+ 
+
+ align:start position:0%
+remarkable advances in in Aeronautics
+and aerospace so they do the they do the
+
+ align:start position:0%
+and aerospace so they do the they do the
+ 
+
+ align:start position:0%
+and aerospace so they do the they do the
+u2 they do the sr-71 blackbird which
+
+ align:start position:0%
+u2 they do the sr-71 blackbird which
+ 
+
+ align:start position:0%
+u2 they do the sr-71 blackbird which
+many people who this day think is the
+
+ align:start position:0%
+many people who this day think is the
+ 
+
+ align:start position:0%
+many people who this day think is the
+most remarkable plane ever built but
+
+ align:start position:0%
+most remarkable plane ever built but
+ 
+
+ align:start position:0%
+most remarkable plane ever built but
+then a whole sequence of other aircraft
+
+ align:start position:0%
+then a whole sequence of other aircraft
+ 
+
+ align:start position:0%
+then a whole sequence of other aircraft
+and they do stealth right they're the
+
+ align:start position:0%
+and they do stealth right they're the
+ 
+
+ align:start position:0%
+and they do stealth right they're the
+implementers of a lot of the stealth
+
+ align:start position:0%
+implementers of a lot of the stealth
+ 
+
+ align:start position:0%
+implementers of a lot of the stealth
+technology so that's an example of how a
+
+ align:start position:0%
+technology so that's an example of how a
+ 
+
+ align:start position:0%
+technology so that's an example of how a
+corporation is able to create an entity
+
+ align:start position:0%
+corporation is able to create an entity
+ 
+
+ align:start position:0%
+corporation is able to create an entity
+that can move through a series of great
+
+ align:start position:0%
+that can move through a series of great
+ 
+
+ align:start position:0%
+that can move through a series of great
+groups and keep innovating that's kind
+
+ align:start position:0%
+groups and keep innovating that's kind
+ 
+
+ align:start position:0%
+groups and keep innovating that's kind
+of held up as a kind of iconic model so
+
+ align:start position:0%
+of held up as a kind of iconic model so
+ 
+
+ align:start position:0%
+of held up as a kind of iconic model so
+it is possible so when you're the small
+
+ align:start position:0%
+it is possible so when you're the small
+ 
+
+ align:start position:0%
+it is possible so when you're the small
+companies that you all set up become
+
+ align:start position:0%
+companies that you all set up become
+ 
+
+ align:start position:0%
+companies that you all set up become
+major corporations you know read read
+
+ align:start position:0%
+major corporations you know read read
+ 
+
+ align:start position:0%
+major corporations you know read read
+about skunk works because that'll be
+
+ align:start position:0%
+about skunk works because that'll be
+ 
+
+ align:start position:0%
+about skunk works because that'll be
+your clue to continue to survival it
+
+ align:start position:0%
+your clue to continue to survival it
+ 
+
+ align:start position:0%
+your clue to continue to survival it
+wasn't fun
+
+ align:start position:0%
+wasn't fun
+ 
+
+ align:start position:0%
+wasn't fun
+fights analog devices just up the street
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we how about a closing thought for us
+
+ align:start position:0%
+we how about a closing thought for us
+ 
+
+ align:start position:0%
+we how about a closing thought for us
+about this amazing crowd let's see I
+
+ align:start position:0%
+about this amazing crowd let's see I
+ 
+
+ align:start position:0%
+about this amazing crowd let's see I
+think that Craig is right when he says
+
+ align:start position:0%
+think that Craig is right when he says
+ 
+
+ align:start position:0%
+think that Craig is right when he says
+you have to take risks you have to take
+
+ align:start position:0%
+you have to take risks you have to take
+ 
+
+ align:start position:0%
+you have to take risks you have to take
+risks or else you're not gonna do
+
+ align:start position:0%
+risks or else you're not gonna do
+ 
+
+ align:start position:0%
+risks or else you're not gonna do
+anything worth writing about and that's
+
+ align:start position:0%
+anything worth writing about and that's
+ 
+
+ align:start position:0%
+anything worth writing about and that's
+a great way to close
\ No newline at end of file
diff --git a/dFF2DuEv-2c.txt b/dFF2DuEv-2c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7d991036fb1fb7cee4031e0b322142dceb423315
--- /dev/null
+++ b/dFF2DuEv-2c.txt
@@ -0,0 +1,16891 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu what we're going to be doing
+
+ align:start position:0%
+ocw.mit.edu what we're going to be doing
+ 
+
+ align:start position:0%
+ocw.mit.edu what we're going to be doing
+over the next few days um uh today and
+
+ align:start position:0%
+over the next few days um uh today and
+ 
+
+ align:start position:0%
+over the next few days um uh today and
+on Tuesday is really diving into the uh
+
+ align:start position:0%
+on Tuesday is really diving into the uh
+ 
+
+ align:start position:0%
+on Tuesday is really diving into the uh
+device fundamentals and then on Tuesday
+
+ align:start position:0%
+device fundamentals and then on Tuesday
+ 
+
+ align:start position:0%
+device fundamentals and then on Tuesday
+the materials fundamentals of how a
+
+ align:start position:0%
+the materials fundamentals of how a
+ 
+
+ align:start position:0%
+the materials fundamentals of how a
+solar cell device really works and uh
+
+ align:start position:0%
+solar cell device really works and uh
+ 
+
+ align:start position:0%
+solar cell device really works and uh
+what we've done so far is uh skimmed
+
+ align:start position:0%
+what we've done so far is uh skimmed
+ 
+
+ align:start position:0%
+what we've done so far is uh skimmed
+along at a very high level um
+
+ align:start position:0%
+along at a very high level um
+ 
+
+ align:start position:0%
+along at a very high level um
+using only the necessary physics and
+
+ align:start position:0%
+using only the necessary physics and
+ 
+
+ align:start position:0%
+using only the necessary physics and
+nothing more to describe how a solar
+
+ align:start position:0%
+nothing more to describe how a solar
+ 
+
+ align:start position:0%
+nothing more to describe how a solar
+cell works uh because we want to give
+
+ align:start position:0%
+cell works uh because we want to give
+ 
+
+ align:start position:0%
+cell works uh because we want to give
+you an intuition about solar cell device
+
+ align:start position:0%
+you an intuition about solar cell device
+ 
+
+ align:start position:0%
+you an intuition about solar cell device
+operation uh the alternative way of
+
+ align:start position:0%
+operation uh the alternative way of
+ 
+
+ align:start position:0%
+operation uh the alternative way of
+teaching PV is that we go heavy on the
+
+ align:start position:0%
+teaching PV is that we go heavy on the
+ 
+
+ align:start position:0%
+teaching PV is that we go heavy on the
+device physics up front front uh you're
+
+ align:start position:0%
+device physics up front front uh you're
+ 
+
+ align:start position:0%
+device physics up front front uh you're
+completely overloaded your RAM is is is
+
+ align:start position:0%
+completely overloaded your RAM is is is
+ 
+
+ align:start position:0%
+completely overloaded your RAM is is is
+completely full uh and by the time we
+
+ align:start position:0%
+completely full uh and by the time we
+ 
+
+ align:start position:0%
+completely full uh and by the time we
+actually get to IV curves you you're
+
+ align:start position:0%
+actually get to IV curves you you're
+ 
+
+ align:start position:0%
+actually get to IV curves you you're
+completely lost so hopefully you have
+
+ align:start position:0%
+completely lost so hopefully you have
+ 
+
+ align:start position:0%
+completely lost so hopefully you have
+some intuitive sense now about how a PV
+
+ align:start position:0%
+some intuitive sense now about how a PV
+ 
+
+ align:start position:0%
+some intuitive sense now about how a PV
+device works now we're going to be doing
+
+ align:start position:0%
+device works now we're going to be doing
+ 
+
+ align:start position:0%
+device works now we're going to be doing
+some deep dives into some advanced
+
+ align:start position:0%
+some deep dives into some advanced
+ 
+
+ align:start position:0%
+some deep dives into some advanced
+concepts so that we really uh have a
+
+ align:start position:0%
+concepts so that we really uh have a
+ 
+
+ align:start position:0%
+concepts so that we really uh have a
+sophisticated understanding of how a
+
+ align:start position:0%
+sophisticated understanding of how a
+ 
+
+ align:start position:0%
+sophisticated understanding of how a
+solar cell works so uh let's dive into
+
+ align:start position:0%
+solar cell works so uh let's dive into
+ 
+
+ align:start position:0%
+solar cell works so uh let's dive into
+uh the lecture material toward a 1D
+
+ align:start position:0%
+uh the lecture material toward a 1D
+ 
+
+ align:start position:0%
+uh the lecture material toward a 1D
+device model we want to be able to
+
+ align:start position:0%
+device model we want to be able to
+ 
+
+ align:start position:0%
+device model we want to be able to
+create a one-dimensional model that
+
+ align:start position:0%
+create a one-dimensional model that
+ 
+
+ align:start position:0%
+create a one-dimensional model that
+describes how a solar cell operates so
+
+ align:start position:0%
+describes how a solar cell operates so
+ 
+
+ align:start position:0%
+describes how a solar cell operates so
+we want to capture all of the necessary
+
+ align:start position:0%
+we want to capture all of the necessary
+ 
+
+ align:start position:0%
+we want to capture all of the necessary
+physics uh from the from the materials
+
+ align:start position:0%
+physics uh from the from the materials
+ 
+
+ align:start position:0%
+physics uh from the from the materials
+and the device uh to describe the IV
+
+ align:start position:0%
+and the device uh to describe the IV
+ 
+
+ align:start position:0%
+and the device uh to describe the IV
+characteristics of a solar cell so what
+
+ align:start position:0%
+characteristics of a solar cell so what
+ 
+
+ align:start position:0%
+characteristics of a solar cell so what
+we'll do at the very beginning is start
+
+ align:start position:0%
+we'll do at the very beginning is start
+ 
+
+ align:start position:0%
+we'll do at the very beginning is start
+with a little bit of nomenclature so
+
+ align:start position:0%
+with a little bit of nomenclature so
+ 
+
+ align:start position:0%
+with a little bit of nomenclature so
+that we understand what we're talking
+
+ align:start position:0%
+that we understand what we're talking
+ 
+
+ align:start position:0%
+that we understand what we're talking
+about in terms of energy conversion
+
+ align:start position:0%
+about in terms of energy conversion
+ 
+
+ align:start position:0%
+about in terms of energy conversion
+efficiency and Quantum efficiency and
+
+ align:start position:0%
+efficiency and Quantum efficiency and
+ 
+
+ align:start position:0%
+efficiency and Quantum efficiency and
+then we'll start describing the
+
+ align:start position:0%
+then we'll start describing the
+ 
+
+ align:start position:0%
+then we'll start describing the
+different parameters that affect uh
+
+ align:start position:0%
+different parameters that affect uh
+ 
+
+ align:start position:0%
+different parameters that affect uh
+energy conversion efficiency and Quantum
+
+ align:start position:0%
+energy conversion efficiency and Quantum
+ 
+
+ align:start position:0%
+energy conversion efficiency and Quantum
+efficiency here so one of the first key
+
+ align:start position:0%
+efficiency here so one of the first key
+ 
+
+ align:start position:0%
+efficiency here so one of the first key
+Concepts that's very very important to
+
+ align:start position:0%
+Concepts that's very very important to
+ 
+
+ align:start position:0%
+Concepts that's very very important to
+understand is that energy conversion
+
+ align:start position:0%
+understand is that energy conversion
+ 
+
+ align:start position:0%
+understand is that energy conversion
+efficiency is not the same thing as
+
+ align:start position:0%
+efficiency is not the same thing as
+ 
+
+ align:start position:0%
+efficiency is not the same thing as
+quantum efficiency you'll hear these two
+
+ align:start position:0%
+quantum efficiency you'll hear these two
+ 
+
+ align:start position:0%
+quantum efficiency you'll hear these two
+terms used quite frequently in the PB
+
+ align:start position:0%
+terms used quite frequently in the PB
+ 
+
+ align:start position:0%
+terms used quite frequently in the PB
+Community uh now I would say we're we're
+
+ align:start position:0%
+Community uh now I would say we're we're
+ 
+
+ align:start position:0%
+Community uh now I would say we're we're
+really starting to get sophisticated
+
+ align:start position:0%
+really starting to get sophisticated
+ 
+
+ align:start position:0%
+really starting to get sophisticated
+about their use in the very beginning of
+
+ align:start position:0%
+about their use in the very beginning of
+ 
+
+ align:start position:0%
+about their use in the very beginning of
+the of the field well let's put it this
+
+ align:start position:0%
+the of the field well let's put it this
+ 
+
+ align:start position:0%
+the of the field well let's put it this
+way in the third wave of PV which began
+
+ align:start position:0%
+way in the third wave of PV which began
+ 
+
+ align:start position:0%
+way in the third wave of PV which began
+at around late 1990s early 2000s um
+
+ align:start position:0%
+at around late 1990s early 2000s um
+ 
+
+ align:start position:0%
+at around late 1990s early 2000s um
+which was uh really when say some of the
+
+ align:start position:0%
+which was uh really when say some of the
+ 
+
+ align:start position:0%
+which was uh really when say some of the
+novel materials uh Quantum dot-based
+
+ align:start position:0%
+novel materials uh Quantum dot-based
+ 
+
+ align:start position:0%
+novel materials uh Quantum dot-based
+solar cells uh some Modern organic
+
+ align:start position:0%
+solar cells uh some Modern organic
+ 
+
+ align:start position:0%
+solar cells uh some Modern organic
+material-based solar cells really
+
+ align:start position:0%
+material-based solar cells really
+ 
+
+ align:start position:0%
+material-based solar cells really
+started to take off there wasn't that
+
+ align:start position:0%
+started to take off there wasn't that
+ 
+
+ align:start position:0%
+started to take off there wasn't that
+sophistic at of of understanding of of
+
+ align:start position:0%
+sophistic at of of understanding of of
+ 
+
+ align:start position:0%
+sophistic at of of understanding of of
+some of the nomenclature in PV and so
+
+ align:start position:0%
+some of the nomenclature in PV and so
+ 
+
+ align:start position:0%
+some of the nomenclature in PV and so
+terms were used in a confusing way when
+
+ align:start position:0%
+terms were used in a confusing way when
+ 
+
+ align:start position:0%
+terms were used in a confusing way when
+you read some of the papers back from
+
+ align:start position:0%
+you read some of the papers back from
+ 
+
+ align:start position:0%
+you read some of the papers back from
+the early 2000s you might pick up on
+
+ align:start position:0%
+the early 2000s you might pick up on
+ 
+
+ align:start position:0%
+the early 2000s you might pick up on
+some of this uh and so that's why I have
+
+ align:start position:0%
+some of this uh and so that's why I have
+ 
+
+ align:start position:0%
+some of this uh and so that's why I have
+this slide right here describing very
+
+ align:start position:0%
+this slide right here describing very
+ 
+
+ align:start position:0%
+this slide right here describing very
+clearly what is quantum efficiency and
+
+ align:start position:0%
+clearly what is quantum efficiency and
+ 
+
+ align:start position:0%
+clearly what is quantum efficiency and
+what is energy conversion efficiency um
+
+ align:start position:0%
+what is energy conversion efficiency um
+ 
+
+ align:start position:0%
+what is energy conversion efficiency um
+so energy conversion efficiency is
+
+ align:start position:0%
+so energy conversion efficiency is
+ 
+
+ align:start position:0%
+so energy conversion efficiency is
+pretty easy to understand we've been
+
+ align:start position:0%
+pretty easy to understand we've been
+ 
+
+ align:start position:0%
+pretty easy to understand we've been
+talking about that all class we've been
+
+ align:start position:0%
+talking about that all class we've been
+ 
+
+ align:start position:0%
+talking about that all class we've been
+talking about how a photon comes in with
+
+ align:start position:0%
+talking about how a photon comes in with
+ 
+
+ align:start position:0%
+talking about how a photon comes in with
+a certain amount of energy and you
+
+ align:start position:0%
+a certain amount of energy and you
+ 
+
+ align:start position:0%
+a certain amount of energy and you
+extract electrons from your solar cell
+
+ align:start position:0%
+extract electrons from your solar cell
+ 
+
+ align:start position:0%
+extract electrons from your solar cell
+device that have a certain amount of
+
+ align:start position:0%
+device that have a certain amount of
+ 
+
+ align:start position:0%
+device that have a certain amount of
+energy and that ratio would be the
+
+ align:start position:0%
+energy and that ratio would be the
+ 
+
+ align:start position:0%
+energy and that ratio would be the
+energy conversion efficiency is
+
+ align:start position:0%
+energy conversion efficiency is
+ 
+
+ align:start position:0%
+energy conversion efficiency is
+essentially uh the energy coming out
+
+ align:start position:0%
+essentially uh the energy coming out
+ 
+
+ align:start position:0%
+essentially uh the energy coming out
+divided by the energy going in so if for
+
+ align:start position:0%
+divided by the energy going in so if for
+ 
+
+ align:start position:0%
+divided by the energy going in so if for
+example one Photon comes in with three
+
+ align:start position:0%
+example one Photon comes in with three
+ 
+
+ align:start position:0%
+example one Photon comes in with three
+EV and generates an electron whole pair
+
+ align:start position:0%
+EV and generates an electron whole pair
+ 
+
+ align:start position:0%
+EV and generates an electron whole pair
+which is then extracted from the device
+
+ align:start position:0%
+which is then extracted from the device
+ 
+
+ align:start position:0%
+which is then extracted from the device
+with a voltage of say uh6 volts uh we
+
+ align:start position:0%
+with a voltage of say uh6 volts uh we
+ 
+
+ align:start position:0%
+with a voltage of say uh6 volts uh we
+would have an energy conversion
+
+ align:start position:0%
+would have an energy conversion
+ 
+
+ align:start position:0%
+would have an energy conversion
+efficiency less than one somewhere
+
+ align:start position:0%
+efficiency less than one somewhere
+ 
+
+ align:start position:0%
+efficiency less than one somewhere
+around 15% or so whereas if we uh if we
+
+ align:start position:0%
+around 15% or so whereas if we uh if we
+ 
+
+ align:start position:0%
+around 15% or so whereas if we uh if we
+uh looked at Quantum efficiency and
+
+ align:start position:0%
+uh looked at Quantum efficiency and
+ 
+
+ align:start position:0%
+uh looked at Quantum efficiency and
+Define quantum efficiency as the number
+
+ align:start position:0%
+Define quantum efficiency as the number
+ 
+
+ align:start position:0%
+Define quantum efficiency as the number
+of electrons out per incident Photon
+
+ align:start position:0%
+of electrons out per incident Photon
+ 
+
+ align:start position:0%
+of electrons out per incident Photon
+that means if we have one Photon coming
+
+ align:start position:0%
+that means if we have one Photon coming
+ 
+
+ align:start position:0%
+that means if we have one Photon coming
+in and one electron coming out of our
+
+ align:start position:0%
+in and one electron coming out of our
+ 
+
+ align:start position:0%
+in and one electron coming out of our
+device we have a Quantum efficiency of
+
+ align:start position:0%
+device we have a Quantum efficiency of
+ 
+
+ align:start position:0%
+device we have a Quantum efficiency of
+one or 100% so Quantum efficiency can be
+
+ align:start position:0%
+one or 100% so Quantum efficiency can be
+ 
+
+ align:start position:0%
+one or 100% so Quantum efficiency can be
+thought of as collection efficiency it
+
+ align:start position:0%
+thought of as collection efficiency it
+ 
+
+ align:start position:0%
+thought of as collection efficiency it
+means how many electron whole pairs were
+
+ align:start position:0%
+means how many electron whole pairs were
+ 
+
+ align:start position:0%
+means how many electron whole pairs were
+generated inside of the device and how
+
+ align:start position:0%
+generated inside of the device and how
+ 
+
+ align:start position:0%
+generated inside of the device and how
+many were collected coming out of the
+
+ align:start position:0%
+many were collected coming out of the
+ 
+
+ align:start position:0%
+many were collected coming out of the
+device um there's a little bit more T in
+
+ align:start position:0%
+device um there's a little bit more T in
+ 
+
+ align:start position:0%
+device um there's a little bit more T in
+that dealing with reflectivity off the
+
+ align:start position:0%
+that dealing with reflectivity off the
+ 
+
+ align:start position:0%
+that dealing with reflectivity off the
+surface I'll get to that in a slide or
+
+ align:start position:0%
+surface I'll get to that in a slide or
+ 
+
+ align:start position:0%
+surface I'll get to that in a slide or
+two but it can be thought of roughly as
+
+ align:start position:0%
+two but it can be thought of roughly as
+ 
+
+ align:start position:0%
+two but it can be thought of roughly as
+collection efficiency as whereas energy
+
+ align:start position:0%
+collection efficiency as whereas energy
+ 
+
+ align:start position:0%
+collection efficiency as whereas energy
+conversion efficiency is really what you
+
+ align:start position:0%
+conversion efficiency is really what you
+ 
+
+ align:start position:0%
+conversion efficiency is really what you
+think of in terms of thermodynamic
+
+ align:start position:0%
+think of in terms of thermodynamic
+ 
+
+ align:start position:0%
+think of in terms of thermodynamic
+efficiency of a device
+
+ align:start position:0%
+efficiency of a device
+ 
+
+ align:start position:0%
+efficiency of a device
+why is this important well uh there are
+
+ align:start position:0%
+why is this important well uh there are
+ 
+
+ align:start position:0%
+why is this important well uh there are
+papers out there this is an old one I
+
+ align:start position:0%
+papers out there this is an old one I
+ 
+
+ align:start position:0%
+papers out there this is an old one I
+think in in in nature materials if I'm
+
+ align:start position:0%
+think in in in nature materials if I'm
+ 
+
+ align:start position:0%
+think in in in nature materials if I'm
+not mistaken um that that uh started
+
+ align:start position:0%
+not mistaken um that that uh started
+ 
+
+ align:start position:0%
+not mistaken um that that uh started
+using a bunch of terms right so under 0
+
+ align:start position:0%
+using a bunch of terms right so under 0
+ 
+
+ align:start position:0%
+using a bunch of terms right so under 0
+or under five volts bias an illumination
+
+ align:start position:0%
+or under five volts bias an illumination
+ 
+
+ align:start position:0%
+or under five volts bias an illumination
+from a 975 nanometer laser so nothing
+
+ align:start position:0%
+from a 975 nanometer laser so nothing
+ 
+
+ align:start position:0%
+from a 975 nanometer laser so nothing
+like a polychromatic solar Spectrum this
+
+ align:start position:0%
+like a polychromatic solar Spectrum this
+ 
+
+ align:start position:0%
+like a polychromatic solar Spectrum this
+is a monochromatic light source our
+
+ align:start position:0%
+is a monochromatic light source our
+ 
+
+ align:start position:0%
+is a monochromatic light source our
+detectors show an internal Quantum
+
+ align:start position:0%
+detectors show an internal Quantum
+ 
+
+ align:start position:0%
+detectors show an internal Quantum
+efficiency of
+
+ align:start position:0%
+efficiency of
+ 
+
+ align:start position:0%
+efficiency of
+3% the photovoltaic response under this
+
+ align:start position:0%
+3% the photovoltaic response under this
+ 
+
+ align:start position:0%
+3% the photovoltaic response under this
+monochromatic light results in a maximum
+
+ align:start position:0%
+monochromatic light results in a maximum
+ 
+
+ align:start position:0%
+monochromatic light results in a maximum
+open circuit voltage of so and so a
+
+ align:start position:0%
+open circuit voltage of so and so a
+ 
+
+ align:start position:0%
+open circuit voltage of so and so a
+short circuit current of 350 nanoamps
+
+ align:start position:0%
+short circuit current of 350 nanoamps
+ 
+
+ align:start position:0%
+short circuit current of 350 nanoamps
+very very tiny and a short circuit
+
+ align:start position:0%
+very very tiny and a short circuit
+ 
+
+ align:start position:0%
+very very tiny and a short circuit
+current internal Quantum efficiency of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.006% so what they're talking about
+
+ align:start position:0%
+0.006% so what they're talking about
+ 
+
+ align:start position:0%
+0.006% so what they're talking about
+here is a a Quantum efficiency right of
+
+ align:start position:0%
+here is a a Quantum efficiency right of
+ 
+
+ align:start position:0%
+here is a a Quantum efficiency right of
+0.06% as we've already done just by the
+
+ align:start position:0%
+0.06% as we've already done just by the
+ 
+
+ align:start position:0%
+0.06% as we've already done just by the
+simple example of the 3v photon coming
+
+ align:start position:0%
+simple example of the 3v photon coming
+ 
+
+ align:start position:0%
+simple example of the 3v photon coming
+in exciting electron whole pair um
+
+ align:start position:0%
+in exciting electron whole pair um
+ 
+
+ align:start position:0%
+in exciting electron whole pair um
+Quantum efficiency of one but energy
+
+ align:start position:0%
+Quantum efficiency of one but energy
+ 
+
+ align:start position:0%
+Quantum efficiency of one but energy
+conversion efficiency below 20% we can
+
+ align:start position:0%
+conversion efficiency below 20% we can
+ 
+
+ align:start position:0%
+conversion efficiency below 20% we can
+already guess that the energy conversion
+
+ align:start position:0%
+already guess that the energy conversion
+ 
+
+ align:start position:0%
+already guess that the energy conversion
+efficiency of a device like this even
+
+ align:start position:0%
+efficiency of a device like this even
+ 
+
+ align:start position:0%
+efficiency of a device like this even
+for monochromatic light is going to be
+
+ align:start position:0%
+for monochromatic light is going to be
+ 
+
+ align:start position:0%
+for monochromatic light is going to be
+very low right so what what the reason
+
+ align:start position:0%
+very low right so what what the reason
+ 
+
+ align:start position:0%
+very low right so what what the reason
+I'm I'm highlighting this abstract right
+
+ align:start position:0%
+I'm I'm highlighting this abstract right
+ 
+
+ align:start position:0%
+I'm I'm highlighting this abstract right
+here is because it's a great example of
+
+ align:start position:0%
+here is because it's a great example of
+ 
+
+ align:start position:0%
+here is because it's a great example of
+um the uh plethora of different terms
+
+ align:start position:0%
+um the uh plethora of different terms
+ 
+
+ align:start position:0%
+um the uh plethora of different terms
+that you could find in reading a paper
+
+ align:start position:0%
+that you could find in reading a paper
+ 
+
+ align:start position:0%
+that you could find in reading a paper
+right and if you focus on just a few of
+
+ align:start position:0%
+right and if you focus on just a few of
+ 
+
+ align:start position:0%
+right and if you focus on just a few of
+them uh like oh uh 3% wow that's awesome
+
+ align:start position:0%
+them uh like oh uh 3% wow that's awesome
+ 
+
+ align:start position:0%
+them uh like oh uh 3% wow that's awesome
+3% device efficiency no it's not energy
+
+ align:start position:0%
+3% device efficiency no it's not energy
+ 
+
+ align:start position:0%
+3% device efficiency no it's not energy
+conversion efficiency that's the uh
+
+ align:start position:0%
+conversion efficiency that's the uh
+ 
+
+ align:start position:0%
+conversion efficiency that's the uh
+Quantum efficiency under a very specific
+
+ align:start position:0%
+Quantum efficiency under a very specific
+ 
+
+ align:start position:0%
+Quantum efficiency under a very specific
+bias condition reverse bias it's like a
+
+ align:start position:0%
+bias condition reverse bias it's like a
+ 
+
+ align:start position:0%
+bias condition reverse bias it's like a
+photod detector not a not a solar cell
+
+ align:start position:0%
+photod detector not a not a solar cell
+ 
+
+ align:start position:0%
+photod detector not a not a solar cell
+not under forward bias conditions okay
+
+ align:start position:0%
+not under forward bias conditions okay
+ 
+
+ align:start position:0%
+not under forward bias conditions okay
+so what does this really mean this
+
+ align:start position:0%
+so what does this really mean this
+ 
+
+ align:start position:0%
+so what does this really mean this
+0.006% uh shortcircuit internal Quantum
+
+ align:start position:0%
+0.006% uh shortcircuit internal Quantum
+ 
+
+ align:start position:0%
+0.006% uh shortcircuit internal Quantum
+efficiency well we defined our energy
+
+ align:start position:0%
+efficiency well we defined our energy
+ 
+
+ align:start position:0%
+efficiency well we defined our energy
+conversion efficiency or solar
+
+ align:start position:0%
+conversion efficiency or solar
+ 
+
+ align:start position:0%
+conversion efficiency or solar
+conversion efficiency as power out
+
+ align:start position:0%
+conversion efficiency as power out
+ 
+
+ align:start position:0%
+conversion efficiency as power out
+divided by power in uh that was done in
+
+ align:start position:0%
+divided by power in uh that was done in
+ 
+
+ align:start position:0%
+divided by power in uh that was done in
+the previous lectures um the power out
+
+ align:start position:0%
+the previous lectures um the power out
+ 
+
+ align:start position:0%
+the previous lectures um the power out
+would be the power and the uh the the
+
+ align:start position:0%
+would be the power and the uh the the
+ 
+
+ align:start position:0%
+would be the power and the uh the the
+current and the voltage product at the
+
+ align:start position:0%
+current and the voltage product at the
+ 
+
+ align:start position:0%
+current and the voltage product at the
+maximum power point divided by the solar
+
+ align:start position:0%
+maximum power point divided by the solar
+ 
+
+ align:start position:0%
+maximum power point divided by the solar
+flux coming in um and that would be
+
+ align:start position:0%
+flux coming in um and that would be
+ 
+
+ align:start position:0%
+flux coming in um and that would be
+equivalent to the fill Factor times the
+
+ align:start position:0%
+equivalent to the fill Factor times the
+ 
+
+ align:start position:0%
+equivalent to the fill Factor times the
+short circuit current times the open
+
+ align:start position:0%
+short circuit current times the open
+ 
+
+ align:start position:0%
+short circuit current times the open
+circuit voltage and typical values for
+
+ align:start position:0%
+circuit voltage and typical values for
+ 
+
+ align:start position:0%
+circuit voltage and typical values for
+energy conversion efficiency are in the
+
+ align:start position:0%
+energy conversion efficiency are in the
+ 
+
+ align:start position:0%
+energy conversion efficiency are in the
+12 to 20% range I would say uh maybe
+
+ align:start position:0%
+12 to 20% range I would say uh maybe
+ 
+
+ align:start position:0%
+12 to 20% range I would say uh maybe
+less than 10% for emerging Technologies
+
+ align:start position:0%
+less than 10% for emerging Technologies
+ 
+
+ align:start position:0%
+less than 10% for emerging Technologies
+but but these are are typical values and
+
+ align:start position:0%
+but but these are are typical values and
+ 
+
+ align:start position:0%
+but but these are are typical values and
+um the uh solar flux the illumination
+
+ align:start position:0%
+um the uh solar flux the illumination
+ 
+
+ align:start position:0%
+um the uh solar flux the illumination
+intensity might vary as well but
+
+ align:start position:0%
+intensity might vary as well but
+ 
+
+ align:start position:0%
+intensity might vary as well but
+typically we talk about one sun or am
+
+ align:start position:0%
+typically we talk about one sun or am
+ 
+
+ align:start position:0%
+typically we talk about one sun or am
+1.5 uh illumination condition right so
+
+ align:start position:0%
+1.5 uh illumination condition right so
+ 
+
+ align:start position:0%
+1.5 uh illumination condition right so
+that's our our Spectrum at at am 1.5
+
+ align:start position:0%
+that's our our Spectrum at at am 1.5
+ 
+
+ align:start position:0%
+that's our our Spectrum at at am 1.5
+conditions what we did on homework
+
+ align:start position:0%
+conditions what we did on homework
+ 
+
+ align:start position:0%
+conditions what we did on homework
+number one now the quantum efficiency uh
+
+ align:start position:0%
+number one now the quantum efficiency uh
+ 
+
+ align:start position:0%
+number one now the quantum efficiency uh
+has two flavors one we'll call external
+
+ align:start position:0%
+has two flavors one we'll call external
+ 
+
+ align:start position:0%
+has two flavors one we'll call external
+Quantum efficiency and the other
+
+ align:start position:0%
+Quantum efficiency and the other
+ 
+
+ align:start position:0%
+Quantum efficiency and the other
+internal Quantum efficiency and they're
+
+ align:start position:0%
+internal Quantum efficiency and they're
+ 
+
+ align:start position:0%
+internal Quantum efficiency and they're
+basically the difference between them is
+
+ align:start position:0%
+basically the difference between them is
+ 
+
+ align:start position:0%
+basically the difference between them is
+the reflectance off the front surface of
+
+ align:start position:0%
+the reflectance off the front surface of
+ 
+
+ align:start position:0%
+the reflectance off the front surface of
+the device the internal Quantum
+
+ align:start position:0%
+the device the internal Quantum
+ 
+
+ align:start position:0%
+the device the internal Quantum
+efficiency um uh essentially factors out
+
+ align:start position:0%
+efficiency um uh essentially factors out
+ 
+
+ align:start position:0%
+efficiency um uh essentially factors out
+the reflectance the external Quantum
+
+ align:start position:0%
+the reflectance the external Quantum
+ 
+
+ align:start position:0%
+the reflectance the external Quantum
+efficiency is really um taking
+
+ align:start position:0%
+efficiency is really um taking
+ 
+
+ align:start position:0%
+efficiency is really um taking
+reflectance into account as well so
+
+ align:start position:0%
+reflectance into account as well so
+ 
+
+ align:start position:0%
+reflectance into account as well so
+external Quantum efficiency is defined
+
+ align:start position:0%
+external Quantum efficiency is defined
+ 
+
+ align:start position:0%
+external Quantum efficiency is defined
+as electrons out per photons toward the
+
+ align:start position:0%
+as electrons out per photons toward the
+ 
+
+ align:start position:0%
+as electrons out per photons toward the
+device we say photons in but this is
+
+ align:start position:0%
+device we say photons in but this is
+ 
+
+ align:start position:0%
+device we say photons in but this is
+really how many photons are impingent
+
+ align:start position:0%
+really how many photons are impingent
+ 
+
+ align:start position:0%
+really how many photons are impingent
+upon the device itself some of those
+
+ align:start position:0%
+upon the device itself some of those
+ 
+
+ align:start position:0%
+upon the device itself some of those
+photons will be reflected off the front
+
+ align:start position:0%
+photons will be reflected off the front
+ 
+
+ align:start position:0%
+photons will be reflected off the front
+surface other photons will go into the
+
+ align:start position:0%
+surface other photons will go into the
+ 
+
+ align:start position:0%
+surface other photons will go into the
+device and generate electron hold pairs
+
+ align:start position:0%
+device and generate electron hold pairs
+ 
+
+ align:start position:0%
+device and generate electron hold pairs
+or some will go straight through the
+
+ align:start position:0%
+or some will go straight through the
+ 
+
+ align:start position:0%
+or some will go straight through the
+device and be absorbed in the back
+
+ align:start position:0%
+device and be absorbed in the back
+ 
+
+ align:start position:0%
+device and be absorbed in the back
+surface or so forth so the eqe external
+
+ align:start position:0%
+surface or so forth so the eqe external
+ 
+
+ align:start position:0%
+surface or so forth so the eqe external
+Quantum efficiency typical Peak values
+
+ align:start position:0%
+Quantum efficiency typical Peak values
+ 
+
+ align:start position:0%
+Quantum efficiency typical Peak values
+range between 60 and 90% depending on
+
+ align:start position:0%
+range between 60 and 90% depending on
+ 
+
+ align:start position:0%
+range between 60 and 90% depending on
+the reflectivity uh for moderate
+
+ align:start position:0%
+the reflectivity uh for moderate
+ 
+
+ align:start position:0%
+the reflectivity uh for moderate
+efficiency devices
+
+ align:start position:0%
+efficiency devices
+ 
+
+ align:start position:0%
+efficiency devices
+right so the reason Peak values range
+
+ align:start position:0%
+right so the reason Peak values range
+ 
+
+ align:start position:0%
+right so the reason Peak values range
+from 60 to 90 is because there's going
+
+ align:start position:0%
+from 60 to 90 is because there's going
+ 
+
+ align:start position:0%
+from 60 to 90 is because there's going
+to be some band of wavelengths at which
+
+ align:start position:0%
+to be some band of wavelengths at which
+ 
+
+ align:start position:0%
+to be some band of wavelengths at which
+the solar cell really responds well it's
+
+ align:start position:0%
+the solar cell really responds well it's
+ 
+
+ align:start position:0%
+the solar cell really responds well it's
+really efficient at converting that
+
+ align:start position:0%
+really efficient at converting that
+ 
+
+ align:start position:0%
+really efficient at converting that
+those photons into electron hole Pairs
+
+ align:start position:0%
+those photons into electron hole Pairs
+ 
+
+ align:start position:0%
+those photons into electron hole Pairs
+and where the Sun instead of a beautiful
+
+ align:start position:0%
+and where the Sun instead of a beautiful
+ 
+
+ align:start position:0%
+and where the Sun instead of a beautiful
+polychromatic black body emission Source
+
+ align:start position:0%
+polychromatic black body emission Source
+ 
+
+ align:start position:0%
+polychromatic black body emission Source
+if the sun were a monochromatic light
+
+ align:start position:0%
+if the sun were a monochromatic light
+ 
+
+ align:start position:0%
+if the sun were a monochromatic light
+source tuned to that particular
+
+ align:start position:0%
+source tuned to that particular
+ 
+
+ align:start position:0%
+source tuned to that particular
+wavelength the solar cell would be
+
+ align:start position:0%
+wavelength the solar cell would be
+ 
+
+ align:start position:0%
+wavelength the solar cell would be
+Wicked efficient but it's not so um this
+
+ align:start position:0%
+Wicked efficient but it's not so um this
+ 
+
+ align:start position:0%
+Wicked efficient but it's not so um this
+is this is why e Q is is an interesting
+
+ align:start position:0%
+is this is why e Q is is an interesting
+ 
+
+ align:start position:0%
+is this is why e Q is is an interesting
+parameter because it tells you the
+
+ align:start position:0%
+parameter because it tells you the
+ 
+
+ align:start position:0%
+parameter because it tells you the
+response of the solar cell to different
+
+ align:start position:0%
+response of the solar cell to different
+ 
+
+ align:start position:0%
+response of the solar cell to different
+spectral conditions and that's why we
+
+ align:start position:0%
+spectral conditions and that's why we
+ 
+
+ align:start position:0%
+spectral conditions and that's why we
+sometimes call it spectral response of a
+
+ align:start position:0%
+sometimes call it spectral response of a
+ 
+
+ align:start position:0%
+sometimes call it spectral response of a
+solar cell device by the way those who
+
+ align:start position:0%
+solar cell device by the way those who
+ 
+
+ align:start position:0%
+solar cell device by the way those who
+need notes um if you would be so kind as
+
+ align:start position:0%
+need notes um if you would be so kind as
+ 
+
+ align:start position:0%
+need notes um if you would be so kind as
+to raise your hand Joe will uh pass them
+
+ align:start position:0%
+to raise your hand Joe will uh pass them
+ 
+
+ align:start position:0%
+to raise your hand Joe will uh pass them
+around as well so we can have uh enough
+
+ align:start position:0%
+around as well so we can have uh enough
+ 
+
+ align:start position:0%
+around as well so we can have uh enough
+for everybody to write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down any questions as far on uh eqe
+
+ align:start position:0%
+down any questions as far on uh eqe
+ 
+
+ align:start position:0%
+down any questions as far on uh eqe
+external Quantum efficiency the
+
+ align:start position:0%
+external Quantum efficiency the
+ 
+
+ align:start position:0%
+external Quantum efficiency the
+difference between QE and the difference
+
+ align:start position:0%
+difference between QE and the difference
+ 
+
+ align:start position:0%
+difference between QE and the difference
+between uh ECE or um shall we say the
+
+ align:start position:0%
+between uh ECE or um shall we say the
+ 
+
+ align:start position:0%
+between uh ECE or um shall we say the
+energy conversion
+
+ align:start position:0%
+energy conversion
+ 
+
+ align:start position:0%
+energy conversion
+efficiency okay efficiencies they uh
+
+ align:start position:0%
+efficiency okay efficiencies they uh
+ 
+
+ align:start position:0%
+efficiency okay efficiencies they uh
+also include the subb photons right or
+
+ align:start position:0%
+also include the subb photons right or
+ 
+
+ align:start position:0%
+also include the subb photons right or
+do they just include photons which have
+
+ align:start position:0%
+do they just include photons which have
+ 
+
+ align:start position:0%
+do they just include photons which have
+the potential to make an electronal pair
+
+ align:start position:0%
+the potential to make an electronal pair
+ 
+
+ align:start position:0%
+the potential to make an electronal pair
+in principle QE um or sorry eqe should
+
+ align:start position:0%
+in principle QE um or sorry eqe should
+ 
+
+ align:start position:0%
+in principle QE um or sorry eqe should
+have eqe as a function of Lambda really
+
+ align:start position:0%
+have eqe as a function of Lambda really
+ 
+
+ align:start position:0%
+have eqe as a function of Lambda really
+and uh the photon in uh is going to be
+
+ align:start position:0%
+and uh the photon in uh is going to be
+ 
+
+ align:start position:0%
+and uh the photon in uh is going to be
+obviously uh at a certain wavelength
+
+ align:start position:0%
+obviously uh at a certain wavelength
+ 
+
+ align:start position:0%
+obviously uh at a certain wavelength
+usually uh I've rarely heard
+
+ align:start position:0%
+usually uh I've rarely heard
+ 
+
+ align:start position:0%
+usually uh I've rarely heard
+eqe uh given in a polychromatic sense
+
+ align:start position:0%
+eqe uh given in a polychromatic sense
+ 
+
+ align:start position:0%
+eqe uh given in a polychromatic sense
+where they take an entire solar spectrum
+
+ align:start position:0%
+where they take an entire solar spectrum
+ 
+
+ align:start position:0%
+where they take an entire solar spectrum
+and measure the quantum efficiency
+
+ align:start position:0%
+and measure the quantum efficiency
+ 
+
+ align:start position:0%
+and measure the quantum efficiency
+average usually Quantum efficiency is is
+
+ align:start position:0%
+average usually Quantum efficiency is is
+ 
+
+ align:start position:0%
+average usually Quantum efficiency is is
+is measured wavelength by wavelength and
+
+ align:start position:0%
+is measured wavelength by wavelength and
+ 
+
+ align:start position:0%
+is measured wavelength by wavelength and
+so you might uh change your your your
+
+ align:start position:0%
+so you might uh change your your your
+ 
+
+ align:start position:0%
+so you might uh change your your your
+monochrometer settings 20 or 30 times
+
+ align:start position:0%
+monochrometer settings 20 or 30 times
+ 
+
+ align:start position:0%
+monochrometer settings 20 or 30 times
+over or even more over a Quantum
+
+ align:start position:0%
+over or even more over a Quantum
+ 
+
+ align:start position:0%
+over or even more over a Quantum
+efficiency measurement to really map out
+
+ align:start position:0%
+efficiency measurement to really map out
+ 
+
+ align:start position:0%
+efficiency measurement to really map out
+the entire solar Spectrum from short
+
+ align:start position:0%
+the entire solar Spectrum from short
+ 
+
+ align:start position:0%
+the entire solar Spectrum from short
+wavelength in the ultraviolet all the
+
+ align:start position:0%
+wavelength in the ultraviolet all the
+ 
+
+ align:start position:0%
+wavelength in the ultraviolet all the
+way to longer wavelength in the infrared
+
+ align:start position:0%
+way to longer wavelength in the infrared
+ 
+
+ align:start position:0%
+way to longer wavelength in the infrared
+and you're absolutely right some of
+
+ align:start position:0%
+and you're absolutely right some of
+ 
+
+ align:start position:0%
+and you're absolutely right some of
+those wavelengths the photo response of
+
+ align:start position:0%
+those wavelengths the photo response of
+ 
+
+ align:start position:0%
+those wavelengths the photo response of
+the solar cell will be very close to
+
+ align:start position:0%
+the solar cell will be very close to
+ 
+
+ align:start position:0%
+the solar cell will be very close to
+zero because it just doesn't respond
+
+ align:start position:0%
+zero because it just doesn't respond
+ 
+
+ align:start position:0%
+zero because it just doesn't respond
+well at that wavelength maybe the
+
+ align:start position:0%
+well at that wavelength maybe the
+ 
+
+ align:start position:0%
+well at that wavelength maybe the
+wavelength is too short and it's being
+
+ align:start position:0%
+wavelength is too short and it's being
+ 
+
+ align:start position:0%
+wavelength is too short and it's being
+absorbed by some surface layer or maybe
+
+ align:start position:0%
+absorbed by some surface layer or maybe
+ 
+
+ align:start position:0%
+absorbed by some surface layer or maybe
+the wavelength is too long and it's just
+
+ align:start position:0%
+the wavelength is too long and it's just
+ 
+
+ align:start position:0%
+the wavelength is too long and it's just
+going straight through uh sub Bap Photon
+
+ align:start position:0%
+going straight through uh sub Bap Photon
+ 
+
+ align:start position:0%
+going straight through uh sub Bap Photon
+whereas energy conversion efficiency is
+
+ align:start position:0%
+whereas energy conversion efficiency is
+ 
+
+ align:start position:0%
+whereas energy conversion efficiency is
+really taking the entire solar spectrum
+
+ align:start position:0%
+really taking the entire solar spectrum
+ 
+
+ align:start position:0%
+really taking the entire solar spectrum
+and uh matching uh or or testing the uh
+
+ align:start position:0%
+and uh matching uh or or testing the uh
+ 
+
+ align:start position:0%
+and uh matching uh or or testing the uh
+the energy the the power coming out of
+
+ align:start position:0%
+the energy the the power coming out of
+ 
+
+ align:start position:0%
+the energy the the power coming out of
+the solar cell versus the power going in
+
+ align:start position:0%
+the solar cell versus the power going in
+ 
+
+ align:start position:0%
+the solar cell versus the power going in
+so a typical Quantum efficiency curve
+
+ align:start position:0%
+so a typical Quantum efficiency curve
+ 
+
+ align:start position:0%
+so a typical Quantum efficiency curve
+might look something like this let's
+
+ align:start position:0%
+might look something like this let's
+ 
+
+ align:start position:0%
+might look something like this let's
+walk through the axes first and then
+
+ align:start position:0%
+walk through the axes first and then
+ 
+
+ align:start position:0%
+walk through the axes first and then
+talk about the curve so the axes we have
+
+ align:start position:0%
+talk about the curve so the axes we have
+ 
+
+ align:start position:0%
+talk about the curve so the axes we have
+wavelength on the x-axis on the obsa and
+
+ align:start position:0%
+wavelength on the x-axis on the obsa and
+ 
+
+ align:start position:0%
+wavelength on the x-axis on the obsa and
+on the ordinate we have Quantum
+
+ align:start position:0%
+on the ordinate we have Quantum
+ 
+
+ align:start position:0%
+on the ordinate we have Quantum
+efficiency wavelength is varying from
+
+ align:start position:0%
+efficiency wavelength is varying from
+ 
+
+ align:start position:0%
+efficiency wavelength is varying from
+let's say the uh ultraviolet to the
+
+ align:start position:0%
+let's say the uh ultraviolet to the
+ 
+
+ align:start position:0%
+let's say the uh ultraviolet to the
+infrared and Beyond uh well beyond the
+
+ align:start position:0%
+infrared and Beyond uh well beyond the
+ 
+
+ align:start position:0%
+infrared and Beyond uh well beyond the
+red uh into the near infrared and
+
+ align:start position:0%
+red uh into the near infrared and
+ 
+
+ align:start position:0%
+red uh into the near infrared and
+probably ending somewhere around the mid
+
+ align:start position:0%
+probably ending somewhere around the mid
+ 
+
+ align:start position:0%
+probably ending somewhere around the mid
+infrared and Quantum efficiency extends
+
+ align:start position:0%
+infrared and Quantum efficiency extends
+ 
+
+ align:start position:0%
+infrared and Quantum efficiency extends
+from uh 0 to one in other words from 0%
+
+ align:start position:0%
+from uh 0 to one in other words from 0%
+ 
+
+ align:start position:0%
+from uh 0 to one in other words from 0%
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+100% And we have this box that's
+
+ align:start position:0%
+100% And we have this box that's
+ 
+
+ align:start position:0%
+100% And we have this box that's
+represented by this uh maroon line right
+
+ align:start position:0%
+represented by this uh maroon line right
+ 
+
+ align:start position:0%
+represented by this uh maroon line right
+here uh entitled ideal Quantum
+
+ align:start position:0%
+here uh entitled ideal Quantum
+ 
+
+ align:start position:0%
+here uh entitled ideal Quantum
+efficiency
+
+ align:start position:0%
+efficiency
+ 
+
+ align:start position:0%
+efficiency
+and this would be if uh at the band Gap
+
+ align:start position:0%
+and this would be if uh at the band Gap
+ 
+
+ align:start position:0%
+and this would be if uh at the band Gap
+energy all of a sudden our Quantum
+
+ align:start position:0%
+energy all of a sudden our Quantum
+ 
+
+ align:start position:0%
+energy all of a sudden our Quantum
+efficiency turned on Boop to 100% and
+
+ align:start position:0%
+efficiency turned on Boop to 100% and
+ 
+
+ align:start position:0%
+efficiency turned on Boop to 100% and
+cut across and this was the assumption
+
+ align:start position:0%
+cut across and this was the assumption
+ 
+
+ align:start position:0%
+cut across and this was the assumption
+that we made in our homework that the
+
+ align:start position:0%
+that we made in our homework that the
+ 
+
+ align:start position:0%
+that we made in our homework that the
+solar cell device would respond in this
+
+ align:start position:0%
+solar cell device would respond in this
+ 
+
+ align:start position:0%
+solar cell device would respond in this
+ideal manner in reality uh at longer
+
+ align:start position:0%
+ideal manner in reality uh at longer
+ 
+
+ align:start position:0%
+ideal manner in reality uh at longer
+wavelengths here what's going on why
+
+ align:start position:0%
+wavelengths here what's going on why
+ 
+
+ align:start position:0%
+wavelengths here what's going on why
+would there be a decrease of the quantum
+
+ align:start position:0%
+would there be a decrease of the quantum
+ 
+
+ align:start position:0%
+would there be a decrease of the quantum
+efficiency at longer
+
+ align:start position:0%
+efficiency at longer
+ 
+
+ align:start position:0%
+efficiency at longer
+wavelengths what what effect is
+
+ align:start position:0%
+wavelengths what what effect is
+ 
+
+ align:start position:0%
+wavelengths what what effect is
+happening there AB yeah the absorption
+
+ align:start position:0%
+happening there AB yeah the absorption
+ 
+
+ align:start position:0%
+happening there AB yeah the absorption
+coefficient is dropping uh and and this
+
+ align:start position:0%
+coefficient is dropping uh and and this
+ 
+
+ align:start position:0%
+coefficient is dropping uh and and this
+light is starting to go straight through
+
+ align:start position:0%
+light is starting to go straight through
+ 
+
+ align:start position:0%
+light is starting to go straight through
+the device there is a growing fraction
+
+ align:start position:0%
+the device there is a growing fraction
+ 
+
+ align:start position:0%
+the device there is a growing fraction
+of photons that are not being absorbed
+
+ align:start position:0%
+of photons that are not being absorbed
+ 
+
+ align:start position:0%
+of photons that are not being absorbed
+by the solar cell device in the very
+
+ align:start position:0%
+by the solar cell device in the very
+ 
+
+ align:start position:0%
+by the solar cell device in the very
+short wavelengths right here as I said
+
+ align:start position:0%
+short wavelengths right here as I said
+ 
+
+ align:start position:0%
+short wavelengths right here as I said
+before uh often times there's a dead
+
+ align:start position:0%
+before uh often times there's a dead
+ 
+
+ align:start position:0%
+before uh often times there's a dead
+layer right near the surface of the
+
+ align:start position:0%
+layer right near the surface of the
+ 
+
+ align:start position:0%
+layer right near the surface of the
+device that's impeding uh good uh
+
+ align:start position:0%
+device that's impeding uh good uh
+ 
+
+ align:start position:0%
+device that's impeding uh good uh
+electron whole pair charge separation
+
+ align:start position:0%
+electron whole pair charge separation
+ 
+
+ align:start position:0%
+electron whole pair charge separation
+and eventually collection and right here
+
+ align:start position:0%
+and eventually collection and right here
+ 
+
+ align:start position:0%
+and eventually collection and right here
+in the middle there's a slow but steady
+
+ align:start position:0%
+in the middle there's a slow but steady
+ 
+
+ align:start position:0%
+in the middle there's a slow but steady
+decrease of the quantum efficiency
+
+ align:start position:0%
+decrease of the quantum efficiency
+ 
+
+ align:start position:0%
+decrease of the quantum efficiency
+typically these are photons that are
+
+ align:start position:0%
+typically these are photons that are
+ 
+
+ align:start position:0%
+typically these are photons that are
+being absorbed in the absorber layer and
+
+ align:start position:0%
+being absorbed in the absorber layer and
+ 
+
+ align:start position:0%
+being absorbed in the absorber layer and
+if you think about your solar cell and
+
+ align:start position:0%
+if you think about your solar cell and
+ 
+
+ align:start position:0%
+if you think about your solar cell and
+cross-section here's your solar cell and
+
+ align:start position:0%
+cross-section here's your solar cell and
+ 
+
+ align:start position:0%
+cross-section here's your solar cell and
+cross-section these are photons being
+
+ align:start position:0%
+cross-section these are photons being
+ 
+
+ align:start position:0%
+cross-section these are photons being
+absorbed in the absorber layer
+
+ align:start position:0%
+absorbed in the absorber layer
+ 
+
+ align:start position:0%
+absorbed in the absorber layer
+generating electron whole paars which
+
+ align:start position:0%
+generating electron whole paars which
+ 
+
+ align:start position:0%
+generating electron whole paars which
+are then being separated by The Junction
+
+ align:start position:0%
+are then being separated by The Junction
+ 
+
+ align:start position:0%
+are then being separated by The Junction
+right and as we go to longer and longer
+
+ align:start position:0%
+right and as we go to longer and longer
+ 
+
+ align:start position:0%
+right and as we go to longer and longer
+wavelengths if you remember your Optical
+
+ align:start position:0%
+wavelengths if you remember your Optical
+ 
+
+ align:start position:0%
+wavelengths if you remember your Optical
+absorption coefficient begins dropping
+
+ align:start position:0%
+absorption coefficient begins dropping
+ 
+
+ align:start position:0%
+absorption coefficient begins dropping
+that means that the penetration depth of
+
+ align:start position:0%
+that means that the penetration depth of
+ 
+
+ align:start position:0%
+that means that the penetration depth of
+the light the average penetration depth
+
+ align:start position:0%
+the light the average penetration depth
+ 
+
+ align:start position:0%
+the light the average penetration depth
+of the light is increasing and so the
+
+ align:start position:0%
+of the light is increasing and so the
+ 
+
+ align:start position:0%
+of the light is increasing and so the
+average distance that the electron hold
+
+ align:start position:0%
+average distance that the electron hold
+ 
+
+ align:start position:0%
+average distance that the electron hold
+pairs are being generated from The
+
+ align:start position:0%
+pairs are being generated from The
+ 
+
+ align:start position:0%
+pairs are being generated from The
+Junction is increasing so in other words
+
+ align:start position:0%
+Junction is increasing so in other words
+ 
+
+ align:start position:0%
+Junction is increasing so in other words
+as we go from short wavelengths to
+
+ align:start position:0%
+as we go from short wavelengths to
+ 
+
+ align:start position:0%
+as we go from short wavelengths to
+longer wavelengths the distance from
+
+ align:start position:0%
+longer wavelengths the distance from
+ 
+
+ align:start position:0%
+longer wavelengths the distance from
+which the electron hole pairs are being
+
+ align:start position:0%
+which the electron hole pairs are being
+ 
+
+ align:start position:0%
+which the electron hole pairs are being
+generated from The Junction is
+
+ align:start position:0%
+generated from The Junction is
+ 
+
+ align:start position:0%
+generated from The Junction is
+increasing that means that the electron
+
+ align:start position:0%
+increasing that means that the electron
+ 
+
+ align:start position:0%
+increasing that means that the electron
+hole pairs generated at these
+
+ align:start position:0%
+hole pairs generated at these
+ 
+
+ align:start position:0%
+hole pairs generated at these
+wavelengths have further to travel to
+
+ align:start position:0%
+wavelengths have further to travel to
+ 
+
+ align:start position:0%
+wavelengths have further to travel to
+reach the junction than those electron
+
+ align:start position:0%
+reach the junction than those electron
+ 
+
+ align:start position:0%
+reach the junction than those electron
+hole pairs generated at these
+
+ align:start position:0%
+hole pairs generated at these
+ 
+
+ align:start position:0%
+hole pairs generated at these
+wavelengths closer to the front surface
+
+ align:start position:0%
+wavelengths closer to the front surface
+ 
+
+ align:start position:0%
+wavelengths closer to the front surface
+and since there's a finite probability
+
+ align:start position:0%
+and since there's a finite probability
+ 
+
+ align:start position:0%
+and since there's a finite probability
+that the electron whole pair will
+
+ align:start position:0%
+that the electron whole pair will
+ 
+
+ align:start position:0%
+that the electron whole pair will
+recombine as it travels through the
+
+ align:start position:0%
+recombine as it travels through the
+ 
+
+ align:start position:0%
+recombine as it travels through the
+material that's why you get this very
+
+ align:start position:0%
+material that's why you get this very
+ 
+
+ align:start position:0%
+material that's why you get this very
+slow uh but steady uh increase of
+
+ align:start position:0%
+slow uh but steady uh increase of
+ 
+
+ align:start position:0%
+slow uh but steady uh increase of
+quantum efficiency over the mid uh
+
+ align:start position:0%
+quantum efficiency over the mid uh
+ 
+
+ align:start position:0%
+quantum efficiency over the mid uh
+wavelength range and uh on Tuesday we'll
+
+ align:start position:0%
+wavelength range and uh on Tuesday we'll
+ 
+
+ align:start position:0%
+wavelength range and uh on Tuesday we'll
+talk more about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that internal Quantum efficiency so for
+
+ align:start position:0%
+that internal Quantum efficiency so for
+ 
+
+ align:start position:0%
+that internal Quantum efficiency so for
+those who say well you know um there's
+
+ align:start position:0%
+those who say well you know um there's
+ 
+
+ align:start position:0%
+those who say well you know um there's
+this there's a certain Delta right here
+
+ align:start position:0%
+this there's a certain Delta right here
+ 
+
+ align:start position:0%
+this there's a certain Delta right here
+between one and my maximum uh uh
+
+ align:start position:0%
+between one and my maximum uh uh
+ 
+
+ align:start position:0%
+between one and my maximum uh uh
+response here my maximum Quantum
+
+ align:start position:0%
+response here my maximum Quantum
+ 
+
+ align:start position:0%
+response here my maximum Quantum
+efficiency and I suspect that's really
+
+ align:start position:0%
+efficiency and I suspect that's really
+ 
+
+ align:start position:0%
+efficiency and I suspect that's really
+due to the fact that a certain uh
+
+ align:start position:0%
+due to the fact that a certain uh
+ 
+
+ align:start position:0%
+due to the fact that a certain uh
+percentage of my photons are being
+
+ align:start position:0%
+percentage of my photons are being
+ 
+
+ align:start position:0%
+percentage of my photons are being
+reflected off the front surface I I know
+
+ align:start position:0%
+reflected off the front surface I I know
+ 
+
+ align:start position:0%
+reflected off the front surface I I know
+how to calculate reflectance we did that
+
+ align:start position:0%
+how to calculate reflectance we did that
+ 
+
+ align:start position:0%
+how to calculate reflectance we did that
+in uh lecture number two or three I
+
+ align:start position:0%
+in uh lecture number two or three I
+ 
+
+ align:start position:0%
+in uh lecture number two or three I
+believe uh so we know how to calculate
+
+ align:start position:0%
+believe uh so we know how to calculate
+ 
+
+ align:start position:0%
+believe uh so we know how to calculate
+reflectance off the front surface we can
+
+ align:start position:0%
+reflectance off the front surface we can
+ 
+
+ align:start position:0%
+reflectance off the front surface we can
+also measure reflectance using a spectr
+
+ align:start position:0%
+also measure reflectance using a spectr
+ 
+
+ align:start position:0%
+also measure reflectance using a spectr
+photometer and what we can do is
+
+ align:start position:0%
+photometer and what we can do is
+ 
+
+ align:start position:0%
+photometer and what we can do is
+normalize the effect of reflectance out
+
+ align:start position:0%
+normalize the effect of reflectance out
+ 
+
+ align:start position:0%
+normalize the effect of reflectance out
+by dividing our external Quantum
+
+ align:start position:0%
+by dividing our external Quantum
+ 
+
+ align:start position:0%
+by dividing our external Quantum
+efficiency by 1 minus r what in effect
+
+ align:start position:0%
+efficiency by 1 minus r what in effect
+ 
+
+ align:start position:0%
+efficiency by 1 minus r what in effect
+we're doing is we're normalizing the
+
+ align:start position:0%
+we're doing is we're normalizing the
+ 
+
+ align:start position:0%
+we're doing is we're normalizing the
+effect of reflectance out of our
+
+ align:start position:0%
+effect of reflectance out of our
+ 
+
+ align:start position:0%
+effect of reflectance out of our
+measurement so now we're only
+
+ align:start position:0%
+measurement so now we're only
+ 
+
+ align:start position:0%
+measurement so now we're only
+considering those photons that get into
+
+ align:start position:0%
+considering those photons that get into
+ 
+
+ align:start position:0%
+considering those photons that get into
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+device if you want you can think about
+
+ align:start position:0%
+device if you want you can think about
+ 
+
+ align:start position:0%
+device if you want you can think about
+the cases there if reflectance is zero
+
+ align:start position:0%
+the cases there if reflectance is zero
+ 
+
+ align:start position:0%
+the cases there if reflectance is zero
+that means your EQ is equal to your iqe
+
+ align:start position:0%
+that means your EQ is equal to your iqe
+ 
+
+ align:start position:0%
+that means your EQ is equal to your iqe
+your internal Quantum efficiency is
+
+ align:start position:0%
+your internal Quantum efficiency is
+ 
+
+ align:start position:0%
+your internal Quantum efficiency is
+equal to the external Quantum efficiency
+
+ align:start position:0%
+equal to the external Quantum efficiency
+ 
+
+ align:start position:0%
+equal to the external Quantum efficiency
+but if reflectance is say 50% if 50% of
+
+ align:start position:0%
+but if reflectance is say 50% if 50% of
+ 
+
+ align:start position:0%
+but if reflectance is say 50% if 50% of
+your photons are being reflected off the
+
+ align:start position:0%
+your photons are being reflected off the
+ 
+
+ align:start position:0%
+your photons are being reflected off the
+front surface of your device now your
+
+ align:start position:0%
+front surface of your device now your
+ 
+
+ align:start position:0%
+front surface of your device now your
+iqe is probably going to be double your
+
+ align:start position:0%
+iqe is probably going to be double your
+ 
+
+ align:start position:0%
+iqe is probably going to be double your
+external Quantum
+
+ align:start position:0%
+external Quantum
+ 
+
+ align:start position:0%
+external Quantum
+efficiency and so now uh this is an
+
+ align:start position:0%
+efficiency and so now uh this is an
+ 
+
+ align:start position:0%
+efficiency and so now uh this is an
+interesting um uh parameter because for
+
+ align:start position:0%
+interesting um uh parameter because for
+ 
+
+ align:start position:0%
+interesting um uh parameter because for
+example in our lab scale devices when
+
+ align:start position:0%
+example in our lab scale devices when
+ 
+
+ align:start position:0%
+example in our lab scale devices when
+we're testing them often times we don't
+
+ align:start position:0%
+we're testing them often times we don't
+ 
+
+ align:start position:0%
+we're testing them often times we don't
+optimize for optical properties
+
+ align:start position:0%
+optimize for optical properties
+ 
+
+ align:start position:0%
+optimize for optical properties
+sometimes we do but many times we're
+
+ align:start position:0%
+sometimes we do but many times we're
+ 
+
+ align:start position:0%
+sometimes we do but many times we're
+we're focused on the material we're
+
+ align:start position:0%
+we're focused on the material we're
+ 
+
+ align:start position:0%
+we're focused on the material we're
+focused on the junction and we don't
+
+ align:start position:0%
+focused on the junction and we don't
+ 
+
+ align:start position:0%
+focused on the junction and we don't
+bother to put the perfect anti
+
+ align:start position:0%
+bother to put the perfect anti
+ 
+
+ align:start position:0%
+bother to put the perfect anti
+reflective cating on it would take too
+
+ align:start position:0%
+reflective cating on it would take too
+ 
+
+ align:start position:0%
+reflective cating on it would take too
+long to fabricate it and so iqe gives us
+
+ align:start position:0%
+long to fabricate it and so iqe gives us
+ 
+
+ align:start position:0%
+long to fabricate it and so iqe gives us
+a good metric of how the solar cell is
+
+ align:start position:0%
+a good metric of how the solar cell is
+ 
+
+ align:start position:0%
+a good metric of how the solar cell is
+responding if we were to go through all
+
+ align:start position:0%
+responding if we were to go through all
+ 
+
+ align:start position:0%
+responding if we were to go through all
+the effort to make the light capture
+
+ align:start position:0%
+the effort to make the light capture
+ 
+
+ align:start position:0%
+the effort to make the light capture
+ideal for our
+
+ align:start position:0%
+ideal for our
+ 
+
+ align:start position:0%
+ideal for our
+device okay and that's why we sometimes
+
+ align:start position:0%
+device okay and that's why we sometimes
+ 
+
+ align:start position:0%
+device okay and that's why we sometimes
+use or report iqe in uh in studies and
+
+ align:start position:0%
+use or report iqe in uh in studies and
+ 
+
+ align:start position:0%
+use or report iqe in uh in studies and
+typical Peak values are between 80 and
+
+ align:start position:0%
+typical Peak values are between 80 and
+ 
+
+ align:start position:0%
+typical Peak values are between 80 and
+98% for moderate efficiency devices uh
+
+ align:start position:0%
+98% for moderate efficiency devices uh
+ 
+
+ align:start position:0%
+98% for moderate efficiency devices uh
+so uh it would essentially the curve
+
+ align:start position:0%
+so uh it would essentially the curve
+ 
+
+ align:start position:0%
+so uh it would essentially the curve
+would look very much like the eqe curve
+
+ align:start position:0%
+would look very much like the eqe curve
+ 
+
+ align:start position:0%
+would look very much like the eqe curve
+it just be boosted up by 1 over 1us
+
+ align:start position:0%
+it just be boosted up by 1 over 1us
+ 
+
+ align:start position:0%
+it just be boosted up by 1 over 1us
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+okay so um so so any questions so far
+
+ align:start position:0%
+okay so um so so any questions so far
+ 
+
+ align:start position:0%
+okay so um so so any questions so far
+make sure we're on the same page
+
+ align:start position:0%
+make sure we're on the same page
+ 
+
+ align:start position:0%
+make sure we're on the same page
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and absolutely so uh iqe is a function
+
+ align:start position:0%
+and absolutely so uh iqe is a function
+ 
+
+ align:start position:0%
+and absolutely so uh iqe is a function
+of wavelength uh our reflectivity is
+
+ align:start position:0%
+of wavelength uh our reflectivity is
+ 
+
+ align:start position:0%
+of wavelength uh our reflectivity is
+also going to be a strong function of
+
+ align:start position:0%
+also going to be a strong function of
+ 
+
+ align:start position:0%
+also going to be a strong function of
+wavelength because the real component of
+
+ align:start position:0%
+wavelength because the real component of
+ 
+
+ align:start position:0%
+wavelength because the real component of
+the refractive index is changing as a
+
+ align:start position:0%
+the refractive index is changing as a
+ 
+
+ align:start position:0%
+the refractive index is changing as a
+function of wavelength yep
+
+ align:start position:0%
+function of wavelength yep
+ 
+
+ align:start position:0%
+function of wavelength yep
+absolutely okay so this gives you a a
+
+ align:start position:0%
+absolutely okay so this gives you a a
+ 
+
+ align:start position:0%
+absolutely okay so this gives you a a
+sense sorry for the uh poor choice of
+
+ align:start position:0%
+sense sorry for the uh poor choice of
+ 
+
+ align:start position:0%
+sense sorry for the uh poor choice of
+the reflectivity colors right here this
+
+ align:start position:0%
+the reflectivity colors right here this
+ 
+
+ align:start position:0%
+the reflectivity colors right here this
+baby blue which is almost impossible to
+
+ align:start position:0%
+baby blue which is almost impossible to
+ 
+
+ align:start position:0%
+baby blue which is almost impossible to
+see but I've just traced it out with my
+
+ align:start position:0%
+see but I've just traced it out with my
+ 
+
+ align:start position:0%
+see but I've just traced it out with my
+finger that denotes the reflectivity as
+
+ align:start position:0%
+finger that denotes the reflectivity as
+ 
+
+ align:start position:0%
+finger that denotes the reflectivity as
+a function of wavelength from some data
+
+ align:start position:0%
+a function of wavelength from some data
+ 
+
+ align:start position:0%
+a function of wavelength from some data
+that I took as a graduate student so um
+
+ align:start position:0%
+that I took as a graduate student so um
+ 
+
+ align:start position:0%
+that I took as a graduate student so um
+you have some typical um uh uh Quantum
+
+ align:start position:0%
+you have some typical um uh uh Quantum
+ 
+
+ align:start position:0%
+you have some typical um uh uh Quantum
+efficiency curves right here and in the
+
+ align:start position:0%
+efficiency curves right here and in the
+ 
+
+ align:start position:0%
+efficiency curves right here and in the
+the quantum efficiency curves that are
+
+ align:start position:0%
+the quantum efficiency curves that are
+ 
+
+ align:start position:0%
+the quantum efficiency curves that are
+shown are for a pretty poor quality
+
+ align:start position:0%
+shown are for a pretty poor quality
+ 
+
+ align:start position:0%
+shown are for a pretty poor quality
+device and um in this particular case I
+
+ align:start position:0%
+device and um in this particular case I
+ 
+
+ align:start position:0%
+device and um in this particular case I
+I measured Quantum efficiency under
+
+ align:start position:0%
+I measured Quantum efficiency under
+ 
+
+ align:start position:0%
+I measured Quantum efficiency under
+short circuit conditions but with
+
+ align:start position:0%
+short circuit conditions but with
+ 
+
+ align:start position:0%
+short circuit conditions but with
+different illumination intensities so
+
+ align:start position:0%
+different illumination intensities so
+ 
+
+ align:start position:0%
+different illumination intensities so
+going from zero Sun illumination all the
+
+ align:start position:0%
+going from zero Sun illumination all the
+ 
+
+ align:start position:0%
+going from zero Sun illumination all the
+way up to one Sun illumination but this
+
+ align:start position:0%
+way up to one Sun illumination but this
+ 
+
+ align:start position:0%
+way up to one Sun illumination but this
+the device was still in short circuit
+
+ align:start position:0%
+the device was still in short circuit
+ 
+
+ align:start position:0%
+the device was still in short circuit
+conditions so what I was doing in effect
+
+ align:start position:0%
+conditions so what I was doing in effect
+ 
+
+ align:start position:0%
+conditions so what I was doing in effect
+was flooding the device with more and
+
+ align:start position:0%
+was flooding the device with more and
+ 
+
+ align:start position:0%
+was flooding the device with more and
+more and more carriers and I got this
+
+ align:start position:0%
+more and more carriers and I got this
+ 
+
+ align:start position:0%
+more and more carriers and I got this
+boost here in the middle wavelength uh
+
+ align:start position:0%
+boost here in the middle wavelength uh
+ 
+
+ align:start position:0%
+boost here in the middle wavelength uh
+range I still was limited by my surface
+
+ align:start position:0%
+range I still was limited by my surface
+ 
+
+ align:start position:0%
+range I still was limited by my surface
+I was still limited by my band Gap and
+
+ align:start position:0%
+I was still limited by my band Gap and
+ 
+
+ align:start position:0%
+I was still limited by my band Gap and
+non-absorption effects over here but in
+
+ align:start position:0%
+non-absorption effects over here but in
+ 
+
+ align:start position:0%
+non-absorption effects over here but in
+the middle I was was able to get this
+
+ align:start position:0%
+the middle I was was able to get this
+ 
+
+ align:start position:0%
+the middle I was was able to get this
+boost in performance uh simply because I
+
+ align:start position:0%
+boost in performance uh simply because I
+ 
+
+ align:start position:0%
+boost in performance uh simply because I
+was filling in uh trap States inside of
+
+ align:start position:0%
+was filling in uh trap States inside of
+ 
+
+ align:start position:0%
+was filling in uh trap States inside of
+the material this is an advanced concept
+
+ align:start position:0%
+the material this is an advanced concept
+ 
+
+ align:start position:0%
+the material this is an advanced concept
+that we're going to get to uh over the
+
+ align:start position:0%
+that we're going to get to uh over the
+ 
+
+ align:start position:0%
+that we're going to get to uh over the
+next few lectures but it gives you a
+
+ align:start position:0%
+next few lectures but it gives you a
+ 
+
+ align:start position:0%
+next few lectures but it gives you a
+sense of what a QE curve might look like
+
+ align:start position:0%
+sense of what a QE curve might look like
+ 
+
+ align:start position:0%
+sense of what a QE curve might look like
+for a device what the reflectivity might
+
+ align:start position:0%
+for a device what the reflectivity might
+ 
+
+ align:start position:0%
+for a device what the reflectivity might
+look like um and and these curves right
+
+ align:start position:0%
+look like um and and these curves right
+ 
+
+ align:start position:0%
+look like um and and these curves right
+here were iqe or internal Quantum
+
+ align:start position:0%
+here were iqe or internal Quantum
+ 
+
+ align:start position:0%
+here were iqe or internal Quantum
+efficiency okay so um you know take
+
+ align:start position:0%
+efficiency okay so um you know take
+ 
+
+ align:start position:0%
+efficiency okay so um you know take
+efficiency with a grain of Sal when you
+
+ align:start position:0%
+efficiency with a grain of Sal when you
+ 
+
+ align:start position:0%
+efficiency with a grain of Sal when you
+hear somebody reporting an efficiency
+
+ align:start position:0%
+hear somebody reporting an efficiency
+ 
+
+ align:start position:0%
+hear somebody reporting an efficiency
+value uh ask think about what efficiency
+
+ align:start position:0%
+value uh ask think about what efficiency
+ 
+
+ align:start position:0%
+value uh ask think about what efficiency
+is being measured is it uh energy
+
+ align:start position:0%
+is being measured is it uh energy
+ 
+
+ align:start position:0%
+is being measured is it uh energy
+conversion efficiency is it quantum
+
+ align:start position:0%
+conversion efficiency is it quantum
+ 
+
+ align:start position:0%
+conversion efficiency is it quantum
+efficiency internal external what
+
+ align:start position:0%
+efficiency internal external what
+ 
+
+ align:start position:0%
+efficiency internal external what
+wavelengths uh what is the nature of the
+
+ align:start position:0%
+wavelengths uh what is the nature of the
+ 
+
+ align:start position:0%
+wavelengths uh what is the nature of the
+light being used right is it is it a one
+
+ align:start position:0%
+light being used right is it is it a one
+ 
+
+ align:start position:0%
+light being used right is it is it a one
+Sun uh illumination source that has been
+
+ align:start position:0%
+Sun uh illumination source that has been
+ 
+
+ align:start position:0%
+Sun uh illumination source that has been
+well calibrated to within 2% spectral
+
+ align:start position:0%
+well calibrated to within 2% spectral
+ 
+
+ align:start position:0%
+well calibrated to within 2% spectral
+Fidelity uh spatial uniformity temporal
+
+ align:start position:0%
+Fidelity uh spatial uniformity temporal
+ 
+
+ align:start position:0%
+Fidelity uh spatial uniformity temporal
+stability is it a really bonafit good
+
+ align:start position:0%
+stability is it a really bonafit good
+ 
+
+ align:start position:0%
+stability is it a really bonafit good
+light source or is this uh some
+
+ align:start position:0%
+light source or is this uh some
+ 
+
+ align:start position:0%
+light source or is this uh some
+monochromatic light source that somebody
+
+ align:start position:0%
+monochromatic light source that somebody
+ 
+
+ align:start position:0%
+monochromatic light source that somebody
+set up because they knew aha my solar
+
+ align:start position:0%
+set up because they knew aha my solar
+ 
+
+ align:start position:0%
+set up because they knew aha my solar
+cell really responds well to say 500
+
+ align:start position:0%
+cell really responds well to say 500
+ 
+
+ align:start position:0%
+cell really responds well to say 500
+nanometers light right so I'm going to
+
+ align:start position:0%
+nanometers light right so I'm going to
+ 
+
+ align:start position:0%
+nanometers light right so I'm going to
+test my I'm going to report my values
+
+ align:start position:0%
+test my I'm going to report my values
+ 
+
+ align:start position:0%
+test my I'm going to report my values
+right at that wavelength you have to
+
+ align:start position:0%
+right at that wavelength you have to
+ 
+
+ align:start position:0%
+right at that wavelength you have to
+take it with a grain of salt um and uh
+
+ align:start position:0%
+take it with a grain of salt um and uh
+ 
+
+ align:start position:0%
+take it with a grain of salt um and uh
+yeah exactly what is the intensity of
+
+ align:start position:0%
+yeah exactly what is the intensity of
+ 
+
+ align:start position:0%
+yeah exactly what is the intensity of
+the light that's being used as well
+
+ align:start position:0%
+the light that's being used as well
+ 
+
+ align:start position:0%
+the light that's being used as well
+that's very important as we just saw
+
+ align:start position:0%
+that's very important as we just saw
+ 
+
+ align:start position:0%
+that's very important as we just saw
+right over here because the bulk
+
+ align:start position:0%
+right over here because the bulk
+ 
+
+ align:start position:0%
+right over here because the bulk
+material uh is going to respond
+
+ align:start position:0%
+material uh is going to respond
+ 
+
+ align:start position:0%
+material uh is going to respond
+differently there are certain trap
+
+ align:start position:0%
+differently there are certain trap
+ 
+
+ align:start position:0%
+differently there are certain trap
+States for electrons inside of the
+
+ align:start position:0%
+States for electrons inside of the
+ 
+
+ align:start position:0%
+States for electrons inside of the
+material and as you add more and more
+
+ align:start position:0%
+material and as you add more and more
+ 
+
+ align:start position:0%
+material and as you add more and more
+light you're flooding those traps they
+
+ align:start position:0%
+light you're flooding those traps they
+ 
+
+ align:start position:0%
+light you're flooding those traps they
+become filled and the electrons can move
+
+ align:start position:0%
+become filled and the electrons can move
+ 
+
+ align:start position:0%
+become filled and the electrons can move
+through the material more easily right
+
+ align:start position:0%
+through the material more easily right
+ 
+
+ align:start position:0%
+through the material more easily right
+that's why you get this boost of
+
+ align:start position:0%
+that's why you get this boost of
+ 
+
+ align:start position:0%
+that's why you get this boost of
+response as you increase the
+
+ align:start position:0%
+response as you increase the
+ 
+
+ align:start position:0%
+response as you increase the
+illumination intensity in this
+
+ align:start position:0%
+illumination intensity in this
+ 
+
+ align:start position:0%
+illumination intensity in this
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+experiment so these are all questions
+
+ align:start position:0%
+experiment so these are all questions
+ 
+
+ align:start position:0%
+experiment so these are all questions
+that you should ask yourselves when you
+
+ align:start position:0%
+that you should ask yourselves when you
+ 
+
+ align:start position:0%
+that you should ask yourselves when you
+see Quantum efficiency uh internal
+
+ align:start position:0%
+see Quantum efficiency uh internal
+ 
+
+ align:start position:0%
+see Quantum efficiency uh internal
+Quantum uh external Quantum efficiency
+
+ align:start position:0%
+Quantum uh external Quantum efficiency
+ 
+
+ align:start position:0%
+Quantum uh external Quantum efficiency
+values reported and or energy conversion
+
+ align:start position:0%
+values reported and or energy conversion
+ 
+
+ align:start position:0%
+values reported and or energy conversion
+efficiencies is what is what is really
+
+ align:start position:0%
+efficiencies is what is what is really
+ 
+
+ align:start position:0%
+efficiencies is what is what is really
+happening what are they majoring this
+
+ align:start position:0%
+happening what are they majoring this
+ 
+
+ align:start position:0%
+happening what are they majoring this
+right here a paper out of Paul lotus'
+
+ align:start position:0%
+right here a paper out of Paul lotus'
+ 
+
+ align:start position:0%
+right here a paper out of Paul lotus'
+lab from 2002 was in my humble opinion
+
+ align:start position:0%
+lab from 2002 was in my humble opinion
+ 
+
+ align:start position:0%
+lab from 2002 was in my humble opinion
+an excellent example of honest
+
+ align:start position:0%
+an excellent example of honest
+ 
+
+ align:start position:0%
+an excellent example of honest
+efficiency reporting um first off they
+
+ align:start position:0%
+efficiency reporting um first off they
+ 
+
+ align:start position:0%
+efficiency reporting um first off they
+uh you know they they picked their
+
+ align:start position:0%
+uh you know they they picked their
+ 
+
+ align:start position:0%
+uh you know they they picked their
+highest values and and put their best
+
+ align:start position:0%
+highest values and and put their best
+ 
+
+ align:start position:0%
+highest values and and put their best
+foot forward and said look we have a
+
+ align:start position:0%
+foot forward and said look we have a
+ 
+
+ align:start position:0%
+foot forward and said look we have a
+Quantum efficiency over 54% uh and a
+
+ align:start position:0%
+Quantum efficiency over 54% uh and a
+ 
+
+ align:start position:0%
+Quantum efficiency over 54% uh and a
+monochromatic power conversion
+
+ align:start position:0%
+monochromatic power conversion
+ 
+
+ align:start position:0%
+monochromatic power conversion
+efficiency of 6.9% under very low
+
+ align:start position:0%
+efficiency of 6.9% under very low
+ 
+
+ align:start position:0%
+efficiency of 6.9% under very low
+intensity light um uh at 55 nmet right
+
+ align:start position:0%
+intensity light um uh at 55 nmet right
+ 
+
+ align:start position:0%
+intensity light um uh at 55 nmet right
+so first off they put their best foot
+
+ align:start position:0%
+so first off they put their best foot
+ 
+
+ align:start position:0%
+so first off they put their best foot
+forward and said under optimal
+
+ align:start position:0%
+forward and said under optimal
+ 
+
+ align:start position:0%
+forward and said under optimal
+conditions monochromatic light that's
+
+ align:start position:0%
+conditions monochromatic light that's
+ 
+
+ align:start position:0%
+conditions monochromatic light that's
+what we get but also under air mass 1.5
+
+ align:start position:0%
+what we get but also under air mass 1.5
+ 
+
+ align:start position:0%
+what we get but also under air mass 1.5
+Global solar conditions under the
+
+ align:start position:0%
+Global solar conditions under the
+ 
+
+ align:start position:0%
+Global solar conditions under the
+standard solar Spectrum we obtained an
+
+ align:start position:0%
+standard solar Spectrum we obtained an
+ 
+
+ align:start position:0%
+standard solar Spectrum we obtained an
+energy conversion effic or a power
+
+ align:start position:0%
+energy conversion effic or a power
+ 
+
+ align:start position:0%
+energy conversion effic or a power
+conversion efficiency of
+
+ align:start position:0%
+conversion efficiency of
+ 
+
+ align:start position:0%
+conversion efficiency of
+1.7% so both values are put there out on
+
+ align:start position:0%
+1.7% so both values are put there out on
+ 
+
+ align:start position:0%
+1.7% so both values are put there out on
+the table and they say look here's
+
+ align:start position:0%
+the table and they say look here's
+ 
+
+ align:start position:0%
+the table and they say look here's
+here's a characterization of our device
+
+ align:start position:0%
+here's a characterization of our device
+ 
+
+ align:start position:0%
+here's a characterization of our device
+so I I really like this pay-per-view it
+
+ align:start position:0%
+so I I really like this pay-per-view it
+ 
+
+ align:start position:0%
+so I I really like this pay-per-view it
+was back in 2002 right at the beginning
+
+ align:start position:0%
+was back in 2002 right at the beginning
+ 
+
+ align:start position:0%
+was back in 2002 right at the beginning
+of the the new wave of of of new
+
+ align:start position:0%
+of the the new wave of of of new
+ 
+
+ align:start position:0%
+of the the new wave of of of new
+materials in PV uh so to speak this this
+
+ align:start position:0%
+materials in PV uh so to speak this this
+ 
+
+ align:start position:0%
+materials in PV uh so to speak this this
+third wave of PV uh in in the United
+
+ align:start position:0%
+third wave of PV uh in in the United
+ 
+
+ align:start position:0%
+third wave of PV uh in in the United
+States and it was a beautiful example of
+
+ align:start position:0%
+States and it was a beautiful example of
+ 
+
+ align:start position:0%
+States and it was a beautiful example of
+a really well reported uh carefully
+
+ align:start position:0%
+a really well reported uh carefully
+ 
+
+ align:start position:0%
+a really well reported uh carefully
+described uh
+
+ align:start position:0%
+described uh
+ 
+
+ align:start position:0%
+described uh
+efficiency any further uh thoughts or
+
+ align:start position:0%
+efficiency any further uh thoughts or
+ 
+
+ align:start position:0%
+efficiency any further uh thoughts or
+comments before we jump on to the next
+
+ align:start position:0%
+comments before we jump on to the next
+ 
+
+ align:start position:0%
+comments before we jump on to the next
+uh topics of the day how do you have a
+
+ align:start position:0%
+uh topics of the day how do you have a
+ 
+
+ align:start position:0%
+uh topics of the day how do you have a
+QE curve for zero Suns I noticed on your
+
+ align:start position:0%
+QE curve for zero Suns I noticed on your
+ 
+
+ align:start position:0%
+QE curve for zero Suns I noticed on your
+PL or is that kind of an extrap yeah so
+
+ align:start position:0%
+PL or is that kind of an extrap yeah so
+ 
+
+ align:start position:0%
+PL or is that kind of an extrap yeah so
+these are this is the bias condition uh
+
+ align:start position:0%
+these are this is the bias condition uh
+ 
+
+ align:start position:0%
+these are this is the bias condition uh
+sorry the bias lighting condition not
+
+ align:start position:0%
+sorry the bias lighting condition not
+ 
+
+ align:start position:0%
+sorry the bias lighting condition not
+the bias voltage as in uh battery but
+
+ align:start position:0%
+the bias voltage as in uh battery but
+ 
+
+ align:start position:0%
+the bias voltage as in uh battery but
+bias lighting is in I I shine a a a
+
+ align:start position:0%
+bias lighting is in I I shine a a a
+ 
+
+ align:start position:0%
+bias lighting is in I I shine a a a
+light source a polychromatic light
+
+ align:start position:0%
+light source a polychromatic light
+ 
+
+ align:start position:0%
+light source a polychromatic light
+source at at my material I believe in
+
+ align:start position:0%
+source at at my material I believe in
+ 
+
+ align:start position:0%
+source at at my material I believe in
+that case it was a hen lamp with a
+
+ align:start position:0%
+that case it was a hen lamp with a
+ 
+
+ align:start position:0%
+that case it was a hen lamp with a
+series of filters to simulate the the
+
+ align:start position:0%
+series of filters to simulate the the
+ 
+
+ align:start position:0%
+series of filters to simulate the the
+solar spectrum and um obviously you you
+
+ align:start position:0%
+solar spectrum and um obviously you you
+ 
+
+ align:start position:0%
+solar spectrum and um obviously you you
+you can't measure a Quantum efficiency
+
+ align:start position:0%
+you can't measure a Quantum efficiency
+ 
+
+ align:start position:0%
+you can't measure a Quantum efficiency
+without having some light involved um
+
+ align:start position:0%
+without having some light involved um
+ 
+
+ align:start position:0%
+without having some light involved um
+and so the light that was being
+
+ align:start position:0%
+and so the light that was being
+ 
+
+ align:start position:0%
+and so the light that was being
+generated by the monochrometer was much
+
+ align:start position:0%
+generated by the monochrometer was much
+ 
+
+ align:start position:0%
+generated by the monochrometer was much
+lower in intensity than uh these uh
+
+ align:start position:0%
+lower in intensity than uh these uh
+ 
+
+ align:start position:0%
+lower in intensity than uh these uh
+illumination intensities here and so it
+
+ align:start position:0%
+illumination intensities here and so it
+ 
+
+ align:start position:0%
+illumination intensities here and so it
+was more of a pertubation on top of a
+
+ align:start position:0%
+was more of a pertubation on top of a
+ 
+
+ align:start position:0%
+was more of a pertubation on top of a
+steadystate background and we ran the
+
+ align:start position:0%
+steadystate background and we ran the
+ 
+
+ align:start position:0%
+steadystate background and we ran the
+measurement in exactly those conditions
+
+ align:start position:0%
+measurement in exactly those conditions
+ 
+
+ align:start position:0%
+measurement in exactly those conditions
+we had a steady state background light
+
+ align:start position:0%
+we had a steady state background light
+ 
+
+ align:start position:0%
+we had a steady state background light
+and then we chopped uh the monochrometer
+
+ align:start position:0%
+and then we chopped uh the monochrometer
+ 
+
+ align:start position:0%
+and then we chopped uh the monochrometer
+light coming in uh and used the lock and
+
+ align:start position:0%
+light coming in uh and used the lock and
+ 
+
+ align:start position:0%
+light coming in uh and used the lock and
+amplifier to track that particular
+
+ align:start position:0%
+amplifier to track that particular
+ 
+
+ align:start position:0%
+amplifier to track that particular
+frequency so we're able to detect the
+
+ align:start position:0%
+frequency so we're able to detect the
+ 
+
+ align:start position:0%
+frequency so we're able to detect the
+small perturbation due to the
+
+ align:start position:0%
+small perturbation due to the
+ 
+
+ align:start position:0%
+small perturbation due to the
+monochromatic light coming in on top of
+
+ align:start position:0%
+monochromatic light coming in on top of
+ 
+
+ align:start position:0%
+monochromatic light coming in on top of
+the study
+
+ align:start position:0%
+the study
+ 
+
+ align:start position:0%
+the study
+background yeah there's no International
+
+ align:start position:0%
+background yeah there's no International
+ 
+
+ align:start position:0%
+background yeah there's no International
+standard to report efficiency or
+
+ align:start position:0%
+standard to report efficiency or
+ 
+
+ align:start position:0%
+standard to report efficiency or
+convention uh there are uh there are
+
+ align:start position:0%
+convention uh there are uh there are
+ 
+
+ align:start position:0%
+convention uh there are uh there are
+conventions International conventions to
+
+ align:start position:0%
+conventions International conventions to
+ 
+
+ align:start position:0%
+conventions International conventions to
+report uh energy conversion efficiencies
+
+ align:start position:0%
+report uh energy conversion efficiencies
+ 
+
+ align:start position:0%
+report uh energy conversion efficiencies
+and I believe there might also be for uh
+
+ align:start position:0%
+and I believe there might also be for uh
+ 
+
+ align:start position:0%
+and I believe there might also be for uh
+Quantum efficiencies as well let me look
+
+ align:start position:0%
+Quantum efficiencies as well let me look
+ 
+
+ align:start position:0%
+Quantum efficiencies as well let me look
+into that um why don't we take note of
+
+ align:start position:0%
+into that um why don't we take note of
+ 
+
+ align:start position:0%
+into that um why don't we take note of
+that and bring back the precise ASM
+
+ align:start position:0%
+that and bring back the precise ASM
+ 
+
+ align:start position:0%
+that and bring back the precise ASM
+standards next time uh and I believe
+
+ align:start position:0%
+standards next time uh and I believe
+ 
+
+ align:start position:0%
+standards next time uh and I believe
+also there are uh other entities like
+
+ align:start position:0%
+also there are uh other entities like
+ 
+
+ align:start position:0%
+also there are uh other entities like
+IEC uh that have their own systems for
+
+ align:start position:0%
+IEC uh that have their own systems for
+ 
+
+ align:start position:0%
+IEC uh that have their own systems for
+it um there are about four four
+
+ align:start position:0%
+it um there are about four four
+ 
+
+ align:start position:0%
+it um there are about four four
+Laboratories worldwide that
+
+ align:start position:0%
+Laboratories worldwide that
+ 
+
+ align:start position:0%
+Laboratories worldwide that
+are authorized to give uh standard
+
+ align:start position:0%
+are authorized to give uh standard
+ 
+
+ align:start position:0%
+are authorized to give uh standard
+efficiency measurements so they have
+
+ align:start position:0%
+efficiency measurements so they have
+ 
+
+ align:start position:0%
+efficiency measurements so they have
+very carefully calibrated uh um Quantum
+
+ align:start position:0%
+very carefully calibrated uh um Quantum
+ 
+
+ align:start position:0%
+very carefully calibrated uh um Quantum
+efficiency measurement devices very
+
+ align:start position:0%
+efficiency measurement devices very
+ 
+
+ align:start position:0%
+efficiency measurement devices very
+carefully calibrated solar simulators
+
+ align:start position:0%
+carefully calibrated solar simulators
+ 
+
+ align:start position:0%
+carefully calibrated solar simulators
+and um if you really think you have a
+
+ align:start position:0%
+and um if you really think you have a
+ 
+
+ align:start position:0%
+and um if you really think you have a
+record efficiency cell you should get it
+
+ align:start position:0%
+record efficiency cell you should get it
+ 
+
+ align:start position:0%
+record efficiency cell you should get it
+checked at one of those Laboratories you
+
+ align:start position:0%
+checked at one of those Laboratories you
+ 
+
+ align:start position:0%
+checked at one of those Laboratories you
+shouldn't just uh report what you have
+
+ align:start position:0%
+shouldn't just uh report what you have
+ 
+
+ align:start position:0%
+shouldn't just uh report what you have
+coming off of your lab-based system or
+
+ align:start position:0%
+coming off of your lab-based system or
+ 
+
+ align:start position:0%
+coming off of your lab-based system or
+you may even want to go around to a few
+
+ align:start position:0%
+you may even want to go around to a few
+ 
+
+ align:start position:0%
+you may even want to go around to a few
+different Labs here at MIT first yeah
+
+ align:start position:0%
+different Labs here at MIT first yeah
+ 
+
+ align:start position:0%
+different Labs here at MIT first yeah
+one might have a better better
+
+ align:start position:0%
+one might have a better better
+ 
+
+ align:start position:0%
+one might have a better better
+calibrated solar simulator than another
+
+ align:start position:0%
+calibrated solar simulator than another
+ 
+
+ align:start position:0%
+calibrated solar simulator than another
+what we're going to do now is dive into
+
+ align:start position:0%
+what we're going to do now is dive into
+ 
+
+ align:start position:0%
+what we're going to do now is dive into
+uh some of the common factors that cause
+
+ align:start position:0%
+uh some of the common factors that cause
+ 
+
+ align:start position:0%
+uh some of the common factors that cause
+solar cell IV curves to deviate from
+
+ align:start position:0%
+solar cell IV curves to deviate from
+ 
+
+ align:start position:0%
+solar cell IV curves to deviate from
+normal ideal diode model we're going to
+
+ align:start position:0%
+normal ideal diode model we're going to
+ 
+
+ align:start position:0%
+normal ideal diode model we're going to
+talk about shun and series resistance uh
+
+ align:start position:0%
+talk about shun and series resistance uh
+ 
+
+ align:start position:0%
+talk about shun and series resistance uh
+recombination currents um maybe we'll
+
+ align:start position:0%
+recombination currents um maybe we'll
+ 
+
+ align:start position:0%
+recombination currents um maybe we'll
+get to current crowding some other
+
+ align:start position:0%
+get to current crowding some other
+ 
+
+ align:start position:0%
+get to current crowding some other
+effects uh basically what we're doing
+
+ align:start position:0%
+effects uh basically what we're doing
+ 
+
+ align:start position:0%
+effects uh basically what we're doing
+now in number two is we're beginning to
+
+ align:start position:0%
+now in number two is we're beginning to
+ 
+
+ align:start position:0%
+now in number two is we're beginning to
+say okay now that we understand an ideal
+
+ align:start position:0%
+say okay now that we understand an ideal
+ 
+
+ align:start position:0%
+say okay now that we understand an ideal
+di now that we have an ideal picture of
+
+ align:start position:0%
+di now that we have an ideal picture of
+ 
+
+ align:start position:0%
+di now that we have an ideal picture of
+how our solar cell works let's bring it
+
+ align:start position:0%
+how our solar cell works let's bring it
+ 
+
+ align:start position:0%
+how our solar cell works let's bring it
+down to real life and talk about all the
+
+ align:start position:0%
+down to real life and talk about all the
+ 
+
+ align:start position:0%
+down to real life and talk about all the
+things that can go wrong because when
+
+ align:start position:0%
+things that can go wrong because when
+ 
+
+ align:start position:0%
+things that can go wrong because when
+you try to make a solar cell in the lab
+
+ align:start position:0%
+you try to make a solar cell in the lab
+ 
+
+ align:start position:0%
+you try to make a solar cell in the lab
+these are the things that are going to
+
+ align:start position:0%
+these are the things that are going to
+ 
+
+ align:start position:0%
+these are the things that are going to
+start um nipping at your heels so to
+
+ align:start position:0%
+start um nipping at your heels so to
+ 
+
+ align:start position:0%
+start um nipping at your heels so to
+speak so we'll start out with an
+
+ align:start position:0%
+speak so we'll start out with an
+ 
+
+ align:start position:0%
+speak so we'll start out with an
+equivalent circuit diagram of a solar
+
+ align:start position:0%
+equivalent circuit diagram of a solar
+ 
+
+ align:start position:0%
+equivalent circuit diagram of a solar
+cell device and this might be new to
+
+ align:start position:0%
+cell device and this might be new to
+ 
+
+ align:start position:0%
+cell device and this might be new to
+some folks um but it's it's all stuff
+
+ align:start position:0%
+some folks um but it's it's all stuff
+ 
+
+ align:start position:0%
+some folks um but it's it's all stuff
+you've seen so far what we have over
+
+ align:start position:0%
+you've seen so far what we have over
+ 
+
+ align:start position:0%
+you've seen so far what we have over
+here is the current generation source of
+
+ align:start position:0%
+here is the current generation source of
+ 
+
+ align:start position:0%
+here is the current generation source of
+the it's the solar cell operating under
+
+ align:start position:0%
+the it's the solar cell operating under
+ 
+
+ align:start position:0%
+the it's the solar cell operating under
+forward bias conditions under
+
+ align:start position:0%
+forward bias conditions under
+ 
+
+ align:start position:0%
+forward bias conditions under
+illumination generating a voltage in a
+
+ align:start position:0%
+illumination generating a voltage in a
+ 
+
+ align:start position:0%
+illumination generating a voltage in a
+current we have a diode here that
+
+ align:start position:0%
+current we have a diode here that
+ 
+
+ align:start position:0%
+current we have a diode here that
+prevents the backflow of current and
+
+ align:start position:0%
+prevents the backflow of current and
+ 
+
+ align:start position:0%
+prevents the backflow of current and
+forces the current to go out through the
+
+ align:start position:0%
+forces the current to go out through the
+ 
+
+ align:start position:0%
+forces the current to go out through the
+external circuit Loop right and it
+
+ align:start position:0%
+external circuit Loop right and it
+ 
+
+ align:start position:0%
+external circuit Loop right and it
+forces it to drive the external load
+
+ align:start position:0%
+forces it to drive the external load
+ 
+
+ align:start position:0%
+forces it to drive the external load
+which would be attached to that little
+
+ align:start position:0%
+which would be attached to that little
+ 
+
+ align:start position:0%
+which would be attached to that little
+circle over there and that other little
+
+ align:start position:0%
+circle over there and that other little
+ 
+
+ align:start position:0%
+circle over there and that other little
+circle over there so you can imagine an
+
+ align:start position:0%
+circle over there so you can imagine an
+ 
+
+ align:start position:0%
+circle over there so you can imagine an
+external circuit attaching itself right
+
+ align:start position:0%
+external circuit attaching itself right
+ 
+
+ align:start position:0%
+external circuit attaching itself right
+there so uh the diode if the diode
+
+ align:start position:0%
+there so uh the diode if the diode
+ 
+
+ align:start position:0%
+there so uh the diode if the diode
+quality is high if it's good it will
+
+ align:start position:0%
+quality is high if it's good it will
+ 
+
+ align:start position:0%
+quality is high if it's good it will
+prevent the backflow of current if the
+
+ align:start position:0%
+prevent the backflow of current if the
+ 
+
+ align:start position:0%
+prevent the backflow of current if the
+diode quality is poor uh you will have
+
+ align:start position:0%
+diode quality is poor uh you will have
+ 
+
+ align:start position:0%
+diode quality is poor uh you will have
+so-called leakage current current
+
+ align:start position:0%
+so-called leakage current current
+ 
+
+ align:start position:0%
+so-called leakage current current
+leaking into the diode uh back if you
+
+ align:start position:0%
+leaking into the diode uh back if you
+ 
+
+ align:start position:0%
+leaking into the diode uh back if you
+want to think about it in forward bias
+
+ align:start position:0%
+want to think about it in forward bias
+ 
+
+ align:start position:0%
+want to think about it in forward bias
+conditions here's your solar cell
+
+ align:start position:0%
+conditions here's your solar cell
+ 
+
+ align:start position:0%
+conditions here's your solar cell
+forward bias you have light electrons
+
+ align:start position:0%
+forward bias you have light electrons
+ 
+
+ align:start position:0%
+forward bias you have light electrons
+coming in separated by the electron by
+
+ align:start position:0%
+coming in separated by the electron by
+ 
+
+ align:start position:0%
+coming in separated by the electron by
+the electric field instead of powering
+
+ align:start position:0%
+the electric field instead of powering
+ 
+
+ align:start position:0%
+the electric field instead of powering
+the external load and coming back into
+
+ align:start position:0%
+the external load and coming back into
+ 
+
+ align:start position:0%
+the external load and coming back into
+the device through the back leakage
+
+ align:start position:0%
+the device through the back leakage
+ 
+
+ align:start position:0%
+the device through the back leakage
+current would be the electrons going
+
+ align:start position:0%
+current would be the electrons going
+ 
+
+ align:start position:0%
+current would be the electrons going
+back up the barrier right going back
+
+ align:start position:0%
+back up the barrier right going back
+ 
+
+ align:start position:0%
+back up the barrier right going back
+into the base of the device uh the
+
+ align:start position:0%
+into the base of the device uh the
+ 
+
+ align:start position:0%
+into the base of the device uh the
+so-called diffusion current so this is
+
+ align:start position:0%
+so-called diffusion current so this is
+ 
+
+ align:start position:0%
+so-called diffusion current so this is
+that diode right here representing the
+
+ align:start position:0%
+that diode right here representing the
+ 
+
+ align:start position:0%
+that diode right here representing the
+diffusion current or the uh the in that
+
+ align:start position:0%
+diffusion current or the uh the in that
+ 
+
+ align:start position:0%
+diffusion current or the uh the in that
+particular case inal uh the equivalent
+
+ align:start position:0%
+particular case inal uh the equivalent
+ 
+
+ align:start position:0%
+particular case inal uh the equivalent
+circuit diagram this is representing the
+
+ align:start position:0%
+circuit diagram this is representing the
+ 
+
+ align:start position:0%
+circuit diagram this is representing the
+resistance to diffusion if you will so
+
+ align:start position:0%
+resistance to diffusion if you will so
+ 
+
+ align:start position:0%
+resistance to diffusion if you will so
+we have this uh voltage and and current
+
+ align:start position:0%
+we have this uh voltage and and current
+ 
+
+ align:start position:0%
+we have this uh voltage and and current
+being generated by the solar cell and
+
+ align:start position:0%
+being generated by the solar cell and
+ 
+
+ align:start position:0%
+being generated by the solar cell and
+that would be described by the ideal
+
+ align:start position:0%
+that would be described by the ideal
+ 
+
+ align:start position:0%
+that would be described by the ideal
+diode equation my apologies there should
+
+ align:start position:0%
+diode equation my apologies there should
+ 
+
+ align:start position:0%
+diode equation my apologies there should
+be actually X of this minus one right
+
+ align:start position:0%
+be actually X of this minus one right
+ 
+
+ align:start position:0%
+be actually X of this minus one right
+there we should take note of that and
+
+ align:start position:0%
+there we should take note of that and
+ 
+
+ align:start position:0%
+there we should take note of that and
+corrected I just happen to notice that
+
+ align:start position:0%
+corrected I just happen to notice that
+ 
+
+ align:start position:0%
+corrected I just happen to notice that
+um okay so the ideal diode equation is
+
+ align:start position:0%
+um okay so the ideal diode equation is
+ 
+
+ align:start position:0%
+um okay so the ideal diode equation is
+right here and uh this is the current
+
+ align:start position:0%
+right here and uh this is the current
+ 
+
+ align:start position:0%
+right here and uh this is the current
+density versus voltage so we have uh in
+
+ align:start position:0%
+density versus voltage so we have uh in
+ 
+
+ align:start position:0%
+density versus voltage so we have uh in
+uh uh linear log scale or or or or axis
+
+ align:start position:0%
+uh uh linear log scale or or or or axis
+ 
+
+ align:start position:0%
+uh uh linear log scale or or or or axis
+we have a straight line uh that would on
+
+ align:start position:0%
+we have a straight line uh that would on
+ 
+
+ align:start position:0%
+we have a straight line uh that would on
+a linear linear scale we would have an
+
+ align:start position:0%
+a linear linear scale we would have an
+ 
+
+ align:start position:0%
+a linear linear scale we would have an
+exponential curve right so an
+
+ align:start position:0%
+exponential curve right so an
+ 
+
+ align:start position:0%
+exponential curve right so an
+exponential function exponential curve
+
+ align:start position:0%
+exponential function exponential curve
+ 
+
+ align:start position:0%
+exponential function exponential curve
+up here and a straight line in linear
+
+ align:start position:0%
+up here and a straight line in linear
+ 
+
+ align:start position:0%
+up here and a straight line in linear
+log uh scale I'm trying to sensitize you
+
+ align:start position:0%
+log uh scale I'm trying to sensitize you
+ 
+
+ align:start position:0%
+log uh scale I'm trying to sensitize you
+to the two ways of looking at this both
+
+ align:start position:0%
+to the two ways of looking at this both
+ 
+
+ align:start position:0%
+to the two ways of looking at this both
+uh a linear scale and a log scale of
+
+ align:start position:0%
+uh a linear scale and a log scale of
+ 
+
+ align:start position:0%
+uh a linear scale and a log scale of
+current in the y- AIS because both will
+
+ align:start position:0%
+current in the y- AIS because both will
+ 
+
+ align:start position:0%
+current in the y- AIS because both will
+tell us something from the linear scale
+
+ align:start position:0%
+tell us something from the linear scale
+ 
+
+ align:start position:0%
+tell us something from the linear scale
+up here on the upper right it will be
+
+ align:start position:0%
+up here on the upper right it will be
+ 
+
+ align:start position:0%
+up here on the upper right it will be
+very easy for us to see the fill Factor
+
+ align:start position:0%
+very easy for us to see the fill Factor
+ 
+
+ align:start position:0%
+very easy for us to see the fill Factor
+we can just glance at that curve and see
+
+ align:start position:0%
+we can just glance at that curve and see
+ 
+
+ align:start position:0%
+we can just glance at that curve and see
+oh it looks really box-like it must have
+
+ align:start position:0%
+oh it looks really box-like it must have
+ 
+
+ align:start position:0%
+oh it looks really box-like it must have
+a large fill factor from this curve down
+
+ align:start position:0%
+a large fill factor from this curve down
+ 
+
+ align:start position:0%
+a large fill factor from this curve down
+here we can begin to see deviations from
+
+ align:start position:0%
+here we can begin to see deviations from
+ 
+
+ align:start position:0%
+here we can begin to see deviations from
+ideality if anything causes this curve
+
+ align:start position:0%
+ideality if anything causes this curve
+ 
+
+ align:start position:0%
+ideality if anything causes this curve
+to bend up or down either down here or
+
+ align:start position:0%
+to bend up or down either down here or
+ 
+
+ align:start position:0%
+to bend up or down either down here or
+up here we're going to see it really
+
+ align:start position:0%
+up here we're going to see it really
+ 
+
+ align:start position:0%
+up here we're going to see it really
+quick on the linear on the log scale and
+
+ align:start position:0%
+quick on the linear on the log scale and
+ 
+
+ align:start position:0%
+quick on the linear on the log scale and
+that's why looking at the IV curve in
+
+ align:start position:0%
+that's why looking at the IV curve in
+ 
+
+ align:start position:0%
+that's why looking at the IV curve in
+both ways is helpful it's uh a method of
+
+ align:start position:0%
+both ways is helpful it's uh a method of
+ 
+
+ align:start position:0%
+both ways is helpful it's uh a method of
+diagnosing the problem
+
+ align:start position:0%
+diagnosing the problem
+ 
+
+ align:start position:0%
+diagnosing the problem
+quickly so what we're going to do now is
+
+ align:start position:0%
+quickly so what we're going to do now is
+ 
+
+ align:start position:0%
+quickly so what we're going to do now is
+to take our equivalent circuit and begin
+
+ align:start position:0%
+to take our equivalent circuit and begin
+ 
+
+ align:start position:0%
+to take our equivalent circuit and begin
+adding a few things to it that represent
+
+ align:start position:0%
+adding a few things to it that represent
+ 
+
+ align:start position:0%
+adding a few things to it that represent
+realistic uh effects that we might see
+
+ align:start position:0%
+realistic uh effects that we might see
+ 
+
+ align:start position:0%
+realistic uh effects that we might see
+in in a real device so the first thing
+
+ align:start position:0%
+in in a real device so the first thing
+ 
+
+ align:start position:0%
+in in a real device so the first thing
+that we might do is say well listen a
+
+ align:start position:0%
+that we might do is say well listen a
+ 
+
+ align:start position:0%
+that we might do is say well listen a
+real device has a finite series
+
+ align:start position:0%
+real device has a finite series
+ 
+
+ align:start position:0%
+real device has a finite series
+resistance and that can come from a
+
+ align:start position:0%
+resistance and that can come from a
+ 
+
+ align:start position:0%
+resistance and that can come from a
+variety of sources we'll talk about
+
+ align:start position:0%
+variety of sources we'll talk about
+ 
+
+ align:start position:0%
+variety of sources we'll talk about
+those in a few minutes but we might add
+
+ align:start position:0%
+those in a few minutes but we might add
+ 
+
+ align:start position:0%
+those in a few minutes but we might add
+a series resistance component right up
+
+ align:start position:0%
+a series resistance component right up
+ 
+
+ align:start position:0%
+a series resistance component right up
+there so let's look back I'm going to
+
+ align:start position:0%
+there so let's look back I'm going to
+ 
+
+ align:start position:0%
+there so let's look back I'm going to
+flip back and forth between the two
+
+ align:start position:0%
+flip back and forth between the two
+ 
+
+ align:start position:0%
+flip back and forth between the two
+slides just so folks can really see what
+
+ align:start position:0%
+slides just so folks can really see what
+ 
+
+ align:start position:0%
+slides just so folks can really see what
+the difference is this was the ideal
+
+ align:start position:0%
+the difference is this was the ideal
+ 
+
+ align:start position:0%
+the difference is this was the ideal
+case that's the with series resistance
+
+ align:start position:0%
+case that's the with series resistance
+ 
+
+ align:start position:0%
+case that's the with series resistance
+again ideal with series resistance up
+
+ align:start position:0%
+again ideal with series resistance up
+ 
+
+ align:start position:0%
+again ideal with series resistance up
+there in the equivalent circuit great so
+
+ align:start position:0%
+there in the equivalent circuit great so
+ 
+
+ align:start position:0%
+there in the equivalent circuit great so
+what have we done well we've added a
+
+ align:start position:0%
+what have we done well we've added a
+ 
+
+ align:start position:0%
+what have we done well we've added a
+series resistance component which is
+
+ align:start position:0%
+series resistance component which is
+ 
+
+ align:start position:0%
+series resistance component which is
+essentially dropping the voltage output
+
+ align:start position:0%
+essentially dropping the voltage output
+ 
+
+ align:start position:0%
+essentially dropping the voltage output
+of our solar cell and notice what else
+
+ align:start position:0%
+of our solar cell and notice what else
+ 
+
+ align:start position:0%
+of our solar cell and notice what else
+happened now we have a nonlinear
+
+ align:start position:0%
+happened now we have a nonlinear
+ 
+
+ align:start position:0%
+happened now we have a nonlinear
+equation our current density is a
+
+ align:start position:0%
+equation our current density is a
+ 
+
+ align:start position:0%
+equation our current density is a
+function of our current
+
+ align:start position:0%
+function of our current
+ 
+
+ align:start position:0%
+function of our current
+density right so this is becoming more
+
+ align:start position:0%
+density right so this is becoming more
+ 
+
+ align:start position:0%
+density right so this is becoming more
+difficult to uh uh uh to solve um
+
+ align:start position:0%
+difficult to uh uh uh to solve um
+ 
+
+ align:start position:0%
+difficult to uh uh uh to solve um
+analytically uh and what is happening to
+
+ align:start position:0%
+analytically uh and what is happening to
+ 
+
+ align:start position:0%
+analytically uh and what is happening to
+RV characteristics well let's uh look uh
+
+ align:start position:0%
+RV characteristics well let's uh look uh
+ 
+
+ align:start position:0%
+RV characteristics well let's uh look uh
+we'll go back once again to our ideal
+
+ align:start position:0%
+we'll go back once again to our ideal
+ 
+
+ align:start position:0%
+we'll go back once again to our ideal
+diod equation right here we have a very
+
+ align:start position:0%
+diod equation right here we have a very
+ 
+
+ align:start position:0%
+diod equation right here we have a very
+sharp box- like IV curve under the ideal
+
+ align:start position:0%
+sharp box- like IV curve under the ideal
+ 
+
+ align:start position:0%
+sharp box- like IV curve under the ideal
+conditions now when we introduced the
+
+ align:start position:0%
+conditions now when we introduced the
+ 
+
+ align:start position:0%
+conditions now when we introduced the
+series resistance component we begun
+
+ align:start position:0%
+series resistance component we begun
+ 
+
+ align:start position:0%
+series resistance component we begun
+smoothing out that IV curve the fill
+
+ align:start position:0%
+smoothing out that IV curve the fill
+ 
+
+ align:start position:0%
+smoothing out that IV curve the fill
+Factor has dropped take a look ideal
+
+ align:start position:0%
+Factor has dropped take a look ideal
+ 
+
+ align:start position:0%
+Factor has dropped take a look ideal
+conditions sharp very large fill Factor
+
+ align:start position:0%
+conditions sharp very large fill Factor
+ 
+
+ align:start position:0%
+conditions sharp very large fill Factor
+now we've added the series resistance
+
+ align:start position:0%
+now we've added the series resistance
+ 
+
+ align:start position:0%
+now we've added the series resistance
+component The Fill Factor has begun
+
+ align:start position:0%
+component The Fill Factor has begun
+ 
+
+ align:start position:0%
+component The Fill Factor has begun
+dropping if we look at it in log scale
+
+ align:start position:0%
+dropping if we look at it in log scale
+ 
+
+ align:start position:0%
+dropping if we look at it in log scale
+it's very easy to detect that series
+
+ align:start position:0%
+it's very easy to detect that series
+ 
+
+ align:start position:0%
+it's very easy to detect that series
+resistance we can see it right here this
+
+ align:start position:0%
+resistance we can see it right here this
+ 
+
+ align:start position:0%
+resistance we can see it right here this
+used to be our curve right so again this
+
+ align:start position:0%
+used to be our curve right so again this
+ 
+
+ align:start position:0%
+used to be our curve right so again this
+was the ideal case straight line again
+
+ align:start position:0%
+was the ideal case straight line again
+ 
+
+ align:start position:0%
+was the ideal case straight line again
+again this is log of current versus
+
+ align:start position:0%
+again this is log of current versus
+ 
+
+ align:start position:0%
+again this is log of current versus
+linear voltage so the x- axis of the two
+
+ align:start position:0%
+linear voltage so the x- axis of the two
+ 
+
+ align:start position:0%
+linear voltage so the x- axis of the two
+plots here are the same I'm only
+
+ align:start position:0%
+plots here are the same I'm only
+ 
+
+ align:start position:0%
+plots here are the same I'm only
+changing the y- axis from linear scale
+
+ align:start position:0%
+changing the y- axis from linear scale
+ 
+
+ align:start position:0%
+changing the y- axis from linear scale
+up there to log scale down here and
+
+ align:start position:0%
+up there to log scale down here and
+ 
+
+ align:start position:0%
+up there to log scale down here and
+notice what happens if I add the series
+
+ align:start position:0%
+notice what happens if I add the series
+ 
+
+ align:start position:0%
+notice what happens if I add the series
+resistance component now I begin
+
+ align:start position:0%
+resistance component now I begin
+ 
+
+ align:start position:0%
+resistance component now I begin
+dropping
+
+ align:start position:0%
+dropping
+ 
+
+ align:start position:0%
+dropping
+off so this is a Telltale sign when you
+
+ align:start position:0%
+off so this is a Telltale sign when you
+ 
+
+ align:start position:0%
+off so this is a Telltale sign when you
+take an IV curve and you see that that
+
+ align:start position:0%
+take an IV curve and you see that that
+ 
+
+ align:start position:0%
+take an IV curve and you see that that
+you know you have some series resistance
+
+ align:start position:0%
+you know you have some series resistance
+ 
+
+ align:start position:0%
+you know you have some series resistance
+effect inside of your external circuit
+
+ align:start position:0%
+effect inside of your external circuit
+ 
+
+ align:start position:0%
+effect inside of your external circuit
+or your solar cell from combination of
+
+ align:start position:0%
+or your solar cell from combination of
+ 
+
+ align:start position:0%
+or your solar cell from combination of
+of the two yes Ashley so the this curve
+
+ align:start position:0%
+of the two yes Ashley so the this curve
+ 
+
+ align:start position:0%
+of the two yes Ashley so the this curve
+it looks like the Ser resistance really
+
+ align:start position:0%
+it looks like the Ser resistance really
+ 
+
+ align:start position:0%
+it looks like the Ser resistance really
+only starts to have an effect once you
+
+ align:start position:0%
+only starts to have an effect once you
+ 
+
+ align:start position:0%
+only starts to have an effect once you
+have a higher voltage absolutely and
+
+ align:start position:0%
+have a higher voltage absolutely and
+ 
+
+ align:start position:0%
+have a higher voltage absolutely and
+that you can begin to see directly from
+
+ align:start position:0%
+that you can begin to see directly from
+ 
+
+ align:start position:0%
+that you can begin to see directly from
+the equation right here as well uh take
+
+ align:start position:0%
+the equation right here as well uh take
+ 
+
+ align:start position:0%
+the equation right here as well uh take
+the limit of of low voltage and the
+
+ align:start position:0%
+the limit of of low voltage and the
+ 
+
+ align:start position:0%
+the limit of of low voltage and the
+limit of high voltage or another way to
+
+ align:start position:0%
+limit of high voltage or another way to
+ 
+
+ align:start position:0%
+limit of high voltage or another way to
+put it would be the high current really
+
+ align:start position:0%
+put it would be the high current really
+ 
+
+ align:start position:0%
+put it would be the high current really
+um and and that uh the high current to
+
+ align:start position:0%
+um and and that uh the high current to
+ 
+
+ align:start position:0%
+um and and that uh the high current to
+voltage ratio only begins to take on up
+
+ align:start position:0%
+voltage ratio only begins to take on up
+ 
+
+ align:start position:0%
+voltage ratio only begins to take on up
+at higher voltages because of the
+
+ align:start position:0%
+at higher voltages because of the
+ 
+
+ align:start position:0%
+at higher voltages because of the
+exponential function of that
+
+ align:start position:0%
+exponential function of that
+ 
+
+ align:start position:0%
+exponential function of that
+curve so that's a very very important
+
+ align:start position:0%
+curve so that's a very very important
+ 
+
+ align:start position:0%
+curve so that's a very very important
+and astute observation that the series
+
+ align:start position:0%
+and astute observation that the series
+ 
+
+ align:start position:0%
+and astute observation that the series
+resistance begins to kill you at High
+
+ align:start position:0%
+resistance begins to kill you at High
+ 
+
+ align:start position:0%
+resistance begins to kill you at High
+forward bias voltage conditions you hope
+
+ align:start position:0%
+forward bias voltage conditions you hope
+ 
+
+ align:start position:0%
+forward bias voltage conditions you hope
+that you design your solar cell in such
+
+ align:start position:0%
+that you design your solar cell in such
+ 
+
+ align:start position:0%
+that you design your solar cell in such
+a way that the series resistance only
+
+ align:start position:0%
+a way that the series resistance only
+ 
+
+ align:start position:0%
+a way that the series resistance only
+really begins to kick in above the
+
+ align:start position:0%
+really begins to kick in above the
+ 
+
+ align:start position:0%
+really begins to kick in above the
+maximum PowerPoint
+
+ align:start position:0%
+maximum PowerPoint
+ 
+
+ align:start position:0%
+maximum PowerPoint
+voltage that's the goal and this is this
+
+ align:start position:0%
+voltage that's the goal and this is this
+ 
+
+ align:start position:0%
+voltage that's the goal and this is this
+is not voltage out this is voltage
+
+ align:start position:0%
+is not voltage out this is voltage
+ 
+
+ align:start position:0%
+is not voltage out this is voltage
+applied to the battery uh no this is
+
+ align:start position:0%
+applied to the battery uh no this is
+ 
+
+ align:start position:0%
+applied to the battery uh no this is
+this is the voltage uh that is is is
+
+ align:start position:0%
+this is the voltage uh that is is is
+ 
+
+ align:start position:0%
+this is the voltage uh that is is is
+being measured across the solar cell
+
+ align:start position:0%
+being measured across the solar cell
+ 
+
+ align:start position:0%
+being measured across the solar cell
+outut the output voltage yeah mhm or the
+
+ align:start position:0%
+outut the output voltage yeah mhm or the
+ 
+
+ align:start position:0%
+outut the output voltage yeah mhm or the
+yes the the the um
+
+ align:start position:0%
+yes the the the um
+ 
+
+ align:start position:0%
+yes the the the um
+you can think of this as as the uh the
+
+ align:start position:0%
+you can think of this as as the uh the
+ 
+
+ align:start position:0%
+you can think of this as as the uh the
+biasing condition of your solar cell
+
+ align:start position:0%
+biasing condition of your solar cell
+ 
+
+ align:start position:0%
+biasing condition of your solar cell
+device the two are almost equivalent the
+
+ align:start position:0%
+device the two are almost equivalent the
+ 
+
+ align:start position:0%
+device the two are almost equivalent the
+only difference is you have that series
+
+ align:start position:0%
+only difference is you have that series
+ 
+
+ align:start position:0%
+only difference is you have that series
+resistance in series there so you have
+
+ align:start position:0%
+resistance in series there so you have
+ 
+
+ align:start position:0%
+resistance in series there so you have
+to be careful whether you're talking
+
+ align:start position:0%
+to be careful whether you're talking
+ 
+
+ align:start position:0%
+to be careful whether you're talking
+about the uh voltage here at the solar
+
+ align:start position:0%
+about the uh voltage here at the solar
+ 
+
+ align:start position:0%
+about the uh voltage here at the solar
+cell itself across a junction uh or the
+
+ align:start position:0%
+cell itself across a junction uh or the
+ 
+
+ align:start position:0%
+cell itself across a junction uh or the
+voltage coming out of your device uh
+
+ align:start position:0%
+voltage coming out of your device uh
+ 
+
+ align:start position:0%
+voltage coming out of your device uh
+that is affected by that series
+
+ align:start position:0%
+that is affected by that series
+ 
+
+ align:start position:0%
+that is affected by that series
+resistance as
+
+ align:start position:0%
+resistance as
+ 
+
+ align:start position:0%
+resistance as
+well so think of it as uh doing that IV
+
+ align:start position:0%
+well so think of it as uh doing that IV
+ 
+
+ align:start position:0%
+well so think of it as uh doing that IV
+sweep that we did in class the other day
+
+ align:start position:0%
+sweep that we did in class the other day
+ 
+
+ align:start position:0%
+sweep that we did in class the other day
+right so you're taking the IV sweep of
+
+ align:start position:0%
+right so you're taking the IV sweep of
+ 
+
+ align:start position:0%
+right so you're taking the IV sweep of
+your device and you're seeing the impact
+
+ align:start position:0%
+your device and you're seeing the impact
+ 
+
+ align:start position:0%
+your device and you're seeing the impact
+of the series resistance in the output
+
+ align:start position:0%
+of the series resistance in the output
+ 
+
+ align:start position:0%
+of the series resistance in the output
+voltage that you're measuring of your
+
+ align:start position:0%
+voltage that you're measuring of your
+ 
+
+ align:start position:0%
+voltage that you're measuring of your
+solar cell device just like we did in
+
+ align:start position:0%
+solar cell device just like we did in
+ 
+
+ align:start position:0%
+solar cell device just like we did in
+class so again uh series resistance will
+
+ align:start position:0%
+class so again uh series resistance will
+ 
+
+ align:start position:0%
+class so again uh series resistance will
+affect you at some point it is almost
+
+ align:start position:0%
+affect you at some point it is almost
+ 
+
+ align:start position:0%
+affect you at some point it is almost
+inevitable but you have to design your
+
+ align:start position:0%
+inevitable but you have to design your
+ 
+
+ align:start position:0%
+inevitable but you have to design your
+solar cell such that it affects you only
+
+ align:start position:0%
+solar cell such that it affects you only
+ 
+
+ align:start position:0%
+solar cell such that it affects you only
+after the maximum power
+
+ align:start position:0%
+after the maximum power
+ 
+
+ align:start position:0%
+after the maximum power
+point likewise we're going to introduce
+
+ align:start position:0%
+point likewise we're going to introduce
+ 
+
+ align:start position:0%
+point likewise we're going to introduce
+another resistance term inside of our
+
+ align:start position:0%
+another resistance term inside of our
+ 
+
+ align:start position:0%
+another resistance term inside of our
+equivalent circuit diagram what we call
+
+ align:start position:0%
+equivalent circuit diagram what we call
+ 
+
+ align:start position:0%
+equivalent circuit diagram what we call
+a shunt resistance let me back up one
+
+ align:start position:0%
+a shunt resistance let me back up one
+ 
+
+ align:start position:0%
+a shunt resistance let me back up one
+step here this was just with series
+
+ align:start position:0%
+step here this was just with series
+ 
+
+ align:start position:0%
+step here this was just with series
+resistance now I've added a shunt
+
+ align:start position:0%
+resistance now I've added a shunt
+ 
+
+ align:start position:0%
+resistance now I've added a shunt
+resistance term here as well
+
+ align:start position:0%
+resistance term here as well
+ 
+
+ align:start position:0%
+resistance term here as well
+and whereas we wanted our our series
+
+ align:start position:0%
+and whereas we wanted our our series
+ 
+
+ align:start position:0%
+and whereas we wanted our our series
+resistance to be small right the smaller
+
+ align:start position:0%
+resistance to be small right the smaller
+ 
+
+ align:start position:0%
+resistance to be small right the smaller
+our series resistance the smaller our
+
+ align:start position:0%
+our series resistance the smaller our
+ 
+
+ align:start position:0%
+our series resistance the smaller our
+series resistance the less this effect
+
+ align:start position:0%
+series resistance the less this effect
+ 
+
+ align:start position:0%
+series resistance the less this effect
+would be the more ideal this curve would
+
+ align:start position:0%
+would be the more ideal this curve would
+ 
+
+ align:start position:0%
+would be the more ideal this curve would
+be we want our shunt resistance to be
+
+ align:start position:0%
+be we want our shunt resistance to be
+ 
+
+ align:start position:0%
+be we want our shunt resistance to be
+large because we want to prevent the
+
+ align:start position:0%
+large because we want to prevent the
+ 
+
+ align:start position:0%
+large because we want to prevent the
+current from flowing inside of the
+
+ align:start position:0%
+current from flowing inside of the
+ 
+
+ align:start position:0%
+current from flowing inside of the
+device and back to uh back to the the
+
+ align:start position:0%
+device and back to uh back to the the
+ 
+
+ align:start position:0%
+device and back to uh back to the the
+base instead we want the current to flow
+
+ align:start position:0%
+base instead we want the current to flow
+ 
+
+ align:start position:0%
+base instead we want the current to flow
+through the external circuit so we want
+
+ align:start position:0%
+through the external circuit so we want
+ 
+
+ align:start position:0%
+through the external circuit so we want
+the shunt resistance to be large in
+
+ align:start position:0%
+the shunt resistance to be large in
+ 
+
+ align:start position:0%
+the shunt resistance to be large in
+other words we don't want our solar cell
+
+ align:start position:0%
+other words we don't want our solar cell
+ 
+
+ align:start position:0%
+other words we don't want our solar cell
+device to be full of shunts that's
+
+ align:start position:0%
+device to be full of shunts that's
+ 
+
+ align:start position:0%
+device to be full of shunts that's
+pretty obvious okay so what does shunt
+
+ align:start position:0%
+pretty obvious okay so what does shunt
+ 
+
+ align:start position:0%
+pretty obvious okay so what does shunt
+resistance do to you well if we compare
+
+ align:start position:0%
+resistance do to you well if we compare
+ 
+
+ align:start position:0%
+resistance do to you well if we compare
+the IV curves once again uh between the
+
+ align:start position:0%
+the IV curves once again uh between the
+ 
+
+ align:start position:0%
+the IV curves once again uh between the
+solar cell just with the series
+
+ align:start position:0%
+solar cell just with the series
+ 
+
+ align:start position:0%
+solar cell just with the series
+resistance we had a very uh low uh uh
+
+ align:start position:0%
+resistance we had a very uh low uh uh
+ 
+
+ align:start position:0%
+resistance we had a very uh low uh uh
+forward current here under under low
+
+ align:start position:0%
+forward current here under under low
+ 
+
+ align:start position:0%
+forward current here under under low
+forward bias conditions if we have a a
+
+ align:start position:0%
+forward bias conditions if we have a a
+ 
+
+ align:start position:0%
+forward bias conditions if we have a a
+very poor shunt uh if we have a plethora
+
+ align:start position:0%
+very poor shunt uh if we have a plethora
+ 
+
+ align:start position:0%
+very poor shunt uh if we have a plethora
+of shunt Pathways in our device we're
+
+ align:start position:0%
+of shunt Pathways in our device we're
+ 
+
+ align:start position:0%
+of shunt Pathways in our device we're
+going to get current flowing through our
+
+ align:start position:0%
+going to get current flowing through our
+ 
+
+ align:start position:0%
+going to get current flowing through our
+device even at low uh bias conditions
+
+ align:start position:0%
+device even at low uh bias conditions
+ 
+
+ align:start position:0%
+device even at low uh bias conditions
+that's because the p injunction is weak
+
+ align:start position:0%
+that's because the p injunction is weak
+ 
+
+ align:start position:0%
+that's because the p injunction is weak
+and even though we have a very large
+
+ align:start position:0%
+and even though we have a very large
+ 
+
+ align:start position:0%
+and even though we have a very large
+field in there there are some regions
+
+ align:start position:0%
+field in there there are some regions
+ 
+
+ align:start position:0%
+field in there there are some regions
+where the field is much smaller because
+
+ align:start position:0%
+where the field is much smaller because
+ 
+
+ align:start position:0%
+where the field is much smaller because
+of the shunt pathway and current is
+
+ align:start position:0%
+of the shunt pathway and current is
+ 
+
+ align:start position:0%
+of the shunt pathway and current is
+going to be flowing through there
+
+ align:start position:0%
+going to be flowing through there
+ 
+
+ align:start position:0%
+going to be flowing through there
+diffusion current will be flowing
+
+ align:start position:0%
+diffusion current will be flowing
+ 
+
+ align:start position:0%
+diffusion current will be flowing
+through that shunt pathway so think of
+
+ align:start position:0%
+through that shunt pathway so think of
+ 
+
+ align:start position:0%
+through that shunt pathway so think of
+this as being a very strong diode right
+
+ align:start position:0%
+this as being a very strong diode right
+ 
+
+ align:start position:0%
+this as being a very strong diode right
+in the absence of shunt resistance you
+
+ align:start position:0%
+in the absence of shunt resistance you
+ 
+
+ align:start position:0%
+in the absence of shunt resistance you
+have a very strong diode you have uh in
+
+ align:start position:0%
+have a very strong diode you have uh in
+ 
+
+ align:start position:0%
+have a very strong diode you have uh in
+your p p type region in your n and that
+
+ align:start position:0%
+your p p type region in your n and that
+ 
+
+ align:start position:0%
+your p p type region in your n and that
+large barrier is preventing the
+
+ align:start position:0%
+large barrier is preventing the
+ 
+
+ align:start position:0%
+large barrier is preventing the
+diffusion of electrons back into the
+
+ align:start position:0%
+diffusion of electrons back into the
+ 
+
+ align:start position:0%
+diffusion of electrons back into the
+device it's preventing this from rising
+
+ align:start position:0%
+device it's preventing this from rising
+ 
+
+ align:start position:0%
+device it's preventing this from rising
+keeping it low and and that can only
+
+ align:start position:0%
+keeping it low and and that can only
+ 
+
+ align:start position:0%
+keeping it low and and that can only
+happen when the p and Junction uh
+
+ align:start position:0%
+happen when the p and Junction uh
+ 
+
+ align:start position:0%
+happen when the p and Junction uh
+barrier is uniform throughout your
+
+ align:start position:0%
+barrier is uniform throughout your
+ 
+
+ align:start position:0%
+barrier is uniform throughout your
+entire device if you have one region of
+
+ align:start position:0%
+entire device if you have one region of
+ 
+
+ align:start position:0%
+entire device if you have one region of
+your device that is poor that has a
+
+ align:start position:0%
+your device that is poor that has a
+ 
+
+ align:start position:0%
+your device that is poor that has a
+shunt pathway maybe you have a piece of
+
+ align:start position:0%
+shunt pathway maybe you have a piece of
+ 
+
+ align:start position:0%
+shunt pathway maybe you have a piece of
+metal that fired through the junction
+
+ align:start position:0%
+metal that fired through the junction
+ 
+
+ align:start position:0%
+metal that fired through the junction
+and is making good omic contact to both
+
+ align:start position:0%
+and is making good omic contact to both
+ 
+
+ align:start position:0%
+and is making good omic contact to both
+sides if you have a shunt pathway now
+
+ align:start position:0%
+sides if you have a shunt pathway now
+ 
+
+ align:start position:0%
+sides if you have a shunt pathway now
+the current can flow even under small
+
+ align:start position:0%
+the current can flow even under small
+ 
+
+ align:start position:0%
+the current can flow even under small
+bias conditions the diffusion current
+
+ align:start position:0%
+bias conditions the diffusion current
+ 
+
+ align:start position:0%
+bias conditions the diffusion current
+can flow into your device and that of
+
+ align:start position:0%
+can flow into your device and that of
+ 
+
+ align:start position:0%
+can flow into your device and that of
+course uh drops on on on on the linear
+
+ align:start position:0%
+course uh drops on on on on the linear
+ 
+
+ align:start position:0%
+course uh drops on on on on the linear
+log scale right up here you hardly
+
+ align:start position:0%
+log scale right up here you hardly
+ 
+
+ align:start position:0%
+log scale right up here you hardly
+detect it notice if we go back and forth
+
+ align:start position:0%
+detect it notice if we go back and forth
+ 
+
+ align:start position:0%
+detect it notice if we go back and forth
+between with and without shunt
+
+ align:start position:0%
+between with and without shunt
+ 
+
+ align:start position:0%
+between with and without shunt
+resistance you can hardly detect it
+
+ align:start position:0%
+resistance you can hardly detect it
+ 
+
+ align:start position:0%
+resistance you can hardly detect it
+right here until you start getting to
+
+ align:start position:0%
+right here until you start getting to
+ 
+
+ align:start position:0%
+right here until you start getting to
+some really leaky diodes in which case
+
+ align:start position:0%
+some really leaky diodes in which case
+ 
+
+ align:start position:0%
+some really leaky diodes in which case
+you begin to impact your fill Factor as
+
+ align:start position:0%
+you begin to impact your fill Factor as
+ 
+
+ align:start position:0%
+you begin to impact your fill Factor as
+well so shunt resistance is is important
+
+ align:start position:0%
+well so shunt resistance is is important
+ 
+
+ align:start position:0%
+well so shunt resistance is is important
+for a solar cell device that it not be
+
+ align:start position:0%
+for a solar cell device that it not be
+ 
+
+ align:start position:0%
+for a solar cell device that it not be
+too too high um because at some point it
+
+ align:start position:0%
+too too high um because at some point it
+ 
+
+ align:start position:0%
+too too high um because at some point it
+does begin impacting your fill factor
+
+ align:start position:0%
+does begin impacting your fill factor
+ 
+
+ align:start position:0%
+does begin impacting your fill factor
+sorry the shunt resistance not be too
+
+ align:start position:0%
+sorry the shunt resistance not be too
+ 
+
+ align:start position:0%
+sorry the shunt resistance not be too
+too too low yes uh your shun resistance
+
+ align:start position:0%
+too too low yes uh your shun resistance
+ 
+
+ align:start position:0%
+too too low yes uh your shun resistance
+can't be too too low because at some
+
+ align:start position:0%
+can't be too too low because at some
+ 
+
+ align:start position:0%
+can't be too too low because at some
+point it will begin impacting your fill
+
+ align:start position:0%
+point it will begin impacting your fill
+ 
+
+ align:start position:0%
+point it will begin impacting your fill
+Factor but more importantly shunt
+
+ align:start position:0%
+Factor but more importantly shunt
+ 
+
+ align:start position:0%
+Factor but more importantly shunt
+resistance is usually indicative of some
+
+ align:start position:0%
+resistance is usually indicative of some
+ 
+
+ align:start position:0%
+resistance is usually indicative of some
+localized failure in your PN Jun it's
+
+ align:start position:0%
+localized failure in your PN Jun it's
+ 
+
+ align:start position:0%
+localized failure in your PN Jun it's
+usually not homogeneously distributed
+
+ align:start position:0%
+usually not homogeneously distributed
+ 
+
+ align:start position:0%
+usually not homogeneously distributed
+throughout the entire pan Junction maybe
+
+ align:start position:0%
+throughout the entire pan Junction maybe
+ 
+
+ align:start position:0%
+throughout the entire pan Junction maybe
+your first solar cell device you ever
+
+ align:start position:0%
+your first solar cell device you ever
+ 
+
+ align:start position:0%
+your first solar cell device you ever
+make might be affected by that but as
+
+ align:start position:0%
+make might be affected by that but as
+ 
+
+ align:start position:0%
+make might be affected by that but as
+you get better and better you'll you'll
+
+ align:start position:0%
+you get better and better you'll you'll
+ 
+
+ align:start position:0%
+you get better and better you'll you'll
+you'll start making higher quality
+
+ align:start position:0%
+you'll start making higher quality
+ 
+
+ align:start position:0%
+you'll start making higher quality
+Junctions and usually the shunt
+
+ align:start position:0%
+Junctions and usually the shunt
+ 
+
+ align:start position:0%
+Junctions and usually the shunt
+resistance is indicative of of one
+
+ align:start position:0%
+resistance is indicative of of one
+ 
+
+ align:start position:0%
+resistance is indicative of of one
+little spot and what happens at that one
+
+ align:start position:0%
+little spot and what happens at that one
+ 
+
+ align:start position:0%
+little spot and what happens at that one
+little spot well current is flowing in
+
+ align:start position:0%
+little spot well current is flowing in
+ 
+
+ align:start position:0%
+little spot well current is flowing in
+from the entire emitter region into that
+
+ align:start position:0%
+from the entire emitter region into that
+ 
+
+ align:start position:0%
+from the entire emitter region into that
+one little shunt and locally heating up
+
+ align:start position:0%
+one little shunt and locally heating up
+ 
+
+ align:start position:0%
+one little shunt and locally heating up
+your device and so that's why people
+
+ align:start position:0%
+your device and so that's why people
+ 
+
+ align:start position:0%
+your device and so that's why people
+worry about shunts in industry is
+
+ align:start position:0%
+worry about shunts in industry is
+ 
+
+ align:start position:0%
+worry about shunts in industry is
+because if you have current crowding
+
+ align:start position:0%
+because if you have current crowding
+ 
+
+ align:start position:0%
+because if you have current crowding
+into that one little spot it's heating
+
+ align:start position:0%
+into that one little spot it's heating
+ 
+
+ align:start position:0%
+into that one little spot it's heating
+up it's becoming a hot spot and it can
+
+ align:start position:0%
+up it's becoming a hot spot and it can
+ 
+
+ align:start position:0%
+up it's becoming a hot spot and it can
+even melt the encapsulate materials in
+
+ align:start position:0%
+even melt the encapsulate materials in
+ 
+
+ align:start position:0%
+even melt the encapsulate materials in
+your module perhaps even uh create a a
+
+ align:start position:0%
+your module perhaps even uh create a a
+ 
+
+ align:start position:0%
+your module perhaps even uh create a a
+fire in extreme conditions and so uh
+
+ align:start position:0%
+fire in extreme conditions and so uh
+ 
+
+ align:start position:0%
+fire in extreme conditions and so uh
+when you test the solar cell devices um
+
+ align:start position:0%
+when you test the solar cell devices um
+ 
+
+ align:start position:0%
+when you test the solar cell devices um
+typically the IV tester will throw out
+
+ align:start position:0%
+typically the IV tester will throw out
+ 
+
+ align:start position:0%
+typically the IV tester will throw out
+uh well will will measure the shunt
+
+ align:start position:0%
+uh well will will measure the shunt
+ 
+
+ align:start position:0%
+uh well will will measure the shunt
+resistance in a solar cell by looking at
+
+ align:start position:0%
+resistance in a solar cell by looking at
+ 
+
+ align:start position:0%
+resistance in a solar cell by looking at
+what's happening under very small bias
+
+ align:start position:0%
+what's happening under very small bias
+ 
+
+ align:start position:0%
+what's happening under very small bias
+conditions right here and comparing it
+
+ align:start position:0%
+conditions right here and comparing it
+ 
+
+ align:start position:0%
+conditions right here and comparing it
+against the healthy cell that it would
+
+ align:start position:0%
+against the healthy cell that it would
+ 
+
+ align:start position:0%
+against the healthy cell that it would
+expect and if it finds cells with high
+
+ align:start position:0%
+expect and if it finds cells with high
+ 
+
+ align:start position:0%
+expect and if it finds cells with high
+uh shunt leakage current in other words
+
+ align:start position:0%
+uh shunt leakage current in other words
+ 
+
+ align:start position:0%
+uh shunt leakage current in other words
+low shunt resistance it will advise the
+
+ align:start position:0%
+low shunt resistance it will advise the
+ 
+
+ align:start position:0%
+low shunt resistance it will advise the
+the the tester and sorder to throw out
+
+ align:start position:0%
+the the tester and sorder to throw out
+ 
+
+ align:start position:0%
+the the tester and sorder to throw out
+those cells and so they'll be put into
+
+ align:start position:0%
+those cells and so they'll be put into
+ 
+
+ align:start position:0%
+those cells and so they'll be put into
+the scrap
+
+ align:start position:0%
+the scrap
+ 
+
+ align:start position:0%
+the scrap
+pile and so the shunt resistance
+
+ align:start position:0%
+pile and so the shunt resistance
+ 
+
+ align:start position:0%
+pile and so the shunt resistance
+manifests itself right here in the ideal
+
+ align:start position:0%
+manifests itself right here in the ideal
+ 
+
+ align:start position:0%
+manifests itself right here in the ideal
+diode equation uh in this term right
+
+ align:start position:0%
+diode equation uh in this term right
+ 
+
+ align:start position:0%
+diode equation uh in this term right
+there so it's essentially in add- on
+
+ align:start position:0%
+there so it's essentially in add- on
+ 
+
+ align:start position:0%
+there so it's essentially in add- on
+term after your exponential uh looking
+
+ align:start position:0%
+term after your exponential uh looking
+ 
+
+ align:start position:0%
+term after your exponential uh looking
+something like this essentially at uh
+
+ align:start position:0%
+something like this essentially at uh
+ 
+
+ align:start position:0%
+something like this essentially at uh
+low bias conditions you can extrapolate
+
+ align:start position:0%
+low bias conditions you can extrapolate
+ 
+
+ align:start position:0%
+low bias conditions you can extrapolate
+this point right here determine the
+
+ align:start position:0%
+this point right here determine the
+ 
+
+ align:start position:0%
+this point right here determine the
+slope of that point and find uh the
+
+ align:start position:0%
+slope of that point and find uh the
+ 
+
+ align:start position:0%
+slope of that point and find uh the
+shunt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistance and uh likewise you'll notice
+
+ align:start position:0%
+resistance and uh likewise you'll notice
+ 
+
+ align:start position:0%
+resistance and uh likewise you'll notice
+that the shunt resistance really isn't
+
+ align:start position:0%
+that the shunt resistance really isn't
+ 
+
+ align:start position:0%
+that the shunt resistance really isn't
+impacting you up
+
+ align:start position:0%
+impacting you up
+ 
+
+ align:start position:0%
+impacting you up
+here uh the the shunt resistance really
+
+ align:start position:0%
+here uh the the shunt resistance really
+ 
+
+ align:start position:0%
+here uh the the shunt resistance really
+isn't impacting you at higher forward
+
+ align:start position:0%
+isn't impacting you at higher forward
+ 
+
+ align:start position:0%
+isn't impacting you at higher forward
+bias conditions uh that's mostly series
+
+ align:start position:0%
+bias conditions uh that's mostly series
+ 
+
+ align:start position:0%
+bias conditions uh that's mostly series
+resistance and the illumination current
+
+ align:start position:0%
+resistance and the illumination current
+ 
+
+ align:start position:0%
+resistance and the illumination current
+that's overwhelming uh any shun pathway
+
+ align:start position:0%
+that's overwhelming uh any shun pathway
+ 
+
+ align:start position:0%
+that's overwhelming uh any shun pathway
+Ashley yeah do you know for for I don't
+
+ align:start position:0%
+Ashley yeah do you know for for I don't
+ 
+
+ align:start position:0%
+Ashley yeah do you know for for I don't
+know a high quality manufacturer how
+
+ align:start position:0%
+know a high quality manufacturer how
+ 
+
+ align:start position:0%
+know a high quality manufacturer how
+what percentage of produced cells get
+
+ align:start position:0%
+what percentage of produced cells get
+ 
+
+ align:start position:0%
+what percentage of produced cells get
+tossed because of very low the uh
+
+ align:start position:0%
+tossed because of very low the uh
+ 
+
+ align:start position:0%
+tossed because of very low the uh
+manufacturing yields of um a well oiled
+
+ align:start position:0%
+manufacturing yields of um a well oiled
+ 
+
+ align:start position:0%
+manufacturing yields of um a well oiled
+manufacturing line I I say oiled in a
+
+ align:start position:0%
+manufacturing line I I say oiled in a
+ 
+
+ align:start position:0%
+manufacturing line I I say oiled in a
+figurative sense we're not typically
+
+ align:start position:0%
+figurative sense we're not typically
+ 
+
+ align:start position:0%
+figurative sense we're not typically
+yeah some of the parts I suppose use oil
+
+ align:start position:0%
+yeah some of the parts I suppose use oil
+ 
+
+ align:start position:0%
+yeah some of the parts I suppose use oil
+um we in in a well functioning
+
+ align:start position:0%
+um we in in a well functioning
+ 
+
+ align:start position:0%
+um we in in a well functioning
+manufacuring line uh the yields are
+
+ align:start position:0%
+manufacuring line uh the yields are
+ 
+
+ align:start position:0%
+manufacuring line uh the yields are
+upwards of 95% for sell fabrication so
+
+ align:start position:0%
+upwards of 95% for sell fabrication so
+ 
+
+ align:start position:0%
+upwards of 95% for sell fabrication so
+it's a very small percentage uh you
+
+ align:start position:0%
+it's a very small percentage uh you
+ 
+
+ align:start position:0%
+it's a very small percentage uh you
+typically see this when you're
+
+ align:start position:0%
+typically see this when you're
+ 
+
+ align:start position:0%
+typically see this when you're
+developing a new process and that's why
+
+ align:start position:0%
+developing a new process and that's why
+ 
+
+ align:start position:0%
+developing a new process and that's why
+I'm informing all of you about this is
+
+ align:start position:0%
+I'm informing all of you about this is
+ 
+
+ align:start position:0%
+I'm informing all of you about this is
+because we're all developing new
+
+ align:start position:0%
+because we're all developing new
+ 
+
+ align:start position:0%
+because we're all developing new
+processes here right we're all working
+
+ align:start position:0%
+processes here right we're all working
+ 
+
+ align:start position:0%
+processes here right we're all working
+on new solar cell devices and it's it's
+
+ align:start position:0%
+on new solar cell devices and it's it's
+ 
+
+ align:start position:0%
+on new solar cell devices and it's it's
+very important to be aware of of of
+
+ align:start position:0%
+very important to be aware of of of
+ 
+
+ align:start position:0%
+very important to be aware of of of
+what's going wrong in your device not
+
+ align:start position:0%
+what's going wrong in your device not
+ 
+
+ align:start position:0%
+what's going wrong in your device not
+just that you're getting a low
+
+ align:start position:0%
+just that you're getting a low
+ 
+
+ align:start position:0%
+just that you're getting a low
+efficiency because this is a first step
+
+ align:start position:0%
+efficiency because this is a first step
+ 
+
+ align:start position:0%
+efficiency because this is a first step
+to troubleshooting y this why is it bad
+
+ align:start position:0%
+to troubleshooting y this why is it bad
+ 
+
+ align:start position:0%
+to troubleshooting y this why is it bad
+that we have a high current density is
+
+ align:start position:0%
+that we have a high current density is
+ 
+
+ align:start position:0%
+that we have a high current density is
+not the current density going AC uh why
+
+ align:start position:0%
+not the current density going AC uh why
+ 
+
+ align:start position:0%
+not the current density going AC uh why
+is it bad that we have a high current
+
+ align:start position:0%
+is it bad that we have a high current
+ 
+
+ align:start position:0%
+is it bad that we have a high current
+density why don't we go back to a simple
+
+ align:start position:0%
+density why don't we go back to a simple
+ 
+
+ align:start position:0%
+density why don't we go back to a simple
+case right here where we have uh series
+
+ align:start position:0%
+case right here where we have uh series
+ 
+
+ align:start position:0%
+case right here where we have uh series
+resistance for instance right and so at
+
+ align:start position:0%
+resistance for instance right and so at
+ 
+
+ align:start position:0%
+resistance for instance right and so at
+at say 0.5 volts forward bias we now
+
+ align:start position:0%
+at say 0.5 volts forward bias we now
+ 
+
+ align:start position:0%
+at say 0.5 volts forward bias we now
+have with the series resistance a higher
+
+ align:start position:0%
+have with the series resistance a higher
+ 
+
+ align:start position:0%
+have with the series resistance a higher
+uh forward current we'll call it a dark
+
+ align:start position:0%
+uh forward current we'll call it a dark
+ 
+
+ align:start position:0%
+uh forward current we'll call it a dark
+forward current because we're measuring
+
+ align:start position:0%
+forward current because we're measuring
+ 
+
+ align:start position:0%
+forward current because we're measuring
+this in the dark that's why we have zero
+
+ align:start position:0%
+this in the dark that's why we have zero
+ 
+
+ align:start position:0%
+this in the dark that's why we have zero
+here and it's forward current meaning
+
+ align:start position:0%
+here and it's forward current meaning
+ 
+
+ align:start position:0%
+here and it's forward current meaning
+it's going it's like a diffusion current
+
+ align:start position:0%
+it's going it's like a diffusion current
+ 
+
+ align:start position:0%
+it's going it's like a diffusion current
+going from the emitter back into the
+
+ align:start position:0%
+going from the emitter back into the
+ 
+
+ align:start position:0%
+going from the emitter back into the
+base um and so we have a higher dark
+
+ align:start position:0%
+base um and so we have a higher dark
+ 
+
+ align:start position:0%
+base um and so we have a higher dark
+forward current here in the dark with
+
+ align:start position:0%
+forward current here in the dark with
+ 
+
+ align:start position:0%
+forward current here in the dark with
+the series resistance than if we didn't
+
+ align:start position:0%
+the series resistance than if we didn't
+ 
+
+ align:start position:0%
+the series resistance than if we didn't
+have the series resistance right so let
+
+ align:start position:0%
+have the series resistance right so let
+ 
+
+ align:start position:0%
+have the series resistance right so let
+me do that again we're up here at say uh
+
+ align:start position:0%
+me do that again we're up here at say uh
+ 
+
+ align:start position:0%
+me do that again we're up here at say uh
+1 * 10us 2 milliamps per CM whereas
+
+ align:start position:0%
+1 * 10us 2 milliamps per CM whereas
+ 
+
+ align:start position:0%
+1 * 10us 2 milliamps per CM whereas
+before we were down at around maybe a
+
+ align:start position:0%
+before we were down at around maybe a
+ 
+
+ align:start position:0%
+before we were down at around maybe a
+quarter right so why is that bad that's
+
+ align:start position:0%
+quarter right so why is that bad that's
+ 
+
+ align:start position:0%
+quarter right so why is that bad that's
+bad because when we illuminate our solar
+
+ align:start position:0%
+bad because when we illuminate our solar
+ 
+
+ align:start position:0%
+bad because when we illuminate our solar
+cell device we are going to be shifting
+
+ align:start position:0%
+cell device we are going to be shifting
+ 
+
+ align:start position:0%
+cell device we are going to be shifting
+that curve down and that's going to
+
+ align:start position:0%
+that curve down and that's going to
+ 
+
+ align:start position:0%
+that curve down and that's going to
+reduce the total current output at the
+
+ align:start position:0%
+reduce the total current output at the
+ 
+
+ align:start position:0%
+reduce the total current output at the
+maximum power point so anything that
+
+ align:start position:0%
+maximum power point so anything that
+ 
+
+ align:start position:0%
+maximum power point so anything that
+goes up here when it's shifted or
+
+ align:start position:0%
+goes up here when it's shifted or
+ 
+
+ align:start position:0%
+goes up here when it's shifted or
+transposed by a finite fixed amount it
+
+ align:start position:0%
+transposed by a finite fixed amount it
+ 
+
+ align:start position:0%
+transposed by a finite fixed amount it
+will be closer to the zero point of
+
+ align:start position:0%
+will be closer to the zero point of
+ 
+
+ align:start position:0%
+will be closer to the zero point of
+current than it used to be that's why
+
+ align:start position:0%
+current than it used to be that's why
+ 
+
+ align:start position:0%
+current than it used to be that's why
+it's bad so anything anything that
+
+ align:start position:0%
+it's bad so anything anything that
+ 
+
+ align:start position:0%
+it's bad so anything anything that
+increases um that blue curve and shifts
+
+ align:start position:0%
+increases um that blue curve and shifts
+ 
+
+ align:start position:0%
+increases um that blue curve and shifts
+it up in the dark is going to be bad for
+
+ align:start position:0%
+it up in the dark is going to be bad for
+ 
+
+ align:start position:0%
+it up in the dark is going to be bad for
+our solar cell in an ideal case we want
+
+ align:start position:0%
+our solar cell in an ideal case we want
+ 
+
+ align:start position:0%
+our solar cell in an ideal case we want
+our dark forward current to be as small
+
+ align:start position:0%
+our dark forward current to be as small
+ 
+
+ align:start position:0%
+our dark forward current to be as small
+as possible we want our J knot to be as
+
+ align:start position:0%
+as possible we want our J knot to be as
+ 
+
+ align:start position:0%
+as possible we want our J knot to be as
+Tiny as
+
+ align:start position:0%
+Tiny as
+ 
+
+ align:start position:0%
+Tiny as
+possible for a good solar cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+device
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good let me uh show you dynamically
+
+ align:start position:0%
+okay good let me uh show you dynamically
+ 
+
+ align:start position:0%
+okay good let me uh show you dynamically
+what happens um in a solar cell oopsie
+
+ align:start position:0%
+what happens um in a solar cell oopsie
+ 
+
+ align:start position:0%
+what happens um in a solar cell oopsie
+sorry about that here we go so this is
+
+ align:start position:0%
+sorry about that here we go so this is
+ 
+
+ align:start position:0%
+sorry about that here we go so this is
+uh pbcd Raman uh and a beautiful example
+
+ align:start position:0%
+uh pbcd Raman uh and a beautiful example
+ 
+
+ align:start position:0%
+uh pbcd Raman uh and a beautiful example
+of in this particular case looks like
+
+ align:start position:0%
+of in this particular case looks like
+ 
+
+ align:start position:0%
+of in this particular case looks like
+series resistance so now we're at 1 ohm
+
+ align:start position:0%
+series resistance so now we're at 1 ohm
+ 
+
+ align:start position:0%
+series resistance so now we're at 1 ohm
+series resistance for the entire device
+
+ align:start position:0%
+series resistance for the entire device
+ 
+
+ align:start position:0%
+series resistance for the entire device
+the ideal solar cell is shown in red the
+
+ align:start position:0%
+the ideal solar cell is shown in red the
+ 
+
+ align:start position:0%
+the ideal solar cell is shown in red the
+IV curve for the ideal solar cell is
+
+ align:start position:0%
+IV curve for the ideal solar cell is
+ 
+
+ align:start position:0%
+IV curve for the ideal solar cell is
+shown in red uh it would be a short
+
+ align:start position:0%
+shown in red uh it would be a short
+ 
+
+ align:start position:0%
+shown in red uh it would be a short
+circuit current of 35 milliamps per
+
+ align:start position:0%
+circuit current of 35 milliamps per
+ 
+
+ align:start position:0%
+circuit current of 35 milliamps per
+square cimeter an open circuit voltage
+
+ align:start position:0%
+square cimeter an open circuit voltage
+ 
+
+ align:start position:0%
+square cimeter an open circuit voltage
+of 624 molts and a fill factor of 83%
+
+ align:start position:0%
+of 624 molts and a fill factor of 83%
+ 
+
+ align:start position:0%
+of 624 molts and a fill factor of 83%
+ideal solar cell the real solar cell now
+
+ align:start position:0%
+ideal solar cell the real solar cell now
+ 
+
+ align:start position:0%
+ideal solar cell the real solar cell now
+with 1 ohm series resistance The Fill
+
+ align:start position:0%
+with 1 ohm series resistance The Fill
+ 
+
+ align:start position:0%
+with 1 ohm series resistance The Fill
+Factor has dropped by 5% down absolute
+
+ align:start position:0%
+Factor has dropped by 5% down absolute
+ 
+
+ align:start position:0%
+Factor has dropped by 5% down absolute
+down to
+
+ align:start position:0%
+down to
+ 
+
+ align:start position:0%
+down to
+78% and now I'm going to increase the
+
+ align:start position:0%
+78% and now I'm going to increase the
+ 
+
+ align:start position:0%
+78% and now I'm going to increase the
+fill Factor what would you expect to
+
+ align:start position:0%
+fill Factor what would you expect to
+ 
+
+ align:start position:0%
+fill Factor what would you expect to
+happen to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve flattens right the fill Factor
+
+ align:start position:0%
+curve flattens right the fill Factor
+ 
+
+ align:start position:0%
+curve flattens right the fill Factor
+drops so let me start increasing the
+
+ align:start position:0%
+drops so let me start increasing the
+ 
+
+ align:start position:0%
+drops so let me start increasing the
+series resistance by manually dragging
+
+ align:start position:0%
+series resistance by manually dragging
+ 
+
+ align:start position:0%
+series resistance by manually dragging
+this forward so now we're at around
+
+ align:start position:0%
+this forward so now we're at around
+ 
+
+ align:start position:0%
+this forward so now we're at around
+two 3 4 five 7 8 9 10 so now we're at 10
+
+ align:start position:0%
+two 3 4 five 7 8 9 10 so now we're at 10
+ 
+
+ align:start position:0%
+two 3 4 five 7 8 9 10 so now we're at 10
+ohms series resistance that means we
+
+ align:start position:0%
+ohms series resistance that means we
+ 
+
+ align:start position:0%
+ohms series resistance that means we
+have a large resistance across inside of
+
+ align:start position:0%
+have a large resistance across inside of
+ 
+
+ align:start position:0%
+have a large resistance across inside of
+our solar cell device at some point and
+
+ align:start position:0%
+our solar cell device at some point and
+ 
+
+ align:start position:0%
+our solar cell device at some point and
+our fill Factor has now dropped uh
+
+ align:start position:0%
+our fill Factor has now dropped uh
+ 
+
+ align:start position:0%
+our fill Factor has now dropped uh
+precipitously and if you remember that
+
+ align:start position:0%
+precipitously and if you remember that
+ 
+
+ align:start position:0%
+precipitously and if you remember that
+efficiency is proportional to fill
+
+ align:start position:0%
+efficiency is proportional to fill
+ 
+
+ align:start position:0%
+efficiency is proportional to fill
+factor that means we have a problem with
+
+ align:start position:0%
+factor that means we have a problem with
+ 
+
+ align:start position:0%
+factor that means we have a problem with
+our device we're really dropping the
+
+ align:start position:0%
+our device we're really dropping the
+ 
+
+ align:start position:0%
+our device we're really dropping the
+maximum power point we're really
+
+ align:start position:0%
+maximum power point we're really
+ 
+
+ align:start position:0%
+maximum power point we're really
+dropping the uh operating point of our
+
+ align:start position:0%
+dropping the uh operating point of our
+ 
+
+ align:start position:0%
+dropping the uh operating point of our
+solar cell so the if you were to do an
+
+ align:start position:0%
+solar cell so the if you were to do an
+ 
+
+ align:start position:0%
+solar cell so the if you were to do an
+extreme condition um you know you you
+
+ align:start position:0%
+extreme condition um you know you you
+ 
+
+ align:start position:0%
+extreme condition um you know you you
+you might have so much serious
+
+ align:start position:0%
+you might have so much serious
+ 
+
+ align:start position:0%
+you might have so much serious
+resistance that your IV curve looks like
+
+ align:start position:0%
+resistance that your IV curve looks like
+ 
+
+ align:start position:0%
+resistance that your IV curve looks like
+a straight line you have an omic
+
+ align:start position:0%
+a straight line you have an omic
+ 
+
+ align:start position:0%
+a straight line you have an omic
+resistor now
+
+ align:start position:0%
+resistor now
+ 
+
+ align:start position:0%
+resistor now
+the uh resistance component is swamping
+
+ align:start position:0%
+the uh resistance component is swamping
+ 
+
+ align:start position:0%
+the uh resistance component is swamping
+out any diod likee behavior of a solar
+
+ align:start position:0%
+out any diod likee behavior of a solar
+ 
+
+ align:start position:0%
+out any diod likee behavior of a solar
+cell and that's why you have a line
+
+ align:start position:0%
+cell and that's why you have a line
+ 
+
+ align:start position:0%
+cell and that's why you have a line
+likewise you're dropping the total
+
+ align:start position:0%
+likewise you're dropping the total
+ 
+
+ align:start position:0%
+likewise you're dropping the total
+current output of your device right
+
+ align:start position:0%
+current output of your device right
+ 
+
+ align:start position:0%
+current output of your device right
+because you have a resistor in series
+
+ align:start position:0%
+because you have a resistor in series
+ 
+
+ align:start position:0%
+because you have a resistor in series
+now is preventing the current flow okay
+
+ align:start position:0%
+now is preventing the current flow okay
+ 
+
+ align:start position:0%
+now is preventing the current flow okay
+so that's um again an extreme case of
+
+ align:start position:0%
+so that's um again an extreme case of
+ 
+
+ align:start position:0%
+so that's um again an extreme case of
+what can happen in a shunt resistance uh
+
+ align:start position:0%
+what can happen in a shunt resistance uh
+ 
+
+ align:start position:0%
+what can happen in a shunt resistance uh
+let me show you that as well so we have
+
+ align:start position:0%
+let me show you that as well so we have
+ 
+
+ align:start position:0%
+let me show you that as well so we have
+another beautiful uh example of shunt
+
+ align:start position:0%
+another beautiful uh example of shunt
+ 
+
+ align:start position:0%
+another beautiful uh example of shunt
+resistance um here now we start out with
+
+ align:start position:0%
+resistance um here now we start out with
+ 
+
+ align:start position:0%
+resistance um here now we start out with
+a very high shunt resistance because in
+
+ align:start position:0%
+a very high shunt resistance because in
+ 
+
+ align:start position:0%
+a very high shunt resistance because in
+our equivalent circuit diagram if we go
+
+ align:start position:0%
+our equivalent circuit diagram if we go
+ 
+
+ align:start position:0%
+our equivalent circuit diagram if we go
+back up here we have a large barrier
+
+ align:start position:0%
+back up here we have a large barrier
+ 
+
+ align:start position:0%
+back up here we have a large barrier
+that prevents the current from flowing
+
+ align:start position:0%
+that prevents the current from flowing
+ 
+
+ align:start position:0%
+that prevents the current from flowing
+back internally inside of the device the
+
+ align:start position:0%
+back internally inside of the device the
+ 
+
+ align:start position:0%
+back internally inside of the device the
+current is forced to go outside through
+
+ align:start position:0%
+current is forced to go outside through
+ 
+
+ align:start position:0%
+current is forced to go outside through
+the external circuit but as we drop that
+
+ align:start position:0%
+the external circuit but as we drop that
+ 
+
+ align:start position:0%
+the external circuit but as we drop that
+red shunt resistance component right
+
+ align:start position:0%
+red shunt resistance component right
+ 
+
+ align:start position:0%
+red shunt resistance component right
+there as we uh decrease the magnitude of
+
+ align:start position:0%
+there as we uh decrease the magnitude of
+ 
+
+ align:start position:0%
+there as we uh decrease the magnitude of
+the shunt resistance we will allow the
+
+ align:start position:0%
+the shunt resistance we will allow the
+ 
+
+ align:start position:0%
+the shunt resistance we will allow the
+current to flow inside of the device now
+
+ align:start position:0%
+current to flow inside of the device now
+ 
+
+ align:start position:0%
+current to flow inside of the device now
+we have internal current loops and that
+
+ align:start position:0%
+we have internal current loops and that
+ 
+
+ align:start position:0%
+we have internal current loops and that
+means that we no longer are forcing the
+
+ align:start position:0%
+means that we no longer are forcing the
+ 
+
+ align:start position:0%
+means that we no longer are forcing the
+current to go outside through the
+
+ align:start position:0%
+current to go outside through the
+ 
+
+ align:start position:0%
+current to go outside through the
+external circuit and somewhere around uh
+
+ align:start position:0%
+external circuit and somewhere around uh
+ 
+
+ align:start position:0%
+external circuit and somewhere around uh
+between a th000
+
+ align:start position:0%
+between a th000
+ 
+
+ align:start position:0%
+between a th000
+100 ohms for our shunt resistance we
+
+ align:start position:0%
+100 ohms for our shunt resistance we
+ 
+
+ align:start position:0%
+100 ohms for our shunt resistance we
+really begin to see that drop in fill
+
+ align:start position:0%
+really begin to see that drop in fill
+ 
+
+ align:start position:0%
+really begin to see that drop in fill
+factor and as expected it's really
+
+ align:start position:0%
+factor and as expected it's really
+ 
+
+ align:start position:0%
+factor and as expected it's really
+beginning to impact us at the lower bias
+
+ align:start position:0%
+beginning to impact us at the lower bias
+ 
+
+ align:start position:0%
+beginning to impact us at the lower bias
+voltages down here like we saw and at
+
+ align:start position:0%
+voltages down here like we saw and at
+ 
+
+ align:start position:0%
+voltages down here like we saw and at
+some point we dropped the shunt
+
+ align:start position:0%
+some point we dropped the shunt
+ 
+
+ align:start position:0%
+some point we dropped the shunt
+resistance so much that uh now the
+
+ align:start position:0%
+resistance so much that uh now the
+ 
+
+ align:start position:0%
+resistance so much that uh now the
+voltage across our solar cell is even
+
+ align:start position:0%
+voltage across our solar cell is even
+ 
+
+ align:start position:0%
+voltage across our solar cell is even
+suffering because there's uh not enough
+
+ align:start position:0%
+suffering because there's uh not enough
+ 
+
+ align:start position:0%
+suffering because there's uh not enough
+separation of charge sustained uh to
+
+ align:start position:0%
+separation of charge sustained uh to
+ 
+
+ align:start position:0%
+separation of charge sustained uh to
+make that voltage uh large because the
+
+ align:start position:0%
+make that voltage uh large because the
+ 
+
+ align:start position:0%
+make that voltage uh large because the
+current is being shunted back inside the
+
+ align:start position:0%
+current is being shunted back inside the
+ 
+
+ align:start position:0%
+current is being shunted back inside the
+device
+
+ align:start position:0%
+device
+ 
+
+ align:start position:0%
+device
+and again we we have what appears to be
+
+ align:start position:0%
+and again we we have what appears to be
+ 
+
+ align:start position:0%
+and again we we have what appears to be
+a very a linear IV curve so you can see
+
+ align:start position:0%
+a very a linear IV curve so you can see
+ 
+
+ align:start position:0%
+a very a linear IV curve so you can see
+when you when you measure your solar
+
+ align:start position:0%
+when you when you measure your solar
+ 
+
+ align:start position:0%
+when you when you measure your solar
+cell and you test it and you get a
+
+ align:start position:0%
+cell and you test it and you get a
+ 
+
+ align:start position:0%
+cell and you test it and you get a
+linear IV curve instead of that nice
+
+ align:start position:0%
+linear IV curve instead of that nice
+ 
+
+ align:start position:0%
+linear IV curve instead of that nice
+exponential you have to do a little bit
+
+ align:start position:0%
+exponential you have to do a little bit
+ 
+
+ align:start position:0%
+exponential you have to do a little bit
+of troubleshooting to figure out what
+
+ align:start position:0%
+of troubleshooting to figure out what
+ 
+
+ align:start position:0%
+of troubleshooting to figure out what
+exactly is going on
+
+ align:start position:0%
+exactly is going on
+ 
+
+ align:start position:0%
+exactly is going on
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good so uh key concept so far um we can
+
+ align:start position:0%
+good so uh key concept so far um we can
+ 
+
+ align:start position:0%
+good so uh key concept so far um we can
+add the effects of parallel resistance
+
+ align:start position:0%
+add the effects of parallel resistance
+ 
+
+ align:start position:0%
+add the effects of parallel resistance
+um what we typically refer to as shunt
+
+ align:start position:0%
+um what we typically refer to as shunt
+ 
+
+ align:start position:0%
+um what we typically refer to as shunt
+resistance is also called parallel
+
+ align:start position:0%
+resistance is also called parallel
+ 
+
+ align:start position:0%
+resistance is also called parallel
+resistance because uh it appears in
+
+ align:start position:0%
+resistance because uh it appears in
+ 
+
+ align:start position:0%
+resistance because uh it appears in
+parallel with our uh the diode inside of
+
+ align:start position:0%
+parallel with our uh the diode inside of
+ 
+
+ align:start position:0%
+parallel with our uh the diode inside of
+the device right so um we can have a
+
+ align:start position:0%
+the device right so um we can have a
+ 
+
+ align:start position:0%
+the device right so um we can have a
+parallel or shunt resistance and series
+
+ align:start position:0%
+parallel or shunt resistance and series
+ 
+
+ align:start position:0%
+parallel or shunt resistance and series
+resistance in our devices and as an
+
+ align:start position:0%
+resistance in our devices and as an
+ 
+
+ align:start position:0%
+resistance in our devices and as an
+advanced concept I really wanted to
+
+ align:start position:0%
+advanced concept I really wanted to
+ 
+
+ align:start position:0%
+advanced concept I really wanted to
+expose you once uh and we can talk more
+
+ align:start position:0%
+expose you once uh and we can talk more
+ 
+
+ align:start position:0%
+expose you once uh and we can talk more
+about this in in office hours um to the
+
+ align:start position:0%
+about this in in office hours um to the
+ 
+
+ align:start position:0%
+about this in in office hours um to the
+notion that in addition to uh just
+
+ align:start position:0%
+notion that in addition to uh just
+ 
+
+ align:start position:0%
+notion that in addition to uh just
+having one saturation current you could
+
+ align:start position:0%
+having one saturation current you could
+ 
+
+ align:start position:0%
+having one saturation current you could
+Envision different saturation currents
+
+ align:start position:0%
+Envision different saturation currents
+ 
+
+ align:start position:0%
+Envision different saturation currents
+coming from different regions of your
+
+ align:start position:0%
+coming from different regions of your
+ 
+
+ align:start position:0%
+coming from different regions of your
+solar cell device let me walk you
+
+ align:start position:0%
+solar cell device let me walk you
+ 
+
+ align:start position:0%
+solar cell device let me walk you
+through that under low bias conditions
+
+ align:start position:0%
+through that under low bias conditions
+ 
+
+ align:start position:0%
+through that under low bias conditions
+where we have a large uh uh uh built-in
+
+ align:start position:0%
+where we have a large uh uh uh built-in
+ 
+
+ align:start position:0%
+where we have a large uh uh uh built-in
+uh uh field and we have very low bias
+
+ align:start position:0%
+uh uh field and we have very low bias
+ 
+
+ align:start position:0%
+uh uh field and we have very low bias
+conditions as we for bias obviously the
+
+ align:start position:0%
+conditions as we for bias obviously the
+ 
+
+ align:start position:0%
+conditions as we for bias obviously the
+field is going to be decreasing the
+
+ align:start position:0%
+field is going to be decreasing the
+ 
+
+ align:start position:0%
+field is going to be decreasing the
+barrier height is going to be decreasing
+
+ align:start position:0%
+barrier height is going to be decreasing
+ 
+
+ align:start position:0%
+barrier height is going to be decreasing
+as well so under low forward bias
+
+ align:start position:0%
+as well so under low forward bias
+ 
+
+ align:start position:0%
+as well so under low forward bias
+conditions current is going to have a
+
+ align:start position:0%
+conditions current is going to have a
+ 
+
+ align:start position:0%
+conditions current is going to have a
+hard time getting all the way up into
+
+ align:start position:0%
+hard time getting all the way up into
+ 
+
+ align:start position:0%
+hard time getting all the way up into
+the base and recombining inside of the
+
+ align:start position:0%
+the base and recombining inside of the
+ 
+
+ align:start position:0%
+the base and recombining inside of the
+base but some of the current could
+
+ align:start position:0%
+base but some of the current could
+ 
+
+ align:start position:0%
+base but some of the current could
+recombine in the space charge region of
+
+ align:start position:0%
+recombine in the space charge region of
+ 
+
+ align:start position:0%
+recombine in the space charge region of
+our device and that's why under low
+
+ align:start position:0%
+our device and that's why under low
+ 
+
+ align:start position:0%
+our device and that's why under low
+forward bias conditions we might have
+
+ align:start position:0%
+forward bias conditions we might have
+ 
+
+ align:start position:0%
+forward bias conditions we might have
+what is called the jot2 current or
+
+ align:start position:0%
+what is called the jot2 current or
+ 
+
+ align:start position:0%
+what is called the jot2 current or
+recombination current in the space
+
+ align:start position:0%
+recombination current in the space
+ 
+
+ align:start position:0%
+recombination current in the space
+charge region and then the are high
+
+ align:start position:0%
+charge region and then the are high
+ 
+
+ align:start position:0%
+charge region and then the are high
+forward bias conditions when a lot of
+
+ align:start position:0%
+forward bias conditions when a lot of
+ 
+
+ align:start position:0%
+forward bias conditions when a lot of
+the carriers can diffuse into the bulk
+
+ align:start position:0%
+the carriers can diffuse into the bulk
+ 
+
+ align:start position:0%
+the carriers can diffuse into the bulk
+and recombine inside of the bulk we
+
+ align:start position:0%
+and recombine inside of the bulk we
+ 
+
+ align:start position:0%
+and recombine inside of the bulk we
+might be driven by different
+
+ align:start position:0%
+might be driven by different
+ 
+
+ align:start position:0%
+might be driven by different
+recombination mechanisms uh bulk
+
+ align:start position:0%
+recombination mechanisms uh bulk
+ 
+
+ align:start position:0%
+recombination mechanisms uh bulk
+recombination mechanisms so that's
+
+ align:start position:0%
+recombination mechanisms so that's
+ 
+
+ align:start position:0%
+recombination mechanisms so that's
+sometimes where you see uh what is
+
+ align:start position:0%
+sometimes where you see uh what is
+ 
+
+ align:start position:0%
+sometimes where you see uh what is
+called a two diode model for a solar
+
+ align:start position:0%
+called a two diode model for a solar
+ 
+
+ align:start position:0%
+called a two diode model for a solar
+cell and the two diode model for a solar
+
+ align:start position:0%
+cell and the two diode model for a solar
+ 
+
+ align:start position:0%
+cell and the two diode model for a solar
+cell would look very much like this
+
+ align:start position:0%
+cell would look very much like this
+ 
+
+ align:start position:0%
+cell would look very much like this
+except you'd have two two diodes uh one
+
+ align:start position:0%
+except you'd have two two diodes uh one
+ 
+
+ align:start position:0%
+except you'd have two two diodes uh one
+right next to the other um one that
+
+ align:start position:0%
+right next to the other um one that
+ 
+
+ align:start position:0%
+right next to the other um one that
+would affect you at low bias conditions
+
+ align:start position:0%
+would affect you at low bias conditions
+ 
+
+ align:start position:0%
+would affect you at low bias conditions
+the other one at large bias conditions
+
+ align:start position:0%
+the other one at large bias conditions
+ 
+
+ align:start position:0%
+the other one at large bias conditions
+you might see this in your research it's
+
+ align:start position:0%
+you might see this in your research it's
+ 
+
+ align:start position:0%
+you might see this in your research it's
+really an advanced concept more targeted
+
+ align:start position:0%
+really an advanced concept more targeted
+ 
+
+ align:start position:0%
+really an advanced concept more targeted
+toward the The Graduate students here
+
+ align:start position:0%
+toward the The Graduate students here
+ 
+
+ align:start position:0%
+toward the The Graduate students here
+another thing you might see Pop Up is
+
+ align:start position:0%
+another thing you might see Pop Up is
+ 
+
+ align:start position:0%
+another thing you might see Pop Up is
+this ideality Factor showing up right
+
+ align:start position:0%
+this ideality Factor showing up right
+ 
+
+ align:start position:0%
+this ideality Factor showing up right
+down here the ideality factor is a slope
+
+ align:start position:0%
+down here the ideality factor is a slope
+ 
+
+ align:start position:0%
+down here the ideality factor is a slope
+Factor what that means is um here if we
+
+ align:start position:0%
+Factor what that means is um here if we
+ 
+
+ align:start position:0%
+Factor what that means is um here if we
+go back to this if you change your
+
+ align:start position:0%
+go back to this if you change your
+ 
+
+ align:start position:0%
+go back to this if you change your
+ideality Factor you're changing the
+
+ align:start position:0%
+ideality Factor you're changing the
+ 
+
+ align:start position:0%
+ideality Factor you're changing the
+slope in log scale it still be a
+
+ align:start position:0%
+slope in log scale it still be a
+ 
+
+ align:start position:0%
+slope in log scale it still be a
+straight line but if your ideality
+
+ align:start position:0%
+straight line but if your ideality
+ 
+
+ align:start position:0%
+straight line but if your ideality
+Factor increases you would get something
+
+ align:start position:0%
+Factor increases you would get something
+ 
+
+ align:start position:0%
+Factor increases you would get something
+like this if it decreases the slope
+
+ align:start position:0%
+like this if it decreases the slope
+ 
+
+ align:start position:0%
+like this if it decreases the slope
+would uh increase right because you have
+
+ align:start position:0%
+would uh increase right because you have
+ 
+
+ align:start position:0%
+would uh increase right because you have
+the equation dependent on one over uh
+
+ align:start position:0%
+the equation dependent on one over uh
+ 
+
+ align:start position:0%
+the equation dependent on one over uh
+this parameter okay so um the ideality
+
+ align:start position:0%
+this parameter okay so um the ideality
+ 
+
+ align:start position:0%
+this parameter okay so um the ideality
+factor is important as well because it
+
+ align:start position:0%
+factor is important as well because it
+ 
+
+ align:start position:0%
+factor is important as well because it
+indicates the type of recombination
+
+ align:start position:0%
+indicates the type of recombination
+ 
+
+ align:start position:0%
+indicates the type of recombination
+mechanism that's driving the current
+
+ align:start position:0%
+mechanism that's driving the current
+ 
+
+ align:start position:0%
+mechanism that's driving the current
+inside of that region of the device and
+
+ align:start position:0%
+inside of that region of the device and
+ 
+
+ align:start position:0%
+inside of that region of the device and
+if anybody ever comes across this in
+
+ align:start position:0%
+if anybody ever comes across this in
+ 
+
+ align:start position:0%
+if anybody ever comes across this in
+their research come talk to me I'd be
+
+ align:start position:0%
+their research come talk to me I'd be
+ 
+
+ align:start position:0%
+their research come talk to me I'd be
+happy to uh to point you in the right
+
+ align:start position:0%
+happy to uh to point you in the right
+ 
+
+ align:start position:0%
+happy to uh to point you in the right
+directions or you could look up the
+
+ align:start position:0%
+directions or you could look up the
+ 
+
+ align:start position:0%
+directions or you could look up the
+thesis of Keith Macintosh from
+
+ align:start position:0%
+thesis of Keith Macintosh from
+ 
+
+ align:start position:0%
+thesis of Keith Macintosh from
+University of New South Wales um
+
+ align:start position:0%
+University of New South Wales um
+ 
+
+ align:start position:0%
+University of New South Wales um
+excellent excellent thesis entitled
+
+ align:start position:0%
+excellent excellent thesis entitled
+ 
+
+ align:start position:0%
+excellent excellent thesis entitled
+humps lumps and bumps um a
+
+ align:start position:0%
+humps lumps and bumps um a
+ 
+
+ align:start position:0%
+humps lumps and bumps um a
+threedimensional threedimensional
+
+ align:start position:0%
+threedimensional threedimensional
+ 
+
+ align:start position:0%
+threedimensional threedimensional
+effects of the current voltage curve of
+
+ align:start position:0%
+effects of the current voltage curve of
+ 
+
+ align:start position:0%
+effects of the current voltage curve of
+silicon solar cells some of which might
+
+ align:start position:0%
+silicon solar cells some of which might
+ 
+
+ align:start position:0%
+silicon solar cells some of which might
+apply as well to other material systems
+
+ align:start position:0%
+apply as well to other material systems
+ 
+
+ align:start position:0%
+apply as well to other material systems
+as well and you can tell where the lumps
+
+ align:start position:0%
+as well and you can tell where the lumps
+ 
+
+ align:start position:0%
+as well and you can tell where the lumps
+humps and bumps comes from it's really
+
+ align:start position:0%
+humps and bumps comes from it's really
+ 
+
+ align:start position:0%
+humps and bumps comes from it's really
+these uh lumps humps and bumps in the IV
+
+ align:start position:0%
+these uh lumps humps and bumps in the IV
+ 
+
+ align:start position:0%
+these uh lumps humps and bumps in the IV
+curve that he's talking about excellent
+
+ align:start position:0%
+curve that he's talking about excellent
+ 
+
+ align:start position:0%
+curve that he's talking about excellent
+read very good thesis um highly
+
+ align:start position:0%
+read very good thesis um highly
+ 
+
+ align:start position:0%
+read very good thesis um highly
+recommended for those who want to look
+
+ align:start position:0%
+recommended for those who want to look
+ 
+
+ align:start position:0%
+recommended for those who want to look
+into their IV curves a little bit more
+
+ align:start position:0%
+into their IV curves a little bit more
+ 
+
+ align:start position:0%
+into their IV curves a little bit more
+it's kind of like looking into the tea
+
+ align:start position:0%
+it's kind of like looking into the tea
+ 
+
+ align:start position:0%
+it's kind of like looking into the tea
+leaves right because there are a number
+
+ align:start position:0%
+leaves right because there are a number
+ 
+
+ align:start position:0%
+leaves right because there are a number
+of things that can be affecting the IV
+
+ align:start position:0%
+of things that can be affecting the IV
+ 
+
+ align:start position:0%
+of things that can be affecting the IV
+curves we'll get to some of those uh on
+
+ align:start position:0%
+curves we'll get to some of those uh on
+ 
+
+ align:start position:0%
+curves we'll get to some of those uh on
+on Tuesday as well these are um IV
+
+ align:start position:0%
+on Tuesday as well these are um IV
+ 
+
+ align:start position:0%
+on Tuesday as well these are um IV
+curves again in in in log scale on the
+
+ align:start position:0%
+curves again in in in log scale on the
+ 
+
+ align:start position:0%
+curves again in in in log scale on the
+ordinate linear scale on the abscissa
+
+ align:start position:0%
+ordinate linear scale on the abscissa
+ 
+
+ align:start position:0%
+ordinate linear scale on the abscissa
+you notice there's little commas here
+
+ align:start position:0%
+you notice there's little commas here
+ 
+
+ align:start position:0%
+you notice there's little commas here
+because I took this data in Germany so
+
+ align:start position:0%
+because I took this data in Germany so
+ 
+
+ align:start position:0%
+because I took this data in Germany so
+the decimal place is written as a comma
+
+ align:start position:0%
+the decimal place is written as a comma
+ 
+
+ align:start position:0%
+the decimal place is written as a comma
+uh the um the IV curves uh vary in in in
+
+ align:start position:0%
+uh the um the IV curves uh vary in in in
+ 
+
+ align:start position:0%
+uh the um the IV curves uh vary in in in
+shape and in style let's look at this
+
+ align:start position:0%
+shape and in style let's look at this
+ 
+
+ align:start position:0%
+shape and in style let's look at this
+one right here this black one um it
+
+ align:start position:0%
+one right here this black one um it
+ 
+
+ align:start position:0%
+one right here this black one um it
+starts up like this and then it goes
+
+ align:start position:0%
+starts up like this and then it goes
+ 
+
+ align:start position:0%
+starts up like this and then it goes
+flat for a while and then it becomes
+
+ align:start position:0%
+flat for a while and then it becomes
+ 
+
+ align:start position:0%
+flat for a while and then it becomes
+series it's dominated way up at higher
+
+ align:start position:0%
+series it's dominated way up at higher
+ 
+
+ align:start position:0%
+series it's dominated way up at higher
+bias voltages whereas uh this blue curve
+
+ align:start position:0%
+bias voltages whereas uh this blue curve
+ 
+
+ align:start position:0%
+bias voltages whereas uh this blue curve
+right here this one uh again you have
+
+ align:start position:0%
+right here this one uh again you have
+ 
+
+ align:start position:0%
+right here this one uh again you have
+the effect of shunt resistance at lower
+
+ align:start position:0%
+the effect of shunt resistance at lower
+ 
+
+ align:start position:0%
+the effect of shunt resistance at lower
+bias voltages then you have one diode
+
+ align:start position:0%
+bias voltages then you have one diode
+ 
+
+ align:start position:0%
+bias voltages then you have one diode
+two diodes and eventually the series
+
+ align:start position:0%
+two diodes and eventually the series
+ 
+
+ align:start position:0%
+two diodes and eventually the series
+resistance component coming in as well
+
+ align:start position:0%
+resistance component coming in as well
+ 
+
+ align:start position:0%
+resistance component coming in as well
+or perhaps it's a large shunt as well
+
+ align:start position:0%
+or perhaps it's a large shunt as well
+ 
+
+ align:start position:0%
+or perhaps it's a large shunt as well
+you don't really know until you start
+
+ align:start position:0%
+you don't really know until you start
+ 
+
+ align:start position:0%
+you don't really know until you start
+fitting it and modeling it and maybe
+
+ align:start position:0%
+fitting it and modeling it and maybe
+ 
+
+ align:start position:0%
+fitting it and modeling it and maybe
+measuring the temperature dependence and
+
+ align:start position:0%
+measuring the temperature dependence and
+ 
+
+ align:start position:0%
+measuring the temperature dependence and
+so forth so this gives you a sense of
+
+ align:start position:0%
+so forth so this gives you a sense of
+ 
+
+ align:start position:0%
+so forth so this gives you a sense of
+the the real life uh uh diod IV curves
+
+ align:start position:0%
+the the real life uh uh diod IV curves
+ 
+
+ align:start position:0%
+the the real life uh uh diod IV curves
+that you might get over the course of
+
+ align:start position:0%
+that you might get over the course of
+ 
+
+ align:start position:0%
+that you might get over the course of
+your research and uh gives you some
+
+ align:start position:0%
+your research and uh gives you some
+ 
+
+ align:start position:0%
+your research and uh gives you some
+tools uh to use to begin parsing through
+
+ align:start position:0%
+tools uh to use to begin parsing through
+ 
+
+ align:start position:0%
+tools uh to use to begin parsing through
+and figuring out what's going wrong
+
+ align:start position:0%
+and figuring out what's going wrong
+ 
+
+ align:start position:0%
+and figuring out what's going wrong
+let's talk about that let's talk about
+
+ align:start position:0%
+let's talk about that let's talk about
+ 
+
+ align:start position:0%
+let's talk about that let's talk about
+solving problems so fill Factor what can
+
+ align:start position:0%
+solving problems so fill Factor what can
+ 
+
+ align:start position:0%
+solving problems so fill Factor what can
+impact the fill Factor well we talked
+
+ align:start position:0%
+impact the fill Factor well we talked
+ 
+
+ align:start position:0%
+impact the fill Factor well we talked
+about uh the need for a high fill factor
+
+ align:start position:0%
+about uh the need for a high fill factor
+ 
+
+ align:start position:0%
+about uh the need for a high fill factor
+to produce a high power cell very easy
+
+ align:start position:0%
+to produce a high power cell very easy
+ 
+
+ align:start position:0%
+to produce a high power cell very easy
+to understand the larger the fill Factor
+
+ align:start position:0%
+to understand the larger the fill Factor
+ 
+
+ align:start position:0%
+to understand the larger the fill Factor
+the larger the maximum
+
+ align:start position:0%
+the larger the maximum
+ 
+
+ align:start position:0%
+the larger the maximum
+PowerPoint if you have a low fill Factor
+
+ align:start position:0%
+PowerPoint if you have a low fill Factor
+ 
+
+ align:start position:0%
+PowerPoint if you have a low fill Factor
+your maximum PowerPoint is going to drop
+
+ align:start position:0%
+your maximum PowerPoint is going to drop
+ 
+
+ align:start position:0%
+your maximum PowerPoint is going to drop
+let me show you back and forth Good
+
+ align:start position:0%
+let me show you back and forth Good
+ 
+
+ align:start position:0%
+let me show you back and forth Good
+device bad device large fill Factor low
+
+ align:start position:0%
+device bad device large fill Factor low
+ 
+
+ align:start position:0%
+device bad device large fill Factor low
+fill Factor High maximum power point
+
+ align:start position:0%
+fill Factor High maximum power point
+ 
+
+ align:start position:0%
+fill Factor High maximum power point
+lower maximum power
+
+ align:start position:0%
+lower maximum power
+ 
+
+ align:start position:0%
+lower maximum power
+point okay we talked about this okay so
+
+ align:start position:0%
+point okay we talked about this okay so
+ 
+
+ align:start position:0%
+point okay we talked about this okay so
+causes of shun resistance physical
+
+ align:start position:0%
+causes of shun resistance physical
+ 
+
+ align:start position:0%
+causes of shun resistance physical
+causes I alluded to this earlier but
+
+ align:start position:0%
+causes I alluded to this earlier but
+ 
+
+ align:start position:0%
+causes I alluded to this earlier but
+let's imagine you have that weak spot in
+
+ align:start position:0%
+let's imagine you have that weak spot in
+ 
+
+ align:start position:0%
+let's imagine you have that weak spot in
+your P injunction this is meant to
+
+ align:start position:0%
+your P injunction this is meant to
+ 
+
+ align:start position:0%
+your P injunction this is meant to
+represent the P Junction in two
+
+ align:start position:0%
+represent the P Junction in two
+ 
+
+ align:start position:0%
+represent the P Junction in two
+Dimensions now right so so far we've
+
+ align:start position:0%
+Dimensions now right so so far we've
+ 
+
+ align:start position:0%
+Dimensions now right so so far we've
+only taken a cross-section like this now
+
+ align:start position:0%
+only taken a cross-section like this now
+ 
+
+ align:start position:0%
+only taken a cross-section like this now
+you have a real device in 2D and what
+
+ align:start position:0%
+you have a real device in 2D and what
+ 
+
+ align:start position:0%
+you have a real device in 2D and what
+this is meant to represent is some local
+
+ align:start position:0%
+this is meant to represent is some local
+ 
+
+ align:start position:0%
+this is meant to represent is some local
+weakness in the P Junction and the
+
+ align:start position:0%
+weakness in the P Junction and the
+ 
+
+ align:start position:0%
+weakness in the P Junction and the
+current is now flowing through that
+
+ align:start position:0%
+current is now flowing through that
+ 
+
+ align:start position:0%
+current is now flowing through that
+local weakness weakness so that's uh a
+
+ align:start position:0%
+local weakness weakness so that's uh a
+ 
+
+ align:start position:0%
+local weakness weakness so that's uh a
+representation uh in a in a 2d energy
+
+ align:start position:0%
+representation uh in a in a 2d energy
+ 
+
+ align:start position:0%
+representation uh in a in a 2d energy
+band diagram E versus X versus y right
+
+ align:start position:0%
+band diagram E versus X versus y right
+ 
+
+ align:start position:0%
+band diagram E versus X versus y right
+of uh of of a shunt in realistic
+
+ align:start position:0%
+of uh of of a shunt in realistic
+ 
+
+ align:start position:0%
+of uh of of a shunt in realistic
+conditions so uh shunt uh series
+
+ align:start position:0%
+conditions so uh shunt uh series
+ 
+
+ align:start position:0%
+conditions so uh shunt uh series
+resistance on the other uh hand we we
+
+ align:start position:0%
+resistance on the other uh hand we we
+ 
+
+ align:start position:0%
+resistance on the other uh hand we we
+talked about the effect of High series
+
+ align:start position:0%
+talked about the effect of High series
+ 
+
+ align:start position:0%
+talked about the effect of High series
+resistance and we're going to calculate
+
+ align:start position:0%
+resistance and we're going to calculate
+ 
+
+ align:start position:0%
+resistance and we're going to calculate
+the series resistance for a solar cell
+
+ align:start position:0%
+the series resistance for a solar cell
+ 
+
+ align:start position:0%
+the series resistance for a solar cell
+in part because this is asked for you on
+
+ align:start position:0%
+in part because this is asked for you on
+ 
+
+ align:start position:0%
+in part because this is asked for you on
+your homework assignment at least The
+
+ align:start position:0%
+your homework assignment at least The
+ 
+
+ align:start position:0%
+your homework assignment at least The
+Graduate students have a problem uh
+
+ align:start position:0%
+Graduate students have a problem uh
+ 
+
+ align:start position:0%
+Graduate students have a problem uh
+pertaining to this so let's talk about
+
+ align:start position:0%
+pertaining to this so let's talk about
+ 
+
+ align:start position:0%
+pertaining to this so let's talk about
+the different uh components of series
+
+ align:start position:0%
+the different uh components of series
+ 
+
+ align:start position:0%
+the different uh components of series
+resistance we have a bulk current and an
+
+ align:start position:0%
+resistance we have a bulk current and an
+ 
+
+ align:start position:0%
+resistance we have a bulk current and an
+lateral current inside of a typical
+
+ align:start position:0%
+lateral current inside of a typical
+ 
+
+ align:start position:0%
+lateral current inside of a typical
+solar cell device so sunlight comes in
+
+ align:start position:0%
+solar cell device so sunlight comes in
+ 
+
+ align:start position:0%
+solar cell device so sunlight comes in
+shines generates electron whole pairs
+
+ align:start position:0%
+shines generates electron whole pairs
+ 
+
+ align:start position:0%
+shines generates electron whole pairs
+these electrons will diffuse to the the
+
+ align:start position:0%
+these electrons will diffuse to the the
+ 
+
+ align:start position:0%
+these electrons will diffuse to the the
+the the junction region and then they'll
+
+ align:start position:0%
+the the junction region and then they'll
+ 
+
+ align:start position:0%
+the the junction region and then they'll
+drift Across The Junction wind up in in
+
+ align:start position:0%
+drift Across The Junction wind up in in
+ 
+
+ align:start position:0%
+drift Across The Junction wind up in in
+the submitter uh front surface region
+
+ align:start position:0%
+the submitter uh front surface region
+ 
+
+ align:start position:0%
+the submitter uh front surface region
+and eventually through lateral uh uh
+
+ align:start position:0%
+and eventually through lateral uh uh
+ 
+
+ align:start position:0%
+and eventually through lateral uh uh
+diffusion reach the contacts and be
+
+ align:start position:0%
+diffusion reach the contacts and be
+ 
+
+ align:start position:0%
+diffusion reach the contacts and be
+pulled out of the device so uh we have
+
+ align:start position:0%
+pulled out of the device so uh we have
+ 
+
+ align:start position:0%
+pulled out of the device so uh we have
+to consider these two different
+
+ align:start position:0%
+to consider these two different
+ 
+
+ align:start position:0%
+to consider these two different
+components uh and pretty much the
+
+ align:start position:0%
+components uh and pretty much the
+ 
+
+ align:start position:0%
+components uh and pretty much the
+current all the way from the back
+
+ align:start position:0%
+current all the way from the back
+ 
+
+ align:start position:0%
+current all the way from the back
+contact to the front contact any one of
+
+ align:start position:0%
+contact to the front contact any one of
+ 
+
+ align:start position:0%
+contact to the front contact any one of
+those things could contribute to series
+
+ align:start position:0%
+those things could contribute to series
+ 
+
+ align:start position:0%
+those things could contribute to series
+resistance in an additive sense so to
+
+ align:start position:0%
+resistance in an additive sense so to
+ 
+
+ align:start position:0%
+resistance in an additive sense so to
+put that pictorially we have bulk
+
+ align:start position:0%
+put that pictorially we have bulk
+ 
+
+ align:start position:0%
+put that pictorially we have bulk
+resistance AIT sheet resistance the
+
+ align:start position:0%
+resistance AIT sheet resistance the
+ 
+
+ align:start position:0%
+resistance AIT sheet resistance the
+contact resistance and then line losses
+
+ align:start position:0%
+contact resistance and then line losses
+ 
+
+ align:start position:0%
+contact resistance and then line losses
+uh out of plane as we travel along those
+
+ align:start position:0%
+uh out of plane as we travel along those
+ 
+
+ align:start position:0%
+uh out of plane as we travel along those
+uh front contact
+
+ align:start position:0%
+uh front contact
+ 
+
+ align:start position:0%
+uh front contact
+metalization so bulk resistance this is
+
+ align:start position:0%
+metalization so bulk resistance this is
+ 
+
+ align:start position:0%
+metalization so bulk resistance this is
+another way to State how to choose an
+
+ align:start position:0%
+another way to State how to choose an
+ 
+
+ align:start position:0%
+another way to State how to choose an
+absorber thickness so we've talked about
+
+ align:start position:0%
+absorber thickness so we've talked about
+ 
+
+ align:start position:0%
+absorber thickness so we've talked about
+choosing absorber thicknesses in other
+
+ align:start position:0%
+choosing absorber thicknesses in other
+ 
+
+ align:start position:0%
+choosing absorber thicknesses in other
+words we've talked about choosing the
+
+ align:start position:0%
+words we've talked about choosing the
+ 
+
+ align:start position:0%
+words we've talked about choosing the
+thickness of our solar cell device based
+
+ align:start position:0%
+thickness of our solar cell device based
+ 
+
+ align:start position:0%
+thickness of our solar cell device based
+on how much light we want to capture
+
+ align:start position:0%
+on how much light we want to capture
+ 
+
+ align:start position:0%
+on how much light we want to capture
+based on the optical absorption
+
+ align:start position:0%
+based on the optical absorption
+ 
+
+ align:start position:0%
+based on the optical absorption
+coefficients well guess what this is a
+
+ align:start position:0%
+coefficients well guess what this is a
+ 
+
+ align:start position:0%
+coefficients well guess what this is a
+co-optimization problem we also have to
+
+ align:start position:0%
+co-optimization problem we also have to
+ 
+
+ align:start position:0%
+co-optimization problem we also have to
+worry about the finite resistance of the
+
+ align:start position:0%
+worry about the finite resistance of the
+ 
+
+ align:start position:0%
+worry about the finite resistance of the
+bulk material and we have to spec the
+
+ align:start position:0%
+bulk material and we have to spec the
+ 
+
+ align:start position:0%
+bulk material and we have to spec the
+thickness accordingly so that we don't
+
+ align:start position:0%
+thickness accordingly so that we don't
+ 
+
+ align:start position:0%
+thickness accordingly so that we don't
+wind up with too thick of a bulk
+
+ align:start position:0%
+wind up with too thick of a bulk
+ 
+
+ align:start position:0%
+wind up with too thick of a bulk
+material and the series resistance
+
+ align:start position:0%
+material and the series resistance
+ 
+
+ align:start position:0%
+material and the series resistance
+component will be too large so how to
+
+ align:start position:0%
+component will be too large so how to
+ 
+
+ align:start position:0%
+component will be too large so how to
+choose the appropriate absorber
+
+ align:start position:0%
+choose the appropriate absorber
+ 
+
+ align:start position:0%
+choose the appropriate absorber
+thickness let's talk about that for a
+
+ align:start position:0%
+thickness let's talk about that for a
+ 
+
+ align:start position:0%
+thickness let's talk about that for a
+minute so you can measure a parameter in
+
+ align:start position:0%
+minute so you can measure a parameter in
+ 
+
+ align:start position:0%
+minute so you can measure a parameter in
+the bulk called
+
+ align:start position:0%
+the bulk called
+ 
+
+ align:start position:0%
+the bulk called
+resistivity resistivity will be given as
+
+ align:start position:0%
+resistivity resistivity will be given as
+ 
+
+ align:start position:0%
+resistivity resistivity will be given as
+a function of of Q which is the charge
+
+ align:start position:0%
+a function of of Q which is the charge
+ 
+
+ align:start position:0%
+a function of of Q which is the charge
+mu which is the carrier Mobility which
+
+ align:start position:0%
+mu which is the carrier Mobility which
+ 
+
+ align:start position:0%
+mu which is the carrier Mobility which
+means how easy is it for that carrier to
+
+ align:start position:0%
+means how easy is it for that carrier to
+ 
+
+ align:start position:0%
+means how easy is it for that carrier to
+move around the lce and N being the
+
+ align:start position:0%
+move around the lce and N being the
+ 
+
+ align:start position:0%
+move around the lce and N being the
+carrier density so let's think that
+
+ align:start position:0%
+carrier density so let's think that
+ 
+
+ align:start position:0%
+carrier density so let's think that
+through resistivity if our carrier
+
+ align:start position:0%
+through resistivity if our carrier
+ 
+
+ align:start position:0%
+through resistivity if our carrier
+density goes up if we have more carriers
+
+ align:start position:0%
+density goes up if we have more carriers
+ 
+
+ align:start position:0%
+density goes up if we have more carriers
+to transport the charge the resistivity
+
+ align:start position:0%
+to transport the charge the resistivity
+ 
+
+ align:start position:0%
+to transport the charge the resistivity
+should go down that makes sense check if
+
+ align:start position:0%
+should go down that makes sense check if
+ 
+
+ align:start position:0%
+should go down that makes sense check if
+the mobility goes up meaning it's easier
+
+ align:start position:0%
+the mobility goes up meaning it's easier
+ 
+
+ align:start position:0%
+the mobility goes up meaning it's easier
+for the carriers to move around the
+
+ align:start position:0%
+for the carriers to move around the
+ 
+
+ align:start position:0%
+for the carriers to move around the
+lattice then the resistivity should go
+
+ align:start position:0%
+lattice then the resistivity should go
+ 
+
+ align:start position:0%
+lattice then the resistivity should go
+down check okay so that makes good
+
+ align:start position:0%
+down check okay so that makes good
+ 
+
+ align:start position:0%
+down check okay so that makes good
+intuitive sense now the base resistance
+
+ align:start position:0%
+intuitive sense now the base resistance
+ 
+
+ align:start position:0%
+intuitive sense now the base resistance
+in other words the resistance that we
+
+ align:start position:0%
+in other words the resistance that we
+ 
+
+ align:start position:0%
+in other words the resistance that we
+should have as current travels across
+
+ align:start position:0%
+should have as current travels across
+ 
+
+ align:start position:0%
+should have as current travels across
+the base across the the absorber of our
+
+ align:start position:0%
+the base across the the absorber of our
+ 
+
+ align:start position:0%
+the base across the the absorber of our
+material which we also call the base of
+
+ align:start position:0%
+material which we also call the base of
+ 
+
+ align:start position:0%
+material which we also call the base of
+our solar cell so as the total
+
+ align:start position:0%
+our solar cell so as the total
+ 
+
+ align:start position:0%
+our solar cell so as the total
+resistance as current goes across the
+
+ align:start position:0%
+resistance as current goes across the
+ 
+
+ align:start position:0%
+resistance as current goes across the
+base should be given as row which is a
+
+ align:start position:0%
+base should be given as row which is a
+ 
+
+ align:start position:0%
+base should be given as row which is a
+fundamental material
+
+ align:start position:0%
+fundamental material
+ 
+
+ align:start position:0%
+fundamental material
+parameter combined with some geometric
+
+ align:start position:0%
+parameter combined with some geometric
+ 
+
+ align:start position:0%
+parameter combined with some geometric
+parameters that Define the size of our
+
+ align:start position:0%
+parameters that Define the size of our
+ 
+
+ align:start position:0%
+parameters that Define the size of our
+solar cell so L is going to be the
+
+ align:start position:0%
+solar cell so L is going to be the
+ 
+
+ align:start position:0%
+solar cell so L is going to be the
+length of the conductive path which
+
+ align:start position:0%
+length of the conductive path which
+ 
+
+ align:start position:0%
+length of the conductive path which
+typically would be given as the
+
+ align:start position:0%
+typically would be given as the
+ 
+
+ align:start position:0%
+typically would be given as the
+thickness of the device and a is the
+
+ align:start position:0%
+thickness of the device and a is the
+ 
+
+ align:start position:0%
+thickness of the device and a is the
+area of current flow in other words the
+
+ align:start position:0%
+area of current flow in other words the
+ 
+
+ align:start position:0%
+area of current flow in other words the
+Dimension or size of our solar cell
+
+ align:start position:0%
+Dimension or size of our solar cell
+ 
+
+ align:start position:0%
+Dimension or size of our solar cell
+device so to minimize base resistance we
+
+ align:start position:0%
+device so to minimize base resistance we
+ 
+
+ align:start position:0%
+device so to minimize base resistance we
+want to have a very thin solar cell
+
+ align:start position:0%
+want to have a very thin solar cell
+ 
+
+ align:start position:0%
+want to have a very thin solar cell
+device but wait a second if we make it
+
+ align:start position:0%
+device but wait a second if we make it
+ 
+
+ align:start position:0%
+device but wait a second if we make it
+very thin then what
+
+ align:start position:0%
+very thin then what
+ 
+
+ align:start position:0%
+very thin then what
+happens a less absorption so we have to
+
+ align:start position:0%
+happens a less absorption so we have to
+ 
+
+ align:start position:0%
+happens a less absorption so we have to
+make it a certain thickness to get a
+
+ align:start position:0%
+make it a certain thickness to get a
+ 
+
+ align:start position:0%
+make it a certain thickness to get a
+good enough absorption then we can
+
+ align:start position:0%
+good enough absorption then we can
+ 
+
+ align:start position:0%
+good enough absorption then we can
+compensate if we still need to drop the
+
+ align:start position:0%
+compensate if we still need to drop the
+ 
+
+ align:start position:0%
+compensate if we still need to drop the
+base resistance we can increase the area
+
+ align:start position:0%
+base resistance we can increase the area
+ 
+
+ align:start position:0%
+base resistance we can increase the area
+of the base right and so far um that
+
+ align:start position:0%
+of the base right and so far um that
+ 
+
+ align:start position:0%
+of the base right and so far um that
+makes good sense there's nothing else uh
+
+ align:start position:0%
+makes good sense there's nothing else uh
+ 
+
+ align:start position:0%
+makes good sense there's nothing else uh
+tugging uh for the area to be in the the
+
+ align:start position:0%
+tugging uh for the area to be in the the
+ 
+
+ align:start position:0%
+tugging uh for the area to be in the the
+other direction right so we can make
+
+ align:start position:0%
+other direction right so we can make
+ 
+
+ align:start position:0%
+other direction right so we can make
+this solar cell infinitely large um
+
+ align:start position:0%
+this solar cell infinitely large um
+ 
+
+ align:start position:0%
+this solar cell infinitely large um
+thick as we want it to be to absorb all
+
+ align:start position:0%
+thick as we want it to be to absorb all
+ 
+
+ align:start position:0%
+thick as we want it to be to absorb all
+the light great okay hold on to that
+
+ align:start position:0%
+the light great okay hold on to that
+ 
+
+ align:start position:0%
+the light great okay hold on to that
+thought because we're going to have
+
+ align:start position:0%
+thought because we're going to have
+ 
+
+ align:start position:0%
+thought because we're going to have
+another constraining parameter that
+
+ align:start position:0%
+another constraining parameter that
+ 
+
+ align:start position:0%
+another constraining parameter that
+pushes Us in the opposite way in a few
+
+ align:start position:0%
+pushes Us in the opposite way in a few
+ 
+
+ align:start position:0%
+pushes Us in the opposite way in a few
+slides all right so the emitter sheet
+
+ align:start position:0%
+slides all right so the emitter sheet
+ 
+
+ align:start position:0%
+slides all right so the emitter sheet
+resistance um in other words how to
+
+ align:start position:0%
+resistance um in other words how to
+ 
+
+ align:start position:0%
+resistance um in other words how to
+design front contact metalization
+
+ align:start position:0%
+design front contact metalization
+ 
+
+ align:start position:0%
+design front contact metalization
+emitter sheet resistance refers to the
+
+ align:start position:0%
+emitter sheet resistance refers to the
+ 
+
+ align:start position:0%
+emitter sheet resistance refers to the
+resistance of lateral current that the
+
+ align:start position:0%
+resistance of lateral current that the
+ 
+
+ align:start position:0%
+resistance of lateral current that the
+carriers will experience as they move
+
+ align:start position:0%
+carriers will experience as they move
+ 
+
+ align:start position:0%
+carriers will experience as they move
+laterally to reach the front contacts
+
+ align:start position:0%
+laterally to reach the front contacts
+ 
+
+ align:start position:0%
+laterally to reach the front contacts
+and again we go back to this fundamental
+
+ align:start position:0%
+and again we go back to this fundamental
+ 
+
+ align:start position:0%
+and again we go back to this fundamental
+material parameter uh where we have uh
+
+ align:start position:0%
+material parameter uh where we have uh
+ 
+
+ align:start position:0%
+material parameter uh where we have uh
+resistivity as a function of mobility
+
+ align:start position:0%
+resistivity as a function of mobility
+ 
+
+ align:start position:0%
+resistivity as a function of mobility
+and total dopent concentration sorry for
+
+ align:start position:0%
+and total dopent concentration sorry for
+ 
+
+ align:start position:0%
+and total dopent concentration sorry for
+some reason I used the big n here in a
+
+ align:start position:0%
+some reason I used the big n here in a
+ 
+
+ align:start position:0%
+some reason I used the big n here in a
+little end on the previous slide but
+
+ align:start position:0%
+little end on the previous slide but
+ 
+
+ align:start position:0%
+little end on the previous slide but
+it's the same thing it's carrier density
+
+ align:start position:0%
+it's the same thing it's carrier density
+ 
+
+ align:start position:0%
+it's the same thing it's carrier density
+so again our resistivity is a function
+
+ align:start position:0%
+so again our resistivity is a function
+ 
+
+ align:start position:0%
+so again our resistivity is a function
+of carrier mobility and carrier
+
+ align:start position:0%
+of carrier mobility and carrier
+ 
+
+ align:start position:0%
+of carrier mobility and carrier
+concentration how easy it is for the
+
+ align:start position:0%
+concentration how easy it is for the
+ 
+
+ align:start position:0%
+concentration how easy it is for the
+carriers to move and how many of them
+
+ align:start position:0%
+carriers to move and how many of them
+ 
+
+ align:start position:0%
+carriers to move and how many of them
+are there for a thin layer a sheet
+
+ align:start position:0%
+are there for a thin layer a sheet
+ 
+
+ align:start position:0%
+are there for a thin layer a sheet
+resistance can be described as the
+
+ align:start position:0%
+resistance can be described as the
+ 
+
+ align:start position:0%
+resistance can be described as the
+integral of the resistivity by the
+
+ align:start position:0%
+integral of the resistivity by the
+ 
+
+ align:start position:0%
+integral of the resistivity by the
+thickness of that layer or to put it
+
+ align:start position:0%
+thickness of that layer or to put it
+ 
+
+ align:start position:0%
+thickness of that layer or to put it
+more simply if you have a uniform layer
+
+ align:start position:0%
+more simply if you have a uniform layer
+ 
+
+ align:start position:0%
+more simply if you have a uniform layer
+you simply multiply the the denominator
+
+ align:start position:0%
+you simply multiply the the denominator
+ 
+
+ align:start position:0%
+you simply multiply the the denominator
+here by thickness so this this can be
+
+ align:start position:0%
+here by thickness so this this can be
+ 
+
+ align:start position:0%
+here by thickness so this this can be
+thought of in the following way if we
+
+ align:start position:0%
+thought of in the following way if we
+ 
+
+ align:start position:0%
+thought of in the following way if we
+have a thicker uh emitter thicker
+
+ align:start position:0%
+have a thicker uh emitter thicker
+ 
+
+ align:start position:0%
+have a thicker uh emitter thicker
+emitter right we will be dropping the
+
+ align:start position:0%
+emitter right we will be dropping the
+ 
+
+ align:start position:0%
+emitter right we will be dropping the
+emitter sheet resistance we will be
+
+ align:start position:0%
+emitter sheet resistance we will be
+ 
+
+ align:start position:0%
+emitter sheet resistance we will be
+dropping the uh resistance component uh
+
+ align:start position:0%
+dropping the uh resistance component uh
+ 
+
+ align:start position:0%
+dropping the uh resistance component uh
+that carriers uh experience as they
+
+ align:start position:0%
+that carriers uh experience as they
+ 
+
+ align:start position:0%
+that carriers uh experience as they
+travel laterally through this and that
+
+ align:start position:0%
+travel laterally through this and that
+ 
+
+ align:start position:0%
+travel laterally through this and that
+makes sense because in effect as we
+
+ align:start position:0%
+makes sense because in effect as we
+ 
+
+ align:start position:0%
+makes sense because in effect as we
+increase the thickness of this emitter
+
+ align:start position:0%
+increase the thickness of this emitter
+ 
+
+ align:start position:0%
+increase the thickness of this emitter
+region we're increasing the total
+
+ align:start position:0%
+region we're increasing the total
+ 
+
+ align:start position:0%
+region we're increasing the total
+cross-sectional area for the charges to
+
+ align:start position:0%
+cross-sectional area for the charges to
+ 
+
+ align:start position:0%
+cross-sectional area for the charges to
+travel through right
+
+ align:start position:0%
+travel through right
+ 
+
+ align:start position:0%
+travel through right
+so folks with me so far for the emitter
+
+ align:start position:0%
+so folks with me so far for the emitter
+ 
+
+ align:start position:0%
+so folks with me so far for the emitter
+sheet resistance to be uh low we need
+
+ align:start position:0%
+sheet resistance to be uh low we need
+ 
+
+ align:start position:0%
+sheet resistance to be uh low we need
+the thickness to be good enough uh the
+
+ align:start position:0%
+the thickness to be good enough uh the
+ 
+
+ align:start position:0%
+the thickness to be good enough uh the
+thickness to be thick enough the carrier
+
+ align:start position:0%
+thickness to be thick enough the carrier
+ 
+
+ align:start position:0%
+thickness to be thick enough the carrier
+density to be high enough and the
+
+ align:start position:0%
+density to be high enough and the
+ 
+
+ align:start position:0%
+density to be high enough and the
+mobility to be large enough and often
+
+ align:start position:0%
+mobility to be large enough and often
+ 
+
+ align:start position:0%
+mobility to be large enough and often
+times uh the resistivity of a material
+
+ align:start position:0%
+times uh the resistivity of a material
+ 
+
+ align:start position:0%
+times uh the resistivity of a material
+you might spend months trying to
+
+ align:start position:0%
+you might spend months trying to
+ 
+
+ align:start position:0%
+you might spend months trying to
+optimize the resistivity of your emitter
+
+ align:start position:0%
+optimize the resistivity of your emitter
+ 
+
+ align:start position:0%
+optimize the resistivity of your emitter
+region for those doing thinfilm
+
+ align:start position:0%
+region for those doing thinfilm
+ 
+
+ align:start position:0%
+region for those doing thinfilm
+materials you might be working on zinc
+
+ align:start position:0%
+materials you might be working on zinc
+ 
+
+ align:start position:0%
+materials you might be working on zinc
+oxide uh aluminum doped or Florine doped
+
+ align:start position:0%
+oxide uh aluminum doped or Florine doped
+ 
+
+ align:start position:0%
+oxide uh aluminum doped or Florine doped
+zinc oxide for instance and after months
+
+ align:start position:0%
+zinc oxide for instance and after months
+ 
+
+ align:start position:0%
+zinc oxide for instance and after months
+of tuning the temperature and the oxygen
+
+ align:start position:0%
+of tuning the temperature and the oxygen
+ 
+
+ align:start position:0%
+of tuning the temperature and the oxygen
+partial pressure during the deposition
+
+ align:start position:0%
+partial pressure during the deposition
+ 
+
+ align:start position:0%
+partial pressure during the deposition
+process you're there and you have what
+
+ align:start position:0%
+process you're there and you have what
+ 
+
+ align:start position:0%
+process you're there and you have what
+you have you have a certain carry
+
+ align:start position:0%
+you have you have a certain carry
+ 
+
+ align:start position:0%
+you have you have a certain carry
+density and a certain mobility and you
+
+ align:start position:0%
+density and a certain mobility and you
+ 
+
+ align:start position:0%
+density and a certain mobility and you
+can't do much more than vary the
+
+ align:start position:0%
+can't do much more than vary the
+ 
+
+ align:start position:0%
+can't do much more than vary the
+geometric parameter varying the
+
+ align:start position:0%
+geometric parameter varying the
+ 
+
+ align:start position:0%
+geometric parameter varying the
+thickness so what next if my thickness
+
+ align:start position:0%
+thickness so what next if my thickness
+ 
+
+ align:start position:0%
+thickness so what next if my thickness
+is too big on my emitter if my thickness
+
+ align:start position:0%
+is too big on my emitter if my thickness
+ 
+
+ align:start position:0%
+is too big on my emitter if my thickness
+is too big I'm going to be absorbing all
+
+ align:start position:0%
+is too big I'm going to be absorbing all
+ 
+
+ align:start position:0%
+is too big I'm going to be absorbing all
+of my short wavelength photons in the
+
+ align:start position:0%
+of my short wavelength photons in the
+ 
+
+ align:start position:0%
+of my short wavelength photons in the
+front surface of my
+
+ align:start position:0%
+front surface of my
+ 
+
+ align:start position:0%
+front surface of my
+device and maybe the current collection
+
+ align:start position:0%
+device and maybe the current collection
+ 
+
+ align:start position:0%
+device and maybe the current collection
+probability from that layer up here that
+
+ align:start position:0%
+probability from that layer up here that
+ 
+
+ align:start position:0%
+probability from that layer up here that
+has a very high uh uh uh uh uh carrier
+
+ align:start position:0%
+has a very high uh uh uh uh uh carrier
+ 
+
+ align:start position:0%
+has a very high uh uh uh uh uh carrier
+density is not going to be as large in
+
+ align:start position:0%
+density is not going to be as large in
+ 
+
+ align:start position:0%
+density is not going to be as large in
+other words the current collection
+
+ align:start position:0%
+other words the current collection
+ 
+
+ align:start position:0%
+other words the current collection
+efficiency won't be as large as if I
+
+ align:start position:0%
+efficiency won't be as large as if I
+ 
+
+ align:start position:0%
+efficiency won't be as large as if I
+generated the carriers here in the bulk
+
+ align:start position:0%
+generated the carriers here in the bulk
+ 
+
+ align:start position:0%
+generated the carriers here in the bulk
+because of an effect called a Rec
+
+ align:start position:0%
+because of an effect called a Rec
+ 
+
+ align:start position:0%
+because of an effect called a Rec
+combination which we get to in a few
+
+ align:start position:0%
+combination which we get to in a few
+ 
+
+ align:start position:0%
+combination which we get to in a few
+lectures so this uh front surface region
+
+ align:start position:0%
+lectures so this uh front surface region
+ 
+
+ align:start position:0%
+lectures so this uh front surface region
+here often times is considered a dead
+
+ align:start position:0%
+here often times is considered a dead
+ 
+
+ align:start position:0%
+here often times is considered a dead
+layer to a solar cell its electrical
+
+ align:start position:0%
+layer to a solar cell its electrical
+ 
+
+ align:start position:0%
+layer to a solar cell its electrical
+properties are very very poor so if I
+
+ align:start position:0%
+properties are very very poor so if I
+ 
+
+ align:start position:0%
+properties are very very poor so if I
+make this layer too thick sure I get rid
+
+ align:start position:0%
+make this layer too thick sure I get rid
+ 
+
+ align:start position:0%
+make this layer too thick sure I get rid
+of my emitter sheet resistance term but
+
+ align:start position:0%
+of my emitter sheet resistance term but
+ 
+
+ align:start position:0%
+of my emitter sheet resistance term but
+at the same time I'm killing my Quantum
+
+ align:start position:0%
+at the same time I'm killing my Quantum
+ 
+
+ align:start position:0%
+at the same time I'm killing my Quantum
+efficiency in the short
+
+ align:start position:0%
+efficiency in the short
+ 
+
+ align:start position:0%
+efficiency in the short
+wavelengths because I'm not able to
+
+ align:start position:0%
+wavelengths because I'm not able to
+ 
+
+ align:start position:0%
+wavelengths because I'm not able to
+absorb those short wavelength photons
+
+ align:start position:0%
+absorb those short wavelength photons
+ 
+
+ align:start position:0%
+absorb those short wavelength photons
+and convert them efficiency efficiently
+
+ align:start position:0%
+and convert them efficiency efficiently
+ 
+
+ align:start position:0%
+and convert them efficiency efficiently
+into electron hole
+
+ align:start position:0%
+into electron hole
+ 
+
+ align:start position:0%
+into electron hole
+pairs so this is a story about
+
+ align:start position:0%
+pairs so this is a story about
+ 
+
+ align:start position:0%
+pairs so this is a story about
+co-optimization of different device
+
+ align:start position:0%
+co-optimization of different device
+ 
+
+ align:start position:0%
+co-optimization of different device
+parameters so let's let's keep this
+
+ align:start position:0%
+parameters so let's let's keep this
+ 
+
+ align:start position:0%
+parameters so let's let's keep this
+thought for a minute and let's now try
+
+ align:start position:0%
+thought for a minute and let's now try
+ 
+
+ align:start position:0%
+thought for a minute and let's now try
+to calculate the total power loss due to
+
+ align:start position:0%
+to calculate the total power loss due to
+ 
+
+ align:start position:0%
+to calculate the total power loss due to
+the emitter sheet resistance because now
+
+ align:start position:0%
+the emitter sheet resistance because now
+ 
+
+ align:start position:0%
+the emitter sheet resistance because now
+we have this weird unit of ohms per
+
+ align:start position:0%
+we have this weird unit of ohms per
+ 
+
+ align:start position:0%
+we have this weird unit of ohms per
+square in reality it's ohms but when we
+
+ align:start position:0%
+square in reality it's ohms but when we
+ 
+
+ align:start position:0%
+square in reality it's ohms but when we
+take think about emitter sheet
+
+ align:start position:0%
+take think about emitter sheet
+ 
+
+ align:start position:0%
+take think about emitter sheet
+resistance since we're thinking about a
+
+ align:start position:0%
+resistance since we're thinking about a
+ 
+
+ align:start position:0%
+resistance since we're thinking about a
+square of the material um we have units
+
+ align:start position:0%
+square of the material um we have units
+ 
+
+ align:start position:0%
+square of the material um we have units
+of ohms per square square being a
+
+ align:start position:0%
+of ohms per square square being a
+ 
+
+ align:start position:0%
+of ohms per square square being a
+unitless parameter uh so it has uh let's
+
+ align:start position:0%
+unitless parameter uh so it has uh let's
+ 
+
+ align:start position:0%
+unitless parameter uh so it has uh let's
+see resistivity had units of ohm
+
+ align:start position:0%
+see resistivity had units of ohm
+ 
+
+ align:start position:0%
+see resistivity had units of ohm
+centimeter we divided our resistivity by
+
+ align:start position:0%
+centimeter we divided our resistivity by
+ 
+
+ align:start position:0%
+centimeter we divided our resistivity by
+our thickness of that emitter region so
+
+ align:start position:0%
+our thickness of that emitter region so
+ 
+
+ align:start position:0%
+our thickness of that emitter region so
+our units became ohms and and ohms per
+
+ align:start position:0%
+our units became ohms and and ohms per
+ 
+
+ align:start position:0%
+our units became ohms and and ohms per
+square here is the the units typically
+
+ align:start position:0%
+square here is the the units typically
+ 
+
+ align:start position:0%
+square here is the the units typically
+given for meter sheet resistance and um
+
+ align:start position:0%
+given for meter sheet resistance and um
+ 
+
+ align:start position:0%
+given for meter sheet resistance and um
+and now we have to convert this into
+
+ align:start position:0%
+and now we have to convert this into
+ 
+
+ align:start position:0%
+and now we have to convert this into
+some meaningful parameter uh for actual
+
+ align:start position:0%
+some meaningful parameter uh for actual
+ 
+
+ align:start position:0%
+some meaningful parameter uh for actual
+solar cell device so if you want to
+
+ align:start position:0%
+solar cell device so if you want to
+ 
+
+ align:start position:0%
+solar cell device so if you want to
+calculate the fraction of power lost due
+
+ align:start position:0%
+calculate the fraction of power lost due
+ 
+
+ align:start position:0%
+calculate the fraction of power lost due
+to this emitter sheet resistance it's
+
+ align:start position:0%
+to this emitter sheet resistance it's
+ 
+
+ align:start position:0%
+to this emitter sheet resistance it's
+fairly straightforward we would have to
+
+ align:start position:0%
+fairly straightforward we would have to
+ 
+
+ align:start position:0%
+fairly straightforward we would have to
+think about the current uh since power
+
+ align:start position:0%
+think about the current uh since power
+ 
+
+ align:start position:0%
+think about the current uh since power
+is i^ s r we have to think about the
+
+ align:start position:0%
+is i^ s r we have to think about the
+ 
+
+ align:start position:0%
+is i^ s r we have to think about the
+current as a function of the resistance
+
+ align:start position:0%
+current as a function of the resistance
+ 
+
+ align:start position:0%
+current as a function of the resistance
+right as a function of the position here
+
+ align:start position:0%
+right as a function of the position here
+ 
+
+ align:start position:0%
+right as a function of the position here
+we're integrating over uh y y being uh
+
+ align:start position:0%
+we're integrating over uh y y being uh
+ 
+
+ align:start position:0%
+we're integrating over uh y y being uh
+the lateral Dimension and we're
+
+ align:start position:0%
+the lateral Dimension and we're
+ 
+
+ align:start position:0%
+the lateral Dimension and we're
+integrating imagine the separation
+
+ align:start position:0%
+integrating imagine the separation
+ 
+
+ align:start position:0%
+integrating imagine the separation
+between contacts is s so here's one
+
+ align:start position:0%
+between contacts is s so here's one
+ 
+
+ align:start position:0%
+between contacts is s so here's one
+contact metal finger here's the next
+
+ align:start position:0%
+contact metal finger here's the next
+ 
+
+ align:start position:0%
+contact metal finger here's the next
+contact metal finger it's extracting
+
+ align:start position:0%
+contact metal finger it's extracting
+ 
+
+ align:start position:0%
+contact metal finger it's extracting
+charge from the material and we have a a
+
+ align:start position:0%
+charge from the material and we have a a
+ 
+
+ align:start position:0%
+charge from the material and we have a a
+certain distance s right here between
+
+ align:start position:0%
+certain distance s right here between
+ 
+
+ align:start position:0%
+certain distance s right here between
+them so the maximum distance that the
+
+ align:start position:0%
+them so the maximum distance that the
+ 
+
+ align:start position:0%
+them so the maximum distance that the
+current would travel in principle would
+
+ align:start position:0%
+current would travel in principle would
+ 
+
+ align:start position:0%
+current would travel in principle would
+be S / 2 since any current that reaches
+
+ align:start position:0%
+be S / 2 since any current that reaches
+ 
+
+ align:start position:0%
+be S / 2 since any current that reaches
+the emitter over here will be collected
+
+ align:start position:0%
+the emitter over here will be collected
+ 
+
+ align:start position:0%
+the emitter over here will be collected
+by this contact grid and any electrons
+
+ align:start position:0%
+by this contact grid and any electrons
+ 
+
+ align:start position:0%
+by this contact grid and any electrons
+reaching the emitter over here will be
+
+ align:start position:0%
+reaching the emitter over here will be
+ 
+
+ align:start position:0%
+reaching the emitter over here will be
+collected by that contact grid
+
+ align:start position:0%
+collected by that contact grid
+ 
+
+ align:start position:0%
+collected by that contact grid
+finger okay so now we have our current
+
+ align:start position:0%
+finger okay so now we have our current
+ 
+
+ align:start position:0%
+finger okay so now we have our current
+uh we can translate that into here where
+
+ align:start position:0%
+uh we can translate that into here where
+ 
+
+ align:start position:0%
+uh we can translate that into here where
+we have our b b being the uh vertical
+
+ align:start position:0%
+we have our b b being the uh vertical
+ 
+
+ align:start position:0%
+we have our b b being the uh vertical
+Dimension um y being the horizontal
+
+ align:start position:0%
+Dimension um y being the horizontal
+ 
+
+ align:start position:0%
+Dimension um y being the horizontal
+Dimension here um and we would get uh
+
+ align:start position:0%
+Dimension here um and we would get uh
+ 
+
+ align:start position:0%
+Dimension here um and we would get uh
+this equation coming out right on the
+
+ align:start position:0%
+this equation coming out right on the
+ 
+
+ align:start position:0%
+this equation coming out right on the
+other side which is a function of the
+
+ align:start position:0%
+other side which is a function of the
+ 
+
+ align:start position:0%
+other side which is a function of the
+separation of our contact metalization
+
+ align:start position:0%
+separation of our contact metalization
+ 
+
+ align:start position:0%
+separation of our contact metalization
+fingers to the cube to the third power
+
+ align:start position:0%
+fingers to the cube to the third power
+ 
+
+ align:start position:0%
+fingers to the cube to the third power
+so the power loss coming from the solar
+
+ align:start position:0%
+so the power loss coming from the solar
+ 
+
+ align:start position:0%
+so the power loss coming from the solar
+cell device as we separate our contact
+
+ align:start position:0%
+cell device as we separate our contact
+ 
+
+ align:start position:0%
+cell device as we separate our contact
+metalization by a small amount this
+
+ align:start position:0%
+metalization by a small amount this
+ 
+
+ align:start position:0%
+metalization by a small amount this
+power loss is going to go up very
+
+ align:start position:0%
+power loss is going to go up very
+ 
+
+ align:start position:0%
+power loss is going to go up very
+quickly that's a really deep point to to
+
+ align:start position:0%
+quickly that's a really deep point to to
+ 
+
+ align:start position:0%
+quickly that's a really deep point to to
+to recognize here because what this
+
+ align:start position:0%
+to recognize here because what this
+ 
+
+ align:start position:0%
+to recognize here because what this
+means in effect is that we can lose a
+
+ align:start position:0%
+means in effect is that we can lose a
+ 
+
+ align:start position:0%
+means in effect is that we can lose a
+lot of power very quickly in our solar
+
+ align:start position:0%
+lot of power very quickly in our solar
+ 
+
+ align:start position:0%
+lot of power very quickly in our solar
+cell device if we place our contact
+
+ align:start position:0%
+cell device if we place our contact
+ 
+
+ align:start position:0%
+cell device if we place our contact
+fingers too far apart due to this
+
+ align:start position:0%
+fingers too far apart due to this
+ 
+
+ align:start position:0%
+fingers too far apart due to this
+emitter sheet resistance effect due to
+
+ align:start position:0%
+emitter sheet resistance effect due to
+ 
+
+ align:start position:0%
+emitter sheet resistance effect due to
+the row Subs which is our emitter sheet
+
+ align:start position:0%
+the row Subs which is our emitter sheet
+ 
+
+ align:start position:0%
+the row Subs which is our emitter sheet
+resistance or emitter sheet resistance
+
+ align:start position:0%
+resistance or emitter sheet resistance
+ 
+
+ align:start position:0%
+resistance or emitter sheet resistance
+right here okay so then if we uh divide
+
+ align:start position:0%
+right here okay so then if we uh divide
+ 
+
+ align:start position:0%
+right here okay so then if we uh divide
+the power loss by the maximum power
+
+ align:start position:0%
+the power loss by the maximum power
+ 
+
+ align:start position:0%
+the power loss by the maximum power
+point we essentially get a normalized
+
+ align:start position:0%
+point we essentially get a normalized
+ 
+
+ align:start position:0%
+point we essentially get a normalized
+power loss um and so if you want to say
+
+ align:start position:0%
+power loss um and so if you want to say
+ 
+
+ align:start position:0%
+power loss um and so if you want to say
+limit this ratio to a certain fraction
+
+ align:start position:0%
+limit this ratio to a certain fraction
+ 
+
+ align:start position:0%
+limit this ratio to a certain fraction
+say 4% of total power is lost due to M
+
+ align:start position:0%
+say 4% of total power is lost due to M
+ 
+
+ align:start position:0%
+say 4% of total power is lost due to M
+sheet resistance now we can Define the
+
+ align:start position:0%
+sheet resistance now we can Define the
+ 
+
+ align:start position:0%
+sheet resistance now we can Define the
+geometric parameter the distance between
+
+ align:start position:0%
+geometric parameter the distance between
+ 
+
+ align:start position:0%
+geometric parameter the distance between
+the contact metal that we need to do to
+
+ align:start position:0%
+the contact metal that we need to do to
+ 
+
+ align:start position:0%
+the contact metal that we need to do to
+do in an actual solar cell and if you
+
+ align:start position:0%
+do in an actual solar cell and if you
+ 
+
+ align:start position:0%
+do in an actual solar cell and if you
+run through the
+
+ align:start position:0%
+run through the
+ 
+
+ align:start position:0%
+run through the
+calculations uh with a typical uh set of
+
+ align:start position:0%
+calculations uh with a typical uh set of
+ 
+
+ align:start position:0%
+calculations uh with a typical uh set of
+parameters for a silicon based solar
+
+ align:start position:0%
+parameters for a silicon based solar
+ 
+
+ align:start position:0%
+parameters for a silicon based solar
+cell you'll find up find out that your
+
+ align:start position:0%
+cell you'll find up find out that your
+ 
+
+ align:start position:0%
+cell you'll find up find out that your
+uh uh metalization finger should be
+
+ align:start position:0%
+uh uh metalization finger should be
+ 
+
+ align:start position:0%
+uh uh metalization finger should be
+separated on the order of 4 mm and if
+
+ align:start position:0%
+separated on the order of 4 mm and if
+ 
+
+ align:start position:0%
+separated on the order of 4 mm and if
+you remember the real solar cell devices
+
+ align:start position:0%
+you remember the real solar cell devices
+ 
+
+ align:start position:0%
+you remember the real solar cell devices
+that you saw embedded in that module the
+
+ align:start position:0%
+that you saw embedded in that module the
+ 
+
+ align:start position:0%
+that you saw embedded in that module the
+separation of the fingers is just about
+
+ align:start position:0%
+separation of the fingers is just about
+ 
+
+ align:start position:0%
+separation of the fingers is just about
+4 millim so this is where that finger
+
+ align:start position:0%
+4 millim so this is where that finger
+ 
+
+ align:start position:0%
+4 millim so this is where that finger
+separation comes from in one case you'd
+
+ align:start position:0%
+separation comes from in one case you'd
+ 
+
+ align:start position:0%
+separation comes from in one case you'd
+want to have your fingers spaced really
+
+ align:start position:0%
+want to have your fingers spaced really
+ 
+
+ align:start position:0%
+want to have your fingers spaced really
+really close together to minimize the
+
+ align:start position:0%
+really close together to minimize the
+ 
+
+ align:start position:0%
+really close together to minimize the
+emitter sheet resistance but on the
+
+ align:start position:0%
+emitter sheet resistance but on the
+ 
+
+ align:start position:0%
+emitter sheet resistance but on the
+other hand if you place your fingers too
+
+ align:start position:0%
+other hand if you place your fingers too
+ 
+
+ align:start position:0%
+other hand if you place your fingers too
+close together you're shading the front
+
+ align:start position:0%
+close together you're shading the front
+ 
+
+ align:start position:0%
+close together you're shading the front
+surface of your solar cell with metal
+
+ align:start position:0%
+surface of your solar cell with metal
+ 
+
+ align:start position:0%
+surface of your solar cell with metal
+and light's not going to get in to
+
+ align:start position:0%
+and light's not going to get in to
+ 
+
+ align:start position:0%
+and light's not going to get in to
+generate electron hole pairs so that's
+
+ align:start position:0%
+generate electron hole pairs so that's
+ 
+
+ align:start position:0%
+generate electron hole pairs so that's
+the optimization function that's run
+
+ align:start position:0%
+the optimization function that's run
+ 
+
+ align:start position:0%
+the optimization function that's run
+right there wow so far we I'm counting
+
+ align:start position:0%
+right there wow so far we I'm counting
+ 
+
+ align:start position:0%
+right there wow so far we I'm counting
+three or four of these different
+
+ align:start position:0%
+three or four of these different
+ 
+
+ align:start position:0%
+three or four of these different
+parameters tugging in different
+
+ align:start position:0%
+parameters tugging in different
+ 
+
+ align:start position:0%
+parameters tugging in different
+directions right so you can begin to
+
+ align:start position:0%
+directions right so you can begin to
+ 
+
+ align:start position:0%
+directions right so you can begin to
+sense how constrained the solar cell
+
+ align:start position:0%
+sense how constrained the solar cell
+ 
+
+ align:start position:0%
+sense how constrained the solar cell
+device is in terms of optimization of
+
+ align:start position:0%
+device is in terms of optimization of
+ 
+
+ align:start position:0%
+device is in terms of optimization of
+all these parameters and how easy it is
+
+ align:start position:0%
+all these parameters and how easy it is
+ 
+
+ align:start position:0%
+all these parameters and how easy it is
+to make a very low efficiency device as
+
+ align:start position:0%
+to make a very low efficiency device as
+ 
+
+ align:start position:0%
+to make a very low efficiency device as
+a result how difficult it is to make a
+
+ align:start position:0%
+a result how difficult it is to make a
+ 
+
+ align:start position:0%
+a result how difficult it is to make a
+high efficiency device so um this is
+
+ align:start position:0%
+high efficiency device so um this is
+ 
+
+ align:start position:0%
+high efficiency device so um this is
+interesting um so we have now the
+
+ align:start position:0%
+interesting um so we have now the
+ 
+
+ align:start position:0%
+interesting um so we have now the
+spacing the appropriate spacing between
+
+ align:start position:0%
+spacing the appropriate spacing between
+ 
+
+ align:start position:0%
+spacing the appropriate spacing between
+uh uh fingers it's about 4 mm which
+
+ align:start position:0%
+uh uh fingers it's about 4 mm which
+ 
+
+ align:start position:0%
+uh uh fingers it's about 4 mm which
+means if we're going to be making a
+
+ align:start position:0%
+means if we're going to be making a
+ 
+
+ align:start position:0%
+means if we're going to be making a
+solar cell device say a thin film solar
+
+ align:start position:0%
+solar cell device say a thin film solar
+ 
+
+ align:start position:0%
+solar cell device say a thin film solar
+cell device on a sheet of glass with
+
+ align:start position:0%
+cell device on a sheet of glass with
+ 
+
+ align:start position:0%
+cell device on a sheet of glass with
+some transparent conducting uh material
+
+ align:start position:0%
+some transparent conducting uh material
+ 
+
+ align:start position:0%
+some transparent conducting uh material
+some transparent conducting oxy now we
+
+ align:start position:0%
+some transparent conducting oxy now we
+ 
+
+ align:start position:0%
+some transparent conducting oxy now we
+have our solar cell device we have their
+
+ align:start position:0%
+have our solar cell device we have their
+ 
+
+ align:start position:0%
+have our solar cell device we have their
+front surface here and we have let's say
+
+ align:start position:0%
+front surface here and we have let's say
+ 
+
+ align:start position:0%
+front surface here and we have let's say
+something else on top um we have to
+
+ align:start position:0%
+something else on top um we have to
+ 
+
+ align:start position:0%
+something else on top um we have to
+limit how wide we make that device
+
+ align:start position:0%
+limit how wide we make that device
+ 
+
+ align:start position:0%
+limit how wide we make that device
+otherwise we could be limited by our uh
+
+ align:start position:0%
+otherwise we could be limited by our uh
+ 
+
+ align:start position:0%
+otherwise we could be limited by our uh
+emitter sheet our sheet resistance in
+
+ align:start position:0%
+emitter sheet our sheet resistance in
+ 
+
+ align:start position:0%
+emitter sheet our sheet resistance in
+say the zinc oxide layer of our device
+
+ align:start position:0%
+say the zinc oxide layer of our device
+ 
+
+ align:start position:0%
+say the zinc oxide layer of our device
+and this is interesting now
+
+ align:start position:0%
+and this is interesting now
+ 
+
+ align:start position:0%
+and this is interesting now
+because uh previously for the bulk
+
+ align:start position:0%
+because uh previously for the bulk
+ 
+
+ align:start position:0%
+because uh previously for the bulk
+resistance let's think back over to our
+
+ align:start position:0%
+resistance let's think back over to our
+ 
+
+ align:start position:0%
+resistance let's think back over to our
+bulk resistance we wanted our area to be
+
+ align:start position:0%
+bulk resistance we wanted our area to be
+ 
+
+ align:start position:0%
+bulk resistance we wanted our area to be
+large because we wanted to minimize the
+
+ align:start position:0%
+large because we wanted to minimize the
+ 
+
+ align:start position:0%
+large because we wanted to minimize the
+bulk resistance now we want the area to
+
+ align:start position:0%
+bulk resistance now we want the area to
+ 
+
+ align:start position:0%
+bulk resistance now we want the area to
+be small so that we minimize our M sheet
+
+ align:start position:0%
+be small so that we minimize our M sheet
+ 
+
+ align:start position:0%
+be small so that we minimize our M sheet
+resistance so you can see how the the
+
+ align:start position:0%
+resistance so you can see how the the
+ 
+
+ align:start position:0%
+resistance so you can see how the the
+the current traveling in two orthogonal
+
+ align:start position:0%
+the current traveling in two orthogonal
+ 
+
+ align:start position:0%
+the current traveling in two orthogonal
+directions inside of our device is
+
+ align:start position:0%
+directions inside of our device is
+ 
+
+ align:start position:0%
+directions inside of our device is
+really causing us problems because we're
+
+ align:start position:0%
+really causing us problems because we're
+ 
+
+ align:start position:0%
+really causing us problems because we're
+having to optimize the same parameter in
+
+ align:start position:0%
+having to optimize the same parameter in
+ 
+
+ align:start position:0%
+having to optimize the same parameter in
+different directions for
+
+ align:start position:0%
+different directions for
+ 
+
+ align:start position:0%
+different directions for
+each It's Tricky uh and I'm providing
+
+ align:start position:0%
+each It's Tricky uh and I'm providing
+ 
+
+ align:start position:0%
+each It's Tricky uh and I'm providing
+you the tools here to be able to sit
+
+ align:start position:0%
+you the tools here to be able to sit
+ 
+
+ align:start position:0%
+you the tools here to be able to sit
+down and calculate out uh what is the
+
+ align:start position:0%
+down and calculate out uh what is the
+ 
+
+ align:start position:0%
+down and calculate out uh what is the
+optimal thickness what is the optimal uh
+
+ align:start position:0%
+optimal thickness what is the optimal uh
+ 
+
+ align:start position:0%
+optimal thickness what is the optimal uh
+thickness of your emitter uh of your
+
+ align:start position:0%
+thickness of your emitter uh of your
+ 
+
+ align:start position:0%
+thickness of your emitter uh of your
+base and what is the optimal lateral
+
+ align:start position:0%
+base and what is the optimal lateral
+ 
+
+ align:start position:0%
+base and what is the optimal lateral
+dimensions of your solar cell device to
+
+ align:start position:0%
+dimensions of your solar cell device to
+ 
+
+ align:start position:0%
+dimensions of your solar cell device to
+simultaneously minimize your bulk
+
+ align:start position:0%
+simultaneously minimize your bulk
+ 
+
+ align:start position:0%
+simultaneously minimize your bulk
+resistance and your emitter uh
+
+ align:start position:0%
+resistance and your emitter uh
+ 
+
+ align:start position:0%
+resistance and your emitter uh
+resistance inside of a device and you
+
+ align:start position:0%
+resistance inside of a device and you
+ 
+
+ align:start position:0%
+resistance inside of a device and you
+can do it all now with equations that I
+
+ align:start position:0%
+can do it all now with equations that I
+ 
+
+ align:start position:0%
+can do it all now with equations that I
+just gave you so it's pretty cool at
+
+ align:start position:0%
+just gave you so it's pretty cool at
+ 
+
+ align:start position:0%
+just gave you so it's pretty cool at
+least the first
+
+ align:start position:0%
+least the first
+ 
+
+ align:start position:0%
+least the first
+order how did you define again yeah
+
+ align:start position:0%
+order how did you define again yeah
+ 
+
+ align:start position:0%
+order how did you define again yeah
+absolutely so B was a lateral a vertical
+
+ align:start position:0%
+absolutely so B was a lateral a vertical
+ 
+
+ align:start position:0%
+absolutely so B was a lateral a vertical
+Dimension B is just given as the
+
+ align:start position:0%
+Dimension B is just given as the
+ 
+
+ align:start position:0%
+Dimension B is just given as the
+distance here
+
+ align:start position:0%
+distance here
+ 
+
+ align:start position:0%
+distance here
+yeah that's that's going across if you
+
+ align:start position:0%
+yeah that's that's going across if you
+ 
+
+ align:start position:0%
+yeah that's that's going across if you
+look down your you're looking down on
+
+ align:start position:0%
+look down your you're looking down on
+ 
+
+ align:start position:0%
+look down your you're looking down on
+your on your solar cell so the p and
+
+ align:start position:0%
+your on your solar cell so the p and
+ 
+
+ align:start position:0%
+your on your solar cell so the p and
+Junction would be planer uh to this view
+
+ align:start position:0%
+Junction would be planer uh to this view
+ 
+
+ align:start position:0%
+Junction would be planer uh to this view
+right here y some to the board
+
+ align:start position:0%
+right here y some to the board
+ 
+
+ align:start position:0%
+right here y some to the board
+yep so bird's eye view on the solar cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other
+
+ align:start position:0%
+any other
+ 
+
+ align:start position:0%
+any other
+questions okay so um contact resistance
+
+ align:start position:0%
+questions okay so um contact resistance
+ 
+
+ align:start position:0%
+questions okay so um contact resistance
+this is the next thing that can kill a
+
+ align:start position:0%
+this is the next thing that can kill a
+ 
+
+ align:start position:0%
+this is the next thing that can kill a
+solar cell device uh contact resistance
+
+ align:start position:0%
+solar cell device uh contact resistance
+ 
+
+ align:start position:0%
+solar cell device uh contact resistance
+we want to minimize the contact
+
+ align:start position:0%
+we want to minimize the contact
+ 
+
+ align:start position:0%
+we want to minimize the contact
+resistance but the first step to
+
+ align:start position:0%
+resistance but the first step to
+ 
+
+ align:start position:0%
+resistance but the first step to
+minimizing is to measure to know what
+
+ align:start position:0%
+minimizing is to measure to know what
+ 
+
+ align:start position:0%
+minimizing is to measure to know what
+your contact resistance really is and uh
+
+ align:start position:0%
+your contact resistance really is and uh
+ 
+
+ align:start position:0%
+your contact resistance really is and uh
+one simple way to measure contact
+
+ align:start position:0%
+one simple way to measure contact
+ 
+
+ align:start position:0%
+one simple way to measure contact
+resistance is to take a cross-section of
+
+ align:start position:0%
+resistance is to take a cross-section of
+ 
+
+ align:start position:0%
+resistance is to take a cross-section of
+your solar cell device where you've
+
+ align:start position:0%
+your solar cell device where you've
+ 
+
+ align:start position:0%
+your solar cell device where you've
+deposited say four metal fingers on it
+
+ align:start position:0%
+deposited say four metal fingers on it
+ 
+
+ align:start position:0%
+deposited say four metal fingers on it
+and they're appropriately spaced by how
+
+ align:start position:0%
+and they're appropriately spaced by how
+ 
+
+ align:start position:0%
+and they're appropriately spaced by how
+many millimeters or so um so you have a
+
+ align:start position:0%
+many millimeters or so um so you have a
+ 
+
+ align:start position:0%
+many millimeters or so um so you have a
+certain contact resistance right here uh
+
+ align:start position:0%
+certain contact resistance right here uh
+ 
+
+ align:start position:0%
+certain contact resistance right here uh
+between the uh the metal and your U
+
+ align:start position:0%
+between the uh the metal and your U
+ 
+
+ align:start position:0%
+between the uh the metal and your U
+semiconductor material that's denoted as
+
+ align:start position:0%
+semiconductor material that's denoted as
+ 
+
+ align:start position:0%
+semiconductor material that's denoted as
+R subc and then there's a certain uh
+
+ align:start position:0%
+R subc and then there's a certain uh
+ 
+
+ align:start position:0%
+R subc and then there's a certain uh
+emitter resistance that we just talked
+
+ align:start position:0%
+emitter resistance that we just talked
+ 
+
+ align:start position:0%
+emitter resistance that we just talked
+about R subm right here um and if you
+
+ align:start position:0%
+about R subm right here um and if you
+ 
+
+ align:start position:0%
+about R subm right here um and if you
+were to measure the um the current
+
+ align:start position:0%
+were to measure the um the current
+ 
+
+ align:start position:0%
+were to measure the um the current
+passing through uh here to here or
+
+ align:start position:0%
+passing through uh here to here or
+ 
+
+ align:start position:0%
+passing through uh here to here or
+another way to say it is the resistance
+
+ align:start position:0%
+another way to say it is the resistance
+ 
+
+ align:start position:0%
+another way to say it is the resistance
+for current to pass from this point to
+
+ align:start position:0%
+for current to pass from this point to
+ 
+
+ align:start position:0%
+for current to pass from this point to
+that point you might get um let's say
+
+ align:start position:0%
+that point you might get um let's say
+ 
+
+ align:start position:0%
+that point you might get um let's say
+this data point right here a total
+
+ align:start position:0%
+this data point right here a total
+ 
+
+ align:start position:0%
+this data point right here a total
+resistance value of some value and a
+
+ align:start position:0%
+resistance value of some value and a
+ 
+
+ align:start position:0%
+resistance value of some value and a
+distance between uh the two probes of
+
+ align:start position:0%
+distance between uh the two probes of
+ 
+
+ align:start position:0%
+distance between uh the two probes of
+say one times uh D subf where D subf is
+
+ align:start position:0%
+say one times uh D subf where D subf is
+ 
+
+ align:start position:0%
+say one times uh D subf where D subf is
+the unit distance between two adjacent
+
+ align:start position:0%
+the unit distance between two adjacent
+ 
+
+ align:start position:0%
+the unit distance between two adjacent
+uh contact metalization fingers now if
+
+ align:start position:0%
+uh contact metalization fingers now if
+ 
+
+ align:start position:0%
+uh contact metalization fingers now if
+we measure the resistance between this
+
+ align:start position:0%
+we measure the resistance between this
+ 
+
+ align:start position:0%
+we measure the resistance between this
+point and that point we might wind up
+
+ align:start position:0%
+point and that point we might wind up
+ 
+
+ align:start position:0%
+point and that point we might wind up
+with that data point right here
+
+ align:start position:0%
+with that data point right here
+ 
+
+ align:start position:0%
+with that data point right here
+and if we measure the resistance between
+
+ align:start position:0%
+and if we measure the resistance between
+ 
+
+ align:start position:0%
+and if we measure the resistance between
+this point and that point we already did
+
+ align:start position:0%
+this point and that point we already did
+ 
+
+ align:start position:0%
+this point and that point we already did
+that this point and that point we might
+
+ align:start position:0%
+that this point and that point we might
+ 
+
+ align:start position:0%
+that this point and that point we might
+wind up with that data point right here
+
+ align:start position:0%
+wind up with that data point right here
+ 
+
+ align:start position:0%
+wind up with that data point right here
+and so forth and what's happening well
+
+ align:start position:0%
+and so forth and what's happening well
+ 
+
+ align:start position:0%
+and so forth and what's happening well
+as the current goes into the device it
+
+ align:start position:0%
+as the current goes into the device it
+ 
+
+ align:start position:0%
+as the current goes into the device it
+passes once through the contact
+
+ align:start position:0%
+passes once through the contact
+ 
+
+ align:start position:0%
+passes once through the contact
+resistance a certain n * R sub em n
+
+ align:start position:0%
+resistance a certain n * R sub em n
+ 
+
+ align:start position:0%
+resistance a certain n * R sub em n
+being the number of uh metalization
+
+ align:start position:0%
+being the number of uh metalization
+ 
+
+ align:start position:0%
+being the number of uh metalization
+number of hops the number of times we
+
+ align:start position:0%
+number of hops the number of times we
+ 
+
+ align:start position:0%
+number of hops the number of times we
+travel a distance DF and then it goes
+
+ align:start position:0%
+travel a distance DF and then it goes
+ 
+
+ align:start position:0%
+travel a distance DF and then it goes
+out the other side again traveling
+
+ align:start position:0%
+out the other side again traveling
+ 
+
+ align:start position:0%
+out the other side again traveling
+through uh the contact resistance so the
+
+ align:start position:0%
+through uh the contact resistance so the
+ 
+
+ align:start position:0%
+through uh the contact resistance so the
+slope of this line here should be equal
+
+ align:start position:0%
+slope of this line here should be equal
+ 
+
+ align:start position:0%
+slope of this line here should be equal
+to the emitter
+
+ align:start position:0%
+to the emitter
+ 
+
+ align:start position:0%
+to the emitter
+resistance and the offset The Intercept
+
+ align:start position:0%
+resistance and the offset The Intercept
+ 
+
+ align:start position:0%
+resistance and the offset The Intercept
+at uh x equals 0 here The Intercept
+
+ align:start position:0%
+at uh x equals 0 here The Intercept
+ 
+
+ align:start position:0%
+at uh x equals 0 here The Intercept
+should be two times the contact
+
+ align:start position:0%
+should be two times the contact
+ 
+
+ align:start position:0%
+should be two times the contact
+resistance because in principle that
+
+ align:start position:0%
+resistance because in principle that
+ 
+
+ align:start position:0%
+resistance because in principle that
+would be the equivalent of current going
+
+ align:start position:0%
+would be the equivalent of current going
+ 
+
+ align:start position:0%
+would be the equivalent of current going
+in and going back out through this
+
+ align:start position:0%
+in and going back out through this
+ 
+
+ align:start position:0%
+in and going back out through this
+contact resistance right here through
+
+ align:start position:0%
+contact resistance right here through
+ 
+
+ align:start position:0%
+contact resistance right here through
+the same one not traveling at all
+
+ align:start position:0%
+the same one not traveling at all
+ 
+
+ align:start position:0%
+the same one not traveling at all
+through the emitter obviously since
+
+ align:start position:0%
+through the emitter obviously since
+ 
+
+ align:start position:0%
+through the emitter obviously since
+that's impossible to measure we have to
+
+ align:start position:0%
+that's impossible to measure we have to
+ 
+
+ align:start position:0%
+that's impossible to measure we have to
+determine that through extrapolation
+
+ align:start position:0%
+determine that through extrapolation
+ 
+
+ align:start position:0%
+determine that through extrapolation
+back to the the y- axis so this
+
+ align:start position:0%
+back to the the y- axis so this
+ 
+
+ align:start position:0%
+back to the the y- axis so this
+so-called tlm method the transmission
+
+ align:start position:0%
+so-called tlm method the transmission
+ 
+
+ align:start position:0%
+so-called tlm method the transmission
+line method is a method that is used to
+
+ align:start position:0%
+line method is a method that is used to
+ 
+
+ align:start position:0%
+line method is a method that is used to
+determine the contact resistance of a
+
+ align:start position:0%
+determine the contact resistance of a
+ 
+
+ align:start position:0%
+determine the contact resistance of a
+solar cell device um you could either
+
+ align:start position:0%
+solar cell device um you could either
+ 
+
+ align:start position:0%
+solar cell device um you could either
+perform it linearly in this fashion
+
+ align:start position:0%
+perform it linearly in this fashion
+ 
+
+ align:start position:0%
+perform it linearly in this fashion
+right here or using a circular uh uh
+
+ align:start position:0%
+right here or using a circular uh uh
+ 
+
+ align:start position:0%
+right here or using a circular uh uh
+essentially an array of concentric
+
+ align:start position:0%
+essentially an array of concentric
+ 
+
+ align:start position:0%
+essentially an array of concentric
+circles and the latter method is
+
+ align:start position:0%
+circles and the latter method is
+ 
+
+ align:start position:0%
+circles and the latter method is
+typically preferred uh especially in
+
+ align:start position:0%
+typically preferred uh especially in
+ 
+
+ align:start position:0%
+typically preferred uh especially in
+thin film
+
+ align:start position:0%
+thin film
+ 
+
+ align:start position:0%
+thin film
+devices so this is how you measure the
+
+ align:start position:0%
+devices so this is how you measure the
+ 
+
+ align:start position:0%
+devices so this is how you measure the
+contact resistance um and then there are
+
+ align:start position:0%
+contact resistance um and then there are
+ 
+
+ align:start position:0%
+contact resistance um and then there are
+line losses so what can oh let me back
+
+ align:start position:0%
+line losses so what can oh let me back
+ 
+
+ align:start position:0%
+line losses so what can oh let me back
+up one step what can affect the contact
+
+ align:start position:0%
+up one step what can affect the contact
+ 
+
+ align:start position:0%
+up one step what can affect the contact
+resistance typically what affects
+
+ align:start position:0%
+resistance typically what affects
+ 
+
+ align:start position:0%
+resistance typically what affects
+contact resistance is the uh uh Atomic
+
+ align:start position:0%
+contact resistance is the uh uh Atomic
+ 
+
+ align:start position:0%
+contact resistance is the uh uh Atomic
+interface between your metal and your
+
+ align:start position:0%
+interface between your metal and your
+ 
+
+ align:start position:0%
+interface between your metal and your
+semiconductor whether it's an organic or
+
+ align:start position:0%
+semiconductor whether it's an organic or
+ 
+
+ align:start position:0%
+semiconductor whether it's an organic or
+an inorganic semiconductor bless you so
+
+ align:start position:0%
+an inorganic semiconductor bless you so
+ 
+
+ align:start position:0%
+an inorganic semiconductor bless you so
+the uh the the interface here is what
+
+ align:start position:0%
+the uh the the interface here is what
+ 
+
+ align:start position:0%
+the uh the the interface here is what
+determines uh the contact resistance
+
+ align:start position:0%
+determines uh the contact resistance
+ 
+
+ align:start position:0%
+determines uh the contact resistance
+typically and of course the dopent
+
+ align:start position:0%
+typically and of course the dopent
+ 
+
+ align:start position:0%
+typically and of course the dopent
+density uh within your uh
+
+ align:start position:0%
+density uh within your uh
+ 
+
+ align:start position:0%
+density uh within your uh
+semiconductor so components of the
+
+ align:start position:0%
+semiconductor so components of the
+ 
+
+ align:start position:0%
+semiconductor so components of the
+series resistance and the line losses so
+
+ align:start position:0%
+series resistance and the line losses so
+ 
+
+ align:start position:0%
+series resistance and the line losses so
+line losses are essentially the uh
+
+ align:start position:0%
+line losses are essentially the uh
+ 
+
+ align:start position:0%
+line losses are essentially the uh
+losses
+
+ align:start position:0%
+losses
+ 
+
+ align:start position:0%
+losses
+um in the contact metalization lines out
+
+ align:start position:0%
+um in the contact metalization lines out
+ 
+
+ align:start position:0%
+um in the contact metalization lines out
+of plane uh what can cause uh a
+
+ align:start position:0%
+of plane uh what can cause uh a
+ 
+
+ align:start position:0%
+of plane uh what can cause uh a
+resistance in the contact metalization
+
+ align:start position:0%
+resistance in the contact metalization
+ 
+
+ align:start position:0%
+resistance in the contact metalization
+line well intuitively we know that okay
+
+ align:start position:0%
+line well intuitively we know that okay
+ 
+
+ align:start position:0%
+line well intuitively we know that okay
+if the line is too small if the
+
+ align:start position:0%
+if the line is too small if the
+ 
+
+ align:start position:0%
+if the line is too small if the
+cross-section of that line is too tiny
+
+ align:start position:0%
+cross-section of that line is too tiny
+ 
+
+ align:start position:0%
+cross-section of that line is too tiny
+then there's going to be uh High
+
+ align:start position:0%
+then there's going to be uh High
+ 
+
+ align:start position:0%
+then there's going to be uh High
+Resistance uh to current travel along
+
+ align:start position:0%
+Resistance uh to current travel along
+ 
+
+ align:start position:0%
+Resistance uh to current travel along
+that line and indeed that's the case who
+
+ align:start position:0%
+that line and indeed that's the case who
+ 
+
+ align:start position:0%
+that line and indeed that's the case who
+we have the same exact equation as we
+
+ align:start position:0%
+we have the same exact equation as we
+ 
+
+ align:start position:0%
+we have the same exact equation as we
+had for our base resistance now it's
+
+ align:start position:0%
+had for our base resistance now it's
+ 
+
+ align:start position:0%
+had for our base resistance now it's
+applied to the line because in principle
+
+ align:start position:0%
+applied to the line because in principle
+ 
+
+ align:start position:0%
+applied to the line because in principle
+it's the same thing we have current
+
+ align:start position:0%
+it's the same thing we have current
+ 
+
+ align:start position:0%
+it's the same thing we have current
+traveling through uh in in One Direction
+
+ align:start position:0%
+traveling through uh in in One Direction
+ 
+
+ align:start position:0%
+traveling through uh in in One Direction
+along a a constrained uh um
+
+ align:start position:0%
+along a a constrained uh um
+ 
+
+ align:start position:0%
+along a a constrained uh um
+cross-sectional area a certain distance
+
+ align:start position:0%
+cross-sectional area a certain distance
+ 
+
+ align:start position:0%
+cross-sectional area a certain distance
+a certain length so we have now our
+
+ align:start position:0%
+a certain length so we have now our
+ 
+
+ align:start position:0%
+a certain length so we have now our
+resistivity given by the metal obviously
+
+ align:start position:0%
+resistivity given by the metal obviously
+ 
+
+ align:start position:0%
+resistivity given by the metal obviously
+because now we're talking about the
+
+ align:start position:0%
+because now we're talking about the
+ 
+
+ align:start position:0%
+because now we're talking about the
+metal itself not the semiconductor
+
+ align:start position:0%
+metal itself not the semiconductor
+ 
+
+ align:start position:0%
+metal itself not the semiconductor
+anymore current traveling along the
+
+ align:start position:0%
+anymore current traveling along the
+ 
+
+ align:start position:0%
+anymore current traveling along the
+contact metal so the the row becomes the
+
+ align:start position:0%
+contact metal so the the row becomes the
+ 
+
+ align:start position:0%
+contact metal so the the row becomes the
+resistivity of the metal the a becomes
+
+ align:start position:0%
+resistivity of the metal the a becomes
+ 
+
+ align:start position:0%
+resistivity of the metal the a becomes
+the cross-sectional area of the contact
+
+ align:start position:0%
+the cross-sectional area of the contact
+ 
+
+ align:start position:0%
+the cross-sectional area of the contact
+finger and the L is the length of the
+
+ align:start position:0%
+finger and the L is the length of the
+ 
+
+ align:start position:0%
+finger and the L is the length of the
+conductive path in other words how long
+
+ align:start position:0%
+conductive path in other words how long
+ 
+
+ align:start position:0%
+conductive path in other words how long
+how long does the current have to travel
+
+ align:start position:0%
+how long does the current have to travel
+ 
+
+ align:start position:0%
+how long does the current have to travel
+along that contact metal before it
+
+ align:start position:0%
+along that contact metal before it
+ 
+
+ align:start position:0%
+along that contact metal before it
+reaches a highway a bus bar one of those
+
+ align:start position:0%
+reaches a highway a bus bar one of those
+ 
+
+ align:start position:0%
+reaches a highway a bus bar one of those
+really thick uh strips of metal on our
+
+ align:start position:0%
+really thick uh strips of metal on our
+ 
+
+ align:start position:0%
+really thick uh strips of metal on our
+solar cell device
+
+ align:start position:0%
+solar cell device
+ 
+
+ align:start position:0%
+solar cell device
+um in which case it's Home Free so the r
+
+ align:start position:0%
+um in which case it's Home Free so the r
+ 
+
+ align:start position:0%
+um in which case it's Home Free so the r
+the the the the the row rather the uh
+
+ align:start position:0%
+the the the the the row rather the uh
+ 
+
+ align:start position:0%
+the the the the the row rather the uh
+metal resistivity resistivities of
+
+ align:start position:0%
+metal resistivity resistivities of
+ 
+
+ align:start position:0%
+metal resistivity resistivities of
+several uh uh metals and non-metal
+
+ align:start position:0%
+several uh uh metals and non-metal
+ 
+
+ align:start position:0%
+several uh uh metals and non-metal
+materials are given here um that's
+
+ align:start position:0%
+materials are given here um that's
+ 
+
+ align:start position:0%
+materials are given here um that's
+typically why you see silver contact
+
+ align:start position:0%
+typically why you see silver contact
+ 
+
+ align:start position:0%
+typically why you see silver contact
+metalization used for uh solar cells
+
+ align:start position:0%
+metalization used for uh solar cells
+ 
+
+ align:start position:0%
+metalization used for uh solar cells
+it's because it has a very low
+
+ align:start position:0%
+it's because it has a very low
+ 
+
+ align:start position:0%
+it's because it has a very low
+resistivity which means that the
+
+ align:start position:0%
+resistivity which means that the
+ 
+
+ align:start position:0%
+resistivity which means that the
+resistance line losses will be
+
+ align:start position:0%
+resistance line losses will be
+ 
+
+ align:start position:0%
+resistance line losses will be
+small now what is the problem with
+
+ align:start position:0%
+small now what is the problem with
+ 
+
+ align:start position:0%
+small now what is the problem with
+silver does anybody know what percentage
+
+ align:start position:0%
+silver does anybody know what percentage
+ 
+
+ align:start position:0%
+silver does anybody know what percentage
+of the world's silver right now
+
+ align:start position:0%
+of the world's silver right now
+ 
+
+ align:start position:0%
+of the world's silver right now
+manufactured each year is currently
+
+ align:start position:0%
+manufactured each year is currently
+ 
+
+ align:start position:0%
+manufactured each year is currently
+being used for contact metalization on
+
+ align:start position:0%
+being used for contact metalization on
+ 
+
+ align:start position:0%
+being used for contact metalization on
+solar
+
+ align:start position:0%
+solar
+ 
+
+ align:start position:0%
+solar
+cells take a number guess a little lower
+
+ align:start position:0%
+cells take a number guess a little lower
+ 
+
+ align:start position:0%
+cells take a number guess a little lower
+um but but in that order of magnitude so
+
+ align:start position:0%
+um but but in that order of magnitude so
+ 
+
+ align:start position:0%
+um but but in that order of magnitude so
+he said 30 uh somewhere upwards of 10%
+
+ align:start position:0%
+he said 30 uh somewhere upwards of 10%
+ 
+
+ align:start position:0%
+he said 30 uh somewhere upwards of 10%
+right it be your guess so around 10% um
+
+ align:start position:0%
+right it be your guess so around 10% um
+ 
+
+ align:start position:0%
+right it be your guess so around 10% um
+and of course PV is growing at
+
+ align:start position:0%
+and of course PV is growing at
+ 
+
+ align:start position:0%
+and of course PV is growing at
+accumulative annual growth rates in the
+
+ align:start position:0%
+accumulative annual growth rates in the
+ 
+
+ align:start position:0%
+accumulative annual growth rates in the
+several tens of percents per year so
+
+ align:start position:0%
+several tens of percents per year so
+ 
+
+ align:start position:0%
+several tens of percents per year so
+silver utilization is expected to
+
+ align:start position:0%
+silver utilization is expected to
+ 
+
+ align:start position:0%
+silver utilization is expected to
+continue to increase so either we mine
+
+ align:start position:0%
+continue to increase so either we mine
+ 
+
+ align:start position:0%
+continue to increase so either we mine
+more silver or we mer we we venture to
+
+ align:start position:0%
+more silver or we mer we we venture to
+ 
+
+ align:start position:0%
+more silver or we mer we we venture to
+another contact metal uh material and
+
+ align:start position:0%
+another contact metal uh material and
+ 
+
+ align:start position:0%
+another contact metal uh material and
+that's why you see folks looking at the
+
+ align:start position:0%
+that's why you see folks looking at the
+ 
+
+ align:start position:0%
+that's why you see folks looking at the
+copper nickel which is similar in
+
+ align:start position:0%
+copper nickel which is similar in
+ 
+
+ align:start position:0%
+copper nickel which is similar in
+electronic structure it's one uh element
+
+ align:start position:0%
+electronic structure it's one uh element
+ 
+
+ align:start position:0%
+electronic structure it's one uh element
+to the left of copper on the periodic
+
+ align:start position:0%
+to the left of copper on the periodic
+ 
+
+ align:start position:0%
+to the left of copper on the periodic
+table and and other uh metal
+
+ align:start position:0%
+table and and other uh metal
+ 
+
+ align:start position:0%
+table and and other uh metal
+Alternatives yes yeah where does Nickel
+
+ align:start position:0%
+Alternatives yes yeah where does Nickel
+ 
+
+ align:start position:0%
+Alternatives yes yeah where does Nickel
+fall on this res resistivity chart I
+
+ align:start position:0%
+fall on this res resistivity chart I
+ 
+
+ align:start position:0%
+fall on this res resistivity chart I
+have to give you the exact number but if
+
+ align:start position:0%
+have to give you the exact number but if
+ 
+
+ align:start position:0%
+have to give you the exact number but if
+I were to venture a guess what you're
+
+ align:start position:0%
+I were to venture a guess what you're
+ 
+
+ align:start position:0%
+I were to venture a guess what you're
+noticing over here um are several of the
+
+ align:start position:0%
+noticing over here um are several of the
+ 
+
+ align:start position:0%
+noticing over here um are several of the
+um metals that fall in the noble metal
+
+ align:start position:0%
+um metals that fall in the noble metal
+ 
+
+ align:start position:0%
+um metals that fall in the noble metal
+category uh these are far to the right
+
+ align:start position:0%
+category uh these are far to the right
+ 
+
+ align:start position:0%
+category uh these are far to the right
+on the 3D series uh so if you pict the
+
+ align:start position:0%
+on the 3D series uh so if you pict the
+ 
+
+ align:start position:0%
+on the 3D series uh so if you pict the
+periodic table again far in the 3D
+
+ align:start position:0%
+periodic table again far in the 3D
+ 
+
+ align:start position:0%
+periodic table again far in the 3D
+series you have that Dell uh orbital
+
+ align:start position:0%
+series you have that Dell uh orbital
+ 
+
+ align:start position:0%
+series you have that Dell uh orbital
+completely filled and those outermost
+
+ align:start position:0%
+completely filled and those outermost
+ 
+
+ align:start position:0%
+completely filled and those outermost
+electrons are then screened by all the
+
+ align:start position:0%
+electrons are then screened by all the
+ 
+
+ align:start position:0%
+electrons are then screened by all the
+other electrons in the system and very
+
+ align:start position:0%
+other electrons in the system and very
+ 
+
+ align:start position:0%
+other electrons in the system and very
+Loosely bound so you can remove the
+
+ align:start position:0%
+Loosely bound so you can remove the
+ 
+
+ align:start position:0%
+Loosely bound so you can remove the
+electrons fairly easily um it's one of
+
+ align:start position:0%
+electrons fairly easily um it's one of
+ 
+
+ align:start position:0%
+electrons fairly easily um it's one of
+the reasons why these uh these these
+
+ align:start position:0%
+the reasons why these uh these these
+ 
+
+ align:start position:0%
+the reasons why these uh these these
+elements in that class have a higher
+
+ align:start position:0%
+elements in that class have a higher
+ 
+
+ align:start position:0%
+elements in that class have a higher
+conductivity a lower resistivity yep
+
+ align:start position:0%
+conductivity a lower resistivity yep
+ 
+
+ align:start position:0%
+conductivity a lower resistivity yep
+question copper doesn't seem that much
+
+ align:start position:0%
+question copper doesn't seem that much
+ 
+
+ align:start position:0%
+question copper doesn't seem that much
+worse than Sil reason so um yes
+
+ align:start position:0%
+worse than Sil reason so um yes
+ 
+
+ align:start position:0%
+worse than Sil reason so um yes
+absolutely uh copper doesn't seem so
+
+ align:start position:0%
+absolutely uh copper doesn't seem so
+ 
+
+ align:start position:0%
+absolutely uh copper doesn't seem so
+much worse than silver uh so uh the uh
+
+ align:start position:0%
+much worse than silver uh so uh the uh
+ 
+
+ align:start position:0%
+much worse than silver uh so uh the uh
+contact metallization pastes to date
+
+ align:start position:0%
+contact metallization pastes to date
+ 
+
+ align:start position:0%
+contact metallization pastes to date
+have mostly been using silver uh copper
+
+ align:start position:0%
+have mostly been using silver uh copper
+ 
+
+ align:start position:0%
+have mostly been using silver uh copper
+uh can oxidized fairly easily um so
+
+ align:start position:0%
+uh can oxidized fairly easily um so
+ 
+
+ align:start position:0%
+uh can oxidized fairly easily um so
+that's one one downside of copper uh
+
+ align:start position:0%
+that's one one downside of copper uh
+ 
+
+ align:start position:0%
+that's one one downside of copper uh
+another uh problem with copper is that
+
+ align:start position:0%
+another uh problem with copper is that
+ 
+
+ align:start position:0%
+another uh problem with copper is that
+it's a very fast diffuser uh it's very
+
+ align:start position:0%
+it's a very fast diffuser uh it's very
+ 
+
+ align:start position:0%
+it's a very fast diffuser uh it's very
+tiny uh and so the elastic strain energy
+
+ align:start position:0%
+tiny uh and so the elastic strain energy
+ 
+
+ align:start position:0%
+tiny uh and so the elastic strain energy
+term as it tries to move through a
+
+ align:start position:0%
+term as it tries to move through a
+ 
+
+ align:start position:0%
+term as it tries to move through a
+lattice is very small uh and as a result
+
+ align:start position:0%
+lattice is very small uh and as a result
+ 
+
+ align:start position:0%
+lattice is very small uh and as a result
+it goes deep so when you fire your
+
+ align:start position:0%
+it goes deep so when you fire your
+ 
+
+ align:start position:0%
+it goes deep so when you fire your
+contact metalization when you create the
+
+ align:start position:0%
+contact metalization when you create the
+ 
+
+ align:start position:0%
+contact metalization when you create the
+contact between your metal and your
+
+ align:start position:0%
+contact between your metal and your
+ 
+
+ align:start position:0%
+contact between your metal and your
+semiconductor underneath you run the
+
+ align:start position:0%
+semiconductor underneath you run the
+ 
+
+ align:start position:0%
+semiconductor underneath you run the
+risk of having atoms diffuse into your
+
+ align:start position:0%
+risk of having atoms diffuse into your
+ 
+
+ align:start position:0%
+risk of having atoms diffuse into your
+device and uh hurting the efficiency uh
+
+ align:start position:0%
+device and uh hurting the efficiency uh
+ 
+
+ align:start position:0%
+device and uh hurting the efficiency uh
+hurting the uh ability of the solar cell
+
+ align:start position:0%
+hurting the uh ability of the solar cell
+ 
+
+ align:start position:0%
+hurting the uh ability of the solar cell
+to collect carriers we'll hear more
+
+ align:start position:0%
+to collect carriers we'll hear more
+ 
+
+ align:start position:0%
+to collect carriers we'll hear more
+about that on Tuesday so it becomes an
+
+ align:start position:0%
+about that on Tuesday so it becomes an
+ 
+
+ align:start position:0%
+about that on Tuesday so it becomes an
+impurity yeah exactly it becomes an
+
+ align:start position:0%
+impurity yeah exactly it becomes an
+ 
+
+ align:start position:0%
+impurity yeah exactly it becomes an
+impurity in this case unintentional so
+
+ align:start position:0%
+impurity in this case unintentional so
+ 
+
+ align:start position:0%
+impurity in this case unintentional so
+uh just remember where the contact is
+
+ align:start position:0%
+uh just remember where the contact is
+ 
+
+ align:start position:0%
+uh just remember where the contact is
+right here in the emitter okay if it
+
+ align:start position:0%
+right here in the emitter okay if it
+ 
+
+ align:start position:0%
+right here in the emitter okay if it
+diffuses into the emitter it's okay the
+
+ align:start position:0%
+diffuses into the emitter it's okay the
+ 
+
+ align:start position:0%
+diffuses into the emitter it's okay the
+electrons at this point are the majority
+
+ align:start position:0%
+electrons at this point are the majority
+ 
+
+ align:start position:0%
+electrons at this point are the majority
+carriers but if the metal diffuses all
+
+ align:start position:0%
+carriers but if the metal diffuses all
+ 
+
+ align:start position:0%
+carriers but if the metal diffuses all
+the way into the bulk the electrons
+
+ align:start position:0%
+the way into the bulk the electrons
+ 
+
+ align:start position:0%
+the way into the bulk the electrons
+inside of the bulk and here are minority
+
+ align:start position:0%
+inside of the bulk and here are minority
+ 
+
+ align:start position:0%
+inside of the bulk and here are minority
+carriers and they can be impacted by the
+
+ align:start position:0%
+carriers and they can be impacted by the
+ 
+
+ align:start position:0%
+carriers and they can be impacted by the
+presence of of that copper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there all right so um I wanted to get
+
+ align:start position:0%
+there all right so um I wanted to get
+ 
+
+ align:start position:0%
+there all right so um I wanted to get
+through at least one more uh point to
+
+ align:start position:0%
+through at least one more uh point to
+ 
+
+ align:start position:0%
+through at least one more uh point to
+really set us up well uh on Tuesday we
+
+ align:start position:0%
+really set us up well uh on Tuesday we
+ 
+
+ align:start position:0%
+really set us up well uh on Tuesday we
+want to be able to calculate the firmy
+
+ align:start position:0%
+want to be able to calculate the firmy
+ 
+
+ align:start position:0%
+want to be able to calculate the firmy
+energy of a solar cell as a function of
+
+ align:start position:0%
+energy of a solar cell as a function of
+ 
+
+ align:start position:0%
+energy of a solar cell as a function of
+dopen concentration illumination
+
+ align:start position:0%
+dopen concentration illumination
+ 
+
+ align:start position:0%
+dopen concentration illumination
+condition and temperature so so far
+
+ align:start position:0%
+condition and temperature so so far
+ 
+
+ align:start position:0%
+condition and temperature so so far
+we've really talked about the fmy energy
+
+ align:start position:0%
+we've really talked about the fmy energy
+ 
+
+ align:start position:0%
+we've really talked about the fmy energy
+the chemical potential inside of a solar
+
+ align:start position:0%
+the chemical potential inside of a solar
+ 
+
+ align:start position:0%
+the chemical potential inside of a solar
+cell in handwavy terms we've talked
+
+ align:start position:0%
+cell in handwavy terms we've talked
+ 
+
+ align:start position:0%
+cell in handwavy terms we've talked
+about General Trends about how as we add
+
+ align:start position:0%
+about General Trends about how as we add
+ 
+
+ align:start position:0%
+about General Trends about how as we add
+more electrons to our system Say by
+
+ align:start position:0%
+more electrons to our system Say by
+ 
+
+ align:start position:0%
+more electrons to our system Say by
+doping we shift The Firm energy up
+
+ align:start position:0%
+doping we shift The Firm energy up
+ 
+
+ align:start position:0%
+doping we shift The Firm energy up
+because the average Ensemble energy of
+
+ align:start position:0%
+because the average Ensemble energy of
+ 
+
+ align:start position:0%
+because the average Ensemble energy of
+the electrons is increasing um but now
+
+ align:start position:0%
+the electrons is increasing um but now
+ 
+
+ align:start position:0%
+the electrons is increasing um but now
+we're going to be calculating it and
+
+ align:start position:0%
+we're going to be calculating it and
+ 
+
+ align:start position:0%
+we're going to be calculating it and
+determining how to calculate it so the
+
+ align:start position:0%
+determining how to calculate it so the
+ 
+
+ align:start position:0%
+determining how to calculate it so the
+question is um you know calculating fir
+
+ align:start position:0%
+question is um you know calculating fir
+ 
+
+ align:start position:0%
+question is um you know calculating fir
+energy so let's introduce A New Concept
+
+ align:start position:0%
+energy so let's introduce A New Concept
+ 
+
+ align:start position:0%
+energy so let's introduce A New Concept
+here so far we've talked about an energy
+
+ align:start position:0%
+here so far we've talked about an energy
+ 
+
+ align:start position:0%
+here so far we've talked about an energy
+band diagram and drawn our veence band
+
+ align:start position:0%
+band diagram and drawn our veence band
+ 
+
+ align:start position:0%
+band diagram and drawn our veence band
+and drawn our conduction band and of
+
+ align:start position:0%
+and drawn our conduction band and of
+ 
+
+ align:start position:0%
+and drawn our conduction band and of
+course the band Gap in between them
+
+ align:start position:0%
+course the band Gap in between them
+ 
+
+ align:start position:0%
+course the band Gap in between them
+we've drawn the veence band and
+
+ align:start position:0%
+we've drawn the veence band and
+ 
+
+ align:start position:0%
+we've drawn the veence band and
+conduction bands as if they were just
+
+ align:start position:0%
+conduction bands as if they were just
+ 
+
+ align:start position:0%
+conduction bands as if they were just
+Continuum uh density of States as if
+
+ align:start position:0%
+Continuum uh density of States as if
+ 
+
+ align:start position:0%
+Continuum uh density of States as if
+they were just these blocks where
+
+ align:start position:0%
+they were just these blocks where
+ 
+
+ align:start position:0%
+they were just these blocks where
+electrons could Pile in
+
+ align:start position:0%
+electrons could Pile in
+ 
+
+ align:start position:0%
+electrons could Pile in
+um in reality we have what's called a
+
+ align:start position:0%
+um in reality we have what's called a
+ 
+
+ align:start position:0%
+um in reality we have what's called a
+density of States um in the veilance
+
+ align:start position:0%
+density of States um in the veilance
+ 
+
+ align:start position:0%
+density of States um in the veilance
+band and a density of states in the
+
+ align:start position:0%
+band and a density of states in the
+ 
+
+ align:start position:0%
+band and a density of states in the
+conduction band uh if you want to think
+
+ align:start position:0%
+conduction band uh if you want to think
+ 
+
+ align:start position:0%
+conduction band uh if you want to think
+about electrons as cars the density of
+
+ align:start position:0%
+about electrons as cars the density of
+ 
+
+ align:start position:0%
+about electrons as cars the density of
+States could be considered the uh number
+
+ align:start position:0%
+States could be considered the uh number
+ 
+
+ align:start position:0%
+States could be considered the uh number
+of uh parking spaces there are per floor
+
+ align:start position:0%
+of uh parking spaces there are per floor
+ 
+
+ align:start position:0%
+of uh parking spaces there are per floor
+in a parking garage right as you
+
+ align:start position:0%
+in a parking garage right as you
+ 
+
+ align:start position:0%
+in a parking garage right as you
+increase the energy and in the case of a
+
+ align:start position:0%
+increase the energy and in the case of a
+ 
+
+ align:start position:0%
+increase the energy and in the case of a
+parking garage you increase your
+
+ align:start position:0%
+parking garage you increase your
+ 
+
+ align:start position:0%
+parking garage you increase your
+potential energy as you move your car
+
+ align:start position:0%
+potential energy as you move your car
+ 
+
+ align:start position:0%
+potential energy as you move your car
+higher and higher um and here you would
+
+ align:start position:0%
+higher and higher um and here you would
+ 
+
+ align:start position:0%
+higher and higher um and here you would
+be increasing the energy of the
+
+ align:start position:0%
+be increasing the energy of the
+ 
+
+ align:start position:0%
+be increasing the energy of the
+electrons as you go higher and higher
+
+ align:start position:0%
+electrons as you go higher and higher
+ 
+
+ align:start position:0%
+electrons as you go higher and higher
+the increase in the energy of holes as
+
+ align:start position:0%
+the increase in the energy of holes as
+ 
+
+ align:start position:0%
+the increase in the energy of holes as
+they go lower and lower so we have a
+
+ align:start position:0%
+they go lower and lower so we have a
+ 
+
+ align:start position:0%
+they go lower and lower so we have a
+certain density of states that is
+
+ align:start position:0%
+certain density of states that is
+ 
+
+ align:start position:0%
+certain density of states that is
+allowed uh inside of our semiconductor
+
+ align:start position:0%
+allowed uh inside of our semiconductor
+ 
+
+ align:start position:0%
+allowed uh inside of our semiconductor
+and there is a very small density of
+
+ align:start position:0%
+and there is a very small density of
+ 
+
+ align:start position:0%
+and there is a very small density of
+states right at the band Edge and that
+
+ align:start position:0%
+states right at the band Edge and that
+ 
+
+ align:start position:0%
+states right at the band Edge and that
+density of States typically increases as
+
+ align:start position:0%
+density of States typically increases as
+ 
+
+ align:start position:0%
+density of States typically increases as
+you go deeper and deeper into the
+
+ align:start position:0%
+you go deeper and deeper into the
+ 
+
+ align:start position:0%
+you go deeper and deeper into the
+bands so now um in at at at room temp at
+
+ align:start position:0%
+bands so now um in at at at room temp at
+ 
+
+ align:start position:0%
+bands so now um in at at at room temp at
+absolute zero and the person who
+
+ align:start position:0%
+absolute zero and the person who
+ 
+
+ align:start position:0%
+absolute zero and the person who
+probably knows more about absolute zero
+
+ align:start position:0%
+probably knows more about absolute zero
+ 
+
+ align:start position:0%
+probably knows more about absolute zero
+than anybody else here in this room is
+
+ align:start position:0%
+than anybody else here in this room is
+ 
+
+ align:start position:0%
+than anybody else here in this room is
+Christy Simmons in the back who for her
+
+ align:start position:0%
+Christy Simmons in the back who for her
+ 
+
+ align:start position:0%
+Christy Simmons in the back who for her
+PhD uh would work on very low
+
+ align:start position:0%
+PhD uh would work on very low
+ 
+
+ align:start position:0%
+PhD uh would work on very low
+temperature experiments down into the
+
+ align:start position:0%
+temperature experiments down into the
+ 
+
+ align:start position:0%
+temperature experiments down into the
+what tens of Melvin range tens of Melvin
+
+ align:start position:0%
+what tens of Melvin range tens of Melvin
+ 
+
+ align:start position:0%
+what tens of Melvin range tens of Melvin
+range it's very very cold um and if you
+
+ align:start position:0%
+range it's very very cold um and if you
+ 
+
+ align:start position:0%
+range it's very very cold um and if you
+cool things down if you cool things down
+
+ align:start position:0%
+cool things down if you cool things down
+ 
+
+ align:start position:0%
+cool things down if you cool things down
+a lot uh all the electrons that were
+
+ align:start position:0%
+a lot uh all the electrons that were
+ 
+
+ align:start position:0%
+a lot uh all the electrons that were
+excited will drop down say into the
+
+ align:start position:0%
+excited will drop down say into the
+ 
+
+ align:start position:0%
+excited will drop down say into the
+valence band right here and what this is
+
+ align:start position:0%
+valence band right here and what this is
+ 
+
+ align:start position:0%
+valence band right here and what this is
+represented is is a fil filled veence
+
+ align:start position:0%
+represented is is a fil filled veence
+ 
+
+ align:start position:0%
+represented is is a fil filled veence
+band right there and as you begin
+
+ align:start position:0%
+band right there and as you begin
+ 
+
+ align:start position:0%
+band right there and as you begin
+heating uh your system up some of the
+
+ align:start position:0%
+heating uh your system up some of the
+ 
+
+ align:start position:0%
+heating uh your system up some of the
+electrons will have the thermal energy
+
+ align:start position:0%
+electrons will have the thermal energy
+ 
+
+ align:start position:0%
+electrons will have the thermal energy
+to be excited across the bandap so
+
+ align:start position:0%
+to be excited across the bandap so
+ 
+
+ align:start position:0%
+to be excited across the bandap so
+thermally excited electrons here
+
+ align:start position:0%
+thermally excited electrons here
+ 
+
+ align:start position:0%
+thermally excited electrons here
+represented um in your conduction band
+
+ align:start position:0%
+represented um in your conduction band
+ 
+
+ align:start position:0%
+represented um in your conduction band
+so we have a certain number of thermally
+
+ align:start position:0%
+so we have a certain number of thermally
+ 
+
+ align:start position:0%
+so we have a certain number of thermally
+excited electrons here uh up into the uh
+
+ align:start position:0%
+excited electrons here uh up into the uh
+ 
+
+ align:start position:0%
+excited electrons here uh up into the uh
+up into the conduction
+
+ align:start position:0%
+up into the conduction
+ 
+
+ align:start position:0%
+up into the conduction
+band oh and um these carriers these
+
+ align:start position:0%
+band oh and um these carriers these
+ 
+
+ align:start position:0%
+band oh and um these carriers these
+carriers will call intrinsic carriers
+
+ align:start position:0%
+carriers will call intrinsic carriers
+ 
+
+ align:start position:0%
+carriers will call intrinsic carriers
+because they're not added by dopin we're
+
+ align:start position:0%
+because they're not added by dopin we're
+ 
+
+ align:start position:0%
+because they're not added by dopin we're
+not adding anything to the semiconductor
+
+ align:start position:0%
+not adding anything to the semiconductor
+ 
+
+ align:start position:0%
+not adding anything to the semiconductor
+to create dopin to uh generate new
+
+ align:start position:0%
+to create dopin to uh generate new
+ 
+
+ align:start position:0%
+to create dopin to uh generate new
+carriers these are intrinsic carriers
+
+ align:start position:0%
+carriers these are intrinsic carriers
+ 
+
+ align:start position:0%
+carriers these are intrinsic carriers
+because they came from the veence band
+
+ align:start position:0%
+because they came from the veence band
+ 
+
+ align:start position:0%
+because they came from the veence band
+went up to the conduction band so if we
+
+ align:start position:0%
+went up to the conduction band so if we
+ 
+
+ align:start position:0%
+went up to the conduction band so if we
+plot intrinsic carrier concentration as
+
+ align:start position:0%
+plot intrinsic carrier concentration as
+ 
+
+ align:start position:0%
+plot intrinsic carrier concentration as
+a function of temperature we see a curve
+
+ align:start position:0%
+a function of temperature we see a curve
+ 
+
+ align:start position:0%
+a function of temperature we see a curve
+that looks like this and it follows this
+
+ align:start position:0%
+that looks like this and it follows this
+ 
+
+ align:start position:0%
+that looks like this and it follows this
+expression right here which is called an
+
+ align:start position:0%
+expression right here which is called an
+ 
+
+ align:start position:0%
+expression right here which is called an
+uranous equation in a generic form um in
+
+ align:start position:0%
+uranous equation in a generic form um in
+ 
+
+ align:start position:0%
+uranous equation in a generic form um in
+this case it would be intrinsic carrier
+
+ align:start position:0%
+this case it would be intrinsic carrier
+ 
+
+ align:start position:0%
+this case it would be intrinsic carrier
+concentration as a function of
+
+ align:start position:0%
+concentration as a function of
+ 
+
+ align:start position:0%
+concentration as a function of
+temperature we'd have to substitute this
+
+ align:start position:0%
+temperature we'd have to substitute this
+ 
+
+ align:start position:0%
+temperature we'd have to substitute this
+big n here for intrinsic carrier
+
+ align:start position:0%
+big n here for intrinsic carrier
+ 
+
+ align:start position:0%
+big n here for intrinsic carrier
+concentration some exponential preactor
+
+ align:start position:0%
+concentration some exponential preactor
+ 
+
+ align:start position:0%
+concentration some exponential preactor
+and in an activation energy the
+
+ align:start position:0%
+and in an activation energy the
+ 
+
+ align:start position:0%
+and in an activation energy the
+activation energy being the energy
+
+ align:start position:0%
+activation energy being the energy
+ 
+
+ align:start position:0%
+activation energy being the energy
+needed to create that free carrier right
+
+ align:start position:0%
+needed to create that free carrier right
+ 
+
+ align:start position:0%
+needed to create that free carrier right
+the bang Gap energy in this case the
+
+ align:start position:0%
+the bang Gap energy in this case the
+ 
+
+ align:start position:0%
+the bang Gap energy in this case the
+activation energy divided by KBT the um
+
+ align:start position:0%
+activation energy divided by KBT the um
+ 
+
+ align:start position:0%
+activation energy divided by KBT the um
+KBT being boltzman's constant time
+
+ align:start position:0%
+KBT being boltzman's constant time
+ 
+
+ align:start position:0%
+KBT being boltzman's constant time
+temperature in Calvin now if we plot the
+
+ align:start position:0%
+temperature in Calvin now if we plot the
+ 
+
+ align:start position:0%
+temperature in Calvin now if we plot the
+the same functions that we just saw in
+
+ align:start position:0%
+the same functions that we just saw in
+ 
+
+ align:start position:0%
+the same functions that we just saw in
+the previous slide a little differently
+
+ align:start position:0%
+the previous slide a little differently
+ 
+
+ align:start position:0%
+the previous slide a little differently
+we plot 1/ T say 1 over T right there
+
+ align:start position:0%
+we plot 1/ T say 1 over T right there
+ 
+
+ align:start position:0%
+we plot 1/ T say 1 over T right there
+and we plot the log of this value so
+
+ align:start position:0%
+and we plot the log of this value so
+ 
+
+ align:start position:0%
+and we plot the log of this value so
+again log of this value we can read the
+
+ align:start position:0%
+again log of this value we can read the
+ 
+
+ align:start position:0%
+again log of this value we can read the
+activation energy off of the slope of
+
+ align:start position:0%
+activation energy off of the slope of
+ 
+
+ align:start position:0%
+activation energy off of the slope of
+this graph so that's why you typically
+
+ align:start position:0%
+this graph so that's why you typically
+ 
+
+ align:start position:0%
+this graph so that's why you typically
+see uranous plots plotted in this way 1
+
+ align:start position:0%
+see uranous plots plotted in this way 1
+ 
+
+ align:start position:0%
+see uranous plots plotted in this way 1
+overt versus log of parameter because
+
+ align:start position:0%
+overt versus log of parameter because
+ 
+
+ align:start position:0%
+overt versus log of parameter because
+you can read the activation energy
+
+ align:start position:0%
+you can read the activation energy
+ 
+
+ align:start position:0%
+you can read the activation energy
+straight off of the graph it becomes
+
+ align:start position:0%
+straight off of the graph it becomes
+ 
+
+ align:start position:0%
+straight off of the graph it becomes
+very easy to see the carrier
+
+ align:start position:0%
+very easy to see the carrier
+ 
+
+ align:start position:0%
+very easy to see the carrier
+concentration so again at Absolute Zero
+
+ align:start position:0%
+concentration so again at Absolute Zero
+ 
+
+ align:start position:0%
+concentration so again at Absolute Zero
+at Absolute Zero we have um uh uh here
+
+ align:start position:0%
+at Absolute Zero we have um uh uh here
+ 
+
+ align:start position:0%
+at Absolute Zero we have um uh uh here
+the veilance band completely filled the
+
+ align:start position:0%
+the veilance band completely filled the
+ 
+
+ align:start position:0%
+the veilance band completely filled the
+conduction band completely empty in our
+
+ align:start position:0%
+conduction band completely empty in our
+ 
+
+ align:start position:0%
+conduction band completely empty in our
+semiconductor and the probability of
+
+ align:start position:0%
+semiconductor and the probability of
+ 
+
+ align:start position:0%
+semiconductor and the probability of
+occupancy of a state inside of our
+
+ align:start position:0%
+occupancy of a state inside of our
+ 
+
+ align:start position:0%
+occupancy of a state inside of our
+semiconductor is given by this box
+
+ align:start position:0%
+semiconductor is given by this box
+ 
+
+ align:start position:0%
+semiconductor is given by this box
+function right here now let's look at
+
+ align:start position:0%
+function right here now let's look at
+ 
+
+ align:start position:0%
+function right here now let's look at
+what happens when we Heat this up when
+
+ align:start position:0%
+what happens when we Heat this up when
+ 
+
+ align:start position:0%
+what happens when we Heat this up when
+we heat the sample up some of the
+
+ align:start position:0%
+we heat the sample up some of the
+ 
+
+ align:start position:0%
+we heat the sample up some of the
+electrons that were in the higher energy
+
+ align:start position:0%
+electrons that were in the higher energy
+ 
+
+ align:start position:0%
+electrons that were in the higher energy
+states are going to be excited so they
+
+ align:start position:0%
+states are going to be excited so they
+ 
+
+ align:start position:0%
+states are going to be excited so they
+used to be here in lower energy States
+
+ align:start position:0%
+used to be here in lower energy States
+ 
+
+ align:start position:0%
+used to be here in lower energy States
+they're going to be excited the higher
+
+ align:start position:0%
+they're going to be excited the higher
+ 
+
+ align:start position:0%
+they're going to be excited the higher
+energy states
+
+ align:start position:0%
+energy states
+ 
+
+ align:start position:0%
+energy states
+and the area of this little shape right
+
+ align:start position:0%
+and the area of this little shape right
+ 
+
+ align:start position:0%
+and the area of this little shape right
+here is equal to the area of that little
+
+ align:start position:0%
+here is equal to the area of that little
+ 
+
+ align:start position:0%
+here is equal to the area of that little
+shape right here because we have
+
+ align:start position:0%
+shape right here because we have
+ 
+
+ align:start position:0%
+shape right here because we have
+conservation of number of electrons in
+
+ align:start position:0%
+conservation of number of electrons in
+ 
+
+ align:start position:0%
+conservation of number of electrons in
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+system if we multiply this by the
+
+ align:start position:0%
+system if we multiply this by the
+ 
+
+ align:start position:0%
+system if we multiply this by the
+density of States this is the density of
+
+ align:start position:0%
+density of States this is the density of
+ 
+
+ align:start position:0%
+density of States this is the density of
+states in the veilance band minimized
+
+ align:start position:0%
+states in the veilance band minimized
+ 
+
+ align:start position:0%
+states in the veilance band minimized
+here at the band edges uh and and
+
+ align:start position:0%
+here at the band edges uh and and
+ 
+
+ align:start position:0%
+here at the band edges uh and and
+increasing as we go deeper into the
+
+ align:start position:0%
+increasing as we go deeper into the
+ 
+
+ align:start position:0%
+increasing as we go deeper into the
+bands for the valance band and the
+
+ align:start position:0%
+bands for the valance band and the
+ 
+
+ align:start position:0%
+bands for the valance band and the
+conduction band so we take our
+
+ align:start position:0%
+conduction band so we take our
+ 
+
+ align:start position:0%
+conduction band so we take our
+probability distribution function
+
+ align:start position:0%
+probability distribution function
+ 
+
+ align:start position:0%
+probability distribution function
+multiply it by the density of states and
+
+ align:start position:0%
+multiply it by the density of states and
+ 
+
+ align:start position:0%
+multiply it by the density of states and
+we get the occupied density of states in
+
+ align:start position:0%
+we get the occupied density of states in
+ 
+
+ align:start position:0%
+we get the occupied density of states in
+our semiconductor so now we see that
+
+ align:start position:0%
+our semiconductor so now we see that
+ 
+
+ align:start position:0%
+our semiconductor so now we see that
+there's some uh number of missing
+
+ align:start position:0%
+there's some uh number of missing
+ 
+
+ align:start position:0%
+there's some uh number of missing
+electrons that are now in the conduction
+
+ align:start position:0%
+electrons that are now in the conduction
+ 
+
+ align:start position:0%
+electrons that are now in the conduction
+band they used to be in the valence band
+
+ align:start position:0%
+band they used to be in the valence band
+ 
+
+ align:start position:0%
+band they used to be in the valence band
+at very low temperature but now as we
+
+ align:start position:0%
+at very low temperature but now as we
+ 
+
+ align:start position:0%
+at very low temperature but now as we
+increase the temperature they've had the
+
+ align:start position:0%
+increase the temperature they've had the
+ 
+
+ align:start position:0%
+increase the temperature they've had the
+thermal energy to excite across given
+
+ align:start position:0%
+thermal energy to excite across given
+ 
+
+ align:start position:0%
+thermal energy to excite across given
+this probability distribution
+
+ align:start position:0%
+this probability distribution
+ 
+
+ align:start position:0%
+this probability distribution
+function and these carriers are now free
+
+ align:start position:0%
+function and these carriers are now free
+ 
+
+ align:start position:0%
+function and these carriers are now free
+to conduct charge inside of our
+
+ align:start position:0%
+to conduct charge inside of our
+ 
+
+ align:start position:0%
+to conduct charge inside of our
+system so what can we do with this
+
+ align:start position:0%
+system so what can we do with this
+ 
+
+ align:start position:0%
+system so what can we do with this
+framework with this understanding well
+
+ align:start position:0%
+framework with this understanding well
+ 
+
+ align:start position:0%
+framework with this understanding well
+um we can uh we can look at this uh
+
+ align:start position:0%
+um we can uh we can look at this uh
+ 
+
+ align:start position:0%
+um we can uh we can look at this uh
+function here and ask ourselves what is
+
+ align:start position:0%
+function here and ask ourselves what is
+ 
+
+ align:start position:0%
+function here and ask ourselves what is
+the name of that function it's called
+
+ align:start position:0%
+the name of that function it's called
+ 
+
+ align:start position:0%
+the name of that function it's called
+the firir distribution and it's given by
+
+ align:start position:0%
+the firir distribution and it's given by
+ 
+
+ align:start position:0%
+the firir distribution and it's given by
+this equation right here we'll notice in
+
+ align:start position:0%
+this equation right here we'll notice in
+ 
+
+ align:start position:0%
+this equation right here we'll notice in
+the firir distribution we'll notice that
+
+ align:start position:0%
+the firir distribution we'll notice that
+ 
+
+ align:start position:0%
+the firir distribution we'll notice that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+equation um approximates to an
+
+ align:start position:0%
+equation um approximates to an
+ 
+
+ align:start position:0%
+equation um approximates to an
+exponential equation as we M move
+
+ align:start position:0%
+exponential equation as we M move
+ 
+
+ align:start position:0%
+exponential equation as we M move
+further and further away from the firm
+
+ align:start position:0%
+further and further away from the firm
+ 
+
+ align:start position:0%
+further and further away from the firm
+energy The Firm energy being defined as
+
+ align:start position:0%
+energy The Firm energy being defined as
+ 
+
+ align:start position:0%
+energy The Firm energy being defined as
+this energy right here if we move
+
+ align:start position:0%
+this energy right here if we move
+ 
+
+ align:start position:0%
+this energy right here if we move
+further way down here or further way up
+
+ align:start position:0%
+further way down here or further way up
+ 
+
+ align:start position:0%
+further way down here or further way up
+here this starts looking awful lot like
+
+ align:start position:0%
+here this starts looking awful lot like
+ 
+
+ align:start position:0%
+here this starts looking awful lot like
+an exponential meaning this right here
+
+ align:start position:0%
+an exponential meaning this right here
+ 
+
+ align:start position:0%
+an exponential meaning this right here
+and this right here start looking like
+
+ align:start position:0%
+and this right here start looking like
+ 
+
+ align:start position:0%
+and this right here start looking like
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+functions okay so let's um do a quick
+
+ align:start position:0%
+functions okay so let's um do a quick
+ 
+
+ align:start position:0%
+functions okay so let's um do a quick
+little gunan experiment a quick little
+
+ align:start position:0%
+little gunan experiment a quick little
+ 
+
+ align:start position:0%
+little gunan experiment a quick little
+thought experiment about what happens
+
+ align:start position:0%
+thought experiment about what happens
+ 
+
+ align:start position:0%
+thought experiment about what happens
+when we heat up a semiconductor and how
+
+ align:start position:0%
+when we heat up a semiconductor and how
+ 
+
+ align:start position:0%
+when we heat up a semiconductor and how
+would this impact how would these free
+
+ align:start position:0%
+would this impact how would these free
+ 
+
+ align:start position:0%
+would this impact how would these free
+carriers right here impact um the uh the
+
+ align:start position:0%
+carriers right here impact um the uh the
+ 
+
+ align:start position:0%
+carriers right here impact um the uh the
+noise say in in in a camera a a CCD
+
+ align:start position:0%
+noise say in in in a camera a a CCD
+ 
+
+ align:start position:0%
+noise say in in in a camera a a CCD
+based camera a charge couple display
+
+ align:start position:0%
+based camera a charge couple display
+ 
+
+ align:start position:0%
+based camera a charge couple display
+camera which functions not so different
+
+ align:start position:0%
+camera which functions not so different
+ 
+
+ align:start position:0%
+camera which functions not so different
+from a solar cell device except that
+
+ align:start position:0%
+from a solar cell device except that
+ 
+
+ align:start position:0%
+from a solar cell device except that
+it's biased a little differently than
+
+ align:start position:0%
+it's biased a little differently than
+ 
+
+ align:start position:0%
+it's biased a little differently than
+actual solar cell device but it could be
+
+ align:start position:0%
+actual solar cell device but it could be
+ 
+
+ align:start position:0%
+actual solar cell device but it could be
+like a PN Junction uh P to be more
+
+ align:start position:0%
+like a PN Junction uh P to be more
+ 
+
+ align:start position:0%
+like a PN Junction uh P to be more
+precise so we have um
+
+ align:start position:0%
+precise so we have um
+ 
+
+ align:start position:0%
+precise so we have um
+our little camera right here and inside
+
+ align:start position:0%
+our little camera right here and inside
+ 
+
+ align:start position:0%
+our little camera right here and inside
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a the camera is typically placed inside
+
+ align:start position:0%
+a the camera is typically placed inside
+ 
+
+ align:start position:0%
+a the camera is typically placed inside
+of a liquid nitrogen Durer if we want
+
+ align:start position:0%
+of a liquid nitrogen Durer if we want
+ 
+
+ align:start position:0%
+of a liquid nitrogen Durer if we want
+very high performance uh these are not
+
+ align:start position:0%
+very high performance uh these are not
+ 
+
+ align:start position:0%
+very high performance uh these are not
+your typical handheld cameras that you
+
+ align:start position:0%
+your typical handheld cameras that you
+ 
+
+ align:start position:0%
+your typical handheld cameras that you
+would use for shots in the street these
+
+ align:start position:0%
+would use for shots in the street these
+ 
+
+ align:start position:0%
+would use for shots in the street these
+are cameras that we use in the
+
+ align:start position:0%
+are cameras that we use in the
+ 
+
+ align:start position:0%
+are cameras that we use in the
+laboratory for detecting very faint
+
+ align:start position:0%
+laboratory for detecting very faint
+ 
+
+ align:start position:0%
+laboratory for detecting very faint
+signals inside of our uh semiconductor
+
+ align:start position:0%
+signals inside of our uh semiconductor
+ 
+
+ align:start position:0%
+signals inside of our uh semiconductor
+systems and we typically cool our
+
+ align:start position:0%
+systems and we typically cool our
+ 
+
+ align:start position:0%
+systems and we typically cool our
+cameras down why because we want to
+
+ align:start position:0%
+cameras down why because we want to
+ 
+
+ align:start position:0%
+cameras down why because we want to
+minimize the density of these intrinsic
+
+ align:start position:0%
+minimize the density of these intrinsic
+ 
+
+ align:start position:0%
+minimize the density of these intrinsic
+carriers
+
+ align:start position:0%
+carriers
+ 
+
+ align:start position:0%
+carriers
+because any Photon that comes into our
+
+ align:start position:0%
+because any Photon that comes into our
+ 
+
+ align:start position:0%
+because any Photon that comes into our
+system we want to be able to count it
+
+ align:start position:0%
+system we want to be able to count it
+ 
+
+ align:start position:0%
+system we want to be able to count it
+and to detect it and not have to detect
+
+ align:start position:0%
+and to detect it and not have to detect
+ 
+
+ align:start position:0%
+and to detect it and not have to detect
+a very small signal on top of a large
+
+ align:start position:0%
+a very small signal on top of a large
+ 
+
+ align:start position:0%
+a very small signal on top of a large
+background noise of thermally excited
+
+ align:start position:0%
+background noise of thermally excited
+ 
+
+ align:start position:0%
+background noise of thermally excited
+carriers in a solar cell device um the
+
+ align:start position:0%
+carriers in a solar cell device um the
+ 
+
+ align:start position:0%
+carriers in a solar cell device um the
+intrinsic carrier concentration is
+
+ align:start position:0%
+intrinsic carrier concentration is
+ 
+
+ align:start position:0%
+intrinsic carrier concentration is
+typically much much less than the uh
+
+ align:start position:0%
+typically much much less than the uh
+ 
+
+ align:start position:0%
+typically much much less than the uh
+dopent concentration so the intrinsic
+
+ align:start position:0%
+dopent concentration so the intrinsic
+ 
+
+ align:start position:0%
+dopent concentration so the intrinsic
+carrier concentration matters less for
+
+ align:start position:0%
+carrier concentration matters less for
+ 
+
+ align:start position:0%
+carrier concentration matters less for
+our semiconductors than it does for a
+
+ align:start position:0%
+our semiconductors than it does for a
+ 
+
+ align:start position:0%
+our semiconductors than it does for a
+photo detector uh like this and that's
+
+ align:start position:0%
+photo detector uh like this and that's
+ 
+
+ align:start position:0%
+photo detector uh like this and that's
+why thankfully we don't have to cool our
+
+ align:start position:0%
+why thankfully we don't have to cool our
+ 
+
+ align:start position:0%
+why thankfully we don't have to cool our
+solar cells with li nitrogen
+
+ align:start position:0%
+solar cells with li nitrogen
+ 
+
+ align:start position:0%
+solar cells with li nitrogen
+so um in terms of of of uh intrinsic
+
+ align:start position:0%
+so um in terms of of of uh intrinsic
+ 
+
+ align:start position:0%
+so um in terms of of of uh intrinsic
+carriers let's dwell there just a little
+
+ align:start position:0%
+carriers let's dwell there just a little
+ 
+
+ align:start position:0%
+carriers let's dwell there just a little
+bit longer transistors are made of what
+
+ align:start position:0%
+bit longer transistors are made of what
+ 
+
+ align:start position:0%
+bit longer transistors are made of what
+semiconductor material to uh have uh
+
+ align:start position:0%
+semiconductor material to uh have uh
+ 
+
+ align:start position:0%
+semiconductor material to uh have uh
+less electronic noise uh to experience
+
+ align:start position:0%
+less electronic noise uh to experience
+ 
+
+ align:start position:0%
+less electronic noise uh to experience
+okay so what semiconductor material
+
+ align:start position:0%
+okay so what semiconductor material
+ 
+
+ align:start position:0%
+okay so what semiconductor material
+geranium or silicon would experience
+
+ align:start position:0%
+geranium or silicon would experience
+ 
+
+ align:start position:0%
+geranium or silicon would experience
+less electronic noise at room
+
+ align:start position:0%
+less electronic noise at room
+ 
+
+ align:start position:0%
+less electronic noise at room
+temperature and let me give you a hint
+
+ align:start position:0%
+temperature and let me give you a hint
+ 
+
+ align:start position:0%
+temperature and let me give you a hint
+silicon has a band gap of 1.1 EV
+
+ align:start position:0%
+silicon has a band gap of 1.1 EV
+ 
+
+ align:start position:0%
+silicon has a band gap of 1.1 EV
+germanium has a band gap of 0.67 EV
+
+ align:start position:0%
+germanium has a band gap of 0.67 EV
+ 
+
+ align:start position:0%
+germanium has a band gap of 0.67 EV
+which of the two is going to have
+
+ align:start position:0%
+which of the two is going to have
+ 
+
+ align:start position:0%
+which of the two is going to have
+greater electronic noise at room
+
+ align:start position:0%
+greater electronic noise at room
+ 
+
+ align:start position:0%
+greater electronic noise at room
+temperature germanium because as a
+
+ align:start position:0%
+temperature germanium because as a
+ 
+
+ align:start position:0%
+temperature germanium because as a
+smaller band Gap it's going to be easier
+
+ align:start position:0%
+smaller band Gap it's going to be easier
+ 
+
+ align:start position:0%
+smaller band Gap it's going to be easier
+for the carriers where you go all the
+
+ align:start position:0%
+for the carriers where you go all the
+ 
+
+ align:start position:0%
+for the carriers where you go all the
+way back here it's going to be easier
+
+ align:start position:0%
+way back here it's going to be easier
+ 
+
+ align:start position:0%
+way back here it's going to be easier
+for carriers to hop across because the
+
+ align:start position:0%
+for carriers to hop across because the
+ 
+
+ align:start position:0%
+for carriers to hop across because the
+band Gap is smaller another way to look
+
+ align:start position:0%
+band Gap is smaller another way to look
+ 
+
+ align:start position:0%
+band Gap is smaller another way to look
+at it is on the uranous plot you'll have
+
+ align:start position:0%
+at it is on the uranous plot you'll have
+ 
+
+ align:start position:0%
+at it is on the uranous plot you'll have
+a higher carrier concentration because
+
+ align:start position:0%
+a higher carrier concentration because
+ 
+
+ align:start position:0%
+a higher carrier concentration because
+your slope is smaller your activation
+
+ align:start position:0%
+your slope is smaller your activation
+ 
+
+ align:start position:0%
+your slope is smaller your activation
+energy is smaller and as a result you'll
+
+ align:start position:0%
+energy is smaller and as a result you'll
+ 
+
+ align:start position:0%
+energy is smaller and as a result you'll
+have a higher uh if the band Gap shrinks
+
+ align:start position:0%
+have a higher uh if the band Gap shrinks
+ 
+
+ align:start position:0%
+have a higher uh if the band Gap shrinks
+you'll have a higher carrier density
+
+ align:start position:0%
+you'll have a higher carrier density
+ 
+
+ align:start position:0%
+you'll have a higher carrier density
+here in the conduction band let me show
+
+ align:start position:0%
+here in the conduction band let me show
+ 
+
+ align:start position:0%
+here in the conduction band let me show
+you that in pictoral form so this is the
+
+ align:start position:0%
+you that in pictoral form so this is the
+ 
+
+ align:start position:0%
+you that in pictoral form so this is the
+Silicon band Gap this is the density of
+
+ align:start position:0%
+Silicon band Gap this is the density of
+ 
+
+ align:start position:0%
+Silicon band Gap this is the density of
+thermally excited carriers for silicon
+
+ align:start position:0%
+thermally excited carriers for silicon
+ 
+
+ align:start position:0%
+thermally excited carriers for silicon
+now we shrink the band Gap boom We
+
+ align:start position:0%
+now we shrink the band Gap boom We
+ 
+
+ align:start position:0%
+now we shrink the band Gap boom We
+Shrunk it same probability distribution
+
+ align:start position:0%
+Shrunk it same probability distribution
+ 
+
+ align:start position:0%
+Shrunk it same probability distribution
+function because we're at the same
+
+ align:start position:0%
+function because we're at the same
+ 
+
+ align:start position:0%
+function because we're at the same
+temperature but now we have a smaller
+
+ align:start position:0%
+temperature but now we have a smaller
+ 
+
+ align:start position:0%
+temperature but now we have a smaller
+band Gap so we have a higher density of
+
+ align:start position:0%
+band Gap so we have a higher density of
+ 
+
+ align:start position:0%
+band Gap so we have a higher density of
+free carriers and true story geranium
+
+ align:start position:0%
+free carriers and true story geranium
+ 
+
+ align:start position:0%
+free carriers and true story geranium
+was one of the first crystals to be uh
+
+ align:start position:0%
+was one of the first crystals to be uh
+ 
+
+ align:start position:0%
+was one of the first crystals to be uh
+purified uh during the early days of
+
+ align:start position:0%
+purified uh during the early days of
+ 
+
+ align:start position:0%
+purified uh during the early days of
+semiconductors and silicon was following
+
+ align:start position:0%
+semiconductors and silicon was following
+ 
+
+ align:start position:0%
+semiconductors and silicon was following
+germanium uh and silicon was ultimately
+
+ align:start position:0%
+germanium uh and silicon was ultimately
+ 
+
+ align:start position:0%
+germanium uh and silicon was ultimately
+chosen as the uh material of choice for
+
+ align:start position:0%
+chosen as the uh material of choice for
+ 
+
+ align:start position:0%
+chosen as the uh material of choice for
+transistors because the intrinsic
+
+ align:start position:0%
+transistors because the intrinsic
+ 
+
+ align:start position:0%
+transistors because the intrinsic
+carrier concentration of geranium was
+
+ align:start position:0%
+carrier concentration of geranium was
+ 
+
+ align:start position:0%
+carrier concentration of geranium was
+just too high for most uh applications
+
+ align:start position:0%
+just too high for most uh applications
+ 
+
+ align:start position:0%
+just too high for most uh applications
+and so you can see the intrinsic carrier
+
+ align:start position:0%
+and so you can see the intrinsic carrier
+ 
+
+ align:start position:0%
+and so you can see the intrinsic carrier
+concentration at room temperature of
+
+ align:start position:0%
+concentration at room temperature of
+ 
+
+ align:start position:0%
+concentration at room temperature of
+silicon is around 10 10 whereas for
+
+ align:start position:0%
+silicon is around 10 10 whereas for
+ 
+
+ align:start position:0%
+silicon is around 10 10 whereas for
+geranium is around 10^ 13 uh three
+
+ align:start position:0%
+geranium is around 10^ 13 uh three
+ 
+
+ align:start position:0%
+geranium is around 10^ 13 uh three
+orders of magnitude higher so yes
+
+ align:start position:0%
+orders of magnitude higher so yes
+ 
+
+ align:start position:0%
+orders of magnitude higher so yes
+question last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wey
+
+ align:start position:0%
+wey
+ 
+
+ align:start position:0%
+wey
+cells would be a much better choice than
+
+ align:start position:0%
+cells would be a much better choice than
+ 
+
+ align:start position:0%
+cells would be a much better choice than
+I'm just assuming is that more like a
+
+ align:start position:0%
+I'm just assuming is that more like a
+ 
+
+ align:start position:0%
+I'm just assuming is that more like a
+cost thing it would be mostly a cost
+
+ align:start position:0%
+cost thing it would be mostly a cost
+ 
+
+ align:start position:0%
+cost thing it would be mostly a cost
+thing absolutely um and so you do see
+
+ align:start position:0%
+thing absolutely um and so you do see
+ 
+
+ align:start position:0%
+thing absolutely um and so you do see
+solar cells like concentric is one
+
+ align:start position:0%
+solar cells like concentric is one
+ 
+
+ align:start position:0%
+solar cells like concentric is one
+company that's commercializing Gallum
+
+ align:start position:0%
+company that's commercializing Gallum
+ 
+
+ align:start position:0%
+company that's commercializing Gallum
+aride based solar cells but they have to
+
+ align:start position:0%
+aride based solar cells but they have to
+ 
+
+ align:start position:0%
+aride based solar cells but they have to
+uh concentrate the sunlight into very
+
+ align:start position:0%
+uh concentrate the sunlight into very
+ 
+
+ align:start position:0%
+uh concentrate the sunlight into very
+small area devices because the devices
+
+ align:start position:0%
+small area devices because the devices
+ 
+
+ align:start position:0%
+small area devices because the devices
+cost so much to make per unit area so
+
+ align:start position:0%
+cost so much to make per unit area so
+ 
+
+ align:start position:0%
+cost so much to make per unit area so
+they take cheap plastic and and
+
+ align:start position:0%
+they take cheap plastic and and
+ 
+
+ align:start position:0%
+they take cheap plastic and and
+concentrate the sunlight
+
+ align:start position:0%
+concentrate the sunlight
+ 
+
+ align:start position:0%
+concentrate the sunlight
+down yeah and here's Gallum arsenide the
+
+ align:start position:0%
+down yeah and here's Gallum arsenide the
+ 
+
+ align:start position:0%
+down yeah and here's Gallum arsenide the
+intrinsic carrier concentration is even
+
+ align:start position:0%
+intrinsic carrier concentration is even
+ 
+
+ align:start position:0%
+intrinsic carrier concentration is even
+less than that of silicon because the
+
+ align:start position:0%
+less than that of silicon because the
+ 
+
+ align:start position:0%
+less than that of silicon because the
+band Gap is 1.4 EV instead of
+
+ align:start position:0%
+band Gap is 1.4 EV instead of
+ 
+
+ align:start position:0%
+band Gap is 1.4 EV instead of
+1.1 okay so I think this is a good place
+
+ align:start position:0%
+1.1 okay so I think this is a good place
+ 
+
+ align:start position:0%
+1.1 okay so I think this is a good place
+to stop I'm still not through all the
+
+ align:start position:0%
+to stop I'm still not through all the
+ 
+
+ align:start position:0%
+to stop I'm still not through all the
+material um oh we wanted to do one demo
+
+ align:start position:0%
+material um oh we wanted to do one demo
+ 
+
+ align:start position:0%
+material um oh we wanted to do one demo
+yeah uh do you want to do it first thing
+
+ align:start position:0%
+yeah uh do you want to do it first thing
+ 
+
+ align:start position:0%
+yeah uh do you want to do it first thing
+next lecture that's fine got ah we we do
+
+ align:start position:0%
+next lecture that's fine got ah we we do
+ 
+
+ align:start position:0%
+next lecture that's fine got ah we we do
+have five more minutes before 10 after
+
+ align:start position:0%
+have five more minutes before 10 after
+ 
+
+ align:start position:0%
+have five more minutes before 10 after
+okay why don't we do a quick demo then
+
+ align:start position:0%
+okay why don't we do a quick demo then
+ 
+
+ align:start position:0%
+okay why don't we do a quick demo then
+um so what we're going to do is Joe sets
+
+ align:start position:0%
+um so what we're going to do is Joe sets
+ 
+
+ align:start position:0%
+um so what we're going to do is Joe sets
+us up is I'll I'll I'll verly describe
+
+ align:start position:0%
+us up is I'll I'll I'll verly describe
+ 
+
+ align:start position:0%
+us up is I'll I'll I'll verly describe
+what's going to happen here um we are
+
+ align:start position:0%
+what's going to happen here um we are
+ 
+
+ align:start position:0%
+what's going to happen here um we are
+going to take uh this actually let me go
+
+ align:start position:0%
+going to take uh this actually let me go
+ 
+
+ align:start position:0%
+going to take uh this actually let me go
+back to the affir distribution function
+
+ align:start position:0%
+back to the affir distribution function
+ 
+
+ align:start position:0%
+back to the affir distribution function
+this function right here as we increase
+
+ align:start position:0%
+this function right here as we increase
+ 
+
+ align:start position:0%
+this function right here as we increase
+temperature what happens to this this
+
+ align:start position:0%
+temperature what happens to this this
+ 
+
+ align:start position:0%
+temperature what happens to this this
+will look more and more
+
+ align:start position:0%
+will look more and more
+ 
+
+ align:start position:0%
+will look more and more
+uh shall we say uh flat it won't
+
+ align:start position:0%
+uh shall we say uh flat it won't
+ 
+
+ align:start position:0%
+uh shall we say uh flat it won't
+actually go flat but it'll become more
+
+ align:start position:0%
+actually go flat but it'll become more
+ 
+
+ align:start position:0%
+actually go flat but it'll become more
+and more diagonal as opposed to box like
+
+ align:start position:0%
+and more diagonal as opposed to box like
+ 
+
+ align:start position:0%
+and more diagonal as opposed to box like
+in function what that means is the
+
+ align:start position:0%
+in function what that means is the
+ 
+
+ align:start position:0%
+in function what that means is the
+density of carriers the density of free
+
+ align:start position:0%
+density of carriers the density of free
+ 
+
+ align:start position:0%
+density of carriers the density of free
+carriers will increase with temperature
+
+ align:start position:0%
+carriers will increase with temperature
+ 
+
+ align:start position:0%
+carriers will increase with temperature
+and because of the uranous dependence
+
+ align:start position:0%
+and because of the uranous dependence
+ 
+
+ align:start position:0%
+and because of the uranous dependence
+here we have an exponential increase of
+
+ align:start position:0%
+here we have an exponential increase of
+ 
+
+ align:start position:0%
+here we have an exponential increase of
+the number of free carriers with
+
+ align:start position:0%
+the number of free carriers with
+ 
+
+ align:start position:0%
+the number of free carriers with
+temperature uh because the function
+
+ align:start position:0%
+temperature uh because the function
+ 
+
+ align:start position:0%
+temperature uh because the function
+right around this region right here
+
+ align:start position:0%
+right around this region right here
+ 
+
+ align:start position:0%
+right around this region right here
+which impacts the uh electron
+
+ align:start position:0%
+which impacts the uh electron
+ 
+
+ align:start position:0%
+which impacts the uh electron
+concentration the conduction band uh
+
+ align:start position:0%
+concentration the conduction band uh
+ 
+
+ align:start position:0%
+concentration the conduction band uh
+this small portion of the fidi equation
+
+ align:start position:0%
+this small portion of the fidi equation
+ 
+
+ align:start position:0%
+this small portion of the fidi equation
+can be approximated by an exponential if
+
+ align:start position:0%
+can be approximated by an exponential if
+ 
+
+ align:start position:0%
+can be approximated by an exponential if
+we have an increasing temperature we
+
+ align:start position:0%
+we have an increasing temperature we
+ 
+
+ align:start position:0%
+we have an increasing temperature we
+should have a drastically increasing
+
+ align:start position:0%
+should have a drastically increasing
+ 
+
+ align:start position:0%
+should have a drastically increasing
+carrier density and let's see if that's
+
+ align:start position:0%
+carrier density and let's see if that's
+ 
+
+ align:start position:0%
+carrier density and let's see if that's
+indeed the case what we have is a piece
+
+ align:start position:0%
+indeed the case what we have is a piece
+ 
+
+ align:start position:0%
+indeed the case what we have is a piece
+of intrinsic silicon uh just with a a
+
+ align:start position:0%
+of intrinsic silicon uh just with a a
+ 
+
+ align:start position:0%
+of intrinsic silicon uh just with a a
+battery pack attached so we have a a
+
+ align:start position:0%
+battery pack attached so we have a a
+ 
+
+ align:start position:0%
+battery pack attached so we have a a
+field across that piece of intrinsic
+
+ align:start position:0%
+field across that piece of intrinsic
+ 
+
+ align:start position:0%
+field across that piece of intrinsic
+silicon oops here we go and we are going
+
+ align:start position:0%
+silicon oops here we go and we are going
+ 
+
+ align:start position:0%
+silicon oops here we go and we are going
+to apply again that field across the
+
+ align:start position:0%
+to apply again that field across the
+ 
+
+ align:start position:0%
+to apply again that field across the
+intrinsic piece of silicon a certain
+
+ align:start position:0%
+intrinsic piece of silicon a certain
+ 
+
+ align:start position:0%
+intrinsic piece of silicon a certain
+current will flow through it um and then
+
+ align:start position:0%
+current will flow through it um and then
+ 
+
+ align:start position:0%
+current will flow through it um and then
+Joe has a heat gun so he's going to heat
+
+ align:start position:0%
+Joe has a heat gun so he's going to heat
+ 
+
+ align:start position:0%
+Joe has a heat gun so he's going to heat
+up the Silicon
+
+ align:start position:0%
+up the Silicon
+ 
+
+ align:start position:0%
+up the Silicon
+uh and see what happens as the fidra uh
+
+ align:start position:0%
+uh and see what happens as the fidra uh
+ 
+
+ align:start position:0%
+uh and see what happens as the fidra uh
+equation here is affected by temperature
+
+ align:start position:0%
+equation here is affected by temperature
+ 
+
+ align:start position:0%
+equation here is affected by temperature
+we should have an increasing density of
+
+ align:start position:0%
+we should have an increasing density of
+ 
+
+ align:start position:0%
+we should have an increasing density of
+carriers in the conduction band uh so
+
+ align:start position:0%
+carriers in the conduction band uh so
+ 
+
+ align:start position:0%
+carriers in the conduction band uh so
+let's see if that's indeed the case can
+
+ align:start position:0%
+let's see if that's indeed the case can
+ 
+
+ align:start position:0%
+let's see if that's indeed the case can
+somebody read off what the uh current is
+
+ align:start position:0%
+somebody read off what the uh current is
+ 
+
+ align:start position:0%
+somebody read off what the uh current is
+currently measuring there on our current
+
+ align:start position:0%
+currently measuring there on our current
+ 
+
+ align:start position:0%
+currently measuring there on our current
+meter it's about 9.8 microamps right now
+
+ align:start position:0%
+meter it's about 9.8 microamps right now
+ 
+
+ align:start position:0%
+meter it's about 9.8 microamps right now
+9.8 microamps so this battery pack of 3
+
+ align:start position:0%
+9.8 microamps so this battery pack of 3
+ 
+
+ align:start position:0%
+9.8 microamps so this battery pack of 3
+volts right here is um is forcing a
+
+ align:start position:0%
+volts right here is um is forcing a
+ 
+
+ align:start position:0%
+volts right here is um is forcing a
+current of 9.8 microamps across that
+
+ align:start position:0%
+current of 9.8 microamps across that
+ 
+
+ align:start position:0%
+current of 9.8 microamps across that
+little slab of silicon
+
+ align:start position:0%
+little slab of silicon
+ 
+
+ align:start position:0%
+little slab of silicon
+uh that is SED right here and so Joe is
+
+ align:start position:0%
+uh that is SED right here and so Joe is
+ 
+
+ align:start position:0%
+uh that is SED right here and so Joe is
+going to apply the heat gun and if none
+
+ align:start position:0%
+going to apply the heat gun and if none
+ 
+
+ align:start position:0%
+going to apply the heat gun and if none
+of the contacts pop off uh let's see
+
+ align:start position:0%
+of the contacts pop off uh let's see
+ 
+
+ align:start position:0%
+of the contacts pop off uh let's see
+what uh let's see what will happen so we
+
+ align:start position:0%
+what uh let's see what will happen so we
+ 
+
+ align:start position:0%
+what uh let's see what will happen so we
+expect the resistivity uh to go what
+
+ align:start position:0%
+expect the resistivity uh to go what
+ 
+
+ align:start position:0%
+expect the resistivity uh to go what
+down and the conductivity to go up all
+
+ align:start position:0%
+down and the conductivity to go up all
+ 
+
+ align:start position:0%
+down and the conductivity to go up all
+right so let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so what's happening there
+
+ align:start position:0%
+here so what's happening there
+ 
+
+ align:start position:0%
+here so what's happening there
+folks it's going up so that's the
+
+ align:start position:0%
+folks it's going up so that's the
+ 
+
+ align:start position:0%
+folks it's going up so that's the
+uh so it went up to around 50 microG and
+
+ align:start position:0%
+uh so it went up to around 50 microG and
+ 
+
+ align:start position:0%
+uh so it went up to around 50 microG and
+you can see it's dropping R
+
+ align:start position:0%
+you can see it's dropping R
+ 
+
+ align:start position:0%
+you can see it's dropping R
+dramatically so the current that the
+
+ align:start position:0%
+dramatically so the current that the
+ 
+
+ align:start position:0%
+dramatically so the current that the
+material is able to pass through is
+
+ align:start position:0%
+material is able to pass through is
+ 
+
+ align:start position:0%
+material is able to pass through is
+increasing as a result of uh the
+
+ align:start position:0%
+increasing as a result of uh the
+ 
+
+ align:start position:0%
+increasing as a result of uh the
+increasing temperature because you're
+
+ align:start position:0%
+increasing temperature because you're
+ 
+
+ align:start position:0%
+increasing temperature because you're
+exciting more carriers into the
+
+ align:start position:0%
+exciting more carriers into the
+ 
+
+ align:start position:0%
+exciting more carriers into the
+conduction band leaving more holes in
+
+ align:start position:0%
+conduction band leaving more holes in
+ 
+
+ align:start position:0%
+conduction band leaving more holes in
+the veilance band and these are free
+
+ align:start position:0%
+the veilance band and these are free
+ 
+
+ align:start position:0%
+the veilance band and these are free
+charge carriers that are able to conduct
+
+ align:start position:0%
+charge carriers that are able to conduct
+ 
+
+ align:start position:0%
+charge carriers that are able to conduct
+charge through the
+
+ align:start position:0%
+charge through the
+ 
+
+ align:start position:0%
+charge through the
+material cool okay so uh with that I
+
+ align:start position:0%
+material cool okay so uh with that I
+ 
+
+ align:start position:0%
+material cool okay so uh with that I
+will leave you and we'll return Tuesday
+
+ align:start position:0%
+will leave you and we'll return Tuesday
+ 
+
+ align:start position:0%
+will leave you and we'll return Tuesday
+and Joe will give a fantastic lecture on
+
+ align:start position:0%
+and Joe will give a fantastic lecture on
+ 
+
+ align:start position:0%
+and Joe will give a fantastic lecture on
+uh device physics as well uh since will
+
+ align:start position:0%
+uh device physics as well uh since will
+ 
+
+ align:start position:0%
+uh device physics as well uh since will
+be at a kickoff meeting at for a big NSF
+
+ align:start position:0%
+be at a kickoff meeting at for a big NSF
+ 
+
+ align:start position:0%
+be at a kickoff meeting at for a big NSF
+related Center in Phoenix Arizona but it
+
+ align:start position:0%
+related Center in Phoenix Arizona but it
+ 
+
+ align:start position:0%
+related Center in Phoenix Arizona but it
+will be a great lecture uh you won't
+
+ align:start position:0%
+will be a great lecture uh you won't
+ 
+
+ align:start position:0%
+will be a great lecture uh you won't
+want to miss it and uh look forward to
+
+ align:start position:0%
+want to miss it and uh look forward to
+ 
+
+ align:start position:0%
+want to miss it and uh look forward to
+seeing you on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tuesday
\ No newline at end of file
diff --git a/dgSFOyxFHW8.txt b/dgSFOyxFHW8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..51a1dbd5047c18db27d95041b8afbdebbf71ad79
--- /dev/null
+++ b/dgSFOyxFHW8.txt
@@ -0,0 +1,1731 @@
+align:start position:0%
+ 
+And uh our our last um speaker for this
+
+ align:start position:0%
+And uh our our last um speaker for this
+ 
+
+ align:start position:0%
+And uh our our last um speaker for this
+session is Jonathan
+
+ align:start position:0%
+session is Jonathan
+ 
+
+ align:start position:0%
+session is Jonathan
+>> Buunor.
+
+ align:start position:0%
+>> Buunor.
+ 
+
+ align:start position:0%
+>> Buunor.
+I'm looking for a
+
+ align:start position:0%
+I'm looking for a
+ 
+
+ align:start position:0%
+I'm looking for a
+>> slide changer. This one
+
+ align:start position:0%
+>> slide changer. This one
+ 
+
+ align:start position:0%
+>> slide changer. This one
+>> is this the slide flipper?
+
+ align:start position:0%
+>> is this the slide flipper?
+ 
+
+ align:start position:0%
+>> is this the slide flipper?
+>> Yes. Okay,
+
+ align:start position:0%
+>> Yes. Okay,
+ 
+
+ align:start position:0%
+>> Yes. Okay,
+>> you got it.
+
+ align:start position:0%
+>> you got it.
+ 
+
+ align:start position:0%
+>> you got it.
+>> All right. Yeah. So, my my name is
+
+ align:start position:0%
+>> All right. Yeah. So, my my name is
+ 
+
+ align:start position:0%
+>> All right. Yeah. So, my my name is
+Jonathan Municore. I'm a assistant
+
+ align:start position:0%
+Jonathan Municore. I'm a assistant
+ 
+
+ align:start position:0%
+Jonathan Municore. I'm a assistant
+professor at Boston University School of
+
+ align:start position:0%
+professor at Boston University School of
+ 
+
+ align:start position:0%
+professor at Boston University School of
+Public Health. And uh my my goal in the
+
+ align:start position:0%
+Public Health. And uh my my goal in the
+ 
+
+ align:start position:0%
+Public Health. And uh my my goal in the
+next 10 minutes is to not only uh
+
+ align:start position:0%
+next 10 minutes is to not only uh
+ 
+
+ align:start position:0%
+next 10 minutes is to not only uh
+convince you that a person from public
+
+ align:start position:0%
+convince you that a person from public
+ 
+
+ align:start position:0%
+convince you that a person from public
+health belongs in the room, but also to
+
+ align:start position:0%
+health belongs in the room, but also to
+ 
+
+ align:start position:0%
+health belongs in the room, but also to
+uh convince you that you all are
+
+ align:start position:0%
+uh convince you that you all are
+ 
+
+ align:start position:0%
+uh convince you that you all are
+secretly um going to be public health
+
+ align:start position:0%
+secretly um going to be public health
+ 
+
+ align:start position:0%
+secretly um going to be public health
+professionals. Um so uh where I wanted
+
+ align:start position:0%
+professionals. Um so uh where I wanted
+ 
+
+ align:start position:0%
+professionals. Um so uh where I wanted
+to start was to look at this um process.
+
+ align:start position:0%
+to start was to look at this um process.
+ 
+
+ align:start position:0%
+to start was to look at this um process.
+This is how like uh EPA other
+
+ align:start position:0%
+This is how like uh EPA other
+ 
+
+ align:start position:0%
+This is how like uh EPA other
+environmental agencies um like help
+
+ align:start position:0%
+environmental agencies um like help
+ 
+
+ align:start position:0%
+environmental agencies um like help
+public health environmental health
+
+ align:start position:0%
+public health environmental health
+ 
+
+ align:start position:0%
+public health environmental health
+professionals look at um just hazards in
+
+ align:start position:0%
+professionals look at um just hazards in
+ 
+
+ align:start position:0%
+professionals look at um just hazards in
+the world. Um we do a lot of very fancy
+
+ align:start position:0%
+the world. Um we do a lot of very fancy
+ 
+
+ align:start position:0%
+the world. Um we do a lot of very fancy
+stuff but very often it breaks down into
+
+ align:start position:0%
+stuff but very often it breaks down into
+ 
+
+ align:start position:0%
+stuff but very often it breaks down into
+these four basic steps which is to start
+
+ align:start position:0%
+these four basic steps which is to start
+ 
+
+ align:start position:0%
+these four basic steps which is to start
+it start on the left to ask like is
+
+ align:start position:0%
+it start on the left to ask like is
+ 
+
+ align:start position:0%
+it start on the left to ask like is
+there some kind of pollutant a stressor
+
+ align:start position:0%
+there some kind of pollutant a stressor
+ 
+
+ align:start position:0%
+there some kind of pollutant a stressor
+something like that that people are
+
+ align:start position:0%
+something like that that people are
+ 
+
+ align:start position:0%
+something like that that people are
+being exposed to that might cause a
+
+ align:start position:0%
+being exposed to that might cause a
+ 
+
+ align:start position:0%
+being exposed to that might cause a
+problem could be you know air pollutant
+
+ align:start position:0%
+problem could be you know air pollutant
+ 
+
+ align:start position:0%
+problem could be you know air pollutant
+uh water pollutant heat um a safety
+
+ align:start position:0%
+uh water pollutant heat um a safety
+ 
+
+ align:start position:0%
+uh water pollutant heat um a safety
+issue um anything like anything that
+
+ align:start position:0%
+issue um anything like anything that
+ 
+
+ align:start position:0%
+issue um anything like anything that
+could harm people should go in that box.
+
+ align:start position:0%
+could harm people should go in that box.
+ 
+
+ align:start position:0%
+could harm people should go in that box.
+Um, next up is this dose response
+
+ align:start position:0%
+Um, next up is this dose response
+ 
+
+ align:start position:0%
+Um, next up is this dose response
+assessment. Um, where this is really
+
+ align:start position:0%
+assessment. Um, where this is really
+ 
+
+ align:start position:0%
+assessment. Um, where this is really
+just a process of asking like if there's
+
+ align:start position:0%
+just a process of asking like if there's
+ 
+
+ align:start position:0%
+just a process of asking like if there's
+a certain amount of this thing in the
+
+ align:start position:0%
+a certain amount of this thing in the
+ 
+
+ align:start position:0%
+a certain amount of this thing in the
+environment, what are the health
+
+ align:start position:0%
+environment, what are the health
+ 
+
+ align:start position:0%
+environment, what are the health
+problems at different levels of
+
+ align:start position:0%
+problems at different levels of
+ 
+
+ align:start position:0%
+problems at different levels of
+exposures? So like air high levels of
+
+ align:start position:0%
+exposures? So like air high levels of
+ 
+
+ align:start position:0%
+exposures? So like air high levels of
+air pollution or worse than uh lower
+
+ align:start position:0%
+air pollution or worse than uh lower
+ 
+
+ align:start position:0%
+air pollution or worse than uh lower
+levels of air pollution. Same goes for
+
+ align:start position:0%
+levels of air pollution. Same goes for
+ 
+
+ align:start position:0%
+levels of air pollution. Same goes for
+water pollution um and that kind of
+
+ align:start position:0%
+water pollution um and that kind of
+ 
+
+ align:start position:0%
+water pollution um and that kind of
+thing. The uh third step that goes in
+
+ align:start position:0%
+thing. The uh third step that goes in
+ 
+
+ align:start position:0%
+thing. The uh third step that goes in
+parallel with that is this exposure
+
+ align:start position:0%
+parallel with that is this exposure
+ 
+
+ align:start position:0%
+parallel with that is this exposure
+assessment step that asks um okay so we
+
+ align:start position:0%
+assessment step that asks um okay so we
+ 
+
+ align:start position:0%
+assessment step that asks um okay so we
+know that there's a thing that is bad.
+
+ align:start position:0%
+know that there's a thing that is bad.
+ 
+
+ align:start position:0%
+know that there's a thing that is bad.
+um how many people are exposed to it?
+
+ align:start position:0%
+um how many people are exposed to it?
+ 
+
+ align:start position:0%
+um how many people are exposed to it?
+How long are they exposed to it? Are
+
+ align:start position:0%
+How long are they exposed to it? Are
+ 
+
+ align:start position:0%
+How long are they exposed to it? Are
+there certain like um susceptible
+
+ align:start position:0%
+there certain like um susceptible
+ 
+
+ align:start position:0%
+there certain like um susceptible
+windows or susceptible populations like
+
+ align:start position:0%
+windows or susceptible populations like
+ 
+
+ align:start position:0%
+windows or susceptible populations like
+infants or um marginalized communities
+
+ align:start position:0%
+infants or um marginalized communities
+ 
+
+ align:start position:0%
+infants or um marginalized communities
+that are um exposed to this? And then in
+
+ align:start position:0%
+that are um exposed to this? And then in
+ 
+
+ align:start position:0%
+that are um exposed to this? And then in
+the end we have this fourth step called
+
+ align:start position:0%
+the end we have this fourth step called
+ 
+
+ align:start position:0%
+the end we have this fourth step called
+risk characterization which um basically
+
+ align:start position:0%
+risk characterization which um basically
+ 
+
+ align:start position:0%
+risk characterization which um basically
+just asks like how big of a deal is this
+
+ align:start position:0%
+just asks like how big of a deal is this
+ 
+
+ align:start position:0%
+just asks like how big of a deal is this
+anyway? Um, so what I've done and do
+
+ align:start position:0%
+anyway? Um, so what I've done and do
+ 
+
+ align:start position:0%
+anyway? Um, so what I've done and do
+occasionally is I put this uh flip these
+
+ align:start position:0%
+occasionally is I put this uh flip these
+ 
+
+ align:start position:0%
+occasionally is I put this uh flip these
+these four steps to look like one of
+
+ align:start position:0%
+these four steps to look like one of
+ 
+
+ align:start position:0%
+these four steps to look like one of
+these hazmat placards that you'll see on
+
+ align:start position:0%
+these hazmat placards that you'll see on
+ 
+
+ align:start position:0%
+these hazmat placards that you'll see on
+um like the the trucks going down the
+
+ align:start position:0%
+um like the the trucks going down the
+ 
+
+ align:start position:0%
+um like the the trucks going down the
+highway or whatever. Um and then um
+
+ align:start position:0%
+highway or whatever. Um and then um
+ 
+
+ align:start position:0%
+highway or whatever. Um and then um
+again here's a simple versions. Is there
+
+ align:start position:0%
+again here's a simple versions. Is there
+ 
+
+ align:start position:0%
+again here's a simple versions. Is there
+some is there something that might be
+
+ align:start position:0%
+some is there something that might be
+ 
+
+ align:start position:0%
+some is there something that might be
+harmful? How harmful is it if you're
+
+ align:start position:0%
+harmful? How harmful is it if you're
+ 
+
+ align:start position:0%
+harmful? How harmful is it if you're
+exposed? Uh how many people are exposed
+
+ align:start position:0%
+exposed? Uh how many people are exposed
+ 
+
+ align:start position:0%
+exposed? Uh how many people are exposed
+to it? And how big of a deal is this
+
+ align:start position:0%
+to it? And how big of a deal is this
+ 
+
+ align:start position:0%
+to it? And how big of a deal is this
+really? So four basic questions. Um now
+
+ align:start position:0%
+really? So four basic questions. Um now
+ 
+
+ align:start position:0%
+really? So four basic questions. Um now
+uh you can overlay this look at the full
+
+ align:start position:0%
+uh you can overlay this look at the full
+ 
+
+ align:start position:0%
+uh you can overlay this look at the full
+life cycle. This is supply chain of
+
+ align:start position:0%
+life cycle. This is supply chain of
+ 
+
+ align:start position:0%
+life cycle. This is supply chain of
+natural gas starting from your wells and
+
+ align:start position:0%
+natural gas starting from your wells and
+ 
+
+ align:start position:0%
+natural gas starting from your wells and
+everything on the left over to the
+
+ align:start position:0%
+everything on the left over to the
+ 
+
+ align:start position:0%
+everything on the left over to the
+right. Um all the gas consumers like
+
+ align:start position:0%
+right. Um all the gas consumers like
+ 
+
+ align:start position:0%
+right. Um all the gas consumers like
+your commercial buildings, your um
+
+ align:start position:0%
+your commercial buildings, your um
+ 
+
+ align:start position:0%
+your commercial buildings, your um
+residences, uh the use of gas and power
+
+ align:start position:0%
+residences, uh the use of gas and power
+ 
+
+ align:start position:0%
+residences, uh the use of gas and power
+plants and all the pipelines, storage
+
+ align:start position:0%
+plants and all the pipelines, storage
+ 
+
+ align:start position:0%
+plants and all the pipelines, storage
+facilities, compressor stations, um
+
+ align:start position:0%
+facilities, compressor stations, um
+ 
+
+ align:start position:0%
+facilities, compressor stations, um
+processing stations, LG terminals,
+
+ align:start position:0%
+processing stations, LG terminals,
+ 
+
+ align:start position:0%
+processing stations, LG terminals,
+whatever else it is that is in between a
+
+ align:start position:0%
+whatever else it is that is in between a
+ 
+
+ align:start position:0%
+whatever else it is that is in between a
+well and your stove or your furnace. And
+
+ align:start position:0%
+well and your stove or your furnace. And
+ 
+
+ align:start position:0%
+well and your stove or your furnace. And
+uh we take our little hazmat placard and
+
+ align:start position:0%
+uh we take our little hazmat placard and
+ 
+
+ align:start position:0%
+uh we take our little hazmat placard and
+say, okay, how bad is all this anyway?
+
+ align:start position:0%
+say, okay, how bad is all this anyway?
+ 
+
+ align:start position:0%
+say, okay, how bad is all this anyway?
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+and I'll argue to you that uh there are
+
+ align:start position:0%
+and I'll argue to you that uh there are
+ 
+
+ align:start position:0%
+and I'll argue to you that uh there are
+hazards present across the entire supply
+
+ align:start position:0%
+hazards present across the entire supply
+ 
+
+ align:start position:0%
+hazards present across the entire supply
+chain. Um we know very little about most
+
+ align:start position:0%
+chain. Um we know very little about most
+ 
+
+ align:start position:0%
+chain. Um we know very little about most
+of these. Um which is, you know, this
+
+ align:start position:0%
+of these. Um which is, you know, this
+ 
+
+ align:start position:0%
+of these. Um which is, you know, this
+could potentially be my whole research
+
+ align:start position:0%
+could potentially be my whole research
+ 
+
+ align:start position:0%
+could potentially be my whole research
+career as a public health professional.
+
+ align:start position:0%
+career as a public health professional.
+ 
+
+ align:start position:0%
+career as a public health professional.
+Um and but uh I'm going to talk in
+
+ align:start position:0%
+Um and but uh I'm going to talk in
+ 
+
+ align:start position:0%
+Um and but uh I'm going to talk in
+detail about a couple of these different
+
+ align:start position:0%
+detail about a couple of these different
+ 
+
+ align:start position:0%
+detail about a couple of these different
+end points just to explain that um what
+
+ align:start position:0%
+end points just to explain that um what
+ 
+
+ align:start position:0%
+end points just to explain that um what
+you all are doing like you know all
+
+ align:start position:0%
+you all are doing like you know all
+ 
+
+ align:start position:0%
+you all are doing like you know all
+about the climate hazards. Um you're
+
+ align:start position:0%
+about the climate hazards. Um you're
+ 
+
+ align:start position:0%
+about the climate hazards. Um you're
+also doing a lot for uh for public
+
+ align:start position:0%
+also doing a lot for uh for public
+ 
+
+ align:start position:0%
+also doing a lot for uh for public
+health. So I'm going to start on the
+
+ align:start position:0%
+health. So I'm going to start on the
+ 
+
+ align:start position:0%
+health. So I'm going to start on the
+production side of things. Uh this is a
+
+ align:start position:0%
+production side of things. Uh this is a
+ 
+
+ align:start position:0%
+production side of things. Uh this is a
+map of every single uh oil and gas well
+
+ align:start position:0%
+map of every single uh oil and gas well
+ 
+
+ align:start position:0%
+map of every single uh oil and gas well
+in the United States. Um you may have
+
+ align:start position:0%
+in the United States. Um you may have
+ 
+
+ align:start position:0%
+in the United States. Um you may have
+noticed that there's a lot of them. Um,
+
+ align:start position:0%
+noticed that there's a lot of them. Um,
+ 
+
+ align:start position:0%
+noticed that there's a lot of them. Um,
+and a natural question that you should
+
+ align:start position:0%
+and a natural question that you should
+ 
+
+ align:start position:0%
+and a natural question that you should
+be asking yourself is, okay, so how big
+
+ align:start position:0%
+be asking yourself is, okay, so how big
+ 
+
+ align:start position:0%
+be asking yourself is, okay, so how big
+of a deal is this really? Um, going
+
+ align:start position:0%
+of a deal is this really? Um, going
+ 
+
+ align:start position:0%
+of a deal is this really? Um, going
+through a hazard assessment, there's
+
+ align:start position:0%
+through a hazard assessment, there's
+ 
+
+ align:start position:0%
+through a hazard assessment, there's
+like a lot of things that could be you
+
+ align:start position:0%
+like a lot of things that could be you
+ 
+
+ align:start position:0%
+like a lot of things that could be you
+could potentially be exposed to. Um,
+
+ align:start position:0%
+could potentially be exposed to. Um,
+ 
+
+ align:start position:0%
+could potentially be exposed to. Um,
+being I mostly focus on sort of regional
+
+ align:start position:0%
+being I mostly focus on sort of regional
+ 
+
+ align:start position:0%
+being I mostly focus on sort of regional
+air pollution. Um so I did a study that
+
+ align:start position:0%
+air pollution. Um so I did a study that
+ 
+
+ align:start position:0%
+air pollution. Um so I did a study that
+was focusing on the regional air
+
+ align:start position:0%
+was focusing on the regional air
+ 
+
+ align:start position:0%
+was focusing on the regional air
+pollution aspects of this and basically
+
+ align:start position:0%
+pollution aspects of this and basically
+ 
+
+ align:start position:0%
+pollution aspects of this and basically
+found that there are um a lot of uh
+
+ align:start position:0%
+found that there are um a lot of uh
+ 
+
+ align:start position:0%
+found that there are um a lot of uh
+violations of the national ambient air
+
+ align:start position:0%
+violations of the national ambient air
+ 
+
+ align:start position:0%
+violations of the national ambient air
+quality standards in the US that are due
+
+ align:start position:0%
+quality standards in the US that are due
+ 
+
+ align:start position:0%
+quality standards in the US that are due
+to the air pollution from oil and gas
+
+ align:start position:0%
+to the air pollution from oil and gas
+ 
+
+ align:start position:0%
+to the air pollution from oil and gas
+extraction. Um there's a big kind of
+
+ align:start position:0%
+extraction. Um there's a big kind of
+ 
+
+ align:start position:0%
+extraction. Um there's a big kind of
+plume of ozone in the middle of the
+
+ align:start position:0%
+plume of ozone in the middle of the
+ 
+
+ align:start position:0%
+plume of ozone in the middle of the
+country over the oil and gas um
+
+ align:start position:0%
+country over the oil and gas um
+ 
+
+ align:start position:0%
+country over the oil and gas um
+production there. Um there's NO2 which
+
+ align:start position:0%
+production there. Um there's NO2 which
+ 
+
+ align:start position:0%
+production there. Um there's NO2 which
+we're concerned about from a respiratory
+
+ align:start position:0%
+we're concerned about from a respiratory
+ 
+
+ align:start position:0%
+we're concerned about from a respiratory
+health standpoint. um this tends to be
+
+ align:start position:0%
+health standpoint. um this tends to be
+ 
+
+ align:start position:0%
+health standpoint. um this tends to be
+more concentrated in production areas
+
+ align:start position:0%
+more concentrated in production areas
+ 
+
+ align:start position:0%
+more concentrated in production areas
+and then PM2.5 which is our standard um
+
+ align:start position:0%
+and then PM2.5 which is our standard um
+ 
+
+ align:start position:0%
+and then PM2.5 which is our standard um
+aerosol um somewhere in between. So
+
+ align:start position:0%
+aerosol um somewhere in between. So
+ 
+
+ align:start position:0%
+aerosol um somewhere in between. So
+that's great. Um and then running it
+
+ align:start position:0%
+that's great. Um and then running it
+ 
+
+ align:start position:0%
+that's great. Um and then running it
+running it through all the science that
+
+ align:start position:0%
+running it through all the science that
+ 
+
+ align:start position:0%
+running it through all the science that
+we have about who lives where and what
+
+ align:start position:0%
+we have about who lives where and what
+ 
+
+ align:start position:0%
+we have about who lives where and what
+the health impacts of these different
+
+ align:start position:0%
+the health impacts of these different
+ 
+
+ align:start position:0%
+the health impacts of these different
+pollutants are. Um we have about 7,500
+
+ align:start position:0%
+pollutants are. Um we have about 7,500
+ 
+
+ align:start position:0%
+pollutants are. Um we have about 7,500
+deaths per year in the United States due
+
+ align:start position:0%
+deaths per year in the United States due
+ 
+
+ align:start position:0%
+deaths per year in the United States due
+to air pollution from oil and gas
+
+ align:start position:0%
+to air pollution from oil and gas
+ 
+
+ align:start position:0%
+to air pollution from oil and gas
+production. um about 410,000 asthma
+
+ align:start position:0%
+production. um about 410,000 asthma
+ 
+
+ align:start position:0%
+production. um about 410,000 asthma
+attacks and 220 uh these are children
+
+ align:start position:0%
+attacks and 220 uh these are children
+ 
+
+ align:start position:0%
+attacks and 220 uh these are children
+that are newly diagnosed with asthma per
+
+ align:start position:0%
+that are newly diagnosed with asthma per
+ 
+
+ align:start position:0%
+that are newly diagnosed with asthma per
+year due to oil and gas just the
+
+ align:start position:0%
+year due to oil and gas just the
+ 
+
+ align:start position:0%
+year due to oil and gas just the
+production side pollution in the US. Um
+
+ align:start position:0%
+production side pollution in the US. Um
+ 
+
+ align:start position:0%
+production side pollution in the US. Um
+so toting up all the health damages um
+
+ align:start position:0%
+so toting up all the health damages um
+ 
+
+ align:start position:0%
+so toting up all the health damages um
+on top of this there's like emergency
+
+ align:start position:0%
+on top of this there's like emergency
+ 
+
+ align:start position:0%
+on top of this there's like emergency
+department visits, hospitalizations,
+
+ align:start position:0%
+department visits, hospitalizations,
+ 
+
+ align:start position:0%
+department visits, hospitalizations,
+heart attacks, strokes um a whole
+
+ align:start position:0%
+heart attacks, strokes um a whole
+ 
+
+ align:start position:0%
+heart attacks, strokes um a whole
+growing menu of health outcomes that are
+
+ align:start position:0%
+growing menu of health outcomes that are
+ 
+
+ align:start position:0%
+growing menu of health outcomes that are
+related to um air pollution. And uh we
+
+ align:start position:0%
+related to um air pollution. And uh we
+ 
+
+ align:start position:0%
+related to um air pollution. And uh we
+can put a price tag on this of about 77
+
+ align:start position:0%
+can put a price tag on this of about 77
+ 
+
+ align:start position:0%
+can put a price tag on this of about 77
+billion with a B dollars yearly due to
+
+ align:start position:0%
+billion with a B dollars yearly due to
+ 
+
+ align:start position:0%
+billion with a B dollars yearly due to
+production of oil and gas. Um and as
+
+ align:start position:0%
+production of oil and gas. Um and as
+ 
+
+ align:start position:0%
+production of oil and gas. Um and as
+you've heard um geothermal will be able
+
+ align:start position:0%
+you've heard um geothermal will be able
+ 
+
+ align:start position:0%
+you've heard um geothermal will be able
+to kind of put a dent in that. So that's
+
+ align:start position:0%
+to kind of put a dent in that. So that's
+ 
+
+ align:start position:0%
+to kind of put a dent in that. So that's
+just the production side. Um and I'm
+
+ align:start position:0%
+just the production side. Um and I'm
+ 
+
+ align:start position:0%
+just the production side. Um and I'm
+going to move over to the other end of
+
+ align:start position:0%
+going to move over to the other end of
+ 
+
+ align:start position:0%
+going to move over to the other end of
+this which is the stove. Um they do emit
+
+ align:start position:0%
+this which is the stove. Um they do emit
+ 
+
+ align:start position:0%
+this which is the stove. Um they do emit
+air pollution. Um there's benzene which
+
+ align:start position:0%
+air pollution. Um there's benzene which
+ 
+
+ align:start position:0%
+air pollution. Um there's benzene which
+is a carcinogen so it causes cancer.
+
+ align:start position:0%
+is a carcinogen so it causes cancer.
+ 
+
+ align:start position:0%
+is a carcinogen so it causes cancer.
+There's a whole lot of volatile organic
+
+ align:start position:0%
+There's a whole lot of volatile organic
+ 
+
+ align:start position:0%
+There's a whole lot of volatile organic
+compounds that come along with that.
+
+ align:start position:0%
+compounds that come along with that.
+ 
+
+ align:start position:0%
+compounds that come along with that.
+there's NO2 when you burn it again and
+
+ align:start position:0%
+there's NO2 when you burn it again and
+ 
+
+ align:start position:0%
+there's NO2 when you burn it again and
+methane which is the greenhouse gas that
+
+ align:start position:0%
+methane which is the greenhouse gas that
+ 
+
+ align:start position:0%
+methane which is the greenhouse gas that
+we're all worried about from a climate
+
+ align:start position:0%
+we're all worried about from a climate
+ 
+
+ align:start position:0%
+we're all worried about from a climate
+standpoint. Um so Zand, myself and maybe
+
+ align:start position:0%
+standpoint. Um so Zand, myself and maybe
+ 
+
+ align:start position:0%
+standpoint. Um so Zand, myself and maybe
+a few other people in the room, Nathan
+
+ align:start position:0%
+a few other people in the room, Nathan
+ 
+
+ align:start position:0%
+a few other people in the room, Nathan
+um were involved in a study that um
+
+ align:start position:0%
+um were involved in a study that um
+ 
+
+ align:start position:0%
+um were involved in a study that um
+basically sampled gas around Boston. So
+
+ align:start position:0%
+basically sampled gas around Boston. So
+ 
+
+ align:start position:0%
+basically sampled gas around Boston. So
+we put it in a canister, sent it to a
+
+ align:start position:0%
+we put it in a canister, sent it to a
+ 
+
+ align:start position:0%
+we put it in a canister, sent it to a
+lab and they told us what was in it. Um
+
+ align:start position:0%
+lab and they told us what was in it. Um
+ 
+
+ align:start position:0%
+lab and they told us what was in it. Um
+and uh it looked like an organic
+
+ align:start position:0%
+and uh it looked like an organic
+ 
+
+ align:start position:0%
+and uh it looked like an organic
+chemistry textbook. Um there was uh a
+
+ align:start position:0%
+chemistry textbook. Um there was uh a
+ 
+
+ align:start position:0%
+chemistry textbook. Um there was uh a
+lot of methane as expected, a lot of
+
+ align:start position:0%
+lot of methane as expected, a lot of
+ 
+
+ align:start position:0%
+lot of methane as expected, a lot of
+ethane as expected, but a whole lot of
+
+ align:start position:0%
+ethane as expected, but a whole lot of
+ 
+
+ align:start position:0%
+ethane as expected, but a whole lot of
+things that were not methane and they
+
+ align:start position:0%
+things that were not methane and they
+ 
+
+ align:start position:0%
+things that were not methane and they
+were not ethane. Um we got hexane,
+
+ align:start position:0%
+were not ethane. Um we got hexane,
+ 
+
+ align:start position:0%
+were not ethane. Um we got hexane,
+benzene, taluine and heptine,
+
+ align:start position:0%
+benzene, taluine and heptine,
+ 
+
+ align:start position:0%
+benzene, taluine and heptine,
+carcinogenic, uh MPY, carcinogenic,
+
+ align:start position:0%
+carcinogenic, uh MPY, carcinogenic,
+ 
+
+ align:start position:0%
+carcinogenic, uh MPY, carcinogenic,
+carcinogenic xylene, and then all these
+
+ align:start position:0%
+carcinogenic xylene, and then all these
+ 
+
+ align:start position:0%
+carcinogenic xylene, and then all these
+other things that are also uh
+
+ align:start position:0%
+other things that are also uh
+ 
+
+ align:start position:0%
+other things that are also uh
+carcinogenic. Um so they went on to keep
+
+ align:start position:0%
+carcinogenic. Um so they went on to keep
+ 
+
+ align:start position:0%
+carcinogenic. Um so they went on to keep
+doing this kind of research. Uh turns
+
+ align:start position:0%
+doing this kind of research. Uh turns
+ 
+
+ align:start position:0%
+doing this kind of research. Uh turns
+out that Boston is not the only place
+
+ align:start position:0%
+out that Boston is not the only place
+ 
+
+ align:start position:0%
+out that Boston is not the only place
+that has a problem. Um it's uh there's
+
+ align:start position:0%
+that has a problem. Um it's uh there's
+ 
+
+ align:start position:0%
+that has a problem. Um it's uh there's
+also issues related to these odorants um
+
+ align:start position:0%
+also issues related to these odorants um
+ 
+
+ align:start position:0%
+also issues related to these odorants um
+which is the chemical that is uh
+
+ align:start position:0%
+which is the chemical that is uh
+ 
+
+ align:start position:0%
+which is the chemical that is uh
+intentionally added to the gas stream so
+
+ align:start position:0%
+intentionally added to the gas stream so
+ 
+
+ align:start position:0%
+intentionally added to the gas stream so
+we can smell it when it leaks. Um turns
+
+ align:start position:0%
+we can smell it when it leaks. Um turns
+ 
+
+ align:start position:0%
+we can smell it when it leaks. Um turns
+out that humans don't like how it smells
+
+ align:start position:0%
+out that humans don't like how it smells
+ 
+
+ align:start position:0%
+out that humans don't like how it smells
+because it is a respiratory irritant.
+
+ align:start position:0%
+because it is a respiratory irritant.
+ 
+
+ align:start position:0%
+because it is a respiratory irritant.
+It's harmful. Um and potentially there's
+
+ align:start position:0%
+It's harmful. Um and potentially there's
+ 
+
+ align:start position:0%
+It's harmful. Um and potentially there's
+other health issues related to it. Um
+
+ align:start position:0%
+other health issues related to it. Um
+ 
+
+ align:start position:0%
+other health issues related to it. Um
+but it is uh present in all the gas
+
+ align:start position:0%
+but it is uh present in all the gas
+ 
+
+ align:start position:0%
+but it is uh present in all the gas
+everywhere. Um and again looking at just
+
+ align:start position:0%
+everywhere. Um and again looking at just
+ 
+
+ align:start position:0%
+everywhere. Um and again looking at just
+benzene again um basically every single
+
+ align:start position:0%
+benzene again um basically every single
+ 
+
+ align:start position:0%
+benzene again um basically every single
+canister they sent to a lab had some
+
+ align:start position:0%
+canister they sent to a lab had some
+ 
+
+ align:start position:0%
+canister they sent to a lab had some
+amount of benzene in it. Um Boston is
+
+ align:start position:0%
+amount of benzene in it. Um Boston is
+ 
+
+ align:start position:0%
+amount of benzene in it. Um Boston is
+actually on the lowest end of the
+
+ align:start position:0%
+actually on the lowest end of the
+ 
+
+ align:start position:0%
+actually on the lowest end of the
+spectrum as far as um benzene
+
+ align:start position:0%
+spectrum as far as um benzene
+ 
+
+ align:start position:0%
+spectrum as far as um benzene
+concentrations. The highest in the US is
+
+ align:start position:0%
+concentrations. The highest in the US is
+ 
+
+ align:start position:0%
+concentrations. The highest in the US is
+Los Angeles and the highest of places in
+
+ align:start position:0%
+Los Angeles and the highest of places in
+ 
+
+ align:start position:0%
+Los Angeles and the highest of places in
+the uh in North America that they
+
+ align:start position:0%
+the uh in North America that they
+ 
+
+ align:start position:0%
+the uh in North America that they
+sampled was uh Vancouver and Los
+
+ align:start position:0%
+sampled was uh Vancouver and Los
+ 
+
+ align:start position:0%
+sampled was uh Vancouver and Los
+Angeles. So, um,
+
+ align:start position:0%
+Angeles. So, um,
+ 
+
+ align:start position:0%
+Angeles. So, um,
+you know, I could go on for hours about
+
+ align:start position:0%
+you know, I could go on for hours about
+ 
+
+ align:start position:0%
+you know, I could go on for hours about
+every single one of these spots, but,
+
+ align:start position:0%
+every single one of these spots, but,
+ 
+
+ align:start position:0%
+every single one of these spots, but,
+um, I I just wanted to give folks kind
+
+ align:start position:0%
+um, I I just wanted to give folks kind
+ 
+
+ align:start position:0%
+um, I I just wanted to give folks kind
+of a small snapshot of the types of
+
+ align:start position:0%
+of a small snapshot of the types of
+ 
+
+ align:start position:0%
+of a small snapshot of the types of
+health hazards that you all are helping
+
+ align:start position:0%
+health hazards that you all are helping
+ 
+
+ align:start position:0%
+health hazards that you all are helping
+to prevent by switching over to
+
+ align:start position:0%
+to prevent by switching over to
+ 
+
+ align:start position:0%
+to prevent by switching over to
+geothermal. Um because if you uh change
+
+ align:start position:0%
+geothermal. Um because if you uh change
+ 
+
+ align:start position:0%
+geothermal. Um because if you uh change
+what's going on on the right side of the
+
+ align:start position:0%
+what's going on on the right side of the
+ 
+
+ align:start position:0%
+what's going on on the right side of the
+supply chain, you're having ripple
+
+ align:start position:0%
+supply chain, you're having ripple
+ 
+
+ align:start position:0%
+supply chain, you're having ripple
+effects all the way across the supply
+
+ align:start position:0%
+effects all the way across the supply
+ 
+
+ align:start position:0%
+effects all the way across the supply
+chain and reducing air pollution,
+
+ align:start position:0%
+chain and reducing air pollution,
+ 
+
+ align:start position:0%
+chain and reducing air pollution,
+reducing safety hazards due to gas
+
+ align:start position:0%
+reducing safety hazards due to gas
+ 
+
+ align:start position:0%
+reducing safety hazards due to gas
+storage, which I could talk for hours
+
+ align:start position:0%
+storage, which I could talk for hours
+ 
+
+ align:start position:0%
+storage, which I could talk for hours
+about. Um reducing use of pipelines,
+
+ align:start position:0%
+about. Um reducing use of pipelines,
+ 
+
+ align:start position:0%
+about. Um reducing use of pipelines,
+reducing compressor station pollution,
+
+ align:start position:0%
+reducing compressor station pollution,
+ 
+
+ align:start position:0%
+reducing compressor station pollution,
+um and you know, really being a public
+
+ align:start position:0%
+um and you know, really being a public
+ 
+
+ align:start position:0%
+um and you know, really being a public
+health resource. So that's it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Thank you so much. I am feeling really
+
+ align:start position:0%
+>> Thank you so much. I am feeling really
+ 
+
+ align:start position:0%
+>> Thank you so much. I am feeling really
+grateful for those three amazing talks
+
+ align:start position:0%
+grateful for those three amazing talks
+ 
+
+ align:start position:0%
+grateful for those three amazing talks
+to start our day.
\ No newline at end of file
diff --git a/e10dswn-grA.txt b/e10dswn-grA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..31cc6bea7cc318448536f61be2fdcdff87222347
--- /dev/null
+++ b/e10dswn-grA.txt
@@ -0,0 +1,16097 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu welcome back to 6890 uh
+
+ align:start position:0%
+ocw.mit.edu welcome back to 6890 uh
+ 
+
+ align:start position:0%
+ocw.mit.edu welcome back to 6890 uh
+today we will do many more hardness
+
+ align:start position:0%
+today we will do many more hardness
+ 
+
+ align:start position:0%
+today we will do many more hardness
+proofs uh mostly of games and puzzles uh
+
+ align:start position:0%
+proofs uh mostly of games and puzzles uh
+ 
+
+ align:start position:0%
+proofs uh mostly of games and puzzles uh
+and some graph theoretic problems uh all
+
+ align:start position:0%
+and some graph theoretic problems uh all
+ 
+
+ align:start position:0%
+and some graph theoretic problems uh all
+reducing from three Set uh we're going
+
+ align:start position:0%
+reducing from three Set uh we're going
+ 
+
+ align:start position:0%
+reducing from three Set uh we're going
+to continue where we left off last time
+
+ align:start position:0%
+to continue where we left off last time
+ 
+
+ align:start position:0%
+to continue where we left off last time
+which was with this picture which also
+
+ align:start position:0%
+which was with this picture which also
+ 
+
+ align:start position:0%
+which was with this picture which also
+comes from lecture one uh which is how
+
+ align:start position:0%
+comes from lecture one uh which is how
+ 
+
+ align:start position:0%
+comes from lecture one uh which is how
+to prove Super Mario Brothers is NP hard
+
+ align:start position:0%
+to prove Super Mario Brothers is NP hard
+ 
+
+ align:start position:0%
+to prove Super Mario Brothers is NP hard
+we had two main gadgets the variable
+
+ align:start position:0%
+we had two main gadgets the variable
+ 
+
+ align:start position:0%
+we had two main gadgets the variable
+Gadget which uh forces your player to
+
+ align:start position:0%
+Gadget which uh forces your player to
+ 
+
+ align:start position:0%
+Gadget which uh forces your player to
+choose going left or right and the
+
+ align:start position:0%
+choose going left or right and the
+ 
+
+ align:start position:0%
+choose going left or right and the
+Clause Gadget which uh could be visited
+
+ align:start position:0%
+Clause Gadget which uh could be visited
+ 
+
+ align:start position:0%
+Clause Gadget which uh could be visited
+in three three different ways in order
+
+ align:start position:0%
+in three three different ways in order
+ 
+
+ align:start position:0%
+in three three different ways in order
+to enable it these each contained an
+
+ align:start position:0%
+to enable it these each contained an
+ 
+
+ align:start position:0%
+to enable it these each contained an
+invincibility star so if later you come
+
+ align:start position:0%
+invincibility star so if later you come
+ 
+
+ align:start position:0%
+invincibility star so if later you come
+through to Traverse the gadget you can
+
+ align:start position:0%
+through to Traverse the gadget you can
+ 
+
+ align:start position:0%
+through to Traverse the gadget you can
+get through all these fireb bars if and
+
+ align:start position:0%
+get through all these fireb bars if and
+ 
+
+ align:start position:0%
+get through all these fireb bars if and
+only if there was at least one star
+
+ align:start position:0%
+only if there was at least one star
+ 
+
+ align:start position:0%
+only if there was at least one star
+there so that was a regular three set
+
+ align:start position:0%
+there so that was a regular three set
+ 
+
+ align:start position:0%
+there so that was a regular three set
+clause and then there's the connectivity
+
+ align:start position:0%
+clause and then there's the connectivity
+ 
+
+ align:start position:0%
+clause and then there's the connectivity
+in between and so in particular you need
+
+ align:start position:0%
+in between and so in particular you need
+ 
+
+ align:start position:0%
+in between and so in particular you need
+a crossover Gadget with this setup but
+
+ align:start position:0%
+a crossover Gadget with this setup but
+ 
+
+ align:start position:0%
+a crossover Gadget with this setup but
+the general idea is you visit variable
+
+ align:start position:0%
+the general idea is you visit variable
+ 
+
+ align:start position:0%
+the general idea is you visit variable
+visit all the Clauses that are in it uh
+
+ align:start position:0%
+visit all the Clauses that are in it uh
+ 
+
+ align:start position:0%
+visit all the Clauses that are in it uh
+that include that literal the one you
+
+ align:start position:0%
+that include that literal the one you
+ 
+
+ align:start position:0%
+that include that literal the one you
+you get to choose only one then you go
+
+ align:start position:0%
+you get to choose only one then you go
+ 
+
+ align:start position:0%
+you get to choose only one then you go
+to the next variable next variable and
+
+ align:start position:0%
+to the next variable next variable and
+ 
+
+ align:start position:0%
+to the next variable next variable and
+then you Trav all the Clauses that you
+
+ align:start position:0%
+then you Trav all the Clauses that you
+ 
+
+ align:start position:0%
+then you Trav all the Clauses that you
+can get to finish if and only if uh the
+
+ align:start position:0%
+can get to finish if and only if uh the
+ 
+
+ align:start position:0%
+can get to finish if and only if uh the
+three step formula was satisfiable this
+
+ align:start position:0%
+three step formula was satisfiable this
+ 
+
+ align:start position:0%
+three step formula was satisfiable this
+is a general uh construction or approach
+
+ align:start position:0%
+is a general uh construction or approach
+ 
+
+ align:start position:0%
+is a general uh construction or approach
+for platform video games that's what we
+
+ align:start position:0%
+for platform video games that's what we
+ 
+
+ align:start position:0%
+for platform video games that's what we
+uh were presenting it as in a recent
+
+ align:start position:0%
+uh were presenting it as in a recent
+ 
+
+ align:start position:0%
+uh were presenting it as in a recent
+paper uh I thought I'd show you a few
+
+ align:start position:0%
+paper uh I thought I'd show you a few
+ 
+
+ align:start position:0%
+paper uh I thought I'd show you a few
+other uh Nintendo games you can prove
+
+ align:start position:0%
+other uh Nintendo games you can prove
+ 
+
+ align:start position:0%
+other uh Nintendo games you can prove
+hard with this technique uh this is the
+
+ align:start position:0%
+hard with this technique uh this is the
+ 
+
+ align:start position:0%
+hard with this technique uh this is the
+Clause gadget for Super Mario World uh
+
+ align:start position:0%
+Clause gadget for Super Mario World uh
+ 
+
+ align:start position:0%
+Clause gadget for Super Mario World uh
+so in Super Mario World there are these
+
+ align:start position:0%
+so in Super Mario World there are these
+ 
+
+ align:start position:0%
+so in Super Mario World there are these
+great uh question mark blocks and in
+
+ align:start position:0%
+great uh question mark blocks and in
+ 
+
+ align:start position:0%
+great uh question mark blocks and in
+particular uh pow blocks which go back
+
+ align:start position:0%
+particular uh pow blocks which go back
+ 
+
+ align:start position:0%
+particular uh pow blocks which go back
+to the original uh Mario Brothers
+
+ align:start position:0%
+to the original uh Mario Brothers
+ 
+
+ align:start position:0%
+to the original uh Mario Brothers
+without the super how many people played
+
+ align:start position:0%
+without the super how many people played
+ 
+
+ align:start position:0%
+without the super how many people played
+Mario Brothers kind of old really old
+
+ align:start position:0%
+Mario Brothers kind of old really old
+ 
+
+ align:start position:0%
+Mario Brothers kind of old really old
+school pre Super Mario and uh anyway it
+
+ align:start position:0%
+school pre Super Mario and uh anyway it
+ 
+
+ align:start position:0%
+school pre Super Mario and uh anyway it
+doesn't matter exactly where it comes
+
+ align:start position:0%
+doesn't matter exactly where it comes
+ 
+
+ align:start position:0%
+doesn't matter exactly where it comes
+from it does something completely
+
+ align:start position:0%
+from it does something completely
+ 
+
+ align:start position:0%
+from it does something completely
+different in Super Mario World um which
+
+ align:start position:0%
+different in Super Mario World um which
+ 
+
+ align:start position:0%
+different in Super Mario World um which
+is turns all coins into walkable things
+
+ align:start position:0%
+is turns all coins into walkable things
+ 
+
+ align:start position:0%
+is turns all coins into walkable things
+you can walk on for like 10 seconds uh
+
+ align:start position:0%
+you can walk on for like 10 seconds uh
+ 
+
+ align:start position:0%
+you can walk on for like 10 seconds uh
+but you can't normally hit a question
+
+ align:start position:0%
+but you can't normally hit a question
+ 
+
+ align:start position:0%
+but you can't normally hit a question
+mark block except from the bottom
+
+ align:start position:0%
+mark block except from the bottom
+ 
+
+ align:start position:0%
+mark block except from the bottom
+there's no way to do that here but if
+
+ align:start position:0%
+there's no way to do that here but if
+ 
+
+ align:start position:0%
+there's no way to do that here but if
+you can visit one of these three places
+
+ align:start position:0%
+you can visit one of these three places
+ 
+
+ align:start position:0%
+you can visit one of these three places
+you can send one of these turtle shells
+
+ align:start position:0%
+you can send one of these turtle shells
+ 
+
+ align:start position:0%
+you can send one of these turtle shells
+flying and it will hit this and bring
+
+ align:start position:0%
+flying and it will hit this and bring
+ 
+
+ align:start position:0%
+flying and it will hit this and bring
+the PO block off and then disappear so
+
+ align:start position:0%
+the PO block off and then disappear so
+ 
+
+ align:start position:0%
+the PO block off and then disappear so
+that later when you try to Traverse this
+
+ align:start position:0%
+that later when you try to Traverse this
+ 
+
+ align:start position:0%
+that later when you try to Traverse this
+Clause Gadget if there's a PO block you
+
+ align:start position:0%
+Clause Gadget if there's a PO block you
+ 
+
+ align:start position:0%
+Clause Gadget if there's a PO block you
+can turn these into Sol solid things for
+
+ align:start position:0%
+can turn these into Sol solid things for
+ 
+
+ align:start position:0%
+can turn these into Sol solid things for
+long enough you can get a cross but no
+
+ align:start position:0%
+long enough you can get a cross but no
+ 
+
+ align:start position:0%
+long enough you can get a cross but no
+longer than that so in the next Gadget
+
+ align:start position:0%
+longer than that so in the next Gadget
+ 
+
+ align:start position:0%
+longer than that so in the next Gadget
+you need another po block and so on so
+
+ align:start position:0%
+you need another po block and so on so
+ 
+
+ align:start position:0%
+you need another po block and so on so
+that's Claus gadget for Super Mario
+
+ align:start position:0%
+that's Claus gadget for Super Mario
+ 
+
+ align:start position:0%
+that's Claus gadget for Super Mario
+World um the other gadgets are pretty
+
+ align:start position:0%
+World um the other gadgets are pretty
+ 
+
+ align:start position:0%
+World um the other gadgets are pretty
+similar so I'll just show you that one
+
+ align:start position:0%
+similar so I'll just show you that one
+ 
+
+ align:start position:0%
+similar so I'll just show you that one
+does the Star Trek not work uh
+
+ align:start position:0%
+does the Star Trek not work uh
+ 
+
+ align:start position:0%
+does the Star Trek not work uh
+I guess you could also do the Star trick
+
+ align:start position:0%
+I guess you could also do the Star trick
+ 
+
+ align:start position:0%
+I guess you could also do the Star trick
+but I think we drew this figure before
+
+ align:start position:0%
+but I think we drew this figure before
+ 
+
+ align:start position:0%
+but I think we drew this figure before
+we did the Star trick so we thought oh
+
+ align:start position:0%
+we did the Star trick so we thought oh
+ 
+
+ align:start position:0%
+we did the Star trick so we thought oh
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+cooler
+
+ align:start position:0%
+cooler
+ 
+
+ align:start position:0%
+cooler
+yeah um now one thing I I thought I'd
+
+ align:start position:0%
+yeah um now one thing I I thought I'd
+ 
+
+ align:start position:0%
+yeah um now one thing I I thought I'd
+mention uh briefly is uh some fun
+
+ align:start position:0%
+mention uh briefly is uh some fun
+ 
+
+ align:start position:0%
+mention uh briefly is uh some fun
+glitches you can do in real Super Mario
+
+ align:start position:0%
+glitches you can do in real Super Mario
+ 
+
+ align:start position:0%
+glitches you can do in real Super Mario
+Brothers as implemented on the ROMs um
+
+ align:start position:0%
+Brothers as implemented on the ROMs um
+ 
+
+ align:start position:0%
+Brothers as implemented on the ROMs um
+you can do these crazy things like jump
+
+ align:start position:0%
+you can do these crazy things like jump
+ 
+
+ align:start position:0%
+you can do these crazy things like jump
+off of walls you're not supposed to be
+
+ align:start position:0%
+off of walls you're not supposed to be
+ 
+
+ align:start position:0%
+off of walls you're not supposed to be
+able to do this and this level would be
+
+ align:start position:0%
+able to do this and this level would be
+ 
+
+ align:start position:0%
+able to do this and this level would be
+unsolvable in the way you normally think
+
+ align:start position:0%
+unsolvable in the way you normally think
+ 
+
+ align:start position:0%
+unsolvable in the way you normally think
+about uh Super Mario Brothers but there
+
+ align:start position:0%
+about uh Super Mario Brothers but there
+ 
+
+ align:start position:0%
+about uh Super Mario Brothers but there
+happens to be this fun sub pixel
+
+ align:start position:0%
+happens to be this fun sub pixel
+ 
+
+ align:start position:0%
+happens to be this fun sub pixel
+resolution I think this is usually done
+
+ align:start position:0%
+resolution I think this is usually done
+ 
+
+ align:start position:0%
+resolution I think this is usually done
+very hard to do with a real controller
+
+ align:start position:0%
+very hard to do with a real controller
+ 
+
+ align:start position:0%
+very hard to do with a real controller
+but much easier to do when you can slow
+
+ align:start position:0%
+but much easier to do when you can slow
+ 
+
+ align:start position:0%
+but much easier to do when you can slow
+things down a 100 times and every frame
+
+ align:start position:0%
+things down a 100 times and every frame
+ 
+
+ align:start position:0%
+things down a 100 times and every frame
+you have a choice of whether to push a
+
+ align:start position:0%
+you have a choice of whether to push a
+ 
+
+ align:start position:0%
+you have a choice of whether to push a
+particular button that's called to Tool
+
+ align:start position:0%
+particular button that's called to Tool
+ 
+
+ align:start position:0%
+particular button that's called to Tool
+assisted speedruns usually um and so you
+
+ align:start position:0%
+assisted speedruns usually um and so you
+ 
+
+ align:start position:0%
+assisted speedruns usually um and so you
+might I don't know if you consider this
+
+ align:start position:0%
+might I don't know if you consider this
+ 
+
+ align:start position:0%
+might I don't know if you consider this
+real Super Mario Brothers or not it
+
+ align:start position:0%
+real Super Mario Brothers or not it
+ 
+
+ align:start position:0%
+real Super Mario Brothers or not it
+depends on your notion of reality
+
+ align:start position:0%
+depends on your notion of reality
+ 
+
+ align:start position:0%
+depends on your notion of reality
+whether you more a mathematician or a
+
+ align:start position:0%
+whether you more a mathematician or a
+ 
+
+ align:start position:0%
+whether you more a mathematician or a
+gamer I guess uh but you can try to
+
+ align:start position:0%
+gamer I guess uh but you can try to
+ 
+
+ align:start position:0%
+gamer I guess uh but you can try to
+modify the gadgets so that uh wall
+
+ align:start position:0%
+modify the gadgets so that uh wall
+ 
+
+ align:start position:0%
+modify the gadgets so that uh wall
+jumping doesn't help you uh so you could
+
+ align:start position:0%
+jumping doesn't help you uh so you could
+ 
+
+ align:start position:0%
+jumping doesn't help you uh so you could
+imagine trying to jump up these walls
+
+ align:start position:0%
+imagine trying to jump up these walls
+ 
+
+ align:start position:0%
+imagine trying to jump up these walls
+but if there's things in the way
+
+ align:start position:0%
+but if there's things in the way
+ 
+
+ align:start position:0%
+but if there's things in the way
+prevents it so if you just add that to
+
+ align:start position:0%
+prevents it so if you just add that to
+ 
+
+ align:start position:0%
+prevents it so if you just add that to
+every vertical tunnel that will uh
+
+ align:start position:0%
+every vertical tunnel that will uh
+ 
+
+ align:start position:0%
+every vertical tunnel that will uh
+prevent going back up the tunnels which
+
+ align:start position:0%
+prevent going back up the tunnels which
+ 
+
+ align:start position:0%
+prevent going back up the tunnels which
+is important for the variable gadgets we
+
+ align:start position:0%
+is important for the variable gadgets we
+ 
+
+ align:start position:0%
+is important for the variable gadgets we
+don't want to be able to reverse our
+
+ align:start position:0%
+don't want to be able to reverse our
+ 
+
+ align:start position:0%
+don't want to be able to reverse our
+decision and later choose the opposite
+
+ align:start position:0%
+decision and later choose the opposite
+ 
+
+ align:start position:0%
+decision and later choose the opposite
+variable setting here's another fun set
+
+ align:start position:0%
+variable setting here's another fun set
+ 
+
+ align:start position:0%
+variable setting here's another fun set
+of uh um cheats where you you jump
+
+ align:start position:0%
+of uh um cheats where you you jump
+ 
+
+ align:start position:0%
+of uh um cheats where you you jump
+through the walls this one is apparently
+
+ align:start position:0%
+through the walls this one is apparently
+ 
+
+ align:start position:0%
+through the walls this one is apparently
+somewhat doable on a real controller uh
+
+ align:start position:0%
+somewhat doable on a real controller uh
+ 
+
+ align:start position:0%
+somewhat doable on a real controller uh
+but still quite challenging um I think
+
+ align:start position:0%
+but still quite challenging um I think
+ 
+
+ align:start position:0%
+but still quite challenging um I think
+the one of the general ideas is the
+
+ align:start position:0%
+the one of the general ideas is the
+ 
+
+ align:start position:0%
+the one of the general ideas is the
+Collision detection is not super good in
+
+ align:start position:0%
+Collision detection is not super good in
+ 
+
+ align:start position:0%
+Collision detection is not super good in
+the game as implemented uh so if you
+
+ align:start position:0%
+the game as implemented uh so if you
+ 
+
+ align:start position:0%
+the game as implemented uh so if you
+time if you get just the right geometry
+
+ align:start position:0%
+time if you get just the right geometry
+ 
+
+ align:start position:0%
+time if you get just the right geometry
+you can walk through the walls there's
+
+ align:start position:0%
+you can walk through the walls there's
+ 
+
+ align:start position:0%
+you can walk through the walls there's
+instructions
+
+ align:start position:0%
+instructions
+ 
+
+ align:start position:0%
+instructions
+for um so this is obviously problematic
+
+ align:start position:0%
+for um so this is obviously problematic
+ 
+
+ align:start position:0%
+for um so this is obviously problematic
+because all of our gadgets involve walls
+
+ align:start position:0%
+because all of our gadgets involve walls
+ 
+
+ align:start position:0%
+because all of our gadgets involve walls
+so if you can walk through them
+
+ align:start position:0%
+so if you can walk through them
+ 
+
+ align:start position:0%
+so if you can walk through them
+not very uh interesting so a general
+
+ align:start position:0%
+not very uh interesting so a general
+ 
+
+ align:start position:0%
+not very uh interesting so a general
+approach is to just add lots of
+
+ align:start position:0%
+approach is to just add lots of
+ 
+
+ align:start position:0%
+approach is to just add lots of
+monsters into the walls so even if you
+
+ align:start position:0%
+monsters into the walls so even if you
+ 
+
+ align:start position:0%
+monsters into the walls so even if you
+could walk through you become small
+
+ align:start position:0%
+could walk through you become small
+ 
+
+ align:start position:0%
+could walk through you become small
+Mario and then that's not an option um I
+
+ align:start position:0%
+Mario and then that's not an option um I
+ 
+
+ align:start position:0%
+Mario and then that's not an option um I
+should say these have not been
+
+ align:start position:0%
+should say these have not been
+ 
+
+ align:start position:0%
+should say these have not been
+thoroughly tested so it's plausible you
+
+ align:start position:0%
+thoroughly tested so it's plausible you
+ 
+
+ align:start position:0%
+thoroughly tested so it's plausible you
+can walk through the wall in such a way
+
+ align:start position:0%
+can walk through the wall in such a way
+ 
+
+ align:start position:0%
+can walk through the wall in such a way
+that maybe you kill the monster or there
+
+ align:start position:0%
+that maybe you kill the monster or there
+ 
+
+ align:start position:0%
+that maybe you kill the monster or there
+may be other glitches that we don't know
+
+ align:start position:0%
+may be other glitches that we don't know
+ 
+
+ align:start position:0%
+may be other glitches that we don't know
+about and so uh you might consider this
+
+ align:start position:0%
+about and so uh you might consider this
+ 
+
+ align:start position:0%
+about and so uh you might consider this
+a work in progress but generally I would
+
+ align:start position:0%
+a work in progress but generally I would
+ 
+
+ align:start position:0%
+a work in progress but generally I would
+believe you can modify the proof to work
+
+ align:start position:0%
+believe you can modify the proof to work
+ 
+
+ align:start position:0%
+believe you can modify the proof to work
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+real Super Mario Brothers as implemented
+
+ align:start position:0%
+real Super Mario Brothers as implemented
+ 
+
+ align:start position:0%
+real Super Mario Brothers as implemented
+in real physics of course generalized to
+
+ align:start position:0%
+in real physics of course generalized to
+ 
+
+ align:start position:0%
+in real physics of course generalized to
+an end byend screen and so on so uh what
+
+ align:start position:0%
+an end byend screen and so on so uh what
+ 
+
+ align:start position:0%
+an end byend screen and so on so uh what
+exactly you call real is uh is
+
+ align:start position:0%
+exactly you call real is uh is
+ 
+
+ align:start position:0%
+exactly you call real is uh is
+challenging there uh but that's Super
+
+ align:start position:0%
+challenging there uh but that's Super
+ 
+
+ align:start position:0%
+challenging there uh but that's Super
+Mario Brothers just uh some more fun
+
+ align:start position:0%
+Mario Brothers just uh some more fun
+ 
+
+ align:start position:0%
+Mario Brothers just uh some more fun
+stuff in the
+
+ align:start position:0%
+stuff in the
+ 
+
+ align:start position:0%
+stuff in the
+paper um let me talk a little bit about
+
+ align:start position:0%
+paper um let me talk a little bit about
+ 
+
+ align:start position:0%
+paper um let me talk a little bit about
+Legend of Zelda uh this is what it looks
+
+ align:start position:0%
+Legend of Zelda uh this is what it looks
+ 
+
+ align:start position:0%
+Legend of Zelda uh this is what it looks
+like in case you've never seen it and uh
+
+ align:start position:0%
+like in case you've never seen it and uh
+ 
+
+ align:start position:0%
+like in case you've never seen it and uh
+this is the original Legend of Zelda
+
+ align:start position:0%
+this is the original Legend of Zelda
+ 
+
+ align:start position:0%
+this is the original Legend of Zelda
+you're a little character you can walk
+
+ align:start position:0%
+you're a little character you can walk
+ 
+
+ align:start position:0%
+you're a little character you can walk
+around and this is what I would say is a
+
+ align:start position:0%
+around and this is what I would say is a
+ 
+
+ align:start position:0%
+around and this is what I would say is a
+typical block pushing puzzle in Legend
+
+ align:start position:0%
+typical block pushing puzzle in Legend
+ 
+
+ align:start position:0%
+typical block pushing puzzle in Legend
+of Sala which is try all the blocks and
+
+ align:start position:0%
+of Sala which is try all the blocks and
+ 
+
+ align:start position:0%
+of Sala which is try all the blocks and
+hope that one of them pushes
+
+ align:start position:0%
+hope that one of them pushes
+ 
+
+ align:start position:0%
+hope that one of them pushes
+and um I I have to say I watched an
+
+ align:start position:0%
+and um I I have to say I watched an
+ 
+
+ align:start position:0%
+and um I I have to say I watched an
+entire I don't know how long it was five
+
+ align:start position:0%
+entire I don't know how long it was five
+ 
+
+ align:start position:0%
+entire I don't know how long it was five
+hours of walk through Legend of Zelda
+
+ align:start position:0%
+hours of walk through Legend of Zelda
+ 
+
+ align:start position:0%
+hours of walk through Legend of Zelda
+one to find whether there are any more
+
+ align:start position:0%
+one to find whether there are any more
+ 
+
+ align:start position:0%
+one to find whether there are any more
+complicated block pushing puzzles I
+
+ align:start position:0%
+complicated block pushing puzzles I
+ 
+
+ align:start position:0%
+complicated block pushing puzzles I
+swear I remember a slightly more
+
+ align:start position:0%
+swear I remember a slightly more
+ 
+
+ align:start position:0%
+swear I remember a slightly more
+complicated one but I could not find it
+
+ align:start position:0%
+complicated one but I could not find it
+ 
+
+ align:start position:0%
+complicated one but I could not find it
+it's possible skipped in this particular
+
+ align:start position:0%
+it's possible skipped in this particular
+ 
+
+ align:start position:0%
+it's possible skipped in this particular
+walkth through um this well okay it just
+
+ align:start position:0%
+walkth through um this well okay it just
+ 
+
+ align:start position:0%
+walkth through um this well okay it just
+takes a long time but you get all right
+
+ align:start position:0%
+takes a long time but you get all right
+ 
+
+ align:start position:0%
+takes a long time but you get all right
+we're almost done you get an idea of how
+
+ align:start position:0%
+we're almost done you get an idea of how
+ 
+
+ align:start position:0%
+we're almost done you get an idea of how
+uh of what the game is like you've got a
+
+ align:start position:0%
+uh of what the game is like you've got a
+ 
+
+ align:start position:0%
+uh of what the game is like you've got a
+sword whatever that won't be
+
+ align:start position:0%
+sword whatever that won't be
+ 
+
+ align:start position:0%
+sword whatever that won't be
+particularly relevant to our reductions
+
+ align:start position:0%
+particularly relevant to our reductions
+ 
+
+ align:start position:0%
+particularly relevant to our reductions
+there will be no monsters in our
+
+ align:start position:0%
+there will be no monsters in our
+ 
+
+ align:start position:0%
+there will be no monsters in our
+reductions in this case I think you just
+
+ align:start position:0%
+reductions in this case I think you just
+ 
+
+ align:start position:0%
+reductions in this case I think you just
+have to wait a really long time or
+
+ align:start position:0%
+have to wait a really long time or
+ 
+
+ align:start position:0%
+have to wait a really long time or
+possibly kill the the hand that comes
+
+ align:start position:0%
+possibly kill the the hand that comes
+ 
+
+ align:start position:0%
+possibly kill the the hand that comes
+out then you can push that block he
+
+ align:start position:0%
+out then you can push that block he
+ 
+
+ align:start position:0%
+out then you can push that block he
+actually tried to push in the beginning
+
+ align:start position:0%
+actually tried to push in the beginning
+ 
+
+ align:start position:0%
+actually tried to push in the beginning
+but it wouldn't move anyway that's
+
+ align:start position:0%
+but it wouldn't move anyway that's
+ 
+
+ align:start position:0%
+but it wouldn't move anyway that's
+Legend of Zelda uh the the uh here's a
+
+ align:start position:0%
+Legend of Zelda uh the the uh here's a
+ 
+
+ align:start position:0%
+Legend of Zelda uh the the uh here's a
+slightly more interesting one this is
+
+ align:start position:0%
+slightly more interesting one this is
+ 
+
+ align:start position:0%
+slightly more interesting one this is
+what I remember normally you push one
+
+ align:start position:0%
+what I remember normally you push one
+ 
+
+ align:start position:0%
+what I remember normally you push one
+two three and then you push this to the
+
+ align:start position:0%
+two three and then you push this to the
+ 
+
+ align:start position:0%
+two three and then you push this to the
+side in this particular particular case
+
+ align:start position:0%
+side in this particular particular case
+ 
+
+ align:start position:0%
+side in this particular particular case
+blocks are not pushable sideways which
+
+ align:start position:0%
+blocks are not pushable sideways which
+ 
+
+ align:start position:0%
+blocks are not pushable sideways which
+is really annoying so you actually have
+
+ align:start position:0%
+is really annoying so you actually have
+ 
+
+ align:start position:0%
+is really annoying so you actually have
+to solve it a different way if you watch
+
+ align:start position:0%
+to solve it a different way if you watch
+ 
+
+ align:start position:0%
+to solve it a different way if you watch
+this video at this point he's like oh my
+
+ align:start position:0%
+this video at this point he's like oh my
+ 
+
+ align:start position:0%
+this video at this point he's like oh my
+God this was the simplest blocking push
+
+ align:start position:0%
+God this was the simplest blocking push
+ 
+
+ align:start position:0%
+God this was the simplest blocking push
+block pushing puzzle ever and I solved
+
+ align:start position:0%
+block pushing puzzle ever and I solved
+ 
+
+ align:start position:0%
+block pushing puzzle ever and I solved
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+yay it's like after half an hour of
+
+ align:start position:0%
+yay it's like after half an hour of
+ 
+
+ align:start position:0%
+yay it's like after half an hour of
+trying other things um that's the the
+
+ align:start position:0%
+trying other things um that's the the
+ 
+
+ align:start position:0%
+trying other things um that's the the
+joy of Legend of Zelda very fun puzzles
+
+ align:start position:0%
+joy of Legend of Zelda very fun puzzles
+ 
+
+ align:start position:0%
+joy of Legend of Zelda very fun puzzles
+so to speak uh so the point is you have
+
+ align:start position:0%
+so to speak uh so the point is you have
+ 
+
+ align:start position:0%
+so to speak uh so the point is you have
+block pushing puzzles we already know uh
+
+ align:start position:0%
+block pushing puzzles we already know uh
+ 
+
+ align:start position:0%
+block pushing puzzles we already know uh
+oh sorry here's one more I guess this
+
+ align:start position:0%
+oh sorry here's one more I guess this
+ 
+
+ align:start position:0%
+oh sorry here's one more I guess this
+these are in Legend of Zelda linked to
+
+ align:start position:0%
+these are in Legend of Zelda linked to
+ 
+
+ align:start position:0%
+these are in Legend of Zelda linked to
+the Past uh so it has a slightly more
+
+ align:start position:0%
+the Past uh so it has a slightly more
+ 
+
+ align:start position:0%
+the Past uh so it has a slightly more
+comp There's an actual slightly
+
+ align:start position:0%
+comp There's an actual slightly
+ 
+
+ align:start position:0%
+comp There's an actual slightly
+non-trivial block pushing puzzle um but
+
+ align:start position:0%
+non-trivial block pushing puzzle um but
+ 
+
+ align:start position:0%
+non-trivial block pushing puzzle um but
+in general we know push one is hard uh
+
+ align:start position:0%
+in general we know push one is hard uh
+ 
+
+ align:start position:0%
+in general we know push one is hard uh
+most versions of Legend of Zelda are
+
+ align:start position:0%
+most versions of Legend of Zelda are
+ 
+
+ align:start position:0%
+most versions of Legend of Zelda are
+slightly more restrictive than uh push
+
+ align:start position:0%
+slightly more restrictive than uh push
+ 
+
+ align:start position:0%
+slightly more restrictive than uh push
+one I would call them push once blocks
+
+ align:start position:0%
+one I would call them push once blocks
+ 
+
+ align:start position:0%
+one I would call them push once blocks
+where uh you can only push one uh at a
+
+ align:start position:0%
+where uh you can only push one uh at a
+ 
+
+ align:start position:0%
+where uh you can only push one uh at a
+time that's your strength but also you
+
+ align:start position:0%
+time that's your strength but also you
+ 
+
+ align:start position:0%
+time that's your strength but also you
+can only push a block once you can never
+
+ align:start position:0%
+can only push a block once you can never
+ 
+
+ align:start position:0%
+can only push a block once you can never
+push it a second time or push it back or
+
+ align:start position:0%
+push it a second time or push it back or
+ 
+
+ align:start position:0%
+push it a second time or push it back or
+do anything like that and uh with some
+
+ align:start position:0%
+do anything like that and uh with some
+ 
+
+ align:start position:0%
+do anything like that and uh with some
+slight this is the gadget we saw before
+
+ align:start position:0%
+slight this is the gadget we saw before
+ 
+
+ align:start position:0%
+slight this is the gadget we saw before
+with some slight tweaks you can make the
+
+ align:start position:0%
+with some slight tweaks you can make the
+ 
+
+ align:start position:0%
+with some slight tweaks you can make the
+lock still work when you only allowed to
+
+ align:start position:0%
+lock still work when you only allowed to
+ 
+
+ align:start position:0%
+lock still work when you only allowed to
+push each block once so um that proves
+
+ align:start position:0%
+push each block once so um that proves
+ 
+
+ align:start position:0%
+push each block once so um that proves
+that most versions of Legends of Zelda
+
+ align:start position:0%
+that most versions of Legends of Zelda
+ 
+
+ align:start position:0%
+that most versions of Legends of Zelda
+are at least MP hard uh because they
+
+ align:start position:0%
+are at least MP hard uh because they
+ 
+
+ align:start position:0%
+are at least MP hard uh because they
+include block pushing um but it would be
+
+ align:start position:0%
+include block pushing um but it would be
+ 
+
+ align:start position:0%
+include block pushing um but it would be
+nice to uh understand other senses in
+
+ align:start position:0%
+nice to uh understand other senses in
+ 
+
+ align:start position:0%
+nice to uh understand other senses in
+which these kinds of games are hard
+
+ align:start position:0%
+which these kinds of games are hard
+ 
+
+ align:start position:0%
+which these kinds of games are hard
+without using block pushing so here's
+
+ align:start position:0%
+without using block pushing so here's
+ 
+
+ align:start position:0%
+without using block pushing so here's
+another feature called the um the hook
+
+ align:start position:0%
+another feature called the um the hook
+ 
+
+ align:start position:0%
+another feature called the um the hook
+shot so you select it then if there's a
+
+ align:start position:0%
+shot so you select it then if there's a
+ 
+
+ align:start position:0%
+shot so you select it then if there's a
+object on the other side you can hook
+
+ align:start position:0%
+object on the other side you can hook
+ 
+
+ align:start position:0%
+object on the other side you can hook
+shot to that side so in you can't walk
+
+ align:start position:0%
+shot to that side so in you can't walk
+ 
+
+ align:start position:0%
+shot to that side so in you can't walk
+over the cavern but you can hook shot
+
+ align:start position:0%
+over the cavern but you can hook shot
+ 
+
+ align:start position:0%
+over the cavern but you can hook shot
+across here here it is again as long as
+
+ align:start position:0%
+across here here it is again as long as
+ 
+
+ align:start position:0%
+across here here it is again as long as
+there's an object over there you can
+
+ align:start position:0%
+there's an object over there you can
+ 
+
+ align:start position:0%
+there's an object over there you can
+also pick up objects and Destroy them uh
+
+ align:start position:0%
+also pick up objects and Destroy them uh
+ 
+
+ align:start position:0%
+also pick up objects and Destroy them uh
+so does that make it hard with no
+
+ align:start position:0%
+so does that make it hard with no
+ 
+
+ align:start position:0%
+so does that make it hard with no
+pushing blocks well little bit of
+
+ align:start position:0%
+pushing blocks well little bit of
+ 
+
+ align:start position:0%
+pushing blocks well little bit of
+pushing blocks here's a simple proof
+
+ align:start position:0%
+pushing blocks here's a simple proof
+ 
+
+ align:start position:0%
+pushing blocks here's a simple proof
+using that uh structure so here's a
+
+ align:start position:0%
+using that uh structure so here's a
+ 
+
+ align:start position:0%
+using that uh structure so here's a
+variable uh you go from top to bottom so
+
+ align:start position:0%
+variable uh you go from top to bottom so
+ 
+
+ align:start position:0%
+variable uh you go from top to bottom so
+you're over here uh treasure chests are
+
+ align:start position:0%
+you're over here uh treasure chests are
+ 
+
+ align:start position:0%
+you're over here uh treasure chests are
+something that you can hook shot onto to
+
+ align:start position:0%
+something that you can hook shot onto to
+ 
+
+ align:start position:0%
+something that you can hook shot onto to
+go over the cavern and here you have a
+
+ align:start position:0%
+go over the cavern and here you have a
+ 
+
+ align:start position:0%
+go over the cavern and here you have a
+choice you can go left or you can go
+
+ align:start position:0%
+choice you can go left or you can go
+ 
+
+ align:start position:0%
+choice you can go left or you can go
+right but then you can't back up because
+
+ align:start position:0%
+right but then you can't back up because
+ 
+
+ align:start position:0%
+right but then you can't back up because
+there's no object here to hook shot onto
+
+ align:start position:0%
+there's no object here to hook shot onto
+ 
+
+ align:start position:0%
+there's no object here to hook shot onto
+you can only do it
+
+ align:start position:0%
+you can only do it
+ 
+
+ align:start position:0%
+you can only do it
+orthogonally um here's a clause if you
+
+ align:start position:0%
+orthogonally um here's a clause if you
+ 
+
+ align:start position:0%
+orthogonally um here's a clause if you
+come down any one of these paths then
+
+ align:start position:0%
+come down any one of these paths then
+ 
+
+ align:start position:0%
+come down any one of these paths then
+you can push this block One Step um and
+
+ align:start position:0%
+you can push this block One Step um and
+ 
+
+ align:start position:0%
+you can push this block One Step um and
+then you'll be able to hook shot from
+
+ align:start position:0%
+then you'll be able to hook shot from
+ 
+
+ align:start position:0%
+then you'll be able to hook shot from
+the right uh to get onto this platform
+
+ align:start position:0%
+the right uh to get onto this platform
+ 
+
+ align:start position:0%
+the right uh to get onto this platform
+and then continue to the left uh and a
+
+ align:start position:0%
+and then continue to the left uh and a
+ 
+
+ align:start position:0%
+and then continue to the left uh and a
+crossover is really easy in this world
+
+ align:start position:0%
+crossover is really easy in this world
+ 
+
+ align:start position:0%
+crossover is really easy in this world
+so this there's you could come up with
+
+ align:start position:0%
+so this there's you could come up with
+ 
+
+ align:start position:0%
+so this there's you could come up with
+lots of different NP hardness proofs so
+
+ align:start position:0%
+lots of different NP hardness proofs so
+ 
+
+ align:start position:0%
+lots of different NP hardness proofs so
+this was a a fun one for a link to the
+
+ align:start position:0%
+this was a a fun one for a link to the
+ 
+
+ align:start position:0%
+this was a a fun one for a link to the
+past which is the first one first game
+
+ align:start position:0%
+past which is the first one first game
+ 
+
+ align:start position:0%
+past which is the first one first game
+that has that hook shot this is Metroid
+
+ align:start position:0%
+that has that hook shot this is Metroid
+ 
+
+ align:start position:0%
+that has that hook shot this is Metroid
+if you've never played most of the time
+
+ align:start position:0%
+if you've never played most of the time
+ 
+
+ align:start position:0%
+if you've never played most of the time
+you spend going up and down elevator
+
+ align:start position:0%
+you spend going up and down elevator
+ 
+
+ align:start position:0%
+you spend going up and down elevator
+shafts and there are these monsters
+
+ align:start position:0%
+shafts and there are these monsters
+ 
+
+ align:start position:0%
+shafts and there are these monsters
+which you can shoot um and then there's
+
+ align:start position:0%
+which you can shoot um and then there's
+ 
+
+ align:start position:0%
+which you can shoot um and then there's
+also this ability to become a one by one
+
+ align:start position:0%
+also this ability to become a one by one
+ 
+
+ align:start position:0%
+also this ability to become a one by one
+block instead of a 2 by one block and
+
+ align:start position:0%
+block instead of a 2 by one block and
+ 
+
+ align:start position:0%
+block instead of a 2 by one block and
+roll through small things when you're in
+
+ align:start position:0%
+roll through small things when you're in
+ 
+
+ align:start position:0%
+roll through small things when you're in
+that position uh in a certain part of
+
+ align:start position:0%
+that position uh in a certain part of
+ 
+
+ align:start position:0%
+that position uh in a certain part of
+the game you're not allowed to shoot
+
+ align:start position:0%
+the game you're not allowed to shoot
+ 
+
+ align:start position:0%
+the game you're not allowed to shoot
+okay so that's the situation we're going
+
+ align:start position:0%
+okay so that's the situation we're going
+ 
+
+ align:start position:0%
+okay so that's the situation we're going
+to imagine um um so here is a clause and
+
+ align:start position:0%
+to imagine um um so here is a clause and
+ 
+
+ align:start position:0%
+to imagine um um so here is a clause and
+a crossover I mean the the variable
+
+ align:start position:0%
+a crossover I mean the the variable
+ 
+
+ align:start position:0%
+a crossover I mean the the variable
+Gadget is the same as Mario you fall
+
+ align:start position:0%
+Gadget is the same as Mario you fall
+ 
+
+ align:start position:0%
+Gadget is the same as Mario you fall
+left or fall right you can't go back up
+
+ align:start position:0%
+left or fall right you can't go back up
+ 
+
+ align:start position:0%
+left or fall right you can't go back up
+uh because you have a limited jump
+
+ align:start position:0%
+uh because you have a limited jump
+ 
+
+ align:start position:0%
+uh because you have a limited jump
+height so let's do the Clause first um
+
+ align:start position:0%
+height so let's do the Clause first um
+ 
+
+ align:start position:0%
+height so let's do the Clause first um
+there are three different ways to visit
+
+ align:start position:0%
+there are three different ways to visit
+ 
+
+ align:start position:0%
+there are three different ways to visit
+it uh when you're setting your variables
+
+ align:start position:0%
+it uh when you're setting your variables
+ 
+
+ align:start position:0%
+it uh when you're setting your variables
+if you can get here you can aim upwards
+
+ align:start position:0%
+if you can get here you can aim upwards
+ 
+
+ align:start position:0%
+if you can get here you can aim upwards
+and just shoot all of these things it
+
+ align:start position:0%
+and just shoot all of these things it
+ 
+
+ align:start position:0%
+and just shoot all of these things it
+would take a few minutes but you get rid
+
+ align:start position:0%
+would take a few minutes but you get rid
+ 
+
+ align:start position:0%
+would take a few minutes but you get rid
+of All These Guys these guys just walk
+
+ align:start position:0%
+of All These Guys these guys just walk
+ 
+
+ align:start position:0%
+of All These Guys these guys just walk
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+constantly and then to Traverse you're
+
+ align:start position:0%
+constantly and then to Traverse you're
+ 
+
+ align:start position:0%
+constantly and then to Traverse you're
+going to be coming through here in ball
+
+ align:start position:0%
+going to be coming through here in ball
+ 
+
+ align:start position:0%
+going to be coming through here in ball
+mode there no way to I guess here you
+
+ align:start position:0%
+mode there no way to I guess here you
+ 
+
+ align:start position:0%
+mode there no way to I guess here you
+could briefly stand up but you can't
+
+ align:start position:0%
+could briefly stand up but you can't
+ 
+
+ align:start position:0%
+could briefly stand up but you can't
+shoot down in original Metroid so you
+
+ align:start position:0%
+shoot down in original Metroid so you
+ 
+
+ align:start position:0%
+shoot down in original Metroid so you
+want to roll over here but you would
+
+ align:start position:0%
+want to roll over here but you would
+ 
+
+ align:start position:0%
+want to roll over here but you would
+take too much damage uh maybe you only
+
+ align:start position:0%
+take too much damage uh maybe you only
+ 
+
+ align:start position:0%
+take too much damage uh maybe you only
+have one hit point left so if there's
+
+ align:start position:0%
+have one hit point left so if there's
+ 
+
+ align:start position:0%
+have one hit point left so if there's
+any of these guys left you have to visit
+
+ align:start position:0%
+any of these guys left you have to visit
+ 
+
+ align:start position:0%
+any of these guys left you have to visit
+at least one of these to kill all the
+
+ align:start position:0%
+at least one of these to kill all the
+ 
+
+ align:start position:0%
+at least one of these to kill all the
+monsters and then get through okay
+
+ align:start position:0%
+monsters and then get through okay
+ 
+
+ align:start position:0%
+monsters and then get through okay
+that's Clause crossover is a little more
+
+ align:start position:0%
+that's Clause crossover is a little more
+ 
+
+ align:start position:0%
+that's Clause crossover is a little more
+challenging um in this case we set
+
+ align:start position:0%
+challenging um in this case we set
+ 
+
+ align:start position:0%
+challenging um in this case we set
+things up the idea is you come in here
+
+ align:start position:0%
+things up the idea is you come in here
+ 
+
+ align:start position:0%
+things up the idea is you come in here
+and you want to leave out there uh so
+
+ align:start position:0%
+and you want to leave out there uh so
+ 
+
+ align:start position:0%
+and you want to leave out there uh so
+it's unidirectional you can't go up in
+
+ align:start position:0%
+it's unidirectional you can't go up in
+ 
+
+ align:start position:0%
+it's unidirectional you can't go up in
+this gadget and the idea is there's a
+
+ align:start position:0%
+this gadget and the idea is there's a
+ 
+
+ align:start position:0%
+this gadget and the idea is there's a
+little Gap uh and it's moving this way
+
+ align:start position:0%
+little Gap uh and it's moving this way
+ 
+
+ align:start position:0%
+little Gap uh and it's moving this way
+as the monsters move around so you wait
+
+ align:start position:0%
+as the monsters move around so you wait
+ 
+
+ align:start position:0%
+as the monsters move around so you wait
+for the Gap to come here then you go
+
+ align:start position:0%
+for the Gap to come here then you go
+ 
+
+ align:start position:0%
+for the Gap to come here then you go
+down and then you basically forced in
+
+ align:start position:0%
+down and then you basically forced in
+ 
+
+ align:start position:0%
+down and then you basically forced in
+timing when you fall down this
+
+ align:start position:0%
+timing when you fall down this
+ 
+
+ align:start position:0%
+timing when you fall down this
+Cavern and it's set up so that by the
+
+ align:start position:0%
+Cavern and it's set up so that by the
+ 
+
+ align:start position:0%
+Cavern and it's set up so that by the
+time that hap by this time this thing
+
+ align:start position:0%
+time that hap by this time this thing
+ 
+
+ align:start position:0%
+time that hap by this time this thing
+gets to here uh these guys will have
+
+ align:start position:0%
+gets to here uh these guys will have
+ 
+
+ align:start position:0%
+gets to here uh these guys will have
+come to the other side and then you have
+
+ align:start position:0%
+come to the other side and then you have
+ 
+
+ align:start position:0%
+come to the other side and then you have
+to roll to the right in order to avoid
+
+ align:start position:0%
+to roll to the right in order to avoid
+ 
+
+ align:start position:0%
+to roll to the right in order to avoid
+taking damage from these guys who are
+
+ align:start position:0%
+taking damage from these guys who are
+ 
+
+ align:start position:0%
+taking damage from these guys who are
+going around the other way and similarly
+
+ align:start position:0%
+going around the other way and similarly
+ 
+
+ align:start position:0%
+going around the other way and similarly
+in the other direction
+
+ align:start position:0%
+in the other direction
+ 
+
+ align:start position:0%
+in the other direction
+uh so you have to get the timing right
+
+ align:start position:0%
+uh so you have to get the timing right
+ 
+
+ align:start position:0%
+uh so you have to get the timing right
+and we haven't exactly tested this yet
+
+ align:start position:0%
+and we haven't exactly tested this yet
+ 
+
+ align:start position:0%
+and we haven't exactly tested this yet
+but it should be approximately correct
+
+ align:start position:0%
+but it should be approximately correct
+ 
+
+ align:start position:0%
+but it should be approximately correct
+um and that will force a crossover
+
+ align:start position:0%
+um and that will force a crossover
+ 
+
+ align:start position:0%
+um and that will force a crossover
+should be a simpler way but that's the
+
+ align:start position:0%
+should be a simpler way but that's the
+ 
+
+ align:start position:0%
+should be a simpler way but that's the
+best crossover we have
+
+ align:start position:0%
+best crossover we have
+ 
+
+ align:start position:0%
+best crossover we have
+currently uh so Metroid is NP here we
+
+ align:start position:0%
+currently uh so Metroid is NP here we
+ 
+
+ align:start position:0%
+currently uh so Metroid is NP here we
+actually claim mp completeness uh
+
+ align:start position:0%
+actually claim mp completeness uh
+ 
+
+ align:start position:0%
+actually claim mp completeness uh
+because there isn't too much state to
+
+ align:start position:0%
+because there isn't too much state to
+ 
+
+ align:start position:0%
+because there isn't too much state to
+the game um uh so the the issue here is
+
+ align:start position:0%
+the game um uh so the the issue here is
+ 
+
+ align:start position:0%
+the game um uh so the the issue here is
+is the length of a solution polinomial
+
+ align:start position:0%
+is the length of a solution polinomial
+ 
+
+ align:start position:0%
+is the length of a solution polinomial
+length if it is then we know it's NP
+
+ align:start position:0%
+length if it is then we know it's NP
+ 
+
+ align:start position:0%
+length if it is then we know it's NP
+then it's in NP and NP complete um and
+
+ align:start position:0%
+then it's in NP and NP complete um and
+ 
+
+ align:start position:0%
+then it's in NP and NP complete um and
+here you can kill each monster only once
+
+ align:start position:0%
+here you can kill each monster only once
+ 
+
+ align:start position:0%
+here you can kill each monster only once
+uh so that's that's the idea uh for and
+
+ align:start position:0%
+uh so that's that's the idea uh for and
+ 
+
+ align:start position:0%
+uh so that's that's the idea uh for and
+the amount of State you have is just
+
+ align:start position:0%
+the amount of State you have is just
+ 
+
+ align:start position:0%
+the amount of State you have is just
+your position and what items you
+
+ align:start position:0%
+your position and what items you
+ 
+
+ align:start position:0%
+your position and what items you
+currently have so you should be able to
+
+ align:start position:0%
+currently have so you should be able to
+ 
+
+ align:start position:0%
+currently have so you should be able to
+solve this in NP and that sort of
+
+ align:start position:0%
+solve this in NP and that sort of
+ 
+
+ align:start position:0%
+solve this in NP and that sort of
+settles the complexity most of these
+
+ align:start position:0%
+settles the complexity most of these
+ 
+
+ align:start position:0%
+settles the complexity most of these
+other problems could potentially be
+
+ align:start position:0%
+other problems could potentially be
+ 
+
+ align:start position:0%
+other problems could potentially be
+harder than NP and we have some other
+
+ align:start position:0%
+harder than NP and we have some other
+ 
+
+ align:start position:0%
+harder than NP and we have some other
+results like that which we may get to
+
+ align:start position:0%
+results like that which we may get to
+ 
+
+ align:start position:0%
+results like that which we may get to
+when we're talking about ppace but today
+
+ align:start position:0%
+when we're talking about ppace but today
+ 
+
+ align:start position:0%
+when we're talking about ppace but today
+is about
+
+ align:start position:0%
+is about
+ 
+
+ align:start position:0%
+is about
+NP uh here's Donkey Kong Country if you
+
+ align:start position:0%
+NP uh here's Donkey Kong Country if you
+ 
+
+ align:start position:0%
+NP uh here's Donkey Kong Country if you
+haven't played I this is a speedrun
+
+ align:start position:0%
+haven't played I this is a speedrun
+ 
+
+ align:start position:0%
+haven't played I this is a speedrun
+uh and uh you can kill monsters by
+
+ align:start position:0%
+uh and uh you can kill monsters by
+ 
+
+ align:start position:0%
+uh and uh you can kill monsters by
+Rolling most of the time you're jumping
+
+ align:start position:0%
+Rolling most of the time you're jumping
+ 
+
+ align:start position:0%
+Rolling most of the time you're jumping
+um and collecting bananas uh there are
+
+ align:start position:0%
+um and collecting bananas uh there are
+ 
+
+ align:start position:0%
+um and collecting bananas uh there are
+these bees that if you touch them you
+
+ align:start position:0%
+these bees that if you touch them you
+ 
+
+ align:start position:0%
+these bees that if you touch them you
+die or uh you sort of have two hit
+
+ align:start position:0%
+die or uh you sort of have two hit
+ 
+
+ align:start position:0%
+die or uh you sort of have two hit
+points and then there are these barrels
+
+ align:start position:0%
+points and then there are these barrels
+ 
+
+ align:start position:0%
+points and then there are these barrels
+you can pick up that's a giant bee you
+
+ align:start position:0%
+you can pick up that's a giant bee you
+ 
+
+ align:start position:0%
+you can pick up that's a giant bee you
+can pick up some certain barrels and
+
+ align:start position:0%
+can pick up some certain barrels and
+ 
+
+ align:start position:0%
+can pick up some certain barrels and
+then throw them at a monster and in this
+
+ align:start position:0%
+then throw them at a monster and in this
+ 
+
+ align:start position:0%
+then throw them at a monster and in this
+case damage usually kill them then there
+
+ align:start position:0%
+case damage usually kill them then there
+ 
+
+ align:start position:0%
+case damage usually kill them then there
+are these other types of barrels that
+
+ align:start position:0%
+are these other types of barrels that
+ 
+
+ align:start position:0%
+are these other types of barrels that
+when you touch them they shoot you in a
+
+ align:start position:0%
+when you touch them they shoot you in a
+ 
+
+ align:start position:0%
+when you touch them they shoot you in a
+predefined direction and let you collect
+
+ align:start position:0%
+predefined direction and let you collect
+ 
+
+ align:start position:0%
+predefined direction and let you collect
+lots of bananas
+
+ align:start position:0%
+lots of bananas
+ 
+
+ align:start position:0%
+lots of bananas
+okay so that's those are the rules of
+
+ align:start position:0%
+okay so that's those are the rules of
+ 
+
+ align:start position:0%
+okay so that's those are the rules of
+Donkey Kong in a nutshell um in a banana
+
+ align:start position:0%
+Donkey Kong in a nutshell um in a banana
+ 
+
+ align:start position:0%
+Donkey Kong in a nutshell um in a banana
+shell
+
+ align:start position:0%
+shell
+ 
+
+ align:start position:0%
+shell
+I so in a banana peel thank you um so
+
+ align:start position:0%
+I so in a banana peel thank you um so
+ 
+
+ align:start position:0%
+I so in a banana peel thank you um so
+here's a simple Crossover with that
+
+ align:start position:0%
+here's a simple Crossover with that
+ 
+
+ align:start position:0%
+here's a simple Crossover with that
+setup uh you just have these barrels
+
+ align:start position:0%
+setup uh you just have these barrels
+ 
+
+ align:start position:0%
+setup uh you just have these barrels
+that shoot you in a predefined direction
+
+ align:start position:0%
+that shoot you in a predefined direction
+ 
+
+ align:start position:0%
+that shoot you in a predefined direction
+and force you to go through this
+
+ align:start position:0%
+and force you to go through this
+ 
+
+ align:start position:0%
+and force you to go through this
+intersection without any choice when
+
+ align:start position:0%
+intersection without any choice when
+ 
+
+ align:start position:0%
+intersection without any choice when
+you're when you're being shot you cannot
+
+ align:start position:0%
+you're when you're being shot you cannot
+ 
+
+ align:start position:0%
+you're when you're being shot you cannot
+move uh so that's easy uh again
+
+ align:start position:0%
+move uh so that's easy uh again
+ 
+
+ align:start position:0%
+move uh so that's easy uh again
+variables the same as Mario you fall
+
+ align:start position:0%
+variables the same as Mario you fall
+ 
+
+ align:start position:0%
+variables the same as Mario you fall
+left or fall right and a clause uh it's
+
+ align:start position:0%
+left or fall right and a clause uh it's
+ 
+
+ align:start position:0%
+left or fall right and a clause uh it's
+a little hard to see with the background
+
+ align:start position:0%
+a little hard to see with the background
+ 
+
+ align:start position:0%
+a little hard to see with the background
+here but um there's a little ledge here
+
+ align:start position:0%
+here but um there's a little ledge here
+ 
+
+ align:start position:0%
+here but um there's a little ledge here
+and you can come down this way pick up
+
+ align:start position:0%
+and you can come down this way pick up
+ 
+
+ align:start position:0%
+and you can come down this way pick up
+this barrel and throw it over here and
+
+ align:start position:0%
+this barrel and throw it over here and
+ 
+
+ align:start position:0%
+this barrel and throw it over here and
+it will eventually hit this uh B so that
+
+ align:start position:0%
+it will eventually hit this uh B so that
+ 
+
+ align:start position:0%
+it will eventually hit this uh B so that
+later you can Traverse this gadget
+
+ align:start position:0%
+later you can Traverse this gadget
+ 
+
+ align:start position:0%
+later you can Traverse this gadget
+without dying from the B so not drawn is
+
+ align:start position:0%
+without dying from the B so not drawn is
+ 
+
+ align:start position:0%
+without dying from the B so not drawn is
+uh a platform that you need to or maybe
+
+ align:start position:0%
+uh a platform that you need to or maybe
+ 
+
+ align:start position:0%
+uh a platform that you need to or maybe
+you're falling all the way through these
+
+ align:start position:0%
+you're falling all the way through these
+ 
+
+ align:start position:0%
+you're falling all the way through these
+things uh if you set up all the Clauses
+
+ align:start position:0%
+things uh if you set up all the Clauses
+ 
+
+ align:start position:0%
+things uh if you set up all the Clauses
+vertically if there's any B left you
+
+ align:start position:0%
+vertically if there's any B left you
+ 
+
+ align:start position:0%
+vertically if there's any B left you
+will die otherwise not and so you have
+
+ align:start position:0%
+will die otherwise not and so you have
+ 
+
+ align:start position:0%
+will die otherwise not and so you have
+to visit at at least one of these three
+
+ align:start position:0%
+to visit at at least one of these three
+ 
+
+ align:start position:0%
+to visit at at least one of these three
+barrels to kill the
+
+ align:start position:0%
+barrels to kill the
+ 
+
+ align:start position:0%
+barrels to kill the
+bee so uh and I think this is a
+
+ align:start position:0%
+bee so uh and I think this is a
+ 
+
+ align:start position:0%
+bee so uh and I think this is a
+mechanism to prevent you from carrying
+
+ align:start position:0%
+mechanism to prevent you from carrying
+ 
+
+ align:start position:0%
+mechanism to prevent you from carrying
+this Barrel anywhere else uh like
+
+ align:start position:0%
+this Barrel anywhere else uh like
+ 
+
+ align:start position:0%
+this Barrel anywhere else uh like
+climbing up or
+
+ align:start position:0%
+climbing up or
+ 
+
+ align:start position:0%
+climbing up or
+something anyway that's Donkey Kong
+
+ align:start position:0%
+something anyway that's Donkey Kong
+ 
+
+ align:start position:0%
+something anyway that's Donkey Kong
+Country I think there's one more
+
+ align:start position:0%
+Country I think there's one more
+ 
+
+ align:start position:0%
+Country I think there's one more
+Pokemon uh I'm kind of embarrassed I've
+
+ align:start position:0%
+Pokemon uh I'm kind of embarrassed I've
+ 
+
+ align:start position:0%
+Pokemon uh I'm kind of embarrassed I've
+never actually played a Pokemon game I
+
+ align:start position:0%
+never actually played a Pokemon game I
+ 
+
+ align:start position:0%
+never actually played a Pokemon game I
+don't know if I should admit this but I
+
+ align:start position:0%
+don't know if I should admit this but I
+ 
+
+ align:start position:0%
+don't know if I should admit this but I
+need to sit down and play them all some
+
+ align:start position:0%
+need to sit down and play them all some
+ 
+
+ align:start position:0%
+need to sit down and play them all some
+some weekend um I did watch Twitch play
+
+ align:start position:0%
+some weekend um I did watch Twitch play
+ 
+
+ align:start position:0%
+some weekend um I did watch Twitch play
+it for a
+
+ align:start position:0%
+it for a
+ 
+
+ align:start position:0%
+it for a
+while going back to the previous slide
+
+ align:start position:0%
+while going back to the previous slide
+ 
+
+ align:start position:0%
+while going back to the previous slide
+in in some of the other
+
+ align:start position:0%
+in in some of the other
+ 
+
+ align:start position:0%
+in in some of the other
+gadgets uh if we satisfied a clause
+
+ align:start position:0%
+gadgets uh if we satisfied a clause
+ 
+
+ align:start position:0%
+gadgets uh if we satisfied a clause
+there was no way to uh you there was a
+
+ align:start position:0%
+there was no way to uh you there was a
+ 
+
+ align:start position:0%
+there was no way to uh you there was a
+barrier between uh setting the clause
+
+ align:start position:0%
+barrier between uh setting the clause
+ 
+
+ align:start position:0%
+barrier between uh setting the clause
+and going through the rest of that thing
+
+ align:start position:0%
+and going through the rest of that thing
+ 
+
+ align:start position:0%
+and going through the rest of that thing
+right so potentially you could get to
+
+ align:start position:0%
+right so potentially you could get to
+ 
+
+ align:start position:0%
+right so potentially you could get to
+the last Clause here kill the bee and
+
+ align:start position:0%
+the last Clause here kill the bee and
+ 
+
+ align:start position:0%
+the last Clause here kill the bee and
+just walk forward without killing the
+
+ align:start position:0%
+just walk forward without killing the
+ 
+
+ align:start position:0%
+just walk forward without killing the
+rest of the stuff
+
+ align:start position:0%
+rest of the stuff
+ 
+
+ align:start position:0%
+rest of the stuff
+uh good question okay yeah I think
+
+ align:start position:0%
+uh good question okay yeah I think
+ 
+
+ align:start position:0%
+uh good question okay yeah I think
+probably the right way to set this up uh
+
+ align:start position:0%
+probably the right way to set this up uh
+ 
+
+ align:start position:0%
+probably the right way to set this up uh
+I'm not quite sure how to do it directly
+
+ align:start position:0%
+I'm not quite sure how to do it directly
+ 
+
+ align:start position:0%
+I'm not quite sure how to do it directly
+from the drawing but an easy way to do
+
+ align:start position:0%
+from the drawing but an easy way to do
+ 
+
+ align:start position:0%
+from the drawing but an easy way to do
+it would be there's there's no floor
+
+ align:start position:0%
+it would be there's there's no floor
+ 
+
+ align:start position:0%
+it would be there's there's no floor
+below here uh and at the end when you
+
+ align:start position:0%
+below here uh and at the end when you
+ 
+
+ align:start position:0%
+below here uh and at the end when you
+solved all the things there is one of
+
+ align:start position:0%
+solved all the things there is one of
+ 
+
+ align:start position:0%
+solved all the things there is one of
+these barrels that shoots you straight
+
+ align:start position:0%
+these barrels that shoots you straight
+ 
+
+ align:start position:0%
+these barrels that shoots you straight
+to the left until you get to the
+
+ align:start position:0%
+to the left until you get to the
+ 
+
+ align:start position:0%
+to the left until you get to the
+finish uh so you if you tried to exit
+
+ align:start position:0%
+finish uh so you if you tried to exit
+ 
+
+ align:start position:0%
+finish uh so you if you tried to exit
+the claws early you would just fall to
+
+ align:start position:0%
+the claws early you would just fall to
+ 
+
+ align:start position:0%
+the claws early you would just fall to
+your death because there's only one
+
+ align:start position:0%
+your death because there's only one
+ 
+
+ align:start position:0%
+your death because there's only one
+barrel shooting way over on the right
+
+ align:start position:0%
+barrel shooting way over on the right
+ 
+
+ align:start position:0%
+barrel shooting way over on the right
+that be one solution I forget exactly
+
+ align:start position:0%
+that be one solution I forget exactly
+ 
+
+ align:start position:0%
+that be one solution I forget exactly
+what's in the paper but wouldn't
+
+ align:start position:0%
+what's in the paper but wouldn't
+ 
+
+ align:start position:0%
+what's in the paper but wouldn't
+surprise me if it's that yeah good
+
+ align:start position:0%
+surprise me if it's that yeah good
+ 
+
+ align:start position:0%
+surprise me if it's that yeah good
+question you definitely don't want to be
+
+ align:start position:0%
+question you definitely don't want to be
+ 
+
+ align:start position:0%
+question you definitely don't want to be
+able to just visit the last Clause kill
+
+ align:start position:0%
+able to just visit the last Clause kill
+ 
+
+ align:start position:0%
+able to just visit the last Clause kill
+the guy and then exit that would be that
+
+ align:start position:0%
+the guy and then exit that would be that
+ 
+
+ align:start position:0%
+the guy and then exit that would be that
+would be cheating but in these proofs
+
+ align:start position:0%
+would be cheating but in these proofs
+ 
+
+ align:start position:0%
+would be cheating but in these proofs
+that's always what you have to worry
+
+ align:start position:0%
+that's always what you have to worry
+ 
+
+ align:start position:0%
+that's always what you have to worry
+about is this type of cheating other
+
+ align:start position:0%
+about is this type of cheating other
+ 
+
+ align:start position:0%
+about is this type of cheating other
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+cool uh Pokemon time um so
+
+ align:start position:0%
+cool uh Pokemon time um so
+ 
+
+ align:start position:0%
+cool uh Pokemon time um so
+uh Pokemon is a somewhat complicated
+
+ align:start position:0%
+uh Pokemon is a somewhat complicated
+ 
+
+ align:start position:0%
+uh Pokemon is a somewhat complicated
+game um a lot of different abilities and
+
+ align:start position:0%
+game um a lot of different abilities and
+ 
+
+ align:start position:0%
+game um a lot of different abilities and
+so on so we had to abstract things away
+
+ align:start position:0%
+so on so we had to abstract things away
+ 
+
+ align:start position:0%
+so on so we had to abstract things away
+and in these pictures there are two
+
+ align:start position:0%
+and in these pictures there are two
+ 
+
+ align:start position:0%
+and in these pictures there are two
+types of uh I haven't defined any of the
+
+ align:start position:0%
+types of uh I haven't defined any of the
+ 
+
+ align:start position:0%
+types of uh I haven't defined any of the
+rules yet you are a little uh person
+
+ align:start position:0%
+rules yet you are a little uh person
+ 
+
+ align:start position:0%
+rules yet you are a little uh person
+walking around here uh you're carrying
+
+ align:start position:0%
+walking around here uh you're carrying
+ 
+
+ align:start position:0%
+walking around here uh you're carrying
+Pokemon whatever uh and there are these
+
+ align:start position:0%
+Pokemon whatever uh and there are these
+ 
+
+ align:start position:0%
+Pokemon whatever uh and there are these
+these characters called trainers and uh
+
+ align:start position:0%
+these characters called trainers and uh
+ 
+
+ align:start position:0%
+these characters called trainers and uh
+the the red trainers are called weak
+
+ align:start position:0%
+the the red trainers are called weak
+ 
+
+ align:start position:0%
+the the red trainers are called weak
+trainers these are people that when you
+
+ align:start position:0%
+trainers these are people that when you
+ 
+
+ align:start position:0%
+trainers these are people that when you
+visit they just sort of deactivate you
+
+ align:start position:0%
+visit they just sort of deactivate you
+ 
+
+ align:start position:0%
+visit they just sort of deactivate you
+beat them and then there's blue trainers
+
+ align:start position:0%
+beat them and then there's blue trainers
+ 
+
+ align:start position:0%
+beat them and then there's blue trainers
+we'll call them strong trainers those
+
+ align:start position:0%
+we'll call them strong trainers those
+ 
+
+ align:start position:0%
+we'll call them strong trainers those
+are ones that no matter how no matter
+
+ align:start position:0%
+are ones that no matter how no matter
+ 
+
+ align:start position:0%
+are ones that no matter how no matter
+when or how you try to play them you
+
+ align:start position:0%
+when or how you try to play them you
+ 
+
+ align:start position:0%
+when or how you try to play them you
+always die and so you fail so you never
+
+ align:start position:0%
+always die and so you fail so you never
+ 
+
+ align:start position:0%
+always die and so you fail so you never
+want to visit blue trainer uh now
+
+ align:start position:0%
+want to visit blue trainer uh now
+ 
+
+ align:start position:0%
+want to visit blue trainer uh now
+trainers have two kinds of uh let's talk
+
+ align:start position:0%
+trainers have two kinds of uh let's talk
+ 
+
+ align:start position:0%
+trainers have two kinds of uh let's talk
+about variables maybe this is an easy
+
+ align:start position:0%
+about variables maybe this is an easy
+ 
+
+ align:start position:0%
+about variables maybe this is an easy
+situation uh so variable you want to
+
+ align:start position:0%
+situation uh so variable you want to
+ 
+
+ align:start position:0%
+situation uh so variable you want to
+come in the in and either leave in the
+
+ align:start position:0%
+come in the in and either leave in the
+ 
+
+ align:start position:0%
+come in the in and either leave in the
+false or leave in the true and there are
+
+ align:start position:0%
+false or leave in the true and there are
+ 
+
+ align:start position:0%
+false or leave in the true and there are
+two ways to activate a trainer one is to
+
+ align:start position:0%
+two ways to activate a trainer one is to
+ 
+
+ align:start position:0%
+two ways to activate a trainer one is to
+walk into their field of view so when
+
+ align:start position:0%
+walk into their field of view so when
+ 
+
+ align:start position:0%
+walk into their field of view so when
+you which are drawn with these
+
+ align:start position:0%
+you which are drawn with these
+ 
+
+ align:start position:0%
+you which are drawn with these
+rectangles if you walk to this position
+
+ align:start position:0%
+rectangles if you walk to this position
+ 
+
+ align:start position:0%
+rectangles if you walk to this position
+the trainer will walk to you
+
+ align:start position:0%
+the trainer will walk to you
+ 
+
+ align:start position:0%
+the trainer will walk to you
+and then you fight the trainer okay and
+
+ align:start position:0%
+and then you fight the trainer okay and
+ 
+
+ align:start position:0%
+and then you fight the trainer okay and
+because it's red you'll win and so in
+
+ align:start position:0%
+because it's red you'll win and so in
+ 
+
+ align:start position:0%
+because it's red you'll win and so in
+that case the trainer has moved here
+
+ align:start position:0%
+that case the trainer has moved here
+ 
+
+ align:start position:0%
+that case the trainer has moved here
+trainers are obstacles so you can uh you
+
+ align:start position:0%
+trainers are obstacles so you can uh you
+ 
+
+ align:start position:0%
+trainers are obstacles so you can uh you
+can't get to the true anymore you have
+
+ align:start position:0%
+can't get to the true anymore you have
+ 
+
+ align:start position:0%
+can't get to the true anymore you have
+to go around to false the other way you
+
+ align:start position:0%
+to go around to false the other way you
+ 
+
+ align:start position:0%
+to go around to false the other way you
+can visit a trainer is to talk to them
+
+ align:start position:0%
+can visit a trainer is to talk to them
+ 
+
+ align:start position:0%
+can visit a trainer is to talk to them
+from the side or from behind so you can
+
+ align:start position:0%
+from the side or from behind so you can
+ 
+
+ align:start position:0%
+from the side or from behind so you can
+walk here talk to the trainer beat them
+
+ align:start position:0%
+walk here talk to the trainer beat them
+ 
+
+ align:start position:0%
+walk here talk to the trainer beat them
+then they deactivate then you can walk
+
+ align:start position:0%
+then they deactivate then you can walk
+ 
+
+ align:start position:0%
+then they deactivate then you can walk
+this way and you can only fight them
+
+ align:start position:0%
+this way and you can only fight them
+ 
+
+ align:start position:0%
+this way and you can only fight them
+once then it's it's they won't move
+
+ align:start position:0%
+once then it's it's they won't move
+ 
+
+ align:start position:0%
+once then it's it's they won't move
+anymore so uh that forces you to do true
+
+ align:start position:0%
+anymore so uh that forces you to do true
+ 
+
+ align:start position:0%
+anymore so uh that forces you to do true
+or false and then commit to that
+
+ align:start position:0%
+or false and then commit to that
+ 
+
+ align:start position:0%
+or false and then commit to that
+decision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um and these are obviously
+
+ align:start position:0%
+okay um and these are obviously
+ 
+
+ align:start position:0%
+okay um and these are obviously
+obstacles they're immovable all right so
+
+ align:start position:0%
+obstacles they're immovable all right so
+ 
+
+ align:start position:0%
+obstacles they're immovable all right so
+the idea with a clause
+
+ align:start position:0%
+the idea with a clause
+ 
+
+ align:start position:0%
+the idea with a clause
+is uh the following you're when you're
+
+ align:start position:0%
+is uh the following you're when you're
+ 
+
+ align:start position:0%
+is uh the following you're when you're
+TR traversing the Clause at the end you
+
+ align:start position:0%
+TR traversing the Clause at the end you
+ 
+
+ align:start position:0%
+TR traversing the Clause at the end you
+want to walk through here and leave and
+
+ align:start position:0%
+want to walk through here and leave and
+ 
+
+ align:start position:0%
+want to walk through here and leave and
+the worry is this position if this
+
+ align:start position:0%
+the worry is this position if this
+ 
+
+ align:start position:0%
+the worry is this position if this
+trainer uh can come to you you will
+
+ align:start position:0%
+trainer uh can come to you you will
+ 
+
+ align:start position:0%
+trainer uh can come to you you will
+die okay
+
+ align:start position:0%
+die okay
+ 
+
+ align:start position:0%
+die okay
+so uh that will be possible exactly when
+
+ align:start position:0%
+so uh that will be possible exactly when
+ 
+
+ align:start position:0%
+so uh that will be possible exactly when
+all of these guys are out of the way
+
+ align:start position:0%
+all of these guys are out of the way
+ 
+
+ align:start position:0%
+all of these guys are out of the way
+when will they come out of the way when
+
+ align:start position:0%
+when will they come out of the way when
+ 
+
+ align:start position:0%
+when will they come out of the way when
+you walk through them and none of them
+
+ align:start position:0%
+you walk through them and none of them
+ 
+
+ align:start position:0%
+you walk through them and none of them
+have been activated yet so then they
+
+ align:start position:0%
+have been activated yet so then they
+ 
+
+ align:start position:0%
+have been activated yet so then they
+will walk one space to you you'll win
+
+ align:start position:0%
+will walk one space to you you'll win
+ 
+
+ align:start position:0%
+will walk one space to you you'll win
+but uh it's
+
+ align:start position:0%
+but uh it's
+ 
+
+ align:start position:0%
+but uh it's
+temporary you win the battle lose the
+
+ align:start position:0%
+temporary you win the battle lose the
+ 
+
+ align:start position:0%
+temporary you win the battle lose the
+war because when you get here then this
+
+ align:start position:0%
+war because when you get here then this
+ 
+
+ align:start position:0%
+war because when you get here then this
+guy can walk through uh but these serve
+
+ align:start position:0%
+guy can walk through uh but these serve
+ 
+
+ align:start position:0%
+guy can walk through uh but these serve
+as obstacles otherwise so um if you can
+
+ align:start position:0%
+as obstacles otherwise so um if you can
+ 
+
+ align:start position:0%
+as obstacles otherwise so um if you can
+come down one of these paths and visit
+
+ align:start position:0%
+come down one of these paths and visit
+ 
+
+ align:start position:0%
+come down one of these paths and visit
+the trainer early then later when you
+
+ align:start position:0%
+the trainer early then later when you
+ 
+
+ align:start position:0%
+the trainer early then later when you
+come through they will not move towards
+
+ align:start position:0%
+come through they will not move towards
+ 
+
+ align:start position:0%
+come through they will not move towards
+you they will stay an obstacle for this
+
+ align:start position:0%
+you they will stay an obstacle for this
+ 
+
+ align:start position:0%
+you they will stay an obstacle for this
+guy and so this I cannot walk to you
+
+ align:start position:0%
+guy and so this I cannot walk to you
+ 
+
+ align:start position:0%
+guy and so this I cannot walk to you
+this is just to make a barrier uh and
+
+ align:start position:0%
+this is just to make a barrier uh and
+ 
+
+ align:start position:0%
+this is just to make a barrier uh and
+then then you can get through okay
+
+ align:start position:0%
+then then you can get through okay
+ 
+
+ align:start position:0%
+then then you can get through okay
+crossover you get the idea right uh we
+
+ align:start position:0%
+crossover you get the idea right uh we
+ 
+
+ align:start position:0%
+crossover you get the idea right uh we
+could try to walk through it but it's
+
+ align:start position:0%
+could try to walk through it but it's
+ 
+
+ align:start position:0%
+could try to walk through it but it's
+definitely complicated General we want
+
+ align:start position:0%
+definitely complicated General we want
+ 
+
+ align:start position:0%
+definitely complicated General we want
+to go from X to X prime or Y to Y Prime
+
+ align:start position:0%
+to go from X to X prime or Y to Y Prime
+ 
+
+ align:start position:0%
+to go from X to X prime or Y to Y Prime
+again it's
+
+ align:start position:0%
+again it's
+ 
+
+ align:start position:0%
+again it's
+directional uh and now that I know the
+
+ align:start position:0%
+directional uh and now that I know the
+ 
+
+ align:start position:0%
+directional uh and now that I know the
+right color assignment red is weak I
+
+ align:start position:0%
+right color assignment red is weak I
+ 
+
+ align:start position:0%
+right color assignment red is weak I
+would guess
+
+ align:start position:0%
+would guess
+ 
+
+ align:start position:0%
+would guess
+uh yeah this guy has an obstacle but as
+
+ align:start position:0%
+uh yeah this guy has an obstacle but as
+ 
+
+ align:start position:0%
+uh yeah this guy has an obstacle but as
+soon as you go this way this guy moves
+
+ align:start position:0%
+soon as you go this way this guy moves
+ 
+
+ align:start position:0%
+soon as you go this way this guy moves
+out of the way so it kind of closes off
+
+ align:start position:0%
+out of the way so it kind of closes off
+ 
+
+ align:start position:0%
+out of the way so it kind of closes off
+trying to return this way so once you
+
+ align:start position:0%
+trying to return this way so once you
+ 
+
+ align:start position:0%
+trying to return this way so once you
+come through here this uh would be a
+
+ align:start position:0%
+come through here this uh would be a
+ 
+
+ align:start position:0%
+come through here this uh would be a
+problem to come back so that kind of
+
+ align:start position:0%
+problem to come back so that kind of
+ 
+
+ align:start position:0%
+problem to come back so that kind of
+cuts you off from going back and uh it's
+
+ align:start position:0%
+cuts you off from going back and uh it's
+ 
+
+ align:start position:0%
+cuts you off from going back and uh it's
+kind of like the crossover we saw with
+
+ align:start position:0%
+kind of like the crossover we saw with
+ 
+
+ align:start position:0%
+kind of like the crossover we saw with
+push one 2D I
+
+ align:start position:0%
+push one 2D I
+ 
+
+ align:start position:0%
+push one 2D I
+believe uh then you probably go here
+
+ align:start position:0%
+believe uh then you probably go here
+ 
+
+ align:start position:0%
+believe uh then you probably go here
+similar thing happens go this guy will
+
+ align:start position:0%
+similar thing happens go this guy will
+ 
+
+ align:start position:0%
+similar thing happens go this guy will
+approach come to you uh and then you can
+
+ align:start position:0%
+approach come to you uh and then you can
+ 
+
+ align:start position:0%
+approach come to you uh and then you can
+escape when you get here this guy will
+
+ align:start position:0%
+escape when you get here this guy will
+ 
+
+ align:start position:0%
+escape when you get here this guy will
+come all the way down oh that looks bad
+
+ align:start position:0%
+come all the way down oh that looks bad
+ 
+
+ align:start position:0%
+come all the way down oh that looks bad
+can yeah so probably we should have
+
+ align:start position:0%
+can yeah so probably we should have
+ 
+
+ align:start position:0%
+can yeah so probably we should have
+talked to him early so then we can come
+
+ align:start position:0%
+talked to him early so then we can come
+ 
+
+ align:start position:0%
+talked to him early so then we can come
+through here without any trouble
+
+ align:start position:0%
+through here without any trouble
+ 
+
+ align:start position:0%
+through here without any trouble
+succeeded in getting down to Y Prime you
+
+ align:start position:0%
+succeeded in getting down to Y Prime you
+ 
+
+ align:start position:0%
+succeeded in getting down to Y Prime you
+have to check that you can't get to X
+
+ align:start position:0%
+have to check that you can't get to X
+ 
+
+ align:start position:0%
+have to check that you can't get to X
+Prime this looks like a impossible Nexus
+
+ align:start position:0%
+Prime this looks like a impossible Nexus
+ 
+
+ align:start position:0%
+Prime this looks like a impossible Nexus
+to get through but these guys can walk
+
+ align:start position:0%
+to get through but these guys can walk
+ 
+
+ align:start position:0%
+to get through but these guys can walk
+through that's the reason they're there
+
+ align:start position:0%
+through that's the reason they're there
+ 
+
+ align:start position:0%
+through that's the reason they're there
+instead of just being
+
+ align:start position:0%
+instead of just being
+ 
+
+ align:start position:0%
+instead of just being
+obstacles uh left left to right should
+
+ align:start position:0%
+obstacles uh left left to right should
+ 
+
+ align:start position:0%
+obstacles uh left left to right should
+be sorry they can only see you like five
+
+ align:start position:0%
+be sorry they can only see you like five
+ 
+
+ align:start position:0%
+be sorry they can only see you like five
+or six piles away this is a generalized
+
+ align:start position:0%
+or six piles away this is a generalized
+ 
+
+ align:start position:0%
+or six piles away this is a generalized
+Pokemon yeah it would be nice I mean
+
+ align:start position:0%
+Pokemon yeah it would be nice I mean
+ 
+
+ align:start position:0%
+Pokemon yeah it would be nice I mean
+obviously this is a bounded visibility
+
+ align:start position:0%
+obviously this is a bounded visibility
+ 
+
+ align:start position:0%
+obviously this is a bounded visibility
+it would be nice to get it to get that
+
+ align:start position:0%
+it would be nice to get it to get that
+ 
+
+ align:start position:0%
+it would be nice to get it to get that
+bound smaller uh but at least this shows
+
+ align:start position:0%
+bound smaller uh but at least this shows
+ 
+
+ align:start position:0%
+bound smaller uh but at least this shows
+constant visibility is enough these
+
+ align:start position:0%
+constant visibility is enough these
+ 
+
+ align:start position:0%
+constant visibility is enough these
+gadgets are all
+
+ align:start position:0%
+gadgets are all
+ 
+
+ align:start position:0%
+gadgets are all
+local uh it would maybe also be nice are
+
+ align:start position:0%
+local uh it would maybe also be nice are
+ 
+
+ align:start position:0%
+local uh it would maybe also be nice are
+they all the
+
+ align:start position:0%
+they all the
+ 
+
+ align:start position:0%
+they all the
+same it's just some fix so it would be
+
+ align:start position:0%
+same it's just some fix so it would be
+ 
+
+ align:start position:0%
+same it's just some fix so it would be
+nice if they were also all the same uh
+
+ align:start position:0%
+nice if they were also all the same uh
+ 
+
+ align:start position:0%
+nice if they were also all the same uh
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+does not currently hold but wouldn't
+
+ align:start position:0%
+does not currently hold but wouldn't
+ 
+
+ align:start position:0%
+does not currently hold but wouldn't
+surprise me if that well yeah
+
+ align:start position:0%
+surprise me if that well yeah
+ 
+
+ align:start position:0%
+surprise me if that well yeah
+tricky all right uh I'll just mention uh
+
+ align:start position:0%
+tricky all right uh I'll just mention uh
+ 
+
+ align:start position:0%
+tricky all right uh I'll just mention uh
+for a little bit of Pokemon cred this is
+
+ align:start position:0%
+for a little bit of Pokemon cred this is
+ 
+
+ align:start position:0%
+for a little bit of Pokemon cred this is
+one uh paragraph of our paper uh where
+
+ align:start position:0%
+one uh paragraph of our paper uh where
+ 
+
+ align:start position:0%
+one uh paragraph of our paper uh where
+we con
+
+ align:start position:0%
+we con
+ 
+
+ align:start position:0%
+we con
+construct construct the weak and the
+
+ align:start position:0%
+construct construct the weak and the
+ 
+
+ align:start position:0%
+construct construct the weak and the
+strong trainers um to use using exactly
+
+ align:start position:0%
+strong trainers um to use using exactly
+ 
+
+ align:start position:0%
+strong trainers um to use using exactly
+the setup that's available in various
+
+ align:start position:0%
+the setup that's available in various
+ 
+
+ align:start position:0%
+the setup that's available in various
+Pokemon games I I I believe in every
+
+ align:start position:0%
+Pokemon games I I I believe in every
+ 
+
+ align:start position:0%
+Pokemon games I I I believe in every
+single game there are enough uh
+
+ align:start position:0%
+single game there are enough uh
+ 
+
+ align:start position:0%
+single game there are enough uh
+abilities that you can set up uh so that
+
+ align:start position:0%
+abilities that you can set up uh so that
+ 
+
+ align:start position:0%
+abilities that you can set up uh so that
+you either Force the bad guy to all he
+
+ align:start position:0%
+you either Force the bad guy to all he
+ 
+
+ align:start position:0%
+you either Force the bad guy to all he
+can do is self-destruct or uh all he can
+
+ align:start position:0%
+can do is self-destruct or uh all he can
+ 
+
+ align:start position:0%
+can do is self-destruct or uh all he can
+do is kill you and you lose that sort of
+
+ align:start position:0%
+do is kill you and you lose that sort of
+ 
+
+ align:start position:0%
+do is kill you and you lose that sort of
+thing uh but it take requires some
+
+ align:start position:0%
+thing uh but it take requires some
+ 
+
+ align:start position:0%
+thing uh but it take requires some
+Pokemon expertise with which uh uh Alan
+
+ align:start position:0%
+Pokemon expertise with which uh uh Alan
+ 
+
+ align:start position:0%
+Pokemon expertise with which uh uh Alan
+guo had in this case he's a PhD student
+
+ align:start position:0%
+guo had in this case he's a PhD student
+ 
+
+ align:start position:0%
+guo had in this case he's a PhD student
+in Cale
+
+ align:start position:0%
+in Cale
+ 
+
+ align:start position:0%
+in Cale
+here okay um any other questions about
+
+ align:start position:0%
+here okay um any other questions about
+ 
+
+ align:start position:0%
+here okay um any other questions about
+uh Nintendo games before we move on yeah
+
+ align:start position:0%
+uh Nintendo games before we move on yeah
+ 
+
+ align:start position:0%
+uh Nintendo games before we move on yeah
+uh this is a common sort of fork
+
+ align:start position:0%
+uh this is a common sort of fork
+ 
+
+ align:start position:0%
+uh this is a common sort of fork
+specific in generation one can miss with
+
+ align:start position:0%
+specific in generation one can miss with
+ 
+
+ align:start position:0%
+specific in generation one can miss with
+a one and 255 CH yeah chess even if
+
+ align:start position:0%
+a one and 255 CH yeah chess even if
+ 
+
+ align:start position:0%
+a one and 255 CH yeah chess even if
+their accuracy is 100% uh how do you
+
+ align:start position:0%
+their accuracy is 100% uh how do you
+ 
+
+ align:start position:0%
+their accuracy is 100% uh how do you
+deal with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sestru SRU miss it doesn't die no but
+
+ align:start position:0%
+sestru SRU miss it doesn't die no but
+ 
+
+ align:start position:0%
+sestru SRU miss it doesn't die no but
+self-destruct doesn't matter whether it
+
+ align:start position:0%
+self-destruct doesn't matter whether it
+ 
+
+ align:start position:0%
+self-destruct doesn't matter whether it
+does damage right it's just kind of you
+
+ align:start position:0%
+does damage right it's just kind of you
+ 
+
+ align:start position:0%
+does damage right it's just kind of you
+self-destruct you die yeah I think I
+
+ align:start position:0%
+self-destruct you die yeah I think I
+ 
+
+ align:start position:0%
+self-destruct you die yeah I think I
+think self-destruct but the death
+
+ align:start position:0%
+think self-destruct but the death
+ 
+
+ align:start position:0%
+think self-destruct but the death
+doesn't actually happen if the attack
+
+ align:start position:0%
+doesn't actually happen if the attack
+ 
+
+ align:start position:0%
+doesn't actually happen if the attack
+misses can you no it does does really
+
+ align:start position:0%
+misses can you no it does does really
+ 
+
+ align:start position:0%
+misses can you no it does does really
+okay yeah it
+
+ align:start position:0%
+okay yeah it
+ 
+
+ align:start position:0%
+okay yeah it
+does we'll have to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+play all right um the next game I'm
+
+ align:start position:0%
+play all right um the next game I'm
+ 
+
+ align:start position:0%
+play all right um the next game I'm
+going to talk about is a sort of
+
+ align:start position:0%
+going to talk about is a sort of
+ 
+
+ align:start position:0%
+going to talk about is a sort of
+physical game that you play on usually a
+
+ align:start position:0%
+physical game that you play on usually a
+ 
+
+ align:start position:0%
+physical game that you play on usually a
+go board with go Stones uh so there are
+
+ align:start position:0%
+go board with go Stones uh so there are
+ 
+
+ align:start position:0%
+go board with go Stones uh so there are
+white stones and black Stones this is is
+
+ align:start position:0%
+white stones and black Stones this is is
+ 
+
+ align:start position:0%
+white stones and black Stones this is is
+invented by this guy John Conway um as
+
+ align:start position:0%
+invented by this guy John Conway um as
+ 
+
+ align:start position:0%
+invented by this guy John Conway um as
+if you've ever played Conway's Game of
+
+ align:start position:0%
+if you've ever played Conway's Game of
+ 
+
+ align:start position:0%
+if you've ever played Conway's Game of
+Life it's not that's a zero player game
+
+ align:start position:0%
+Life it's not that's a zero player game
+ 
+
+ align:start position:0%
+Life it's not that's a zero player game
+this is an actual two-player game and
+
+ align:start position:0%
+this is an actual two-player game and
+ 
+
+ align:start position:0%
+this is an actual two-player game and
+quite challenging in here's the the
+
+ align:start position:0%
+quite challenging in here's the the
+ 
+
+ align:start position:0%
+quite challenging in here's the the
+general idea there's a right player
+
+ align:start position:0%
+general idea there's a right player
+ 
+
+ align:start position:0%
+general idea there's a right player
+trying to get the white ball that's the
+
+ align:start position:0%
+trying to get the white ball that's the
+ 
+
+ align:start position:0%
+trying to get the white ball that's the
+football this is philosopher football if
+
+ align:start position:0%
+football this is philosopher football if
+ 
+
+ align:start position:0%
+football this is philosopher football if
+you will um you're trying to get this
+
+ align:start position:0%
+you will um you're trying to get this
+ 
+
+ align:start position:0%
+you will um you're trying to get this
+ball over to that goal and the left
+
+ align:start position:0%
+ball over to that goal and the left
+ 
+
+ align:start position:0%
+ball over to that goal and the left
+player is trying to get the ball to the
+
+ align:start position:0%
+player is trying to get the ball to the
+ 
+
+ align:start position:0%
+player is trying to get the ball to the
+right goal then there are these uh black
+
+ align:start position:0%
+right goal then there are these uh black
+ 
+
+ align:start position:0%
+right goal then there are these uh black
+pieces which are called men those are
+
+ align:start position:0%
+pieces which are called men those are
+ 
+
+ align:start position:0%
+pieces which are called men those are
+the players of the game so to speak um
+
+ align:start position:0%
+the players of the game so to speak um
+ 
+
+ align:start position:0%
+the players of the game so to speak um
+and there are two types of move in this
+
+ align:start position:0%
+and there are two types of move in this
+ 
+
+ align:start position:0%
+and there are two types of move in this
+game one move you can do is just place a
+
+ align:start position:0%
+game one move you can do is just place a
+ 
+
+ align:start position:0%
+game one move you can do is just place a
+black stone anywhere on the board that's
+
+ align:start position:0%
+black stone anywhere on the board that's
+ 
+
+ align:start position:0%
+black stone anywhere on the board that's
+currently empty and the other type of
+
+ align:start position:0%
+currently empty and the other type of
+ 
+
+ align:start position:0%
+currently empty and the other type of
+move is the more complicated one this is
+
+ align:start position:0%
+move is the more complicated one this is
+ 
+
+ align:start position:0%
+move is the more complicated one this is
+called kicking the ball you can take the
+
+ align:start position:0%
+called kicking the ball you can take the
+ 
+
+ align:start position:0%
+called kicking the ball you can take the
+white piece and you can jump it over a
+
+ align:start position:0%
+white piece and you can jump it over a
+ 
+
+ align:start position:0%
+white piece and you can jump it over a
+string of black of consecutive black
+
+ align:start position:0%
+string of black of consecutive black
+ 
+
+ align:start position:0%
+string of black of consecutive black
+pieces those pieces are immediately
+
+ align:start position:0%
+pieces those pieces are immediately
+ 
+
+ align:start position:0%
+pieces those pieces are immediately
+removed so the these gray shading means
+
+ align:start position:0%
+removed so the these gray shading means
+ 
+
+ align:start position:0%
+removed so the these gray shading means
+they've been removed from the board uh
+
+ align:start position:0%
+they've been removed from the board uh
+ 
+
+ align:start position:0%
+they've been removed from the board uh
+but in the same move you can do several
+
+ align:start position:0%
+but in the same move you can do several
+ 
+
+ align:start position:0%
+but in the same move you can do several
+such jumps so I can jump here then I can
+
+ align:start position:0%
+such jumps so I can jump here then I can
+ 
+
+ align:start position:0%
+such jumps so I can jump here then I can
+jump here uh then I can jump here uh
+
+ align:start position:0%
+jump here uh then I can jump here uh
+ 
+
+ align:start position:0%
+jump here uh then I can jump here uh
+then I can jump here and everything I
+
+ align:start position:0%
+then I can jump here and everything I
+ 
+
+ align:start position:0%
+then I can jump here and everything I
+jump over in this case I won uh if I'm
+
+ align:start position:0%
+jump over in this case I won uh if I'm
+ 
+
+ align:start position:0%
+jump over in this case I won uh if I'm
+the right player I got to that position
+
+ align:start position:0%
+the right player I got to that position
+ 
+
+ align:start position:0%
+the right player I got to that position
+so this is why the right player from the
+
+ align:start position:0%
+so this is why the right player from the
+ 
+
+ align:start position:0%
+so this is why the right player from the
+original position maybe they wanted to
+
+ align:start position:0%
+original position maybe they wanted to
+ 
+
+ align:start position:0%
+original position maybe they wanted to
+place this Stone uh because that would
+
+ align:start position:0%
+place this Stone uh because that would
+ 
+
+ align:start position:0%
+place this Stone uh because that would
+enable in their next move you can't
+
+ align:start position:0%
+enable in their next move you can't
+ 
+
+ align:start position:0%
+enable in their next move you can't
+place a black stone and then jump you
+
+ align:start position:0%
+place a black stone and then jump you
+ 
+
+ align:start position:0%
+place a black stone and then jump you
+can do one or the other so you could try
+
+ align:start position:0%
+can do one or the other so you could try
+ 
+
+ align:start position:0%
+can do one or the other so you could try
+to place this position place the stone
+
+ align:start position:0%
+to place this position place the stone
+ 
+
+ align:start position:0%
+to place this position place the stone
+hoping that in your next turn you'll be
+
+ align:start position:0%
+hoping that in your next turn you'll be
+ 
+
+ align:start position:0%
+hoping that in your next turn you'll be
+able to do this jump and win uh but uh
+
+ align:start position:0%
+able to do this jump and win uh but uh
+ 
+
+ align:start position:0%
+able to do this jump and win uh but uh
+instead from this position the left
+
+ align:start position:0%
+instead from this position the left
+ 
+
+ align:start position:0%
+instead from this position the left
+player could say oh I'll just add this
+
+ align:start position:0%
+player could say oh I'll just add this
+ 
+
+ align:start position:0%
+player could say oh I'll just add this
+Stone and then I in my next move I'll be
+
+ align:start position:0%
+Stone and then I in my next move I'll be
+ 
+
+ align:start position:0%
+Stone and then I in my next move I'll be
+able to jump to the right right side U
+
+ align:start position:0%
+able to jump to the right right side U
+ 
+
+ align:start position:0%
+able to jump to the right right side U
+that's I think unblockable so left wins
+
+ align:start position:0%
+that's I think unblockable so left wins
+ 
+
+ align:start position:0%
+that's I think unblockable so left wins
+yay um so that's that's a setup uh now
+
+ align:start position:0%
+yay um so that's that's a setup uh now
+ 
+
+ align:start position:0%
+yay um so that's that's a setup uh now
+this is a fairly complicated game uh you
+
+ align:start position:0%
+this is a fairly complicated game uh you
+ 
+
+ align:start position:0%
+this is a fairly complicated game uh you
+can get to the same position multiple
+
+ align:start position:0%
+can get to the same position multiple
+ 
+
+ align:start position:0%
+can get to the same position multiple
+times uh and so it's actually open how
+
+ align:start position:0%
+times uh and so it's actually open how
+ 
+
+ align:start position:0%
+times uh and so it's actually open how
+hard this game is I think there's an
+
+ align:start position:0%
+hard this game is I think there's an
+ 
+
+ align:start position:0%
+hard this game is I think there's an
+upper bound of it being solvable in
+
+ align:start position:0%
+upper bound of it being solvable in
+ 
+
+ align:start position:0%
+upper bound of it being solvable in
+exponential time so it's in exp what Sol
+
+ align:start position:0%
+exponential time so it's in exp what Sol
+ 
+
+ align:start position:0%
+exponential time so it's in exp what Sol
+so you given a position you want to know
+
+ align:start position:0%
+so you given a position you want to know
+ 
+
+ align:start position:0%
+so you given a position you want to know
+whether left or right will win from this
+
+ align:start position:0%
+whether left or right will win from this
+ 
+
+ align:start position:0%
+whether left or right will win from this
+position is it possible that it doesn't
+
+ align:start position:0%
+position is it possible that it doesn't
+ 
+
+ align:start position:0%
+position is it possible that it doesn't
+terminate uh it could be Tai is the
+
+ align:start position:0%
+terminate uh it could be Tai is the
+ 
+
+ align:start position:0%
+terminate uh it could be Tai is the
+right answer y so that's tricky uh it
+
+ align:start position:0%
+right answer y so that's tricky uh it
+ 
+
+ align:start position:0%
+right answer y so that's tricky uh it
+there is a PE Bas hardness result
+
+ align:start position:0%
+there is a PE Bas hardness result
+ 
+
+ align:start position:0%
+there is a PE Bas hardness result
+relatively recent uh but an old result
+
+ align:start position:0%
+relatively recent uh but an old result
+ 
+
+ align:start position:0%
+relatively recent uh but an old result
+of ours uh with David Epstein uh is that
+
+ align:start position:0%
+of ours uh with David Epstein uh is that
+ 
+
+ align:start position:0%
+of ours uh with David Epstein uh is that
+just determining whether you can win in
+
+ align:start position:0%
+just determining whether you can win in
+ 
+
+ align:start position:0%
+just determining whether you can win in
+one move is NP complete so that that's a
+
+ align:start position:0%
+one move is NP complete so that that's a
+ 
+
+ align:start position:0%
+one move is NP complete so that that's a
+relatively clean thing you don't have to
+
+ align:start position:0%
+relatively clean thing you don't have to
+ 
+
+ align:start position:0%
+relatively clean thing you don't have to
+worry about non-termination or that sort
+
+ align:start position:0%
+worry about non-termination or that sort
+ 
+
+ align:start position:0%
+worry about non-termination or that sort
+of thing it's just one player's move
+
+ align:start position:0%
+of thing it's just one player's move
+ 
+
+ align:start position:0%
+of thing it's just one player's move
+uh here everything is uh reversed we
+
+ align:start position:0%
+uh here everything is uh reversed we
+ 
+
+ align:start position:0%
+uh here everything is uh reversed we
+have the black uh the ball is black in
+
+ align:start position:0%
+have the black uh the ball is black in
+ 
+
+ align:start position:0%
+have the black uh the ball is black in
+this case I'm not sure if there's a
+
+ align:start position:0%
+this case I'm not sure if there's a
+ 
+
+ align:start position:0%
+this case I'm not sure if there's a
+consistent uh notion anyway uh and this
+
+ align:start position:0%
+consistent uh notion anyway uh and this
+ 
+
+ align:start position:0%
+consistent uh notion anyway uh and this
+is actually our reduction all in one
+
+ align:start position:0%
+is actually our reduction all in one
+ 
+
+ align:start position:0%
+is actually our reduction all in one
+slide um it's pretty simple so this is
+
+ align:start position:0%
+slide um it's pretty simple so this is
+ 
+
+ align:start position:0%
+slide um it's pretty simple so this is
+what we call the mate in one problem and
+
+ align:start position:0%
+what we call the mate in one problem and
+ 
+
+ align:start position:0%
+what we call the mate in one problem and
+you can take lots of different games and
+
+ align:start position:0%
+you can take lots of different games and
+ 
+
+ align:start position:0%
+you can take lots of different games and
+make them really clean well-defined
+
+ align:start position:0%
+make them really clean well-defined
+ 
+
+ align:start position:0%
+make them really clean well-defined
+puzzles if you just ask can I win in one
+
+ align:start position:0%
+puzzles if you just ask can I win in one
+ 
+
+ align:start position:0%
+puzzles if you just ask can I win in one
+move even games that involve cards and
+
+ align:start position:0%
+move even games that involve cards and
+ 
+
+ align:start position:0%
+move even games that involve cards and
+Randomness and weird stuff uh in one
+
+ align:start position:0%
+Randomness and weird stuff uh in one
+ 
+
+ align:start position:0%
+Randomness and weird stuff uh in one
+move usually doesn't involve those at
+
+ align:start position:0%
+move usually doesn't involve those at
+ 
+
+ align:start position:0%
+move usually doesn't involve those at
+all anyway here we're getting rid of uh
+
+ align:start position:0%
+all anyway here we're getting rid of uh
+ 
+
+ align:start position:0%
+all anyway here we're getting rid of uh
+the loopiness of the game and not having
+
+ align:start position:0%
+the loopiness of the game and not having
+ 
+
+ align:start position:0%
+the loopiness of the game and not having
+to worry about that so um there's sort
+
+ align:start position:0%
+to worry about that so um there's sort
+ 
+
+ align:start position:0%
+to worry about that so um there's sort
+of two parts to this proof the variable
+
+ align:start position:0%
+of two parts to this proof the variable
+ 
+
+ align:start position:0%
+of two parts to this proof the variable
+traversal and the Clause traversal but
+
+ align:start position:0%
+traversal and the Clause traversal but
+ 
+
+ align:start position:0%
+traversal and the Clause traversal but
+here we have a kind of very different
+
+ align:start position:0%
+here we have a kind of very different
+ 
+
+ align:start position:0%
+here we have a kind of very different
+way of connecting things together we
+
+ align:start position:0%
+way of connecting things together we
+ 
+
+ align:start position:0%
+way of connecting things together we
+have a giant Matrix if you will um we're
+
+ align:start position:0%
+have a giant Matrix if you will um we're
+ 
+
+ align:start position:0%
+have a giant Matrix if you will um we're
+starting up here and we have a choice
+
+ align:start position:0%
+starting up here and we have a choice
+ 
+
+ align:start position:0%
+starting up here and we have a choice
+whether we if we want to set X1 to true
+
+ align:start position:0%
+whether we if we want to set X1 to true
+ 
+
+ align:start position:0%
+whether we if we want to set X1 to true
+we're just going to go to the right uh
+
+ align:start position:0%
+we're just going to go to the right uh
+ 
+
+ align:start position:0%
+we're just going to go to the right uh
+by sequence of jumps we jump here then
+
+ align:start position:0%
+by sequence of jumps we jump here then
+ 
+
+ align:start position:0%
+by sequence of jumps we jump here then
+here then here every time we stop we
+
+ align:start position:0%
+here then here every time we stop we
+ 
+
+ align:start position:0%
+here then here every time we stop we
+have no choice if we want to keep going
+
+ align:start position:0%
+have no choice if we want to keep going
+ 
+
+ align:start position:0%
+have no choice if we want to keep going
+our goal is to get to
+
+ align:start position:0%
+our goal is to get to
+ 
+
+ align:start position:0%
+our goal is to get to
+somewhere one of the edges of the board
+
+ align:start position:0%
+somewhere one of the edges of the board
+ 
+
+ align:start position:0%
+somewhere one of the edges of the board
+I think the bottom Edge yeah bottom Edge
+
+ align:start position:0%
+I think the bottom Edge yeah bottom Edge
+ 
+
+ align:start position:0%
+I think the bottom Edge yeah bottom Edge
+is the one that's hard to get
+
+ align:start position:0%
+is the one that's hard to get
+ 
+
+ align:start position:0%
+is the one that's hard to get
+to uh so every time we jump to the right
+
+ align:start position:0%
+to uh so every time we jump to the right
+ 
+
+ align:start position:0%
+to uh so every time we jump to the right
+here we don't have a choice we have to
+
+ align:start position:0%
+here we don't have a choice we have to
+ 
+
+ align:start position:0%
+here we don't have a choice we have to
+keep jumping to the right uh but over
+
+ align:start position:0%
+keep jumping to the right uh but over
+ 
+
+ align:start position:0%
+keep jumping to the right uh but over
+here we have a choice we could go down
+
+ align:start position:0%
+here we have a choice we could go down
+ 
+
+ align:start position:0%
+here we have a choice we could go down
+and then jump to the right and get over
+
+ align:start position:0%
+and then jump to the right and get over
+ 
+
+ align:start position:0%
+and then jump to the right and get over
+here and that will do different things
+
+ align:start position:0%
+here and that will do different things
+ 
+
+ align:start position:0%
+here and that will do different things
+in the middle in general that is our
+
+ align:start position:0%
+in the middle in general that is our
+ 
+
+ align:start position:0%
+in the middle in general that is our
+setting of X1 then we're going to do the
+
+ align:start position:0%
+setting of X1 then we're going to do the
+ 
+
+ align:start position:0%
+setting of X1 then we're going to do the
+same thing coming back for X2 of two
+
+ align:start position:0%
+same thing coming back for X2 of two
+ 
+
+ align:start position:0%
+same thing coming back for X2 of two
+choices then the same thing going back
+
+ align:start position:0%
+choices then the same thing going back
+ 
+
+ align:start position:0%
+choices then the same thing going back
+for X3 uh and then we get to this corner
+
+ align:start position:0%
+for X3 uh and then we get to this corner
+ 
+
+ align:start position:0%
+for X3 uh and then we get to this corner
+so that's forced other than these
+
+ align:start position:0%
+so that's forced other than these
+ 
+
+ align:start position:0%
+so that's forced other than these
+choices binary
+
+ align:start position:0%
+choices binary
+ 
+
+ align:start position:0%
+choices binary
+choices uh now uh we have our first
+
+ align:start position:0%
+choices uh now uh we have our first
+ 
+
+ align:start position:0%
+choices uh now uh we have our first
+Clause let's say X1 negated or X2
+
+ align:start position:0%
+Clause let's say X1 negated or X2
+ 
+
+ align:start position:0%
+Clause let's say X1 negated or X2
+negated or X3 negated we want one of
+
+ align:start position:0%
+negated or X3 negated we want one of
+ 
+
+ align:start position:0%
+negated or X3 negated we want one of
+those things to be true and uh so the
+
+ align:start position:0%
+those things to be true and uh so the
+ 
+
+ align:start position:0%
+those things to be true and uh so the
+idea is we're going to choose whichever
+
+ align:start position:0%
+idea is we're going to choose whichever
+ 
+
+ align:start position:0%
+idea is we're going to choose whichever
+one uh has been set correctly and then
+
+ align:start position:0%
+one uh has been set correctly and then
+ 
+
+ align:start position:0%
+one uh has been set correctly and then
+we will go up that channel and get to
+
+ align:start position:0%
+we will go up that channel and get to
+ 
+
+ align:start position:0%
+we will go up that channel and get to
+the top again it's pretty much symmetric
+
+ align:start position:0%
+the top again it's pretty much symmetric
+ 
+
+ align:start position:0%
+the top again it's pretty much symmetric
+so every time we jump over a bunch of
+
+ align:start position:0%
+so every time we jump over a bunch of
+ 
+
+ align:start position:0%
+so every time we jump over a bunch of
+pieces whenever we stop we can't go left
+
+ align:start position:0%
+pieces whenever we stop we can't go left
+ 
+
+ align:start position:0%
+pieces whenever we stop we can't go left
+or right we have to keep going up so we
+
+ align:start position:0%
+or right we have to keep going up so we
+ 
+
+ align:start position:0%
+or right we have to keep going up so we
+have to make it all the
+
+ align:start position:0%
+have to make it all the
+ 
+
+ align:start position:0%
+have to make it all the
+way in fact uh each of these columns
+
+ align:start position:0%
+way in fact uh each of these columns
+ 
+
+ align:start position:0%
+way in fact uh each of these columns
+will be completely filled except for one
+
+ align:start position:0%
+will be completely filled except for one
+ 
+
+ align:start position:0%
+will be completely filled except for one
+intersection which is the thing that
+
+ align:start position:0%
+intersection which is the thing that
+ 
+
+ align:start position:0%
+intersection which is the thing that
+makes it false so here we want X2 to be
+
+ align:start position:0%
+makes it false so here we want X2 to be
+ 
+
+ align:start position:0%
+makes it false so here we want X2 to be
+false so if we happen to follow the true
+
+ align:start position:0%
+false so if we happen to follow the true
+ 
+
+ align:start position:0%
+false so if we happen to follow the true
+path where X2 is true we won't make it
+
+ align:start position:0%
+path where X2 is true we won't make it
+ 
+
+ align:start position:0%
+path where X2 is true we won't make it
+because this uh piece will already have
+
+ align:start position:0%
+because this uh piece will already have
+ 
+
+ align:start position:0%
+because this uh piece will already have
+been removed when we came through here
+
+ align:start position:0%
+been removed when we came through here
+ 
+
+ align:start position:0%
+been removed when we came through here
+and so if we try to take this path we'll
+
+ align:start position:0%
+and so if we try to take this path we'll
+ 
+
+ align:start position:0%
+and so if we try to take this path we'll
+get stuck here there won't be any piece
+
+ align:start position:0%
+get stuck here there won't be any piece
+ 
+
+ align:start position:0%
+get stuck here there won't be any piece
+above us okay as long as that didn't
+
+ align:start position:0%
+above us okay as long as that didn't
+ 
+
+ align:start position:0%
+above us okay as long as that didn't
+happen as long as this this row was not
+
+ align:start position:0%
+happen as long as this this row was not
+ 
+
+ align:start position:0%
+happen as long as this this row was not
+chosen then we can take this column and
+
+ align:start position:0%
+chosen then we can take this column and
+ 
+
+ align:start position:0%
+chosen then we can take this column and
+just make it all the way up to the top
+
+ align:start position:0%
+just make it all the way up to the top
+ 
+
+ align:start position:0%
+just make it all the way up to the top
+so we're going to be able to take one of
+
+ align:start position:0%
+so we're going to be able to take one of
+ 
+
+ align:start position:0%
+so we're going to be able to take one of
+these three paths if and only if at
+
+ align:start position:0%
+these three paths if and only if at
+ 
+
+ align:start position:0%
+these three paths if and only if at
+least one of these things is true that's
+
+ align:start position:0%
+least one of these things is true that's
+ 
+
+ align:start position:0%
+least one of these things is true that's
+the first Clause uh then we do the same
+
+ align:start position:0%
+the first Clause uh then we do the same
+ 
+
+ align:start position:0%
+the first Clause uh then we do the same
+thing for the second clause and if all
+
+ align:start position:0%
+thing for the second clause and if all
+ 
+
+ align:start position:0%
+thing for the second clause and if all
+the Clauses are true we will be able to
+
+ align:start position:0%
+the Clauses are true we will be able to
+ 
+
+ align:start position:0%
+the Clauses are true we will be able to
+get here and then we can jump down and
+
+ align:start position:0%
+get here and then we can jump down and
+ 
+
+ align:start position:0%
+get here and then we can jump down and
+get to the Finish Line and win in one
+
+ align:start position:0%
+get to the Finish Line and win in one
+ 
+
+ align:start position:0%
+get to the Finish Line and win in one
+move one
+
+ align:start position:0%
+move one
+ 
+
+ align:start position:0%
+move one
+move okay so that's uh m one is MP
+
+ align:start position:0%
+move okay so that's uh m one is MP
+ 
+
+ align:start position:0%
+move okay so that's uh m one is MP
+complete uh I have one other example of
+
+ align:start position:0%
+complete uh I have one other example of
+ 
+
+ align:start position:0%
+complete uh I have one other example of
+a mate one result it's actually not a
+
+ align:start position:0%
+a mate one result it's actually not a
+ 
+
+ align:start position:0%
+a mate one result it's actually not a
+hardness result but it's kind of fun so
+
+ align:start position:0%
+hardness result but it's kind of fun so
+ 
+
+ align:start position:0%
+hardness result but it's kind of fun so
+I thought I would talk about a non
+
+ align:start position:0%
+I thought I would talk about a non
+ 
+
+ align:start position:0%
+I thought I would talk about a non
+hardness result for once which is
+
+ align:start position:0%
+hardness result for once which is
+ 
+
+ align:start position:0%
+hardness result for once which is
+Checkers Checkers is another game where
+
+ align:start position:0%
+Checkers Checkers is another game where
+ 
+
+ align:start position:0%
+Checkers Checkers is another game where
+in one move you can do a lot of jumps
+
+ align:start position:0%
+in one move you can do a lot of jumps
+ 
+
+ align:start position:0%
+in one move you can do a lot of jumps
+especially if you have a king uh then
+
+ align:start position:0%
+especially if you have a king uh then
+ 
+
+ align:start position:0%
+especially if you have a king uh then
+you can potentially win and by killing a
+
+ align:start position:0%
+you can potentially win and by killing a
+ 
+
+ align:start position:0%
+you can potentially win and by killing a
+lot of pieces all at once and this is
+
+ align:start position:0%
+lot of pieces all at once and this is
+ 
+
+ align:start position:0%
+lot of pieces all at once and this is
+considered back in 1978 this is the same
+
+ align:start position:0%
+considered back in 1978 this is the same
+ 
+
+ align:start position:0%
+considered back in 1978 this is the same
+paper that proves Checkers is X time
+
+ align:start position:0%
+paper that proves Checkers is X time
+ 
+
+ align:start position:0%
+paper that proves Checkers is X time
+complete which we will get to at some
+
+ align:start position:0%
+complete which we will get to at some
+ 
+
+ align:start position:0%
+complete which we will get to at some
+point uh but for now let's think about
+
+ align:start position:0%
+point uh but for now let's think about
+ 
+
+ align:start position:0%
+point uh but for now let's think about
+the main one problem this turns out to
+
+ align:start position:0%
+the main one problem this turns out to
+ 
+
+ align:start position:0%
+the main one problem this turns out to
+be easy unlike
+
+ align:start position:0%
+be easy unlike
+ 
+
+ align:start position:0%
+be easy unlike
+football so uh Checkers I assume you've
+
+ align:start position:0%
+football so uh Checkers I assume you've
+ 
+
+ align:start position:0%
+football so uh Checkers I assume you've
+all played Checkers you can only move
+
+ align:start position:0%
+all played Checkers you can only move
+ 
+
+ align:start position:0%
+all played Checkers you can only move
+diagonally on the black squares um so
+
+ align:start position:0%
+diagonally on the black squares um so
+ 
+
+ align:start position:0%
+diagonally on the black squares um so
+you can recast that into an orthogonal
+
+ align:start position:0%
+you can recast that into an orthogonal
+ 
+
+ align:start position:0%
+you can recast that into an orthogonal
+problem where the pieces can only move
+
+ align:start position:0%
+problem where the pieces can only move
+ 
+
+ align:start position:0%
+problem where the pieces can only move
+orthogonally up uh or or right or vice
+
+ align:start position:0%
+orthogonally up uh or or right or vice
+ 
+
+ align:start position:0%
+orthogonally up uh or or right or vice
+versa except King pieces they can just
+
+ align:start position:0%
+versa except King pieces they can just
+ 
+
+ align:start position:0%
+versa except King pieces they can just
+move orthogonally and the interesting
+
+ align:start position:0%
+move orthogonally and the interesting
+ 
+
+ align:start position:0%
+move orthogonally and the interesting
+part is when you can jump over a piece
+
+ align:start position:0%
+part is when you can jump over a piece
+ 
+
+ align:start position:0%
+part is when you can jump over a piece
+of another color so if there was a black
+
+ align:start position:0%
+of another color so if there was a black
+ 
+
+ align:start position:0%
+of another color so if there was a black
+piece here this one can jump over um and
+
+ align:start position:0%
+piece here this one can jump over um and
+ 
+
+ align:start position:0%
+piece here this one can jump over um and
+in general if you have a sequence of
+
+ align:start position:0%
+in general if you have a sequence of
+ 
+
+ align:start position:0%
+in general if you have a sequence of
+jumps you can make then you can do all
+
+ align:start position:0%
+jumps you can make then you can do all
+ 
+
+ align:start position:0%
+jumps you can make then you can do all
+of them at once so the problem looks
+
+ align:start position:0%
+of them at once so the problem looks
+ 
+
+ align:start position:0%
+of them at once so the problem looks
+something like this if you have a black
+
+ align:start position:0%
+something like this if you have a black
+ 
+
+ align:start position:0%
+something like this if you have a black
+piece and let's say black to move uh if
+
+ align:start position:0%
+piece and let's say black to move uh if
+ 
+
+ align:start position:0%
+piece and let's say black to move uh if
+there are a bunch of white pieces you
+
+ align:start position:0%
+there are a bunch of white pieces you
+ 
+
+ align:start position:0%
+there are a bunch of white pieces you
+can jump over them um and the key thing
+
+ align:start position:0%
+can jump over them um and the key thing
+ 
+
+ align:start position:0%
+can jump over them um and the key thing
+to notice again as soon as you jump over
+
+ align:start position:0%
+to notice again as soon as you jump over
+ 
+
+ align:start position:0%
+to notice again as soon as you jump over
+a piece it disappears so you can't reuse
+
+ align:start position:0%
+a piece it disappears so you can't reuse
+ 
+
+ align:start position:0%
+a piece it disappears so you can't reuse
+it in the same move or I guess you can't
+
+ align:start position:0%
+it in the same move or I guess you can't
+ 
+
+ align:start position:0%
+it in the same move or I guess you can't
+reuse it in general um the key thing is
+
+ align:start position:0%
+reuse it in general um the key thing is
+ 
+
+ align:start position:0%
+reuse it in general um the key thing is
+that the jumps preserve the parity the
+
+ align:start position:0%
+that the jumps preserve the parity the
+ 
+
+ align:start position:0%
+that the jumps preserve the parity the
+even or oddness of of both your x
+
+ align:start position:0%
+even or oddness of of both your x
+ 
+
+ align:start position:0%
+even or oddness of of both your x
+coordinate and your y-coordinate so
+
+ align:start position:0%
+coordinate and your y-coordinate so
+ 
+
+ align:start position:0%
+coordinate and your y-coordinate so
+you're moving around on this reduced
+
+ align:start position:0%
+you're moving around on this reduced
+ 
+
+ align:start position:0%
+you're moving around on this reduced
+grid and so you can take a picture like
+
+ align:start position:0%
+grid and so you can take a picture like
+ 
+
+ align:start position:0%
+grid and so you can take a picture like
+this and turn it into a graph where the
+
+ align:start position:0%
+this and turn it into a graph where the
+ 
+
+ align:start position:0%
+this and turn it into a graph where the
+potential positions for you uh which are
+
+ align:start position:0%
+potential positions for you uh which are
+ 
+
+ align:start position:0%
+potential positions for you uh which are
+drawn with this kind of pattern even
+
+ align:start position:0%
+drawn with this kind of pattern even
+ 
+
+ align:start position:0%
+drawn with this kind of pattern even
+same uh par of of uh rows and columns uh
+
+ align:start position:0%
+same uh par of of uh rows and columns uh
+ 
+
+ align:start position:0%
+same uh par of of uh rows and columns uh
+you can make those the vertices of your
+
+ align:start position:0%
+you can make those the vertices of your
+ 
+
+ align:start position:0%
+you can make those the vertices of your
+graph and then there's an edge between
+
+ align:start position:0%
+graph and then there's an edge between
+ 
+
+ align:start position:0%
+graph and then there's an edge between
+them if there's a white uh Stone in
+
+ align:start position:0%
+them if there's a white uh Stone in
+ 
+
+ align:start position:0%
+them if there's a white uh Stone in
+between that you could jump
+
+ align:start position:0%
+between that you could jump
+ 
+
+ align:start position:0%
+between that you could jump
+over so then given this graph the
+
+ align:start position:0%
+over so then given this graph the
+ 
+
+ align:start position:0%
+over so then given this graph the
+question is can you visit all of the
+
+ align:start position:0%
+question is can you visit all of the
+ 
+
+ align:start position:0%
+question is can you visit all of the
+edges of the graph with a single path
+
+ align:start position:0%
+edges of the graph with a single path
+ 
+
+ align:start position:0%
+edges of the graph with a single path
+and that is the oiler tour problem or
+
+ align:start position:0%
+and that is the oiler tour problem or
+ 
+
+ align:start position:0%
+and that is the oiler tour problem or
+the oiler path problem and it's easy to
+
+ align:start position:0%
+the oiler path problem and it's easy to
+ 
+
+ align:start position:0%
+the oiler path problem and it's easy to
+solve that in polinomial time you look
+
+ align:start position:0%
+solve that in polinomial time you look
+ 
+
+ align:start position:0%
+solve that in polinomial time you look
+for odd degree vertices there should be
+
+ align:start position:0%
+for odd degree vertices there should be
+ 
+
+ align:start position:0%
+for odd degree vertices there should be
+at most two of them and you better be at
+
+ align:start position:0%
+at most two of them and you better be at
+ 
+
+ align:start position:0%
+at most two of them and you better be at
+one of
+
+ align:start position:0%
+one of
+ 
+
+ align:start position:0%
+one of
+them uh or there's zero of them then
+
+ align:start position:0%
+them uh or there's zero of them then
+ 
+
+ align:start position:0%
+them uh or there's zero of them then
+you're happy so that's how to solve mate
+
+ align:start position:0%
+you're happy so that's how to solve mate
+ 
+
+ align:start position:0%
+you're happy so that's how to solve mate
+and one and Checkers in case you ever
+
+ align:start position:0%
+and one and Checkers in case you ever
+ 
+
+ align:start position:0%
+and one and Checkers in case you ever
+get to those difficult Checkers end
+
+ align:start position:0%
+get to those difficult Checkers end
+ 
+
+ align:start position:0%
+get to those difficult Checkers end
+games then now you can decide how to win
+
+ align:start position:0%
+games then now you can decide how to win
+ 
+
+ align:start position:0%
+games then now you can decide how to win
+or not in one move two moves is left to
+
+ align:start position:0%
+or not in one move two moves is left to
+ 
+
+ align:start position:0%
+or not in one move two moves is left to
+you all right um so next topic is uh
+
+ align:start position:0%
+you all right um so next topic is uh
+ 
+
+ align:start position:0%
+you all right um so next topic is uh
+called Crypt rhythms this is comes from
+
+ align:start position:0%
+called Crypt rhythms this is comes from
+ 
+
+ align:start position:0%
+called Crypt rhythms this is comes from
+the recreational math world and they're
+
+ align:start position:0%
+the recreational math world and they're
+ 
+
+ align:start position:0%
+the recreational math world and they're
+kind of fun you've probably seen this
+
+ align:start position:0%
+kind of fun you've probably seen this
+ 
+
+ align:start position:0%
+kind of fun you've probably seen this
+you may have seen this one if you've
+
+ align:start position:0%
+you may have seen this one if you've
+ 
+
+ align:start position:0%
+you may have seen this one if you've
+seen any Crypt Rhythm uh it's a classic
+
+ align:start position:0%
+seen any Crypt Rhythm uh it's a classic
+ 
+
+ align:start position:0%
+seen any Crypt Rhythm uh it's a classic
+goes back to 1979 from this book by
+
+ align:start position:0%
+goes back to 1979 from this book by
+ 
+
+ align:start position:0%
+goes back to 1979 from this book by
+madaki
+
+ align:start position:0%
+madaki
+ 
+
+ align:start position:0%
+madaki
+uh and the idea is this is an arithmetic
+
+ align:start position:0%
+uh and the idea is this is an arithmetic
+ 
+
+ align:start position:0%
+uh and the idea is this is an arithmetic
+formula Send Plus more equals money and
+
+ align:start position:0%
+formula Send Plus more equals money and
+ 
+
+ align:start position:0%
+formula Send Plus more equals money and
+each of these letters represents a digit
+
+ align:start position:0%
+each of these letters represents a digit
+ 
+
+ align:start position:0%
+each of these letters represents a digit
+0 through N9 and so the two M's
+
+ align:start position:0%
+0 through N9 and so the two M's
+ 
+
+ align:start position:0%
+0 through N9 and so the two M's
+represent the same digit and so on the
+
+ align:start position:0%
+represent the same digit and so on the
+ 
+
+ align:start position:0%
+represent the same digit and so on the
+two n's represent the same digit the two
+
+ align:start position:0%
+two n's represent the same digit the two
+ 
+
+ align:start position:0%
+two n's represent the same digit the two
+o's represent the same digit and
+
+ align:start position:0%
+o's represent the same digit and
+ 
+
+ align:start position:0%
+o's represent the same digit and
+furthermore m is different from o is
+
+ align:start position:0%
+furthermore m is different from o is
+ 
+
+ align:start position:0%
+furthermore m is different from o is
+different from R so it's it's a bje
+
+ align:start position:0%
+different from R so it's it's a bje
+ 
+
+ align:start position:0%
+different from R so it's it's a bje
+between the letters that appear in this
+
+ align:start position:0%
+between the letters that appear in this
+ 
+
+ align:start position:0%
+between the letters that appear in this
+puzzle and some subset of 0 through 9
+
+ align:start position:0%
+puzzle and some subset of 0 through 9
+ 
+
+ align:start position:0%
+puzzle and some subset of 0 through 9
+and actually has a unique solution uh
+
+ align:start position:0%
+and actually has a unique solution uh
+ 
+
+ align:start position:0%
+and actually has a unique solution uh
+this is it you could verify it but I'll
+
+ align:start position:0%
+this is it you could verify it but I'll
+ 
+
+ align:start position:0%
+this is it you could verify it but I'll
+leave it as a puzzle so don't look at
+
+ align:start position:0%
+leave it as a puzzle so don't look at
+ 
+
+ align:start position:0%
+leave it as a puzzle so don't look at
+that too long in case you want to solve
+
+ align:start position:0%
+that too long in case you want to solve
+ 
+
+ align:start position:0%
+that too long in case you want to solve
+it um it is doable but you know the
+
+ align:start position:0%
+it um it is doable but you know the
+ 
+
+ align:start position:0%
+it um it is doable but you know the
+tricky part of things like the carries
+
+ align:start position:0%
+tricky part of things like the carries
+ 
+
+ align:start position:0%
+tricky part of things like the carries
+in the addition which make it not just a
+
+ align:start position:0%
+in the addition which make it not just a
+ 
+
+ align:start position:0%
+in the addition which make it not just a
+a simple linear system to solve and in
+
+ align:start position:0%
+a simple linear system to solve and in
+ 
+
+ align:start position:0%
+a simple linear system to solve and in
+fact these puzzles uh generalize to an
+
+ align:start position:0%
+fact these puzzles uh generalize to an
+ 
+
+ align:start position:0%
+fact these puzzles uh generalize to an
+arbitrary base are and be complete if
+
+ align:start position:0%
+arbitrary base are and be complete if
+ 
+
+ align:start position:0%
+arbitrary base are and be complete if
+you do it in uh base 10 then there's
+
+ align:start position:0%
+you do it in uh base 10 then there's
+ 
+
+ align:start position:0%
+you do it in uh base 10 then there's
+only at most 10 factorial possible
+
+ align:start position:0%
+only at most 10 factorial possible
+ 
+
+ align:start position:0%
+only at most 10 factorial possible
+solutions so that's constant and that's
+
+ align:start position:0%
+solutions so that's constant and that's
+ 
+
+ align:start position:0%
+solutions so that's constant and that's
+considered fast and indeed in real
+
+ align:start position:0%
+considered fast and indeed in real
+ 
+
+ align:start position:0%
+considered fast and indeed in real
+computers you can solve 10 factorial
+
+ align:start position:0%
+computers you can solve 10 factorial
+ 
+
+ align:start position:0%
+computers you can solve 10 factorial
+reasonably um so uh for generalized base
+
+ align:start position:0%
+reasonably um so uh for generalized base
+ 
+
+ align:start position:0%
+reasonably um so uh for generalized base
+here is a proof this is actually David
+
+ align:start position:0%
+here is a proof this is actually David
+ 
+
+ align:start position:0%
+here is a proof this is actually David
+Epstein who was a co-author in the
+
+ align:start position:0%
+Epstein who was a co-author in the
+ 
+
+ align:start position:0%
+Epstein who was a co-author in the
+previous result this is his first Theory
+
+ align:start position:0%
+previous result this is his first Theory
+ 
+
+ align:start position:0%
+previous result this is his first Theory
+paper on cak
+
+ align:start position:0%
+paper on cak
+ 
+
+ align:start position:0%
+paper on cak
+news and uh proved that it's strongly NP
+
+ align:start position:0%
+news and uh proved that it's strongly NP
+ 
+
+ align:start position:0%
+news and uh proved that it's strongly NP
+complete meaning even if the base is
+
+ align:start position:0%
+complete meaning even if the base is
+ 
+
+ align:start position:0%
+complete meaning even if the base is
+polinomial the problem is NP hard and it
+
+ align:start position:0%
+polinomial the problem is NP hard and it
+ 
+
+ align:start position:0%
+polinomial the problem is NP hard and it
+looks really
+
+ align:start position:0%
+looks really
+ 
+
+ align:start position:0%
+looks really
+messy uh but actually it's fairly simple
+
+ align:start position:0%
+messy uh but actually it's fairly simple
+ 
+
+ align:start position:0%
+messy uh but actually it's fairly simple
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+um let me start with this gadget this is
+
+ align:start position:0%
+um let me start with this gadget this is
+ 
+
+ align:start position:0%
+um let me start with this gadget this is
+an easy one uh so there's no notion of
+
+ align:start position:0%
+an easy one uh so there's no notion of
+ 
+
+ align:start position:0%
+an easy one uh so there's no notion of
+zero or one in this gadget but uh zero
+
+ align:start position:0%
+zero or one in this gadget but uh zero
+ 
+
+ align:start position:0%
+zero or one in this gadget but uh zero
+is just a letter and one is just a
+
+ align:start position:0%
+is just a letter and one is just a
+ 
+
+ align:start position:0%
+is just a letter and one is just a
+letter but at with this gadget in place
+
+ align:start position:0%
+letter but at with this gadget in place
+ 
+
+ align:start position:0%
+letter but at with this gadget in place
+Z is zero and one is one because zero is
+
+ align:start position:0%
+Z is zero and one is one because zero is
+ 
+
+ align:start position:0%
+Z is zero and one is one because zero is
+the only possible digit when you add it
+
+ align:start position:0%
+the only possible digit when you add it
+ 
+
+ align:start position:0%
+the only possible digit when you add it
+with yourself you get it again okay it
+
+ align:start position:0%
+with yourself you get it again okay it
+ 
+
+ align:start position:0%
+with yourself you get it again okay it
+is the identity in in additive ring so
+
+ align:start position:0%
+is the identity in in additive ring so
+ 
+
+ align:start position:0%
+is the identity in in additive ring so
+that force is Zer to be zero and and
+
+ align:start position:0%
+that force is Zer to be zero and and
+ 
+
+ align:start position:0%
+that force is Zer to be zero and and
+then here um we're adding p with p p are
+
+ align:start position:0%
+then here um we're adding p with p p are
+ 
+
+ align:start position:0%
+then here um we're adding p with p p are
+just arbitrary things sort of don't care
+
+ align:start position:0%
+just arbitrary things sort of don't care
+ 
+
+ align:start position:0%
+just arbitrary things sort of don't care
+what they are we get something q and
+
+ align:start position:0%
+what they are we get something q and
+ 
+
+ align:start position:0%
+what they are we get something q and
+over here we add Z to zero and we get
+
+ align:start position:0%
+over here we add Z to zero and we get
+ 
+
+ align:start position:0%
+over here we add Z to zero and we get
+one that's only going to be possible if
+
+ align:start position:0%
+one that's only going to be possible if
+ 
+
+ align:start position:0%
+one that's only going to be possible if
+there's a carry in this column and
+
+ align:start position:0%
+there's a carry in this column and
+ 
+
+ align:start position:0%
+there's a carry in this column and
+Carries can be only one they can be zero
+
+ align:start position:0%
+Carries can be only one they can be zero
+ 
+
+ align:start position:0%
+Carries can be only one they can be zero
+or one so that forces we know it's not
+
+ align:start position:0%
+or one so that forces we know it's not
+ 
+
+ align:start position:0%
+or one so that forces we know it's not
+zero because one is different from zero
+
+ align:start position:0%
+zero because one is different from zero
+ 
+
+ align:start position:0%
+zero because one is different from zero
+therefore one is one okay symbol one is
+
+ align:start position:0%
+therefore one is one okay symbol one is
+ 
+
+ align:start position:0%
+therefore one is one okay symbol one is
+the value one the number one all right
+
+ align:start position:0%
+the value one the number one all right
+ 
+
+ align:start position:0%
+the value one the number one all right
+so that gives us some infrastructure and
+
+ align:start position:0%
+so that gives us some infrastructure and
+ 
+
+ align:start position:0%
+so that gives us some infrastructure and
+the zeros are really helpful CU it lets
+
+ align:start position:0%
+the zeros are really helpful CU it lets
+ 
+
+ align:start position:0%
+the zeros are really helpful CU it lets
+us space out gadgets and guarantee that
+
+ align:start position:0%
+us space out gadgets and guarantee that
+ 
+
+ align:start position:0%
+us space out gadgets and guarantee that
+there's no carry between them this is
+
+ align:start position:0%
+there's no carry between them this is
+ 
+
+ align:start position:0%
+there's no carry between them this is
+supposed to be a variable Gadget there's
+
+ align:start position:0%
+supposed to be a variable Gadget there's
+ 
+
+ align:start position:0%
+supposed to be a variable Gadget there's
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+VI and there's VI bar so let's see what
+
+ align:start position:0%
+VI and there's VI bar so let's see what
+ 
+
+ align:start position:0%
+VI and there's VI bar so let's see what
+what happens let's do the VI Part first
+
+ align:start position:0%
+what happens let's do the VI Part first
+ 
+
+ align:start position:0%
+what happens let's do the VI Part first
+so this this formula says that bi equals
+
+ align:start position:0%
+so this this formula says that bi equals
+ 
+
+ align:start position:0%
+so this this formula says that bi equals
+twice Ai and there's guaranteed to be no
+
+ align:start position:0%
+twice Ai and there's guaranteed to be no
+ 
+
+ align:start position:0%
+twice Ai and there's guaranteed to be no
+carry because of this this is a little
+
+ align:start position:0%
+carry because of this this is a little
+ 
+
+ align:start position:0%
+carry because of this this is a little
+tricky we add Yi to Yi we get zi so
+
+ align:start position:0%
+tricky we add Yi to Yi we get zi so
+ 
+
+ align:start position:0%
+tricky we add Yi to Yi we get zi so
+there may be a carry or not
+
+ align:start position:0%
+there may be a carry or not
+ 
+
+ align:start position:0%
+there may be a carry or not
+here then we add bi to bi and we get VI
+
+ align:start position:0%
+here then we add bi to bi and we get VI
+ 
+
+ align:start position:0%
+here then we add bi to bi and we get VI
+so VI is going to be 2 * bi Plus either
+
+ align:start position:0%
+so VI is going to be 2 * bi Plus either
+ 
+
+ align:start position:0%
+so VI is going to be 2 * bi Plus either
+zero or one that's going to be our
+
+ align:start position:0%
+zero or one that's going to be our
+ 
+
+ align:start position:0%
+zero or one that's going to be our
+binary choice we can set up the Yi to
+
+ align:start position:0%
+binary choice we can set up the Yi to
+ 
+
+ align:start position:0%
+binary choice we can set up the Yi to
+either carry or not we'll call that c c
+
+ align:start position:0%
+either carry or not we'll call that c c
+ 
+
+ align:start position:0%
+either carry or not we'll call that c c
+in this formulation C is the carry in
+
+ align:start position:0%
+in this formulation C is the carry in
+ 
+
+ align:start position:0%
+in this formulation C is the carry in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+operation
+
+ align:start position:0%
+operation
+ 
+
+ align:start position:0%
+operation
+uh okay and bi is 2 * AI so this is four
+
+ align:start position:0%
+uh okay and bi is 2 * AI so this is four
+ 
+
+ align:start position:0%
+uh okay and bi is 2 * AI so this is four
+time AI plus
+
+ align:start position:0%
+time AI plus
+ 
+
+ align:start position:0%
+time AI plus
+C which is01 and what we're going to
+
+ align:start position:0%
+C which is01 and what we're going to
+ 
+
+ align:start position:0%
+C which is01 and what we're going to
+think about is uh modulo 4 this is
+
+ align:start position:0%
+think about is uh modulo 4 this is
+ 
+
+ align:start position:0%
+think about is uh modulo 4 this is
+congruent to
+
+ align:start position:0%
+congruent to
+ 
+
+ align:start position:0%
+congruent to
+C so we're going to treat all of our
+
+ align:start position:0%
+C so we're going to treat all of our
+ 
+
+ align:start position:0%
+C so we're going to treat all of our
+variable assignments modu of 4 and
+
+ align:start position:0%
+variable assignments modu of 4 and
+ 
+
+ align:start position:0%
+variable assignments modu of 4 and
+they're always going to be Z or one the
+
+ align:start position:0%
+they're always going to be Z or one the
+ 
+
+ align:start position:0%
+they're always going to be Z or one the
+claim is VI became this and the claim is
+
+ align:start position:0%
+claim is VI became this and the claim is
+ 
+
+ align:start position:0%
+claim is VI became this and the claim is
+that this part makes VI bar the
+
+ align:start position:0%
+that this part makes VI bar the
+ 
+
+ align:start position:0%
+that this part makes VI bar the
+opposite and you can work through the
+
+ align:start position:0%
+opposite and you can work through the
+ 
+
+ align:start position:0%
+opposite and you can work through the
+arithmetic uh as I did in the notes um
+
+ align:start position:0%
+arithmetic uh as I did in the notes um
+ 
+
+ align:start position:0%
+arithmetic uh as I did in the notes um
+you end up VI bar has to be um 4 *
+
+ align:start position:0%
+you end up VI bar has to be um 4 *
+ 
+
+ align:start position:0%
+you end up VI bar has to be um 4 *
+something which is CI so we don't sort
+
+ align:start position:0%
+something which is CI so we don't sort
+ 
+
+ align:start position:0%
+something which is CI so we don't sort
+of don't care what that is uh we'll set
+
+ align:start position:0%
+of don't care what that is uh we'll set
+ 
+
+ align:start position:0%
+of don't care what that is uh we'll set
+it at the very end uh plus 3 C + 1 if C
+
+ align:start position:0%
+it at the very end uh plus 3 C + 1 if C
+ 
+
+ align:start position:0%
+it at the very end uh plus 3 C + 1 if C
+is 1 this is four and this becomes zero
+
+ align:start position:0%
+is 1 this is four and this becomes zero
+ 
+
+ align:start position:0%
+is 1 this is four and this becomes zero
+uh if C is zero this becomes one mod 4
+
+ align:start position:0%
+uh if C is zero this becomes one mod 4
+ 
+
+ align:start position:0%
+uh if C is zero this becomes one mod 4
+so uh in general it's 1 minus C it's the
+
+ align:start position:0%
+so uh in general it's 1 minus C it's the
+ 
+
+ align:start position:0%
+so uh in general it's 1 minus C it's the
+opposite Choice from what VI was uh that
+
+ align:start position:0%
+opposite Choice from what VI was uh that
+ 
+
+ align:start position:0%
+opposite Choice from what VI was uh that
+becomes VI bar so that's cool we've got
+
+ align:start position:0%
+becomes VI bar so that's cool we've got
+ 
+
+ align:start position:0%
+becomes VI bar so that's cool we've got
+VI and we've got VI bar we can duplicate
+
+ align:start position:0%
+VI and we've got VI bar we can duplicate
+ 
+
+ align:start position:0%
+VI and we've got VI bar we can duplicate
+our variables for free because we can
+
+ align:start position:0%
+our variables for free because we can
+ 
+
+ align:start position:0%
+our variables for free because we can
+just use that same letter VI in many
+
+ align:start position:0%
+just use that same letter VI in many
+ 
+
+ align:start position:0%
+just use that same letter VI in many
+different places and then we just need a
+
+ align:start position:0%
+different places and then we just need a
+ 
+
+ align:start position:0%
+different places and then we just need a
+clause
+
+ align:start position:0%
+clause
+ 
+
+ align:start position:0%
+clause
+Gadget um
+
+ align:start position:0%
+Gadget um
+ 
+
+ align:start position:0%
+Gadget um
+and so uh the work is kind of similar
+
+ align:start position:0%
+and so uh the work is kind of similar
+ 
+
+ align:start position:0%
+and so uh the work is kind of similar
+similar kind of tricks we add VI fi to
+
+ align:start position:0%
+similar kind of tricks we add VI fi to
+ 
+
+ align:start position:0%
+similar kind of tricks we add VI fi to
+itself we get GI we add GI to itself we
+
+ align:start position:0%
+itself we get GI we add GI to itself we
+ 
+
+ align:start position:0%
+itself we get GI we add GI to itself we
+get hi so at this point we have four
+
+ align:start position:0%
+get hi so at this point we have four
+ 
+
+ align:start position:0%
+get hi so at this point we have four
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+fi uh plus possibly one carry this wi
+
+ align:start position:0%
+fi uh plus possibly one carry this wi
+ 
+
+ align:start position:0%
+fi uh plus possibly one carry this wi
+might carry or not so uh we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi is 4 *
+
+ align:start position:0%
+hi is 4 *
+ 
+
+ align:start position:0%
+hi is 4 *
+fi plus
+
+ align:start position:0%
+fi plus
+ 
+
+ align:start position:0%
+fi plus
+01 then we add hi to one and we get TI
+
+ align:start position:0%
+01 then we add hi to one and we get TI
+ 
+
+ align:start position:0%
+01 then we add hi to one and we get TI
+plus there might be a carry from this
+
+ align:start position:0%
+plus there might be a carry from this
+ 
+
+ align:start position:0%
+plus there might be a carry from this
+column so that's
+
+ align:start position:0%
+column so that's
+ 
+
+ align:start position:0%
+column so that's
+TI is going to be hi + 1 plus a
+
+ align:start position:0%
+TI is going to be hi + 1 plus a
+ 
+
+ align:start position:0%
+TI is going to be hi + 1 plus a
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+carry hi is this thing so we end up with
+
+ align:start position:0%
+carry hi is this thing so we end up with
+ 
+
+ align:start position:0%
+carry hi is this thing so we end up with
+4 *
+
+ align:start position:0%
+4 *
+ 
+
+ align:start position:0%
+4 *
+fi +
+
+ align:start position:0%
+fi +
+ 
+
+ align:start position:0%
+fi +
+1+ uh 0 or one or two depending on how
+
+ align:start position:0%
+1+ uh 0 or one or two depending on how
+ 
+
+ align:start position:0%
+1+ uh 0 or one or two depending on how
+many carries we've had total which is 4
+
+ align:start position:0%
+many carries we've had total which is 4
+ 
+
+ align:start position:0%
+many carries we've had total which is 4
+* fi plus one or 2 or
+
+ align:start position:0%
+* fi plus one or 2 or
+ 
+
+ align:start position:0%
+* fi plus one or 2 or
+three and modul of 4 that is one or two
+
+ align:start position:0%
+three and modul of 4 that is one or two
+ 
+
+ align:start position:0%
+three and modul of 4 that is one or two
+or three this is going to be the number
+
+ align:start position:0%
+or three this is going to be the number
+ 
+
+ align:start position:0%
+or three this is going to be the number
+of true variables in our Clause cuz in
+
+ align:start position:0%
+of true variables in our Clause cuz in
+ 
+
+ align:start position:0%
+of true variables in our Clause cuz in
+the end we just add VI plus VB we get
+
+ align:start position:0%
+the end we just add VI plus VB we get
+ 
+
+ align:start position:0%
+the end we just add VI plus VB we get
+this thing we add add VC for our three
+
+ align:start position:0%
+this thing we add add VC for our three
+ 
+
+ align:start position:0%
+this thing we add add VC for our three
+variables VA a b and c we get
+
+ align:start position:0%
+variables VA a b and c we get
+ 
+
+ align:start position:0%
+variables VA a b and c we get
+TI and TI was that
+
+ align:start position:0%
+TI and TI was that
+ 
+
+ align:start position:0%
+TI and TI was that
+thing so if we just think about things
+
+ align:start position:0%
+thing so if we just think about things
+ 
+
+ align:start position:0%
+thing so if we just think about things
+modul 4 that means V VA plus VB plus VC
+
+ align:start position:0%
+modul 4 that means V VA plus VB plus VC
+ 
+
+ align:start position:0%
+modul 4 that means V VA plus VB plus VC
+should be one two or three mod
+
+ align:start position:0%
+should be one two or three mod
+ 
+
+ align:start position:0%
+should be one two or three mod
+four okay now the reason we have this
+
+ align:start position:0%
+four okay now the reason we have this
+ 
+
+ align:start position:0%
+four okay now the reason we have this
+junk and the
+
+ align:start position:0%
+junk and the
+ 
+
+ align:start position:0%
+junk and the
+junks uh well okay there's there's the
+
+ align:start position:0%
+junks uh well okay there's there's the
+ 
+
+ align:start position:0%
+junks uh well okay there's there's the
+not modulo 4 part the part when you
+
+ align:start position:0%
+not modulo 4 part the part when you
+ 
+
+ align:start position:0%
+not modulo 4 part the part when you
+divide by four that's sort of tricky uh
+
+ align:start position:0%
+divide by four that's sort of tricky uh
+ 
+
+ align:start position:0%
+divide by four that's sort of tricky uh
+but at this point at least you should be
+
+ align:start position:0%
+but at this point at least you should be
+ 
+
+ align:start position:0%
+but at this point at least you should be
+convinced that um if there's a solution
+
+ align:start position:0%
+convinced that um if there's a solution
+ 
+
+ align:start position:0%
+convinced that um if there's a solution
+to this problem then there must be a
+
+ align:start position:0%
+to this problem then there must be a
+ 
+
+ align:start position:0%
+to this problem then there must be a
+solution to the original Three side
+
+ align:start position:0%
+solution to the original Three side
+ 
+
+ align:start position:0%
+solution to the original Three side
+instance the reverse is less clear if
+
+ align:start position:0%
+instance the reverse is less clear if
+ 
+
+ align:start position:0%
+instance the reverse is less clear if
+you have a solution to the three side
+
+ align:start position:0%
+you have a solution to the three side
+ 
+
+ align:start position:0%
+you have a solution to the three side
+instance you have to be able to set all
+
+ align:start position:0%
+instance you have to be able to set all
+ 
+
+ align:start position:0%
+instance you have to be able to set all
+these variables to make everything work
+
+ align:start position:0%
+these variables to make everything work
+ 
+
+ align:start position:0%
+these variables to make everything work
+out that's a little more tedious um for
+
+ align:start position:0%
+out that's a little more tedious um for
+ 
+
+ align:start position:0%
+out that's a little more tedious um for
+fun I mean this is an old proof 1987 uh
+
+ align:start position:0%
+fun I mean this is an old proof 1987 uh
+ 
+
+ align:start position:0%
+fun I mean this is an old proof 1987 uh
+and I was just looking at it uh again
+
+ align:start position:0%
+and I was just looking at it uh again
+ 
+
+ align:start position:0%
+and I was just looking at it uh again
+today I think and or I think this is
+
+ align:start position:0%
+today I think and or I think this is
+ 
+
+ align:start position:0%
+today I think and or I think this is
+yesterday I think I can simplify it a
+
+ align:start position:0%
+yesterday I think I can simplify it a
+ 
+
+ align:start position:0%
+yesterday I think I can simplify it a
+little bit instead of using regular
+
+ align:start position:0%
+little bit instead of using regular
+ 
+
+ align:start position:0%
+little bit instead of using regular
+three set where you have all these
+
+ align:start position:0%
+three set where you have all these
+ 
+
+ align:start position:0%
+three set where you have all these
+choices one two or three things are true
+
+ align:start position:0%
+choices one two or three things are true
+ 
+
+ align:start position:0%
+choices one two or three things are true
+if you use exactly one three set one and
+
+ align:start position:0%
+if you use exactly one three set one and
+ 
+
+ align:start position:0%
+if you use exactly one three set one and
+three Set uh it should be a lot easier
+
+ align:start position:0%
+three Set uh it should be a lot easier
+ 
+
+ align:start position:0%
+three Set uh it should be a lot easier
+so gadgets are smaller uh with one and
+
+ align:start position:0%
+so gadgets are smaller uh with one and
+ 
+
+ align:start position:0%
+so gadgets are smaller uh with one and
+three set we don't need negation so I
+
+ align:start position:0%
+three set we don't need negation so I
+ 
+
+ align:start position:0%
+three set we don't need negation so I
+just need the VI Part which we did
+
+ align:start position:0%
+just need the VI Part which we did
+ 
+
+ align:start position:0%
+just need the VI Part which we did
+explicitly over here so that's kind of
+
+ align:start position:0%
+explicitly over here so that's kind of
+ 
+
+ align:start position:0%
+explicitly over here so that's kind of
+nifty um and for exactly one threat we
+
+ align:start position:0%
+nifty um and for exactly one threat we
+ 
+
+ align:start position:0%
+nifty um and for exactly one threat we
+we don't need to have all those carries
+
+ align:start position:0%
+we don't need to have all those carries
+ 
+
+ align:start position:0%
+we don't need to have all those carries
+we just need to build four time
+
+ align:start position:0%
+we just need to build four time
+ 
+
+ align:start position:0%
+we just need to build four time
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+sorry that should be fi here uh we add
+
+ align:start position:0%
+sorry that should be fi here uh we add
+ 
+
+ align:start position:0%
+sorry that should be fi here uh we add
+fi to itself we add GI to itself so we
+
+ align:start position:0%
+fi to itself we add GI to itself so we
+ 
+
+ align:start position:0%
+fi to itself we add GI to itself so we
+here we have four * fi um and then we
+
+ align:start position:0%
+here we have four * fi um and then we
+ 
+
+ align:start position:0%
+here we have four * fi um and then we
+add one so this will be This Ti will be
+
+ align:start position:0%
+add one so this will be This Ti will be
+ 
+
+ align:start position:0%
+add one so this will be This Ti will be
+one mod 4 and then we add the variables
+
+ align:start position:0%
+one mod 4 and then we add the variables
+ 
+
+ align:start position:0%
+one mod 4 and then we add the variables
+up and we should get exactly one mod 4
+
+ align:start position:0%
+up and we should get exactly one mod 4
+ 
+
+ align:start position:0%
+up and we should get exactly one mod 4
+now admittedly I haven't checked the
+
+ align:start position:0%
+now admittedly I haven't checked the
+ 
+
+ align:start position:0%
+now admittedly I haven't checked the
+second half of the proof with this
+
+ align:start position:0%
+second half of the proof with this
+ 
+
+ align:start position:0%
+second half of the proof with this
+construction but seems plausible this
+
+ align:start position:0%
+construction but seems plausible this
+ 
+
+ align:start position:0%
+construction but seems plausible this
+would be a somewhat simpler proof so
+
+ align:start position:0%
+would be a somewhat simpler proof so
+ 
+
+ align:start position:0%
+would be a somewhat simpler proof so
+shows you the power of all the different
+
+ align:start position:0%
+shows you the power of all the different
+ 
+
+ align:start position:0%
+shows you the power of all the different
+versions of threat we saw last
+
+ align:start position:0%
+versions of threat we saw last
+ 
+
+ align:start position:0%
+versions of threat we saw last
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+um now I can tell you a little bit about
+
+ align:start position:0%
+um now I can tell you a little bit about
+ 
+
+ align:start position:0%
+um now I can tell you a little bit about
+the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+um I have some of the details written
+
+ align:start position:0%
+um I have some of the details written
+ 
+
+ align:start position:0%
+um I have some of the details written
+down here so the other direction is we
+
+ align:start position:0%
+down here so the other direction is we
+ 
+
+ align:start position:0%
+down here so the other direction is we
+need to check that if there's a
+
+ align:start position:0%
+need to check that if there's a
+ 
+
+ align:start position:0%
+need to check that if there's a
+satisfying assignment to threat or one
+
+ align:start position:0%
+satisfying assignment to threat or one
+ 
+
+ align:start position:0%
+satisfying assignment to threat or one
+and threat that we can actually
+
+ align:start position:0%
+and threat that we can actually
+ 
+
+ align:start position:0%
+and threat that we can actually
+construct these numbers uh that the base
+
+ align:start position:0%
+construct these numbers uh that the base
+ 
+
+ align:start position:0%
+construct these numbers uh that the base
+is only
+
+ align:start position:0%
+is only
+ 
+
+ align:start position:0%
+is only
+polinomial uh the trickiest part part is
+
+ align:start position:0%
+polinomial uh the trickiest part part is
+ 
+
+ align:start position:0%
+polinomial uh the trickiest part part is
+to get all of these numbers to be
+
+ align:start position:0%
+to get all of these numbers to be
+ 
+
+ align:start position:0%
+to get all of these numbers to be
+distinct from each
+
+ align:start position:0%
+distinct from each
+ 
+
+ align:start position:0%
+distinct from each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+um what Bas you the base will be
+
+ align:start position:0%
+um what Bas you the base will be
+ 
+
+ align:start position:0%
+um what Bas you the base will be
+something like n
+
+ align:start position:0%
+something like n
+ 
+
+ align:start position:0%
+something like n
+cubed it turns out and uh I'll tell you
+
+ align:start position:0%
+cubed it turns out and uh I'll tell you
+ 
+
+ align:start position:0%
+cubed it turns out and uh I'll tell you
+one trick is we have all these AI b i
+
+ align:start position:0%
+one trick is we have all these AI b i
+ 
+
+ align:start position:0%
+one trick is we have all these AI b i
+and CIS we can guarantee they are all
+
+ align:start position:0%
+and CIS we can guarantee they are all
+ 
+
+ align:start position:0%
+and CIS we can guarantee they are all
+different from each other that all the
+
+ align:start position:0%
+different from each other that all the
+ 
+
+ align:start position:0%
+different from each other that all the
+A's are different from all the B's or
+
+ align:start position:0%
+A's are different from all the B's or
+ 
+
+ align:start position:0%
+A's are different from all the B's or
+different from all the C's uh by
+
+ align:start position:0%
+different from all the C's uh by
+ 
+
+ align:start position:0%
+different from all the C's uh by
+distinguishing by saying all A's get
+
+ align:start position:0%
+distinguishing by saying all A's get
+ 
+
+ align:start position:0%
+distinguishing by saying all A's get
+this right all A's will be 2 34 66 or 98
+
+ align:start position:0%
+this right all A's will be 2 34 66 or 98
+ 
+
+ align:start position:0%
+this right all A's will be 2 34 66 or 98
+mod
+
+ align:start position:0%
+mod
+ 
+
+ align:start position:0%
+mod
+128 and in general uh those are
+
+ align:start position:0%
+128 and in general uh those are
+ 
+
+ align:start position:0%
+128 and in general uh those are
+particular numbers set up to make this
+
+ align:start position:0%
+particular numbers set up to make this
+ 
+
+ align:start position:0%
+particular numbers set up to make this
+construction work out I didn't check
+
+ align:start position:0%
+construction work out I didn't check
+ 
+
+ align:start position:0%
+construction work out I didn't check
+them all but I believe them um in
+
+ align:start position:0%
+them all but I believe them um in
+ 
+
+ align:start position:0%
+them all but I believe them um in
+general we're going to distinguish all
+
+ align:start position:0%
+general we're going to distinguish all
+ 
+
+ align:start position:0%
+general we're going to distinguish all
+the letters by how they be how what they
+
+ align:start position:0%
+the letters by how they be how what they
+ 
+
+ align:start position:0%
+the letters by how they be how what they
+are mod 128 so given a number between 0
+
+ align:start position:0%
+are mod 128 so given a number between 0
+ 
+
+ align:start position:0%
+are mod 128 so given a number between 0
+and 127 there's a unique letter of the
+
+ align:start position:0%
+and 127 there's a unique letter of the
+ 
+
+ align:start position:0%
+and 127 there's a unique letter of the
+regular English letter alphabet the A's
+
+ align:start position:0%
+regular English letter alphabet the A's
+ 
+
+ align:start position:0%
+regular English letter alphabet the A's
+the B's the Y's the Z's and so on uh
+
+ align:start position:0%
+the B's the Y's the Z's and so on uh
+ 
+
+ align:start position:0%
+the B's the Y's the Z's and so on uh
+that it is assigned to and I'll tell you
+
+ align:start position:0%
+that it is assigned to and I'll tell you
+ 
+
+ align:start position:0%
+that it is assigned to and I'll tell you
+in particular the
+
+ align:start position:0%
+in particular the
+ 
+
+ align:start position:0%
+in particular the
+vi and the vi bars are going to be I
+
+ align:start position:0%
+vi and the vi bars are going to be I
+ 
+
+ align:start position:0%
+vi and the vi bars are going to be I
+think eight or
+
+ align:start position:0%
+think eight or
+ 
+
+ align:start position:0%
+think eight or
+nine mod
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+128 uh and the eight is if it's
+
+ align:start position:0%
+128 uh and the eight is if it's
+ 
+
+ align:start position:0%
+128 uh and the eight is if it's
+false and the nine is if it's true
+
+ align:start position:0%
+false and the nine is if it's true
+ 
+
+ align:start position:0%
+false and the nine is if it's true
+because remember modulo 4 we want this
+
+ align:start position:0%
+because remember modulo 4 we want this
+ 
+
+ align:start position:0%
+because remember modulo 4 we want this
+to be zero and we want this to be one so
+
+ align:start position:0%
+to be zero and we want this to be one so
+ 
+
+ align:start position:0%
+to be zero and we want this to be one so
+there's a bunch of choices like that
+
+ align:start position:0%
+there's a bunch of choices like that
+ 
+
+ align:start position:0%
+there's a bunch of choices like that
+some of them are unique we can always
+
+ align:start position:0%
+some of them are unique we can always
+ 
+
+ align:start position:0%
+some of them are unique we can always
+guarantee forget which ones the CIS are
+
+ align:start position:0%
+guarantee forget which ones the CIS are
+ 
+
+ align:start position:0%
+guarantee forget which ones the CIS are
+all something mod 128 so the mod 128
+
+ align:start position:0%
+all something mod 128 so the mod 128
+ 
+
+ align:start position:0%
+all something mod 128 so the mod 128
+will tell you sort of what letter of the
+
+ align:start position:0%
+will tell you sort of what letter of the
+ 
+
+ align:start position:0%
+will tell you sort of what letter of the
+English alphabet it is and then it's a
+
+ align:start position:0%
+English alphabet it is and then it's a
+ 
+
+ align:start position:0%
+English alphabet it is and then it's a
+matter of deciding the high order bits
+
+ align:start position:0%
+matter of deciding the high order bits
+ 
+
+ align:start position:0%
+matter of deciding the high order bits
+uh your number divided by 128 and take
+
+ align:start position:0%
+uh your number divided by 128 and take
+ 
+
+ align:start position:0%
+uh your number divided by 128 and take
+the floor uh what that is we set to make
+
+ align:start position:0%
+the floor uh what that is we set to make
+ 
+
+ align:start position:0%
+the floor uh what that is we set to make
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+distinct and um the heart of the proof I
+
+ align:start position:0%
+distinct and um the heart of the proof I
+ 
+
+ align:start position:0%
+distinct and um the heart of the proof I
+will say is to make sure that the uh
+
+ align:start position:0%
+will say is to make sure that the uh
+ 
+
+ align:start position:0%
+will say is to make sure that the uh
+VIIs are all
+
+ align:start position:0%
+VIIs are all
+ 
+
+ align:start position:0%
+VIIs are all
+different um
+
+ align:start position:0%
+different um
+ 
+
+ align:start position:0%
+different um
+um or let's say that the ti are
+
+ align:start position:0%
+um or let's say that the ti are
+ 
+
+ align:start position:0%
+um or let's say that the ti are
+different so we have we have the
+
+ align:start position:0%
+different so we have we have the
+ 
+
+ align:start position:0%
+different so we have we have the
+variables here we're adding them up and
+
+ align:start position:0%
+variables here we're adding them up and
+ 
+
+ align:start position:0%
+variables here we're adding them up and
+we get TI and we need those all of the
+
+ align:start position:0%
+we get TI and we need those all of the
+ 
+
+ align:start position:0%
+we get TI and we need those all of the
+ti there's one TI per Clause we need
+
+ align:start position:0%
+ti there's one TI per Clause we need
+ 
+
+ align:start position:0%
+ti there's one TI per Clause we need
+them all to be different which means no
+
+ align:start position:0%
+them all to be different which means no
+ 
+
+ align:start position:0%
+them all to be different which means no
+matter which triple of VI we get we
+
+ align:start position:0%
+matter which triple of VI we get we
+ 
+
+ align:start position:0%
+matter which triple of VI we get we
+should get a different sum of the
+
+ align:start position:0%
+should get a different sum of the
+ 
+
+ align:start position:0%
+should get a different sum of the
+triples so this is a problem of uh set
+
+ align:start position:0%
+triples so this is a problem of uh set
+ 
+
+ align:start position:0%
+triples so this is a problem of uh set
+VI and VI Prime uh divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+128 so
+
+ align:start position:0%
+128 so
+ 
+
+ align:start position:0%
+128 so
+that VI plus
+
+ align:start position:0%
+that VI plus
+ 
+
+ align:start position:0%
+that VI plus
+VJ plus
+
+ align:start position:0%
+VJ plus
+ 
+
+ align:start position:0%
+VJ plus
+VK uh are all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distinct and at this point epin says oh
+
+ align:start position:0%
+distinct and at this point epin says oh
+ 
+
+ align:start position:0%
+distinct and at this point epin says oh
+there's a result by Bose and Chala from
+
+ align:start position:0%
+there's a result by Bose and Chala from
+ 
+
+ align:start position:0%
+there's a result by Bose and Chala from
+1959 that says you can always choose
+
+ align:start position:0%
+1959 that says you can always choose
+ 
+
+ align:start position:0%
+1959 that says you can always choose
+these guys um if there's n of them that
+
+ align:start position:0%
+these guys um if there's n of them that
+ 
+
+ align:start position:0%
+these guys um if there's n of them that
+you need to choose then n cubed
+
+ align:start position:0%
+you need to choose then n cubed
+ 
+
+ align:start position:0%
+you need to choose then n cubed
+different integers suffice to make this
+
+ align:start position:0%
+different integers suffice to make this
+ 
+
+ align:start position:0%
+different integers suffice to make this
+true uh that's if you know the
+
+ align:start position:0%
+true uh that's if you know the
+ 
+
+ align:start position:0%
+true uh that's if you know the
+literature super well but there's an
+
+ align:start position:0%
+literature super well but there's an
+ 
+
+ align:start position:0%
+literature super well but there's an
+easy proof uh that polinomial is enough
+
+ align:start position:0%
+easy proof uh that polinomial is enough
+ 
+
+ align:start position:0%
+easy proof uh that polinomial is enough
+here and those of you who are in
+
+ align:start position:0%
+here and those of you who are in
+ 
+
+ align:start position:0%
+here and those of you who are in
+6851 should be able to construct one
+
+ align:start position:0%
+6851 should be able to construct one
+ 
+
+ align:start position:0%
+6851 should be able to construct one
+because this is essentially Fusion trees
+
+ align:start position:0%
+because this is essentially Fusion trees
+ 
+
+ align:start position:0%
+because this is essentially Fusion trees
+uh but in general imagine that you've
+
+ align:start position:0%
+uh but in general imagine that you've
+ 
+
+ align:start position:0%
+uh but in general imagine that you've
+chosen um by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction I'll call them V less than I
+
+ align:start position:0%
+induction I'll call them V less than I
+ 
+
+ align:start position:0%
+induction I'll call them V less than I
+and Let's ignore the primes let's just
+
+ align:start position:0%
+and Let's ignore the primes let's just
+ 
+
+ align:start position:0%
+and Let's ignore the primes let's just
+say we've constructed all the things up
+
+ align:start position:0%
+say we've constructed all the things up
+ 
+
+ align:start position:0%
+say we've constructed all the things up
+to vus one and now we want to
+
+ align:start position:0%
+to vus one and now we want to
+ 
+
+ align:start position:0%
+to vus one and now we want to
+choose
+
+ align:start position:0%
+choose
+ 
+
+ align:start position:0%
+choose
+VI uh and it needs to
+
+ align:start position:0%
+VI uh and it needs to
+ 
+
+ align:start position:0%
+VI uh and it needs to
+avoid uh certain values I think if it
+
+ align:start position:0%
+avoid uh certain values I think if it
+ 
+
+ align:start position:0%
+avoid uh certain values I think if it
+avoids VJ plus
+
+ align:start position:0%
+avoids VJ plus
+ 
+
+ align:start position:0%
+avoids VJ plus
+VK minus v l minus VM minus
+
+ align:start position:0%
+VK minus v l minus VM minus
+ 
+
+ align:start position:0%
+VK minus v l minus VM minus
+VP for all j k l m p less than
+
+ align:start position:0%
+VP for all j k l m p less than
+ 
+
+ align:start position:0%
+VP for all j k l m p less than
+I then no triple should sum to any other
+
+ align:start position:0%
+I then no triple should sum to any other
+ 
+
+ align:start position:0%
+I then no triple should sum to any other
+triple because if we add uh I think I
+
+ align:start position:0%
+triple because if we add uh I think I
+ 
+
+ align:start position:0%
+triple because if we add uh I think I
+maybe I have those signs slightly off so
+
+ align:start position:0%
+maybe I have those signs slightly off so
+ 
+
+ align:start position:0%
+maybe I have those signs slightly off so
+I wanted
+
+ align:start position:0%
+I wanted
+ 
+
+ align:start position:0%
+I wanted
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+this yeah so let's do one more plus okay
+
+ align:start position:0%
+this yeah so let's do one more plus okay
+ 
+
+ align:start position:0%
+this yeah so let's do one more plus okay
+so suppose I had an equation like this
+
+ align:start position:0%
+so suppose I had an equation like this
+ 
+
+ align:start position:0%
+so suppose I had an equation like this
+um I claim that's bad because if I move
+
+ align:start position:0%
+um I claim that's bad because if I move
+ 
+
+ align:start position:0%
+um I claim that's bad because if I move
+these guys over to the left left hand
+
+ align:start position:0%
+these guys over to the left left hand
+ 
+
+ align:start position:0%
+these guys over to the left left hand
+side that's a triple of V's that sums to
+
+ align:start position:0%
+side that's a triple of V's that sums to
+ 
+
+ align:start position:0%
+side that's a triple of V's that sums to
+another triple of V's so as long as I
+
+ align:start position:0%
+another triple of V's so as long as I
+ 
+
+ align:start position:0%
+another triple of V's so as long as I
+choose my new value V uh sorry this
+
+ align:start position:0%
+choose my new value V uh sorry this
+ 
+
+ align:start position:0%
+choose my new value V uh sorry this
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+VI is the one I'm choosing as long as I
+
+ align:start position:0%
+VI is the one I'm choosing as long as I
+ 
+
+ align:start position:0%
+VI is the one I'm choosing as long as I
+choose VI to be
+
+ align:start position:0%
+choose VI to be
+ 
+
+ align:start position:0%
+choose VI to be
+different uh from all all such sums and
+
+ align:start position:0%
+different uh from all all such sums and
+ 
+
+ align:start position:0%
+different uh from all all such sums and
+they're only like less than n the 5th
+
+ align:start position:0%
+they're only like less than n the 5th
+ 
+
+ align:start position:0%
+they're only like less than n the 5th
+such
+
+ align:start position:0%
+such
+ 
+
+ align:start position:0%
+such
+sums because there're only n of these
+
+ align:start position:0%
+sums because there're only n of these
+ 
+
+ align:start position:0%
+sums because there're only n of these
+different things then uh I'm okay and so
+
+ align:start position:0%
+different things then uh I'm okay and so
+ 
+
+ align:start position:0%
+different things then uh I'm okay and so
+by pigeon hle Principle as long as I
+
+ align:start position:0%
+by pigeon hle Principle as long as I
+ 
+
+ align:start position:0%
+by pigeon hle Principle as long as I
+have a range that is at least n the 5th
+
+ align:start position:0%
+have a range that is at least n the 5th
+ 
+
+ align:start position:0%
+have a range that is at least n the 5th
+in size then I can always choose VI to
+
+ align:start position:0%
+in size then I can always choose VI to
+ 
+
+ align:start position:0%
+in size then I can always choose VI to
+avoid all those conflicts okay so that's
+
+ align:start position:0%
+avoid all those conflicts okay so that's
+ 
+
+ align:start position:0%
+avoid all those conflicts okay so that's
+a really easy proof that n the 5th is
+
+ align:start position:0%
+a really easy proof that n the 5th is
+ 
+
+ align:start position:0%
+a really easy proof that n the 5th is
+enough in fact n cubed is enough but
+
+ align:start position:0%
+enough in fact n cubed is enough but
+ 
+
+ align:start position:0%
+enough in fact n cubed is enough but
+this is a hardness proof all we need is
+
+ align:start position:0%
+this is a hardness proof all we need is
+ 
+
+ align:start position:0%
+this is a hardness proof all we need is
+strong hardness we just need n cubed
+
+ align:start position:0%
+strong hardness we just need n cubed
+ 
+
+ align:start position:0%
+strong hardness we just need n cubed
+that's just fine or n to the fifth any
+
+ align:start position:0%
+that's just fine or n to the fifth any
+ 
+
+ align:start position:0%
+that's just fine or n to the fifth any
+polinomial would be
+
+ align:start position:0%
+polinomial would be
+ 
+
+ align:start position:0%
+polinomial would be
+okay so that's a sketch of the reverse
+
+ align:start position:0%
+okay so that's a sketch of the reverse
+ 
+
+ align:start position:0%
+okay so that's a sketch of the reverse
+direction for this proof there are some
+
+ align:start position:0%
+direction for this proof there are some
+ 
+
+ align:start position:0%
+direction for this proof there are some
+more details to make sure everything
+
+ align:start position:0%
+more details to make sure everything
+ 
+
+ align:start position:0%
+more details to make sure everything
+adds up right mod 128 and that you can
+
+ align:start position:0%
+adds up right mod 128 and that you can
+ 
+
+ align:start position:0%
+adds up right mod 128 and that you can
+make all the AIS different and so on but
+
+ align:start position:0%
+make all the AIS different and so on but
+ 
+
+ align:start position:0%
+make all the AIS different and so on but
+the hard part is the vi seems
+
+ align:start position:0%
+the hard part is the vi seems
+ 
+
+ align:start position:0%
+the hard part is the vi seems
+believable questions about Cryptor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rhythms okay
+
+ align:start position:0%
+rhythms okay
+ 
+
+ align:start position:0%
+rhythms okay
+uh cool next uh is an origami proof so
+
+ align:start position:0%
+uh cool next uh is an origami proof so
+ 
+
+ align:start position:0%
+uh cool next uh is an origami proof so
+uh here's sort of the motivating problem
+
+ align:start position:0%
+uh here's sort of the motivating problem
+ 
+
+ align:start position:0%
+uh here's sort of the motivating problem
+I give you some crease pattern which is
+
+ align:start position:0%
+I give you some crease pattern which is
+ 
+
+ align:start position:0%
+I give you some crease pattern which is
+just a graph drawn in the plane no
+
+ align:start position:0%
+just a graph drawn in the plane no
+ 
+
+ align:start position:0%
+just a graph drawn in the plane no
+Crossings and all the edges are straight
+
+ align:start position:0%
+Crossings and all the edges are straight
+ 
+
+ align:start position:0%
+Crossings and all the edges are straight
+segments and you want to fold it into a
+
+ align:start position:0%
+segments and you want to fold it into a
+ 
+
+ align:start position:0%
+segments and you want to fold it into a
+flat
+
+ align:start position:0%
+flat
+ 
+
+ align:start position:0%
+flat
+origami or flat folded state would be
+
+ align:start position:0%
+origami or flat folded state would be
+ 
+
+ align:start position:0%
+origami or flat folded state would be
+the more technical term so this is an
+
+ align:start position:0%
+the more technical term so this is an
+ 
+
+ align:start position:0%
+the more technical term so this is an
+example of what's called an origami
+
+ align:start position:0%
+example of what's called an origami
+ 
+
+ align:start position:0%
+example of what's called an origami
+tessellation but in general what you're
+
+ align:start position:0%
+tessellation but in general what you're
+ 
+
+ align:start position:0%
+tessellation but in general what you're
+allowed to do uh the red lines here mean
+
+ align:start position:0%
+allowed to do uh the red lines here mean
+ 
+
+ align:start position:0%
+allowed to do uh the red lines here mean
+that you fold as a mountain by 180 uh
+
+ align:start position:0%
+that you fold as a mountain by 180 uh
+ 
+
+ align:start position:0%
+that you fold as a mountain by 180 uh
+180° and the blue lines mean you fold a
+
+ align:start position:0%
+180° and the blue lines mean you fold a
+ 
+
+ align:start position:0%
+180° and the blue lines mean you fold a
+valley 180° so they're specifying the
+
+ align:start position:0%
+valley 180° so they're specifying the
+ 
+
+ align:start position:0%
+valley 180° so they're specifying the
+relative orientation but in flat folding
+
+ align:start position:0%
+relative orientation but in flat folding
+ 
+
+ align:start position:0%
+relative orientation but in flat folding
+you're only allowed to go plus or minus
+
+ align:start position:0%
+you're only allowed to go plus or minus
+ 
+
+ align:start position:0%
+you're only allowed to go plus or minus
+180 and then it has to exist now the
+
+ align:start position:0%
+180 and then it has to exist now the
+ 
+
+ align:start position:0%
+180 and then it has to exist now the
+rules for paper are twofold one is that
+
+ align:start position:0%
+rules for paper are twofold one is that
+ 
+
+ align:start position:0%
+rules for paper are twofold one is that
+it doesn't stretch it's an isometric
+
+ align:start position:0%
+it doesn't stretch it's an isometric
+ 
+
+ align:start position:0%
+it doesn't stretch it's an isometric
+mapping of the piece of paper each of
+
+ align:start position:0%
+mapping of the piece of paper each of
+ 
+
+ align:start position:0%
+mapping of the piece of paper each of
+these little polygons is just uh rotated
+
+ align:start position:0%
+these little polygons is just uh rotated
+ 
+
+ align:start position:0%
+these little polygons is just uh rotated
+translated reflected possibly over here
+
+ align:start position:0%
+translated reflected possibly over here
+ 
+
+ align:start position:0%
+translated reflected possibly over here
+they fit together so you don't tear the
+
+ align:start position:0%
+they fit together so you don't tear the
+ 
+
+ align:start position:0%
+they fit together so you don't tear the
+paper they fit together at all the
+
+ align:start position:0%
+paper they fit together at all the
+ 
+
+ align:start position:0%
+paper they fit together at all the
+creases um and there are no Crossings
+
+ align:start position:0%
+creases um and there are no Crossings
+ 
+
+ align:start position:0%
+creases um and there are no Crossings
+because paper can't intersect itself so
+
+ align:start position:0%
+because paper can't intersect itself so
+ 
+
+ align:start position:0%
+because paper can't intersect itself so
+um the geometry is basically determined
+
+ align:start position:0%
+um the geometry is basically determined
+ 
+
+ align:start position:0%
+um the geometry is basically determined
+if you if you say okay I'm going to view
+
+ align:start position:0%
+if you if you say okay I'm going to view
+ 
+
+ align:start position:0%
+if you if you say okay I'm going to view
+this panel as being fixed it doesn't
+
+ align:start position:0%
+this panel as being fixed it doesn't
+ 
+
+ align:start position:0%
+this panel as being fixed it doesn't
+move then this one is going to be a
+
+ align:start position:0%
+move then this one is going to be a
+ 
+
+ align:start position:0%
+move then this one is going to be a
+reflection through this line flipped
+
+ align:start position:0%
+reflection through this line flipped
+ 
+
+ align:start position:0%
+reflection through this line flipped
+over and in general all of these other
+
+ align:start position:0%
+over and in general all of these other
+ 
+
+ align:start position:0%
+over and in general all of these other
+polygons just have to be Reflections
+
+ align:start position:0%
+polygons just have to be Reflections
+ 
+
+ align:start position:0%
+polygons just have to be Reflections
+because every time you fold on a line
+
+ align:start position:0%
+because every time you fold on a line
+ 
+
+ align:start position:0%
+because every time you fold on a line
+and the rules of the game here is you
+
+ align:start position:0%
+and the rules of the game here is you
+ 
+
+ align:start position:0%
+and the rules of the game here is you
+have to fold everywhere there is a
+
+ align:start position:0%
+have to fold everywhere there is a
+ 
+
+ align:start position:0%
+have to fold everywhere there is a
+crease um you can figure out this
+
+ align:start position:0%
+crease um you can figure out this
+ 
+
+ align:start position:0%
+crease um you can figure out this
+polygon will end up here uh relative to
+
+ align:start position:0%
+polygon will end up here uh relative to
+ 
+
+ align:start position:0%
+polygon will end up here uh relative to
+some original polygon so you can figure
+
+ align:start position:0%
+some original polygon so you can figure
+ 
+
+ align:start position:0%
+some original polygon so you can figure
+out pretty much what this looks like as
+
+ align:start position:0%
+out pretty much what this looks like as
+ 
+
+ align:start position:0%
+out pretty much what this looks like as
+an x-ray diagram and the hard part
+
+ align:start position:0%
+an x-ray diagram and the hard part
+ 
+
+ align:start position:0%
+an x-ray diagram and the hard part
+becomes how are how are layers stacked
+
+ align:start position:0%
+becomes how are how are layers stacked
+ 
+
+ align:start position:0%
+becomes how are how are layers stacked
+is this one on top of this one or is
+
+ align:start position:0%
+is this one on top of this one or is
+ 
+
+ align:start position:0%
+is this one on top of this one or is
+this one on top of that one
+
+ align:start position:0%
+this one on top of that one
+ 
+
+ align:start position:0%
+this one on top of that one
+that's why the problem is empty complete
+
+ align:start position:0%
+that's why the problem is empty complete
+ 
+
+ align:start position:0%
+that's why the problem is empty complete
+is that last step deciding which layers
+
+ align:start position:0%
+is that last step deciding which layers
+ 
+
+ align:start position:0%
+is that last step deciding which layers
+are on top of the other in general
+
+ align:start position:0%
+are on top of the other in general
+ 
+
+ align:start position:0%
+are on top of the other in general
+Whenever two layers of paper partially
+
+ align:start position:0%
+Whenever two layers of paper partially
+ 
+
+ align:start position:0%
+Whenever two layers of paper partially
+overlap you have to decide which is on
+
+ align:start position:0%
+overlap you have to decide which is on
+ 
+
+ align:start position:0%
+overlap you have to decide which is on
+top of the other and then there's some
+
+ align:start position:0%
+top of the other and then there's some
+ 
+
+ align:start position:0%
+top of the other and then there's some
+obvious constraints like um get my hands
+
+ align:start position:0%
+obvious constraints like um get my hands
+ 
+
+ align:start position:0%
+obvious constraints like um get my hands
+oriented this is okay but this is not
+
+ align:start position:0%
+oriented this is okay but this is not
+ 
+
+ align:start position:0%
+oriented this is okay but this is not
+okay right if there's one crease of
+
+ align:start position:0%
+okay right if there's one crease of
+ 
+
+ align:start position:0%
+okay right if there's one crease of
+paper here and another crease of paper
+
+ align:start position:0%
+paper here and another crease of paper
+ 
+
+ align:start position:0%
+paper here and another crease of paper
+here then these locally intersect so
+
+ align:start position:0%
+here then these locally intersect so
+ 
+
+ align:start position:0%
+here then these locally intersect so
+this is okay this is okay this is not
+
+ align:start position:0%
+this is okay this is okay this is not
+ 
+
+ align:start position:0%
+this is okay this is okay this is not
+okay that's the rules uh we don't need
+
+ align:start position:0%
+okay that's the rules uh we don't need
+ 
+
+ align:start position:0%
+okay that's the rules uh we don't need
+to know those rules super precisely to
+
+ align:start position:0%
+to know those rules super precisely to
+ 
+
+ align:start position:0%
+to know those rules super precisely to
+understand this proof fairly intuitively
+
+ align:start position:0%
+understand this proof fairly intuitively
+ 
+
+ align:start position:0%
+understand this proof fairly intuitively
+because everything's going to be small
+
+ align:start position:0%
+because everything's going to be small
+ 
+
+ align:start position:0%
+because everything's going to be small
+and quite local uh the basic idea is the
+
+ align:start position:0%
+and quite local uh the basic idea is the
+ 
+
+ align:start position:0%
+and quite local uh the basic idea is the
+following you take um a piece of
+
+ align:start position:0%
+following you take um a piece of
+ 
+
+ align:start position:0%
+following you take um a piece of
+paper and you fold it along two parallel
+
+ align:start position:0%
+paper and you fold it along two parallel
+ 
+
+ align:start position:0%
+paper and you fold it along two parallel
+lines so fold along this line and then
+
+ align:start position:0%
+lines so fold along this line and then
+ 
+
+ align:start position:0%
+lines so fold along this line and then
+along this
+
+ align:start position:0%
+along this
+ 
+
+ align:start position:0%
+along this
+line okay and this is called a pleat and
+
+ align:start position:0%
+line okay and this is called a pleat and
+ 
+
+ align:start position:0%
+line okay and this is called a pleat and
+there are two ways to do it you could do
+
+ align:start position:0%
+there are two ways to do it you could do
+ 
+
+ align:start position:0%
+there are two ways to do it you could do
+one mountain one Valley or you could do
+
+ align:start position:0%
+one mountain one Valley or you could do
+ 
+
+ align:start position:0%
+one mountain one Valley or you could do
+the other one mountain and the other one
+
+ align:start position:0%
+the other one mountain and the other one
+ 
+
+ align:start position:0%
+the other one mountain and the other one
+Valley you can't make them both
+
+ align:start position:0%
+Valley you can't make them both
+ 
+
+ align:start position:0%
+Valley you can't make them both
+mountains because then you'd locally
+
+ align:start position:0%
+mountains because then you'd locally
+ 
+
+ align:start position:0%
+mountains because then you'd locally
+intersect
+
+ align:start position:0%
+intersect
+ 
+
+ align:start position:0%
+intersect
+yourself okay so it could be this way or
+
+ align:start position:0%
+yourself okay so it could be this way or
+ 
+
+ align:start position:0%
+yourself okay so it could be this way or
+it could be the other way I just had it
+
+ align:start position:0%
+it could be the other way I just had it
+ 
+
+ align:start position:0%
+it could be the other way I just had it
+uh little
+
+ align:start position:0%
+uh little
+ 
+
+ align:start position:0%
+uh little
+tedious um and so you have to make that
+
+ align:start position:0%
+tedious um and so you have to make that
+ 
+
+ align:start position:0%
+tedious um and so you have to make that
+choice which one is a mountain which one
+
+ align:start position:0%
+choice which one is a mountain which one
+ 
+
+ align:start position:0%
+choice which one is a mountain which one
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+valley uh that's going to be our truth
+
+ align:start position:0%
+valley uh that's going to be our truth
+ 
+
+ align:start position:0%
+valley uh that's going to be our truth
+signal one we're going to consider one
+
+ align:start position:0%
+signal one we're going to consider one
+ 
+
+ align:start position:0%
+signal one we're going to consider one
+option true the other option false
+
+ align:start position:0%
+option true the other option false
+ 
+
+ align:start position:0%
+option true the other option false
+and as a point of notation we're going
+
+ align:start position:0%
+and as a point of notation we're going
+ 
+
+ align:start position:0%
+and as a point of notation we're going
+to have an arrow in every one of these
+
+ align:start position:0%
+to have an arrow in every one of these
+ 
+
+ align:start position:0%
+to have an arrow in every one of these
+uh we call them wire gadgets and general
+
+ align:start position:0%
+uh we call them wire gadgets and general
+ 
+
+ align:start position:0%
+uh we call them wire gadgets and general
+wires are how we have truth segments
+
+ align:start position:0%
+wires are how we have truth segments
+ 
+
+ align:start position:0%
+wires are how we have truth segments
+truth settings um and so relative to the
+
+ align:start position:0%
+truth settings um and so relative to the
+ 
+
+ align:start position:0%
+truth settings um and so relative to the
+orientation of this Arrow if it's Valley
+
+ align:start position:0%
+orientation of this Arrow if it's Valley
+ 
+
+ align:start position:0%
+orientation of this Arrow if it's Valley
+on the left blue is Valley uh because I
+
+ align:start position:0%
+on the left blue is Valley uh because I
+ 
+
+ align:start position:0%
+on the left blue is Valley uh because I
+guess rivers are in valleys then we'll
+
+ align:start position:0%
+guess rivers are in valleys then we'll
+ 
+
+ align:start position:0%
+guess rivers are in valleys then we'll
+consider it true if there's blue on the
+
+ align:start position:0%
+consider it true if there's blue on the
+ 
+
+ align:start position:0%
+consider it true if there's blue on the
+right we'll consider it false question
+
+ align:start position:0%
+right we'll consider it false question
+ 
+
+ align:start position:0%
+right we'll consider it false question
+just a question about the setup like
+
+ align:start position:0%
+just a question about the setup like
+ 
+
+ align:start position:0%
+just a question about the setup like
+once you draw all the red and blue lines
+
+ align:start position:0%
+once you draw all the red and blue lines
+ 
+
+ align:start position:0%
+once you draw all the red and blue lines
+if there's just one unique answer uh no
+
+ align:start position:0%
+if there's just one unique answer uh no
+ 
+
+ align:start position:0%
+if there's just one unique answer uh no
+the answer is not necessarily unique but
+
+ align:start position:0%
+the answer is not necessarily unique but
+ 
+
+ align:start position:0%
+the answer is not necessarily unique but
+there will be a unique yes or no answer
+
+ align:start position:0%
+there will be a unique yes or no answer
+ 
+
+ align:start position:0%
+there will be a unique yes or no answer
+either it will be flat foldable or not
+
+ align:start position:0%
+either it will be flat foldable or not
+ 
+
+ align:start position:0%
+either it will be flat foldable or not
+but there actually may be many flat
+
+ align:start position:0%
+but there actually may be many flat
+ 
+
+ align:start position:0%
+but there actually may be many flat
+foldings consistent with a given
+
+ align:start position:0%
+foldings consistent with a given
+ 
+
+ align:start position:0%
+foldings consistent with a given
+Mountain Valley assignment in general so
+
+ align:start position:0%
+Mountain Valley assignment in general so
+ 
+
+ align:start position:0%
+Mountain Valley assignment in general so
+we're not worrying about that too much
+
+ align:start position:0%
+we're not worrying about that too much
+ 
+
+ align:start position:0%
+we're not worrying about that too much
+here um we're just worrying about
+
+ align:start position:0%
+here um we're just worrying about
+ 
+
+ align:start position:0%
+here um we're just worrying about
+whether it is feasible whether there's
+
+ align:start position:0%
+whether it is feasible whether there's
+ 
+
+ align:start position:0%
+whether it is feasible whether there's
+some ordering that makes things work
+
+ align:start position:0%
+some ordering that makes things work
+ 
+
+ align:start position:0%
+some ordering that makes things work
+out okay so the idea is this could be
+
+ align:start position:0%
+out okay so the idea is this could be
+ 
+
+ align:start position:0%
+out okay so the idea is this could be
+your variable
+
+ align:start position:0%
+your variable
+ 
+
+ align:start position:0%
+your variable
+some reductions have variable gadgets
+
+ align:start position:0%
+some reductions have variable gadgets
+ 
+
+ align:start position:0%
+some reductions have variable gadgets
+some don't this one is just going to
+
+ align:start position:0%
+some don't this one is just going to
+ 
+
+ align:start position:0%
+some don't this one is just going to
+have a wire the idea is if you say well
+
+ align:start position:0%
+have a wire the idea is if you say well
+ 
+
+ align:start position:0%
+have a wire the idea is if you say well
+there's a plead over here in the paper
+
+ align:start position:0%
+there's a plead over here in the paper
+ 
+
+ align:start position:0%
+there's a plead over here in the paper
+then it could be pleaded one way or the
+
+ align:start position:0%
+then it could be pleaded one way or the
+ 
+
+ align:start position:0%
+then it could be pleaded one way or the
+other and um that serves as a variable
+
+ align:start position:0%
+other and um that serves as a variable
+ 
+
+ align:start position:0%
+other and um that serves as a variable
+that you choose make one choice the
+
+ align:start position:0%
+that you choose make one choice the
+ 
+
+ align:start position:0%
+that you choose make one choice the
+other what we'd like is to make take
+
+ align:start position:0%
+other what we'd like is to make take
+ 
+
+ align:start position:0%
+other what we'd like is to make take
+that truth value and duplicate it make
+
+ align:start position:0%
+that truth value and duplicate it make
+ 
+
+ align:start position:0%
+that truth value and duplicate it make
+many copies but that's not the next
+
+ align:start position:0%
+many copies but that's not the next
+ 
+
+ align:start position:0%
+many copies but that's not the next
+Gadget the next Gadget is a not all
+
+ align:start position:0%
+Gadget the next Gadget is a not all
+ 
+
+ align:start position:0%
+Gadget the next Gadget is a not all
+equal Clause Gadget so this is going to
+
+ align:start position:0%
+equal Clause Gadget so this is going to
+ 
+
+ align:start position:0%
+equal Clause Gadget so this is going to
+be a reduction from not all equal three
+
+ align:start position:0%
+be a reduction from not all equal three
+ 
+
+ align:start position:0%
+be a reduction from not all equal three
+set and I have the gadget pre-old fold
+
+ align:start position:0%
+set and I have the gadget pre-old fold
+ 
+
+ align:start position:0%
+set and I have the gadget pre-old fold
+it here um so this is uh what in origami
+
+ align:start position:0%
+it here um so this is uh what in origami
+ 
+
+ align:start position:0%
+it here um so this is uh what in origami
+world is called a triangular twist it's
+
+ align:start position:0%
+world is called a triangular twist it's
+ 
+
+ align:start position:0%
+world is called a triangular twist it's
+a slightly weird triangular twist in
+
+ align:start position:0%
+a slightly weird triangular twist in
+ 
+
+ align:start position:0%
+a slightly weird triangular twist in
+that this is 35° instead
+
+ align:start position:0%
+that this is 35° instead
+ 
+
+ align:start position:0%
+that this is 35° instead
+of 30 be the usual one uh and that is so
+
+ align:start position:0%
+of 30 be the usual one uh and that is so
+ 
+
+ align:start position:0%
+of 30 be the usual one uh and that is so
+it's just a little bit larger and that
+
+ align:start position:0%
+it's just a little bit larger and that
+ 
+
+ align:start position:0%
+it's just a little bit larger and that
+causes a problem so this is an example
+
+ align:start position:0%
+causes a problem so this is an example
+ 
+
+ align:start position:0%
+causes a problem so this is an example
+of a valid flat folding of that Gadget
+
+ align:start position:0%
+of a valid flat folding of that Gadget
+ 
+
+ align:start position:0%
+of a valid flat folding of that Gadget
+and if you look at the three ple the
+
+ align:start position:0%
+and if you look at the three ple the
+ 
+
+ align:start position:0%
+and if you look at the three ple the
+three pleats that are coming in notice
+
+ align:start position:0%
+three pleats that are coming in notice
+ 
+
+ align:start position:0%
+three pleats that are coming in notice
+the arrows are all pointing in so it's
+
+ align:start position:0%
+the arrows are all pointing in so it's
+ 
+
+ align:start position:0%
+the arrows are all pointing in so it's
+sort of symmetric uh it's going to be
+
+ align:start position:0%
+sort of symmetric uh it's going to be
+ 
+
+ align:start position:0%
+sort of symmetric uh it's going to be
+one of the valid ones um so I guess it's
+
+ align:start position:0%
+one of the valid ones um so I guess it's
+ 
+
+ align:start position:0%
+one of the valid ones um so I guess it's
+actually written on the diagram here
+
+ align:start position:0%
+actually written on the diagram here
+ 
+
+ align:start position:0%
+actually written on the diagram here
+this one is considered true uh because
+
+ align:start position:0%
+this one is considered true uh because
+ 
+
+ align:start position:0%
+this one is considered true uh because
+there's a valley on your right this one
+
+ align:start position:0%
+there's a valley on your right this one
+ 
+
+ align:start position:0%
+there's a valley on your right this one
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+considered false because there's a
+
+ align:start position:0%
+considered false because there's a
+ 
+
+ align:start position:0%
+considered false because there's a
+valley on your oh I'm so
+
+ align:start position:0%
+valley on your oh I'm so
+ 
+
+ align:start position:0%
+valley on your oh I'm so
+confused uh on your right yeah and this
+
+ align:start position:0%
+confused uh on your right yeah and this
+ 
+
+ align:start position:0%
+confused uh on your right yeah and this
+one is considered true because there's a
+
+ align:start position:0%
+one is considered true because there's a
+ 
+
+ align:start position:0%
+one is considered true because there's a
+valley on your left sorry false cuz
+
+ align:start position:0%
+valley on your left sorry false cuz
+ 
+
+ align:start position:0%
+valley on your left sorry false cuz
+because there's a valley on your right
+
+ align:start position:0%
+because there's a valley on your right
+ 
+
+ align:start position:0%
+because there's a valley on your right
+if you're walking down the arrow then
+
+ align:start position:0%
+if you're walking down the arrow then
+ 
+
+ align:start position:0%
+if you're walking down the arrow then
+the right hand side has a valley uh and
+
+ align:start position:0%
+the right hand side has a valley uh and
+ 
+
+ align:start position:0%
+the right hand side has a valley uh and
+so this happens to fold because they're
+
+ align:start position:0%
+so this happens to fold because they're
+ 
+
+ align:start position:0%
+so this happens to fold because they're
+not all the same if you tried to make
+
+ align:start position:0%
+not all the same if you tried to make
+ 
+
+ align:start position:0%
+not all the same if you tried to make
+them all the same which would be like
+
+ align:start position:0%
+them all the same which would be like
+ 
+
+ align:start position:0%
+them all the same which would be like
+reversing the
+
+ align:start position:0%
+reversing the
+ 
+
+ align:start position:0%
+reversing the
+true uh it's going to look something
+
+ align:start position:0%
+true uh it's going to look something
+ 
+
+ align:start position:0%
+true uh it's going to look something
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay which it's actually easier to
+
+ align:start position:0%
+this okay which it's actually easier to
+ 
+
+ align:start position:0%
+this okay which it's actually easier to
+see back here so now they're all trying
+
+ align:start position:0%
+see back here so now they're all trying
+ 
+
+ align:start position:0%
+see back here so now they're all trying
+to fold the same way uh but the problem
+
+ align:start position:0%
+to fold the same way uh but the problem
+ 
+
+ align:start position:0%
+to fold the same way uh but the problem
+is on this side sorry these guys will
+
+ align:start position:0%
+is on this side sorry these guys will
+ 
+
+ align:start position:0%
+is on this side sorry these guys will
+all come and intersect in the center and
+
+ align:start position:0%
+all come and intersect in the center and
+ 
+
+ align:start position:0%
+all come and intersect in the center and
+it's uh I think we have a diagram here
+
+ align:start position:0%
+it's uh I think we have a diagram here
+ 
+
+ align:start position:0%
+it's uh I think we have a diagram here
+and sort of in x-ray this is what must
+
+ align:start position:0%
+and sort of in x-ray this is what must
+ 
+
+ align:start position:0%
+and sort of in x-ray this is what must
+happen and there's this little area of
+
+ align:start position:0%
+happen and there's this little area of
+ 
+
+ align:start position:0%
+happen and there's this little area of
+intersection where you cannot resolve
+
+ align:start position:0%
+intersection where you cannot resolve
+ 
+
+ align:start position:0%
+intersection where you cannot resolve
+which of these three things are on top
+
+ align:start position:0%
+which of these three things are on top
+ 
+
+ align:start position:0%
+which of these three things are on top
+of each other because this one wants to
+
+ align:start position:0%
+of each other because this one wants to
+ 
+
+ align:start position:0%
+of each other because this one wants to
+be on top of this one wants to be on top
+
+ align:start position:0%
+be on top of this one wants to be on top
+ 
+
+ align:start position:0%
+be on top of this one wants to be on top
+of this one wants to be on top of this
+
+ align:start position:0%
+of this one wants to be on top of this
+ 
+
+ align:start position:0%
+of this one wants to be on top of this
+one so there's a cycle of constraints no
+
+ align:start position:0%
+one so there's a cycle of constraints no
+ 
+
+ align:start position:0%
+one so there's a cycle of constraints no
+one can be on top of each other at in
+
+ align:start position:0%
+one can be on top of each other at in
+ 
+
+ align:start position:0%
+one can be on top of each other at in
+this little region in the regular
+
+ align:start position:0%
+this little region in the regular
+ 
+
+ align:start position:0%
+this little region in the regular
+triangle twist this is a point and
+
+ align:start position:0%
+triangle twist this is a point and
+ 
+
+ align:start position:0%
+triangle twist this is a point and
+everything's fine but but the way these
+
+ align:start position:0%
+everything's fine but but the way these
+ 
+
+ align:start position:0%
+everything's fine but but the way these
+angles are set up there's this area of
+
+ align:start position:0%
+angles are set up there's this area of
+ 
+
+ align:start position:0%
+angles are set up there's this area of
+overlap and in that one situation you're
+
+ align:start position:0%
+overlap and in that one situation you're
+ 
+
+ align:start position:0%
+overlap and in that one situation you're
+toast so if they're all true but of
+
+ align:start position:0%
+toast so if they're all true but of
+ 
+
+ align:start position:0%
+toast so if they're all true but of
+course everything's symmetric if you
+
+ align:start position:0%
+course everything's symmetric if you
+ 
+
+ align:start position:0%
+course everything's symmetric if you
+flip it over then it's the same if
+
+ align:start position:0%
+flip it over then it's the same if
+ 
+
+ align:start position:0%
+flip it over then it's the same if
+they're all false so you forbid all true
+
+ align:start position:0%
+they're all false so you forbid all true
+ 
+
+ align:start position:0%
+they're all false so you forbid all true
+you forbid all false everything else
+
+ align:start position:0%
+you forbid all false everything else
+ 
+
+ align:start position:0%
+you forbid all false everything else
+will work so this is not all equal this
+
+ align:start position:0%
+will work so this is not all equal this
+ 
+
+ align:start position:0%
+will work so this is not all equal this
+will be flat foldable locally if and
+
+ align:start position:0%
+will be flat foldable locally if and
+ 
+
+ align:start position:0%
+will be flat foldable locally if and
+only if uh those those variable
+
+ align:start position:0%
+only if uh those those variable
+ 
+
+ align:start position:0%
+only if uh those those variable
+assignments are not all
+
+ align:start position:0%
+assignments are not all
+ 
+
+ align:start position:0%
+assignments are not all
+equal okay now uh we need a couple more
+
+ align:start position:0%
+equal okay now uh we need a couple more
+ 
+
+ align:start position:0%
+equal okay now uh we need a couple more
+gadgets for this to work one is the
+
+ align:start position:0%
+gadgets for this to work one is the
+ 
+
+ align:start position:0%
+gadgets for this to work one is the
+ability to duplicate a signal and the
+
+ align:start position:0%
+ability to duplicate a signal and the
+ 
+
+ align:start position:0%
+ability to duplicate a signal and the
+other is a
+
+ align:start position:0%
+other is a
+ 
+
+ align:start position:0%
+other is a
+crossover so here is uh this is a proof
+
+ align:start position:0%
+crossover so here is uh this is a proof
+ 
+
+ align:start position:0%
+crossover so here is uh this is a proof
+by burn and hay by the way this is I
+
+ align:start position:0%
+by burn and hay by the way this is I
+ 
+
+ align:start position:0%
+by burn and hay by the way this is I
+think the first or second paper in
+
+ align:start position:0%
+think the first or second paper in
+ 
+
+ align:start position:0%
+think the first or second paper in
+computational origami so got things off
+
+ align:start position:0%
+computational origami so got things off
+ 
+
+ align:start position:0%
+computational origami so got things off
+to an exciting start uh this is a uh
+
+ align:start position:0%
+to an exciting start uh this is a uh
+ 
+
+ align:start position:0%
+to an exciting start uh this is a uh
+splitter negation Gadget uh this is what
+
+ align:start position:0%
+splitter negation Gadget uh this is what
+ 
+
+ align:start position:0%
+splitter negation Gadget uh this is what
+it folds like it looks a little bit
+
+ align:start position:0%
+it folds like it looks a little bit
+ 
+
+ align:start position:0%
+it folds like it looks a little bit
+weird uh cuz my paper is a little bit
+
+ align:start position:0%
+weird uh cuz my paper is a little bit
+ 
+
+ align:start position:0%
+weird uh cuz my paper is a little bit
+small but uh the point is there's
+
+ align:start position:0%
+small but uh the point is there's
+ 
+
+ align:start position:0%
+small but uh the point is there's
+essentially only one way to fold this
+
+ align:start position:0%
+essentially only one way to fold this
+ 
+
+ align:start position:0%
+essentially only one way to fold this
+and if you take 6849 you'll know this
+
+ align:start position:0%
+and if you take 6849 you'll know this
+ 
+
+ align:start position:0%
+and if you take 6849 you'll know this
+little local analysis that forces
+
+ align:start position:0%
+little local analysis that forces
+ 
+
+ align:start position:0%
+little local analysis that forces
+different mountains and valleys to be
+
+ align:start position:0%
+different mountains and valleys to be
+ 
+
+ align:start position:0%
+different mountains and valleys to be
+the same for example these two have to
+
+ align:start position:0%
+the same for example these two have to
+ 
+
+ align:start position:0%
+the same for example these two have to
+be opposite which forces if this is a
+
+ align:start position:0%
+be opposite which forces if this is a
+ 
+
+ align:start position:0%
+be opposite which forces if this is a
+true this one must be a false uh so
+
+ align:start position:0%
+true this one must be a false uh so
+ 
+
+ align:start position:0%
+true this one must be a false uh so
+that's your negation and also uh from a
+
+ align:start position:0%
+that's your negation and also uh from a
+ 
+
+ align:start position:0%
+that's your negation and also uh from a
+local analysis of this vertex if this
+
+ align:start position:0%
+local analysis of this vertex if this
+ 
+
+ align:start position:0%
+local analysis of this vertex if this
+one is true this one must be
+
+ align:start position:0%
+one is true this one must be
+ 
+
+ align:start position:0%
+one is true this one must be
+true and it works and it also works in
+
+ align:start position:0%
+true and it works and it also works in
+ 
+
+ align:start position:0%
+true and it works and it also works in
+the inverse setup that's always going to
+
+ align:start position:0%
+the inverse setup that's always going to
+ 
+
+ align:start position:0%
+the inverse setup that's always going to
+be true uh a natural reason for us to be
+
+ align:start position:0%
+be true uh a natural reason for us to be
+ 
+
+ align:start position:0%
+be true uh a natural reason for us to be
+using not all equal three side here is
+
+ align:start position:0%
+using not all equal three side here is
+ 
+
+ align:start position:0%
+using not all equal three side here is
+there's really no preference between
+
+ align:start position:0%
+there's really no preference between
+ 
+
+ align:start position:0%
+there's really no preference between
+true and false there sort of there not
+
+ align:start position:0%
+true and false there sort of there not
+ 
+
+ align:start position:0%
+true and false there sort of there not
+really a logical notion it's more like
+
+ align:start position:0%
+really a logical notion it's more like
+ 
+
+ align:start position:0%
+really a logical notion it's more like
+red and blue literally red and blue um
+
+ align:start position:0%
+red and blue literally red and blue um
+ 
+
+ align:start position:0%
+red and blue literally red and blue um
+so notal equal is the one that's nice
+
+ align:start position:0%
+so notal equal is the one that's nice
+ 
+
+ align:start position:0%
+so notal equal is the one that's nice
+and symmetric it has no preference
+
+ align:start position:0%
+and symmetric it has no preference
+ 
+
+ align:start position:0%
+and symmetric it has no preference
+between red and blue and so we're seeing
+
+ align:start position:0%
+between red and blue and so we're seeing
+ 
+
+ align:start position:0%
+between red and blue and so we're seeing
+that here because everything's
+
+ align:start position:0%
+that here because everything's
+ 
+
+ align:start position:0%
+that here because everything's
+invertible we want that symmetry between
+
+ align:start position:0%
+invertible we want that symmetry between
+ 
+
+ align:start position:0%
+invertible we want that symmetry between
+red and blue so that would be one reason
+
+ align:start position:0%
+red and blue so that would be one reason
+ 
+
+ align:start position:0%
+red and blue so that would be one reason
+to guess not all equal 3at is a good
+
+ align:start position:0%
+to guess not all equal 3at is a good
+ 
+
+ align:start position:0%
+to guess not all equal 3at is a good
+choice here at least for that wire uh so
+
+ align:start position:0%
+choice here at least for that wire uh so
+ 
+
+ align:start position:0%
+choice here at least for that wire uh so
+cool if we have a signal we can make a
+
+ align:start position:0%
+cool if we have a signal we can make a
+ 
+
+ align:start position:0%
+cool if we have a signal we can make a
+copy we also uh well we sort of get two
+
+ align:start position:0%
+copy we also uh well we sort of get two
+ 
+
+ align:start position:0%
+copy we also uh well we sort of get two
+copies one of them happens to be negated
+
+ align:start position:0%
+copies one of them happens to be negated
+ 
+
+ align:start position:0%
+copies one of them happens to be negated
+with this particular choice of Arrow
+
+ align:start position:0%
+with this particular choice of Arrow
+ 
+
+ align:start position:0%
+with this particular choice of Arrow
+orientation um if we oriented the arrow
+
+ align:start position:0%
+orientation um if we oriented the arrow
+ 
+
+ align:start position:0%
+orientation um if we oriented the arrow
+the other way you could call that a copy
+
+ align:start position:0%
+the other way you could call that a copy
+ 
+
+ align:start position:0%
+the other way you could call that a copy
+but we don't want to take a wire that's
+
+ align:start position:0%
+but we don't want to take a wire that's
+ 
+
+ align:start position:0%
+but we don't want to take a wire that's
+pointing backwards so because we need to
+
+ align:start position:0%
+pointing backwards so because we need to
+ 
+
+ align:start position:0%
+pointing backwards so because we need to
+attach this to something else uh these
+
+ align:start position:0%
+attach this to something else uh these
+ 
+
+ align:start position:0%
+attach this to something else uh these
+all have very particular angles but it
+
+ align:start position:0%
+all have very particular angles but it
+ 
+
+ align:start position:0%
+all have very particular angles but it
+turns out that will be okay one more
+
+ align:start position:0%
+turns out that will be okay one more
+ 
+
+ align:start position:0%
+turns out that will be okay one more
+Gadget is a crossover Gadget this is
+
+ align:start position:0%
+Gadget is a crossover Gadget this is
+ 
+
+ align:start position:0%
+Gadget is a crossover Gadget this is
+very simple it is just one oh this is uh
+
+ align:start position:0%
+very simple it is just one oh this is uh
+ 
+
+ align:start position:0%
+very simple it is just one oh this is uh
+not the pre-folded one you do one pleat
+
+ align:start position:0%
+not the pre-folded one you do one pleat
+ 
+
+ align:start position:0%
+not the pre-folded one you do one pleat
+and then you do the other pleet uh and
+
+ align:start position:0%
+and then you do the other pleet uh and
+ 
+
+ align:start position:0%
+and then you do the other pleet uh and
+you can see from the crease pattern you
+
+ align:start position:0%
+you can see from the crease pattern you
+ 
+
+ align:start position:0%
+you can see from the crease pattern you
+have to do this pleet and then do this
+
+ align:start position:0%
+have to do this pleet and then do this
+ 
+
+ align:start position:0%
+have to do this pleet and then do this
+ple but it's completely independent I
+
+ align:start position:0%
+ple but it's completely independent I
+ 
+
+ align:start position:0%
+ple but it's completely independent I
+could do each ple either way it doesn't
+
+ align:start position:0%
+could do each ple either way it doesn't
+ 
+
+ align:start position:0%
+could do each ple either way it doesn't
+affect the other one so that's crossover
+
+ align:start position:0%
+affect the other one so that's crossover
+ 
+
+ align:start position:0%
+affect the other one so that's crossover
+done easy this works with pretty much
+
+ align:start position:0%
+done easy this works with pretty much
+ 
+
+ align:start position:0%
+done easy this works with pretty much
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+angles uh and then it's just a matter of
+
+ align:start position:0%
+angles uh and then it's just a matter of
+ 
+
+ align:start position:0%
+angles uh and then it's just a matter of
+checking that you can fit all the
+
+ align:start position:0%
+checking that you can fit all the
+ 
+
+ align:start position:0%
+checking that you can fit all the
+gadgets together um this is something we
+
+ align:start position:0%
+gadgets together um this is something we
+ 
+
+ align:start position:0%
+gadgets together um this is something we
+did in our book to get a picture of how
+
+ align:start position:0%
+did in our book to get a picture of how
+ 
+
+ align:start position:0%
+did in our book to get a picture of how
+everything works but in general the idea
+
+ align:start position:0%
+everything works but in general the idea
+ 
+
+ align:start position:0%
+everything works but in general the idea
+is on the left side of the page we have
+
+ align:start position:0%
+is on the left side of the page we have
+ 
+
+ align:start position:0%
+is on the left side of the page we have
+all of our variables those are just
+
+ align:start position:0%
+all of our variables those are just
+ 
+
+ align:start position:0%
+all of our variables those are just
+wires so they can go one way or the
+
+ align:start position:0%
+wires so they can go one way or the
+ 
+
+ align:start position:0%
+wires so they can go one way or the
+other so the idea is uh here is X2 we
+
+ align:start position:0%
+other so the idea is uh here is X2 we
+ 
+
+ align:start position:0%
+other so the idea is uh here is X2 we
+just I just want to bend it so it's
+
+ align:start position:0%
+just I just want to bend it so it's
+ 
+
+ align:start position:0%
+just I just want to bend it so it's
+pointing down Wards so I'm going to use
+
+ align:start position:0%
+pointing down Wards so I'm going to use
+ 
+
+ align:start position:0%
+pointing down Wards so I'm going to use
+the splitter SL negation Gadget so we
+
+ align:start position:0%
+the splitter SL negation Gadget so we
+ 
+
+ align:start position:0%
+the splitter SL negation Gadget so we
+get this copy of X2 just going off it's
+
+ align:start position:0%
+get this copy of X2 just going off it's
+ 
+
+ align:start position:0%
+get this copy of X2 just going off it's
+going to go up to the top of the page no
+
+ align:start position:0%
+going to go up to the top of the page no
+ 
+
+ align:start position:0%
+going to go up to the top of the page no
+big deal just throw it away then we're
+
+ align:start position:0%
+big deal just throw it away then we're
+ 
+
+ align:start position:0%
+big deal just throw it away then we're
+going to go over here something happens
+
+ align:start position:0%
+going to go over here something happens
+ 
+
+ align:start position:0%
+going to go over here something happens
+to cross us but we don't care uh now
+
+ align:start position:0%
+to cross us but we don't care uh now
+ 
+
+ align:start position:0%
+to cross us but we don't care uh now
+what I would like to do looks like this
+
+ align:start position:0%
+what I would like to do looks like this
+ 
+
+ align:start position:0%
+what I would like to do looks like this
+Clause involves X2 so I'm going to do
+
+ align:start position:0%
+Clause involves X2 so I'm going to do
+ 
+
+ align:start position:0%
+Clause involves X2 so I'm going to do
+this funny kind of turnaround
+
+ align:start position:0%
+this funny kind of turnaround
+ 
+
+ align:start position:0%
+this funny kind of turnaround
+thingy uh which will end up making a
+
+ align:start position:0%
+thingy uh which will end up making a
+ 
+
+ align:start position:0%
+thingy uh which will end up making a
+copy of this variable pointing straight
+
+ align:start position:0%
+copy of this variable pointing straight
+ 
+
+ align:start position:0%
+copy of this variable pointing straight
+up and also we'll make a copy of the
+
+ align:start position:0%
+up and also we'll make a copy of the
+ 
+
+ align:start position:0%
+up and also we'll make a copy of the
+variable pointing in this direction and
+
+ align:start position:0%
+variable pointing in this direction and
+ 
+
+ align:start position:0%
+variable pointing in this direction and
+so in general I'm going to keep doing
+
+ align:start position:0%
+so in general I'm going to keep doing
+ 
+
+ align:start position:0%
+so in general I'm going to keep doing
+that uh and whenever I need a copy I'll
+
+ align:start position:0%
+that uh and whenever I need a copy I'll
+ 
+
+ align:start position:0%
+that uh and whenever I need a copy I'll
+just use an appropriate parity of turns
+
+ align:start position:0%
+just use an appropriate parity of turns
+ 
+
+ align:start position:0%
+just use an appropriate parity of turns
+to get a positive copy uh so this is
+
+ align:start position:0%
+to get a positive copy uh so this is
+ 
+
+ align:start position:0%
+to get a positive copy uh so this is
+negated uh and then this is a copy of
+
+ align:start position:0%
+negated uh and then this is a copy of
+ 
+
+ align:start position:0%
+negated uh and then this is a copy of
+the negation and then we flip it one two
+
+ align:start position:0%
+the negation and then we flip it one two
+ 
+
+ align:start position:0%
+the negation and then we flip it one two
+three times so in the end it should be
+
+ align:start position:0%
+three times so in the end it should be
+ 
+
+ align:start position:0%
+three times so in the end it should be
+positive this is the tricky part to
+
+ align:start position:0%
+positive this is the tricky part to
+ 
+
+ align:start position:0%
+positive this is the tricky part to
+check here we have uh a not all equal
+
+ align:start position:0%
+check here we have uh a not all equal
+ 
+
+ align:start position:0%
+check here we have uh a not all equal
+threat Clause where three things come
+
+ align:start position:0%
+threat Clause where three things come
+ 
+
+ align:start position:0%
+threat Clause where three things come
+together and that's going to be foldable
+
+ align:start position:0%
+together and that's going to be foldable
+ 
+
+ align:start position:0%
+together and that's going to be foldable
+if and only if the three variables that
+
+ align:start position:0%
+if and only if the three variables that
+ 
+
+ align:start position:0%
+if and only if the three variables that
+that we're combining have a reasonable
+
+ align:start position:0%
+that we're combining have a reasonable
+ 
+
+ align:start position:0%
+that we're combining have a reasonable
+assignment and then we just have to copy
+
+ align:start position:0%
+assignment and then we just have to copy
+ 
+
+ align:start position:0%
+assignment and then we just have to copy
+all these things and get them to meet
+
+ align:start position:0%
+all these things and get them to meet
+ 
+
+ align:start position:0%
+all these things and get them to meet
+all at the those nexuses at the top so
+
+ align:start position:0%
+all at the those nexuses at the top so
+ 
+
+ align:start position:0%
+all at the those nexuses at the top so
+definitely tricky to make sure this
+
+ align:start position:0%
+definitely tricky to make sure this
+ 
+
+ align:start position:0%
+definitely tricky to make sure this
+works to guarantee all of the
+
+ align:start position:0%
+works to guarantee all of the
+ 
+
+ align:start position:0%
+works to guarantee all of the
+coordinates can be encoded with a
+
+ align:start position:0%
+coordinates can be encoded with a
+ 
+
+ align:start position:0%
+coordinates can be encoded with a
+polinomial number of bits and therefore
+
+ align:start position:0%
+polinomial number of bits and therefore
+ 
+
+ align:start position:0%
+polinomial number of bits and therefore
+this is a strongly NP hard proof but I'm
+
+ align:start position:0%
+this is a strongly NP hard proof but I'm
+ 
+
+ align:start position:0%
+this is a strongly NP hard proof but I'm
+going to wave my hands at those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+details
+
+ align:start position:0%
+details
+ 
+
+ align:start position:0%
+details
+questions the if it's any constellation
+
+ align:start position:0%
+questions the if it's any constellation
+ 
+
+ align:start position:0%
+questions the if it's any constellation
+the original proof also alwayss it
+
+ align:start position:0%
+the original proof also alwayss it
+ 
+
+ align:start position:0%
+the original proof also alwayss it
+handed these details but if you have a
+
+ align:start position:0%
+handed these details but if you have a
+ 
+
+ align:start position:0%
+handed these details but if you have a
+fold pattern like this can you tell what
+
+ align:start position:0%
+fold pattern like this can you tell what
+ 
+
+ align:start position:0%
+fold pattern like this can you tell what
+order you would need to do the folds in
+
+ align:start position:0%
+order you would need to do the folds in
+ 
+
+ align:start position:0%
+order you would need to do the folds in
+there's no such thing as order of the
+
+ align:start position:0%
+there's no such thing as order of the
+ 
+
+ align:start position:0%
+there's no such thing as order of the
+folds here all of the folds would be
+
+ align:start position:0%
+folds here all of the folds would be
+ 
+
+ align:start position:0%
+folds here all of the folds would be
+folded simultaneously more or less
+
+ align:start position:0%
+folded simultaneously more or less
+ 
+
+ align:start position:0%
+folded simultaneously more or less
+instantaneously instantaneously to make
+
+ align:start position:0%
+instantaneously instantaneously to make
+ 
+
+ align:start position:0%
+instantaneously instantaneously to make
+it even more precise so here was really
+
+ align:start position:0%
+it even more precise so here was really
+ 
+
+ align:start position:0%
+it even more precise so here was really
+a question of whether there is a flat
+
+ align:start position:0%
+a question of whether there is a flat
+ 
+
+ align:start position:0%
+a question of whether there is a flat
+folded State we're not worried about the
+
+ align:start position:0%
+folded State we're not worried about the
+ 
+
+ align:start position:0%
+folded State we're not worried about the
+motion to get there that's another topic
+
+ align:start position:0%
+motion to get there that's another topic
+ 
+
+ align:start position:0%
+motion to get there that's another topic
+which you should take a49 if you're
+
+ align:start position:0%
+which you should take a49 if you're
+ 
+
+ align:start position:0%
+which you should take a49 if you're
+curious about um but these kinds of
+
+ align:start position:0%
+curious about um but these kinds of
+ 
+
+ align:start position:0%
+curious about um but these kinds of
+patterns there you can't do one thing
+
+ align:start position:0%
+patterns there you can't do one thing
+ 
+
+ align:start position:0%
+patterns there you can't do one thing
+because there's no pleat that goes all
+
+ align:start position:0%
+because there's no pleat that goes all
+ 
+
+ align:start position:0%
+because there's no pleat that goes all
+the way so that's life unlike the
+
+ align:start position:0%
+the way so that's life unlike the
+ 
+
+ align:start position:0%
+the way so that's life unlike the
+folding problem we saw two classes ago
+
+ align:start position:0%
+folding problem we saw two classes ago
+ 
+
+ align:start position:0%
+folding problem we saw two classes ago
+the map folding where we're were doing
+
+ align:start position:0%
+the map folding where we're were doing
+ 
+
+ align:start position:0%
+the map folding where we're were doing
+one then the other there in the notion
+
+ align:start position:0%
+one then the other there in the notion
+ 
+
+ align:start position:0%
+one then the other there in the notion
+of simple folds there's an ordering but
+
+ align:start position:0%
+of simple folds there's an ordering but
+ 
+
+ align:start position:0%
+of simple folds there's an ordering but
+in general origami there is no
+
+ align:start position:0%
+in general origami there is no
+ 
+
+ align:start position:0%
+in general origami there is no
+ordering
+
+ align:start position:0%
+ordering
+ 
+
+ align:start position:0%
+ordering
+cool good that is origami stuff um the
+
+ align:start position:0%
+cool good that is origami stuff um the
+ 
+
+ align:start position:0%
+cool good that is origami stuff um the
+next topic is a more kind of graph
+
+ align:start position:0%
+next topic is a more kind of graph
+ 
+
+ align:start position:0%
+next topic is a more kind of graph
+theoretic basic question uh but it will
+
+ align:start position:0%
+theoretic basic question uh but it will
+ 
+
+ align:start position:0%
+theoretic basic question uh but it will
+also relate to a puzzle um and this the
+
+ align:start position:0%
+also relate to a puzzle um and this the
+ 
+
+ align:start position:0%
+also relate to a puzzle um and this the
+idea of vertex disjoint paths this is in
+
+ align:start position:0%
+idea of vertex disjoint paths this is in
+ 
+
+ align:start position:0%
+idea of vertex disjoint paths this is in
+uh Jason Lynch's early work before he
+
+ align:start position:0%
+uh Jason Lynch's early work before he
+ 
+
+ align:start position:0%
+uh Jason Lynch's early work before he
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+born I assume no relation um 1975 uh so
+
+ align:start position:0%
+born I assume no relation um 1975 uh so
+ 
+
+ align:start position:0%
+born I assume no relation um 1975 uh so
+early days of NP completeness uh this
+
+ align:start position:0%
+early days of NP completeness uh this
+ 
+
+ align:start position:0%
+early days of NP completeness uh this
+problem vertex disjoint paths uh in a
+
+ align:start position:0%
+problem vertex disjoint paths uh in a
+ 
+
+ align:start position:0%
+problem vertex disjoint paths uh in a
+graph As proved and be complete so uh
+
+ align:start position:0%
+graph As proved and be complete so uh
+ 
+
+ align:start position:0%
+graph As proved and be complete so uh
+the problem is I give you a bunch of
+
+ align:start position:0%
+the problem is I give you a bunch of
+ 
+
+ align:start position:0%
+the problem is I give you a bunch of
+terminal pairs via V1 V1 Prime V2 V2
+
+ align:start position:0%
+terminal pairs via V1 V1 Prime V2 V2
+ 
+
+ align:start position:0%
+terminal pairs via V1 V1 Prime V2 V2
+Prime and so on C1 C1 prime a bunch ofir
+
+ align:start position:0%
+Prime and so on C1 C1 prime a bunch ofir
+ 
+
+ align:start position:0%
+Prime and so on C1 C1 prime a bunch ofir
+pairs of vertices and I want to connect
+
+ align:start position:0%
+pairs of vertices and I want to connect
+ 
+
+ align:start position:0%
+pairs of vertices and I want to connect
+the pairs by paths so I want to find a
+
+ align:start position:0%
+the pairs by paths so I want to find a
+ 
+
+ align:start position:0%
+the pairs by paths so I want to find a
+path from V1 to V1 Prime and so on so
+
+ align:start position:0%
+path from V1 to V1 Prime and so on so
+ 
+
+ align:start position:0%
+path from V1 to V1 Prime and so on so
+that those paths are all vertex
+
+ align:start position:0%
+that those paths are all vertex
+ 
+
+ align:start position:0%
+that those paths are all vertex
+disjoint here's the hardness proof super
+
+ align:start position:0%
+disjoint here's the hardness proof super
+ 
+
+ align:start position:0%
+disjoint here's the hardness proof super
+simple this is like one of the easiest
+
+ align:start position:0%
+simple this is like one of the easiest
+ 
+
+ align:start position:0%
+simple this is like one of the easiest
+thre Set uh reductions this is not the
+
+ align:start position:0%
+thre Set uh reductions this is not the
+ 
+
+ align:start position:0%
+thre Set uh reductions this is not the
+end of their paper they do more
+
+ align:start position:0%
+end of their paper they do more
+ 
+
+ align:start position:0%
+end of their paper they do more
+interesting things which I will get to
+
+ align:start position:0%
+interesting things which I will get to
+ 
+
+ align:start position:0%
+interesting things which I will get to
+but first let's understand this one so
+
+ align:start position:0%
+but first let's understand this one so
+ 
+
+ align:start position:0%
+but first let's understand this one so
+uh this is a graph and I've drawn it in
+
+ align:start position:0%
+uh this is a graph and I've drawn it in
+ 
+
+ align:start position:0%
+uh this is a graph and I've drawn it in
+a funny way uh these are vertices these
+
+ align:start position:0%
+a funny way uh these are vertices these
+ 
+
+ align:start position:0%
+a funny way uh these are vertices these
+are vertices these are not vertices
+
+ align:start position:0%
+are vertices these are not vertices
+ 
+
+ align:start position:0%
+are vertices these are not vertices
+those are just in the plane they happen
+
+ align:start position:0%
+those are just in the plane they happen
+ 
+
+ align:start position:0%
+those are just in the plane they happen
+to cross but there's no vertex there so
+
+ align:start position:0%
+to cross but there's no vertex there so
+ 
+
+ align:start position:0%
+to cross but there's no vertex there so
+it's just a straight path all the way
+
+ align:start position:0%
+it's just a straight path all the way
+ 
+
+ align:start position:0%
+it's just a straight path all the way
+through um kind of similar to what we
+
+ align:start position:0%
+through um kind of similar to what we
+ 
+
+ align:start position:0%
+through um kind of similar to what we
+did with football the idea is that if
+
+ align:start position:0%
+did with football the idea is that if
+ 
+
+ align:start position:0%
+did with football the idea is that if
+from V1 to V1 Prime there are two paths
+
+ align:start position:0%
+from V1 to V1 Prime there are two paths
+ 
+
+ align:start position:0%
+from V1 to V1 Prime there are two paths
+at least that stay here you could try to
+
+ align:start position:0%
+at least that stay here you could try to
+ 
+
+ align:start position:0%
+at least that stay here you could try to
+go into a clause path and wreck havoc
+
+ align:start position:0%
+go into a clause path and wreck havoc
+ 
+
+ align:start position:0%
+go into a clause path and wreck havoc
+but I think you will be doomed I hope so
+
+ align:start position:0%
+but I think you will be doomed I hope so
+ 
+
+ align:start position:0%
+but I think you will be doomed I hope so
+the idea is V1 uh maybe you choose the
+
+ align:start position:0%
+the idea is V1 uh maybe you choose the
+ 
+
+ align:start position:0%
+the idea is V1 uh maybe you choose the
+blue path that will prevent C3 from
+
+ align:start position:0%
+blue path that will prevent C3 from
+ 
+
+ align:start position:0%
+blue path that will prevent C3 from
+using that path because there's an
+
+ align:start position:0%
+using that path because there's an
+ 
+
+ align:start position:0%
+using that path because there's an
+intersection here it won't prevent
+
+ align:start position:0%
+intersection here it won't prevent
+ 
+
+ align:start position:0%
+intersection here it won't prevent
+anybody else because there's no other
+
+ align:start position:0%
+anybody else because there's no other
+ 
+
+ align:start position:0%
+anybody else because there's no other
+vertices here so I use the blue path C3
+
+ align:start position:0%
+vertices here so I use the blue path C3
+ 
+
+ align:start position:0%
+vertices here so I use the blue path C3
+cannot use that path if I use the red
+
+ align:start position:0%
+cannot use that path if I use the red
+ 
+
+ align:start position:0%
+cannot use that path if I use the red
+path C1 can't use this one C2 can't use
+
+ align:start position:0%
+path C1 can't use this one C2 can't use
+ 
+
+ align:start position:0%
+path C1 can't use this one C2 can't use
+this one so again we are blocking the
+
+ align:start position:0%
+this one so again we are blocking the
+ 
+
+ align:start position:0%
+this one so again we are blocking the
+thing that it would be setting false so
+
+ align:start position:0%
+thing that it would be setting false so
+ 
+
+ align:start position:0%
+thing that it would be setting false so
+that means uh let's say red I forget in
+
+ align:start position:0%
+that means uh let's say red I forget in
+ 
+
+ align:start position:0%
+that means uh let's say red I forget in
+this picture let's say red is
+
+ align:start position:0%
+this picture let's say red is
+ 
+
+ align:start position:0%
+this picture let's say red is
+true uh then C1 has a V1 bar in it uh C1
+
+ align:start position:0%
+true uh then C1 has a V1 bar in it uh C1
+ 
+
+ align:start position:0%
+true uh then C1 has a V1 bar in it uh C1
+is happy if you choose the blue path but
+
+ align:start position:0%
+is happy if you choose the blue path but
+ 
+
+ align:start position:0%
+is happy if you choose the blue path but
+it's not happy if you choose the red
+
+ align:start position:0%
+it's not happy if you choose the red
+ 
+
+ align:start position:0%
+it's not happy if you choose the red
+path now C1 to C1 Prime only has to be
+
+ align:start position:0%
+path now C1 to C1 Prime only has to be
+ 
+
+ align:start position:0%
+path now C1 to C1 Prime only has to be
+happy uh if one of these three things
+
+ align:start position:0%
+happy uh if one of these three things
+ 
+
+ align:start position:0%
+happy uh if one of these three things
+are happy that's three set at least one
+
+ align:start position:0%
+are happy that's three set at least one
+ 
+
+ align:start position:0%
+are happy that's three set at least one
+of the things should be set correctly
+
+ align:start position:0%
+of the things should be set correctly
+ 
+
+ align:start position:0%
+of the things should be set correctly
+then there is a path from C1 to C1 prime
+
+ align:start position:0%
+then there is a path from C1 to C1 prime
+ 
+
+ align:start position:0%
+then there is a path from C1 to C1 prime
+otherwise there'll be vertex
+
+ align:start position:0%
+otherwise there'll be vertex
+ 
+
+ align:start position:0%
+otherwise there'll be vertex
+intersections you won't have vertex
+
+ align:start position:0%
+intersections you won't have vertex
+ 
+
+ align:start position:0%
+intersections you won't have vertex
+distrain paths okay so in a graph done
+
+ align:start position:0%
+distrain paths okay so in a graph done
+ 
+
+ align:start position:0%
+distrain paths okay so in a graph done
+now let's make it a planer graph where
+
+ align:start position:0%
+now let's make it a planer graph where
+ 
+
+ align:start position:0%
+now let's make it a planer graph where
+things get fun so this is the original
+
+ align:start position:0%
+things get fun so this is the original
+ 
+
+ align:start position:0%
+things get fun so this is the original
+Gadget I've stared at it for many hours
+
+ align:start position:0%
+Gadget I've stared at it for many hours
+ 
+
+ align:start position:0%
+Gadget I've stared at it for many hours
+but it's it's actually pretty simple
+
+ align:start position:0%
+but it's it's actually pretty simple
+ 
+
+ align:start position:0%
+but it's it's actually pretty simple
+after you stare at it for enough hours
+
+ align:start position:0%
+after you stare at it for enough hours
+ 
+
+ align:start position:0%
+after you stare at it for enough hours
+let me try to convince you of that uh so
+
+ align:start position:0%
+let me try to convince you of that uh so
+ 
+
+ align:start position:0%
+let me try to convince you of that uh so
+we're going to follow I'm going to
+
+ align:start position:0%
+we're going to follow I'm going to
+ 
+
+ align:start position:0%
+we're going to follow I'm going to
+follow the same kind of outline
+
+ align:start position:0%
+follow the same kind of outline
+ 
+
+ align:start position:0%
+follow the same kind of outline
+here uh but we have to get rid of these
+
+ align:start position:0%
+here uh but we have to get rid of these
+ 
+
+ align:start position:0%
+here uh but we have to get rid of these
+These are fine those are intersections
+
+ align:start position:0%
+These are fine those are intersections
+ 
+
+ align:start position:0%
+These are fine those are intersections
+okay but these crossovers we need to
+
+ align:start position:0%
+okay but these crossovers we need to
+ 
+
+ align:start position:0%
+okay but these crossovers we need to
+build a crossover Gadget so the idea is
+
+ align:start position:0%
+build a crossover Gadget so the idea is
+ 
+
+ align:start position:0%
+build a crossover Gadget so the idea is
+instead of V1 to V1 Prime being a single
+
+ align:start position:0%
+instead of V1 to V1 Prime being a single
+ 
+
+ align:start position:0%
+instead of V1 to V1 Prime being a single
+path that's that's going to be a problem
+
+ align:start position:0%
+path that's that's going to be a problem
+ 
+
+ align:start position:0%
+path that's that's going to be a problem
+instead of that I'm going to have it be
+
+ align:start position:0%
+instead of that I'm going to have it be
+ 
+
+ align:start position:0%
+instead of that I'm going to have it be
+several paths and they are going to be
+
+ align:start position:0%
+several paths and they are going to be
+ 
+
+ align:start position:0%
+several paths and they are going to be
+uh nested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brackets
+
+ align:start position:0%
+brackets
+ 
+
+ align:start position:0%
+brackets
+CH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay this is the kind of um thing
+
+ align:start position:0%
+uh okay this is the kind of um thing
+ 
+
+ align:start position:0%
+uh okay this is the kind of um thing
+we're imagining we have some vertex
+
+ align:start position:0%
+we're imagining we have some vertex
+ 
+
+ align:start position:0%
+we're imagining we have some vertex
+pairs which can connect like
+
+ align:start position:0%
+pairs which can connect like
+ 
+
+ align:start position:0%
+pairs which can connect like
+this and there are two ways to connect
+
+ align:start position:0%
+this and there are two ways to connect
+ 
+
+ align:start position:0%
+this and there are two ways to connect
+them in this in what we'll end up being
+
+ align:start position:0%
+them in this in what we'll end up being
+ 
+
+ align:start position:0%
+them in this in what we'll end up being
+the diagram we could connect
+
+ align:start position:0%
+the diagram we could connect
+ 
+
+ align:start position:0%
+the diagram we could connect
+them uh like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this notice I'm still connecting the
+
+ align:start position:0%
+this notice I'm still connecting the
+ 
+
+ align:start position:0%
+this notice I'm still connecting the
+same pairs if I do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and the whites do not intersect
+
+ align:start position:0%
+right and the whites do not intersect
+ 
+
+ align:start position:0%
+right and the whites do not intersect
+each other their vertex is joint the
+
+ align:start position:0%
+each other their vertex is joint the
+ 
+
+ align:start position:0%
+each other their vertex is joint the
+Reds do not intersect each other their
+
+ align:start position:0%
+Reds do not intersect each other their
+ 
+
+ align:start position:0%
+Reds do not intersect each other their
+vertex is joint but if you tried to
+
+ align:start position:0%
+vertex is joint but if you tried to
+ 
+
+ align:start position:0%
+vertex is joint but if you tried to
+switch from right to Red you'd get
+
+ align:start position:0%
+switch from right to Red you'd get
+ 
+
+ align:start position:0%
+switch from right to Red you'd get
+intersections right so with the same
+
+ align:start position:0%
+intersections right so with the same
+ 
+
+ align:start position:0%
+intersections right so with the same
+there's exactly two settings here so
+
+ align:start position:0%
+there's exactly two settings here so
+ 
+
+ align:start position:0%
+there's exactly two settings here so
+this is a wire once I choose over here
+
+ align:start position:0%
+this is a wire once I choose over here
+ 
+
+ align:start position:0%
+this is a wire once I choose over here
+white or red all the others are forced
+
+ align:start position:0%
+white or red all the others are forced
+ 
+
+ align:start position:0%
+white or red all the others are forced
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+alternate uh sorry once I choose up or
+
+ align:start position:0%
+alternate uh sorry once I choose up or
+ 
+
+ align:start position:0%
+alternate uh sorry once I choose up or
+down the rest are forced to alternate up
+
+ align:start position:0%
+down the rest are forced to alternate up
+ 
+
+ align:start position:0%
+down the rest are forced to alternate up
+or down if I choose white here they're
+
+ align:start position:0%
+or down if I choose white here they're
+ 
+
+ align:start position:0%
+or down if I choose white here they're
+all white I choose red they're all red
+
+ align:start position:0%
+all white I choose red they're all red
+ 
+
+ align:start position:0%
+all white I choose red they're all red
+this is independent for each variable so
+
+ align:start position:0%
+this is independent for each variable so
+ 
+
+ align:start position:0%
+this is independent for each variable so
+independent for each wire so that's
+
+ align:start position:0%
+independent for each wire so that's
+ 
+
+ align:start position:0%
+independent for each wire so that's
+what's going on here and if you look
+
+ align:start position:0%
+what's going on here and if you look
+ 
+
+ align:start position:0%
+what's going on here and if you look
+closely at the Bold lines you've got a
+
+ align:start position:0%
+closely at the Bold lines you've got a
+ 
+
+ align:start position:0%
+closely at the Bold lines you've got a
+bracket here from V1 to X1 then you've
+
+ align:start position:0%
+bracket here from V1 to X1 then you've
+ 
+
+ align:start position:0%
+bracket here from V1 to X1 then you've
+got a bracket here from X2 to X3 then a
+
+ align:start position:0%
+got a bracket here from X2 to X3 then a
+ 
+
+ align:start position:0%
+got a bracket here from X2 to X3 then a
+bracket here from X4 but in general
+
+ align:start position:0%
+bracket here from X4 but in general
+ 
+
+ align:start position:0%
+bracket here from X4 but in general
+there would be lots of those
+
+ align:start position:0%
+there would be lots of those
+ 
+
+ align:start position:0%
+there would be lots of those
+brackets going all the way down the the
+
+ align:start position:0%
+brackets going all the way down the the
+ 
+
+ align:start position:0%
+brackets going all the way down the the
+picture and the cool thing about this is
+
+ align:start position:0%
+picture and the cool thing about this is
+ 
+
+ align:start position:0%
+picture and the cool thing about this is
+you get uh the ability to cross over
+
+ align:start position:0%
+you get uh the ability to cross over
+ 
+
+ align:start position:0%
+you get uh the ability to cross over
+because now if I just restrict this
+
+ align:start position:0%
+because now if I just restrict this
+ 
+
+ align:start position:0%
+because now if I just restrict this
+picture it's hard to see if I just
+
+ align:start position:0%
+picture it's hard to see if I just
+ 
+
+ align:start position:0%
+picture it's hard to see if I just
+restrict to the white
+
+ align:start position:0%
+restrict to the white
+ 
+
+ align:start position:0%
+restrict to the white
+part uh you can go from top to bottom
+
+ align:start position:0%
+part uh you can go from top to bottom
+ 
+
+ align:start position:0%
+part uh you can go from top to bottom
+you just need an appropriate kind of
+
+ align:start position:0%
+you just need an appropriate kind of
+ 
+
+ align:start position:0%
+you just need an appropriate kind of
+zigzag that will let you go from up here
+
+ align:start position:0%
+zigzag that will let you go from up here
+ 
+
+ align:start position:0%
+zigzag that will let you go from up here
+to down there without intersections and
+
+ align:start position:0%
+to down there without intersections and
+ 
+
+ align:start position:0%
+to down there without intersections and
+that's what's happening with this line
+
+ align:start position:0%
+that's what's happening with this line
+ 
+
+ align:start position:0%
+that's what's happening with this line
+it's going over around the brackets and
+
+ align:start position:0%
+it's going over around the brackets and
+ 
+
+ align:start position:0%
+it's going over around the brackets and
+down and so the C1 to C1 Prime can
+
+ align:start position:0%
+down and so the C1 to C1 Prime can
+ 
+
+ align:start position:0%
+down and so the C1 to C1 Prime can
+remain a single path it can always get
+
+ align:start position:0%
+remain a single path it can always get
+ 
+
+ align:start position:0%
+remain a single path it can always get
+through uh if you have this gadget then
+
+ align:start position:0%
+through uh if you have this gadget then
+ 
+
+ align:start position:0%
+through uh if you have this gadget then
+you can have an intersection with no
+
+ align:start position:0%
+you can have an intersection with no
+ 
+
+ align:start position:0%
+you can have an intersection with no
+trouble um but V1 is still communicating
+
+ align:start position:0%
+trouble um but V1 is still communicating
+ 
+
+ align:start position:0%
+trouble um but V1 is still communicating
+information down the line of one setting
+
+ align:start position:0%
+information down the line of one setting
+ 
+
+ align:start position:0%
+information down the line of one setting
+or the other zero or
+
+ align:start position:0%
+or the other zero or
+ 
+
+ align:start position:0%
+or the other zero or
+one okay that's there's some details to
+
+ align:start position:0%
+one okay that's there's some details to
+ 
+
+ align:start position:0%
+one okay that's there's some details to
+check there but uh that's the idea okay
+
+ align:start position:0%
+check there but uh that's the idea okay
+ 
+
+ align:start position:0%
+check there but uh that's the idea okay
+and that's the end of the Lynch paper
+
+ align:start position:0%
+and that's the end of the Lynch paper
+ 
+
+ align:start position:0%
+and that's the end of the Lynch paper
+now uh we were looking at this earlier
+
+ align:start position:0%
+now uh we were looking at this earlier
+ 
+
+ align:start position:0%
+now uh we were looking at this earlier
+this year and we can prove an even
+
+ align:start position:0%
+this year and we can prove an even
+ 
+
+ align:start position:0%
+this year and we can prove an even
+stronger result which is what you might
+
+ align:start position:0%
+stronger result which is what you might
+ 
+
+ align:start position:0%
+stronger result which is what you might
+call planer vertex disjoint paths in a
+
+ align:start position:0%
+call planer vertex disjoint paths in a
+ 
+
+ align:start position:0%
+call planer vertex disjoint paths in a
+rectangle uh but it's not so the idea is
+
+ align:start position:0%
+rectangle uh but it's not so the idea is
+ 
+
+ align:start position:0%
+rectangle uh but it's not so the idea is
+you have a rectangle of 1x one squares
+
+ align:start position:0%
+you have a rectangle of 1x one squares
+ 
+
+ align:start position:0%
+you have a rectangle of 1x one squares
+each 1X one square could be a terminal
+
+ align:start position:0%
+each 1X one square could be a terminal
+ 
+
+ align:start position:0%
+each 1X one square could be a terminal
+and a teral pair or it could just be a
+
+ align:start position:0%
+and a teral pair or it could just be a
+ 
+
+ align:start position:0%
+and a teral pair or it could just be a
+blank space that you can R paths through
+
+ align:start position:0%
+blank space that you can R paths through
+ 
+
+ align:start position:0%
+blank space that you can R paths through
+and my
+
+ align:start position:0%
+and my
+ 
+
+ align:start position:0%
+and my
+goal uh is to find vertex D joint paths
+
+ align:start position:0%
+goal uh is to find vertex D joint paths
+ 
+
+ align:start position:0%
+goal uh is to find vertex D joint paths
+connecting all the terminal pairs but
+
+ align:start position:0%
+connecting all the terminal pairs but
+ 
+
+ align:start position:0%
+connecting all the terminal pairs but
+furthermore I want every square of the
+
+ align:start position:0%
+furthermore I want every square of the
+ 
+
+ align:start position:0%
+furthermore I want every square of the
+grid to be occupied by a path so it's
+
+ align:start position:0%
+grid to be occupied by a path so it's
+ 
+
+ align:start position:0%
+grid to be occupied by a path so it's
+sort of it's not quite hamiltonian path
+
+ align:start position:0%
+sort of it's not quite hamiltonian path
+ 
+
+ align:start position:0%
+sort of it's not quite hamiltonian path
+it's like you have a bunch of paths
+
+ align:start position:0%
+it's like you have a bunch of paths
+ 
+
+ align:start position:0%
+it's like you have a bunch of paths
+where uh that collectively fill the
+
+ align:start position:0%
+where uh that collectively fill the
+ 
+
+ align:start position:0%
+where uh that collectively fill the
+entire
+
+ align:start position:0%
+entire
+ 
+
+ align:start position:0%
+entire
+grid why uh it's motivated by a puzzle
+
+ align:start position:0%
+grid why uh it's motivated by a puzzle
+ 
+
+ align:start position:0%
+grid why uh it's motivated by a puzzle
+but it's natural enough this is a more
+
+ align:start position:0%
+but it's natural enough this is a more
+ 
+
+ align:start position:0%
+but it's natural enough this is a more
+specialized version
+
+ align:start position:0%
+specialized version
+ 
+
+ align:start position:0%
+specialized version
+um so this is also EMP hard and we're
+
+ align:start position:0%
+um so this is also EMP hard and we're
+ 
+
+ align:start position:0%
+um so this is also EMP hard and we're
+going to mimic the same proof and this
+
+ align:start position:0%
+going to mimic the same proof and this
+ 
+
+ align:start position:0%
+going to mimic the same proof and this
+for example is a gadget to do say this
+
+ align:start position:0%
+for example is a gadget to do say this
+ 
+
+ align:start position:0%
+for example is a gadget to do say this
+little picture where you have two
+
+ align:start position:0%
+little picture where you have two
+ 
+
+ align:start position:0%
+little picture where you have two
+choices so maybe uh the V1 dot is
+
+ align:start position:0%
+choices so maybe uh the V1 dot is
+ 
+
+ align:start position:0%
+choices so maybe uh the V1 dot is
+actually here and the idea is you could
+
+ align:start position:0%
+actually here and the idea is you could
+ 
+
+ align:start position:0%
+actually here and the idea is you could
+either follow this path or you could
+
+ align:start position:0%
+either follow this path or you could
+ 
+
+ align:start position:0%
+either follow this path or you could
+follow this path and uh what's also
+
+ align:start position:0%
+follow this path and uh what's also
+ 
+
+ align:start position:0%
+follow this path and uh what's also
+drawn here are lots of other terminal
+
+ align:start position:0%
+drawn here are lots of other terminal
+ 
+
+ align:start position:0%
+drawn here are lots of other terminal
+pairs these are what you might call
+
+ align:start position:0%
+pairs these are what you might call
+ 
+
+ align:start position:0%
+pairs these are what you might call
+adjacent terminal pairs what you might
+
+ align:start position:0%
+adjacent terminal pairs what you might
+ 
+
+ align:start position:0%
+adjacent terminal pairs what you might
+also call obstacles because the paths
+
+ align:start position:0%
+also call obstacles because the paths
+ 
+
+ align:start position:0%
+also call obstacles because the paths
+have to be vertex joint no path can go
+
+ align:start position:0%
+have to be vertex joint no path can go
+ 
+
+ align:start position:0%
+have to be vertex joint no path can go
+through a
+
+ align:start position:0%
+through a
+ 
+
+ align:start position:0%
+through a
+terminal any of these dots serve as
+
+ align:start position:0%
+terminal any of these dots serve as
+ 
+
+ align:start position:0%
+terminal any of these dots serve as
+obstacles so we effectively simulate
+
+ align:start position:0%
+obstacles so we effectively simulate
+ 
+
+ align:start position:0%
+obstacles so we effectively simulate
+this blank space that you're not allowed
+
+ align:start position:0%
+this blank space that you're not allowed
+ 
+
+ align:start position:0%
+this blank space that you're not allowed
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+touch okay uh now the fun part is now
+
+ align:start position:0%
+touch okay uh now the fun part is now
+ 
+
+ align:start position:0%
+touch okay uh now the fun part is now
+maybe those terminal pairs are connected
+
+ align:start position:0%
+maybe those terminal pairs are connected
+ 
+
+ align:start position:0%
+maybe those terminal pairs are connected
+by the single edge that joins them and
+
+ align:start position:0%
+by the single edge that joins them and
+ 
+
+ align:start position:0%
+by the single edge that joins them and
+so doesn't get in the way but there are
+
+ align:start position:0%
+so doesn't get in the way but there are
+ 
+
+ align:start position:0%
+so doesn't get in the way but there are
+other possibilities drawn with these
+
+ align:start position:0%
+other possibilities drawn with these
+ 
+
+ align:start position:0%
+other possibilities drawn with these
+blue lines so instead of going here I
+
+ align:start position:0%
+blue lines so instead of going here I
+ 
+
+ align:start position:0%
+blue lines so instead of going here I
+could do this instead of going here I
+
+ align:start position:0%
+could do this instead of going here I
+ 
+
+ align:start position:0%
+could do this instead of going here I
+could do this and this and then if you
+
+ align:start position:0%
+could do this and this and then if you
+ 
+
+ align:start position:0%
+could do this and this and then if you
+look at this pict picture every pixel
+
+ align:start position:0%
+look at this pict picture every pixel
+ 
+
+ align:start position:0%
+look at this pict picture every pixel
+has a path through
+
+ align:start position:0%
+has a path through
+ 
+
+ align:start position:0%
+has a path through
+it in this case and then here's the
+
+ align:start position:0%
+it in this case and then here's the
+ 
+
+ align:start position:0%
+it in this case and then here's the
+other case again and now I'll fill this
+
+ align:start position:0%
+other case again and now I'll fill this
+ 
+
+ align:start position:0%
+other case again and now I'll fill this
+this these two pixels with this pair and
+
+ align:start position:0%
+this these two pixels with this pair and
+ 
+
+ align:start position:0%
+this these two pixels with this pair and
+now every pixel has a path through it
+
+ align:start position:0%
+now every pixel has a path through it
+ 
+
+ align:start position:0%
+now every pixel has a path through it
+that's my goal is to make sure every
+
+ align:start position:0%
+that's my goal is to make sure every
+ 
+
+ align:start position:0%
+that's my goal is to make sure every
+pixel has a path through it so we're
+
+ align:start position:0%
+pixel has a path through it so we're
+ 
+
+ align:start position:0%
+pixel has a path through it so we're
+just trying to preserve all the
+
+ align:start position:0%
+just trying to preserve all the
+ 
+
+ align:start position:0%
+just trying to preserve all the
+solutions we have here but with the
+
+ align:start position:0%
+solutions we have here but with the
+ 
+
+ align:start position:0%
+solutions we have here but with the
+additional constraint that all of the
+
+ align:start position:0%
+additional constraint that all of the
+ 
+
+ align:start position:0%
+additional constraint that all of the
+because we already know this is
+
+ align:start position:0%
+because we already know this is
+ 
+
+ align:start position:0%
+because we already know this is
+simulating uh three sets we already know
+
+ align:start position:0%
+simulating uh three sets we already know
+ 
+
+ align:start position:0%
+simulating uh three sets we already know
+it's hard uh we just now want to have
+
+ align:start position:0%
+it's hard uh we just now want to have
+ 
+
+ align:start position:0%
+it's hard uh we just now want to have
+this extra constraint that every pixel
+
+ align:start position:0%
+this extra constraint that every pixel
+ 
+
+ align:start position:0%
+this extra constraint that every pixel
+has a path through it and that we live
+
+ align:start position:0%
+has a path through it and that we live
+ 
+
+ align:start position:0%
+has a path through it and that we live
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+rectangle so this looks good um as you
+
+ align:start position:0%
+rectangle so this looks good um as you
+ 
+
+ align:start position:0%
+rectangle so this looks good um as you
+might imagine there's a little bit of
+
+ align:start position:0%
+might imagine there's a little bit of
+ 
+
+ align:start position:0%
+might imagine there's a little bit of
+finesse to make these gadgets work uh
+
+ align:start position:0%
+finesse to make these gadgets work uh
+ 
+
+ align:start position:0%
+finesse to make these gadgets work uh
+you notice some of these guys are
+
+ align:start position:0%
+you notice some of these guys are
+ 
+
+ align:start position:0%
+you notice some of these guys are
+oriented horizontally some of them are
+
+ align:start position:0%
+oriented horizontally some of them are
+ 
+
+ align:start position:0%
+oriented horizontally some of them are
+oriented vertically that's to make it
+
+ align:start position:0%
+oriented vertically that's to make it
+ 
+
+ align:start position:0%
+oriented vertically that's to make it
+work uh but this was easy uh what you're
+
+ align:start position:0%
+work uh but this was easy uh what you're
+ 
+
+ align:start position:0%
+work uh but this was easy uh what you're
+about to see is less easy so let's do
+
+ align:start position:0%
+about to see is less easy so let's do
+ 
+
+ align:start position:0%
+about to see is less easy so let's do
+the crossover Gadget because that's like
+
+ align:start position:0%
+the crossover Gadget because that's like
+ 
+
+ align:start position:0%
+the crossover Gadget because that's like
+the heart of everything and when we were
+
+ align:start position:0%
+the heart of everything and when we were
+ 
+
+ align:start position:0%
+the heart of everything and when we were
+starting on this uh I think this is in
+
+ align:start position:0%
+starting on this uh I think this is in
+ 
+
+ align:start position:0%
+starting on this uh I think this is in
+May uh I was very happy when I could
+
+ align:start position:0%
+May uh I was very happy when I could
+ 
+
+ align:start position:0%
+May uh I was very happy when I could
+finally draw this picture uh sorry this
+
+ align:start position:0%
+finally draw this picture uh sorry this
+ 
+
+ align:start position:0%
+finally draw this picture uh sorry this
+is actually the final Gadget which works
+
+ align:start position:0%
+is actually the final Gadget which works
+ 
+
+ align:start position:0%
+is actually the final Gadget which works
+um but you can see the same kind of
+
+ align:start position:0%
+um but you can see the same kind of
+ 
+
+ align:start position:0%
+um but you can see the same kind of
+picture uh we've got a bracket here that
+
+ align:start position:0%
+picture uh we've got a bracket here that
+ 
+
+ align:start position:0%
+picture uh we've got a bracket here that
+corresponds to this bracket here as
+
+ align:start position:0%
+corresponds to this bracket here as
+ 
+
+ align:start position:0%
+corresponds to this bracket here as
+another bracket here I've just sort of
+
+ align:start position:0%
+another bracket here I've just sort of
+ 
+
+ align:start position:0%
+another bracket here I've just sort of
+rounded it to integer coordinates and
+
+ align:start position:0%
+rounded it to integer coordinates and
+ 
+
+ align:start position:0%
+rounded it to integer coordinates and
+made sure that everything else can be
+
+ align:start position:0%
+made sure that everything else can be
+ 
+
+ align:start position:0%
+made sure that everything else can be
+filled in Easy right uh as a to uh in
+
+ align:start position:0%
+filled in Easy right uh as a to uh in
+ 
+
+ align:start position:0%
+filled in Easy right uh as a to uh in
+the sake of Education let me show you
+
+ align:start position:0%
+the sake of Education let me show you
+ 
+
+ align:start position:0%
+the sake of Education let me show you
+all the things that went wrong in this
+
+ align:start position:0%
+all the things that went wrong in this
+ 
+
+ align:start position:0%
+all the things that went wrong in this
+proof and because it was only a few
+
+ align:start position:0%
+proof and because it was only a few
+ 
+
+ align:start position:0%
+proof and because it was only a few
+months ago I mostly remember everything
+
+ align:start position:0%
+months ago I mostly remember everything
+ 
+
+ align:start position:0%
+months ago I mostly remember everything
+that went wrong which was a lot um so
+
+ align:start position:0%
+that went wrong which was a lot um so
+ 
+
+ align:start position:0%
+that went wrong which was a lot um so
+this was an early version of the gadget
+
+ align:start position:0%
+this was an early version of the gadget
+ 
+
+ align:start position:0%
+this was an early version of the gadget
+not actually the first one but it serves
+
+ align:start position:0%
+not actually the first one but it serves
+ 
+
+ align:start position:0%
+not actually the first one but it serves
+its purpose uh so here we have the two
+
+ align:start position:0%
+its purpose uh so here we have the two
+ 
+
+ align:start position:0%
+its purpose uh so here we have the two
+settings corresponding to these two
+
+ align:start position:0%
+settings corresponding to these two
+ 
+
+ align:start position:0%
+settings corresponding to these two
+settings the up and the down setting the
+
+ align:start position:0%
+settings the up and the down setting the
+ 
+
+ align:start position:0%
+settings the up and the down setting the
+true and the false setting we've got
+
+ align:start position:0%
+true and the false setting we've got
+ 
+
+ align:start position:0%
+true and the false setting we've got
+this path coming through in both cases
+
+ align:start position:0%
+this path coming through in both cases
+ 
+
+ align:start position:0%
+this path coming through in both cases
+it takes a slightly different path over
+
+ align:start position:0%
+it takes a slightly different path over
+ 
+
+ align:start position:0%
+it takes a slightly different path over
+here uh but the and the brackets are
+
+ align:start position:0%
+here uh but the and the brackets are
+ 
+
+ align:start position:0%
+here uh but the and the brackets are
+flipped
+
+ align:start position:0%
+flipped
+ 
+
+ align:start position:0%
+flipped
+uh so the first thing I want to point
+
+ align:start position:0%
+uh so the first thing I want to point
+ 
+
+ align:start position:0%
+uh so the first thing I want to point
+out are these circled nodes um the
+
+ align:start position:0%
+out are these circled nodes um the
+ 
+
+ align:start position:0%
+out are these circled nodes um the
+obvious way to draw this picture is with
+
+ align:start position:0%
+obvious way to draw this picture is with
+ 
+
+ align:start position:0%
+obvious way to draw this picture is with
+all of the terminals in the center row
+
+ align:start position:0%
+all of the terminals in the center row
+ 
+
+ align:start position:0%
+all of the terminals in the center row
+that would be reasonable they're not
+
+ align:start position:0%
+that would be reasonable they're not
+ 
+
+ align:start position:0%
+that would be reasonable they're not
+drawn that way here because imagine at
+
+ align:start position:0%
+drawn that way here because imagine at
+ 
+
+ align:start position:0%
+drawn that way here because imagine at
+this point we're down here and we have
+
+ align:start position:0%
+this point we're down here and we have
+ 
+
+ align:start position:0%
+this point we're down here and we have
+this big path over here then there'll be
+
+ align:start position:0%
+this big path over here then there'll be
+ 
+
+ align:start position:0%
+this big path over here then there'll be
+three pixels here which somehow have to
+
+ align:start position:0%
+three pixels here which somehow have to
+ 
+
+ align:start position:0%
+three pixels here which somehow have to
+be filled and that is trouble because
+
+ align:start position:0%
+be filled and that is trouble because
+ 
+
+ align:start position:0%
+be filled and that is trouble because
+three is odd okay so this is what you
+
+ align:start position:0%
+three is odd okay so this is what you
+ 
+
+ align:start position:0%
+three is odd okay so this is what you
+might call issue one the empty space
+
+ align:start position:0%
+might call issue one the empty space
+ 
+
+ align:start position:0%
+might call issue one the empty space
+wherever you have empty space any group
+
+ align:start position:0%
+wherever you have empty space any group
+ 
+
+ align:start position:0%
+wherever you have empty space any group
+should have even area uh because if you
+
+ align:start position:0%
+should have even area uh because if you
+ 
+
+ align:start position:0%
+should have even area uh because if you
+look at two guys that say are adjacent
+
+ align:start position:0%
+look at two guys that say are adjacent
+ 
+
+ align:start position:0%
+look at two guys that say are adjacent
+and you uh replace them with some other
+
+ align:start position:0%
+and you uh replace them with some other
+ 
+
+ align:start position:0%
+and you uh replace them with some other
+path together that forms a polygon and
+
+ align:start position:0%
+path together that forms a polygon and
+ 
+
+ align:start position:0%
+path together that forms a polygon and
+in the Square grid every polygon has
+
+ align:start position:0%
+in the Square grid every polygon has
+ 
+
+ align:start position:0%
+in the Square grid every polygon has
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+area so you will never fill exactly
+
+ align:start position:0%
+area so you will never fill exactly
+ 
+
+ align:start position:0%
+area so you will never fill exactly
+three spaces and so the the major
+
+ align:start position:0%
+three spaces and so the the major
+ 
+
+ align:start position:0%
+three spaces and so the the major
+Revolution which I spent many hours
+
+ align:start position:0%
+Revolution which I spent many hours
+ 
+
+ align:start position:0%
+Revolution which I spent many hours
+figuring out is if I just move these
+
+ align:start position:0%
+figuring out is if I just move these
+ 
+
+ align:start position:0%
+figuring out is if I just move these
+points up one spot everything just works
+
+ align:start position:0%
+points up one spot everything just works
+ 
+
+ align:start position:0%
+points up one spot everything just works
+uh so happy uh so I figure okay proof's
+
+ align:start position:0%
+uh so happy uh so I figure okay proof's
+ 
+
+ align:start position:0%
+uh so happy uh so I figure okay proof's
+done I drew these two figures and uh
+
+ align:start position:0%
+done I drew these two figures and uh
+ 
+
+ align:start position:0%
+done I drew these two figures and uh
+forgot about it then uh a couple months
+
+ align:start position:0%
+forgot about it then uh a couple months
+ 
+
+ align:start position:0%
+forgot about it then uh a couple months
+later we went to write the paper uh and
+
+ align:start position:0%
+later we went to write the paper uh and
+ 
+
+ align:start position:0%
+later we went to write the paper uh and
+then we get to issue two so issue two is
+
+ align:start position:0%
+then we get to issue two so issue two is
+ 
+
+ align:start position:0%
+then we get to issue two so issue two is
+well this was great this this works fine
+
+ align:start position:0%
+well this was great this this works fine
+ 
+
+ align:start position:0%
+well this was great this this works fine
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+um the Clause path is present if the
+
+ align:start position:0%
+um the Clause path is present if the
+ 
+
+ align:start position:0%
+um the Clause path is present if the
+Clause chooses this vertical path this
+
+ align:start position:0%
+Clause chooses this vertical path this
+ 
+
+ align:start position:0%
+Clause chooses this vertical path this
+will fill everything this will F fill
+
+ align:start position:0%
+will fill everything this will F fill
+ 
+
+ align:start position:0%
+will fill everything this will F fill
+everything but what if the Clause path
+
+ align:start position:0%
+everything but what if the Clause path
+ 
+
+ align:start position:0%
+everything but what if the Clause path
+is absent Clause has three choices it
+
+ align:start position:0%
+is absent Clause has three choices it
+ 
+
+ align:start position:0%
+is absent Clause has three choices it
+may not choose this vertical path so
+
+ align:start position:0%
+may not choose this vertical path so
+ 
+
+ align:start position:0%
+may not choose this vertical path so
+then somehow this stuff has to be
+
+ align:start position:0%
+then somehow this stuff has to be
+ 
+
+ align:start position:0%
+then somehow this stuff has to be
+covered using all the extra filler
+
+ align:start position:0%
+covered using all the extra filler
+ 
+
+ align:start position:0%
+covered using all the extra filler
+stuff okay and uh here I couldn't quite
+
+ align:start position:0%
+stuff okay and uh here I couldn't quite
+ 
+
+ align:start position:0%
+stuff okay and uh here I couldn't quite
+figure out how to fill these things like
+
+ align:start position:0%
+figure out how to fill these things like
+ 
+
+ align:start position:0%
+figure out how to fill these things like
+well maybe I should add a couple more
+
+ align:start position:0%
+well maybe I should add a couple more
+ 
+
+ align:start position:0%
+well maybe I should add a couple more
+rows in the middle that didn't seem to
+
+ align:start position:0%
+rows in the middle that didn't seem to
+ 
+
+ align:start position:0%
+rows in the middle that didn't seem to
+help uh I would I thought this one was
+
+ align:start position:0%
+help uh I would I thought this one was
+ 
+
+ align:start position:0%
+help uh I would I thought this one was
+okay it looks fine until I noticed that
+
+ align:start position:0%
+okay it looks fine until I noticed that
+ 
+
+ align:start position:0%
+okay it looks fine until I noticed that
+well either I connect these two dots by
+
+ align:start position:0%
+well either I connect these two dots by
+ 
+
+ align:start position:0%
+well either I connect these two dots by
+a length to path or I connect it by this
+
+ align:start position:0%
+a length to path or I connect it by this
+ 
+
+ align:start position:0%
+a length to path or I connect it by this
+path but in that case this pixel is
+
+ align:start position:0%
+path but in that case this pixel is
+ 
+
+ align:start position:0%
+path but in that case this pixel is
+uncovered by
+
+ align:start position:0%
+uncovered by
+ 
+
+ align:start position:0%
+uncovered by
+paths so uh and this is bad because
+
+ align:start position:0%
+paths so uh and this is bad because
+ 
+
+ align:start position:0%
+paths so uh and this is bad because
+there's exactly one such pixel which
+
+ align:start position:0%
+there's exactly one such pixel which
+ 
+
+ align:start position:0%
+there's exactly one such pixel which
+means I have another parody problem
+
+ align:start position:0%
+means I have another parody problem
+ 
+
+ align:start position:0%
+means I have another parody problem
+again so uh I think what we ended up
+
+ align:start position:0%
+again so uh I think what we ended up
+ 
+
+ align:start position:0%
+again so uh I think what we ended up
+doing um and you know when you're really
+
+ align:start position:0%
+doing um and you know when you're really
+ 
+
+ align:start position:0%
+doing um and you know when you're really
+doing it you don't immediately realize
+
+ align:start position:0%
+doing it you don't immediately realize
+ 
+
+ align:start position:0%
+doing it you don't immediately realize
+it's a parody problem you have to like I
+
+ align:start position:0%
+it's a parody problem you have to like I
+ 
+
+ align:start position:0%
+it's a parody problem you have to like I
+I've tried trying to fix this many many
+
+ align:start position:0%
+I've tried trying to fix this many many
+ 
+
+ align:start position:0%
+I've tried trying to fix this many many
+times and every single time I have like
+
+ align:start position:0%
+times and every single time I have like
+ 
+
+ align:start position:0%
+times and every single time I have like
+one pixel on covered they like H bet
+
+ align:start position:0%
+one pixel on covered they like H bet
+ 
+
+ align:start position:0%
+one pixel on covered they like H bet
+there's a theorem here and then I proved
+
+ align:start position:0%
+there's a theorem here and then I proved
+ 
+
+ align:start position:0%
+there's a theorem here and then I proved
+oh yeah it's got to change parody so
+
+ align:start position:0%
+oh yeah it's got to change parody so
+ 
+
+ align:start position:0%
+oh yeah it's got to change parody so
+what we ended up doing was adding a row
+
+ align:start position:0%
+what we ended up doing was adding a row
+ 
+
+ align:start position:0%
+what we ended up doing was adding a row
+down here uh make this path slightly
+
+ align:start position:0%
+down here uh make this path slightly
+ 
+
+ align:start position:0%
+down here uh make this path slightly
+longer that that adds exactly one
+
+ align:start position:0%
+longer that that adds exactly one
+ 
+
+ align:start position:0%
+longer that that adds exactly one
+uncovered pixel so it should fix the
+
+ align:start position:0%
+uncovered pixel so it should fix the
+ 
+
+ align:start position:0%
+uncovered pixel so it should fix the
+parody problem uh many hours later we
+
+ align:start position:0%
+parody problem uh many hours later we
+ 
+
+ align:start position:0%
+parody problem uh many hours later we
+came up with this um so this is good
+
+ align:start position:0%
+came up with this um so this is good
+ 
+
+ align:start position:0%
+came up with this um so this is good
+every pixel is covered in all four cases
+
+ align:start position:0%
+every pixel is covered in all four cases
+ 
+
+ align:start position:0%
+every pixel is covered in all four cases
+so we have the bottom row is that the
+
+ align:start position:0%
+so we have the bottom row is that the
+ 
+
+ align:start position:0%
+so we have the bottom row is that the
+top the CLA path is in and the top row
+
+ align:start position:0%
+top the CLA path is in and the top row
+ 
+
+ align:start position:0%
+top the CLA path is in and the top row
+is the CLA path is out and as you can
+
+ align:start position:0%
+is the CLA path is out and as you can
+ 
+
+ align:start position:0%
+is the CLA path is out and as you can
+see lots of careful orientations of
+
+ align:start position:0%
+see lots of careful orientations of
+ 
+
+ align:start position:0%
+see lots of careful orientations of
+these little terminal pairs to make sure
+
+ align:start position:0%
+these little terminal pairs to make sure
+ 
+
+ align:start position:0%
+these little terminal pairs to make sure
+in all cases you can cover everything
+
+ align:start position:0%
+in all cases you can cover everything
+ 
+
+ align:start position:0%
+in all cases you can cover everything
+this is frustrating because you fixed
+
+ align:start position:0%
+this is frustrating because you fixed
+ 
+
+ align:start position:0%
+this is frustrating because you fixed
+one and then you switch to the other
+
+ align:start position:0%
+one and then you switch to the other
+ 
+
+ align:start position:0%
+one and then you switch to the other
+layer and say oh I broke this other one
+
+ align:start position:0%
+layer and say oh I broke this other one
+ 
+
+ align:start position:0%
+layer and say oh I broke this other one
+I rotated these guys and now it's not
+
+ align:start position:0%
+I rotated these guys and now it's not
+ 
+
+ align:start position:0%
+I rotated these guys and now it's not
+possible to do this so you better and it
+
+ align:start position:0%
+possible to do this so you better and it
+ 
+
+ align:start position:0%
+possible to do this so you better and it
+would be like you rotate this and then
+
+ align:start position:0%
+would be like you rotate this and then
+ 
+
+ align:start position:0%
+would be like you rotate this and then
+rotate that and rotate this and you
+
+ align:start position:0%
+rotate that and rotate this and you
+ 
+
+ align:start position:0%
+rotate that and rotate this and you
+luckily no bad Cycles happen you could
+
+ align:start position:0%
+luckily no bad Cycles happen you could
+ 
+
+ align:start position:0%
+luckily no bad Cycles happen you could
+always resolve it and so finally we got
+
+ align:start position:0%
+always resolve it and so finally we got
+ 
+
+ align:start position:0%
+always resolve it and so finally we got
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+picture except for issue three uh which
+
+ align:start position:0%
+picture except for issue three uh which
+ 
+
+ align:start position:0%
+picture except for issue three uh which
+is another parody problem it's blown
+
+ align:start position:0%
+is another parody problem it's blown
+ 
+
+ align:start position:0%
+is another parody problem it's blown
+away it's like every day uh there was
+
+ align:start position:0%
+away it's like every day uh there was
+ 
+
+ align:start position:0%
+away it's like every day uh there was
+another parody problem wri of course the
+
+ align:start position:0%
+another parody problem wri of course the
+ 
+
+ align:start position:0%
+another parody problem wri of course the
+deadline is like tomorrow at this point
+
+ align:start position:0%
+deadline is like tomorrow at this point
+ 
+
+ align:start position:0%
+deadline is like tomorrow at this point
+luckily I started three days ahead
+
+ align:start position:0%
+luckily I started three days ahead
+ 
+
+ align:start position:0%
+luckily I started three days ahead
+so there were exactly three
+
+ align:start position:0%
+so there were exactly three
+ 
+
+ align:start position:0%
+so there were exactly three
+issues so uh remember this gadget which
+
+ align:start position:0%
+issues so uh remember this gadget which
+ 
+
+ align:start position:0%
+issues so uh remember this gadget which
+was the choice uh I didn't say this is
+
+ align:start position:0%
+was the choice uh I didn't say this is
+ 
+
+ align:start position:0%
+was the choice uh I didn't say this is
+like a variable choice you have two
+
+ align:start position:0%
+like a variable choice you have two
+ 
+
+ align:start position:0%
+like a variable choice you have two
+choices if you want a clause choice you
+
+ align:start position:0%
+choices if you want a clause choice you
+ 
+
+ align:start position:0%
+choices if you want a clause choice you
+connect two of these gadgets together
+
+ align:start position:0%
+connect two of these gadgets together
+ 
+
+ align:start position:0%
+connect two of these gadgets together
+and then you have three different paths
+
+ align:start position:0%
+and then you have three different paths
+ 
+
+ align:start position:0%
+and then you have three different paths
+you might follow if you stare at this
+
+ align:start position:0%
+you might follow if you stare at this
+ 
+
+ align:start position:0%
+you might follow if you stare at this
+enough and I just wanted to make sure
+
+ align:start position:0%
+enough and I just wanted to make sure
+ 
+
+ align:start position:0%
+enough and I just wanted to make sure
+okay can I plug these together I thought
+
+ align:start position:0%
+okay can I plug these together I thought
+ 
+
+ align:start position:0%
+okay can I plug these together I thought
+okay I'll just copy the paste and lay
+
+ align:start position:0%
+okay I'll just copy the paste and lay
+ 
+
+ align:start position:0%
+okay I'll just copy the paste and lay
+things out and I had a parity problem
+
+ align:start position:0%
+things out and I had a parity problem
+ 
+
+ align:start position:0%
+things out and I had a parity problem
+it's like oh man what's going on well if
+
+ align:start position:0%
+it's like oh man what's going on well if
+ 
+
+ align:start position:0%
+it's like oh man what's going on well if
+you look here uh this is at one column
+
+ align:start position:0%
+you look here uh this is at one column
+ 
+
+ align:start position:0%
+you look here uh this is at one column
+and this is a column uh four positions
+
+ align:start position:0%
+and this is a column uh four positions
+ 
+
+ align:start position:0%
+and this is a column uh four positions
+over so in particular the two choices
+
+ align:start position:0%
+over so in particular the two choices
+ 
+
+ align:start position:0%
+over so in particular the two choices
+here uh have the same parody I don't I
+
+ align:start position:0%
+here uh have the same parody I don't I
+ 
+
+ align:start position:0%
+here uh have the same parody I don't I
+think it's mod two not mod four but
+
+ align:start position:0%
+think it's mod two not mod four but
+ 
+
+ align:start position:0%
+think it's mod two not mod four but
+could double check uh and you just
+
+ align:start position:0%
+could double check uh and you just
+ 
+
+ align:start position:0%
+could double check uh and you just
+cannot build this if you want these
+
+ align:start position:0%
+cannot build this if you want these
+ 
+
+ align:start position:0%
+cannot build this if you want these
+things to be in odd distance apart
+
+ align:start position:0%
+things to be in odd distance apart
+ 
+
+ align:start position:0%
+things to be in odd distance apart
+um cuz parody so and then you look at
+
+ align:start position:0%
+um cuz parody so and then you look at
+ 
+
+ align:start position:0%
+um cuz parody so and then you look at
+this gadget and you realize it has an
+
+ align:start position:0%
+this gadget and you realize it has an
+ 
+
+ align:start position:0%
+this gadget and you realize it has an
+odd number of columns we made it an even
+
+ align:start position:0%
+odd number of columns we made it an even
+ 
+
+ align:start position:0%
+odd number of columns we made it an even
+number of rows when we added that last
+
+ align:start position:0%
+number of rows when we added that last
+ 
+
+ align:start position:0%
+number of rows when we added that last
+row uh but now it has an odd number of
+
+ align:start position:0%
+row uh but now it has an odd number of
+ 
+
+ align:start position:0%
+row uh but now it has an odd number of
+columns which is kind of weird but
+
+ align:start position:0%
+columns which is kind of weird but
+ 
+
+ align:start position:0%
+columns which is kind of weird but
+that's life so uh we need to make it
+
+ align:start position:0%
+that's life so uh we need to make it
+ 
+
+ align:start position:0%
+that's life so uh we need to make it
+even and so I think if you focus right
+
+ align:start position:0%
+even and so I think if you focus right
+ 
+
+ align:start position:0%
+even and so I think if you focus right
+here we add another column sorry it's
+
+ align:start position:0%
+here we add another column sorry it's
+ 
+
+ align:start position:0%
+here we add another column sorry it's
+now right here so there used to be two
+
+ align:start position:0%
+now right here so there used to be two
+ 
+
+ align:start position:0%
+now right here so there used to be two
+now now there are three we have this
+
+ align:start position:0%
+now now there are three we have this
+ 
+
+ align:start position:0%
+now now there are three we have this
+little trick to kind of fill things in
+
+ align:start position:0%
+little trick to kind of fill things in
+ 
+
+ align:start position:0%
+little trick to kind of fill things in
+and not too much changed I think I also
+
+ align:start position:0%
+and not too much changed I think I also
+ 
+
+ align:start position:0%
+and not too much changed I think I also
+cleaned up the gadget I removed a couple
+
+ align:start position:0%
+cleaned up the gadget I removed a couple
+ 
+
+ align:start position:0%
+cleaned up the gadget I removed a couple
+extra columns on the right but the key
+
+ align:start position:0%
+extra columns on the right but the key
+ 
+
+ align:start position:0%
+extra columns on the right but the key
+thing was to add a new column uh that
+
+ align:start position:0%
+thing was to add a new column uh that
+ 
+
+ align:start position:0%
+thing was to add a new column uh that
+fixed the par now the number of columns
+
+ align:start position:0%
+fixed the par now the number of columns
+ 
+
+ align:start position:0%
+fixed the par now the number of columns
+is even and now you have to prove this
+
+ align:start position:0%
+is even and now you have to prove this
+ 
+
+ align:start position:0%
+is even and now you have to prove this
+but it's pretty easy to check you can
+
+ align:start position:0%
+but it's pretty easy to check you can
+ 
+
+ align:start position:0%
+but it's pretty easy to check you can
+plug it into you can combine these
+
+ align:start position:0%
+plug it into you can combine these
+ 
+
+ align:start position:0%
+plug it into you can combine these
+gadgets together and uh they match up
+
+ align:start position:0%
+gadgets together and uh they match up
+ 
+
+ align:start position:0%
+gadgets together and uh they match up
+and then if you have blank space it's
+
+ align:start position:0%
+and then if you have blank space it's
+ 
+
+ align:start position:0%
+and then if you have blank space it's
+also even by even and so you it always
+
+ align:start position:0%
+also even by even and so you it always
+ 
+
+ align:start position:0%
+also even by even and so you it always
+has a perfect matching and so you can
+
+ align:start position:0%
+has a perfect matching and so you can
+ 
+
+ align:start position:0%
+has a perfect matching and so you can
+fill in any blank space with extra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairs those are the
+
+ align:start position:0%
+pairs those are the
+ 
+
+ align:start position:0%
+pairs those are the
+gadgets
+
+ align:start position:0%
+gadgets
+ 
+
+ align:start position:0%
+gadgets
+except uh there's one more issue I
+
+ align:start position:0%
+except uh there's one more issue I
+ 
+
+ align:start position:0%
+except uh there's one more issue I
+haven't mentioned yeah there's a parody
+
+ align:start position:0%
+haven't mentioned yeah there's a parody
+ 
+
+ align:start position:0%
+haven't mentioned yeah there's a parody
+problem with your parody problems
+
+ align:start position:0%
+problem with your parody problems
+ 
+
+ align:start position:0%
+problem with your parody problems
+there's only an odd number of only an
+
+ align:start position:0%
+there's only an odd number of only an
+ 
+
+ align:start position:0%
+there's only an odd number of only an
+odd number of parody problems luckily
+
+ align:start position:0%
+odd number of parody problems luckily
+ 
+
+ align:start position:0%
+odd number of parody problems luckily
+the next problem is not a parody problem
+
+ align:start position:0%
+the next problem is not a parody problem
+ 
+
+ align:start position:0%
+the next problem is not a parody problem
+or unluck I don't know yeah um and this
+
+ align:start position:0%
+or unluck I don't know yeah um and this
+ 
+
+ align:start position:0%
+or unluck I don't know yeah um and this
+it wasn't really a problem I knew it was
+
+ align:start position:0%
+it wasn't really a problem I knew it was
+ 
+
+ align:start position:0%
+it wasn't really a problem I knew it was
+going to happen I just had to draw the
+
+ align:start position:0%
+going to happen I just had to draw the
+ 
+
+ align:start position:0%
+going to happen I just had to draw the
+figure uh but it's good for exercise
+
+ align:start position:0%
+figure uh but it's good for exercise
+ 
+
+ align:start position:0%
+figure uh but it's good for exercise
+think about what what could possibly be
+
+ align:start position:0%
+think about what what could possibly be
+ 
+
+ align:start position:0%
+think about what what could possibly be
+missing we've spent all this time doing
+
+ align:start position:0%
+missing we've spent all this time doing
+ 
+
+ align:start position:0%
+missing we've spent all this time doing
+crossover gadgets but there's also the
+
+ align:start position:0%
+crossover gadgets but there's also the
+ 
+
+ align:start position:0%
+crossover gadgets but there's also the
+case where the wires cross and we
+
+ align:start position:0%
+case where the wires cross and we
+ 
+
+ align:start position:0%
+case where the wires cross and we
+actually want the vertical wire to block
+
+ align:start position:0%
+actually want the vertical wire to block
+ 
+
+ align:start position:0%
+actually want the vertical wire to block
+the horizontal wire in a particular
+
+ align:start position:0%
+the horizontal wire in a particular
+ 
+
+ align:start position:0%
+the horizontal wire in a particular
+choice this is actually really easy to
+
+ align:start position:0%
+choice this is actually really easy to
+ 
+
+ align:start position:0%
+choice this is actually really easy to
+do so here's the the gadget I was just
+
+ align:start position:0%
+do so here's the the gadget I was just
+ 
+
+ align:start position:0%
+do so here's the the gadget I was just
+showing you without all the stuff filled
+
+ align:start position:0%
+showing you without all the stuff filled
+ 
+
+ align:start position:0%
+showing you without all the stuff filled
+in those are just the terminal Pairs and
+
+ align:start position:0%
+in those are just the terminal Pairs and
+ 
+
+ align:start position:0%
+in those are just the terminal Pairs and
+you know this guy goes to the left this
+
+ align:start position:0%
+you know this guy goes to the left this
+ 
+
+ align:start position:0%
+you know this guy goes to the left this
+guy goes to here this guy goes to the
+
+ align:start position:0%
+guy goes to here this guy goes to the
+ 
+
+ align:start position:0%
+guy goes to here this guy goes to the
+right um if you just add in an extra
+
+ align:start position:0%
+right um if you just add in an extra
+ 
+
+ align:start position:0%
+right um if you just add in an extra
+pair here or an extra pair here you will
+
+ align:start position:0%
+pair here or an extra pair here you will
+ 
+
+ align:start position:0%
+pair here or an extra pair here you will
+block blue or red correspondingly so if
+
+ align:start position:0%
+block blue or red correspondingly so if
+ 
+
+ align:start position:0%
+block blue or red correspondingly so if
+we go to the previous slide here blue
+
+ align:start position:0%
+we go to the previous slide here blue
+ 
+
+ align:start position:0%
+we go to the previous slide here blue
+goes through this position but red does
+
+ align:start position:0%
+goes through this position but red does
+ 
+
+ align:start position:0%
+goes through this position but red does
+not and uh down here uh blue does not go
+
+ align:start position:0%
+not and uh down here uh blue does not go
+ 
+
+ align:start position:0%
+not and uh down here uh blue does not go
+through this position but red does and
+
+ align:start position:0%
+through this position but red does and
+ 
+
+ align:start position:0%
+through this position but red does and
+so if you add in this extra little pair
+
+ align:start position:0%
+so if you add in this extra little pair
+ 
+
+ align:start position:0%
+so if you add in this extra little pair
+you will force red or blue at that
+
+ align:start position:0%
+you will force red or blue at that
+ 
+
+ align:start position:0%
+you will force red or blue at that
+intersection and that was the little
+
+ align:start position:0%
+intersection and that was the little
+ 
+
+ align:start position:0%
+intersection and that was the little
+squares in the overall diagram so if you
+
+ align:start position:0%
+squares in the overall diagram so if you
+ 
+
+ align:start position:0%
+squares in the overall diagram so if you
+choose this vertical path you force the
+
+ align:start position:0%
+choose this vertical path you force the
+ 
+
+ align:start position:0%
+choose this vertical path you force the
+horizontal path to be the other
+
+ align:start position:0%
+horizontal path to be the other
+ 
+
+ align:start position:0%
+horizontal path to be the other
+thing that's the
+
+ align:start position:0%
+thing that's the
+ 
+
+ align:start position:0%
+thing that's the
+proof I hope there are no more
+
+ align:start position:0%
+proof I hope there are no more
+ 
+
+ align:start position:0%
+proof I hope there are no more
+issues uh but it was it was exciting so
+
+ align:start position:0%
+issues uh but it was it was exciting so
+ 
+
+ align:start position:0%
+issues uh but it was it was exciting so
+just to give you a flavor for parody
+
+ align:start position:0%
+just to give you a flavor for parody
+ 
+
+ align:start position:0%
+just to give you a flavor for parody
+issues they are all over the place
+
+ align:start position:0%
+issues they are all over the place
+ 
+
+ align:start position:0%
+issues they are all over the place
+especially when you're on a grid be
+
+ align:start position:0%
+especially when you're on a grid be
+ 
+
+ align:start position:0%
+especially when you're on a grid be
+careful of them that's the life lesson
+
+ align:start position:0%
+careful of them that's the life lesson
+ 
+
+ align:start position:0%
+careful of them that's the life lesson
+um I'll tell you a little bit about
+
+ align:start position:0%
+um I'll tell you a little bit about
+ 
+
+ align:start position:0%
+um I'll tell you a little bit about
+where this kind of problem comes from
+
+ align:start position:0%
+where this kind of problem comes from
+ 
+
+ align:start position:0%
+where this kind of problem comes from
+the earliest reference we know is by Sam
+
+ align:start position:0%
+the earliest reference we know is by Sam
+ 
+
+ align:start position:0%
+the earliest reference we know is by Sam
+Lloyd famous puzzle designer in 1897 he
+
+ align:start position:0%
+Lloyd famous puzzle designer in 1897 he
+ 
+
+ align:start position:0%
+Lloyd famous puzzle designer in 1897 he
+he posed this puzzle incredibly
+
+ align:start position:0%
+he posed this puzzle incredibly
+ 
+
+ align:start position:0%
+he posed this puzzle incredibly
+complicated puzzle I mean lots of stuff
+
+ align:start position:0%
+complicated puzzle I mean lots of stuff
+ 
+
+ align:start position:0%
+complicated puzzle I mean lots of stuff
+in it um and then I think the next issue
+
+ align:start position:0%
+in it um and then I think the next issue
+ 
+
+ align:start position:0%
+in it um and then I think the next issue
+he published the solution which is this
+
+ align:start position:0%
+he published the solution which is this
+ 
+
+ align:start position:0%
+he published the solution which is this
+um hopefully I remember the problem so
+
+ align:start position:0%
+um hopefully I remember the problem so
+ 
+
+ align:start position:0%
+um hopefully I remember the problem so
+you have these houses and you'll notice
+
+ align:start position:0%
+you have these houses and you'll notice
+ 
+
+ align:start position:0%
+you have these houses and you'll notice
+each house faces an
+
+ align:start position:0%
+each house faces an
+ 
+
+ align:start position:0%
+each house faces an
+exit and uh what you'd like is for each
+
+ align:start position:0%
+exit and uh what you'd like is for each
+ 
+
+ align:start position:0%
+exit and uh what you'd like is for each
+house to be connected via Pathway to the
+
+ align:start position:0%
+house to be connected via Pathway to the
+ 
+
+ align:start position:0%
+house to be connected via Pathway to the
+exit um but if you just did that that
+
+ align:start position:0%
+exit um but if you just did that that
+ 
+
+ align:start position:0%
+exit um but if you just did that that
+they would intersect each other so you
+
+ align:start position:0%
+they would intersect each other so you
+ 
+
+ align:start position:0%
+they would intersect each other so you
+want vertex disjoint paths in the grid
+
+ align:start position:0%
+want vertex disjoint paths in the grid
+ 
+
+ align:start position:0%
+want vertex disjoint paths in the grid
+from the houses to the exit that they
+
+ align:start position:0%
+from the houses to the exit that they
+ 
+
+ align:start position:0%
+from the houses to the exit that they
+face so that is a terminal pair vertex
+
+ align:start position:0%
+face so that is a terminal pair vertex
+ 
+
+ align:start position:0%
+face so that is a terminal pair vertex
+dis joint path problem now he didn't
+
+ align:start position:0%
+dis joint path problem now he didn't
+ 
+
+ align:start position:0%
+dis joint path problem now he didn't
+specify that those paths should fill the
+
+ align:start position:0%
+specify that those paths should fill the
+ 
+
+ align:start position:0%
+specify that those paths should fill the
+entire grid but they almost do other
+
+ align:start position:0%
+entire grid but they almost do other
+ 
+
+ align:start position:0%
+entire grid but they almost do other
+than this little corner uh they do and
+
+ align:start position:0%
+than this little corner uh they do and
+ 
+
+ align:start position:0%
+than this little corner uh they do and
+this you know a few little Corners at
+
+ align:start position:0%
+this you know a few little Corners at
+ 
+
+ align:start position:0%
+this you know a few little Corners at
+the extremes and you can fix it instead
+
+ align:start position:0%
+the extremes and you can fix it instead
+ 
+
+ align:start position:0%
+the extremes and you can fix it instead
+of going like this you can go Zig Zig
+
+ align:start position:0%
+of going like this you can go Zig Zig
+ 
+
+ align:start position:0%
+of going like this you can go Zig Zig
+Zig Zig and Zig Zig Zig Zig Zig and uh
+
+ align:start position:0%
+Zig Zig and Zig Zig Zig Zig Zig and uh
+ 
+
+ align:start position:0%
+Zig Zig and Zig Zig Zig Zig Zig and uh
+make it into a solution to the problem I
+
+ align:start position:0%
+make it into a solution to the problem I
+ 
+
+ align:start position:0%
+make it into a solution to the problem I
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+said okay so that's
+
+ align:start position:0%
+said okay so that's
+ 
+
+ align:start position:0%
+said okay so that's
+1897 um in modern terms this is known as
+
+ align:start position:0%
+1897 um in modern terms this is known as
+ 
+
+ align:start position:0%
+1897 um in modern terms this is known as
+the number link puzzle uh nickoli is a
+
+ align:start position:0%
+the number link puzzle uh nickoli is a
+ 
+
+ align:start position:0%
+the number link puzzle uh nickoli is a
+famous uh Japanese puzzle publisher
+
+ align:start position:0%
+famous uh Japanese puzzle publisher
+ 
+
+ align:start position:0%
+famous uh Japanese puzzle publisher
+these are two nickoli books that uh we
+
+ align:start position:0%
+these are two nickoli books that uh we
+ 
+
+ align:start position:0%
+these are two nickoli books that uh we
+got in our last trip to Japan a couple
+
+ align:start position:0%
+got in our last trip to Japan a couple
+ 
+
+ align:start position:0%
+got in our last trip to Japan a couple
+of months ago uh these are both for the
+
+ align:start position:0%
+of months ago uh these are both for the
+ 
+
+ align:start position:0%
+of months ago uh these are both for the
+number link puzzle so you turn to an
+
+ align:start position:0%
+number link puzzle so you turn to an
+ 
+
+ align:start position:0%
+number link puzzle so you turn to an
+arbitrary
+
+ align:start position:0%
+arbitrary
+ 
+
+ align:start position:0%
+arbitrary
+page and you have some
+
+ align:start position:0%
+page and you have some
+ 
+
+ align:start position:0%
+page and you have some
+uh picture like this which uh here's an
+
+ align:start position:0%
+uh picture like this which uh here's an
+ 
+
+ align:start position:0%
+uh picture like this which uh here's an
+example you have pairs you have a bunch
+
+ align:start position:0%
+example you have pairs you have a bunch
+ 
+
+ align:start position:0%
+example you have pairs you have a bunch
+of numbers and blank spaces the idea is
+
+ align:start position:0%
+of numbers and blank spaces the idea is
+ 
+
+ align:start position:0%
+of numbers and blank spaces the idea is
+that there's exactly two of each number
+
+ align:start position:0%
+that there's exactly two of each number
+ 
+
+ align:start position:0%
+that there's exactly two of each number
+those are your terminal pairs you want
+
+ align:start position:0%
+those are your terminal pairs you want
+ 
+
+ align:start position:0%
+those are your terminal pairs you want
+to find vertex dis joint paths that
+
+ align:start position:0%
+to find vertex dis joint paths that
+ 
+
+ align:start position:0%
+to find vertex dis joint paths that
+connect them and yeah in the back
+
+ align:start position:0%
+connect them and yeah in the back
+ 
+
+ align:start position:0%
+connect them and yeah in the back
+there's Solutions so if you can't solve
+
+ align:start position:0%
+there's Solutions so if you can't solve
+ 
+
+ align:start position:0%
+there's Solutions so if you can't solve
+one um they have easy ones medium ones
+
+ align:start position:0%
+one um they have easy ones medium ones
+ 
+
+ align:start position:0%
+one um they have easy ones medium ones
+hard ones uh so how hard is it and P
+
+ align:start position:0%
+hard ones uh so how hard is it and P
+ 
+
+ align:start position:0%
+hard ones uh so how hard is it and P
+hard uh because this is exactly the
+
+ align:start position:0%
+hard uh because this is exactly the
+ 
+
+ align:start position:0%
+hard uh because this is exactly the
+problem we were just solving if you want
+
+ align:start position:0%
+problem we were just solving if you want
+ 
+
+ align:start position:0%
+problem we were just solving if you want
+to find ver
+
+ align:start position:0%
+to find ver
+ 
+
+ align:start position:0%
+to find ver
+just trint paths in the grid um there is
+
+ align:start position:0%
+just trint paths in the grid um there is
+ 
+
+ align:start position:0%
+just trint paths in the grid um there is
+this issue of whether you are specified
+
+ align:start position:0%
+this issue of whether you are specified
+ 
+
+ align:start position:0%
+this issue of whether you are specified
+as one of the constraints that you must
+
+ align:start position:0%
+as one of the constraints that you must
+ 
+
+ align:start position:0%
+as one of the constraints that you must
+um visit every square
+
+ align:start position:0%
+um visit every square
+ 
+
+ align:start position:0%
+um visit every square
+but do a quick quick visual scan here
+
+ align:start position:0%
+but do a quick quick visual scan here
+ 
+
+ align:start position:0%
+but do a quick quick visual scan here
+and every solution that I see every
+
+ align:start position:0%
+and every solution that I see every
+ 
+
+ align:start position:0%
+and every solution that I see every
+Square happens to be
+
+ align:start position:0%
+Square happens to be
+ 
+
+ align:start position:0%
+Square happens to be
+filled okay now that might be the way
+
+ align:start position:0%
+filled okay now that might be the way
+ 
+
+ align:start position:0%
+filled okay now that might be the way
+that they design the puzzles the only
+
+ align:start position:0%
+that they design the puzzles the only
+ 
+
+ align:start position:0%
+that they design the puzzles the only
+way to solve them is for the every
+
+ align:start position:0%
+way to solve them is for the every
+ 
+
+ align:start position:0%
+way to solve them is for the every
+Square squ to be filled or it might be
+
+ align:start position:0%
+Square squ to be filled or it might be
+ 
+
+ align:start position:0%
+Square squ to be filled or it might be
+that's a constraint to the puzzle and
+
+ align:start position:0%
+that's a constraint to the puzzle and
+ 
+
+ align:start position:0%
+that's a constraint to the puzzle and
+different writeups suggest different
+
+ align:start position:0%
+different writeups suggest different
+ 
+
+ align:start position:0%
+different writeups suggest different
+ways but what we proved is both ways
+
+ align:start position:0%
+ways but what we proved is both ways
+ 
+
+ align:start position:0%
+ways but what we proved is both ways
+it's hard whether you give that as a
+
+ align:start position:0%
+it's hard whether you give that as a
+ 
+
+ align:start position:0%
+it's hard whether you give that as a
+specification or you make it possible to
+
+ align:start position:0%
+specification or you make it possible to
+ 
+
+ align:start position:0%
+specification or you make it possible to
+do uh it it is NP hard because we
+
+ align:start position:0%
+do uh it it is NP hard because we
+ 
+
+ align:start position:0%
+do uh it it is NP hard because we
+started from a reduction that didn't
+
+ align:start position:0%
+started from a reduction that didn't
+ 
+
+ align:start position:0%
+started from a reduction that didn't
+have to fill every pixel and we turn it
+
+ align:start position:0%
+have to fill every pixel and we turn it
+ 
+
+ align:start position:0%
+have to fill every pixel and we turn it
+into one that could fill every pixel if
+
+ align:start position:0%
+into one that could fill every pixel if
+ 
+
+ align:start position:0%
+into one that could fill every pixel if
+you wanted so yeah there's a sense in
+
+ align:start position:0%
+you wanted so yeah there's a sense in
+ 
+
+ align:start position:0%
+you wanted so yeah there's a sense in
+which these puzzles are sparer in terms
+
+ align:start position:0%
+which these puzzles are sparer in terms
+ 
+
+ align:start position:0%
+which these puzzles are sparer in terms
+of the number of vertices than your
+
+ align:start position:0%
+of the number of vertices than your
+ 
+
+ align:start position:0%
+of the number of vertices than your
+reduction is it possible that you could
+
+ align:start position:0%
+reduction is it possible that you could
+ 
+
+ align:start position:0%
+reduction is it possible that you could
+Define it in such a way that these are
+
+ align:start position:0%
+Define it in such a way that these are
+ 
+
+ align:start position:0%
+Define it in such a way that these are
+polom solvable it's an interesting
+
+ align:start position:0%
+polom solvable it's an interesting
+ 
+
+ align:start position:0%
+polom solvable it's an interesting
+question um so our our reduction has
+
+ align:start position:0%
+question um so our our reduction has
+ 
+
+ align:start position:0%
+question um so our our reduction has
+most of the cells filled with terminal
+
+ align:start position:0%
+most of the cells filled with terminal
+ 
+
+ align:start position:0%
+most of the cells filled with terminal
+filled with numbers um these you could
+
+ align:start position:0%
+filled with numbers um these you could
+ 
+
+ align:start position:0%
+filled with numbers um these you could
+say if you have an N byn grid maybe
+
+ align:start position:0%
+say if you have an N byn grid maybe
+ 
+
+ align:start position:0%
+say if you have an N byn grid maybe
+these only have order n numbers whereas
+
+ align:start position:0%
+these only have order n numbers whereas
+ 
+
+ align:start position:0%
+these only have order n numbers whereas
+we have order n squ numbers that would
+
+ align:start position:0%
+we have order n squ numbers that would
+ 
+
+ align:start position:0%
+we have order n squ numbers that would
+be interesting I don't know the
+
+ align:start position:0%
+be interesting I don't know the
+ 
+
+ align:start position:0%
+be interesting I don't know the
+complexity the one thing that's known as
+
+ align:start position:0%
+complexity the one thing that's known as
+ 
+
+ align:start position:0%
+complexity the one thing that's known as
+for one terminal pair it's polinomial
+
+ align:start position:0%
+for one terminal pair it's polinomial
+ 
+
+ align:start position:0%
+for one terminal pair it's polinomial
+time I think even two terminal pairs is
+
+ align:start position:0%
+time I think even two terminal pairs is
+ 
+
+ align:start position:0%
+time I think even two terminal pairs is
+an open problem so that would be you
+
+ align:start position:0%
+an open problem so that would be you
+ 
+
+ align:start position:0%
+an open problem so that would be you
+need to solve that before you could
+
+ align:start position:0%
+need to solve that before you could
+ 
+
+ align:start position:0%
+need to solve that before you could
+solve n terminal pairs SP an N
+
+ align:start position:0%
+solve n terminal pairs SP an N
+ 
+
+ align:start position:0%
+solve n terminal pairs SP an N
+byn uh so I don't know how many people
+
+ align:start position:0%
+byn uh so I don't know how many people
+ 
+
+ align:start position:0%
+byn uh so I don't know how many people
+worked on Tu terminal pairs I thought
+
+ align:start position:0%
+worked on Tu terminal pairs I thought
+ 
+
+ align:start position:0%
+worked on Tu terminal pairs I thought
+about a little bit it seems very
+
+ align:start position:0%
+about a little bit it seems very
+ 
+
+ align:start position:0%
+about a little bit it seems very
+difficult uh anyway little more to this
+
+ align:start position:0%
+difficult uh anyway little more to this
+ 
+
+ align:start position:0%
+difficult uh anyway little more to this
+story um we first in fact we first
+
+ align:start position:0%
+story um we first in fact we first
+ 
+
+ align:start position:0%
+story um we first in fact we first
+encountered number Link in the form of
+
+ align:start position:0%
+encountered number Link in the form of
+ 
+
+ align:start position:0%
+encountered number Link in the form of
+an Android game called Flow Free which
+
+ align:start position:0%
+an Android game called Flow Free which
+ 
+
+ align:start position:0%
+an Android game called Flow Free which
+some of you may have played it was it
+
+ align:start position:0%
+some of you may have played it was it
+ 
+
+ align:start position:0%
+some of you may have played it was it
+became popular for a few months there um
+
+ align:start position:0%
+became popular for a few months there um
+ 
+
+ align:start position:0%
+became popular for a few months there um
+and but it is exactly number link as
+
+ align:start position:0%
+and but it is exactly number link as
+ 
+
+ align:start position:0%
+and but it is exactly number link as
+I've defined it and once you know that
+
+ align:start position:0%
+I've defined it and once you know that
+ 
+
+ align:start position:0%
+I've defined it and once you know that
+uh then you there's also number link and
+
+ align:start position:0%
+uh then you there's also number link and
+ 
+
+ align:start position:0%
+uh then you there's also number link and
+a zillion other clones and I don't think
+
+ align:start position:0%
+a zillion other clones and I don't think
+ 
+
+ align:start position:0%
+a zillion other clones and I don't think
+nickol Le publishes any of these so but
+
+ align:start position:0%
+nickol Le publishes any of these so but
+ 
+
+ align:start position:0%
+nickol Le publishes any of these so but
+it's all from 1897 so unclear what the
+
+ align:start position:0%
+it's all from 1897 so unclear what the
+ 
+
+ align:start position:0%
+it's all from 1897 so unclear what the
+copyright is here um uh but in
+
+ align:start position:0%
+copyright is here um uh but in
+ 
+
+ align:start position:0%
+copyright is here um uh but in
+particular number link I like it has the
+
+ align:start position:0%
+particular number link I like it has the
+ 
+
+ align:start position:0%
+particular number link I like it has the
+nicest gooey uh but in the beginning
+
+ align:start position:0%
+nicest gooey uh but in the beginning
+ 
+
+ align:start position:0%
+nicest gooey uh but in the beginning
+tutorial it says well there's actually
+
+ align:start position:0%
+tutorial it says well there's actually
+ 
+
+ align:start position:0%
+tutorial it says well there's actually
+two modes you can play there's zigzag
+
+ align:start position:0%
+two modes you can play there's zigzag
+ 
+
+ align:start position:0%
+two modes you can play there's zigzag
+mode where you can draw pads however you
+
+ align:start position:0%
+mode where you can draw pads however you
+ 
+
+ align:start position:0%
+mode where you can draw pads however you
+want that's what I've been talking about
+
+ align:start position:0%
+want that's what I've been talking about
+ 
+
+ align:start position:0%
+want that's what I've been talking about
+CU graph theoretically that's the
+
+ align:start position:0%
+CU graph theoretically that's the
+ 
+
+ align:start position:0%
+CU graph theoretically that's the
+natural thing thing then there's this
+
+ align:start position:0%
+natural thing thing then there's this
+ 
+
+ align:start position:0%
+natural thing thing then there's this
+other Mode called classic mode where uh
+
+ align:start position:0%
+other Mode called classic mode where uh
+ 
+
+ align:start position:0%
+other Mode called classic mode where uh
+whenever if you draw a complicated path
+
+ align:start position:0%
+whenever if you draw a complicated path
+ 
+
+ align:start position:0%
+whenever if you draw a complicated path
+it gets short Auto shrinked is the
+
+ align:start position:0%
+it gets short Auto shrinked is the
+ 
+
+ align:start position:0%
+it gets short Auto shrinked is the
+technical term uh now again it's hard to
+
+ align:start position:0%
+technical term uh now again it's hard to
+ 
+
+ align:start position:0%
+technical term uh now again it's hard to
+have an authority here on like what are
+
+ align:start position:0%
+have an authority here on like what are
+ 
+
+ align:start position:0%
+have an authority here on like what are
+the rules of number link uh but one
+
+ align:start position:0%
+the rules of number link uh but one
+ 
+
+ align:start position:0%
+the rules of number link uh but one
+definition is you consider all possible
+
+ align:start position:0%
+definition is you consider all possible
+ 
+
+ align:start position:0%
+definition is you consider all possible
+paths uh between these pairs that have
+
+ align:start position:0%
+paths uh between these pairs that have
+ 
+
+ align:start position:0%
+paths uh between these pairs that have
+the same topology like you could try to
+
+ align:start position:0%
+the same topology like you could try to
+ 
+
+ align:start position:0%
+the same topology like you could try to
+go you can try to go this way or you
+
+ align:start position:0%
+go you can try to go this way or you
+ 
+
+ align:start position:0%
+go you can try to go this way or you
+could try to go this way here you have
+
+ align:start position:0%
+could try to go this way here you have
+ 
+
+ align:start position:0%
+could try to go this way here you have
+these two guys on your right hand side
+
+ align:start position:0%
+these two guys on your right hand side
+ 
+
+ align:start position:0%
+these two guys on your right hand side
+here you have them on the left hand side
+
+ align:start position:0%
+here you have them on the left hand side
+ 
+
+ align:start position:0%
+here you have them on the left hand side
+in general that's called the homotopy
+
+ align:start position:0%
+in general that's called the homotopy
+ 
+
+ align:start position:0%
+in general that's called the homotopy
+type of that path consider all paths
+
+ align:start position:0%
+type of that path consider all paths
+ 
+
+ align:start position:0%
+type of that path consider all paths
+with the same homotopy path homotopy
+
+ align:start position:0%
+with the same homotopy path homotopy
+ 
+
+ align:start position:0%
+with the same homotopy path homotopy
+type your path should be shortest among
+
+ align:start position:0%
+type your path should be shortest among
+ 
+
+ align:start position:0%
+type your path should be shortest among
+all such paths that is one notion of
+
+ align:start position:0%
+all such paths that is one notion of
+ 
+
+ align:start position:0%
+all such paths that is one notion of
+Auto shrink I don't know if that's the
+
+ align:start position:0%
+Auto shrink I don't know if that's the
+ 
+
+ align:start position:0%
+Auto shrink I don't know if that's the
+official one but it is a that has to do
+
+ align:start position:0%
+official one but it is a that has to do
+ 
+
+ align:start position:0%
+official one but it is a that has to do
+the order in which you set the things
+
+ align:start position:0%
+the order in which you set the things
+ 
+
+ align:start position:0%
+the order in which you set the things
+this description suggests a particular
+
+ align:start position:0%
+this description suggests a particular
+ 
+
+ align:start position:0%
+this description suggests a particular
+order yeah uh so you'd also maybe need a
+
+ align:start position:0%
+order yeah uh so you'd also maybe need a
+ 
+
+ align:start position:0%
+order yeah uh so you'd also maybe need a
+proper ordering yeah so there's the one
+
+ align:start position:0%
+proper ordering yeah so there's the one
+ 
+
+ align:start position:0%
+proper ordering yeah so there's the one
+to the one here there's
+
+ align:start position:0%
+to the one here there's
+ 
+
+ align:start position:0%
+to the one here there's
+multiple ways to well the other way
+
+ align:start position:0%
+multiple ways to well the other way
+ 
+
+ align:start position:0%
+multiple ways to well the other way
+there's multiple ways to get through
+
+ align:start position:0%
+there's multiple ways to get through
+ 
+
+ align:start position:0%
+there's multiple ways to get through
+that square grid I think you can go down
+
+ align:start position:0%
+that square grid I think you can go down
+ 
+
+ align:start position:0%
+that square grid I think you can go down
+and all the way around or you can go
+
+ align:start position:0%
+and all the way around or you can go
+ 
+
+ align:start position:0%
+and all the way around or you can go
+right these would both be the same
+
+ align:start position:0%
+right these would both be the same
+ 
+
+ align:start position:0%
+right these would both be the same
+length and I think those are both
+
+ align:start position:0%
+length and I think those are both
+ 
+
+ align:start position:0%
+length and I think those are both
+considered valid although you have to
+
+ align:start position:0%
+considered valid although you have to
+ 
+
+ align:start position:0%
+considered valid although you have to
+play this particular wouldn't either of
+
+ align:start position:0%
+play this particular wouldn't either of
+ 
+
+ align:start position:0%
+play this particular wouldn't either of
+those it would take the one you chose
+
+ align:start position:0%
+those it would take the one you chose
+ 
+
+ align:start position:0%
+those it would take the one you chose
+right okay so you have still have some
+
+ align:start position:0%
+right okay so you have still have some
+ 
+
+ align:start position:0%
+right okay so you have still have some
+flexibility there are multiple shortest
+
+ align:start position:0%
+flexibility there are multiple shortest
+ 
+
+ align:start position:0%
+flexibility there are multiple shortest
+paths in this world because we're
+
+ align:start position:0%
+paths in this world because we're
+ 
+
+ align:start position:0%
+paths in this world because we're
+Manhattan
+
+ align:start position:0%
+Manhattan
+ 
+
+ align:start position:0%
+Manhattan
+metric uh so this raises the issue of Cl
+
+ align:start position:0%
+metric uh so this raises the issue of Cl
+ 
+
+ align:start position:0%
+metric uh so this raises the issue of Cl
+classic number link and most of the
+
+ align:start position:0%
+classic number link and most of the
+ 
+
+ align:start position:0%
+classic number link and most of the
+puzzles I think all the puzzles I
+
+ align:start position:0%
+puzzles I think all the puzzles I
+ 
+
+ align:start position:0%
+puzzles I think all the puzzles I
+haven't checked every single one
+
+ align:start position:0%
+haven't checked every single one
+ 
+
+ align:start position:0%
+haven't checked every single one
+actually follow these rules uh but again
+
+ align:start position:0%
+actually follow these rules uh but again
+ 
+
+ align:start position:0%
+actually follow these rules uh but again
+I I'm not clear what the rules actually
+
+ align:start position:0%
+I I'm not clear what the rules actually
+ 
+
+ align:start position:0%
+I I'm not clear what the rules actually
+are whether they require this or this uh
+
+ align:start position:0%
+are whether they require this or this uh
+ 
+
+ align:start position:0%
+are whether they require this or this uh
+but luckily there's another paper that
+
+ align:start position:0%
+but luckily there's another paper that
+ 
+
+ align:start position:0%
+but luckily there's another paper that
+covers that case uh it's in Japanese but
+
+ align:start position:0%
+covers that case uh it's in Japanese but
+ 
+
+ align:start position:0%
+covers that case uh it's in Japanese but
+it uh sets up uh the ru
+
+ align:start position:0%
+it uh sets up uh the ru
+ 
+
+ align:start position:0%
+it uh sets up uh the ru
+a it considers the model where you the
+
+ align:start position:0%
+a it considers the model where you the
+ 
+
+ align:start position:0%
+a it considers the model where you the
+classic mode where you have to uh do
+
+ align:start position:0%
+classic mode where you have to uh do
+ 
+
+ align:start position:0%
+classic mode where you have to uh do
+some kind of locally shortest paths and
+
+ align:start position:0%
+some kind of locally shortest paths and
+ 
+
+ align:start position:0%
+some kind of locally shortest paths and
+the gadgets critically exploit that
+
+ align:start position:0%
+the gadgets critically exploit that
+ 
+
+ align:start position:0%
+the gadgets critically exploit that
+feature uh it's a reduction from planer
+
+ align:start position:0%
+feature uh it's a reduction from planer
+ 
+
+ align:start position:0%
+feature uh it's a reduction from planer
+3at we might look at it when we get to
+
+ align:start position:0%
+3at we might look at it when we get to
+ 
+
+ align:start position:0%
+3at we might look at it when we get to
+planer 3at which is the next class or
+
+ align:start position:0%
+planer 3at which is the next class or
+ 
+
+ align:start position:0%
+planer 3at which is the next class or
+two uh or not there's a ton of planer
+
+ align:start position:0%
+two uh or not there's a ton of planer
+ 
+
+ align:start position:0%
+two uh or not there's a ton of planer
+threat proofs but anyway that's been
+
+ align:start position:0%
+threat proofs but anyway that's been
+ 
+
+ align:start position:0%
+threat proofs but anyway that's been
+covered already the actual order of
+
+ align:start position:0%
+covered already the actual order of
+ 
+
+ align:start position:0%
+covered already the actual order of
+events is we proved our result and then
+
+ align:start position:0%
+events is we proved our result and then
+ 
+
+ align:start position:0%
+events is we proved our result and then
+we're like uh oh this is number link uh
+
+ align:start position:0%
+we're like uh oh this is number link uh
+ 
+
+ align:start position:0%
+we're like uh oh this is number link uh
+oh number link is MP complete and that
+
+ align:start position:0%
+oh number link is MP complete and that
+ 
+
+ align:start position:0%
+oh number link is MP complete and that
+was known a few years ago oh good thing
+
+ align:start position:0%
+was known a few years ago oh good thing
+ 
+
+ align:start position:0%
+was known a few years ago oh good thing
+it's a different game that we studed uh
+
+ align:start position:0%
+it's a different game that we studed uh
+ 
+
+ align:start position:0%
+it's a different game that we studed uh
+so there are two versions of number link
+
+ align:start position:0%
+so there are two versions of number link
+ 
+
+ align:start position:0%
+so there are two versions of number link
+now they're both heart so that's the
+
+ align:start position:0%
+now they're both heart so that's the
+ 
+
+ align:start position:0%
+now they're both heart so that's the
+good news and that's all for
+
+ align:start position:0%
+good news and that's all for
+ 
+
+ align:start position:0%
+good news and that's all for
+today this is the Super Mario Brothers
+
+ align:start position:0%
+today this is the Super Mario Brothers
+ 
+
+ align:start position:0%
+today this is the Super Mario Brothers
+edition of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
\ No newline at end of file
diff --git a/eO3RNUAFtDE.txt b/eO3RNUAFtDE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3e7afc03a02d2b273d387ad8e1bb4b2afd03ec18
--- /dev/null
+++ b/eO3RNUAFtDE.txt
@@ -0,0 +1,10595 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu good evening people I've
+
+ align:start position:0%
+ocw.mit.edu good evening people I've
+ 
+
+ align:start position:0%
+ocw.mit.edu good evening people I've
+I've placed so much emphasis on
+
+ align:start position:0%
+I've placed so much emphasis on
+ 
+
+ align:start position:0%
+I've placed so much emphasis on
+Renard's camera because I think it so uh
+
+ align:start position:0%
+Renard's camera because I think it so uh
+ 
+
+ align:start position:0%
+Renard's camera because I think it so uh
+fundamentally expresses uh his sense of
+
+ align:start position:0%
+fundamentally expresses uh his sense of
+ 
+
+ align:start position:0%
+fundamentally expresses uh his sense of
+experience and if you become attentive
+
+ align:start position:0%
+experience and if you become attentive
+ 
+
+ align:start position:0%
+experience and if you become attentive
+to the really quiet and subtle ways in
+
+ align:start position:0%
+to the really quiet and subtle ways in
+ 
+
+ align:start position:0%
+to the really quiet and subtle ways in
+which renoir's camera is almost always
+
+ align:start position:0%
+which renoir's camera is almost always
+ 
+
+ align:start position:0%
+which renoir's camera is almost always
+in action is a part of the story in some
+
+ align:start position:0%
+in action is a part of the story in some
+ 
+
+ align:start position:0%
+in action is a part of the story in some
+sense uh you can begin to capture
+
+ align:start position:0%
+sense uh you can begin to capture
+ 
+
+ align:start position:0%
+sense uh you can begin to capture
+something of his importance in the
+
+ align:start position:0%
+something of his importance in the
+ 
+
+ align:start position:0%
+something of his importance in the
+history of Cinema uh because no director
+
+ align:start position:0%
+history of Cinema uh because no director
+ 
+
+ align:start position:0%
+history of Cinema uh because no director
+uh or Apprentice director who ever uh
+
+ align:start position:0%
+uh or Apprentice director who ever uh
+ 
+
+ align:start position:0%
+uh or Apprentice director who ever uh
+studied or looked at that uh renoir's
+
+ align:start position:0%
+studied or looked at that uh renoir's
+ 
+
+ align:start position:0%
+studied or looked at that uh renoir's
+films came away from it the same uh and
+
+ align:start position:0%
+films came away from it the same uh and
+ 
+
+ align:start position:0%
+films came away from it the same uh and
+his influence is almost impossible to
+
+ align:start position:0%
+his influence is almost impossible to
+ 
+
+ align:start position:0%
+his influence is almost impossible to
+fully measure there there are there are
+
+ align:start position:0%
+fully measure there there are there are
+ 
+
+ align:start position:0%
+fully measure there there are there are
+no uh cinematic Traditions after Renoir
+
+ align:start position:0%
+no uh cinematic Traditions after Renoir
+ 
+
+ align:start position:0%
+no uh cinematic Traditions after Renoir
+that haven't at least in some degree
+
+ align:start position:0%
+that haven't at least in some degree
+ 
+
+ align:start position:0%
+that haven't at least in some degree
+even if not directly then indirectly
+
+ align:start position:0%
+even if not directly then indirectly
+ 
+
+ align:start position:0%
+even if not directly then indirectly
+through other people who have been
+
+ align:start position:0%
+through other people who have been
+ 
+
+ align:start position:0%
+through other people who have been
+influenced by him uh um U been shaped by
+
+ align:start position:0%
+influenced by him uh um U been shaped by
+ 
+
+ align:start position:0%
+influenced by him uh um U been shaped by
+renoir's uh example and I wanted to give
+
+ align:start position:0%
+renoir's uh example and I wanted to give
+ 
+
+ align:start position:0%
+renoir's uh example and I wanted to give
+you one more instance of renoir's camera
+
+ align:start position:0%
+you one more instance of renoir's camera
+ 
+
+ align:start position:0%
+you one more instance of renoir's camera
+this from a film I've mentioned but not
+
+ align:start position:0%
+this from a film I've mentioned but not
+ 
+
+ align:start position:0%
+this from a film I've mentioned but not
+shown you it's from the last of his
+
+ align:start position:0%
+shown you it's from the last of his
+ 
+
+ align:start position:0%
+shown you it's from the last of his
+great French films some people many
+
+ align:start position:0%
+great French films some people many
+ 
+
+ align:start position:0%
+great French films some people many
+people would say it's his greatest film
+
+ align:start position:0%
+people would say it's his greatest film
+ 
+
+ align:start position:0%
+people would say it's his greatest film
+one of the great masterpieces in the
+
+ align:start position:0%
+one of the great masterpieces in the
+ 
+
+ align:start position:0%
+one of the great masterpieces in the
+history of movies the rules of the game
+
+ align:start position:0%
+history of movies the rules of the game
+ 
+
+ align:start position:0%
+history of movies the rules of the game
+the only reason I don't show it in our
+
+ align:start position:0%
+the only reason I don't show it in our
+ 
+
+ align:start position:0%
+the only reason I don't show it in our
+course is that it's in many ways a more
+
+ align:start position:0%
+course is that it's in many ways a more
+ 
+
+ align:start position:0%
+course is that it's in many ways a more
+difficult a more complex film than Grand
+
+ align:start position:0%
+difficult a more complex film than Grand
+ 
+
+ align:start position:0%
+difficult a more complex film than Grand
+Illusion and there's a there's a there's
+
+ align:start position:0%
+Illusion and there's a there's a there's
+ 
+
+ align:start position:0%
+Illusion and there's a there's a there's
+a grand Clarity or Simplicity of a
+
+ align:start position:0%
+a grand Clarity or Simplicity of a
+ 
+
+ align:start position:0%
+a grand Clarity or Simplicity of a
+certain kind not a Simplicity of
+
+ align:start position:0%
+certain kind not a Simplicity of
+ 
+
+ align:start position:0%
+certain kind not a Simplicity of
+character or of vision or of theme but a
+
+ align:start position:0%
+character or of vision or of theme but a
+ 
+
+ align:start position:0%
+character or of vision or of theme but a
+Simplicity of intention
+
+ align:start position:0%
+Simplicity of intention
+ 
+
+ align:start position:0%
+Simplicity of intention
+that becomes clear at least after the
+
+ align:start position:0%
+that becomes clear at least after the
+ 
+
+ align:start position:0%
+that becomes clear at least after the
+fact in Grand delusion it's a more
+
+ align:start position:0%
+fact in Grand delusion it's a more
+ 
+
+ align:start position:0%
+fact in Grand delusion it's a more
+accessible film especially for Americans
+
+ align:start position:0%
+accessible film especially for Americans
+ 
+
+ align:start position:0%
+accessible film especially for Americans
+I think uh the the uh the the rules of
+
+ align:start position:0%
+I think uh the the uh the the rules of
+ 
+
+ align:start position:0%
+I think uh the the uh the the rules of
+the game much more profoundly uh is
+
+ align:start position:0%
+the game much more profoundly uh is
+ 
+
+ align:start position:0%
+the game much more profoundly uh is
+a a meditation on the a theme that is
+
+ align:start position:0%
+a a meditation on the a theme that is
+ 
+
+ align:start position:0%
+a a meditation on the a theme that is
+also present in Grand Illusion as you'll
+
+ align:start position:0%
+also present in Grand Illusion as you'll
+ 
+
+ align:start position:0%
+also present in Grand Illusion as you'll
+see this evening uh the theme of
+
+ align:start position:0%
+see this evening uh the theme of
+ 
+
+ align:start position:0%
+see this evening uh the theme of
+historical transition but it's a much
+
+ align:start position:0%
+historical transition but it's a much
+ 
+
+ align:start position:0%
+historical transition but it's a much
+more complex and and uh extended medit
+
+ align:start position:0%
+more complex and and uh extended medit
+ 
+
+ align:start position:0%
+more complex and and uh extended medit
+on what was happening to French society
+
+ align:start position:0%
+on what was happening to French society
+ 
+
+ align:start position:0%
+on what was happening to French society
+uh in the in this in this immense
+
+ align:start position:0%
+uh in the in this in this immense
+ 
+
+ align:start position:0%
+uh in the in this in this immense
+transition that took place at the
+
+ align:start position:0%
+transition that took place at the
+ 
+
+ align:start position:0%
+transition that took place at the
+beginning of the 20th century
+
+ align:start position:0%
+beginning of the 20th century
+ 
+
+ align:start position:0%
+beginning of the 20th century
+essentially it's a transition as you'll
+
+ align:start position:0%
+essentially it's a transition as you'll
+ 
+
+ align:start position:0%
+essentially it's a transition as you'll
+see dramatized in um the film we're
+
+ align:start position:0%
+see dramatized in um the film we're
+ 
+
+ align:start position:0%
+see dramatized in um the film we're
+showing tonight um Grand delusion it's a
+
+ align:start position:0%
+showing tonight um Grand delusion it's a
+ 
+
+ align:start position:0%
+showing tonight um Grand delusion it's a
+it's a transition from an aristocratic
+
+ align:start position:0%
+it's a transition from an aristocratic
+ 
+
+ align:start position:0%
+it's a transition from an aristocratic
+to a middle class culture from from from
+
+ align:start position:0%
+to a middle class culture from from from
+ 
+
+ align:start position:0%
+to a middle class culture from from from
+a from from a from an aristocratic
+
+ align:start position:0%
+a from from a from an aristocratic
+ 
+
+ align:start position:0%
+a from from a from an aristocratic
+dispensation to a quasi Democratic or
+
+ align:start position:0%
+dispensation to a quasi Democratic or
+ 
+
+ align:start position:0%
+dispensation to a quasi Democratic or
+more democratic dispens ens ation uh and
+
+ align:start position:0%
+more democratic dispens ens ation uh and
+ 
+
+ align:start position:0%
+more democratic dispens ens ation uh and
+and uh this was a topic uh which which
+
+ align:start position:0%
+and uh this was a topic uh which which
+ 
+
+ align:start position:0%
+and uh this was a topic uh which which
+preoccupied many directors Renoir
+
+ align:start position:0%
+preoccupied many directors Renoir
+ 
+
+ align:start position:0%
+preoccupied many directors Renoir
+especially and is a kind of central
+
+ align:start position:0%
+especially and is a kind of central
+ 
+
+ align:start position:0%
+especially and is a kind of central
+Topic in both rules of the game and
+
+ align:start position:0%
+Topic in both rules of the game and
+ 
+
+ align:start position:0%
+Topic in both rules of the game and
+Grand Illusion this scene from uh rules
+
+ align:start position:0%
+Grand Illusion this scene from uh rules
+ 
+
+ align:start position:0%
+Grand Illusion this scene from uh rules
+of the game is maybe his least subtle in
+
+ align:start position:0%
+of the game is maybe his least subtle in
+ 
+
+ align:start position:0%
+of the game is maybe his least subtle in
+some ways or rather the subtlety is
+
+ align:start position:0%
+some ways or rather the subtlety is
+ 
+
+ align:start position:0%
+some ways or rather the subtlety is
+harder to see if you're just looking at
+
+ align:start position:0%
+harder to see if you're just looking at
+ 
+
+ align:start position:0%
+harder to see if you're just looking at
+a clip the subtlety in is involved in
+
+ align:start position:0%
+a clip the subtlety in is involved in
+ 
+
+ align:start position:0%
+a clip the subtlety in is involved in
+the characters themselves who have
+
+ align:start position:0%
+the characters themselves who have
+ 
+
+ align:start position:0%
+the characters themselves who have
+already in some degree been established
+
+ align:start position:0%
+already in some degree been established
+ 
+
+ align:start position:0%
+already in some degree been established
+in a kind of individ uality which then
+
+ align:start position:0%
+in a kind of individ uality which then
+ 
+
+ align:start position:0%
+in a kind of individ uality which then
+further expresses itself in the scene
+
+ align:start position:0%
+further expresses itself in the scene
+ 
+
+ align:start position:0%
+further expresses itself in the scene
+you're going to see uh the basic
+
+ align:start position:0%
+you're going to see uh the basic
+ 
+
+ align:start position:0%
+you're going to see uh the basic
+situation of uh uh the rules of the game
+
+ align:start position:0%
+situation of uh uh the rules of the game
+ 
+
+ align:start position:0%
+situation of uh uh the rules of the game
+is a is a classically uh uh powerful one
+
+ align:start position:0%
+is a is a classically uh uh powerful one
+ 
+
+ align:start position:0%
+is a is a classically uh uh powerful one
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+it it's essentially a weekend of
+
+ align:start position:0%
+it it's essentially a weekend of
+ 
+
+ align:start position:0%
+it it's essentially a weekend of
+festivities a a marquee a grand figure
+
+ align:start position:0%
+festivities a a marquee a grand figure
+ 
+
+ align:start position:0%
+festivities a a marquee a grand figure
+at U presumably who owns a uh a
+
+ align:start position:0%
+at U presumably who owns a uh a
+ 
+
+ align:start position:0%
+at U presumably who owns a uh a
+remarkable Chateau invites a group many
+
+ align:start position:0%
+remarkable Chateau invites a group many
+ 
+
+ align:start position:0%
+remarkable Chateau invites a group many
+invites some friends for a weekend of
+
+ align:start position:0%
+invites some friends for a weekend of
+ 
+
+ align:start position:0%
+invites some friends for a weekend of
+games and shooting of hunting uh at his
+
+ align:start position:0%
+games and shooting of hunting uh at his
+ 
+
+ align:start position:0%
+games and shooting of hunting uh at his
+great Chateau in the country and uh uh
+
+ align:start position:0%
+great Chateau in the country and uh uh
+ 
+
+ align:start position:0%
+great Chateau in the country and uh uh
+the the the film is a kind of series of
+
+ align:start position:0%
+the the the film is a kind of series of
+ 
+
+ align:start position:0%
+the the the film is a kind of series of
+Tableau or a series of festivities all
+
+ align:start position:0%
+Tableau or a series of festivities all
+ 
+
+ align:start position:0%
+Tableau or a series of festivities all
+of which are cankered or damaged in some
+
+ align:start position:0%
+of which are cankered or damaged in some
+ 
+
+ align:start position:0%
+of which are cankered or damaged in some
+way it's as if we have a sense that each
+
+ align:start position:0%
+way it's as if we have a sense that each
+ 
+
+ align:start position:0%
+way it's as if we have a sense that each
+of the festivities or festivals that are
+
+ align:start position:0%
+of the festivities or festivals that are
+ 
+
+ align:start position:0%
+of the festivities or festivals that are
+dramatized in the rules of the game are
+
+ align:start position:0%
+dramatized in the rules of the game are
+ 
+
+ align:start position:0%
+dramatized in the rules of the game are
+diminished versions of something that in
+
+ align:start position:0%
+diminished versions of something that in
+ 
+
+ align:start position:0%
+diminished versions of something that in
+the past had great Authority power and
+
+ align:start position:0%
+the past had great Authority power and
+ 
+
+ align:start position:0%
+the past had great Authority power and
+cultural centrality but has but have
+
+ align:start position:0%
+cultural centrality but has but have
+ 
+
+ align:start position:0%
+cultural centrality but has but have
+become now diminished and even and even
+
+ align:start position:0%
+become now diminished and even and even
+ 
+
+ align:start position:0%
+become now diminished and even and even
+parodically uh uh reduced versions of
+
+ align:start position:0%
+parodically uh uh reduced versions of
+ 
+
+ align:start position:0%
+parodically uh uh reduced versions of
+what they had been when they were part
+
+ align:start position:0%
+what they had been when they were part
+ 
+
+ align:start position:0%
+what they had been when they were part
+of a coherent culture it's almost as if
+
+ align:start position:0%
+of a coherent culture it's almost as if
+ 
+
+ align:start position:0%
+of a coherent culture it's almost as if
+these festivals and rituals have become
+
+ align:start position:0%
+these festivals and rituals have become
+ 
+
+ align:start position:0%
+these festivals and rituals have become
+have been Rec are recognized by the film
+
+ align:start position:0%
+have been Rec are recognized by the film
+ 
+
+ align:start position:0%
+have been Rec are recognized by the film
+although not necessarily by the
+
+ align:start position:0%
+although not necessarily by the
+ 
+
+ align:start position:0%
+although not necessarily by the
+characters inside the film as vestiges
+
+ align:start position:0%
+characters inside the film as vestiges
+ 
+
+ align:start position:0%
+characters inside the film as vestiges
+of a time that has now passed and the
+
+ align:start position:0%
+of a time that has now passed and the
+ 
+
+ align:start position:0%
+of a time that has now passed and the
+most dramatic instance of this subject
+
+ align:start position:0%
+most dramatic instance of this subject
+ 
+
+ align:start position:0%
+most dramatic instance of this subject
+of the of the or embodiment of this
+
+ align:start position:0%
+of the of the or embodiment of this
+ 
+
+ align:start position:0%
+of the of the or embodiment of this
+theme is the senior going to see it's
+
+ align:start position:0%
+theme is the senior going to see it's
+ 
+
+ align:start position:0%
+theme is the senior going to see it's
+the hunting scene uh and uh I I I I I
+
+ align:start position:0%
+the hunting scene uh and uh I I I I I
+ 
+
+ align:start position:0%
+the hunting scene uh and uh I I I I I
+don't I I want you to sort of at least
+
+ align:start position:0%
+don't I I want you to sort of at least
+ 
+
+ align:start position:0%
+don't I I want you to sort of at least
+get a sense of it not not only because
+
+ align:start position:0%
+get a sense of it not not only because
+ 
+
+ align:start position:0%
+get a sense of it not not only because
+it's an important film and I'd like to
+
+ align:start position:0%
+it's an important film and I'd like to
+ 
+
+ align:start position:0%
+it's an important film and I'd like to
+fix it in your mind maybe give you a
+
+ align:start position:0%
+fix it in your mind maybe give you a
+ 
+
+ align:start position:0%
+fix it in your mind maybe give you a
+taste of it so you'll go out and look at
+
+ align:start position:0%
+taste of it so you'll go out and look at
+ 
+
+ align:start position:0%
+taste of it so you'll go out and look at
+the film yourself uh these two these two
+
+ align:start position:0%
+the film yourself uh these two these two
+ 
+
+ align:start position:0%
+the film yourself uh these two these two
+films Grand Illusion and and uh rules of
+
+ align:start position:0%
+films Grand Illusion and and uh rules of
+ 
+
+ align:start position:0%
+films Grand Illusion and and uh rules of
+the game are certainly the Pinnacle of
+
+ align:start position:0%
+the game are certainly the Pinnacle of
+ 
+
+ align:start position:0%
+the game are certainly the Pinnacle of
+renoir's Art and people who know these
+
+ align:start position:0%
+renoir's Art and people who know these
+ 
+
+ align:start position:0%
+renoir's Art and people who know these
+films deeply know something important
+
+ align:start position:0%
+films deeply know something important
+ 
+
+ align:start position:0%
+films deeply know something important
+about film know something important
+
+ align:start position:0%
+about film know something important
+ 
+
+ align:start position:0%
+about film know something important
+about what works of art are
+
+ align:start position:0%
+about what works of art are
+ 
+
+ align:start position:0%
+about what works of art are
+so I want you to see it for that reason
+
+ align:start position:0%
+so I want you to see it for that reason
+ 
+
+ align:start position:0%
+so I want you to see it for that reason
+but I also want you to see it to get one
+
+ align:start position:0%
+but I also want you to see it to get one
+ 
+
+ align:start position:0%
+but I also want you to see it to get one
+more experience outside of grand
+
+ align:start position:0%
+more experience outside of grand
+ 
+
+ align:start position:0%
+more experience outside of grand
+delusion of the way renoir's camera
+
+ align:start position:0%
+delusion of the way renoir's camera
+ 
+
+ align:start position:0%
+delusion of the way renoir's camera
+behaves and especially the way it
+
+ align:start position:0%
+behaves and especially the way it
+ 
+
+ align:start position:0%
+behaves and especially the way it
+establishes a relationship between
+
+ align:start position:0%
+establishes a relationship between
+ 
+
+ align:start position:0%
+establishes a relationship between
+character and and ground between
+
+ align:start position:0%
+character and and ground between
+ 
+
+ align:start position:0%
+character and and ground between
+character and environment and here of
+
+ align:start position:0%
+character and environment and here of
+ 
+
+ align:start position:0%
+character and environment and here of
+course the camera's job is not only to
+
+ align:start position:0%
+course the camera's job is not only to
+ 
+
+ align:start position:0%
+course the camera's job is not only to
+tell us something about the relations
+
+ align:start position:0%
+tell us something about the relations
+ 
+
+ align:start position:0%
+tell us something about the relations
+among the characters and to show us
+
+ align:start position:0%
+among the characters and to show us
+ 
+
+ align:start position:0%
+among the characters and to show us
+their interactions uh in in as
+
+ align:start position:0%
+their interactions uh in in as
+ 
+
+ align:start position:0%
+their interactions uh in in as
+economically powerful a way as possible
+
+ align:start position:0%
+economically powerful a way as possible
+ 
+
+ align:start position:0%
+economically powerful a way as possible
+but also to give us a sense of this of
+
+ align:start position:0%
+but also to give us a sense of this of
+ 
+
+ align:start position:0%
+but also to give us a sense of this of
+this Grand ritual gone bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all freeze it one second this the
+
+ align:start position:0%
+okay all freeze it one second this the
+ 
+
+ align:start position:0%
+okay all freeze it one second this the
+character who that little character
+
+ align:start position:0%
+character who that little character
+ 
+
+ align:start position:0%
+character who that little character
+who's giving instructions you will
+
+ align:start position:0%
+who's giving instructions you will
+ 
+
+ align:start position:0%
+who's giving instructions you will
+recognize him his the actor's name is
+
+ align:start position:0%
+recognize him his the actor's name is
+ 
+
+ align:start position:0%
+recognize him his the actor's name is
+Dalo and he's the one who plays rosenal
+
+ align:start position:0%
+Dalo and he's the one who plays rosenal
+ 
+
+ align:start position:0%
+Dalo and he's the one who plays rosenal
+in Grand Illusion in this film he plays
+
+ align:start position:0%
+in Grand Illusion in this film he plays
+ 
+
+ align:start position:0%
+in Grand Illusion in this film he plays
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Marquee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see how powerful it is not to have
+
+ align:start position:0%
+you see how powerful it is not to have
+ 
+
+ align:start position:0%
+you see how powerful it is not to have
+fake
+
+ align:start position:0%
+fake
+ 
+
+ align:start position:0%
+fake
+music what just the effect of that is on
+
+ align:start position:0%
+music what just the effect of that is on
+ 
+
+ align:start position:0%
+music what just the effect of that is on
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+film I shouldn't say fake music non-
+
+ align:start position:0%
+film I shouldn't say fake music non-
+ 
+
+ align:start position:0%
+film I shouldn't say fake music non-
+diagetic music music That's not part of
+
+ align:start position:0%
+diagetic music music That's not part of
+ 
+
+ align:start position:0%
+diagetic music music That's not part of
+the scene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Doo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ricky
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+freeze it for a second I wish we had
+
+ align:start position:0%
+freeze it for a second I wish we had
+ 
+
+ align:start position:0%
+freeze it for a second I wish we had
+time to dwell on this and I won't do
+
+ align:start position:0%
+time to dwell on this and I won't do
+ 
+
+ align:start position:0%
+time to dwell on this and I won't do
+this too much because I'll run out of
+
+ align:start position:0%
+this too much because I'll run out of
+ 
+
+ align:start position:0%
+this too much because I'll run out of
+time for what I need to tell you but
+
+ align:start position:0%
+time for what I need to tell you but
+ 
+
+ align:start position:0%
+time for what I need to tell you but
+tell me what you see here quickly make
+
+ align:start position:0%
+tell me what you see here quickly make
+ 
+
+ align:start position:0%
+tell me what you see here quickly make
+some conclusions about what what about
+
+ align:start position:0%
+some conclusions about what what about
+ 
+
+ align:start position:0%
+some conclusions about what what about
+this great ritual immediately what would
+
+ align:start position:0%
+this great ritual immediately what would
+ 
+
+ align:start position:0%
+this great ritual immediately what would
+we think if we watching if we're
+
+ align:start position:0%
+we think if we watching if we're
+ 
+
+ align:start position:0%
+we think if we watching if we're
+watching this what's one conclusion you
+
+ align:start position:0%
+watching this what's one conclusion you
+ 
+
+ align:start position:0%
+watching this what's one conclusion you
+draw from this
+
+ align:start position:0%
+draw from this
+ 
+
+ align:start position:0%
+draw from this
+is this uh is this is this hunting uh uh
+
+ align:start position:0%
+is this uh is this is this hunting uh uh
+ 
+
+ align:start position:0%
+is this uh is this is this hunting uh uh
+the the the activity of of of brave
+
+ align:start position:0%
+the the the activity of of of brave
+ 
+
+ align:start position:0%
+the the the activity of of of brave
+pionering souls who are confronting the
+
+ align:start position:0%
+pionering souls who are confronting the
+ 
+
+ align:start position:0%
+pionering souls who are confronting the
+dangers of the
+
+ align:start position:0%
+dangers of the
+ 
+
+ align:start position:0%
+dangers of the
+Wilderness right it's it's an
+
+ align:start position:0%
+Wilderness right it's it's an
+ 
+
+ align:start position:0%
+Wilderness right it's it's an
+unbelievably uh controlled and in many
+
+ align:start position:0%
+unbelievably uh controlled and in many
+ 
+
+ align:start position:0%
+unbelievably uh controlled and in many
+ways murderous environment isn't it what
+
+ align:start position:0%
+ways murderous environment isn't it what
+ 
+
+ align:start position:0%
+ways murderous environment isn't it what
+have we begun to feel about these about
+
+ align:start position:0%
+have we begun to feel about these about
+ 
+
+ align:start position:0%
+have we begun to feel about these about
+these creatures that are being flushed
+
+ align:start position:0%
+these creatures that are being flushed
+ 
+
+ align:start position:0%
+these creatures that are being flushed
+out tremendous sympathy for them right
+
+ align:start position:0%
+out tremendous sympathy for them right
+ 
+
+ align:start position:0%
+out tremendous sympathy for them right
+we're hostile to the adults right were
+
+ align:start position:0%
+we're hostile to the adults right were
+ 
+
+ align:start position:0%
+we're hostile to the adults right were
+hostile to the human beings in the scene
+
+ align:start position:0%
+hostile to the human beings in the scene
+ 
+
+ align:start position:0%
+hostile to the human beings in the scene
+we think there's something to matter
+
+ align:start position:0%
+we think there's something to matter
+ 
+
+ align:start position:0%
+we think there's something to matter
+with this and of course it's not in the
+
+ align:start position:0%
+with this and of course it's not in the
+ 
+
+ align:start position:0%
+with this and of course it's not in the
+olden days in the day in the presumably
+
+ align:start position:0%
+olden days in the day in the presumably
+ 
+
+ align:start position:0%
+olden days in the day in the presumably
+in the days when when such hunts
+
+ align:start position:0%
+in the days when when such hunts
+ 
+
+ align:start position:0%
+in the days when when such hunts
+occurred in a more in a more coherent
+
+ align:start position:0%
+occurred in a more in a more coherent
+ 
+
+ align:start position:0%
+occurred in a more in a more coherent
+and less and and less forced way you
+
+ align:start position:0%
+and less and and less forced way you
+ 
+
+ align:start position:0%
+and less and and less forced way you
+didn't need beaters to go around in the
+
+ align:start position:0%
+didn't need beaters to go around in the
+ 
+
+ align:start position:0%
+didn't need beaters to go around in the
+woods making noise to scare the few re
+
+ align:start position:0%
+woods making noise to scare the few re
+ 
+
+ align:start position:0%
+woods making noise to scare the few re
+the few vestiges of rabbits and other
+
+ align:start position:0%
+the few vestiges of rabbits and other
+ 
+
+ align:start position:0%
+the few vestiges of rabbits and other
+game out into the open so people with
+
+ align:start position:0%
+game out into the open so people with
+ 
+
+ align:start position:0%
+game out into the open so people with
+giant guns could kill them right because
+
+ align:start position:0%
+giant guns could kill them right because
+ 
+
+ align:start position:0%
+giant guns could kill them right because
+the place was teaming with in the 16th
+
+ align:start position:0%
+the place was teaming with in the 16th
+ 
+
+ align:start position:0%
+the place was teaming with in the 16th
+or the 15th century or the 18 Century
+
+ align:start position:0%
+or the 15th century or the 18 Century
+ 
+
+ align:start position:0%
+or the 15th century or the 18 Century
+the these fields were teaming with game
+
+ align:start position:0%
+the these fields were teaming with game
+ 
+
+ align:start position:0%
+the these fields were teaming with game
+now in the 20th century you have to beat
+
+ align:start position:0%
+now in the 20th century you have to beat
+ 
+
+ align:start position:0%
+now in the 20th century you have to beat
+the sticks to get them to come out what
+
+ align:start position:0%
+the sticks to get them to come out what
+ 
+
+ align:start position:0%
+the sticks to get them to come out what
+a parody of what an actual hunt would be
+
+ align:start position:0%
+a parody of what an actual hunt would be
+ 
+
+ align:start position:0%
+a parody of what an actual hunt would be
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead when this film was made I forgot
+
+ align:start position:0%
+ahead when this film was made I forgot
+ 
+
+ align:start position:0%
+ahead when this film was made I forgot
+the number I have it in my notes but I
+
+ align:start position:0%
+the number I have it in my notes but I
+ 
+
+ align:start position:0%
+the number I have it in my notes but I
+couldn't find them there I left them in
+
+ align:start position:0%
+couldn't find them there I left them in
+ 
+
+ align:start position:0%
+couldn't find them there I left them in
+my office a a certain number of these
+
+ align:start position:0%
+my office a a certain number of these
+ 
+
+ align:start position:0%
+my office a a certain number of these
+animals were actually killed in the in
+
+ align:start position:0%
+animals were actually killed in the in
+ 
+
+ align:start position:0%
+animals were actually killed in the in
+the in the of the film I forgot the
+
+ align:start position:0%
+the in the of the film I forgot the
+ 
+
+ align:start position:0%
+the in the of the film I forgot the
+number but it's a significant
+
+ align:start position:0%
+number but it's a significant
+ 
+
+ align:start position:0%
+number but it's a significant
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+number today they when they made such a
+
+ align:start position:0%
+number today they when they made such a
+ 
+
+ align:start position:0%
+number today they when they made such a
+film There are rules that don't allow
+
+ align:start position:0%
+film There are rules that don't allow
+ 
+
+ align:start position:0%
+film There are rules that don't allow
+them to kill
+
+ align:start position:0%
+them to kill
+ 
+
+ align:start position:0%
+them to kill
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you get some sense of how powerful
+
+ align:start position:0%
+okay you get some sense of how powerful
+ 
+
+ align:start position:0%
+okay you get some sense of how powerful
+a saturnist but also how quiet a
+
+ align:start position:0%
+a saturnist but also how quiet a
+ 
+
+ align:start position:0%
+a saturnist but also how quiet a
+saturnist he can be it's not as if the
+
+ align:start position:0%
+saturnist he can be it's not as if the
+ 
+
+ align:start position:0%
+saturnist he can be it's not as if the
+film it's not as if there's someone
+
+ align:start position:0%
+film it's not as if there's someone
+ 
+
+ align:start position:0%
+film it's not as if there's someone
+there saying isn't this horrible he's
+
+ align:start position:0%
+there saying isn't this horrible he's
+ 
+
+ align:start position:0%
+there saying isn't this horrible he's
+leaving it to the audience to figure out
+
+ align:start position:0%
+leaving it to the audience to figure out
+ 
+
+ align:start position:0%
+leaving it to the audience to figure out
+although it doesn't take too much to
+
+ align:start position:0%
+although it doesn't take too much to
+ 
+
+ align:start position:0%
+although it doesn't take too much to
+figure it out does it what what what you
+
+ align:start position:0%
+figure it out does it what what what you
+ 
+
+ align:start position:0%
+figure it out does it what what what you
+can't pick up from this it makes maybe
+
+ align:start position:0%
+can't pick up from this it makes maybe
+ 
+
+ align:start position:0%
+can't pick up from this it makes maybe
+the scene that I've shown you may make
+
+ align:start position:0%
+the scene that I've shown you may make
+ 
+
+ align:start position:0%
+the scene that I've shown you may make
+the scene seem cruder than it is
+
+ align:start position:0%
+the scene seem cruder than it is
+ 
+
+ align:start position:0%
+the scene seem cruder than it is
+virtually all the characters faces that
+
+ align:start position:0%
+virtually all the characters faces that
+ 
+
+ align:start position:0%
+virtually all the characters faces that
+you've seen many most of them anyway are
+
+ align:start position:0%
+you've seen many most of them anyway are
+ 
+
+ align:start position:0%
+you've seen many most of them anyway are
+major characters in the film and even by
+
+ align:start position:0%
+major characters in the film and even by
+ 
+
+ align:start position:0%
+major characters in the film and even by
+this time in the film you've gotten to
+
+ align:start position:0%
+this time in the film you've gotten to
+ 
+
+ align:start position:0%
+this time in the film you've gotten to
+know some of them quite well so they've
+
+ align:start position:0%
+know some of them quite well so they've
+ 
+
+ align:start position:0%
+know some of them quite well so they've
+been humanized and individual ated and
+
+ align:start position:0%
+been humanized and individual ated and
+ 
+
+ align:start position:0%
+been humanized and individual ated and
+that makes the brutality to which they
+
+ align:start position:0%
+that makes the brutality to which they
+ 
+
+ align:start position:0%
+that makes the brutality to which they
+are mostly oblivious of what's Happening
+
+ align:start position:0%
+are mostly oblivious of what's Happening
+ 
+
+ align:start position:0%
+are mostly oblivious of what's Happening
+even more powerful you don't hate the
+
+ align:start position:0%
+even more powerful you don't hate the
+ 
+
+ align:start position:0%
+even more powerful you don't hate the
+characters who are doing this shooting
+
+ align:start position:0%
+characters who are doing this shooting
+ 
+
+ align:start position:0%
+characters who are doing this shooting
+you know them for the comic and and
+
+ align:start position:0%
+you know them for the comic and and
+ 
+
+ align:start position:0%
+you know them for the comic and and
+damaged and ambitious and idealistic and
+
+ align:start position:0%
+damaged and ambitious and idealistic and
+ 
+
+ align:start position:0%
+damaged and ambitious and idealistic and
+and foolish characters they've already
+
+ align:start position:0%
+and foolish characters they've already
+ 
+
+ align:start position:0%
+and foolish characters they've already
+shown themselves to be by the time they
+
+ align:start position:0%
+shown themselves to be by the time they
+ 
+
+ align:start position:0%
+shown themselves to be by the time they
+get into this scene it's almost as if
+
+ align:start position:0%
+get into this scene it's almost as if
+ 
+
+ align:start position:0%
+get into this scene it's almost as if
+they themselves are also victims of this
+
+ align:start position:0%
+they themselves are also victims of this
+ 
+
+ align:start position:0%
+they themselves are also victims of this
+ritual they're part of so there's a kind
+
+ align:start position:0%
+ritual they're part of so there's a kind
+ 
+
+ align:start position:0%
+ritual they're part of so there's a kind
+of subtlety that you can't pick up on
+
+ align:start position:0%
+of subtlety that you can't pick up on
+ 
+
+ align:start position:0%
+of subtlety that you can't pick up on
+just watching the clip that that uh is
+
+ align:start position:0%
+just watching the clip that that uh is
+ 
+
+ align:start position:0%
+just watching the clip that that uh is
+present for any for any audience member
+
+ align:start position:0%
+present for any for any audience member
+ 
+
+ align:start position:0%
+present for any for any audience member
+but I wanted you to see the this scene
+
+ align:start position:0%
+but I wanted you to see the this scene
+ 
+
+ align:start position:0%
+but I wanted you to see the this scene
+also in part again to show you how
+
+ align:start position:0%
+also in part again to show you how
+ 
+
+ align:start position:0%
+also in part again to show you how
+powerfully uh Ren War's camera is able
+
+ align:start position:0%
+powerfully uh Ren War's camera is able
+ 
+
+ align:start position:0%
+powerfully uh Ren War's camera is able
+to uh create emotional and intellectual
+
+ align:start position:0%
+to uh create emotional and intellectual
+ 
+
+ align:start position:0%
+to uh create emotional and intellectual
+responses in the audience in a way that
+
+ align:start position:0%
+responses in the audience in a way that
+ 
+
+ align:start position:0%
+responses in the audience in a way that
+is in some sense diametrically opposed
+
+ align:start position:0%
+is in some sense diametrically opposed
+ 
+
+ align:start position:0%
+is in some sense diametrically opposed
+to what we might call expressionist
+
+ align:start position:0%
+to what we might call expressionist
+ 
+
+ align:start position:0%
+to what we might call expressionist
+directors like Hitchcock or eisenstein
+
+ align:start position:0%
+directors like Hitchcock or eisenstein
+ 
+
+ align:start position:0%
+directors like Hitchcock or eisenstein
+might do by manipulating our our our
+
+ align:start position:0%
+might do by manipulating our our our
+ 
+
+ align:start position:0%
+might do by manipulating our our our
+attitudes by uh constant by very rapid
+
+ align:start position:0%
+attitudes by uh constant by very rapid
+ 
+
+ align:start position:0%
+attitudes by uh constant by very rapid
+edit and and by giving us high or low
+
+ align:start position:0%
+edit and and by giving us high or low
+ 
+
+ align:start position:0%
+edit and and by giving us high or low
+angle shots that control our emotional
+
+ align:start position:0%
+angle shots that control our emotional
+ 
+
+ align:start position:0%
+angle shots that control our emotional
+response because of the way we're seeing
+
+ align:start position:0%
+response because of the way we're seeing
+ 
+
+ align:start position:0%
+response because of the way we're seeing
+things uh uh renoir's strategies can be
+
+ align:start position:0%
+things uh uh renoir's strategies can be
+ 
+
+ align:start position:0%
+things uh uh renoir's strategies can be
+just as powerful in terms of emotional
+
+ align:start position:0%
+just as powerful in terms of emotional
+ 
+
+ align:start position:0%
+just as powerful in terms of emotional
+and moral reaction but Renoir Renoir
+
+ align:start position:0%
+and moral reaction but Renoir Renoir
+ 
+
+ align:start position:0%
+and moral reaction but Renoir Renoir
+strategy is quite different present the
+
+ align:start position:0%
+strategy is quite different present the
+ 
+
+ align:start position:0%
+strategy is quite different present the
+evidence in some sense to the to the
+
+ align:start position:0%
+evidence in some sense to the to the
+ 
+
+ align:start position:0%
+evidence in some sense to the to the
+audience keep keep the keep the camera
+
+ align:start position:0%
+audience keep keep the keep the camera
+ 
+
+ align:start position:0%
+audience keep keep the keep the camera
+at at a level that allows the full
+
+ align:start position:0%
+at at a level that allows the full
+ 
+
+ align:start position:0%
+at at a level that allows the full
+action to be taken in I I hope you
+
+ align:start position:0%
+action to be taken in I I hope you
+ 
+
+ align:start position:0%
+action to be taken in I I hope you
+realize that there were relatively few
+
+ align:start position:0%
+realize that there were relatively few
+ 
+
+ align:start position:0%
+realize that there were relatively few
+Cuts in that scene and in in most of uh
+
+ align:start position:0%
+Cuts in that scene and in in most of uh
+ 
+
+ align:start position:0%
+Cuts in that scene and in in most of uh
+renoir's work the number of edits is
+
+ align:start position:0%
+renoir's work the number of edits is
+ 
+
+ align:start position:0%
+renoir's work the number of edits is
+relatively small compared to the number
+
+ align:start position:0%
+relatively small compared to the number
+ 
+
+ align:start position:0%
+relatively small compared to the number
+of scenes that are extended the number
+
+ align:start position:0%
+of scenes that are extended the number
+ 
+
+ align:start position:0%
+of scenes that are extended the number
+the the the long the amount of long
+
+ align:start position:0%
+the the the long the amount of long
+ 
+
+ align:start position:0%
+the the the long the amount of long
+takes that we have and there are certain
+
+ align:start position:0%
+takes that we have and there are certain
+ 
+
+ align:start position:0%
+takes that we have and there are certain
+moments in the in the film where he will
+
+ align:start position:0%
+moments in the in the film where he will
+ 
+
+ align:start position:0%
+moments in the in the film where he will
+vary this strategy for example and you
+
+ align:start position:0%
+vary this strategy for example and you
+ 
+
+ align:start position:0%
+vary this strategy for example and you
+might want to watch for this in
+
+ align:start position:0%
+might want to watch for this in
+ 
+
+ align:start position:0%
+might want to watch for this in
+tonight's film there's one moment in
+
+ align:start position:0%
+tonight's film there's one moment in
+ 
+
+ align:start position:0%
+tonight's film there's one moment in
+tonight's film
+
+ align:start position:0%
+tonight's film
+ 
+
+ align:start position:0%
+tonight's film
+uh where uh an interview between two of
+
+ align:start position:0%
+uh where uh an interview between two of
+ 
+
+ align:start position:0%
+uh where uh an interview between two of
+the central characters the the German
+
+ align:start position:0%
+the central characters the the German
+ 
+
+ align:start position:0%
+the central characters the the German
+prison Warden uh
+
+ align:start position:0%
+prison Warden uh
+ 
+
+ align:start position:0%
+prison Warden uh
+played by Eric Von scheim uh and the the
+
+ align:start position:0%
+played by Eric Von scheim uh and the the
+ 
+
+ align:start position:0%
+played by Eric Von scheim uh and the the
+the French Aristocrat um named dubu
+
+ align:start position:0%
+the French Aristocrat um named dubu
+ 
+
+ align:start position:0%
+the French Aristocrat um named dubu
+played by an actor named defres defr and
+
+ align:start position:0%
+played by an actor named defres defr and
+ 
+
+ align:start position:0%
+played by an actor named defres defr and
+and U uh in this scene between the
+
+ align:start position:0%
+and U uh in this scene between the
+ 
+
+ align:start position:0%
+and U uh in this scene between the
+German and the Frenchman one of the
+
+ align:start position:0%
+German and the Frenchman one of the
+ 
+
+ align:start position:0%
+German and the Frenchman one of the
+things we recognize is because they
+
+ align:start position:0%
+things we recognize is because they
+ 
+
+ align:start position:0%
+things we recognize is because they
+belong to the aristocratic class they
+
+ align:start position:0%
+belong to the aristocratic class they
+ 
+
+ align:start position:0%
+belong to the aristocratic class they
+have a lot in common what they speak
+
+ align:start position:0%
+have a lot in common what they speak
+ 
+
+ align:start position:0%
+have a lot in common what they speak
+English for example they because they
+
+ align:start position:0%
+English for example they because they
+ 
+
+ align:start position:0%
+English for example they because they
+both know English right even though
+
+ align:start position:0%
+both know English right even though
+ 
+
+ align:start position:0%
+both know English right even though
+one's a German and one's a Frenchman and
+
+ align:start position:0%
+one's a German and one's a Frenchman and
+ 
+
+ align:start position:0%
+one's a German and one's a Frenchman and
+there is a sense in the film of a very
+
+ align:start position:0%
+there is a sense in the film of a very
+ 
+
+ align:start position:0%
+there is a sense in the film of a very
+powerful one that's established that
+
+ align:start position:0%
+powerful one that's established that
+ 
+
+ align:start position:0%
+powerful one that's established that
+they have in in some sense a greater
+
+ align:start position:0%
+they have in in some sense a greater
+ 
+
+ align:start position:0%
+they have in in some sense a greater
+connection to each other than they have
+
+ align:start position:0%
+connection to each other than they have
+ 
+
+ align:start position:0%
+connection to each other than they have
+with their own uh uh uh with other
+
+ align:start position:0%
+with their own uh uh uh with other
+ 
+
+ align:start position:0%
+with their own uh uh uh with other
+soldiers of of in in their own armies uh
+
+ align:start position:0%
+soldiers of of in in their own armies uh
+ 
+
+ align:start position:0%
+soldiers of of in in their own armies uh
+and the film is the film meditates on
+
+ align:start position:0%
+and the film is the film meditates on
+ 
+
+ align:start position:0%
+and the film is the film meditates on
+these distinctions and especially on
+
+ align:start position:0%
+these distinctions and especially on
+ 
+
+ align:start position:0%
+these distinctions and especially on
+this uh conundrum of social class in
+
+ align:start position:0%
+this uh conundrum of social class in
+ 
+
+ align:start position:0%
+this uh conundrum of social class in
+rather a complex way as as I'll suggest
+
+ align:start position:0%
+rather a complex way as as I'll suggest
+ 
+
+ align:start position:0%
+rather a complex way as as I'll suggest
+well in the very first scene between um
+
+ align:start position:0%
+well in the very first scene between um
+ 
+
+ align:start position:0%
+well in the very first scene between um
+uh uh Balu and ralen Stein the German
+
+ align:start position:0%
+uh uh Balu and ralen Stein the German
+ 
+
+ align:start position:0%
+uh uh Balu and ralen Stein the German
+and the Frenchmen um um
+
+ align:start position:0%
+and the Frenchmen um um
+ 
+
+ align:start position:0%
+and the Frenchmen um um
+Renoir uses a fairly standard procedure
+
+ align:start position:0%
+Renoir uses a fairly standard procedure
+ 
+
+ align:start position:0%
+Renoir uses a fairly standard procedure
+much more common to other directors it's
+
+ align:start position:0%
+much more common to other directors it's
+ 
+
+ align:start position:0%
+much more common to other directors it's
+sometimes called a shot counter shot
+
+ align:start position:0%
+sometimes called a shot counter shot
+ 
+
+ align:start position:0%
+sometimes called a shot counter shot
+style so that when you're it's
+
+ align:start position:0%
+style so that when you're it's
+ 
+
+ align:start position:0%
+style so that when you're it's
+especially common on American television
+
+ align:start position:0%
+especially common on American television
+ 
+
+ align:start position:0%
+especially common on American television
+but it was it's common in the movies too
+
+ align:start position:0%
+but it was it's common in the movies too
+ 
+
+ align:start position:0%
+but it was it's common in the movies too
+in which when you see characters in
+
+ align:start position:0%
+in which when you see characters in
+ 
+
+ align:start position:0%
+in which when you see characters in
+conversation uh you'll get relatively
+
+ align:start position:0%
+conversation uh you'll get relatively
+ 
+
+ align:start position:0%
+conversation uh you'll get relatively
+rapid cutting and you look at one face
+
+ align:start position:0%
+rapid cutting and you look at one face
+ 
+
+ align:start position:0%
+rapid cutting and you look at one face
+then then the camera will shift and you
+
+ align:start position:0%
+then then the camera will shift and you
+ 
+
+ align:start position:0%
+then then the camera will shift and you
+look back at the other face there'll be
+
+ align:start position:0%
+look back at the other face there'll be
+ 
+
+ align:start position:0%
+look back at the other face there'll be
+a cut and you'll look at right and you
+
+ align:start position:0%
+a cut and you'll look at right and you
+ 
+
+ align:start position:0%
+a cut and you'll look at right and you
+you'll constantly shift back and forth
+
+ align:start position:0%
+you'll constantly shift back and forth
+ 
+
+ align:start position:0%
+you'll constantly shift back and forth
+this shot counter shot style uh but he
+
+ align:start position:0%
+this shot counter shot style uh but he
+ 
+
+ align:start position:0%
+this shot counter shot style uh but he
+renir uses this kind of style rarely
+
+ align:start position:0%
+renir uses this kind of style rarely
+ 
+
+ align:start position:0%
+renir uses this kind of style rarely
+because it involves the first of all it
+
+ align:start position:0%
+because it involves the first of all it
+ 
+
+ align:start position:0%
+because it involves the first of all it
+involves the idea of cutting it involves
+
+ align:start position:0%
+involves the idea of cutting it involves
+ 
+
+ align:start position:0%
+involves the idea of cutting it involves
+the idea of separation why use shot
+
+ align:start position:0%
+the idea of separation why use shot
+ 
+
+ align:start position:0%
+the idea of separation why use shot
+counter shot Renoir would say when I can
+
+ align:start position:0%
+counter shot Renoir would say when I can
+ 
+
+ align:start position:0%
+counter shot Renoir would say when I can
+move my camera like this and show the
+
+ align:start position:0%
+move my camera like this and show the
+ 
+
+ align:start position:0%
+move my camera like this and show the
+two characters together and move it and
+
+ align:start position:0%
+two characters together and move it and
+ 
+
+ align:start position:0%
+two characters together and move it and
+move it around in another way and show
+
+ align:start position:0%
+move it around in another way and show
+ 
+
+ align:start position:0%
+move it around in another way and show
+the back of one character's head and the
+
+ align:start position:0%
+the back of one character's head and the
+ 
+
+ align:start position:0%
+the back of one character's head and the
+way the other is re in other words if
+
+ align:start position:0%
+way the other is re in other words if
+ 
+
+ align:start position:0%
+way the other is re in other words if
+the camera if the camera's part of the
+
+ align:start position:0%
+the camera if the camera's part of the
+ 
+
+ align:start position:0%
+the camera if the camera's part of the
+action a fluid part of the action
+
+ align:start position:0%
+action a fluid part of the action
+ 
+
+ align:start position:0%
+action a fluid part of the action
+there's more I can show you more about
+
+ align:start position:0%
+there's more I can show you more about
+ 
+
+ align:start position:0%
+there's more I can show you more about
+character renmore would say but in that
+
+ align:start position:0%
+character renmore would say but in that
+ 
+
+ align:start position:0%
+character renmore would say but in that
+particular scene he doesn't do it in
+
+ align:start position:0%
+particular scene he doesn't do it in
+ 
+
+ align:start position:0%
+particular scene he doesn't do it in
+this first interview extended interview
+
+ align:start position:0%
+this first interview extended interview
+ 
+
+ align:start position:0%
+this first interview extended interview
+it lasts about 2 minutes and 45 seconds
+
+ align:start position:0%
+it lasts about 2 minutes and 45 seconds
+ 
+
+ align:start position:0%
+it lasts about 2 minutes and 45 seconds
+and it uses 21 shots 21 separate shots
+
+ align:start position:0%
+and it uses 21 shots 21 separate shots
+ 
+
+ align:start position:0%
+and it uses 21 shots 21 separate shots
+in 2 minutes and 45 seconds for Renoir
+
+ align:start position:0%
+in 2 minutes and 45 seconds for Renoir
+ 
+
+ align:start position:0%
+in 2 minutes and 45 seconds for Renoir
+that's a tremendous number of edits
+
+ align:start position:0%
+that's a tremendous number of edits
+ 
+
+ align:start position:0%
+that's a tremendous number of edits
+right and one way you can tell that this
+
+ align:start position:0%
+right and one way you can tell that this
+ 
+
+ align:start position:0%
+right and one way you can tell that this
+is a and what what why would he do it
+
+ align:start position:0%
+is a and what what why would he do it
+ 
+
+ align:start position:0%
+is a and what what why would he do it
+there because it's very unusual for him
+
+ align:start position:0%
+there because it's very unusual for him
+ 
+
+ align:start position:0%
+there because it's very unusual for him
+to use this shot counter shot style in
+
+ align:start position:0%
+to use this shot counter shot style in
+ 
+
+ align:start position:0%
+to use this shot counter shot style in
+the film why would he do it he wants to
+
+ align:start position:0%
+the film why would he do it he wants to
+ 
+
+ align:start position:0%
+the film why would he do it he wants to
+emphasize their separation their
+
+ align:start position:0%
+emphasize their separation their
+ 
+
+ align:start position:0%
+emphasize their separation their
+isolation from each other their distance
+
+ align:start position:0%
+isolation from each other their distance
+ 
+
+ align:start position:0%
+isolation from each other their distance
+from each other right and and there is a
+
+ align:start position:0%
+from each other right and and there is a
+ 
+
+ align:start position:0%
+from each other right and and there is a
+later scene in the film uh near the very
+
+ align:start position:0%
+later scene in the film uh near the very
+ 
+
+ align:start position:0%
+later scene in the film uh near the very
+end the film uh again between du and uh
+
+ align:start position:0%
+end the film uh again between du and uh
+ 
+
+ align:start position:0%
+end the film uh again between du and uh
+uh uh uh uh and another character uh but
+
+ align:start position:0%
+uh uh uh uh and another character uh but
+ 
+
+ align:start position:0%
+uh uh uh uh and another character uh but
+this one between du and marel the French
+
+ align:start position:0%
+this one between du and marel the French
+ 
+
+ align:start position:0%
+this one between du and marel the French
+working man who working class figure
+
+ align:start position:0%
+working man who working class figure
+ 
+
+ align:start position:0%
+working man who working class figure
+who's who's on the French side just
+
+ align:start position:0%
+who's who's on the French side just
+ 
+
+ align:start position:0%
+who's who's on the French side just
+before there's an attempted escape and
+
+ align:start position:0%
+before there's an attempted escape and
+ 
+
+ align:start position:0%
+before there's an attempted escape and
+that scene is almost as long it's 2
+
+ align:start position:0%
+that scene is almost as long it's 2
+ 
+
+ align:start position:0%
+that scene is almost as long it's 2
+minutes and and 20 seconds long but that
+
+ align:start position:0%
+minutes and and 20 seconds long but that
+ 
+
+ align:start position:0%
+minutes and and 20 seconds long but that
+scene only has three separate edits in
+
+ align:start position:0%
+scene only has three separate edits in
+ 
+
+ align:start position:0%
+scene only has three separate edits in
+it and you might compare it the farewell
+
+ align:start position:0%
+it and you might compare it the farewell
+ 
+
+ align:start position:0%
+it and you might compare it the farewell
+scene is a very obvious one and you'll
+
+ align:start position:0%
+scene is a very obvious one and you'll
+ 
+
+ align:start position:0%
+scene is a very obvious one and you'll
+you'll recognize it when you see it and
+
+ align:start position:0%
+you'll recognize it when you see it and
+ 
+
+ align:start position:0%
+you'll recognize it when you see it and
+and and of course the reason is that he
+
+ align:start position:0%
+and and of course the reason is that he
+ 
+
+ align:start position:0%
+and and of course the reason is that he
+wants to emphasize in so far as it's
+
+ align:start position:0%
+wants to emphasize in so far as it's
+ 
+
+ align:start position:0%
+wants to emphasize in so far as it's
+possible that they are together he wants
+
+ align:start position:0%
+possible that they are together he wants
+ 
+
+ align:start position:0%
+possible that they are together he wants
+to minimize the sense of isolation uh in
+
+ align:start position:0%
+to minimize the sense of isolation uh in
+ 
+
+ align:start position:0%
+to minimize the sense of isolation uh in
+that sequence again I mention this
+
+ align:start position:0%
+that sequence again I mention this
+ 
+
+ align:start position:0%
+that sequence again I mention this
+because I want you to become as
+
+ align:start position:0%
+because I want you to become as
+ 
+
+ align:start position:0%
+because I want you to become as
+attentive as possible without destroying
+
+ align:start position:0%
+attentive as possible without destroying
+ 
+
+ align:start position:0%
+attentive as possible without destroying
+your enjoyment of the film to the
+
+ align:start position:0%
+your enjoyment of the film to the
+ 
+
+ align:start position:0%
+your enjoyment of the film to the
+camera's way of Behaving uh so U one of
+
+ align:start position:0%
+camera's way of Behaving uh so U one of
+ 
+
+ align:start position:0%
+camera's way of Behaving uh so U one of
+the ways to summarize what I'm trying to
+
+ align:start position:0%
+the ways to summarize what I'm trying to
+ 
+
+ align:start position:0%
+the ways to summarize what I'm trying to
+say about the way the camera Works in
+
+ align:start position:0%
+say about the way the camera Works in
+ 
+
+ align:start position:0%
+say about the way the camera Works in
+Renoir I want to remind you that even in
+
+ align:start position:0%
+Renoir I want to remind you that even in
+ 
+
+ align:start position:0%
+Renoir I want to remind you that even in
+his darkest films uh um the his his
+
+ align:start position:0%
+his darkest films uh um the his his
+ 
+
+ align:start position:0%
+his darkest films uh um the his his
+camera work carries an undercurrent of
+
+ align:start position:0%
+camera work carries an undercurrent of
+ 
+
+ align:start position:0%
+camera work carries an undercurrent of
+excitement even sometimes a kind of Joy
+
+ align:start position:0%
+excitement even sometimes a kind of Joy
+ 
+
+ align:start position:0%
+excitement even sometimes a kind of Joy
+at the sheer particular the
+
+ align:start position:0%
+at the sheer particular the
+ 
+
+ align:start position:0%
+at the sheer particular the
+particularity of the world um uh you can
+
+ align:start position:0%
+particularity of the world um uh you can
+ 
+
+ align:start position:0%
+particularity of the world um uh you can
+you can sense his his awareness of
+
+ align:start position:0%
+you can sense his his awareness of
+ 
+
+ align:start position:0%
+you can sense his his awareness of
+ambigu of human ambiguity and his Wonder
+
+ align:start position:0%
+ambigu of human ambiguity and his Wonder
+ 
+
+ align:start position:0%
+ambigu of human ambiguity and his Wonder
+at the texture of the visible world uh
+
+ align:start position:0%
+at the texture of the visible world uh
+ 
+
+ align:start position:0%
+at the texture of the visible world uh
+all through his films of the French of
+
+ align:start position:0%
+all through his films of the French of
+ 
+
+ align:start position:0%
+all through his films of the French of
+his of his so-called French period and
+
+ align:start position:0%
+his of his so-called French period and
+ 
+
+ align:start position:0%
+his of his so-called French period and
+especially in the film you're going to
+
+ align:start position:0%
+especially in the film you're going to
+ 
+
+ align:start position:0%
+especially in the film you're going to
+see tonight which is in many ways in
+
+ align:start position:0%
+see tonight which is in many ways in
+ 
+
+ align:start position:0%
+see tonight which is in many ways in
+environments that are very un poetic
+
+ align:start position:0%
+environments that are very un poetic
+ 
+
+ align:start position:0%
+environments that are very un poetic
+right there the entire film takes place
+
+ align:start position:0%
+right there the entire film takes place
+ 
+
+ align:start position:0%
+right there the entire film takes place
+in a series of prison camps the entire
+
+ align:start position:0%
+in a series of prison camps the entire
+ 
+
+ align:start position:0%
+in a series of prison camps the entire
+film is about these French prisoners of
+
+ align:start position:0%
+film is about these French prisoners of
+ 
+
+ align:start position:0%
+film is about these French prisoners of
+War there's an introduction or prologue
+
+ align:start position:0%
+War there's an introduction or prologue
+ 
+
+ align:start position:0%
+War there's an introduction or prologue
+before they're captured and then after
+
+ align:start position:0%
+before they're captured and then after
+ 
+
+ align:start position:0%
+before they're captured and then after
+they're captured we see them in a series
+
+ align:start position:0%
+they're captured we see them in a series
+ 
+
+ align:start position:0%
+they're captured we see them in a series
+of prison camps uh um and and uh uh it's
+
+ align:start position:0%
+of prison camps uh um and and uh uh it's
+ 
+
+ align:start position:0%
+of prison camps uh um and and uh uh it's
+quite an
+
+ align:start position:0%
+quite an
+ 
+
+ align:start position:0%
+quite an
+amazing experience in some ways to watch
+
+ align:start position:0%
+amazing experience in some ways to watch
+ 
+
+ align:start position:0%
+amazing experience in some ways to watch
+renoir's camera discover the complexity
+
+ align:start position:0%
+renoir's camera discover the complexity
+ 
+
+ align:start position:0%
+renoir's camera discover the complexity
+of even the uh of of of of a of of of a
+
+ align:start position:0%
+of even the uh of of of of a of of of a
+ 
+
+ align:start position:0%
+of even the uh of of of of a of of of a
+of a world that seems in on the surface
+
+ align:start position:0%
+of a world that seems in on the surface
+ 
+
+ align:start position:0%
+of a world that seems in on the surface
+to be so un promising uh and so
+
+ align:start position:0%
+to be so un promising uh and so
+ 
+
+ align:start position:0%
+to be so un promising uh and so
+uninteresting so lacking in texture uh
+
+ align:start position:0%
+uninteresting so lacking in texture uh
+ 
+
+ align:start position:0%
+uninteresting so lacking in texture uh
+we we can think of U we can think of
+
+ align:start position:0%
+we we can think of U we can think of
+ 
+
+ align:start position:0%
+we we can think of U we can think of
+renoir's camera as shy timid in a sense
+
+ align:start position:0%
+renoir's camera as shy timid in a sense
+ 
+
+ align:start position:0%
+renoir's camera as shy timid in a sense
+capable of embarrassment even there's
+
+ align:start position:0%
+capable of embarrassment even there's
+ 
+
+ align:start position:0%
+capable of embarrassment even there's
+one moment in the rules of the game
+
+ align:start position:0%
+one moment in the rules of the game
+ 
+
+ align:start position:0%
+one moment in the rules of the game
+which partly involves a a kind of it has
+
+ align:start position:0%
+which partly involves a a kind of it has
+ 
+
+ align:start position:0%
+which partly involves a a kind of it has
+a farce Dimension so that they when the
+
+ align:start position:0%
+a farce Dimension so that they when the
+ 
+
+ align:start position:0%
+a farce Dimension so that they when the
+when all the guests in the in the great
+
+ align:start position:0%
+when all the guests in the in the great
+ 
+
+ align:start position:0%
+when all the guests in the in the great
+state the in the great um uh estate or
+
+ align:start position:0%
+state the in the great um uh estate or
+ 
+
+ align:start position:0%
+state the in the great um uh estate or
+Castle uh go to sleep at night they
+
+ align:start position:0%
+Castle uh go to sleep at night they
+ 
+
+ align:start position:0%
+Castle uh go to sleep at night they
+there there's a they sort of come out of
+
+ align:start position:0%
+there there's a they sort of come out of
+ 
+
+ align:start position:0%
+there there's a they sort of come out of
+their rooms and start you know changing
+
+ align:start position:0%
+their rooms and start you know changing
+ 
+
+ align:start position:0%
+their rooms and start you know changing
+bed partners and things like that they
+
+ align:start position:0%
+bed partners and things like that they
+ 
+
+ align:start position:0%
+bed partners and things like that they
+they have various liaison and there's a
+
+ align:start position:0%
+they have various liaison and there's a
+ 
+
+ align:start position:0%
+they have various liaison and there's a
+moment when the camera is in the this
+
+ align:start position:0%
+moment when the camera is in the this
+ 
+
+ align:start position:0%
+moment when the camera is in the this
+long hallway and one of the lovers comes
+
+ align:start position:0%
+long hallway and one of the lovers comes
+ 
+
+ align:start position:0%
+long hallway and one of the lovers comes
+out to meet another lover and the C it
+
+ align:start position:0%
+out to meet another lover and the C it
+ 
+
+ align:start position:0%
+out to meet another lover and the C it
+looks as if the camera actually backs
+
+ align:start position:0%
+looks as if the camera actually backs
+ 
+
+ align:start position:0%
+looks as if the camera actually backs
+away in embarrassment and looks away as
+
+ align:start position:0%
+away in embarrassment and looks away as
+ 
+
+ align:start position:0%
+away in embarrassment and looks away as
+if it says oh that's inappropriate for
+
+ align:start position:0%
+if it says oh that's inappropriate for
+ 
+
+ align:start position:0%
+if it says oh that's inappropriate for
+me to be looking at so there's the
+
+ align:start position:0%
+me to be looking at so there's the
+ 
+
+ align:start position:0%
+me to be looking at so there's the
+camera is humanized in a very uh uh
+
+ align:start position:0%
+camera is humanized in a very uh uh
+ 
+
+ align:start position:0%
+camera is humanized in a very uh uh
+subtle quiet way all the way through
+
+ align:start position:0%
+subtle quiet way all the way through
+ 
+
+ align:start position:0%
+subtle quiet way all the way through
+renoir's uh uh work uh so we can think
+
+ align:start position:0%
+renoir's uh uh work uh so we can think
+ 
+
+ align:start position:0%
+renoir's uh uh work uh so we can think
+of his camera as shy as embarrassed
+
+ align:start position:0%
+of his camera as shy as embarrassed
+ 
+
+ align:start position:0%
+of his camera as shy as embarrassed
+reluctant to overhear or to intrude um
+
+ align:start position:0%
+reluctant to overhear or to intrude um
+ 
+
+ align:start position:0%
+reluctant to overhear or to intrude um
+there are even moments when it is
+
+ align:start position:0%
+there are even moments when it is
+ 
+
+ align:start position:0%
+there are even moments when it is
+distracted or drawn to an apparently
+
+ align:start position:0%
+distracted or drawn to an apparently
+ 
+
+ align:start position:0%
+distracted or drawn to an apparently
+irrelevant element uh times when the
+
+ align:start position:0%
+irrelevant element uh times when the
+ 
+
+ align:start position:0%
+irrelevant element uh times when the
+camera hesitates or even appears to
+
+ align:start position:0%
+camera hesitates or even appears to
+ 
+
+ align:start position:0%
+camera hesitates or even appears to
+change its mind an uncertain camera then
+
+ align:start position:0%
+change its mind an uncertain camera then
+ 
+
+ align:start position:0%
+change its mind an uncertain camera then
+always adjusting to a world that is
+
+ align:start position:0%
+always adjusting to a world that is
+ 
+
+ align:start position:0%
+always adjusting to a world that is
+itself always shifting and changing and
+
+ align:start position:0%
+itself always shifting and changing and
+ 
+
+ align:start position:0%
+itself always shifting and changing and
+of course that's the deepest argument
+
+ align:start position:0%
+of course that's the deepest argument
+ 
+
+ align:start position:0%
+of course that's the deepest argument
+for why this the camera is so Restless
+
+ align:start position:0%
+for why this the camera is so Restless
+ 
+
+ align:start position:0%
+for why this the camera is so Restless
+remember it's not obtrusive it's not
+
+ align:start position:0%
+remember it's not obtrusive it's not
+ 
+
+ align:start position:0%
+remember it's not obtrusive it's not
+like you feel the camera swinging wildly
+
+ align:start position:0%
+like you feel the camera swinging wildly
+ 
+
+ align:start position:0%
+like you feel the camera swinging wildly
+not at all you have to pay attention
+
+ align:start position:0%
+not at all you have to pay attention
+ 
+
+ align:start position:0%
+not at all you have to pay attention
+sometime you won't even be aware of the
+
+ align:start position:0%
+sometime you won't even be aware of the
+ 
+
+ align:start position:0%
+sometime you won't even be aware of the
+fact of how quietly and subtly the
+
+ align:start position:0%
+fact of how quietly and subtly the
+ 
+
+ align:start position:0%
+fact of how quietly and subtly the
+camera but it's as if the camera is
+
+ align:start position:0%
+camera but it's as if the camera is
+ 
+
+ align:start position:0%
+camera but it's as if the camera is
+always making adjustments as if it's
+
+ align:start position:0%
+always making adjustments as if it's
+ 
+
+ align:start position:0%
+always making adjustments as if it's
+always alive to the changing character
+
+ align:start position:0%
+always alive to the changing character
+ 
+
+ align:start position:0%
+always alive to the changing character
+of what it's looking at and that very
+
+ align:start position:0%
+of what it's looking at and that very
+ 
+
+ align:start position:0%
+of what it's looking at and that very
+aliveness reminds you of how complex
+
+ align:start position:0%
+aliveness reminds you of how complex
+ 
+
+ align:start position:0%
+aliveness reminds you of how complex
+reality is because reality itself is
+
+ align:start position:0%
+reality is because reality itself is
+ 
+
+ align:start position:0%
+reality is because reality itself is
+always shifting and changing um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this describes I think something of
+
+ align:start position:0%
+um this describes I think something of
+ 
+
+ align:start position:0%
+um this describes I think something of
+what is meant by renoir's realism but
+
+ align:start position:0%
+what is meant by renoir's realism but
+ 
+
+ align:start position:0%
+what is meant by renoir's realism but
+there's a kind of lyric element as I've
+
+ align:start position:0%
+there's a kind of lyric element as I've
+ 
+
+ align:start position:0%
+there's a kind of lyric element as I've
+mentioned a kind of even a kind of
+
+ align:start position:0%
+mentioned a kind of even a kind of
+ 
+
+ align:start position:0%
+mentioned a kind of even a kind of
+Tranquility or pleasure or Joy
+
+ align:start position:0%
+Tranquility or pleasure or Joy
+ 
+
+ align:start position:0%
+Tranquility or pleasure or Joy
+celebratory impulse in his camera's gaze
+
+ align:start position:0%
+celebratory impulse in his camera's gaze
+ 
+
+ align:start position:0%
+celebratory impulse in his camera's gaze
+that qualifies or sweetens his realism
+
+ align:start position:0%
+that qualifies or sweetens his realism
+ 
+
+ align:start position:0%
+that qualifies or sweetens his realism
+of space and character and we need to be
+
+ align:start position:0%
+of space and character and we need to be
+ 
+
+ align:start position:0%
+of space and character and we need to be
+aware of that too one way to crystallize
+
+ align:start position:0%
+aware of that too one way to crystallize
+ 
+
+ align:start position:0%
+aware of that too one way to crystallize
+this is to suggest that once we become
+
+ align:start position:0%
+this is to suggest that once we become
+ 
+
+ align:start position:0%
+this is to suggest that once we become
+attuned to the camera's forms of
+
+ align:start position:0%
+attuned to the camera's forms of
+ 
+
+ align:start position:0%
+attuned to the camera's forms of
+attention that's a good phrase the
+
+ align:start position:0%
+attention that's a good phrase the
+ 
+
+ align:start position:0%
+attention that's a good phrase the
+camera's forms of attention uh there a
+
+ align:start position:0%
+camera's forms of attention uh there a
+ 
+
+ align:start position:0%
+camera's forms of attention uh there a
+wonderful book about poetry called forms
+
+ align:start position:0%
+wonderful book about poetry called forms
+ 
+
+ align:start position:0%
+wonderful book about poetry called forms
+of attention right lyric poetry is
+
+ align:start position:0%
+of attention right lyric poetry is
+ 
+
+ align:start position:0%
+of attention right lyric poetry is
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+
+ align:start position:0%
+constit it's a special kind of attention
+ 
+
+ align:start position:0%
+constit it's a special kind of attention
+we can say that that renoir's
+
+ align:start position:0%
+we can say that that renoir's
+ 
+
+ align:start position:0%
+we can say that that renoir's
+camera is is engaged constantly in these
+
+ align:start position:0%
+camera is is engaged constantly in these
+ 
+
+ align:start position:0%
+camera is is engaged constantly in these
+forms of attention um um once we become
+
+ align:start position:0%
+forms of attention um um once we become
+ 
+
+ align:start position:0%
+forms of attention um um once we become
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+
+ align:start position:0%
+aware of that of that of the camera's
+ 
+
+ align:start position:0%
+aware of that of that of the camera's
+interest in that uh we become aware of a
+
+ align:start position:0%
+interest in that uh we become aware of a
+ 
+
+ align:start position:0%
+interest in that uh we become aware of a
+quiet continuous struggle a loving
+
+ align:start position:0%
+quiet continuous struggle a loving
+ 
+
+ align:start position:0%
+quiet continuous struggle a loving
+contest almost between the multiple
+
+ align:start position:0%
+contest almost between the multiple
+ 
+
+ align:start position:0%
+contest almost between the multiple
+points of interest in the scene and the
+
+ align:start position:0%
+points of interest in the scene and the
+ 
+
+ align:start position:0%
+points of interest in the scene and the
+camera's reluctant gently hesitant
+
+ align:start position:0%
+camera's reluctant gently hesitant
+ 
+
+ align:start position:0%
+camera's reluctant gently hesitant
+choices the menu of things to see and
+
+ align:start position:0%
+choices the menu of things to see and
+ 
+
+ align:start position:0%
+choices the menu of things to see and
+hear R Wars films keep telling
+
+ align:start position:0%
+hear R Wars films keep telling
+ 
+
+ align:start position:0%
+hear R Wars films keep telling
+us is too rich to be fully captured even
+
+ align:start position:0%
+us is too rich to be fully captured even
+ 
+
+ align:start position:0%
+us is too rich to be fully captured even
+by the most generous eye and that's what
+
+ align:start position:0%
+by the most generous eye and that's what
+ 
+
+ align:start position:0%
+by the most generous eye and that's what
+I mean when I say that visual style can
+
+ align:start position:0%
+I mean when I say that visual style can
+ 
+
+ align:start position:0%
+I mean when I say that visual style can
+be understood as a form of moral style
+
+ align:start position:0%
+be understood as a form of moral style
+ 
+
+ align:start position:0%
+be understood as a form of moral style
+right uh I want to say a few more words
+
+ align:start position:0%
+right uh I want to say a few more words
+ 
+
+ align:start position:0%
+right uh I want to say a few more words
+about uh Grand delusion itself to help
+
+ align:start position:0%
+about uh Grand delusion itself to help
+ 
+
+ align:start position:0%
+about uh Grand delusion itself to help
+frame your uh experience of it uh it's
+
+ align:start position:0%
+frame your uh experience of it uh it's
+ 
+
+ align:start position:0%
+frame your uh experience of it uh it's
+not a complex film but it's a deep and
+
+ align:start position:0%
+not a complex film but it's a deep and
+ 
+
+ align:start position:0%
+not a complex film but it's a deep and
+beautiful one and I think you'll all
+
+ align:start position:0%
+beautiful one and I think you'll all
+ 
+
+ align:start position:0%
+beautiful one and I think you'll all
+find it very memorable first a word
+
+ align:start position:0%
+find it very memorable first a word
+ 
+
+ align:start position:0%
+find it very memorable first a word
+about the actors um or or maybe I should
+
+ align:start position:0%
+about the actors um or or maybe I should
+ 
+
+ align:start position:0%
+about the actors um or or maybe I should
+say one other word about about Renoir
+
+ align:start position:0%
+say one other word about about Renoir
+ 
+
+ align:start position:0%
+say one other word about about Renoir
+himself because it Bears on his actors
+
+ align:start position:0%
+himself because it Bears on his actors
+ 
+
+ align:start position:0%
+himself because it Bears on his actors
+as I implied or I think suggested this
+
+ align:start position:0%
+as I implied or I think suggested this
+ 
+
+ align:start position:0%
+as I implied or I think suggested this
+afternoon one of the most distinctive
+
+ align:start position:0%
+afternoon one of the most distinctive
+ 
+
+ align:start position:0%
+afternoon one of the most distinctive
+features of renoir's practice and follow
+
+ align:start position:0%
+features of renoir's practice and follow
+ 
+
+ align:start position:0%
+features of renoir's practice and follow
+if you think about the way his camera
+
+ align:start position:0%
+if you think about the way his camera
+ 
+
+ align:start position:0%
+if you think about the way his camera
+behaves you can see how logically
+
+ align:start position:0%
+behaves you can see how logically
+ 
+
+ align:start position:0%
+behaves you can see how logically
+connected these elements are was that he
+
+ align:start position:0%
+connected these elements are was that he
+ 
+
+ align:start position:0%
+connected these elements are was that he
+was an improvisational director he
+
+ align:start position:0%
+was an improvisational director he
+ 
+
+ align:start position:0%
+was an improvisational director he
+collaborated with his actors with his
+
+ align:start position:0%
+collaborated with his actors with his
+ 
+
+ align:start position:0%
+collaborated with his actors with his
+performers he didn't come in with an
+
+ align:start position:0%
+performers he didn't come in with an
+ 
+
+ align:start position:0%
+performers he didn't come in with an
+absolutely fixed script he's he's like
+
+ align:start position:0%
+absolutely fixed script he's he's like
+ 
+
+ align:start position:0%
+absolutely fixed script he's he's like
+the anti- Hitchcock
+
+ align:start position:0%
+the anti- Hitchcock
+ 
+
+ align:start position:0%
+the anti- Hitchcock
+Hitchcock has solved all his problems
+
+ align:start position:0%
+Hitchcock has solved all his problems
+ 
+
+ align:start position:0%
+Hitchcock has solved all his problems
+before he's come in to do his shooting
+
+ align:start position:0%
+before he's come in to do his shooting
+ 
+
+ align:start position:0%
+before he's come in to do his shooting
+Renoir has just begun the process of
+
+ align:start position:0%
+Renoir has just begun the process of
+ 
+
+ align:start position:0%
+Renoir has just begun the process of
+making his movie when he he has an idea
+
+ align:start position:0%
+making his movie when he he has an idea
+ 
+
+ align:start position:0%
+making his movie when he he has an idea
+of his subject matter he knows what he's
+
+ align:start position:0%
+of his subject matter he knows what he's
+ 
+
+ align:start position:0%
+of his subject matter he knows what he's
+doing he knows he I don't mean that he's
+
+ align:start position:0%
+doing he knows he I don't mean that he's
+ 
+
+ align:start position:0%
+doing he knows he I don't mean that he's
+working completely blind but he
+
+ align:start position:0%
+working completely blind but he
+ 
+
+ align:start position:0%
+working completely blind but he
+allows Discovery to take place in the
+
+ align:start position:0%
+allows Discovery to take place in the
+ 
+
+ align:start position:0%
+allows Discovery to take place in the
+course of the making of the movies of
+
+ align:start position:0%
+course of the making of the movies of
+ 
+
+ align:start position:0%
+course of the making of the movies of
+his movies and he's very deeply involved
+
+ align:start position:0%
+his movies and he's very deeply involved
+ 
+
+ align:start position:0%
+his movies and he's very deeply involved
+in collaborating with his performers so
+
+ align:start position:0%
+in collaborating with his performers so
+ 
+
+ align:start position:0%
+in collaborating with his performers so
+that for example um when he had already
+
+ align:start position:0%
+that for example um when he had already
+ 
+
+ align:start position:0%
+that for example um when he had already
+begun working on the movie I I don't
+
+ align:start position:0%
+begun working on the movie I I don't
+ 
+
+ align:start position:0%
+begun working on the movie I I don't
+think they they hadn't beun I don't
+
+ align:start position:0%
+think they they hadn't beun I don't
+ 
+
+ align:start position:0%
+think they they hadn't beun I don't
+think they'd begun shooting it yet but
+
+ align:start position:0%
+think they'd begun shooting it yet but
+ 
+
+ align:start position:0%
+think they'd begun shooting it yet but
+they were very far along in creating the
+
+ align:start position:0%
+they were very far along in creating the
+ 
+
+ align:start position:0%
+they were very far along in creating the
+movie and in casting the movie when they
+
+ align:start position:0%
+movie and in casting the movie when they
+ 
+
+ align:start position:0%
+movie and in casting the movie when they
+discovered that Eric Von stroheim who
+
+ align:start position:0%
+discovered that Eric Von stroheim who
+ 
+
+ align:start position:0%
+discovered that Eric Von stroheim who
+was all already by then by the time this
+
+ align:start position:0%
+was all already by then by the time this
+ 
+
+ align:start position:0%
+was all already by then by the time this
+film was made a very well-known actor
+
+ align:start position:0%
+film was made a very well-known actor
+ 
+
+ align:start position:0%
+film was made a very well-known actor
+and director much in fact incredibly
+
+ align:start position:0%
+and director much in fact incredibly
+ 
+
+ align:start position:0%
+and director much in fact incredibly
+admired director uh both both an actor
+
+ align:start position:0%
+admired director uh both both an actor
+ 
+
+ align:start position:0%
+admired director uh both both an actor
+and a director uh uh agreed to join the
+
+ align:start position:0%
+and a director uh uh agreed to join the
+ 
+
+ align:start position:0%
+and a director uh uh agreed to join the
+film and when he agreed to join the film
+
+ align:start position:0%
+film and when he agreed to join the film
+ 
+
+ align:start position:0%
+film and when he agreed to join the film
+he and Renoir began to collaborate on
+
+ align:start position:0%
+he and Renoir began to collaborate on
+ 
+
+ align:start position:0%
+he and Renoir began to collaborate on
+expanding the role that on scheim plays
+
+ align:start position:0%
+expanding the role that on scheim plays
+ 
+
+ align:start position:0%
+expanding the role that on scheim plays
+and you'll understand what an what what
+
+ align:start position:0%
+and you'll understand what an what what
+ 
+
+ align:start position:0%
+and you'll understand what an what what
+an immensely helpful contribution to the
+
+ align:start position:0%
+an immensely helpful contribution to the
+ 
+
+ align:start position:0%
+an immensely helpful contribution to the
+what what could we call it to the
+
+ align:start position:0%
+what what could we call it to the
+ 
+
+ align:start position:0%
+what what could we call it to the
+Ecology of the movie to the sense of the
+
+ align:start position:0%
+Ecology of the movie to the sense of the
+ 
+
+ align:start position:0%
+Ecology of the movie to the sense of the
+movie uh uh Von stroheim May because his
+
+ align:start position:0%
+movie uh uh Von stroheim May because his
+ 
+
+ align:start position:0%
+movie uh uh Von stroheim May because his
+because he's one of the dominant
+
+ align:start position:0%
+because he's one of the dominant
+ 
+
+ align:start position:0%
+because he's one of the dominant
+characters his his if if we if we if we
+
+ align:start position:0%
+characters his his if if we if we if we
+ 
+
+ align:start position:0%
+characters his his if if we if we if we
+try to imagine Grand Illusion with a
+
+ align:start position:0%
+try to imagine Grand Illusion with a
+ 
+
+ align:start position:0%
+try to imagine Grand Illusion with a
+much reduced role for the Von stroheim
+
+ align:start position:0%
+much reduced role for the Von stroheim
+ 
+
+ align:start position:0%
+much reduced role for the Von stroheim
+character it's a much lesser film you
+
+ align:start position:0%
+character it's a much lesser film you
+ 
+
+ align:start position:0%
+character it's a much lesser film you
+could so you can recognize what an and
+
+ align:start position:0%
+could so you can recognize what an and
+ 
+
+ align:start position:0%
+could so you can recognize what an and
+uh what an extraordinary contribution V
+
+ align:start position:0%
+uh what an extraordinary contribution V
+ 
+
+ align:start position:0%
+uh what an extraordinary contribution V
+strohi made now he not only made
+
+ align:start position:0%
+strohi made now he not only made
+ 
+
+ align:start position:0%
+strohi made now he not only made
+contributions to questions about the
+
+ align:start position:0%
+contributions to questions about the
+ 
+
+ align:start position:0%
+contributions to questions about the
+dialogue what the character would say
+
+ align:start position:0%
+dialogue what the character would say
+ 
+
+ align:start position:0%
+dialogue what the character would say
+expanded the role but even made
+
+ align:start position:0%
+expanded the role but even made
+ 
+
+ align:start position:0%
+expanded the role but even made
+suggestions about how the character
+
+ align:start position:0%
+suggestions about how the character
+ 
+
+ align:start position:0%
+suggestions about how the character
+would look what what what uh cut how the
+
+ align:start position:0%
+would look what what what uh cut how the
+ 
+
+ align:start position:0%
+would look what what what uh cut how the
+character would be customed and I think
+
+ align:start position:0%
+character would be customed and I think
+ 
+
+ align:start position:0%
+character would be customed and I think
+it was Von stroheim who emphasi who who
+
+ align:start position:0%
+it was Von stroheim who emphasi who who
+ 
+
+ align:start position:0%
+it was Von stroheim who emphasi who who
+who emphasized even more fully than
+
+ align:start position:0%
+who emphasized even more fully than
+ 
+
+ align:start position:0%
+who emphasized even more fully than
+Renoir had originally intended that the
+
+ align:start position:0%
+Renoir had originally intended that the
+ 
+
+ align:start position:0%
+Renoir had originally intended that the
+Von stroheim character is a war Casualty
+
+ align:start position:0%
+Von stroheim character is a war Casualty
+ 
+
+ align:start position:0%
+Von stroheim character is a war Casualty
+that he has a ram rod up his back that
+
+ align:start position:0%
+that he has a ram rod up his back that
+ 
+
+ align:start position:0%
+that he has a ram rod up his back that
+he can he has to wear gloves because his
+
+ align:start position:0%
+he can he has to wear gloves because his
+ 
+
+ align:start position:0%
+he can he has to wear gloves because his
+hands are horribly burned he's a
+
+ align:start position:0%
+hands are horribly burned he's a
+ 
+
+ align:start position:0%
+hands are horribly burned he's a
+and that's why he's now running prison
+
+ align:start position:0%
+and that's why he's now running prison
+ 
+
+ align:start position:0%
+and that's why he's now running prison
+camps because he's not useful for
+
+ align:start position:0%
+camps because he's not useful for
+ 
+
+ align:start position:0%
+camps because he's not useful for
+anything else right and there's the
+
+ align:start position:0%
+anything else right and there's the
+ 
+
+ align:start position:0%
+anything else right and there's the
+sense that he's a damaged U uh uh um
+
+ align:start position:0%
+sense that he's a damaged U uh uh um
+ 
+
+ align:start position:0%
+sense that he's a damaged U uh uh um
+wounded figure even from the very
+
+ align:start position:0%
+wounded figure even from the very
+ 
+
+ align:start position:0%
+wounded figure even from the very
+beginning of the film when we when we
+
+ align:start position:0%
+beginning of the film when we when we
+ 
+
+ align:start position:0%
+beginning of the film when we when we
+first meet him uh but one of so that's
+
+ align:start position:0%
+first meet him uh but one of so that's
+ 
+
+ align:start position:0%
+first meet him uh but one of so that's
+important in itself but there's a second
+
+ align:start position:0%
+important in itself but there's a second
+ 
+
+ align:start position:0%
+important in itself but there's a second
+thing about F stran that I want to
+
+ align:start position:0%
+thing about F stran that I want to
+ 
+
+ align:start position:0%
+thing about F stran that I want to
+emphasize to you to it shows you how uh
+
+ align:start position:0%
+emphasize to you to it shows you how uh
+ 
+
+ align:start position:0%
+emphasize to you to it shows you how uh
+subtly Renoir was aware of how he could
+
+ align:start position:0%
+subtly Renoir was aware of how he could
+ 
+
+ align:start position:0%
+subtly Renoir was aware of how he could
+utilize all the elements available to
+
+ align:start position:0%
+utilize all the elements available to
+ 
+
+ align:start position:0%
+utilize all the elements available to
+him as a filmmaker Von stroheim was
+
+ align:start position:0%
+him as a filmmaker Von stroheim was
+ 
+
+ align:start position:0%
+him as a filmmaker Von stroheim was
+especially well known as an actor for
+
+ align:start position:0%
+especially well known as an actor for
+ 
+
+ align:start position:0%
+especially well known as an actor for
+roles in which he would play this was
+
+ align:start position:0%
+roles in which he would play this was
+ 
+
+ align:start position:0%
+roles in which he would play this was
+especially true in roles he played in
+
+ align:start position:0%
+especially true in roles he played in
+ 
+
+ align:start position:0%
+especially true in roles he played in
+the United States in which he would play
+
+ align:start position:0%
+the United States in which he would play
+ 
+
+ align:start position:0%
+the United States in which he would play
+a dangerous scary martinet a kind of a
+
+ align:start position:0%
+a dangerous scary martinet a kind of a
+ 
+
+ align:start position:0%
+a dangerous scary martinet a kind of a
+kind of uh there there were even hints
+
+ align:start position:0%
+kind of uh there there were even hints
+ 
+
+ align:start position:0%
+kind of uh there there were even hints
+of s masochism about the role sometime
+
+ align:start position:0%
+of s masochism about the role sometime
+ 
+
+ align:start position:0%
+of s masochism about the role sometime
+so he would play he would play uh uh
+
+ align:start position:0%
+so he would play he would play uh uh
+ 
+
+ align:start position:0%
+so he would play he would play uh uh
+brutal brutal prison camp wardens right
+
+ align:start position:0%
+brutal brutal prison camp wardens right
+ 
+
+ align:start position:0%
+brutal brutal prison camp wardens right
+or brutal police types brutal BR
+
+ align:start position:0%
+or brutal police types brutal BR
+ 
+
+ align:start position:0%
+or brutal police types brutal BR
+militarist types right uh violent
+
+ align:start position:0%
+militarist types right uh violent
+ 
+
+ align:start position:0%
+militarist types right uh violent
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+
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+
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+
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+fact he he was understood also as a
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+
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+
+ align:start position:0%
+villain he often played roles that were
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+recognizably evil roles he came to be
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+
+ align:start position:0%
+recognizably evil roles he came to be
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+
+ align:start position:0%
+known as the man you love to hate that
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+
+ align:start position:0%
+known as the man you love to hate that
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+
+ align:start position:0%
+was like his sort of it was a sort of
+ 
+
+ align:start position:0%
+was like his sort of it was a sort of
+motto that was attached to his to his
+
+ align:start position:0%
+motto that was attached to his to his
+ 
+
+ align:start position:0%
+motto that was attached to his to his
+name and when you watch Grand Illusion
+
+ align:start position:0%
+name and when you watch Grand Illusion
+ 
+
+ align:start position:0%
+name and when you watch Grand Illusion
+one of the things I hope you'll think
+
+ align:start position:0%
+one of the things I hope you'll think
+ 
+
+ align:start position:0%
+one of the things I hope you'll think
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+
+ align:start position:0%
+about is the comple the complex way in
+ 
+
+ align:start position:0%
+about is the comple the complex way in
+which that inherited idea of the Von
+
+ align:start position:0%
+which that inherited idea of the Von
+ 
+
+ align:start position:0%
+which that inherited idea of the Von
+stroheim character is complicated
+
+ align:start position:0%
+stroheim character is complicated
+ 
+
+ align:start position:0%
+stroheim character is complicated
+undermined and humanized because in many
+
+ align:start position:0%
+undermined and humanized because in many
+ 
+
+ align:start position:0%
+undermined and humanized because in many
+ways he still is the villain in the
+
+ align:start position:0%
+ways he still is the villain in the
+ 
+
+ align:start position:0%
+ways he still is the villain in the
+piece but he's a humanized villain he's
+
+ align:start position:0%
+piece but he's a humanized villain he's
+ 
+
+ align:start position:0%
+piece but he's a humanized villain he's
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+
+ align:start position:0%
+a he becomes a complex character as much
+ 
+
+ align:start position:0%
+a he becomes a complex character as much
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+
+ align:start position:0%
+a victim of what's Happening happening
+ 
+
+ align:start position:0%
+a victim of what's Happening happening
+of his as much a victim of history as
+
+ align:start position:0%
+of his as much a victim of history as
+ 
+
+ align:start position:0%
+of his as much a victim of history as
+any of the other characters in the film
+
+ align:start position:0%
+any of the other characters in the film
+ 
+
+ align:start position:0%
+any of the other characters in the film
+so uh there's a sense in which this in
+
+ align:start position:0%
+so uh there's a sense in which this in
+ 
+
+ align:start position:0%
+so uh there's a sense in which this in
+which what what Renoir and Von stroheim
+
+ align:start position:0%
+which what what Renoir and Von stroheim
+ 
+
+ align:start position:0%
+which what what Renoir and Von stroheim
+together are doing is taking the Persona
+
+ align:start position:0%
+together are doing is taking the Persona
+ 
+
+ align:start position:0%
+together are doing is taking the Persona
+that Von stroheim had established and
+
+ align:start position:0%
+that Von stroheim had established and
+ 
+
+ align:start position:0%
+that Von stroheim had established and
+undercutting it undermining it in some
+
+ align:start position:0%
+undercutting it undermining it in some
+ 
+
+ align:start position:0%
+undercutting it undermining it in some
+in some slight way creating a much
+
+ align:start position:0%
+in some slight way creating a much
+ 
+
+ align:start position:0%
+in some slight way creating a much
+greater resonance for the character
+
+ align:start position:0%
+greater resonance for the character
+ 
+
+ align:start position:0%
+greater resonance for the character
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+
+ align:start position:0%
+exactly because of the ways in which he
+ 
+
+ align:start position:0%
+exactly because of the ways in which he
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+
+ align:start position:0%
+first that appears to fulfill the
+ 
+
+ align:start position:0%
+first that appears to fulfill the
+expectations that he's an evil villain
+
+ align:start position:0%
+expectations that he's an evil villain
+ 
+
+ align:start position:0%
+expectations that he's an evil villain
+and then as the film goes on this sense
+
+ align:start position:0%
+and then as the film goes on this sense
+ 
+
+ align:start position:0%
+and then as the film goes on this sense
+is undermined complicated and you
+
+ align:start position:0%
+is undermined complicated and you
+ 
+
+ align:start position:0%
+is undermined complicated and you
+realize that he's a he's a human being
+
+ align:start position:0%
+realize that he's a he's a human being
+ 
+
+ align:start position:0%
+realize that he's a he's a human being
+with W with with with powers of
+
+ align:start position:0%
+with W with with with powers of
+ 
+
+ align:start position:0%
+with W with with with powers of
+generosity although also certain
+
+ align:start position:0%
+generosity although also certain
+ 
+
+ align:start position:0%
+generosity although also certain
+limitations uh he's pre he's a German
+
+ align:start position:0%
+limitations uh he's pre he's a German
+ 
+
+ align:start position:0%
+limitations uh he's pre he's a German
+he's a Prejudice he has he doesn't
+
+ align:start position:0%
+he's a Prejudice he has he doesn't
+ 
+
+ align:start position:0%
+he's a Prejudice he has he doesn't
+really like the French especially
+
+ align:start position:0%
+really like the French especially
+ 
+
+ align:start position:0%
+really like the French especially
+doesn't like workingclass people most
+
+ align:start position:0%
+doesn't like workingclass people most
+ 
+
+ align:start position:0%
+doesn't like workingclass people most
+especially doesn't like Jews right I
+
+ align:start position:0%
+especially doesn't like Jews right I
+ 
+
+ align:start position:0%
+especially doesn't like Jews right I
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+
+ align:start position:0%
+mean it's not he's an imperfect
+ 
+
+ align:start position:0%
+mean it's not he's an imperfect
+character but you see that he's deeply
+
+ align:start position:0%
+character but you see that he's deeply
+ 
+
+ align:start position:0%
+character but you see that he's deeply
+humanized and something of the same kind
+
+ align:start position:0%
+humanized and something of the same kind
+ 
+
+ align:start position:0%
+humanized and something of the same kind
+of thing happens in the film's treatment
+
+ align:start position:0%
+of thing happens in the film's treatment
+ 
+
+ align:start position:0%
+of thing happens in the film's treatment
+of the Jeong gabang character the the
+
+ align:start position:0%
+of the Jeong gabang character the the
+ 
+
+ align:start position:0%
+of the Jeong gabang character the the
+really he he's the character who plays
+
+ align:start position:0%
+really he he's the character who plays
+ 
+
+ align:start position:0%
+really he he's the character who plays
+marishal the actor who plays marishal
+
+ align:start position:0%
+marishal the actor who plays marishal
+ 
+
+ align:start position:0%
+marishal the actor who plays marishal
+the workingclass um um Frenchman who
+
+ align:start position:0%
+the workingclass um um Frenchman who
+ 
+
+ align:start position:0%
+the workingclass um um Frenchman who
+along with du and and uh the uh the Jew
+
+ align:start position:0%
+along with du and and uh the uh the Jew
+ 
+
+ align:start position:0%
+along with du and and uh the uh the Jew
+played by the Jew played by
+
+ align:start position:0%
+played by the Jew played by
+ 
+
+ align:start position:0%
+played by the Jew played by
+Dalo character called rosental these
+
+ align:start position:0%
+Dalo character called rosental these
+ 
+
+ align:start position:0%
+Dalo character called rosental these
+three are the central uh French
+
+ align:start position:0%
+three are the central uh French
+ 
+
+ align:start position:0%
+three are the central uh French
+characters and we see them moving from
+
+ align:start position:0%
+characters and we see them moving from
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+
+ align:start position:0%
+characters and we see them moving from
+prison camp to prison camp through the
+
+ align:start position:0%
+prison camp to prison camp through the
+ 
+
+ align:start position:0%
+prison camp to prison camp through the
+film that that group is the central uh
+
+ align:start position:0%
+film that that group is the central uh
+ 
+
+ align:start position:0%
+film that that group is the central uh
+group of the film and we follow them as
+
+ align:start position:0%
+group of the film and we follow them as
+ 
+
+ align:start position:0%
+group of the film and we follow them as
+the film goes on uh the gabang character
+
+ align:start position:0%
+the film goes on uh the gabang character
+ 
+
+ align:start position:0%
+the film goes on uh the gabang character
+too was the in many ways the most famous
+
+ align:start position:0%
+too was the in many ways the most famous
+ 
+
+ align:start position:0%
+too was the in many ways the most famous
+actor of of if not in Europe certainly
+
+ align:start position:0%
+actor of of if not in Europe certainly
+ 
+
+ align:start position:0%
+actor of of if not in Europe certainly
+in France of the late 20s and 30s major
+
+ align:start position:0%
+in France of the late 20s and 30s major
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+
+ align:start position:0%
+in France of the late 20s and 30s major
+major figure uh and he he was especially
+
+ align:start position:0%
+major figure uh and he he was especially
+ 
+
+ align:start position:0%
+major figure uh and he he was especially
+associated with workingclass roles and
+
+ align:start position:0%
+associated with workingclass roles and
+ 
+
+ align:start position:0%
+associated with workingclass roles and
+most especially associated with roles he
+
+ align:start position:0%
+most especially associated with roles he
+ 
+
+ align:start position:0%
+most especially associated with roles he
+was like an early Jack Nicholson an even
+
+ align:start position:0%
+was like an early Jack Nicholson an even
+ 
+
+ align:start position:0%
+was like an early Jack Nicholson an even
+more powerful version of it because he
+
+ align:start position:0%
+more powerful version of it because he
+ 
+
+ align:start position:0%
+more powerful version of it because he
+became famous for these moments in the
+
+ align:start position:0%
+became famous for these moments in the
+ 
+
+ align:start position:0%
+became famous for these moments in the
+films when he would go nuts when he
+
+ align:start position:0%
+films when he would go nuts when he
+ 
+
+ align:start position:0%
+films when he would go nuts when he
+would have a fit when he would start
+
+ align:start position:0%
+would have a fit when he would start
+ 
+
+ align:start position:0%
+would have a fit when he would start
+screaming or he would lose it right he
+
+ align:start position:0%
+screaming or he would lose it right he
+ 
+
+ align:start position:0%
+screaming or he would lose it right he
+would he would rant or Rave or and and
+
+ align:start position:0%
+would he would rant or Rave or and and
+ 
+
+ align:start position:0%
+would he would rant or Rave or and and
+in some of the films in some films he
+
+ align:start position:0%
+in some of the films in some films he
+ 
+
+ align:start position:0%
+in some of the films in some films he
+was in he would have a a climactic scene
+
+ align:start position:0%
+was in he would have a a climactic scene
+ 
+
+ align:start position:0%
+was in he would have a a climactic scene
+this may be in fact where the uh uh
+
+ align:start position:0%
+this may be in fact where the uh uh
+ 
+
+ align:start position:0%
+this may be in fact where the uh uh
+stereotype began he would have a
+
+ align:start position:0%
+stereotype began he would have a
+ 
+
+ align:start position:0%
+stereotype began he would have a
+climactic scene often he was like he
+
+ align:start position:0%
+climactic scene often he was like he
+ 
+
+ align:start position:0%
+climactic scene often he was like he
+would be a suicidal proletarian right a
+
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+would be a suicidal proletarian right a
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+would be a suicidal proletarian right a
+suicidal worker up against the forces of
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+ align:start position:0%
+suicidal worker up against the forces of
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+
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+suicidal worker up against the forces of
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+capitalism or the forces of the police
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+
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+right the gabang character had frequent
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+
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+right the gabang character had frequent
+roles like this uh in which he would in
+
+ align:start position:0%
+roles like this uh in which he would in
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+
+ align:start position:0%
+roles like this uh in which he would in
+which he would U uh essentially Lo lose
+
+ align:start position:0%
+which he would U uh essentially Lo lose
+ 
+
+ align:start position:0%
+which he would U uh essentially Lo lose
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+all rational control and rant and Rave
+ 
+
+ align:start position:0%
+all rational control and rant and Rave
+and scream sometimes die right uh and he
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+and scream sometimes die right uh and he
+ 
+
+ align:start position:0%
+and scream sometimes die right uh and he
+he was so famous for this and this was
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+he was so famous for this and this was
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+
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+he was so famous for this and this was
+such a fundamental part of his Persona
+
+ align:start position:0%
+such a fundamental part of his Persona
+ 
+
+ align:start position:0%
+such a fundamental part of his Persona
+that he uh had written into most of his
+
+ align:start position:0%
+that he uh had written into most of his
+ 
+
+ align:start position:0%
+that he uh had written into most of his
+contracts that he had to have a scene in
+
+ align:start position:0%
+contracts that he had to have a scene in
+ 
+
+ align:start position:0%
+contracts that he had to have a scene in
+which he did this he had to have at
+
+ align:start position:0%
+which he did this he had to have at
+ 
+
+ align:start position:0%
+which he did this he had to have at
+least one scene in the film in which he
+
+ align:start position:0%
+least one scene in the film in which he
+ 
+
+ align:start position:0%
+least one scene in the film in which he
+sort of went kukamonga in which he in
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+ align:start position:0%
+sort of went kukamonga in which he in
+ 
+
+ align:start position:0%
+sort of went kukamonga in which he in
+which he lost it right now one of the
+
+ align:start position:0%
+which he lost it right now one of the
+ 
+
+ align:start position:0%
+which he lost it right now one of the
+most subtle things about this film is
+
+ align:start position:0%
+most subtle things about this film is
+ 
+
+ align:start position:0%
+most subtle things about this film is
+there is such a moment in this film
+
+ align:start position:0%
+there is such a moment in this film
+ 
+
+ align:start position:0%
+there is such a moment in this film
+watch for youan because it's so quiet
+
+ align:start position:0%
+watch for youan because it's so quiet
+ 
+
+ align:start position:0%
+watch for youan because it's so quiet
+compared to what you might expect that
+
+ align:start position:0%
+compared to what you might expect that
+ 
+
+ align:start position:0%
+compared to what you might expect that
+you might miss it but it's really there
+
+ align:start position:0%
+you might miss it but it's really there
+ 
+
+ align:start position:0%
+you might miss it but it's really there
+and in fact the way in which it both
+
+ align:start position:0%
+and in fact the way in which it both
+ 
+
+ align:start position:0%
+and in fact the way in which it both
+fulfills but also undermines our
+
+ align:start position:0%
+fulfills but also undermines our
+ 
+
+ align:start position:0%
+fulfills but also undermines our
+expectations about this character again
+
+ align:start position:0%
+expectations about this character again
+ 
+
+ align:start position:0%
+expectations about this character again
+tells us something about the way in
+
+ align:start position:0%
+tells us something about the way in
+ 
+
+ align:start position:0%
+tells us something about the way in
+which Renoir and his collaborating
+
+ align:start position:0%
+which Renoir and his collaborating
+ 
+
+ align:start position:0%
+which Renoir and his collaborating
+actors were able to create immensely
+
+ align:start position:0%
+actors were able to create immensely
+ 
+
+ align:start position:0%
+actors were able to create immensely
+nuanced meanings uh possibilities out of
+
+ align:start position:0%
+nuanced meanings uh possibilities out of
+ 
+
+ align:start position:0%
+nuanced meanings uh possibilities out of
+the raw material of their of not only of
+
+ align:start position:0%
+the raw material of their of not only of
+ 
+
+ align:start position:0%
+the raw material of their of not only of
+the story of the film and of the setting
+
+ align:start position:0%
+the story of the film and of the setting
+ 
+
+ align:start position:0%
+the story of the film and of the setting
+of the film but even the past history of
+
+ align:start position:0%
+of the film but even the past history of
+ 
+
+ align:start position:0%
+of the film but even the past history of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+performers I want to say just a couple
+
+ align:start position:0%
+performers I want to say just a couple
+ 
+
+ align:start position:0%
+performers I want to say just a couple
+of things about some of the dominant um
+
+ align:start position:0%
+of things about some of the dominant um
+ 
+
+ align:start position:0%
+of things about some of the dominant um
+uh themes in the film to help uh
+
+ align:start position:0%
+uh themes in the film to help uh
+ 
+
+ align:start position:0%
+uh themes in the film to help uh
+organize your experience of it and I'm
+
+ align:start position:0%
+organize your experience of it and I'm
+ 
+
+ align:start position:0%
+organize your experience of it and I'm
+borrowing here or deeply influenced here
+
+ align:start position:0%
+borrowing here or deeply influenced here
+ 
+
+ align:start position:0%
+borrowing here or deeply influenced here
+by two critics especially although I
+
+ align:start position:0%
+by two critics especially although I
+ 
+
+ align:start position:0%
+by two critics especially although I
+mean I I perhaps I should say
+
+ align:start position:0%
+mean I I perhaps I should say
+ 
+
+ align:start position:0%
+mean I I perhaps I should say
+parenthetically uh you should probably
+
+ align:start position:0%
+parenthetically uh you should probably
+ 
+
+ align:start position:0%
+parenthetically uh you should probably
+uh uh assume that almost anything I say
+
+ align:start position:0%
+uh uh assume that almost anything I say
+ 
+
+ align:start position:0%
+uh uh assume that almost anything I say
+has been said by someone else somewhere
+
+ align:start position:0%
+has been said by someone else somewhere
+ 
+
+ align:start position:0%
+has been said by someone else somewhere
+some at some time in the past and words
+
+ align:start position:0%
+some at some time in the past and words
+ 
+
+ align:start position:0%
+some at some time in the past and words
+the job of a teacher as I conceive it is
+
+ align:start position:0%
+the job of a teacher as I conceive it is
+ 
+
+ align:start position:0%
+the job of a teacher as I conceive it is
+not to come up with totally original
+
+ align:start position:0%
+not to come up with totally original
+ 
+
+ align:start position:0%
+not to come up with totally original
+arguments every time because no one can
+
+ align:start position:0%
+arguments every time because no one can
+ 
+
+ align:start position:0%
+arguments every time because no one can
+be so original as to say everything
+
+ align:start position:0%
+be so original as to say everything
+ 
+
+ align:start position:0%
+be so original as to say everything
+that's wonderful about particular text
+
+ align:start position:0%
+that's wonderful about particular text
+ 
+
+ align:start position:0%
+that's wonderful about particular text
+or about a whole phenomenon like the
+
+ align:start position:0%
+or about a whole phenomenon like the
+ 
+
+ align:start position:0%
+or about a whole phenomenon like the
+movies right so a good teacher draws on
+
+ align:start position:0%
+movies right so a good teacher draws on
+ 
+
+ align:start position:0%
+movies right so a good teacher draws on
+that and I I when I really am drawing on
+
+ align:start position:0%
+that and I I when I really am drawing on
+ 
+
+ align:start position:0%
+that and I I when I really am drawing on
+a on a prior scholar who I know has uh
+
+ align:start position:0%
+a on a prior scholar who I know has uh
+ 
+
+ align:start position:0%
+a on a prior scholar who I know has uh
+shaped the arguments I'm making or has
+
+ align:start position:0%
+shaped the arguments I'm making or has
+ 
+
+ align:start position:0%
+shaped the arguments I'm making or has
+given me the the categories I'm using I
+
+ align:start position:0%
+given me the the categories I'm using I
+ 
+
+ align:start position:0%
+given me the the categories I'm using I
+mention them by name but of course I've
+
+ align:start position:0%
+mention them by name but of course I've
+ 
+
+ align:start position:0%
+mention them by name but of course I've
+been teaching for so long that much of
+
+ align:start position:0%
+been teaching for so long that much of
+ 
+
+ align:start position:0%
+been teaching for so long that much of
+this must now be uh U and unconsciously
+
+ align:start position:0%
+this must now be uh U and unconsciously
+ 
+
+ align:start position:0%
+this must now be uh U and unconsciously
+absorbed into my into my psyche and I
+
+ align:start position:0%
+absorbed into my into my psyche and I
+ 
+
+ align:start position:0%
+absorbed into my into my psyche and I
+don't always know this so I I'm not
+
+ align:start position:0%
+don't always know this so I I'm not
+ 
+
+ align:start position:0%
+don't always know this so I I'm not
+saying that those moments where I
+
+ align:start position:0%
+saying that those moments where I
+ 
+
+ align:start position:0%
+saying that those moments where I
+haven't made this acknowledgement are
+
+ align:start position:0%
+haven't made this acknowledgement are
+ 
+
+ align:start position:0%
+haven't made this acknowledgement are
+free of such influence quite the
+
+ align:start position:0%
+free of such influence quite the
+ 
+
+ align:start position:0%
+free of such influence quite the
+opposite but I do want to mention two
+
+ align:start position:0%
+opposite but I do want to mention two
+ 
+
+ align:start position:0%
+opposite but I do want to mention two
+Scholars who have especially influenced
+
+ align:start position:0%
+Scholars who have especially influenced
+ 
+
+ align:start position:0%
+Scholars who have especially influenced
+me on on uh Renoir uh because virtually
+
+ align:start position:0%
+me on on uh Renoir uh because virtually
+ 
+
+ align:start position:0%
+me on on uh Renoir uh because virtually
+all the things I've told you about
+
+ align:start position:0%
+all the things I've told you about
+ 
+
+ align:start position:0%
+all the things I've told you about
+Renoir although I've made the ideas my
+
+ align:start position:0%
+Renoir although I've made the ideas my
+ 
+
+ align:start position:0%
+Renoir although I've made the ideas my
+own come from these one is a a Frenchman
+
+ align:start position:0%
+own come from these one is a a Frenchman
+ 
+
+ align:start position:0%
+own come from these one is a a Frenchman
+named Alexander
+
+ align:start position:0%
+named Alexander
+ 
+
+ align:start position:0%
+named Alexander
+sansi uh and wrote a wonderful book on
+
+ align:start position:0%
+sansi uh and wrote a wonderful book on
+ 
+
+ align:start position:0%
+sansi uh and wrote a wonderful book on
+on I think it's several volume book on
+
+ align:start position:0%
+on I think it's several volume book on
+ 
+
+ align:start position:0%
+on I think it's several volume book on
+on Renoir that taught me a tremendous
+
+ align:start position:0%
+on Renoir that taught me a tremendous
+ 
+
+ align:start position:0%
+on Renoir that taught me a tremendous
+amount of especially about his French uh
+
+ align:start position:0%
+amount of especially about his French uh
+ 
+
+ align:start position:0%
+amount of especially about his French uh
+period and the other is the is the uh uh
+
+ align:start position:0%
+period and the other is the is the uh uh
+ 
+
+ align:start position:0%
+period and the other is the is the uh uh
+California scholar now California
+
+ align:start position:0%
+California scholar now California
+ 
+
+ align:start position:0%
+California scholar now California
+scholar Leo Brody one of whose essays
+
+ align:start position:0%
+scholar Leo Brody one of whose essays
+ 
+
+ align:start position:0%
+scholar Leo Brody one of whose essays
+I've asked you to read in this course
+
+ align:start position:0%
+I've asked you to read in this course
+ 
+
+ align:start position:0%
+I've asked you to read in this course
+and he's written a wonderful book on
+
+ align:start position:0%
+and he's written a wonderful book on
+ 
+
+ align:start position:0%
+and he's written a wonderful book on
+Renoir uh and uh although I have read
+
+ align:start position:0%
+Renoir uh and uh although I have read
+ 
+
+ align:start position:0%
+Renoir uh and uh although I have read
+the book I learned more about Renoir
+
+ align:start position:0%
+the book I learned more about Renoir
+ 
+
+ align:start position:0%
+the book I learned more about Renoir
+from Brody in conversation because he
+
+ align:start position:0%
+from Brody in conversation because he
+ 
+
+ align:start position:0%
+from Brody in conversation because he
+was my colleague many years ago when we
+
+ align:start position:0%
+was my colleague many years ago when we
+ 
+
+ align:start position:0%
+was my colleague many years ago when we
+were teaching together in the English
+
+ align:start position:0%
+were teaching together in the English
+ 
+
+ align:start position:0%
+were teaching together in the English
+Department at Yale and he's one of the
+
+ align:start position:0%
+Department at Yale and he's one of the
+ 
+
+ align:start position:0%
+Department at Yale and he's one of the
+people who turned me into a person
+
+ align:start position:0%
+people who turned me into a person
+ 
+
+ align:start position:0%
+people who turned me into a person
+interested in movies interested in film
+
+ align:start position:0%
+interested in movies interested in film
+ 
+
+ align:start position:0%
+interested in movies interested in film
+so Leo Brody b r a u d y Alexander sansi
+
+ align:start position:0%
+so Leo Brody b r a u d y Alexander sansi
+ 
+
+ align:start position:0%
+so Leo Brody b r a u d y Alexander sansi
+s s o n
+
+ align:start position:0%
+s s o n
+ 
+
+ align:start position:0%
+s s o n
+ke the two
+
+ align:start position:0%
+ke the two
+ 
+
+ align:start position:0%
+ke the two
+principal Scholars and critics behind
+
+ align:start position:0%
+principal Scholars and critics behind
+ 
+
+ align:start position:0%
+principal Scholars and critics behind
+what I've been saying both this
+
+ align:start position:0%
+what I've been saying both this
+ 
+
+ align:start position:0%
+what I've been saying both this
+afternoon and this
+
+ align:start position:0%
+afternoon and this
+ 
+
+ align:start position:0%
+afternoon and this
+evening dominant themes one the prison
+
+ align:start position:0%
+evening dominant themes one the prison
+ 
+
+ align:start position:0%
+evening dominant themes one the prison
+camp as a microcosm right uh there's a
+
+ align:start position:0%
+camp as a microcosm right uh there's a
+ 
+
+ align:start position:0%
+camp as a microcosm right uh there's a
+wonderful passage at one point in the in
+
+ align:start position:0%
+wonderful passage at one point in the in
+ 
+
+ align:start position:0%
+wonderful passage at one point in the in
+the movie where one of the characters
+
+ align:start position:0%
+the movie where one of the characters
+ 
+
+ align:start position:0%
+the movie where one of the characters
+said everyone would die of the disease
+
+ align:start position:0%
+said everyone would die of the disease
+ 
+
+ align:start position:0%
+said everyone would die of the disease
+of his class if the war did not
+
+ align:start position:0%
+of his class if the war did not
+ 
+
+ align:start position:0%
+of his class if the war did not
+reconcile all
+
+ align:start position:0%
+reconcile all
+ 
+
+ align:start position:0%
+reconcile all
+microbes and think about the
+
+ align:start position:0%
+microbes and think about the
+ 
+
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+microbes and think about the
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+
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+implications of that words the idea is
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+
+ align:start position:0%
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+
+ align:start position:0%
+that what the what one of the things
+ 
+
+ align:start position:0%
+that what the what one of the things
+that makes this prison camp such a
+
+ align:start position:0%
+that makes this prison camp such a
+ 
+
+ align:start position:0%
+that makes this prison camp such a
+fascinating place is that it is in some
+
+ align:start position:0%
+fascinating place is that it is in some
+ 
+
+ align:start position:0%
+fascinating place is that it is in some
+sense a microcosm of the larger
+
+ align:start position:0%
+sense a microcosm of the larger
+ 
+
+ align:start position:0%
+sense a microcosm of the larger
+world and and in especially if you if
+
+ align:start position:0%
+world and and in especially if you if
+ 
+
+ align:start position:0%
+world and and in especially if you if
+you think of the prison camp Beyond just
+
+ align:start position:0%
+you think of the prison camp Beyond just
+ 
+
+ align:start position:0%
+you think of the prison camp Beyond just
+the the the uh grouping of the French
+
+ align:start position:0%
+the the the uh grouping of the French
+ 
+
+ align:start position:0%
+the the the uh grouping of the French
+soldiers whom the French prisoners whom
+
+ align:start position:0%
+soldiers whom the French prisoners whom
+ 
+
+ align:start position:0%
+soldiers whom the French prisoners whom
+we follow primarily what you can
+
+ align:start position:0%
+we follow primarily what you can
+ 
+
+ align:start position:0%
+we follow primarily what you can
+recognize this you back away because we
+
+ align:start position:0%
+recognize this you back away because we
+ 
+
+ align:start position:0%
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+
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+
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+we are told about and we meet and we see
+briefly some of the other prisoners
+
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+briefly some of the other prisoners
+ 
+
+ align:start position:0%
+briefly some of the other prisoners
+there are there are Russian prisoners
+
+ align:start position:0%
+there are there are Russian prisoners
+ 
+
+ align:start position:0%
+there are there are Russian prisoners
+and other kinds of prisoners as well
+
+ align:start position:0%
+and other kinds of prisoners as well
+ 
+
+ align:start position:0%
+and other kinds of prisoners as well
+there uh other kinds of prisoners as
+
+ align:start position:0%
+there uh other kinds of prisoners as
+ 
+
+ align:start position:0%
+there uh other kinds of prisoners as
+well there's a there's a sense that that
+
+ align:start position:0%
+well there's a there's a sense that that
+ 
+
+ align:start position:0%
+well there's a there's a sense that that
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+
+ align:start position:0%
+that the prison camp is a kind of
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+
+ align:start position:0%
+that the prison camp is a kind of
+microcosm at least of Europe if not of
+
+ align:start position:0%
+microcosm at least of Europe if not of
+ 
+
+ align:start position:0%
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+
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+if not of the world as a whole and more
+ 
+
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+if not of the world as a whole and more
+specifically the way in which the prison
+
+ align:start position:0%
+specifically the way in which the prison
+ 
+
+ align:start position:0%
+specifically the way in which the prison
+camp is a microcosm for the social
+
+ align:start position:0%
+camp is a microcosm for the social
+ 
+
+ align:start position:0%
+camp is a microcosm for the social
+striations that organize outer Society
+
+ align:start position:0%
+striations that organize outer Society
+ 
+
+ align:start position:0%
+striations that organize outer Society
+there's a working class there's a
+
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+there's a working class there's a
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+
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+there's a working class there's a
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+
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+there's it seems to be a middle class
+ 
+
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+there's it seems to be a middle class
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+
+ align:start position:0%
+you'll notice that there's a scholar who
+ 
+
+ align:start position:0%
+you'll notice that there's a scholar who
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+
+ align:start position:0%
+right who who who has a copy of pindar
+ 
+
+ align:start position:0%
+right who who who has a copy of pindar
+the the the great ancient uh uh poet uh
+
+ align:start position:0%
+the the the great ancient uh uh poet uh
+ 
+
+ align:start position:0%
+the the the great ancient uh uh poet uh
+who think and who who who Treasures his
+
+ align:start position:0%
+who think and who who who Treasures his
+ 
+
+ align:start position:0%
+who think and who who who Treasures his
+work on pin he's one of my favorite
+
+ align:start position:0%
+work on pin he's one of my favorite
+ 
+
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+work on pin he's one of my favorite
+minor characters in the film because of
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+minor characters in the film because of
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+
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+minor characters in the film because of
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+
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+his commitment to literature despite the
+ 
+
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+his commitment to literature despite the
+war and despite the miseries of prison
+
+ align:start position:0%
+war and despite the miseries of prison
+ 
+
+ align:start position:0%
+war and despite the miseries of prison
+camp right uh uh and what you what you
+
+ align:start position:0%
+camp right uh uh and what you what you
+ 
+
+ align:start position:0%
+camp right uh uh and what you what you
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+
+ align:start position:0%
+can see is in a certain sense is that
+ 
+
+ align:start position:0%
+can see is in a certain sense is that
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+
+ align:start position:0%
+Renoir is delighted by the idea that a
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+
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+Renoir is delighted by the idea that a
+that a that a kind of microcosm is
+
+ align:start position:0%
+that a that a kind of microcosm is
+ 
+
+ align:start position:0%
+that a that a kind of microcosm is
+created and if you watch variations
+
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+created and if you watch variations
+ 
+
+ align:start position:0%
+created and if you watch variations
+amongst the Frenchmen and again if you
+
+ align:start position:0%
+amongst the Frenchmen and again if you
+ 
+
+ align:start position:0%
+amongst the Frenchmen and again if you
+think about that fragment of a scene I
+
+ align:start position:0%
+think about that fragment of a scene I
+ 
+
+ align:start position:0%
+think about that fragment of a scene I
+showed you this afternoon of these
+
+ align:start position:0%
+showed you this afternoon of these
+ 
+
+ align:start position:0%
+showed you this afternoon of these
+characters at dinner table in the in uh
+
+ align:start position:0%
+characters at dinner table in the in uh
+ 
+
+ align:start position:0%
+characters at dinner table in the in uh
+in the uh in the prison camp you'll
+
+ align:start position:0%
+in the uh in the prison camp you'll
+ 
+
+ align:start position:0%
+in the uh in the prison camp you'll
+begin to see more fully how powerfully
+
+ align:start position:0%
+begin to see more fully how powerfully
+ 
+
+ align:start position:0%
+begin to see more fully how powerfully
+and interestingly complexly he
+
+ align:start position:0%
+and interestingly complexly he
+ 
+
+ align:start position:0%
+and interestingly complexly he
+differentiates his characters from each
+
+ align:start position:0%
+differentiates his characters from each
+ 
+
+ align:start position:0%
+differentiates his characters from each
+other uh uh that fragment that you saw I
+
+ align:start position:0%
+other uh uh that fragment that you saw I
+ 
+
+ align:start position:0%
+other uh uh that fragment that you saw I
+hope you realized one of the characters
+
+ align:start position:0%
+hope you realized one of the characters
+ 
+
+ align:start position:0%
+hope you realized one of the characters
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+
+ align:start position:0%
+was an actor and you could tell that you
+ 
+
+ align:start position:0%
+was an actor and you could tell that you
+it becomes clearer if you watch the
+
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+it becomes clearer if you watch the
+ 
+
+ align:start position:0%
+it becomes clearer if you watch the
+whole scene but he's a he's a very
+
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+whole scene but he's a he's a very
+ 
+
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+whole scene but he's a he's a very
+histrionic and Theatrical character he
+
+ align:start position:0%
+histrionic and Theatrical character he
+ 
+
+ align:start position:0%
+histrionic and Theatrical character he
+bursts into to song all the time right
+
+ align:start position:0%
+bursts into to song all the time right
+ 
+
+ align:start position:0%
+bursts into to song all the time right
+uh and then there's the Aristocrat who's
+
+ align:start position:0%
+uh and then there's the Aristocrat who's
+ 
+
+ align:start position:0%
+uh and then there's the Aristocrat who's
+looking down his monacle very very uh uh
+
+ align:start position:0%
+looking down his monacle very very uh uh
+ 
+
+ align:start position:0%
+looking down his monacle very very uh uh
+uh austerely and it seems his lip seems
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+uh austerely and it seems his lip seems
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+
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+uh austerely and it seems his lip seems
+curled in a permanent uh gesture of
+
+ align:start position:0%
+curled in a permanent uh gesture of
+ 
+
+ align:start position:0%
+curled in a permanent uh gesture of
+condescension uh uh and so forth uh
+
+ align:start position:0%
+condescension uh uh and so forth uh
+ 
+
+ align:start position:0%
+condescension uh uh and so forth uh
+watch how how how richly how complexly
+
+ align:start position:0%
+watch how how how richly how complexly
+ 
+
+ align:start position:0%
+watch how how how richly how complexly
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+
+ align:start position:0%
+the characters are distinguished from
+ 
+
+ align:start position:0%
+the characters are distinguished from
+each other by social class by profession
+
+ align:start position:0%
+each other by social class by profession
+ 
+
+ align:start position:0%
+each other by social class by profession
+by uh and so and so forth I don't want
+
+ align:start position:0%
+by uh and so and so forth I don't want
+ 
+
+ align:start position:0%
+by uh and so and so forth I don't want
+to romanticize or idealize what I'm this
+
+ align:start position:0%
+to romanticize or idealize what I'm this
+ 
+
+ align:start position:0%
+to romanticize or idealize what I'm this
+argument because I'm not suggesting that
+
+ align:start position:0%
+argument because I'm not suggesting that
+ 
+
+ align:start position:0%
+argument because I'm not suggesting that
+when he says it's a microcosm of the
+
+ align:start position:0%
+when he says it's a microcosm of the
+ 
+
+ align:start position:0%
+when he says it's a microcosm of the
+world he wants to celebrate that
+
+ align:start position:0%
+world he wants to celebrate that
+ 
+
+ align:start position:0%
+world he wants to celebrate that
+microcosm although he he's interested in
+
+ align:start position:0%
+microcosm although he he's interested in
+ 
+
+ align:start position:0%
+microcosm although he he's interested in
+it uh Renoir is also aware of the
+
+ align:start position:0%
+it uh Renoir is also aware of the
+ 
+
+ align:start position:0%
+it uh Renoir is also aware of the
+limitations that it's not as if he's
+
+ align:start position:0%
+limitations that it's not as if he's
+ 
+
+ align:start position:0%
+limitations that it's not as if he's
+suggesting that this is a perfect
+
+ align:start position:0%
+suggesting that this is a perfect
+ 
+
+ align:start position:0%
+suggesting that this is a perfect
+community at all one reason is they're
+
+ align:start position:0%
+community at all one reason is they're
+ 
+
+ align:start position:0%
+community at all one reason is they're
+forced together but they're being forced
+
+ align:start position:0%
+forced together but they're being forced
+ 
+
+ align:start position:0%
+forced together but they're being forced
+together uh makes them share forces them
+
+ align:start position:0%
+together uh makes them share forces them
+ 
+
+ align:start position:0%
+together uh makes them share forces them
+to come out of their limitations in
+
+ align:start position:0%
+to come out of their limitations in
+ 
+
+ align:start position:0%
+to come out of their limitations in
+certain way to overcome certain of their
+
+ align:start position:0%
+certain way to overcome certain of their
+ 
+
+ align:start position:0%
+certain way to overcome certain of their
+prejudices although never fully right
+
+ align:start position:0%
+prejudices although never fully right
+ 
+
+ align:start position:0%
+prejudices although never fully right
+but what it also does is reveal them and
+
+ align:start position:0%
+but what it also does is reveal them and
+ 
+
+ align:start position:0%
+but what it also does is reveal them and
+we can and we can see how both processes
+
+ align:start position:0%
+we can and we can see how both processes
+ 
+
+ align:start position:0%
+we can and we can see how both processes
+the the the the process of sort of
+
+ align:start position:0%
+the the the the process of sort of
+ 
+
+ align:start position:0%
+the the the the process of sort of
+adjusting uh to people different from
+
+ align:start position:0%
+adjusting uh to people different from
+ 
+
+ align:start position:0%
+adjusting uh to people different from
+yourself and maybe overcoming some of
+
+ align:start position:0%
+yourself and maybe overcoming some of
+ 
+
+ align:start position:0%
+yourself and maybe overcoming some of
+your class or racial prejudices is a
+
+ align:start position:0%
+your class or racial prejudices is a
+ 
+
+ align:start position:0%
+your class or racial prejudices is a
+part of the experience that the
+
+ align:start position:0%
+part of the experience that the
+ 
+
+ align:start position:0%
+part of the experience that the
+characters in the film have but another
+
+ align:start position:0%
+characters in the film have but another
+ 
+
+ align:start position:0%
+characters in the film have but another
+part of the experiences that they come
+
+ align:start position:0%
+part of the experiences that they come
+ 
+
+ align:start position:0%
+part of the experiences that they come
+up against the differences between them
+
+ align:start position:0%
+up against the differences between them
+ 
+
+ align:start position:0%
+up against the differences between them
+some of which can never be breached let
+
+ align:start position:0%
+some of which can never be breached let
+ 
+
+ align:start position:0%
+some of which can never be breached let
+me mention one scene which dramatizes
+
+ align:start position:0%
+me mention one scene which dramatizes
+ 
+
+ align:start position:0%
+me mention one scene which dramatizes
+this ambig ambiguity very deeply there's
+
+ align:start position:0%
+this ambig ambiguity very deeply there's
+ 
+
+ align:start position:0%
+this ambig ambiguity very deeply there's
+one moment in the film very powerful
+
+ align:start position:0%
+one moment in the film very powerful
+ 
+
+ align:start position:0%
+one moment in the film very powerful
+moment I think uh in which one charact
+
+ align:start position:0%
+moment I think uh in which one charact
+ 
+
+ align:start position:0%
+moment I think uh in which one charact
+in which the mar the the character
+
+ align:start position:0%
+in which the mar the the character
+ 
+
+ align:start position:0%
+in which the mar the the character
+played by um uh gabah the marelle
+
+ align:start position:0%
+played by um uh gabah the marelle
+ 
+
+ align:start position:0%
+played by um uh gabah the marelle
+character is wounded in a good part of
+
+ align:start position:0%
+character is wounded in a good part of
+ 
+
+ align:start position:0%
+character is wounded in a good part of
+the early part of the film and in fact
+
+ align:start position:0%
+the early part of the film and in fact
+ 
+
+ align:start position:0%
+the early part of the film and in fact
+in in the dinner scene that I showed you
+
+ align:start position:0%
+in in the dinner scene that I showed you
+ 
+
+ align:start position:0%
+in in the dinner scene that I showed you
+this afternoon uh you'll see that at a
+
+ align:start position:0%
+this afternoon uh you'll see that at a
+ 
+
+ align:start position:0%
+this afternoon uh you'll see that at a
+certain point his comrade sitting at the
+
+ align:start position:0%
+certain point his comrade sitting at the
+ 
+
+ align:start position:0%
+certain point his comrade sitting at the
+table cuts his meat for him because his
+
+ align:start position:0%
+table cuts his meat for him because his
+ 
+
+ align:start position:0%
+table cuts his meat for him because his
+hand is injured and uh I don't know if
+
+ align:start position:0%
+hand is injured and uh I don't know if
+ 
+
+ align:start position:0%
+hand is injured and uh I don't know if
+it's in this scene or a subsequent scene
+
+ align:start position:0%
+it's in this scene or a subsequent scene
+ 
+
+ align:start position:0%
+it's in this scene or a subsequent scene
+there's a moment when another character
+
+ align:start position:0%
+there's a moment when another character
+ 
+
+ align:start position:0%
+there's a moment when another character
+in the film washes marelle's feet why is
+
+ align:start position:0%
+in the film washes marelle's feet why is
+ 
+
+ align:start position:0%
+in the film washes marelle's feet why is
+foot
+
+ align:start position:0%
+foot
+ 
+
+ align:start position:0%
+foot
+washing uh instantly a symbolic thing
+
+ align:start position:0%
+washing uh instantly a symbolic thing
+ 
+
+ align:start position:0%
+washing uh instantly a symbolic thing
+who knows the
+
+ align:start position:0%
+who knows the
+ 
+
+ align:start position:0%
+who knows the
+answer likey all right there's a scene
+
+ align:start position:0%
+answer likey all right there's a scene
+ 
+
+ align:start position:0%
+answer likey all right there's a scene
+in the Bible in in in the 12th chapter
+
+ align:start position:0%
+in the Bible in in in the 12th chapter
+ 
+
+ align:start position:0%
+in the Bible in in in the 12th chapter
+of John uh in which in which in which
+
+ align:start position:0%
+of John uh in which in which in which
+ 
+
+ align:start position:0%
+of John uh in which in which in which
+Mary or Martha I can't remember which
+
+ align:start position:0%
+Mary or Martha I can't remember which
+ 
+
+ align:start position:0%
+Mary or Martha I can't remember which
+washes Christ's feet and then in the
+
+ align:start position:0%
+washes Christ's feet and then in the
+ 
+
+ align:start position:0%
+washes Christ's feet and then in the
+very next chapter and uh in the very
+
+ align:start position:0%
+very next chapter and uh in the very
+ 
+
+ align:start position:0%
+very next chapter and uh in the very
+next chapter it at the Last Supper
+
+ align:start position:0%
+next chapter it at the Last Supper
+ 
+
+ align:start position:0%
+next chapter it at the Last Supper
+Christ himself washes the feet of his
+
+ align:start position:0%
+Christ himself washes the feet of his
+ 
+
+ align:start position:0%
+Christ himself washes the feet of his
+disciples and in fact the washing of
+
+ align:start position:0%
+disciples and in fact the washing of
+ 
+
+ align:start position:0%
+disciples and in fact the washing of
+feet uh is is in Catholic and in certain
+
+ align:start position:0%
+feet uh is is in Catholic and in certain
+ 
+
+ align:start position:0%
+feet uh is is in Catholic and in certain
+other Christian uh um rituals uh an
+
+ align:start position:0%
+other Christian uh um rituals uh an
+ 
+
+ align:start position:0%
+other Christian uh um rituals uh an
+actual official ritual it used to be
+
+ align:start position:0%
+actual official ritual it used to be
+ 
+
+ align:start position:0%
+actual official ritual it used to be
+much more common than it is today but
+
+ align:start position:0%
+much more common than it is today but
+ 
+
+ align:start position:0%
+much more common than it is today but
+it's still done in certain Catholic
+
+ align:start position:0%
+it's still done in certain Catholic
+ 
+
+ align:start position:0%
+it's still done in certain Catholic
+countries uh uh at the at the Advent of
+
+ align:start position:0%
+countries uh uh at the at the Advent of
+ 
+
+ align:start position:0%
+countries uh uh at the at the Advent of
+the holy of Holy Week uh uh so it's a
+
+ align:start position:0%
+the holy of Holy Week uh uh so it's a
+ 
+
+ align:start position:0%
+the holy of Holy Week uh uh so it's a
+deeply symbolic act in which in which
+
+ align:start position:0%
+deeply symbolic act in which in which
+ 
+
+ align:start position:0%
+deeply symbolic act in which in which
+Christ himself is washing the feet of
+
+ align:start position:0%
+Christ himself is washing the feet of
+ 
+
+ align:start position:0%
+Christ himself is washing the feet of
+his disciples and and he and the message
+
+ align:start position:0%
+his disciples and and he and the message
+ 
+
+ align:start position:0%
+his disciples and and he and the message
+he gives is everyone uh uh you should
+
+ align:start position:0%
+he gives is everyone uh uh you should
+ 
+
+ align:start position:0%
+he gives is everyone uh uh you should
+now do this to your to your fellows uh
+
+ align:start position:0%
+now do this to your to your fellows uh
+ 
+
+ align:start position:0%
+now do this to your to your fellows uh
+uh the implication being no one is
+
+ align:start position:0%
+uh the implication being no one is
+ 
+
+ align:start position:0%
+uh the implication being no one is
+better than anyone else the implication
+
+ align:start position:0%
+better than anyone else the implication
+ 
+
+ align:start position:0%
+better than anyone else the implication
+a radical a radically democratic Vision
+
+ align:start position:0%
+a radical a radically democratic Vision
+ 
+
+ align:start position:0%
+a radical a radically democratic Vision
+in some sense of of of uh of God's love
+
+ align:start position:0%
+in some sense of of of uh of God's love
+ 
+
+ align:start position:0%
+in some sense of of of uh of God's love
+uh and uh where has this practice been
+
+ align:start position:0%
+uh and uh where has this practice been
+ 
+
+ align:start position:0%
+uh and uh where has this practice been
+recently very dramatically and publicly
+
+ align:start position:0%
+recently very dramatically and publicly
+ 
+
+ align:start position:0%
+recently very dramatically and publicly
+revived who's been doing it the Pope the
+
+ align:start position:0%
+revived who's been doing it the Pope the
+ 
+
+ align:start position:0%
+revived who's been doing it the Pope the
+new pope haven't you read about this the
+
+ align:start position:0%
+new pope haven't you read about this the
+ 
+
+ align:start position:0%
+new pope haven't you read about this the
+new pope has been doing this he's uh uh
+
+ align:start position:0%
+new pope has been doing this he's uh uh
+ 
+
+ align:start position:0%
+new pope has been doing this he's uh uh
+uh washing the feet of
+
+ align:start position:0%
+uh washing the feet of
+ 
+
+ align:start position:0%
+uh washing the feet of
+parishioners a symbolic gesture in which
+
+ align:start position:0%
+parishioners a symbolic gesture in which
+ 
+
+ align:start position:0%
+parishioners a symbolic gesture in which
+in which God's Emissary on Earth is
+
+ align:start position:0%
+in which God's Emissary on Earth is
+ 
+
+ align:start position:0%
+in which God's Emissary on Earth is
+behaving with the humility that Jesus
+
+ align:start position:0%
+behaving with the humility that Jesus
+ 
+
+ align:start position:0%
+behaving with the humility that Jesus
+Christ himself so what so the foot
+
+ align:start position:0%
+Christ himself so what so the foot
+ 
+
+ align:start position:0%
+Christ himself so what so the foot
+washing scene in in uh in in in uh U our
+
+ align:start position:0%
+washing scene in in uh in in in uh U our
+ 
+
+ align:start position:0%
+washing scene in in uh in in in uh U our
+film has this sort of resonance to it
+
+ align:start position:0%
+film has this sort of resonance to it
+ 
+
+ align:start position:0%
+film has this sort of resonance to it
+even though there's no there's no openly
+
+ align:start position:0%
+even though there's no there's no openly
+ 
+
+ align:start position:0%
+even though there's no there's no openly
+religious reference but of but it has a
+
+ align:start position:0%
+religious reference but of but it has a
+ 
+
+ align:start position:0%
+religious reference but of but it has a
+similar kind of significance and and and
+
+ align:start position:0%
+similar kind of significance and and and
+ 
+
+ align:start position:0%
+similar kind of significance and and and
+they're carrying on a kind of
+
+ align:start position:0%
+they're carrying on a kind of
+ 
+
+ align:start position:0%
+they're carrying on a kind of
+conversation as the as the feet are
+
+ align:start position:0%
+conversation as the as the feet are
+ 
+
+ align:start position:0%
+conversation as the as the feet are
+being washed and what you feel is boy
+
+ align:start position:0%
+being washed and what you feel is boy
+ 
+
+ align:start position:0%
+being washed and what you feel is boy
+what a moving scene uh nobody is in the
+
+ align:start position:0%
+what a moving scene uh nobody is in the
+ 
+
+ align:start position:0%
+what a moving scene uh nobody is in the
+man who's doing the washing doesn't feel
+
+ align:start position:0%
+man who's doing the washing doesn't feel
+ 
+
+ align:start position:0%
+man who's doing the washing doesn't feel
+that he's being condescended to or that
+
+ align:start position:0%
+that he's being condescended to or that
+ 
+
+ align:start position:0%
+that he's being condescended to or that
+he's being diminished in any way by
+
+ align:start position:0%
+he's being diminished in any way by
+ 
+
+ align:start position:0%
+he's being diminished in any way by
+doing it the man whose feet are being
+
+ align:start position:0%
+doing it the man whose feet are being
+ 
+
+ align:start position:0%
+doing it the man whose feet are being
+washed is not embarrassed to have it
+
+ align:start position:0%
+washed is not embarrassed to have it
+ 
+
+ align:start position:0%
+washed is not embarrassed to have it
+happen what a scene of solidarity and
+
+ align:start position:0%
+happen what a scene of solidarity and
+ 
+
+ align:start position:0%
+happen what a scene of solidarity and
+Community uh and and you could turn this
+
+ align:start position:0%
+Community uh and and you could turn this
+ 
+
+ align:start position:0%
+Community uh and and you could turn this
+you could become very you could you
+
+ align:start position:0%
+you could become very you could you
+ 
+
+ align:start position:0%
+you could become very you could you
+could wax very poetic about what a scene
+
+ align:start position:0%
+could wax very poetic about what a scene
+ 
+
+ align:start position:0%
+could wax very poetic about what a scene
+of community and yet watch how the scene
+
+ align:start position:0%
+of community and yet watch how the scene
+ 
+
+ align:start position:0%
+of community and yet watch how the scene
+ends there's a moment at which after
+
+ align:start position:0%
+ends there's a moment at which after
+ 
+
+ align:start position:0%
+ends there's a moment at which after
+they as he's drying his feet uh the the
+
+ align:start position:0%
+they as he's drying his feet uh the the
+ 
+
+ align:start position:0%
+they as he's drying his feet uh the the
+uh the foot washer uh marelle asked the
+
+ align:start position:0%
+uh the foot washer uh marelle asked the
+ 
+
+ align:start position:0%
+uh the foot washer uh marelle asked the
+foot washer what do you do for a living
+
+ align:start position:0%
+foot washer what do you do for a living
+ 
+
+ align:start position:0%
+foot washer what do you do for a living
+and at some point during their
+
+ align:start position:0%
+and at some point during their
+ 
+
+ align:start position:0%
+and at some point during their
+conversation he says oh I I he says I am
+
+ align:start position:0%
+conversation he says oh I I he says I am
+ 
+
+ align:start position:0%
+conversation he says oh I I he says I am
+a I I I am a cadas what that means is
+
+ align:start position:0%
+a I I I am a cadas what that means is
+ 
+
+ align:start position:0%
+a I I I am a cadas what that means is
+something like City Planning he's a city
+
+ align:start position:0%
+something like City Planning he's a city
+ 
+
+ align:start position:0%
+something like City Planning he's a city
+planner and so the Marell character
+
+ align:start position:0%
+planner and so the Marell character
+ 
+
+ align:start position:0%
+planner and so the Marell character
+hears this and they go on that at the
+
+ align:start position:0%
+hears this and they go on that at the
+ 
+
+ align:start position:0%
+hears this and they go on that at the
+very end of the scene marichelle turns
+
+ align:start position:0%
+very end of the scene marichelle turns
+ 
+
+ align:start position:0%
+very end of the scene marichelle turns
+to his foot washer and he says what does
+
+ align:start position:0%
+to his foot washer and he says what does
+ 
+
+ align:start position:0%
+to his foot washer and he says what does
+that mean
+
+ align:start position:0%
+that mean
+ 
+
+ align:start position:0%
+that mean
+kadas the implication being that their
+
+ align:start position:0%
+kadas the implication being that their
+ 
+
+ align:start position:0%
+kadas the implication being that their
+vocabularies aren't even the same that
+
+ align:start position:0%
+vocabularies aren't even the same that
+ 
+
+ align:start position:0%
+vocabularies aren't even the same that
+they what it what it dramatizes is the
+
+ align:start position:0%
+they what it what it dramatizes is the
+ 
+
+ align:start position:0%
+they what it what it dramatizes is the
+distance between them he's been sitting
+
+ align:start position:0%
+distance between them he's been sitting
+ 
+
+ align:start position:0%
+distance between them he's been sitting
+there having this conversation with him
+
+ align:start position:0%
+there having this conversation with him
+ 
+
+ align:start position:0%
+there having this conversation with him
+but he didn't even say GE I have no idea
+
+ align:start position:0%
+but he didn't even say GE I have no idea
+ 
+
+ align:start position:0%
+but he didn't even say GE I have no idea
+what that word means I certainly have no
+
+ align:start position:0%
+what that word means I certainly have no
+ 
+
+ align:start position:0%
+what that word means I certainly have no
+idea what you do for a living it's a way
+
+ align:start position:0%
+idea what you do for a living it's a way
+ 
+
+ align:start position:0%
+idea what you do for a living it's a way
+of reminding us yes they've come
+
+ align:start position:0%
+of reminding us yes they've come
+ 
+
+ align:start position:0%
+of reminding us yes they've come
+together yes they're sharing space yes
+
+ align:start position:0%
+together yes they're sharing space yes
+ 
+
+ align:start position:0%
+together yes they're sharing space yes
+they they're doing something very uh um
+
+ align:start position:0%
+they they're doing something very uh um
+ 
+
+ align:start position:0%
+they they're doing something very uh um
+that dramatizes human solidarity and yet
+
+ align:start position:0%
+that dramatizes human solidarity and yet
+ 
+
+ align:start position:0%
+that dramatizes human solidarity and yet
+all also how separated they are again
+
+ align:start position:0%
+all also how separated they are again
+ 
+
+ align:start position:0%
+all also how separated they are again
+and again in the film we have this sort
+
+ align:start position:0%
+and again in the film we have this sort
+ 
+
+ align:start position:0%
+and again in the film we have this sort
+of double experience in which we see
+
+ align:start position:0%
+of double experience in which we see
+ 
+
+ align:start position:0%
+of double experience in which we see
+characters uh um make contact with each
+
+ align:start position:0%
+characters uh um make contact with each
+ 
+
+ align:start position:0%
+characters uh um make contact with each
+other or even sacrifice for each other
+
+ align:start position:0%
+other or even sacrifice for each other
+ 
+
+ align:start position:0%
+other or even sacrifice for each other
+and at the same time we're aware of
+
+ align:start position:0%
+and at the same time we're aware of
+ 
+
+ align:start position:0%
+and at the same time we're aware of
+their differences watch for this it's
+
+ align:start position:0%
+their differences watch for this it's
+ 
+
+ align:start position:0%
+their differences watch for this it's
+very powerful and moving in words it's a
+
+ align:start position:0%
+very powerful and moving in words it's a
+ 
+
+ align:start position:0%
+very powerful and moving in words it's a
+form of moral realism in which the film
+
+ align:start position:0%
+form of moral realism in which the film
+ 
+
+ align:start position:0%
+form of moral realism in which the film
+refuses to simplify what it wants to say
+
+ align:start position:0%
+refuses to simplify what it wants to say
+ 
+
+ align:start position:0%
+refuses to simplify what it wants to say
+about Human Experience very powerful
+
+ align:start position:0%
+about Human Experience very powerful
+ 
+
+ align:start position:0%
+about Human Experience very powerful
+example of this in the relationship
+
+ align:start position:0%
+example of this in the relationship
+ 
+
+ align:start position:0%
+example of this in the relationship
+between the Jew rosental who of his
+
+ align:start position:0%
+between the Jew rosental who of his
+ 
+
+ align:start position:0%
+between the Jew rosental who of his
+wealth he's the heir of a department
+
+ align:start position:0%
+wealth he's the heir of a department
+ 
+
+ align:start position:0%
+wealth he's the heir of a department
+store Fortune right uh but because he's
+
+ align:start position:0%
+store Fortune right uh but because he's
+ 
+
+ align:start position:0%
+store Fortune right uh but because he's
+a Jew he and and because he's nvo reach
+
+ align:start position:0%
+a Jew he and and because he's nvo reach
+ 
+
+ align:start position:0%
+a Jew he and and because he's nvo reach
+he can never be part of the aristocracy
+
+ align:start position:0%
+he can never be part of the aristocracy
+ 
+
+ align:start position:0%
+he can never be part of the aristocracy
+uh uh his relation to the marishal
+
+ align:start position:0%
+uh uh his relation to the marishal
+ 
+
+ align:start position:0%
+uh uh his relation to the marishal
+character is very complex marelle as I
+
+ align:start position:0%
+character is very complex marelle as I
+ 
+
+ align:start position:0%
+character is very complex marelle as I
+mentioned this afternoon retains a kind
+
+ align:start position:0%
+mentioned this afternoon retains a kind
+ 
+
+ align:start position:0%
+mentioned this afternoon retains a kind
+of working class French workingclass
+
+ align:start position:0%
+of working class French workingclass
+ 
+
+ align:start position:0%
+of working class French workingclass
+characteristic anti-Semitism and and
+
+ align:start position:0%
+characteristic anti-Semitism and and
+ 
+
+ align:start position:0%
+characteristic anti-Semitism and and
+there are moments when you can feel the
+
+ align:start position:0%
+there are moments when you can feel the
+ 
+
+ align:start position:0%
+there are moments when you can feel the
+hostility between them when the two of
+
+ align:start position:0%
+hostility between them when the two of
+ 
+
+ align:start position:0%
+hostility between them when the two of
+them finally try to make an escape from
+
+ align:start position:0%
+them finally try to make an escape from
+ 
+
+ align:start position:0%
+them finally try to make an escape from
+the prison and they actually are away
+
+ align:start position:0%
+the prison and they actually are away
+ 
+
+ align:start position:0%
+the prison and they actually are away
+from one of the prisons for a while and
+
+ align:start position:0%
+from one of the prisons for a while and
+ 
+
+ align:start position:0%
+from one of the prisons for a while and
+you see the the the rosentel character
+
+ align:start position:0%
+you see the the the rosentel character
+ 
+
+ align:start position:0%
+you see the the the rosentel character
+hurts his foot and there's a moment in
+
+ align:start position:0%
+hurts his foot and there's a moment in
+ 
+
+ align:start position:0%
+hurts his foot and there's a moment in
+which it looks like gee if if the
+
+ align:start position:0%
+which it looks like gee if if the
+ 
+
+ align:start position:0%
+which it looks like gee if if the
+marelle character stays with him he's
+
+ align:start position:0%
+marelle character stays with him he's
+ 
+
+ align:start position:0%
+marelle character stays with him he's
+putting himself in danger as well and
+
+ align:start position:0%
+putting himself in danger as well and
+ 
+
+ align:start position:0%
+putting himself in danger as well and
+they get into a fight and one of them
+
+ align:start position:0%
+they get into a fight and one of them
+ 
+
+ align:start position:0%
+they get into a fight and one of them
+said the Roso says go away leave me
+
+ align:start position:0%
+said the Roso says go away leave me
+ 
+
+ align:start position:0%
+said the Roso says go away leave me
+alone leave and marelle says all right I
+
+ align:start position:0%
+alone leave and marelle says all right I
+ 
+
+ align:start position:0%
+alone leave and marelle says all right I
+will and it's a very wonderful scene
+
+ align:start position:0%
+will and it's a very wonderful scene
+ 
+
+ align:start position:0%
+will and it's a very wonderful scene
+because they start singing at each other
+
+ align:start position:0%
+because they start singing at each other
+ 
+
+ align:start position:0%
+because they start singing at each other
+and it's a form of singing hostility so
+
+ align:start position:0%
+and it's a form of singing hostility so
+ 
+
+ align:start position:0%
+and it's a form of singing hostility so
+there's a comic Dimension to it too it's
+
+ align:start position:0%
+there's a comic Dimension to it too it's
+ 
+
+ align:start position:0%
+there's a comic Dimension to it too it's
+really rich but what is also being
+
+ align:start position:0%
+really rich but what is also being
+ 
+
+ align:start position:0%
+really rich but what is also being
+dramatized there are the limitations of
+
+ align:start position:0%
+dramatized there are the limitations of
+ 
+
+ align:start position:0%
+dramatized there are the limitations of
+the characters are marelle's
+
+ align:start position:0%
+the characters are marelle's
+ 
+
+ align:start position:0%
+the characters are marelle's
+anti-Semitism Rises come comes to the
+
+ align:start position:0%
+anti-Semitism Rises come comes to the
+ 
+
+ align:start position:0%
+anti-Semitism Rises come comes to the
+surface their hostility toward each
+
+ align:start position:0%
+surface their hostility toward each
+ 
+
+ align:start position:0%
+surface their hostility toward each
+other comes to the surface at that
+
+ align:start position:0%
+other comes to the surface at that
+ 
+
+ align:start position:0%
+other comes to the surface at that
+moment although of course they also
+
+ align:start position:0%
+moment although of course they also
+ 
+
+ align:start position:0%
+moment although of course they also
+overcome it and there are many other
+
+ align:start position:0%
+overcome it and there are many other
+ 
+
+ align:start position:0%
+overcome it and there are many other
+such moments in the film uh the
+
+ align:start position:0%
+such moments in the film uh the
+ 
+
+ align:start position:0%
+such moments in the film uh the
+relationship between de and his German
+
+ align:start position:0%
+relationship between de and his German
+ 
+
+ align:start position:0%
+relationship between de and his German
+counterpart the
+
+ align:start position:0%
+counterpart the
+ 
+
+ align:start position:0%
+counterpart the
+Aristocrat um uh um the aristocratic
+
+ align:start position:0%
+Aristocrat um uh um the aristocratic
+ 
+
+ align:start position:0%
+Aristocrat um uh um the aristocratic
+German uh uh is also a version of this
+
+ align:start position:0%
+German uh uh is also a version of this
+ 
+
+ align:start position:0%
+German uh uh is also a version of this
+of this kind of thing so a as I've
+
+ align:start position:0%
+of this kind of thing so a as I've
+ 
+
+ align:start position:0%
+of this kind of thing so a as I've
+already implied a second central theme
+
+ align:start position:0%
+already implied a second central theme
+ 
+
+ align:start position:0%
+already implied a second central theme
+of the film has to do with what we met
+
+ align:start position:0%
+of the film has to do with what we met
+ 
+
+ align:start position:0%
+of the film has to do with what we met
+my might call uh barriers and boundaries
+
+ align:start position:0%
+my might call uh barriers and boundaries
+ 
+
+ align:start position:0%
+my might call uh barriers and boundaries
+there's the barrier of social class
+
+ align:start position:0%
+there's the barrier of social class
+ 
+
+ align:start position:0%
+there's the barrier of social class
+which I've mentioned already there's the
+
+ align:start position:0%
+which I've mentioned already there's the
+ 
+
+ align:start position:0%
+which I've mentioned already there's the
+barrier of of language and culture right
+
+ align:start position:0%
+barrier of of language and culture right
+ 
+
+ align:start position:0%
+barrier of of language and culture right
+the Germans and the French are at War
+
+ align:start position:0%
+the Germans and the French are at War
+ 
+
+ align:start position:0%
+the Germans and the French are at War
+right uh the Russians don't speak the
+
+ align:start position:0%
+right uh the Russians don't speak the
+ 
+
+ align:start position:0%
+right uh the Russians don't speak the
+same language as the Germans the English
+
+ align:start position:0%
+same language as the Germans the English
+ 
+
+ align:start position:0%
+same language as the Germans the English
+don't speak the same language as the
+
+ align:start position:0%
+don't speak the same language as the
+ 
+
+ align:start position:0%
+don't speak the same language as the
+French and again and again the what
+
+ align:start position:0%
+French and again and again the what
+ 
+
+ align:start position:0%
+French and again and again the what
+separates people is dramatized for us
+
+ align:start position:0%
+separates people is dramatized for us
+ 
+
+ align:start position:0%
+separates people is dramatized for us
+although there's also a longing in the
+
+ align:start position:0%
+although there's also a longing in the
+ 
+
+ align:start position:0%
+although there's also a longing in the
+film to transcend these boundaries they
+
+ align:start position:0%
+film to transcend these boundaries they
+ 
+
+ align:start position:0%
+film to transcend these boundaries they
+always they don't can't always be
+
+ align:start position:0%
+always they don't can't always be
+ 
+
+ align:start position:0%
+always they don't can't always be
+transcended sometimes these boundaries
+
+ align:start position:0%
+transcended sometimes these boundaries
+ 
+
+ align:start position:0%
+transcended sometimes these boundaries
+are shown to be foolish and trivial or
+
+ align:start position:0%
+are shown to be foolish and trivial or
+ 
+
+ align:start position:0%
+are shown to be foolish and trivial or
+or or or at best unhelpful right uh uh
+
+ align:start position:0%
+or or or at best unhelpful right uh uh
+ 
+
+ align:start position:0%
+or or or at best unhelpful right uh uh
+and we can think of many there are many
+
+ align:start position:0%
+and we can think of many there are many
+ 
+
+ align:start position:0%
+and we can think of many there are many
+examples in the film uh both of language
+
+ align:start position:0%
+examples in the film uh both of language
+ 
+
+ align:start position:0%
+examples in the film uh both of language
+and of geography as well as of social
+
+ align:start position:0%
+and of geography as well as of social
+ 
+
+ align:start position:0%
+and of geography as well as of social
+class but let me mention just U two of
+
+ align:start position:0%
+class but let me mention just U two of
+ 
+
+ align:start position:0%
+class but let me mention just U two of
+them there's one wonderful moment in the
+
+ align:start position:0%
+them there's one wonderful moment in the
+ 
+
+ align:start position:0%
+them there's one wonderful moment in the
+film The French prisoners have been
+
+ align:start position:0%
+film The French prisoners have been
+ 
+
+ align:start position:0%
+film The French prisoners have been
+digging a tunnel an escape tunnel uh and
+
+ align:start position:0%
+digging a tunnel an escape tunnel uh and
+ 
+
+ align:start position:0%
+digging a tunnel an escape tunnel uh and
+they've almost completed the tunnel when
+
+ align:start position:0%
+they've almost completed the tunnel when
+ 
+
+ align:start position:0%
+they've almost completed the tunnel when
+the Germans come and say all right we're
+
+ align:start position:0%
+the Germans come and say all right we're
+ 
+
+ align:start position:0%
+the Germans come and say all right we're
+moving you out of your barracks and
+
+ align:start position:0%
+moving you out of your barracks and
+ 
+
+ align:start position:0%
+moving you out of your barracks and
+we're putting these English prisoners in
+
+ align:start position:0%
+we're putting these English prisoners in
+ 
+
+ align:start position:0%
+we're putting these English prisoners in
+it's very so the French are very unhappy
+
+ align:start position:0%
+it's very so the French are very unhappy
+ 
+
+ align:start position:0%
+it's very so the French are very unhappy
+about this because they've almost
+
+ align:start position:0%
+about this because they've almost
+ 
+
+ align:start position:0%
+about this because they've almost
+completed their tunnel so at Great
+
+ align:start position:0%
+completed their tunnel so at Great
+ 
+
+ align:start position:0%
+completed their tunnel so at Great
+danger to himself the marishal character
+
+ align:start position:0%
+danger to himself the marishal character
+ 
+
+ align:start position:0%
+danger to himself the marishal character
+breaks
+
+ align:start position:0%
+breaks
+ 
+
+ align:start position:0%
+breaks
+ranks drop try he does it kind of trick
+
+ align:start position:0%
+ranks drop try he does it kind of trick
+ 
+
+ align:start position:0%
+ranks drop try he does it kind of trick
+where he drops his suitcase I think or
+
+ align:start position:0%
+where he drops his suitcase I think or
+ 
+
+ align:start position:0%
+where he drops his suitcase I think or
+someone and he bends over to try to pick
+
+ align:start position:0%
+someone and he bends over to try to pick
+ 
+
+ align:start position:0%
+someone and he bends over to try to pick
+it up to give him an excuse to talk to
+
+ align:start position:0%
+it up to give him an excuse to talk to
+ 
+
+ align:start position:0%
+it up to give him an excuse to talk to
+the English prisoners who are going to
+
+ align:start position:0%
+the English prisoners who are going to
+ 
+
+ align:start position:0%
+the English prisoners who are going to
+change places with them he wants to tell
+
+ align:start position:0%
+change places with them he wants to tell
+ 
+
+ align:start position:0%
+change places with them he wants to tell
+the English prisoners there's a tunnel
+
+ align:start position:0%
+the English prisoners there's a tunnel
+ 
+
+ align:start position:0%
+the English prisoners there's a tunnel
+you can escape right uh but it turns out
+
+ align:start position:0%
+you can escape right uh but it turns out
+ 
+
+ align:start position:0%
+you can escape right uh but it turns out
+he's not able to give him the message
+
+ align:start position:0%
+he's not able to give him the message
+ 
+
+ align:start position:0%
+he's not able to give him the message
+because the English don't understand
+
+ align:start position:0%
+because the English don't understand
+ 
+
+ align:start position:0%
+because the English don't understand
+French and he can't speak English so so
+
+ align:start position:0%
+French and he can't speak English so so
+ 
+
+ align:start position:0%
+French and he can't speak English so so
+they the English prisoners end up going
+
+ align:start position:0%
+they the English prisoners end up going
+ 
+
+ align:start position:0%
+they the English prisoners end up going
+into them but without ever knowing that
+
+ align:start position:0%
+into them but without ever knowing that
+ 
+
+ align:start position:0%
+into them but without ever knowing that
+there's a tunnel waiting for them that
+
+ align:start position:0%
+there's a tunnel waiting for them that
+ 
+
+ align:start position:0%
+there's a tunnel waiting for them that
+it's almost ready ready to be completed
+
+ align:start position:0%
+it's almost ready ready to be completed
+ 
+
+ align:start position:0%
+it's almost ready ready to be completed
+an example of the barrier that language
+
+ align:start position:0%
+an example of the barrier that language
+ 
+
+ align:start position:0%
+an example of the barrier that language
+uh the the way language separates people
+
+ align:start position:0%
+uh the the way language separates people
+ 
+
+ align:start position:0%
+uh the the way language separates people
+and in many in many ways can be said to
+
+ align:start position:0%
+and in many in many ways can be said to
+ 
+
+ align:start position:0%
+and in many in many ways can be said to
+be frustrating uh one more example at
+
+ align:start position:0%
+be frustrating uh one more example at
+ 
+
+ align:start position:0%
+be frustrating uh one more example at
+the very end of the film there's a
+
+ align:start position:0%
+the very end of the film there's a
+ 
+
+ align:start position:0%
+the very end of the film there's a
+moment when the two the two characters
+
+ align:start position:0%
+moment when the two the two characters
+ 
+
+ align:start position:0%
+moment when the two the two characters
+marishal and rosenal are making their
+
+ align:start position:0%
+marishal and rosenal are making their
+ 
+
+ align:start position:0%
+marishal and rosenal are making their
+escape across a great field a Great
+
+ align:start position:0%
+escape across a great field a Great
+ 
+
+ align:start position:0%
+escape across a great field a Great
+White Field of snow uh and they're
+
+ align:start position:0%
+White Field of snow uh and they're
+ 
+
+ align:start position:0%
+White Field of snow uh and they're
+running across the field and so and the
+
+ align:start position:0%
+running across the field and so and the
+ 
+
+ align:start position:0%
+running across the field and so and the
+camera backs up and we see them being
+
+ align:start position:0%
+camera backs up and we see them being
+ 
+
+ align:start position:0%
+camera backs up and we see them being
+watched by German soldiers one of the
+
+ align:start position:0%
+watched by German soldiers one of the
+ 
+
+ align:start position:0%
+watched by German soldiers one of the
+soldiers picks up his rifle he says
+
+ align:start position:0%
+soldiers picks up his rifle he says
+ 
+
+ align:start position:0%
+soldiers picks up his rifle he says
+they're making an escape and he starts
+
+ align:start position:0%
+they're making an escape and he starts
+ 
+
+ align:start position:0%
+they're making an escape and he starts
+to aim at him then all of a sudden he
+
+ align:start position:0%
+to aim at him then all of a sudden he
+ 
+
+ align:start position:0%
+to aim at him then all of a sudden he
+stops I think I can't remember the ex
+
+ align:start position:0%
+stops I think I can't remember the ex
+ 
+
+ align:start position:0%
+stops I think I can't remember the ex
+watch for this how it happens I think
+
+ align:start position:0%
+watch for this how it happens I think
+ 
+
+ align:start position:0%
+watch for this how it happens I think
+his partner says wait a minute hold off
+
+ align:start position:0%
+his partner says wait a minute hold off
+ 
+
+ align:start position:0%
+his partner says wait a minute hold off
+why doesn't he shoot and then we see
+
+ align:start position:0%
+why doesn't he shoot and then we see
+ 
+
+ align:start position:0%
+why doesn't he shoot and then we see
+marelle and rosental could disappear or
+
+ align:start position:0%
+marelle and rosental could disappear or
+ 
+
+ align:start position:0%
+marelle and rosental could disappear or
+cross the cross an invisible boundary
+
+ align:start position:0%
+cross the cross an invisible boundary
+ 
+
+ align:start position:0%
+cross the cross an invisible boundary
+and the and the Germans says well
+
+ align:start position:0%
+and the and the Germans says well
+ 
+
+ align:start position:0%
+and the and the Germans says well
+they've crossed the border they're no
+
+ align:start position:0%
+they've crossed the border they're no
+ 
+
+ align:start position:0%
+they've crossed the border they're no
+longer in Germany I can't shoot them
+
+ align:start position:0%
+longer in Germany I can't shoot them
+ 
+
+ align:start position:0%
+longer in Germany I can't shoot them
+they're in they're now in Belgium but
+
+ align:start position:0%
+they're in they're now in Belgium but
+ 
+
+ align:start position:0%
+they're in they're now in Belgium but
+the fact is there's no boundary there
+
+ align:start position:0%
+the fact is there's no boundary there
+ 
+
+ align:start position:0%
+the fact is there's no boundary there
+it's all snow it's a snowy field right
+
+ align:start position:0%
+it's all snow it's a snowy field right
+ 
+
+ align:start position:0%
+it's all snow it's a snowy field right
+how arbitrary that boundary is well
+
+ align:start position:0%
+how arbitrary that boundary is well
+ 
+
+ align:start position:0%
+how arbitrary that boundary is well
+again and again in the film we have this
+
+ align:start position:0%
+again and again in the film we have this
+ 
+
+ align:start position:0%
+again and again in the film we have this
+theme of barriers and boundaries what
+
+ align:start position:0%
+theme of barriers and boundaries what
+ 
+
+ align:start position:0%
+theme of barriers and boundaries what
+separates us uh and also one last thing
+
+ align:start position:0%
+separates us uh and also one last thing
+ 
+
+ align:start position:0%
+separates us uh and also one last thing
+about the question of social class maybe
+
+ align:start position:0%
+about the question of social class maybe
+ 
+
+ align:start position:0%
+about the question of social class maybe
+the most disturbing and Powerful Insight
+
+ align:start position:0%
+the most disturbing and Powerful Insight
+ 
+
+ align:start position:0%
+the most disturbing and Powerful Insight
+that the film has about social class one
+
+ align:start position:0%
+that the film has about social class one
+ 
+
+ align:start position:0%
+that the film has about social class one
+that Americans tend to resist but I
+
+ align:start position:0%
+that Americans tend to resist but I
+ 
+
+ align:start position:0%
+that Americans tend to resist but I
+encourage you not to resist it those of
+
+ align:start position:0%
+encourage you not to resist it those of
+ 
+
+ align:start position:0%
+encourage you not to resist it those of
+you not from the United States will
+
+ align:start position:0%
+you not from the United States will
+ 
+
+ align:start position:0%
+you not from the United States will
+perhaps understand this more easily
+
+ align:start position:0%
+perhaps understand this more easily
+ 
+
+ align:start position:0%
+perhaps understand this more easily
+although Americans need to understand it
+
+ align:start position:0%
+although Americans need to understand it
+ 
+
+ align:start position:0%
+although Americans need to understand it
+is the extent to which one social class
+
+ align:start position:0%
+is the extent to which one social class
+ 
+
+ align:start position:0%
+is the extent to which one social class
+shapes one's identity that is to say one
+
+ align:start position:0%
+shapes one's identity that is to say one
+ 
+
+ align:start position:0%
+shapes one's identity that is to say one
+of the things we feel in this film is
+
+ align:start position:0%
+of the things we feel in this film is
+ 
+
+ align:start position:0%
+of the things we feel in this film is
+that well Jew's nature is a function of
+
+ align:start position:0%
+that well Jew's nature is a function of
+ 
+
+ align:start position:0%
+that well Jew's nature is a function of
+his having been raised as an aristocrat
+
+ align:start position:0%
+his having been raised as an aristocrat
+ 
+
+ align:start position:0%
+his having been raised as an aristocrat
+there are wonderful scenes between du
+
+ align:start position:0%
+there are wonderful scenes between du
+ 
+
+ align:start position:0%
+there are wonderful scenes between du
+and marel where marel says to him
+
+ align:start position:0%
+and marel where marel says to him
+ 
+
+ align:start position:0%
+and marel where marel says to him
+there's a wall between us uh and uh
+
+ align:start position:0%
+there's a wall between us uh and uh
+ 
+
+ align:start position:0%
+there's a wall between us uh and uh
+you're so undemonstrative and you
+
+ align:start position:0%
+you're so undemonstrative and you
+ 
+
+ align:start position:0%
+you're so undemonstrative and you
+marelle doesn't trust him because he
+
+ align:start position:0%
+marelle doesn't trust him because he
+ 
+
+ align:start position:0%
+marelle doesn't trust him because he
+because he belongs to belongs to a
+
+ align:start position:0%
+because he belongs to belongs to a
+ 
+
+ align:start position:0%
+because he belongs to belongs to a
+different class even though of course
+
+ align:start position:0%
+different class even though of course
+ 
+
+ align:start position:0%
+different class even though of course
+they're Frenchmen after all and in the
+
+ align:start position:0%
+they're Frenchmen after all and in the
+ 
+
+ align:start position:0%
+they're Frenchmen after all and in the
+end nationality Trump's class in this in
+
+ align:start position:0%
+end nationality Trump's class in this in
+ 
+
+ align:start position:0%
+end nationality Trump's class in this in
+this film uh as you'll as you'll see uh
+
+ align:start position:0%
+this film uh as you'll as you'll see uh
+ 
+
+ align:start position:0%
+this film uh as you'll as you'll see uh
+but in this kind in this in this sort of
+
+ align:start position:0%
+but in this kind in this in this sort of
+ 
+
+ align:start position:0%
+but in this kind in this in this sort of
+uh distinction or difference between
+
+ align:start position:0%
+uh distinction or difference between
+ 
+
+ align:start position:0%
+uh distinction or difference between
+marelle and duio we have another
+
+ align:start position:0%
+marelle and duio we have another
+ 
+
+ align:start position:0%
+marelle and duio we have another
+expression of this of this sense of of
+
+ align:start position:0%
+expression of this of this sense of of
+ 
+
+ align:start position:0%
+expression of this of this sense of of
+of this idea or this recognition that
+
+ align:start position:0%
+of this idea or this recognition that
+ 
+
+ align:start position:0%
+of this idea or this recognition that
+one's personality
+
+ align:start position:0%
+one's personality
+ 
+
+ align:start position:0%
+one's personality
+itself what one likes and dislikes one's
+
+ align:start position:0%
+itself what one likes and dislikes one's
+ 
+
+ align:start position:0%
+itself what one likes and dislikes one's
+fundamental nature is in part shaped by
+
+ align:start position:0%
+fundamental nature is in part shaped by
+ 
+
+ align:start position:0%
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+one deep Grand but horrible illusion is
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+
+ align:start position:0%
+the film I haven't mentioned yet and
+ 
+
+ align:start position:0%
+the film I haven't mentioned yet and
+it's it's maybe the most memorable
+
+ align:start position:0%
+it's it's maybe the most memorable
+ 
+
+ align:start position:0%
+it's it's maybe the most memorable
+interlude in the film is after marishal
+
+ align:start position:0%
+interlude in the film is after marishal
+ 
+
+ align:start position:0%
+interlude in the film is after marishal
+and Rosenthal make their escape from one
+
+ align:start position:0%
+and Rosenthal make their escape from one
+ 
+
+ align:start position:0%
+and Rosenthal make their escape from one
+of the prison camps they're on the Run
+
+ align:start position:0%
+of the prison camps they're on the Run
+ 
+
+ align:start position:0%
+of the prison camps they're on the Run
+they can't be they they but they're in
+
+ align:start position:0%
+they can't be they they but they're in
+ 
+
+ align:start position:0%
+they can't be they they but they're in
+Germany and they're it's the middle of
+
+ align:start position:0%
+Germany and they're it's the middle of
+ 
+
+ align:start position:0%
+Germany and they're it's the middle of
+winter and they managed to find uh uh uh
+
+ align:start position:0%
+winter and they managed to find uh uh uh
+ 
+
+ align:start position:0%
+winter and they managed to find uh uh uh
+safety in the home of a of of a German
+
+ align:start position:0%
+safety in the home of a of of a German
+ 
+
+ align:start position:0%
+safety in the home of a of of a German
+woman who is whose husband is away at
+
+ align:start position:0%
+woman who is whose husband is away at
+ 
+
+ align:start position:0%
+woman who is whose husband is away at
+the war uh perhaps dead and uh she she
+
+ align:start position:0%
+the war uh perhaps dead and uh she she
+ 
+
+ align:start position:0%
+the war uh perhaps dead and uh she she
+is there trying to manage a farm with
+
+ align:start position:0%
+is there trying to manage a farm with
+ 
+
+ align:start position:0%
+is there trying to manage a farm with
+her young daughter Elsie and Elsa and
+
+ align:start position:0%
+her young daughter Elsie and Elsa and
+ 
+
+ align:start position:0%
+her young daughter Elsie and Elsa and
+and marishal and rosenal spend the
+
+ align:start position:0%
+and marishal and rosenal spend the
+ 
+
+ align:start position:0%
+and marishal and rosenal spend the
+winter with them and and they get and
+
+ align:start position:0%
+winter with them and and they get and
+ 
+
+ align:start position:0%
+winter with them and and they get and
+it's it's an idol in the winter so think
+
+ align:start position:0%
+it's it's an idol in the winter so think
+ 
+
+ align:start position:0%
+it's it's an idol in the winter so think
+about what and F is very moving and
+
+ align:start position:0%
+about what and F is very moving and
+ 
+
+ align:start position:0%
+about what and F is very moving and
+again the barriers of language are
+
+ align:start position:0%
+again the barriers of language are
+ 
+
+ align:start position:0%
+again the barriers of language are
+present there at the very end of the of
+
+ align:start position:0%
+present there at the very end of the of
+ 
+
+ align:start position:0%
+present there at the very end of the of
+their Idol in the woods we have marishal
+
+ align:start position:0%
+their Idol in the woods we have marishal
+ 
+
+ align:start position:0%
+their Idol in the woods we have marishal
+say to to the child I think her name is
+
+ align:start position:0%
+say to to the child I think her name is
+ 
+
+ align:start position:0%
+say to to the child I think her name is
+I I called her Elsa I think it's LTI um
+
+ align:start position:0%
+I I called her Elsa I think it's LTI um
+ 
+
+ align:start position:0%
+I I called her Elsa I think it's LTI um
+he says he looks at the girl he says
+
+ align:start position:0%
+he says he looks at the girl he says
+ 
+
+ align:start position:0%
+he says he looks at the girl he says
+says he he tried in bad German he says
+
+ align:start position:0%
+says he he tried in bad German he says
+ 
+
+ align:start position:0%
+says he he tried in bad German he says
+LTI has blow he says blue eyes but he's
+
+ align:start position:0%
+LTI has blow he says blue eyes but he's
+ 
+
+ align:start position:0%
+LTI has blow he says blue eyes but he's
+very proud of himself for having been
+
+ align:start position:0%
+very proud of himself for having been
+ 
+
+ align:start position:0%
+very proud of himself for having been
+able to articulate two German words but
+
+ align:start position:0%
+able to articulate two German words but
+ 
+
+ align:start position:0%
+able to articulate two German words but
+the fact that he's done that is a mark
+
+ align:start position:0%
+the fact that he's done that is a mark
+ 
+
+ align:start position:0%
+the fact that he's done that is a mark
+of his having you reached out and and
+
+ align:start position:0%
+of his having you reached out and and
+ 
+
+ align:start position:0%
+of his having you reached out and and
+the implication more than an implication
+
+ align:start position:0%
+the implication more than an implication
+ 
+
+ align:start position:0%
+the implication more than an implication
+is he becomes the woman's lover uh uh uh
+
+ align:start position:0%
+is he becomes the woman's lover uh uh uh
+ 
+
+ align:start position:0%
+is he becomes the woman's lover uh uh uh
+uh while they're while they spend the
+
+ align:start position:0%
+uh while they're while they spend the
+ 
+
+ align:start position:0%
+uh while they're while they spend the
+winter in this and and the German woman
+
+ align:start position:0%
+winter in this and and the German woman
+ 
+
+ align:start position:0%
+winter in this and and the German woman
+uh at a certain point when they first
+
+ align:start position:0%
+uh at a certain point when they first
+ 
+
+ align:start position:0%
+uh at a certain point when they first
+take refuge in her place the door a
+
+ align:start position:0%
+take refuge in her place the door a
+ 
+
+ align:start position:0%
+take refuge in her place the door a
+German Soldier searching for these guys
+
+ align:start position:0%
+German Soldier searching for these guys
+ 
+
+ align:start position:0%
+German Soldier searching for these guys
+comes to the comes to the door comes to
+
+ align:start position:0%
+comes to the comes to the door comes to
+ 
+
+ align:start position:0%
+comes to the comes to the door comes to
+the window and speaks to the Widow and
+
+ align:start position:0%
+the window and speaks to the Widow and
+ 
+
+ align:start position:0%
+the window and speaks to the Widow and
+the Widow protects them right so so a
+
+ align:start position:0%
+the Widow protects them right so so a
+ 
+
+ align:start position:0%
+the Widow protects them right so so a
+second Grand Illusion may very well be
+
+ align:start position:0%
+second Grand Illusion may very well be
+ 
+
+ align:start position:0%
+second Grand Illusion may very well be
+look this is a very lovely story but how
+
+ align:start position:0%
+look this is a very lovely story but how
+ 
+
+ align:start position:0%
+look this is a very lovely story but how
+believable is it Germans French soldiers
+
+ align:start position:0%
+believable is it Germans French soldiers
+ 
+
+ align:start position:0%
+believable is it Germans French soldiers
+on the run from a prison camp find find
+
+ align:start position:0%
+on the run from a prison camp find find
+ 
+
+ align:start position:0%
+on the run from a prison camp find find
+a a farmhouse in which a German Widow
+
+ align:start position:0%
+a a farmhouse in which a German Widow
+ 
+
+ align:start position:0%
+a a farmhouse in which a German Widow
+takes them in and protects them from the
+
+ align:start position:0%
+takes them in and protects them from the
+ 
+
+ align:start position:0%
+takes them in and protects them from the
+German soldiers that would be it's a
+
+ align:start position:0%
+German soldiers that would be it's a
+ 
+
+ align:start position:0%
+German soldiers that would be it's a
+nice story but is it a grand ill if it
+
+ align:start position:0%
+nice story but is it a grand ill if it
+ 
+
+ align:start position:0%
+nice story but is it a grand ill if it
+is an illusion maybe it's a grand one a
+
+ align:start position:0%
+is an illusion maybe it's a grand one a
+ 
+
+ align:start position:0%
+is an illusion maybe it's a grand one a
+wonderful one not just a large one but a
+
+ align:start position:0%
+wonderful one not just a large one but a
+ 
+
+ align:start position:0%
+wonderful one not just a large one but a
+valuable one right so that's a second
+
+ align:start position:0%
+valuable one right so that's a second
+ 
+
+ align:start position:0%
+valuable one right so that's a second
+way in which the the uh title resonates
+
+ align:start position:0%
+way in which the the uh title resonates
+ 
+
+ align:start position:0%
+way in which the the uh title resonates
+for me um um uh the third Grand Illusion
+
+ align:start position:0%
+for me um um uh the third Grand Illusion
+ 
+
+ align:start position:0%
+for me um um uh the third Grand Illusion
+has to do with the community of the
+
+ align:start position:0%
+has to do with the community of the
+ 
+
+ align:start position:0%
+has to do with the community of the
+Prisoners the solidarity and Community
+
+ align:start position:0%
+Prisoners the solidarity and Community
+ 
+
+ align:start position:0%
+Prisoners the solidarity and Community
+that's dramatized in the film in the end
+
+ align:start position:0%
+that's dramatized in the film in the end
+ 
+
+ align:start position:0%
+that's dramatized in the film in the end
+the duj character sacrifices himself for
+
+ align:start position:0%
+the duj character sacrifices himself for
+ 
+
+ align:start position:0%
+the duj character sacrifices himself for
+the good of the others something that we
+
+ align:start position:0%
+the good of the others something that we
+ 
+
+ align:start position:0%
+the good of the others something that we
+might find surprising at first given his
+
+ align:start position:0%
+might find surprising at first given his
+ 
+
+ align:start position:0%
+might find surprising at first given his
+distance from the other characters um um
+
+ align:start position:0%
+distance from the other characters um um
+ 
+
+ align:start position:0%
+distance from the other characters um um
+and uh there is a sense all the way
+
+ align:start position:0%
+and uh there is a sense all the way
+ 
+
+ align:start position:0%
+and uh there is a sense all the way
+through the film that the that that a
+
+ align:start position:0%
+through the film that the that that a
+ 
+
+ align:start position:0%
+through the film that the that that a
+kind of Comm
+
+ align:start position:0%
+kind of Comm
+ 
+
+ align:start position:0%
+kind of Comm
+or solidarity has been established
+
+ align:start position:0%
+or solidarity has been established
+ 
+
+ align:start position:0%
+or solidarity has been established
+amongst the men especially amongst the
+
+ align:start position:0%
+amongst the men especially amongst the
+ 
+
+ align:start position:0%
+amongst the men especially amongst the
+Frenchmen uh and especially that a kind
+
+ align:start position:0%
+Frenchmen uh and especially that a kind
+ 
+
+ align:start position:0%
+Frenchmen uh and especially that a kind
+of friendship between uh between
+
+ align:start position:0%
+of friendship between uh between
+ 
+
+ align:start position:0%
+of friendship between uh between
+rosental and Marell has been forged well
+
+ align:start position:0%
+rosental and Marell has been forged well
+ 
+
+ align:start position:0%
+rosental and Marell has been forged well
+again maybe that's a Grand Illusion the
+
+ align:start position:0%
+again maybe that's a Grand Illusion the
+ 
+
+ align:start position:0%
+again maybe that's a Grand Illusion the
+idea that you can transcend social class
+
+ align:start position:0%
+idea that you can transcend social class
+ 
+
+ align:start position:0%
+idea that you can transcend social class
+that you can transcend the uh ethnic uh
+
+ align:start position:0%
+that you can transcend the uh ethnic uh
+ 
+
+ align:start position:0%
+that you can transcend the uh ethnic uh
+prejudices into which you are born and
+
+ align:start position:0%
+prejudices into which you are born and
+ 
+
+ align:start position:0%
+prejudices into which you are born and
+and to which you've been uh um
+
+ align:start position:0%
+and to which you've been uh um
+ 
+
+ align:start position:0%
+and to which you've been uh um
+U with which you've been brainwashed so
+
+ align:start position:0%
+U with which you've been brainwashed so
+ 
+
+ align:start position:0%
+U with which you've been brainwashed so
+that's another kind kind of potential
+
+ align:start position:0%
+that's another kind kind of potential
+ 
+
+ align:start position:0%
+that's another kind kind of potential
+Grand Illusion and then finally the
+
+ align:start position:0%
+Grand Illusion and then finally the
+ 
+
+ align:start position:0%
+Grand Illusion and then finally the
+fourth example I would give the F the
+
+ align:start position:0%
+fourth example I would give the F the
+ 
+
+ align:start position:0%
+fourth example I would give the F the
+fourth Nuance that one could add to the
+
+ align:start position:0%
+fourth Nuance that one could add to the
+ 
+
+ align:start position:0%
+fourth Nuance that one could add to the
+title The Grand Illusion of movies
+
+ align:start position:0%
+title The Grand Illusion of movies
+ 
+
+ align:start position:0%
+title The Grand Illusion of movies
+themselves what are movies but Grand
+
+ align:start position:0%
+themselves what are movies but Grand
+ 
+
+ align:start position:0%
+themselves what are movies but Grand
+Illusions right they're
+
+ align:start position:0%
+Illusions right they're
+ 
+
+ align:start position:0%
+Illusions right they're
+two-dimensional not threedimensional but
+
+ align:start position:0%
+two-dimensional not threedimensional but
+ 
+
+ align:start position:0%
+two-dimensional not threedimensional but
+when we watch them we feel we've entered
+
+ align:start position:0%
+when we watch them we feel we've entered
+ 
+
+ align:start position:0%
+when we watch them we feel we've entered
+into a real world the Grand Illusion of
+
+ align:start position:0%
+into a real world the Grand Illusion of
+ 
+
+ align:start position:0%
+into a real world the Grand Illusion of
+movies themselves is part of what the
+
+ align:start position:0%
+movies themselves is part of what the
+ 
+
+ align:start position:0%
+movies themselves is part of what the
+title alludes to well something of the
+
+ align:start position:0%
+title alludes to well something of the
+ 
+
+ align:start position:0%
+title alludes to well something of the
+complexity and maturity of Renard vision
+
+ align:start position:0%
+complexity and maturity of Renard vision
+ 
+
+ align:start position:0%
+complexity and maturity of Renard vision
+of experience sense of human character
+
+ align:start position:0%
+of experience sense of human character
+ 
+
+ align:start position:0%
+of experience sense of human character
+and sense of history is embodied then in
+
+ align:start position:0%
+and sense of history is embodied then in
+ 
+
+ align:start position:0%
+and sense of history is embodied then in
+the complexity of the title of his
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+movie
\ No newline at end of file
diff --git a/eRCN3daFCmU.txt b/eRCN3daFCmU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5df605a054ed5374553f73fbf5a646db925ef447
--- /dev/null
+++ b/eRCN3daFCmU.txt
@@ -0,0 +1,2369 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROF.
+
+JERISON: So, we're ready to
+begin Lecture 10, and what I'm
+
+going to begin with is
+by finishing up some
+
+things from last time.
+
+We'll talk about approximations,
+and I want to
+
+fill in a number of comments and
+get you a little bit more
+
+oriented in the point of view
+that I'm trying to express
+
+about approximations.
+
+So, first of all, I want to
+remind you of the actual
+
+applied example that I
+wrote down last time.
+
+So that was this
+business here.
+
+There was something from
+special relativity.
+
+And the approximation that
+we used was the linear
+
+approximation, with a - 1/2
+power that comes out to be t(
+
+1 1/2 v^2 / C^2).
+
+I want to reiterate why
+this is a useful way
+
+of thinking of things.
+
+And why this is that this
+comes up in real life.
+
+Why this is maybe more important
+than everything that
+
+I've taught you about
+technically so far.
+
+So, first of all, what this is
+telling us is the change in t
+
+/ t, if you do the arithmetic
+here and subtract t that's
+
+using the change in
+t is t' - t here.
+
+If you work that out, this is
+approximately the same as 1/2
+
+(v^2 / C^2).
+
+So what is this saying?
+
+This is saying that if you have
+this satellite, which is
+
+going at speed v, and little c
+is the speed of light, then
+
+the change in the watch down
+here on earth, relative to the
+
+time on the satellite, is going
+to be proportional to
+
+this ratio here.
+
+So, physically, this
+makes sense.
+
+This is time divided by time.
+
+And this is velocity squared
+divided by velocity squared.
+
+So, in each case, the
+units divide out.
+
+So this is a dimensionless
+quantity.
+
+And this is a dimensionless
+quantity.
+
+And the only point here that
+we're trying to make is just
+
+this notion of proportionality.
+
+So I want to write this down.
+
+Just, in summary.
+
+So the error fraction, if you
+like, which is sort of the
+
+number of significant digits
+that we have in our
+
+measurement, is proportional,
+in this
+
+case, to this quantity.
+
+It happens to be proportional
+to this quantity here.
+
+And the factor is, happens
+to be, 1/2.
+
+So these proportionality
+factors are what
+
+we're looking for.
+
+Their rates of change.
+
+Their rates of change of
+something with respect to
+
+something else.
+
+Now, on your homework,
+you have something
+
+rather similar to this.
+
+So in Problem, on Part 2b, Part
+II, Problem 1, there's
+
+the speed of a pitch, right?
+
+And the speed of the pitch is
+changing depending on how high
+
+the mound is.
+
+And the point here is that
+that's approximately
+
+proportional to the change in
+the height of the mound.
+
+In that problem, we had this
+delta h, that was the x
+
+variable in that problem.
+
+And what you're trying to
+figure out is what the
+
+constant of proportionality
+is.
+
+That's what you're aiming
+for in this problem.
+
+So there's a linear
+relationship, approximately,
+
+to all intents and purposes
+this is an equality.
+
+Because the lower
+order terms are
+
+unimportant for the problem.
+
+Just as over here, this function
+is a little bit
+
+complicated.
+
+This function is a little
+more simple.
+
+For the purposes of this
+problem, they are the same.
+
+Because the errors are
+negligible for the particular
+
+problem that we're working on.
+
+So we might as well work with
+the simpler relationship.
+
+And similarly, over here, so
+you could do this with, in
+
+this case with square roots,
+it's not so hard here with
+
+reciprocals of square roots.
+
+It's also not terribly hard
+to do it numerically.
+
+And the reason why we're not
+doing it numerically is that,
+
+as I say, this is something
+that happens all across
+
+engineering.
+
+People are looking for these
+linear relationships between
+
+the change in some input and
+the change in the output.
+
+And if you don't make these
+simplifications, then when you
+
+get, say, a dozen of them
+together, you can't figure out
+
+what's going on.
+
+In this case the design of the
+
+satellite, it's very important.
+
+The speed actually isn't
+just one speed.
+
+Because it's the relative speed
+of u to the satellite.
+
+And you might be, it depends
+on your angle of sight with
+
+the satellite what
+the speed is.
+
+So it varies quite a bit.
+
+So you really need this
+rule of thumb.
+
+Then there are all
+kinds of other
+
+considerations in this question.
+
+Like, for example, there's the
+fact that we're sitting on
+
+Earth and so we're rotating
+around on what's called a
+
+non-inertial frame.
+
+So there's the question
+of that acceleration.
+
+There's the question that the
+gravity that I experience here
+
+on Earth is not the same
+as up at the satellite.
+
+And that also creates a
+difference in time, as a
+
+result of general relativity.
+
+So all of these considerations
+come down to formulas which
+
+are this complicated or
+maybe a tiny bit more.
+
+Not really that much.
+
+And then people simplify them
+enormously to these very
+
+simple-minded rules.
+
+And they don't keep track
+of what's going on.
+
+So in order to design the
+system, you must make these
+
+simplifications, otherwise you
+can't even think about
+
+what's going on.
+
+This comes up in everything.
+
+In weather forecasting,
+economic forecasting.
+
+Figuring out whether there's
+going to be an asteroid that's
+
+going to hit the Earth.
+
+Every single one of these things
+involves dozens of
+
+these considerations.
+
+OK, there was a question
+that I saw, here.
+
+Yes.
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: Yeah.
+
+Basically, any problem where
+you have a derivative, the
+
+rate of change also depends upon
+what the base point is.
+
+That's the question.
+
+You're saying, doesn't this
+delta v also depend, I had a
+
+base point in that problem.
+
+I happened to decide that
+pitchers pitch on average
+
+about 90 miles an hour.
+
+Whereas, in fact, some pitchers
+pitch at 100 miles an
+
+hour, some pitch at 80 miles
+an hour, and of course they
+
+vary the speed of the pitch.
+
+And so, this varies
+a little bit.
+
+In fact, that's sort of
+a second order effect.
+
+It does change the constant
+of proportionality.
+
+It's a rate of change at
+a different base point.
+
+Which we're considering fixed.
+
+In fact, that's sort of
+a second order effect.
+
+When you actually do the
+computations, what you
+
+discover is that it doesn't
+make that much difference.
+
+To the a.
+
+And that's something that
+you get from experience.
+
+That it turns out, which
+things matter and
+
+which things don't.
+
+And yet again, that's exactly
+the same sort of consideration
+
+but at the next order of what
+I'm talking about here is.
+
+You have to have enough
+experience with numbers to
+
+know that if you take, if you
+vary something a little bit
+
+it's not going to change
+the answer that you're
+
+looking for very much.
+
+And that's exactly the point
+that I'm making.
+
+So I can't make them all at
+once, all such points.
+
+So that's my pitch for
+understanding things from this
+
+point of view.
+
+Now, we're going to go
+on, now, to quadratic
+
+approximations, which are a
+little more complicated.
+
+So, we talked a little bit about
+this last time but I
+
+didn't finish.
+
+So I want to finish this up.
+
+And the first thing that I
+should say is that you use the
+
+when the linear approximation
+is not enough.
+
+OK, so, that's something that
+you really need to get a
+
+little experience with.
+
+In economics, I told you they
+use logarithms. So sometimes
+
+they use log linear functions.
+
+Sometimes they use log quadratic
+functions when the
+
+log linear ones don't work.
+
+So most modeling in
+economics is with
+
+log quadratic functions.
+
+And if you've made it
+any more complicated
+
+than that, it's useless.
+
+And it's a mess.
+
+And people don't do it.
+
+So they stick with the quadratic
+ones, typically.
+
+So the basic formula here, and
+I'm going to take the base
+
+point to be 0, is that f (
+x ) is approximately f
+
+( 0 ) f' ( 0 )x.
+
+That's the linear part.
+
+Plus this extra term.
+
+Which is f'' ( 0 ) / 2x^2.
+
+And this is supposed to
+work for x near 0.
+
+So it shows in the base point
+as simply as possible.
+
+So here's more or less where
+we left off last time.
+
+And one thing that I said I was
+going to explain, which I
+
+will now, is why it's
+(1/2) f'' ( 0 ).
+
+So we need to know that.
+
+So let's work that out
+here first of all.
+
+So I'm just going to
+do it by example.
+
+So if you like, the answer is
+just, well, what happens when
+
+you have a parabola?
+
+A parabola's a quadratic.
+
+It had better, its quadratic
+approximation
+
+had better be itself.
+
+It's got to be the best one.
+
+So it's got to be itself.
+
+So this formula, if it's
+going to work, has
+
+to work on the nose.
+
+For quadratic functions.
+
+So, let's take a look.
+
+If I differentiate,
+I get b 2cx.
+
+If I differentiate a second
+time, I get 2c.
+
+And now let's plug it in.
+
+Well, we can recover, what is
+it that we want to recover?
+
+We want to recover these numbers
+a, b and c using the
+
+derivatives evaluated at 0.
+
+So let's see.
+
+It's pretty easy, actually.
+f ( 0 ) = a.
+
+That's on the nose.
+
+If you plug in x = 0 here,
+these terms drop
+
+out and you get a.
+
+And now, f' ( 0 ), whoops
+that was wrong.
+
+So I wrote f' but what
+I meant was f.
+
+So f ( 0 ) is a.
+
+Let's back up. f ( 0 ) is a, so
+if I plug in x = 0 I get a.
+
+Now, f' ( 0 ), that's this next
+formula here, f' ( 0 ), I
+
+plug in 0 here, and I get b.
+
+That's also good.
+
+And that's exactly what the
+linear approximation is
+
+supposed to be.
+
+But now you notice, f'' is 2c.
+
+So to recover c, I better
+take half of it.
+
+And that's it.
+
+That's the reason.
+
+There's no chance that any
+other formula could work.
+
+And this one does.
+
+So that's the explanation
+for the formula.
+
+And now I remind you that I
+had a collection of basic
+
+formulas written on the board.
+
+And I want to just make sure
+we know all of them again.
+
+So, first of all, there was
+sine x is approximately x.
+
+Cosine x is approximately
+1 - 1/2 x^2.
+
+And e ^ x is approximately
+1 x 1/2 x^2.
+
+So those were three that
+I mentioned last time.
+
+And, again, this is
+all for x near 0.
+
+All for x near 0 only.
+
+These are wildly wrong, Far
+away, but near 0 they're nice,
+
+good, quadratic approximations.
+
+Now, the other two
+approximations that I want to
+
+mention are the logarithm and we
+use the base point shifted.
+
+So we can put it at x near 0.
+
+And this one - sorry,
+this is an
+
+approximately equals sign there.
+
+Turns out to be x - 1/2 x^2.
+
+And the last one is one (1 x)
+^ r, which turns out to be 1
+
+rx r ( r - 1) / 2x^2.
+
+Now, eventually, your mind will
+converge on all of these
+
+and you'll find them relatively
+easy to memorize.
+
+But it'll take some
+getting used to.
+
+And I'm not claiming that you
+should recognize them and
+
+understand them all now.
+
+But I'm going to put a giant
+box around this.
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: Yes.
+
+So the question was, you get all
+of these if you use that
+
+equation there.
+
+That's exactly what are you
+going to do. so I already did
+
+it actually for these
+three, last time.
+
+But I didn't do it yet
+for these two.
+
+But I will do it in
+about two minutes.
+
+Well, maybe five minutes.
+
+But first I want to explain just
+a few things about these.
+
+They all follow from
+the basic formula.
+
+In fact, that one deserves a
+pink box too, doesn't it.
+
+That one's pretty important.
+
+Alright.
+
+Yeah.
+
+Maybe even some little
+sparkles.
+
+Alright.
+
+OK.
+
+So that's pretty important.
+
+Almost as important as
+the more basic one
+
+without this term here.
+
+So now, let me just tell you
+a little bit more about the
+
+significance.
+
+Again, this is just to reinforce
+something that we've
+
+already done.
+
+But it's closely related to
+what you're doing on your
+
+problem set.
+
+So it's worth your while
+to recall this.
+
+So, there's this expression
+that we were dealing with.
+
+And we talked about
+it in lecture.
+
+And we showed that this tends
+to e as k goes to infinity.
+
+So that's what we showed
+in lecture.
+
+And the way that we did that
+was, we took the logarithm and
+
+we wrote it as k times, sorry,
+the ln of 1 (1 / k).
+
+And then we evaluated
+the limit of this.
+
+And I want to do this limit
+again, using linear
+
+approximation.
+
+To show you how easy it is.
+
+If you just remember the
+linear approximation.
+
+And then we'll explain
+where the quadratic
+
+approximation comes in.
+
+So I claim that this
+is approximately
+
+equal to k ( 1 / k).
+
+Now, why is that?
+
+Well, that's just this
+linear approximation.
+
+So what did I use here?
+
+I used ln of 1 x is
+approximately x.
+
+For x = 1 / k.
+
+That's what I used in this
+approximation here.
+
+And that's the linear
+approximation
+
+to the natural logarithm.
+
+And this number is relatively
+easy to evaluate.
+
+I know how to do it.
+
+It's equal to 1.
+
+That's the same, well, so
+where does this work?
+
+This works where this
+thing is near 0.
+
+Which is when k is going
+to infinity.
+
+This thing is working only when
+k is going to infinity.
+
+So what it's really saying, this
+approximation formula,
+
+it's really saying that as we
+go to infinity, in k, this
+
+thing is going to 1.
+
+As k goes to infinity.
+
+So that's what it's saying.
+
+That's the substance there.
+
+And that's how we want to use
+it, in many instances.
+
+Just to evaluate limits.
+
+We also want to realize that
+it's nearby when k is pretty
+
+large, like 100 or something
+like that.
+
+Now, so that's the idea of
+the linear approximation.
+
+Now, if you want to get the rate
+of convergence here, so
+
+the rate of what's called
+convergence.
+
+So convergence means how fast
+this is going towards that.
+
+What I have to do is take
+the difference.
+
+I have to take ln ak, and I have
+to subtract 1 from it.
+
+And I know that this is going to
+0, and the question is how
+
+big is this.
+
+We want it to be very small.
+
+And the answer we're going to
+get, so the answer just uses
+
+the quadratic approximation.
+
+So if I just have a little bit
+more detail, then this
+
+expression here, in other words,
+I have the next higher
+
+order term.
+
+This is like 1 / k, this
+is like 1 / k^2.
+
+Then I can understand how big
+the difference is between the
+
+expression that I've
+got and its limit.
+
+And so that's what's
+on your homework.
+
+This is on your problem set.
+
+OK, so that is more or less an
+explanation for one of the
+
+things that quadratic
+approximations are good for.
+
+And I'm going to give you
+one more illustration.
+
+One more illustration.
+
+And then we'll actually
+check these formulas.
+
+Yeah, another question.
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: That's a very
+good question here.
+
+When they, which in this case
+means maybe, me, when I give
+
+you a question, does one specify
+whether you want to
+
+use a linear or a quadratic
+approximation.
+
+The answer is, in real life
+when you're faced with a
+
+problem like this, where some
+satellite is orbiting and you
+
+want to know the effects of
+gravity or something like
+
+that, nobody is going to
+tell you anything.
+
+They're not even going to tell
+you whether a linear
+
+approximation is relevant, or
+a quadratic or anything.
+
+So you're on your own.
+
+When I give you a question, at
+least for right now, I'm
+
+always going to tell you.
+
+But as time goes on I'd like you
+to get used to when it's
+
+enough to get away with a
+linear approximation.
+
+And you should only use a
+quadratic approximation if
+
+somebody forces you to.
+
+You should always start trying
+with a linear one.
+
+Because the quadratic ones are
+much more complicated as
+
+you'll see in this
+next example.
+
+OK, so the example that I want
+to use is, you're going to be
+
+stuck with it because I'm asking
+for the quadratic.
+
+So we're going to find the
+quadratic approximation near,
+
+for x near 0.
+
+To what?
+
+Well, this is the same function
+that we used in the
+
+last lecture.
+
+I think this was it. e
+^ - 3x (1 x) ^ - 1/2.
+
+OK.
+
+So, unfortunately, I stuck it in
+the wrong place to be able
+
+to fit this very long
+formula here.
+
+So I'm going to switch it.
+
+I'm just going to
+write it here.
+
+And we're going to just
+do the approximation.
+
+So we're going to say quadratic,
+in parentheses.
+
+And we'll say x near 0.
+
+So that's what I want.
+
+So now, here's what
+I have to do.
+
+Well, I have to write in the
+quadratic approximation for e
+
+^ - 3x, and I'm going to use
+this formula right here.
+
+And so that's (1 (-
+3x) (- 3x)^2 / 2).
+
+And the other factor, I'm going
+to have to use this
+
+formula down here. because
+r is - 1/2.
+
+And so that's (1 - 1/2 x 1/2
+( - 1/2)( - 3/2)x^2).
+
+So this is the r term, and
+this is the r - 1 term.
+
+And now I'm going to do
+something which is the only
+
+good thing about quadratic
+approximations.
+
+They're messy, they're long,
+there's nothing particularly
+
+good about them.
+
+But there is one good
+thing about them.
+
+Which is that you always get
+to ignore the higher order
+
+terms. So even though this
+looks like a very ugly
+
+multiplication, I can
+do it in my head.
+
+Just watching it.
+
+Because I get a 1 * 1, I'm
+forced with that term here.
+
+And then I get the cross terms
+which are linear, which is -
+
+3x - 1/2 x.
+
+We already did that when we
+calculated the linear
+
+approximation, so that's
+this times the 1 and
+
+this times that 1.
+
+And now I have three
+
+cross-terms which are quadratic.
+
+So one of them is these two
+linear terms are multiplying.
+
+So that's plus 3/2 x^2.
+
+That's (- 3)( - 1/2).
+
+And then there's this term,
+multiplying the 1,
+
+that's plus 9/2 x^2.
+
+And then there's one
+last term, which is
+
+this monster here.
+
+Multiplying 1, and
+that is - 3/8.
+
+So the great thing is, we drop
+x^3, x ^ 4, etc., terms. Yeah?
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: OK, well
+so copy it down.
+
+And you work it out as
+I'm doing it now.
+
+So what I did is, I
+multiplied 1 by 1.
+
+I'm using the distributive
+law here.
+
+That was this one.
+
+I multiplied this 3x by this
+one, that was that term.
+
+I multiplied this by this,
+that's that term.
+
+And then I multiplied
+this by this.
+
+In other words, 2 x terms
+that gave me an x^2
+
+and a (- 3)( - 1/2).
+
+And I'm going to stop
+at that point.
+
+Because the point is it's
+just all the rest of the
+
+terms that come up.
+
+Now, the reason, the only reason
+why it's easy is that I
+
+only have to go up to
+x squared term.
+
+I don't have to do
+the higher ones.
+
+Another question,
+way back here.
+
+Yeah, right there.
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: OK.
+
+So somebody can check
+my arithmetic, too.
+
+Good.
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: Why do I get to drop
+all the higher-order terms.
+
+So, that's because the situation
+where I'm going to
+
+apply this is the situation
+in which x is, say, 1/100.
+
+So if here's about 1/100.
+
+Here's something which is
+on the order of 100.
+
+This is on the order
+of 1/100^2.
+
+1/100^2, all of these terms.
+Now, these cubic and quartic
+
+terms are of the order
+of 1/100^3.
+
+That's 10 ^ - 6.
+
+And the point is that I'm
+not claiming that I
+
+have an exact answer.
+
+And I'm going to drop things
+of that order of magnitude.
+
+So I'm saving everything
+up to 4 decimal places.
+
+I'm throwing away things which
+are 6 decimal places out.
+
+Does that answer
+your question?
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: So.
+
+That's the situation, and now
+you can combine the terms. I
+
+mean, it's not very
+impressive here.
+
+This is equal to 1 - 7/2
+x, maybe 51/8 x^2.
+
+If I've made that, if those
+minus signs hadn't canceled, I
+
+would have gotten the
+wrong answer here.
+
+Anyway.
+
+So, this is a 2 here, sorry.
+
+7/2.
+
+This is the linear approximation
+we got last time
+
+and here's the extra information
+that we got from
+
+this calculation.
+
+Which is this 51/8 term.
+
+Right, you have to accept that
+there's a certain degree of
+
+complexity to this problem and
+the answer is sufficiently
+
+complicated so it can't be less
+arithmetic because we get
+
+this peculiar 51/8
+there, right.
+
+So one of the things to realize
+is that these kinds of
+
+problems, because they involve
+many, many terms are always
+
+going to involve a little bit
+of complicated arithmetic.
+
+Last little bit, I did promise
+you that I was going to derive
+
+these two relations,
+as I said.
+
+Did the ones in the
+left column.
+
+So let's carry that out.
+
+And as someone just pointed out,
+it all comes from this
+
+formula here.
+
+So let's just check it.
+
+So we'll start with
+the ln function.
+
+This is the function, f,
+and then f' is 1/1 x.
+
+And f'', so this is f', this
+is f'', is - 1/1 x^2.
+
+And now I have to
+plug in x = 0.
+
+So at x = 0 this is
+ln 1, which is 0.
+
+So this is at x = 0.
+
+I'm getting 0 here, I plug
+in 0 and I get 1.
+
+And here, I plug in
+0 and I get - 1.
+
+So now I go and I look up at
+that formula, which is way in
+
+that upper corner there.
+
+And I see that the coefficient
+on the constant is 0.
+
+The coefficient on x is 1.
+
+And then the other coefficient,
+the very last
+
+one, is - 1/2.
+
+So this is the - 1 here.
+
+And then in the formula,
+there's a 2 in the
+
+denominator.
+
+So it's half of whatever
+I get for this second
+
+derivative, at 0.
+
+So this is the approximation
+formula, which is way up in
+
+that corner there.
+
+Similarly, if I do it for
+(1 x) ^ r, I have to
+
+differentiate that I get r( 1
+x) ^ r - 1, and then r ( r -
+
+1( x 1) ^ r - 2.
+
+So here are the derivatives.
+
+And so if I evaluate them
+at x = 0, I get 1.
+
+That's 1 ^ r = 1.
+
+And here I get r.
+(1 ^ r - 1)r.
+
+And here, I plug in x = 0
+and I get r ( r - 1).
+
+So again, the pattern is
+right above it here.
+
+The 1 is there, the
+r is there.
+
+And then instead of r ( r
+- 1), I have half that.
+
+For the coefficient.
+
+So these are just examples.
+
+Obviously if we had a more
+complicated functional, we
+
+might carry this out.
+
+But as a practical matter, we
+try to stick with the ones in
+
+the pink box and just use
+algebra to get other formulas.
+
+So I want to shift gears now and
+treat the subject that was
+
+supposed to be this lecture.
+
+And we're not quite caught up,
+but we will try to do our best
+
+to do as much as we can today.
+
+So the next topic is
+curve sketching.
+
+And so let's get started
+with that.
+
+So now, happily in this subject,
+there are more
+
+pictures and it's a little
+bit more geometric.
+
+And there's relatively
+little computation.
+
+So let's hope we can do this.
+
+So I want to, so here
+we go, we'll
+
+start with curve sketching.
+
+And the goal here
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: So that's like,
+liner, the last time.
+
+That's kind of sketchy
+spelling, isn't it?
+
+Yeah, there are certain kinds of
+things which I can't spell.
+
+But, alright.
+
+Sketching.
+
+Alright.
+
+So here's our goal.
+
+Our goal is to draw the graph
+of f, using f' and f''.
+
+Whether they're positive
+or negative.
+
+So that's it.
+
+This is the goal here.
+
+However, there is a
+big warning that I
+
+want to give you.
+
+And this is one that
+unfortunately I now have to
+
+make you unlearn, especially
+those that you that have
+
+actually had a little bit of
+calculus before, I want to
+
+make you unlearn some of your
+instincts that you developed.
+
+So this will be harder for those
+of you who have actually
+
+done this before.
+
+But for the rest of you, it
+will be relatively easy.
+
+Which is, don't abandon your
+precalculus skills.
+
+And common sense.
+
+So there's a great deal of
+common sense in this.
+
+And it actually trumps
+some of the calculus.
+
+The calculus just fills
+in what you
+
+didn't quite know yet.
+
+So I will try to illustrate
+this.
+
+And because we're running a bit
+late, I won't get to the
+
+some of the main punchlines
+until next lecture.
+
+But I want you to do it.
+
+So for now, I'm just going to
+tell you about the general
+
+principles.
+
+And in the process I'm going to
+introduce the terminology.
+
+Just, the words that we need
+to use to describe what is
+
+that we're doing.
+
+And there's also a certain
+amount of carelessness with
+
+that in many of the treatments
+that you'll see.
+
+And a lot of hastiness.
+
+So just be a little patient
+and we will do this.
+
+So, the first principle
+is the following.
+
+If f' is positive, then
+f is increasing.
+
+That's a straightforward idea,
+and it's closely related to
+
+this tangent line approximation
+or the linear
+
+approximation that I just did.
+
+You can just imagine.
+
+Here's the tangent line,
+here's the function.
+
+And if the tangent line is
+pointing up, then the function
+
+is also going up, too.
+
+So that's all that's
+going on here.
+
+Similarly, if f' is negative,
+then f is decreasing.
+
+And that's the basic idea.
+
+Now, the second step is also
+fairly straightforward.
+
+It's just a second order effect
+of the same type.
+
+If you have f'' as positive,
+then that means that f' is
+
+increasing.
+
+That's the same principle
+applied one step up.
+
+Right?
+
+Because if f'' is positive,
+that means it's the
+
+derivative of f'.
+
+So it's the same principle
+just repeated.
+
+And now I just want to draw
+a picture of this.
+
+Here's a picture
+of it, I claim.
+
+And it looks like something's
+going down.
+
+And I did that on purpose.
+
+But there is something that's
+increasing here.
+
+Which is, the slope is very
+steep negative here.
+
+And it's less steep negative
+over here.
+
+So we have the slope which
+is some negative
+
+number, say, - 4.
+
+And here it's - 3.
+
+So it's increasing.
+
+It's getting less negative,
+and maybe eventually it'll
+
+curve up the other way.
+
+And this is a picture of what
+I'm talking about here.
+
+That's what it means to say
+that f' is increasing.
+
+The slope is getting larger.
+
+And the way to describe a curve
+like this is that it's
+
+concave. So f is concave up.
+
+And similarly, f'' negative is
+going to be the same thing as
+
+f concave, or implies
+f concave down.
+
+So those are the ways in which
+derivatives will help us
+
+qualitatively to draw graphs.
+
+But as I said before, we still
+have to use a little bit of
+
+common sense when we
+draw the graphs.
+
+These are just the additional
+bits of help that
+
+we have from calculus.
+
+In drawing pictures.
+
+So I'm going to go through
+one example to
+
+introduce all the notations.
+
+And then eventually, so probably
+at the beginning of
+
+next time, I'll give you a
+systematic strategy that's
+
+going to work when what I'm
+describing now goes wrong, or
+
+a little bit wrong.
+
+So let's begin with a
+straightforward example.
+
+So, the first example that I'll
+give you is the function
+
+f (x) = 3x - x^3.
+
+Just, as I said, to be able to
+introduce all the notations.
+
+Now, if you differentiate
+it, you get 3 - 3x^2.
+
+And I can factor that.
+
+This is 3 ( 1 - x)( 1 x).
+
+OK?
+
+And so, I can decide whether
+the derivative
+
+is positive or negative.
+
+Easily enough.
+
+Namely, just staring at this,
+I can see that when -1 < x <
+
+1, in that range there, both
+these numbers, both these
+
+factors, are positive.
+
+1 - x is a positive number and
+1 x is a positive number.
+
+So, in this range, f'
+( x ) is positive.
+
+So this thing is, so
+f is increasing.
+
+And similarly, in the other
+ranges, if x is very, very
+
+large, this becomes, if it
+crosses 1, in fact, this
+
+becomes, this factor becomes
+negative and
+
+this one stays positive.
+
+So when x > 1, we have that
+f ' (x) is negative.
+
+And so f is decreasing.
+
+And the same thing goes
+for the other side.
+
+When it's less than - 1, that
+also works this way.
+
+Because when it's less
+than - 1, this
+
+number factors positive.
+
+But the other one is negative.
+
+So in both of these cases, we
+get that it's decreasing.
+
+So now, here's the schematic
+picture of this function.
+
+So here's - 1, here's 1.
+
+It's going to go
+down, up, down.
+
+That's what it's doing.
+
+Maybe I'll just leave
+it alone like this.
+
+That's what it looks like.
+
+So, this is the kind of
+information we can get right
+
+off the bat.
+
+And you notice immediately that
+it's very important, from
+
+the features of the function,
+the sort of key features of
+
+the function that we see here,
+are these two places.
+
+Maybe I'll even mark them
+in a, like this.
+
+And these things are
+turning points.
+
+So what are they?
+
+Well, they're just the
+points where the
+
+derivative changes sign.
+
+Where it's negative here and
+it's positive there, so there
+
+it must be 0.
+
+So we have a definition, and
+this is the most important
+
+definition in this subject,
+which is that is if f' (x0) =
+
+0, we call x0 a critical
+point.
+
+The word 'turning point' is
+not used just because, in
+
+fact, it doesn't have to turn
+around at those points.
+
+But certainly, if it turns
+around then this will happen.
+
+And we also have another
+notation, which is the number
+
+y0 which is f ( x0 ) is called
+a critical value.
+
+So these are the key numbers
+that we're going to have to
+
+work out in order to understand
+what the function
+
+looks like.
+
+So what I'm going to do
+is just plot them.
+
+We're going to plot
+the critical
+
+points and the values.
+
+Well, we found the critical
+points relatively easily.
+
+I didn't write it down here
+but it's pretty obvious.
+
+If you set f(x) = 0, that
+implies that (1 - x)( 1 x) =
+
+0, which implies that
+x is or - 1.
+
+So those are known as
+the critical points.
+
+And now, in order to get the
+critical values here, I have
+
+to plug in f (1), for instance,
+the function is 3x -
+
+x^2, so there's this 3 *
+1 - 1^3, which is 2.
+
+And f ( - 1), which is 3 ( -
+1) - (- 1)^3, which is - 2.
+
+And so I can plot the
+function here.
+
+So here's the point - 1 and
+here's, up here, is 2.
+
+So this is - whoops,
+which one is it?
+
+Yeah.
+
+This is - 1, so it's
+down here.
+
+So it's (- 1, - 2).
+
+And then over here, I have
+the point (1, 2).
+
+Alright, now, what information
+do I get from - so I've now
+
+plotted two, I claim, very
+interesting points.
+
+What information do
+I get from this?
+
+The answer is, I know something
+very nearby.
+
+Because I've already checked
+that the thing is coming down
+
+from the left, and
+coming back up.
+
+And so it must be shaped
+like this.
+
+Over here.
+
+The tangent line is 0, it's
+going to be level there.
+
+And similarly over here,
+it's going to do that.
+
+So this is what we know
+so far, based
+
+on what we've computed.
+
+Question.
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: The question
+is, what happens if
+
+there's a sharp corner.
+
+The answer is, calculus, it's
+not called a critical point.
+
+It's a something else.
+
+And it's a very important
+point, too.
+
+And we will be discussing
+those kinds of points.
+
+There are much more dramatic
+instances of that.
+
+That's part of what we're
+going to say.
+
+But I just want to save
+that, alright.
+
+We will be discussing.
+
+Yeah.
+
+Question.
+
+STUDENT: [INAUDIBLE]
+
+PROF.
+
+JERISON: The question that was
+asked was, how did I know at
+
+the critical point that it's
+concave down over here and
+
+concave up over here.
+
+The answer is that I actually
+did not use the second
+
+derivative yet.
+
+What I used is another
+piece of information.
+
+I used the information that
+I derived over here.
+
+That f' is positive, where
+f' is positive
+
+and where it's negative.
+
+So what I know is that the graph
+is going down to the
+
+left of - 1.
+
+It's going up to the
+right, here.
+
+It's going up here and it's
+going down there.
+
+I did not use the second
+derivative.
+
+I used the first derivative.
+
+OK, but I didn't just use the
+fact that there was a turning
+
+point here.
+
+So, actually, I was using
+the fact that it
+
+was a turning point.
+
+I wasn't using the fact
+that it had the
+
+second derivative, though.
+
+OK.
+
+For now.
+
+You can also see it by the
+second derivative as well.
+
+So now, the next thing that
+I'd like to do, I need to
+
+finish off this graph.
+
+And I just want to do it a
+little bit carefully here.
+
+In the order that
+is reasonable.
+
+Now, you might happen to notice,
+and there's nothing
+
+wrong with this, so let's
+even fill in a guess.
+
+In order to fill in a guess,
+though, and have it be even
+
+vaguely right, I do have to
+notice that this thing
+
+crosses, this function
+crosses the origin.
+
+The function f(x) = 3x - x^3
+happens also have the property
+
+that f ( 0 ) = 0.
+
+Again, common sense.
+
+You're allowed to use
+your common sense.
+
+You're allowed to notice
+a value of the
+
+function and put it in.
+
+So there's nothing
+wrong with that.
+
+If you happen to have
+such a value.
+
+So, now we can guess what
+our function is
+
+going to look like.
+
+It's going to maybe come
+down like this.
+
+Come up like this.
+
+And come down like this.
+
+That could be what
+it looks like.
+
+But, you know, another
+possibility is it sort of
+
+comes along here and
+goes out that way.
+
+Comes along here and goes
+out that way, who knows?
+
+It happens, by the way, that
+it's an odd function.
+
+Right?
+
+Those are all odd powers.
+
+So, actually, it's symmetric
+on the right half
+
+and the left half.
+
+And crosses at 0.
+
+So everything that we do on the
+right is going to be the
+
+same as what happens
+on the left.
+
+That's another piece
+of common sense.
+
+You want to make use of that as
+much as possible, whenever
+
+you're drawing anything.
+
+Don't want to throw
+out information.
+
+So this function happens
+to be odd.
+
+Odd, and f ( 0 ) = 0.
+
+I'm considering those to be
+kinds of precalculus skills
+
+that I want you to use
+as much as you can.
+
+So now, here's the first feature
+which is unfortunately
+
+ignored in most discussions
+of functions.
+
+And it's strange, because
+nowadays we
+
+have graphing things.
+
+And it's really the only part
+of the exercise that you
+
+couldn't do, at least on this
+relatively simpleminded level,
+
+with a graphing calculator.
+
+And that is what I would call
+the ends of the problem.
+
+So what happens off the screen,
+is the question.
+
+And that basically is the
+theoretical part of the
+
+problem that you have
+to address.
+
+You can program this.
+
+You can draw all the pictures
+that you want.
+
+But what you won't see is
+what's off the screen.
+
+You need to know something
+to figure out
+
+what's off the screen.
+
+So, in this case, I'm talking
+about what's off the screen
+
+going to the right, or
+going to the left.
+
+So let's check the ends.
+
+So here, let's just
+take a look.
+
+We have the function f(x), which
+is, sorry, 3x - x^3.
+
+Again this is a precalculus
+sort of thing.
+
+And we're imagining now,
+let's just do x
+
+goes to plus infinity.
+
+So what happens here.
+
+When x is gigantic, this term
+is completely negligible.
+
+And it just behaves like -
+x^3, which goes to minus
+
+infinity as x goes
+to plus infinity.
+
+And similarly, f (x) goes to
+plus infinity if x goes to
+
+minus infinity.
+
+Now let me pull down this
+picture again, and show you
+
+what piece of the information
+we've got.
+
+We now know that it is
+heading up this way.
+
+It doesn't go like this,
+it goes up like that.
+
+And I'm going to put an
+arrow for it, And it's
+
+going down like this.
+
+Heading down to minus infinity
+as x goes out
+
+farther to the right.
+
+And going out to plus infinity
+as x goes farther to the left.
+
+So now there's hardly
+anything left of
+
+this function to describe.
+
+There's really nothing left
+except maybe decoration.
+
+And we kind of like that
+decoration, so we will pay
+
+attention to it.
+
+And to do that, we'll have to
+check the second derivative.
+
+So if we differentiate a
+second time, the first
+
+derivative was, remember,
+3 - 3x^2.
+
+So the second derivative
+is - 6x.
+
+So now we notice that f'' (x) is
+negative if x is positive.
+
+And f'' ( x) is positive
+if x is negative.
+
+And so in this part
+it's concave down.
+
+And in this part it's
+concave up.
+
+And now I'm going to switch
+the boards so that
+
+you'll, and draw it.
+
+And you see that it was begging
+to be this way.
+
+So we'll fill in the
+rest of it here.
+
+Maybe in a nice color here.
+
+So this is the whole graph and
+this is the correct graph.
+
+It comes down in one swoop down
+here, and comes up here.
+
+And then it changes to concave
+down right at the origin.
+
+So this point is of interest,
+not only because it's the
+
+place where it crosses the axis,
+but it's also what's
+
+called an inflection point.
+
+Inflection point, that's a point
+where because f'' at
+
+that place is equal to 0.
+
+So it's a place where the
+second derivative is 0.
+
+We also consider those to
+be interesting points.
+
+Now, so let me just making
+one closing remark here.
+
+Which is that all of this
+information fits together.
+
+And we're going to have much,
+much harder examples of this
+
+where you'll actually have to
+think about what's going on.
+
+But there's a lot of stuff
+protecting you.
+
+And functions will behave
+themselves and turn around
+
+appropriately.
+
+Anyway, we'll talk about
+it next time.
\ No newline at end of file
diff --git a/ekgSqnLd0Ls.txt b/ekgSqnLd0Ls.txt
new file mode 100644
index 0000000000000000000000000000000000000000..714303ae50fc3815d6784591c81cd01a108af550
--- /dev/null
+++ b/ekgSqnLd0Ls.txt
@@ -0,0 +1,11264 @@
+align:start position:0%
+ 
+hello everybody we're going to be
+
+ align:start position:0%
+hello everybody we're going to be
+ 
+
+ align:start position:0%
+hello everybody we're going to be
+looking today at how we can use machine
+
+ align:start position:0%
+looking today at how we can use machine
+ 
+
+ align:start position:0%
+looking today at how we can use machine
+learning and artificial intelligence in
+
+ align:start position:0%
+learning and artificial intelligence in
+ 
+
+ align:start position:0%
+learning and artificial intelligence in
+order to learn more about musical
+
+ align:start position:0%
+order to learn more about musical
+ 
+
+ align:start position:0%
+order to learn more about musical
+behavior and music theory and just music
+
+ align:start position:0%
+behavior and music theory and just music
+ 
+
+ align:start position:0%
+behavior and music theory and just music
+in general our first task is going to be
+
+ align:start position:0%
+in general our first task is going to be
+ 
+
+ align:start position:0%
+in general our first task is going to be
+how do we transform music into formats
+
+ align:start position:0%
+how do we transform music into formats
+ 
+
+ align:start position:0%
+how do we transform music into formats
+that computers can learn from because a
+
+ align:start position:0%
+that computers can learn from because a
+ 
+
+ align:start position:0%
+that computers can learn from because a
+score alone is not something that can be
+
+ align:start position:0%
+score alone is not something that can be
+ 
+
+ align:start position:0%
+score alone is not something that can be
+used for artificial intelligence and so
+
+ align:start position:0%
+used for artificial intelligence and so
+ 
+
+ align:start position:0%
+used for artificial intelligence and so
+our first task is going to be
+
+ align:start position:0%
+our first task is going to be
+ 
+
+ align:start position:0%
+our first task is going to be
+understanding how feature extraction the
+
+ align:start position:0%
+understanding how feature extraction the
+ 
+
+ align:start position:0%
+understanding how feature extraction the
+conversion of musical scores into
+
+ align:start position:0%
+conversion of musical scores into
+ 
+
+ align:start position:0%
+conversion of musical scores into
+intelligent numerical data how feature
+
+ align:start position:0%
+intelligent numerical data how feature
+ 
+
+ align:start position:0%
+intelligent numerical data how feature
+extraction is able to make machine
+
+ align:start position:0%
+extraction is able to make machine
+ 
+
+ align:start position:0%
+extraction is able to make machine
+learning possible so go ahead and load
+
+ align:start position:0%
+learning possible so go ahead and load
+ 
+
+ align:start position:0%
+learning possible so go ahead and load
+up juper notebook and follow along as we
+
+ align:start position:0%
+up juper notebook and follow along as we
+ 
+
+ align:start position:0%
+up juper notebook and follow along as we
+do some work with music 21 first
+
+ align:start position:0%
+do some work with music 21 first
+ 
+
+ align:start position:0%
+do some work with music 21 first
+separate from the music 21 machine
+
+ align:start position:0%
+separate from the music 21 machine
+ 
+
+ align:start position:0%
+separate from the music 21 machine
+learning tool kit and then with music 21
+
+ align:start position:0%
+learning tool kit and then with music 21
+ 
+
+ align:start position:0%
+learning tool kit and then with music 21
+features in order to learn more about
+
+ align:start position:0%
+features in order to learn more about
+ 
+
+ align:start position:0%
+features in order to learn more about
+some genres and other ways of
+
+ align:start position:0%
+some genres and other ways of
+ 
+
+ align:start position:0%
+some genres and other ways of
+classifying
+
+ align:start position:0%
+classifying
+ 
+
+ align:start position:0%
+classifying
+music so go ahead and start Jupiter
+
+ align:start position:0%
+music so go ahead and start Jupiter
+ 
+
+ align:start position:0%
+music so go ahead and start Jupiter
+notebook and we're going to create uh
+
+ align:start position:0%
+notebook and we're going to create uh
+ 
+
+ align:start position:0%
+notebook and we're going to create uh
+the first step which is to understand
+
+ align:start position:0%
+the first step which is to understand
+ 
+
+ align:start position:0%
+the first step which is to understand
+what features are so I'll I know why we
+
+ align:start position:0%
+what features are so I'll I know why we
+ 
+
+ align:start position:0%
+what features are so I'll I know why we
+might want to extract them so what is a
+
+ align:start position:0%
+might want to extract them so what is a
+ 
+
+ align:start position:0%
+might want to extract them so what is a
+feature that's the first thing we're
+
+ align:start position:0%
+feature that's the first thing we're
+ 
+
+ align:start position:0%
+feature that's the first thing we're
+going to work on feature is something
+
+ align:start position:0%
+going to work on feature is something
+ 
+
+ align:start position:0%
+going to work on feature is something
+really really really basic let's say
+
+ align:start position:0%
+really really really basic let's say
+ 
+
+ align:start position:0%
+really really really basic let's say
+that we have a piece um will load from
+
+ align:start position:0%
+that we have a piece um will load from
+ 
+
+ align:start position:0%
+that we have a piece um will load from
+music 21 Corpus our favorite B Corral so
+
+ align:start position:0%
+music 21 Corpus our favorite B Corral so
+ 
+
+ align:start position:0%
+music 21 Corpus our favorite B Corral so
+you don't even need to know what comes
+
+ align:start position:0%
+you don't even need to know what comes
+ 
+
+ align:start position:0%
+you don't even need to know what comes
+up from this Corpus pars BL bwv 66.
+
+ align:start position:0%
+up from this Corpus pars BL bwv 66.
+ 
+
+ align:start position:0%
+up from this Corpus pars BL bwv 66.
+six and just to remind yourselves how it
+
+ align:start position:0%
+six and just to remind yourselves how it
+ 
+
+ align:start position:0%
+six and just to remind yourselves how it
+goes here's the
+
+ align:start position:0%
+goes here's the
+ 
+
+ align:start position:0%
+goes here's the
+buck so great let's go ahead
+
+ align:start position:0%
+buck so great let's go ahead
+ 
+
+ align:start position:0%
+buck so great let's go ahead
+and choose a feature from the this um
+
+ align:start position:0%
+and choose a feature from the this um
+ 
+
+ align:start position:0%
+and choose a feature from the this um
+from this let's do the parts feature and
+
+ align:start position:0%
+from this let's do the parts feature and
+ 
+
+ align:start position:0%
+from this let's do the parts feature and
+we'll call it num Parts equals 4 and
+
+ align:start position:0%
+we'll call it num Parts equals 4 and
+ 
+
+ align:start position:0%
+we'll call it num Parts equals 4 and
+let's do the time
+
+ align:start position:0%
+let's do the time
+ 
+
+ align:start position:0%
+let's do the time
+signature numerator
+
+ align:start position:0%
+signature numerator
+ 
+
+ align:start position:0%
+signature numerator
+feature equal
+
+ align:start position:0%
+feature equal
+ 
+
+ align:start position:0%
+feature equal
+4 there we've now extracted manually two
+
+ align:start position:0%
+4 there we've now extracted manually two
+ 
+
+ align:start position:0%
+4 there we've now extracted manually two
+features from this
+
+ align:start position:0%
+features from this
+ 
+
+ align:start position:0%
+features from this
+Coral feature extraction is the
+
+ align:start position:0%
+Coral feature extraction is the
+ 
+
+ align:start position:0%
+Coral feature extraction is the
+conversion of musical elements or any
+
+ align:start position:0%
+conversion of musical elements or any
+ 
+
+ align:start position:0%
+conversion of musical elements or any
+element but musical feature extraction
+
+ align:start position:0%
+element but musical feature extraction
+ 
+
+ align:start position:0%
+element but musical feature extraction
+is a conversion of musical elements into
+
+ align:start position:0%
+is a conversion of musical elements into
+ 
+
+ align:start position:0%
+is a conversion of musical elements into
+single numbers or lists arays vectors of
+
+ align:start position:0%
+single numbers or lists arays vectors of
+ 
+
+ align:start position:0%
+single numbers or lists arays vectors of
+numbers it is thus the most boring thing
+
+ align:start position:0%
+numbers it is thus the most boring thing
+ 
+
+ align:start position:0%
+numbers it is thus the most boring thing
+in the world as you've just
+
+ align:start position:0%
+in the world as you've just
+ 
+
+ align:start position:0%
+in the world as you've just
+seen it is just a bunch of numbers
+
+ align:start position:0%
+seen it is just a bunch of numbers
+ 
+
+ align:start position:0%
+seen it is just a bunch of numbers
+feature extraction sucks out the
+
+ align:start position:0%
+feature extraction sucks out the
+ 
+
+ align:start position:0%
+feature extraction sucks out the
+lifeblood of Music it takes everything
+
+ align:start position:0%
+lifeblood of Music it takes everything
+ 
+
+ align:start position:0%
+lifeblood of Music it takes everything
+that's beautiful in music and turns it
+
+ align:start position:0%
+that's beautiful in music and turns it
+ 
+
+ align:start position:0%
+that's beautiful in music and turns it
+into a bunch of numbers it is the life
+
+ align:start position:0%
+into a bunch of numbers it is the life
+ 
+
+ align:start position:0%
+into a bunch of numbers it is the life
+sucker it is the zombie of the musical
+
+ align:start position:0%
+sucker it is the zombie of the musical
+ 
+
+ align:start position:0%
+sucker it is the zombie of the musical
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+but but there are tons of amazing
+
+ align:start position:0%
+but but there are tons of amazing
+ 
+
+ align:start position:0%
+but but there are tons of amazing
+machine learning and artificial
+
+ align:start position:0%
+machine learning and artificial
+ 
+
+ align:start position:0%
+machine learning and artificial
+intelligence and deep learning
+
+ align:start position:0%
+intelligence and deep learning
+ 
+
+ align:start position:0%
+intelligence and deep learning
+algorithms in the world as far as I know
+
+ align:start position:0%
+algorithms in the world as far as I know
+ 
+
+ align:start position:0%
+algorithms in the world as far as I know
+they all have one thing in common they
+
+ align:start position:0%
+they all have one thing in common they
+ 
+
+ align:start position:0%
+they all have one thing in common they
+only work on collections of single
+
+ align:start position:0%
+only work on collections of single
+ 
+
+ align:start position:0%
+only work on collections of single
+numbers or vectors of
+
+ align:start position:0%
+numbers or vectors of
+ 
+
+ align:start position:0%
+numbers or vectors of
+numbers I'm not a machine learning
+
+ align:start position:0%
+numbers I'm not a machine learning
+ 
+
+ align:start position:0%
+numbers I'm not a machine learning
+expert so maybe there are algorithms
+
+ align:start position:0%
+expert so maybe there are algorithms
+ 
+
+ align:start position:0%
+expert so maybe there are algorithms
+that work on two or multi-dimensional
+
+ align:start position:0%
+that work on two or multi-dimensional
+ 
+
+ align:start position:0%
+that work on two or multi-dimensional
+arrays of numbers that would be amazing
+
+ align:start position:0%
+arrays of numbers that would be amazing
+ 
+
+ align:start position:0%
+arrays of numbers that would be amazing
+for Machine Vision or what we do but
+
+ align:start position:0%
+for Machine Vision or what we do but
+ 
+
+ align:start position:0%
+for Machine Vision or what we do but
+nothing as far as I know in the
+
+ align:start position:0%
+nothing as far as I know in the
+ 
+
+ align:start position:0%
+nothing as far as I know in the
+artificial intelligence World works on
+
+ align:start position:0%
+artificial intelligence World works on
+ 
+
+ align:start position:0%
+artificial intelligence World works on
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+notation or
+
+ align:start position:0%
+notation or
+ 
+
+ align:start position:0%
+notation or
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sound so if we're going to work on doing
+
+ align:start position:0%
+sound so if we're going to work on doing
+ 
+
+ align:start position:0%
+sound so if we're going to work on doing
+artificial intelligence or predictions
+
+ align:start position:0%
+artificial intelligence or predictions
+ 
+
+ align:start position:0%
+artificial intelligence or predictions
+or anything super amazing on music
+
+ align:start position:0%
+or anything super amazing on music
+ 
+
+ align:start position:0%
+or anything super amazing on music
+notation at least at present we need to
+
+ align:start position:0%
+notation at least at present we need to
+ 
+
+ align:start position:0%
+notation at least at present we need to
+convert music to
+
+ align:start position:0%
+convert music to
+ 
+
+ align:start position:0%
+convert music to
+numbers so that's what feature
+
+ align:start position:0%
+numbers so that's what feature
+ 
+
+ align:start position:0%
+numbers so that's what feature
+extraction is basic feature extraction
+
+ align:start position:0%
+extraction is basic feature extraction
+ 
+
+ align:start position:0%
+extraction is basic feature extraction
+is pretty
+
+ align:start position:0%
+is pretty
+ 
+
+ align:start position:0%
+is pretty
+simple so in this case let's just
+
+ align:start position:0%
+simple so in this case let's just
+ 
+
+ align:start position:0%
+simple so in this case let's just
+extract
+
+ align:start position:0%
+extract
+ 
+
+ align:start position:0%
+extract
+automatically the meter from this piece
+
+ align:start position:0%
+automatically the meter from this piece
+ 
+
+ align:start position:0%
+automatically the meter from this piece
+so we'll uh write something that does it
+
+ align:start position:0%
+so we'll uh write something that does it
+ 
+
+ align:start position:0%
+so we'll uh write something that does it
+we'll import from the typing module
+
+ align:start position:0%
+we'll import from the typing module
+ 
+
+ align:start position:0%
+we'll import from the typing module
+because we like to do things like this
+
+ align:start position:0%
+because we like to do things like this
+ 
+
+ align:start position:0%
+because we like to do things like this
+turn python which is a weakly typed
+
+ align:start position:0%
+turn python which is a weakly typed
+ 
+
+ align:start position:0%
+turn python which is a weakly typed
+language into slightly stronger typed so
+
+ align:start position:0%
+language into slightly stronger typed so
+ 
+
+ align:start position:0%
+language into slightly stronger typed so
+that we can um understand a little bit
+
+ align:start position:0%
+that we can um understand a little bit
+ 
+
+ align:start position:0%
+that we can um understand a little bit
+better um what's going to go on so we'll
+
+ align:start position:0%
+better um what's going to go on so we'll
+ 
+
+ align:start position:0%
+better um what's going to go on so we'll
+also import from music 21 the meter and
+
+ align:start position:0%
+also import from music 21 the meter and
+ 
+
+ align:start position:0%
+also import from music 21 the meter and
+stream modules now let's write something
+
+ align:start position:0%
+stream modules now let's write something
+ 
+
+ align:start position:0%
+stream modules now let's write something
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+extract extract meter which takes in a
+
+ align:start position:0%
+extract extract meter which takes in a
+ 
+
+ align:start position:0%
+extract extract meter which takes in a
+variable score which is a
+
+ align:start position:0%
+variable score which is a
+ 
+
+ align:start position:0%
+variable score which is a
+stream. stream object maybe it should be
+
+ align:start position:0%
+stream. stream object maybe it should be
+ 
+
+ align:start position:0%
+stream. stream object maybe it should be
+a stream. score object but let's keep it
+
+ align:start position:0%
+a stream. score object but let's keep it
+ 
+
+ align:start position:0%
+a stream. score object but let's keep it
+flexible and it returns a tupple of two
+
+ align:start position:0%
+flexible and it returns a tupple of two
+ 
+
+ align:start position:0%
+flexible and it returns a tupple of two
+integers and we'll say here that returns
+
+ align:start position:0%
+integers and we'll say here that returns
+ 
+
+ align:start position:0%
+integers and we'll say here that returns
+a two tle of the
+
+ align:start position:0%
+a two tle of the
+ 
+
+ align:start position:0%
+a two tle of the
+numerator and
+
+ align:start position:0%
+numerator and
+ 
+
+ align:start position:0%
+numerator and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+denominator of the first time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signature
+
+ align:start position:0%
+signature
+ 
+
+ align:start position:0%
+signature
+siger found in a
+
+ align:start position:0%
+siger found in a
+ 
+
+ align:start position:0%
+siger found in a
+score returns 0 comma 0 if the score has
+
+ align:start position:0%
+score returns 0 comma 0 if the score has
+ 
+
+ align:start position:0%
+score returns 0 comma 0 if the score has
+no meter why do we return 0 comma 0 if
+
+ align:start position:0%
+no meter why do we return 0 comma 0 if
+ 
+
+ align:start position:0%
+no meter why do we return 0 comma 0 if
+there's no meter in feature extraction
+
+ align:start position:0%
+there's no meter in feature extraction
+ 
+
+ align:start position:0%
+there's no meter in feature extraction
+it's generally assumed that we want to
+
+ align:start position:0%
+it's generally assumed that we want to
+ 
+
+ align:start position:0%
+it's generally assumed that we want to
+return out of bound number rather than
+
+ align:start position:0%
+return out of bound number rather than
+ 
+
+ align:start position:0%
+return out of bound number rather than
+raising exception if there's a
+
+ align:start position:0%
+raising exception if there's a
+ 
+
+ align:start position:0%
+raising exception if there's a
+mistake and the reason is you'd hate to
+
+ align:start position:0%
+mistake and the reason is you'd hate to
+ 
+
+ align:start position:0%
+mistake and the reason is you'd hate to
+be running extract meter on hundreds or
+
+ align:start position:0%
+be running extract meter on hundreds or
+ 
+
+ align:start position:0%
+be running extract meter on hundreds or
+thousands of pieces and you're always
+
+ align:start position:0%
+thousands of pieces and you're always
+ 
+
+ align:start position:0%
+thousands of pieces and you're always
+getting 4 comma 4 or 3 comma 4 or 6
+
+ align:start position:0%
+getting 4 comma 4 or 3 comma 4 or 6
+ 
+
+ align:start position:0%
+getting 4 comma 4 or 3 comma 4 or 6
+comma 8 or even something wacky like 11
+
+ align:start position:0%
+comma 8 or even something wacky like 11
+ 
+
+ align:start position:0%
+comma 8 or even something wacky like 11
+comma 32 and you it's all working
+
+ align:start position:0%
+comma 32 and you it's all working
+ 
+
+ align:start position:0%
+comma 32 and you it's all working
+successfully only to have your entire
+
+ align:start position:0%
+successfully only to have your entire
+ 
+
+ align:start position:0%
+successfully only to have your entire
+feature construction artificial
+
+ align:start position:0%
+feature construction artificial
+ 
+
+ align:start position:0%
+feature construction artificial
+intelligence pipeline fail if there's
+
+ align:start position:0%
+intelligence pipeline fail if there's
+ 
+
+ align:start position:0%
+intelligence pipeline fail if there's
+one piece that doesn't have a time
+
+ align:start position:0%
+one piece that doesn't have a time
+ 
+
+ align:start position:0%
+one piece that doesn't have a time
+signature like let's say it's Gregorian
+
+ align:start position:0%
+signature like let's say it's Gregorian
+ 
+
+ align:start position:0%
+signature like let's say it's Gregorian
+chant or some kind of trans
+
+ align:start position:0%
+chant or some kind of trans
+ 
+
+ align:start position:0%
+chant or some kind of trans
+meditation so that's why we're going to
+
+ align:start position:0%
+meditation so that's why we're going to
+ 
+
+ align:start position:0%
+meditation so that's why we're going to
+be putting returning 0 comma 0 on the
+
+ align:start position:0%
+be putting returning 0 comma 0 on the
+ 
+
+ align:start position:0%
+be putting returning 0 comma 0 on the
+other hand maybe it's a bad assumption
+
+ align:start position:0%
+other hand maybe it's a bad assumption
+ 
+
+ align:start position:0%
+other hand maybe it's a bad assumption
+and we should raise exceptions when
+
+ align:start position:0%
+and we should raise exceptions when
+ 
+
+ align:start position:0%
+and we should raise exceptions when
+something's not right and then we should
+
+ align:start position:0%
+something's not right and then we should
+ 
+
+ align:start position:0%
+something's not right and then we should
+fix our work rather than hiding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+errors but we'll get to that in just a
+
+ align:start position:0%
+errors but we'll get to that in just a
+ 
+
+ align:start position:0%
+errors but we'll get to that in just a
+bit first meter but first let's see how
+
+ align:start position:0%
+bit first meter but first let's see how
+ 
+
+ align:start position:0%
+bit first meter but first let's see how
+we do this so let's just remind
+
+ align:start position:0%
+we do this so let's just remind
+ 
+
+ align:start position:0%
+we do this so let's just remind
+ourselves we can take from anything get
+
+ align:start position:0%
+ourselves we can take from anything get
+ 
+
+ align:start position:0%
+ourselves we can take from anything get
+Elements by class meter. time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signature and if we do not have the any
+
+ align:start position:0%
+signature and if we do not have the any
+ 
+
+ align:start position:0%
+signature and if we do not have the any
+the first meter will
+
+ align:start position:0%
+the first meter will
+ 
+
+ align:start position:0%
+the first meter will
+return 0 comma
+
+ align:start position:0%
+return 0 comma
+ 
+
+ align:start position:0%
+return 0 comma
+0 and otherwise we'll return the first
+
+ align:start position:0%
+0 and otherwise we'll return the first
+ 
+
+ align:start position:0%
+0 and otherwise we'll return the first
+meters numerator and the first
+
+ align:start position:0%
+meters numerator and the first
+ 
+
+ align:start position:0%
+meters numerator and the first
+meters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denominator we're kind of hiding an
+
+ align:start position:0%
+denominator we're kind of hiding an
+ 
+
+ align:start position:0%
+denominator we're kind of hiding an
+error in our encoding um is that the
+
+ align:start position:0%
+error in our encoding um is that the
+ 
+
+ align:start position:0%
+error in our encoding um is that the
+right thing to do and I think this is
+
+ align:start position:0%
+right thing to do and I think this is
+ 
+
+ align:start position:0%
+right thing to do and I think this is
+something that when we're talking about
+
+ align:start position:0%
+something that when we're talking about
+ 
+
+ align:start position:0%
+something that when we're talking about
+it and I would love to talk to anybody
+
+ align:start position:0%
+it and I would love to talk to anybody
+ 
+
+ align:start position:0%
+it and I would love to talk to anybody
+directly about about ethics and morality
+
+ align:start position:0%
+directly about about ethics and morality
+ 
+
+ align:start position:0%
+directly about about ethics and morality
+and sort of what who artificial
+
+ align:start position:0%
+and sort of what who artificial
+ 
+
+ align:start position:0%
+and sort of what who artificial
+intelligence is working for because I
+
+ align:start position:0%
+intelligence is working for because I
+ 
+
+ align:start position:0%
+intelligence is working for because I
+think there are often important
+
+ align:start position:0%
+think there are often important
+ 
+
+ align:start position:0%
+think there are often important
+considerations of artificial
+
+ align:start position:0%
+considerations of artificial
+ 
+
+ align:start position:0%
+considerations of artificial
+intelligence with moral and ethical
+
+ align:start position:0%
+intelligence with moral and ethical
+ 
+
+ align:start position:0%
+intelligence with moral and ethical
+consequences when we hide things that it
+
+ align:start position:0%
+consequences when we hide things that it
+ 
+
+ align:start position:0%
+consequences when we hide things that it
+can't do and so I want you if you're
+
+ align:start position:0%
+can't do and so I want you if you're
+ 
+
+ align:start position:0%
+can't do and so I want you if you're
+going to be somebody who's going to be
+
+ align:start position:0%
+going to be somebody who's going to be
+ 
+
+ align:start position:0%
+going to be somebody who's going to be
+working with artificial intelligence and
+
+ align:start position:0%
+working with artificial intelligence and
+ 
+
+ align:start position:0%
+working with artificial intelligence and
+the rest of your life and Technology to
+
+ align:start position:0%
+the rest of your life and Technology to
+ 
+
+ align:start position:0%
+the rest of your life and Technology to
+think about such things maybe we
+
+ align:start position:0%
+think about such things maybe we
+ 
+
+ align:start position:0%
+think about such things maybe we
+shouldn't be hiding our error so
+
+ align:start position:0%
+shouldn't be hiding our error so
+ 
+
+ align:start position:0%
+shouldn't be hiding our error so
+much okay so we have this extract meter
+
+ align:start position:0%
+much okay so we have this extract meter
+ 
+
+ align:start position:0%
+much okay so we have this extract meter
+to get back to this whoops um doesn't
+
+ align:start position:0%
+to get back to this whoops um doesn't
+ 
+
+ align:start position:0%
+to get back to this whoops um doesn't
+matter if you put a parenthesis around a
+
+ align:start position:0%
+matter if you put a parenthesis around a
+ 
+
+ align:start position:0%
+matter if you put a parenthesis around a
+tupple when you return it but if you
+
+ align:start position:0%
+tupple when you return it but if you
+ 
+
+ align:start position:0%
+tupple when you return it but if you
+start with one you have to do the other
+
+ align:start position:0%
+start with one you have to do the other
+ 
+
+ align:start position:0%
+start with one you have to do the other
+okay so let's take this B Corral and
+
+ align:start position:0%
+okay so let's take this B Corral and
+ 
+
+ align:start position:0%
+okay so let's take this B Corral and
+let's run extract
+
+ align:start position:0%
+let's run extract
+ 
+
+ align:start position:0%
+let's run extract
+meter on the B
+
+ align:start position:0%
+meter on the B
+ 
+
+ align:start position:0%
+meter on the B
+oh0 comma 0 oh I know why because we
+
+ align:start position:0%
+oh0 comma 0 oh I know why because we
+ 
+
+ align:start position:0%
+oh0 comma 0 oh I know why because we
+forgot to do
+
+ align:start position:0%
+forgot to do
+ 
+
+ align:start position:0%
+forgot to do
+recurse you know flat would do just as
+
+ align:start position:0%
+recurse you know flat would do just as
+ 
+
+ align:start position:0%
+recurse you know flat would do just as
+well but recurse is a little bit faster
+
+ align:start position:0%
+well but recurse is a little bit faster
+ 
+
+ align:start position:0%
+well but recurse is a little bit faster
+and oh by the way something I didn't
+
+ align:start position:0%
+and oh by the way something I didn't
+ 
+
+ align:start position:0%
+and oh by the way something I didn't
+mention uh you might have seen that
+
+ align:start position:0%
+mention uh you might have seen that
+ 
+
+ align:start position:0%
+mention uh you might have seen that
+we're sending in the class actual class
+
+ align:start position:0%
+we're sending in the class actual class
+ 
+
+ align:start position:0%
+we're sending in the class actual class
+meter. time signature we could also put
+
+ align:start position:0%
+meter. time signature we could also put
+ 
+
+ align:start position:0%
+meter. time signature we could also put
+in the um strin time signature doesn't
+
+ align:start position:0%
+in the um strin time signature doesn't
+ 
+
+ align:start position:0%
+in the um strin time signature doesn't
+matter either way there um but this
+
+ align:start position:0%
+matter either way there um but this
+ 
+
+ align:start position:0%
+matter either way there um but this
+actually doesn't get us the first meter
+
+ align:start position:0%
+actually doesn't get us the first meter
+ 
+
+ align:start position:0%
+actually doesn't get us the first meter
+this gets us all the meters and so if
+
+ align:start position:0%
+this gets us all the meters and so if
+ 
+
+ align:start position:0%
+this gets us all the meters and so if
+there are no
+
+ align:start position:0%
+there are no
+ 
+
+ align:start position:0%
+there are no
+meters that says if there's not a single
+
+ align:start position:0%
+meters that says if there's not a single
+ 
+
+ align:start position:0%
+meters that says if there's not a single
+one return that we'll call First
+
+ align:start position:0%
+one return that we'll call First
+ 
+
+ align:start position:0%
+one return that we'll call First
+meter the first of all meters so of
+
+ align:start position:0%
+meter the first of all meters so of
+ 
+
+ align:start position:0%
+meter the first of all meters so of
+course it's number zero now that's
+
+ align:start position:0%
+course it's number zero now that's
+ 
+
+ align:start position:0%
+course it's number zero now that's
+should be there now extract meter Bo
+
+ align:start position:0%
+should be there now extract meter Bo
+ 
+
+ align:start position:0%
+should be there now extract meter Bo
+fantastic returns four comma
+
+ align:start position:0%
+fantastic returns four comma
+ 
+
+ align:start position:0%
+fantastic returns four comma
+4 so why would we want to extract the
+
+ align:start position:0%
+4 so why would we want to extract the
+ 
+
+ align:start position:0%
+4 so why would we want to extract the
+meter as two numbers as part of future
+
+ align:start position:0%
+meter as two numbers as part of future
+ 
+
+ align:start position:0%
+meter as two numbers as part of future
+extraction we might do it as part of a
+
+ align:start position:0%
+extraction we might do it as part of a
+ 
+
+ align:start position:0%
+extraction we might do it as part of a
+series of features in order to make a
+
+ align:start position:0%
+series of features in order to make a
+ 
+
+ align:start position:0%
+series of features in order to make a
+prediction about a piece let's say we
+
+ align:start position:0%
+prediction about a piece let's say we
+ 
+
+ align:start position:0%
+prediction about a piece let's say we
+wanted to predict if a piece of music is
+
+ align:start position:0%
+wanted to predict if a piece of music is
+ 
+
+ align:start position:0%
+wanted to predict if a piece of music is
+a waltz or not so we might first think
+
+ align:start position:0%
+a waltz or not so we might first think
+ 
+
+ align:start position:0%
+a waltz or not so we might first think
+is this a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+waltz or is this a Walts
+
+ align:start position:0%
+waltz or is this a Walts
+ 
+
+ align:start position:0%
+waltz or is this a Walts
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+is this a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Walts so what makes something a Walts
+
+ align:start position:0%
+Walts so what makes something a Walts
+ 
+
+ align:start position:0%
+Walts so what makes something a Walts
+well it probably has something to do
+
+ align:start position:0%
+well it probably has something to do
+ 
+
+ align:start position:0%
+well it probably has something to do
+with a meter we fortunately already have
+
+ align:start position:0%
+with a meter we fortunately already have
+ 
+
+ align:start position:0%
+with a meter we fortunately already have
+a meter extraction for types cure for
+
+ align:start position:0%
+a meter extraction for types cure for
+ 
+
+ align:start position:0%
+a meter extraction for types cure for
+the piece and now we can use this to try
+
+ align:start position:0%
+the piece and now we can use this to try
+ 
+
+ align:start position:0%
+the piece and now we can use this to try
+to figure out if something is a Walter
+
+ align:start position:0%
+to figure out if something is a Walter
+ 
+
+ align:start position:0%
+to figure out if something is a Walter
+not so we would assume that the
+
+ align:start position:0%
+not so we would assume that the
+ 
+
+ align:start position:0%
+not so we would assume that the
+prevailing time signature in a piece and
+
+ align:start position:0%
+prevailing time signature in a piece and
+ 
+
+ align:start position:0%
+prevailing time signature in a piece and
+the opening time signature in a piece if
+
+ align:start position:0%
+the opening time signature in a piece if
+ 
+
+ align:start position:0%
+the opening time signature in a piece if
+it's a Walt would be 34 and therefore
+
+ align:start position:0%
+it's a Walt would be 34 and therefore
+ 
+
+ align:start position:0%
+it's a Walt would be 34 and therefore
+our extraction should be 3 comma
+
+ align:start position:0%
+our extraction should be 3 comma
+ 
+
+ align:start position:0%
+our extraction should be 3 comma
+4 that is the worst assumption ever the
+
+ align:start position:0%
+4 that is the worst assumption ever the
+ 
+
+ align:start position:0%
+4 that is the worst assumption ever the
+most famous Walts of all time Johan
+
+ align:start position:0%
+most famous Walts of all time Johan
+ 
+
+ align:start position:0%
+most famous Walts of all time Johan
+truss's blue Dan Waltz which you just
+
+ align:start position:0%
+truss's blue Dan Waltz which you just
+ 
+
+ align:start position:0%
+truss's blue Dan Waltz which you just
+heard doesn't start in 34 it starts with
+
+ align:start position:0%
+heard doesn't start in 34 it starts with
+ 
+
+ align:start position:0%
+heard doesn't start in 34 it starts with
+a slow introduction in 68
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time I happen to have a random Waltz on
+
+ align:start position:0%
+time I happen to have a random Waltz on
+ 
+
+ align:start position:0%
+time I happen to have a random Waltz on
+my computer it's Yan strauss's Waltz
+
+ align:start position:0%
+my computer it's Yan strauss's Waltz
+ 
+
+ align:start position:0%
+my computer it's Yan strauss's Waltz
+called on the blue denu it's not in the
+
+ align:start position:0%
+called on the blue denu it's not in the
+ 
+
+ align:start position:0%
+called on the blue denu it's not in the
+music 21 Corpus but it's instead on my
+
+ align:start position:0%
+music 21 Corpus but it's instead on my
+ 
+
+ align:start position:0%
+music 21 Corpus but it's instead on my
+hard drive on my desktop so I'll need to
+
+ align:start position:0%
+hard drive on my desktop so I'll need to
+ 
+
+ align:start position:0%
+hard drive on my desktop so I'll need to
+import the converter module from music
+
+ align:start position:0%
+import the converter module from music
+ 
+
+ align:start position:0%
+import the converter module from music
+21 I mean it's just a wrapper around
+
+ align:start position:0%
+21 I mean it's just a wrapper around
+ 
+
+ align:start position:0%
+21 I mean it's just a wrapper around
+loading things and stuff and now instead
+
+ align:start position:0%
+loading things and stuff and now instead
+ 
+
+ align:start position:0%
+loading things and stuff and now instead
+of using Corpus parse I'll use converter
+
+ align:start position:0%
+of using Corpus parse I'll use converter
+ 
+
+ align:start position:0%
+of using Corpus parse I'll use converter
+dopar I'll give um the full file name to
+
+ align:start position:0%
+dopar I'll give um the full file name to
+ 
+
+ align:start position:0%
+dopar I'll give um the full file name to
+file path to my um to my
+
+ align:start position:0%
+file path to my um to my
+ 
+
+ align:start position:0%
+file path to my um to my
+Walts it's a music XML
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+file oh great so the guy who's making
+
+ align:start position:0%
+file oh great so the guy who's making
+ 
+
+ align:start position:0%
+file oh great so the guy who's making
+this recording just goes online grabs a
+
+ align:start position:0%
+this recording just goes online grabs a
+ 
+
+ align:start position:0%
+this recording just goes online grabs a
+random music XML copy of the blue danu
+
+ align:start position:0%
+random music XML copy of the blue danu
+ 
+
+ align:start position:0%
+random music XML copy of the blue danu
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+internet and this version skips the
+
+ align:start position:0%
+internet and this version skips the
+ 
+
+ align:start position:0%
+internet and this version skips the
+introduction completely so it has 34
+
+ align:start position:0%
+introduction completely so it has 34
+ 
+
+ align:start position:0%
+introduction completely so it has 34
+when it should have gotten 68 so it's
+
+ align:start position:0%
+when it should have gotten 68 so it's
+ 
+
+ align:start position:0%
+when it should have gotten 68 so it's
+going to get the right answer but for
+
+ align:start position:0%
+going to get the right answer but for
+ 
+
+ align:start position:0%
+going to get the right answer but for
+all the wrong reasons have you ever
+
+ align:start position:0%
+all the wrong reasons have you ever
+ 
+
+ align:start position:0%
+all the wrong reasons have you ever
+heard the expression goo garbage in
+
+ align:start position:0%
+heard the expression goo garbage in
+ 
+
+ align:start position:0%
+heard the expression goo garbage in
+equals garbage
+
+ align:start position:0%
+equals garbage
+ 
+
+ align:start position:0%
+equals garbage
+out let's not do that in our own work
+
+ align:start position:0%
+out let's not do that in our own work
+ 
+
+ align:start position:0%
+out let's not do that in our own work
+what we're learning from in this
+
+ align:start position:0%
+what we're learning from in this
+ 
+
+ align:start position:0%
+what we're learning from in this
+tutorial let's instead make the world of
+
+ align:start position:0%
+tutorial let's instead make the world of
+ 
+
+ align:start position:0%
+tutorial let's instead make the world of
+artificial intelligence a better place
+
+ align:start position:0%
+artificial intelligence a better place
+ 
+
+ align:start position:0%
+artificial intelligence a better place
+and always check whether our training
+
+ align:start position:0%
+and always check whether our training
+ 
+
+ align:start position:0%
+and always check whether our training
+data is correct whether this is actually
+
+ align:start position:0%
+data is correct whether this is actually
+ 
+
+ align:start position:0%
+data is correct whether this is actually
+a score of the Blue danu rather than
+
+ align:start position:0%
+a score of the Blue danu rather than
+ 
+
+ align:start position:0%
+a score of the Blue danu rather than
+just the main theme of it let's check
+
+ align:start position:0%
+just the main theme of it let's check
+ 
+
+ align:start position:0%
+just the main theme of it let's check
+things like this before we use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it great so it's in 34 so our extract
+
+ align:start position:0%
+it great so it's in 34 so our extract
+ 
+
+ align:start position:0%
+it great so it's in 34 so our extract
+meter function is going to return 34
+
+ align:start position:0%
+meter function is going to return 34
+ 
+
+ align:start position:0%
+meter function is going to return 34
+let's try that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops sorry don't give the answer give
+
+ align:start position:0%
+oops sorry don't give the answer give
+ 
+
+ align:start position:0%
+oops sorry don't give the answer give
+the question there we go so now we have
+
+ align:start position:0%
+the question there we go so now we have
+ 
+
+ align:start position:0%
+the question there we go so now we have
+our first feature that might help
+
+ align:start position:0%
+our first feature that might help
+ 
+
+ align:start position:0%
+our first feature that might help
+identify a Walt it's Tim
+
+ align:start position:0%
+identify a Walt it's Tim
+ 
+
+ align:start position:0%
+identify a Walt it's Tim
+signature now let's do something a
+
+ align:start position:0%
+signature now let's do something a
+ 
+
+ align:start position:0%
+signature now let's do something a
+little bit more advanced and let's let's
+
+ align:start position:0%
+little bit more advanced and let's let's
+ 
+
+ align:start position:0%
+little bit more advanced and let's let's
+look at this piece and see H is there
+
+ align:start position:0%
+look at this piece and see H is there
+ 
+
+ align:start position:0%
+look at this piece and see H is there
+anything that seems to happen pretty
+
+ align:start position:0%
+anything that seems to happen pretty
+ 
+
+ align:start position:0%
+anything that seems to happen pretty
+often well it looks like the last beat
+
+ align:start position:0%
+often well it looks like the last beat
+ 
+
+ align:start position:0%
+often well it looks like the last beat
+beat three of the piece or offset two is
+
+ align:start position:0%
+beat three of the piece or offset two is
+ 
+
+ align:start position:0%
+beat three of the piece or offset two is
+more often higher than offset one I
+
+ align:start position:0%
+more often higher than offset one I
+ 
+
+ align:start position:0%
+more often higher than offset one I
+don't know if that's true but that that
+
+ align:start position:0%
+don't know if that's true but that that
+ 
+
+ align:start position:0%
+don't know if that's true but that that
+looks like something that's a
+
+ align:start position:0%
+looks like something that's a
+ 
+
+ align:start position:0%
+looks like something that's a
+possibility so we'll create sort of a
+
+ align:start position:0%
+possibility so we'll create sort of a
+ 
+
+ align:start position:0%
+possibility so we'll create sort of a
+more sophisticated feature extractor
+
+ align:start position:0%
+more sophisticated feature extractor
+ 
+
+ align:start position:0%
+more sophisticated feature extractor
+which uh Returns the proportion of all
+
+ align:start position:0%
+which uh Returns the proportion of all
+ 
+
+ align:start position:0%
+which uh Returns the proportion of all
+the measures where beat 3 is above beat
+
+ align:start position:0%
+the measures where beat 3 is above beat
+ 
+
+ align:start position:0%
+the measures where beat 3 is above beat
+1 first we'll make the assumption that
+
+ align:start position:0%
+1 first we'll make the assumption that
+ 
+
+ align:start position:0%
+1 first we'll make the assumption that
+beat 1 is always at offset zero and beat
+
+ align:start position:0%
+beat 1 is always at offset zero and beat
+ 
+
+ align:start position:0%
+beat 1 is always at offset zero and beat
+3 is at offset to these aren't very good
+
+ align:start position:0%
+3 is at offset to these aren't very good
+ 
+
+ align:start position:0%
+3 is at offset to these aren't very good
+assumptions uh but maybe together with
+
+ align:start position:0%
+assumptions uh but maybe together with
+ 
+
+ align:start position:0%
+assumptions uh but maybe together with
+searching for meter they'll too will
+
+ align:start position:0%
+searching for meter they'll too will
+ 
+
+ align:start position:0%
+searching for meter they'll too will
+make a good case for whether something
+
+ align:start position:0%
+make a good case for whether something
+ 
+
+ align:start position:0%
+make a good case for whether something
+is a waltz or not so here we go uh if
+
+ align:start position:0%
+is a waltz or not so here we go uh if
+ 
+
+ align:start position:0%
+is a waltz or not so here we go uh if
+we're going to we're going to eventually
+
+ align:start position:0%
+we're going to we're going to eventually
+ 
+
+ align:start position:0%
+we're going to we're going to eventually
+write something uh proportion uh prop
+
+ align:start position:0%
+write something uh proportion uh prop
+ 
+
+ align:start position:0%
+write something uh proportion uh prop
+proportion of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bat3 above beat one which is going to
+
+ align:start position:0%
+bat3 above beat one which is going to
+ 
+
+ align:start position:0%
+bat3 above beat one which is going to
+take a score stream stream and it's
+
+ align:start position:0%
+take a score stream stream and it's
+ 
+
+ align:start position:0%
+take a score stream stream and it's
+going to return a float because it's a
+
+ align:start position:0%
+going to return a float because it's a
+ 
+
+ align:start position:0%
+going to return a float because it's a
+proportion and I'll just say pass now
+
+ align:start position:0%
+proportion and I'll just say pass now
+ 
+
+ align:start position:0%
+proportion and I'll just say pass now
+because in order to write this of of
+
+ align:start position:0%
+because in order to write this of of
+ 
+
+ align:start position:0%
+because in order to write this of of
+course uh we're going to need something
+
+ align:start position:0%
+course uh we're going to need something
+ 
+
+ align:start position:0%
+course uh we're going to need something
+that figures out for any given measure
+
+ align:start position:0%
+that figures out for any given measure
+ 
+
+ align:start position:0%
+that figures out for any given measure
+if beat 3 is above beat
+
+ align:start position:0%
+if beat 3 is above beat
+ 
+
+ align:start position:0%
+if beat 3 is above beat
+one for a single measure for one measure
+
+ align:start position:0%
+one for a single measure for one measure
+ 
+
+ align:start position:0%
+one for a single measure for one measure
+so we'll take an M which will be a
+
+ align:start position:0%
+so we'll take an M which will be a
+ 
+
+ align:start position:0%
+so we'll take an M which will be a
+stream. measure and this is going to
+
+ align:start position:0%
+stream. measure and this is going to
+ 
+
+ align:start position:0%
+stream. measure and this is going to
+return true or false oops it's going to
+
+ align:start position:0%
+return true or false oops it's going to
+ 
+
+ align:start position:0%
+return true or false oops it's going to
+return true or false someday we going to
+
+ align:start position:0%
+return true or false someday we going to
+ 
+
+ align:start position:0%
+return true or false someday we going to
+have an incredible production crew
+
+ align:start position:0%
+have an incredible production crew
+ 
+
+ align:start position:0%
+have an incredible production crew
+that's going to edit out all these
+
+ align:start position:0%
+that's going to edit out all these
+ 
+
+ align:start position:0%
+that's going to edit out all these
+mistakes but I don't have that yet so
+
+ align:start position:0%
+mistakes but I don't have that yet so
+ 
+
+ align:start position:0%
+mistakes but I don't have that yet so
+we'll say that measures notes are get
+
+ align:start position:0%
+we'll say that measures notes are get
+ 
+
+ align:start position:0%
+we'll say that measures notes are get
+all the elements by class note and that
+
+ align:start position:0%
+all the elements by class note and that
+ 
+
+ align:start position:0%
+all the elements by class note and that
+returns this stream iterator for now I'm
+
+ align:start position:0%
+returns this stream iterator for now I'm
+ 
+
+ align:start position:0%
+returns this stream iterator for now I'm
+going to say recast that stream iterator
+
+ align:start position:0%
+going to say recast that stream iterator
+ 
+
+ align:start position:0%
+going to say recast that stream iterator
+as another stream uh you can do this
+
+ align:start position:0%
+as another stream uh you can do this
+ 
+
+ align:start position:0%
+as another stream uh you can do this
+with any of the get something bu
+
+ align:start position:0%
+with any of the get something bu
+ 
+
+ align:start position:0%
+with any of the get something bu
+something uh classes in music 21 great
+
+ align:start position:0%
+something uh classes in music 21 great
+ 
+
+ align:start position:0%
+something uh classes in music 21 great
+so within this is now a stream of just
+
+ align:start position:0%
+so within this is now a stream of just
+ 
+
+ align:start position:0%
+so within this is now a stream of just
+nothing but notes and so I can say the
+
+ align:start position:0%
+nothing but notes and so I can say the
+ 
+
+ align:start position:0%
+nothing but notes and so I can say the
+first notes are those notes
+
+ align:start position:0%
+first notes are those notes
+ 
+
+ align:start position:0%
+first notes are those notes
+that appear at an offset
+
+ align:start position:0%
+that appear at an offset
+ 
+
+ align:start position:0%
+that appear at an offset
+zero and if there's no note there return
+
+ align:start position:0%
+zero and if there's no note there return
+ 
+
+ align:start position:0%
+zero and if there's no note there return
+fulse great now we'll check bat3 notes
+
+ align:start position:0%
+fulse great now we'll check bat3 notes
+ 
+
+ align:start position:0%
+fulse great now we'll check bat3 notes
+are those
+
+ align:start position:0%
+are those
+ 
+
+ align:start position:0%
+are those
+notes
+
+ align:start position:0%
+notes
+ 
+
+ align:start position:0%
+notes
+that are at offset 2 and that began at
+
+ align:start position:0%
+that are at offset 2 and that began at
+ 
+
+ align:start position:0%
+that are at offset 2 and that began at
+offset 2 so that should work pretty well
+
+ align:start position:0%
+offset 2 so that should work pretty well
+ 
+
+ align:start position:0%
+offset 2 so that should work pretty well
+and if there's no note
+
+ align:start position:0%
+and if there's no note
+ 
+
+ align:start position:0%
+and if there's no note
+that satisfies that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition we're going to return false
+
+ align:start position:0%
+condition we're going to return false
+ 
+
+ align:start position:0%
+condition we're going to return false
+again but what if there is more than one
+
+ align:start position:0%
+again but what if there is more than one
+ 
+
+ align:start position:0%
+again but what if there is more than one
+note at the beginning of the measure or
+
+ align:start position:0%
+note at the beginning of the measure or
+ 
+
+ align:start position:0%
+note at the beginning of the measure or
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+bat3 so we have to make sure that first
+
+ align:start position:0%
+bat3 so we have to make sure that first
+ 
+
+ align:start position:0%
+bat3 so we have to make sure that first
+note is the first of the beat3
+
+ align:start position:0%
+note is the first of the beat3
+ 
+
+ align:start position:0%
+note is the first of the beat3
+notes and the beat3 note not is the
+
+ align:start position:0%
+notes and the beat3 note not is the
+ 
+
+ align:start position:0%
+notes and the beat3 note not is the
+first of the beat3 notes not the third
+
+ align:start position:0%
+first of the beat3 notes not the third
+ 
+
+ align:start position:0%
+first of the beat3 notes not the third
+the first now we'll go ahead and say if
+
+ align:start position:0%
+the first now we'll go ahead and say if
+ 
+
+ align:start position:0%
+the first now we'll go ahead and say if
+the first note pitch is lower and we're
+
+ align:start position:0%
+the first note pitch is lower and we're
+ 
+
+ align:start position:0%
+the first note pitch is lower and we're
+going to measure the pitch by pitch
+
+ align:start position:0%
+going to measure the pitch by pitch
+ 
+
+ align:start position:0%
+going to measure the pitch by pitch
+space or midi number uh is less than the
+
+ align:start position:0%
+space or midi number uh is less than the
+ 
+
+ align:start position:0%
+space or midi number uh is less than the
+beat3
+
+ align:start position:0%
+beat3
+ 
+
+ align:start position:0%
+beat3
+notes pit space will return false
+
+ align:start position:0%
+notes pit space will return false
+ 
+
+ align:start position:0%
+notes pit space will return false
+otherwise we're going to return true
+
+ align:start position:0%
+otherwise we're going to return true
+ 
+
+ align:start position:0%
+otherwise we're going to return true
+um great we'll let's be good we'll make
+
+ align:start position:0%
+um great we'll let's be good we'll make
+ 
+
+ align:start position:0%
+um great we'll let's be good we'll make
+this a second thing we'll put cut and
+
+ align:start position:0%
+this a second thing we'll put cut and
+ 
+
+ align:start position:0%
+this a second thing we'll put cut and
+paste that there Meanwhile we're going
+
+ align:start position:0%
+paste that there Meanwhile we're going
+ 
+
+ align:start position:0%
+paste that there Meanwhile we're going
+to um let's write a little test on this
+
+ align:start position:0%
+to um let's write a little test on this
+ 
+
+ align:start position:0%
+to um let's write a little test on this
+so we have blue um let's get measure
+
+ align:start position:0%
+so we have blue um let's get measure
+ 
+
+ align:start position:0%
+so we have blue um let's get measure
+zero so
+
+ align:start position:0%
+zero so
+ 
+
+ align:start position:0%
+zero so
+m0 actually it's measure one so blue.
+
+ align:start position:0%
+m0 actually it's measure one so blue.
+ 
+
+ align:start position:0%
+m0 actually it's measure one so blue.
+measure one and we'll
+
+ align:start position:0%
+measure one and we'll
+ 
+
+ align:start position:0%
+measure one and we'll
+see is
+
+ align:start position:0%
+see is
+ 
+
+ align:start position:0%
+see is
+beat3 above beat 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little elements
+
+ align:start position:0%
+little elements
+ 
+
+ align:start position:0%
+little elements
+you so this
+
+ align:start position:0%
+you so this
+ 
+
+ align:start position:0%
+you so this
+fight this is why we test things great
+
+ align:start position:0%
+fight this is why we test things great
+ 
+
+ align:start position:0%
+fight this is why we test things great
+is beat three above beat one in
+
+ align:start position:0%
+is beat three above beat one in
+ 
+
+ align:start position:0%
+is beat three above beat one in
+measure one actually is
+
+ align:start position:0%
+measure one actually is
+ 
+
+ align:start position:0%
+measure one actually is
+huh oh I know what it is we have a
+
+ align:start position:0%
+huh oh I know what it is we have a
+ 
+
+ align:start position:0%
+huh oh I know what it is we have a
+reverse of a sign it if this pitch is
+
+ align:start position:0%
+reverse of a sign it if this pitch is
+ 
+
+ align:start position:0%
+reverse of a sign it if this pitch is
+greater than or equal then we returned
+
+ align:start position:0%
+greater than or equal then we returned
+ 
+
+ align:start position:0%
+greater than or equal then we returned
+false actually if it's yeah the equal
+
+ align:start position:0%
+false actually if it's yeah the equal
+ 
+
+ align:start position:0%
+false actually if it's yeah the equal
+sign there and now that's working
+
+ align:start position:0%
+sign there and now that's working
+ 
+
+ align:start position:0%
+sign there and now that's working
+measure two should be true also measure
+
+ align:start position:0%
+measure two should be true also measure
+ 
+
+ align:start position:0%
+measure two should be true also measure
+three should be false let's make sure
+
+ align:start position:0%
+three should be false let's make sure
+ 
+
+ align:start position:0%
+three should be false let's make sure
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+works yep and false great so that seems
+
+ align:start position:0%
+works yep and false great so that seems
+ 
+
+ align:start position:0%
+works yep and false great so that seems
+to be working um here's the irony uh
+
+ align:start position:0%
+to be working um here's the irony uh
+ 
+
+ align:start position:0%
+to be working um here's the irony uh
+actually except for the fact that our
+
+ align:start position:0%
+actually except for the fact that our
+ 
+
+ align:start position:0%
+actually except for the fact that our
+label would be completely wrong uh
+
+ align:start position:0%
+label would be completely wrong uh
+ 
+
+ align:start position:0%
+label would be completely wrong uh
+having every single thing that should be
+
+ align:start position:0%
+having every single thing that should be
+ 
+
+ align:start position:0%
+having every single thing that should be
+false be true and true be false probably
+
+ align:start position:0%
+false be true and true be false probably
+ 
+
+ align:start position:0%
+false be true and true be false probably
+wouldn't change our answers very much
+
+ align:start position:0%
+wouldn't change our answers very much
+ 
+
+ align:start position:0%
+wouldn't change our answers very much
+but who knows we call this is beat three
+
+ align:start position:0%
+but who knows we call this is beat three
+ 
+
+ align:start position:0%
+but who knows we call this is beat three
+above beat one in one
+
+ align:start position:0%
+above beat one in one
+ 
+
+ align:start position:0%
+above beat one in one
+measure it better do what it says okay
+
+ align:start position:0%
+measure it better do what it says okay
+ 
+
+ align:start position:0%
+measure it better do what it says okay
+great now we're going to get the
+
+ align:start position:0%
+great now we're going to get the
+ 
+
+ align:start position:0%
+great now we're going to get the
+proportion that is U the proportion of
+
+ align:start position:0%
+proportion that is U the proportion of
+ 
+
+ align:start position:0%
+proportion that is U the proportion of
+measures in this piece where B3 is above
+
+ align:start position:0%
+measures in this piece where B3 is above
+ 
+
+ align:start position:0%
+measures in this piece where B3 is above
+B1 so
+
+ align:start position:0%
+B1 so
+ 
+
+ align:start position:0%
+B1 so
+we'll keep track of the total number of
+
+ align:start position:0%
+we'll keep track of the total number of
+ 
+
+ align:start position:0%
+we'll keep track of the total number of
+measures equals z the total we'll call
+
+ align:start position:0%
+measures equals z the total we'll call
+ 
+
+ align:start position:0%
+measures equals z the total we'll call
+them Walts like measures those where
+
+ align:start position:0%
+them Walts like measures those where
+ 
+
+ align:start position:0%
+them Walts like measures those where
+beat 3 is above beat one we'll call it
+
+ align:start position:0%
+beat 3 is above beat one we'll call it
+ 
+
+ align:start position:0%
+beat 3 is above beat one we'll call it
+zero for every measure in the score
+
+ align:start position:0%
+zero for every measure in the score
+ 
+
+ align:start position:0%
+zero for every measure in the score
+recurse get Elements by class
+
+ align:start position:0%
+recurse get Elements by class
+ 
+
+ align:start position:0%
+recurse get Elements by class
+measure um there's a reason why we'll
+
+ align:start position:0%
+measure um there's a reason why we'll
+ 
+
+ align:start position:0%
+measure um there's a reason why we'll
+use get Elements by class measure
+
+ align:start position:0%
+use get Elements by class measure
+ 
+
+ align:start position:0%
+use get Elements by class measure
+instead of measure 0 1 2 3 so mostly to
+
+ align:start position:0%
+instead of measure 0 1 2 3 so mostly to
+ 
+
+ align:start position:0%
+instead of measure 0 1 2 3 so mostly to
+do with the fact that sometimes there's
+
+ align:start position:0%
+do with the fact that sometimes there's
+ 
+
+ align:start position:0%
+do with the fact that sometimes there's
+two measure 3es or they're missing
+
+ align:start position:0%
+two measure 3es or they're missing
+ 
+
+ align:start position:0%
+two measure 3es or they're missing
+Measure 11 or something like that with
+
+ align:start position:0%
+Measure 11 or something like that with
+ 
+
+ align:start position:0%
+Measure 11 or something like that with
+there's measure 5 a and 5B if there's a
+
+ align:start position:0%
+there's measure 5 a and 5B if there's a
+ 
+
+ align:start position:0%
+there's measure 5 a and 5B if there's a
+first ending or something like that
+
+ align:start position:0%
+first ending or something like that
+ 
+
+ align:start position:0%
+first ending or something like that
+anyhow so we're going for every measure
+
+ align:start position:0%
+anyhow so we're going for every measure
+ 
+
+ align:start position:0%
+anyhow so we're going for every measure
+we increment the total number of
+
+ align:start position:0%
+we increment the total number of
+ 
+
+ align:start position:0%
+we increment the total number of
+measures by one and now um we look at
+
+ align:start position:0%
+measures by one and now um we look at
+ 
+
+ align:start position:0%
+measures by one and now um we look at
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure and we say if that's true then
+
+ align:start position:0%
+measure and we say if that's true then
+ 
+
+ align:start position:0%
+measure and we say if that's true then
+the total Walts
+
+ align:start position:0%
+the total Walts
+ 
+
+ align:start position:0%
+the total Walts
+like measures plus equal one and we're
+
+ align:start position:0%
+like measures plus equal one and we're
+ 
+
+ align:start position:0%
+like measures plus equal one and we're
+going to return the
+
+ align:start position:0%
+going to return the
+ 
+
+ align:start position:0%
+going to return the
+total WTS like measures divided by the
+
+ align:start position:0%
+total WTS like measures divided by the
+ 
+
+ align:start position:0%
+total WTS like measures divided by the
+total measures
+
+ align:start position:0%
+total measures
+ 
+
+ align:start position:0%
+total measures
+uh we're coding pretty fast so we'll
+
+ align:start position:0%
+uh we're coding pretty fast so we'll
+ 
+
+ align:start position:0%
+uh we're coding pretty fast so we'll
+just put as a to-do later um what if
+
+ align:start position:0%
+just put as a to-do later um what if
+ 
+
+ align:start position:0%
+just put as a to-do later um what if
+there are no total measures always make
+
+ align:start position:0%
+there are no total measures always make
+ 
+
+ align:start position:0%
+there are no total measures always make
+sure that we don't do a division by zero
+
+ align:start position:0%
+sure that we don't do a division by zero
+ 
+
+ align:start position:0%
+sure that we don't do a division by zero
+measure uh error but that can be a later
+
+ align:start position:0%
+measure uh error but that can be a later
+ 
+
+ align:start position:0%
+measure uh error but that can be a later
+thing so let's check this um
+
+ align:start position:0%
+thing so let's check this um
+ 
+
+ align:start position:0%
+thing so let's check this um
+proportion of beat 3
+
+ align:start position:0%
+proportion of beat 3
+ 
+
+ align:start position:0%
+proportion of beat 3
+above beat one in the blue danu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+26% not really true seems a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low one two
+
+ align:start position:0%
+low one two
+ 
+
+ align:start position:0%
+low one two
+down well we'll check that later turns
+
+ align:start position:0%
+down well we'll check that later turns
+ 
+
+ align:start position:0%
+down well we'll check that later turns
+out it's not not that bad and BWB U
+
+ align:start position:0%
+out it's not not that bad and BWB U
+ 
+
+ align:start position:0%
+out it's not not that bad and BWB U
+sorry Buck CL this time it's actually
+
+ align:start position:0%
+sorry Buck CL this time it's actually
+ 
+
+ align:start position:0%
+sorry Buck CL this time it's actually
+even a little bit more interesting okay
+
+ align:start position:0%
+even a little bit more interesting okay
+ 
+
+ align:start position:0%
+even a little bit more interesting okay
+so in any case this is a feature we've
+
+ align:start position:0%
+so in any case this is a feature we've
+ 
+
+ align:start position:0%
+so in any case this is a feature we've
+just defined this particular feature
+
+ align:start position:0%
+just defined this particular feature
+ 
+
+ align:start position:0%
+just defined this particular feature
+figures out how often beat 3 is above
+
+ align:start position:0%
+figures out how often beat 3 is above
+ 
+
+ align:start position:0%
+figures out how often beat 3 is above
+beat one great what we can do now is
+
+ align:start position:0%
+beat one great what we can do now is
+ 
+
+ align:start position:0%
+beat one great what we can do now is
+these are individual features let's
+
+ align:start position:0%
+these are individual features let's
+ 
+
+ align:start position:0%
+these are individual features let's
+create something that does chains a
+
+ align:start position:0%
+create something that does chains a
+ 
+
+ align:start position:0%
+create something that does chains a
+whole bunch of features together well
+
+ align:start position:0%
+whole bunch of features together well
+ 
+
+ align:start position:0%
+whole bunch of features together well
+not this one whole bunch of features
+
+ align:start position:0%
+not this one whole bunch of features
+ 
+
+ align:start position:0%
+not this one whole bunch of features
+we'll
+
+ align:start position:0%
+we'll
+ 
+
+ align:start position:0%
+we'll
+get four features so we'll
+
+ align:start position:0%
+get four features so we'll
+ 
+
+ align:start position:0%
+get four features so we'll
+say our feature
+
+ align:start position:0%
+say our feature
+ 
+
+ align:start position:0%
+say our feature
+extractor will take in a
+
+ align:start position:0%
+extractor will take in a
+ 
+
+ align:start position:0%
+extractor will take in a
+score and it's going to return a tupple
+
+ align:start position:0%
+score and it's going to return a tupple
+ 
+
+ align:start position:0%
+score and it's going to return a tupple
+of a string an INT an INT a float and a
+
+ align:start position:0%
+of a string an INT an INT a float and a
+ 
+
+ align:start position:0%
+of a string an INT an INT a float and a
+b end okay what the heck what are these
+
+ align:start position:0%
+b end okay what the heck what are these
+ 
+
+ align:start position:0%
+b end okay what the heck what are these
+things going to be so first what we're
+
+ align:start position:0%
+things going to be so first what we're
+ 
+
+ align:start position:0%
+things going to be so first what we're
+going to do is we're going to take in
+
+ align:start position:0%
+going to do is we're going to take in
+ 
+
+ align:start position:0%
+going to do is we're going to take in
+score and we're going to
+
+ align:start position:0%
+score and we're going to
+ 
+
+ align:start position:0%
+score and we're going to
+um well we're going to say the file
+
+ align:start position:0%
+um well we're going to say the file
+ 
+
+ align:start position:0%
+um well we're going to say the file
+name of the score is going to be that
+
+ align:start position:0%
+name of the score is going to be that
+ 
+
+ align:start position:0%
+name of the score is going to be that
+first string um and you can get the file
+
+ align:start position:0%
+first string um and you can get the file
+ 
+
+ align:start position:0%
+first string um and you can get the file
+name from any music 21 core by getting
+
+ align:start position:0%
+name from any music 21 core by getting
+ 
+
+ align:start position:0%
+name from any music 21 core by getting
+his file path which is a path lip and
+
+ align:start position:0%
+his file path which is a path lip and
+ 
+
+ align:start position:0%
+his file path which is a path lip and
+getting the name which gets rid of all
+
+ align:start position:0%
+getting the name which gets rid of all
+ 
+
+ align:start position:0%
+getting the name which gets rid of all
+the directories and stuff great so we'll
+
+ align:start position:0%
+the directories and stuff great so we'll
+ 
+
+ align:start position:0%
+the directories and stuff great so we'll
+get the file name of something and we'll
+
+ align:start position:0%
+get the file name of something and we'll
+ 
+
+ align:start position:0%
+get the file name of something and we'll
+get the next thing we're going to get
+
+ align:start position:0%
+get the next thing we're going to get
+ 
+
+ align:start position:0%
+get the next thing we're going to get
+these two ins which are going to be the
+
+ align:start position:0%
+these two ins which are going to be the
+ 
+
+ align:start position:0%
+these two ins which are going to be the
+meter so we'll say the meter
+
+ align:start position:0%
+meter so we'll say the meter
+ 
+
+ align:start position:0%
+meter so we'll say the meter
+feature is where I get that from
+
+ align:start position:0%
+feature is where I get that from
+ 
+
+ align:start position:0%
+feature is where I get that from
+extract extract meter on that
+
+ align:start position:0%
+extract extract meter on that
+ 
+
+ align:start position:0%
+extract extract meter on that
+score next we're going to get this float
+
+ align:start position:0%
+score next we're going to get this float
+ 
+
+ align:start position:0%
+score next we're going to get this float
+which is going to be the beat 3
+
+ align:start position:0%
+which is going to be the beat 3
+ 
+
+ align:start position:0%
+which is going to be the beat 3
+feature so we'll get the beat3
+
+ align:start position:0%
+feature so we'll get the beat3
+ 
+
+ align:start position:0%
+feature so we'll get the beat3
+feature is the proportion propor sh why
+
+ align:start position:0%
+feature is the proportion propor sh why
+ 
+
+ align:start position:0%
+feature is the proportion propor sh why
+do I keep doing this beat three above
+
+ align:start position:0%
+do I keep doing this beat three above
+ 
+
+ align:start position:0%
+do I keep doing this beat three above
+beat one for that score great super oops
+
+ align:start position:0%
+beat one for that score great super oops
+ 
+
+ align:start position:0%
+beat one for that score great super oops
+I hit shift enter then we want to get
+
+ align:start position:0%
+I hit shift enter then we want to get
+ 
+
+ align:start position:0%
+I hit shift enter then we want to get
+the Boolean what we're going to do is if
+
+ align:start position:0%
+the Boolean what we're going to do is if
+ 
+
+ align:start position:0%
+the Boolean what we're going to do is if
+we're training a data set we're going to
+
+ align:start position:0%
+we're training a data set we're going to
+ 
+
+ align:start position:0%
+we're training a data set we're going to
+know whether or not something is a waltz
+
+ align:start position:0%
+know whether or not something is a waltz
+ 
+
+ align:start position:0%
+know whether or not something is a waltz
+so we'll say that Boolean is going to be
+
+ align:start position:0%
+so we'll say that Boolean is going to be
+ 
+
+ align:start position:0%
+so we'll say that Boolean is going to be
+true or false on whether something is a
+
+ align:start position:0%
+true or false on whether something is a
+ 
+
+ align:start position:0%
+true or false on whether something is a
+waltz and so we could say is
+
+ align:start position:0%
+waltz and so we could say is
+ 
+
+ align:start position:0%
+waltz and so we could say is
+Waltz
+
+ align:start position:0%
+Waltz
+ 
+
+ align:start position:0%
+Waltz
+equals if true if Waltz is in the file
+
+ align:start position:0%
+equals if true if Waltz is in the file
+ 
+
+ align:start position:0%
+equals if true if Waltz is in the file
+name or if lowercase vaults is in the
+
+ align:start position:0%
+name or if lowercase vaults is in the
+ 
+
+ align:start position:0%
+name or if lowercase vaults is in the
+file
+
+ align:start position:0%
+file
+ 
+
+ align:start position:0%
+file
+name file name so then we know the file
+
+ align:start position:0%
+name file name so then we know the file
+ 
+
+ align:start position:0%
+name file name so then we know the file
+name numerator and
+
+ align:start position:0%
+name numerator and
+ 
+
+ align:start position:0%
+name numerator and
+denominator a float of the proportion
+
+ align:start position:0%
+denominator a float of the proportion
+ 
+
+ align:start position:0%
+denominator a float of the proportion
+beat3 and whether or not science Walts
+
+ align:start position:0%
+beat3 and whether or not science Walts
+ 
+
+ align:start position:0%
+beat3 and whether or not science Walts
+this last particular um thing we'll some
+
+ align:start position:0%
+this last particular um thing we'll some
+ 
+
+ align:start position:0%
+this last particular um thing we'll some
+call this instead of is Walter sign
+
+ align:start position:0%
+call this instead of is Walter sign
+ 
+
+ align:start position:0%
+call this instead of is Walter sign
+we'll use generic term ground truth
+
+ align:start position:0%
+we'll use generic term ground truth
+ 
+
+ align:start position:0%
+we'll use generic term ground truth
+we'll also see it called the class so
+
+ align:start position:0%
+we'll also see it called the class so
+ 
+
+ align:start position:0%
+we'll also see it called the class so
+whether it's belongs to the waltz class
+
+ align:start position:0%
+whether it's belongs to the waltz class
+ 
+
+ align:start position:0%
+whether it's belongs to the waltz class
+or not so we can call it Walt or non-
+
+ align:start position:0%
+or not so we can call it Walt or non-
+ 
+
+ align:start position:0%
+or not so we can call it Walt or non-
+waltz or true false something like that
+
+ align:start position:0%
+waltz or true false something like that
+ 
+
+ align:start position:0%
+waltz or true false something like that
+now we want to return all these things
+
+ align:start position:0%
+now we want to return all these things
+ 
+
+ align:start position:0%
+now we want to return all these things
+as a tupple so tuples are created
+
+ align:start position:0%
+as a tupple so tuples are created
+ 
+
+ align:start position:0%
+as a tupple so tuples are created
+with a comma or with a parenthesis so
+
+ align:start position:0%
+with a comma or with a parenthesis so
+ 
+
+ align:start position:0%
+with a comma or with a parenthesis so
+we'll use the parenthesis the file name
+
+ align:start position:0%
+we'll use the parenthesis the file name
+ 
+
+ align:start position:0%
+we'll use the parenthesis the file name
+the meter features first argument which
+
+ align:start position:0%
+the meter features first argument which
+ 
+
+ align:start position:0%
+the meter features first argument which
+is the numerator meter
+
+ align:start position:0%
+is the numerator meter
+ 
+
+ align:start position:0%
+is the numerator meter
+features second argument which is the
+
+ align:start position:0%
+features second argument which is the
+ 
+
+ align:start position:0%
+features second argument which is the
+denominator the beat3
+
+ align:start position:0%
+denominator the beat3
+ 
+
+ align:start position:0%
+denominator the beat3
+feature and the ground
+
+ align:start position:0%
+feature and the ground
+ 
+
+ align:start position:0%
+feature and the ground
+truth so let's see we'll run this
+
+ align:start position:0%
+truth so let's see we'll run this
+ 
+
+ align:start position:0%
+truth so let's see we'll run this
+feature ex let's call extractor let's
+
+ align:start position:0%
+feature ex let's call extractor let's
+ 
+
+ align:start position:0%
+feature ex let's call extractor let's
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+snap it properly F feature extractor on
+
+ align:start position:0%
+snap it properly F feature extractor on
+ 
+
+ align:start position:0%
+snap it properly F feature extractor on
+the blue denu
+
+ align:start position:0%
+the blue denu
+ 
+
+ align:start position:0%
+the blue denu
+and uh I still didn't spell it right why
+
+ align:start position:0%
+and uh I still didn't spell it right why
+ 
+
+ align:start position:0%
+and uh I still didn't spell it right why
+do I copy and paste there we
+
+ align:start position:0%
+do I copy and paste there we
+ 
+
+ align:start position:0%
+do I copy and paste there we
+go oh we can see blue Denny Waltz was in
+
+ align:start position:0%
+go oh we can see blue Denny Waltz was in
+ 
+
+ align:start position:0%
+go oh we can see blue Denny Waltz was in
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+four 26% has this beat proportion and
+
+ align:start position:0%
+four 26% has this beat proportion and
+ 
+
+ align:start position:0%
+four 26% has this beat proportion and
+true it is a Walt let's run our feature
+
+ align:start position:0%
+true it is a Walt let's run our feature
+ 
+
+ align:start position:0%
+true it is a Walt let's run our feature
+extract
+
+ align:start position:0%
+extract
+ 
+
+ align:start position:0%
+extract
+Tour on BW on
+
+ align:start position:0%
+Tour on BW on
+ 
+
+ align:start position:0%
+Tour on BW on
+B we'll see file name 44 35 false
+
+ align:start position:0%
+B we'll see file name 44 35 false
+ 
+
+ align:start position:0%
+B we'll see file name 44 35 false
+great So eventually we would want to
+
+ align:start position:0%
+great So eventually we would want to
+ 
+
+ align:start position:0%
+great So eventually we would want to
+have a computer system that can
+
+ align:start position:0%
+have a computer system that can
+ 
+
+ align:start position:0%
+have a computer system that can
+distinguish between one up between a
+
+ align:start position:0%
+distinguish between one up between a
+ 
+
+ align:start position:0%
+distinguish between one up between a
+waltz and not by learning all this
+
+ align:start position:0%
+waltz and not by learning all this
+ 
+
+ align:start position:0%
+waltz and not by learning all this
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+unfortunately I don't have enough waltes
+
+ align:start position:0%
+unfortunately I don't have enough waltes
+ 
+
+ align:start position:0%
+unfortunately I don't have enough waltes
+in my data set to do this so we're going
+
+ align:start position:0%
+in my data set to do this so we're going
+ 
+
+ align:start position:0%
+in my data set to do this so we're going
+to move to the next best thing we're
+
+ align:start position:0%
+to move to the next best thing we're
+ 
+
+ align:start position:0%
+to move to the next best thing we're
+going to get a jig so let's go ahead and
+
+ align:start position:0%
+going to get a jig so let's go ahead and
+ 
+
+ align:start position:0%
+going to get a jig so let's go ahead and
+um and grab a particular jig we have all
+
+ align:start position:0%
+um and grab a particular jig we have all
+ 
+
+ align:start position:0%
+um and grab a particular jig we have all
+of these jigs in this um in this data
+
+ align:start position:0%
+of these jigs in this um in this data
+ 
+
+ align:start position:0%
+of these jigs in this um in this data
+set which is really useful for people to
+
+ align:start position:0%
+set which is really useful for people to
+ 
+
+ align:start position:0%
+set which is really useful for people to
+know it's called
+
+ align:start position:0%
+know it's called
+ 
+
+ align:start position:0%
+know it's called
+Ryan's uh
+
+ align:start position:0%
+Ryan's uh
+ 
+
+ align:start position:0%
+Ryan's uh
+Mammoth
+
+ align:start position:0%
+Mammoth
+ 
+
+ align:start position:0%
+Mammoth
+collection it's for 19th century thing
+
+ align:start position:0%
+collection it's for 19th century thing
+ 
+
+ align:start position:0%
+collection it's for 19th century thing
+you can look it up it's very famous hi I
+
+ align:start position:0%
+you can look it up it's very famous hi I
+ 
+
+ align:start position:0%
+you can look it up it's very famous hi I
+wanted to jump in for a second and say
+
+ align:start position:0%
+wanted to jump in for a second and say
+ 
+
+ align:start position:0%
+wanted to jump in for a second and say
+something about this collection I'm
+
+ align:start position:0%
+something about this collection I'm
+ 
+
+ align:start position:0%
+something about this collection I'm
+planning on not using it again soon
+
+ align:start position:0%
+planning on not using it again soon
+ 
+
+ align:start position:0%
+planning on not using it again soon
+since I made this video I've realized
+
+ align:start position:0%
+since I made this video I've realized
+ 
+
+ align:start position:0%
+since I made this video I've realized
+that within Ryan's Mammoth collection
+
+ align:start position:0%
+that within Ryan's Mammoth collection
+ 
+
+ align:start position:0%
+that within Ryan's Mammoth collection
+there is a lot of what are called
+
+ align:start position:0%
+there is a lot of what are called
+ 
+
+ align:start position:0%
+there is a lot of what are called
+minstral songs that is songs that were
+
+ align:start position:0%
+minstral songs that is songs that were
+ 
+
+ align:start position:0%
+minstral songs that is songs that were
+performed um in the style of negro
+
+ align:start position:0%
+performed um in the style of negro
+ 
+
+ align:start position:0%
+performed um in the style of negro
+Melodies but by uh by white performers
+
+ align:start position:0%
+Melodies but by uh by white performers
+ 
+
+ align:start position:0%
+Melodies but by uh by white performers
+often in blackace and with texts which
+
+ align:start position:0%
+often in blackace and with texts which
+ 
+
+ align:start position:0%
+often in blackace and with texts which
+are not included in this collection
+
+ align:start position:0%
+are not included in this collection
+ 
+
+ align:start position:0%
+are not included in this collection
+thank goodness but with texts that uh
+
+ align:start position:0%
+thank goodness but with texts that uh
+ 
+
+ align:start position:0%
+thank goodness but with texts that uh
+denigrated uh Black Americans and black
+
+ align:start position:0%
+denigrated uh Black Americans and black
+ 
+
+ align:start position:0%
+denigrated uh Black Americans and black
+experience so I'm going to try to uh
+
+ align:start position:0%
+experience so I'm going to try to uh
+ 
+
+ align:start position:0%
+experience so I'm going to try to uh
+change this example as soon as I can and
+
+ align:start position:0%
+change this example as soon as I can and
+ 
+
+ align:start position:0%
+change this example as soon as I can and
+my apologies
+
+ align:start position:0%
+my apologies
+ 
+
+ align:start position:0%
+my apologies
+for what I didn't know then and what I
+
+ align:start position:0%
+for what I didn't know then and what I
+ 
+
+ align:start position:0%
+for what I didn't know then and what I
+know now and what I plan to continue to
+
+ align:start position:0%
+know now and what I plan to continue to
+ 
+
+ align:start position:0%
+know now and what I plan to continue to
+do to make computational musicology a
+
+ align:start position:0%
+do to make computational musicology a
+ 
+
+ align:start position:0%
+do to make computational musicology a
+more welcoming
+
+ align:start position:0%
+more welcoming
+ 
+
+ align:start position:0%
+more welcoming
+place we're going to be looking at the
+
+ align:start position:0%
+place we're going to be looking at the
+ 
+
+ align:start position:0%
+place we're going to be looking at the
+blooming Meadows Chi so um let's just
+
+ align:start position:0%
+blooming Meadows Chi so um let's just
+ 
+
+ align:start position:0%
+blooming Meadows Chi so um let's just
+we'll load that um
+
+ align:start position:0%
+we'll load that um
+ 
+
+ align:start position:0%
+we'll load that um
+blooming Corpus
+
+ align:start position:0%
+blooming Corpus
+ 
+
+ align:start position:0%
+blooming Corpus
+pars blo Meadow jig don't need the ABC
+
+ align:start position:0%
+pars blo Meadow jig don't need the ABC
+ 
+
+ align:start position:0%
+pars blo Meadow jig don't need the ABC
+you can leave it in however you want
+
+ align:start position:0%
+you can leave it in however you want
+ 
+
+ align:start position:0%
+you can leave it in however you want
+let's look at
+
+ align:start position:0%
+let's look at
+ 
+
+ align:start position:0%
+let's look at
+this in case you haven't seen a jig in a
+
+ align:start position:0%
+this in case you haven't seen a jig in a
+ 
+
+ align:start position:0%
+this in case you haven't seen a jig in a
+while it's kind of helpful for
+
+ align:start position:0%
+while it's kind of helpful for
+ 
+
+ align:start position:0%
+while it's kind of helpful for
+understanding so
+
+ align:start position:0%
+understanding so
+ 
+
+ align:start position:0%
+understanding so
+jig we speaking of 68 we got these
+
+ align:start position:0%
+jig we speaking of 68 we got these
+ 
+
+ align:start position:0%
+jig we speaking of 68 we got these
+violin bow marks we could use that as a
+
+ align:start position:0%
+violin bow marks we could use that as a
+ 
+
+ align:start position:0%
+violin bow marks we could use that as a
+feature extractor if it has violin
+
+ align:start position:0%
+feature extractor if it has violin
+ 
+
+ align:start position:0%
+feature extractor if it has violin
+markings it's more likely to be a jig if
+
+ align:start position:0%
+markings it's more likely to be a jig if
+ 
+
+ align:start position:0%
+markings it's more likely to be a jig if
+it doesn't it's less likely lots of Bo
+
+ align:start position:0%
+it doesn't it's less likely lots of Bo
+ 
+
+ align:start position:0%
+it doesn't it's less likely lots of Bo
+pieces of violin bow marks the boach
+
+ align:start position:0%
+pieces of violin bow marks the boach
+ 
+
+ align:start position:0%
+pieces of violin bow marks the boach
+violin part just they're not all jigs
+
+ align:start position:0%
+violin part just they're not all jigs
+ 
+
+ align:start position:0%
+violin part just they're not all jigs
+but you know so it's not going to be
+
+ align:start position:0%
+but you know so it's not going to be
+ 
+
+ align:start position:0%
+but you know so it's not going to be
+perfect but all these things kind of
+
+ align:start position:0%
+perfect but all these things kind of
+ 
+
+ align:start position:0%
+perfect but all these things kind of
+help but maybe that meter extractor 68
+
+ align:start position:0%
+help but maybe that meter extractor 68
+ 
+
+ align:start position:0%
+help but maybe that meter extractor 68
+is going to be a little bit
+
+ align:start position:0%
+is going to be a little bit
+ 
+
+ align:start position:0%
+is going to be a little bit
+helpful so I happen to know that this
+
+ align:start position:0%
+helpful so I happen to know that this
+ 
+
+ align:start position:0%
+helpful so I happen to know that this
+little piece is a jig it's kind of nice
+
+ align:start position:0%
+little piece is a jig it's kind of nice
+ 
+
+ align:start position:0%
+little piece is a jig it's kind of nice
+short piece but there's a whole bunch of
+
+ align:start position:0%
+short piece but there's a whole bunch of
+ 
+
+ align:start position:0%
+short piece but there's a whole bunch of
+things so we're going to get from Ryan
+
+ align:start position:0%
+things so we're going to get from Ryan
+ 
+
+ align:start position:0%
+things so we're going to get from Ryan
+MTH collection and we'll use a different
+
+ align:start position:0%
+MTH collection and we'll use a different
+ 
+
+ align:start position:0%
+MTH collection and we'll use a different
+thing uh that we've used before into
+
+ align:start position:0%
+thing uh that we've used before into
+ 
+
+ align:start position:0%
+thing uh that we've used before into
+Corpus pars we're going to search
+
+ align:start position:0%
+Corpus pars we're going to search
+ 
+
+ align:start position:0%
+Corpus pars we're going to search
+everything for Ryan um I think
+
+ align:start position:0%
+everything for Ryan um I think
+ 
+
+ align:start position:0%
+everything for Ryan um I think
+everything in there is uh is part of
+
+ align:start position:0%
+everything in there is uh is part of
+ 
+
+ align:start position:0%
+everything in there is uh is part of
+this Ryan's mavi collection and we'll
+
+ align:start position:0%
+this Ryan's mavi collection and we'll
+ 
+
+ align:start position:0%
+this Ryan's mavi collection and we'll
+see that within Ryan there's going to be
+
+ align:start position:0%
+see that within Ryan there's going to be
+ 
+
+ align:start position:0%
+see that within Ryan there's going to be
+quite a number of pieces
+
+ align:start position:0%
+quite a number of pieces
+ 
+
+ align:start position:0%
+quite a number of pieces
+1,63 you'll see the first time you use
+
+ align:start position:0%
+1,63 you'll see the first time you use
+ 
+
+ align:start position:0%
+1,63 you'll see the first time you use
+Corpus search you um it takes some time
+
+ align:start position:0%
+Corpus search you um it takes some time
+ 
+
+ align:start position:0%
+Corpus search you um it takes some time
+but you can um you can use after the
+
+ align:start position:0%
+but you can um you can use after the
+ 
+
+ align:start position:0%
+but you can um you can use after the
+after you do it once it's often quite a
+
+ align:start position:0%
+after you do it once it's often quite a
+ 
+
+ align:start position:0%
+after you do it once it's often quite a
+bit faster super
+
+ align:start position:0%
+bit faster super
+ 
+
+ align:start position:0%
+bit faster super
+fast there we go okay so we're going to
+
+ align:start position:0%
+fast there we go okay so we're going to
+ 
+
+ align:start position:0%
+fast there we go okay so we're going to
+um have use that beat3 feature why not I
+
+ align:start position:0%
+um have use that beat3 feature why not I
+ 
+
+ align:start position:0%
+um have use that beat3 feature why not I
+mean we already have a feature and we're
+
+ align:start position:0%
+mean we already have a feature and we're
+ 
+
+ align:start position:0%
+mean we already have a feature and we're
+going to use the meter feature but let's
+
+ align:start position:0%
+going to use the meter feature but let's
+ 
+
+ align:start position:0%
+going to use the meter feature but let's
+use one more thing I've heard that jigs
+
+ align:start position:0%
+use one more thing I've heard that jigs
+ 
+
+ align:start position:0%
+use one more thing I've heard that jigs
+tend to come in a
+
+ align:start position:0%
+tend to come in a
+ 
+
+ align:start position:0%
+tend to come in a
+few in a few Keys a few key signatures
+
+ align:start position:0%
+few in a few Keys a few key signatures
+ 
+
+ align:start position:0%
+few in a few Keys a few key signatures
+um maybe one flat one sharp you know
+
+ align:start position:0%
+um maybe one flat one sharp you know
+ 
+
+ align:start position:0%
+um maybe one flat one sharp you know
+they don't tend to come in five flats
+
+ align:start position:0%
+they don't tend to come in five flats
+ 
+
+ align:start position:0%
+they don't tend to come in five flats
+that's kind of a hard thing for violin
+
+ align:start position:0%
+that's kind of a hard thing for violin
+ 
+
+ align:start position:0%
+that's kind of a hard thing for violin
+so let's go ahead and create um a sharp
+
+ align:start position:0%
+so let's go ahead and create um a sharp
+ 
+
+ align:start position:0%
+so let's go ahead and create um a sharp
+extractor so we'll call it uh we just
+
+ align:start position:0%
+extractor so we'll call it uh we just
+ 
+
+ align:start position:0%
+extractor so we'll call it uh we just
+called get
+
+ align:start position:0%
+called get
+ 
+
+ align:start position:0%
+called get
+Sharps because we'll just remind
+
+ align:start position:0%
+Sharps because we'll just remind
+ 
+
+ align:start position:0%
+Sharps because we'll just remind
+ourselves that feature extractor is
+
+ align:start position:0%
+ourselves that feature extractor is
+ 
+
+ align:start position:0%
+ourselves that feature extractor is
+nothing more than something that takes
+
+ align:start position:0%
+nothing more than something that takes
+ 
+
+ align:start position:0%
+nothing more than something that takes
+in a score some other piece of data and
+
+ align:start position:0%
+in a score some other piece of data and
+ 
+
+ align:start position:0%
+in a score some other piece of data and
+returns numbers in this case an integer
+
+ align:start position:0%
+returns numbers in this case an integer
+ 
+
+ align:start position:0%
+returns numbers in this case an integer
+uh we'll just TR put a try thing we'll
+
+ align:start position:0%
+uh we'll just TR put a try thing we'll
+ 
+
+ align:start position:0%
+uh we'll just TR put a try thing we'll
+return the score we're going to go
+
+ align:start position:0%
+return the score we're going to go
+ 
+
+ align:start position:0%
+return the score we're going to go
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+recurse get all the elements okay use
+
+ align:start position:0%
+recurse get all the elements okay use
+ 
+
+ align:start position:0%
+recurse get all the elements okay use
+plural This Time by class key
+
+ align:start position:0%
+plural This Time by class key
+ 
+
+ align:start position:0%
+plural This Time by class key
+signature get the first one and return
+
+ align:start position:0%
+signature get the first one and return
+ 
+
+ align:start position:0%
+signature get the first one and return
+the number of Sharps remember if it's
+
+ align:start position:0%
+the number of Sharps remember if it's
+ 
+
+ align:start position:0%
+the number of Sharps remember if it's
+two Flats Sharps will be -2 and in case
+
+ align:start position:0%
+two Flats Sharps will be -2 and in case
+ 
+
+ align:start position:0%
+two Flats Sharps will be -2 and in case
+we can't find it uh might be an index
+
+ align:start position:0%
+we can't find it uh might be an index
+ 
+
+ align:start position:0%
+we can't find it uh might be an index
+error because uh there's zero um you can
+
+ align:start position:0%
+error because uh there's zero um you can
+ 
+
+ align:start position:0%
+error because uh there's zero um you can
+always in your own code that you don't
+
+ align:start position:0%
+always in your own code that you don't
+ 
+
+ align:start position:0%
+always in your own code that you don't
+turn in um and you don't put sign there
+
+ align:start position:0%
+turn in um and you don't put sign there
+ 
+
+ align:start position:0%
+turn in um and you don't put sign there
+you can just say except all
+
+ align:start position:0%
+you can just say except all
+ 
+
+ align:start position:0%
+you can just say except all
+errors return zero let's double check
+
+ align:start position:0%
+errors return zero let's double check
+ 
+
+ align:start position:0%
+errors return zero let's double check
+this um do we call it yeah
+
+ align:start position:0%
+this um do we call it yeah
+ 
+
+ align:start position:0%
+this um do we call it yeah
+blooming
+
+ align:start position:0%
+blooming
+ 
+
+ align:start position:0%
+blooming
+Sharps
+
+ align:start position:0%
+Sharps
+ 
+
+ align:start position:0%
+Sharps
+blooming get one let's remind ourselves
+
+ align:start position:0%
+blooming get one let's remind ourselves
+ 
+
+ align:start position:0%
+blooming get one let's remind ourselves
+blue denu should also be one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great and that Bo piece should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three super okay so that seems to work a
+
+ align:start position:0%
+three super okay so that seems to work a
+ 
+
+ align:start position:0%
+three super okay so that seems to work a
+little bit now let's write our feature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extractor or our multifeature extractor
+
+ align:start position:0%
+extractor or our multifeature extractor
+ 
+
+ align:start position:0%
+extractor or our multifeature extractor
+never really sure if our if feature
+
+ align:start position:0%
+never really sure if our if feature
+ 
+
+ align:start position:0%
+never really sure if our if feature
+extractor just refers to sign that gets
+
+ align:start position:0%
+extractor just refers to sign that gets
+ 
+
+ align:start position:0%
+extractor just refers to sign that gets
+one feature like get sharps or sign that
+
+ align:start position:0%
+one feature like get sharps or sign that
+ 
+
+ align:start position:0%
+one feature like get sharps or sign that
+gets a whole bunch features people
+
+ align:start position:0%
+gets a whole bunch features people
+ 
+
+ align:start position:0%
+gets a whole bunch features people
+aren't really clear on that so we're
+
+ align:start position:0%
+aren't really clear on that so we're
+ 
+
+ align:start position:0%
+aren't really clear on that so we're
+going to return again the string it's
+
+ align:start position:0%
+going to return again the string it's
+ 
+
+ align:start position:0%
+going to return again the string it's
+going to be the file name uh two
+
+ align:start position:0%
+going to be the file name uh two
+ 
+
+ align:start position:0%
+going to be the file name uh two
+integers for the metered mearian
+
+ align:start position:0%
+integers for the metered mearian
+ 
+
+ align:start position:0%
+integers for the metered mearian
+denominator pretty important float for
+
+ align:start position:0%
+denominator pretty important float for
+ 
+
+ align:start position:0%
+denominator pretty important float for
+that kind of silly uh beat3 thing but
+
+ align:start position:0%
+that kind of silly uh beat3 thing but
+ 
+
+ align:start position:0%
+that kind of silly uh beat3 thing but
+we'll add one more integer on
+
+ align:start position:0%
+we'll add one more integer on
+ 
+
+ align:start position:0%
+we'll add one more integer on
+um whether or not um yeah on the number
+
+ align:start position:0%
+um whether or not um yeah on the number
+ 
+
+ align:start position:0%
+um whether or not um yeah on the number
+of Sharps and instead returning a
+
+ align:start position:0%
+of Sharps and instead returning a
+ 
+
+ align:start position:0%
+of Sharps and instead returning a
+Boolean at the end we're going to switch
+
+ align:start position:0%
+Boolean at the end we're going to switch
+ 
+
+ align:start position:0%
+Boolean at the end we're going to switch
+this last little thing to returning an
+
+ align:start position:0%
+this last little thing to returning an
+ 
+
+ align:start position:0%
+this last little thing to returning an
+integer for whether or not something is
+
+ align:start position:0%
+integer for whether or not something is
+ 
+
+ align:start position:0%
+integer for whether or not something is
+a jig the ground truth and it's because
+
+ align:start position:0%
+a jig the ground truth and it's because
+ 
+
+ align:start position:0%
+a jig the ground truth and it's because
+most of the machine learning toolkits
+
+ align:start position:0%
+most of the machine learning toolkits
+ 
+
+ align:start position:0%
+most of the machine learning toolkits
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+um like working with numbers so might as
+
+ align:start position:0%
+um like working with numbers so might as
+ 
+
+ align:start position:0%
+um like working with numbers so might as
+well make our ground truth a number uh
+
+ align:start position:0%
+well make our ground truth a number uh
+ 
+
+ align:start position:0%
+well make our ground truth a number uh
+make a file name the file path name
+
+ align:start position:0%
+make a file name the file path name
+ 
+
+ align:start position:0%
+make a file name the file path name
+again as before you don't really need
+
+ align:start position:0%
+again as before you don't really need
+ 
+
+ align:start position:0%
+again as before you don't really need
+that there but it's going to be really
+
+ align:start position:0%
+that there but it's going to be really
+ 
+
+ align:start position:0%
+that there but it's going to be really
+helpful for figuring out why something's
+
+ align:start position:0%
+helpful for figuring out why something's
+ 
+
+ align:start position:0%
+helpful for figuring out why something's
+working or what particular pieces are
+
+ align:start position:0%
+working or what particular pieces are
+ 
+
+ align:start position:0%
+working or what particular pieces are
+wrong or right IOP I still had propor
+
+ align:start position:0%
+wrong or right IOP I still had propor
+ 
+
+ align:start position:0%
+wrong or right IOP I still had propor
+shot in my uh we in my clip board but
+
+ align:start position:0%
+shot in my uh we in my clip board but
+ 
+
+ align:start position:0%
+shot in my uh we in my clip board but
+okay so proportion B3 above B1 I always
+
+ align:start position:0%
+okay so proportion B3 above B1 I always
+ 
+
+ align:start position:0%
+okay so proportion B3 above B1 I always
+hit shift enter too early Sharps feature
+
+ align:start position:0%
+hit shift enter too early Sharps feature
+ 
+
+ align:start position:0%
+hit shift enter too early Sharps feature
+is better be get Sharps from score add
+
+ align:start position:0%
+is better be get Sharps from score add
+ 
+
+ align:start position:0%
+is better be get Sharps from score add
+our ground truth this case we said it's
+
+ align:start position:0%
+our ground truth this case we said it's
+ 
+
+ align:start position:0%
+our ground truth this case we said it's
+going to be an integer so we'll say int
+
+ align:start position:0%
+going to be an integer so we'll say int
+ 
+
+ align:start position:0%
+going to be an integer so we'll say int
+jig in file name or jig in file name two
+
+ align:start position:0%
+jig in file name or jig in file name two
+ 
+
+ align:start position:0%
+jig in file name or jig in file name two
+things to know one python int on true on
+
+ align:start position:0%
+things to know one python int on true on
+ 
+
+ align:start position:0%
+things to know one python int on true on
+int on true returns one int on false
+
+ align:start position:0%
+int on true returns one int on false
+ 
+
+ align:start position:0%
+int on true returns one int on false
+returns zero in fact uh in earlier
+
+ align:start position:0%
+returns zero in fact uh in earlier
+ 
+
+ align:start position:0%
+returns zero in fact uh in earlier
+versions of python true and false were
+
+ align:start position:0%
+versions of python true and false were
+ 
+
+ align:start position:0%
+versions of python true and false were
+just kind of aliases for one and zero
+
+ align:start position:0%
+just kind of aliases for one and zero
+ 
+
+ align:start position:0%
+just kind of aliases for one and zero
+thankfully that's a little bit better uh
+
+ align:start position:0%
+thankfully that's a little bit better uh
+ 
+
+ align:start position:0%
+thankfully that's a little bit better uh
+the other thing is again this what we've
+
+ align:start position:0%
+the other thing is again this what we've
+ 
+
+ align:start position:0%
+the other thing is again this what we've
+learned about garbage in garbage out I
+
+ align:start position:0%
+learned about garbage in garbage out I
+ 
+
+ align:start position:0%
+learned about garbage in garbage out I
+don't actually know if every single
+
+ align:start position:0%
+don't actually know if every single
+ 
+
+ align:start position:0%
+don't actually know if every single
+thing in uh this collection that has a
+
+ align:start position:0%
+thing in uh this collection that has a
+ 
+
+ align:start position:0%
+thing in uh this collection that has a
+word jig in its title is a jig and I
+
+ align:start position:0%
+word jig in its title is a jig and I
+ 
+
+ align:start position:0%
+word jig in its title is a jig and I
+definitely don't know that there's every
+
+ align:start position:0%
+definitely don't know that there's every
+ 
+
+ align:start position:0%
+definitely don't know that there's every
+piece in this collection that isn't a
+
+ align:start position:0%
+piece in this collection that isn't a
+ 
+
+ align:start position:0%
+piece in this collection that isn't a
+jig or that is a jig has jig in the
+
+ align:start position:0%
+jig or that is a jig has jig in the
+ 
+
+ align:start position:0%
+jig or that is a jig has jig in the
+title or that yeah that there might be
+
+ align:start position:0%
+title or that yeah that there might be
+ 
+
+ align:start position:0%
+title or that yeah that there might be
+jigs that don't have jig in the the
+
+ align:start position:0%
+jigs that don't have jig in the the
+ 
+
+ align:start position:0%
+jigs that don't have jig in the the
+title just as most rag rags in rag time
+
+ align:start position:0%
+title just as most rag rags in rag time
+ 
+
+ align:start position:0%
+title just as most rag rags in rag time
+in Scott Joplin have rag in their title
+
+ align:start position:0%
+in Scott Joplin have rag in their title
+ 
+
+ align:start position:0%
+in Scott Joplin have rag in their title
+Maple Leaf Rag so on but some of them
+
+ align:start position:0%
+Maple Leaf Rag so on but some of them
+ 
+
+ align:start position:0%
+Maple Leaf Rag so on but some of them
+don't the Entertainer is a rag it
+
+ align:start position:0%
+don't the Entertainer is a rag it
+ 
+
+ align:start position:0%
+don't the Entertainer is a rag it
+doesn't have rag in his title so so our
+
+ align:start position:0%
+doesn't have rag in his title so so our
+ 
+
+ align:start position:0%
+doesn't have rag in his title so so our
+ground truth isn't exactly the world's
+
+ align:start position:0%
+ground truth isn't exactly the world's
+ 
+
+ align:start position:0%
+ground truth isn't exactly the world's
+gospel truth this is something that that
+
+ align:start position:0%
+gospel truth this is something that that
+ 
+
+ align:start position:0%
+gospel truth this is something that that
+people neglect all the time in machine
+
+ align:start position:0%
+people neglect all the time in machine
+ 
+
+ align:start position:0%
+people neglect all the time in machine
+learning they keep training the computer
+
+ align:start position:0%
+learning they keep training the computer
+ 
+
+ align:start position:0%
+learning they keep training the computer
+to replicate
+
+ align:start position:0%
+to replicate
+ 
+
+ align:start position:0%
+to replicate
+truths that aren't necessarily true and
+
+ align:start position:0%
+truths that aren't necessarily true and
+ 
+
+ align:start position:0%
+truths that aren't necessarily true and
+you'll see this all over the place I was
+
+ align:start position:0%
+you'll see this all over the place I was
+ 
+
+ align:start position:0%
+you'll see this all over the place I was
+just working with uh Master student on a
+
+ align:start position:0%
+just working with uh Master student on a
+ 
+
+ align:start position:0%
+just working with uh Master student on a
+project where we're trying to train
+
+ align:start position:0%
+project where we're trying to train
+ 
+
+ align:start position:0%
+project where we're trying to train
+Optical music recognition to produce the
+
+ align:start position:0%
+Optical music recognition to produce the
+ 
+
+ align:start position:0%
+Optical music recognition to produce the
+exact ground truth that we had found
+
+ align:start position:0%
+exact ground truth that we had found
+ 
+
+ align:start position:0%
+exact ground truth that we had found
+encoded the thing is the ground truth
+
+ align:start position:0%
+encoded the thing is the ground truth
+ 
+
+ align:start position:0%
+encoded the thing is the ground truth
+had lots of Errors too so that's theci
+
+ align:start position:0%
+had lots of Errors too so that's theci
+ 
+
+ align:start position:0%
+had lots of Errors too so that's theci
+to know anyhow getting back to what are
+
+ align:start position:0%
+to know anyhow getting back to what are
+ 
+
+ align:start position:0%
+to know anyhow getting back to what are
+we going to return take a second see if
+
+ align:start position:0%
+we going to return take a second see if
+ 
+
+ align:start position:0%
+we going to return take a second see if
+you can figure this out based on what
+
+ align:start position:0%
+you can figure this out based on what
+ 
+
+ align:start position:0%
+you can figure this out based on what
+we've said return value is and what
+
+ align:start position:0%
+we've said return value is and what
+ 
+
+ align:start position:0%
+we've said return value is and what
+we've defined here great so we're going
+
+ align:start position:0%
+we've defined here great so we're going
+ 
+
+ align:start position:0%
+we've defined here great so we're going
+to return the file name meter
+
+ align:start position:0%
+to return the file name meter
+ 
+
+ align:start position:0%
+to return the file name meter
+feature zero meter feature one P3
+
+ align:start position:0%
+feature zero meter feature one P3
+ 
+
+ align:start position:0%
+feature zero meter feature one P3
+feature Sharps feature and the ground
+
+ align:start position:0%
+feature Sharps feature and the ground
+ 
+
+ align:start position:0%
+feature Sharps feature and the ground
+truth
+
+ align:start position:0%
+truth
+ 
+
+ align:start position:0%
+truth
+great okay so now we just need to
+
+ align:start position:0%
+great okay so now we just need to
+ 
+
+ align:start position:0%
+great okay so now we just need to
+iterate over everything I want to show
+
+ align:start position:0%
+iterate over everything I want to show
+ 
+
+ align:start position:0%
+iterate over everything I want to show
+something when you iterate over a corpus
+
+ align:start position:0%
+something when you iterate over a corpus
+ 
+
+ align:start position:0%
+something when you iterate over a corpus
+search object object there's this thing
+
+ align:start position:0%
+search object object there's this thing
+ 
+
+ align:start position:0%
+search object object there's this thing
+called a metadata bundle that is to say
+
+ align:start position:0%
+called a metadata bundle that is to say
+ 
+
+ align:start position:0%
+called a metadata bundle that is to say
+you haven't actually parsed 1,63 pieces
+
+ align:start position:0%
+you haven't actually parsed 1,63 pieces
+ 
+
+ align:start position:0%
+you haven't actually parsed 1,63 pieces
+it just knows about the existence of
+
+ align:start position:0%
+it just knows about the existence of
+ 
+
+ align:start position:0%
+it just knows about the existence of
+1,63 pieces so when we say for um bundle
+
+ align:start position:0%
+1,63 pieces so when we say for um bundle
+ 
+
+ align:start position:0%
+1,63 pieces so when we say for um bundle
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+Ryan we can print the
+
+ align:start position:0%
+Ryan we can print the
+ 
+
+ align:start position:0%
+Ryan we can print the
+bundle and we can see that we have all
+
+ align:start position:0%
+bundle and we can see that we have all
+ 
+
+ align:start position:0%
+bundle and we can see that we have all
+of these um different Ines for
+
+ align:start position:0%
+of these um different Ines for
+ 
+
+ align:start position:0%
+of these um different Ines for
+pieces so what we'll do go ahead and do
+
+ align:start position:0%
+pieces so what we'll do go ahead and do
+ 
+
+ align:start position:0%
+pieces so what we'll do go ahead and do
+is instead of um getting but not actual
+
+ align:start position:0%
+is instead of um getting but not actual
+ 
+
+ align:start position:0%
+is instead of um getting but not actual
+pieces so to get the pieces we can say
+
+ align:start position:0%
+pieces so to get the pieces we can say
+ 
+
+ align:start position:0%
+pieces so to get the pieces we can say
+um piece pars equals bundle actually we
+
+ align:start position:0%
+um piece pars equals bundle actually we
+ 
+
+ align:start position:0%
+um piece pars equals bundle actually we
+call it to bundle say metadata
+
+ align:start position:0%
+call it to bundle say metadata
+ 
+
+ align:start position:0%
+call it to bundle say metadata
+entry since out in there metadata entry
+
+ align:start position:0%
+entry since out in there metadata entry
+ 
+
+ align:start position:0%
+entry since out in there metadata entry
+in Ryan
+
+ align:start position:0%
+in Ryan
+ 
+
+ align:start position:0%
+in Ryan
+entry piece pars is the metadata entry.
+
+ align:start position:0%
+entry piece pars is the metadata entry.
+ 
+
+ align:start position:0%
+entry piece pars is the metadata entry.
+parse that's going to take some
+
+ align:start position:0%
+parse that's going to take some
+ 
+
+ align:start position:0%
+parse that's going to take some
+time then we're going to print out the
+
+ align:start position:0%
+time then we're going to print out the
+ 
+
+ align:start position:0%
+time then we're going to print out the
+feature extraction
+
+ align:start position:0%
+feature extraction
+ 
+
+ align:start position:0%
+feature extraction
+on the piece
+
+ align:start position:0%
+on the piece
+ 
+
+ align:start position:0%
+on the piece
+pars you're going to learn to use this
+
+ align:start position:0%
+pars you're going to learn to use this
+ 
+
+ align:start position:0%
+pars you're going to learn to use this
+little button in a second because the
+
+ align:start position:0%
+little button in a second because the
+ 
+
+ align:start position:0%
+little button in a second because the
+stop button because it's going to take
+
+ align:start position:0%
+stop button because it's going to take
+ 
+
+ align:start position:0%
+stop button because it's going to take
+some time if you hit run but you're
+
+ align:start position:0%
+some time if you hit run but you're
+ 
+
+ align:start position:0%
+some time if you hit run but you're
+going to have to do it in a little bit
+
+ align:start position:0%
+going to have to do it in a little bit
+ 
+
+ align:start position:0%
+going to have to do it in a little bit
+oops feature extractor used to call it
+
+ align:start position:0%
+oops feature extractor used to call it
+ 
+
+ align:start position:0%
+oops feature extractor used to call it
+feature extraction but that
+
+ align:start position:0%
+feature extraction but that
+ 
+
+ align:start position:0%
+feature extraction but that
+and extract meter exact meter extract
+
+ align:start position:0%
+and extract meter exact meter extract
+ 
+
+ align:start position:0%
+and extract meter exact meter extract
+meter here we go so we're going to put
+
+ align:start position:0%
+meter here we go so we're going to put
+ 
+
+ align:start position:0%
+meter here we go so we're going to put
+this back here and uh let's go ahead and
+
+ align:start position:0%
+this back here and uh let's go ahead and
+ 
+
+ align:start position:0%
+this back here and uh let's go ahead and
+run this
+
+ align:start position:0%
+run this
+ 
+
+ align:start position:0%
+run this
+oops oh my goodness I cannot spell
+
+ align:start position:0%
+oops oh my goodness I cannot spell
+ 
+
+ align:start position:0%
+oops oh my goodness I cannot spell
+anything today okay here we go let's go
+
+ align:start position:0%
+anything today okay here we go let's go
+ 
+
+ align:start position:0%
+anything today okay here we go let's go
+ahead and runting this it shows that
+
+ align:start position:0%
+ahead and runting this it shows that
+ 
+
+ align:start position:0%
+ahead and runting this it shows that
+adil's hornpipe is I don't know this
+
+ align:start position:0%
+adil's hornpipe is I don't know this
+ 
+
+ align:start position:0%
+adil's hornpipe is I don't know this
+piece but it's in
+
+ align:start position:0%
+piece but it's in
+ 
+
+ align:start position:0%
+piece but it's in
+22 really seldom does beat three um is
+
+ align:start position:0%
+22 really seldom does beat three um is
+ 
+
+ align:start position:0%
+22 really seldom does beat three um is
+uh was offset two higher than offset one
+
+ align:start position:0%
+uh was offset two higher than offset one
+ 
+
+ align:start position:0%
+uh was offset two higher than offset one
+wow that is really really low and um
+
+ align:start position:0%
+wow that is really really low and um
+ 
+
+ align:start position:0%
+wow that is really really low and um
+it's in one sharp oh good Flats do work
+
+ align:start position:0%
+it's in one sharp oh good Flats do work
+ 
+
+ align:start position:0%
+it's in one sharp oh good Flats do work
+and it is zero it is not a jig it is a
+
+ align:start position:0%
+and it is zero it is not a jig it is a
+ 
+
+ align:start position:0%
+and it is zero it is not a jig it is a
+hornpipe I know we all know these
+
+ align:start position:0%
+hornpipe I know we all know these
+ 
+
+ align:start position:0%
+hornpipe I know we all know these
+differences between reels and hornpipes
+
+ align:start position:0%
+differences between reels and hornpipes
+ 
+
+ align:start position:0%
+differences between reels and hornpipes
+and Jigs and all these things um well
+
+ align:start position:0%
+and Jigs and all these things um well
+ 
+
+ align:start position:0%
+and Jigs and all these things um well
+maybe some of us got our Pirates like
+
+ align:start position:0%
+maybe some of us got our Pirates like
+ 
+
+ align:start position:0%
+maybe some of us got our Pirates like
+okay we can see here Bano o barley meal
+
+ align:start position:0%
+okay we can see here Bano o barley meal
+ 
+
+ align:start position:0%
+okay we can see here Bano o barley meal
+jig uh which is in
+
+ align:start position:0%
+jig uh which is in
+ 
+
+ align:start position:0%
+jig uh which is in
+68 has this feature it's in two sharps
+
+ align:start position:0%
+68 has this feature it's in two sharps
+ 
+
+ align:start position:0%
+68 has this feature it's in two sharps
+and there's a one here so is a jig so
+
+ align:start position:0%
+and there's a one here so is a jig so
+ 
+
+ align:start position:0%
+and there's a one here so is a jig so
+that works pretty well and we can scroll
+
+ align:start position:0%
+that works pretty well and we can scroll
+ 
+
+ align:start position:0%
+that works pretty well and we can scroll
+all the way through wow there's a lot of
+
+ align:start position:0%
+all the way through wow there's a lot of
+ 
+
+ align:start position:0%
+all the way through wow there's a lot of
+pieces okay great and some of them are
+
+ align:start position:0%
+pieces okay great and some of them are
+ 
+
+ align:start position:0%
+pieces okay great and some of them are
+jigs some of them are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not okay so now we've extracted all this
+
+ align:start position:0%
+not okay so now we've extracted all this
+ 
+
+ align:start position:0%
+not okay so now we've extracted all this
+data if we put all of this into some
+
+ align:start position:0%
+data if we put all of this into some
+ 
+
+ align:start position:0%
+data if we put all of this into some
+sort of file somewhere um we will have
+
+ align:start position:0%
+sort of file somewhere um we will have
+ 
+
+ align:start position:0%
+sort of file somewhere um we will have
+it all done so I'm going to take a two
+
+ align:start position:0%
+it all done so I'm going to take a two
+ 
+
+ align:start position:0%
+it all done so I'm going to take a two
+second break and show how we move from
+
+ align:start position:0%
+second break and show how we move from
+ 
+
+ align:start position:0%
+second break and show how we move from
+feature abstraction to machine
+
+ align:start position:0%
+feature abstraction to machine
+ 
+
+ align:start position:0%
+feature abstraction to machine
+learning okay one of the most important
+
+ align:start position:0%
+learning okay one of the most important
+ 
+
+ align:start position:0%
+learning okay one of the most important
+things we're going to be thinking about
+
+ align:start position:0%
+things we're going to be thinking about
+ 
+
+ align:start position:0%
+things we're going to be thinking about
+when we think about machine learning is
+
+ align:start position:0%
+when we think about machine learning is
+ 
+
+ align:start position:0%
+when we think about machine learning is
+that we're going to be training the
+
+ align:start position:0%
+that we're going to be training the
+ 
+
+ align:start position:0%
+that we're going to be training the
+computer on a certain set of data
+
+ align:start position:0%
+computer on a certain set of data
+ 
+
+ align:start position:0%
+computer on a certain set of data
+training our algorithms training our
+
+ align:start position:0%
+training our algorithms training our
+ 
+
+ align:start position:0%
+training our algorithms training our
+neural networks or whatever artificial
+
+ align:start position:0%
+neural networks or whatever artificial
+ 
+
+ align:start position:0%
+neural networks or whatever artificial
+intelligence and machine learning
+
+ align:start position:0%
+intelligence and machine learning
+ 
+
+ align:start position:0%
+intelligence and machine learning
+algorithm we choose to use on some
+
+ align:start position:0%
+algorithm we choose to use on some
+ 
+
+ align:start position:0%
+algorithm we choose to use on some
+portion of the data and then we want to
+
+ align:start position:0%
+portion of the data and then we want to
+ 
+
+ align:start position:0%
+portion of the data and then we want to
+see how good is the computer doing so
+
+ align:start position:0%
+see how good is the computer doing so
+ 
+
+ align:start position:0%
+see how good is the computer doing so
+we're going to hold out some portion of
+
+ align:start position:0%
+we're going to hold out some portion of
+ 
+
+ align:start position:0%
+we're going to hold out some portion of
+the data to be our test to see well if
+
+ align:start position:0%
+the data to be our test to see well if
+ 
+
+ align:start position:0%
+the data to be our test to see well if
+the training data is somewhat like the
+
+ align:start position:0%
+the training data is somewhat like the
+ 
+
+ align:start position:0%
+the training data is somewhat like the
+test data but the computer seen the
+
+ align:start position:0%
+test data but the computer seen the
+ 
+
+ align:start position:0%
+test data but the computer seen the
+training data and it hasn't seen the
+
+ align:start position:0%
+training data and it hasn't seen the
+ 
+
+ align:start position:0%
+training data and it hasn't seen the
+test data how well does it learn from
+
+ align:start position:0%
+test data how well does it learn from
+ 
+
+ align:start position:0%
+test data how well does it learn from
+the training data in order to make um
+
+ align:start position:0%
+the training data in order to make um
+ 
+
+ align:start position:0%
+the training data in order to make um
+identifications in the test data and
+
+ align:start position:0%
+identifications in the test data and
+ 
+
+ align:start position:0%
+identifications in the test data and
+there are lots of different ways of
+
+ align:start position:0%
+there are lots of different ways of
+ 
+
+ align:start position:0%
+there are lots of different ways of
+doing this please take a machine
+
+ align:start position:0%
+doing this please take a machine
+ 
+
+ align:start position:0%
+doing this please take a machine
+learning class take an artificial
+
+ align:start position:0%
+learning class take an artificial
+ 
+
+ align:start position:0%
+learning class take an artificial
+intelligence class so you can learn
+
+ align:start position:0%
+intelligence class so you can learn
+ 
+
+ align:start position:0%
+intelligence class so you can learn
+about one hold out out cross validation
+
+ align:start position:0%
+about one hold out out cross validation
+ 
+
+ align:start position:0%
+about one hold out out cross validation
+or on10th uh hold out lots of different
+
+ align:start position:0%
+or on10th uh hold out lots of different
+ 
+
+ align:start position:0%
+or on10th uh hold out lots of different
+ways that we can do this better than
+
+ align:start position:0%
+ways that we can do this better than
+ 
+
+ align:start position:0%
+ways that we can do this better than
+what we're going to do but instead for
+
+ align:start position:0%
+what we're going to do but instead for
+ 
+
+ align:start position:0%
+what we're going to do but instead for
+now to make things very simple for those
+
+ align:start position:0%
+now to make things very simple for those
+ 
+
+ align:start position:0%
+now to make things very simple for those
+who for whom this is going to be your
+
+ align:start position:0%
+who for whom this is going to be your
+ 
+
+ align:start position:0%
+who for whom this is going to be your
+first introduction to artificial
+
+ align:start position:0%
+first introduction to artificial
+ 
+
+ align:start position:0%
+first introduction to artificial
+intelligence and machine learning what
+
+ align:start position:0%
+intelligence and machine learning what
+ 
+
+ align:start position:0%
+intelligence and machine learning what
+we're going to do is we're going to
+
+ align:start position:0%
+we're going to do is we're going to
+ 
+
+ align:start position:0%
+we're going to do is we're going to
+divide all of our training data into two
+
+ align:start position:0%
+divide all of our training data into two
+ 
+
+ align:start position:0%
+divide all of our training data into two
+parts all of our data into half of it as
+
+ align:start position:0%
+parts all of our data into half of it as
+ 
+
+ align:start position:0%
+parts all of our data into half of it as
+the test data and half of it as the
+
+ align:start position:0%
+the test data and half of it as the
+ 
+
+ align:start position:0%
+the test data and half of it as the
+training data and I'm just going to go
+
+ align:start position:0%
+training data and I'm just going to go
+ 
+
+ align:start position:0%
+training data and I'm just going to go
+through and almost always do everything
+
+ align:start position:0%
+through and almost always do everything
+ 
+
+ align:start position:0%
+through and almost always do everything
+in up this one to test this one training
+
+ align:start position:0%
+in up this one to test this one training
+ 
+
+ align:start position:0%
+in up this one to test this one training
+this one test this one training it's
+
+ align:start position:0%
+this one test this one training it's
+ 
+
+ align:start position:0%
+this one test this one training it's
+just going to make things easier but
+
+ align:start position:0%
+just going to make things easier but
+ 
+
+ align:start position:0%
+just going to make things easier but
+there are better ways to do
+
+ align:start position:0%
+there are better ways to do
+ 
+
+ align:start position:0%
+there are better ways to do
+it not for now let's get to some
+
+ align:start position:0%
+it not for now let's get to some
+ 
+
+ align:start position:0%
+it not for now let's get to some
+artificial intelligence and machine
+
+ align:start position:0%
+artificial intelligence and machine
+ 
+
+ align:start position:0%
+artificial intelligence and machine
+learning okay let's go ahead and and
+
+ align:start position:0%
+learning okay let's go ahead and and
+ 
+
+ align:start position:0%
+learning okay let's go ahead and and
+open up two files for writing I'm going
+
+ align:start position:0%
+open up two files for writing I'm going
+ 
+
+ align:start position:0%
+open up two files for writing I'm going
+to call
+
+ align:start position:0%
+to call
+ 
+
+ align:start position:0%
+to call
+them uh they're on my desktop o now you
+
+ align:start position:0%
+them uh they're on my desktop o now you
+ 
+
+ align:start position:0%
+them uh they're on my desktop o now you
+know my secret secret path um we'll call
+
+ align:start position:0%
+know my secret secret path um we'll call
+ 
+
+ align:start position:0%
+know my secret secret path um we'll call
+it train data. tab we're going to open
+
+ align:start position:0%
+it train data. tab we're going to open
+ 
+
+ align:start position:0%
+it train data. tab we're going to open
+this for writing and we'll call it as
+
+ align:start position:0%
+this for writing and we'll call it as
+ 
+
+ align:start position:0%
+this for writing and we'll call it as
+training if you're not familiar with
+
+ align:start position:0%
+training if you're not familiar with
+ 
+
+ align:start position:0%
+training if you're not familiar with
+python um file handles please take a
+
+ align:start position:0%
+python um file handles please take a
+ 
+
+ align:start position:0%
+python um file handles please take a
+second to look this up because otherwise
+
+ align:start position:0%
+second to look this up because otherwise
+ 
+
+ align:start position:0%
+second to look this up because otherwise
+this won't make much sense but
+
+ align:start position:0%
+this won't make much sense but
+ 
+
+ align:start position:0%
+this won't make much sense but
+essentially we're going to have um two
+
+ align:start position:0%
+essentially we're going to have um two
+ 
+
+ align:start position:0%
+essentially we're going to have um two
+files so we're going to be able to write
+
+ align:start position:0%
+files so we're going to be able to write
+ 
+
+ align:start position:0%
+files so we're going to be able to write
+two going back and forth one versus the
+
+ align:start position:0%
+two going back and forth one versus the
+ 
+
+ align:start position:0%
+two going back and forth one versus the
+other there's going to be better ways of
+
+ align:start position:0%
+other there's going to be better ways of
+ 
+
+ align:start position:0%
+other there's going to be better ways of
+doing this but this how we're going to
+
+ align:start position:0%
+doing this but this how we're going to
+ 
+
+ align:start position:0%
+doing this but this how we're going to
+do it first okay we're going to need to
+
+ align:start position:0%
+do it first okay we're going to need to
+ 
+
+ align:start position:0%
+do it first okay we're going to need to
+say uh for a lot of various algorithms
+
+ align:start position:0%
+say uh for a lot of various algorithms
+ 
+
+ align:start position:0%
+say uh for a lot of various algorithms
+we're going to need to be able to say
+
+ align:start position:0%
+we're going to need to be able to say
+ 
+
+ align:start position:0%
+we're going to need to be able to say
+what our column names are so we'll say
+
+ align:start position:0%
+what our column names are so we'll say
+ 
+
+ align:start position:0%
+what our column names are so we'll say
+our columns are going to be a series of
+
+ align:start position:0%
+our columns are going to be a series of
+ 
+
+ align:start position:0%
+our columns are going to be a series of
+tab separated values so that's what
+
+ align:start position:0%
+tab separated values so that's what
+ 
+
+ align:start position:0%
+tab separated values so that's what
+these tab files are going to be series
+
+ align:start position:0%
+these tab files are going to be series
+ 
+
+ align:start position:0%
+these tab files are going to be series
+of tab separated values that join these
+
+ align:start position:0%
+of tab separated values that join these
+ 
+
+ align:start position:0%
+of tab separated values that join these
+um titles file
+
+ align:start position:0%
+um titles file
+ 
+
+ align:start position:0%
+um titles file
+name numerator doesn't matter what these
+
+ align:start position:0%
+name numerator doesn't matter what these
+ 
+
+ align:start position:0%
+name numerator doesn't matter what these
+are called
+
+ align:start position:0%
+are called
+ 
+
+ align:start position:0%
+are called
+denominator beat3 proportion I'm not
+
+ align:start position:0%
+denominator beat3 proportion I'm not
+ 
+
+ align:start position:0%
+denominator beat3 proportion I'm not
+going to make myself type that again and
+
+ align:start position:0%
+going to make myself type that again and
+ 
+
+ align:start position:0%
+going to make myself type that again and
+we'll say is jig at the end for a ground
+
+ align:start position:0%
+we'll say is jig at the end for a ground
+ 
+
+ align:start position:0%
+we'll say is jig at the end for a ground
+truth fantastic okay those are columns
+
+ align:start position:0%
+truth fantastic okay those are columns
+ 
+
+ align:start position:0%
+truth fantastic okay those are columns
+and first I'm going to do is write to
+
+ align:start position:0%
+and first I'm going to do is write to
+ 
+
+ align:start position:0%
+and first I'm going to do is write to
+each of our
+
+ align:start position:0%
+each of our
+ 
+
+ align:start position:0%
+each of our
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+files write our columns with a line
+
+ align:start position:0%
+files write our columns with a line
+ 
+
+ align:start position:0%
+files write our columns with a line
+break at the
+
+ align:start position:0%
+break at the
+ 
+
+ align:start position:0%
+break at the
+end go testing is going to write columns
+
+ align:start position:0%
+end go testing is going to write columns
+ 
+
+ align:start position:0%
+end go testing is going to write columns
+with a line break at the end great now
+
+ align:start position:0%
+with a line break at the end great now
+ 
+
+ align:start position:0%
+with a line break at the end great now
+we want to describe what kind of value
+
+ align:start position:0%
+we want to describe what kind of value
+ 
+
+ align:start position:0%
+we want to describe what kind of value
+what kind of value um will a machine
+
+ align:start position:0%
+what kind of value um will a machine
+ 
+
+ align:start position:0%
+what kind of value um will a machine
+learning toolkit expect to get from file
+
+ align:start position:0%
+learning toolkit expect to get from file
+ 
+
+ align:start position:0%
+learning toolkit expect to get from file
+name uh stram numerator integer beat3
+
+ align:start position:0%
+name uh stram numerator integer beat3
+ 
+
+ align:start position:0%
+name uh stram numerator integer beat3
+float things like that so we'll say our
+
+ align:start position:0%
+float things like that so we'll say our
+ 
+
+ align:start position:0%
+float things like that so we'll say our
+descriptions are going to be and these
+
+ align:start position:0%
+descriptions are going to be and these
+ 
+
+ align:start position:0%
+descriptions are going to be and these
+are pretty standard formats but they're
+
+ align:start position:0%
+are pretty standard formats but they're
+ 
+
+ align:start position:0%
+are pretty standard formats but they're
+not python so look at this it's not Str
+
+ align:start position:0%
+not python so look at this it's not Str
+ 
+
+ align:start position:0%
+not python so look at this it's not Str
+it's string and we'll say that our
+
+ align:start position:0%
+it's string and we'll say that our
+ 
+
+ align:start position:0%
+it's string and we'll say that our
+integers are discrete data with a I not
+
+ align:start position:0%
+integers are discrete data with a I not
+ 
+
+ align:start position:0%
+integers are discrete data with a I not
+discrete like indiscrete
+
+ align:start position:0%
+discrete like indiscrete
+ 
+
+ align:start position:0%
+discrete like indiscrete
+but okay I won't make a joke but discret
+
+ align:start position:0%
+but okay I won't make a joke but discret
+ 
+
+ align:start position:0%
+but okay I won't make a joke but discret
+like integer values uh but beat3 data
+
+ align:start position:0%
+like integer values uh but beat3 data
+ 
+
+ align:start position:0%
+like integer values uh but beat3 data
+can be continuous it can be 1.2 1.21 so
+
+ align:start position:0%
+can be continuous it can be 1.2 1.21 so
+ 
+
+ align:start position:0%
+can be continuous it can be 1.2 1.21 so
+on and then another discrete data for
+
+ align:start position:0%
+on and then another discrete data for
+ 
+
+ align:start position:0%
+on and then another discrete data for
+the number Sharps and then for is J it's
+
+ align:start position:0%
+the number Sharps and then for is J it's
+ 
+
+ align:start position:0%
+the number Sharps and then for is J it's
+also it's 01 so it's going to be
+
+ align:start position:0%
+also it's 01 so it's going to be
+ 
+
+ align:start position:0%
+also it's 01 so it's going to be
+discrete data fantastic we're going to
+
+ align:start position:0%
+discrete data fantastic we're going to
+ 
+
+ align:start position:0%
+discrete data fantastic we're going to
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+these to these files the descriptions
+
+ align:start position:0%
+these to these files the descriptions
+ 
+
+ align:start position:0%
+these to these files the descriptions
+also boom okay
+
+ align:start position:0%
+also boom okay
+ 
+
+ align:start position:0%
+also boom okay
+great this um we also tend to put these
+
+ align:start position:0%
+great this um we also tend to put these
+ 
+
+ align:start position:0%
+great this um we also tend to put these
+meta variables in and they say um if
+
+ align:start position:0%
+meta variables in and they say um if
+ 
+
+ align:start position:0%
+meta variables in and they say um if
+anything is special if anything is
+
+ align:start position:0%
+anything is special if anything is
+ 
+
+ align:start position:0%
+anything is special if anything is
+unlike the rest well the ones that are
+
+ align:start position:0%
+unlike the rest well the ones that are
+ 
+
+ align:start position:0%
+unlike the rest well the ones that are
+special is the first thing string is
+
+ align:start position:0%
+special is the first thing string is
+ 
+
+ align:start position:0%
+special is the first thing string is
+just a meta data that is to say it just
+
+ align:start position:0%
+just a meta data that is to say it just
+ 
+
+ align:start position:0%
+just a meta data that is to say it just
+means um something so that we can more
+
+ align:start position:0%
+means um something so that we can more
+ 
+
+ align:start position:0%
+means um something so that we can more
+easily diagnose uh problems and look
+
+ align:start position:0%
+easily diagnose uh problems and look
+ 
+
+ align:start position:0%
+easily diagnose uh problems and look
+things up later we don't actually need
+
+ align:start position:0%
+things up later we don't actually need
+ 
+
+ align:start position:0%
+things up later we don't actually need
+it we're not going to study the file
+
+ align:start position:0%
+it we're not going to study the file
+ 
+
+ align:start position:0%
+it we're not going to study the file
+name um and then these are just normal
+
+ align:start position:0%
+name um and then these are just normal
+ 
+
+ align:start position:0%
+name um and then these are just normal
+things numerator denominator beat three
+
+ align:start position:0%
+things numerator denominator beat three
+ 
+
+ align:start position:0%
+things numerator denominator beat three
+number of Sharps and then at the very
+
+ align:start position:0%
+number of Sharps and then at the very
+ 
+
+ align:start position:0%
+number of Sharps and then at the very
+end the final thing is our class the
+
+ align:start position:0%
+end the final thing is our class the
+ 
+
+ align:start position:0%
+end the final thing is our class the
+thing that's we're trying to learn we're
+
+ align:start position:0%
+thing that's we're trying to learn we're
+ 
+
+ align:start position:0%
+thing that's we're trying to learn we're
+trying to learn does this
+
+ align:start position:0%
+trying to learn does this
+ 
+
+ align:start position:0%
+trying to learn does this
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+98.1
+
+ align:start position:0%
+98.1
+ 
+
+ align:start position:0%
+98.1
+11112 describe a jig or not the class of
+
+ align:start position:0%
+11112 describe a jig or not the class of
+ 
+
+ align:start position:0%
+11112 describe a jig or not the class of
+objects that is a jig great so these are
+
+ align:start position:0%
+objects that is a jig great so these are
+ 
+
+ align:start position:0%
+objects that is a jig great so these are
+our meta variables and we're going to
+
+ align:start position:0%
+our meta variables and we're going to
+ 
+
+ align:start position:0%
+our meta variables and we're going to
+write them to again our see do I still
+
+ align:start position:0%
+write them to again our see do I still
+ 
+
+ align:start position:0%
+write them to again our see do I still
+have that
+
+ align:start position:0%
+have that
+ 
+
+ align:start position:0%
+have that
+no going to write that to our training
+
+ align:start position:0%
+no going to write that to our training
+ 
+
+ align:start position:0%
+no going to write that to our training
+and to our testing
+
+ align:start position:0%
+and to our testing
+ 
+
+ align:start position:0%
+and to our testing
+great um here I can kind of do this
+
+ align:start position:0%
+great um here I can kind of do this
+ 
+
+ align:start position:0%
+great um here I can kind of do this
+anyhow we can
+
+ align:start position:0%
+anyhow we can
+ 
+
+ align:start position:0%
+anyhow we can
+cat that file this is a um these magic
+
+ align:start position:0%
+cat that file this is a um these magic
+ 
+
+ align:start position:0%
+cat that file this is a um these magic
+things are stuff you can do in Jupiter
+
+ align:start position:0%
+things are stuff you can do in Jupiter
+ 
+
+ align:start position:0%
+things are stuff you can do in Jupiter
+that you can't in normal python um but
+
+ align:start position:0%
+that you can't in normal python um but
+ 
+
+ align:start position:0%
+that you can't in normal python um but
+it'll see train
+
+ align:start position:0%
+it'll see train
+ 
+
+ align:start position:0%
+it'll see train
+data tab yep we can kind of see what
+
+ align:start position:0%
+data tab yep we can kind of see what
+ 
+
+ align:start position:0%
+data tab yep we can kind of see what
+we've written out there okay great now
+
+ align:start position:0%
+we've written out there okay great now
+ 
+
+ align:start position:0%
+we've written out there okay great now
+we're going to take this and we're going
+
+ align:start position:0%
+we're going to take this and we're going
+ 
+
+ align:start position:0%
+we're going to take this and we're going
+to write more things it we're going to
+
+ align:start position:0%
+to write more things it we're going to
+ 
+
+ align:start position:0%
+to write more things it we're going to
+write to um these into these two files
+
+ align:start position:0%
+write to um these into these two files
+ 
+
+ align:start position:0%
+write to um these into these two files
+information about from our feature
+
+ align:start position:0%
+information about from our feature
+ 
+
+ align:start position:0%
+information about from our feature
+extractions so we're going to go back
+
+ align:start position:0%
+extractions so we're going to go back
+ 
+
+ align:start position:0%
+extractions so we're going to go back
+for each piece in ryion um
+
+ align:start position:0%
+for each piece in ryion um
+ 
+
+ align:start position:0%
+for each piece in ryion um
+enumerate Ryan um and enumerate says our
+
+ align:start position:0%
+enumerate Ryan um and enumerate says our
+ 
+
+ align:start position:0%
+enumerate Ryan um and enumerate says our
+first thing goes into piece and we'll
+
+ align:start position:0%
+first thing goes into piece and we'll
+ 
+
+ align:start position:0%
+first thing goes into piece and we'll
+call it I actually we'll not call it
+
+ align:start position:0%
+call it I actually we'll not call it
+ 
+
+ align:start position:0%
+call it I actually we'll not call it
+piece we'll call it uh metad data entry
+
+ align:start position:0%
+piece we'll call it uh metad data entry
+ 
+
+ align:start position:0%
+piece we'll call it uh metad data entry
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+uh we'll say piece pars is our
+
+ align:start position:0%
+uh we'll say piece pars is our
+ 
+
+ align:start position:0%
+uh we'll say piece pars is our
+metadata entry
+
+ align:start position:0%
+metadata entry
+ 
+
+ align:start position:0%
+metadata entry
+parse great and our
+
+ align:start position:0%
+parse great and our
+ 
+
+ align:start position:0%
+parse great and our
+features are our featured
+
+ align:start position:0%
+features are our featured
+ 
+
+ align:start position:0%
+features are our featured
+extractor on pie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pars pie pars and now we're going to uh
+
+ align:start position:0%
+pars pie pars and now we're going to uh
+ 
+
+ align:start position:0%
+pars pie pars and now we're going to uh
+create make a string out of that feature
+
+ align:start position:0%
+create make a string out of that feature
+ 
+
+ align:start position:0%
+create make a string out of that feature
+string equals tab separated version of
+
+ align:start position:0%
+string equals tab separated version of
+ 
+
+ align:start position:0%
+string equals tab separated version of
+the string value of each element for the
+
+ align:start position:0%
+the string value of each element for the
+ 
+
+ align:start position:0%
+the string value of each element for the
+element in features okay yeah we should
+
+ align:start position:0%
+element in features okay yeah we should
+ 
+
+ align:start position:0%
+element in features okay yeah we should
+call it
+
+ align:start position:0%
+call it
+ 
+
+ align:start position:0%
+call it
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+fantastic and if I is
+
+ align:start position:0%
+fantastic and if I is
+ 
+
+ align:start position:0%
+fantastic and if I is
+even no if I is odd uh we'll write it to
+
+ align:start position:0%
+even no if I is odd uh we'll write it to
+ 
+
+ align:start position:0%
+even no if I is odd uh we'll write it to
+the training
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data with uh new
+
+ align:start position:0%
+data with uh new
+ 
+
+ align:start position:0%
+data with uh new
+line and
+
+ align:start position:0%
+line and
+ 
+
+ align:start position:0%
+line and
+otherwise we'll write it to the testing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data with a new line great hopefully I
+
+ align:start position:0%
+data with a new line great hopefully I
+ 
+
+ align:start position:0%
+data with a new line great hopefully I
+didn't type anything wrong we'll find
+
+ align:start position:0%
+didn't type anything wrong we'll find
+ 
+
+ align:start position:0%
+didn't type anything wrong we'll find
+out in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second great it seems to be working it's
+
+ align:start position:0%
+second great it seems to be working it's
+ 
+
+ align:start position:0%
+second great it seems to be working it's
+slow one of the things I'm going to
+
+ align:start position:0%
+slow one of the things I'm going to
+ 
+
+ align:start position:0%
+slow one of the things I'm going to
+eventually learn is that everything's
+
+ align:start position:0%
+eventually learn is that everything's
+ 
+
+ align:start position:0%
+eventually learn is that everything's
+slower when I'm screen recording so uh
+
+ align:start position:0%
+slower when I'm screen recording so uh
+ 
+
+ align:start position:0%
+slower when I'm screen recording so uh
+we could see that yep there's a bunch of
+
+ align:start position:0%
+we could see that yep there's a bunch of
+ 
+
+ align:start position:0%
+we could see that yep there's a bunch of
+of things in here most important one can
+
+ align:start position:0%
+of things in here most important one can
+ 
+
+ align:start position:0%
+of things in here most important one can
+we get a jig good it has a one at the
+
+ align:start position:0%
+we get a jig good it has a one at the
+ 
+
+ align:start position:0%
+we get a jig good it has a one at the
+end if it's a jig zero at the end if
+
+ align:start position:0%
+end if it's a jig zero at the end if
+ 
+
+ align:start position:0%
+end if it's a jig zero at the end if
+it's something else oh these jigs are 68
+
+ align:start position:0%
+it's something else oh these jigs are 68
+ 
+
+ align:start position:0%
+it's something else oh these jigs are 68
+oh look there's a jig it begins in 98 so
+
+ align:start position:0%
+oh look there's a jig it begins in 98 so
+ 
+
+ align:start position:0%
+oh look there's a jig it begins in 98 so
+maybe it's the eight that's more
+
+ align:start position:0%
+maybe it's the eight that's more
+ 
+
+ align:start position:0%
+maybe it's the eight that's more
+important I don't know we'll see if the
+
+ align:start position:0%
+important I don't know we'll see if the
+ 
+
+ align:start position:0%
+important I don't know we'll see if the
+computer can figure this out uh we don't
+
+ align:start position:0%
+computer can figure this out uh we don't
+ 
+
+ align:start position:0%
+computer can figure this out uh we don't
+need to look at all 1,000 entries
+
+ align:start position:0%
+need to look at all 1,000 entries
+ 
+
+ align:start position:0%
+need to look at all 1,000 entries
+Jupiter does a nice way of not putting
+
+ align:start position:0%
+Jupiter does a nice way of not putting
+ 
+
+ align:start position:0%
+Jupiter does a nice way of not putting
+that all together okay great so now we
+
+ align:start position:0%
+that all together okay great so now we
+ 
+
+ align:start position:0%
+that all together okay great so now we
+have something that we can feed into an
+
+ align:start position:0%
+have something that we can feed into an
+ 
+
+ align:start position:0%
+have something that we can feed into an
+artificial intelligence classification
+
+ align:start position:0%
+artificial intelligence classification
+ 
+
+ align:start position:0%
+artificial intelligence classification
+program so we don't have one so we're
+
+ align:start position:0%
+program so we don't have one so we're
+ 
+
+ align:start position:0%
+program so we don't have one so we're
+going to write one of our own so we're
+
+ align:start position:0%
+going to write one of our own so we're
+ 
+
+ align:start position:0%
+going to write one of our own so we're
+going to say neural network ah just
+
+ align:start position:0%
+going to say neural network ah just
+ 
+
+ align:start position:0%
+going to say neural network ah just
+kidding no that's not what this class is
+
+ align:start position:0%
+kidding no that's not what this class is
+ 
+
+ align:start position:0%
+kidding no that's not what this class is
+about that's other classes we're going
+
+ align:start position:0%
+about that's other classes we're going
+ 
+
+ align:start position:0%
+about that's other classes we're going
+to install one so go ahead and install
+
+ align:start position:0%
+to install one so go ahead and install
+ 
+
+ align:start position:0%
+to install one so go ahead and install
+Orange 3 which is a really great pass
+
+ align:start position:0%
+Orange 3 which is a really great pass
+ 
+
+ align:start position:0%
+Orange 3 which is a really great pass
+package oh hey I already have installed
+
+ align:start position:0%
+package oh hey I already have installed
+ 
+
+ align:start position:0%
+package oh hey I already have installed
+yours probably takes a little bit longer
+
+ align:start position:0%
+yours probably takes a little bit longer
+ 
+
+ align:start position:0%
+yours probably takes a little bit longer
+than that great
+
+ align:start position:0%
+than that great
+ 
+
+ align:start position:0%
+than that great
+super so now I have orange 3 um orange 3
+
+ align:start position:0%
+super so now I have orange 3 um orange 3
+ 
+
+ align:start position:0%
+super so now I have orange 3 um orange 3
+names it stuff kind of funny um so I
+
+ align:start position:0%
+names it stuff kind of funny um so I
+ 
+
+ align:start position:0%
+names it stuff kind of funny um so I
+always because I've been using it for a
+
+ align:start position:0%
+always because I've been using it for a
+ 
+
+ align:start position:0%
+always because I've been using it for a
+long time I just imported it it's not
+
+ align:start position:0%
+long time I just imported it it's not
+ 
+
+ align:start position:0%
+long time I just imported it it's not
+Orange 3 let's call it orange great now
+
+ align:start position:0%
+Orange 3 let's call it orange great now
+ 
+
+ align:start position:0%
+Orange 3 let's call it orange great now
+what we're going to do is we're going to
+
+ align:start position:0%
+what we're going to do is we're going to
+ 
+
+ align:start position:0%
+what we're going to do is we're going to
+load in our training
+
+ align:start position:0%
+load in our training
+ 
+
+ align:start position:0%
+load in our training
+data from an orange data table based on
+
+ align:start position:0%
+data from an orange data table based on
+ 
+
+ align:start position:0%
+data from an orange data table based on
+that information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so train data.
+
+ align:start position:0%
+so train data.
+ 
+
+ align:start position:0%
+so train data.
+tab uh I reverted myself to using camel
+
+ align:start position:0%
+tab uh I reverted myself to using camel
+ 
+
+ align:start position:0%
+tab uh I reverted myself to using camel
+case things I probably shouldn't but I'm
+
+ align:start position:0%
+case things I probably shouldn't but I'm
+ 
+
+ align:start position:0%
+case things I probably shouldn't but I'm
+not going to
+
+ align:start position:0%
+not going to
+ 
+
+ align:start position:0%
+not going to
+rewrite everything now though it doesn't
+
+ align:start position:0%
+rewrite everything now though it doesn't
+ 
+
+ align:start position:0%
+rewrite everything now though it doesn't
+look like much but I have a lot in my
+
+ align:start position:0%
+look like much but I have a lot in my
+ 
+
+ align:start position:0%
+look like much but I have a lot in my
+sleeve okay so we're going to load those
+
+ align:start position:0%
+sleeve okay so we're going to load those
+ 
+
+ align:start position:0%
+sleeve okay so we're going to load those
+two great um we can look at train data
+
+ align:start position:0%
+two great um we can look at train data
+ 
+
+ align:start position:0%
+two great um we can look at train data
+little bit yep whole bunch of stuff uh
+
+ align:start position:0%
+little bit yep whole bunch of stuff uh
+ 
+
+ align:start position:0%
+little bit yep whole bunch of stuff uh
+these are I think map plot live is type
+
+ align:start position:0%
+these are I think map plot live is type
+ 
+
+ align:start position:0%
+these are I think map plot live is type
+things okay great so what we want to do
+
+ align:start position:0%
+things okay great so what we want to do
+ 
+
+ align:start position:0%
+things okay great so what we want to do
+is um create a bunch of Learners things
+
+ align:start position:0%
+is um create a bunch of Learners things
+ 
+
+ align:start position:0%
+is um create a bunch of Learners things
+that can classify and understand data
+
+ align:start position:0%
+that can classify and understand data
+ 
+
+ align:start position:0%
+that can classify and understand data
+and try to make guesses about things our
+
+ align:start position:0%
+and try to make guesses about things our
+ 
+
+ align:start position:0%
+and try to make guesses about things our
+first learner is kind of like the
+
+ align:start position:0%
+first learner is kind of like the
+ 
+
+ align:start position:0%
+first learner is kind of like the
+placebo of Learners uh it's called the
+
+ align:start position:0%
+placebo of Learners uh it's called the
+ 
+
+ align:start position:0%
+placebo of Learners uh it's called the
+majority learner uh and there's other
+
+ align:start position:0%
+majority learner uh and there's other
+ 
+
+ align:start position:0%
+majority learner uh and there's other
+ways of doing this but we'll use this
+
+ align:start position:0%
+ways of doing this but we'll use this
+ 
+
+ align:start position:0%
+ways of doing this but we'll use this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and the majority learner is um is is
+
+ align:start position:0%
+and the majority learner is um is is
+ 
+
+ align:start position:0%
+and the majority learner is um is is
+pretty cool it just looks at the data it
+
+ align:start position:0%
+pretty cool it just looks at the data it
+ 
+
+ align:start position:0%
+pretty cool it just looks at the data it
+um it looks at what we put in the
+
+ align:start position:0%
+um it looks at what we put in the
+ 
+
+ align:start position:0%
+um it looks at what we put in the
+training data and it says you know what
+
+ align:start position:0%
+training data and it says you know what
+ 
+
+ align:start position:0%
+training data and it says you know what
+there's about three times as many things
+
+ align:start position:0%
+there's about three times as many things
+ 
+
+ align:start position:0%
+there's about three times as many things
+that are not jigs as there are jigs so I
+
+ align:start position:0%
+that are not jigs as there are jigs so I
+ 
+
+ align:start position:0%
+that are not jigs as there are jigs so I
+can get three out of four right if I
+
+ align:start position:0%
+can get three out of four right if I
+ 
+
+ align:start position:0%
+can get three out of four right if I
+just learn to always vote with majority
+
+ align:start position:0%
+just learn to always vote with majority
+ 
+
+ align:start position:0%
+just learn to always vote with majority
+I don't know anything about music but
+
+ align:start position:0%
+I don't know anything about music but
+ 
+
+ align:start position:0%
+I don't know anything about music but
+I'll just say I'll always say that's not
+
+ align:start position:0%
+I'll just say I'll always say that's not
+ 
+
+ align:start position:0%
+I'll just say I'll always say that's not
+a jig and you know what I'll usually be
+
+ align:start position:0%
+a jig and you know what I'll usually be
+ 
+
+ align:start position:0%
+a jig and you know what I'll usually be
+right um so never classify things
+
+ align:start position:0%
+right um so never classify things
+ 
+
+ align:start position:0%
+right um so never classify things
+according to hey uh is this right or
+
+ align:start position:0%
+according to hey uh is this right or
+ 
+
+ align:start position:0%
+according to hey uh is this right or
+wrong you know did did it get it right
+
+ align:start position:0%
+wrong you know did did it get it right
+ 
+
+ align:start position:0%
+wrong you know did did it get it right
+more than half the time no classify how
+
+ align:start position:0%
+more than half the time no classify how
+ 
+
+ align:start position:0%
+more than half the time no classify how
+you're doing against did it do did it do
+
+ align:start position:0%
+you're doing against did it do did it do
+ 
+
+ align:start position:0%
+you're doing against did it do did it do
+better than the majority learner
+
+ align:start position:0%
+better than the majority learner
+ 
+
+ align:start position:0%
+better than the majority learner
+correct um you're going to now if you
+
+ align:start position:0%
+correct um you're going to now if you
+ 
+
+ align:start position:0%
+correct um you're going to now if you
+don't know what this is we're going to
+
+ align:start position:0%
+don't know what this is we're going to
+ 
+
+ align:start position:0%
+don't know what this is we're going to
+learn what um in uh uh K nearest
+
+ align:start position:0%
+learn what um in uh uh K nearest
+ 
+
+ align:start position:0%
+learn what um in uh uh K nearest
+neighbors is KNN learner uh
+
+ align:start position:0%
+neighbors is KNN learner uh
+ 
+
+ align:start position:0%
+neighbors is KNN learner uh
+classification
+
+ align:start position:0%
+classification
+ 
+
+ align:start position:0%
+classification
+classification
+
+ align:start position:0%
+classification
+ 
+
+ align:start position:0%
+classification
+KNN learner and this is a pretty
+
+ align:start position:0%
+KNN learner and this is a pretty
+ 
+
+ align:start position:0%
+KNN learner and this is a pretty
+standard artificial intelligence
+
+ align:start position:0%
+standard artificial intelligence
+ 
+
+ align:start position:0%
+standard artificial intelligence
+learning algorithm um and so I'm not
+
+ align:start position:0%
+learning algorithm um and so I'm not
+ 
+
+ align:start position:0%
+learning algorithm um and so I'm not
+going to say too much about that so we
+
+ align:start position:0%
+going to say too much about that so we
+ 
+
+ align:start position:0%
+going to say too much about that so we
+have we create a kind of learner thing
+
+ align:start position:0%
+have we create a kind of learner thing
+ 
+
+ align:start position:0%
+have we create a kind of learner thing
+and our classifier is a learner that's
+
+ align:start position:0%
+and our classifier is a learner that's
+ 
+
+ align:start position:0%
+and our classifier is a learner that's
+been that's going to work on a
+
+ align:start position:0%
+been that's going to work on a
+ 
+
+ align:start position:0%
+been that's going to work on a
+particular set of data our training data
+
+ align:start position:0%
+particular set of data our training data
+ 
+
+ align:start position:0%
+particular set of data our training data
+okay good so we create a learner create
+
+ align:start position:0%
+okay good so we create a learner create
+ 
+
+ align:start position:0%
+okay good so we create a learner create
+a classifier hasn't actually learned
+
+ align:start position:0%
+a classifier hasn't actually learned
+ 
+
+ align:start position:0%
+a classifier hasn't actually learned
+anything yet but it's going to be ready
+
+ align:start position:0%
+anything yet but it's going to be ready
+ 
+
+ align:start position:0%
+anything yet but it's going to be ready
+for for doing that okay
+
+ align:start position:0%
+for for doing that okay
+ 
+
+ align:start position:0%
+for for doing that okay
+um now we're going to check how often
+
+ align:start position:0%
+um now we're going to check how often
+ 
+
+ align:start position:0%
+um now we're going to check how often
+does the majority learner get things uh
+
+ align:start position:0%
+does the majority learner get things uh
+ 
+
+ align:start position:0%
+does the majority learner get things uh
+how many times does it get it correct
+
+ align:start position:0%
+how many times does it get it correct
+ 
+
+ align:start position:0%
+how many times does it get it correct
+and how many times does um the kers
+
+ align:start position:0%
+and how many times does um the kers
+ 
+
+ align:start position:0%
+and how many times does um the kers
+neighbors learner get things
+
+ align:start position:0%
+neighbors learner get things
+ 
+
+ align:start position:0%
+neighbors learner get things
+correct and how many total things are
+
+ align:start position:0%
+correct and how many total things are
+ 
+
+ align:start position:0%
+correct and how many total things are
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+uh we get that as I need floats still
+
+ align:start position:0%
+uh we get that as I need floats still
+ 
+
+ align:start position:0%
+uh we get that as I need floats still
+thinking too much how to think like
+
+ align:start position:0%
+thinking too much how to think like
+ 
+
+ align:start position:0%
+thinking too much how to think like
+python
+
+ align:start position:0%
+python
+ 
+
+ align:start position:0%
+python
+Tu so how many test data there
+
+ align:start position:0%
+Tu so how many test data there
+ 
+
+ align:start position:0%
+Tu so how many test data there
+are go ah and see okay 532 in the test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data the training data does not need to
+
+ align:start position:0%
+data the training data does not need to
+ 
+
+ align:start position:0%
+data the training data does not need to
+be exactly the same size or even close
+
+ align:start position:0%
+be exactly the same size or even close
+ 
+
+ align:start position:0%
+be exactly the same size or even close
+the same size as the test data
+
+ align:start position:0%
+the same size as the test data
+ 
+
+ align:start position:0%
+the same size as the test data
+but in this case they are great so now
+
+ align:start position:0%
+but in this case they are great so now
+ 
+
+ align:start position:0%
+but in this case they are great so now
+we're going to iterate through each of
+
+ align:start position:0%
+we're going to iterate through each of
+ 
+
+ align:start position:0%
+we're going to iterate through each of
+the rows
+
+ align:start position:0%
+the rows
+ 
+
+ align:start position:0%
+the rows
+um of um of our test data not our
+
+ align:start position:0%
+um of um of our test data not our
+ 
+
+ align:start position:0%
+um of um of our test data not our
+training
+
+ align:start position:0%
+training
+ 
+
+ align:start position:0%
+training
+data so we're going to know what row
+
+ align:start position:0%
+data so we're going to know what row
+ 
+
+ align:start position:0%
+data so we're going to know what row
+number we are on I and then test row and
+
+ align:start position:0%
+number we are on I and then test row and
+ 
+
+ align:start position:0%
+number we are on I and then test row and
+then the majority learner is going to
+
+ align:start position:0%
+then the majority learner is going to
+ 
+
+ align:start position:0%
+then the majority learner is going to
+make a guess based on the data in the
+
+ align:start position:0%
+make a guess based on the data in the
+ 
+
+ align:start position:0%
+make a guess based on the data in the
+test row wh the majority learner is
+
+ align:start position:0%
+test row wh the majority learner is
+ 
+
+ align:start position:0%
+test row wh the majority learner is
+really stupid so its guess is always
+
+ align:start position:0%
+really stupid so its guess is always
+ 
+
+ align:start position:0%
+really stupid so its guess is always
+going to be it's not a jig then Ker's
+
+ align:start position:0%
+going to be it's not a jig then Ker's
+ 
+
+ align:start position:0%
+going to be it's not a jig then Ker's
+neighbor is going to make a guess and
+
+ align:start position:0%
+neighbor is going to make a guess and
+ 
+
+ align:start position:0%
+neighbor is going to make a guess and
+we're hope that K's neighbor is making a
+
+ align:start position:0%
+we're hope that K's neighbor is making a
+ 
+
+ align:start position:0%
+we're hope that K's neighbor is making a
+guess based on some intelligence that it
+
+ align:start position:0%
+guess based on some intelligence that it
+ 
+
+ align:start position:0%
+guess based on some intelligence that it
+has or fake intelligence I mean it's
+
+ align:start position:0%
+has or fake intelligence I mean it's
+ 
+
+ align:start position:0%
+has or fake intelligence I mean it's
+called artificial intelligence for a
+
+ align:start position:0%
+called artificial intelligence for a
+ 
+
+ align:start position:0%
+called artificial intelligence for a
+reason and then we get to see in this
+
+ align:start position:0%
+reason and then we get to see in this
+ 
+
+ align:start position:0%
+reason and then we get to see in this
+case what the actual answer is with the
+
+ align:start position:0%
+case what the actual answer is with the
+ 
+
+ align:start position:0%
+case what the actual answer is with the
+class whether it's a jig or not so
+
+ align:start position:0%
+class whether it's a jig or not so
+ 
+
+ align:start position:0%
+class whether it's a jig or not so
+that's our real answer so we know this
+
+ align:start position:0%
+that's our real answer so we know this
+ 
+
+ align:start position:0%
+that's our real answer so we know this
+but K nearest neighbor is not allowed to
+
+ align:start position:0%
+but K nearest neighbor is not allowed to
+ 
+
+ align:start position:0%
+but K nearest neighbor is not allowed to
+look at this we really hope the
+
+ align:start position:0%
+look at this we really hope the
+ 
+
+ align:start position:0%
+look at this we really hope the
+computer's not peing uh otherwise all
+
+ align:start position:0%
+computer's not peing uh otherwise all
+ 
+
+ align:start position:0%
+computer's not peing uh otherwise all
+artificial intelligence is kind of
+
+ align:start position:0%
+artificial intelligence is kind of
+ 
+
+ align:start position:0%
+artificial intelligence is kind of
+screwed okay we'll just print out some
+
+ align:start position:0%
+screwed okay we'll just print out some
+ 
+
+ align:start position:0%
+screwed okay we'll just print out some
+test data that um the
+
+ align:start position:0%
+test data that um the
+ 
+
+ align:start position:0%
+test data that um the
+row I is
+
+ align:start position:0%
+row I is
+ 
+
+ align:start position:0%
+row I is
+uh a little bit of the information about
+
+ align:start position:0%
+uh a little bit of the information about
+ 
+
+ align:start position:0%
+uh a little bit of the information about
+our set that should be good gri will'll
+
+ align:start position:0%
+our set that should be good gri will'll
+ 
+
+ align:start position:0%
+our set that should be good gri will'll
+print out that the answer to row I
+
+ align:start position:0%
+print out that the answer to row I
+ 
+
+ align:start position:0%
+print out that the answer to row I
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jig
+
+ align:start position:0%
+jig
+ 
+
+ align:start position:0%
+jig
+give whe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer I think that works else not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and then we'll put in a tab we'll
+
+ align:start position:0%
+and and then we'll put in a tab we'll
+ 
+
+ align:start position:0%
+and and then we'll put in a tab we'll
+say k neighbor got it right or wrong
+
+ align:start position:0%
+say k neighbor got it right or wrong
+ 
+
+ align:start position:0%
+say k neighbor got it right or wrong
+correct right if k&n's if the K nearest
+
+ align:start position:0%
+correct right if k&n's if the K nearest
+ 
+
+ align:start position:0%
+correct right if k&n's if the K nearest
+neighbor's guess is the same as the real
+
+ align:start position:0%
+neighbor's guess is the same as the real
+ 
+
+ align:start position:0%
+neighbor's guess is the same as the real
+answer else
+
+ align:start position:0%
+answer else
+ 
+
+ align:start position:0%
+answer else
+wrong that's some pretty tough stuff
+
+ align:start position:0%
+wrong that's some pretty tough stuff
+ 
+
+ align:start position:0%
+wrong that's some pretty tough stuff
+Oran can't even get that right good
+
+ align:start position:0%
+Oran can't even get that right good
+ 
+
+ align:start position:0%
+Oran can't even get that right good
+okay um we'll print a blank line after
+
+ align:start position:0%
+okay um we'll print a blank line after
+ 
+
+ align:start position:0%
+okay um we'll print a blank line after
+that if the majority guesss if the
+
+ align:start position:0%
+that if the majority guesss if the
+ 
+
+ align:start position:0%
+that if the majority guesss if the
+majority guessed
+
+ align:start position:0%
+majority guessed
+ 
+
+ align:start position:0%
+majority guessed
+right then the majority correct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+INR if k n
+
+ align:start position:0%
+INR if k n
+ 
+
+ align:start position:0%
+INR if k n
+neighbors guess is
+
+ align:start position:0%
+neighbors guess is
+ 
+
+ align:start position:0%
+neighbors guess is
+right so we're just checking at this
+
+ align:start position:0%
+right so we're just checking at this
+ 
+
+ align:start position:0%
+right so we're just checking at this
+point how how good is this cares
+
+ align:start position:0%
+point how how good is this cares
+ 
+
+ align:start position:0%
+point how how good is this cares
+neighbors correct okay this going to be
+
+ align:start position:0%
+neighbors correct okay this going to be
+ 
+
+ align:start position:0%
+neighbors correct okay this going to be
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+great so we'll go ahead and let that run
+
+ align:start position:0%
+great so we'll go ahead and let that run
+ 
+
+ align:start position:0%
+great so we'll go ahead and let that run
+oops uh claes are very nice oops they
+
+ align:start position:0%
+oops uh claes are very nice oops they
+ 
+
+ align:start position:0%
+oops uh claes are very nice oops they
+screw siging up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um oops there we go uh I have to cast
+
+ align:start position:0%
+um oops there we go uh I have to cast
+ 
+
+ align:start position:0%
+um oops there we go uh I have to cast
+this as a list because where is it this
+
+ align:start position:0%
+this as a list because where is it this
+ 
+
+ align:start position:0%
+this as a list because where is it this
+data can't be sliced but lists can okay
+
+ align:start position:0%
+data can't be sliced but lists can okay
+ 
+
+ align:start position:0%
+data can't be sliced but lists can okay
+so that going on you know I probably
+
+ align:start position:0%
+so that going on you know I probably
+ 
+
+ align:start position:0%
+so that going on you know I probably
+need to reset my data so let's go ahead
+
+ align:start position:0%
+need to reset my data so let's go ahead
+ 
+
+ align:start position:0%
+need to reset my data so let's go ahead
+and do that it's going to be printing
+
+ align:start position:0%
+and do that it's going to be printing
+ 
+
+ align:start position:0%
+and do that it's going to be printing
+cool not jig K neighbors got it wrong
+
+ align:start position:0%
+cool not jig K neighbors got it wrong
+ 
+
+ align:start position:0%
+cool not jig K neighbors got it wrong
+not jig Kors got it right good good so
+
+ align:start position:0%
+not jig Kors got it right good good so
+ 
+
+ align:start position:0%
+not jig Kors got it right good good so
+hey see a lot of got it right I like
+
+ align:start position:0%
+hey see a lot of got it right I like
+ 
+
+ align:start position:0%
+hey see a lot of got it right I like
+that I like that okay here's the Moment
+
+ align:start position:0%
+that I like that okay here's the Moment
+ 
+
+ align:start position:0%
+that I like that okay here's the Moment
+of Truth um without machine
+
+ align:start position:0%
+of Truth um without machine
+ 
+
+ align:start position:0%
+of Truth um without machine
+learning there's a majority learner
+
+ align:start position:0%
+learning there's a majority learner
+ 
+
+ align:start position:0%
+learning there's a majority learner
+majority
+
+ align:start position:0%
+majority
+ 
+
+ align:start position:0%
+majority
+correct always put things into um into
+
+ align:start position:0%
+correct always put things into um into
+ 
+
+ align:start position:0%
+correct always put things into um into
+uh percentages always round your
+
+ align:start position:0%
+uh percentages always round your
+ 
+
+ align:start position:0%
+uh percentages always round your
+percentages toci reasonable nobody wants
+
+ align:start position:0%
+percentages toci reasonable nobody wants
+ 
+
+ align:start position:0%
+percentages toci reasonable nobody wants
+to see all those dangling digits okay so
+
+ align:start position:0%
+to see all those dangling digits okay so
+ 
+
+ align:start position:0%
+to see all those dangling digits okay so
+it got that number right and we'll say
+
+ align:start position:0%
+it got that number right and we'll say
+ 
+
+ align:start position:0%
+it got that number right and we'll say
+with K andn Machine learning we got the
+
+ align:start position:0%
+with K andn Machine learning we got the
+ 
+
+ align:start position:0%
+with K andn Machine learning we got the
+KNN correct how well do we
+
+ align:start position:0%
+KNN correct how well do we
+ 
+
+ align:start position:0%
+KNN correct how well do we
+do without machine learning got it 77%
+
+ align:start position:0%
+do without machine learning got it 77%
+ 
+
+ align:start position:0%
+do without machine learning got it 77%
+right K nearest neighbors got it 95%
+
+ align:start position:0%
+right K nearest neighbors got it 95%
+ 
+
+ align:start position:0%
+right K nearest neighbors got it 95%
+right wow okay that's pretty awesome
+
+ align:start position:0%
+right wow okay that's pretty awesome
+ 
+
+ align:start position:0%
+right wow okay that's pretty awesome
+that's a lot better than I thought when
+
+ align:start position:0%
+that's a lot better than I thought when
+ 
+
+ align:start position:0%
+that's a lot better than I thought when
+I um when I thought I would do this um
+
+ align:start position:0%
+I um when I thought I would do this um
+ 
+
+ align:start position:0%
+I um when I thought I would do this um
+by the way one of the things we can do
+
+ align:start position:0%
+by the way one of the things we can do
+ 
+
+ align:start position:0%
+by the way one of the things we can do
+you you probably want to keep track of
+
+ align:start position:0%
+you you probably want to keep track of
+ 
+
+ align:start position:0%
+you you probably want to keep track of
+your uh of your data and don't um don't
+
+ align:start position:0%
+your uh of your data and don't um don't
+ 
+
+ align:start position:0%
+your uh of your data and don't um don't
+do this but we'll just go ahead and
+
+ align:start position:0%
+do this but we'll just go ahead and
+ 
+
+ align:start position:0%
+do this but we'll just go ahead and
+check does it make a difference if we
+
+ align:start position:0%
+check does it make a difference if we
+ 
+
+ align:start position:0%
+check does it make a difference if we
+swap the training and the test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data oops not training data training
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data do we get a fluke
+
+ align:start position:0%
+data do we get a fluke
+ 
+
+ align:start position:0%
+data do we get a fluke
+and we can go ahead and
+
+ align:start position:0%
+and we can go ahead and
+ 
+
+ align:start position:0%
+and we can go ahead and
+run 72 and 94 so yeah still pretty good
+
+ align:start position:0%
+run 72 and 94 so yeah still pretty good
+ 
+
+ align:start position:0%
+run 72 and 94 so yeah still pretty good
+doesn't matter which one we do I'm going
+
+ align:start position:0%
+doesn't matter which one we do I'm going
+ 
+
+ align:start position:0%
+doesn't matter which one we do I'm going
+to switch that back because I will
+
+ align:start position:0%
+to switch that back because I will
+ 
+
+ align:start position:0%
+to switch that back because I will
+totally uh make that mistake but yeah so
+
+ align:start position:0%
+totally uh make that mistake but yeah so
+ 
+
+ align:start position:0%
+totally uh make that mistake but yeah so
+we're doing really well with this so
+
+ align:start position:0%
+we're doing really well with this so
+ 
+
+ align:start position:0%
+we're doing really well with this so
+this is how you can do artificial
+
+ align:start position:0%
+this is how you can do artificial
+ 
+
+ align:start position:0%
+this is how you can do artificial
+intelligence with machine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+learning but that's been a little bit
+
+ align:start position:0%
+learning but that's been a little bit
+ 
+
+ align:start position:0%
+learning but that's been a little bit
+hard so
+
+ align:start position:0%
+hard so
+ 
+
+ align:start position:0%
+hard so
+fortunately music 21 has some tools to
+
+ align:start position:0%
+fortunately music 21 has some tools to
+ 
+
+ align:start position:0%
+fortunately music 21 has some tools to
+make a lot of these things even easier
+
+ align:start position:0%
+make a lot of these things even easier
+ 
+
+ align:start position:0%
+make a lot of these things even easier
+here so music 21 feature extraction will
+
+ align:start position:0%
+here so music 21 feature extraction will
+ 
+
+ align:start position:0%
+here so music 21 feature extraction will
+be the last topic that we're going to
+
+ align:start position:0%
+be the last topic that we're going to
+ 
+
+ align:start position:0%
+be the last topic that we're going to
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+today so we can go ahead and import from
+
+ align:start position:0%
+today so we can go ahead and import from
+ 
+
+ align:start position:0%
+today so we can go ahead and import from
+music 21 the features
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+module great so within the features
+
+ align:start position:0%
+module great so within the features
+ 
+
+ align:start position:0%
+module great so within the features
+module there are things called data sets
+
+ align:start position:0%
+module there are things called data sets
+ 
+
+ align:start position:0%
+module there are things called data sets
+so let's create um um training
+
+ align:start position:0%
+so let's create um um training
+ 
+
+ align:start position:0%
+so let's create um um training
+set which will be a data set um with a
+
+ align:start position:0%
+set which will be a data set um with a
+ 
+
+ align:start position:0%
+set which will be a data set um with a
+class label of is jig we call ground
+
+ align:start position:0%
+class label of is jig we call ground
+ 
+
+ align:start position:0%
+class label of is jig we call ground
+trth or whatever and we'll create an
+
+ align:start position:0%
+trth or whatever and we'll create an
+ 
+
+ align:start position:0%
+trth or whatever and we'll create an
+identical one U for our test
+
+ align:start position:0%
+identical one U for our test
+ 
+
+ align:start position:0%
+identical one U for our test
+set testing set great so these are just
+
+ align:start position:0%
+set testing set great so these are just
+ 
+
+ align:start position:0%
+set testing set great so these are just
+um things that are ready to
+
+ align:start position:0%
+um things that are ready to
+ 
+
+ align:start position:0%
+um things that are ready to
+add two important things a set of data
+
+ align:start position:0%
+add two important things a set of data
+ 
+
+ align:start position:0%
+add two important things a set of data
+that is Stream So a whole bunch of
+
+ align:start position:0%
+that is Stream So a whole bunch of
+ 
+
+ align:start position:0%
+that is Stream So a whole bunch of
+streams uh will be added to both the
+
+ align:start position:0%
+streams uh will be added to both the
+ 
+
+ align:start position:0%
+streams uh will be added to both the
+training and the test set and also a set
+
+ align:start position:0%
+training and the test set and also a set
+ 
+
+ align:start position:0%
+training and the test set and also a set
+of feature
+
+ align:start position:0%
+of feature
+ 
+
+ align:start position:0%
+of feature
+extractors I'm not going to explain
+
+ align:start position:0%
+extractors I'm not going to explain
+ 
+
+ align:start position:0%
+extractors I'm not going to explain
+today how to write new feature
+
+ align:start position:0%
+today how to write new feature
+ 
+
+ align:start position:0%
+today how to write new feature
+extractors in the way music 21 expects
+
+ align:start position:0%
+extractors in the way music 21 expects
+ 
+
+ align:start position:0%
+extractors in the way music 21 expects
+them but they're basically pretty
+
+ align:start position:0%
+them but they're basically pretty
+ 
+
+ align:start position:0%
+them but they're basically pretty
+similar to what we've just been writing
+
+ align:start position:0%
+similar to what we've just been writing
+ 
+
+ align:start position:0%
+similar to what we've just been writing
+with functions except they're kind of
+
+ align:start position:0%
+with functions except they're kind of
+ 
+
+ align:start position:0%
+with functions except they're kind of
+expected to be
+
+ align:start position:0%
+expected to be
+ 
+
+ align:start position:0%
+expected to be
+classes but we don't really have to
+
+ align:start position:0%
+classes but we don't really have to
+ 
+
+ align:start position:0%
+classes but we don't really have to
+because music 21 has a whole bunch of
+
+ align:start position:0%
+because music 21 has a whole bunch of
+ 
+
+ align:start position:0%
+because music 21 has a whole bunch of
+features
+
+ align:start position:0%
+features
+ 
+
+ align:start position:0%
+features
+extractors some of them come from this
+
+ align:start position:0%
+extractors some of them come from this
+ 
+
+ align:start position:0%
+extractors some of them come from this
+amazing toolkit called J symbolic or the
+
+ align:start position:0%
+amazing toolkit called J symbolic or the
+ 
+
+ align:start position:0%
+amazing toolkit called J symbolic or the
+reinterpretations of Corey McKay's J
+
+ align:start position:0%
+reinterpretations of Corey McKay's J
+ 
+
+ align:start position:0%
+reinterpretations of Corey McKay's J
+symbolic toolkit which is in Java and um
+
+ align:start position:0%
+symbolic toolkit which is in Java and um
+ 
+
+ align:start position:0%
+symbolic toolkit which is in Java and um
+they have numbers like D1 is the overall
+
+ align:start position:0%
+they have numbers like D1 is the overall
+ 
+
+ align:start position:0%
+they have numbers like D1 is the overall
+dynamic range features not all of them
+
+ align:start position:0%
+dynamic range features not all of them
+ 
+
+ align:start position:0%
+dynamic range features not all of them
+have been implemented um eyes are
+
+ align:start position:0%
+have been implemented um eyes are
+ 
+
+ align:start position:0%
+have been implemented um eyes are
+instrument features you can probably see
+
+ align:start position:0%
+instrument features you can probably see
+ 
+
+ align:start position:0%
+instrument features you can probably see
+that um the percentage of all notes
+
+ align:start position:0%
+that um the percentage of all notes
+ 
+
+ align:start position:0%
+that um the percentage of all notes
+being played by electric guitars
+
+ align:start position:0%
+being played by electric guitars
+ 
+
+ align:start position:0%
+being played by electric guitars
+if you know something about jigs is
+
+ align:start position:0%
+if you know something about jigs is
+ 
+
+ align:start position:0%
+if you know something about jigs is
+probably not going to be very helpful to
+
+ align:start position:0%
+probably not going to be very helpful to
+ 
+
+ align:start position:0%
+probably not going to be very helpful to
+um to classifying whether or not
+
+ align:start position:0%
+um to classifying whether or not
+ 
+
+ align:start position:0%
+um to classifying whether or not
+something is a jig but maybe the average
+
+ align:start position:0%
+something is a jig but maybe the average
+ 
+
+ align:start position:0%
+something is a jig but maybe the average
+melodic interval will tell you something
+
+ align:start position:0%
+melodic interval will tell you something
+ 
+
+ align:start position:0%
+melodic interval will tell you something
+like that or how often there are melodic
+
+ align:start position:0%
+like that or how often there are melodic
+ 
+
+ align:start position:0%
+like that or how often there are melodic
+thirds or melodic fifths or maybe you
+
+ align:start position:0%
+thirds or melodic fifths or maybe you
+ 
+
+ align:start position:0%
+thirds or melodic fifths or maybe you
+know other things might tell sign so
+
+ align:start position:0%
+know other things might tell sign so
+ 
+
+ align:start position:0%
+know other things might tell sign so
+these are Melody features pitch features
+
+ align:start position:0%
+these are Melody features pitch features
+ 
+
+ align:start position:0%
+these are Melody features pitch features
+and so on um there's Rhythm features
+
+ align:start position:0%
+and so on um there's Rhythm features
+ 
+
+ align:start position:0%
+and so on um there's Rhythm features
+that's going to be pretty important um
+
+ align:start position:0%
+that's going to be pretty important um
+ 
+
+ align:start position:0%
+that's going to be pretty important um
+uh where do we have r31 initial time
+
+ align:start position:0%
+uh where do we have r31 initial time
+ 
+
+ align:start position:0%
+uh where do we have r31 initial time
+signature feature R32 compound or simple
+
+ align:start position:0%
+signature feature R32 compound or simple
+ 
+
+ align:start position:0%
+signature feature R32 compound or simple
+meure features and so on so we could add
+
+ align:start position:0%
+meure features and so on so we could add
+ 
+
+ align:start position:0%
+meure features and so on so we could add
+a bunch of these features in and we
+
+ align:start position:0%
+a bunch of these features in and we
+ 
+
+ align:start position:0%
+a bunch of these features in and we
+remember the names and within the music
+
+ align:start position:0%
+remember the names and within the music
+ 
+
+ align:start position:0%
+remember the names and within the music
+21 documentation there will be um
+
+ align:start position:0%
+21 documentation there will be um
+ 
+
+ align:start position:0%
+21 documentation there will be um
+certain things that will tell you you
+
+ align:start position:0%
+certain things that will tell you you
+ 
+
+ align:start position:0%
+certain things that will tell you you
+know uh triple meter features set to one
+
+ align:start position:0%
+know uh triple meter features set to one
+ 
+
+ align:start position:0%
+know uh triple meter features set to one
+if the numerator of the initial time
+
+ align:start position:0%
+if the numerator of the initial time
+ 
+
+ align:start position:0%
+if the numerator of the initial time
+signature is three or zero otherwise and
+
+ align:start position:0%
+signature is three or zero otherwise and
+ 
+
+ align:start position:0%
+signature is three or zero otherwise and
+this shows you how how it can work um so
+
+ align:start position:0%
+this shows you how how it can work um so
+ 
+
+ align:start position:0%
+this shows you how how it can work um so
+we can give a particular piece and it
+
+ align:start position:0%
+we can give a particular piece and it
+ 
+
+ align:start position:0%
+we can give a particular piece and it
+will tell us that BWB 66.6 is zero not
+
+ align:start position:0%
+will tell us that BWB 66.6 is zero not
+ 
+
+ align:start position:0%
+will tell us that BWB 66.6 is zero not
+in triple meter okay um we've already
+
+ align:start position:0%
+in triple meter okay um we've already
+ 
+
+ align:start position:0%
+in triple meter okay um we've already
+done something really really great um
+
+ align:start position:0%
+done something really really great um
+ 
+
+ align:start position:0%
+done something really really great um
+and so I will tell you that if we use
+
+ align:start position:0%
+and so I will tell you that if we use
+ 
+
+ align:start position:0%
+and so I will tell you that if we use
+this very similar feature extractors the
+
+ align:start position:0%
+this very similar feature extractors the
+ 
+
+ align:start position:0%
+this very similar feature extractors the
+ones we did before we're going to get
+
+ align:start position:0%
+ones we did before we're going to get
+ 
+
+ align:start position:0%
+ones we did before we're going to get
+the same um the same results but one of
+
+ align:start position:0%
+the same um the same results but one of
+ 
+
+ align:start position:0%
+the same um the same results but one of
+the other things we can do is we can
+
+ align:start position:0%
+the other things we can do is we can
+ 
+
+ align:start position:0%
+the other things we can do is we can
+just use a whole bunch of pretty random
+
+ align:start position:0%
+just use a whole bunch of pretty random
+ 
+
+ align:start position:0%
+just use a whole bunch of pretty random
+ones so we'll get um these features by
+
+ align:start position:0%
+ones so we'll get um these features by
+ 
+
+ align:start position:0%
+ones so we'll get um these features by
+ID and these are a bunch of features
+
+ align:start position:0%
+ID and these are a bunch of features
+ 
+
+ align:start position:0%
+ID and these are a bunch of features
+that I used to classify um various
+
+ align:start position:0%
+that I used to classify um various
+ 
+
+ align:start position:0%
+that I used to classify um various
+pieces of I think it was 16th 15th
+
+ align:start position:0%
+pieces of I think it was 16th 15th
+ 
+
+ align:start position:0%
+pieces of I think it was 16th 15th
+century music no 16th century music so
+
+ align:start position:0%
+century music no 16th century music so
+ 
+
+ align:start position:0%
+century music no 16th century music so
+they're not exactly super tuned for what
+
+ align:start position:0%
+they're not exactly super tuned for what
+ 
+
+ align:start position:0%
+they're not exactly super tuned for what
+we're going to do um um a lot of them
+
+ align:start position:0%
+we're going to do um um a lot of them
+ 
+
+ align:start position:0%
+we're going to do um um a lot of them
+are melodic features and so on uh well
+
+ align:start position:0%
+are melodic features and so on uh well
+ 
+
+ align:start position:0%
+are melodic features and so on uh well
+you see scroll over see which ones
+
+ align:start position:0%
+you see scroll over see which ones
+ 
+
+ align:start position:0%
+you see scroll over see which ones
+haven't done pitch features pitch
+
+ align:start position:0%
+haven't done pitch features pitch
+ 
+
+ align:start position:0%
+haven't done pitch features pitch
+feature
+
+ align:start position:0%
+feature
+ 
+
+ align:start position:0%
+feature
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+10 R up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+feature wa we guys see what they
+
+ align:start position:0%
+feature wa we guys see what they
+ 
+
+ align:start position:0%
+feature wa we guys see what they
+are I'm already going to tell you uh no
+
+ align:start position:0%
+are I'm already going to tell you uh no
+ 
+
+ align:start position:0%
+are I'm already going to tell you uh no
+surprise these aren't going to work
+
+ align:start position:0%
+surprise these aren't going to work
+ 
+
+ align:start position:0%
+surprise these aren't going to work
+nearly as well as the ones we just made
+
+ align:start position:0%
+nearly as well as the ones we just made
+ 
+
+ align:start position:0%
+nearly as well as the ones we just made
+um note dens feature isn't going to help
+
+ align:start position:0%
+um note dens feature isn't going to help
+ 
+
+ align:start position:0%
+um note dens feature isn't going to help
+us very much I would have thought range
+
+ align:start position:0%
+us very much I would have thought range
+ 
+
+ align:start position:0%
+us very much I would have thought range
+might have told us something about a jig
+
+ align:start position:0%
+might have told us something about a jig
+ 
+
+ align:start position:0%
+might have told us something about a jig
+but maybe it's not um some people will
+
+ align:start position:0%
+but maybe it's not um some people will
+ 
+
+ align:start position:0%
+but maybe it's not um some people will
+tell you hey just throw lots of feature
+
+ align:start position:0%
+tell you hey just throw lots of feature
+ 
+
+ align:start position:0%
+tell you hey just throw lots of feature
+extractors in um it can't hurt it kind
+
+ align:start position:0%
+extractors in um it can't hurt it kind
+ 
+
+ align:start position:0%
+extractors in um it can't hurt it kind
+of can but because we often don't have
+
+ align:start position:0%
+of can but because we often don't have
+ 
+
+ align:start position:0%
+of can but because we often don't have
+enough data to make use of all these
+
+ align:start position:0%
+enough data to make use of all these
+ 
+
+ align:start position:0%
+enough data to make use of all these
+features but let's give it a shot we're
+
+ align:start position:0%
+features but let's give it a shot we're
+ 
+
+ align:start position:0%
+features but let's give it a shot we're
+going to add these feature
+
+ align:start position:0%
+going to add these feature
+ 
+
+ align:start position:0%
+going to add these feature
+extractors to um our training set and to
+
+ align:start position:0%
+extractors to um our training set and to
+ 
+
+ align:start position:0%
+extractors to um our training set and to
+to our testing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set okay so our training set and testing
+
+ align:start position:0%
+set okay so our training set and testing
+ 
+
+ align:start position:0%
+set okay so our training set and testing
+set any uh is now ready to go where any
+
+ align:start position:0%
+set any uh is now ready to go where any
+ 
+
+ align:start position:0%
+set any uh is now ready to go where any
+stream we add to these sets we're going
+
+ align:start position:0%
+stream we add to these sets we're going
+ 
+
+ align:start position:0%
+stream we add to these sets we're going
+to um going to have these feature
+
+ align:start position:0%
+to um going to have these feature
+ 
+
+ align:start position:0%
+to um going to have these feature
+extractors added to them so we'll say is
+
+ align:start position:0%
+extractors added to them so we'll say is
+ 
+
+ align:start position:0%
+extractors added to them so we'll say is
+for I add metad dat entry in a
+
+ align:start position:0%
+for I add metad dat entry in a
+ 
+
+ align:start position:0%
+for I add metad dat entry in a
+numerate
+
+ align:start position:0%
+numerate
+ 
+
+ align:start position:0%
+numerate
+uh Ryan again P's part
+
+ align:start position:0%
+uh Ryan again P's part
+ 
+
+ align:start position:0%
+uh Ryan again P's part
+equals metad dat
+
+ align:start position:0%
+equals metad dat
+ 
+
+ align:start position:0%
+equals metad dat
+entry.
+
+ align:start position:0%
+entry.
+ 
+
+ align:start position:0%
+entry.
+parse if I is odd then training or test
+
+ align:start position:0%
+parse if I is odd then training or test
+ 
+
+ align:start position:0%
+parse if I is odd then training or test
+will be we'll we'll set um so we only
+
+ align:start position:0%
+will be we'll we'll set um so we only
+ 
+
+ align:start position:0%
+will be we'll we'll set um so we only
+have to write things once we'll set our
+
+ align:start position:0%
+have to write things once we'll set our
+ 
+
+ align:start position:0%
+have to write things once we'll set our
+training or test set will be the
+
+ align:start position:0%
+training or test set will be the
+ 
+
+ align:start position:0%
+training or test set will be the
+training set in this case otherwise our
+
+ align:start position:0%
+training set in this case otherwise our
+ 
+
+ align:start position:0%
+training set in this case otherwise our
+training or test will be our testing
+
+ align:start position:0%
+training or test will be our testing
+ 
+
+ align:start position:0%
+training or test will be our testing
+set great uh file name is the pie PAR
+
+ align:start position:0%
+set great uh file name is the pie PAR
+ 
+
+ align:start position:0%
+set great uh file name is the pie PAR
+file path name is jig same thing we were
+
+ align:start position:0%
+file path name is jig same thing we were
+ 
+
+ align:start position:0%
+file path name is jig same thing we were
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+before here we're not going to um music
+
+ align:start position:0%
+before here we're not going to um music
+ 
+
+ align:start position:0%
+before here we're not going to um music
+21 smart enough it doesn't need us to
+
+ align:start position:0%
+21 smart enough it doesn't need us to
+ 
+
+ align:start position:0%
+21 smart enough it doesn't need us to
+cast this to an integer that'll figure
+
+ align:start position:0%
+cast this to an integer that'll figure
+ 
+
+ align:start position:0%
+cast this to an integer that'll figure
+out what to do itself
+
+ align:start position:0%
+out what to do itself
+ 
+
+ align:start position:0%
+out what to do itself
+okay we going say what row are we is
+
+ align:start position:0%
+okay we going say what row are we is
+ 
+
+ align:start position:0%
+okay we going say what row are we is
+this a jig and what's its file name
+
+ align:start position:0%
+this a jig and what's its file name
+ 
+
+ align:start position:0%
+this a jig and what's its file name
+that's easy part and then whatever
+
+ align:start position:0%
+that's easy part and then whatever
+ 
+
+ align:start position:0%
+that's easy part and then whatever
+dating data set we're working with
+
+ align:start position:0%
+dating data set we're working with
+ 
+
+ align:start position:0%
+dating data set we're working with
+training or test we're going to add
+
+ align:start position:0%
+training or test we're going to add
+ 
+
+ align:start position:0%
+training or test we're going to add
+the data from the here's a stream our
+
+ align:start position:0%
+the data from the here's a stream our
+ 
+
+ align:start position:0%
+the data from the here's a stream our
+score whatever you call it class value
+
+ align:start position:0%
+score whatever you call it class value
+ 
+
+ align:start position:0%
+score whatever you call it class value
+what is what is the right answer it's
+
+ align:start position:0%
+what is what is the right answer it's
+ 
+
+ align:start position:0%
+what is what is the right answer it's
+whether or not this is a jig and then
+
+ align:start position:0%
+whether or not this is a jig and then
+ 
+
+ align:start position:0%
+whether or not this is a jig and then
+the identification for this will be the
+
+ align:start position:0%
+the identification for this will be the
+ 
+
+ align:start position:0%
+the identification for this will be the
+file name okay boom it's going to go
+
+ align:start position:0%
+file name okay boom it's going to go
+ 
+
+ align:start position:0%
+file name okay boom it's going to go
+through it has 1,000 of these to run so
+
+ align:start position:0%
+through it has 1,000 of these to run so
+ 
+
+ align:start position:0%
+through it has 1,000 of these to run so
+I'm not going to wait for all of it to
+
+ align:start position:0%
+I'm not going to wait for all of it to
+ 
+
+ align:start position:0%
+I'm not going to wait for all of it to
+um happen I'm going to stop for a second
+
+ align:start position:0%
+um happen I'm going to stop for a second
+ 
+
+ align:start position:0%
+um happen I'm going to stop for a second
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+because we don't have all that time in
+
+ align:start position:0%
+because we don't have all that time in
+ 
+
+ align:start position:0%
+because we don't have all that time in
+the world um that's part of the reason
+
+ align:start position:0%
+the world um that's part of the reason
+ 
+
+ align:start position:0%
+the world um that's part of the reason
+why we also don't want to do everything
+
+ align:start position:0%
+why we also don't want to do everything
+ 
+
+ align:start position:0%
+why we also don't want to do everything
+but our that small training set we're
+
+ align:start position:0%
+but our that small training set we're
+ 
+
+ align:start position:0%
+but our that small training set we're
+going to process and we're going to take
+
+ align:start position:0%
+going to process and we're going to take
+ 
+
+ align:start position:0%
+going to process and we're going to take
+that training set and write it out to
+
+ align:start position:0%
+that training set and write it out to
+ 
+
+ align:start position:0%
+that training set and write it out to
+train
+
+ align:start position:0%
+train
+ 
+
+ align:start position:0%
+train
+to. no we're not you should do that
+
+ align:start position:0%
+to. no we're not you should do that
+ 
+
+ align:start position:0%
+to. no we're not you should do that
+because you have time to wait but uh
+
+ align:start position:0%
+because you have time to wait but uh
+ 
+
+ align:start position:0%
+because you have time to wait but uh
+nobody wants us do that we'll do the
+
+ align:start position:0%
+nobody wants us do that we'll do the
+ 
+
+ align:start position:0%
+nobody wants us do that we'll do the
+same thing with the testing set process
+
+ align:start position:0%
+same thing with the testing set process
+ 
+
+ align:start position:0%
+same thing with the testing set process
+and then testing set
+
+ align:start position:0%
+and then testing set
+ 
+
+ align:start position:0%
+and then testing set
+we're going to write that to test
+
+ align:start position:0%
+we're going to write that to test
+ 
+
+ align:start position:0%
+we're going to write that to test
+2.tap I'm not doing that right now
+
+ align:start position:0%
+2.tap I'm not doing that right now
+ 
+
+ align:start position:0%
+2.tap I'm not doing that right now
+because like they do in those old
+
+ align:start position:0%
+because like they do in those old
+ 
+
+ align:start position:0%
+because like they do in those old
+cooking shows um I've already done all
+
+ align:start position:0%
+cooking shows um I've already done all
+ 
+
+ align:start position:0%
+cooking shows um I've already done all
+this and I'm going to uh load it from
+
+ align:start position:0%
+this and I'm going to uh load it from
+ 
+
+ align:start position:0%
+this and I'm going to uh load it from
+what I've already done
+
+ align:start position:0%
+what I've already done
+ 
+
+ align:start position:0%
+what I've already done
+so um you know what I mean the old
+
+ align:start position:0%
+so um you know what I mean the old
+ 
+
+ align:start position:0%
+so um you know what I mean the old
+cooking shows where they put they put
+
+ align:start position:0%
+cooking shows where they put they put
+ 
+
+ align:start position:0%
+cooking shows where they put they put
+the turkey raw turkey in the oven and
+
+ align:start position:0%
+the turkey raw turkey in the oven and
+ 
+
+ align:start position:0%
+the turkey raw turkey in the oven and
+then they just immediately go to the
+
+ align:start position:0%
+then they just immediately go to the
+ 
+
+ align:start position:0%
+then they just immediately go to the
+other oven and the turkey son. sorry all
+
+ align:start position:0%
+other oven and the turkey son. sorry all
+ 
+
+ align:start position:0%
+other oven and the turkey son. sorry all
+right I you know you all can read my
+
+ align:start position:0%
+right I you know you all can read my
+ 
+
+ align:start position:0%
+right I you know you all can read my
+mind right that's that's
+
+ align:start position:0%
+mind right that's that's
+ 
+
+ align:start position:0%
+mind right that's that's
+what that's what you pay me to do make
+
+ align:start position:0%
+what that's what you pay me to do make
+ 
+
+ align:start position:0%
+what that's what you pay me to do make
+you read my mind to not actually
+
+ align:start position:0%
+you read my mind to not actually
+ 
+
+ align:start position:0%
+you read my mind to not actually
+teach that's fantastic um okay a no
+
+ align:start position:0%
+teach that's fantastic um okay a no
+ 
+
+ align:start position:0%
+teach that's fantastic um okay a no
+enough I'll make this line up so I
+
+ align:start position:0%
+enough I'll make this line up so I
+ 
+
+ align:start position:0%
+enough I'll make this line up so I
+don't so I don't make any
+
+ align:start position:0%
+don't so I don't make any
+ 
+
+ align:start position:0%
+don't so I don't make any
+typos on my
+
+ align:start position:0%
+typos on my
+ 
+
+ align:start position:0%
+typos on my
+desktop test 2.tap that's why it broke
+
+ align:start position:0%
+desktop test 2.tap that's why it broke
+ 
+
+ align:start position:0%
+desktop test 2.tap that's why it broke
+okay so again we're going to do
+
+ align:start position:0%
+okay so again we're going to do
+ 
+
+ align:start position:0%
+okay so again we're going to do
+everything as before why do everything
+
+ align:start position:0%
+everything as before why do everything
+ 
+
+ align:start position:0%
+everything as before why do everything
+as before when you can't just copy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and because now we've already written
+
+ align:start position:0%
+and because now we've already written
+ 
+
+ align:start position:0%
+and because now we've already written
+everything out for um yeah this this
+
+ align:start position:0%
+everything out for um yeah this this
+ 
+
+ align:start position:0%
+everything out for um yeah this this
+whole process and right thing takes care
+
+ align:start position:0%
+whole process and right thing takes care
+ 
+
+ align:start position:0%
+whole process and right thing takes care
+of everything we did before where we
+
+ align:start position:0%
+of everything we did before where we
+ 
+
+ align:start position:0%
+of everything we did before where we
+where is that where we had to Define we
+
+ align:start position:0%
+where is that where we had to Define we
+ 
+
+ align:start position:0%
+where is that where we had to Define we
+had to open our datas we had to Define
+
+ align:start position:0%
+had to open our datas we had to Define
+ 
+
+ align:start position:0%
+had to open our datas we had to Define
+our columns we had to write that out
+
+ align:start position:0%
+our columns we had to write that out
+ 
+
+ align:start position:0%
+our columns we had to write that out
+Define our description write out all our
+
+ align:start position:0%
+Define our description write out all our
+ 
+
+ align:start position:0%
+Define our description write out all our
+meta things um extract write our feature
+
+ align:start position:0%
+meta things um extract write our feature
+ 
+
+ align:start position:0%
+meta things um extract write our feature
+extractors do all that
+
+ align:start position:0%
+extractors do all that
+ 
+
+ align:start position:0%
+extractors do all that
+stuff these little um process and then
+
+ align:start position:0%
+stuff these little um process and then
+ 
+
+ align:start position:0%
+stuff these little um process and then
+write did all that for us so now we're
+
+ align:start position:0%
+write did all that for us so now we're
+ 
+
+ align:start position:0%
+write did all that for us so now we're
+we're actually back on to
+
+ align:start position:0%
+we're actually back on to
+ 
+
+ align:start position:0%
+we're actually back on to
+uh uh feature extraction is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done let's do machine learning anybody
+
+ align:start position:0%
+done let's do machine learning anybody
+ 
+
+ align:start position:0%
+done let's do machine learning anybody
+who tells you that the machine learn
+
+ align:start position:0%
+who tells you that the machine learn
+ 
+
+ align:start position:0%
+who tells you that the machine learn
+learning is the only hard part and that
+
+ align:start position:0%
+learning is the only hard part and that
+ 
+
+ align:start position:0%
+learning is the only hard part and that
+feature extraction uh is easy stuff uh
+
+ align:start position:0%
+feature extraction uh is easy stuff uh
+ 
+
+ align:start position:0%
+feature extraction uh is easy stuff uh
+is lying to you or is doesn't know what
+
+ align:start position:0%
+is lying to you or is doesn't know what
+ 
+
+ align:start position:0%
+is lying to you or is doesn't know what
+they're talking about or whatever
+
+ align:start position:0%
+they're talking about or whatever
+ 
+
+ align:start position:0%
+they're talking about or whatever
+because um feature extraction and doing
+
+ align:start position:0%
+because um feature extraction and doing
+ 
+
+ align:start position:0%
+because um feature extraction and doing
+it right is really really hard okay so
+
+ align:start position:0%
+it right is really really hard okay so
+ 
+
+ align:start position:0%
+it right is really really hard okay so
+we're going to cop basically copy and
+
+ align:start position:0%
+we're going to cop basically copy and
+ 
+
+ align:start position:0%
+we're going to cop basically copy and
+paste everything that um that we did
+
+ align:start position:0%
+paste everything that um that we did
+ 
+
+ align:start position:0%
+paste everything that um that we did
+before totals something like
+
+ align:start position:0%
+before totals something like
+ 
+
+ align:start position:0%
+before totals something like
+that great we're going to run this
+
+ align:start position:0%
+that great we're going to run this
+ 
+
+ align:start position:0%
+that great we're going to run this
+again and then we're going
+
+ align:start position:0%
+again and then we're going
+ 
+
+ align:start position:0%
+again and then we're going
+to print everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+afterwards great and that's going to go
+
+ align:start position:0%
+afterwards great and that's going to go
+ 
+
+ align:start position:0%
+afterwards great and that's going to go
+through and uh it's going to print a
+
+ align:start position:0%
+through and uh it's going to print a
+ 
+
+ align:start position:0%
+through and uh it's going to print a
+couple things what are we
+
+ align:start position:0%
+couple things what are we
+ 
+
+ align:start position:0%
+couple things what are we
+doing oh has to we giving it a lot more
+
+ align:start position:0%
+doing oh has to we giving it a lot more
+ 
+
+ align:start position:0%
+doing oh has to we giving it a lot more
+things to train on so a lot more data
+
+ align:start position:0%
+things to train on so a lot more data
+ 
+
+ align:start position:0%
+things to train on so a lot more data
+these are much bigger files because of
+
+ align:start position:0%
+these are much bigger files because of
+ 
+
+ align:start position:0%
+these are much bigger files because of
+all the different feature extractors so
+
+ align:start position:0%
+all the different feature extractors so
+ 
+
+ align:start position:0%
+all the different feature extractors so
+it takes a while you can see in all this
+
+ align:start position:0%
+it takes a while you can see in all this
+ 
+
+ align:start position:0%
+it takes a while you can see in all this
+time it's just done one
+
+ align:start position:0%
+time it's just done one
+ 
+
+ align:start position:0%
+time it's just done one
+row and two rows are we going to wait
+
+ align:start position:0%
+row and two rows are we going to wait
+ 
+
+ align:start position:0%
+row and two rows are we going to wait
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+uh you know oh I think it's like an hour
+
+ align:start position:0%
+uh you know oh I think it's like an hour
+ 
+
+ align:start position:0%
+uh you know oh I think it's like an hour
+and a half and I ran this at like 2 in
+
+ align:start position:0%
+and a half and I ran this at like 2 in
+ 
+
+ align:start position:0%
+and a half and I ran this at like 2 in
+the morning are we going to wait an hour
+
+ align:start position:0%
+the morning are we going to wait an hour
+ 
+
+ align:start position:0%
+the morning are we going to wait an hour
+and a half we can all do that no I'm
+
+ align:start position:0%
+and a half we can all do that no I'm
+ 
+
+ align:start position:0%
+and a half we can all do that no I'm
+going to hit stop for a second on the
+
+ align:start position:0%
+going to hit stop for a second on the
+ 
+
+ align:start position:0%
+going to hit stop for a second on the
+recording and then I'm going to load up
+
+ align:start position:0%
+recording and then I'm going to load up
+ 
+
+ align:start position:0%
+recording and then I'm going to load up
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+results okay here are the results I
+
+ align:start position:0%
+results okay here are the results I
+ 
+
+ align:start position:0%
+results okay here are the results I
+got again our majority learner got 77%
+
+ align:start position:0%
+got again our majority learner got 77%
+ 
+
+ align:start position:0%
+got again our majority learner got 77%
+right and our K nearest neighbors super
+
+ align:start position:0%
+right and our K nearest neighbors super
+ 
+
+ align:start position:0%
+right and our K nearest neighbors super
+intelligent artificial
+
+ align:start position:0%
+intelligent artificial
+ 
+
+ align:start position:0%
+intelligent artificial
+intelligence only got 4% better I mean I
+
+ align:start position:0%
+intelligence only got 4% better I mean I
+ 
+
+ align:start position:0%
+intelligence only got 4% better I mean I
+don't even know if that meets the margin
+
+ align:start position:0%
+don't even know if that meets the margin
+ 
+
+ align:start position:0%
+don't even know if that meets the margin
+of error in a political poll or
+
+ align:start position:0%
+of error in a political poll or
+ 
+
+ align:start position:0%
+of error in a political poll or
+something so all that extra time didn't
+
+ align:start position:0%
+something so all that extra time didn't
+ 
+
+ align:start position:0%
+something so all that extra time didn't
+actually improve anything what's
+
+ align:start position:0%
+actually improve anything what's
+ 
+
+ align:start position:0%
+actually improve anything what's
+important is always to choose your um
+
+ align:start position:0%
+important is always to choose your um
+ 
+
+ align:start position:0%
+important is always to choose your um
+choose your
+
+ align:start position:0%
+choose your
+ 
+
+ align:start position:0%
+choose your
+feature extractors well the fact that I
+
+ align:start position:0%
+feature extractors well the fact that I
+ 
+
+ align:start position:0%
+feature extractors well the fact that I
+didn't include that one simple extractor
+
+ align:start position:0%
+didn't include that one simple extractor
+ 
+
+ align:start position:0%
+didn't include that one simple extractor
+about the time signature made all the
+
+ align:start position:0%
+about the time signature made all the
+ 
+
+ align:start position:0%
+about the time signature made all the
+difference in the world I think um okay
+
+ align:start position:0%
+difference in the world I think um okay
+ 
+
+ align:start position:0%
+difference in the world I think um okay
+I just want to show that there's um you
+
+ align:start position:0%
+I just want to show that there's um you
+ 
+
+ align:start position:0%
+I just want to show that there's um you
+can uh you can print all of the
+
+ align:start position:0%
+can uh you can print all of the
+ 
+
+ align:start position:0%
+can uh you can print all of the
+different features onto various charts
+
+ align:start position:0%
+different features onto various charts
+ 
+
+ align:start position:0%
+different features onto various charts
+and zoom in and stuff like that if
+
+ align:start position:0%
+and zoom in and stuff like that if
+ 
+
+ align:start position:0%
+and zoom in and stuff like that if
+people want to do that but that'll be
+
+ align:start position:0%
+people want to do that but that'll be
+ 
+
+ align:start position:0%
+people want to do that but that'll be
+something for another
+
+ align:start position:0%
+something for another
+ 
+
+ align:start position:0%
+something for another
+time this is what is available to you
+
+ align:start position:0%
+time this is what is available to you
+ 
+
+ align:start position:0%
+time this is what is available to you
+now um maybe not this kind of low-level
+
+ align:start position:0%
+now um maybe not this kind of low-level
+ 
+
+ align:start position:0%
+now um maybe not this kind of low-level
+one but using the these feature
+
+ align:start position:0%
+one but using the these feature
+ 
+
+ align:start position:0%
+one but using the these feature
+extractors simple ones like Sharps and
+
+ align:start position:0%
+extractors simple ones like Sharps and
+ 
+
+ align:start position:0%
+extractors simple ones like Sharps and
+meter and uh what was that percentage of
+
+ align:start position:0%
+meter and uh what was that percentage of
+ 
+
+ align:start position:0%
+meter and uh what was that percentage of
+compound time range features things like
+
+ align:start position:0%
+compound time range features things like
+ 
+
+ align:start position:0%
+compound time range features things like
+that in order to classify pieces is
+
+ align:start position:0%
+that in order to classify pieces is
+ 
+
+ align:start position:0%
+that in order to classify pieces is
+incredibly powerful and when put
+
+ align:start position:0%
+incredibly powerful and when put
+ 
+
+ align:start position:0%
+incredibly powerful and when put
+together with the right machine learning
+
+ align:start position:0%
+together with the right machine learning
+ 
+
+ align:start position:0%
+together with the right machine learning
+and artificial intelligence algorithm
+
+ align:start position:0%
+and artificial intelligence algorithm
+ 
+
+ align:start position:0%
+and artificial intelligence algorithm
+there's a lot of possibilities for the
+
+ align:start position:0%
+there's a lot of possibilities for the
+ 
+
+ align:start position:0%
+there's a lot of possibilities for the
+future of computational Music
+
+ align:start position:0%
+future of computational Music
+ 
+
+ align:start position:0%
+future of computational Music
+analysis this lecture is run pretty darn
+
+ align:start position:0%
+analysis this lecture is run pretty darn
+ 
+
+ align:start position:0%
+analysis this lecture is run pretty darn
+long so I'm going to say for a second
+
+ align:start position:0%
+long so I'm going to say for a second
+ 
+
+ align:start position:0%
+long so I'm going to say for a second
+little supplement on what are some of
+
+ align:start position:0%
+little supplement on what are some of
+ 
+
+ align:start position:0%
+little supplement on what are some of
+the things that I have learned through
+
+ align:start position:0%
+the things that I have learned through
+ 
+
+ align:start position:0%
+the things that I have learned through
+using computational artificial
+
+ align:start position:0%
+using computational artificial
+ 
+
+ align:start position:0%
+using computational artificial
+intelligence what are some of the
+
+ align:start position:0%
+intelligence what are some of the
+ 
+
+ align:start position:0%
+intelligence what are some of the
+projects other people have done and why
+
+ align:start position:0%
+projects other people have done and why
+ 
+
+ align:start position:0%
+projects other people have done and why
+the world of the-art blackbox deep
+
+ align:start position:0%
+the world of the-art blackbox deep
+ 
+
+ align:start position:0%
+the world of the-art blackbox deep
+learning or um other sophisticated
+
+ align:start position:0%
+learning or um other sophisticated
+ 
+
+ align:start position:0%
+learning or um other sophisticated
+algorithms might not always be the best
+
+ align:start position:0%
+algorithms might not always be the best
+ 
+
+ align:start position:0%
+algorithms might not always be the best
+ones that we want to use when we're
+
+ align:start position:0%
+ones that we want to use when we're
+ 
+
+ align:start position:0%
+ones that we want to use when we're
+doing artificial intelligence and
+
+ align:start position:0%
+doing artificial intelligence and
+ 
+
+ align:start position:0%
+doing artificial intelligence and
+machine learning techniques on musical
+
+ align:start position:0%
+machine learning techniques on musical
+ 
+
+ align:start position:0%
+machine learning techniques on musical
+scores but we'll leave that for another
+
+ align:start position:0%
+scores but we'll leave that for another
+ 
+
+ align:start position:0%
+scores but we'll leave that for another
+time thank you so much for listening go
+
+ align:start position:0%
+time thank you so much for listening go
+ 
+
+ align:start position:0%
+time thank you so much for listening go
+ahead and play around with some data
+
+ align:start position:0%
+ahead and play around with some data
+ 
+
+ align:start position:0%
+ahead and play around with some data
+sets you've learned how to use Corpus
+
+ align:start position:0%
+sets you've learned how to use Corpus
+ 
+
+ align:start position:0%
+sets you've learned how to use Corpus
+search to be able to find various pieces
+
+ align:start position:0%
+search to be able to find various pieces
+ 
+
+ align:start position:0%
+search to be able to find various pieces
+on there's a music 21 uh I think chapter
+
+ align:start position:0%
+on there's a music 21 uh I think chapter
+ 
+
+ align:start position:0%
+on there's a music 21 uh I think chapter
+users guide chapter and tutorial on how
+
+ align:start position:0%
+users guide chapter and tutorial on how
+ 
+
+ align:start position:0%
+users guide chapter and tutorial on how
+to do more interesting things with that
+
+ align:start position:0%
+to do more interesting things with that
+ 
+
+ align:start position:0%
+to do more interesting things with that
+there's the paper written with Chris ARA
+
+ align:start position:0%
+there's the paper written with Chris ARA
+ 
+
+ align:start position:0%
+there's the paper written with Chris ARA
+and Lisa Friedland on using feature
+
+ align:start position:0%
+and Lisa Friedland on using feature
+ 
+
+ align:start position:0%
+and Lisa Friedland on using feature
+extractors with music 21 and there's
+
+ align:start position:0%
+extractors with music 21 and there's
+ 
+
+ align:start position:0%
+extractors with music 21 and there's
+also some other um music 21 feature
+
+ align:start position:0%
+also some other um music 21 feature
+ 
+
+ align:start position:0%
+also some other um music 21 feature
+extractor papers that were written with
+
+ align:start position:0%
+extractor papers that were written with
+ 
+
+ align:start position:0%
+extractor papers that were written with
+MIT undergraduate europs on how we can
+
+ align:start position:0%
+MIT undergraduate europs on how we can
+ 
+
+ align:start position:0%
+MIT undergraduate europs on how we can
+use feature extraction to go beyond what
+
+ align:start position:0%
+use feature extraction to go beyond what
+ 
+
+ align:start position:0%
+use feature extraction to go beyond what
+we can do with midi to really look at
+
+ align:start position:0%
+we can do with midi to really look at
+ 
+
+ align:start position:0%
+we can do with midi to really look at
+the Nuance of musical scores in feature
+
+ align:start position:0%
+the Nuance of musical scores in feature
+ 
+
+ align:start position:0%
+the Nuance of musical scores in feature
+extraction I'll be sending all those
+
+ align:start position:0%
+extraction I'll be sending all those
+ 
+
+ align:start position:0%
+extraction I'll be sending all those
+around the meantime please go back
+
+ align:start position:0%
+around the meantime please go back
+ 
+
+ align:start position:0%
+around the meantime please go back
+through your the most interesting parts
+
+ align:start position:0%
+through your the most interesting parts
+ 
+
+ align:start position:0%
+through your the most interesting parts
+of this lecture to you hit pause and
+
+ align:start position:0%
+of this lecture to you hit pause and
+ 
+
+ align:start position:0%
+of this lecture to you hit pause and
+play around with your own data
+
+ align:start position:0%
+play around with your own data
+ 
+
+ align:start position:0%
+play around with your own data
+sense good luck in applying this to
+
+ align:start position:0%
+sense good luck in applying this to
+ 
+
+ align:start position:0%
+sense good luck in applying this to
+Future projects
\ No newline at end of file
diff --git a/fGUaxrIejr4.txt b/fGUaxrIejr4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5452112480f79f2ca48ee1703714487bd4a73e39
--- /dev/null
+++ b/fGUaxrIejr4.txt
@@ -0,0 +1,2802 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK, let's start.
+
+So we've been trying to
+understand critical points.
+
+And this refers to the
+experimental observation
+
+that in a number
+of systems we can
+
+be changing some parameters,
+such as temperature,
+
+and you encounter a transition
+to some other type of behavior
+
+at some point.
+
+So the temperature, let's
+say, in this behavior
+
+is the control parameter.
+
+And you have to
+see, for example,
+
+this will be normal to
+superfluid transition.
+
+You have one now [INAUDIBLE]
+change temperature and going
+
+through this point.
+
+For other systems,
+such as magnets,
+
+you actually have two knobs.
+
+There is also the
+magnetic field.
+
+And there, you have
+to turn two knobs
+
+in order to end at
+this critical point,
+
+also in the case of the liquid
+gas system in the pressure
+
+temperature plane, you
+have to tune two things
+
+to get this point.
+
+And the interesting thing
+was that in the vicinity
+
+of his point, the singular
+parts of various thermodynamic
+
+quantities are interestingly
+independent of the type
+
+of material.
+
+So if we, for example, establish
+a coordinate at t and h
+
+describing deviations
+from this critical point,
+
+we have, let's say,
+the singular part
+
+of free energy as a
+function of t and h
+
+has a form like t to
+the 2 minus alpha,
+
+some scaling function
+ht to the delta,
+
+and these exponents, alpha
+and delta, other things
+
+that are universe.
+
+For example, we
+could get from that
+
+by taking two derivatives with
+respect to h, the singularity
+
+and the divergence of
+the susceptibility.
+
+And we said that the
+diverging susceptibility also
+
+immediately tells you that
+there is a correlation then
+
+that diverges, and
+in particular, we
+
+indicated its divergence
+to an exponent u.
+
+WE could for that also
+establish a scaling form
+
+on how the correlation
+then diverges
+
+on approaching this point
+generally in the ht plane.
+
+So this was the general picture.
+
+And building on that, we made
+one observation last time,
+
+which is that any point when
+you are away from h and t
+
+equals to 0, you have
+a correlation length.
+
+And then we concluded that if
+you are at t and h equals to 0,
+
+you have a form of
+scaling vertices.
+
+And basically what
+that means is that when
+
+you are at that point,
+you look at your system,
+
+it's a fluctuating system,
+and the fluctuations are
+
+such that you can't
+associate a scale with them.
+
+The scale has already
+gone into the correlation
+
+length that is infinite.
+
+And we said that
+therefore, if I were
+
+to look at some kind of
+a correlation function,
+
+such as a magnetization
+in the case of a magnet,
+
+that the only way that
+it became its separation
+
+is as a power of a distance.
+
+And this clearly has
+a property that if we
+
+were to rescale x and
+y by a certain amount,
+
+this correlation function
+nearly gets multiplied
+
+by a factor that is
+dependent on this rescale.
+
+And this is after
+we do the averaging,
+
+so it's a kind of
+statistical self-singularity,
+
+as opposed to some factor such
+as Sierpinkski gasket, which
+
+are identically and
+deterministically
+
+self-similar in that each
+piece, if you blow it up,
+
+looks like the entire thing.
+
+So what we have in our system
+is that if we have, let's say,
+
+a box which could be
+containing our liquid gas
+
+system at its critical
+point, or maybe a magnet
+
+at its critical point, will
+have a statistical field,
+
+this m of x.
+
+And it will fluctuate
+across the system.
+
+So maybe this would be a picture
+of the density fluctuation.
+
+What I can do is to take a scan
+along some particular axis--
+
+let's call it x-- and plot
+what the fluctuations are
+
+of this magnetization.
+
+Let's say m of x.
+
+Now the average
+will be 0, but it
+
+will have fluctuations
+around the average.
+
+And so maybe it
+will look something
+
+like this-- kind of like
+a picture of a mountain,
+
+for example.
+
+Now one thing that
+we should remember
+
+is that this object would
+be piece of iron or nickle,
+
+and clearly I don't
+really mean that this
+
+is what is going on at
+the scale of a single atom
+
+or molecule of my substance.
+
+I had to do some kind
+of averaging in order
+
+to get the statistical field
+that I'm presenting here.
+
+So let's keep in
+mind that there is,
+
+in fact, some implicit
+analog of lattice size
+
+or some implicit
+shortest distance,
+
+shortest wavelength that I
+allow for my frustrations.
+
+Now I can sort of make this
+idea of scale invariance
+
+of a set of pictures, such
+as this one, more precise,
+
+as follows, by going
+through a procedure
+
+that I will call renormalization
+that has the following three
+
+steps.
+
+So the first step, what I will
+do is to coarse-grain further.
+
+And by this, I mean averaging
+m of x over a scale ta.
+
+So previously, I had done my
+averaging of whatever means,
+
+et cetera.
+
+We're giving contribution
+to the overall magnetization
+
+over some number,
+let's 100 by 100 by 100
+
+spins and a was my
+scaling distance.
+
+Why should I choose 100?
+
+Why not choose 200, some factor
+of what I had originally?
+
+So coarse-graining means
+increasing this minimum length
+
+scale from a to ba.
+
+And then I define a
+coarse-grained version
+
+of my field.
+
+So previously, I had m of x.
+
+Now I have m tilda of x, which
+is obtained by averaging,
+
+let's say, over volume around
+the point x that I had before.
+
+And this volume is a box
+of dimension ba to the d.
+
+And then I basically
+average over that.
+
+I guess let's call it
+original distance a equals 1,
+
+so I don't really have to bother
+by the dimensionality of y,
+
+et cetera.
+
+OK?
+
+So if I were to apply
+that to the picture
+
+that I have up
+there, what do I get?
+
+I will get an m tilda
+as a function of x.
+
+And essentially,
+let's say if I were
+
+to choose a factor
+of b that was like 2,
+
+I would take the average
+of the fluctuations
+
+that they have over 2 of
+those of those intervals.
+
+And so the picture
+that I would get it
+
+would be kind of a
+smoothened out version
+
+of what I have
+before over there.
+
+I will still have
+some fluctuations,
+
+but kind of ironed out.
+
+And basically,
+essentially, it means
+
+that if you were to imagine
+having taken a photograph,
+
+previously you had the
+pixel size that was 1.
+
+Now your pixel size is larger.
+
+It is factor of b.
+
+So it's this kind of
+detuning and averaging
+
+of the fluctuations
+that has gone.
+
+And so you have here now b.
+
+Now if I were to give you
+a photograph like that
+
+and a photograph
+like this, you would
+
+say that they are not identical.
+
+One of them is clearly much
+grainier than the other.
+
+So I say, OK, I can restore
+some amount of similarity
+
+between them by
+doing a rescaling.
+
+So I call a new variable x prime
+to be my old variable x divided
+
+by a factor of b.
+
+So when I do that
+to this picture,
+
+I will get m tilda as
+a function of x prime.
+
+x prime can go in further
+less, because all I do
+
+is I take this and squeeze
+it by a factor of b.
+
+So I will get a
+picture that maybe
+
+looks something like this.
+
+Now if I were to look at this
+picture and this picture,
+
+you would also see a difference.
+
+That is, there is a contrast.
+
+So here, there would be,
+let's say, black and white.
+
+And as you scan the
+picture, you sort of see
+
+some variation of
+black and white.
+
+If you look at this, you say
+the contrast is just too big.
+
+You have big fluctuations
+as you go across
+
+compared to what
+I had over there.
+
+So there's another step, which
+is called renormalize, which
+
+is that you define
+m prime to be m
+
+by a change of
+contrast factor zeta.
+
+So you take a knob that
+corresponds to contrast
+
+and you reduce it
+until you see pictures
+
+that kind of statistically look
+like what you started with.
+
+So in order to sort of generate
+pictures that are self-similar,
+
+you have this one knob.
+
+Basically, scaling variance
+means the change of size.
+
+But there is associated
+with change of size
+
+a change of contrast
+for whatever variable
+
+you are looking at.
+
+It turns out that that
+change of contrast
+
+would eventually map to
+one of these exponents
+
+that we have over there.
+
+Yes.
+
+STUDENT: Are you
+using m or n tilda?
+
+PROFESSOR: m tilda, thank you.
+
+So I guess the green
+is m tilda of x prime,
+
+and the pink is m
+prime of x prime.
+
+So what I have done
+mathematically is as follows.
+
+I have defined an
+m prime of x prime,
+
+which is 1 over zeta,
+this contrast factor
+
+b to the d because of the
+averaging over a volume
+
+that involved b to the d pixels
+of the original field centered
+
+at a location that
+was bx prime plus y.
+
+So in principle, I
+can go and generate
+
+lots and lots of configurations
+of my magnetization,
+
+or lots and lots of pictures
+of a system at the liquid gas
+
+critical point, or
+magnetic systems
+
+at their critical point.
+
+I can generate lots and
+lots of these pictures
+
+and construct this
+transformation.
+
+And associated with
+this transformation
+
+is a change of
+probability, because there
+
+was some probability--
+let's call it P old,
+
+that was describing my
+original configurations m of x.
+
+Let's forget the vector
+notation for the time being.
+
+Then there will be, after this
+transformation, probability
+
+that describes these
+configurations m
+
+prime of x prime.
+
+Now you know that
+averaging is not something
+
+that you can reverse.
+
+So this transformation
+going from here and here,
+
+I cannot go back.
+
+There are many
+configurations over here
+
+that would correspond
+to the same average,
+
+like up, down or down,
+up would give you
+
+the same average, right?
+
+So a number of
+possibilities here
+
+have to be summed up to
+generate for you this object.
+
+Now the statement of
+self-similarity presumably
+
+is that this weight is
+the same as this weight.
+
+You can't tell apart that
+you generated configurations
+
+before or after that scaling.
+
+So this is same
+at critical point.
+
+I've not constructed
+either weight,
+
+so it really doesn't
+amount to much.
+
+But Kadanoff
+introduced this concept
+
+of doing this and thinking of
+it as a kind of group operation
+
+called renormalization
+group that I
+
+describe a little bit better
+and evolve the description as we
+
+go along.
+
+So if I look at my
+original system,
+
+I said that
+self-similarity occurs,
+
+let's say, exactly at this
+point that corresponds to t
+
+and h equals to 0.
+
+Now presumably, I
+can, in some sense,
+
+force these things, if I were
+to take its log, for example.
+
+I can construct some
+kind of a weight that
+
+is associated with
+m, and this would
+
+be a new weight that is
+associated with m prime.
+
+Presumably, right at
+the critical point,
+
+these two would be
+the same weight,
+
+and it would be the
+same Hamiltonian.
+
+What happens, if I
+do this procedure,
+
+to a system that is initially
+away from the critical point?
+
+So my initial system is
+characterized by deviations t
+
+and h from this scale
+in variant ways, which
+
+means that over here I
+have a correlation length.
+
+Now I go through all of
+these transformations.
+
+I can do those
+transformations also
+
+for a point that is not
+at the critical point.
+
+But at the end of
+the day, I certainly
+
+will not get back
+my original weight,
+
+because I look at the picture
+after this transformation.
+
+Before the transformation, I
+had a long correlation length,
+
+let's say a mile.
+
+When I do this transformation,
+that correlation length
+
+is reduced by a factor of b.
+
+So the new system has deviated
+more from the critical point.
+
+Because the further you go
+away from the critical point,
+
+you have a larger
+correlation length.
+
+So the idea is that right
+at the critical point,
+
+the two weights are the same.
+
+Deviation from
+the critical point
+
+is described by these
+two parameters, t and h.
+
+And if you do the
+renormalization procedure
+
+on a Hamiltonian
+that deviates, you
+
+will get a Hamiltonian
+that more deviates, still
+
+describable by parameters
+t and h that have changed.
+
+So again, this says
+that c was, in fact,
+
+b times c of t
+prime and h prime,
+
+and t prime and h
+prime are further away.
+
+Now the next thing that Kadanoff
+said was, OK, therefore there
+
+is a transformation
+that tells me
+
+after I do a rescaling
+by a factor of b how
+
+the new t and the new h depend
+on the old t and the old h.
+
+So there is a mapping
+in this space.
+
+So a point that was
+here will go over there.
+
+Maybe a point that is
+here will map over there.
+
+A point that is here
+will map over here.
+
+So there is a mapping
+that tells you
+
+how th get transformed
+under this procedure.
+
+Actually the reason this is
+called a renormalization group,
+
+groups we are really
+thinking usually
+
+in terms of operations
+that are invertible.
+
+This transformation
+is not invertible.
+
+But this is a mapping.
+
+So potentially this
+mapping is invertible.
+
+You can say that if this
+point came from this point
+
+under inversion, it will go
+back to the original point,
+
+and so forth.
+
+The next part of the argument
+is what did we do over here?
+
+We got rid of some short
+wavelength fluctuations.
+
+Now one of the things that I
+said right at the beginning
+
+was that as long as you are
+getting rid of short scale
+
+fluctuations, you are summing
+over a cube that his 100
+
+square, 200 cube.
+
+It doesn't matter,
+100 cube, 200 cube--
+
+you are doing some
+analytical function.
+
+So the transformation
+that relates these
+
+to these, the old to new,
+should be analytical,
+
+and hence you should be able to
+write a Taylor series for it.
+
+So let's try to make a
+Taylor series for this.
+
+Taylor series start
+with a constant.
+
+But we know that the constant
+has to be 0 in both cases
+
+because the starting
+point was the point that
+
+was scale invariant and
+was mapping onto itself.
+
+So the first thing that I can
+write down are linear terms.
+
+So there could be a term
+that is proportional to t.
+
+There could be a term
+that is proportional to h.
+
+There could be a term here
+that is proportional to h.
+
+There could be a term
+that is proportional--
+
+well, let's call this t.
+
+Let's call this h.
+
+And then there
+will be terms that
+
+will be order of t
+squared and higher.
+
+So I just did an
+analytical expansion,
+
+justified by this summing over
+just finite degrees of freedom
+
+at short scale.
+
+Now if I have a structure,
+such as the one that I
+
+have over there, I
+also know some things
+
+on the basis of symmetry.
+
+Like if I'm on the line that
+corresponds to h equals to 0,
+
+there is no difference
+between up and down.
+
+Under rescaling, I still
+don't know the difference
+
+between up and down.
+
+So I should not generate
+an h if h was originally 0
+
+just because t deviated from 0.
+
+So by symmetry, that
+has to be absent.
+
+And similarly, by
+symmetry, there
+
+is no difference between
+h positive and h negative.
+
+As far as t is concerned, h and
+minus h should behave the same.
+
+So this series should start at
+order of h squared and not h,
+
+so that term should be absent.
+
+So at this level, we have a nice
+separation into t prime is at
+
+and h Prime.
+
+Is dh.
+
+Now we know
+something more, which
+
+is that the procedure
+that we are doing
+
+has some kind of a group
+character, in that if I,
+
+let's say, originally
+transform by some factor b1,
+
+change by a factor of 2,
+then change by a factor of 3,
+
+the answer is equivalent to
+changing by a factor of 2
+
+times 3, or 3 times 2.
+
+Doesn't matter in
+which order I do them.
+
+So also, I would get,
+if I were to do b1 first
+
+and b2 later, it would
+be the same thing.
+
+So what does that imply?
+
+That if I do two of
+these transformation,
+
+I find that my new t is obtained
+in one case by the product,
+
+in the other case by the
+product of the two a's.
+
+So that's, again, some
+kind of a group character.
+
+And furthermore, if I don't
+change the length scale,
+
+everything should
+stay where it is.
+
+So you glance at
+those, and you find
+
+that there is only
+one possibility,
+
+that a as a function of b
+should be b to some power.
+
+So you know therefore
+that at the lowest
+
+order under rescaling
+by a factor of b,
+
+t prime should be b
+to some y-- I called
+
+it yt-- times t
+plus higher orders,
+
+while h prime is b to some other
+power of yh times h plus higher
+
+orders.
+
+And you say, OK, fine.
+
+What's this good for?
+
+Well, let's take a look
+at what we did over there.
+
+We said that I take some bunch
+of initial configurations,
+
+sum their weights
+to get the weight
+
+of the new configuration.
+
+What happens if I sum over
+all initial configurations?
+
+Well, if I sum over all
+initial configuration,
+
+I will get the
+partition function.
+
+Now essentially,
+all the original
+
+configurations I
+regrouped and put
+
+into these coarse-grained
+configurations that
+
+are weighted this way.
+
+So there could be
+an overall constant
+
+that emerges from this.
+
+But this really implies that
+the singular part of log z,
+
+and presumably this
+depends on how far
+
+away I am from the
+critical point,
+
+is the same as log z that
+singular after I do this t
+
+prime and h prime.
+
+Now there is one other
+issue, which is extensivity.
+
+Up to signs, factors
+of beta, et cetera,
+
+this is b times an
+intensive free energy,
+
+which is a function of t and h.
+
+So this is the same as v prime,
+because the volume shrunk.
+
+I took all of my scales and
+shrunk it by a factor of v,
+
+v prime, f of t
+prime and h prime.
+
+So now let's go this way.
+
+Note that v prime is
+the original v divided
+
+by b to the d scaling factor.
+
+So you do the
+divisions here, and you
+
+find that f as a
+function of t and h
+
+is the ratio of v prime to
+v, which is b to the minus d,
+
+f as a function of
+t prime and h prime.
+
+But t prime we said to lowest
+order is b to the yt t.
+
+h prime is b to the yh h.
+
+This is actually the
+more correct form
+
+of writing a
+homogeneous function.
+
+So previously in
+last lecture, we
+
+assumed that the free energy
+had a homogeneous form.
+
+Now subject to these
+conditions and assumptions
+
+of renormalization
+group, we have
+
+concluded that it should
+have that homogeneous form.
+
+Now you say this
+homogeneous form does not
+
+look like the
+homogeneous forms that I
+
+had written for you before.
+
+I say, OK.
+
+Presumably this is true
+for any factor of b
+
+that I want to choose.
+
+Let me choose a b, a rescaling
+factor such that v to the yt t
+
+is of the order of 1.
+
+Could be 1, could be pi.
+
+I don't care.
+
+Which means that
+I chose a factor
+
+of b that will scale with t
+as t to the minus 1 over yt.
+
+I put this b-- this expression
+is true for all choices of b.
+
+If I chose that particular
+value, what I get
+
+is t to the d over
+yt, some function.
+
+First argument has now
+become 1 or some constant.
+
+Really it only depends
+on the second argument
+
+in the combination h and t
+to the power of yh over yt.
+
+So you can see that
+this is, in fact,
+
+the same as the first
+line that I have above.
+
+And I have identified
+that 2 minus alpha
+
+would be related to
+this factor of yt, which
+
+is how you would scale
+under renormalization,
+
+the parameters t and h.
+
+And the gap exponent is related
+to the ratio of yh over yt.
+
+Similarly, we had that
+the correlation length--
+
+I have a line there.
+
+Psi of t and h is b psi
+of t prime and h prime.
+
+So I have that psi as
+a function of t and h
+
+is b times psi as a function of
+b to the yt t, b to the yh h.
+
+So that's also correct.
+
+I can again choose this value
+of v, substitute it over there.
+
+What do I get?
+
+I get that psi as a
+function of t and h
+
+would be t to the
+minus 1 over yt,
+
+some scaling function-- let's
+call it g psi-- of, again, h
+
+to the power of yh over yt.
+
+So I have got an answer
+that nu should be 1 over yt.
+
+I can get the scaling form
+for the correlation length.
+
+I identify the divergence
+of correlation length
+
+with inverse of this.
+
+And by the way, I get, if I
+substitute nu as 1 over yt
+
+here, the Josephson hyperscale
+in relation to minus alpha
+
+equals to b.
+
+I can go further if I want.
+
+I can calculate magnetization
+as a function of t and h,
+
+would correspond to
+basically the behaviors
+
+that we identify with exponents
+beta or delta as d log z.
+
+Yeah, let's say f by dh.
+
+If I take a
+derivative over there,
+
+you can immediately
+see that what
+
+that gives me is b to the
+power of yh minus d, and then
+
+some scaling function which is
+the derivative of this scaling
+
+function b the yt
+t, b to the yh h.
+
+And again, if I
+make this choice,
+
+then this goes over to t to the
+power of d minus yh over yt,
+
+and then some scaling
+function of h t to the delta.
+
+So I can continue with my table.
+
+And for example,
+I will have beta
+
+to be d minus yh divided by yt.
+
+I can go and calculate
+delta, et cetera.
+
+Actually I was a
+little bit careless
+
+with this factor
+zeta, which presumably
+
+is implicit in all of these
+transformations that I have.
+
+And I have to do special
+things to figure out
+
+what zeta is so that I will
+get self-similarity right
+
+at the critical point.
+
+But we can see that
+already we have
+
+the analog of a rescaling for m.
+
+And so it is easy to sort of
+look at those two equations
+
+and identify that my zeta
+should be precisely this one.
+
+So the zeta is not
+independent of the relevance
+
+of the magnetic field.
+
+And if you think about it, the
+field and the magnetization
+
+are conjugate variables in the
+sense that in the weight here,
+
+I will have a term that is like
+hm-- integrated, of course.
+
+And so hm integrated,
+you can see
+
+that up to a factor of b
+to the d from integration,
+
+the dimensionality that I assign
+to h and the dimensionality
+
+that I assign to m
+should be related.
+
+And not only for
+the magnetization,
+
+but for any pair of variables
+that are so conjugate--
+
+there's some f, and
+there's some x--
+
+there will be a corresponding
+relation between what
+
+would happen to this x at the
+critical point and this factor
+
+f when I deviate from
+the critical point.
+
+So all of this is
+kind of nice, but it's
+
+a little bit hand waving.
+
+I essentially traded one set of
+assumptions about homogeneity
+
+and scaling of free
+energy correlation length
+
+to some other set of assumptions
+about two parameters moving
+
+away from a scale
+invariant critical point.
+
+I didn't calculate anything
+about what the scale invariant
+
+probability is.
+
+I didn't show that, indeed,
+two parameters are sufficient,
+
+that this kind of scaling
+takes place, et cetera.
+
+So we need to be
+much more precise
+
+if we want to do, ultimately,
+calculations that give us
+
+what these numbers
+yt and yh are.
+
+So let's try to put
+this hand waving
+
+on a little bit
+more firm setting.
+
+So let's see how
+we should proceed.
+
+We start with some experimental
+system, critical point.
+
+So I tell you that somebody in
+the experiment, the liquid gas
+
+system, they saw a diverging
+correlation length,
+
+critical opalescence, et cetera.
+
+So then I associate
+with that some kind
+
+of a statistical field.
+
+And let's kind of
+stick with the notation
+
+that we have for the magnet.
+
+Let's call it m of x.
+
+And in general, this
+would be the part
+
+where one needs to put
+in a lot of thinking.
+
+That is, the experimentalist
+comes and tells you
+
+that I see a system that
+undergoes a phase transition.
+
+There are some
+response functions
+
+that are divergent, et cetera.
+
+You have to put in some
+thinking to think about what
+
+the appropriate
+order parameter is.
+
+And based on that order
+parameter or statistical field,
+
+you construct the most
+general weight consistent
+
+with symmetries, with
+not only asymmetries
+
+but the kind of assumptions that
+we have been putting in play.
+
+So we put in assumptions
+about locality, symmetry.
+
+Stability is, of
+course, paramount.
+
+But there is a list of things
+that you have to think about.
+
+So once you do
+that you say, OK, I
+
+associate with my
+configurations m of x some set
+
+of probabilities.
+
+Probabilities are
+certainly positive.
+
+So I can take its log, call its
+minus its log to be some kind
+
+of a weight, beta h, that
+governs these m of x's.
+
+If I say that I'm
+obeying locality,
+
+then I would write the answer,
+for example, like this.
+
+But it doesn't have to be.
+
+I have to write some
+particular example.
+
+But you may construct
+your example
+
+depending on the
+system of interest.
+
+And let's say we are looking
+at something like a superfluid,
+
+maybe, that we don't even have
+the analog of magnetic field,
+
+and we go and
+construct terms that
+
+are symmetric and made
+for a two component m.
+
+And I will write a
+few of these terms
+
+to emphasize that this is,
+in principle, a long list.
+
+There's coefficient
+of m to the sixth.
+
+We saw that the gradient
+terms could start with this k.
+
+But maybe there's a
+higher order gradient,
+
+and there's essentially
+and infinity of terms
+
+that you can write down that
+are consistent with these
+
+assumptions that you
+have made so far.
+
+So you say, OK.
+
+Now I take this, and implicit
+in all of these calculations
+
+is, indeed, some kind
+of a short scale cutoff.
+
+To construct the
+statistical field,
+
+I do apply the three steps of
+RG-- renormalization group,
+
+as I described before.
+
+And this will give me
+a new configuration
+
+for each of the
+old configurations
+
+through the formula that
+I gave you over there.
+
+So in principle, this is just
+a transformation from one
+
+set of variables to a
+new set of variables.
+
+So if I do this
+transformation, I
+
+can calculate the weight
+of the new configurations,
+
+m prime of x prime.
+
+I can take minus
+the log of that.
+
+And again, up to
+some constant, it
+
+will be the same
+as a probability.
+
+So there could be,
+in this procedure,
+
+some set of constants
+that are generated
+
+that don't depend on m.
+
+And then there
+will be a function
+
+that depends on m
+prime of x prime.
+
+Now the statement
+is that since I
+
+wrote the most general function
+over here, whatever I put here
+
+will have to have exactly
+the same form, because I said
+
+put anything that
+you can think of that
+
+is consistent with
+symmetries over here.
+
+So you put everything there.
+
+What I put here should have
+exactly the same functional
+
+form, but with coefficients
+that have changed.
+
+So you basically
+prime everything,
+
+but you have this whole thing.
+
+Now this may seem like
+truly difficult thing.
+
+But we will actually do this.
+
+We will carry out this
+transformation explicitly
+
+in particular cases.
+
+And we will show that this
+transformation amounts
+
+to constructing a rescaling of
+each one of these parameters--
+
+t prime, u prime, v prime, k
+prime, l prime, and so forth--
+
+as functions of
+the old parameters.
+
+So this is, if you
+like, a mapping.
+
+You take some set of
+parameters-- t, u, v, k, l,
+
+blah, blah, blah-- and
+you construct a mapping,
+
+s prime, which is some
+function of the original set
+
+of parameters.
+
+So this is a huge
+dimensional space.
+
+Any points that you start
+on the transformation
+
+will go to another point.
+
+But the key is that we
+wrote the most general form
+
+that we could, so we had
+to stay within this space.
+
+So why are you doing this?
+
+Well, I started by saying that
+the key to this whole thing
+
+is have to having a handle as
+to what this self-similar scale
+
+invariant probability is.
+
+I can't construct
+that just by guessing.
+
+But I can do what we
+usually do, let's say,
+
+in constructing wave functions
+in quantum mechanics that
+
+have some particular symmetry.
+
+Maybe you start with
+some wave function that
+
+doesn't have the full
+symmetry, and then
+
+you rotate it and
+rotate it again,
+
+and you average
+over all of them,
+
+and you end up with
+some function that
+
+has the right symmetry.
+
+So we start with a
+weight that I don't
+
+know whether it has the
+property that I want.
+
+And I apply the action
+of the group, which
+
+is this scaling
+variance, to see what
+
+happens to it under
+that transformation.
+
+But the point that
+I am interested,
+
+or the behavior that
+I am interested,
+
+is where I basically get
+the same probability back.
+
+So I'm very interested
+at the point where,
+
+under the transformation,
+I go back to myself.
+
+And that's called a fixed point.
+
+So S is a shorthand for this
+infinite vector of parameters.
+
+I want to find the point s
+star in this parameter space.
+
+Actually, let me call
+this transformation R
+
+and indicate that I'm
+renormalizing by a scale b,
+
+such that, when I
+renormalize by a scale
+
+b, my original
+set of parameters,
+
+if I am at this fixed point,
+I will end up at that point.
+
+So clearly, this
+is a system that
+
+has exactly these properties
+that I was harping in
+
+at the beginning.
+
+This is the point that
+is truly scale invariant.
+
+That's the point that
+I want to get at.
+
+So again, once we have
+done this transformation
+
+in a specific case, we'll figure
+out what this fixed point is.
+
+But for the time being,
+let's think a little bit away
+
+from this and deviate
+from fixed point.
+
+So I start with
+an initial point S
+
+that is, let's write it, S
+star plus a little bit away.
+
+Just like in the
+picture that I have
+
+here, I started
+with a fixed point,
+
+and I said I go
+away by an amount
+
+that I had parameterized
+by t and h.
+
+Now I have essentially
+a whole line
+
+of deviations forming a vector.
+
+I act with Rb on this, and I
+note that if delta S goes to 0,
+
+then I should go back to S star.
+
+But if delta S is
+small, maybe I can
+
+look at the delta
+S prime, which is
+
+a linearized version of
+these transformations.
+
+So basically these
+transformations
+
+are highly nonlinear just as
+the transformation over here,
+
+in principle, would have
+been highly nonlinear.
+
+But then I expanded it around
+the point t and h equals to 0.
+
+Similarly, I'm assuming
+that this delta S is small,
+
+and therefore delta S prime
+can be related to delta S
+
+through the action of a matrix
+that is a linearized version.
+
+Let's call it here RL of b.
+
+So this is a linearized
+transformation,
+
+which means that
+it's really a matrix.
+
+In this particular case, in
+principle, I started with a 2
+
+by 2 matrix.
+
+The off diagonal
+terms were 0, so it
+
+was only the diagonal
+terms that mattered.
+
+But in general, it
+would be a matrix,
+
+which would be the
+square of whatever
+
+the size of the parameter
+space is that I am looking at.
+
+Now then you have
+a matrix, it's good
+
+always to think in terms of its
+eigenvalues and eigendirection.
+
+In this problem that
+I had over here,
+
+symmetries had already
+diagonalized the matrix.
+
+I didn't have off
+diagonal terms.
+
+But I don't know here.
+
+It could be all kinds
+of off diagonal terms.
+
+So the properties are
+captured by diagonalize, RL,
+
+which means that I find a set
+of vectors in this space--
+
+let's call them Oi-- such
+that under action of this,
+
+I will get lambda Oi, lambda i.
+
+Of course, the transformation
+depends on the rescaling
+
+parameter, so there
+should be a b here.
+
+Now of course, you will get
+a totally different matrix
+
+for each b.
+
+So is it really hopeless that
+for each b I have to look
+
+at a new matrix, new
+diagonalization, et cetera?
+
+Well, exactly this thing
+that we had over here
+
+now comes into
+play, because I know
+
+that if I make a
+transformation size b1 followed
+
+by a transformation size b2,
+the answer is a transformation
+
+size b1, b2.
+
+And it doesn't matter
+in which order I do it.
+
+AUDIENCE: Can't you just mix
+notation, because L used to be
+
+[INAUDIBLE]?
+
+PROFESSOR: Sorry.
+
+So in particular, I see
+that these linearized
+
+matrices commute with each
+other for different values of b.
+
+And again, from your
+quantum mechanics,
+
+you probably know that
+if matrices commute then
+
+they have the same eigenvectors.
+
+So essentially, I was correct
+here in putting no index b
+
+on these eigenvectors,
+because it's
+
+independent of eigenvector,
+whereas the eigenvalues,
+
+in principle, depend on b.
+
+And how they depend on
+b is also determined
+
+by this transformation, that is
+lambda i of b1, lambda i of b2
+
+should be the same
+thing as lambda b1, b2.
+
+And of course, lambda
+i of 1 should be 1.
+
+If you don't change scale,
+nothing should change.
+
+And this is exactly the
+same set of conditions
+
+as we have over
+here, which means
+
+that we know that the
+eigenvalue's lambda i can
+
+be written as b to the
+power of some set of yi.
+
+So we just generalized
+what we had done before,
+
+now to this space that
+includes many parameters.
+
+So the story is now
+something like this.
+
+There is this
+multi-dimensional space
+
+with lots and lots
+of parameters--
+
+t, u, v, blah, blah,
+blah, many of them.
+
+And somewhere in this space
+of parameters, presumably
+
+there is a fixed point, S star.
+
+Now in the vicinity
+of that S star,
+
+I have established that there
+are some particular directions
+
+that I can obtain by
+diagonalizing this.
+
+So let's imagine that
+this is one direction,
+
+this is another direction,
+this is a third direction.
+
+And that if I start
+with a beta h-- well,
+
+actually, let's do this.
+
+That is, if I start with an S
+that is S star plus whatever
+
+is a projection of
+my components are
+
+along these different
+dimensions, so let's call them,
+
+let's say, ai along
+these Oi hat-- just
+
+make sure we kind of
+think of them as vectors--
+
+that under rescaling,
+I will go to S
+
+prime, which is S star plus
+sum over i, ai b to the yi Oi.
+
+That is, some of
+these directions,
+
+the component will get
+stretched if yi is positive.
+
+It will get diminished
+if yi is negative.
+
+And so now some notation
+comes into play.
+
+If yi is positive, the
+corresponding direction
+
+is called relevant.
+
+Eigendirection is relevant.
+
+If yi is negative, the
+corresponding eigendirection
+
+is irrelevant.
+
+And very occasionally,
+we may run into the case
+
+where yi is 0.
+
+And there is a terminology.
+
+The corresponding
+eigendirection is marginal.
+
+And what that means is that I
+need to resort to higher order
+
+terms to see whether it
+is attracted or repelled
+
+by the fixed point.
+
+So we need higher orders.
+
+After all, so far I have only
+linearized the transformation.
+
+Now the set of irrelevant
+directions to this particular S
+
+fixed point, S star, defines
+basing of attraction of S star.
+
+So let me go back to the
+picture that I have over here
+
+and be precise and use the arrow
+going away as an indication
+
+that the corresponding
+b is positive,
+
+and I'm forced out
+along this direction.
+
+Let me choose going
+in as an indicator
+
+that the corresponding
+y is negative.
+
+And as I make b
+larger and larger,
+
+I shrink along this axis.
+
+So in this three
+dimensional representation
+
+that I have over there, I have
+one relevant direction and two
+
+irrelevant directions.
+
+The two irrelevant directions
+will define the plane
+
+in this three
+dimensional space, which
+
+is the basing of attraction.
+
+So basically these
+two define a surface,
+
+and presumably any point that
+is in this surface in the three
+
+dimensional picture
+under looking
+
+at larger and larger
+things will get
+
+attracted to the fixed point.
+
+If you are away
+from the surface,
+
+maybe you will approach
+here, and then you
+
+will be pushed out.
+
+All right, fine.
+
+Now let's go and look
+at the following.
+
+We have a formula,
+psi of t and h.
+
+Or quite generally,
+psi under rescaling
+
+is b times the new psi.
+
+Or the new psi under any one
+of these transformation, psi
+
+prime, is the old psi divided
+by the old correlation
+
+length divided by a factor of b.
+
+So if I look at
+the fixed point--
+
+so if I ask what is psi
+at the fixed point--
+
+then under the transformation,
+I have the same parameters.
+
+So psi at the fixed
+point should be
+
+the psi of the fixed
+point divided by b.
+
+There are only two
+solutions to this.
+
+Either psi of S star is 0 or
+psi of S star is infinite.
+
+Now we introduce physics.
+
+Psi being 0 means
+that I have units
+
+that are completely
+uncorrelated to each other.
+
+Each one of them does
+whatever it wants.
+
+So this describes
+essentially, let's say,
+
+a system of infinite
+temperature.
+
+Every degree of freedom
+does whatever it wants.
+
+Well, I should say this
+corresponds to disordered
+
+or ordered phases.
+
+Because after all,
+we said that when
+
+we go to the
+ordered states also,
+
+there is an overall
+magnetization,
+
+but fluctuations around
+the overall magnetization
+
+have only a finite
+correlation length.
+
+And as you go further and
+further into the ordered phase,
+
+that correlation
+length shrinks to 0.
+
+So there is a similarity
+between what goes on
+
+at very high
+temperature and what
+
+goes on at very
+low temperature as
+
+far as the correlation of
+fluctuations is concerned.
+
+There is, of course,
+a long range order
+
+in one case that is
+absent in the other.
+
+But the correlation
+of fluctuations
+
+in both of those cases
+basically becomes
+
+finite, and under rescaling,
+goes all the way to 0.
+
+And clearly this is
+the interesting case,
+
+where it corresponds
+to critical point.
+
+So we've established that,
+once we found this fixed point,
+
+that those set of parameters
+are what can give us the scale
+
+invariant behavioral
+that we want.
+
+Now this list is
+hundreds of parameters.
+
+So this point corresponds
+to a very special point
+
+in this hundreds
+of parameter space.
+
+So let's say there is one
+point somewhere there which
+
+is the fixed point.
+
+And then you take
+your magnet and you
+
+change your critical
+temperature,
+
+are we going to hit that point?
+
+The answer is, no.
+
+Generically, you are not
+going to hit that point.
+
+But that's no problem.
+
+Why?
+
+Because if this
+basing of attraction.
+
+Because for any point on basing
+of attraction, I do rescaling,
+
+and I find that psi
+prime is psi over b.
+
+It becomes smaller.
+
+So you generically
+tend to become smaller.
+
+But ultimately, you
+end up at this point.
+
+And this point, the
+correlation length is infinite.
+
+So any point on this basing
+of attraction, in fact,
+
+has infinite correlation length.
+
+So every point on the basis
+of psi prime equals to psi,
+
+and hence psi has
+to be infinite.
+
+Yes.
+
+AUDIENCE: Question.
+
+Why should there be
+only one fixed point?
+
+PROFESSOR: There is no reason.
+
+AUDIENCE: OK.
+
+So this is just an example?
+
+PROFESSOR: Yeah.
+
+So locally, let's say that
+we found such a fixed point.
+
+Maybe globally, there
+is hundreds of them.
+
+I don't know.
+
+So that will always be
+a question in our minds.
+
+So if I just write down for
+you the most general set
+
+of transformations, who
+knows what's happening?
+
+Ultimately, we have to
+be guided by physics.
+
+We have to say that, if in the
+space of all parametrization,
+
+there are some that have
+no physical correspondence,
+
+we throw them out,
+we seek things
+
+that can be matched to
+our physical system.
+
+Yes?
+
+AUDIENCE: If there are
+multiple fixed points,
+
+do the planes of the
+basing of attraction
+
+have to be parallel
+to each other?
+
+PROFESSOR: They may have
+to have some conditions
+
+on non-intersecting or whatever.
+
+These are only linear in the
+vicinity of the fixed point.
+
+So in principle, they could
+be highly curved surfaces
+
+with all kinds of structures
+and things that I don't know.
+
+Yes?
+
+AUDIENCE: Is there any reason
+why you might or might not
+
+have attracting point
+that is actually
+
+a more complicated
+structure, like say,
+
+a limit cycle or
+even a [INAUDIBLE]?
+
+PROFESSOR: Yeah.
+
+So again, we are governed
+ultimately by physics.
+
+When I write these
+equations, they
+
+are as general as equations as
+the people in dynamical systems
+
+use that also includes
+cycles, chaotic attractors,
+
+all kinds of strange things.
+
+And we have to hope that
+when we apply this procedure
+
+to an appropriate
+physical system,
+
+the kind of
+equations that we get
+
+are such that their behavior
+is indicative of the physics.
+
+So there is one case I know
+where people sort of found
+
+chaotic renormalization
+group trajectories
+
+for some kind of a
+[INAUDIBLE] system.
+
+But always, again, this is
+a very general procedure.
+
+We have to limit
+mathematics, ultimately,
+
+by what the physical process is.
+
+So it's good that you know
+that these equations can
+
+do all kinds of strange things.
+
+But then we take a
+particular physical system,
+
+we have to beat on them
+until they behave properly.
+
+So let's imagine that we have
+a situation, such as this,
+
+where we have three parameters.
+
+Two of them are irrelevant.
+
+One of them is relevant.
+
+Then presumably, I
+take my physical system
+
+at some temperature
+and it would correspond
+
+to being on some point
+in this phase diagram.
+
+Some color that we don't have.
+
+Let's say over here.
+
+And I change the temperature.
+
+And I will take
+some trajectory--
+
+in this case, three
+dimensional space.
+
+And this is a line in this
+three dimensional space.
+
+And experimentally, I've
+been told that if I take,
+
+let's say, my piece of iron
+and I change temperature,
+
+at some point I go
+through a point that
+
+has infinite correlations.
+
+So I have to conclude that
+my trajectory for iron
+
+will intersect with
+surface at some point.
+
+And I'll say, OK, I take nickel.
+
+Nickel would be something else.
+
+And I change
+temperature of nickel,
+
+and I will be doing something
+completely different.
+
+But that experimentalist
+also has a point
+
+where you have
+ferromagnetic transition,
+
+so it must hit this surface.
+
+Then you do cobalt, where
+some other trajectory
+
+comes and hits off the surface.
+
+Now what we now
+know is that when
+
+we rescale the system
+sufficiently, all of them
+
+ultimately are described
+at the point where
+
+they have infinite
+correlation length by what
+
+is going on over here.
+
+So if I take iron,
+nickel, cobalt, clearly
+
+at the level of
+atoms and molecules,
+
+they are very different
+from each other.
+
+And the difference between
+ironness, nickelness,
+
+cobaltness is really in all of
+these irrelevant parameters.
+
+And as I go and look at
+larger and larger scale,
+
+they all diminish and go away.
+
+And at large scale,
+I see the same thing,
+
+where all of the individual
+details has been washed out.
+
+So this is able to capture
+the idea of universality.
+
+But there is a very
+important caveat
+
+to this, which is that
+the experimental system,
+
+whether you take iron or
+cobalt or some mixture
+
+of these different elements,
+you change one parameter
+
+temperature, and you always see
+a transition from, let's say,
+
+paramagnetic to
+ferromagnetic behavior.
+
+Now if I have, say, a line
+here in three dimensional space
+
+and I draw another
+line that corresponds
+
+to change in temperature,
+I will not intersect it.
+
+I have to do something very
+special to intersect that line.
+
+So in order that genetically I
+have a phase transition-- which
+
+is what my experimentalist
+friends tell me--
+
+I know that I can only have
+one relevant direction,
+
+because the dimensionality
+of the basing of attraction
+
+is the dimensionality of
+the space minus however
+
+many relevant directions I have.
+
+And I've been told
+by experimentalists
+
+that they exchange
+one parameters,
+
+and generically they
+hit the surface.
+
+So that's part of the story.
+
+I better find a theory that,
+at the end of the day, when
+
+I do all of this, I
+find a fixed point that
+
+not only is well-behaved
+and is not a limit cycle,
+
+but also a fixed point
+that has one and only one
+
+relevant direction, if
+that's the physical system
+
+that I'm describing.
+
+Now of course, maybe that
+was for the superfluid, where
+
+they could only
+change temperature,
+
+and you have a situation where
+the magnet comes into play
+
+and they say, oh, actually we
+also have the magnetic field.
+
+And we really have to go
+to the space of zero field.
+
+And then if I expand
+my space of parameters
+
+here to include terms
+that break the symmetry,
+
+in that generalized
+space, I should only
+
+have two relevant directions.
+
+So it is kind of strange story,
+that all we are doing here
+
+is mathematics.
+
+But at the end of
+the day, we have
+
+to get the mathematics to have
+very specific properties that
+
+are dictated by very rough
+things about experiments.
+
+So this was kind of
+conceptually rich.
+
+So I'll let you digest
+that for a while.
+
+And next lecture, we will start
+actually doing this procedure
+
+and finding these kinds
+of [INAUDIBLE] relations.
\ No newline at end of file
diff --git a/fW9ZyXvdCwE.txt b/fW9ZyXvdCwE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9e5001342e44c28066a65bb828969955e6b94418
--- /dev/null
+++ b/fW9ZyXvdCwE.txt
@@ -0,0 +1,1747 @@
+align:start position:0%
+ 
+welcome back to ag20 special relativity
+
+ align:start position:0%
+welcome back to ag20 special relativity
+ 
+
+ align:start position:0%
+welcome back to ag20 special relativity
+in this short video we look at the
+
+ align:start position:0%
+in this short video we look at the
+ 
+
+ align:start position:0%
+in this short video we look at the
+historic backdrop the time in which
+
+ align:start position:0%
+historic backdrop the time in which
+ 
+
+ align:start position:0%
+historic backdrop the time in which
+Einstein was able to develop the theory
+
+ align:start position:0%
+Einstein was able to develop the theory
+ 
+
+ align:start position:0%
+Einstein was able to develop the theory
+of special relativity what were people
+
+ align:start position:0%
+of special relativity what were people
+ 
+
+ align:start position:0%
+of special relativity what were people
+thinking what was you know the physics
+
+ align:start position:0%
+thinking what was you know the physics
+ 
+
+ align:start position:0%
+thinking what was you know the physics
+landscape of the time
+
+ align:start position:0%
+landscape of the time
+ 
+
+ align:start position:0%
+landscape of the time
+how was technology developed and and how
+
+ align:start position:0%
+how was technology developed and and how
+ 
+
+ align:start position:0%
+how was technology developed and and how
+did all those things come together for
+
+ align:start position:0%
+did all those things come together for
+ 
+
+ align:start position:0%
+did all those things come together for
+Ein to thrive and come forward with
+
+ align:start position:0%
+Ein to thrive and come forward with
+ 
+
+ align:start position:0%
+Ein to thrive and come forward with
+those important discoveries in
+
+ align:start position:0%
+those important discoveries in
+ 
+
+ align:start position:0%
+those important discoveries in
+physics we have to go back to 1900
+
+ align:start position:0%
+physics we have to go back to 1900
+ 
+
+ align:start position:0%
+physics we have to go back to 1900
+around that time in which Einstein was
+
+ align:start position:0%
+around that time in which Einstein was
+ 
+
+ align:start position:0%
+around that time in which Einstein was
+able to you
+
+ align:start position:0%
+able to you
+ 
+
+ align:start position:0%
+able to you
+know break through break out um and come
+
+ align:start position:0%
+know break through break out um and come
+ 
+
+ align:start position:0%
+know break through break out um and come
+up with completely new ideas and and pH
+
+ align:start position:0%
+up with completely new ideas and and pH
+ 
+
+ align:start position:0%
+up with completely new ideas and and pH
+um before we go into the discussion of
+
+ align:start position:0%
+um before we go into the discussion of
+ 
+
+ align:start position:0%
+um before we go into the discussion of
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+timelines um I'd like you to be invited
+
+ align:start position:0%
+timelines um I'd like you to be invited
+ 
+
+ align:start position:0%
+timelines um I'd like you to be invited
+to come to Geneva to Switzerland to burn
+
+ align:start position:0%
+to come to Geneva to Switzerland to burn
+ 
+
+ align:start position:0%
+to come to Geneva to Switzerland to burn
+to Zurich to the places in which this
+
+ align:start position:0%
+to Zurich to the places in which this
+ 
+
+ align:start position:0%
+to Zurich to the places in which this
+all happened um especially burn is a is
+
+ align:start position:0%
+all happened um especially burn is a is
+ 
+
+ align:start position:0%
+all happened um especially burn is a is
+a historic town wasn't destroyed in the
+
+ align:start position:0%
+a historic town wasn't destroyed in the
+ 
+
+ align:start position:0%
+a historic town wasn't destroyed in the
+second world war and if you walk down
+
+ align:start position:0%
+second world war and if you walk down
+ 
+
+ align:start position:0%
+second world war and if you walk down
+the streets um here is a picture of me
+
+ align:start position:0%
+the streets um here is a picture of me
+ 
+
+ align:start position:0%
+the streets um here is a picture of me
+two years ago in front of the Einstein
+
+ align:start position:0%
+two years ago in front of the Einstein
+ 
+
+ align:start position:0%
+two years ago in front of the Einstein
+house you know the streets are basically
+
+ align:start position:0%
+house you know the streets are basically
+ 
+
+ align:start position:0%
+house you know the streets are basically
+unchanged for the last 100 150 years so
+
+ align:start position:0%
+unchanged for the last 100 150 years so
+ 
+
+ align:start position:0%
+unchanged for the last 100 150 years so
+you look up into the window and you see
+
+ align:start position:0%
+you look up into the window and you see
+ 
+
+ align:start position:0%
+you look up into the window and you see
+Einstein looking down at
+
+ align:start position:0%
+Einstein looking down at
+ 
+
+ align:start position:0%
+Einstein looking down at
+you um so if you go back 200 years um in
+
+ align:start position:0%
+you um so if you go back 200 years um in
+ 
+
+ align:start position:0%
+you um so if you go back 200 years um in
+Italy people like VTA and others started
+
+ align:start position:0%
+Italy people like VTA and others started
+ 
+
+ align:start position:0%
+Italy people like VTA and others started
+to make use of electromagnetic effects
+
+ align:start position:0%
+to make use of electromagnetic effects
+ 
+
+ align:start position:0%
+to make use of electromagnetic effects
+the first batteries were developed and a
+
+ align:start position:0%
+the first batteries were developed and a
+ 
+
+ align:start position:0%
+the first batteries were developed and a
+theory of wave a wave theory of light
+
+ align:start position:0%
+theory of wave a wave theory of light
+ 
+
+ align:start position:0%
+theory of wave a wave theory of light
+was developed that then LED you know in
+
+ align:start position:0%
+was developed that then LED you know in
+ 
+
+ align:start position:0%
+was developed that then LED you know in
+the you know slowly developed into a Ser
+
+ align:start position:0%
+the you know slowly developed into a Ser
+ 
+
+ align:start position:0%
+the you know slowly developed into a Ser
+of electromagnetism and the
+
+ align:start position:0%
+of electromagnetism and the
+ 
+
+ align:start position:0%
+of electromagnetism and the
+understanding of those phenomena in the
+
+ align:start position:0%
+understanding of those phenomena in the
+ 
+
+ align:start position:0%
+understanding of those phenomena in the
+very same time in Europe the first
+
+ align:start position:0%
+very same time in Europe the first
+ 
+
+ align:start position:0%
+very same time in Europe the first
+railroad systems were developed um
+
+ align:start position:0%
+railroad systems were developed um
+ 
+
+ align:start position:0%
+railroad systems were developed um
+electromagnetic induction was understood
+
+ align:start position:0%
+electromagnetic induction was understood
+ 
+
+ align:start position:0%
+electromagnetic induction was understood
+and then in 1860s in the 1860s Maxwell
+
+ align:start position:0%
+and then in 1860s in the 1860s Maxwell
+ 
+
+ align:start position:0%
+and then in 1860s in the 1860s Maxwell
+was able to put all of those Concepts
+
+ align:start position:0%
+was able to put all of those Concepts
+ 
+
+ align:start position:0%
+was able to put all of those Concepts
+together in his famous Maxville
+
+ align:start position:0%
+together in his famous Maxville
+ 
+
+ align:start position:0%
+together in his famous Maxville
+equations which are discuss discussed at
+
+ align:start position:0%
+equations which are discuss discussed at
+ 
+
+ align:start position:0%
+equations which are discuss discussed at
+length in
+
+ align:start position:0%
+length in
+ 
+
+ align:start position:0%
+length in
+802 people were then because of the
+
+ align:start position:0%
+802 people were then because of the
+ 
+
+ align:start position:0%
+802 people were then because of the
+railroads um but also because of graphic
+
+ align:start position:0%
+railroads um but also because of graphic
+ 
+
+ align:start position:0%
+railroads um but also because of graphic
+cables able to communicate and move over
+
+ align:start position:0%
+cables able to communicate and move over
+ 
+
+ align:start position:0%
+cables able to communicate and move over
+larger distance in shorter amount of
+
+ align:start position:0%
+larger distance in shorter amount of
+ 
+
+ align:start position:0%
+larger distance in shorter amount of
+time and that led to the need of
+
+ align:start position:0%
+time and that led to the need of
+ 
+
+ align:start position:0%
+time and that led to the need of
+synchronizing clocks uh to that point in
+
+ align:start position:0%
+synchronizing clocks uh to that point in
+ 
+
+ align:start position:0%
+synchronizing clocks uh to that point in
+each Town had one or few clock towers
+
+ align:start position:0%
+each Town had one or few clock towers
+ 
+
+ align:start position:0%
+each Town had one or few clock towers
+and you just read off the time and
+
+ align:start position:0%
+and you just read off the time and
+ 
+
+ align:start position:0%
+and you just read off the time and
+that's the time of day there was no need
+
+ align:start position:0%
+that's the time of day there was no need
+ 
+
+ align:start position:0%
+that's the time of day there was no need
+to be able to tell what time is it in
+
+ align:start position:0%
+to be able to tell what time is it in
+ 
+
+ align:start position:0%
+to be able to tell what time is it in
+London when you have your breakfast in
+
+ align:start position:0%
+London when you have your breakfast in
+ 
+
+ align:start position:0%
+London when you have your breakfast in
+Munich or uh what time you know the
+
+ align:start position:0%
+Munich or uh what time you know the
+ 
+
+ align:start position:0%
+Munich or uh what time you know the
+store opens in a different city there
+
+ align:start position:0%
+store opens in a different city there
+ 
+
+ align:start position:0%
+store opens in a different city there
+was no need for this kind of
+
+ align:start position:0%
+was no need for this kind of
+ 
+
+ align:start position:0%
+was no need for this kind of
+synchronization but with the expansion
+
+ align:start position:0%
+synchronization but with the expansion
+ 
+
+ align:start position:0%
+synchronization but with the expansion
+of railroad specifically there was a
+
+ align:start position:0%
+of railroad specifically there was a
+ 
+
+ align:start position:0%
+of railroad specifically there was a
+need to understand when a train when a
+
+ align:start position:0%
+need to understand when a train when a
+ 
+
+ align:start position:0%
+need to understand when a train when a
+when a uh train is on a track and such
+
+ align:start position:0%
+when a uh train is on a track and such
+ 
+
+ align:start position:0%
+when a uh train is on a track and such
+that it doesn't intersect with another
+
+ align:start position:0%
+that it doesn't intersect with another
+ 
+
+ align:start position:0%
+that it doesn't intersect with another
+train and you know avoiding collisions
+
+ align:start position:0%
+train and you know avoiding collisions
+ 
+
+ align:start position:0%
+train and you know avoiding collisions
+you also want to know when you have to
+
+ align:start position:0%
+you also want to know when you have to
+ 
+
+ align:start position:0%
+you also want to know when you have to
+be at a train station in order to catch
+
+ align:start position:0%
+be at a train station in order to catch
+ 
+
+ align:start position:0%
+be at a train station in order to catch
+the train uh those things became
+
+ align:start position:0%
+the train uh those things became
+ 
+
+ align:start position:0%
+the train uh those things became
+important and they led to patents filed
+
+ align:start position:0%
+important and they led to patents filed
+ 
+
+ align:start position:0%
+important and they led to patents filed
+around the this time and also later on
+
+ align:start position:0%
+around the this time and also later on
+ 
+
+ align:start position:0%
+around the this time and also later on
+on the theory of light people developed
+
+ align:start position:0%
+on the theory of light people developed
+ 
+
+ align:start position:0%
+on the theory of light people developed
+all kinds of ideas and conflicting ideas
+
+ align:start position:0%
+all kinds of ideas and conflicting ideas
+ 
+
+ align:start position:0%
+all kinds of ideas and conflicting ideas
+for example mechanical models of Light
+
+ align:start position:0%
+for example mechanical models of Light
+ 
+
+ align:start position:0%
+for example mechanical models of Light
+which relied on the existence of the
+
+ align:start position:0%
+which relied on the existence of the
+ 
+
+ align:start position:0%
+which relied on the existence of the
+medium in which light travels and we'll
+
+ align:start position:0%
+medium in which light travels and we'll
+ 
+
+ align:start position:0%
+medium in which light travels and we'll
+discuss this at length in the
+
+ align:start position:0%
+discuss this at length in the
+ 
+
+ align:start position:0%
+discuss this at length in the
+1818 um there's a new phenomena in the
+
+ align:start position:0%
+1818 um there's a new phenomena in the
+ 
+
+ align:start position:0%
+1818 um there's a new phenomena in the
+structure of physics after this point
+
+ align:start position:0%
+structure of physics after this point
+ 
+
+ align:start position:0%
+structure of physics after this point
+there was a professor of physics at an
+
+ align:start position:0%
+there was a professor of physics at an
+ 
+
+ align:start position:0%
+there was a professor of physics at an
+Institute he had a share and everybody
+
+ align:start position:0%
+Institute he had a share and everybody
+ 
+
+ align:start position:0%
+Institute he had a share and everybody
+was working for them um but then you
+
+ align:start position:0%
+was working for them um but then you
+ 
+
+ align:start position:0%
+was working for them um but then you
+know there was a a change in in in the
+
+ align:start position:0%
+know there was a a change in in in the
+ 
+
+ align:start position:0%
+know there was a a change in in in the
+way physics research was conducted such
+
+ align:start position:0%
+way physics research was conducted such
+ 
+
+ align:start position:0%
+way physics research was conducted such
+that started to be a division of labor
+
+ align:start position:0%
+that started to be a division of labor
+ 
+
+ align:start position:0%
+that started to be a division of labor
+between experimental physicist and
+
+ align:start position:0%
+between experimental physicist and
+ 
+
+ align:start position:0%
+between experimental physicist and
+theoretical
+
+ align:start position:0%
+theoretical
+ 
+
+ align:start position:0%
+theoretical
+physicist around this time Thomas Edison
+
+ align:start position:0%
+physicist around this time Thomas Edison
+ 
+
+ align:start position:0%
+physicist around this time Thomas Edison
+uh developed light bulbs uh meaning that
+
+ align:start position:0%
+uh developed light bulbs uh meaning that
+ 
+
+ align:start position:0%
+uh developed light bulbs uh meaning that
+light and electricity those two things
+
+ align:start position:0%
+light and electricity those two things
+ 
+
+ align:start position:0%
+light and electricity those two things
+became more woven together um
+
+ align:start position:0%
+became more woven together um
+ 
+
+ align:start position:0%
+became more woven together um
+electromagnetic waves were discovered
+
+ align:start position:0%
+electromagnetic waves were discovered
+ 
+
+ align:start position:0%
+electromagnetic waves were discovered
+and Michaelson and moley conducted the
+
+ align:start position:0%
+and Michaelson and moley conducted the
+ 
+
+ align:start position:0%
+and Michaelson and moley conducted the
+experiment and they did find they did
+
+ align:start position:0%
+experiment and they did find they did
+ 
+
+ align:start position:0%
+experiment and they did find they did
+not find a medium which carried light
+
+ align:start position:0%
+not find a medium which carried light
+ 
+
+ align:start position:0%
+not find a medium which carried light
+waves and we'll discuss the Michaels and
+
+ align:start position:0%
+waves and we'll discuss the Michaels and
+ 
+
+ align:start position:0%
+waves and we'll discuss the Michaels and
+mole experiment in much more depth um
+
+ align:start position:0%
+mole experiment in much more depth um
+ 
+
+ align:start position:0%
+mole experiment in much more depth um
+but this was basically the backdrop you
+
+ align:start position:0%
+but this was basically the backdrop you
+ 
+
+ align:start position:0%
+but this was basically the backdrop you
+know Michaelson and moley uh the idea of
+
+ align:start position:0%
+know Michaelson and moley uh the idea of
+ 
+
+ align:start position:0%
+know Michaelson and moley uh the idea of
+electromagnetic waves how do they
+
+ align:start position:0%
+electromagnetic waves how do they
+ 
+
+ align:start position:0%
+electromagnetic waves how do they
+actually travel uh what is the speed in
+
+ align:start position:0%
+actually travel uh what is the speed in
+ 
+
+ align:start position:0%
+actually travel uh what is the speed in
+which they travel what are the medium
+
+ align:start position:0%
+which they travel what are the medium
+ 
+
+ align:start position:0%
+which they travel what are the medium
+and how does this all interact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Einstein was born into this he was
+
+ align:start position:0%
+so Einstein was born into this he was
+ 
+
+ align:start position:0%
+so Einstein was born into this he was
+born in ol a German Town a small German
+
+ align:start position:0%
+born in ol a German Town a small German
+ 
+
+ align:start position:0%
+born in ol a German Town a small German
+Town on March 14th
+
+ align:start position:0%
+Town on March 14th
+ 
+
+ align:start position:0%
+Town on March 14th
+1879 on P day um he spent his youth in
+
+ align:start position:0%
+1879 on P day um he spent his youth in
+ 
+
+ align:start position:0%
+1879 on P day um he spent his youth in
+Munich where his father he was um he had
+
+ align:start position:0%
+Munich where his father he was um he had
+ 
+
+ align:start position:0%
+Munich where his father he was um he had
+an electrical company a company which uh
+
+ align:start position:0%
+an electrical company a company which uh
+ 
+
+ align:start position:0%
+an electrical company a company which uh
+provided electrical services for example
+
+ align:start position:0%
+provided electrical services for example
+ 
+
+ align:start position:0%
+provided electrical services for example
+for the octob October Fest in Munich um
+
+ align:start position:0%
+for the octob October Fest in Munich um
+ 
+
+ align:start position:0%
+for the octob October Fest in Munich um
+and his business went up and down and
+
+ align:start position:0%
+and his business went up and down and
+ 
+
+ align:start position:0%
+and his business went up and down and
+had to be located later into Italy um
+
+ align:start position:0%
+had to be located later into Italy um
+ 
+
+ align:start position:0%
+had to be located later into Italy um
+was difficult and interesting time so
+
+ align:start position:0%
+was difficult and interesting time so
+ 
+
+ align:start position:0%
+was difficult and interesting time so
+Einstein went to school in Munich in a
+
+ align:start position:0%
+Einstein went to school in Munich in a
+ 
+
+ align:start position:0%
+Einstein went to school in Munich in a
+gymnasium in in Munich uh and at some
+
+ align:start position:0%
+gymnasium in in Munich uh and at some
+ 
+
+ align:start position:0%
+gymnasium in in Munich uh and at some
+point it was time for him to go to
+
+ align:start position:0%
+point it was time for him to go to
+ 
+
+ align:start position:0%
+point it was time for him to go to
+military service and he avoided this by
+
+ align:start position:0%
+military service and he avoided this by
+ 
+
+ align:start position:0%
+military service and he avoided this by
+becoming stateless uh he then wanted to
+
+ align:start position:0%
+becoming stateless uh he then wanted to
+ 
+
+ align:start position:0%
+becoming stateless uh he then wanted to
+enroll in uh in University uh in
+
+ align:start position:0%
+enroll in uh in University uh in
+ 
+
+ align:start position:0%
+enroll in uh in University uh in
+Switzerland poly
+
+ align:start position:0%
+Switzerland poly
+ 
+
+ align:start position:0%
+Switzerland poly
+technique in um but he wasn't quite
+
+ align:start position:0%
+technique in um but he wasn't quite
+ 
+
+ align:start position:0%
+technique in um but he wasn't quite
+admitted uh
+
+ align:start position:0%
+admitted uh
+ 
+
+ align:start position:0%
+admitted uh
+mainly because his French wasn't quite
+
+ align:start position:0%
+mainly because his French wasn't quite
+ 
+
+ align:start position:0%
+mainly because his French wasn't quite
+sufficient so he had to go an extra
+
+ align:start position:0%
+sufficient so he had to go an extra
+ 
+
+ align:start position:0%
+sufficient so he had to go an extra
+round of studying in order to be then
+
+ align:start position:0%
+round of studying in order to be then
+ 
+
+ align:start position:0%
+round of studying in order to be then
+admitted to as a poly Technic one of his
+
+ align:start position:0%
+admitted to as a poly Technic one of his
+ 
+
+ align:start position:0%
+admitted to as a poly Technic one of his
+mentors at the time was hair Professor
+
+ align:start position:0%
+mentors at the time was hair Professor
+ 
+
+ align:start position:0%
+mentors at the time was hair Professor
+vber uh he was a leading physicist there
+
+ align:start position:0%
+vber uh he was a leading physicist there
+ 
+
+ align:start position:0%
+vber uh he was a leading physicist there
+and they had an interesting relationship
+
+ align:start position:0%
+and they had an interesting relationship
+ 
+
+ align:start position:0%
+and they had an interesting relationship
+which I come back to in a little while
+
+ align:start position:0%
+which I come back to in a little while
+ 
+
+ align:start position:0%
+which I come back to in a little while
+while studying in um in uh in in
+
+ align:start position:0%
+while studying in um in uh in in
+ 
+
+ align:start position:0%
+while studying in um in uh in in
+in in Zurich
+
+ align:start position:0%
+in in Zurich
+ 
+
+ align:start position:0%
+in in Zurich
+um Einstein met his wife miva
+
+ align:start position:0%
+um Einstein met his wife miva
+ 
+
+ align:start position:0%
+um Einstein met his wife miva
+marage um she was also a physics student
+
+ align:start position:0%
+marage um she was also a physics student
+ 
+
+ align:start position:0%
+marage um she was also a physics student
+one of the few female physics students
+
+ align:start position:0%
+one of the few female physics students
+ 
+
+ align:start position:0%
+one of the few female physics students
+there and they fell in love and they uh
+
+ align:start position:0%
+there and they fell in love and they uh
+ 
+
+ align:start position:0%
+there and they fell in love and they uh
+married and they had had a child
+
+ align:start position:0%
+married and they had had a child
+ 
+
+ align:start position:0%
+married and they had had a child
+together or children together in 1900 um
+
+ align:start position:0%
+together or children together in 1900 um
+ 
+
+ align:start position:0%
+together or children together in 1900 um
+Einstein graduated um he wasn't the best
+
+ align:start position:0%
+Einstein graduated um he wasn't the best
+ 
+
+ align:start position:0%
+Einstein graduated um he wasn't the best
+student in class um neither was miva
+
+ align:start position:0%
+student in class um neither was miva
+ 
+
+ align:start position:0%
+student in class um neither was miva
+marriage and he had a hard time finding
+
+ align:start position:0%
+marriage and he had a hard time finding
+ 
+
+ align:start position:0%
+marriage and he had a hard time finding
+a career so he wanted to stay at the UN
+
+ align:start position:0%
+a career so he wanted to stay at the UN
+ 
+
+ align:start position:0%
+a career so he wanted to stay at the UN
+University and enter an academic career
+
+ align:start position:0%
+University and enter an academic career
+ 
+
+ align:start position:0%
+University and enter an academic career
+and that required the mentors to be uh
+
+ align:start position:0%
+and that required the mentors to be uh
+ 
+
+ align:start position:0%
+and that required the mentors to be uh
+in favor of this and since Einstein
+
+ align:start position:0%
+in favor of this and since Einstein
+ 
+
+ align:start position:0%
+in favor of this and since Einstein
+didn't quite develop a good relationship
+
+ align:start position:0%
+didn't quite develop a good relationship
+ 
+
+ align:start position:0%
+didn't quite develop a good relationship
+with professor wber and the other um
+
+ align:start position:0%
+with professor wber and the other um
+ 
+
+ align:start position:0%
+with professor wber and the other um
+professors around uh they didn't want
+
+ align:start position:0%
+professors around uh they didn't want
+ 
+
+ align:start position:0%
+professors around uh they didn't want
+him there they didn't promote his career
+
+ align:start position:0%
+him there they didn't promote his career
+ 
+
+ align:start position:0%
+him there they didn't promote his career
+so he didn't know quite what to do um
+
+ align:start position:0%
+so he didn't know quite what to do um
+ 
+
+ align:start position:0%
+so he didn't know quite what to do um
+went back to his parents to Italy and
+
+ align:start position:0%
+went back to his parents to Italy and
+ 
+
+ align:start position:0%
+went back to his parents to Italy and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and this didn't get any traction from
+
+ align:start position:0%
+and this didn't get any traction from
+ 
+
+ align:start position:0%
+and this didn't get any traction from
+where he was and he was quite anxious
+
+ align:start position:0%
+where he was and he was quite anxious
+ 
+
+ align:start position:0%
+where he was and he was quite anxious
+about this and it just visible in
+
+ align:start position:0%
+about this and it just visible in
+ 
+
+ align:start position:0%
+about this and it just visible in
+letters he but he had good friends there
+
+ align:start position:0%
+letters he but he had good friends there
+ 
+
+ align:start position:0%
+letters he but he had good friends there
+um he had a good friend Marcel Crossman
+
+ align:start position:0%
+um he had a good friend Marcel Crossman
+ 
+
+ align:start position:0%
+um he had a good friend Marcel Crossman
+specifically who helped him get into
+
+ align:start position:0%
+specifically who helped him get into
+ 
+
+ align:start position:0%
+specifically who helped him get into
+after some back and forth a position as
+
+ align:start position:0%
+after some back and forth a position as
+ 
+
+ align:start position:0%
+after some back and forth a position as
+a lower level patent clerk um in a patn
+
+ align:start position:0%
+a lower level patent clerk um in a patn
+ 
+
+ align:start position:0%
+a lower level patent clerk um in a patn
+office in burn and so this was a
+
+ align:start position:0%
+office in burn and so this was a
+ 
+
+ align:start position:0%
+office in burn and so this was a
+starting point for career so he had this
+
+ align:start position:0%
+starting point for career so he had this
+ 
+
+ align:start position:0%
+starting point for career so he had this
+you know was a pattern clerk he had a
+
+ align:start position:0%
+you know was a pattern clerk he had a
+ 
+
+ align:start position:0%
+you know was a pattern clerk he had a
+lot of time on his hand Beyond say and
+
+ align:start position:0%
+lot of time on his hand Beyond say and
+ 
+
+ align:start position:0%
+lot of time on his hand Beyond say and
+they started something which was called
+
+ align:start position:0%
+they started something which was called
+ 
+
+ align:start position:0%
+they started something which was called
+the um um Olympia Academy which uh you
+
+ align:start position:0%
+the um um Olympia Academy which uh you
+ 
+
+ align:start position:0%
+the um um Olympia Academy which uh you
+know consisted of a group of people who
+
+ align:start position:0%
+know consisted of a group of people who
+ 
+
+ align:start position:0%
+know consisted of a group of people who
+studied with and Friends of Einstein
+
+ align:start position:0%
+studied with and Friends of Einstein
+ 
+
+ align:start position:0%
+studied with and Friends of Einstein
+including um Marcel Crosman and they
+
+ align:start position:0%
+including um Marcel Crosman and they
+ 
+
+ align:start position:0%
+including um Marcel Crosman and they
+talked and spent time took long walks uh
+
+ align:start position:0%
+talked and spent time took long walks uh
+ 
+
+ align:start position:0%
+talked and spent time took long walks uh
+you know spend time drinking partying if
+
+ align:start position:0%
+you know spend time drinking partying if
+ 
+
+ align:start position:0%
+you know spend time drinking partying if
+you want um and but specifically talking
+
+ align:start position:0%
+you want um and but specifically talking
+ 
+
+ align:start position:0%
+you want um and but specifically talking
+about physics um and in this framework
+
+ align:start position:0%
+about physics um and in this framework
+ 
+
+ align:start position:0%
+about physics um and in this framework
+Einstein was able to develop his
+
+ align:start position:0%
+Einstein was able to develop his
+ 
+
+ align:start position:0%
+Einstein was able to develop his
+ideas and then 1905 came uh not in a
+
+ align:start position:0%
+ideas and then 1905 came uh not in a
+ 
+
+ align:start position:0%
+ideas and then 1905 came uh not in a
+sudden but in 1905 he was able out of
+
+ align:start position:0%
+sudden but in 1905 he was able out of
+ 
+
+ align:start position:0%
+sudden but in 1905 he was able out of
+this context to develop develop five
+
+ align:start position:0%
+this context to develop develop five
+ 
+
+ align:start position:0%
+this context to develop develop five
+very very important paper the first one
+
+ align:start position:0%
+very very important paper the first one
+ 
+
+ align:start position:0%
+very very important paper the first one
+was on light Quantum um he was able to
+
+ align:start position:0%
+was on light Quantum um he was able to
+ 
+
+ align:start position:0%
+was on light Quantum um he was able to
+describe the emission and absorption of
+
+ align:start position:0%
+describe the emission and absorption of
+ 
+
+ align:start position:0%
+describe the emission and absorption of
+light in April then which was part of
+
+ align:start position:0%
+light in April then which was part of
+ 
+
+ align:start position:0%
+light in April then which was part of
+his PhD seases he was able to uh
+
+ align:start position:0%
+his PhD seases he was able to uh
+ 
+
+ align:start position:0%
+his PhD seases he was able to uh
+characterize the size of molecules and
+
+ align:start position:0%
+characterize the size of molecules and
+ 
+
+ align:start position:0%
+characterize the size of molecules and
+in may he was able to show the existence
+
+ align:start position:0%
+in may he was able to show the existence
+ 
+
+ align:start position:0%
+in may he was able to show the existence
+of atoms he was basically demonstrating
+
+ align:start position:0%
+of atoms he was basically demonstrating
+ 
+
+ align:start position:0%
+of atoms he was basically demonstrating
+this by following Browning random motion
+
+ align:start position:0%
+this by following Browning random motion
+ 
+
+ align:start position:0%
+this by following Browning random motion
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+atoms and then in June he wrote a paper
+
+ align:start position:0%
+atoms and then in June he wrote a paper
+ 
+
+ align:start position:0%
+atoms and then in June he wrote a paper
+named electrodynamics of moving bodies
+
+ align:start position:0%
+named electrodynamics of moving bodies
+ 
+
+ align:start position:0%
+named electrodynamics of moving bodies
+and that is the paper in which he
+
+ align:start position:0%
+and that is the paper in which he
+ 
+
+ align:start position:0%
+and that is the paper in which he
+discovers or describes special
+
+ align:start position:0%
+discovers or describes special
+ 
+
+ align:start position:0%
+discovers or describes special
+relativity on further review he
+
+ align:start position:0%
+relativity on further review he
+ 
+
+ align:start position:0%
+relativity on further review he
+discovered that there's a consequent of
+
+ align:start position:0%
+discovered that there's a consequent of
+ 
+
+ align:start position:0%
+discovered that there's a consequent of
+special relative ity that energy and
+
+ align:start position:0%
+special relative ity that energy and
+ 
+
+ align:start position:0%
+special relative ity that energy and
+mass are equivalent in this famous
+
+ align:start position:0%
+mass are equivalent in this famous
+ 
+
+ align:start position:0%
+mass are equivalent in this famous
+equation eal mc² and we'll come to this
+
+ align:start position:0%
+equation eal mc² and we'll come to this
+ 
+
+ align:start position:0%
+equation eal mc² and we'll come to this
+as well so this is basically the
+
+ align:start position:0%
+as well so this is basically the
+ 
+
+ align:start position:0%
+as well so this is basically the
+framework of of this lecture um if you
+
+ align:start position:0%
+framework of of this lecture um if you
+ 
+
+ align:start position:0%
+framework of of this lecture um if you
+then move forward into general
+
+ align:start position:0%
+then move forward into general
+ 
+
+ align:start position:0%
+then move forward into general
+relativity which was developed by
+
+ align:start position:0%
+relativity which was developed by
+ 
+
+ align:start position:0%
+relativity which was developed by
+Einstein in
+
+ align:start position:0%
+Einstein in
+ 
+
+ align:start position:0%
+Einstein in
+1915 um you can then again follow the
+
+ align:start position:0%
+1915 um you can then again follow the
+ 
+
+ align:start position:0%
+1915 um you can then again follow the
+developments of Science of quantum
+
+ align:start position:0%
+developments of Science of quantum
+ 
+
+ align:start position:0%
+developments of Science of quantum
+mechanics of general relativity and the
+
+ align:start position:0%
+mechanics of general relativity and the
+ 
+
+ align:start position:0%
+mechanics of general relativity and the
+conundrum of describing those two
+
+ align:start position:0%
+conundrum of describing those two
+ 
+
+ align:start position:0%
+conundrum of describing those two
+concepts at the very same time in which
+
+ align:start position:0%
+concepts at the very same time in which
+ 
+
+ align:start position:0%
+concepts at the very same time in which
+then Einstein lived and moved his career
+
+ align:start position:0%
+then Einstein lived and moved his career
+ 
+
+ align:start position:0%
+then Einstein lived and moved his career
+developed then from there
+
+ align:start position:0%
+developed then from there
+ 
+
+ align:start position:0%
+developed then from there
+on not instantly but systematically he
+
+ align:start position:0%
+on not instantly but systematically he
+ 
+
+ align:start position:0%
+on not instantly but systematically he
+had a call as a professor in uh in
+
+ align:start position:0%
+had a call as a professor in uh in
+ 
+
+ align:start position:0%
+had a call as a professor in uh in
+Berlin later on and uh after the Nazis
+
+ align:start position:0%
+Berlin later on and uh after the Nazis
+ 
+
+ align:start position:0%
+Berlin later on and uh after the Nazis
+took over in Germany decided to free
+
+ align:start position:0%
+took over in Germany decided to free
+ 
+
+ align:start position:0%
+took over in Germany decided to free
+Germany and he went moved to the United
+
+ align:start position:0%
+Germany and he went moved to the United
+ 
+
+ align:start position:0%
+Germany and he went moved to the United
+States where he took on a position in
+
+ align:start position:0%
+States where he took on a position in
+ 
+
+ align:start position:0%
+States where he took on a position in
+Princeton um the rest is history as you
+
+ align:start position:0%
+Princeton um the rest is history as you
+ 
+
+ align:start position:0%
+Princeton um the rest is history as you
+want and we'll hear more about this uh
+
+ align:start position:0%
+want and we'll hear more about this uh
+ 
+
+ align:start position:0%
+want and we'll hear more about this uh
+tomorrow
\ No newline at end of file
diff --git a/fXlzY2l1-4w.txt b/fXlzY2l1-4w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ed2dd1dacffb67990c08f2b5c5ef2730689ca1ae
--- /dev/null
+++ b/fXlzY2l1-4w.txt
@@ -0,0 +1,2531 @@
+align:start position:0%
+ 
+we spoke about the hydrogen atom and in
+
+ align:start position:0%
+we spoke about the hydrogen atom and in
+ 
+
+ align:start position:0%
+we spoke about the hydrogen atom and in
+the hydrogen atom we drew the spectrum
+
+ align:start position:0%
+the hydrogen atom we drew the spectrum
+ 
+
+ align:start position:0%
+the hydrogen atom we drew the spectrum
+so the table the data of spectrum of a
+
+ align:start position:0%
+so the table the data of spectrum of a
+ 
+
+ align:start position:0%
+so the table the data of spectrum of a
+quantum system so this is a question
+
+ align:start position:0%
+quantum system so this is a question
+ 
+
+ align:start position:0%
+quantum system so this is a question
+that they want you in general to be
+
+ align:start position:0%
+that they want you in general to be
+ 
+
+ align:start position:0%
+that they want you in general to be
+aware of what do we mean by a diagram of
+
+ align:start position:0%
+aware of what do we mean by a diagram of
+ 
+
+ align:start position:0%
+aware of what do we mean by a diagram of
+the energy levels in a central potential
+
+ align:start position:0%
+the energy levels in a central potential
+ 
+
+ align:start position:0%
+the energy levels in a central potential
+so this is something we did for the
+
+ align:start position:0%
+so this is something we did for the
+ 
+
+ align:start position:0%
+so this is something we did for the
+hydrogen atom but in general the diagram
+
+ align:start position:0%
+hydrogen atom but in general the diagram
+ 
+
+ align:start position:0%
+hydrogen atom but in general the diagram
+of energy eigenstates in a central
+
+ align:start position:0%
+of energy eigenstates in a central
+ 
+
+ align:start position:0%
+of energy eigenstates in a central
+potential looks like this you put the
+
+ align:start position:0%
+potential looks like this you put the
+ 
+
+ align:start position:0%
+potential looks like this you put the
+energies here and they could be bound
+
+ align:start position:0%
+energies here and they could be bound
+ 
+
+ align:start position:0%
+energies here and they could be bound
+states that have negative energy they
+
+ align:start position:0%
+states that have negative energy they
+ 
+
+ align:start position:0%
+states that have negative energy they
+could be even bound States with positive
+
+ align:start position:0%
+could be even bound States with positive
+ 
+
+ align:start position:0%
+could be even bound States with positive
+energy depending on the system you are
+
+ align:start position:0%
+energy depending on the system you are
+ 
+
+ align:start position:0%
+energy depending on the system you are
+discussing like you remember the
+
+ align:start position:0%
+discussing like you remember the
+ 
+
+ align:start position:0%
+discussing like you remember the
+harmonic oscillator the potential is
+
+ align:start position:0%
+harmonic oscillator the potential is
+ 
+
+ align:start position:0%
+harmonic oscillator the potential is
+naturally defined to be positive and all
+
+ align:start position:0%
+naturally defined to be positive and all
+ 
+
+ align:start position:0%
+naturally defined to be positive and all
+these energy states that harmonic
+
+ align:start position:0%
+these energy states that harmonic
+ 
+
+ align:start position:0%
+these energy states that harmonic
+oscillator has represent bound States
+
+ align:start position:0%
+oscillator has represent bound States
+ 
+
+ align:start position:0%
+oscillator has represent bound States
+there normalizable wave function in fact
+
+ align:start position:0%
+there normalizable wave function in fact
+ 
+
+ align:start position:0%
+there normalizable wave function in fact
+you don't have scattering States because
+
+ align:start position:0%
+you don't have scattering States because
+ 
+
+ align:start position:0%
+you don't have scattering States because
+the potential just reaches forever so in
+
+ align:start position:0%
+the potential just reaches forever so in
+ 
+
+ align:start position:0%
+the potential just reaches forever so in
+general for a central potential however
+
+ align:start position:0%
+general for a central potential however
+ 
+
+ align:start position:0%
+general for a central potential however
+of the the system is shown like that and
+
+ align:start position:0%
+of the the system is shown like that and
+ 
+
+ align:start position:0%
+of the the system is shown like that and
+we plot here L but L is not a continuous
+
+ align:start position:0%
+we plot here L but L is not a continuous
+ 
+
+ align:start position:0%
+we plot here L but L is not a continuous
+variable so we'll put like l equals 0
+
+ align:start position:0%
+variable so we'll put like l equals 0
+ 
+
+ align:start position:0%
+variable so we'll put like l equals 0
+here l equals 1 l equals 2 l equals 3
+
+ align:start position:0%
+here l equals 1 l equals 2 l equals 3
+ 
+
+ align:start position:0%
+here l equals 1 l equals 2 l equals 3
+and then you start plotting the energy
+
+ align:start position:0%
+and then you start plotting the energy
+ 
+
+ align:start position:0%
+and then you start plotting the energy
+levels you solve the radial equation
+
+ align:start position:0%
+levels you solve the radial equation
+ 
+
+ align:start position:0%
+levels you solve the radial equation
+remember the radial equation is a
+
+ align:start position:0%
+remember the radial equation is a
+ 
+
+ align:start position:0%
+remember the radial equation is a
+Schrodinger equation minus h squared
+
+ align:start position:0%
+Schrodinger equation minus h squared
+ 
+
+ align:start position:0%
+Schrodinger equation minus h squared
+over 2m these second you the R squared
+
+ align:start position:0%
+over 2m these second you the R squared
+ 
+
+ align:start position:0%
+over 2m these second you the R squared
+plus V effective of R u equals EU and V
+
+ align:start position:0%
+plus V effective of R u equals EU and V
+ 
+
+ align:start position:0%
+plus V effective of R u equals EU and V
+effective of R is the V of R that your
+
+ align:start position:0%
+effective of R is the V of R that your
+ 
+
+ align:start position:0%
+effective of R is the V of R that your
+system had plus a contribution for
+
+ align:start position:0%
+system had plus a contribution for
+ 
+
+ align:start position:0%
+system had plus a contribution for
+angular momentum to sew up this radial
+
+ align:start position:0%
+angular momentum to sew up this radial
+ 
+
+ align:start position:0%
+angular momentum to sew up this radial
+equation is a collection of radial
+
+ align:start position:0%
+equation is a collection of radial
+ 
+
+ align:start position:0%
+equation is a collection of radial
+equations with try to emphasize that
+
+ align:start position:0%
+equations with try to emphasize that
+ 
+
+ align:start position:0%
+equations with try to emphasize that
+many times already and you solve it
+
+ align:start position:0%
+many times already and you solve it
+ 
+
+ align:start position:0%
+many times already and you solve it
+first for l equals 0 and for a liquid
+
+ align:start position:0%
+first for l equals 0 and for a liquid
+ 
+
+ align:start position:0%
+first for l equals 0 and for a liquid
+one for L equal 2 you go on and on
+
+ align:start position:0%
+one for L equal 2 you go on and on
+ 
+
+ align:start position:0%
+one for L equal 2 you go on and on
+so you solve it for l equals 0 as an as
+
+ align:start position:0%
+so you solve it for l equals 0 as an as
+ 
+
+ align:start position:0%
+so you solve it for l equals 0 as an as
+and just like us in any one dimensional
+
+ align:start position:0%
+and just like us in any one dimensional
+ 
+
+ align:start position:0%
+and just like us in any one dimensional
+problem for l equals 0 you solve this
+
+ align:start position:0%
+problem for l equals 0 you solve this
+ 
+
+ align:start position:0%
+problem for l equals 0 you solve this
+equation and you find energy levels so
+
+ align:start position:0%
+equation and you find energy levels so
+ 
+
+ align:start position:0%
+equation and you find energy levels so
+you sketch them like that those are the
+
+ align:start position:0%
+you sketch them like that those are the
+ 
+
+ align:start position:0%
+you sketch them like that those are the
+energy levels for l equals 0 this is the
+
+ align:start position:0%
+energy levels for l equals 0 this is the
+ 
+
+ align:start position:0%
+energy levels for l equals 0 this is the
+ground state of the l equals 0 radial
+
+ align:start position:0%
+ground state of the l equals 0 radial
+ 
+
+ align:start position:0%
+ground state of the l equals 0 radial
+equation now just to remind you this is
+
+ align:start position:0%
+equation now just to remind you this is
+ 
+
+ align:start position:0%
+equation now just to remind you this is
+the hard part of solving the Schrodinger
+
+ align:start position:0%
+the hard part of solving the Schrodinger
+ 
+
+ align:start position:0%
+the hard part of solving the Schrodinger
+equation because at the end of the day
+
+ align:start position:0%
+equation because at the end of the day
+ 
+
+ align:start position:0%
+equation because at the end of the day
+the PSI is U of R over R times some ylm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the L that you have here determines
+
+ align:start position:0%
+so the L that you have here determines
+ 
+
+ align:start position:0%
+so the L that you have here determines
+the Y and the M is arbitrary in fact the
+
+ align:start position:0%
+the Y and the M is arbitrary in fact the
+ 
+
+ align:start position:0%
+the Y and the M is arbitrary in fact the
+you doesn't know about the M value so
+
+ align:start position:0%
+you doesn't know about the M value so
+ 
+
+ align:start position:0%
+you doesn't know about the M value so
+here you have this energy levels and
+
+ align:start position:0%
+here you have this energy levels and
+ 
+
+ align:start position:0%
+here you have this energy levels and
+then what happened with the with this
+
+ align:start position:0%
+then what happened with the with this
+ 
+
+ align:start position:0%
+then what happened with the with this
+hydrogen atom is you keep solving of
+
+ align:start position:0%
+hydrogen atom is you keep solving of
+ 
+
+ align:start position:0%
+hydrogen atom is you keep solving of
+course for all the else and in general
+
+ align:start position:0%
+course for all the else and in general
+ 
+
+ align:start position:0%
+course for all the else and in general
+when you solve for L equal 1 you may
+
+ align:start position:0%
+when you solve for L equal 1 you may
+ 
+
+ align:start position:0%
+when you solve for L equal 1 you may
+find some levels like this it's a
+
+ align:start position:0%
+find some levels like this it's a
+ 
+
+ align:start position:0%
+find some levels like this it's a
+miracle
+
+ align:start position:0%
+miracle
+ 
+
+ align:start position:0%
+miracle
+when the levels coincide there's no
+
+ align:start position:0%
+when the levels coincide there's no
+ 
+
+ align:start position:0%
+when the levels coincide there's no
+reason why they should coincide they
+
+ align:start position:0%
+reason why they should coincide they
+ 
+
+ align:start position:0%
+reason why they should coincide they
+happen to coincide for the hydrogen atom
+
+ align:start position:0%
+happen to coincide for the hydrogen atom
+ 
+
+ align:start position:0%
+happen to coincide for the hydrogen atom
+and that's because of a very special
+
+ align:start position:0%
+and that's because of a very special
+ 
+
+ align:start position:0%
+and that's because of a very special
+symmetry of the 1 over R potential orbit
+
+ align:start position:0%
+symmetry of the 1 over R potential orbit
+ 
+
+ align:start position:0%
+symmetry of the 1 over R potential orbit
+then for L equal to you solve it and for
+
+ align:start position:0%
+then for L equal to you solve it and for
+ 
+
+ align:start position:0%
+then for L equal to you solve it and for
+L equal 3 you solve and you find the
+
+ align:start position:0%
+L equal 3 you solve and you find the
+ 
+
+ align:start position:0%
+L equal 3 you solve and you find the
+station that's the diagram of states of
+
+ align:start position:0%
+station that's the diagram of states of
+ 
+
+ align:start position:0%
+station that's the diagram of states of
+a central potential for the hydrogen
+
+ align:start position:0%
+a central potential for the hydrogen
+ 
+
+ align:start position:0%
+a central potential for the hydrogen
+atom of course they first all the
+
+ align:start position:0%
+atom of course they first all the
+ 
+
+ align:start position:0%
+atom of course they first all the
+energies were negative and the energy
+
+ align:start position:0%
+energies were negative and the energy
+ 
+
+ align:start position:0%
+energies were negative and the energy
+levels coincide so
+
+ align:start position:0%
+levels coincide so
+ 
+
+ align:start position:0%
+levels coincide so
+this is the ground state of the l equals
+
+ align:start position:0%
+this is the ground state of the l equals
+ 
+
+ align:start position:0%
+this is the ground state of the l equals
+0 radio equation this is the ground
+
+ align:start position:0%
+0 radio equation this is the ground
+ 
+
+ align:start position:0%
+0 radio equation this is the ground
+state of the L equal 1 radial equation
+
+ align:start position:0%
+state of the L equal 1 radial equation
+ 
+
+ align:start position:0%
+state of the L equal 1 radial equation
+this is a grunt sense of the L equal to
+
+ align:start position:0%
+this is a grunt sense of the L equal to
+ 
+
+ align:start position:0%
+this is a grunt sense of the L equal to
+radial equation this is the ground state
+
+ align:start position:0%
+radial equation this is the ground state
+ 
+
+ align:start position:0%
+radial equation this is the ground state
+of the whole system so this is what we
+
+ align:start position:0%
+of the whole system so this is what we
+ 
+
+ align:start position:0%
+of the whole system so this is what we
+call plotting the spectrum in a in a
+
+ align:start position:0%
+call plotting the spectrum in a in a
+ 
+
+ align:start position:0%
+call plotting the spectrum in a in a
+radial potential problem and it's a
+
+ align:start position:0%
+radial potential problem and it's a
+ 
+
+ align:start position:0%
+radial potential problem and it's a
+generic form so we were doing this for
+
+ align:start position:0%
+generic form so we were doing this for
+ 
+
+ align:start position:0%
+generic form so we were doing this for
+the hydrogen atom last time to try to
+
+ align:start position:0%
+the hydrogen atom last time to try to
+ 
+
+ align:start position:0%
+the hydrogen atom last time to try to
+understand the various orbits and we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the hydrogen atom V of R was a
+
+ align:start position:0%
+for the hydrogen atom V of R was a
+ 
+
+ align:start position:0%
+for the hydrogen atom V of R was a
+potential like this minus e squared over
+
+ align:start position:0%
+potential like this minus e squared over
+ 
+
+ align:start position:0%
+potential like this minus e squared over
+R and then you have sometimes the L
+
+ align:start position:0%
+R and then you have sometimes the L
+ 
+
+ align:start position:0%
+R and then you have sometimes the L
+contribution that this function diverges
+
+ align:start position:0%
+contribution that this function diverges
+ 
+
+ align:start position:0%
+contribution that this function diverges
+towards the origin 1 over R squared and
+
+ align:start position:0%
+towards the origin 1 over R squared and
+ 
+
+ align:start position:0%
+towards the origin 1 over R squared and
+by the time you add them together this
+
+ align:start position:0%
+by the time you add them together this
+ 
+
+ align:start position:0%
+by the time you add them together this
+is the original potential so this could
+
+ align:start position:0%
+is the original potential so this could
+ 
+
+ align:start position:0%
+is the original potential so this could
+be thought as L equals 0 case then when
+
+ align:start position:0%
+be thought as L equals 0 case then when
+ 
+
+ align:start position:0%
+be thought as L equals 0 case then when
+if you have L sub L over here and some
+
+ align:start position:0%
+if you have L sub L over here and some
+ 
+
+ align:start position:0%
+if you have L sub L over here and some
+other L maybe like that these are the
+
+ align:start position:0%
+other L maybe like that these are the
+ 
+
+ align:start position:0%
+other L maybe like that these are the
+various potentials that you get and in
+
+ align:start position:0%
+various potentials that you get and in
+ 
+
+ align:start position:0%
+various potentials that you get and in
+general you may want to figure out for
+
+ align:start position:0%
+general you may want to figure out for
+ 
+
+ align:start position:0%
+general you may want to figure out for
+example if you have an energy level some
+
+ align:start position:0%
+example if you have an energy level some
+ 
+
+ align:start position:0%
+example if you have an energy level some
+particular energy what are the turning
+
+ align:start position:0%
+particular energy what are the turning
+ 
+
+ align:start position:0%
+particular energy what are the turning
+point so let's consider for that case
+
+ align:start position:0%
+point so let's consider for that case
+ 
+
+ align:start position:0%
+point so let's consider for that case
+it's just one curve that we care about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the electron will be going from some
+
+ align:start position:0%
+and the electron will be going from some
+ 
+
+ align:start position:0%
+and the electron will be going from some
+value of the radius so this is the plot
+
+ align:start position:0%
+value of the radius so this is the plot
+ 
+
+ align:start position:0%
+value of the radius so this is the plot
+of the effective potential as a function
+
+ align:start position:0%
+of the effective potential as a function
+ 
+
+ align:start position:0%
+of the effective potential as a function
+of radius it will go from one to another
+
+ align:start position:0%
+of radius it will go from one to another
+ 
+
+ align:start position:0%
+of radius it will go from one to another
+they could be called R minus 2r plus and
+
+ align:start position:0%
+they could be called R minus 2r plus and
+ 
+
+ align:start position:0%
+they could be called R minus 2r plus and
+our semi classical interpretation which
+
+ align:start position:0%
+our semi classical interpretation which
+ 
+
+ align:start position:0%
+our semi classical interpretation which
+is roughly good if you're talking about
+
+ align:start position:0%
+is roughly good if you're talking about
+ 
+
+ align:start position:0%
+is roughly good if you're talking about
+high quantum
+
+ align:start position:0%
+high quantum
+ 
+
+ align:start position:0%
+high quantum
+numbers hi principal quantum numbers
+
+ align:start position:0%
+numbers hi principal quantum numbers
+ 
+
+ align:start position:0%
+numbers hi principal quantum numbers
+high l quantum numbers is that you have
+
+ align:start position:0%
+high l quantum numbers is that you have
+ 
+
+ align:start position:0%
+high l quantum numbers is that you have
+an ellipse on the radial distance to the
+
+ align:start position:0%
+an ellipse on the radial distance to the
+ 
+
+ align:start position:0%
+an ellipse on the radial distance to the
+center where the proton is located go
+
+ align:start position:0%
+center where the proton is located go
+ 
+
+ align:start position:0%
+center where the proton is located go
+from our plus to our minus the electron
+
+ align:start position:0%
+from our plus to our minus the electron
+ 
+
+ align:start position:0%
+from our plus to our minus the electron
+is bouncing back and forth that is the
+
+ align:start position:0%
+is bouncing back and forth that is the
+ 
+
+ align:start position:0%
+is bouncing back and forth that is the
+classical picture in the quantum
+
+ align:start position:0%
+classical picture in the quantum
+ 
+
+ align:start position:0%
+classical picture in the quantum
+mechanical picture you expect something
+
+ align:start position:0%
+mechanical picture you expect something
+ 
+
+ align:start position:0%
+mechanical picture you expect something
+somewhat similar there's going to be a
+
+ align:start position:0%
+somewhat similar there's going to be a
+ 
+
+ align:start position:0%
+somewhat similar there's going to be a
+wave function maybe a wave function here
+
+ align:start position:0%
+wave function maybe a wave function here
+ 
+
+ align:start position:0%
+wave function maybe a wave function here
+sy squared and it's it's going to be
+
+ align:start position:0%
+sy squared and it's it's going to be
+ 
+
+ align:start position:0%
+sy squared and it's it's going to be
+vanishing Li small before this point and
+
+ align:start position:0%
+vanishing Li small before this point and
+ 
+
+ align:start position:0%
+vanishing Li small before this point and
+then by the time you get here it's going
+
+ align:start position:0%
+then by the time you get here it's going
+ 
+
+ align:start position:0%
+then by the time you get here it's going
+to be very fast or and then decay again
+
+ align:start position:0%
+to be very fast or and then decay again
+ 
+
+ align:start position:0%
+to be very fast or and then decay again
+so the probability distribution will
+
+ align:start position:0%
+so the probability distribution will
+ 
+
+ align:start position:0%
+so the probability distribution will
+sort of mimic the time spent by the
+
+ align:start position:0%
+sort of mimic the time spent by the
+ 
+
+ align:start position:0%
+sort of mimic the time spent by the
+particles we used to argue before so
+
+ align:start position:0%
+particles we used to argue before so
+ 
+
+ align:start position:0%
+particles we used to argue before so
+let's do a little exercise of
+
+ align:start position:0%
+let's do a little exercise of
+ 
+
+ align:start position:0%
+let's do a little exercise of
+calculating the the turning points so
+
+ align:start position:0%
+calculating the the turning points so
+ 
+
+ align:start position:0%
+calculating the the turning points so
+how do we do that well we set H squared
+
+ align:start position:0%
+how do we do that well we set H squared
+ 
+
+ align:start position:0%
+how do we do that well we set H squared
+L times L plus 1 over 2m R squared minus
+
+ align:start position:0%
+L times L plus 1 over 2m R squared minus
+ 
+
+ align:start position:0%
+L times L plus 1 over 2m R squared minus
+e squared over R that's the effective
+
+ align:start position:0%
+e squared over R that's the effective
+ 
+
+ align:start position:0%
+e squared over R that's the effective
+potential equal to the energy of some
+
+ align:start position:0%
+potential equal to the energy of some
+ 
+
+ align:start position:0%
+potential equal to the energy of some
+level and principal quantum number n so
+
+ align:start position:0%
+level and principal quantum number n so
+ 
+
+ align:start position:0%
+level and principal quantum number n so
+it will be minus e squared over 2 a 0 1
+
+ align:start position:0%
+it will be minus e squared over 2 a 0 1
+ 
+
+ align:start position:0%
+it will be minus e squared over 2 a 0 1
+over m squared that's the value of the
+
+ align:start position:0%
+over m squared that's the value of the
+ 
+
+ align:start position:0%
+over m squared that's the value of the
+energy M and the solutions of this
+
+ align:start position:0%
+energy M and the solutions of this
+ 
+
+ align:start position:0%
+energy M and the solutions of this
+quadratic equation are going to give us
+
+ align:start position:0%
+quadratic equation are going to give us
+ 
+
+ align:start position:0%
+quadratic equation are going to give us
+the R plus and the R minus of the orbit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's probably worthwhile to do a little
+
+ align:start position:0%
+it's probably worthwhile to do a little
+ 
+
+ align:start position:0%
+it's probably worthwhile to do a little
+transformation and to say are equal 0
+
+ align:start position:0%
+transformation and to say are equal 0
+ 
+
+ align:start position:0%
+transformation and to say are equal 0
+times X where X is unit 3 and then the
+
+ align:start position:0%
+times X where X is unit 3 and then the
+ 
+
+ align:start position:0%
+times X where X is unit 3 and then the
+equation becomes H squared L times L
+
+ align:start position:0%
+equation becomes H squared L times L
+ 
+
+ align:start position:0%
+equation becomes H squared L times L
+plus 1 over 2m a squared is 0 squared
+
+ align:start position:0%
+plus 1 over 2m a squared is 0 squared
+ 
+
+ align:start position:0%
+plus 1 over 2m a squared is 0 squared
+times L times L plus 1 over x squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus y squared over a not X is equal to
+
+ align:start position:0%
+minus y squared over a not X is equal to
+ 
+
+ align:start position:0%
+minus y squared over a not X is equal to
+minus e squared over 2a not 1 over m
+
+ align:start position:0%
+minus e squared over 2a not 1 over m
+ 
+
+ align:start position:0%
+minus e squared over 2a not 1 over m
+squared so we unit should work out we
+
+ align:start position:0%
+squared so we unit should work out we
+ 
+
+ align:start position:0%
+squared so we unit should work out we
+should get a nice equation without unit
+
+ align:start position:0%
+should get a nice equation without unit
+ 
+
+ align:start position:0%
+should get a nice equation without unit
+so what must be happening is that the
+
+ align:start position:0%
+so what must be happening is that the
+ 
+
+ align:start position:0%
+so what must be happening is that the
+coefficient in front of here H squared
+
+ align:start position:0%
+coefficient in front of here H squared
+ 
+
+ align:start position:0%
+coefficient in front of here H squared
+2m a 0 squared let's take the other a 0
+
+ align:start position:0%
+2m a 0 squared let's take the other a 0
+ 
+
+ align:start position:0%
+2m a 0 squared let's take the other a 0
+and separate it out and transform this
+
+ align:start position:0%
+and separate it out and transform this
+ 
+
+ align:start position:0%
+and separate it out and transform this
+remember a 0 was H squared over m e
+
+ align:start position:0%
+remember a 0 was H squared over m e
+ 
+
+ align:start position:0%
+remember a 0 was H squared over m e
+squared so so here we get h squared over
+
+ align:start position:0%
+squared so so here we get h squared over
+ 
+
+ align:start position:0%
+squared so so here we get h squared over
+2m a 0 and that is 0 now has an H
+
+ align:start position:0%
+2m a 0 and that is 0 now has an H
+ 
+
+ align:start position:0%
+2m a 0 and that is 0 now has an H
+squared and there's M e squared so the
+
+ align:start position:0%
+squared and there's M e squared so the
+ 
+
+ align:start position:0%
+squared and there's M e squared so the
+h-word cancels the M cancels this is e
+
+ align:start position:0%
+h-word cancels the M cancels this is e
+ 
+
+ align:start position:0%
+h-word cancels the M cancels this is e
+squared over 2a 0 so this whole
+
+ align:start position:0%
+squared over 2a 0 so this whole
+ 
+
+ align:start position:0%
+squared over 2a 0 so this whole
+coefficient is e squared over 2a 0 which
+
+ align:start position:0%
+coefficient is e squared over 2a 0 which
+ 
+
+ align:start position:0%
+coefficient is e squared over 2a 0 which
+is nice because now the e squared over a
+
+ align:start position:0%
+is nice because now the e squared over a
+ 
+
+ align:start position:0%
+is nice because now the e squared over a
+0 the e squared over 2a squared over
+
+ align:start position:0%
+0 the e squared over 2a squared over
+ 
+
+ align:start position:0%
+0 the e squared over 2a squared over
+easy
+
+ align:start position:0%
+easy
+ 
+
+ align:start position:0%
+easy
+your counsel and we get a L times L plus
+
+ align:start position:0%
+your counsel and we get a L times L plus
+ 
+
+ align:start position:0%
+your counsel and we get a L times L plus
+one over x squared I've cancelled all
+
+ align:start position:0%
+one over x squared I've cancelled all
+ 
+
+ align:start position:0%
+one over x squared I've cancelled all
+this factor -2 over X is equal to minus
+
+ align:start position:0%
+this factor -2 over X is equal to minus
+ 
+
+ align:start position:0%
+this factor -2 over X is equal to minus
+1 over N squared so I multiplied by the
+
+ align:start position:0%
+1 over N squared so I multiplied by the
+ 
+
+ align:start position:0%
+1 over N squared so I multiplied by the
+inverse of this quantity it clears up
+
+ align:start position:0%
+inverse of this quantity it clears up
+ 
+
+ align:start position:0%
+inverse of this quantity it clears up
+the factor in the first term it produces
+
+ align:start position:0%
+the factor in the first term it produces
+ 
+
+ align:start position:0%
+the factor in the first term it produces
+an extra factor of 2 in the second term
+
+ align:start position:0%
+an extra factor of 2 in the second term
+ 
+
+ align:start position:0%
+an extra factor of 2 in the second term
+and you've got a nice simple quadratic
+
+ align:start position:0%
+and you've got a nice simple quadratic
+ 
+
+ align:start position:0%
+and you've got a nice simple quadratic
+equation yes um oh there's no no such
+
+ align:start position:0%
+equation yes um oh there's no no such
+ 
+
+ align:start position:0%
+equation yes um oh there's no no such
+thing there's too many of them thank you
+
+ align:start position:0%
+thing there's too many of them thank you
+ 
+
+ align:start position:0%
+thing there's too many of them thank you
+very much yes too many 1 over x squared
+
+ align:start position:0%
+very much yes too many 1 over x squared
+ 
+
+ align:start position:0%
+very much yes too many 1 over x squared
+thank you so let's move this to the
+
+ align:start position:0%
+thank you so let's move this to the
+ 
+
+ align:start position:0%
+thank you so let's move this to the
+other side plus 1 over N squared equals
+
+ align:start position:0%
+other side plus 1 over N squared equals
+ 
+
+ align:start position:0%
+other side plus 1 over N squared equals
+0 so you have this is the main equation
+
+ align:start position:0%
+0 so you have this is the main equation
+ 
+
+ align:start position:0%
+0 so you have this is the main equation
+and we can write this up well the
+
+ align:start position:0%
+and we can write this up well the
+ 
+
+ align:start position:0%
+and we can write this up well the
+solution for 1 over X is a quadratic
+
+ align:start position:0%
+solution for 1 over X is a quadratic
+ 
+
+ align:start position:0%
+solution for 1 over X is a quadratic
+equation in 1 over X so it's some I'll
+
+ align:start position:0%
+equation in 1 over X so it's some I'll
+ 
+
+ align:start position:0%
+equation in 1 over X so it's some I'll
+write it here 1 plus minus square root
+
+ align:start position:0%
+write it here 1 plus minus square root
+ 
+
+ align:start position:0%
+write it here 1 plus minus square root
+of 1 minus L times L plus 1 over N
+
+ align:start position:0%
+of 1 minus L times L plus 1 over N
+ 
+
+ align:start position:0%
+of 1 minus L times L plus 1 over N
+squared divided by L times L plus 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's just from the quadratic formula
+
+ align:start position:0%
+that's just from the quadratic formula
+ 
+
+ align:start position:0%
+that's just from the quadratic formula
+so then you invert it so X is now L
+
+ align:start position:0%
+so then you invert it so X is now L
+ 
+
+ align:start position:0%
+so then you invert it so X is now L
+times L plus 1 over 1 plus minus square
+
+ align:start position:0%
+times L plus 1 over 1 plus minus square
+ 
+
+ align:start position:0%
+times L plus 1 over 1 plus minus square
+root of 1 minus L L plus 1 over N
+
+ align:start position:0%
+root of 1 minus L L plus 1 over N
+ 
+
+ align:start position:0%
+root of 1 minus L L plus 1 over N
+squared and we multiplied by the
+
+ align:start position:0%
+squared and we multiplied by the
+ 
+
+ align:start position:0%
+squared and we multiplied by the
+opposite factor to clear the square root
+
+ align:start position:0%
+opposite factor to clear the square root
+ 
+
+ align:start position:0%
+opposite factor to clear the square root
+so 1 minus plus square root of 1 minus L
+
+ align:start position:0%
+so 1 minus plus square root of 1 minus L
+ 
+
+ align:start position:0%
+so 1 minus plus square root of 1 minus L
+times L plus 1 over N squared and the
+
+ align:start position:0%
+times L plus 1 over N squared and the
+ 
+
+ align:start position:0%
+times L plus 1 over N squared and the
+same factor here 1 minus plus square
+
+ align:start position:0%
+same factor here 1 minus plus square
+ 
+
+ align:start position:0%
+same factor here 1 minus plus square
+root of 1 minus ll plus 1 over N squared
+
+ align:start position:0%
+root of 1 minus ll plus 1 over N squared
+ 
+
+ align:start position:0%
+root of 1 minus ll plus 1 over N squared
+all these things but that's not so bad
+
+ align:start position:0%
+all these things but that's not so bad
+ 
+
+ align:start position:0%
+all these things but that's not so bad
+you get L times L plus 1 times this
+
+ align:start position:0%
+you get L times L plus 1 times this
+ 
+
+ align:start position:0%
+you get L times L plus 1 times this
+factor that you had in the numerator
+
+ align:start position:0%
+factor that you had in the numerator
+ 
+
+ align:start position:0%
+factor that you had in the numerator
+that still is the same 1 minus L L plus
+
+ align:start position:0%
+that still is the same 1 minus L L plus
+ 
+
+ align:start position:0%
+that still is the same 1 minus L L plus
+1 over N squared
+
+ align:start position:0%
+1 over N squared
+ 
+
+ align:start position:0%
+1 over N squared
+now we're after a kind of an interesting
+
+ align:start position:0%
+now we're after a kind of an interesting
+ 
+
+ align:start position:0%
+now we're after a kind of an interesting
+piece of information the to the sizes of
+
+ align:start position:0%
+piece of information the to the sizes of
+ 
+
+ align:start position:0%
+piece of information the to the sizes of
+the lip so it's worth simplifying what
+
+ align:start position:0%
+the lip so it's worth simplifying what
+ 
+
+ align:start position:0%
+the lip so it's worth simplifying what
+you got this this equation is not nice
+
+ align:start position:0%
+you got this this equation is not nice
+ 
+
+ align:start position:0%
+you got this this equation is not nice
+enough so we're simplifying and in the
+
+ align:start position:0%
+enough so we're simplifying and in the
+ 
+
+ align:start position:0%
+enough so we're simplifying and in the
+denominator you have a plus B times a
+
+ align:start position:0%
+denominator you have a plus B times a
+ 
+
+ align:start position:0%
+denominator you have a plus B times a
+minus B so it's 1 minus 1 minus L L plus
+
+ align:start position:0%
+minus B so it's 1 minus 1 minus L L plus
+ 
+
+ align:start position:0%
+minus B so it's 1 minus 1 minus L L plus
+1 over m squared and the good thing is
+
+ align:start position:0%
+1 over m squared and the good thing is
+ 
+
+ align:start position:0%
+1 over m squared and the good thing is
+that the denominator the 1 cancels and
+
+ align:start position:0%
+that the denominator the 1 cancels and
+ 
+
+ align:start position:0%
+that the denominator the 1 cancels and
+you get the plus L times L plus 1 over N
+
+ align:start position:0%
+you get the plus L times L plus 1 over N
+ 
+
+ align:start position:0%
+you get the plus L times L plus 1 over N
+squared that cancels that one so that at
+
+ align:start position:0%
+squared that cancels that one so that at
+ 
+
+ align:start position:0%
+squared that cancels that one so that at
+the end of the day we get a pretty nice
+
+ align:start position:0%
+the end of the day we get a pretty nice
+ 
+
+ align:start position:0%
+the end of the day we get a pretty nice
+formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the formulas X is equal to N squared 1
+
+ align:start position:0%
+the formulas X is equal to N squared 1
+ 
+
+ align:start position:0%
+the formulas X is equal to N squared 1
+minus plus 1 minus L times L plus 1 over
+
+ align:start position:0%
+minus plus 1 minus L times L plus 1 over
+ 
+
+ align:start position:0%
+minus plus 1 minus L times L plus 1 over
+N squared like that so if we wish it so
+
+ align:start position:0%
+N squared like that so if we wish it so
+ 
+
+ align:start position:0%
+N squared like that so if we wish it so
+our plus/minus is X multiplied by a
+
+ align:start position:0%
+our plus/minus is X multiplied by a
+ 
+
+ align:start position:0%
+our plus/minus is X multiplied by a
+naught so it's N squared a naught 1
+
+ align:start position:0%
+naught so it's N squared a naught 1
+ 
+
+ align:start position:0%
+naught so it's N squared a naught 1
+minus plus square root of 1 minus L
+
+ align:start position:0%
+minus plus square root of 1 minus L
+ 
+
+ align:start position:0%
+minus plus square root of 1 minus L
+times L plus 1 over N squared okay so
+
+ align:start position:0%
+times L plus 1 over N squared okay so
+ 
+
+ align:start position:0%
+times L plus 1 over N squared okay so
+the ellipse is defined by those two
+
+ align:start position:0%
+the ellipse is defined by those two
+ 
+
+ align:start position:0%
+the ellipse is defined by those two
+values that we have here but the
+
+ align:start position:0%
+values that we have here but the
+ 
+
+ align:start position:0%
+values that we have here but the
+surprising thing is that the some old
+
+ align:start position:0%
+surprising thing is that the some old
+ 
+
+ align:start position:0%
+surprising thing is that the some old
+ellipse and its eccentricity is
+
+ align:start position:0%
+ellipse and its eccentricity is
+ 
+
+ align:start position:0%
+ellipse and its eccentricity is
+dramatically affected by the values of L
+
+ align:start position:0%
+dramatically affected by the values of L
+ 
+
+ align:start position:0%
+dramatically affected by the values of L
+in fact for L equal largest L will be
+
+ align:start position:0%
+in fact for L equal largest L will be
+ 
+
+ align:start position:0%
+in fact for L equal largest L will be
+comparable to n remember L can go up to
+
+ align:start position:0%
+comparable to n remember L can go up to
+ 
+
+ align:start position:0%
+comparable to n remember L can go up to
+n minus 1 so at that point this is
+
+ align:start position:0%
+n minus 1 so at that point this is
+ 
+
+ align:start position:0%
+n minus 1 so at that point this is
+essentially 1 you cancel this and
+
+ align:start position:0%
+essentially 1 you cancel this and
+ 
+
+ align:start position:0%
+essentially 1 you cancel this and
+there's nothing here so there so our
+
+ align:start position:0%
+there's nothing here so there so our
+ 
+
+ align:start position:0%
+there's nothing here so there so our
+plus in our mind has become about the
+
+ align:start position:0%
+plus in our mind has become about the
+ 
+
+ align:start position:0%
+plus in our mind has become about the
+same for l equals n minus 1 our plus is
+
+ align:start position:0%
+same for l equals n minus 1 our plus is
+ 
+
+ align:start position:0%
+same for l equals n minus 1 our plus is
+almost the same as our minus on the
+
+ align:start position:0%
+almost the same as our minus on the
+ 
+
+ align:start position:0%
+almost the same as our minus on the
+orbit is circular completely circular on
+
+ align:start position:0%
+orbit is circular completely circular on
+ 
+
+ align:start position:0%
+orbit is circular completely circular on
+the other hand for l equals 0 the orbit
+
+ align:start position:0%
+the other hand for l equals 0 the orbit
+ 
+
+ align:start position:0%
+the other hand for l equals 0 the orbit
+is completely elliptical in that the
+
+ align:start position:0%
+is completely elliptical in that the
+ 
+
+ align:start position:0%
+is completely elliptical in that the
+radius for l equals 0 this is 0 1 plus
+
+ align:start position:0%
+radius for l equals 0 this is 0 1 plus
+ 
+
+ align:start position:0%
+radius for l equals 0 this is 0 1 plus
+minus 1 so some times is twice this
+
+ align:start position:0%
+minus 1 so some times is twice this
+ 
+
+ align:start position:0%
+minus 1 so some times is twice this
+value sometimes it's 0
+
+ align:start position:0%
+value sometimes it's 0
+ 
+
+ align:start position:0%
+value sometimes it's 0
+so you have the case where our minus can
+
+ align:start position:0%
+so you have the case where our minus can
+ 
+
+ align:start position:0%
+so you have the case where our minus can
+be 0 and you have just an orbit that
+
+ align:start position:0%
+be 0 and you have just an orbit that
+ 
+
+ align:start position:0%
+be 0 and you have just an orbit that
+this like that our minus 0 so extremely
+
+ align:start position:0%
+this like that our minus 0 so extremely
+ 
+
+ align:start position:0%
+this like that our minus 0 so extremely
+elliptical of course that is the semi
+
+ align:start position:0%
+elliptical of course that is the semi
+ 
+
+ align:start position:0%
+elliptical of course that is the semi
+classical approximation so it's more
+
+ align:start position:0%
+classical approximation so it's more
+ 
+
+ align:start position:0%
+classical approximation so it's more
+reliable when you have a reasonable L
+
+ align:start position:0%
+reliable when you have a reasonable L
+ 
+
+ align:start position:0%
+reliable when you have a reasonable L
+undone and finally we can say here for
+
+ align:start position:0%
+undone and finally we can say here for
+ 
+
+ align:start position:0%
+undone and finally we can say here for
+example one interesting thing that our
+
+ align:start position:0%
+example one interesting thing that our
+ 
+
+ align:start position:0%
+example one interesting thing that our
+plus plus our - over 2 which is this our
+
+ align:start position:0%
+plus plus our - over 2 which is this our
+ 
+
+ align:start position:0%
+plus plus our - over 2 which is this our
+plus plus or minus is the total longest
+
+ align:start position:0%
+plus plus or minus is the total longest
+ 
+
+ align:start position:0%
+plus plus or minus is the total longest
+axis of the lips / to the center of the
+
+ align:start position:0%
+axis of the lips / to the center of the
+ 
+
+ align:start position:0%
+axis of the lips / to the center of the
+lips not the focus that distance is
+
+ align:start position:0%
+lips not the focus that distance is
+ 
+
+ align:start position:0%
+lips not the focus that distance is
+independent of L so you'll have N
+
+ align:start position:0%
+independent of L so you'll have N
+ 
+
+ align:start position:0%
+independent of L so you'll have N
+squared a 0 so a typical red burg atom
+
+ align:start position:0%
+squared a 0 so a typical red burg atom
+ 
+
+ align:start position:0%
+squared a 0 so a typical red burg atom
+will have n equal 100 so this is an
+
+ align:start position:0%
+will have n equal 100 so this is an
+ 
+
+ align:start position:0%
+will have n equal 100 so this is an
+example n equal 100 l equals 60 in which
+
+ align:start position:0%
+example n equal 100 l equals 60 in which
+ 
+
+ align:start position:0%
+example n equal 100 l equals 60 in which
+case of the ARP for n equal 100 are plus
+
+ align:start position:0%
+case of the ARP for n equal 100 are plus
+ 
+
+ align:start position:0%
+case of the ARP for n equal 100 are plus
+minus is equal to 10,000 a 0 M squared a
+
+ align:start position:0%
+minus is equal to 10,000 a 0 M squared a
+ 
+
+ align:start position:0%
+minus is equal to 10,000 a 0 M squared a
+0 times this factor which in one case is
+
+ align:start position:0%
+0 times this factor which in one case is
+ 
+
+ align:start position:0%
+0 times this factor which in one case is
+1.8 and in the other case is 0.2 that's
+
+ align:start position:0%
+1.8 and in the other case is 0.2 that's
+ 
+
+ align:start position:0%
+1.8 and in the other case is 0.2 that's
+what you get for L equal 60 and n equal
+
+ align:start position:0%
+what you get for L equal 60 and n equal
+ 
+
+ align:start position:0%
+what you get for L equal 60 and n equal
+100 so this this orbit we have our plus
+
+ align:start position:0%
+100 so this this orbit we have our plus
+ 
+
+ align:start position:0%
+100 so this this orbit we have our plus
+about 18,000 a 0 on arm
+
+ align:start position:0%
+about 18,000 a 0 on arm
+ 
+
+ align:start position:0%
+about 18,000 a 0 on arm
+- about two thousand zero and all of our
+
+ align:start position:0%
+- about two thousand zero and all of our
+ 
+
+ align:start position:0%
+- about two thousand zero and all of our
+orbits satisfy this property that if you
+
+ align:start position:0%
+orbits satisfy this property that if you
+ 
+
+ align:start position:0%
+orbits satisfy this property that if you
+have this hour - an hour plus all of the
+
+ align:start position:0%
+have this hour - an hour plus all of the
+ 
+
+ align:start position:0%
+have this hour - an hour plus all of the
+orbits with different L have the same
+
+ align:start position:0%
+orbits with different L have the same
+ 
+
+ align:start position:0%
+orbits with different L have the same
+hour plus plus or minus so if this is
+
+ align:start position:0%
+hour plus plus or minus so if this is
+ 
+
+ align:start position:0%
+hour plus plus or minus so if this is
+the total length of the major axis when
+
+ align:start position:0%
+the total length of the major axis when
+ 
+
+ align:start position:0%
+the total length of the major axis when
+the orbit becomes circular it's the same
+
+ align:start position:0%
+the orbit becomes circular it's the same
+ 
+
+ align:start position:0%
+the orbit becomes circular it's the same
+and this distance when the orbit becomes
+
+ align:start position:0%
+and this distance when the orbit becomes
+ 
+
+ align:start position:0%
+and this distance when the orbit becomes
+very elliptical is the same as well I
+
+ align:start position:0%
+very elliptical is the same as well I
+ 
+
+ align:start position:0%
+very elliptical is the same as well I
+mentioned last time that this nice
+
+ align:start position:0%
+mentioned last time that this nice
+ 
+
+ align:start position:0%
+mentioned last time that this nice
+property is degeneracy we're here if
+
+ align:start position:0%
+property is degeneracy we're here if
+ 
+
+ align:start position:0%
+property is degeneracy we're here if
+you're keeping em fixed but changing L
+
+ align:start position:0%
+you're keeping em fixed but changing L
+ 
+
+ align:start position:0%
+you're keeping em fixed but changing L
+you're going from all these ellipses
+
+ align:start position:0%
+you're going from all these ellipses
+ 
+
+ align:start position:0%
+you're going from all these ellipses
+this is for l equals n minus 1 and this
+
+ align:start position:0%
+this is for l equals n minus 1 and this
+ 
+
+ align:start position:0%
+this is for l equals n minus 1 and this
+one is for l equals 0 on all these
+
+ align:start position:0%
+one is for l equals 0 on all these
+ 
+
+ align:start position:0%
+one is for l equals 0 on all these
+ellipses are here and they all those are
+
+ align:start position:0%
+ellipses are here and they all those are
+ 
+
+ align:start position:0%
+ellipses are here and they all those are
+all the semi-classical picture of those
+
+ align:start position:0%
+all the semi-classical picture of those
+ 
+
+ align:start position:0%
+all the semi-classical picture of those
+degenerate states in the diagram of the
+
+ align:start position:0%
+degenerate states in the diagram of the
+ 
+
+ align:start position:0%
+degenerate states in the diagram of the
+hydrogen atom the diagram of the
+
+ align:start position:0%
+hydrogen atom the diagram of the
+ 
+
+ align:start position:0%
+hydrogen atom the diagram of the
+hydrogen atom was something like this
+
+ align:start position:0%
+hydrogen atom was something like this
+ 
+
+ align:start position:0%
+hydrogen atom was something like this
+and and you're looking at all the
+
+ align:start position:0%
+and and you're looking at all the
+ 
+
+ align:start position:0%
+and and you're looking at all the
+degenerate states that you have there
+
+ align:start position:0%
+degenerate states that you have there
+ 
+
+ align:start position:0%
+degenerate states that you have there
+and they are degenerate and you would
+
+ align:start position:0%
+and they are degenerate and you would
+ 
+
+ align:start position:0%
+and they are degenerate and you would
+say well why are ellipses that look like
+
+ align:start position:0%
+say well why are ellipses that look like
+ 
+
+ align:start position:0%
+say well why are ellipses that look like
+that the generate well even Kepler
+
+ align:start position:0%
+that the generate well even Kepler
+ 
+
+ align:start position:0%
+that the generate well even Kepler
+apparently knew that in Kepler's laws
+
+ align:start position:0%
+apparently knew that in Kepler's laws
+ 
+
+ align:start position:0%
+apparently knew that in Kepler's laws
+that he observed that the period of
+
+ align:start position:0%
+that he observed that the period of
+ 
+
+ align:start position:0%
+that he observed that the period of
+motion of an orbit just depended on the
+
+ align:start position:0%
+motion of an orbit just depended on the
+ 
+
+ align:start position:0%
+motion of an orbit just depended on the
+semi-major axis so periods are related
+
+ align:start position:0%
+semi-major axis so periods are related
+ 
+
+ align:start position:0%
+semi-major axis so periods are related
+to energy
+
+ align:start position:0%
+to energy
+ 
+
+ align:start position:0%
+to energy
+and it's reasonable the wigs have this
+
+ align:start position:0%
+and it's reasonable the wigs have this
+ 
+
+ align:start position:0%
+and it's reasonable the wigs have this
+thing in quantum mechanics
+
+ align:start position:0%
+thing in quantum mechanics
+ 
+
+ align:start position:0%
+thing in quantum mechanics
+now these degeneracies I want to just
+
+ align:start position:0%
+now these degeneracies I want to just
+ 
+
+ align:start position:0%
+now these degeneracies I want to just
+finish up by emphasizing what you have
+
+ align:start position:0%
+finish up by emphasizing what you have
+ 
+
+ align:start position:0%
+finish up by emphasizing what you have
+here when somebody asks what is the
+
+ align:start position:0%
+here when somebody asks what is the
+ 
+
+ align:start position:0%
+here when somebody asks what is the
+number of states you have here well you
+
+ align:start position:0%
+number of states you have here well you
+ 
+
+ align:start position:0%
+number of states you have here well you
+have to be a little precise on what
+
+ align:start position:0%
+have to be a little precise on what
+ 
+
+ align:start position:0%
+have to be a little precise on what
+you're counting the number of full
+
+ align:start position:0%
+you're counting the number of full
+ 
+
+ align:start position:0%
+you're counting the number of full
+physical states of the quantum system is
+
+ align:start position:0%
+physical states of the quantum system is
+ 
+
+ align:start position:0%
+physical states of the quantum system is
+one here one here one here but each one
+
+ align:start position:0%
+one here one here one here but each one
+ 
+
+ align:start position:0%
+one here one here one here but each one
+of these corresponds to l equals one so
+
+ align:start position:0%
+of these corresponds to l equals one so
+ 
+
+ align:start position:0%
+of these corresponds to l equals one so
+each one of this is triply degenerate
+
+ align:start position:0%
+each one of this is triply degenerate
+ 
+
+ align:start position:0%
+each one of this is triply degenerate
+because M can be minus 1 0 & 1 so here
+
+ align:start position:0%
+because M can be minus 1 0 & 1 so here
+ 
+
+ align:start position:0%
+because M can be minus 1 0 & 1 so here
+three states three stage three states
+
+ align:start position:0%
+three states three stage three states
+ 
+
+ align:start position:0%
+three states three stage three states
+here this is five states five states
+
+ align:start position:0%
+here this is five states five states
+ 
+
+ align:start position:0%
+here this is five states five states
+five stages they'll all have L equal to
+
+ align:start position:0%
+five stages they'll all have L equal to
+ 
+
+ align:start position:0%
+five stages they'll all have L equal to
+and L equal to goes M from minus 2 to
+
+ align:start position:0%
+and L equal to goes M from minus 2 to
+ 
+
+ align:start position:0%
+and L equal to goes M from minus 2 to
+plus 2 so you know we don't actually put
+
+ align:start position:0%
+plus 2 so you know we don't actually put
+ 
+
+ align:start position:0%
+plus 2 so you know we don't actually put
+three things here I think that would be
+
+ align:start position:0%
+three things here I think that would be
+ 
+
+ align:start position:0%
+three things here I think that would be
+confusing we could not put five and we
+
+ align:start position:0%
+confusing we could not put five and we
+ 
+
+ align:start position:0%
+confusing we could not put five and we
+cannot see but it should be remembered
+
+ align:start position:0%
+cannot see but it should be remembered
+ 
+
+ align:start position:0%
+cannot see but it should be remembered
+that this there's the implicit extra
+
+ align:start position:0%
+that this there's the implicit extra
+ 
+
+ align:start position:0%
+that this there's the implicit extra
+degeneracy here associated with the
+
+ align:start position:0%
+degeneracy here associated with the
+ 
+
+ align:start position:0%
+degeneracy here associated with the
+azimuthal quantum number that we
+
+ align:start position:0%
+azimuthal quantum number that we
+ 
+
+ align:start position:0%
+azimuthal quantum number that we
+sometimes just don't represent it in a
+
+ align:start position:0%
+sometimes just don't represent it in a
+ 
+
+ align:start position:0%
+sometimes just don't represent it in a
+figure
\ No newline at end of file
diff --git a/fn2UGyk5DP4.txt b/fn2UGyk5DP4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e0a6df6256dd77fdbe3a69053b8f7b38bbdc962e
--- /dev/null
+++ b/fn2UGyk5DP4.txt
@@ -0,0 +1,9683 @@
+align:start position:0%
+ 
+hi last time we had looked at how we
+
+ align:start position:0%
+hi last time we had looked at how we
+ 
+
+ align:start position:0%
+hi last time we had looked at how we
+might select the compensation for an
+
+ align:start position:0%
+might select the compensation for an
+ 
+
+ align:start position:0%
+might select the compensation for an
+externally compensated operational
+
+ align:start position:0%
+externally compensated operational
+ 
+
+ align:start position:0%
+externally compensated operational
+amplifier as a function of its
+
+ align:start position:0%
+amplifier as a function of its
+ 
+
+ align:start position:0%
+amplifier as a function of its
+application we were using an available
+
+ align:start position:0%
+application we were using an available
+ 
+
+ align:start position:0%
+application we were using an available
+integrated circuit operational amplifier
+
+ align:start position:0%
+integrated circuit operational amplifier
+ 
+
+ align:start position:0%
+integrated circuit operational amplifier
+the type 101 a that is compensated by
+
+ align:start position:0%
+the type 101 a that is compensated by
+ 
+
+ align:start position:0%
+the type 101 a that is compensated by
+means of a minor loop and we discussed
+
+ align:start position:0%
+means of a minor loop and we discussed
+ 
+
+ align:start position:0%
+means of a minor loop and we discussed
+how that minor loop worked and in fact
+
+ align:start position:0%
+how that minor loop worked and in fact
+ 
+
+ align:start position:0%
+how that minor loop worked and in fact
+how we chose compensating in admittances
+
+ align:start position:0%
+how we chose compensating in admittances
+ 
+
+ align:start position:0%
+how we chose compensating in admittances
+or compensating two-port networks as a
+
+ align:start position:0%
+or compensating two-port networks as a
+ 
+
+ align:start position:0%
+or compensating two-port networks as a
+function of the desired closed loop or
+
+ align:start position:0%
+function of the desired closed loop or
+ 
+
+ align:start position:0%
+function of the desired closed loop or
+as a function of the desired open-loop
+
+ align:start position:0%
+as a function of the desired open-loop
+ 
+
+ align:start position:0%
+as a function of the desired open-loop
+transfer function of the amplifier today
+
+ align:start position:0%
+transfer function of the amplifier today
+ 
+
+ align:start position:0%
+transfer function of the amplifier today
+I'd like to continue and look at several
+
+ align:start position:0%
+I'd like to continue and look at several
+ 
+
+ align:start position:0%
+I'd like to continue and look at several
+other types of compensation that we're
+
+ align:start position:0%
+other types of compensation that we're
+ 
+
+ align:start position:0%
+other types of compensation that we're
+able to use if you recall the comparison
+
+ align:start position:0%
+able to use if you recall the comparison
+ 
+
+ align:start position:0%
+able to use if you recall the comparison
+that we were going against was an
+
+ align:start position:0%
+that we were going against was an
+ 
+
+ align:start position:0%
+that we were going against was an
+amplifier that had fixed compensation
+
+ align:start position:0%
+amplifier that had fixed compensation
+ 
+
+ align:start position:0%
+amplifier that had fixed compensation
+something like a 741 type operational
+
+ align:start position:0%
+something like a 741 type operational
+ 
+
+ align:start position:0%
+something like a 741 type operational
+amplifier normally when a manufacturer
+
+ align:start position:0%
+amplifier normally when a manufacturer
+ 
+
+ align:start position:0%
+amplifier normally when a manufacturer
+designs an operational amplifier with
+
+ align:start position:0%
+designs an operational amplifier with
+ 
+
+ align:start position:0%
+designs an operational amplifier with
+fixed compensation he chooses to use
+
+ align:start position:0%
+fixed compensation he chooses to use
+ 
+
+ align:start position:0%
+fixed compensation he chooses to use
+single pole compensation and normally
+
+ align:start position:0%
+single pole compensation and normally
+ 
+
+ align:start position:0%
+single pole compensation and normally
+the constant associated with that single
+
+ align:start position:0%
+the constant associated with that single
+ 
+
+ align:start position:0%
+the constant associated with that single
+pole compensation will be selected so
+
+ align:start position:0%
+pole compensation will be selected so
+ 
+
+ align:start position:0%
+pole compensation will be selected so
+that the amplifier goes through unity
+
+ align:start position:0%
+that the amplifier goes through unity
+ 
+
+ align:start position:0%
+that the amplifier goes through unity
+gain with adequate phase margin as a
+
+ align:start position:0%
+gain with adequate phase margin as a
+ 
+
+ align:start position:0%
+gain with adequate phase margin as a
+consequence when you have such a single
+
+ align:start position:0%
+consequence when you have such a single
+ 
+
+ align:start position:0%
+consequence when you have such a single
+pole Titan amplifier its unity gains
+
+ align:start position:0%
+pole Titan amplifier its unity gains
+ 
+
+ align:start position:0%
+pole Titan amplifier its unity gains
+stable you can use it in the connection
+
+ align:start position:0%
+stable you can use it in the connection
+ 
+
+ align:start position:0%
+stable you can use it in the connection
+that where the output is connected
+
+ align:start position:0%
+that where the output is connected
+ 
+
+ align:start position:0%
+that where the output is connected
+directly back to the inverting input and
+
+ align:start position:0%
+directly back to the inverting input and
+ 
+
+ align:start position:0%
+directly back to the inverting input and
+it will remain stable and that's a
+
+ align:start position:0%
+it will remain stable and that's a
+ 
+
+ align:start position:0%
+it will remain stable and that's a
+perfectly acceptable general
+
+ align:start position:0%
+perfectly acceptable general
+ 
+
+ align:start position:0%
+perfectly acceptable general
+purpose compensation for many
+
+ align:start position:0%
+purpose compensation for many
+ 
+
+ align:start position:0%
+purpose compensation for many
+applications however the difficulty is
+
+ align:start position:0%
+applications however the difficulty is
+ 
+
+ align:start position:0%
+applications however the difficulty is
+that it's really overly conservative for
+
+ align:start position:0%
+that it's really overly conservative for
+ 
+
+ align:start position:0%
+that it's really overly conservative for
+many other and more demanding types of
+
+ align:start position:0%
+many other and more demanding types of
+ 
+
+ align:start position:0%
+many other and more demanding types of
+applications we saw that one of the
+
+ align:start position:0%
+applications we saw that one of the
+ 
+
+ align:start position:0%
+applications we saw that one of the
+things we can do is stay with single
+
+ align:start position:0%
+things we can do is stay with single
+ 
+
+ align:start position:0%
+things we can do is stay with single
+pole compensation that is used a single
+
+ align:start position:0%
+pole compensation that is used a single
+ 
+
+ align:start position:0%
+pole compensation that is used a single
+capacitor to compensate the amplifier
+
+ align:start position:0%
+capacitor to compensate the amplifier
+ 
+
+ align:start position:0%
+capacitor to compensate the amplifier
+but change the magnitude of the
+
+ align:start position:0%
+but change the magnitude of the
+ 
+
+ align:start position:0%
+but change the magnitude of the
+capacitor we found that if we did that
+
+ align:start position:0%
+capacitor we found that if we did that
+ 
+
+ align:start position:0%
+capacitor we found that if we did that
+and in fact changed the capacitor size
+
+ align:start position:0%
+and in fact changed the capacitor size
+ 
+
+ align:start position:0%
+and in fact changed the capacitor size
+as we change the desired closed-loop
+
+ align:start position:0%
+as we change the desired closed-loop
+ 
+
+ align:start position:0%
+as we change the desired closed-loop
+gain we were able to get very dramatic
+
+ align:start position:0%
+gain we were able to get very dramatic
+ 
+
+ align:start position:0%
+gain we were able to get very dramatic
+improvements in the band width of our
+
+ align:start position:0%
+improvements in the band width of our
+ 
+
+ align:start position:0%
+improvements in the band width of our
+externally compensated amplifier
+
+ align:start position:0%
+externally compensated amplifier
+ 
+
+ align:start position:0%
+externally compensated amplifier
+compared to that of a 741 we then looked
+
+ align:start position:0%
+compared to that of a 741 we then looked
+ 
+
+ align:start position:0%
+compared to that of a 741 we then looked
+at another type of compensation to Cole
+
+ align:start position:0%
+at another type of compensation to Cole
+ 
+
+ align:start position:0%
+at another type of compensation to Cole
+compensation where the amplifier
+
+ align:start position:0%
+compensation where the amplifier
+ 
+
+ align:start position:0%
+compensation where the amplifier
+roll-off goes as 1 over s squared at
+
+ align:start position:0%
+roll-off goes as 1 over s squared at
+ 
+
+ align:start position:0%
+roll-off goes as 1 over s squared at
+frequencies well below crossover and
+
+ align:start position:0%
+frequencies well below crossover and
+ 
+
+ align:start position:0%
+frequencies well below crossover and
+then we add a 0 so that crossover is
+
+ align:start position:0%
+then we add a 0 so that crossover is
+ 
+
+ align:start position:0%
+then we add a 0 so that crossover is
+accomplished with a slope of 1 over s
+
+ align:start position:0%
+accomplished with a slope of 1 over s
+ 
+
+ align:start position:0%
+accomplished with a slope of 1 over s
+and again we found out that that sort of
+
+ align:start position:0%
+and again we found out that that sort of
+ 
+
+ align:start position:0%
+and again we found out that that sort of
+compensation could yield very greatly
+
+ align:start position:0%
+compensation could yield very greatly
+ 
+
+ align:start position:0%
+compensation could yield very greatly
+improved the sensitivity over a wide
+
+ align:start position:0%
+improved the sensitivity over a wide
+ 
+
+ align:start position:0%
+improved the sensitivity over a wide
+range of frequencies compared to that
+
+ align:start position:0%
+range of frequencies compared to that
+ 
+
+ align:start position:0%
+range of frequencies compared to that
+which we could achieve with single pole
+
+ align:start position:0%
+which we could achieve with single pole
+ 
+
+ align:start position:0%
+which we could achieve with single pole
+compensation let's consider another
+
+ align:start position:0%
+compensation let's consider another
+ 
+
+ align:start position:0%
+compensation let's consider another
+possible situation suppose we have our
+
+ align:start position:0%
+possible situation suppose we have our
+ 
+
+ align:start position:0%
+possible situation suppose we have our
+operational amplifier and in fact
+
+ align:start position:0%
+operational amplifier and in fact
+ 
+
+ align:start position:0%
+operational amplifier and in fact
+compensated to have a single pole
+
+ align:start position:0%
+compensated to have a single pole
+ 
+
+ align:start position:0%
+compensated to have a single pole
+roll-off so that gets us a 1 over s kind
+
+ align:start position:0%
+roll-off so that gets us a 1 over s kind
+ 
+
+ align:start position:0%
+roll-off so that gets us a 1 over s kind
+of roll-off in our loop and to the
+
+ align:start position:0%
+of roll-off in our loop and to the
+ 
+
+ align:start position:0%
+of roll-off in our loop and to the
+extent that we can ignore other energy
+
+ align:start position:0%
+extent that we can ignore other energy
+ 
+
+ align:start position:0%
+extent that we can ignore other energy
+storage mechanisms in the amplifier
+
+ align:start position:0%
+storage mechanisms in the amplifier
+ 
+
+ align:start position:0%
+storage mechanisms in the amplifier
+while we get approximately 90 degrees of
+
+ align:start position:0%
+while we get approximately 90 degrees of
+ 
+
+ align:start position:0%
+while we get approximately 90 degrees of
+phase margin with this kind of
+
+ align:start position:0%
+phase margin with this kind of
+ 
+
+ align:start position:0%
+phase margin with this kind of
+compensation if we use purely resistive
+
+ align:start position:0%
+compensation if we use purely resistive
+ 
+
+ align:start position:0%
+compensation if we use purely resistive
+feedback however consider what happens
+
+ align:start position:0%
+feedback however consider what happens
+ 
+
+ align:start position:0%
+feedback however consider what happens
+if we load the amplifier with a
+
+ align:start position:0%
+if we load the amplifier with a
+ 
+
+ align:start position:0%
+if we load the amplifier with a
+capacitor and that's a fairly frequently
+
+ align:start position:0%
+capacitor and that's a fairly frequently
+ 
+
+ align:start position:0%
+capacitor and that's a fairly frequently
+occurring situation we can certainly
+
+ align:start position:0%
+occurring situation we can certainly
+ 
+
+ align:start position:0%
+occurring situation we can certainly
+think for example of power supplies
+
+ align:start position:0%
+think for example of power supplies
+ 
+
+ align:start position:0%
+think for example of power supplies
+where a capacitive load is used
+
+ align:start position:0%
+where a capacitive load is used
+ 
+
+ align:start position:0%
+where a capacitive load is used
+routinely we've already looked at one
+
+ align:start position:0%
+routinely we've already looked at one
+ 
+
+ align:start position:0%
+routinely we've already looked at one
+aspect of that problem but if we're not
+
+ align:start position:0%
+aspect of that problem but if we're not
+ 
+
+ align:start position:0%
+aspect of that problem but if we're not
+able to force a dominant pole at the
+
+ align:start position:0%
+able to force a dominant pole at the
+ 
+
+ align:start position:0%
+able to force a dominant pole at the
+output as we suggested earlier why here
+
+ align:start position:0%
+output as we suggested earlier why here
+ 
+
+ align:start position:0%
+output as we suggested earlier why here
+we have a situation where we have the
+
+ align:start position:0%
+we have a situation where we have the
+ 
+
+ align:start position:0%
+we have a situation where we have the
+passive load another possibility is a
+
+ align:start position:0%
+passive load another possibility is a
+ 
+
+ align:start position:0%
+passive load another possibility is a
+circuit known as a sample-and-hold
+
+ align:start position:0%
+circuit known as a sample-and-hold
+ 
+
+ align:start position:0%
+circuit known as a sample-and-hold
+where one takes an amplifier connects a
+
+ align:start position:0%
+where one takes an amplifier connects a
+ 
+
+ align:start position:0%
+where one takes an amplifier connects a
+capacitor to it so that the capacitor
+
+ align:start position:0%
+capacitor to it so that the capacitor
+ 
+
+ align:start position:0%
+capacitor to it so that the capacitor
+can be charged to some input voltage
+
+ align:start position:0%
+can be charged to some input voltage
+ 
+
+ align:start position:0%
+can be charged to some input voltage
+applied to the amplifier and then at
+
+ align:start position:0%
+applied to the amplifier and then at
+ 
+
+ align:start position:0%
+applied to the amplifier and then at
+some later time removes the
+
+ align:start position:0%
+some later time removes the
+ 
+
+ align:start position:0%
+some later time removes the
+passenger so that the value of the
+
+ align:start position:0%
+passenger so that the value of the
+ 
+
+ align:start position:0%
+passenger so that the value of the
+voltage is maintained that sort of a
+
+ align:start position:0%
+voltage is maintained that sort of a
+ 
+
+ align:start position:0%
+voltage is maintained that sort of a
+circuit is called the sample-and-hold
+
+ align:start position:0%
+circuit is called the sample-and-hold
+ 
+
+ align:start position:0%
+circuit is called the sample-and-hold
+but again it involves a capacitive load
+
+ align:start position:0%
+but again it involves a capacitive load
+ 
+
+ align:start position:0%
+but again it involves a capacitive load
+on an operational amplifier the
+
+ align:start position:0%
+on an operational amplifier the
+ 
+
+ align:start position:0%
+on an operational amplifier the
+operational amplifier has finite output
+
+ align:start position:0%
+operational amplifier has finite output
+ 
+
+ align:start position:0%
+operational amplifier has finite output
+resistance and consequently adding a
+
+ align:start position:0%
+resistance and consequently adding a
+ 
+
+ align:start position:0%
+resistance and consequently adding a
+capacitor to its output gives us an
+
+ align:start position:0%
+capacitor to its output gives us an
+ 
+
+ align:start position:0%
+capacitor to its output gives us an
+additional pole and so now we have a two
+
+ align:start position:0%
+additional pole and so now we have a two
+ 
+
+ align:start position:0%
+additional pole and so now we have a two
+pole kind of loop transmission and
+
+ align:start position:0%
+pole kind of loop transmission and
+ 
+
+ align:start position:0%
+pole kind of loop transmission and
+certainly if the additional pole that we
+
+ align:start position:0%
+certainly if the additional pole that we
+ 
+
+ align:start position:0%
+certainly if the additional pole that we
+add occurs well below crossover the
+
+ align:start position:0%
+add occurs well below crossover the
+ 
+
+ align:start position:0%
+add occurs well below crossover the
+stability of the amplifier is very
+
+ align:start position:0%
+stability of the amplifier is very
+ 
+
+ align:start position:0%
+stability of the amplifier is very
+severely compromised I'd like to look at
+
+ align:start position:0%
+severely compromised I'd like to look at
+ 
+
+ align:start position:0%
+severely compromised I'd like to look at
+that we have the same demonstration
+
+ align:start position:0%
+that we have the same demonstration
+ 
+
+ align:start position:0%
+that we have the same demonstration
+setup that we used last time just a
+
+ align:start position:0%
+setup that we used last time just a
+ 
+
+ align:start position:0%
+setup that we used last time just a
+power supply a signal generator which in
+
+ align:start position:0%
+power supply a signal generator which in
+ 
+
+ align:start position:0%
+power supply a signal generator which in
+this case will be applying a square wave
+
+ align:start position:0%
+this case will be applying a square wave
+ 
+
+ align:start position:0%
+this case will be applying a square wave
+to the amplifier we're testing an
+
+ align:start position:0%
+to the amplifier we're testing an
+ 
+
+ align:start position:0%
+to the amplifier we're testing an
+oscilloscope to look at the output of
+
+ align:start position:0%
+oscilloscope to look at the output of
+ 
+
+ align:start position:0%
+oscilloscope to look at the output of
+the amplifier and this time we're using
+
+ align:start position:0%
+the amplifier and this time we're using
+ 
+
+ align:start position:0%
+the amplifier and this time we're using
+this particular amplifier and have it
+
+ align:start position:0%
+this particular amplifier and have it
+ 
+
+ align:start position:0%
+this particular amplifier and have it
+connected simply as a unity gain
+
+ align:start position:0%
+connected simply as a unity gain
+ 
+
+ align:start position:0%
+connected simply as a unity gain
+follower in other words we apply the
+
+ align:start position:0%
+follower in other words we apply the
+ 
+
+ align:start position:0%
+follower in other words we apply the
+input signal to the non-inverting input
+
+ align:start position:0%
+input signal to the non-inverting input
+ 
+
+ align:start position:0%
+input signal to the non-inverting input
+terminal of the operational amplifier we
+
+ align:start position:0%
+terminal of the operational amplifier we
+ 
+
+ align:start position:0%
+terminal of the operational amplifier we
+take the output and bring it directly
+
+ align:start position:0%
+take the output and bring it directly
+ 
+
+ align:start position:0%
+take the output and bring it directly
+back to the inverting input terminal and
+
+ align:start position:0%
+back to the inverting input terminal and
+ 
+
+ align:start position:0%
+back to the inverting input terminal and
+at present we have the amplifier
+
+ align:start position:0%
+at present we have the amplifier
+ 
+
+ align:start position:0%
+at present we have the amplifier
+compensated for single pole operation
+
+ align:start position:0%
+compensated for single pole operation
+ 
+
+ align:start position:0%
+compensated for single pole operation
+and we see the resultant step response
+
+ align:start position:0%
+and we see the resultant step response
+ 
+
+ align:start position:0%
+and we see the resultant step response
+on the oscilloscope we're using about a
+
+ align:start position:0%
+on the oscilloscope we're using about a
+ 
+
+ align:start position:0%
+on the oscilloscope we're using about a
+twenty Pico farad capacitor with this
+
+ align:start position:0%
+twenty Pico farad capacitor with this
+ 
+
+ align:start position:0%
+twenty Pico farad capacitor with this
+particular amplifier which is the same
+
+ align:start position:0%
+particular amplifier which is the same
+ 
+
+ align:start position:0%
+particular amplifier which is the same
+one we used in the last series of
+
+ align:start position:0%
+one we used in the last series of
+ 
+
+ align:start position:0%
+one we used in the last series of
+demonstrations we get a rise time ten to
+
+ align:start position:0%
+demonstrations we get a rise time ten to
+ 
+
+ align:start position:0%
+demonstrations we get a rise time ten to
+90 percent rise time of about 200
+
+ align:start position:0%
+90 percent rise time of about 200
+ 
+
+ align:start position:0%
+90 percent rise time of about 200
+nanoseconds with that single pole with
+
+ align:start position:0%
+nanoseconds with that single pole with
+ 
+
+ align:start position:0%
+nanoseconds with that single pole with
+that value for single pole compensation
+
+ align:start position:0%
+that value for single pole compensation
+ 
+
+ align:start position:0%
+that value for single pole compensation
+implying with the crossover frequency
+
+ align:start position:0%
+implying with the crossover frequency
+ 
+
+ align:start position:0%
+implying with the crossover frequency
+for this configuration is somewhere in
+
+ align:start position:0%
+for this configuration is somewhere in
+ 
+
+ align:start position:0%
+for this configuration is somewhere in
+the order of two megahertz and this is
+
+ align:start position:0%
+the order of two megahertz and this is
+ 
+
+ align:start position:0%
+the order of two megahertz and this is
+operating without any capacitive load
+
+ align:start position:0%
+operating without any capacitive load
+ 
+
+ align:start position:0%
+operating without any capacitive load
+now let's see what happens when I throw
+
+ align:start position:0%
+now let's see what happens when I throw
+ 
+
+ align:start position:0%
+now let's see what happens when I throw
+this switch and first we'll connect 0.01
+
+ align:start position:0%
+this switch and first we'll connect 0.01
+ 
+
+ align:start position:0%
+this switch and first we'll connect 0.01
+micro farad capacitor to the output of
+
+ align:start position:0%
+micro farad capacitor to the output of
+ 
+
+ align:start position:0%
+micro farad capacitor to the output of
+the amplifier and we notice that in
+
+ align:start position:0%
+the amplifier and we notice that in
+ 
+
+ align:start position:0%
+the amplifier and we notice that in
+addition to the we get a tremendous
+
+ align:start position:0%
+addition to the we get a tremendous
+ 
+
+ align:start position:0%
+addition to the we get a tremendous
+amount of overshoot we get a very much
+
+ align:start position:0%
+amount of overshoot we get a very much
+ 
+
+ align:start position:0%
+amount of overshoot we get a very much
+more poorly damped system than we had
+
+ align:start position:0%
+more poorly damped system than we had
+ 
+
+ align:start position:0%
+more poorly damped system than we had
+before comparing again these two cases
+
+ align:start position:0%
+before comparing again these two cases
+ 
+
+ align:start position:0%
+before comparing again these two cases
+here's no capacitive load here's a no 1
+
+ align:start position:0%
+here's no capacitive load here's a no 1
+ 
+
+ align:start position:0%
+here's no capacitive load here's a no 1
+microfarad capacitive load applied to
+
+ align:start position:0%
+microfarad capacitive load applied to
+ 
+
+ align:start position:0%
+microfarad capacitive load applied to
+the amplifier we get a considerable
+
+ align:start position:0%
+the amplifier we get a considerable
+ 
+
+ align:start position:0%
+the amplifier we get a considerable
+overshoot quite a poorly damped response
+
+ align:start position:0%
+overshoot quite a poorly damped response
+ 
+
+ align:start position:0%
+overshoot quite a poorly damped response
+and the settling time is of course very
+
+ align:start position:0%
+and the settling time is of course very
+ 
+
+ align:start position:0%
+and the settling time is of course very
+very dramatically increased before
+
+ align:start position:0%
+very dramatically increased before
+ 
+
+ align:start position:0%
+very dramatically increased before
+settling time was with several hundred
+
+ align:start position:0%
+settling time was with several hundred
+ 
+
+ align:start position:0%
+settling time was with several hundred
+nano seconds here we see that the
+
+ align:start position:0%
+nano seconds here we see that the
+ 
+
+ align:start position:0%
+nano seconds here we see that the
+amplifier is still ringing at ten
+
+ align:start position:0%
+amplifier is still ringing at ten
+ 
+
+ align:start position:0%
+amplifier is still ringing at ten
+microseconds the horizontal division one
+
+ align:start position:0%
+microseconds the horizontal division one
+ 
+
+ align:start position:0%
+microseconds the horizontal division one
+horizontal division corresponds to two
+
+ align:start position:0%
+horizontal division corresponds to two
+ 
+
+ align:start position:0%
+horizontal division corresponds to two
+microseconds so we see that the
+
+ align:start position:0%
+microseconds so we see that the
+ 
+
+ align:start position:0%
+microseconds so we see that the
+amplifier is ringing for at least ten
+
+ align:start position:0%
+amplifier is ringing for at least ten
+ 
+
+ align:start position:0%
+amplifier is ringing for at least ten
+microseconds we can make matters even
+
+ align:start position:0%
+microseconds we can make matters even
+ 
+
+ align:start position:0%
+microseconds we can make matters even
+worse let me load the amplifier with a
+
+ align:start position:0%
+worse let me load the amplifier with a
+ 
+
+ align:start position:0%
+worse let me load the amplifier with a
+tenth of a micro farad capacitor and we
+
+ align:start position:0%
+tenth of a micro farad capacitor and we
+ 
+
+ align:start position:0%
+tenth of a micro farad capacitor and we
+do that we'll have to slow down the
+
+ align:start position:0%
+do that we'll have to slow down the
+ 
+
+ align:start position:0%
+do that we'll have to slow down the
+signal generator just a bit here again
+
+ align:start position:0%
+signal generator just a bit here again
+ 
+
+ align:start position:0%
+signal generator just a bit here again
+we notice a further deterioration of
+
+ align:start position:0%
+we notice a further deterioration of
+ 
+
+ align:start position:0%
+we notice a further deterioration of
+relative stability considerable
+
+ align:start position:0%
+relative stability considerable
+ 
+
+ align:start position:0%
+relative stability considerable
+overshoot we're now at ten microseconds
+
+ align:start position:0%
+overshoot we're now at ten microseconds
+ 
+
+ align:start position:0%
+overshoot we're now at ten microseconds
+per division and we notice that the
+
+ align:start position:0%
+per division and we notice that the
+ 
+
+ align:start position:0%
+per division and we notice that the
+response still is wiggling a hundred
+
+ align:start position:0%
+response still is wiggling a hundred
+ 
+
+ align:start position:0%
+response still is wiggling a hundred
+microseconds later so the settling time
+
+ align:start position:0%
+microseconds later so the settling time
+ 
+
+ align:start position:0%
+microseconds later so the settling time
+of this amplifier has been deteriorated
+
+ align:start position:0%
+of this amplifier has been deteriorated
+ 
+
+ align:start position:0%
+of this amplifier has been deteriorated
+to more than one hundred microseconds
+
+ align:start position:0%
+to more than one hundred microseconds
+ 
+
+ align:start position:0%
+to more than one hundred microseconds
+with the addition of the tenth micro
+
+ align:start position:0%
+with the addition of the tenth micro
+ 
+
+ align:start position:0%
+with the addition of the tenth micro
+farad load capacitor we can also notice
+
+ align:start position:0%
+farad load capacitor we can also notice
+ 
+
+ align:start position:0%
+farad load capacitor we can also notice
+the ring frequency we're now at at two
+
+ align:start position:0%
+the ring frequency we're now at at two
+ 
+
+ align:start position:0%
+the ring frequency we're now at at two
+microseconds per division so the ring
+
+ align:start position:0%
+microseconds per division so the ring
+ 
+
+ align:start position:0%
+microseconds per division so the ring
+frequency is somewhere in the order of
+
+ align:start position:0%
+frequency is somewhere in the order of
+ 
+
+ align:start position:0%
+frequency is somewhere in the order of
+200 kilohertz for this particular
+
+ align:start position:0%
+200 kilohertz for this particular
+ 
+
+ align:start position:0%
+200 kilohertz for this particular
+amplifier we can explain why that
+
+ align:start position:0%
+amplifier we can explain why that
+ 
+
+ align:start position:0%
+amplifier we can explain why that
+happens let's look at the amplifier
+
+ align:start position:0%
+happens let's look at the amplifier
+ 
+
+ align:start position:0%
+happens let's look at the amplifier
+open-loop transfer function in the
+
+ align:start position:0%
+open-loop transfer function in the
+ 
+
+ align:start position:0%
+open-loop transfer function in the
+absence of a capacitive load here we we
+
+ align:start position:0%
+absence of a capacitive load here we we
+ 
+
+ align:start position:0%
+absence of a capacitive load here we we
+have chosen single pole compensation for
+
+ align:start position:0%
+have chosen single pole compensation for
+ 
+
+ align:start position:0%
+have chosen single pole compensation for
+this particular amplifier with the
+
+ align:start position:0%
+this particular amplifier with the
+ 
+
+ align:start position:0%
+this particular amplifier with the
+twenty Pico farad compensating capacitor
+
+ align:start position:0%
+twenty Pico farad compensating capacitor
+ 
+
+ align:start position:0%
+twenty Pico farad compensating capacitor
+that we're using crossover occurs at
+
+ align:start position:0%
+that we're using crossover occurs at
+ 
+
+ align:start position:0%
+that we're using crossover occurs at
+about two megahertz or 1.2 times 10 to
+
+ align:start position:0%
+about two megahertz or 1.2 times 10 to
+ 
+
+ align:start position:0%
+about two megahertz or 1.2 times 10 to
+the seventh radians per second so this
+
+ align:start position:0%
+the seventh radians per second so this
+ 
+
+ align:start position:0%
+the seventh radians per second so this
+is the open-loop transfer function of
+
+ align:start position:0%
+is the open-loop transfer function of
+ 
+
+ align:start position:0%
+is the open-loop transfer function of
+the amplifier a single pole roll-off
+
+ align:start position:0%
+the amplifier a single pole roll-off
+ 
+
+ align:start position:0%
+the amplifier a single pole roll-off
+over a wide range of frequencies when we
+
+ align:start position:0%
+over a wide range of frequencies when we
+ 
+
+ align:start position:0%
+over a wide range of frequencies when we
+have no capacitive load the output
+
+ align:start position:0%
+have no capacitive load the output
+ 
+
+ align:start position:0%
+have no capacitive load the output
+resistance of the amplifier is somewhere
+
+ align:start position:0%
+resistance of the amplifier is somewhere
+ 
+
+ align:start position:0%
+resistance of the amplifier is somewhere
+on the order of a hundred ohms and
+
+ align:start position:0%
+on the order of a hundred ohms and
+ 
+
+ align:start position:0%
+on the order of a hundred ohms and
+consequently when we load the amplifier
+
+ align:start position:0%
+consequently when we load the amplifier
+ 
+
+ align:start position:0%
+consequently when we load the amplifier
+with a tenth of a micro farad capacitor
+
+ align:start position:0%
+with a tenth of a micro farad capacitor
+ 
+
+ align:start position:0%
+with a tenth of a micro farad capacitor
+we'll put in another poll with a time
+
+ align:start position:0%
+we'll put in another poll with a time
+ 
+
+ align:start position:0%
+we'll put in another poll with a time
+constant of 10 microseconds in other
+
+ align:start position:0%
+constant of 10 microseconds in other
+ 
+
+ align:start position:0%
+constant of 10 microseconds in other
+words we'll add a poll at 10 to the
+
+ align:start position:0%
+words we'll add a poll at 10 to the
+ 
+
+ align:start position:0%
+words we'll add a poll at 10 to the
+fifth radians per second back about in
+
+ align:start position:0%
+fifth radians per second back about in
+ 
+
+ align:start position:0%
+fifth radians per second back about in
+here if we add one additional poll to
+
+ align:start position:0%
+here if we add one additional poll to
+ 
+
+ align:start position:0%
+here if we add one additional poll to
+the open-loop transfer function of the
+
+ align:start position:0%
+the open-loop transfer function of the
+ 
+
+ align:start position:0%
+the open-loop transfer function of the
+amplifier our resultant a of s will be
+
+ align:start position:0%
+amplifier our resultant a of s will be
+ 
+
+ align:start position:0%
+amplifier our resultant a of s will be
+this we notice that the magnitude of the
+
+ align:start position:0%
+this we notice that the magnitude of the
+ 
+
+ align:start position:0%
+this we notice that the magnitude of the
+open-loop gain at the frequency where
+
+ align:start position:0%
+open-loop gain at the frequency where
+ 
+
+ align:start position:0%
+open-loop gain at the frequency where
+the pole is located is about 120 it's
+
+ align:start position:0%
+the pole is located is about 120 it's
+ 
+
+ align:start position:0%
+the pole is located is about 120 it's
+back a factor of 120 from the unity gain
+
+ align:start position:0%
+back a factor of 120 from the unity gain
+ 
+
+ align:start position:0%
+back a factor of 120 from the unity gain
+frequency that results with sing it with
+
+ align:start position:0%
+frequency that results with sing it with
+ 
+
+ align:start position:0%
+frequency that results with sing it with
+a single pole roll-off we cross over at
+
+ align:start position:0%
+a single pole roll-off we cross over at
+ 
+
+ align:start position:0%
+a single pole roll-off we cross over at
+the geometric mean between this
+
+ align:start position:0%
+the geometric mean between this
+ 
+
+ align:start position:0%
+the geometric mean between this
+frequency and the original frequency
+
+ align:start position:0%
+frequency and the original frequency
+ 
+
+ align:start position:0%
+frequency and the original frequency
+since where the original crossover
+
+ align:start position:0%
+since where the original crossover
+ 
+
+ align:start position:0%
+since where the original crossover
+frequency since we're falling off as 1
+
+ align:start position:0%
+frequency since we're falling off as 1
+ 
+
+ align:start position:0%
+frequency since we're falling off as 1
+over s squared and so we cross over
+
+ align:start position:0%
+over s squared and so we cross over
+ 
+
+ align:start position:0%
+over s squared and so we cross over
+somewhere on the order of 10 to the 6th
+
+ align:start position:0%
+somewhere on the order of 10 to the 6th
+ 
+
+ align:start position:0%
+somewhere on the order of 10 to the 6th
+radians per second or maybe a little bit
+
+ align:start position:0%
+radians per second or maybe a little bit
+ 
+
+ align:start position:0%
+radians per second or maybe a little bit
+higher than that and that corresponds to
+
+ align:start position:0%
+higher than that and that corresponds to
+ 
+
+ align:start position:0%
+higher than that and that corresponds to
+the roughly 200 kilohertz ring frequency
+
+ align:start position:0%
+the roughly 200 kilohertz ring frequency
+ 
+
+ align:start position:0%
+the roughly 200 kilohertz ring frequency
+that we saw on the oscilloscope trace
+
+ align:start position:0%
+that we saw on the oscilloscope trace
+ 
+
+ align:start position:0%
+that we saw on the oscilloscope trace
+furthermore notice that we cross over
+
+ align:start position:0%
+furthermore notice that we cross over
+ 
+
+ align:start position:0%
+furthermore notice that we cross over
+after we've been rolling off as 1 over s
+
+ align:start position:0%
+after we've been rolling off as 1 over s
+ 
+
+ align:start position:0%
+after we've been rolling off as 1 over s
+squared for about a factor of 10 from
+
+ align:start position:0%
+squared for about a factor of 10 from
+ 
+
+ align:start position:0%
+squared for about a factor of 10 from
+this frequency to this one there's been
+
+ align:start position:0%
+this frequency to this one there's been
+ 
+
+ align:start position:0%
+this frequency to this one there's been
+a long one over s squared region and if
+
+ align:start position:0%
+a long one over s squared region and if
+ 
+
+ align:start position:0%
+a long one over s squared region and if
+you consider the implications of that
+
+ align:start position:0%
+you consider the implications of that
+ 
+
+ align:start position:0%
+you consider the implications of that
+why we would anticipate a phase margin
+
+ align:start position:0%
+why we would anticipate a phase margin
+ 
+
+ align:start position:0%
+why we would anticipate a phase margin
+of somewhere in the order of a tenth of
+
+ align:start position:0%
+of somewhere in the order of a tenth of
+ 
+
+ align:start position:0%
+of somewhere in the order of a tenth of
+a Radian roughly 5 degrees because we're
+
+ align:start position:0%
+a Radian roughly 5 degrees because we're
+ 
+
+ align:start position:0%
+a Radian roughly 5 degrees because we're
+crossing over a factor of 10 beyond the
+
+ align:start position:0%
+crossing over a factor of 10 beyond the
+ 
+
+ align:start position:0%
+crossing over a factor of 10 beyond the
+second pole we'd certainly expect that
+
+ align:start position:0%
+second pole we'd certainly expect that
+ 
+
+ align:start position:0%
+second pole we'd certainly expect that
+that sort of phase margin would result
+
+ align:start position:0%
+that sort of phase margin would result
+ 
+
+ align:start position:0%
+that sort of phase margin would result
+in very marginally stable performance
+
+ align:start position:0%
+in very marginally stable performance
+ 
+
+ align:start position:0%
+in very marginally stable performance
+and that's what we see in the step
+
+ align:start position:0%
+and that's what we see in the step
+ 
+
+ align:start position:0%
+and that's what we see in the step
+response
+
+ align:start position:0%
+response
+ 
+
+ align:start position:0%
+response
+well how might we improve the situation
+
+ align:start position:0%
+well how might we improve the situation
+ 
+
+ align:start position:0%
+well how might we improve the situation
+the thing to do is to attempt to make
+
+ align:start position:0%
+the thing to do is to attempt to make
+ 
+
+ align:start position:0%
+the thing to do is to attempt to make
+the open-loop transfer function of the
+
+ align:start position:0%
+the open-loop transfer function of the
+ 
+
+ align:start position:0%
+the open-loop transfer function of the
+amplifier in the absence of load include
+
+ align:start position:0%
+amplifier in the absence of load include
+ 
+
+ align:start position:0%
+amplifier in the absence of load include
+a 0 in other words start out with an
+
+ align:start position:0%
+a 0 in other words start out with an
+ 
+
+ align:start position:0%
+a 0 in other words start out with an
+open-loop transfer function that rolls
+
+ align:start position:0%
+open-loop transfer function that rolls
+ 
+
+ align:start position:0%
+open-loop transfer function that rolls
+off is 1 over s at low frequencies but
+
+ align:start position:0%
+off is 1 over s at low frequencies but
+ 
+
+ align:start position:0%
+off is 1 over s at low frequencies but
+then at some higher frequency flattens
+
+ align:start position:0%
+then at some higher frequency flattens
+ 
+
+ align:start position:0%
+then at some higher frequency flattens
+out if we can do that if we can add a 0
+
+ align:start position:0%
+out if we can do that if we can add a 0
+ 
+
+ align:start position:0%
+out if we can do that if we can add a 0
+we presumably could use that 0 to
+
+ align:start position:0%
+we presumably could use that 0 to
+ 
+
+ align:start position:0%
+we presumably could use that 0 to
+somehow
+
+ align:start position:0%
+somehow
+ 
+
+ align:start position:0%
+somehow
+offset the effects of the pole that we
+
+ align:start position:0%
+offset the effects of the pole that we
+ 
+
+ align:start position:0%
+offset the effects of the pole that we
+get when we add capacitive loading we
+
+ align:start position:0%
+get when we add capacitive loading we
+ 
+
+ align:start position:0%
+get when we add capacitive loading we
+might for example attempt to line up the
+
+ align:start position:0%
+might for example attempt to line up the
+ 
+
+ align:start position:0%
+might for example attempt to line up the
+zero in the unloaded open-loop transfer
+
+ align:start position:0%
+zero in the unloaded open-loop transfer
+ 
+
+ align:start position:0%
+zero in the unloaded open-loop transfer
+function with the pole actually we find
+
+ align:start position:0%
+function with the pole actually we find
+ 
+
+ align:start position:0%
+function with the pole actually we find
+out that there may be a little better
+
+ align:start position:0%
+out that there may be a little better
+ 
+
+ align:start position:0%
+out that there may be a little better
+thing to do than that but but
+
+ align:start position:0%
+thing to do than that but but
+ 
+
+ align:start position:0%
+thing to do than that but but
+effectively what we can do is use this
+
+ align:start position:0%
+effectively what we can do is use this
+ 
+
+ align:start position:0%
+effectively what we can do is use this
+zero in an attempt to offset the effect
+
+ align:start position:0%
+zero in an attempt to offset the effect
+ 
+
+ align:start position:0%
+zero in an attempt to offset the effect
+of the pole that results from capacitive
+
+ align:start position:0%
+of the pole that results from capacitive
+ 
+
+ align:start position:0%
+of the pole that results from capacitive
+loading if we can choose compensating
+
+ align:start position:0%
+loading if we can choose compensating
+ 
+
+ align:start position:0%
+loading if we can choose compensating
+admittance or a compensating network to
+
+ align:start position:0%
+admittance or a compensating network to
+ 
+
+ align:start position:0%
+admittance or a compensating network to
+give us this sort of ideal open-loop
+
+ align:start position:0%
+give us this sort of ideal open-loop
+ 
+
+ align:start position:0%
+give us this sort of ideal open-loop
+transfer function we can look at the
+
+ align:start position:0%
+transfer function we can look at the
+ 
+
+ align:start position:0%
+transfer function we can look at the
+result in a little bit more detail here
+
+ align:start position:0%
+result in a little bit more detail here
+ 
+
+ align:start position:0%
+result in a little bit more detail here
+here again we have the assumed
+
+ align:start position:0%
+here again we have the assumed
+ 
+
+ align:start position:0%
+here again we have the assumed
+uncompensated transfer function of the
+
+ align:start position:0%
+uncompensated transfer function of the
+ 
+
+ align:start position:0%
+uncompensated transfer function of the
+amplifier we have the approximation the
+
+ align:start position:0%
+amplifier we have the approximation the
+ 
+
+ align:start position:0%
+amplifier we have the approximation the
+ideal open-loop transfer function that's
+
+ align:start position:0%
+ideal open-loop transfer function that's
+ 
+
+ align:start position:0%
+ideal open-loop transfer function that's
+simply related to the transconductance
+
+ align:start position:0%
+simply related to the transconductance
+ 
+
+ align:start position:0%
+simply related to the transconductance
+of the first stage and the compensating
+
+ align:start position:0%
+of the first stage and the compensating
+ 
+
+ align:start position:0%
+of the first stage and the compensating
+admittance or the short-circuit transfer
+
+ align:start position:0%
+admittance or the short-circuit transfer
+ 
+
+ align:start position:0%
+admittance or the short-circuit transfer
+admittance of the compensating Network
+
+ align:start position:0%
+admittance of the compensating Network
+ 
+
+ align:start position:0%
+admittance of the compensating Network
+that approximation where we'd like to
+
+ align:start position:0%
+that approximation where we'd like to
+ 
+
+ align:start position:0%
+that approximation where we'd like to
+have have a 1 over s roll-off at low
+
+ align:start position:0%
+have have a 1 over s roll-off at low
+ 
+
+ align:start position:0%
+have have a 1 over s roll-off at low
+frequencies and then flattened out at
+
+ align:start position:0%
+frequencies and then flattened out at
+ 
+
+ align:start position:0%
+frequencies and then flattened out at
+higher frequencies the intersection of
+
+ align:start position:0%
+higher frequencies the intersection of
+ 
+
+ align:start position:0%
+higher frequencies the intersection of
+that with the uncompensated curve
+
+ align:start position:0%
+that with the uncompensated curve
+ 
+
+ align:start position:0%
+that with the uncompensated curve
+choosing the lower of the curves at all
+
+ align:start position:0%
+choosing the lower of the curves at all
+ 
+
+ align:start position:0%
+choosing the lower of the curves at all
+frequencies gives us a good estimation
+
+ align:start position:0%
+frequencies gives us a good estimation
+ 
+
+ align:start position:0%
+frequencies gives us a good estimation
+of the actual open-loop gain of the
+
+ align:start position:0%
+of the actual open-loop gain of the
+ 
+
+ align:start position:0%
+of the actual open-loop gain of the
+amplifier and so between possibly this
+
+ align:start position:0%
+amplifier and so between possibly this
+ 
+
+ align:start position:0%
+amplifier and so between possibly this
+frequency and this frequency we find out
+
+ align:start position:0%
+frequency and this frequency we find out
+ 
+
+ align:start position:0%
+frequency and this frequency we find out
+that we are able to control the transfer
+
+ align:start position:0%
+that we are able to control the transfer
+ 
+
+ align:start position:0%
+that we are able to control the transfer
+function of the amplifier by the
+
+ align:start position:0%
+function of the amplifier by the
+ 
+
+ align:start position:0%
+function of the amplifier by the
+compensating Network we get the single
+
+ align:start position:0%
+compensating Network we get the single
+ 
+
+ align:start position:0%
+compensating Network we get the single
+pole roll-off at low frequencies the
+
+ align:start position:0%
+pole roll-off at low frequencies the
+ 
+
+ align:start position:0%
+pole roll-off at low frequencies the
+zero that we hope to use to compensate
+
+ align:start position:0%
+zero that we hope to use to compensate
+ 
+
+ align:start position:0%
+zero that we hope to use to compensate
+the pole resulting from capacitive
+
+ align:start position:0%
+the pole resulting from capacitive
+ 
+
+ align:start position:0%
+the pole resulting from capacitive
+loading again we see the effect on on
+
+ align:start position:0%
+loading again we see the effect on on
+ 
+
+ align:start position:0%
+loading again we see the effect on on
+phase the uncompensated phase of course
+
+ align:start position:0%
+phase the uncompensated phase of course
+ 
+
+ align:start position:0%
+phase the uncompensated phase of course
+rolling off are the approximation
+
+ align:start position:0%
+rolling off are the approximation
+ 
+
+ align:start position:0%
+rolling off are the approximation
+indicating we'd have minus 90 degrees a
+
+ align:start position:0%
+indicating we'd have minus 90 degrees a
+ 
+
+ align:start position:0%
+indicating we'd have minus 90 degrees a
+phase shift at low frequencies
+
+ align:start position:0%
+phase shift at low frequencies
+ 
+
+ align:start position:0%
+phase shift at low frequencies
+corresponding to the 1 over s roll-off
+
+ align:start position:0%
+corresponding to the 1 over s roll-off
+ 
+
+ align:start position:0%
+corresponding to the 1 over s roll-off
+and increasing actually to 0 degrees in
+
+ align:start position:0%
+and increasing actually to 0 degrees in
+ 
+
+ align:start position:0%
+and increasing actually to 0 degrees in
+reality we don't achieve that but we get
+
+ align:start position:0%
+reality we don't achieve that but we get
+ 
+
+ align:start position:0%
+reality we don't achieve that but we get
+a an actual compensated phase curve that
+
+ align:start position:0%
+a an actual compensated phase curve that
+ 
+
+ align:start position:0%
+a an actual compensated phase curve that
+looks something like Slyke so at very
+
+ align:start position:0%
+looks something like Slyke so at very
+ 
+
+ align:start position:0%
+looks something like Slyke so at very
+low frequencies at 0 it then dips down
+
+ align:start position:0%
+low frequencies at 0 it then dips down
+ 
+
+ align:start position:0%
+low frequencies at 0 it then dips down
+close to minus 90
+
+ align:start position:0%
+close to minus 90
+ 
+
+ align:start position:0%
+close to minus 90
+agrees over a wide range of frequencies
+
+ align:start position:0%
+agrees over a wide range of frequencies
+ 
+
+ align:start position:0%
+agrees over a wide range of frequencies
+heads back more positive in the vicinity
+
+ align:start position:0%
+heads back more positive in the vicinity
+ 
+
+ align:start position:0%
+heads back more positive in the vicinity
+of the zero and eventually falls off
+
+ align:start position:0%
+of the zero and eventually falls off
+ 
+
+ align:start position:0%
+of the zero and eventually falls off
+again at higher frequencies so this then
+
+ align:start position:0%
+again at higher frequencies so this then
+ 
+
+ align:start position:0%
+again at higher frequencies so this then
+is the kind of an open-loop transfer
+
+ align:start position:0%
+is the kind of an open-loop transfer
+ 
+
+ align:start position:0%
+is the kind of an open-loop transfer
+function we'd expect from the amplifier
+
+ align:start position:0%
+function we'd expect from the amplifier
+ 
+
+ align:start position:0%
+function we'd expect from the amplifier
+if we could select a compensating or a
+
+ align:start position:0%
+if we could select a compensating or a
+ 
+
+ align:start position:0%
+if we could select a compensating or a
+compensating network that had a
+
+ align:start position:0%
+compensating network that had a
+ 
+
+ align:start position:0%
+compensating network that had a
+short-circuit transfer admittance such
+
+ align:start position:0%
+short-circuit transfer admittance such
+ 
+
+ align:start position:0%
+short-circuit transfer admittance such
+the G sub M over to YC had this form how
+
+ align:start position:0%
+the G sub M over to YC had this form how
+ 
+
+ align:start position:0%
+the G sub M over to YC had this form how
+do we accomplish that well let's see
+
+ align:start position:0%
+do we accomplish that well let's see
+ 
+
+ align:start position:0%
+do we accomplish that well let's see
+we'd like to have G M over to YC of s
+
+ align:start position:0%
+we'd like to have G M over to YC of s
+ 
+
+ align:start position:0%
+we'd like to have G M over to YC of s
+have the general form K over s times a0
+
+ align:start position:0%
+have the general form K over s times a0
+ 
+
+ align:start position:0%
+have the general form K over s times a0
+we can do that without even resorting to
+
+ align:start position:0%
+we can do that without even resorting to
+ 
+
+ align:start position:0%
+we can do that without even resorting to
+a true two-port we can do it is simply a
+
+ align:start position:0%
+a true two-port we can do it is simply a
+ 
+
+ align:start position:0%
+a true two-port we can do it is simply a
+series combination of a resistor and a
+
+ align:start position:0%
+series combination of a resistor and a
+ 
+
+ align:start position:0%
+series combination of a resistor and a
+capacitor if we look at the simple RC
+
+ align:start position:0%
+capacitor if we look at the simple RC
+ 
+
+ align:start position:0%
+capacitor if we look at the simple RC
+connection and write its admittance we
+
+ align:start position:0%
+connection and write its admittance we
+ 
+
+ align:start position:0%
+connection and write its admittance we
+find that the admittance of that network
+
+ align:start position:0%
+find that the admittance of that network
+ 
+
+ align:start position:0%
+find that the admittance of that network
+is simply CS over RCS plus 1
+
+ align:start position:0%
+is simply CS over RCS plus 1
+ 
+
+ align:start position:0%
+is simply CS over RCS plus 1
+consequently G sub M over 2 YC has the
+
+ align:start position:0%
+consequently G sub M over 2 YC has the
+ 
+
+ align:start position:0%
+consequently G sub M over 2 YC has the
+general form that we'd like and what we
+
+ align:start position:0%
+general form that we'd like and what we
+ 
+
+ align:start position:0%
+general form that we'd like and what we
+might do then is for example choose a 0
+
+ align:start position:0%
+might do then is for example choose a 0
+ 
+
+ align:start position:0%
+might do then is for example choose a 0
+location as I've shown it somewhere out
+
+ align:start position:0%
+location as I've shown it somewhere out
+ 
+
+ align:start position:0%
+location as I've shown it somewhere out
+in here if we did that we'd use that
+
+ align:start position:0%
+in here if we did that we'd use that
+ 
+
+ align:start position:0%
+in here if we did that we'd use that
+zero from the compensated amplifier
+
+ align:start position:0%
+zero from the compensated amplifier
+ 
+
+ align:start position:0%
+zero from the compensated amplifier
+open-loop transfer function in the
+
+ align:start position:0%
+open-loop transfer function in the
+ 
+
+ align:start position:0%
+open-loop transfer function in the
+absence of load we use that zero to
+
+ align:start position:0%
+absence of load we use that zero to
+ 
+
+ align:start position:0%
+absence of load we use that zero to
+offset the effects of the pole that
+
+ align:start position:0%
+offset the effects of the pole that
+ 
+
+ align:start position:0%
+offset the effects of the pole that
+resulted from capacitive loading as a
+
+ align:start position:0%
+resulted from capacitive loading as a
+ 
+
+ align:start position:0%
+resulted from capacitive loading as a
+result R over overall loop transmission
+
+ align:start position:0%
+result R over overall loop transmission
+ 
+
+ align:start position:0%
+result R over overall loop transmission
+or the negative of the loop transmission
+
+ align:start position:0%
+or the negative of the loop transmission
+ 
+
+ align:start position:0%
+or the negative of the loop transmission
+might look something like that the hope
+
+ align:start position:0%
+might look something like that the hope
+ 
+
+ align:start position:0%
+might look something like that the hope
+is that of course we greatly improve the
+
+ align:start position:0%
+is that of course we greatly improve the
+ 
+
+ align:start position:0%
+is that of course we greatly improve the
+phase margin by virtue of having added
+
+ align:start position:0%
+phase margin by virtue of having added
+ 
+
+ align:start position:0%
+phase margin by virtue of having added
+this zero to the loop transmission let's
+
+ align:start position:0%
+this zero to the loop transmission let's
+ 
+
+ align:start position:0%
+this zero to the loop transmission let's
+see how that works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here again we have the amplifier as we
+
+ align:start position:0%
+here again we have the amplifier as we
+ 
+
+ align:start position:0%
+here again we have the amplifier as we
+left it with the tenth micro farad
+
+ align:start position:0%
+left it with the tenth micro farad
+ 
+
+ align:start position:0%
+left it with the tenth micro farad
+capacitor load and considerable ringing
+
+ align:start position:0%
+capacitor load and considerable ringing
+ 
+
+ align:start position:0%
+capacitor load and considerable ringing
+and what I'm going to do is add a
+
+ align:start position:0%
+and what I'm going to do is add a
+ 
+
+ align:start position:0%
+and what I'm going to do is add a
+network that consists of a series
+
+ align:start position:0%
+network that consists of a series
+ 
+
+ align:start position:0%
+network that consists of a series
+connection of a resistor and a capacitor
+
+ align:start position:0%
+connection of a resistor and a capacitor
+ 
+
+ align:start position:0%
+connection of a resistor and a capacitor
+actually there's a third little
+
+ align:start position:0%
+actually there's a third little
+ 
+
+ align:start position:0%
+actually there's a third little
+capacitor here and I'll apologize for
+
+ align:start position:0%
+capacitor here and I'll apologize for
+ 
+
+ align:start position:0%
+capacitor here and I'll apologize for
+that we'll see in a moment why we want
+
+ align:start position:0%
+that we'll see in a moment why we want
+ 
+
+ align:start position:0%
+that we'll see in a moment why we want
+to have that that third element to the
+
+ align:start position:0%
+to have that that third element to the
+ 
+
+ align:start position:0%
+to have that that third element to the
+the second capacitor woman we'll see
+
+ align:start position:0%
+the second capacitor woman we'll see
+ 
+
+ align:start position:0%
+the second capacitor woman we'll see
+what we do with that in a moment but
+
+ align:start position:0%
+what we do with that in a moment but
+ 
+
+ align:start position:0%
+what we do with that in a moment but
+starting out we simply have the series
+
+ align:start position:0%
+starting out we simply have the series
+ 
+
+ align:start position:0%
+starting out we simply have the series
+resistor capacitor combination that I
+
+ align:start position:0%
+resistor capacitor combination that I
+ 
+
+ align:start position:0%
+resistor capacitor combination that I
+mentioned and what I'd like to do is
+
+ align:start position:0%
+mentioned and what I'd like to do is
+ 
+
+ align:start position:0%
+mentioned and what I'd like to do is
+look back at the oscilloscope trace and
+
+ align:start position:0%
+look back at the oscilloscope trace and
+ 
+
+ align:start position:0%
+look back at the oscilloscope trace and
+recall that the settling time with one
+
+ align:start position:0%
+recall that the settling time with one
+ 
+
+ align:start position:0%
+recall that the settling time with one
+over s compensation is about or is in
+
+ align:start position:0%
+over s compensation is about or is in
+ 
+
+ align:start position:0%
+over s compensation is about or is in
+excess of 100 microseconds and now let's
+
+ align:start position:0%
+excess of 100 microseconds and now let's
+ 
+
+ align:start position:0%
+excess of 100 microseconds and now let's
+go to the compensation that includes a
+
+ align:start position:0%
+go to the compensation that includes a
+ 
+
+ align:start position:0%
+go to the compensation that includes a
+zero I'll remove the single capacitor
+
+ align:start position:0%
+zero I'll remove the single capacitor
+ 
+
+ align:start position:0%
+zero I'll remove the single capacitor
+that was doing the compensation before
+
+ align:start position:0%
+that was doing the compensation before
+ 
+
+ align:start position:0%
+that was doing the compensation before
+and I'll put in the series RC connection
+
+ align:start position:0%
+and I'll put in the series RC connection
+ 
+
+ align:start position:0%
+and I'll put in the series RC connection
+and when we do that we notice a very
+
+ align:start position:0%
+and when we do that we notice a very
+ 
+
+ align:start position:0%
+and when we do that we notice a very
+dramatic improvement in performance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're now able to go to a much faster
+
+ align:start position:0%
+we're now able to go to a much faster
+ 
+
+ align:start position:0%
+we're now able to go to a much faster
+time scale and we notice for example
+
+ align:start position:0%
+time scale and we notice for example
+ 
+
+ align:start position:0%
+time scale and we notice for example
+that the trace has certainly virtually
+
+ align:start position:0%
+that the trace has certainly virtually
+ 
+
+ align:start position:0%
+that the trace has certainly virtually
+completely settled three or four
+
+ align:start position:0%
+completely settled three or four
+ 
+
+ align:start position:0%
+completely settled three or four
+divisions after the start of the
+
+ align:start position:0%
+divisions after the start of the
+ 
+
+ align:start position:0%
+divisions after the start of the
+transient we're two microseconds per
+
+ align:start position:0%
+transient we're two microseconds per
+ 
+
+ align:start position:0%
+transient we're two microseconds per
+division this time and consequently
+
+ align:start position:0%
+division this time and consequently
+ 
+
+ align:start position:0%
+division this time and consequently
+we're settling in in somewhere on the
+
+ align:start position:0%
+we're settling in in somewhere on the
+ 
+
+ align:start position:0%
+we're settling in in somewhere on the
+order of six to eight microseconds the
+
+ align:start position:0%
+order of six to eight microseconds the
+ 
+
+ align:start position:0%
+order of six to eight microseconds the
+basic transient is a very good one a
+
+ align:start position:0%
+basic transient is a very good one a
+ 
+
+ align:start position:0%
+basic transient is a very good one a
+very pleasant one the overshoot is oh I
+
+ align:start position:0%
+very pleasant one the overshoot is oh I
+ 
+
+ align:start position:0%
+very pleasant one the overshoot is oh I
+don't know 20 percent possibly of the
+
+ align:start position:0%
+don't know 20 percent possibly of the
+ 
+
+ align:start position:0%
+don't know 20 percent possibly of the
+amplitude of the step or something like
+
+ align:start position:0%
+amplitude of the step or something like
+ 
+
+ align:start position:0%
+amplitude of the step or something like
+that so we've very dramatically improved
+
+ align:start position:0%
+that so we've very dramatically improved
+ 
+
+ align:start position:0%
+that so we've very dramatically improved
+the phase margin of the system is
+
+ align:start position:0%
+the phase margin of the system is
+ 
+
+ align:start position:0%
+the phase margin of the system is
+evidenced at least by its step response
+
+ align:start position:0%
+evidenced at least by its step response
+ 
+
+ align:start position:0%
+evidenced at least by its step response
+but there's one bad thing remaining we
+
+ align:start position:0%
+but there's one bad thing remaining we
+ 
+
+ align:start position:0%
+but there's one bad thing remaining we
+notice that there's a series of little
+
+ align:start position:0%
+notice that there's a series of little
+ 
+
+ align:start position:0%
+notice that there's a series of little
+teeth on the trailing edge of the
+
+ align:start position:0%
+teeth on the trailing edge of the
+ 
+
+ align:start position:0%
+teeth on the trailing edge of the
+transient actually they exist on the
+
+ align:start position:0%
+transient actually they exist on the
+ 
+
+ align:start position:0%
+transient actually they exist on the
+leading edge too if you look at it
+
+ align:start position:0%
+leading edge too if you look at it
+ 
+
+ align:start position:0%
+leading edge too if you look at it
+carefully and so the the transient
+
+ align:start position:0%
+carefully and so the the transient
+ 
+
+ align:start position:0%
+carefully and so the the transient
+response of this setup or this
+
+ align:start position:0%
+response of this setup or this
+ 
+
+ align:start position:0%
+response of this setup or this
+configuration is almost
+
+ align:start position:0%
+configuration is almost
+ 
+
+ align:start position:0%
+configuration is almost
+right just doesn't quite make it and I'd
+
+ align:start position:0%
+right just doesn't quite make it and I'd
+ 
+
+ align:start position:0%
+right just doesn't quite make it and I'd
+like to think a little bit about why we
+
+ align:start position:0%
+like to think a little bit about why we
+ 
+
+ align:start position:0%
+like to think a little bit about why we
+might have that problem why do we get
+
+ align:start position:0%
+might have that problem why do we get
+ 
+
+ align:start position:0%
+might have that problem why do we get
+the teeth in this kind of compensation
+
+ align:start position:0%
+the teeth in this kind of compensation
+ 
+
+ align:start position:0%
+the teeth in this kind of compensation
+well what we're doing is using a network
+
+ align:start position:0%
+well what we're doing is using a network
+ 
+
+ align:start position:0%
+well what we're doing is using a network
+of the general type shown of course and
+
+ align:start position:0%
+of the general type shown of course and
+ 
+
+ align:start position:0%
+of the general type shown of course and
+the important part of this network is
+
+ align:start position:0%
+the important part of this network is
+ 
+
+ align:start position:0%
+the important part of this network is
+that at high frequencies or at least as
+
+ align:start position:0%
+that at high frequencies or at least as
+ 
+
+ align:start position:0%
+that at high frequencies or at least as
+far as the teeth are concerned at high
+
+ align:start position:0%
+far as the teeth are concerned at high
+ 
+
+ align:start position:0%
+far as the teeth are concerned at high
+frequencies this network looks resistive
+
+ align:start position:0%
+frequencies this network looks resistive
+ 
+
+ align:start position:0%
+frequencies this network looks resistive
+in contrast to either of the two other
+
+ align:start position:0%
+in contrast to either of the two other
+ 
+
+ align:start position:0%
+in contrast to either of the two other
+kinds of compensating networks we've
+
+ align:start position:0%
+kinds of compensating networks we've
+ 
+
+ align:start position:0%
+kinds of compensating networks we've
+looked at either the single capacitor or
+
+ align:start position:0%
+looked at either the single capacitor or
+ 
+
+ align:start position:0%
+looked at either the single capacitor or
+the t network that had two capacitors
+
+ align:start position:0%
+the t network that had two capacitors
+ 
+
+ align:start position:0%
+the t network that had two capacitors
+across the top of the T both of those
+
+ align:start position:0%
+across the top of the T both of those
+ 
+
+ align:start position:0%
+across the top of the T both of those
+networks look capacitive at high
+
+ align:start position:0%
+networks look capacitive at high
+ 
+
+ align:start position:0%
+networks look capacitive at high
+frequencies this one looks resistive
+
+ align:start position:0%
+frequencies this one looks resistive
+ 
+
+ align:start position:0%
+frequencies this one looks resistive
+between the terminals in other words
+
+ align:start position:0%
+between the terminals in other words
+ 
+
+ align:start position:0%
+between the terminals in other words
+when we use this for compensation around
+
+ align:start position:0%
+when we use this for compensation around
+ 
+
+ align:start position:0%
+when we use this for compensation around
+the second stage that local feedback
+
+ align:start position:0%
+the second stage that local feedback
+ 
+
+ align:start position:0%
+the second stage that local feedback
+path the minor loop feedback path looks
+
+ align:start position:0%
+path the minor loop feedback path looks
+ 
+
+ align:start position:0%
+path the minor loop feedback path looks
+resistive at high frequencies let's see
+
+ align:start position:0%
+resistive at high frequencies let's see
+ 
+
+ align:start position:0%
+resistive at high frequencies let's see
+what that does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I've showed a simplified model for
+
+ align:start position:0%
+here I've showed a simplified model for
+ 
+
+ align:start position:0%
+here I've showed a simplified model for
+the second stage of our operational
+
+ align:start position:0%
+the second stage of our operational
+ 
+
+ align:start position:0%
+the second stage of our operational
+amplifier the input of the second stage
+
+ align:start position:0%
+amplifier the input of the second stage
+ 
+
+ align:start position:0%
+amplifier the input of the second stage
+which if you recall is driven by a
+
+ align:start position:0%
+which if you recall is driven by a
+ 
+
+ align:start position:0%
+which if you recall is driven by a
+differential first stage in the
+
+ align:start position:0%
+differential first stage in the
+ 
+
+ align:start position:0%
+differential first stage in the
+operational amplifier generally looks
+
+ align:start position:0%
+operational amplifier generally looks
+ 
+
+ align:start position:0%
+operational amplifier generally looks
+like a parallel combination of an input
+
+ align:start position:0%
+like a parallel combination of an input
+ 
+
+ align:start position:0%
+like a parallel combination of an input
+resistance and an input capacitance and
+
+ align:start position:0%
+resistance and an input capacitance and
+ 
+
+ align:start position:0%
+resistance and an input capacitance and
+then we have a generator that gives us
+
+ align:start position:0%
+then we have a generator that gives us
+ 
+
+ align:start position:0%
+then we have a generator that gives us
+an output voltage from the second stage
+
+ align:start position:0%
+an output voltage from the second stage
+ 
+
+ align:start position:0%
+an output voltage from the second stage
+proportional to the voltage at the input
+
+ align:start position:0%
+proportional to the voltage at the input
+ 
+
+ align:start position:0%
+proportional to the voltage at the input
+to the second stage but there's also
+
+ align:start position:0%
+to the second stage but there's also
+ 
+
+ align:start position:0%
+to the second stage but there's also
+typically a single pole associated with
+
+ align:start position:0%
+typically a single pole associated with
+ 
+
+ align:start position:0%
+typically a single pole associated with
+that transfer function
+
+ align:start position:0%
+that transfer function
+ 
+
+ align:start position:0%
+that transfer function
+the physical reason for this pole is
+
+ align:start position:0%
+the physical reason for this pole is
+ 
+
+ align:start position:0%
+the physical reason for this pole is
+normally capacitive loading or at least
+
+ align:start position:0%
+normally capacitive loading or at least
+ 
+
+ align:start position:0%
+normally capacitive loading or at least
+one possibility is capacitive loading at
+
+ align:start position:0%
+one possibility is capacitive loading at
+ 
+
+ align:start position:0%
+one possibility is capacitive loading at
+the output of the second stage itself
+
+ align:start position:0%
+the output of the second stage itself
+ 
+
+ align:start position:0%
+the output of the second stage itself
+not at the output of the overall
+
+ align:start position:0%
+not at the output of the overall
+ 
+
+ align:start position:0%
+not at the output of the overall
+operational amplifier but rather at the
+
+ align:start position:0%
+operational amplifier but rather at the
+ 
+
+ align:start position:0%
+operational amplifier but rather at the
+output of the second stage itself and so
+
+ align:start position:0%
+output of the second stage itself and so
+ 
+
+ align:start position:0%
+output of the second stage itself and so
+that gives us a pole and now we put a
+
+ align:start position:0%
+that gives us a pole and now we put a
+ 
+
+ align:start position:0%
+that gives us a pole and now we put a
+minor loop from the output of the second
+
+ align:start position:0%
+minor loop from the output of the second
+ 
+
+ align:start position:0%
+minor loop from the output of the second
+stage back to its input well if at
+
+ align:start position:0%
+stage back to its input well if at
+ 
+
+ align:start position:0%
+stage back to its input well if at
+crossover in the minor loop this network
+
+ align:start position:0%
+crossover in the minor loop this network
+ 
+
+ align:start position:0%
+crossover in the minor loop this network
+looks principally capacitive from here
+
+ align:start position:0%
+looks principally capacitive from here
+ 
+
+ align:start position:0%
+looks principally capacitive from here
+to here in other words if it looks like
+
+ align:start position:0%
+to here in other words if it looks like
+ 
+
+ align:start position:0%
+to here in other words if it looks like
+a single capacitor or if it looks like a
+
+ align:start position:0%
+a single capacitor or if it looks like a
+ 
+
+ align:start position:0%
+a single capacitor or if it looks like a
+tea that has two capacitors across the
+
+ align:start position:0%
+tea that has two capacitors across the
+ 
+
+ align:start position:0%
+tea that has two capacitors across the
+top and a single resistor down on the
+
+ align:start position:0%
+top and a single resistor down on the
+ 
+
+ align:start position:0%
+top and a single resistor down on the
+the vertical portion of the tea then at
+
+ align:start position:0%
+the vertical portion of the tea then at
+ 
+
+ align:start position:0%
+the vertical portion of the tea then at
+high frequencies we get simply an
+
+ align:start position:0%
+high frequencies we get simply an
+ 
+
+ align:start position:0%
+high frequencies we get simply an
+attenuation between this voltage and
+
+ align:start position:0%
+attenuation between this voltage and
+ 
+
+ align:start position:0%
+attenuation between this voltage and
+this one we basically have a capacitive
+
+ align:start position:0%
+this one we basically have a capacitive
+ 
+
+ align:start position:0%
+this one we basically have a capacitive
+divider at high frequencies that
+
+ align:start position:0%
+divider at high frequencies that
+ 
+
+ align:start position:0%
+divider at high frequencies that
+involves the effective capacitance from
+
+ align:start position:0%
+involves the effective capacitance from
+ 
+
+ align:start position:0%
+involves the effective capacitance from
+this point to this point in the
+
+ align:start position:0%
+this point to this point in the
+ 
+
+ align:start position:0%
+this point to this point in the
+compensating Network working with the
+
+ align:start position:0%
+compensating Network working with the
+ 
+
+ align:start position:0%
+compensating Network working with the
+input capacitance to the second stage so
+
+ align:start position:0%
+input capacitance to the second stage so
+ 
+
+ align:start position:0%
+input capacitance to the second stage so
+we get simply some fraction of the
+
+ align:start position:0%
+we get simply some fraction of the
+ 
+
+ align:start position:0%
+we get simply some fraction of the
+voltage at the output of the second
+
+ align:start position:0%
+voltage at the output of the second
+ 
+
+ align:start position:0%
+voltage at the output of the second
+stage applied back to its input that's
+
+ align:start position:0%
+stage applied back to its input that's
+ 
+
+ align:start position:0%
+stage applied back to its input that's
+fine if we look at the minor loop the
+
+ align:start position:0%
+fine if we look at the minor loop the
+ 
+
+ align:start position:0%
+fine if we look at the minor loop the
+minor loop is quite well behaved under
+
+ align:start position:0%
+minor loop is quite well behaved under
+ 
+
+ align:start position:0%
+minor loop is quite well behaved under
+those conditions because we have
+
+ align:start position:0%
+those conditions because we have
+ 
+
+ align:start position:0%
+those conditions because we have
+effectively a single pole roll-off this
+
+ align:start position:0%
+effectively a single pole roll-off this
+ 
+
+ align:start position:0%
+effectively a single pole roll-off this
+pole in the minor loop in the vicinity
+
+ align:start position:0%
+pole in the minor loop in the vicinity
+ 
+
+ align:start position:0%
+pole in the minor loop in the vicinity
+of the minor loop crossover however
+
+ align:start position:0%
+of the minor loop crossover however
+ 
+
+ align:start position:0%
+of the minor loop crossover however
+consider what happens if at the
+
+ align:start position:0%
+consider what happens if at the
+ 
+
+ align:start position:0%
+consider what happens if at the
+crossover frequency of the minor loop
+
+ align:start position:0%
+crossover frequency of the minor loop
+ 
+
+ align:start position:0%
+crossover frequency of the minor loop
+this network looks basically resistive
+
+ align:start position:0%
+this network looks basically resistive
+ 
+
+ align:start position:0%
+this network looks basically resistive
+if it looks effectively like a resistor
+
+ align:start position:0%
+if it looks effectively like a resistor
+ 
+
+ align:start position:0%
+if it looks effectively like a resistor
+between here and here then it's entirely
+
+ align:start position:0%
+between here and here then it's entirely
+ 
+
+ align:start position:0%
+between here and here then it's entirely
+possible that we get an additional pole
+
+ align:start position:0%
+possible that we get an additional pole
+ 
+
+ align:start position:0%
+possible that we get an additional pole
+in the Meyer loop transponder leuk leuk
+
+ align:start position:0%
+in the Meyer loop transponder leuk leuk
+ 
+
+ align:start position:0%
+in the Meyer loop transponder leuk leuk
+transmission that reflects the loading
+
+ align:start position:0%
+transmission that reflects the loading
+ 
+
+ align:start position:0%
+transmission that reflects the loading
+of the input capacitance of the second
+
+ align:start position:0%
+of the input capacitance of the second
+ 
+
+ align:start position:0%
+of the input capacitance of the second
+stage working on that resistance we'd
+
+ align:start position:0%
+stage working on that resistance we'd
+ 
+
+ align:start position:0%
+stage working on that resistance we'd
+simply get an RC transfer function from
+
+ align:start position:0%
+simply get an RC transfer function from
+ 
+
+ align:start position:0%
+simply get an RC transfer function from
+here to here we combine that with one
+
+ align:start position:0%
+here to here we combine that with one
+ 
+
+ align:start position:0%
+here to here we combine that with one
+additional pole in the open-loop
+
+ align:start position:0%
+additional pole in the open-loop
+ 
+
+ align:start position:0%
+additional pole in the open-loop
+transfer function of the second stage
+
+ align:start position:0%
+transfer function of the second stage
+ 
+
+ align:start position:0%
+transfer function of the second stage
+and we find out that that we end up with
+
+ align:start position:0%
+and we find out that that we end up with
+ 
+
+ align:start position:0%
+and we find out that that we end up with
+a two pole roll-off if that two pole
+
+ align:start position:0%
+a two pole roll-off if that two pole
+ 
+
+ align:start position:0%
+a two pole roll-off if that two pole
+roll-off occurs or is in in progress in
+
+ align:start position:0%
+roll-off occurs or is in in progress in
+ 
+
+ align:start position:0%
+roll-off occurs or is in in progress in
+the vicinity of the monitor loop
+
+ align:start position:0%
+the vicinity of the monitor loop
+ 
+
+ align:start position:0%
+the vicinity of the monitor loop
+crossover why we can have very low phase
+
+ align:start position:0%
+crossover why we can have very low phase
+ 
+
+ align:start position:0%
+crossover why we can have very low phase
+margin in the minor loop and I think
+
+ align:start position:0%
+margin in the minor loop and I think
+ 
+
+ align:start position:0%
+margin in the minor loop and I think
+that's what gives us the T that we see
+
+ align:start position:0%
+that's what gives us the T that we see
+ 
+
+ align:start position:0%
+that's what gives us the T that we see
+in the transient response I think that's
+
+ align:start position:0%
+in the transient response I think that's
+ 
+
+ align:start position:0%
+in the transient response I think that's
+sign of impending minor loop instability
+
+ align:start position:0%
+sign of impending minor loop instability
+ 
+
+ align:start position:0%
+sign of impending minor loop instability
+I think that what's happening is that if
+
+ align:start position:0%
+I think that what's happening is that if
+ 
+
+ align:start position:0%
+I think that what's happening is that if
+we could physically reach into the
+
+ align:start position:0%
+we could physically reach into the
+ 
+
+ align:start position:0%
+we could physically reach into the
+amplifier and look at the actual output
+
+ align:start position:0%
+amplifier and look at the actual output
+ 
+
+ align:start position:0%
+amplifier and look at the actual output
+of the second stage it'd be isolating
+
+ align:start position:0%
+of the second stage it'd be isolating
+ 
+
+ align:start position:0%
+of the second stage it'd be isolating
+quite violently an awful lot of
+
+ align:start position:0%
+quite violently an awful lot of
+ 
+
+ align:start position:0%
+quite violently an awful lot of
+overshoot and so forth we see some
+
+ align:start position:0%
+overshoot and so forth we see some
+ 
+
+ align:start position:0%
+overshoot and so forth we see some
+remain of that because we're looking at
+
+ align:start position:0%
+remain of that because we're looking at
+ 
+
+ align:start position:0%
+remain of that because we're looking at
+this through a low pass filter we go
+
+ align:start position:0%
+this through a low pass filter we go
+ 
+
+ align:start position:0%
+this through a low pass filter we go
+ahead and remember we have a tenth of a
+
+ align:start position:0%
+ahead and remember we have a tenth of a
+ 
+
+ align:start position:0%
+ahead and remember we have a tenth of a
+micro farad capacity of the Ring
+
+ align:start position:0%
+micro farad capacity of the Ring
+ 
+
+ align:start position:0%
+micro farad capacity of the Ring
+frequency at present is several
+
+ align:start position:0%
+frequency at present is several
+ 
+
+ align:start position:0%
+frequency at present is several
+megahertz were at at two microseconds
+
+ align:start position:0%
+megahertz were at at two microseconds
+ 
+
+ align:start position:0%
+megahertz were at at two microseconds
+per division the frequency of the teeth
+
+ align:start position:0%
+per division the frequency of the teeth
+ 
+
+ align:start position:0%
+per division the frequency of the teeth
+is is several megahertz and we're
+
+ align:start position:0%
+is is several megahertz and we're
+ 
+
+ align:start position:0%
+is is several megahertz and we're
+looking at that through a very low pass
+
+ align:start position:0%
+looking at that through a very low pass
+ 
+
+ align:start position:0%
+looking at that through a very low pass
+filter because of the output resistance
+
+ align:start position:0%
+filter because of the output resistance
+ 
+
+ align:start position:0%
+filter because of the output resistance
+of the operational amplifier and and the
+
+ align:start position:0%
+of the operational amplifier and and the
+ 
+
+ align:start position:0%
+of the operational amplifier and and the
+tenth micro farad capacitor flowed that
+
+ align:start position:0%
+tenth micro farad capacitor flowed that
+ 
+
+ align:start position:0%
+tenth micro farad capacitor flowed that
+we've seen and so we see just a little
+
+ align:start position:0%
+we've seen and so we see just a little
+ 
+
+ align:start position:0%
+we've seen and so we see just a little
+remnant of this large oscillation that's
+
+ align:start position:0%
+remnant of this large oscillation that's
+ 
+
+ align:start position:0%
+remnant of this large oscillation that's
+occurring at the actual output of the
+
+ align:start position:0%
+occurring at the actual output of the
+ 
+
+ align:start position:0%
+occurring at the actual output of the
+second stage before the final buffer
+
+ align:start position:0%
+second stage before the final buffer
+ 
+
+ align:start position:0%
+second stage before the final buffer
+amplifier associated with the op-amp and
+
+ align:start position:0%
+amplifier associated with the op-amp and
+ 
+
+ align:start position:0%
+amplifier associated with the op-amp and
+there's some non-linearity to some
+
+ align:start position:0%
+there's some non-linearity to some
+ 
+
+ align:start position:0%
+there's some non-linearity to some
+crossover problems and so forth but I
+
+ align:start position:0%
+crossover problems and so forth but I
+ 
+
+ align:start position:0%
+crossover problems and so forth but I
+believe that the teeth reflect an
+
+ align:start position:0%
+believe that the teeth reflect an
+ 
+
+ align:start position:0%
+believe that the teeth reflect an
+impending minor loop instability the way
+
+ align:start position:0%
+impending minor loop instability the way
+ 
+
+ align:start position:0%
+impending minor loop instability the way
+to get around that the way to improve
+
+ align:start position:0%
+to get around that the way to improve
+ 
+
+ align:start position:0%
+to get around that the way to improve
+the situation is to consider what would
+
+ align:start position:0%
+the situation is to consider what would
+ 
+
+ align:start position:0%
+the situation is to consider what would
+happen if we added one more capacitor
+
+ align:start position:0%
+happen if we added one more capacitor
+ 
+
+ align:start position:0%
+happen if we added one more capacitor
+here now what we'd like to do is
+
+ align:start position:0%
+here now what we'd like to do is
+ 
+
+ align:start position:0%
+here now what we'd like to do is
+maintain the general feature associated
+
+ align:start position:0%
+maintain the general feature associated
+ 
+
+ align:start position:0%
+maintain the general feature associated
+with the transfer function we had
+
+ align:start position:0%
+with the transfer function we had
+ 
+
+ align:start position:0%
+with the transfer function we had
+mentioned earlier and what that
+
+ align:start position:0%
+mentioned earlier and what that
+ 
+
+ align:start position:0%
+mentioned earlier and what that
+means is that this capacitor must be
+
+ align:start position:0%
+means is that this capacitor must be
+ 
+
+ align:start position:0%
+means is that this capacitor must be
+much smaller than our original capacitor
+
+ align:start position:0%
+much smaller than our original capacitor
+ 
+
+ align:start position:0%
+much smaller than our original capacitor
+so we might call this some big capacitor
+
+ align:start position:0%
+so we might call this some big capacitor
+ 
+
+ align:start position:0%
+so we might call this some big capacitor
+and this some small or s is probably a
+
+ align:start position:0%
+and this some small or s is probably a
+ 
+
+ align:start position:0%
+and this some small or s is probably a
+poor choice see little and the ratio
+
+ align:start position:0%
+poor choice see little and the ratio
+ 
+
+ align:start position:0%
+poor choice see little and the ratio
+between C big and C little should be
+
+ align:start position:0%
+between C big and C little should be
+ 
+
+ align:start position:0%
+between C big and C little should be
+quite great the reason being that when
+
+ align:start position:0%
+quite great the reason being that when
+ 
+
+ align:start position:0%
+quite great the reason being that when
+we add C little the effect on the ideal
+
+ align:start position:0%
+we add C little the effect on the ideal
+ 
+
+ align:start position:0%
+we add C little the effect on the ideal
+open-loop transfer function of the
+
+ align:start position:0%
+open-loop transfer function of the
+ 
+
+ align:start position:0%
+open-loop transfer function of the
+operational amplifier is to add an
+
+ align:start position:0%
+operational amplifier is to add an
+ 
+
+ align:start position:0%
+operational amplifier is to add an
+additional pole maybe out here we'd like
+
+ align:start position:0%
+additional pole maybe out here we'd like
+ 
+
+ align:start position:0%
+additional pole maybe out here we'd like
+to make sure that that pole occurs well
+
+ align:start position:0%
+to make sure that that pole occurs well
+ 
+
+ align:start position:0%
+to make sure that that pole occurs well
+after crossover in the overall loop so
+
+ align:start position:0%
+after crossover in the overall loop so
+ 
+
+ align:start position:0%
+after crossover in the overall loop so
+that we don't compromise the stability
+
+ align:start position:0%
+that we don't compromise the stability
+ 
+
+ align:start position:0%
+that we don't compromise the stability
+of the overall loop we only want to use
+
+ align:start position:0%
+of the overall loop we only want to use
+ 
+
+ align:start position:0%
+of the overall loop we only want to use
+this capacitor to improve the stability
+
+ align:start position:0%
+this capacitor to improve the stability
+ 
+
+ align:start position:0%
+this capacitor to improve the stability
+of the minor loop and in this particular
+
+ align:start position:0%
+of the minor loop and in this particular
+ 
+
+ align:start position:0%
+of the minor loop and in this particular
+setup we've chosen our small capacitor
+
+ align:start position:0%
+setup we've chosen our small capacitor
+ 
+
+ align:start position:0%
+setup we've chosen our small capacitor
+here to be roughly 1/10 of the value of
+
+ align:start position:0%
+here to be roughly 1/10 of the value of
+ 
+
+ align:start position:0%
+here to be roughly 1/10 of the value of
+the big capacitor and that results in a
+
+ align:start position:0%
+the big capacitor and that results in a
+ 
+
+ align:start position:0%
+the big capacitor and that results in a
+very good compromise between maintaining
+
+ align:start position:0%
+very good compromise between maintaining
+ 
+
+ align:start position:0%
+very good compromise between maintaining
+stability in the minor loop and yet not
+
+ align:start position:0%
+stability in the minor loop and yet not
+ 
+
+ align:start position:0%
+stability in the minor loop and yet not
+compromising the stability of the
+
+ align:start position:0%
+compromising the stability of the
+ 
+
+ align:start position:0%
+compromising the stability of the
+overall loop so let's now add that
+
+ align:start position:0%
+overall loop so let's now add that
+ 
+
+ align:start position:0%
+overall loop so let's now add that
+capacitor when we do that we notice the
+
+ align:start position:0%
+capacitor when we do that we notice the
+ 
+
+ align:start position:0%
+capacitor when we do that we notice the
+basic transient response remains the
+
+ align:start position:0%
+basic transient response remains the
+ 
+
+ align:start position:0%
+basic transient response remains the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+we have about the 20% overshoot or there
+
+ align:start position:0%
+we have about the 20% overshoot or there
+ 
+
+ align:start position:0%
+we have about the 20% overshoot or there
+abouts but the teeth have completely
+
+ align:start position:0%
+abouts but the teeth have completely
+ 
+
+ align:start position:0%
+abouts but the teeth have completely
+gone away we've we've eliminated the
+
+ align:start position:0%
+gone away we've we've eliminated the
+ 
+
+ align:start position:0%
+gone away we've we've eliminated the
+minor loop problem by making the
+
+ align:start position:0%
+minor loop problem by making the
+ 
+
+ align:start position:0%
+minor loop problem by making the
+compensating Network look capacitive at
+
+ align:start position:0%
+compensating Network look capacitive at
+ 
+
+ align:start position:0%
+compensating Network look capacitive at
+the crossover frequency of the minor
+
+ align:start position:0%
+the crossover frequency of the minor
+ 
+
+ align:start position:0%
+the crossover frequency of the minor
+loop that frequency of course is much
+
+ align:start position:0%
+loop that frequency of course is much
+ 
+
+ align:start position:0%
+loop that frequency of course is much
+higher than the overall crossover
+
+ align:start position:0%
+higher than the overall crossover
+ 
+
+ align:start position:0%
+higher than the overall crossover
+frequency let's doing once more let's
+
+ align:start position:0%
+frequency let's doing once more let's
+ 
+
+ align:start position:0%
+frequency let's doing once more let's
+take out that capacitor the teeth come
+
+ align:start position:0%
+take out that capacitor the teeth come
+ 
+
+ align:start position:0%
+take out that capacitor the teeth come
+we add the capacitor back in simply move
+
+ align:start position:0%
+we add the capacitor back in simply move
+ 
+
+ align:start position:0%
+we add the capacitor back in simply move
+this lead over the minor loop whoops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's really a matter of placement the
+
+ align:start position:0%
+it's really a matter of placement the
+ 
+
+ align:start position:0%
+it's really a matter of placement the
+minor loop gets much better behaved and
+
+ align:start position:0%
+minor loop gets much better behaved and
+ 
+
+ align:start position:0%
+minor loop gets much better behaved and
+we really haven't significantly changed
+
+ align:start position:0%
+we really haven't significantly changed
+ 
+
+ align:start position:0%
+we really haven't significantly changed
+the overall features we haven't changed
+
+ align:start position:0%
+the overall features we haven't changed
+ 
+
+ align:start position:0%
+the overall features we haven't changed
+things significantly in the vicinity of
+
+ align:start position:0%
+things significantly in the vicinity of
+ 
+
+ align:start position:0%
+things significantly in the vicinity of
+the major loop crossover what's the
+
+ align:start position:0%
+the major loop crossover what's the
+ 
+
+ align:start position:0%
+the major loop crossover what's the
+difficulty with this kind of
+
+ align:start position:0%
+difficulty with this kind of
+ 
+
+ align:start position:0%
+difficulty with this kind of
+compensation well one of the things is
+
+ align:start position:0%
+compensation well one of the things is
+ 
+
+ align:start position:0%
+compensation well one of the things is
+it's very very special purpose we have
+
+ align:start position:0%
+it's very very special purpose we have
+ 
+
+ align:start position:0%
+it's very very special purpose we have
+already looked at one over s squared
+
+ align:start position:0%
+already looked at one over s squared
+ 
+
+ align:start position:0%
+already looked at one over s squared
+compensation and found out that it was
+
+ align:start position:0%
+compensation and found out that it was
+ 
+
+ align:start position:0%
+compensation and found out that it was
+somewhat special purpose here we're
+
+ align:start position:0%
+somewhat special purpose here we're
+ 
+
+ align:start position:0%
+somewhat special purpose here we're
+tailoring compensation to a specific
+
+ align:start position:0%
+tailoring compensation to a specific
+ 
+
+ align:start position:0%
+tailoring compensation to a specific
+load in particular a capacitive load and
+
+ align:start position:0%
+load in particular a capacitive load and
+ 
+
+ align:start position:0%
+load in particular a capacitive load and
+we're choosing the zero associated with
+
+ align:start position:0%
+we're choosing the zero associated with
+ 
+
+ align:start position:0%
+we're choosing the zero associated with
+this form of compensation to bear some
+
+ align:start position:0%
+this form of compensation to bear some
+ 
+
+ align:start position:0%
+this form of compensation to bear some
+relationship to the pole caused by the
+
+ align:start position:0%
+relationship to the pole caused by the
+ 
+
+ align:start position:0%
+relationship to the pole caused by the
+capacitive load what happens if we take
+
+ align:start position:0%
+capacitive load what happens if we take
+ 
+
+ align:start position:0%
+capacitive load what happens if we take
+the capacitive load away well the system
+
+ align:start position:0%
+the capacitive load away well the system
+ 
+
+ align:start position:0%
+the capacitive load away well the system
+goes unstable we can see that let me go
+
+ align:start position:0%
+goes unstable we can see that let me go
+ 
+
+ align:start position:0%
+goes unstable we can see that let me go
+back to zero capacitive load and we
+
+ align:start position:0%
+back to zero capacitive load and we
+ 
+
+ align:start position:0%
+back to zero capacitive load and we
+notice even if we eliminate the input Y
+
+ align:start position:0%
+notice even if we eliminate the input Y
+ 
+
+ align:start position:0%
+notice even if we eliminate the input Y
+the amplifier is oscillating
+
+ align:start position:0%
+the amplifier is oscillating
+ 
+
+ align:start position:0%
+the amplifier is oscillating
+I'm sure whether we can sync on that or
+
+ align:start position:0%
+I'm sure whether we can sync on that or
+ 
+
+ align:start position:0%
+I'm sure whether we can sync on that or
+not sure here the amplifier is
+
+ align:start position:0%
+not sure here the amplifier is
+ 
+
+ align:start position:0%
+not sure here the amplifier is
+oscillating at quite a high frequency
+
+ align:start position:0%
+oscillating at quite a high frequency
+ 
+
+ align:start position:0%
+oscillating at quite a high frequency
+several megahertz reflecting the fact
+
+ align:start position:0%
+several megahertz reflecting the fact
+ 
+
+ align:start position:0%
+several megahertz reflecting the fact
+that we've taken away the capacitive
+
+ align:start position:0%
+that we've taken away the capacitive
+ 
+
+ align:start position:0%
+that we've taken away the capacitive
+load which in Canessa Cerie for
+
+ align:start position:0%
+load which in Canessa Cerie for
+ 
+
+ align:start position:0%
+load which in Canessa Cerie for
+stabilization when we use this sort of
+
+ align:start position:0%
+stabilization when we use this sort of
+ 
+
+ align:start position:0%
+stabilization when we use this sort of
+compensation let's put the capacitive
+
+ align:start position:0%
+compensation let's put the capacitive
+ 
+
+ align:start position:0%
+compensation let's put the capacitive
+load back on that the amplifier is now
+
+ align:start position:0%
+load back on that the amplifier is now
+ 
+
+ align:start position:0%
+load back on that the amplifier is now
+well-behaved and we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get our well damped response back the
+
+ align:start position:0%
+get our well damped response back the
+ 
+
+ align:start position:0%
+get our well damped response back the
+amplifier will oscillate even if we load
+
+ align:start position:0%
+amplifier will oscillate even if we load
+ 
+
+ align:start position:0%
+amplifier will oscillate even if we load
+it with a capacitor other than the
+
+ align:start position:0%
+it with a capacitor other than the
+ 
+
+ align:start position:0%
+it with a capacitor other than the
+intended one if we go to the O one micro
+
+ align:start position:0%
+intended one if we go to the O one micro
+ 
+
+ align:start position:0%
+intended one if we go to the O one micro
+farad capacitor load once again the
+
+ align:start position:0%
+farad capacitor load once again the
+ 
+
+ align:start position:0%
+farad capacitor load once again the
+amplifier is oscillating presumably at a
+
+ align:start position:0%
+amplifier is oscillating presumably at a
+ 
+
+ align:start position:0%
+amplifier is oscillating presumably at a
+different frequency
+
+ align:start position:0%
+different frequency
+ 
+
+ align:start position:0%
+different frequency
+but once again oscillating so if we go
+
+ align:start position:0%
+but once again oscillating so if we go
+ 
+
+ align:start position:0%
+but once again oscillating so if we go
+back to the capacitive load we designed
+
+ align:start position:0%
+back to the capacitive load we designed
+ 
+
+ align:start position:0%
+back to the capacitive load we designed
+the compensation for things are fine but
+
+ align:start position:0%
+the compensation for things are fine but
+ 
+
+ align:start position:0%
+the compensation for things are fine but
+if we change the magnitude of that
+
+ align:start position:0%
+if we change the magnitude of that
+ 
+
+ align:start position:0%
+if we change the magnitude of that
+capacitive load or if we eliminate it
+
+ align:start position:0%
+capacitive load or if we eliminate it
+ 
+
+ align:start position:0%
+capacitive load or if we eliminate it
+entirely things get much worse so that's
+
+ align:start position:0%
+entirely things get much worse so that's
+ 
+
+ align:start position:0%
+entirely things get much worse so that's
+one of the problems with this form of
+
+ align:start position:0%
+one of the problems with this form of
+ 
+
+ align:start position:0%
+one of the problems with this form of
+compensation I'd like to look at one
+
+ align:start position:0%
+compensation I'd like to look at one
+ 
+
+ align:start position:0%
+compensation I'd like to look at one
+final form of compensation we found out
+
+ align:start position:0%
+final form of compensation we found out
+ 
+
+ align:start position:0%
+final form of compensation we found out
+that one way to offset the effects of an
+
+ align:start position:0%
+that one way to offset the effects of an
+ 
+
+ align:start position:0%
+that one way to offset the effects of an
+additional pole in the loop is to add a
+
+ align:start position:0%
+additional pole in the loop is to add a
+ 
+
+ align:start position:0%
+additional pole in the loop is to add a
+zero that's what we were doing here but
+
+ align:start position:0%
+zero that's what we were doing here but
+ 
+
+ align:start position:0%
+zero that's what we were doing here but
+now let me pose a different problem
+
+ align:start position:0%
+now let me pose a different problem
+ 
+
+ align:start position:0%
+now let me pose a different problem
+suppose we anticipate an additional pole
+
+ align:start position:0%
+suppose we anticipate an additional pole
+ 
+
+ align:start position:0%
+suppose we anticipate an additional pole
+in our loop transmission but we don't
+
+ align:start position:0%
+in our loop transmission but we don't
+ 
+
+ align:start position:0%
+in our loop transmission but we don't
+know the frequency at which that pole
+
+ align:start position:0%
+know the frequency at which that pole
+ 
+
+ align:start position:0%
+know the frequency at which that pole
+will be located so what we're looking
+
+ align:start position:0%
+will be located so what we're looking
+ 
+
+ align:start position:0%
+will be located so what we're looking
+here for now is really compensation for
+
+ align:start position:0%
+here for now is really compensation for
+ 
+
+ align:start position:0%
+here for now is really compensation for
+those who don't know what they're doing
+
+ align:start position:0%
+those who don't know what they're doing
+ 
+
+ align:start position:0%
+those who don't know what they're doing
+possibly or something where we have a
+
+ align:start position:0%
+possibly or something where we have a
+ 
+
+ align:start position:0%
+possibly or something where we have a
+system that has certain uncertain
+
+ align:start position:0%
+system that has certain uncertain
+ 
+
+ align:start position:0%
+system that has certain uncertain
+parameters some uncertain parameters how
+
+ align:start position:0%
+parameters some uncertain parameters how
+ 
+
+ align:start position:0%
+parameters some uncertain parameters how
+might we compensate in that case it's
+
+ align:start position:0%
+might we compensate in that case it's
+ 
+
+ align:start position:0%
+might we compensate in that case it's
+not but this is a more than academic
+
+ align:start position:0%
+not but this is a more than academic
+ 
+
+ align:start position:0%
+not but this is a more than academic
+interest there are certain elements
+
+ align:start position:0%
+interest there are certain elements
+ 
+
+ align:start position:0%
+interest there are certain elements
+which in fact have dynamics that vary as
+
+ align:start position:0%
+which in fact have dynamics that vary as
+ 
+
+ align:start position:0%
+which in fact have dynamics that vary as
+a function of conditions for example a
+
+ align:start position:0%
+a function of conditions for example a
+ 
+
+ align:start position:0%
+a function of conditions for example a
+very simple example is that of a power
+
+ align:start position:0%
+very simple example is that of a power
+ 
+
+ align:start position:0%
+very simple example is that of a power
+supply again if you build a power supply
+
+ align:start position:0%
+supply again if you build a power supply
+ 
+
+ align:start position:0%
+supply again if you build a power supply
+into some system why people go ahead and
+
+ align:start position:0%
+into some system why people go ahead and
+ 
+
+ align:start position:0%
+into some system why people go ahead and
+connect loads to the power supply very
+
+ align:start position:0%
+connect loads to the power supply very
+ 
+
+ align:start position:0%
+connect loads to the power supply very
+frequently those loads include their own
+
+ align:start position:0%
+frequently those loads include their own
+ 
+
+ align:start position:0%
+frequently those loads include their own
+decoupling capacitors consequently you
+
+ align:start position:0%
+decoupling capacitors consequently you
+ 
+
+ align:start position:0%
+decoupling capacitors consequently you
+can add a great deal of capacitance to
+
+ align:start position:0%
+can add a great deal of capacitance to
+ 
+
+ align:start position:0%
+can add a great deal of capacitance to
+the output of the power supply you don't
+
+ align:start position:0%
+the output of the power supply you don't
+ 
+
+ align:start position:0%
+the output of the power supply you don't
+necessarily know the exact amount you
+
+ align:start position:0%
+necessarily know the exact amount you
+ 
+
+ align:start position:0%
+necessarily know the exact amount you
+can bound put a lower bound on it by by
+
+ align:start position:0%
+can bound put a lower bound on it by by
+ 
+
+ align:start position:0%
+can bound put a lower bound on it by by
+including some capacitance internally
+
+ align:start position:0%
+including some capacitance internally
+ 
+
+ align:start position:0%
+including some capacitance internally
+but you're never sure what the total
+
+ align:start position:0%
+but you're never sure what the total
+ 
+
+ align:start position:0%
+but you're never sure what the total
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+capacitance how large the load capacitor
+
+ align:start position:0%
+capacitance how large the load capacitor
+ 
+
+ align:start position:0%
+capacitance how large the load capacitor
+can be there's another possibility
+
+ align:start position:0%
+can be there's another possibility
+ 
+
+ align:start position:0%
+can be there's another possibility
+there's an element that's quite
+
+ align:start position:0%
+there's an element that's quite
+ 
+
+ align:start position:0%
+there's an element that's quite
+frequently used as a gain control
+
+ align:start position:0%
+frequently used as a gain control
+ 
+
+ align:start position:0%
+frequently used as a gain control
+element that consists of a photo
+
+ align:start position:0%
+element that consists of a photo
+ 
+
+ align:start position:0%
+element that consists of a photo
+resistor illuminated by a lamp and by
+
+ align:start position:0%
+resistor illuminated by a lamp and by
+ 
+
+ align:start position:0%
+resistor illuminated by a lamp and by
+changing the illumination you change the
+
+ align:start position:0%
+changing the illumination you change the
+ 
+
+ align:start position:0%
+changing the illumination you change the
+value of the resistor you're able to use
+
+ align:start position:0%
+value of the resistor you're able to use
+ 
+
+ align:start position:0%
+value of the resistor you're able to use
+that as some sort of a gain control
+
+ align:start position:0%
+that as some sort of a gain control
+ 
+
+ align:start position:0%
+that as some sort of a gain control
+mechanism build a feedback loop that
+
+ align:start position:0%
+mechanism build a feedback loop that
+ 
+
+ align:start position:0%
+mechanism build a feedback loop that
+adjusts lamp intensity in order to get a
+
+ align:start position:0%
+adjusts lamp intensity in order to get a
+ 
+
+ align:start position:0%
+adjusts lamp intensity in order to get a
+desired signal level out of an overall
+
+ align:start position:0%
+desired signal level out of an overall
+ 
+
+ align:start position:0%
+desired signal level out of an overall
+system for example well the nature of
+
+ align:start position:0%
+system for example well the nature of
+ 
+
+ align:start position:0%
+system for example well the nature of
+the photo resistors used in those
+
+ align:start position:0%
+the photo resistors used in those
+ 
+
+ align:start position:0%
+the photo resistors used in those
+devices is such that as you change
+
+ align:start position:0%
+devices is such that as you change
+ 
+
+ align:start position:0%
+devices is such that as you change
+illumination the time constant the pole
+
+ align:start position:0%
+illumination the time constant the pole
+ 
+
+ align:start position:0%
+illumination the time constant the pole
+associated with that transfer function
+
+ align:start position:0%
+associated with that transfer function
+ 
+
+ align:start position:0%
+associated with that transfer function
+the transfer function relating light to
+
+ align:start position:0%
+the transfer function relating light to
+ 
+
+ align:start position:0%
+the transfer function relating light to
+resistance value changes that the time
+
+ align:start position:0%
+resistance value changes that the time
+ 
+
+ align:start position:0%
+resistance value changes that the time
+constant is actually lower at low
+
+ align:start position:0%
+constant is actually lower at low
+ 
+
+ align:start position:0%
+constant is actually lower at low
+illumination levels than it is at high
+
+ align:start position:0%
+illumination levels than it is at high
+ 
+
+ align:start position:0%
+illumination levels than it is at high
+lumen illumination levels another
+
+ align:start position:0%
+lumen illumination levels another
+ 
+
+ align:start position:0%
+lumen illumination levels another
+problem exists in that kind of a loop in
+
+ align:start position:0%
+problem exists in that kind of a loop in
+ 
+
+ align:start position:0%
+problem exists in that kind of a loop in
+that the gain the loop transmission in
+
+ align:start position:0%
+that the gain the loop transmission in
+ 
+
+ align:start position:0%
+that the gain the loop transmission in
+these sort of gain control loops is
+
+ align:start position:0%
+these sort of gain control loops is
+ 
+
+ align:start position:0%
+these sort of gain control loops is
+always a function of operating
+
+ align:start position:0%
+always a function of operating
+ 
+
+ align:start position:0%
+always a function of operating
+conditions it's a function of the amount
+
+ align:start position:0%
+conditions it's a function of the amount
+ 
+
+ align:start position:0%
+conditions it's a function of the amount
+of gain control that's that's present at
+
+ align:start position:0%
+of gain control that's that's present at
+ 
+
+ align:start position:0%
+of gain control that's that's present at
+a given moment and so here you have a
+
+ align:start position:0%
+a given moment and so here you have a
+ 
+
+ align:start position:0%
+a given moment and so here you have a
+loop that has to on certain variables
+
+ align:start position:0%
+loop that has to on certain variables
+ 
+
+ align:start position:0%
+loop that has to on certain variables
+one the location of a pole another one
+
+ align:start position:0%
+one the location of a pole another one
+ 
+
+ align:start position:0%
+one the location of a pole another one
+being the loop transmission magnitude
+
+ align:start position:0%
+being the loop transmission magnitude
+ 
+
+ align:start position:0%
+being the loop transmission magnitude
+and what I'd like to look at now is a
+
+ align:start position:0%
+and what I'd like to look at now is a
+ 
+
+ align:start position:0%
+and what I'd like to look at now is a
+fourth and final form of compensation
+
+ align:start position:0%
+fourth and final form of compensation
+ 
+
+ align:start position:0%
+fourth and final form of compensation
+that will allow us to maintain a good
+
+ align:start position:0%
+that will allow us to maintain a good
+ 
+
+ align:start position:0%
+that will allow us to maintain a good
+degree of stability in view of these
+
+ align:start position:0%
+degree of stability in view of these
+ 
+
+ align:start position:0%
+degree of stability in view of these
+sorts of uncertain parameters the the
+
+ align:start position:0%
+sorts of uncertain parameters the the
+ 
+
+ align:start position:0%
+sorts of uncertain parameters the the
+test configuration that we're going to
+
+ align:start position:0%
+test configuration that we're going to
+ 
+
+ align:start position:0%
+test configuration that we're going to
+look at is as follows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we build up a loop that allows us
+
+ align:start position:0%
+here we build up a loop that allows us
+ 
+
+ align:start position:0%
+here we build up a loop that allows us
+to very easily add a pole to the
+
+ align:start position:0%
+to very easily add a pole to the
+ 
+
+ align:start position:0%
+to very easily add a pole to the
+open-loop transfer function of the
+
+ align:start position:0%
+open-loop transfer function of the
+ 
+
+ align:start position:0%
+open-loop transfer function of the
+operational amplifier that's used and
+
+ align:start position:0%
+operational amplifier that's used and
+ 
+
+ align:start position:0%
+operational amplifier that's used and
+furthermore vary its location over a
+
+ align:start position:0%
+furthermore vary its location over a
+ 
+
+ align:start position:0%
+furthermore vary its location over a
+very wide range of frequencies here we
+
+ align:start position:0%
+very wide range of frequencies here we
+ 
+
+ align:start position:0%
+very wide range of frequencies here we
+have the operational amplifier that
+
+ align:start position:0%
+have the operational amplifier that
+ 
+
+ align:start position:0%
+have the operational amplifier that
+we're using with its compensating
+
+ align:start position:0%
+we're using with its compensating
+ 
+
+ align:start position:0%
+we're using with its compensating
+network at its output we add an R and C
+
+ align:start position:0%
+network at its output we add an R and C
+ 
+
+ align:start position:0%
+network at its output we add an R and C
+and we're able to adjust the values of
+
+ align:start position:0%
+and we're able to adjust the values of
+ 
+
+ align:start position:0%
+and we're able to adjust the values of
+the R and C change the values so that we
+
+ align:start position:0%
+the R and C change the values so that we
+ 
+
+ align:start position:0%
+the R and C change the values so that we
+can add an additional pole to the loop
+
+ align:start position:0%
+can add an additional pole to the loop
+ 
+
+ align:start position:0%
+can add an additional pole to the loop
+transmission at over a very wide range
+
+ align:start position:0%
+transmission at over a very wide range
+ 
+
+ align:start position:0%
+transmission at over a very wide range
+of frequencies by appropriately
+
+ align:start position:0%
+of frequencies by appropriately
+ 
+
+ align:start position:0%
+of frequencies by appropriately
+selecting the R 1 C 1 product we then
+
+ align:start position:0%
+selecting the R 1 C 1 product we then
+ 
+
+ align:start position:0%
+selecting the R 1 C 1 product we then
+have a buffer amplifier a little unity
+
+ align:start position:0%
+have a buffer amplifier a little unity
+ 
+
+ align:start position:0%
+have a buffer amplifier a little unity
+gain follower that has a bandwidth much
+
+ align:start position:0%
+gain follower that has a bandwidth much
+ 
+
+ align:start position:0%
+gain follower that has a bandwidth much
+much greater than the actual operational
+
+ align:start position:0%
+much greater than the actual operational
+ 
+
+ align:start position:0%
+much greater than the actual operational
+amplifier we're using and we just use
+
+ align:start position:0%
+amplifier we're using and we just use
+ 
+
+ align:start position:0%
+amplifier we're using and we just use
+this to prevent any loading on the RC
+
+ align:start position:0%
+this to prevent any loading on the RC
+ 
+
+ align:start position:0%
+this to prevent any loading on the RC
+network a little resistor that's
+
+ align:start position:0%
+network a little resistor that's
+ 
+
+ align:start position:0%
+network a little resistor that's
+recommended by the manufacturer when one
+
+ align:start position:0%
+recommended by the manufacturer when one
+ 
+
+ align:start position:0%
+recommended by the manufacturer when one
+uses this amplifier and then we close
+
+ align:start position:0%
+uses this amplifier and then we close
+ 
+
+ align:start position:0%
+uses this amplifier and then we close
+the overall feedback loop so we have the
+
+ align:start position:0%
+the overall feedback loop so we have the
+ 
+
+ align:start position:0%
+the overall feedback loop so we have the
+dynamics of this amplifier is such that
+
+ align:start position:0%
+dynamics of this amplifier is such that
+ 
+
+ align:start position:0%
+dynamics of this amplifier is such that
+it's basically transparent consequently
+
+ align:start position:0%
+it's basically transparent consequently
+ 
+
+ align:start position:0%
+it's basically transparent consequently
+we have a loop transmission in this loop
+
+ align:start position:0%
+we have a loop transmission in this loop
+ 
+
+ align:start position:0%
+we have a loop transmission in this loop
+that's that of the operational amplifier
+
+ align:start position:0%
+that's that of the operational amplifier
+ 
+
+ align:start position:0%
+that's that of the operational amplifier
+times 1 over R 1 C 1 s plus 1 the
+
+ align:start position:0%
+times 1 over R 1 C 1 s plus 1 the
+ 
+
+ align:start position:0%
+times 1 over R 1 C 1 s plus 1 the
+low-pass characteristic of this network
+
+ align:start position:0%
+low-pass characteristic of this network
+ 
+
+ align:start position:0%
+low-pass characteristic of this network
+and say what we're going to do is
+
+ align:start position:0%
+and say what we're going to do is
+ 
+
+ align:start position:0%
+and say what we're going to do is
+attempt to come up with a compensation
+
+ align:start position:0%
+attempt to come up with a compensation
+ 
+
+ align:start position:0%
+attempt to come up with a compensation
+where we maintain adequate stability
+
+ align:start position:0%
+where we maintain adequate stability
+ 
+
+ align:start position:0%
+where we maintain adequate stability
+over a very wide range of R 1 C 1
+
+ align:start position:0%
+over a very wide range of R 1 C 1
+ 
+
+ align:start position:0%
+over a very wide range of R 1 C 1
+products the difficulty of course is
+
+ align:start position:0%
+products the difficulty of course is
+ 
+
+ align:start position:0%
+products the difficulty of course is
+that if we use a single pole
+
+ align:start position:0%
+that if we use a single pole
+ 
+
+ align:start position:0%
+that if we use a single pole
+compensation with a fixed value of
+
+ align:start position:0%
+compensation with a fixed value of
+ 
+
+ align:start position:0%
+compensation with a fixed value of
+capacitor why certain values of the R 1
+
+ align:start position:0%
+capacitor why certain values of the R 1
+ 
+
+ align:start position:0%
+capacitor why certain values of the R 1
+C 1 product will cause us to crossover
+
+ align:start position:0%
+C 1 product will cause us to crossover
+ 
+
+ align:start position:0%
+C 1 product will cause us to crossover
+in a 1 over s squared region in fact
+
+ align:start position:0%
+in a 1 over s squared region in fact
+ 
+
+ align:start position:0%
+in a 1 over s squared region in fact
+it's certainly possible to have very
+
+ align:start position:0%
+it's certainly possible to have very
+ 
+
+ align:start position:0%
+it's certainly possible to have very
+very long regions of 1 over s squared
+
+ align:start position:0%
+very long regions of 1 over s squared
+ 
+
+ align:start position:0%
+very long regions of 1 over s squared
+roll-off with appropriate choices of the
+
+ align:start position:0%
+roll-off with appropriate choices of the
+ 
+
+ align:start position:0%
+roll-off with appropriate choices of the
+R 1 C 1 product and so we can get very
+
+ align:start position:0%
+R 1 C 1 product and so we can get very
+ 
+
+ align:start position:0%
+R 1 C 1 product and so we can get very
+very low phase margins in that sort of a
+
+ align:start position:0%
+very low phase margins in that sort of a
+ 
+
+ align:start position:0%
+very low phase margins in that sort of a
+system if we choose compensation that
+
+ align:start position:0%
+system if we choose compensation that
+ 
+
+ align:start position:0%
+system if we choose compensation that
+includes a zero we're again in trouble
+
+ align:start position:0%
+includes a zero we're again in trouble
+ 
+
+ align:start position:0%
+includes a zero we're again in trouble
+because we saw in last demonstration
+
+ align:start position:0%
+because we saw in last demonstration
+ 
+
+ align:start position:0%
+because we saw in last demonstration
+that we have to tailor the location of a
+
+ align:start position:0%
+that we have to tailor the location of a
+ 
+
+ align:start position:0%
+that we have to tailor the location of a
+zero in that kind of compensation
+
+ align:start position:0%
+zero in that kind of compensation
+ 
+
+ align:start position:0%
+zero in that kind of compensation
+civically the load capacitance we're
+
+ align:start position:0%
+civically the load capacitance we're
+ 
+
+ align:start position:0%
+civically the load capacitance we're
+going to have and if we used it in this
+
+ align:start position:0%
+going to have and if we used it in this
+ 
+
+ align:start position:0%
+going to have and if we used it in this
+configuration why what we'd have to do
+
+ align:start position:0%
+configuration why what we'd have to do
+ 
+
+ align:start position:0%
+configuration why what we'd have to do
+is is tailor the zero location to the
+
+ align:start position:0%
+is is tailor the zero location to the
+ 
+
+ align:start position:0%
+is is tailor the zero location to the
+precise value of the r1 c1 product that
+
+ align:start position:0%
+precise value of the r1 c1 product that
+ 
+
+ align:start position:0%
+precise value of the r1 c1 product that
+used at least within a factor of two or
+
+ align:start position:0%
+used at least within a factor of two or
+ 
+
+ align:start position:0%
+used at least within a factor of two or
+three and if we state is one of the
+
+ align:start position:0%
+three and if we state is one of the
+ 
+
+ align:start position:0%
+three and if we state is one of the
+rules of the game or one of the
+
+ align:start position:0%
+rules of the game or one of the
+ 
+
+ align:start position:0%
+rules of the game or one of the
+uncertainties here that that the we
+
+ align:start position:0%
+uncertainties here that that the we
+ 
+
+ align:start position:0%
+uncertainties here that that the we
+don't know the r1 c1 product beforehand
+
+ align:start position:0%
+don't know the r1 c1 product beforehand
+ 
+
+ align:start position:0%
+don't know the r1 c1 product beforehand
+while we're not able to use that sort of
+
+ align:start position:0%
+while we're not able to use that sort of
+ 
+
+ align:start position:0%
+while we're not able to use that sort of
+compensation let me suggest another
+
+ align:start position:0%
+compensation let me suggest another
+ 
+
+ align:start position:0%
+compensation let me suggest another
+approach suppose we could come up with
+
+ align:start position:0%
+approach suppose we could come up with
+ 
+
+ align:start position:0%
+approach suppose we could come up with
+way of compensating the amplifier such
+
+ align:start position:0%
+way of compensating the amplifier such
+ 
+
+ align:start position:0%
+way of compensating the amplifier such
+that it's open loop transfer function
+
+ align:start position:0%
+that it's open loop transfer function
+ 
+
+ align:start position:0%
+that it's open loop transfer function
+rolled off proportional to 1 over the
+
+ align:start position:0%
+rolled off proportional to 1 over the
+ 
+
+ align:start position:0%
+rolled off proportional to 1 over the
+square root of s if we did that let's
+
+ align:start position:0%
+square root of s if we did that let's
+ 
+
+ align:start position:0%
+square root of s if we did that let's
+see what's the characteristics that are
+
+ align:start position:0%
+see what's the characteristics that are
+ 
+
+ align:start position:0%
+see what's the characteristics that are
+that's associated with a 1 over the
+
+ align:start position:0%
+that's associated with a 1 over the
+ 
+
+ align:start position:0%
+that's associated with a 1 over the
+square root of s roll off
+
+ align:start position:0%
+square root of s roll off
+ 
+
+ align:start position:0%
+square root of s roll off
+well the phase shift associated with the
+
+ align:start position:0%
+well the phase shift associated with the
+ 
+
+ align:start position:0%
+well the phase shift associated with the
+amplifier itself with its open-loop
+
+ align:start position:0%
+amplifier itself with its open-loop
+ 
+
+ align:start position:0%
+amplifier itself with its open-loop
+transfer function would always be minus
+
+ align:start position:0%
+transfer function would always be minus
+ 
+
+ align:start position:0%
+transfer function would always be minus
+45 degrees that's the angle associated
+
+ align:start position:0%
+45 degrees that's the angle associated
+ 
+
+ align:start position:0%
+45 degrees that's the angle associated
+with a 1 over radical S transfer
+
+ align:start position:0%
+with a 1 over radical S transfer
+ 
+
+ align:start position:0%
+with a 1 over radical S transfer
+function however the magnitude would
+
+ align:start position:0%
+function however the magnitude would
+ 
+
+ align:start position:0%
+function however the magnitude would
+drop off and and that means that if we
+
+ align:start position:0%
+drop off and and that means that if we
+ 
+
+ align:start position:0%
+drop off and and that means that if we
+designed our 1 over radical s amplifier
+
+ align:start position:0%
+designed our 1 over radical s amplifier
+ 
+
+ align:start position:0%
+designed our 1 over radical s amplifier
+properly we could arrange to have it go
+
+ align:start position:0%
+properly we could arrange to have it go
+ 
+
+ align:start position:0%
+properly we could arrange to have it go
+through unity gain at a sufficiently low
+
+ align:start position:0%
+through unity gain at a sufficiently low
+ 
+
+ align:start position:0%
+through unity gain at a sufficiently low
+frequency so that it would be stable
+
+ align:start position:0%
+frequency so that it would be stable
+ 
+
+ align:start position:0%
+frequency so that it would be stable
+without an additional pole added to its
+
+ align:start position:0%
+without an additional pole added to its
+ 
+
+ align:start position:0%
+without an additional pole added to its
+loop transmission yet if we added
+
+ align:start position:0%
+loop transmission yet if we added
+ 
+
+ align:start position:0%
+loop transmission yet if we added
+another pole to the loop transmission in
+
+ align:start position:0%
+another pole to the loop transmission in
+ 
+
+ align:start position:0%
+another pole to the loop transmission in
+addition to the 1 over s roll radical S
+
+ align:start position:0%
+addition to the 1 over s roll radical S
+ 
+
+ align:start position:0%
+addition to the 1 over s roll radical S
+roll-off Y we could be assured of at
+
+ align:start position:0%
+roll-off Y we could be assured of at
+ 
+
+ align:start position:0%
+roll-off Y we could be assured of at
+least 45 degrees of phase margin
+
+ align:start position:0%
+least 45 degrees of phase margin
+ 
+
+ align:start position:0%
+least 45 degrees of phase margin
+regardless of the location of the
+
+ align:start position:0%
+regardless of the location of the
+ 
+
+ align:start position:0%
+regardless of the location of the
+additional pole the the pole could give
+
+ align:start position:0%
+additional pole the the pole could give
+ 
+
+ align:start position:0%
+additional pole the the pole could give
+us at most minus 90 degrees a phase
+
+ align:start position:0%
+us at most minus 90 degrees a phase
+ 
+
+ align:start position:0%
+us at most minus 90 degrees a phase
+shift that combined with the 45 degrees
+
+ align:start position:0%
+shift that combined with the 45 degrees
+ 
+
+ align:start position:0%
+shift that combined with the 45 degrees
+of negative phase shift associated with
+
+ align:start position:0%
+of negative phase shift associated with
+ 
+
+ align:start position:0%
+of negative phase shift associated with
+the 1 over radical S roll-off would give
+
+ align:start position:0%
+the 1 over radical S roll-off would give
+ 
+
+ align:start position:0%
+the 1 over radical S roll-off would give
+us at most 135 degrees of negative phase
+
+ align:start position:0%
+us at most 135 degrees of negative phase
+ 
+
+ align:start position:0%
+us at most 135 degrees of negative phase
+shift associated with the AF product and
+
+ align:start position:0%
+shift associated with the AF product and
+ 
+
+ align:start position:0%
+shift associated with the AF product and
+so we have at least 45 degrees of phase
+
+ align:start position:0%
+so we have at least 45 degrees of phase
+ 
+
+ align:start position:0%
+so we have at least 45 degrees of phase
+margin we could have more depending on
+
+ align:start position:0%
+margin we could have more depending on
+ 
+
+ align:start position:0%
+margin we could have more depending on
+the exact value of the R 1 C 1 product
+
+ align:start position:0%
+the exact value of the R 1 C 1 product
+ 
+
+ align:start position:0%
+the exact value of the R 1 C 1 product
+but we're guaranteed to have at least 45
+
+ align:start position:0%
+but we're guaranteed to have at least 45
+ 
+
+ align:start position:0%
+but we're guaranteed to have at least 45
+degrees of phase margin well that's fine
+
+ align:start position:0%
+degrees of phase margin well that's fine
+ 
+
+ align:start position:0%
+degrees of phase margin well that's fine
+the only bad news is that one can't
+
+ align:start position:0%
+the only bad news is that one can't
+ 
+
+ align:start position:0%
+the only bad news is that one can't
+realize a radical s Condor 1 over
+
+ align:start position:0%
+realize a radical s Condor 1 over
+ 
+
+ align:start position:0%
+realize a radical s Condor 1 over
+radical s kind of roll
+
+ align:start position:0%
+radical s kind of roll
+ 
+
+ align:start position:0%
+radical s kind of roll
+as a collection of lumped elements there
+
+ align:start position:0%
+as a collection of lumped elements there
+ 
+
+ align:start position:0%
+as a collection of lumped elements there
+are distributed systems that can give us
+
+ align:start position:0%
+are distributed systems that can give us
+ 
+
+ align:start position:0%
+are distributed systems that can give us
+that sort of a transfer function or
+
+ align:start position:0%
+that sort of a transfer function or
+ 
+
+ align:start position:0%
+that sort of a transfer function or
+transfer admittance but you can't do
+
+ align:start position:0%
+transfer admittance but you can't do
+ 
+
+ align:start position:0%
+transfer admittance but you can't do
+that as a as a collection of lumped
+
+ align:start position:0%
+that as a as a collection of lumped
+ 
+
+ align:start position:0%
+that as a as a collection of lumped
+elements but you can approximate it
+
+ align:start position:0%
+elements but you can approximate it
+ 
+
+ align:start position:0%
+elements but you can approximate it
+quite well and the way you do the
+
+ align:start position:0%
+quite well and the way you do the
+ 
+
+ align:start position:0%
+quite well and the way you do the
+approximation is as follows we've
+
+ align:start position:0%
+approximation is as follows we've
+ 
+
+ align:start position:0%
+approximation is as follows we've
+already looked at what happens if you
+
+ align:start position:0%
+already looked at what happens if you
+ 
+
+ align:start position:0%
+already looked at what happens if you
+take a single RC and we found out that
+
+ align:start position:0%
+take a single RC and we found out that
+ 
+
+ align:start position:0%
+take a single RC and we found out that
+in that case one over Y sub C looks
+
+ align:start position:0%
+in that case one over Y sub C looks
+ 
+
+ align:start position:0%
+in that case one over Y sub C looks
+something like so
+
+ align:start position:0%
+something like so
+ 
+
+ align:start position:0%
+something like so
+well now what I can do is add another
+
+ align:start position:0%
+well now what I can do is add another
+ 
+
+ align:start position:0%
+well now what I can do is add another
+parallel branch we might start out with
+
+ align:start position:0%
+parallel branch we might start out with
+ 
+
+ align:start position:0%
+parallel branch we might start out with
+this being a relatively large capacitor
+
+ align:start position:0%
+this being a relatively large capacitor
+ 
+
+ align:start position:0%
+this being a relatively large capacitor
+that gives us the 1 over s roll-off here
+
+ align:start position:0%
+that gives us the 1 over s roll-off here
+ 
+
+ align:start position:0%
+that gives us the 1 over s roll-off here
+we then get to a point the frequency
+
+ align:start position:0%
+we then get to a point the frequency
+ 
+
+ align:start position:0%
+we then get to a point the frequency
+where the admittance of the capacitor
+
+ align:start position:0%
+where the admittance of the capacitor
+ 
+
+ align:start position:0%
+where the admittance of the capacitor
+equals the conductance of this element
+
+ align:start position:0%
+equals the conductance of this element
+ 
+
+ align:start position:0%
+equals the conductance of this element
+and then things fall on a level off the
+
+ align:start position:0%
+and then things fall on a level off the
+ 
+
+ align:start position:0%
+and then things fall on a level off the
+admittance gets no lower we mine now
+
+ align:start position:0%
+admittance gets no lower we mine now
+ 
+
+ align:start position:0%
+admittance gets no lower we mine now
+could add a smaller capacitor and maybe
+
+ align:start position:0%
+could add a smaller capacitor and maybe
+ 
+
+ align:start position:0%
+could add a smaller capacitor and maybe
+another resistor and now what would
+
+ align:start position:0%
+another resistor and now what would
+ 
+
+ align:start position:0%
+another resistor and now what would
+happen is that that at some higher
+
+ align:start position:0%
+happen is that that at some higher
+ 
+
+ align:start position:0%
+happen is that that at some higher
+frequency this capacitor would become
+
+ align:start position:0%
+frequency this capacitor would become
+ 
+
+ align:start position:0%
+frequency this capacitor would become
+important it would now shunt this path
+
+ align:start position:0%
+important it would now shunt this path
+ 
+
+ align:start position:0%
+important it would now shunt this path
+both this capacitor and this resistor
+
+ align:start position:0%
+both this capacitor and this resistor
+ 
+
+ align:start position:0%
+both this capacitor and this resistor
+are smaller in value than their the
+
+ align:start position:0%
+are smaller in value than their the
+ 
+
+ align:start position:0%
+are smaller in value than their the
+corresponding elements in the top rung
+
+ align:start position:0%
+corresponding elements in the top rung
+ 
+
+ align:start position:0%
+corresponding elements in the top rung
+and the net result there might be to
+
+ align:start position:0%
+and the net result there might be to
+ 
+
+ align:start position:0%
+and the net result there might be to
+give us another region of one over s
+
+ align:start position:0%
+give us another region of one over s
+ 
+
+ align:start position:0%
+give us another region of one over s
+roll-off and then another flat region
+
+ align:start position:0%
+roll-off and then another flat region
+ 
+
+ align:start position:0%
+roll-off and then another flat region
+and I think now you can see what we
+
+ align:start position:0%
+and I think now you can see what we
+ 
+
+ align:start position:0%
+and I think now you can see what we
+might do we continue to build up our
+
+ align:start position:0%
+might do we continue to build up our
+ 
+
+ align:start position:0%
+might do we continue to build up our
+network with parallel RC chunks and the
+
+ align:start position:0%
+network with parallel RC chunks and the
+ 
+
+ align:start position:0%
+network with parallel RC chunks and the
+result on one over YC is to have a 1
+
+ align:start position:0%
+result on one over YC is to have a 1
+ 
+
+ align:start position:0%
+result on one over YC is to have a 1
+over s roll-off a flat region a 1 over s
+
+ align:start position:0%
+over s roll-off a flat region a 1 over s
+ 
+
+ align:start position:0%
+over s roll-off a flat region a 1 over s
+roll-off a flat region and so forth and
+
+ align:start position:0%
+roll-off a flat region and so forth and
+ 
+
+ align:start position:0%
+roll-off a flat region and so forth and
+if we space the poles and zeros
+
+ align:start position:0%
+if we space the poles and zeros
+ 
+
+ align:start position:0%
+if we space the poles and zeros
+associated with this transfer function
+
+ align:start position:0%
+associated with this transfer function
+ 
+
+ align:start position:0%
+associated with this transfer function
+closely enough we'd begin to approximate
+
+ align:start position:0%
+closely enough we'd begin to approximate
+ 
+
+ align:start position:0%
+closely enough we'd begin to approximate
+a 1 over radical S roll-off we'd roll
+
+ align:start position:0%
+a 1 over radical S roll-off we'd roll
+ 
+
+ align:start position:0%
+a 1 over radical S roll-off we'd roll
+off as 1 over s half the time on
+
+ align:start position:0%
+off as 1 over s half the time on
+ 
+
+ align:start position:0%
+off as 1 over s half the time on
+logarithmic coordinates B flat half the
+
+ align:start position:0%
+logarithmic coordinates B flat half the
+ 
+
+ align:start position:0%
+logarithmic coordinates B flat half the
+time 1
+
+ align:start position:0%
+time 1
+ 
+
+ align:start position:0%
+time 1
+erratic of one over s and so forth and
+
+ align:start position:0%
+erratic of one over s and so forth and
+ 
+
+ align:start position:0%
+erratic of one over s and so forth and
+begin to approximate a one over radical
+
+ align:start position:0%
+begin to approximate a one over radical
+ 
+
+ align:start position:0%
+begin to approximate a one over radical
+s roll-off so what we would choose to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is use a network it looks something like
+
+ align:start position:0%
+is use a network it looks something like
+ 
+
+ align:start position:0%
+is use a network it looks something like
+this if alphas a number larger than one
+
+ align:start position:0%
+this if alphas a number larger than one
+ 
+
+ align:start position:0%
+this if alphas a number larger than one
+if we start in the middle for example
+
+ align:start position:0%
+if we start in the middle for example
+ 
+
+ align:start position:0%
+if we start in the middle for example
+both resistors and capacitors get larger
+
+ align:start position:0%
+both resistors and capacitors get larger
+ 
+
+ align:start position:0%
+both resistors and capacitors get larger
+as we go this way in the ladder as we go
+
+ align:start position:0%
+as we go this way in the ladder as we go
+ 
+
+ align:start position:0%
+as we go this way in the ladder as we go
+to higher rungs and the ladder resistors
+
+ align:start position:0%
+to higher rungs and the ladder resistors
+ 
+
+ align:start position:0%
+to higher rungs and the ladder resistors
+and capacitors get smaller and you can
+
+ align:start position:0%
+and capacitors get smaller and you can
+ 
+
+ align:start position:0%
+and capacitors get smaller and you can
+chase that through and analyze that sort
+
+ align:start position:0%
+chase that through and analyze that sort
+ 
+
+ align:start position:0%
+chase that through and analyze that sort
+of a network the thing we're really
+
+ align:start position:0%
+of a network the thing we're really
+ 
+
+ align:start position:0%
+of a network the thing we're really
+interested in getting out of this
+
+ align:start position:0%
+interested in getting out of this
+ 
+
+ align:start position:0%
+interested in getting out of this
+network is 45 degrees of phase margin in
+
+ align:start position:0%
+network is 45 degrees of phase margin in
+ 
+
+ align:start position:0%
+network is 45 degrees of phase margin in
+our eventual system in other words we
+
+ align:start position:0%
+our eventual system in other words we
+ 
+
+ align:start position:0%
+our eventual system in other words we
+want the transfer admittance of that
+
+ align:start position:0%
+want the transfer admittance of that
+ 
+
+ align:start position:0%
+want the transfer admittance of that
+thing to have 45 degrees of actually
+
+ align:start position:0%
+thing to have 45 degrees of actually
+ 
+
+ align:start position:0%
+thing to have 45 degrees of actually
+positive phase shift if you look at the
+
+ align:start position:0%
+positive phase shift if you look at the
+ 
+
+ align:start position:0%
+positive phase shift if you look at the
+actual phase shift associated with the
+
+ align:start position:0%
+actual phase shift associated with the
+ 
+
+ align:start position:0%
+actual phase shift associated with the
+transfer admittance of course it ripples
+
+ align:start position:0%
+transfer admittance of course it ripples
+ 
+
+ align:start position:0%
+transfer admittance of course it ripples
+when you're when the transfer admittance
+
+ align:start position:0%
+when you're when the transfer admittance
+ 
+
+ align:start position:0%
+when you're when the transfer admittance
+is going as radical as asks why you have
+
+ align:start position:0%
+is going as radical as asks why you have
+ 
+
+ align:start position:0%
+is going as radical as asks why you have
+90 degrees of phase shift or approaching
+
+ align:start position:0%
+90 degrees of phase shift or approaching
+ 
+
+ align:start position:0%
+90 degrees of phase shift or approaching
+90 degrees of phase shift when the
+
+ align:start position:0%
+90 degrees of phase shift when the
+ 
+
+ align:start position:0%
+90 degrees of phase shift when the
+transfer admittance is constant with
+
+ align:start position:0%
+transfer admittance is constant with
+ 
+
+ align:start position:0%
+transfer admittance is constant with
+frequency you're approaching zero
+
+ align:start position:0%
+frequency you're approaching zero
+ 
+
+ align:start position:0%
+frequency you're approaching zero
+degrees of phase shift and in general
+
+ align:start position:0%
+degrees of phase shift and in general
+ 
+
+ align:start position:0%
+degrees of phase shift and in general
+just as the roll-off of that Network
+
+ align:start position:0%
+just as the roll-off of that Network
+ 
+
+ align:start position:0%
+just as the roll-off of that Network
+ripples so does the phase and you can
+
+ align:start position:0%
+ripples so does the phase and you can
+ 
+
+ align:start position:0%
+ripples so does the phase and you can
+control the amount of ripple really by
+
+ align:start position:0%
+control the amount of ripple really by
+ 
+
+ align:start position:0%
+control the amount of ripple really by
+the closeness of spacing a pole and zero
+
+ align:start position:0%
+the closeness of spacing a pole and zero
+ 
+
+ align:start position:0%
+the closeness of spacing a pole and zero
+pairs or equivalently by the choice of
+
+ align:start position:0%
+pairs or equivalently by the choice of
+ 
+
+ align:start position:0%
+pairs or equivalently by the choice of
+the quantity alpha in this network well
+
+ align:start position:0%
+the quantity alpha in this network well
+ 
+
+ align:start position:0%
+the quantity alpha in this network well
+it turns out that if you use only one
+
+ align:start position:0%
+it turns out that if you use only one
+ 
+
+ align:start position:0%
+it turns out that if you use only one
+pole and one zero per decade you get a
+
+ align:start position:0%
+pole and one zero per decade you get a
+ 
+
+ align:start position:0%
+pole and one zero per decade you get a
+very very good approximation to 45
+
+ align:start position:0%
+very very good approximation to 45
+ 
+
+ align:start position:0%
+very very good approximation to 45
+degrees of phase shift associated with
+
+ align:start position:0%
+degrees of phase shift associated with
+ 
+
+ align:start position:0%
+degrees of phase shift associated with
+the transfer admittance you can choose
+
+ align:start position:0%
+the transfer admittance you can choose
+ 
+
+ align:start position:0%
+the transfer admittance you can choose
+that or you can can look at that
+
+ align:start position:0%
+that or you can can look at that
+ 
+
+ align:start position:0%
+that or you can can look at that
+situation users say a value of alpha
+
+ align:start position:0%
+situation users say a value of alpha
+ 
+
+ align:start position:0%
+situation users say a value of alpha
+that's the square root of 10 which gives
+
+ align:start position:0%
+that's the square root of 10 which gives
+ 
+
+ align:start position:0%
+that's the square root of 10 which gives
+you one pole and one zero in the
+
+ align:start position:0%
+you one pole and one zero in the
+ 
+
+ align:start position:0%
+you one pole and one zero in the
+transfer admittance of the network per
+
+ align:start position:0%
+transfer admittance of the network per
+ 
+
+ align:start position:0%
+transfer admittance of the network per
+decade and frequency and you find out
+
+ align:start position:0%
+decade and frequency and you find out
+ 
+
+ align:start position:0%
+decade and frequency and you find out
+that the peak to peak ripple associated
+
+ align:start position:0%
+that the peak to peak ripple associated
+ 
+
+ align:start position:0%
+that the peak to peak ripple associated
+with the phase shift of that network is
+
+ align:start position:0%
+with the phase shift of that network is
+ 
+
+ align:start position:0%
+with the phase shift of that network is
+only three degrees
+
+ align:start position:0%
+only three degrees
+ 
+
+ align:start position:0%
+only three degrees
+so we can approximate 45 degrees the
+
+ align:start position:0%
+so we can approximate 45 degrees the
+ 
+
+ align:start position:0%
+so we can approximate 45 degrees the
+desired value and the peak to peak
+
+ align:start position:0%
+desired value and the peak to peak
+ 
+
+ align:start position:0%
+desired value and the peak to peak
+ripple associated without approximation
+
+ align:start position:0%
+ripple associated without approximation
+ 
+
+ align:start position:0%
+ripple associated without approximation
+assuming that all of the elements had
+
+ align:start position:0%
+assuming that all of the elements had
+ 
+
+ align:start position:0%
+assuming that all of the elements had
+had the specified values there's no
+
+ align:start position:0%
+had the specified values there's no
+ 
+
+ align:start position:0%
+had the specified values there's no
+component tolerance would only be 3
+
+ align:start position:0%
+component tolerance would only be 3
+ 
+
+ align:start position:0%
+component tolerance would only be 3
+degrees well in order to see how that
+
+ align:start position:0%
+degrees well in order to see how that
+ 
+
+ align:start position:0%
+degrees well in order to see how that
+works we've built up such a network and
+
+ align:start position:0%
+works we've built up such a network and
+ 
+
+ align:start position:0%
+works we've built up such a network and
+and here we have they look a little bit
+
+ align:start position:0%
+and here we have they look a little bit
+ 
+
+ align:start position:0%
+and here we have they look a little bit
+unwieldy this happens to be an 11 wrong
+
+ align:start position:0%
+unwieldy this happens to be an 11 wrong
+ 
+
+ align:start position:0%
+unwieldy this happens to be an 11 wrong
+ladder and what we have are of course
+
+ align:start position:0%
+ladder and what we have are of course
+ 
+
+ align:start position:0%
+ladder and what we have are of course
+simply 11 parallel RC sections this
+
+ align:start position:0%
+simply 11 parallel RC sections this
+ 
+
+ align:start position:0%
+simply 11 parallel RC sections this
+network gives us a 1 over radical s
+
+ align:start position:0%
+network gives us a 1 over radical s
+ 
+
+ align:start position:0%
+network gives us a 1 over radical s
+roll-off from several megahertz to
+
+ align:start position:0%
+roll-off from several megahertz to
+ 
+
+ align:start position:0%
+roll-off from several megahertz to
+fractions of a Hertz again using one RC
+
+ align:start position:0%
+fractions of a Hertz again using one RC
+ 
+
+ align:start position:0%
+fractions of a Hertz again using one RC
+section per decade we get that sort of
+
+ align:start position:0%
+section per decade we get that sort of
+ 
+
+ align:start position:0%
+section per decade we get that sort of
+performance with this kind of a network
+
+ align:start position:0%
+performance with this kind of a network
+ 
+
+ align:start position:0%
+performance with this kind of a network
+what I'd like to do is is investigate
+
+ align:start position:0%
+what I'd like to do is is investigate
+ 
+
+ align:start position:0%
+what I'd like to do is is investigate
+how that sort of a network stabilizes a
+
+ align:start position:0%
+how that sort of a network stabilizes a
+ 
+
+ align:start position:0%
+how that sort of a network stabilizes a
+system pretty much independent of where
+
+ align:start position:0%
+system pretty much independent of where
+ 
+
+ align:start position:0%
+system pretty much independent of where
+we locate an additional pole in the loop
+
+ align:start position:0%
+we locate an additional pole in the loop
+ 
+
+ align:start position:0%
+we locate an additional pole in the loop
+here we have our experimental setup this
+
+ align:start position:0%
+here we have our experimental setup this
+ 
+
+ align:start position:0%
+here we have our experimental setup this
+is a little bit different from the the
+
+ align:start position:0%
+is a little bit different from the the
+ 
+
+ align:start position:0%
+is a little bit different from the the
+past one what I have once again is is
+
+ align:start position:0%
+past one what I have once again is is
+ 
+
+ align:start position:0%
+past one what I have once again is is
+the power supply powering everything a
+
+ align:start position:0%
+the power supply powering everything a
+ 
+
+ align:start position:0%
+the power supply powering everything a
+generator that lets us put steps into
+
+ align:start position:0%
+generator that lets us put steps into
+ 
+
+ align:start position:0%
+generator that lets us put steps into
+our circuit we've changed the board in
+
+ align:start position:0%
+our circuit we've changed the board in
+ 
+
+ align:start position:0%
+our circuit we've changed the board in
+this case here's the circuit itself we
+
+ align:start position:0%
+this case here's the circuit itself we
+ 
+
+ align:start position:0%
+this case here's the circuit itself we
+have the 301 a or the 101 a type app
+
+ align:start position:0%
+have the 301 a or the 101 a type app
+ 
+
+ align:start position:0%
+have the 301 a or the 101 a type app
+let's buffer amplifier and a series of
+
+ align:start position:0%
+let's buffer amplifier and a series of
+ 
+
+ align:start position:0%
+let's buffer amplifier and a series of
+switches on the front the first of all
+
+ align:start position:0%
+switches on the front the first of all
+ 
+
+ align:start position:0%
+switches on the front the first of all
+let us select from various types of
+
+ align:start position:0%
+let us select from various types of
+ 
+
+ align:start position:0%
+let us select from various types of
+compensation also let us select the R 1
+
+ align:start position:0%
+compensation also let us select the R 1
+ 
+
+ align:start position:0%
+compensation also let us select the R 1
+C 1 product so that's what these three
+
+ align:start position:0%
+C 1 product so that's what these three
+ 
+
+ align:start position:0%
+C 1 product so that's what these three
+switches do and what I'd like to
+
+ align:start position:0%
+switches do and what I'd like to
+ 
+
+ align:start position:0%
+switches do and what I'd like to
+initially look at is the behavior of the
+
+ align:start position:0%
+initially look at is the behavior of the
+ 
+
+ align:start position:0%
+initially look at is the behavior of the
+system when we have a single pole
+
+ align:start position:0%
+system when we have a single pole
+ 
+
+ align:start position:0%
+system when we have a single pole
+roll-off associated with the amplifier
+
+ align:start position:0%
+roll-off associated with the amplifier
+ 
+
+ align:start position:0%
+roll-off associated with the amplifier
+and we get that by moving the right hat
+
+ align:start position:0%
+and we get that by moving the right hat
+ 
+
+ align:start position:0%
+and we get that by moving the right hat
+or having the right hand switch in the
+
+ align:start position:0%
+or having the right hand switch in the
+ 
+
+ align:start position:0%
+or having the right hand switch in the
+upward position and we now have removed
+
+ align:start position:0%
+upward position and we now have removed
+ 
+
+ align:start position:0%
+upward position and we now have removed
+the additional pole in the loop the R is
+
+ align:start position:0%
+the additional pole in the loop the R is
+ 
+
+ align:start position:0%
+the additional pole in the loop the R is
+quite small in the seasoned open circuit
+
+ align:start position:0%
+quite small in the seasoned open circuit
+ 
+
+ align:start position:0%
+quite small in the seasoned open circuit
+so we've now removed the additional pole
+
+ align:start position:0%
+so we've now removed the additional pole
+ 
+
+ align:start position:0%
+so we've now removed the additional pole
+and the result of that of course is to
+
+ align:start position:0%
+and the result of that of course is to
+ 
+
+ align:start position:0%
+and the result of that of course is to
+give us effectively an exponential kind
+
+ align:start position:0%
+give us effectively an exponential kind
+ 
+
+ align:start position:0%
+give us effectively an exponential kind
+of response we'd expect when when our
+
+ align:start position:0%
+of response we'd expect when when our
+ 
+
+ align:start position:0%
+of response we'd expect when when our
+blue
+
+ align:start position:0%
+blue
+ 
+
+ align:start position:0%
+blue
+was rolling off as one over s or
+
+ align:start position:0%
+was rolling off as one over s or
+ 
+
+ align:start position:0%
+was rolling off as one over s or
+proportional to 1 over s we get a have a
+
+ align:start position:0%
+proportional to 1 over s we get a have a
+ 
+
+ align:start position:0%
+proportional to 1 over s we get a have a
+first-order system we've chosen numbers
+
+ align:start position:0%
+first-order system we've chosen numbers
+ 
+
+ align:start position:0%
+first-order system we've chosen numbers
+so the crossover in the loop occurs well
+
+ align:start position:0%
+so the crossover in the loop occurs well
+ 
+
+ align:start position:0%
+so the crossover in the loop occurs well
+below any additional phase shifts
+
+ align:start position:0%
+below any additional phase shifts
+ 
+
+ align:start position:0%
+below any additional phase shifts
+associated with the amplifier itself so
+
+ align:start position:0%
+associated with the amplifier itself so
+ 
+
+ align:start position:0%
+associated with the amplifier itself so
+we get a response that looks very very
+
+ align:start position:0%
+we get a response that looks very very
+ 
+
+ align:start position:0%
+we get a response that looks very very
+nearly first-order now let's begin to
+
+ align:start position:0%
+nearly first-order now let's begin to
+ 
+
+ align:start position:0%
+nearly first-order now let's begin to
+add additional poles let me start out
+
+ align:start position:0%
+add additional poles let me start out
+ 
+
+ align:start position:0%
+add additional poles let me start out
+putting in a pole at a megahertz well
+
+ align:start position:0%
+putting in a pole at a megahertz well
+ 
+
+ align:start position:0%
+putting in a pole at a megahertz well
+that doesn't really have much effect on
+
+ align:start position:0%
+that doesn't really have much effect on
+ 
+
+ align:start position:0%
+that doesn't really have much effect on
+the response and say here's a pole going
+
+ align:start position:0%
+the response and say here's a pole going
+ 
+
+ align:start position:0%
+the response and say here's a pole going
+into the megahertz that's actually
+
+ align:start position:0%
+into the megahertz that's actually
+ 
+
+ align:start position:0%
+into the megahertz that's actually
+beyond crossover in this loop and so
+
+ align:start position:0%
+beyond crossover in this loop and so
+ 
+
+ align:start position:0%
+beyond crossover in this loop and so
+there's very little change and there's
+
+ align:start position:0%
+there's very little change and there's
+ 
+
+ align:start position:0%
+there's very little change and there's
+the response we see just a hint of
+
+ align:start position:0%
+the response we see just a hint of
+ 
+
+ align:start position:0%
+the response we see just a hint of
+overshoot but really nothing very
+
+ align:start position:0%
+overshoot but really nothing very
+ 
+
+ align:start position:0%
+overshoot but really nothing very
+dramatic let me move the additional pole
+
+ align:start position:0%
+dramatic let me move the additional pole
+ 
+
+ align:start position:0%
+dramatic let me move the additional pole
+back to a hundred kilohertz by
+
+ align:start position:0%
+back to a hundred kilohertz by
+ 
+
+ align:start position:0%
+back to a hundred kilohertz by
+appropriate choice of the r1 c1 product
+
+ align:start position:0%
+appropriate choice of the r1 c1 product
+ 
+
+ align:start position:0%
+appropriate choice of the r1 c1 product
+I do that by throwing this middle switch
+
+ align:start position:0%
+I do that by throwing this middle switch
+ 
+
+ align:start position:0%
+I do that by throwing this middle switch
+down well now things are getting worse
+
+ align:start position:0%
+down well now things are getting worse
+ 
+
+ align:start position:0%
+down well now things are getting worse
+now the pole actually is occurring in
+
+ align:start position:0%
+now the pole actually is occurring in
+ 
+
+ align:start position:0%
+now the pole actually is occurring in
+the vicinity of crossover in the overall
+
+ align:start position:0%
+the vicinity of crossover in the overall
+ 
+
+ align:start position:0%
+the vicinity of crossover in the overall
+loop and so now we're down to something
+
+ align:start position:0%
+loop and so now we're down to something
+ 
+
+ align:start position:0%
+loop and so now we're down to something
+on the order of 40 degrees 30 degrees of
+
+ align:start position:0%
+on the order of 40 degrees 30 degrees of
+ 
+
+ align:start position:0%
+on the order of 40 degrees 30 degrees of
+phase margin possibly as I say the pole
+
+ align:start position:0%
+phase margin possibly as I say the pole
+ 
+
+ align:start position:0%
+phase margin possibly as I say the pole
+is probably actually a little bit above
+
+ align:start position:0%
+is probably actually a little bit above
+ 
+
+ align:start position:0%
+is probably actually a little bit above
+crossover and so we we get some
+
+ align:start position:0%
+crossover and so we we get some
+ 
+
+ align:start position:0%
+crossover and so we we get some
+significant overshoot let me move the
+
+ align:start position:0%
+significant overshoot let me move the
+ 
+
+ align:start position:0%
+significant overshoot let me move the
+pole down another decade to 10 kilohertz
+
+ align:start position:0%
+pole down another decade to 10 kilohertz
+ 
+
+ align:start position:0%
+pole down another decade to 10 kilohertz
+this is again lowering or increasing the
+
+ align:start position:0%
+this is again lowering or increasing the
+ 
+
+ align:start position:0%
+this is again lowering or increasing the
+value of the r1 c1 product things get
+
+ align:start position:0%
+value of the r1 c1 product things get
+ 
+
+ align:start position:0%
+value of the r1 c1 product things get
+much worse now we're not settling by the
+
+ align:start position:0%
+much worse now we're not settling by the
+ 
+
+ align:start position:0%
+much worse now we're not settling by the
+time the square wave comes along let me
+
+ align:start position:0%
+time the square wave comes along let me
+ 
+
+ align:start position:0%
+time the square wave comes along let me
+slow the generator but now we have
+
+ align:start position:0%
+slow the generator but now we have
+ 
+
+ align:start position:0%
+slow the generator but now we have
+considerable overshoot we're putting in
+
+ align:start position:0%
+considerable overshoot we're putting in
+ 
+
+ align:start position:0%
+considerable overshoot we're putting in
+a three division step and we're getting
+
+ align:start position:0%
+a three division step and we're getting
+ 
+
+ align:start position:0%
+a three division step and we're getting
+60% overshoot or something like that
+
+ align:start position:0%
+60% overshoot or something like that
+ 
+
+ align:start position:0%
+60% overshoot or something like that
+very prolonged transient very poorly
+
+ align:start position:0%
+very prolonged transient very poorly
+ 
+
+ align:start position:0%
+very prolonged transient very poorly
+damn let's try it just one more time
+
+ align:start position:0%
+damn let's try it just one more time
+ 
+
+ align:start position:0%
+damn let's try it just one more time
+that was it with a 10 kilohertz pole
+
+ align:start position:0%
+that was it with a 10 kilohertz pole
+ 
+
+ align:start position:0%
+that was it with a 10 kilohertz pole
+location here's one at 1 kilohertz again
+
+ align:start position:0%
+location here's one at 1 kilohertz again
+ 
+
+ align:start position:0%
+location here's one at 1 kilohertz again
+things haven't quite settled out let me
+
+ align:start position:0%
+things haven't quite settled out let me
+ 
+
+ align:start position:0%
+things haven't quite settled out let me
+slow the generator even further we can
+
+ align:start position:0%
+slow the generator even further we can
+ 
+
+ align:start position:0%
+slow the generator even further we can
+see once again very very nearly a
+
+ align:start position:0%
+see once again very very nearly a
+ 
+
+ align:start position:0%
+see once again very very nearly a
+hundred percent overshoot something like
+
+ align:start position:0%
+hundred percent overshoot something like
+ 
+
+ align:start position:0%
+hundred percent overshoot something like
+90 percent overshoot a very very
+
+ align:start position:0%
+90 percent overshoot a very very
+ 
+
+ align:start position:0%
+90 percent overshoot a very very
+prolonged settling
+
+ align:start position:0%
+prolonged settling
+ 
+
+ align:start position:0%
+prolonged settling
+let's see if we can do it just one more
+
+ align:start position:0%
+let's see if we can do it just one more
+ 
+
+ align:start position:0%
+let's see if we can do it just one more
+time move the pole down to a hundred
+
+ align:start position:0%
+time move the pole down to a hundred
+ 
+
+ align:start position:0%
+time move the pole down to a hundred
+Hertz and I don't know whether we can
+
+ align:start position:0%
+Hertz and I don't know whether we can
+ 
+
+ align:start position:0%
+Hertz and I don't know whether we can
+slow things enough to observe that or
+
+ align:start position:0%
+slow things enough to observe that or
+ 
+
+ align:start position:0%
+slow things enough to observe that or
+not but I'm just going to lower drive
+
+ align:start position:0%
+not but I'm just going to lower drive
+ 
+
+ align:start position:0%
+not but I'm just going to lower drive
+frequencies at present and here we see a
+
+ align:start position:0%
+frequencies at present and here we see a
+ 
+
+ align:start position:0%
+frequencies at present and here we see a
+very very poorly damped transient let's
+
+ align:start position:0%
+very very poorly damped transient let's
+ 
+
+ align:start position:0%
+very very poorly damped transient let's
+go back to one that's a little bit
+
+ align:start position:0%
+go back to one that's a little bit
+ 
+
+ align:start position:0%
+go back to one that's a little bit
+easier to observe here we are again with
+
+ align:start position:0%
+easier to observe here we are again with
+ 
+
+ align:start position:0%
+easier to observe here we are again with
+a transient response that corresponds to
+
+ align:start position:0%
+a transient response that corresponds to
+ 
+
+ align:start position:0%
+a transient response that corresponds to
+a 1 kilohertz pole location associated
+
+ align:start position:0%
+a 1 kilohertz pole location associated
+ 
+
+ align:start position:0%
+a 1 kilohertz pole location associated
+with R 1 C 1 so we see that when we use
+
+ align:start position:0%
+with R 1 C 1 so we see that when we use
+ 
+
+ align:start position:0%
+with R 1 C 1 so we see that when we use
+that sort of compensation the one over s
+
+ align:start position:0%
+that sort of compensation the one over s
+ 
+
+ align:start position:0%
+that sort of compensation the one over s
+compensation in the loop where we can
+
+ align:start position:0%
+compensation in the loop where we can
+ 
+
+ align:start position:0%
+compensation in the loop where we can
+add an additional pole we're able to get
+
+ align:start position:0%
+add an additional pole we're able to get
+ 
+
+ align:start position:0%
+add an additional pole we're able to get
+into very very severe stability problems
+
+ align:start position:0%
+into very very severe stability problems
+ 
+
+ align:start position:0%
+into very very severe stability problems
+we have another version of the one over
+
+ align:start position:0%
+we have another version of the one over
+ 
+
+ align:start position:0%
+we have another version of the one over
+radical S Network here somewhat better
+
+ align:start position:0%
+radical S Network here somewhat better
+ 
+
+ align:start position:0%
+radical S Network here somewhat better
+behaved Network or at least easier to
+
+ align:start position:0%
+behaved Network or at least easier to
+ 
+
+ align:start position:0%
+behaved Network or at least easier to
+use rather than have it spread out and
+
+ align:start position:0%
+use rather than have it spread out and
+ 
+
+ align:start position:0%
+use rather than have it spread out and
+in the Jacob's Ladder kind of
+
+ align:start position:0%
+in the Jacob's Ladder kind of
+ 
+
+ align:start position:0%
+in the Jacob's Ladder kind of
+configuration this is a little bit
+
+ align:start position:0%
+configuration this is a little bit
+ 
+
+ align:start position:0%
+configuration this is a little bit
+easier to use in our test setup let's go
+
+ align:start position:0%
+easier to use in our test setup let's go
+ 
+
+ align:start position:0%
+easier to use in our test setup let's go
+back to the situation where we have the
+
+ align:start position:0%
+back to the situation where we have the
+ 
+
+ align:start position:0%
+back to the situation where we have the
+the actual the R 1 C 1 pole located at
+
+ align:start position:0%
+the actual the R 1 C 1 pole located at
+ 
+
+ align:start position:0%
+the actual the R 1 C 1 pole located at
+very high frequencies and then let me
+
+ align:start position:0%
+very high frequencies and then let me
+ 
+
+ align:start position:0%
+very high frequencies and then let me
+add the network that compensates our
+
+ align:start position:0%
+add the network that compensates our
+ 
+
+ align:start position:0%
+add the network that compensates our
+loop for one over radical s behavior and
+
+ align:start position:0%
+loop for one over radical s behavior and
+ 
+
+ align:start position:0%
+loop for one over radical s behavior and
+let's look at at that response
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens here is that we get a very
+
+ align:start position:0%
+what happens here is that we get a very
+ 
+
+ align:start position:0%
+what happens here is that we get a very
+long tail if you will we spoke a little
+
+ align:start position:0%
+long tail if you will we spoke a little
+ 
+
+ align:start position:0%
+long tail if you will we spoke a little
+bit about this prolonged settling
+
+ align:start position:0%
+bit about this prolonged settling
+ 
+
+ align:start position:0%
+bit about this prolonged settling
+transient that results when we have a
+
+ align:start position:0%
+transient that results when we have a
+ 
+
+ align:start position:0%
+transient that results when we have a
+pole 0 doublet we looked at that in
+
+ align:start position:0%
+pole 0 doublet we looked at that in
+ 
+
+ align:start position:0%
+pole 0 doublet we looked at that in
+conjunction with the one over s squared
+
+ align:start position:0%
+conjunction with the one over s squared
+ 
+
+ align:start position:0%
+conjunction with the one over s squared
+compensation last time I mentioned the
+
+ align:start position:0%
+compensation last time I mentioned the
+ 
+
+ align:start position:0%
+compensation last time I mentioned the
+same kind of thing happens with a lag
+
+ align:start position:0%
+same kind of thing happens with a lag
+ 
+
+ align:start position:0%
+same kind of thing happens with a lag
+Network well here we have an extreme
+
+ align:start position:0%
+Network well here we have an extreme
+ 
+
+ align:start position:0%
+Network well here we have an extreme
+example of this kind of thing the effect
+
+ align:start position:0%
+example of this kind of thing the effect
+ 
+
+ align:start position:0%
+example of this kind of thing the effect
+of using the one over the approximation
+
+ align:start position:0%
+of using the one over the approximation
+ 
+
+ align:start position:0%
+of using the one over the approximation
+to the 1 over radical s roll-off is that
+
+ align:start position:0%
+to the 1 over radical s roll-off is that
+ 
+
+ align:start position:0%
+to the 1 over radical s roll-off is that
+we end up with an open-loop transfer
+
+ align:start position:0%
+we end up with an open-loop transfer
+ 
+
+ align:start position:0%
+we end up with an open-loop transfer
+function that has a poles and zeros
+
+ align:start position:0%
+function that has a poles and zeros
+ 
+
+ align:start position:0%
+function that has a poles and zeros
+alternated along the negative real axis
+
+ align:start position:0%
+alternated along the negative real axis
+ 
+
+ align:start position:0%
+alternated along the negative real axis
+and if we draw a root locus diagram for
+
+ align:start position:0%
+and if we draw a root locus diagram for
+ 
+
+ align:start position:0%
+and if we draw a root locus diagram for
+that we end up with a very large
+
+ align:start position:0%
+that we end up with a very large
+ 
+
+ align:start position:0%
+that we end up with a very large
+collection of pole 0 doublets in this
+
+ align:start position:0%
+collection of pole 0 doublets in this
+ 
+
+ align:start position:0%
+collection of pole 0 doublets in this
+case 11 and we get a very very long
+
+ align:start position:0%
+case 11 and we get a very very long
+ 
+
+ align:start position:0%
+case 11 and we get a very very long
+tortured settling to final value and we
+
+ align:start position:0%
+tortured settling to final value and we
+ 
+
+ align:start position:0%
+tortured settling to final value and we
+can see that final value is is has not
+
+ align:start position:0%
+can see that final value is is has not
+ 
+
+ align:start position:0%
+can see that final value is is has not
+even been reached here yet we go half
+
+ align:start position:0%
+even been reached here yet we go half
+ 
+
+ align:start position:0%
+even been reached here yet we go half
+way or so to final value quite quickly
+
+ align:start position:0%
+way or so to final value quite quickly
+ 
+
+ align:start position:0%
+way or so to final value quite quickly
+we go half way in a few microseconds
+
+ align:start position:0%
+we go half way in a few microseconds
+ 
+
+ align:start position:0%
+we go half way in a few microseconds
+we're 5 microseconds per division one
+
+ align:start position:0%
+we're 5 microseconds per division one
+ 
+
+ align:start position:0%
+we're 5 microseconds per division one
+and a half divisions vertically is half
+
+ align:start position:0%
+and a half divisions vertically is half
+ 
+
+ align:start position:0%
+and a half divisions vertically is half
+a final value but 500 microseconds later
+
+ align:start position:0%
+a final value but 500 microseconds later
+ 
+
+ align:start position:0%
+a final value but 500 microseconds later
+we're still settling and in fact if we
+
+ align:start position:0%
+we're still settling and in fact if we
+ 
+
+ align:start position:0%
+we're still settling and in fact if we
+examine things very carefully half a
+
+ align:start position:0%
+examine things very carefully half a
+ 
+
+ align:start position:0%
+examine things very carefully half a
+millisecond there are 5 milliseconds
+
+ align:start position:0%
+millisecond there are 5 milliseconds
+ 
+
+ align:start position:0%
+millisecond there are 5 milliseconds
+later the transient response is still
+
+ align:start position:0%
+later the transient response is still
+ 
+
+ align:start position:0%
+later the transient response is still
+settling and that reflects the
+
+ align:start position:0%
+settling and that reflects the
+ 
+
+ align:start position:0%
+settling and that reflects the
+collection of closely spaced called zero
+
+ align:start position:0%
+collection of closely spaced called zero
+ 
+
+ align:start position:0%
+collection of closely spaced called zero
+doublets that result when this sort of
+
+ align:start position:0%
+doublets that result when this sort of
+ 
+
+ align:start position:0%
+doublets that result when this sort of
+compensation is used the good news is
+
+ align:start position:0%
+compensation is used the good news is
+ 
+
+ align:start position:0%
+compensation is used the good news is
+that we get very dramatically improved
+
+ align:start position:0%
+that we get very dramatically improved
+ 
+
+ align:start position:0%
+that we get very dramatically improved
+stability as we add capacitive loads or
+
+ align:start position:0%
+stability as we add capacitive loads or
+ 
+
+ align:start position:0%
+stability as we add capacitive loads or
+an additional pole in the loop
+
+ align:start position:0%
+an additional pole in the loop
+ 
+
+ align:start position:0%
+an additional pole in the loop
+transmission let me first of all add the
+
+ align:start position:0%
+transmission let me first of all add the
+ 
+
+ align:start position:0%
+transmission let me first of all add the
+pole at at a hundred or at one megahertz
+
+ align:start position:0%
+pole at at a hundred or at one megahertz
+ 
+
+ align:start position:0%
+pole at at a hundred or at one megahertz
+again not much happens that is a
+
+ align:start position:0%
+again not much happens that is a
+ 
+
+ align:start position:0%
+again not much happens that is a
+sufficiently high frequency so that not
+
+ align:start position:0%
+sufficiently high frequency so that not
+ 
+
+ align:start position:0%
+sufficiently high frequency so that not
+much changes but now let's go to 100
+
+ align:start position:0%
+much changes but now let's go to 100
+ 
+
+ align:start position:0%
+much changes but now let's go to 100
+kilohertz and this was a case where we
+
+ align:start position:0%
+kilohertz and this was a case where we
+ 
+
+ align:start position:0%
+kilohertz and this was a case where we
+were beginning to get measurable
+
+ align:start position:0%
+were beginning to get measurable
+ 
+
+ align:start position:0%
+were beginning to get measurable
+significant overshoot when we used one
+
+ align:start position:0%
+significant overshoot when we used one
+ 
+
+ align:start position:0%
+significant overshoot when we used one
+over s compensation
+
+ align:start position:0%
+over s compensation
+ 
+
+ align:start position:0%
+over s compensation
+here things are still very well-behaved
+
+ align:start position:0%
+here things are still very well-behaved
+ 
+
+ align:start position:0%
+here things are still very well-behaved
+in fact we really can't discern any
+
+ align:start position:0%
+in fact we really can't discern any
+ 
+
+ align:start position:0%
+in fact we really can't discern any
+overshoot a little ripple but but we
+
+ align:start position:0%
+overshoot a little ripple but but we
+ 
+
+ align:start position:0%
+overshoot a little ripple but but we
+really don't see any overshoot
+
+ align:start position:0%
+really don't see any overshoot
+ 
+
+ align:start position:0%
+really don't see any overshoot
+let's move the pole back to 10 kilohertz
+
+ align:start position:0%
+let's move the pole back to 10 kilohertz
+ 
+
+ align:start position:0%
+let's move the pole back to 10 kilohertz
+getting a little bit of overshoot but
+
+ align:start position:0%
+getting a little bit of overshoot but
+ 
+
+ align:start position:0%
+getting a little bit of overshoot but
+very very well-behaved response now
+
+ align:start position:0%
+very very well-behaved response now
+ 
+
+ align:start position:0%
+very very well-behaved response now
+let's go to a kilohertz rather than 10
+
+ align:start position:0%
+let's go to a kilohertz rather than 10
+ 
+
+ align:start position:0%
+let's go to a kilohertz rather than 10
+kilohertz do this okay there we are with
+
+ align:start position:0%
+kilohertz do this okay there we are with
+ 
+
+ align:start position:0%
+kilohertz do this okay there we are with
+the network giving us a pole at at one
+
+ align:start position:0%
+the network giving us a pole at at one
+ 
+
+ align:start position:0%
+the network giving us a pole at at one
+kilohertz very well behaved response
+
+ align:start position:0%
+kilohertz very well behaved response
+ 
+
+ align:start position:0%
+kilohertz very well behaved response
+reflecting the approximately 45 degrees
+
+ align:start position:0%
+reflecting the approximately 45 degrees
+ 
+
+ align:start position:0%
+reflecting the approximately 45 degrees
+of phase margin let's go to a hundred
+
+ align:start position:0%
+of phase margin let's go to a hundred
+ 
+
+ align:start position:0%
+of phase margin let's go to a hundred
+Hertz things get slower fact much slower
+
+ align:start position:0%
+Hertz things get slower fact much slower
+ 
+
+ align:start position:0%
+Hertz things get slower fact much slower
+but the basic shape of the response now
+
+ align:start position:0%
+but the basic shape of the response now
+ 
+
+ align:start position:0%
+but the basic shape of the response now
+remains almost invariant here's the
+
+ align:start position:0%
+remains almost invariant here's the
+ 
+
+ align:start position:0%
+remains almost invariant here's the
+response with the RC pole located at a
+
+ align:start position:0%
+response with the RC pole located at a
+ 
+
+ align:start position:0%
+response with the RC pole located at a
+hundred Hertz here's the response with
+
+ align:start position:0%
+hundred Hertz here's the response with
+ 
+
+ align:start position:0%
+hundred Hertz here's the response with
+it located to the kilohertz comparable
+
+ align:start position:0%
+it located to the kilohertz comparable
+ 
+
+ align:start position:0%
+it located to the kilohertz comparable
+kinds of responses in terms of stability
+
+ align:start position:0%
+kinds of responses in terms of stability
+ 
+
+ align:start position:0%
+kinds of responses in terms of stability
+a little bit more overshoot here I think
+
+ align:start position:0%
+a little bit more overshoot here I think
+ 
+
+ align:start position:0%
+a little bit more overshoot here I think
+that reflects the ripple in the phase
+
+ align:start position:0%
+that reflects the ripple in the phase
+ 
+
+ align:start position:0%
+that reflects the ripple in the phase
+curve and probably the ripple is more
+
+ align:start position:0%
+curve and probably the ripple is more
+ 
+
+ align:start position:0%
+curve and probably the ripple is more
+than three degrees peak to peak because
+
+ align:start position:0%
+than three degrees peak to peak because
+ 
+
+ align:start position:0%
+than three degrees peak to peak because
+of component tolerances let's locate the
+
+ align:start position:0%
+of component tolerances let's locate the
+ 
+
+ align:start position:0%
+of component tolerances let's locate the
+pole at ten Hertz we weren't even able
+
+ align:start position:0%
+pole at ten Hertz we weren't even able
+ 
+
+ align:start position:0%
+pole at ten Hertz we weren't even able
+to do that with one over s compensation
+
+ align:start position:0%
+to do that with one over s compensation
+ 
+
+ align:start position:0%
+to do that with one over s compensation
+things do get slower but we have a still
+
+ align:start position:0%
+things do get slower but we have a still
+ 
+
+ align:start position:0%
+things do get slower but we have a still
+a very well behaved response not
+
+ align:start position:0%
+a very well behaved response not
+ 
+
+ align:start position:0%
+a very well behaved response not
+excessive overshoot and so we're able to
+
+ align:start position:0%
+excessive overshoot and so we're able to
+ 
+
+ align:start position:0%
+excessive overshoot and so we're able to
+stabilize the system notice that as we
+
+ align:start position:0%
+stabilize the system notice that as we
+ 
+
+ align:start position:0%
+stabilize the system notice that as we
+did this I've been moving the pole over
+
+ align:start position:0%
+did this I've been moving the pole over
+ 
+
+ align:start position:0%
+did this I've been moving the pole over
+five decades I started at a megahertz
+
+ align:start position:0%
+five decades I started at a megahertz
+ 
+
+ align:start position:0%
+five decades I started at a megahertz
+got all the way down to ten Hertz and we
+
+ align:start position:0%
+got all the way down to ten Hertz and we
+ 
+
+ align:start position:0%
+got all the way down to ten Hertz and we
+still get very very acceptable transient
+
+ align:start position:0%
+still get very very acceptable transient
+ 
+
+ align:start position:0%
+still get very very acceptable transient
+response so as the pole moves over in
+
+ align:start position:0%
+response so as the pole moves over in
+ 
+
+ align:start position:0%
+response so as the pole moves over in
+this case ten decades in frequency we
+
+ align:start position:0%
+this case ten decades in frequency we
+ 
+
+ align:start position:0%
+this case ten decades in frequency we
+still get very acceptable performance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well one may question the practicality
+
+ align:start position:0%
+well one may question the practicality
+ 
+
+ align:start position:0%
+well one may question the practicality
+of using this sort of a network to
+
+ align:start position:0%
+of using this sort of a network to
+ 
+
+ align:start position:0%
+of using this sort of a network to
+compensate an operational amplifier
+
+ align:start position:0%
+compensate an operational amplifier
+ 
+
+ align:start position:0%
+compensate an operational amplifier
+fortunately there's a middle ground we
+
+ align:start position:0%
+fortunately there's a middle ground we
+ 
+
+ align:start position:0%
+fortunately there's a middle ground we
+found out that an approximation that
+
+ align:start position:0%
+found out that an approximation that
+ 
+
+ align:start position:0%
+found out that an approximation that
+uses one pole in one zero per decade did
+
+ align:start position:0%
+uses one pole in one zero per decade did
+ 
+
+ align:start position:0%
+uses one pole in one zero per decade did
+a pretty good job let's consider a very
+
+ align:start position:0%
+a pretty good job let's consider a very
+ 
+
+ align:start position:0%
+a pretty good job let's consider a very
+crude approximation to the ladder just a
+
+ align:start position:0%
+crude approximation to the ladder just a
+ 
+
+ align:start position:0%
+crude approximation to the ladder just a
+two wrong ladder and in fact let's
+
+ align:start position:0%
+two wrong ladder and in fact let's
+ 
+
+ align:start position:0%
+two wrong ladder and in fact let's
+choose things such that the capacitors
+
+ align:start position:0%
+choose things such that the capacitors
+ 
+
+ align:start position:0%
+choose things such that the capacitors
+have a ratio of ten to one by doing that
+
+ align:start position:0%
+have a ratio of ten to one by doing that
+ 
+
+ align:start position:0%
+have a ratio of ten to one by doing that
+we can end up with a very crude
+
+ align:start position:0%
+we can end up with a very crude
+ 
+
+ align:start position:0%
+we can end up with a very crude
+approximation to the one over radical s
+
+ align:start position:0%
+approximation to the one over radical s
+ 
+
+ align:start position:0%
+approximation to the one over radical s
+roll-off let's see what I've shown here
+
+ align:start position:0%
+roll-off let's see what I've shown here
+ 
+
+ align:start position:0%
+roll-off let's see what I've shown here
+normalized to attend to the sixth Radian
+
+ align:start position:0%
+normalized to attend to the sixth Radian
+ 
+
+ align:start position:0%
+normalized to attend to the sixth Radian
+per second crossover frequency is first
+
+ align:start position:0%
+per second crossover frequency is first
+ 
+
+ align:start position:0%
+per second crossover frequency is first
+of all a transfer function that's
+
+ align:start position:0%
+of all a transfer function that's
+ 
+
+ align:start position:0%
+of all a transfer function that's
+falling off as 1 over s that has minus
+
+ align:start position:0%
+falling off as 1 over s that has minus
+ 
+
+ align:start position:0%
+falling off as 1 over s that has minus
+90 degrees a phase shift at all
+
+ align:start position:0%
+90 degrees a phase shift at all
+ 
+
+ align:start position:0%
+90 degrees a phase shift at all
+frequencies I then show a network or an
+
+ align:start position:0%
+frequencies I then show a network or an
+ 
+
+ align:start position:0%
+frequencies I then show a network or an
+amplifier that's rolling off as 1 over
+
+ align:start position:0%
+amplifier that's rolling off as 1 over
+ 
+
+ align:start position:0%
+amplifier that's rolling off as 1 over
+radical s that has minus 45 degrees a
+
+ align:start position:0%
+radical s that has minus 45 degrees a
+ 
+
+ align:start position:0%
+radical s that has minus 45 degrees a
+phase shift at all frequencies here I
+
+ align:start position:0%
+phase shift at all frequencies here I
+ 
+
+ align:start position:0%
+phase shift at all frequencies here I
+show a transfer function that rolls off
+
+ align:start position:0%
+show a transfer function that rolls off
+ 
+
+ align:start position:0%
+show a transfer function that rolls off
+as 1 over s from the unity gain
+
+ align:start position:0%
+as 1 over s from the unity gain
+ 
+
+ align:start position:0%
+as 1 over s from the unity gain
+frequency back to a decade below the
+
+ align:start position:0%
+frequency back to a decade below the
+ 
+
+ align:start position:0%
+frequency back to a decade below the
+unity gain frequency it then flattens
+
+ align:start position:0%
+unity gain frequency it then flattens
+ 
+
+ align:start position:0%
+unity gain frequency it then flattens
+out for another decade from here to here
+
+ align:start position:0%
+out for another decade from here to here
+ 
+
+ align:start position:0%
+out for another decade from here to here
+and then once again rolls off as 1 over
+
+ align:start position:0%
+and then once again rolls off as 1 over
+ 
+
+ align:start position:0%
+and then once again rolls off as 1 over
+s below that so this is a very crude
+
+ align:start position:0%
+s below that so this is a very crude
+ 
+
+ align:start position:0%
+s below that so this is a very crude
+approximation to the 1 over radical s
+
+ align:start position:0%
+approximation to the 1 over radical s
+ 
+
+ align:start position:0%
+approximation to the 1 over radical s
+kind of roll off the corresponding phase
+
+ align:start position:0%
+kind of roll off the corresponding phase
+ 
+
+ align:start position:0%
+kind of roll off the corresponding phase
+characteristics are like this but that's
+
+ align:start position:0%
+characteristics are like this but that's
+ 
+
+ align:start position:0%
+characteristics are like this but that's
+a very achievable Network we can do that
+
+ align:start position:0%
+a very achievable Network we can do that
+ 
+
+ align:start position:0%
+a very achievable Network we can do that
+as a say with with just two capacitors
+
+ align:start position:0%
+as a say with with just two capacitors
+ 
+
+ align:start position:0%
+as a say with with just two capacitors
+and a resistor as I've shown and let's
+
+ align:start position:0%
+and a resistor as I've shown and let's
+ 
+
+ align:start position:0%
+and a resistor as I've shown and let's
+look at the results of that let me
+
+ align:start position:0%
+look at the results of that let me
+ 
+
+ align:start position:0%
+look at the results of that let me
+remove the one over radical s kind of
+
+ align:start position:0%
+remove the one over radical s kind of
+ 
+
+ align:start position:0%
+remove the one over radical s kind of
+Network this one let's go back to the
+
+ align:start position:0%
+Network this one let's go back to the
+ 
+
+ align:start position:0%
+Network this one let's go back to the
+very high frequency location for the RC
+
+ align:start position:0%
+very high frequency location for the RC
+ 
+
+ align:start position:0%
+very high frequency location for the RC
+pole
+
+ align:start position:0%
+pole
+ 
+
+ align:start position:0%
+pole
+and let's speed up things now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what we find is again a delayed
+
+ align:start position:0%
+well what we find is again a delayed
+ 
+
+ align:start position:0%
+well what we find is again a delayed
+settling time this sort of compensation
+
+ align:start position:0%
+settling time this sort of compensation
+ 
+
+ align:start position:0%
+settling time this sort of compensation
+again gives us a pole-zero doublet if we
+
+ align:start position:0%
+again gives us a pole-zero doublet if we
+ 
+
+ align:start position:0%
+again gives us a pole-zero doublet if we
+look at it we get to about 90% of final
+
+ align:start position:0%
+look at it we get to about 90% of final
+ 
+
+ align:start position:0%
+look at it we get to about 90% of final
+value very quickly on the leading edge
+
+ align:start position:0%
+value very quickly on the leading edge
+ 
+
+ align:start position:0%
+value very quickly on the leading edge
+but it takes us much much longer the
+
+ align:start position:0%
+but it takes us much much longer the
+ 
+
+ align:start position:0%
+but it takes us much much longer the
+response is basically two Exponential's
+
+ align:start position:0%
+response is basically two Exponential's
+ 
+
+ align:start position:0%
+response is basically two Exponential's
+one of which has a much longer time
+
+ align:start position:0%
+one of which has a much longer time
+ 
+
+ align:start position:0%
+one of which has a much longer time
+constant than the other one and we see
+
+ align:start position:0%
+constant than the other one and we see
+ 
+
+ align:start position:0%
+constant than the other one and we see
+the quite prolonged settling to final
+
+ align:start position:0%
+the quite prolonged settling to final
+ 
+
+ align:start position:0%
+the quite prolonged settling to final
+value let's begin to add the pole this
+
+ align:start position:0%
+value let's begin to add the pole this
+ 
+
+ align:start position:0%
+value let's begin to add the pole this
+is with the additional pole loop at
+
+ align:start position:0%
+is with the additional pole loop at
+ 
+
+ align:start position:0%
+is with the additional pole loop at
+infinite frequency effectively now let's
+
+ align:start position:0%
+infinite frequency effectively now let's
+ 
+
+ align:start position:0%
+infinite frequency effectively now let's
+go ahead and add the pole at one
+
+ align:start position:0%
+go ahead and add the pole at one
+ 
+
+ align:start position:0%
+go ahead and add the pole at one
+megahertz again not much effect we see
+
+ align:start position:0%
+megahertz again not much effect we see
+ 
+
+ align:start position:0%
+megahertz again not much effect we see
+just a little peaking we can begin to
+
+ align:start position:0%
+just a little peaking we can begin to
+ 
+
+ align:start position:0%
+just a little peaking we can begin to
+lower the location of the additional
+
+ align:start position:0%
+lower the location of the additional
+ 
+
+ align:start position:0%
+lower the location of the additional
+pole in the loop here's 100 kilohertz
+
+ align:start position:0%
+pole in the loop here's 100 kilohertz
+ 
+
+ align:start position:0%
+pole in the loop here's 100 kilohertz
+well behaved 10 kilohertz notice this is
+
+ align:start position:0%
+well behaved 10 kilohertz notice this is
+ 
+
+ align:start position:0%
+well behaved 10 kilohertz notice this is
+actually better damped than the one
+
+ align:start position:0%
+actually better damped than the one
+ 
+
+ align:start position:0%
+actually better damped than the one
+corresponding to the pole location at
+
+ align:start position:0%
+corresponding to the pole location at
+ 
+
+ align:start position:0%
+corresponding to the pole location at
+100 kilohertz that's not surprising the
+
+ align:start position:0%
+100 kilohertz that's not surprising the
+ 
+
+ align:start position:0%
+100 kilohertz that's not surprising the
+phase of this network this very simple
+
+ align:start position:0%
+phase of this network this very simple
+ 
+
+ align:start position:0%
+phase of this network this very simple
+approximation to a 1 over radical S
+
+ align:start position:0%
+approximation to a 1 over radical S
+ 
+
+ align:start position:0%
+approximation to a 1 over radical S
+network change is far more violently as
+
+ align:start position:0%
+network change is far more violently as
+ 
+
+ align:start position:0%
+network change is far more violently as
+a function of frequency then does the
+
+ align:start position:0%
+a function of frequency then does the
+ 
+
+ align:start position:0%
+a function of frequency then does the
+one over radical s approximation using
+
+ align:start position:0%
+one over radical s approximation using
+ 
+
+ align:start position:0%
+one over radical s approximation using
+the much better
+
+ align:start position:0%
+the much better
+ 
+
+ align:start position:0%
+the much better
+ladder with considerably more and larger
+
+ align:start position:0%
+ladder with considerably more and larger
+ 
+
+ align:start position:0%
+ladder with considerably more and larger
+number of rungs so it's not surprising
+
+ align:start position:0%
+number of rungs so it's not surprising
+ 
+
+ align:start position:0%
+number of rungs so it's not surprising
+that relative stability is is more
+
+ align:start position:0%
+that relative stability is is more
+ 
+
+ align:start position:0%
+that relative stability is is more
+dependent on the exact location of the
+
+ align:start position:0%
+dependent on the exact location of the
+ 
+
+ align:start position:0%
+dependent on the exact location of the
+additional pole here's one of the
+
+ align:start position:0%
+additional pole here's one of the
+ 
+
+ align:start position:0%
+additional pole here's one of the
+kilohertz have to slow things down again
+
+ align:start position:0%
+kilohertz have to slow things down again
+ 
+
+ align:start position:0%
+kilohertz have to slow things down again
+relative to the pole location at 10
+
+ align:start position:0%
+relative to the pole location at 10
+ 
+
+ align:start position:0%
+relative to the pole location at 10
+kilohertz we have poor stability at a
+
+ align:start position:0%
+kilohertz we have poor stability at a
+ 
+
+ align:start position:0%
+kilohertz we have poor stability at a
+hundred Hertz considerably poor
+
+ align:start position:0%
+hundred Hertz considerably poor
+ 
+
+ align:start position:0%
+hundred Hertz considerably poor
+stability once again and beyond this we
+
+ align:start position:0%
+stability once again and beyond this we
+ 
+
+ align:start position:0%
+stability once again and beyond this we
+begin to lose things quite dramatically
+
+ align:start position:0%
+begin to lose things quite dramatically
+ 
+
+ align:start position:0%
+begin to lose things quite dramatically
+but again at this point the one over s
+
+ align:start position:0%
+but again at this point the one over s
+ 
+
+ align:start position:0%
+but again at this point the one over s
+compensation was had just completely
+
+ align:start position:0%
+compensation was had just completely
+ 
+
+ align:start position:0%
+compensation was had just completely
+lost in fact we had a lot of trouble
+
+ align:start position:0%
+lost in fact we had a lot of trouble
+ 
+
+ align:start position:0%
+lost in fact we had a lot of trouble
+with one over s compensation when we
+
+ align:start position:0%
+with one over s compensation when we
+ 
+
+ align:start position:0%
+with one over s compensation when we
+located the pole at one kilohertz here
+
+ align:start position:0%
+located the pole at one kilohertz here
+ 
+
+ align:start position:0%
+located the pole at one kilohertz here
+the thing I hear the
+
+ align:start position:0%
+the thing I hear the
+ 
+
+ align:start position:0%
+the thing I hear the
+system is very well behaved with this
+
+ align:start position:0%
+system is very well behaved with this
+ 
+
+ align:start position:0%
+system is very well behaved with this
+very simple compensating network when
+
+ align:start position:0%
+very simple compensating network when
+ 
+
+ align:start position:0%
+very simple compensating network when
+the poles of 1 kilohertz if you look at
+
+ align:start position:0%
+the poles of 1 kilohertz if you look at
+ 
+
+ align:start position:0%
+the poles of 1 kilohertz if you look at
+at this in in detail you find that you
+
+ align:start position:0%
+at this in in detail you find that you
+ 
+
+ align:start position:0%
+at this in in detail you find that you
+can maintain something like 30 degrees
+
+ align:start position:0%
+can maintain something like 30 degrees
+ 
+
+ align:start position:0%
+can maintain something like 30 degrees
+of phase margin as a minimum until you
+
+ align:start position:0%
+of phase margin as a minimum until you
+ 
+
+ align:start position:0%
+of phase margin as a minimum until you
+move the additional pole back to
+
+ align:start position:0%
+move the additional pole back to
+ 
+
+ align:start position:0%
+move the additional pole back to
+somewhere on the order of a kilohertz or
+
+ align:start position:0%
+somewhere on the order of a kilohertz or
+ 
+
+ align:start position:0%
+somewhere on the order of a kilohertz or
+actually below that so you're able to
+
+ align:start position:0%
+actually below that so you're able to
+ 
+
+ align:start position:0%
+actually below that so you're able to
+move the pole from crossover back by
+
+ align:start position:0%
+move the pole from crossover back by
+ 
+
+ align:start position:0%
+move the pole from crossover back by
+approximately three decades before you
+
+ align:start position:0%
+approximately three decades before you
+ 
+
+ align:start position:0%
+approximately three decades before you
+begin to get into serious stability
+
+ align:start position:0%
+begin to get into serious stability
+ 
+
+ align:start position:0%
+begin to get into serious stability
+problems the implication is that we can
+
+ align:start position:0%
+problems the implication is that we can
+ 
+
+ align:start position:0%
+problems the implication is that we can
+design for a system with an uncertain
+
+ align:start position:0%
+design for a system with an uncertain
+ 
+
+ align:start position:0%
+design for a system with an uncertain
+pole location where the pole location
+
+ align:start position:0%
+pole location where the pole location
+ 
+
+ align:start position:0%
+pole location where the pole location
+varies over as much as three decades and
+
+ align:start position:0%
+varies over as much as three decades and
+ 
+
+ align:start position:0%
+varies over as much as three decades and
+still get acceptable stability with a
+
+ align:start position:0%
+still get acceptable stability with a
+ 
+
+ align:start position:0%
+still get acceptable stability with a
+very very simple compensating Network
+
+ align:start position:0%
+very very simple compensating Network
+ 
+
+ align:start position:0%
+very very simple compensating Network
+independent of the actual location of
+
+ align:start position:0%
+independent of the actual location of
+ 
+
+ align:start position:0%
+independent of the actual location of
+the pole to summarize very quickly we've
+
+ align:start position:0%
+the pole to summarize very quickly we've
+ 
+
+ align:start position:0%
+the pole to summarize very quickly we've
+compared special-purpose compensation
+
+ align:start position:0%
+compared special-purpose compensation
+ 
+
+ align:start position:0%
+compared special-purpose compensation
+compensation tailored to the specific
+
+ align:start position:0%
+compensation tailored to the specific
+ 
+
+ align:start position:0%
+compensation tailored to the specific
+application and we've we've compared
+
+ align:start position:0%
+application and we've we've compared
+ 
+
+ align:start position:0%
+application and we've we've compared
+that with what happens when we live with
+
+ align:start position:0%
+that with what happens when we live with
+ 
+
+ align:start position:0%
+that with what happens when we live with
+sort of the manufacturers recommendation
+
+ align:start position:0%
+sort of the manufacturers recommendation
+ 
+
+ align:start position:0%
+sort of the manufacturers recommendation
+in an internally compensated operational
+
+ align:start position:0%
+in an internally compensated operational
+ 
+
+ align:start position:0%
+in an internally compensated operational
+amplifier we found that we can either
+
+ align:start position:0%
+amplifier we found that we can either
+ 
+
+ align:start position:0%
+amplifier we found that we can either
+use single pole compensation where we
+
+ align:start position:0%
+use single pole compensation where we
+ 
+
+ align:start position:0%
+use single pole compensation where we
+tailor the constant associated with the
+
+ align:start position:0%
+tailor the constant associated with the
+ 
+
+ align:start position:0%
+tailor the constant associated with the
+compensation to the specific feedback
+
+ align:start position:0%
+compensation to the specific feedback
+ 
+
+ align:start position:0%
+compensation to the specific feedback
+attenuation used we improve performance
+
+ align:start position:0%
+attenuation used we improve performance
+ 
+
+ align:start position:0%
+attenuation used we improve performance
+compared to fixed single pole
+
+ align:start position:0%
+compared to fixed single pole
+ 
+
+ align:start position:0%
+compared to fixed single pole
+compensation we can use two pole
+
+ align:start position:0%
+compensation we can use two pole
+ 
+
+ align:start position:0%
+compensation we can use two pole
+compensation which gets us greatly
+
+ align:start position:0%
+compensation which gets us greatly
+ 
+
+ align:start position:0%
+compensation which gets us greatly
+improved these sensitivity compared to
+
+ align:start position:0%
+improved these sensitivity compared to
+ 
+
+ align:start position:0%
+improved these sensitivity compared to
+single pole compensation over a wide
+
+ align:start position:0%
+single pole compensation over a wide
+ 
+
+ align:start position:0%
+single pole compensation over a wide
+range of frequencies we can use
+
+ align:start position:0%
+range of frequencies we can use
+ 
+
+ align:start position:0%
+range of frequencies we can use
+compensation that includes a zero and
+
+ align:start position:0%
+compensation that includes a zero and
+ 
+
+ align:start position:0%
+compensation that includes a zero and
+that allows us to make up for one
+
+ align:start position:0%
+that allows us to make up for one
+ 
+
+ align:start position:0%
+that allows us to make up for one
+additional pole in the loop but it's
+
+ align:start position:0%
+additional pole in the loop but it's
+ 
+
+ align:start position:0%
+additional pole in the loop but it's
+dependent on our a good knowledge of
+
+ align:start position:0%
+dependent on our a good knowledge of
+ 
+
+ align:start position:0%
+dependent on our a good knowledge of
+where the additional pole is located and
+
+ align:start position:0%
+where the additional pole is located and
+ 
+
+ align:start position:0%
+where the additional pole is located and
+finally we're able to use a slow roll
+
+ align:start position:0%
+finally we're able to use a slow roll
+ 
+
+ align:start position:0%
+finally we're able to use a slow roll
+off kind of compensation that rolls off
+
+ align:start position:0%
+off kind of compensation that rolls off
+ 
+
+ align:start position:0%
+off kind of compensation that rolls off
+somewhere between 1 / s + and 0 and with
+
+ align:start position:0%
+somewhere between 1 / s + and 0 and with
+ 
+
+ align:start position:0%
+somewhere between 1 / s + and 0 and with
+that we're able to tolerate an
+
+ align:start position:0%
+that we're able to tolerate an
+ 
+
+ align:start position:0%
+that we're able to tolerate an
+additional pole added to the loop
+
+ align:start position:0%
+additional pole added to the loop
+ 
+
+ align:start position:0%
+additional pole added to the loop
+transmission over a very very wide range
+
+ align:start position:0%
+transmission over a very very wide range
+ 
+
+ align:start position:0%
+transmission over a very very wide range
+frequency's and still maintain
+
+ align:start position:0%
+frequency's and still maintain
+ 
+
+ align:start position:0%
+frequency's and still maintain
+acceptable stability that concludes this
+
+ align:start position:0%
+acceptable stability that concludes this
+ 
+
+ align:start position:0%
+acceptable stability that concludes this
+series of examples compensating the LM
+
+ align:start position:0%
+series of examples compensating the LM
+ 
+
+ align:start position:0%
+series of examples compensating the LM
+101 a type operational amplifier thank
+
+ align:start position:0%
+101 a type operational amplifier thank
+ 
+
+ align:start position:0%
+101 a type operational amplifier thank
+you
\ No newline at end of file
diff --git a/fnodeNO6gaQ.txt b/fnodeNO6gaQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3cd98e97a0468d612402351d3d6925f1179e2d5e
--- /dev/null
+++ b/fnodeNO6gaQ.txt
@@ -0,0 +1,8387 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu what are tool activities and
+
+ align:start position:0%
+ocw.mit.edu what are tool activities and
+ 
+
+ align:start position:0%
+ocw.mit.edu what are tool activities and
+why does Lawrence call them tool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+activities this should be an easy
+
+ align:start position:0%
+activities this should be an easy
+ 
+
+ align:start position:0%
+activities this should be an easy
+question if you're doing any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reading what does he mean by Tool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+activities I know some of you
+
+ align:start position:0%
+activities I know some of you
+ 
+
+ align:start position:0%
+activities I know some of you
+know you know you don't
+
+ align:start position:0%
+know you know you don't
+ 
+
+ align:start position:0%
+know you know you don't
+remember I guess you were doing homework
+
+ align:start position:0%
+remember I guess you were doing homework
+ 
+
+ align:start position:0%
+remember I guess you were doing homework
+instead of
+
+ align:start position:0%
+instead of
+ 
+
+ align:start position:0%
+instead of
+reading all right tool activities mean
+
+ align:start position:0%
+reading all right tool activities mean
+ 
+
+ align:start position:0%
+reading all right tool activities mean
+multi-purpose actions they're
+
+ align:start position:0%
+multi-purpose actions they're
+ 
+
+ align:start position:0%
+multi-purpose actions they're
+instinctive action
+
+ align:start position:0%
+instinctive action
+ 
+
+ align:start position:0%
+instinctive action
+patterns they do have a motivational
+
+ align:start position:0%
+patterns they do have a motivational
+ 
+
+ align:start position:0%
+patterns they do have a motivational
+component so they're classified as fixed
+
+ align:start position:0%
+component so they're classified as fixed
+ 
+
+ align:start position:0%
+component so they're classified as fixed
+action patterns rather than reflexes but
+
+ align:start position:0%
+action patterns rather than reflexes but
+ 
+
+ align:start position:0%
+action patterns rather than reflexes but
+they refer to multi-purpose actions that
+
+ align:start position:0%
+they refer to multi-purpose actions that
+ 
+
+ align:start position:0%
+they refer to multi-purpose actions that
+the very same they're components of many
+
+ align:start position:0%
+the very same they're components of many
+ 
+
+ align:start position:0%
+the very same they're components of many
+different fixed action
+
+ align:start position:0%
+different fixed action
+ 
+
+ align:start position:0%
+different fixed action
+patterns but they're also fixed action
+
+ align:start position:0%
+patterns but they're also fixed action
+ 
+
+ align:start position:0%
+patterns but they're also fixed action
+patterns of their own like
+
+ align:start position:0%
+patterns of their own like
+ 
+
+ align:start position:0%
+patterns of their own like
+Locomotion you know we use locomotion as
+
+ align:start position:0%
+Locomotion you know we use locomotion as
+ 
+
+ align:start position:0%
+Locomotion you know we use locomotion as
+part of the repetitive Behavior behind
+
+ align:start position:0%
+part of the repetitive Behavior behind
+ 
+
+ align:start position:0%
+part of the repetitive Behavior behind
+any almost very many other fixed
+
+ align:start position:0%
+any almost very many other fixed
+ 
+
+ align:start position:0%
+any almost very many other fixed
+action and the same is true of
+
+ align:start position:0%
+action and the same is true of
+ 
+
+ align:start position:0%
+action and the same is true of
+the orienting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+movements we'd make orienting
+
+ align:start position:0%
+movements we'd make orienting
+ 
+
+ align:start position:0%
+movements we'd make orienting
+movements in response to stimuli it's
+
+ align:start position:0%
+movements in response to stimuli it's
+ 
+
+ align:start position:0%
+movements in response to stimuli it's
+true and that makes them seem like
+
+ align:start position:0%
+true and that makes them seem like
+ 
+
+ align:start position:0%
+true and that makes them seem like
+reflexes but in fact they're part of
+
+ align:start position:0%
+reflexes but in fact they're part of
+ 
+
+ align:start position:0%
+reflexes but in fact they're part of
+many fixed action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patterns and we don't just fit without
+
+ align:start position:0%
+patterns and we don't just fit without
+ 
+
+ align:start position:0%
+patterns and we don't just fit without
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+stimuli you know even if none of you are
+
+ align:start position:0%
+stimuli you know even if none of you are
+ 
+
+ align:start position:0%
+stimuli you know even if none of you are
+moving and I'm I don't just stare at
+
+ align:start position:0%
+moving and I'm I don't just stare at
+ 
+
+ align:start position:0%
+moving and I'm I don't just stare at
+one's place my eyes are always roaming
+
+ align:start position:0%
+one's place my eyes are always roaming
+ 
+
+ align:start position:0%
+one's place my eyes are always roaming
+around I'm making orienting
+
+ align:start position:0%
+around I'm making orienting
+ 
+
+ align:start position:0%
+around I'm making orienting
+movements grasping with the hands is the
+
+ align:start position:0%
+movements grasping with the hands is the
+ 
+
+ align:start position:0%
+movements grasping with the hands is the
+same so each of
+
+ align:start position:0%
+same so each of
+ 
+
+ align:start position:0%
+same so each of
+these major types of activities are tool
+
+ align:start position:0%
+these major types of activities are tool
+ 
+
+ align:start position:0%
+these major types of activities are tool
+activities and there's actually many
+
+ align:start position:0%
+activities and there's actually many
+ 
+
+ align:start position:0%
+activities and there's actually many
+variet ities of each one for a
+
+ align:start position:0%
+variet ities of each one for a
+ 
+
+ align:start position:0%
+variet ities of each one for a
+Locomotion is easiest to talk about
+
+ align:start position:0%
+Locomotion is easiest to talk about
+ 
+
+ align:start position:0%
+Locomotion is easiest to talk about
+there because we Define the various
+
+ align:start position:0%
+there because we Define the various
+ 
+
+ align:start position:0%
+there because we Define the various
+Gates especially in four-legged animals
+
+ align:start position:0%
+Gates especially in four-legged animals
+ 
+
+ align:start position:0%
+Gates especially in four-legged animals
+but humans still have various types of
+
+ align:start position:0%
+but humans still have various types of
+ 
+
+ align:start position:0%
+but humans still have various types of
+walking and running various speeds of
+
+ align:start position:0%
+walking and running various speeds of
+ 
+
+ align:start position:0%
+walking and running various speeds of
+running okay now what about the action
+
+ align:start position:0%
+running okay now what about the action
+ 
+
+ align:start position:0%
+running okay now what about the action
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+potential Behind These and
+
+ align:start position:0%
+potential Behind These and
+ 
+
+ align:start position:0%
+potential Behind These and
+other exaction
+
+ align:start position:0%
+other exaction
+ 
+
+ align:start position:0%
+other exaction
+patterns
+
+ align:start position:0%
+patterns
+ 
+
+ align:start position:0%
+patterns
+we know
+
+ align:start position:0%
+we know
+ 
+
+ align:start position:0%
+we know
+that if they're like most fixed action
+
+ align:start position:0%
+that if they're like most fixed action
+ 
+
+ align:start position:0%
+that if they're like most fixed action
+patterns the the action specific
+
+ align:start position:0%
+patterns the the action specific
+ 
+
+ align:start position:0%
+patterns the the action specific
+potential meaning the level of
+
+ align:start position:0%
+potential meaning the level of
+ 
+
+ align:start position:0%
+potential meaning the level of
+motivation builds up over time well it
+
+ align:start position:0%
+motivation builds up over time well it
+ 
+
+ align:start position:0%
+motivation builds up over time well it
+doesn't build up at the same rate for
+
+ align:start position:0%
+doesn't build up at the same rate for
+ 
+
+ align:start position:0%
+doesn't build up at the same rate for
+different fix action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patterns it tends to build up at a rate
+
+ align:start position:0%
+patterns it tends to build up at a rate
+ 
+
+ align:start position:0%
+patterns it tends to build up at a rate
+proportional to how often the pattern
+
+ align:start position:0%
+proportional to how often the pattern
+ 
+
+ align:start position:0%
+proportional to how often the pattern
+the the movement is
+
+ align:start position:0%
+the the movement is
+ 
+
+ align:start position:0%
+the the movement is
+needed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know that many of these fixed
+
+ align:start position:0%
+and we know that many of these fixed
+ 
+
+ align:start position:0%
+and we know that many of these fixed
+action patterns like predatory behavior
+
+ align:start position:0%
+action patterns like predatory behavior
+ 
+
+ align:start position:0%
+action patterns like predatory behavior
+in the cat are actually a series of
+
+ align:start position:0%
+in the cat are actually a series of
+ 
+
+ align:start position:0%
+in the cat are actually a series of
+fixed they're inherited as a s as a
+
+ align:start position:0%
+fixed they're inherited as a s as a
+ 
+
+ align:start position:0%
+fixed they're inherited as a s as a
+series of different fixed action
+
+ align:start position:0%
+series of different fixed action
+ 
+
+ align:start position:0%
+series of different fixed action
+patterns but they become linked during
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+development that is habits form
+
+ align:start position:0%
+development that is habits form
+ 
+
+ align:start position:0%
+development that is habits form
+depending on the experience of the
+
+ align:start position:0%
+depending on the experience of the
+ 
+
+ align:start position:0%
+depending on the experience of the
+animal usually with the mother in the
+
+ align:start position:0%
+animal usually with the mother in the
+ 
+
+ align:start position:0%
+animal usually with the mother in the
+case of predatory
+
+ align:start position:0%
+case of predatory
+ 
+
+ align:start position:0%
+case of predatory
+cats
+
+ align:start position:0%
+cats
+ 
+
+ align:start position:0%
+cats
+uh and the the various patterns become
+
+ align:start position:0%
+uh and the the various patterns become
+ 
+
+ align:start position:0%
+uh and the the various patterns become
+linked so then they're normally doing
+
+ align:start position:0%
+linked so then they're normally doing
+ 
+
+ align:start position:0%
+linked so then they're normally doing
+them the searching Locomotion and
+
+ align:start position:0%
+them the searching Locomotion and
+ 
+
+ align:start position:0%
+them the searching Locomotion and
+searching then stalking then bouncing
+
+ align:start position:0%
+searching then stalking then bouncing
+ 
+
+ align:start position:0%
+searching then stalking then bouncing
+and then the killing bite usually in
+
+ align:start position:0%
+and then the killing bite usually in
+ 
+
+ align:start position:0%
+and then the killing bite usually in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how frequently does the
+
+ align:start position:0%
+so how frequently does the
+ 
+
+ align:start position:0%
+so how frequently does the
+cat
+
+ align:start position:0%
+cat
+ 
+
+ align:start position:0%
+cat
+perform each of these
+
+ align:start position:0%
+perform each of these
+ 
+
+ align:start position:0%
+perform each of these
+behaviors
+
+ align:start position:0%
+behaviors
+ 
+
+ align:start position:0%
+behaviors
+well they perform stalking a lot more
+
+ align:start position:0%
+well they perform stalking a lot more
+ 
+
+ align:start position:0%
+well they perform stalking a lot more
+than they pounce because they have to
+
+ align:start position:0%
+than they pounce because they have to
+ 
+
+ align:start position:0%
+than they pounce because they have to
+stalk they have to search for prey the
+
+ align:start position:0%
+stalk they have to search for prey the
+ 
+
+ align:start position:0%
+stalk they have to search for prey the
+most before they find it so they're
+
+ align:start position:0%
+most before they find it so they're
+ 
+
+ align:start position:0%
+most before they find it so they're
+going to spend the most time doing that
+
+ align:start position:0%
+going to spend the most time doing that
+ 
+
+ align:start position:0%
+going to spend the most time doing that
+and then when when they see them they
+
+ align:start position:0%
+and then when when they see them they
+ 
+
+ align:start position:0%
+and then when when they see them they
+have to stalk them and they're going to
+
+ align:start position:0%
+have to stalk them and they're going to
+ 
+
+ align:start position:0%
+have to stalk them and they're going to
+do that a lot more than they will
+
+ align:start position:0%
+do that a lot more than they will
+ 
+
+ align:start position:0%
+do that a lot more than they will
+actually pounce because they don't get
+
+ align:start position:0%
+actually pounce because they don't get
+ 
+
+ align:start position:0%
+actually pounce because they don't get
+the opportunity to pounce that often
+
+ align:start position:0%
+the opportunity to pounce that often
+ 
+
+ align:start position:0%
+the opportunity to pounce that often
+okay the animals move away the animals
+
+ align:start position:0%
+okay the animals move away the animals
+ 
+
+ align:start position:0%
+okay the animals move away the animals
+smell them and run away and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forth and of course the The Killing bite
+
+ align:start position:0%
+forth and of course the The Killing bite
+ 
+
+ align:start position:0%
+forth and of course the The Killing bite
+is executed the least
+
+ align:start position:0%
+is executed the least
+ 
+
+ align:start position:0%
+is executed the least
+frequently because sometimes when they
+
+ align:start position:0%
+frequently because sometimes when they
+ 
+
+ align:start position:0%
+frequently because sometimes when they
+pounce on an animal the animal still
+
+ align:start position:0%
+pounce on an animal the animal still
+ 
+
+ align:start position:0%
+pounce on an animal the animal still
+escapes we talk about Escape Behavior
+
+ align:start position:0%
+escapes we talk about Escape Behavior
+ 
+
+ align:start position:0%
+escapes we talk about Escape Behavior
+you'll see examples of that on
+
+ align:start position:0%
+you'll see examples of that on
+ 
+
+ align:start position:0%
+you'll see examples of that on
+videos so that's the action that's done
+
+ align:start position:0%
+videos so that's the action that's done
+ 
+
+ align:start position:0%
+videos so that's the action that's done
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+least well that means that the action
+
+ align:start position:0%
+least well that means that the action
+ 
+
+ align:start position:0%
+least well that means that the action
+specific potential the motivation to do
+
+ align:start position:0%
+specific potential the motivation to do
+ 
+
+ align:start position:0%
+specific potential the motivation to do
+those different things building up at a
+
+ align:start position:0%
+those different things building up at a
+ 
+
+ align:start position:0%
+those different things building up at a
+different rate they're much more
+
+ align:start position:0%
+different rate they're much more
+ 
+
+ align:start position:0%
+different rate they're much more
+motivated to do searching
+
+ align:start position:0%
+motivated to do searching
+ 
+
+ align:start position:0%
+motivated to do searching
+Locomotion than they are those other
+
+ align:start position:0%
+Locomotion than they are those other
+ 
+
+ align:start position:0%
+Locomotion than they are those other
+things because they have to do it the
+
+ align:start position:0%
+things because they have to do it the
+ 
+
+ align:start position:0%
+things because they have to do it the
+most
+
+ align:start position:0%
+most
+ 
+
+ align:start position:0%
+most
+we'll come back to
+
+ align:start position:0%
+we'll come back to
+ 
+
+ align:start position:0%
+we'll come back to
+this but for those frequently used
+
+ align:start position:0%
+this but for those frequently used
+ 
+
+ align:start position:0%
+this but for those frequently used
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+patterns the uh thresholds can be
+
+ align:start position:0%
+patterns the uh thresholds can be
+ 
+
+ align:start position:0%
+patterns the uh thresholds can be
+lowered quite frequently take for
+
+ align:start position:0%
+lowered quite frequently take for
+ 
+
+ align:start position:0%
+lowered quite frequently take for
+example uh flying in a little rent say
+
+ align:start position:0%
+example uh flying in a little rent say
+ 
+
+ align:start position:0%
+example uh flying in a little rent say
+and compare it to flying in a
+
+ align:start position:0%
+and compare it to flying in a
+ 
+
+ align:start position:0%
+and compare it to flying in a
+goose you know that little Ren Can't
+
+ align:start position:0%
+goose you know that little Ren Can't
+ 
+
+ align:start position:0%
+goose you know that little Ren Can't
+Stop for more than a few seconds before
+
+ align:start position:0%
+Stop for more than a few seconds before
+ 
+
+ align:start position:0%
+Stop for more than a few seconds before
+he's flying
+
+ align:start position:0%
+he's flying
+ 
+
+ align:start position:0%
+he's flying
+again they they flit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around very
+
+ align:start position:0%
+around very
+ 
+
+ align:start position:0%
+around very
+frequently whereas the goose once he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flies I don't want to mute it I just
+
+ align:start position:0%
+flies I don't want to mute it I just
+ 
+
+ align:start position:0%
+flies I don't want to mute it I just
+want to turn the amplitude down but this
+
+ align:start position:0%
+want to turn the amplitude down but this
+ 
+
+ align:start position:0%
+want to turn the amplitude down but this
+isn't
+
+ align:start position:0%
+isn't
+ 
+
+ align:start position:0%
+isn't
+there we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go okay so the goose when he flies he
+
+ align:start position:0%
+go okay so the goose when he flies he
+ 
+
+ align:start position:0%
+go okay so the goose when he flies he
+won't fly again for quite a while unless
+
+ align:start position:0%
+won't fly again for quite a while unless
+ 
+
+ align:start position:0%
+won't fly again for quite a while unless
+a stimulus like a predator you know
+
+ align:start position:0%
+a stimulus like a predator you know
+ 
+
+ align:start position:0%
+a stimulus like a predator you know
+causes a rapid rise in the motivation to
+
+ align:start position:0%
+causes a rapid rise in the motivation to
+ 
+
+ align:start position:0%
+causes a rapid rise in the motivation to
+fly but in most cases uh if he's not
+
+ align:start position:0%
+fly but in most cases uh if he's not
+ 
+
+ align:start position:0%
+fly but in most cases uh if he's not
+being disturbed by Predators he won't
+
+ align:start position:0%
+being disturbed by Predators he won't
+ 
+
+ align:start position:0%
+being disturbed by Predators he won't
+fly again for quite a while whereas the
+
+ align:start position:0%
+fly again for quite a while whereas the
+ 
+
+ align:start position:0%
+fly again for quite a while whereas the
+ren is flying much more so the the rate
+
+ align:start position:0%
+ren is flying much more so the the rate
+ 
+
+ align:start position:0%
+ren is flying much more so the the rate
+of build up is different from species to
+
+ align:start position:0%
+of build up is different from species to
+ 
+
+ align:start position:0%
+of build up is different from species to
+species for the very same action pattern
+
+ align:start position:0%
+species for the very same action pattern
+ 
+
+ align:start position:0%
+species for the very same action pattern
+and it's different for different fixed
+
+ align:start position:0%
+and it's different for different fixed
+ 
+
+ align:start position:0%
+and it's different for different fixed
+action patterns in the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+species let's talk about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+threshold for this responding to stimuli
+
+ align:start position:0%
+threshold for this responding to stimuli
+ 
+
+ align:start position:0%
+threshold for this responding to stimuli
+that elicit a fixed action
+
+ align:start position:0%
+that elicit a fixed action
+ 
+
+ align:start position:0%
+that elicit a fixed action
+pattern as the motivation builds up the
+
+ align:start position:0%
+pattern as the motivation builds up the
+ 
+
+ align:start position:0%
+pattern as the motivation builds up the
+threshold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the amount of stimulation
+
+ align:start position:0%
+the amount of stimulation
+ 
+
+ align:start position:0%
+the amount of stimulation
+needed to get the action
+
+ align:start position:0%
+needed to get the action
+ 
+
+ align:start position:0%
+needed to get the action
+pattern that uh goes
+
+ align:start position:0%
+pattern that uh goes
+ 
+
+ align:start position:0%
+pattern that uh goes
+down look at hunger and feeding we've
+
+ align:start position:0%
+down look at hunger and feeding we've
+ 
+
+ align:start position:0%
+down look at hunger and feeding we've
+mentioned this before and it's obvious
+
+ align:start position:0%
+mentioned this before and it's obvious
+ 
+
+ align:start position:0%
+mentioned this before and it's obvious
+when you think about it when the
+
+ align:start position:0%
+when you think about it when the
+ 
+
+ align:start position:0%
+when you think about it when the
+hungrier the animal or person
+
+ align:start position:0%
+hungrier the animal or person
+ 
+
+ align:start position:0%
+hungrier the animal or person
+is the less discriminating he is why do
+
+ align:start position:0%
+is the less discriminating he is why do
+ 
+
+ align:start position:0%
+is the less discriminating he is why do
+we have dessert at the end of a meal
+
+ align:start position:0%
+we have dessert at the end of a meal
+ 
+
+ align:start position:0%
+we have dessert at the end of a meal
+we're not as
+
+ align:start position:0%
+we're not as
+ 
+
+ align:start position:0%
+we're not as
+hungry so it's often the most palatable
+
+ align:start position:0%
+hungry so it's often the most palatable
+ 
+
+ align:start position:0%
+hungry so it's often the most palatable
+thing of course there are exceptions but
+
+ align:start position:0%
+thing of course there are exceptions but
+ 
+
+ align:start position:0%
+thing of course there are exceptions but
+most of us like sweet
+
+ align:start position:0%
+most of us like sweet
+ 
+
+ align:start position:0%
+most of us like sweet
+things some countries don't even serve
+
+ align:start position:0%
+things some countries don't even serve
+ 
+
+ align:start position:0%
+things some countries don't even serve
+theer like in China an American
+
+ align:start position:0%
+theer like in China an American
+ 
+
+ align:start position:0%
+theer like in China an American
+habit okay but of course it occurs in in
+
+ align:start position:0%
+habit okay but of course it occurs in in
+ 
+
+ align:start position:0%
+habit okay but of course it occurs in in
+many countries that have it the dessert
+
+ align:start position:0%
+many countries that have it the dessert
+ 
+
+ align:start position:0%
+many countries that have it the dessert
+is last because it's the most palatable
+
+ align:start position:0%
+is last because it's the most palatable
+ 
+
+ align:start position:0%
+is last because it's the most palatable
+thing and uh they they will still eat
+
+ align:start position:0%
+thing and uh they they will still eat
+ 
+
+ align:start position:0%
+thing and uh they they will still eat
+dessert even though they're not hungry
+
+ align:start position:0%
+dessert even though they're not hungry
+ 
+
+ align:start position:0%
+dessert even though they're not hungry
+for food other Foods
+
+ align:start position:0%
+for food other Foods
+ 
+
+ align:start position:0%
+for food other Foods
+anymore and as I mentioned if you have a
+
+ align:start position:0%
+anymore and as I mentioned if you have a
+ 
+
+ align:start position:0%
+anymore and as I mentioned if you have a
+child that's very finicky that's because
+
+ align:start position:0%
+child that's very finicky that's because
+ 
+
+ align:start position:0%
+child that's very finicky that's because
+he's still
+
+ align:start position:0%
+he's still
+ 
+
+ align:start position:0%
+he's still
+welled much less finicky if he's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hungry and if you don't like certain and
+
+ align:start position:0%
+hungry and if you don't like certain and
+ 
+
+ align:start position:0%
+hungry and if you don't like certain and
+certain something and all your friends
+
+ align:start position:0%
+certain something and all your friends
+ 
+
+ align:start position:0%
+certain something and all your friends
+do like it well just don't eat for a
+
+ align:start position:0%
+do like it well just don't eat for a
+ 
+
+ align:start position:0%
+do like it well just don't eat for a
+while if you want to start liking
+
+ align:start position:0%
+while if you want to start liking
+ 
+
+ align:start position:0%
+while if you want to start liking
+it and then you'll get used to
+
+ align:start position:0%
+it and then you'll get used to
+ 
+
+ align:start position:0%
+it and then you'll get used to
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I thought I'd never like beer I hated
+
+ align:start position:0%
+I thought I'd never like beer I hated
+ 
+
+ align:start position:0%
+I thought I'd never like beer I hated
+beer when I was a kid brother would be
+
+ align:start position:0%
+beer when I was a kid brother would be
+ 
+
+ align:start position:0%
+beer when I was a kid brother would be
+drinking beer
+
+ align:start position:0%
+drinking beer
+ 
+
+ align:start position:0%
+drinking beer
+couldn't stand the stuff but then on a
+
+ align:start position:0%
+couldn't stand the stuff but then on a
+ 
+
+ align:start position:0%
+couldn't stand the stuff but then on a
+real hot day you get really
+
+ align:start position:0%
+real hot day you get really
+ 
+
+ align:start position:0%
+real hot day you get really
+thirsty and your much your thresholds
+
+ align:start position:0%
+thirsty and your much your thresholds
+ 
+
+ align:start position:0%
+thirsty and your much your thresholds
+are lowered okay your thresholds for
+
+ align:start position:0%
+are lowered okay your thresholds for
+ 
+
+ align:start position:0%
+are lowered okay your thresholds for
+drinking and so you like it a little
+
+ align:start position:0%
+drinking and so you like it a little
+ 
+
+ align:start position:0%
+drinking and so you like it a little
+better and then I got used to it now I
+
+ align:start position:0%
+better and then I got used to it now I
+ 
+
+ align:start position:0%
+better and then I got used to it now I
+can drink beer still don't like it as
+
+ align:start position:0%
+can drink beer still don't like it as
+ 
+
+ align:start position:0%
+can drink beer still don't like it as
+well as some people people do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay breeding sexual attraction really
+
+ align:start position:0%
+okay breeding sexual attraction really
+ 
+
+ align:start position:0%
+okay breeding sexual attraction really
+obvious a horse breeder if he wants his
+
+ align:start position:0%
+obvious a horse breeder if he wants his
+ 
+
+ align:start position:0%
+obvious a horse breeder if he wants his
+Mar if he he's got a stallion let's say
+
+ align:start position:0%
+Mar if he he's got a stallion let's say
+ 
+
+ align:start position:0%
+Mar if he he's got a stallion let's say
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+he's wants to breed that stallion if the
+
+ align:start position:0%
+he's wants to breed that stallion if the
+ 
+
+ align:start position:0%
+he's wants to breed that stallion if the
+stallion is worth a lot he gets money
+
+ align:start position:0%
+stallion is worth a lot he gets money
+ 
+
+ align:start position:0%
+stallion is worth a lot he gets money
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+that but if he's being paid that
+
+ align:start position:0%
+that but if he's being paid that
+ 
+
+ align:start position:0%
+that but if he's being paid that
+stallion has to perform so what does he
+
+ align:start position:0%
+stallion has to perform so what does he
+ 
+
+ align:start position:0%
+stallion has to perform so what does he
+do he he does not let that stallion
+
+ align:start position:0%
+do he he does not let that stallion
+ 
+
+ align:start position:0%
+do he he does not let that stallion
+copulate for a long period of time so he
+
+ align:start position:0%
+copulate for a long period of time so he
+ 
+
+ align:start position:0%
+copulate for a long period of time so he
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+motivation to breed builds up in the
+
+ align:start position:0%
+motivation to breed builds up in the
+ 
+
+ align:start position:0%
+motivation to breed builds up in the
+animal and if you build it up enough I
+
+ align:start position:0%
+animal and if you build it up enough I
+ 
+
+ align:start position:0%
+animal and if you build it up enough I
+mean he'll breed with a
+
+ align:start position:0%
+mean he'll breed with a
+ 
+
+ align:start position:0%
+mean he'll breed with a
+mule that's how you get
+
+ align:start position:0%
+mule that's how you get
+ 
+
+ align:start position:0%
+mule that's how you get
+donkeys and and so that's important and
+
+ align:start position:0%
+donkeys and and so that's important and
+ 
+
+ align:start position:0%
+donkeys and and so that's important and
+it happens in humans too there's an
+
+ align:start position:0%
+it happens in humans too there's an
+ 
+
+ align:start position:0%
+it happens in humans too there's an
+amusing story there in the Lawrence
+
+ align:start position:0%
+amusing story there in the Lawrence
+ 
+
+ align:start position:0%
+amusing story there in the Lawrence
+reading about story told to Lawrence by
+
+ align:start position:0%
+reading about story told to Lawrence by
+ 
+
+ align:start position:0%
+reading about story told to Lawrence by
+a ship captain he knew and how he felt
+
+ align:start position:0%
+a ship captain he knew and how he felt
+ 
+
+ align:start position:0%
+a ship captain he knew and how he felt
+after being at sea for a long time he
+
+ align:start position:0%
+after being at sea for a long time he
+ 
+
+ align:start position:0%
+after being at sea for a long time he
+came back and he said every woman in
+
+ align:start position:0%
+came back and he said every woman in
+ 
+
+ align:start position:0%
+came back and he said every woman in
+town looks like hell on of
+
+ align:start position:0%
+town looks like hell on of
+ 
+
+ align:start position:0%
+town looks like hell on of
+TR but after I'd been here a couple
+
+ align:start position:0%
+TR but after I'd been here a couple
+ 
+
+ align:start position:0%
+TR but after I'd been here a couple
+weeks he said so many ugly
+
+ align:start position:0%
+weeks he said so many ugly
+ 
+
+ align:start position:0%
+weeks he said so many ugly
+ones What's happen threshold
+
+ align:start position:0%
+ones What's happen threshold
+ 
+
+ align:start position:0%
+ones What's happen threshold
+Loring okay
+
+ align:start position:0%
+Loring okay
+ 
+
+ align:start position:0%
+Loring okay
+so and this really explains to a large
+
+ align:start position:0%
+so and this really explains to a large
+ 
+
+ align:start position:0%
+so and this really explains to a large
+degree the phenomenon we
+
+ align:start position:0%
+degree the phenomenon we
+ 
+
+ align:start position:0%
+degree the phenomenon we
+call INB back
+
+ align:start position:0%
+call INB back
+ 
+
+ align:start position:0%
+call INB back
+reaction vacuum activity another term
+
+ align:start position:0%
+reaction vacuum activity another term
+ 
+
+ align:start position:0%
+reaction vacuum activity another term
+used in
+
+ align:start position:0%
+used in
+ 
+
+ align:start position:0%
+used in
+ethology it literally
+
+ align:start position:0%
+ethology it literally
+ 
+
+ align:start position:0%
+ethology it literally
+means when an instinctive Behavior
+
+ align:start position:0%
+means when an instinctive Behavior
+ 
+
+ align:start position:0%
+means when an instinctive Behavior
+pattern that occurs without any stimulus
+
+ align:start position:0%
+pattern that occurs without any stimulus
+ 
+
+ align:start position:0%
+pattern that occurs without any stimulus
+that would that would be the literal
+
+ align:start position:0%
+that would that would be the literal
+ 
+
+ align:start position:0%
+that would that would be the literal
+meaning of vacuum
+
+ align:start position:0%
+meaning of vacuum
+ 
+
+ align:start position:0%
+meaning of vacuum
+activity but in that in fact it seems to
+
+ align:start position:0%
+activity but in that in fact it seems to
+ 
+
+ align:start position:0%
+activity but in that in fact it seems to
+be a case of extreme threshold
+
+ align:start position:0%
+be a case of extreme threshold
+ 
+
+ align:start position:0%
+be a case of extreme threshold
+lowering the thresholds can get so low
+
+ align:start position:0%
+lowering the thresholds can get so low
+ 
+
+ align:start position:0%
+lowering the thresholds can get so low
+that we don't even notice the stimuli
+
+ align:start position:0%
+that we don't even notice the stimuli
+ 
+
+ align:start position:0%
+that we don't even notice the stimuli
+the animals are responding to and
+
+ align:start position:0%
+the animals are responding to and
+ 
+
+ align:start position:0%
+the animals are responding to and
+Lawrence talks about his when he was
+
+ align:start position:0%
+Lawrence talks about his when he was
+ 
+
+ align:start position:0%
+Lawrence talks about his when he was
+young he had a pet
+
+ align:start position:0%
+young he had a pet
+ 
+
+ align:start position:0%
+young he had a pet
+Starling and uh he could be eating
+
+ align:start position:0%
+Starling and uh he could be eating
+ 
+
+ align:start position:0%
+Starling and uh he could be eating
+dinner with his family and uh that he
+
+ align:start position:0%
+dinner with his family and uh that he
+ 
+
+ align:start position:0%
+dinner with his family and uh that he
+would notice that the Starling seemed to
+
+ align:start position:0%
+would notice that the Starling seemed to
+ 
+
+ align:start position:0%
+would notice that the Starling seemed to
+be catching and feeding on flies up near
+
+ align:start position:0%
+be catching and feeding on flies up near
+ 
+
+ align:start position:0%
+be catching and feeding on flies up near
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+ceiling and he couldn't see the Flies so
+
+ align:start position:0%
+ceiling and he couldn't see the Flies so
+ 
+
+ align:start position:0%
+ceiling and he couldn't see the Flies so
+he tried getting a ladder and going up
+
+ align:start position:0%
+he tried getting a ladder and going up
+ 
+
+ align:start position:0%
+he tried getting a ladder and going up
+there to see if we're in flies and he
+
+ align:start position:0%
+there to see if we're in flies and he
+ 
+
+ align:start position:0%
+there to see if we're in flies and he
+convinced himself that there were none
+
+ align:start position:0%
+convinced himself that there were none
+ 
+
+ align:start position:0%
+convinced himself that there were none
+you know and yet the Starling was there
+
+ align:start position:0%
+you know and yet the Starling was there
+ 
+
+ align:start position:0%
+you know and yet the Starling was there
+showing the fixed action pattern of
+
+ align:start position:0%
+showing the fixed action pattern of
+ 
+
+ align:start position:0%
+showing the fixed action pattern of
+searching for catching and and eating
+
+ align:start position:0%
+searching for catching and and eating
+ 
+
+ align:start position:0%
+searching for catching and and eating
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Flies so that's called invacuo
+
+ align:start position:0%
+Flies so that's called invacuo
+ 
+
+ align:start position:0%
+Flies so that's called invacuo
+activity or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactions uh some of you that if you
+
+ align:start position:0%
+reactions uh some of you that if you
+ 
+
+ align:start position:0%
+reactions uh some of you that if you
+keep rats uh or mice and cages and they
+
+ align:start position:0%
+keep rats uh or mice and cages and they
+ 
+
+ align:start position:0%
+keep rats uh or mice and cages and they
+don't have any nesting material they
+
+ align:start position:0%
+don't have any nesting material they
+ 
+
+ align:start position:0%
+don't have any nesting material they
+have a motivation to nest and if they're
+
+ align:start position:0%
+have a motivation to nest and if they're
+ 
+
+ align:start position:0%
+have a motivation to nest and if they're
+deprived of nesting material for a long
+
+ align:start position:0%
+deprived of nesting material for a long
+ 
+
+ align:start position:0%
+deprived of nesting material for a long
+period of time they'll try to build a
+
+ align:start position:0%
+period of time they'll try to build a
+ 
+
+ align:start position:0%
+period of time they'll try to build a
+nest with their own tail you know
+
+ align:start position:0%
+nest with their own tail you know
+ 
+
+ align:start position:0%
+nest with their own tail you know
+and canaries will
+
+ align:start position:0%
+and canaries will
+ 
+
+ align:start position:0%
+and canaries will
+do build nests with their own
+
+ align:start position:0%
+do build nests with their own
+ 
+
+ align:start position:0%
+do build nests with their own
+feathers and
+
+ align:start position:0%
+feathers and
+ 
+
+ align:start position:0%
+feathers and
+uh male or Drakes when they're in
+
+ align:start position:0%
+uh male or Drakes when they're in
+ 
+
+ align:start position:0%
+uh male or Drakes when they're in
+a their highly
+
+ align:start position:0%
+a their highly
+ 
+
+ align:start position:0%
+a their highly
+motivated uh to mate they're also very
+
+ align:start position:0%
+motivated uh to mate they're also very
+ 
+
+ align:start position:0%
+motivated uh to mate they're also very
+aggressive against other males and they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh they'll actually attack their own
+
+ align:start position:0%
+uh they'll actually attack their own
+ 
+
+ align:start position:0%
+uh they'll actually attack their own
+Tails because the thresholds are so low
+
+ align:start position:0%
+Tails because the thresholds are so low
+ 
+
+ align:start position:0%
+Tails because the thresholds are so low
+it doesn't take much of a
+
+ align:start position:0%
+it doesn't take much of a
+ 
+
+ align:start position:0%
+it doesn't take much of a
+stimulus you know they just need certain
+
+ align:start position:0%
+stimulus you know they just need certain
+ 
+
+ align:start position:0%
+stimulus you know they just need certain
+key
+
+ align:start position:0%
+key
+ 
+
+ align:start position:0%
+key
+stimuli and if thresholds are low enough
+
+ align:start position:0%
+stimuli and if thresholds are low enough
+ 
+
+ align:start position:0%
+stimuli and if thresholds are low enough
+their own tail will be enough to elicit
+
+ align:start position:0%
+their own tail will be enough to elicit
+ 
+
+ align:start position:0%
+their own tail will be enough to elicit
+the behavior ostriches deprived of their
+
+ align:start position:0%
+the behavior ostriches deprived of their
+ 
+
+ align:start position:0%
+the behavior ostriches deprived of their
+usual method of feeding
+
+ align:start position:0%
+usual method of feeding
+ 
+
+ align:start position:0%
+usual method of feeding
+of grass they will pluck grass that is
+
+ align:start position:0%
+of grass they will pluck grass that is
+ 
+
+ align:start position:0%
+of grass they will pluck grass that is
+not not even
+
+ align:start position:0%
+not not even
+ 
+
+ align:start position:0%
+not not even
+there the same true is you will notice
+
+ align:start position:0%
+there the same true is you will notice
+ 
+
+ align:start position:0%
+there the same true is you will notice
+this in rodents if you don't you know we
+
+ align:start position:0%
+this in rodents if you don't you know we
+ 
+
+ align:start position:0%
+this in rodents if you don't you know we
+give them Road uh Rat pellets we call
+
+ align:start position:0%
+give them Road uh Rat pellets we call
+ 
+
+ align:start position:0%
+give them Road uh Rat pellets we call
+them well why do we give them food
+
+ align:start position:0%
+them well why do we give them food
+ 
+
+ align:start position:0%
+them well why do we give them food
+that's so
+
+ align:start position:0%
+that's so
+ 
+
+ align:start position:0%
+that's so
+hard in fact it's mixed with material
+
+ align:start position:0%
+hard in fact it's mixed with material
+ 
+
+ align:start position:0%
+hard in fact it's mixed with material
+that grinds their teeth down well they
+
+ align:start position:0%
+that grinds their teeth down well they
+ 
+
+ align:start position:0%
+that grinds their teeth down well they
+have to because in the case of rodents
+
+ align:start position:0%
+have to because in the case of rodents
+ 
+
+ align:start position:0%
+have to because in the case of rodents
+the teeth keep growing these Insider
+
+ align:start position:0%
+the teeth keep growing these Insider
+ 
+
+ align:start position:0%
+the teeth keep growing these Insider
+teeth on both bottom and top same is
+
+ align:start position:0%
+teeth on both bottom and top same is
+ 
+
+ align:start position:0%
+teeth on both bottom and top same is
+true of hamsters and mice they just keep
+
+ align:start position:0%
+true of hamsters and mice they just keep
+ 
+
+ align:start position:0%
+true of hamsters and mice they just keep
+growing so they're highly motivated to
+
+ align:start position:0%
+growing so they're highly motivated to
+ 
+
+ align:start position:0%
+growing so they're highly motivated to
+GW and if you deprive them of things to
+
+ align:start position:0%
+GW and if you deprive them of things to
+ 
+
+ align:start position:0%
+GW and if you deprive them of things to
+GW on let's say say you're feeding them
+
+ align:start position:0%
+GW on let's say say you're feeding them
+ 
+
+ align:start position:0%
+GW on let's say say you're feeding them
+wet Mash or something they can't wear
+
+ align:start position:0%
+wet Mash or something they can't wear
+ 
+
+ align:start position:0%
+wet Mash or something they can't wear
+their teeth down they will chew on the
+
+ align:start position:0%
+their teeth down they will chew on the
+ 
+
+ align:start position:0%
+their teeth down they will chew on the
+on the metal cage you know they'll chew
+
+ align:start position:0%
+on the metal cage you know they'll chew
+ 
+
+ align:start position:0%
+on the metal cage you know they'll chew
+on anything they can get their teeth
+
+ align:start position:0%
+on anything they can get their teeth
+ 
+
+ align:start position:0%
+on anything they can get their teeth
+around reminds me of some dogs
+
+ align:start position:0%
+around reminds me of some dogs
+ 
+
+ align:start position:0%
+around reminds me of some dogs
+I I don't know what their fixed action
+
+ align:start position:0%
+I I don't know what their fixed action
+ 
+
+ align:start position:0%
+I I don't know what their fixed action
+patterns how much of it's nesting or
+
+ align:start position:0%
+patterns how much of it's nesting or
+ 
+
+ align:start position:0%
+patterns how much of it's nesting or
+whatever but some dogs also can mess up
+
+ align:start position:0%
+whatever but some dogs also can mess up
+ 
+
+ align:start position:0%
+whatever but some dogs also can mess up
+your house quite a bit because of what
+
+ align:start position:0%
+your house quite a bit because of what
+ 
+
+ align:start position:0%
+your house quite a bit because of what
+they do to to shoes blankets and so
+
+ align:start position:0%
+they do to to shoes blankets and so
+ 
+
+ align:start position:0%
+they do to to shoes blankets and so
+forth so with a lot of thresold lowering
+
+ align:start position:0%
+forth so with a lot of thresold lowering
+ 
+
+ align:start position:0%
+forth so with a lot of thresold lowering
+you all all you need is a very small
+
+ align:start position:0%
+you all all you need is a very small
+ 
+
+ align:start position:0%
+you all all you need is a very small
+stimulus it's it's almost like an
+
+ align:start position:0%
+stimulus it's it's almost like an
+ 
+
+ align:start position:0%
+stimulus it's it's almost like an
+internal
+
+ align:start position:0%
+internal
+ 
+
+ align:start position:0%
+internal
+Reservoir um that's sort of a metaphor
+
+ align:start position:0%
+Reservoir um that's sort of a metaphor
+ 
+
+ align:start position:0%
+Reservoir um that's sort of a metaphor
+for the the action specific potential
+
+ align:start position:0%
+for the the action specific potential
+ 
+
+ align:start position:0%
+for the the action specific potential
+builds up to a point it just starts
+
+ align:start position:0%
+builds up to a point it just starts
+ 
+
+ align:start position:0%
+builds up to a point it just starts
+spilling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over now we talked last time about the
+
+ align:start position:0%
+over now we talked last time about the
+ 
+
+ align:start position:0%
+over now we talked last time about the
+different components of fixed action
+
+ align:start position:0%
+different components of fixed action
+ 
+
+ align:start position:0%
+different components of fixed action
+patterns and we'll use these terms a
+
+ align:start position:0%
+patterns and we'll use these terms a
+ 
+
+ align:start position:0%
+patterns and we'll use these terms a
+lot uh there was a component that wasn't
+
+ align:start position:0%
+lot uh there was a component that wasn't
+ 
+
+ align:start position:0%
+lot uh there was a component that wasn't
+defined for a long time until the
+
+ align:start position:0%
+defined for a long time until the
+ 
+
+ align:start position:0%
+defined for a long time until the
+skywall Craig uh defined it it
+
+ align:start position:0%
+skywall Craig uh defined it it
+ 
+
+ align:start position:0%
+skywall Craig uh defined it it
+corresponds to the level of uh
+
+ align:start position:0%
+corresponds to the level of uh
+ 
+
+ align:start position:0%
+corresponds to the level of uh
+the action specific potential but before
+
+ align:start position:0%
+the action specific potential but before
+ 
+
+ align:start position:0%
+the action specific potential but before
+they even use that theoretical term this
+
+ align:start position:0%
+they even use that theoretical term this
+ 
+
+ align:start position:0%
+they even use that theoretical term this
+Behavior had been described what is it
+
+ align:start position:0%
+Behavior had been described what is it
+ 
+
+ align:start position:0%
+Behavior had been described what is it
+what did Craig talk
+
+ align:start position:0%
+what did Craig talk
+ 
+
+ align:start position:0%
+what did Craig talk
+about appetitive Behavior It's usually
+
+ align:start position:0%
+about appetitive Behavior It's usually
+ 
+
+ align:start position:0%
+about appetitive Behavior It's usually
+the app appetitive behavior of some sort
+
+ align:start position:0%
+the app appetitive behavior of some sort
+ 
+
+ align:start position:0%
+the app appetitive behavior of some sort
+usually Locomotion and searching
+
+ align:start position:0%
+usually Locomotion and searching
+ 
+
+ align:start position:0%
+usually Locomotion and searching
+behavior and
+
+ align:start position:0%
+behavior and
+ 
+
+ align:start position:0%
+behavior and
+orienting is has the lowest threshold so
+
+ align:start position:0%
+orienting is has the lowest threshold so
+ 
+
+ align:start position:0%
+orienting is has the lowest threshold so
+when an animal gets hungry he the the
+
+ align:start position:0%
+when an animal gets hungry he the the
+ 
+
+ align:start position:0%
+when an animal gets hungry he the the
+action the the the movement that's part
+
+ align:start position:0%
+action the the the movement that's part
+ 
+
+ align:start position:0%
+action the the the movement that's part
+of the the series of actions that
+
+ align:start position:0%
+of the the series of actions that
+ 
+
+ align:start position:0%
+of the the series of actions that
+compose a fixed action
+
+ align:start position:0%
+compose a fixed action
+ 
+
+ align:start position:0%
+compose a fixed action
+pattern the part with the lowest
+
+ align:start position:0%
+pattern the part with the lowest
+ 
+
+ align:start position:0%
+pattern the part with the lowest
+threshold is repetitive Behavior
+
+ align:start position:0%
+threshold is repetitive Behavior
+ 
+
+ align:start position:0%
+threshold is repetitive Behavior
+searching Behavior so they literally
+
+ align:start position:0%
+searching Behavior so they literally
+ 
+
+ align:start position:0%
+searching Behavior so they literally
+search for the stimulus that will lead
+
+ align:start position:0%
+search for the stimulus that will lead
+ 
+
+ align:start position:0%
+search for the stimulus that will lead
+to the rest of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+and finding appetitive behavior for
+
+ align:start position:0%
+and finding appetitive behavior for
+ 
+
+ align:start position:0%
+and finding appetitive behavior for
+some fix action patterns especially in
+
+ align:start position:0%
+some fix action patterns especially in
+ 
+
+ align:start position:0%
+some fix action patterns especially in
+humans has been led to quite a bit of
+
+ align:start position:0%
+humans has been led to quite a bit of
+ 
+
+ align:start position:0%
+humans has been led to quite a bit of
+controversy and the controversy that
+
+ align:start position:0%
+controversy and the controversy that
+ 
+
+ align:start position:0%
+controversy and the controversy that
+Lawrence got into
+
+ align:start position:0%
+Lawrence got into
+ 
+
+ align:start position:0%
+Lawrence got into
+concerned what he called an appetite for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aggression for example the second one
+
+ align:start position:0%
+aggression for example the second one
+ 
+
+ align:start position:0%
+aggression for example the second one
+the grayle gander you know when he's in
+
+ align:start position:0%
+the grayle gander you know when he's in
+ 
+
+ align:start position:0%
+the grayle gander you know when he's in
+an aggressive mood because he's in the
+
+ align:start position:0%
+an aggressive mood because he's in the
+ 
+
+ align:start position:0%
+an aggressive mood because he's in the
+mating mood
+
+ align:start position:0%
+mating mood
+ 
+
+ align:start position:0%
+mating mood
+uh he literally looks for other
+
+ align:start position:0%
+uh he literally looks for other
+ 
+
+ align:start position:0%
+uh he literally looks for other
+ganders to fight with okay and there's
+
+ align:start position:0%
+ganders to fight with okay and there's
+ 
+
+ align:start position:0%
+ganders to fight with okay and there's
+other many many animals are like this
+
+ align:start position:0%
+other many many animals are like this
+ 
+
+ align:start position:0%
+other many many animals are like this
+and so he applied this to humans he said
+
+ align:start position:0%
+and so he applied this to humans he said
+ 
+
+ align:start position:0%
+and so he applied this to humans he said
+think of the young men roam the streets
+
+ align:start position:0%
+think of the young men roam the streets
+ 
+
+ align:start position:0%
+think of the young men roam the streets
+looking for trouble what are they doing
+
+ align:start position:0%
+looking for trouble what are they doing
+ 
+
+ align:start position:0%
+looking for trouble what are they doing
+it's the same thing they have a
+
+ align:start position:0%
+it's the same thing they have a
+ 
+
+ align:start position:0%
+it's the same thing they have a
+motivation to get into
+
+ align:start position:0%
+motivation to get into
+ 
+
+ align:start position:0%
+motivation to get into
+fights maybe maybe our aggressive video
+
+ align:start position:0%
+fights maybe maybe our aggressive video
+ 
+
+ align:start position:0%
+fights maybe maybe our aggressive video
+games are able to satisfy that urge for
+
+ align:start position:0%
+games are able to satisfy that urge for
+ 
+
+ align:start position:0%
+games are able to satisfy that urge for
+most of a lot of young men but if you
+
+ align:start position:0%
+most of a lot of young men but if you
+ 
+
+ align:start position:0%
+most of a lot of young men but if you
+look at aggressive video games and see
+
+ align:start position:0%
+look at aggressive video games and see
+ 
+
+ align:start position:0%
+look at aggressive video games and see
+who plays them you'll see it's much more
+
+ align:start position:0%
+who plays them you'll see it's much more
+ 
+
+ align:start position:0%
+who plays them you'll see it's much more
+males than females so there are girls
+
+ align:start position:0%
+males than females so there are girls
+ 
+
+ align:start position:0%
+males than females so there are girls
+that do it
+
+ align:start position:0%
+that do it
+ 
+
+ align:start position:0%
+that do it
+too and uh young men that seem to have
+
+ align:start position:0%
+too and uh young men that seem to have
+ 
+
+ align:start position:0%
+too and uh young men that seem to have
+no real desire to fight at all can get
+
+ align:start position:0%
+no real desire to fight at all can get
+ 
+
+ align:start position:0%
+no real desire to fight at all can get
+extremely involved in these games and
+
+ align:start position:0%
+extremely involved in these games and
+ 
+
+ align:start position:0%
+extremely involved in these games and
+they can feel great Triumph when they
+
+ align:start position:0%
+they can feel great Triumph when they
+ 
+
+ align:start position:0%
+they can feel great Triumph when they
+win I remember when my son was growing
+
+ align:start position:0%
+win I remember when my son was growing
+ 
+
+ align:start position:0%
+win I remember when my son was growing
+up uh this was long before he came came
+
+ align:start position:0%
+up uh this was long before he came came
+ 
+
+ align:start position:0%
+up uh this was long before he came came
+to MIT uh he went to the MIT camp and
+
+ align:start position:0%
+to MIT uh he went to the MIT camp and
+ 
+
+ align:start position:0%
+to MIT uh he went to the MIT camp and
+the counselor found out that all the
+
+ align:start position:0%
+the counselor found out that all the
+ 
+
+ align:start position:0%
+the counselor found out that all the
+young men in his group uh were mostly
+
+ align:start position:0%
+young men in his group uh were mostly
+ 
+
+ align:start position:0%
+young men in his group uh were mostly
+Middle School age they love this
+
+ align:start position:0%
+Middle School age they love this
+ 
+
+ align:start position:0%
+Middle School age they love this
+particular video game that he also
+
+ align:start position:0%
+particular video game that he also
+ 
+
+ align:start position:0%
+particular video game that he also
+played it's like many many MIT students
+
+ align:start position:0%
+played it's like many many MIT students
+ 
+
+ align:start position:0%
+played it's like many many MIT students
+so he organized the tournament and the
+
+ align:start position:0%
+so he organized the tournament and the
+ 
+
+ align:start position:0%
+so he organized the tournament and the
+kids got go involved in it you know and
+
+ align:start position:0%
+kids got go involved in it you know and
+ 
+
+ align:start position:0%
+kids got go involved in it you know and
+my son I could tell he's not aggressive
+
+ align:start position:0%
+my son I could tell he's not aggressive
+ 
+
+ align:start position:0%
+my son I could tell he's not aggressive
+but he felt great great Triumph when he
+
+ align:start position:0%
+but he felt great great Triumph when he
+ 
+
+ align:start position:0%
+but he felt great great Triumph when he
+beat the counselor in the first part of
+
+ align:start position:0%
+beat the counselor in the first part of
+ 
+
+ align:start position:0%
+beat the counselor in the first part of
+the tournament of course they continued
+
+ align:start position:0%
+the tournament of course they continued
+ 
+
+ align:start position:0%
+the tournament of course they continued
+the tournament and the counselor beat
+
+ align:start position:0%
+the tournament and the counselor beat
+ 
+
+ align:start position:0%
+the tournament and the counselor beat
+him the second time but you could tell
+
+ align:start position:0%
+him the second time but you could tell
+ 
+
+ align:start position:0%
+him the second time but you could tell
+that he had that a
+
+ align:start position:0%
+that he had that a
+ 
+
+ align:start position:0%
+that he had that a
+drive that was this all happened after
+
+ align:start position:0%
+drive that was this all happened after
+ 
+
+ align:start position:0%
+drive that was this all happened after
+Lawrence of course had done his studies
+
+ align:start position:0%
+Lawrence of course had done his studies
+ 
+
+ align:start position:0%
+Lawrence of course had done his studies
+I don't know what he would say
+
+ align:start position:0%
+I don't know what he would say
+ 
+
+ align:start position:0%
+I don't know what he would say
+about the motivation behind doing these
+
+ align:start position:0%
+about the motivation behind doing these
+ 
+
+ align:start position:0%
+about the motivation behind doing these
+video games but I'm sure what I'm saying
+
+ align:start position:0%
+video games but I'm sure what I'm saying
+ 
+
+ align:start position:0%
+video games but I'm sure what I'm saying
+is some part of the explanation many
+
+ align:start position:0%
+is some part of the explanation many
+ 
+
+ align:start position:0%
+is some part of the explanation many
+experiments done with Jewel fish because
+
+ align:start position:0%
+experiments done with Jewel fish because
+ 
+
+ align:start position:0%
+experiments done with Jewel fish because
+of their fighting behavior and one in
+
+ align:start position:0%
+of their fighting behavior and one in
+ 
+
+ align:start position:0%
+of their fighting behavior and one in
+one of the
+
+ align:start position:0%
+one of the
+ 
+
+ align:start position:0%
+one of the
+experiments male Jewish jewfish that
+
+ align:start position:0%
+experiments male Jewish jewfish that
+ 
+
+ align:start position:0%
+experiments male Jewish jewfish that
+wanted to fight he would could teach
+
+ align:start position:0%
+wanted to fight he would could teach
+ 
+
+ align:start position:0%
+wanted to fight he would could teach
+them a maaz when the only reward was
+
+ align:start position:0%
+them a maaz when the only reward was
+ 
+
+ align:start position:0%
+them a maaz when the only reward was
+getting a a visual view of another Jewel
+
+ align:start position:0%
+getting a a visual view of another Jewel
+ 
+
+ align:start position:0%
+getting a a visual view of another Jewel
+a male Jew Jewel fish also in the
+
+ align:start position:0%
+a male Jew Jewel fish also in the
+ 
+
+ align:start position:0%
+a male Jew Jewel fish also in the
+fighting they change coloration when
+
+ align:start position:0%
+fighting they change coloration when
+ 
+
+ align:start position:0%
+fighting they change coloration when
+they're in that mood and uh just seeing
+
+ align:start position:0%
+they're in that mood and uh just seeing
+ 
+
+ align:start position:0%
+they're in that mood and uh just seeing
+the other male and being able to attack
+
+ align:start position:0%
+the other male and being able to attack
+ 
+
+ align:start position:0%
+the other male and being able to attack
+the glass see they they didn't actually
+
+ align:start position:0%
+the glass see they they didn't actually
+ 
+
+ align:start position:0%
+the glass see they they didn't actually
+fight you didn't need to get them to
+
+ align:start position:0%
+fight you didn't need to get them to
+ 
+
+ align:start position:0%
+fight you didn't need to get them to
+fight to to get that reward and so it
+
+ align:start position:0%
+fight to to get that reward and so it
+ 
+
+ align:start position:0%
+fight to to get that reward and so it
+might seem strange to you but being
+
+ align:start position:0%
+might seem strange to you but being
+ 
+
+ align:start position:0%
+might seem strange to you but being
+hungry can is necessary to be rewarded
+
+ align:start position:0%
+hungry can is necessary to be rewarded
+ 
+
+ align:start position:0%
+hungry can is necessary to be rewarded
+by truth so actually we like to be
+
+ align:start position:0%
+by truth so actually we like to be
+ 
+
+ align:start position:0%
+by truth so actually we like to be
+hungry just not too
+
+ align:start position:0%
+hungry just not too
+ 
+
+ align:start position:0%
+hungry just not too
+hungry okay
+
+ align:start position:0%
+hungry okay
+ 
+
+ align:start position:0%
+hungry okay
+because without being hungry food isn't
+
+ align:start position:0%
+because without being hungry food isn't
+ 
+
+ align:start position:0%
+because without being hungry food isn't
+rewarding and it's the same for the
+
+ align:start position:0%
+rewarding and it's the same for the
+ 
+
+ align:start position:0%
+rewarding and it's the same for the
+aggressive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dve so I just discussed briefly here the
+
+ align:start position:0%
+dve so I just discussed briefly here the
+ 
+
+ align:start position:0%
+dve so I just discussed briefly here the
+reactions people have had against that
+
+ align:start position:0%
+reactions people have had against that
+ 
+
+ align:start position:0%
+reactions people have had against that
+remember for a long time uh especially
+
+ align:start position:0%
+remember for a long time uh especially
+ 
+
+ align:start position:0%
+remember for a long time uh especially
+in America and in Russia there was a
+
+ align:start position:0%
+in America and in Russia there was a
+ 
+
+ align:start position:0%
+in America and in Russia there was a
+pretty strong bias that against any
+
+ align:start position:0%
+pretty strong bias that against any
+ 
+
+ align:start position:0%
+pretty strong bias that against any
+behavior that couldn't be explained in
+
+ align:start position:0%
+behavior that couldn't be explained in
+ 
+
+ align:start position:0%
+behavior that couldn't be explained in
+terms of a stimulus response model you
+
+ align:start position:0%
+terms of a stimulus response model you
+ 
+
+ align:start position:0%
+terms of a stimulus response model you
+know people come to believe that a
+
+ align:start position:0%
+know people come to believe that a
+ 
+
+ align:start position:0%
+know people come to believe that a
+certain model is adequate to explain all
+
+ align:start position:0%
+certain model is adequate to explain all
+ 
+
+ align:start position:0%
+certain model is adequate to explain all
+Behavior they don't like it and there's
+
+ align:start position:0%
+Behavior they don't like it and there's
+ 
+
+ align:start position:0%
+Behavior they don't like it and there's
+some behavior that can't be explained so
+
+ align:start position:0%
+some behavior that can't be explained so
+ 
+
+ align:start position:0%
+some behavior that can't be explained so
+they're going to try to find some way to
+
+ align:start position:0%
+they're going to try to find some way to
+ 
+
+ align:start position:0%
+they're going to try to find some way to
+explain it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away and uh so how could there be an
+
+ align:start position:0%
+away and uh so how could there be an
+ 
+
+ align:start position:0%
+away and uh so how could there be an
+appetite for aggression it has must be a
+
+ align:start position:0%
+appetite for aggression it has must be a
+ 
+
+ align:start position:0%
+appetite for aggression it has must be a
+stimulus and yes there's all they're
+
+ align:start position:0%
+stimulus and yes there's all they're
+ 
+
+ align:start position:0%
+stimulus and yes there's all they're
+always responding to some stimuli but
+
+ align:start position:0%
+always responding to some stimuli but
+ 
+
+ align:start position:0%
+always responding to some stimuli but
+the stimulus can be minimal and the
+
+ align:start position:0%
+the stimulus can be minimal and the
+ 
+
+ align:start position:0%
+the stimulus can be minimal and the
+thresholds can change drastically due to
+
+ align:start position:0%
+thresholds can change drastically due to
+ 
+
+ align:start position:0%
+thresholds can change drastically due to
+an internal State that's
+
+ align:start position:0%
+an internal State that's
+ 
+
+ align:start position:0%
+an internal State that's
+changing and of course we know there was
+
+ align:start position:0%
+changing and of course we know there was
+ 
+
+ align:start position:0%
+changing and of course we know there was
+a bias against instinctive behavior in
+
+ align:start position:0%
+a bias against instinctive behavior in
+ 
+
+ align:start position:0%
+a bias against instinctive behavior in
+general especially in humans but not
+
+ align:start position:0%
+general especially in humans but not
+ 
+
+ align:start position:0%
+general especially in humans but not
+only in humans they I I read studies in
+
+ align:start position:0%
+only in humans they I I read studies in
+ 
+
+ align:start position:0%
+only in humans they I I read studies in
+written in the 30s especially uh before
+
+ align:start position:0%
+written in the 30s especially uh before
+ 
+
+ align:start position:0%
+written in the 30s especially uh before
+World War II where people experimenters
+
+ align:start position:0%
+World War II where people experimenters
+ 
+
+ align:start position:0%
+World War II where people experimenters
+went to Great length to try to proed
+
+ align:start position:0%
+went to Great length to try to proed
+ 
+
+ align:start position:0%
+went to Great length to try to proed
+that some behavior that appeared seemed
+
+ align:start position:0%
+that some behavior that appeared seemed
+ 
+
+ align:start position:0%
+that some behavior that appeared seemed
+to have be innate because it appeared in
+
+ align:start position:0%
+to have be innate because it appeared in
+ 
+
+ align:start position:0%
+to have be innate because it appeared in
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+early uh was actually learned in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+utero it was believed that for example
+
+ align:start position:0%
+utero it was believed that for example
+ 
+
+ align:start position:0%
+utero it was believed that for example
+the the birds that have to Peck their
+
+ align:start position:0%
+the the birds that have to Peck their
+ 
+
+ align:start position:0%
+the the birds that have to Peck their
+way out of an egg they actually learned
+
+ align:start position:0%
+way out of an egg they actually learned
+ 
+
+ align:start position:0%
+way out of an egg they actually learned
+to do that in the uterus or in the egg
+
+ align:start position:0%
+to do that in the uterus or in the egg
+ 
+
+ align:start position:0%
+to do that in the uterus or in the egg
+before they were before they had and
+
+ align:start position:0%
+before they were before they had and
+ 
+
+ align:start position:0%
+before they were before they had and
+they went to Great length to show that
+
+ align:start position:0%
+they went to Great length to show that
+ 
+
+ align:start position:0%
+they went to Great length to show that
+there could be such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experience now people are are not quite
+
+ align:start position:0%
+experience now people are are not quite
+ 
+
+ align:start position:0%
+experience now people are are not quite
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+extreme
+
+ align:start position:0%
+extreme
+ 
+
+ align:start position:0%
+extreme
+although there are still people in the
+
+ align:start position:0%
+although there are still people in the
+ 
+
+ align:start position:0%
+although there are still people in the
+humanities and even in
+
+ align:start position:0%
+humanities and even in
+ 
+
+ align:start position:0%
+humanities and even in
+sociology that believe that all that
+
+ align:start position:0%
+sociology that believe that all that
+ 
+
+ align:start position:0%
+sociology that believe that all that
+unlearn behavior is not important in
+
+ align:start position:0%
+unlearn behavior is not important in
+ 
+
+ align:start position:0%
+unlearn behavior is not important in
+explaining human
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior so let's go back to this topic
+
+ align:start position:0%
+behavior so let's go back to this topic
+ 
+
+ align:start position:0%
+behavior so let's go back to this topic
+of internal Readiness the action
+
+ align:start position:0%
+of internal Readiness the action
+ 
+
+ align:start position:0%
+of internal Readiness the action
+specific potential and how it varies
+
+ align:start position:0%
+specific potential and how it varies
+ 
+
+ align:start position:0%
+specific potential and how it varies
+just to give some
+
+ align:start position:0%
+just to give some
+ 
+
+ align:start position:0%
+just to give some
+examples I mentioned how flying builds
+
+ align:start position:0%
+examples I mentioned how flying builds
+ 
+
+ align:start position:0%
+examples I mentioned how flying builds
+up the different rates and different
+
+ align:start position:0%
+up the different rates and different
+ 
+
+ align:start position:0%
+up the different rates and different
+birds uh but take the example uh I think
+
+ align:start position:0%
+birds uh but take the example uh I think
+ 
+
+ align:start position:0%
+birds uh but take the example uh I think
+this is described in the Lawrence
+
+ align:start position:0%
+this is described in the Lawrence
+ 
+
+ align:start position:0%
+this is described in the Lawrence
+chapter uh from Paul leusen studies of
+
+ align:start position:0%
+chapter uh from Paul leusen studies of
+ 
+
+ align:start position:0%
+chapter uh from Paul leusen studies of
+cats leus studied a number of different
+
+ align:start position:0%
+cats leus studied a number of different
+ 
+
+ align:start position:0%
+cats leus studied a number of different
+species of cats uh found the same fix
+
+ align:start position:0%
+species of cats uh found the same fix
+ 
+
+ align:start position:0%
+species of cats uh found the same fix
+action patterns with slight variations
+
+ align:start position:0%
+action patterns with slight variations
+ 
+
+ align:start position:0%
+action patterns with slight variations
+of course in different species of cat
+
+ align:start position:0%
+of course in different species of cat
+ 
+
+ align:start position:0%
+of course in different species of cat
+including the very large Asian and
+
+ align:start position:0%
+including the very large Asian and
+ 
+
+ align:start position:0%
+including the very large Asian and
+African cats and domestic cats in
+
+ align:start position:0%
+African cats and domestic cats in
+ 
+
+ align:start position:0%
+African cats and domestic cats in
+America and Europe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and if you have a cat that a hunter
+
+ align:start position:0%
+uh and if you have a cat that a hunter
+ 
+
+ align:start position:0%
+uh and if you have a cat that a hunter
+that is he's been exposed to hunting
+
+ align:start position:0%
+that is he's been exposed to hunting
+ 
+
+ align:start position:0%
+that is he's been exposed to hunting
+when he was he's watched his mother hunt
+
+ align:start position:0%
+when he was he's watched his mother hunt
+ 
+
+ align:start position:0%
+when he was he's watched his mother hunt
+he will become a hunter okay and if he's
+
+ align:start position:0%
+he will become a hunter okay and if he's
+ 
+
+ align:start position:0%
+he will become a hunter okay and if he's
+deprived of hunting for a long period
+
+ align:start position:0%
+deprived of hunting for a long period
+ 
+
+ align:start position:0%
+deprived of hunting for a long period
+what does that Cat do if you put him in
+
+ align:start position:0%
+what does that Cat do if you put him in
+ 
+
+ align:start position:0%
+what does that Cat do if you put him in
+a room full of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mice well he he will initially attack
+
+ align:start position:0%
+mice well he he will initially attack
+ 
+
+ align:start position:0%
+mice well he he will initially attack
+and kill a few of those mice then what
+
+ align:start position:0%
+and kill a few of those mice then what
+ 
+
+ align:start position:0%
+and kill a few of those mice then what
+does he
+
+ align:start position:0%
+does he
+ 
+
+ align:start position:0%
+does he
+do does he just stop no he continues to
+
+ align:start position:0%
+do does he just stop no he continues to
+ 
+
+ align:start position:0%
+do does he just stop no he continues to
+stalk and pounce on mice but he stops
+
+ align:start position:0%
+stalk and pounce on mice but he stops
+ 
+
+ align:start position:0%
+stalk and pounce on mice but he stops
+executing the killing bite he will jump
+
+ align:start position:0%
+executing the killing bite he will jump
+ 
+
+ align:start position:0%
+executing the killing bite he will jump
+on them and SWAT them with his
+
+ align:start position:0%
+on them and SWAT them with his
+ 
+
+ align:start position:0%
+on them and SWAT them with his
+paws and it looks like he's playing with
+
+ align:start position:0%
+paws and it looks like he's playing with
+ 
+
+ align:start position:0%
+paws and it looks like he's playing with
+them and then eventually he will stalk
+
+ align:start position:0%
+them and then eventually he will stalk
+ 
+
+ align:start position:0%
+them and then eventually he will stalk
+them but he won't even
+
+ align:start position:0%
+them but he won't even
+ 
+
+ align:start position:0%
+them but he won't even
+p and then eventually he will just he
+
+ align:start position:0%
+p and then eventually he will just he
+ 
+
+ align:start position:0%
+p and then eventually he will just he
+appears to be searching for them he's
+
+ align:start position:0%
+appears to be searching for them he's
+ 
+
+ align:start position:0%
+appears to be searching for them he's
+very alert picks up his ears he's
+
+ align:start position:0%
+very alert picks up his ears he's
+ 
+
+ align:start position:0%
+very alert picks up his ears he's
+watching them he's showing all the
+
+ align:start position:0%
+watching them he's showing all the
+ 
+
+ align:start position:0%
+watching them he's showing all the
+orienting movements of a searching cat
+
+ align:start position:0%
+orienting movements of a searching cat
+ 
+
+ align:start position:0%
+orienting movements of a searching cat
+but now he's not doing any of those
+
+ align:start position:0%
+but now he's not doing any of those
+ 
+
+ align:start position:0%
+but now he's not doing any of those
+things and eventually ACC course he'll
+
+ align:start position:0%
+things and eventually ACC course he'll
+ 
+
+ align:start position:0%
+things and eventually ACC course he'll
+go to
+
+ align:start position:0%
+go to
+ 
+
+ align:start position:0%
+go to
+sleep so that because the the rate at
+
+ align:start position:0%
+sleep so that because the the rate at
+ 
+
+ align:start position:0%
+sleep so that because the the rate at
+which the action specific potential
+
+ align:start position:0%
+which the action specific potential
+ 
+
+ align:start position:0%
+which the action specific potential
+behind each of those fix action patterns
+
+ align:start position:0%
+behind each of those fix action patterns
+ 
+
+ align:start position:0%
+behind each of those fix action patterns
+that have been combined in attack
+
+ align:start position:0%
+that have been combined in attack
+ 
+
+ align:start position:0%
+that have been combined in attack
+behavior of the cat builds up at a
+
+ align:start position:0%
+behavior of the cat builds up at a
+ 
+
+ align:start position:0%
+behavior of the cat builds up at a
+different rate depending on how
+
+ align:start position:0%
+different rate depending on how
+ 
+
+ align:start position:0%
+different rate depending on how
+frequently it's needed in natural life
+
+ align:start position:0%
+frequently it's needed in natural life
+ 
+
+ align:start position:0%
+frequently it's needed in natural life
+of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+animals can you answer this question for
+
+ align:start position:0%
+animals can you answer this question for
+ 
+
+ align:start position:0%
+animals can you answer this question for
+me is it true that cats or dogs hunt
+
+ align:start position:0%
+me is it true that cats or dogs hunt
+ 
+
+ align:start position:0%
+me is it true that cats or dogs hunt
+only in order to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eat and describing experiment to test
+
+ align:start position:0%
+eat and describing experiment to test
+ 
+
+ align:start position:0%
+eat and describing experiment to test
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+idea do they hunt only in order to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eat does a cat that's a r and we know he
+
+ align:start position:0%
+eat does a cat that's a r and we know he
+ 
+
+ align:start position:0%
+eat does a cat that's a r and we know he
+hunts for rats and mice does he do that
+
+ align:start position:0%
+hunts for rats and mice does he do that
+ 
+
+ align:start position:0%
+hunts for rats and mice does he do that
+just in order to eat does he do it
+
+ align:start position:0%
+just in order to eat does he do it
+ 
+
+ align:start position:0%
+just in order to eat does he do it
+because he's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hungry well for one thing how can that
+
+ align:start position:0%
+hungry well for one thing how can that
+ 
+
+ align:start position:0%
+hungry well for one thing how can that
+be people that keep pet cats are feeding
+
+ align:start position:0%
+be people that keep pet cats are feeding
+ 
+
+ align:start position:0%
+be people that keep pet cats are feeding
+them they feed them every day these are
+
+ align:start position:0%
+them they feed them every day these are
+ 
+
+ align:start position:0%
+them they feed them every day these are
+not hungry cats well do they just go out
+
+ align:start position:0%
+not hungry cats well do they just go out
+ 
+
+ align:start position:0%
+not hungry cats well do they just go out
+near feeding time
+
+ align:start position:0%
+near feeding time
+ 
+
+ align:start position:0%
+near feeding time
+no well how can you prove that the
+
+ align:start position:0%
+no well how can you prove that the
+ 
+
+ align:start position:0%
+no well how can you prove that the
+motivation to eat and the motivation to
+
+ align:start position:0%
+motivation to eat and the motivation to
+ 
+
+ align:start position:0%
+motivation to eat and the motivation to
+hunt are quite
+
+ align:start position:0%
+hunt are quite
+ 
+
+ align:start position:0%
+hunt are quite
+separate well you can get that a deprive
+
+ align:start position:0%
+separate well you can get that a deprive
+ 
+
+ align:start position:0%
+separate well you can get that a deprive
+the cat of abil of opportunities to
+
+ align:start position:0%
+the cat of abil of opportunities to
+ 
+
+ align:start position:0%
+the cat of abil of opportunities to
+hunt so his eagerness to hunt builds
+
+ align:start position:0%
+hunt so his eagerness to hunt builds
+ 
+
+ align:start position:0%
+hunt so his eagerness to hunt builds
+up okay
+
+ align:start position:0%
+up okay
+ 
+
+ align:start position:0%
+up okay
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+we put him in a situation where he has
+
+ align:start position:0%
+we put him in a situation where he has
+ 
+
+ align:start position:0%
+we put him in a situation where he has
+to say cross
+
+ align:start position:0%
+to say cross
+ 
+
+ align:start position:0%
+to say cross
+over a dish of tuna fish his favorite
+
+ align:start position:0%
+over a dish of tuna fish his favorite
+ 
+
+ align:start position:0%
+over a dish of tuna fish his favorite
+food just in order to get out and
+
+ align:start position:0%
+food just in order to get out and
+ 
+
+ align:start position:0%
+food just in order to get out and
+Hunt what does he do does he run to the
+
+ align:start position:0%
+Hunt what does he do does he run to the
+ 
+
+ align:start position:0%
+Hunt what does he do does he run to the
+tuna
+
+ align:start position:0%
+tuna
+ 
+
+ align:start position:0%
+tuna
+fish no he'll leap right over it to get
+
+ align:start position:0%
+fish no he'll leap right over it to get
+ 
+
+ align:start position:0%
+fish no he'll leap right over it to get
+out there and hunt and that's been seen
+
+ align:start position:0%
+out there and hunt and that's been seen
+ 
+
+ align:start position:0%
+out there and hunt and that's been seen
+in brain stimulation studies where you
+
+ align:start position:0%
+in brain stimulation studies where you
+ 
+
+ align:start position:0%
+in brain stimulation studies where you
+can stimulate the mood that causes them
+
+ align:start position:0%
+can stimulate the mood that causes them
+ 
+
+ align:start position:0%
+can stimulate the mood that causes them
+to be to go into a hunting mood they'll
+
+ align:start position:0%
+to be to go into a hunting mood they'll
+ 
+
+ align:start position:0%
+to be to go into a hunting mood they'll
+leap over dishes everything just to get
+
+ align:start position:0%
+leap over dishes everything just to get
+ 
+
+ align:start position:0%
+leap over dishes everything just to get
+at a mouse or a
+
+ align:start position:0%
+at a mouse or a
+ 
+
+ align:start position:0%
+at a mouse or a
+rat because the motivation to hunt is
+
+ align:start position:0%
+rat because the motivation to hunt is
+ 
+
+ align:start position:0%
+rat because the motivation to hunt is
+quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separate so it's pretty easy to do an
+
+ align:start position:0%
+separate so it's pretty easy to do an
+ 
+
+ align:start position:0%
+separate so it's pretty easy to do an
+experiment to show that and it has
+
+ align:start position:0%
+experiment to show that and it has
+ 
+
+ align:start position:0%
+experiment to show that and it has
+certainly been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done and similar we can talk about
+
+ align:start position:0%
+done and similar we can talk about
+ 
+
+ align:start position:0%
+done and similar we can talk about
+species that they
+
+ align:start position:0%
+species that they
+ 
+
+ align:start position:0%
+species that they
+don't they don't hunt and kill in the
+
+ align:start position:0%
+don't they don't hunt and kill in the
+ 
+
+ align:start position:0%
+don't they don't hunt and kill in the
+same way that the cats do but they still
+
+ align:start position:0%
+same way that the cats do but they still
+ 
+
+ align:start position:0%
+same way that the cats do but they still
+hunt uh for insects like Lawrence's
+
+ align:start position:0%
+hunt uh for insects like Lawrence's
+ 
+
+ align:start position:0%
+hunt uh for insects like Lawrence's
+starlings uh those
+
+ align:start position:0%
+starlings uh those
+ 
+
+ align:start position:0%
+starlings uh those
+starlings normally when they feed they
+
+ align:start position:0%
+starlings normally when they feed they
+ 
+
+ align:start position:0%
+starlings normally when they feed they
+are poking their bills into the bark of
+
+ align:start position:0%
+are poking their bills into the bark of
+ 
+
+ align:start position:0%
+are poking their bills into the bark of
+trees
+
+ align:start position:0%
+trees
+ 
+
+ align:start position:0%
+trees
+or in leaves and they're poking using
+
+ align:start position:0%
+or in leaves and they're poking using
+ 
+
+ align:start position:0%
+or in leaves and they're poking using
+their bills to poke well if you feed the
+
+ align:start position:0%
+their bills to poke well if you feed the
+ 
+
+ align:start position:0%
+their bills to poke well if you feed the
+it's a pet Starling and you're feeding
+
+ align:start position:0%
+it's a pet Starling and you're feeding
+ 
+
+ align:start position:0%
+it's a pet Starling and you're feeding
+him all the time so he's not hungry that
+
+ align:start position:0%
+him all the time so he's not hungry that
+ 
+
+ align:start position:0%
+him all the time so he's not hungry that
+animal will feed in order to
+
+ align:start position:0%
+animal will feed in order to
+ 
+
+ align:start position:0%
+animal will feed in order to
+poke was the normal sequence who be
+
+ align:start position:0%
+poke was the normal sequence who be
+ 
+
+ align:start position:0%
+poke was the normal sequence who be
+poking in order to get food but now he
+
+ align:start position:0%
+poking in order to get food but now he
+ 
+
+ align:start position:0%
+poking in order to get food but now he
+will he will feed just to be able to
+
+ align:start position:0%
+will he will feed just to be able to
+ 
+
+ align:start position:0%
+will he will feed just to be able to
+poke the cactus uh Finch and the
+
+ align:start position:0%
+poke the cactus uh Finch and the
+ 
+
+ align:start position:0%
+poke the cactus uh Finch and the
+Galapagos is a very interesting
+
+ align:start position:0%
+Galapagos is a very interesting
+ 
+
+ align:start position:0%
+Galapagos is a very interesting
+bird here here you see the a finch and
+
+ align:start position:0%
+bird here here you see the a finch and
+ 
+
+ align:start position:0%
+bird here here you see the a finch and
+it looks like he's got this long
+
+ align:start position:0%
+it looks like he's got this long
+ 
+
+ align:start position:0%
+it looks like he's got this long
+extension of his beak it what it is is a
+
+ align:start position:0%
+extension of his beak it what it is is a
+ 
+
+ align:start position:0%
+extension of his beak it what it is is a
+a cactus thorn
+
+ align:start position:0%
+a cactus thorn
+ 
+
+ align:start position:0%
+a cactus thorn
+that the the bird has found and he uses
+
+ align:start position:0%
+that the the bird has found and he uses
+ 
+
+ align:start position:0%
+that the the bird has found and he uses
+that and all Cactus finches do this they
+
+ align:start position:0%
+that and all Cactus finches do this they
+ 
+
+ align:start position:0%
+that and all Cactus finches do this they
+get that thorn and they use that to poke
+
+ align:start position:0%
+get that thorn and they use that to poke
+ 
+
+ align:start position:0%
+get that thorn and they use that to poke
+deeper into crevices in Cactus and other
+
+ align:start position:0%
+deeper into crevices in Cactus and other
+ 
+
+ align:start position:0%
+deeper into crevices in Cactus and other
+places in order to get food and if you
+
+ align:start position:0%
+places in order to get food and if you
+ 
+
+ align:start position:0%
+places in order to get food and if you
+deprive that Cactus Finch of opportunity
+
+ align:start position:0%
+deprive that Cactus Finch of opportunity
+ 
+
+ align:start position:0%
+deprive that Cactus Finch of opportunity
+to use the thorn that
+
+ align:start position:0%
+to use the thorn that
+ 
+
+ align:start position:0%
+to use the thorn that
+way they will they're highly motivated
+
+ align:start position:0%
+way they will they're highly motivated
+ 
+
+ align:start position:0%
+way they will they're highly motivated
+to do that okay and even if he's wellfed
+
+ align:start position:0%
+to do that okay and even if he's wellfed
+ 
+
+ align:start position:0%
+to do that okay and even if he's wellfed
+he will take the he will search for The
+
+ align:start position:0%
+he will take the he will search for The
+ 
+
+ align:start position:0%
+he will take the he will search for The
+Thorn take the thorn and he'll be out
+
+ align:start position:0%
+Thorn take the thorn and he'll be out
+ 
+
+ align:start position:0%
+Thorn take the thorn and he'll be out
+poking okay because it's a separate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motivation okay now I want to talk
+
+ align:start position:0%
+motivation okay now I want to talk
+ 
+
+ align:start position:0%
+motivation okay now I want to talk
+specifically about the sensory side of
+
+ align:start position:0%
+specifically about the sensory side of
+ 
+
+ align:start position:0%
+specifically about the sensory side of
+these innate behavior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patterns we call the mechanism on that
+
+ align:start position:0%
+patterns we call the mechanism on that
+ 
+
+ align:start position:0%
+patterns we call the mechanism on that
+side the inate releasing mechanism that
+
+ align:start position:0%
+side the inate releasing mechanism that
+ 
+
+ align:start position:0%
+side the inate releasing mechanism that
+was a theoretical term introduced by
+
+ align:start position:0%
+was a theoretical term introduced by
+ 
+
+ align:start position:0%
+was a theoretical term introduced by
+ethologists who did not actually study
+
+ align:start position:0%
+ethologists who did not actually study
+ 
+
+ align:start position:0%
+ethologists who did not actually study
+the nervous
+
+ align:start position:0%
+the nervous
+ 
+
+ align:start position:0%
+the nervous
+system okay but they knew there was an
+
+ align:start position:0%
+system okay but they knew there was an
+ 
+
+ align:start position:0%
+system okay but they knew there was an
+innate releasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mechanism I've seen this
+
+ align:start position:0%
+mechanism I've seen this
+ 
+
+ align:start position:0%
+mechanism I've seen this
+statement and I want you to criticize it
+
+ align:start position:0%
+statement and I want you to criticize it
+ 
+
+ align:start position:0%
+statement and I want you to criticize it
+the innate releasing mechanism responds
+
+ align:start position:0%
+the innate releasing mechanism responds
+ 
+
+ align:start position:0%
+the innate releasing mechanism responds
+to complex stimulus configurations and
+
+ align:start position:0%
+to complex stimulus configurations and
+ 
+
+ align:start position:0%
+to complex stimulus configurations and
+triggers the behavioral response from
+
+ align:start position:0%
+triggers the behavioral response from
+ 
+
+ align:start position:0%
+triggers the behavioral response from
+the organism M sort of a definition of
+
+ align:start position:0%
+the organism M sort of a definition of
+ 
+
+ align:start position:0%
+the organism M sort of a definition of
+innate behavior in some people's view
+
+ align:start position:0%
+innate behavior in some people's view
+ 
+
+ align:start position:0%
+innate behavior in some people's view
+but what's wrong with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it there's a couple of glaring things
+
+ align:start position:0%
+it there's a couple of glaring things
+ 
+
+ align:start position:0%
+it there's a couple of glaring things
+wrong with it first of
+
+ align:start position:0%
+wrong with it first of
+ 
+
+ align:start position:0%
+wrong with it first of
+all these innate releasing mechanis
+
+ align:start position:0%
+all these innate releasing mechanis
+ 
+
+ align:start position:0%
+all these innate releasing mechanis
+mechanisms are at
+
+ align:start position:0%
+mechanisms are at
+ 
+
+ align:start position:0%
+mechanisms are at
+least at the onset when the animal is
+
+ align:start position:0%
+least at the onset when the animal is
+ 
+
+ align:start position:0%
+least at the onset when the animal is
+Young are not responding to complex
+
+ align:start position:0%
+Young are not responding to complex
+ 
+
+ align:start position:0%
+Young are not responding to complex
+stimulus configuration they're
+
+ align:start position:0%
+stimulus configuration they're
+ 
+
+ align:start position:0%
+stimulus configuration they're
+responding to very simple
+
+ align:start position:0%
+responding to very simple
+ 
+
+ align:start position:0%
+responding to very simple
+stimuli and if the response is say of
+
+ align:start position:0%
+stimuli and if the response is say of
+ 
+
+ align:start position:0%
+stimuli and if the response is say of
+the young to the
+
+ align:start position:0%
+the young to the
+ 
+
+ align:start position:0%
+the young to the
+mother he doesn't respond to her as a as
+
+ align:start position:0%
+mother he doesn't respond to her as a as
+ 
+
+ align:start position:0%
+mother he doesn't respond to her as a as
+an individual he responds to specific
+
+ align:start position:0%
+an individual he responds to specific
+ 
+
+ align:start position:0%
+an individual he responds to specific
+stimuli presented by that mother like
+
+ align:start position:0%
+stimuli presented by that mother like
+ 
+
+ align:start position:0%
+stimuli presented by that mother like
+the Herring GS responding to the orange
+
+ align:start position:0%
+the Herring GS responding to the orange
+ 
+
+ align:start position:0%
+the Herring GS responding to the orange
+spot on the mother's beak and an earn
+
+ align:start position:0%
+spot on the mother's beak and an earn
+ 
+
+ align:start position:0%
+spot on the mother's beak and an earn
+spot on a pencil will elicit the same
+
+ align:start position:0%
+spot on a pencil will elicit the same
+ 
+
+ align:start position:0%
+spot on a pencil will elicit the same
+kind of gaping behavior for feeding
+
+ align:start position:0%
+kind of gaping behavior for feeding
+ 
+
+ align:start position:0%
+kind of gaping behavior for feeding
+so the stimulus is generally very simple
+
+ align:start position:0%
+so the stimulus is generally very simple
+ 
+
+ align:start position:0%
+so the stimulus is generally very simple
+and they can be multiple but they're
+
+ align:start position:0%
+and they can be multiple but they're
+ 
+
+ align:start position:0%
+and they can be multiple but they're
+very simple
+
+ align:start position:0%
+very simple
+ 
+
+ align:start position:0%
+very simple
+stimuli so that's the first thing that's
+
+ align:start position:0%
+stimuli so that's the first thing that's
+ 
+
+ align:start position:0%
+stimuli so that's the first thing that's
+wrong with it and now I what about the I
+
+ align:start position:0%
+wrong with it and now I what about the I
+ 
+
+ align:start position:0%
+wrong with it and now I what about the I
+say elicits the behavior as if we're
+
+ align:start position:0%
+say elicits the behavior as if we're
+ 
+
+ align:start position:0%
+say elicits the behavior as if we're
+talking about a reflex but we're not
+
+ align:start position:0%
+talking about a reflex but we're not
+ 
+
+ align:start position:0%
+talking about a reflex but we're not
+talking about reflexes the response will
+
+ align:start position:0%
+talking about reflexes the response will
+ 
+
+ align:start position:0%
+talking about reflexes the response will
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+occur if the motivation level isn't high
+
+ align:start position:0%
+occur if the motivation level isn't high
+ 
+
+ align:start position:0%
+occur if the motivation level isn't high
+that action specific
+
+ align:start position:0%
+that action specific
+ 
+
+ align:start position:0%
+that action specific
+potential okay so there's no inevitable
+
+ align:start position:0%
+potential okay so there's no inevitable
+ 
+
+ align:start position:0%
+potential okay so there's no inevitable
+elicitation of these fixed action
+
+ align:start position:0%
+elicitation of these fixed action
+ 
+
+ align:start position:0%
+elicitation of these fixed action
+patterns the fixed motor component the
+
+ align:start position:0%
+patterns the fixed motor component the
+ 
+
+ align:start position:0%
+patterns the fixed motor component the
+fixed motor pattern component of a fixed
+
+ align:start position:0%
+fixed motor pattern component of a fixed
+ 
+
+ align:start position:0%
+fixed motor pattern component of a fixed
+action pattern that's what's wrong with
+
+ align:start position:0%
+action pattern that's what's wrong with
+ 
+
+ align:start position:0%
+action pattern that's what's wrong with
+the statement we're not dealing with
+
+ align:start position:0%
+the statement we're not dealing with
+ 
+
+ align:start position:0%
+the statement we're not dealing with
+reflexes so let's just give examples of
+
+ align:start position:0%
+reflexes so let's just give examples of
+ 
+
+ align:start position:0%
+reflexes so let's just give examples of
+the Simplicity of the key steami we
+
+ align:start position:0%
+the Simplicity of the key steami we
+ 
+
+ align:start position:0%
+the Simplicity of the key steami we
+talked about the I just mentioned the
+
+ align:start position:0%
+talked about the I just mentioned the
+ 
+
+ align:start position:0%
+talked about the I just mentioned the
+hering gull chicks uh you remember the
+
+ align:start position:0%
+hering gull chicks uh you remember the
+ 
+
+ align:start position:0%
+hering gull chicks uh you remember the
+stickleback fish very simple stimuli in
+
+ align:start position:0%
+stickleback fish very simple stimuli in
+ 
+
+ align:start position:0%
+stickleback fish very simple stimuli in
+the the female that the male responds to
+
+ align:start position:0%
+the the female that the male responds to
+ 
+
+ align:start position:0%
+the the female that the male responds to
+in order to
+
+ align:start position:0%
+in order to
+ 
+
+ align:start position:0%
+in order to
+initiate
+
+ align:start position:0%
+initiate
+ 
+
+ align:start position:0%
+initiate
+his specific actions and leading the
+
+ align:start position:0%
+his specific actions and leading the
+ 
+
+ align:start position:0%
+his specific actions and leading the
+female to his net in order to get her to
+
+ align:start position:0%
+female to his net in order to get her to
+ 
+
+ align:start position:0%
+female to his net in order to get her to
+lay eggs in
+
+ align:start position:0%
+lay eggs in
+ 
+
+ align:start position:0%
+lay eggs in
+it they're not complex
+
+ align:start position:0%
+it they're not complex
+ 
+
+ align:start position:0%
+it they're not complex
+stimuli it's very simple
+
+ align:start position:0%
+stimuli it's very simple
+ 
+
+ align:start position:0%
+stimuli it's very simple
+shapes that are resembled in some
+
+ align:start position:0%
+shapes that are resembled in some
+ 
+
+ align:start position:0%
+shapes that are resembled in some
+way a fish with a SW swollen belly they
+
+ align:start position:0%
+way a fish with a SW swollen belly they
+ 
+
+ align:start position:0%
+way a fish with a SW swollen belly they
+don't even have to look much much like
+
+ align:start position:0%
+don't even have to look much much like
+ 
+
+ align:start position:0%
+don't even have to look much much like
+fish to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us Lawrence mentions the uh the stinging
+
+ align:start position:0%
+us Lawrence mentions the uh the stinging
+ 
+
+ align:start position:0%
+us Lawrence mentions the uh the stinging
+response of the female common tick this
+
+ align:start position:0%
+response of the female common tick this
+ 
+
+ align:start position:0%
+response of the female common tick this
+was an example he got from
+
+ align:start position:0%
+was an example he got from
+ 
+
+ align:start position:0%
+was an example he got from
+yakob in
+
+ align:start position:0%
+yakob in
+ 
+
+ align:start position:0%
+yakob in
+199 uh very simple stimuli elicit that
+
+ align:start position:0%
+199 uh very simple stimuli elicit that
+ 
+
+ align:start position:0%
+199 uh very simple stimuli elicit that
+stinging response of the tick a body
+
+ align:start position:0%
+stinging response of the tick a body
+ 
+
+ align:start position:0%
+stinging response of the tick a body
+temperature of about
+
+ align:start position:0%
+temperature of about
+ 
+
+ align:start position:0%
+temperature of about
+37° and the smell of butyric acid that's
+
+ align:start position:0%
+37° and the smell of butyric acid that's
+ 
+
+ align:start position:0%
+37° and the smell of butyric acid that's
+all it takes and uh we know that the
+
+ align:start position:0%
+all it takes and uh we know that the
+ 
+
+ align:start position:0%
+all it takes and uh we know that the
+tick can fall from a bush onto an
+
+ align:start position:0%
+tick can fall from a bush onto an
+ 
+
+ align:start position:0%
+tick can fall from a bush onto an
+animal and uh we don't think the tick is
+
+ align:start position:0%
+animal and uh we don't think the tick is
+ 
+
+ align:start position:0%
+animal and uh we don't think the tick is
+detecting surface temperatures at a
+
+ align:start position:0%
+detecting surface temperatures at a
+ 
+
+ align:start position:0%
+detecting surface temperatures at a
+distance it probably responds to the
+
+ align:start position:0%
+distance it probably responds to the
+ 
+
+ align:start position:0%
+distance it probably responds to the
+odor of animals passing but then the
+
+ align:start position:0%
+odor of animals passing but then the
+ 
+
+ align:start position:0%
+odor of animals passing but then the
+animal bumps the bush and so forth and
+
+ align:start position:0%
+animal bumps the bush and so forth and
+ 
+
+ align:start position:0%
+animal bumps the bush and so forth and
+the ticks fall onto
+
+ align:start position:0%
+the ticks fall onto
+ 
+
+ align:start position:0%
+the ticks fall onto
+them the stingy response though is
+
+ align:start position:0%
+them the stingy response though is
+ 
+
+ align:start position:0%
+them the stingy response though is
+triggered by those two stimuli that I
+
+ align:start position:0%
+triggered by those two stimuli that I
+ 
+
+ align:start position:0%
+triggered by those two stimuli that I
+mentioned surface temperature plus the
+
+ align:start position:0%
+mentioned surface temperature plus the
+ 
+
+ align:start position:0%
+mentioned surface temperature plus the
+odor you can see the size of it this is
+
+ align:start position:0%
+odor you can see the size of it this is
+ 
+
+ align:start position:0%
+odor you can see the size of it this is
+the tip of a ballpoint pen this is a
+
+ align:start position:0%
+the tip of a ballpoint pen this is a
+ 
+
+ align:start position:0%
+the tip of a ballpoint pen this is a
+tick from a dog and here are some deer
+
+ align:start position:0%
+tick from a dog and here are some deer
+ 
+
+ align:start position:0%
+tick from a dog and here are some deer
+ticks which are a little
+
+ align:start position:0%
+ticks which are a little
+ 
+
+ align:start position:0%
+ticks which are a little
+smaller known for spreading diseases
+
+ align:start position:0%
+smaller known for spreading diseases
+ 
+
+ align:start position:0%
+smaller known for spreading diseases
+like lime's disease it's spread by deer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ticks so the other he talks about the
+
+ align:start position:0%
+ticks so the other he talks about the
+ 
+
+ align:start position:0%
+ticks so the other he talks about the
+common Cricket females response to in
+
+ align:start position:0%
+common Cricket females response to in
+ 
+
+ align:start position:0%
+common Cricket females response to in
+males she's responding to the specific
+
+ align:start position:0%
+males she's responding to the specific
+ 
+
+ align:start position:0%
+males she's responding to the specific
+pitch of the M's courtship song and
+
+ align:start position:0%
+pitch of the M's courtship song and
+ 
+
+ align:start position:0%
+pitch of the M's courtship song and
+different species of crickets have
+
+ align:start position:0%
+different species of crickets have
+ 
+
+ align:start position:0%
+different species of crickets have
+slightly different pitches of
+
+ align:start position:0%
+slightly different pitches of
+ 
+
+ align:start position:0%
+slightly different pitches of
+sound so females of their own species
+
+ align:start position:0%
+sound so females of their own species
+ 
+
+ align:start position:0%
+sound so females of their own species
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+respond just if the pitch is right and
+
+ align:start position:0%
+respond just if the pitch is right and
+ 
+
+ align:start position:0%
+respond just if the pitch is right and
+that's there's something very similar in
+
+ align:start position:0%
+that's there's something very similar in
+ 
+
+ align:start position:0%
+that's there's something very similar in
+mosquitoes the male responds to specific
+
+ align:start position:0%
+mosquitoes the male responds to specific
+ 
+
+ align:start position:0%
+mosquitoes the male responds to specific
+frequencies of the female's Wing beads
+
+ align:start position:0%
+frequencies of the female's Wing beads
+ 
+
+ align:start position:0%
+frequencies of the female's Wing beads
+that buzzing sound we hear when we hear
+
+ align:start position:0%
+that buzzing sound we hear when we hear
+ 
+
+ align:start position:0%
+that buzzing sound we hear when we hear
+a female flying around that's a very
+
+ align:start position:0%
+a female flying around that's a very
+ 
+
+ align:start position:0%
+a female flying around that's a very
+meaningful stimulus for the the male uh
+
+ align:start position:0%
+meaningful stimulus for the the male uh
+ 
+
+ align:start position:0%
+meaningful stimulus for the the male uh
+looking for a female to meet
+
+ align:start position:0%
+looking for a female to meet
+ 
+
+ align:start position:0%
+looking for a female to meet
+with so the stimuli are are very
+
+ align:start position:0%
+with so the stimuli are are very
+ 
+
+ align:start position:0%
+with so the stimuli are are very
+simple let's talk about the contribution
+
+ align:start position:0%
+simple let's talk about the contribution
+ 
+
+ align:start position:0%
+simple let's talk about the contribution
+of Jerry lethon here at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MIT he died just a couple of years ago
+
+ align:start position:0%
+MIT he died just a couple of years ago
+ 
+
+ align:start position:0%
+MIT he died just a couple of years ago
+um but that was long after his
+
+ align:start position:0%
+um but that was long after his
+ 
+
+ align:start position:0%
+um but that was long after his
+retirement from
+
+ align:start position:0%
+retirement from
+ 
+
+ align:start position:0%
+retirement from
+MIT uh back in
+
+ align:start position:0%
+MIT uh back in
+ 
+
+ align:start position:0%
+MIT uh back in
+the 1959 he published a paper that's one
+
+ align:start position:0%
+the 1959 he published a paper that's one
+ 
+
+ align:start position:0%
+the 1959 he published a paper that's one
+of the most highly cited papers in
+
+ align:start position:0%
+of the most highly cited papers in
+ 
+
+ align:start position:0%
+of the most highly cited papers in
+neuroscience and the title was pretty
+
+ align:start position:0%
+neuroscience and the title was pretty
+ 
+
+ align:start position:0%
+neuroscience and the title was pretty
+far out what the frogs ey tells the
+
+ align:start position:0%
+far out what the frogs ey tells the
+ 
+
+ align:start position:0%
+far out what the frogs ey tells the
+Frog's
+
+ align:start position:0%
+Frog's
+ 
+
+ align:start position:0%
+Frog's
+brain and uh it's a very scholarly paper
+
+ align:start position:0%
+brain and uh it's a very scholarly paper
+ 
+
+ align:start position:0%
+brain and uh it's a very scholarly paper
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+reports uh systematically the
+
+ align:start position:0%
+reports uh systematically the
+ 
+
+ align:start position:0%
+reports uh systematically the
+experiments that he did with machira
+
+ align:start position:0%
+experiments that he did with machira
+ 
+
+ align:start position:0%
+experiments that he did with machira
+South American scientist Warren
+
+ align:start position:0%
+South American scientist Warren
+ 
+
+ align:start position:0%
+South American scientist Warren
+mccullock and uh pittz who was another
+
+ align:start position:0%
+mccullock and uh pittz who was another
+ 
+
+ align:start position:0%
+mccullock and uh pittz who was another
+MIT scientist an
+
+ align:start position:0%
+MIT scientist an
+ 
+
+ align:start position:0%
+MIT scientist an
+engineer
+
+ align:start position:0%
+engineer
+ 
+
+ align:start position:0%
+engineer
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+and this is what they were studying they
+
+ align:start position:0%
+and this is what they were studying they
+ 
+
+ align:start position:0%
+and this is what they were studying they
+were studying
+
+ align:start position:0%
+were studying
+ 
+
+ align:start position:0%
+were studying
+basically they were inspired by the
+
+ align:start position:0%
+basically they were inspired by the
+ 
+
+ align:start position:0%
+basically they were inspired by the
+behavior of the fraud this frog is
+
+ align:start position:0%
+behavior of the fraud this frog is
+ 
+
+ align:start position:0%
+behavior of the fraud this frog is
+responding to the visual stimulus of
+
+ align:start position:0%
+responding to the visual stimulus of
+ 
+
+ align:start position:0%
+responding to the visual stimulus of
+that bug on the leag
+
+ align:start position:0%
+that bug on the leag
+ 
+
+ align:start position:0%
+that bug on the leag
+the bug was flying landed on the leaf
+
+ align:start position:0%
+the bug was flying landed on the leaf
+ 
+
+ align:start position:0%
+the bug was flying landed on the leaf
+the Frog
+
+ align:start position:0%
+the Frog
+ 
+
+ align:start position:0%
+the Frog
+waited he might have made an orienting
+
+ align:start position:0%
+waited he might have made an orienting
+ 
+
+ align:start position:0%
+waited he might have made an orienting
+movement towards
+
+ align:start position:0%
+movement towards
+ 
+
+ align:start position:0%
+movement towards
+that bug and then he simply Waits until
+
+ align:start position:0%
+that bug and then he simply Waits until
+ 
+
+ align:start position:0%
+that bug and then he simply Waits until
+the bug is still and then out comes his
+
+ align:start position:0%
+the bug is still and then out comes his
+ 
+
+ align:start position:0%
+the bug is still and then out comes his
+tongue sticky on the
+
+ align:start position:0%
+tongue sticky on the
+ 
+
+ align:start position:0%
+tongue sticky on the
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+uh and they're normally they're pretty
+
+ align:start position:0%
+uh and they're normally they're pretty
+ 
+
+ align:start position:0%
+uh and they're normally they're pretty
+accurate they only flip their tongue out
+
+ align:start position:0%
+accurate they only flip their tongue out
+ 
+
+ align:start position:0%
+accurate they only flip their tongue out
+when the they're close enough to the uh
+
+ align:start position:0%
+when the they're close enough to the uh
+ 
+
+ align:start position:0%
+when the they're close enough to the uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+bug okay so what Leon did he recording
+
+ align:start position:0%
+bug okay so what Leon did he recording
+ 
+
+ align:start position:0%
+bug okay so what Leon did he recording
+electrically you used tiny electrodes in
+
+ align:start position:0%
+electrically you used tiny electrodes in
+ 
+
+ align:start position:0%
+electrically you used tiny electrodes in
+the Frog's
+
+ align:start position:0%
+the Frog's
+ 
+
+ align:start position:0%
+the Frog's
+brain sometimes he did it just from the
+
+ align:start position:0%
+brain sometimes he did it just from the
+ 
+
+ align:start position:0%
+brain sometimes he did it just from the
+stump of the optic nerve because he was
+
+ align:start position:0%
+stump of the optic nerve because he was
+ 
+
+ align:start position:0%
+stump of the optic nerve because he was
+really recording from the accents coming
+
+ align:start position:0%
+really recording from the accents coming
+ 
+
+ align:start position:0%
+really recording from the accents coming
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+retina so it was the activity of retinal
+
+ align:start position:0%
+retina so it was the activity of retinal
+ 
+
+ align:start position:0%
+retina so it was the activity of retinal
+gangling so this was the information
+
+ align:start position:0%
+gangling so this was the information
+ 
+
+ align:start position:0%
+gangling so this was the information
+that reach the midbrain tectum the roof
+
+ align:start position:0%
+that reach the midbrain tectum the roof
+ 
+
+ align:start position:0%
+that reach the midbrain tectum the roof
+of the midbrain where orany
+
+ align:start position:0%
+of the midbrain where orany
+ 
+
+ align:start position:0%
+of the midbrain where orany
+movements are re are
+
+ align:start position:0%
+movements are re are
+ 
+
+ align:start position:0%
+movements are re are
+caused and only after the animal orients
+
+ align:start position:0%
+caused and only after the animal orients
+ 
+
+ align:start position:0%
+caused and only after the animal orients
+and brings it to us the stimulus to a
+
+ align:start position:0%
+and brings it to us the stimulus to a
+ 
+
+ align:start position:0%
+and brings it to us the stimulus to a
+certain part of the
+
+ align:start position:0%
+certain part of the
+ 
+
+ align:start position:0%
+certain part of the
+tectum that then you get the uh tongue
+
+ align:start position:0%
+tectum that then you get the uh tongue
+ 
+
+ align:start position:0%
+tectum that then you get the uh tongue
+flick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+response so he was recording from the
+
+ align:start position:0%
+response so he was recording from the
+ 
+
+ align:start position:0%
+response so he was recording from the
+terminal Arbors of aoms coming from the
+
+ align:start position:0%
+terminal Arbors of aoms coming from the
+ 
+
+ align:start position:0%
+terminal Arbors of aoms coming from the
+retina
+
+ align:start position:0%
+retina
+ 
+
+ align:start position:0%
+retina
+there was argument about that for a
+
+ align:start position:0%
+there was argument about that for a
+ 
+
+ align:start position:0%
+there was argument about that for a
+while but he knew when he wrote that
+
+ align:start position:0%
+while but he knew when he wrote that
+ 
+
+ align:start position:0%
+while but he knew when he wrote that
+paper what he must be recording from
+
+ align:start position:0%
+paper what he must be recording from
+ 
+
+ align:start position:0%
+paper what he must be recording from
+because he had recorded even from aons
+
+ align:start position:0%
+because he had recorded even from aons
+ 
+
+ align:start position:0%
+because he had recorded even from aons
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+nerve and he showed four actually there
+
+ align:start position:0%
+nerve and he showed four actually there
+ 
+
+ align:start position:0%
+nerve and he showed four actually there
+were five types of of axons but four
+
+ align:start position:0%
+were five types of of axons but four
+ 
+
+ align:start position:0%
+were five types of of axons but four
+major ones that he described in great
+
+ align:start position:0%
+major ones that he described in great
+ 
+
+ align:start position:0%
+major ones that he described in great
+detail the one that's the most well
+
+ align:start position:0%
+detail the one that's the most well
+ 
+
+ align:start position:0%
+detail the one that's the most well
+known we called Bug
+
+ align:start position:0%
+known we called Bug
+ 
+
+ align:start position:0%
+known we called Bug
+detectors he didn't call it that in the
+
+ align:start position:0%
+detectors he didn't call it that in the
+ 
+
+ align:start position:0%
+detectors he didn't call it that in the
+paper he called them net convexity
+
+ align:start position:0%
+paper he called them net convexity
+ 
+
+ align:start position:0%
+paper he called them net convexity
+detector tors but he did in his
+
+ align:start position:0%
+detector tors but he did in his
+ 
+
+ align:start position:0%
+detector tors but he did in his
+discussion uh his discussion with these
+
+ align:start position:0%
+discussion uh his discussion with these
+ 
+
+ align:start position:0%
+discussion uh his discussion with these
+other scientists he did talk about that
+
+ align:start position:0%
+other scientists he did talk about that
+ 
+
+ align:start position:0%
+other scientists he did talk about that
+what he had given was sort of a a
+
+ align:start position:0%
+what he had given was sort of a a
+ 
+
+ align:start position:0%
+what he had given was sort of a a
+detailed scientific description of a
+
+ align:start position:0%
+detailed scientific description of a
+ 
+
+ align:start position:0%
+detailed scientific description of a
+bug the kind of stimulus that the bug
+
+ align:start position:0%
+bug the kind of stimulus that the bug
+ 
+
+ align:start position:0%
+bug the kind of stimulus that the bug
+presented to the
+
+ align:start position:0%
+presented to the
+ 
+
+ align:start position:0%
+presented to the
+Frog they those acents were part of what
+
+ align:start position:0%
+Frog they those acents were part of what
+ 
+
+ align:start position:0%
+Frog they those acents were part of what
+we call an innate releasing mechanism
+
+ align:start position:0%
+we call an innate releasing mechanism
+ 
+
+ align:start position:0%
+we call an innate releasing mechanism
+for detecting and orienting towards prey
+
+ align:start position:0%
+for detecting and orienting towards prey
+ 
+
+ align:start position:0%
+for detecting and orienting towards prey
+he found another major type that has a
+
+ align:start position:0%
+he found another major type that has a
+ 
+
+ align:start position:0%
+he found another major type that has a
+easily uh discerned function was he
+
+ align:start position:0%
+easily uh discerned function was he
+ 
+
+ align:start position:0%
+easily uh discerned function was he
+called a a dimming detector and it's
+
+ align:start position:0%
+called a a dimming detector and it's
+ 
+
+ align:start position:0%
+called a a dimming detector and it's
+interesting that the dimming detectors
+
+ align:start position:0%
+interesting that the dimming detectors
+ 
+
+ align:start position:0%
+interesting that the dimming detectors
+were uh the activity of much larger axon
+
+ align:start position:0%
+were uh the activity of much larger axon
+ 
+
+ align:start position:0%
+were uh the activity of much larger axon
+very the most rapidly conducting axon in
+
+ align:start position:0%
+very the most rapidly conducting axon in
+ 
+
+ align:start position:0%
+very the most rapidly conducting axon in
+the optic nerve and that's interesting
+
+ align:start position:0%
+the optic nerve and that's interesting
+ 
+
+ align:start position:0%
+the optic nerve and that's interesting
+because these are responding to sudden
+
+ align:start position:0%
+because these are responding to sudden
+ 
+
+ align:start position:0%
+because these are responding to sudden
+dim of the field of the sort that occurs
+
+ align:start position:0%
+dim of the field of the sort that occurs
+ 
+
+ align:start position:0%
+dim of the field of the sort that occurs
+when there's approaching
+
+ align:start position:0%
+when there's approaching
+ 
+
+ align:start position:0%
+when there's approaching
+predator and so the Frog responds in a
+
+ align:start position:0%
+predator and so the Frog responds in a
+ 
+
+ align:start position:0%
+predator and so the Frog responds in a
+completely different way and note that
+
+ align:start position:0%
+completely different way and note that
+ 
+
+ align:start position:0%
+completely different way and note that
+it's very
+
+ align:start position:0%
+it's very
+ 
+
+ align:start position:0%
+it's very
+fast speed is always at a premium when
+
+ align:start position:0%
+fast speed is always at a premium when
+ 
+
+ align:start position:0%
+fast speed is always at a premium when
+it concerns escape from predators so the
+
+ align:start position:0%
+it concerns escape from predators so the
+ 
+
+ align:start position:0%
+it concerns escape from predators so the
+fastest conducting ones were responding
+
+ align:start position:0%
+fastest conducting ones were responding
+ 
+
+ align:start position:0%
+fastest conducting ones were responding
+to the dimming which would be a visual
+
+ align:start position:0%
+to the dimming which would be a visual
+ 
+
+ align:start position:0%
+to the dimming which would be a visual
+stimulus indicating the very likely
+
+ align:start position:0%
+stimulus indicating the very likely
+ 
+
+ align:start position:0%
+stimulus indicating the very likely
+indicating a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Predator okay now because the key
+
+ align:start position:0%
+Predator okay now because the key
+ 
+
+ align:start position:0%
+Predator okay now because the key
+stimuli are so simple you can get very
+
+ align:start position:0%
+stimuli are so simple you can get very
+ 
+
+ align:start position:0%
+stimuli are so simple you can get very
+maladaptive responses in some cases and
+
+ align:start position:0%
+maladaptive responses in some cases and
+ 
+
+ align:start position:0%
+maladaptive responses in some cases and
+these are a couple that he describes
+
+ align:start position:0%
+these are a couple that he describes
+ 
+
+ align:start position:0%
+these are a couple that he describes
+first of all turkey chicks I'll say a
+
+ align:start position:0%
+first of all turkey chicks I'll say a
+ 
+
+ align:start position:0%
+first of all turkey chicks I'll say a
+little more about turkey chicks
+
+ align:start position:0%
+little more about turkey chicks
+ 
+
+ align:start position:0%
+little more about turkey chicks
+responses to Predators but first what
+
+ align:start position:0%
+responses to Predators but first what
+ 
+
+ align:start position:0%
+responses to Predators but first what
+Lawrence says they respond the very same
+
+ align:start position:0%
+Lawrence says they respond the very same
+ 
+
+ align:start position:0%
+Lawrence says they respond the very same
+way to a fat ply crawling across the
+
+ align:start position:0%
+way to a fat ply crawling across the
+ 
+
+ align:start position:0%
+way to a fat ply crawling across the
+ceiling as they do to a hawk flying
+
+ align:start position:0%
+ceiling as they do to a hawk flying
+ 
+
+ align:start position:0%
+ceiling as they do to a hawk flying
+overhead they don't
+
+ align:start position:0%
+overhead they don't
+ 
+
+ align:start position:0%
+overhead they don't
+discriminate so they make maladaptive
+
+ align:start position:0%
+discriminate so they make maladaptive
+ 
+
+ align:start position:0%
+discriminate so they make maladaptive
+Escape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+responses and he says that young
+
+ align:start position:0%
+responses and he says that young
+ 
+
+ align:start position:0%
+responses and he says that young
+kestrels have an innate response to
+
+ align:start position:0%
+kestrels have an innate response to
+ 
+
+ align:start position:0%
+kestrels have an innate response to
+water they'll make bathing movements but
+
+ align:start position:0%
+water they'll make bathing movements but
+ 
+
+ align:start position:0%
+water they'll make bathing movements but
+they'll do the same thing just to
+
+ align:start position:0%
+they'll do the same thing just to
+ 
+
+ align:start position:0%
+they'll do the same thing just to
+they'll respond to the stimuli from a
+
+ align:start position:0%
+they'll respond to the stimuli from a
+ 
+
+ align:start position:0%
+they'll respond to the stimuli from a
+marble
+
+ align:start position:0%
+marble
+ 
+
+ align:start position:0%
+marble
+tabletop because of the glassy
+
+ align:start position:0%
+tabletop because of the glassy
+ 
+
+ align:start position:0%
+tabletop because of the glassy
+surface that's the only stimulus needed
+
+ align:start position:0%
+surface that's the only stimulus needed
+ 
+
+ align:start position:0%
+surface that's the only stimulus needed
+to elicit the bathing response was
+
+ align:start position:0%
+to elicit the bathing response was
+ 
+
+ align:start position:0%
+to elicit the bathing response was
+obviously not very adaptive these are
+
+ align:start position:0%
+obviously not very adaptive these are
+ 
+
+ align:start position:0%
+obviously not very adaptive these are
+just showing older Kestrel there's the
+
+ align:start position:0%
+just showing older Kestrel there's the
+ 
+
+ align:start position:0%
+just showing older Kestrel there's the
+turkey baby now a little more about that
+
+ align:start position:0%
+turkey baby now a little more about that
+ 
+
+ align:start position:0%
+turkey baby now a little more about that
+this is an experiment
+
+ align:start position:0%
+this is an experiment
+ 
+
+ align:start position:0%
+this is an experiment
+done not too long ago 2001 in the
+
+ align:start position:0%
+done not too long ago 2001 in the
+ 
+
+ align:start position:0%
+done not too long ago 2001 in the
+journal
+
+ align:start position:0%
+journal
+ 
+
+ align:start position:0%
+journal
+Behavior where some nice experiments
+
+ align:start position:0%
+Behavior where some nice experiments
+ 
+
+ align:start position:0%
+Behavior where some nice experiments
+were done
+
+ align:start position:0%
+were done
+ 
+
+ align:start position:0%
+were done
+on turkey chicks why did they use the
+
+ align:start position:0%
+on turkey chicks why did they use the
+ 
+
+ align:start position:0%
+on turkey chicks why did they use the
+this particular particular turkey chick
+
+ align:start position:0%
+this particular particular turkey chick
+ 
+
+ align:start position:0%
+this particular particular turkey chick
+because it was
+
+ align:start position:0%
+because it was
+ 
+
+ align:start position:0%
+because it was
+born uh it was
+
+ align:start position:0%
+born uh it was
+ 
+
+ align:start position:0%
+born uh it was
+hatched
+
+ align:start position:0%
+hatched
+ 
+
+ align:start position:0%
+hatched
+from slightly below ground and the
+
+ align:start position:0%
+from slightly below ground and the
+ 
+
+ align:start position:0%
+from slightly below ground and the
+ground warms up and the Egg ha hatches
+
+ align:start position:0%
+ground warms up and the Egg ha hatches
+ 
+
+ align:start position:0%
+ground warms up and the Egg ha hatches
+no parents around they just hatch and
+
+ align:start position:0%
+no parents around they just hatch and
+ 
+
+ align:start position:0%
+no parents around they just hatch and
+the eggs are deposited separately so
+
+ align:start position:0%
+the eggs are deposited separately so
+ 
+
+ align:start position:0%
+the eggs are deposited separately so
+there's no siblings around either so
+
+ align:start position:0%
+there's no siblings around either so
+ 
+
+ align:start position:0%
+there's no siblings around either so
+they're not exposed to any social cues
+
+ align:start position:0%
+they're not exposed to any social cues
+ 
+
+ align:start position:0%
+they're not exposed to any social cues
+that could teach them anything about
+
+ align:start position:0%
+that could teach them anything about
+ 
+
+ align:start position:0%
+that could teach them anything about
+Predators so if they're going to be able
+
+ align:start position:0%
+Predators so if they're going to be able
+ 
+
+ align:start position:0%
+Predators so if they're going to be able
+to escape from predators when they're
+
+ align:start position:0%
+to escape from predators when they're
+ 
+
+ align:start position:0%
+to escape from predators when they're
+first hatched you know the response has
+
+ align:start position:0%
+first hatched you know the response has
+ 
+
+ align:start position:0%
+first hatched you know the response has
+to be innate and that's why they pick
+
+ align:start position:0%
+to be innate and that's why they pick
+ 
+
+ align:start position:0%
+to be innate and that's why they pick
+this little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chick uh they live solitarily of course
+
+ align:start position:0%
+chick uh they live solitarily of course
+ 
+
+ align:start position:0%
+chick uh they live solitarily of course
+except when they need to
+
+ align:start position:0%
+except when they need to
+ 
+
+ align:start position:0%
+except when they need to
+make they kept them in a large outdo
+
+ align:start position:0%
+make they kept them in a large outdo
+ 
+
+ align:start position:0%
+make they kept them in a large outdo
+door
+
+ align:start position:0%
+door
+ 
+
+ align:start position:0%
+door
+Avery set in a natural rainforest
+
+ align:start position:0%
+Avery set in a natural rainforest
+ 
+
+ align:start position:0%
+Avery set in a natural rainforest
+habitat similar to where they would
+
+ align:start position:0%
+habitat similar to where they would
+ 
+
+ align:start position:0%
+habitat similar to where they would
+normally be found now in these graphs
+
+ align:start position:0%
+normally be found now in these graphs
+ 
+
+ align:start position:0%
+normally be found now in these graphs
+each black bar
+
+ align:start position:0%
+each black bar
+ 
+
+ align:start position:0%
+each black bar
+shows the
+
+ align:start position:0%
+shows the
+ 
+
+ align:start position:0%
+shows the
+amount of a certain kind of behavior
+
+ align:start position:0%
+amount of a certain kind of behavior
+ 
+
+ align:start position:0%
+amount of a certain kind of behavior
+they saw uh in in this case running
+
+ align:start position:0%
+they saw uh in in this case running
+ 
+
+ align:start position:0%
+they saw uh in in this case running
+Behavior okay so the animal is running
+
+ align:start position:0%
+Behavior okay so the animal is running
+ 
+
+ align:start position:0%
+Behavior okay so the animal is running
+in response to the stimuli listed here
+
+ align:start position:0%
+in response to the stimuli listed here
+ 
+
+ align:start position:0%
+in response to the stimuli listed here
+the first bars there are response to a
+
+ align:start position:0%
+the first bars there are response to a
+ 
+
+ align:start position:0%
+the first bars there are response to a
+live cat walking through the the Avy the
+
+ align:start position:0%
+live cat walking through the the Avy the
+ 
+
+ align:start position:0%
+live cat walking through the the Avy the
+second one to a live dog
+
+ align:start position:0%
+second one to a live dog
+ 
+
+ align:start position:0%
+second one to a live dog
+the third one to a snake model okay they
+
+ align:start position:0%
+the third one to a snake model okay they
+ 
+
+ align:start position:0%
+the third one to a snake model okay they
+didn't use a live snake but they had a
+
+ align:start position:0%
+didn't use a live snake but they had a
+ 
+
+ align:start position:0%
+didn't use a live snake but they had a
+model of a snake Okay and as you know
+
+ align:start position:0%
+model of a snake Okay and as you know
+ 
+
+ align:start position:0%
+model of a snake Okay and as you know
+models of snakes can look exactly like a
+
+ align:start position:0%
+models of snakes can look exactly like a
+ 
+
+ align:start position:0%
+models of snakes can look exactly like a
+snake Okay those are the three stimuli
+
+ align:start position:0%
+snake Okay those are the three stimuli
+ 
+
+ align:start position:0%
+snake Okay those are the three stimuli
+that caus the most
+
+ align:start position:0%
+that caus the most
+ 
+
+ align:start position:0%
+that caus the most
+running the stimuli that corresponded to
+
+ align:start position:0%
+running the stimuli that corresponded to
+ 
+
+ align:start position:0%
+running the stimuli that corresponded to
+a model of a Raptor so it's a hawk
+
+ align:start position:0%
+a model of a Raptor so it's a hawk
+ 
+
+ align:start position:0%
+a model of a Raptor so it's a hawk
+model looked like a hawk shape gliding
+
+ align:start position:0%
+model looked like a hawk shape gliding
+ 
+
+ align:start position:0%
+model looked like a hawk shape gliding
+overhead didn't cause the running what
+
+ align:start position:0%
+overhead didn't cause the running what
+ 
+
+ align:start position:0%
+overhead didn't cause the running what
+it did what it did cause was the second
+
+ align:start position:0%
+it did what it did cause was the second
+ 
+
+ align:start position:0%
+it did what it did cause was the second
+response here crouching more crouching
+
+ align:start position:0%
+response here crouching more crouching
+ 
+
+ align:start position:0%
+response here crouching more crouching
+in response to that overhead stimulus
+
+ align:start position:0%
+in response to that overhead stimulus
+ 
+
+ align:start position:0%
+in response to that overhead stimulus
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+any than than in any of the other
+
+ align:start position:0%
+any than than in any of the other
+ 
+
+ align:start position:0%
+any than than in any of the other
+stimuli a little more to cats than to
+
+ align:start position:0%
+stimuli a little more to cats than to
+ 
+
+ align:start position:0%
+stimuli a little more to cats than to
+dogs but mostly to the Raptors but now
+
+ align:start position:0%
+dogs but mostly to the Raptors but now
+ 
+
+ align:start position:0%
+dogs but mostly to the Raptors but now
+notice another thing oh this this one
+
+ align:start position:0%
+notice another thing oh this this one
+ 
+
+ align:start position:0%
+notice another thing oh this this one
+here uh when they they suddenly appear
+
+ align:start position:0%
+here uh when they they suddenly appear
+ 
+
+ align:start position:0%
+here uh when they they suddenly appear
+very Vigilant with their head up and
+
+ align:start position:0%
+very Vigilant with their head up and
+ 
+
+ align:start position:0%
+very Vigilant with their head up and
+they search most with their eyes that
+
+ align:start position:0%
+they search most with their eyes that
+ 
+
+ align:start position:0%
+they search most with their eyes that
+response was elicited most by
+
+ align:start position:0%
+response was elicited most by
+ 
+
+ align:start position:0%
+response was elicited most by
+recordings not of turkey sounds but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of alarm calls of strong birds that live
+
+ align:start position:0%
+of alarm calls of strong birds that live
+ 
+
+ align:start position:0%
+of alarm calls of strong birds that live
+in that
+
+ align:start position:0%
+in that
+ 
+
+ align:start position:0%
+in that
+Forest indicating that these birds
+
+ align:start position:0%
+Forest indicating that these birds
+ 
+
+ align:start position:0%
+Forest indicating that these birds
+almost as soon as they're hatched
+
+ align:start position:0%
+almost as soon as they're hatched
+ 
+
+ align:start position:0%
+almost as soon as they're hatched
+respond to those alarm
+
+ align:start position:0%
+respond to those alarm
+ 
+
+ align:start position:0%
+respond to those alarm
+calls not to turkey calls but to alarm
+
+ align:start position:0%
+calls not to turkey calls but to alarm
+ 
+
+ align:start position:0%
+calls not to turkey calls but to alarm
+calls of other birds birds that live in
+
+ align:start position:0%
+calls of other birds birds that live in
+ 
+
+ align:start position:0%
+calls of other birds birds that live in
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+place and they're responding mostly by
+
+ align:start position:0%
+place and they're responding mostly by
+ 
+
+ align:start position:0%
+place and they're responding mostly by
+that vigilance Behavior what they're
+
+ align:start position:0%
+that vigilance Behavior what they're
+ 
+
+ align:start position:0%
+that vigilance Behavior what they're
+looking for of course
+
+ align:start position:0%
+looking for of course
+ 
+
+ align:start position:0%
+looking for of course
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Predators but now there's a black bar
+
+ align:start position:0%
+Predators but now there's a black bar
+ 
+
+ align:start position:0%
+Predators but now there's a black bar
+and a white bar the black bar is to
+
+ align:start position:0%
+and a white bar the black bar is to
+ 
+
+ align:start position:0%
+and a white bar the black bar is to
+their the live cat and mouse or their
+
+ align:start position:0%
+their the live cat and mouse or their
+ 
+
+ align:start position:0%
+their the live cat and mouse or their
+realistic model the white bars are the
+
+ align:start position:0%
+realistic model the white bars are the
+ 
+
+ align:start position:0%
+realistic model the white bars are the
+response to control stimuli the control
+
+ align:start position:0%
+response to control stimuli the control
+ 
+
+ align:start position:0%
+response to control stimuli the control
+stimuli were in the case of the cat dog
+
+ align:start position:0%
+stimuli were in the case of the cat dog
+ 
+
+ align:start position:0%
+stimuli were in the case of the cat dog
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+us and Raptor they're just cardboard
+
+ align:start position:0%
+us and Raptor they're just cardboard
+ 
+
+ align:start position:0%
+us and Raptor they're just cardboard
+boxes they colored the cardboard
+
+ align:start position:0%
+boxes they colored the cardboard
+ 
+
+ align:start position:0%
+boxes they colored the cardboard
+boxes so they were they controlled for
+
+ align:start position:0%
+boxes so they were they controlled for
+ 
+
+ align:start position:0%
+boxes so they were they controlled for
+the color but not detail for shape and
+
+ align:start position:0%
+the color but not detail for shape and
+ 
+
+ align:start position:0%
+the color but not detail for shape and
+you can see they're usually responding
+
+ align:start position:0%
+you can see they're usually responding
+ 
+
+ align:start position:0%
+you can see they're usually responding
+the same way to the boxes in the case of
+
+ align:start position:0%
+the same way to the boxes in the case of
+ 
+
+ align:start position:0%
+the same way to the boxes in the case of
+the snake they used just a simple
+
+ align:start position:0%
+the snake they used just a simple
+ 
+
+ align:start position:0%
+the snake they used just a simple
+cardboard
+
+ align:start position:0%
+cardboard
+ 
+
+ align:start position:0%
+cardboard
+cylinder that was very effective but
+
+ align:start position:0%
+cylinder that was very effective but
+ 
+
+ align:start position:0%
+cylinder that was very effective but
+there were exceptions to that
+
+ align:start position:0%
+there were exceptions to that
+ 
+
+ align:start position:0%
+there were exceptions to that
+in other words the only thing about this
+
+ align:start position:0%
+in other words the only thing about this
+ 
+
+ align:start position:0%
+in other words the only thing about this
+one that made it a raptor was that it
+
+ align:start position:0%
+one that made it a raptor was that it
+ 
+
+ align:start position:0%
+one that made it a raptor was that it
+was up here and it was about the right
+
+ align:start position:0%
+was up here and it was about the right
+ 
+
+ align:start position:0%
+was up here and it was about the right
+bead of movement and the right side
+
+ align:start position:0%
+bead of movement and the right side
+ 
+
+ align:start position:0%
+bead of movement and the right side
+that's all that was required but notice
+
+ align:start position:0%
+that's all that was required but notice
+ 
+
+ align:start position:0%
+that's all that was required but notice
+here this is the recordings of sound
+
+ align:start position:0%
+here this is the recordings of sound
+ 
+
+ align:start position:0%
+here this is the recordings of sound
+here there was a significant difference
+
+ align:start position:0%
+here there was a significant difference
+ 
+
+ align:start position:0%
+here there was a significant difference
+between the experimental sounds the
+
+ align:start position:0%
+between the experimental sounds the
+ 
+
+ align:start position:0%
+between the experimental sounds the
+recording of the actual alarm calls and
+
+ align:start position:0%
+recording of the actual alarm calls and
+ 
+
+ align:start position:0%
+recording of the actual alarm calls and
+just white noise cuz white noise was the
+
+ align:start position:0%
+just white noise cuz white noise was the
+ 
+
+ align:start position:0%
+just white noise cuz white noise was the
+control here okay so there they have a
+
+ align:start position:0%
+control here okay so there they have a
+ 
+
+ align:start position:0%
+control here okay so there they have a
+specific response specific
+
+ align:start position:0%
+specific response specific
+ 
+
+ align:start position:0%
+specific response specific
+differences and perhaps in the case of
+
+ align:start position:0%
+differences and perhaps in the case of
+ 
+
+ align:start position:0%
+differences and perhaps in the case of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Raptor um there as I mentioned once
+
+ align:start position:0%
+Raptor um there as I mentioned once
+ 
+
+ align:start position:0%
+Raptor um there as I mentioned once
+before in the class there is some
+
+ align:start position:0%
+before in the class there is some
+ 
+
+ align:start position:0%
+before in the class there is some
+evidence that they
+
+ align:start position:0%
+evidence that they
+ 
+
+ align:start position:0%
+evidence that they
+U they have some specificity of response
+
+ align:start position:0%
+U they have some specificity of response
+ 
+
+ align:start position:0%
+U they have some specificity of response
+but you can see here they couldn't
+
+ align:start position:0%
+but you can see here they couldn't
+ 
+
+ align:start position:0%
+but you can see here they couldn't
+confirm it that they it had anything to
+
+ align:start position:0%
+confirm it that they it had anything to
+ 
+
+ align:start position:0%
+confirm it that they it had anything to
+do with the hawk
+
+ align:start position:0%
+do with the hawk
+ 
+
+ align:start position:0%
+do with the hawk
+shap that doesn't mean that later on
+
+ align:start position:0%
+shap that doesn't mean that later on
+ 
+
+ align:start position:0%
+shap that doesn't mean that later on
+doesn't because they can habituate to
+
+ align:start position:0%
+doesn't because they can habituate to
+ 
+
+ align:start position:0%
+doesn't because they can habituate to
+other shapes and they and not to the uh
+
+ align:start position:0%
+other shapes and they and not to the uh
+ 
+
+ align:start position:0%
+other shapes and they and not to the uh
+the hawk if their experience is teaching
+
+ align:start position:0%
+the hawk if their experience is teaching
+ 
+
+ align:start position:0%
+the hawk if their experience is teaching
+them something else but it's interesting
+
+ align:start position:0%
+them something else but it's interesting
+ 
+
+ align:start position:0%
+them something else but it's interesting
+how non-specific some of these fixed
+
+ align:start position:0%
+how non-specific some of these fixed
+ 
+
+ align:start position:0%
+how non-specific some of these fixed
+action the key stimuli can be they're
+
+ align:start position:0%
+action the key stimuli can be they're
+ 
+
+ align:start position:0%
+action the key stimuli can be they're
+very very
+
+ align:start position:0%
+very very
+ 
+
+ align:start position:0%
+very very
+simple what we see is the hawk what they
+
+ align:start position:0%
+simple what we see is the hawk what they
+ 
+
+ align:start position:0%
+simple what we see is the hawk what they
+see is just something up there that's
+
+ align:start position:0%
+see is just something up there that's
+ 
+
+ align:start position:0%
+see is just something up there that's
+about the size of a hawk and moving in a
+
+ align:start position:0%
+about the size of a hawk and moving in a
+ 
+
+ align:start position:0%
+about the size of a hawk and moving in a
+certain way okay
+
+ align:start position:0%
+certain way okay
+ 
+
+ align:start position:0%
+certain way okay
+do humans show maladaptive responses to
+
+ align:start position:0%
+do humans show maladaptive responses to
+ 
+
+ align:start position:0%
+do humans show maladaptive responses to
+key stimuli
+
+ align:start position:0%
+key stimuli
+ 
+
+ align:start position:0%
+key stimuli
+tuo they certainly do we eat too much
+
+ align:start position:0%
+tuo they certainly do we eat too much
+ 
+
+ align:start position:0%
+tuo they certainly do we eat too much
+sugar we eat high fat foods because it
+
+ align:start position:0%
+sugar we eat high fat foods because it
+ 
+
+ align:start position:0%
+sugar we eat high fat foods because it
+tastes better and the restaurants always
+
+ align:start position:0%
+tastes better and the restaurants always
+ 
+
+ align:start position:0%
+tastes better and the restaurants always
+add extra sugar and
+
+ align:start position:0%
+add extra sugar and
+ 
+
+ align:start position:0%
+add extra sugar and
+fat restaurants are a horror horror for
+
+ align:start position:0%
+fat restaurants are a horror horror for
+ 
+
+ align:start position:0%
+fat restaurants are a horror horror for
+diabetics I've learned that I always
+
+ align:start position:0%
+diabetics I've learned that I always
+ 
+
+ align:start position:0%
+diabetics I've learned that I always
+have trouble with my blood sugar after
+
+ align:start position:0%
+have trouble with my blood sugar after
+ 
+
+ align:start position:0%
+have trouble with my blood sugar after
+eating at a restaurant so I ose my
+
+ align:start position:0%
+eating at a restaurant so I ose my
+ 
+
+ align:start position:0%
+eating at a restaurant so I ose my
+restaurants very very carefully and
+
+ align:start position:0%
+restaurants very very carefully and
+ 
+
+ align:start position:0%
+restaurants very very carefully and
+generally won't go to them at
+
+ align:start position:0%
+generally won't go to them at
+ 
+
+ align:start position:0%
+generally won't go to them at
+all what about other things I picked
+
+ align:start position:0%
+all what about other things I picked
+ 
+
+ align:start position:0%
+all what about other things I picked
+this quote from the internet that I
+
+ align:start position:0%
+this quote from the internet that I
+ 
+
+ align:start position:0%
+this quote from the internet that I
+found this just couple just last year
+
+ align:start position:0%
+found this just couple just last year
+ 
+
+ align:start position:0%
+found this just couple just last year
+like all animals humans have instincts
+
+ align:start position:0%
+like all animals humans have instincts
+ 
+
+ align:start position:0%
+like all animals humans have instincts
+genetically hard hardwired behaviors
+
+ align:start position:0%
+genetically hard hardwired behaviors
+ 
+
+ align:start position:0%
+genetically hard hardwired behaviors
+that enhance our ability to cope with
+
+ align:start position:0%
+that enhance our ability to cope with
+ 
+
+ align:start position:0%
+that enhance our ability to cope with
+vital environmental contingencies our
+
+ align:start position:0%
+vital environmental contingencies our
+ 
+
+ align:start position:0%
+vital environmental contingencies our
+innate fear of snakes is an
+
+ align:start position:0%
+innate fear of snakes is an
+ 
+
+ align:start position:0%
+innate fear of snakes is an
+example other instincts including denial
+
+ align:start position:0%
+example other instincts including denial
+ 
+
+ align:start position:0%
+example other instincts including denial
+Revenge tribal loyalty greed and our
+
+ align:start position:0%
+Revenge tribal loyalty greed and our
+ 
+
+ align:start position:0%
+Revenge tribal loyalty greed and our
+urge to procreate now threaten our very
+
+ align:start position:0%
+urge to procreate now threaten our very
+ 
+
+ align:start position:0%
+urge to procreate now threaten our very
+existence in other words it's important
+
+ align:start position:0%
+existence in other words it's important
+ 
+
+ align:start position:0%
+existence in other words it's important
+we come to
+
+ align:start position:0%
+we come to
+ 
+
+ align:start position:0%
+we come to
+understand our own fixed action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patterns let's talk about one more thing
+
+ align:start position:0%
+patterns let's talk about one more thing
+ 
+
+ align:start position:0%
+patterns let's talk about one more thing
+here Lawrence's discussion of the
+
+ align:start position:0%
+here Lawrence's discussion of the
+ 
+
+ align:start position:0%
+here Lawrence's discussion of the
+transposability of key stimuli all he
+
+ align:start position:0%
+transposability of key stimuli all he
+ 
+
+ align:start position:0%
+transposability of key stimuli all he
+means is that animals are
+
+ align:start position:0%
+means is that animals are
+ 
+
+ align:start position:0%
+means is that animals are
+responding not the exact size of the
+
+ align:start position:0%
+responding not the exact size of the
+ 
+
+ align:start position:0%
+responding not the exact size of the
+stimuli usually doesn't matter but it's
+
+ align:start position:0%
+stimuli usually doesn't matter but it's
+ 
+
+ align:start position:0%
+stimuli usually doesn't matter but it's
+the if it's the configuration at all
+
+ align:start position:0%
+the if it's the configuration at all
+ 
+
+ align:start position:0%
+the if it's the configuration at all
+this is unlike in those turkeys where
+
+ align:start position:0%
+this is unlike in those turkeys where
+ 
+
+ align:start position:0%
+this is unlike in those turkeys where
+the size and movement were seem to be
+
+ align:start position:0%
+the size and movement were seem to be
+ 
+
+ align:start position:0%
+the size and movement were seem to be
+critical but in most cases it's the
+
+ align:start position:0%
+critical but in most cases it's the
+ 
+
+ align:start position:0%
+critical but in most cases it's the
+relationship between stimuli just like
+
+ align:start position:0%
+relationship between stimuli just like
+ 
+
+ align:start position:0%
+relationship between stimuli just like
+the relationship between sounds in a
+
+ align:start position:0%
+the relationship between sounds in a
+ 
+
+ align:start position:0%
+the relationship between sounds in a
+song We recognize the song even though
+
+ align:start position:0%
+song We recognize the song even though
+ 
+
+ align:start position:0%
+song We recognize the song even though
+the pitch may vary a lot and the
+
+ align:start position:0%
+the pitch may vary a lot and the
+ 
+
+ align:start position:0%
+the pitch may vary a lot and the
+loudness may vary a lot we can still
+
+ align:start position:0%
+loudness may vary a lot we can still
+ 
+
+ align:start position:0%
+loudness may vary a lot we can still
+recognize
+
+ align:start position:0%
+recognize
+ 
+
+ align:start position:0%
+recognize
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+uh and you can use dummy stimuli I just
+
+ align:start position:0%
+uh and you can use dummy stimuli I just
+ 
+
+ align:start position:0%
+uh and you can use dummy stimuli I just
+drew some of these uh most little birds
+
+ align:start position:0%
+drew some of these uh most little birds
+ 
+
+ align:start position:0%
+drew some of these uh most little birds
+uh nesting crushes they respond to any
+
+ align:start position:0%
+uh nesting crushes they respond to any
+ 
+
+ align:start position:0%
+uh nesting crushes they respond to any
+stimulus that's even remotely similar to
+
+ align:start position:0%
+stimulus that's even remotely similar to
+ 
+
+ align:start position:0%
+stimulus that's even remotely similar to
+a bird all it has to have is a a top
+
+ align:start position:0%
+a bird all it has to have is a a top
+ 
+
+ align:start position:0%
+a bird all it has to have is a a top
+part that's about one3 the size of the
+
+ align:start position:0%
+part that's about one3 the size of the
+ 
+
+ align:start position:0%
+part that's about one3 the size of the
+bottom part and they will show gaping
+
+ align:start position:0%
+bottom part and they will show gaping
+ 
+
+ align:start position:0%
+bottom part and they will show gaping
+it's about all they all they require
+
+ align:start position:0%
+it's about all they all they require
+ 
+
+ align:start position:0%
+it's about all they all they require
+seems very stupid what they're doing but
+
+ align:start position:0%
+seems very stupid what they're doing but
+ 
+
+ align:start position:0%
+seems very stupid what they're doing but
+that's all that's required and if you
+
+ align:start position:0%
+that's all that's required and if you
+ 
+
+ align:start position:0%
+that's all that's required and if you
+have two sticks like this they're
+
+ align:start position:0%
+have two sticks like this they're
+ 
+
+ align:start position:0%
+have two sticks like this they're
+presented like this they'll always
+
+ align:start position:0%
+presented like this they'll always
+ 
+
+ align:start position:0%
+presented like this they'll always
+respond to the upper one if they're
+
+ align:start position:0%
+respond to the upper one if they're
+ 
+
+ align:start position:0%
+respond to the upper one if they're
+presented once much closer then they
+
+ align:start position:0%
+presented once much closer then they
+ 
+
+ align:start position:0%
+presented once much closer then they
+will respond if it's presented
+
+ align:start position:0%
+will respond if it's presented
+ 
+
+ align:start position:0%
+will respond if it's presented
+horizontally anyway they'll respond to
+
+ align:start position:0%
+horizontally anyway they'll respond to
+ 
+
+ align:start position:0%
+horizontally anyway they'll respond to
+the uh the nearer one but if they're
+
+ align:start position:0%
+the uh the nearer one but if they're
+ 
+
+ align:start position:0%
+the uh the nearer one but if they're
+presented like this even though this is
+
+ align:start position:0%
+presented like this even though this is
+ 
+
+ align:start position:0%
+presented like this even though this is
+near they'll still go for the upper one
+
+ align:start position:0%
+near they'll still go for the upper one
+ 
+
+ align:start position:0%
+near they'll still go for the upper one
+because it it's just a matter of
+
+ align:start position:0%
+because it it's just a matter of
+ 
+
+ align:start position:0%
+because it it's just a matter of
+probabilities what they're likely to
+
+ align:start position:0%
+probabilities what they're likely to
+ 
+
+ align:start position:0%
+probabilities what they're likely to
+encounter in that Nest when they're
+
+ align:start position:0%
+encounter in that Nest when they're
+ 
+
+ align:start position:0%
+encounter in that Nest when they're
+feeding and these simple stimulus
+
+ align:start position:0%
+feeding and these simple stimulus
+ 
+
+ align:start position:0%
+feeding and these simple stimulus
+properties have been exploited by other
+
+ align:start position:0%
+properties have been exploited by other
+ 
+
+ align:start position:0%
+properties have been exploited by other
+birds birds like the Kaku that lay their
+
+ align:start position:0%
+birds birds like the Kaku that lay their
+ 
+
+ align:start position:0%
+birds birds like the Kaku that lay their
+nest in other birds
+
+ align:start position:0%
+nest in other birds
+ 
+
+ align:start position:0%
+nest in other birds
+nest because those other birds
+
+ align:start position:0%
+nest because those other birds
+ 
+
+ align:start position:0%
+nest because those other birds
+respond to the egg in fact if it's a
+
+ align:start position:0%
+respond to the egg in fact if it's a
+ 
+
+ align:start position:0%
+respond to the egg in fact if it's a
+little larger they might respond better
+
+ align:start position:0%
+little larger they might respond better
+ 
+
+ align:start position:0%
+little larger they might respond better
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+it often the eggs depending on the the
+
+ align:start position:0%
+it often the eggs depending on the the
+ 
+
+ align:start position:0%
+it often the eggs depending on the the
+uh parasitic bird uh resembles their egg
+
+ align:start position:0%
+uh parasitic bird uh resembles their egg
+ 
+
+ align:start position:0%
+uh parasitic bird uh resembles their egg
+in the case of the caku it doesn't
+
+ align:start position:0%
+in the case of the caku it doesn't
+ 
+
+ align:start position:0%
+in the case of the caku it doesn't
+always in the case of the white bird the
+
+ align:start position:0%
+always in the case of the white bird the
+ 
+
+ align:start position:0%
+always in the case of the white bird the
+egg mimics their own the Egg of the
+
+ align:start position:0%
+egg mimics their own the Egg of the
+ 
+
+ align:start position:0%
+egg mimics their own the Egg of the
+species they they Cooling and getting to
+
+ align:start position:0%
+species they they Cooling and getting to
+ 
+
+ align:start position:0%
+species they they Cooling and getting to
+raise their young and even their babies
+
+ align:start position:0%
+raise their young and even their babies
+ 
+
+ align:start position:0%
+raise their young and even their babies
+look like the other species for a while
+
+ align:start position:0%
+look like the other species for a while
+ 
+
+ align:start position:0%
+look like the other species for a while
+whdas are much more innocuous in that
+
+ align:start position:0%
+whdas are much more innocuous in that
+ 
+
+ align:start position:0%
+whdas are much more innocuous in that
+they don't destroy the other birds in
+
+ align:start position:0%
+they don't destroy the other birds in
+ 
+
+ align:start position:0%
+they don't destroy the other birds in
+the nest but the cuu is horrible you
+
+ align:start position:0%
+the nest but the cuu is horrible you
+ 
+
+ align:start position:0%
+the nest but the cuu is horrible you
+know it puts its egg in there and it
+
+ align:start position:0%
+know it puts its egg in there and it
+ 
+
+ align:start position:0%
+know it puts its egg in there and it
+hatches at least one of those eggs won't
+
+ align:start position:0%
+hatches at least one of those eggs won't
+ 
+
+ align:start position:0%
+hatches at least one of those eggs won't
+even survive the the the chick won't
+
+ align:start position:0%
+even survive the the the chick won't
+ 
+
+ align:start position:0%
+even survive the the the chick won't
+even survive and in many cases no other
+
+ align:start position:0%
+even survive and in many cases no other
+ 
+
+ align:start position:0%
+even survive and in many cases no other
+little birds will survive just the caku
+
+ align:start position:0%
+little birds will survive just the caku
+ 
+
+ align:start position:0%
+little birds will survive just the caku
+so why do they do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it Lauren says there it's their Vice
+
+ align:start position:0%
+it Lauren says there it's their Vice
+ 
+
+ align:start position:0%
+it Lauren says there it's their Vice
+they they can't you know a vice is
+
+ align:start position:0%
+they they can't you know a vice is
+ 
+
+ align:start position:0%
+they they can't you know a vice is
+you're following an instinct that's bad
+
+ align:start position:0%
+you're following an instinct that's bad
+ 
+
+ align:start position:0%
+you're following an instinct that's bad
+for you he says a vice of these birds is
+
+ align:start position:0%
+for you he says a vice of these birds is
+ 
+
+ align:start position:0%
+for you he says a vice of these birds is
+they they respond to the gaping response
+
+ align:start position:0%
+they they respond to the gaping response
+ 
+
+ align:start position:0%
+they they respond to the gaping response
+of these look at look at the gape here
+
+ align:start position:0%
+of these look at look at the gape here
+ 
+
+ align:start position:0%
+of these look at look at the gape here
+of the kuu here's this enormous chick
+
+ align:start position:0%
+of the kuu here's this enormous chick
+ 
+
+ align:start position:0%
+of the kuu here's this enormous chick
+with this huge gape and there's the Reed
+
+ align:start position:0%
+with this huge gape and there's the Reed
+ 
+
+ align:start position:0%
+with this huge gape and there's the Reed
+warbler feeding
+
+ align:start position:0%
+warbler feeding
+ 
+
+ align:start position:0%
+warbler feeding
+him that's his vice he can't
+
+ align:start position:0%
+him that's his vice he can't
+ 
+
+ align:start position:0%
+him that's his vice he can't
+resist okay so think about why they why
+
+ align:start position:0%
+resist okay so think about why they why
+ 
+
+ align:start position:0%
+resist okay so think about why they why
+don't the birds evolve some way to avoid
+
+ align:start position:0%
+don't the birds evolve some way to avoid
+ 
+
+ align:start position:0%
+don't the birds evolve some way to avoid
+this being taken advantage of and having
+
+ align:start position:0%
+this being taken advantage of and having
+ 
+
+ align:start position:0%
+this being taken advantage of and having
+their own reproduction go
+
+ align:start position:0%
+their own reproduction go
+ 
+
+ align:start position:0%
+their own reproduction go
+down because another bird they're
+
+ align:start position:0%
+down because another bird they're
+ 
+
+ align:start position:0%
+down because another bird they're
+raising other Bird's chicks we'll talk
+
+ align:start position:0%
+raising other Bird's chicks we'll talk
+ 
+
+ align:start position:0%
+raising other Bird's chicks we'll talk
+about that next time
\ No newline at end of file
diff --git a/fp7wylcPRKM.txt b/fp7wylcPRKM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7f10238ae75c55cd22096b61fce4568b3efebb33
--- /dev/null
+++ b/fp7wylcPRKM.txt
@@ -0,0 +1,1819 @@
+align:start position:0%
+ 
+okay so as Kristen said I'm barbert Huey
+
+ align:start position:0%
+okay so as Kristen said I'm barbert Huey
+ 
+
+ align:start position:0%
+okay so as Kristen said I'm barbert Huey
+I teach in the mechanical engineering
+
+ align:start position:0%
+I teach in the mechanical engineering
+ 
+
+ align:start position:0%
+I teach in the mechanical engineering
+department at MIT and I thought you
+
+ align:start position:0%
+department at MIT and I thought you
+ 
+
+ align:start position:0%
+department at MIT and I thought you
+might wanted to see a little bit about
+
+ align:start position:0%
+might wanted to see a little bit about
+ 
+
+ align:start position:0%
+might wanted to see a little bit about
+me so I was more or less from New Jersey
+
+ align:start position:0%
+me so I was more or less from New Jersey
+ 
+
+ align:start position:0%
+me so I was more or less from New Jersey
+I was born in Philadelphia lived in New
+
+ align:start position:0%
+I was born in Philadelphia lived in New
+ 
+
+ align:start position:0%
+I was born in Philadelphia lived in New
+Jersey and outside of
+
+ align:start position:0%
+Jersey and outside of
+ 
+
+ align:start position:0%
+Jersey and outside of
+Philadelphia there we go moved back and
+
+ align:start position:0%
+Philadelphia there we go moved back and
+ 
+
+ align:start position:0%
+Philadelphia there we go moved back and
+forth about 2 and2 years briefly mov to
+
+ align:start position:0%
+forth about 2 and2 years briefly mov to
+ 
+
+ align:start position:0%
+forth about 2 and2 years briefly mov to
+Southern California when
+
+ align:start position:0%
+Southern California when
+ 
+
+ align:start position:0%
+Southern California when
+and in I was undergraduate where I went
+
+ align:start position:0%
+and in I was undergraduate where I went
+ 
+
+ align:start position:0%
+and in I was undergraduate where I went
+in as a physics major I had always loved
+
+ align:start position:0%
+in as a physics major I had always loved
+ 
+
+ align:start position:0%
+in as a physics major I had always loved
+math and physics I ended up coming out
+
+ align:start position:0%
+math and physics I ended up coming out
+ 
+
+ align:start position:0%
+math and physics I ended up coming out
+with with an engineering Physics degree
+
+ align:start position:0%
+with with an engineering Physics degree
+ 
+
+ align:start position:0%
+with with an engineering Physics degree
+in the mechanical and aerospace
+
+ align:start position:0%
+in the mechanical and aerospace
+ 
+
+ align:start position:0%
+in the mechanical and aerospace
+engineering department which was awesome
+
+ align:start position:0%
+engineering department which was awesome
+ 
+
+ align:start position:0%
+engineering department which was awesome
+for what I'm doing now and also for a
+
+ align:start position:0%
+for what I'm doing now and also for a
+ 
+
+ align:start position:0%
+for what I'm doing now and also for a
+lot of the research I did um before I
+
+ align:start position:0%
+lot of the research I did um before I
+ 
+
+ align:start position:0%
+lot of the research I did um before I
+came back to MIT and then I came up to
+
+ align:start position:0%
+came back to MIT and then I came up to
+ 
+
+ align:start position:0%
+came back to MIT and then I came up to
+Boston to get my PhD in physics at MIT
+
+ align:start position:0%
+Boston to get my PhD in physics at MIT
+ 
+
+ align:start position:0%
+Boston to get my PhD in physics at MIT
+very highly esoteric subject that was
+
+ align:start position:0%
+very highly esoteric subject that was
+ 
+
+ align:start position:0%
+very highly esoteric subject that was
+great fun involving quantum mechanics
+
+ align:start position:0%
+great fun involving quantum mechanics
+ 
+
+ align:start position:0%
+great fun involving quantum mechanics
+but not terribly useful and then I
+
+ align:start position:0%
+but not terribly useful and then I
+ 
+
+ align:start position:0%
+but not terribly useful and then I
+worked for a couple small companies in
+
+ align:start position:0%
+worked for a couple small companies in
+ 
+
+ align:start position:0%
+worked for a couple small companies in
+the area mostly doing um applications of
+
+ align:start position:0%
+the area mostly doing um applications of
+ 
+
+ align:start position:0%
+the area mostly doing um applications of
+particle accelerators to medicine and
+
+ align:start position:0%
+particle accelerators to medicine and
+ 
+
+ align:start position:0%
+particle accelerators to medicine and
+actually a lot of it I know you're
+
+ align:start position:0%
+actually a lot of it I know you're
+ 
+
+ align:start position:0%
+actually a lot of it I know you're
+spending the day on sort of Imaging and
+
+ align:start position:0%
+spending the day on sort of Imaging and
+ 
+
+ align:start position:0%
+spending the day on sort of Imaging and
+image processing I did a lot with
+
+ align:start position:0%
+image processing I did a lot with
+ 
+
+ align:start position:0%
+image processing I did a lot with
+positron emission tomography images
+
+ align:start position:0%
+positron emission tomography images
+ 
+
+ align:start position:0%
+positron emission tomography images
+magnetic MRI images things like that and
+
+ align:start position:0%
+magnetic MRI images things like that and
+ 
+
+ align:start position:0%
+magnetic MRI images things like that and
+then in 2002 I came back to MIT to teach
+
+ align:start position:0%
+then in 2002 I came back to MIT to teach
+ 
+
+ align:start position:0%
+then in 2002 I came back to MIT to teach
+the undergraduate measurement and
+
+ align:start position:0%
+the undergraduate measurement and
+ 
+
+ align:start position:0%
+the undergraduate measurement and
+instrumentation class where I basically
+
+ align:start position:0%
+instrumentation class where I basically
+ 
+
+ align:start position:0%
+instrumentation class where I basically
+teach students how to do experiments and
+
+ align:start position:0%
+teach students how to do experiments and
+ 
+
+ align:start position:0%
+teach students how to do experiments and
+we have a project we call go forth and
+
+ align:start position:0%
+we have a project we call go forth and
+ 
+
+ align:start position:0%
+we have a project we call go forth and
+measure where each student picks their
+
+ align:start position:0%
+measure where each student picks their
+ 
+
+ align:start position:0%
+measure where each student picks their
+own project and does something actually
+
+ align:start position:0%
+own project and does something actually
+ 
+
+ align:start position:0%
+own project and does something actually
+Kristen what was your go forth and
+
+ align:start position:0%
+Kristen what was your go forth and
+ 
+
+ align:start position:0%
+Kristen what was your go forth and
+measure
+
+ align:start position:0%
+measure
+ 
+
+ align:start position:0%
+measure
+what was your go forth and measure
+
+ align:start position:0%
+what was your go forth and measure
+ 
+
+ align:start position:0%
+what was your go forth and measure
+project me you oh does anyone like to
+
+ align:start position:0%
+project me you oh does anyone like to
+ 
+
+ align:start position:0%
+project me you oh does anyone like to
+run here track awesome me too I did um I
+
+ align:start position:0%
+run here track awesome me too I did um I
+ 
+
+ align:start position:0%
+run here track awesome me too I did um I
+took a pressure sensor and put it inside
+
+ align:start position:0%
+took a pressure sensor and put it inside
+ 
+
+ align:start position:0%
+took a pressure sensor and put it inside
+a sneaker and I tried running on
+
+ align:start position:0%
+a sneaker and I tried running on
+ 
+
+ align:start position:0%
+a sneaker and I tried running on
+different surfaces and compared the
+
+ align:start position:0%
+different surfaces and compared the
+ 
+
+ align:start position:0%
+different surfaces and compared the
+impact of running on a treadmill versus
+
+ align:start position:0%
+impact of running on a treadmill versus
+ 
+
+ align:start position:0%
+impact of running on a treadmill versus
+running on
+
+ align:start position:0%
+running on
+ 
+
+ align:start position:0%
+running on
+concrete and we have a lot of really
+
+ align:start position:0%
+concrete and we have a lot of really
+ 
+
+ align:start position:0%
+concrete and we have a lot of really
+cool projects like that where people do
+
+ align:start position:0%
+cool projects like that where people do
+ 
+
+ align:start position:0%
+cool projects like that where people do
+everyday things that they're interested
+
+ align:start position:0%
+everyday things that they're interested
+ 
+
+ align:start position:0%
+everyday things that they're interested
+in including food things like that so
+
+ align:start position:0%
+in including food things like that so
+ 
+
+ align:start position:0%
+in including food things like that so
+anyways back to the women's technology
+
+ align:start position:0%
+anyways back to the women's technology
+ 
+
+ align:start position:0%
+anyways back to the women's technology
+program so I came to MIT in 2002 in 2006
+
+ align:start position:0%
+program so I came to MIT in 2002 in 2006
+ 
+
+ align:start position:0%
+program so I came to MIT in 2002 in 2006
+I was asked to expand the existing
+
+ align:start position:0%
+I was asked to expand the existing
+ 
+
+ align:start position:0%
+I was asked to expand the existing
+women's Technology Program which was
+
+ align:start position:0%
+women's Technology Program which was
+ 
+
+ align:start position:0%
+women's Technology Program which was
+founded in 2002 in electrical
+
+ align:start position:0%
+founded in 2002 in electrical
+ 
+
+ align:start position:0%
+founded in 2002 in electrical
+engineering and computer science so most
+
+ align:start position:0%
+engineering and computer science so most
+ 
+
+ align:start position:0%
+engineering and computer science so most
+of what you're doing today would fit
+
+ align:start position:0%
+of what you're doing today would fit
+ 
+
+ align:start position:0%
+of what you're doing today would fit
+more in that um and then we expanded it
+
+ align:start position:0%
+more in that um and then we expanded it
+ 
+
+ align:start position:0%
+more in that um and then we expanded it
+to mechanical engineering and the goal
+
+ align:start position:0%
+to mechanical engineering and the goal
+ 
+
+ align:start position:0%
+to mechanical engineering and the goal
+is to spark high school girls interest
+
+ align:start position:0%
+is to spark high school girls interest
+ 
+
+ align:start position:0%
+is to spark high school girls interest
+in studying engineering and computer
+
+ align:start position:0%
+in studying engineering and computer
+ 
+
+ align:start position:0%
+in studying engineering and computer
+science which is I think exactly the
+
+ align:start position:0%
+science which is I think exactly the
+ 
+
+ align:start position:0%
+science which is I think exactly the
+goal of this program
+
+ align:start position:0%
+goal of this program
+ 
+
+ align:start position:0%
+goal of this program
+too so our approach is to pick girls to
+
+ align:start position:0%
+too so our approach is to pick girls to
+ 
+
+ align:start position:0%
+too so our approach is to pick girls to
+pick students who are rising High School
+
+ align:start position:0%
+pick students who are rising High School
+ 
+
+ align:start position:0%
+pick students who are rising High School
+seniors who are really good and really
+
+ align:start position:0%
+seniors who are really good and really
+ 
+
+ align:start position:0%
+seniors who are really good and really
+interested in math and science but don't
+
+ align:start position:0%
+interested in math and science but don't
+ 
+
+ align:start position:0%
+interested in math and science but don't
+really have a background in engineering
+
+ align:start position:0%
+really have a background in engineering
+ 
+
+ align:start position:0%
+really have a background in engineering
+have maybe heard of engineering people
+
+ align:start position:0%
+have maybe heard of engineering people
+ 
+
+ align:start position:0%
+have maybe heard of engineering people
+maybe tell them you should think about
+
+ align:start position:0%
+maybe tell them you should think about
+ 
+
+ align:start position:0%
+maybe tell them you should think about
+engineering but they don't really know
+
+ align:start position:0%
+engineering but they don't really know
+ 
+
+ align:start position:0%
+engineering but they don't really know
+what it is they haven't taken a lot of
+
+ align:start position:0%
+what it is they haven't taken a lot of
+ 
+
+ align:start position:0%
+what it is they haven't taken a lot of
+engineering classes they're just curious
+
+ align:start position:0%
+engineering classes they're just curious
+ 
+
+ align:start position:0%
+engineering classes they're just curious
+and not sure what they want to major in
+
+ align:start position:0%
+and not sure what they want to major in
+ 
+
+ align:start position:0%
+and not sure what they want to major in
+so we give them a four-week exposure to
+
+ align:start position:0%
+so we give them a four-week exposure to
+ 
+
+ align:start position:0%
+so we give them a four-week exposure to
+engineering there are two curriculum
+
+ align:start position:0%
+engineering there are two curriculum
+ 
+
+ align:start position:0%
+engineering there are two curriculum
+tracks electrical engineering and
+
+ align:start position:0%
+tracks electrical engineering and
+ 
+
+ align:start position:0%
+tracks electrical engineering and
+computer science and then the one that I
+
+ align:start position:0%
+computer science and then the one that I
+ 
+
+ align:start position:0%
+computer science and then the one that I
+run which is mechanical engineering I
+
+ align:start position:0%
+run which is mechanical engineering I
+ 
+
+ align:start position:0%
+run which is mechanical engineering I
+don't have a lot of time so I can't go
+
+ align:start position:0%
+don't have a lot of time so I can't go
+ 
+
+ align:start position:0%
+don't have a lot of time so I can't go
+into too much detail but I'll be happy
+
+ align:start position:0%
+into too much detail but I'll be happy
+ 
+
+ align:start position:0%
+into too much detail but I'll be happy
+happy to answer questions about what we
+
+ align:start position:0%
+happy to answer questions about what we
+ 
+
+ align:start position:0%
+happy to answer questions about what we
+do in them they're mostly Hands-On
+
+ align:start position:0%
+do in them they're mostly Hands-On
+ 
+
+ align:start position:0%
+do in them they're mostly Hands-On
+classes like what you're doing today we
+
+ align:start position:0%
+classes like what you're doing today we
+ 
+
+ align:start position:0%
+classes like what you're doing today we
+of course especially in mechanical
+
+ align:start position:0%
+of course especially in mechanical
+ 
+
+ align:start position:0%
+of course especially in mechanical
+engineering have to teach them a lot of
+
+ align:start position:0%
+engineering have to teach them a lot of
+ 
+
+ align:start position:0%
+engineering have to teach them a lot of
+physics because you can't do much in
+
+ align:start position:0%
+physics because you can't do much in
+ 
+
+ align:start position:0%
+physics because you can't do much in
+mechanical engineering until you have
+
+ align:start position:0%
+mechanical engineering until you have
+ 
+
+ align:start position:0%
+mechanical engineering until you have
+physics but physics is fun it really is
+
+ align:start position:0%
+physics but physics is fun it really is
+ 
+
+ align:start position:0%
+physics but physics is fun it really is
+um and then we try to correct ideas
+
+ align:start position:0%
+um and then we try to correct ideas
+ 
+
+ align:start position:0%
+um and then we try to correct ideas
+about what Engineers are like and what
+
+ align:start position:0%
+about what Engineers are like and what
+ 
+
+ align:start position:0%
+about what Engineers are like and what
+they do and the students give us
+
+ align:start position:0%
+they do and the students give us
+ 
+
+ align:start position:0%
+they do and the students give us
+wonderful quotes such as that they
+
+ align:start position:0%
+wonderful quotes such as that they
+ 
+
+ align:start position:0%
+wonderful quotes such as that they
+realize engineering has so much more
+
+ align:start position:0%
+realize engineering has so much more
+ 
+
+ align:start position:0%
+realize engineering has so much more
+depth and so many more applications
+
+ align:start position:0%
+depth and so many more applications
+ 
+
+ align:start position:0%
+depth and so many more applications
+coming in they have some of the
+
+ align:start position:0%
+coming in they have some of the
+ 
+
+ align:start position:0%
+coming in they have some of the
+preconceptions that you might have which
+
+ align:start position:0%
+preconceptions that you might have which
+ 
+
+ align:start position:0%
+preconceptions that you might have which
+is the Engineers work alone you know
+
+ align:start position:0%
+is the Engineers work alone you know
+ 
+
+ align:start position:0%
+is the Engineers work alone you know
+it's not very exciting not very people
+
+ align:start position:0%
+it's not very exciting not very people
+ 
+
+ align:start position:0%
+it's not very exciting not very people
+oriented but in fact it is you work a
+
+ align:start position:0%
+oriented but in fact it is you work a
+ 
+
+ align:start position:0%
+oriented but in fact it is you work a
+lot in teams as I think you're doing
+
+ align:start position:0%
+lot in teams as I think you're doing
+ 
+
+ align:start position:0%
+lot in teams as I think you're doing
+today and you get to do a whole range of
+
+ align:start position:0%
+today and you get to do a whole range of
+ 
+
+ align:start position:0%
+today and you get to do a whole range of
+applications and make products that are
+
+ align:start position:0%
+applications and make products that are
+ 
+
+ align:start position:0%
+applications and make products that are
+helpful to
+
+ align:start position:0%
+helpful to
+ 
+
+ align:start position:0%
+helpful to
+people we also want to increase
+
+ align:start position:0%
+people we also want to increase
+ 
+
+ align:start position:0%
+people we also want to increase
+confidence of the students by exposing
+
+ align:start position:0%
+confidence of the students by exposing
+ 
+
+ align:start position:0%
+confidence of the students by exposing
+them to female Engineers of all ages
+
+ align:start position:0%
+them to female Engineers of all ages
+ 
+
+ align:start position:0%
+them to female Engineers of all ages
+give them an opportunity to live away
+
+ align:start position:0%
+give them an opportunity to live away
+ 
+
+ align:start position:0%
+give them an opportunity to live away
+from home so it's four weeks living away
+
+ align:start position:0%
+from home so it's four weeks living away
+ 
+
+ align:start position:0%
+from home so it's four weeks living away
+from home you live in the the students
+
+ align:start position:0%
+from home you live in the the students
+ 
+
+ align:start position:0%
+from home you live in the the students
+live in the MIT dorms they live with MIT
+
+ align:start position:0%
+live in the MIT dorms they live with MIT
+ 
+
+ align:start position:0%
+live in the MIT dorms they live with MIT
+undergrads or recent graduates who help
+
+ align:start position:0%
+undergrads or recent graduates who help
+ 
+
+ align:start position:0%
+undergrads or recent graduates who help
+them with their homework and also do
+
+ align:start position:0%
+them with their homework and also do
+ 
+
+ align:start position:0%
+them with their homework and also do
+social outings and everything and the
+
+ align:start position:0%
+social outings and everything and the
+ 
+
+ align:start position:0%
+social outings and everything and the
+classes are taught by graduate students
+
+ align:start position:0%
+classes are taught by graduate students
+ 
+
+ align:start position:0%
+classes are taught by graduate students
+in uh mechanical engineering or
+
+ align:start position:0%
+in uh mechanical engineering or
+ 
+
+ align:start position:0%
+in uh mechanical engineering or
+eecs and uh oh I already said some of
+
+ align:start position:0%
+eecs and uh oh I already said some of
+ 
+
+ align:start position:0%
+eecs and uh oh I already said some of
+this um so again it's a Hands-On uh
+
+ align:start position:0%
+this um so again it's a Hands-On uh
+ 
+
+ align:start position:0%
+this um so again it's a Hands-On uh
+there's 40 students in the ECS track and
+
+ align:start position:0%
+there's 40 students in the ECS track and
+ 
+
+ align:start position:0%
+there's 40 students in the ECS track and
+20 students in the mechanical
+
+ align:start position:0%
+20 students in the mechanical
+ 
+
+ align:start position:0%
+20 students in the mechanical
+engineering track so there's 60 students
+
+ align:start position:0%
+engineering track so there's 60 students
+ 
+
+ align:start position:0%
+engineering track so there's 60 students
+total uh we have Hands-On lab classes
+
+ align:start position:0%
+total uh we have Hands-On lab classes
+ 
+
+ align:start position:0%
+total uh we have Hands-On lab classes
+with projects in mechanical engineering
+
+ align:start position:0%
+with projects in mechanical engineering
+ 
+
+ align:start position:0%
+with projects in mechanical engineering
+we like to have a sort of Capstone
+
+ align:start position:0%
+we like to have a sort of Capstone
+ 
+
+ align:start position:0%
+we like to have a sort of Capstone
+project at the end of each week which
+
+ align:start position:0%
+project at the end of each week which
+ 
+
+ align:start position:0%
+project at the end of each week which
+ranges from building cranes that cons
+
+ align:start position:0%
+ranges from building cranes that cons
+ 
+
+ align:start position:0%
+ranges from building cranes that cons
+sust stay a certain amount of weight uh
+
+ align:start position:0%
+sust stay a certain amount of weight uh
+ 
+
+ align:start position:0%
+sust stay a certain amount of weight uh
+through doing oral presentations making
+
+ align:start position:0%
+through doing oral presentations making
+ 
+
+ align:start position:0%
+through doing oral presentations making
+a poster presentation and then there are
+
+ align:start position:0%
+a poster presentation and then there are
+ 
+
+ align:start position:0%
+a poster presentation and then there are
+two special final week presentations
+
+ align:start position:0%
+two special final week presentations
+ 
+
+ align:start position:0%
+two special final week presentations
+where the eec students build DC motors
+
+ align:start position:0%
+where the eec students build DC motors
+ 
+
+ align:start position:0%
+where the eec students build DC motors
+and the uh wtm students build rub
+
+ align:start position:0%
+and the uh wtm students build rub
+ 
+
+ align:start position:0%
+and the uh wtm students build rub
+Goldberg machines which are basically
+
+ align:start position:0%
+Goldberg machines which are basically
+ 
+
+ align:start position:0%
+Goldberg machines which are basically
+just Chain Reaction machines but the
+
+ align:start position:0%
+just Chain Reaction machines but the
+ 
+
+ align:start position:0%
+just Chain Reaction machines but the
+thing we do to make it possibly a little
+
+ align:start position:0%
+thing we do to make it possibly a little
+ 
+
+ align:start position:0%
+thing we do to make it possibly a little
+more interesting is they have to figure
+
+ align:start position:0%
+more interesting is they have to figure
+ 
+
+ align:start position:0%
+more interesting is they have to figure
+out what's going on in every step so
+
+ align:start position:0%
+out what's going on in every step so
+ 
+
+ align:start position:0%
+out what's going on in every step so
+it's not just trial and error they have
+
+ align:start position:0%
+it's not just trial and error they have
+ 
+
+ align:start position:0%
+it's not just trial and error they have
+to apply the design principles we've
+
+ align:start position:0%
+to apply the design principles we've
+ 
+
+ align:start position:0%
+to apply the design principles we've
+taught them they have to use the physics
+
+ align:start position:0%
+taught them they have to use the physics
+ 
+
+ align:start position:0%
+taught them they have to use the physics
+and the science we've taught them to
+
+ align:start position:0%
+and the science we've taught them to
+ 
+
+ align:start position:0%
+and the science we've taught them to
+figure out what's going on
+
+ align:start position:0%
+figure out what's going on
+ 
+
+ align:start position:0%
+figure out what's going on
+and then make their machine run and we
+
+ align:start position:0%
+and then make their machine run and we
+ 
+
+ align:start position:0%
+and then make their machine run and we
+also do a lot of faculty and Industry
+
+ align:start position:0%
+also do a lot of faculty and Industry
+ 
+
+ align:start position:0%
+also do a lot of faculty and Industry
+guest speakers and tours um we also have
+
+ align:start position:0%
+guest speakers and tours um we also have
+ 
+
+ align:start position:0%
+guest speakers and tours um we also have
+uh as I said MIT students and Rec recent
+
+ align:start position:0%
+uh as I said MIT students and Rec recent
+ 
+
+ align:start position:0%
+uh as I said MIT students and Rec recent
+graduates are the instructors and also
+
+ align:start position:0%
+graduates are the instructors and also
+ 
+
+ align:start position:0%
+graduates are the instructors and also
+the the tutors that live with the
+
+ align:start position:0%
+the the tutors that live with the
+ 
+
+ align:start position:0%
+the the tutors that live with the
+students and these are some photos from
+
+ align:start position:0%
+students and these are some photos from
+ 
+
+ align:start position:0%
+students and these are some photos from
+the motor building for the ECS so this
+
+ align:start position:0%
+the motor building for the ECS so this
+ 
+
+ align:start position:0%
+the motor building for the ECS so this
+is actually the professor who runs it
+
+ align:start position:0%
+is actually the professor who runs it
+ 
+
+ align:start position:0%
+is actually the professor who runs it
+they figure out the design of their
+
+ align:start position:0%
+they figure out the design of their
+ 
+
+ align:start position:0%
+they figure out the design of their
+motor then they do all the Machining
+
+ align:start position:0%
+motor then they do all the Machining
+ 
+
+ align:start position:0%
+motor then they do all the Machining
+they build them in pairs so that's one
+
+ align:start position:0%
+they build them in pairs so that's one
+ 
+
+ align:start position:0%
+they build them in pairs so that's one
+of the completed Motors and they use
+
+ align:start position:0%
+of the completed Motors and they use
+ 
+
+ align:start position:0%
+of the completed Motors and they use
+actually the mechanical engineering shop
+
+ align:start position:0%
+actually the mechanical engineering shop
+ 
+
+ align:start position:0%
+actually the mechanical engineering shop
+to do all
+
+ align:start position:0%
+to do all
+ 
+
+ align:start position:0%
+to do all
+this and then here's some photographs
+
+ align:start position:0%
+this and then here's some photographs
+ 
+
+ align:start position:0%
+this and then here's some photographs
+from the me track where you see a r
+
+ align:start position:0%
+from the me track where you see a r
+ 
+
+ align:start position:0%
+from the me track where you see a r
+Goldberg machine dominoes are of course
+
+ align:start position:0%
+Goldberg machine dominoes are of course
+ 
+
+ align:start position:0%
+Goldberg machine dominoes are of course
+often used uh various types of trip
+
+ align:start position:0%
+often used uh various types of trip
+ 
+
+ align:start position:0%
+often used uh various types of trip
+wires and things uh uh usually pendulums
+
+ align:start position:0%
+wires and things uh uh usually pendulums
+ 
+
+ align:start position:0%
+wires and things uh uh usually pendulums
+and slinkies used and then there's a
+
+ align:start position:0%
+and slinkies used and then there's a
+ 
+
+ align:start position:0%
+and slinkies used and then there's a
+final step they can decide this one for
+
+ align:start position:0%
+final step they can decide this one for
+ 
+
+ align:start position:0%
+final step they can decide this one for
+their final step they pulled aside a
+
+ align:start position:0%
+their final step they pulled aside a
+ 
+
+ align:start position:0%
+their final step they pulled aside a
+curtain that then showed a photograph of
+
+ align:start position:0%
+curtain that then showed a photograph of
+ 
+
+ align:start position:0%
+curtain that then showed a photograph of
+all the students and
+
+ align:start position:0%
+all the students and
+ 
+
+ align:start position:0%
+all the students and
+staff so since 2002 uh reminder again me
+
+ align:start position:0%
+staff so since 2002 uh reminder again me
+ 
+
+ align:start position:0%
+staff so since 2002 uh reminder again me
+started in 2006 but e start in 2002 up
+
+ align:start position:0%
+started in 2006 but e start in 2002 up
+ 
+
+ align:start position:0%
+started in 2006 but e start in 2002 up
+through last summer we've had 744
+
+ align:start position:0%
+through last summer we've had 744
+ 
+
+ align:start position:0%
+through last summer we've had 744
+females uh finish the program uh they
+
+ align:start position:0%
+females uh finish the program uh they
+ 
+
+ align:start position:0%
+females uh finish the program uh they
+all have a they say wtp has a big impact
+
+ align:start position:0%
+all have a they say wtp has a big impact
+ 
+
+ align:start position:0%
+all have a they say wtp has a big impact
+on them many of them as I'll show on the
+
+ align:start position:0%
+on them many of them as I'll show on the
+ 
+
+ align:start position:0%
+on them many of them as I'll show on the
+next slide many of them go into into
+
+ align:start position:0%
+next slide many of them go into into
+ 
+
+ align:start position:0%
+next slide many of them go into into
+engineering some of them after going
+
+ align:start position:0%
+engineering some of them after going
+ 
+
+ align:start position:0%
+engineering some of them after going
+through wtp decide that they actually
+
+ align:start position:0%
+through wtp decide that they actually
+ 
+
+ align:start position:0%
+through wtp decide that they actually
+don't like engineering it's not for them
+
+ align:start position:0%
+don't like engineering it's not for them
+ 
+
+ align:start position:0%
+don't like engineering it's not for them
+that's a perfectly great outcome for us
+
+ align:start position:0%
+that's a perfectly great outcome for us
+ 
+
+ align:start position:0%
+that's a perfectly great outcome for us
+as well because then they have learned
+
+ align:start position:0%
+as well because then they have learned
+ 
+
+ align:start position:0%
+as well because then they have learned
+and save their parents money of sending
+
+ align:start position:0%
+and save their parents money of sending
+ 
+
+ align:start position:0%
+and save their parents money of sending
+them to an engineering school they've
+
+ align:start position:0%
+them to an engineering school they've
+ 
+
+ align:start position:0%
+them to an engineering school they've
+learned oh I don't really like
+
+ align:start position:0%
+learned oh I don't really like
+ 
+
+ align:start position:0%
+learned oh I don't really like
+engineering I want to do something else
+
+ align:start position:0%
+engineering I want to do something else
+ 
+
+ align:start position:0%
+engineering I want to do something else
+so so either outcome is fine we just
+
+ align:start position:0%
+so so either outcome is fine we just
+ 
+
+ align:start position:0%
+so so either outcome is fine we just
+want to expose them and give them a real
+
+ align:start position:0%
+want to expose them and give them a real
+ 
+
+ align:start position:0%
+want to expose them and give them a real
+more realistic view of what engineering
+
+ align:start position:0%
+more realistic view of what engineering
+ 
+
+ align:start position:0%
+more realistic view of what engineering
+actually is many of them would not have
+
+ align:start position:0%
+actually is many of them would not have
+ 
+
+ align:start position:0%
+actually is many of them would not have
+thought of an engineering major or
+
+ align:start position:0%
+thought of an engineering major or
+ 
+
+ align:start position:0%
+thought of an engineering major or
+applying to
+
+ align:start position:0%
+applying to
+ 
+
+ align:start position:0%
+applying to
+MIT and as you see actually many of them
+
+ align:start position:0%
+MIT and as you see actually many of them
+ 
+
+ align:start position:0%
+MIT and as you see actually many of them
+end up apply uh majoring in either
+
+ align:start position:0%
+end up apply uh majoring in either
+ 
+
+ align:start position:0%
+end up apply uh majoring in either
+engineering or computer science more
+
+ align:start position:0%
+engineering or computer science more
+ 
+
+ align:start position:0%
+engineering or computer science more
+than 60% of the alumni have majored or
+
+ align:start position:0%
+than 60% of the alumni have majored or
+ 
+
+ align:start position:0%
+than 60% of the alumni have majored or
+are majoring in engineering or computer
+
+ align:start position:0%
+are majoring in engineering or computer
+ 
+
+ align:start position:0%
+are majoring in engineering or computer
+science many others in U science math uh
+
+ align:start position:0%
+science many others in U science math uh
+ 
+
+ align:start position:0%
+science many others in U science math uh
+a big bunch in business and then a few
+
+ align:start position:0%
+a big bunch in business and then a few
+ 
+
+ align:start position:0%
+a big bunch in business and then a few
+of others so it's highly successful for
+
+ align:start position:0%
+of others so it's highly successful for
+ 
+
+ align:start position:0%
+of others so it's highly successful for
+its goal which really is to get girls
+
+ align:start position:0%
+its goal which really is to get girls
+ 
+
+ align:start position:0%
+its goal which really is to get girls
+interested in majoring and Engineering
+
+ align:start position:0%
+interested in majoring and Engineering
+ 
+
+ align:start position:0%
+interested in majoring and Engineering
+or at the very least to let them know
+
+ align:start position:0%
+or at the very least to let them know
+ 
+
+ align:start position:0%
+or at the very least to let them know
+what engineering is about and this is uh
+
+ align:start position:0%
+what engineering is about and this is uh
+ 
+
+ align:start position:0%
+what engineering is about and this is uh
+I think the class of 2014 probably and
+
+ align:start position:0%
+I think the class of 2014 probably and
+ 
+
+ align:start position:0%
+I think the class of 2014 probably and
+that's our website and so if you have
+
+ align:start position:0%
+that's our website and so if you have
+ 
+
+ align:start position:0%
+that's our website and so if you have
+any question oh no acknowledgements
+
+ align:start position:0%
+any question oh no acknowledgements
+ 
+
+ align:start position:0%
+any question oh no acknowledgements
+first uh I H I couldn't do this alone
+
+ align:start position:0%
+first uh I H I couldn't do this alone
+ 
+
+ align:start position:0%
+first uh I H I couldn't do this alone
+there's a woman who runs the ECS uh
+
+ align:start position:0%
+there's a woman who runs the ECS uh
+ 
+
+ align:start position:0%
+there's a woman who runs the ECS uh
+program and the whole program the Emy
+
+ align:start position:0%
+program and the whole program the Emy
+ 
+
+ align:start position:0%
+program and the whole program the Emy
+program is funded by an amazing woman
+
+ align:start position:0%
+program is funded by an amazing woman
+ 
+
+ align:start position:0%
+program is funded by an amazing woman
+who's in her actually I think she just
+
+ align:start position:0%
+who's in her actually I think she just
+ 
+
+ align:start position:0%
+who's in her actually I think she just
+turned 80 who is a mechanical engineer
+
+ align:start position:0%
+turned 80 who is a mechanical engineer
+ 
+
+ align:start position:0%
+turned 80 who is a mechanical engineer
+and she funds our program and then
+
+ align:start position:0%
+and she funds our program and then
+ 
+
+ align:start position:0%
+and she funds our program and then
+various other people so any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+nothing
+
+ align:start position:0%
+nothing
+ 
+
+ align:start position:0%
+nothing
+okay okay and uh if you are not I know
+
+ align:start position:0%
+okay okay and uh if you are not I know
+ 
+
+ align:start position:0%
+okay okay and uh if you are not I know
+there are some Juniors here which
+
+ align:start position:0%
+there are some Juniors here which
+ 
+
+ align:start position:0%
+there are some Juniors here which
+unfortunately you've missed the deadline
+
+ align:start position:0%
+unfortunately you've missed the deadline
+ 
+
+ align:start position:0%
+unfortunately you've missed the deadline
+for this summer but if you are not a
+
+ align:start position:0%
+for this summer but if you are not a
+ 
+
+ align:start position:0%
+for this summer but if you are not a
+junior if you're a e8th n9th or 10th
+
+ align:start position:0%
+junior if you're a e8th n9th or 10th
+ 
+
+ align:start position:0%
+junior if you're a e8th n9th or 10th
+grader look in around November of your
+
+ align:start position:0%
+grader look in around November of your
+ 
+
+ align:start position:0%
+grader look in around November of your
+junior year on that
+
+ align:start position:0%
+junior year on that
+ 
+
+ align:start position:0%
+junior year on that
+website right there and look for our
+
+ align:start position:0%
+website right there and look for our
+ 
+
+ align:start position:0%
+website right there and look for our
+application information and the
+
+ align:start position:0%
+application information and the
+ 
+
+ align:start position:0%
+application information and the
+applications are usually do at the
+
+ align:start position:0%
+applications are usually do at the
+ 
+
+ align:start position:0%
+applications are usually do at the
+beginning of January okay okay
+
+ align:start position:0%
+beginning of January okay okay
+ 
+
+ align:start position:0%
+beginning of January okay okay
+[Applause]
\ No newline at end of file
diff --git a/g2mOvmC1TKc.txt b/g2mOvmC1TKc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bd105842b47c14c176604d1a7175c8feea95a761
--- /dev/null
+++ b/g2mOvmC1TKc.txt
@@ -0,0 +1,395 @@
+align:start position:0%
+ 
+now we can use the unique path
+
+ align:start position:0%
+now we can use the unique path
+ 
+
+ align:start position:0%
+now we can use the unique path
+characterization of trees to very
+
+ align:start position:0%
+characterization of trees to very
+ 
+
+ align:start position:0%
+characterization of trees to very
+quickly figure out that every tree is is
+
+ align:start position:0%
+quickly figure out that every tree is is
+ 
+
+ align:start position:0%
+quickly figure out that every tree is is
+two colorable so we know that a tree is
+
+ align:start position:0%
+two colorable so we know that a tree is
+ 
+
+ align:start position:0%
+two colorable so we know that a tree is
+a graph with unique paths between every
+
+ align:start position:0%
+a graph with unique paths between every
+ 
+
+ align:start position:0%
+a graph with unique paths between every
+pair of vertices and as a consequence
+
+ align:start position:0%
+pair of vertices and as a consequence
+ 
+
+ align:start position:0%
+pair of vertices and as a consequence
+the chromatic number of a tree with two
+
+ align:start position:0%
+the chromatic number of a tree with two
+ 
+
+ align:start position:0%
+the chromatic number of a tree with two
+or more vertices is
+
+ align:start position:0%
+or more vertices is
+ 
+
+ align:start position:0%
+or more vertices is
+two um the proof is just to show you uh
+
+ align:start position:0%
+two um the proof is just to show you uh
+ 
+
+ align:start position:0%
+two um the proof is just to show you uh
+how to color it you K clearly can't get
+
+ align:start position:0%
+how to color it you K clearly can't get
+ 
+
+ align:start position:0%
+how to color it you K clearly can't get
+by with one color if you've got any two
+
+ align:start position:0%
+by with one color if you've got any two
+ 
+
+ align:start position:0%
+by with one color if you've got any two
+adjacent vertices uh the two-c colable
+
+ align:start position:0%
+adjacent vertices uh the two-c colable
+ 
+
+ align:start position:0%
+adjacent vertices uh the two-c colable
+way is that you just choose an arbitrary
+
+ align:start position:0%
+way is that you just choose an arbitrary
+ 
+
+ align:start position:0%
+way is that you just choose an arbitrary
+vertex um and call it the root but you
+
+ align:start position:0%
+vertex um and call it the root but you
+ 
+
+ align:start position:0%
+vertex um and call it the root but you
+make the arbitrary choice on what the
+
+ align:start position:0%
+make the arbitrary choice on what the
+ 
+
+ align:start position:0%
+make the arbitrary choice on what the
+root is and uh there's a unique path
+
+ align:start position:0%
+root is and uh there's a unique path
+ 
+
+ align:start position:0%
+root is and uh there's a unique path
+from every vertex from the root to every
+
+ align:start position:0%
+from every vertex from the root to every
+ 
+
+ align:start position:0%
+from every vertex from the root to every
+vertex using this unique path
+
+ align:start position:0%
+vertex using this unique path
+ 
+
+ align:start position:0%
+vertex using this unique path
+characterization and so we're just going
+
+ align:start position:0%
+characterization and so we're just going
+ 
+
+ align:start position:0%
+characterization and so we're just going
+to color vertices by whether the path
+
+ align:start position:0%
+to color vertices by whether the path
+ 
+
+ align:start position:0%
+to color vertices by whether the path
+from the root is of odd or even length
+
+ align:start position:0%
+from the root is of odd or even length
+ 
+
+ align:start position:0%
+from the root is of odd or even length
+if it's of even length color it red and
+
+ align:start position:0%
+if it's of even length color it red and
+ 
+
+ align:start position:0%
+if it's of even length color it red and
+if it's odd length color it blue colored
+
+ align:start position:0%
+if it's odd length color it blue colored
+ 
+
+ align:start position:0%
+if it's odd length color it blue colored
+green and so we wind up alter
+
+ align:start position:0%
+green and so we wind up alter
+ 
+
+ align:start position:0%
+green and so we wind up alter
+red and green and the fact is that uh
+
+ align:start position:0%
+red and green and the fact is that uh
+ 
+
+ align:start position:0%
+red and green and the fact is that uh
+adjacent nodes are going to be at a
+
+ align:start position:0%
+adjacent nodes are going to be at a
+ 
+
+ align:start position:0%
+adjacent nodes are going to be at a
+distance where one is an odd distance
+
+ align:start position:0%
+distance where one is an odd distance
+ 
+
+ align:start position:0%
+distance where one is an odd distance
+and one is an even distance which is why
+
+ align:start position:0%
+and one is an even distance which is why
+ 
+
+ align:start position:0%
+and one is an even distance which is why
+this method of coloring is going to work
+
+ align:start position:0%
+this method of coloring is going to work
+ 
+
+ align:start position:0%
+this method of coloring is going to work
+a general property of two coloring is
+
+ align:start position:0%
+a general property of two coloring is
+ 
+
+ align:start position:0%
+a general property of two coloring is
+that it to figure out whether or not a
+
+ align:start position:0%
+that it to figure out whether or not a
+ 
+
+ align:start position:0%
+that it to figure out whether or not a
+graph is two colorable and how to do it
+
+ align:start position:0%
+graph is two colorable and how to do it
+ 
+
+ align:start position:0%
+graph is two colorable and how to do it
+is you just start uh pick an arbitrary
+
+ align:start position:0%
+is you just start uh pick an arbitrary
+ 
+
+ align:start position:0%
+is you just start uh pick an arbitrary
+vertex give it a color it red and then
+
+ align:start position:0%
+vertex give it a color it red and then
+ 
+
+ align:start position:0%
+vertex give it a color it red and then
+color all the vertices adjacent to it
+
+ align:start position:0%
+color all the vertices adjacent to it
+ 
+
+ align:start position:0%
+color all the vertices adjacent to it
+green and keep going in that way uh
+
+ align:start position:0%
+green and keep going in that way uh
+ 
+
+ align:start position:0%
+green and keep going in that way uh
+coloring a Vertex with a color different
+
+ align:start position:0%
+coloring a Vertex with a color different
+ 
+
+ align:start position:0%
+coloring a Vertex with a color different
+from an adjac bent vertex that's colored
+
+ align:start position:0%
+from an adjac bent vertex that's colored
+ 
+
+ align:start position:0%
+from an adjac bent vertex that's colored
+until you get stuck if you don't get
+
+ align:start position:0%
+until you get stuck if you don't get
+ 
+
+ align:start position:0%
+until you get stuck if you don't get
+stuck it's too colorable and if it's not
+
+ align:start position:0%
+stuck it's too colorable and if it's not
+ 
+
+ align:start position:0%
+stuck it's too colorable and if it's not
+too colorable you're guaranteed to get
+
+ align:start position:0%
+too colorable you're guaranteed to get
+ 
+
+ align:start position:0%
+too colorable you're guaranteed to get
+stuck so it's a very easy way to figure
+
+ align:start position:0%
+stuck so it's a very easy way to figure
+ 
+
+ align:start position:0%
+stuck so it's a very easy way to figure
+out if a graph is two colorable uh
+
+ align:start position:0%
+out if a graph is two colorable uh
+ 
+
+ align:start position:0%
+out if a graph is two colorable uh
+another characterization that of two
+
+ align:start position:0%
+another characterization that of two
+ 
+
+ align:start position:0%
+another characterization that of two
+colorability in general is that um a
+
+ align:start position:0%
+colorability in general is that um a
+ 
+
+ align:start position:0%
+colorability in general is that um a
+graph is too colorable providing that
+
+ align:start position:0%
+graph is too colorable providing that
+ 
+
+ align:start position:0%
+graph is too colorable providing that
+all the cycles that it has if any are of
+
+ align:start position:0%
+all the cycles that it has if any are of
+ 
+
+ align:start position:0%
+all the cycles that it has if any are of
+even length of course a tree has no
+
+ align:start position:0%
+even length of course a tree has no
+ 
+
+ align:start position:0%
+even length of course a tree has no
+Cycles so that makes it too colorable
+
+ align:start position:0%
+Cycles so that makes it too colorable
+ 
+
+ align:start position:0%
+Cycles so that makes it too colorable
+for sure
\ No newline at end of file
diff --git a/ggxY20cXql8.txt b/ggxY20cXql8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4d5a216192053f9514edaa4786db931fd4f00f51
--- /dev/null
+++ b/ggxY20cXql8.txt
@@ -0,0 +1,1843 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: I apologize to
+those of you watching on
+
+OpenCourseWare.
+
+I forgot to turn on
+my microphone.
+
+And you missed some incredibly
+brilliant things.
+
+But such is life.
+
+Let me go back to where I was,
+which was we we're looking at
+
+this code to find the cube
+root of a perfect cube.
+
+We saw this last week, and
+indeed, you also saw it in
+
+recitation.
+
+I'm not going to belabor it.
+
+I do want to ask you the
+question, for what values will
+
+this program terminate?
+
+That is to say the only
+input is to x.
+
+For what values of
+x is this program
+
+guaranteed to always stop?
+
+Anybody want to volunteer
+an answer to that?
+
+Ask a simpler question.
+
+Let's assume that
+x is a number.
+
+In fact, let's assume
+it's an integer.
+
+Will it terminate for all
+positive integers, all
+
+positive values of x?
+
+Yeah.
+
+All negative values?
+
+As far as I can tell.
+
+How about 0?
+
+Yeah.
+
+So in fact, it terminates
+for all values of x.
+
+How do I know that?
+
+And that's a key question.
+
+I know that because I've used,
+and I mean by used as a mental
+
+tool, something in my head,
+the notion of a
+
+decrementing function.
+
+And every time I write a loop,
+I think about one of these,
+
+because that explains to
+me why the loop is
+
+guaranteed to terminate.
+
+We'll go over here where we have
+a bigger board and look
+
+at the properties that
+a decrementing
+
+function needs to have.
+
+One, it will map some
+set of program
+
+variables to an integer.
+
+Two, when the loop is entered
+for the first time or when I
+
+encountered the test of the loop
+for the first time, its
+
+value is non-negative.
+
+Three, when its value gets to
+be less than or equal to 0,
+
+the loop terminates.
+
+And finally four, it's
+decreased each
+
+time through the loop.
+
+So what we see is if it starts
+to be a positive value or
+
+non-negative, and it's decreased
+every time I execute
+
+the body of a loop, that
+eventually, it's got to reach
+
+0 or something less than 0.
+
+And when it does,
+the loop stops.
+
+If such a function exists, then
+the loop is guaranteed to
+
+always terminate.
+
+Now, of course, one can count up
+to a value instead of down.
+
+But there's always a trick we
+can use of subtracting to make
+
+it the same.
+
+So what's the decrementing
+function for this loop?
+
+How did I know it will
+always terminate?
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Answer equals
+answer plus 1.
+
+I don't think so.
+
+Does that satisfy all
+of these properties?
+
+Remember, a function is going
+to map some set of program
+
+variables to an integer.
+
+So what are the interesting
+program variables here?
+
+Well, there are only
+two, ans and x.
+
+Right?
+
+At least, that's
+all I can see.
+
+So what would be an interesting
+function?
+
+Somebody?
+
+Surely, there's someone who
+can figure this out.
+
+Yes?
+
+Or no, you're just scratching
+your head.
+
+You fooled me.
+
+I can't see because of the
+light, but I'm sure there must
+
+be dozens of hands up if
+I could only see them.
+
+Actually, I don't see
+any hands up.
+
+This is not so hard, guys.
+
+It's the absolute value of
+x minus answer cubed.
+
+So what does this
+value start at?
+
+Let's pick a value.
+
+Suppose that x is equal to 8.
+
+What is the initial value of
+the decrementing function?
+
+Wow.
+
+Come on.
+
+Let's be a little cooperative,
+please.
+
+Yes?
+
+AUDIENCE: So it's 8, answer
+is 0 and absolute
+
+value of x is 8.
+
+PROFESSOR: So it's 8 minus
+0, which is equal to 8.
+
+So it satisfies conditions
+one and conditions two.
+
+What happens to this value every
+time through the loop?
+
+Does x change?
+
+Does answer change?
+
+And how does it change?
+
+It's increasing.
+
+What does answer start at?
+
+It starts at 0, and
+it increases.
+
+So I know that answer cubed
+will always be positive.
+
+Right?
+
+So I know that every
+time through the
+
+loop, it will be 8.
+
+The first time through,
+it'll be 8 minus 1
+
+cubed, which is 7.
+
+And then the next time through,
+it'll be 8 minus 2
+
+cubed, which is 0.
+
+And then, I exit the loop.
+
+And it's that kind of reasoning
+that I used to
+
+convince myself that this
+loop terminates.
+
+And every time I write a loop,
+and I hope every time you
+
+write a loop, you will think
+about what's the reason the
+
+loop is going to terminate.
+
+And you will do it by thinking
+about what the decrementing
+
+function is.
+
+People get me on that?
+
+And whoever finally answered
+a question surely
+
+deserves to be fed.
+
+I obviously have to bring better
+candy to encourage
+
+better responses.
+
+Now, let's go back and look
+at the program itself.
+
+Now that we know it stops, and
+you can take my word for it
+
+that it actually computes the
+correct answer, let's think
+
+about what kind of algorithm
+this is.
+
+What's the method?
+
+This is an example of
+guess and check.
+
+And it's a particular kind
+called exhaustive enumeration.
+
+Each time through the loop, I'm
+taking a guess at to what
+
+the value is, and I'm checking
+whether it's true.
+
+But I'm enumerating
+the guesses in a
+
+very systematic way.
+
+They're not just
+random guesses.
+
+I'm enumerating all the
+possible answers.
+
+If I get through the entire
+space of answers, or possible
+
+answers, and I don't find a
+solution, then I know that it
+
+doesn't exist, and it's
+not a perfect cube.
+
+So that's why it's called
+exhaustive enumeration because
+
+I'm exhausting the space
+of possible answers.
+
+Does that makes sense
+to everyone?
+
+So let's try it.
+
+Let's try it with say a very
+large value of x, because
+
+that's always an issue, of
+course, when we do exhaustive
+
+enumeration.
+
+So I'm going to enter
+this value.
+
+Is that a perfect cube?
+
+Who thinks it is?
+
+Who can tell me what it is?
+
+What's the cube root of that?
+
+Well, this is a question I did
+not expect you to answer.
+
+But it's 1,251.
+
+That'll be in the first quiz,
+so make a note of it.
+
+Notice how quickly the
+computer did this.
+
+It found the cube
+root of quite a
+
+large number very quickly.
+
+And so while one might
+initially think that
+
+exhaustive enumeration is a
+silly technique because takes
+
+a lot of guesses, for an awful
+lot of problems, we can
+
+actually just write a pretty
+stupid program that's solves
+
+it by exhaustive enumeration.
+
+We typically refer to such
+programs as brute force.
+
+And brute force is often
+exactly the right
+
+way to solve a problem.
+
+Why does it work?
+
+Because computers
+are really fast.
+
+How fast are computers?
+
+Well, today, a good computer
+can execute in a single
+
+processor in the order of 100
+million instructions a second.
+
+How fast is that?
+
+And now, we're going to see if
+Mitchell has answered the
+
+question I asked in the
+way in the class.
+
+How many instructions can a
+computer execute between the
+
+time I say something and the
+time the people in the back
+
+row hear it?
+
+Mitch thinks it's 400 million
+instructions.
+
+I think that's about right.
+
+It's hundreds of millions
+at any rate.
+
+It's kind of amazing between the
+time I say something and
+
+the time you hear it, hundreds
+of millions of instructions.
+
+It's mind boggling
+how fast that is.
+
+And that's why we can often use
+these kind of solutions.
+
+Next lecture, actually, even
+a little bit later in this
+
+lecture, I hope to get to an
+example of why that doesn't
+
+really get the job done,
+at least not always.
+
+Before I do that, I want
+to look at one
+
+more programming construct.
+
+And that's a variant
+on the while loop.
+
+So if we think about what the
+while loop we were just
+
+looking at did or does, as the
+decrementing function told us,
+
+it's looking at all the possible
+values of answer
+
+ranging from 0 to the
+absolute value of x.
+
+And at each step testing and
+doing something, we can
+
+abstract this process using
+something called a for loop.
+
+So let's look at this code.
+
+It's essentially exactly
+the same algorithm.
+
+I got bored of typing ans
+times ans times ans.
+
+So I used a Python notation
+for exponentiation, which
+
+you'll see is star, star.
+
+Now, be easier to read
+if I get rid of that.
+
+But other than that, the
+interesting thing I did was
+
+replace the while
+loop by a for.
+
+So you'll see this line of code
+there, for ans in range 0
+
+to abs of x plus 1.
+
+What that says is range is a
+built-in function of Python
+
+that generates, in this case,
+a sequence of integers,
+
+something called a tuple, which
+we'll be looking at in a
+
+lecture or so.
+
+But for now, it's pretty simple
+to think about what you
+
+get is if you look at the
+expression range of x to y,
+
+that gives me a sequence
+of values, x, x plus 1
+
+up to y minus 1.
+
+Notice not up to y, but
+up to y minus 1.
+
+So it gives me a sequence
+of length y--
+
+well, assuming that's 0.
+
+Right?
+
+It doesn't have to be 0.
+
+It can be anything.
+
+It can be another
+value as well.
+
+0 in my example.
+
+And then, the for loop executes
+it on this value and
+
+the next iteration on this
+value, and finally, at the
+
+very end on that value.
+
+So it executes it one iteration
+of the loop on each
+
+value in this sequence
+of values generated
+
+by the range statement.
+
+And normally, it does
+all of them.
+
+However, you'll see I've added
+something called a break here,
+
+a command in Python.
+
+And what break says
+is exit the loop.
+
+So it exits it prematurely
+without executing all of the
+
+values generated by range.
+
+You can nest loops just like
+you nest if statements.
+
+And if you do that break,
+always executes--
+
+always exits rather the
+innermost loop.
+
+So what this does is it's
+generates a set
+
+of values to test.
+
+It checks whether or not
+it's got the answer.
+
+If it does, it terminates
+the loop.
+
+And eventually, you
+exit the loop.
+
+And then, it just checks as
+before whether or not it found
+
+a correct answer and does
+the right thing.
+
+So you'll find, particularly
+when you're iterating over
+
+integers, but later we'll see
+when you're iterating over a
+
+lot of other kinds of things,
+for loops are a very
+
+convenient shorthand.
+
+There's nothing you can't
+do with a while loop.
+
+You don't need for loops.
+
+But they do make life easy.
+
+And over the semester, I think
+you'll end up writing a lot
+
+more for loops than you
+will while loops.
+
+Any questions about this?
+
+If not, I'm going to
+move right along.
+
+So this is the moment.
+
+I'm going to move right along.
+
+So we've now got a program that
+does something really
+
+silly, really.
+
+It finds cube roots
+of perfect cubes.
+
+Well, that's not typically
+useful.
+
+Right?
+
+You've even got these $0.50 four
+function calculators that
+
+find square roots.
+
+And they don't insist that you
+only give it perfect squares.
+
+So now, let's think about how
+we would take this kind of
+
+program, and indeed, this kind
+of method of writing programs
+
+and use it to find--
+
+for now, we'll look at the
+square root of any number, of
+
+any floating point number.
+
+Well, the first question we need
+to ask is what do I mean?
+
+That's kind of a subtle
+question.
+
+What does it mean to find the
+square root of a number?
+
+What does it mean, for
+example, to find the
+
+square root of 2?
+
+Well, we know that that was an
+endless series of digits
+
+before we can find the
+square root of 2.
+
+Right?
+
+It does not have
+a nice answer.
+
+So we can't just say we have to
+find something that if we
+
+multiply it by itself,
+it will equal 2.
+
+Because we can't find
+such a thing.
+
+So we've got to think
+about a different
+
+notion of what we mean.
+
+Furthermore, even for some
+numbers which there is a
+
+square root, it might be a
+million decimal places long,
+
+and consequently, really
+hard to find.
+
+So we need to think
+about a different
+
+kind of concept here.
+
+And it's the concept of an
+approximation, finding an
+
+answer that is good enough.
+
+So what should we do here?
+
+How do we think about this?
+
+Typically, what we do when we
+think about an approximation
+
+is we define how good
+an approximation
+
+we're willing to accept.
+
+So for example, we might want
+to say, I want to find a
+
+square root that lies
+within epsilon of
+
+the true square root.
+
+So find a y such that y times
+y is equal to what?
+
+What does it mean?
+
+How would I express it within
+epsilon of the perfect answer?
+
+I don't want to say it's equal
+to x, because that may be
+
+impossible or too time
+consuming to find.
+
+So really, what I mean is
+x plus or minus epsilon.
+
+So that's what I'm asking.
+
+Find one that's close enough.
+
+And that's what the next
+piece of code I
+
+want to show you does.
+
+Excuse me.
+
+So I'm starting, just giving it
+a value for x, so I don't
+
+have to keep typing one in.
+
+Let's say it's 25.
+
+I'm going to take epsilon
+to be 0.01.
+
+So I want it within that
+distance of the true answer.
+
+I'm going to keep track of the
+number of guesses here, not
+
+because we need it to actually
+compute the answer, but
+
+because I want to then discuss
+how many iterations of the
+
+loop we're doing.
+
+We're going to start by setting
+my first guess at 0.0.
+
+Again, this is going to be
+exhaustive enumeration.
+
+Then, I'm going to essentially
+encode this as a test of my
+
+while loop while the absolute
+value of answer squared minus
+
+x is greater than or equal to
+epsilon, and answer is less
+
+than equal to x.
+
+So it's now a more
+complicated test.
+
+I've got a Boolean value.
+
+Two things have to be true to
+execute the body of the loop.
+
+I'm going to increment answer
+by a tiny amount, increment
+
+the number of guesses just so
+I can keep track of it.
+
+Maybe I'm going to comment
+this out for the first go
+
+around just so we don't see too
+many print statements and
+
+keep doing it.
+
+And then when I'm done I'm going
+to see whether or not
+
+what I found is indeed a square
+root or close enough.
+
+So if we think about why this
+loop terminates, why am I
+
+guaranteed that this loop
+will terminate?
+
+What's my decrementing
+function here?
+
+Somebody?
+
+What's the decrementing
+function?
+
+What am I guaranteed to reduce
+each time through, and when I
+
+get through, I'm done?
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+answer squared minus
+x1 times 1.
+
+PROFESSOR: No.
+
+Close, sort of.
+
+But I appreciate
+you're trying.
+
+That's worth something
+just for the effort.
+
+Somebody else.
+
+Remember, if we look at the
+properties it has to have,
+
+it's going to guarantee me that
+when it gets to the right
+
+value, I exit the loop, which
+suggests it's going to
+
+certainly be part of the
+test of the while.
+
+Just look at this piece
+over here at the end.
+
+Answer starts at 0.
+
+I keep incrementing it.
+
+Eventually, answer minus x
+will hit a value, right?
+
+Eventually, I'll get to
+the point that this
+
+condition must be true--
+
+must be false rather.
+
+And then, I exit the loop.
+
+So this piece is not
+really the key.
+
+It's this piece that guarantees
+me I'm going to get
+
+out eventually.
+
+This piece can get
+me out sooner.
+
+It's kind of an optimization,
+if you will.
+
+So I'm just going to go until
+I find the answer.
+
+Let's see what happens
+when I run it.
+
+It tells me that 4.99, et cetera
+is close to the square
+
+root of 25.
+
+So there are some things
+to note about this.
+
+First, it didn't find 5, 25
+happens to be a perfect
+
+square, yet I didn't find it.
+
+Is that OK?
+
+Yeah.
+
+Because that wasn't
+what I said.
+
+What I said is find
+a y that has these
+
+properties over here.
+
+And I did.
+
+I didn't say find the y that
+gets closest to the
+
+square root of x.
+
+I said find one that has
+these properties.
+
+Effectively, what this is is a
+specification of the problem.
+
+And I've now written a piece
+of code that meets the
+
+specification.
+
+It does what I set out to do,
+and that's good enough.
+
+Now, let's turn this print
+statement back on.
+
+It took almost 1/2 million
+guesses to get there.
+
+But it was still blindingly
+fast.
+
+So once again, exhaustive
+enumeration seems to be OK.
+
+Suppose, however, I choose
+a bigger number.
+
+Now, first, let's choose
+something that doesn't have a
+
+good answer.
+
+Let's see what it
+does for that.
+
+All right.
+
+Pretty good.
+
+Also pretty fast.
+
+Not too many guesses.
+
+But now, let's try this one.
+
+Well, it's going to wait.
+
+It's going to get done, but it's
+going to take a little
+
+bit longer than maybe
+we want it to take.
+
+Why is it taking so long?
+
+There it is.
+
+It found an answer, which
+I think is good.
+
+But as you can see, it
+took quite a few
+
+guesses to get there.
+
+So why?
+
+Well, let me first ask
+this question.
+
+Can we look at the code and
+anticipate how many guesses
+
+it's going to have to take?
+
+We're going back to this issue
+of computational complexity,
+
+but here, not of the problem
+but of the solution.
+
+So this is algorithmic
+analysis.
+
+We're analyzing the algorithm,
+this exhaustive enumeration
+
+algorithm, and trying to figure
+out how long it's
+
+likely to take to run.
+
+Well, what does the running
+time of this
+
+algorithm depend upon?
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: It depends on
+the actual square root.
+
+Yes.
+
+But in particular, the distance
+of the actual square
+
+root from the starting point.
+
+So that's one factor
+it depends on.
+
+But that's not the
+only factor.
+
+What else does it depend on?
+
+Oh, do we have an injury?
+
+We had a dropped pass and
+a deflection there.
+
+All right.
+
+Yes?
+
+AUDIENCE: It depends on the
+level of accuracy, so how you
+
+define epsilon.
+
+PROFESSOR: It depends upon
+the value of epsilon.
+
+Absolutely.
+
+How long it takes to run.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Someone with
+a concern for safety.
+
+it depends upon the actual value
+of epsilon, because if
+
+epsilon is small, we may have
+to take more steps to get a
+
+precise enough answer.
+
+And it depends upon
+one more thing.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE] the
+increment that [INAUDIBLE]?
+
+PROFESSOR: The increment.
+
+Exactly.
+
+Because the number of times we
+go through the loop is going
+
+to be related to how
+big a step we
+
+take each time through.
+
+No applause?
+
+Thank you.
+
+So it depends upon all
+of these things.
+
+And here, since we're trying
+to find a pretty [? big ?]
+
+square root and a sort of
+precise answer, but we're
+
+taking tiny steps, it's
+going to take a
+
+long time to execute.
+
+So we could make it faster.
+
+For example, suppose I change
+the step size to this.
+
+Plus equal by says increment
+the value by whatever the
+
+right side is.
+
+So I'm going to increment
+it by 1.
+
+Wow, it was really fast.
+
+But it didn't work.
+
+It failed.
+
+That's not so good.
+
+So I can't just do that.
+
+And of course, it's not
+surprising, because I ended up
+
+jumping all over the answer.
+
+I could make epsilon smaller,
+but that seems like cheating.
+
+So really, what I need to do is
+find a better algorithm, a
+
+better way to attack
+the problem.
+
+Fortunately, I don't
+have to invent it.
+
+Some people a lot smarter than
+I am figured out a long time
+
+ago a good method for solving
+this kind of problem.
+
+And they're doing it
+using something
+
+called bisection search.
+
+As we look at this particular
+implementation of it, we're
+
+going to use two algorithmic
+techniques that you'll use
+
+over and over again because
+they're generally useful.
+
+So the first one related to
+bisection search is we'll cut
+
+the search space in half
+each iteration.
+
+So with my brute force
+algorithm, we're trimming the
+
+search base only a little
+bit each step.
+
+So if we think about it, what it
+looks like, we had a space
+
+of values to search
+for the answer.
+
+And I started here.
+
+And each step, I just trimmed
+off a tiny, tiny little bit,
+
+0.001, leaving me a lot
+of space to search.
+
+And that's why it
+took so long.
+
+When I do bisection search, the
+basic idea is each step I
+
+want to cut the search
+space in half.
+
+Get rid of half of the search
+space each time.
+
+So one way I could do
+it is I start with a
+
+guess say in the middle.
+
+Just pick some guess that's in
+the middle of my search space.
+
+And now I say is it too
+high or too low?
+
+I can easily answer
+that question.
+
+I square it.
+
+See is my result bigger than
+the actual square root or
+
+smaller than the actual
+square root?
+
+That tells me whether my guess
+is too big or too small.
+
+Once I know that, I know which
+side of the guess the right
+
+answer is on.
+
+So if I knew that my guess was
+too big, then I know there's
+
+no point in looking over
+here for my next guess.
+
+So I can get rid of this
+whole half in one step.
+
+Now, what should my
+next guess be?
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: My next
+guess should be
+
+half way through there.
+
+Exactly.
+
+And now, let's say this time
+my answer is too small.
+
+Then I know I can
+get rid of this.
+
+So now, I'm very quickly pruning
+my search space.
+
+If I think about that, how many
+times am I likely to have
+
+to prune it?
+
+It's much faster, right?
+
+As we'll see later, it's
+basically log base 2.
+
+If I have some number of
+values to look at--
+
+and by the way, how many values
+do I have in my search
+
+space to start with?
+
+What determines it?
+
+Clearly, the first value and the
+last value, but also, how
+
+small I'm dividing it up.
+
+Right?
+
+So I have to think
+about that too.
+
+What is the precision with
+which I do this.
+
+Am I looking at every
+one millionth of a
+
+number or every 0.01?
+
+That will tell me
+how big it is.
+
+Once I know how big my search
+space is, I know that if I
+
+search it linearly looking at
+every value, my worst cases, I
+
+look at everything until
+I get to the end.
+
+Well, my best case is
+I get lucky, and my
+
+first guess is right.
+
+But if I use bisection search,
+my worst case is going to be
+
+log number of values
+in that space.
+
+Because each time, I throw
+half of them away.
+
+We'll see that in more
+detail later on.
+
+Let's go back and look
+at the code now.
+
+So it starts as before with
+a value for epsilon.
+
+But now, I'm going to take a
+lower bound, here, and an
+
+upper bound on my
+search space.
+
+I'm going to say my initial
+guess will be the upper bound
+
+plus the lower bound
+over 2 halfway
+
+through my search space.
+
+And then, I'm just going to work
+my way through it until I
+
+get to the answer or
+don't find it.
+
+So should we look at what's
+going on here?
+
+Let's try this.
+
+Well, let's first make sure it
+works for a small value.
+
+Never test your program first
+on something big.
+
+Always try your program in
+something small first.
+
+Let's try it on that.
+
+Got an answer.
+
+Notice that it's different from
+the answer we got last
+
+time we looked for the
+square root of 25.
+
+But that's OK, because it's
+still meets the specification.
+
+It's still within epsilon of
+the actual square root.
+
+And I didn't have to say that
+I wanted it below or the
+
+square root or above, just
+said within epsilon.
+
+Sure enough, different
+algorithm, different answer,
+
+but equally good, but
+a lot faster.
+
+Now let's try it for
+the big value.
+
+Wow, that was a lot
+faster, wasn't it?
+
+It got me an answer.
+
+Probably, not exactly
+the same answer as
+
+before but pretty close.
+
+But it did it in only
+26 guesses.
+
+Pretty cool.
+
+And in fact, we'll see over and
+over again that bisection
+
+search is a really good
+technique for
+
+finding quick answers.
+
+And again, why is it 26?
+
+Well, we had some number of
+guesses to start with.
+
+After 1, it was half as big,
+then a quarter is big, and
+
+eventually, log 2 of the size.
+
+But what was the size?
+
+Was it the number 12345?
+
+No.
+
+We already sort of talked
+about that.
+
+What was it?
+
+Let's look at the code, and
+let's think about what was the
+
+size of our initial
+search space.
+
+It's a little bit tricky to
+think about this, right?
+
+Now, we have to think a little
+bit harder about when we exit
+
+the loop, because in
+fundamentally, that's telling
+
+me the size of the
+search space.
+
+So what determined the size
+of the search space?
+
+Well, we talked about the upper
+and the lower bound.
+
+But what's telling me
+roughly speaking how
+
+many divisions I have?
+
+It's epsilon.
+
+It's not 0.01 because when
+I square it, it has to be
+
+smaller than 0.01.
+
+But that tells me roughly
+how many I have.
+
+And so it's going to be roughly
+12345 divided by 0.01
+
+squared, which turns out to
+be 26.897 more or less.
+
+So we could predict it.
+
+And son of a gun, when we ran
+it, we actually matched the
+
+prediction.
+
+That's the great thing about
+algorithmic analysis.
+
+We can actually get accurate
+guesses as to how long a
+
+program is likely
+to take to run.
+
+This is an important thing
+because sometimes we do that
+
+and we say, oh, it's going
+to take a year.
+
+I better not even try.
+
+I better find a smarter
+algorithm.
+
+Or we do it and say, well, it's
+going to take almost no
+
+time at all.
+
+I'm not going to waste
+my time looking
+
+for a smarter algorithm.
+
+I'm going to live with
+the one I've got.
+
+It's important, and again, as
+I said, it's a topic we're
+
+going to get back to.
+
+Of course, whether it's
+26, 27, or even 50
+
+doesn't really matter.
+
+What matters is it's
+not a billion.
+
+Right?
+
+Because we don't really care
+small differences.
+
+Whether it takes 25 or it
+takes 50 will be an
+
+imperceptible difference.
+
+It's whether it's a huge
+difference that matters.
+
+And that's really the kind of
+things we're going after is
+
+orders of magnitude.
+
+Now, I have a question
+about this program.
+
+I've been obsessing about
+whether it's fast enough.
+
+And we've shown it is.
+
+But does it work?
+
+Kind of more important.
+
+It's always possible to write
+a really fast program that
+
+gives you the wrong answer.
+
+The problem is to write a fast
+program that give you the
+
+right answer.
+
+Does this program always work?
+
+Well, it worked for 25.
+
+It worked for 12345.
+
+Is that good enough?
+
+Probably not.
+
+We might want to try it
+in some other values.
+
+I'll ask a simpler question.
+
+Does it always work on
+positive values?
+
+All right.
+
+I'll give you a hint.
+
+No.
+
+It does not.
+
+I'm not going to, however,
+tell you why it doesn't,
+
+because I want you to
+think about it.
+
+And I want you to
+tell me why it
+
+doesn't in the next lecture.
+
+But because I'm not a complete
+sadist, I'll give you a hint.
+
+When we use bisection search, or
+for that matter, any search
+
+method, we are depending upon
+the fact that the answer lies
+
+somewhere in the region
+we're searching.
+
+If indeed the answer is out
+here or out here, then it
+
+doesn't matter how carefully
+I search this region.
+
+I'm not going to find
+the answer.
+
+And so this program doesn't work
+on some potential values
+
+of x because the actual square
+root of x will not lie in the
+
+region that the program
+is searching.
+
+I leave it to you to think about
+what such values are.
+
+And we can talk about that
+on the next lecture.
+
+Suppose I want to use this
+program to find the cube root.
+
+Suppose it worked, and
+I want it to use it
+
+to find a cube root.
+
+What would I have to change?
+
+How would I change it, so it
+found cube roots instead of
+
+square roots?
+
+Well, I can take it up.
+
+I could use cut and paste, and
+paste it into my editor and
+
+get a new program.
+
+And how would I change
+that new program to
+
+make it do cube roots?
+
+Not very hard.
+
+Think only two places
+have to get changed.
+
+That's for the simplicity,
+say cube
+
+roots of positive numbers.
+
+I think you said the
+right thing.
+
+All I have to do is change that
+two to a three and that
+
+two to a three, and I'm done.
+
+And I should probably change the
+message to say cube root.
+
+Pretty easy.
+
+On the other hand, suppose I
+also want it to find the
+
+fourth root, and the fifth
+root, and the sixth root,
+
+however many roots.
+
+Well, I'm going to get pretty
+tired of cutting, and pasting,
+
+and building a whole
+bunch of things.
+
+So really, what I want to do
+is find a way to write the
+
+code that will find the nth root
+of a number for any n.
+
+To do that, I'm going
+to introduce a
+
+new programming concept.
+
+And that concept is
+the function.
+
+And that will be the main topic
+of Thursday's lecture.
\ No newline at end of file
diff --git a/hmJMaVYiqwM.txt b/hmJMaVYiqwM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e355a788d822057338a0f6a5762b369df74df64e
--- /dev/null
+++ b/hmJMaVYiqwM.txt
@@ -0,0 +1,3131 @@
+align:start position:0%
+ 
+I swore to myself that if I became a
+
+ align:start position:0%
+I swore to myself that if I became a
+ 
+
+ align:start position:0%
+I swore to myself that if I became a
+lecturer I would never more my students
+
+ align:start position:0%
+lecturer I would never more my students
+ 
+
+ align:start position:0%
+lecturer I would never more my students
+that that was a worse sin than almost
+
+ align:start position:0%
+that that was a worse sin than almost
+ 
+
+ align:start position:0%
+that that was a worse sin than almost
+any other a teacher could commit was to
+
+ align:start position:0%
+any other a teacher could commit was to
+ 
+
+ align:start position:0%
+any other a teacher could commit was to
+be boring today on the podcast the film
+
+ align:start position:0%
+be boring today on the podcast the film
+ 
+
+ align:start position:0%
+be boring today on the podcast the film
+experience in this episode we'll explore
+
+ align:start position:0%
+experience in this episode we'll explore
+ 
+
+ align:start position:0%
+experience in this episode we'll explore
+what it takes to reframe historical
+
+ align:start position:0%
+what it takes to reframe historical
+ 
+
+ align:start position:0%
+what it takes to reframe historical
+artifacts things like classic plays
+
+ align:start position:0%
+artifacts things like classic plays
+ 
+
+ align:start position:0%
+artifacts things like classic plays
+books and films for a modern audience
+
+ align:start position:0%
+books and films for a modern audience
+ 
+
+ align:start position:0%
+books and films for a modern audience
+and I said to him what did you actually
+
+ align:start position:0%
+and I said to him what did you actually
+ 
+
+ align:start position:0%
+and I said to him what did you actually
+think Shakespeare's environment was he
+
+ align:start position:0%
+think Shakespeare's environment was he
+ 
+
+ align:start position:0%
+think Shakespeare's environment was he
+somehow had managed to disconnect the
+
+ align:start position:0%
+somehow had managed to disconnect the
+ 
+
+ align:start position:0%
+somehow had managed to disconnect the
+literary power of Shakespeare from the
+
+ align:start position:0%
+literary power of Shakespeare from the
+ 
+
+ align:start position:0%
+literary power of Shakespeare from the
+fact that it was done on this incredibly
+
+ align:start position:0%
+fact that it was done on this incredibly
+ 
+
+ align:start position:0%
+fact that it was done on this incredibly
+popular stage and it was so sensational
+
+ align:start position:0%
+popular stage and it was so sensational
+ 
+
+ align:start position:0%
+popular stage and it was so sensational
+and it was so much more like television
+
+ align:start position:0%
+and it was so much more like television
+ 
+
+ align:start position:0%
+and it was so much more like television
+or the movies than it was like some
+
+ align:start position:0%
+or the movies than it was like some
+ 
+
+ align:start position:0%
+or the movies than it was like some
+process of sitting in a in a library in
+
+ align:start position:0%
+process of sitting in a in a library in
+ 
+
+ align:start position:0%
+process of sitting in a in a library in
+wood-paneled splendor reading words in
+
+ align:start position:0%
+wood-paneled splendor reading words in
+ 
+
+ align:start position:0%
+wood-paneled splendor reading words in
+silence that's not what Shakespeare was
+
+ align:start position:0%
+silence that's not what Shakespeare was
+ 
+
+ align:start position:0%
+silence that's not what Shakespeare was
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+how can we compare media so that
+
+ align:start position:0%
+how can we compare media so that
+ 
+
+ align:start position:0%
+how can we compare media so that
+students today might better understand
+
+ align:start position:0%
+students today might better understand
+ 
+
+ align:start position:0%
+students today might better understand
+what it originally was
+
+ align:start position:0%
+what it originally was
+ 
+
+ align:start position:0%
+what it originally was
+welcome to chalk radio a podcast about
+
+ align:start position:0%
+welcome to chalk radio a podcast about
+ 
+
+ align:start position:0%
+welcome to chalk radio a podcast about
+inspired teaching at MIT
+
+ align:start position:0%
+inspired teaching at MIT
+ 
+
+ align:start position:0%
+inspired teaching at MIT
+I'm your host Sarah Hansen from MIT
+
+ align:start position:0%
+I'm your host Sarah Hansen from MIT
+ 
+
+ align:start position:0%
+I'm your host Sarah Hansen from MIT
+OpenCourseWare my guest today is a
+
+ align:start position:0%
+OpenCourseWare my guest today is a
+ 
+
+ align:start position:0%
+OpenCourseWare my guest today is a
+longtime professor at MIT I'm David
+
+ align:start position:0%
+longtime professor at MIT I'm David
+ 
+
+ align:start position:0%
+longtime professor at MIT I'm David
+Thorburn I'm a professor of literature
+
+ align:start position:0%
+Thorburn I'm a professor of literature
+ 
+
+ align:start position:0%
+Thorburn I'm a professor of literature
+and comparative media I've taught the
+
+ align:start position:0%
+and comparative media I've taught the
+ 
+
+ align:start position:0%
+and comparative media I've taught the
+film experience for 39 years at MIT
+
+ align:start position:0%
+film experience for 39 years at MIT
+ 
+
+ align:start position:0%
+film experience for 39 years at MIT
+we'll be talking about professor Thor
+
+ align:start position:0%
+we'll be talking about professor Thor
+ 
+
+ align:start position:0%
+we'll be talking about professor Thor
+Byrnes class 21 l01 won the film
+
+ align:start position:0%
+Byrnes class 21 l01 won the film
+ 
+
+ align:start position:0%
+Byrnes class 21 l01 won the film
+experience and like all of the classes
+
+ align:start position:0%
+experience and like all of the classes
+ 
+
+ align:start position:0%
+experience and like all of the classes
+we talked about on this podcast you can
+
+ align:start position:0%
+we talked about on this podcast you can
+ 
+
+ align:start position:0%
+we talked about on this podcast you can
+check out the film experience on OCW
+
+ align:start position:0%
+check out the film experience on OCW
+ 
+
+ align:start position:0%
+check out the film experience on OCW
+website at ocw.mit.edu professor
+
+ align:start position:0%
+website at ocw.mit.edu professor
+ 
+
+ align:start position:0%
+website at ocw.mit.edu professor
+Thorburn made a splash in the academic
+
+ align:start position:0%
+Thorburn made a splash in the academic
+ 
+
+ align:start position:0%
+Thorburn made a splash in the academic
+world by bringing in media that
+
+ align:start position:0%
+world by bringing in media that
+ 
+
+ align:start position:0%
+world by bringing in media that
+traditionally hadn't existed there we'll
+
+ align:start position:0%
+traditionally hadn't existed there we'll
+ 
+
+ align:start position:0%
+traditionally hadn't existed there we'll
+start with how this all came about
+
+ align:start position:0%
+start with how this all came about
+ 
+
+ align:start position:0%
+start with how this all came about
+and what it was like for him to
+
+ align:start position:0%
+and what it was like for him to
+ 
+
+ align:start position:0%
+and what it was like for him to
+challenge what might be considered
+
+ align:start position:0%
+challenge what might be considered
+ 
+
+ align:start position:0%
+challenge what might be considered
+unholy in the sacred space of the
+
+ align:start position:0%
+unholy in the sacred space of the
+ 
+
+ align:start position:0%
+unholy in the sacred space of the
+classroom the story of what made me into
+
+ align:start position:0%
+classroom the story of what made me into
+ 
+
+ align:start position:0%
+classroom the story of what made me into
+a film scholar or a media scholar is at
+
+ align:start position:0%
+a film scholar or a media scholar is at
+ 
+
+ align:start position:0%
+a film scholar or a media scholar is at
+least interesting to me and so it still
+
+ align:start position:0%
+least interesting to me and so it still
+ 
+
+ align:start position:0%
+least interesting to me and so it still
+surprises me I had been teaching at Yale
+
+ align:start position:0%
+surprises me I had been teaching at Yale
+ 
+
+ align:start position:0%
+surprises me I had been teaching at Yale
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+for seven or eight years and I was
+
+ align:start position:0%
+for seven or eight years and I was
+ 
+
+ align:start position:0%
+for seven or eight years and I was
+offered a chance to do a visitation at
+
+ align:start position:0%
+offered a chance to do a visitation at
+ 
+
+ align:start position:0%
+offered a chance to do a visitation at
+the University of California in Santa
+
+ align:start position:0%
+the University of California in Santa
+ 
+
+ align:start position:0%
+the University of California in Santa
+Barbara and I was trying to introduce
+
+ align:start position:0%
+Barbara and I was trying to introduce
+ 
+
+ align:start position:0%
+Barbara and I was trying to introduce
+the students to the idea of conventions
+
+ align:start position:0%
+the students to the idea of conventions
+ 
+
+ align:start position:0%
+the students to the idea of conventions
+what it means when you begin a story
+
+ align:start position:0%
+what it means when you begin a story
+ 
+
+ align:start position:0%
+what it means when you begin a story
+once upon a time and every story begins
+
+ align:start position:0%
+once upon a time and every story begins
+ 
+
+ align:start position:0%
+once upon a time and every story begins
+that way or what it means when you say
+
+ align:start position:0%
+that way or what it means when you say
+ 
+
+ align:start position:0%
+that way or what it means when you say
+they lived happily ever after to take
+
+ align:start position:0%
+they lived happily ever after to take
+ 
+
+ align:start position:0%
+they lived happily ever after to take
+the simplest example of what a
+
+ align:start position:0%
+the simplest example of what a
+ 
+
+ align:start position:0%
+the simplest example of what a
+convention is I was trying to illustrate
+
+ align:start position:0%
+convention is I was trying to illustrate
+ 
+
+ align:start position:0%
+convention is I was trying to illustrate
+how in fact we internalize these things
+
+ align:start position:0%
+how in fact we internalize these things
+ 
+
+ align:start position:0%
+how in fact we internalize these things
+and we understand the conventions of the
+
+ align:start position:0%
+and we understand the conventions of the
+ 
+
+ align:start position:0%
+and we understand the conventions of the
+narratives of our own time in our blood
+
+ align:start position:0%
+narratives of our own time in our blood
+ 
+
+ align:start position:0%
+narratives of our own time in our blood
+without even thinking about it
+
+ align:start position:0%
+without even thinking about it
+ 
+
+ align:start position:0%
+without even thinking about it
+so what I needed to illustrate the
+
+ align:start position:0%
+so what I needed to illustrate the
+ 
+
+ align:start position:0%
+so what I needed to illustrate the
+principle were shared texts so I began
+
+ align:start position:0%
+principle were shared texts so I began
+ 
+
+ align:start position:0%
+principle were shared texts so I began
+by asking them this was in the 1970s in
+
+ align:start position:0%
+by asking them this was in the 1970s in
+ 
+
+ align:start position:0%
+by asking them this was in the 1970s in
+the early 1970s and I asked the students
+
+ align:start position:0%
+the early 1970s and I asked the students
+ 
+
+ align:start position:0%
+the early 1970s and I asked the students
+there these are bright california public
+
+ align:start position:0%
+there these are bright california public
+ 
+
+ align:start position:0%
+there these are bright california public
+school students how many of you have
+
+ align:start position:0%
+school students how many of you have
+ 
+
+ align:start position:0%
+school students how many of you have
+ever seen a John Wayne movie maybe 15%
+
+ align:start position:0%
+ever seen a John Wayne movie maybe 15%
+ 
+
+ align:start position:0%
+ever seen a John Wayne movie maybe 15%
+of the students raised their hand then I
+
+ align:start position:0%
+of the students raised their hand then I
+ 
+
+ align:start position:0%
+of the students raised their hand then I
+said well how many of you have read
+
+ align:start position:0%
+said well how many of you have read
+ 
+
+ align:start position:0%
+said well how many of you have read
+Huckleberry Finn maybe 30% I tried other
+
+ align:start position:0%
+Huckleberry Finn maybe 30% I tried other
+ 
+
+ align:start position:0%
+Huckleberry Finn maybe 30% I tried other
+novels classic novels I tried
+
+ align:start position:0%
+novels classic novels I tried
+ 
+
+ align:start position:0%
+novels classic novels I tried
+Shakespeare plays I was at a lot member
+
+ align:start position:0%
+Shakespeare plays I was at a lot member
+ 
+
+ align:start position:0%
+Shakespeare plays I was at a lot member
+this is in the early seventies finally I
+
+ align:start position:0%
+this is in the early seventies finally I
+ 
+
+ align:start position:0%
+this is in the early seventies finally I
+said how many of you have seen all in
+
+ align:start position:0%
+said how many of you have seen all in
+ 
+
+ align:start position:0%
+said how many of you have seen all in
+the family for those in the audience too
+
+ align:start position:0%
+the family for those in the audience too
+ 
+
+ align:start position:0%
+the family for those in the audience too
+young to know this all in the family was
+
+ align:start position:0%
+young to know this all in the family was
+ 
+
+ align:start position:0%
+young to know this all in the family was
+a television program a classic and
+
+ align:start position:0%
+a television program a classic and
+ 
+
+ align:start position:0%
+a television program a classic and
+transforming one that appeared in 1971
+
+ align:start position:0%
+transforming one that appeared in 1971
+ 
+
+ align:start position:0%
+transforming one that appeared in 1971
+on American television and involved a
+
+ align:start position:0%
+on American television and involved a
+ 
+
+ align:start position:0%
+on American television and involved a
+working-class hero who had never such
+
+ align:start position:0%
+working-class hero who had never such
+ 
+
+ align:start position:0%
+working-class hero who had never such
+characters had never appeared on
+
+ align:start position:0%
+characters had never appeared on
+ 
+
+ align:start position:0%
+characters had never appeared on
+television before was a very important
+
+ align:start position:0%
+television before was a very important
+ 
+
+ align:start position:0%
+television before was a very important
+program and of course a hundred percent
+
+ align:start position:0%
+program and of course a hundred percent
+ 
+
+ align:start position:0%
+program and of course a hundred percent
+of the class had seen it and I began to
+
+ align:start position:0%
+of the class had seen it and I began to
+ 
+
+ align:start position:0%
+of the class had seen it and I began to
+take my examples from television
+
+ align:start position:0%
+take my examples from television
+ 
+
+ align:start position:0%
+take my examples from television
+programs and I became either this
+
+ align:start position:0%
+programs and I became either this
+ 
+
+ align:start position:0%
+programs and I became either this
+maybe I worried on me as the term went
+
+ align:start position:0%
+maybe I worried on me as the term went
+ 
+
+ align:start position:0%
+maybe I worried on me as the term went
+on and I what I realized was that the
+
+ align:start position:0%
+on and I what I realized was that the
+ 
+
+ align:start position:0%
+on and I what I realized was that the
+literature of our own day the story
+
+ align:start position:0%
+literature of our own day the story
+ 
+
+ align:start position:0%
+literature of our own day the story
+forms that belong to my students and to
+
+ align:start position:0%
+forms that belong to my students and to
+ 
+
+ align:start position:0%
+forms that belong to my students and to
+the generation of kids I was teaching
+
+ align:start position:0%
+the generation of kids I was teaching
+ 
+
+ align:start position:0%
+the generation of kids I was teaching
+were visual not literary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I became interested in television as
+
+ align:start position:0%
+so I became interested in television as
+ 
+
+ align:start position:0%
+so I became interested in television as
+a narrative medium and then I came to
+
+ align:start position:0%
+a narrative medium and then I came to
+ 
+
+ align:start position:0%
+a narrative medium and then I came to
+realize as I began to think more
+
+ align:start position:0%
+realize as I began to think more
+ 
+
+ align:start position:0%
+realize as I began to think more
+seriously about the role of television
+
+ align:start position:0%
+seriously about the role of television
+ 
+
+ align:start position:0%
+seriously about the role of television
+in American like remember by 1970
+
+ align:start position:0%
+in American like remember by 1970
+ 
+
+ align:start position:0%
+in American like remember by 1970
+American television was the dominant
+
+ align:start position:0%
+American television was the dominant
+ 
+
+ align:start position:0%
+American television was the dominant
+form of entertainment and narrative in
+
+ align:start position:0%
+form of entertainment and narrative in
+ 
+
+ align:start position:0%
+form of entertainment and narrative in
+American life and in fact this initial
+
+ align:start position:0%
+American life and in fact this initial
+ 
+
+ align:start position:0%
+American life and in fact this initial
+understanding out of which my whole
+
+ align:start position:0%
+understanding out of which my whole
+ 
+
+ align:start position:0%
+understanding out of which my whole
+interest in media developed has shaped I
+
+ align:start position:0%
+interest in media developed has shaped I
+ 
+
+ align:start position:0%
+interest in media developed has shaped I
+realized now just in talking about this
+
+ align:start position:0%
+realized now just in talking about this
+ 
+
+ align:start position:0%
+realized now just in talking about this
+my way of teaching the film experience
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when I got back to Yale after my years
+
+ align:start position:0%
+when I got back to Yale after my years
+ 
+
+ align:start position:0%
+when I got back to Yale after my years
+visitation I introduced a course called
+
+ align:start position:0%
+visitation I introduced a course called
+ 
+
+ align:start position:0%
+visitation I introduced a course called
+literature and popular culture in which
+
+ align:start position:0%
+literature and popular culture in which
+ 
+
+ align:start position:0%
+literature and popular culture in which
+I explored these ideas in greater depth
+
+ align:start position:0%
+I explored these ideas in greater depth
+ 
+
+ align:start position:0%
+I explored these ideas in greater depth
+I read some bestsellers I ended the
+
+ align:start position:0%
+I read some bestsellers I ended the
+ 
+
+ align:start position:0%
+I read some bestsellers I ended the
+course by looking at the honeymooners
+
+ align:start position:0%
+course by looking at the honeymooners
+ 
+
+ align:start position:0%
+course by looking at the honeymooners
+and I remember I was teaching the course
+
+ align:start position:0%
+and I remember I was teaching the course
+ 
+
+ align:start position:0%
+and I remember I was teaching the course
+in a room at Yale College Kalindi
+
+ align:start position:0%
+in a room at Yale College Kalindi
+ 
+
+ align:start position:0%
+in a room at Yale College Kalindi
+Chittenden Hall in which legendary
+
+ align:start position:0%
+Chittenden Hall in which legendary
+ 
+
+ align:start position:0%
+Chittenden Hall in which legendary
+figures had laid lectured on Shakespeare
+
+ align:start position:0%
+figures had laid lectured on Shakespeare
+ 
+
+ align:start position:0%
+figures had laid lectured on Shakespeare
+and one of these legendary professors
+
+ align:start position:0%
+and one of these legendary professors
+ 
+
+ align:start position:0%
+and one of these legendary professors
+the man who had actually hired me at
+
+ align:start position:0%
+the man who had actually hired me at
+ 
+
+ align:start position:0%
+the man who had actually hired me at
+Yale Maynard Mack of great a great
+
+ align:start position:0%
+Yale Maynard Mack of great a great
+ 
+
+ align:start position:0%
+Yale Maynard Mack of great a great
+literary scholar poaches headed and
+
+ align:start position:0%
+literary scholar poaches headed and
+ 
+
+ align:start position:0%
+literary scholar poaches headed and
+while I was teaching the honeymooners
+
+ align:start position:0%
+while I was teaching the honeymooners
+ 
+
+ align:start position:0%
+while I was teaching the honeymooners
+and then later called me into his office
+
+ align:start position:0%
+and then later called me into his office
+ 
+
+ align:start position:0%
+and then later called me into his office
+and expressed great disappointment over
+
+ align:start position:0%
+and expressed great disappointment over
+ 
+
+ align:start position:0%
+and expressed great disappointment over
+the fact that I was polluting this this
+
+ align:start position:0%
+the fact that I was polluting this this
+ 
+
+ align:start position:0%
+the fact that I was polluting this this
+environment so then I and when we then
+
+ align:start position:0%
+environment so then I and when we then
+ 
+
+ align:start position:0%
+environment so then I and when we then
+had a serious conversation and I said to
+
+ align:start position:0%
+had a serious conversation and I said to
+ 
+
+ align:start position:0%
+had a serious conversation and I said to
+him what did you what did he actually
+
+ align:start position:0%
+him what did you what did he actually
+ 
+
+ align:start position:0%
+him what did you what did he actually
+think Shakespeare's environment was and
+
+ align:start position:0%
+think Shakespeare's environment was and
+ 
+
+ align:start position:0%
+think Shakespeare's environment was and
+that was when it struck me how narrow my
+
+ align:start position:0%
+that was when it struck me how narrow my
+ 
+
+ align:start position:0%
+that was when it struck me how narrow my
+education had been because he really had
+
+ align:start position:0%
+education had been because he really had
+ 
+
+ align:start position:0%
+education had been because he really had
+not even though he was a great man and
+
+ align:start position:0%
+not even though he was a great man and
+ 
+
+ align:start position:0%
+not even though he was a great man and
+agreed he knew the history but he
+
+ align:start position:0%
+agreed he knew the history but he
+ 
+
+ align:start position:0%
+agreed he knew the history but he
+somehow had managed to disconnect the
+
+ align:start position:0%
+somehow had managed to disconnect the
+ 
+
+ align:start position:0%
+somehow had managed to disconnect the
+literary power of Shakespeare from the
+
+ align:start position:0%
+literary power of Shakespeare from the
+ 
+
+ align:start position:0%
+literary power of Shakespeare from the
+fact that it was done on this incredibly
+
+ align:start position:0%
+fact that it was done on this incredibly
+ 
+
+ align:start position:0%
+fact that it was done on this incredibly
+popular stage and it was so sensational
+
+ align:start position:0%
+popular stage and it was so sensational
+ 
+
+ align:start position:0%
+popular stage and it was so sensational
+and it was so much more like a
+
+ align:start position:0%
+and it was so much more like a
+ 
+
+ align:start position:0%
+and it was so much more like a
+television or the movies than it was
+
+ align:start position:0%
+television or the movies than it was
+ 
+
+ align:start position:0%
+television or the movies than it was
+like some process of sitting in a in a
+
+ align:start position:0%
+like some process of sitting in a in a
+ 
+
+ align:start position:0%
+like some process of sitting in a in a
+library with wood-paneled splendor
+
+ align:start position:0%
+library with wood-paneled splendor
+ 
+
+ align:start position:0%
+library with wood-paneled splendor
+reading words in silence that's not what
+
+ align:start position:0%
+reading words in silence that's not what
+ 
+
+ align:start position:0%
+reading words in silence that's not what
+Shakespeare was
+
+ align:start position:0%
+Shakespeare was
+ 
+
+ align:start position:0%
+Shakespeare was
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+part of why we wanted to talk about
+
+ align:start position:0%
+part of why we wanted to talk about
+ 
+
+ align:start position:0%
+part of why we wanted to talk about
+professor Thor Barton's film experience
+
+ align:start position:0%
+professor Thor Barton's film experience
+ 
+
+ align:start position:0%
+professor Thor Barton's film experience
+class is because teaching film changes
+
+ align:start position:0%
+class is because teaching film changes
+ 
+
+ align:start position:0%
+class is because teaching film changes
+as technology and student life evolve
+
+ align:start position:0%
+as technology and student life evolve
+ 
+
+ align:start position:0%
+as technology and student life evolve
+I asked him what this evolution means
+
+ align:start position:0%
+I asked him what this evolution means
+ 
+
+ align:start position:0%
+I asked him what this evolution means
+for the ways in which he presents his
+
+ align:start position:0%
+for the ways in which he presents his
+ 
+
+ align:start position:0%
+for the ways in which he presents his
+materials his answer start from the very
+
+ align:start position:0%
+materials his answer start from the very
+ 
+
+ align:start position:0%
+materials his answer start from the very
+beginning when I begin the film
+
+ align:start position:0%
+beginning when I begin the film
+ 
+
+ align:start position:0%
+beginning when I begin the film
+experience I asked the students to do
+
+ align:start position:0%
+experience I asked the students to do
+ 
+
+ align:start position:0%
+experience I asked the students to do
+something they find increasingly
+
+ align:start position:0%
+something they find increasingly
+ 
+
+ align:start position:0%
+something they find increasingly
+difficult in the old days before the
+
+ align:start position:0%
+difficult in the old days before the
+ 
+
+ align:start position:0%
+difficult in the old days before the
+proliferation of smartphones and visual
+
+ align:start position:0%
+proliferation of smartphones and visual
+ 
+
+ align:start position:0%
+proliferation of smartphones and visual
+media all over the place and everyone
+
+ align:start position:0%
+media all over the place and everyone
+ 
+
+ align:start position:0%
+media all over the place and everyone
+being able to make his own video and so
+
+ align:start position:0%
+being able to make his own video and so
+ 
+
+ align:start position:0%
+being able to make his own video and so
+forth and the you know the ubiquity of
+
+ align:start position:0%
+forth and the you know the ubiquity of
+ 
+
+ align:start position:0%
+forth and the you know the ubiquity of
+DVDs before those days I was able to
+
+ align:start position:0%
+DVDs before those days I was able to
+ 
+
+ align:start position:0%
+DVDs before those days I was able to
+tell the students look we live in an
+
+ align:start position:0%
+tell the students look we live in an
+ 
+
+ align:start position:0%
+tell the students look we live in an
+audio-visual age we live in a televisual
+
+ align:start position:0%
+audio-visual age we live in a televisual
+ 
+
+ align:start position:0%
+audio-visual age we live in a televisual
+age I want you to think that stuff away
+
+ align:start position:0%
+age I want you to think that stuff away
+ 
+
+ align:start position:0%
+age I want you to think that stuff away
+I want you to get think yourself back to
+
+ align:start position:0%
+I want you to get think yourself back to
+ 
+
+ align:start position:0%
+I want you to get think yourself back to
+an age before people understood that
+
+ align:start position:0%
+an age before people understood that
+ 
+
+ align:start position:0%
+an age before people understood that
+there is such a thing as a film and
+
+ align:start position:0%
+there is such a thing as a film and
+ 
+
+ align:start position:0%
+there is such a thing as a film and
+think about the original meaning of
+
+ align:start position:0%
+think about the original meaning of
+ 
+
+ align:start position:0%
+think about the original meaning of
+movie is go back to the roots meaning
+
+ align:start position:0%
+movie is go back to the roots meaning
+ 
+
+ align:start position:0%
+movie is go back to the roots meaning
+it's a metaphor that is a dead metaphor
+
+ align:start position:0%
+it's a metaphor that is a dead metaphor
+ 
+
+ align:start position:0%
+it's a metaphor that is a dead metaphor
+for us but it actually it's it tells you
+
+ align:start position:0%
+for us but it actually it's it tells you
+ 
+
+ align:start position:0%
+for us but it actually it's it tells you
+what the most fundamental aspect of the
+
+ align:start position:0%
+what the most fundamental aspect of the
+ 
+
+ align:start position:0%
+what the most fundamental aspect of the
+movies were for the original audiences
+
+ align:start position:0%
+movies were for the original audiences
+ 
+
+ align:start position:0%
+movies were for the original audiences
+and why they were so fascinated by the
+
+ align:start position:0%
+and why they were so fascinated by the
+ 
+
+ align:start position:0%
+and why they were so fascinated by the
+capacity of this new technology to
+
+ align:start position:0%
+capacity of this new technology to
+ 
+
+ align:start position:0%
+capacity of this new technology to
+capture motion it seemed like and it was
+
+ align:start position:0%
+capture motion it seemed like and it was
+ 
+
+ align:start position:0%
+capture motion it seemed like and it was
+a tremendous new advance in technologies
+
+ align:start position:0%
+a tremendous new advance in technologies
+ 
+
+ align:start position:0%
+a tremendous new advance in technologies
+of the representation of human
+
+ align:start position:0%
+of the representation of human
+ 
+
+ align:start position:0%
+of the representation of human
+experience because it captured humans in
+
+ align:start position:0%
+experience because it captured humans in
+ 
+
+ align:start position:0%
+experience because it captured humans in
+motion it captured the movements of the
+
+ align:start position:0%
+motion it captured the movements of the
+ 
+
+ align:start position:0%
+motion it captured the movements of the
+world the first films as I try to show
+
+ align:start position:0%
+world the first films as I try to show
+ 
+
+ align:start position:0%
+world the first films as I try to show
+my students were so preoccupied by this
+
+ align:start position:0%
+my students were so preoccupied by this
+ 
+
+ align:start position:0%
+my students were so preoccupied by this
+wondrous capacity of the medium that
+
+ align:start position:0%
+wondrous capacity of the medium that
+ 
+
+ align:start position:0%
+wondrous capacity of the medium that
+it's almost the only thing they filmed
+
+ align:start position:0%
+it's almost the only thing they filmed
+ 
+
+ align:start position:0%
+it's almost the only thing they filmed
+and you can see the evolution of the
+
+ align:start position:0%
+and you can see the evolution of the
+ 
+
+ align:start position:0%
+and you can see the evolution of the
+medium embodied in the way in which
+
+ align:start position:0%
+medium embodied in the way in which
+ 
+
+ align:start position:0%
+medium embodied in the way in which
+after an initial profound fascination
+
+ align:start position:0%
+after an initial profound fascination
+ 
+
+ align:start position:0%
+after an initial profound fascination
+with the novelty of movement begins to
+
+ align:start position:0%
+with the novelty of movement begins to
+ 
+
+ align:start position:0%
+with the novelty of movement begins to
+wear off other properties of the film
+
+ align:start position:0%
+wear off other properties of the film
+ 
+
+ align:start position:0%
+wear off other properties of the film
+medium begin to be discovered so I tell
+
+ align:start position:0%
+medium begin to be discovered so I tell
+ 
+
+ align:start position:0%
+medium begin to be discovered so I tell
+my students this principle and I asked
+
+ align:start position:0%
+my students this principle and I asked
+ 
+
+ align:start position:0%
+my students this principle and I asked
+them to try to think their way back into
+
+ align:start position:0%
+them to try to think their way back into
+ 
+
+ align:start position:0%
+them to try to think their way back into
+the attitude of these first viewers who
+
+ align:start position:0%
+the attitude of these first viewers who
+ 
+
+ align:start position:0%
+the attitude of these first viewers who
+didn't know about the visual media to
+
+ align:start position:0%
+didn't know about the visual media to
+ 
+
+ align:start position:0%
+didn't know about the visual media to
+play a kind of thought experiment today
+
+ align:start position:0%
+play a kind of thought experiment today
+ 
+
+ align:start position:0%
+play a kind of thought experiment today
+it's much harder to make them play that
+
+ align:start position:0%
+it's much harder to make them play that
+ 
+
+ align:start position:0%
+it's much harder to make them play that
+experiment because I have to tell them
+
+ align:start position:0%
+experiment because I have to tell them
+ 
+
+ align:start position:0%
+experiment because I have to tell them
+as I do in that first lecture think
+
+ align:start position:0%
+as I do in that first lecture think
+ 
+
+ align:start position:0%
+as I do in that first lecture think
+away your iPad's imagine a world without
+
+ align:start position:0%
+away your iPad's imagine a world without
+ 
+
+ align:start position:0%
+away your iPad's imagine a world without
+iPads imagine a world without
+
+ align:start position:0%
+iPads imagine a world without
+ 
+
+ align:start position:0%
+iPads imagine a world without
+smartphones imagine a world without
+
+ align:start position:0%
+smartphones imagine a world without
+ 
+
+ align:start position:0%
+smartphones imagine a world without
+instant communication and of course this
+
+ align:start position:0%
+instant communication and of course this
+ 
+
+ align:start position:0%
+instant communication and of course this
+is much harder for the students to do
+
+ align:start position:0%
+is much harder for the students to do
+ 
+
+ align:start position:0%
+is much harder for the students to do
+and of course at one level they are much
+
+ align:start position:0%
+and of course at one level they are much
+ 
+
+ align:start position:0%
+and of course at one level they are much
+more capable of processing audio visual
+
+ align:start position:0%
+more capable of processing audio visual
+ 
+
+ align:start position:0%
+more capable of processing audio visual
+information than I am and then my and my
+
+ align:start position:0%
+information than I am and then my and my
+ 
+
+ align:start position:0%
+information than I am and then my and my
+parents generation and then and and all
+
+ align:start position:0%
+parents generation and then and and all
+ 
+
+ align:start position:0%
+parents generation and then and and all
+of the generations older than their
+
+ align:start position:0%
+of the generations older than their
+ 
+
+ align:start position:0%
+of the generations older than their
+because they've grown up in an
+
+ align:start position:0%
+because they've grown up in an
+ 
+
+ align:start position:0%
+because they've grown up in an
+environment in which essentially they're
+
+ align:start position:0%
+environment in which essentially they're
+ 
+
+ align:start position:0%
+environment in which essentially they're
+surrounded 24/7 by audio visual stimuli
+
+ align:start position:0%
+surrounded 24/7 by audio visual stimuli
+ 
+
+ align:start position:0%
+surrounded 24/7 by audio visual stimuli
+by audio visual signals this many people
+
+ align:start position:0%
+by audio visual signals this many people
+ 
+
+ align:start position:0%
+by audio visual signals this many people
+might see this as dangerous perhaps it
+
+ align:start position:0%
+might see this as dangerous perhaps it
+ 
+
+ align:start position:0%
+might see this as dangerous perhaps it
+is but it develops new capacities and
+
+ align:start position:0%
+is but it develops new capacities and
+ 
+
+ align:start position:0%
+is but it develops new capacities and
+the and one can see this in the history
+
+ align:start position:0%
+the and one can see this in the history
+ 
+
+ align:start position:0%
+the and one can see this in the history
+of television in which at a certain
+
+ align:start position:0%
+of television in which at a certain
+ 
+
+ align:start position:0%
+of television in which at a certain
+point there are certain kinds of
+
+ align:start position:0%
+point there are certain kinds of
+ 
+
+ align:start position:0%
+point there are certain kinds of
+television programs that become too
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+ align:start position:0%
+television programs that become too
+ 
+
+ align:start position:0%
+television programs that become too
+complex for older generations and only
+
+ align:start position:0%
+complex for older generations and only
+ 
+
+ align:start position:0%
+complex for older generations and only
+the younger generation that was used to
+
+ align:start position:0%
+the younger generation that was used to
+ 
+
+ align:start position:0%
+the younger generation that was used to
+going to the movies and had been
+
+ align:start position:0%
+going to the movies and had been
+ 
+
+ align:start position:0%
+going to the movies and had been
+watching television and had been
+
+ align:start position:0%
+watching television and had been
+ 
+
+ align:start position:0%
+watching television and had been
+watching MTV they were able to
+
+ align:start position:0%
+watching MTV they were able to
+ 
+
+ align:start position:0%
+watching MTV they were able to
+understand this very easily
+
+ align:start position:0%
+understand this very easily
+ 
+
+ align:start position:0%
+understand this very easily
+professor Thor burns class includes a
+
+ align:start position:0%
+professor Thor burns class includes a
+ 
+
+ align:start position:0%
+professor Thor burns class includes a
+two-hour lecture with one more hour of
+
+ align:start position:0%
+two-hour lecture with one more hour of
+ 
+
+ align:start position:0%
+two-hour lecture with one more hour of
+discussion in our conversation he talked
+
+ align:start position:0%
+discussion in our conversation he talked
+ 
+
+ align:start position:0%
+discussion in our conversation he talked
+about the changing popular opinion
+
+ align:start position:0%
+about the changing popular opinion
+ 
+
+ align:start position:0%
+about the changing popular opinion
+surrounding lectures namely that their
+
+ align:start position:0%
+surrounding lectures namely that their
+ 
+
+ align:start position:0%
+surrounding lectures namely that their
+outdated and less effective than other
+
+ align:start position:0%
+outdated and less effective than other
+ 
+
+ align:start position:0%
+outdated and less effective than other
+styles of teaching in short he disagrees
+
+ align:start position:0%
+styles of teaching in short he disagrees
+ 
+
+ align:start position:0%
+styles of teaching in short he disagrees
+I'll let him explain I've thought a lot
+
+ align:start position:0%
+I'll let him explain I've thought a lot
+ 
+
+ align:start position:0%
+I'll let him explain I've thought a lot
+about what it means to lecture to
+
+ align:start position:0%
+about what it means to lecture to
+ 
+
+ align:start position:0%
+about what it means to lecture to
+undergraduates I hated bad lectures I
+
+ align:start position:0%
+undergraduates I hated bad lectures I
+ 
+
+ align:start position:0%
+undergraduates I hated bad lectures I
+thought they were the the pits of higher
+
+ align:start position:0%
+thought they were the the pits of higher
+ 
+
+ align:start position:0%
+thought they were the the pits of higher
+education and I swore to myself that if
+
+ align:start position:0%
+education and I swore to myself that if
+ 
+
+ align:start position:0%
+education and I swore to myself that if
+I became a lecturer I would never more
+
+ align:start position:0%
+I became a lecturer I would never more
+ 
+
+ align:start position:0%
+I became a lecturer I would never more
+my students that that was a worse sin
+
+ align:start position:0%
+my students that that was a worse sin
+ 
+
+ align:start position:0%
+my students that that was a worse sin
+than almost any other a teacher could
+
+ align:start position:0%
+than almost any other a teacher could
+ 
+
+ align:start position:0%
+than almost any other a teacher could
+commit was to be boring and I have also
+
+ align:start position:0%
+commit was to be boring and I have also
+ 
+
+ align:start position:0%
+commit was to be boring and I have also
+felt that in recent years especially
+
+ align:start position:0%
+felt that in recent years especially
+ 
+
+ align:start position:0%
+felt that in recent years especially
+although it's always been an
+
+ align:start position:0%
+although it's always been an
+ 
+
+ align:start position:0%
+although it's always been an
+undercurrent in education there's been a
+
+ align:start position:0%
+undercurrent in education there's been a
+ 
+
+ align:start position:0%
+undercurrent in education there's been a
+kind of growing negative feeling about
+
+ align:start position:0%
+kind of growing negative feeling about
+ 
+
+ align:start position:0%
+kind of growing negative feeling about
+lectures as if they're they're hurting
+
+ align:start position:0%
+lectures as if they're they're hurting
+ 
+
+ align:start position:0%
+lectures as if they're they're hurting
+students into a herd experience and it
+
+ align:start position:0%
+students into a herd experience and it
+ 
+
+ align:start position:0%
+students into a herd experience and it
+doesn't give them hands-on experience
+
+ align:start position:0%
+doesn't give them hands-on experience
+ 
+
+ align:start position:0%
+doesn't give them hands-on experience
+and I think intellectually that's a
+
+ align:start position:0%
+and I think intellectually that's a
+ 
+
+ align:start position:0%
+and I think intellectually that's a
+foolish perspective professors know more
+
+ align:start position:0%
+foolish perspective professors know more
+ 
+
+ align:start position:0%
+foolish perspective professors know more
+than students it's appropriate for
+
+ align:start position:0%
+than students it's appropriate for
+ 
+
+ align:start position:0%
+than students it's appropriate for
+students to listen to professors
+
+ align:start position:0%
+students to listen to professors
+ 
+
+ align:start position:0%
+students to listen to professors
+sometimes professors should take the
+
+ align:start position:0%
+sometimes professors should take the
+ 
+
+ align:start position:0%
+sometimes professors should take the
+responsibility of taught when they talk
+
+ align:start position:0%
+responsibility of taught when they talk
+ 
+
+ align:start position:0%
+responsibility of taught when they talk
+to students
+
+ align:start position:0%
+to students
+ 
+
+ align:start position:0%
+to students
+very seriously and in the in a small
+
+ align:start position:0%
+very seriously and in the in a small
+ 
+
+ align:start position:0%
+very seriously and in the in a small
+classroom they should certainly
+
+ align:start position:0%
+classroom they should certainly
+ 
+
+ align:start position:0%
+classroom they should certainly
+encourage discussion and interaction and
+
+ align:start position:0%
+encourage discussion and interaction and
+ 
+
+ align:start position:0%
+encourage discussion and interaction and
+I think at my best I'm not sure I always
+
+ align:start position:0%
+I think at my best I'm not sure I always
+ 
+
+ align:start position:0%
+I think at my best I'm not sure I always
+am at my best I know I'm not but when I
+
+ align:start position:0%
+am at my best I know I'm not but when I
+ 
+
+ align:start position:0%
+am at my best I know I'm not but when I
+am at my best I think I'm doing
+
+ align:start position:0%
+am at my best I think I'm doing
+ 
+
+ align:start position:0%
+am at my best I think I'm doing
+something that that can't be captured in
+
+ align:start position:0%
+something that that can't be captured in
+ 
+
+ align:start position:0%
+something that that can't be captured in
+printed form or couldn't be captured if
+
+ align:start position:0%
+printed form or couldn't be captured if
+ 
+
+ align:start position:0%
+printed form or couldn't be captured if
+you gave the students a transcript of
+
+ align:start position:0%
+you gave the students a transcript of
+ 
+
+ align:start position:0%
+you gave the students a transcript of
+what you had done which is that I'm
+
+ align:start position:0%
+what you had done which is that I'm
+ 
+
+ align:start position:0%
+what you had done which is that I'm
+modeling thinking I'm modeling how you
+
+ align:start position:0%
+modeling thinking I'm modeling how you
+ 
+
+ align:start position:0%
+modeling thinking I'm modeling how you
+make connections it seemed to me as I
+
+ align:start position:0%
+make connections it seemed to me as I
+ 
+
+ align:start position:0%
+make connections it seemed to me as I
+thought about the most inspiring
+
+ align:start position:0%
+thought about the most inspiring
+ 
+
+ align:start position:0%
+thought about the most inspiring
+lectures that I had as an undergraduate
+
+ align:start position:0%
+lectures that I had as an undergraduate
+ 
+
+ align:start position:0%
+lectures that I had as an undergraduate
+there was one professor I had especially
+
+ align:start position:0%
+there was one professor I had especially
+ 
+
+ align:start position:0%
+there was one professor I had especially
+he's now dead but he was a wonderfully
+
+ align:start position:0%
+he's now dead but he was a wonderfully
+ 
+
+ align:start position:0%
+he's now dead but he was a wonderfully
+inspiring man's name was Lawrence
+
+ align:start position:0%
+inspiring man's name was Lawrence
+ 
+
+ align:start position:0%
+inspiring man's name was Lawrence
+Holland his lecturer was on American
+
+ align:start position:0%
+Holland his lecturer was on American
+ 
+
+ align:start position:0%
+Holland his lecturer was on American
+literature and his strategy in lectures
+
+ align:start position:0%
+literature and his strategy in lectures
+ 
+
+ align:start position:0%
+literature and his strategy in lectures
+I've tried to copy one thing he always
+
+ align:start position:0%
+I've tried to copy one thing he always
+ 
+
+ align:start position:0%
+I've tried to copy one thing he always
+did was he presented an outline it
+
+ align:start position:0%
+did was he presented an outline it
+ 
+
+ align:start position:0%
+did was he presented an outline it
+wasn't it was not the text of the
+
+ align:start position:0%
+wasn't it was not the text of the
+ 
+
+ align:start position:0%
+wasn't it was not the text of the
+lecture but it was three or four central
+
+ align:start position:0%
+lecture but it was three or four central
+ 
+
+ align:start position:0%
+lecture but it was three or four central
+digestible points that organized the
+
+ align:start position:0%
+digestible points that organized the
+ 
+
+ align:start position:0%
+digestible points that organized the
+lecture in sequence it didn't capture
+
+ align:start position:0%
+lecture in sequence it didn't capture
+ 
+
+ align:start position:0%
+lecture in sequence it didn't capture
+the whole lecture but if you could use
+
+ align:start position:0%
+the whole lecture but if you could use
+ 
+
+ align:start position:0%
+the whole lecture but if you could use
+that sheet to organize your
+
+ align:start position:0%
+that sheet to organize your
+ 
+
+ align:start position:0%
+that sheet to organize your
+understanding of the lecture I thought
+
+ align:start position:0%
+understanding of the lecture I thought
+ 
+
+ align:start position:0%
+understanding of the lecture I thought
+that was a wonderfully helpful I found
+
+ align:start position:0%
+that was a wonderfully helpful I found
+ 
+
+ align:start position:0%
+that was a wonderfully helpful I found
+it wonderfully helpful but the both for
+
+ align:start position:0%
+it wonderfully helpful but the both for
+ 
+
+ align:start position:0%
+it wonderfully helpful but the both for
+review but also because what it showed
+
+ align:start position:0%
+review but also because what it showed
+ 
+
+ align:start position:0%
+review but also because what it showed
+me was that Professor Holland had
+
+ align:start position:0%
+me was that Professor Holland had
+ 
+
+ align:start position:0%
+me was that Professor Holland had
+planned what he was doing that he was
+
+ align:start position:0%
+planned what he was doing that he was
+ 
+
+ align:start position:0%
+planned what he was doing that he was
+presenting material to me that he had
+
+ align:start position:0%
+presenting material to me that he had
+ 
+
+ align:start position:0%
+presenting material to me that he had
+thought long about that he had organized
+
+ align:start position:0%
+thought long about that he had organized
+ 
+
+ align:start position:0%
+thought long about that he had organized
+in a serious way but the second great
+
+ align:start position:0%
+in a serious way but the second great
+ 
+
+ align:start position:0%
+in a serious way but the second great
+thing about Larry Holland's lectures was
+
+ align:start position:0%
+thing about Larry Holland's lectures was
+ 
+
+ align:start position:0%
+thing about Larry Holland's lectures was
+that they were not completely written
+
+ align:start position:0%
+that they were not completely written
+ 
+
+ align:start position:0%
+that they were not completely written
+out there were parts of them that were
+
+ align:start position:0%
+out there were parts of them that were
+ 
+
+ align:start position:0%
+out there were parts of them that were
+written out very eloquent moments often
+
+ align:start position:0%
+written out very eloquent moments often
+ 
+
+ align:start position:0%
+written out very eloquent moments often
+at the beginning at the end and I've
+
+ align:start position:0%
+at the beginning at the end and I've
+ 
+
+ align:start position:0%
+at the beginning at the end and I've
+sometimes imitated that but the greatest
+
+ align:start position:0%
+sometimes imitated that but the greatest
+ 
+
+ align:start position:0%
+sometimes imitated that but the greatest
+part of his lectures with his lecture
+
+ align:start position:0%
+part of his lectures with his lecture
+ 
+
+ align:start position:0%
+part of his lectures with his lecture
+seemed spontaneous even though he was
+
+ align:start position:0%
+seemed spontaneous even though he was
+ 
+
+ align:start position:0%
+seemed spontaneous even though he was
+following his lecture it seemed as if he
+
+ align:start position:0%
+following his lecture it seemed as if he
+ 
+
+ align:start position:0%
+following his lecture it seemed as if he
+was not he was speaking to me and I
+
+ align:start position:0%
+was not he was speaking to me and I
+ 
+
+ align:start position:0%
+was not he was speaking to me and I
+tried to capture I've never been as good
+
+ align:start position:0%
+tried to capture I've never been as good
+ 
+
+ align:start position:0%
+tried to capture I've never been as good
+as he was there was a kind of passion a
+
+ align:start position:0%
+as he was there was a kind of passion a
+ 
+
+ align:start position:0%
+as he was there was a kind of passion a
+kind of feeling in what he did and I
+
+ align:start position:0%
+kind of feeling in what he did and I
+ 
+
+ align:start position:0%
+kind of feeling in what he did and I
+realized that the another aspect of what
+
+ align:start position:0%
+realized that the another aspect of what
+ 
+
+ align:start position:0%
+realized that the another aspect of what
+he was showing me was how not just
+
+ align:start position:0%
+he was showing me was how not just
+ 
+
+ align:start position:0%
+he was showing me was how not just
+intellectually engaged but how
+
+ align:start position:0%
+intellectually engaged but how
+ 
+
+ align:start position:0%
+intellectually engaged but how
+passionate
+
+ align:start position:0%
+passionate
+ 
+
+ align:start position:0%
+passionate
+engaged how emotionally valuable
+
+ align:start position:0%
+engaged how emotionally valuable
+ 
+
+ align:start position:0%
+engaged how emotionally valuable
+studying literature could be maybe the
+
+ align:start position:0%
+studying literature could be maybe the
+ 
+
+ align:start position:0%
+studying literature could be maybe the
+most telling feature of this course is
+
+ align:start position:0%
+most telling feature of this course is
+ 
+
+ align:start position:0%
+most telling feature of this course is
+its intended outcome for students
+
+ align:start position:0%
+its intended outcome for students
+ 
+
+ align:start position:0%
+its intended outcome for students
+professor Thorburn isn't trying to
+
+ align:start position:0%
+professor Thorburn isn't trying to
+ 
+
+ align:start position:0%
+professor Thorburn isn't trying to
+create film critics or even experts in
+
+ align:start position:0%
+create film critics or even experts in
+ 
+
+ align:start position:0%
+create film critics or even experts in
+his classes his school is much more
+
+ align:start position:0%
+his classes his school is much more
+ 
+
+ align:start position:0%
+his classes his school is much more
+significant one of the ways of the study
+
+ align:start position:0%
+significant one of the ways of the study
+ 
+
+ align:start position:0%
+significant one of the ways of the study
+of literature the study of film differs
+
+ align:start position:0%
+of literature the study of film differs
+ 
+
+ align:start position:0%
+of literature the study of film differs
+from the study of technical things and
+
+ align:start position:0%
+from the study of technical things and
+ 
+
+ align:start position:0%
+from the study of technical things and
+the reason I teach it is that it belongs
+
+ align:start position:0%
+the reason I teach it is that it belongs
+ 
+
+ align:start position:0%
+the reason I teach it is that it belongs
+to everyone that it's valuable for
+
+ align:start position:0%
+to everyone that it's valuable for
+ 
+
+ align:start position:0%
+to everyone that it's valuable for
+everyone not everyone needs to know
+
+ align:start position:0%
+everyone not everyone needs to know
+ 
+
+ align:start position:0%
+everyone not everyone needs to know
+about quantum mechanics but I believe
+
+ align:start position:0%
+about quantum mechanics but I believe
+ 
+
+ align:start position:0%
+about quantum mechanics but I believe
+everyone should and if they don't I feel
+
+ align:start position:0%
+everyone should and if they don't I feel
+ 
+
+ align:start position:0%
+everyone should and if they don't I feel
+they're impoverished know how to read a
+
+ align:start position:0%
+they're impoverished know how to read a
+ 
+
+ align:start position:0%
+they're impoverished know how to read a
+good story
+
+ align:start position:0%
+good story
+ 
+
+ align:start position:0%
+good story
+enjoy plays know how to enjoy the movies
+
+ align:start position:0%
+enjoy plays know how to enjoy the movies
+ 
+
+ align:start position:0%
+enjoy plays know how to enjoy the movies
+so I feel that what I'm giving my
+
+ align:start position:0%
+so I feel that what I'm giving my
+ 
+
+ align:start position:0%
+so I feel that what I'm giving my
+students is in some sense something even
+
+ align:start position:0%
+students is in some sense something even
+ 
+
+ align:start position:0%
+students is in some sense something even
+more valuable to them because it will be
+
+ align:start position:0%
+more valuable to them because it will be
+ 
+
+ align:start position:0%
+more valuable to them because it will be
+something that they'll have with them
+
+ align:start position:0%
+something that they'll have with them
+ 
+
+ align:start position:0%
+something that they'll have with them
+for their whole lives their whole career
+
+ align:start position:0%
+for their whole lives their whole career
+ 
+
+ align:start position:0%
+for their whole lives their whole career
+one of the things MIT students sometimes
+
+ align:start position:0%
+one of the things MIT students sometimes
+ 
+
+ align:start position:0%
+one of the things MIT students sometimes
+often do not realize is that a very
+
+ align:start position:0%
+often do not realize is that a very
+ 
+
+ align:start position:0%
+often do not realize is that a very
+large number of them do not end up
+
+ align:start position:0%
+large number of them do not end up
+ 
+
+ align:start position:0%
+large number of them do not end up
+making their living in the areas in
+
+ align:start position:0%
+making their living in the areas in
+ 
+
+ align:start position:0%
+making their living in the areas in
+which they majored but all of them end
+
+ align:start position:0%
+which they majored but all of them end
+ 
+
+ align:start position:0%
+which they majored but all of them end
+up wanting to go to the movies all of
+
+ align:start position:0%
+up wanting to go to the movies all of
+ 
+
+ align:start position:0%
+up wanting to go to the movies all of
+them end up with a capacity to read and
+
+ align:start position:0%
+them end up with a capacity to read and
+ 
+
+ align:start position:0%
+them end up with a capacity to read and
+enjoy literature and I hope that coming
+
+ align:start position:0%
+enjoy literature and I hope that coming
+ 
+
+ align:start position:0%
+enjoy literature and I hope that coming
+out of my classes they'll do those
+
+ align:start position:0%
+out of my classes they'll do those
+ 
+
+ align:start position:0%
+out of my classes they'll do those
+things with greater joy and with greater
+
+ align:start position:0%
+things with greater joy and with greater
+ 
+
+ align:start position:0%
+things with greater joy and with greater
+intelligence but one thing I've thought
+
+ align:start position:0%
+intelligence but one thing I've thought
+ 
+
+ align:start position:0%
+intelligence but one thing I've thought
+about that you know I don't know I I
+
+ align:start position:0%
+about that you know I don't know I I
+ 
+
+ align:start position:0%
+about that you know I don't know I I
+don't I haven't actually said this in in
+
+ align:start position:0%
+don't I haven't actually said this in in
+ 
+
+ align:start position:0%
+don't I haven't actually said this in in
+in my courses yet but I I think implicit
+
+ align:start position:0%
+in my courses yet but I I think implicit
+ 
+
+ align:start position:0%
+in my courses yet but I I think implicit
+in my film course is an admiration for a
+
+ align:start position:0%
+in my film course is an admiration for a
+ 
+
+ align:start position:0%
+in my film course is an admiration for a
+certain kind of achievement an
+
+ align:start position:0%
+certain kind of achievement an
+ 
+
+ align:start position:0%
+certain kind of achievement an
+admiration for a certain kind of artist
+
+ align:start position:0%
+admiration for a certain kind of artist
+ 
+
+ align:start position:0%
+admiration for a certain kind of artist
+an artist like Jean Renoir the great
+
+ align:start position:0%
+an artist like Jean Renoir the great
+ 
+
+ align:start position:0%
+an artist like Jean Renoir the great
+filmmaker or Monet the great painter
+
+ align:start position:0%
+filmmaker or Monet the great painter
+ 
+
+ align:start position:0%
+filmmaker or Monet the great painter
+whose Cathedral series I often talk
+
+ align:start position:0%
+whose Cathedral series I often talk
+ 
+
+ align:start position:0%
+whose Cathedral series I often talk
+about in my teaching and I realized that
+
+ align:start position:0%
+about in my teaching and I realized that
+ 
+
+ align:start position:0%
+about in my teaching and I realized that
+I shouldn't leave it implicit because I
+
+ align:start position:0%
+I shouldn't leave it implicit because I
+ 
+
+ align:start position:0%
+I shouldn't leave it implicit because I
+want to set up as a candidate for their
+
+ align:start position:0%
+want to set up as a candidate for their
+ 
+
+ align:start position:0%
+want to set up as a candidate for their
+admiration an alternative
+
+ align:start position:0%
+admiration an alternative
+ 
+
+ align:start position:0%
+admiration an alternative
+to Wall Street an alternative to
+
+ align:start position:0%
+to Wall Street an alternative to
+ 
+
+ align:start position:0%
+to Wall Street an alternative to
+entrepreneurial genius
+
+ align:start position:0%
+entrepreneurial genius
+ 
+
+ align:start position:0%
+entrepreneurial genius
+I admire John Renoir is genius or Orson
+
+ align:start position:0%
+I admire John Renoir is genius or Orson
+ 
+
+ align:start position:0%
+I admire John Renoir is genius or Orson
+Welles is genius or James Joyce's genius
+
+ align:start position:0%
+Welles is genius or James Joyce's genius
+ 
+
+ align:start position:0%
+Welles is genius or James Joyce's genius
+universe is more than I admire what
+
+ align:start position:0%
+universe is more than I admire what
+ 
+
+ align:start position:0%
+universe is more than I admire what
+entrepreneurs do I respect what
+
+ align:start position:0%
+entrepreneurs do I respect what
+ 
+
+ align:start position:0%
+entrepreneurs do I respect what
+entrepreneurs do but I am in awe of what
+
+ align:start position:0%
+entrepreneurs do but I am in awe of what
+ 
+
+ align:start position:0%
+entrepreneurs do but I am in awe of what
+great artists do and of what great
+
+ align:start position:0%
+great artists do and of what great
+ 
+
+ align:start position:0%
+great artists do and of what great
+doctors do what while we're on the
+
+ align:start position:0%
+doctors do what while we're on the
+ 
+
+ align:start position:0%
+doctors do what while we're on the
+subject we become so preoccupied by what
+
+ align:start position:0%
+subject we become so preoccupied by what
+ 
+
+ align:start position:0%
+subject we become so preoccupied by what
+we might call commercial or financial
+
+ align:start position:0%
+we might call commercial or financial
+ 
+
+ align:start position:0%
+we might call commercial or financial
+success instead of the kind of lasting
+
+ align:start position:0%
+success instead of the kind of lasting
+ 
+
+ align:start position:0%
+success instead of the kind of lasting
+success that great art or the practice
+
+ align:start position:0%
+success that great art or the practice
+ 
+
+ align:start position:0%
+success that great art or the practice
+of medicine or the practice of Nursing
+
+ align:start position:0%
+of medicine or the practice of Nursing
+ 
+
+ align:start position:0%
+of medicine or the practice of Nursing
+or dare I say it the practice of
+
+ align:start position:0%
+or dare I say it the practice of
+ 
+
+ align:start position:0%
+or dare I say it the practice of
+teaching might also embody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+professor Thorburn shares additional
+
+ align:start position:0%
+professor Thorburn shares additional
+ 
+
+ align:start position:0%
+professor Thorburn shares additional
+thoughts on teaching the film experience
+
+ align:start position:0%
+thoughts on teaching the film experience
+ 
+
+ align:start position:0%
+thoughts on teaching the film experience
+in a series of videos within the
+
+ align:start position:0%
+in a series of videos within the
+ 
+
+ align:start position:0%
+in a series of videos within the
+instructor insight section of is OCW
+
+ align:start position:0%
+instructor insight section of is OCW
+ 
+
+ align:start position:0%
+instructor insight section of is OCW
+course you can find them at ocw.mit.edu
+
+ align:start position:0%
+course you can find them at ocw.mit.edu
+ 
+
+ align:start position:0%
+course you can find them at ocw.mit.edu
+and while you're there
+
+ align:start position:0%
+and while you're there
+ 
+
+ align:start position:0%
+and while you're there
+download the teaching resources from his
+
+ align:start position:0%
+download the teaching resources from his
+ 
+
+ align:start position:0%
+download the teaching resources from his
+course and find so many other materials
+
+ align:start position:0%
+course and find so many other materials
+ 
+
+ align:start position:0%
+course and find so many other materials
+shared by faculty across all of the
+
+ align:start position:0%
+shared by faculty across all of the
+ 
+
+ align:start position:0%
+shared by faculty across all of the
+schools at MIT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you for listening we're so glad
+
+ align:start position:0%
+thank you for listening we're so glad
+ 
+
+ align:start position:0%
+thank you for listening we're so glad
+that you're tuning into what makes MIT
+
+ align:start position:0%
+that you're tuning into what makes MIT
+ 
+
+ align:start position:0%
+that you're tuning into what makes MIT
+is such an exciting place to learn
+
+ align:start position:0%
+is such an exciting place to learn
+ 
+
+ align:start position:0%
+is such an exciting place to learn
+conversations with people passionate
+
+ align:start position:0%
+conversations with people passionate
+ 
+
+ align:start position:0%
+conversations with people passionate
+about impacting the world in positive
+
+ align:start position:0%
+about impacting the world in positive
+ 
+
+ align:start position:0%
+about impacting the world in positive
+ways we hope you'll open MIT to more
+
+ align:start position:0%
+ways we hope you'll open MIT to more
+ 
+
+ align:start position:0%
+ways we hope you'll open MIT to more
+people by sharing this podcast and OCW
+
+ align:start position:0%
+people by sharing this podcast and OCW
+ 
+
+ align:start position:0%
+people by sharing this podcast and OCW
+with your own colleagues and friends
+
+ align:start position:0%
+with your own colleagues and friends
+ 
+
+ align:start position:0%
+with your own colleagues and friends
+until next time I'm Sarah Hansen from
+
+ align:start position:0%
+until next time I'm Sarah Hansen from
+ 
+
+ align:start position:0%
+until next time I'm Sarah Hansen from
+MIT OpenCourseWare
+
+ align:start position:0%
+MIT OpenCourseWare
+ 
+
+ align:start position:0%
+MIT OpenCourseWare
+[Music]
\ No newline at end of file
diff --git a/hqiH39PShmA.txt b/hqiH39PShmA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b99fa0e8bfe9632c22625633b2682d1509327c1a
--- /dev/null
+++ b/hqiH39PShmA.txt
@@ -0,0 +1,643 @@
+align:start position:0%
+ 
+in this recitation we're going to talk
+
+ align:start position:0%
+in this recitation we're going to talk
+ 
+
+ align:start position:0%
+in this recitation we're going to talk
+about predictive coding an emerging use
+
+ align:start position:0%
+about predictive coding an emerging use
+ 
+
+ align:start position:0%
+about predictive coding an emerging use
+of text analytics in the area of
+
+ align:start position:0%
+of text analytics in the area of
+ 
+
+ align:start position:0%
+of text analytics in the area of
+criminal justice we'll start with the
+
+ align:start position:0%
+criminal justice we'll start with the
+ 
+
+ align:start position:0%
+criminal justice we'll start with the
+story of Enron a United States energy
+
+ align:start position:0%
+story of Enron a United States energy
+ 
+
+ align:start position:0%
+story of Enron a United States energy
+company based out of Houston Texas that
+
+ align:start position:0%
+company based out of Houston Texas that
+ 
+
+ align:start position:0%
+company based out of Houston Texas that
+was involved in a number of electricity
+
+ align:start position:0%
+was involved in a number of electricity
+ 
+
+ align:start position:0%
+was involved in a number of electricity
+production and distribution markets in
+
+ align:start position:0%
+production and distribution markets in
+ 
+
+ align:start position:0%
+production and distribution markets in
+the early 2000s and Ron was a hot
+
+ align:start position:0%
+the early 2000s and Ron was a hot
+ 
+
+ align:start position:0%
+the early 2000s and Ron was a hot
+company with a market capitalization
+
+ align:start position:0%
+company with a market capitalization
+ 
+
+ align:start position:0%
+company with a market capitalization
+exceeding 60 billion dollars and Forbes
+
+ align:start position:0%
+exceeding 60 billion dollars and Forbes
+ 
+
+ align:start position:0%
+exceeding 60 billion dollars and Forbes
+magazine ranked it as the most
+
+ align:start position:0%
+magazine ranked it as the most
+ 
+
+ align:start position:0%
+magazine ranked it as the most
+innovative US company six years in a row
+
+ align:start position:0%
+innovative US company six years in a row
+ 
+
+ align:start position:0%
+innovative US company six years in a row
+now all that changed in 2001 with the
+
+ align:start position:0%
+now all that changed in 2001 with the
+ 
+
+ align:start position:0%
+now all that changed in 2001 with the
+news of widespread accounting fraud at
+
+ align:start position:0%
+news of widespread accounting fraud at
+ 
+
+ align:start position:0%
+news of widespread accounting fraud at
+the firm this massive fraud led to
+
+ align:start position:0%
+the firm this massive fraud led to
+ 
+
+ align:start position:0%
+the firm this massive fraud led to
+Enron's bankruptcy the largest ever at
+
+ align:start position:0%
+Enron's bankruptcy the largest ever at
+ 
+
+ align:start position:0%
+Enron's bankruptcy the largest ever at
+the time and led to Enron's accounting
+
+ align:start position:0%
+the time and led to Enron's accounting
+ 
+
+ align:start position:0%
+the time and led to Enron's accounting
+firm Arthur Andersen dissolving to this
+
+ align:start position:0%
+firm Arthur Andersen dissolving to this
+ 
+
+ align:start position:0%
+firm Arthur Andersen dissolving to this
+day and Ron remains a symbol of
+
+ align:start position:0%
+day and Ron remains a symbol of
+ 
+
+ align:start position:0%
+day and Ron remains a symbol of
+corporate greed and corruption
+
+ align:start position:0%
+corporate greed and corruption
+ 
+
+ align:start position:0%
+corporate greed and corruption
+now while Enron's collapse stemmed
+
+ align:start position:0%
+now while Enron's collapse stemmed
+ 
+
+ align:start position:0%
+now while Enron's collapse stemmed
+largely from accounting fraud the firm
+
+ align:start position:0%
+largely from accounting fraud the firm
+ 
+
+ align:start position:0%
+largely from accounting fraud the firm
+also faced sanctions for its involvement
+
+ align:start position:0%
+also faced sanctions for its involvement
+ 
+
+ align:start position:0%
+also faced sanctions for its involvement
+in the California electricity crisis
+
+ align:start position:0%
+in the California electricity crisis
+ 
+
+ align:start position:0%
+in the California electricity crisis
+California is the most populous state in
+
+ align:start position:0%
+California is the most populous state in
+ 
+
+ align:start position:0%
+California is the most populous state in
+the United States and in 2000 to 2001 it
+
+ align:start position:0%
+the United States and in 2000 to 2001 it
+ 
+
+ align:start position:0%
+the United States and in 2000 to 2001 it
+had a number of power blackouts despite
+
+ align:start position:0%
+had a number of power blackouts despite
+ 
+
+ align:start position:0%
+had a number of power blackouts despite
+having sufficient generating capacity it
+
+ align:start position:0%
+having sufficient generating capacity it
+ 
+
+ align:start position:0%
+having sufficient generating capacity it
+later surfaced that Enron played a key
+
+ align:start position:0%
+later surfaced that Enron played a key
+ 
+
+ align:start position:0%
+later surfaced that Enron played a key
+role in this energy crisis by
+
+ align:start position:0%
+role in this energy crisis by
+ 
+
+ align:start position:0%
+role in this energy crisis by
+artificially reducing power supply to
+
+ align:start position:0%
+artificially reducing power supply to
+ 
+
+ align:start position:0%
+artificially reducing power supply to
+spiked prices and then make me a profit
+
+ align:start position:0%
+spiked prices and then make me a profit
+ 
+
+ align:start position:0%
+spiked prices and then make me a profit
+from this market instability the Federal
+
+ align:start position:0%
+from this market instability the Federal
+ 
+
+ align:start position:0%
+from this market instability the Federal
+Energy Regulatory Commission or FERC
+
+ align:start position:0%
+Energy Regulatory Commission or FERC
+ 
+
+ align:start position:0%
+Energy Regulatory Commission or FERC
+investigated and Ron's involvement in
+
+ align:start position:0%
+investigated and Ron's involvement in
+ 
+
+ align:start position:0%
+investigated and Ron's involvement in
+the crisis and this investigation
+
+ align:start position:0%
+the crisis and this investigation
+ 
+
+ align:start position:0%
+the crisis and this investigation
+eventually led to a one point five two
+
+ align:start position:0%
+eventually led to a one point five two
+ 
+
+ align:start position:0%
+eventually led to a one point five two
+billion dollar sentiment settlement
+
+ align:start position:0%
+billion dollar sentiment settlement
+ 
+
+ align:start position:0%
+billion dollar sentiment settlement
+Burks investigation into Enron will be
+
+ align:start position:0%
+Burks investigation into Enron will be
+ 
+
+ align:start position:0%
+Burks investigation into Enron will be
+the topic of today's recitation now
+
+ align:start position:0%
+the topic of today's recitation now
+ 
+
+ align:start position:0%
+the topic of today's recitation now
+Enron was a huge company and its
+
+ align:start position:0%
+Enron was a huge company and its
+ 
+
+ align:start position:0%
+Enron was a huge company and its
+corporate servers contain millions of
+
+ align:start position:0%
+corporate servers contain millions of
+ 
+
+ align:start position:0%
+corporate servers contain millions of
+emails and other electronic files
+
+ align:start position:0%
+emails and other electronic files
+ 
+
+ align:start position:0%
+emails and other electronic files
+sifting through these documents to find
+
+ align:start position:0%
+sifting through these documents to find
+ 
+
+ align:start position:0%
+sifting through these documents to find
+the ones relevant to an investigation is
+
+ align:start position:0%
+the ones relevant to an investigation is
+ 
+
+ align:start position:0%
+the ones relevant to an investigation is
+no simple task in law this electronic
+
+ align:start position:0%
+no simple task in law this electronic
+ 
+
+ align:start position:0%
+no simple task in law this electronic
+document retrieval process is called the
+
+ align:start position:0%
+document retrieval process is called the
+ 
+
+ align:start position:0%
+document retrieval process is called the
+e-discovery problem and relevant files
+
+ align:start position:0%
+e-discovery problem and relevant files
+ 
+
+ align:start position:0%
+e-discovery problem and relevant files
+are called
+
+ align:start position:0%
+are called
+ 
+
+ align:start position:0%
+are called
+responsive documents traditionally the
+
+ align:start position:0%
+responsive documents traditionally the
+ 
+
+ align:start position:0%
+responsive documents traditionally the
+e-discovery problem has been solved by
+
+ align:start position:0%
+e-discovery problem has been solved by
+ 
+
+ align:start position:0%
+e-discovery problem has been solved by
+using a keyword search in our case
+
+ align:start position:0%
+using a keyword search in our case
+ 
+
+ align:start position:0%
+using a keyword search in our case
+perhaps searching for phrases like
+
+ align:start position:0%
+perhaps searching for phrases like
+ 
+
+ align:start position:0%
+perhaps searching for phrases like
+electricity bid or energy schedule file
+
+ align:start position:0%
+electricity bid or energy schedule file
+ 
+
+ align:start position:0%
+electricity bid or energy schedule file
+by an expensive and time-consuming
+
+ align:start position:0%
+by an expensive and time-consuming
+ 
+
+ align:start position:0%
+by an expensive and time-consuming
+manual review process in which attorneys
+
+ align:start position:0%
+manual review process in which attorneys
+ 
+
+ align:start position:0%
+manual review process in which attorneys
+read through thousands of documents to
+
+ align:start position:0%
+read through thousands of documents to
+ 
+
+ align:start position:0%
+read through thousands of documents to
+determine which ones are responsive
+
+ align:start position:0%
+determine which ones are responsive
+ 
+
+ align:start position:0%
+determine which ones are responsive
+however predictive coding is a new
+
+ align:start position:0%
+however predictive coding is a new
+ 
+
+ align:start position:0%
+however predictive coding is a new
+technique in which attorneys manually
+
+ align:start position:0%
+technique in which attorneys manually
+ 
+
+ align:start position:0%
+technique in which attorneys manually
+label some documents and then use text
+
+ align:start position:0%
+label some documents and then use text
+ 
+
+ align:start position:0%
+label some documents and then use text
+analytics models trained on the manually
+
+ align:start position:0%
+analytics models trained on the manually
+ 
+
+ align:start position:0%
+analytics models trained on the manually
+labeled documents to predict which of
+
+ align:start position:0%
+labeled documents to predict which of
+ 
+
+ align:start position:0%
+labeled documents to predict which of
+the remaining documents are responsive
+
+ align:start position:0%
+the remaining documents are responsive
+ 
+
+ align:start position:0%
+the remaining documents are responsive
+now as part of its investigation the
+
+ align:start position:0%
+now as part of its investigation the
+ 
+
+ align:start position:0%
+now as part of its investigation the
+FERC released hundreds of thousands of
+
+ align:start position:0%
+FERC released hundreds of thousands of
+ 
+
+ align:start position:0%
+FERC released hundreds of thousands of
+emails from top executives at Enron
+
+ align:start position:0%
+emails from top executives at Enron
+ 
+
+ align:start position:0%
+emails from top executives at Enron
+creating the largest publicly available
+
+ align:start position:0%
+creating the largest publicly available
+ 
+
+ align:start position:0%
+creating the largest publicly available
+set of emails today we will use this
+
+ align:start position:0%
+set of emails today we will use this
+ 
+
+ align:start position:0%
+set of emails today we will use this
+data set called the Enron corpus to
+
+ align:start position:0%
+data set called the Enron corpus to
+ 
+
+ align:start position:0%
+data set called the Enron corpus to
+perform predictive coding in this
+
+ align:start position:0%
+perform predictive coding in this
+ 
+
+ align:start position:0%
+perform predictive coding in this
+recitation our data set contains just
+
+ align:start position:0%
+recitation our data set contains just
+ 
+
+ align:start position:0%
+recitation our data set contains just
+two fields email which is the text of
+
+ align:start position:0%
+two fields email which is the text of
+ 
+
+ align:start position:0%
+two fields email which is the text of
+the email in question and responsive
+
+ align:start position:0%
+the email in question and responsive
+ 
+
+ align:start position:0%
+the email in question and responsive
+which is whether the email relates to
+
+ align:start position:0%
+which is whether the email relates to
+ 
+
+ align:start position:0%
+which is whether the email relates to
+energy schedules or bids the labels for
+
+ align:start position:0%
+energy schedules or bids the labels for
+ 
+
+ align:start position:0%
+energy schedules or bids the labels for
+these emails were made by attorneys as
+
+ align:start position:0%
+these emails were made by attorneys as
+ 
+
+ align:start position:0%
+these emails were made by attorneys as
+part of the 2010 text retrieval
+
+ align:start position:0%
+part of the 2010 text retrieval
+ 
+
+ align:start position:0%
+part of the 2010 text retrieval
+conference legal track a predictive
+
+ align:start position:0%
+conference legal track a predictive
+ 
+
+ align:start position:0%
+conference legal track a predictive
+coding competition
\ No newline at end of file
diff --git a/iB6SuG7wh5U.txt b/iB6SuG7wh5U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..df8c390875df9c9fc2a4c678a080ba64ce6f60a6
--- /dev/null
+++ b/iB6SuG7wh5U.txt
@@ -0,0 +1,15979 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see what i have in mind today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+is to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make a an assignment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that will be due
+
+ align:start position:0%
+that will be due
+ 
+
+ align:start position:0%
+that will be due
+tuesday
+
+ align:start position:0%
+tuesday
+ 
+
+ align:start position:0%
+tuesday
+now here's what i want to do with that
+
+ align:start position:0%
+now here's what i want to do with that
+ 
+
+ align:start position:0%
+now here's what i want to do with that
+assignment
+
+ align:start position:0%
+assignment
+ 
+
+ align:start position:0%
+assignment
+i want you to write up an analysis of
+
+ align:start position:0%
+i want you to write up an analysis of
+ 
+
+ align:start position:0%
+i want you to write up an analysis of
+the a7d case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i want you to allow something um
+
+ align:start position:0%
+i want you to allow something um
+ 
+
+ align:start position:0%
+i want you to allow something um
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh isn't entirely scholarly it won't
+
+ align:start position:0%
+uh isn't entirely scholarly it won't
+ 
+
+ align:start position:0%
+uh isn't entirely scholarly it won't
+sound entirely scholarly to you at first
+
+ align:start position:0%
+sound entirely scholarly to you at first
+ 
+
+ align:start position:0%
+sound entirely scholarly to you at first
+i want to micromanage
+
+ align:start position:0%
+i want to micromanage
+ 
+
+ align:start position:0%
+i want to micromanage
+this homework assignment i want to tell
+
+ align:start position:0%
+this homework assignment i want to tell
+ 
+
+ align:start position:0%
+this homework assignment i want to tell
+you exactly what i want done all right
+
+ align:start position:0%
+you exactly what i want done all right
+ 
+
+ align:start position:0%
+you exactly what i want done all right
+now the reason for that is
+
+ align:start position:0%
+now the reason for that is
+ 
+
+ align:start position:0%
+now the reason for that is
+that once you see what i think is a good
+
+ align:start position:0%
+that once you see what i think is a good
+ 
+
+ align:start position:0%
+that once you see what i think is a good
+way to lay out something
+
+ align:start position:0%
+way to lay out something
+ 
+
+ align:start position:0%
+way to lay out something
+now you can start talking about how you
+
+ align:start position:0%
+now you can start talking about how you
+ 
+
+ align:start position:0%
+now you can start talking about how you
+want to lay it out
+
+ align:start position:0%
+want to lay it out
+ 
+
+ align:start position:0%
+want to lay it out
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh then you can start talking to me
+
+ align:start position:0%
+and uh then you can start talking to me
+ 
+
+ align:start position:0%
+and uh then you can start talking to me
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um that you want to lay it out a
+
+ align:start position:0%
+um that you want to lay it out a
+ 
+
+ align:start position:0%
+um that you want to lay it out a
+different way how can i respond to that
+
+ align:start position:0%
+different way how can i respond to that
+ 
+
+ align:start position:0%
+different way how can i respond to that
+and that kind of thing but let's see it
+
+ align:start position:0%
+and that kind of thing but let's see it
+ 
+
+ align:start position:0%
+and that kind of thing but let's see it
+one way first
+
+ align:start position:0%
+one way first
+ 
+
+ align:start position:0%
+one way first
+for and tear it up
+
+ align:start position:0%
+for and tear it up
+ 
+
+ align:start position:0%
+for and tear it up
+okay and when you turn that thing in
+
+ align:start position:0%
+okay and when you turn that thing in
+ 
+
+ align:start position:0%
+okay and when you turn that thing in
+tuesday
+
+ align:start position:0%
+tuesday
+ 
+
+ align:start position:0%
+tuesday
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll have a format and some ideas that
+
+ align:start position:0%
+you'll have a format and some ideas that
+ 
+
+ align:start position:0%
+you'll have a format and some ideas that
+just laid out
+
+ align:start position:0%
+just laid out
+ 
+
+ align:start position:0%
+just laid out
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so my philosophy is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a classroom
+
+ align:start position:0%
+in a classroom
+ 
+
+ align:start position:0%
+in a classroom
+imitate
+
+ align:start position:0%
+imitate
+ 
+
+ align:start position:0%
+imitate
+then liberate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now what i want to do today is to is
+
+ align:start position:0%
+now what i want to do today is to is
+ 
+
+ align:start position:0%
+now what i want to do today is to is
+actually just to lay out this
+
+ align:start position:0%
+actually just to lay out this
+ 
+
+ align:start position:0%
+actually just to lay out this
+this um
+
+ align:start position:0%
+this um
+ 
+
+ align:start position:0%
+this um
+this analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then at the end then i want to discuss
+
+ align:start position:0%
+then at the end then i want to discuss
+ 
+
+ align:start position:0%
+then at the end then i want to discuss
+to some extent
+
+ align:start position:0%
+to some extent
+ 
+
+ align:start position:0%
+to some extent
+this movie
+
+ align:start position:0%
+this movie
+ 
+
+ align:start position:0%
+this movie
+and then i want to deal with some um
+
+ align:start position:0%
+and then i want to deal with some um
+ 
+
+ align:start position:0%
+and then i want to deal with some um
+pedagogic issues i've got the
+
+ align:start position:0%
+pedagogic issues i've got the
+ 
+
+ align:start position:0%
+pedagogic issues i've got the
+percentages for the grades laid out all
+
+ align:start position:0%
+percentages for the grades laid out all
+ 
+
+ align:start position:0%
+percentages for the grades laid out all
+of that okay so give me a uh
+
+ align:start position:0%
+of that okay so give me a uh
+ 
+
+ align:start position:0%
+of that okay so give me a uh
+15 minute high sign before the class is
+
+ align:start position:0%
+15 minute high sign before the class is
+ 
+
+ align:start position:0%
+15 minute high sign before the class is
+over that'll give me five minutes to
+
+ align:start position:0%
+over that'll give me five minutes to
+ 
+
+ align:start position:0%
+over that'll give me five minutes to
+stop and 10 minutes to do
+
+ align:start position:0%
+stop and 10 minutes to do
+ 
+
+ align:start position:0%
+stop and 10 minutes to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see this all right
+
+ align:start position:0%
+you see this all right
+ 
+
+ align:start position:0%
+you see this all right
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first thing i'd like you to do in this
+
+ align:start position:0%
+first thing i'd like you to do in this
+ 
+
+ align:start position:0%
+first thing i'd like you to do in this
+homework assignment is to state your
+
+ align:start position:0%
+homework assignment is to state your
+ 
+
+ align:start position:0%
+homework assignment is to state your
+purpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then state your objectives those are the
+
+ align:start position:0%
+then state your objectives those are the
+ 
+
+ align:start position:0%
+then state your objectives those are the
+main parts
+
+ align:start position:0%
+main parts
+ 
+
+ align:start position:0%
+main parts
+of the paper
+
+ align:start position:0%
+of the paper
+ 
+
+ align:start position:0%
+of the paper
+that will develop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+purpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+i want you to give me a rationale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is why you're doing it why you're
+
+ align:start position:0%
+that is why you're doing it why you're
+ 
+
+ align:start position:0%
+that is why you're doing it why you're
+setting it up the way you're doing it
+
+ align:start position:0%
+setting it up the way you're doing it
+ 
+
+ align:start position:0%
+setting it up the way you're doing it
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then lastly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want you to tell me
+
+ align:start position:0%
+i want you to tell me
+ 
+
+ align:start position:0%
+i want you to tell me
+write down tell me something about the
+
+ align:start position:0%
+write down tell me something about the
+ 
+
+ align:start position:0%
+write down tell me something about the
+scope of your
+
+ align:start position:0%
+scope of your
+ 
+
+ align:start position:0%
+scope of your
+of your uh analysis now here's the
+
+ align:start position:0%
+of your uh analysis now here's the
+ 
+
+ align:start position:0%
+of your uh analysis now here's the
+beauty of this
+
+ align:start position:0%
+beauty of this
+ 
+
+ align:start position:0%
+beauty of this
+this tells you what we're going to do
+
+ align:start position:0%
+this tells you what we're going to do
+ 
+
+ align:start position:0%
+this tells you what we're going to do
+what you're going to do this tells me
+
+ align:start position:0%
+what you're going to do this tells me
+ 
+
+ align:start position:0%
+what you're going to do this tells me
+what you are going to do
+
+ align:start position:0%
+what you are going to do
+ 
+
+ align:start position:0%
+what you are going to do
+and of all the things that come to my
+
+ align:start position:0%
+and of all the things that come to my
+ 
+
+ align:start position:0%
+and of all the things that come to my
+mind when you've told me what you're
+
+ align:start position:0%
+mind when you've told me what you're
+ 
+
+ align:start position:0%
+mind when you've told me what you're
+going to do you've got to tell me what
+
+ align:start position:0%
+going to do you've got to tell me what
+ 
+
+ align:start position:0%
+going to do you've got to tell me what
+it is that you're not that not going to
+
+ align:start position:0%
+it is that you're not that not going to
+ 
+
+ align:start position:0%
+it is that you're not that not going to
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you see the metaphysics in that
+
+ align:start position:0%
+okay you see the metaphysics in that
+ 
+
+ align:start position:0%
+okay you see the metaphysics in that
+you say what a thing is and then to
+
+ align:start position:0%
+you say what a thing is and then to
+ 
+
+ align:start position:0%
+you say what a thing is and then to
+sharpen your meaning you say what it
+
+ align:start position:0%
+sharpen your meaning you say what it
+ 
+
+ align:start position:0%
+sharpen your meaning you say what it
+isn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the second thing is
+
+ align:start position:0%
+the second thing is
+ 
+
+ align:start position:0%
+the second thing is
+to lay out your argument
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+categories of objectives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then at the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+give me a summary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and conclusions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically what you want to do is to tell
+
+ align:start position:0%
+basically what you want to do is to tell
+ 
+
+ align:start position:0%
+basically what you want to do is to tell
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+uh did you fulfill your purpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+what i want you to do in this purpose
+
+ align:start position:0%
+what i want you to do in this purpose
+ 
+
+ align:start position:0%
+what i want you to do in this purpose
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is to say that you want to
+
+ align:start position:0%
+is to say that you want to
+ 
+
+ align:start position:0%
+is to say that you want to
+do a moral analysis
+
+ align:start position:0%
+do a moral analysis
+ 
+
+ align:start position:0%
+do a moral analysis
+of the a7d case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the scope is
+
+ align:start position:0%
+and the scope is
+ 
+
+ align:start position:0%
+and the scope is
+that you're going to do that analysis
+
+ align:start position:0%
+that you're going to do that analysis
+ 
+
+ align:start position:0%
+that you're going to do that analysis
+twice
+
+ align:start position:0%
+twice
+ 
+
+ align:start position:0%
+twice
+one using a utilitarian
+
+ align:start position:0%
+one using a utilitarian
+ 
+
+ align:start position:0%
+one using a utilitarian
+utilitarian
+
+ align:start position:0%
+utilitarian
+ 
+
+ align:start position:0%
+utilitarian
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+and the other one is to use what's
+
+ align:start position:0%
+and the other one is to use what's
+ 
+
+ align:start position:0%
+and the other one is to use what's
+called a deontological
+
+ align:start position:0%
+called a deontological
+ 
+
+ align:start position:0%
+called a deontological
+analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're going to use uh mil and
+
+ align:start position:0%
+okay so we're going to use uh mil and
+ 
+
+ align:start position:0%
+okay so we're going to use uh mil and
+kant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in your conclusions
+
+ align:start position:0%
+in your conclusions
+ 
+
+ align:start position:0%
+in your conclusions
+i want you to evaluate both methods
+
+ align:start position:0%
+i want you to evaluate both methods
+ 
+
+ align:start position:0%
+i want you to evaluate both methods
+relative to the a7d case
+
+ align:start position:0%
+relative to the a7d case
+ 
+
+ align:start position:0%
+relative to the a7d case
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now i can tell you what you might want
+
+ align:start position:0%
+now i can tell you what you might want
+ 
+
+ align:start position:0%
+now i can tell you what you might want
+to put in there
+
+ align:start position:0%
+to put in there
+ 
+
+ align:start position:0%
+to put in there
+that you can see already
+
+ align:start position:0%
+that you can see already
+ 
+
+ align:start position:0%
+that you can see already
+and that is
+
+ align:start position:0%
+and that is
+ 
+
+ align:start position:0%
+and that is
+that one of the problems you're going to
+
+ align:start position:0%
+that one of the problems you're going to
+ 
+
+ align:start position:0%
+that one of the problems you're going to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+with the utilitarian approach
+
+ align:start position:0%
+with the utilitarian approach
+ 
+
+ align:start position:0%
+with the utilitarian approach
+as applied to the a7d case is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that nobody got hurt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you're going to have to tell me
+
+ align:start position:0%
+okay so you're going to have to tell me
+ 
+
+ align:start position:0%
+okay so you're going to have to tell me
+is that a powerful method relative to
+
+ align:start position:0%
+is that a powerful method relative to
+ 
+
+ align:start position:0%
+is that a powerful method relative to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+case all right
+
+ align:start position:0%
+case all right
+ 
+
+ align:start position:0%
+case all right
+uh one of the problems you're going to
+
+ align:start position:0%
+uh one of the problems you're going to
+ 
+
+ align:start position:0%
+uh one of the problems you're going to
+find with the uh
+
+ align:start position:0%
+find with the uh
+ 
+
+ align:start position:0%
+find with the uh
+deontological approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i is that
+
+ align:start position:0%
+i is that
+ 
+
+ align:start position:0%
+i is that
+you're going to find it hard to say one
+
+ align:start position:0%
+you're going to find it hard to say one
+ 
+
+ align:start position:0%
+you're going to find it hard to say one
+should never lie about anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you're going to have conflicts
+
+ align:start position:0%
+because you're going to have conflicts
+ 
+
+ align:start position:0%
+because you're going to have conflicts
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+uh telling the truth all of the time
+
+ align:start position:0%
+uh telling the truth all of the time
+ 
+
+ align:start position:0%
+uh telling the truth all of the time
+we're going to have to ask ourselves is
+
+ align:start position:0%
+we're going to have to ask ourselves is
+ 
+
+ align:start position:0%
+we're going to have to ask ourselves is
+that possible in real life
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+in your
+
+ align:start position:0%
+in your
+ 
+
+ align:start position:0%
+in your
+back matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of course you're going to have what
+
+ align:start position:0%
+of course you're going to have what
+ 
+
+ align:start position:0%
+of course you're going to have what
+references
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+i would like to see at least one
+
+ align:start position:0%
+i would like to see at least one
+ 
+
+ align:start position:0%
+i would like to see at least one
+reference
+
+ align:start position:0%
+reference
+ 
+
+ align:start position:0%
+reference
+it's not this book
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+lastly this is a little uh something new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i haven't lectured on this but i this
+
+ align:start position:0%
+i haven't lectured on this but i this
+ 
+
+ align:start position:0%
+i haven't lectured on this but i this
+can be pedestrian
+
+ align:start position:0%
+can be pedestrian
+ 
+
+ align:start position:0%
+can be pedestrian
+uh and that is to take what you have
+
+ align:start position:0%
+uh and that is to take what you have
+ 
+
+ align:start position:0%
+uh and that is to take what you have
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+and see if you can analyze your paper
+
+ align:start position:0%
+and see if you can analyze your paper
+ 
+
+ align:start position:0%
+and see if you can analyze your paper
+in storied terms
+
+ align:start position:0%
+in storied terms
+ 
+
+ align:start position:0%
+in storied terms
+does it have a beginning does it have a
+
+ align:start position:0%
+does it have a beginning does it have a
+ 
+
+ align:start position:0%
+does it have a beginning does it have a
+middle does it have an end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does it make a point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh look where i'm pointing
+
+ align:start position:0%
+uh look where i'm pointing
+ 
+
+ align:start position:0%
+uh look where i'm pointing
+does it make a point
+
+ align:start position:0%
+does it make a point
+ 
+
+ align:start position:0%
+does it make a point
+is there a point of view
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay remember from um
+
+ align:start position:0%
+okay remember from um
+ 
+
+ align:start position:0%
+okay remember from um
+from uh moby dick
+
+ align:start position:0%
+from uh moby dick
+ 
+
+ align:start position:0%
+from uh moby dick
+does anybody remember the first sentence
+
+ align:start position:0%
+does anybody remember the first sentence
+ 
+
+ align:start position:0%
+does anybody remember the first sentence
+in moby dick
+
+ align:start position:0%
+in moby dick
+ 
+
+ align:start position:0%
+in moby dick
+call me ishmael
+
+ align:start position:0%
+call me ishmael
+ 
+
+ align:start position:0%
+call me ishmael
+tells you what point of view you're
+
+ align:start position:0%
+tells you what point of view you're
+ 
+
+ align:start position:0%
+tells you what point of view you're
+looking at the story from
+
+ align:start position:0%
+looking at the story from
+ 
+
+ align:start position:0%
+looking at the story from
+you can see that if it was somebody else
+
+ align:start position:0%
+you can see that if it was somebody else
+ 
+
+ align:start position:0%
+you can see that if it was somebody else
+the story would be played out a little
+
+ align:start position:0%
+the story would be played out a little
+ 
+
+ align:start position:0%
+the story would be played out a little
+bit differently ahab would tell a
+
+ align:start position:0%
+bit differently ahab would tell a
+ 
+
+ align:start position:0%
+bit differently ahab would tell a
+different story with me
+
+ align:start position:0%
+different story with me
+ 
+
+ align:start position:0%
+different story with me
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh give me your point of view
+
+ align:start position:0%
+so uh give me your point of view
+ 
+
+ align:start position:0%
+so uh give me your point of view
+and give me your voice is it first
+
+ align:start position:0%
+and give me your voice is it first
+ 
+
+ align:start position:0%
+and give me your voice is it first
+person second person third person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then put anything else in there that
+
+ align:start position:0%
+and then put anything else in there that
+ 
+
+ align:start position:0%
+and then put anything else in there that
+you can tell me
+
+ align:start position:0%
+you can tell me
+ 
+
+ align:start position:0%
+you can tell me
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+uh what you have just done
+
+ align:start position:0%
+uh what you have just done
+ 
+
+ align:start position:0%
+uh what you have just done
+can be looked at as a story
+
+ align:start position:0%
+can be looked at as a story
+ 
+
+ align:start position:0%
+can be looked at as a story
+now that gets you ready for something
+
+ align:start position:0%
+now that gets you ready for something
+ 
+
+ align:start position:0%
+now that gets you ready for something
+we're going to cover later
+
+ align:start position:0%
+we're going to cover later
+ 
+
+ align:start position:0%
+we're going to cover later
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+what i would like to do now unless you
+
+ align:start position:0%
+what i would like to do now unless you
+ 
+
+ align:start position:0%
+what i would like to do now unless you
+have any questions let me see if you got
+
+ align:start position:0%
+have any questions let me see if you got
+ 
+
+ align:start position:0%
+have any questions let me see if you got
+any questions that's what
+
+ align:start position:0%
+any questions that's what
+ 
+
+ align:start position:0%
+any questions that's what
+any questions yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two sequential sections one with the
+
+ align:start position:0%
+two sequential sections one with the
+ 
+
+ align:start position:0%
+two sequential sections one with the
+first analysis and one is the second
+
+ align:start position:0%
+first analysis and one is the second
+ 
+
+ align:start position:0%
+first analysis and one is the second
+analysis as opposed to
+
+ align:start position:0%
+analysis as opposed to
+ 
+
+ align:start position:0%
+analysis as opposed to
+as opposed to like
+
+ align:start position:0%
+as opposed to like
+ 
+
+ align:start position:0%
+as opposed to like
+parallel
+
+ align:start position:0%
+parallel
+ 
+
+ align:start position:0%
+parallel
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+oh you mean
+
+ align:start position:0%
+oh you mean
+ 
+
+ align:start position:0%
+oh you mean
+in one paragraph
+
+ align:start position:0%
+in one paragraph
+ 
+
+ align:start position:0%
+in one paragraph
+contrasting the methods that's your
+
+ align:start position:0%
+contrasting the methods that's your
+ 
+
+ align:start position:0%
+contrasting the methods that's your
+style
+
+ align:start position:0%
+style
+ 
+
+ align:start position:0%
+style
+no no it's not i mean i could do it
+
+ align:start position:0%
+no no it's not i mean i could do it
+ 
+
+ align:start position:0%
+no no it's not i mean i could do it
+either way i'm just trying to get a
+
+ align:start position:0%
+either way i'm just trying to get a
+ 
+
+ align:start position:0%
+either way i'm just trying to get a
+clearer picture you decide that okay you
+
+ align:start position:0%
+clearer picture you decide that okay you
+ 
+
+ align:start position:0%
+clearer picture you decide that okay you
+just said how you want to do it now i
+
+ align:start position:0%
+just said how you want to do it now i
+ 
+
+ align:start position:0%
+just said how you want to do it now i
+think that in these objectives one of
+
+ align:start position:0%
+think that in these objectives one of
+ 
+
+ align:start position:0%
+think that in these objectives one of
+the things you want to do is to state
+
+ align:start position:0%
+the things you want to do is to state
+ 
+
+ align:start position:0%
+the things you want to do is to state
+the case
+
+ align:start position:0%
+the case
+ 
+
+ align:start position:0%
+the case
+a summary of the a7b case
+
+ align:start position:0%
+a summary of the a7b case
+ 
+
+ align:start position:0%
+a summary of the a7b case
+okay so you want the facts
+
+ align:start position:0%
+okay so you want the facts
+ 
+
+ align:start position:0%
+okay so you want the facts
+then so that might be objective one
+
+ align:start position:0%
+then so that might be objective one
+ 
+
+ align:start position:0%
+then so that might be objective one
+objective two
+
+ align:start position:0%
+objective two
+ 
+
+ align:start position:0%
+objective two
+would be a utilitarian analysis
+
+ align:start position:0%
+would be a utilitarian analysis
+ 
+
+ align:start position:0%
+would be a utilitarian analysis
+i tell you what let's keep them separate
+
+ align:start position:0%
+i tell you what let's keep them separate
+ 
+
+ align:start position:0%
+i tell you what let's keep them separate
+i change that let's keep them separate
+
+ align:start position:0%
+i change that let's keep them separate
+ 
+
+ align:start position:0%
+i change that let's keep them separate
+objective two will be utilitarian
+
+ align:start position:0%
+objective two will be utilitarian
+ 
+
+ align:start position:0%
+objective two will be utilitarian
+objective three will be uh d'angelo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+you may feel compelled to put in another
+
+ align:start position:0%
+you may feel compelled to put in another
+ 
+
+ align:start position:0%
+you may feel compelled to put in another
+objective but i think the three will do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+summary of the case
+
+ align:start position:0%
+summary of the case
+ 
+
+ align:start position:0%
+summary of the case
+analysis one analysis two
+
+ align:start position:0%
+analysis one analysis two
+ 
+
+ align:start position:0%
+analysis one analysis two
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+uh i would expect something like this
+
+ align:start position:0%
+uh i would expect something like this
+ 
+
+ align:start position:0%
+uh i would expect something like this
+the whole thing
+
+ align:start position:0%
+the whole thing
+ 
+
+ align:start position:0%
+the whole thing
+to be about
+
+ align:start position:0%
+to be about
+ 
+
+ align:start position:0%
+to be about
+three pages
+
+ align:start position:0%
+three pages
+ 
+
+ align:start position:0%
+three pages
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now if you get two pages and can't think
+
+ align:start position:0%
+now if you get two pages and can't think
+ 
+
+ align:start position:0%
+now if you get two pages and can't think
+of anything else in put in there please
+
+ align:start position:0%
+of anything else in put in there please
+ 
+
+ align:start position:0%
+of anything else in put in there please
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+put any uh
+
+ align:start position:0%
+put any uh
+ 
+
+ align:start position:0%
+put any uh
+thing else in there
+
+ align:start position:0%
+thing else in there
+ 
+
+ align:start position:0%
+thing else in there
+if it goes over
+
+ align:start position:0%
+if it goes over
+ 
+
+ align:start position:0%
+if it goes over
+five pages submit it if it goes to ten
+
+ align:start position:0%
+five pages submit it if it goes to ten
+ 
+
+ align:start position:0%
+five pages submit it if it goes to ten
+pages
+
+ align:start position:0%
+pages
+ 
+
+ align:start position:0%
+pages
+we got a problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+talk to me about it
+
+ align:start position:0%
+talk to me about it
+ 
+
+ align:start position:0%
+talk to me about it
+uh it might be something that you didn't
+
+ align:start position:0%
+uh it might be something that you didn't
+ 
+
+ align:start position:0%
+uh it might be something that you didn't
+need to say but if you really feel
+
+ align:start position:0%
+need to say but if you really feel
+ 
+
+ align:start position:0%
+need to say but if you really feel
+compelled to say ten pages worth of
+
+ align:start position:0%
+compelled to say ten pages worth of
+ 
+
+ align:start position:0%
+compelled to say ten pages worth of
+stuff then fine the only thing that was
+
+ align:start position:0%
+stuff then fine the only thing that was
+ 
+
+ align:start position:0%
+stuff then fine the only thing that was
+really going to irritate me about 10
+
+ align:start position:0%
+really going to irritate me about 10
+ 
+
+ align:start position:0%
+really going to irritate me about 10
+pages is if you download nine pages of
+
+ align:start position:0%
+pages is if you download nine pages of
+ 
+
+ align:start position:0%
+pages is if you download nine pages of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+i mean if you're writing out of your
+
+ align:start position:0%
+i mean if you're writing out of your
+ 
+
+ align:start position:0%
+i mean if you're writing out of your
+heart
+
+ align:start position:0%
+heart
+ 
+
+ align:start position:0%
+heart
+and i'll know the difference
+
+ align:start position:0%
+and i'll know the difference
+ 
+
+ align:start position:0%
+and i'll know the difference
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+then we need to talk about it
+
+ align:start position:0%
+then we need to talk about it
+ 
+
+ align:start position:0%
+then we need to talk about it
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+and i'm going to grade this but i'm
+
+ align:start position:0%
+and i'm going to grade this but i'm
+ 
+
+ align:start position:0%
+and i'm going to grade this but i'm
+going to like i said i'm going to
+
+ align:start position:0%
+going to like i said i'm going to
+ 
+
+ align:start position:0%
+going to like i said i'm going to
+micromanage this
+
+ align:start position:0%
+micromanage this
+ 
+
+ align:start position:0%
+micromanage this
+this this first one there's only one
+
+ align:start position:0%
+this this first one there's only one
+ 
+
+ align:start position:0%
+this this first one there's only one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+after references
+
+ align:start position:0%
+after references
+ 
+
+ align:start position:0%
+after references
+are you hoping that we'll look more into
+
+ align:start position:0%
+are you hoping that we'll look more into
+ 
+
+ align:start position:0%
+are you hoping that we'll look more into
+the facts of the case or good question
+
+ align:start position:0%
+the facts of the case or good question
+ 
+
+ align:start position:0%
+the facts of the case or good question
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+deontological and
+
+ align:start position:0%
+deontological and
+ 
+
+ align:start position:0%
+deontological and
+i'm looking up
+
+ align:start position:0%
+i'm looking up
+ 
+
+ align:start position:0%
+i'm looking up
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+uh now what i'm getting ready to do now
+
+ align:start position:0%
+uh now what i'm getting ready to do now
+ 
+
+ align:start position:0%
+uh now what i'm getting ready to do now
+is to go more deeply into those methods
+
+ align:start position:0%
+is to go more deeply into those methods
+ 
+
+ align:start position:0%
+is to go more deeply into those methods
+now look at chapter six
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh actually when i say look at chapter
+
+ align:start position:0%
+uh actually when i say look at chapter
+ 
+
+ align:start position:0%
+uh actually when i say look at chapter
+six that's not what i mean
+
+ align:start position:0%
+six that's not what i mean
+ 
+
+ align:start position:0%
+six that's not what i mean
+look at the table of contents
+
+ align:start position:0%
+look at the table of contents
+ 
+
+ align:start position:0%
+look at the table of contents
+and look at the citations chapter six
+
+ align:start position:0%
+and look at the citations chapter six
+ 
+
+ align:start position:0%
+and look at the citations chapter six
+okay what's the title
+
+ align:start position:0%
+okay what's the title
+ 
+
+ align:start position:0%
+okay what's the title
+honestly integrity
+
+ align:start position:0%
+honestly integrity
+ 
+
+ align:start position:0%
+honestly integrity
+all right that's not what i want okay
+
+ align:start position:0%
+all right that's not what i want okay
+ 
+
+ align:start position:0%
+all right that's not what i want okay
+i've got uh
+
+ align:start position:0%
+i've got uh
+ 
+
+ align:start position:0%
+i've got uh
+i was looking at the old version
+
+ align:start position:0%
+i was looking at the old version
+ 
+
+ align:start position:0%
+i was looking at the old version
+of this book
+
+ align:start position:0%
+of this book
+ 
+
+ align:start position:0%
+of this book
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+there was a there's a section called um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh which is chapter six called tests in
+
+ align:start position:0%
+uh which is chapter six called tests in
+ 
+
+ align:start position:0%
+uh which is chapter six called tests in
+moral problem solving do you have a
+
+ align:start position:0%
+moral problem solving do you have a
+ 
+
+ align:start position:0%
+moral problem solving do you have a
+chapter like that
+
+ align:start position:0%
+chapter like that
+ 
+
+ align:start position:0%
+chapter like that
+we have methods for moral problem
+
+ align:start position:0%
+we have methods for moral problem
+ 
+
+ align:start position:0%
+we have methods for moral problem
+solving what's the one right after that
+
+ align:start position:0%
+solving what's the one right after that
+ 
+
+ align:start position:0%
+solving what's the one right after that
+organizing principles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the one so it's chapter four
+
+ align:start position:0%
+that's the one so it's chapter four
+ 
+
+ align:start position:0%
+that's the one so it's chapter four
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+uh and chapter four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what what they call respect for persons
+
+ align:start position:0%
+what what they call respect for persons
+ 
+
+ align:start position:0%
+what what they call respect for persons
+is kant's
+
+ align:start position:0%
+is kant's
+ 
+
+ align:start position:0%
+is kant's
+kind is one particular case
+
+ align:start position:0%
+kind is one particular case
+ 
+
+ align:start position:0%
+kind is one particular case
+but is the deontological approach
+
+ align:start position:0%
+but is the deontological approach
+ 
+
+ align:start position:0%
+but is the deontological approach
+and then utilitarianism i think they
+
+ align:start position:0%
+and then utilitarianism i think they
+ 
+
+ align:start position:0%
+and then utilitarianism i think they
+spell it out
+
+ align:start position:0%
+spell it out
+ 
+
+ align:start position:0%
+spell it out
+right there
+
+ align:start position:0%
+right there
+ 
+
+ align:start position:0%
+right there
+so but i'm going to cover i'm going to
+
+ align:start position:0%
+so but i'm going to cover i'm going to
+ 
+
+ align:start position:0%
+so but i'm going to cover i'm going to
+cover that material
+
+ align:start position:0%
+cover that material
+ 
+
+ align:start position:0%
+cover that material
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but i'm going to cover it in a way that
+
+ align:start position:0%
+but i'm going to cover it in a way that
+ 
+
+ align:start position:0%
+but i'm going to cover it in a way that
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+makes best sense for me as a teacher
+
+ align:start position:0%
+makes best sense for me as a teacher
+ 
+
+ align:start position:0%
+makes best sense for me as a teacher
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+particularly because there's some
+
+ align:start position:0%
+particularly because there's some
+ 
+
+ align:start position:0%
+particularly because there's some
+subtleties in this
+
+ align:start position:0%
+subtleties in this
+ 
+
+ align:start position:0%
+subtleties in this
+in uh this material that i think that uh
+
+ align:start position:0%
+in uh this material that i think that uh
+ 
+
+ align:start position:0%
+in uh this material that i think that uh
+you ought to pick up and secondly
+
+ align:start position:0%
+you ought to pick up and secondly
+ 
+
+ align:start position:0%
+you ought to pick up and secondly
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most most philosophers complain that
+
+ align:start position:0%
+most most philosophers complain that
+ 
+
+ align:start position:0%
+most most philosophers complain that
+kant is very hard to understand
+
+ align:start position:0%
+kant is very hard to understand
+ 
+
+ align:start position:0%
+kant is very hard to understand
+now not all philosophers believe he's
+
+ align:start position:0%
+now not all philosophers believe he's
+ 
+
+ align:start position:0%
+now not all philosophers believe he's
+hard to understand
+
+ align:start position:0%
+hard to understand
+ 
+
+ align:start position:0%
+hard to understand
+british philosophers believe he's hard
+
+ align:start position:0%
+british philosophers believe he's hard
+ 
+
+ align:start position:0%
+british philosophers believe he's hard
+to believe but they they they think he's
+
+ align:start position:0%
+to believe but they they they think he's
+ 
+
+ align:start position:0%
+to believe but they they they think he's
+impossible to understand because they
+
+ align:start position:0%
+impossible to understand because they
+ 
+
+ align:start position:0%
+impossible to understand because they
+don't they don't see it
+
+ align:start position:0%
+don't they don't see it
+ 
+
+ align:start position:0%
+don't they don't see it
+right so you've got to ask the germans
+
+ align:start position:0%
+right so you've got to ask the germans
+ 
+
+ align:start position:0%
+right so you've got to ask the germans
+do they have a hard time right they
+
+ align:start position:0%
+do they have a hard time right they
+ 
+
+ align:start position:0%
+do they have a hard time right they
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+all right so what some of them some of
+
+ align:start position:0%
+all right so what some of them some of
+ 
+
+ align:start position:0%
+all right so what some of them some of
+them blame it on the translations no
+
+ align:start position:0%
+them blame it on the translations no
+ 
+
+ align:start position:0%
+them blame it on the translations no
+it's not got it so what i'm going to try
+
+ align:start position:0%
+it's not got it so what i'm going to try
+ 
+
+ align:start position:0%
+it's not got it so what i'm going to try
+to do is to lay out
+
+ align:start position:0%
+to do is to lay out
+ 
+
+ align:start position:0%
+to do is to lay out
+these two
+
+ align:start position:0%
+these two
+ 
+
+ align:start position:0%
+these two
+approaches
+
+ align:start position:0%
+approaches
+ 
+
+ align:start position:0%
+approaches
+in a context
+
+ align:start position:0%
+in a context
+ 
+
+ align:start position:0%
+in a context
+so that you can see the meaning of it
+
+ align:start position:0%
+so that you can see the meaning of it
+ 
+
+ align:start position:0%
+so that you can see the meaning of it
+and i think once you get this context
+
+ align:start position:0%
+and i think once you get this context
+ 
+
+ align:start position:0%
+and i think once you get this context
+and the meaning of it the stuff
+
+ align:start position:0%
+and the meaning of it the stuff
+ 
+
+ align:start position:0%
+and the meaning of it the stuff
+falls out pretty clearly it falls out
+
+ align:start position:0%
+falls out pretty clearly it falls out
+ 
+
+ align:start position:0%
+falls out pretty clearly it falls out
+clearly to me
+
+ align:start position:0%
+clearly to me
+ 
+
+ align:start position:0%
+clearly to me
+and i've been successful in the argument
+
+ align:start position:0%
+and i've been successful in the argument
+ 
+
+ align:start position:0%
+and i've been successful in the argument
+arguing it
+
+ align:start position:0%
+arguing it
+ 
+
+ align:start position:0%
+arguing it
+let me try it with you okay
+
+ align:start position:0%
+let me try it with you okay
+ 
+
+ align:start position:0%
+let me try it with you okay
+so let's see if the context is going to
+
+ align:start position:0%
+so let's see if the context is going to
+ 
+
+ align:start position:0%
+so let's see if the context is going to
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so with that i'll that's what i'll cover
+
+ align:start position:0%
+so with that i'll that's what i'll cover
+ 
+
+ align:start position:0%
+so with that i'll that's what i'll cover
+now any more questions or
+
+ align:start position:0%
+now any more questions or
+ 
+
+ align:start position:0%
+now any more questions or
+comments
+
+ align:start position:0%
+comments
+ 
+
+ align:start position:0%
+comments
+whenever i ask for questions i'm also
+
+ align:start position:0%
+whenever i ask for questions i'm also
+ 
+
+ align:start position:0%
+whenever i ask for questions i'm also
+leaving the possibilities of them for
+
+ align:start position:0%
+leaving the possibilities of them for
+ 
+
+ align:start position:0%
+leaving the possibilities of them for
+comments
+
+ align:start position:0%
+comments
+ 
+
+ align:start position:0%
+comments
+okay graduate class right
+
+ align:start position:0%
+okay graduate class right
+ 
+
+ align:start position:0%
+okay graduate class right
+comment
+
+ align:start position:0%
+comment
+ 
+
+ align:start position:0%
+comment
+undergraduates they don't have any
+
+ align:start position:0%
+undergraduates they don't have any
+ 
+
+ align:start position:0%
+undergraduates they don't have any
+authority
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say what do you say i remember the day
+
+ align:start position:0%
+say what do you say i remember the day
+ 
+
+ align:start position:0%
+say what do you say i remember the day
+huh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i was told about this professor at
+
+ align:start position:0%
+i was told about this professor at
+ 
+
+ align:start position:0%
+i was told about this professor at
+oberlin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who would uh
+
+ align:start position:0%
+who would uh
+ 
+
+ align:start position:0%
+who would uh
+cut a philosophy professor
+
+ align:start position:0%
+cut a philosophy professor
+ 
+
+ align:start position:0%
+cut a philosophy professor
+who would come into class
+
+ align:start position:0%
+who would come into class
+ 
+
+ align:start position:0%
+who would come into class
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+lie down on his desk
+
+ align:start position:0%
+lie down on his desk
+ 
+
+ align:start position:0%
+lie down on his desk
+and put his robe book on his chest
+
+ align:start position:0%
+and put his robe book on his chest
+ 
+
+ align:start position:0%
+and put his robe book on his chest
+and say now when somebody says something
+
+ align:start position:0%
+and say now when somebody says something
+ 
+
+ align:start position:0%
+and say now when somebody says something
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+i'll give you a grade
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nobody asked if he was really asleep
+
+ align:start position:0%
+nobody asked if he was really asleep
+ 
+
+ align:start position:0%
+nobody asked if he was really asleep
+back down there but the students would
+
+ align:start position:0%
+back down there but the students would
+ 
+
+ align:start position:0%
+back down there but the students would
+start to discover it was really
+
+ align:start position:0%
+start to discover it was really
+ 
+
+ align:start position:0%
+start to discover it was really
+intimidating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm not going to do that because i might
+
+ align:start position:0%
+i'm not going to do that because i might
+ 
+
+ align:start position:0%
+i'm not going to do that because i might
+wind up going right to sleep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but i guess the main point of what i
+
+ align:start position:0%
+but i guess the main point of what i
+ 
+
+ align:start position:0%
+but i guess the main point of what i
+just said is that i really do appreciate
+
+ align:start position:0%
+just said is that i really do appreciate
+ 
+
+ align:start position:0%
+just said is that i really do appreciate
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imaginative pedagogy i really do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think 325 on purpose for the because
+
+ align:start position:0%
+i think 325 on purpose for the because
+ 
+
+ align:start position:0%
+i think 325 on purpose for the because
+of the council yes
+
+ align:start position:0%
+of the council yes
+ 
+
+ align:start position:0%
+of the council yes
+yeah but i put circa if they said uh
+
+ align:start position:0%
+yeah but i put circa if they said uh
+ 
+
+ align:start position:0%
+yeah but i put circa if they said uh
+fourth century
+
+ align:start position:0%
+fourth century
+ 
+
+ align:start position:0%
+fourth century
+they put up a circle there but 325
+
+ align:start position:0%
+they put up a circle there but 325
+ 
+
+ align:start position:0%
+they put up a circle there but 325
+because of the council
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's see how we're doing can we
+
+ align:start position:0%
+uh let's see how we're doing can we
+ 
+
+ align:start position:0%
+uh let's see how we're doing can we
+tell me about these lights
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if can you see it better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you turn the front ones off
+
+ align:start position:0%
+if you turn the front ones off
+ 
+
+ align:start position:0%
+if you turn the front ones off
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+better yes uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roman empire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roughly 325 a.d the color coding is in
+
+ align:start position:0%
+roughly 325 a.d the color coding is in
+ 
+
+ align:start position:0%
+roughly 325 a.d the color coding is in
+this particular uh
+
+ align:start position:0%
+this particular uh
+ 
+
+ align:start position:0%
+this particular uh
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+is there just to show the differences of
+
+ align:start position:0%
+is there just to show the differences of
+ 
+
+ align:start position:0%
+is there just to show the differences of
+the provinces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this being read and this being red and
+
+ align:start position:0%
+this being read and this being red and
+ 
+
+ align:start position:0%
+this being read and this being red and
+this being red has nothing to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and in 325 a d
+
+ align:start position:0%
+and in 325 a d
+ 
+
+ align:start position:0%
+and in 325 a d
+was when
+
+ align:start position:0%
+was when
+ 
+
+ align:start position:0%
+was when
+was right after constantine the great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unified the empire
+
+ align:start position:0%
+unified the empire
+ 
+
+ align:start position:0%
+unified the empire
+and made christianity the state religion
+
+ align:start position:0%
+and made christianity the state religion
+ 
+
+ align:start position:0%
+and made christianity the state religion
+of the roman empire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now unified the empire
+
+ align:start position:0%
+now unified the empire
+ 
+
+ align:start position:0%
+now unified the empire
+the empire is divided east and west
+
+ align:start position:0%
+the empire is divided east and west
+ 
+
+ align:start position:0%
+the empire is divided east and west
+in at least three ways geographically
+
+ align:start position:0%
+in at least three ways geographically
+ 
+
+ align:start position:0%
+in at least three ways geographically
+culturally
+
+ align:start position:0%
+culturally
+ 
+
+ align:start position:0%
+culturally
+and politically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is divided east and west
+
+ align:start position:0%
+it is divided east and west
+ 
+
+ align:start position:0%
+it is divided east and west
+geographically pretty much along
+
+ align:start position:0%
+geographically pretty much along
+ 
+
+ align:start position:0%
+geographically pretty much along
+this vertical line that you can just
+
+ align:start position:0%
+this vertical line that you can just
+ 
+
+ align:start position:0%
+this vertical line that you can just
+barely see here
+
+ align:start position:0%
+barely see here
+ 
+
+ align:start position:0%
+barely see here
+where you've got greece on one side
+
+ align:start position:0%
+where you've got greece on one side
+ 
+
+ align:start position:0%
+where you've got greece on one side
+uh and all of what we now call turkey
+
+ align:start position:0%
+uh and all of what we now call turkey
+ 
+
+ align:start position:0%
+uh and all of what we now call turkey
+and the middle east
+
+ align:start position:0%
+and the middle east
+ 
+
+ align:start position:0%
+and the middle east
+and some of
+
+ align:start position:0%
+and some of
+ 
+
+ align:start position:0%
+and some of
+egypt
+
+ align:start position:0%
+egypt
+ 
+
+ align:start position:0%
+egypt
+and the west is north africa
+
+ align:start position:0%
+and the west is north africa
+ 
+
+ align:start position:0%
+and the west is north africa
+and spain and
+
+ align:start position:0%
+and spain and
+ 
+
+ align:start position:0%
+and spain and
+france and england and italy
+
+ align:start position:0%
+france and england and italy
+ 
+
+ align:start position:0%
+france and england and italy
+and others
+
+ align:start position:0%
+and others
+ 
+
+ align:start position:0%
+and others
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+culturally
+
+ align:start position:0%
+culturally
+ 
+
+ align:start position:0%
+culturally
+this is the most important part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have you ever seen have you ever read
+
+ align:start position:0%
+have you ever seen have you ever read
+ 
+
+ align:start position:0%
+have you ever seen have you ever read
+the new york the new yorker magazine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+do you like the covers
+
+ align:start position:0%
+do you like the covers
+ 
+
+ align:start position:0%
+do you like the covers
+the covers always have some kind of
+
+ align:start position:0%
+the covers always have some kind of
+ 
+
+ align:start position:0%
+the covers always have some kind of
+message
+
+ align:start position:0%
+message
+ 
+
+ align:start position:0%
+message
+ostensibly if you're a new yorker it
+
+ align:start position:0%
+ostensibly if you're a new yorker it
+ 
+
+ align:start position:0%
+ostensibly if you're a new yorker it
+picks up better you can understand it
+
+ align:start position:0%
+picks up better you can understand it
+ 
+
+ align:start position:0%
+picks up better you can understand it
+better than other people
+
+ align:start position:0%
+better than other people
+ 
+
+ align:start position:0%
+better than other people
+well there's a cover
+
+ align:start position:0%
+well there's a cover
+ 
+
+ align:start position:0%
+well there's a cover
+and it's done by steinberg i should have
+
+ align:start position:0%
+and it's done by steinberg i should have
+ 
+
+ align:start position:0%
+and it's done by steinberg i should have
+brought it in i have
+
+ align:start position:0%
+brought it in i have
+ 
+
+ align:start position:0%
+brought it in i have
+the big poster of it in my uh at my uh
+
+ align:start position:0%
+the big poster of it in my uh at my uh
+ 
+
+ align:start position:0%
+the big poster of it in my uh at my uh
+on my apartment i carry wherever i go
+
+ align:start position:0%
+on my apartment i carry wherever i go
+ 
+
+ align:start position:0%
+on my apartment i carry wherever i go
+now if i'm at a hotel but if i'm going
+
+ align:start position:0%
+now if i'm at a hotel but if i'm going
+ 
+
+ align:start position:0%
+now if i'm at a hotel but if i'm going
+to stay at some point
+
+ align:start position:0%
+to stay at some point
+ 
+
+ align:start position:0%
+to stay at some point
+i carry that and put it on the wall it's
+
+ align:start position:0%
+i carry that and put it on the wall it's
+ 
+
+ align:start position:0%
+i carry that and put it on the wall it's
+about this tall
+
+ align:start position:0%
+about this tall
+ 
+
+ align:start position:0%
+about this tall
+and i have uh
+
+ align:start position:0%
+and i have uh
+ 
+
+ align:start position:0%
+and i have uh
+it's numb he's numbered his uh posters i
+
+ align:start position:0%
+it's numb he's numbered his uh posters i
+ 
+
+ align:start position:0%
+it's numb he's numbered his uh posters i
+have something around 355.
+
+ align:start position:0%
+have something around 355.
+ 
+
+ align:start position:0%
+have something around 355.
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it's an original
+
+ align:start position:0%
+it's an original
+ 
+
+ align:start position:0%
+it's an original
+and it's the 355th one
+
+ align:start position:0%
+and it's the 355th one
+ 
+
+ align:start position:0%
+and it's the 355th one
+that he did
+
+ align:start position:0%
+that he did
+ 
+
+ align:start position:0%
+that he did
+and what it does is it's just incredible
+
+ align:start position:0%
+and what it does is it's just incredible
+ 
+
+ align:start position:0%
+and what it does is it's just incredible
+uh it has a picture it's called i think
+
+ align:start position:0%
+uh it has a picture it's called i think
+ 
+
+ align:start position:0%
+uh it has a picture it's called i think
+it's called the new yorker's view of the
+
+ align:start position:0%
+it's called the new yorker's view of the
+ 
+
+ align:start position:0%
+it's called the new yorker's view of the
+world it has a picture of
+
+ align:start position:0%
+world it has a picture of
+ 
+
+ align:start position:0%
+world it has a picture of
+some buildings in new york city
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then that's the foreground
+
+ align:start position:0%
+and then that's the foreground
+ 
+
+ align:start position:0%
+and then that's the foreground
+then then as you go up you go back
+
+ align:start position:0%
+then then as you go up you go back
+ 
+
+ align:start position:0%
+then then as you go up you go back
+so as you go up the next thing is the um
+
+ align:start position:0%
+so as you go up the next thing is the um
+ 
+
+ align:start position:0%
+so as you go up the next thing is the um
+hudson river
+
+ align:start position:0%
+hudson river
+ 
+
+ align:start position:0%
+hudson river
+and everything else is wilderness
+
+ align:start position:0%
+and everything else is wilderness
+ 
+
+ align:start position:0%
+and everything else is wilderness
+there's a little place over there they
+
+ align:start position:0%
+there's a little place over there they
+ 
+
+ align:start position:0%
+there's a little place over there they
+say chicago
+
+ align:start position:0%
+say chicago
+ 
+
+ align:start position:0%
+say chicago
+there's a little hill over there and
+
+ align:start position:0%
+there's a little hill over there and
+ 
+
+ align:start position:0%
+there's a little hill over there and
+they say los angeles
+
+ align:start position:0%
+they say los angeles
+ 
+
+ align:start position:0%
+they say los angeles
+there's a pond up here called the
+
+ align:start position:0%
+there's a pond up here called the
+ 
+
+ align:start position:0%
+there's a pond up here called the
+pacific ocean
+
+ align:start position:0%
+pacific ocean
+ 
+
+ align:start position:0%
+pacific ocean
+and then there's some land and there's a
+
+ align:start position:0%
+and then there's some land and there's a
+ 
+
+ align:start position:0%
+and then there's some land and there's a
+little word says japan and uss i mean
+
+ align:start position:0%
+little word says japan and uss i mean
+ 
+
+ align:start position:0%
+little word says japan and uss i mean
+the new york
+
+ align:start position:0%
+the new york
+ 
+
+ align:start position:0%
+the new york
+picture of the world is that everything
+
+ align:start position:0%
+picture of the world is that everything
+ 
+
+ align:start position:0%
+picture of the world is that everything
+that is civilization and that is
+
+ align:start position:0%
+that is civilization and that is
+ 
+
+ align:start position:0%
+that is civilization and that is
+happening is here when you walk across
+
+ align:start position:0%
+happening is here when you walk across
+ 
+
+ align:start position:0%
+happening is here when you walk across
+when you get out of
+
+ align:start position:0%
+when you get out of
+ 
+
+ align:start position:0%
+when you get out of
+one of those bridges
+
+ align:start position:0%
+one of those bridges
+ 
+
+ align:start position:0%
+one of those bridges
+then you're in the wasteland
+
+ align:start position:0%
+then you're in the wasteland
+ 
+
+ align:start position:0%
+then you're in the wasteland
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+people who lived in the eastern part of
+
+ align:start position:0%
+people who lived in the eastern part of
+ 
+
+ align:start position:0%
+people who lived in the eastern part of
+the empire felt that way about the west
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this was this this was
+
+ align:start position:0%
+this was this this was
+ 
+
+ align:start position:0%
+this was this this was
+high culture over here
+
+ align:start position:0%
+high culture over here
+ 
+
+ align:start position:0%
+high culture over here
+this was on the wasteland over there
+
+ align:start position:0%
+this was on the wasteland over there
+ 
+
+ align:start position:0%
+this was on the wasteland over there
+even rome forget about what they say
+
+ align:start position:0%
+even rome forget about what they say
+ 
+
+ align:start position:0%
+even rome forget about what they say
+about hollywood
+
+ align:start position:0%
+about hollywood
+ 
+
+ align:start position:0%
+about hollywood
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the romans any one of them who had
+
+ align:start position:0%
+and the romans any one of them who had
+ 
+
+ align:start position:0%
+and the romans any one of them who had
+been out to the east
+
+ align:start position:0%
+been out to the east
+ 
+
+ align:start position:0%
+been out to the east
+felt pretty much the same way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they didn't even speak the same language
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the west the
+
+ align:start position:0%
+in the west the
+ 
+
+ align:start position:0%
+in the west the
+the language of choice mainly of the
+
+ align:start position:0%
+the language of choice mainly of the
+ 
+
+ align:start position:0%
+the language of choice mainly of the
+scholars and the uh upper classes
+
+ align:start position:0%
+scholars and the uh upper classes
+ 
+
+ align:start position:0%
+scholars and the uh upper classes
+uh but uh of anybody else who could
+
+ align:start position:0%
+uh but uh of anybody else who could
+ 
+
+ align:start position:0%
+uh but uh of anybody else who could
+speak uh latin was the language of the
+
+ align:start position:0%
+speak uh latin was the language of the
+ 
+
+ align:start position:0%
+speak uh latin was the language of the
+realm in the west
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what was the language of the realm in
+
+ align:start position:0%
+what was the language of the realm in
+ 
+
+ align:start position:0%
+what was the language of the realm in
+the east it was not that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you want to guess
+
+ align:start position:0%
+you want to guess
+ 
+
+ align:start position:0%
+you want to guess
+persian
+
+ align:start position:0%
+persian
+ 
+
+ align:start position:0%
+persian
+that's a good guess
+
+ align:start position:0%
+that's a good guess
+ 
+
+ align:start position:0%
+that's a good guess
+she said persia
+
+ align:start position:0%
+she said persia
+ 
+
+ align:start position:0%
+she said persia
+would you say hebrew
+
+ align:start position:0%
+would you say hebrew
+ 
+
+ align:start position:0%
+would you say hebrew
+sure okay
+
+ align:start position:0%
+sure okay
+ 
+
+ align:start position:0%
+sure okay
+greek greek
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it was greek that's why they call
+
+ align:start position:0%
+right it was greek that's why they call
+ 
+
+ align:start position:0%
+right it was greek that's why they call
+it the the hellenistic part
+
+ align:start position:0%
+it the the hellenistic part
+ 
+
+ align:start position:0%
+it the the hellenistic part
+of the empire
+
+ align:start position:0%
+of the empire
+ 
+
+ align:start position:0%
+of the empire
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in the west
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the people out here were just like
+
+ align:start position:0%
+the the people out here were just like
+ 
+
+ align:start position:0%
+the the people out here were just like
+the romans
+
+ align:start position:0%
+the romans
+ 
+
+ align:start position:0%
+the romans
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+made the impact they were very
+
+ align:start position:0%
+made the impact they were very
+ 
+
+ align:start position:0%
+made the impact they were very
+uh concerned about
+
+ align:start position:0%
+uh concerned about
+ 
+
+ align:start position:0%
+uh concerned about
+militarism
+
+ align:start position:0%
+militarism
+ 
+
+ align:start position:0%
+militarism
+okay because at this time
+
+ align:start position:0%
+okay because at this time
+ 
+
+ align:start position:0%
+okay because at this time
+there was a great flood of
+
+ align:start position:0%
+there was a great flood of
+ 
+
+ align:start position:0%
+there was a great flood of
+several waves
+
+ align:start position:0%
+several waves
+ 
+
+ align:start position:0%
+several waves
+i don't want to use the word
+
+ align:start position:0%
+i don't want to use the word
+ 
+
+ align:start position:0%
+i don't want to use the word
+several waves of people coming in
+
+ align:start position:0%
+several waves of people coming in
+ 
+
+ align:start position:0%
+several waves of people coming in
+to this part of europe
+
+ align:start position:0%
+to this part of europe
+ 
+
+ align:start position:0%
+to this part of europe
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+asia
+
+ align:start position:0%
+asia
+ 
+
+ align:start position:0%
+asia
+the teutonic tribes
+
+ align:start position:0%
+the teutonic tribes
+ 
+
+ align:start position:0%
+the teutonic tribes
+now they came in in more than one way
+
+ align:start position:0%
+now they came in in more than one way
+ 
+
+ align:start position:0%
+now they came in in more than one way
+there was an earlier wave where they
+
+ align:start position:0%
+there was an earlier wave where they
+ 
+
+ align:start position:0%
+there was an earlier wave where they
+came in
+
+ align:start position:0%
+came in
+ 
+
+ align:start position:0%
+came in
+and occupied these northern parts
+
+ align:start position:0%
+and occupied these northern parts
+ 
+
+ align:start position:0%
+and occupied these northern parts
+vikings
+
+ align:start position:0%
+vikings
+ 
+
+ align:start position:0%
+vikings
+but the big waves came in around this
+
+ align:start position:0%
+but the big waves came in around this
+ 
+
+ align:start position:0%
+but the big waves came in around this
+round this time
+
+ align:start position:0%
+round this time
+ 
+
+ align:start position:0%
+round this time
+and we know why they came in
+
+ align:start position:0%
+and we know why they came in
+ 
+
+ align:start position:0%
+and we know why they came in
+it was a big drought out here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the historians and anthropologists that
+
+ align:start position:0%
+the historians and anthropologists that
+ 
+
+ align:start position:0%
+the historians and anthropologists that
+i read
+
+ align:start position:0%
+i read
+ 
+
+ align:start position:0%
+i read
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when they say that they don't know why
+
+ align:start position:0%
+when they say that they don't know why
+ 
+
+ align:start position:0%
+when they say that they don't know why
+somebody migrated from one area to
+
+ align:start position:0%
+somebody migrated from one area to
+ 
+
+ align:start position:0%
+somebody migrated from one area to
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+it does not mean that they don't have
+
+ align:start position:0%
+it does not mean that they don't have
+ 
+
+ align:start position:0%
+it does not mean that they don't have
+some idea about why they do it
+
+ align:start position:0%
+some idea about why they do it
+ 
+
+ align:start position:0%
+some idea about why they do it
+it's usually some
+
+ align:start position:0%
+it's usually some
+ 
+
+ align:start position:0%
+it's usually some
+drought or disease
+
+ align:start position:0%
+drought or disease
+ 
+
+ align:start position:0%
+drought or disease
+or population expansion
+
+ align:start position:0%
+or population expansion
+ 
+
+ align:start position:0%
+or population expansion
+of some sort or persecution by somebody
+
+ align:start position:0%
+of some sort or persecution by somebody
+ 
+
+ align:start position:0%
+of some sort or persecution by somebody
+else further out
+
+ align:start position:0%
+else further out
+ 
+
+ align:start position:0%
+else further out
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right but this time they pretty much
+
+ align:start position:0%
+all right but this time they pretty much
+ 
+
+ align:start position:0%
+all right but this time they pretty much
+know it was they had a series of bad
+
+ align:start position:0%
+know it was they had a series of bad
+ 
+
+ align:start position:0%
+know it was they had a series of bad
+droughts up in asia
+
+ align:start position:0%
+droughts up in asia
+ 
+
+ align:start position:0%
+droughts up in asia
+and great numbers of people came
+
+ align:start position:0%
+and great numbers of people came
+ 
+
+ align:start position:0%
+and great numbers of people came
+in here
+
+ align:start position:0%
+in here
+ 
+
+ align:start position:0%
+in here
+and they were all your your goths
+
+ align:start position:0%
+and they were all your your goths
+ 
+
+ align:start position:0%
+and they were all your your goths
+which include the ostrogoths and the
+
+ align:start position:0%
+which include the ostrogoths and the
+ 
+
+ align:start position:0%
+which include the ostrogoths and the
+visigoth
+
+ align:start position:0%
+visigoth
+ 
+
+ align:start position:0%
+visigoth
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+vandals
+
+ align:start position:0%
+vandals
+ 
+
+ align:start position:0%
+vandals
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+all of these people came in from this
+
+ align:start position:0%
+all of these people came in from this
+ 
+
+ align:start position:0%
+all of these people came in from this
+area here and they terrified the empire
+
+ align:start position:0%
+area here and they terrified the empire
+ 
+
+ align:start position:0%
+area here and they terrified the empire
+because they had a fighting nature to
+
+ align:start position:0%
+because they had a fighting nature to
+ 
+
+ align:start position:0%
+because they had a fighting nature to
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and they would raid over these borders
+
+ align:start position:0%
+and they would raid over these borders
+ 
+
+ align:start position:0%
+and they would raid over these borders
+okay and in 410 a.d alaric the goth
+
+ align:start position:0%
+okay and in 410 a.d alaric the goth
+ 
+
+ align:start position:0%
+okay and in 410 a.d alaric the goth
+sacked rome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the cultural point that i want to
+
+ align:start position:0%
+here's the cultural point that i want to
+ 
+
+ align:start position:0%
+here's the cultural point that i want to
+carry into the universities
+
+ align:start position:0%
+carry into the universities
+ 
+
+ align:start position:0%
+carry into the universities
+and it's going to be one of my major
+
+ align:start position:0%
+and it's going to be one of my major
+ 
+
+ align:start position:0%
+and it's going to be one of my major
+points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in this lecture
+
+ align:start position:0%
+uh in this lecture
+ 
+
+ align:start position:0%
+uh in this lecture
+here it
+
+ align:start position:0%
+here it
+ 
+
+ align:start position:0%
+here it
+is okay ready
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the period
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between 650
+
+ align:start position:0%
+between 650
+ 
+
+ align:start position:0%
+between 650
+bc and 650 a.d all your major religions
+
+ align:start position:0%
+bc and 650 a.d all your major religions
+ 
+
+ align:start position:0%
+bc and 650 a.d all your major religions
+except two
+
+ align:start position:0%
+except two
+ 
+
+ align:start position:0%
+except two
+were found
+
+ align:start position:0%
+were found
+ 
+
+ align:start position:0%
+were found
+in these areas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+judaism was
+
+ align:start position:0%
+judaism was
+ 
+
+ align:start position:0%
+judaism was
+founded before all that
+
+ align:start position:0%
+founded before all that
+ 
+
+ align:start position:0%
+founded before all that
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+islam was founded
+
+ align:start position:0%
+islam was founded
+ 
+
+ align:start position:0%
+islam was founded
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+but everything else was
+
+ align:start position:0%
+but everything else was
+ 
+
+ align:start position:0%
+but everything else was
+coming around this time not just there
+
+ align:start position:0%
+coming around this time not just there
+ 
+
+ align:start position:0%
+coming around this time not just there
+but when you think of buddhism buddhism
+
+ align:start position:0%
+but when you think of buddhism buddhism
+ 
+
+ align:start position:0%
+but when you think of buddhism buddhism
+it was the whole world
+
+ align:start position:0%
+it was the whole world
+ 
+
+ align:start position:0%
+it was the whole world
+it was it was very broad
+
+ align:start position:0%
+it was it was very broad
+ 
+
+ align:start position:0%
+it was it was very broad
+it was a very magical period
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when christianity was formed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there was there were some issues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of the issues was this
+
+ align:start position:0%
+and one of the issues was this
+ 
+
+ align:start position:0%
+and one of the issues was this
+all right this is going to be a
+
+ align:start position:0%
+all right this is going to be a
+ 
+
+ align:start position:0%
+all right this is going to be a
+theological point but i'm going to make
+
+ align:start position:0%
+theological point but i'm going to make
+ 
+
+ align:start position:0%
+theological point but i'm going to make
+it an educational point that's going to
+
+ align:start position:0%
+it an educational point that's going to
+ 
+
+ align:start position:0%
+it an educational point that's going to
+last us last you for the rest of your
+
+ align:start position:0%
+last us last you for the rest of your
+ 
+
+ align:start position:0%
+last us last you for the rest of your
+career
+
+ align:start position:0%
+career
+ 
+
+ align:start position:0%
+career
+the theological point is this
+
+ align:start position:0%
+the theological point is this
+ 
+
+ align:start position:0%
+the theological point is this
+the question
+
+ align:start position:0%
+the question
+ 
+
+ align:start position:0%
+the question
+which is most important or which comes
+
+ align:start position:0%
+which is most important or which comes
+ 
+
+ align:start position:0%
+which is most important or which comes
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+faith
+
+ align:start position:0%
+faith
+ 
+
+ align:start position:0%
+faith
+or works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you have it in your mind
+
+ align:start position:0%
+do you have it in your mind
+ 
+
+ align:start position:0%
+do you have it in your mind
+that you are a good person and that will
+
+ align:start position:0%
+that you are a good person and that will
+ 
+
+ align:start position:0%
+that you are a good person and that will
+cause you to do good things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or you'd best do good things otherwise
+
+ align:start position:0%
+or you'd best do good things otherwise
+ 
+
+ align:start position:0%
+or you'd best do good things otherwise
+you won't get into the
+
+ align:start position:0%
+you won't get into the
+ 
+
+ align:start position:0%
+you won't get into the
+you won't get salvation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in the east
+
+ align:start position:0%
+now in the east
+ 
+
+ align:start position:0%
+now in the east
+when all of these religions were vying
+
+ align:start position:0%
+when all of these religions were vying
+ 
+
+ align:start position:0%
+when all of these religions were vying
+with one another
+
+ align:start position:0%
+with one another
+ 
+
+ align:start position:0%
+with one another
+and i say that that there were people uh
+
+ align:start position:0%
+and i say that that there were people uh
+ 
+
+ align:start position:0%
+and i say that that there were people uh
+long before this time who knew that
+
+ align:start position:0%
+long before this time who knew that
+ 
+
+ align:start position:0%
+long before this time who knew that
+paganism
+
+ align:start position:0%
+paganism
+ 
+
+ align:start position:0%
+paganism
+could not last the romans
+
+ align:start position:0%
+could not last the romans
+ 
+
+ align:start position:0%
+could not last the romans
+in peace time because paganism was a
+
+ align:start position:0%
+in peace time because paganism was a
+ 
+
+ align:start position:0%
+in peace time because paganism was a
+warrior religion
+
+ align:start position:0%
+warrior religion
+ 
+
+ align:start position:0%
+warrior religion
+and i think that many of these religions
+
+ align:start position:0%
+and i think that many of these religions
+ 
+
+ align:start position:0%
+and i think that many of these religions
+were vying with each other it to be the
+
+ align:start position:0%
+were vying with each other it to be the
+ 
+
+ align:start position:0%
+were vying with each other it to be the
+state religion of the roman empire they
+
+ align:start position:0%
+state religion of the roman empire they
+ 
+
+ align:start position:0%
+state religion of the roman empire they
+just didn't know when it was going to
+
+ align:start position:0%
+just didn't know when it was going to
+ 
+
+ align:start position:0%
+just didn't know when it was going to
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+now that's my take on it i emphasize the
+
+ align:start position:0%
+now that's my take on it i emphasize the
+ 
+
+ align:start position:0%
+now that's my take on it i emphasize the
+word m-y
+
+ align:start position:0%
+word m-y
+ 
+
+ align:start position:0%
+word m-y
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in the east
+
+ align:start position:0%
+but in the east
+ 
+
+ align:start position:0%
+but in the east
+the problem of getting people to accept
+
+ align:start position:0%
+the problem of getting people to accept
+ 
+
+ align:start position:0%
+the problem of getting people to accept
+your religion was a problem of reason
+
+ align:start position:0%
+your religion was a problem of reason
+ 
+
+ align:start position:0%
+your religion was a problem of reason
+you had to argue with them
+
+ align:start position:0%
+you had to argue with them
+ 
+
+ align:start position:0%
+you had to argue with them
+because all of them had studied all of
+
+ align:start position:0%
+because all of them had studied all of
+ 
+
+ align:start position:0%
+because all of them had studied all of
+your intellectuals
+
+ align:start position:0%
+your intellectuals
+ 
+
+ align:start position:0%
+your intellectuals
+had studied greek philosophy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they knew all about
+
+ align:start position:0%
+they knew all about
+ 
+
+ align:start position:0%
+they knew all about
+plato and aristotle
+
+ align:start position:0%
+plato and aristotle
+ 
+
+ align:start position:0%
+plato and aristotle
+and all of these people and so you had
+
+ align:start position:0%
+and all of these people and so you had
+ 
+
+ align:start position:0%
+and all of these people and so you had
+to sit down and reason it out with
+
+ align:start position:0%
+to sit down and reason it out with
+ 
+
+ align:start position:0%
+to sit down and reason it out with
+you had to get their faith before you
+
+ align:start position:0%
+you had to get their faith before you
+ 
+
+ align:start position:0%
+you had to get their faith before you
+could get their works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess what in the west
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you had to get their works
+
+ align:start position:0%
+you had to get their works
+ 
+
+ align:start position:0%
+you had to get their works
+all right people they want to hear about
+
+ align:start position:0%
+all right people they want to hear about
+ 
+
+ align:start position:0%
+all right people they want to hear about
+all of this theorizing
+
+ align:start position:0%
+all of this theorizing
+ 
+
+ align:start position:0%
+all of this theorizing
+what do you want me to do
+
+ align:start position:0%
+what do you want me to do
+ 
+
+ align:start position:0%
+what do you want me to do
+so works came before
+
+ align:start position:0%
+so works came before
+ 
+
+ align:start position:0%
+so works came before
+faith in the west
+
+ align:start position:0%
+faith in the west
+ 
+
+ align:start position:0%
+faith in the west
+faith came before works in the east
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what does that have to do with
+
+ align:start position:0%
+now what does that have to do with
+ 
+
+ align:start position:0%
+now what does that have to do with
+universities
+
+ align:start position:0%
+universities
+ 
+
+ align:start position:0%
+universities
+well as you saw from the film
+
+ align:start position:0%
+well as you saw from the film
+ 
+
+ align:start position:0%
+well as you saw from the film
+uh whatever had whatever theologians
+
+ align:start position:0%
+uh whatever had whatever theologians
+ 
+
+ align:start position:0%
+uh whatever had whatever theologians
+theologians were thinking about had
+
+ align:start position:0%
+theologians were thinking about had
+ 
+
+ align:start position:0%
+theologians were thinking about had
+something to do with the universities
+
+ align:start position:0%
+something to do with the universities
+ 
+
+ align:start position:0%
+something to do with the universities
+they were the professors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this is around 1500
+
+ align:start position:0%
+this is around 1500
+ 
+
+ align:start position:0%
+this is around 1500
+a.d
+
+ align:start position:0%
+a.d
+ 
+
+ align:start position:0%
+a.d
+and now i want you to put in your mind
+
+ align:start position:0%
+and now i want you to put in your mind
+ 
+
+ align:start position:0%
+and now i want you to put in your mind
+that film that i showed
+
+ align:start position:0%
+that film that i showed
+ 
+
+ align:start position:0%
+that film that i showed
+where julius ii
+
+ align:start position:0%
+where julius ii
+ 
+
+ align:start position:0%
+where julius ii
+is the warrior pope
+
+ align:start position:0%
+is the warrior pope
+ 
+
+ align:start position:0%
+is the warrior pope
+this is during his time
+
+ align:start position:0%
+this is during his time
+ 
+
+ align:start position:0%
+this is during his time
+actually circa 1500 is pretty much his
+
+ align:start position:0%
+actually circa 1500 is pretty much his
+ 
+
+ align:start position:0%
+actually circa 1500 is pretty much his
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+right this is a map of europe it's kind
+
+ align:start position:0%
+right this is a map of europe it's kind
+ 
+
+ align:start position:0%
+right this is a map of europe it's kind
+of hard to see but you don't need this
+
+ align:start position:0%
+of hard to see but you don't need this
+ 
+
+ align:start position:0%
+of hard to see but you don't need this
+i'll
+
+ align:start position:0%
+i'll
+ 
+
+ align:start position:0%
+i'll
+see for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is a map of the universities in
+
+ align:start position:0%
+this is a map of the universities in
+ 
+
+ align:start position:0%
+this is a map of the universities in
+europe at that time it was about 75 of
+
+ align:start position:0%
+europe at that time it was about 75 of
+ 
+
+ align:start position:0%
+europe at that time it was about 75 of
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh this part
+
+ align:start position:0%
+uh this part
+ 
+
+ align:start position:0%
+uh this part
+of the map including
+
+ align:start position:0%
+of the map including
+ 
+
+ align:start position:0%
+of the map including
+most of
+
+ align:start position:0%
+most of
+ 
+
+ align:start position:0%
+most of
+italy
+
+ align:start position:0%
+italy
+ 
+
+ align:start position:0%
+italy
+but certainly all of what we call
+
+ align:start position:0%
+but certainly all of what we call
+ 
+
+ align:start position:0%
+but certainly all of what we call
+germania was what is called the holy
+
+ align:start position:0%
+germania was what is called the holy
+ 
+
+ align:start position:0%
+germania was what is called the holy
+roman
+
+ align:start position:0%
+roman
+ 
+
+ align:start position:0%
+roman
+empire that was established after
+
+ align:start position:0%
+empire that was established after
+ 
+
+ align:start position:0%
+empire that was established after
+the roman empire had fallen
+
+ align:start position:0%
+the roman empire had fallen
+ 
+
+ align:start position:0%
+the roman empire had fallen
+after islam had come in
+
+ align:start position:0%
+after islam had come in
+ 
+
+ align:start position:0%
+after islam had come in
+and after islam had pretty much gone
+
+ align:start position:0%
+and after islam had pretty much gone
+ 
+
+ align:start position:0%
+and after islam had pretty much gone
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+charlemagne came to power in around 1800
+
+ align:start position:0%
+charlemagne came to power in around 1800
+ 
+
+ align:start position:0%
+charlemagne came to power in around 1800
+and depending on who you talked to was
+
+ align:start position:0%
+and depending on who you talked to was
+ 
+
+ align:start position:0%
+and depending on who you talked to was
+either charlemagne or otto the first
+
+ align:start position:0%
+either charlemagne or otto the first
+ 
+
+ align:start position:0%
+either charlemagne or otto the first
+that began the holy roman empire if you
+
+ align:start position:0%
+that began the holy roman empire if you
+ 
+
+ align:start position:0%
+that began the holy roman empire if you
+talk to a frenchman guess what the
+
+ align:start position:0%
+talk to a frenchman guess what the
+ 
+
+ align:start position:0%
+talk to a frenchman guess what the
+frenchman will say
+
+ align:start position:0%
+frenchman will say
+ 
+
+ align:start position:0%
+frenchman will say
+if you talk to a german what will the
+
+ align:start position:0%
+if you talk to a german what will the
+ 
+
+ align:start position:0%
+if you talk to a german what will the
+germans say i told the person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's important for me to say
+
+ align:start position:0%
+it's important for me to say
+ 
+
+ align:start position:0%
+it's important for me to say
+that this is what the germans in the
+
+ align:start position:0%
+that this is what the germans in the
+ 
+
+ align:start position:0%
+that this is what the germans in the
+20th century called
+
+ align:start position:0%
+20th century called
+ 
+
+ align:start position:0%
+20th century called
+the first reich
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you had an emperor that was located up
+
+ align:start position:0%
+you had an emperor that was located up
+ 
+
+ align:start position:0%
+you had an emperor that was located up
+around in here
+
+ align:start position:0%
+around in here
+ 
+
+ align:start position:0%
+around in here
+and guess who the high priest of the
+
+ align:start position:0%
+and guess who the high priest of the
+ 
+
+ align:start position:0%
+and guess who the high priest of the
+empire was
+
+ align:start position:0%
+empire was
+ 
+
+ align:start position:0%
+empire was
+the pope
+
+ align:start position:0%
+the pope
+ 
+
+ align:start position:0%
+the pope
+and then you had everybody else so there
+
+ align:start position:0%
+and then you had everybody else so there
+ 
+
+ align:start position:0%
+and then you had everybody else so there
+is remember the three principles of
+
+ align:start position:0%
+is remember the three principles of
+ 
+
+ align:start position:0%
+is remember the three principles of
+social order
+
+ align:start position:0%
+social order
+ 
+
+ align:start position:0%
+social order
+regal
+
+ align:start position:0%
+regal
+ 
+
+ align:start position:0%
+regal
+priestly
+
+ align:start position:0%
+priestly
+ 
+
+ align:start position:0%
+priestly
+and popular
+
+ align:start position:0%
+and popular
+ 
+
+ align:start position:0%
+and popular
+the regal principle was the
+
+ align:start position:0%
+the regal principle was the
+ 
+
+ align:start position:0%
+the regal principle was the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+emperor
+
+ align:start position:0%
+emperor
+ 
+
+ align:start position:0%
+emperor
+the priestly principle was the pope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the uh popular principle was
+
+ align:start position:0%
+the uh popular principle was
+ 
+
+ align:start position:0%
+the uh popular principle was
+that if you belong to the empire you
+
+ align:start position:0%
+that if you belong to the empire you
+ 
+
+ align:start position:0%
+that if you belong to the empire you
+would be safe from
+
+ align:start position:0%
+would be safe from
+ 
+
+ align:start position:0%
+would be safe from
+marauders you can enjoy some of the
+
+ align:start position:0%
+marauders you can enjoy some of the
+ 
+
+ align:start position:0%
+marauders you can enjoy some of the
+wealth of the empire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there it is
+
+ align:start position:0%
+okay so there it is
+ 
+
+ align:start position:0%
+okay so there it is
+and this is the mood in which these
+
+ align:start position:0%
+and this is the mood in which these
+ 
+
+ align:start position:0%
+and this is the mood in which these
+universities were founded now here comes
+
+ align:start position:0%
+universities were founded now here comes
+ 
+
+ align:start position:0%
+universities were founded now here comes
+my point
+
+ align:start position:0%
+my point
+ 
+
+ align:start position:0%
+my point
+right here it comes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first universities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that were founded in and were founded in
+
+ align:start position:0%
+that were founded in and were founded in
+ 
+
+ align:start position:0%
+that were founded in and were founded in
+in italy before this
+
+ align:start position:0%
+in italy before this
+ 
+
+ align:start position:0%
+in italy before this
+time we're talking about
+
+ align:start position:0%
+time we're talking about
+ 
+
+ align:start position:0%
+time we're talking about
+around just around the time and just
+
+ align:start position:0%
+around just around the time and just
+ 
+
+ align:start position:0%
+around just around the time and just
+before the time of the name of the rose
+
+ align:start position:0%
+before the time of the name of the rose
+ 
+
+ align:start position:0%
+before the time of the name of the rose
+which depending on who you're talking
+
+ align:start position:0%
+which depending on who you're talking
+ 
+
+ align:start position:0%
+which depending on who you're talking
+about 1100 1200
+
+ align:start position:0%
+about 1100 1200
+ 
+
+ align:start position:0%
+about 1100 1200
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+these universities
+
+ align:start position:0%
+these universities
+ 
+
+ align:start position:0%
+these universities
+in italy they were bologna
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and elsewhere
+
+ align:start position:0%
+and elsewhere
+ 
+
+ align:start position:0%
+and elsewhere
+they were
+
+ align:start position:0%
+they were
+ 
+
+ align:start position:0%
+they were
+universities that taught medicine
+
+ align:start position:0%
+universities that taught medicine
+ 
+
+ align:start position:0%
+universities that taught medicine
+law
+
+ align:start position:0%
+law
+ 
+
+ align:start position:0%
+law
+theology
+
+ align:start position:0%
+theology
+ 
+
+ align:start position:0%
+theology
+or ministry and or administration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this is what
+
+ align:start position:0%
+this is what
+ 
+
+ align:start position:0%
+this is what
+gets me excited
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they were right close to the pope
+
+ align:start position:0%
+they were right close to the pope
+ 
+
+ align:start position:0%
+they were right close to the pope
+and it made sense for those institutions
+
+ align:start position:0%
+and it made sense for those institutions
+ 
+
+ align:start position:0%
+and it made sense for those institutions
+to be institutions focusing on works
+
+ align:start position:0%
+to be institutions focusing on works
+ 
+
+ align:start position:0%
+to be institutions focusing on works
+the practical arts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if engine if if engineering was a
+
+ align:start position:0%
+so if engine if if engineering was a
+ 
+
+ align:start position:0%
+so if engine if if engineering was a
+learning discipline at that time and was
+
+ align:start position:0%
+learning discipline at that time and was
+ 
+
+ align:start position:0%
+learning discipline at that time and was
+taught at a university where would it
+
+ align:start position:0%
+taught at a university where would it
+ 
+
+ align:start position:0%
+taught at a university where would it
+most likely have been founded
+
+ align:start position:0%
+most likely have been founded
+ 
+
+ align:start position:0%
+most likely have been founded
+down there near the pope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that
+
+ align:start position:0%
+uh that
+ 
+
+ align:start position:0%
+uh that
+is important about this time
+
+ align:start position:0%
+is important about this time
+ 
+
+ align:start position:0%
+is important about this time
+that made
+
+ align:start position:0%
+that made
+ 
+
+ align:start position:0%
+that made
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+professors interested get interested in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greek philosophy
+
+ align:start position:0%
+greek philosophy
+ 
+
+ align:start position:0%
+greek philosophy
+remember from your film
+
+ align:start position:0%
+remember from your film
+ 
+
+ align:start position:0%
+remember from your film
+who was the bad guy
+
+ align:start position:0%
+who was the bad guy
+ 
+
+ align:start position:0%
+who was the bad guy
+in the film
+
+ align:start position:0%
+in the film
+ 
+
+ align:start position:0%
+in the film
+the venerable yorkie
+
+ align:start position:0%
+the venerable yorkie
+ 
+
+ align:start position:0%
+the venerable yorkie
+and why was he the bad guy
+
+ align:start position:0%
+and why was he the bad guy
+ 
+
+ align:start position:0%
+and why was he the bad guy
+tell me in your own words
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why did you commit all those murders
+
+ align:start position:0%
+why did you commit all those murders
+ 
+
+ align:start position:0%
+why did you commit all those murders
+he was afraid
+
+ align:start position:0%
+he was afraid
+ 
+
+ align:start position:0%
+he was afraid
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+knowledge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+aristotle
+
+ align:start position:0%
+aristotle
+ 
+
+ align:start position:0%
+aristotle
+yeah let's keep talking just keep going
+
+ align:start position:0%
+yeah let's keep talking just keep going
+ 
+
+ align:start position:0%
+yeah let's keep talking just keep going
+you can't say too much duration of
+
+ align:start position:0%
+you can't say too much duration of
+ 
+
+ align:start position:0%
+you can't say too much duration of
+people's minds
+
+ align:start position:0%
+people's minds
+ 
+
+ align:start position:0%
+people's minds
+people's sense of joy and
+
+ align:start position:0%
+people's sense of joy and
+ 
+
+ align:start position:0%
+people's sense of joy and
+people's desire to search for new
+
+ align:start position:0%
+people's desire to search for new
+ 
+
+ align:start position:0%
+people's desire to search for new
+knowledge he was afraid of all those
+
+ align:start position:0%
+knowledge he was afraid of all those
+ 
+
+ align:start position:0%
+knowledge he was afraid of all those
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+destroying
+
+ align:start position:0%
+destroying
+ 
+
+ align:start position:0%
+destroying
+the church and
+
+ align:start position:0%
+the church and
+ 
+
+ align:start position:0%
+the church and
+yeah civilizations he knew it
+
+ align:start position:0%
+yeah civilizations he knew it
+ 
+
+ align:start position:0%
+yeah civilizations he knew it
+keep trying
+
+ align:start position:0%
+keep trying
+ 
+
+ align:start position:0%
+keep trying
+let's go have some more ideas you see
+
+ align:start position:0%
+let's go have some more ideas you see
+ 
+
+ align:start position:0%
+let's go have some more ideas you see
+you saw that
+
+ align:start position:0%
+you saw that
+ 
+
+ align:start position:0%
+you saw that
+come on tell me what do you think about
+
+ align:start position:0%
+come on tell me what do you think about
+ 
+
+ align:start position:0%
+come on tell me what do you think about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+were you impressed i mean did this movie
+
+ align:start position:0%
+were you impressed i mean did this movie
+ 
+
+ align:start position:0%
+were you impressed i mean did this movie
+make an impact on you
+
+ align:start position:0%
+make an impact on you
+ 
+
+ align:start position:0%
+make an impact on you
+it did
+
+ align:start position:0%
+it did
+ 
+
+ align:start position:0%
+it did
+and i did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice that in the eastern part of the
+
+ align:start position:0%
+notice that in the eastern part of the
+ 
+
+ align:start position:0%
+notice that in the eastern part of the
+empire everybody study group over here
+
+ align:start position:0%
+empire everybody study group over here
+ 
+
+ align:start position:0%
+empire everybody study group over here
+they were terrified
+
+ align:start position:0%
+they were terrified
+ 
+
+ align:start position:0%
+they were terrified
+well one of the things one of the ways
+
+ align:start position:0%
+well one of the things one of the ways
+ 
+
+ align:start position:0%
+well one of the things one of the ways
+you can talk about the terror of it all
+
+ align:start position:0%
+you can talk about the terror of it all
+ 
+
+ align:start position:0%
+you can talk about the terror of it all
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+reason
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was challenging faith
+
+ align:start position:0%
+was challenging faith
+ 
+
+ align:start position:0%
+was challenging faith
+don't tell me
+
+ align:start position:0%
+don't tell me
+ 
+
+ align:start position:0%
+don't tell me
+anything and tell me that my faith has
+
+ align:start position:0%
+anything and tell me that my faith has
+ 
+
+ align:start position:0%
+anything and tell me that my faith has
+to make it so
+
+ align:start position:0%
+to make it so
+ 
+
+ align:start position:0%
+to make it so
+appeal to my reason
+
+ align:start position:0%
+appeal to my reason
+ 
+
+ align:start position:0%
+appeal to my reason
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that was sort of sean connery's
+
+ align:start position:0%
+that was sort of sean connery's
+ 
+
+ align:start position:0%
+that was sort of sean connery's
+character yes
+
+ align:start position:0%
+character yes
+ 
+
+ align:start position:0%
+character yes
+uh a word or two about sean connelly's
+
+ align:start position:0%
+uh a word or two about sean connelly's
+ 
+
+ align:start position:0%
+uh a word or two about sean connelly's
+character yes okay this is uh
+
+ align:start position:0%
+character yes okay this is uh
+ 
+
+ align:start position:0%
+character yes okay this is uh
+this is uh hollywood has its best in my
+
+ align:start position:0%
+this is uh hollywood has its best in my
+ 
+
+ align:start position:0%
+this is uh hollywood has its best in my
+judgment
+
+ align:start position:0%
+judgment
+ 
+
+ align:start position:0%
+judgment
+sean connery's character was a
+
+ align:start position:0%
+sean connery's character was a
+ 
+
+ align:start position:0%
+sean connery's character was a
+conflation of more than one person
+
+ align:start position:0%
+conflation of more than one person
+ 
+
+ align:start position:0%
+conflation of more than one person
+but i think the main character main
+
+ align:start position:0%
+but i think the main character main
+ 
+
+ align:start position:0%
+but i think the main character main
+person that
+
+ align:start position:0%
+person that
+ 
+
+ align:start position:0%
+person that
+alberto echo had in mind
+
+ align:start position:0%
+alberto echo had in mind
+ 
+
+ align:start position:0%
+alberto echo had in mind
+was a man named called william of occult
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+william of arkham uh you can read about
+
+ align:start position:0%
+william of arkham uh you can read about
+ 
+
+ align:start position:0%
+william of arkham uh you can read about
+him and the philosophies that he had
+
+ align:start position:0%
+him and the philosophies that he had
+ 
+
+ align:start position:0%
+him and the philosophies that he had
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and william of arkham and others were
+
+ align:start position:0%
+and william of arkham and others were
+ 
+
+ align:start position:0%
+and william of arkham and others were
+the were belonged to one of two
+
+ align:start position:0%
+the were belonged to one of two
+ 
+
+ align:start position:0%
+the were belonged to one of two
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+oh oh i'm doing this
+
+ align:start position:0%
+oh oh i'm doing this
+ 
+
+ align:start position:0%
+oh oh i'm doing this
+this thing is leaking
+
+ align:start position:0%
+this thing is leaking
+ 
+
+ align:start position:0%
+this thing is leaking
+uh one of two sects
+
+ align:start position:0%
+uh one of two sects
+ 
+
+ align:start position:0%
+uh one of two sects
+they were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh actually i don't want to throw it
+
+ align:start position:0%
+uh actually i don't want to throw it
+ 
+
+ align:start position:0%
+uh actually i don't want to throw it
+away i want to wipe this off
+
+ align:start position:0%
+away i want to wipe this off
+ 
+
+ align:start position:0%
+away i want to wipe this off
+nobody has any tissues in there got any
+
+ align:start position:0%
+nobody has any tissues in there got any
+ 
+
+ align:start position:0%
+nobody has any tissues in there got any
+tissues this thing is leaking um
+
+ align:start position:0%
+tissues this thing is leaking um
+ 
+
+ align:start position:0%
+tissues this thing is leaking um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the franciscans
+
+ align:start position:0%
+the franciscans
+ 
+
+ align:start position:0%
+the franciscans
+and the dominicans could you pick them
+
+ align:start position:0%
+and the dominicans could you pick them
+ 
+
+ align:start position:0%
+and the dominicans could you pick them
+out in the film
+
+ align:start position:0%
+out in the film
+ 
+
+ align:start position:0%
+out in the film
+the franciscans were
+
+ align:start position:0%
+the franciscans were
+ 
+
+ align:start position:0%
+the franciscans were
+the poor ones thank you
+
+ align:start position:0%
+the poor ones thank you
+ 
+
+ align:start position:0%
+the poor ones thank you
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+they were just the
+
+ align:start position:0%
+they were just the
+ 
+
+ align:start position:0%
+they were just the
+plain cowl we're talking about the film
+
+ align:start position:0%
+plain cowl we're talking about the film
+ 
+
+ align:start position:0%
+plain cowl we're talking about the film
+uh and uh the
+
+ align:start position:0%
+uh and uh the
+ 
+
+ align:start position:0%
+uh and uh the
+flamboyant ones were the benedictines
+
+ align:start position:0%
+flamboyant ones were the benedictines
+ 
+
+ align:start position:0%
+flamboyant ones were the benedictines
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh actually um they reflect
+
+ align:start position:0%
+uh actually um they reflect
+ 
+
+ align:start position:0%
+uh actually um they reflect
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+for the most part
+
+ align:start position:0%
+for the most part
+ 
+
+ align:start position:0%
+for the most part
+uh class differences of the members
+
+ align:start position:0%
+uh class differences of the members
+ 
+
+ align:start position:0%
+uh class differences of the members
+uh the benedictines for the most part
+
+ align:start position:0%
+uh the benedictines for the most part
+ 
+
+ align:start position:0%
+uh the benedictines for the most part
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+
+ align:start position:0%
+were people who came from wealthy
+ 
+
+ align:start position:0%
+were people who came from wealthy
+families
+
+ align:start position:0%
+families
+ 
+
+ align:start position:0%
+families
+and the uh augustinians
+
+ align:start position:0%
+and the uh augustinians
+ 
+
+ align:start position:0%
+and the uh augustinians
+were were
+
+ align:start position:0%
+were were
+ 
+
+ align:start position:0%
+were were
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say augustinians i should have
+
+ align:start position:0%
+let's say augustinians i should have
+ 
+
+ align:start position:0%
+let's say augustinians i should have
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+franciscans
+
+ align:start position:0%
+franciscans
+ 
+
+ align:start position:0%
+franciscans
+i'm sorry franciscans
+
+ align:start position:0%
+i'm sorry franciscans
+ 
+
+ align:start position:0%
+i'm sorry franciscans
+uh were mainly did not come from those
+
+ align:start position:0%
+uh were mainly did not come from those
+ 
+
+ align:start position:0%
+uh were mainly did not come from those
+families
+
+ align:start position:0%
+families
+ 
+
+ align:start position:0%
+families
+which meant that their competition
+
+ align:start position:0%
+which meant that their competition
+ 
+
+ align:start position:0%
+which meant that their competition
+for intellectual equality
+
+ align:start position:0%
+for intellectual equality
+ 
+
+ align:start position:0%
+for intellectual equality
+was keen
+
+ align:start position:0%
+was keen
+ 
+
+ align:start position:0%
+was keen
+and the franciscans enjoyed beating
+
+ align:start position:0%
+and the franciscans enjoyed beating
+ 
+
+ align:start position:0%
+and the franciscans enjoyed beating
+benedict
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happened was that the benedictines
+
+ align:start position:0%
+what happened was that the benedictines
+ 
+
+ align:start position:0%
+what happened was that the benedictines
+and the franciscans
+
+ align:start position:0%
+and the franciscans
+ 
+
+ align:start position:0%
+and the franciscans
+were at first
+
+ align:start position:0%
+were at first
+ 
+
+ align:start position:0%
+were at first
+together in the faculties particularly
+
+ align:start position:0%
+together in the faculties particularly
+ 
+
+ align:start position:0%
+together in the faculties particularly
+at the university of paris and then the
+
+ align:start position:0%
+at the university of paris and then the
+ 
+
+ align:start position:0%
+at the university of paris and then the
+franciscans
+
+ align:start position:0%
+franciscans
+ 
+
+ align:start position:0%
+franciscans
+uh decided to go off
+
+ align:start position:0%
+uh decided to go off
+ 
+
+ align:start position:0%
+uh decided to go off
+and they established cambridge and
+
+ align:start position:0%
+and they established cambridge and
+ 
+
+ align:start position:0%
+and they established cambridge and
+oxford
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now because science and arist
+
+ align:start position:0%
+now because science and arist
+ 
+
+ align:start position:0%
+now because science and arist
+had become
+
+ align:start position:0%
+had become
+ 
+
+ align:start position:0%
+had become
+the new vogue in those days we
+
+ align:start position:0%
+the new vogue in those days we
+ 
+
+ align:start position:0%
+the new vogue in those days we
+had just discovered the americas
+
+ align:start position:0%
+had just discovered the americas
+ 
+
+ align:start position:0%
+had just discovered the americas
+we're creating a new middle class
+
+ align:start position:0%
+we're creating a new middle class
+ 
+
+ align:start position:0%
+we're creating a new middle class
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+notion of science and exploration are
+
+ align:start position:0%
+notion of science and exploration are
+ 
+
+ align:start position:0%
+notion of science and exploration are
+now important
+
+ align:start position:0%
+now important
+ 
+
+ align:start position:0%
+now important
+that's why uh the venerable yorkie was
+
+ align:start position:0%
+that's why uh the venerable yorkie was
+ 
+
+ align:start position:0%
+that's why uh the venerable yorkie was
+having a hard time because people
+
+ align:start position:0%
+having a hard time because people
+ 
+
+ align:start position:0%
+having a hard time because people
+thought that well we need to learn
+
+ align:start position:0%
+thought that well we need to learn
+ 
+
+ align:start position:0%
+thought that well we need to learn
+aristotle now
+
+ align:start position:0%
+aristotle now
+ 
+
+ align:start position:0%
+aristotle now
+right and the benedictines and the
+
+ align:start position:0%
+right and the benedictines and the
+ 
+
+ align:start position:0%
+right and the benedictines and the
+franciscans believe that
+
+ align:start position:0%
+franciscans believe that
+ 
+
+ align:start position:0%
+franciscans believe that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the further they got away
+
+ align:start position:0%
+so the further they got away
+ 
+
+ align:start position:0%
+so the further they got away
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+the pope
+
+ align:start position:0%
+the pope
+ 
+
+ align:start position:0%
+the pope
+the more successful they were in
+
+ align:start position:0%
+the more successful they were in
+ 
+
+ align:start position:0%
+the more successful they were in
+studying and teaching aristotle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the same time something very
+
+ align:start position:0%
+at the same time something very
+ 
+
+ align:start position:0%
+at the same time something very
+interesting was happening over
+
+ align:start position:0%
+interesting was happening over
+ 
+
+ align:start position:0%
+interesting was happening over
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we're now talking about the
+
+ align:start position:0%
+we're now talking about the
+ 
+
+ align:start position:0%
+we're now talking about the
+what happened to the what what was going
+
+ align:start position:0%
+what happened to the what what was going
+ 
+
+ align:start position:0%
+what happened to the what what was going
+on how did christianity take with the
+
+ align:start position:0%
+on how did christianity take with the
+ 
+
+ align:start position:0%
+on how did christianity take with the
+goths
+
+ align:start position:0%
+goths
+ 
+
+ align:start position:0%
+goths
+and uh some of the other tribes that i
+
+ align:start position:0%
+and uh some of the other tribes that i
+ 
+
+ align:start position:0%
+and uh some of the other tribes that i
+said had just started coming in
+
+ align:start position:0%
+said had just started coming in
+ 
+
+ align:start position:0%
+said had just started coming in
+uh in the early part early early part of
+
+ align:start position:0%
+uh in the early part early early part of
+ 
+
+ align:start position:0%
+uh in the early part early early part of
+the fourth century
+
+ align:start position:0%
+the fourth century
+ 
+
+ align:start position:0%
+the fourth century
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separate the fur these
+
+ align:start position:0%
+separate the fur these
+ 
+
+ align:start position:0%
+separate the fur these
+these are what they thought were the way
+
+ align:start position:0%
+these are what they thought were the way
+ 
+
+ align:start position:0%
+these are what they thought were the way
+the world was divided up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just take a little look at that
+
+ align:start position:0%
+and just take a little look at that
+ 
+
+ align:start position:0%
+and just take a little look at that
+separate the first one and the last one
+
+ align:start position:0%
+separate the first one and the last one
+ 
+
+ align:start position:0%
+separate the first one and the last one
+from the middle
+
+ align:start position:0%
+from the middle
+ 
+
+ align:start position:0%
+from the middle
+the first one
+
+ align:start position:0%
+the first one
+ 
+
+ align:start position:0%
+the first one
+sky gods
+
+ align:start position:0%
+sky gods
+ 
+
+ align:start position:0%
+sky gods
+came in from christianity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the last
+
+ align:start position:0%
+the last
+ 
+
+ align:start position:0%
+the last
+the realm of dead
+
+ align:start position:0%
+the realm of dead
+ 
+
+ align:start position:0%
+the realm of dead
+hell this word h-e-l
+
+ align:start position:0%
+hell this word h-e-l
+ 
+
+ align:start position:0%
+hell this word h-e-l
+is supposed to be where h-e-l-l came
+
+ align:start position:0%
+is supposed to be where h-e-l-l came
+ 
+
+ align:start position:0%
+is supposed to be where h-e-l-l came
+from but it also came in from christian
+
+ align:start position:0%
+from but it also came in from christian
+ 
+
+ align:start position:0%
+from but it also came in from christian
+the middle was what the goth had before
+
+ align:start position:0%
+the middle was what the goth had before
+ 
+
+ align:start position:0%
+the middle was what the goth had before
+they even came over
+
+ align:start position:0%
+they even came over
+ 
+
+ align:start position:0%
+they even came over
+to europe
+
+ align:start position:0%
+to europe
+ 
+
+ align:start position:0%
+to europe
+and well the point i want to make is
+
+ align:start position:0%
+and well the point i want to make is
+ 
+
+ align:start position:0%
+and well the point i want to make is
+that when christianity
+
+ align:start position:0%
+that when christianity
+ 
+
+ align:start position:0%
+that when christianity
+was introduced
+
+ align:start position:0%
+was introduced
+ 
+
+ align:start position:0%
+was introduced
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the goths
+
+ align:start position:0%
+the goths
+ 
+
+ align:start position:0%
+the goths
+and others in the
+
+ align:start position:0%
+and others in the
+ 
+
+ align:start position:0%
+and others in the
+germanic part of europe and eastern
+
+ align:start position:0%
+germanic part of europe and eastern
+ 
+
+ align:start position:0%
+germanic part of europe and eastern
+europe it never fully overtook people's
+
+ align:start position:0%
+europe it never fully overtook people's
+ 
+
+ align:start position:0%
+europe it never fully overtook people's
+thinking
+
+ align:start position:0%
+thinking
+ 
+
+ align:start position:0%
+thinking
+the middle part remained
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there's something very significant
+
+ align:start position:0%
+now there's something very significant
+ 
+
+ align:start position:0%
+now there's something very significant
+about this middle part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very significant
+
+ align:start position:0%
+very significant
+ 
+
+ align:start position:0%
+very significant
+very significant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is that when you look at
+
+ align:start position:0%
+and that is that when you look at
+ 
+
+ align:start position:0%
+and that is that when you look at
+their village pagan religion and ask who
+
+ align:start position:0%
+their village pagan religion and ask who
+ 
+
+ align:start position:0%
+their village pagan religion and ask who
+which of the gods lives live in those
+
+ align:start position:0%
+which of the gods lives live in those
+ 
+
+ align:start position:0%
+which of the gods lives live in those
+parts of the world
+
+ align:start position:0%
+parts of the world
+ 
+
+ align:start position:0%
+parts of the world
+what you're going to find is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one
+
+ align:start position:0%
+that one
+ 
+
+ align:start position:0%
+that one
+m-a-n-i-g manic
+
+ align:start position:0%
+m-a-n-i-g manic
+ 
+
+ align:start position:0%
+m-a-n-i-g manic
+i don't know if it's pronounced manic or
+
+ align:start position:0%
+i don't know if it's pronounced manic or
+ 
+
+ align:start position:0%
+i don't know if it's pronounced manic or
+maddening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but look at it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the individual has will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+christianity
+
+ align:start position:0%
+christianity
+ 
+
+ align:start position:0%
+christianity
+at least during these times would
+
+ align:start position:0%
+at least during these times would
+ 
+
+ align:start position:0%
+at least during these times would
+attribute
+
+ align:start position:0%
+attribute
+ 
+
+ align:start position:0%
+attribute
+will to god god had will
+
+ align:start position:0%
+will to god god had will
+ 
+
+ align:start position:0%
+will to god god had will
+but here
+
+ align:start position:0%
+but here
+ 
+
+ align:start position:0%
+but here
+they are talking about
+
+ align:start position:0%
+they are talking about
+ 
+
+ align:start position:0%
+they are talking about
+every human being having a will and that
+
+ align:start position:0%
+every human being having a will and that
+ 
+
+ align:start position:0%
+every human being having a will and that
+will being a part of your body
+
+ align:start position:0%
+will being a part of your body
+ 
+
+ align:start position:0%
+will being a part of your body
+and it even goes further than that the
+
+ align:start position:0%
+and it even goes further than that the
+ 
+
+ align:start position:0%
+and it even goes further than that the
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+could overdo the orla
+
+ align:start position:0%
+could overdo the orla
+ 
+
+ align:start position:0%
+could overdo the orla
+which was
+
+ align:start position:0%
+which was
+ 
+
+ align:start position:0%
+which was
+the god of your destiny
+
+ align:start position:0%
+the god of your destiny
+ 
+
+ align:start position:0%
+the god of your destiny
+and that is
+
+ align:start position:0%
+and that is
+ 
+
+ align:start position:0%
+and that is
+you could say that i have destiny and i
+
+ align:start position:0%
+you could say that i have destiny and i
+ 
+
+ align:start position:0%
+you could say that i have destiny and i
+have faith out in front of me and there
+
+ align:start position:0%
+have faith out in front of me and there
+ 
+
+ align:start position:0%
+have faith out in front of me and there
+are these gods who
+
+ align:start position:0%
+are these gods who
+ 
+
+ align:start position:0%
+are these gods who
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+that this is where i am going in this
+
+ align:start position:0%
+that this is where i am going in this
+ 
+
+ align:start position:0%
+that this is where i am going in this
+life
+
+ align:start position:0%
+life
+ 
+
+ align:start position:0%
+life
+but guess how you could oh how a human
+
+ align:start position:0%
+but guess how you could oh how a human
+ 
+
+ align:start position:0%
+but guess how you could oh how a human
+being could overcome the gods
+
+ align:start position:0%
+being could overcome the gods
+ 
+
+ align:start position:0%
+being could overcome the gods
+with the will
+
+ align:start position:0%
+with the will
+ 
+
+ align:start position:0%
+with the will
+i will it not i will not go that way
+
+ align:start position:0%
+i will it not i will not go that way
+ 
+
+ align:start position:0%
+i will it not i will not go that way
+free will
+
+ align:start position:0%
+free will
+ 
+
+ align:start position:0%
+free will
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+do you see it coming that's the basis of
+
+ align:start position:0%
+do you see it coming that's the basis of
+ 
+
+ align:start position:0%
+do you see it coming that's the basis of
+constant deontology he lived in this
+
+ align:start position:0%
+constant deontology he lived in this
+ 
+
+ align:start position:0%
+constant deontology he lived in this
+area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the point i'm gonna make
+
+ align:start position:0%
+that's the point i'm gonna make
+ 
+
+ align:start position:0%
+that's the point i'm gonna make
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it was out of this thinking about the
+
+ align:start position:0%
+it was out of this thinking about the
+ 
+
+ align:start position:0%
+it was out of this thinking about the
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+took on in the west
+
+ align:start position:0%
+took on in the west
+ 
+
+ align:start position:0%
+took on in the west
+the notion
+
+ align:start position:0%
+the notion
+ 
+
+ align:start position:0%
+the notion
+that faith is more important than works
+
+ align:start position:0%
+that faith is more important than works
+ 
+
+ align:start position:0%
+that faith is more important than works
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+faith is of the mind just like the will
+
+ align:start position:0%
+faith is of the mind just like the will
+ 
+
+ align:start position:0%
+faith is of the mind just like the will
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it was luther martin luther
+
+ align:start position:0%
+and it was luther martin luther
+ 
+
+ align:start position:0%
+and it was luther martin luther
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+started the
+
+ align:start position:0%
+started the
+ 
+
+ align:start position:0%
+started the
+reformation with his 95 theses the most
+
+ align:start position:0%
+reformation with his 95 theses the most
+ 
+
+ align:start position:0%
+reformation with his 95 theses the most
+important one being
+
+ align:start position:0%
+important one being
+ 
+
+ align:start position:0%
+important one being
+you this it's between you and god to
+
+ align:start position:0%
+you this it's between you and god to
+ 
+
+ align:start position:0%
+you this it's between you and god to
+decide whether or not you're good not
+
+ align:start position:0%
+decide whether or not you're good not
+ 
+
+ align:start position:0%
+decide whether or not you're good not
+the pope
+
+ align:start position:0%
+the pope
+ 
+
+ align:start position:0%
+the pope
+not the pope judging what you do
+
+ align:start position:0%
+not the pope judging what you do
+ 
+
+ align:start position:0%
+not the pope judging what you do
+and you and what you do mainly is
+
+ align:start position:0%
+and you and what you do mainly is
+ 
+
+ align:start position:0%
+and you and what you do mainly is
+paying those tithes okay
+
+ align:start position:0%
+paying those tithes okay
+ 
+
+ align:start position:0%
+paying those tithes okay
+at a time when there's a new middle
+
+ align:start position:0%
+at a time when there's a new middle
+ 
+
+ align:start position:0%
+at a time when there's a new middle
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+that wants to enjoy the money they're
+
+ align:start position:0%
+that wants to enjoy the money they're
+ 
+
+ align:start position:0%
+that wants to enjoy the money they're
+making they don't have a whole lot of
+
+ align:start position:0%
+making they don't have a whole lot of
+ 
+
+ align:start position:0%
+making they don't have a whole lot of
+money to be given over to the pope
+
+ align:start position:0%
+money to be given over to the pope
+ 
+
+ align:start position:0%
+money to be given over to the pope
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so martin lu martin luther
+
+ align:start position:0%
+so martin lu martin luther
+ 
+
+ align:start position:0%
+so martin lu martin luther
+was just acting out of
+
+ align:start position:0%
+was just acting out of
+ 
+
+ align:start position:0%
+was just acting out of
+what was ordinary and normal for people
+
+ align:start position:0%
+what was ordinary and normal for people
+ 
+
+ align:start position:0%
+what was ordinary and normal for people
+around him at the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now i think that's the end of that
+
+ align:start position:0%
+so now i think that's the end of that
+ 
+
+ align:start position:0%
+so now i think that's the end of that
+show now i want to talk a little bit in
+
+ align:start position:0%
+show now i want to talk a little bit in
+ 
+
+ align:start position:0%
+show now i want to talk a little bit in
+depth about the two points of view
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and i want to say how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want you to put those points of view
+
+ align:start position:0%
+i want you to put those points of view
+ 
+
+ align:start position:0%
+i want you to put those points of view
+into this homework assignment
+
+ align:start position:0%
+into this homework assignment
+ 
+
+ align:start position:0%
+into this homework assignment
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's start with
+
+ align:start position:0%
+let's start with
+ 
+
+ align:start position:0%
+let's start with
+utilitarianism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've had a pedestrian discussion of
+
+ align:start position:0%
+we've had a pedestrian discussion of
+ 
+
+ align:start position:0%
+we've had a pedestrian discussion of
+utilitarianism
+
+ align:start position:0%
+utilitarianism
+ 
+
+ align:start position:0%
+utilitarianism
+now let's
+
+ align:start position:0%
+now let's
+ 
+
+ align:start position:0%
+now let's
+go a little deeper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and before the class is all over we'll
+
+ align:start position:0%
+and before the class is all over we'll
+ 
+
+ align:start position:0%
+and before the class is all over we'll
+go one more step in depth
+
+ align:start position:0%
+go one more step in depth
+ 
+
+ align:start position:0%
+go one more step in depth
+and we'll take something back that we
+
+ align:start position:0%
+and we'll take something back that we
+ 
+
+ align:start position:0%
+and we'll take something back that we
+said before we'll shape it right
+
+ align:start position:0%
+said before we'll shape it right
+ 
+
+ align:start position:0%
+said before we'll shape it right
+but this is the next step
+
+ align:start position:0%
+but this is the next step
+ 
+
+ align:start position:0%
+but this is the next step
+you'll be 90 there
+
+ align:start position:0%
+you'll be 90 there
+ 
+
+ align:start position:0%
+you'll be 90 there
+the rest of it is just
+
+ align:start position:0%
+the rest of it is just
+ 
+
+ align:start position:0%
+the rest of it is just
+gonna be icing on the cake this will get
+
+ align:start position:0%
+gonna be icing on the cake this will get
+ 
+
+ align:start position:0%
+gonna be icing on the cake this will get
+you 90 there
+
+ align:start position:0%
+you 90 there
+ 
+
+ align:start position:0%
+you 90 there
+all right we're in
+
+ align:start position:0%
+all right we're in
+ 
+
+ align:start position:0%
+all right we're in
+a place in the world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're in england
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where they're teaching greek philosophy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+they are still motivated
+
+ align:start position:0%
+they are still motivated
+ 
+
+ align:start position:0%
+they are still motivated
+by the notion that works are more
+
+ align:start position:0%
+by the notion that works are more
+ 
+
+ align:start position:0%
+by the notion that works are more
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+than faith
+
+ align:start position:0%
+than faith
+ 
+
+ align:start position:0%
+than faith
+so when they teach science
+
+ align:start position:0%
+so when they teach science
+ 
+
+ align:start position:0%
+so when they teach science
+what are they going to be interested in
+
+ align:start position:0%
+what are they going to be interested in
+ 
+
+ align:start position:0%
+what are they going to be interested in
+empirical science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're going to be
+
+ align:start position:0%
+they're going to be
+ 
+
+ align:start position:0%
+they're going to be
+interested in rational science and
+
+ align:start position:0%
+interested in rational science and
+ 
+
+ align:start position:0%
+interested in rational science and
+mathematics too
+
+ align:start position:0%
+mathematics too
+ 
+
+ align:start position:0%
+mathematics too
+okay let's not
+
+ align:start position:0%
+okay let's not
+ 
+
+ align:start position:0%
+okay let's not
+forget that one of the best
+
+ align:start position:0%
+forget that one of the best
+ 
+
+ align:start position:0%
+forget that one of the best
+mathematicians around
+
+ align:start position:0%
+mathematicians around
+ 
+
+ align:start position:0%
+mathematicians around
+uh in uh
+
+ align:start position:0%
+uh in uh
+ 
+
+ align:start position:0%
+uh in uh
+our olden days was a guy by the name of
+
+ align:start position:0%
+our olden days was a guy by the name of
+ 
+
+ align:start position:0%
+our olden days was a guy by the name of
+bishop george barkley
+
+ align:start position:0%
+bishop george barkley
+ 
+
+ align:start position:0%
+bishop george barkley
+okay so it doesn't apply to all of them
+
+ align:start position:0%
+okay so it doesn't apply to all of them
+ 
+
+ align:start position:0%
+okay so it doesn't apply to all of them
+but basically they're in an environment
+
+ align:start position:0%
+but basically they're in an environment
+ 
+
+ align:start position:0%
+but basically they're in an environment
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+works is still more important than faith
+
+ align:start position:0%
+works is still more important than faith
+ 
+
+ align:start position:0%
+works is still more important than faith
+so when they start talking about science
+
+ align:start position:0%
+so when they start talking about science
+ 
+
+ align:start position:0%
+so when they start talking about science
+they're going to talk about rational
+
+ align:start position:0%
+they're going to talk about rational
+ 
+
+ align:start position:0%
+they're going to talk about rational
+science a little bit
+
+ align:start position:0%
+science a little bit
+ 
+
+ align:start position:0%
+science a little bit
+the theory
+
+ align:start position:0%
+the theory
+ 
+
+ align:start position:0%
+the theory
+but they're mainly going to be
+
+ align:start position:0%
+but they're mainly going to be
+ 
+
+ align:start position:0%
+but they're mainly going to be
+interested in
+
+ align:start position:0%
+interested in
+ 
+
+ align:start position:0%
+interested in
+empirical science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mainly interested in empirical signs
+
+ align:start position:0%
+mainly interested in empirical signs
+ 
+
+ align:start position:0%
+mainly interested in empirical signs
+when they get to ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're going to be mainly interested in
+
+ align:start position:0%
+they're going to be mainly interested in
+ 
+
+ align:start position:0%
+they're going to be mainly interested in
+and a
+
+ align:start position:0%
+and a
+ 
+
+ align:start position:0%
+and a
+in ethical arguments that have is
+
+ align:start position:0%
+in ethical arguments that have is
+ 
+
+ align:start position:0%
+in ethical arguments that have is
+its basis and root
+
+ align:start position:0%
+its basis and root
+ 
+
+ align:start position:0%
+its basis and root
+in facts
+
+ align:start position:0%
+in facts
+ 
+
+ align:start position:0%
+in facts
+not ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here let's characterize the times
+
+ align:start position:0%
+now here let's characterize the times
+ 
+
+ align:start position:0%
+now here let's characterize the times
+uh john stuart mill gives gets all the
+
+ align:start position:0%
+uh john stuart mill gives gets all the
+ 
+
+ align:start position:0%
+uh john stuart mill gives gets all the
+credit
+
+ align:start position:0%
+credit
+ 
+
+ align:start position:0%
+credit
+for utilitarianism a lot of utilitarians
+
+ align:start position:0%
+for utilitarianism a lot of utilitarians
+ 
+
+ align:start position:0%
+for utilitarianism a lot of utilitarians
+before him
+
+ align:start position:0%
+before him
+ 
+
+ align:start position:0%
+before him
+uh he gets the credit because he more or
+
+ align:start position:0%
+uh he gets the credit because he more or
+ 
+
+ align:start position:0%
+uh he gets the credit because he more or
+less perfected the uh the theory
+
+ align:start position:0%
+less perfected the uh the theory
+ 
+
+ align:start position:0%
+less perfected the uh the theory
+but the one that i want to talk about
+
+ align:start position:0%
+but the one that i want to talk about
+ 
+
+ align:start position:0%
+but the one that i want to talk about
+which is not one of the first but what
+
+ align:start position:0%
+which is not one of the first but what
+ 
+
+ align:start position:0%
+which is not one of the first but what
+really gives it
+
+ align:start position:0%
+really gives it
+ 
+
+ align:start position:0%
+really gives it
+its context is a man named jeremy
+
+ align:start position:0%
+its context is a man named jeremy
+ 
+
+ align:start position:0%
+its context is a man named jeremy
+bentham
+
+ align:start position:0%
+bentham
+ 
+
+ align:start position:0%
+bentham
+i'd like you to know that name
+
+ align:start position:0%
+i'd like you to know that name
+ 
+
+ align:start position:0%
+i'd like you to know that name
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and here's why he gives the context
+
+ align:start position:0%
+and here's why he gives the context
+ 
+
+ align:start position:0%
+and here's why he gives the context
+jeremy bentham
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh did most of his writing
+
+ align:start position:0%
+uh did most of his writing
+ 
+
+ align:start position:0%
+uh did most of his writing
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+around 1800 a little bit before a little
+
+ align:start position:0%
+around 1800 a little bit before a little
+ 
+
+ align:start position:0%
+around 1800 a little bit before a little
+bit after
+
+ align:start position:0%
+bit after
+ 
+
+ align:start position:0%
+bit after
+and let's talk about 1800
+
+ align:start position:0%
+and let's talk about 1800
+ 
+
+ align:start position:0%
+and let's talk about 1800
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+less than 30 years before
+
+ align:start position:0%
+less than 30 years before
+ 
+
+ align:start position:0%
+less than 30 years before
+1776 we have the american revolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1789 we've got the french revolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1803 the holy roman empire collapses
+
+ align:start position:0%
+1803 the holy roman empire collapses
+ 
+
+ align:start position:0%
+1803 the holy roman empire collapses
+you get the feeling there's a whole lot
+
+ align:start position:0%
+you get the feeling there's a whole lot
+ 
+
+ align:start position:0%
+you get the feeling there's a whole lot
+of revolution going on
+
+ align:start position:0%
+of revolution going on
+ 
+
+ align:start position:0%
+of revolution going on
+and the revolutionaries are coming up
+
+ align:start position:0%
+and the revolutionaries are coming up
+ 
+
+ align:start position:0%
+and the revolutionaries are coming up
+with new philosophies for their new
+
+ align:start position:0%
+with new philosophies for their new
+ 
+
+ align:start position:0%
+with new philosophies for their new
+government
+
+ align:start position:0%
+government
+ 
+
+ align:start position:0%
+government
+jeremy bentham was interested in new
+
+ align:start position:0%
+jeremy bentham was interested in new
+ 
+
+ align:start position:0%
+jeremy bentham was interested in new
+laws
+
+ align:start position:0%
+laws
+ 
+
+ align:start position:0%
+laws
+for the english people they did not have
+
+ align:start position:0%
+for the english people they did not have
+ 
+
+ align:start position:0%
+for the english people they did not have
+a revolution
+
+ align:start position:0%
+a revolution
+ 
+
+ align:start position:0%
+a revolution
+it should have been but
+
+ align:start position:0%
+it should have been but
+ 
+
+ align:start position:0%
+it should have been but
+would have done a lot of good would have
+
+ align:start position:0%
+would have done a lot of good would have
+ 
+
+ align:start position:0%
+would have done a lot of good would have
+done a lot of good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there was a guy by the name of uh i
+
+ align:start position:0%
+but there was a guy by the name of uh i
+ 
+
+ align:start position:0%
+but there was a guy by the name of uh i
+just learned about him it turns out
+
+ align:start position:0%
+just learned about him it turns out
+ 
+
+ align:start position:0%
+just learned about him it turns out
+my stepson's elementary school was named
+
+ align:start position:0%
+my stepson's elementary school was named
+ 
+
+ align:start position:0%
+my stepson's elementary school was named
+edmund burke school
+
+ align:start position:0%
+edmund burke school
+ 
+
+ align:start position:0%
+edmund burke school
+and edmund burke wrote a paper
+
+ align:start position:0%
+and edmund burke wrote a paper
+ 
+
+ align:start position:0%
+and edmund burke wrote a paper
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+to the aristocrats in england
+
+ align:start position:0%
+to the aristocrats in england
+ 
+
+ align:start position:0%
+to the aristocrats in england
+saying don't worry we're not going to
+
+ align:start position:0%
+saying don't worry we're not going to
+ 
+
+ align:start position:0%
+saying don't worry we're not going to
+have a revolution over here
+
+ align:start position:0%
+have a revolution over here
+ 
+
+ align:start position:0%
+have a revolution over here
+turned out he was right but it turned
+
+ align:start position:0%
+turned out he was right but it turned
+ 
+
+ align:start position:0%
+turned out he was right but it turned
+out he was wrong in another way it just
+
+ align:start position:0%
+out he was wrong in another way it just
+ 
+
+ align:start position:0%
+out he was wrong in another way it just
+was not a founder things did change
+
+ align:start position:0%
+was not a founder things did change
+ 
+
+ align:start position:0%
+was not a founder things did change
+dramatically
+
+ align:start position:0%
+dramatically
+ 
+
+ align:start position:0%
+dramatically
+and they were called the reforms of the
+
+ align:start position:0%
+and they were called the reforms of the
+ 
+
+ align:start position:0%
+and they were called the reforms of the
+1830s jeremy bentham was one of the
+
+ align:start position:0%
+1830s jeremy bentham was one of the
+ 
+
+ align:start position:0%
+1830s jeremy bentham was one of the
+leaders jeremy bentham was interested
+
+ align:start position:0%
+leaders jeremy bentham was interested
+ 
+
+ align:start position:0%
+leaders jeremy bentham was interested
+well his his movement was primarily
+
+ align:start position:0%
+well his his movement was primarily
+ 
+
+ align:start position:0%
+well his his movement was primarily
+interested in new laws
+
+ align:start position:0%
+interested in new laws
+ 
+
+ align:start position:0%
+interested in new laws
+particularly laws favoring the upper
+
+ align:start position:0%
+particularly laws favoring the upper
+ 
+
+ align:start position:0%
+particularly laws favoring the upper
+middle class
+
+ align:start position:0%
+middle class
+ 
+
+ align:start position:0%
+middle class
+as opposed to the aristocrats
+
+ align:start position:0%
+as opposed to the aristocrats
+ 
+
+ align:start position:0%
+as opposed to the aristocrats
+jerry jeremy bentham's starting point
+
+ align:start position:0%
+jerry jeremy bentham's starting point
+ 
+
+ align:start position:0%
+jerry jeremy bentham's starting point
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+morality ethics
+
+ align:start position:0%
+morality ethics
+ 
+
+ align:start position:0%
+morality ethics
+that what he wanted to say was that when
+
+ align:start position:0%
+that what he wanted to say was that when
+ 
+
+ align:start position:0%
+that what he wanted to say was that when
+we build these new laws we want them
+
+ align:start position:0%
+we build these new laws we want them
+ 
+
+ align:start position:0%
+we build these new laws we want them
+grounded in ethics they have to be right
+
+ align:start position:0%
+grounded in ethics they have to be right
+ 
+
+ align:start position:0%
+grounded in ethics they have to be right
+right you get the context now
+
+ align:start position:0%
+right you get the context now
+ 
+
+ align:start position:0%
+right you get the context now
+right so what he wants to do is to come
+
+ align:start position:0%
+right so what he wants to do is to come
+ 
+
+ align:start position:0%
+right so what he wants to do is to come
+up with an ethical theory
+
+ align:start position:0%
+up with an ethical theory
+ 
+
+ align:start position:0%
+up with an ethical theory
+that is compelling upon the people
+
+ align:start position:0%
+that is compelling upon the people
+ 
+
+ align:start position:0%
+that is compelling upon the people
+around him
+
+ align:start position:0%
+around him
+ 
+
+ align:start position:0%
+around him
+what would that ethical theory have to
+
+ align:start position:0%
+what would that ethical theory have to
+ 
+
+ align:start position:0%
+what would that ethical theory have to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+be grounded on facts
+
+ align:start position:0%
+be grounded on facts
+ 
+
+ align:start position:0%
+be grounded on facts
+not on ideas
+
+ align:start position:0%
+not on ideas
+ 
+
+ align:start position:0%
+not on ideas
+and here's the way the utilitarians did
+
+ align:start position:0%
+and here's the way the utilitarians did
+ 
+
+ align:start position:0%
+and here's the way the utilitarians did
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they got their clipboards
+
+ align:start position:0%
+they got their clipboards
+ 
+
+ align:start position:0%
+they got their clipboards
+and their pencils
+
+ align:start position:0%
+and their pencils
+ 
+
+ align:start position:0%
+and their pencils
+and they went out
+
+ align:start position:0%
+and they went out
+ 
+
+ align:start position:0%
+and they went out
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+the world and ask people questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they did not sit down under a tree
+
+ align:start position:0%
+they did not sit down under a tree
+ 
+
+ align:start position:0%
+they did not sit down under a tree
+with a loaf of bread
+
+ align:start position:0%
+with a loaf of bread
+ 
+
+ align:start position:0%
+with a loaf of bread
+and a bottle of wine and think through a
+
+ align:start position:0%
+and a bottle of wine and think through a
+ 
+
+ align:start position:0%
+and a bottle of wine and think through a
+great idea
+
+ align:start position:0%
+great idea
+ 
+
+ align:start position:0%
+great idea
+they went out and here's what they did
+
+ align:start position:0%
+they went out and here's what they did
+ 
+
+ align:start position:0%
+they went out and here's what they did
+they just asked themselves they used a
+
+ align:start position:0%
+they just asked themselves they used a
+ 
+
+ align:start position:0%
+they just asked themselves they used a
+method by plato
+
+ align:start position:0%
+method by plato
+ 
+
+ align:start position:0%
+method by plato
+they asked themselves
+
+ align:start position:0%
+they asked themselves
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+
+ align:start position:0%
+they asked themselves
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+
+ align:start position:0%
+they ask people
+ 
+
+ align:start position:0%
+they ask people
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+why do you do why did you choose to do x
+
+ align:start position:0%
+why do you do why did you choose to do x
+ 
+
+ align:start position:0%
+why do you do why did you choose to do x
+instead of y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay they might ask you a question like
+
+ align:start position:0%
+okay they might ask you a question like
+ 
+
+ align:start position:0%
+okay they might ask you a question like
+why are you uh in graduate school
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make up an answer don't give me the
+
+ align:start position:0%
+make up an answer don't give me the
+ 
+
+ align:start position:0%
+make up an answer don't give me the
+truth you'll just make up an answer a
+
+ align:start position:0%
+truth you'll just make up an answer a
+ 
+
+ align:start position:0%
+truth you'll just make up an answer a
+reason why i'm in graduate school
+
+ align:start position:0%
+reason why i'm in graduate school
+ 
+
+ align:start position:0%
+reason why i'm in graduate school
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+i want to make more money when i get out
+
+ align:start position:0%
+i want to make more money when i get out
+ 
+
+ align:start position:0%
+i want to make more money when i get out
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and they did something then they did
+
+ align:start position:0%
+and they did something then they did
+ 
+
+ align:start position:0%
+and they did something then they did
+something it sounds like actually i
+
+ align:start position:0%
+something it sounds like actually i
+ 
+
+ align:start position:0%
+something it sounds like actually i
+understand that plato got his method of
+
+ align:start position:0%
+understand that plato got his method of
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+
+ align:start position:0%
+understand that plato got his method of
+ends and means from watching
+
+ align:start position:0%
+ends and means from watching
+ 
+
+ align:start position:0%
+ends and means from watching
+mothers uh quiz children
+
+ align:start position:0%
+mothers uh quiz children
+ 
+
+ align:start position:0%
+mothers uh quiz children
+i know as watching children quiz their
+
+ align:start position:0%
+i know as watching children quiz their
+ 
+
+ align:start position:0%
+i know as watching children quiz their
+mothers
+
+ align:start position:0%
+mothers
+ 
+
+ align:start position:0%
+mothers
+because a child at the right age i think
+
+ align:start position:0%
+because a child at the right age i think
+ 
+
+ align:start position:0%
+because a child at the right age i think
+it's about three
+
+ align:start position:0%
+it's about three
+ 
+
+ align:start position:0%
+it's about three
+when you tell them to do something
+
+ align:start position:0%
+when you tell them to do something
+ 
+
+ align:start position:0%
+when you tell them to do something
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+
+ align:start position:0%
+they'll say why
+ 
+
+ align:start position:0%
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+then when you tell them why guess what
+
+ align:start position:0%
+then when you tell them why guess what
+ 
+
+ align:start position:0%
+then when you tell them why guess what
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+ align:start position:0%
+they'll say why
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+
+ align:start position:0%
+they'll say why
+okay
+
+ align:start position:0%
+okay
+ 
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+ align:start position:0%
+okay
+because
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+ align:start position:0%
+because
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+ align:start position:0%
+because
+and what what plato would do is it ask
+
+ align:start position:0%
+and what what plato would do is it ask
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+
+ align:start position:0%
+and what what plato would do is it ask
+you something and then you say then you
+
+ align:start position:0%
+you something and then you say then you
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+you something and then you say then you
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+
+ align:start position:0%
+give an answer then they say why didn't
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+
+ align:start position:0%
+give an answer then they say why didn't
+you give another answer
+
+ align:start position:0%
+you give another answer
+ 
+
+ align:start position:0%
+you give another answer
+and he would keep asking why until you
+
+ align:start position:0%
+and he would keep asking why until you
+ 
+
+ align:start position:0%
+and he would keep asking why until you
+stop giving
+
+ align:start position:0%
+stop giving
+ 
+
+ align:start position:0%
+stop giving
+new answers
+
+ align:start position:0%
+new answers
+ 
+
+ align:start position:0%
+new answers
+that last answer is what they called an
+
+ align:start position:0%
+that last answer is what they called an
+ 
+
+ align:start position:0%
+that last answer is what they called an
+end the rest of it was means to ends
+
+ align:start position:0%
+end the rest of it was means to ends
+ 
+
+ align:start position:0%
+end the rest of it was means to ends
+it's a theory called teleology
+
+ align:start position:0%
+it's a theory called teleology
+ 
+
+ align:start position:0%
+it's a theory called teleology
+i'd like for you to know this word
+
+ align:start position:0%
+i'd like for you to know this word
+ 
+
+ align:start position:0%
+i'd like for you to know this word
+i'd like for you to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in your homework assignment
+
+ align:start position:0%
+in your homework assignment
+ 
+
+ align:start position:0%
+in your homework assignment
+study of ends and means
+
+ align:start position:0%
+study of ends and means
+ 
+
+ align:start position:0%
+study of ends and means
+so what they what they came back from
+
+ align:start position:0%
+so what they what they came back from
+ 
+
+ align:start position:0%
+so what they what they came back from
+the field with was two things number one
+
+ align:start position:0%
+the field with was two things number one
+ 
+
+ align:start position:0%
+the field with was two things number one
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+that the it now listen to me carefully
+
+ align:start position:0%
+that the it now listen to me carefully
+ 
+
+ align:start position:0%
+that the it now listen to me carefully
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
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+
+ align:start position:0%
+you're to get this kind of language when
+ 
+
+ align:start position:0%
+you're to get this kind of language when
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+
+ align:start position:0%
+you read philosophies
+ 
+
+ align:start position:0%
+you read philosophies
+the end of life
+
+ align:start position:0%
+the end of life
+ 
+
+ align:start position:0%
+the end of life
+is happiness not the end meaning death
+
+ align:start position:0%
+is happiness not the end meaning death
+ 
+
+ align:start position:0%
+is happiness not the end meaning death
+but the end
+
+ align:start position:0%
+but the end
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+
+ align:start position:0%
+but the end
+meaning
+
+ align:start position:0%
+meaning
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+
+ align:start position:0%
+meaning
+in relationship to means okay when you
+
+ align:start position:0%
+in relationship to means okay when you
+ 
+
+ align:start position:0%
+in relationship to means okay when you
+ask people why are they living
+
+ align:start position:0%
+ask people why are they living
+ 
+
+ align:start position:0%
+ask people why are they living
+and what are they how do they make their
+
+ align:start position:0%
+and what are they how do they make their
+ 
+
+ align:start position:0%
+and what are they how do they make their
+decisions
+
+ align:start position:0%
+decisions
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+ align:start position:0%
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+they came up with in the end
+
+ align:start position:0%
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+
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+
+ align:start position:0%
+when you got down to the end when
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+
+ align:start position:0%
+when you got down to the end when
+they've asked you why and you after a
+
+ align:start position:0%
+they've asked you why and you after a
+ 
+
+ align:start position:0%
+they've asked you why and you after a
+while you just keep saying the same
+
+ align:start position:0%
+while you just keep saying the same
+ 
+
+ align:start position:0%
+while you just keep saying the same
+thing over and over again in the end
+
+ align:start position:0%
+thing over and over again in the end
+ 
+
+ align:start position:0%
+thing over and over again in the end
+they said it was pleasure as opposed to
+
+ align:start position:0%
+they said it was pleasure as opposed to
+ 
+
+ align:start position:0%
+they said it was pleasure as opposed to
+pain
+
+ align:start position:0%
+pain
+ 
+
+ align:start position:0%
+pain
+it was happiness
+
+ align:start position:0%
+it was happiness
+ 
+
+ align:start position:0%
+it was happiness
+as opposed to unhappiness
+
+ align:start position:0%
+as opposed to unhappiness
+ 
+
+ align:start position:0%
+as opposed to unhappiness
+well down to that
+
+ align:start position:0%
+well down to that
+ 
+
+ align:start position:0%
+well down to that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+then they ask them
+
+ align:start position:0%
+then they ask them
+ 
+
+ align:start position:0%
+then they ask them
+well what are the kinds of things out
+
+ align:start position:0%
+well what are the kinds of things out
+ 
+
+ align:start position:0%
+well what are the kinds of things out
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+in the world that you think are good
+
+ align:start position:0%
+in the world that you think are good
+ 
+
+ align:start position:0%
+in the world that you think are good
+and which are things that you think are
+
+ align:start position:0%
+and which are things that you think are
+ 
+
+ align:start position:0%
+and which are things that you think are
+bad
+
+ align:start position:0%
+bad
+ 
+
+ align:start position:0%
+bad
+which are the things that you think are
+
+ align:start position:0%
+which are the things that you think are
+ 
+
+ align:start position:0%
+which are the things that you think are
+moral which are the things that you
+
+ align:start position:0%
+moral which are the things that you
+ 
+
+ align:start position:0%
+moral which are the things that you
+think are
+
+ align:start position:0%
+think are
+ 
+
+ align:start position:0%
+think are
+immoral they just ask people
+
+ align:start position:0%
+immoral they just ask people
+ 
+
+ align:start position:0%
+immoral they just ask people
+and there was a collection of things
+
+ align:start position:0%
+and there was a collection of things
+ 
+
+ align:start position:0%
+and there was a collection of things
+that most people sort of sort of agreed
+
+ align:start position:0%
+that most people sort of sort of agreed
+ 
+
+ align:start position:0%
+that most people sort of sort of agreed
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+uh it's wrong to murder somebody just
+
+ align:start position:0%
+uh it's wrong to murder somebody just
+ 
+
+ align:start position:0%
+uh it's wrong to murder somebody just
+because i feel okay things like that
+
+ align:start position:0%
+because i feel okay things like that
+ 
+
+ align:start position:0%
+because i feel okay things like that
+then they came back and they said
+
+ align:start position:0%
+then they came back and they said
+ 
+
+ align:start position:0%
+then they came back and they said
+which of
+
+ align:start position:0%
+which of
+ 
+
+ align:start position:0%
+which of
+uh how can i organize my life in terms
+
+ align:start position:0%
+uh how can i organize my life in terms
+ 
+
+ align:start position:0%
+uh how can i organize my life in terms
+of ends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that respect those morals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the answer was
+
+ align:start position:0%
+and the answer was
+ 
+
+ align:start position:0%
+and the answer was
+act
+
+ align:start position:0%
+act
+ 
+
+ align:start position:0%
+act
+in such a way that i not only
+
+ align:start position:0%
+in such a way that i not only
+ 
+
+ align:start position:0%
+in such a way that i not only
+try to maximize my own happiness
+
+ align:start position:0%
+try to maximize my own happiness
+ 
+
+ align:start position:0%
+try to maximize my own happiness
+but maximize the happiness among all the
+
+ align:start position:0%
+but maximize the happiness among all the
+ 
+
+ align:start position:0%
+but maximize the happiness among all the
+affected parties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of my actions all the parties affected
+
+ align:start position:0%
+of my actions all the parties affected
+ 
+
+ align:start position:0%
+of my actions all the parties affected
+by my action
+
+ align:start position:0%
+by my action
+ 
+
+ align:start position:0%
+by my action
+okay let's pause for a second let's try
+
+ align:start position:0%
+okay let's pause for a second let's try
+ 
+
+ align:start position:0%
+okay let's pause for a second let's try
+to interrogate this idea i mean sorry i
+
+ align:start position:0%
+to interrogate this idea i mean sorry i
+ 
+
+ align:start position:0%
+to interrogate this idea i mean sorry i
+don't i'm sorry i didn't want to say
+
+ align:start position:0%
+don't i'm sorry i didn't want to say
+ 
+
+ align:start position:0%
+don't i'm sorry i didn't want to say
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+it is an idea but let's
+
+ align:start position:0%
+it is an idea but let's
+ 
+
+ align:start position:0%
+it is an idea but let's
+let's interrogate utilitarian
+
+ align:start position:0%
+let's interrogate utilitarian
+ 
+
+ align:start position:0%
+let's interrogate utilitarian
+utilitarianism a little bit
+
+ align:start position:0%
+utilitarianism a little bit
+ 
+
+ align:start position:0%
+utilitarianism a little bit
+let's interrogate all that
+
+ align:start position:0%
+let's interrogate all that
+ 
+
+ align:start position:0%
+let's interrogate all that
+i'll play the game but i want you to get
+
+ align:start position:0%
+i'll play the game but i want you to get
+ 
+
+ align:start position:0%
+i'll play the game but i want you to get
+into it at your own leisure and i want
+
+ align:start position:0%
+into it at your own leisure and i want
+ 
+
+ align:start position:0%
+into it at your own leisure and i want
+you all to be a little bit more
+
+ align:start position:0%
+you all to be a little bit more
+ 
+
+ align:start position:0%
+you all to be a little bit more
+aggressive
+
+ align:start position:0%
+aggressive
+ 
+
+ align:start position:0%
+aggressive
+about getting into these conversations
+
+ align:start position:0%
+about getting into these conversations
+ 
+
+ align:start position:0%
+about getting into these conversations
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+not necessarily the day but as you go to
+
+ align:start position:0%
+not necessarily the day but as you go to
+ 
+
+ align:start position:0%
+not necessarily the day but as you go to
+particularly taking credit okay
+
+ align:start position:0%
+particularly taking credit okay
+ 
+
+ align:start position:0%
+particularly taking credit okay
+and this is where you really want to
+
+ align:start position:0%
+and this is where you really want to
+ 
+
+ align:start position:0%
+and this is where you really want to
+interrogate this thing okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want to start out with what i think is
+
+ align:start position:0%
+i want to start out with what i think is
+ 
+
+ align:start position:0%
+i want to start out with what i think is
+the hard question the hardest question
+
+ align:start position:0%
+the hard question the hardest question
+ 
+
+ align:start position:0%
+the hard question the hardest question
+why should i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximize your happiness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there are two ways to answer that
+
+ align:start position:0%
+now there are two ways to answer that
+ 
+
+ align:start position:0%
+now there are two ways to answer that
+question what you think is a good answer
+
+ align:start position:0%
+question what you think is a good answer
+ 
+
+ align:start position:0%
+question what you think is a good answer
+to the question
+
+ align:start position:0%
+to the question
+ 
+
+ align:start position:0%
+to the question
+or what you think that
+
+ align:start position:0%
+or what you think that
+ 
+
+ align:start position:0%
+or what you think that
+a utilitarian would say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm really interested in last one
+
+ align:start position:0%
+i'm really interested in last one
+ 
+
+ align:start position:0%
+i'm really interested in last one
+you understood yeah i'm not i'm not
+
+ align:start position:0%
+you understood yeah i'm not i'm not
+ 
+
+ align:start position:0%
+you understood yeah i'm not i'm not
+that's not a that's not a uh
+
+ align:start position:0%
+that's not a that's not a uh
+ 
+
+ align:start position:0%
+that's not a that's not a uh
+historical question
+
+ align:start position:0%
+historical question
+ 
+
+ align:start position:0%
+historical question
+why should i care about your health why
+
+ align:start position:0%
+why should i care about your health why
+ 
+
+ align:start position:0%
+why should i care about your health why
+should i maximize the happiness of all
+
+ align:start position:0%
+should i maximize the happiness of all
+ 
+
+ align:start position:0%
+should i maximize the happiness of all
+the affected parties so the utilitarian
+
+ align:start position:0%
+the affected parties so the utilitarian
+ 
+
+ align:start position:0%
+the affected parties so the utilitarian
+would say
+
+ align:start position:0%
+would say
+ 
+
+ align:start position:0%
+would say
+i think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i should maximize other people's
+
+ align:start position:0%
+i should maximize other people's
+ 
+
+ align:start position:0%
+i should maximize other people's
+happiness because later on they will
+
+ align:start position:0%
+happiness because later on they will
+ 
+
+ align:start position:0%
+happiness because later on they will
+take action that affects me and if in
+
+ align:start position:0%
+take action that affects me and if in
+ 
+
+ align:start position:0%
+take action that affects me and if in
+the past i have made them happy then
+
+ align:start position:0%
+the past i have made them happy then
+ 
+
+ align:start position:0%
+the past i have made them happy then
+they will take action to make me that's
+
+ align:start position:0%
+they will take action to make me that's
+ 
+
+ align:start position:0%
+they will take action to make me that's
+a good utilitarian answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well then my my then i would say well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+is that really the first principle
+
+ align:start position:0%
+is that really the first principle
+ 
+
+ align:start position:0%
+is that really the first principle
+is it really the first principle
+
+ align:start position:0%
+is it really the first principle
+ 
+
+ align:start position:0%
+is it really the first principle
+maximizing the happiness of all affected
+
+ align:start position:0%
+maximizing the happiness of all affected
+ 
+
+ align:start position:0%
+maximizing the happiness of all affected
+persons when actually what you just said
+
+ align:start position:0%
+persons when actually what you just said
+ 
+
+ align:start position:0%
+persons when actually what you just said
+was the end is your own personal
+
+ align:start position:0%
+was the end is your own personal
+ 
+
+ align:start position:0%
+was the end is your own personal
+happiness
+
+ align:start position:0%
+happiness
+ 
+
+ align:start position:0%
+happiness
+why not say maximize my own personal
+
+ align:start position:0%
+why not say maximize my own personal
+ 
+
+ align:start position:0%
+why not say maximize my own personal
+happiness and then reason it out
+
+ align:start position:0%
+happiness and then reason it out
+ 
+
+ align:start position:0%
+happiness and then reason it out
+that in a society i cannot maximize my
+
+ align:start position:0%
+that in a society i cannot maximize my
+ 
+
+ align:start position:0%
+that in a society i cannot maximize my
+own personal happiness without trying to
+
+ align:start position:0%
+own personal happiness without trying to
+ 
+
+ align:start position:0%
+own personal happiness without trying to
+help maximize other people's happiness
+
+ align:start position:0%
+help maximize other people's happiness
+ 
+
+ align:start position:0%
+help maximize other people's happiness
+too that's not the end
+
+ align:start position:0%
+too that's not the end
+ 
+
+ align:start position:0%
+too that's not the end
+the end
+
+ align:start position:0%
+the end
+ 
+
+ align:start position:0%
+the end
+is your personal happiness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well then let's be bold maybe the
+
+ align:start position:0%
+okay well then let's be bold maybe the
+ 
+
+ align:start position:0%
+okay well then let's be bold maybe the
+utilitarians got it wrong hold on a
+
+ align:start position:0%
+utilitarians got it wrong hold on a
+ 
+
+ align:start position:0%
+utilitarians got it wrong hold on a
+minute
+
+ align:start position:0%
+minute
+ 
+
+ align:start position:0%
+minute
+i'll pass this around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all they do in this book is tear up
+
+ align:start position:0%
+all they do in this book is tear up
+ 
+
+ align:start position:0%
+all they do in this book is tear up
+utilitarians
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh let's tear it up answer my
+
+ align:start position:0%
+okay so uh let's tear it up answer my
+ 
+
+ align:start position:0%
+okay so uh let's tear it up answer my
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+maximizing the happiness of all the
+
+ align:start position:0%
+maximizing the happiness of all the
+ 
+
+ align:start position:0%
+maximizing the happiness of all the
+affected parties according to what you
+
+ align:start position:0%
+affected parties according to what you
+ 
+
+ align:start position:0%
+affected parties according to what you
+just said is not the end
+
+ align:start position:0%
+just said is not the end
+ 
+
+ align:start position:0%
+just said is not the end
+maximizing my own in other words there
+
+ align:start position:0%
+maximizing my own in other words there
+ 
+
+ align:start position:0%
+maximizing my own in other words there
+is a branch and a philosophy of ethics
+
+ align:start position:0%
+is a branch and a philosophy of ethics
+ 
+
+ align:start position:0%
+is a branch and a philosophy of ethics
+called hedonism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bentham was a hedonist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can we escape hedonism
+
+ align:start position:0%
+can we escape hedonism
+ 
+
+ align:start position:0%
+can we escape hedonism
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense to other utilitarianism and you
+
+ align:start position:0%
+sense to other utilitarianism and you
+ 
+
+ align:start position:0%
+sense to other utilitarianism and you
+can't just maximize your own happiness
+
+ align:start position:0%
+can't just maximize your own happiness
+ 
+
+ align:start position:0%
+can't just maximize your own happiness
+without worrying about others
+
+ align:start position:0%
+without worrying about others
+ 
+
+ align:start position:0%
+without worrying about others
+i agree but my problem is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my problem is
+
+ align:start position:0%
+my problem is
+ 
+
+ align:start position:0%
+my problem is
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the end of hedonism
+
+ align:start position:0%
+the end of hedonism
+ 
+
+ align:start position:0%
+the end of hedonism
+is not this maximization of everybody's
+
+ align:start position:0%
+is not this maximization of everybody's
+ 
+
+ align:start position:0%
+is not this maximization of everybody's
+happiness the end of
+
+ align:start position:0%
+happiness the end of
+ 
+
+ align:start position:0%
+happiness the end of
+hedonism is maximization of my happiness
+
+ align:start position:0%
+hedonism is maximization of my happiness
+ 
+
+ align:start position:0%
+hedonism is maximization of my happiness
+even though
+
+ align:start position:0%
+even though
+ 
+
+ align:start position:0%
+even though
+maximizing your happiness is a means
+
+ align:start position:0%
+maximizing your happiness is a means
+ 
+
+ align:start position:0%
+maximizing your happiness is a means
+to maximizing my happiness so why don't
+
+ align:start position:0%
+to maximizing my happiness so why don't
+ 
+
+ align:start position:0%
+to maximizing my happiness so why don't
+we just
+
+ align:start position:0%
+we just
+ 
+
+ align:start position:0%
+we just
+call a state of spain
+
+ align:start position:0%
+call a state of spain
+ 
+
+ align:start position:0%
+call a state of spain
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+he we don't want to be utilitarians we
+
+ align:start position:0%
+he we don't want to be utilitarians we
+ 
+
+ align:start position:0%
+he we don't want to be utilitarians we
+want to be hedonists
+
+ align:start position:0%
+want to be hedonists
+ 
+
+ align:start position:0%
+want to be hedonists
+and we want to maximize our own
+
+ align:start position:0%
+and we want to maximize our own
+ 
+
+ align:start position:0%
+and we want to maximize our own
+individual at the end of hedonism is to
+
+ align:start position:0%
+individual at the end of hedonism is to
+ 
+
+ align:start position:0%
+individual at the end of hedonism is to
+maximize our own individual
+
+ align:start position:0%
+maximize our own individual
+ 
+
+ align:start position:0%
+maximize our own individual
+pleasure or happiness and the smart
+
+ align:start position:0%
+pleasure or happiness and the smart
+ 
+
+ align:start position:0%
+pleasure or happiness and the smart
+thing to do is to help maximize others
+
+ align:start position:0%
+thing to do is to help maximize others
+ 
+
+ align:start position:0%
+thing to do is to help maximize others
+if we can do it why not just say that
+
+ align:start position:0%
+if we can do it why not just say that
+ 
+
+ align:start position:0%
+if we can do it why not just say that
+why don't we just come back and tell the
+
+ align:start position:0%
+why don't we just come back and tell the
+ 
+
+ align:start position:0%
+why don't we just come back and tell the
+lie we want to maximize everybody's
+
+ align:start position:0%
+lie we want to maximize everybody's
+ 
+
+ align:start position:0%
+lie we want to maximize everybody's
+happiness
+
+ align:start position:0%
+happiness
+ 
+
+ align:start position:0%
+happiness
+i've been in a
+
+ align:start position:0%
+i've been in a
+ 
+
+ align:start position:0%
+i've been in a
+devil's advocate
+
+ align:start position:0%
+devil's advocate
+ 
+
+ align:start position:0%
+devil's advocate
+maybe they got it wrong what if we place
+
+ align:start position:0%
+maybe they got it wrong what if we place
+ 
+
+ align:start position:0%
+maybe they got it wrong what if we place
+equal value
+
+ align:start position:0%
+equal value
+ 
+
+ align:start position:0%
+equal value
+on social order
+
+ align:start position:0%
+on social order
+ 
+
+ align:start position:0%
+on social order
+value on our own happiness and social
+
+ align:start position:0%
+value on our own happiness and social
+ 
+
+ align:start position:0%
+value on our own happiness and social
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+and so then
+
+ align:start position:0%
+and so then
+ 
+
+ align:start position:0%
+and so then
+you need
+
+ align:start position:0%
+you need
+ 
+
+ align:start position:0%
+you need
+everyone's happiness to be happening
+
+ align:start position:0%
+everyone's happiness to be happening
+ 
+
+ align:start position:0%
+everyone's happiness to be happening
+in order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+somebody saying something like that i
+
+ align:start position:0%
+somebody saying something like that i
+ 
+
+ align:start position:0%
+somebody saying something like that i
+can't remember who it was
+
+ align:start position:0%
+can't remember who it was
+ 
+
+ align:start position:0%
+can't remember who it was
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but if you said that
+
+ align:start position:0%
+but if you said that
+ 
+
+ align:start position:0%
+but if you said that
+the question would not be the question
+
+ align:start position:0%
+the question would not be the question
+ 
+
+ align:start position:0%
+the question would not be the question
+of reason the question would be compel
+
+ align:start position:0%
+of reason the question would be compel
+ 
+
+ align:start position:0%
+of reason the question would be compel
+compulsion
+
+ align:start position:0%
+compulsion
+ 
+
+ align:start position:0%
+compulsion
+how many people gonna buy that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you gotta give me an end i'm not gonna
+
+ align:start position:0%
+you gotta give me an end i'm not gonna
+ 
+
+ align:start position:0%
+you gotta give me an end i'm not gonna
+believe you got two independent
+
+ align:start position:0%
+believe you got two independent
+ 
+
+ align:start position:0%
+believe you got two independent
+equally valuable
+
+ align:start position:0%
+equally valuable
+ 
+
+ align:start position:0%
+equally valuable
+ends i'm just not going to believe it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fear
+
+ align:start position:0%
+fear
+ 
+
+ align:start position:0%
+fear
+faith
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+there is a certain amount of faith in
+
+ align:start position:0%
+there is a certain amount of faith in
+ 
+
+ align:start position:0%
+there is a certain amount of faith in
+all of this uh because there's this
+
+ align:start position:0%
+all of this uh because there's this
+ 
+
+ align:start position:0%
+all of this uh because there's this
+unwritten well it is written it is it is
+
+ align:start position:0%
+unwritten well it is written it is it is
+ 
+
+ align:start position:0%
+unwritten well it is written it is it is
+written and you have to read it when you
+
+ align:start position:0%
+written and you have to read it when you
+ 
+
+ align:start position:0%
+written and you have to read it when you
+read these uh people
+
+ align:start position:0%
+read these uh people
+ 
+
+ align:start position:0%
+read these uh people
+uh they will all say that what we're
+
+ align:start position:0%
+uh they will all say that what we're
+ 
+
+ align:start position:0%
+uh they will all say that what we're
+talking about applies to rational
+
+ align:start position:0%
+talking about applies to rational
+ 
+
+ align:start position:0%
+talking about applies to rational
+persons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+does not apply to children
+
+ align:start position:0%
+does not apply to children
+ 
+
+ align:start position:0%
+does not apply to children
+does not apply to schizophrenics
+
+ align:start position:0%
+does not apply to schizophrenics
+ 
+
+ align:start position:0%
+does not apply to schizophrenics
+but it doesn't apply to a whole lot of
+
+ align:start position:0%
+but it doesn't apply to a whole lot of
+ 
+
+ align:start position:0%
+but it doesn't apply to a whole lot of
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+people it doesn't apply to faith
+
+ align:start position:0%
+people it doesn't apply to faith
+ 
+
+ align:start position:0%
+people it doesn't apply to faith
+and it does not apply there's another
+
+ align:start position:0%
+and it does not apply there's another
+ 
+
+ align:start position:0%
+and it does not apply there's another
+category of person out here or a
+
+ align:start position:0%
+category of person out here or a
+ 
+
+ align:start position:0%
+category of person out here or a
+category
+
+ align:start position:0%
+category
+ 
+
+ align:start position:0%
+category
+that we all find ourselves in from time
+
+ align:start position:0%
+that we all find ourselves in from time
+ 
+
+ align:start position:0%
+that we all find ourselves in from time
+to time
+
+ align:start position:0%
+to time
+ 
+
+ align:start position:0%
+to time
+that's the category when we say i will
+
+ align:start position:0%
+that's the category when we say i will
+ 
+
+ align:start position:0%
+that's the category when we say i will
+allow my emotions to take charge of my
+
+ align:start position:0%
+allow my emotions to take charge of my
+ 
+
+ align:start position:0%
+allow my emotions to take charge of my
+reasons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you don't believe it is there a dance
+
+ align:start position:0%
+if you don't believe it is there a dance
+ 
+
+ align:start position:0%
+if you don't believe it is there a dance
+department here at mit
+
+ align:start position:0%
+department here at mit
+ 
+
+ align:start position:0%
+department here at mit
+is there a art department
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in architecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll find that uh
+
+ align:start position:0%
+you'll find that uh
+ 
+
+ align:start position:0%
+you'll find that uh
+there's something more important than
+
+ align:start position:0%
+there's something more important than
+ 
+
+ align:start position:0%
+there's something more important than
+faith and reason
+
+ align:start position:0%
+faith and reason
+ 
+
+ align:start position:0%
+faith and reason
+that's being able to anybody you know a
+
+ align:start position:0%
+that's being able to anybody you know a
+ 
+
+ align:start position:0%
+that's being able to anybody you know a
+frenchman
+
+ align:start position:0%
+frenchman
+ 
+
+ align:start position:0%
+frenchman
+a frenchman a frenchman
+
+ align:start position:0%
+a frenchman a frenchman
+ 
+
+ align:start position:0%
+a frenchman a frenchman
+a friend from france
+
+ align:start position:0%
+a friend from france
+ 
+
+ align:start position:0%
+a friend from france
+talk to a freshman see what they find
+
+ align:start position:0%
+talk to a freshman see what they find
+ 
+
+ align:start position:0%
+talk to a freshman see what they find
+out is the most important thing in life
+
+ align:start position:0%
+out is the most important thing in life
+ 
+
+ align:start position:0%
+out is the most important thing in life
+might not be reason might not be faith
+
+ align:start position:0%
+might not be reason might not be faith
+ 
+
+ align:start position:0%
+might not be reason might not be faith
+either
+
+ align:start position:0%
+either
+ 
+
+ align:start position:0%
+either
+it might be stuff that comes from your
+
+ align:start position:0%
+it might be stuff that comes from your
+ 
+
+ align:start position:0%
+it might be stuff that comes from your
+heart
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh a word that they will use from time
+
+ align:start position:0%
+uh a word that they will use from time
+ 
+
+ align:start position:0%
+uh a word that they will use from time
+to time that i don't like to use because
+
+ align:start position:0%
+to time that i don't like to use because
+ 
+
+ align:start position:0%
+to time that i don't like to use because
+it isn't strong enough
+
+ align:start position:0%
+it isn't strong enough
+ 
+
+ align:start position:0%
+it isn't strong enough
+uh is intuition
+
+ align:start position:0%
+uh is intuition
+ 
+
+ align:start position:0%
+uh is intuition
+but that's not really what it is
+
+ align:start position:0%
+but that's not really what it is
+ 
+
+ align:start position:0%
+but that's not really what it is
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+okay all right here's what i think that
+
+ align:start position:0%
+okay all right here's what i think that
+ 
+
+ align:start position:0%
+okay all right here's what i think that
+uh a
+
+ align:start position:0%
+uh a
+ 
+
+ align:start position:0%
+uh a
+utilitarian will say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+might have some compulsion
+
+ align:start position:0%
+might have some compulsion
+ 
+
+ align:start position:0%
+might have some compulsion
+uh i invite you to read more
+
+ align:start position:0%
+uh i invite you to read more
+ 
+
+ align:start position:0%
+uh i invite you to read more
+and to bring this up again and take me
+
+ align:start position:0%
+and to bring this up again and take me
+ 
+
+ align:start position:0%
+and to bring this up again and take me
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+in this okay but i think that a
+
+ align:start position:0%
+in this okay but i think that a
+ 
+
+ align:start position:0%
+in this okay but i think that a
+utilitarian will say well look
+
+ align:start position:0%
+utilitarian will say well look
+ 
+
+ align:start position:0%
+utilitarian will say well look
+i didn't make up this whole business of
+
+ align:start position:0%
+i didn't make up this whole business of
+ 
+
+ align:start position:0%
+i didn't make up this whole business of
+morals i went and asked you before i put
+
+ align:start position:0%
+morals i went and asked you before i put
+ 
+
+ align:start position:0%
+morals i went and asked you before i put
+this theory together
+
+ align:start position:0%
+this theory together
+ 
+
+ align:start position:0%
+this theory together
+you told me already what you thought was
+
+ align:start position:0%
+you told me already what you thought was
+ 
+
+ align:start position:0%
+you told me already what you thought was
+were morals and right and wrong all i'm
+
+ align:start position:0%
+were morals and right and wrong all i'm
+ 
+
+ align:start position:0%
+were morals and right and wrong all i'm
+doing is putting it into a logical
+
+ align:start position:0%
+doing is putting it into a logical
+ 
+
+ align:start position:0%
+doing is putting it into a logical
+irrational order
+
+ align:start position:0%
+irrational order
+ 
+
+ align:start position:0%
+irrational order
+so the utilitarian will blame you for
+
+ align:start position:0%
+so the utilitarian will blame you for
+ 
+
+ align:start position:0%
+so the utilitarian will blame you for
+the whole thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but what is the end
+
+ align:start position:0%
+but what is the end
+ 
+
+ align:start position:0%
+but what is the end
+that doesn't
+
+ align:start position:0%
+that doesn't
+ 
+
+ align:start position:0%
+that doesn't
+i'm not understanding how that solves
+
+ align:start position:0%
+i'm not understanding how that solves
+ 
+
+ align:start position:0%
+i'm not understanding how that solves
+the problem you pointed out right
+
+ align:start position:0%
+the problem you pointed out right
+ 
+
+ align:start position:0%
+the problem you pointed out right
+there's a i think the best way to
+
+ align:start position:0%
+there's a i think the best way to
+ 
+
+ align:start position:0%
+there's a i think the best way to
+explain that one is by uh
+
+ align:start position:0%
+explain that one is by uh
+ 
+
+ align:start position:0%
+explain that one is by uh
+a person uh
+
+ align:start position:0%
+a person uh
+ 
+
+ align:start position:0%
+a person uh
+named schopenhauer
+
+ align:start position:0%
+named schopenhauer
+ 
+
+ align:start position:0%
+named schopenhauer
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now schopenhauer tells a story
+
+ align:start position:0%
+now schopenhauer tells a story
+ 
+
+ align:start position:0%
+now schopenhauer tells a story
+schopenhauer says he's
+
+ align:start position:0%
+schopenhauer says he's
+ 
+
+ align:start position:0%
+schopenhauer says he's
+walking along one day
+
+ align:start position:0%
+walking along one day
+ 
+
+ align:start position:0%
+walking along one day
+uh and gets to a bridge
+
+ align:start position:0%
+uh and gets to a bridge
+ 
+
+ align:start position:0%
+uh and gets to a bridge
+and there's some other people on the
+
+ align:start position:0%
+and there's some other people on the
+ 
+
+ align:start position:0%
+and there's some other people on the
+bridge
+
+ align:start position:0%
+bridge
+ 
+
+ align:start position:0%
+bridge
+and one person gets up and decides to
+
+ align:start position:0%
+and one person gets up and decides to
+ 
+
+ align:start position:0%
+and one person gets up and decides to
+commit suicide and tries to jump off the
+
+ align:start position:0%
+commit suicide and tries to jump off the
+ 
+
+ align:start position:0%
+commit suicide and tries to jump off the
+bridge
+
+ align:start position:0%
+bridge
+ 
+
+ align:start position:0%
+bridge
+just as he gets uh gets off the bridge
+
+ align:start position:0%
+just as he gets uh gets off the bridge
+ 
+
+ align:start position:0%
+just as he gets uh gets off the bridge
+another person runs over and grabs him
+
+ align:start position:0%
+another person runs over and grabs him
+ 
+
+ align:start position:0%
+another person runs over and grabs him
+by the nape of the neck and holds
+
+ align:start position:0%
+by the nape of the neck and holds
+ 
+
+ align:start position:0%
+by the nape of the neck and holds
+and then everybody else pulls them all
+
+ align:start position:0%
+and then everybody else pulls them all
+ 
+
+ align:start position:0%
+and then everybody else pulls them all
+back in
+
+ align:start position:0%
+back in
+ 
+
+ align:start position:0%
+back in
+and chopin our asked the guy i said
+
+ align:start position:0%
+and chopin our asked the guy i said
+ 
+
+ align:start position:0%
+and chopin our asked the guy i said
+why did you do that why did you risk
+
+ align:start position:0%
+why did you do that why did you risk
+ 
+
+ align:start position:0%
+why did you do that why did you risk
+your life for this guy when
+
+ align:start position:0%
+your life for this guy when
+ 
+
+ align:start position:0%
+your life for this guy when
+you almost went over if we weren't here
+
+ align:start position:0%
+you almost went over if we weren't here
+ 
+
+ align:start position:0%
+you almost went over if we weren't here
+to pull you back you'd have gone too his
+
+ align:start position:0%
+to pull you back you'd have gone too his
+ 
+
+ align:start position:0%
+to pull you back you'd have gone too his
+answer was i could not live with myself
+
+ align:start position:0%
+answer was i could not live with myself
+ 
+
+ align:start position:0%
+answer was i could not live with myself
+if i hadn't tried
+
+ align:start position:0%
+if i hadn't tried
+ 
+
+ align:start position:0%
+if i hadn't tried
+so the point is very much like what you
+
+ align:start position:0%
+so the point is very much like what you
+ 
+
+ align:start position:0%
+so the point is very much like what you
+had said before some people cannot
+
+ align:start position:0%
+had said before some people cannot
+ 
+
+ align:start position:0%
+had said before some people cannot
+separate their individual cells from
+
+ align:start position:0%
+separate their individual cells from
+ 
+
+ align:start position:0%
+separate their individual cells from
+your individual self
+
+ align:start position:0%
+your individual self
+ 
+
+ align:start position:0%
+your individual self
+better stated better stated some people
+
+ align:start position:0%
+better stated better stated some people
+ 
+
+ align:start position:0%
+better stated better stated some people
+cannot separate their feelings of
+
+ align:start position:0%
+cannot separate their feelings of
+ 
+
+ align:start position:0%
+cannot separate their feelings of
+pain and happiness from your feelings as
+
+ align:start position:0%
+pain and happiness from your feelings as
+ 
+
+ align:start position:0%
+pain and happiness from your feelings as
+pain it happens i'm sitting here uh
+
+ align:start position:0%
+pain it happens i'm sitting here uh
+ 
+
+ align:start position:0%
+pain it happens i'm sitting here uh
+eating a hamburger feeling good you're
+
+ align:start position:0%
+eating a hamburger feeling good you're
+ 
+
+ align:start position:0%
+eating a hamburger feeling good you're
+sitting there starving i can't enjoy my
+
+ align:start position:0%
+sitting there starving i can't enjoy my
+ 
+
+ align:start position:0%
+sitting there starving i can't enjoy my
+hamburger
+
+ align:start position:0%
+hamburger
+ 
+
+ align:start position:0%
+hamburger
+so it is some people just do not see
+
+ align:start position:0%
+so it is some people just do not see
+ 
+
+ align:start position:0%
+so it is some people just do not see
+that there is a difference between your
+
+ align:start position:0%
+that there is a difference between your
+ 
+
+ align:start position:0%
+that there is a difference between your
+pain and their own
+
+ align:start position:0%
+pain and their own
+ 
+
+ align:start position:0%
+pain and their own
+it's called empathy
+
+ align:start position:0%
+it's called empathy
+ 
+
+ align:start position:0%
+it's called empathy
+and other things well then you say well
+
+ align:start position:0%
+and other things well then you say well
+ 
+
+ align:start position:0%
+and other things well then you say well
+what about people who are not empathetic
+
+ align:start position:0%
+what about people who are not empathetic
+ 
+
+ align:start position:0%
+what about people who are not empathetic
+now here's what i think a good bentham
+
+ align:start position:0%
+now here's what i think a good bentham
+ 
+
+ align:start position:0%
+now here's what i think a good bentham
+utilitarian would say
+
+ align:start position:0%
+utilitarian would say
+ 
+
+ align:start position:0%
+utilitarian would say
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+this is only the starting point for laws
+
+ align:start position:0%
+this is only the starting point for laws
+ 
+
+ align:start position:0%
+this is only the starting point for laws
+we're going to force you to be this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the whole point for him was to get
+
+ align:start position:0%
+okay the whole point for him was to get
+ 
+
+ align:start position:0%
+okay the whole point for him was to get
+a good sound basis for
+
+ align:start position:0%
+a good sound basis for
+ 
+
+ align:start position:0%
+a good sound basis for
+law that was enforceable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i really think
+
+ align:start position:0%
+and i really think
+ 
+
+ align:start position:0%
+and i really think
+that a utilitarian
+
+ align:start position:0%
+that a utilitarian
+ 
+
+ align:start position:0%
+that a utilitarian
+who doesn't see it that way is going to
+
+ align:start position:0%
+who doesn't see it that way is going to
+ 
+
+ align:start position:0%
+who doesn't see it that way is going to
+offer you an argument that you won't
+
+ align:start position:0%
+offer you an argument that you won't
+ 
+
+ align:start position:0%
+offer you an argument that you won't
+find compelling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's let's let's go back across the
+
+ align:start position:0%
+now let's let's let's go back across the
+ 
+
+ align:start position:0%
+now let's let's let's go back across the
+wall
+
+ align:start position:0%
+wall
+ 
+
+ align:start position:0%
+wall
+uh there was a man who wrote his
+
+ align:start position:0%
+uh there was a man who wrote his
+ 
+
+ align:start position:0%
+uh there was a man who wrote his
+kant wrote his most important piece
+
+ align:start position:0%
+kant wrote his most important piece
+ 
+
+ align:start position:0%
+kant wrote his most important piece
+and if i got it right 17
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around 1776 i was going to say 1780.
+
+ align:start position:0%
+around 1776 i was going to say 1780.
+ 
+
+ align:start position:0%
+around 1776 i was going to say 1780.
+but yeah which one
+
+ align:start position:0%
+but yeah which one
+ 
+
+ align:start position:0%
+but yeah which one
+critique
+
+ align:start position:0%
+critique
+ 
+
+ align:start position:0%
+critique
+so we're talking about the same period
+
+ align:start position:0%
+so we're talking about the same period
+ 
+
+ align:start position:0%
+so we're talking about the same period
+of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a lot of things were going on
+
+ align:start position:0%
+so a lot of things were going on
+ 
+
+ align:start position:0%
+so a lot of things were going on
+intellectually in these times
+
+ align:start position:0%
+intellectually in these times
+ 
+
+ align:start position:0%
+intellectually in these times
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now we're going to go over to
+
+ align:start position:0%
+so now we're going to go over to
+ 
+
+ align:start position:0%
+so now we're going to go over to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i'm going to call it germania
+
+ align:start position:0%
+i'm going to call it germania
+ 
+
+ align:start position:0%
+i'm going to call it germania
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and we're going to go to a little town
+
+ align:start position:0%
+and we're going to go to a little town
+ 
+
+ align:start position:0%
+and we're going to go to a little town
+called krona's cronie kronigsberg
+
+ align:start position:0%
+called krona's cronie kronigsberg
+ 
+
+ align:start position:0%
+called krona's cronie kronigsberg
+i get that right cronig's bird
+
+ align:start position:0%
+i get that right cronig's bird
+ 
+
+ align:start position:0%
+i get that right cronig's bird
+the o has the um lot on top of
+
+ align:start position:0%
+the o has the um lot on top of
+ 
+
+ align:start position:0%
+the o has the um lot on top of
+know you're german you tell me how to
+
+ align:start position:0%
+know you're german you tell me how to
+ 
+
+ align:start position:0%
+know you're german you tell me how to
+pronounce it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and it's a small college town and
+
+ align:start position:0%
+and it's a small college town and
+ 
+
+ align:start position:0%
+and it's a small college town and
+there's a man named man there named
+
+ align:start position:0%
+there's a man named man there named
+ 
+
+ align:start position:0%
+there's a man named man there named
+emmanuel kant
+
+ align:start position:0%
+emmanuel kant
+ 
+
+ align:start position:0%
+emmanuel kant
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+emmanuel kant uh
+
+ align:start position:0%
+emmanuel kant uh
+ 
+
+ align:start position:0%
+emmanuel kant uh
+in his whole life has never left that
+
+ align:start position:0%
+in his whole life has never left that
+ 
+
+ align:start position:0%
+in his whole life has never left that
+little town
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he's going to talk about the nature of
+
+ align:start position:0%
+he's going to talk about the nature of
+ 
+
+ align:start position:0%
+he's going to talk about the nature of
+humanity but he's never left that little
+
+ align:start position:0%
+humanity but he's never left that little
+ 
+
+ align:start position:0%
+humanity but he's never left that little
+town
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+emmanuel kant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+now here's what i think helps me see
+
+ align:start position:0%
+now here's what i think helps me see
+ 
+
+ align:start position:0%
+now here's what i think helps me see
+what emmanuel kant says
+
+ align:start position:0%
+what emmanuel kant says
+ 
+
+ align:start position:0%
+what emmanuel kant says
+may not help you but try to see it
+
+ align:start position:0%
+may not help you but try to see it
+ 
+
+ align:start position:0%
+may not help you but try to see it
+through my eyes first
+
+ align:start position:0%
+through my eyes first
+ 
+
+ align:start position:0%
+through my eyes first
+then tear it up
+
+ align:start position:0%
+then tear it up
+ 
+
+ align:start position:0%
+then tear it up
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+emanuel kahn was first and foremost a
+
+ align:start position:0%
+emanuel kahn was first and foremost a
+ 
+
+ align:start position:0%
+emanuel kahn was first and foremost a
+professor
+
+ align:start position:0%
+professor
+ 
+
+ align:start position:0%
+professor
+of logic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he was a logician
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+he looks at this
+
+ align:start position:0%
+he looks at this
+ 
+
+ align:start position:0%
+he looks at this
+question of teleology about why people
+
+ align:start position:0%
+question of teleology about why people
+ 
+
+ align:start position:0%
+question of teleology about why people
+act in certain ways
+
+ align:start position:0%
+act in certain ways
+ 
+
+ align:start position:0%
+act in certain ways
+and he can find he says that he's just
+
+ align:start position:0%
+and he can find he says that he's just
+ 
+
+ align:start position:0%
+and he can find he says that he's just
+looked at the universe of what everybody
+
+ align:start position:0%
+looked at the universe of what everybody
+ 
+
+ align:start position:0%
+looked at the universe of what everybody
+says about ends and means and he can
+
+ align:start position:0%
+says about ends and means and he can
+ 
+
+ align:start position:0%
+says about ends and means and he can
+find only one end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that human beings are capable of
+
+ align:start position:0%
+that human beings are capable of
+ 
+
+ align:start position:0%
+that human beings are capable of
+and he says that human beings
+
+ align:start position:0%
+and he says that human beings
+ 
+
+ align:start position:0%
+and he says that human beings
+remember that uh
+
+ align:start position:0%
+remember that uh
+ 
+
+ align:start position:0%
+remember that uh
+piece i had up here
+
+ align:start position:0%
+piece i had up here
+ 
+
+ align:start position:0%
+piece i had up here
+about the gothic
+
+ align:start position:0%
+about the gothic
+ 
+
+ align:start position:0%
+about the gothic
+religion
+
+ align:start position:0%
+religion
+ 
+
+ align:start position:0%
+religion
+he says that every human being
+
+ align:start position:0%
+he says that every human being
+ 
+
+ align:start position:0%
+he says that every human being
+has the capacity
+
+ align:start position:0%
+has the capacity
+ 
+
+ align:start position:0%
+has the capacity
+hi
+
+ align:start position:0%
+hi
+ 
+
+ align:start position:0%
+hi
+we ought to hear five of
+
+ align:start position:0%
+we ought to hear five of
+ 
+
+ align:start position:0%
+we ought to hear five of
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+i have a class yeah okay so we're out of
+
+ align:start position:0%
+i have a class yeah okay so we're out of
+ 
+
+ align:start position:0%
+i have a class yeah okay so we're out of
+here five of them
+
+ align:start position:0%
+here five of them
+ 
+
+ align:start position:0%
+here five of them
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+emmanuel khan says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+every person has the will
+
+ align:start position:0%
+every person has the will
+ 
+
+ align:start position:0%
+every person has the will
+the capability called the will
+
+ align:start position:0%
+the capability called the will
+ 
+
+ align:start position:0%
+the capability called the will
+to do to act
+
+ align:start position:0%
+to do to act
+ 
+
+ align:start position:0%
+to do to act
+and he says now you understand this you
+
+ align:start position:0%
+and he says now you understand this you
+ 
+
+ align:start position:0%
+and he says now you understand this you
+have to understand this
+
+ align:start position:0%
+have to understand this
+ 
+
+ align:start position:0%
+have to understand this
+that that will
+
+ align:start position:0%
+that that will
+ 
+
+ align:start position:0%
+that that will
+is not
+
+ align:start position:0%
+is not
+ 
+
+ align:start position:0%
+is not
+the effect of any other cause
+
+ align:start position:0%
+the effect of any other cause
+ 
+
+ align:start position:0%
+the effect of any other cause
+nobody else
+
+ align:start position:0%
+nobody else
+ 
+
+ align:start position:0%
+nobody else
+including god
+
+ align:start position:0%
+including god
+ 
+
+ align:start position:0%
+including god
+gave you that will
+
+ align:start position:0%
+gave you that will
+ 
+
+ align:start position:0%
+gave you that will
+that was yours
+
+ align:start position:0%
+that was yours
+ 
+
+ align:start position:0%
+that was yours
+that's the end
+
+ align:start position:0%
+that's the end
+ 
+
+ align:start position:0%
+that's the end
+so he says now let's see if we can build
+
+ align:start position:0%
+so he says now let's see if we can build
+ 
+
+ align:start position:0%
+so he says now let's see if we can build
+up an ethical system based on the will
+
+ align:start position:0%
+up an ethical system based on the will
+ 
+
+ align:start position:0%
+up an ethical system based on the will
+notice the will is in the mind
+
+ align:start position:0%
+notice the will is in the mind
+ 
+
+ align:start position:0%
+notice the will is in the mind
+i'm not going out here to make any tests
+
+ align:start position:0%
+i'm not going out here to make any tests
+ 
+
+ align:start position:0%
+i'm not going out here to make any tests
+i've never left this little village
+
+ align:start position:0%
+i've never left this little village
+ 
+
+ align:start position:0%
+i've never left this little village
+not village a little town little college
+
+ align:start position:0%
+not village a little town little college
+ 
+
+ align:start position:0%
+not village a little town little college
+town i don't have to leave i don't have
+
+ align:start position:0%
+town i don't have to leave i don't have
+ 
+
+ align:start position:0%
+town i don't have to leave i don't have
+to get my clipboard and ask anybody
+
+ align:start position:0%
+to get my clipboard and ask anybody
+ 
+
+ align:start position:0%
+to get my clipboard and ask anybody
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+because if it's in my mind it's in yours
+
+ align:start position:0%
+because if it's in my mind it's in yours
+ 
+
+ align:start position:0%
+because if it's in my mind it's in yours
+that i can talk about the mind as a
+
+ align:start position:0%
+that i can talk about the mind as a
+ 
+
+ align:start position:0%
+that i can talk about the mind as a
+universe okay i shouldn't use that word
+
+ align:start position:0%
+universe okay i shouldn't use that word
+ 
+
+ align:start position:0%
+universe okay i shouldn't use that word
+over here okay so he says what about the
+
+ align:start position:0%
+over here okay so he says what about the
+ 
+
+ align:start position:0%
+over here okay so he says what about the
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+all right i have the will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to act this way or that way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he's a logician
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he's looking for first principles
+
+ align:start position:0%
+and he's looking for first principles
+ 
+
+ align:start position:0%
+and he's looking for first principles
+like a mathematician would look for
+
+ align:start position:0%
+like a mathematician would look for
+ 
+
+ align:start position:0%
+like a mathematician would look for
+axioms
+
+ align:start position:0%
+axioms
+ 
+
+ align:start position:0%
+axioms
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+he says
+
+ align:start position:0%
+he says
+ 
+
+ align:start position:0%
+he says
+if i have the will
+
+ align:start position:0%
+if i have the will
+ 
+
+ align:start position:0%
+if i have the will
+to act this way or that way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i act
+
+ align:start position:0%
+i act
+ 
+
+ align:start position:0%
+i act
+this way but then i don't act that way
+
+ align:start position:0%
+this way but then i don't act that way
+ 
+
+ align:start position:0%
+this way but then i don't act that way
+why is it that i make this choice
+
+ align:start position:0%
+why is it that i make this choice
+ 
+
+ align:start position:0%
+why is it that i make this choice
+instead of that
+
+ align:start position:0%
+instead of that
+ 
+
+ align:start position:0%
+instead of that
+okay so it's free will
+
+ align:start position:0%
+okay so it's free will
+ 
+
+ align:start position:0%
+okay so it's free will
+but a logician is asking why did i make
+
+ align:start position:0%
+but a logician is asking why did i make
+ 
+
+ align:start position:0%
+but a logician is asking why did i make
+this choice
+
+ align:start position:0%
+this choice
+ 
+
+ align:start position:0%
+this choice
+instead of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then he does something that
+
+ align:start position:0%
+and then he does something that
+ 
+
+ align:start position:0%
+and then he does something that
+lets you know how deep he's trying to
+
+ align:start position:0%
+lets you know how deep he's trying to
+ 
+
+ align:start position:0%
+lets you know how deep he's trying to
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+he's saying i have the will
+
+ align:start position:0%
+he's saying i have the will
+ 
+
+ align:start position:0%
+he's saying i have the will
+to hold out this piece of chalk and drop
+
+ align:start position:0%
+to hold out this piece of chalk and drop
+ 
+
+ align:start position:0%
+to hold out this piece of chalk and drop
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+after that piece of chalk after i let
+
+ align:start position:0%
+after that piece of chalk after i let
+ 
+
+ align:start position:0%
+after that piece of chalk after i let
+that piece of truck
+
+ align:start position:0%
+that piece of truck
+ 
+
+ align:start position:0%
+that piece of truck
+chalk drop
+
+ align:start position:0%
+chalk drop
+ 
+
+ align:start position:0%
+chalk drop
+that piece of chalk it is subject to
+
+ align:start position:0%
+that piece of chalk it is subject to
+ 
+
+ align:start position:0%
+that piece of chalk it is subject to
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+to some laws of nature
+
+ align:start position:0%
+to some laws of nature
+ 
+
+ align:start position:0%
+to some laws of nature
+law of gravitation that govern what
+
+ align:start position:0%
+law of gravitation that govern what
+ 
+
+ align:start position:0%
+law of gravitation that govern what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+while my i was acting upon my will
+
+ align:start position:0%
+while my i was acting upon my will
+ 
+
+ align:start position:0%
+while my i was acting upon my will
+my will has some laws
+
+ align:start position:0%
+my will has some laws
+ 
+
+ align:start position:0%
+my will has some laws
+but i invent those laws
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somebody else invented
+
+ align:start position:0%
+somebody else invented
+ 
+
+ align:start position:0%
+somebody else invented
+law of gravitation
+
+ align:start position:0%
+law of gravitation
+ 
+
+ align:start position:0%
+law of gravitation
+but i invent the laws by which i will
+
+ align:start position:0%
+but i invent the laws by which i will
+ 
+
+ align:start position:0%
+but i invent the laws by which i will
+choose to do this instead of doing that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which laws what laws shall i adopt
+
+ align:start position:0%
+which laws what laws shall i adopt
+ 
+
+ align:start position:0%
+which laws what laws shall i adopt
+then he asks one more question and gets
+
+ align:start position:0%
+then he asks one more question and gets
+ 
+
+ align:start position:0%
+then he asks one more question and gets
+to the final part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i i want some basic laws i want the
+
+ align:start position:0%
+well i i want some basic laws i want the
+ 
+
+ align:start position:0%
+well i i want some basic laws i want the
+fundamental laws i want something that's
+
+ align:start position:0%
+fundamental laws i want something that's
+ 
+
+ align:start position:0%
+fundamental laws i want something that's
+on the level of an axiom in mathematics
+
+ align:start position:0%
+on the level of an axiom in mathematics
+ 
+
+ align:start position:0%
+on the level of an axiom in mathematics
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what he says is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what he says is
+
+ align:start position:0%
+what he says is
+ 
+
+ align:start position:0%
+what he says is
+see if i can put it in these in the
+
+ align:start position:0%
+see if i can put it in these in the
+ 
+
+ align:start position:0%
+see if i can put it in these in the
+right words because
+
+ align:start position:0%
+right words because
+ 
+
+ align:start position:0%
+right words because
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this has to be done right
+
+ align:start position:0%
+this has to be done right
+ 
+
+ align:start position:0%
+this has to be done right
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what he says is that i want some laws
+
+ align:start position:0%
+what he says is that i want some laws
+ 
+
+ align:start position:0%
+what he says is that i want some laws
+that tell me
+
+ align:start position:0%
+that tell me
+ 
+
+ align:start position:0%
+that tell me
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+i should
+
+ align:start position:0%
+i should
+ 
+
+ align:start position:0%
+i should
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+or tell me what i should not do
+
+ align:start position:0%
+or tell me what i should not do
+ 
+
+ align:start position:0%
+or tell me what i should not do
+i'm going to call these imperatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here's the subtlety about
+
+ align:start position:0%
+now here's the subtlety about
+ 
+
+ align:start position:0%
+now here's the subtlety about
+these imperatives
+
+ align:start position:0%
+these imperatives
+ 
+
+ align:start position:0%
+these imperatives
+now listen to me careful this is a
+
+ align:start position:0%
+now listen to me careful this is a
+ 
+
+ align:start position:0%
+now listen to me careful this is a
+subtlety i think it's a subtlety because
+
+ align:start position:0%
+subtlety i think it's a subtlety because
+ 
+
+ align:start position:0%
+subtlety i think it's a subtlety because
+philosophers tend to take it for granted
+
+ align:start position:0%
+philosophers tend to take it for granted
+ 
+
+ align:start position:0%
+philosophers tend to take it for granted
+i think it's the difference between life
+
+ align:start position:0%
+i think it's the difference between life
+ 
+
+ align:start position:0%
+i think it's the difference between life
+and death death for us in the class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an imperative is something that you
+
+ align:start position:0%
+an imperative is something that you
+ 
+
+ align:start position:0%
+an imperative is something that you
+should do
+
+ align:start position:0%
+should do
+ 
+
+ align:start position:0%
+should do
+all of the time
+
+ align:start position:0%
+all of the time
+ 
+
+ align:start position:0%
+all of the time
+not when the situation arises that's
+
+ align:start position:0%
+not when the situation arises that's
+ 
+
+ align:start position:0%
+not when the situation arises that's
+empirical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you should never lie
+
+ align:start position:0%
+you should never lie
+ 
+
+ align:start position:0%
+you should never lie
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+wait till the occasion comes you should
+
+ align:start position:0%
+wait till the occasion comes you should
+ 
+
+ align:start position:0%
+wait till the occasion comes you should
+what can i write down as an imperative
+
+ align:start position:0%
+what can i write down as an imperative
+ 
+
+ align:start position:0%
+what can i write down as an imperative
+that i should always do
+
+ align:start position:0%
+that i should always do
+ 
+
+ align:start position:0%
+that i should always do
+or that i should never do
+
+ align:start position:0%
+or that i should never do
+ 
+
+ align:start position:0%
+or that i should never do
+that's an imperative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i should treat
+
+ align:start position:0%
+if i should treat
+ 
+
+ align:start position:0%
+if i should treat
+if i should try to maximize
+
+ align:start position:0%
+if i should try to maximize
+ 
+
+ align:start position:0%
+if i should try to maximize
+your happiness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order that we all maximize our habits
+
+ align:start position:0%
+in order that we all maximize our habits
+ 
+
+ align:start position:0%
+in order that we all maximize our habits
+then emmanuel khan is going to say well
+
+ align:start position:0%
+then emmanuel khan is going to say well
+ 
+
+ align:start position:0%
+then emmanuel khan is going to say well
+that's an empirical test that lasts for
+
+ align:start position:0%
+that's an empirical test that lasts for
+ 
+
+ align:start position:0%
+that's an empirical test that lasts for
+that particular instance that's not a
+
+ align:start position:0%
+that particular instance that's not a
+ 
+
+ align:start position:0%
+that particular instance that's not a
+general you can't that's not a general
+
+ align:start position:0%
+general you can't that's not a general
+ 
+
+ align:start position:0%
+general you can't that's not a general
+principle of of of the will
+
+ align:start position:0%
+principle of of of the will
+ 
+
+ align:start position:0%
+principle of of of the will
+what is a general principle of the will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he's a logician
+
+ align:start position:0%
+he's a logician
+ 
+
+ align:start position:0%
+he's a logician
+his logic
+
+ align:start position:0%
+his logic
+ 
+
+ align:start position:0%
+his logic
+what can i do here's the way he would
+
+ align:start position:0%
+what can i do here's the way he would
+ 
+
+ align:start position:0%
+what can i do here's the way he would
+like his way emmanuel kant would say why
+
+ align:start position:0%
+like his way emmanuel kant would say why
+ 
+
+ align:start position:0%
+like his way emmanuel kant would say why
+you should never lie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why should you no no i got a battle
+
+ align:start position:0%
+why should you no no i got a battle
+ 
+
+ align:start position:0%
+why should you no no i got a battle
+steal why should you never steal why
+
+ align:start position:0%
+steal why should you never steal why
+ 
+
+ align:start position:0%
+steal why should you never steal why
+should god i better stay why should you
+
+ align:start position:0%
+should god i better stay why should you
+ 
+
+ align:start position:0%
+should god i better stay why should you
+never steal
+
+ align:start position:0%
+never steal
+ 
+
+ align:start position:0%
+never steal
+why should i always act so that i never
+
+ align:start position:0%
+why should i always act so that i never
+ 
+
+ align:start position:0%
+why should i always act so that i never
+steal
+
+ align:start position:0%
+steal
+ 
+
+ align:start position:0%
+steal
+every day
+
+ align:start position:0%
+every day
+ 
+
+ align:start position:0%
+every day
+all the time
+
+ align:start position:0%
+all the time
+ 
+
+ align:start position:0%
+all the time
+now here's the way kant would argue that
+
+ align:start position:0%
+now here's the way kant would argue that
+ 
+
+ align:start position:0%
+now here's the way kant would argue that
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+got nothing to do with whether or not it
+
+ align:start position:0%
+got nothing to do with whether or not it
+ 
+
+ align:start position:0%
+got nothing to do with whether or not it
+makes other people mad
+
+ align:start position:0%
+makes other people mad
+ 
+
+ align:start position:0%
+makes other people mad
+and whether or not they're gonna hurt me
+
+ align:start position:0%
+and whether or not they're gonna hurt me
+ 
+
+ align:start position:0%
+and whether or not they're gonna hurt me
+so that i will not maximize my pleasure
+
+ align:start position:0%
+so that i will not maximize my pleasure
+ 
+
+ align:start position:0%
+so that i will not maximize my pleasure
+he's a logician
+
+ align:start position:0%
+he's a logician
+ 
+
+ align:start position:0%
+he's a logician
+kant will say that stealing
+
+ align:start position:0%
+kant will say that stealing
+ 
+
+ align:start position:0%
+kant will say that stealing
+implies property
+
+ align:start position:0%
+implies property
+ 
+
+ align:start position:0%
+implies property
+and if i steal all of your property and
+
+ align:start position:0%
+and if i steal all of your property and
+ 
+
+ align:start position:0%
+and if i steal all of your property and
+all of your property and all your
+
+ align:start position:0%
+all of your property and all your
+ 
+
+ align:start position:0%
+all of your property and all your
+property and all your property and all
+
+ align:start position:0%
+property and all your property and all
+ 
+
+ align:start position:0%
+property and all your property and all
+your property the time will come when i
+
+ align:start position:0%
+your property the time will come when i
+ 
+
+ align:start position:0%
+your property the time will come when i
+cannot act
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that i will uh steal
+
+ align:start position:0%
+that i will uh steal
+ 
+
+ align:start position:0%
+that i will uh steal
+because there's nothing for me to steal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i say that i can see how he's let me
+
+ align:start position:0%
+if i say that i can see how he's let me
+ 
+
+ align:start position:0%
+if i say that i can see how he's let me
+say that again can you say it better
+
+ align:start position:0%
+say that again can you say it better
+ 
+
+ align:start position:0%
+say that again can you say it better
+so you're saying the choice is the
+
+ align:start position:0%
+so you're saying the choice is the
+ 
+
+ align:start position:0%
+so you're saying the choice is the
+imperative is either you should not
+
+ align:start position:0%
+imperative is either you should not
+ 
+
+ align:start position:0%
+imperative is either you should not
+steal all the time or you shouldn't
+
+ align:start position:0%
+steal all the time or you shouldn't
+ 
+
+ align:start position:0%
+steal all the time or you shouldn't
+steal all the time right and if you go
+
+ align:start position:0%
+steal all the time right and if you go
+ 
+
+ align:start position:0%
+steal all the time right and if you go
+with you should steal all the time
+
+ align:start position:0%
+with you should steal all the time
+ 
+
+ align:start position:0%
+with you should steal all the time
+when you can never do that anymore
+
+ align:start position:0%
+when you can never do that anymore
+ 
+
+ align:start position:0%
+when you can never do that anymore
+logically but if you go with you should
+
+ align:start position:0%
+logically but if you go with you should
+ 
+
+ align:start position:0%
+logically but if you go with you should
+not steal
+
+ align:start position:0%
+not steal
+ 
+
+ align:start position:0%
+not steal
+for the for one's entire life right it
+
+ align:start position:0%
+for the for one's entire life right it
+ 
+
+ align:start position:0%
+for the for one's entire life right it
+is always possible it's always possible
+
+ align:start position:0%
+is always possible it's always possible
+ 
+
+ align:start position:0%
+is always possible it's always possible
+not to steal
+
+ align:start position:0%
+not to steal
+ 
+
+ align:start position:0%
+not to steal
+logically okay logically meaning from
+
+ align:start position:0%
+logically okay logically meaning from
+ 
+
+ align:start position:0%
+logically okay logically meaning from
+the branch
+
+ align:start position:0%
+the branch
+ 
+
+ align:start position:0%
+the branch
+of learn the learned discipline called
+
+ align:start position:0%
+of learn the learned discipline called
+ 
+
+ align:start position:0%
+of learn the learned discipline called
+logic
+
+ align:start position:0%
+logic
+ 
+
+ align:start position:0%
+logic
+okay not in terms of something genetic
+
+ align:start position:0%
+okay not in terms of something genetic
+ 
+
+ align:start position:0%
+okay not in terms of something genetic
+that we call reasoning out of the brain
+
+ align:start position:0%
+that we call reasoning out of the brain
+ 
+
+ align:start position:0%
+that we call reasoning out of the brain
+and people can come up with i'm talking
+
+ align:start position:0%
+and people can come up with i'm talking
+ 
+
+ align:start position:0%
+and people can come up with i'm talking
+about opening a book that has logic on
+
+ align:start position:0%
+about opening a book that has logic on
+ 
+
+ align:start position:0%
+about opening a book that has logic on
+the in the title
+
+ align:start position:0%
+the in the title
+ 
+
+ align:start position:0%
+the in the title
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right he's a logician
+
+ align:start position:0%
+all right he's a logician
+ 
+
+ align:start position:0%
+all right he's a logician
+so a lot so he is going to say that the
+
+ align:start position:0%
+so a lot so he is going to say that the
+ 
+
+ align:start position:0%
+so a lot so he is going to say that the
+fundamental principles
+
+ align:start position:0%
+fundamental principles
+ 
+
+ align:start position:0%
+fundamental principles
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+principles of logic
+
+ align:start position:0%
+principles of logic
+ 
+
+ align:start position:0%
+principles of logic
+and then he's going to say
+
+ align:start position:0%
+and then he's going to say
+ 
+
+ align:start position:0%
+and then he's going to say
+that everybody should reason that way
+
+ align:start position:0%
+that everybody should reason that way
+ 
+
+ align:start position:0%
+that everybody should reason that way
+look at logic now
+
+ align:start position:0%
+look at logic now
+ 
+
+ align:start position:0%
+look at logic now
+logic is not going to give you some
+
+ align:start position:0%
+logic is not going to give you some
+ 
+
+ align:start position:0%
+logic is not going to give you some
+alternatives not all that's not always
+
+ align:start position:0%
+alternatives not all that's not always
+ 
+
+ align:start position:0%
+alternatives not all that's not always
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+but the basic ideas that he's talking
+
+ align:start position:0%
+but the basic ideas that he's talking
+ 
+
+ align:start position:0%
+but the basic ideas that he's talking
+about when it comes to imperatives
+
+ align:start position:0%
+about when it comes to imperatives
+ 
+
+ align:start position:0%
+about when it comes to imperatives
+is always true
+
+ align:start position:0%
+is always true
+ 
+
+ align:start position:0%
+is always true
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what he is trying to do is give you
+
+ align:start position:0%
+so what he is trying to do is give you
+ 
+
+ align:start position:0%
+so what he is trying to do is give you
+some imperatives the kind of imperative
+
+ align:start position:0%
+some imperatives the kind of imperative
+ 
+
+ align:start position:0%
+some imperatives the kind of imperative
+where i said
+
+ align:start position:0%
+where i said
+ 
+
+ align:start position:0%
+where i said
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+do x because
+
+ align:start position:0%
+do x because
+ 
+
+ align:start position:0%
+do x because
+uh y will help maximize your pleasure
+
+ align:start position:0%
+uh y will help maximize your pleasure
+ 
+
+ align:start position:0%
+uh y will help maximize your pleasure
+he's going to call that a hypothetical
+
+ align:start position:0%
+he's going to call that a hypothetical
+ 
+
+ align:start position:0%
+he's going to call that a hypothetical
+imperative
+
+ align:start position:0%
+imperative
+ 
+
+ align:start position:0%
+imperative
+never lie he's going to call that guess
+
+ align:start position:0%
+never lie he's going to call that guess
+ 
+
+ align:start position:0%
+never lie he's going to call that guess
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+categorical imperative
+
+ align:start position:0%
+categorical imperative
+ 
+
+ align:start position:0%
+categorical imperative
+i want you to know those terms
+
+ align:start position:0%
+i want you to know those terms
+ 
+
+ align:start position:0%
+i want you to know those terms
+the categorical imperative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he's going to build up a system of
+
+ align:start position:0%
+so he's going to build up a system of
+ 
+
+ align:start position:0%
+so he's going to build up a system of
+logic
+
+ align:start position:0%
+logic
+ 
+
+ align:start position:0%
+logic
+based on the equivalence of axioms
+
+ align:start position:0%
+based on the equivalence of axioms
+ 
+
+ align:start position:0%
+based on the equivalence of axioms
+called these categorical imperatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that those imperatives are
+
+ align:start position:0%
+and that those imperatives are
+ 
+
+ align:start position:0%
+and that those imperatives are
+imperative upon you all of the time
+
+ align:start position:0%
+imperative upon you all of the time
+ 
+
+ align:start position:0%
+imperative upon you all of the time
+by reason of logic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right my last piece on this is
+
+ align:start position:0%
+right my last piece on this is
+ 
+
+ align:start position:0%
+right my last piece on this is
+the same question uh belligerent
+
+ align:start position:0%
+the same question uh belligerent
+ 
+
+ align:start position:0%
+the same question uh belligerent
+question i asked of the utilitarian
+
+ align:start position:0%
+question i asked of the utilitarian
+ 
+
+ align:start position:0%
+question i asked of the utilitarian
+why should i
+
+ align:start position:0%
+why should i
+ 
+
+ align:start position:0%
+why should i
+maximize your
+
+ align:start position:0%
+maximize your
+ 
+
+ align:start position:0%
+maximize your
+happiness
+
+ align:start position:0%
+happiness
+ 
+
+ align:start position:0%
+happiness
+or the happiness of all of the affected
+
+ align:start position:0%
+or the happiness of all of the affected
+ 
+
+ align:start position:0%
+or the happiness of all of the affected
+parties i'm going to ask kant
+
+ align:start position:0%
+parties i'm going to ask kant
+ 
+
+ align:start position:0%
+parties i'm going to ask kant
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+why should i be logical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll tell you what khan is going to say
+
+ align:start position:0%
+i'll tell you what khan is going to say
+ 
+
+ align:start position:0%
+i'll tell you what khan is going to say
+khan is going to go all the way back to
+
+ align:start position:0%
+khan is going to go all the way back to
+ 
+
+ align:start position:0%
+khan is going to go all the way back to
+the stoics now for me those were the
+
+ align:start position:0%
+the stoics now for me those were the
+ 
+
+ align:start position:0%
+the stoics now for me those were the
+real philosophers
+
+ align:start position:0%
+real philosophers
+ 
+
+ align:start position:0%
+real philosophers
+the stoics
+
+ align:start position:0%
+the stoics
+ 
+
+ align:start position:0%
+the stoics
+not because their ideas were any good
+
+ align:start position:0%
+not because their ideas were any good
+ 
+
+ align:start position:0%
+not because their ideas were any good
+but because
+
+ align:start position:0%
+but because
+ 
+
+ align:start position:0%
+but because
+they did not eat
+
+ align:start position:0%
+they did not eat
+ 
+
+ align:start position:0%
+they did not eat
+unless they stood up
+
+ align:start position:0%
+unless they stood up
+ 
+
+ align:start position:0%
+unless they stood up
+in a crowd and debated a point
+
+ align:start position:0%
+in a crowd and debated a point
+ 
+
+ align:start position:0%
+in a crowd and debated a point
+and if they won the crowd will give them
+
+ align:start position:0%
+and if they won the crowd will give them
+ 
+
+ align:start position:0%
+and if they won the crowd will give them
+some money that's the only way they can
+
+ align:start position:0%
+some money that's the only way they can
+ 
+
+ align:start position:0%
+some money that's the only way they can
+feed themselves
+
+ align:start position:0%
+feed themselves
+ 
+
+ align:start position:0%
+feed themselves
+so that's from real philosophy
+
+ align:start position:0%
+so that's from real philosophy
+ 
+
+ align:start position:0%
+so that's from real philosophy
+where you say you say joel that's all
+
+ align:start position:0%
+where you say you say joel that's all
+ 
+
+ align:start position:0%
+where you say you say joel that's all
+well i mean to
+
+ align:start position:0%
+well i mean to
+ 
+
+ align:start position:0%
+well i mean to
+convince people that's that's a
+
+ align:start position:0%
+convince people that's that's a
+ 
+
+ align:start position:0%
+convince people that's that's a
+politician's job
+
+ align:start position:0%
+politician's job
+ 
+
+ align:start position:0%
+politician's job
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so uh there was this story about this uh
+
+ align:start position:0%
+so uh there was this story about this uh
+ 
+
+ align:start position:0%
+so uh there was this story about this uh
+stoic
+
+ align:start position:0%
+stoic
+ 
+
+ align:start position:0%
+stoic
+talking about reason and logic
+
+ align:start position:0%
+talking about reason and logic
+ 
+
+ align:start position:0%
+talking about reason and logic
+and somebody in the crowd said wait a
+
+ align:start position:0%
+and somebody in the crowd said wait a
+ 
+
+ align:start position:0%
+and somebody in the crowd said wait a
+minute hold on hold on put his hands
+
+ align:start position:0%
+minute hold on hold on put his hands
+ 
+
+ align:start position:0%
+minute hold on hold on put his hands
+folded his hands across his chest
+
+ align:start position:0%
+folded his hands across his chest
+ 
+
+ align:start position:0%
+folded his hands across his chest
+became very confident looked at that
+
+ align:start position:0%
+became very confident looked at that
+ 
+
+ align:start position:0%
+became very confident looked at that
+philosopher and said
+
+ align:start position:0%
+philosopher and said
+ 
+
+ align:start position:0%
+philosopher and said
+why should i be logical
+
+ align:start position:0%
+why should i be logical
+ 
+
+ align:start position:0%
+why should i be logical
+and the philosopher said
+
+ align:start position:0%
+and the philosopher said
+ 
+
+ align:start position:0%
+and the philosopher said
+do you want a logical answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the answer was yes
+
+ align:start position:0%
+the answer was yes
+ 
+
+ align:start position:0%
+the answer was yes
+the basic idea was
+
+ align:start position:0%
+the basic idea was
+ 
+
+ align:start position:0%
+the basic idea was
+you should be logical because you compel
+
+ align:start position:0%
+you should be logical because you compel
+ 
+
+ align:start position:0%
+you should be logical because you compel
+me to be logical
+
+ align:start position:0%
+me to be logical
+ 
+
+ align:start position:0%
+me to be logical
+you're going to compel all of us to be
+
+ align:start position:0%
+you're going to compel all of us to be
+ 
+
+ align:start position:0%
+you're going to compel all of us to be
+logical how you get to be so high and
+
+ align:start position:0%
+logical how you get to be so high and
+ 
+
+ align:start position:0%
+logical how you get to be so high and
+mighty that you can be the only one in
+
+ align:start position:0%
+mighty that you can be the only one in
+ 
+
+ align:start position:0%
+mighty that you can be the only one in
+here who's not logical
+
+ align:start position:0%
+here who's not logical
+ 
+
+ align:start position:0%
+here who's not logical
+okay so that's what he means when he
+
+ align:start position:0%
+okay so that's what he means when he
+ 
+
+ align:start position:0%
+okay so that's what he means when he
+says universal
+
+ align:start position:0%
+says universal
+ 
+
+ align:start position:0%
+says universal
+it's got to apply
+
+ align:start position:0%
+it's got to apply
+ 
+
+ align:start position:0%
+it's got to apply
+whatever you do has got to apply to
+
+ align:start position:0%
+whatever you do has got to apply to
+ 
+
+ align:start position:0%
+whatever you do has got to apply to
+everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you make these analyses
+
+ align:start position:0%
+so when you make these analyses
+ 
+
+ align:start position:0%
+so when you make these analyses
+and we
+
+ align:start position:0%
+and we
+ 
+
+ align:start position:0%
+and we
+of of the a7d case
+
+ align:start position:0%
+of of the a7d case
+ 
+
+ align:start position:0%
+of of the a7d case
+when you get to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deontological analysis
+
+ align:start position:0%
+deontological analysis
+ 
+
+ align:start position:0%
+deontological analysis
+don't give me anything that tests
+
+ align:start position:0%
+don't give me anything that tests
+ 
+
+ align:start position:0%
+don't give me anything that tests
+facts don't give me any
+
+ align:start position:0%
+facts don't give me any
+ 
+
+ align:start position:0%
+facts don't give me any
+tests based on facts
+
+ align:start position:0%
+tests based on facts
+ 
+
+ align:start position:0%
+tests based on facts
+try your best i i'm
+
+ align:start position:0%
+try your best i i'm
+ 
+
+ align:start position:0%
+try your best i i'm
+going to assume that you haven't had a
+
+ align:start position:0%
+going to assume that you haven't had a
+ 
+
+ align:start position:0%
+going to assume that you haven't had a
+formal course in logic
+
+ align:start position:0%
+formal course in logic
+ 
+
+ align:start position:0%
+formal course in logic
+that's okay
+
+ align:start position:0%
+that's okay
+ 
+
+ align:start position:0%
+that's okay
+at least give it a try
+
+ align:start position:0%
+at least give it a try
+ 
+
+ align:start position:0%
+at least give it a try
+go back and see if you can put this
+
+ align:start position:0%
+go back and see if you can put this
+ 
+
+ align:start position:0%
+go back and see if you can put this
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+in logical terms all right if you can't
+
+ align:start position:0%
+in logical terms all right if you can't
+ 
+
+ align:start position:0%
+in logical terms all right if you can't
+say so
+
+ align:start position:0%
+say so
+ 
+
+ align:start position:0%
+say so
+but say that kant would you don't know
+
+ align:start position:0%
+but say that kant would you don't know
+ 
+
+ align:start position:0%
+but say that kant would you don't know
+how that's what he would do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now since time is just i i
+
+ align:start position:0%
+all right now since time is just i i
+ 
+
+ align:start position:0%
+all right now since time is just i i
+calculated i got one more minute
+
+ align:start position:0%
+calculated i got one more minute
+ 
+
+ align:start position:0%
+calculated i got one more minute
+all right i promise to do something that
+
+ align:start position:0%
+all right i promise to do something that
+ 
+
+ align:start position:0%
+all right i promise to do something that
+i didn't do yet and that was put the
+
+ align:start position:0%
+i didn't do yet and that was put the
+ 
+
+ align:start position:0%
+i didn't do yet and that was put the
+grades
+
+ align:start position:0%
+grades
+ 
+
+ align:start position:0%
+grades
+uh and uh
+
+ align:start position:0%
+uh and uh
+ 
+
+ align:start position:0%
+uh and uh
+dr moses um
+
+ align:start position:0%
+dr moses um
+ 
+
+ align:start position:0%
+dr moses um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+presentation
+
+ align:start position:0%
+presentation
+ 
+
+ align:start position:0%
+presentation
+in the email okay i'm gonna do it today
+
+ align:start position:0%
+in the email okay i'm gonna do it today
+ 
+
+ align:start position:0%
+in the email okay i'm gonna do it today
+tomorrow gotta cover that
+
+ align:start position:0%
+tomorrow gotta cover that
+ 
+
+ align:start position:0%
+tomorrow gotta cover that
+and give me this homework on tuesday
+
+ align:start position:0%
+and give me this homework on tuesday
+ 
+
+ align:start position:0%
+and give me this homework on tuesday
+and then we'll start talking about some
+
+ align:start position:0%
+and then we'll start talking about some
+ 
+
+ align:start position:0%
+and then we'll start talking about some
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+some matters of the calendar
+
+ align:start position:0%
+some matters of the calendar
+ 
+
+ align:start position:0%
+some matters of the calendar
+when the test is coming up and all of
+
+ align:start position:0%
+when the test is coming up and all of
+ 
+
+ align:start position:0%
+when the test is coming up and all of
+that kind of stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+question maybe it's not quickly yeah in
+
+ align:start position:0%
+question maybe it's not quickly yeah in
+ 
+
+ align:start position:0%
+question maybe it's not quickly yeah in
+terms of the
+
+ align:start position:0%
+terms of the
+ 
+
+ align:start position:0%
+terms of the
+imperatives
+
+ align:start position:0%
+imperatives
+ 
+
+ align:start position:0%
+imperatives
+is there a difference between having an
+
+ align:start position:0%
+is there a difference between having an
+ 
+
+ align:start position:0%
+is there a difference between having an
+imperative and the ability to fulfill
+
+ align:start position:0%
+imperative and the ability to fulfill
+ 
+
+ align:start position:0%
+imperative and the ability to fulfill
+the impairment so for example if
+
+ align:start position:0%
+the impairment so for example if
+ 
+
+ align:start position:0%
+the impairment so for example if
+the imperative is i'm going to steal
+
+ align:start position:0%
+the imperative is i'm going to steal
+ 
+
+ align:start position:0%
+the imperative is i'm going to steal
+and i'm always going to steal
+
+ align:start position:0%
+and i'm always going to steal
+ 
+
+ align:start position:0%
+and i'm always going to steal
+and maybe there's some point in time
+
+ align:start position:0%
+and maybe there's some point in time
+ 
+
+ align:start position:0%
+and maybe there's some point in time
+when there's nothing not just you but i
+
+ align:start position:0%
+when there's nothing not just you but i
+ 
+
+ align:start position:0%
+when there's nothing not just you but i
+can still have the imperative that i'm
+
+ align:start position:0%
+can still have the imperative that i'm
+ 
+
+ align:start position:0%
+can still have the imperative that i'm
+gonna steal just that i can't fulfill it
+
+ align:start position:0%
+gonna steal just that i can't fulfill it
+ 
+
+ align:start position:0%
+gonna steal just that i can't fulfill it
+there's nothing left to steal until
+
+ align:start position:0%
+there's nothing left to steal until
+ 
+
+ align:start position:0%
+there's nothing left to steal until
+someone makes something and then i'll
+
+ align:start position:0%
+someone makes something and then i'll
+ 
+
+ align:start position:0%
+someone makes something and then i'll
+steal it right so is there a difference
+
+ align:start position:0%
+steal it right so is there a difference
+ 
+
+ align:start position:0%
+steal it right so is there a difference
+between just having a party with
+
+ align:start position:0%
+between just having a party with
+ 
+
+ align:start position:0%
+between just having a party with
+fulfillment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now uh i'm not going to answer
+
+ align:start position:0%
+right now uh i'm not going to answer
+ 
+
+ align:start position:0%
+right now uh i'm not going to answer
+your question directly
+
+ align:start position:0%
+your question directly
+ 
+
+ align:start position:0%
+your question directly
+because that presumes that there's uh
+
+ align:start position:0%
+because that presumes that there's uh
+ 
+
+ align:start position:0%
+because that presumes that there's uh
+that there's a unique answer to this to
+
+ align:start position:0%
+that there's a unique answer to this to
+ 
+
+ align:start position:0%
+that there's a unique answer to this to
+your question what i'm going to do is
+
+ align:start position:0%
+your question what i'm going to do is
+ 
+
+ align:start position:0%
+your question what i'm going to do is
+say but i think
+
+ align:start position:0%
+say but i think
+ 
+
+ align:start position:0%
+say but i think
+kant and other
+
+ align:start position:0%
+kant and other
+ 
+
+ align:start position:0%
+kant and other
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+logists will say
+
+ align:start position:0%
+logists will say
+ 
+
+ align:start position:0%
+logists will say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what they will say is that uh they're
+
+ align:start position:0%
+what they will say is that uh they're
+ 
+
+ align:start position:0%
+what they will say is that uh they're
+gonna assume
+
+ align:start position:0%
+gonna assume
+ 
+
+ align:start position:0%
+gonna assume
+that the will
+
+ align:start position:0%
+that the will
+ 
+
+ align:start position:0%
+that the will
+at first it's all powerful they're not
+
+ align:start position:0%
+at first it's all powerful they're not
+ 
+
+ align:start position:0%
+at first it's all powerful they're not
+going to limit that right now
+
+ align:start position:0%
+going to limit that right now
+ 
+
+ align:start position:0%
+going to limit that right now
+and say that you have the power to do
+
+ align:start position:0%
+and say that you have the power to do
+ 
+
+ align:start position:0%
+and say that you have the power to do
+these things the question is will you
+
+ align:start position:0%
+these things the question is will you
+ 
+
+ align:start position:0%
+these things the question is will you
+make the choice
+
+ align:start position:0%
+make the choice
+ 
+
+ align:start position:0%
+make the choice
+to do it
+
+ align:start position:0%
+to do it
+ 
+
+ align:start position:0%
+to do it
+so they're going to eliminate that eye
+
+ align:start position:0%
+so they're going to eliminate that eye
+ 
+
+ align:start position:0%
+so they're going to eliminate that eye
+priority i shouldn't sit up
+
+ align:start position:0%
+priority i shouldn't sit up
+ 
+
+ align:start position:0%
+priority i shouldn't sit up
+they're going to eliminate that before
+
+ align:start position:0%
+they're going to eliminate that before
+ 
+
+ align:start position:0%
+they're going to eliminate that before
+they get into the argument
+
+ align:start position:0%
+they get into the argument
+ 
+
+ align:start position:0%
+they get into the argument
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the rest of us are going to have to deal
+
+ align:start position:0%
+the rest of us are going to have to deal
+ 
+
+ align:start position:0%
+the rest of us are going to have to deal
+with that on a case-by-case basis
+
+ align:start position:0%
+with that on a case-by-case basis
+ 
+
+ align:start position:0%
+with that on a case-by-case basis
+and let's see how far you can make that
+
+ align:start position:0%
+and let's see how far you can make that
+ 
+
+ align:start position:0%
+and let's see how far you can make that
+argument and the question is can you
+
+ align:start position:0%
+argument and the question is can you
+ 
+
+ align:start position:0%
+argument and the question is can you
+make it compelling now just like dr
+
+ align:start position:0%
+make it compelling now just like dr
+ 
+
+ align:start position:0%
+make it compelling now just like dr
+mozambique we're talking at the
+
+ align:start position:0%
+mozambique we're talking at the
+ 
+
+ align:start position:0%
+mozambique we're talking at the
+beginning of the class
+
+ align:start position:0%
+beginning of the class
+ 
+
+ align:start position:0%
+beginning of the class
+you could probably make that case
+
+ align:start position:0%
+you could probably make that case
+ 
+
+ align:start position:0%
+you could probably make that case
+um i'm going to be
+
+ align:start position:0%
+um i'm going to be
+ 
+
+ align:start position:0%
+um i'm going to be
+you could probably you'll be you'll be
+
+ align:start position:0%
+you could probably you'll be you'll be
+ 
+
+ align:start position:0%
+you could probably you'll be you'll be
+more likely to make that case in germany
+
+ align:start position:0%
+more likely to make that case in germany
+ 
+
+ align:start position:0%
+more likely to make that case in germany
+than you would in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today even now the world is globalizing
+
+ align:start position:0%
+today even now the world is globalizing
+ 
+
+ align:start position:0%
+today even now the world is globalizing
+and it doesn't apply to everybody
+
+ align:start position:0%
+and it doesn't apply to everybody
+ 
+
+ align:start position:0%
+and it doesn't apply to everybody
+okay but it depends on who you're
+
+ align:start position:0%
+okay but it depends on who you're
+ 
+
+ align:start position:0%
+okay but it depends on who you're
+talking to there's some orientations
+
+ align:start position:0%
+talking to there's some orientations
+ 
+
+ align:start position:0%
+talking to there's some orientations
+that are going to seem more sensitive
+
+ align:start position:0%
+that are going to seem more sensitive
+ 
+
+ align:start position:0%
+that are going to seem more sensitive
+you're not going to make a utilitarian
+
+ align:start position:0%
+you're not going to make a utilitarian
+ 
+
+ align:start position:0%
+you're not going to make a utilitarian
+culture is not going to see any point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can have a brainstorming discussion
+
+ align:start position:0%
+we can have a brainstorming discussion
+ 
+
+ align:start position:0%
+we can have a brainstorming discussion
+next time we can devote most of the
+
+ align:start position:0%
+next time we can devote most of the
+ 
+
+ align:start position:0%
+next time we can devote most of the
+class to that i won't talk most of it
+
+ align:start position:0%
+class to that i won't talk most of it
+ 
+
+ align:start position:0%
+class to that i won't talk most of it
+how about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+thank you all very much
+
+ align:start position:0%
+thank you all very much
+ 
+
+ align:start position:0%
+thank you all very much
+you got something for me
+
+ align:start position:0%
+you got something for me
+ 
+
+ align:start position:0%
+you got something for me
+um i was just gonna ask if it would
+
+ align:start position:0%
+um i was just gonna ask if it would
+ 
+
+ align:start position:0%
+um i was just gonna ask if it would
+i know the first time we did a little
+
+ align:start position:0%
+i know the first time we did a little
+ 
+
+ align:start position:0%
+i know the first time we did a little
+paragraph about the a7d case we weren't
+
+ align:start position:0%
+paragraph about the a7d case we weren't
+ 
+
+ align:start position:0%
+paragraph about the a7d case we weren't
+supposed to like do a lot of reading or
+
+ align:start position:0%
+supposed to like do a lot of reading or
+ 
+
+ align:start position:0%
+supposed to like do a lot of reading or
+look at examples right is it okay to do
+
+ align:start position:0%
+look at examples right is it okay to do
+ 
+
+ align:start position:0%
+look at examples right is it okay to do
+that now like to use our book
+
+ align:start position:0%
+that now like to use our book
+ 
+
+ align:start position:0%
+that now like to use our book
+a lot of reading means use the book and
+
+ align:start position:0%
+a lot of reading means use the book and
+ 
+
+ align:start position:0%
+a lot of reading means use the book and
+use at least one other reference right
+
+ align:start position:0%
+use at least one other reference right
+ 
+
+ align:start position:0%
+use at least one other reference right
+okay that's all that means right now
+
+ align:start position:0%
+okay that's all that means right now
+ 
+
+ align:start position:0%
+okay that's all that means right now
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and it means chapter four okay that's
+
+ align:start position:0%
+and it means chapter four okay that's
+ 
+
+ align:start position:0%
+and it means chapter four okay that's
+all it means thanks
\ No newline at end of file
diff --git a/iqSMRO78UD0.txt b/iqSMRO78UD0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1fcfcf43f4b2350bad50d0aa4a0c1e685acd6a36
--- /dev/null
+++ b/iqSMRO78UD0.txt
@@ -0,0 +1,14851 @@
+align:start position:0%
+ 
+okay so let's start uh thank you
+
+ align:start position:0%
+okay so let's start uh thank you
+ 
+
+ align:start position:0%
+okay so let's start uh thank you
+everyone for coming uh this is going to
+
+ align:start position:0%
+everyone for coming uh this is going to
+ 
+
+ align:start position:0%
+everyone for coming uh this is going to
+be a advanced class on cryptography
+
+ align:start position:0%
+be a advanced class on cryptography
+ 
+
+ align:start position:0%
+be a advanced class on cryptography
+those who do not have background on
+
+ align:start position:0%
+those who do not have background on
+ 
+
+ align:start position:0%
+those who do not have background on
+cryptography it's okay it's not actually
+
+ align:start position:0%
+cryptography it's okay it's not actually
+ 
+
+ align:start position:0%
+cryptography it's okay it's not actually
+hardcore cryptography this is actually a
+
+ align:start position:0%
+hardcore cryptography this is actually a
+ 
+
+ align:start position:0%
+hardcore cryptography this is actually a
+class on the evolution of proofs in
+
+ align:start position:0%
+class on the evolution of proofs in
+ 
+
+ align:start position:0%
+class on the evolution of proofs in
+computer science so this class is really
+
+ align:start position:0%
+computer science so this class is really
+ 
+
+ align:start position:0%
+computer science so this class is really
+about proofs uh that's what we're going
+
+ align:start position:0%
+about proofs uh that's what we're going
+ 
+
+ align:start position:0%
+about proofs uh that's what we're going
+to learn and kind of how kind of proofs
+
+ align:start position:0%
+to learn and kind of how kind of proofs
+ 
+
+ align:start position:0%
+to learn and kind of how kind of proofs
+evolved with the years starting from
+
+ align:start position:0%
+evolved with the years starting from
+ 
+
+ align:start position:0%
+evolved with the years starting from
+kind of the 80s mid 80s all the way to
+
+ align:start position:0%
+kind of the 80s mid 80s all the way to
+ 
+
+ align:start position:0%
+kind of the 80s mid 80s all the way to
+today and how we think about proofs
+
+ align:start position:0%
+today and how we think about proofs
+ 
+
+ align:start position:0%
+today and how we think about proofs
+differently today so this is uh what
+
+ align:start position:0%
+differently today so this is uh what
+ 
+
+ align:start position:0%
+differently today so this is uh what
+this class is about actually before I I
+
+ align:start position:0%
+this class is about actually before I I
+ 
+
+ align:start position:0%
+this class is about actually before I I
+go into kind of the content of the class
+
+ align:start position:0%
+go into kind of the content of the class
+ 
+
+ align:start position:0%
+go into kind of the content of the class
+and what what I'm going to be teaching
+
+ align:start position:0%
+and what what I'm going to be teaching
+ 
+
+ align:start position:0%
+and what what I'm going to be teaching
+first of all quick question how many
+
+ align:start position:0%
+first of all quick question how many
+ 
+
+ align:start position:0%
+first of all quick question how many
+students here are not MIT students but
+
+ align:start position:0%
+students here are not MIT students but
+ 
+
+ align:start position:0%
+students here are not MIT students but
+cross register students okay h a bunch
+
+ align:start position:0%
+cross register students okay h a bunch
+ 
+
+ align:start position:0%
+cross register students okay h a bunch
+so you guys have access so I hope I made
+
+ align:start position:0%
+so you guys have access so I hope I made
+ 
+
+ align:start position:0%
+so you guys have access so I hope I made
+the the website public it's on canvas uh
+
+ align:start position:0%
+the the website public it's on canvas uh
+ 
+
+ align:start position:0%
+the the website public it's on canvas uh
+but now I think it should be public so
+
+ align:start position:0%
+but now I think it should be public so
+ 
+
+ align:start position:0%
+but now I think it should be public so
+uh you know you should have access if
+
+ align:start position:0%
+uh you know you should have access if
+ 
+
+ align:start position:0%
+uh you know you should have access if
+anyone has problems with accessing the
+
+ align:start position:0%
+anyone has problems with accessing the
+ 
+
+ align:start position:0%
+anyone has problems with accessing the
+website just let me know I'll try to fix
+
+ align:start position:0%
+website just let me know I'll try to fix
+ 
+
+ align:start position:0%
+website just let me know I'll try to fix
+it um so this class is meeting once a
+
+ align:start position:0%
+it um so this class is meeting once a
+ 
+
+ align:start position:0%
+it um so this class is meeting once a
+week weekly from 1: to 4: p.m. uh in
+
+ align:start position:0%
+week weekly from 1: to 4: p.m. uh in
+ 
+
+ align:start position:0%
+week weekly from 1: to 4: p.m. uh in
+terms of expectations or what uh so you
+
+ align:start position:0%
+terms of expectations or what uh so you
+ 
+
+ align:start position:0%
+terms of expectations or what uh so you
+know the expectations that you'll enjoy
+
+ align:start position:0%
+know the expectations that you'll enjoy
+ 
+
+ align:start position:0%
+know the expectations that you'll enjoy
+it I hope you will I think it's really
+
+ align:start position:0%
+it I hope you will I think it's really
+ 
+
+ align:start position:0%
+it I hope you will I think it's really
+really beautiful material uh but beyond
+
+ align:start position:0%
+really beautiful material uh but beyond
+ 
+
+ align:start position:0%
+really beautiful material uh but beyond
+having fun uh I want to ask uh I have uh
+
+ align:start position:0%
+having fun uh I want to ask uh I have uh
+ 
+
+ align:start position:0%
+having fun uh I want to ask uh I have uh
+two uh kind of uh requirements from you
+
+ align:start position:0%
+two uh kind of uh requirements from you
+ 
+
+ align:start position:0%
+two uh kind of uh requirements from you
+guys so one I want to have scribe notes
+
+ align:start position:0%
+guys so one I want to have scribe notes
+ 
+
+ align:start position:0%
+guys so one I want to have scribe notes
+for the classes uh I I have written
+
+ align:start position:0%
+for the classes uh I I have written
+ 
+
+ align:start position:0%
+for the classes uh I I have written
+notes I can give it to you uh to help
+
+ align:start position:0%
+notes I can give it to you uh to help
+ 
+
+ align:start position:0%
+notes I can give it to you uh to help
+you out but uh so we have about actually
+
+ align:start position:0%
+you out but uh so we have about actually
+ 
+
+ align:start position:0%
+you out but uh so we have about actually
+we we have 11 classes total in in this
+
+ align:start position:0%
+we we have 11 classes total in in this
+ 
+
+ align:start position:0%
+we we have 11 classes total in in this
+class but uh we're going to have a bunch
+
+ align:start position:0%
+class but uh we're going to have a bunch
+ 
+
+ align:start position:0%
+class but uh we're going to have a bunch
+of uh like one one day we're going to
+
+ align:start position:0%
+of uh like one one day we're going to
+ 
+
+ align:start position:0%
+of uh like one one day we're going to
+have a guest lecture uh by odv who's in
+
+ align:start position:0%
+have a guest lecture uh by odv who's in
+ 
+
+ align:start position:0%
+have a guest lecture uh by odv who's in
+he has a beautiful result he's going to
+
+ align:start position:0%
+he has a beautiful result he's going to
+ 
+
+ align:start position:0%
+he has a beautiful result he's going to
+come here uh on October 6 and presented
+
+ align:start position:0%
+come here uh on October 6 and presented
+ 
+
+ align:start position:0%
+come here uh on October 6 and presented
+to us so uh we won't H that won't need
+
+ align:start position:0%
+to us so uh we won't H that won't need
+ 
+
+ align:start position:0%
+to us so uh we won't H that won't need
+to be described and then there one day
+
+ align:start position:0%
+to be described and then there one day
+ 
+
+ align:start position:0%
+to be described and then there one day
+there's a crypto day which also won't
+
+ align:start position:0%
+there's a crypto day which also won't
+ 
+
+ align:start position:0%
+there's a crypto day which also won't
+need to be described well uh there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more anybody wants to
+
+ align:start position:0%
+more anybody wants to
+ 
+
+ align:start position:0%
+more anybody wants to
+sit uh but for the rest we'll need
+
+ align:start position:0%
+sit uh but for the rest we'll need
+ 
+
+ align:start position:0%
+sit uh but for the rest we'll need
+scribe notes I'm happy if you want to do
+
+ align:start position:0%
+scribe notes I'm happy if you want to do
+ 
+
+ align:start position:0%
+scribe notes I'm happy if you want to do
+it in pairs uh to describe unless will
+
+ align:start position:0%
+it in pairs uh to describe unless will
+ 
+
+ align:start position:0%
+it in pairs uh to describe unless will
+run out of people and then we'll need to
+
+ align:start position:0%
+run out of people and then we'll need to
+ 
+
+ align:start position:0%
+run out of people and then we'll need to
+keep it for one uh so that's one
+
+ align:start position:0%
+keep it for one uh so that's one
+ 
+
+ align:start position:0%
+keep it for one uh so that's one
+requirement and then I was told that I
+
+ align:start position:0%
+requirement and then I was told that I
+ 
+
+ align:start position:0%
+requirement and then I was told that I
+need to do something more you know
+
+ align:start position:0%
+need to do something more you know
+ 
+
+ align:start position:0%
+need to do something more you know
+that's not enough so we'll do a p set
+
+ align:start position:0%
+that's not enough so we'll do a p set
+ 
+
+ align:start position:0%
+that's not enough so we'll do a p set
+sometime in the middle of the course
+
+ align:start position:0%
+sometime in the middle of the course
+ 
+
+ align:start position:0%
+sometime in the middle of the course
+okay uh it won't be anything too
+
+ align:start position:0%
+okay uh it won't be anything too
+ 
+
+ align:start position:0%
+okay uh it won't be anything too
+difficult it's mainly to make sure
+
+ align:start position:0%
+difficult it's mainly to make sure
+ 
+
+ align:start position:0%
+difficult it's mainly to make sure
+you're on board uh but I really do
+
+ align:start position:0%
+you're on board uh but I really do
+ 
+
+ align:start position:0%
+you're on board uh but I really do
+recommend that before class every time
+
+ align:start position:0%
+recommend that before class every time
+ 
+
+ align:start position:0%
+recommend that before class every time
+before so here's a real homework okay uh
+
+ align:start position:0%
+before so here's a real homework okay uh
+ 
+
+ align:start position:0%
+before so here's a real homework okay uh
+every time before you come to class in
+
+ align:start position:0%
+every time before you come to class in
+ 
+
+ align:start position:0%
+every time before you come to class in
+the website there's reading I really
+
+ align:start position:0%
+the website there's reading I really
+ 
+
+ align:start position:0%
+the website there's reading I really
+recommend you look at the reading and
+
+ align:start position:0%
+recommend you look at the reading and
+ 
+
+ align:start position:0%
+recommend you look at the reading and
+try to read I so there's beautiful uh
+
+ align:start position:0%
+try to read I so there's beautiful uh
+ 
+
+ align:start position:0%
+try to read I so there's beautiful uh
+survey by Justin Taylor uh there's a
+
+ align:start position:0%
+survey by Justin Taylor uh there's a
+ 
+
+ align:start position:0%
+survey by Justin Taylor uh there's a
+link uh on the website uh the survey is
+
+ align:start position:0%
+link uh on the website uh the survey is
+ 
+
+ align:start position:0%
+link uh on the website uh the survey is
+on proof system it's more of kind of the
+
+ align:start position:0%
+on proof system it's more of kind of the
+ 
+
+ align:start position:0%
+on proof system it's more of kind of the
+applied side of proof system this is a
+
+ align:start position:0%
+applied side of proof system this is a
+ 
+
+ align:start position:0%
+applied side of proof system this is a
+more Theory class but he does have
+
+ align:start position:0%
+more Theory class but he does have
+ 
+
+ align:start position:0%
+more Theory class but he does have
+really beautifully written sections that
+
+ align:start position:0%
+really beautifully written sections that
+ 
+
+ align:start position:0%
+really beautifully written sections that
+are very theoretical that I'm going to
+
+ align:start position:0%
+are very theoretical that I'm going to
+ 
+
+ align:start position:0%
+are very theoretical that I'm going to
+link to uh so I recommend or I you can
+
+ align:start position:0%
+link to uh so I recommend or I you can
+ 
+
+ align:start position:0%
+link to uh so I recommend or I you can
+think of it as informal homework before
+
+ align:start position:0%
+think of it as informal homework before
+ 
+
+ align:start position:0%
+think of it as informal homework before
+class to do the reading I think it will
+
+ align:start position:0%
+class to do the reading I think it will
+ 
+
+ align:start position:0%
+class to do the reading I think it will
+be very helpful to uh for understanding
+
+ align:start position:0%
+be very helpful to uh for understanding
+ 
+
+ align:start position:0%
+be very helpful to uh for understanding
+this class and also after the you know
+
+ align:start position:0%
+this class and also after the you know
+ 
+
+ align:start position:0%
+this class and also after the you know
+the lecture to look at the reading and I
+
+ align:start position:0%
+the lecture to look at the reading and I
+ 
+
+ align:start position:0%
+the lecture to look at the reading and I
+think it'll be very very
+
+ align:start position:0%
+think it'll be very very
+ 
+
+ align:start position:0%
+think it'll be very very
+helpful okay so uh any questions about
+
+ align:start position:0%
+helpful okay so uh any questions about
+ 
+
+ align:start position:0%
+helpful okay so uh any questions about
+bureaucracy
+
+ align:start position:0%
+bureaucracy
+ 
+
+ align:start position:0%
+bureaucracy
+stuff okay so let me tell you a little
+
+ align:start position:0%
+stuff okay so let me tell you a little
+ 
+
+ align:start position:0%
+stuff okay so let me tell you a little
+bit more about about what the class is
+
+ align:start position:0%
+bit more about about what the class is
+ 
+
+ align:start position:0%
+bit more about about what the class is
+actually about so you know proofs is
+
+ align:start position:0%
+actually about so you know proofs is
+ 
+
+ align:start position:0%
+actually about so you know proofs is
+something that has been studied in
+
+ align:start position:0%
+something that has been studied in
+ 
+
+ align:start position:0%
+something that has been studied in
+mathematics for thousands of years uh
+
+ align:start position:0%
+mathematics for thousands of years uh
+ 
+
+ align:start position:0%
+mathematics for thousands of years uh
+and usually when people think about what
+
+ align:start position:0%
+and usually when people think about what
+ 
+
+ align:start position:0%
+and usually when people think about what
+a proof is uh you know a proof you write
+
+ align:start position:0%
+a proof is uh you know a proof you write
+ 
+
+ align:start position:0%
+a proof is uh you know a proof you write
+kind of line by line and you can verify
+
+ align:start position:0%
+kind of line by line and you can verify
+ 
+
+ align:start position:0%
+kind of line by line and you can verify
+it kind of line by line to make sure the
+
+ align:start position:0%
+it kind of line by line to make sure the
+ 
+
+ align:start position:0%
+it kind of line by line to make sure the
+proof is correct that's how you know
+
+ align:start position:0%
+proof is correct that's how you know
+ 
+
+ align:start position:0%
+proof is correct that's how you know
+most people think of what a proof is
+
+ align:start position:0%
+most people think of what a proof is
+ 
+
+ align:start position:0%
+most people think of what a proof is
+okay starting from the mid 80s in
+
+ align:start position:0%
+okay starting from the mid 80s in
+ 
+
+ align:start position:0%
+okay starting from the mid 80s in
+computer science and particular Le in
+
+ align:start position:0%
+computer science and particular Le in
+ 
+
+ align:start position:0%
+computer science and particular Le in
+cryptography the way we thought about
+
+ align:start position:0%
+cryptography the way we thought about
+ 
+
+ align:start position:0%
+cryptography the way we thought about
+proofs changed started changing this is
+
+ align:start position:0%
+proofs changed started changing this is
+ 
+
+ align:start position:0%
+proofs changed started changing this is
+uh came uh about because of the idea of
+
+ align:start position:0%
+uh came uh about because of the idea of
+ 
+
+ align:start position:0%
+uh came uh about because of the idea of
+zero knowledge proof so there was a hope
+
+ align:start position:0%
+zero knowledge proof so there was a hope
+ 
+
+ align:start position:0%
+zero knowledge proof so there was a hope
+to kind of construct proofs that reveal
+
+ align:start position:0%
+to kind of construct proofs that reveal
+ 
+
+ align:start position:0%
+to kind of construct proofs that reveal
+no information about why the claim is
+
+ align:start position:0%
+no information about why the claim is
+ 
+
+ align:start position:0%
+no information about why the claim is
+true and uh in around 85 uh godas M and
+
+ align:start position:0%
+true and uh in around 85 uh godas M and
+ 
+
+ align:start position:0%
+true and uh in around 85 uh godas M and
+roov kind of constructed the first zero
+
+ align:start position:0%
+roov kind of constructed the first zero
+ 
+
+ align:start position:0%
+roov kind of constructed the first zero
+knowledge proof by the way this class is
+
+ align:start position:0%
+knowledge proof by the way this class is
+ 
+
+ align:start position:0%
+knowledge proof by the way this class is
+not about zero knowledge actually it's
+
+ align:start position:0%
+not about zero knowledge actually it's
+ 
+
+ align:start position:0%
+not about zero knowledge actually it's
+not about crypto per se it's just about
+
+ align:start position:0%
+not about crypto per se it's just about
+ 
+
+ align:start position:0%
+not about crypto per se it's just about
+kind of coming up with new proof systems
+
+ align:start position:0%
+kind of coming up with new proof systems
+ 
+
+ align:start position:0%
+kind of coming up with new proof systems
+you have a
+
+ align:start position:0%
+you have a
+ 
+
+ align:start position:0%
+you have a
+question um but they constructed they
+
+ align:start position:0%
+question um but they constructed they
+ 
+
+ align:start position:0%
+question um but they constructed they
+want to construct these proofs that
+
+ align:start position:0%
+want to construct these proofs that
+ 
+
+ align:start position:0%
+want to construct these proofs that
+reveal no information and to do that
+
+ align:start position:0%
+reveal no information and to do that
+ 
+
+ align:start position:0%
+reveal no information and to do that
+they needed to change the model turns
+
+ align:start position:0%
+they needed to change the model turns
+ 
+
+ align:start position:0%
+they needed to change the model turns
+out they could not do it using kind of
+
+ align:start position:0%
+out they could not do it using kind of
+ 
+
+ align:start position:0%
+out they could not do it using kind of
+what we think of a classical proof and
+
+ align:start position:0%
+what we think of a classical proof and
+ 
+
+ align:start position:0%
+what we think of a classical proof and
+the way they changed the model is by
+
+ align:start position:0%
+the way they changed the model is by
+ 
+
+ align:start position:0%
+the way they changed the model is by
+defining a new uh proof system a new
+
+ align:start position:0%
+defining a new uh proof system a new
+ 
+
+ align:start position:0%
+defining a new uh proof system a new
+model uh which is called interactive
+
+ align:start position:0%
+model uh which is called interactive
+ 
+
+ align:start position:0%
+model uh which is called interactive
+proofs we're going to talk about this
+
+ align:start position:0%
+proofs we're going to talk about this
+ 
+
+ align:start position:0%
+proofs we're going to talk about this
+today okay but they Define this notion
+
+ align:start position:0%
+today okay but they Define this notion
+ 
+
+ align:start position:0%
+today okay but they Define this notion
+of interactive proof so the we're going
+
+ align:start position:0%
+of interactive proof so the we're going
+ 
+
+ align:start position:0%
+of interactive proof so the we're going
+to start this course by talking about
+
+ align:start position:0%
+to start this course by talking about
+ 
+
+ align:start position:0%
+to start this course by talking about
+what interactive proofs are okay uh and
+
+ align:start position:0%
+what interactive proofs are okay uh and
+ 
+
+ align:start position:0%
+what interactive proofs are okay uh and
+we're going to construct interactive
+
+ align:start position:0%
+we're going to construct interactive
+ 
+
+ align:start position:0%
+we're going to construct interactive
+proofs in the 80s and 90s when people
+
+ align:start position:0%
+proofs in the 80s and 90s when people
+ 
+
+ align:start position:0%
+proofs in the 80s and 90s when people
+thought about interactive proofs usually
+
+ align:start position:0%
+thought about interactive proofs usually
+ 
+
+ align:start position:0%
+thought about interactive proofs usually
+the model is we think of the verifier as
+
+ align:start position:0%
+the model is we think of the verifier as
+ 
+
+ align:start position:0%
+the model is we think of the verifier as
+being efficient for us efficient means
+
+ align:start position:0%
+being efficient for us efficient means
+ 
+
+ align:start position:0%
+being efficient for us efficient means
+polinomial time okay but of course uh
+
+ align:start position:0%
+polinomial time okay but of course uh
+ 
+
+ align:start position:0%
+polinomial time okay but of course uh
+you know in practice it has more
+
+ align:start position:0%
+you know in practice it has more
+ 
+
+ align:start position:0%
+you know in practice it has more
+specific meaning but for now think of
+
+ align:start position:0%
+specific meaning but for now think of
+ 
+
+ align:start position:0%
+specific meaning but for now think of
+efficient as being pomal time and the
+
+ align:start position:0%
+efficient as being pomal time and the
+ 
+
+ align:start position:0%
+efficient as being pomal time and the
+verifier can be all powerful so the the
+
+ align:start position:0%
+verifier can be all powerful so the the
+ 
+
+ align:start position:0%
+verifier can be all powerful so the the
+time complexity of the prover was not
+
+ align:start position:0%
+time complexity of the prover was not
+ 
+
+ align:start position:0%
+time complexity of the prover was not
+even a consideration actually they
+
+ align:start position:0%
+even a consideration actually they
+ 
+
+ align:start position:0%
+even a consideration actually they
+called the prover Merlin like he's a
+
+ align:start position:0%
+called the prover Merlin like he's a
+ 
+
+ align:start position:0%
+called the prover Merlin like he's a
+wizard can do whatever the hell he wants
+
+ align:start position:0%
+wizard can do whatever the hell he wants
+ 
+
+ align:start position:0%
+wizard can do whatever the hell he wants
+like in infinite
+
+ align:start position:0%
+like in infinite
+ 
+
+ align:start position:0%
+like in infinite
+power what we're going to talk about
+
+ align:start position:0%
+power what we're going to talk about
+ 
+
+ align:start position:0%
+power what we're going to talk about
+about after introducing this model and
+
+ align:start position:0%
+about after introducing this model and
+ 
+
+ align:start position:0%
+about after introducing this model and
+giving some protocols we're going to
+
+ align:start position:0%
+giving some protocols we're going to
+ 
+
+ align:start position:0%
+giving some protocols we're going to
+talk about the model of doubly efficient
+
+ align:start position:0%
+talk about the model of doubly efficient
+ 
+
+ align:start position:0%
+talk about the model of doubly efficient
+interactive proofs and here what we we
+
+ align:start position:0%
+interactive proofs and here what we we
+ 
+
+ align:start position:0%
+interactive proofs and here what we we
+say no the appr is not all powerful we
+
+ align:start position:0%
+say no the appr is not all powerful we
+ 
+
+ align:start position:0%
+say no the appr is not all powerful we
+don't have all powerful machines in the
+
+ align:start position:0%
+don't have all powerful machines in the
+ 
+
+ align:start position:0%
+don't have all powerful machines in the
+world every machine is bounded so what
+
+ align:start position:0%
+world every machine is bounded so what
+ 
+
+ align:start position:0%
+world every machine is bounded so what
+we want yes the verifier should be very
+
+ align:start position:0%
+we want yes the verifier should be very
+ 
+
+ align:start position:0%
+we want yes the verifier should be very
+efficient but the Prov should not be all
+
+ align:start position:0%
+efficient but the Prov should not be all
+ 
+
+ align:start position:0%
+efficient but the Prov should not be all
+powerful either so we care about the
+
+ align:start position:0%
+powerful either so we care about the
+ 
+
+ align:start position:0%
+powerful either so we care about the
+Prov running time too that's what called
+
+ align:start position:0%
+Prov running time too that's what called
+ 
+
+ align:start position:0%
+Prov running time too that's what called
+double efficient interactive proofs
+
+ align:start position:0%
+double efficient interactive proofs
+ 
+
+ align:start position:0%
+double efficient interactive proofs
+we're going to construct double
+
+ align:start position:0%
+we're going to construct double
+ 
+
+ align:start position:0%
+we're going to construct double
+efficient interactive proof uh we're
+
+ align:start position:0%
+efficient interactive proof uh we're
+ 
+
+ align:start position:0%
+efficient interactive proof uh we're
+going to show the GK protocol specific
+
+ align:start position:0%
+going to show the GK protocol specific
+ 
+
+ align:start position:0%
+going to show the GK protocol specific
+protocol and then we're going to show
+
+ align:start position:0%
+protocol and then we're going to show
+ 
+
+ align:start position:0%
+protocol and then we're going to show
+application of this protocol and we're
+
+ align:start position:0%
+application of this protocol and we're
+ 
+
+ align:start position:0%
+application of this protocol and we're
+going to see application to really nice
+
+ align:start position:0%
+going to see application to really nice
+ 
+
+ align:start position:0%
+going to see application to really nice
+kind of models such that PCP which is
+
+ align:start position:0%
+kind of models such that PCP which is
+ 
+
+ align:start position:0%
+kind of models such that PCP which is
+probabilistically checkable proofs nip
+
+ align:start position:0%
+probabilistically checkable proofs nip
+ 
+
+ align:start position:0%
+probabilistically checkable proofs nip
+multi prooof interactive proofs and
+
+ align:start position:0%
+multi prooof interactive proofs and
+ 
+
+ align:start position:0%
+multi prooof interactive proofs and
+particular we're going to show how to
+
+ align:start position:0%
+particular we're going to show how to
+ 
+
+ align:start position:0%
+particular we're going to show how to
+use this to get a a kind of we proove a
+
+ align:start position:0%
+use this to get a a kind of we proove a
+ 
+
+ align:start position:0%
+use this to get a a kind of we proove a
+celebrated result which is the IP equals
+
+ align:start position:0%
+celebrated result which is the IP equals
+ 
+
+ align:start position:0%
+celebrated result which is the IP equals
+ppace theorem of Shamir okay so this if
+
+ align:start position:0%
+ppace theorem of Shamir okay so this if
+ 
+
+ align:start position:0%
+ppace theorem of Shamir okay so this if
+you don't know any of these buzzwords
+
+ align:start position:0%
+you don't know any of these buzzwords
+ 
+
+ align:start position:0%
+you don't know any of these buzzwords
+I'll explain everything this is I'm just
+
+ align:start position:0%
+I'll explain everything this is I'm just
+ 
+
+ align:start position:0%
+I'll explain everything this is I'm just
+kind of doing a very quick overview for
+
+ align:start position:0%
+kind of doing a very quick overview for
+ 
+
+ align:start position:0%
+kind of doing a very quick overview for
+those who kind of heard these buzzwords
+
+ align:start position:0%
+those who kind of heard these buzzwords
+ 
+
+ align:start position:0%
+those who kind of heard these buzzwords
+a little bit and so you'll know what to
+
+ align:start position:0%
+a little bit and so you'll know what to
+ 
+
+ align:start position:0%
+a little bit and so you'll know what to
+expect okay so up to here no crypto at
+
+ align:start position:0%
+expect okay so up to here no crypto at
+ 
+
+ align:start position:0%
+expect okay so up to here no crypto at
+all this is not at all about crypto it's
+
+ align:start position:0%
+all this is not at all about crypto it's
+ 
+
+ align:start position:0%
+all this is not at all about crypto it's
+just about proof systems then we're
+
+ align:start position:0%
+just about proof systems then we're
+ 
+
+ align:start position:0%
+just about proof systems then we're
+going to show how to use cryptography to
+
+ align:start position:0%
+going to show how to use cryptography to
+ 
+
+ align:start position:0%
+going to show how to use cryptography to
+get our proofs more succinct okay and
+
+ align:start position:0%
+get our proofs more succinct okay and
+ 
+
+ align:start position:0%
+get our proofs more succinct okay and
+then we're going to kind of uh leave the
+
+ align:start position:0%
+then we're going to kind of uh leave the
+ 
+
+ align:start position:0%
+then we're going to kind of uh leave the
+idea the stand the classical idea of a
+
+ align:start position:0%
+idea the stand the classical idea of a
+ 
+
+ align:start position:0%
+idea the stand the classical idea of a
+proof that if the theorem is false there
+
+ align:start position:0%
+proof that if the theorem is false there
+ 
+
+ align:start position:0%
+proof that if the theorem is false there
+you can't cheat it's possible to cheat
+
+ align:start position:0%
+you can't cheat it's possible to cheat
+ 
+
+ align:start position:0%
+you can't cheat it's possible to cheat
+like there's no fake proof there's no
+
+ align:start position:0%
+like there's no fake proof there's no
+ 
+
+ align:start position:0%
+like there's no fake proof there's no
+false proof okay every there's no if the
+
+ align:start position:0%
+false proof okay every there's no if the
+ 
+
+ align:start position:0%
+false proof okay every there's no if the
+theorem is incorrect there's no proof
+
+ align:start position:0%
+theorem is incorrect there's no proof
+ 
+
+ align:start position:0%
+theorem is incorrect there's no proof
+period we're going to use crypto to say
+
+ align:start position:0%
+period we're going to use crypto to say
+ 
+
+ align:start position:0%
+period we're going to use crypto to say
+ah maybe they're false proof but they're
+
+ align:start position:0%
+ah maybe they're false proof but they're
+ 
+
+ align:start position:0%
+ah maybe they're false proof but they're
+very hard to find so the only way you
+
+ align:start position:0%
+very hard to find so the only way you
+ 
+
+ align:start position:0%
+very hard to find so the only way you
+can find a convincing proof to a false
+
+ align:start position:0%
+can find a convincing proof to a false
+ 
+
+ align:start position:0%
+can find a convincing proof to a false
+statement is by breaking kind of a hard
+
+ align:start position:0%
+statement is by breaking kind of a hard
+ 
+
+ align:start position:0%
+statement is by breaking kind of a hard
+uh cryptographic problem you can Factor
+
+ align:start position:0%
+uh cryptographic problem you can Factor
+ 
+
+ align:start position:0%
+uh cryptographic problem you can Factor
+large numbers you can break latus
+
+ align:start position:0%
+large numbers you can break latus
+ 
+
+ align:start position:0%
+large numbers you can break latus
+assumptions and so on okay so we're
+
+ align:start position:0%
+assumptions and so on okay so we're
+ 
+
+ align:start position:0%
+assumptions and so on okay so we're
+going to use a cryptography to make our
+
+ align:start position:0%
+going to use a cryptography to make our
+ 
+
+ align:start position:0%
+going to use a cryptography to make our
+proofs more succinct but then what what
+
+ align:start position:0%
+proofs more succinct but then what what
+ 
+
+ align:start position:0%
+proofs more succinct but then what what
+going on here is are proofs who can make
+
+ align:start position:0%
+going on here is are proofs who can make
+ 
+
+ align:start position:0%
+going on here is are proofs who can make
+them succinct but they're still
+
+ align:start position:0%
+them succinct but they're still
+ 
+
+ align:start position:0%
+them succinct but they're still
+interactive and then we're going to show
+
+ align:start position:0%
+interactive and then we're going to show
+ 
+
+ align:start position:0%
+interactive and then we're going to show
+how to use this beautiful F Cham
+
+ align:start position:0%
+how to use this beautiful F Cham
+ 
+
+ align:start position:0%
+how to use this beautiful F Cham
+Paradigm which is a paradigm for
+
+ align:start position:0%
+Paradigm which is a paradigm for
+ 
+
+ align:start position:0%
+Paradigm which is a paradigm for
+reducing interaction and we're going to
+
+ align:start position:0%
+reducing interaction and we're going to
+ 
+
+ align:start position:0%
+reducing interaction and we're going to
+kind of study the security of this
+
+ align:start position:0%
+kind of study the security of this
+ 
+
+ align:start position:0%
+kind of study the security of this
+Paradigm and show how to make this
+
+ align:start position:0%
+Paradigm and show how to make this
+ 
+
+ align:start position:0%
+Paradigm and show how to make this
+Paradigm secure okay so these are kind
+
+ align:start position:0%
+Paradigm secure okay so these are kind
+ 
+
+ align:start position:0%
+Paradigm secure okay so these are kind
+of results that have happened very
+
+ align:start position:0%
+of results that have happened very
+ 
+
+ align:start position:0%
+of results that have happened very
+recently actually one of the students
+
+ align:start position:0%
+recently actually one of the students
+ 
+
+ align:start position:0%
+recently actually one of the students
+here Alex Lombardi at MIT uh was V not
+
+ align:start position:0%
+here Alex Lombardi at MIT uh was V not
+ 
+
+ align:start position:0%
+here Alex Lombardi at MIT uh was V not
+student was uh one of the people who
+
+ align:start position:0%
+student was uh one of the people who
+ 
+
+ align:start position:0%
+student was uh one of the people who
+came show kind of the security of this
+
+ align:start position:0%
+came show kind of the security of this
+ 
+
+ align:start position:0%
+came show kind of the security of this
+Paradigm so we're going show it we're
+
+ align:start position:0%
+Paradigm so we're going show it we're
+ 
+
+ align:start position:0%
+Paradigm so we're going show it we're
+going to use it then to show how to get
+
+ align:start position:0%
+going to use it then to show how to get
+ 
+
+ align:start position:0%
+going to use it then to show how to get
+our doubly efficient interactive proof
+
+ align:start position:0%
+our doubly efficient interactive proof
+ 
+
+ align:start position:0%
+our doubly efficient interactive proof
+how to make it non interactive anymore
+
+ align:start position:0%
+how to make it non interactive anymore
+ 
+
+ align:start position:0%
+how to make it non interactive anymore
+so make it completely
+
+ align:start position:0%
+so make it completely
+ 
+
+ align:start position:0%
+so make it completely
+non-interactive we're going to also show
+
+ align:start position:0%
+non-interactive we're going to also show
+ 
+
+ align:start position:0%
+non-interactive we're going to also show
+to use this fimir Paradigm to do kind of
+
+ align:start position:0%
+to use this fimir Paradigm to do kind of
+ 
+
+ align:start position:0%
+to use this fimir Paradigm to do kind of
+batch proofs uh non-interactively in
+
+ align:start position:0%
+batch proofs uh non-interactively in
+ 
+
+ align:start position:0%
+batch proofs uh non-interactively in
+very succinct way so taking a bunch of
+
+ align:start position:0%
+very succinct way so taking a bunch of
+ 
+
+ align:start position:0%
+very succinct way so taking a bunch of
+claims and kind of giving one uh short
+
+ align:start position:0%
+claims and kind of giving one uh short
+ 
+
+ align:start position:0%
+claims and kind of giving one uh short
+proof from them and finally we're going
+
+ align:start position:0%
+proof from them and finally we're going
+ 
+
+ align:start position:0%
+proof from them and finally we're going
+to show how to use that to go all the
+
+ align:start position:0%
+to show how to use that to go all the
+ 
+
+ align:start position:0%
+to show how to use that to go all the
+way to what's called a snar which is a
+
+ align:start position:0%
+way to what's called a snar which is a
+ 
+
+ align:start position:0%
+way to what's called a snar which is a
+succinct non-interactive argument
+
+ align:start position:0%
+succinct non-interactive argument
+ 
+
+ align:start position:0%
+succinct non-interactive argument
+argument is just another word for a
+
+ align:start position:0%
+argument is just another word for a
+ 
+
+ align:start position:0%
+argument is just another word for a
+computationally soundproof so this is
+
+ align:start position:0%
+computationally soundproof so this is
+ 
+
+ align:start position:0%
+computationally soundproof so this is
+kind of very very high level of what you
+
+ align:start position:0%
+kind of very very high level of what you
+ 
+
+ align:start position:0%
+kind of very very high level of what you
+should expect uh uh to learn in this
+
+ align:start position:0%
+should expect uh uh to learn in this
+ 
+
+ align:start position:0%
+should expect uh uh to learn in this
+class if you didn't understand a word
+
+ align:start position:0%
+class if you didn't understand a word
+ 
+
+ align:start position:0%
+class if you didn't understand a word
+what I said then this is what the hope
+
+ align:start position:0%
+what I said then this is what the hope
+ 
+
+ align:start position:0%
+what I said then this is what the hope
+the goal is that you will understand
+
+ align:start position:0%
+the goal is that you will understand
+ 
+
+ align:start position:0%
+the goal is that you will understand
+this by the end of this
+
+ align:start position:0%
+this by the end of this
+ 
+
+ align:start position:0%
+this by the end of this
+class okay uh questions before I start
+
+ align:start position:0%
+class okay uh questions before I start
+ 
+
+ align:start position:0%
+class okay uh questions before I start
+okay I need a volunteer to scribe for
+
+ align:start position:0%
+okay I need a volunteer to scribe for
+ 
+
+ align:start position:0%
+okay I need a volunteer to scribe for
+today oh fantastic thanks okay so with
+
+ align:start position:0%
+today oh fantastic thanks okay so with
+ 
+
+ align:start position:0%
+today oh fantastic thanks okay so with
+that let let's start so let's start with
+
+ align:start position:0%
+that let let's start so let's start with
+ 
+
+ align:start position:0%
+that let let's start so let's start with
+the notion of of interactive proofs and
+
+ align:start position:0%
+the notion of of interactive proofs and
+ 
+
+ align:start position:0%
+the notion of of interactive proofs and
+before I go to interactive proofs let me
+
+ align:start position:0%
+before I go to interactive proofs let me
+ 
+
+ align:start position:0%
+before I go to interactive proofs let me
+just you know even before intive proofs
+
+ align:start position:0%
+just you know even before intive proofs
+ 
+
+ align:start position:0%
+just you know even before intive proofs
+let's look at the class NP
+
+ align:start position:0%
+let's look at the class NP
+ 
+
+ align:start position:0%
+let's look at the class NP
+non-deterministic pomal time even this
+
+ align:start position:0%
+non-deterministic pomal time even this
+ 
+
+ align:start position:0%
+non-deterministic pomal time even this
+class is about proof system right so
+
+ align:start position:0%
+class is about proof system right so
+ 
+
+ align:start position:0%
+class is about proof system right so
+what is this this class is trying
+
+ align:start position:0%
+what is this this class is trying
+ 
+
+ align:start position:0%
+what is this this class is trying
+to by the way there's another chair here
+
+ align:start position:0%
+to by the way there's another chair here
+ 
+
+ align:start position:0%
+to by the way there's another chair here
+for those who don't have a chair there's
+
+ align:start position:0%
+for those who don't have a chair there's
+ 
+
+ align:start position:0%
+for those who don't have a chair there's
+one right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great great so even before we go to the
+
+ align:start position:0%
+great great so even before we go to the
+ 
+
+ align:start position:0%
+great great so even before we go to the
+interactive setting let's even think of
+
+ align:start position:0%
+interactive setting let's even think of
+ 
+
+ align:start position:0%
+interactive setting let's even think of
+the class NP what is the class NP if you
+
+ align:start position:0%
+the class NP what is the class NP if you
+ 
+
+ align:start position:0%
+the class NP what is the class NP if you
+think about it it's all the
+
+ align:start position:0%
+think about it it's all the
+ 
+
+ align:start position:0%
+think about it it's all the
+languages that have a proof that's the
+
+ align:start position:0%
+languages that have a proof that's the
+ 
+
+ align:start position:0%
+languages that have a proof that's the
+witness that can be verified by
+
+ align:start position:0%
+witness that can be verified by
+ 
+
+ align:start position:0%
+witness that can be verified by
+polinomial time okay so we want to think
+
+ align:start position:0%
+polinomial time okay so we want to think
+ 
+
+ align:start position:0%
+polinomial time okay so we want to think
+with the here's the the framework for
+
+ align:start position:0%
+with the here's the the framework for
+ 
+
+ align:start position:0%
+with the here's the the framework for
+this class is the following we want to
+
+ align:start position:0%
+this class is the following we want to
+ 
+
+ align:start position:0%
+this class is the following we want to
+ask I we have the verifiers are pomal
+
+ align:start position:0%
+ask I we have the verifiers are pomal
+ 
+
+ align:start position:0%
+ask I we have the verifiers are pomal
+time or even like there there you know
+
+ align:start position:0%
+time or even like there there you know
+ 
+
+ align:start position:0%
+time or even like there there you know
+they're very efficient what can you
+
+ align:start position:0%
+they're very efficient what can you
+ 
+
+ align:start position:0%
+they're very efficient what can you
+prove to these
+
+ align:start position:0%
+prove to these
+ 
+
+ align:start position:0%
+prove to these
+verifiers okay so that's exactly what NP
+
+ align:start position:0%
+verifiers okay so that's exactly what NP
+ 
+
+ align:start position:0%
+verifiers okay so that's exactly what NP
+captures NP is all the
+
+ align:start position:0%
+captures NP is all the
+ 
+
+ align:start position:0%
+captures NP is all the
+languages that you can prove membership
+
+ align:start position:0%
+languages that you can prove membership
+ 
+
+ align:start position:0%
+languages that you can prove membership
+in the language to pomal time
+
+ align:start position:0%
+in the language to pomal time
+ 
+
+ align:start position:0%
+in the language to pomal time
+verifier okay so NP is exactly the
+
+ align:start position:0%
+verifier okay so NP is exactly the
+ 
+
+ align:start position:0%
+verifier okay so NP is exactly the
+set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+languages m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ship can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proved in poly time so for or can
+
+ align:start position:0%
+proved in poly time so for or can
+ 
+
+ align:start position:0%
+proved in poly time so for or can
+prove or can prove to a PO time maybe I
+
+ align:start position:0%
+prove or can prove to a PO time maybe I
+ 
+
+ align:start position:0%
+prove or can prove to a PO time maybe I
+should say can proved
+
+ align:start position:0%
+should say can proved
+ 
+
+ align:start position:0%
+should say can proved
+to a polinomial Time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+verifier so uh poal time verifier can
+
+ align:start position:0%
+verifier so uh poal time verifier can
+ 
+
+ align:start position:0%
+verifier so uh poal time verifier can
+verify membership in the language so far
+
+ align:start position:0%
+verify membership in the language so far
+ 
+
+ align:start position:0%
+verify membership in the language so far
+so good okay but NP is not that rich
+
+ align:start position:0%
+so good okay but NP is not that rich
+ 
+
+ align:start position:0%
+so good okay but NP is not that rich
+okay so we want more more than NP okay
+
+ align:start position:0%
+okay so we want more more than NP okay
+ 
+
+ align:start position:0%
+okay so we want more more than NP okay
+so let's so okay so one thing we can add
+
+ align:start position:0%
+so let's so okay so one thing we can add
+ 
+
+ align:start position:0%
+so let's so okay so one thing we can add
+so what is the class IP the first thing
+
+ align:start position:0%
+so what is the class IP the first thing
+ 
+
+ align:start position:0%
+so what is the class IP the first thing
+that so IP interactive proofs and two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components so in NP the proof is
+
+ align:start position:0%
+components so in NP the proof is
+ 
+
+ align:start position:0%
+components so in NP the proof is
+classical it's the class of languages
+
+ align:start position:0%
+classical it's the class of languages
+ 
+
+ align:start position:0%
+classical it's the class of languages
+for which a membership can be proved
+
+ align:start position:0%
+for which a membership can be proved
+ 
+
+ align:start position:0%
+for which a membership can be proved
+using a classical
+
+ align:start position:0%
+using a classical
+ 
+
+ align:start position:0%
+using a classical
+proof okay like a proof that you know
+
+ align:start position:0%
+proof okay like a proof that you know
+ 
+
+ align:start position:0%
+proof okay like a proof that you know
+you can verify just like running a
+
+ align:start position:0%
+you can verify just like running a
+ 
+
+ align:start position:0%
+you can verify just like running a
+touring machine okay interactive proofs
+
+ align:start position:0%
+touring machine okay interactive proofs
+ 
+
+ align:start position:0%
+touring machine okay interactive proofs
+are different in two ways first of all
+
+ align:start position:0%
+are different in two ways first of all
+ 
+
+ align:start position:0%
+are different in two ways first of all
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+allow
+
+ align:start position:0%
+allow
+ 
+
+ align:start position:0%
+allow
+interaction between the prover and the
+
+ align:start position:0%
+interaction between the prover and the
+ 
+
+ align:start position:0%
+interaction between the prover and the
+verifier they can talk back and
+
+ align:start position:0%
+verifier they can talk back and
+ 
+
+ align:start position:0%
+verifier they can talk back and
+forth
+
+ align:start position:0%
+forth
+ 
+
+ align:start position:0%
+forth
+importantly we allow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+randomization now note what do I mean
+
+ align:start position:0%
+randomization now note what do I mean
+ 
+
+ align:start position:0%
+randomization now note what do I mean
+randomization the verifier can be
+
+ align:start position:0%
+randomization the verifier can be
+ 
+
+ align:start position:0%
+randomization the verifier can be
+randomized and there can be some chance
+
+ align:start position:0%
+randomized and there can be some chance
+ 
+
+ align:start position:0%
+randomized and there can be some chance
+that the theorem is uh false and he'll
+
+ align:start position:0%
+that the theorem is uh false and he'll
+ 
+
+ align:start position:0%
+that the theorem is uh false and he'll
+accept but that's very very small okay
+
+ align:start position:0%
+accept but that's very very small okay
+ 
+
+ align:start position:0%
+accept but that's very very small okay
+we can make it kind of if the
+
+ align:start position:0%
+we can make it kind of if the
+ 
+
+ align:start position:0%
+we can make it kind of if the
+communication complexity is let's say n
+
+ align:start position:0%
+communication complexity is let's say n
+ 
+
+ align:start position:0%
+communication complexity is let's say n
+we can make you'll you'll accept the
+
+ align:start position:0%
+we can make you'll you'll accept the
+ 
+
+ align:start position:0%
+we can make you'll you'll accept the
+false statement probability something
+
+ align:start position:0%
+false statement probability something
+ 
+
+ align:start position:0%
+false statement probability something
+like 2 Theus n so we can make it very
+
+ align:start position:0%
+like 2 Theus n so we can make it very
+ 
+
+ align:start position:0%
+like 2 Theus n so we can make it very
+very small but there is a nonzero chance
+
+ align:start position:0%
+very small but there is a nonzero chance
+ 
+
+ align:start position:0%
+very small but there is a nonzero chance
+that you'll accept false statement okay
+
+ align:start position:0%
+that you'll accept false statement okay
+ 
+
+ align:start position:0%
+that you'll accept false statement okay
+so in that sense we weakened the
+
+ align:start position:0%
+so in that sense we weakened the
+ 
+
+ align:start position:0%
+so in that sense we weakened the
+model now note if there's no
+
+ align:start position:0%
+model now note if there's no
+ 
+
+ align:start position:0%
+model now note if there's no
+randomization if we force the
+
+ align:start position:0%
+randomization if we force the
+ 
+
+ align:start position:0%
+randomization if we force the
+verifier to be deterministic if the
+
+ align:start position:0%
+verifier to be deterministic if the
+ 
+
+ align:start position:0%
+verifier to be deterministic if the
+interaction so again the interactive
+
+ align:start position:0%
+interaction so again the interactive
+ 
+
+ align:start position:0%
+interaction so again the interactive
+proof is a kind of
+
+ align:start position:0%
+proof is a kind of
+ 
+
+ align:start position:0%
+proof is a kind of
+interactive protocol between approver
+
+ align:start position:0%
+interactive protocol between approver
+ 
+
+ align:start position:0%
+interactive protocol between approver
+and verifier if the approver knew what
+
+ align:start position:0%
+and verifier if the approver knew what
+ 
+
+ align:start position:0%
+and verifier if the approver knew what
+the verifier is going to send if he was
+
+ align:start position:0%
+the verifier is going to send if he was
+ 
+
+ align:start position:0%
+the verifier is going to send if he was
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+deterministic then the pro can just
+
+ align:start position:0%
+deterministic then the pro can just
+ 
+
+ align:start position:0%
+deterministic then the pro can just
+generate the entire transcript and give
+
+ align:start position:0%
+generate the entire transcript and give
+ 
+
+ align:start position:0%
+generate the entire transcript and give
+it as a proof so it will really be
+
+ align:start position:0%
+it as a proof so it will really be
+ 
+
+ align:start position:0%
+it as a proof so it will really be
+NP there's no point of this
+
+ align:start position:0%
+NP there's no point of this
+ 
+
+ align:start position:0%
+NP there's no point of this
+interaction so really the power of this
+
+ align:start position:0%
+interaction so really the power of this
+ 
+
+ align:start position:0%
+interaction so really the power of this
+IP comes from the fact that the verifier
+
+ align:start position:0%
+IP comes from the fact that the verifier
+ 
+
+ align:start position:0%
+IP comes from the fact that the verifier
+is interacted it comes from the fact
+
+ align:start position:0%
+is interacted it comes from the fact
+ 
+
+ align:start position:0%
+is interacted it comes from the fact
+that the verifier is interactive is is
+
+ align:start position:0%
+that the verifier is interactive is is
+ 
+
+ align:start position:0%
+that the verifier is interactive is is
+randomized sorry is randomized and the
+
+ align:start position:0%
+randomized sorry is randomized and the
+ 
+
+ align:start position:0%
+randomized sorry is randomized and the
+pro doesn't know what this Randomness is
+
+ align:start position:0%
+pro doesn't know what this Randomness is
+ 
+
+ align:start position:0%
+pro doesn't know what this Randomness is
+going to be so if I'm trying to prove to
+
+ align:start position:0%
+going to be so if I'm trying to prove to
+ 
+
+ align:start position:0%
+going to be so if I'm trying to prove to
+you a
+
+ align:start position:0%
+you a
+ 
+
+ align:start position:0%
+you a
+statement I send you my first message I
+
+ align:start position:0%
+statement I send you my first message I
+ 
+
+ align:start position:0%
+statement I send you my first message I
+don't know what question you're going to
+
+ align:start position:0%
+don't know what question you're going to
+ 
+
+ align:start position:0%
+don't know what question you're going to
+ask me you're going answer some random
+
+ align:start position:0%
+ask me you're going answer some random
+ 
+
+ align:start position:0%
+ask me you're going answer some random
+questions and I'll need to give an
+
+ align:start position:0%
+questions and I'll need to give an
+ 
+
+ align:start position:0%
+questions and I'll need to give an
+answer and then I don't know what the
+
+ align:start position:0%
+answer and then I don't know what the
+ 
+
+ align:start position:0%
+answer and then I don't know what the
+next question if I knew all your
+
+ align:start position:0%
+next question if I knew all your
+ 
+
+ align:start position:0%
+next question if I knew all your
+question in advance then there's no
+
+ align:start position:0%
+question in advance then there's no
+ 
+
+ align:start position:0%
+question in advance then there's no
+point it's like it loses the power okay
+
+ align:start position:0%
+point it's like it loses the power okay
+ 
+
+ align:start position:0%
+point it's like it loses the power okay
+so really the power comes from the fact
+
+ align:start position:0%
+so really the power comes from the fact
+ 
+
+ align:start position:0%
+so really the power comes from the fact
+that there's interraction in the PO
+
+ align:start position:0%
+that there's interraction in the PO
+ 
+
+ align:start position:0%
+that there's interraction in the PO
+cannot predict ahead of time what
+
+ align:start position:0%
+cannot predict ahead of time what
+ 
+
+ align:start position:0%
+cannot predict ahead of time what
+questions he's going to get from the
+
+ align:start position:0%
+questions he's going to get from the
+ 
+
+ align:start position:0%
+questions he's going to get from the
+verifier okay so any any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions Okay so
+
+ align:start position:0%
+questions Okay so
+ 
+
+ align:start position:0%
+questions Okay so
+I can I did Define this formul yet I'll
+
+ align:start position:0%
+I can I did Define this formul yet I'll
+ 
+
+ align:start position:0%
+I can I did Define this formul yet I'll
+Define it formally in a bit but I hope I
+
+ align:start position:0%
+Define it formally in a bit but I hope I
+ 
+
+ align:start position:0%
+Define it formally in a bit but I hope I
+convinced you that like without
+
+ align:start position:0%
+convinced you that like without
+ 
+
+ align:start position:0%
+convinced you that like without
+Randomness this model is really useless
+
+ align:start position:0%
+Randomness this model is really useless
+ 
+
+ align:start position:0%
+Randomness this model is really useless
+okay there's no point how about just how
+
+ align:start position:0%
+okay there's no point how about just how
+ 
+
+ align:start position:0%
+okay there's no point how about just how
+about without inaction let's say I had
+
+ align:start position:0%
+about without inaction let's say I had
+ 
+
+ align:start position:0%
+about without inaction let's say I had
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+Randomness do I get more and actually so
+
+ align:start position:0%
+Randomness do I get more and actually so
+ 
+
+ align:start position:0%
+Randomness do I get more and actually so
+what what if we allow only
+
+ align:start position:0%
+what what if we allow only
+ 
+
+ align:start position:0%
+what what if we allow only
+Randomness so
+
+ align:start position:0%
+Randomness so
+ 
+
+ align:start position:0%
+Randomness so
+proofs so let's talk about
+
+ align:start position:0%
+proofs so let's talk about
+ 
+
+ align:start position:0%
+proofs so let's talk about
+non-interactive proofs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the verifier V is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+randomized by the way I forgot to say
+
+ align:start position:0%
+randomized by the way I forgot to say
+ 
+
+ align:start position:0%
+randomized by the way I forgot to say
+please stop me at any point and ask me
+
+ align:start position:0%
+please stop me at any point and ask me
+ 
+
+ align:start position:0%
+please stop me at any point and ask me
+questions I like questions questions are
+
+ align:start position:0%
+questions I like questions questions are
+ 
+
+ align:start position:0%
+questions I like questions questions are
+good for me to kind of SL me down it
+
+ align:start position:0%
+good for me to kind of SL me down it
+ 
+
+ align:start position:0%
+good for me to kind of SL me down it
+gives you an opportunity to digest so
+
+ align:start position:0%
+gives you an opportunity to digest so
+ 
+
+ align:start position:0%
+gives you an opportunity to digest so
+it's a great thing so please just at any
+
+ align:start position:0%
+it's a great thing so please just at any
+ 
+
+ align:start position:0%
+it's a great thing so please just at any
+point stop me with questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so uh good so what what
+
+ align:start position:0%
+questions okay so uh good so what what
+ 
+
+ align:start position:0%
+questions okay so uh good so what what
+about if we so we said if we get rid of
+
+ align:start position:0%
+about if we so we said if we get rid of
+ 
+
+ align:start position:0%
+about if we so we said if we get rid of
+Randomness we get nothing what if we get
+
+ align:start position:0%
+Randomness we get nothing what if we get
+ 
+
+ align:start position:0%
+Randomness we get nothing what if we get
+rid of interaction and we just allow
+
+ align:start position:0%
+rid of interaction and we just allow
+ 
+
+ align:start position:0%
+rid of interaction and we just allow
+Randomness do we get more and actually
+
+ align:start position:0%
+Randomness do we get more and actually
+ 
+
+ align:start position:0%
+Randomness do we get more and actually
+we do get more okay and actually this
+
+ align:start position:0%
+we do get more okay and actually this
+ 
+
+ align:start position:0%
+we do get more okay and actually this
+complexity test is a name this is ma for
+
+ align:start position:0%
+complexity test is a name this is ma for
+ 
+
+ align:start position:0%
+complexity test is a name this is ma for
+Merlin Arthur Arthur is known as a
+
+ align:start position:0%
+Merlin Arthur Arthur is known as a
+ 
+
+ align:start position:0%
+Merlin Arthur Arthur is known as a
+verify Merin is known as aover so kind
+
+ align:start position:0%
+verify Merin is known as aover so kind
+ 
+
+ align:start position:0%
+verify Merin is known as aover so kind
+of the approver sends a message Arthur
+
+ align:start position:0%
+of the approver sends a message Arthur
+ 
+
+ align:start position:0%
+of the approver sends a message Arthur
+the verifier can kind of toss coins and
+
+ align:start position:0%
+the verifier can kind of toss coins and
+ 
+
+ align:start position:0%
+the verifier can kind of toss coins and
+based on that decide if to accept or not
+
+ align:start position:0%
+based on that decide if to accept or not
+ 
+
+ align:start position:0%
+based on that decide if to accept or not
+but anyway the non the non-interactive
+
+ align:start position:0%
+but anyway the non the non-interactive
+ 
+
+ align:start position:0%
+but anyway the non the non-interactive
+randomized version is uh believe to be I
+
+ align:start position:0%
+randomized version is uh believe to be I
+ 
+
+ align:start position:0%
+randomized version is uh believe to be I
+mean it may be more powerful than NP we
+
+ align:start position:0%
+mean it may be more powerful than NP we
+ 
+
+ align:start position:0%
+mean it may be more powerful than NP we
+actually don't know but it seems there's
+
+ align:start position:0%
+actually don't know but it seems there's
+ 
+
+ align:start position:0%
+actually don't know but it seems there's
+some more power and actually let me give
+
+ align:start position:0%
+some more power and actually let me give
+ 
+
+ align:start position:0%
+some more power and actually let me give
+you an example this is example that will
+
+ align:start position:0%
+you an example this is example that will
+ 
+
+ align:start position:0%
+you an example this is example that will
+kind of be useful for us later so it's
+
+ align:start position:0%
+kind of be useful for us later so it's
+ 
+
+ align:start position:0%
+kind of be useful for us later so it's
+not only an example but let me give you
+
+ align:start position:0%
+not only an example but let me give you
+ 
+
+ align:start position:0%
+not only an example but let me give you
+an example where kind of Randomness can
+
+ align:start position:0%
+an example where kind of Randomness can
+ 
+
+ align:start position:0%
+an example where kind of Randomness can
+be helpful for us okay so suppose you
+
+ align:start position:0%
+be helpful for us okay so suppose you
+ 
+
+ align:start position:0%
+be helpful for us okay so suppose you
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+verify let's say you have two n byn
+
+ align:start position:0%
+verify let's say you have two n byn
+ 
+
+ align:start position:0%
+verify let's say you have two n byn
+matrices A and B these are n byn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrices let's say over Z1 or over a
+
+ align:start position:0%
+matrices let's say over Z1 or over a
+ 
+
+ align:start position:0%
+matrices let's say over Z1 or over a
+finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field and let's say you want to verify
+
+ align:start position:0%
+field and let's say you want to verify
+ 
+
+ align:start position:0%
+field and let's say you want to verify
+suppose you want to
+
+ align:start position:0%
+suppose you want to
+ 
+
+ align:start position:0%
+suppose you want to
+verify that some Matrix C is equal to a
+
+ align:start position:0%
+verify that some Matrix C is equal to a
+ 
+
+ align:start position:0%
+verify that some Matrix C is equal to a
+*
+
+ align:start position:0%
+*
+ 
+
+ align:start position:0%
+*
+B so you're also given let's say
+
+ align:start position:0%
+B so you're also given let's say
+ 
+
+ align:start position:0%
+B so you're also given let's say
+C you want to so you you need to verify
+
+ align:start position:0%
+C you want to so you you need to verify
+ 
+
+ align:start position:0%
+C you want to so you you need to verify
+task of matrix
+
+ align:start position:0%
+task of matrix
+ 
+
+ align:start position:0%
+task of matrix
+multiplication okay we can do it
+
+ align:start position:0%
+multiplication okay we can do it
+ 
+
+ align:start position:0%
+multiplication okay we can do it
+efficiently in general the best known
+
+ align:start position:0%
+efficiently in general the best known
+ 
+
+ align:start position:0%
+efficiently in general the best known
+algorithm is something like order uh o
+
+ align:start position:0%
+algorithm is something like order uh o
+ 
+
+ align:start position:0%
+algorithm is something like order uh o
+of n to the 2 3 6 maybe something like
+
+ align:start position:0%
+of n to the 2 3 6 maybe something like
+ 
+
+ align:start position:0%
+of n to the 2 3 6 maybe something like
+that that's the best known matrix
+
+ align:start position:0%
+that that's the best known matrix
+ 
+
+ align:start position:0%
+that that's the best known matrix
+multiplication
+
+ align:start position:0%
+multiplication
+ 
+
+ align:start position:0%
+multiplication
+algorithm why you looking me the number
+
+ align:start position:0%
+algorithm why you looking me the number
+ 
+
+ align:start position:0%
+algorithm why you looking me the number
+yeah close uh let but turns out that if
+
+ align:start position:0%
+yeah close uh let but turns out that if
+ 
+
+ align:start position:0%
+yeah close uh let but turns out that if
+using randomization
+
+ align:start position:0%
+using randomization
+ 
+
+ align:start position:0%
+using randomization
+you can do it more efficiently okay so
+
+ align:start position:0%
+you can do it more efficiently okay so
+ 
+
+ align:start position:0%
+you can do it more efficiently okay so
+let's show how you can verify that a
+
+ align:start position:0%
+let's show how you can verify that a
+ 
+
+ align:start position:0%
+let's show how you can verify that a
+matrix C is a product of two matrices A
+
+ align:start position:0%
+matrix C is a product of two matrices A
+ 
+
+ align:start position:0%
+matrix C is a product of two matrices A
+and B in time order and
+
+ align:start position:0%
+and B in time order and
+ 
+
+ align:start position:0%
+and B in time order and
+squared okay so kind of the best you can
+
+ align:start position:0%
+squared okay so kind of the best you can
+ 
+
+ align:start position:0%
+squared okay so kind of the best you can
+do because you need to read the the
+
+ align:start position:0%
+do because you need to read the the
+ 
+
+ align:start position:0%
+do because you need to read the the
+input okay so how will you do that
+
+ align:start position:0%
+input okay so how will you do that
+ 
+
+ align:start position:0%
+input okay so how will you do that
+here's the idea so here's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+randomized algorithm for verifying this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's assume that F first assume this
+
+ align:start position:0%
+so let's assume that F first assume this
+ 
+
+ align:start position:0%
+so let's assume that F first assume this
+is kind of without lots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generality that f is much bigger than
+
+ align:start position:0%
+generality that f is much bigger than
+ 
+
+ align:start position:0%
+generality that f is much bigger than
+n if not you can take kind of an
+
+ align:start position:0%
+n if not you can take kind of an
+ 
+
+ align:start position:0%
+n if not you can take kind of an
+extension field of that okay embedded in
+
+ align:start position:0%
+extension field of that okay embedded in
+ 
+
+ align:start position:0%
+extension field of that okay embedded in
+a much bigger field so just let's assume
+
+ align:start position:0%
+a much bigger field so just let's assume
+ 
+
+ align:start position:0%
+a much bigger field so just let's assume
+if those who are not kind of comfortable
+
+ align:start position:0%
+if those who are not kind of comfortable
+ 
+
+ align:start position:0%
+if those who are not kind of comfortable
+with extension field let's assume it's
+
+ align:start position:0%
+with extension field let's assume it's
+ 
+
+ align:start position:0%
+with extension field let's assume it's
+just much
+
+ align:start position:0%
+just much
+ 
+
+ align:start position:0%
+just much
+bigger okay then what do you do here's
+
+ align:start position:0%
+bigger okay then what do you do here's
+ 
+
+ align:start position:0%
+bigger okay then what do you do here's
+my algorithm what I'm going to do I'm
+
+ align:start position:0%
+my algorithm what I'm going to do I'm
+ 
+
+ align:start position:0%
+my algorithm what I'm going to do I'm
+going to choose a random element in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field I'm going to consider X which is
+
+ align:start position:0%
+field I'm going to consider X which is
+ 
+
+ align:start position:0%
+field I'm going to consider X which is
+just uh 1 r r 2 up to R to the N minus
+
+ align:start position:0%
+just uh 1 r r 2 up to R to the N minus
+ 
+
+ align:start position:0%
+just uh 1 r r 2 up to R to the N minus
+one okay so all the powers of R I chose
+
+ align:start position:0%
+one okay so all the powers of R I chose
+ 
+
+ align:start position:0%
+one okay so all the powers of R I chose
+a random R in the field I look at all
+
+ align:start position:0%
+a random R in the field I look at all
+ 
+
+ align:start position:0%
+a random R in the field I look at all
+the powers of
+
+ align:start position:0%
+the powers of
+ 
+
+ align:start position:0%
+the powers of
+R and then what do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly and then I'm going to
+
+ align:start position:0%
+exactly and then I'm going to
+ 
+
+ align:start position:0%
+exactly and then I'm going to
+check if C * X I guess
+
+ align:start position:0%
+check if C * X I guess
+ 
+
+ align:start position:0%
+check if C * X I guess
+transpose because I wrote it is equal to
+
+ align:start position:0%
+transpose because I wrote it is equal to
+ 
+
+ align:start position:0%
+transpose because I wrote it is equal to
+a b *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X that's my
+
+ align:start position:0%
+X that's my
+ 
+
+ align:start position:0%
+X that's my
+algorithm okay so note
+
+ align:start position:0%
+algorithm okay so note
+ 
+
+ align:start position:0%
+algorithm okay so note
+uh yeah
+
+ align:start position:0%
+uh yeah
+ 
+
+ align:start position:0%
+uh yeah
+so so note this is just a vector and
+
+ align:start position:0%
+so so note this is just a vector and
+ 
+
+ align:start position:0%
+so so note this is just a vector and
+Vector times Matrix mult so to multiply
+
+ align:start position:0%
+Vector times Matrix mult so to multiply
+ 
+
+ align:start position:0%
+Vector times Matrix mult so to multiply
+a matrix by Vector is time n squ as
+
+ align:start position:0%
+a matrix by Vector is time n squ as
+ 
+
+ align:start position:0%
+a matrix by Vector is time n squ as
+opposed to you know the N to the 23 six
+
+ align:start position:0%
+opposed to you know the N to the 23 six
+ 
+
+ align:start position:0%
+opposed to you know the N to the 23 six
+so this is more efficient why is it okay
+
+ align:start position:0%
+so this is more efficient why is it okay
+ 
+
+ align:start position:0%
+so this is more efficient why is it okay
+why why so of course it's complete if
+
+ align:start position:0%
+why why so of course it's complete if
+ 
+
+ align:start position:0%
+why why so of course it's complete if
+these are equal I'm going to accept Okay
+
+ align:start position:0%
+these are equal I'm going to accept Okay
+ 
+
+ align:start position:0%
+these are equal I'm going to accept Okay
+but if they're not
+
+ align:start position:0%
+but if they're not
+ 
+
+ align:start position:0%
+but if they're not
+equal so so why why is it uh sound so
+
+ align:start position:0%
+equal so so why why is it uh sound so
+ 
+
+ align:start position:0%
+equal so so why why is it uh sound so
+maybe you can convince me let's say
+
+ align:start position:0%
+maybe you can convince me let's say
+ 
+
+ align:start position:0%
+maybe you can convince me let's say
+they're not equal maybe you can still
+
+ align:start position:0%
+they're not equal maybe you can still
+ 
+
+ align:start position:0%
+they're not equal maybe you can still
+convince me that they're equal that
+
+ align:start position:0%
+convince me that they're equal that
+ 
+
+ align:start position:0%
+convince me that they're equal that
+would be a problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the size of the field iser than n
+
+ align:start position:0%
+yeah the size of the field iser than n
+ 
+
+ align:start position:0%
+yeah the size of the field iser than n
+it's that like fantastic fantastic so
+
+ align:start position:0%
+it's that like fantastic fantastic so
+ 
+
+ align:start position:0%
+it's that like fantastic fantastic so
+here's let me just repeat what you said
+
+ align:start position:0%
+here's let me just repeat what you said
+ 
+
+ align:start position:0%
+here's let me just repeat what you said
+a b bit more formly so suppose they're
+
+ align:start position:0%
+a b bit more formly so suppose they're
+ 
+
+ align:start position:0%
+a b bit more formly so suppose they're
+not equal there's one row that they're
+
+ align:start position:0%
+not equal there's one row that they're
+ 
+
+ align:start position:0%
+not equal there's one row that they're
+not equal on right let's focus on that
+
+ align:start position:0%
+not equal on right let's focus on that
+ 
+
+ align:start position:0%
+not equal on right let's focus on that
+row so you can think of what when I do c
+
+ align:start position:0%
+row so you can think of what when I do c
+ 
+
+ align:start position:0%
+row so you can think of what when I do c
+* X let's let's say C1 like the first
+
+ align:start position:0%
+* X let's let's say C1 like the first
+ 
+
+ align:start position:0%
+* X let's let's say C1 like the first
+row of C when I do c *
+
+ align:start position:0%
+row of C when I do c *
+ 
+
+ align:start position:0%
+row of C when I do c *
+X this is you can think of this as I
+
+ align:start position:0%
+X this is you can think of this as I
+ 
+
+ align:start position:0%
+X this is you can think of this as I
+take I look at this the row as a polom
+
+ align:start position:0%
+take I look at this the row as a polom
+ 
+
+ align:start position:0%
+take I look at this the row as a polom
+so if you look at the first row maybe
+
+ align:start position:0%
+so if you look at the first row maybe
+ 
+
+ align:start position:0%
+so if you look at the first row maybe
+I'll write it as C11 up to or C10 up to
+
+ align:start position:0%
+I'll write it as C11 up to or C10 up to
+ 
+
+ align:start position:0%
+I'll write it as C11 up to or C10 up to
+C1 n minus one okay let's look at this n
+
+ align:start position:0%
+C1 n minus one okay let's look at this n
+ 
+
+ align:start position:0%
+C1 n minus one okay let's look at this n
+row when I multiply by X which is one r
+
+ align:start position:0%
+row when I multiply by X which is one r
+ 
+
+ align:start position:0%
+row when I multiply by X which is one r
+r squ this is nothing but some C 1 i x
+
+ align:start position:0%
+r squ this is nothing but some C 1 i x
+ 
+
+ align:start position:0%
+r squ this is nothing but some C 1 i x
+to the I or sorry R to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I so now what do I check so now you know
+
+ align:start position:0%
+I so now what do I check so now you know
+ 
+
+ align:start position:0%
+I so now what do I check so now you know
+if this row let's say it is different
+
+ align:start position:0%
+if this row let's say it is different
+ 
+
+ align:start position:0%
+if this row let's say it is different
+than the row
+
+ align:start position:0%
+than the row
+ 
+
+ align:start position:0%
+than the row
+here then I have two different
+
+ align:start position:0%
+here then I have two different
+ 
+
+ align:start position:0%
+here then I have two different
+pols right so if I write if I write the
+
+ align:start position:0%
+pols right so if I write if I write the
+ 
+
+ align:start position:0%
+pols right so if I write if I write the
+row there let's say as I don't know D1
+
+ align:start position:0%
+row there let's say as I don't know D1
+ 
+
+ align:start position:0%
+row there let's say as I don't know D1
+d0 or d10 up to D1 n minus one let's say
+
+ align:start position:0%
+d0 or d10 up to D1 n minus one let's say
+ 
+
+ align:start position:0%
+d0 or d10 up to D1 n minus one let's say
+this is the row corresponding to a *
+
+ align:start position:0%
+this is the row corresponding to a *
+ 
+
+ align:start position:0%
+this is the row corresponding to a *
+B if these are different if these are
+
+ align:start position:0%
+B if these are different if these are
+ 
+
+ align:start position:0%
+B if these are different if these are
+different then I have two different
+
+ align:start position:0%
+different then I have two different
+ 
+
+ align:start position:0%
+different then I have two different
+pols that agree in a random out two
+
+ align:start position:0%
+pols that agree in a random out two
+ 
+
+ align:start position:0%
+pols that agree in a random out two
+random degree n minus one pols so the
+
+ align:start position:0%
+random degree n minus one pols so the
+ 
+
+ align:start position:0%
+random degree n minus one pols so the
+polinomial is defined by this row these
+
+ align:start position:0%
+polinomial is defined by this row these
+ 
+
+ align:start position:0%
+polinomial is defined by this row these
+are the coefficients of the polinomial
+
+ align:start position:0%
+are the coefficients of the polinomial
+ 
+
+ align:start position:0%
+are the coefficients of the polinomial
+they're n coefficient so it's a degree n
+
+ align:start position:0%
+they're n coefficient so it's a degree n
+ 
+
+ align:start position:0%
+they're n coefficient so it's a degree n
+minus one polom so
+
+ align:start position:0%
+minus one polom so
+ 
+
+ align:start position:0%
+minus one polom so
+when when would I S when would I accept
+
+ align:start position:0%
+when when would I S when would I accept
+ 
+
+ align:start position:0%
+when when would I S when would I accept
+a false claim if there exist two things
+
+ align:start position:0%
+a false claim if there exist two things
+ 
+
+ align:start position:0%
+a false claim if there exist two things
+that are equal that are different to
+
+ align:start position:0%
+that are equal that are different to
+ 
+
+ align:start position:0%
+that are equal that are different to
+there exists a row in in C that's
+
+ align:start position:0%
+there exists a row in in C that's
+ 
+
+ align:start position:0%
+there exists a row in in C that's
+different than a row in a *
+
+ align:start position:0%
+different than a row in a *
+ 
+
+ align:start position:0%
+different than a row in a *
+B so there exists a polinomial degree in
+
+ align:start position:0%
+B so there exists a polinomial degree in
+ 
+
+ align:start position:0%
+B so there exists a polinomial degree in
+minus one here and a different
+
+ align:start position:0%
+minus one here and a different
+ 
+
+ align:start position:0%
+minus one here and a different
+polinomial degree and minus one and
+
+ align:start position:0%
+polinomial degree and minus one and
+ 
+
+ align:start position:0%
+polinomial degree and minus one and
+these two pols are equal and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are but what is the probability that two
+
+ align:start position:0%
+are but what is the probability that two
+ 
+
+ align:start position:0%
+are but what is the probability that two
+distinct polinomial of degree n minus
+
+ align:start position:0%
+distinct polinomial of degree n minus
+ 
+
+ align:start position:0%
+distinct polinomial of degree n minus
+one are equal it's just this happens
+
+ align:start position:0%
+one are equal it's just this happens
+ 
+
+ align:start position:0%
+one are equal it's just this happens
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+probability at most n minus one the
+
+ align:start position:0%
+probability at most n minus one the
+ 
+
+ align:start position:0%
+probability at most n minus one the
+degree divided by the field
+
+ align:start position:0%
+degree divided by the field
+ 
+
+ align:start position:0%
+degree divided by the field
+sides right two pooms agree two distinct
+
+ align:start position:0%
+sides right two pooms agree two distinct
+ 
+
+ align:start position:0%
+sides right two pooms agree two distinct
+pols agree on at most or the fraction
+
+ align:start position:0%
+pols agree on at most or the fraction
+ 
+
+ align:start position:0%
+pols agree on at most or the fraction
+not they agree on at most n minus one
+
+ align:start position:0%
+not they agree on at most n minus one
+ 
+
+ align:start position:0%
+not they agree on at most n minus one
+points and which is nus one over F
+
+ align:start position:0%
+points and which is nus one over F
+ 
+
+ align:start position:0%
+points and which is nus one over F
+fraction of
+
+ align:start position:0%
+fraction of
+ 
+
+ align:start position:0%
+fraction of
+the of the field
+
+ align:start position:0%
+the of the field
+ 
+
+ align:start position:0%
+the of the field
+so so that so I'll I'll reject with this
+
+ align:start position:0%
+so so that so I'll I'll reject with this
+ 
+
+ align:start position:0%
+so so that so I'll I'll reject with this
+probability and if we're not happy with
+
+ align:start position:0%
+probability and if we're not happy with
+ 
+
+ align:start position:0%
+probability and if we're not happy with
+this F is f is not big enough for us
+
+ align:start position:0%
+this F is f is not big enough for us
+ 
+
+ align:start position:0%
+this F is f is not big enough for us
+then we do everything over a bigger
+
+ align:start position:0%
+then we do everything over a bigger
+ 
+
+ align:start position:0%
+then we do everything over a bigger
+extension field so we can except so our
+
+ align:start position:0%
+extension field so we can except so our
+ 
+
+ align:start position:0%
+extension field so we can except so our
+rejection probability will be uh high if
+
+ align:start position:0%
+rejection probability will be uh high if
+ 
+
+ align:start position:0%
+rejection probability will be uh high if
+if if the claims
+
+ align:start position:0%
+if if the claims
+ 
+
+ align:start position:0%
+if if the claims
+Falls any any questions about
+
+ align:start position:0%
+Falls any any questions about
+ 
+
+ align:start position:0%
+Falls any any questions about
+this okay so so far what we saw is that
+
+ align:start position:0%
+this okay so so far what we saw is that
+ 
+
+ align:start position:0%
+this okay so so far what we saw is that
+when oh yeah oh yes please thank you
+
+ align:start position:0%
+when oh yeah oh yes please thank you
+ 
+
+ align:start position:0%
+when oh yeah oh yes please thank you
+is this is not short zipa short zipa is
+
+ align:start position:0%
+is this is not short zipa short zipa is
+ 
+
+ align:start position:0%
+is this is not short zipa short zipa is
+similar but in a multivariant setting so
+
+ align:start position:0%
+similar but in a multivariant setting so
+ 
+
+ align:start position:0%
+similar but in a multivariant setting so
+this good so let me that's a good
+
+ align:start position:0%
+this good so let me that's a good
+ 
+
+ align:start position:0%
+this good so let me that's a good
+question so thank you so uh I just want
+
+ align:start position:0%
+question so thank you so uh I just want
+ 
+
+ align:start position:0%
+question so thank you so uh I just want
+to say oh by the way I should tell you
+
+ align:start position:0%
+to say oh by the way I should tell you
+ 
+
+ align:start position:0%
+to say oh by the way I should tell you
+guys this this uh this is being recorded
+
+ align:start position:0%
+guys this this uh this is being recorded
+ 
+
+ align:start position:0%
+guys this this uh this is being recorded
+I hope it's okay with you you're not
+
+ align:start position:0%
+I hope it's okay with you you're not
+ 
+
+ align:start position:0%
+I hope it's okay with you you're not
+being recorded it's supposed I'm
+
+ align:start position:0%
+being recorded it's supposed I'm
+ 
+
+ align:start position:0%
+being recorded it's supposed I'm
+supposed to be the one being recorded
+
+ align:start position:0%
+supposed to be the one being recorded
+ 
+
+ align:start position:0%
+supposed to be the one being recorded
+but I think you should know that there's
+
+ align:start position:0%
+but I think you should know that there's
+ 
+
+ align:start position:0%
+but I think you should know that there's
+a cameraman behind you uh but actually I
+
+ align:start position:0%
+a cameraman behind you uh but actually I
+ 
+
+ align:start position:0%
+a cameraman behind you uh but actually I
+don't I don't think I'm going to put
+
+ align:start position:0%
+don't I don't think I'm going to put
+ 
+
+ align:start position:0%
+don't I don't think I'm going to put
+this public I mean it's in the website
+
+ align:start position:0%
+this public I mean it's in the website
+ 
+
+ align:start position:0%
+this public I mean it's in the website
+for us well now the website is public so
+
+ align:start position:0%
+for us well now the website is public so
+ 
+
+ align:start position:0%
+for us well now the website is public so
+it will be public
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I can make it private if you prefer if
+
+ align:start position:0%
+I I can make it private if you prefer if
+ 
+
+ align:start position:0%
+I I can make it private if you prefer if
+if people come to me and ask for it to
+
+ align:start position:0%
+if people come to me and ask for it to
+ 
+
+ align:start position:0%
+if people come to me and ask for it to
+be private I'll make it private um okay
+
+ align:start position:0%
+be private I'll make it private um okay
+ 
+
+ align:start position:0%
+be private I'll make it private um okay
+uh so uh good so the question was was
+
+ align:start position:0%
+uh so uh good so the question was was
+ 
+
+ align:start position:0%
+uh so uh good so the question was was
+this short zipa and the answer exact
+
+ align:start position:0%
+this short zipa and the answer exact
+ 
+
+ align:start position:0%
+this short zipa and the answer exact
+short zipa is a multivariate version of
+
+ align:start position:0%
+short zipa is a multivariate version of
+ 
+
+ align:start position:0%
+short zipa is a multivariate version of
+this okay this is for the single variate
+
+ align:start position:0%
+this okay this is for the single variate
+ 
+
+ align:start position:0%
+this okay this is for the single variate
+case so the fact that two univariate
+
+ align:start position:0%
+case so the fact that two univariate
+ 
+
+ align:start position:0%
+case so the fact that two univariate
+polinomial of degree D distinct they're
+
+ align:start position:0%
+polinomial of degree D distinct they're
+ 
+
+ align:start position:0%
+polinomial of degree D distinct they're
+equal and a random value their equal and
+
+ align:start position:0%
+equal and a random value their equal and
+ 
+
+ align:start position:0%
+equal and a random value their equal and
+most D element D being the degree uh is
+
+ align:start position:0%
+most D element D being the degree uh is
+ 
+
+ align:start position:0%
+most D element D being the degree uh is
+uh is kind of I don't remember theorem
+
+ align:start position:0%
+uh is kind of I don't remember theorem
+ 
+
+ align:start position:0%
+uh is kind of I don't remember theorem
+like basic something
+
+ align:start position:0%
+like basic something
+ 
+
+ align:start position:0%
+like basic something
+M you say interation yeah but CH is
+
+ align:start position:0%
+M you say interation yeah but CH is
+ 
+
+ align:start position:0%
+M you say interation yeah but CH is
+exactly that but the multivariant
+
+ align:start position:0%
+exactly that but the multivariant
+ 
+
+ align:start position:0%
+exactly that but the multivariant
+setting so a generalization of exactly
+
+ align:start position:0%
+setting so a generalization of exactly
+ 
+
+ align:start position:0%
+setting so a generalization of exactly
+exactly the tral is exactly
+
+ align:start position:0%
+exactly the tral is exactly
+ 
+
+ align:start position:0%
+exactly the tral is exactly
+generalization of this the it will come
+
+ align:start position:0%
+generalization of this the it will come
+ 
+
+ align:start position:0%
+generalization of this the it will come
+up actually later in this class so yeah
+
+ align:start position:0%
+up actually later in this class so yeah
+ 
+
+ align:start position:0%
+up actually later in this class so yeah
+we'll talk about that great any other
+
+ align:start position:0%
+we'll talk about that great any other
+ 
+
+ align:start position:0%
+we'll talk about that great any other
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah good good good very good question
+
+ align:start position:0%
+yeah good good good very good question
+ 
+
+ align:start position:0%
+yeah good good good very good question
+so the question is can are do we have
+
+ align:start position:0%
+so the question is can are do we have
+ 
+
+ align:start position:0%
+so the question is can are do we have
+examples where Randomness gives you more
+
+ align:start position:0%
+examples where Randomness gives you more
+ 
+
+ align:start position:0%
+examples where Randomness gives you more
+speed up than just kind of pathetic this
+
+ align:start position:0%
+speed up than just kind of pathetic this
+ 
+
+ align:start position:0%
+speed up than just kind of pathetic this
+is not very interesting right so or in
+
+ align:start position:0%
+is not very interesting right so or in
+ 
+
+ align:start position:0%
+is not very interesting right so or in
+other words let me rephrase your
+
+ align:start position:0%
+other words let me rephrase your
+ 
+
+ align:start position:0%
+other words let me rephrase your
+question is the class ma different than
+
+ align:start position:0%
+question is the class ma different than
+ 
+
+ align:start position:0%
+question is the class ma different than
+NP that's the question we don't
+
+ align:start position:0%
+NP that's the question we don't
+ 
+
+ align:start position:0%
+NP that's the question we don't
+know so ma said that the
+
+ align:start position:0%
+know so ma said that the
+ 
+
+ align:start position:0%
+know so ma said that the
+verif yeah so the yeah so all and okay
+
+ align:start position:0%
+verif yeah so the yeah so all and okay
+ 
+
+ align:start position:0%
+verif yeah so the yeah so all and okay
+so yeah so let me explain uh there's a
+
+ align:start position:0%
+so yeah so let me explain uh there's a
+ 
+
+ align:start position:0%
+so yeah so let me explain uh there's a
+kind of there's this class called like m
+
+ align:start position:0%
+kind of there's this class called like m
+ 
+
+ align:start position:0%
+kind of there's this class called like m
+a m a ma a as many as you want and the
+
+ align:start position:0%
+a m a ma a as many as you want and the
+ 
+
+ align:start position:0%
+a m a ma a as many as you want and the
+idea is m means Merlin speaks mlin is
+
+ align:start position:0%
+idea is m means Merlin speaks mlin is
+ 
+
+ align:start position:0%
+idea is m means Merlin speaks mlin is
+the approver he's the wizard a means
+
+ align:start position:0%
+the approver he's the wizard a means
+ 
+
+ align:start position:0%
+the approver he's the wizard a means
+Arthur the king he's the verifier
+
+ align:start position:0%
+Arthur the king he's the verifier
+ 
+
+ align:start position:0%
+Arthur the king he's the verifier
+answers M speaks a answers M speak a
+
+ align:start position:0%
+answers M speaks a answers M speak a
+ 
+
+ align:start position:0%
+answers M speaks a answers M speak a
+answers so there's kind of these classes
+
+ align:start position:0%
+answers so there's kind of these classes
+ 
+
+ align:start position:0%
+answers so there's kind of these classes
+uh you know Ma a ma ma ma
+
+ align:start position:0%
+uh you know Ma a ma ma ma
+ 
+
+ align:start position:0%
+uh you know Ma a ma ma ma
+uh here ma a means M the Merlin speaks
+
+ align:start position:0%
+uh here ma a means M the Merlin speaks
+ 
+
+ align:start position:0%
+uh here ma a means M the Merlin speaks
+Arthur kind of uses Randomness and then
+
+ align:start position:0%
+Arthur kind of uses Randomness and then
+ 
+
+ align:start position:0%
+Arthur kind of uses Randomness and then
+kind of sends Randomness well he doesn't
+
+ align:start position:0%
+kind of sends Randomness well he doesn't
+ 
+
+ align:start position:0%
+kind of sends Randomness well he doesn't
+speak mlin doesn't speak again so but
+
+ align:start position:0%
+speak mlin doesn't speak again so but
+ 
+
+ align:start position:0%
+speak mlin doesn't speak again so but
+Merlin speaks Arthur chooses coins and
+
+ align:start position:0%
+Merlin speaks Arthur chooses coins and
+ 
+
+ align:start position:0%
+Merlin speaks Arthur chooses coins and
+then there's a verdict function that
+
+ align:start position:0%
+then there's a verdict function that
+ 
+
+ align:start position:0%
+then there's a verdict function that
+decides to accept or
+
+ align:start position:0%
+decides to accept or
+ 
+
+ align:start position:0%
+decides to accept or
+reject okay and we don't know if ma is
+
+ align:start position:0%
+reject okay and we don't know if ma is
+ 
+
+ align:start position:0%
+reject okay and we don't know if ma is
+different than NP yes so this actually
+
+ align:start position:0%
+different than NP yes so this actually
+ 
+
+ align:start position:0%
+different than NP yes so this actually
+is a you know po identity testing right
+
+ align:start position:0%
+is a you know po identity testing right
+ 
+
+ align:start position:0%
+is a you know po identity testing right
+right like you saying this is like poom
+
+ align:start position:0%
+right like you saying this is like poom
+ 
+
+ align:start position:0%
+right like you saying this is like poom
+identity yes I give you a circuit
+
+ align:start position:0%
+identity yes I give you a circuit
+ 
+
+ align:start position:0%
+identity yes I give you a circuit
+supp I claim
+
+ align:start position:0%
+supp I claim
+ 
+
+ align:start position:0%
+supp I claim
+that you can check it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clearly right right
+
+ align:start position:0%
+clearly right right
+ 
+
+ align:start position:0%
+clearly right right
+right right but uh oh you're saying
+
+ align:start position:0%
+right right but uh oh you're saying
+ 
+
+ align:start position:0%
+right right but uh oh you're saying
+you're saying sorry you're saying to
+
+ align:start position:0%
+you're saying sorry you're saying to
+ 
+
+ align:start position:0%
+you're saying sorry you're saying to
+test whether a circuit is a identically
+
+ align:start position:0%
+test whether a circuit is a identically
+ 
+
+ align:start position:0%
+test whether a circuit is a identically
+zero but wait oh you're giving us just
+
+ align:start position:0%
+zero but wait oh you're giving us just
+ 
+
+ align:start position:0%
+zero but wait oh you're giving us just
+as as a circuit as a circuit testing if
+
+ align:start position:0%
+as as a circuit as a circuit testing if
+ 
+
+ align:start position:0%
+as as a circuit as a circuit testing if
+it's identically zero
+
+ align:start position:0%
+it's identically zero
+ 
+
+ align:start position:0%
+it's identically zero
+but if it needs to be low degree because
+
+ align:start position:0%
+but if it needs to be low degree because
+ 
+
+ align:start position:0%
+but if it needs to be low degree because
+otherwise so like it's syntactically low
+
+ align:start position:0%
+otherwise so like it's syntactically low
+ 
+
+ align:start position:0%
+otherwise so like it's syntactically low
+degree right low dep or something right
+
+ align:start position:0%
+degree right low dep or something right
+ 
+
+ align:start position:0%
+degree right low dep or something right
+low depth aritic CC low depth like log
+
+ align:start position:0%
+low depth aritic CC low depth like log
+ 
+
+ align:start position:0%
+low depth aritic CC low depth like log
+log depth arithmetic circuit then you're
+
+ align:start position:0%
+log depth arithmetic circuit then you're
+ 
+
+ align:start position:0%
+log depth arithmetic circuit then you're
+saying it has polinomial degree it has
+
+ align:start position:0%
+saying it has polinomial degree it has
+ 
+
+ align:start position:0%
+saying it has polinomial degree it has
+polinomial degree you can test it by
+
+ align:start position:0%
+polinomial degree you can test it by
+ 
+
+ align:start position:0%
+polinomial degree you can test it by
+taking a large field it's sent field you
+
+ align:start position:0%
+taking a large field it's sent field you
+ 
+
+ align:start position:0%
+taking a large field it's sent field you
+can test you don't know how to predict
+
+ align:start position:0%
+can test you don't know how to predict
+ 
+
+ align:start position:0%
+can test you don't know how to predict
+if it's yes good we don't know how to D
+
+ align:start position:0%
+if it's yes good we don't know how to D
+ 
+
+ align:start position:0%
+if it's yes good we don't know how to D
+randomize it how to Der randomize
+
+ align:start position:0%
+randomize it how to Der randomize
+ 
+
+ align:start position:0%
+randomize it how to Der randomize
+randomize it then there are circulars
+
+ align:start position:0%
+randomize it then there are circulars
+ 
+
+ align:start position:0%
+randomize it then there are circulars
+which means you can randomize everything
+
+ align:start position:0%
+which means you can randomize everything
+ 
+
+ align:start position:0%
+which means you can randomize everything
+probably right more
+
+ align:start position:0%
+probably right more
+ 
+
+ align:start position:0%
+probably right more
+less you
+
+ align:start position:0%
+less you
+ 
+
+ align:start position:0%
+less you
+get yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Al no why why is it n so so you look at
+
+ align:start position:0%
+Al no why why is it n so so you look at
+ 
+
+ align:start position:0%
+Al no why why is it n so so you look at
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CL also right okay okay yeah yeah yeah
+
+ align:start position:0%
+CL also right okay okay yeah yeah yeah
+ 
+
+ align:start position:0%
+CL also right okay okay yeah yeah yeah
+yeah yeah you're right it's in BPP
+
+ align:start position:0%
+yeah yeah you're right it's in BPP
+ 
+
+ align:start position:0%
+yeah yeah you're right it's in BPP
+yeah so I just wanted to make the point
+
+ align:start position:0%
+yeah so I just wanted to make the point
+ 
+
+ align:start position:0%
+yeah so I just wanted to make the point
+that I describe is essentially the the
+
+ align:start position:0%
+that I describe is essentially the the
+ 
+
+ align:start position:0%
+that I describe is essentially the the
+only canonical problem in okay yeah yeah
+
+ align:start position:0%
+only canonical problem in okay yeah yeah
+ 
+
+ align:start position:0%
+only canonical problem in okay yeah yeah
+up to up to details which I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think thanks thanks yeah okay so uh okay
+
+ align:start position:0%
+think thanks thanks yeah okay so uh okay
+ 
+
+ align:start position:0%
+think thanks thanks yeah okay so uh okay
+so now let's go in ahead and just Define
+
+ align:start position:0%
+so now let's go in ahead and just Define
+ 
+
+ align:start position:0%
+so now let's go in ahead and just Define
+this class of NP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh of of Ip are interactive proofs so
+
+ align:start position:0%
+uh of of Ip are interactive proofs so
+ 
+
+ align:start position:0%
+uh of of Ip are interactive proofs so
+and then we'll show how kind of uh an
+
+ align:start position:0%
+and then we'll show how kind of uh an
+ 
+
+ align:start position:0%
+and then we'll show how kind of uh an
+actual uh to and we'll actually show why
+
+ align:start position:0%
+actual uh to and we'll actually show why
+ 
+
+ align:start position:0%
+actual uh to and we'll actually show why
+we believe this class is more powerful
+
+ align:start position:0%
+we believe this class is more powerful
+ 
+
+ align:start position:0%
+we believe this class is more powerful
+then NP will give kind of a a protocol
+
+ align:start position:0%
+then NP will give kind of a a protocol
+ 
+
+ align:start position:0%
+then NP will give kind of a a protocol
+that solves a problem that seems pretty
+
+ align:start position:0%
+that solves a problem that seems pretty
+ 
+
+ align:start position:0%
+that solves a problem that seems pretty
+hard so let's
+
+ align:start position:0%
+hard so let's
+ 
+
+ align:start position:0%
+hard so let's
+see so here is the so what is an
+
+ align:start position:0%
+see so here is the so what is an
+ 
+
+ align:start position:0%
+see so here is the so what is an
+interactive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof an interractive proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+IP this is a
+
+ align:start position:0%
+IP this is a
+ 
+
+ align:start position:0%
+IP this is a
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protocol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between and
+
+ align:start position:0%
+between and
+ 
+
+ align:start position:0%
+between and
+possibly all powerful okay I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+aover
+
+ align:start position:0%
+aover
+ 
+
+ align:start position:0%
+aover
+P okay so P can be run as long as he
+
+ align:start position:0%
+P okay so P can be run as long as he
+ 
+
+ align:start position:0%
+P okay so P can be run as long as he
+wants and a poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+verifier
+
+ align:start position:0%
+verifier
+ 
+
+ align:start position:0%
+verifier
+v such that here's the requirement want
+
+ align:start position:0%
+v such that here's the requirement want
+ 
+
+ align:start position:0%
+v such that here's the requirement want
+from from the protocol we want to say
+
+ align:start position:0%
+from from the protocol we want to say
+ 
+
+ align:start position:0%
+from from the protocol we want to say
+that a so interactive protocol let's say
+
+ align:start position:0%
+that a so interactive protocol let's say
+ 
+
+ align:start position:0%
+that a so interactive protocol let's say
+for H sorry between a
+
+ align:start position:0%
+for H sorry between a
+ 
+
+ align:start position:0%
+for H sorry between a
+p for a language l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for some
+
+ align:start position:0%
+for some
+ 
+
+ align:start position:0%
+for some
+language or some problem l so the
+
+ align:start position:0%
+language or some problem l so the
+ 
+
+ align:start position:0%
+language or some problem l so the
+problem correspondent is membership in L
+
+ align:start position:0%
+problem correspondent is membership in L
+ 
+
+ align:start position:0%
+problem correspondent is membership in L
+that's a problem is X a member not a
+
+ align:start position:0%
+that's a problem is X a member not a
+ 
+
+ align:start position:0%
+that's a problem is X a member not a
+member so an interactive proof should
+
+ align:start position:0%
+member so an interactive proof should
+ 
+
+ align:start position:0%
+member so an interactive proof should
+satisfy the following so it's a protocol
+
+ align:start position:0%
+satisfy the following so it's a protocol
+ 
+
+ align:start position:0%
+satisfy the following so it's a protocol
+such that it should have two properties
+
+ align:start position:0%
+such that it should have two properties
+ 
+
+ align:start position:0%
+such that it should have two properties
+completeness and
+
+ align:start position:0%
+completeness and
+ 
+
+ align:start position:0%
+completeness and
+soundness completeness says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if x is in the language the PO
+
+ align:start position:0%
+that if x is in the language the PO
+ 
+
+ align:start position:0%
+that if x is in the language the PO
+should convince you to
+
+ align:start position:0%
+should convince you to
+ 
+
+ align:start position:0%
+should convince you to
+accept Okay so if for every X in the
+
+ align:start position:0%
+accept Okay so if for every X in the
+ 
+
+ align:start position:0%
+accept Okay so if for every X in the
+language if you look if you denote let's
+
+ align:start position:0%
+language if you look if you denote let's
+ 
+
+ align:start position:0%
+language if you look if you denote let's
+say by T the transcript so let's say
+
+ align:start position:0%
+say by T the transcript so let's say
+ 
+
+ align:start position:0%
+say by T the transcript so let's say
+p uh and V which has secret Randomness
+
+ align:start position:0%
+p uh and V which has secret Randomness
+ 
+
+ align:start position:0%
+p uh and V which has secret Randomness
+the prover doesn't know what it is ahead
+
+ align:start position:0%
+the prover doesn't know what it is ahead
+ 
+
+ align:start position:0%
+the prover doesn't know what it is ahead
+of time and input X let's run this
+
+ align:start position:0%
+of time and input X let's run this
+ 
+
+ align:start position:0%
+of time and input X let's run this
+protocol we get a transcript
+
+ align:start position:0%
+protocol we get a transcript
+ 
+
+ align:start position:0%
+protocol we get a transcript
+okay so the it's an interactive protocol
+
+ align:start position:0%
+okay so the it's an interactive protocol
+ 
+
+ align:start position:0%
+okay so the it's an interactive protocol
+it actually think can think of it the
+
+ align:start position:0%
+it actually think can think of it the
+ 
+
+ align:start position:0%
+it actually think can think of it the
+protocol consists in two phases first
+
+ align:start position:0%
+protocol consists in two phases first
+ 
+
+ align:start position:0%
+protocol consists in two phases first
+there's interaction between the they
+
+ align:start position:0%
+there's interaction between the they
+ 
+
+ align:start position:0%
+there's interaction between the they
+talk back and forth let's denote the
+
+ align:start position:0%
+talk back and forth let's denote the
+ 
+
+ align:start position:0%
+talk back and forth let's denote the
+transcript by T okay often denot like
+
+ align:start position:0%
+transcript by T okay often denot like
+ 
+
+ align:start position:0%
+transcript by T okay often denot like
+like PV that's kind of the protocol the
+
+ align:start position:0%
+like PV that's kind of the protocol the
+ 
+
+ align:start position:0%
+like PV that's kind of the protocol the
+Prov has are both of them know the input
+
+ align:start position:0%
+Prov has are both of them know the input
+ 
+
+ align:start position:0%
+Prov has are both of them know the input
+X they generate a transcript and at the
+
+ align:start position:0%
+X they generate a transcript and at the
+ 
+
+ align:start position:0%
+X they generate a transcript and at the
+end the
+
+ align:start position:0%
+end the
+ 
+
+ align:start position:0%
+end the
+probability that V with his input with
+
+ align:start position:0%
+probability that V with his input with
+ 
+
+ align:start position:0%
+probability that V with his input with
+his uh he gets the transcript the r
+
+ align:start position:0%
+his uh he gets the transcript the r
+ 
+
+ align:start position:0%
+his uh he gets the transcript the r
+Randomness in X the probability that he
+
+ align:start position:0%
+Randomness in X the probability that he
+ 
+
+ align:start position:0%
+Randomness in X the probability that he
+accepts outputs one when we say output
+
+ align:start position:0%
+accepts outputs one when we say output
+ 
+
+ align:start position:0%
+accepts outputs one when we say output
+one we usually mean he
+
+ align:start position:0%
+one we usually mean he
+ 
+
+ align:start position:0%
+one we usually mean he
+accepts is large okay let me call a
+
+ align:start position:0%
+accepts is large okay let me call a
+ 
+
+ align:start position:0%
+accepts is large okay let me call a
+least
+
+ align:start position:0%
+least
+ 
+
+ align:start position:0%
+least
+C so and C is going to be a completeness
+
+ align:start position:0%
+C so and C is going to be a completeness
+ 
+
+ align:start position:0%
+C so and C is going to be a completeness
+parameter so a protocol between p and v
+
+ align:start position:0%
+parameter so a protocol between p and v
+ 
+
+ align:start position:0%
+parameter so a protocol between p and v
+for language L with completeness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soundness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S ah yes I do mean all AC now oh thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you thanks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L okay so if it's in the language he's
+
+ align:start position:0%
+L okay so if it's in the language he's
+ 
+
+ align:start position:0%
+L okay so if it's in the language he's
+accepted with high probability there's
+
+ align:start position:0%
+accepted with high probability there's
+ 
+
+ align:start position:0%
+accepted with high probability there's
+some complet this parameter C and most
+
+ align:start position:0%
+some complet this parameter C and most
+ 
+
+ align:start position:0%
+some complet this parameter C and most
+of what we see in class that AC is one
+
+ align:start position:0%
+of what we see in class that AC is one
+ 
+
+ align:start position:0%
+of what we see in class that AC is one
+okay you accept with probability one and
+
+ align:start position:0%
+okay you accept with probability one and
+ 
+
+ align:start position:0%
+okay you accept with probability one and
+sist
+
+ align:start position:0%
+sist
+ 
+
+ align:start position:0%
+sist
+says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this sist says that for any X not in the
+
+ align:start position:0%
+this sist says that for any X not in the
+ 
+
+ align:start position:0%
+this sist says that for any X not in the
+language
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for every X that's not in the
+
+ align:start position:0%
+for every X that's not in the
+ 
+
+ align:start position:0%
+for every X that's not in the
+language no matter how you try to cheat
+
+ align:start position:0%
+language no matter how you try to cheat
+ 
+
+ align:start position:0%
+language no matter how you try to cheat
+you'll fail okay so for any cheating
+
+ align:start position:0%
+you'll fail okay so for any cheating
+ 
+
+ align:start position:0%
+you'll fail okay so for any cheating
+prover or for any P star because it can
+
+ align:start position:0%
+prover or for any P star because it can
+ 
+
+ align:start position:0%
+prover or for any P star because it can
+be any any Prov that tries to convince
+
+ align:start position:0%
+be any any Prov that tries to convince
+ 
+
+ align:start position:0%
+be any any Prov that tries to convince
+me to
+
+ align:start position:0%
+me to
+ 
+
+ align:start position:0%
+me to
+accept if we the probability for the
+
+ align:start position:0%
+accept if we the probability for the
+ 
+
+ align:start position:0%
+accept if we the probability for the
+same t as above the probability that the
+
+ align:start position:0%
+same t as above the probability that the
+ 
+
+ align:start position:0%
+same t as above the probability that the
+verifier given the transcript the
+
+ align:start position:0%
+verifier given the transcript the
+ 
+
+ align:start position:0%
+verifier given the transcript the
+randomness in X outputs one accepts is
+
+ align:start position:0%
+randomness in X outputs one accepts is
+ 
+
+ align:start position:0%
+randomness in X outputs one accepts is
+at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s okay so that's if you if it's in the
+
+ align:start position:0%
+s okay so that's if you if it's in the
+ 
+
+ align:start position:0%
+s okay so that's if you if it's in the
+language you should be accept with high
+
+ align:start position:0%
+language you should be accept with high
+ 
+
+ align:start position:0%
+language you should be accept with high
+probability C is high if it's not in the
+
+ align:start position:0%
+probability C is high if it's not in the
+ 
+
+ align:start position:0%
+probability C is high if it's not in the
+language you should accept with small
+
+ align:start position:0%
+language you should accept with small
+ 
+
+ align:start position:0%
+language you should accept with small
+probability s is
+
+ align:start position:0%
+probability s is
+ 
+
+ align:start position:0%
+probability s is
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+okay question about the
+
+ align:start position:0%
+okay question about the
+ 
+
+ align:start position:0%
+okay question about the
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+yeah is there any restriction on S and C
+
+ align:start position:0%
+yeah is there any restriction on S and C
+ 
+
+ align:start position:0%
+yeah is there any restriction on S and C
+or they just right great question uh
+
+ align:start position:0%
+or they just right great question uh
+ 
+
+ align:start position:0%
+or they just right great question uh
+what are snc are they constant so that
+
+ align:start position:0%
+what are snc are they constant so that
+ 
+
+ align:start position:0%
+what are snc are they constant so that
+was my next remark which means that the
+
+ align:start position:0%
+was my next remark which means that the
+ 
+
+ align:start position:0%
+was my next remark which means that the
+question was right in place uh so often
+
+ align:start position:0%
+question was right in place uh so often
+ 
+
+ align:start position:0%
+question was right in place uh so often
+if you look at the literature there
+
+ align:start position:0%
+if you look at the literature there
+ 
+
+ align:start position:0%
+if you look at the literature there
+won't be a mention of s and C and C will
+
+ align:start position:0%
+won't be a mention of s and C and C will
+ 
+
+ align:start position:0%
+won't be a mention of s and C and C will
+be taken to be 2/3 and that's will be
+
+ align:start position:0%
+be taken to be 2/3 and that's will be
+ 
+
+ align:start position:0%
+be taken to be 2/3 and that's will be
+taken to be one3 that's kind of a
+
+ align:start position:0%
+taken to be one3 that's kind of a
+ 
+
+ align:start position:0%
+taken to be one3 that's kind of a
+canonical so when people say there's an
+
+ align:start position:0%
+canonical so when people say there's an
+ 
+
+ align:start position:0%
+canonical so when people say there's an
+inter here's an interactive proof often
+
+ align:start position:0%
+inter here's an interactive proof often
+ 
+
+ align:start position:0%
+inter here's an interactive proof often
+you think of s as 1/3 and C as 2/3 and
+
+ align:start position:0%
+you think of s as 1/3 and C as 2/3 and
+ 
+
+ align:start position:0%
+you think of s as 1/3 and C as 2/3 and
+this seems like very arbitrary and you
+
+ align:start position:0%
+this seems like very arbitrary and you
+ 
+
+ align:start position:0%
+this seems like very arbitrary and you
+should be be alarmed so what what you
+
+ align:start position:0%
+should be be alarmed so what what you
+ 
+
+ align:start position:0%
+should be be alarmed so what what you
+know where do this PL come
+
+ align:start position:0%
+know where do this PL come
+ 
+
+ align:start position:0%
+know where do this PL come
+from I don't I think it's
+
+ align:start position:0%
+from I don't I think it's
+ 
+
+ align:start position:0%
+from I don't I think it's
+theed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly exactly so the reason why we
+
+ align:start position:0%
+exactly exactly so the reason why we
+ 
+
+ align:start position:0%
+exactly exactly so the reason why we
+don't care so much about these constants
+
+ align:start position:0%
+don't care so much about these constants
+ 
+
+ align:start position:0%
+don't care so much about these constants
+is because if you have an interactive
+
+ align:start position:0%
+is because if you have an interactive
+ 
+
+ align:start position:0%
+is because if you have an interactive
+proof with a gap between CNS so for
+
+ align:start position:0%
+proof with a gap between CNS so for
+ 
+
+ align:start position:0%
+proof with a gap between CNS so for
+example 1/3 and 2/3 what we're going to
+
+ align:start position:0%
+example 1/3 and 2/3 what we're going to
+ 
+
+ align:start position:0%
+example 1/3 and 2/3 what we're going to
+do is repeat the protocol so let's say
+
+ align:start position:0%
+do is repeat the protocol so let's say
+ 
+
+ align:start position:0%
+do is repeat the protocol so let's say
+that it's 1/3 and 23 let's repeat the
+
+ align:start position:0%
+that it's 1/3 and 23 let's repeat the
+ 
+
+ align:start position:0%
+that it's 1/3 and 23 let's repeat the
+protocol let's say n times and then
+
+ align:start position:0%
+protocol let's say n times and then
+ 
+
+ align:start position:0%
+protocol let's say n times and then
+we're going to accept if you're closer
+
+ align:start position:0%
+we're going to accept if you're closer
+ 
+
+ align:start position:0%
+we're going to accept if you're closer
+to C and reject if you're closer to to s
+
+ align:start position:0%
+to C and reject if you're closer to to s
+ 
+
+ align:start position:0%
+to C and reject if you're closer to to s
+or if so in other words if you if more
+
+ align:start position:0%
+or if so in other words if you if more
+ 
+
+ align:start position:0%
+or if so in other words if you if more
+than C uh plus s over two like right in
+
+ align:start position:0%
+than C uh plus s over two like right in
+ 
+
+ align:start position:0%
+than C uh plus s over two like right in
+the middle if more than C plus s over
+
+ align:start position:0%
+the middle if more than C plus s over
+ 
+
+ align:start position:0%
+the middle if more than C plus s over
+two are accepted you're going to accept
+
+ align:start position:0%
+two are accepted you're going to accept
+ 
+
+ align:start position:0%
+two are accepted you're going to accept
+if less you're going to reject in in
+
+ align:start position:0%
+if less you're going to reject in in
+ 
+
+ align:start position:0%
+if less you're going to reject in in
+this case of 2/3 and third if let's say
+
+ align:start position:0%
+this case of 2/3 and third if let's say
+ 
+
+ align:start position:0%
+this case of 2/3 and third if let's say
+more than half repeat it many many many
+
+ align:start position:0%
+more than half repeat it many many many
+ 
+
+ align:start position:0%
+more than half repeat it many many many
+times you should accept if it's in the
+
+ align:start position:0%
+times you should accept if it's in the
+ 
+
+ align:start position:0%
+times you should accept if it's in the
+language you should expect to see about
+
+ align:start position:0%
+language you should expect to see about
+ 
+
+ align:start position:0%
+language you should expect to see about
+two3 acceptance if it's not in the
+
+ align:start position:0%
+two3 acceptance if it's not in the
+ 
+
+ align:start position:0%
+two3 acceptance if it's not in the
+language you should expect to see one
+
+ align:start position:0%
+language you should expect to see one
+ 
+
+ align:start position:0%
+language you should expect to see one
+third of them being accepted and if you
+
+ align:start position:0%
+third of them being accepted and if you
+ 
+
+ align:start position:0%
+third of them being accepted and if you
+repeat enough times by the laws of large
+
+ align:start position:0%
+repeat enough times by the laws of large
+ 
+
+ align:start position:0%
+repeat enough times by the laws of large
+numbers you're going to kind of get
+
+ align:start position:0%
+numbers you're going to kind of get
+ 
+
+ align:start position:0%
+numbers you're going to kind of get
+closer and closer to the expectation so
+
+ align:start position:0%
+closer and closer to the expectation so
+ 
+
+ align:start position:0%
+closer and closer to the expectation so
+you're going to be either very close to
+
+ align:start position:0%
+you're going to be either very close to
+ 
+
+ align:start position:0%
+you're going to be either very close to
+the 2/3 if you're in the language or
+
+ align:start position:0%
+the 2/3 if you're in the language or
+ 
+
+ align:start position:0%
+the 2/3 if you're in the language or
+very close to the one3 if you're outside
+
+ align:start position:0%
+very close to the one3 if you're outside
+ 
+
+ align:start position:0%
+very close to the one3 if you're outside
+the language and the the uh like the the
+
+ align:start position:0%
+the language and the the uh like the the
+ 
+
+ align:start position:0%
+the language and the the uh like the the
+there's very strong concentration so if
+
+ align:start position:0%
+there's very strong concentration so if
+ 
+
+ align:start position:0%
+there's very strong concentration so if
+you repeat it let's say n times then now
+
+ align:start position:0%
+you repeat it let's say n times then now
+ 
+
+ align:start position:0%
+you repeat it let's say n times then now
+you're can to be accepted or your the
+
+ align:start position:0%
+you're can to be accepted or your the
+ 
+
+ align:start position:0%
+you're can to be accepted or your the
+soundness and uh completeness Gap would
+
+ align:start position:0%
+soundness and uh completeness Gap would
+ 
+
+ align:start position:0%
+soundness and uh completeness Gap would
+be something like 2 the minus n versus 1
+
+ align:start position:0%
+be something like 2 the minus n versus 1
+ 
+
+ align:start position:0%
+be something like 2 the minus n versus 1
+minus 2 the minus n so you can really
+
+ align:start position:0%
+minus 2 the minus n so you can really
+ 
+
+ align:start position:0%
+minus 2 the minus n so you can really
+kind of uh very fast make these things
+
+ align:start position:0%
+kind of uh very fast make these things
+ 
+
+ align:start position:0%
+kind of uh very fast make these things
+go to zero and one which is why often we
+
+ align:start position:0%
+go to zero and one which is why often we
+ 
+
+ align:start position:0%
+go to zero and one which is why often we
+don't really care about these and you
+
+ align:start position:0%
+don't really care about these and you
+ 
+
+ align:start position:0%
+don't really care about these and you
+can think of them very close to zero and
+
+ align:start position:0%
+can think of them very close to zero and
+ 
+
+ align:start position:0%
+can think of them very close to zero and
+very close to one so if it's in the
+
+ align:start position:0%
+very close to one so if it's in the
+ 
+
+ align:start position:0%
+very close to one so if it's in the
+language you accept probability almost
+
+ align:start position:0%
+language you accept probability almost
+ 
+
+ align:start position:0%
+language you accept probability almost
+one if it's not the language you reject
+
+ align:start position:0%
+one if it's not the language you reject
+ 
+
+ align:start position:0%
+one if it's not the language you reject
+you accept probility almost zero
+
+ align:start position:0%
+you accept probility almost zero
+ 
+
+ align:start position:0%
+you accept probility almost zero
+okay great okay any question about kind
+
+ align:start position:0%
+okay great okay any question about kind
+ 
+
+ align:start position:0%
+okay great okay any question about kind
+of what an interactive uh proof
+
+ align:start position:0%
+of what an interactive uh proof
+ 
+
+ align:start position:0%
+of what an interactive uh proof
+is okay I just want to mention one thing
+
+ align:start position:0%
+is okay I just want to mention one thing
+ 
+
+ align:start position:0%
+is okay I just want to mention one thing
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+notation like PV on input X is
+
+ align:start position:0%
+notation like PV on input X is
+ 
+
+ align:start position:0%
+notation like PV on input X is
+overloaded we use this notation to
+
+ align:start position:0%
+overloaded we use this notation to
+ 
+
+ align:start position:0%
+overloaded we use this notation to
+denote the transcript we also use this
+
+ align:start position:0%
+denote the transcript we also use this
+ 
+
+ align:start position:0%
+denote the transcript we also use this
+notation to denote the verdict function
+
+ align:start position:0%
+notation to denote the verdict function
+ 
+
+ align:start position:0%
+notation to denote the verdict function
+whether V accepts or not and also I'll
+
+ align:start position:0%
+whether V accepts or not and also I'll
+ 
+
+ align:start position:0%
+whether V accepts or not and also I'll
+use that in class and also wherever you
+
+ align:start position:0%
+use that in class and also wherever you
+ 
+
+ align:start position:0%
+use that in class and also wherever you
+read you'll see both of them kind of
+
+ align:start position:0%
+read you'll see both of them kind of
+ 
+
+ align:start position:0%
+read you'll see both of them kind of
+used so it's good to get used to so this
+
+ align:start position:0%
+used so it's good to get used to so this
+ 
+
+ align:start position:0%
+used so it's good to get used to so this
+sometimes denotes the entire transcript
+
+ align:start position:0%
+sometimes denotes the entire transcript
+ 
+
+ align:start position:0%
+sometimes denotes the entire transcript
+sometimes it's just the notes the
+
+ align:start position:0%
+sometimes it's just the notes the
+ 
+
+ align:start position:0%
+sometimes it's just the notes the
+acceptance or ejection bit of of the
+
+ align:start position:0%
+acceptance or ejection bit of of the
+ 
+
+ align:start position:0%
+acceptance or ejection bit of of the
+verifier and it'll be clear in the
+
+ align:start position:0%
+verifier and it'll be clear in the
+ 
+
+ align:start position:0%
+verifier and it'll be clear in the
+context okay so now the question you
+
+ align:start position:0%
+context okay so now the question you
+ 
+
+ align:start position:0%
+context okay so now the question you
+should ask is okay is this uh is this
+
+ align:start position:0%
+should ask is okay is this uh is this
+ 
+
+ align:start position:0%
+should ask is okay is this uh is this
+model more expressive than
+
+ align:start position:0%
+model more expressive than
+ 
+
+ align:start position:0%
+model more expressive than
+NP what can we do with this model how
+
+ align:start position:0%
+NP what can we do with this model how
+ 
+
+ align:start position:0%
+NP what can we do with this model how
+can what's the power of this
+
+ align:start position:0%
+can what's the power of this
+ 
+
+ align:start position:0%
+can what's the power of this
+m so let me actually go to the punchline
+
+ align:start position:0%
+m so let me actually go to the punchline
+ 
+
+ align:start position:0%
+m so let me actually go to the punchline
+and say there's a celebrated result by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Shamir from 92 I
+
+ align:start position:0%
+Shamir from 92 I
+ 
+
+ align:start position:0%
+Shamir from 92 I
+believe and he showed ex he oh this
+
+ align:start position:0%
+believe and he showed ex he oh this
+ 
+
+ align:start position:0%
+believe and he showed ex he oh this
+model is very very powerful and actually
+
+ align:start position:0%
+model is very very powerful and actually
+ 
+
+ align:start position:0%
+model is very very powerful and actually
+you can prove any P space computation in
+
+ align:start position:0%
+you can prove any P space computation in
+ 
+
+ align:start position:0%
+you can prove any P space computation in
+this model namely if I want to prove to
+
+ align:start position:0%
+this model namely if I want to prove to
+ 
+
+ align:start position:0%
+this model namely if I want to prove to
+you any language in P space take any
+
+ align:start position:0%
+you any language in P space take any
+ 
+
+ align:start position:0%
+you any language in P space take any
+language in P space I can prove
+
+ align:start position:0%
+language in P space I can prove
+ 
+
+ align:start position:0%
+language in P space I can prove
+membership in this language to a
+
+ align:start position:0%
+membership in this language to a
+ 
+
+ align:start position:0%
+membership in this language to a
+verifier that only runs in polinomial
+
+ align:start position:0%
+verifier that only runs in polinomial
+ 
+
+ align:start position:0%
+verifier that only runs in polinomial
+time so that's sh so b space we believe
+
+ align:start position:0%
+time so that's sh so b space we believe
+ 
+
+ align:start position:0%
+time so that's sh so b space we believe
+is much much kind of more expressive
+
+ align:start position:0%
+is much much kind of more expressive
+ 
+
+ align:start position:0%
+is much much kind of more expressive
+stronger than NP we actually don't know
+
+ align:start position:0%
+stronger than NP we actually don't know
+ 
+
+ align:start position:0%
+stronger than NP we actually don't know
+how to prove it by the way but we
+
+ align:start position:0%
+how to prove it by the way but we
+ 
+
+ align:start position:0%
+how to prove it by the way but we
+believe that's the
+
+ align:start position:0%
+believe that's the
+ 
+
+ align:start position:0%
+believe that's the
+case uh so we believe this is a much
+
+ align:start position:0%
+case uh so we believe this is a much
+ 
+
+ align:start position:0%
+case uh so we believe this is a much
+stronger kind of uh proof
+
+ align:start position:0%
+stronger kind of uh proof
+ 
+
+ align:start position:0%
+stronger kind of uh proof
+system okay actually before I I'm going
+
+ align:start position:0%
+system okay actually before I I'm going
+ 
+
+ align:start position:0%
+system okay actually before I I'm going
+to show you actually now I'm going to
+
+ align:start position:0%
+to show you actually now I'm going to
+ 
+
+ align:start position:0%
+to show you actually now I'm going to
+give you an example of the kind of the
+
+ align:start position:0%
+give you an example of the kind of the
+ 
+
+ align:start position:0%
+give you an example of the kind of the
+power of this proof system but before I
+
+ align:start position:0%
+power of this proof system but before I
+ 
+
+ align:start position:0%
+power of this proof system but before I
+go into kind of the technicality I want
+
+ align:start position:0%
+go into kind of the technicality I want
+ 
+
+ align:start position:0%
+go into kind of the technicality I want
+to step back for a second and kind of
+
+ align:start position:0%
+to step back for a second and kind of
+ 
+
+ align:start position:0%
+to step back for a second and kind of
+think a little bit about the story here
+
+ align:start position:0%
+think a little bit about the story here
+ 
+
+ align:start position:0%
+think a little bit about the story here
+which is a very nice story so you know
+
+ align:start position:0%
+which is a very nice story so you know
+ 
+
+ align:start position:0%
+which is a very nice story so you know
+this introduction of uh interactive
+
+ align:start position:0%
+this introduction of uh interactive
+ 
+
+ align:start position:0%
+this introduction of uh interactive
+proofs this model came about for the
+
+ align:start position:0%
+proofs this model came about for the
+ 
+
+ align:start position:0%
+proofs this model came about for the
+goal of doing zero knowledge nobody
+
+ align:start position:0%
+goal of doing zero knowledge nobody
+ 
+
+ align:start position:0%
+goal of doing zero knowledge nobody
+thought at that point about whether you
+
+ align:start position:0%
+thought at that point about whether you
+ 
+
+ align:start position:0%
+thought at that point about whether you
+can prove more languages not more
+
+ align:start position:0%
+can prove more languages not more
+ 
+
+ align:start position:0%
+can prove more languages not more
+languag which is the only thing you want
+
+ align:start position:0%
+languag which is the only thing you want
+ 
+
+ align:start position:0%
+languag which is the only thing you want
+is to hide okay I just want to hide why
+
+ align:start position:0%
+is to hide okay I just want to hide why
+ 
+
+ align:start position:0%
+is to hide okay I just want to hide why
+a theorem is true I want to hide the
+
+ align:start position:0%
+a theorem is true I want to hide the
+ 
+
+ align:start position:0%
+a theorem is true I want to hide the
+proof I want to convince you but hide
+
+ align:start position:0%
+proof I want to convince you but hide
+ 
+
+ align:start position:0%
+proof I want to convince you but hide
+that was the only goal uh that kind of
+
+ align:start position:0%
+that was the only goal uh that kind of
+ 
+
+ align:start position:0%
+that was the only goal uh that kind of
+introduced this model and it's kind of
+
+ align:start position:0%
+introduced this model and it's kind of
+ 
+
+ align:start position:0%
+introduced this model and it's kind of
+interesting how kind of very F like also
+
+ align:start position:0%
+interesting how kind of very F like also
+ 
+
+ align:start position:0%
+interesting how kind of very F like also
+who cares about zero knowledge this is a
+
+ align:start position:0%
+who cares about zero knowledge this is a
+ 
+
+ align:start position:0%
+who cares about zero knowledge this is a
+really interesting model let's see what
+
+ align:start position:0%
+really interesting model let's see what
+ 
+
+ align:start position:0%
+really interesting model let's see what
+we can do with it and this kind of open
+
+ align:start position:0%
+we can do with it and this kind of open
+ 
+
+ align:start position:0%
+we can do with it and this kind of open
+our eyes just the idea that we can shift
+
+ align:start position:0%
+our eyes just the idea that we can shift
+ 
+
+ align:start position:0%
+our eyes just the idea that we can shift
+from the traditional way of thinking
+
+ align:start position:0%
+from the traditional way of thinking
+ 
+
+ align:start position:0%
+from the traditional way of thinking
+about proofs to this attractive and
+
+ align:start position:0%
+about proofs to this attractive and
+ 
+
+ align:start position:0%
+about proofs to this attractive and
+randomized randomized land kind of
+
+ align:start position:0%
+randomized randomized land kind of
+ 
+
+ align:start position:0%
+randomized randomized land kind of
+brought about a lot of really really
+
+ align:start position:0%
+brought about a lot of really really
+ 
+
+ align:start position:0%
+brought about a lot of really really
+beautiful and fascinating results
+
+ align:start position:0%
+beautiful and fascinating results
+ 
+
+ align:start position:0%
+beautiful and fascinating results
+including the fact this is the first
+
+ align:start position:0%
+including the fact this is the first
+ 
+
+ align:start position:0%
+including the fact this is the first
+time to realize wow we can prove a lot
+
+ align:start position:0%
+time to realize wow we can prove a lot
+ 
+
+ align:start position:0%
+time to realize wow we can prove a lot
+of ver to a polinomial Time verifier
+
+ align:start position:0%
+of ver to a polinomial Time verifier
+ 
+
+ align:start position:0%
+of ver to a polinomial Time verifier
+much more than what was believed to
+
+ align:start position:0%
+much more than what was believed to
+ 
+
+ align:start position:0%
+much more than what was believed to
+be a what we believed we can do with a
+
+ align:start position:0%
+be a what we believed we can do with a
+ 
+
+ align:start position:0%
+be a what we believed we can do with a
+classical
+
+ align:start position:0%
+classical
+ 
+
+ align:start position:0%
+classical
+proof so this was kind of really I think
+
+ align:start position:0%
+proof so this was kind of really I think
+ 
+
+ align:start position:0%
+proof so this was kind of really I think
+eye opening and very interesting so okay
+
+ align:start position:0%
+eye opening and very interesting so okay
+ 
+
+ align:start position:0%
+eye opening and very interesting so okay
+so now I'm GNA convince you try to
+
+ align:start position:0%
+so now I'm GNA convince you try to
+ 
+
+ align:start position:0%
+so now I'm GNA convince you try to
+convince you of why this
+
+ align:start position:0%
+convince you of why this
+ 
+
+ align:start position:0%
+convince you of why this
+a proof system this model is so powerful
+
+ align:start position:0%
+a proof system this model is so powerful
+ 
+
+ align:start position:0%
+a proof system this model is so powerful
+by giving you an example of things of a
+
+ align:start position:0%
+by giving you an example of things of a
+ 
+
+ align:start position:0%
+by giving you an example of things of a
+problem that I can prove to you using an
+
+ align:start position:0%
+problem that I can prove to you using an
+ 
+
+ align:start position:0%
+problem that I can prove to you using an
+interactive proof that we really don't
+
+ align:start position:0%
+interactive proof that we really don't
+ 
+
+ align:start position:0%
+interactive proof that we really don't
+know how to prove using a classical
+
+ align:start position:0%
+know how to prove using a classical
+ 
+
+ align:start position:0%
+know how to prove using a classical
+proof okay so let me give you the
+
+ align:start position:0%
+proof okay so let me give you the
+ 
+
+ align:start position:0%
+proof okay so let me give you the
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example so the protocol is called Su
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protocol and this I'm going to give you
+
+ align:start position:0%
+protocol and this I'm going to give you
+ 
+
+ align:start position:0%
+protocol and this I'm going to give you
+an interactive this is an interactive
+
+ align:start position:0%
+an interactive this is an interactive
+ 
+
+ align:start position:0%
+an interactive this is an interactive
+proof for the following problem so take
+
+ align:start position:0%
+proof for the following problem so take
+ 
+
+ align:start position:0%
+proof for the following problem so take
+any degree
+
+ align:start position:0%
+any degree
+ 
+
+ align:start position:0%
+any degree
+fix or okay
+
+ align:start position:0%
+fix or okay
+ 
+
+ align:start position:0%
+fix or okay
+given a
+
+ align:start position:0%
+given a
+ 
+
+ align:start position:0%
+given a
+polinomial
+
+ align:start position:0%
+polinomial
+ 
+
+ align:start position:0%
+polinomial
+F let's say from F to the N so
+
+ align:start position:0%
+F let's say from F to the N so
+ 
+
+ align:start position:0%
+F let's say from F to the N so
+multivariate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polinomial of let's take degree D in
+
+ align:start position:0%
+polinomial of let's take degree D in
+ 
+
+ align:start position:0%
+polinomial of let's take degree D in
+each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable okay I want a proof
+
+ align:start position:0%
+variable okay I want a proof
+ 
+
+ align:start position:0%
+variable okay I want a proof
+that sum of f B1
+
+ align:start position:0%
+that sum of f B1
+ 
+
+ align:start position:0%
+that sum of f B1
+or let me just make sure how do I wrot
+
+ align:start position:0%
+or let me just make sure how do I wrot
+ 
+
+ align:start position:0%
+or let me just make sure how do I wrot
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+down okay
+
+ align:start position:0%
+down okay
+ 
+
+ align:start position:0%
+down okay
+sorry so take any fix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any subset h and
+
+ align:start position:0%
+any subset h and
+ 
+
+ align:start position:0%
+any subset h and
+f you can think of H 01 you can think of
+
+ align:start position:0%
+f you can think of H 01 you can think of
+ 
+
+ align:start position:0%
+f you can think of H 01 you can think of
+a bigger
+
+ align:start position:0%
+a bigger
+ 
+
+ align:start position:0%
+a bigger
+set I want to I want you to convince me
+
+ align:start position:0%
+set I want to I want you to convince me
+ 
+
+ align:start position:0%
+set I want to I want you to convince me
+that Su F of H1 up to hm
+
+ align:start position:0%
+that Su F of H1 up to hm
+ 
+
+ align:start position:0%
+that Su F of H1 up to hm
+for all H1 up to
+
+ align:start position:0%
+for all H1 up to
+ 
+
+ align:start position:0%
+for all H1 up to
+hm in
+
+ align:start position:0%
+hm in
+ 
+
+ align:start position:0%
+hm in
+h is equals some value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta okay so there's a fixed polinomial
+
+ align:start position:0%
+beta okay so there's a fixed polinomial
+ 
+
+ align:start position:0%
+beta okay so there's a fixed polinomial
+F let's say I know this polinomial I
+
+ align:start position:0%
+F let's say I know this polinomial I
+ 
+
+ align:start position:0%
+F let's say I know this polinomial I
+either it actually has a succinct
+
+ align:start position:0%
+either it actually has a succinct
+ 
+
+ align:start position:0%
+either it actually has a succinct
+circuit or maybe I have Oracle access to
+
+ align:start position:0%
+circuit or maybe I have Oracle access to
+ 
+
+ align:start position:0%
+circuit or maybe I have Oracle access to
+it so I'm a
+
+ align:start position:0%
+it so I'm a
+ 
+
+ align:start position:0%
+it so I'm a
+verifier I'm a verifier I have let's say
+
+ align:start position:0%
+verifier I'm a verifier I have let's say
+ 
+
+ align:start position:0%
+verifier I'm a verifier I have let's say
+I have Oracle access to this polinomial
+
+ align:start position:0%
+I have Oracle access to this polinomial
+ 
+
+ align:start position:0%
+I have Oracle access to this polinomial
+or there are some sync way to compute it
+
+ align:start position:0%
+or there are some sync way to compute it
+ 
+
+ align:start position:0%
+or there are some sync way to compute it
+so I can compute this polinomial easily
+
+ align:start position:0%
+so I can compute this polinomial easily
+ 
+
+ align:start position:0%
+so I can compute this polinomial easily
+let's think for now I have Oracle access
+
+ align:start position:0%
+let's think for now I have Oracle access
+ 
+
+ align:start position:0%
+let's think for now I have Oracle access
+to it so I can kind of query it in some
+
+ align:start position:0%
+to it so I can kind of query it in some
+ 
+
+ align:start position:0%
+to it so I can kind of query it in some
+point and after that and get back an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer I want you to I want prove you
+
+ align:start position:0%
+answer I want you to I want prove you
+ 
+
+ align:start position:0%
+answer I want you to I want prove you
+you're going to prove to me that the sum
+
+ align:start position:0%
+you're going to prove to me that the sum
+ 
+
+ align:start position:0%
+you're going to prove to me that the sum
+of this polinomial and H to the m points
+
+ align:start position:0%
+of this polinomial and H to the m points
+ 
+
+ align:start position:0%
+of this polinomial and H to the m points
+and all the points there some set H you
+
+ align:start position:0%
+and all the points there some set H you
+ 
+
+ align:start position:0%
+and all the points there some set H you
+can think of H as 01 you can think of it
+
+ align:start position:0%
+can think of H as 01 you can think of it
+ 
+
+ align:start position:0%
+can think of H as 01 you can think of it
+bigger and I want you to sum this iial
+
+ align:start position:0%
+bigger and I want you to sum this iial
+ 
+
+ align:start position:0%
+bigger and I want you to sum this iial
+on all the elements in the set H to the
+
+ align:start position:0%
+on all the elements in the set H to the
+ 
+
+ align:start position:0%
+on all the elements in the set H to the
+N okay all of this is done over some
+
+ align:start position:0%
+N okay all of this is done over some
+ 
+
+ align:start position:0%
+N okay all of this is done over some
+finite field
+
+ align:start position:0%
+finite field
+ 
+
+ align:start position:0%
+finite field
+F and there's a result beta I want to
+
+ align:start position:0%
+F and there's a result beta I want to
+ 
+
+ align:start position:0%
+F and there's a result beta I want to
+prove that this sum is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta okay that's that's I I'm going to
+
+ align:start position:0%
+beta okay that's that's I I'm going to
+ 
+
+ align:start position:0%
+beta okay that's that's I I'm going to
+show you an interactive proof for this
+
+ align:start position:0%
+show you an interactive proof for this
+ 
+
+ align:start position:0%
+show you an interactive proof for this
+langage now before kind of you guys are
+
+ align:start position:0%
+langage now before kind of you guys are
+ 
+
+ align:start position:0%
+langage now before kind of you guys are
+like seriously why do I care about this
+
+ align:start position:0%
+like seriously why do I care about this
+ 
+
+ align:start position:0%
+like seriously why do I care about this
+language is it interesting where did I
+
+ align:start position:0%
+language is it interesting where did I
+ 
+
+ align:start position:0%
+language is it interesting where did I
+come up with this thing let me tell you
+
+ align:start position:0%
+come up with this thing let me tell you
+ 
+
+ align:start position:0%
+come up with this thing let me tell you
+I think this is
+
+ align:start position:0%
+I think this is
+ 
+
+ align:start position:0%
+I think this is
+the most important protocol in all the
+
+ align:start position:0%
+the most important protocol in all the
+ 
+
+ align:start position:0%
+the most important protocol in all the
+literature and pro systems okay we all
+
+ align:start position:0%
+literature and pro systems okay we all
+ 
+
+ align:start position:0%
+literature and pro systems okay we all
+use this protocol all the time it turns
+
+ align:start position:0%
+use this protocol all the time it turns
+ 
+
+ align:start position:0%
+use this protocol all the time it turns
+out to be super super influential okay
+
+ align:start position:0%
+out to be super super influential okay
+ 
+
+ align:start position:0%
+out to be super super influential okay
+every single thing we'll use from now on
+
+ align:start position:0%
+every single thing we'll use from now on
+ 
+
+ align:start position:0%
+every single thing we'll use from now on
+relies on this protocol okay so it turns
+
+ align:start position:0%
+relies on this protocol okay so it turns
+ 
+
+ align:start position:0%
+relies on this protocol okay so it turns
+out and I'm going to convince you that
+
+ align:start position:0%
+out and I'm going to convince you that
+ 
+
+ align:start position:0%
+out and I'm going to convince you that
+later uh but that this is a very very
+
+ align:start position:0%
+later uh but that this is a very very
+ 
+
+ align:start position:0%
+later uh but that this is a very very
+important actually problem okay if you
+
+ align:start position:0%
+important actually problem okay if you
+ 
+
+ align:start position:0%
+important actually problem okay if you
+have interactive proof for this problem
+
+ align:start position:0%
+have interactive proof for this problem
+ 
+
+ align:start position:0%
+have interactive proof for this problem
+you it kind of gives you rise attrative
+
+ align:start position:0%
+you it kind of gives you rise attrative
+ 
+
+ align:start position:0%
+you it kind of gives you rise attrative
+proof for many many many other
+
+ align:start position:0%
+proof for many many many other
+ 
+
+ align:start position:0%
+proof for many many many other
+problems okay actually we use this if
+
+ align:start position:0%
+problems okay actually we use this if
+ 
+
+ align:start position:0%
+problems okay actually we use this if
+you give me an interactive proof for
+
+ align:start position:0%
+you give me an interactive proof for
+ 
+
+ align:start position:0%
+you give me an interactive proof for
+this problem I can use it to get an
+
+ align:start position:0%
+this problem I can use it to get an
+ 
+
+ align:start position:0%
+this problem I can use it to get an
+interactive proof for all P
+
+ align:start position:0%
+interactive proof for all P
+ 
+
+ align:start position:0%
+interactive proof for all P
+space in kind of a blackbox way so
+
+ align:start position:0%
+space in kind of a blackbox way so
+ 
+
+ align:start position:0%
+space in kind of a blackbox way so
+really this is the heart of coming up
+
+ align:start position:0%
+really this is the heart of coming up
+ 
+
+ align:start position:0%
+really this is the heart of coming up
+with interactive proofs this is the most
+
+ align:start position:0%
+with interactive proofs this is the most
+ 
+
+ align:start position:0%
+with interactive proofs this is the most
+important interactive
+
+ align:start position:0%
+important interactive
+ 
+
+ align:start position:0%
+important interactive
+proof okay so with that let me show you
+
+ align:start position:0%
+proof okay so with that let me show you
+ 
+
+ align:start position:0%
+proof okay so with that let me show you
+the interactive proof for proving
+
+ align:start position:0%
+the interactive proof for proving
+ 
+
+ align:start position:0%
+the interactive proof for proving
+this okay any questions before we jump
+
+ align:start position:0%
+this okay any questions before we jump
+ 
+
+ align:start position:0%
+this okay any questions before we jump
+yeah just H is like one
+
+ align:start position:0%
+yeah just H is like one
+ 
+
+ align:start position:0%
+yeah just H is like one
+dimension exactly H exactly you can
+
+ align:start position:0%
+dimension exactly H exactly you can
+ 
+
+ align:start position:0%
+dimension exactly H exactly you can
+think of H is 01 for example you can
+
+ align:start position:0%
+think of H is 01 for example you can
+ 
+
+ align:start position:0%
+think of H is 01 for example you can
+think of H 012 yeah I mean if two is in
+
+ align:start position:0%
+think of H 012 yeah I mean if two is in
+ 
+
+ align:start position:0%
+think of H 012 yeah I mean if two is in
+the field yeah it's a onedimensional
+
+ align:start position:0%
+the field yeah it's a onedimensional
+ 
+
+ align:start position:0%
+the field yeah it's a onedimensional
+thing right and you sum over so as a the
+
+ align:start position:0%
+thing right and you sum over so as a the
+ 
+
+ align:start position:0%
+thing right and you sum over so as a the
+you sum here over H to the m sides of H
+
+ align:start position:0%
+you sum here over H to the m sides of H
+ 
+
+ align:start position:0%
+you sum here over H to the m sides of H
+to the m elements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it can be you sum over all of them
+
+ align:start position:0%
+uh it can be you sum over all of them
+ 
+
+ align:start position:0%
+uh it can be you sum over all of them
+you sum over also like z z z z z one
+
+ align:start position:0%
+you sum over also like z z z z z one
+ 
+
+ align:start position:0%
+you sum over also like z z z z z one
+yeah all yeah H one and each2 do not
+
+ align:start position:0%
+yeah all yeah H one and each2 do not
+ 
+
+ align:start position:0%
+yeah all yeah H one and each2 do not
+need to be distinct at all yeah exactly
+
+ align:start position:0%
+need to be distinct at all yeah exactly
+ 
+
+ align:start position:0%
+need to be distinct at all yeah exactly
+over all possible yeah you Su over H to
+
+ align:start position:0%
+over all possible yeah you Su over H to
+ 
+
+ align:start position:0%
+over all possible yeah you Su over H to
+the m elements each one all all the
+
+ align:start position:0%
+the m elements each one all all the
+ 
+
+ align:start position:0%
+the m elements each one all all the
+possibilities good other
+
+ align:start position:0%
+possibilities good other
+ 
+
+ align:start position:0%
+possibilities good other
+questions thank you yes so degree D in
+
+ align:start position:0%
+questions thank you yes so degree D in
+ 
+
+ align:start position:0%
+questions thank you yes so degree D in
+each variable just means like any
+
+ align:start position:0%
+each variable just means like any
+ 
+
+ align:start position:0%
+each variable just means like any
+variable is exp exactly so yeah let me
+
+ align:start position:0%
+variable is exp exactly so yeah let me
+ 
+
+ align:start position:0%
+variable is exp exactly so yeah let me
+good good great so degree D in each
+
+ align:start position:0%
+good good great so degree D in each
+ 
+
+ align:start position:0%
+good good great so degree D in each
+variable means f is a polinomial so you
+
+ align:start position:0%
+variable means f is a polinomial so you
+ 
+
+ align:start position:0%
+variable means f is a polinomial so you
+can write it as a sum of monomials each
+
+ align:start position:0%
+can write it as a sum of monomials each
+ 
+
+ align:start position:0%
+can write it as a sum of monomials each
+monomial each uh H variable has a degree
+
+ align:start position:0%
+monomial each uh H variable has a degree
+ 
+
+ align:start position:0%
+monomial each uh H variable has a degree
+so I want say if you look at all the
+
+ align:start position:0%
+so I want say if you look at all the
+ 
+
+ align:start position:0%
+so I want say if you look at all the
+monomials each variable has a degree and
+
+ align:start position:0%
+monomials each variable has a degree and
+ 
+
+ align:start position:0%
+monomials each variable has a degree and
+most be in each of the
+
+ align:start position:0%
+most be in each of the
+ 
+
+ align:start position:0%
+most be in each of the
+monomials okay great questions thank you
+
+ align:start position:0%
+monomials okay great questions thank you
+ 
+
+ align:start position:0%
+monomials okay great questions thank you
+any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay great so let me give you
+
+ align:start position:0%
+questions okay great so let me give you
+ 
+
+ align:start position:0%
+questions okay great so let me give you
+uh the protocol a
+
+ align:start position:0%
+uh the protocol a
+ 
+
+ align:start position:0%
+uh the protocol a
+so let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it by the way I want to tell you I get
+
+ align:start position:0%
+it by the way I want to tell you I get
+ 
+
+ align:start position:0%
+it by the way I want to tell you I get
+such satisfactions from your questions
+
+ align:start position:0%
+such satisfactions from your questions
+ 
+
+ align:start position:0%
+such satisfactions from your questions
+so if you just want to make me happy
+
+ align:start position:0%
+so if you just want to make me happy
+ 
+
+ align:start position:0%
+so if you just want to make me happy
+which is a great goal on its own and you
+
+ align:start position:0%
+which is a great goal on its own and you
+ 
+
+ align:start position:0%
+which is a great goal on its own and you
+should ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ready for the protocol okay Pro
+
+ align:start position:0%
+ready for the protocol okay Pro
+ 
+
+ align:start position:0%
+ready for the protocol okay Pro
+convinces a
+
+ align:start position:0%
+convinces a
+ 
+
+ align:start position:0%
+convinces a
+verifier that the sum F on H1 up to
+
+ align:start position:0%
+verifier that the sum F on H1 up to
+ 
+
+ align:start position:0%
+verifier that the sum F on H1 up to
+hn is equal to
+
+ align:start position:0%
+hn is equal to
+ 
+
+ align:start position:0%
+hn is equal to
+Beta where the H is are all elements in
+
+ align:start position:0%
+Beta where the H is are all elements in
+ 
+
+ align:start position:0%
+Beta where the H is are all elements in
+this set H which is in the field we have
+
+ align:start position:0%
+this set H which is in the field we have
+ 
+
+ align:start position:0%
+this set H which is in the field we have
+some fixed field that we're looking over
+
+ align:start position:0%
+some fixed field that we're looking over
+ 
+
+ align:start position:0%
+some fixed field that we're looking over
+okay how would he prove what would what
+
+ align:start position:0%
+okay how would he prove what would what
+ 
+
+ align:start position:0%
+okay how would he prove what would what
+would he do so here is the idea the idea
+
+ align:start position:0%
+would he do so here is the idea the idea
+ 
+
+ align:start position:0%
+would he do so here is the idea the idea
+is the prover will first
+
+ align:start position:0%
+is the prover will first
+ 
+
+ align:start position:0%
+is the prover will first
+send this sum this polinomial but where
+
+ align:start position:0%
+send this sum this polinomial but where
+ 
+
+ align:start position:0%
+send this sum this polinomial but where
+the first variable is EMP is open so he
+
+ align:start position:0%
+the first variable is EMP is open so he
+ 
+
+ align:start position:0%
+the first variable is EMP is open so he
+will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compute he will compute some only over
+
+ align:start position:0%
+compute he will compute some only over
+ 
+
+ align:start position:0%
+compute he will compute some only over
+H2 up to
+
+ align:start position:0%
+H2 up to
+ 
+
+ align:start position:0%
+H2 up to
+hm f of x this is a variable H2 up to hn
+
+ align:start position:0%
+hm f of x this is a variable H2 up to hn
+ 
+
+ align:start position:0%
+hm f of x this is a variable H2 up to hn
+and he will send this over let's call
+
+ align:start position:0%
+and he will send this over let's call
+ 
+
+ align:start position:0%
+and he will send this over let's call
+this G1 of
+
+ align:start position:0%
+this G1 of
+ 
+
+ align:start position:0%
+this G1 of
+X so he sends a univariate
+
+ align:start position:0%
+X so he sends a univariate
+ 
+
+ align:start position:0%
+X so he sends a univariate
+polinomial okay where he sums over H2 to
+
+ align:start position:0%
+polinomial okay where he sums over H2 to
+ 
+
+ align:start position:0%
+polinomial okay where he sums over H2 to
+hm but leaves the first variable
+
+ align:start position:0%
+hm but leaves the first variable
+ 
+
+ align:start position:0%
+hm but leaves the first variable
+open okay what is the degree of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polinomial D very good so this is a
+
+ align:start position:0%
+polinomial D very good so this is a
+ 
+
+ align:start position:0%
+polinomial D very good so this is a
+degree d
+
+ align:start position:0%
+degree d
+ 
+
+ align:start position:0%
+degree d
+polinomial the verifier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+checks that G1 is of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degree at most D if not he rejects
+
+ align:start position:0%
+degree at most D if not he rejects
+ 
+
+ align:start position:0%
+degree at most D if not he rejects
+because he knows that this is a degree D
+
+ align:start position:0%
+because he knows that this is a degree D
+ 
+
+ align:start position:0%
+because he knows that this is a degree D
+polinomial multivaried
+
+ align:start position:0%
+polinomial multivaried
+ 
+
+ align:start position:0%
+polinomial multivaried
+polinomial so he knows that each
+
+ align:start position:0%
+polinomial so he knows that each
+ 
+
+ align:start position:0%
+polinomial so he knows that each
+variable is the degree most D so if you
+
+ align:start position:0%
+variable is the degree most D so if you
+ 
+
+ align:start position:0%
+variable is the degree most D so if you
+s something degree like you're cheating
+
+ align:start position:0%
+s something degree like you're cheating
+ 
+
+ align:start position:0%
+s something degree like you're cheating
+here so it's going to be reject
+
+ align:start position:0%
+here so it's going to be reject
+ 
+
+ align:start position:0%
+here so it's going to be reject
+you he he will also
+
+ align:start position:0%
+you he he will also
+ 
+
+ align:start position:0%
+you he he will also
+check that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some G1 of H I guess one let me call
+
+ align:start position:0%
+some G1 of H I guess one let me call
+ 
+
+ align:start position:0%
+some G1 of H I guess one let me call
+H1 that if you take G1 and you sum it
+
+ align:start position:0%
+H1 that if you take G1 and you sum it
+ 
+
+ align:start position:0%
+H1 that if you take G1 and you sum it
+over all possible H's in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h what does he expect to get what would
+
+ align:start position:0%
+h what does he expect to get what would
+ 
+
+ align:start position:0%
+h what does he expect to get what would
+he check
+
+ align:start position:0%
+he check
+ 
+
+ align:start position:0%
+he check
+for exactly beta
+
+ align:start position:0%
+for exactly beta
+ 
+
+ align:start position:0%
+for exactly beta
+because the claim is beta so he checks
+
+ align:start position:0%
+because the claim is beta so he checks
+ 
+
+ align:start position:0%
+because the claim is beta so he checks
+that this is a degree
+
+ align:start position:0%
+that this is a degree
+ 
+
+ align:start position:0%
+that this is a degree
+mosd that when you sun over hes you get
+
+ align:start position:0%
+mosd that when you sun over hes you get
+ 
+
+ align:start position:0%
+mosd that when you sun over hes you get
+what was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claimed okay if he's if this does not
+
+ align:start position:0%
+claimed okay if he's if this does not
+ 
+
+ align:start position:0%
+claimed okay if he's if this does not
+hold then he reject he say b i reject
+
+ align:start position:0%
+hold then he reject he say b i reject
+ 
+
+ align:start position:0%
+hold then he reject he say b i reject
+you not going to continue if this holds
+
+ align:start position:0%
+you not going to continue if this holds
+ 
+
+ align:start position:0%
+you not going to continue if this holds
+then he chooses a
+
+ align:start position:0%
+then he chooses a
+ 
+
+ align:start position:0%
+then he chooses a
+random T1 in the
+
+ align:start position:0%
+random T1 in the
+ 
+
+ align:start position:0%
+random T1 in the
+field this is often a notation left
+
+ align:start position:0%
+field this is often a notation left
+ 
+
+ align:start position:0%
+field this is often a notation left
+arrow that we use for choosing a random
+
+ align:start position:0%
+arrow that we use for choosing a random
+ 
+
+ align:start position:0%
+arrow that we use for choosing a random
+okay so he uses a he chooses a random a
+
+ align:start position:0%
+okay so he uses a he chooses a random a
+ 
+
+ align:start position:0%
+okay so he uses a he chooses a random a
+T1 a random element in the field not an
+
+ align:start position:0%
+T1 a random element in the field not an
+ 
+
+ align:start position:0%
+T1 a random element in the field not an
+H but in The Big Field okay you need to
+
+ align:start position:0%
+H but in The Big Field okay you need to
+ 
+
+ align:start position:0%
+H but in The Big Field okay you need to
+think of this field as being big well
+
+ align:start position:0%
+think of this field as being big well
+ 
+
+ align:start position:0%
+think of this field as being big well
+that will the bigger the field the
+
+ align:start position:0%
+that will the bigger the field the
+ 
+
+ align:start position:0%
+that will the bigger the field the
+better the soundless will
+
+ align:start position:0%
+better the soundless will
+ 
+
+ align:start position:0%
+better the soundless will
+get okay so he chooses a random T1 in
+
+ align:start position:0%
+get okay so he chooses a random T1 in
+ 
+
+ align:start position:0%
+get okay so he chooses a random T1 in
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field good then what happens the the PO
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in some sense this reduces the problem
+
+ align:start position:0%
+in some sense this reduces the problem
+ 
+
+ align:start position:0%
+in some sense this reduces the problem
+from checking that this sum is beta to
+
+ align:start position:0%
+from checking that this sum is beta to
+ 
+
+ align:start position:0%
+from checking that this sum is beta to
+checking
+
+ align:start position:0%
+checking
+ 
+
+ align:start position:0%
+checking
+sum let me WR here to checking that sum
+
+ align:start position:0%
+sum let me WR here to checking that sum
+ 
+
+ align:start position:0%
+sum let me WR here to checking that sum
+of f t t is fixed or T1 you call it and
+
+ align:start position:0%
+of f t t is fixed or T1 you call it and
+ 
+
+ align:start position:0%
+of f t t is fixed or T1 you call it and
+then H2 up to
+
+ align:start position:0%
+then H2 up to
+ 
+
+ align:start position:0%
+then H2 up to
+hn is this fixed I don't know G1 of
+
+ align:start position:0%
+hn is this fixed I don't know G1 of
+ 
+
+ align:start position:0%
+hn is this fixed I don't know G1 of
+T1 we kind of reduce the problem to this
+
+ align:start position:0%
+T1 we kind of reduce the problem to this
+ 
+
+ align:start position:0%
+T1 we kind of reduce the problem to this
+problem which is of one dimension less
+
+ align:start position:0%
+problem which is of one dimension less
+ 
+
+ align:start position:0%
+problem which is of one dimension less
+because the sum is only over M minus one
+
+ align:start position:0%
+because the sum is only over M minus one
+ 
+
+ align:start position:0%
+because the sum is only over M minus one
+variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes good what what are we going to put
+
+ align:start position:0%
+yes good what what are we going to put
+ 
+
+ align:start position:0%
+yes good what what are we going to put
+polinomial in very good question when I
+
+ align:start position:0%
+polinomial in very good question when I
+ 
+
+ align:start position:0%
+polinomial in very good question when I
+said that verifier is polinomial time
+
+ align:start position:0%
+said that verifier is polinomial time
+ 
+
+ align:start position:0%
+said that verifier is polinomial time
+polinomial in what so he's going to he's
+
+ align:start position:0%
+polinomial in what so he's going to he's
+ 
+
+ align:start position:0%
+polinomial in what so he's going to he's
+going to be polinomial okay we think of
+
+ align:start position:0%
+going to be polinomial okay we think of
+ 
+
+ align:start position:0%
+going to be polinomial okay we think of
+F I said f can be as Oracle axis to it
+
+ align:start position:0%
+F I said f can be as Oracle axis to it
+ 
+
+ align:start position:0%
+F I said f can be as Oracle axis to it
+so what poom what so he was he what
+
+ align:start position:0%
+so what poom what so he was he what
+ 
+
+ align:start position:0%
+so what poom what so he was he what
+we're we're going to analyze his runtime
+
+ align:start position:0%
+we're we're going to analyze his runtime
+ 
+
+ align:start position:0%
+we're we're going to analyze his runtime
+in a bit but his runtime will depend
+
+ align:start position:0%
+in a bit but his runtime will depend
+ 
+
+ align:start position:0%
+in a bit but his runtime will depend
+polinomial on M which is the number of
+
+ align:start position:0%
+polinomial on M which is the number of
+ 
+
+ align:start position:0%
+polinomial on M which is the number of
+variables and on the
+
+ align:start position:0%
+variables and on the
+ 
+
+ align:start position:0%
+variables and on the
+degree and we think of a in these in to
+
+ align:start position:0%
+degree and we think of a in these in to
+ 
+
+ align:start position:0%
+degree and we think of a in these in to
+today and act like throughout the course
+
+ align:start position:0%
+today and act like throughout the course
+ 
+
+ align:start position:0%
+today and act like throughout the course
+and it's common in this field we think
+
+ align:start position:0%
+and it's common in this field we think
+ 
+
+ align:start position:0%
+and it's common in this field we think
+of f like that he can add and multiply
+
+ align:start position:0%
+of f like that he can add and multiply
+ 
+
+ align:start position:0%
+of f like that he can add and multiply
+things in or order one time like it's a
+
+ align:start position:0%
+things in or order one time like it's a
+ 
+
+ align:start position:0%
+things in or order one time like it's a
+constant uh and typically these fields
+
+ align:start position:0%
+constant uh and typically these fields
+ 
+
+ align:start position:0%
+constant uh and typically these fields
+are going to be take polylog but we
+
+ align:start position:0%
+are going to be take polylog but we
+ 
+
+ align:start position:0%
+are going to be take polylog but we
+don't want to run you know chase after
+
+ align:start position:0%
+don't want to run you know chase after
+ 
+
+ align:start position:0%
+don't want to run you know chase after
+these polog terms so we're not going to
+
+ align:start position:0%
+these polog terms so we're not going to
+ 
+
+ align:start position:0%
+these polog terms so we're not going to
+consider them really sometimes we do
+
+ align:start position:0%
+consider them really sometimes we do
+ 
+
+ align:start position:0%
+consider them really sometimes we do
+sometimes we don't depends but beyond
+
+ align:start position:0%
+sometimes we don't depends but beyond
+ 
+
+ align:start position:0%
+sometimes we don't depends but beyond
+the so if you want to be kind of very
+
+ align:start position:0%
+the so if you want to be kind of very
+ 
+
+ align:start position:0%
+the so if you want to be kind of very
+pedantic then
+
+ align:start position:0%
+pedantic then
+ 
+
+ align:start position:0%
+pedantic then
+you log
+
+ align:start position:0%
+you log
+ 
+
+ align:start position:0%
+you log
+F also H maybe yes thank
+
+ align:start position:0%
+F also H maybe yes thank
+ 
+
+ align:start position:0%
+F also H maybe yes thank
+you yes of course thanks sua the size of
+
+ align:start position:0%
+you yes of course thanks sua the size of
+ 
+
+ align:start position:0%
+you yes of course thanks sua the size of
+H and log
+
+ align:start position:0%
+H and log
+ 
+
+ align:start position:0%
+H and log
+F that's what's going to happen but you
+
+ align:start position:0%
+F that's what's going to happen but you
+ 
+
+ align:start position:0%
+F that's what's going to happen but you
+right that here the polinomial time
+
+ align:start position:0%
+right that here the polinomial time
+ 
+
+ align:start position:0%
+right that here the polinomial time
+doesn't really apply here because you I
+
+ align:start position:0%
+doesn't really apply here because you I
+ 
+
+ align:start position:0%
+doesn't really apply here because you I
+said that he has oralis so we polinomial
+
+ align:start position:0%
+said that he has oralis so we polinomial
+ 
+
+ align:start position:0%
+said that he has oralis so we polinomial
+over so this is this is what he's going
+
+ align:start position:0%
+over so this is this is what he's going
+ 
+
+ align:start position:0%
+over so this is this is what he's going
+to be after but when we're going to use
+
+ align:start position:0%
+to be after but when we're going to use
+ 
+
+ align:start position:0%
+to be after but when we're going to use
+him for applications you'll see it will
+
+ align:start position:0%
+him for applications you'll see it will
+ 
+
+ align:start position:0%
+him for applications you'll see it will
+correspond to polinomial time but we're
+
+ align:start position:0%
+correspond to polinomial time but we're
+ 
+
+ align:start position:0%
+correspond to polinomial time but we're
+going to go over this uh when when uh
+
+ align:start position:0%
+going to go over this uh when when uh
+ 
+
+ align:start position:0%
+going to go over this uh when when uh
+when we analyze the
+
+ align:start position:0%
+when we analyze the
+ 
+
+ align:start position:0%
+when we analyze the
+protocol okay so let's uh okay so let's
+
+ align:start position:0%
+protocol okay so let's uh okay so let's
+ 
+
+ align:start position:0%
+protocol okay so let's uh okay so let's
+just uh uh continue so where let me
+
+ align:start position:0%
+just uh uh continue so where let me
+ 
+
+ align:start position:0%
+just uh uh continue so where let me
+actually start it so what's let me even
+
+ align:start position:0%
+actually start it so what's let me even
+ 
+
+ align:start position:0%
+actually start it so what's let me even
+say before I continue the protocol let's
+
+ align:start position:0%
+say before I continue the protocol let's
+ 
+
+ align:start position:0%
+say before I continue the protocol let's
+continue the protocol with kind of a
+
+ align:start position:0%
+continue the protocol with kind of a
+ 
+
+ align:start position:0%
+continue the protocol with kind of a
+high level idea of what we're trying to
+
+ align:start position:0%
+high level idea of what we're trying to
+ 
+
+ align:start position:0%
+high level idea of what we're trying to
+do here the idea is the
+
+ align:start position:0%
+do here the idea is the
+ 
+
+ align:start position:0%
+do here the idea is the
+following we want to catch aover
+
+ align:start position:0%
+following we want to catch aover
+ 
+
+ align:start position:0%
+following we want to catch aover
+cheating that's the goal of a proof
+
+ align:start position:0%
+cheating that's the goal of a proof
+ 
+
+ align:start position:0%
+cheating that's the goal of a proof
+right we want to catch you if you're
+
+ align:start position:0%
+right we want to catch you if you're
+ 
+
+ align:start position:0%
+right we want to catch you if you're
+cheating so suppose aover is cheating
+
+ align:start position:0%
+cheating so suppose aover is cheating
+ 
+
+ align:start position:0%
+cheating so suppose aover is cheating
+here how will how will he C we catch it
+
+ align:start position:0%
+here how will how will he C we catch it
+ 
+
+ align:start position:0%
+here how will how will he C we catch it
+the way we're going to catch it is when
+
+ align:start position:0%
+the way we're going to catch it is when
+ 
+
+ align:start position:0%
+the way we're going to catch it is when
+tell you know what give me this
+
+ align:start position:0%
+tell you know what give me this
+ 
+
+ align:start position:0%
+tell you know what give me this
+G1 okay now he cannot give me an the
+
+ align:start position:0%
+G1 okay now he cannot give me an the
+ 
+
+ align:start position:0%
+G1 okay now he cannot give me an the
+actual true G1 Because the actual true
+
+ align:start position:0%
+actual true G1 Because the actual true
+ 
+
+ align:start position:0%
+actual true G1 Because the actual true
+G1 will not sum up to Beta beta is the
+
+ align:start position:0%
+G1 will not sum up to Beta beta is the
+ 
+
+ align:start position:0%
+G1 will not sum up to Beta beta is the
+false thing so right so if it if a po
+
+ align:start position:0%
+false thing so right so if it if a po
+ 
+
+ align:start position:0%
+false thing so right so if it if a po
+cheats if he try let I'm trying to kind
+
+ align:start position:0%
+cheats if he try let I'm trying to kind
+ 
+
+ align:start position:0%
+cheats if he try let I'm trying to kind
+of let's come up with this protocol
+
+ align:start position:0%
+of let's come up with this protocol
+ 
+
+ align:start position:0%
+of let's come up with this protocol
+together with kind of the goal of trying
+
+ align:start position:0%
+together with kind of the goal of trying
+ 
+
+ align:start position:0%
+together with kind of the goal of trying
+to catch the the approver so how do we
+
+ align:start position:0%
+to catch the the approver so how do we
+ 
+
+ align:start position:0%
+to catch the the approver so how do we
+catch aover cheating so the IDE is will
+
+ align:start position:0%
+catch aover cheating so the IDE is will
+ 
+
+ align:start position:0%
+catch aover cheating so the IDE is will
+tell me you know what give me this some
+
+ align:start position:0%
+tell me you know what give me this some
+ 
+
+ align:start position:0%
+tell me you know what give me this some
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+open I'm going to check that this sum
+
+ align:start position:0%
+open I'm going to check that this sum
+ 
+
+ align:start position:0%
+open I'm going to check that this sum
+with like that the sum of G1 is equal to
+
+ align:start position:0%
+with like that the sum of G1 is equal to
+ 
+
+ align:start position:0%
+with like that the sum of G1 is equal to
+Beta and then it's low
+
+ align:start position:0%
+Beta and then it's low
+ 
+
+ align:start position:0%
+Beta and then it's low
+degree if it passes then this G1 cannot
+
+ align:start position:0%
+degree if it passes then this G1 cannot
+ 
+
+ align:start position:0%
+degree if it passes then this G1 cannot
+be the true true G1 it can't actually be
+
+ align:start position:0%
+be the true true G1 it can't actually be
+ 
+
+ align:start position:0%
+be the true true G1 it can't actually be
+the real sum of f because the real sum
+
+ align:start position:0%
+the real sum of f because the real sum
+ 
+
+ align:start position:0%
+the real sum of f because the real sum
+of f is not beta he's cheating so this
+
+ align:start position:0%
+of f is not beta he's cheating so this
+ 
+
+ align:start position:0%
+of f is not beta he's cheating so this
+must be a
+
+ align:start position:0%
+must be a
+ 
+
+ align:start position:0%
+must be a
+cheat now when we send in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T1 and we consider kind of so now we
+
+ align:start position:0%
+T1 and we consider kind of so now we
+ 
+
+ align:start position:0%
+T1 and we consider kind of so now we
+send T1 and we kind of reduce the claim
+
+ align:start position:0%
+send T1 and we kind of reduce the claim
+ 
+
+ align:start position:0%
+send T1 and we kind of reduce the claim
+to claiming this
+
+ align:start position:0%
+to claiming this
+ 
+
+ align:start position:0%
+to claiming this
+but with very high probability G1 is
+
+ align:start position:0%
+but with very high probability G1 is
+ 
+
+ align:start position:0%
+but with very high probability G1 is
+also a cheat
+
+ align:start position:0%
+also a cheat
+ 
+
+ align:start position:0%
+also a cheat
+because G1 G1 T1 is a cheat so G1 T1 is
+
+ align:start position:0%
+because G1 G1 T1 is a cheat so G1 T1 is
+ 
+
+ align:start position:0%
+because G1 G1 T1 is a cheat so G1 T1 is
+not really the sum because they're
+
+ align:start position:0%
+not really the sum because they're
+ 
+
+ align:start position:0%
+not really the sum because they're
+different G1 is different than that so
+
+ align:start position:0%
+different G1 is different than that so
+ 
+
+ align:start position:0%
+different G1 is different than that so
+we know that if they're different they
+
+ align:start position:0%
+we know that if they're different they
+ 
+
+ align:start position:0%
+we know that if they're different they
+agree only on D elements okay two
+
+ align:start position:0%
+agree only on D elements okay two
+ 
+
+ align:start position:0%
+agree only on D elements okay two
+distinct polom age only on D elements
+
+ align:start position:0%
+distinct polom age only on D elements
+ 
+
+ align:start position:0%
+distinct polom age only on D elements
+what's the probability that this1 is one
+
+ align:start position:0%
+what's the probability that this1 is one
+ 
+
+ align:start position:0%
+what's the probability that this1 is one
+of the D very small
+
+ align:start position:0%
+of the D very small
+ 
+
+ align:start position:0%
+of the D very small
+DF Okay so think of is really large
+
+ align:start position:0%
+DF Okay so think of is really large
+ 
+
+ align:start position:0%
+DF Okay so think of is really large
+great so this is also false actually you
+
+ align:start position:0%
+great so this is also false actually you
+ 
+
+ align:start position:0%
+great so this is also false actually you
+know he give me G one it's actually not
+
+ align:start position:0%
+know he give me G one it's actually not
+ 
+
+ align:start position:0%
+know he give me G one it's actually not
+the real life he's going to claim it's
+
+ align:start position:0%
+the real life he's going to claim it's
+ 
+
+ align:start position:0%
+the real life he's going to claim it's
+the real life but I know it's not now
+
+ align:start position:0%
+the real life but I know it's not now
+ 
+
+ align:start position:0%
+the real life but I know it's not now
+I'm going to tell him next thing I'm
+
+ align:start position:0%
+I'm going to tell him next thing I'm
+ 
+
+ align:start position:0%
+I'm going to tell him next thing I'm
+going to tell him okay give me G2 G2 is
+
+ align:start position:0%
+going to tell him okay give me G2 G2 is
+ 
+
+ align:start position:0%
+going to tell him okay give me G2 G2 is
+G2 of
+
+ align:start position:0%
+G2 of
+ 
+
+ align:start position:0%
+G2 of
+X is some it should be some f T1 I'm
+
+ align:start position:0%
+X is some it should be some f T1 I'm
+ 
+
+ align:start position:0%
+X is some it should be some f T1 I'm
+going to only sum over H3 up to hm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the X2 the two is going to be open and
+
+ align:start position:0%
+the X2 the two is going to be open and
+ 
+
+ align:start position:0%
+the X2 the two is going to be open and
+then H3 after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H okay so we started by getting rid of
+
+ align:start position:0%
+H okay so we started by getting rid of
+ 
+
+ align:start position:0%
+H okay so we started by getting rid of
+the summing over
+
+ align:start position:0%
+the summing over
+ 
+
+ align:start position:0%
+the summing over
+H1 we gave him the univ pomal or we
+
+ align:start position:0%
+H1 we gave him the univ pomal or we
+ 
+
+ align:start position:0%
+H1 we gave him the univ pomal or we
+chose our R T1 now we're getting rid of
+
+ align:start position:0%
+chose our R T1 now we're getting rid of
+ 
+
+ align:start position:0%
+chose our R T1 now we're getting rid of
+summing over the second
+
+ align:start position:0%
+summing over the second
+ 
+
+ align:start position:0%
+summing over the second
+coordinate we're asking for a univ
+
+ align:start position:0%
+coordinate we're asking for a univ
+ 
+
+ align:start position:0%
+coordinate we're asking for a univ
+polinomial G2 what do we check we check
+
+ align:start position:0%
+polinomial G2 what do we check we check
+ 
+
+ align:start position:0%
+polinomial G2 what do we check we check
+so the verifier checks that
+
+ align:start position:0%
+so the verifier checks that
+ 
+
+ align:start position:0%
+so the verifier checks that
+G2 is of
+
+ align:start position:0%
+G2 is of
+ 
+
+ align:start position:0%
+G2 is of
+degree and most D and what else does he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check very good so sum G2 and
+
+ align:start position:0%
+check very good so sum G2 and
+ 
+
+ align:start position:0%
+check very good so sum G2 and
+H maybe I'll write H2 is equal to what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly G1 of
+
+ align:start position:0%
+exactly G1 of
+ 
+
+ align:start position:0%
+exactly G1 of
+T1 so essentially we kind of you know we
+
+ align:start position:0%
+T1 so essentially we kind of you know we
+ 
+
+ align:start position:0%
+T1 so essentially we kind of you know we
+check this for exactly as we did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before okay so now note if in the honest
+
+ align:start position:0%
+before okay so now note if in the honest
+ 
+
+ align:start position:0%
+before okay so now note if in the honest
+case of course that's that's the case G2
+
+ align:start position:0%
+case of course that's that's the case G2
+ 
+
+ align:start position:0%
+case of course that's that's the case G2
+of course is degree at most D because f
+
+ align:start position:0%
+of course is degree at most D because f
+ 
+
+ align:start position:0%
+of course is degree at most D because f
+is degree at most D and when you sum
+
+ align:start position:0%
+is degree at most D and when you sum
+ 
+
+ align:start position:0%
+is degree at most D and when you sum
+with over over all of H2 you should get
+
+ align:start position:0%
+with over over all of H2 you should get
+ 
+
+ align:start position:0%
+with over over all of H2 you should get
+exactly G1 and T that's how
+
+ align:start position:0%
+exactly G1 and T that's how
+ 
+
+ align:start position:0%
+exactly G1 and T that's how
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+great if he's if this does not hold he
+
+ align:start position:0%
+great if he's if this does not hold he
+ 
+
+ align:start position:0%
+great if he's if this does not hold he
+immediately aborts and say I reject you
+
+ align:start position:0%
+immediately aborts and say I reject you
+ 
+
+ align:start position:0%
+immediately aborts and say I reject you
+if he's happy he's going to send T2 at
+
+ align:start position:0%
+if he's happy he's going to send T2 at
+ 
+
+ align:start position:0%
+if he's happy he's going to send T2 at
+random from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field what am I going to reply with what
+
+ align:start position:0%
+field what am I going to reply with what
+ 
+
+ align:start position:0%
+field what am I going to reply with what
+what should the Prov reply with
+
+ align:start position:0%
+what should the Prov reply with
+ 
+
+ align:start position:0%
+what should the Prov reply with
+so let's see
+
+ align:start position:0%
+so let's see
+ 
+
+ align:start position:0%
+so let's see
+G3 of X is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what very
+
+ align:start position:0%
+what very
+ 
+
+ align:start position:0%
+what very
+good very good F of T1 T2 X and H4 up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hm yeah again we take essentially what
+
+ align:start position:0%
+hm yeah again we take essentially what
+ 
+
+ align:start position:0%
+hm yeah again we take essentially what
+happened here we reduced after T2 we
+
+ align:start position:0%
+happened here we reduced after T2 we
+ 
+
+ align:start position:0%
+happened here we reduced after T2 we
+reduced the problem to proving a sum
+
+ align:start position:0%
+reduced the problem to proving a sum
+ 
+
+ align:start position:0%
+reduced the problem to proving a sum
+check over sum F1 T1 T2 H3 up to hm and
+
+ align:start position:0%
+check over sum F1 T1 T2 H3 up to hm and
+ 
+
+ align:start position:0%
+check over sum F1 T1 T2 H3 up to hm and
+we need to check whether this is equal
+
+ align:start position:0%
+we need to check whether this is equal
+ 
+
+ align:start position:0%
+we need to check whether this is equal
+to a G2 of
+
+ align:start position:0%
+to a G2 of
+ 
+
+ align:start position:0%
+to a G2 of
+H2 of T2 sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so again each time we kind of layer
+
+ align:start position:0%
+okay so again each time we kind of layer
+ 
+
+ align:start position:0%
+okay so again each time we kind of layer
+kind of get rid of one variable in the
+
+ align:start position:0%
+kind of get rid of one variable in the
+ 
+
+ align:start position:0%
+kind of get rid of one variable in the
+sum check we start with an narate sum
+
+ align:start position:0%
+sum check we start with an narate sum
+ 
+
+ align:start position:0%
+sum check we start with an narate sum
+check and each round we get rid of one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable okay last one what do we check
+
+ align:start position:0%
+variable okay last one what do we check
+ 
+
+ align:start position:0%
+variable okay last one what do we check
+here we got G3 what do we check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the
+
+ align:start position:0%
+what is the
+ 
+
+ align:start position:0%
+what is the
+g33 exactly so first that G3 is low
+
+ align:start position:0%
+g33 exactly so first that G3 is low
+ 
+
+ align:start position:0%
+g33 exactly so first that G3 is low
+degree is
+
+ align:start position:0%
+degree is
+ 
+
+ align:start position:0%
+degree is
+degree most and some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G3 is
+
+ align:start position:0%
+G3 is
+ 
+
+ align:start position:0%
+G3 is
+G2 and we continueing this way until we
+
+ align:start position:0%
+G2 and we continueing this way until we
+ 
+
+ align:start position:0%
+G2 and we continueing this way until we
+continue continue continue until we got
+
+ align:start position:0%
+continue continue continue until we got
+ 
+
+ align:start position:0%
+continue continue continue until we got
+rid of everything so in the last round
+
+ align:start position:0%
+rid of everything so in the last round
+ 
+
+ align:start position:0%
+rid of everything so in the last round
+what will happen in the last round in
+
+ align:start position:0%
+what will happen in the last round in
+ 
+
+ align:start position:0%
+what will happen in the last round in
+the last
+
+ align:start position:0%
+the last
+ 
+
+ align:start position:0%
+the last
+round we will send
+
+ align:start position:0%
+round we will send
+ 
+
+ align:start position:0%
+round we will send
+g m minus one
+
+ align:start position:0%
+g m minus one
+ 
+
+ align:start position:0%
+g m minus one
+GM of like
+
+ align:start position:0%
+GM of like
+ 
+
+ align:start position:0%
+GM of like
+GMX which is f of T1 up to TN minus1
+
+ align:start position:0%
+GMX which is f of T1 up to TN minus1
+ 
+
+ align:start position:0%
+GMX which is f of T1 up to TN minus1
+X that's what he should check that's
+
+ align:start position:0%
+X that's what he should check that's
+ 
+
+ align:start position:0%
+X that's what he should check that's
+what you should send if you're honest
+
+ align:start position:0%
+what you should send if you're honest
+ 
+
+ align:start position:0%
+what you should send if you're honest
+that's what you send you peeled out off
+
+ align:start position:0%
+that's what you send you peeled out off
+ 
+
+ align:start position:0%
+that's what you send you peeled out off
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+finally you're left with a with a GM
+
+ align:start position:0%
+finally you're left with a with a GM
+ 
+
+ align:start position:0%
+finally you're left with a with a GM
+which is F and M minus one X and then
+
+ align:start position:0%
+which is F and M minus one X and then
+ 
+
+ align:start position:0%
+which is F and M minus one X and then
+the verifier is done he'll choose a
+
+ align:start position:0%
+the verifier is done he'll choose a
+ 
+
+ align:start position:0%
+the verifier is done he'll choose a
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+TM and he will check whether this is
+
+ align:start position:0%
+TM and he will check whether this is
+ 
+
+ align:start position:0%
+TM and he will check whether this is
+indeed F of T1 of the TM we assumed he
+
+ align:start position:0%
+indeed F of T1 of the TM we assumed he
+ 
+
+ align:start position:0%
+indeed F of T1 of the TM we assumed he
+has Oracle access so we can check if
+
+ align:start position:0%
+has Oracle access so we can check if
+ 
+
+ align:start position:0%
+has Oracle access so we can check if
+this value is T1 of the TM okay so
+
+ align:start position:0%
+this value is T1 of the TM okay so
+ 
+
+ align:start position:0%
+this value is T1 of the TM okay so
+finally this is this and
+
+ align:start position:0%
+finally this is this and
+ 
+
+ align:start position:0%
+finally this is this and
+verifier I'm out of room but maybe I'll
+
+ align:start position:0%
+verifier I'm out of room but maybe I'll
+ 
+
+ align:start position:0%
+verifier I'm out of room but maybe I'll
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+here V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chooses uh random TM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+checks that g m of
+
+ align:start position:0%
+checks that g m of
+ 
+
+ align:start position:0%
+checks that g m of
+TM is equal to the Oracle he has F on T1
+
+ align:start position:0%
+TM is equal to the Oracle he has F on T1
+ 
+
+ align:start position:0%
+TM is equal to the Oracle he has F on T1
+up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protocol I'll give you a minute to
+
+ align:start position:0%
+protocol I'll give you a minute to
+ 
+
+ align:start position:0%
+protocol I'll give you a minute to
+appreciate the beauty while I eras the
+
+ align:start position:0%
+appreciate the beauty while I eras the
+ 
+
+ align:start position:0%
+appreciate the beauty while I eras the
+board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+a you're asking can I have a different
+
+ align:start position:0%
+a you're asking can I have a different
+ 
+
+ align:start position:0%
+a you're asking can I have a different
+set I can I can have a different set yes
+
+ align:start position:0%
+set I can I can have a different set yes
+ 
+
+ align:start position:0%
+set I can I can have a different set yes
+yeah so the question was do do the hes
+
+ align:start position:0%
+yeah so the question was do do the hes
+ 
+
+ align:start position:0%
+yeah so the question was do do the hes
+have to be identical and the answers
+
+ align:start position:0%
+have to be identical and the answers
+ 
+
+ align:start position:0%
+have to be identical and the answers
+they don't have to be identical you can
+
+ align:start position:0%
+they don't have to be identical you can
+ 
+
+ align:start position:0%
+they don't have to be identical you can
+take a we didn't use that anywhere and
+
+ align:start position:0%
+take a we didn't use that anywhere and
+ 
+
+ align:start position:0%
+take a we didn't use that anywhere and
+yeah it's somehow yeah somehow we always
+
+ align:start position:0%
+yeah it's somehow yeah somehow we always
+ 
+
+ align:start position:0%
+yeah it's somehow yeah somehow we always
+use it when it is but uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but that's a very good point because
+
+ align:start position:0%
+but but that's a very good point because
+ 
+
+ align:start position:0%
+but but that's a very good point because
+it's like it seems more General it seems
+
+ align:start position:0%
+it's like it seems more General it seems
+ 
+
+ align:start position:0%
+it's like it seems more General it seems
+like it can be useful but somehow we
+
+ align:start position:0%
+like it can be useful but somehow we
+ 
+
+ align:start position:0%
+like it can be useful but somehow we
+don't use it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but that's a very good good point
+
+ align:start position:0%
+uh but that's a very good good point
+ 
+
+ align:start position:0%
+uh but that's a very good good point
+yeah you can the hes does not have to be
+
+ align:start position:0%
+yeah you can the hes does not have to be
+ 
+
+ align:start position:0%
+yeah you can the hes does not have to be
+the same age you can be some over H1 of
+
+ align:start position:0%
+the same age you can be some over H1 of
+ 
+
+ align:start position:0%
+the same age you can be some over H1 of
+hm so particular H would be equal right
+
+ align:start position:0%
+hm so particular H would be equal right
+ 
+
+ align:start position:0%
+hm so particular H would be equal right
+okay H could be equal uh to F yes H
+
+ align:start position:0%
+okay H could be equal uh to F yes H
+ 
+
+ align:start position:0%
+okay H could be equal uh to F yes H
+could be equal to f um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do you
+
+ align:start position:0%
+how do you
+ 
+
+ align:start position:0%
+how do you
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+G1 sorry first line Su G1 H1 you will
+
+ align:start position:0%
+G1 sorry first line Su G1 H1 you will
+ 
+
+ align:start position:0%
+G1 sorry first line Su G1 H1 you will
+take time propal yeah but let's say
+
+ align:start position:0%
+take time propal yeah but let's say
+ 
+
+ align:start position:0%
+take time propal yeah but let's say
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+okay again
+
+ align:start position:0%
+okay again
+ 
+
+ align:start position:0%
+okay again
+s yeah so let's we'll talk about
+
+ align:start position:0%
+s yeah so let's we'll talk about
+ 
+
+ align:start position:0%
+s yeah so let's we'll talk about
+soundness in a minute uh actually
+
+ align:start position:0%
+soundness in a minute uh actually
+ 
+
+ align:start position:0%
+soundness in a minute uh actually
+um if f is degree D the sist won't
+
+ align:start position:0%
+um if f is degree D the sist won't
+ 
+
+ align:start position:0%
+um if f is degree D the sist won't
+Decay I actually I think actually a okay
+
+ align:start position:0%
+Decay I actually I think actually a okay
+ 
+
+ align:start position:0%
+Decay I actually I think actually a okay
+let's talk about soundness and then
+
+ align:start position:0%
+let's talk about soundness and then
+ 
+
+ align:start position:0%
+let's talk about soundness and then
+we'll see actually the soundness won't
+
+ align:start position:0%
+we'll see actually the soundness won't
+ 
+
+ align:start position:0%
+we'll see actually the soundness won't
+uh in general usually when H is big in
+
+ align:start position:0%
+uh in general usually when H is big in
+ 
+
+ align:start position:0%
+uh in general usually when H is big in
+applications what happens often is when
+
+ align:start position:0%
+applications what happens often is when
+ 
+
+ align:start position:0%
+applications what happens often is when
+you take big H the F turns out to be
+
+ align:start position:0%
+you take big H the F turns out to be
+ 
+
+ align:start position:0%
+you take big H the F turns out to be
+degree H or H minus one so when we use
+
+ align:start position:0%
+degree H or H minus one so when we use
+ 
+
+ align:start position:0%
+degree H or H minus one so when we use
+this protocol so you know as I said this
+
+ align:start position:0%
+this protocol so you know as I said this
+ 
+
+ align:start position:0%
+this protocol so you know as I said this
+problem I'm say why do I care about this
+
+ align:start position:0%
+problem I'm say why do I care about this
+ 
+
+ align:start position:0%
+problem I'm say why do I care about this
+problem who cares about this problem so
+
+ align:start position:0%
+problem who cares about this problem so
+ 
+
+ align:start position:0%
+problem who cares about this problem so
+it turns out we care a lot it comes up
+
+ align:start position:0%
+it turns out we care a lot it comes up
+ 
+
+ align:start position:0%
+it turns out we care a lot it comes up
+all the time the way we use it in pra
+
+ align:start position:0%
+all the time the way we use it in pra
+ 
+
+ align:start position:0%
+all the time the way we use it in pra
+like the way it comes up is the F that
+
+ align:start position:0%
+like the way it comes up is the F that
+ 
+
+ align:start position:0%
+like the way it comes up is the F that
+we use usually is of degree hus one and
+
+ align:start position:0%
+we use usually is of degree hus one and
+ 
+
+ align:start position:0%
+we use usually is of degree hus one and
+each variable we use it in a way that
+
+ align:start position:0%
+each variable we use it in a way that
+ 
+
+ align:start position:0%
+each variable we use it in a way that
+that turns out to be the degree of F and
+
+ align:start position:0%
+that turns out to be the degree of F and
+ 
+
+ align:start position:0%
+that turns out to be the degree of F and
+the soundness decades with a degree so
+
+ align:start position:0%
+the soundness decades with a degree so
+ 
+
+ align:start position:0%
+the soundness decades with a degree so
+if the H is Big the soundness if the
+
+ align:start position:0%
+if the H is Big the soundness if the
+ 
+
+ align:start position:0%
+if the H is Big the soundness if the
+degree is Big the soundness is big but
+
+ align:start position:0%
+degree is Big the soundness is big but
+ 
+
+ align:start position:0%
+degree is Big the soundness is big but
+actually if your promis that the degree
+
+ align:start position:0%
+actually if your promis that the degree
+ 
+
+ align:start position:0%
+actually if your promis that the degree
+is small then we're good we we'll
+
+ align:start position:0%
+is small then we're good we we'll
+ 
+
+ align:start position:0%
+is small then we're good we we'll
+analyze it right now yeah can you say
+
+ align:start position:0%
+analyze it right now yeah can you say
+ 
+
+ align:start position:0%
+analyze it right now yeah can you say
+something about like what's so special
+
+ align:start position:0%
+something about like what's so special
+ 
+
+ align:start position:0%
+something about like what's so special
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes great question love the question
+
+ align:start position:0%
+yes yes great question love the question
+ 
+
+ align:start position:0%
+yes yes great question love the question
+so what what's so fascinating about
+
+ align:start position:0%
+so what what's so fascinating about
+ 
+
+ align:start position:0%
+so what what's so fascinating about
+polinomial that comes up here so the
+
+ align:start position:0%
+polinomial that comes up here so the
+ 
+
+ align:start position:0%
+polinomial that comes up here so the
+what it's kind of why is this so
+
+ align:start position:0%
+what it's kind of why is this so
+ 
+
+ align:start position:0%
+what it's kind of why is this so
+interesting why is colonial so so
+
+ align:start position:0%
+interesting why is colonial so so
+ 
+
+ align:start position:0%
+interesting why is colonial so so
+important you know that this comes up
+
+ align:start position:0%
+important you know that this comes up
+ 
+
+ align:start position:0%
+important you know that this comes up
+everywhere so here's my take and uh on
+
+ align:start position:0%
+everywhere so here's my take and uh on
+ 
+
+ align:start position:0%
+everywhere so here's my take and uh on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+question everything can be okay first of
+
+ align:start position:0%
+question everything can be okay first of
+ 
+
+ align:start position:0%
+question everything can be okay first of
+all pooms are and St they're very very
+
+ align:start position:0%
+all pooms are and St they're very very
+ 
+
+ align:start position:0%
+all pooms are and St they're very very
+useful because of their their power of
+
+ align:start position:0%
+useful because of their their power of
+ 
+
+ align:start position:0%
+useful because of their their power of
+error correction so in other words what
+
+ align:start position:0%
+error correction so in other words what
+ 
+
+ align:start position:0%
+error correction so in other words what
+happens if you cheat it once we're going
+
+ align:start position:0%
+happens if you cheat it once we're going
+ 
+
+ align:start position:0%
+happens if you cheat it once we're going
+to amplify your cheat that's kind kind
+
+ align:start position:0%
+to amplify your cheat that's kind kind
+ 
+
+ align:start position:0%
+to amplify your cheat that's kind kind
+of what we do here right you cheat it
+
+ align:start position:0%
+of what we do here right you cheat it
+ 
+
+ align:start position:0%
+of what we do here right you cheat it
+once we're g to like for a random Point
+
+ align:start position:0%
+once we're g to like for a random Point
+ 
+
+ align:start position:0%
+once we're g to like for a random Point
+T you're if if you're low degree this
+
+ align:start position:0%
+T you're if if you're low degree this
+ 
+
+ align:start position:0%
+T you're if if you're low degree this
+we're assuming that this Pro gives kind
+
+ align:start position:0%
+we're assuming that this Pro gives kind
+ 
+
+ align:start position:0%
+we're assuming that this Pro gives kind
+of low degree low degree low degree all
+
+ align:start position:0%
+of low degree low degree low degree all
+ 
+
+ align:start position:0%
+of low degree low degree low degree all
+the time if you give low degree low
+
+ align:start position:0%
+the time if you give low degree low
+ 
+
+ align:start position:0%
+the time if you give low degree low
+degree low degree and you cheated then
+
+ align:start position:0%
+degree low degree and you cheated then
+ 
+
+ align:start position:0%
+degree low degree and you cheated then
+the cheat must be kind of corresponding
+
+ align:start position:0%
+the cheat must be kind of corresponding
+ 
+
+ align:start position:0%
+the cheat must be kind of corresponding
+a che a random Point like at the end a
+
+ align:start position:0%
+a che a random Point like at the end a
+ 
+
+ align:start position:0%
+a che a random Point like at the end a
+random Point T1 the TM you should be
+
+ align:start position:0%
+random Point T1 the TM you should be
+ 
+
+ align:start position:0%
+random Point T1 the TM you should be
+different and that's kind of we'll
+
+ align:start position:0%
+different and that's kind of we'll
+ 
+
+ align:start position:0%
+different and that's kind of we'll
+analyze this this is just intuition but
+
+ align:start position:0%
+analyze this this is just intuition but
+ 
+
+ align:start position:0%
+analyze this this is just intuition but
+that kind of the beauty of polinomial
+
+ align:start position:0%
+that kind of the beauty of polinomial
+ 
+
+ align:start position:0%
+that kind of the beauty of polinomial
+that if you're wrong you're wrong almost
+
+ align:start position:0%
+that if you're wrong you're wrong almost
+ 
+
+ align:start position:0%
+that if you're wrong you're wrong almost
+everywhere because if if it's not the
+
+ align:start position:0%
+everywhere because if if it's not the
+ 
+
+ align:start position:0%
+everywhere because if if it's not the
+correct polinomial then it's different
+
+ align:start position:0%
+correct polinomial then it's different
+ 
+
+ align:start position:0%
+correct polinomial then it's different
+from the correct bomal almost everywhere
+
+ align:start position:0%
+from the correct bomal almost everywhere
+ 
+
+ align:start position:0%
+from the correct bomal almost everywhere
+that's the short zip for the multivaried
+
+ align:start position:0%
+that's the short zip for the multivaried
+ 
+
+ align:start position:0%
+that's the short zip for the multivaried
+case for the single varied case it's
+
+ align:start position:0%
+case for the single varied case it's
+ 
+
+ align:start position:0%
+case for the single varied case it's
+just the the interpolation I guess it's
+
+ align:start position:0%
+just the the interpolation I guess it's
+ 
+
+ align:start position:0%
+just the the interpolation I guess it's
+called but okay now you're saying okay
+
+ align:start position:0%
+called but okay now you're saying okay
+ 
+
+ align:start position:0%
+called but okay now you're saying okay
+but that just pomal why am I saying
+
+ align:start position:0%
+but that just pomal why am I saying
+ 
+
+ align:start position:0%
+but that just pomal why am I saying
+comes what's so special about polinomial
+
+ align:start position:0%
+comes what's so special about polinomial
+ 
+
+ align:start position:0%
+comes what's so special about polinomial
+like why why are they so General okay if
+
+ align:start position:0%
+like why why are they so General okay if
+ 
+
+ align:start position:0%
+like why why are they so General okay if
+you happen to have a polinomial good
+
+ align:start position:0%
+you happen to have a polinomial good
+ 
+
+ align:start position:0%
+you happen to have a polinomial good
+good for you you won because it has such
+
+ align:start position:0%
+good for you you won because it has such
+ 
+
+ align:start position:0%
+good for you you won because it has such
+air crafting guarantees you're you're
+
+ align:start position:0%
+air crafting guarantees you're you're
+ 
+
+ align:start position:0%
+air crafting guarantees you're you're
+lucky it's your lucky day but what if
+
+ align:start position:0%
+lucky it's your lucky day but what if
+ 
+
+ align:start position:0%
+lucky it's your lucky day but what if
+it's like why is every day a lucky day
+
+ align:start position:0%
+it's like why is every day a lucky day
+ 
+
+ align:start position:0%
+it's like why is every day a lucky day
+kind of thing why is the poal come up
+
+ align:start position:0%
+kind of thing why is the poal come up
+ 
+
+ align:start position:0%
+kind of thing why is the poal come up
+come up everywhere and the answer is
+
+ align:start position:0%
+come up everywhere and the answer is
+ 
+
+ align:start position:0%
+come up everywhere and the answer is
+that you can actually embed many many
+
+ align:start position:0%
+that you can actually embed many many
+ 
+
+ align:start position:0%
+that you can actually embed many many
+problems into pols so there's a way
+
+ align:start position:0%
+problems into pols so there's a way
+ 
+
+ align:start position:0%
+problems into pols so there's a way
+there's a technique which we'll call low
+
+ align:start position:0%
+there's a technique which we'll call low
+ 
+
+ align:start position:0%
+there's a technique which we'll call low
+degree extension we'll see that pretty
+
+ align:start position:0%
+degree extension we'll see that pretty
+ 
+
+ align:start position:0%
+degree extension we'll see that pretty
+soon soon if not today then tomorrow
+
+ align:start position:0%
+soon soon if not today then tomorrow
+ 
+
+ align:start position:0%
+soon soon if not today then tomorrow
+then next week where uh a a you can kind
+
+ align:start position:0%
+then next week where uh a a you can kind
+ 
+
+ align:start position:0%
+then next week where uh a a you can kind
+of convert many problems into
+
+ align:start position:0%
+of convert many problems into
+ 
+
+ align:start position:0%
+of convert many problems into
+polinomial and then use the sum check so
+
+ align:start position:0%
+polinomial and then use the sum check so
+ 
+
+ align:start position:0%
+polinomial and then use the sum check so
+that's often what we do we take a
+
+ align:start position:0%
+that's often what we do we take a
+ 
+
+ align:start position:0%
+that's often what we do we take a
+problem we embed it into a polom we kind
+
+ align:start position:0%
+problem we embed it into a polom we kind
+ 
+
+ align:start position:0%
+problem we embed it into a polom we kind
+of extend it to look like a polinomial
+
+ align:start position:0%
+of extend it to look like a polinomial
+ 
+
+ align:start position:0%
+of extend it to look like a polinomial
+of low degree and then we use subject to
+
+ align:start position:0%
+of low degree and then we use subject to
+ 
+
+ align:start position:0%
+of low degree and then we use subject to
+it so that's how it will come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up any any more questions before a
+
+ align:start position:0%
+up any any more questions before a
+ 
+
+ align:start position:0%
+up any any more questions before a
+before we analyze the subject protocol
+
+ align:start position:0%
+before we analyze the subject protocol
+ 
+
+ align:start position:0%
+before we analyze the subject protocol
+questions on the protocol
+
+ align:start position:0%
+questions on the protocol
+ 
+
+ align:start position:0%
+questions on the protocol
+itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or oh oh you're asking what you're
+
+ align:start position:0%
+or oh oh you're asking what you're
+ 
+
+ align:start position:0%
+or oh oh you're asking what you're
+asking you're saying this sum check do I
+
+ align:start position:0%
+asking you're saying this sum check do I
+ 
+
+ align:start position:0%
+asking you're saying this sum check do I
+really need this specific kind of a
+
+ align:start position:0%
+really need this specific kind of a
+ 
+
+ align:start position:0%
+really need this specific kind of a
+polinomial code or can I do using
+
+ align:start position:0%
+polinomial code or can I do using
+ 
+
+ align:start position:0%
+polinomial code or can I do using
+arbitrary codes kind of thing okay so
+
+ align:start position:0%
+arbitrary codes kind of thing okay so
+ 
+
+ align:start position:0%
+arbitrary codes kind of thing okay so
+actually this is a great great question
+
+ align:start position:0%
+actually this is a great great question
+ 
+
+ align:start position:0%
+actually this is a great great question
+uh there's a paper by or
+
+ align:start position:0%
+uh there's a paper by or
+ 
+
+ align:start position:0%
+uh there's a paper by or
+from several years ago I remember
+
+ align:start position:0%
+from several years ago I remember
+ 
+
+ align:start position:0%
+from several years ago I remember
+exactly where he shows how to do a sum
+
+ align:start position:0%
+exactly where he shows how to do a sum
+ 
+
+ align:start position:0%
+exactly where he shows how to do a sum
+check over more General codes not any
+
+ align:start position:0%
+check over more General codes not any
+ 
+
+ align:start position:0%
+check over more General codes not any
+kind of code but more General than that
+
+ align:start position:0%
+kind of code but more General than that
+ 
+
+ align:start position:0%
+kind of code but more General than that
+thing like tensor codes or Rachel do you
+
+ align:start position:0%
+thing like tensor codes or Rachel do you
+ 
+
+ align:start position:0%
+thing like tensor codes or Rachel do you
+remember you looked into it yeah t
+
+ align:start position:0%
+remember you looked into it yeah t
+ 
+
+ align:start position:0%
+remember you looked into it yeah t
+tensor
+
+ align:start position:0%
+tensor
+ 
+
+ align:start position:0%
+tensor
+codes yeah so so he generalized it not
+
+ align:start position:0%
+codes yeah so so he generalized it not
+ 
+
+ align:start position:0%
+codes yeah so so he generalized it not
+to any code but he G the generalization
+
+ align:start position:0%
+to any code but he G the generalization
+ 
+
+ align:start position:0%
+to any code but he G the generalization
+this OC to work for big for a larger
+
+ align:start position:0%
+this OC to work for big for a larger
+ 
+
+ align:start position:0%
+this OC to work for big for a larger
+family
+
+ align:start position:0%
+family
+ 
+
+ align:start position:0%
+family
+of to ask the question what does it mean
+
+ align:start position:0%
+of to ask the question what does it mean
+ 
+
+ align:start position:0%
+of to ask the question what does it mean
+for the subject protocol to work for
+
+ align:start position:0%
+for the subject protocol to work for
+ 
+
+ align:start position:0%
+for the subject protocol to work for
+okay more good good good so you can
+
+ align:start position:0%
+okay more good good good so you can
+ 
+
+ align:start position:0%
+okay more good good good so you can
+think of it is I'm proving something
+
+ align:start position:0%
+think of it is I'm proving something
+ 
+
+ align:start position:0%
+think of it is I'm proving something
+about uh I don't remember exactly how
+
+ align:start position:0%
+about uh I don't remember exactly how
+ 
+
+ align:start position:0%
+about uh I don't remember exactly how
+his formalization was but it's like uh
+
+ align:start position:0%
+his formalization was but it's like uh
+ 
+
+ align:start position:0%
+his formalization was but it's like uh
+I'm proving something about a code
+
+ align:start position:0%
+I'm proving something about a code
+ 
+
+ align:start position:0%
+I'm proving something about a code
+word and I want kind of reinterpret this
+
+ align:start position:0%
+word and I want kind of reinterpret this
+ 
+
+ align:start position:0%
+word and I want kind of reinterpret this
+you can reinterpret this as a because
+
+ align:start position:0%
+you can reinterpret this as a because
+ 
+
+ align:start position:0%
+you can reinterpret this as a because
+you can think of the this F as being an
+
+ align:start position:0%
+you can think of the this F as being an
+ 
+
+ align:start position:0%
+you can think of the this F as being an
+aircraf in code so does it work only for
+
+ align:start position:0%
+aircraf in code so does it work only for
+ 
+
+ align:start position:0%
+aircraf in code so does it work only for
+this kind of read M this is called the
+
+ align:start position:0%
+this kind of read M this is called the
+ 
+
+ align:start position:0%
+this kind of read M this is called the
+read does it work only for read can you
+
+ align:start position:0%
+read does it work only for read can you
+ 
+
+ align:start position:0%
+read does it work only for read can you
+do it for arbitrary codes uh and he
+
+ align:start position:0%
+do it for arbitrary codes uh and he
+ 
+
+ align:start position:0%
+do it for arbitrary codes uh and he
+proves it for for arbitrary codes so
+
+ align:start position:0%
+proves it for for arbitrary codes so
+ 
+
+ align:start position:0%
+proves it for for arbitrary codes so
+this is kind of there's kind of a any
+
+ align:start position:0%
+this is kind of there's kind of a any
+ 
+
+ align:start position:0%
+this is kind of there's kind of a any
+polinomial is an air correcting code
+
+ align:start position:0%
+polinomial is an air correcting code
+ 
+
+ align:start position:0%
+polinomial is an air correcting code
+it's a type of air crafting code H for a
+
+ align:start position:0%
+it's a type of air crafting code H for a
+ 
+
+ align:start position:0%
+it's a type of air crafting code H for a
+multivaried case it's called read Muller
+
+ align:start position:0%
+multivaried case it's called read Muller
+ 
+
+ align:start position:0%
+multivaried case it's called read Muller
+for univ case is called re Solomon and
+
+ align:start position:0%
+for univ case is called re Solomon and
+ 
+
+ align:start position:0%
+for univ case is called re Solomon and
+so when the subject protocol for V think
+
+ align:start position:0%
+so when the subject protocol for V think
+ 
+
+ align:start position:0%
+so when the subject protocol for V think
+it is this protocol for read more codes
+
+ align:start position:0%
+it is this protocol for read more codes
+ 
+
+ align:start position:0%
+it is this protocol for read more codes
+and then you can ask is there a analog
+
+ align:start position:0%
+and then you can ask is there a analog
+ 
+
+ align:start position:0%
+and then you can ask is there a analog
+for other codes and actually there is
+
+ align:start position:0%
+for other codes and actually there is
+ 
+
+ align:start position:0%
+for other codes and actually there is
+there are analogs out there
+
+ align:start position:0%
+there are analogs out there
+ 
+
+ align:start position:0%
+there are analogs out there
+yeah okay any other questions
+
+ align:start position:0%
+yeah okay any other questions
+ 
+
+ align:start position:0%
+yeah okay any other questions
+yeah making the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of that wouldn't like point of doing
+
+ align:start position:0%
+of that wouldn't like point of doing
+ 
+
+ align:start position:0%
+of that wouldn't like point of doing
+this because of like the size of H the
+
+ align:start position:0%
+this because of like the size of H the
+ 
+
+ align:start position:0%
+this because of like the size of H the
+log okay you're right so okay you're
+
+ align:start position:0%
+log okay you're right so okay you're
+ 
+
+ align:start position:0%
+log okay you're right so okay you're
+right so if there okay so the let me go
+
+ align:start position:0%
+right so if there okay so the let me go
+ 
+
+ align:start position:0%
+right so if there okay so the let me go
+back so the question is what what should
+
+ align:start position:0%
+back so the question is what what should
+ 
+
+ align:start position:0%
+back so the question is what what should
+this H be you know what is this H and
+
+ align:start position:0%
+this H be you know what is this H and
+ 
+
+ align:start position:0%
+this H be you know what is this H and
+the answer is this H can actually be all
+
+ align:start position:0%
+the answer is this H can actually be all
+ 
+
+ align:start position:0%
+the answer is this H can actually be all
+of f of course if it's all of f the
+
+ align:start position:0%
+of f of course if it's all of f the
+ 
+
+ align:start position:0%
+of f of course if it's all of f the
+verifier runs in time which is like the
+
+ align:start position:0%
+verifier runs in time which is like the
+ 
+
+ align:start position:0%
+verifier runs in time which is like the
+size of f because he checks you know Su
+
+ align:start position:0%
+size of f because he checks you know Su
+ 
+
+ align:start position:0%
+size of f because he checks you know Su
+over H if it's all of f you run the time
+
+ align:start position:0%
+over H if it's all of f you run the time
+ 
+
+ align:start position:0%
+over H if it's all of f you run the time
+all of f but maybe f is not that big
+
+ align:start position:0%
+all of f but maybe f is not that big
+ 
+
+ align:start position:0%
+all of f but maybe f is not that big
+maybe f is polinomial even if f is
+
+ align:start position:0%
+maybe f is polinomial even if f is
+ 
+
+ align:start position:0%
+maybe f is polinomial even if f is
+polinomial size still checking this sum
+
+ align:start position:0%
+polinomial size still checking this sum
+ 
+
+ align:start position:0%
+polinomial size still checking this sum
+is much bigger than F right it's like H
+
+ align:start position:0%
+is much bigger than F right it's like H
+ 
+
+ align:start position:0%
+is much bigger than F right it's like H
+to the n like f to the m m can be big so
+
+ align:start position:0%
+to the n like f to the m m can be big so
+ 
+
+ align:start position:0%
+to the n like f to the m m can be big so
+the the hardness does not come only from
+
+ align:start position:0%
+the the hardness does not come only from
+ 
+
+ align:start position:0%
+the the hardness does not come only from
+f it comes from M it's exponential in M
+
+ align:start position:0%
+f it comes from M it's exponential in M
+ 
+
+ align:start position:0%
+f it comes from M it's exponential in M
+it's the M that kind of makes it very
+
+ align:start position:0%
+it's the M that kind of makes it very
+ 
+
+ align:start position:0%
+it's the M that kind of makes it very
+hard and so H can be as large as the
+
+ align:start position:0%
+hard and so H can be as large as the
+ 
+
+ align:start position:0%
+hard and so H can be as large as the
+entire field and you can run some check
+
+ align:start position:0%
+entire field and you can run some check
+ 
+
+ align:start position:0%
+entire field and you can run some check
+over that too there's um it's still an
+
+ align:start position:0%
+over that too there's um it's still an
+ 
+
+ align:start position:0%
+over that too there's um it's still an
+interesting protocol yeah but if we that
+
+ align:start position:0%
+interesting protocol yeah but if we that
+ 
+
+ align:start position:0%
+interesting protocol yeah but if we that
+would we need to do an extension or
+
+ align:start position:0%
+would we need to do an extension or
+ 
+
+ align:start position:0%
+would we need to do an extension or
+something that good so okay the good so
+
+ align:start position:0%
+something that good so okay the good so
+ 
+
+ align:start position:0%
+something that good so okay the good so
+the question is wait do we get any
+
+ align:start position:0%
+the question is wait do we get any
+ 
+
+ align:start position:0%
+the question is wait do we get any
+aircraft in guarantees here because uh
+
+ align:start position:0%
+aircraft in guarantees here because uh
+ 
+
+ align:start position:0%
+aircraft in guarantees here because uh
+if we're doing over all of that and I
+
+ align:start position:0%
+if we're doing over all of that and I
+ 
+
+ align:start position:0%
+if we're doing over all of that and I
+think the answer is yes we we don't need
+
+ align:start position:0%
+think the answer is yes we we don't need
+ 
+
+ align:start position:0%
+think the answer is yes we we don't need
+to extend it further because as we see
+
+ align:start position:0%
+to extend it further because as we see
+ 
+
+ align:start position:0%
+to extend it further because as we see
+now we'll see now when we analyze it the
+
+ align:start position:0%
+now we'll see now when we analyze it the
+ 
+
+ align:start position:0%
+now we'll see now when we analyze it the
+soundless error goes down with something
+
+ align:start position:0%
+soundless error goes down with something
+ 
+
+ align:start position:0%
+soundless error goes down with something
+like d over f h does not come into play
+
+ align:start position:0%
+like d over f h does not come into play
+ 
+
+ align:start position:0%
+like d over f h does not come into play
+there but we'll see that let's let's see
+
+ align:start position:0%
+there but we'll see that let's let's see
+ 
+
+ align:start position:0%
+there but we'll see that let's let's see
+that together I I right I agree when you
+
+ align:start position:0%
+that together I I right I agree when you
+ 
+
+ align:start position:0%
+that together I I right I agree when you
+say that yeah that should right it
+
+ align:start position:0%
+say that yeah that should right it
+ 
+
+ align:start position:0%
+say that yeah that should right it
+should things should degrade with age
+
+ align:start position:0%
+should things should degrade with age
+ 
+
+ align:start position:0%
+should things should degrade with age
+but actually they don't so we'll see
+
+ align:start position:0%
+but actually they don't so we'll see
+ 
+
+ align:start position:0%
+but actually they don't so we'll see
+that now when we when we analyze
+
+ align:start position:0%
+that now when we when we analyze
+ 
+
+ align:start position:0%
+that now when we when we analyze
+it okay okay any any these are great
+
+ align:start position:0%
+it okay okay any any these are great
+ 
+
+ align:start position:0%
+it okay okay any any these are great
+great questions so thank you any other
+
+ align:start position:0%
+great questions so thank you any other
+ 
+
+ align:start position:0%
+great questions so thank you any other
+questions before we go to the
+
+ align:start position:0%
+questions before we go to the
+ 
+
+ align:start position:0%
+questions before we go to the
+analysis okay so actually before we do
+
+ align:start position:0%
+analysis okay so actually before we do
+ 
+
+ align:start position:0%
+analysis okay so actually before we do
+soundness let's just first do a sanity
+
+ align:start position:0%
+soundness let's just first do a sanity
+ 
+
+ align:start position:0%
+soundness let's just first do a sanity
+check on the com on the kind of
+
+ align:start position:0%
+check on the com on the kind of
+ 
+
+ align:start position:0%
+check on the com on the kind of
+communication complexity and the the
+
+ align:start position:0%
+communication complexity and the the
+ 
+
+ align:start position:0%
+communication complexity and the the
+runtime and so on so first let's see
+
+ align:start position:0%
+runtime and so on so first let's see
+ 
+
+ align:start position:0%
+runtime and so on so first let's see
+this protocol has n rounds each round we
+
+ align:start position:0%
+this protocol has n rounds each round we
+ 
+
+ align:start position:0%
+this protocol has n rounds each round we
+kind of get rid of one VAR one sum in
+
+ align:start position:0%
+kind of get rid of one VAR one sum in
+ 
+
+ align:start position:0%
+kind of get rid of one VAR one sum in
+the sum check right so
+
+ align:start position:0%
+the sum check right so
+ 
+
+ align:start position:0%
+the sum check right so
+the so uh the communication complexity
+
+ align:start position:0%
+the so uh the communication complexity
+ 
+
+ align:start position:0%
+the so uh the communication complexity
+so our round
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complexity is M rounds M back and forth
+
+ align:start position:0%
+complexity is M rounds M back and forth
+ 
+
+ align:start position:0%
+complexity is M rounds M back and forth
+M to m i don't if you want to count each
+
+ align:start position:0%
+M to m i don't if you want to count each
+ 
+
+ align:start position:0%
+M to m i don't if you want to count each
+one or round is one two so let me just
+
+ align:start position:0%
+one or round is one two so let me just
+ 
+
+ align:start position:0%
+one or round is one two so let me just
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+order uh the the communication
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complexity is what um uh so each time uh
+
+ align:start position:0%
+complexity is what um uh so each time uh
+ 
+
+ align:start position:0%
+complexity is what um uh so each time uh
+po one polinomial is s and one field
+
+ align:start position:0%
+po one polinomial is s and one field
+ 
+
+ align:start position:0%
+po one polinomial is s and one field
+element so it's really a polinomial is a
+
+ align:start position:0%
+element so it's really a polinomial is a
+ 
+
+ align:start position:0%
+element so it's really a polinomial is a
+degree d right so it's just uh D field
+
+ align:start position:0%
+degree d right so it's just uh D field
+ 
+
+ align:start position:0%
+degree d right so it's just uh D field
+elements each time times
+
+ align:start position:0%
+elements each time times
+ 
+
+ align:start position:0%
+elements each time times
+n so fine we can do times you know log F
+
+ align:start position:0%
+n so fine we can do times you know log F
+ 
+
+ align:start position:0%
+n so fine we can do times you know log F
+if you want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to so that's the communication
+
+ align:start position:0%
+to so that's the communication
+ 
+
+ align:start position:0%
+to so that's the communication
+complexity okay what about the verifier
+
+ align:start position:0%
+complexity okay what about the verifier
+ 
+
+ align:start position:0%
+complexity okay what about the verifier
+run time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+verifier he gets a polinomial degree D
+
+ align:start position:0%
+verifier he gets a polinomial degree D
+ 
+
+ align:start position:0%
+verifier he gets a polinomial degree D
+polinomial so D essentially field
+
+ align:start position:0%
+polinomial so D essentially field
+ 
+
+ align:start position:0%
+polinomial so D essentially field
+elements or D plus1 field elements and
+
+ align:start position:0%
+elements or D plus1 field elements and
+ 
+
+ align:start position:0%
+elements or D plus1 field elements and
+he just sums them up he checks that it's
+
+ align:start position:0%
+he just sums them up he checks that it's
+ 
+
+ align:start position:0%
+he just sums them up he checks that it's
+a degree D and sums them up that's all
+
+ align:start position:0%
+a degree D and sums them up that's all
+ 
+
+ align:start position:0%
+a degree D and sums them up that's all
+he does so it's really essentially the
+
+ align:start position:0%
+he does so it's really essentially the
+ 
+
+ align:start position:0%
+he does so it's really essentially the
+same for M rounds he has a degree D
+
+ align:start position:0%
+same for M rounds he has a degree D
+ 
+
+ align:start position:0%
+same for M rounds he has a degree D
+polinomial and he sums them I should put
+
+ align:start position:0%
+polinomial and he sums them I should put
+ 
+
+ align:start position:0%
+polinomial and he sums them I should put
+here maybe po log then because the sum I
+
+ align:start position:0%
+here maybe po log then because the sum I
+ 
+
+ align:start position:0%
+here maybe po log then because the sum I
+I'm assuming addition multiplication
+
+ align:start position:0%
+I'm assuming addition multiplication
+ 
+
+ align:start position:0%
+I'm assuming addition multiplication
+take poly log F again as I said often I
+
+ align:start position:0%
+take poly log F again as I said often I
+ 
+
+ align:start position:0%
+take poly log F again as I said often I
+think maybe even in the notes justtin
+
+ align:start position:0%
+think maybe even in the notes justtin
+ 
+
+ align:start position:0%
+think maybe even in the notes justtin
+Taylor's notes this is omitted it's like
+
+ align:start position:0%
+Taylor's notes this is omitted it's like
+ 
+
+ align:start position:0%
+Taylor's notes this is omitted it's like
+the feel thing of is one operation so
+
+ align:start position:0%
+the feel thing of is one operation so
+ 
+
+ align:start position:0%
+the feel thing of is one operation so
+just so you know if you read things
+
+ align:start position:0%
+just so you know if you read things
+ 
+
+ align:start position:0%
+just so you know if you read things
+often you won't see this part question
+
+ align:start position:0%
+often you won't see this part question
+ 
+
+ align:start position:0%
+often you won't see this part question
+ver the verifier also needs to choose
+
+ align:start position:0%
+ver the verifier also needs to choose
+ 
+
+ align:start position:0%
+ver the verifier also needs to choose
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T yeah exactly so some over H is like H
+
+ align:start position:0%
+T yeah exactly so some over H is like H
+ 
+
+ align:start position:0%
+T yeah exactly so some over H is like H
+additions okay okay yeah he you sorry
+
+ align:start position:0%
+additions okay okay yeah he you sorry
+ 
+
+ align:start position:0%
+additions okay okay yeah he you sorry
+yeah so okay good uh you're saying he
+
+ align:start position:0%
+yeah so okay good uh you're saying he
+ 
+
+ align:start position:0%
+yeah so okay good uh you're saying he
+needs to compute uh it's still yeah so
+
+ align:start position:0%
+needs to compute uh it's still yeah so
+ 
+
+ align:start position:0%
+needs to compute uh it's still yeah so
+right so the the ver far he gets a
+
+ align:start position:0%
+right so the the ver far he gets a
+ 
+
+ align:start position:0%
+right so the the ver far he gets a
+polinomial he needs to evaluate the
+
+ align:start position:0%
+polinomial he needs to evaluate the
+ 
+
+ align:start position:0%
+polinomial he needs to evaluate the
+polinomial in h so yeah so for M rounds
+
+ align:start position:0%
+polinomial in h so yeah so for M rounds
+ 
+
+ align:start position:0%
+polinomial in h so yeah so for M rounds
+he gets a degree D polinomial he needs
+
+ align:start position:0%
+he gets a degree D polinomial he needs
+ 
+
+ align:start position:0%
+he gets a degree D polinomial he needs
+to evaluate
+
+ align:start position:0%
+to evaluate
+ 
+
+ align:start position:0%
+to evaluate
+it oh sorry this does not have
+
+ align:start position:0%
+it oh sorry this does not have
+ 
+
+ align:start position:0%
+it oh sorry this does not have
+H yeah you need to evaluate it in in uh
+
+ align:start position:0%
+H yeah you need to evaluate it in in uh
+ 
+
+ align:start position:0%
+H yeah you need to evaluate it in in uh
+H
+
+ align:start position:0%
+H
+ 
+
+ align:start position:0%
+H
+points the degree D polinomial and then
+
+ align:start position:0%
+points the degree D polinomial and then
+ 
+
+ align:start position:0%
+points the degree D polinomial and then
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+log thanks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good thanks a lot good catch that's
+
+ align:start position:0%
+good thanks a lot good catch that's
+ 
+
+ align:start position:0%
+good thanks a lot good catch that's
+awesome okay great so that's the
+
+ align:start position:0%
+awesome okay great so that's the
+ 
+
+ align:start position:0%
+awesome okay great so that's the
+verifier as I said the PO we care less
+
+ align:start position:0%
+verifier as I said the PO we care less
+ 
+
+ align:start position:0%
+verifier as I said the PO we care less
+about but just you know if you want to
+
+ align:start position:0%
+about but just you know if you want to
+ 
+
+ align:start position:0%
+about but just you know if you want to
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+and and by the way this is assuming the
+
+ align:start position:0%
+and and by the way this is assuming the
+ 
+
+ align:start position:0%
+and and by the way this is assuming the
+verifier has access to F he knows f f is
+
+ align:start position:0%
+verifier has access to F he knows f f is
+ 
+
+ align:start position:0%
+verifier has access to F he knows f f is
+kind of he has Oracle access to it
+
+ align:start position:0%
+kind of he has Oracle access to it
+ 
+
+ align:start position:0%
+kind of he has Oracle access to it
+because of course at the end he needs to
+
+ align:start position:0%
+because of course at the end he needs to
+ 
+
+ align:start position:0%
+because of course at the end he needs to
+check equality with f so this we just
+
+ align:start position:0%
+check equality with f so this we just
+ 
+
+ align:start position:0%
+check equality with f so this we just
+assume he has oral access to F and then
+
+ align:start position:0%
+assume he has oral access to F and then
+ 
+
+ align:start position:0%
+assume he has oral access to F and then
+the prover what he does he need to do
+
+ align:start position:0%
+the prover what he does he need to do
+ 
+
+ align:start position:0%
+the prover what he does he need to do
+well he needs to do this computation so
+
+ align:start position:0%
+well he needs to do this computation so
+ 
+
+ align:start position:0%
+well he needs to do this computation so
+he runs in time like H to the m he needs
+
+ align:start position:0%
+he runs in time like H to the m he needs
+ 
+
+ align:start position:0%
+he runs in time like H to the m he needs
+to do all the sum he needs to run so the
+
+ align:start position:0%
+to do all the sum he needs to run so the
+ 
+
+ align:start position:0%
+to do all the sum he needs to run so the
+polinomial so it's called a t subf is
+
+ align:start position:0%
+polinomial so it's called a t subf is
+ 
+
+ align:start position:0%
+polinomial so it's called a t subf is
+the time to run uh to compute F so we
+
+ align:start position:0%
+the time to run uh to compute F so we
+ 
+
+ align:start position:0%
+the time to run uh to compute F so we
+need to compute F uh he needs to uh do
+
+ align:start position:0%
+need to compute F uh he needs to uh do
+ 
+
+ align:start position:0%
+need to compute F uh he needs to uh do
+the sum overall fs and he does that kind
+
+ align:start position:0%
+the sum overall fs and he does that kind
+ 
+
+ align:start position:0%
+the sum overall fs and he does that kind
+of a d m times right something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this A and polog H polog F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+yeah so that's the pro ver test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes no good good good good good great
+
+ align:start position:0%
+yes no good good good good good great
+ 
+
+ align:start position:0%
+yes no good good good good good great
+question no so you're okay so even if V
+
+ align:start position:0%
+question no so you're okay so even if V
+ 
+
+ align:start position:0%
+question no so you're okay so even if V
+has random Oracle access to F he can
+
+ align:start position:0%
+has random Oracle access to F he can
+ 
+
+ align:start position:0%
+has random Oracle access to F he can
+compute this entire thing but it will
+
+ align:start position:0%
+compute this entire thing but it will
+ 
+
+ align:start position:0%
+compute this entire thing but it will
+take him time H to the end because he
+
+ align:start position:0%
+take him time H to the end because he
+ 
+
+ align:start position:0%
+take him time H to the end because he
+needs to computer some so the the goal
+
+ align:start position:0%
+needs to computer some so the the goal
+ 
+
+ align:start position:0%
+needs to computer some so the the goal
+he needs to check so let's say Computing
+
+ align:start position:0%
+he needs to check so let's say Computing
+ 
+
+ align:start position:0%
+he needs to check so let's say Computing
+F once it takes the one time you can
+
+ align:start position:0%
+F once it takes the one time you can
+ 
+
+ align:start position:0%
+F once it takes the one time you can
+kind of ask but to check the sum he
+
+ align:start position:0%
+kind of ask but to check the sum he
+ 
+
+ align:start position:0%
+kind of ask but to check the sum he
+needs to
+
+ align:start position:0%
+needs to
+ 
+
+ align:start position:0%
+needs to
+ask this an H to the m question now
+
+ align:start position:0%
+ask this an H to the m question now
+ 
+
+ align:start position:0%
+ask this an H to the m question now
+think of H of them is
+
+ align:start position:0%
+think of H of them is
+ 
+
+ align:start position:0%
+think of H of them is
+huge even if a even if H is two think of
+
+ align:start position:0%
+huge even if a even if H is two think of
+ 
+
+ align:start position:0%
+huge even if a even if H is two think of
+M as being Big M is like n variable so
+
+ align:start position:0%
+M as being Big M is like n variable so
+ 
+
+ align:start position:0%
+M as being Big M is like n variable so
+it's like exponential that's it great
+
+ align:start position:0%
+it's like exponential that's it great
+ 
+
+ align:start position:0%
+it's like exponential that's it great
+question but should I think of the
+
+ align:start position:0%
+question but should I think of the
+ 
+
+ align:start position:0%
+question but should I think of the
+description of f Pol or good so you can
+
+ align:start position:0%
+description of f Pol or good so you can
+ 
+
+ align:start position:0%
+description of f Pol or good so you can
+okay there's two options you can think
+
+ align:start position:0%
+okay there's two options you can think
+ 
+
+ align:start position:0%
+okay there's two options you can think
+of the description of f as being
+
+ align:start position:0%
+of the description of f as being
+ 
+
+ align:start position:0%
+of the description of f as being
+polinomial that's one option or that you
+
+ align:start position:0%
+polinomial that's one option or that you
+ 
+
+ align:start position:0%
+polinomial that's one option or that you
+can compute F in it's like described by
+
+ align:start position:0%
+can compute F in it's like described by
+ 
+
+ align:start position:0%
+can compute F in it's like described by
+a polinomial size circuit or you can
+
+ align:start position:0%
+a polinomial size circuit or you can
+ 
+
+ align:start position:0%
+a polinomial size circuit or you can
+think it can be large but the verifier
+
+ align:start position:0%
+think it can be large but the verifier
+ 
+
+ align:start position:0%
+think it can be large but the verifier
+has access to it somehow the verifier
+
+ align:start position:0%
+has access to it somehow the verifier
+ 
+
+ align:start position:0%
+has access to it somehow the verifier
+has like a trusted Oracle that computes
+
+ align:start position:0%
+has like a trusted Oracle that computes
+ 
+
+ align:start position:0%
+has like a trusted Oracle that computes
+app for
+
+ align:start position:0%
+app for
+ 
+
+ align:start position:0%
+app for
+him
+
+ align:start position:0%
+him
+ 
+
+ align:start position:0%
+him
+okay great okay so now the
+
+ align:start position:0%
+okay great okay so now the
+ 
+
+ align:start position:0%
+okay great okay so now the
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yes good yeah this is just sorry this
+
+ align:start position:0%
+yes good yeah this is just sorry this
+ 
+
+ align:start position:0%
+yes good yeah this is just sorry this
+it's just the time it takes to compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F thanks
+
+ align:start position:0%
+F thanks
+ 
+
+ align:start position:0%
+F thanks
+yeah because he needs to comp the
+
+ align:start position:0%
+yeah because he needs to comp the
+ 
+
+ align:start position:0%
+yeah because he needs to comp the
+approver supposedly doesn't have he
+
+ align:start position:0%
+approver supposedly doesn't have he
+ 
+
+ align:start position:0%
+approver supposedly doesn't have he
+needs to actually do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computation okay great yes um whereing
+
+ align:start position:0%
+computation okay great yes um whereing
+ 
+
+ align:start position:0%
+computation okay great yes um whereing
+that into account the theover finding G
+
+ align:start position:0%
+that into account the theover finding G
+ 
+
+ align:start position:0%
+that into account the theover finding G
+of One X like don't they have to combine
+
+ align:start position:0%
+of One X like don't they have to combine
+ 
+
+ align:start position:0%
+of One X like don't they have to combine
+a bunch of terms order of oh yeah but uh
+
+ align:start position:0%
+a bunch of terms order of oh yeah but uh
+ 
+
+ align:start position:0%
+a bunch of terms order of oh yeah but uh
+he runs in time F anyway f is much
+
+ align:start position:0%
+he runs in time F anyway f is much
+ 
+
+ align:start position:0%
+he runs in time F anyway f is much
+bigger than D so the degree is also
+
+ align:start position:0%
+bigger than D so the degree is also
+ 
+
+ align:start position:0%
+bigger than D so the degree is also
+always much smaller
+
+ align:start position:0%
+always much smaller
+ 
+
+ align:start position:0%
+always much smaller
+F so it's I'm kind of lumping it in yeah
+
+ align:start position:0%
+F so it's I'm kind of lumping it in yeah
+ 
+
+ align:start position:0%
+F so it's I'm kind of lumping it in yeah
+thanks great question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah something else again you're saying
+
+ align:start position:0%
+yeah something else again you're saying
+ 
+
+ align:start position:0%
+yeah something else again you're saying
+if you you want to be even you you're
+
+ align:start position:0%
+if you you want to be even you you're
+ 
+
+ align:start position:0%
+if you you want to be even you you're
+saying let's say the verifier wants to
+
+ align:start position:0%
+saying let's say the verifier wants to
+ 
+
+ align:start position:0%
+saying let's say the verifier wants to
+be even more efficient than this then
+
+ align:start position:0%
+be even more efficient than this then
+ 
+
+ align:start position:0%
+be even more efficient than this then
+what can you do can I choose H to be
+
+ align:start position:0%
+what can you do can I choose H to be
+ 
+
+ align:start position:0%
+what can you do can I choose H to be
+like special structure okay but you're
+
+ align:start position:0%
+like special structure okay but you're
+ 
+
+ align:start position:0%
+like special structure okay but you're
+changing the problem you what you're
+
+ align:start position:0%
+changing the problem you what you're
+ 
+
+ align:start position:0%
+changing the problem you what you're
+saying is so the problem is H is given
+
+ align:start position:0%
+saying is so the problem is H is given
+ 
+
+ align:start position:0%
+saying is so the problem is H is given
+to us and you want to prove now you're
+
+ align:start position:0%
+to us and you want to prove now you're
+ 
+
+ align:start position:0%
+to us and you want to prove now you're
+saying maybe if H has a special
+
+ align:start position:0%
+saying maybe if H has a special
+ 
+
+ align:start position:0%
+saying maybe if H has a special
+structure maybe we can be even more
+
+ align:start position:0%
+structure maybe we can be even more
+ 
+
+ align:start position:0%
+structure maybe we can be even more
+efficient is what you're saying
+
+ align:start position:0%
+efficient is what you're saying
+ 
+
+ align:start position:0%
+efficient is what you're saying
+a good question a I haven't thought
+
+ align:start position:0%
+a good question a I haven't thought
+ 
+
+ align:start position:0%
+a good question a I haven't thought
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+itation yeah like you can probably uh
+
+ align:start position:0%
+itation yeah like you can probably uh
+ 
+
+ align:start position:0%
+itation yeah like you can probably uh
+yeah yeah probably you can you can so V
+
+ align:start position:0%
+yeah yeah probably you can you can so V
+ 
+
+ align:start position:0%
+yeah yeah probably you can you can so V
+not was saying you can probably batch
+
+ align:start position:0%
+not was saying you can probably batch
+ 
+
+ align:start position:0%
+not was saying you can probably batch
+things or probably yeah I think if you
+
+ align:start position:0%
+things or probably yeah I think if you
+ 
+
+ align:start position:0%
+things or probably yeah I think if you
+can choose H if H is of a certain
+
+ align:start position:0%
+can choose H if H is of a certain
+ 
+
+ align:start position:0%
+can choose H if H is of a certain
+structure then I think you can do better
+
+ align:start position:0%
+structure then I think you can do better
+ 
+
+ align:start position:0%
+structure then I think you can do better
+but this is kind of your the verifier
+
+ align:start position:0%
+but this is kind of your the verifier
+ 
+
+ align:start position:0%
+but this is kind of your the verifier
+doesn't choose it like that's what's
+
+ align:start position:0%
+doesn't choose it like that's what's
+ 
+
+ align:start position:0%
+doesn't choose it like that's what's
+given them great okay
+
+ align:start position:0%
+given them great okay
+ 
+
+ align:start position:0%
+given them great okay
+great okay any more any more a
+
+ align:start position:0%
+great okay any more any more a
+ 
+
+ align:start position:0%
+great okay any more any more a
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh okay it's degree D but it's m
+
+ align:start position:0%
+yeah oh okay it's degree D but it's m
+ 
+
+ align:start position:0%
+yeah oh okay it's degree D but it's m
+variables so in General Degree D
+
+ align:start position:0%
+variables so in General Degree D
+ 
+
+ align:start position:0%
+variables so in General Degree D
+polinomial with m variables can have
+
+ align:start position:0%
+polinomial with m variables can have
+ 
+
+ align:start position:0%
+polinomial with m variables can have
+size like m to the D so which is can be
+
+ align:start position:0%
+size like m to the D so which is can be
+ 
+
+ align:start position:0%
+size like m to the D so which is can be
+very big great question a d to the m
+
+ align:start position:0%
+very big great question a d to the m
+ 
+
+ align:start position:0%
+very big great question a d to the m
+sorry yeah great great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question okay okay so let's go to
+
+ align:start position:0%
+question okay okay so let's go to
+ 
+
+ align:start position:0%
+question okay okay so let's go to
+completeness and soundness then so what
+
+ align:start position:0%
+completeness and soundness then so what
+ 
+
+ align:start position:0%
+completeness and soundness then so what
+is the completeness of this protocol if
+
+ align:start position:0%
+is the completeness of this protocol if
+ 
+
+ align:start position:0%
+is the completeness of this protocol if
+let's say the pro is honest the
+
+ align:start position:0%
+let's say the pro is honest the
+ 
+
+ align:start position:0%
+let's say the pro is honest the
+statement is correct with what
+
+ align:start position:0%
+statement is correct with what
+ 
+
+ align:start position:0%
+statement is correct with what
+probability will the verifier
+
+ align:start position:0%
+probability will the verifier
+ 
+
+ align:start position:0%
+probability will the verifier
+accept one exactly because you'll just
+
+ align:start position:0%
+accept one exactly because you'll just
+ 
+
+ align:start position:0%
+accept one exactly because you'll just
+be honest you always give the C nomial
+
+ align:start position:0%
+be honest you always give the C nomial
+ 
+
+ align:start position:0%
+be honest you always give the C nomial
+always be Lo degree will always sum to
+
+ align:start position:0%
+always be Lo degree will always sum to
+ 
+
+ align:start position:0%
+always be Lo degree will always sum to
+what it should be and you always going
+
+ align:start position:0%
+what it should be and you always going
+ 
+
+ align:start position:0%
+what it should be and you always going
+accept it that's easy the hard part is
+
+ align:start position:0%
+accept it that's easy the hard part is
+ 
+
+ align:start position:0%
+accept it that's easy the hard part is
+soundness so let's do the soundness and
+
+ align:start position:0%
+soundness so let's do the soundness and
+ 
+
+ align:start position:0%
+soundness so let's do the soundness and
+then after soundness we'll take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a okay so for sound this here's the idea
+
+ align:start position:0%
+a okay so for sound this here's the idea
+ 
+
+ align:start position:0%
+a okay so for sound this here's the idea
+suppose so let's look at it fix suppose
+
+ align:start position:0%
+suppose so let's look at it fix suppose
+ 
+
+ align:start position:0%
+suppose so let's look at it fix suppose
+there's a cheating
+
+ align:start position:0%
+there's a cheating
+ 
+
+ align:start position:0%
+there's a cheating
+prover that generates a false clip so
+
+ align:start position:0%
+prover that generates a false clip so
+ 
+
+ align:start position:0%
+prover that generates a false clip so
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the claim is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+false mainly this sum of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is actually not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big okay so we start with the false CL
+
+ align:start position:0%
+big okay so we start with the false CL
+ 
+
+ align:start position:0%
+big okay so we start with the false CL
+the first thing we know is that and so
+
+ align:start position:0%
+the first thing we know is that and so
+ 
+
+ align:start position:0%
+the first thing we know is that and so
+fix any so you you fix a claim that's
+
+ align:start position:0%
+fix any so you you fix a claim that's
+ 
+
+ align:start position:0%
+fix any so you you fix a claim that's
+false fix any piece
+
+ align:start position:0%
+false fix any piece
+ 
+
+ align:start position:0%
+false fix any piece
+he tries to cheat let's show that he he
+
+ align:start position:0%
+he tries to cheat let's show that he he
+ 
+
+ align:start position:0%
+he tries to cheat let's show that he he
+fails like he won't succeed or succeed
+
+ align:start position:0%
+fails like he won't succeed or succeed
+ 
+
+ align:start position:0%
+fails like he won't succeed or succeed
+very small probability the field is
+
+ align:start position:0%
+very small probability the field is
+ 
+
+ align:start position:0%
+very small probability the field is
+large enough so let's
+
+ align:start position:0%
+large enough so let's
+ 
+
+ align:start position:0%
+large enough so let's
+see first the first thing I want to
+
+ align:start position:0%
+see first the first thing I want to
+ 
+
+ align:start position:0%
+see first the first thing I want to
+point out which I mentioned before is G1
+
+ align:start position:0%
+point out which I mentioned before is G1
+ 
+
+ align:start position:0%
+point out which I mentioned before is G1
+must be false G so it must be the case
+
+ align:start position:0%
+must be false G so it must be the case
+ 
+
+ align:start position:0%
+must be false G so it must be the case
+no matter how he cheats and he gives me
+
+ align:start position:0%
+no matter how he cheats and he gives me
+ 
+
+ align:start position:0%
+no matter how he cheats and he gives me
+a bad G1 okay it cannot if he's accepted
+
+ align:start position:0%
+a bad G1 okay it cannot if he's accepted
+ 
+
+ align:start position:0%
+a bad G1 okay it cannot if he's accepted
+if the Prov is accepted then G1 cannot
+
+ align:start position:0%
+if the Prov is accepted then G1 cannot
+ 
+
+ align:start position:0%
+if the Prov is accepted then G1 cannot
+be sum of
+
+ align:start position:0%
+be sum of
+ 
+
+ align:start position:0%
+be sum of
+a call
+
+ align:start position:0%
+a call
+ 
+
+ align:start position:0%
+a call
+g1x is not sum of f H2 up to
+
+ align:start position:0%
+g1x is not sum of f H2 up to
+ 
+
+ align:start position:0%
+g1x is not sum of f H2 up to
+hm because I'm going to check that it's
+
+ align:start position:0%
+hm because I'm going to check that it's
+ 
+
+ align:start position:0%
+hm because I'm going to check that it's
+equal to Beta but the sum of f is not
+
+ align:start position:0%
+equal to Beta but the sum of f is not
+ 
+
+ align:start position:0%
+equal to Beta but the sum of f is not
+beta so the G that he gives me cannot be
+
+ align:start position:0%
+beta so the G that he gives me cannot be
+ 
+
+ align:start position:0%
+beta so the G that he gives me cannot be
+the correct F like the correct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G okay so in other words he starts the
+
+ align:start position:0%
+G okay so in other words he starts the
+ 
+
+ align:start position:0%
+G okay so in other words he starts the
+protocol by a cheat a the first message
+
+ align:start position:0%
+protocol by a cheat a the first message
+ 
+
+ align:start position:0%
+protocol by a cheat a the first message
+is not the correct
+
+ align:start position:0%
+is not the correct
+ 
+
+ align:start position:0%
+is not the correct
+polinomial okay because the correct
+
+ align:start position:0%
+polinomial okay because the correct
+ 
+
+ align:start position:0%
+polinomial okay because the correct
+polinomial if you Summit you'll get the
+
+ align:start position:0%
+polinomial if you Summit you'll get the
+ 
+
+ align:start position:0%
+polinomial if you Summit you'll get the
+real beta not the fake
+
+ align:start position:0%
+real beta not the fake
+ 
+
+ align:start position:0%
+real beta not the fake
+beta okay that he
+
+ align:start position:0%
+beta okay that he
+ 
+
+ align:start position:0%
+beta okay that he
+claimed okay however at the end of the
+
+ align:start position:0%
+claimed okay however at the end of the
+ 
+
+ align:start position:0%
+claimed okay however at the end of the
+day if you're
+
+ align:start position:0%
+day if you're
+ 
+
+ align:start position:0%
+day if you're
+accepted the final check when you check
+
+ align:start position:0%
+accepted the final check when you check
+ 
+
+ align:start position:0%
+accepted the final check when you check
+then you check with respect to the
+
+ align:start position:0%
+then you check with respect to the
+ 
+
+ align:start position:0%
+then you check with respect to the
+honest F right and that verifies so at
+
+ align:start position:0%
+honest F right and that verifies so at
+ 
+
+ align:start position:0%
+honest F right and that verifies so at
+the end of the day when you left with G
+
+ align:start position:0%
+the end of the day when you left with G
+ 
+
+ align:start position:0%
+the end of the day when you left with G
+to the like the last one GM to the TM
+
+ align:start position:0%
+to the like the last one GM to the TM
+ 
+
+ align:start position:0%
+to the like the last one GM to the TM
+that's actually
+
+ align:start position:0%
+that's actually
+ 
+
+ align:start position:0%
+that's actually
+honest so somewh the protocol you had to
+
+ align:start position:0%
+honest so somewh the protocol you had to
+ 
+
+ align:start position:0%
+honest so somewh the protocol you had to
+move from a
+
+ align:start position:0%
+move from a
+ 
+
+ align:start position:0%
+move from a
+bad G to a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G okay so again here's the
+
+ align:start position:0%
+G okay so again here's the
+ 
+
+ align:start position:0%
+G okay so again here's the
+claim so I want to argue if so let there
+
+ align:start position:0%
+claim so I want to argue if so let there
+ 
+
+ align:start position:0%
+claim so I want to argue if so let there
+I want to argue there must exist a round
+
+ align:start position:0%
+I want to argue there must exist a round
+ 
+
+ align:start position:0%
+I want to argue there must exist a round
+such that around let's say I so to Pro
+
+ align:start position:0%
+such that around let's say I so to Pro
+ 
+
+ align:start position:0%
+such that around let's say I so to Pro
+to cheat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there must exist around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I such
+
+ align:start position:0%
+I such
+ 
+
+ align:start position:0%
+I such
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+GI is false so GI is not sum of
+
+ align:start position:0%
+GI is false so GI is not sum of
+ 
+
+ align:start position:0%
+GI is false so GI is not sum of
+T1 t i-1 x h i +1 up to hm this is what
+
+ align:start position:0%
+T1 t i-1 x h i +1 up to hm this is what
+ 
+
+ align:start position:0%
+T1 t i-1 x h i +1 up to hm this is what
+it should be but it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and yet at some point but g i +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is actually equal to oh I forgot
+
+ align:start position:0%
+one is actually equal to oh I forgot
+ 
+
+ align:start position:0%
+one is actually equal to oh I forgot
+f is actually equal to some f T1 up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ti so to cheat you must go so you start
+
+ align:start position:0%
+ti so to cheat you must go so you start
+ 
+
+ align:start position:0%
+ti so to cheat you must go so you start
+with with you start with an
+
+ align:start position:0%
+with with you start with an
+ 
+
+ align:start position:0%
+with with you start with an
+incorrect A A polom we know that's for
+
+ align:start position:0%
+incorrect A A polom we know that's for
+ 
+
+ align:start position:0%
+incorrect A A polom we know that's for
+sure because you assuming you're you're
+
+ align:start position:0%
+sure because you assuming you're you're
+ 
+
+ align:start position:0%
+sure because you assuming you're you're
+accepted if you're accepted G1 is false
+
+ align:start position:0%
+accepted if you're accepted G1 is false
+ 
+
+ align:start position:0%
+accepted if you're accepted G1 is false
+now either now G2 is true and then I'll
+
+ align:start position:0%
+now either now G2 is true and then I'll
+ 
+
+ align:start position:0%
+now either now G2 is true and then I'll
+show that happens with very small
+
+ align:start position:0%
+show that happens with very small
+ 
+
+ align:start position:0%
+show that happens with very small
+probability or G2 is also false if G2 is
+
+ align:start position:0%
+probability or G2 is also false if G2 is
+ 
+
+ align:start position:0%
+probability or G2 is also false if G2 is
+false I G3 is true I'm going to show
+
+ align:start position:0%
+false I G3 is true I'm going to show
+ 
+
+ align:start position:0%
+false I G3 is true I'm going to show
+that happens with very small probability
+
+ align:start position:0%
+that happens with very small probability
+ 
+
+ align:start position:0%
+that happens with very small probability
+or G or G3 is false until we're left
+
+ align:start position:0%
+or G or G3 is false until we're left
+ 
+
+ align:start position:0%
+or G or G3 is false until we're left
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+GM which again let but it's still I'm
+
+ align:start position:0%
+GM which again let but it's still I'm
+ 
+
+ align:start position:0%
+GM which again let but it's still I'm
+going to argue that if G minus one was
+
+ align:start position:0%
+going to argue that if G minus one was
+ 
+
+ align:start position:0%
+going to argue that if G minus one was
+false GM is also false with very high
+
+ align:start position:0%
+false GM is also false with very high
+ 
+
+ align:start position:0%
+false GM is also false with very high
+probability but if GM is
+
+ align:start position:0%
+probability but if GM is
+ 
+
+ align:start position:0%
+probability but if GM is
+false you're not going to be if GM is
+
+ align:start position:0%
+false you're not going to be if GM is
+ 
+
+ align:start position:0%
+false you're not going to be if GM is
+actually not
+
+ align:start position:0%
+actually not
+ 
+
+ align:start position:0%
+actually not
+F then for random T the probability that
+
+ align:start position:0%
+F then for random T the probability that
+ 
+
+ align:start position:0%
+F then for random T the probability that
+you'll get f is very very you'll be
+
+ align:start position:0%
+you'll get f is very very you'll be
+ 
+
+ align:start position:0%
+you'll get f is very very you'll be
+consistent with f is very very small
+
+ align:start position:0%
+consistent with f is very very small
+ 
+
+ align:start position:0%
+consistent with f is very very small
+because these are two different
+
+ align:start position:0%
+because these are two different
+ 
+
+ align:start position:0%
+because these are two different
+polinomial and they agree only on D
+
+ align:start position:0%
+polinomial and they agree only on D
+ 
+
+ align:start position:0%
+polinomial and they agree only on D
+points so what's the probability that I
+
+ align:start position:0%
+points so what's the probability that I
+ 
+
+ align:start position:0%
+points so what's the probability that I
+chose one of these D's one of these
+
+ align:start position:0%
+chose one of these D's one of these
+ 
+
+ align:start position:0%
+chose one of these D's one of these
+points D over f
+
+ align:start position:0%
+points D over f
+ 
+
+ align:start position:0%
+points D over f
+okay so let me let me be a little more
+
+ align:start position:0%
+okay so let me let me be a little more
+ 
+
+ align:start position:0%
+okay so let me let me be a little more
+formal
+
+ align:start position:0%
+formal
+ 
+
+ align:start position:0%
+formal
+now okay so I want to argue that part me
+
+ align:start position:0%
+now okay so I want to argue that part me
+ 
+
+ align:start position:0%
+now okay so I want to argue that part me
+argue that so first to cheat there must
+
+ align:start position:0%
+argue that so first to cheat there must
+ 
+
+ align:start position:0%
+argue that so first to cheat there must
+exist some round where we go from F from
+
+ align:start position:0%
+exist some round where we go from F from
+ 
+
+ align:start position:0%
+exist some round where we go from F from
+from false to true because the final
+
+ align:start position:0%
+from false to true because the final
+ 
+
+ align:start position:0%
+from false to true because the final
+final check must be true otherwise
+
+ align:start position:0%
+final check must be true otherwise
+ 
+
+ align:start position:0%
+final check must be true otherwise
+you're I'm going to check you with the
+
+ align:start position:0%
+you're I'm going to check you with the
+ 
+
+ align:start position:0%
+you're I'm going to check you with the
+true so there must exist a around that
+
+ align:start position:0%
+true so there must exist a around that
+ 
+
+ align:start position:0%
+true so there must exist a around that
+you go from false to True let's see
+
+ align:start position:0%
+you go from false to True let's see
+ 
+
+ align:start position:0%
+you go from false to True let's see
+what's the probability of going from
+
+ align:start position:0%
+what's the probability of going from
+ 
+
+ align:start position:0%
+what's the probability of going from
+false to true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so good so what's the probability so
+
+ align:start position:0%
+so good so what's the probability so
+ 
+
+ align:start position:0%
+so good so what's the probability so
+let's denote this event let's knowe this
+
+ align:start position:0%
+let's denote this event let's knowe this
+ 
+
+ align:start position:0%
+let's denote this event let's knowe this
+event by
+
+ align:start position:0%
+event by
+ 
+
+ align:start position:0%
+event by
+bi now let's see what's the probability
+
+ align:start position:0%
+bi now let's see what's the probability
+ 
+
+ align:start position:0%
+bi now let's see what's the probability
+that this events happen this is kind of
+
+ align:start position:0%
+that this events happen this is kind of
+ 
+
+ align:start position:0%
+that this events happen this is kind of
+a bad event an event that you go from a
+
+ align:start position:0%
+a bad event an event that you go from a
+ 
+
+ align:start position:0%
+a bad event an event that you go from a
+bad incorrect a false to true that's for
+
+ align:start position:0%
+bad incorrect a false to true that's for
+ 
+
+ align:start position:0%
+bad incorrect a false to true that's for
+the ver part it's a very bad event
+
+ align:start position:0%
+the ver part it's a very bad event
+ 
+
+ align:start position:0%
+the ver part it's a very bad event
+because then he accepts a false
+
+ align:start position:0%
+because then he accepts a false
+ 
+
+ align:start position:0%
+because then he accepts a false
+statement what is the probability that
+
+ align:start position:0%
+statement what is the probability that
+ 
+
+ align:start position:0%
+statement what is the probability that
+this bad event happen so the
+
+ align:start position:0%
+this bad event happen so the
+ 
+
+ align:start position:0%
+this bad event happen so the
+probability of
+
+ align:start position:0%
+probability of
+ 
+
+ align:start position:0%
+probability of
+B I want to argue is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most D over F let's see
+
+ align:start position:0%
+most D over F let's see
+ 
+
+ align:start position:0%
+most D over F let's see
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+so when is let's see when is GI + one
+
+ align:start position:0%
+so when is let's see when is GI + one
+ 
+
+ align:start position:0%
+so when is let's see when is GI + one
+true we're sending here like the very
+
+ align:start position:0%
+true we're sending here like the very
+ 
+
+ align:start position:0%
+true we're sending here like the very
+the probability let's fix like we fixed
+
+ align:start position:0%
+the probability let's fix like we fixed
+ 
+
+ align:start position:0%
+the probability let's fix like we fixed
+already T1 of the ti plus1 that's fixed
+
+ align:start position:0%
+already T1 of the ti plus1 that's fixed
+ 
+
+ align:start position:0%
+already T1 of the ti plus1 that's fixed
+okay so fix and I don't care how t one
+
+ align:start position:0%
+okay so fix and I don't care how t one
+ 
+
+ align:start position:0%
+okay so fix and I don't care how t one
+up to t i minus one this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defines like the what the prover
+
+ align:start position:0%
+defines like the what the prover
+ 
+
+ align:start position:0%
+defines like the what the prover
+gives GI in the protocol the cheating
+
+ align:start position:0%
+gives GI in the protocol the cheating
+ 
+
+ align:start position:0%
+gives GI in the protocol the cheating
+prover gives in the
+
+ align:start position:0%
+prover gives in the
+ 
+
+ align:start position:0%
+prover gives in the
+protocol okay
+
+ align:start position:0%
+protocol okay
+ 
+
+ align:start position:0%
+protocol okay
+now now the verifier chooses a random t
+
+ align:start position:0%
+now now the verifier chooses a random t
+ 
+
+ align:start position:0%
+now now the verifier chooses a random t
+a random uh so good so this defines GI
+
+ align:start position:0%
+a random uh so good so this defines GI
+ 
+
+ align:start position:0%
+a random uh so good so this defines GI
+which is uh okay this is my G now the
+
+ align:start position:0%
+which is uh okay this is my G now the
+ 
+
+ align:start position:0%
+which is uh okay this is my G now the
+prover the verifier the probability over
+
+ align:start position:0%
+prover the verifier the probability over
+ 
+
+ align:start position:0%
+prover the verifier the probability over
+TI that the verifier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chooses This Ti tells you if GI this
+
+ align:start position:0%
+chooses This Ti tells you if GI this
+ 
+
+ align:start position:0%
+chooses This Ti tells you if GI this
+defines GI +
+
+ align:start position:0%
+defines GI +
+ 
+
+ align:start position:0%
+defines GI +
+one but when it's
+
+ align:start position:0%
+one but when it's
+ 
+
+ align:start position:0%
+one but when it's
+if what do we know about when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we know that because the verifier is
+
+ align:start position:0%
+if we know that because the verifier is
+ 
+
+ align:start position:0%
+if we know that because the verifier is
+accepted we know that some g i +1 of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H is equal to
+
+ align:start position:0%
+H is equal to
+ 
+
+ align:start position:0%
+H is equal to
+GI which is the wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polinomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NTI and this is the wrong polinomial so
+
+ align:start position:0%
+NTI and this is the wrong polinomial so
+ 
+
+ align:start position:0%
+NTI and this is the wrong polinomial so
+what is the probability that for so so
+
+ align:start position:0%
+what is the probability that for so so
+ 
+
+ align:start position:0%
+what is the probability that for so so
+in other words J + one is the wrong
+
+ align:start position:0%
+in other words J + one is the wrong
+ 
+
+ align:start position:0%
+in other words J + one is the wrong
+polom
+
+ align:start position:0%
+polom
+ 
+
+ align:start position:0%
+polom
+what is the probability that for a
+
+ align:start position:0%
+what is the probability that for a
+ 
+
+ align:start position:0%
+what is the probability that for a
+random T it will be the right
+
+ align:start position:0%
+random T it will be the right
+ 
+
+ align:start position:0%
+random T it will be the right
+one D over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F because two polinomial that are
+
+ align:start position:0%
+F because two polinomial that are
+ 
+
+ align:start position:0%
+F because two polinomial that are
+different agree on it most D points I
+
+ align:start position:0%
+different agree on it most D points I
+ 
+
+ align:start position:0%
+different agree on it most D points I
+chose a random point the probability
+
+ align:start position:0%
+chose a random point the probability
+ 
+
+ align:start position:0%
+chose a random point the probability
+that it's one of these D is D over
+
+ align:start position:0%
+that it's one of these D is D over
+ 
+
+ align:start position:0%
+that it's one of these D is D over
+F so what is the probability that you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cheat at this is the
+
+ align:start position:0%
+cheat at this is the
+ 
+
+ align:start position:0%
+cheat at this is the
+probability that there exist some
+
+ align:start position:0%
+probability that there exist some
+ 
+
+ align:start position:0%
+probability that there exist some
+I such that bi holds a bad event holds
+
+ align:start position:0%
+I such that bi holds a bad event holds
+ 
+
+ align:start position:0%
+I such that bi holds a bad event holds
+namely there exists an eye that you go
+
+ align:start position:0%
+namely there exists an eye that you go
+ 
+
+ align:start position:0%
+namely there exists an eye that you go
+from True from false to
+
+ align:start position:0%
+from True from false to
+ 
+
+ align:start position:0%
+from True from false to
+true and that IE by the union bound this
+
+ align:start position:0%
+true and that IE by the union bound this
+ 
+
+ align:start position:0%
+true and that IE by the union bound this
+is at most M number of rounds Times the
+
+ align:start position:0%
+is at most M number of rounds Times the
+ 
+
+ align:start position:0%
+is at most M number of rounds Times the
+probability of one of a specific b b me
+
+ align:start position:0%
+probability of one of a specific b b me
+ 
+
+ align:start position:0%
+probability of one of a specific b b me
+which is D over
+
+ align:start position:0%
+which is D over
+ 
+
+ align:start position:0%
+which is D over
+F so just just note H actually doesn't
+
+ align:start position:0%
+F so just just note H actually doesn't
+ 
+
+ align:start position:0%
+F so just just note H actually doesn't
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+up in the soundness this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soundness okay so the sinus needs M time
+
+ align:start position:0%
+soundness okay so the sinus needs M time
+ 
+
+ align:start position:0%
+soundness okay so the sinus needs M time
+D to be significantly smaller than the
+
+ align:start position:0%
+D to be significantly smaller than the
+ 
+
+ align:start position:0%
+D to be significantly smaller than the
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+size that's all that's important for
+
+ align:start position:0%
+size that's all that's important for
+ 
+
+ align:start position:0%
+size that's all that's important for
+sence yeah so Point like
+
+ align:start position:0%
+sence yeah so Point like
+ 
+
+ align:start position:0%
+sence yeah so Point like
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have exact exactly the point is if
+
+ align:start position:0%
+have exact exactly the point is if
+ 
+
+ align:start position:0%
+have exact exactly the point is if
+you're not happy if f is not large
+
+ align:start position:0%
+you're not happy if f is not large
+ 
+
+ align:start position:0%
+you're not happy if f is not large
+enough if it's not much bigger than m
+
+ align:start position:0%
+enough if it's not much bigger than m
+ 
+
+ align:start position:0%
+enough if it's not much bigger than m
+the m * D then you just make it bigger
+
+ align:start position:0%
+the m * D then you just make it bigger
+ 
+
+ align:start position:0%
+the m * D then you just make it bigger
+you can take you can take extension
+
+ align:start position:0%
+you can take you can take extension
+ 
+
+ align:start position:0%
+you can take you can take extension
+Fields you can take so you just kind of
+
+ align:start position:0%
+Fields you can take so you just kind of
+ 
+
+ align:start position:0%
+Fields you can take so you just kind of
+artificially increase F so that F will
+
+ align:start position:0%
+artificially increase F so that F will
+ 
+
+ align:start position:0%
+artificially increase F so that F will
+be much larger than M * D and hence
+
+ align:start position:0%
+be much larger than M * D and hence
+ 
+
+ align:start position:0%
+be much larger than M * D and hence
+you'll get a small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+applications what happens is given H
+
+ align:start position:0%
+applications what happens is given H
+ 
+
+ align:start position:0%
+applications what happens is given H
+right and the degree happens to be uh H
+
+ align:start position:0%
+right and the degree happens to be uh H
+ 
+
+ align:start position:0%
+right and the degree happens to be uh H
+ESS or h that's why it doesn't make
+
+ align:start position:0%
+ESS or h that's why it doesn't make
+ 
+
+ align:start position:0%
+ESS or h that's why it doesn't make
+sense for H and to be the same but you
+
+ align:start position:0%
+sense for H and to be the same but you
+ 
+
+ align:start position:0%
+sense for H and to be the same but you
+can dis exactly can dis 100% so let me
+
+ align:start position:0%
+can dis exactly can dis 100% so let me
+ 
+
+ align:start position:0%
+can dis exactly can dis 100% so let me
+repeat it because I'm recorded you're
+
+ align:start position:0%
+repeat it because I'm recorded you're
+ 
+
+ align:start position:0%
+repeat it because I'm recorded you're
+not yeah because that's a very good
+
+ align:start position:0%
+not yeah because that's a very good
+ 
+
+ align:start position:0%
+not yeah because that's a very good
+point the the point is for Su in general
+
+ align:start position:0%
+point the the point is for Su in general
+ 
+
+ align:start position:0%
+point the the point is for Su in general
+it makes sense to consider any ag even H
+
+ align:start position:0%
+it makes sense to consider any ag even H
+ 
+
+ align:start position:0%
+it makes sense to consider any ag even H
+which is of size f is interesting for
+
+ align:start position:0%
+which is of size f is interesting for
+ 
+
+ align:start position:0%
+which is of size f is interesting for
+the Su protocol okay in application
+
+ align:start position:0%
+the Su protocol okay in application
+ 
+
+ align:start position:0%
+the Su protocol okay in application
+because as long as the D is small of
+
+ align:start position:0%
+because as long as the D is small of
+ 
+
+ align:start position:0%
+because as long as the D is small of
+course in applications often it turns
+
+ align:start position:0%
+course in applications often it turns
+ 
+
+ align:start position:0%
+course in applications often it turns
+out that the when we use the sub check
+
+ align:start position:0%
+out that the when we use the sub check
+ 
+
+ align:start position:0%
+out that the when we use the sub check
+it turns out that the D is often equal
+
+ align:start position:0%
+it turns out that the D is often equal
+ 
+
+ align:start position:0%
+it turns out that the D is often equal
+to the size of
+
+ align:start position:0%
+to the size of
+ 
+
+ align:start position:0%
+to the size of
+H okay because we kind of do the slow
+
+ align:start position:0%
+H okay because we kind of do the slow
+ 
+
+ align:start position:0%
+H okay because we kind of do the slow
+degree extension which makes the field
+
+ align:start position:0%
+degree extension which makes the field
+ 
+
+ align:start position:0%
+degree extension which makes the field
+as large as
+
+ align:start position:0%
+as large as
+ 
+
+ align:start position:0%
+as large as
+H and then if a if if we take H which
+
+ align:start position:0%
+H and then if a if if we take H which
+ 
+
+ align:start position:0%
+H and then if a if if we take H which
+becomes the degree to be F this is
+
+ align:start position:0%
+becomes the degree to be F this is
+ 
+
+ align:start position:0%
+becomes the degree to be F this is
+Meaningful
+
+ align:start position:0%
+Meaningful
+ 
+
+ align:start position:0%
+Meaningful
+meaningless so for
+
+ align:start position:0%
+meaningless so for
+ 
+
+ align:start position:0%
+meaningless so for
+application often indeed H is small but
+
+ align:start position:0%
+application often indeed H is small but
+ 
+
+ align:start position:0%
+application often indeed H is small but
+for the sum of prot it's own you can
+
+ align:start position:0%
+for the sum of prot it's own you can
+ 
+
+ align:start position:0%
+for the sum of prot it's own you can
+make you can take eight to be the entire
+
+ align:start position:0%
+make you can take eight to be the entire
+ 
+
+ align:start position:0%
+make you can take eight to be the entire
+field yes is it that find F like it's
+
+ align:start position:0%
+field yes is it that find F like it's
+ 
+
+ align:start position:0%
+field yes is it that find F like it's
+easy to put another yeah okay good good
+
+ align:start position:0%
+easy to put another yeah okay good good
+ 
+
+ align:start position:0%
+easy to put another yeah okay good good
+good yes exactly so let me yeah so it
+
+ align:start position:0%
+good yes exactly so let me yeah so it
+ 
+
+ align:start position:0%
+good yes exactly so let me yeah so it
+there's kind of uh you can take so this
+
+ align:start position:0%
+there's kind of uh you can take so this
+ 
+
+ align:start position:0%
+there's kind of uh you can take so this
+is a fact from mathematics you can take
+
+ align:start position:0%
+is a fact from mathematics you can take
+ 
+
+ align:start position:0%
+is a fact from mathematics you can take
+any finite field and embed it into a
+
+ align:start position:0%
+any finite field and embed it into a
+ 
+
+ align:start position:0%
+any finite field and embed it into a
+bigger finite field and how big is the
+
+ align:start position:0%
+bigger finite field and how big is the
+ 
+
+ align:start position:0%
+bigger finite field and how big is the
+bigger finite field kind of as big as
+
+ align:start position:0%
+bigger finite field kind of as big as
+ 
+
+ align:start position:0%
+bigger finite field kind of as big as
+you want so you can take any Loosely
+
+ align:start position:0%
+you want so you can take any Loosely
+ 
+
+ align:start position:0%
+you want so you can take any Loosely
+speaking you can take any F and embed it
+
+ align:start position:0%
+speaking you can take any F and embed it
+ 
+
+ align:start position:0%
+speaking you can take any F and embed it
+into kind of a field F to the
+
+ align:start position:0%
+into kind of a field F to the
+ 
+
+ align:start position:0%
+into kind of a field F to the
+N uh so when you can take n as big as
+
+ align:start position:0%
+N uh so when you can take n as big as
+ 
+
+ align:start position:0%
+N uh so when you can take n as big as
+you want so you can kind of that's
+
+ align:start position:0%
+you want so you can kind of that's
+ 
+
+ align:start position:0%
+you want so you can kind of that's
+what's called an extension
+
+ align:start position:0%
+what's called an extension
+ 
+
+ align:start position:0%
+what's called an extension
+field so you can kind of extend it to as
+
+ align:start position:0%
+field so you can kind of extend it to as
+ 
+
+ align:start position:0%
+field so you can kind of extend it to as
+large size as you want while still
+
+ align:start position:0%
+large size as you want while still
+ 
+
+ align:start position:0%
+large size as you want while still
+keeping f as a sub field so operations
+
+ align:start position:0%
+keeping f as a sub field so operations
+ 
+
+ align:start position:0%
+keeping f as a sub field so operations
+in F kind of behave exactly as they did
+
+ align:start position:0%
+in F kind of behave exactly as they did
+ 
+
+ align:start position:0%
+in F kind of behave exactly as they did
+before so without ruing the sum or
+
+ align:start position:0%
+before so without ruing the sum or
+ 
+
+ align:start position:0%
+before so without ruing the sum or
+anything like
+
+ align:start position:0%
+anything like
+ 
+
+ align:start position:0%
+anything like
+that this Anis right is it really the
+
+ align:start position:0%
+that this Anis right is it really the
+ 
+
+ align:start position:0%
+that this Anis right is it really the
+case that there is actually a chea
+
+ align:start position:0%
+case that there is actually a chea
+ 
+
+ align:start position:0%
+case that there is actually a chea
+strategy that succeeds with yes this
+
+ align:start position:0%
+strategy that succeeds with yes this
+ 
+
+ align:start position:0%
+strategy that succeeds with yes this
+yeah this good this analysis is really
+
+ align:start position:0%
+yeah this good this analysis is really
+ 
+
+ align:start position:0%
+yeah this good this analysis is really
+tight so I mean if if I'm malicious you
+
+ align:start position:0%
+tight so I mean if if I'm malicious you
+ 
+
+ align:start position:0%
+tight so I mean if if I'm malicious you
+know I can always hope for the best if
+
+ align:start position:0%
+know I can always hope for the best if
+ 
+
+ align:start position:0%
+know I can always hope for the best if
+it happens to be I'm malicious I give
+
+ align:start position:0%
+it happens to be I'm malicious I give
+ 
+
+ align:start position:0%
+it happens to be I'm malicious I give
+you the wrong polinomial look you may
+
+ align:start position:0%
+you the wrong polinomial look you may
+ 
+
+ align:start position:0%
+you the wrong polinomial look you may
+find so I want to go from the wrong Pol
+
+ align:start position:0%
+find so I want to go from the wrong Pol
+ 
+
+ align:start position:0%
+find so I want to go from the wrong Pol
+to the true polinomial that's what to
+
+ align:start position:0%
+to the true polinomial that's what to
+ 
+
+ align:start position:0%
+to the true polinomial that's what to
+cheat right that's what I want to do now
+
+ align:start position:0%
+cheat right that's what I want to do now
+ 
+
+ align:start position:0%
+cheat right that's what I want to do now
+the the my wrong poal and the true
+
+ align:start position:0%
+the the my wrong poal and the true
+ 
+
+ align:start position:0%
+the the my wrong poal and the true
+polinomial they agree the points any two
+
+ align:start position:0%
+polinomial they agree the points any two
+ 
+
+ align:start position:0%
+polinomial they agree the points any two
+pomal can agree on the points so as long
+
+ align:start position:0%
+pomal can agree on the points so as long
+ 
+
+ align:start position:0%
+pomal can agree on the points so as long
+as the verifier I'm lucky enough that
+
+ align:start position:0%
+as the verifier I'm lucky enough that
+ 
+
+ align:start position:0%
+as the verifier I'm lucky enough that
+this T is one of the deep points I mean
+
+ align:start position:0%
+this T is one of the deep points I mean
+ 
+
+ align:start position:0%
+this T is one of the deep points I mean
+look I got a good pomal I'll continue
+
+ align:start position:0%
+look I got a good pomal I'll continue
+ 
+
+ align:start position:0%
+look I got a good pomal I'll continue
+with a good pomal till the end of now
+
+ align:start position:0%
+with a good pomal till the end of now
+ 
+
+ align:start position:0%
+with a good pomal till the end of now
+I'm I'm in kind of a h La La Land you
+
+ align:start position:0%
+I'm I'm in kind of a h La La Land you
+ 
+
+ align:start position:0%
+I'm I'm in kind of a h La La Land you
+know I'm happy uh the problem is the
+
+ align:start position:0%
+know I'm happy uh the problem is the
+ 
+
+ align:start position:0%
+know I'm happy uh the problem is the
+chance each one the chance that you'll
+
+ align:start position:0%
+chance each one the chance that you'll
+ 
+
+ align:start position:0%
+chance each one the chance that you'll
+give me a t that's one of the D points
+
+ align:start position:0%
+give me a t that's one of the D points
+ 
+
+ align:start position:0%
+give me a t that's one of the D points
+is only D over F and a union bound over
+
+ align:start position:0%
+is only D over F and a union bound over
+ 
+
+ align:start position:0%
+is only D over F and a union bound over
+everything it's n times D over F and if
+
+ align:start position:0%
+everything it's n times D over F and if
+ 
+
+ align:start position:0%
+everything it's n times D over F and if
+f is much much bigger than n times D
+
+ align:start position:0%
+f is much much bigger than n times D
+ 
+
+ align:start position:0%
+f is much much bigger than n times D
+then you know uh the chances that the
+
+ align:start position:0%
+then you know uh the chances that the
+ 
+
+ align:start position:0%
+then you know uh the chances that the
+Prov will Su will be in this L land is
+
+ align:start position:0%
+Prov will Su will be in this L land is
+ 
+
+ align:start position:0%
+Prov will Su will be in this L land is
+very small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any any questions further questions
+
+ align:start position:0%
+okay any any questions further questions
+ 
+
+ align:start position:0%
+okay any any questions further questions
+about the subject
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protocol okay so let's take maybe kind
+
+ align:start position:0%
+protocol okay so let's take maybe kind
+ 
+
+ align:start position:0%
+protocol okay so let's take maybe kind
+of a five minute break to stretch and so
+
+ align:start position:0%
+of a five minute break to stretch and so
+ 
+
+ align:start position:0%
+of a five minute break to stretch and so
+on and then we'll show application we'll
+
+ align:start position:0%
+on and then we'll show application we'll
+ 
+
+ align:start position:0%
+on and then we'll show application we'll
+start showing applications for this
\ No newline at end of file
diff --git a/jJvVmdkiD3Y.txt b/jJvVmdkiD3Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1b1d87ac73548ef96abcd1cca514f1840b8815b9
--- /dev/null
+++ b/jJvVmdkiD3Y.txt
@@ -0,0 +1,11467 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so I should probably
+
+ align:start position:0%
+ocw.mit.edu okay so I should probably
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so I should probably
+get started um so I just wanted to
+
+ align:start position:0%
+get started um so I just wanted to
+ 
+
+ align:start position:0%
+get started um so I just wanted to
+mentioned this Friday the libraries are
+
+ align:start position:0%
+mentioned this Friday the libraries are
+ 
+
+ align:start position:0%
+mentioned this Friday the libraries are
+having furry Friday so you know they
+
+ align:start position:0%
+having furry Friday so you know they
+ 
+
+ align:start position:0%
+having furry Friday so you know they
+have therapy dogs come and if you like
+
+ align:start position:0%
+have therapy dogs come and if you like
+ 
+
+ align:start position:0%
+have therapy dogs come and if you like
+dogs it's kind of fun to go get cuddled
+
+ align:start position:0%
+dogs it's kind of fun to go get cuddled
+ 
+
+ align:start position:0%
+dogs it's kind of fun to go get cuddled
+by the dog the other thing I wanted to
+
+ align:start position:0%
+by the dog the other thing I wanted to
+ 
+
+ align:start position:0%
+by the dog the other thing I wanted to
+mention um you know last term there was
+
+ align:start position:0%
+mention um you know last term there was
+ 
+
+ align:start position:0%
+mention um you know last term there was
+a student taking 3032 who was interested
+
+ align:start position:0%
+a student taking 3032 who was interested
+ 
+
+ align:start position:0%
+a student taking 3032 who was interested
+in art and I kept trying to find art
+
+ align:start position:0%
+in art and I kept trying to find art
+ 
+
+ align:start position:0%
+in art and I kept trying to find art
+pictures for him and he's not here but I
+
+ align:start position:0%
+pictures for him and he's not here but I
+ 
+
+ align:start position:0%
+pictures for him and he's not here but I
+thought everybody else kind of liked the
+
+ align:start position:0%
+thought everybody else kind of liked the
+ 
+
+ align:start position:0%
+thought everybody else kind of liked the
+art too so I belong to the Peabody Essex
+
+ align:start position:0%
+art too so I belong to the Peabody Essex
+ 
+
+ align:start position:0%
+art too so I belong to the Peabody Essex
+Museum in Salem Mass and they have an
+
+ align:start position:0%
+Museum in Salem Mass and they have an
+ 
+
+ align:start position:0%
+Museum in Salem Mass and they have an
+exhibit right now on wood and on sort of
+
+ align:start position:0%
+exhibit right now on wood and on sort of
+ 
+
+ align:start position:0%
+exhibit right now on wood and on sort of
+using wood is a sculptural material and
+
+ align:start position:0%
+using wood is a sculptural material and
+ 
+
+ align:start position:0%
+using wood is a sculptural material and
+this is kind of one of their posters to
+
+ align:start position:0%
+this is kind of one of their posters to
+ 
+
+ align:start position:0%
+this is kind of one of their posters to
+advertise it uh so this thing was carved
+
+ align:start position:0%
+advertise it uh so this thing was carved
+ 
+
+ align:start position:0%
+advertise it uh so this thing was carved
+out of a single piece of wood I think um
+
+ align:start position:0%
+out of a single piece of wood I think um
+ 
+
+ align:start position:0%
+out of a single piece of wood I think um
+and they've got lots of other sort of
+
+ align:start position:0%
+and they've got lots of other sort of
+ 
+
+ align:start position:0%
+and they've got lots of other sort of
+sculptural wood so I thought you might
+
+ align:start position:0%
+sculptural wood so I thought you might
+ 
+
+ align:start position:0%
+sculptural wood so I thought you might
+like to see that um if you wanted to go
+
+ align:start position:0%
+like to see that um if you wanted to go
+ 
+
+ align:start position:0%
+like to see that um if you wanted to go
+to Salem there's a couple of options if
+
+ align:start position:0%
+to Salem there's a couple of options if
+ 
+
+ align:start position:0%
+to Salem there's a couple of options if
+you don't have a car you can take the
+
+ align:start position:0%
+you don't have a car you can take the
+ 
+
+ align:start position:0%
+you don't have a car you can take the
+commuter rail to Salem you can also take
+
+ align:start position:0%
+commuter rail to Salem you can also take
+ 
+
+ align:start position:0%
+commuter rail to Salem you can also take
+the ferry and if you take the ferry to
+
+ align:start position:0%
+the ferry and if you take the ferry to
+ 
+
+ align:start position:0%
+the ferry and if you take the ferry to
+Salem you can it's like a f minute walk
+
+ align:start position:0%
+Salem you can it's like a f minute walk
+ 
+
+ align:start position:0%
+Salem you can it's like a f minute walk
+to where the ferry lets you off to get
+
+ align:start position:0%
+to where the ferry lets you off to get
+ 
+
+ align:start position:0%
+to where the ferry lets you off to get
+to the PE body essics and it's a kind of
+
+ align:start position:0%
+to the PE body essics and it's a kind of
+ 
+
+ align:start position:0%
+to the PE body essics and it's a kind of
+neat Museum it's not too big it's kind
+
+ align:start position:0%
+neat Museum it's not too big it's kind
+ 
+
+ align:start position:0%
+neat Museum it's not too big it's kind
+of small um but it's it's a beautiful
+
+ align:start position:0%
+of small um but it's it's a beautiful
+ 
+
+ align:start position:0%
+of small um but it's it's a beautiful
+building and they have neat stuff there
+
+ align:start position:0%
+building and they have neat stuff there
+ 
+
+ align:start position:0%
+building and they have neat stuff there
+so you could go to the peab essics
+
+ align:start position:0%
+so you could go to the peab essics
+ 
+
+ align:start position:0%
+so you could go to the peab essics
+museum H very nice yeah you've been
+
+ align:start position:0%
+museum H very nice yeah you've been
+ 
+
+ align:start position:0%
+museum H very nice yeah you've been
+there yeah it's really nice yeah okay so
+
+ align:start position:0%
+there yeah it's really nice yeah okay so
+ 
+
+ align:start position:0%
+there yeah it's really nice yeah okay so
+I was going to talk about honeycomb like
+
+ align:start position:0%
+I was going to talk about honeycomb like
+ 
+
+ align:start position:0%
+I was going to talk about honeycomb like
+materials in nature today and I'm going
+
+ align:start position:0%
+materials in nature today and I'm going
+ 
+
+ align:start position:0%
+materials in nature today and I'm going
+to talk about wood today and I I might
+
+ align:start position:0%
+to talk about wood today and I I might
+ 
+
+ align:start position:0%
+to talk about wood today and I I might
+finish this today I might not and then I
+
+ align:start position:0%
+finish this today I might not and then I
+ 
+
+ align:start position:0%
+finish this today I might not and then I
+was going to talk about cork for a
+
+ align:start position:0%
+was going to talk about cork for a
+ 
+
+ align:start position:0%
+was going to talk about cork for a
+little bit um on Wednesday and then
+
+ align:start position:0%
+little bit um on Wednesday and then
+ 
+
+ align:start position:0%
+little bit um on Wednesday and then
+we'll start talking about Foams after
+
+ align:start position:0%
+we'll start talking about Foams after
+ 
+
+ align:start position:0%
+we'll start talking about Foams after
+that um so I have a couple of sort of
+
+ align:start position:0%
+that um so I have a couple of sort of
+ 
+
+ align:start position:0%
+that um so I have a couple of sort of
+cute little language historically things
+
+ align:start position:0%
+cute little language historically things
+ 
+
+ align:start position:0%
+cute little language historically things
+and you know how I like that stuff too
+
+ align:start position:0%
+and you know how I like that stuff too
+ 
+
+ align:start position:0%
+and you know how I like that stuff too
+so I have two things about um about
+
+ align:start position:0%
+so I have two things about um about
+ 
+
+ align:start position:0%
+so I have two things about um about
+words that are related to Wood so the
+
+ align:start position:0%
+words that are related to Wood so the
+ 
+
+ align:start position:0%
+words that are related to Wood so the
+word materials do you know where the
+
+ align:start position:0%
+word materials do you know where the
+ 
+
+ align:start position:0%
+word materials do you know where the
+word materials comes from it's uh it
+
+ align:start position:0%
+word materials comes from it's uh it
+ 
+
+ align:start position:0%
+word materials comes from it's uh it
+comes from the Latin so there's a Latin
+
+ align:start position:0%
+comes from the Latin so there's a Latin
+ 
+
+ align:start position:0%
+comes from the Latin so there's a Latin
+materias Materia and materias Materia
+
+ align:start position:0%
+materias Materia and materias Materia
+ 
+
+ align:start position:0%
+materias Materia and materias Materia
+means wood or the trunk of a tree so
+
+ align:start position:0%
+means wood or the trunk of a tree so
+ 
+
+ align:start position:0%
+means wood or the trunk of a tree so
+when you you know if you think of
+
+ align:start position:0%
+when you you know if you think of
+ 
+
+ align:start position:0%
+when you you know if you think of
+studying materials you know in olden
+
+ align:start position:0%
+studying materials you know in olden
+ 
+
+ align:start position:0%
+studying materials you know in olden
+times that was like studying wood and
+
+ align:start position:0%
+times that was like studying wood and
+ 
+
+ align:start position:0%
+times that was like studying wood and
+another cute thing that I found was that
+
+ align:start position:0%
+another cute thing that I found was that
+ 
+
+ align:start position:0%
+another cute thing that I found was that
+in Old Irish the names of the first few
+
+ align:start position:0%
+in Old Irish the names of the first few
+ 
+
+ align:start position:0%
+in Old Irish the names of the first few
+letters of the alphabet are named after
+
+ align:start position:0%
+letters of the alphabet are named after
+ 
+
+ align:start position:0%
+letters of the alphabet are named after
+trees so the letter A that's called alum
+
+ align:start position:0%
+trees so the letter A that's called alum
+ 
+
+ align:start position:0%
+trees so the letter A that's called alum
+in Old Irish and Alum is the word for
+
+ align:start position:0%
+in Old Irish and Alum is the word for
+ 
+
+ align:start position:0%
+in Old Irish and Alum is the word for
+Elm and B is I don't know if I'm saying
+
+ align:start position:0%
+Elm and B is I don't know if I'm saying
+ 
+
+ align:start position:0%
+Elm and B is I don't know if I'm saying
+these right it's called Beth and that's
+
+ align:start position:0%
+these right it's called Beth and that's
+ 
+
+ align:start position:0%
+these right it's called Beth and that's
+the word for Birch and C is call that's
+
+ align:start position:0%
+the word for Birch and C is call that's
+ 
+
+ align:start position:0%
+the word for Birch and C is call that's
+the word for Hazel and D is dare and
+
+ align:start position:0%
+the word for Hazel and D is dare and
+ 
+
+ align:start position:0%
+the word for Hazel and D is dare and
+that's the word for Oak and so they sort
+
+ align:start position:0%
+that's the word for Oak and so they sort
+ 
+
+ align:start position:0%
+that's the word for Oak and so they sort
+of named the letters of the alphabet
+
+ align:start position:0%
+of named the letters of the alphabet
+ 
+
+ align:start position:0%
+of named the letters of the alphabet
+after after different kinds of trees
+
+ align:start position:0%
+after after different kinds of trees
+ 
+
+ align:start position:0%
+after after different kinds of trees
+different kinds of woods so I just
+
+ align:start position:0%
+different kinds of woods so I just
+ 
+
+ align:start position:0%
+different kinds of woods so I just
+thought those were kind of interesting
+
+ align:start position:0%
+thought those were kind of interesting
+ 
+
+ align:start position:0%
+thought those were kind of interesting
+historical
+
+ align:start position:0%
+historical
+ 
+
+ align:start position:0%
+historical
+things okay so I wanted to start by
+
+ align:start position:0%
+things okay so I wanted to start by
+ 
+
+ align:start position:0%
+things okay so I wanted to start by
+talking about wood structure and then
+
+ align:start position:0%
+talking about wood structure and then
+ 
+
+ align:start position:0%
+talking about wood structure and then
+we're going to look at how wood deforms
+
+ align:start position:0%
+we're going to look at how wood deforms
+ 
+
+ align:start position:0%
+we're going to look at how wood deforms
+and fails and talk about um the data
+
+ align:start position:0%
+and fails and talk about um the data
+ 
+
+ align:start position:0%
+and fails and talk about um the data
+that people have measured for the wood
+
+ align:start position:0%
+that people have measured for the wood
+ 
+
+ align:start position:0%
+that people have measured for the wood
+properties things like stiffness and
+
+ align:start position:0%
+properties things like stiffness and
+ 
+
+ align:start position:0%
+properties things like stiffness and
+strength and then we'll talk a little
+
+ align:start position:0%
+strength and then we'll talk a little
+ 
+
+ align:start position:0%
+strength and then we'll talk a little
+bit about how the honeycomb models can
+
+ align:start position:0%
+bit about how the honeycomb models can
+ 
+
+ align:start position:0%
+bit about how the honeycomb models can
+be applied to understanding the
+
+ align:start position:0%
+be applied to understanding the
+ 
+
+ align:start position:0%
+be applied to understanding the
+mechanical properties of woods so this
+
+ align:start position:0%
+mechanical properties of woods so this
+ 
+
+ align:start position:0%
+mechanical properties of woods so this
+is kind of a generic trunk of the tree
+
+ align:start position:0%
+is kind of a generic trunk of the tree
+ 
+
+ align:start position:0%
+is kind of a generic trunk of the tree
+here and we're defining three axes the
+
+ align:start position:0%
+here and we're defining three axes the
+ 
+
+ align:start position:0%
+here and we're defining three axes the
+radial axis comes radially out of the
+
+ align:start position:0%
+radial axis comes radially out of the
+ 
+
+ align:start position:0%
+radial axis comes radially out of the
+tree there's the tangential axis so
+
+ align:start position:0%
+tree there's the tangential axis so
+ 
+
+ align:start position:0%
+tree there's the tangential axis so
+that's the X1 and the X2 axes and then
+
+ align:start position:0%
+that's the X1 and the X2 axes and then
+ 
+
+ align:start position:0%
+that's the X1 and the X2 axes and then
+there the longitudinal or the axial axis
+
+ align:start position:0%
+there the longitudinal or the axial axis
+ 
+
+ align:start position:0%
+there the longitudinal or the axial axis
+X3 so if you think of the wood as being
+
+ align:start position:0%
+X3 so if you think of the wood as being
+ 
+
+ align:start position:0%
+X3 so if you think of the wood as being
+in a very very simple way just like the
+
+ align:start position:0%
+in a very very simple way just like the
+ 
+
+ align:start position:0%
+in a very very simple way just like the
+honeycomb uh the radial would be this
+
+ align:start position:0%
+honeycomb uh the radial would be this
+ 
+
+ align:start position:0%
+honeycomb uh the radial would be this
+way on the tangential would be that way
+
+ align:start position:0%
+way on the tangential would be that way
+ 
+
+ align:start position:0%
+way on the tangential would be that way
+on and the axial would be that way on
+
+ align:start position:0%
+on and the axial would be that way on
+ 
+
+ align:start position:0%
+on and the axial would be that way on
+okay so it's it's like that and if you
+
+ align:start position:0%
+okay so it's it's like that and if you
+ 
+
+ align:start position:0%
+okay so it's it's like that and if you
+neglect the the growth rings you can say
+
+ align:start position:0%
+neglect the the growth rings you can say
+ 
+
+ align:start position:0%
+neglect the the growth rings you can say
+that the wood's orthotropic and that's
+
+ align:start position:0%
+that the wood's orthotropic and that's
+ 
+
+ align:start position:0%
+that the wood's orthotropic and that's
+typically what people do they neglect
+
+ align:start position:0%
+typically what people do they neglect
+ 
+
+ align:start position:0%
+typically what people do they neglect
+the growth rings and they say that it's
+
+ align:start position:0%
+the growth rings and they say that it's
+ 
+
+ align:start position:0%
+the growth rings and they say that it's
+orthotropic and the density of the woods
+
+ align:start position:0%
+orthotropic and the density of the woods
+ 
+
+ align:start position:0%
+orthotropic and the density of the woods
+the relative density ranges from about
+
+ align:start position:0%
+the relative density ranges from about
+ 
+
+ align:start position:0%
+the relative density ranges from about
+5% for balsa wood to about 80% % for
+
+ align:start position:0%
+5% for balsa wood to about 80% % for
+ 
+
+ align:start position:0%
+5% for balsa wood to about 80% % for
+lignum vti so I brought in some pieces
+
+ align:start position:0%
+lignum vti so I brought in some pieces
+ 
+
+ align:start position:0%
+lignum vti so I brought in some pieces
+of wood so this is balsa wood you're
+
+ align:start position:0%
+of wood so this is balsa wood you're
+ 
+
+ align:start position:0%
+of wood so this is balsa wood you're
+probably familiar you know making
+
+ align:start position:0%
+probably familiar you know making
+ 
+
+ align:start position:0%
+probably familiar you know making
+different kinds of models with Balsa so
+
+ align:start position:0%
+different kinds of models with Balsa so
+ 
+
+ align:start position:0%
+different kinds of models with Balsa so
+Balsa is very light grows in Ecuador and
+
+ align:start position:0%
+Balsa is very light grows in Ecuador and
+ 
+
+ align:start position:0%
+Balsa is very light grows in Ecuador and
+um it's the lightest wood and this is
+
+ align:start position:0%
+um it's the lightest wood and this is
+ 
+
+ align:start position:0%
+um it's the lightest wood and this is
+lignum Vita you're probably not so
+
+ align:start position:0%
+lignum Vita you're probably not so
+ 
+
+ align:start position:0%
+lignum Vita you're probably not so
+familiar with that this actually grows
+
+ align:start position:0%
+familiar with that this actually grows
+ 
+
+ align:start position:0%
+familiar with that this actually grows
+in Florida and it's the densest wood it
+
+ align:start position:0%
+in Florida and it's the densest wood it
+ 
+
+ align:start position:0%
+in Florida and it's the densest wood it
+has a relative density of 08 and it's so
+
+ align:start position:0%
+has a relative density of 08 and it's so
+ 
+
+ align:start position:0%
+has a relative density of 08 and it's so
+dense that if you put it in water it
+
+ align:start position:0%
+dense that if you put it in water it
+ 
+
+ align:start position:0%
+dense that if you put it in water it
+sinks so it's it's a very dense wood
+
+ align:start position:0%
+sinks so it's it's a very dense wood
+ 
+
+ align:start position:0%
+sinks so it's it's a very dense wood
+um and the way the wood cells grow is
+
+ align:start position:0%
+um and the way the wood cells grow is
+ 
+
+ align:start position:0%
+um and the way the wood cells grow is
+that if if you if you look at the sort
+
+ align:start position:0%
+that if if you if you look at the sort
+ 
+
+ align:start position:0%
+that if if you if you look at the sort
+of structure here of the tree there's
+
+ align:start position:0%
+of structure here of the tree there's
+ 
+
+ align:start position:0%
+of structure here of the tree there's
+the bark on the outside here and then
+
+ align:start position:0%
+the bark on the outside here and then
+ 
+
+ align:start position:0%
+the bark on the outside here and then
+there's the kind of wood cells inside
+
+ align:start position:0%
+there's the kind of wood cells inside
+ 
+
+ align:start position:0%
+there's the kind of wood cells inside
+the bark and there's a layer of cells in
+
+ align:start position:0%
+the bark and there's a layer of cells in
+ 
+
+ align:start position:0%
+the bark and there's a layer of cells in
+between the bark and the wood called the
+
+ align:start position:0%
+between the bark and the wood called the
+ 
+
+ align:start position:0%
+between the bark and the wood called the
+cambia layer and that's really the layer
+
+ align:start position:0%
+cambia layer and that's really the layer
+ 
+
+ align:start position:0%
+cambia layer and that's really the layer
+of cells that are alive and are dividing
+
+ align:start position:0%
+of cells that are alive and are dividing
+ 
+
+ align:start position:0%
+of cells that are alive and are dividing
+so if you think of the the wood cells
+
+ align:start position:0%
+so if you think of the the wood cells
+ 
+
+ align:start position:0%
+so if you think of the the wood cells
+there's uh they're living when they're
+
+ align:start position:0%
+there's uh they're living when they're
+ 
+
+ align:start position:0%
+there's uh they're living when they're
+in that little cambial layer there and
+
+ align:start position:0%
+in that little cambial layer there and
+ 
+
+ align:start position:0%
+in that little cambial layer there and
+they're dividing and that cambia layer
+
+ align:start position:0%
+they're dividing and that cambia layer
+ 
+
+ align:start position:0%
+they're dividing and that cambia layer
+the cells have a plasma membrane and a
+
+ align:start position:0%
+the cells have a plasma membrane and a
+ 
+
+ align:start position:0%
+the cells have a plasma membrane and a
+prot plast and then they they sort of
+
+ align:start position:0%
+prot plast and then they they sort of
+ 
+
+ align:start position:0%
+prot plast and then they they sort of
+exude the plant cell wall so a little
+
+ align:start position:0%
+exude the plant cell wall so a little
+ 
+
+ align:start position:0%
+exude the plant cell wall so a little
+like bone cells like if you think of
+
+ align:start position:0%
+like bone cells like if you think of
+ 
+
+ align:start position:0%
+like bone cells like if you think of
+bone in your body there's osteoblasts
+
+ align:start position:0%
+bone in your body there's osteoblasts
+ 
+
+ align:start position:0%
+bone in your body there's osteoblasts
+and osteoclasts different kinds of bone
+
+ align:start position:0%
+and osteoclasts different kinds of bone
+ 
+
+ align:start position:0%
+and osteoclasts different kinds of bone
+cells but the bone cells uh secrete the
+
+ align:start position:0%
+cells but the bone cells uh secrete the
+ 
+
+ align:start position:0%
+cells but the bone cells uh secrete the
+sort of collagen and the calcium
+
+ align:start position:0%
+sort of collagen and the calcium
+ 
+
+ align:start position:0%
+sort of collagen and the calcium
+phosphate that are the sort of hard
+
+ align:start position:0%
+phosphate that are the sort of hard
+ 
+
+ align:start position:0%
+phosphate that are the sort of hard
+mineral part of the bone that you think
+
+ align:start position:0%
+mineral part of the bone that you think
+ 
+
+ align:start position:0%
+mineral part of the bone that you think
+about the bone and that's not a living
+
+ align:start position:0%
+about the bone and that's not a living
+ 
+
+ align:start position:0%
+about the bone and that's not a living
+thing the cells are the living thing
+
+ align:start position:0%
+thing the cells are the living thing
+ 
+
+ align:start position:0%
+thing the cells are the living thing
+that's like an extracellular Matrix and
+
+ align:start position:0%
+that's like an extracellular Matrix and
+ 
+
+ align:start position:0%
+that's like an extracellular Matrix and
+the trees it's a little bit the same so
+
+ align:start position:0%
+the trees it's a little bit the same so
+ 
+
+ align:start position:0%
+the trees it's a little bit the same so
+there's the the living cells that are
+
+ align:start position:0%
+there's the the living cells that are
+ 
+
+ align:start position:0%
+there's the the living cells that are
+just under the bark and they have this
+
+ align:start position:0%
+just under the bark and they have this
+ 
+
+ align:start position:0%
+just under the bark and they have this
+plasma membrane and the protoplasm and
+
+ align:start position:0%
+plasma membrane and the protoplasm and
+ 
+
+ align:start position:0%
+plasma membrane and the protoplasm and
+over a few weeks they excrete the plant
+
+ align:start position:0%
+over a few weeks they excrete the plant
+ 
+
+ align:start position:0%
+over a few weeks they excrete the plant
+cell wall and then they die so the
+
+ align:start position:0%
+cell wall and then they die so the
+ 
+
+ align:start position:0%
+cell wall and then they die so the
+living cells die and you're left with
+
+ align:start position:0%
+living cells die and you're left with
+ 
+
+ align:start position:0%
+living cells die and you're left with
+the plant cell walls and then as the
+
+ align:start position:0%
+the plant cell walls and then as the
+ 
+
+ align:start position:0%
+the plant cell walls and then as the
+plant you know as the tree grows uh
+
+ align:start position:0%
+plant you know as the tree grows uh
+ 
+
+ align:start position:0%
+plant you know as the tree grows uh
+these you're always having a layer of
+
+ align:start position:0%
+these you're always having a layer of
+ 
+
+ align:start position:0%
+these you're always having a layer of
+these cambial cells and it forms bark on
+
+ align:start position:0%
+these cambial cells and it forms bark on
+ 
+
+ align:start position:0%
+these cambial cells and it forms bark on
+the outside and wood on the inside so
+
+ align:start position:0%
+the outside and wood on the inside so
+ 
+
+ align:start position:0%
+the outside and wood on the inside so
+there sort of a layer of cells that are
+
+ align:start position:0%
+there sort of a layer of cells that are
+ 
+
+ align:start position:0%
+there sort of a layer of cells that are
+differentiated such that on the outer
+
+ align:start position:0%
+differentiated such that on the outer
+ 
+
+ align:start position:0%
+differentiated such that on the outer
+layer they form the bark and on the
+
+ align:start position:0%
+layer they form the bark and on the
+ 
+
+ align:start position:0%
+layer they form the bark and on the
+inner layer they form the wood and as
+
+ align:start position:0%
+inner layer they form the wood and as
+ 
+
+ align:start position:0%
+inner layer they form the wood and as
+the wood you know as the tree grows that
+
+ align:start position:0%
+the wood you know as the tree grows that
+ 
+
+ align:start position:0%
+the wood you know as the tree grows that
+cambal layer is kind of expanding out
+
+ align:start position:0%
+cambal layer is kind of expanding out
+ 
+
+ align:start position:0%
+cambal layer is kind of expanding out
+radially so let me let me write some of
+
+ align:start position:0%
+radially so let me let me write some of
+ 
+
+ align:start position:0%
+radially so let me let me write some of
+these things
+
+ align:start position:0%
+these things
+ 
+
+ align:start position:0%
+these things
+down uh let's see
+
+ align:start position:0%
+down uh let's see
+ 
+
+ align:start position:0%
+down uh let's see
+okay okay so let me just write down
+
+ align:start position:0%
+okay okay so let me just write down
+ 
+
+ align:start position:0%
+okay okay so let me just write down
+those two little word things just cuz I
+
+ align:start position:0%
+those two little word things just cuz I
+ 
+
+ align:start position:0%
+those two little word things just cuz I
+think they're
+
+ align:start position:0%
+think they're
+ 
+
+ align:start position:0%
+think they're
+cute so the word materials is from the
+
+ align:start position:0%
+cute so the word materials is from the
+ 
+
+ align:start position:0%
+cute so the word materials is from the
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Latin material
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Materia and that means wood or the trunk
+
+ align:start position:0%
+Materia and that means wood or the trunk
+ 
+
+ align:start position:0%
+Materia and that means wood or the trunk
+of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree and here's the little old Irish
+
+ align:start position:0%
+tree and here's the little old Irish
+ 
+
+ align:start position:0%
+tree and here's the little old Irish
+thing it's not like I think you know I'm
+
+ align:start position:0%
+thing it's not like I think you know I'm
+ 
+
+ align:start position:0%
+thing it's not like I think you know I'm
+not going to put this on the test or
+
+ align:start position:0%
+not going to put this on the test or
+ 
+
+ align:start position:0%
+not going to put this on the test or
+something I just thought it was cute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so the letter A
+
+ align:start position:0%
+um so the letter A
+ 
+
+ align:start position:0%
+um so the letter A
+is alum which is
+
+ align:start position:0%
+is alum which is
+ 
+
+ align:start position:0%
+is alum which is
+Elm letter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B is be which is
+
+ align:start position:0%
+B is be which is
+ 
+
+ align:start position:0%
+B is be which is
+birch letter
+
+ align:start position:0%
+birch letter
+ 
+
+ align:start position:0%
+birch letter
+C was call was
+
+ align:start position:0%
+C was call was
+ 
+
+ align:start position:0%
+C was call was
+Hazel and D was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dare and that's Oak okay that's just
+
+ align:start position:0%
+dare and that's Oak okay that's just
+ 
+
+ align:start position:0%
+dare and that's Oak okay that's just
+just for general interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then the wood structure we can think
+
+ align:start position:0%
+so then the wood structure we can think
+ 
+
+ align:start position:0%
+so then the wood structure we can think
+of it as orthotropic if we ignore the um
+
+ align:start position:0%
+of it as orthotropic if we ignore the um
+ 
+
+ align:start position:0%
+of it as orthotropic if we ignore the um
+growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rings and if you have a a sort of large
+
+ align:start position:0%
+rings and if you have a a sort of large
+ 
+
+ align:start position:0%
+rings and if you have a a sort of large
+diameter tree and you take a piece of
+
+ align:start position:0%
+diameter tree and you take a piece of
+ 
+
+ align:start position:0%
+diameter tree and you take a piece of
+wood um you know not from the very
+
+ align:start position:0%
+wood um you know not from the very
+ 
+
+ align:start position:0%
+wood um you know not from the very
+center but from somewhere sort of near
+
+ align:start position:0%
+center but from somewhere sort of near
+ 
+
+ align:start position:0%
+center but from somewhere sort of near
+the outside then that's not a bad
+
+ align:start position:0%
+the outside then that's not a bad
+ 
+
+ align:start position:0%
+the outside then that's not a bad
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+and the relative density of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+woods ranges from about 005 for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Balsa to about 8 for lignum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VII any Latin Scholars here they I took
+
+ align:start position:0%
+VII any Latin Scholars here they I took
+ 
+
+ align:start position:0%
+VII any Latin Scholars here they I took
+one year of Latin in high school they
+
+ align:start position:0%
+one year of Latin in high school they
+ 
+
+ align:start position:0%
+one year of Latin in high school they
+took Latin no no Latin so I think this
+
+ align:start position:0%
+took Latin no no Latin so I think this
+ 
+
+ align:start position:0%
+took Latin no no Latin so I think this
+means lignum V I think is Tree of Life V
+
+ align:start position:0%
+means lignum V I think is Tree of Life V
+ 
+
+ align:start position:0%
+means lignum V I think is Tree of Life V
+is the sort of
+
+ align:start position:0%
+is the sort of
+ 
+
+ align:start position:0%
+is the sort of
+life and when it has this ending AE it
+
+ align:start position:0%
+life and when it has this ending AE it
+ 
+
+ align:start position:0%
+life and when it has this ending AE it
+means of life so I think that's the tree
+
+ align:start position:0%
+means of life so I think that's the tree
+ 
+
+ align:start position:0%
+means of life so I think that's the tree
+of life is lignum
+
+ align:start position:0%
+of life is lignum
+ 
+
+ align:start position:0%
+of life is lignum
+V so trees have a cambia layer beneath
+
+ align:start position:0%
+V so trees have a cambia layer beneath
+ 
+
+ align:start position:0%
+V so trees have a cambia layer beneath
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bark and the cell division occurs in
+
+ align:start position:0%
+bark and the cell division occurs in
+ 
+
+ align:start position:0%
+bark and the cell division occurs in
+that cambal layer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the new cells on the outer part turn
+
+ align:start position:0%
+so the new cells on the outer part turn
+ 
+
+ align:start position:0%
+so the new cells on the outer part turn
+into bark and the new cells on the inner
+
+ align:start position:0%
+into bark and the new cells on the inner
+ 
+
+ align:start position:0%
+into bark and the new cells on the inner
+part turn into wood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then we have the living plant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells that have the plasma
+
+ align:start position:0%
+cells that have the plasma
+ 
+
+ align:start position:0%
+cells that have the plasma
+membrane and the protoplast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and those cells then secrete the plant
+
+ align:start position:0%
+and those cells then secrete the plant
+ 
+
+ align:start position:0%
+and those cells then secrete the plant
+cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wall which sort of surrounds them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in trees the living cells lay down
+
+ align:start position:0%
+so in trees the living cells lay down
+ 
+
+ align:start position:0%
+so in trees the living cells lay down
+the plant cell wall over a period of a
+
+ align:start position:0%
+the plant cell wall over a period of a
+ 
+
+ align:start position:0%
+the plant cell wall over a period of a
+few weeks and then the living cells die
+
+ align:start position:0%
+few weeks and then the living cells die
+ 
+
+ align:start position:0%
+few weeks and then the living cells die
+oops back here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you always retain a layer of those
+
+ align:start position:0%
+and you always retain a layer of those
+ 
+
+ align:start position:0%
+and you always retain a layer of those
+cambial cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you may have heard if you have a tree
+
+ align:start position:0%
+so you may have heard if you have a tree
+ 
+
+ align:start position:0%
+so you may have heard if you have a tree
+and you you know you cut a ring around
+
+ align:start position:0%
+and you you know you cut a ring around
+ 
+
+ align:start position:0%
+and you you know you cut a ring around
+the tree and through the bark if you go
+
+ align:start position:0%
+the tree and through the bark if you go
+ 
+
+ align:start position:0%
+the tree and through the bark if you go
+into those cambial cells and you destroy
+
+ align:start position:0%
+into those cambial cells and you destroy
+ 
+
+ align:start position:0%
+into those cambial cells and you destroy
+them you kill the tree because you're
+
+ align:start position:0%
+them you kill the tree because you're
+ 
+
+ align:start position:0%
+them you kill the tree because you're
+killing that layer of living
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then we want to look at the the
+
+ align:start position:0%
+so then we want to look at the the
+ 
+
+ align:start position:0%
+so then we want to look at the the
+cellular structure of the woods as well
+
+ align:start position:0%
+cellular structure of the woods as well
+ 
+
+ align:start position:0%
+cellular structure of the woods as well
+and I've got a couple of slides here
+
+ align:start position:0%
+and I've got a couple of slides here
+ 
+
+ align:start position:0%
+and I've got a couple of slides here
+this one is of soft woods and soft Woods
+
+ align:start position:0%
+this one is of soft woods and soft Woods
+ 
+
+ align:start position:0%
+this one is of soft woods and soft Woods
+have two types of cells they have
+
+ align:start position:0%
+have two types of cells they have
+ 
+
+ align:start position:0%
+have two types of cells they have
+trachead which are the bulk of these
+
+ align:start position:0%
+trachead which are the bulk of these
+ 
+
+ align:start position:0%
+trachead which are the bulk of these
+cells here and the trachead provide
+
+ align:start position:0%
+cells here and the trachead provide
+ 
+
+ align:start position:0%
+cells here and the trachead provide
+structural support and the trachead have
+
+ align:start position:0%
+structural support and the trachead have
+ 
+
+ align:start position:0%
+structural support and the trachead have
+little holes along the length of them at
+
+ align:start position:0%
+little holes along the length of them at
+ 
+
+ align:start position:0%
+little holes along the length of them at
+their ends called pits and those pits
+
+ align:start position:0%
+their ends called pits and those pits
+ 
+
+ align:start position:0%
+their ends called pits and those pits
+allow fluid transport um up and down the
+
+ align:start position:0%
+allow fluid transport um up and down the
+ 
+
+ align:start position:0%
+allow fluid transport um up and down the
+tree and then the softwood also has
+
+ align:start position:0%
+tree and then the softwood also has
+ 
+
+ align:start position:0%
+tree and then the softwood also has
+these Ray cells here so those are
+
+ align:start position:0%
+these Ray cells here so those are
+ 
+
+ align:start position:0%
+these Ray cells here so those are
+examples of Ray cells so this is a
+
+ align:start position:0%
+examples of Ray cells so this is a
+ 
+
+ align:start position:0%
+examples of Ray cells so this is a
+transverse section this is a
+
+ align:start position:0%
+transverse section this is a
+ 
+
+ align:start position:0%
+transverse section this is a
+longitudinal section here and the rays
+
+ align:start position:0%
+longitudinal section here and the rays
+ 
+
+ align:start position:0%
+longitudinal section here and the rays
+are penous cells which store sugars so
+
+ align:start position:0%
+are penous cells which store sugars so
+ 
+
+ align:start position:0%
+are penous cells which store sugars so
+softwoods have trachs and rays and then
+
+ align:start position:0%
+softwoods have trachs and rays and then
+ 
+
+ align:start position:0%
+softwoods have trachs and rays and then
+Hardwoods here's an example of a
+
+ align:start position:0%
+Hardwoods here's an example of a
+ 
+
+ align:start position:0%
+Hardwoods here's an example of a
+hardwood Oak they have three types of
+
+ align:start position:0%
+hardwood Oak they have three types of
+ 
+
+ align:start position:0%
+hardwood Oak they have three types of
+cells there's cells called fibers so
+
+ align:start position:0%
+cells there's cells called fibers so
+ 
+
+ align:start position:0%
+cells there's cells called fibers so
+these guys all in here would be fibers
+
+ align:start position:0%
+these guys all in here would be fibers
+ 
+
+ align:start position:0%
+these guys all in here would be fibers
+they provide the structural support they
+
+ align:start position:0%
+they provide the structural support they
+ 
+
+ align:start position:0%
+they provide the structural support they
+have vessels these really large cells
+
+ align:start position:0%
+have vessels these really large cells
+ 
+
+ align:start position:0%
+have vessels these really large cells
+that provide fluid transport up and down
+
+ align:start position:0%
+that provide fluid transport up and down
+ 
+
+ align:start position:0%
+that provide fluid transport up and down
+the tree and they also have Rays so
+
+ align:start position:0%
+the tree and they also have Rays so
+ 
+
+ align:start position:0%
+the tree and they also have Rays so
+here's some rays here and again those
+
+ align:start position:0%
+here's some rays here and again those
+ 
+
+ align:start position:0%
+here's some rays here and again those
+rays are parous cells that store sugars
+
+ align:start position:0%
+rays are parous cells that store sugars
+ 
+
+ align:start position:0%
+rays are parous cells that store sugars
+in the tree so let me just write down
+
+ align:start position:0%
+in the tree so let me just write down
+ 
+
+ align:start position:0%
+in the tree so let me just write down
+what all these cells are so
+
+ align:start position:0%
+what all these cells are so
+ 
+
+ align:start position:0%
+what all these cells are so
+in so in soft Woods the most of the
+
+ align:start position:0%
+in so in soft Woods the most of the
+ 
+
+ align:start position:0%
+in so in soft Woods the most of the
+cells are these trads so they make up
+
+ align:start position:0%
+cells are these trads so they make up
+ 
+
+ align:start position:0%
+cells are these trads so they make up
+the bulk of the tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh something like 90% of the tree and
+
+ align:start position:0%
+uh something like 90% of the tree and
+ 
+
+ align:start position:0%
+uh something like 90% of the tree and
+they provide structural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+support they have holes in the cell wall
+
+ align:start position:0%
+support they have holes in the cell wall
+ 
+
+ align:start position:0%
+support they have holes in the cell wall
+for fluid transport and those are called
+
+ align:start position:0%
+for fluid transport and those are called
+ 
+
+ align:start position:0%
+for fluid transport and those are called
+pits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and to give you some idea what size they
+
+ align:start position:0%
+and to give you some idea what size they
+ 
+
+ align:start position:0%
+and to give you some idea what size they
+are they're a few millimeters long so
+
+ align:start position:0%
+are they're a few millimeters long so
+ 
+
+ align:start position:0%
+are they're a few millimeters long so
+something like 2 and 1/2 to 7 mm
+
+ align:start position:0%
+something like 2 and 1/2 to 7 mm
+ 
+
+ align:start position:0%
+something like 2 and 1/2 to 7 mm
+long and then there're tens of microns
+
+ align:start position:0%
+long and then there're tens of microns
+ 
+
+ align:start position:0%
+long and then there're tens of microns
+in the other two directions so there's
+
+ align:start position:0%
+in the other two directions so there's
+ 
+
+ align:start position:0%
+in the other two directions so there's
+something like 20 to 80 microns
+
+ align:start position:0%
+something like 20 to 80 microns
+ 
+
+ align:start position:0%
+something like 20 to 80 microns
+across and the cell wall thickness T is
+
+ align:start position:0%
+across and the cell wall thickness T is
+ 
+
+ align:start position:0%
+across and the cell wall thickness T is
+usually a few microns so something
+
+ align:start position:0%
+usually a few microns so something
+ 
+
+ align:start position:0%
+usually a few microns so something
+between about 2 and seven microns so
+
+ align:start position:0%
+between about 2 and seven microns so
+ 
+
+ align:start position:0%
+between about 2 and seven microns so
+typically the denser the wood the
+
+ align:start position:0%
+typically the denser the wood the
+ 
+
+ align:start position:0%
+typically the denser the wood the
+thicker the cell wall is going to be
+
+ align:start position:0%
+thicker the cell wall is going to be
+ 
+
+ align:start position:0%
+thicker the cell wall is going to be
+oops let see if I can put the Rays down
+
+ align:start position:0%
+oops let see if I can put the Rays down
+ 
+
+ align:start position:0%
+oops let see if I can put the Rays down
+here put on the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board so the rays are parous cells that
+
+ align:start position:0%
+board so the rays are parous cells that
+ 
+
+ align:start position:0%
+board so the rays are parous cells that
+store
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sugar okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the hardwoods have three types
+
+ align:start position:0%
+and then the hardwoods have three types
+ 
+
+ align:start position:0%
+and then the hardwoods have three types
+of cells they have the fibers that
+
+ align:start position:0%
+of cells they have the fibers that
+ 
+
+ align:start position:0%
+of cells they have the fibers that
+provide the structural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+support and the amount of cells that are
+
+ align:start position:0%
+support and the amount of cells that are
+ 
+
+ align:start position:0%
+support and the amount of cells that are
+fibers varies depending on the species
+
+ align:start position:0%
+fibers varies depending on the species
+ 
+
+ align:start position:0%
+fibers varies depending on the species
+but it's usually somewhere around 35 to
+
+ align:start position:0%
+but it's usually somewhere around 35 to
+ 
+
+ align:start position:0%
+but it's usually somewhere around 35 to
+70% of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and then they have the vessels
+
+ align:start position:0%
+cells and then they have the vessels
+ 
+
+ align:start position:0%
+cells and then they have the vessels
+which are the sap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+channels that provides for the
+
+ align:start position:0%
+channels that provides for the
+ 
+
+ align:start position:0%
+channels that provides for the
+conduction of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fluids and that's between about 6 and
+
+ align:start position:0%
+fluids and that's between about 6 and
+ 
+
+ align:start position:0%
+fluids and that's between about 6 and
+55% of the cells
+
+ align:start position:0%
+55% of the cells
+ 
+
+ align:start position:0%
+55% of the cells
+and then again there's rays that store
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sugars they usually make up about 10 to
+
+ align:start position:0%
+sugars they usually make up about 10 to
+ 
+
+ align:start position:0%
+sugars they usually make up about 10 to
+30% of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells so there's the structure of the
+
+ align:start position:0%
+cells so there's the structure of the
+ 
+
+ align:start position:0%
+cells so there's the structure of the
+sort of cellular structure that this
+
+ align:start position:0%
+sort of cellular structure that this
+ 
+
+ align:start position:0%
+sort of cellular structure that this
+kind of length scale of sort tens of
+
+ align:start position:0%
+kind of length scale of sort tens of
+ 
+
+ align:start position:0%
+kind of length scale of sort tens of
+microns and then there's also a
+
+ align:start position:0%
+microns and then there's also a
+ 
+
+ align:start position:0%
+microns and then there's also a
+structure within the cell wall itself
+
+ align:start position:0%
+structure within the cell wall itself
+ 
+
+ align:start position:0%
+structure within the cell wall itself
+and the cell wall itself um is made up
+
+ align:start position:0%
+and the cell wall itself um is made up
+ 
+
+ align:start position:0%
+and the cell wall itself um is made up
+of cellulose fibral in a matrix of
+
+ align:start position:0%
+of cellulose fibral in a matrix of
+ 
+
+ align:start position:0%
+of cellulose fibral in a matrix of
+lignan and something called
+
+ align:start position:0%
+lignan and something called
+ 
+
+ align:start position:0%
+lignan and something called
+hemicellulose so if you look at the
+
+ align:start position:0%
+hemicellulose so if you look at the
+ 
+
+ align:start position:0%
+hemicellulose so if you look at the
+cellulose structure the cellulose has um
+
+ align:start position:0%
+cellulose structure the cellulose has um
+ 
+
+ align:start position:0%
+cellulose structure the cellulose has um
+a regular structure sort of periodic
+
+ align:start position:0%
+a regular structure sort of periodic
+ 
+
+ align:start position:0%
+a regular structure sort of periodic
+lattice uh and it's crystallin for most
+
+ align:start position:0%
+lattice uh and it's crystallin for most
+ 
+
+ align:start position:0%
+lattice uh and it's crystallin for most
+of the length of the fibral so this is
+
+ align:start position:0%
+of the length of the fibral so this is
+ 
+
+ align:start position:0%
+of the length of the fibral so this is
+the the structure of the the cellulose
+
+ align:start position:0%
+the the structure of the the cellulose
+ 
+
+ align:start position:0%
+the the structure of the the cellulose
+here and uh this is showing at a
+
+ align:start position:0%
+here and uh this is showing at a
+ 
+
+ align:start position:0%
+here and uh this is showing at a
+slightly larger length scale if might
+
+ align:start position:0%
+slightly larger length scale if might
+ 
+
+ align:start position:0%
+slightly larger length scale if might
+have a crystalline region here and then
+
+ align:start position:0%
+have a crystalline region here and then
+ 
+
+ align:start position:0%
+have a crystalline region here and then
+a non-crystalline region here and these
+
+ align:start position:0%
+a non-crystalline region here and these
+ 
+
+ align:start position:0%
+a non-crystalline region here and these
+macrofibrils which are made up of
+
+ align:start position:0%
+macrofibrils which are made up of
+ 
+
+ align:start position:0%
+macrofibrils which are made up of
+bundles of microf fibral are about uh 10
+
+ align:start position:0%
+bundles of microf fibral are about uh 10
+ 
+
+ align:start position:0%
+bundles of microf fibral are about uh 10
+to 25 nanm and each one of the microf
+
+ align:start position:0%
+to 25 nanm and each one of the microf
+ 
+
+ align:start position:0%
+to 25 nanm and each one of the microf
+fibral might be 3 to four nanm across so
+
+ align:start position:0%
+fibral might be 3 to four nanm across so
+ 
+
+ align:start position:0%
+fibral might be 3 to four nanm across so
+you have these cellulose fibers and then
+
+ align:start position:0%
+you have these cellulose fibers and then
+ 
+
+ align:start position:0%
+you have these cellulose fibers and then
+the cell wall is made up of different
+
+ align:start position:0%
+the cell wall is made up of different
+ 
+
+ align:start position:0%
+the cell wall is made up of different
+layers so there's What's called the
+
+ align:start position:0%
+layers so there's What's called the
+ 
+
+ align:start position:0%
+layers so there's What's called the
+primary wall here which has a random
+
+ align:start position:0%
+primary wall here which has a random
+ 
+
+ align:start position:0%
+primary wall here which has a random
+arrangement of the cellulose fibral then
+
+ align:start position:0%
+arrangement of the cellulose fibral then
+ 
+
+ align:start position:0%
+arrangement of the cellulose fibral then
+there's an outer layer here these are
+
+ align:start position:0%
+there's an outer layer here these are
+ 
+
+ align:start position:0%
+there's an outer layer here these are
+all called secondary layers this is s uh
+
+ align:start position:0%
+all called secondary layers this is s uh
+ 
+
+ align:start position:0%
+all called secondary layers this is s uh
+let's see that's
+
+ align:start position:0%
+let's see that's
+ 
+
+ align:start position:0%
+let's see that's
+S1 yeah that's S1 uh and it has this
+
+ align:start position:0%
+S1 yeah that's S1 uh and it has this
+ 
+
+ align:start position:0%
+S1 yeah that's S1 uh and it has this
+arrangement of the uh fibral then
+
+ align:start position:0%
+arrangement of the uh fibral then
+ 
+
+ align:start position:0%
+arrangement of the uh fibral then
+there's a a layer called S2 and it's
+
+ align:start position:0%
+there's a a layer called S2 and it's
+ 
+
+ align:start position:0%
+there's a a layer called S2 and it's
+generally the thickest layer in the cell
+
+ align:start position:0%
+generally the thickest layer in the cell
+ 
+
+ align:start position:0%
+generally the thickest layer in the cell
+wall and the cellulose fibral are
+
+ align:start position:0%
+wall and the cellulose fibral are
+ 
+
+ align:start position:0%
+wall and the cellulose fibral are
+aligned not perfectly vertical but a
+
+ align:start position:0%
+aligned not perfectly vertical but a
+ 
+
+ align:start position:0%
+aligned not perfectly vertical but a
+little off the vertical and the angle
+
+ align:start position:0%
+little off the vertical and the angle
+ 
+
+ align:start position:0%
+little off the vertical and the angle
+between the vertical and the orientation
+
+ align:start position:0%
+between the vertical and the orientation
+ 
+
+ align:start position:0%
+between the vertical and the orientation
+of the cellulose fibers is called the
+
+ align:start position:0%
+of the cellulose fibers is called the
+ 
+
+ align:start position:0%
+of the cellulose fibers is called the
+microfibrillar angle and then there's a
+
+ align:start position:0%
+microfibrillar angle and then there's a
+ 
+
+ align:start position:0%
+microfibrillar angle and then there's a
+third third layer here S3 with again a
+
+ align:start position:0%
+third third layer here S3 with again a
+ 
+
+ align:start position:0%
+third third layer here S3 with again a
+different winding of the fibers so
+
+ align:start position:0%
+different winding of the fibers so
+ 
+
+ align:start position:0%
+different winding of the fibers so
+because the S2 layer is the thickest
+
+ align:start position:0%
+because the S2 layer is the thickest
+ 
+
+ align:start position:0%
+because the S2 layer is the thickest
+layer and because the fibral are closest
+
+ align:start position:0%
+layer and because the fibral are closest
+ 
+
+ align:start position:0%
+layer and because the fibral are closest
+to the vertical axis the S2 layer
+
+ align:start position:0%
+to the vertical axis the S2 layer
+ 
+
+ align:start position:0%
+to the vertical axis the S2 layer
+actually contributes the most to the um
+
+ align:start position:0%
+actually contributes the most to the um
+ 
+
+ align:start position:0%
+actually contributes the most to the um
+longitudinal modulus and stiffness of
+
+ align:start position:0%
+longitudinal modulus and stiffness of
+ 
+
+ align:start position:0%
+longitudinal modulus and stiffness of
+the and strength of the cell wall so
+
+ align:start position:0%
+the and strength of the cell wall so
+ 
+
+ align:start position:0%
+the and strength of the cell wall so
+that's kind of the layer of of the cell
+
+ align:start position:0%
+that's kind of the layer of of the cell
+ 
+
+ align:start position:0%
+that's kind of the layer of of the cell
+arrangement of the cell wall and then so
+
+ align:start position:0%
+arrangement of the cell wall and then so
+ 
+
+ align:start position:0%
+arrangement of the cell wall and then so
+that one cell would have that another
+
+ align:start position:0%
+that one cell would have that another
+ 
+
+ align:start position:0%
+that one cell would have that another
+cell would have that and in between the
+
+ align:start position:0%
+cell would have that and in between the
+ 
+
+ align:start position:0%
+cell would have that and in between the
+two there's a layer called the middle
+
+ align:start position:0%
+two there's a layer called the middle
+ 
+
+ align:start position:0%
+two there's a layer called the middle
+Lela that kind of glues them together so
+
+ align:start position:0%
+Lela that kind of glues them together so
+ 
+
+ align:start position:0%
+Lela that kind of glues them together so
+that's the arrangement of the
+
+ align:start position:0%
+that's the arrangement of the
+ 
+
+ align:start position:0%
+that's the arrangement of the
+cells um so oops let me scoot over here
+
+ align:start position:0%
+cells um so oops let me scoot over here
+ 
+
+ align:start position:0%
+cells um so oops let me scoot over here
+so the cells are often modeled as a
+
+ align:start position:0%
+so the cells are often modeled as a
+ 
+
+ align:start position:0%
+so the cells are often modeled as a
+fiber reinforced composite um that has
+
+ align:start position:0%
+fiber reinforced composite um that has
+ 
+
+ align:start position:0%
+fiber reinforced composite um that has
+four layers to
+
+ align:start position:0%
+four layers to
+ 
+
+ align:start position:0%
+four layers to
+it and in each layer there's different
+
+ align:start position:0%
+it and in each layer there's different
+ 
+
+ align:start position:0%
+it and in each layer there's different
+volume fraction of the fibers and
+
+ align:start position:0%
+volume fraction of the fibers and
+ 
+
+ align:start position:0%
+volume fraction of the fibers and
+different orientation of the fibers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the cell wall has this fiber
+
+ align:start position:0%
+okay so the cell wall has this fiber
+ 
+
+ align:start position:0%
+okay so the cell wall has this fiber
+reinforced structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's the
+
+ align:start position:0%
+there's the
+ 
+
+ align:start position:0%
+there's the
+cellulose
+
+ align:start position:0%
+cellulose
+ 
+
+ align:start position:0%
+cellulose
+fibers in a matrix of Li and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hemicellulose and there's four layers
+
+ align:start position:0%
+hemicellulose and there's four layers
+ 
+
+ align:start position:0%
+hemicellulose and there's four layers
+each with the fibers in a different
+
+ align:start position:0%
+each with the fibers in a different
+ 
+
+ align:start position:0%
+each with the fibers in a different
+orientation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's the middle Lela between
+
+ align:start position:0%
+and then there's the middle Lela between
+ 
+
+ align:start position:0%
+and then there's the middle Lela between
+the two cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in doing the modeling of of a
+
+ align:start position:0%
+so in doing the modeling of of a
+ 
+
+ align:start position:0%
+so in doing the modeling of of a
+material like wood you need to know what
+
+ align:start position:0%
+material like wood you need to know what
+ 
+
+ align:start position:0%
+material like wood you need to know what
+the properties of a cell wall material
+
+ align:start position:0%
+the properties of a cell wall material
+ 
+
+ align:start position:0%
+the properties of a cell wall material
+are because obviously the properties of
+
+ align:start position:0%
+are because obviously the properties of
+ 
+
+ align:start position:0%
+are because obviously the properties of
+the wood would depend on the cell wall
+
+ align:start position:0%
+the wood would depend on the cell wall
+ 
+
+ align:start position:0%
+the wood would depend on the cell wall
+properties and it turns out that they're
+
+ align:start position:0%
+properties and it turns out that they're
+ 
+
+ align:start position:0%
+properties and it turns out that they're
+similar they're not exactly the same but
+
+ align:start position:0%
+similar they're not exactly the same but
+ 
+
+ align:start position:0%
+similar they're not exactly the same but
+they're similar in different species of
+
+ align:start position:0%
+they're similar in different species of
+ 
+
+ align:start position:0%
+they're similar in different species of
+wood so we're going to call
+
+ align:start position:0%
+wood so we're going to call
+ 
+
+ align:start position:0%
+wood so we're going to call
+them more or less the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the density of the solid
+
+ align:start position:0%
+so the density of the solid
+ 
+
+ align:start position:0%
+so the density of the solid
+is500 kg per cubic
+
+ align:start position:0%
+is500 kg per cubic
+ 
+
+ align:start position:0%
+is500 kg per cubic
+meter the modulus of the solid in the
+
+ align:start position:0%
+meter the modulus of the solid in the
+ 
+
+ align:start position:0%
+meter the modulus of the solid in the
+axial direction is 35 Gap
+
+ align:start position:0%
+axial direction is 35 Gap
+ 
+
+ align:start position:0%
+axial direction is 35 Gap
+pascals the modulus in the tangential
+
+ align:start position:0%
+pascals the modulus in the tangential
+ 
+
+ align:start position:0%
+pascals the modulus in the tangential
+direction or transverse direction is 10
+
+ align:start position:0%
+direction or transverse direction is 10
+ 
+
+ align:start position:0%
+direction or transverse direction is 10
+Gap pascals and the strength of the
+
+ align:start position:0%
+Gap pascals and the strength of the
+ 
+
+ align:start position:0%
+Gap pascals and the strength of the
+solid in the axial
+
+ align:start position:0%
+solid in the axial
+ 
+
+ align:start position:0%
+solid in the axial
+direction is 350 megap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pascals and the strength in the
+
+ align:start position:0%
+pascals and the strength in the
+ 
+
+ align:start position:0%
+pascals and the strength in the
+transverse direction is about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+135 so here a means axial
+
+ align:start position:0%
+135 so here a means axial
+ 
+
+ align:start position:0%
+135 so here a means axial
+Direction and T is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transverse and just for
+
+ align:start position:0%
+transverse and just for
+ 
+
+ align:start position:0%
+transverse and just for
+comparison if you just look at
+
+ align:start position:0%
+comparison if you just look at
+ 
+
+ align:start position:0%
+comparison if you just look at
+cellulose cellulose has some pretty
+
+ align:start position:0%
+cellulose cellulose has some pretty
+ 
+
+ align:start position:0%
+cellulose cellulose has some pretty
+amazing properties the modulus of
+
+ align:start position:0%
+amazing properties the modulus of
+ 
+
+ align:start position:0%
+amazing properties the modulus of
+cellulose is about 140 gigap pascals
+
+ align:start position:0%
+cellulose is about 140 gigap pascals
+ 
+
+ align:start position:0%
+cellulose is about 140 gigap pascals
+which is very high for a polymer and the
+
+ align:start position:0%
+which is very high for a polymer and the
+ 
+
+ align:start position:0%
+which is very high for a polymer and the
+strength of cellulose fibers run between
+
+ align:start position:0%
+strength of cellulose fibers run between
+ 
+
+ align:start position:0%
+strength of cellulose fibers run between
+about 700 and
+
+ align:start position:0%
+about 700 and
+ 
+
+ align:start position:0%
+about 700 and
+900 megap pascals so the cellulose
+
+ align:start position:0%
+900 megap pascals so the cellulose
+ 
+
+ align:start position:0%
+900 megap pascals so the cellulose
+fibers have very impressive properties
+
+ align:start position:0%
+fibers have very impressive properties
+ 
+
+ align:start position:0%
+fibers have very impressive properties
+and that's one of the things that gives
+
+ align:start position:0%
+and that's one of the things that gives
+ 
+
+ align:start position:0%
+and that's one of the things that gives
+wood very good properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the next thing is I want to
+
+ align:start position:0%
+right so the next thing is I want to
+ 
+
+ align:start position:0%
+right so the next thing is I want to
+show you some stress strain curves for
+
+ align:start position:0%
+show you some stress strain curves for
+ 
+
+ align:start position:0%
+show you some stress strain curves for
+wood and you'll see how similar they are
+
+ align:start position:0%
+wood and you'll see how similar they are
+ 
+
+ align:start position:0%
+wood and you'll see how similar they are
+to the Honeycombs that we looked at
+
+ align:start position:0%
+to the Honeycombs that we looked at
+ 
+
+ align:start position:0%
+to the Honeycombs that we looked at
+before um and then we'll look at how the
+
+ align:start position:0%
+before um and then we'll look at how the
+ 
+
+ align:start position:0%
+before um and then we'll look at how the
+cells are deforming as they're getting
+
+ align:start position:0%
+cells are deforming as they're getting
+ 
+
+ align:start position:0%
+cells are deforming as they're getting
+loaded and from that we're going to do
+
+ align:start position:0%
+loaded and from that we're going to do
+ 
+
+ align:start position:0%
+loaded and from that we're going to do
+some modeling
+
+ align:start position:0%
+some modeling
+ 
+
+ align:start position:0%
+some modeling
+okay so let me just wait till people
+
+ align:start position:0%
+okay so let me just wait till people
+ 
+
+ align:start position:0%
+okay so let me just wait till people
+have caught up are we caught
+
+ align:start position:0%
+have caught up are we caught
+ 
+
+ align:start position:0%
+have caught up are we caught
+up more or less okay okay so these are
+
+ align:start position:0%
+up more or less okay okay so these are
+ 
+
+ align:start position:0%
+up more or less okay okay so these are
+all compression curves so I'm just going
+
+ align:start position:0%
+all compression curves so I'm just going
+ 
+
+ align:start position:0%
+all compression curves so I'm just going
+to talk about compression so these are
+
+ align:start position:0%
+to talk about compression so these are
+ 
+
+ align:start position:0%
+to talk about compression so these are
+curves for different types of woods and
+
+ align:start position:0%
+curves for different types of woods and
+ 
+
+ align:start position:0%
+curves for different types of woods and
+on the left the wood is loaded in in the
+
+ align:start position:0%
+on the left the wood is loaded in in the
+ 
+
+ align:start position:0%
+on the left the wood is loaded in in the
+tangential Direction so in terms of you
+
+ align:start position:0%
+tangential Direction so in terms of you
+ 
+
+ align:start position:0%
+tangential Direction so in terms of you
+know this sort of honeycomb model it's
+
+ align:start position:0%
+know this sort of honeycomb model it's
+ 
+
+ align:start position:0%
+know this sort of honeycomb model it's
+loading it kind of this this way on like
+
+ align:start position:0%
+loading it kind of this this way on like
+ 
+
+ align:start position:0%
+loading it kind of this this way on like
+that and on the right are a set of
+
+ align:start position:0%
+that and on the right are a set of
+ 
+
+ align:start position:0%
+that and on the right are a set of
+Curves for wood loaded in axial
+
+ align:start position:0%
+Curves for wood loaded in axial
+ 
+
+ align:start position:0%
+Curves for wood loaded in axial
+compression so in axial compression
+
+ align:start position:0%
+compression so in axial compression
+ 
+
+ align:start position:0%
+compression so in axial compression
+we're loading it that way on okay and
+
+ align:start position:0%
+we're loading it that way on okay and
+ 
+
+ align:start position:0%
+we're loading it that way on okay and
+we've got different species here so the
+
+ align:start position:0%
+we've got different species here so the
+ 
+
+ align:start position:0%
+we've got different species here so the
+lowest density is Balsa around about 100
+
+ align:start position:0%
+lowest density is Balsa around about 100
+ 
+
+ align:start position:0%
+lowest density is Balsa around about 100
+kg per cubic meter the densest species
+
+ align:start position:0%
+kg per cubic meter the densest species
+ 
+
+ align:start position:0%
+kg per cubic meter the densest species
+on this plot is Beach which is around
+
+ align:start position:0%
+on this plot is Beach which is around
+ 
+
+ align:start position:0%
+on this plot is Beach which is around
+700 kilog per cubic meter and then
+
+ align:start position:0%
+700 kilog per cubic meter and then
+ 
+
+ align:start position:0%
+700 kilog per cubic meter and then
+there's pine and Willow some other
+
+ align:start position:0%
+there's pine and Willow some other
+ 
+
+ align:start position:0%
+there's pine and Willow some other
+species in between here so you can see
+
+ align:start position:0%
+species in between here so you can see
+ 
+
+ align:start position:0%
+species in between here so you can see
+the shapes of the curve look just like
+
+ align:start position:0%
+the shapes of the curve look just like
+ 
+
+ align:start position:0%
+the shapes of the curve look just like
+the um curves that we had for the
+
+ align:start position:0%
+the um curves that we had for the
+ 
+
+ align:start position:0%
+the um curves that we had for the
+Honeycombs so here there's a linear
+
+ align:start position:0%
+Honeycombs so here there's a linear
+ 
+
+ align:start position:0%
+Honeycombs so here there's a linear
+elastic bit there's a stress plateau and
+
+ align:start position:0%
+elastic bit there's a stress plateau and
+ 
+
+ align:start position:0%
+elastic bit there's a stress plateau and
+there's a densification bit so and then
+
+ align:start position:0%
+there's a densification bit so and then
+ 
+
+ align:start position:0%
+there's a densification bit so and then
+as the density goes up the it gets
+
+ align:start position:0%
+as the density goes up the it gets
+ 
+
+ align:start position:0%
+as the density goes up the it gets
+stiffer and the strain at which the
+
+ align:start position:0%
+stiffer and the strain at which the
+ 
+
+ align:start position:0%
+stiffer and the strain at which the
+densification occurs uh gets smaller and
+
+ align:start position:0%
+densification occurs uh gets smaller and
+ 
+
+ align:start position:0%
+densification occurs uh gets smaller and
+the strength gets higher uh and if we
+
+ align:start position:0%
+the strength gets higher uh and if we
+ 
+
+ align:start position:0%
+the strength gets higher uh and if we
+look at the
+
+ align:start position:0%
+look at the
+ 
+
+ align:start position:0%
+look at the
+axial properties the shape of the curve
+
+ align:start position:0%
+axial properties the shape of the curve
+ 
+
+ align:start position:0%
+axial properties the shape of the curve
+is similar we get linear elastic stress
+
+ align:start position:0%
+is similar we get linear elastic stress
+ 
+
+ align:start position:0%
+is similar we get linear elastic stress
+plateau densification uh but if you look
+
+ align:start position:0%
+plateau densification uh but if you look
+ 
+
+ align:start position:0%
+plateau densification uh but if you look
+at the scale here this scale goes from 0
+
+ align:start position:0%
+at the scale here this scale goes from 0
+ 
+
+ align:start position:0%
+at the scale here this scale goes from 0
+to 100 whereas that scale went from 0 to
+
+ align:start position:0%
+to 100 whereas that scale went from 0 to
+ 
+
+ align:start position:0%
+to 100 whereas that scale went from 0 to
+20 and so this this stiffness and the
+
+ align:start position:0%
+20 and so this this stiffness and the
+ 
+
+ align:start position:0%
+20 and so this this stiffness and the
+strength along the grain are much higher
+
+ align:start position:0%
+strength along the grain are much higher
+ 
+
+ align:start position:0%
+strength along the grain are much higher
+than they are across the Grain and you
+
+ align:start position:0%
+than they are across the Grain and you
+ 
+
+ align:start position:0%
+than they are across the Grain and you
+probably already know that wood is
+
+ align:start position:0%
+probably already know that wood is
+ 
+
+ align:start position:0%
+probably already know that wood is
+stronger and stiffer along the grain
+
+ align:start position:0%
+stronger and stiffer along the grain
+ 
+
+ align:start position:0%
+stronger and stiffer along the grain
+than across the grain okay so that's
+
+ align:start position:0%
+than across the grain okay so that's
+ 
+
+ align:start position:0%
+than across the grain okay so that's
+when the stress strin curves looked like
+
+ align:start position:0%
+when the stress strin curves looked like
+ 
+
+ align:start position:0%
+when the stress strin curves looked like
+and the fact that we're getting the
+
+ align:start position:0%
+and the fact that we're getting the
+ 
+
+ align:start position:0%
+and the fact that we're getting the
+curves that look like that makes us
+
+ align:start position:0%
+curves that look like that makes us
+ 
+
+ align:start position:0%
+curves that look like that makes us
+think maybe the mechanisms of
+
+ align:start position:0%
+think maybe the mechanisms of
+ 
+
+ align:start position:0%
+think maybe the mechanisms of
+deformation and failure similar to the
+
+ align:start position:0%
+deformation and failure similar to the
+ 
+
+ align:start position:0%
+deformation and failure similar to the
+honeycomb 2 so here's a here's a set of
+
+ align:start position:0%
+honeycomb 2 so here's a here's a set of
+ 
+
+ align:start position:0%
+honeycomb 2 so here's a here's a set of
+Curves for Balsa all plotted on the same
+
+ align:start position:0%
+Curves for Balsa all plotted on the same
+ 
+
+ align:start position:0%
+Curves for Balsa all plotted on the same
+scale and again you can see the the for
+
+ align:start position:0%
+scale and again you can see the the for
+ 
+
+ align:start position:0%
+scale and again you can see the the for
+loading across the grain either in the
+
+ align:start position:0%
+loading across the grain either in the
+ 
+
+ align:start position:0%
+loading across the grain either in the
+radial or the tangential Direction the
+
+ align:start position:0%
+radial or the tangential Direction the
+ 
+
+ align:start position:0%
+radial or the tangential Direction the
+stiffness and the strength is a lot less
+
+ align:start position:0%
+stiffness and the strength is a lot less
+ 
+
+ align:start position:0%
+stiffness and the strength is a lot less
+than if you load it in the axial
+
+ align:start position:0%
+than if you load it in the axial
+ 
+
+ align:start position:0%
+than if you load it in the axial
+Direction so a number of years ago we
+
+ align:start position:0%
+Direction so a number of years ago we
+ 
+
+ align:start position:0%
+Direction so a number of years ago we
+had a project on Balsa and the thing we
+
+ align:start position:0%
+had a project on Balsa and the thing we
+ 
+
+ align:start position:0%
+had a project on Balsa and the thing we
+were interested in doing was looking at
+
+ align:start position:0%
+were interested in doing was looking at
+ 
+
+ align:start position:0%
+were interested in doing was looking at
+how the cells deformed and failed and
+
+ align:start position:0%
+how the cells deformed and failed and
+ 
+
+ align:start position:0%
+how the cells deformed and failed and
+because bals is a low density wood it
+
+ align:start position:0%
+because bals is a low density wood it
+ 
+
+ align:start position:0%
+because bals is a low density wood it
+was easier to see the deformation in the
+
+ align:start position:0%
+was easier to see the deformation in the
+ 
+
+ align:start position:0%
+was easier to see the deformation in the
+cells because the cell walls were thin
+
+ align:start position:0%
+cells because the cell walls were thin
+ 
+
+ align:start position:0%
+cells because the cell walls were thin
+so that's why we chose Balsa I actually
+
+ align:start position:0%
+so that's why we chose Balsa I actually
+ 
+
+ align:start position:0%
+so that's why we chose Balsa I actually
+have a project on Balsa right now and um
+
+ align:start position:0%
+have a project on Balsa right now and um
+ 
+
+ align:start position:0%
+have a project on Balsa right now and um
+Sardar my postto is doing more detailed
+
+ align:start position:0%
+Sardar my postto is doing more detailed
+ 
+
+ align:start position:0%
+Sardar my postto is doing more detailed
+kind of finite element modeling trying
+
+ align:start position:0%
+kind of finite element modeling trying
+ 
+
+ align:start position:0%
+kind of finite element modeling trying
+to represent the structure of Balsa and
+
+ align:start position:0%
+to represent the structure of Balsa and
+ 
+
+ align:start position:0%
+to represent the structure of Balsa and
+I think I mentioned the reason we're
+
+ align:start position:0%
+I think I mentioned the reason we're
+ 
+
+ align:start position:0%
+I think I mentioned the reason we're
+interested in it is that Balsa is used
+
+ align:start position:0%
+interested in it is that Balsa is used
+ 
+
+ align:start position:0%
+interested in it is that Balsa is used
+as a core in Sandwich panels in wind
+
+ align:start position:0%
+as a core in Sandwich panels in wind
+ 
+
+ align:start position:0%
+as a core in Sandwich panels in wind
+turbine blades and uh it's it's actually
+
+ align:start position:0%
+turbine blades and uh it's it's actually
+ 
+
+ align:start position:0%
+turbine blades and uh it's it's actually
+the best material that they can find
+
+ align:start position:0%
+the best material that they can find
+ 
+
+ align:start position:0%
+the best material that they can find
+it's better than any engineering
+
+ align:start position:0%
+it's better than any engineering
+ 
+
+ align:start position:0%
+it's better than any engineering
+material so that's
+
+ align:start position:0%
+material so that's
+ 
+
+ align:start position:0%
+material so that's
+comparing the three curves for Balsa and
+
+ align:start position:0%
+comparing the three curves for Balsa and
+ 
+
+ align:start position:0%
+comparing the three curves for Balsa and
+then if you look um at a specimen that's
+
+ align:start position:0%
+then if you look um at a specimen that's
+ 
+
+ align:start position:0%
+then if you look um at a specimen that's
+loaded in the sem you can uh with a
+
+ align:start position:0%
+loaded in the sem you can uh with a
+ 
+
+ align:start position:0%
+loaded in the sem you can uh with a
+loading stage you can measure the stress
+
+ align:start position:0%
+loading stage you can measure the stress
+ 
+
+ align:start position:0%
+loading stage you can measure the stress
+strain curve and you can take
+
+ align:start position:0%
+strain curve and you can take
+ 
+
+ align:start position:0%
+strain curve and you can take
+photographs of what the cellular
+
+ align:start position:0%
+photographs of what the cellular
+ 
+
+ align:start position:0%
+photographs of what the cellular
+structure looks like at different stages
+
+ align:start position:0%
+structure looks like at different stages
+ 
+
+ align:start position:0%
+structure looks like at different stages
+of loading so here this picture one is
+
+ align:start position:0%
+of loading so here this picture one is
+ 
+
+ align:start position:0%
+of loading so here this picture one is
+unloaded and these four Images here are
+
+ align:start position:0%
+unloaded and these four Images here are
+ 
+
+ align:start position:0%
+unloaded and these four Images here are
+looking at the same section of cells the
+
+ align:start position:0%
+looking at the same section of cells the
+ 
+
+ align:start position:0%
+looking at the same section of cells the
+same area of cells and you can see
+
+ align:start position:0%
+same area of cells and you can see
+ 
+
+ align:start position:0%
+same area of cells and you can see
+there's a big vessel here and that's the
+
+ align:start position:0%
+there's a big vessel here and that's the
+ 
+
+ align:start position:0%
+there's a big vessel here and that's the
+same vessel there so here this image two
+
+ align:start position:0%
+same vessel there so here this image two
+ 
+
+ align:start position:0%
+same vessel there so here this image two
+is at this point on the stress strain
+
+ align:start position:0%
+is at this point on the stress strain
+ 
+
+ align:start position:0%
+is at this point on the stress strain
+curve here's three at that point and
+
+ align:start position:0%
+curve here's three at that point and
+ 
+
+ align:start position:0%
+curve here's three at that point and
+four is at that point so if you look at
+
+ align:start position:0%
+four is at that point so if you look at
+ 
+
+ align:start position:0%
+four is at that point so if you look at
+this carefully and I've got another
+
+ align:start position:0%
+this carefully and I've got another
+ 
+
+ align:start position:0%
+this carefully and I've got another
+higher meg picture I'll show you in a
+
+ align:start position:0%
+higher meg picture I'll show you in a
+ 
+
+ align:start position:0%
+higher meg picture I'll show you in a
+second um you can see that what's
+
+ align:start position:0%
+second um you can see that what's
+ 
+
+ align:start position:0%
+second um you can see that what's
+happening is the cell walls are bending
+
+ align:start position:0%
+happening is the cell walls are bending
+ 
+
+ align:start position:0%
+happening is the cell walls are bending
+so it's kind of like taking my honeycomb
+
+ align:start position:0%
+so it's kind of like taking my honeycomb
+ 
+
+ align:start position:0%
+so it's kind of like taking my honeycomb
+like this and I'm doing that to it and
+
+ align:start position:0%
+like this and I'm doing that to it and
+ 
+
+ align:start position:0%
+like this and I'm doing that to it and
+the cell walls are bending so just the
+
+ align:start position:0%
+the cell walls are bending so just the
+ 
+
+ align:start position:0%
+the cell walls are bending so just the
+same as the honeycomb and then
+
+ align:start position:0%
+same as the honeycomb and then
+ 
+
+ align:start position:0%
+same as the honeycomb and then
+eventually if I load it enough you get
+
+ align:start position:0%
+eventually if I load it enough you get
+ 
+
+ align:start position:0%
+eventually if I load it enough you get
+to this sort of densified stage and
+
+ align:start position:0%
+to this sort of densified stage and
+ 
+
+ align:start position:0%
+to this sort of densified stage and
+you're doing this and the stress strain
+
+ align:start position:0%
+you're doing this and the stress strain
+ 
+
+ align:start position:0%
+you're doing this and the stress strain
+curve increases sharply so here you can
+
+ align:start position:0%
+curve increases sharply so here you can
+ 
+
+ align:start position:0%
+curve increases sharply so here you can
+see how the cells have densified over
+
+ align:start position:0%
+see how the cells have densified over
+ 
+
+ align:start position:0%
+see how the cells have densified over
+here it kind of looks a lot like my
+
+ align:start position:0%
+here it kind of looks a lot like my
+ 
+
+ align:start position:0%
+here it kind of looks a lot like my
+honeycomb when I oops maybe I do it this
+
+ align:start position:0%
+honeycomb when I oops maybe I do it this
+ 
+
+ align:start position:0%
+honeycomb when I oops maybe I do it this
+way when I smush it up like that it
+
+ align:start position:0%
+way when I smush it up like that it
+ 
+
+ align:start position:0%
+way when I smush it up like that it
+looks kind of
+
+ align:start position:0%
+looks kind of
+ 
+
+ align:start position:0%
+looks kind of
+similar so if we look at the higher mag
+
+ align:start position:0%
+similar so if we look at the higher mag
+ 
+
+ align:start position:0%
+similar so if we look at the higher mag
+picture again these four Images are the
+
+ align:start position:0%
+picture again these four Images are the
+ 
+
+ align:start position:0%
+picture again these four Images are the
+same area of the cells and you can if
+
+ align:start position:0%
+same area of the cells and you can if
+ 
+
+ align:start position:0%
+same area of the cells and you can if
+you look at that little bit of crud
+
+ align:start position:0%
+you look at that little bit of crud
+ 
+
+ align:start position:0%
+you look at that little bit of crud
+that's the same on all four of them
+
+ align:start position:0%
+that's the same on all four of them
+ 
+
+ align:start position:0%
+that's the same on all four of them
+there so this is the unloaded one and
+
+ align:start position:0%
+there so this is the unloaded one and
+ 
+
+ align:start position:0%
+there so this is the unloaded one and
+these were loaded from top to bottom and
+
+ align:start position:0%
+these were loaded from top to bottom and
+ 
+
+ align:start position:0%
+these were loaded from top to bottom and
+this is loaded uh to some extent that's
+
+ align:start position:0%
+this is loaded uh to some extent that's
+ 
+
+ align:start position:0%
+this is loaded uh to some extent that's
+loaded more and that's loaded more so if
+
+ align:start position:0%
+loaded more and that's loaded more so if
+ 
+
+ align:start position:0%
+loaded more and that's loaded more so if
+you look at this cell here it's got this
+
+ align:start position:0%
+you look at this cell here it's got this
+ 
+
+ align:start position:0%
+you look at this cell here it's got this
+little tear on it so you can sort of
+
+ align:start position:0%
+little tear on it so you can sort of
+ 
+
+ align:start position:0%
+little tear on it so you can sort of
+find it again if you look at that cell
+
+ align:start position:0%
+find it again if you look at that cell
+ 
+
+ align:start position:0%
+find it again if you look at that cell
+there that's what it looks like unloaded
+
+ align:start position:0%
+there that's what it looks like unloaded
+ 
+
+ align:start position:0%
+there that's what it looks like unloaded
+and here you can see see that wall there
+
+ align:start position:0%
+and here you can see see that wall there
+ 
+
+ align:start position:0%
+and here you can see see that wall there
+you can see how it's bent up so it's
+
+ align:start position:0%
+you can see how it's bent up so it's
+ 
+
+ align:start position:0%
+you can see how it's bent up so it's
+bent like the honeycomb walls and here
+
+ align:start position:0%
+bent like the honeycomb walls and here
+ 
+
+ align:start position:0%
+bent like the honeycomb walls and here
+that's bent even more and eventually it
+
+ align:start position:0%
+that's bent even more and eventually it
+ 
+
+ align:start position:0%
+that's bent even more and eventually it
+sort of has this sort of a shape here
+
+ align:start position:0%
+sort of has this sort of a shape here
+ 
+
+ align:start position:0%
+sort of has this sort of a shape here
+and you know it's formed a it's to form
+
+ align:start position:0%
+and you know it's formed a it's to form
+ 
+
+ align:start position:0%
+and you know it's formed a it's to form
+permanently it's formed one of these
+
+ align:start position:0%
+permanently it's formed one of these
+ 
+
+ align:start position:0%
+permanently it's formed one of these
+plastic hinges so it's like the aluminum
+
+ align:start position:0%
+plastic hinges so it's like the aluminum
+ 
+
+ align:start position:0%
+plastic hinges so it's like the aluminum
+Honeycombs almost that it's failed like
+
+ align:start position:0%
+Honeycombs almost that it's failed like
+ 
+
+ align:start position:0%
+Honeycombs almost that it's failed like
+that so in the balwood when we load it
+
+ align:start position:0%
+that so in the balwood when we load it
+ 
+
+ align:start position:0%
+that so in the balwood when we load it
+uh in the tangential direction we're
+
+ align:start position:0%
+uh in the tangential direction we're
+ 
+
+ align:start position:0%
+uh in the tangential direction we're
+getting bending of the cell walls and
+
+ align:start position:0%
+getting bending of the cell walls and
+ 
+
+ align:start position:0%
+getting bending of the cell walls and
+then yielding and plastic hinges forming
+
+ align:start position:0%
+then yielding and plastic hinges forming
+ 
+
+ align:start position:0%
+then yielding and plastic hinges forming
+just the same as we would in aluminum
+
+ align:start position:0%
+just the same as we would in aluminum
+ 
+
+ align:start position:0%
+just the same as we would in aluminum
+honeycomb okay are we good with that
+
+ align:start position:0%
+honeycomb okay are we good with that
+ 
+
+ align:start position:0%
+honeycomb okay are we good with that
+I'll go through the all three directions
+
+ align:start position:0%
+I'll go through the all three directions
+ 
+
+ align:start position:0%
+I'll go through the all three directions
+and then I'll write down the
+
+ align:start position:0%
+and then I'll write down the
+ 
+
+ align:start position:0%
+and then I'll write down the
+notes um so this is loading the Bala in
+
+ align:start position:0%
+notes um so this is loading the Bala in
+ 
+
+ align:start position:0%
+notes um so this is loading the Bala in
+the radial
+
+ align:start position:0%
+the radial
+ 
+
+ align:start position:0%
+the radial
+Direction and these things here are the
+
+ align:start position:0%
+Direction and these things here are the
+ 
+
+ align:start position:0%
+Direction and these things here are the
+Rays okay so we're loading it in that
+
+ align:start position:0%
+Rays okay so we're loading it in that
+ 
+
+ align:start position:0%
+Rays okay so we're loading it in that
+direction and here you see uh this also
+
+ align:start position:0%
+direction and here you see uh this also
+ 
+
+ align:start position:0%
+direction and here you see uh this also
+bending occurs but the Rays act a little
+
+ align:start position:0%
+bending occurs but the Rays act a little
+ 
+
+ align:start position:0%
+bending occurs but the Rays act a little
+bit like fiber reinforcement so the rays
+
+ align:start position:0%
+bit like fiber reinforcement so the rays
+ 
+
+ align:start position:0%
+bit like fiber reinforcement so the rays
+are a little bit stiffer and they sort
+
+ align:start position:0%
+are a little bit stiffer and they sort
+ 
+
+ align:start position:0%
+are a little bit stiffer and they sort
+of reinforce the thing a bit and this is
+
+ align:start position:0%
+of reinforce the thing a bit and this is
+ 
+
+ align:start position:0%
+of reinforce the thing a bit and this is
+the loading platin here and you can kind
+
+ align:start position:0%
+the loading platin here and you can kind
+ 
+
+ align:start position:0%
+the loading platin here and you can kind
+of see that the failure starts at the
+
+ align:start position:0%
+of see that the failure starts at the
+ 
+
+ align:start position:0%
+of see that the failure starts at the
+loading platin and as you sort of load
+
+ align:start position:0%
+loading platin and as you sort of load
+ 
+
+ align:start position:0%
+loading platin and as you sort of load
+it more it progresses in from the
+
+ align:start position:0%
+it more it progresses in from the
+ 
+
+ align:start position:0%
+it more it progresses in from the
+loading plan so we're going to look at
+
+ align:start position:0%
+loading plan so we're going to look at
+ 
+
+ align:start position:0%
+loading plan so we're going to look at
+the modeling of the BSA in the radial
+
+ align:start position:0%
+the modeling of the BSA in the radial
+ 
+
+ align:start position:0%
+the modeling of the BSA in the radial
+Direction and we're going to count for
+
+ align:start position:0%
+Direction and we're going to count for
+ 
+
+ align:start position:0%
+Direction and we're going to count for
+the Rays at least in a crude way and
+
+ align:start position:0%
+the Rays at least in a crude way and
+ 
+
+ align:start position:0%
+the Rays at least in a crude way and
+then when you load the balla in the
+
+ align:start position:0%
+then when you load the balla in the
+ 
+
+ align:start position:0%
+then when you load the balla in the
+axial Direction um initially you don't
+
+ align:start position:0%
+axial Direction um initially you don't
+ 
+
+ align:start position:0%
+axial Direction um initially you don't
+really see much happening so if one is
+
+ align:start position:0%
+really see much happening so if one is
+ 
+
+ align:start position:0%
+really see much happening so if one is
+unloaded one's down here and two is at
+
+ align:start position:0%
+unloaded one's down here and two is at
+ 
+
+ align:start position:0%
+unloaded one's down here and two is at
+this peak stress up here and really if
+
+ align:start position:0%
+this peak stress up here and really if
+ 
+
+ align:start position:0%
+this peak stress up here and really if
+you look between one and two you just
+
+ align:start position:0%
+you look between one and two you just
+ 
+
+ align:start position:0%
+you look between one and two you just
+don't see an awful lot of difference and
+
+ align:start position:0%
+don't see an awful lot of difference and
+ 
+
+ align:start position:0%
+don't see an awful lot of difference and
+that's because what you're doing is
+
+ align:start position:0%
+that's because what you're doing is
+ 
+
+ align:start position:0%
+that's because what you're doing is
+you're taking the wood and you're
+
+ align:start position:0%
+you're taking the wood and you're
+ 
+
+ align:start position:0%
+you're taking the wood and you're
+loading it this way on and it's so stiff
+
+ align:start position:0%
+loading it this way on and it's so stiff
+ 
+
+ align:start position:0%
+loading it this way on and it's so stiff
+you just don't see much deformation so
+
+ align:start position:0%
+you just don't see much deformation so
+ 
+
+ align:start position:0%
+you just don't see much deformation so
+there's not really much to see but then
+
+ align:start position:0%
+there's not really much to see but then
+ 
+
+ align:start position:0%
+there's not really much to see but then
+eventually you start something starts to
+
+ align:start position:0%
+eventually you start something starts to
+ 
+
+ align:start position:0%
+eventually you start something starts to
+fail and in this case what fails are the
+
+ align:start position:0%
+fail and in this case what fails are the
+ 
+
+ align:start position:0%
+fail and in this case what fails are the
+end caps so the Balsa would you know has
+
+ align:start position:0%
+end caps so the Balsa would you know has
+ 
+
+ align:start position:0%
+end caps so the Balsa would you know has
+these long cells here but then at the
+
+ align:start position:0%
+these long cells here but then at the
+ 
+
+ align:start position:0%
+these long cells here but then at the
+end of the cells there's little caps on
+
+ align:start position:0%
+end of the cells there's little caps on
+ 
+
+ align:start position:0%
+end of the cells there's little caps on
+the ends and the cells kind of fit
+
+ align:start position:0%
+the ends and the cells kind of fit
+ 
+
+ align:start position:0%
+the ends and the cells kind of fit
+together like that so that eventually if
+
+ align:start position:0%
+together like that so that eventually if
+ 
+
+ align:start position:0%
+together like that so that eventually if
+you keep smooshing it those end caps
+
+ align:start position:0%
+you keep smooshing it those end caps
+ 
+
+ align:start position:0%
+you keep smooshing it those end caps
+start to fail and you can see here oops
+
+ align:start position:0%
+start to fail and you can see here oops
+ 
+
+ align:start position:0%
+start to fail and you can see here oops
+wrong button here you can see how bright
+
+ align:start position:0%
+wrong button here you can see how bright
+ 
+
+ align:start position:0%
+wrong button here you can see how bright
+it gets and the cells are starting to
+
+ align:start position:0%
+it gets and the cells are starting to
+ 
+
+ align:start position:0%
+it gets and the cells are starting to
+crush together and kind of fail those
+
+ align:start position:0%
+crush together and kind of fail those
+ 
+
+ align:start position:0%
+crush together and kind of fail those
+endcaps and in fact each one of these
+
+ align:start position:0%
+endcaps and in fact each one of these
+ 
+
+ align:start position:0%
+endcaps and in fact each one of these
+serrations here if you look at say from
+
+ align:start position:0%
+serrations here if you look at say from
+ 
+
+ align:start position:0%
+serrations here if you look at say from
+that Peak up to that Peak that
+
+ align:start position:0%
+that Peak up to that Peak that
+ 
+
+ align:start position:0%
+that Peak up to that Peak that
+corresponds to a length of about the
+
+ align:start position:0%
+corresponds to a length of about the
+ 
+
+ align:start position:0%
+corresponds to a length of about the
+length of the cell or the length of the
+
+ align:start position:0%
+length of the cell or the length of the
+ 
+
+ align:start position:0%
+length of the cell or the length of the
+cell between the end caps so so in axial
+
+ align:start position:0%
+cell between the end caps so so in axial
+ 
+
+ align:start position:0%
+cell between the end caps so so in axial
+deformation you're you're just actually
+
+ align:start position:0%
+deformation you're you're just actually
+ 
+
+ align:start position:0%
+deformation you're you're just actually
+deforming the cells until you break
+
+ align:start position:0%
+deforming the cells until you break
+ 
+
+ align:start position:0%
+deforming the cells until you break
+those endcaps if you look at denser
+
+ align:start position:0%
+those endcaps if you look at denser
+ 
+
+ align:start position:0%
+those endcaps if you look at denser
+woods they fail in slightly different
+
+ align:start position:0%
+woods they fail in slightly different
+ 
+
+ align:start position:0%
+woods they fail in slightly different
+ways this is a Douglas fur which is much
+
+ align:start position:0%
+ways this is a Douglas fur which is much
+ 
+
+ align:start position:0%
+ways this is a Douglas fur which is much
+denser uh this this particular specimen
+
+ align:start position:0%
+denser uh this this particular specimen
+ 
+
+ align:start position:0%
+denser uh this this particular specimen
+the whole thing is kind of buckled over
+
+ align:start position:0%
+the whole thing is kind of buckled over
+ 
+
+ align:start position:0%
+the whole thing is kind of buckled over
+so it's not really so representative of
+
+ align:start position:0%
+so it's not really so representative of
+ 
+
+ align:start position:0%
+so it's not really so representative of
+the this the structure itself uh this is
+
+ align:start position:0%
+the this the structure itself uh this is
+ 
+
+ align:start position:0%
+the this the structure itself uh this is
+Douglas fur in radial compression and
+
+ align:start position:0%
+Douglas fur in radial compression and
+ 
+
+ align:start position:0%
+Douglas fur in radial compression and
+you can see this picture looks just like
+
+ align:start position:0%
+you can see this picture looks just like
+ 
+
+ align:start position:0%
+you can see this picture looks just like
+what I showed you for the balls of wood
+
+ align:start position:0%
+what I showed you for the balls of wood
+ 
+
+ align:start position:0%
+what I showed you for the balls of wood
+that sort of propagation of the failure
+
+ align:start position:0%
+that sort of propagation of the failure
+ 
+
+ align:start position:0%
+that sort of propagation of the failure
+and uh these are the oops these long
+
+ align:start position:0%
+and uh these are the oops these long
+ 
+
+ align:start position:0%
+and uh these are the oops these long
+things here are the Rays uh and this is
+
+ align:start position:0%
+things here are the Rays uh and this is
+ 
+
+ align:start position:0%
+things here are the Rays uh and this is
+a Norway Spruce in axial compression and
+
+ align:start position:0%
+a Norway Spruce in axial compression and
+ 
+
+ align:start position:0%
+a Norway Spruce in axial compression and
+this is fairly common in in denser Woods
+
+ align:start position:0%
+this is fairly common in in denser Woods
+ 
+
+ align:start position:0%
+this is fairly common in in denser Woods
+you get this um buckling formation and
+
+ align:start position:0%
+you get this um buckling formation and
+ 
+
+ align:start position:0%
+you get this um buckling formation and
+what happens is I think you get some
+
+ align:start position:0%
+what happens is I think you get some
+ 
+
+ align:start position:0%
+what happens is I think you get some
+yielding of the cell walls initially uh
+
+ align:start position:0%
+yielding of the cell walls initially uh
+ 
+
+ align:start position:0%
+yielding of the cell walls initially uh
+but that leads to um buckling like a
+
+ align:start position:0%
+but that leads to um buckling like a
+ 
+
+ align:start position:0%
+but that leads to um buckling like a
+plastic buckling and you can see on this
+
+ align:start position:0%
+plastic buckling and you can see on this
+ 
+
+ align:start position:0%
+plastic buckling and you can see on this
+higher mag picture down here you get
+
+ align:start position:0%
+higher mag picture down here you get
+ 
+
+ align:start position:0%
+higher mag picture down here you get
+these really small wavelength U Buckles
+
+ align:start position:0%
+these really small wavelength U Buckles
+ 
+
+ align:start position:0%
+these really small wavelength U Buckles
+in the cell wall and the two you you got
+
+ align:start position:0%
+in the cell wall and the two you you got
+ 
+
+ align:start position:0%
+in the cell wall and the two you you got
+a plane that kind of shears over itself
+
+ align:start position:0%
+a plane that kind of shears over itself
+ 
+
+ align:start position:0%
+a plane that kind of shears over itself
+and you can see in the top image that
+
+ align:start position:0%
+and you can see in the top image that
+ 
+
+ align:start position:0%
+and you can see in the top image that
+the you know this top half has sheared
+
+ align:start position:0%
+the you know this top half has sheared
+ 
+
+ align:start position:0%
+the you know this top half has sheared
+over relative to the bottom half and all
+
+ align:start position:0%
+over relative to the bottom half and all
+ 
+
+ align:start position:0%
+over relative to the bottom half and all
+the deformation is in this little band
+
+ align:start position:0%
+the deformation is in this little band
+ 
+
+ align:start position:0%
+the deformation is in this little band
+here so this you know this stuff here is
+
+ align:start position:0%
+here so this you know this stuff here is
+ 
+
+ align:start position:0%
+here so this you know this stuff here is
+all going on in that band up there okay
+
+ align:start position:0%
+all going on in that band up there okay
+ 
+
+ align:start position:0%
+all going on in that band up there okay
+so let me write down some notes about um
+
+ align:start position:0%
+so let me write down some notes about um
+ 
+
+ align:start position:0%
+so let me write down some notes about um
+how these things to form and fail uh and
+
+ align:start position:0%
+how these things to form and fail uh and
+ 
+
+ align:start position:0%
+how these things to form and fail uh and
+then we'll get to the modeling a little
+
+ align:start position:0%
+then we'll get to the modeling a little
+ 
+
+ align:start position:0%
+then we'll get to the modeling a little
+bit okay so we can say the stress strain
+
+ align:start position:0%
+bit okay so we can say the stress strain
+ 
+
+ align:start position:0%
+bit okay so we can say the stress strain
+curves resemble those for Honeycombs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll say the mechanisms of
+
+ align:start position:0%
+and I'll say the mechanisms of
+ 
+
+ align:start position:0%
+and I'll say the mechanisms of
+deformation and
+
+ align:start position:0%
+deformation and
+ 
+
+ align:start position:0%
+deformation and
+failure are most easily identified in
+
+ align:start position:0%
+failure are most easily identified in
+ 
+
+ align:start position:0%
+failure are most easily identified in
+low density Ballwood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for Balsa if we look at the
+
+ align:start position:0%
+so for Balsa if we look at the
+ 
+
+ align:start position:0%
+so for Balsa if we look at the
+tangential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loading we see bending of the cell walls
+
+ align:start position:0%
+loading we see bending of the cell walls
+ 
+
+ align:start position:0%
+loading we see bending of the cell walls
+and then eventually plastic yielding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for radial loading the ray Act is
+
+ align:start position:0%
+and for radial loading the ray Act is
+ 
+
+ align:start position:0%
+and for radial loading the ray Act is
+reinforcing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for axial loading you get axial
+
+ align:start position:0%
+and for axial loading you get axial
+ 
+
+ align:start position:0%
+and for axial loading you get axial
+deformation and then failure of the endc
+
+ align:start position:0%
+deformation and then failure of the endc
+ 
+
+ align:start position:0%
+deformation and then failure of the endc
+caps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll just say failure by plastic
+
+ align:start position:0%
+and I'll just say failure by plastic
+ 
+
+ align:start position:0%
+and I'll just say failure by plastic
+buckling is also
+
+ align:start position:0%
+buckling is also
+ 
+
+ align:start position:0%
+buckling is also
+observed say in the denser
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Woods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oops where's my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CER Heroes any right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so then we can look at some
+
+ align:start position:0%
+all right so then we can look at some
+ 
+
+ align:start position:0%
+all right so then we can look at some
+data for the properties of of woods and
+
+ align:start position:0%
+data for the properties of of woods and
+ 
+
+ align:start position:0%
+data for the properties of of woods and
+these charts plot relative Young's
+
+ align:start position:0%
+these charts plot relative Young's
+ 
+
+ align:start position:0%
+these charts plot relative Young's
+modulus and relative strength against
+
+ align:start position:0%
+modulus and relative strength against
+ 
+
+ align:start position:0%
+modulus and relative strength against
+relative density so here the modulus of
+
+ align:start position:0%
+relative density so here the modulus of
+ 
+
+ align:start position:0%
+relative density so here the modulus of
+the wood is divided by the modulus of
+
+ align:start position:0%
+the wood is divided by the modulus of
+ 
+
+ align:start position:0%
+the wood is divided by the modulus of
+the solid cell wall material and here
+
+ align:start position:0%
+the solid cell wall material and here
+ 
+
+ align:start position:0%
+the solid cell wall material and here
+we've we've normalized everything by the
+
+ align:start position:0%
+we've we've normalized everything by the
+ 
+
+ align:start position:0%
+we've we've normalized everything by the
+modulus of the solid cell wall material
+
+ align:start position:0%
+modulus of the solid cell wall material
+ 
+
+ align:start position:0%
+modulus of the solid cell wall material
+in the axial Direction because the cell
+
+ align:start position:0%
+in the axial Direction because the cell
+ 
+
+ align:start position:0%
+in the axial Direction because the cell
+wall itself is
+
+ align:start position:0%
+wall itself is
+ 
+
+ align:start position:0%
+wall itself is
+anisotropic um and so here's the
+
+ align:start position:0%
+anisotropic um and so here's the
+ 
+
+ align:start position:0%
+anisotropic um and so here's the
+relative modulus and here's the relative
+
+ align:start position:0%
+relative modulus and here's the relative
+ 
+
+ align:start position:0%
+relative modulus and here's the relative
+density these are log log plots and we
+
+ align:start position:0%
+density these are log log plots and we
+ 
+
+ align:start position:0%
+density these are log log plots and we
+see that when we load the wood in the
+
+ align:start position:0%
+see that when we load the wood in the
+ 
+
+ align:start position:0%
+see that when we load the wood in the
+axial Direction the modul just linearly
+
+ align:start position:0%
+axial Direction the modul just linearly
+ 
+
+ align:start position:0%
+axial Direction the modul just linearly
+related to the density and we Lo when we
+
+ align:start position:0%
+related to the density and we Lo when we
+ 
+
+ align:start position:0%
+related to the density and we Lo when we
+load it across the grain it varies with
+
+ align:start position:0%
+load it across the grain it varies with
+ 
+
+ align:start position:0%
+load it across the grain it varies with
+the cube of the relative density so do
+
+ align:start position:0%
+the cube of the relative density so do
+ 
+
+ align:start position:0%
+the cube of the relative density so do
+you remember our little honeycomb models
+
+ align:start position:0%
+you remember our little honeycomb models
+ 
+
+ align:start position:0%
+you remember our little honeycomb models
+if I took the honeycomb and I loaded at
+
+ align:start position:0%
+if I took the honeycomb and I loaded at
+ 
+
+ align:start position:0%
+if I took the honeycomb and I loaded at
+this way it went as the cube of T over L
+
+ align:start position:0%
+this way it went as the cube of T over L
+ 
+
+ align:start position:0%
+this way it went as the cube of T over L
+and that's because of the bending and so
+
+ align:start position:0%
+and that's because of the bending and so
+ 
+
+ align:start position:0%
+and that's because of the bending and so
+the wood doesn't lie perfectly on that
+
+ align:start position:0%
+the wood doesn't lie perfectly on that
+ 
+
+ align:start position:0%
+the wood doesn't lie perfectly on that
+Cube line but it's it's fairly close and
+
+ align:start position:0%
+Cube line but it's it's fairly close and
+ 
+
+ align:start position:0%
+Cube line but it's it's fairly close and
+then similarly if we took the honeycomb
+
+ align:start position:0%
+then similarly if we took the honeycomb
+ 
+
+ align:start position:0%
+then similarly if we took the honeycomb
+and we loaded it this way on and it
+
+ align:start position:0%
+and we loaded it this way on and it
+ 
+
+ align:start position:0%
+and we loaded it this way on and it
+deformed actually the modulus depended
+
+ align:start position:0%
+deformed actually the modulus depended
+ 
+
+ align:start position:0%
+deformed actually the modulus depended
+linearly on the um density so you get
+
+ align:start position:0%
+linearly on the um density so you get
+ 
+
+ align:start position:0%
+linearly on the um density so you get
+the same kind of relationships there and
+
+ align:start position:0%
+the same kind of relationships there and
+ 
+
+ align:start position:0%
+the same kind of relationships there and
+then if you look at the strength the
+
+ align:start position:0%
+then if you look at the strength the
+ 
+
+ align:start position:0%
+then if you look at the strength the
+strength along the grain goes linearly
+
+ align:start position:0%
+strength along the grain goes linearly
+ 
+
+ align:start position:0%
+strength along the grain goes linearly
+uh and the strength across the grain
+
+ align:start position:0%
+uh and the strength across the grain
+ 
+
+ align:start position:0%
+uh and the strength across the grain
+goes with the square and uh we'll see
+
+ align:start position:0%
+goes with the square and uh we'll see
+ 
+
+ align:start position:0%
+goes with the square and uh we'll see
+when we get to the modeling in a minute
+
+ align:start position:0%
+when we get to the modeling in a minute
+ 
+
+ align:start position:0%
+when we get to the modeling in a minute
+that if we loaded say an aluminum
+
+ align:start position:0%
+that if we loaded say an aluminum
+ 
+
+ align:start position:0%
+that if we loaded say an aluminum
+honeycomb this way on the strength would
+
+ align:start position:0%
+honeycomb this way on the strength would
+ 
+
+ align:start position:0%
+honeycomb this way on the strength would
+go linearly with the density if we're
+
+ align:start position:0%
+go linearly with the density if we're
+ 
+
+ align:start position:0%
+go linearly with the density if we're
+just yielding the cell walls and if we
+
+ align:start position:0%
+just yielding the cell walls and if we
+ 
+
+ align:start position:0%
+just yielding the cell walls and if we
+loaded it this way on it went as the
+
+ align:start position:0%
+loaded it this way on it went as the
+ 
+
+ align:start position:0%
+loaded it this way on it went as the
+square of T overl so it these things
+
+ align:start position:0%
+square of T overl so it these things
+ 
+
+ align:start position:0%
+square of T overl so it these things
+kind of correspond and you can see the
+
+ align:start position:0%
+kind of correspond and you can see the
+ 
+
+ align:start position:0%
+kind of correspond and you can see the
+structure of the wood is a lot more
+
+ align:start position:0%
+structure of the wood is a lot more
+ 
+
+ align:start position:0%
+structure of the wood is a lot more
+complicated than just a simple honeycomb
+
+ align:start position:0%
+complicated than just a simple honeycomb
+ 
+
+ align:start position:0%
+complicated than just a simple honeycomb
+and so these models are sort of first
+
+ align:start position:0%
+and so these models are sort of first
+ 
+
+ align:start position:0%
+and so these models are sort of first
+order and they're fairly crude they
+
+ align:start position:0%
+order and they're fairly crude they
+ 
+
+ align:start position:0%
+order and they're fairly crude they
+don't try to capture every detail of the
+
+ align:start position:0%
+don't try to capture every detail of the
+ 
+
+ align:start position:0%
+don't try to capture every detail of the
+wood structure uh but they can give you
+
+ align:start position:0%
+wood structure uh but they can give you
+ 
+
+ align:start position:0%
+wood structure uh but they can give you
+a a sense of where the wood properties
+
+ align:start position:0%
+a a sense of where the wood properties
+ 
+
+ align:start position:0%
+a a sense of where the wood properties
+are coming from so let me just write
+
+ align:start position:0%
+are coming from so let me just write
+ 
+
+ align:start position:0%
+are coming from so let me just write
+down some of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observations so the data for the wood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the modulus along the grain goes
+
+ align:start position:0%
+the modulus along the grain goes
+ 
+
+ align:start position:0%
+the modulus along the grain goes
+linearly with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density it goes more or less as the cube
+
+ align:start position:0%
+density it goes more or less as the cube
+ 
+
+ align:start position:0%
+density it goes more or less as the cube
+for loading in the tangential Direction
+
+ align:start position:0%
+for loading in the tangential Direction
+ 
+
+ align:start position:0%
+for loading in the tangential Direction
+and The radial direction is somewhat
+
+ align:start position:0%
+and The radial direction is somewhat
+ 
+
+ align:start position:0%
+and The radial direction is somewhat
+stiffer than that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the strength in the axial
+
+ align:start position:0%
+the strength in the axial
+ 
+
+ align:start position:0%
+the strength in the axial
+Direction goes linearly with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strength across the grain goes with the
+
+ align:start position:0%
+strength across the grain goes with the
+ 
+
+ align:start position:0%
+strength across the grain goes with the
+square of the density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's data for the poson
+
+ align:start position:0%
+and then there's data for the poson
+ 
+
+ align:start position:0%
+and then there's data for the poson
+ratios
+
+ align:start position:0%
+ratios
+ 
+
+ align:start position:0%
+ratios
+too so let me just write them down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the modeling based on the honeycomb
+
+ align:start position:0%
+so the modeling based on the honeycomb
+ 
+
+ align:start position:0%
+so the modeling based on the honeycomb
+is sort of a simplified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model that gives you kind of a first
+
+ align:start position:0%
+model that gives you kind of a first
+ 
+
+ align:start position:0%
+model that gives you kind of a first
+ordered description of the
+
+ align:start position:0%
+ordered description of the
+ 
+
+ align:start position:0%
+ordered description of the
+behavior and it doesn't really attempt
+
+ align:start position:0%
+behavior and it doesn't really attempt
+ 
+
+ align:start position:0%
+behavior and it doesn't really attempt
+to capture all the details of the uh
+
+ align:start position:0%
+to capture all the details of the uh
+ 
+
+ align:start position:0%
+to capture all the details of the uh
+softwood and hardwood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure and in the equations I'm going
+
+ align:start position:0%
+structure and in the equations I'm going
+ 
+
+ align:start position:0%
+structure and in the equations I'm going
+to take the cell wall properties along
+
+ align:start position:0%
+to take the cell wall properties along
+ 
+
+ align:start position:0%
+to take the cell wall properties along
+the grain
+
+ align:start position:0%
+the grain
+ 
+
+ align:start position:0%
+the grain
+or along the axial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction and we're going to have a
+
+ align:start position:0%
+Direction and we're going to have a
+ 
+
+ align:start position:0%
+Direction and we're going to have a
+bunch of constants that describe the
+
+ align:start position:0%
+bunch of constants that describe the
+ 
+
+ align:start position:0%
+bunch of constants that describe the
+cell geometry and those constants are
+
+ align:start position:0%
+cell geometry and those constants are
+ 
+
+ align:start position:0%
+cell geometry and those constants are
+also going to reflect the cell wall an
+
+ align:start position:0%
+also going to reflect the cell wall an
+ 
+
+ align:start position:0%
+also going to reflect the cell wall an
+isotropy and an an isotropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can model the wood structure as
+
+ align:start position:0%
+so we can model the wood structure as
+ 
+
+ align:start position:0%
+so we can model the wood structure as
+something that's a bit more of a
+
+ align:start position:0%
+something that's a bit more of a
+ 
+
+ align:start position:0%
+something that's a bit more of a
+simplified thing just like this and we
+
+ align:start position:0%
+simplified thing just like this and we
+ 
+
+ align:start position:0%
+simplified thing just like this and we
+say we've got cells that are roughly
+
+ align:start position:0%
+say we've got cells that are roughly
+ 
+
+ align:start position:0%
+say we've got cells that are roughly
+hexagonal and then we've got some cells
+
+ align:start position:0%
+hexagonal and then we've got some cells
+ 
+
+ align:start position:0%
+hexagonal and then we've got some cells
+that are more or less rectangular that
+
+ align:start position:0%
+that are more or less rectangular that
+ 
+
+ align:start position:0%
+that are more or less rectangular that
+are the ray cells and if you look at
+
+ align:start position:0%
+are the ray cells and if you look at
+ 
+
+ align:start position:0%
+are the ray cells and if you look at
+lots of micrographs you can get some
+
+ align:start position:0%
+lots of micrographs you can get some
+ 
+
+ align:start position:0%
+lots of micrographs you can get some
+idea what the dimensions of the cells
+
+ align:start position:0%
+idea what the dimensions of the cells
+ 
+
+ align:start position:0%
+idea what the dimensions of the cells
+are and these Dimensions were measured
+
+ align:start position:0%
+are and these Dimensions were measured
+ 
+
+ align:start position:0%
+are and these Dimensions were measured
+for a particular density of bolts of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wood so if we look at the linear elastic
+
+ align:start position:0%
+wood so if we look at the linear elastic
+ 
+
+ align:start position:0%
+wood so if we look at the linear elastic
+modui we can start off with a tangential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loading and if we have the tangential
+
+ align:start position:0%
+loading and if we have the tangential
+ 
+
+ align:start position:0%
+loading and if we have the tangential
+loading we can model it as a honey comb
+
+ align:start position:0%
+loading we can model it as a honey comb
+ 
+
+ align:start position:0%
+loading we can model it as a honey comb
+loaded in the plane and we get cell wall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bending and from the cell wall bending
+
+ align:start position:0%
+bending and from the cell wall bending
+ 
+
+ align:start position:0%
+bending and from the cell wall bending
+and the honeycomb model you would get
+
+ align:start position:0%
+and the honeycomb model you would get
+ 
+
+ align:start position:0%
+and the honeycomb model you would get
+that the tangential modulus varies with
+
+ align:start position:0%
+that the tangential modulus varies with
+ 
+
+ align:start position:0%
+that the tangential modulus varies with
+the relative density
+
+ align:start position:0%
+the relative density
+ 
+
+ align:start position:0%
+the relative density
+cubed and the the structure is not quite
+
+ align:start position:0%
+cubed and the the structure is not quite
+ 
+
+ align:start position:0%
+cubed and the the structure is not quite
+that simple there's Ray cells there's
+
+ align:start position:0%
+that simple there's Ray cells there's
+ 
+
+ align:start position:0%
+that simple there's Ray cells there's
+end caps and they act to stiffen it a
+
+ align:start position:0%
+end caps and they act to stiffen it a
+ 
+
+ align:start position:0%
+end caps and they act to stiffen it a
+little bit and the data lie a little bit
+
+ align:start position:0%
+little bit and the data lie a little bit
+ 
+
+ align:start position:0%
+little bit and the data lie a little bit
+above this line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if we look at the radial loading
+
+ align:start position:0%
+then if we look at the radial loading
+ 
+
+ align:start position:0%
+then if we look at the radial loading
+the the Rays kind of line up with the
+
+ align:start position:0%
+the the Rays kind of line up with the
+ 
+
+ align:start position:0%
+the the Rays kind of line up with the
+radial Direction and the Rays act as
+
+ align:start position:0%
+radial Direction and the Rays act as
+ 
+
+ align:start position:0%
+radial Direction and the Rays act as
+reinforcing plates and so you can just
+
+ align:start position:0%
+reinforcing plates and so you can just
+ 
+
+ align:start position:0%
+reinforcing plates and so you can just
+use kind of an upper bound Composites
+
+ align:start position:0%
+use kind of an upper bound Composites
+ 
+
+ align:start position:0%
+use kind of an upper bound Composites
+idea to get the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modulus and the Rays tend to be a bit
+
+ align:start position:0%
+modulus and the Rays tend to be a bit
+ 
+
+ align:start position:0%
+modulus and the Rays tend to be a bit
+denser than the fibers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I say VR is the volume fraction of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rays and R is the ratio of the relative
+
+ align:start position:0%
+rays and R is the ratio of the relative
+ 
+
+ align:start position:0%
+rays and R is the ratio of the relative
+density of the Rays compared to the
+
+ align:start position:0%
+density of the Rays compared to the
+ 
+
+ align:start position:0%
+density of the Rays compared to the
+fibers so it's row over row s for the
+
+ align:start position:0%
+fibers so it's row over row s for the
+ 
+
+ align:start position:0%
+fibers so it's row over row s for the
+Rays divided by row over row
+
+ align:start position:0%
+Rays divided by row over row
+ 
+
+ align:start position:0%
+Rays divided by row over row
+s for the
+
+ align:start position:0%
+s for the
+ 
+
+ align:start position:0%
+s for the
+fibers and that varies a little bit from
+
+ align:start position:0%
+fibers and that varies a little bit from
+ 
+
+ align:start position:0%
+fibers and that varies a little bit from
+one species to another one specimen to
+
+ align:start position:0%
+one species to another one specimen to
+ 
+
+ align:start position:0%
+one species to another one specimen to
+another but it's something a little over
+
+ align:start position:0%
+another but it's something a little over
+ 
+
+ align:start position:0%
+another but it's something a little over
+one something between one and two then I
+
+ align:start position:0%
+one something between one and two then I
+ 
+
+ align:start position:0%
+one something between one and two then I
+can say the modulus in the radial
+
+ align:start position:0%
+can say the modulus in the radial
+ 
+
+ align:start position:0%
+can say the modulus in the radial
+direction is the volume fraction of the
+
+ align:start position:0%
+direction is the volume fraction of the
+ 
+
+ align:start position:0%
+direction is the volume fraction of the
+Rays time R cubed time the tangential
+
+ align:start position:0%
+Rays time R cubed time the tangential
+ 
+
+ align:start position:0%
+Rays time R cubed time the tangential
+modulus plus 1 minus the volume fraction
+
+ align:start position:0%
+modulus plus 1 minus the volume fraction
+ 
+
+ align:start position:0%
+modulus plus 1 minus the volume fraction
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+rays times the tangential modulus and
+
+ align:start position:0%
+rays times the tangential modulus and
+ 
+
+ align:start position:0%
+rays times the tangential modulus and
+that works out to be about 1.5
+
+ align:start position:0%
+that works out to be about 1.5
+ 
+
+ align:start position:0%
+that works out to be about 1.5
+* the tangential modulus I wanted to
+
+ align:start position:0%
+* the tangential modulus I wanted to
+ 
+
+ align:start position:0%
+* the tangential modulus I wanted to
+work this out in terms of the tangential
+
+ align:start position:0%
+work this out in terms of the tangential
+ 
+
+ align:start position:0%
+work this out in terms of the tangential
+modulus so I've put this in terms of the
+
+ align:start position:0%
+modulus so I've put this in terms of the
+ 
+
+ align:start position:0%
+modulus so I've put this in terms of the
+tangential modulus in the first term
+
+ align:start position:0%
+tangential modulus in the first term
+ 
+
+ align:start position:0%
+tangential modulus in the first term
+there so we get that the radial modulus
+
+ align:start position:0%
+there so we get that the radial modulus
+ 
+
+ align:start position:0%
+there so we get that the radial modulus
+is slightly larger than the tangential
+
+ align:start position:0%
+is slightly larger than the tangential
+ 
+
+ align:start position:0%
+is slightly larger than the tangential
+but also goes roughly as the cube of the
+
+ align:start position:0%
+but also goes roughly as the cube of the
+ 
+
+ align:start position:0%
+but also goes roughly as the cube of the
+density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then for the axial loading we just
+
+ align:start position:0%
+and then for the axial loading we just
+ 
+
+ align:start position:0%
+and then for the axial loading we just
+have axial deformation in the cell wall
+
+ align:start position:0%
+have axial deformation in the cell wall
+ 
+
+ align:start position:0%
+have axial deformation in the cell wall
+and the and the young modules just
+
+ align:start position:0%
+and the and the young modules just
+ 
+
+ align:start position:0%
+and the and the young modules just
+varies linearly with the density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are kind of simple models but
+
+ align:start position:0%
+so these are kind of simple models but
+ 
+
+ align:start position:0%
+so these are kind of simple models but
+they kind of explain to first order the
+
+ align:start position:0%
+they kind of explain to first order the
+ 
+
+ align:start position:0%
+they kind of explain to first order the
+density dependence of the wood moduli
+
+ align:start position:0%
+density dependence of the wood moduli
+ 
+
+ align:start position:0%
+density dependence of the wood moduli
+and the anisotropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's kind of nice cuz they're fairly
+
+ align:start position:0%
+so it's kind of nice cuz they're fairly
+ 
+
+ align:start position:0%
+so it's kind of nice cuz they're fairly
+simple models and that gives you kind of
+
+ align:start position:0%
+simple models and that gives you kind of
+ 
+
+ align:start position:0%
+simple models and that gives you kind of
+a big picture so if you wanted to know
+
+ align:start position:0%
+a big picture so if you wanted to know
+ 
+
+ align:start position:0%
+a big picture so if you wanted to know
+the modulus of a particular piece of
+
+ align:start position:0%
+the modulus of a particular piece of
+ 
+
+ align:start position:0%
+the modulus of a particular piece of
+wood this probably isn't the best way to
+
+ align:start position:0%
+wood this probably isn't the best way to
+ 
+
+ align:start position:0%
+wood this probably isn't the best way to
+figure it out but if you wanted to kind
+
+ align:start position:0%
+figure it out but if you wanted to kind
+ 
+
+ align:start position:0%
+figure it out but if you wanted to kind
+of compare how the woods behave in
+
+ align:start position:0%
+of compare how the woods behave in
+ 
+
+ align:start position:0%
+of compare how the woods behave in
+general and how does the density affect
+
+ align:start position:0%
+general and how does the density affect
+ 
+
+ align:start position:0%
+general and how does the density affect
+the properties and why are they an
+
+ align:start position:0%
+the properties and why are they an
+ 
+
+ align:start position:0%
+the properties and why are they an
+isotropic this is a pretty good way to
+
+ align:start position:0%
+isotropic this is a pretty good way to
+ 
+
+ align:start position:0%
+isotropic this is a pretty good way to
+do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we could also look at the puin ratios
+
+ align:start position:0%
+we could also look at the puin ratios
+ 
+
+ align:start position:0%
+we could also look at the puin ratios
+and just because I didn't want to write
+
+ align:start position:0%
+and just because I didn't want to write
+ 
+
+ align:start position:0%
+and just because I didn't want to write
+them down again I've just left on what
+
+ align:start position:0%
+them down again I've just left on what
+ 
+
+ align:start position:0%
+them down again I've just left on what
+the data were down here but let me just
+
+ align:start position:0%
+the data were down here but let me just
+ 
+
+ align:start position:0%
+the data were down here but let me just
+write what the model would give
+
+ align:start position:0%
+write what the model would give
+ 
+
+ align:start position:0%
+write what the model would give
+us uh for new RT and new
+
+ align:start position:0%
+us uh for new RT and new
+ 
+
+ align:start position:0%
+us uh for new RT and new
+TR the model would give us one if we had
+
+ align:start position:0%
+TR the model would give us one if we had
+ 
+
+ align:start position:0%
+TR the model would give us one if we had
+regular hexagonal cells uh and these are
+
+ align:start position:0%
+regular hexagonal cells uh and these are
+ 
+
+ align:start position:0%
+regular hexagonal cells uh and these are
+the values we get here this might be you
+
+ align:start position:0%
+the values we get here this might be you
+ 
+
+ align:start position:0%
+the values we get here this might be you
+know 6.7 would be a typical value
+
+ align:start position:0%
+know 6.7 would be a typical value
+ 
+
+ align:start position:0%
+know 6.7 would be a typical value
+somewhere around 04 in there so they're
+
+ align:start position:0%
+somewhere around 04 in there so they're
+ 
+
+ align:start position:0%
+somewhere around 04 in there so they're
+not quite one but they're close to it
+
+ align:start position:0%
+not quite one but they're close to it
+ 
+
+ align:start position:0%
+not quite one but they're close to it
+and I think uh the reason they're a
+
+ align:start position:0%
+and I think uh the reason they're a
+ 
+
+ align:start position:0%
+and I think uh the reason they're a
+little less is because the Rays and the
+
+ align:start position:0%
+little less is because the Rays and the
+ 
+
+ align:start position:0%
+little less is because the Rays and the
+end caps provide some constraint and you
+
+ align:start position:0%
+end caps provide some constraint and you
+ 
+
+ align:start position:0%
+end caps provide some constraint and you
+don't you know if you have the honeycomb
+
+ align:start position:0%
+don't you know if you have the honeycomb
+ 
+
+ align:start position:0%
+don't you know if you have the honeycomb
+if I just had these cells and I I
+
+ align:start position:0%
+if I just had these cells and I I
+ 
+
+ align:start position:0%
+if I just had these cells and I I
+squeeze it like this these guys can move
+
+ align:start position:0%
+squeeze it like this these guys can move
+ 
+
+ align:start position:0%
+squeeze it like this these guys can move
+out and if it's a regular hexagonal
+
+ align:start position:0%
+out and if it's a regular hexagonal
+ 
+
+ align:start position:0%
+out and if it's a regular hexagonal
+honeycomb The Strain that I'm applying
+
+ align:start position:0%
+honeycomb The Strain that I'm applying
+ 
+
+ align:start position:0%
+honeycomb The Strain that I'm applying
+here is equal to the strain going out
+
+ align:start position:0%
+here is equal to the strain going out
+ 
+
+ align:start position:0%
+here is equal to the strain going out
+that way but if I have Rays this way
+
+ align:start position:0%
+that way but if I have Rays this way
+ 
+
+ align:start position:0%
+that way but if I have Rays this way
+that sort of constrain it or encaps uh
+
+ align:start position:0%
+that sort of constrain it or encaps uh
+ 
+
+ align:start position:0%
+that sort of constrain it or encaps uh
+it means that the plus ratio is going to
+
+ align:start position:0%
+it means that the plus ratio is going to
+ 
+
+ align:start position:0%
+it means that the plus ratio is going to
+be a little bit
+
+ align:start position:0%
+be a little bit
+ 
+
+ align:start position:0%
+be a little bit
+less so I'll just say constraining
+
+ align:start position:0%
+less so I'll just say constraining
+ 
+
+ align:start position:0%
+less so I'll just say constraining
+effect of the end caps and
+
+ align:start position:0%
+effect of the end caps and
+ 
+
+ align:start position:0%
+effect of the end caps and
+Rays constraining
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then for
+
+ align:start position:0%
+then for
+ 
+
+ align:start position:0%
+then for
+new ra and new
+
+ align:start position:0%
+new ra and new
+ 
+
+ align:start position:0%
+new ra and new
+ta the model
+
+ align:start position:0%
+ta the model
+ 
+
+ align:start position:0%
+ta the model
+says the value we would get be zero and
+
+ align:start position:0%
+says the value we would get be zero and
+ 
+
+ align:start position:0%
+says the value we would get be zero and
+these are pretty close to zero they're
+
+ align:start position:0%
+these are pretty close to zero they're
+ 
+
+ align:start position:0%
+these are pretty close to zero they're
+not quite zero but pretty
+
+ align:start position:0%
+not quite zero but pretty
+ 
+
+ align:start position:0%
+not quite zero but pretty
+close and then the last
+
+ align:start position:0%
+close and then the last
+ 
+
+ align:start position:0%
+close and then the last
+pair new a
+
+ align:start position:0%
+pair new a
+ 
+
+ align:start position:0%
+pair new a
+r and new a
+
+ align:start position:0%
+r and new a
+ 
+
+ align:start position:0%
+r and new a
+t the model says that we would get new
+
+ align:start position:0%
+t the model says that we would get new
+ 
+
+ align:start position:0%
+t the model says that we would get new
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solid and the data is close to
+
+ align:start position:0%
+solid and the data is close to
+ 
+
+ align:start position:0%
+solid and the data is close to
+0.4 which you might expect would be
+
+ align:start position:0%
+0.4 which you might expect would be
+ 
+
+ align:start position:0%
+0.4 which you might expect would be
+about the new of the solid so again
+
+ align:start position:0%
+about the new of the solid so again
+ 
+
+ align:start position:0%
+about the new of the solid so again
+there's some variation in the proon
+
+ align:start position:0%
+there's some variation in the proon
+ 
+
+ align:start position:0%
+there's some variation in the proon
+ratios not all just one number but you
+
+ align:start position:0%
+ratios not all just one number but you
+ 
+
+ align:start position:0%
+ratios not all just one number but you
+can see you know these these ones here
+
+ align:start position:0%
+can see you know these these ones here
+ 
+
+ align:start position:0%
+can see you know these these ones here
+are about zero and that's roughly what
+
+ align:start position:0%
+are about zero and that's roughly what
+ 
+
+ align:start position:0%
+are about zero and that's roughly what
+the model says these ones here are
+
+ align:start position:0%
+the model says these ones here are
+ 
+
+ align:start position:0%
+the model says these ones here are
+closer to one uh and then these ones
+
+ align:start position:0%
+closer to one uh and then these ones
+ 
+
+ align:start position:0%
+closer to one uh and then these ones
+here are closer to what you might expect
+
+ align:start position:0%
+here are closer to what you might expect
+ 
+
+ align:start position:0%
+here are closer to what you might expect
+for a solid material so it gives you the
+
+ align:start position:0%
+for a solid material so it gives you the
+ 
+
+ align:start position:0%
+for a solid material so it gives you the
+kind of General general idea are we good
+
+ align:start position:0%
+kind of General general idea are we good
+ 
+
+ align:start position:0%
+kind of General general idea are we good
+we're good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so we can do a similar thing for
+
+ align:start position:0%
+yeah so we can do a similar thing for
+ 
+
+ align:start position:0%
+yeah so we can do a similar thing for
+the compressive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strength uh so for tangential loading we
+
+ align:start position:0%
+strength uh so for tangential loading we
+ 
+
+ align:start position:0%
+strength uh so for tangential loading we
+get plas the hinges forming in the men
+
+ align:start position:0%
+get plas the hinges forming in the men
+ 
+
+ align:start position:0%
+get plas the hinges forming in the men
+cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+walls just like in an aluminum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+honeycomb and we get that the
+
+ align:start position:0%
+honeycomb and we get that the
+ 
+
+ align:start position:0%
+honeycomb and we get that the
+strength over the cell wall
+
+ align:start position:0%
+strength over the cell wall
+ 
+
+ align:start position:0%
+strength over the cell wall
+strength goes into the relative density
+
+ align:start position:0%
+strength goes into the relative density
+ 
+
+ align:start position:0%
+strength goes into the relative density
+squared so just like the honeycomb for
+
+ align:start position:0%
+squared so just like the honeycomb for
+ 
+
+ align:start position:0%
+squared so just like the honeycomb for
+the radial loading we can do the
+
+ align:start position:0%
+the radial loading we can do the
+ 
+
+ align:start position:0%
+the radial loading we can do the
+Composites thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again so we can say the strength in the
+
+ align:start position:0%
+again so we can say the strength in the
+ 
+
+ align:start position:0%
+again so we can say the strength in the
+radial direction is about equal to the
+
+ align:start position:0%
+radial direction is about equal to the
+ 
+
+ align:start position:0%
+radial direction is about equal to the
+volume fraction of rays time r squared
+
+ align:start position:0%
+volume fraction of rays time r squared
+ 
+
+ align:start position:0%
+volume fraction of rays time r squared
+time the tangential strength plus 1
+
+ align:start position:0%
+time the tangential strength plus 1
+ 
+
+ align:start position:0%
+time the tangential strength plus 1
+minus the volume fraction of rays time
+
+ align:start position:0%
+minus the volume fraction of rays time
+ 
+
+ align:start position:0%
+minus the volume fraction of rays time
+the tangential strength and for
+
+ align:start position:0%
+the tangential strength and for
+ 
+
+ align:start position:0%
+the tangential strength and for
+Balsa we have some values here VR is
+
+ align:start position:0%
+Balsa we have some values here VR is
+ 
+
+ align:start position:0%
+Balsa we have some values here VR is
+about equal to one or
+
+ align:start position:0%
+about equal to one or
+ 
+
+ align:start position:0%
+about equal to one or
+0.14 R is about equal to two and so the
+
+ align:start position:0%
+0.14 R is about equal to two and so the
+ 
+
+ align:start position:0%
+0.14 R is about equal to two and so the
+radial
+
+ align:start position:0%
+radial
+ 
+
+ align:start position:0%
+radial
+strength is about equal to 1.4 * the
+
+ align:start position:0%
+strength is about equal to 1.4 * the
+ 
+
+ align:start position:0%
+strength is about equal to 1.4 * the
+tangential and in higher density Woods
+
+ align:start position:0%
+tangential and in higher density Woods
+ 
+
+ align:start position:0%
+tangential and in higher density Woods
+the value of R is a little bit smaller
+
+ align:start position:0%
+the value of R is a little bit smaller
+ 
+
+ align:start position:0%
+the value of R is a little bit smaller
+and in general the radial strength is a
+
+ align:start position:0%
+and in general the radial strength is a
+ 
+
+ align:start position:0%
+and in general the radial strength is a
+bit larger than the tangential and both
+
+ align:start position:0%
+bit larger than the tangential and both
+ 
+
+ align:start position:0%
+bit larger than the tangential and both
+depend on the density squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+then and then for axial
+
+ align:start position:0%
+then and then for axial
+ 
+
+ align:start position:0%
+then and then for axial
+loading if the failure is initiated by
+
+ align:start position:0%
+loading if the failure is initiated by
+ 
+
+ align:start position:0%
+loading if the failure is initiated by
+yielding the cell walls then the actual
+
+ align:start position:0%
+yielding the cell walls then the actual
+ 
+
+ align:start position:0%
+yielding the cell walls then the actual
+strength is just going to depend
+
+ align:start position:0%
+strength is just going to depend
+ 
+
+ align:start position:0%
+strength is just going to depend
+linearly on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density okay
+
+ align:start position:0%
+density okay
+ 
+
+ align:start position:0%
+density okay
+so the idea with these models isn't that
+
+ align:start position:0%
+so the idea with these models isn't that
+ 
+
+ align:start position:0%
+so the idea with these models isn't that
+they kind of describe a particular um
+
+ align:start position:0%
+they kind of describe a particular um
+ 
+
+ align:start position:0%
+they kind of describe a particular um
+you know particular piece of wood
+
+ align:start position:0%
+you know particular piece of wood
+ 
+
+ align:start position:0%
+you know particular piece of wood
+exactly it's more that it gives you a
+
+ align:start position:0%
+exactly it's more that it gives you a
+ 
+
+ align:start position:0%
+exactly it's more that it gives you a
+general picture of how the cells are
+
+ align:start position:0%
+general picture of how the cells are
+ 
+
+ align:start position:0%
+general picture of how the cells are
+deforming and failing and how the
+
+ align:start position:0%
+deforming and failing and how the
+ 
+
+ align:start position:0%
+deforming and failing and how the
+properties scale with density and why
+
+ align:start position:0%
+properties scale with density and why
+ 
+
+ align:start position:0%
+properties scale with density and why
+the woods an isotropic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are we good y caught up okay so there's
+
+ align:start position:0%
+are we good y caught up okay so there's
+ 
+
+ align:start position:0%
+are we good y caught up okay so there's
+a couple more sort of interesting things
+
+ align:start position:0%
+a couple more sort of interesting things
+ 
+
+ align:start position:0%
+a couple more sort of interesting things
+we can do uh with looking at the wood
+
+ align:start position:0%
+we can do uh with looking at the wood
+ 
+
+ align:start position:0%
+we can do uh with looking at the wood
+properties so we've been talking about
+
+ align:start position:0%
+properties so we've been talking about
+ 
+
+ align:start position:0%
+properties so we've been talking about
+how to model the cellular structure but
+
+ align:start position:0%
+how to model the cellular structure but
+ 
+
+ align:start position:0%
+how to model the cellular structure but
+people have also looked at how to model
+
+ align:start position:0%
+people have also looked at how to model
+ 
+
+ align:start position:0%
+people have also looked at how to model
+the cell wall as a fiber composite and
+
+ align:start position:0%
+the cell wall as a fiber composite and
+ 
+
+ align:start position:0%
+the cell wall as a fiber composite and
+this plot and the next one kind of show
+
+ align:start position:0%
+this plot and the next one kind of show
+ 
+
+ align:start position:0%
+this plot and the next one kind of show
+you how you can can combine all of that
+
+ align:start position:0%
+you how you can can combine all of that
+ 
+
+ align:start position:0%
+you how you can can combine all of that
+together so remember I said the modulus
+
+ align:start position:0%
+together so remember I said the modulus
+ 
+
+ align:start position:0%
+together so remember I said the modulus
+of the cellulose was around 140 gigap
+
+ align:start position:0%
+of the cellulose was around 140 gigap
+ 
+
+ align:start position:0%
+of the cellulose was around 140 gigap
+pascals so here's the modulus of the
+
+ align:start position:0%
+pascals so here's the modulus of the
+ 
+
+ align:start position:0%
+pascals so here's the modulus of the
+cellulose um at least the crystalline
+
+ align:start position:0%
+cellulose um at least the crystalline
+ 
+
+ align:start position:0%
+cellulose um at least the crystalline
+part of the cellulose plotted in that
+
+ align:start position:0%
+part of the cellulose plotted in that
+ 
+
+ align:start position:0%
+part of the cellulose plotted in that
+little envelope there the ligan and the
+
+ align:start position:0%
+little envelope there the ligan and the
+ 
+
+ align:start position:0%
+little envelope there the ligan and the
+hemicellulose have a modulus around two
+
+ align:start position:0%
+hemicellulose have a modulus around two
+ 
+
+ align:start position:0%
+hemicellulose have a modulus around two
+or 3 gigap Pascal so it's down there and
+
+ align:start position:0%
+or 3 gigap Pascal so it's down there and
+ 
+
+ align:start position:0%
+or 3 gigap Pascal so it's down there and
+if you made Composites with cellulose
+
+ align:start position:0%
+if you made Composites with cellulose
+ 
+
+ align:start position:0%
+if you made Composites with cellulose
+fibers in ligan and hemicellulose Matrix
+
+ align:start position:0%
+fibers in ligan and hemicellulose Matrix
+ 
+
+ align:start position:0%
+fibers in ligan and hemicellulose Matrix
+those Composites would have a modulus
+
+ align:start position:0%
+those Composites would have a modulus
+ 
+
+ align:start position:0%
+those Composites would have a modulus
+that fell in this envelope here they've
+
+ align:start position:0%
+that fell in this envelope here they've
+ 
+
+ align:start position:0%
+that fell in this envelope here they've
+got to be in between those two limits
+
+ align:start position:0%
+got to be in between those two limits
+ 
+
+ align:start position:0%
+got to be in between those two limits
+right the modulus have to be between
+
+ align:start position:0%
+right the modulus have to be between
+ 
+
+ align:start position:0%
+right the modulus have to be between
+those two limits the density have to be
+
+ align:start position:0%
+those two limits the density have to be
+ 
+
+ align:start position:0%
+those two limits the density have to be
+within the densities of the
+
+ align:start position:0%
+within the densities of the
+ 
+
+ align:start position:0%
+within the densities of the
+constituents and if you look at the
+
+ align:start position:0%
+constituents and if you look at the
+ 
+
+ align:start position:0%
+constituents and if you look at the
+modulus of the wood cell wall it lies in
+
+ align:start position:0%
+modulus of the wood cell wall it lies in
+ 
+
+ align:start position:0%
+modulus of the wood cell wall it lies in
+this envelope here the along the grain
+
+ align:start position:0%
+this envelope here the along the grain
+ 
+
+ align:start position:0%
+this envelope here the along the grain
+would be here and then across the grain
+
+ align:start position:0%
+would be here and then across the grain
+ 
+
+ align:start position:0%
+would be here and then across the grain
+is further down here so the cell wall
+
+ align:start position:0%
+is further down here so the cell wall
+ 
+
+ align:start position:0%
+is further down here so the cell wall
+modulus is in here and then if you take
+
+ align:start position:0%
+modulus is in here and then if you take
+ 
+
+ align:start position:0%
+modulus is in here and then if you take
+that cell wall and you make it into the
+
+ align:start position:0%
+that cell wall and you make it into the
+ 
+
+ align:start position:0%
+that cell wall and you make it into the
+honeycomb type material that wood is if
+
+ align:start position:0%
+honeycomb type material that wood is if
+ 
+
+ align:start position:0%
+honeycomb type material that wood is if
+you load it along the grain you're going
+
+ align:start position:0%
+you load it along the grain you're going
+ 
+
+ align:start position:0%
+you load it along the grain you're going
+to get this linear dependence of U
+
+ align:start position:0%
+to get this linear dependence of U
+ 
+
+ align:start position:0%
+to get this linear dependence of U
+modulus on density and if you load it
+
+ align:start position:0%
+modulus on density and if you load it
+ 
+
+ align:start position:0%
+modulus on density and if you load it
+across the Grain in the radial or the
+
+ align:start position:0%
+across the Grain in the radial or the
+ 
+
+ align:start position:0%
+across the Grain in the radial or the
+tangential Direction you're going to get
+
+ align:start position:0%
+tangential Direction you're going to get
+ 
+
+ align:start position:0%
+tangential Direction you're going to get
+this Cube dependence here so here's a
+
+ align:start position:0%
+this Cube dependence here so here's a
+ 
+
+ align:start position:0%
+this Cube dependence here so here's a
+set of data for different Woods of
+
+ align:start position:0%
+set of data for different Woods of
+ 
+
+ align:start position:0%
+set of data for different Woods of
+different densities and that envelope
+
+ align:start position:0%
+different densities and that envelope
+ 
+
+ align:start position:0%
+different densities and that envelope
+kind of um encompasses all of them uh
+
+ align:start position:0%
+kind of um encompasses all of them uh
+ 
+
+ align:start position:0%
+kind of um encompasses all of them uh
+but if you if you look at the slope of
+
+ align:start position:0%
+but if you if you look at the slope of
+ 
+
+ align:start position:0%
+but if you if you look at the slope of
+that data it's roughly equal to a slope
+
+ align:start position:0%
+that data it's roughly equal to a slope
+ 
+
+ align:start position:0%
+that data it's roughly equal to a slope
+of one and so it corresponds to that
+
+ align:start position:0%
+of one and so it corresponds to that
+ 
+
+ align:start position:0%
+of one and so it corresponds to that
+equation there and similarly here's a a
+
+ align:start position:0%
+equation there and similarly here's a a
+ 
+
+ align:start position:0%
+equation there and similarly here's a a
+set of data for different species of
+
+ align:start position:0%
+set of data for different species of
+ 
+
+ align:start position:0%
+set of data for different species of
+woods of different densities loaded
+
+ align:start position:0%
+woods of different densities loaded
+ 
+
+ align:start position:0%
+woods of different densities loaded
+perpendicular to the Grain and they lie
+
+ align:start position:0%
+perpendicular to the Grain and they lie
+ 
+
+ align:start position:0%
+perpendicular to the Grain and they lie
+on a line that has more or less a slope
+
+ align:start position:0%
+on a line that has more or less a slope
+ 
+
+ align:start position:0%
+on a line that has more or less a slope
+of three and this set of data here along
+
+ align:start position:0%
+of three and this set of data here along
+ 
+
+ align:start position:0%
+of three and this set of data here along
+the grain intersects the wood cell wall
+
+ align:start position:0%
+the grain intersects the wood cell wall
+ 
+
+ align:start position:0%
+the grain intersects the wood cell wall
+sort of towards the top of that envelope
+
+ align:start position:0%
+sort of towards the top of that envelope
+ 
+
+ align:start position:0%
+sort of towards the top of that envelope
+and this set of data here intersects
+
+ align:start position:0%
+and this set of data here intersects
+ 
+
+ align:start position:0%
+and this set of data here intersects
+closer to the bottom of that set of that
+
+ align:start position:0%
+closer to the bottom of that set of that
+ 
+
+ align:start position:0%
+closer to the bottom of that set of that
+envelope for the C wall material so this
+
+ align:start position:0%
+envelope for the C wall material so this
+ 
+
+ align:start position:0%
+envelope for the C wall material so this
+gives a way of sort of putting
+
+ align:start position:0%
+gives a way of sort of putting
+ 
+
+ align:start position:0%
+gives a way of sort of putting
+everything together on one plot the cell
+
+ align:start position:0%
+everything together on one plot the cell
+ 
+
+ align:start position:0%
+everything together on one plot the cell
+wall as well as the cellular structure
+
+ align:start position:0%
+wall as well as the cellular structure
+ 
+
+ align:start position:0%
+wall as well as the cellular structure
+so that plot does it for the modulus and
+
+ align:start position:0%
+so that plot does it for the modulus and
+ 
+
+ align:start position:0%
+so that plot does it for the modulus and
+you can do the same kind of thing for
+
+ align:start position:0%
+you can do the same kind of thing for
+ 
+
+ align:start position:0%
+you can do the same kind of thing for
+the strength here's the cellulose up
+
+ align:start position:0%
+the strength here's the cellulose up
+ 
+
+ align:start position:0%
+the strength here's the cellulose up
+here here's the lignin down there here's
+
+ align:start position:0%
+here here's the lignin down there here's
+ 
+
+ align:start position:0%
+here here's the lignin down there here's
+the wood cell wall but composite made
+
+ align:start position:0%
+the wood cell wall but composite made
+ 
+
+ align:start position:0%
+the wood cell wall but composite made
+from those two and then here's data for
+
+ align:start position:0%
+from those two and then here's data for
+ 
+
+ align:start position:0%
+from those two and then here's data for
+different kinds of woods loaded along
+
+ align:start position:0%
+different kinds of woods loaded along
+ 
+
+ align:start position:0%
+different kinds of woods loaded along
+the Grain and for loaded across the
+
+ align:start position:0%
+the Grain and for loaded across the
+ 
+
+ align:start position:0%
+the Grain and for loaded across the
+grain so it gives you a way of kind of
+
+ align:start position:0%
+grain so it gives you a way of kind of
+ 
+
+ align:start position:0%
+grain so it gives you a way of kind of
+putting all of this modeling into one
+
+ align:start position:0%
+putting all of this modeling into one
+ 
+
+ align:start position:0%
+putting all of this modeling into one
+set of plots uh so let me just write a
+
+ align:start position:0%
+set of plots uh so let me just write a
+ 
+
+ align:start position:0%
+set of plots uh so let me just write a
+couple of little things about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so we could say you could model the
+
+ align:start position:0%
+that so we could say you could model the
+ 
+
+ align:start position:0%
+that so we could say you could model the
+cell wall as a fiber composite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can use the composite upper and
+
+ align:start position:0%
+and you can use the composite upper and
+ 
+
+ align:start position:0%
+and you can use the composite upper and
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+bounds to give an envelope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you can also
+
+ align:start position:0%
+and then you can also
+ 
+
+ align:start position:0%
+and then you can also
+show the cellular solids models on the
+
+ align:start position:0%
+show the cellular solids models on the
+ 
+
+ align:start position:0%
+show the cellular solids models on the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plot so overall it shows you how the
+
+ align:start position:0%
+plot so overall it shows you how the
+ 
+
+ align:start position:0%
+plot so overall it shows you how the
+hierarchical structure fits together um
+
+ align:start position:0%
+hierarchical structure fits together um
+ 
+
+ align:start position:0%
+hierarchical structure fits together um
+can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modeled
+
+ align:start position:0%
+modeled
+ 
+
+ align:start position:0%
+modeled
+okay now there's some more cute things
+
+ align:start position:0%
+okay now there's some more cute things
+ 
+
+ align:start position:0%
+okay now there's some more cute things
+we can see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh so another thing I wanted to talk
+
+ align:start position:0%
+oh so another thing I wanted to talk
+ 
+
+ align:start position:0%
+oh so another thing I wanted to talk
+about about is material selection
+
+ align:start position:0%
+about about is material selection
+ 
+
+ align:start position:0%
+about about is material selection
+because it turns out wood is very good
+
+ align:start position:0%
+because it turns out wood is very good
+ 
+
+ align:start position:0%
+because it turns out wood is very good
+compared to other materials in certain
+
+ align:start position:0%
+compared to other materials in certain
+ 
+
+ align:start position:0%
+compared to other materials in certain
+applications so we're going to look at
+
+ align:start position:0%
+applications so we're going to look at
+ 
+
+ align:start position:0%
+applications so we're going to look at
+say having a beam of a given stiffness
+
+ align:start position:0%
+say having a beam of a given stiffness
+ 
+
+ align:start position:0%
+say having a beam of a given stiffness
+and a given span and say it's just a
+
+ align:start position:0%
+and a given span and say it's just a
+ 
+
+ align:start position:0%
+and a given span and say it's just a
+rectangular or a square cross-section
+
+ align:start position:0%
+rectangular or a square cross-section
+ 
+
+ align:start position:0%
+rectangular or a square cross-section
+beam of edge length T and the question
+
+ align:start position:0%
+beam of edge length T and the question
+ 
+
+ align:start position:0%
+beam of edge length T and the question
+is what material would minimize the mass
+
+ align:start position:0%
+is what material would minimize the mass
+ 
+
+ align:start position:0%
+is what material would minimize the mass
+of the beam so say we have you know some
+
+ align:start position:0%
+of the beam so say we have you know some
+ 
+
+ align:start position:0%
+of the beam so say we have you know some
+span we have to have it's got to have
+
+ align:start position:0%
+span we have to have it's got to have
+ 
+
+ align:start position:0%
+span we have to have it's got to have
+some rectangular cross-section um some
+
+ align:start position:0%
+some rectangular cross-section um some
+ 
+
+ align:start position:0%
+some rectangular cross-section um some
+given stiffness and the question is
+
+ align:start position:0%
+given stiffness and the question is
+ 
+
+ align:start position:0%
+given stiffness and the question is
+what's the material that minimizes the
+
+ align:start position:0%
+what's the material that minimizes the
+ 
+
+ align:start position:0%
+what's the material that minimizes the
+mass so there's a little short
+
+ align:start position:0%
+mass so there's a little short
+ 
+
+ align:start position:0%
+mass so there's a little short
+calculation we can do to figure that out
+
+ align:start position:0%
+calculation we can do to figure that out
+ 
+
+ align:start position:0%
+calculation we can do to figure that out
+and then I've got another plot and you
+
+ align:start position:0%
+and then I've got another plot and you
+ 
+
+ align:start position:0%
+and then I've got another plot and you
+can compare different materials on this
+
+ align:start position:0%
+can compare different materials on this
+ 
+
+ align:start position:0%
+can compare different materials on this
+other plot and you'll see how how good
+
+ align:start position:0%
+other plot and you'll see how how good
+ 
+
+ align:start position:0%
+other plot and you'll see how how good
+wood is compared to other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+materials so for a beam of a given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stiffness a given
+
+ align:start position:0%
+stiffness a given
+ 
+
+ align:start position:0%
+stiffness a given
+span and say it's a square cross-section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the question is what material
+
+ align:start position:0%
+then the question is what material
+ 
+
+ align:start position:0%
+then the question is what material
+minimizes the mass of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam you guys okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the mass is just going to be the
+
+ align:start position:0%
+so the mass is just going to be the
+ 
+
+ align:start position:0%
+so the mass is just going to be the
+density * T ^2 *
+
+ align:start position:0%
+density * T ^2 *
+ 
+
+ align:start position:0%
+density * T ^2 *
+L and if it's a beam say it's got some
+
+ align:start position:0%
+L and if it's a beam say it's got some
+ 
+
+ align:start position:0%
+L and if it's a beam say it's got some
+Central load on it concentrated load the
+
+ align:start position:0%
+Central load on it concentrated load the
+ 
+
+ align:start position:0%
+Central load on it concentrated load the
+deflection is going to go as PL
+
+ align:start position:0%
+deflection is going to go as PL
+ 
+
+ align:start position:0%
+deflection is going to go as PL
+cubed divided by some constant and
+
+ align:start position:0%
+cubed divided by some constant and
+ 
+
+ align:start position:0%
+cubed divided by some constant and
+divided by the Young's modulus and the
+
+ align:start position:0%
+divided by the Young's modulus and the
+ 
+
+ align:start position:0%
+divided by the Young's modulus and the
+moment of inertia
+
+ align:start position:0%
+moment of inertia
+ 
+
+ align:start position:0%
+moment of inertia
+I so the stiffness if I just rearrange
+
+ align:start position:0%
+I so the stiffness if I just rearrange
+ 
+
+ align:start position:0%
+I so the stiffness if I just rearrange
+this the stiffness p over Delta
+
+ align:start position:0%
+this the stiffness p over Delta
+ 
+
+ align:start position:0%
+this the stiffness p over Delta
+that's going to go as u p over
+
+ align:start position:0%
+that's going to go as u p over
+ 
+
+ align:start position:0%
+that's going to go as u p over
+Delta CI and I is going to go as t to
+
+ align:start position:0%
+Delta CI and I is going to go as t to
+ 
+
+ align:start position:0%
+Delta CI and I is going to go as t to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+4th over L cubed and then I can solve
+
+ align:start position:0%
+4th over L cubed and then I can solve
+ 
+
+ align:start position:0%
+4th over L cubed and then I can solve
+that for t^2 and I I want t^2 because
+
+ align:start position:0%
+that for t^2 and I I want t^2 because
+ 
+
+ align:start position:0%
+that for t^2 and I I want t^2 because
+I'm going to plug it back into the
+
+ align:start position:0%
+I'm going to plug it back into the
+ 
+
+ align:start position:0%
+I'm going to plug it back into the
+equation for the mass so if I solve this
+
+ align:start position:0%
+equation for the mass so if I solve this
+ 
+
+ align:start position:0%
+equation for the mass so if I solve this
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+t^2 I've got my stiffness p over Delta
+
+ align:start position:0%
+t^2 I've got my stiffness p over Delta
+ 
+
+ align:start position:0%
+t^2 I've got my stiffness p over Delta
+I've got L cubed divided by c
+
+ align:start position:0%
+I've got L cubed divided by c
+ 
+
+ align:start position:0%
+I've got L cubed divided by c
+e and then I take that whole thing the
+
+ align:start position:0%
+e and then I take that whole thing the
+ 
+
+ align:start position:0%
+e and then I take that whole thing the
+1/2 power like that and then I plug the
+
+ align:start position:0%
+1/2 power like that and then I plug the
+ 
+
+ align:start position:0%
+1/2 power like that and then I plug the
+t^2 back into the little equation for
+
+ align:start position:0%
+t^2 back into the little equation for
+ 
+
+ align:start position:0%
+t^2 back into the little equation for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+mass so I've got
+
+ align:start position:0%
+mass so I've got
+ 
+
+ align:start position:0%
+mass so I've got
+density p over Delta * L cubed over c
+
+ align:start position:0%
+density p over Delta * L cubed over c
+ 
+
+ align:start position:0%
+density p over Delta * L cubed over c
+e and we take that whole thing to 1 half
+
+ align:start position:0%
+e and we take that whole thing to 1 half
+ 
+
+ align:start position:0%
+e and we take that whole thing to 1 half
+power we have another L and so to
+
+ align:start position:0%
+power we have another L and so to
+ 
+
+ align:start position:0%
+power we have another L and so to
+minimize the mass you want to look at
+
+ align:start position:0%
+minimize the mass you want to look at
+ 
+
+ align:start position:0%
+minimize the mass you want to look at
+the material properties and here the
+
+ align:start position:0%
+the material properties and here the
+ 
+
+ align:start position:0%
+the material properties and here the
+material properties of the density and
+
+ align:start position:0%
+material properties of the density and
+ 
+
+ align:start position:0%
+material properties of the density and
+the Young's modulus
+
+ align:start position:0%
+the Young's modulus
+ 
+
+ align:start position:0%
+the Young's modulus
+and to to minimize the mass you want to
+
+ align:start position:0%
+and to to minimize the mass you want to
+ 
+
+ align:start position:0%
+and to to minimize the mass you want to
+minimize row E to2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power or conversely you want to maximize
+
+ align:start position:0%
+power or conversely you want to maximize
+ 
+
+ align:start position:0%
+power or conversely you want to maximize
+e to the 1/2 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row okay so if you just had if you had a
+
+ align:start position:0%
+row okay so if you just had if you had a
+ 
+
+ align:start position:0%
+row okay so if you just had if you had a
+bar that you were just pulling on you
+
+ align:start position:0%
+bar that you were just pulling on you
+ 
+
+ align:start position:0%
+bar that you were just pulling on you
+would just want to maximize e over row
+
+ align:start position:0%
+would just want to maximize e over row
+ 
+
+ align:start position:0%
+would just want to maximize e over row
+but if it's a beam in bending it works
+
+ align:start position:0%
+but if it's a beam in bending it works
+ 
+
+ align:start position:0%
+but if it's a beam in bending it works
+out that you want to maximize e to the
+
+ align:start position:0%
+out that you want to maximize e to the
+ 
+
+ align:start position:0%
+out that you want to maximize e to the
+1/2 over row and if we look at the next
+
+ align:start position:0%
+1/2 over row and if we look at the next
+ 
+
+ align:start position:0%
+1/2 over row and if we look at the next
+slide this next slide then
+
+ align:start position:0%
+slide this next slide then
+ 
+
+ align:start position:0%
+slide this next slide then
+plots on a log log scale it plots the
+
+ align:start position:0%
+plots on a log log scale it plots the
+ 
+
+ align:start position:0%
+plots on a log log scale it plots the
+modulus on this axis and the density on
+
+ align:start position:0%
+modulus on this axis and the density on
+ 
+
+ align:start position:0%
+modulus on this axis and the density on
+that axis and here this plotted uh data
+
+ align:start position:0%
+that axis and here this plotted uh data
+ 
+
+ align:start position:0%
+that axis and here this plotted uh data
+for lots of different materials so
+
+ align:start position:0%
+for lots of different materials so
+ 
+
+ align:start position:0%
+for lots of different materials so
+there's engineering Alloys metals are up
+
+ align:start position:0%
+there's engineering Alloys metals are up
+ 
+
+ align:start position:0%
+there's engineering Alloys metals are up
+here engineering Ceramics are here
+
+ align:start position:0%
+here engineering Ceramics are here
+ 
+
+ align:start position:0%
+here engineering Ceramics are here
+Composites are here polymers are down
+
+ align:start position:0%
+Composites are here polymers are down
+ 
+
+ align:start position:0%
+Composites are here polymers are down
+here elastomer is way down here foamy
+
+ align:start position:0%
+here elastomer is way down here foamy
+ 
+
+ align:start position:0%
+here elastomer is way down here foamy
+things down here and this envelope here
+
+ align:start position:0%
+things down here and this envelope here
+ 
+
+ align:start position:0%
+things down here and this envelope here
+is woods and notice the log scale here
+
+ align:start position:0%
+is woods and notice the log scale here
+ 
+
+ align:start position:0%
+is woods and notice the log scale here
+the the lowest stiffness polymer Foams
+
+ align:start position:0%
+the the lowest stiffness polymer Foams
+ 
+
+ align:start position:0%
+the the lowest stiffness polymer Foams
+here are 01 gigap Pascal and diamond is
+
+ align:start position:0%
+here are 01 gigap Pascal and diamond is
+ 
+
+ align:start position:0%
+here are 01 gigap Pascal and diamond is
+up here at a th000 gigap pascal so
+
+ align:start position:0%
+up here at a th000 gigap pascal so
+ 
+
+ align:start position:0%
+up here at a th000 gigap pascal so
+there's like five orders of magnitude
+
+ align:start position:0%
+there's like five orders of magnitude
+ 
+
+ align:start position:0%
+there's like five orders of magnitude
+difference in the modulus
+
+ align:start position:0%
+difference in the modulus
+ 
+
+ align:start position:0%
+difference in the modulus
+here so then if you look at the bottom
+
+ align:start position:0%
+here so then if you look at the bottom
+ 
+
+ align:start position:0%
+here so then if you look at the bottom
+right corner here there's a bunch of
+
+ align:start position:0%
+right corner here there's a bunch of
+ 
+
+ align:start position:0%
+right corner here there's a bunch of
+dashed lines lines and this red one here
+
+ align:start position:0%
+dashed lines lines and this red one here
+ 
+
+ align:start position:0%
+dashed lines lines and this red one here
+is e to 1/2 over row so if it's log log
+
+ align:start position:0%
+is e to 1/2 over row so if it's log log
+ 
+
+ align:start position:0%
+is e to 1/2 over row so if it's log log
+plot e to 1/2 over row is going to show
+
+ align:start position:0%
+plot e to 1/2 over row is going to show
+ 
+
+ align:start position:0%
+plot e to 1/2 over row is going to show
+up as a straight line and every point on
+
+ align:start position:0%
+up as a straight line and every point on
+ 
+
+ align:start position:0%
+up as a straight line and every point on
+that line has the same value of e to the
+
+ align:start position:0%
+that line has the same value of e to the
+ 
+
+ align:start position:0%
+that line has the same value of e to the
+1/2 over
+
+ align:start position:0%
+1/2 over
+ 
+
+ align:start position:0%
+1/2 over
+row and the material that would be the
+
+ align:start position:0%
+row and the material that would be the
+ 
+
+ align:start position:0%
+row and the material that would be the
+best um for a beam of a given stiffness
+
+ align:start position:0%
+best um for a beam of a given stiffness
+ 
+
+ align:start position:0%
+best um for a beam of a given stiffness
+would be the one that has the biggest
+
+ align:start position:0%
+would be the one that has the biggest
+ 
+
+ align:start position:0%
+would be the one that has the biggest
+value of e to the 1/2 over row and if I
+
+ align:start position:0%
+value of e to the 1/2 over row and if I
+ 
+
+ align:start position:0%
+value of e to the 1/2 over row and if I
+move the line up to the top left here
+
+ align:start position:0%
+move the line up to the top left here
+ 
+
+ align:start position:0%
+move the line up to the top left here
+I'm increasing e I'm decreasing row it's
+
+ align:start position:0%
+I'm increasing e I'm decreasing row it's
+ 
+
+ align:start position:0%
+I'm increasing e I'm decreasing row it's
+got the biggest value of e to the 1/2
+
+ align:start position:0%
+got the biggest value of e to the 1/2
+ 
+
+ align:start position:0%
+got the biggest value of e to the 1/2
+over row so the materials that are on
+
+ align:start position:0%
+over row so the materials that are on
+ 
+
+ align:start position:0%
+over row so the materials that are on
+this line here they all have the same
+
+ align:start position:0%
+this line here they all have the same
+ 
+
+ align:start position:0%
+this line here they all have the same
+value of e to the 1/2 over row and
+
+ align:start position:0%
+value of e to the 1/2 over row and
+ 
+
+ align:start position:0%
+value of e to the 1/2 over row and
+they've got the biggest value well
+
+ align:start position:0%
+they've got the biggest value well
+ 
+
+ align:start position:0%
+they've got the biggest value well
+virtually the biggest value uh so let's
+
+ align:start position:0%
+virtually the biggest value uh so let's
+ 
+
+ align:start position:0%
+virtually the biggest value uh so let's
+look at what those materials are there's
+
+ align:start position:0%
+look at what those materials are there's
+ 
+
+ align:start position:0%
+look at what those materials are there's
+there's things like engineering Ceramics
+
+ align:start position:0%
+there's things like engineering Ceramics
+ 
+
+ align:start position:0%
+there's things like engineering Ceramics
+like diamond that maybe are not the most
+
+ align:start position:0%
+like diamond that maybe are not the most
+ 
+
+ align:start position:0%
+like diamond that maybe are not the most
+convenient thing to make our beam out of
+
+ align:start position:0%
+convenient thing to make our beam out of
+ 
+
+ align:start position:0%
+convenient thing to make our beam out of
+and tend to be brittle and might break
+
+ align:start position:0%
+and tend to be brittle and might break
+ 
+
+ align:start position:0%
+and tend to be brittle and might break
+so they have some issues there's
+
+ align:start position:0%
+so they have some issues there's
+ 
+
+ align:start position:0%
+so they have some issues there's
+engineering Composites so things like uh
+
+ align:start position:0%
+engineering Composites so things like uh
+ 
+
+ align:start position:0%
+engineering Composites so things like uh
+carbon fiber reinforced Plastics and at
+
+ align:start position:0%
+carbon fiber reinforced Plastics and at
+ 
+
+ align:start position:0%
+carbon fiber reinforced Plastics and at
+this sort of tip of the Composites
+
+ align:start position:0%
+this sort of tip of the Composites
+ 
+
+ align:start position:0%
+this sort of tip of the Composites
+there'd be things like un uni
+
+ align:start position:0%
+there'd be things like un uni
+ 
+
+ align:start position:0%
+there'd be things like un uni
+unidirectional um fiber composites
+
+ align:start position:0%
+unidirectional um fiber composites
+ 
+
+ align:start position:0%
+unidirectional um fiber composites
+and then here's the woods down here so
+
+ align:start position:0%
+and then here's the woods down here so
+ 
+
+ align:start position:0%
+and then here's the woods down here so
+the woods have the same performance
+
+ align:start position:0%
+the woods have the same performance
+ 
+
+ align:start position:0%
+the woods have the same performance
+Index this is called the same value of e
+
+ align:start position:0%
+Index this is called the same value of e
+ 
+
+ align:start position:0%
+Index this is called the same value of e
+to the 1/2 over row as the best
+
+ align:start position:0%
+to the 1/2 over row as the best
+ 
+
+ align:start position:0%
+to the 1/2 over row as the best
+engineering Composites and so they have
+
+ align:start position:0%
+engineering Composites and so they have
+ 
+
+ align:start position:0%
+engineering Composites and so they have
+very good properties for their weight
+
+ align:start position:0%
+very good properties for their weight
+ 
+
+ align:start position:0%
+very good properties for their weight
+and one of the interesting things is if
+
+ align:start position:0%
+and one of the interesting things is if
+ 
+
+ align:start position:0%
+and one of the interesting things is if
+you look at this performance index of e
+
+ align:start position:0%
+you look at this performance index of e
+ 
+
+ align:start position:0%
+you look at this performance index of e
+to the 1/2 over
+
+ align:start position:0%
+to the 1/2 over
+ 
+
+ align:start position:0%
+to the 1/2 over
+row this is the performance index for
+
+ align:start position:0%
+row this is the performance index for
+ 
+
+ align:start position:0%
+row this is the performance index for
+the wood this is for the solid cell wall
+
+ align:start position:0%
+the wood this is for the solid cell wall
+ 
+
+ align:start position:0%
+the wood this is for the solid cell wall
+material that the woods made from so e
+
+ align:start position:0%
+material that the woods made from so e
+ 
+
+ align:start position:0%
+material that the woods made from so e
+to 1/2 uh of the solid over rope the
+
+ align:start position:0%
+to 1/2 uh of the solid over rope the
+ 
+
+ align:start position:0%
+to 1/2 uh of the solid over rope the
+solid and from the modeling of the wood
+
+ align:start position:0%
+solid and from the modeling of the wood
+ 
+
+ align:start position:0%
+solid and from the modeling of the wood
+just looking at the axial modulus this
+
+ align:start position:0%
+just looking at the axial modulus this
+ 
+
+ align:start position:0%
+just looking at the axial modulus this
+thing here is equal to that times row s
+
+ align:start position:0%
+thing here is equal to that times row s
+ 
+
+ align:start position:0%
+thing here is equal to that times row s
+over row so if you look at this this is
+
+ align:start position:0%
+over row so if you look at this this is
+ 
+
+ align:start position:0%
+over row so if you look at this this is
+the performance index for the wood this
+
+ align:start position:0%
+the performance index for the wood this
+ 
+
+ align:start position:0%
+the performance index for the wood this
+is the solid it's made from this number
+
+ align:start position:0%
+is the solid it's made from this number
+ 
+
+ align:start position:0%
+is the solid it's made from this number
+here is bigger than one right because
+
+ align:start position:0%
+here is bigger than one right because
+ 
+
+ align:start position:0%
+here is bigger than one right because
+the density of the solid is bigger than
+
+ align:start position:0%
+the density of the solid is bigger than
+ 
+
+ align:start position:0%
+the density of the solid is bigger than
+the density of the wood and so this is
+
+ align:start position:0%
+the density of the wood and so this is
+ 
+
+ align:start position:0%
+the density of the wood and so this is
+saying the wood is more efficient than
+
+ align:start position:0%
+saying the wood is more efficient than
+ 
+
+ align:start position:0%
+saying the wood is more efficient than
+the thing that it's made from than the
+
+ align:start position:0%
+the thing that it's made from than the
+ 
+
+ align:start position:0%
+the thing that it's made from than the
+solid that it's made from and so that's
+
+ align:start position:0%
+solid that it's made from and so that's
+ 
+
+ align:start position:0%
+solid that it's made from and so that's
+the the sort of plot for the stiffness
+
+ align:start position:0%
+the the sort of plot for the stiffness
+ 
+
+ align:start position:0%
+the the sort of plot for the stiffness
+and there's a similar plot for the
+
+ align:start position:0%
+and there's a similar plot for the
+ 
+
+ align:start position:0%
+and there's a similar plot for the
+strength that if you do this same little
+
+ align:start position:0%
+strength that if you do this same little
+ 
+
+ align:start position:0%
+strength that if you do this same little
+kind of calculation you find that the
+
+ align:start position:0%
+kind of calculation you find that the
+ 
+
+ align:start position:0%
+kind of calculation you find that the
+performance index for the strength is
+
+ align:start position:0%
+performance index for the strength is
+ 
+
+ align:start position:0%
+performance index for the strength is
+some failure strength raised to the 2/3
+
+ align:start position:0%
+some failure strength raised to the 2/3
+ 
+
+ align:start position:0%
+some failure strength raised to the 2/3
+power over row and again here we're
+
+ align:start position:0%
+power over row and again here we're
+ 
+
+ align:start position:0%
+power over row and again here we're
+plotting strength versus density on a
+
+ align:start position:0%
+plotting strength versus density on a
+ 
+
+ align:start position:0%
+plotting strength versus density on a
+log log plot and this red line here is
+
+ align:start position:0%
+log log plot and this red line here is
+ 
+
+ align:start position:0%
+log log plot and this red line here is
+uh the strength of the 2/3 over row and
+
+ align:start position:0%
+uh the strength of the 2/3 over row and
+ 
+
+ align:start position:0%
+uh the strength of the 2/3 over row and
+again if we scoot over here so we have a
+
+ align:start position:0%
+again if we scoot over here so we have a
+ 
+
+ align:start position:0%
+again if we scoot over here so we have a
+parallel line every point on that line
+
+ align:start position:0%
+parallel line every point on that line
+ 
+
+ align:start position:0%
+parallel line every point on that line
+has the same value of the strength um to
+
+ align:start position:0%
+has the same value of the strength um to
+ 
+
+ align:start position:0%
+has the same value of the strength um to
+the 2/3 power over the density and these
+
+ align:start position:0%
+the 2/3 power over the density and these
+ 
+
+ align:start position:0%
+the 2/3 power over the density and these
+are the materials that have the highest
+
+ align:start position:0%
+are the materials that have the highest
+ 
+
+ align:start position:0%
+are the materials that have the highest
+values and again here's engineering
+
+ align:start position:0%
+values and again here's engineering
+ 
+
+ align:start position:0%
+values and again here's engineering
+Composites uh these are Ceramics but the
+
+ align:start position:0%
+Composites uh these are Ceramics but the
+ 
+
+ align:start position:0%
+Composites uh these are Ceramics but the
+Ceramics they have a high compressive
+
+ align:start position:0%
+Ceramics they have a high compressive
+ 
+
+ align:start position:0%
+Ceramics they have a high compressive
+strength but they tend to be brittle so
+
+ align:start position:0%
+strength but they tend to be brittle so
+ 
+
+ align:start position:0%
+strength but they tend to be brittle so
+it's not really a practical strength U
+
+ align:start position:0%
+it's not really a practical strength U
+ 
+
+ align:start position:0%
+it's not really a practical strength U
+these are metals in here and here's the
+
+ align:start position:0%
+these are metals in here and here's the
+ 
+
+ align:start position:0%
+these are metals in here and here's the
+woods down here so it's kind of
+
+ align:start position:0%
+woods down here so it's kind of
+ 
+
+ align:start position:0%
+woods down here so it's kind of
+interesting just to see that the wood
+
+ align:start position:0%
+interesting just to see that the wood
+ 
+
+ align:start position:0%
+interesting just to see that the wood
+has such a good property yes um so why
+
+ align:start position:0%
+has such a good property yes um so why
+ 
+
+ align:start position:0%
+has such a good property yes um so why
+so I like realized like why this is
+
+ align:start position:0%
+so I like realized like why this is
+ 
+
+ align:start position:0%
+so I like realized like why this is
+valuable setting it this setting up the
+
+ align:start position:0%
+valuable setting it this setting up the
+ 
+
+ align:start position:0%
+valuable setting it this setting up the
+problem this way but um if you're
+
+ align:start position:0%
+problem this way but um if you're
+ 
+
+ align:start position:0%
+problem this way but um if you're
+actually trying to design something why
+
+ align:start position:0%
+actually trying to design something why
+ 
+
+ align:start position:0%
+actually trying to design something why
+would you want to fix your cross-section
+
+ align:start position:0%
+would you want to fix your cross-section
+ 
+
+ align:start position:0%
+would you want to fix your cross-section
+oh but you could change your change your
+
+ align:start position:0%
+oh but you could change your change your
+ 
+
+ align:start position:0%
+oh but you could change your change your
+material true and change your
+
+ align:start position:0%
+material true and change your
+ 
+
+ align:start position:0%
+material true and change your
+crosssection so this is the this is the
+
+ align:start position:0%
+crosssection so this is the this is the
+ 
+
+ align:start position:0%
+crosssection so this is the this is the
+starter uh version of this problem and
+
+ align:start position:0%
+starter uh version of this problem and
+ 
+
+ align:start position:0%
+starter uh version of this problem and
+there's another part two of the problem
+
+ align:start position:0%
+there's another part two of the problem
+ 
+
+ align:start position:0%
+there's another part two of the problem
+is to change the shape and you could
+
+ align:start position:0%
+is to change the shape and you could
+ 
+
+ align:start position:0%
+is to change the shape and you could
+look at what shape's efficient there's
+
+ align:start position:0%
+look at what shape's efficient there's
+ 
+
+ align:start position:0%
+look at what shape's efficient there's
+something called a shape factor that
+
+ align:start position:0%
+something called a shape factor that
+ 
+
+ align:start position:0%
+something called a shape factor that
+gives you the efficient shapes so you
+
+ align:start position:0%
+gives you the efficient shapes so you
+ 
+
+ align:start position:0%
+gives you the efficient shapes so you
+could take the material and turn it into
+
+ align:start position:0%
+could take the material and turn it into
+ 
+
+ align:start position:0%
+could take the material and turn it into
+a different shape and have a more
+
+ align:start position:0%
+a different shape and have a more
+ 
+
+ align:start position:0%
+a different shape and have a more
+efficient thing because it was a
+
+ align:start position:0%
+efficient thing because it was a
+ 
+
+ align:start position:0%
+efficient thing because it was a
+different shape so there is a you can't
+
+ align:start position:0%
+different shape so there is a you can't
+ 
+
+ align:start position:0%
+different shape so there is a you can't
+count for if you did if you vared like
+
+ align:start position:0%
+count for if you did if you vared like
+ 
+
+ align:start position:0%
+count for if you did if you vared like
+let's say you made your cross-section
+
+ align:start position:0%
+let's say you made your cross-section
+ 
+
+ align:start position:0%
+let's say you made your cross-section
+smaller like even if it was still Square
+
+ align:start position:0%
+smaller like even if it was still Square
+ 
+
+ align:start position:0%
+smaller like even if it was still Square
+you would just still make it
+
+ align:start position:0%
+you would just still make it
+ 
+
+ align:start position:0%
+you would just still make it
+oh yeah I'm saying we've got a given
+
+ align:start position:0%
+oh yeah I'm saying we've got a given
+ 
+
+ align:start position:0%
+oh yeah I'm saying we've got a given
+stiffness so if we're given a certain
+
+ align:start position:0%
+stiffness so if we're given a certain
+ 
+
+ align:start position:0%
+stiffness so if we're given a certain
+stiffness and a certain span we would
+
+ align:start position:0%
+stiffness and a certain span we would
+ 
+
+ align:start position:0%
+stiffness and a certain span we would
+need a certain cross-section to get to
+
+ align:start position:0%
+need a certain cross-section to get to
+ 
+
+ align:start position:0%
+need a certain cross-section to get to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+stiffness
+
+ align:start position:0%
+stiffness
+ 
+
+ align:start position:0%
+stiffness
+okay yeah are we happy yeah okay okay so
+
+ align:start position:0%
+okay yeah are we happy yeah okay okay so
+ 
+
+ align:start position:0%
+okay yeah are we happy yeah okay okay so
+that's uh one thing um let's see here so
+
+ align:start position:0%
+that's uh one thing um let's see here so
+ 
+
+ align:start position:0%
+that's uh one thing um let's see here so
+let me just write a few more notes about
+
+ align:start position:0%
+let me just write a few more notes about
+ 
+
+ align:start position:0%
+let me just write a few more notes about
+the material selection and then there's
+
+ align:start position:0%
+the material selection and then there's
+ 
+
+ align:start position:0%
+the material selection and then there's
+one more thing I wanted to show you
+
+ align:start position:0%
+one more thing I wanted to show you
+ 
+
+ align:start position:0%
+one more thing I wanted to show you
+about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+woods C's just a constant so it's just
+
+ align:start position:0%
+woods C's just a constant so it's just
+ 
+
+ align:start position:0%
+woods C's just a constant so it's just
+some number so you know if you had a
+
+ align:start position:0%
+some number so you know if you had a
+ 
+
+ align:start position:0%
+some number so you know if you had a
+beam in three-point bending then C would
+
+ align:start position:0%
+beam in three-point bending then C would
+ 
+
+ align:start position:0%
+beam in three-point bending then C would
+be three if you had a beam that was
+
+ align:start position:0%
+be three if you had a beam that was
+ 
+
+ align:start position:0%
+be three if you had a beam that was
+simply supported with a central load C
+
+ align:start position:0%
+simply supported with a central load C
+ 
+
+ align:start position:0%
+simply supported with a central load C
+would be 48 C's just a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+line choice is really just about
+
+ align:start position:0%
+line choice is really just about
+ 
+
+ align:start position:0%
+line choice is really just about
+cost um no it's not about cost there's
+
+ align:start position:0%
+cost um no it's not about cost there's
+ 
+
+ align:start position:0%
+cost um no it's not about cost there's
+nothing on cost here it it's all really
+
+ align:start position:0%
+nothing on cost here it it's all really
+ 
+
+ align:start position:0%
+nothing on cost here it it's all really
+about the properties what's the best
+
+ align:start position:0%
+about the properties what's the best
+ 
+
+ align:start position:0%
+about the properties what's the best
+combination of properties to minimize
+
+ align:start position:0%
+combination of properties to minimize
+ 
+
+ align:start position:0%
+combination of properties to minimize
+the mass and then which the which
+
+ align:start position:0%
+the mass and then which the which
+ 
+
+ align:start position:0%
+the mass and then which the which
+material has that combination of
+
+ align:start position:0%
+material has that combination of
+ 
+
+ align:start position:0%
+material has that combination of
+properties you can you can do charts
+
+ align:start position:0%
+properties you can you can do charts
+ 
+
+ align:start position:0%
+properties you can you can do charts
+like this that include cost um you can
+
+ align:start position:0%
+like this that include cost um you can
+ 
+
+ align:start position:0%
+like this that include cost um you can
+make these charts with whatever property
+
+ align:start position:0%
+make these charts with whatever property
+ 
+
+ align:start position:0%
+make these charts with whatever property
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want I guess
+
+ align:start position:0%
+want I guess
+ 
+
+ align:start position:0%
+want I guess
+the I guess maybe there's a difference
+
+ align:start position:0%
+the I guess maybe there's a difference
+ 
+
+ align:start position:0%
+the I guess maybe there's a difference
+in two or so of
+
+ align:start position:0%
+in two or so of
+ 
+
+ align:start position:0%
+in two or so of
+strength uh between Pine and
+
+ align:start position:0%
+strength uh between Pine and
+ 
+
+ align:start position:0%
+strength uh between Pine and
+Balsa yeah maybe more than that I think
+
+ align:start position:0%
+Balsa yeah maybe more than that I think
+ 
+
+ align:start position:0%
+Balsa yeah maybe more than that I think
+I can't quite see where Pine's close to
+
+ align:start position:0%
+I can't quite see where Pine's close to
+ 
+
+ align:start position:0%
+I can't quite see where Pine's close to
+100 and B is I don't know 20 or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somethinge yeah and it's not I mean the
+
+ align:start position:0%
+somethinge yeah and it's not I mean the
+ 
+
+ align:start position:0%
+somethinge yeah and it's not I mean the
+point of this isn't so much looking at
+
+ align:start position:0%
+point of this isn't so much looking at
+ 
+
+ align:start position:0%
+point of this isn't so much looking at
+the absolute value of the strength it's
+
+ align:start position:0%
+the absolute value of the strength it's
+ 
+
+ align:start position:0%
+the absolute value of the strength it's
+looking at the value of this performance
+
+ align:start position:0%
+looking at the value of this performance
+ 
+
+ align:start position:0%
+looking at the value of this performance
+index and uh what you want to do is
+
+ align:start position:0%
+index and uh what you want to do is
+ 
+
+ align:start position:0%
+index and uh what you want to do is
+maximize that index to get the material
+
+ align:start position:0%
+maximize that index to get the material
+ 
+
+ align:start position:0%
+maximize that index to get the material
+that's going to minimize the mass okay
+
+ align:start position:0%
+that's going to minimize the mass okay
+ 
+
+ align:start position:0%
+that's going to minimize the mass okay
+okay so let me just write a couple notes
+
+ align:start position:0%
+okay so let me just write a couple notes
+ 
+
+ align:start position:0%
+okay so let me just write a couple notes
+about this so we have these These are
+
+ align:start position:0%
+about this so we have these These are
+ 
+
+ align:start position:0%
+about this so we have these These are
+called material selection charts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you plot the log of one property
+
+ align:start position:0%
+so you plot the log of one property
+ 
+
+ align:start position:0%
+so you plot the log of one property
+versus the log of some other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property and then we have a line of
+
+ align:start position:0%
+property and then we have a line of
+ 
+
+ align:start position:0%
+property and then we have a line of
+constant e to the 1/2 over
+
+ align:start position:0%
+constant e to the 1/2 over
+ 
+
+ align:start position:0%
+constant e to the 1/2 over
+row I'll just say it's shown in red
+
+ align:start position:0%
+row I'll just say it's shown in red
+ 
+
+ align:start position:0%
+row I'll just say it's shown in red
+because you're going to have the same
+
+ align:start position:0%
+because you're going to have the same
+ 
+
+ align:start position:0%
+because you're going to have the same
+plots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the materials with the largest
+
+ align:start position:0%
+and the materials with the largest
+ 
+
+ align:start position:0%
+and the materials with the largest
+values are on the upper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left so the woods have similar values to
+
+ align:start position:0%
+left so the woods have similar values to
+ 
+
+ align:start position:0%
+left so the woods have similar values to
+any engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+composits and you can do a similar thing
+
+ align:start position:0%
+composits and you can do a similar thing
+ 
+
+ align:start position:0%
+composits and you can do a similar thing
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strength okay so I have a few more
+
+ align:start position:0%
+strength okay so I have a few more
+ 
+
+ align:start position:0%
+strength okay so I have a few more
+minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I have a few more minuts and I want
+
+ align:start position:0%
+so I have a few more minuts and I want
+ 
+
+ align:start position:0%
+so I have a few more minuts and I want
+to talk about a couple of uses of woods
+
+ align:start position:0%
+to talk about a couple of uses of woods
+ 
+
+ align:start position:0%
+to talk about a couple of uses of woods
+um so one is an old ships so I don't
+
+ align:start position:0%
+um so one is an old ships so I don't
+ 
+
+ align:start position:0%
+um so one is an old ships so I don't
+know if you know Professor Leman has
+
+ align:start position:0%
+know if you know Professor Leman has
+ 
+
+ align:start position:0%
+know if you know Professor Leman has
+this course materials and The Human
+
+ align:start position:0%
+this course materials and The Human
+ 
+
+ align:start position:0%
+this course materials and The Human
+Experience and they talk about sort of
+
+ align:start position:0%
+Experience and they talk about sort of
+ 
+
+ align:start position:0%
+Experience and they talk about sort of
+ancient uses of materials and I did a
+
+ align:start position:0%
+ancient uses of materials and I did a
+ 
+
+ align:start position:0%
+ancient uses of materials and I did a
+section a module on on woods and the use
+
+ align:start position:0%
+section a module on on woods and the use
+ 
+
+ align:start position:0%
+section a module on on woods and the use
+of woods in Old Colonial ships like the
+
+ align:start position:0%
+of woods in Old Colonial ships like the
+ 
+
+ align:start position:0%
+of woods in Old Colonial ships like the
+Constitution that's in in Boston Harbor
+
+ align:start position:0%
+Constitution that's in in Boston Harbor
+ 
+
+ align:start position:0%
+Constitution that's in in Boston Harbor
+so this is kind of a schematic of a an
+
+ align:start position:0%
+so this is kind of a schematic of a an
+ 
+
+ align:start position:0%
+so this is kind of a schematic of a an
+old uh ship and the thing that was
+
+ align:start position:0%
+old uh ship and the thing that was
+ 
+
+ align:start position:0%
+old uh ship and the thing that was
+interesting and the thing that I talked
+
+ align:start position:0%
+interesting and the thing that I talked
+ 
+
+ align:start position:0%
+interesting and the thing that I talked
+about in this module was that people
+
+ align:start position:0%
+about in this module was that people
+ 
+
+ align:start position:0%
+about in this module was that people
+chose particular species for particular
+
+ align:start position:0%
+chose particular species for particular
+ 
+
+ align:start position:0%
+chose particular species for particular
+parts of the boat and they would choose
+
+ align:start position:0%
+parts of the boat and they would choose
+ 
+
+ align:start position:0%
+parts of the boat and they would choose
+a particular species depending on its
+
+ align:start position:0%
+a particular species depending on its
+ 
+
+ align:start position:0%
+a particular species depending on its
+properties and a lot of the hull was
+
+ align:start position:0%
+properties and a lot of the hull was
+ 
+
+ align:start position:0%
+properties and a lot of the hull was
+made of oak so Oaks are very dense wood
+
+ align:start position:0%
+made of oak so Oaks are very dense wood
+ 
+
+ align:start position:0%
+made of oak so Oaks are very dense wood
+uh but they would get something they
+
+ align:start position:0%
+uh but they would get something they
+ 
+
+ align:start position:0%
+uh but they would get something they
+called straight Oak and they would get
+
+ align:start position:0%
+called straight Oak and they would get
+ 
+
+ align:start position:0%
+called straight Oak and they would get
+something they called Compass Oak and
+
+ align:start position:0%
+something they called Compass Oak and
+ 
+
+ align:start position:0%
+something they called Compass Oak and
+you can see this little thing down here
+
+ align:start position:0%
+you can see this little thing down here
+ 
+
+ align:start position:0%
+you can see this little thing down here
+this little kind of schematic here this
+
+ align:start position:0%
+this little kind of schematic here this
+ 
+
+ align:start position:0%
+this little kind of schematic here this
+little sketch
+
+ align:start position:0%
+little sketch
+ 
+
+ align:start position:0%
+little sketch
+uh this is straight Oak just a straight
+
+ align:start position:0%
+uh this is straight Oak just a straight
+ 
+
+ align:start position:0%
+uh this is straight Oak just a straight
+trunk and this thing here would be the
+
+ align:start position:0%
+trunk and this thing here would be the
+ 
+
+ align:start position:0%
+trunk and this thing here would be the
+compass Oak and what they would do is
+
+ align:start position:0%
+compass Oak and what they would do is
+ 
+
+ align:start position:0%
+compass Oak and what they would do is
+they would use the Straight Oak for
+
+ align:start position:0%
+they would use the Straight Oak for
+ 
+
+ align:start position:0%
+they would use the Straight Oak for
+straight parts of the boat so you know
+
+ align:start position:0%
+straight parts of the boat so you know
+ 
+
+ align:start position:0%
+straight parts of the boat so you know
+something like this these pieces here
+
+ align:start position:0%
+something like this these pieces here
+ 
+
+ align:start position:0%
+something like this these pieces here
+and then they would actually look for
+
+ align:start position:0%
+and then they would actually look for
+ 
+
+ align:start position:0%
+and then they would actually look for
+trees that had the curve of the branches
+
+ align:start position:0%
+trees that had the curve of the branches
+ 
+
+ align:start position:0%
+trees that had the curve of the branches
+to match some part of the boat that they
+
+ align:start position:0%
+to match some part of the boat that they
+ 
+
+ align:start position:0%
+to match some part of the boat that they
+were looking for so for instance um if
+
+ align:start position:0%
+were looking for so for instance um if
+ 
+
+ align:start position:0%
+were looking for so for instance um if
+you have the hull out here and the deck
+
+ align:start position:0%
+you have the hull out here and the deck
+ 
+
+ align:start position:0%
+you have the hull out here and the deck
+here and they had their cannons here
+
+ align:start position:0%
+here and they had their cannons here
+ 
+
+ align:start position:0%
+here and they had their cannons here
+there's something called a knee which is
+
+ align:start position:0%
+there's something called a knee which is
+ 
+
+ align:start position:0%
+there's something called a knee which is
+sort of a bracing piece that goes
+
+ align:start position:0%
+sort of a bracing piece that goes
+ 
+
+ align:start position:0%
+sort of a bracing piece that goes
+between the deck and the hull and that
+
+ align:start position:0%
+between the deck and the hull and that
+ 
+
+ align:start position:0%
+between the deck and the hull and that
+bracing piece is curved and they would
+
+ align:start position:0%
+bracing piece is curved and they would
+ 
+
+ align:start position:0%
+bracing piece is curved and they would
+actually look for trees in which the
+
+ align:start position:0%
+actually look for trees in which the
+ 
+
+ align:start position:0%
+actually look for trees in which the
+branches curved at the same kind of
+
+ align:start position:0%
+branches curved at the same kind of
+ 
+
+ align:start position:0%
+branches curved at the same kind of
+curvature as they were looking for in
+
+ align:start position:0%
+curvature as they were looking for in
+ 
+
+ align:start position:0%
+curvature as they were looking for in
+that piece and then they would use it
+
+ align:start position:0%
+that piece and then they would use it
+ 
+
+ align:start position:0%
+that piece and then they would use it
+for that piece and the advantage of this
+
+ align:start position:0%
+for that piece and the advantage of this
+ 
+
+ align:start position:0%
+for that piece and the advantage of this
+is they basically had the grain running
+
+ align:start position:0%
+is they basically had the grain running
+ 
+
+ align:start position:0%
+is they basically had the grain running
+along the curve and so they got the best
+
+ align:start position:0%
+along the curve and so they got the best
+ 
+
+ align:start position:0%
+along the curve and so they got the best
+properties out of the wood by doing that
+
+ align:start position:0%
+properties out of the wood by doing that
+ 
+
+ align:start position:0%
+properties out of the wood by doing that
+so they had this straight Oak and
+
+ align:start position:0%
+so they had this straight Oak and
+ 
+
+ align:start position:0%
+so they had this straight Oak and
+Compass Oak and that was one uh cute
+
+ align:start position:0%
+Compass Oak and that was one uh cute
+ 
+
+ align:start position:0%
+Compass Oak and that was one uh cute
+thing and often they used White Oaks and
+
+ align:start position:0%
+thing and often they used White Oaks and
+ 
+
+ align:start position:0%
+thing and often they used White Oaks and
+I brought a piece of white oak in you
+
+ align:start position:0%
+I brought a piece of white oak in you
+ 
+
+ align:start position:0%
+I brought a piece of white oak in you
+can see how dense it is and the US Navy
+
+ align:start position:0%
+can see how dense it is and the US Navy
+ 
+
+ align:start position:0%
+can see how dense it is and the US Navy
+uh often use something called live o
+
+ align:start position:0%
+uh often use something called live o
+ 
+
+ align:start position:0%
+uh often use something called live o
+Live Oak grows in the South anybody from
+
+ align:start position:0%
+Live Oak grows in the South anybody from
+ 
+
+ align:start position:0%
+Live Oak grows in the South anybody from
+the south you see these big trees with
+
+ align:start position:0%
+the south you see these big trees with
+ 
+
+ align:start position:0%
+the south you see these big trees with
+huge sort of spreading branches those
+
+ align:start position:0%
+huge sort of spreading branches those
+ 
+
+ align:start position:0%
+huge sort of spreading branches those
+are the Live Oaks and apparently the US
+
+ align:start position:0%
+are the Live Oaks and apparently the US
+ 
+
+ align:start position:0%
+are the Live Oaks and apparently the US
+Navy I read somewhere still has a forest
+
+ align:start position:0%
+Navy I read somewhere still has a forest
+ 
+
+ align:start position:0%
+Navy I read somewhere still has a forest
+somewhere with Live Oak for doing things
+
+ align:start position:0%
+somewhere with Live Oak for doing things
+ 
+
+ align:start position:0%
+somewhere with Live Oak for doing things
+like repairing the Constitution so let
+
+ align:start position:0%
+like repairing the Constitution so let
+ 
+
+ align:start position:0%
+like repairing the Constitution so let
+me just pass those guys around so those
+
+ align:start position:0%
+me just pass those guys around so those
+ 
+
+ align:start position:0%
+me just pass those guys around so those
+are a couple of the Oaks they would use
+
+ align:start position:0%
+are a couple of the Oaks they would use
+ 
+
+ align:start position:0%
+are a couple of the Oaks they would use
+for the hull then they would use uh
+
+ align:start position:0%
+for the hull then they would use uh
+ 
+
+ align:start position:0%
+for the hull then they would use uh
+White Pine for the masts and the reason
+
+ align:start position:0%
+White Pine for the masts and the reason
+ 
+
+ align:start position:0%
+White Pine for the masts and the reason
+they use White Pine for the Mast is the
+
+ align:start position:0%
+they use White Pine for the Mast is the
+ 
+
+ align:start position:0%
+they use White Pine for the Mast is the
+white pine grows very very tall and very
+
+ align:start position:0%
+white pine grows very very tall and very
+ 
+
+ align:start position:0%
+white pine grows very very tall and very
+straight and white pine was actually
+
+ align:start position:0%
+straight and white pine was actually
+ 
+
+ align:start position:0%
+straight and white pine was actually
+like a strategic resource in the 1600s
+
+ align:start position:0%
+like a strategic resource in the 1600s
+ 
+
+ align:start position:0%
+like a strategic resource in the 1600s
+and 1700s so and it turns out that when
+
+ align:start position:0%
+and 1700s so and it turns out that when
+ 
+
+ align:start position:0%
+and 1700s so and it turns out that when
+the British royal Navy was um you know
+
+ align:start position:0%
+the British royal Navy was um you know
+ 
+
+ align:start position:0%
+the British royal Navy was um you know
+doing all that Colonial stuff in the 16
+
+ align:start position:0%
+doing all that Colonial stuff in the 16
+ 
+
+ align:start position:0%
+doing all that Colonial stuff in the 16
+1700s Britain actually ran out of trees
+
+ align:start position:0%
+1700s Britain actually ran out of trees
+ 
+
+ align:start position:0%
+1700s Britain actually ran out of trees
+for masts for boats and they would
+
+ align:start position:0%
+for masts for boats and they would
+ 
+
+ align:start position:0%
+for masts for boats and they would
+actually import masts from New England
+
+ align:start position:0%
+actually import masts from New England
+ 
+
+ align:start position:0%
+actually import masts from New England
+and there were these people called
+
+ align:start position:0%
+and there were these people called
+ 
+
+ align:start position:0%
+and there were these people called
+surveyors who would go around and they
+
+ align:start position:0%
+surveyors who would go around and they
+ 
+
+ align:start position:0%
+surveyors who would go around and they
+would Mark certain trees that were
+
+ align:start position:0%
+would Mark certain trees that were
+ 
+
+ align:start position:0%
+would Mark certain trees that were
+supposed to be saved for these masts for
+
+ align:start position:0%
+supposed to be saved for these masts for
+ 
+
+ align:start position:0%
+supposed to be saved for these masts for
+the British royal Navy and the the thing
+
+ align:start position:0%
+the British royal Navy and the the thing
+ 
+
+ align:start position:0%
+the British royal Navy and the the thing
+was that the the size of the boat and
+
+ align:start position:0%
+was that the the size of the boat and
+ 
+
+ align:start position:0%
+was that the the size of the boat and
+how many cannons you could put on the
+
+ align:start position:0%
+how many cannons you could put on the
+ 
+
+ align:start position:0%
+how many cannons you could put on the
+boat depending on how big the Mast was
+
+ align:start position:0%
+boat depending on how big the Mast was
+ 
+
+ align:start position:0%
+boat depending on how big the Mast was
+so the size of the boat depended on this
+
+ align:start position:0%
+so the size of the boat depended on this
+ 
+
+ align:start position:0%
+so the size of the boat depended on this
+the mass because the Mast the Mast
+
+ align:start position:0%
+the mass because the Mast the Mast
+ 
+
+ align:start position:0%
+the mass because the Mast the Mast
+height depended on uh it controlled how
+
+ align:start position:0%
+height depended on uh it controlled how
+ 
+
+ align:start position:0%
+height depended on uh it controlled how
+much sail area you could get so the
+
+ align:start position:0%
+much sail area you could get so the
+ 
+
+ align:start position:0%
+much sail area you could get so the
+taller the mass the more sail the more
+
+ align:start position:0%
+taller the mass the more sail the more
+ 
+
+ align:start position:0%
+taller the mass the more sail the more
+sail the bigger the ship bigger the ship
+
+ align:start position:0%
+sail the bigger the ship bigger the ship
+ 
+
+ align:start position:0%
+sail the bigger the ship bigger the ship
+the more cannons and so having these
+
+ align:start position:0%
+the more cannons and so having these
+ 
+
+ align:start position:0%
+the more cannons and so having these
+tall uh eastern white pines was a sort
+
+ align:start position:0%
+tall uh eastern white pines was a sort
+ 
+
+ align:start position:0%
+tall uh eastern white pines was a sort
+of a strategic resource and I have a
+
+ align:start position:0%
+of a strategic resource and I have a
+ 
+
+ align:start position:0%
+of a strategic resource and I have a
+piece of white pine unfortunately my dog
+
+ align:start position:0%
+piece of white pine unfortunately my dog
+ 
+
+ align:start position:0%
+piece of white pine unfortunately my dog
+got to this one so there's so there's
+
+ align:start position:0%
+got to this one so there's so there's
+ 
+
+ align:start position:0%
+got to this one so there's so there's
+some and be careful it's a bit splintery
+
+ align:start position:0%
+some and be careful it's a bit splintery
+ 
+
+ align:start position:0%
+some and be careful it's a bit splintery
+but you can see it's a lighter kind of
+
+ align:start position:0%
+but you can see it's a lighter kind of
+ 
+
+ align:start position:0%
+but you can see it's a lighter kind of
+wood and if you go around New England uh
+
+ align:start position:0%
+wood and if you go around New England uh
+ 
+
+ align:start position:0%
+wood and if you go around New England uh
+if you go to the Arboretum you can see
+
+ align:start position:0%
+if you go to the Arboretum you can see
+ 
+
+ align:start position:0%
+if you go to the Arboretum you can see
+White Oak and you can see eastern white
+
+ align:start position:0%
+White Oak and you can see eastern white
+ 
+
+ align:start position:0%
+White Oak and you can see eastern white
+pine the other wood they used is lignum
+
+ align:start position:0%
+pine the other wood they used is lignum
+ 
+
+ align:start position:0%
+pine the other wood they used is lignum
+V that first dense one that I passed
+
+ align:start position:0%
+V that first dense one that I passed
+ 
+
+ align:start position:0%
+V that first dense one that I passed
+around and if you notice that lignum V
+
+ align:start position:0%
+around and if you notice that lignum V
+ 
+
+ align:start position:0%
+around and if you notice that lignum V
+it has kind of a waxy feel to it and
+
+ align:start position:0%
+it has kind of a waxy feel to it and
+ 
+
+ align:start position:0%
+it has kind of a waxy feel to it and
+they Ed that in the block and tackle so
+
+ align:start position:0%
+they Ed that in the block and tackle so
+ 
+
+ align:start position:0%
+they Ed that in the block and tackle so
+like pulley and stuff like that and it
+
+ align:start position:0%
+like pulley and stuff like that and it
+ 
+
+ align:start position:0%
+like pulley and stuff like that and it
+was thought to be self-lubricating
+
+ align:start position:0%
+was thought to be self-lubricating
+ 
+
+ align:start position:0%
+was thought to be self-lubricating
+because of that kind of waxy layer on it
+
+ align:start position:0%
+because of that kind of waxy layer on it
+ 
+
+ align:start position:0%
+because of that kind of waxy layer on it
+and because it's very dense if you think
+
+ align:start position:0%
+and because it's very dense if you think
+ 
+
+ align:start position:0%
+and because it's very dense if you think
+of like a block and tackle and you've
+
+ align:start position:0%
+of like a block and tackle and you've
+ 
+
+ align:start position:0%
+of like a block and tackle and you've
+got like a rope going over a pulley
+
+ align:start position:0%
+got like a rope going over a pulley
+ 
+
+ align:start position:0%
+got like a rope going over a pulley
+you've got a pressure from you know
+
+ align:start position:0%
+you've got a pressure from you know
+ 
+
+ align:start position:0%
+you've got a pressure from you know
+everything sort of fitting together
+
+ align:start position:0%
+everything sort of fitting together
+ 
+
+ align:start position:0%
+everything sort of fitting together
+and the bits bearing against each other
+
+ align:start position:0%
+and the bits bearing against each other
+ 
+
+ align:start position:0%
+and the bits bearing against each other
+and the fact that it was very dense made
+
+ align:start position:0%
+and the fact that it was very dense made
+ 
+
+ align:start position:0%
+and the fact that it was very dense made
+it very good for the block and tackle
+
+ align:start position:0%
+it very good for the block and tackle
+ 
+
+ align:start position:0%
+it very good for the block and tackle
+and so they used the lignum V for that
+
+ align:start position:0%
+and so they used the lignum V for that
+ 
+
+ align:start position:0%
+and so they used the lignum V for that
+and there's one other cute story about
+
+ align:start position:0%
+and there's one other cute story about
+ 
+
+ align:start position:0%
+and there's one other cute story about
+lignum vitai um I don't know if any of
+
+ align:start position:0%
+lignum vitai um I don't know if any of
+ 
+
+ align:start position:0%
+lignum vitai um I don't know if any of
+you have ever read Davis sobel's book
+
+ align:start position:0%
+you have ever read Davis sobel's book
+ 
+
+ align:start position:0%
+you have ever read Davis sobel's book
+called longitude anybody read that I'm a
+
+ align:start position:0%
+called longitude anybody read that I'm a
+ 
+
+ align:start position:0%
+called longitude anybody read that I'm a
+sucker for those history of science
+
+ align:start position:0%
+sucker for those history of science
+ 
+
+ align:start position:0%
+sucker for those history of science
+books so her book longitude is about the
+
+ align:start position:0%
+books so her book longitude is about the
+ 
+
+ align:start position:0%
+books so her book longitude is about the
+development of an instrument to measure
+
+ align:start position:0%
+development of an instrument to measure
+ 
+
+ align:start position:0%
+development of an instrument to measure
+longitude they used to be able to
+
+ align:start position:0%
+longitude they used to be able to
+ 
+
+ align:start position:0%
+longitude they used to be able to
+navigate originally they could get the
+
+ align:start position:0%
+navigate originally they could get the
+ 
+
+ align:start position:0%
+navigate originally they could get the
+latitude from the stars but they were
+
+ align:start position:0%
+latitude from the stars but they were
+ 
+
+ align:start position:0%
+latitude from the stars but they were
+really bad at getting the LA itude and
+
+ align:start position:0%
+really bad at getting the LA itude and
+ 
+
+ align:start position:0%
+really bad at getting the LA itude and
+so boats would go off and they wouldn't
+
+ align:start position:0%
+so boats would go off and they wouldn't
+ 
+
+ align:start position:0%
+so boats would go off and they wouldn't
+really be able to figure out where they
+
+ align:start position:0%
+really be able to figure out where they
+ 
+
+ align:start position:0%
+really be able to figure out where they
+were until they had a method to measure
+
+ align:start position:0%
+were until they had a method to measure
+ 
+
+ align:start position:0%
+were until they had a method to measure
+longitude and there was some British I
+
+ align:start position:0%
+longitude and there was some British I
+ 
+
+ align:start position:0%
+longitude and there was some British I
+don't know Board of something or another
+
+ align:start position:0%
+don't know Board of something or another
+ 
+
+ align:start position:0%
+don't know Board of something or another
+they they put forward a prize for
+
+ align:start position:0%
+they they put forward a prize for
+ 
+
+ align:start position:0%
+they they put forward a prize for
+somebody who could produce a way of
+
+ align:start position:0%
+somebody who could produce a way of
+ 
+
+ align:start position:0%
+somebody who could produce a way of
+measuring longitude accurately and there
+
+ align:start position:0%
+measuring longitude accurately and there
+ 
+
+ align:start position:0%
+measuring longitude accurately and there
+was a guy called John Harrison and he
+
+ align:start position:0%
+was a guy called John Harrison and he
+ 
+
+ align:start position:0%
+was a guy called John Harrison and he
+built a clock he built a very accurate
+
+ align:start position:0%
+built a clock he built a very accurate
+ 
+
+ align:start position:0%
+built a clock he built a very accurate
+chronometer and if you knew you know
+
+ align:start position:0%
+chronometer and if you knew you know
+ 
+
+ align:start position:0%
+chronometer and if you knew you know
+when Sunrise was and sunset was and you
+
+ align:start position:0%
+when Sunrise was and sunset was and you
+ 
+
+ align:start position:0%
+when Sunrise was and sunset was and you
+knew the time where you left you could
+
+ align:start position:0%
+knew the time where you left you could
+ 
+
+ align:start position:0%
+knew the time where you left you could
+figure out where you it's kind of like
+
+ align:start position:0%
+figure out where you it's kind of like
+ 
+
+ align:start position:0%
+figure out where you it's kind of like
+time zones you could figure out where
+
+ align:start position:0%
+time zones you could figure out where
+ 
+
+ align:start position:0%
+time zones you could figure out where
+you are today and he built a chronometer
+
+ align:start position:0%
+you are today and he built a chronometer
+ 
+
+ align:start position:0%
+you are today and he built a chronometer
+and one version of his chronometer used
+
+ align:start position:0%
+and one version of his chronometer used
+ 
+
+ align:start position:0%
+and one version of his chronometer used
+the lignum V for the same reason because
+
+ align:start position:0%
+the lignum V for the same reason because
+ 
+
+ align:start position:0%
+the lignum V for the same reason because
+it was very dense and it was very stable
+
+ align:start position:0%
+it was very dense and it was very stable
+ 
+
+ align:start position:0%
+it was very dense and it was very stable
+um and the clock that he eventually won
+
+ align:start position:0%
+um and the clock that he eventually won
+ 
+
+ align:start position:0%
+um and the clock that he eventually won
+the prize with was in the 1700
+
+ align:start position:0%
+the prize with was in the 1700
+ 
+
+ align:start position:0%
+the prize with was in the 1700
+1759 I think he they went on some trip
+
+ align:start position:0%
+1759 I think he they went on some trip
+ 
+
+ align:start position:0%
+1759 I think he they went on some trip
+with it it was 81 days at Sea and it
+
+ align:start position:0%
+with it it was 81 days at Sea and it
+ 
+
+ align:start position:0%
+with it it was 81 days at Sea and it
+lost 5 Seconds over 81 days so that's
+
+ align:start position:0%
+lost 5 Seconds over 81 days so that's
+ 
+
+ align:start position:0%
+lost 5 Seconds over 81 days so that's
+pretty impressive for you know 250 years
+
+ align:start position:0%
+pretty impressive for you know 250 years
+ 
+
+ align:start position:0%
+pretty impressive for you know 250 years
+ago so that was the lignum v in the
+
+ align:start position:0%
+ago so that was the lignum v in the
+ 
+
+ align:start position:0%
+ago so that was the lignum v in the
+clock and I have one more picture and
+
+ align:start position:0%
+clock and I have one more picture and
+ 
+
+ align:start position:0%
+clock and I have one more picture and
+then I can finish up the thing on wood
+
+ align:start position:0%
+then I can finish up the thing on wood
+ 
+
+ align:start position:0%
+then I can finish up the thing on wood
+and we'll start the cork next time
+
+ align:start position:0%
+and we'll start the cork next time
+ 
+
+ align:start position:0%
+and we'll start the cork next time
+so this is another example of using wood
+
+ align:start position:0%
+so this is another example of using wood
+ 
+
+ align:start position:0%
+so this is another example of using wood
+and this is sort of a more modern use so
+
+ align:start position:0%
+and this is sort of a more modern use so
+ 
+
+ align:start position:0%
+and this is sort of a more modern use so
+this bridge here is made with a glue
+
+ align:start position:0%
+this bridge here is made with a glue
+ 
+
+ align:start position:0%
+this bridge here is made with a glue
+laminated wood so this big beam here big
+
+ align:start position:0%
+laminated wood so this big beam here big
+ 
+
+ align:start position:0%
+laminated wood so this big beam here big
+arch is U made up of sections of wood
+
+ align:start position:0%
+arch is U made up of sections of wood
+ 
+
+ align:start position:0%
+arch is U made up of sections of wood
+which are uh glued together and you can
+
+ align:start position:0%
+which are uh glued together and you can
+ 
+
+ align:start position:0%
+which are uh glued together and you can
+glue the sections in a curved shape if
+
+ align:start position:0%
+glue the sections in a curved shape if
+ 
+
+ align:start position:0%
+glue the sections in a curved shape if
+you want and sort of have molds to do
+
+ align:start position:0%
+you want and sort of have molds to do
+ 
+
+ align:start position:0%
+you want and sort of have molds to do
+that and when they make this glue
+
+ align:start position:0%
+that and when they make this glue
+ 
+
+ align:start position:0%
+that and when they make this glue
+laminated wood they cut the defects out
+
+ align:start position:0%
+laminated wood they cut the defects out
+ 
+
+ align:start position:0%
+laminated wood they cut the defects out
+so they cut knots out and they you know
+
+ align:start position:0%
+so they cut knots out and they you know
+ 
+
+ align:start position:0%
+so they cut knots out and they you know
+they control the the pieces of each
+
+ align:start position:0%
+they control the the pieces of each
+ 
+
+ align:start position:0%
+they control the the pieces of each
+laminate that they use uh to get the
+
+ align:start position:0%
+laminate that they use uh to get the
+ 
+
+ align:start position:0%
+laminate that they use uh to get the
+best quality
+
+ align:start position:0%
+best quality
+ 
+
+ align:start position:0%
+best quality
+and the glue laminated wood actually has
+
+ align:start position:0%
+and the glue laminated wood actually has
+ 
+
+ align:start position:0%
+and the glue laminated wood actually has
+better properties than just you know
+
+ align:start position:0%
+better properties than just you know
+ 
+
+ align:start position:0%
+better properties than just you know
+2x4s or whatever you would cut down you
+
+ align:start position:0%
+2x4s or whatever you would cut down you
+ 
+
+ align:start position:0%
+2x4s or whatever you would cut down you
+know Lumber that you would cut from a
+
+ align:start position:0%
+know Lumber that you would cut from a
+ 
+
+ align:start position:0%
+know Lumber that you would cut from a
+tree so glue laminated wood is kind of a
+
+ align:start position:0%
+tree so glue laminated wood is kind of a
+ 
+
+ align:start position:0%
+tree so glue laminated wood is kind of a
+nice uh kind of uh wood structure that's
+
+ align:start position:0%
+nice uh kind of uh wood structure that's
+ 
+
+ align:start position:0%
+nice uh kind of uh wood structure that's
+used now and you see it all the time in
+
+ align:start position:0%
+used now and you see it all the time in
+ 
+
+ align:start position:0%
+used now and you see it all the time in
+things like um ice rink Arenas like
+
+ align:start position:0%
+things like um ice rink Arenas like
+ 
+
+ align:start position:0%
+things like um ice rink Arenas like
+large span it's and it's kind of
+
+ align:start position:0%
+large span it's and it's kind of
+ 
+
+ align:start position:0%
+large span it's and it's kind of
+beautiful you can see the wood grain and
+
+ align:start position:0%
+beautiful you can see the wood grain and
+ 
+
+ align:start position:0%
+beautiful you can see the wood grain and
+the curve in the wood grain when they
+
+ align:start position:0%
+the curve in the wood grain when they
+ 
+
+ align:start position:0%
+the curve in the wood grain when they
+make these things so that's the wood
+
+ align:start position:0%
+make these things so that's the wood
+ 
+
+ align:start position:0%
+make these things so that's the wood
+lecture I'm going to stop there so next
+
+ align:start position:0%
+lecture I'm going to stop there so next
+ 
+
+ align:start position:0%
+lecture I'm going to stop there so next
+time I'll talk about cork I just have a
+
+ align:start position:0%
+time I'll talk about cork I just have a
+ 
+
+ align:start position:0%
+time I'll talk about cork I just have a
+little bit about Cork and then uh we'll
+
+ align:start position:0%
+little bit about Cork and then uh we'll
+ 
+
+ align:start position:0%
+little bit about Cork and then uh we'll
+start talking about foams okay
\ No newline at end of file
diff --git a/jwJrF6kBuJ4.txt b/jwJrF6kBuJ4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dd996d2d8a927c7a0a0934c3ec286854463386be
--- /dev/null
+++ b/jwJrF6kBuJ4.txt
@@ -0,0 +1,4979 @@
+align:start position:0%
+ 
+instead of trying to convince the other
+
+ align:start position:0%
+instead of trying to convince the other
+ 
+
+ align:start position:0%
+instead of trying to convince the other
+person or persuade the other person
+
+ align:start position:0%
+person or persuade the other person
+ 
+
+ align:start position:0%
+person or persuade the other person
+listen help them empty their heart and
+
+ align:start position:0%
+listen help them empty their heart and
+ 
+
+ align:start position:0%
+listen help them empty their heart and
+express why they're frustrated with a
+
+ align:start position:0%
+express why they're frustrated with a
+ 
+
+ align:start position:0%
+express why they're frustrated with a
+situation and then they'll be more
+
+ align:start position:0%
+situation and then they'll be more
+ 
+
+ align:start position:0%
+situation and then they'll be more
+likely to listen to your own experiences
+
+ align:start position:0%
+likely to listen to your own experiences
+ 
+
+ align:start position:0%
+likely to listen to your own experiences
+and more receptive to why you think
+
+ align:start position:0%
+and more receptive to why you think
+ 
+
+ align:start position:0%
+and more receptive to why you think
+climate change
+
+ align:start position:0%
+climate change
+ 
+
+ align:start position:0%
+climate change
+matters and is relevant today on shock
+
+ align:start position:0%
+matters and is relevant today on shock
+ 
+
+ align:start position:0%
+matters and is relevant today on shock
+radio
+
+ align:start position:0%
+radio
+ 
+
+ align:start position:0%
+radio
+we're exploring climate action and how
+
+ align:start position:0%
+we're exploring climate action and how
+ 
+
+ align:start position:0%
+we're exploring climate action and how
+one nonprofit is providing a framework
+
+ align:start position:0%
+one nonprofit is providing a framework
+ 
+
+ align:start position:0%
+one nonprofit is providing a framework
+for young people
+
+ align:start position:0%
+for young people
+ 
+
+ align:start position:0%
+for young people
+to help affect change the thing about
+
+ align:start position:0%
+to help affect change the thing about
+ 
+
+ align:start position:0%
+to help affect change the thing about
+teaching young people
+
+ align:start position:0%
+teaching young people
+ 
+
+ align:start position:0%
+teaching young people
+in particular is that young people are
+
+ align:start position:0%
+in particular is that young people are
+ 
+
+ align:start position:0%
+in particular is that young people are
+open-minded
+
+ align:start position:0%
+open-minded
+ 
+
+ align:start position:0%
+open-minded
+to new material but they're mature
+
+ align:start position:0%
+to new material but they're mature
+ 
+
+ align:start position:0%
+to new material but they're mature
+enough to understand fairly complex
+
+ align:start position:0%
+enough to understand fairly complex
+ 
+
+ align:start position:0%
+enough to understand fairly complex
+concepts
+
+ align:start position:0%
+concepts
+ 
+
+ align:start position:0%
+concepts
+ultimately we hope that ambassadors will
+
+ align:start position:0%
+ultimately we hope that ambassadors will
+ 
+
+ align:start position:0%
+ultimately we hope that ambassadors will
+teach students
+
+ align:start position:0%
+teach students
+ 
+
+ align:start position:0%
+teach students
+students will teach families and
+
+ align:start position:0%
+students will teach families and
+ 
+
+ align:start position:0%
+students will teach families and
+families will demand action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm your host sarah hansen with us today
+
+ align:start position:0%
+i'm your host sarah hansen with us today
+ 
+
+ align:start position:0%
+i'm your host sarah hansen with us today
+is brandon lachinsky
+
+ align:start position:0%
+is brandon lachinsky
+ 
+
+ align:start position:0%
+is brandon lachinsky
+a graduate student in the technology and
+
+ align:start position:0%
+a graduate student in the technology and
+ 
+
+ align:start position:0%
+a graduate student in the technology and
+policy masters program
+
+ align:start position:0%
+policy masters program
+ 
+
+ align:start position:0%
+policy masters program
+and the aeronautics and astronautics
+
+ align:start position:0%
+and the aeronautics and astronautics
+ 
+
+ align:start position:0%
+and the aeronautics and astronautics
+masters program at mit
+
+ align:start position:0%
+masters program at mit
+ 
+
+ align:start position:0%
+masters program at mit
+brandon's also working with a non-profit
+
+ align:start position:0%
+brandon's also working with a non-profit
+ 
+
+ align:start position:0%
+brandon's also working with a non-profit
+called earth dna
+
+ align:start position:0%
+called earth dna
+ 
+
+ align:start position:0%
+called earth dna
+if this organization sounds familiar to
+
+ align:start position:0%
+if this organization sounds familiar to
+ 
+
+ align:start position:0%
+if this organization sounds familiar to
+you it's because our last guest
+
+ align:start position:0%
+you it's because our last guest
+ 
+
+ align:start position:0%
+you it's because our last guest
+professor of astronautics deva newman
+
+ align:start position:0%
+professor of astronautics deva newman
+ 
+
+ align:start position:0%
+professor of astronautics deva newman
+co-founded earth dna it's a global
+
+ align:start position:0%
+co-founded earth dna it's a global
+ 
+
+ align:start position:0%
+co-founded earth dna it's a global
+platform for climate advocacy
+
+ align:start position:0%
+platform for climate advocacy
+ 
+
+ align:start position:0%
+platform for climate advocacy
+and action our guest today
+
+ align:start position:0%
+and action our guest today
+ 
+
+ align:start position:0%
+and action our guest today
+brandon helps create a program called
+
+ align:start position:0%
+brandon helps create a program called
+ 
+
+ align:start position:0%
+brandon helps create a program called
+earth dna
+
+ align:start position:0%
+earth dna
+ 
+
+ align:start position:0%
+earth dna
+ambassadors which provides young people
+
+ align:start position:0%
+ambassadors which provides young people
+ 
+
+ align:start position:0%
+ambassadors which provides young people
+with climate leadership
+
+ align:start position:0%
+with climate leadership
+ 
+
+ align:start position:0%
+with climate leadership
+training in addition to learning about
+
+ align:start position:0%
+training in addition to learning about
+ 
+
+ align:start position:0%
+training in addition to learning about
+the science behind climate change
+
+ align:start position:0%
+the science behind climate change
+ 
+
+ align:start position:0%
+the science behind climate change
+ambassadors also develop skills focused
+
+ align:start position:0%
+ambassadors also develop skills focused
+ 
+
+ align:start position:0%
+ambassadors also develop skills focused
+on communication
+
+ align:start position:0%
+on communication
+ 
+
+ align:start position:0%
+on communication
+negotiation and storytelling
+
+ align:start position:0%
+negotiation and storytelling
+ 
+
+ align:start position:0%
+negotiation and storytelling
+we envision a community of climate
+
+ align:start position:0%
+we envision a community of climate
+ 
+
+ align:start position:0%
+we envision a community of climate
+leaders
+
+ align:start position:0%
+leaders
+ 
+
+ align:start position:0%
+leaders
+who engage their own communities on
+
+ align:start position:0%
+who engage their own communities on
+ 
+
+ align:start position:0%
+who engage their own communities on
+their campuses
+
+ align:start position:0%
+their campuses
+ 
+
+ align:start position:0%
+their campuses
+at their schools on climate change
+
+ align:start position:0%
+at their schools on climate change
+ 
+
+ align:start position:0%
+at their schools on climate change
+current ambassadors
+
+ align:start position:0%
+current ambassadors
+ 
+
+ align:start position:0%
+current ambassadors
+come from different backgrounds whether
+
+ align:start position:0%
+come from different backgrounds whether
+ 
+
+ align:start position:0%
+come from different backgrounds whether
+phd students in immunology
+
+ align:start position:0%
+phd students in immunology
+ 
+
+ align:start position:0%
+phd students in immunology
+or undergraduate students in business
+
+ align:start position:0%
+or undergraduate students in business
+ 
+
+ align:start position:0%
+or undergraduate students in business
+some of them have teaching experience
+
+ align:start position:0%
+some of them have teaching experience
+ 
+
+ align:start position:0%
+some of them have teaching experience
+but not all of them
+
+ align:start position:0%
+but not all of them
+ 
+
+ align:start position:0%
+but not all of them
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+one of the tools that earth dna equips
+
+ align:start position:0%
+one of the tools that earth dna equips
+ 
+
+ align:start position:0%
+one of the tools that earth dna equips
+their ambassadors with
+
+ align:start position:0%
+their ambassadors with
+ 
+
+ align:start position:0%
+their ambassadors with
+is called climate 101
+
+ align:start position:0%
+is called climate 101
+ 
+
+ align:start position:0%
+is called climate 101
+available on mit open courseware and
+
+ align:start position:0%
+available on mit open courseware and
+ 
+
+ align:start position:0%
+available on mit open courseware and
+earthdna.org
+
+ align:start position:0%
+earthdna.org
+ 
+
+ align:start position:0%
+earthdna.org
+it's an interactive workshop that was
+
+ align:start position:0%
+it's an interactive workshop that was
+ 
+
+ align:start position:0%
+it's an interactive workshop that was
+designed to engage communities around
+
+ align:start position:0%
+designed to engage communities around
+ 
+
+ align:start position:0%
+designed to engage communities around
+climate change
+
+ align:start position:0%
+climate change
+ 
+
+ align:start position:0%
+climate change
+and motivate people to act but changing
+
+ align:start position:0%
+and motivate people to act but changing
+ 
+
+ align:start position:0%
+and motivate people to act but changing
+human behavior can be difficult
+
+ align:start position:0%
+human behavior can be difficult
+ 
+
+ align:start position:0%
+human behavior can be difficult
+so climate 101 starts with something a
+
+ align:start position:0%
+so climate 101 starts with something a
+ 
+
+ align:start position:0%
+so climate 101 starts with something a
+bit more approachable
+
+ align:start position:0%
+bit more approachable
+ 
+
+ align:start position:0%
+bit more approachable
+the power of conversation well i think
+
+ align:start position:0%
+the power of conversation well i think
+ 
+
+ align:start position:0%
+the power of conversation well i think
+talking about it is really important
+
+ align:start position:0%
+talking about it is really important
+ 
+
+ align:start position:0%
+talking about it is really important
+because i think that
+
+ align:start position:0%
+because i think that
+ 
+
+ align:start position:0%
+because i think that
+climate change has the stigma about it
+
+ align:start position:0%
+climate change has the stigma about it
+ 
+
+ align:start position:0%
+climate change has the stigma about it
+where if you
+
+ align:start position:0%
+where if you
+ 
+
+ align:start position:0%
+where if you
+even bring it up you're viewed as you
+
+ align:start position:0%
+even bring it up you're viewed as you
+ 
+
+ align:start position:0%
+even bring it up you're viewed as you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+a hippie environmentalist and alarmists
+
+ align:start position:0%
+a hippie environmentalist and alarmists
+ 
+
+ align:start position:0%
+a hippie environmentalist and alarmists
+and all these things
+
+ align:start position:0%
+and all these things
+ 
+
+ align:start position:0%
+and all these things
+and so even by having conversations
+
+ align:start position:0%
+and so even by having conversations
+ 
+
+ align:start position:0%
+and so even by having conversations
+about it and making it normal to have
+
+ align:start position:0%
+about it and making it normal to have
+ 
+
+ align:start position:0%
+about it and making it normal to have
+conversations
+
+ align:start position:0%
+conversations
+ 
+
+ align:start position:0%
+conversations
+about climate change you empower others
+
+ align:start position:0%
+about climate change you empower others
+ 
+
+ align:start position:0%
+about climate change you empower others
+to do that as well and
+
+ align:start position:0%
+to do that as well and
+ 
+
+ align:start position:0%
+to do that as well and
+that's huge because for a lot of people
+
+ align:start position:0%
+that's huge because for a lot of people
+ 
+
+ align:start position:0%
+that's huge because for a lot of people
+they just don't hear about climate
+
+ align:start position:0%
+they just don't hear about climate
+ 
+
+ align:start position:0%
+they just don't hear about climate
+change that often
+
+ align:start position:0%
+change that often
+ 
+
+ align:start position:0%
+change that often
+or if they hear about it it's not
+
+ align:start position:0%
+or if they hear about it it's not
+ 
+
+ align:start position:0%
+or if they hear about it it's not
+necessarily the best information
+
+ align:start position:0%
+necessarily the best information
+ 
+
+ align:start position:0%
+necessarily the best information
+and so if we can have people talking
+
+ align:start position:0%
+and so if we can have people talking
+ 
+
+ align:start position:0%
+and so if we can have people talking
+about climate change in a way that's
+
+ align:start position:0%
+about climate change in a way that's
+ 
+
+ align:start position:0%
+about climate change in a way that's
+personal and meaningful
+
+ align:start position:0%
+personal and meaningful
+ 
+
+ align:start position:0%
+personal and meaningful
+to their family members who might be
+
+ align:start position:0%
+to their family members who might be
+ 
+
+ align:start position:0%
+to their family members who might be
+climate skeptics
+
+ align:start position:0%
+climate skeptics
+ 
+
+ align:start position:0%
+climate skeptics
+that's one of the best ways to create
+
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+
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+ 
+
+ align:start position:0%
+especially in areas where the economy is
+based in
+
+ align:start position:0%
+based in
+ 
+
+ align:start position:0%
+based in
+fossil fuels it can be really difficult
+
+ align:start position:0%
+fossil fuels it can be really difficult
+ 
+
+ align:start position:0%
+fossil fuels it can be really difficult
+because ultimately a climate change
+
+ align:start position:0%
+because ultimately a climate change
+ 
+
+ align:start position:0%
+because ultimately a climate change
+conversation
+
+ align:start position:0%
+conversation
+ 
+
+ align:start position:0%
+conversation
+can amount to an accusation that that
+
+ align:start position:0%
+can amount to an accusation that that
+ 
+
+ align:start position:0%
+can amount to an accusation that that
+person is not just
+
+ align:start position:0%
+person is not just
+ 
+
+ align:start position:0%
+person is not just
+providing food for their family but also
+
+ align:start position:0%
+providing food for their family but also
+ 
+
+ align:start position:0%
+providing food for their family but also
+is damaging the earth and
+
+ align:start position:0%
+is damaging the earth and
+ 
+
+ align:start position:0%
+is damaging the earth and
+harming a lot of people and so it's
+
+ align:start position:0%
+harming a lot of people and so it's
+ 
+
+ align:start position:0%
+harming a lot of people and so it's
+really important to consider all of
+
+ align:start position:0%
+really important to consider all of
+ 
+
+ align:start position:0%
+really important to consider all of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+things as you have these climate change
+
+ align:start position:0%
+things as you have these climate change
+ 
+
+ align:start position:0%
+things as you have these climate change
+conversations
+
+ align:start position:0%
+conversations
+ 
+
+ align:start position:0%
+conversations
+so instead of trying to convince the
+
+ align:start position:0%
+so instead of trying to convince the
+ 
+
+ align:start position:0%
+so instead of trying to convince the
+other person or persuade the other
+
+ align:start position:0%
+other person or persuade the other
+ 
+
+ align:start position:0%
+other person or persuade the other
+person
+
+ align:start position:0%
+person
+ 
+
+ align:start position:0%
+person
+listen help them empty their heart
+
+ align:start position:0%
+listen help them empty their heart
+ 
+
+ align:start position:0%
+listen help them empty their heart
+and express why they're frustrated with
+
+ align:start position:0%
+and express why they're frustrated with
+ 
+
+ align:start position:0%
+and express why they're frustrated with
+a situation and then they'll be more
+
+ align:start position:0%
+a situation and then they'll be more
+ 
+
+ align:start position:0%
+a situation and then they'll be more
+likely to listen to your own experiences
+
+ align:start position:0%
+likely to listen to your own experiences
+ 
+
+ align:start position:0%
+likely to listen to your own experiences
+and more receptive to why you think
+
+ align:start position:0%
+and more receptive to why you think
+ 
+
+ align:start position:0%
+and more receptive to why you think
+climate change
+
+ align:start position:0%
+climate change
+ 
+
+ align:start position:0%
+climate change
+matters and is relevant
+
+ align:start position:0%
+matters and is relevant
+ 
+
+ align:start position:0%
+matters and is relevant
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something else that helps the climate
+
+ align:start position:0%
+something else that helps the climate
+ 
+
+ align:start position:0%
+something else that helps the climate
+101 presentation resonate across
+
+ align:start position:0%
+101 presentation resonate across
+ 
+
+ align:start position:0%
+101 presentation resonate across
+different audiences
+
+ align:start position:0%
+different audiences
+ 
+
+ align:start position:0%
+different audiences
+is the incorporation of local insights
+
+ align:start position:0%
+is the incorporation of local insights
+ 
+
+ align:start position:0%
+is the incorporation of local insights
+this targeted approach helps distill the
+
+ align:start position:0%
+this targeted approach helps distill the
+ 
+
+ align:start position:0%
+this targeted approach helps distill the
+larger sometimes overwhelming issue of
+
+ align:start position:0%
+larger sometimes overwhelming issue of
+ 
+
+ align:start position:0%
+larger sometimes overwhelming issue of
+climate change
+
+ align:start position:0%
+climate change
+ 
+
+ align:start position:0%
+climate change
+into something more digestible one of
+
+ align:start position:0%
+into something more digestible one of
+ 
+
+ align:start position:0%
+into something more digestible one of
+the problems with climate change
+
+ align:start position:0%
+the problems with climate change
+ 
+
+ align:start position:0%
+the problems with climate change
+discussions is that it's a huge problem
+
+ align:start position:0%
+discussions is that it's a huge problem
+ 
+
+ align:start position:0%
+discussions is that it's a huge problem
+right it affects the entire world and
+
+ align:start position:0%
+right it affects the entire world and
+ 
+
+ align:start position:0%
+right it affects the entire world and
+that happens over the course of decades
+
+ align:start position:0%
+that happens over the course of decades
+ 
+
+ align:start position:0%
+that happens over the course of decades
+but people live their lives at home or
+
+ align:start position:0%
+but people live their lives at home or
+ 
+
+ align:start position:0%
+but people live their lives at home or
+in their town
+
+ align:start position:0%
+in their town
+ 
+
+ align:start position:0%
+in their town
+and people live their lives day to day
+
+ align:start position:0%
+and people live their lives day to day
+ 
+
+ align:start position:0%
+and people live their lives day to day
+so when you start talking about these
+
+ align:start position:0%
+so when you start talking about these
+ 
+
+ align:start position:0%
+so when you start talking about these
+massive overwhelming changes
+
+ align:start position:0%
+massive overwhelming changes
+ 
+
+ align:start position:0%
+massive overwhelming changes
+it can be really easy to just dismiss
+
+ align:start position:0%
+it can be really easy to just dismiss
+ 
+
+ align:start position:0%
+it can be really easy to just dismiss
+them as either things
+
+ align:start position:0%
+them as either things
+ 
+
+ align:start position:0%
+them as either things
+that don't affect me or things that i
+
+ align:start position:0%
+that don't affect me or things that i
+ 
+
+ align:start position:0%
+that don't affect me or things that i
+can't do anything about
+
+ align:start position:0%
+can't do anything about
+ 
+
+ align:start position:0%
+can't do anything about
+the idea of creating localized insights
+
+ align:start position:0%
+the idea of creating localized insights
+ 
+
+ align:start position:0%
+the idea of creating localized insights
+and personally meaningful insights is
+
+ align:start position:0%
+and personally meaningful insights is
+ 
+
+ align:start position:0%
+and personally meaningful insights is
+that we need to talk about climate
+
+ align:start position:0%
+that we need to talk about climate
+ 
+
+ align:start position:0%
+that we need to talk about climate
+change in a way that's relevant
+
+ align:start position:0%
+change in a way that's relevant
+ 
+
+ align:start position:0%
+change in a way that's relevant
+to the intended audience and so if we
+
+ align:start position:0%
+to the intended audience and so if we
+ 
+
+ align:start position:0%
+to the intended audience and so if we
+can say for example
+
+ align:start position:0%
+can say for example
+ 
+
+ align:start position:0%
+can say for example
+well here in boston the city was
+
+ align:start position:0%
+well here in boston the city was
+ 
+
+ align:start position:0%
+well here in boston the city was
+actually considering building sea walls
+
+ align:start position:0%
+actually considering building sea walls
+ 
+
+ align:start position:0%
+actually considering building sea walls
+because of anticipated flooding now all
+
+ align:start position:0%
+because of anticipated flooding now all
+ 
+
+ align:start position:0%
+because of anticipated flooding now all
+of a sudden that's something that's
+
+ align:start position:0%
+of a sudden that's something that's
+ 
+
+ align:start position:0%
+of a sudden that's something that's
+happening in my neighborhood
+
+ align:start position:0%
+happening in my neighborhood
+ 
+
+ align:start position:0%
+happening in my neighborhood
+that's something that's like oh my god
+
+ align:start position:0%
+that's something that's like oh my god
+ 
+
+ align:start position:0%
+that's something that's like oh my god
+that's coming for me
+
+ align:start position:0%
+that's coming for me
+ 
+
+ align:start position:0%
+that's coming for me
+that's not the earth is warming by two
+
+ align:start position:0%
+that's not the earth is warming by two
+ 
+
+ align:start position:0%
+that's not the earth is warming by two
+degrees celsius which doesn't really
+
+ align:start position:0%
+degrees celsius which doesn't really
+ 
+
+ align:start position:0%
+degrees celsius which doesn't really
+mean much to me it's
+
+ align:start position:0%
+mean much to me it's
+ 
+
+ align:start position:0%
+mean much to me it's
+oh my god there's going to be flooding
+
+ align:start position:0%
+oh my god there's going to be flooding
+ 
+
+ align:start position:0%
+oh my god there's going to be flooding
+in boston
+
+ align:start position:0%
+in boston
+ 
+
+ align:start position:0%
+in boston
+the more i talked with brandon the more
+
+ align:start position:0%
+the more i talked with brandon the more
+ 
+
+ align:start position:0%
+the more i talked with brandon the more
+i wanted to know what was personally
+
+ align:start position:0%
+i wanted to know what was personally
+ 
+
+ align:start position:0%
+i wanted to know what was personally
+motivating him
+
+ align:start position:0%
+motivating him
+ 
+
+ align:start position:0%
+motivating him
+to engage in climate action work he
+
+ align:start position:0%
+to engage in climate action work he
+ 
+
+ align:start position:0%
+to engage in climate action work he
+began to talk about the
+
+ align:start position:0%
+began to talk about the
+ 
+
+ align:start position:0%
+began to talk about the
+intergenerational experiences
+
+ align:start position:0%
+intergenerational experiences
+ 
+
+ align:start position:0%
+intergenerational experiences
+of his own family a few years ago
+
+ align:start position:0%
+of his own family a few years ago
+ 
+
+ align:start position:0%
+of his own family a few years ago
+my family celebrated its 25th
+
+ align:start position:0%
+my family celebrated its 25th
+ 
+
+ align:start position:0%
+my family celebrated its 25th
+anniversary in the united states
+
+ align:start position:0%
+anniversary in the united states
+ 
+
+ align:start position:0%
+anniversary in the united states
+we were all at my grandparents place
+
+ align:start position:0%
+we were all at my grandparents place
+ 
+
+ align:start position:0%
+we were all at my grandparents place
+seated around this beautiful dining room
+
+ align:start position:0%
+seated around this beautiful dining room
+ 
+
+ align:start position:0%
+seated around this beautiful dining room
+table
+
+ align:start position:0%
+table
+ 
+
+ align:start position:0%
+table
+in front of a gorgeous display case full
+
+ align:start position:0%
+in front of a gorgeous display case full
+ 
+
+ align:start position:0%
+in front of a gorgeous display case full
+of fancy china
+
+ align:start position:0%
+of fancy china
+ 
+
+ align:start position:0%
+of fancy china
+and my grandma was bustling around
+
+ align:start position:0%
+and my grandma was bustling around
+ 
+
+ align:start position:0%
+and my grandma was bustling around
+making sure we all had enough of that
+
+ align:start position:0%
+making sure we all had enough of that
+ 
+
+ align:start position:0%
+making sure we all had enough of that
+fatty and meaty ukrainian food that my
+
+ align:start position:0%
+fatty and meaty ukrainian food that my
+ 
+
+ align:start position:0%
+fatty and meaty ukrainian food that my
+family loves
+
+ align:start position:0%
+family loves
+ 
+
+ align:start position:0%
+family loves
+and my family was telling stories
+
+ align:start position:0%
+and my family was telling stories
+ 
+
+ align:start position:0%
+and my family was telling stories
+stories of my childhood that i'd been
+
+ align:start position:0%
+stories of my childhood that i'd been
+ 
+
+ align:start position:0%
+stories of my childhood that i'd been
+hearing for years
+
+ align:start position:0%
+hearing for years
+ 
+
+ align:start position:0%
+hearing for years
+but stories that helped us reflect on
+
+ align:start position:0%
+but stories that helped us reflect on
+ 
+
+ align:start position:0%
+but stories that helped us reflect on
+what it meant to come to the united
+
+ align:start position:0%
+what it meant to come to the united
+ 
+
+ align:start position:0%
+what it meant to come to the united
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+my grandpa told how he'd only taken one
+
+ align:start position:0%
+my grandpa told how he'd only taken one
+ 
+
+ align:start position:0%
+my grandpa told how he'd only taken one
+flight in his whole life
+
+ align:start position:0%
+flight in his whole life
+ 
+
+ align:start position:0%
+flight in his whole life
+and it was to come to the united states
+
+ align:start position:0%
+and it was to come to the united states
+ 
+
+ align:start position:0%
+and it was to come to the united states
+because the only thing that he feared
+
+ align:start position:0%
+because the only thing that he feared
+ 
+
+ align:start position:0%
+because the only thing that he feared
+more than flying was staying in a
+
+ align:start position:0%
+more than flying was staying in a
+ 
+
+ align:start position:0%
+more than flying was staying in a
+collapsed soviet state
+
+ align:start position:0%
+collapsed soviet state
+ 
+
+ align:start position:0%
+collapsed soviet state
+my grandma how she came to the u.s
+
+ align:start position:0%
+my grandma how she came to the u.s
+ 
+
+ align:start position:0%
+my grandma how she came to the u.s
+without knowing any english and not only
+
+ align:start position:0%
+without knowing any english and not only
+ 
+
+ align:start position:0%
+without knowing any english and not only
+learned english but also learned how to
+
+ align:start position:0%
+learned english but also learned how to
+ 
+
+ align:start position:0%
+learned english but also learned how to
+code
+
+ align:start position:0%
+code
+ 
+
+ align:start position:0%
+code
+and recently retired as a senior
+
+ align:start position:0%
+and recently retired as a senior
+ 
+
+ align:start position:0%
+and recently retired as a senior
+software developer
+
+ align:start position:0%
+software developer
+ 
+
+ align:start position:0%
+software developer
+my mom how she after four months here
+
+ align:start position:0%
+my mom how she after four months here
+ 
+
+ align:start position:0%
+my mom how she after four months here
+was caught stealing a seven dollar
+
+ align:start position:0%
+was caught stealing a seven dollar
+ 
+
+ align:start position:0%
+was caught stealing a seven dollar
+bottle of face cream
+
+ align:start position:0%
+bottle of face cream
+ 
+
+ align:start position:0%
+bottle of face cream
+because she wanted to get a gift for her
+
+ align:start position:0%
+because she wanted to get a gift for her
+ 
+
+ align:start position:0%
+because she wanted to get a gift for her
+mom's birthday and she couldn't afford
+
+ align:start position:0%
+mom's birthday and she couldn't afford
+ 
+
+ align:start position:0%
+mom's birthday and she couldn't afford
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+now my mom went on and started a
+
+ align:start position:0%
+now my mom went on and started a
+ 
+
+ align:start position:0%
+now my mom went on and started a
+business that ended up putting me
+
+ align:start position:0%
+business that ended up putting me
+ 
+
+ align:start position:0%
+business that ended up putting me
+through college
+
+ align:start position:0%
+through college
+ 
+
+ align:start position:0%
+through college
+but even 25 years later she was still so
+
+ align:start position:0%
+but even 25 years later she was still so
+ 
+
+ align:start position:0%
+but even 25 years later she was still so
+embarrassed and ashamed of that moment
+
+ align:start position:0%
+embarrassed and ashamed of that moment
+ 
+
+ align:start position:0%
+embarrassed and ashamed of that moment
+i turned to my dad and i asked him
+
+ align:start position:0%
+i turned to my dad and i asked him
+ 
+
+ align:start position:0%
+i turned to my dad and i asked him
+whether he ever missed
+
+ align:start position:0%
+whether he ever missed
+ 
+
+ align:start position:0%
+whether he ever missed
+the ukraine it's where he grew up it's
+
+ align:start position:0%
+the ukraine it's where he grew up it's
+ 
+
+ align:start position:0%
+the ukraine it's where he grew up it's
+where his friends
+
+ align:start position:0%
+where his friends
+ 
+
+ align:start position:0%
+where his friends
+are and he turned to me and responded in
+
+ align:start position:0%
+are and he turned to me and responded in
+ 
+
+ align:start position:0%
+are and he turned to me and responded in
+russian
+
+ align:start position:0%
+russian
+ 
+
+ align:start position:0%
+russian
+that only in his worst nightmare would
+
+ align:start position:0%
+that only in his worst nightmare would
+ 
+
+ align:start position:0%
+that only in his worst nightmare would
+he ever wake up back in that hell
+
+ align:start position:0%
+he ever wake up back in that hell
+ 
+
+ align:start position:0%
+he ever wake up back in that hell
+and to me that moment really
+
+ align:start position:0%
+and to me that moment really
+ 
+
+ align:start position:0%
+and to me that moment really
+crystallizes this idea that so much
+
+ align:start position:0%
+crystallizes this idea that so much
+ 
+
+ align:start position:0%
+crystallizes this idea that so much
+of who we are and what we have is
+
+ align:start position:0%
+of who we are and what we have is
+ 
+
+ align:start position:0%
+of who we are and what we have is
+determined
+
+ align:start position:0%
+determined
+ 
+
+ align:start position:0%
+determined
+by choices that people make before we're
+
+ align:start position:0%
+by choices that people make before we're
+ 
+
+ align:start position:0%
+by choices that people make before we're
+even born and that's just
+
+ align:start position:0%
+even born and that's just
+ 
+
+ align:start position:0%
+even born and that's just
+such a great injustice and
+
+ align:start position:0%
+such a great injustice and
+ 
+
+ align:start position:0%
+such a great injustice and
+climate change exemplifies that i think
+
+ align:start position:0%
+climate change exemplifies that i think
+ 
+
+ align:start position:0%
+climate change exemplifies that i think
+climate change is
+
+ align:start position:0%
+climate change is
+ 
+
+ align:start position:0%
+climate change is
+one of the great injustices of our time
+
+ align:start position:0%
+one of the great injustices of our time
+ 
+
+ align:start position:0%
+one of the great injustices of our time
+it was created primarily by wealthy
+
+ align:start position:0%
+it was created primarily by wealthy
+ 
+
+ align:start position:0%
+it was created primarily by wealthy
+privileged people in developed nations
+
+ align:start position:0%
+privileged people in developed nations
+ 
+
+ align:start position:0%
+privileged people in developed nations
+and it will primarily affect the
+
+ align:start position:0%
+and it will primarily affect the
+ 
+
+ align:start position:0%
+and it will primarily affect the
+vulnerable the poor
+
+ align:start position:0%
+vulnerable the poor
+ 
+
+ align:start position:0%
+vulnerable the poor
+the sick in many cases people who never
+
+ align:start position:0%
+the sick in many cases people who never
+ 
+
+ align:start position:0%
+the sick in many cases people who never
+even contributed to the problem
+
+ align:start position:0%
+even contributed to the problem
+ 
+
+ align:start position:0%
+even contributed to the problem
+i think that for those of us who have an
+
+ align:start position:0%
+i think that for those of us who have an
+ 
+
+ align:start position:0%
+i think that for those of us who have an
+opportunity
+
+ align:start position:0%
+opportunity
+ 
+
+ align:start position:0%
+opportunity
+to fight that injustice for those of us
+
+ align:start position:0%
+to fight that injustice for those of us
+ 
+
+ align:start position:0%
+to fight that injustice for those of us
+who have benefited
+
+ align:start position:0%
+who have benefited
+ 
+
+ align:start position:0%
+who have benefited
+from being fortunate and from being born
+
+ align:start position:0%
+from being fortunate and from being born
+ 
+
+ align:start position:0%
+from being fortunate and from being born
+in the right place at the right time
+
+ align:start position:0%
+in the right place at the right time
+ 
+
+ align:start position:0%
+in the right place at the right time
+we have a real obligation to help the
+
+ align:start position:0%
+we have a real obligation to help the
+ 
+
+ align:start position:0%
+we have a real obligation to help the
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+who don't necessarily have those
+
+ align:start position:0%
+who don't necessarily have those
+ 
+
+ align:start position:0%
+who don't necessarily have those
+opportunities now reach those same
+
+ align:start position:0%
+opportunities now reach those same
+ 
+
+ align:start position:0%
+opportunities now reach those same
+opportunities
+
+ align:start position:0%
+opportunities
+ 
+
+ align:start position:0%
+opportunities
+and in this case it means doing
+
+ align:start position:0%
+and in this case it means doing
+ 
+
+ align:start position:0%
+and in this case it means doing
+something about
+
+ align:start position:0%
+something about
+ 
+
+ align:start position:0%
+something about
+this massive global problem that will
+
+ align:start position:0%
+this massive global problem that will
+ 
+
+ align:start position:0%
+this massive global problem that will
+eventually affect all of us but is
+
+ align:start position:0%
+eventually affect all of us but is
+ 
+
+ align:start position:0%
+eventually affect all of us but is
+already affecting
+
+ align:start position:0%
+already affecting
+ 
+
+ align:start position:0%
+already affecting
+many of the most vulnerable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one important component in tackling
+
+ align:start position:0%
+one important component in tackling
+ 
+
+ align:start position:0%
+one important component in tackling
+climate change
+
+ align:start position:0%
+climate change
+ 
+
+ align:start position:0%
+climate change
+is recognizing that it's a collective
+
+ align:start position:0%
+is recognizing that it's a collective
+ 
+
+ align:start position:0%
+is recognizing that it's a collective
+issue that affects just about everyone
+
+ align:start position:0%
+issue that affects just about everyone
+ 
+
+ align:start position:0%
+issue that affects just about everyone
+brandon incorporated interactive
+
+ align:start position:0%
+brandon incorporated interactive
+ 
+
+ align:start position:0%
+brandon incorporated interactive
+activities into the climate 101
+
+ align:start position:0%
+activities into the climate 101
+ 
+
+ align:start position:0%
+activities into the climate 101
+curriculum
+
+ align:start position:0%
+curriculum
+ 
+
+ align:start position:0%
+curriculum
+to help simulate how these collective
+
+ align:start position:0%
+to help simulate how these collective
+ 
+
+ align:start position:0%
+to help simulate how these collective
+dilemmas can play out
+
+ align:start position:0%
+dilemmas can play out
+ 
+
+ align:start position:0%
+dilemmas can play out
+these activities are modeled on the
+
+ align:start position:0%
+these activities are modeled on the
+ 
+
+ align:start position:0%
+these activities are modeled on the
+concept of the tragedy of the commons
+
+ align:start position:0%
+concept of the tragedy of the commons
+ 
+
+ align:start position:0%
+concept of the tragedy of the commons
+where people tend to act selfishly when
+
+ align:start position:0%
+where people tend to act selfishly when
+ 
+
+ align:start position:0%
+where people tend to act selfishly when
+they believe that their individual
+
+ align:start position:0%
+they believe that their individual
+ 
+
+ align:start position:0%
+they believe that their individual
+actions
+
+ align:start position:0%
+actions
+ 
+
+ align:start position:0%
+actions
+won't make an impact a classic example
+
+ align:start position:0%
+won't make an impact a classic example
+ 
+
+ align:start position:0%
+won't make an impact a classic example
+of the tragedy of the commons
+
+ align:start position:0%
+of the tragedy of the commons
+ 
+
+ align:start position:0%
+of the tragedy of the commons
+is the gradual overfishing of a public
+
+ align:start position:0%
+is the gradual overfishing of a public
+ 
+
+ align:start position:0%
+is the gradual overfishing of a public
+waterway
+
+ align:start position:0%
+waterway
+ 
+
+ align:start position:0%
+waterway
+and in some ways this concept mirrors
+
+ align:start position:0%
+and in some ways this concept mirrors
+ 
+
+ align:start position:0%
+and in some ways this concept mirrors
+what we've seen throughout the kovit 19
+
+ align:start position:0%
+what we've seen throughout the kovit 19
+ 
+
+ align:start position:0%
+what we've seen throughout the kovit 19
+pandemic
+
+ align:start position:0%
+pandemic
+ 
+
+ align:start position:0%
+pandemic
+while these issues are quite different
+
+ align:start position:0%
+while these issues are quite different
+ 
+
+ align:start position:0%
+while these issues are quite different
+of course they do both require
+
+ align:start position:0%
+of course they do both require
+ 
+
+ align:start position:0%
+of course they do both require
+collaborative efforts to make a real
+
+ align:start position:0%
+collaborative efforts to make a real
+ 
+
+ align:start position:0%
+collaborative efforts to make a real
+difference in tackling them
+
+ align:start position:0%
+difference in tackling them
+ 
+
+ align:start position:0%
+difference in tackling them
+and our everyday choices actually can
+
+ align:start position:0%
+and our everyday choices actually can
+ 
+
+ align:start position:0%
+and our everyday choices actually can
+have an immediate impact
+
+ align:start position:0%
+have an immediate impact
+ 
+
+ align:start position:0%
+have an immediate impact
+i think covid is a really great example
+
+ align:start position:0%
+i think covid is a really great example
+ 
+
+ align:start position:0%
+i think covid is a really great example
+of collective dilemmas
+
+ align:start position:0%
+of collective dilemmas
+ 
+
+ align:start position:0%
+of collective dilemmas
+and in the us in particular we have this
+
+ align:start position:0%
+and in the us in particular we have this
+ 
+
+ align:start position:0%
+and in the us in particular we have this
+very individualist attitude
+
+ align:start position:0%
+very individualist attitude
+ 
+
+ align:start position:0%
+very individualist attitude
+personal liberty above all else and
+
+ align:start position:0%
+personal liberty above all else and
+ 
+
+ align:start position:0%
+personal liberty above all else and
+personal liberty is
+
+ align:start position:0%
+personal liberty is
+ 
+
+ align:start position:0%
+personal liberty is
+obviously super important but we see in
+
+ align:start position:0%
+obviously super important but we see in
+ 
+
+ align:start position:0%
+obviously super important but we see in
+a case like kovid
+
+ align:start position:0%
+a case like kovid
+ 
+
+ align:start position:0%
+a case like kovid
+that when crises arise sometimes
+
+ align:start position:0%
+that when crises arise sometimes
+ 
+
+ align:start position:0%
+that when crises arise sometimes
+we do need to act for the collective
+
+ align:start position:0%
+we do need to act for the collective
+ 
+
+ align:start position:0%
+we do need to act for the collective
+good and that can be really difficult
+
+ align:start position:0%
+good and that can be really difficult
+ 
+
+ align:start position:0%
+good and that can be really difficult
+but climate change is similar the longer
+
+ align:start position:0%
+but climate change is similar the longer
+ 
+
+ align:start position:0%
+but climate change is similar the longer
+we waited to take action on kovid
+
+ align:start position:0%
+we waited to take action on kovid
+ 
+
+ align:start position:0%
+we waited to take action on kovid
+the more drastic the action had to be
+
+ align:start position:0%
+the more drastic the action had to be
+ 
+
+ align:start position:0%
+the more drastic the action had to be
+and with climate change it's similar
+
+ align:start position:0%
+and with climate change it's similar
+ 
+
+ align:start position:0%
+and with climate change it's similar
+had we started really focusing on
+
+ align:start position:0%
+had we started really focusing on
+ 
+
+ align:start position:0%
+had we started really focusing on
+reducing our emissions and transitioning
+
+ align:start position:0%
+reducing our emissions and transitioning
+ 
+
+ align:start position:0%
+reducing our emissions and transitioning
+to renewable energy
+
+ align:start position:0%
+to renewable energy
+ 
+
+ align:start position:0%
+to renewable energy
+as well as making some of the other
+
+ align:start position:0%
+as well as making some of the other
+ 
+
+ align:start position:0%
+as well as making some of the other
+changes we need to make in
+
+ align:start position:0%
+changes we need to make in
+ 
+
+ align:start position:0%
+changes we need to make in
+2000 we could have done it pretty
+
+ align:start position:0%
+2000 we could have done it pretty
+ 
+
+ align:start position:0%
+2000 we could have done it pretty
+gradually and at a reasonable pace
+
+ align:start position:0%
+gradually and at a reasonable pace
+ 
+
+ align:start position:0%
+gradually and at a reasonable pace
+but we waited 20 years and it looks like
+
+ align:start position:0%
+but we waited 20 years and it looks like
+ 
+
+ align:start position:0%
+but we waited 20 years and it looks like
+we're still waiting
+
+ align:start position:0%
+we're still waiting
+ 
+
+ align:start position:0%
+we're still waiting
+so now the action that we have to take
+
+ align:start position:0%
+so now the action that we have to take
+ 
+
+ align:start position:0%
+so now the action that we have to take
+is much more drastic
+
+ align:start position:0%
+is much more drastic
+ 
+
+ align:start position:0%
+is much more drastic
+than had we done it 20 years ago and if
+
+ align:start position:0%
+than had we done it 20 years ago and if
+ 
+
+ align:start position:0%
+than had we done it 20 years ago and if
+we continue to wait
+
+ align:start position:0%
+we continue to wait
+ 
+
+ align:start position:0%
+we continue to wait
+that action will have to be still more
+
+ align:start position:0%
+that action will have to be still more
+ 
+
+ align:start position:0%
+that action will have to be still more
+drastic
+
+ align:start position:0%
+drastic
+ 
+
+ align:start position:0%
+drastic
+so yesterday is better than today and
+
+ align:start position:0%
+so yesterday is better than today and
+ 
+
+ align:start position:0%
+so yesterday is better than today and
+today is better than tomorrow
+
+ align:start position:0%
+today is better than tomorrow
+ 
+
+ align:start position:0%
+today is better than tomorrow
+to quote one of the articles that i read
+
+ align:start position:0%
+to quote one of the articles that i read
+ 
+
+ align:start position:0%
+to quote one of the articles that i read
+regarding kovid
+
+ align:start position:0%
+regarding kovid
+ 
+
+ align:start position:0%
+regarding kovid
+but that also applies equally well to
+
+ align:start position:0%
+but that also applies equally well to
+ 
+
+ align:start position:0%
+but that also applies equally well to
+climate change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many people worry that attention on
+
+ align:start position:0%
+many people worry that attention on
+ 
+
+ align:start position:0%
+many people worry that attention on
+climate change has weakened due to the
+
+ align:start position:0%
+climate change has weakened due to the
+ 
+
+ align:start position:0%
+climate change has weakened due to the
+covet 19 pandemic
+
+ align:start position:0%
+covet 19 pandemic
+ 
+
+ align:start position:0%
+covet 19 pandemic
+but brandon sees a space for optimism
+
+ align:start position:0%
+but brandon sees a space for optimism
+ 
+
+ align:start position:0%
+but brandon sees a space for optimism
+and views these overlapping crises
+
+ align:start position:0%
+and views these overlapping crises
+ 
+
+ align:start position:0%
+and views these overlapping crises
+as an opportunity i think for a lot of
+
+ align:start position:0%
+as an opportunity i think for a lot of
+ 
+
+ align:start position:0%
+as an opportunity i think for a lot of
+climate activists right now is
+
+ align:start position:0%
+climate activists right now is
+ 
+
+ align:start position:0%
+climate activists right now is
+difficult in terms of climate activism
+
+ align:start position:0%
+difficult in terms of climate activism
+ 
+
+ align:start position:0%
+difficult in terms of climate activism
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+covet is a really serious and really
+
+ align:start position:0%
+covet is a really serious and really
+ 
+
+ align:start position:0%
+covet is a really serious and really
+urgent problem
+
+ align:start position:0%
+urgent problem
+ 
+
+ align:start position:0%
+urgent problem
+and it can be hard to spare any
+
+ align:start position:0%
+and it can be hard to spare any
+ 
+
+ align:start position:0%
+and it can be hard to spare any
+attention or any emotion
+
+ align:start position:0%
+attention or any emotion
+ 
+
+ align:start position:0%
+attention or any emotion
+for climate change this other scary
+
+ align:start position:0%
+for climate change this other scary
+ 
+
+ align:start position:0%
+for climate change this other scary
+thing but times of crisis are actually
+
+ align:start position:0%
+thing but times of crisis are actually
+ 
+
+ align:start position:0%
+thing but times of crisis are actually
+times of opportunity
+
+ align:start position:0%
+times of opportunity
+ 
+
+ align:start position:0%
+times of opportunity
+and so right now is a time that people
+
+ align:start position:0%
+and so right now is a time that people
+ 
+
+ align:start position:0%
+and so right now is a time that people
+feel like they need connection and
+
+ align:start position:0%
+feel like they need connection and
+ 
+
+ align:start position:0%
+feel like they need connection and
+purpose
+
+ align:start position:0%
+purpose
+ 
+
+ align:start position:0%
+purpose
+and community and so right now is an
+
+ align:start position:0%
+and community and so right now is an
+ 
+
+ align:start position:0%
+and community and so right now is an
+opportunity for us to continue growing
+
+ align:start position:0%
+opportunity for us to continue growing
+ 
+
+ align:start position:0%
+opportunity for us to continue growing
+and giving people those things and it's
+
+ align:start position:0%
+and giving people those things and it's
+ 
+
+ align:start position:0%
+and giving people those things and it's
+also an opportunity to fight even harder
+
+ align:start position:0%
+also an opportunity to fight even harder
+ 
+
+ align:start position:0%
+also an opportunity to fight even harder
+for some of the changes that we need to
+
+ align:start position:0%
+for some of the changes that we need to
+ 
+
+ align:start position:0%
+for some of the changes that we need to
+make in order to
+
+ align:start position:0%
+make in order to
+ 
+
+ align:start position:0%
+make in order to
+overcome the climate change issue as
+
+ align:start position:0%
+overcome the climate change issue as
+ 
+
+ align:start position:0%
+overcome the climate change issue as
+well as the covet issue
+
+ align:start position:0%
+well as the covet issue
+ 
+
+ align:start position:0%
+well as the covet issue
+much of brandon's work around this
+
+ align:start position:0%
+much of brandon's work around this
+ 
+
+ align:start position:0%
+much of brandon's work around this
+project which inspires others to take a
+
+ align:start position:0%
+project which inspires others to take a
+ 
+
+ align:start position:0%
+project which inspires others to take a
+leadership role in their own way
+
+ align:start position:0%
+leadership role in their own way
+ 
+
+ align:start position:0%
+leadership role in their own way
+has been driven by his own experiences
+
+ align:start position:0%
+has been driven by his own experiences
+ 
+
+ align:start position:0%
+has been driven by his own experiences
+with leaders in his life
+
+ align:start position:0%
+with leaders in his life
+ 
+
+ align:start position:0%
+with leaders in his life
+throughout the covet 19 pandemic he's
+
+ align:start position:0%
+throughout the covet 19 pandemic he's
+ 
+
+ align:start position:0%
+throughout the covet 19 pandemic he's
+found strong leaders and his advisor
+
+ align:start position:0%
+found strong leaders and his advisor
+ 
+
+ align:start position:0%
+found strong leaders and his advisor
+professor david newman at mit
+
+ align:start position:0%
+professor david newman at mit
+ 
+
+ align:start position:0%
+professor david newman at mit
+who you heard from in our last episode
+
+ align:start position:0%
+who you heard from in our last episode
+ 
+
+ align:start position:0%
+who you heard from in our last episode
+and rand wentworth
+
+ align:start position:0%
+and rand wentworth
+ 
+
+ align:start position:0%
+and rand wentworth
+brandon's environmental leadership
+
+ align:start position:0%
+brandon's environmental leadership
+ 
+
+ align:start position:0%
+brandon's environmental leadership
+professor at the harvard kennedy school
+
+ align:start position:0%
+professor at the harvard kennedy school
+ 
+
+ align:start position:0%
+professor at the harvard kennedy school
+they have both been such incredible
+
+ align:start position:0%
+they have both been such incredible
+ 
+
+ align:start position:0%
+they have both been such incredible
+models of what it means to be a leader
+
+ align:start position:0%
+models of what it means to be a leader
+ 
+
+ align:start position:0%
+models of what it means to be a leader
+during a crisis
+
+ align:start position:0%
+during a crisis
+ 
+
+ align:start position:0%
+during a crisis
+they have been hyper attentive to their
+
+ align:start position:0%
+they have been hyper attentive to their
+ 
+
+ align:start position:0%
+they have been hyper attentive to their
+students needs
+
+ align:start position:0%
+students needs
+ 
+
+ align:start position:0%
+students needs
+so empathetic such good listeners
+
+ align:start position:0%
+so empathetic such good listeners
+ 
+
+ align:start position:0%
+so empathetic such good listeners
+adaptive and flexible and positive
+
+ align:start position:0%
+adaptive and flexible and positive
+ 
+
+ align:start position:0%
+adaptive and flexible and positive
+and that has been really inspiring for
+
+ align:start position:0%
+and that has been really inspiring for
+ 
+
+ align:start position:0%
+and that has been really inspiring for
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+empathy is everything and it's just so
+
+ align:start position:0%
+empathy is everything and it's just so
+ 
+
+ align:start position:0%
+empathy is everything and it's just so
+hard right now
+
+ align:start position:0%
+hard right now
+ 
+
+ align:start position:0%
+hard right now
+you know my emotional reserves that i
+
+ align:start position:0%
+you know my emotional reserves that i
+ 
+
+ align:start position:0%
+you know my emotional reserves that i
+usually
+
+ align:start position:0%
+usually
+ 
+
+ align:start position:0%
+usually
+use to accomplish tasks that i don't
+
+ align:start position:0%
+use to accomplish tasks that i don't
+ 
+
+ align:start position:0%
+use to accomplish tasks that i don't
+necessarily find is interesting
+
+ align:start position:0%
+necessarily find is interesting
+ 
+
+ align:start position:0%
+necessarily find is interesting
+are gone at this point i'm just hyper
+
+ align:start position:0%
+are gone at this point i'm just hyper
+ 
+
+ align:start position:0%
+are gone at this point i'm just hyper
+focused on staying sane
+
+ align:start position:0%
+focused on staying sane
+ 
+
+ align:start position:0%
+focused on staying sane
+staying happy staying healthy and
+
+ align:start position:0%
+staying happy staying healthy and
+ 
+
+ align:start position:0%
+staying happy staying healthy and
+rand and deva both really understand
+
+ align:start position:0%
+rand and deva both really understand
+ 
+
+ align:start position:0%
+rand and deva both really understand
+that and they start every meeting
+
+ align:start position:0%
+that and they start every meeting
+ 
+
+ align:start position:0%
+that and they start every meeting
+with a check-in how are you guys what
+
+ align:start position:0%
+with a check-in how are you guys what
+ 
+
+ align:start position:0%
+with a check-in how are you guys what
+can i do to help
+
+ align:start position:0%
+can i do to help
+ 
+
+ align:start position:0%
+can i do to help
+and that's something that i hope to take
+
+ align:start position:0%
+and that's something that i hope to take
+ 
+
+ align:start position:0%
+and that's something that i hope to take
+forward
+
+ align:start position:0%
+forward
+ 
+
+ align:start position:0%
+forward
+as an immediate response in a crisis
+
+ align:start position:0%
+as an immediate response in a crisis
+ 
+
+ align:start position:0%
+as an immediate response in a crisis
+is to figure out okay how are the people
+
+ align:start position:0%
+is to figure out okay how are the people
+ 
+
+ align:start position:0%
+is to figure out okay how are the people
+that are affected by this crisis
+
+ align:start position:0%
+that are affected by this crisis
+ 
+
+ align:start position:0%
+that are affected by this crisis
+doing and what can i do to accommodate
+
+ align:start position:0%
+doing and what can i do to accommodate
+ 
+
+ align:start position:0%
+doing and what can i do to accommodate
+them and to make it easier
+
+ align:start position:0%
+them and to make it easier
+ 
+
+ align:start position:0%
+them and to make it easier
+for them brandon understands that many
+
+ align:start position:0%
+for them brandon understands that many
+ 
+
+ align:start position:0%
+for them brandon understands that many
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+when faced with the covet 19 pandemic as
+
+ align:start position:0%
+when faced with the covet 19 pandemic as
+ 
+
+ align:start position:0%
+when faced with the covet 19 pandemic as
+well as the threat of climate change are
+
+ align:start position:0%
+well as the threat of climate change are
+ 
+
+ align:start position:0%
+well as the threat of climate change are
+experiencing a kind of
+
+ align:start position:0%
+experiencing a kind of
+ 
+
+ align:start position:0%
+experiencing a kind of
+doom fatigue if you seek it out there
+
+ align:start position:0%
+doom fatigue if you seek it out there
+ 
+
+ align:start position:0%
+doom fatigue if you seek it out there
+can be an
+
+ align:start position:0%
+can be an
+ 
+
+ align:start position:0%
+can be an
+overwhelming amount of bad news about
+
+ align:start position:0%
+overwhelming amount of bad news about
+ 
+
+ align:start position:0%
+overwhelming amount of bad news about
+both crises
+
+ align:start position:0%
+both crises
+ 
+
+ align:start position:0%
+both crises
+but brandon is working on reframing this
+
+ align:start position:0%
+but brandon is working on reframing this
+ 
+
+ align:start position:0%
+but brandon is working on reframing this
+thinking into something more
+
+ align:start position:0%
+thinking into something more
+ 
+
+ align:start position:0%
+thinking into something more
+approachable
+
+ align:start position:0%
+approachable
+ 
+
+ align:start position:0%
+approachable
+so that people can carry forward with
+
+ align:start position:0%
+so that people can carry forward with
+ 
+
+ align:start position:0%
+so that people can carry forward with
+important work in their own
+
+ align:start position:0%
+important work in their own
+ 
+
+ align:start position:0%
+important work in their own
+manageable way without feeling like it's
+
+ align:start position:0%
+manageable way without feeling like it's
+ 
+
+ align:start position:0%
+manageable way without feeling like it's
+all just too much to handle
+
+ align:start position:0%
+all just too much to handle
+ 
+
+ align:start position:0%
+all just too much to handle
+there are definitely times when i also
+
+ align:start position:0%
+there are definitely times when i also
+ 
+
+ align:start position:0%
+there are definitely times when i also
+feel like
+
+ align:start position:0%
+feel like
+ 
+
+ align:start position:0%
+feel like
+why am i even bothering there's so
+
+ align:start position:0%
+why am i even bothering there's so
+ 
+
+ align:start position:0%
+why am i even bothering there's so
+much out there to improve
+
+ align:start position:0%
+much out there to improve
+ 
+
+ align:start position:0%
+much out there to improve
+what can i do there's a story
+
+ align:start position:0%
+what can i do there's a story
+ 
+
+ align:start position:0%
+what can i do there's a story
+that i love it's
+
+ align:start position:0%
+that i love it's
+ 
+
+ align:start position:0%
+that i love it's
+told by wangari matai who's a nobel
+
+ align:start position:0%
+told by wangari matai who's a nobel
+ 
+
+ align:start position:0%
+told by wangari matai who's a nobel
+peace prize winner
+
+ align:start position:0%
+peace prize winner
+ 
+
+ align:start position:0%
+peace prize winner
+for her environmental work she tells the
+
+ align:start position:0%
+for her environmental work she tells the
+ 
+
+ align:start position:0%
+for her environmental work she tells the
+story
+
+ align:start position:0%
+story
+ 
+
+ align:start position:0%
+story
+of a great big forest fire and how all
+
+ align:start position:0%
+of a great big forest fire and how all
+ 
+
+ align:start position:0%
+of a great big forest fire and how all
+of the animals
+
+ align:start position:0%
+of the animals
+ 
+
+ align:start position:0%
+of the animals
+are running out of the forest and
+
+ align:start position:0%
+are running out of the forest and
+ 
+
+ align:start position:0%
+are running out of the forest and
+they're standing next to it
+
+ align:start position:0%
+they're standing next to it
+ 
+
+ align:start position:0%
+they're standing next to it
+as it burns but one animal the
+
+ align:start position:0%
+as it burns but one animal the
+ 
+
+ align:start position:0%
+as it burns but one animal the
+hummingbird
+
+ align:start position:0%
+hummingbird
+ 
+
+ align:start position:0%
+hummingbird
+starts going to a nearby lake and
+
+ align:start position:0%
+starts going to a nearby lake and
+ 
+
+ align:start position:0%
+starts going to a nearby lake and
+carrying
+
+ align:start position:0%
+carrying
+ 
+
+ align:start position:0%
+carrying
+one drop of water at a time to douse the
+
+ align:start position:0%
+one drop of water at a time to douse the
+ 
+
+ align:start position:0%
+one drop of water at a time to douse the
+forest fire
+
+ align:start position:0%
+forest fire
+ 
+
+ align:start position:0%
+forest fire
+and all the other animals are asking
+
+ align:start position:0%
+and all the other animals are asking
+ 
+
+ align:start position:0%
+and all the other animals are asking
+what are you doing you're so small
+
+ align:start position:0%
+what are you doing you're so small
+ 
+
+ align:start position:0%
+what are you doing you're so small
+this fire is so big you can't possibly
+
+ align:start position:0%
+this fire is so big you can't possibly
+ 
+
+ align:start position:0%
+this fire is so big you can't possibly
+do anything
+
+ align:start position:0%
+do anything
+ 
+
+ align:start position:0%
+do anything
+about it the elephant is standing there
+
+ align:start position:0%
+about it the elephant is standing there
+ 
+
+ align:start position:0%
+about it the elephant is standing there
+with its big trunk
+
+ align:start position:0%
+with its big trunk
+ 
+
+ align:start position:0%
+with its big trunk
+all the other animals that are also much
+
+ align:start position:0%
+all the other animals that are also much
+ 
+
+ align:start position:0%
+all the other animals that are also much
+bigger just doing nothing
+
+ align:start position:0%
+bigger just doing nothing
+ 
+
+ align:start position:0%
+bigger just doing nothing
+the hummingbird keeps on going and then
+
+ align:start position:0%
+the hummingbird keeps on going and then
+ 
+
+ align:start position:0%
+the hummingbird keeps on going and then
+finally
+
+ align:start position:0%
+finally
+ 
+
+ align:start position:0%
+finally
+without missing a beat the hummingbird
+
+ align:start position:0%
+without missing a beat the hummingbird
+ 
+
+ align:start position:0%
+without missing a beat the hummingbird
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+i'm doing the best i can
+
+ align:start position:0%
+i'm doing the best i can
+ 
+
+ align:start position:0%
+i'm doing the best i can
+and when gary mattai says we should all
+
+ align:start position:0%
+and when gary mattai says we should all
+ 
+
+ align:start position:0%
+and when gary mattai says we should all
+be like hummingbirds
+
+ align:start position:0%
+be like hummingbirds
+ 
+
+ align:start position:0%
+be like hummingbirds
+we should all just do the best that we
+
+ align:start position:0%
+we should all just do the best that we
+ 
+
+ align:start position:0%
+we should all just do the best that we
+can and some days that's not
+
+ align:start position:0%
+can and some days that's not
+ 
+
+ align:start position:0%
+can and some days that's not
+very much at all and that's okay but we
+
+ align:start position:0%
+very much at all and that's okay but we
+ 
+
+ align:start position:0%
+very much at all and that's okay but we
+should all remember
+
+ align:start position:0%
+should all remember
+ 
+
+ align:start position:0%
+should all remember
+that we each can do something and that
+
+ align:start position:0%
+that we each can do something and that
+ 
+
+ align:start position:0%
+that we each can do something and that
+that matters
+
+ align:start position:0%
+that matters
+ 
+
+ align:start position:0%
+that matters
+and that that's enough in that moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in our individual work on climate change
+
+ align:start position:0%
+in our individual work on climate change
+ 
+
+ align:start position:0%
+in our individual work on climate change
+it's okay to take the approach of the
+
+ align:start position:0%
+it's okay to take the approach of the
+ 
+
+ align:start position:0%
+it's okay to take the approach of the
+hummingbird to make a difference
+
+ align:start position:0%
+hummingbird to make a difference
+ 
+
+ align:start position:0%
+hummingbird to make a difference
+if you're interested in becoming an
+
+ align:start position:0%
+if you're interested in becoming an
+ 
+
+ align:start position:0%
+if you're interested in becoming an
+earth dna ambassador or want to learn
+
+ align:start position:0%
+earth dna ambassador or want to learn
+ 
+
+ align:start position:0%
+earth dna ambassador or want to learn
+more about their training program and
+
+ align:start position:0%
+more about their training program and
+ 
+
+ align:start position:0%
+more about their training program and
+materials
+
+ align:start position:0%
+materials
+ 
+
+ align:start position:0%
+materials
+head to earthdna.org ambassadors
+
+ align:start position:0%
+head to earthdna.org ambassadors
+ 
+
+ align:start position:0%
+head to earthdna.org ambassadors
+you can also find the climate 101
+
+ align:start position:0%
+you can also find the climate 101
+ 
+
+ align:start position:0%
+you can also find the climate 101
+presentation slides
+
+ align:start position:0%
+presentation slides
+ 
+
+ align:start position:0%
+presentation slides
+a video of brandon giving the
+
+ align:start position:0%
+a video of brandon giving the
+ 
+
+ align:start position:0%
+a video of brandon giving the
+presentation ambassador program
+
+ align:start position:0%
+presentation ambassador program
+ 
+
+ align:start position:0%
+presentation ambassador program
+application
+
+ align:start position:0%
+application
+ 
+
+ align:start position:0%
+application
+handouts and volunteer resources on our
+
+ align:start position:0%
+handouts and volunteer resources on our
+ 
+
+ align:start position:0%
+handouts and volunteer resources on our
+mit open courseware website
+
+ align:start position:0%
+mit open courseware website
+ 
+
+ align:start position:0%
+mit open courseware website
+and by the way did you know
+
+ align:start position:0%
+and by the way did you know
+ 
+
+ align:start position:0%
+and by the way did you know
+opencourseware is turning 20
+
+ align:start position:0%
+opencourseware is turning 20
+ 
+
+ align:start position:0%
+opencourseware is turning 20
+it's taken a community to bring ocw to
+
+ align:start position:0%
+it's taken a community to bring ocw to
+ 
+
+ align:start position:0%
+it's taken a community to bring ocw to
+this moment
+
+ align:start position:0%
+this moment
+ 
+
+ align:start position:0%
+this moment
+and we want you to be a part of it and
+
+ align:start position:0%
+and we want you to be a part of it and
+ 
+
+ align:start position:0%
+and we want you to be a part of it and
+what comes next
+
+ align:start position:0%
+what comes next
+ 
+
+ align:start position:0%
+what comes next
+please join us for a virtual celebration
+
+ align:start position:0%
+please join us for a virtual celebration
+ 
+
+ align:start position:0%
+please join us for a virtual celebration
+of ocw's impact
+
+ align:start position:0%
+of ocw's impact
+ 
+
+ align:start position:0%
+of ocw's impact
+community and the future of open sharing
+
+ align:start position:0%
+community and the future of open sharing
+ 
+
+ align:start position:0%
+community and the future of open sharing
+on wednesday april 7th
+
+ align:start position:0%
+on wednesday april 7th
+ 
+
+ align:start position:0%
+on wednesday april 7th
+2021 at 12 pm eastern time you can
+
+ align:start position:0%
+2021 at 12 pm eastern time you can
+ 
+
+ align:start position:0%
+2021 at 12 pm eastern time you can
+register using the link in our show
+
+ align:start position:0%
+register using the link in our show
+ 
+
+ align:start position:0%
+register using the link in our show
+notes
+
+ align:start position:0%
+notes
+ 
+
+ align:start position:0%
+notes
+or just tune in live to ocw's youtube
+
+ align:start position:0%
+or just tune in live to ocw's youtube
+ 
+
+ align:start position:0%
+or just tune in live to ocw's youtube
+instagram or facebook pages
+
+ align:start position:0%
+instagram or facebook pages
+ 
+
+ align:start position:0%
+instagram or facebook pages
+thank you for making these first two
+
+ align:start position:0%
+thank you for making these first two
+ 
+
+ align:start position:0%
+thank you for making these first two
+decades possible and thanks so much for
+
+ align:start position:0%
+decades possible and thanks so much for
+ 
+
+ align:start position:0%
+decades possible and thanks so much for
+listening to the chalk radio podcast
+
+ align:start position:0%
+listening to the chalk radio podcast
+ 
+
+ align:start position:0%
+listening to the chalk radio podcast
+until i see you on april 7th signing off
+
+ align:start position:0%
+until i see you on april 7th signing off
+ 
+
+ align:start position:0%
+until i see you on april 7th signing off
+from cambridge massachusetts
+
+ align:start position:0%
+from cambridge massachusetts
+ 
+
+ align:start position:0%
+from cambridge massachusetts
+i'm sarah hansen from mit opencourseware
+
+ align:start position:0%
+i'm sarah hansen from mit opencourseware
+ 
+
+ align:start position:0%
+i'm sarah hansen from mit opencourseware
+mom passed the car
\ No newline at end of file
diff --git a/kEtov6pV_1Q.txt b/kEtov6pV_1Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3c2d625745d48d3d52d399b5ad49affc45e57209
--- /dev/null
+++ b/kEtov6pV_1Q.txt
@@ -0,0 +1,3371 @@
+align:start position:0%
+ 
+hello computational music analysts I'm
+
+ align:start position:0%
+hello computational music analysts I'm
+ 
+
+ align:start position:0%
+hello computational music analysts I'm
+going to talk a little bit today about
+
+ align:start position:0%
+going to talk a little bit today about
+ 
+
+ align:start position:0%
+going to talk a little bit today about
+some topics that are not in themselves
+
+ align:start position:0%
+some topics that are not in themselves
+ 
+
+ align:start position:0%
+some topics that are not in themselves
+essentially computational although
+
+ align:start position:0%
+essentially computational although
+ 
+
+ align:start position:0%
+essentially computational although
+having a computer helps but are really
+
+ align:start position:0%
+having a computer helps but are really
+ 
+
+ align:start position:0%
+having a computer helps but are really
+about the intersection of mathematical
+
+ align:start position:0%
+about the intersection of mathematical
+ 
+
+ align:start position:0%
+about the intersection of mathematical
+and quantitative thinking with music
+
+ align:start position:0%
+and quantitative thinking with music
+ 
+
+ align:start position:0%
+and quantitative thinking with music
+analysis music theory and musicology the
+
+ align:start position:0%
+analysis music theory and musicology the
+ 
+
+ align:start position:0%
+analysis music theory and musicology the
+study of music
+
+ align:start position:0%
+study of music
+ 
+
+ align:start position:0%
+study of music
+history and these are some of the things
+
+ align:start position:0%
+history and these are some of the things
+ 
+
+ align:start position:0%
+history and these are some of the things
+that I've done in my own research that I
+
+ align:start position:0%
+that I've done in my own research that I
+ 
+
+ align:start position:0%
+that I've done in my own research that I
+hope will make you think about some ways
+
+ align:start position:0%
+hope will make you think about some ways
+ 
+
+ align:start position:0%
+hope will make you think about some ways
+that data analysis can go beyond the
+
+ align:start position:0%
+that data analysis can go beyond the
+ 
+
+ align:start position:0%
+that data analysis can go beyond the
+score and tell us something more about
+
+ align:start position:0%
+score and tell us something more about
+ 
+
+ align:start position:0%
+score and tell us something more about
+the history of
+
+ align:start position:0%
+the history of
+ 
+
+ align:start position:0%
+the history of
+music what I'm not doing computational
+
+ align:start position:0%
+music what I'm not doing computational
+ 
+
+ align:start position:0%
+music what I'm not doing computational
+music analysis my other job is as a
+
+ align:start position:0%
+music analysis my other job is as a
+ 
+
+ align:start position:0%
+music analysis my other job is as a
+medieval music researcher and one of the
+
+ align:start position:0%
+medieval music researcher and one of the
+ 
+
+ align:start position:0%
+medieval music researcher and one of the
+certainties I was always taught um about
+
+ align:start position:0%
+certainties I was always taught um about
+ 
+
+ align:start position:0%
+certainties I was always taught um about
+Medieval music is that we've
+
+ align:start position:0%
+Medieval music is that we've
+ 
+
+ align:start position:0%
+Medieval music is that we've
+lost most of it we've lost so much of it
+
+ align:start position:0%
+lost most of it we've lost so much of it
+ 
+
+ align:start position:0%
+lost most of it we've lost so much of it
+and I mean it's it's just incredible how
+
+ align:start position:0%
+and I mean it's it's just incredible how
+ 
+
+ align:start position:0%
+and I mean it's it's just incredible how
+much we have in fact most people always
+
+ align:start position:0%
+much we have in fact most people always
+ 
+
+ align:start position:0%
+much we have in fact most people always
+said that um The Sur the music that
+
+ align:start position:0%
+said that um The Sur the music that
+ 
+
+ align:start position:0%
+said that um The Sur the music that
+survives is just the tip of the iceberg
+
+ align:start position:0%
+survives is just the tip of the iceberg
+ 
+
+ align:start position:0%
+survives is just the tip of the iceberg
+it was first said by a very important
+
+ align:start position:0%
+it was first said by a very important
+ 
+
+ align:start position:0%
+it was first said by a very important
+medieval his U musicologist Nino Perot
+
+ align:start position:0%
+medieval his U musicologist Nino Perot
+ 
+
+ align:start position:0%
+medieval his U musicologist Nino Perot
+uh but this term was picked up from on
+
+ align:start position:0%
+uh but this term was picked up from on
+ 
+
+ align:start position:0%
+uh but this term was picked up from on
+by dozens of other people and so um when
+
+ align:start position:0%
+by dozens of other people and so um when
+ 
+
+ align:start position:0%
+by dozens of other people and so um when
+we think about what's lost it could be
+
+ align:start position:0%
+we think about what's lost it could be
+ 
+
+ align:start position:0%
+we think about what's lost it could be
+number of manuscripts that's lost or it
+
+ align:start position:0%
+number of manuscripts that's lost or it
+ 
+
+ align:start position:0%
+number of manuscripts that's lost or it
+could be things that um were lost
+
+ align:start position:0%
+could be things that um were lost
+ 
+
+ align:start position:0%
+could be things that um were lost
+because they were never written down and
+
+ align:start position:0%
+because they were never written down and
+ 
+
+ align:start position:0%
+because they were never written down and
+we've forgotten them but if we want to
+
+ align:start position:0%
+we've forgotten them but if we want to
+ 
+
+ align:start position:0%
+we've forgotten them but if we want to
+think about even the things that were
+
+ align:start position:0%
+think about even the things that were
+ 
+
+ align:start position:0%
+think about even the things that were
+once written down on songs that were
+
+ align:start position:0%
+once written down on songs that were
+ 
+
+ align:start position:0%
+once written down on songs that were
+once written down the pieces that were
+
+ align:start position:0%
+once written down the pieces that were
+ 
+
+ align:start position:0%
+once written down the pieces that were
+once written down uh how many of them do
+
+ align:start position:0%
+once written down uh how many of them do
+ 
+
+ align:start position:0%
+once written down uh how many of them do
+no longer have any copy of at all um
+
+ align:start position:0%
+no longer have any copy of at all um
+ 
+
+ align:start position:0%
+no longer have any copy of at all um
+what is the tip of the iceberg uh is it
+
+ align:start position:0%
+what is the tip of the iceberg uh is it
+ 
+
+ align:start position:0%
+what is the tip of the iceberg uh is it
+90% that's what a lot of people say you
+
+ align:start position:0%
+90% that's what a lot of people say you
+ 
+
+ align:start position:0%
+90% that's what a lot of people say you
+know the visible part of the iceberg is
+
+ align:start position:0%
+know the visible part of the iceberg is
+ 
+
+ align:start position:0%
+know the visible part of the iceberg is
+is it 99% lost uh 99.9% lost or is one
+
+ align:start position:0%
+is it 99% lost uh 99.9% lost or is one
+ 
+
+ align:start position:0%
+is it 99% lost uh 99.9% lost or is one
+person said basically everything so I'll
+
+ align:start position:0%
+person said basically everything so I'll
+ 
+
+ align:start position:0%
+person said basically everything so I'll
+call that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+99.9999% my friend and former teacher
+
+ align:start position:0%
+99.9999% my friend and former teacher
+ 
+
+ align:start position:0%
+99.9999% my friend and former teacher
+Sean Gallagher once asked me hey would
+
+ align:start position:0%
+Sean Gallagher once asked me hey would
+ 
+
+ align:start position:0%
+Sean Gallagher once asked me hey would
+there be any way you know you're a math
+
+ align:start position:0%
+there be any way you know you're a math
+ 
+
+ align:start position:0%
+there be any way you know you're a math
+guy to prove this to show that it's true
+
+ align:start position:0%
+guy to prove this to show that it's true
+ 
+
+ align:start position:0%
+guy to prove this to show that it's true
+and you know I immediately said no you
+
+ align:start position:0%
+and you know I immediately said no you
+ 
+
+ align:start position:0%
+and you know I immediately said no you
+know there's no way we could do this
+
+ align:start position:0%
+know there's no way we could do this
+ 
+
+ align:start position:0%
+know there's no way we could do this
+then I thought a little bit more and
+
+ align:start position:0%
+then I thought a little bit more and
+ 
+
+ align:start position:0%
+then I thought a little bit more and
+realized there are people who look at um
+
+ align:start position:0%
+realized there are people who look at um
+ 
+
+ align:start position:0%
+realized there are people who look at um
+you know how things get lost and stuff I
+
+ align:start position:0%
+you know how things get lost and stuff I
+ 
+
+ align:start position:0%
+you know how things get lost and stuff I
+uh later on I found this great article
+
+ align:start position:0%
+uh later on I found this great article
+ 
+
+ align:start position:0%
+uh later on I found this great article
+on um what happens in peer-to-peer song
+
+ align:start position:0%
+on um what happens in peer-to-peer song
+ 
+
+ align:start position:0%
+on um what happens in peer-to-peer song
+sharing uh when you just start
+
+ align:start position:0%
+sharing uh when you just start
+ 
+
+ align:start position:0%
+sharing uh when you just start
+disconnecting lots of computers from the
+
+ align:start position:0%
+disconnecting lots of computers from the
+ 
+
+ align:start position:0%
+disconnecting lots of computers from the
+network as happened during the Crackdown
+
+ align:start position:0%
+network as happened during the Crackdown
+ 
+
+ align:start position:0%
+network as happened during the Crackdown
+on napers and things like that and um
+
+ align:start position:0%
+on napers and things like that and um
+ 
+
+ align:start position:0%
+on napers and things like that and um
+and they showed that as you go from if
+
+ align:start position:0%
+and they showed that as you go from if
+ 
+
+ align:start position:0%
+and they showed that as you go from if
+you have a 100,000 computers on a
+
+ align:start position:0%
+you have a 100,000 computers on a
+ 
+
+ align:start position:0%
+you have a 100,000 computers on a
+network you might have five million
+
+ align:start position:0%
+network you might have five million
+ 
+
+ align:start position:0%
+network you might have five million
+songs uh but if the network gets down to
+
+ align:start position:0%
+songs uh but if the network gets down to
+ 
+
+ align:start position:0%
+songs uh but if the network gets down to
+you know maybe 10,000 or 15,000
+
+ align:start position:0%
+you know maybe 10,000 or 15,000
+ 
+
+ align:start position:0%
+you know maybe 10,000 or 15,000
+computers you only lose about half the
+
+ align:start position:0%
+computers you only lose about half the
+ 
+
+ align:start position:0%
+computers you only lose about half the
+song so that was kind of interesting to
+
+ align:start position:0%
+song so that was kind of interesting to
+ 
+
+ align:start position:0%
+song so that was kind of interesting to
+me that was a little bit
+
+ align:start position:0%
+me that was a little bit
+ 
+
+ align:start position:0%
+me that was a little bit
+counterintuitive that you could really
+
+ align:start position:0%
+counterintuitive that you could really
+ 
+
+ align:start position:0%
+counterintuitive that you could really
+lose a lot of nodes on a network and not
+
+ align:start position:0%
+lose a lot of nodes on a network and not
+ 
+
+ align:start position:0%
+lose a lot of nodes on a network and not
+lose a lot of the content there and I
+
+ align:start position:0%
+lose a lot of the content there and I
+ 
+
+ align:start position:0%
+lose a lot of the content there and I
+kind of thought well you know computers
+
+ align:start position:0%
+kind of thought well you know computers
+ 
+
+ align:start position:0%
+kind of thought well you know computers
+might be something like medieval
+
+ align:start position:0%
+might be something like medieval
+ 
+
+ align:start position:0%
+might be something like medieval
+manuscripts that we lose a bunch but
+
+ align:start position:0%
+manuscripts that we lose a bunch but
+ 
+
+ align:start position:0%
+manuscripts that we lose a bunch but
+maybe we still have the songs so I wrote
+
+ align:start position:0%
+maybe we still have the songs so I wrote
+ 
+
+ align:start position:0%
+maybe we still have the songs so I wrote
+two articles about this topic first um
+
+ align:start position:0%
+two articles about this topic first um
+ 
+
+ align:start position:0%
+two articles about this topic first um
+is what I'm really going to be talking
+
+ align:start position:0%
+is what I'm really going to be talking
+ 
+
+ align:start position:0%
+is what I'm really going to be talking
+about now uh it's an article called
+
+ align:start position:0%
+about now uh it's an article called
+ 
+
+ align:start position:0%
+about now uh it's an article called
+tipping the iceberg in a journal called
+
+ align:start position:0%
+tipping the iceberg in a journal called
+ 
+
+ align:start position:0%
+tipping the iceberg in a journal called
+mus discina and another it's a little
+
+ align:start position:0%
+mus discina and another it's a little
+ 
+
+ align:start position:0%
+mus discina and another it's a little
+bit harder to find uh it's called monks
+
+ align:start position:0%
+bit harder to find uh it's called monks
+ 
+
+ align:start position:0%
+bit harder to find uh it's called monks
+manuscripts and other peer-to-peer song
+
+ align:start position:0%
+manuscripts and other peer-to-peer song
+ 
+
+ align:start position:0%
+manuscripts and other peer-to-peer song
+sharing networks of the Middle Ages it's
+
+ align:start position:0%
+sharing networks of the Middle Ages it's
+ 
+
+ align:start position:0%
+sharing networks of the Middle Ages it's
+in a great uh book that the University
+
+ align:start position:0%
+in a great uh book that the University
+ 
+
+ align:start position:0%
+in a great uh book that the University
+of Pennsylvania uh helped publish called
+
+ align:start position:0%
+of Pennsylvania uh helped publish called
+ 
+
+ align:start position:0%
+of Pennsylvania uh helped publish called
+Kus scriptus Technologies of medieval
+
+ align:start position:0%
+Kus scriptus Technologies of medieval
+ 
+
+ align:start position:0%
+Kus scriptus Technologies of medieval
+song like the idea of Technology
+
+ align:start position:0%
+song like the idea of Technology
+ 
+
+ align:start position:0%
+song like the idea of Technology
+existing throughout history anyhow so
+
+ align:start position:0%
+existing throughout history anyhow so
+ 
+
+ align:start position:0%
+existing throughout history anyhow so
+one of the ways that we could do this is
+
+ align:start position:0%
+one of the ways that we could do this is
+ 
+
+ align:start position:0%
+one of the ways that we could do this is
+just you know look at all the records of
+
+ align:start position:0%
+just you know look at all the records of
+ 
+
+ align:start position:0%
+just you know look at all the records of
+missing pieces and see how many of them
+
+ align:start position:0%
+missing pieces and see how many of them
+ 
+
+ align:start position:0%
+missing pieces and see how many of them
+we have and that's kind of sarcastic but
+
+ align:start position:0%
+we have and that's kind of sarcastic but
+ 
+
+ align:start position:0%
+we have and that's kind of sarcastic but
+there are things uh that exist in the
+
+ align:start position:0%
+there are things uh that exist in the
+ 
+
+ align:start position:0%
+there are things uh that exist in the
+world like this um there's a
+
+ align:start position:0%
+world like this um there's a
+ 
+
+ align:start position:0%
+world like this um there's a
+manuscript it's actually only uh I think
+
+ align:start position:0%
+manuscript it's actually only uh I think
+ 
+
+ align:start position:0%
+manuscript it's actually only uh I think
+two or four pages survive now um that
+
+ align:start position:0%
+two or four pages survive now um that
+ 
+
+ align:start position:0%
+two or four pages survive now um that
+was owned by The Duchess of troil so
+
+ align:start position:0%
+was owned by The Duchess of troil so
+ 
+
+ align:start position:0%
+was owned by The Duchess of troil so
+it's often called the tro uh manuscript
+
+ align:start position:0%
+it's often called the tro uh manuscript
+ 
+
+ align:start position:0%
+it's often called the tro uh manuscript
+it's in um it's in the National Library
+
+ align:start position:0%
+it's in um it's in the National Library
+ 
+
+ align:start position:0%
+it's in um it's in the National Library
+of Paris now and if you look at this
+
+ align:start position:0%
+of Paris now and if you look at this
+ 
+
+ align:start position:0%
+of Paris now and if you look at this
+manuscript uh what what we only have a
+
+ align:start position:0%
+manuscript uh what what we only have a
+ 
+
+ align:start position:0%
+manuscript uh what what we only have a
+couple pages of it but we have the
+
+ align:start position:0%
+couple pages of it but we have the
+ 
+
+ align:start position:0%
+couple pages of it but we have the
+entire index the table of contents that
+
+ align:start position:0%
+entire index the table of contents that
+ 
+
+ align:start position:0%
+entire index the table of contents that
+tells you uh what the names of the
+
+ align:start position:0%
+tells you uh what the names of the
+ 
+
+ align:start position:0%
+tells you uh what the names of the
+pieces are and what page they would have
+
+ align:start position:0%
+pieces are and what page they would have
+ 
+
+ align:start position:0%
+pieces are and what page they would have
+been on in the original manuscript so we
+
+ align:start position:0%
+been on in the original manuscript so we
+ 
+
+ align:start position:0%
+been on in the original manuscript so we
+can look at well we don't have this
+
+ align:start position:0%
+can look at well we don't have this
+ 
+
+ align:start position:0%
+can look at well we don't have this
+manuscript but how many of these pieces
+
+ align:start position:0%
+manuscript but how many of these pieces
+ 
+
+ align:start position:0%
+manuscript but how many of these pieces
+do we have we have we lost so we can see
+
+ align:start position:0%
+do we have we have we lost so we can see
+ 
+
+ align:start position:0%
+do we have we have we lost so we can see
+that uh I've marked here these are all
+
+ align:start position:0%
+that uh I've marked here these are all
+ 
+
+ align:start position:0%
+that uh I've marked here these are all
+the pieces that we're pretty sure we
+
+ align:start position:0%
+the pieces that we're pretty sure we
+ 
+
+ align:start position:0%
+the pieces that we're pretty sure we
+don't have copies of and um here's all
+
+ align:start position:0%
+don't have copies of and um here's all
+ 
+
+ align:start position:0%
+don't have copies of and um here's all
+the pieces that we're pretty sure we do
+
+ align:start position:0%
+the pieces that we're pretty sure we do
+ 
+
+ align:start position:0%
+the pieces that we're pretty sure we do
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+copies there's some pieces that we can't
+
+ align:start position:0%
+copies there's some pieces that we can't
+ 
+
+ align:start position:0%
+copies there's some pieces that we can't
+really be sure they're um parts
+
+ align:start position:0%
+really be sure they're um parts
+ 
+
+ align:start position:0%
+really be sure they're um parts
+of Medieval music Traditions like the
+
+ align:start position:0%
+of Medieval music Traditions like the
+ 
+
+ align:start position:0%
+of Medieval music Traditions like the
+mass that have these somewhat generic
+
+ align:start position:0%
+mass that have these somewhat generic
+ 
+
+ align:start position:0%
+mass that have these somewhat generic
+names like k or something kind of like
+
+ align:start position:0%
+names like k or something kind of like
+ 
+
+ align:start position:0%
+names like k or something kind of like
+if we saw oh we lost Symphony well you
+
+ align:start position:0%
+if we saw oh we lost Symphony well you
+ 
+
+ align:start position:0%
+if we saw oh we lost Symphony well you
+know who who Symphony things like that
+
+ align:start position:0%
+know who who Symphony things like that
+ 
+
+ align:start position:0%
+know who who Symphony things like that
+um so when we overlay these two together
+
+ align:start position:0%
+um so when we overlay these two together
+ 
+
+ align:start position:0%
+um so when we overlay these two together
+we see that actually those that survive
+
+ align:start position:0%
+we see that actually those that survive
+ 
+
+ align:start position:0%
+we see that actually those that survive
+really outrank those that don't so so in
+
+ align:start position:0%
+really outrank those that don't so so in
+ 
+
+ align:start position:0%
+really outrank those that don't so so in
+this particular index we have 114
+
+ align:start position:0%
+this particular index we have 114
+ 
+
+ align:start position:0%
+this particular index we have 114
+compositions that um of of which 109 are
+
+ align:start position:0%
+compositions that um of of which 109 are
+ 
+
+ align:start position:0%
+compositions that um of of which 109 are
+identifiable and 68% of them seem to
+
+ align:start position:0%
+identifiable and 68% of them seem to
+ 
+
+ align:start position:0%
+identifiable and 68% of them seem to
+survive or another thing that I looked
+
+ align:start position:0%
+survive or another thing that I looked
+ 
+
+ align:start position:0%
+survive or another thing that I looked
+at was this collection of um sonnets by
+
+ align:start position:0%
+at was this collection of um sonnets by
+ 
+
+ align:start position:0%
+at was this collection of um sonnets by
+a kind of cool but second tier Italian
+
+ align:start position:0%
+a kind of cool but second tier Italian
+ 
+
+ align:start position:0%
+a kind of cool but second tier Italian
+poet named pranii and one of the things
+
+ align:start position:0%
+poet named pranii and one of the things
+ 
+
+ align:start position:0%
+poet named pranii and one of the things
+that um that makes a lot of people think
+
+ align:start position:0%
+that um that makes a lot of people think
+ 
+
+ align:start position:0%
+that um that makes a lot of people think
+he's second tier is is he throws in a
+
+ align:start position:0%
+he's second tier is is he throws in a
+ 
+
+ align:start position:0%
+he's second tier is is he throws in a
+lot of his songs just uh lists of things
+
+ align:start position:0%
+lot of his songs just uh lists of things
+ 
+
+ align:start position:0%
+lot of his songs just uh lists of things
+lists of all the food they eat at lists
+
+ align:start position:0%
+lists of all the food they eat at lists
+ 
+
+ align:start position:0%
+lists of all the food they eat at lists
+of all the dances they they danced that
+
+ align:start position:0%
+of all the dances they they danced that
+ 
+
+ align:start position:0%
+of all the dances they they danced that
+day and in this particular case a list
+
+ align:start position:0%
+day and in this particular case a list
+ 
+
+ align:start position:0%
+day and in this particular case a list
+of all the songs that were sung Begins
+
+ align:start position:0%
+of all the songs that were sung Begins
+ 
+
+ align:start position:0%
+of all the songs that were sung Begins
+the top Bo kind of kind of nice for
+
+ align:start position:0%
+the top Bo kind of kind of nice for
+ 
+
+ align:start position:0%
+the top Bo kind of kind of nice for
+where we're about to be in the year uh
+
+ align:start position:0%
+where we're about to be in the year uh
+ 
+
+ align:start position:0%
+where we're about to be in the year uh
+with the violin Viola something they
+
+ align:start position:0%
+with the violin Viola something they
+ 
+
+ align:start position:0%
+with the violin Viola something they
+made all the May songs like Ros Ki my
+
+ align:start position:0%
+made all the May songs like Ros Ki my
+ 
+
+ align:start position:0%
+made all the May songs like Ros Ki my
+the rose that never changes it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+colors etc etc we can basically figure
+
+ align:start position:0%
+colors etc etc we can basically figure
+ 
+
+ align:start position:0%
+colors etc etc we can basically figure
+out which ones of these um things are
+
+ align:start position:0%
+out which ones of these um things are
+ 
+
+ align:start position:0%
+out which ones of these um things are
+titles of songs and then we can see how
+
+ align:start position:0%
+titles of songs and then we can see how
+ 
+
+ align:start position:0%
+titles of songs and then we can see how
+many of them we know so
+
+ align:start position:0%
+many of them we know so
+ 
+
+ align:start position:0%
+many of them we know so
+Ros is a song that survives so is so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is but some of them like uh toward the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bottom we don't know that song so so we
+
+ align:start position:0%
+bottom we don't know that song so so we
+ 
+
+ align:start position:0%
+bottom we don't know that song so so we
+can look over and again we can see how
+
+ align:start position:0%
+can look over and again we can see how
+ 
+
+ align:start position:0%
+can look over and again we can see how
+many of them survive how many of them
+
+ align:start position:0%
+many of them survive how many of them
+ 
+
+ align:start position:0%
+many of them survive how many of them
+don't survive and then these other four
+
+ align:start position:0%
+don't survive and then these other four
+ 
+
+ align:start position:0%
+don't survive and then these other four
+um where we can argue about um that
+
+ align:start position:0%
+um where we can argue about um that
+ 
+
+ align:start position:0%
+um where we can argue about um that
+there's songs with similar titles are
+
+ align:start position:0%
+there's songs with similar titles are
+ 
+
+ align:start position:0%
+there's songs with similar titles are
+they just being misquoted or um are they
+
+ align:start position:0%
+they just being misquoted or um are they
+ 
+
+ align:start position:0%
+they just being misquoted or um are they
+same or is this really a song things
+
+ align:start position:0%
+same or is this really a song things
+ 
+
+ align:start position:0%
+same or is this really a song things
+like that so uh it's these are the two
+
+ align:start position:0%
+like that so uh it's these are the two
+ 
+
+ align:start position:0%
+like that so uh it's these are the two
+proportions that it could be so
+
+ align:start position:0%
+proportions that it could be so
+ 
+
+ align:start position:0%
+proportions that it could be so
+depending on what we look at there's
+
+ align:start position:0%
+depending on what we look at there's
+ 
+
+ align:start position:0%
+depending on what we look at there's
+somewhere between 16 and 17 compositions
+
+ align:start position:0%
+somewhere between 16 and 17 compositions
+ 
+
+ align:start position:0%
+somewhere between 16 and 17 compositions
+and three to to seven of them are lost
+
+ align:start position:0%
+and three to to seven of them are lost
+ 
+
+ align:start position:0%
+and three to to seven of them are lost
+10 to 12 survive um so that's about 59
+
+ align:start position:0%
+10 to 12 survive um so that's about 59
+ 
+
+ align:start position:0%
+10 to 12 survive um so that's about 59
+to 75% of the songs here
+
+ align:start position:0%
+to 75% of the songs here
+ 
+
+ align:start position:0%
+to 75% of the songs here
+survive if we look at all of the sonnets
+
+ align:start position:0%
+survive if we look at all of the sonnets
+ 
+
+ align:start position:0%
+survive if we look at all of the sonnets
+in this collection by protani there's 59
+
+ align:start position:0%
+in this collection by protani there's 59
+ 
+
+ align:start position:0%
+in this collection by protani there's 59
+identifiable compositions and 40 of them
+
+ align:start position:0%
+identifiable compositions and 40 of them
+ 
+
+ align:start position:0%
+identifiable compositions and 40 of them
+surviv so that's
+
+ align:start position:0%
+surviv so that's
+ 
+
+ align:start position:0%
+surviv so that's
+71% so here's two pieces of evidence um
+
+ align:start position:0%
+71% so here's two pieces of evidence um
+ 
+
+ align:start position:0%
+71% so here's two pieces of evidence um
+both from textual sources to try to see
+
+ align:start position:0%
+both from textual sources to try to see
+ 
+
+ align:start position:0%
+both from textual sources to try to see
+um how how much survives or how much
+
+ align:start position:0%
+um how how much survives or how much
+ 
+
+ align:start position:0%
+um how how much survives or how much
+doesn't but can can we do
+
+ align:start position:0%
+doesn't but can can we do
+ 
+
+ align:start position:0%
+doesn't but can can we do
+better one of the things I thought of
+
+ align:start position:0%
+better one of the things I thought of
+ 
+
+ align:start position:0%
+better one of the things I thought of
+was that there are people who spend a
+
+ align:start position:0%
+was that there are people who spend a
+ 
+
+ align:start position:0%
+was that there are people who spend a
+lot of time trying to count things that
+
+ align:start position:0%
+lot of time trying to count things that
+ 
+
+ align:start position:0%
+lot of time trying to count things that
+are difficult to count because you can't
+
+ align:start position:0%
+are difficult to count because you can't
+ 
+
+ align:start position:0%
+are difficult to count because you can't
+sort of capture them all uh they are the
+
+ align:start position:0%
+sort of capture them all uh they are the
+ 
+
+ align:start position:0%
+sort of capture them all uh they are the
+animal population
+
+ align:start position:0%
+animal population
+ 
+
+ align:start position:0%
+animal population
+biologists they are people who go out
+
+ align:start position:0%
+biologists they are people who go out
+ 
+
+ align:start position:0%
+biologists they are people who go out
+and um they can't capture every deer in
+
+ align:start position:0%
+and um they can't capture every deer in
+ 
+
+ align:start position:0%
+and um they can't capture every deer in
+a forest so what do they do they um they
+
+ align:start position:0%
+a forest so what do they do they um they
+ 
+
+ align:start position:0%
+a forest so what do they do they um they
+might go out here's one way that they do
+
+ align:start position:0%
+might go out here's one way that they do
+ 
+
+ align:start position:0%
+might go out here's one way that they do
+it they may go out at a certain point
+
+ align:start position:0%
+it they may go out at a certain point
+ 
+
+ align:start position:0%
+it they may go out at a certain point
+and go and um capture you know all the
+
+ align:start position:0%
+and go and um capture you know all the
+ 
+
+ align:start position:0%
+and go and um capture you know all the
+deer they can capture in a couple days
+
+ align:start position:0%
+deer they can capture in a couple days
+ 
+
+ align:start position:0%
+deer they can capture in a couple days
+um you know maybe it's let's say it's 10
+
+ align:start position:0%
+um you know maybe it's let's say it's 10
+ 
+
+ align:start position:0%
+um you know maybe it's let's say it's 10
+10 deer and they go and they tag the
+
+ align:start position:0%
+10 deer and they go and they tag the
+ 
+
+ align:start position:0%
+10 deer and they go and they tag the
+deer in some way or something somehow
+
+ align:start position:0%
+deer in some way or something somehow
+ 
+
+ align:start position:0%
+deer in some way or something somehow
+somehow they you know so they can
+
+ align:start position:0%
+somehow they you know so they can
+ 
+
+ align:start position:0%
+somehow they you know so they can
+recognize the same deer again then maybe
+
+ align:start position:0%
+recognize the same deer again then maybe
+ 
+
+ align:start position:0%
+recognize the same deer again then maybe
+you know they let a month go by or
+
+ align:start position:0%
+you know they let a month go by or
+ 
+
+ align:start position:0%
+you know they let a month go by or
+something not too long but more enough
+
+ align:start position:0%
+something not too long but more enough
+ 
+
+ align:start position:0%
+something not too long but more enough
+time that animals can move around and
+
+ align:start position:0%
+time that animals can move around and
+ 
+
+ align:start position:0%
+time that animals can move around and
+stuff and then they go out and they
+
+ align:start position:0%
+stuff and then they go out and they
+ 
+
+ align:start position:0%
+stuff and then they go out and they
+capture deer for a day again and let's
+
+ align:start position:0%
+capture deer for a day again and let's
+ 
+
+ align:start position:0%
+capture deer for a day again and let's
+say you know they capture 10 deer again
+
+ align:start position:0%
+say you know they capture 10 deer again
+ 
+
+ align:start position:0%
+say you know they capture 10 deer again
+uh the point is the second time they do
+
+ align:start position:0%
+uh the point is the second time they do
+ 
+
+ align:start position:0%
+uh the point is the second time they do
+a capture this called capture recapture
+
+ align:start position:0%
+a capture this called capture recapture
+ 
+
+ align:start position:0%
+a capture this called capture recapture
+methods the second time they do it they
+
+ align:start position:0%
+methods the second time they do it they
+ 
+
+ align:start position:0%
+methods the second time they do it they
+look to see how many of the deer that we
+
+ align:start position:0%
+look to see how many of the deer that we
+ 
+
+ align:start position:0%
+look to see how many of the deer that we
+captured the second time did we also
+
+ align:start position:0%
+captured the second time did we also
+ 
+
+ align:start position:0%
+captured the second time did we also
+capture the first time if you think
+
+ align:start position:0%
+capture the first time if you think
+ 
+
+ align:start position:0%
+capture the first time if you think
+about it if you go into a forest and you
+
+ align:start position:0%
+about it if you go into a forest and you
+ 
+
+ align:start position:0%
+about it if you go into a forest and you
+know you you walked around pretty
+
+ align:start position:0%
+know you you walked around pretty
+ 
+
+ align:start position:0%
+know you you walked around pretty
+randomly or something and you all of the
+
+ align:start position:0%
+randomly or something and you all of the
+ 
+
+ align:start position:0%
+randomly or something and you all of the
+deer or nine out of the 10 deer that you
+
+ align:start position:0%
+deer or nine out of the 10 deer that you
+ 
+
+ align:start position:0%
+deer or nine out of the 10 deer that you
+captur the first time you see the same
+
+ align:start position:0%
+captur the first time you see the same
+ 
+
+ align:start position:0%
+captur the first time you see the same
+ones the second time you might think wow
+
+ align:start position:0%
+ones the second time you might think wow
+ 
+
+ align:start position:0%
+ones the second time you might think wow
+we've seen almost all the deer in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forest on the other hand let's say you
+
+ align:start position:0%
+forest on the other hand let's say you
+ 
+
+ align:start position:0%
+forest on the other hand let's say you
+captured 10 deer and none of them that
+
+ align:start position:0%
+captured 10 deer and none of them that
+ 
+
+ align:start position:0%
+captured 10 deer and none of them that
+you captured the second time had the tax
+
+ align:start position:0%
+you captured the second time had the tax
+ 
+
+ align:start position:0%
+you captured the second time had the tax
+you'd be like wow okay I know I've seen
+
+ align:start position:0%
+you'd be like wow okay I know I've seen
+ 
+
+ align:start position:0%
+you'd be like wow okay I know I've seen
+20 deer here but law of averages suggest
+
+ align:start position:0%
+20 deer here but law of averages suggest
+ 
+
+ align:start position:0%
+20 deer here but law of averages suggest
+there's a lot more than 20 deer and in
+
+ align:start position:0%
+there's a lot more than 20 deer and in
+ 
+
+ align:start position:0%
+there's a lot more than 20 deer and in
+fact there's um there's formulas that
+
+ align:start position:0%
+fact there's um there's formulas that
+ 
+
+ align:start position:0%
+fact there's um there's formulas that
+can you can uh that people do with this
+
+ align:start position:0%
+can you can uh that people do with this
+ 
+
+ align:start position:0%
+can you can uh that people do with this
+type of thing
+
+ align:start position:0%
+type of thing
+ 
+
+ align:start position:0%
+type of thing
+um so I tried to figure out you know
+
+ align:start position:0%
+um so I tried to figure out you know
+ 
+
+ align:start position:0%
+um so I tried to figure out you know
+what would be the equivalent in in music
+
+ align:start position:0%
+what would be the equivalent in in music
+ 
+
+ align:start position:0%
+what would be the equivalent in in music
+and so um I started to think you know uh
+
+ align:start position:0%
+and so um I started to think you know uh
+ 
+
+ align:start position:0%
+and so um I started to think you know uh
+let's go and look at some equations we
+
+ align:start position:0%
+let's go and look at some equations we
+ 
+
+ align:start position:0%
+let's go and look at some equations we
+might make uh if we had the number of
+
+ align:start position:0%
+might make uh if we had the number of
+ 
+
+ align:start position:0%
+might make uh if we had the number of
+pieces if we knew the number of pieces
+
+ align:start position:0%
+pieces if we knew the number of pieces
+ 
+
+ align:start position:0%
+pieces if we knew the number of pieces
+that originally existed and we
+
+ align:start position:0%
+that originally existed and we
+ 
+
+ align:start position:0%
+that originally existed and we
+multiplied by the probability that any
+
+ align:start position:0%
+multiplied by the probability that any
+ 
+
+ align:start position:0%
+multiplied by the probability that any
+given piece would be
+
+ align:start position:0%
+given piece would be
+ 
+
+ align:start position:0%
+given piece would be
+missing we would know the total number
+
+ align:start position:0%
+missing we would know the total number
+ 
+
+ align:start position:0%
+missing we would know the total number
+of missing
+
+ align:start position:0%
+of missing
+ 
+
+ align:start position:0%
+of missing
+pieces that's
+
+ align:start position:0%
+pieces that's
+ 
+
+ align:start position:0%
+pieces that's
+fantastic that is a very hard uh
+
+ align:start position:0%
+fantastic that is a very hard uh
+ 
+
+ align:start position:0%
+fantastic that is a very hard uh
+equation it's very hard to argue against
+
+ align:start position:0%
+equation it's very hard to argue against
+ 
+
+ align:start position:0%
+equation it's very hard to argue against
+but it's completely useless right we
+
+ align:start position:0%
+but it's completely useless right we
+ 
+
+ align:start position:0%
+but it's completely useless right we
+don't know the number of pieces
+
+ align:start position:0%
+don't know the number of pieces
+ 
+
+ align:start position:0%
+don't know the number of pieces
+originally we don't know the probability
+
+ align:start position:0%
+originally we don't know the probability
+ 
+
+ align:start position:0%
+originally we don't know the probability
+that any given piece would be missing
+
+ align:start position:0%
+that any given piece would be missing
+ 
+
+ align:start position:0%
+that any given piece would be missing
+and therefore we don't know how many
+
+ align:start position:0%
+and therefore we don't know how many
+ 
+
+ align:start position:0%
+and therefore we don't know how many
+missing pieces are so one equation three
+
+ align:start position:0%
+missing pieces are so one equation three
+ 
+
+ align:start position:0%
+missing pieces are so one equation three
+unknowns we don't know any of
+
+ align:start position:0%
+unknowns we don't know any of
+ 
+
+ align:start position:0%
+unknowns we don't know any of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+but we can think through some of the
+
+ align:start position:0%
+but we can think through some of the
+ 
+
+ align:start position:0%
+but we can think through some of the
+things here um I'm going to go through a
+
+ align:start position:0%
+things here um I'm going to go through a
+ 
+
+ align:start position:0%
+things here um I'm going to go through a
+quicker version of this but I have
+
+ align:start position:0%
+quicker version of this but I have
+ 
+
+ align:start position:0%
+quicker version of this but I have
+elsewhere well I have in my article um a
+
+ align:start position:0%
+elsewhere well I have in my article um a
+ 
+
+ align:start position:0%
+elsewhere well I have in my article um a
+little bit deeper version that talks
+
+ align:start position:0%
+little bit deeper version that talks
+ 
+
+ align:start position:0%
+little bit deeper version that talks
+about all the UN um the assumptions that
+
+ align:start position:0%
+about all the UN um the assumptions that
+ 
+
+ align:start position:0%
+about all the UN um the assumptions that
+could be in play but let's start with um
+
+ align:start position:0%
+could be in play but let's start with um
+ 
+
+ align:start position:0%
+could be in play but let's start with um
+how can we figure F out the probability
+
+ align:start position:0%
+how can we figure F out the probability
+ 
+
+ align:start position:0%
+how can we figure F out the probability
+that we're missing a given piece well
+
+ align:start position:0%
+that we're missing a given piece well
+ 
+
+ align:start position:0%
+that we're missing a given piece well
+here's one model and it's it's kind of a
+
+ align:start position:0%
+here's one model and it's it's kind of a
+ 
+
+ align:start position:0%
+here's one model and it's it's kind of a
+um it's kind of a bad assumption maybe
+
+ align:start position:0%
+um it's kind of a bad assumption maybe
+ 
+
+ align:start position:0%
+um it's kind of a bad assumption maybe
+to start with but here's one model uh
+
+ align:start position:0%
+to start with but here's one model uh
+ 
+
+ align:start position:0%
+to start with but here's one model uh
+what if there's just medieval scribes
+
+ align:start position:0%
+what if there's just medieval scribes
+ 
+
+ align:start position:0%
+what if there's just medieval scribes
+had baskets of pieces you just all the
+
+ align:start position:0%
+had baskets of pieces you just all the
+ 
+
+ align:start position:0%
+had baskets of pieces you just all the
+pieces they knew them all their head
+
+ align:start position:0%
+pieces they knew them all their head
+ 
+
+ align:start position:0%
+pieces they knew them all their head
+there something like that and they kind
+
+ align:start position:0%
+there something like that and they kind
+ 
+
+ align:start position:0%
+there something like that and they kind
+of randomly chose ones that they were
+
+ align:start position:0%
+of randomly chose ones that they were
+ 
+
+ align:start position:0%
+of randomly chose ones that they were
+going to write down well then the
+
+ align:start position:0%
+going to write down well then the
+ 
+
+ align:start position:0%
+going to write down well then the
+probability that a given piece would be
+
+ align:start position:0%
+probability that a given piece would be
+ 
+
+ align:start position:0%
+probability that a given piece would be
+in a particular manuscript is
+
+ align:start position:0%
+in a particular manuscript is
+ 
+
+ align:start position:0%
+in a particular manuscript is
+approximately um the proportion of all
+
+ align:start position:0%
+approximately um the proportion of all
+ 
+
+ align:start position:0%
+approximately um the proportion of all
+of the pieces in the manuscript there's
+
+ align:start position:0%
+of the pieces in the manuscript there's
+ 
+
+ align:start position:0%
+of the pieces in the manuscript there's
+if R sub I is the number of pieces in
+
+ align:start position:0%
+if R sub I is the number of pieces in
+ 
+
+ align:start position:0%
+if R sub I is the number of pieces in
+the manuscript and N is the total of
+
+ align:start position:0%
+the manuscript and N is the total of
+ 
+
+ align:start position:0%
+the manuscript and N is the total of
+pieces originally copied then we would
+
+ align:start position:0%
+pieces originally copied then we would
+ 
+
+ align:start position:0%
+pieces originally copied then we would
+know the probability that a piece would
+
+ align:start position:0%
+know the probability that a piece would
+ 
+
+ align:start position:0%
+know the probability that a piece would
+be in a given manuscript or song book
+
+ align:start position:0%
+be in a given manuscript or song book
+ 
+
+ align:start position:0%
+be in a given manuscript or song book
+it's not exactly that number because you
+
+ align:start position:0%
+it's not exactly that number because you
+ 
+
+ align:start position:0%
+it's not exactly that number because you
+don't do duplication but but it's pretty
+
+ align:start position:0%
+don't do duplication but but it's pretty
+ 
+
+ align:start position:0%
+don't do duplication but but it's pretty
+close um uh it's actually the people
+
+ align:start position:0%
+close um uh it's actually the people
+ 
+
+ align:start position:0%
+close um uh it's actually the people
+have argued against me that you know
+
+ align:start position:0%
+have argued against me that you know
+ 
+
+ align:start position:0%
+have argued against me that you know
+like well you have to correct for that
+
+ align:start position:0%
+like well you have to correct for that
+ 
+
+ align:start position:0%
+like well you have to correct for that
+error but you only have to correct for
+
+ align:start position:0%
+error but you only have to correct for
+ 
+
+ align:start position:0%
+error but you only have to correct for
+the probability of duplication if um if
+
+ align:start position:0%
+the probability of duplication if um if
+ 
+
+ align:start position:0%
+the probability of duplication if um if
+the number piece in that manuscript is
+
+ align:start position:0%
+the number piece in that manuscript is
+ 
+
+ align:start position:0%
+the number piece in that manuscript is
+very is close uh some major uh
+
+ align:start position:0%
+very is close uh some major uh
+ 
+
+ align:start position:0%
+very is close uh some major uh
+percentage of the total number pieces
+
+ align:start position:0%
+percentage of the total number pieces
+ 
+
+ align:start position:0%
+percentage of the total number pieces
+originally copied so um that's already
+
+ align:start position:0%
+originally copied so um that's already
+ 
+
+ align:start position:0%
+originally copied so um that's already
+kind of getting anyhow so this is the
+
+ align:start position:0%
+kind of getting anyhow so this is the
+ 
+
+ align:start position:0%
+kind of getting anyhow so this is the
+probability that given piece would be in
+
+ align:start position:0%
+probability that given piece would be in
+ 
+
+ align:start position:0%
+probability that given piece would be in
+the given manuscript from here we can
+
+ align:start position:0%
+the given manuscript from here we can
+ 
+
+ align:start position:0%
+the given manuscript from here we can
+work out what's the probability the
+
+ align:start position:0%
+work out what's the probability the
+ 
+
+ align:start position:0%
+work out what's the probability the
+piece is not in a given manuscript and
+
+ align:start position:0%
+piece is not in a given manuscript and
+ 
+
+ align:start position:0%
+piece is not in a given manuscript and
+we just subtract that from one great so
+
+ align:start position:0%
+we just subtract that from one great so
+ 
+
+ align:start position:0%
+we just subtract that from one great so
+so that's that's pretty good now let's
+
+ align:start position:0%
+so that's that's pretty good now let's
+ 
+
+ align:start position:0%
+so that's that's pretty good now let's
+say you have two independent manuscripts
+
+ align:start position:0%
+say you have two independent manuscripts
+ 
+
+ align:start position:0%
+say you have two independent manuscripts
+they're being copied in different places
+
+ align:start position:0%
+they're being copied in different places
+ 
+
+ align:start position:0%
+they're being copied in different places
+you know different people whatever
+
+ align:start position:0%
+you know different people whatever
+ 
+
+ align:start position:0%
+you know different people whatever
+something like that what would be the
+
+ align:start position:0%
+something like that what would be the
+ 
+
+ align:start position:0%
+something like that what would be the
+probability that the piece would not be
+
+ align:start position:0%
+probability that the piece would not be
+ 
+
+ align:start position:0%
+probability that the piece would not be
+in any of these two manuscripts and so
+
+ align:start position:0%
+in any of these two manuscripts and so
+ 
+
+ align:start position:0%
+in any of these two manuscripts and so
+you just multiply the probability that
+
+ align:start position:0%
+you just multiply the probability that
+ 
+
+ align:start position:0%
+you just multiply the probability that
+it wouldn't be in one
+
+ align:start position:0%
+it wouldn't be in one
+ 
+
+ align:start position:0%
+it wouldn't be in one
+manuscript and not in the other and so R
+
+ align:start position:0%
+manuscript and not in the other and so R
+ 
+
+ align:start position:0%
+manuscript and not in the other and so R
+sub one and R sub2 they're going to
+
+ align:start position:0%
+sub one and R sub2 they're going to
+ 
+
+ align:start position:0%
+sub one and R sub2 they're going to
+depend on how many pieces are in the
+
+ align:start position:0%
+depend on how many pieces are in the
+ 
+
+ align:start position:0%
+depend on how many pieces are in the
+manuscript but this would be the
+
+ align:start position:0%
+manuscript but this would be the
+ 
+
+ align:start position:0%
+manuscript but this would be the
+probability that some piece existing or
+
+ align:start position:0%
+probability that some piece existing or
+ 
+
+ align:start position:0%
+probability that some piece existing or
+not would be in would not be in any of
+
+ align:start position:0%
+not would be in would not be in any of
+ 
+
+ align:start position:0%
+not would be in would not be in any of
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+manuscripts so there's about 85
+
+ align:start position:0%
+manuscripts so there's about 85
+ 
+
+ align:start position:0%
+manuscripts so there's about 85
+surviving medieval manuscripts in the
+
+ align:start position:0%
+surviving medieval manuscripts in the
+ 
+
+ align:start position:0%
+surviving medieval manuscripts in the
+period I'm most interested in um so of
+
+ align:start position:0%
+period I'm most interested in um so of
+ 
+
+ align:start position:0%
+period I'm most interested in um so of
+Italy from 1370 to
+
+ align:start position:0%
+Italy from 1370 to
+ 
+
+ align:start position:0%
+Italy from 1370 to
+1420 just after the black death and um
+
+ align:start position:0%
+1420 just after the black death and um
+ 
+
+ align:start position:0%
+1420 just after the black death and um
+during the time of the great papal
+
+ align:start position:0%
+during the time of the great papal
+ 
+
+ align:start position:0%
+during the time of the great papal
+Schism so there's about 85 of these
+
+ align:start position:0%
+Schism so there's about 85 of these
+ 
+
+ align:start position:0%
+Schism so there's about 85 of these
+manuscripts so what's the probability
+
+ align:start position:0%
+manuscripts so what's the probability
+ 
+
+ align:start position:0%
+manuscripts so what's the probability
+that any given piece would not be in any
+
+ align:start position:0%
+that any given piece would not be in any
+ 
+
+ align:start position:0%
+that any given piece would not be in any
+of the 85 surviving
+
+ align:start position:0%
+of the 85 surviving
+ 
+
+ align:start position:0%
+of the 85 surviving
+manuscripts and it looks something like
+
+ align:start position:0%
+manuscripts and it looks something like
+ 
+
+ align:start position:0%
+manuscripts and it looks something like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this is something you know that's
+
+ align:start position:0%
+so this is something you know that's
+ 
+
+ align:start position:0%
+so this is something you know that's
+it's a it's a big long um number but you
+
+ align:start position:0%
+it's a it's a big long um number but you
+ 
+
+ align:start position:0%
+it's a it's a big long um number but you
+can see that right at the very end this
+
+ align:start position:0%
+can see that right at the very end this
+ 
+
+ align:start position:0%
+can see that right at the very end this
+whatever this works out to is the equal
+
+ align:start position:0%
+whatever this works out to is the equal
+ 
+
+ align:start position:0%
+whatever this works out to is the equal
+to the probability that a piece would be
+
+ align:start position:0%
+to the probability that a piece would be
+ 
+
+ align:start position:0%
+to the probability that a piece would be
+missing because if a piece is not in any
+
+ align:start position:0%
+missing because if a piece is not in any
+ 
+
+ align:start position:0%
+missing because if a piece is not in any
+of the surviving manuscripts then it's
+
+ align:start position:0%
+of the surviving manuscripts then it's
+ 
+
+ align:start position:0%
+of the surviving manuscripts then it's
+missing to us today so this is kind of
+
+ align:start position:0%
+missing to us today so this is kind of
+ 
+
+ align:start position:0%
+missing to us today so this is kind of
+great we know all these are numbers
+
+ align:start position:0%
+great we know all these are numbers
+ 
+
+ align:start position:0%
+great we know all these are numbers
+because they're simply the number of
+
+ align:start position:0%
+because they're simply the number of
+ 
+
+ align:start position:0%
+because they're simply the number of
+pieces in a manuscript today uh not in
+
+ align:start position:0%
+pieces in a manuscript today uh not in
+ 
+
+ align:start position:0%
+pieces in a manuscript today uh not in
+originally say so we can take this and
+
+ align:start position:0%
+originally say so we can take this and
+ 
+
+ align:start position:0%
+originally say so we can take this and
+we can go back to our original equation
+
+ align:start position:0%
+we can go back to our original equation
+ 
+
+ align:start position:0%
+we can go back to our original equation
+with three
+
+ align:start position:0%
+with three
+ 
+
+ align:start position:0%
+with three
+unknowns and um substitute it into for
+
+ align:start position:0%
+unknowns and um substitute it into for
+ 
+
+ align:start position:0%
+unknowns and um substitute it into for
+that P of M place so we can see that now
+
+ align:start position:0%
+that P of M place so we can see that now
+ 
+
+ align:start position:0%
+that P of M place so we can see that now
+we have one equation and two unknowns um
+
+ align:start position:0%
+we have one equation and two unknowns um
+ 
+
+ align:start position:0%
+we have one equation and two unknowns um
+it's still a pretty honky equation but
+
+ align:start position:0%
+it's still a pretty honky equation but
+ 
+
+ align:start position:0%
+it's still a pretty honky equation but
+uh well that's good one equation two
+
+ align:start position:0%
+uh well that's good one equation two
+ 
+
+ align:start position:0%
+uh well that's good one equation two
+unknowns still two many unknowns right
+
+ align:start position:0%
+unknowns still two many unknowns right
+ 
+
+ align:start position:0%
+unknowns still two many unknowns right
+we need two equations at least if we're
+
+ align:start position:0%
+we need two equations at least if we're
+ 
+
+ align:start position:0%
+we need two equations at least if we're
+going to do two unknowns but we can look
+
+ align:start position:0%
+going to do two unknowns but we can look
+ 
+
+ align:start position:0%
+going to do two unknowns but we can look
+at this last answer this m what are the
+
+ align:start position:0%
+at this last answer this m what are the
+ 
+
+ align:start position:0%
+at this last answer this m what are the
+total number of missing pieces well the
+
+ align:start position:0%
+total number of missing pieces well the
+ 
+
+ align:start position:0%
+total number of missing pieces well the
+total number of missing pieces is just
+
+ align:start position:0%
+total number of missing pieces is just
+ 
+
+ align:start position:0%
+total number of missing pieces is just
+the number of pieces that originally
+
+ align:start position:0%
+the number of pieces that originally
+ 
+
+ align:start position:0%
+the number of pieces that originally
+existed which we don't know minus the
+
+ align:start position:0%
+existed which we don't know minus the
+ 
+
+ align:start position:0%
+existed which we don't know minus the
+number of pieces that survive which we
+
+ align:start position:0%
+number of pieces that survive which we
+ 
+
+ align:start position:0%
+number of pieces that survive which we
+do know if we have a pretty good catalog
+
+ align:start position:0%
+do know if we have a pretty good catalog
+ 
+
+ align:start position:0%
+do know if we have a pretty good catalog
+of everything that survives today then
+
+ align:start position:0%
+of everything that survives today then
+ 
+
+ align:start position:0%
+of everything that survives today then
+we can figure that out so now we go back
+
+ align:start position:0%
+we can figure that out so now we go back
+ 
+
+ align:start position:0%
+we can figure that out so now we go back
+and we see that we have actually just
+
+ align:start position:0%
+and we see that we have actually just
+ 
+
+ align:start position:0%
+and we see that we have actually just
+one equation and one unknown uh it's a
+
+ align:start position:0%
+one equation and one unknown uh it's a
+ 
+
+ align:start position:0%
+one equation and one unknown uh it's a
+pretty big equation um in fact a lot of
+
+ align:start position:0%
+pretty big equation um in fact a lot of
+ 
+
+ align:start position:0%
+pretty big equation um in fact a lot of
+the literature that I was reading from
+
+ align:start position:0%
+the literature that I was reading from
+ 
+
+ align:start position:0%
+the literature that I was reading from
+the 60s and 70s 80s was about okay you
+
+ align:start position:0%
+the 60s and 70s 80s was about okay you
+ 
+
+ align:start position:0%
+the 60s and 70s 80s was about okay you
+can't possibly solve an equation you of
+
+ align:start position:0%
+can't possibly solve an equation you of
+ 
+
+ align:start position:0%
+can't possibly solve an equation you of
+this dimensionality uh exactly so here's
+
+ align:start position:0%
+this dimensionality uh exactly so here's
+ 
+
+ align:start position:0%
+this dimensionality uh exactly so here's
+all the sophisticated math that we can
+
+ align:start position:0%
+all the sophisticated math that we can
+ 
+
+ align:start position:0%
+all the sophisticated math that we can
+do to
+
+ align:start position:0%
+do to
+ 
+
+ align:start position:0%
+do to
+um to try to um you to try to
+
+ align:start position:0%
+um to try to um you to try to
+ 
+
+ align:start position:0%
+um to try to um you to try to
+approximate it but in fact nowadays it's
+
+ align:start position:0%
+approximate it but in fact nowadays it's
+ 
+
+ align:start position:0%
+approximate it but in fact nowadays it's
+it's pretty simple what we can do is we
+
+ align:start position:0%
+it's pretty simple what we can do is we
+ 
+
+ align:start position:0%
+it's pretty simple what we can do is we
+can try different numbers for n the
+
+ align:start position:0%
+can try different numbers for n the
+ 
+
+ align:start position:0%
+can try different numbers for n the
+number of original pieces starting from
+
+ align:start position:0%
+number of original pieces starting from
+ 
+
+ align:start position:0%
+number of original pieces starting from
+you know one more than the numbers
+
+ align:start position:0%
+you know one more than the numbers
+ 
+
+ align:start position:0%
+you know one more than the numbers
+fiving pieces or something try all these
+
+ align:start position:0%
+fiving pieces or something try all these
+ 
+
+ align:start position:0%
+fiving pieces or something try all these
+numbers into here until the left side
+
+ align:start position:0%
+numbers into here until the left side
+ 
+
+ align:start position:0%
+numbers into here until the left side
+and the right side approximately Balan
+
+ align:start position:0%
+and the right side approximately Balan
+ 
+
+ align:start position:0%
+and the right side approximately Balan
+and we can do that with computers so uh
+
+ align:start position:0%
+and we can do that with computers so uh
+ 
+
+ align:start position:0%
+and we can do that with computers so uh
+when I did this I mean it's uh this is
+
+ align:start position:0%
+when I did this I mean it's uh this is
+ 
+
+ align:start position:0%
+when I did this I mean it's uh this is
+article I think like 13 14 years old uh
+
+ align:start position:0%
+article I think like 13 14 years old uh
+ 
+
+ align:start position:0%
+article I think like 13 14 years old uh
+it's before um before python was big so
+
+ align:start position:0%
+it's before um before python was big so
+ 
+
+ align:start position:0%
+it's before um before python was big so
+I used Pearl and I just did find U find
+
+ align:start position:0%
+I used Pearl and I just did find U find
+ 
+
+ align:start position:0%
+I used Pearl and I just did find U find
+and find the hypothetical total number
+
+ align:start position:0%
+and find the hypothetical total number
+ 
+
+ align:start position:0%
+and find the hypothetical total number
+of manuscripts given all the things that
+
+ align:start position:0%
+of manuscripts given all the things that
+ 
+
+ align:start position:0%
+of manuscripts given all the things that
+we know and so on so on and um we're
+
+ align:start position:0%
+we know and so on so on and um we're
+ 
+
+ align:start position:0%
+we know and so on so on and um we're
+able for each of um four
+
+ align:start position:0%
+able for each of um four
+ 
+
+ align:start position:0%
+able for each of um four
+different uh genas these are different
+
+ align:start position:0%
+different uh genas these are different
+ 
+
+ align:start position:0%
+different uh genas these are different
+types of music we're able to figure out
+
+ align:start position:0%
+types of music we're able to figure out
+ 
+
+ align:start position:0%
+types of music we're able to figure out
+what percentage of the pieces are
+
+ align:start position:0%
+what percentage of the pieces are
+ 
+
+ align:start position:0%
+what percentage of the pieces are
+probably missing these are you know I'm
+
+ align:start position:0%
+probably missing these are you know I'm
+ 
+
+ align:start position:0%
+probably missing these are you know I'm
+uh there's error bars on this is rough
+
+ align:start position:0%
+uh there's error bars on this is rough
+ 
+
+ align:start position:0%
+uh there's error bars on this is rough
+guesses um but we can see that the
+
+ align:start position:0%
+guesses um but we can see that the
+ 
+
+ align:start position:0%
+guesses um but we can see that the
+percentage of missing pieces maybe in
+
+ align:start position:0%
+percentage of missing pieces maybe in
+ 
+
+ align:start position:0%
+percentage of missing pieces maybe in
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+one in only one of the genres is it
+
+ align:start position:0%
+one in only one of the genres is it
+ 
+
+ align:start position:0%
+one in only one of the genres is it
+predicted to be more than the number of
+
+ align:start position:0%
+predicted to be more than the number of
+ 
+
+ align:start position:0%
+predicted to be more than the number of
+total number pieces than you know than
+
+ align:start position:0%
+total number pieces than you know than
+ 
+
+ align:start position:0%
+total number pieces than you know than
+the number of surviving pieces in fact
+
+ align:start position:0%
+the number of surviving pieces in fact
+ 
+
+ align:start position:0%
+the number of surviving pieces in fact
+for some of these genres we predict that
+
+ align:start position:0%
+for some of these genres we predict that
+ 
+
+ align:start position:0%
+for some of these genres we predict that
+hey we have almost everything
+
+ align:start position:0%
+hey we have almost everything
+ 
+
+ align:start position:0%
+hey we have almost everything
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+um so one of the things we could look at
+
+ align:start position:0%
+um so one of the things we could look at
+ 
+
+ align:start position:0%
+um so one of the things we could look at
+instead of saying uh how many pieces
+
+ align:start position:0%
+instead of saying uh how many pieces
+ 
+
+ align:start position:0%
+instead of saying uh how many pieces
+were once copied but no longer exist we
+
+ align:start position:0%
+were once copied but no longer exist we
+ 
+
+ align:start position:0%
+were once copied but no longer exist we
+can take that total number and say wow
+
+ align:start position:0%
+can take that total number and say wow
+ 
+
+ align:start position:0%
+can take that total number and say wow
+maybe we have all but 25% of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them now there were a lot of assumptions
+
+ align:start position:0%
+them now there were a lot of assumptions
+ 
+
+ align:start position:0%
+them now there were a lot of assumptions
+that went into that um that scribes are
+
+ align:start position:0%
+that went into that um that scribes are
+ 
+
+ align:start position:0%
+that went into that um that scribes are
+correcting things randomly and so on and
+
+ align:start position:0%
+correcting things randomly and so on and
+ 
+
+ align:start position:0%
+correcting things randomly and so on and
+so forth and that you know that there's
+
+ align:start position:0%
+so forth and that you know that there's
+ 
+
+ align:start position:0%
+so forth and that you know that there's
+not pieces that are more popular than
+
+ align:start position:0%
+not pieces that are more popular than
+ 
+
+ align:start position:0%
+not pieces that are more popular than
+each other and so on and so in the
+
+ align:start position:0%
+each other and so on and so in the
+ 
+
+ align:start position:0%
+each other and so on and so in the
+article that I wrote there's um ways
+
+ align:start position:0%
+article that I wrote there's um ways
+ 
+
+ align:start position:0%
+article that I wrote there's um ways
+that you can compensate for this and
+
+ align:start position:0%
+that you can compensate for this and
+ 
+
+ align:start position:0%
+that you can compensate for this and
+ways that we can test for for instance
+
+ align:start position:0%
+ways that we can test for for instance
+ 
+
+ align:start position:0%
+ways that we can test for for instance
+we can hold out um 10% of the
+
+ align:start position:0%
+we can hold out um 10% of the
+ 
+
+ align:start position:0%
+we can hold out um 10% of the
+manuscripts at random and then say not
+
+ align:start position:0%
+manuscripts at random and then say not
+ 
+
+ align:start position:0%
+manuscripts at random and then say not
+just how many pieces would um would we
+
+ align:start position:0%
+just how many pieces would um would we
+ 
+
+ align:start position:0%
+just how many pieces would um would we
+expect to um would you know would we
+
+ align:start position:0%
+expect to um would you know would we
+ 
+
+ align:start position:0%
+expect to um would you know would we
+expect we lost but if we gained 10 more
+
+ align:start position:0%
+expect we lost but if we gained 10 more
+ 
+
+ align:start position:0%
+expect we lost but if we gained 10 more
+manuscripts how many more pieces would
+
+ align:start position:0%
+manuscripts how many more pieces would
+ 
+
+ align:start position:0%
+manuscripts how many more pieces would
+we expect to have that we didn't know
+
+ align:start position:0%
+we expect to have that we didn't know
+ 
+
+ align:start position:0%
+we expect to have that we didn't know
+already and then we can look at okay now
+
+ align:start position:0%
+already and then we can look at okay now
+ 
+
+ align:start position:0%
+already and then we can look at okay now
+put those 10 men get back and voila uh I
+
+ align:start position:0%
+put those 10 men get back and voila uh I
+ 
+
+ align:start position:0%
+put those 10 men get back and voila uh I
+think I can't remember off the top of my
+
+ align:start position:0%
+think I can't remember off the top of my
+ 
+
+ align:start position:0%
+think I can't remember off the top of my
+head right now I you know one of those
+
+ align:start position:0%
+head right now I you know one of those
+ 
+
+ align:start position:0%
+head right now I you know one of those
+things I published so I don't have to
+
+ align:start position:0%
+things I published so I don't have to
+ 
+
+ align:start position:0%
+things I published so I don't have to
+remember but uh I think that the
+
+ align:start position:0%
+remember but uh I think that the
+ 
+
+ align:start position:0%
+remember but uh I think that the
+percentage of pieces that were lost I
+
+ align:start position:0%
+percentage of pieces that were lost I
+ 
+
+ align:start position:0%
+percentage of pieces that were lost I
+think I think it was you know within 10%
+
+ align:start position:0%
+think I think it was you know within 10%
+ 
+
+ align:start position:0%
+think I think it was you know within 10%
+of something or so so these models were
+
+ align:start position:0%
+of something or so so these models were
+ 
+
+ align:start position:0%
+of something or so so these models were
+pretty pretty good so we can use this
+
+ align:start position:0%
+pretty pretty good so we can use this
+ 
+
+ align:start position:0%
+pretty pretty good so we can use this
+mathematical thinking and just a little
+
+ align:start position:0%
+mathematical thinking and just a little
+ 
+
+ align:start position:0%
+mathematical thinking and just a little
+bit of programming to answer questions
+
+ align:start position:0%
+bit of programming to answer questions
+ 
+
+ align:start position:0%
+bit of programming to answer questions
+that were thought to be completely
+
+ align:start position:0%
+that were thought to be completely
+ 
+
+ align:start position:0%
+that were thought to be completely
+unanswerable in
+
+ align:start position:0%
+unanswerable in
+ 
+
+ align:start position:0%
+unanswerable in
+history thanks
\ No newline at end of file
diff --git a/k_VJo1Vrl6E.txt b/k_VJo1Vrl6E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4926660b59d8ece257008fa7fb54d773badd0c80
--- /dev/null
+++ b/k_VJo1Vrl6E.txt
@@ -0,0 +1,2091 @@
+align:start position:0%
+ 
+so now that we've talked about
+
+ align:start position:0%
+so now that we've talked about
+ 
+
+ align:start position:0%
+so now that we've talked about
+the different dynamics of droplets in
+
+ align:start position:0%
+the different dynamics of droplets in
+ 
+
+ align:start position:0%
+the different dynamics of droplets in
+the air
+
+ align:start position:0%
+the air
+ 
+
+ align:start position:0%
+the air
+we can think about how different types
+
+ align:start position:0%
+we can think about how different types
+ 
+
+ align:start position:0%
+we can think about how different types
+of pathogen can leverage those droplets
+
+ align:start position:0%
+of pathogen can leverage those droplets
+ 
+
+ align:start position:0%
+of pathogen can leverage those droplets
+to transmit
+
+ align:start position:0%
+to transmit
+ 
+
+ align:start position:0%
+to transmit
+from one person to another through
+
+ align:start position:0%
+from one person to another through
+ 
+
+ align:start position:0%
+from one person to another through
+respiration through the air
+
+ align:start position:0%
+respiration through the air
+ 
+
+ align:start position:0%
+respiration through the air
+so let's begin with bacteria so there
+
+ align:start position:0%
+so let's begin with bacteria so there
+ 
+
+ align:start position:0%
+so let's begin with bacteria so there
+are many different kinds of bacteria the
+
+ align:start position:0%
+are many different kinds of bacteria the
+ 
+
+ align:start position:0%
+are many different kinds of bacteria the
+typical size
+
+ align:start position:0%
+typical size
+ 
+
+ align:start position:0%
+typical size
+of a single bacterium is on the order of
+
+ align:start position:0%
+of a single bacterium is on the order of
+ 
+
+ align:start position:0%
+of a single bacterium is on the order of
+several microns so let's just say you
+
+ align:start position:0%
+several microns so let's just say you
+ 
+
+ align:start position:0%
+several microns so let's just say you
+know 1
+
+ align:start position:0%
+know 1
+ 
+
+ align:start position:0%
+know 1
+to 10 microns
+
+ align:start position:0%
+to 10 microns
+ 
+
+ align:start position:0%
+to 10 microns
+on the other hand bacteria can also
+
+ align:start position:0%
+on the other hand bacteria can also
+ 
+
+ align:start position:0%
+on the other hand bacteria can also
+exist in colonies or larger structures
+
+ align:start position:0%
+exist in colonies or larger structures
+ 
+
+ align:start position:0%
+exist in colonies or larger structures
+and that does determine to some extent
+
+ align:start position:0%
+and that does determine to some extent
+ 
+
+ align:start position:0%
+and that does determine to some extent
+what kinds of droplets
+
+ align:start position:0%
+what kinds of droplets
+ 
+
+ align:start position:0%
+what kinds of droplets
+can transmit those bacteria so let's
+
+ align:start position:0%
+can transmit those bacteria so let's
+ 
+
+ align:start position:0%
+can transmit those bacteria so let's
+begin with an example of a large drop
+
+ align:start position:0%
+begin with an example of a large drop
+ 
+
+ align:start position:0%
+begin with an example of a large drop
+bacteria which is typically going to be
+
+ align:start position:0%
+bacteria which is typically going to be
+ 
+
+ align:start position:0%
+bacteria which is typically going to be
+found in large drops
+
+ align:start position:0%
+found in large drops
+ 
+
+ align:start position:0%
+found in large drops
+and that would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the bacteria that causes strep throat
+
+ align:start position:0%
+the bacteria that causes strep throat
+ 
+
+ align:start position:0%
+the bacteria that causes strep throat
+the streptococcus
+
+ align:start position:0%
+the streptococcus
+ 
+
+ align:start position:0%
+the streptococcus
+so the streptococcus bacteria which is
+
+ align:start position:0%
+so the streptococcus bacteria which is
+ 
+
+ align:start position:0%
+so the streptococcus bacteria which is
+shown here
+
+ align:start position:0%
+shown here
+ 
+
+ align:start position:0%
+shown here
+has a typical size that's around two
+
+ align:start position:0%
+has a typical size that's around two
+ 
+
+ align:start position:0%
+has a typical size that's around two
+microns so it's on the smaller end
+
+ align:start position:0%
+microns so it's on the smaller end
+ 
+
+ align:start position:0%
+microns so it's on the smaller end
+and it forms chains
+
+ align:start position:0%
+and it forms chains
+ 
+
+ align:start position:0%
+and it forms chains
+and even larger colonies that may have
+
+ align:start position:0%
+and even larger colonies that may have
+ 
+
+ align:start position:0%
+and even larger colonies that may have
+different structures
+
+ align:start position:0%
+different structures
+ 
+
+ align:start position:0%
+different structures
+and the total size of the colonies can
+
+ align:start position:0%
+and the total size of the colonies can
+ 
+
+ align:start position:0%
+and the total size of the colonies can
+vary
+
+ align:start position:0%
+vary
+ 
+
+ align:start position:0%
+vary
+to be as big as even 500 microns
+
+ align:start position:0%
+to be as big as even 500 microns
+ 
+
+ align:start position:0%
+to be as big as even 500 microns
+so it may not be always that big but it
+
+ align:start position:0%
+so it may not be always that big but it
+ 
+
+ align:start position:0%
+so it may not be always that big but it
+might be let's say 50 to 500 micron
+
+ align:start position:0%
+might be let's say 50 to 500 micron
+ 
+
+ align:start position:0%
+might be let's say 50 to 500 micron
+sort of colonies and they can often be
+
+ align:start position:0%
+sort of colonies and they can often be
+ 
+
+ align:start position:0%
+sort of colonies and they can often be
+these sort of stringy type structures
+
+ align:start position:0%
+these sort of stringy type structures
+ 
+
+ align:start position:0%
+these sort of stringy type structures
+and so as a result those require fairly
+
+ align:start position:0%
+and so as a result those require fairly
+ 
+
+ align:start position:0%
+and so as a result those require fairly
+large droplets
+
+ align:start position:0%
+large droplets
+ 
+
+ align:start position:0%
+large droplets
+now just simply knowing that we have
+
+ align:start position:0%
+now just simply knowing that we have
+ 
+
+ align:start position:0%
+now just simply knowing that we have
+large droplet tells us
+
+ align:start position:0%
+large droplet tells us
+ 
+
+ align:start position:0%
+large droplet tells us
+a lot about how this bacteria can
+
+ align:start position:0%
+a lot about how this bacteria can
+ 
+
+ align:start position:0%
+a lot about how this bacteria can
+actually transmit and what measures must
+
+ align:start position:0%
+actually transmit and what measures must
+ 
+
+ align:start position:0%
+actually transmit and what measures must
+be taken against it
+
+ align:start position:0%
+be taken against it
+ 
+
+ align:start position:0%
+be taken against it
+because as soon as we have large drops
+
+ align:start position:0%
+because as soon as we have large drops
+ 
+
+ align:start position:0%
+because as soon as we have large drops
+then what it means is that we have
+
+ align:start position:0%
+then what it means is that we have
+ 
+
+ align:start position:0%
+then what it means is that we have
+fast settling so we know drops that are
+
+ align:start position:0%
+fast settling so we know drops that are
+ 
+
+ align:start position:0%
+fast settling so we know drops that are
+in this size range are going to fall to
+
+ align:start position:0%
+in this size range are going to fall to
+ 
+
+ align:start position:0%
+in this size range are going to fall to
+the ground within a few seconds
+
+ align:start position:0%
+the ground within a few seconds
+ 
+
+ align:start position:0%
+the ground within a few seconds
+and even if you cough them with a lot of
+
+ align:start position:0%
+and even if you cough them with a lot of
+ 
+
+ align:start position:0%
+and even if you cough them with a lot of
+a big velocity
+
+ align:start position:0%
+a big velocity
+ 
+
+ align:start position:0%
+a big velocity
+which is something we'll talk about
+
+ align:start position:0%
+which is something we'll talk about
+ 
+
+ align:start position:0%
+which is something we'll talk about
+later in this in these lectures
+
+ align:start position:0%
+later in this in these lectures
+ 
+
+ align:start position:0%
+later in this in these lectures
+then still in only a few seconds those
+
+ align:start position:0%
+then still in only a few seconds those
+ 
+
+ align:start position:0%
+then still in only a few seconds those
+droplets can sediment
+
+ align:start position:0%
+droplets can sediment
+ 
+
+ align:start position:0%
+droplets can sediment
+out and they really don't go very far
+
+ align:start position:0%
+out and they really don't go very far
+ 
+
+ align:start position:0%
+out and they really don't go very far
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so they're fast settling and so what
+
+ align:start position:0%
+and so they're fast settling and so what
+ 
+
+ align:start position:0%
+and so they're fast settling and so what
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+is that we have either foam white
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+where those droplets settle on the
+
+ align:start position:0%
+where those droplets settle on the
+ 
+
+ align:start position:0%
+where those droplets settle on the
+ground or on some other surface
+
+ align:start position:0%
+ground or on some other surface
+ 
+
+ align:start position:0%
+ground or on some other surface
+somebody touches that surface touches
+
+ align:start position:0%
+somebody touches that surface touches
+ 
+
+ align:start position:0%
+somebody touches that surface touches
+their eyes and so that's one method of
+
+ align:start position:0%
+their eyes and so that's one method of
+ 
+
+ align:start position:0%
+their eyes and so that's one method of
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+we could also have a direct
+
+ align:start position:0%
+we could also have a direct
+ 
+
+ align:start position:0%
+we could also have a direct
+airborne transmission where
+
+ align:start position:0%
+airborne transmission where
+ 
+
+ align:start position:0%
+airborne transmission where
+let's say i cough or breathe on you and
+
+ align:start position:0%
+let's say i cough or breathe on you and
+ 
+
+ align:start position:0%
+let's say i cough or breathe on you and
+the droplets end up in your face and
+
+ align:start position:0%
+the droplets end up in your face and
+ 
+
+ align:start position:0%
+the droplets end up in your face and
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+directly on your eyes or maybe you
+
+ align:start position:0%
+directly on your eyes or maybe you
+ 
+
+ align:start position:0%
+directly on your eyes or maybe you
+breathe them in so there could be also
+
+ align:start position:0%
+breathe them in so there could be also
+ 
+
+ align:start position:0%
+breathe them in so there could be also
+direct airborne transmission for some of
+
+ align:start position:0%
+direct airborne transmission for some of
+ 
+
+ align:start position:0%
+direct airborne transmission for some of
+the smaller size droplets or for large
+
+ align:start position:0%
+the smaller size droplets or for large
+ 
+
+ align:start position:0%
+the smaller size droplets or for large
+droplets which are ejected from let's
+
+ align:start position:0%
+droplets which are ejected from let's
+ 
+
+ align:start position:0%
+droplets which are ejected from let's
+say a cough or something
+
+ align:start position:0%
+say a cough or something
+ 
+
+ align:start position:0%
+say a cough or something
+and so what that means that the way that
+
+ align:start position:0%
+and so what that means that the way that
+ 
+
+ align:start position:0%
+and so what that means that the way that
+we protect against bacterial
+
+ align:start position:0%
+we protect against bacterial
+ 
+
+ align:start position:0%
+we protect against bacterial
+transmission of disease
+
+ align:start position:0%
+transmission of disease
+ 
+
+ align:start position:0%
+transmission of disease
+is for example for the fomites we will
+
+ align:start position:0%
+is for example for the fomites we will
+ 
+
+ align:start position:0%
+is for example for the fomites we will
+disinfect surfaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can wash hands of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we will avoid touching
+
+ align:start position:0%
+and we will avoid touching
+ 
+
+ align:start position:0%
+and we will avoid touching
+eyes or nose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so those are pretty basic measures at
+
+ align:start position:0%
+so those are pretty basic measures at
+ 
+
+ align:start position:0%
+so those are pretty basic measures at
+the same time if we're worried about the
+
+ align:start position:0%
+the same time if we're worried about the
+ 
+
+ align:start position:0%
+the same time if we're worried about the
+direct
+
+ align:start position:0%
+direct
+ 
+
+ align:start position:0%
+direct
+uh transmission of the droplets from
+
+ align:start position:0%
+uh transmission of the droplets from
+ 
+
+ align:start position:0%
+uh transmission of the droplets from
+especially coughing or sneezing larger
+
+ align:start position:0%
+especially coughing or sneezing larger
+ 
+
+ align:start position:0%
+especially coughing or sneezing larger
+droplets
+
+ align:start position:0%
+droplets
+ 
+
+ align:start position:0%
+droplets
+then what else can we do well we could
+
+ align:start position:0%
+then what else can we do well we could
+ 
+
+ align:start position:0%
+then what else can we do well we could
+have plastic shields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+either worn over the face or maybe a
+
+ align:start position:0%
+either worn over the face or maybe a
+ 
+
+ align:start position:0%
+either worn over the face or maybe a
+barrier between yourself
+
+ align:start position:0%
+barrier between yourself
+ 
+
+ align:start position:0%
+barrier between yourself
+and some other person that you're
+
+ align:start position:0%
+and some other person that you're
+ 
+
+ align:start position:0%
+and some other person that you're
+interacting with to avoid that sort of
+
+ align:start position:0%
+interacting with to avoid that sort of
+ 
+
+ align:start position:0%
+interacting with to avoid that sort of
+projectile transmission of large
+
+ align:start position:0%
+projectile transmission of large
+ 
+
+ align:start position:0%
+projectile transmission of large
+droplets and
+
+ align:start position:0%
+droplets and
+ 
+
+ align:start position:0%
+droplets and
+also we will get the six foot rule
+
+ align:start position:0%
+also we will get the six foot rule
+ 
+
+ align:start position:0%
+also we will get the six foot rule
+which is just an example of a social
+
+ align:start position:0%
+which is just an example of a social
+ 
+
+ align:start position:0%
+which is just an example of a social
+distancing
+
+ align:start position:0%
+distancing
+ 
+
+ align:start position:0%
+distancing
+measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is recommended to avoid this sort
+
+ align:start position:0%
+which is recommended to avoid this sort
+ 
+
+ align:start position:0%
+which is recommended to avoid this sort
+of direct airborne transmission
+
+ align:start position:0%
+of direct airborne transmission
+ 
+
+ align:start position:0%
+of direct airborne transmission
+again coming back to the idea that
+
+ align:start position:0%
+again coming back to the idea that
+ 
+
+ align:start position:0%
+again coming back to the idea that
+droplets of the size typically settle in
+
+ align:start position:0%
+droplets of the size typically settle in
+ 
+
+ align:start position:0%
+droplets of the size typically settle in
+a few seconds
+
+ align:start position:0%
+a few seconds
+ 
+
+ align:start position:0%
+a few seconds
+and if you look at the typical
+
+ align:start position:0%
+and if you look at the typical
+ 
+
+ align:start position:0%
+and if you look at the typical
+velocities of ejection especially from
+
+ align:start position:0%
+velocities of ejection especially from
+ 
+
+ align:start position:0%
+velocities of ejection especially from
+coughs and sneezes
+
+ align:start position:0%
+coughs and sneezes
+ 
+
+ align:start position:0%
+coughs and sneezes
+then they will settle in about six feet
+
+ align:start position:0%
+then they will settle in about six feet
+ 
+
+ align:start position:0%
+then they will settle in about six feet
+or so or about two meters
+
+ align:start position:0%
+or so or about two meters
+ 
+
+ align:start position:0%
+or so or about two meters
+although that's not a hard rule the six
+
+ align:start position:0%
+although that's not a hard rule the six
+ 
+
+ align:start position:0%
+although that's not a hard rule the six
+foot rule happens to be
+
+ align:start position:0%
+foot rule happens to be
+ 
+
+ align:start position:0%
+foot rule happens to be
+for the united states centers for
+
+ align:start position:0%
+for the united states centers for
+ 
+
+ align:start position:0%
+for the united states centers for
+disease control
+
+ align:start position:0%
+disease control
+ 
+
+ align:start position:0%
+disease control
+the cdc but there's also one meter rule
+
+ align:start position:0%
+the cdc but there's also one meter rule
+ 
+
+ align:start position:0%
+the cdc but there's also one meter rule
+which is basically a three-foot rule
+
+ align:start position:0%
+which is basically a three-foot rule
+ 
+
+ align:start position:0%
+which is basically a three-foot rule
+for the world health organization so
+
+ align:start position:0%
+for the world health organization so
+ 
+
+ align:start position:0%
+for the world health organization so
+this is not
+
+ align:start position:0%
+this is not
+ 
+
+ align:start position:0%
+this is not
+you know extremely well-defined what
+
+ align:start position:0%
+you know extremely well-defined what
+ 
+
+ align:start position:0%
+you know extremely well-defined what
+should be the distance but clearly if
+
+ align:start position:0%
+should be the distance but clearly if
+ 
+
+ align:start position:0%
+should be the distance but clearly if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+are able to stay away from people then
+
+ align:start position:0%
+are able to stay away from people then
+ 
+
+ align:start position:0%
+are able to stay away from people then
+even if they're coughing or breathing
+
+ align:start position:0%
+even if they're coughing or breathing
+ 
+
+ align:start position:0%
+even if they're coughing or breathing
+these large droplets
+
+ align:start position:0%
+these large droplets
+ 
+
+ align:start position:0%
+these large droplets
+with only a few seconds of settling time
+
+ align:start position:0%
+with only a few seconds of settling time
+ 
+
+ align:start position:0%
+with only a few seconds of settling time
+those droplets will hit the floor
+
+ align:start position:0%
+those droplets will hit the floor
+ 
+
+ align:start position:0%
+those droplets will hit the floor
+and will not be able to infect you
+
+ align:start position:0%
+and will not be able to infect you
+ 
+
+ align:start position:0%
+and will not be able to infect you
+directly and so it's important to
+
+ align:start position:0%
+directly and so it's important to
+ 
+
+ align:start position:0%
+directly and so it's important to
+maintain that kind of distancing
+
+ align:start position:0%
+maintain that kind of distancing
+ 
+
+ align:start position:0%
+maintain that kind of distancing
+okay now there are also other kinds of
+
+ align:start position:0%
+okay now there are also other kinds of
+ 
+
+ align:start position:0%
+okay now there are also other kinds of
+bacteria
+
+ align:start position:0%
+bacteria
+ 
+
+ align:start position:0%
+bacteria
+that don't form these larger colonies
+
+ align:start position:0%
+that don't form these larger colonies
+ 
+
+ align:start position:0%
+that don't form these larger colonies
+and they remain
+
+ align:start position:0%
+and they remain
+ 
+
+ align:start position:0%
+and they remain
+small even when they're transmitting and
+
+ align:start position:0%
+small even when they're transmitting and
+ 
+
+ align:start position:0%
+small even when they're transmitting and
+a classic example of that which can be
+
+ align:start position:0%
+a classic example of that which can be
+ 
+
+ align:start position:0%
+a classic example of that which can be
+transmitted
+
+ align:start position:0%
+transmitted
+ 
+
+ align:start position:0%
+transmitted
+in small drops is tuberculosis
+
+ align:start position:0%
+in small drops is tuberculosis
+ 
+
+ align:start position:0%
+in small drops is tuberculosis
+in fact the original study in the 1930s
+
+ align:start position:0%
+in fact the original study in the 1930s
+ 
+
+ align:start position:0%
+in fact the original study in the 1930s
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+also involving wells uh was
+
+ align:start position:0%
+also involving wells uh was
+ 
+
+ align:start position:0%
+also involving wells uh was
+for that that led to this essentially
+
+ align:start position:0%
+for that that led to this essentially
+ 
+
+ align:start position:0%
+for that that led to this essentially
+this the distancing rules and the so
+
+ align:start position:0%
+this the distancing rules and the so
+ 
+
+ align:start position:0%
+this the distancing rules and the so
+the sixth rule in particular had to do
+
+ align:start position:0%
+the sixth rule in particular had to do
+ 
+
+ align:start position:0%
+the sixth rule in particular had to do
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+coughing and sneezing and the distance
+
+ align:start position:0%
+coughing and sneezing and the distance
+ 
+
+ align:start position:0%
+coughing and sneezing and the distance
+over which droplets could be transmitted
+
+ align:start position:0%
+over which droplets could be transmitted
+ 
+
+ align:start position:0%
+over which droplets could be transmitted
+containing tuberculosis now tuberculosis
+
+ align:start position:0%
+containing tuberculosis now tuberculosis
+ 
+
+ align:start position:0%
+containing tuberculosis now tuberculosis
+on the other hand
+
+ align:start position:0%
+on the other hand
+ 
+
+ align:start position:0%
+on the other hand
+as you can see um in the image is a
+
+ align:start position:0%
+as you can see um in the image is a
+ 
+
+ align:start position:0%
+as you can see um in the image is a
+rod-like bacteria that's quite small so
+
+ align:start position:0%
+rod-like bacteria that's quite small so
+ 
+
+ align:start position:0%
+rod-like bacteria that's quite small so
+the length
+
+ align:start position:0%
+the length
+ 
+
+ align:start position:0%
+the length
+is several microns typically two to four
+
+ align:start position:0%
+is several microns typically two to four
+ 
+
+ align:start position:0%
+is several microns typically two to four
+but the radius is half a micron or even
+
+ align:start position:0%
+but the radius is half a micron or even
+ 
+
+ align:start position:0%
+but the radius is half a micron or even
+down to 0.2 microns so actually we're
+
+ align:start position:0%
+down to 0.2 microns so actually we're
+ 
+
+ align:start position:0%
+down to 0.2 microns so actually we're
+really talking about hundreds of
+
+ align:start position:0%
+really talking about hundreds of
+ 
+
+ align:start position:0%
+really talking about hundreds of
+nanometers in length
+
+ align:start position:0%
+nanometers in length
+ 
+
+ align:start position:0%
+nanometers in length
+so these are kind of you know little
+
+ align:start position:0%
+so these are kind of you know little
+ 
+
+ align:start position:0%
+so these are kind of you know little
+rods like this
+
+ align:start position:0%
+rods like this
+ 
+
+ align:start position:0%
+rods like this
+and they can be contained in a pretty
+
+ align:start position:0%
+and they can be contained in a pretty
+ 
+
+ align:start position:0%
+and they can be contained in a pretty
+small droplet you know these big
+
+ align:start position:0%
+small droplet you know these big
+ 
+
+ align:start position:0%
+small droplet you know these big
+colonies right
+
+ align:start position:0%
+colonies right
+ 
+
+ align:start position:0%
+colonies right
+of course require something much larger
+
+ align:start position:0%
+of course require something much larger
+ 
+
+ align:start position:0%
+of course require something much larger
+so these droplets could be small
+
+ align:start position:0%
+so these droplets could be small
+ 
+
+ align:start position:0%
+so these droplets could be small
+and so there is a possibility here of
+
+ align:start position:0%
+and so there is a possibility here of
+ 
+
+ align:start position:0%
+and so there is a possibility here of
+larger aerosol transmission by larger i
+
+ align:start position:0%
+larger aerosol transmission by larger i
+ 
+
+ align:start position:0%
+larger aerosol transmission by larger i
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+in the range of sort of 5 to 10 microns
+
+ align:start position:0%
+in the range of sort of 5 to 10 microns
+ 
+
+ align:start position:0%
+in the range of sort of 5 to 10 microns
+so of course tuberculos also can be
+
+ align:start position:0%
+so of course tuberculos also can be
+ 
+
+ align:start position:0%
+so of course tuberculos also can be
+contained in much larger droplets
+
+ align:start position:0%
+contained in much larger droplets
+ 
+
+ align:start position:0%
+contained in much larger droplets
+which you know fall to the ground as
+
+ align:start position:0%
+which you know fall to the ground as
+ 
+
+ align:start position:0%
+which you know fall to the ground as
+we've just been describing
+
+ align:start position:0%
+we've just been describing
+ 
+
+ align:start position:0%
+we've just been describing
+but tuberculosis is a bit different in
+
+ align:start position:0%
+but tuberculosis is a bit different in
+ 
+
+ align:start position:0%
+but tuberculosis is a bit different in
+that these individual
+
+ align:start position:0%
+that these individual
+ 
+
+ align:start position:0%
+that these individual
+bacteria could be transmitted airborne
+
+ align:start position:0%
+bacteria could be transmitted airborne
+ 
+
+ align:start position:0%
+bacteria could be transmitted airborne
+in larger aerosol droplets
+
+ align:start position:0%
+in larger aerosol droplets
+ 
+
+ align:start position:0%
+in larger aerosol droplets
+and in fact that is what is found if you
+
+ align:start position:0%
+and in fact that is what is found if you
+ 
+
+ align:start position:0%
+and in fact that is what is found if you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+this size of droplet then it turns out
+
+ align:start position:0%
+this size of droplet then it turns out
+ 
+
+ align:start position:0%
+this size of droplet then it turns out
+for example if my radius
+
+ align:start position:0%
+for example if my radius
+ 
+
+ align:start position:0%
+for example if my radius
+is let's say greater than 4 microns
+
+ align:start position:0%
+is let's say greater than 4 microns
+ 
+
+ align:start position:0%
+is let's say greater than 4 microns
+then the settling velocity you can find
+
+ align:start position:0%
+then the settling velocity you can find
+ 
+
+ align:start position:0%
+then the settling velocity you can find
+given the density of aqueous fluids
+
+ align:start position:0%
+given the density of aqueous fluids
+ 
+
+ align:start position:0%
+given the density of aqueous fluids
+is around two bigger than two
+
+ align:start position:0%
+is around two bigger than two
+ 
+
+ align:start position:0%
+is around two bigger than two
+millimeters a second
+
+ align:start position:0%
+millimeters a second
+ 
+
+ align:start position:0%
+millimeters a second
+and then the time to drop from a typical
+
+ align:start position:0%
+and then the time to drop from a typical
+ 
+
+ align:start position:0%
+and then the time to drop from a typical
+person's height to the ground
+
+ align:start position:0%
+person's height to the ground
+ 
+
+ align:start position:0%
+person's height to the ground
+is around 15 minutes so these are not
+
+ align:start position:0%
+is around 15 minutes so these are not
+ 
+
+ align:start position:0%
+is around 15 minutes so these are not
+the kind of aerosols that might stick
+
+ align:start position:0%
+the kind of aerosols that might stick
+ 
+
+ align:start position:0%
+the kind of aerosols that might stick
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+for hours like the submicron aerosols
+
+ align:start position:0%
+for hours like the submicron aerosols
+ 
+
+ align:start position:0%
+for hours like the submicron aerosols
+that are also
+
+ align:start position:0%
+that are also
+ 
+
+ align:start position:0%
+that are also
+produced by breathing and which are too
+
+ align:start position:0%
+produced by breathing and which are too
+ 
+
+ align:start position:0%
+produced by breathing and which are too
+small to contain tuberculosis
+
+ align:start position:0%
+small to contain tuberculosis
+ 
+
+ align:start position:0%
+small to contain tuberculosis
+but still these times suggest that
+
+ align:start position:0%
+but still these times suggest that
+ 
+
+ align:start position:0%
+but still these times suggest that
+tuberculosis can linger in the air
+
+ align:start position:0%
+tuberculosis can linger in the air
+ 
+
+ align:start position:0%
+tuberculosis can linger in the air
+and in fact a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+long distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+airborne transmission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not only possible as we've just
+
+ align:start position:0%
+is not only possible as we've just
+ 
+
+ align:start position:0%
+is not only possible as we've just
+argued based on physical rounds but it's
+
+ align:start position:0%
+argued based on physical rounds but it's
+ 
+
+ align:start position:0%
+argued based on physical rounds but it's
+been directly verified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's been done both in human studies
+
+ align:start position:0%
+that's been done both in human studies
+ 
+
+ align:start position:0%
+that's been done both in human studies
+and also in animal studies
+
+ align:start position:0%
+and also in animal studies
+ 
+
+ align:start position:0%
+and also in animal studies
+where they can have two different
+
+ align:start position:0%
+where they can have two different
+ 
+
+ align:start position:0%
+where they can have two different
+compartments with a sick animal such as
+
+ align:start position:0%
+compartments with a sick animal such as
+ 
+
+ align:start position:0%
+compartments with a sick animal such as
+a ferret
+
+ align:start position:0%
+a ferret
+ 
+
+ align:start position:0%
+a ferret
+or some other animal model and the
+
+ align:start position:0%
+or some other animal model and the
+ 
+
+ align:start position:0%
+or some other animal model and the
+disease is spread to another animal
+
+ align:start position:0%
+disease is spread to another animal
+ 
+
+ align:start position:0%
+disease is spread to another animal
+who's had no direct contact but is
+
+ align:start position:0%
+who's had no direct contact but is
+ 
+
+ align:start position:0%
+who's had no direct contact but is
+sharing the same air so the airborne
+
+ align:start position:0%
+sharing the same air so the airborne
+ 
+
+ align:start position:0%
+sharing the same air so the airborne
+transmission is definitely
+
+ align:start position:0%
+transmission is definitely
+ 
+
+ align:start position:0%
+transmission is definitely
+verified in this case and now you might
+
+ align:start position:0%
+verified in this case and now you might
+ 
+
+ align:start position:0%
+verified in this case and now you might
+ask well what are the preventive
+
+ align:start position:0%
+ask well what are the preventive
+ 
+
+ align:start position:0%
+ask well what are the preventive
+measures
+
+ align:start position:0%
+measures
+ 
+
+ align:start position:0%
+measures
+so instead of all of these measures like
+
+ align:start position:0%
+so instead of all of these measures like
+ 
+
+ align:start position:0%
+so instead of all of these measures like
+plastic shields and six foot rule
+
+ align:start position:0%
+plastic shields and six foot rule
+ 
+
+ align:start position:0%
+plastic shields and six foot rule
+if you actually airborne transmission if
+
+ align:start position:0%
+if you actually airborne transmission if
+ 
+
+ align:start position:0%
+if you actually airborne transmission if
+there's a shield then the air is going
+
+ align:start position:0%
+there's a shield then the air is going
+ 
+
+ align:start position:0%
+there's a shield then the air is going
+to go right around the shield and it's
+
+ align:start position:0%
+to go right around the shield and it's
+ 
+
+ align:start position:0%
+to go right around the shield and it's
+going to go everywhere else in the room
+
+ align:start position:0%
+going to go everywhere else in the room
+ 
+
+ align:start position:0%
+going to go everywhere else in the room
+because the air is flowing
+
+ align:start position:0%
+because the air is flowing
+ 
+
+ align:start position:0%
+because the air is flowing
+okay in the same way that when you light
+
+ align:start position:0%
+okay in the same way that when you light
+ 
+
+ align:start position:0%
+okay in the same way that when you light
+a candle and you see where the smoke is
+
+ align:start position:0%
+a candle and you see where the smoke is
+ 
+
+ align:start position:0%
+a candle and you see where the smoke is
+going it quickly spreads around the
+
+ align:start position:0%
+going it quickly spreads around the
+ 
+
+ align:start position:0%
+going it quickly spreads around the
+whole room it doesn't care if there's a
+
+ align:start position:0%
+whole room it doesn't care if there's a
+ 
+
+ align:start position:0%
+whole room it doesn't care if there's a
+shield there as long as there's a way
+
+ align:start position:0%
+shield there as long as there's a way
+ 
+
+ align:start position:0%
+shield there as long as there's a way
+around the shield that's going to find
+
+ align:start position:0%
+around the shield that's going to find
+ 
+
+ align:start position:0%
+around the shield that's going to find
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and so instead when you're trying to
+
+ align:start position:0%
+and so instead when you're trying to
+ 
+
+ align:start position:0%
+and so instead when you're trying to
+protect against airborne transmission
+
+ align:start position:0%
+protect against airborne transmission
+ 
+
+ align:start position:0%
+protect against airborne transmission
+your protective measures are things like
+
+ align:start position:0%
+your protective measures are things like
+ 
+
+ align:start position:0%
+your protective measures are things like
+ventilation so bring in fresh air from
+
+ align:start position:0%
+ventilation so bring in fresh air from
+ 
+
+ align:start position:0%
+ventilation so bring in fresh air from
+outside or opening your windows
+
+ align:start position:0%
+outside or opening your windows
+ 
+
+ align:start position:0%
+outside or opening your windows
+air filtration
+
+ align:start position:0%
+air filtration
+ 
+
+ align:start position:0%
+air filtration
+where you're passing the air through a
+
+ align:start position:0%
+where you're passing the air through a
+ 
+
+ align:start position:0%
+where you're passing the air through a
+filter which is going to filter out the
+
+ align:start position:0%
+filter which is going to filter out the
+ 
+
+ align:start position:0%
+filter which is going to filter out the
+particles by size or by charge
+
+ align:start position:0%
+particles by size or by charge
+ 
+
+ align:start position:0%
+particles by size or by charge
+or some other mechanism like that and
+
+ align:start position:0%
+or some other mechanism like that and
+ 
+
+ align:start position:0%
+or some other mechanism like that and
+also becomes more and more important
+
+ align:start position:0%
+also becomes more and more important
+ 
+
+ align:start position:0%
+also becomes more and more important
+to wear face masks because then at least
+
+ align:start position:0%
+to wear face masks because then at least
+ 
+
+ align:start position:0%
+to wear face masks because then at least
+you can block these droplets at the
+
+ align:start position:0%
+you can block these droplets at the
+ 
+
+ align:start position:0%
+you can block these droplets at the
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+and also at the target as we shall
+
+ align:start position:0%
+and also at the target as we shall
+ 
+
+ align:start position:0%
+and also at the target as we shall
+discuss in much
+
+ align:start position:0%
+discuss in much
+ 
+
+ align:start position:0%
+discuss in much
+more detail so what we see here is just
+
+ align:start position:0%
+more detail so what we see here is just
+ 
+
+ align:start position:0%
+more detail so what we see here is just
+knowing simply the size of the pathogen
+
+ align:start position:0%
+knowing simply the size of the pathogen
+ 
+
+ align:start position:0%
+knowing simply the size of the pathogen
+and understanding the dynamic the
+
+ align:start position:0%
+and understanding the dynamic the
+ 
+
+ align:start position:0%
+and understanding the dynamic the
+physics of droplets
+
+ align:start position:0%
+physics of droplets
+ 
+
+ align:start position:0%
+physics of droplets
+in the air helps us to understand the
+
+ align:start position:0%
+in the air helps us to understand the
+ 
+
+ align:start position:0%
+in the air helps us to understand the
+modes of transmission which are written
+
+ align:start position:0%
+modes of transmission which are written
+ 
+
+ align:start position:0%
+modes of transmission which are written
+here in blue
+
+ align:start position:0%
+here in blue
+ 
+
+ align:start position:0%
+here in blue
+and also the appropriate protective
+
+ align:start position:0%
+and also the appropriate protective
+ 
+
+ align:start position:0%
+and also the appropriate protective
+measures which are written here
+
+ align:start position:0%
+measures which are written here
+ 
+
+ align:start position:0%
+measures which are written here
+in pink to protect against these
+
+ align:start position:0%
+in pink to protect against these
+ 
+
+ align:start position:0%
+in pink to protect against these
+different types
+
+ align:start position:0%
+different types
+ 
+
+ align:start position:0%
+different types
+of transmission
\ No newline at end of file
diff --git a/klubJGAZDOI.txt b/klubJGAZDOI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8a3a3bb265f6fc1c50e8c15faaa248be2d475707
--- /dev/null
+++ b/klubJGAZDOI.txt
@@ -0,0 +1,899 @@
+align:start position:0%
+ 
+visualizing cultures is a web-based
+
+ align:start position:0%
+visualizing cultures is a web-based
+ 
+
+ align:start position:0%
+visualizing cultures is a web-based
+history uh program which John Da and I
+
+ align:start position:0%
+history uh program which John Da and I
+ 
+
+ align:start position:0%
+history uh program which John Da and I
+started in year 2001 John Da is an
+
+ align:start position:0%
+started in year 2001 John Da is an
+ 
+
+ align:start position:0%
+started in year 2001 John Da is an
+eminent historian of modern Japan he won
+
+ align:start position:0%
+eminent historian of modern Japan he won
+ 
+
+ align:start position:0%
+eminent historian of modern Japan he won
+the pillot prize in 1999 for his book
+
+ align:start position:0%
+the pillot prize in 1999 for his book
+ 
+
+ align:start position:0%
+the pillot prize in 1999 for his book
+embracing
+
+ align:start position:0%
+embracing
+ 
+
+ align:start position:0%
+embracing
+defeat I approached John in uh in
+
+ align:start position:0%
+defeat I approached John in uh in
+ 
+
+ align:start position:0%
+defeat I approached John in uh in
+2000 uh when I knew that open course
+
+ align:start position:0%
+2000 uh when I knew that open course
+ 
+
+ align:start position:0%
+2000 uh when I knew that open course
+Weare was about to go up and I told John
+
+ align:start position:0%
+Weare was about to go up and I told John
+ 
+
+ align:start position:0%
+Weare was about to go up and I told John
+that uh I thought that this would be a
+
+ align:start position:0%
+that uh I thought that this would be a
+ 
+
+ align:start position:0%
+that uh I thought that this would be a
+great platform to to do something new
+
+ align:start position:0%
+great platform to to do something new
+ 
+
+ align:start position:0%
+great platform to to do something new
+with history okay specifically to look
+
+ align:start position:0%
+with history okay specifically to look
+ 
+
+ align:start position:0%
+with history okay specifically to look
+at history not just from text which is
+
+ align:start position:0%
+at history not just from text which is
+ 
+
+ align:start position:0%
+at history not just from text which is
+what historians do but from uh looking
+
+ align:start position:0%
+what historians do but from uh looking
+ 
+
+ align:start position:0%
+what historians do but from uh looking
+at images visuals that have been uh
+
+ align:start position:0%
+at images visuals that have been uh
+ 
+
+ align:start position:0%
+at images visuals that have been uh
+produced by uh
+
+ align:start position:0%
+produced by uh
+ 
+
+ align:start position:0%
+produced by uh
+by people from the historical era and to
+
+ align:start position:0%
+by people from the historical era and to
+ 
+
+ align:start position:0%
+by people from the historical era and to
+try to understand what was going
+
+ align:start position:0%
+try to understand what was going
+ 
+
+ align:start position:0%
+try to understand what was going
+on uh
+
+ align:start position:0%
+on uh
+ 
+
+ align:start position:0%
+on uh
+John surprisingly said
+
+ align:start position:0%
+John surprisingly said
+ 
+
+ align:start position:0%
+John surprisingly said
+yes and so we started we didn't quite
+
+ align:start position:0%
+yes and so we started we didn't quite
+ 
+
+ align:start position:0%
+yes and so we started we didn't quite
+know what you know we were doing at
+
+ align:start position:0%
+know what you know we were doing at
+ 
+
+ align:start position:0%
+know what you know we were doing at
+first but uh we got very lucky with our
+
+ align:start position:0%
+first but uh we got very lucky with our
+ 
+
+ align:start position:0%
+first but uh we got very lucky with our
+first unit which is uh uh commer Matthew
+
+ align:start position:0%
+first unit which is uh uh commer Matthew
+ 
+
+ align:start position:0%
+first unit which is uh uh commer Matthew
+Perry's arrival in Japan in 1853 to open
+
+ align:start position:0%
+Perry's arrival in Japan in 1853 to open
+ 
+
+ align:start position:0%
+Perry's arrival in Japan in 1853 to open
+up Japan which had been essentially
+
+ align:start position:0%
+up Japan which had been essentially
+ 
+
+ align:start position:0%
+up Japan which had been essentially
+isolated closed for 250 years and so you
+
+ align:start position:0%
+isolated closed for 250 years and so you
+ 
+
+ align:start position:0%
+isolated closed for 250 years and so you
+have uh America and Japan come clashing
+
+ align:start position:0%
+have uh America and Japan come clashing
+ 
+
+ align:start position:0%
+have uh America and Japan come clashing
+together in this one moment in history
+
+ align:start position:0%
+together in this one moment in history
+ 
+
+ align:start position:0%
+together in this one moment in history
+and from that this explosion of images
+
+ align:start position:0%
+and from that this explosion of images
+ 
+
+ align:start position:0%
+and from that this explosion of images
+from both sides know Americans uh
+
+ align:start position:0%
+from both sides know Americans uh
+ 
+
+ align:start position:0%
+from both sides know Americans uh
+depicting the Japanese uh and Japanese
+
+ align:start position:0%
+depicting the Japanese uh and Japanese
+ 
+
+ align:start position:0%
+depicting the Japanese uh and Japanese
+depicting per and his man and his ships
+
+ align:start position:0%
+depicting per and his man and his ships
+ 
+
+ align:start position:0%
+depicting per and his man and his ships
+it's just
+
+ align:start position:0%
+it's just
+ 
+
+ align:start position:0%
+it's just
+wonderful and what's really uh
+
+ align:start position:0%
+wonderful and what's really uh
+ 
+
+ align:start position:0%
+wonderful and what's really uh
+interesting is that when you look at
+
+ align:start position:0%
+interesting is that when you look at
+ 
+
+ align:start position:0%
+interesting is that when you look at
+images you get to see things that you
+
+ align:start position:0%
+images you get to see things that you
+ 
+
+ align:start position:0%
+images you get to see things that you
+cannot get from written
+
+ align:start position:0%
+cannot get from written
+ 
+
+ align:start position:0%
+cannot get from written
+material uh we found lots of images
+
+ align:start position:0%
+material uh we found lots of images
+ 
+
+ align:start position:0%
+material uh we found lots of images
+where the Japanese were really curious
+
+ align:start position:0%
+where the Japanese were really curious
+ 
+
+ align:start position:0%
+where the Japanese were really curious
+about Paris men and
+
+ align:start position:0%
+about Paris men and
+ 
+
+ align:start position:0%
+about Paris men and
+drawing
+
+ align:start position:0%
+drawing
+ 
+
+ align:start position:0%
+drawing
+uh you know costumes instruments weapons
+
+ align:start position:0%
+uh you know costumes instruments weapons
+ 
+
+ align:start position:0%
+uh you know costumes instruments weapons
+in minute detail and with with notes to
+
+ align:start position:0%
+in minute detail and with with notes to
+ 
+
+ align:start position:0%
+in minute detail and with with notes to
+go along with them showing just sort of
+
+ align:start position:0%
+go along with them showing just sort of
+ 
+
+ align:start position:0%
+go along with them showing just sort of
+sheer curiosity who are these people you
+
+ align:start position:0%
+sheer curiosity who are these people you
+ 
+
+ align:start position:0%
+sheer curiosity who are these people you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+how do they live okay how do they talk
+
+ align:start position:0%
+how do they live okay how do they talk
+ 
+
+ align:start position:0%
+how do they live okay how do they talk
+and you saw the same thing on Perry's
+
+ align:start position:0%
+and you saw the same thing on Perry's
+ 
+
+ align:start position:0%
+and you saw the same thing on Perry's
+side uh Perry brought his own
+
+ align:start position:0%
+side uh Perry brought his own
+ 
+
+ align:start position:0%
+side uh Perry brought his own
+artist haa who was a a
+
+ align:start position:0%
+artist haa who was a a
+ 
+
+ align:start position:0%
+artist haa who was a a
+26-year-old
+
+ align:start position:0%
+26-year-old
+ 
+
+ align:start position:0%
+26-year-old
+um artist uh trained in Germany in sort
+
+ align:start position:0%
+um artist uh trained in Germany in sort
+ 
+
+ align:start position:0%
+um artist uh trained in Germany in sort
+of romantic uh style he just fell in
+
+ align:start position:0%
+of romantic uh style he just fell in
+ 
+
+ align:start position:0%
+of romantic uh style he just fell in
+love with Japan yeah and you can tell
+
+ align:start position:0%
+love with Japan yeah and you can tell
+ 
+
+ align:start position:0%
+love with Japan yeah and you can tell
+that in the images he absolutely fell in
+
+ align:start position:0%
+that in the images he absolutely fell in
+ 
+
+ align:start position:0%
+that in the images he absolutely fell in
+love with with this beautiful country so
+
+ align:start position:0%
+love with with this beautiful country so
+ 
+
+ align:start position:0%
+love with with this beautiful country so
+much so that he would sometimes S Paint
+
+ align:start position:0%
+much so that he would sometimes S Paint
+ 
+
+ align:start position:0%
+much so that he would sometimes S Paint
+himself into the picture interacting
+
+ align:start position:0%
+himself into the picture interacting
+ 
+
+ align:start position:0%
+himself into the picture interacting
+with the Japanese and so what you got
+
+ align:start position:0%
+with the Japanese and so what you got
+ 
+
+ align:start position:0%
+with the Japanese and so what you got
+was this one artist depicting Japan uh
+
+ align:start position:0%
+was this one artist depicting Japan uh
+ 
+
+ align:start position:0%
+was this one artist depicting Japan uh
+in a very beautiful very affectionate uh
+
+ align:start position:0%
+in a very beautiful very affectionate uh
+ 
+
+ align:start position:0%
+in a very beautiful very affectionate uh
+way and that's what the Americans saw of
+
+ align:start position:0%
+way and that's what the Americans saw of
+ 
+
+ align:start position:0%
+way and that's what the Americans saw of
+Japan for the first time this is why
+
+ align:start position:0%
+Japan for the first time this is why
+ 
+
+ align:start position:0%
+Japan for the first time this is why
+even to this day you know in this
+
+ align:start position:0%
+even to this day you know in this
+ 
+
+ align:start position:0%
+even to this day you know in this
+country you have this image of Japan as
+
+ align:start position:0%
+country you have this image of Japan as
+ 
+
+ align:start position:0%
+country you have this image of Japan as
+uh very beautiful very very beautiful
+
+ align:start position:0%
+uh very beautiful very very beautiful
+ 
+
+ align:start position:0%
+uh very beautiful very very beautiful
+nature and it really originates with
+
+ align:start position:0%
+nature and it really originates with
+ 
+
+ align:start position:0%
+nature and it really originates with
+highness paintings and so we very much
+
+ align:start position:0%
+highness paintings and so we very much
+ 
+
+ align:start position:0%
+highness paintings and so we very much
+follow the
+
+ align:start position:0%
+follow the
+ 
+
+ align:start position:0%
+follow the
+ocw principle of uh not only making it
+
+ align:start position:0%
+ocw principle of uh not only making it
+ 
+
+ align:start position:0%
+ocw principle of uh not only making it
+available open and free but that
+
+ align:start position:0%
+available open and free but that
+ 
+
+ align:start position:0%
+available open and free but that
+everything is licensed under Creative
+
+ align:start position:0%
+everything is licensed under Creative
+ 
+
+ align:start position:0%
+everything is licensed under Creative
+Commons so that uh these images okay uh
+
+ align:start position:0%
+Commons so that uh these images okay uh
+ 
+
+ align:start position:0%
+Commons so that uh these images okay uh
+which we got from about 200 museums and
+
+ align:start position:0%
+which we got from about 200 museums and
+ 
+
+ align:start position:0%
+which we got from about 200 museums and
+these are major museums both on MFA
+
+ align:start position:0%
+these are major museums both on MFA
+ 
+
+ align:start position:0%
+these are major museums both on MFA
+Sackler in Washington Hong Kong British
+
+ align:start position:0%
+Sackler in Washington Hong Kong British
+ 
+
+ align:start position:0%
+Sackler in Washington Hong Kong British
+uh Museum uh we asked all of them to
+
+ align:start position:0%
+uh Museum uh we asked all of them to
+ 
+
+ align:start position:0%
+uh Museum uh we asked all of them to
+sign an agreement that we could present
+
+ align:start position:0%
+sign an agreement that we could present
+ 
+
+ align:start position:0%
+sign an agreement that we could present
+their images on open on visualizing
+
+ align:start position:0%
+their images on open on visualizing
+ 
+
+ align:start position:0%
+their images on open on visualizing
+Japan on open coare under creative
+
+ align:start position:0%
+Japan on open coare under creative
+ 
+
+ align:start position:0%
+Japan on open coare under creative
+comments and so uh anyone coming
+
+ align:start position:0%
+comments and so uh anyone coming
+ 
+
+ align:start position:0%
+comments and so uh anyone coming
+in and studying uh visualizing cultures
+
+ align:start position:0%
+in and studying uh visualizing cultures
+ 
+
+ align:start position:0%
+in and studying uh visualizing cultures
+can take images and copy them distribute
+
+ align:start position:0%
+can take images and copy them distribute
+ 
+
+ align:start position:0%
+can take images and copy them distribute
+them alter them uh into their own
+
+ align:start position:0%
+them alter them uh into their own
+ 
+
+ align:start position:0%
+them alter them uh into their own
+material and use them you know however
+
+ align:start position:0%
+material and use them you know however
+ 
+
+ align:start position:0%
+material and use them you know however
+they wish
+
+ align:start position:0%
+they wish
+ 
+
+ align:start position:0%
+they wish
+one of the uh populations that we really
+
+ align:start position:0%
+one of the uh populations that we really
+ 
+
+ align:start position:0%
+one of the uh populations that we really
+wanted to work with were School
+
+ align:start position:0%
+wanted to work with were School
+ 
+
+ align:start position:0%
+wanted to work with were School
+teachers and so we did many many
+
+ align:start position:0%
+teachers and so we did many many
+ 
+
+ align:start position:0%
+teachers and so we did many many
+workshops over the years and we trained
+
+ align:start position:0%
+workshops over the years and we trained
+ 
+
+ align:start position:0%
+workshops over the years and we trained
+face Toof face uh around 2,000 teachers
+
+ align:start position:0%
+face Toof face uh around 2,000 teachers
+ 
+
+ align:start position:0%
+face Toof face uh around 2,000 teachers
+okay this is I we I say we uh we worked
+
+ align:start position:0%
+okay this is I we I say we uh we worked
+ 
+
+ align:start position:0%
+okay this is I we I say we uh we worked
+with a uh uh a a wonderful um group out
+
+ align:start position:0%
+with a uh uh a a wonderful um group out
+ 
+
+ align:start position:0%
+with a uh uh a a wonderful um group out
+of University of Colorado that
+
+ align:start position:0%
+of University of Colorado that
+ 
+
+ align:start position:0%
+of University of Colorado that
+specializes in creating East Asian
+
+ align:start position:0%
+specializes in creating East Asian
+ 
+
+ align:start position:0%
+specializes in creating East Asian
+curriculum and work working with
+
+ align:start position:0%
+curriculum and work working with
+ 
+
+ align:start position:0%
+curriculum and work working with
+teachers directly to help them to
+
+ align:start position:0%
+teachers directly to help them to
+ 
+
+ align:start position:0%
+teachers directly to help them to
+incorporate them into their classroom
+
+ align:start position:0%
+incorporate them into their classroom
+ 
+
+ align:start position:0%
+incorporate them into their classroom
+and so they uh ran this series of
+
+ align:start position:0%
+and so they uh ran this series of
+ 
+
+ align:start position:0%
+and so they uh ran this series of
+workshops all over the country and uh as
+
+ align:start position:0%
+workshops all over the country and uh as
+ 
+
+ align:start position:0%
+workshops all over the country and uh as
+far as I know it's still being
+
+ align:start position:0%
+far as I know it's still being
+ 
+
+ align:start position:0%
+far as I know it's still being
+used so high school teachers uh
+
+ align:start position:0%
+used so high school teachers uh
+ 
+
+ align:start position:0%
+used so high school teachers uh
+University professors tell us that
+
+ align:start position:0%
+University professors tell us that
+ 
+
+ align:start position:0%
+University professors tell us that
+they're um using it uh on a regular
+
+ align:start position:0%
+they're um using it uh on a regular
+ 
+
+ align:start position:0%
+they're um using it uh on a regular
+basis couple years ago a uh University
+
+ align:start position:0%
+basis couple years ago a uh University
+ 
+
+ align:start position:0%
+basis couple years ago a uh University
+um had an opening for assistant
+
+ align:start position:0%
+um had an opening for assistant
+ 
+
+ align:start position:0%
+um had an opening for assistant
+professoring Japanese history and uh uh
+
+ align:start position:0%
+professoring Japanese history and uh uh
+ 
+
+ align:start position:0%
+professoring Japanese history and uh uh
+they had uh four finalists and they
+
+ align:start position:0%
+they had uh four finalists and they
+ 
+
+ align:start position:0%
+they had uh four finalists and they
+asked them how do you teach Japanese
+
+ align:start position:0%
+asked them how do you teach Japanese
+ 
+
+ align:start position:0%
+asked them how do you teach Japanese
+history and three of three of them
+
+ align:start position:0%
+history and three of three of them
+ 
+
+ align:start position:0%
+history and three of three of them
+apparently said they used visualizing
+
+ align:start position:0%
+apparently said they used visualizing
+ 
+
+ align:start position:0%
+apparently said they used visualizing
+cultures
\ No newline at end of file
diff --git a/le8tpXQyYcM.txt b/le8tpXQyYcM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1d06ffeb28caab0abf13a3f54627b3e714739c27
--- /dev/null
+++ b/le8tpXQyYcM.txt
@@ -0,0 +1,1818 @@
+OPERATOR: --
+
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: At the end of the
+lecture on Tuesday, a number
+
+of people asked me questions,
+asked Professor Grimson
+
+questions, which made it clear
+that I had been less than
+
+clear on at least a few things,
+so I want to come back
+
+and revisit a couple of the
+things we talked about at the
+
+end of the lecture.
+
+You'll remember that I had drawn
+this decision tree, in
+
+part because it's an important
+concept I want you to
+
+understand, the concept of
+decision trees, and also to
+
+illustrate, I hope, visually,
+some things related to dynamic
+
+programming.
+
+So we had in that decision tree,
+is we had the weight
+
+vector, and I just given a very
+simple one [5,3,2], and
+
+we had a very simple value
+vector, [9,7,8].
+
+And then the way we drew the
+tree, was we started at the
+
+top, and said all right, we're
+going to first look at item
+
+number 2, which was the third
+item in our list of items, of
+
+course, and say that we had
+five pounds left of weight
+
+that our knapsack that could
+hold, and currently had a
+
+value of 0.
+
+And then we made a decision, to
+not put that last item in
+
+the backpack, and said if we
+made that decision, the next
+
+item we had to consider was
+item 1, we still had five
+
+pounds available, and we still
+had a weight 0 available.
+
+Now I, said the next item to
+consider is item 1, but really
+
+what I meant is, 1 and all of
+the items proceeding it in the
+
+list. This is my shorthand for
+saying the list up to and
+
+including items sub 1,
+kind of a normal way
+
+to think about it.
+
+And then we finish building
+the tree, left first step
+
+first, looking at all the no
+branches, 0,5,0 and then we
+
+were done, that was
+one branch.
+
+We then backed up, and said
+let's look at a yes, we'll
+
+include item number 1.
+
+Well, what happens here, if
+we've included that, it uses
+
+up all the available weight,
+and gave us the value of 9.
+
+STUDENT: [UNINTELLIGIBLE]
+
+PROFESSOR: Pardon?
+
+STUDENT: -- want to be off
+the bottom branch.
+
+PROFESSOR: Yup, Off by 1.
+
+Yeah, I wanted to come off
+this branch, because I've
+
+backtrack just 1, thank you.
+
+And then I backtrack up
+to this branch, and
+
+from here we got 0,2,7.
+
+And I'm not going to draw the
+rest of the tree for you here,
+
+because I drew it last time, and
+you don't need to see the
+
+whole tree.
+
+The point I wanted to make is
+that for every node, except
+
+the leaves, the leaves are the
+bottom of a tree in this case,
+
+computer scientists are weird,
+right, they draw trees where
+
+the root is at the top, and the
+leaves are at the bottom.
+
+And I don't know why, but since
+time immemorial that is
+
+the way computer scientists
+have drawn trees.
+
+That's why we're not biologists,
+I guess.
+
+We don't understand
+these things.
+
+But what I want you to notice is
+that for each node, except
+
+the leaves, the solution for
+that node can be computed from
+
+the solutions from
+it's children.
+
+So in order to look at the
+solution of this node, I
+
+choose one of the solutions of
+it's children, a or b, is the
+
+best solution if I'm here, and
+of course this is the better
+
+of the 2 solutions.
+
+If I look at this node, I get to
+choose its solution as the
+
+better of the solution for
+this node, and this node.
+
+All the way up to the top, where
+when I have to choose
+
+the best solution to the whole
+problem, it's either the best
+
+solution to the left node,
+or the best solution
+
+to the right node.
+
+This happens to be a binary
+decision tree.
+
+There's nothing magic about
+there being only two nodes,
+
+for the knapsack problem, that's
+just the way it works
+
+out, but there are other
+problems where there might be
+
+multiple decisions to make, more
+than a or yes or no, but
+
+it's always the case here that
+I have what we last time
+
+talked about as what?
+
+Optimal sub structure.
+
+As I defined it last time, it
+means that I can solve a
+
+problem by finding the optimal
+solution to smaller sub
+
+problems. Classic divide and
+conquer that we've seen over
+
+and over again in the term.
+
+Take a hard problem, say well,
+I can solve it by solving 2
+
+smaller problems and combine
+their solution, and this case,
+
+the combining is choosing
+the best, it's a or b.
+
+So then, I went directly from
+that way of thinking about the
+
+problem, to this
+straightforward, at the top of
+
+the slide here, also at the
+top of your handout, both
+
+yesterday and today, a
+straightforward implementation
+
+of max val, that basically
+just did this.
+
+And as you might have guessed,
+when you're doing this sort of
+
+thing, recursion is a very
+natural way to implement it.
+
+We then ran this, demonstrated
+that it got the right answer
+
+on problems that were small
+enough that we knew with the
+
+right answer was, ran it on a
+big problem, got what we hoped
+
+was the right answer, but we had
+no good way to check it in
+
+our heads, but noticed it
+took a long time to run.
+
+And then we asked ourselves,
+why did it
+
+take so long to run?
+
+And when we turned on the print
+statement, what we saw
+
+is because it was doing
+the same thing
+
+over and over again.
+
+Because we had a lot of the
+sub-problems were the same.
+
+It was as if, when we went
+through this search tree, we
+
+never remembered what we got
+at the bottom, and we just
+
+re-computed things
+over and over.
+
+So that led us to look at
+memoization, the sort of key
+
+idea behind dynamic programming,
+which says let's
+
+remember the work we've done and
+not do it all over again.
+
+We used a dictionary to
+implement the memo, and that
+
+got us to the fast max val,
+which got called from max val
+
+0, because I wanted to make
+sure I didn't change the
+
+specification of max val by
+introducing this memo that
+
+users shouldn't know even
+exists, because it's part of
+
+the implementation, not part
+of the problem statement.
+
+We did that, and all I did was
+take the original code and
+
+keep track of what I've done,
+and say have I computed this
+
+value before, if so, don't
+compute it again.
+
+And that's the key idea that
+you'll see over and over again
+
+as you solve problems with
+dynamic programming, is you
+
+say, have I already solved this
+problem, if so, let me
+
+look up the answer.
+
+If I haven't solved the problem,
+let me solve it, and
+
+store the answer away
+for later reference.
+
+Very simple idea, and typically
+the beauty of
+
+dynamic programming as you've
+seen here, is not only is the
+
+idea simple, even the
+implementation is simple.
+
+There are a lot of complicated
+algorithmic ideas, dynamic
+
+programming is not
+one of them.
+
+Which is one of the reasons
+we teach it here.
+
+The other reason we teach it
+here, in addition to it being
+
+simple, is that it's
+incredibly useful.
+
+It's probably among the most
+useful ideas there is for
+
+solving complicated problems.
+
+All right, now let's
+look at it.
+
+So here's the fast version, we
+looked at it last time, I'm
+
+not going to bore you by going
+through the details of it
+
+again, but we'll run it.
+
+This was the big example we
+looked at last time, where we
+
+had 30 items we could put in to
+choose from, so when we do
+
+it exponentially, it looks like
+it's 2 to the 30, which
+
+is a big number, but when we ran
+this, it found the answer,
+
+and it took only 1805 calls.
+
+Now I got really excited about
+this because, to me it's
+
+really amazing, that we've
+taken a problem that is
+
+apparently exponential, and
+solved it like that.
+
+And in fact, I could double
+the size of the items to
+
+choose from, and it would
+still run like.
+
+Eh - I'm not very good at
+snapping my fingers -- it
+
+would still run quickly.
+
+All right, so here's the
+question: have I found a way
+
+to solve an inherently
+exponential
+
+problem in linear time.
+
+Because what we'll see here,
+and we saw a little of this
+
+last time, as I double the
+size of the items, I only
+
+really roughly double
+the running time.
+
+Quite amazing.
+
+So have I done that?
+
+Well, I wish I had, because then
+I would be really famous,
+
+and my department head would
+give me a big raise, and all
+
+sorts of wonderful things
+would follow.
+
+But, I'm not famous, and I
+didn't solve that problem.
+
+What's going on?
+
+Well this particular algorithm
+takes roughly, and I'll come
+
+back to the roughly question,
+order (n,s) time, where n is
+
+the number of items in the list
+and s, roughly speaking,
+
+is the size of the knapsack.
+
+We should also observe, that
+it takes order and s space.
+
+Because it's not free to
+store all these values.
+
+So at one level what I'm doing
+is trading time for space.
+
+It can run faster because
+I'm using some
+
+space to save things.
+
+So in this case, we had 30 items
+and the wait was 40,
+
+and, you know, this gives
+us 1200 which is
+
+kind of where we were.
+
+And I'm really emphasizing kind
+of here, because really
+
+what I'm using the available
+size for, is as a proxy for
+
+the number of items that can
+fit in the knapsack.
+
+Because the actual running time
+of this, and the actual
+
+space of this algorithm, is
+governed, interestingly
+
+enough, not by the size of the
+problem alone, but by the size
+
+of the solution.
+
+And I'm going to come
+back to that.
+
+So how long it takes to run is
+related to how many items I
+
+end up being able to fit
+into the knapsack.
+
+If you think about it,
+this make sense.
+
+An entry is made in the memo
+whenever an item, and an
+
+available size pair
+is considered.
+
+As soon as the available size
+goes to 0, I know I can't
+
+enter any more items into
+the memo, right?
+
+So the number of items I have to
+remember is related to how
+
+many items I can fit
+in the knapsack.
+
+And of course, the amount of
+running time is exactly the
+
+number of things I
+have to remember,
+
+almost exactly, right?
+
+So you can see if you think
+about it abstractly, why the
+
+amount of work I have to do here
+will be proportional to
+
+the number of items I can fit
+in, that is to say, the size
+
+of the solution.
+
+This is not the way we'd like
+to talk about complexity.
+
+When we talk about the order,
+or big O, as we keep writing
+
+it, of a problem, we always
+prefer to talk about it in
+
+terms of the size
+of the problem.
+
+And that makes sense because in
+general we don't know the
+
+size of the solution until
+we've solved it.
+
+So we'd much rather define big
+O in terms of the inputs.
+
+What we have here is
+what's called a
+
+pseudo-polynomial algorithm.
+
+You remember a polynomial
+algorithm is an algorithm
+
+that's polynomial in the
+size of the inputs.
+
+Here we have an algorithm that's
+polynomial in the size
+
+of the solution, hence
+the qualifier pseudo.
+
+More formally, and again this is
+not crucial to get all the
+
+details on this, if we think
+about a numerical algorithm, a
+
+pseudo-polynomial algorithm
+has running time that's
+
+polynomial in the numeric
+value of the input.
+
+I'm using a numeric example
+because it's easier to talk
+
+about it that way.
+
+So you might to look at, say,
+an implementation of
+
+factorial, and say its running
+time is proportional to the
+
+numerical value of the number
+who's factorial.
+
+If I'm computing factorial of 8,
+I'll do 8 operations, Right
+
+Factorial of 10, I'll
+do 10 operations.
+
+Now the key issue to think about
+here, is that as we look
+
+at this kind of thing, what
+we'll see is that, if we look
+
+at a numeric value, we know that
+that's exponential number
+
+in the number of digits.
+
+So that's the key thing to think
+about, Right That you
+
+can take a problem, and
+typically, when we're actually
+
+formally looking at
+computational complexity, big
+
+O, what we'll define the in
+terms of, is the size of the
+
+coding of the input.
+
+The number of bits required
+to represent the
+
+input in the computer.
+
+And so when we say something is
+exponential, we're talking
+
+about in terms of the number
+of bits required
+
+to represent it.
+
+Now why am I going through all
+this, maybe I should use the
+
+word pseudo-theory?
+
+Only because I want you to
+understand that when we start
+
+talking about complexity, it
+can be really quite subtle.
+
+And you have to be very careful
+to think about what
+
+you mean, or you can be very
+surprised at how long
+
+something takes to run, or
+how much space it uses.
+
+And you have to understand the
+difference between, are you
+
+defining the performance in
+terms of the size of the
+
+problem, or the size
+of the solution.
+
+When you talk about the size
+of the problem, what do you
+
+mean by that, is it the length
+of an array, is it the size of
+
+the elements of the array,
+and it can matter.
+
+So when we ask you to tell
+us something about the
+
+efficiency, on for example a
+quiz, we want you to be very
+
+careful not to just write
+something like, order n
+
+squared, but to tell
+us what n is.
+
+For example, the number of
+elements in the list. But if
+
+you have a list of lists, maybe
+it's not just the number
+
+elements in the list, maybe
+it depends upon what
+
+the elements are.
+
+So just sort of a warning to try
+and be very careful as you
+
+think about these things,
+all right.
+
+So I haven't done magic, I've
+given you a really fast way to
+
+solve a knapsack problem, but
+it's still exponential deep
+
+down in its heart,
+in something.
+
+All right, in recitation you'll
+get a chance to look at
+
+yet another kind of problem that
+can be solved by dynamic
+
+programming, there
+are many of them.
+
+Before we leave the knapsack
+problem though, I want to take
+
+a couple of minutes to
+look at a slight
+
+variation of the problem.
+
+So let's look at this one.
+
+Suppose I told you that not only
+was there a limit on the
+
+total weight of the items
+in the knapsack,
+
+but also on the volume.
+
+OK, if I gave you a box of
+balloons, the fact that they
+
+didn't weight anything wouldn't
+mean you couldn't
+
+put, you could put lots of them
+in the knapsack, right?
+
+Sometimes it's the volume not
+the weight that matters,
+
+sometimes it's both.
+
+So how would we go about solving
+this problem if I told
+
+you not only was there a maximum
+weight, but there was
+
+a maximum volume.
+
+Well, we want to go back and
+attack it exactly the way we
+
+attacked it the first time,
+which was write some
+
+mathematical formulas.
+
+So you'll remember that when we
+looked at it, we said that
+
+the problem was to maximize the
+sum from i equals 1 to n,
+
+of p sub i, x sub i, maybe it
+should be 0 to n minus 1, but
+
+we won't worry about that.
+
+And we had to do it subject to
+the constraint that the sum
+
+from 1 to n of the weight sub i
+times x sub i, remember x is
+
+0 if it was in, 1 if it wasn't,
+was less than or equal
+
+to the cost, as I wrote it
+this time, which was the
+
+maximum allowable weight.
+
+What do we do if we want to
+add volume, is an issue?
+
+Does this change?
+
+Does the goal change?
+
+You're answering.
+
+Answer out -- no one else can
+see you shake your head.
+
+STUDENT: No.
+
+PROFESSOR: No.
+
+The goal does not change, it's
+still the same goal.
+
+What changes?
+
+STUDENT: The constraints.
+
+PROFESSOR: Yeah, and you
+don't get another bar.
+
+The constraint has to change.
+
+I've added a constraint.
+
+And, what's the constraint
+I've added?
+
+Somebody else -- yeah?
+
+STUDENT: You can't exceed
+the volume that the
+
+knapsack can hold.
+
+PROFESSOR: Right, but can
+you state in this
+
+kind of formal way?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: -- sum from
+i equals 1 to n --
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Let's say v sub i, x
+sub i, is less than or equal
+
+to, we'll write k for the
+total allowable volume.
+
+Exactly.
+
+So the thing to notice here,
+is it's actually quite a
+
+simple little change
+we've made.
+
+I've simply added this one extra
+constraint, nice thing
+
+about thinking about it this
+way is it's easy to think
+
+about it, and what do you think
+I'll have to do if I
+
+want to go change the code?
+
+I'm not going to do it for you,
+but what would I think
+
+about doing when I
+change the code?
+
+Well, let's look at the simple
+version first, because it's
+
+easier to look at.
+
+At the top.
+
+Well basically, all I'd have to
+do is go through and find
+
+every place I checked the
+constraint, and change it.
+
+To incorporate the
+new constraint.
+
+And when I went to the dynamic
+programming problem, what
+
+would I have to do,
+what would change?
+
+The memo would have to change,
+as well as the checks, right?
+
+Because now, I not only would
+have to think about how much
+
+weight did I have available, but
+I have to think about how
+
+much volume did I
+have available.
+
+So whereas before, I had a
+mapping from the item and the
+
+weight available, now I would
+have to have it from a tuple
+
+of the weight and the volume.
+
+Very small changes.
+
+That's one of the things I want
+you to sort of understand
+
+as we look at algorithms, that
+they're very general, and once
+
+you've figured out how to solve
+one problem, you can
+
+often solve another problem
+by a very straightforward
+
+reduction of this
+kind of thing.
+
+All right, any questions
+about that.
+
+Yeah?
+
+STUDENT: I had a question about
+what you were talking
+
+about just before.
+
+PROFESSOR: The
+pseudo-polynomial?
+
+STUDENT: Yes.
+
+PROFESSOR: Ok.
+
+STUDENT: So, how do you come
+to a conclusion as to which
+
+you should use then, if you can
+determine the size based
+
+on solution, or based on input,
+so how do you decide?
+
+PROFESSOR: Great question.
+
+So the question is, how do you
+choose an algorithm, why would
+
+I choose to use a
+pseudo-polynomial algorithm
+
+when I don't know how big the
+solution is likely to be, I
+
+think that's one way
+to think about it.
+
+Well, so if we think about the
+knapsack problem, we can look
+
+at it, and we can ask ourselves,
+well first of all
+
+we know that the brute force
+exponential solution is going
+
+to be a loser if the number
+of items is large.
+
+Fundamentally in this case, what
+I could look at is the
+
+ratio of the number of items to
+the size of the knapsack,
+
+say well, I've got lots items
+to choose from, I probably
+
+won't put them all in.
+
+But even if I did, it
+would still only
+
+be 30 of them, right?
+
+It's hard.
+
+Typically what we'll discover
+is the pseudo-polynomial
+
+algorithms are usually better,
+and in this case, never worse.
+
+So this will never be worse than
+the brute force one. if I
+
+get really unlucky, I end up
+checking the same number of
+
+things, but I'd have to be
+really, it'd have to be a very
+
+strange structure
+to the problem.
+
+So it's almost always the case
+that, if you can find a
+
+solution that uses dynamic
+programming, it will be better
+
+than the brute force, and
+certainly not, well, maybe use
+
+more space, but not
+use more time.
+
+But there is no magic, here, and
+so the question you asked
+
+is a very good question.
+
+And it's sometimes the case in
+real life that you don't know
+
+which is the better algorithm
+on the data you're actually
+
+going to be crunching.
+
+And you pays your money and you
+takes your chances, right?
+
+And if the data is not what you
+think it's going to be,
+
+you may be wrong in your choice,
+so you typically do
+
+have to spend some time thinking
+about it, what's the
+
+data going to actually
+look like.
+
+Very good question.
+
+Anything else?
+
+All right, a couple of closing
+points before we leave this,
+
+things I would like
+you to remember.
+
+In dynamic programming, one of
+the things that's going on is
+
+we're trading time for space.
+
+Dynamic programming is not
+the only time we do that.
+
+We've solved a lot of problems
+that way, in fact, by trading
+
+time for space.
+
+Table look-up, for example,
+right, that if you're going to
+
+have trig tables, you may want
+to compute them all at once
+
+and then just look it up.
+
+So that's one thing.
+
+Two, don't be intimidated by
+exponential problems. There's
+
+a tendency for people to say, oh
+this problem's exponential,
+
+I can't solve it.
+
+Well, I solve 2 or 3 exponential
+problems before
+
+breakfast every day.
+
+You know things like, how to
+find my way to the bathroom is
+
+inherently exponential, but I
+manage to solve it anyway.
+
+Don't be intimidated.
+
+Even though it is apparently
+exponential, a lot of times
+
+you can actually solve
+it much, much faster.
+
+Other issues.
+
+Three: dynamic programming
+is broadly useful.
+
+Whenever you're looking at a
+problem that seems to have a
+
+natural recursive solution,
+think about whether you can
+
+attack it with dynamic
+programming.
+
+If you've got this optimal
+substructure, and overlapping
+
+sub-problems, you can use
+dynamic programming.
+
+So it's good for knapsacks, it's
+good for shortest paths,
+
+it's good for change-making,
+it's good for a whole variety
+
+of problems. And so keep it in
+your toolbox, and when you
+
+have a hard problem to solve,
+one of the first questions you
+
+should ask yourself is, can
+I use dynamic programming?
+
+It's great for string-matching
+problems of a whole variety.
+
+It's hugely useful.
+
+And finally, I want you to keep
+in mind the whole concept
+
+of problem reduction.
+
+I started with this silly
+description of a burglar, and
+
+said : Well this is really the
+knapsack problem, and now I
+
+can go Google the knapsack
+problem and find
+
+code to solve it.
+
+Any time you can reduce
+something to a previously
+
+solved problem, that's good.
+
+And this is a hugely important
+lesson to learn.
+
+People tend not to realize that
+the first question you
+
+should always ask yourself, is
+this really just something
+
+that's well-known in disguise?
+
+Is it a shortest path problem?
+
+Is it a nearest neighbor
+problem?
+
+Is it what string is this
+most similar to problem?
+
+There are scores of
+well-understood problems, but
+
+only really scores, it's not
+thousands of them, and over
+
+time you'll build up a
+vocabulary of these problems,
+
+and when you see something in
+your domain, be it physics or
+
+biology or anything else,
+linguistics, the question you
+
+should ask is can I transform
+this into an existing problem?
+
+Ok, double line.
+
+If there are no questions I'm
+going to make a dramatic
+
+change in topic.
+
+We're going to temporarily get
+off of this more esoteric
+
+stuff, and go back to Python.
+
+And for the next, off and on for
+the next couple of weeks,
+
+we'll be talking about Python
+and program organization.
+
+And what I want to be talking
+about is modules of one sort,
+
+and of course that's because
+what we're interested in is
+
+modularity.
+
+How do we take a complex
+program, again, divide and
+
+conquer, I feel like a 1-trick
+pony, I keep repeating the
+
+same thing over and
+over again.
+
+Divide and conquer to make our
+programs modular so we can
+
+write them a little piece at a
+time and understand them a
+
+little piece at a time.
+
+Now I think of a module as a
+
+collection of related functions.
+
+We've already seen these, and
+we're going to refer to the
+
+functions using dot notation.
+
+We've been doing this all
+term, right, probably
+
+somewhere around lecture 2, we
+said import math, and then
+
+somewhere in our program we
+wrote something like math dot
+
+sqrt of 11, or some
+other number.
+
+And the good news was we didn't
+have to worry about how
+
+math did square root or anything
+like that, we just
+
+got it and we used it.
+
+Now we have the dot notation
+to avoid name conflicts.
+
+Imagine, for example, that in
+my program I wrote something
+
+like import set, because
+somebody had written a module
+
+that implements mathematical
+sets, and somewhere else I'd
+
+written something like import
+table, because someone had
+
+something that implemented
+look-up tables of some sort,
+
+something like dictionaries,
+for example.
+
+And then, I wanted to ask
+something like membership.
+
+Is something in the set, or
+is something in the table?
+
+Well, what I would have written
+is something like
+
+table dot member.
+
+And then the element and
+maybe the table.
+
+And the dot notation was used
+to disambiguate, because I
+
+want the member operation
+from table, not the
+
+member one from set.
+
+This was important because the
+people who implemented table
+
+and set might never have met
+each other, and so they can
+
+hardly have been expected not
+to have used the same name
+
+somewhere by accident.
+
+Hence the use of the
+dot notation.
+
+I now want to talk about a
+particular kind of module, and
+
+those are the modules
+that include
+
+classes or that are classes.
+
+This is a very important concept
+as we'll see, it's why
+
+MIT calls things like 6.00
+subjects, so that they don't
+
+get confused with classes in
+Python, something we really
+
+need to remember here.
+
+Now they can be used in
+different ways, and they have
+
+been historically used
+in different ways.
+
+In this subject we're going to
+emphasize using classes in the
+
+context of what's called
+object-oriented programming.
+
+And if you go look up at Python
+books on the web, or
+
+Java books on the web, about 80%
+of them will include the
+
+word object-oriented
+in their title.
+
+Object-oriented Python
+programming for computer
+
+games, or who knows what else.
+
+And we're going to use this
+object-oriented programming,
+
+typically to create something
+called data abstractions.
+
+And over the next couple of
+days, you'll see what we mean
+
+by this in detail.
+
+A synonym for this is an
+abstract data type.
+
+You'll see both terms used on
+the web, and the literature
+
+etc., and think of them as
+synonyms. Now these ideas of
+
+classes, object-oriented
+programming, data abstraction,
+
+are about 40 years old,
+they're not new ideas.
+
+But they've only been really
+widely accepted in practice
+
+for 10 to 15 years.
+
+It was in the mid-70's, people
+began to write articles
+
+advocating this style of
+programming, and actually
+
+building programming languages,
+notably Smalltalk
+
+and Clue at MIT in fact, that
+provided linguistic support
+
+for the ideas of data
+abstraction and
+
+object-oriented programming.
+
+But it really wasn't until, I
+would say, the arrival of Java
+
+that object-oriented
+programming
+
+caught the popular attention.
+
+And then Java, C++ ,
+Python of, course.
+
+And today nobody advocates a
+programming language that does
+
+not support it in some
+sort of way.
+
+So what is this all about?
+
+What is an object in
+object-oriented programming?
+
+An object is a collection
+of data and functions.
+
+In particular functions that
+operate on the data, perhaps
+
+on other data as well.
+
+The key idea here is to bind
+together the data and the
+
+functions that operate on that
+data as a single thing.
+
+Now typically that's probably
+not the way you've been
+
+thinking about things.
+
+When you think about an int or
+a float or a dictionary or a
+
+list, you knew that there
+were functions
+
+that operated on them.
+
+But when you pass a parameter
+say, a list, you didn't think
+
+that you were not only passing
+the list, you were also
+
+passing the functions
+that operate on the
+
+list. In fact you are.
+
+It often doesn't matter, but
+it sometimes really does.
+
+The advantage of that, is that
+when you pass an object to
+
+another part of the program,
+that part of the program also
+
+gets the ability to perform
+operations on the object.
+
+Now when the only types we're
+dealing with are the built-in
+
+types, the ones that came with
+the programming language, that
+
+doesn't really matter.
+
+Because, well, the programming
+language means everybody has
+
+access to those operations.
+
+But the key idea here is that
+we're going to be generating
+
+user-defined types, we'll invent
+new types, and as we do
+
+that we can't assume that if
+as we pass objects of that
+
+type around, that the
+programming language is giving
+
+us the appropriate operations
+on that type.
+
+This combining of data and
+functions on that data is a
+
+very essence of object-oriented
+programming.
+
+That's really what defines it.
+
+And the word that's often used
+for that is encapsulation.
+
+Think of it as we got a capsule,
+like a pill or
+
+something, and in that capsule
+we've got data and a bunch of
+
+functions, which as we'll
+see are called methods.
+
+Don't worry, it doesn't matter
+that they're called methods,
+
+it's a historical artifact.
+
+All right, so what's
+an example of this?
+
+Well, we could create a circle
+object, that would store a
+
+representation of the circle
+and also provide methods to
+
+operate on it, for example, draw
+the circle on the screen,
+
+return the area of the circle,
+inscribe it in a square, who
+
+knows what you want
+to do with it.
+
+As we talk about this, as people
+talk about this, in the
+
+context of our object-oriented
+programming, they typically
+
+will talk about it in terms
+of message pass, a message
+
+passing metaphor.
+
+I want to mention it's just
+a metaphor, just a way of
+
+thinking about it, it's not
+anything very deep here.
+
+So, the way people will talk
+about this, is one object can
+
+pass a message to another
+object, and the receiving
+
+object responds by executing
+one of its
+
+methods on the object.
+
+So let's think about lists.
+
+So if l is a list, I can
+call something like s
+
+dot sort, l dot sort.
+
+You've seen this.
+
+This says, pass the object l
+the message sort, and that
+
+message says find the method
+sort, and apply it to the
+
+object l, in this case mutating
+the object so that
+
+the elements are now
+in sorted order.
+
+If c is a circle, I might write
+
+something like c dot area.
+
+And this would say, pass to
+the object denoted by the
+
+variable c, the message area,
+which says execute a method
+
+called area, and in this case
+the method might return a
+
+float, rather than have
+a side-effect.
+
+Now again, don't get carried
+away, I almost didn't talk
+
+about this whole message-passing
+paradigm, but
+
+it's so pervasive in the
+world I felt you needed
+
+to hear about it.
+
+But it's nothing very deep, and
+if you want to not think
+
+about messages, and just think
+oh, c has a method area, a
+
+circle has a method area, and
+c as a circle will apply it
+
+and do what it says, you won't
+get in any trouble at all.
+
+Now the next concept to think
+about here, is the notion of
+
+an instance.
+
+So we've already thought about,
+we create instances of
+
+types, so when we looked at
+lists, and we looked at the
+
+notion of aliasing, we used the
+word instance, and said
+
+this is 1 object, this is
+another object, each of those
+
+objects is an instance of
+type list. So now that
+
+gets us to a class.
+
+A class is a collection
+of objects with
+
+characteristics in common.
+
+So you can think of class
+list. What is the
+
+characteristic that all objects
+of class list have in
+
+common, all instances of class
+list? it's the set of methods
+
+that can be applied to lists.
+
+Methods like sort, append,
+other things.
+
+So you should think of all of
+the built-in types we've
+
+talked about as actually just
+built-in classes, like
+
+dictionaries, lists, etc.
+
+The beauty of being able to
+define your own class is you
+
+can now extend the language.
+
+So if, for example, you're in
+the business, God forbid, of
+
+writing financial software
+today, you might decide, I'd
+
+really like to have a class
+called tanking stock, or bad
+
+mortgage, or something like
+that or mortgage, right?
+
+Which would have a bunch of
+operations, like, I won't go
+
+into what they might be.
+
+But you'd like to write your
+program not in terms of floats
+
+and ints and lists, but in terms
+of mortgages, and CDOs,
+
+and all of the objects that you
+read about in the paper,
+
+the types you read about.
+
+And so you get to build your
+own special purpose
+
+programming language that helped
+you solve your problems
+
+in biology or finance or
+whatever, and we'll pick up
+
+here again on Tuesday.
\ No newline at end of file
diff --git a/lm8ywGl9AIQ.txt b/lm8ywGl9AIQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a387f3090f7a620a1e680c1985ac5de376a15d5
--- /dev/null
+++ b/lm8ywGl9AIQ.txt
@@ -0,0 +1,7475 @@
+align:start position:0%
+ 
+I'm a professor in the biology
+
+ align:start position:0%
+I'm a professor in the biology
+ 
+
+ align:start position:0%
+I'm a professor in the biology
+department at MIT and I will be
+
+ align:start position:0%
+department at MIT and I will be
+ 
+
+ align:start position:0%
+department at MIT and I will be
+co-teaching this course with uh Penny
+
+ align:start position:0%
+co-teaching this course with uh Penny
+ 
+
+ align:start position:0%
+co-teaching this course with uh Penny
+Chisum who's a professor in the
+
+ align:start position:0%
+Chisum who's a professor in the
+ 
+
+ align:start position:0%
+Chisum who's a professor in the
+Department of Civil and environmental
+
+ align:start position:0%
+Department of Civil and environmental
+ 
+
+ align:start position:0%
+Department of Civil and environmental
+engineering as well as a a professor in
+
+ align:start position:0%
+engineering as well as a a professor in
+ 
+
+ align:start position:0%
+engineering as well as a a professor in
+biology Department as well uh Penny was
+
+ align:start position:0%
+biology Department as well uh Penny was
+ 
+
+ align:start position:0%
+biology Department as well uh Penny was
+recently featured in the uh journal
+
+ align:start position:0%
+recently featured in the uh journal
+ 
+
+ align:start position:0%
+recently featured in the uh journal
+Nature uh she's a very well-known um
+
+ align:start position:0%
+Nature uh she's a very well-known um
+ 
+
+ align:start position:0%
+Nature uh she's a very well-known um
+ocean oceanographer who's become
+
+ align:start position:0%
+ocean oceanographer who's become
+ 
+
+ align:start position:0%
+ocean oceanographer who's become
+deservedly famous for discovering a very
+
+ align:start position:0%
+deservedly famous for discovering a very
+ 
+
+ align:start position:0%
+deservedly famous for discovering a very
+small bacterium that's capable of
+
+ align:start position:0%
+small bacterium that's capable of
+ 
+
+ align:start position:0%
+small bacterium that's capable of
+carrying out photosynthesis uh for many
+
+ align:start position:0%
+carrying out photosynthesis uh for many
+ 
+
+ align:start position:0%
+carrying out photosynthesis uh for many
+years oceanographers used filters the
+
+ align:start position:0%
+years oceanographers used filters the
+ 
+
+ align:start position:0%
+years oceanographers used filters the
+holes were big enough that this
+
+ align:start position:0%
+holes were big enough that this
+ 
+
+ align:start position:0%
+holes were big enough that this
+bacterium went through and so when they
+
+ align:start position:0%
+bacterium went through and so when they
+ 
+
+ align:start position:0%
+bacterium went through and so when they
+were doing their studies of the ocean
+
+ align:start position:0%
+were doing their studies of the ocean
+ 
+
+ align:start position:0%
+were doing their studies of the ocean
+and how the the biomass that was there
+
+ align:start position:0%
+and how the the biomass that was there
+ 
+
+ align:start position:0%
+and how the the biomass that was there
+and all the fluxes and so on they didn't
+
+ align:start position:0%
+and all the fluxes and so on they didn't
+ 
+
+ align:start position:0%
+and all the fluxes and so on they didn't
+know this organism existed which can
+
+ align:start position:0%
+know this organism existed which can
+ 
+
+ align:start position:0%
+know this organism existed which can
+form up to 50% of the biomass in in
+
+ align:start position:0%
+form up to 50% of the biomass in in
+ 
+
+ align:start position:0%
+form up to 50% of the biomass in in
+parts of the ocean so um Penny's really
+
+ align:start position:0%
+parts of the ocean so um Penny's really
+ 
+
+ align:start position:0%
+parts of the ocean so um Penny's really
+a wonderful lecture a wonderful person
+
+ align:start position:0%
+a wonderful lecture a wonderful person
+ 
+
+ align:start position:0%
+a wonderful lecture a wonderful person
+and she'll be talking teaching the
+
+ align:start position:0%
+and she'll be talking teaching the
+ 
+
+ align:start position:0%
+and she'll be talking teaching the
+component of
+
+ align:start position:0%
+component of
+ 
+
+ align:start position:0%
+component of
+7014 which deals with ecology in the
+
+ align:start position:0%
+7014 which deals with ecology in the
+ 
+
+ align:start position:0%
+7014 which deals with ecology in the
+environment and this is a a section of
+
+ align:start position:0%
+environment and this is a a section of
+ 
+
+ align:start position:0%
+environment and this is a a section of
+7014 that uh is makes it different from
+
+ align:start position:0%
+7014 that uh is makes it different from
+ 
+
+ align:start position:0%
+7014 that uh is makes it different from
+the other two versions 712 and
+
+ align:start position:0%
+the other two versions 712 and
+ 
+
+ align:start position:0%
+the other two versions 712 and
+7013 so for me uh personally this is uh
+
+ align:start position:0%
+7013 so for me uh personally this is uh
+ 
+
+ align:start position:0%
+7013 so for me uh personally this is uh
+an absolutely wonderful uh exciting
+
+ align:start position:0%
+an absolutely wonderful uh exciting
+ 
+
+ align:start position:0%
+an absolutely wonderful uh exciting
+opportunity to be able to teach this
+
+ align:start position:0%
+opportunity to be able to teach this
+ 
+
+ align:start position:0%
+opportunity to be able to teach this
+introductory biology course
+
+ align:start position:0%
+introductory biology course
+ 
+
+ align:start position:0%
+introductory biology course
+uh for some of you I know that biology
+
+ align:start position:0%
+uh for some of you I know that biology
+ 
+
+ align:start position:0%
+uh for some of you I know that biology
+is going to either be a major part of
+
+ align:start position:0%
+is going to either be a major part of
+ 
+
+ align:start position:0%
+is going to either be a major part of
+your career or quite possibly even if
+
+ align:start position:0%
+your career or quite possibly even if
+ 
+
+ align:start position:0%
+your career or quite possibly even if
+you're in engineering or something else
+
+ align:start position:0%
+you're in engineering or something else
+ 
+
+ align:start position:0%
+you're in engineering or something else
+you will find yourselves working with a
+
+ align:start position:0%
+you will find yourselves working with a
+ 
+
+ align:start position:0%
+you will find yourselves working with a
+biological system you can see that
+
+ align:start position:0%
+biological system you can see that
+ 
+
+ align:start position:0%
+biological system you can see that
+happening all over campus these days
+
+ align:start position:0%
+happening all over campus these days
+ 
+
+ align:start position:0%
+happening all over campus these days
+that more and more engineering
+
+ align:start position:0%
+that more and more engineering
+ 
+
+ align:start position:0%
+that more and more engineering
+departments are finding that they're
+
+ align:start position:0%
+departments are finding that they're
+ 
+
+ align:start position:0%
+departments are finding that they're
+working on problems that come from
+
+ align:start position:0%
+working on problems that come from
+ 
+
+ align:start position:0%
+working on problems that come from
+biology or have a biological
+
+ align:start position:0%
+biology or have a biological
+ 
+
+ align:start position:0%
+biology or have a biological
+component um there I'm sure there are at
+
+ align:start position:0%
+component um there I'm sure there are at
+ 
+
+ align:start position:0%
+component um there I'm sure there are at
+least a few of you here who are only
+
+ align:start position:0%
+least a few of you here who are only
+ 
+
+ align:start position:0%
+least a few of you here who are only
+here because it's a a uh required course
+
+ align:start position:0%
+here because it's a a uh required course
+ 
+
+ align:start position:0%
+here because it's a a uh required course
+and you might well wish you were were
+
+ align:start position:0%
+and you might well wish you were were
+ 
+
+ align:start position:0%
+and you might well wish you were were
+somewhere else however I will do my best
+
+ align:start position:0%
+somewhere else however I will do my best
+ 
+
+ align:start position:0%
+somewhere else however I will do my best
+to try to communicate to you why you
+
+ align:start position:0%
+to try to communicate to you why you
+ 
+
+ align:start position:0%
+to try to communicate to you why you
+need to know some biology too I think
+
+ align:start position:0%
+need to know some biology too I think
+ 
+
+ align:start position:0%
+need to know some biology too I think
+most of you know you can hardly pick up
+
+ align:start position:0%
+most of you know you can hardly pick up
+ 
+
+ align:start position:0%
+most of you know you can hardly pick up
+a newspaper uh these days without
+
+ align:start position:0%
+a newspaper uh these days without
+ 
+
+ align:start position:0%
+a newspaper uh these days without
+running into something uh that Demands a
+
+ align:start position:0%
+running into something uh that Demands a
+ 
+
+ align:start position:0%
+running into something uh that Demands a
+a knowledge of biology something about
+
+ align:start position:0%
+a knowledge of biology something about
+ 
+
+ align:start position:0%
+a knowledge of biology something about
+stem cells something about cloning
+
+ align:start position:0%
+stem cells something about cloning
+ 
+
+ align:start position:0%
+stem cells something about cloning
+humans something about a a new drug uh
+
+ align:start position:0%
+humans something about a a new drug uh
+ 
+
+ align:start position:0%
+humans something about a a new drug uh
+lots of things having to do with uh
+
+ align:start position:0%
+lots of things having to do with uh
+ 
+
+ align:start position:0%
+lots of things having to do with uh
+biological effects on the uh on the
+
+ align:start position:0%
+biological effects on the uh on the
+ 
+
+ align:start position:0%
+biological effects on the uh on the
+environment and so on uh you're also
+
+ align:start position:0%
+environment and so on uh you're also
+ 
+
+ align:start position:0%
+environment and so on uh you're also
+going to be confronted with uh decisions
+
+ align:start position:0%
+going to be confronted with uh decisions
+ 
+
+ align:start position:0%
+going to be confronted with uh decisions
+about your health about the health of
+
+ align:start position:0%
+about your health about the health of
+ 
+
+ align:start position:0%
+about your health about the health of
+your loved ones concerning cancer
+
+ align:start position:0%
+your loved ones concerning cancer
+ 
+
+ align:start position:0%
+your loved ones concerning cancer
+concerning uh whether child uh might
+
+ align:start position:0%
+concerning uh whether child uh might
+ 
+
+ align:start position:0%
+concerning uh whether child uh might
+have birth effects all sorts of issues
+
+ align:start position:0%
+have birth effects all sorts of issues
+ 
+
+ align:start position:0%
+have birth effects all sorts of issues
+that will affect your personal lives
+
+ align:start position:0%
+that will affect your personal lives
+ 
+
+ align:start position:0%
+that will affect your personal lives
+that demand an understanding of biology
+
+ align:start position:0%
+that demand an understanding of biology
+ 
+
+ align:start position:0%
+that demand an understanding of biology
+so I feel with some passion that whether
+
+ align:start position:0%
+so I feel with some passion that whether
+ 
+
+ align:start position:0%
+so I feel with some passion that whether
+you're you think you're going to need
+
+ align:start position:0%
+you're you think you're going to need
+ 
+
+ align:start position:0%
+you're you think you're going to need
+biology in your professional career or
+
+ align:start position:0%
+biology in your professional career or
+ 
+
+ align:start position:0%
+biology in your professional career or
+not everyone in this uh institution
+
+ align:start position:0%
+not everyone in this uh institution
+ 
+
+ align:start position:0%
+not everyone in this uh institution
+needs some understanding of biology uh
+
+ align:start position:0%
+needs some understanding of biology uh
+ 
+
+ align:start position:0%
+needs some understanding of biology uh
+to just live their ordinary lives I also
+
+ align:start position:0%
+to just live their ordinary lives I also
+ 
+
+ align:start position:0%
+to just live their ordinary lives I also
+think when as MIT students you're going
+
+ align:start position:0%
+think when as MIT students you're going
+ 
+
+ align:start position:0%
+think when as MIT students you're going
+to be looked at uh as you go through
+
+ align:start position:0%
+to be looked at uh as you go through
+ 
+
+ align:start position:0%
+to be looked at uh as you go through
+your lives as people who are
+
+ align:start position:0%
+your lives as people who are
+ 
+
+ align:start position:0%
+your lives as people who are
+knowledgeable about science and uh and
+
+ align:start position:0%
+knowledgeable about science and uh and
+ 
+
+ align:start position:0%
+knowledgeable about science and uh and
+engineering and you'll be asked
+
+ align:start position:0%
+engineering and you'll be asked
+ 
+
+ align:start position:0%
+engineering and you'll be asked
+questions go far beyond your immediate
+
+ align:start position:0%
+questions go far beyond your immediate
+ 
+
+ align:start position:0%
+questions go far beyond your immediate
+area of expertise and again I think it's
+
+ align:start position:0%
+area of expertise and again I think it's
+ 
+
+ align:start position:0%
+area of expertise and again I think it's
+another reason for needing to know uh
+
+ align:start position:0%
+another reason for needing to know uh
+ 
+
+ align:start position:0%
+another reason for needing to know uh
+some of biology anyway um it's an
+
+ align:start position:0%
+some of biology anyway um it's an
+ 
+
+ align:start position:0%
+some of biology anyway um it's an
+absolutely wonderful time to teach
+
+ align:start position:0%
+absolutely wonderful time to teach
+ 
+
+ align:start position:0%
+absolutely wonderful time to teach
+biology because it's things have just
+
+ align:start position:0%
+biology because it's things have just
+ 
+
+ align:start position:0%
+biology because it's things have just
+been exploding over the last two or
+
+ align:start position:0%
+been exploding over the last two or
+ 
+
+ align:start position:0%
+been exploding over the last two or
+three decades and things are moving
+
+ align:start position:0%
+three decades and things are moving
+ 
+
+ align:start position:0%
+three decades and things are moving
+faster than ever and another wonderful
+
+ align:start position:0%
+faster than ever and another wonderful
+ 
+
+ align:start position:0%
+faster than ever and another wonderful
+thing about teaching biology is that MIT
+
+ align:start position:0%
+thing about teaching biology is that MIT
+ 
+
+ align:start position:0%
+thing about teaching biology is that MIT
+is an absolutely marvelous place to
+
+ align:start position:0%
+is an absolutely marvelous place to
+ 
+
+ align:start position:0%
+is an absolutely marvelous place to
+teach it just to sort of drive this home
+
+ align:start position:0%
+teach it just to sort of drive this home
+ 
+
+ align:start position:0%
+teach it just to sort of drive this home
+in the biology Department alone there
+
+ align:start position:0%
+in the biology Department alone there
+ 
+
+ align:start position:0%
+in the biology Department alone there
+are four Nobel laurates who made got
+
+ align:start position:0%
+are four Nobel laurates who made got
+ 
+
+ align:start position:0%
+are four Nobel laurates who made got
+honored for critical discoveries in
+
+ align:start position:0%
+honored for critical discoveries in
+ 
+
+ align:start position:0%
+honored for critical discoveries in
+biology Goin kurana who's just down the
+
+ align:start position:0%
+biology Goin kurana who's just down the
+ 
+
+ align:start position:0%
+biology Goin kurana who's just down the
+hall from me uh synthesized the first
+
+ align:start position:0%
+hall from me uh synthesized the first
+ 
+
+ align:start position:0%
+hall from me uh synthesized the first
+Gene was a extraordinary feat of
+
+ align:start position:0%
+Gene was a extraordinary feat of
+ 
+
+ align:start position:0%
+Gene was a extraordinary feat of
+synthesis of of organic chemistry
+
+ align:start position:0%
+synthesis of of organic chemistry
+ 
+
+ align:start position:0%
+synthesis of of organic chemistry
+synthesizing DNA when I was an undergrad
+
+ align:start position:0%
+synthesizing DNA when I was an undergrad
+ 
+
+ align:start position:0%
+synthesizing DNA when I was an undergrad
+I I had was a chemistry major um but
+
+ align:start position:0%
+I I had was a chemistry major um but
+ 
+
+ align:start position:0%
+I I had was a chemistry major um but
+I had to take an introductory biology
+
+ align:start position:0%
+I had to take an introductory biology
+ 
+
+ align:start position:0%
+I had to take an introductory biology
+course and at that point the DNA wasn't
+
+ align:start position:0%
+course and at that point the DNA wasn't
+ 
+
+ align:start position:0%
+course and at that point the DNA wasn't
+mentioned in the high school um courses
+
+ align:start position:0%
+mentioned in the high school um courses
+ 
+
+ align:start position:0%
+mentioned in the high school um courses
+so the first time that I heard about DNA
+
+ align:start position:0%
+so the first time that I heard about DNA
+ 
+
+ align:start position:0%
+so the first time that I heard about DNA
+was in my introductory biology course
+
+ align:start position:0%
+was in my introductory biology course
+ 
+
+ align:start position:0%
+was in my introductory biology course
+and that uh determined my career
+
+ align:start position:0%
+and that uh determined my career
+ 
+
+ align:start position:0%
+and that uh determined my career
+Direction I thought that was such a an
+
+ align:start position:0%
+Direction I thought that was such a an
+ 
+
+ align:start position:0%
+Direction I thought that was such a an
+interesting molecule that I wanted to
+
+ align:start position:0%
+interesting molecule that I wanted to
+ 
+
+ align:start position:0%
+interesting molecule that I wanted to
+work on it and I tucked myself into one
+
+ align:start position:0%
+work on it and I tucked myself into one
+ 
+
+ align:start position:0%
+work on it and I tucked myself into one
+of the labs in Ottawa Canada where I
+
+ align:start position:0%
+of the labs in Ottawa Canada where I
+ 
+
+ align:start position:0%
+of the labs in Ottawa Canada where I
+grew up that was trying to synthesize
+
+ align:start position:0%
+grew up that was trying to synthesize
+ 
+
+ align:start position:0%
+grew up that was trying to synthesize
+DNA synthesize pieces of a gene and as I
+
+ align:start position:0%
+DNA synthesize pieces of a gene and as I
+ 
+
+ align:start position:0%
+DNA synthesize pieces of a gene and as I
+turned out later competing
+
+ align:start position:0%
+turned out later competing
+ 
+
+ align:start position:0%
+turned out later competing
+unsuccessfully with my now colleague
+
+ align:start position:0%
+unsuccessfully with my now colleague
+ 
+
+ align:start position:0%
+unsuccessfully with my now colleague
+Goen
+
+ align:start position:0%
+Goen
+ 
+
+ align:start position:0%
+Goen
+Karana uh suumo tagawa uh got a Nobel
+
+ align:start position:0%
+Karana uh suumo tagawa uh got a Nobel
+ 
+
+ align:start position:0%
+Karana uh suumo tagawa uh got a Nobel
+Prize for discovering the amazing
+
+ align:start position:0%
+Prize for discovering the amazing
+ 
+
+ align:start position:0%
+Prize for discovering the amazing
+molecular uh operations that underly the
+
+ align:start position:0%
+molecular uh operations that underly the
+ 
+
+ align:start position:0%
+molecular uh operations that underly the
+diversity of the immune system your
+
+ align:start position:0%
+diversity of the immune system your
+ 
+
+ align:start position:0%
+diversity of the immune system your
+immune system has a capacity to
+
+ align:start position:0%
+immune system has a capacity to
+ 
+
+ align:start position:0%
+immune system has a capacity to
+recognize um viruses and uh bacteria all
+
+ align:start position:0%
+recognize um viruses and uh bacteria all
+ 
+
+ align:start position:0%
+recognize um viruses and uh bacteria all
+sorts of different pathogens and
+
+ align:start position:0%
+sorts of different pathogens and
+ 
+
+ align:start position:0%
+sorts of different pathogens and
+including molecules it can recognize
+
+ align:start position:0%
+including molecules it can recognize
+ 
+
+ align:start position:0%
+including molecules it can recognize
+molecules that haven't even ever been
+
+ align:start position:0%
+molecules that haven't even ever been
+ 
+
+ align:start position:0%
+molecules that haven't even ever been
+synthesized in history
+
+ align:start position:0%
+synthesized in history
+ 
+
+ align:start position:0%
+synthesized in history
+of life and we'll talk towards the end
+
+ align:start position:0%
+of life and we'll talk towards the end
+ 
+
+ align:start position:0%
+of life and we'll talk towards the end
+of the course about the way that happens
+
+ align:start position:0%
+of the course about the way that happens
+ 
+
+ align:start position:0%
+of the course about the way that happens
+and you'll see why susumo got his Nobel
+
+ align:start position:0%
+and you'll see why susumo got his Nobel
+ 
+
+ align:start position:0%
+and you'll see why susumo got his Nobel
+Prize um Phil sharp got his for
+
+ align:start position:0%
+Prize um Phil sharp got his for
+ 
+
+ align:start position:0%
+Prize um Phil sharp got his for
+discovering RNA splicing a completely
+
+ align:start position:0%
+discovering RNA splicing a completely
+ 
+
+ align:start position:0%
+discovering RNA splicing a completely
+unanticipated component of the very
+
+ align:start position:0%
+unanticipated component of the very
+ 
+
+ align:start position:0%
+unanticipated component of the very
+heart of of uh molecular biology and
+
+ align:start position:0%
+heart of of uh molecular biology and
+ 
+
+ align:start position:0%
+heart of of uh molecular biology and
+then Bob horvitz who's a peer of mine we
+
+ align:start position:0%
+then Bob horvitz who's a peer of mine we
+ 
+
+ align:start position:0%
+then Bob horvitz who's a peer of mine we
+started at MIT at the same time and our
+
+ align:start position:0%
+started at MIT at the same time and our
+ 
+
+ align:start position:0%
+started at MIT at the same time and our
+our Labs were side by side for many
+
+ align:start position:0%
+our Labs were side by side for many
+ 
+
+ align:start position:0%
+our Labs were side by side for many
+years got his Nobel 200 for discovering
+
+ align:start position:0%
+years got his Nobel 200 for discovering
+ 
+
+ align:start position:0%
+years got his Nobel 200 for discovering
+a phenomena the general term is uh
+
+ align:start position:0%
+a phenomena the general term is uh
+ 
+
+ align:start position:0%
+a phenomena the general term is uh
+program cell death and it plays all
+
+ align:start position:0%
+program cell death and it plays all
+ 
+
+ align:start position:0%
+program cell death and it plays all
+sorts of important roles in biology from
+
+ align:start position:0%
+sorts of important roles in biology from
+ 
+
+ align:start position:0%
+sorts of important roles in biology from
+scul sculpting the shapes of organs and
+
+ align:start position:0%
+scul sculpting the shapes of organs and
+ 
+
+ align:start position:0%
+scul sculpting the shapes of organs and
+tissues we initially have webs when
+
+ align:start position:0%
+tissues we initially have webs when
+ 
+
+ align:start position:0%
+tissues we initially have webs when
+we're developing between our fingers and
+
+ align:start position:0%
+we're developing between our fingers and
+ 
+
+ align:start position:0%
+we're developing between our fingers and
+those go away because of a kind of
+
+ align:start position:0%
+those go away because of a kind of
+ 
+
+ align:start position:0%
+those go away because of a kind of
+programed cell death that the cells that
+
+ align:start position:0%
+programed cell death that the cells that
+ 
+
+ align:start position:0%
+programed cell death that the cells that
+were making the web disappear uh and
+
+ align:start position:0%
+were making the web disappear uh and
+ 
+
+ align:start position:0%
+were making the web disappear uh and
+another role of that is to prevent
+
+ align:start position:0%
+another role of that is to prevent
+ 
+
+ align:start position:0%
+another role of that is to prevent
+cancer that if cells sense that
+
+ align:start position:0%
+cancer that if cells sense that
+ 
+
+ align:start position:0%
+cancer that if cells sense that
+something is very messed up they have a
+
+ align:start position:0%
+something is very messed up they have a
+ 
+
+ align:start position:0%
+something is very messed up they have a
+sort of suicide program that would uh
+
+ align:start position:0%
+sort of suicide program that would uh
+ 
+
+ align:start position:0%
+sort of suicide program that would uh
+make them destroy themselves and if that
+
+ align:start position:0%
+make them destroy themselves and if that
+ 
+
+ align:start position:0%
+make them destroy themselves and if that
+doesn't happen those could go on and
+
+ align:start position:0%
+doesn't happen those could go on and
+ 
+
+ align:start position:0%
+doesn't happen those could go on and
+become more and more abnormal and
+
+ align:start position:0%
+become more and more abnormal and
+ 
+
+ align:start position:0%
+become more and more abnormal and
+eventually uh turn into uh an invasive
+
+ align:start position:0%
+eventually uh turn into uh an invasive
+ 
+
+ align:start position:0%
+eventually uh turn into uh an invasive
+cancer anyway uh there's a picture of
+
+ align:start position:0%
+cancer anyway uh there's a picture of
+ 
+
+ align:start position:0%
+cancer anyway uh there's a picture of
+Bob uh when we was The Institute was
+
+ align:start position:0%
+Bob uh when we was The Institute was
+ 
+
+ align:start position:0%
+Bob uh when we was The Institute was
+celebrating his um his Nobel Prize he
+
+ align:start position:0%
+celebrating his um his Nobel Prize he
+ 
+
+ align:start position:0%
+celebrating his um his Nobel Prize he
+getting a congratulatory kiss from artha
+
+ align:start position:0%
+getting a congratulatory kiss from artha
+ 
+
+ align:start position:0%
+getting a congratulatory kiss from artha
+Constantine Patton also a professor in
+
+ align:start position:0%
+Constantine Patton also a professor in
+ 
+
+ align:start position:0%
+Constantine Patton also a professor in
+biology Department who happens to be uh
+
+ align:start position:0%
+biology Department who happens to be uh
+ 
+
+ align:start position:0%
+biology Department who happens to be uh
+Bob's wife um most of you know that the
+
+ align:start position:0%
+Bob's wife um most of you know that the
+ 
+
+ align:start position:0%
+Bob's wife um most of you know that the
+human genome has now been sequenced that
+
+ align:start position:0%
+human genome has now been sequenced that
+ 
+
+ align:start position:0%
+human genome has now been sequenced that
+was one of the huge undertakings in most
+
+ align:start position:0%
+was one of the huge undertakings in most
+ 
+
+ align:start position:0%
+was one of the huge undertakings in most
+important undertakings in Modern Biology
+
+ align:start position:0%
+important undertakings in Modern Biology
+ 
+
+ align:start position:0%
+important undertakings in Modern Biology
+over the last while uh it was an
+
+ align:start position:0%
+over the last while uh it was an
+ 
+
+ align:start position:0%
+over the last while uh it was an
+incredible feat each cell has uh as you
+
+ align:start position:0%
+incredible feat each cell has uh as you
+ 
+
+ align:start position:0%
+incredible feat each cell has uh as you
+mostly most of you know 46 chromosomes
+
+ align:start position:0%
+mostly most of you know 46 chromosomes
+ 
+
+ align:start position:0%
+mostly most of you know 46 chromosomes
+that's a total of about 2 meters of DNA
+
+ align:start position:0%
+that's a total of about 2 meters of DNA
+ 
+
+ align:start position:0%
+that's a total of about 2 meters of DNA
+in every human cell and that 2 meters of
+
+ align:start position:0%
+in every human cell and that 2 meters of
+ 
+
+ align:start position:0%
+in every human cell and that 2 meters of
+is composed of about 3 million DNA base
+
+ align:start position:0%
+is composed of about 3 million DNA base
+ 
+
+ align:start position:0%
+is composed of about 3 million DNA base
+pairs these letters A and C that we'll
+
+ align:start position:0%
+pairs these letters A and C that we'll
+ 
+
+ align:start position:0%
+pairs these letters A and C that we'll
+be talking about as we go through the
+
+ align:start position:0%
+be talking about as we go through the
+ 
+
+ align:start position:0%
+be talking about as we go through the
+through the course so to sequence The
+
+ align:start position:0%
+through the course so to sequence The
+ 
+
+ align:start position:0%
+through the course so to sequence The
+genome had to work out the sequence of
+
+ align:start position:0%
+genome had to work out the sequence of
+ 
+
+ align:start position:0%
+genome had to work out the sequence of
+these the exact run of these AGT CS
+
+ align:start position:0%
+these the exact run of these AGT CS
+ 
+
+ align:start position:0%
+these the exact run of these AGT CS
+along the backbone for three uh billion
+
+ align:start position:0%
+along the backbone for three uh billion
+ 
+
+ align:start position:0%
+along the backbone for three uh billion
+uh um base pairs and somewhere that
+
+ align:start position:0%
+uh um base pairs and somewhere that
+ 
+
+ align:start position:0%
+uh um base pairs and somewhere that
+genome encodes somewhere between 20 and
+
+ align:start position:0%
+genome encodes somewhere between 20 and
+ 
+
+ align:start position:0%
+genome encodes somewhere between 20 and
+30,000 genes and we'll be talking about
+
+ align:start position:0%
+30,000 genes and we'll be talking about
+ 
+
+ align:start position:0%
+30,000 genes and we'll be talking about
+the the proteins that are encoded by
+
+ align:start position:0%
+the the proteins that are encoded by
+ 
+
+ align:start position:0%
+the the proteins that are encoded by
+most of those genes and their important
+
+ align:start position:0%
+most of those genes and their important
+ 
+
+ align:start position:0%
+most of those genes and their important
+roles as we go on in the um course what
+
+ align:start position:0%
+roles as we go on in the um course what
+ 
+
+ align:start position:0%
+roles as we go on in the um course what
+some of you may not know is the key role
+
+ align:start position:0%
+some of you may not know is the key role
+ 
+
+ align:start position:0%
+some of you may not know is the key role
+that M uh played in this about a third
+
+ align:start position:0%
+that M uh played in this about a third
+ 
+
+ align:start position:0%
+that M uh played in this about a third
+of the genome was sequenced at the uh
+
+ align:start position:0%
+of the genome was sequenced at the uh
+ 
+
+ align:start position:0%
+of the genome was sequenced at the uh
+the Whitehead uh MIT genome Center and
+
+ align:start position:0%
+the Whitehead uh MIT genome Center and
+ 
+
+ align:start position:0%
+the Whitehead uh MIT genome Center and
+here's some of the robots that were used
+
+ align:start position:0%
+here's some of the robots that were used
+ 
+
+ align:start position:0%
+here's some of the robots that were used
+to sequence that DNA and that sequencing
+
+ align:start position:0%
+to sequence that DNA and that sequencing
+ 
+
+ align:start position:0%
+to sequence that DNA and that sequencing
+effort was led by Eric Lander whose name
+
+ align:start position:0%
+effort was led by Eric Lander whose name
+ 
+
+ align:start position:0%
+effort was led by Eric Lander whose name
+some of you may recognize because he
+
+ align:start position:0%
+some of you may recognize because he
+ 
+
+ align:start position:0%
+some of you may recognize because he
+teaches the fall version of 701 along
+
+ align:start position:0%
+teaches the fall version of 701 along
+ 
+
+ align:start position:0%
+teaches the fall version of 701 along
+with uh Bob
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Weinberg so here just a few examples of
+
+ align:start position:0%
+Weinberg so here just a few examples of
+ 
+
+ align:start position:0%
+Weinberg so here just a few examples of
+why uh I think it's important for you to
+
+ align:start position:0%
+why uh I think it's important for you to
+ 
+
+ align:start position:0%
+why uh I think it's important for you to
+understand uh biology regardless of
+
+ align:start position:0%
+understand uh biology regardless of
+ 
+
+ align:start position:0%
+understand uh biology regardless of
+whether you're uh going to go on and use
+
+ align:start position:0%
+whether you're uh going to go on and use
+ 
+
+ align:start position:0%
+whether you're uh going to go on and use
+it professionally most of you know one
+
+ align:start position:0%
+it professionally most of you know one
+ 
+
+ align:start position:0%
+it professionally most of you know one
+of the biggest challenges we face as
+
+ align:start position:0%
+of the biggest challenges we face as
+ 
+
+ align:start position:0%
+of the biggest challenges we face as
+this planet is this Aid AIDS uh epidemic
+
+ align:start position:0%
+this planet is this Aid AIDS uh epidemic
+ 
+
+ align:start position:0%
+this planet is this Aid AIDS uh epidemic
+it's caused by a certain kind of virus
+
+ align:start position:0%
+it's caused by a certain kind of virus
+ 
+
+ align:start position:0%
+it's caused by a certain kind of virus
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+hiv1 that gets into particular cells of
+
+ align:start position:0%
+hiv1 that gets into particular cells of
+ 
+
+ align:start position:0%
+hiv1 that gets into particular cells of
+your immune system that defend normally
+
+ align:start position:0%
+your immune system that defend normally
+ 
+
+ align:start position:0%
+your immune system that defend normally
+defends us against infection and
+
+ align:start position:0%
+defends us against infection and
+ 
+
+ align:start position:0%
+defends us against infection and
+destroys those and um then people die
+
+ align:start position:0%
+destroys those and um then people die
+ 
+
+ align:start position:0%
+destroys those and um then people die
+from infections by other organisms that
+
+ align:start position:0%
+from infections by other organisms that
+ 
+
+ align:start position:0%
+from infections by other organisms that
+normally you can fight off it's a huge
+
+ align:start position:0%
+normally you can fight off it's a huge
+ 
+
+ align:start position:0%
+normally you can fight off it's a huge
+problem with societ vast societal and
+
+ align:start position:0%
+problem with societ vast societal and
+ 
+
+ align:start position:0%
+problem with societ vast societal and
+economic uh implications and it's one
+
+ align:start position:0%
+economic uh implications and it's one
+ 
+
+ align:start position:0%
+economic uh implications and it's one
+that we're still as a as a mankind still
+
+ align:start position:0%
+that we're still as a as a mankind still
+ 
+
+ align:start position:0%
+that we're still as a as a mankind still
+trying to to deal with grapple with uh
+
+ align:start position:0%
+trying to to deal with grapple with uh
+ 
+
+ align:start position:0%
+trying to to deal with grapple with uh
+here's another example just a couple of
+
+ align:start position:0%
+here's another example just a couple of
+ 
+
+ align:start position:0%
+here's another example just a couple of
+years ago there was the scare of Anthrax
+
+ align:start position:0%
+years ago there was the scare of Anthrax
+ 
+
+ align:start position:0%
+years ago there was the scare of Anthrax
+it's a bacterium that's very pathogenic
+
+ align:start position:0%
+it's a bacterium that's very pathogenic
+ 
+
+ align:start position:0%
+it's a bacterium that's very pathogenic
+can kill its host fairly easily does it
+
+ align:start position:0%
+can kill its host fairly easily does it
+ 
+
+ align:start position:0%
+can kill its host fairly easily does it
+by making uh particular toxins this the
+
+ align:start position:0%
+by making uh particular toxins this the
+ 
+
+ align:start position:0%
+by making uh particular toxins this the
+details shown here don't matter but just
+
+ align:start position:0%
+details shown here don't matter but just
+ 
+
+ align:start position:0%
+details shown here don't matter but just
+reminding you that this is something
+
+ align:start position:0%
+reminding you that this is something
+ 
+
+ align:start position:0%
+reminding you that this is something
+that was in the front pages of the paper
+
+ align:start position:0%
+that was in the front pages of the paper
+ 
+
+ align:start position:0%
+that was in the front pages of the paper
+just a little while ago
+
+ align:start position:0%
+just a little while ago
+ 
+
+ align:start position:0%
+just a little while ago
+um couple of years ago when I was
+
+ align:start position:0%
+um couple of years ago when I was
+ 
+
+ align:start position:0%
+um couple of years ago when I was
+teaching this we had the scare with the
+
+ align:start position:0%
+teaching this we had the scare with the
+ 
+
+ align:start position:0%
+teaching this we had the scare with the
+scar SARS virus that went all the way
+
+ align:start position:0%
+scar SARS virus that went all the way
+ 
+
+ align:start position:0%
+scar SARS virus that went all the way
+during the course when I was teaching it
+
+ align:start position:0%
+during the course when I was teaching it
+ 
+
+ align:start position:0%
+during the course when I was teaching it
+from the initial discovery of the virus
+
+ align:start position:0%
+from the initial discovery of the virus
+ 
+
+ align:start position:0%
+from the initial discovery of the virus
+to the actual sequencing of the genome
+
+ align:start position:0%
+to the actual sequencing of the genome
+ 
+
+ align:start position:0%
+to the actual sequencing of the genome
+which had happened by later on in the
+
+ align:start position:0%
+which had happened by later on in the
+ 
+
+ align:start position:0%
+which had happened by later on in the
+course uh smallpox was a disease we
+
+ align:start position:0%
+course uh smallpox was a disease we
+ 
+
+ align:start position:0%
+course uh smallpox was a disease we
+thought that we' eliminated but now it's
+
+ align:start position:0%
+thought that we' eliminated but now it's
+ 
+
+ align:start position:0%
+thought that we' eliminated but now it's
+come back as a biot terrorism threat and
+
+ align:start position:0%
+come back as a biot terrorism threat and
+ 
+
+ align:start position:0%
+come back as a biot terrorism threat and
+there's increased
+
+ align:start position:0%
+there's increased
+ 
+
+ align:start position:0%
+there's increased
+uh study of of small po pox it's
+
+ align:start position:0%
+uh study of of small po pox it's
+ 
+
+ align:start position:0%
+uh study of of small po pox it's
+something we have to worry about again
+
+ align:start position:0%
+something we have to worry about again
+ 
+
+ align:start position:0%
+something we have to worry about again
+here's another example um this is
+
+ align:start position:0%
+here's another example um this is
+ 
+
+ align:start position:0%
+here's another example um this is
+picture showing the start of a trans
+
+ align:start position:0%
+picture showing the start of a trans
+ 
+
+ align:start position:0%
+picture showing the start of a trans
+genic animal we'll talk about how this
+
+ align:start position:0%
+genic animal we'll talk about how this
+ 
+
+ align:start position:0%
+genic animal we'll talk about how this
+uh process goes later in the course and
+
+ align:start position:0%
+uh process goes later in the course and
+ 
+
+ align:start position:0%
+uh process goes later in the course and
+it's it's related also to this whole
+
+ align:start position:0%
+it's it's related also to this whole
+ 
+
+ align:start position:0%
+it's it's related also to this whole
+issue of cloning uh uh using the sense
+
+ align:start position:0%
+issue of cloning uh uh using the sense
+ 
+
+ align:start position:0%
+issue of cloning uh uh using the sense
+of the word such as in trying to clone a
+
+ align:start position:0%
+of the word such as in trying to clone a
+ 
+
+ align:start position:0%
+of the word such as in trying to clone a
+human or clone an animal to make uh a
+
+ align:start position:0%
+human or clone an animal to make uh a
+ 
+
+ align:start position:0%
+human or clone an animal to make uh a
+genetically identical copy so see there
+
+ align:start position:0%
+genetically identical copy so see there
+ 
+
+ align:start position:0%
+genetically identical copy so see there
+are a couple of different uses so the
+
+ align:start position:0%
+are a couple of different uses so the
+ 
+
+ align:start position:0%
+are a couple of different uses so the
+word cloning as we go through the
+
+ align:start position:0%
+word cloning as we go through the
+ 
+
+ align:start position:0%
+word cloning as we go through the
+course um there's a lot of fuss in the
+
+ align:start position:0%
+course um there's a lot of fuss in the
+ 
+
+ align:start position:0%
+course um there's a lot of fuss in the
+in the news in the newspapers about
+
+ align:start position:0%
+in the news in the newspapers about
+ 
+
+ align:start position:0%
+in the news in the newspapers about
+genetically modified food um and people
+
+ align:start position:0%
+genetically modified food um and people
+ 
+
+ align:start position:0%
+genetically modified food um and people
+have different positions on it here's a
+
+ align:start position:0%
+have different positions on it here's a
+ 
+
+ align:start position:0%
+have different positions on it here's a
+case where I think the benefit of a
+
+ align:start position:0%
+case where I think the benefit of a
+ 
+
+ align:start position:0%
+case where I think the benefit of a
+genetically modified food could hardly
+
+ align:start position:0%
+genetically modified food could hardly
+ 
+
+ align:start position:0%
+genetically modified food could hardly
+be argued with um about two-thirds of
+
+ align:start position:0%
+be argued with um about two-thirds of
+ 
+
+ align:start position:0%
+be argued with um about two-thirds of
+the world's population uses rice as
+
+ align:start position:0%
+the world's population uses rice as
+ 
+
+ align:start position:0%
+the world's population uses rice as
+their primary source of of food one of
+
+ align:start position:0%
+their primary source of of food one of
+ 
+
+ align:start position:0%
+their primary source of of food one of
+the problems with rice is it doesn't
+
+ align:start position:0%
+the problems with rice is it doesn't
+ 
+
+ align:start position:0%
+the problems with rice is it doesn't
+make beta katene beta carotene is what
+
+ align:start position:0%
+make beta katene beta carotene is what
+ 
+
+ align:start position:0%
+make beta katene beta carotene is what
+our bodies take and use to make vitamin
+
+ align:start position:0%
+our bodies take and use to make vitamin
+ 
+
+ align:start position:0%
+our bodies take and use to make vitamin
+A if you have a vitamin A deficiency uh
+
+ align:start position:0%
+A if you have a vitamin A deficiency uh
+ 
+
+ align:start position:0%
+A if you have a vitamin A deficiency uh
+people are prone to infection they have
+
+ align:start position:0%
+people are prone to infection they have
+ 
+
+ align:start position:0%
+people are prone to infection they have
+immune deficiencies in their immune
+
+ align:start position:0%
+immune deficiencies in their immune
+ 
+
+ align:start position:0%
+immune deficiencies in their immune
+system and and blindness and this this
+
+ align:start position:0%
+system and and blindness and this this
+ 
+
+ align:start position:0%
+system and and blindness and this this
+deficiency of vitamin A caused by eating
+
+ align:start position:0%
+deficiency of vitamin A caused by eating
+ 
+
+ align:start position:0%
+deficiency of vitamin A caused by eating
+rice afflicts about 400 million people
+
+ align:start position:0%
+rice afflicts about 400 million people
+ 
+
+ align:start position:0%
+rice afflicts about 400 million people
+worldwide but rice is only
+
+ align:start position:0%
+worldwide but rice is only
+ 
+
+ align:start position:0%
+worldwide but rice is only
+two chemical steps away from being able
+
+ align:start position:0%
+two chemical steps away from being able
+ 
+
+ align:start position:0%
+two chemical steps away from being able
+to make beta katene this is a
+
+ align:start position:0%
+to make beta katene this is a
+ 
+
+ align:start position:0%
+to make beta katene this is a
+genetically modified version of of rice
+
+ align:start position:0%
+genetically modified version of of rice
+ 
+
+ align:start position:0%
+genetically modified version of of rice
+that has those two extra steps inserted
+
+ align:start position:0%
+that has those two extra steps inserted
+ 
+
+ align:start position:0%
+that has those two extra steps inserted
+in it you can see it's golden because
+
+ align:start position:0%
+in it you can see it's golden because
+ 
+
+ align:start position:0%
+in it you can see it's golden because
+it's making beta carotene if people were
+
+ align:start position:0%
+it's making beta carotene if people were
+ 
+
+ align:start position:0%
+it's making beta carotene if people were
+to eat that form of rice then they
+
+ align:start position:0%
+to eat that form of rice then they
+ 
+
+ align:start position:0%
+to eat that form of rice then they
+wouldn't have this problem with vitamin
+
+ align:start position:0%
+wouldn't have this problem with vitamin
+ 
+
+ align:start position:0%
+wouldn't have this problem with vitamin
+A
+
+ align:start position:0%
+A
+ 
+
+ align:start position:0%
+A
+deficiency Penny uh Chisum in her part
+
+ align:start position:0%
+deficiency Penny uh Chisum in her part
+ 
+
+ align:start position:0%
+deficiency Penny uh Chisum in her part
+of the course will be considering things
+
+ align:start position:0%
+of the course will be considering things
+ 
+
+ align:start position:0%
+of the course will be considering things
+at a more Global level uh here's a
+
+ align:start position:0%
+at a more Global level uh here's a
+ 
+
+ align:start position:0%
+at a more Global level uh here's a
+picture of our planet and there issues
+
+ align:start position:0%
+picture of our planet and there issues
+ 
+
+ align:start position:0%
+picture of our planet and there issues
+that you know about there this is a the
+
+ align:start position:0%
+that you know about there this is a the
+ 
+
+ align:start position:0%
+that you know about there this is a the
+carbon dioxide level in the atmosphere
+
+ align:start position:0%
+carbon dioxide level in the atmosphere
+ 
+
+ align:start position:0%
+carbon dioxide level in the atmosphere
+are are rising and uh that's a real
+
+ align:start position:0%
+are are rising and uh that's a real
+ 
+
+ align:start position:0%
+are are rising and uh that's a real
+phenomena that shows from 1960 to
+
+ align:start position:0%
+phenomena that shows from 1960 to
+ 
+
+ align:start position:0%
+phenomena that shows from 1960 to
+1995 uh
+
+ align:start position:0%
+1995 uh
+ 
+
+ align:start position:0%
+1995 uh
+the this is associated with a uh global
+
+ align:start position:0%
+the this is associated with a uh global
+ 
+
+ align:start position:0%
+the this is associated with a uh global
+warming that again is undeniable that
+
+ align:start position:0%
+warming that again is undeniable that
+ 
+
+ align:start position:0%
+warming that again is undeniable that
+it's happening you'll see stuff in the
+
+ align:start position:0%
+it's happening you'll see stuff in the
+ 
+
+ align:start position:0%
+it's happening you'll see stuff in the
+papers uh and these gases particularly
+
+ align:start position:0%
+papers uh and these gases particularly
+ 
+
+ align:start position:0%
+papers uh and these gases particularly
+carbon dioxide and methane that are
+
+ align:start position:0%
+carbon dioxide and methane that are
+ 
+
+ align:start position:0%
+carbon dioxide and methane that are
+known as greenhouse gases are playing a
+
+ align:start position:0%
+known as greenhouse gases are playing a
+ 
+
+ align:start position:0%
+known as greenhouse gases are playing a
+role in that and probably mankind is
+
+ align:start position:0%
+role in that and probably mankind is
+ 
+
+ align:start position:0%
+role in that and probably mankind is
+playing a role in the production of
+
+ align:start position:0%
+playing a role in the production of
+ 
+
+ align:start position:0%
+playing a role in the production of
+those gases and hence in global warming
+
+ align:start position:0%
+those gases and hence in global warming
+ 
+
+ align:start position:0%
+those gases and hence in global warming
+and and Penny will talk to you a little
+
+ align:start position:0%
+and and Penny will talk to you a little
+ 
+
+ align:start position:0%
+and and Penny will talk to you a little
+more about that uh right here at MIT um
+
+ align:start position:0%
+more about that uh right here at MIT um
+ 
+
+ align:start position:0%
+more about that uh right here at MIT um
+Mario Molina in Eeps uh discovered the
+
+ align:start position:0%
+Mario Molina in Eeps uh discovered the
+ 
+
+ align:start position:0%
+Mario Molina in Eeps uh discovered the
+ozone hole got a Nobel Prize for that
+
+ align:start position:0%
+ozone hole got a Nobel Prize for that
+ 
+
+ align:start position:0%
+ozone hole got a Nobel Prize for that
+ozone is important because it absorbs UV
+
+ align:start position:0%
+ozone is important because it absorbs UV
+ 
+
+ align:start position:0%
+ozone is important because it absorbs UV
+uh critical stuff um component of
+
+ align:start position:0%
+uh critical stuff um component of
+ 
+
+ align:start position:0%
+uh critical stuff um component of
+ultraviolet radiation that would damage
+
+ align:start position:0%
+ultraviolet radiation that would damage
+ 
+
+ align:start position:0%
+ultraviolet radiation that would damage
+ourselves if we were exposed to it and
+
+ align:start position:0%
+ourselves if we were exposed to it and
+ 
+
+ align:start position:0%
+ourselves if we were exposed to it and
+because of
+
+ align:start position:0%
+because of
+ 
+
+ align:start position:0%
+because of
+emission of fluorocarbons in the in the
+
+ align:start position:0%
+emission of fluorocarbons in the in the
+ 
+
+ align:start position:0%
+emission of fluorocarbons in the in the
+environment this large hole de developed
+
+ align:start position:0%
+environment this large hole de developed
+ 
+
+ align:start position:0%
+environment this large hole de developed
+over Antarctica if that had spread it
+
+ align:start position:0%
+over Antarctica if that had spread it
+ 
+
+ align:start position:0%
+over Antarctica if that had spread it
+would have been a a real disaster and
+
+ align:start position:0%
+would have been a a real disaster and
+ 
+
+ align:start position:0%
+would have been a a real disaster and
+that seems to be the efforts to cut down
+
+ align:start position:0%
+that seems to be the efforts to cut down
+ 
+
+ align:start position:0%
+that seems to be the efforts to cut down
+and the release of Flur carbon seem to
+
+ align:start position:0%
+and the release of Flur carbon seem to
+ 
+
+ align:start position:0%
+and the release of Flur carbon seem to
+be helping with that but again Penny
+
+ align:start position:0%
+be helping with that but again Penny
+ 
+
+ align:start position:0%
+be helping with that but again Penny
+will have more to say those of you
+
+ align:start position:0%
+will have more to say those of you
+ 
+
+ align:start position:0%
+will have more to say those of you
+who lived around here for a little bit
+
+ align:start position:0%
+who lived around here for a little bit
+ 
+
+ align:start position:0%
+who lived around here for a little bit
+probably know that the fishing industry
+
+ align:start position:0%
+probably know that the fishing industry
+ 
+
+ align:start position:0%
+probably know that the fishing industry
+just locally has had a very hard time as
+
+ align:start position:0%
+just locally has had a very hard time as
+ 
+
+ align:start position:0%
+just locally has had a very hard time as
+a fishing boat just up at glass just up
+
+ align:start position:0%
+a fishing boat just up at glass just up
+ 
+
+ align:start position:0%
+a fishing boat just up at glass just up
+the the coast less than an hour from
+
+ align:start position:0%
+the the coast less than an hour from
+ 
+
+ align:start position:0%
+the the coast less than an hour from
+here and part of the problems again are
+
+ align:start position:0%
+here and part of the problems again are
+ 
+
+ align:start position:0%
+here and part of the problems again are
+caused by mismanagement of the resources
+
+ align:start position:0%
+caused by mismanagement of the resources
+ 
+
+ align:start position:0%
+caused by mismanagement of the resources
+where the the fish have been stocks have
+
+ align:start position:0%
+where the the fish have been stocks have
+ 
+
+ align:start position:0%
+where the the fish have been stocks have
+been over fish so the some of the
+
+ align:start position:0%
+been over fish so the some of the
+ 
+
+ align:start position:0%
+been over fish so the some of the
+Fisheries have come to the point of
+
+ align:start position:0%
+Fisheries have come to the point of
+ 
+
+ align:start position:0%
+Fisheries have come to the point of
+collapse or near the in places such as
+
+ align:start position:0%
+collapse or near the in places such as
+ 
+
+ align:start position:0%
+collapse or near the in places such as
+the grand Banks off of Newland land
+
+ align:start position:0%
+the grand Banks off of Newland land
+ 
+
+ align:start position:0%
+the grand Banks off of Newland land
+there has been a collapse and it's not
+
+ align:start position:0%
+there has been a collapse and it's not
+ 
+
+ align:start position:0%
+there has been a collapse and it's not
+at all clear that it can be reversed and
+
+ align:start position:0%
+at all clear that it can be reversed and
+ 
+
+ align:start position:0%
+at all clear that it can be reversed and
+whether they'll be caught in large
+
+ align:start position:0%
+whether they'll be caught in large
+ 
+
+ align:start position:0%
+whether they'll be caught in large
+quantities ever again
+
+ align:start position:0%
+quantities ever again
+ 
+
+ align:start position:0%
+quantities ever again
+there okay so
+
+ align:start position:0%
+there okay so
+ 
+
+ align:start position:0%
+there okay so
+um a variety of ways that we can can
+
+ align:start position:0%
+um a variety of ways that we can can
+ 
+
+ align:start position:0%
+um a variety of ways that we can can
+study biology and I think I'm going to
+
+ align:start position:0%
+study biology and I think I'm going to
+ 
+
+ align:start position:0%
+study biology and I think I'm going to
+begin by outlining um how we do that
+
+ align:start position:0%
+begin by outlining um how we do that
+ 
+
+ align:start position:0%
+begin by outlining um how we do that
+biology uh is an experimental science
+
+ align:start position:0%
+biology uh is an experimental science
+ 
+
+ align:start position:0%
+biology uh is an experimental science
+it's one of the really
+
+ align:start position:0%
+it's one of the really
+ 
+
+ align:start position:0%
+it's one of the really
+important themes that will
+
+ align:start position:0%
+important themes that will
+ 
+
+ align:start position:0%
+important themes that will
+run through
+
+ align:start position:0%
+run through
+ 
+
+ align:start position:0%
+run through
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course you can't study biology by just
+
+ align:start position:0%
+course you can't study biology by just
+ 
+
+ align:start position:0%
+course you can't study biology by just
+sitting down with a pen and paper room
+
+ align:start position:0%
+sitting down with a pen and paper room
+ 
+
+ align:start position:0%
+sitting down with a pen and paper room
+and thinking you have to get out and
+
+ align:start position:0%
+and thinking you have to get out and
+ 
+
+ align:start position:0%
+and thinking you have to get out and
+find out what's there you need to make
+
+ align:start position:0%
+find out what's there you need to make
+ 
+
+ align:start position:0%
+find out what's there you need to make
+observations you need to try experiments
+
+ align:start position:0%
+observations you need to try experiments
+ 
+
+ align:start position:0%
+observations you need to try experiments
+you need to formulate hypotheses and
+
+ align:start position:0%
+you need to formulate hypotheses and
+ 
+
+ align:start position:0%
+you need to formulate hypotheses and
+test them and either modify your
+
+ align:start position:0%
+test them and either modify your
+ 
+
+ align:start position:0%
+test them and either modify your
+hypothesis or rejected and so on but
+
+ align:start position:0%
+hypothesis or rejected and so on but
+ 
+
+ align:start position:0%
+hypothesis or rejected and so on but
+it's a continue cycle of experimentation
+
+ align:start position:0%
+it's a continue cycle of experimentation
+ 
+
+ align:start position:0%
+it's a continue cycle of experimentation
+and and um making hypotheses and testing
+
+ align:start position:0%
+and and um making hypotheses and testing
+ 
+
+ align:start position:0%
+and and um making hypotheses and testing
+that's the scci scientific method uh at
+
+ align:start position:0%
+that's the scci scientific method uh at
+ 
+
+ align:start position:0%
+that's the scci scientific method uh at
+work and but you can carry that out at
+
+ align:start position:0%
+work and but you can carry that out at
+ 
+
+ align:start position:0%
+work and but you can carry that out at
+different l levels the very highest
+
+ align:start position:0%
+different l levels the very highest
+ 
+
+ align:start position:0%
+different l levels the very highest
+level would be the
+
+ align:start position:0%
+level would be the
+ 
+
+ align:start position:0%
+level would be the
+biosphere there's one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example that's that's Earth it's here
+
+ align:start position:0%
+example that's that's Earth it's here
+ 
+
+ align:start position:0%
+example that's that's Earth it's here
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+um many many uh species of Life uh that
+
+ align:start position:0%
+um many many uh species of Life uh that
+ 
+
+ align:start position:0%
+um many many uh species of Life uh that
+are on there there're many more than
+
+ align:start position:0%
+are on there there're many more than
+ 
+
+ align:start position:0%
+are on there there're many more than
+um than a million
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the estimates of how many there are
+
+ align:start position:0%
+the estimates of how many there are
+ 
+
+ align:start position:0%
+the estimates of how many there are
+range from 10 to in total 10 to the 20
+
+ align:start position:0%
+range from 10 to in total 10 to the 20
+ 
+
+ align:start position:0%
+range from 10 to in total 10 to the 20
+million estimated and one of the the big
+
+ align:start position:0%
+million estimated and one of the the big
+ 
+
+ align:start position:0%
+million estimated and one of the the big
+worries right at the moment is that as
+
+ align:start position:0%
+worries right at the moment is that as
+ 
+
+ align:start position:0%
+worries right at the moment is that as
+rainforests are being depleted Source
+
+ align:start position:0%
+rainforests are being depleted Source
+ 
+
+ align:start position:0%
+rainforests are being depleted Source
+parts of the world that are rich s rich
+
+ align:start position:0%
+parts of the world that are rich s rich
+ 
+
+ align:start position:0%
+parts of the world that are rich s rich
+source of biological diversity uh as
+
+ align:start position:0%
+source of biological diversity uh as
+ 
+
+ align:start position:0%
+source of biological diversity uh as
+those are disappearing we're losing
+
+ align:start position:0%
+those are disappearing we're losing
+ 
+
+ align:start position:0%
+those are disappearing we're losing
+diversity at quite a rate um just couple
+
+ align:start position:0%
+diversity at quite a rate um just couple
+ 
+
+ align:start position:0%
+diversity at quite a rate um just couple
+of years ago I had a chance to fly over
+
+ align:start position:0%
+of years ago I had a chance to fly over
+ 
+
+ align:start position:0%
+of years ago I had a chance to fly over
+a part of Brazil and it was just scary
+
+ align:start position:0%
+a part of Brazil and it was just scary
+ 
+
+ align:start position:0%
+a part of Brazil and it was just scary
+to see from the plane how the rainforest
+
+ align:start position:0%
+to see from the plane how the rainforest
+ 
+
+ align:start position:0%
+to see from the plane how the rainforest
+had just being um cut down and you could
+
+ align:start position:0%
+had just being um cut down and you could
+ 
+
+ align:start position:0%
+had just being um cut down and you could
+just see how fast some of that uh the
+
+ align:start position:0%
+just see how fast some of that uh the
+ 
+
+ align:start position:0%
+just see how fast some of that uh the
+rainforest was disappearing and with it
+
+ align:start position:0%
+rainforest was disappearing and with it
+ 
+
+ align:start position:0%
+rainforest was disappearing and with it
+many different types of uh of species
+
+ align:start position:0%
+many different types of uh of species
+ 
+
+ align:start position:0%
+many different types of uh of species
+that only only can live there um one can
+
+ align:start position:0%
+that only only can live there um one can
+ 
+
+ align:start position:0%
+that only only can live there um one can
+look instead uh going down a level at an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ecosystem which is the is a particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment and the species of Life
+
+ align:start position:0%
+environment and the species of Life
+ 
+
+ align:start position:0%
+environment and the species of Life
+found in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and just to give you a couple of
+
+ align:start position:0%
+it and just to give you a couple of
+ 
+
+ align:start position:0%
+it and just to give you a couple of
+examples of that it could be a uh salt
+
+ align:start position:0%
+examples of that it could be a uh salt
+ 
+
+ align:start position:0%
+examples of that it could be a uh salt
+marsh shown here or here's an
+
+ align:start position:0%
+marsh shown here or here's an
+ 
+
+ align:start position:0%
+marsh shown here or here's an
+interesting environment that Penny
+
+ align:start position:0%
+interesting environment that Penny
+ 
+
+ align:start position:0%
+interesting environment that Penny
+Chisum will tell you more about um this
+
+ align:start position:0%
+Chisum will tell you more about um this
+ 
+
+ align:start position:0%
+Chisum will tell you more about um this
+is a black smoker there's a vent several
+
+ align:start position:0%
+is a black smoker there's a vent several
+ 
+
+ align:start position:0%
+is a black smoker there's a vent several
+miles deep in the Pacific Ocean uh the
+
+ align:start position:0%
+miles deep in the Pacific Ocean uh the
+ 
+
+ align:start position:0%
+miles deep in the Pacific Ocean uh the
+Water temperature that's gushing out of
+
+ align:start position:0%
+Water temperature that's gushing out of
+ 
+
+ align:start position:0%
+Water temperature that's gushing out of
+here is around 360° centigrade and
+
+ align:start position:0%
+here is around 360° centigrade and
+ 
+
+ align:start position:0%
+here is around 360° centigrade and
+there's a particular community of life
+
+ align:start position:0%
+there's a particular community of life
+ 
+
+ align:start position:0%
+there's a particular community of life
+that's able to grow around these around
+
+ align:start position:0%
+that's able to grow around these around
+ 
+
+ align:start position:0%
+that's able to grow around these around
+these uh deep Vents and Penny will tell
+
+ align:start position:0%
+these uh deep Vents and Penny will tell
+ 
+
+ align:start position:0%
+these uh deep Vents and Penny will tell
+you more um more about that then going
+
+ align:start position:0%
+you more um more about that then going
+ 
+
+ align:start position:0%
+you more um more about that then going
+down yet another level you can come to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+population this is interacting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or in breeding uh organisms an example
+
+ align:start position:0%
+or in breeding uh organisms an example
+ 
+
+ align:start position:0%
+or in breeding uh organisms an example
+might be the fiddler crabs in a in a
+
+ align:start position:0%
+might be the fiddler crabs in a in a
+ 
+
+ align:start position:0%
+might be the fiddler crabs in a in a
+salt marsh or or here we see an
+
+ align:start position:0%
+salt marsh or or here we see an
+ 
+
+ align:start position:0%
+salt marsh or or here we see an
+interesting population these are tube
+
+ align:start position:0%
+interesting population these are tube
+ 
+
+ align:start position:0%
+interesting population these are tube
+worms that are up to a meter or more in
+
+ align:start position:0%
+worms that are up to a meter or more in
+ 
+
+ align:start position:0%
+worms that are up to a meter or more in
+length you find down at these um these
+
+ align:start position:0%
+length you find down at these um these
+ 
+
+ align:start position:0%
+length you find down at these um these
+black smokers if we move down yet
+
+ align:start position:0%
+black smokers if we move down yet
+ 
+
+ align:start position:0%
+black smokers if we move down yet
+another level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we come to organisms um organisms have
+
+ align:start position:0%
+we come to organisms um organisms have
+ 
+
+ align:start position:0%
+we come to organisms um organisms have
+uh three important sort of
+
+ align:start position:0%
+uh three important sort of
+ 
+
+ align:start position:0%
+uh three important sort of
+characteristics that we'll talk quite a
+
+ align:start position:0%
+characteristics that we'll talk quite a
+ 
+
+ align:start position:0%
+characteristics that we'll talk quite a
+bit about in this course they carry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out metabolism which is a sum of all the
+
+ align:start position:0%
+out metabolism which is a sum of all the
+ 
+
+ align:start position:0%
+out metabolism which is a sum of all the
+different chemical reactions necessary
+
+ align:start position:0%
+different chemical reactions necessary
+ 
+
+ align:start position:0%
+different chemical reactions necessary
+uh for life they undergo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regulated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+growth and they
+
+ align:start position:0%
+growth and they
+ 
+
+ align:start position:0%
+growth and they
+reproduce and the sort of fundamental
+
+ align:start position:0%
+reproduce and the sort of fundamental
+ 
+
+ align:start position:0%
+reproduce and the sort of fundamental
+unit of of life that we will talk about
+
+ align:start position:0%
+unit of of life that we will talk about
+ 
+
+ align:start position:0%
+unit of of life that we will talk about
+over and over again in this course is
+
+ align:start position:0%
+over and over again in this course is
+ 
+
+ align:start position:0%
+over and over again in this course is
+known as a
+
+ align:start position:0%
+known as a
+ 
+
+ align:start position:0%
+known as a
+cell and life comes in two kinds of
+
+ align:start position:0%
+cell and life comes in two kinds of
+ 
+
+ align:start position:0%
+cell and life comes in two kinds of
+species there's unicellular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+life where
+
+ align:start position:0%
+life where
+ 
+
+ align:start position:0%
+life where
+uh uh the organism is just a single cell
+
+ align:start position:0%
+uh uh the organism is just a single cell
+ 
+
+ align:start position:0%
+uh uh the organism is just a single cell
+and a multicell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multicellular forms of of Life uh that
+
+ align:start position:0%
+multicellular forms of of Life uh that
+ 
+
+ align:start position:0%
+multicellular forms of of Life uh that
+are made of many different types of
+
+ align:start position:0%
+are made of many different types of
+ 
+
+ align:start position:0%
+are made of many different types of
+cells what's a
+
+ align:start position:0%
+cells what's a
+ 
+
+ align:start position:0%
+cells what's a
+cell one of the secrets to life uh it's
+
+ align:start position:0%
+cell one of the secrets to life uh it's
+ 
+
+ align:start position:0%
+cell one of the secrets to life uh it's
+a little tiny bit of the universe that's
+
+ align:start position:0%
+a little tiny bit of the universe that's
+ 
+
+ align:start position:0%
+a little tiny bit of the universe that's
+surrounded by a boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's given the special name of a me a
+
+ align:start position:0%
+it's given the special name of a me a
+ 
+
+ align:start position:0%
+it's given the special name of a me a
+membrane uh it's selective uh not very
+
+ align:start position:0%
+membrane uh it's selective uh not very
+ 
+
+ align:start position:0%
+membrane uh it's selective uh not very
+permeable to most things and cells are
+
+ align:start position:0%
+permeable to most things and cells are
+ 
+
+ align:start position:0%
+permeable to most things and cells are
+able to put little importers and
+
+ align:start position:0%
+able to put little importers and
+ 
+
+ align:start position:0%
+able to put little importers and
+exporters and things that control the
+
+ align:start position:0%
+exporters and things that control the
+ 
+
+ align:start position:0%
+exporters and things that control the
+passage of things across the membrane
+
+ align:start position:0%
+passage of things across the membrane
+ 
+
+ align:start position:0%
+passage of things across the membrane
+and by isolating the inside of a cell
+
+ align:start position:0%
+and by isolating the inside of a cell
+ 
+
+ align:start position:0%
+and by isolating the inside of a cell
+from all the rest of the Universe um
+
+ align:start position:0%
+from all the rest of the Universe um
+ 
+
+ align:start position:0%
+from all the rest of the Universe um
+that's one of the the principles that
+
+ align:start position:0%
+that's one of the the principles that
+ 
+
+ align:start position:0%
+that's one of the the principles that
+makes uh that makes life
+
+ align:start position:0%
+makes uh that makes life
+ 
+
+ align:start position:0%
+makes uh that makes life
+uh possible um we have a couple of
+
+ align:start position:0%
+uh possible um we have a couple of
+ 
+
+ align:start position:0%
+uh possible um we have a couple of
+examples of uh of organisms here here's
+
+ align:start position:0%
+examples of uh of organisms here here's
+ 
+
+ align:start position:0%
+examples of uh of organisms here here's
+some clams that grow down at those black
+
+ align:start position:0%
+some clams that grow down at those black
+ 
+
+ align:start position:0%
+some clams that grow down at those black
+smokers and they can get pretty large
+
+ align:start position:0%
+smokers and they can get pretty large
+ 
+
+ align:start position:0%
+smokers and they can get pretty large
+and I say penny will talk a bit more
+
+ align:start position:0%
+and I say penny will talk a bit more
+ 
+
+ align:start position:0%
+and I say penny will talk a bit more
+about this we have this really amazing
+
+ align:start position:0%
+about this we have this really amazing
+ 
+
+ align:start position:0%
+about this we have this really amazing
+diversity of of life forms that uh we
+
+ align:start position:0%
+diversity of of life forms that uh we
+ 
+
+ align:start position:0%
+diversity of of life forms that uh we
+find on this on this planet however we
+
+ align:start position:0%
+find on this on this planet however we
+ 
+
+ align:start position:0%
+find on this on this planet however we
+can if we think about this division into
+
+ align:start position:0%
+can if we think about this division into
+ 
+
+ align:start position:0%
+can if we think about this division into
+uni
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cellular
+
+ align:start position:0%
+cellular
+ 
+
+ align:start position:0%
+cellular
+multicellular organisms unicellular
+
+ align:start position:0%
+multicellular organisms unicellular
+ 
+
+ align:start position:0%
+multicellular organisms unicellular
+organisms include things that
+
+ align:start position:0%
+organisms include things that
+ 
+
+ align:start position:0%
+organisms include things that
+you're familiar with they're bacteria
+
+ align:start position:0%
+you're familiar with they're bacteria
+ 
+
+ align:start position:0%
+you're familiar with they're bacteria
+there's a picture of just eoli cells and
+
+ align:start position:0%
+there's a picture of just eoli cells and
+ 
+
+ align:start position:0%
+there's a picture of just eoli cells and
+we'll be talking EOL about eoli quite a
+
+ align:start position:0%
+we'll be talking EOL about eoli quite a
+ 
+
+ align:start position:0%
+we'll be talking EOL about eoli quite a
+bit as a model organism as we go through
+
+ align:start position:0%
+bit as a model organism as we go through
+ 
+
+ align:start position:0%
+bit as a model organism as we go through
+the through the course it's been uh by
+
+ align:start position:0%
+the through the course it's been uh by
+ 
+
+ align:start position:0%
+the through the course it's been uh by
+studying eoli
+
+ align:start position:0%
+studying eoli
+ 
+
+ align:start position:0%
+studying eoli
+have learned many important things that
+
+ align:start position:0%
+have learned many important things that
+ 
+
+ align:start position:0%
+have learned many important things that
+apply to to all of life uh another kind
+
+ align:start position:0%
+apply to to all of life uh another kind
+ 
+
+ align:start position:0%
+apply to to all of life uh another kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+important uh single cell organism
+
+ align:start position:0%
+important uh single cell organism
+ 
+
+ align:start position:0%
+important uh single cell organism
+unicellular organism is yeast that's
+
+ align:start position:0%
+unicellular organism is yeast that's
+ 
+
+ align:start position:0%
+unicellular organism is yeast that's
+those are pictures of uh yeast uh sacris
+
+ align:start position:0%
+those are pictures of uh yeast uh sacris
+ 
+
+ align:start position:0%
+those are pictures of uh yeast uh sacris
+that are used in baking bread or in uh
+
+ align:start position:0%
+that are used in baking bread or in uh
+ 
+
+ align:start position:0%
+that are used in baking bread or in uh
+brewing beer or or making wine another
+
+ align:start position:0%
+brewing beer or or making wine another
+ 
+
+ align:start position:0%
+brewing beer or or making wine another
+one you're all familiar
+
+ align:start position:0%
+one you're all familiar
+ 
+
+ align:start position:0%
+one you're all familiar
+with are algae which are single celled
+
+ align:start position:0%
+with are algae which are single celled
+ 
+
+ align:start position:0%
+with are algae which are single celled
+uh organisms that are able to carry out
+
+ align:start position:0%
+uh organisms that are able to carry out
+ 
+
+ align:start position:0%
+uh organisms that are able to carry out
+photosynthesis and we'll be talking
+
+ align:start position:0%
+photosynthesis and we'll be talking
+ 
+
+ align:start position:0%
+photosynthesis and we'll be talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that if uh we think of uh an example of
+
+ align:start position:0%
+that if uh we think of uh an example of
+ 
+
+ align:start position:0%
+that if uh we think of uh an example of
+a of a multicellular organism then there
+
+ align:start position:0%
+a of a multicellular organism then there
+ 
+
+ align:start position:0%
+a of a multicellular organism then there
+we see there are different levels at
+
+ align:start position:0%
+we see there are different levels at
+ 
+
+ align:start position:0%
+we see there are different levels at
+which we can think about this we could
+
+ align:start position:0%
+which we can think about this we could
+ 
+
+ align:start position:0%
+which we can think about this we could
+take uh for example
+
+ align:start position:0%
+take uh for example
+ 
+
+ align:start position:0%
+take uh for example
+uh a picture of me uh just an
+
+ align:start position:0%
+uh a picture of me uh just an
+ 
+
+ align:start position:0%
+uh a picture of me uh just an
+anatomically correct uh diagram
+
+ align:start position:0%
+anatomically correct uh diagram
+ 
+
+ align:start position:0%
+anatomically correct uh diagram
+here that
+
+ align:start position:0%
+here that
+ 
+
+ align:start position:0%
+here that
+I'm made up as you are of about 10 to
+
+ align:start position:0%
+I'm made up as you are of about 10 to
+ 
+
+ align:start position:0%
+I'm made up as you are of about 10 to
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+14th human human
+
+ align:start position:0%
+14th human human
+ 
+
+ align:start position:0%
+14th human human
+cells we all started out as a single uh
+
+ align:start position:0%
+cells we all started out as a single uh
+ 
+
+ align:start position:0%
+cells we all started out as a single uh
+fertilized egg as a fertilized egg which
+
+ align:start position:0%
+fertilized egg as a fertilized egg which
+ 
+
+ align:start position:0%
+fertilized egg as a fertilized egg which
+is a single cell and by the time uh
+
+ align:start position:0%
+is a single cell and by the time uh
+ 
+
+ align:start position:0%
+is a single cell and by the time uh
+we're grown up we have about 10 to the
+
+ align:start position:0%
+we're grown up we have about 10 to the
+ 
+
+ align:start position:0%
+we're grown up we have about 10 to the
+14th human cells just a tremendous
+
+ align:start position:0%
+14th human cells just a tremendous
+ 
+
+ align:start position:0%
+14th human cells just a tremendous
+amount of cell growth that had to happen
+
+ align:start position:0%
+amount of cell growth that had to happen
+ 
+
+ align:start position:0%
+amount of cell growth that had to happen
+and uh specialization the other thing
+
+ align:start position:0%
+and uh specialization the other thing
+ 
+
+ align:start position:0%
+and uh specialization the other thing
+you may not appreciate is that we have
+
+ align:start position:0%
+you may not appreciate is that we have
+ 
+
+ align:start position:0%
+you may not appreciate is that we have
+an ecosystem inside us in our our
+
+ align:start position:0%
+an ecosystem inside us in our our
+ 
+
+ align:start position:0%
+an ecosystem inside us in our our
+gastrointestinal tract the uh this part
+
+ align:start position:0%
+gastrointestinal tract the uh this part
+ 
+
+ align:start position:0%
+gastrointestinal tract the uh this part
+the intestine having the highest
+
+ align:start position:0%
+the intestine having the highest
+ 
+
+ align:start position:0%
+the intestine having the highest
+concentration of microorganisms but
+
+ align:start position:0%
+concentration of microorganisms but
+ 
+
+ align:start position:0%
+concentration of microorganisms but
+they're about 10 to the 14th
+
+ align:start position:0%
+they're about 10 to the 14th
+ 
+
+ align:start position:0%
+they're about 10 to the 14th
+bacteria also inside of our inside of
+
+ align:start position:0%
+bacteria also inside of our inside of
+ 
+
+ align:start position:0%
+bacteria also inside of our inside of
+our gut so we're actually almost the
+
+ align:start position:0%
+our gut so we're actually almost the
+ 
+
+ align:start position:0%
+our gut so we're actually almost the
+same number of human cells and uh
+
+ align:start position:0%
+same number of human cells and uh
+ 
+
+ align:start position:0%
+same number of human cells and uh
+bacterial cells and if we don't have
+
+ align:start position:0%
+bacterial cells and if we don't have
+ 
+
+ align:start position:0%
+bacterial cells and if we don't have
+those bacteria then our Digest systems
+
+ align:start position:0%
+those bacteria then our Digest systems
+ 
+
+ align:start position:0%
+those bacteria then our Digest systems
+don't uh don't work uh well so if we go
+
+ align:start position:0%
+don't uh don't work uh well so if we go
+ 
+
+ align:start position:0%
+don't uh don't work uh well so if we go
+down from a whole organism a whole
+
+ align:start position:0%
+down from a whole organism a whole
+ 
+
+ align:start position:0%
+down from a whole organism a whole
+multicellular organism then a level then
+
+ align:start position:0%
+multicellular organism then a level then
+ 
+
+ align:start position:0%
+multicellular organism then a level then
+we come to uh an
+
+ align:start position:0%
+we come to uh an
+ 
+
+ align:start position:0%
+we come to uh an
+organ and an example of that might be an
+
+ align:start position:0%
+organ and an example of that might be an
+ 
+
+ align:start position:0%
+organ and an example of that might be an
+i and I think we have a a diagram of an
+
+ align:start position:0%
+i and I think we have a a diagram of an
+ 
+
+ align:start position:0%
+i and I think we have a a diagram of an
+i which is made up of of different uh
+
+ align:start position:0%
+i which is made up of of different uh
+ 
+
+ align:start position:0%
+i which is made up of of different uh
+different parts and if we go down
+
+ align:start position:0%
+different parts and if we go down
+ 
+
+ align:start position:0%
+different parts and if we go down
+another level we come to a
+
+ align:start position:0%
+another level we come to a
+ 
+
+ align:start position:0%
+another level we come to a
+tissue which is now you can begin to see
+
+ align:start position:0%
+tissue which is now you can begin to see
+ 
+
+ align:start position:0%
+tissue which is now you can begin to see
+that the tissue is are made up of groups
+
+ align:start position:0%
+that the tissue is are made up of groups
+ 
+
+ align:start position:0%
+that the tissue is are made up of groups
+of specialized cells an example might
+
+ align:start position:0%
+of specialized cells an example might
+ 
+
+ align:start position:0%
+of specialized cells an example might
+be the retina of of an ie and if we
+
+ align:start position:0%
+be the retina of of an ie and if we
+ 
+
+ align:start position:0%
+be the retina of of an ie and if we
+continue to to go downwards we'll get to
+
+ align:start position:0%
+continue to to go downwards we'll get to
+ 
+
+ align:start position:0%
+continue to to go downwards we'll get to
+single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and at this point we're at the
+
+ align:start position:0%
+cells and at this point we're at the
+ 
+
+ align:start position:0%
+cells and at this point we're at the
+same level of detail as when we when we
+
+ align:start position:0%
+same level of detail as when we when we
+ 
+
+ align:start position:0%
+same level of detail as when we when we
+go to when we're talking about a
+
+ align:start position:0%
+go to when we're talking about a
+ 
+
+ align:start position:0%
+go to when we're talking about a
+unicellular um unicellular uh organism
+
+ align:start position:0%
+unicellular um unicellular uh organism
+ 
+
+ align:start position:0%
+unicellular um unicellular uh organism
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+continue down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we can get to um organel uh these
+
+ align:start position:0%
+then we can get to um organel uh these
+ 
+
+ align:start position:0%
+then we can get to um organel uh these
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+um involved in
+
+ align:start position:0%
+um involved in
+ 
+
+ align:start position:0%
+um involved in
+energy uh production uh energy manag
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M mitoch A mitochondrian and a
+
+ align:start position:0%
+M mitoch A mitochondrian and a
+ 
+
+ align:start position:0%
+M mitoch A mitochondrian and a
+chloroplast they're the two principal
+
+ align:start position:0%
+chloroplast they're the two principal
+ 
+
+ align:start position:0%
+chloroplast they're the two principal
+examples of organel that we'll we'll
+
+ align:start position:0%
+examples of organel that we'll we'll
+ 
+
+ align:start position:0%
+examples of organel that we'll we'll
+talk about and if we go down yet another
+
+ align:start position:0%
+talk about and if we go down yet another
+ 
+
+ align:start position:0%
+talk about and if we go down yet another
+level of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organization we get to molecules and
+
+ align:start position:0%
+organization we get to molecules and
+ 
+
+ align:start position:0%
+organization we get to molecules and
+part of the reason that biology has
+
+ align:start position:0%
+part of the reason that biology has
+ 
+
+ align:start position:0%
+part of the reason that biology has
+flourished so well over the last few
+
+ align:start position:0%
+flourished so well over the last few
+ 
+
+ align:start position:0%
+flourished so well over the last few
+decades at MIT is there's been a real
+
+ align:start position:0%
+decades at MIT is there's been a real
+ 
+
+ align:start position:0%
+decades at MIT is there's been a real
+emphasis on looking at things at a
+
+ align:start position:0%
+emphasis on looking at things at a
+ 
+
+ align:start position:0%
+emphasis on looking at things at a
+cellular and molecular level so you're
+
+ align:start position:0%
+cellular and molecular level so you're
+ 
+
+ align:start position:0%
+cellular and molecular level so you're
+going to be hearing a lot about cells
+
+ align:start position:0%
+going to be hearing a lot about cells
+ 
+
+ align:start position:0%
+going to be hearing a lot about cells
+and a lot about uh molecules as we go
+
+ align:start position:0%
+and a lot about uh molecules as we go
+ 
+
+ align:start position:0%
+and a lot about uh molecules as we go
+through this uh through this course
+
+ align:start position:0%
+through this uh through this course
+ 
+
+ align:start position:0%
+through this uh through this course
+here's an example of ropson that's a
+
+ align:start position:0%
+here's an example of ropson that's a
+ 
+
+ align:start position:0%
+here's an example of ropson that's a
+protein we'll be talking what proteins
+
+ align:start position:0%
+protein we'll be talking what proteins
+ 
+
+ align:start position:0%
+protein we'll be talking what proteins
+are but it's a very important class of
+
+ align:start position:0%
+are but it's a very important class of
+ 
+
+ align:start position:0%
+are but it's a very important class of
+molecule in nature in this case proteins
+
+ align:start position:0%
+molecule in nature in this case proteins
+ 
+
+ align:start position:0%
+molecule in nature in this case proteins
+involved in in sensing uh light and
+
+ align:start position:0%
+involved in in sensing uh light and
+ 
+
+ align:start position:0%
+involved in in sensing uh light and
+plays an important part in your vision
+
+ align:start position:0%
+plays an important part in your vision
+ 
+
+ align:start position:0%
+plays an important part in your vision
+here's some another protein you can't
+
+ align:start position:0%
+here's some another protein you can't
+ 
+
+ align:start position:0%
+here's some another protein you can't
+really tell uh what it's doing by just
+
+ align:start position:0%
+really tell uh what it's doing by just
+ 
+
+ align:start position:0%
+really tell uh what it's doing by just
+looking at it but in this case this is
+
+ align:start position:0%
+looking at it but in this case this is
+ 
+
+ align:start position:0%
+looking at it but in this case this is
+one of the is a lethal Factor that's
+
+ align:start position:0%
+one of the is a lethal Factor that's
+ 
+
+ align:start position:0%
+one of the is a lethal Factor that's
+made by Anthrax it's one of the proteins
+
+ align:start position:0%
+made by Anthrax it's one of the proteins
+ 
+
+ align:start position:0%
+made by Anthrax it's one of the proteins
+that Anthrax made makes that's capable
+
+ align:start position:0%
+that Anthrax made makes that's capable
+ 
+
+ align:start position:0%
+that Anthrax made makes that's capable
+of killing you if you get infected with
+
+ align:start position:0%
+of killing you if you get infected with
+ 
+
+ align:start position:0%
+of killing you if you get infected with
+it here's another molecule we'll talk
+
+ align:start position:0%
+it here's another molecule we'll talk
+ 
+
+ align:start position:0%
+it here's another molecule we'll talk
+about in great detail this is DNA it's a
+
+ align:start position:0%
+about in great detail this is DNA it's a
+ 
+
+ align:start position:0%
+about in great detail this is DNA it's a
+you probably all know it's a double
+
+ align:start position:0%
+you probably all know it's a double
+ 
+
+ align:start position:0%
+you probably all know it's a double
+helix two strands of DNA that are held
+
+ align:start position:0%
+helix two strands of DNA that are held
+ 
+
+ align:start position:0%
+helix two strands of DNA that are held
+together by forces will be discussed
+
+ align:start position:0%
+together by forces will be discussed
+ 
+
+ align:start position:0%
+together by forces will be discussed
+it's an absolutely beautiful molecule
+
+ align:start position:0%
+it's an absolutely beautiful molecule
+ 
+
+ align:start position:0%
+it's an absolutely beautiful molecule
+it's fascinated me through all of my
+
+ align:start position:0%
+it's fascinated me through all of my
+ 
+
+ align:start position:0%
+it's fascinated me through all of my
+life and we'll be talking quite a bit
+
+ align:start position:0%
+life and we'll be talking quite a bit
+ 
+
+ align:start position:0%
+life and we'll be talking quite a bit
+about that as the course course goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on okay
+
+ align:start position:0%
+on okay
+ 
+
+ align:start position:0%
+on okay
+so we can if we're thinking about cells
+
+ align:start position:0%
+so we can if we're thinking about cells
+ 
+
+ align:start position:0%
+so we can if we're thinking about cells
+there are two important kinds of cells
+
+ align:start position:0%
+there are two important kinds of cells
+ 
+
+ align:start position:0%
+there are two important kinds of cells
+that one finds on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planet procaryotic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells at least procaryotic organisms
+
+ align:start position:0%
+cells at least procaryotic organisms
+ 
+
+ align:start position:0%
+cells at least procaryotic organisms
+and eukariotic organisms and they each
+
+ align:start position:0%
+and eukariotic organisms and they each
+ 
+
+ align:start position:0%
+and eukariotic organisms and they each
+have are made of cells distinguishable
+
+ align:start position:0%
+have are made of cells distinguishable
+ 
+
+ align:start position:0%
+have are made of cells distinguishable
+from each other i' indicated that a a
+
+ align:start position:0%
+from each other i' indicated that a a
+ 
+
+ align:start position:0%
+from each other i' indicated that a a
+cell is a little bit of the universe
+
+ align:start position:0%
+cell is a little bit of the universe
+ 
+
+ align:start position:0%
+cell is a little bit of the universe
+that's surrounded by a boundary or a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+membrane but inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there some in inside of this is the DNA
+
+ align:start position:0%
+there some in inside of this is the DNA
+ 
+
+ align:start position:0%
+there some in inside of this is the DNA
+which function as the genetic material
+
+ align:start position:0%
+which function as the genetic material
+ 
+
+ align:start position:0%
+which function as the genetic material
+it's the
+
+ align:start position:0%
+it's the
+ 
+
+ align:start position:0%
+it's the
+blueprint for everything that uh that
+
+ align:start position:0%
+blueprint for everything that uh that
+ 
+
+ align:start position:0%
+blueprint for everything that uh that
+cell is going to make and be able to to
+
+ align:start position:0%
+cell is going to make and be able to to
+ 
+
+ align:start position:0%
+cell is going to make and be able to to
+do ultimately everything's encoded there
+
+ align:start position:0%
+do ultimately everything's encoded there
+ 
+
+ align:start position:0%
+do ultimately everything's encoded there
+and in a procaryotic Cell the DNA is
+
+ align:start position:0%
+and in a procaryotic Cell the DNA is
+ 
+
+ align:start position:0%
+and in a procaryotic Cell the DNA is
+free within this uh within this membrane
+
+ align:start position:0%
+free within this uh within this membrane
+ 
+
+ align:start position:0%
+free within this uh within this membrane
+eukaryotic cell also has a membrane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um but the DNA inside is in is uh is
+
+ align:start position:0%
+um but the DNA inside is in is uh is
+ 
+
+ align:start position:0%
+um but the DNA inside is in is uh is
+inside another membrane compartment
+
+ align:start position:0%
+inside another membrane compartment
+ 
+
+ align:start position:0%
+inside another membrane compartment
+known as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleus and this is the DNA uh
+
+ align:start position:0%
+nucleus and this is the DNA uh
+ 
+
+ align:start position:0%
+nucleus and this is the DNA uh
+these procaryotic cells tend to be of
+
+ align:start position:0%
+these procaryotic cells tend to be of
+ 
+
+ align:start position:0%
+these procaryotic cells tend to be of
+the order of uh prometer in length and
+
+ align:start position:0%
+the order of uh prometer in length and
+ 
+
+ align:start position:0%
+the order of uh prometer in length and
+eukariotic cells are usually larger can
+
+ align:start position:0%
+eukariotic cells are usually larger can
+ 
+
+ align:start position:0%
+eukariotic cells are usually larger can
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+uh 10 to 100 parameters um there's quite
+
+ align:start position:0%
+uh 10 to 100 parameters um there's quite
+ 
+
+ align:start position:0%
+uh 10 to 100 parameters um there's quite
+a bit of variation but that gives you at
+
+ align:start position:0%
+a bit of variation but that gives you at
+ 
+
+ align:start position:0%
+a bit of variation but that gives you at
+least some sense of the of the range now
+
+ align:start position:0%
+least some sense of the of the range now
+ 
+
+ align:start position:0%
+least some sense of the of the range now
+I've for years um when I did a diagram
+
+ align:start position:0%
+I've for years um when I did a diagram
+ 
+
+ align:start position:0%
+I've for years um when I did a diagram
+like this I wanted to somehow be able to
+
+ align:start position:0%
+like this I wanted to somehow be able to
+ 
+
+ align:start position:0%
+like this I wanted to somehow be able to
+to show you that these cells were uh
+
+ align:start position:0%
+to show you that these cells were uh
+ 
+
+ align:start position:0%
+to show you that these cells were uh
+interes and just looks on the board so
+
+ align:start position:0%
+interes and just looks on the board so
+ 
+
+ align:start position:0%
+interes and just looks on the board so
+here a couple of pictures just to try
+
+ align:start position:0%
+here a couple of pictures just to try
+ 
+
+ align:start position:0%
+here a couple of pictures just to try
+and do that uh this shows a picture of
+
+ align:start position:0%
+and do that uh this shows a picture of
+ 
+
+ align:start position:0%
+and do that uh this shows a picture of
+eoli uh swimming along and it's um the
+
+ align:start position:0%
+eoli uh swimming along and it's um the
+ 
+
+ align:start position:0%
+eoli uh swimming along and it's um the
+way this image is being taken lets you
+
+ align:start position:0%
+way this image is being taken lets you
+ 
+
+ align:start position:0%
+way this image is being taken lets you
+see what are called fella but which are
+
+ align:start position:0%
+see what are called fella but which are
+ 
+
+ align:start position:0%
+see what are called fella but which are
+basically the uh propellers uh that
+
+ align:start position:0%
+basically the uh propellers uh that
+ 
+
+ align:start position:0%
+basically the uh propellers uh that
+ecoli have that let it swim uh through
+
+ align:start position:0%
+ecoli have that let it swim uh through
+ 
+
+ align:start position:0%
+ecoli have that let it swim uh through
+the water these are uh long structures
+
+ align:start position:0%
+the water these are uh long structures
+ 
+
+ align:start position:0%
+the water these are uh long structures
+made of proteins that are several B
+
+ align:start position:0%
+made of proteins that are several B
+ 
+
+ align:start position:0%
+made of proteins that are several B
+times the body length of the of the
+
+ align:start position:0%
+times the body length of the of the
+ 
+
+ align:start position:0%
+times the body length of the of the
+bacterium and there's a molecular motor
+
+ align:start position:0%
+bacterium and there's a molecular motor
+ 
+
+ align:start position:0%
+bacterium and there's a molecular motor
+embedded in the bacterium that whirls
+
+ align:start position:0%
+embedded in the bacterium that whirls
+ 
+
+ align:start position:0%
+embedded in the bacterium that whirls
+around at about somewhere between 10 and
+
+ align:start position:0%
+around at about somewhere between 10 and
+ 
+
+ align:start position:0%
+around at about somewhere between 10 and
+100,000 000 RPM and that's what drives
+
+ align:start position:0%
+100,000 000 RPM and that's what drives
+ 
+
+ align:start position:0%
+100,000 000 RPM and that's what drives
+the bacterial forward uh so that was a
+
+ align:start position:0%
+the bacterial forward uh so that was a
+ 
+
+ align:start position:0%
+the bacterial forward uh so that was a
+procaryotic cell uh here's a parium this
+
+ align:start position:0%
+procaryotic cell uh here's a parium this
+ 
+
+ align:start position:0%
+procaryotic cell uh here's a parium this
+is a single celled eukaryotic organism
+
+ align:start position:0%
+is a single celled eukaryotic organism
+ 
+
+ align:start position:0%
+is a single celled eukaryotic organism
+and as you can see here it's capable of
+
+ align:start position:0%
+and as you can see here it's capable of
+ 
+
+ align:start position:0%
+and as you can see here it's capable of
+movement as well in this case it has
+
+ align:start position:0%
+movement as well in this case it has
+ 
+
+ align:start position:0%
+movement as well in this case it has
+Sil along the uh outside that allow it
+
+ align:start position:0%
+Sil along the uh outside that allow it
+ 
+
+ align:start position:0%
+Sil along the uh outside that allow it
+to to move here's an interesting one I
+
+ align:start position:0%
+to to move here's an interesting one I
+ 
+
+ align:start position:0%
+to to move here's an interesting one I
+don't know if any of you could guess
+
+ align:start position:0%
+don't know if any of you could guess
+ 
+
+ align:start position:0%
+don't know if any of you could guess
+what these were these were cells from
+
+ align:start position:0%
+what these were these were cells from
+ 
+
+ align:start position:0%
+what these were these were cells from
+the skin of a mouse um they're on a a
+
+ align:start position:0%
+the skin of a mouse um they're on a a
+ 
+
+ align:start position:0%
+the skin of a mouse um they're on a a
+surface augur surface and as you can see
+
+ align:start position:0%
+surface augur surface and as you can see
+ 
+
+ align:start position:0%
+surface augur surface and as you can see
+they too can move there are a couple of
+
+ align:start position:0%
+they too can move there are a couple of
+ 
+
+ align:start position:0%
+they too can move there are a couple of
+things are important about this um I I
+
+ align:start position:0%
+things are important about this um I I
+ 
+
+ align:start position:0%
+things are important about this um I I
+got this uh slide from Linda Griffith
+
+ align:start position:0%
+got this uh slide from Linda Griffith
+ 
+
+ align:start position:0%
+got this uh slide from Linda Griffith
+who's in the biological engineering
+
+ align:start position:0%
+who's in the biological engineering
+ 
+
+ align:start position:0%
+who's in the biological engineering
+department the time I got it for I think
+
+ align:start position:0%
+department the time I got it for I think
+ 
+
+ align:start position:0%
+department the time I got it for I think
+it was in chemical engineering was uh
+
+ align:start position:0%
+it was in chemical engineering was uh
+ 
+
+ align:start position:0%
+it was in chemical engineering was uh
+several years ago when I got this and um
+
+ align:start position:0%
+several years ago when I got this and um
+ 
+
+ align:start position:0%
+several years ago when I got this and um
+what's what was important about this uh
+
+ align:start position:0%
+what's what was important about this uh
+ 
+
+ align:start position:0%
+what's what was important about this uh
+apart from it being a a very nice little
+
+ align:start position:0%
+apart from it being a a very nice little
+ 
+
+ align:start position:0%
+apart from it being a a very nice little
+movie showing you a a Mamon cell uh
+
+ align:start position:0%
+movie showing you a a Mamon cell uh
+ 
+
+ align:start position:0%
+movie showing you a a Mamon cell uh
+moving around was that I got it uh I
+
+ align:start position:0%
+moving around was that I got it uh I
+ 
+
+ align:start position:0%
+moving around was that I got it uh I
+heard saind to show this during one of
+
+ align:start position:0%
+heard saind to show this during one of
+ 
+
+ align:start position:0%
+heard saind to show this during one of
+her research seminars so here is an
+
+ align:start position:0%
+her research seminars so here is an
+ 
+
+ align:start position:0%
+her research seminars so here is an
+engineer at uh MIT who was showing this
+
+ align:start position:0%
+engineer at uh MIT who was showing this
+ 
+
+ align:start position:0%
+engineer at uh MIT who was showing this
+picture as part of her her research talk
+
+ align:start position:0%
+picture as part of her her research talk
+ 
+
+ align:start position:0%
+picture as part of her her research talk
+and I think those of you who are going
+
+ align:start position:0%
+and I think those of you who are going
+ 
+
+ align:start position:0%
+and I think those of you who are going
+on engineering you may be surprised at
+
+ align:start position:0%
+on engineering you may be surprised at
+ 
+
+ align:start position:0%
+on engineering you may be surprised at
+the extent to which you need to know
+
+ align:start position:0%
+the extent to which you need to know
+ 
+
+ align:start position:0%
+the extent to which you need to know
+about uh biology as you go through your
+
+ align:start position:0%
+about uh biology as you go through your
+ 
+
+ align:start position:0%
+about uh biology as you go through your
+your professional careers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um so one of the uh great
+
+ align:start position:0%
+okay um so one of the uh great
+ 
+
+ align:start position:0%
+okay um so one of the uh great
+discoveries that has happened over the
+
+ align:start position:0%
+discoveries that has happened over the
+ 
+
+ align:start position:0%
+discoveries that has happened over the
+last few years that came out of our
+
+ align:start position:0%
+last few years that came out of our
+ 
+
+ align:start position:0%
+last few years that came out of our
+ability to look at DNA and and uh and
+
+ align:start position:0%
+ability to look at DNA and and uh and
+ 
+
+ align:start position:0%
+ability to look at DNA and and uh and
+RNA was the discovery that
+
+ align:start position:0%
+RNA was the discovery that
+ 
+
+ align:start position:0%
+RNA was the discovery that
+that uh the forms of life that are
+
+ align:start position:0%
+that uh the forms of life that are
+ 
+
+ align:start position:0%
+that uh the forms of life that are
+procaryotic
+
+ align:start position:0%
+procaryotic
+ 
+
+ align:start position:0%
+procaryotic
+actually split into two distinct
+
+ align:start position:0%
+actually split into two distinct
+ 
+
+ align:start position:0%
+actually split into two distinct
+kingdoms that are very very different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ARA and the bacteria and just to give
+
+ align:start position:0%
+ARA and the bacteria and just to give
+ 
+
+ align:start position:0%
+ARA and the bacteria and just to give
+you a sense of uh the diversity of Life
+
+ align:start position:0%
+you a sense of uh the diversity of Life
+ 
+
+ align:start position:0%
+you a sense of uh the diversity of Life
+I'll just mention a couple of these
+
+ align:start position:0%
+I'll just mention a couple of these
+ 
+
+ align:start position:0%
+I'll just mention a couple of these
+these ARA uh look like bacteria but
+
+ align:start position:0%
+these ARA uh look like bacteria but
+ 
+
+ align:start position:0%
+these ARA uh look like bacteria but
+there is diverged uh from the bacteria
+
+ align:start position:0%
+there is diverged uh from the bacteria
+ 
+
+ align:start position:0%
+there is diverged uh from the bacteria
+as they are from the UK carots uh so
+
+ align:start position:0%
+as they are from the UK carots uh so
+ 
+
+ align:start position:0%
+as they are from the UK carots uh so
+there were sort of three really major
+
+ align:start position:0%
+there were sort of three really major
+ 
+
+ align:start position:0%
+there were sort of three really major
+kingdoms of life and the ARA many of
+
+ align:start position:0%
+kingdoms of life and the ARA many of
+ 
+
+ align:start position:0%
+kingdoms of life and the ARA many of
+them can live in specialized uh
+
+ align:start position:0%
+them can live in specialized uh
+ 
+
+ align:start position:0%
+them can live in specialized uh
+environments
+
+ align:start position:0%
+environments
+ 
+
+ align:start position:0%
+environments
+for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sulfolobus can live at about 90 de
+
+ align:start position:0%
+sulfolobus can live at about 90 de
+ 
+
+ align:start position:0%
+sulfolobus can live at about 90 de
+centigrade and a pH of somewhere between
+
+ align:start position:0%
+centigrade and a pH of somewhere between
+ 
+
+ align:start position:0%
+centigrade and a pH of somewhere between
+1 and two and so if you see something
+
+ align:start position:0%
+1 and two and so if you see something
+ 
+
+ align:start position:0%
+1 and two and so if you see something
+like a hot springs there are organisms
+
+ align:start position:0%
+like a hot springs there are organisms
+ 
+
+ align:start position:0%
+like a hot springs there are organisms
+such as this that are able to grow in
+
+ align:start position:0%
+such as this that are able to grow in
+ 
+
+ align:start position:0%
+such as this that are able to grow in
+that environment or there are uh
+
+ align:start position:0%
+that environment or there are uh
+ 
+
+ align:start position:0%
+that environment or there are uh
+halophiles salt loving ARA that can grow
+
+ align:start position:0%
+halophiles salt loving ARA that can grow
+ 
+
+ align:start position:0%
+halophiles salt loving ARA that can grow
+in for example in four
+
+ align:start position:0%
+in for example in four
+ 
+
+ align:start position:0%
+in for example in four
+molar sodium chloride and if you've for
+
+ align:start position:0%
+molar sodium chloride and if you've for
+ 
+
+ align:start position:0%
+molar sodium chloride and if you've for
+example ever flown into San Francisco
+
+ align:start position:0%
+example ever flown into San Francisco
+ 
+
+ align:start position:0%
+example ever flown into San Francisco
+Airport coming up from the south over
+
+ align:start position:0%
+Airport coming up from the south over
+ 
+
+ align:start position:0%
+Airport coming up from the south over
+San Jose you've seen things that look
+
+ align:start position:0%
+San Jose you've seen things that look
+ 
+
+ align:start position:0%
+San Jose you've seen things that look
+sort of like these pictures where um
+
+ align:start position:0%
+sort of like these pictures where um
+ 
+
+ align:start position:0%
+sort of like these pictures where um
+seawat is being evaporated down to
+
+ align:start position:0%
+seawat is being evaporated down to
+ 
+
+ align:start position:0%
+seawat is being evaporated down to
+collect the salt and you'll see they're
+
+ align:start position:0%
+collect the salt and you'll see they're
+ 
+
+ align:start position:0%
+collect the salt and you'll see they're
+colored and the reason they're colored
+
+ align:start position:0%
+colored and the reason they're colored
+ 
+
+ align:start position:0%
+colored and the reason they're colored
+is that these uh Halo bacteria are photo
+
+ align:start position:0%
+is that these uh Halo bacteria are photo
+ 
+
+ align:start position:0%
+is that these uh Halo bacteria are photo
+um bacteria that are able to use light
+
+ align:start position:0%
+um bacteria that are able to use light
+ 
+
+ align:start position:0%
+um bacteria that are able to use light
+as an energy source and they make
+
+ align:start position:0%
+as an energy source and they make
+ 
+
+ align:start position:0%
+as an energy source and they make
+pigments that absorb the light and
+
+ align:start position:0%
+pigments that absorb the light and
+ 
+
+ align:start position:0%
+pigments that absorb the light and
+that's why they're why these uh salt
+
+ align:start position:0%
+that's why they're why these uh salt
+ 
+
+ align:start position:0%
+that's why they're why these uh salt
+um areas get get colored a third example
+
+ align:start position:0%
+um areas get get colored a third example
+ 
+
+ align:start position:0%
+um areas get get colored a third example
+would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+methanogens these are uh organisms that
+
+ align:start position:0%
+methanogens these are uh organisms that
+ 
+
+ align:start position:0%
+methanogens these are uh organisms that
+produce methane if you've walked into a
+
+ align:start position:0%
+produce methane if you've walked into a
+ 
+
+ align:start position:0%
+produce methane if you've walked into a
+lake and stepped on the bottom and seen
+
+ align:start position:0%
+lake and stepped on the bottom and seen
+ 
+
+ align:start position:0%
+lake and stepped on the bottom and seen
+little bubbles come up those are uh
+
+ align:start position:0%
+little bubbles come up those are uh
+ 
+
+ align:start position:0%
+little bubbles come up those are uh
+little bubbles of of methane or uh
+
+ align:start position:0%
+little bubbles of of methane or uh
+ 
+
+ align:start position:0%
+little bubbles of of methane or uh
+another place where you find methanogens
+
+ align:start position:0%
+another place where you find methanogens
+ 
+
+ align:start position:0%
+another place where you find methanogens
+are inside of cows now some of you may
+
+ align:start position:0%
+are inside of cows now some of you may
+ 
+
+ align:start position:0%
+are inside of cows now some of you may
+not know uh that a cow is more or less a
+
+ align:start position:0%
+not know uh that a cow is more or less a
+ 
+
+ align:start position:0%
+not know uh that a cow is more or less a
+uh walking uh anerobic
+
+ align:start position:0%
+uh walking uh anerobic
+ 
+
+ align:start position:0%
+uh walking uh anerobic
+fermenter here if we have
+
+ align:start position:0%
+fermenter here if we have
+ 
+
+ align:start position:0%
+fermenter here if we have
+a an anatomically correct uh picture of
+
+ align:start position:0%
+a an anatomically correct uh picture of
+ 
+
+ align:start position:0%
+a an anatomically correct uh picture of
+a of a cow uh the inside of the cow
+
+ align:start position:0%
+a of a cow uh the inside of the cow
+ 
+
+ align:start position:0%
+a of a cow uh the inside of the cow
+there's a large
+
+ align:start position:0%
+there's a large
+ 
+
+ align:start position:0%
+there's a large
+chamber as the rumin which where there's
+
+ align:start position:0%
+chamber as the rumin which where there's
+ 
+
+ align:start position:0%
+chamber as the rumin which where there's
+no oxygen and there's a culture of micro
+
+ align:start position:0%
+no oxygen and there's a culture of micro
+ 
+
+ align:start position:0%
+no oxygen and there's a culture of micro
+organisms there that includes
+
+ align:start position:0%
+organisms there that includes
+ 
+
+ align:start position:0%
+organisms there that includes
+methanogens and it's this combination of
+
+ align:start position:0%
+methanogens and it's this combination of
+ 
+
+ align:start position:0%
+methanogens and it's this combination of
+microorganisms that en cows to uh eat
+
+ align:start position:0%
+microorganisms that en cows to uh eat
+ 
+
+ align:start position:0%
+microorganisms that en cows to uh eat
+grass that we can't manage to uh get
+
+ align:start position:0%
+grass that we can't manage to uh get
+ 
+
+ align:start position:0%
+grass that we can't manage to uh get
+energy from and as a byproduct uh of
+
+ align:start position:0%
+energy from and as a byproduct uh of
+ 
+
+ align:start position:0%
+energy from and as a byproduct uh of
+this specialized type of metabolism
+
+ align:start position:0%
+this specialized type of metabolism
+ 
+
+ align:start position:0%
+this specialized type of metabolism
+produces methane and a cow burps
+
+ align:start position:0%
+produces methane and a cow burps
+ 
+
+ align:start position:0%
+produces methane and a cow burps
+something of the order of 400 liters a
+
+ align:start position:0%
+something of the order of 400 liters a
+ 
+
+ align:start position:0%
+something of the order of 400 liters a
+day of uh of
+
+ align:start position:0%
+day of uh of
+ 
+
+ align:start position:0%
+day of uh of
+methane okay so one last thing then
+
+ align:start position:0%
+methane okay so one last thing then
+ 
+
+ align:start position:0%
+methane okay so one last thing then
+that's just to kind of pull this all
+
+ align:start position:0%
+that's just to kind of pull this all
+ 
+
+ align:start position:0%
+that's just to kind of pull this all
+together is that these organel that I
+
+ align:start position:0%
+together is that these organel that I
+ 
+
+ align:start position:0%
+together is that these organel that I
+mentioned which
+
+ align:start position:0%
+mentioned which
+ 
+
+ align:start position:0%
+mentioned which
+are also membrane compartments that are
+
+ align:start position:0%
+are also membrane compartments that are
+ 
+
+ align:start position:0%
+are also membrane compartments that are
+found in eukariotic cells and either
+
+ align:start position:0%
+found in eukariotic cells and either
+ 
+
+ align:start position:0%
+found in eukariotic cells and either
+could are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mitochondria uh or
+
+ align:start position:0%
+mitochondria uh or
+ 
+
+ align:start position:0%
+mitochondria uh or
+chloroplast uh there's pretty strong
+
+ align:start position:0%
+chloroplast uh there's pretty strong
+ 
+
+ align:start position:0%
+chloroplast uh there's pretty strong
+evidence at this point that these aose
+
+ align:start position:0%
+evidence at this point that these aose
+ 
+
+ align:start position:0%
+evidence at this point that these aose
+from bacteria that were things that that
+
+ align:start position:0%
+from bacteria that were things that that
+ 
+
+ align:start position:0%
+from bacteria that were things that that
+we've uh you're more familiar with
+
+ align:start position:0%
+we've uh you're more familiar with
+ 
+
+ align:start position:0%
+we've uh you're more familiar with
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+like eoli
+
+ align:start position:0%
+like eoli
+ 
+
+ align:start position:0%
+like eoli
+or streptococus
+
+ align:start position:0%
+or streptococus
+ 
+
+ align:start position:0%
+or streptococus
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um causes strep throat or
+
+ align:start position:0%
+um causes strep throat or
+ 
+
+ align:start position:0%
+um causes strep throat or
+um uh the lactic acid bacteria that
+
+ align:start position:0%
+um uh the lactic acid bacteria that
+ 
+
+ align:start position:0%
+um uh the lactic acid bacteria that
+cause the the milk to turn into yogurt
+
+ align:start position:0%
+cause the the milk to turn into yogurt
+ 
+
+ align:start position:0%
+cause the the milk to turn into yogurt
+which some of you probably had for for
+
+ align:start position:0%
+which some of you probably had for for
+ 
+
+ align:start position:0%
+which some of you probably had for for
+lunch today that these organel the
+
+ align:start position:0%
+lunch today that these organel the
+ 
+
+ align:start position:0%
+lunch today that these organel the
+mitochondria and the chloroplast were
+
+ align:start position:0%
+mitochondria and the chloroplast were
+ 
+
+ align:start position:0%
+mitochondria and the chloroplast were
+derived from particular type of bacteria
+
+ align:start position:0%
+derived from particular type of bacteria
+ 
+
+ align:start position:0%
+derived from particular type of bacteria
+that probably first got transiently
+
+ align:start position:0%
+that probably first got transiently
+ 
+
+ align:start position:0%
+that probably first got transiently
+associated with developing eukariotic
+
+ align:start position:0%
+associated with developing eukariotic
+ 
+
+ align:start position:0%
+associated with developing eukariotic
+cells sometime back in evolution and
+
+ align:start position:0%
+cells sometime back in evolution and
+ 
+
+ align:start position:0%
+cells sometime back in evolution and
+eventually became captured and became a
+
+ align:start position:0%
+eventually became captured and became a
+ 
+
+ align:start position:0%
+eventually became captured and became a
+permanent part of the uh of the
+
+ align:start position:0%
+permanent part of the uh of the
+ 
+
+ align:start position:0%
+permanent part of the uh of the
+eukariotic cell the mitochondrian is
+
+ align:start position:0%
+eukariotic cell the mitochondrian is
+ 
+
+ align:start position:0%
+eukariotic cell the mitochondrian is
+thought to derived from something that
+
+ align:start position:0%
+thought to derived from something that
+ 
+
+ align:start position:0%
+thought to derived from something that
+looks like today's present day risia
+
+ align:start position:0%
+looks like today's present day risia
+ 
+
+ align:start position:0%
+looks like today's present day risia
+which we'll talk about that form an
+
+ align:start position:0%
+which we'll talk about that form an
+ 
+
+ align:start position:0%
+which we'll talk about that form an
+intracellular infection of plants a rsia
+
+ align:start position:0%
+intracellular infection of plants a rsia
+ 
+
+ align:start position:0%
+intracellular infection of plants a rsia
+which is a chronic intracellular
+
+ align:start position:0%
+which is a chronic intracellular
+ 
+
+ align:start position:0%
+which is a chronic intracellular
+pathogen the mitochondria looked as
+
+ align:start position:0%
+pathogen the mitochondria looked as
+ 
+
+ align:start position:0%
+pathogen the mitochondria looked as
+though they came from something related
+
+ align:start position:0%
+though they came from something related
+ 
+
+ align:start position:0%
+though they came from something related
+to that the chloroplasts look as though
+
+ align:start position:0%
+to that the chloroplasts look as though
+ 
+
+ align:start position:0%
+to that the chloroplasts look as though
+they came from um a bacterium that was
+
+ align:start position:0%
+they came from um a bacterium that was
+ 
+
+ align:start position:0%
+they came from um a bacterium that was
+able to carry out photosynthesis which
+
+ align:start position:0%
+able to carry out photosynthesis which
+ 
+
+ align:start position:0%
+able to carry out photosynthesis which
+will also be talking about so I want to
+
+ align:start position:0%
+will also be talking about so I want to
+ 
+
+ align:start position:0%
+will also be talking about so I want to
+close by giving you just a quick little
+
+ align:start position:0%
+close by giving you just a quick little
+ 
+
+ align:start position:0%
+close by giving you just a quick little
+snapshot of evolution because I'm hoping
+
+ align:start position:0%
+snapshot of evolution because I'm hoping
+ 
+
+ align:start position:0%
+snapshot of evolution because I'm hoping
+this will maybe make some of the things
+
+ align:start position:0%
+this will maybe make some of the things
+ 
+
+ align:start position:0%
+this will maybe make some of the things
+that we talk about in this course
+
+ align:start position:0%
+that we talk about in this course
+ 
+
+ align:start position:0%
+that we talk about in this course
+clearer so what we're going to
+
+ align:start position:0%
+clearer so what we're going to
+ 
+
+ align:start position:0%
+clearer so what we're going to
+do is we're going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to look back from
+
+ align:start position:0%
+to look back from
+ 
+
+ align:start position:0%
+to look back from
+4.5 billion years ago when the Earth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was the Earth was just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forming so now and I'm just going to try
+
+ align:start position:0%
+forming so now and I'm just going to try
+ 
+
+ align:start position:0%
+forming so now and I'm just going to try
+and give a few uh key things sort of
+
+ align:start position:0%
+and give a few uh key things sort of
+ 
+
+ align:start position:0%
+and give a few uh key things sort of
+landmarks as we as we go along
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so about 4.5 billion years ago there was
+
+ align:start position:0%
+so about 4.5 billion years ago there was
+ 
+
+ align:start position:0%
+so about 4.5 billion years ago there was
+methane carbon
+
+ align:start position:0%
+methane carbon
+ 
+
+ align:start position:0%
+methane carbon
+dioxide ammonium hydrogen gas nitrogen
+
+ align:start position:0%
+dioxide ammonium hydrogen gas nitrogen
+ 
+
+ align:start position:0%
+dioxide ammonium hydrogen gas nitrogen
+gas water but
+
+ align:start position:0%
+gas water but
+ 
+
+ align:start position:0%
+gas water but
+importantly no oxygen at that point now
+
+ align:start position:0%
+importantly no oxygen at that point now
+ 
+
+ align:start position:0%
+importantly no oxygen at that point now
+there's a lot of debate as to how uh
+
+ align:start position:0%
+there's a lot of debate as to how uh
+ 
+
+ align:start position:0%
+there's a lot of debate as to how uh
+life initially came one of the prevalent
+
+ align:start position:0%
+life initially came one of the prevalent
+ 
+
+ align:start position:0%
+life initially came one of the prevalent
+theories at this point is there's
+
+ align:start position:0%
+theories at this point is there's
+ 
+
+ align:start position:0%
+theories at this point is there's
+something called an RNA world this is
+
+ align:start position:0%
+something called an RNA world this is
+ 
+
+ align:start position:0%
+something called an RNA world this is
+just a
+
+ align:start position:0%
+just a
+ 
+
+ align:start position:0%
+just a
+hypothesis in which it's thought that
+
+ align:start position:0%
+hypothesis in which it's thought that
+ 
+
+ align:start position:0%
+hypothesis in which it's thought that
+perhaps the molecule RNA which we'll
+
+ align:start position:0%
+perhaps the molecule RNA which we'll
+ 
+
+ align:start position:0%
+perhaps the molecule RNA which we'll
+talk about played role as both uh an
+
+ align:start position:0%
+talk about played role as both uh an
+ 
+
+ align:start position:0%
+talk about played role as both uh an
+something that was able to catalyze
+
+ align:start position:0%
+something that was able to catalyze
+ 
+
+ align:start position:0%
+something that was able to catalyze
+chemical reactions and therefore did
+
+ align:start position:0%
+chemical reactions and therefore did
+ 
+
+ align:start position:0%
+chemical reactions and therefore did
+things actively and also stored uh
+
+ align:start position:0%
+things actively and also stored uh
+ 
+
+ align:start position:0%
+things actively and also stored uh
+information but in any case the best
+
+ align:start position:0%
+information but in any case the best
+ 
+
+ align:start position:0%
+information but in any case the best
+guess is that the
+
+ align:start position:0%
+guess is that the
+ 
+
+ align:start position:0%
+guess is that the
+first life that
+
+ align:start position:0%
+first life that
+ 
+
+ align:start position:0%
+first life that
+uh was about 3.8 billion years ago
+
+ align:start position:0%
+uh was about 3.8 billion years ago
+ 
+
+ align:start position:0%
+uh was about 3.8 billion years ago
+somewhere in that vicinity it was
+
+ align:start position:0%
+somewhere in that vicinity it was
+ 
+
+ align:start position:0%
+somewhere in that vicinity it was
+something that probably resembled most
+
+ align:start position:0%
+something that probably resembled most
+ 
+
+ align:start position:0%
+something that probably resembled most
+closely a present day bacterium a single
+
+ align:start position:0%
+closely a present day bacterium a single
+ 
+
+ align:start position:0%
+closely a present day bacterium a single
+celled organism something like that now
+
+ align:start position:0%
+celled organism something like that now
+ 
+
+ align:start position:0%
+celled organism something like that now
+initially when life uh got started it's
+
+ align:start position:0%
+initially when life uh got started it's
+ 
+
+ align:start position:0%
+initially when life uh got started it's
+thought that there were a lot of organic
+
+ align:start position:0%
+thought that there were a lot of organic
+ 
+
+ align:start position:0%
+thought that there were a lot of organic
+chemicals that had been made as a
+
+ align:start position:0%
+chemicals that had been made as a
+ 
+
+ align:start position:0%
+chemicals that had been made as a
+consequence of lightning strikes and all
+
+ align:start position:0%
+consequence of lightning strikes and all
+ 
+
+ align:start position:0%
+consequence of lightning strikes and all
+sorts of chemistry that had happened so
+
+ align:start position:0%
+sorts of chemistry that had happened so
+ 
+
+ align:start position:0%
+sorts of chemistry that had happened so
+there was sort of a soup of some kinds
+
+ align:start position:0%
+there was sort of a soup of some kinds
+ 
+
+ align:start position:0%
+there was sort of a soup of some kinds
+of molecules could be used so probably
+
+ align:start position:0%
+of molecules could be used so probably
+ 
+
+ align:start position:0%
+of molecules could be used so probably
+these first organisms were able to
+
+ align:start position:0%
+these first organisms were able to
+ 
+
+ align:start position:0%
+these first organisms were able to
+basically use some preformed nutrients
+
+ align:start position:0%
+basically use some preformed nutrients
+ 
+
+ align:start position:0%
+basically use some preformed nutrients
+and then as the soup began to get
+
+ align:start position:0%
+and then as the soup began to get
+ 
+
+ align:start position:0%
+and then as the soup began to get
+depleted by using it they had learn to
+
+ align:start position:0%
+depleted by using it they had learn to
+ 
+
+ align:start position:0%
+depleted by using it they had learn to
+synthesize at least develop uh systems
+
+ align:start position:0%
+synthesize at least develop uh systems
+ 
+
+ align:start position:0%
+synthesize at least develop uh systems
+uh that would synthesize these building
+
+ align:start position:0%
+uh that would synthesize these building
+ 
+
+ align:start position:0%
+uh that would synthesize these building
+blocks and they also had to begin to
+
+ align:start position:0%
+blocks and they also had to begin to
+ 
+
+ align:start position:0%
+blocks and they also had to begin to
+worry about what to use as energy and so
+
+ align:start position:0%
+worry about what to use as energy and so
+ 
+
+ align:start position:0%
+worry about what to use as energy and so
+somewhere in here there something that
+
+ align:start position:0%
+somewhere in here there something that
+ 
+
+ align:start position:0%
+somewhere in here there something that
+I'll
+
+ align:start position:0%
+I'll
+ 
+
+ align:start position:0%
+I'll
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+uh in a silly way photo synthesis
+
+ align:start position:0%
+uh in a silly way photo synthesis
+ 
+
+ align:start position:0%
+uh in a silly way photo synthesis
+release number one but this was a system
+
+ align:start position:0%
+release number one but this was a system
+ 
+
+ align:start position:0%
+release number one but this was a system
+that enabled the organism to capture
+
+ align:start position:0%
+that enabled the organism to capture
+ 
+
+ align:start position:0%
+that enabled the organism to capture
+sunlight uh from energy uh energy from
+
+ align:start position:0%
+sunlight uh from energy uh energy from
+ 
+
+ align:start position:0%
+sunlight uh from energy uh energy from
+sunlight so that it wasn't now dependent
+
+ align:start position:0%
+sunlight so that it wasn't now dependent
+ 
+
+ align:start position:0%
+sunlight so that it wasn't now dependent
+on getting energy by eating some
+
+ align:start position:0%
+on getting energy by eating some
+ 
+
+ align:start position:0%
+on getting energy by eating some
+pre-formed ingredient was then able to
+
+ align:start position:0%
+pre-formed ingredient was then able to
+ 
+
+ align:start position:0%
+pre-formed ingredient was then able to
+uh take carbon dioxide and make it into
+
+ align:start position:0%
+uh take carbon dioxide and make it into
+ 
+
+ align:start position:0%
+uh take carbon dioxide and make it into
+forms that were useful of carbon that
+
+ align:start position:0%
+forms that were useful of carbon that
+ 
+
+ align:start position:0%
+forms that were useful of carbon that
+were useful for life and It produced a
+
+ align:start position:0%
+were useful for life and It produced a
+ 
+
+ align:start position:0%
+were useful for life and It produced a
+mo such as sulfur as a waste
+
+ align:start position:0%
+mo such as sulfur as a waste
+ 
+
+ align:start position:0%
+mo such as sulfur as a waste
+product there was a bit later in
+
+ align:start position:0%
+product there was a bit later in
+ 
+
+ align:start position:0%
+product there was a bit later in
+evolution somewhere in here something we
+
+ align:start position:0%
+evolution somewhere in here something we
+ 
+
+ align:start position:0%
+evolution somewhere in here something we
+might s think of as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+photosynthesis release
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two this was an improved version of
+
+ align:start position:0%
+two this was an improved version of
+ 
+
+ align:start position:0%
+two this was an improved version of
+photosynthesis it was captured more
+
+ align:start position:0%
+photosynthesis it was captured more
+ 
+
+ align:start position:0%
+photosynthesis it was captured more
+energy uh worked better uh but it
+
+ align:start position:0%
+energy uh worked better uh but it
+ 
+
+ align:start position:0%
+energy uh worked better uh but it
+developed it had a waste product which
+
+ align:start position:0%
+developed it had a waste product which
+ 
+
+ align:start position:0%
+developed it had a waste product which
+was oxygen oxygen hadn't been in our
+
+ align:start position:0%
+was oxygen oxygen hadn't been in our
+ 
+
+ align:start position:0%
+was oxygen oxygen hadn't been in our
+atmosphere and the first thing that sort
+
+ align:start position:0%
+atmosphere and the first thing that sort
+ 
+
+ align:start position:0%
+atmosphere and the first thing that sort
+of happened was that the world started
+
+ align:start position:0%
+of happened was that the world started
+ 
+
+ align:start position:0%
+of happened was that the world started
+to rust all the iron a lot of the iron
+
+ align:start position:0%
+to rust all the iron a lot of the iron
+ 
+
+ align:start position:0%
+to rust all the iron a lot of the iron
+started to interact with the oxygen and
+
+ align:start position:0%
+started to interact with the oxygen and
+ 
+
+ align:start position:0%
+started to interact with the oxygen and
+Penny will tell you that at the the base
+
+ align:start position:0%
+Penny will tell you that at the the base
+ 
+
+ align:start position:0%
+Penny will tell you that at the the base
+of the sea there are huge beds of iron
+
+ align:start position:0%
+of the sea there are huge beds of iron
+ 
+
+ align:start position:0%
+of the sea there are huge beds of iron
+oxide that came from this slow rusting
+
+ align:start position:0%
+oxide that came from this slow rusting
+ 
+
+ align:start position:0%
+oxide that came from this slow rusting
+of the earth and so it took many many uh
+
+ align:start position:0%
+of the earth and so it took many many uh
+ 
+
+ align:start position:0%
+of the earth and so it took many many uh
+years before oxygen levels started to
+
+ align:start position:0%
+years before oxygen levels started to
+ 
+
+ align:start position:0%
+years before oxygen levels started to
+rise as you know there all about it's
+
+ align:start position:0%
+rise as you know there all about it's
+ 
+
+ align:start position:0%
+rise as you know there all about it's
+about 20% of our atmosphere now even at
+
+ align:start position:0%
+about 20% of our atmosphere now even at
+ 
+
+ align:start position:0%
+about 20% of our atmosphere now even at
+this stage it was only a few percent of
+
+ align:start position:0%
+this stage it was only a few percent of
+ 
+
+ align:start position:0%
+this stage it was only a few percent of
+our um made up a few per of our
+
+ align:start position:0%
+our um made up a few per of our
+ 
+
+ align:start position:0%
+our um made up a few per of our
+atmosphere even by here in
+
+ align:start position:0%
+atmosphere even by here in
+ 
+
+ align:start position:0%
+atmosphere even by here in
+evolution um the first eukariotic cell
+
+ align:start position:0%
+evolution um the first eukariotic cell
+ 
+
+ align:start position:0%
+evolution um the first eukariotic cell
+is thought to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have appeared
+
+ align:start position:0%
+have appeared
+ 
+
+ align:start position:0%
+have appeared
+somewhere here again it was likely a
+
+ align:start position:0%
+somewhere here again it was likely a
+ 
+
+ align:start position:0%
+somewhere here again it was likely a
+single celled organism like some of
+
+ align:start position:0%
+single celled organism like some of
+ 
+
+ align:start position:0%
+single celled organism like some of
+those pictures uh I showed you and
+
+ align:start position:0%
+those pictures uh I showed you and
+ 
+
+ align:start position:0%
+those pictures uh I showed you and
+evolution continued to go somewhere
+
+ align:start position:0%
+evolution continued to go somewhere
+ 
+
+ align:start position:0%
+evolution continued to go somewhere
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+a billion a billion years ago sex was
+
+ align:start position:0%
+a billion a billion years ago sex was
+ 
+
+ align:start position:0%
+a billion a billion years ago sex was
+evolved which enabled eukaryotic uh
+
+ align:start position:0%
+evolved which enabled eukaryotic uh
+ 
+
+ align:start position:0%
+evolved which enabled eukaryotic uh
+organisms to exchange genetic material
+
+ align:start position:0%
+organisms to exchange genetic material
+ 
+
+ align:start position:0%
+organisms to exchange genetic material
+and therefore evolve at a a faster rate
+
+ align:start position:0%
+and therefore evolve at a a faster rate
+ 
+
+ align:start position:0%
+and therefore evolve at a a faster rate
+than they could uh
+
+ align:start position:0%
+than they could uh
+ 
+
+ align:start position:0%
+than they could uh
+previously the Cambrian Period was about
+
+ align:start position:0%
+previously the Cambrian Period was about
+ 
+
+ align:start position:0%
+previously the Cambrian Period was about
+a half a billion
+
+ align:start position:0%
+a half a billion
+ 
+
+ align:start position:0%
+a half a billion
+to6 billion uh years ago and there was a
+
+ align:start position:0%
+to6 billion uh years ago and there was a
+ 
+
+ align:start position:0%
+to6 billion uh years ago and there was a
+veritable explosion of of life forms and
+
+ align:start position:0%
+veritable explosion of of life forms and
+ 
+
+ align:start position:0%
+veritable explosion of of life forms and
+you can still see in the fossil records
+
+ align:start position:0%
+you can still see in the fossil records
+ 
+
+ align:start position:0%
+you can still see in the fossil records
+how much diversity was generated at that
+
+ align:start position:0%
+how much diversity was generated at that
+ 
+
+ align:start position:0%
+how much diversity was generated at that
+point some of which went on to become
+
+ align:start position:0%
+point some of which went on to become
+ 
+
+ align:start position:0%
+point some of which went on to become
+life forms that we know and others which
+
+ align:start position:0%
+life forms that we know and others which
+ 
+
+ align:start position:0%
+life forms that we know and others which
+uh probably were more evolutionary dead
+
+ align:start position:0%
+uh probably were more evolutionary dead
+ 
+
+ align:start position:0%
+uh probably were more evolutionary dead
+ends um finally we get to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dinosaurs we about
+
+ align:start position:0%
+dinosaurs we about
+ 
+
+ align:start position:0%
+dinosaurs we about
+245 to 65
+
+ align:start position:0%
+245 to 65
+ 
+
+ align:start position:0%
+245 to 65
+million years ago which should place
+
+ align:start position:0%
+million years ago which should place
+ 
+
+ align:start position:0%
+million years ago which should place
+them somewhere here on this uh on this
+
+ align:start position:0%
+them somewhere here on this uh on this
+ 
+
+ align:start position:0%
+them somewhere here on this uh on this
+timeline so in honor of this course I
+
+ align:start position:0%
+timeline so in honor of this course I
+ 
+
+ align:start position:0%
+timeline so in honor of this course I
+I've commissioned a uh fully uh full
+
+ align:start position:0%
+I've commissioned a uh fully uh full
+ 
+
+ align:start position:0%
+I've commissioned a uh fully uh full
+scale model here of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an we go um so we'll put uh our our
+
+ align:start position:0%
+an we go um so we'll put uh our our
+ 
+
+ align:start position:0%
+an we go um so we'll put uh our our
+dinosaur here if I can get him to stay
+
+ align:start position:0%
+dinosaur here if I can get him to stay
+ 
+
+ align:start position:0%
+dinosaur here if I can get him to stay
+put for a
+
+ align:start position:0%
+put for a
+ 
+
+ align:start position:0%
+put for a
+minute all right and uh at this point in
+
+ align:start position:0%
+minute all right and uh at this point in
+ 
+
+ align:start position:0%
+minute all right and uh at this point in
+evolution things started to get
+
+ align:start position:0%
+evolution things started to get
+ 
+
+ align:start position:0%
+evolution things started to get
+interesting so somewhere about here we
+
+ align:start position:0%
+interesting so somewhere about here we
+ 
+
+ align:start position:0%
+interesting so somewhere about here we
+uh four four million years ago we got
+
+ align:start position:0%
+uh four four million years ago we got
+ 
+
+ align:start position:0%
+uh four four million years ago we got
+the first evidence of of hominoids uh
+
+ align:start position:0%
+the first evidence of of hominoids uh
+ 
+
+ align:start position:0%
+the first evidence of of hominoids uh
+maybe 20 thousand years ago we found the
+
+ align:start position:0%
+maybe 20 thousand years ago we found the
+ 
+
+ align:start position:0%
+maybe 20 thousand years ago we found the
+cave paintings in in France and then
+
+ align:start position:0%
+cave paintings in in France and then
+ 
+
+ align:start position:0%
+cave paintings in in France and then
+there was the Roman Empire and Columbus
+
+ align:start position:0%
+there was the Roman Empire and Columbus
+ 
+
+ align:start position:0%
+there was the Roman Empire and Columbus
+discovered America and uh you were born
+
+ align:start position:0%
+discovered America and uh you were born
+ 
+
+ align:start position:0%
+discovered America and uh you were born
+in the Red Sox W the uh World Series and
+
+ align:start position:0%
+in the Red Sox W the uh World Series and
+ 
+
+ align:start position:0%
+in the Red Sox W the uh World Series and
+uh the Patriots have just won the Super
+
+ align:start position:0%
+uh the Patriots have just won the Super
+ 
+
+ align:start position:0%
+uh the Patriots have just won the Super
+Bowl and we are now here
+
+ align:start position:0%
+Bowl and we are now here
+ 
+
+ align:start position:0%
+Bowl and we are now here
+uh at the peak of evolution uh which is
+
+ align:start position:0%
+uh at the peak of evolution uh which is
+ 
+
+ align:start position:0%
+uh at the peak of evolution uh which is
+as you all know is the MIT student so
+
+ align:start position:0%
+as you all know is the MIT student so
+ 
+
+ align:start position:0%
+as you all know is the MIT student so
+we'll put this our MIT student here who
+
+ align:start position:0%
+we'll put this our MIT student here who
+ 
+
+ align:start position:0%
+we'll put this our MIT student here who
+I can probably not get to stay put
+
+ align:start position:0%
+I can probably not get to stay put
+ 
+
+ align:start position:0%
+I can probably not get to stay put
+because you never get MIT students to
+
+ align:start position:0%
+because you never get MIT students to
+ 
+
+ align:start position:0%
+because you never get MIT students to
+stay anywhere but any case this is sort
+
+ align:start position:0%
+stay anywhere but any case this is sort
+ 
+
+ align:start position:0%
+stay anywhere but any case this is sort
+of a silly demonstration but there's a
+
+ align:start position:0%
+of a silly demonstration but there's a
+ 
+
+ align:start position:0%
+of a silly demonstration but there's a
+very profound uh reason why I'm doing it
+
+ align:start position:0%
+very profound uh reason why I'm doing it
+ 
+
+ align:start position:0%
+very profound uh reason why I'm doing it
+and I must say I don't think I'd ever
+
+ align:start position:0%
+and I must say I don't think I'd ever
+ 
+
+ align:start position:0%
+and I must say I don't think I'd ever
+fully appreciated it until I actually
+
+ align:start position:0%
+fully appreciated it until I actually
+ 
+
+ align:start position:0%
+fully appreciated it until I actually
+thought of doing this this demo for the
+
+ align:start position:0%
+thought of doing this this demo for the
+ 
+
+ align:start position:0%
+thought of doing this this demo for the
+class but what I think you you can see
+
+ align:start position:0%
+class but what I think you you can see
+ 
+
+ align:start position:0%
+class but what I think you you can see
+is that uh Evolution for the most part
+
+ align:start position:0%
+is that uh Evolution for the most part
+ 
+
+ align:start position:0%
+is that uh Evolution for the most part
+happened at the Single Cell level many
+
+ align:start position:0%
+happened at the Single Cell level many
+ 
+
+ align:start position:0%
+happened at the Single Cell level many
+people tended to think oh Evolution that
+
+ align:start position:0%
+people tended to think oh Evolution that
+ 
+
+ align:start position:0%
+people tended to think oh Evolution that
+was about dinosaurs and all that stuff
+
+ align:start position:0%
+was about dinosaurs and all that stuff
+ 
+
+ align:start position:0%
+was about dinosaurs and all that stuff
+you can see the dinosaurs are
+
+ align:start position:0%
+you can see the dinosaurs are
+ 
+
+ align:start position:0%
+you can see the dinosaurs are
+practically now most of evolution
+
+ align:start position:0%
+practically now most of evolution
+ 
+
+ align:start position:0%
+practically now most of evolution
+occurred at the level of single cells
+
+ align:start position:0%
+occurred at the level of single cells
+ 
+
+ align:start position:0%
+occurred at the level of single cells
+that's all this amazing diversity we see
+
+ align:start position:0%
+that's all this amazing diversity we see
+ 
+
+ align:start position:0%
+that's all this amazing diversity we see
+around us was very recent uh um
+
+ align:start position:0%
+around us was very recent uh um
+ 
+
+ align:start position:0%
+around us was very recent uh um
+embellishments in evolution so that
+
+ align:start position:0%
+embellishments in evolution so that
+ 
+
+ align:start position:0%
+embellishments in evolution so that
+means that when you study biology at the
+
+ align:start position:0%
+means that when you study biology at the
+ 
+
+ align:start position:0%
+means that when you study biology at the
+cellular and molecular level you find
+
+ align:start position:0%
+cellular and molecular level you find
+ 
+
+ align:start position:0%
+cellular and molecular level you find
+tremendous commonalities if you look
+
+ align:start position:0%
+tremendous commonalities if you look
+ 
+
+ align:start position:0%
+tremendous commonalities if you look
+inside uh a sulfolobus growing in a hot
+
+ align:start position:0%
+inside uh a sulfolobus growing in a hot
+ 
+
+ align:start position:0%
+inside uh a sulfolobus growing in a hot
+spring you look inside an ecoli you look
+
+ align:start position:0%
+spring you look inside an ecoli you look
+ 
+
+ align:start position:0%
+spring you look inside an ecoli you look
+inside a yeast and you look inside one
+
+ align:start position:0%
+inside a yeast and you look inside one
+ 
+
+ align:start position:0%
+inside a yeast and you look inside one
+of our cells you find that to a huge
+
+ align:start position:0%
+of our cells you find that to a huge
+ 
+
+ align:start position:0%
+of our cells you find that to a huge
+extent uh all the cell many many of the
+
+ align:start position:0%
+extent uh all the cell many many of the
+ 
+
+ align:start position:0%
+extent uh all the cell many many of the
+cellular components are common they
+
+ align:start position:0%
+cellular components are common they
+ 
+
+ align:start position:0%
+cellular components are common they
+arose so early in evolution that they're
+
+ align:start position:0%
+arose so early in evolution that they're
+ 
+
+ align:start position:0%
+arose so early in evolution that they're
+shared by all forms of life of course
+
+ align:start position:0%
+shared by all forms of life of course
+ 
+
+ align:start position:0%
+shared by all forms of life of course
+there's some things that develop later
+
+ align:start position:0%
+there's some things that develop later
+ 
+
+ align:start position:0%
+there's some things that develop later
+and are different but that's one of the
+
+ align:start position:0%
+and are different but that's one of the
+ 
+
+ align:start position:0%
+and are different but that's one of the
+reasons that you can learn so much by
+
+ align:start position:0%
+reasons that you can learn so much by
+ 
+
+ align:start position:0%
+reasons that you can learn so much by
+studying biology at the cellular
+
+ align:start position:0%
+studying biology at the cellular
+ 
+
+ align:start position:0%
+studying biology at the cellular
+molecular level and while we'll why
+
+ align:start position:0%
+molecular level and while we'll why
+ 
+
+ align:start position:0%
+molecular level and while we'll why
+we'll emphasize it a fair bit um in this
+
+ align:start position:0%
+we'll emphasize it a fair bit um in this
+ 
+
+ align:start position:0%
+we'll emphasize it a fair bit um in this
+uh in this course the other thing that
+
+ align:start position:0%
+uh in this course the other thing that
+ 
+
+ align:start position:0%
+uh in this course the other thing that
+I'd U like to make out of this theme
+
+ align:start position:0%
+I'd U like to make out of this theme
+ 
+
+ align:start position:0%
+I'd U like to make out of this theme
+that you'll hear along is in that is
+
+ align:start position:0%
+that you'll hear along is in that is
+ 
+
+ align:start position:0%
+that you'll hear along is in that is
+that organisms U modify their
+
+ align:start position:0%
+that organisms U modify their
+ 
+
+ align:start position:0%
+that organisms U modify their
+environment you can see that in the case
+
+ align:start position:0%
+environment you can see that in the case
+ 
+
+ align:start position:0%
+environment you can see that in the case
+of oxygen back when the Earth formed uh
+
+ align:start position:0%
+of oxygen back when the Earth formed uh
+ 
+
+ align:start position:0%
+of oxygen back when the Earth formed uh
+there was no oxygen in our atmosphere
+
+ align:start position:0%
+there was no oxygen in our atmosphere
+ 
+
+ align:start position:0%
+there was no oxygen in our atmosphere
+now we have a lot of it the reason it's
+
+ align:start position:0%
+now we have a lot of it the reason it's
+ 
+
+ align:start position:0%
+now we have a lot of it the reason it's
+there is because it was generated by uh
+
+ align:start position:0%
+there is because it was generated by uh
+ 
+
+ align:start position:0%
+there is because it was generated by uh
+organisms carrying out photosynthesis
+
+ align:start position:0%
+organisms carrying out photosynthesis
+ 
+
+ align:start position:0%
+organisms carrying out photosynthesis
+and generating oxygen as a waste product
+
+ align:start position:0%
+and generating oxygen as a waste product
+ 
+
+ align:start position:0%
+and generating oxygen as a waste product
+and uh that was an absolutely critical
+
+ align:start position:0%
+and uh that was an absolutely critical
+ 
+
+ align:start position:0%
+and uh that was an absolutely critical
+thing to enable creatures such of
+
+ align:start position:0%
+thing to enable creatures such of
+ 
+
+ align:start position:0%
+thing to enable creatures such of
+ourselves which are dependent on on
+
+ align:start position:0%
+ourselves which are dependent on on
+ 
+
+ align:start position:0%
+ourselves which are dependent on on
+oxygen for our for our just to even be
+
+ align:start position:0%
+oxygen for our for our just to even be
+ 
+
+ align:start position:0%
+oxygen for our for our just to even be
+alive um if we hadn't had this change in
+
+ align:start position:0%
+alive um if we hadn't had this change in
+ 
+
+ align:start position:0%
+alive um if we hadn't had this change in
+environment uh things like us couldn't
+
+ align:start position:0%
+environment uh things like us couldn't
+ 
+
+ align:start position:0%
+environment uh things like us couldn't
+have organisms like us couldn't have
+
+ align:start position:0%
+have organisms like us couldn't have
+ 
+
+ align:start position:0%
+have organisms like us couldn't have
+evolved so anyway um I hope that will
+
+ align:start position:0%
+evolved so anyway um I hope that will
+ 
+
+ align:start position:0%
+evolved so anyway um I hope that will
+give you a little sort of snapshot of
+
+ align:start position:0%
+give you a little sort of snapshot of
+ 
+
+ align:start position:0%
+give you a little sort of snapshot of
+evolution and will help guide your
+
+ align:start position:0%
+evolution and will help guide your
+ 
+
+ align:start position:0%
+evolution and will help guide your
+understanding of this course we'll see
+
+ align:start position:0%
+understanding of this course we'll see
+ 
+
+ align:start position:0%
+understanding of this course we'll see
+you at the next lecture
\ No newline at end of file
diff --git a/m9AJwUCAWGQ.txt b/m9AJwUCAWGQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b7562fe5f0fa07b4d3986e6c5bee8d2a73e572c9
--- /dev/null
+++ b/m9AJwUCAWGQ.txt
@@ -0,0 +1,1807 @@
+The following content is
+provided by MIT OpenCourseWare
+
+under a Creative Commons
+license.
+
+Additional information about
+our license and MIT
+
+OpenCourseWare in general is
+available at ocw.mit.edu.
+
+Where were we,
+last time?
+
+Last time, we said we were
+setting aside the problem of the
+
+structure of the atom.
+We were setting it aside
+
+because we were stuck,
+and what we had to do was to
+
+look at another area of
+discussion.
+
+And that is this wave-particle
+duality of light and matter,
+
+because it is that discussion
+that is going to give us the
+
+clues about how to proceed.
+We are putting aside the
+
+discussion of the structure of
+the atom all the way until next
+
+Wednesday, because next Monday,
+I was reminded,
+
+is a student holiday.
+[APPLAUSE]
+
+And so we started.
+We talked about the wave-like
+
+properties of light.
+We said that the property of
+
+superposition,
+the fact that you can put waves
+
+at the same point in space and
+their amplitudes add.
+
+Since waves have both positive
+and negative amplitude,
+
+that means that you have
+constructive and destructive
+
+interference.
+And it is those interference
+
+phenomena, then,
+that are evidence for wave-like
+
+property.
+And we did the two-slit
+
+experiment to try to give you an
+example of interference
+
+phenomena.
+We were trying to understand
+
+those interference phenomena,
+and did so in terms of this
+
+diagram here.
+The interference phenomena that
+
+we saw was an array,
+actually a row of bright spots,
+
+dark spots, bright spots,
+dark spots.
+
+And we drew these semicircles
+here around each one of the
+
+slits.
+They represent a little bit of
+
+the wave that emanated through
+those slits.
+
+Because those slits are small,
+then, those waves emanated
+
+equally in all directions.
+That is why these semicircles
+
+represent the wave maxima.
+And what we discovered is that
+
+if we looked along this line
+here, this line which led to
+
+this bright spot,
+that all of the waves along
+
+this line were constructively
+interfering.
+
+That is, we had the maximum of
+the two waves at the same point
+
+in space, or the minimum of the
+two waves at the same point in
+
+space.
+And we noticed that everywhere
+
+along this line,
+where we had that constructive
+
+interference,
+the difference in the distance
+
+of the waves traveled was one
+lambda.
+
+We noticed, here,
+that everywhere along this line
+
+that led to a very bright spot,
+we had constructive
+
+interference.
+And the difference in distance
+
+traveled by those two waves was
+two lambda.
+
+And, likewise,
+up here, along this line,
+
+the difference in the distance
+traveled was zero lambda.
+
+And from just that,
+in a sense, qualitative
+
+observation, we drew a
+conclusion.
+
+And that conclusion was in
+order to get maximum
+
+constructive interference,
+a condition that had obtain,
+
+is that the difference in the
+distance traveled by the two
+
+waves has to be an integral
+multiple of the wavelength.
+
+N could be 0,
+1, 2, 3, etc.
+
+And so, the very bright spot
+here that always bisects the two
+
+slits, since N is 0,
+we call that the zero-order
+
+interference feature,
+or the zero-order fraction
+
+feature.
+The bright spot that is either
+
+to the left or to the right or
+up or down of that center bright
+
+spot is the first-order
+diffraction feature or the
+
+first-order interference
+feature.
+
+And then the second bright spot
+up or down from the center is a
+
+second-order diffraction
+feature.
+
+And so on and so on.
+And in recitation section,
+
+what you also should have done,
+is you should have reasoned
+
+through what the condition was
+for destructive interference.
+
+That is in between these bright
+spots, you have dark spots as a
+
+result of destructive
+interference.
+
+And that results because,
+say, right here you get a dark
+
+spot --
+Right here at that point you
+
+would see the maximum of one
+wave at the same point in space
+
+as the minimum of the other,
+and so they exactly cancel.
+
+And so by just analyzing what
+waves were destructively
+
+interfering, you should have
+come up with a general
+
+expression for destructive
+interference,
+
+of N plus one-half,
+that quanity,
+
+times lambda.
+That is your general condition
+
+for destructive interference,
+the difference in the distance
+
+traveled by the two waves.
+This kind of diagram here we
+
+are also going to see on Friday,
+because this interference
+
+phenomenon is the property
+associated with waves.
+
+And what we are going to do is
+see this diagram again when we
+
+scatter electrons for particles.
+We are going to see that
+
+particles, also,
+will destructively and
+
+constructively interfere.
+They also have wave-like
+
+properties.
+That is what we will do on
+
+Friday.
+We have established,
+
+now, the wave-like properties
+of radiation,
+
+so I would like to move on and
+talk about the evidence for the
+
+particle-like nature of
+radiation.
+
+The evidence for the
+particle-like nature of
+
+radiation comes from an effect
+called the photoelectric effect.
+
+Shortly after Thompson
+discovered the electron,
+
+scientists were noticing that
+if you took a metal and shined
+
+radiation on that metal,
+that indeed electrons were
+
+emitted.
+Electrons came off.
+
+These were called
+photoelectrons.
+
+However, the radiation that you
+shined on the metal had to have
+
+a frequency nu that was greater
+than or equal to some threshold
+
+frequency, nu nought.
+That is, if you took radiation
+
+of some frequency here,
+nu, that was less than this
+
+threshold frequency,
+well, you did not get any
+
+electrons off.
+Well, another way to kind of
+
+understand that data or that
+effect is to just plot the
+
+number of the electrons that
+come off as a function of the
+
+frequency of the radiation.
+And so at low frequency,
+
+there are no electrons,
+but all of a sudden you get to
+
+nu nought, and then electrons
+start coming off.
+
+And no matter how high you
+increase the frequency here,
+
+the number of electrons that
+come off remains the same,
+
+remains constant.
+And it turned out that for the
+
+metals that were looked at,
+at that time,
+
+the threshold frequency,
+here, was in the UV range of
+
+the electromagnetic spectrum.
+Well, in addition to just
+
+measuring the number of
+electrons and generally
+
+observing this effect,
+scientists did not understand
+
+what was going on.
+So they just started measuring
+
+everything they could think
+about measuring.
+
+And one quantity that they
+measured was the kinetic energy
+
+of these electrons that were
+being emitted.
+
+And so you take kinetic energy
+here, KE, as a function of the
+
+frequency.
+They found that at low
+
+frequency, again,
+there is no kinetic energy,
+
+because there are no electrons.
+And then at some frequency,
+
+all of a sudden electrons
+started coming off.
+
+And the kinetic energy of those
+electrons seemed to increase
+
+with the frequency once past
+that threshold frequency,
+
+nu nought.
+Well, this was really another
+
+one of these conundrums,
+here, at that time,
+
+because classical physics,
+classical electromagnetism,
+
+classical physics had no way of
+explaining these data.
+
+And, in fact,
+what classical physics
+
+predicted is that the kinetic
+energy of these electrons,
+
+that that kinetic energy should
+have nothing to do with the
+
+frequency of the light.
+That is, the kinetic energy was
+
+constant.
+As you increased the frequency
+
+of the light,
+classical physics would tell
+
+you that the kinetic energy
+should not be affected by the
+
+frequency of the light.
+There was nothing in the
+
+classical way of thinking,
+classical electromagnetism that
+
+connected the frequency of the
+light to the kind of energy,
+
+to the kinetic energy.
+There was no way for blue light
+
+to make the electrons have a
+larger kinetic energy,
+
+and for blue light to have an
+effect on the kinetic energy,
+
+and red light to not have an
+effect on the kinetic energy.
+
+In addition,
+what classical physics
+
+predicted is that the kinetic
+energy of the electrons should
+
+be dependent on the intensity of
+the light.
+
+That is, the more and more
+intense the radiation on the
+
+metal, the more and more kinetic
+energy those electrons should
+
+have.
+Because, after all,
+
+if you increase the intensity
+of the light going into the
+
+metal, you are putting more and
+more energy into it.
+
+That should be reflected in
+just how energetic those
+
+electrons were picked out.
+The more energy in,
+
+the electrons ought to come out
+with larger and larger kinetic
+
+energy.
+Of course, the observation was
+
+that the kinetic energy of the
+electrons had nothing to do with
+
+the intensity of light.
+The kinetic energy of the
+
+electrons did not increase as
+you made the light brighter and
+
+brighter.
+As you put more and more energy
+
+in, the kinetic energy remained
+the same.
+
+It didn't have an effect.
+This was a real conundrum here.
+
+The known classical physics was
+making predictions really just
+
+contrary to what was being
+observed.
+
+These data, here,
+of the kinetic energy versus
+
+the frequency,
+were around for a few years
+
+before Einstein took a look at
+them in 1905,
+
+a hundred years ago.
+And he looked at these data for
+
+many different metals.
+Here is some data for metal A,
+
+for example,
+and here is some data for metal
+
+B.
+And, in both cases,
+
+it certainly looked like the
+kinetic energy was linearly
+
+dependent on the frequency of
+the radiation.
+
+But what was different for the
+two different metals was the
+
+threshold frequency here,
+nu nought.
+
+What Einstein did was,
+he went and fitted a straight
+
+line to these data,
+y equals mx plus b.
+
+And when he did that,
+
+and he went to calculate the
+slope here, m,
+
+of these lines,
+he thought "very interesting."
+
+Because the slope of those
+lines was 6.626x10^-34 joule
+
+seconds.
+The slope of those lines was
+
+something called Planck's
+constant, h.
+
+You say so what?
+Well, the reason he was so
+
+interested in this is because
+just a few years earlier,
+
+there was a scientist by the
+name of Max Planck who was
+
+interested in understanding what
+was called the black-body
+
+radiation data.
+What is a black-body?
+
+Well, let's just,
+for simplicity purposes,
+
+think of the black-body as the
+burner on an electric stove.
+
+What you know is that if you
+turn up the voltage on that
+
+burner, the burner gets hot.
+It increased in temperature.
+
+And you increase the
+temperature, and sooner or
+
+later, that burner is glowing
+bright red.
+
+And you increase the
+temperature some more,
+
+and the burner is glowing a
+brighter red.
+
+And you increase it some more,
+and it is glowing orange.
+
+And you increase it some more,
+which you shouldn't do,
+
+and it's glowing yellow.
+And then if you could increase
+
+it some more,
+it's glowing white.
+
+What is happening,
+as you increase the
+
+temperature, is that the
+radiation from that black-body,
+
+this is the black-body
+radiation, is increasing in
+
+intensity.
+But, more importantly,
+
+the frequency is getting larger
+and larger.
+
+Dark red, bright red,
+orange, yellow,
+
+white, those are all
+frequencies.
+
+The frequency is shifting to
+higher and higher values.
+
+And what was actually done at
+that time is that the intensity
+
+of that black-body radiation,
+oh, and this material is not in
+
+your notes, because you are not
+responsible for it.
+
+I am just trying to make this
+surprise that Einstein noticed
+
+about the slope.
+I am just trying to put it in
+
+some context,
+why he was so surprised and
+
+amazed at it.
+This black-body intensity here,
+
+people had dispersed that
+radiation and looked at the
+
+frequencies that were coming
+off.
+
+This is intensity versus
+frequency.
+
+Here is a general shape of that
+intensity versus frequency.
+
+That was observed for some
+temperature T one.
+
+That was a low temperature.
+And then, when the temperature
+
+was increased and the intensity
+versus frequency was observed,
+
+well, the frequencies generally
+got higher.
+
+This is higher temperature.
+Intensity goes up.
+
+And you increase the
+temperature some more,
+
+and you get even higher
+frequency.
+
+T three is the highest
+temperature.
+
+And that is what the data were.
+What Planck was trying to do
+
+was to understand the origin of
+that black-body radiation.
+
+What he said was that in these
+black-bodies,
+
+in these materials,
+what there must be are
+
+oscillators that are giving off
+this radiation.
+
+But he had another little kick
+to these oscillators.
+
+These oscillators were giving
+off radiation or energy in
+
+chunks, in quanta,
+in particles.
+
+And using that idea,
+plus some statistical
+
+mechanics, he was able to
+calculate the shapes of these
+
+curves.
+That is, he indeed got,
+
+for the lowest temperature
+here, a curve that looked like
+
+this.
+And for T two,
+
+he got a curve that looked like
+this.
+
+And for T three,
+he got a curve that looked like
+
+this.
+He got the shape right,
+
+but he wanted to get the
+intensity right,
+
+too.
+What he realized he had to do
+
+was he essentially needed to
+have a scaling factor,
+
+actually, in front of his
+frequencies of his oscillators.
+
+He wanted a constant.
+And so he said,
+
+what constant do I have to have
+in order to make all of these
+
+data fit the observation?
+That constant is Planck's
+
+constant, his own 6.626x10^-34
+joule seconds.
+
+There it is.
+That is Planck's constant.
+
+That is it.
+There is nothing deeper here.
+
+It is a natural constant.
+It comes from our observations
+
+of the world,
+of nature.
+
+That is it.
+It is a fitting constant.
+
+And so that is why Einstein was
+so amazed, here,
+
+when he realized this number is
+the same as what comes out of
+
+here.
+There must be something very
+
+fundamental about this h,
+this Planck's constant.
+
+That is the story.
+Isn't that amazing?
+
+What Einstein then proceeded to
+do, of course,
+
+is to write down the equation
+of the straight line that he
+
+just put through these data.
+And so that equation is the
+
+kinetic energy equal to nu,
+which is our x,
+
+h, which is the slope.
+And then what he found was that
+
+the intercept here,
+of course, is minus h times nu
+
+nought.
+This is plus minus h times nu
+
+nought.
+And that is the equation of a
+
+straight line.
+Of course, he realized,
+
+if this is energy on this side,
+boy, there better be energy on
+
+this side.
+And so this h times nu
+
+better be an energy.
+And since this nu was the
+
+frequency of the incident
+radiation, therefore,
+
+h times nu better be the energy
+of the incident radiation,
+
+E sub i.
+That is where this expression,
+
+energy equals h times nu
+comes from.
+
+Nothing more.
+That is where it comes from,
+
+the photoelectric effect.
+This was the first time that
+
+there was any relationship
+between the frequency of the
+
+radiation and the energy of the
+radiation.
+
+In classical electromagnetism,
+there is no relationship
+
+between the frequency and the
+energy.
+
+This was the first time in
+which that relationship was
+
+observed.
+And what this is saying is the
+
+following.
+This is saying that you can
+
+have any frequency of radiation
+you want, but the corresponding
+
+energy comes in these chunks of
+h times nu.
+
+h is a quantization constant.
+Radiation, nu,
+
+is continuous,
+but the energy that corresponds
+
+to any given frequency of
+radiation is h times nu.
+
+This E equals h times nu,
+here, is thought of as a
+
+quantum of energy.
+A particle of energy.
+
+A chunk of energy.
+Later on, it became the photon,
+
+the energy of a photon.
+If this h times nu here
+
+was an energy,
+well, this h times nu nought
+
+also better be an  energy.
+
+It is the threshold energy.
+Let's draw an energy level
+
+diagram to try to understand
+that.
+
+I am going to plot an energy
+here.
+
+Let's draw an energy level for
+an electron.
+
+This is an electron,
+here, bound to the metal.
+
+And we know that it takes some
+energy to rip this electron off
+
+of the metal.
+Up here, at higher energy,
+
+is going to be our free
+electron.
+
+I will just call it
+electron-free,
+
+not bound to the metal anymore.
+And the energy that is required
+
+to pull the electron off,
+from the bound state to its
+
+free state, is this threshold
+energy, h times nu nought.
+
+This threshold energy is like
+
+an ionization potential.
+You know what the ionization
+
+potential is.
+Just the energy required to
+
+pull an electron off an atom or
+a molecule.
+
+However, when we are pulling an
+electron off a chunk of a metal,
+
+we actually have another name
+for it.
+
+It is called the work function.
+That is just historical,
+
+but it is the same thing as an
+ionization potential.
+
+And we often give it the symbol
+phi.
+
+That threshold energy,
+ionization energy for a metal,
+
+is the work function,
+here, h times nu,
+
+phi.
+The important point here is
+
+this.
+In order to get an electron off
+
+of the metal,
+what you have to have is
+
+energy, E sub i.
+That energy E sub i has to be
+
+equal to at least the threshold
+energy, h times nu nought.
+
+If you come in with energy of
+
+this radiation,
+of this wavelength and that
+
+frequency, you pulled the
+electron off,
+
+and then the electron is off
+the metal and it just kind of
+
+stays there.
+It doesn't move away.
+
+But you can also come in with
+energy here, E sub i,
+
+that is greater than this work
+function, than the threshold
+
+energy.
+And you can pull the electron
+
+off.
+But then, the electron is
+
+actually going to move away from
+the metal, and the energy with
+
+which it moves away from the
+metal, its kinetic energy,
+
+is just the incident energy
+minus this threshold energy.
+
+It is the excess energy here.
+And I am going to write it as
+
+the kinetic energy.
+From that energy level diagram,
+
+this energy,
+the incident energy,
+
+has to be equal to the work
+function, h nu nought,
+
+plus the kinetic energy.
+
+Or, if I turned this around,
+the kinetic energy is equal to
+
+the incident energy minus h nu
+nought.
+
+The actual expression for the
+energy that Einstein found,
+
+I just turned that equation
+around.
+
+This is an equation that you
+have to know.
+
+I will not give this to you on
+an exam.
+
+Now, you don't have to memorize
+it.
+
+You just have to reason it.
+Draw yourself an energy
+
+diagram.
+You know conservation of
+
+energy.
+The sum of these two energies
+
+has to equal the incident
+energy.
+
+Then you will be all set.
+Now, what is very important
+
+here is the following.
+If I come in with radiation
+
+that is, say,
+a half of the threshold energy.
+
+Suppose I come in with two
+photons, where each photon is
+
+one half h nu --
+
+The bottom line is that you are
+not going to get an electron
+
+off.
+Even though you are coming in
+
+with two photons,
+which together are going to
+
+give you the threshold energy,
+you won't get a photon off.
+
+You have to come in with at
+least the energy of the work
+
+function.
+A photon has to have at least
+
+this energy to get an electron
+off.
+
+That is the particle-like
+nature of radiation.
+
+Energy comes in chunks,
+in particles of energy,
+
+in quanta of energy.
+Likewise, if I came in here
+
+with a photon that had twice the
+energy of the work function or
+
+the threshold energy,
+I would still only get one
+
+electron off.
+I would not get two electrons
+
+off, even though energetically
+you would be able,
+
+in principle,
+to get two electrons off.
+
+But you won't.
+You will only get one electron
+
+off.
+Whenever you send a photon in,
+
+if it has enough energy,
+that is if its energy is equal
+
+to or greater than the work
+function, you will get an
+
+electron off.
+There is one electron for every
+
+photon.
+You never get two electrons for
+
+every photon,
+or you can never get one
+
+electron for two photons that
+are lower energy.
+
+That is the particle quantum
+nature of radiation.
+
+That is important.
+Yes?
+
+What is the form of the photon?
+What do you mean by form?
+
+Oh, you want a picture of the
+photon.
+
+You're looking at them.
+You cannot draw a picture of a
+
+photon because you want to
+relate it to something that is
+
+within your classical
+experience.
+
+And you cannot do that.
+It isn't a classical particle.
+
+That is what you're working
+with right here.
+
+You are trying to use your
+experiences, that are everyday
+
+experiences, to explain
+something that isn't within your
+
+everyday experiences.
+You don't have a frame or a
+
+format to do that.
+Yeah?
+
+Yes.
+If you have a constant flux of
+
+photons onto the surface,
+you will have a constant flux
+
+of electrons.
+Now, there is a probability.
+
+It is not necessarily the case
+that every photon gets in,
+
+will eject electrons,
+because there are other kinds
+
+of competing processes.
+Whatever the rate with which
+
+the photons come in.
+It depends on the flux of the
+
+photons.
+And we will have some problems
+
+like that, where we are going to
+assume that the probability of
+
+the electron coming off is going
+to be one, so one electron for
+
+every photon.
+But, in reality,
+
+there are competing processes.
+Are all electrons being
+
+ejected?
+Actually, some electrons.
+
+Again, this goes to the
+probability.
+
+Some are actually kind of going
+in, too, into deeper the metal.
+
+Not the probability,
+right.
+
+The rate at which the electrons
+come out with is dependent on
+
+the intensity.
+The more photons you send in,
+
+the larger the number of
+photons per second coming in,
+
+the larger the number of
+electrons per second coming out.
+
+This is a plot,
+here, of the energy of the
+
+electrons.
+That's all right.
+
+Other questions?
+Yeah?
+
+Eventually.
+Yes.
+
+Absolutely.
+There are other problems that
+
+will come in.
+Usually, your light source
+
+isn't so energetic that you
+could possibly do that.
+
+Now, also usually what happens
+is that you've got your metal
+
+grounded, so that as you lose
+electrons, new electrons come in
+
+and fill it up to the fermi
+level.
+
+And so you don't charge up your
+sample.
+
+In an experiment,
+if you had your metal just not
+
+grounded and you did shine some
+radiation, what would happen is
+
+the metal would start to charge
+up.
+
+Then, that would make it
+difficult to get electrons off.
+
+Yes?
+
+Yes.
+How strongly those electrons
+
+are bound to the metal depends
+on the electronic structure of
+
+the metal.
+And we are going to talk a
+
+little bit about what determines
+the strength of the interaction
+
+for electrons on atoms and
+molecules, but it is similar to
+
+what it is for metals.
+That is coming in a few days.
+
+Yes?
+
+Yes, there is.
+Right.
+
+You don't actually have to have
+a metal.
+
+You could do it.
+There are usually higher
+
+frequencies on insulators and
+semiconductors,
+
+right.
+It is harder to see the effect,
+
+but it can be done and has been
+done.
+
+Well, what I want to do right
+now is to show you an experiment
+
+we are going to do.
+We are going to do a
+
+photoelectron experiment.
+
+And the experiment is this.
+We have a device up here.
+
+What we have is an aluminum
+plate.
+
+And that aluminum plate is
+mounted on this blue metal rod.
+
+And in the middle of this rod
+is a needle on a pivot.
+
+And this is a fairly
+frictionless pivot.
+
+This black ring,
+here, is just a support
+
+structure, an insulating support
+structure.
+
+What we are going to do is put
+some excess charge on this
+
+aluminum plate.
+And that excess charge is going
+
+to run down this metal rod and
+then onto this needle.
+
+And because that excess charge,
+the electrons on the needle and
+
+the electrons on the metal rod
+are repulsive,
+
+since this is rather
+frictionless,
+
+that needle is going to move
+because of the repulsive
+
+interactions between these
+electrons.
+
+What we're then going to do is
+try to do the photoelectron
+
+experiment.
+We are going to take some UV
+
+radiation and shine it on this
+metal and drive the electrons
+
+off.
+And we should see,
+
+then, the needle swing back to
+its original position.
+
+I need a couple of volunteers
+in order to do this experiment
+
+here.
+Come on up.
+
+All right.
+Fantastic.
+
+I think that is all right.
+Good.
+
+Okay.
+One of you needs to be the
+
+charger, and the other needs to
+be the discharger.
+
+Which one?
+You want to discharge?
+
+Discharge, okay.
+You come over here.
+
+And what you are going to do is
+discharge the aluminum plate
+
+after we get some excess charge
+on it.
+
+You are going to do it just by
+holding it up to here.
+
+You have to get it kind of
+close because it is not a very
+
+intense UV source.
+Could you get the video cam on
+
+the side or on the center to get
+where we are putting it?
+
+I guess we are putting it on
+the side, right?
+
+Okay.
+There we go.
+
+There is the device.
+You are the charger.
+
+What we are going to do,
+to get the excess charge,
+
+we are taking a piece of
+natural fur.
+
+We are going to rub it on this
+Lucite rod.
+
+You have to keep your fingers
+on the yellow tape here.
+
+And we are going to transfer
+some of the natural oils here
+
+onto this rod.
+And there are plenty of
+
+negative ions around here and
+free electrons.
+
+That oil likes those negative
+charges, and so there are going
+
+to be excess negative charges on
+this Lucite rod.
+
+And then you are going to come
+over here and just touch the
+
+edge of this and let the
+electrons flow onto there.
+
+Are you right-handed?
+You have to rub that really,
+
+really hard.
+[LAUGHTER] Great.
+
+Go over there.
+Touch the end.
+
+Cool.
+Why don't you give it another
+
+jolt here and we will really
+move that needle over.
+
+Okay.
+Discharger.
+
+We have to give it another
+jolt.
+
+That is okay.
+You may have touched it with
+
+something else and discharged it
+a little bit.
+
+No, that's okay.
+You have to get the hang of
+
+this, here.
+You are doing fantastic.
+
+Take it off.
+That's what it is.
+
+You are holding it on too long.
+Okay, that is pretty good.
+
+Put it in front there.
+Get it a little bit closer.
+
+Here comes the UV radiation.
+We did it.
+
+Try it again really hard.
+Just touch it.
+
+Take it off.
+Do it again.
+
+You need to do it again.
+You've got to get it right
+
+here.
+Not too much,
+
+not too little.
+Okay.
+
+It is doing it.
+Discharge in front.
+
+Electrons off.
+Now we have to do a control
+
+experiment.
+That is, you have got to charge
+
+it up again, but now,
+when you put the light there,
+
+what I am going to do is hold
+up a Pyrex plate in between the
+
+light and the metal.
+It is going to block the
+
+radiation, and it should not
+discharge.
+
+You need to get on there.
+Fantastic.
+
+There it goes.
+Here is the plate.
+
+Get it to a little bit lower.
+Do a good discharge.
+
+[APPLAUSE] Fantastic.
+Thank you very much.
+
+Thank you for being a good
+sport.
+
+That is the photoelectron
+experiment.
+
+Hey, it works.
+Well, what I want to do now is
+
+just spend a few minutes working
+on a few problems.
+
+I think these are pretty
+straightforward,
+
+but I just want to make sure
+that everybody is on the same
+
+page here in terms of being able
+to do the homework.
+
+Here is the first problem.
+The first problem says,
+
+how many photons?
+And remember what we said a
+
+photon was?
+E equals h nu.
+
+This is the number of joules.
+Implied is the number of joules
+
+per photon, although we don't
+usually write this,
+
+but that is what that is,
+joules per photon.
+
+You may want to write it as you
+do these problems.
+
+How many photons associated
+with radiation of a wavelength
+
+lambda equals one picometer,
+which is 1.0x10^-12 meters,
+
+how many of these do you need
+in order to create,
+
+say, a laser pulse of energy
+that is one joule?
+
+Lasers are pulsed,
+so I am talking about a pulse
+
+of energy, one joule.
+You want to draw yourself a
+
+picture, here.
+We are drawing a picture of one
+
+pulse of energy,
+one joule.
+
+Now, we have not been given the
+frequency, here,
+
+of this radiation,
+but we know the wavelength,
+
+and we know the relationship
+between frequency and
+
+wavelength.
+It is just c over lambda.
+
+I know what lambda is.
+I can calculate nu.
+
+And, when I do that,
+I find that the energy of the
+
+photon, hc over lambda,
+that energy of the
+
+photon is 1.99x10^-13 joules per
+photon.
+
+And I am using one more figure
+than is significant since this
+
+an intermediate step in the
+calculation.
+
+If I want a pulse of one joule
+of energy and I am asked how
+
+many photons do I need to get
+that, and each photon is
+
+1.99x10^-13 joules,
+well, that means that I am
+
+going to need 5.0x10^12 photons.
+There was a question here?
+
+All right.
+Let's work another one.
+
+Here, we want to define what we
+mean by power.
+
+This says the power of
+radiation from the continuous
+
+laser is three milliwatts.
+
+We have some laser,
+and the power of that radiation
+
+coming out is three milliwatts.
+Well, what is power?
+
+Power is energy per unit time.
+It is the energy delivered or
+
+the energy expended per unit
+time.
+
+The unit of power that we are
+going to use is a watt.
+
+A watt is a joule per second.
+We are told that we have
+
+radiation of three milliwatts.
+That is 3.0x10^-3 joules per
+
+second.
+And the question asks,
+
+how long will it take for a
+total energy of one joule to be
+
+supplied?
+Well, one joule.
+
+And we have the rate of energy
+supply as 3x10^-3 joules per
+
+second.
+That gives us 330 seconds.
+
+That is straightforward.
+Finally, we have one more.
+
+It says, how many photons per
+second of, again,
+
+the same radiation,
+of the wavelength of one
+
+picometer.
+That means, again,
+
+we are dealing with photons
+that have an energy of
+
+1.99x10^-13 joules per photon.
+How many photons per second,
+
+the rate of photons at the
+wavelength do you have to have,
+
+or do you have,
+if the power of the radiation
+
+is three milliwatts?
+Well, the power of the
+
+radiation is 3.0x10^-3 joules
+per second, --
+
+-- and we have 1.99x10^-13
+joules per photon.
+
+In order to have this kind of
+power, what we have to have
+
+being emitted is 1.5x10^10
+photons per second.
+
+All right.
+The photoelectric effect is one
+
+of the experiments that
+demonstrated the particle-like
+
+nature of light,
+of radiation.
+
+Particle-like nature because
+you have to have these chunks of
+
+energy to make some process
+occur.
+
+Next time, we are going to look
+at and will just talk briefly
+
+about the other experiments that
+demonstrated the particle-like
+
+nature of radiation.
+And that other experiment is
+
+the demonstration that a photon
+has momentum,
+
+even though it doesn't have any
+mass.
+
+See you Wednesday.
+See you Friday.
\ No newline at end of file
diff --git a/mOa1fZD9qC4.txt b/mOa1fZD9qC4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bdbf30558d8a040f3bcd053be792959bbc396ca8
--- /dev/null
+++ b/mOa1fZD9qC4.txt
@@ -0,0 +1,2587 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ 
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the inductive attenuator demonstrates
+
+ align:start position:0%
+the inductive attenuator demonstrates
+ 
+
+ align:start position:0%
+the inductive attenuator demonstrates
+the lassan nature of magnetic fields in
+
+ align:start position:0%
+the lassan nature of magnetic fields in
+ 
+
+ align:start position:0%
+the lassan nature of magnetic fields in
+free
+
+ align:start position:0%
+free
+ 
+
+ align:start position:0%
+free
+space the way that currents distribute
+
+ align:start position:0%
+space the way that currents distribute
+ 
+
+ align:start position:0%
+space the way that currents distribute
+themselves on the surfaces of perfect
+
+ align:start position:0%
+themselves on the surfaces of perfect
+ 
+
+ align:start position:0%
+themselves on the surfaces of perfect
+conductors and the use of the vector
+
+ align:start position:0%
+conductors and the use of the vector
+ 
+
+ align:start position:0%
+conductors and the use of the vector
+potential in describing magnetic fields
+
+ align:start position:0%
+potential in describing magnetic fields
+ 
+
+ align:start position:0%
+potential in describing magnetic fields
+in two-dimensional
+
+ align:start position:0%
+in two-dimensional
+ 
+
+ align:start position:0%
+in two-dimensional
+systems provided that the magnetic flux
+
+ align:start position:0%
+systems provided that the magnetic flux
+ 
+
+ align:start position:0%
+systems provided that the magnetic flux
+density is in the XY plane and Depends
+
+ align:start position:0%
+density is in the XY plane and Depends
+ 
+
+ align:start position:0%
+density is in the XY plane and Depends
+only on X and Y it can be represented by
+
+ align:start position:0%
+only on X and Y it can be represented by
+ 
+
+ align:start position:0%
+only on X and Y it can be represented by
+one component of the vector potential a
+
+ align:start position:0%
+one component of the vector potential a
+ 
+
+ align:start position:0%
+one component of the vector potential a
+subz in free space the vector potential
+
+ align:start position:0%
+subz in free space the vector potential
+ 
+
+ align:start position:0%
+subz in free space the vector potential
+satisfies llosa's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation separable solutions to Lassa
+
+ align:start position:0%
+equation separable solutions to Lassa
+ 
+
+ align:start position:0%
+equation separable solutions to Lassa
+equation that are periodic in One
+
+ align:start position:0%
+equation that are periodic in One
+ 
+
+ align:start position:0%
+equation that are periodic in One
+Direction decay in a perpendicular
+
+ align:start position:0%
+Direction decay in a perpendicular
+ 
+
+ align:start position:0%
+Direction decay in a perpendicular
+Direction here the direction of
+
+ align:start position:0%
+Direction here the direction of
+ 
+
+ align:start position:0%
+Direction here the direction of
+periodicity is
+
+ align:start position:0%
+periodicity is
+ 
+
+ align:start position:0%
+periodicity is
+X while the hyperbolic sign is a
+
+ align:start position:0%
+X while the hyperbolic sign is a
+ 
+
+ align:start position:0%
+X while the hyperbolic sign is a
+combination of exponentials representing
+
+ align:start position:0%
+combination of exponentials representing
+ 
+
+ align:start position:0%
+combination of exponentials representing
+the decay in the y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction in this model the floor is the
+
+ align:start position:0%
+direction in this model the floor is the
+ 
+
+ align:start position:0%
+direction in this model the floor is the
+XY
+
+ align:start position:0%
+XY
+ 
+
+ align:start position:0%
+XY
+plane the altitude of the surface is the
+
+ align:start position:0%
+plane the altitude of the surface is the
+ 
+
+ align:start position:0%
+plane the altitude of the surface is the
+vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential here's the direction of
+
+ align:start position:0%
+potential here's the direction of
+ 
+
+ align:start position:0%
+potential here's the direction of
+periodicity here's the direction of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Decay because it represents a solution
+
+ align:start position:0%
+Decay because it represents a solution
+ 
+
+ align:start position:0%
+Decay because it represents a solution
+to ll's equation every point on the
+
+ align:start position:0%
+to ll's equation every point on the
+ 
+
+ align:start position:0%
+to ll's equation every point on the
+surface having a positive curvature in
+
+ align:start position:0%
+surface having a positive curvature in
+ 
+
+ align:start position:0%
+surface having a positive curvature in
+the y direction must have a negative
+
+ align:start position:0%
+the y direction must have a negative
+ 
+
+ align:start position:0%
+the y direction must have a negative
+curvature in the X
+
+ align:start position:0%
+curvature in the X
+ 
+
+ align:start position:0%
+curvature in the X
+Direction This Is Why periodicity in One
+
+ align:start position:0%
+Direction This Is Why periodicity in One
+ 
+
+ align:start position:0%
+Direction This Is Why periodicity in One
+Direction implies decay in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other for this solution to llosa's
+
+ align:start position:0%
+other for this solution to llosa's
+ 
+
+ align:start position:0%
+other for this solution to llosa's
+equation three of the rectangular
+
+ align:start position:0%
+equation three of the rectangular
+ 
+
+ align:start position:0%
+equation three of the rectangular
+boundaries have a constant Vector
+
+ align:start position:0%
+boundaries have a constant Vector
+ 
+
+ align:start position:0%
+boundaries have a constant Vector
+potential the fourth is a
+
+ align:start position:0%
+potential the fourth is a
+ 
+
+ align:start position:0%
+potential the fourth is a
+sinusoid in our physical situation this
+
+ align:start position:0%
+sinusoid in our physical situation this
+ 
+
+ align:start position:0%
+sinusoid in our physical situation this
+fourth boundary is elevated to a uniform
+
+ align:start position:0%
+fourth boundary is elevated to a uniform
+ 
+
+ align:start position:0%
+fourth boundary is elevated to a uniform
+Vector potential
+
+ align:start position:0%
+Vector potential
+ 
+
+ align:start position:0%
+Vector potential
+this can be represented by a
+
+ align:start position:0%
+this can be represented by a
+ 
+
+ align:start position:0%
+this can be represented by a
+superposition of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solutions to represent a uniform Vector
+
+ align:start position:0%
+solutions to represent a uniform Vector
+ 
+
+ align:start position:0%
+solutions to represent a uniform Vector
+potential Solutions are added that have
+
+ align:start position:0%
+potential Solutions are added that have
+ 
+
+ align:start position:0%
+potential Solutions are added that have
+a shorter
+
+ align:start position:0%
+a shorter
+ 
+
+ align:start position:0%
+a shorter
+wavelength by the nature of lass's
+
+ align:start position:0%
+wavelength by the nature of lass's
+ 
+
+ align:start position:0%
+wavelength by the nature of lass's
+equation these have a more rapid Decay
+
+ align:start position:0%
+equation these have a more rapid Decay
+ 
+
+ align:start position:0%
+equation these have a more rapid Decay
+than the fundamental in the
+
+ align:start position:0%
+than the fundamental in the
+ 
+
+ align:start position:0%
+than the fundamental in the
+perpendicular y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction here are the magnetic flux
+
+ align:start position:0%
+direction here are the magnetic flux
+ 
+
+ align:start position:0%
+direction here are the magnetic flux
+lines represented by the Vector
+
+ align:start position:0%
+lines represented by the Vector
+ 
+
+ align:start position:0%
+lines represented by the Vector
+potential these are the boundaries where
+
+ align:start position:0%
+potential these are the boundaries where
+ 
+
+ align:start position:0%
+potential these are the boundaries where
+the vector potential is
+
+ align:start position:0%
+the vector potential is
+ 
+
+ align:start position:0%
+the vector potential is
+zero this is the boundary that is
+
+ align:start position:0%
+zero this is the boundary that is
+ 
+
+ align:start position:0%
+zero this is the boundary that is
+elevated in its Vector
+
+ align:start position:0%
+elevated in its Vector
+ 
+
+ align:start position:0%
+elevated in its Vector
+potential a surface of constant Vector
+
+ align:start position:0%
+potential a surface of constant Vector
+ 
+
+ align:start position:0%
+potential a surface of constant Vector
+potential is one that sustains no normal
+
+ align:start position:0%
+potential is one that sustains no normal
+ 
+
+ align:start position:0%
+potential is one that sustains no normal
+component of the magnetic flux
+
+ align:start position:0%
+component of the magnetic flux
+ 
+
+ align:start position:0%
+component of the magnetic flux
+density it can be the surface of a
+
+ align:start position:0%
+density it can be the surface of a
+ 
+
+ align:start position:0%
+density it can be the surface of a
+perfect
+
+ align:start position:0%
+perfect
+ 
+
+ align:start position:0%
+perfect
+conductor here these boundaries of zero
+
+ align:start position:0%
+conductor here these boundaries of zero
+ 
+
+ align:start position:0%
+conductor here these boundaries of zero
+Vector potential are perfect conductors
+
+ align:start position:0%
+Vector potential are perfect conductors
+ 
+
+ align:start position:0%
+Vector potential are perfect conductors
+carrying that surface current necessary
+
+ align:start position:0%
+carrying that surface current necessary
+ 
+
+ align:start position:0%
+carrying that surface current necessary
+to terminate the tangential magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field this boundary of elevated Vector
+
+ align:start position:0%
+field this boundary of elevated Vector
+ 
+
+ align:start position:0%
+field this boundary of elevated Vector
+potential is also a perfect
+
+ align:start position:0%
+potential is also a perfect
+ 
+
+ align:start position:0%
+potential is also a perfect
+conductor the difference between the
+
+ align:start position:0%
+conductor the difference between the
+ 
+
+ align:start position:0%
+conductor the difference between the
+vector potential on this electrode and
+
+ align:start position:0%
+vector potential on this electrode and
+ 
+
+ align:start position:0%
+vector potential on this electrode and
+on the wall is the net magnetic flux per
+
+ align:start position:0%
+on the wall is the net magnetic flux per
+ 
+
+ align:start position:0%
+on the wall is the net magnetic flux per
+unit length passing inward through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gap similarly the difference between the
+
+ align:start position:0%
+Gap similarly the difference between the
+ 
+
+ align:start position:0%
+Gap similarly the difference between the
+electrode Vector potential and the wall
+
+ align:start position:0%
+electrode Vector potential and the wall
+ 
+
+ align:start position:0%
+electrode Vector potential and the wall
+potential here is the net magnetic flux
+
+ align:start position:0%
+potential here is the net magnetic flux
+ 
+
+ align:start position:0%
+potential here is the net magnetic flux
+per unit length passing out
+
+ align:start position:0%
+per unit length passing out
+ 
+
+ align:start position:0%
+per unit length passing out
+outward the surface current passing
+
+ align:start position:0%
+outward the surface current passing
+ 
+
+ align:start position:0%
+outward the surface current passing
+outward on the electrode is returned in
+
+ align:start position:0%
+outward on the electrode is returned in
+ 
+
+ align:start position:0%
+outward on the electrode is returned in
+the side
+
+ align:start position:0%
+the side
+ 
+
+ align:start position:0%
+the side
+walls and bottom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wall in our model lines of constant
+
+ align:start position:0%
+wall in our model lines of constant
+ 
+
+ align:start position:0%
+wall in our model lines of constant
+altitude are lines of constant Vector
+
+ align:start position:0%
+altitude are lines of constant Vector
+ 
+
+ align:start position:0%
+altitude are lines of constant Vector
+potential in two Dimensions lines of
+
+ align:start position:0%
+potential in two Dimensions lines of
+ 
+
+ align:start position:0%
+potential in two Dimensions lines of
+constant a subz are lines of magnetic
+
+ align:start position:0%
+constant a subz are lines of magnetic
+ 
+
+ align:start position:0%
+constant a subz are lines of magnetic
+flux
+
+ align:start position:0%
+flux
+ 
+
+ align:start position:0%
+flux
+density so the wires are the lines of
+
+ align:start position:0%
+density so the wires are the lines of
+ 
+
+ align:start position:0%
+density so the wires are the lines of
+magnetic flux
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density if you're familiar with using a
+
+ align:start position:0%
+density if you're familiar with using a
+ 
+
+ align:start position:0%
+density if you're familiar with using a
+scalar potential to represent an
+
+ align:start position:0%
+scalar potential to represent an
+ 
+
+ align:start position:0%
+scalar potential to represent an
+irrotational electric
+
+ align:start position:0%
+irrotational electric
+ 
+
+ align:start position:0%
+irrotational electric
+field the role played by the scalar
+
+ align:start position:0%
+field the role played by the scalar
+ 
+
+ align:start position:0%
+field the role played by the scalar
+potential is being played here by the
+
+ align:start position:0%
+potential is being played here by the
+ 
+
+ align:start position:0%
+potential is being played here by the
+vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential Lambda is the flux per unit
+
+ align:start position:0%
+potential Lambda is the flux per unit
+ 
+
+ align:start position:0%
+potential Lambda is the flux per unit
+length passing through the gaps at the
+
+ align:start position:0%
+length passing through the gaps at the
+ 
+
+ align:start position:0%
+length passing through the gaps at the
+ends of the top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrode in the Electro quas static
+
+ align:start position:0%
+electrode in the Electro quas static
+ 
+
+ align:start position:0%
+electrode in the Electro quas static
+analog this flux is analogous to the
+
+ align:start position:0%
+analog this flux is analogous to the
+ 
+
+ align:start position:0%
+analog this flux is analogous to the
+voltage between the upper electrode and
+
+ align:start position:0%
+voltage between the upper electrode and
+ 
+
+ align:start position:0%
+voltage between the upper electrode and
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wall the analogy is
+
+ align:start position:0%
+wall the analogy is
+ 
+
+ align:start position:0%
+wall the analogy is
+intriguing it is the potentials that are
+
+ align:start position:0%
+intriguing it is the potentials that are
+ 
+
+ align:start position:0%
+intriguing it is the potentials that are
+analgous in the electr quasy static
+
+ align:start position:0%
+analgous in the electr quasy static
+ 
+
+ align:start position:0%
+analgous in the electr quasy static
+situation the field lines are
+
+ align:start position:0%
+situation the field lines are
+ 
+
+ align:start position:0%
+situation the field lines are
+perpendicular to the lines of constant
+
+ align:start position:0%
+perpendicular to the lines of constant
+ 
+
+ align:start position:0%
+perpendicular to the lines of constant
+scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential here in our Magneto quasy
+
+ align:start position:0%
+potential here in our Magneto quasy
+ 
+
+ align:start position:0%
+potential here in our Magneto quasy
+static situation the lines of constant
+
+ align:start position:0%
+static situation the lines of constant
+ 
+
+ align:start position:0%
+static situation the lines of constant
+Vector potential are the field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lines although we may think of the
+
+ align:start position:0%
+lines although we may think of the
+ 
+
+ align:start position:0%
+lines although we may think of the
+fields as two-dimensional their physical
+
+ align:start position:0%
+fields as two-dimensional their physical
+ 
+
+ align:start position:0%
+fields as two-dimensional their physical
+embodiment is actually
+
+ align:start position:0%
+embodiment is actually
+ 
+
+ align:start position:0%
+embodiment is actually
+three-dimensional here's the driving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrode here are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sidewalls the current outward through
+
+ align:start position:0%
+sidewalls the current outward through
+ 
+
+ align:start position:0%
+sidewalls the current outward through
+the driven electrode
+
+ align:start position:0%
+the driven electrode
+ 
+
+ align:start position:0%
+the driven electrode
+is either returned in the side walls
+
+ align:start position:0%
+is either returned in the side walls
+ 
+
+ align:start position:0%
+is either returned in the side walls
+through connecting
+
+ align:start position:0%
+through connecting
+ 
+
+ align:start position:0%
+through connecting
+wires or is induced in the bottom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wall the current outward through the
+
+ align:start position:0%
+wall the current outward through the
+ 
+
+ align:start position:0%
+wall the current outward through the
+driven electrode is either returned in
+
+ align:start position:0%
+driven electrode is either returned in
+ 
+
+ align:start position:0%
+driven electrode is either returned in
+the sidewalls through connecting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wires or is induced in the bottom wall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over any cross-section the fields are
+
+ align:start position:0%
+over any cross-section the fields are
+ 
+
+ align:start position:0%
+over any cross-section the fields are
+two-
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimensional the closer the bottom
+
+ align:start position:0%
+dimensional the closer the bottom
+ 
+
+ align:start position:0%
+dimensional the closer the bottom
+electrode is to the driving electrode
+
+ align:start position:0%
+electrode is to the driving electrode
+ 
+
+ align:start position:0%
+electrode is to the driving electrode
+the more the current circulating through
+
+ align:start position:0%
+the more the current circulating through
+ 
+
+ align:start position:0%
+the more the current circulating through
+the bottom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrode the current from this 20 khz
+
+ align:start position:0%
+electrode the current from this 20 khz
+ 
+
+ align:start position:0%
+electrode the current from this 20 khz
+Source passes forward through the upper
+
+ align:start position:0%
+Source passes forward through the upper
+ 
+
+ align:start position:0%
+Source passes forward through the upper
+electrode and is returned in the
+
+ align:start position:0%
+electrode and is returned in the
+ 
+
+ align:start position:0%
+electrode and is returned in the
+sidewalls through these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shorts so that we can measure that part
+
+ align:start position:0%
+shorts so that we can measure that part
+ 
+
+ align:start position:0%
+shorts so that we can measure that part
+of the current circulating through the
+
+ align:start position:0%
+of the current circulating through the
+ 
+
+ align:start position:0%
+of the current circulating through the
+bottom
+
+ align:start position:0%
+bottom
+ 
+
+ align:start position:0%
+bottom
+electrode it's insulated from the
+
+ align:start position:0%
+electrode it's insulated from the
+ 
+
+ align:start position:0%
+electrode it's insulated from the
+sidewalls but shorted to them at each
+
+ align:start position:0%
+sidewalls but shorted to them at each
+ 
+
+ align:start position:0%
+sidewalls but shorted to them at each
+end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through this conductor current induced
+
+ align:start position:0%
+through this conductor current induced
+ 
+
+ align:start position:0%
+through this conductor current induced
+in the lower plate can therefore return
+
+ align:start position:0%
+in the lower plate can therefore return
+ 
+
+ align:start position:0%
+in the lower plate can therefore return
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+sidewalls to complete the loop the lower
+
+ align:start position:0%
+sidewalls to complete the loop the lower
+ 
+
+ align:start position:0%
+sidewalls to complete the loop the lower
+plate is also shorted to the sidewalls
+
+ align:start position:0%
+plate is also shorted to the sidewalls
+ 
+
+ align:start position:0%
+plate is also shorted to the sidewalls
+at the far
+
+ align:start position:0%
+at the far
+ 
+
+ align:start position:0%
+at the far
+end presumably these shorts have a
+
+ align:start position:0%
+end presumably these shorts have a
+ 
+
+ align:start position:0%
+end presumably these shorts have a
+sufficiently low impedance that the
+
+ align:start position:0%
+sufficiently low impedance that the
+ 
+
+ align:start position:0%
+sufficiently low impedance that the
+lower plate remains at essentially zero
+
+ align:start position:0%
+lower plate remains at essentially zero
+ 
+
+ align:start position:0%
+lower plate remains at essentially zero
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+potential that is the shorts are good
+
+ align:start position:0%
+potential that is the shorts are good
+ 
+
+ align:start position:0%
+potential that is the shorts are good
+enough that little magnetic flux leaks
+
+ align:start position:0%
+enough that little magnetic flux leaks
+ 
+
+ align:start position:0%
+enough that little magnetic flux leaks
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+gaps between the bottom plate and the
+
+ align:start position:0%
+gaps between the bottom plate and the
+ 
+
+ align:start position:0%
+gaps between the bottom plate and the
+sidewalls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll measure the current induced in the
+
+ align:start position:0%
+we'll measure the current induced in the
+ 
+
+ align:start position:0%
+we'll measure the current induced in the
+lower plate with this current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probe how much total current is induced
+
+ align:start position:0%
+probe how much total current is induced
+ 
+
+ align:start position:0%
+probe how much total current is induced
+in the bottom electrode for a given
+
+ align:start position:0%
+in the bottom electrode for a given
+ 
+
+ align:start position:0%
+in the bottom electrode for a given
+voltage applied to the upper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one this is the actual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+apparatus here are the
+
+ align:start position:0%
+apparatus here are the
+ 
+
+ align:start position:0%
+apparatus here are the
+sidewalls insulated from each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the top
+
+ align:start position:0%
+here's the top
+ 
+
+ align:start position:0%
+here's the top
+plate current from this Source passes
+
+ align:start position:0%
+plate current from this Source passes
+ 
+
+ align:start position:0%
+plate current from this Source passes
+forward through the upper plate and is
+
+ align:start position:0%
+forward through the upper plate and is
+ 
+
+ align:start position:0%
+forward through the upper plate and is
+returned by the shorts through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sidewalls here are the connections at
+
+ align:start position:0%
+sidewalls here are the connections at
+ 
+
+ align:start position:0%
+sidewalls here are the connections at
+the back
+
+ align:start position:0%
+the back
+ 
+
+ align:start position:0%
+the back
+end the source is connected by the
+
+ align:start position:0%
+end the source is connected by the
+ 
+
+ align:start position:0%
+end the source is connected by the
+center conductor of a coaxial cable to
+
+ align:start position:0%
+center conductor of a coaxial cable to
+ 
+
+ align:start position:0%
+center conductor of a coaxial cable to
+the upper elect elod
+
+ align:start position:0%
+the upper elect elod
+ 
+
+ align:start position:0%
+the upper elect elod
+here the driving current is returned to
+
+ align:start position:0%
+here the driving current is returned to
+ 
+
+ align:start position:0%
+here the driving current is returned to
+the source by these
+
+ align:start position:0%
+the source by these
+ 
+
+ align:start position:0%
+the source by these
+wires and the coax Shield
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conductor these leads are connected to
+
+ align:start position:0%
+conductor these leads are connected to
+ 
+
+ align:start position:0%
+conductor these leads are connected to
+the top trace of our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scope the top Trace is the driving
+
+ align:start position:0%
+scope the top Trace is the driving
+ 
+
+ align:start position:0%
+scope the top Trace is the driving
+voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here at the back the bottom plate is
+
+ align:start position:0%
+here at the back the bottom plate is
+ 
+
+ align:start position:0%
+here at the back the bottom plate is
+shorted to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sidewalls it is also shorted at the
+
+ align:start position:0%
+sidewalls it is also shorted at the
+ 
+
+ align:start position:0%
+sidewalls it is also shorted at the
+front through these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wires we measure the current induced in
+
+ align:start position:0%
+wires we measure the current induced in
+ 
+
+ align:start position:0%
+wires we measure the current induced in
+this electrode by means of this current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probe the lower trace on the scope
+
+ align:start position:0%
+probe the lower trace on the scope
+ 
+
+ align:start position:0%
+probe the lower trace on the scope
+represents the output current from the
+
+ align:start position:0%
+represents the output current from the
+ 
+
+ align:start position:0%
+represents the output current from the
+probe it represents the net current
+
+ align:start position:0%
+probe it represents the net current
+ 
+
+ align:start position:0%
+probe it represents the net current
+induced in the lower
+
+ align:start position:0%
+induced in the lower
+ 
+
+ align:start position:0%
+induced in the lower
+electrode here's how the current induced
+
+ align:start position:0%
+electrode here's how the current induced
+ 
+
+ align:start position:0%
+electrode here's how the current induced
+in the lower electrode varies as the
+
+ align:start position:0%
+in the lower electrode varies as the
+ 
+
+ align:start position:0%
+in the lower electrode varies as the
+driving electrode is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lowered as the spacing is increased
+
+ align:start position:0%
+lowered as the spacing is increased
+ 
+
+ align:start position:0%
+lowered as the spacing is increased
+again with the driving voltage
+
+ align:start position:0%
+again with the driving voltage
+ 
+
+ align:start position:0%
+again with the driving voltage
+essentially held fixed the induced
+
+ align:start position:0%
+essentially held fixed the induced
+ 
+
+ align:start position:0%
+essentially held fixed the induced
+current decreases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the driving electrode approaches the
+
+ align:start position:0%
+as the driving electrode approaches the
+ 
+
+ align:start position:0%
+as the driving electrode approaches the
+lower electrode it increases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again with the electrodes this close
+
+ align:start position:0%
+again with the electrodes this close
+ 
+
+ align:start position:0%
+again with the electrodes this close
+almost all of the current in the upper
+
+ align:start position:0%
+almost all of the current in the upper
+ 
+
+ align:start position:0%
+almost all of the current in the upper
+electrode is imaged in the lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrode the current in the lower
+
+ align:start position:0%
+electrode the current in the lower
+ 
+
+ align:start position:0%
+electrode the current in the lower
+electrode is the integral of the
+
+ align:start position:0%
+electrode is the integral of the
+ 
+
+ align:start position:0%
+electrode is the integral of the
+tangential magnetic field intensity over
+
+ align:start position:0%
+tangential magnetic field intensity over
+ 
+
+ align:start position:0%
+tangential magnetic field intensity over
+its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length by the nature of this equation
+
+ align:start position:0%
+length by the nature of this equation
+ 
+
+ align:start position:0%
+length by the nature of this equation
+this field intensity becomes weaker as
+
+ align:start position:0%
+this field intensity becomes weaker as
+ 
+
+ align:start position:0%
+this field intensity becomes weaker as
+the distance between top and bottom
+
+ align:start position:0%
+the distance between top and bottom
+ 
+
+ align:start position:0%
+the distance between top and bottom
+electrodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increases as the distance between
+
+ align:start position:0%
+increases as the distance between
+ 
+
+ align:start position:0%
+increases as the distance between
+electrodes
+
+ align:start position:0%
+electrodes
+ 
+
+ align:start position:0%
+electrodes
+increases the fraction of the current
+
+ align:start position:0%
+increases the fraction of the current
+ 
+
+ align:start position:0%
+increases the fraction of the current
+that returns in the lower electrode is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduced the walls have a width w
+
+ align:start position:0%
+reduced the walls have a width w
+ 
+
+ align:start position:0%
+reduced the walls have a width w
+and are separated by
+
+ align:start position:0%
+and are separated by
+ 
+
+ align:start position:0%
+and are separated by
+a we've been adjusting the distance B
+
+ align:start position:0%
+a we've been adjusting the distance B
+ 
+
+ align:start position:0%
+a we've been adjusting the distance B
+between the exitation and detection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plates our modal Theory tells us that
+
+ align:start position:0%
+plates our modal Theory tells us that
+ 
+
+ align:start position:0%
+plates our modal Theory tells us that
+this output current I sub Z has this
+
+ align:start position:0%
+this output current I sub Z has this
+ 
+
+ align:start position:0%
+this output current I sub Z has this
+dependence on the ac exitation voltage
+
+ align:start position:0%
+dependence on the ac exitation voltage
+ 
+
+ align:start position:0%
+dependence on the ac exitation voltage
+amplitude
+
+ align:start position:0%
+amplitude
+ 
+
+ align:start position:0%
+amplitude
+V here's the dependence on the distance
+
+ align:start position:0%
+V here's the dependence on the distance
+ 
+
+ align:start position:0%
+V here's the dependence on the distance
+between exitation and detection
+
+ align:start position:0%
+between exitation and detection
+ 
+
+ align:start position:0%
+between exitation and detection
+plates the normalizing current I is
+
+ align:start position:0%
+plates the normalizing current I is
+ 
+
+ align:start position:0%
+plates the normalizing current I is
+proportional to the driving voltage
+
+ align:start position:0%
+proportional to the driving voltage
+ 
+
+ align:start position:0%
+proportional to the driving voltage
+V and inversely proportional to the
+
+ align:start position:0%
+V and inversely proportional to the
+ 
+
+ align:start position:0%
+V and inversely proportional to the
+angular frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega to make a quantitative comparison
+
+ align:start position:0%
+Omega to make a quantitative comparison
+ 
+
+ align:start position:0%
+Omega to make a quantitative comparison
+between what we predict and what we
+
+ align:start position:0%
+between what we predict and what we
+ 
+
+ align:start position:0%
+between what we predict and what we
+measure we need to compute the
+
+ align:start position:0%
+measure we need to compute the
+ 
+
+ align:start position:0%
+measure we need to compute the
+normalizing current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I the measured applied voltage V is 8.2
+
+ align:start position:0%
+I the measured applied voltage V is 8.2
+ 
+
+ align:start position:0%
+I the measured applied voltage V is 8.2
+molts
+
+ align:start position:0%
+molts
+ 
+
+ align:start position:0%
+molts
+Peak the W is half a
+
+ align:start position:0%
+Peak the W is half a
+ 
+
+ align:start position:0%
+Peak the W is half a
+meter and the frequency is 20
+
+ align:start position:0%
+meter and the frequency is 20
+ 
+
+ align:start position:0%
+meter and the frequency is 20
+khz so in this case I is 53
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amp with b equal to a the measured
+
+ align:start position:0%
+amp with b equal to a the measured
+ 
+
+ align:start position:0%
+amp with b equal to a the measured
+current I Sub 0 is 2.6 milliamps
+
+ align:start position:0%
+current I Sub 0 is 2.6 milliamps
+ 
+
+ align:start position:0%
+current I Sub 0 is 2.6 milliamps
+Peak so the natural log of this current
+
+ align:start position:0%
+Peak so the natural log of this current
+ 
+
+ align:start position:0%
+Peak so the natural log of this current
+normalized to I is -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+5.3 graphically this is the predicted
+
+ align:start position:0%
+5.3 graphically this is the predicted
+ 
+
+ align:start position:0%
+5.3 graphically this is the predicted
+dependence of output current on the
+
+ align:start position:0%
+dependence of output current on the
+ 
+
+ align:start position:0%
+dependence of output current on the
+distance between upper and lower
+
+ align:start position:0%
+distance between upper and lower
+ 
+
+ align:start position:0%
+distance between upper and lower
+plates the vertical axis is the natural
+
+ align:start position:0%
+plates the vertical axis is the natural
+ 
+
+ align:start position:0%
+plates the vertical axis is the natural
+log of the current in the lower
+
+ align:start position:0%
+log of the current in the lower
+ 
+
+ align:start position:0%
+log of the current in the lower
+electrode normalized to the current I
+
+ align:start position:0%
+electrode normalized to the current I
+ 
+
+ align:start position:0%
+electrode normalized to the current I
+which we just
+
+ align:start position:0%
+which we just
+ 
+
+ align:start position:0%
+which we just
+computed the horizontal axis is the
+
+ align:start position:0%
+computed the horizontal axis is the
+ 
+
+ align:start position:0%
+computed the horizontal axis is the
+distance between lower and upper
+
+ align:start position:0%
+distance between lower and upper
+ 
+
+ align:start position:0%
+distance between lower and upper
+electrodes normalized to the distance
+
+ align:start position:0%
+electrodes normalized to the distance
+ 
+
+ align:start position:0%
+electrodes normalized to the distance
+between the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sidewalls the data point which we've
+
+ align:start position:0%
+sidewalls the data point which we've
+ 
+
+ align:start position:0%
+sidewalls the data point which we've
+just taken was for the electrode spacing
+
+ align:start position:0%
+just taken was for the electrode spacing
+ 
+
+ align:start position:0%
+just taken was for the electrode spacing
+equal to the distance between the
+
+ align:start position:0%
+equal to the distance between the
+ 
+
+ align:start position:0%
+equal to the distance between the
+sidewalls so our data point goes here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here are some other values which we've
+
+ align:start position:0%
+here are some other values which we've
+ 
+
+ align:start position:0%
+here are some other values which we've
+measured the current I Sub Zero in the
+
+ align:start position:0%
+measured the current I Sub Zero in the
+ 
+
+ align:start position:0%
+measured the current I Sub Zero in the
+lower electrode does have the correct
+
+ align:start position:0%
+lower electrode does have the correct
+ 
+
+ align:start position:0%
+lower electrode does have the correct
+variation with spacing between the
+
+ align:start position:0%
+variation with spacing between the
+ 
+
+ align:start position:0%
+variation with spacing between the
+electrodes however it's displaced
+
+ align:start position:0%
+electrodes however it's displaced
+ 
+
+ align:start position:0%
+electrodes however it's displaced
+downward from the predicted curve by
+
+ align:start position:0%
+downward from the predicted curve by
+ 
+
+ align:start position:0%
+downward from the predicted curve by
+essentially a constant factor of eight
+
+ align:start position:0%
+essentially a constant factor of eight
+ 
+
+ align:start position:0%
+essentially a constant factor of eight
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n the main main reason for this
+
+ align:start position:0%
+n the main main reason for this
+ 
+
+ align:start position:0%
+n the main main reason for this
+discrepancy is the flux linked by the
+
+ align:start position:0%
+discrepancy is the flux linked by the
+ 
+
+ align:start position:0%
+discrepancy is the flux linked by the
+wires used to provide the return current
+
+ align:start position:0%
+wires used to provide the return current
+ 
+
+ align:start position:0%
+wires used to provide the return current
+paths the rate of change of this flux
+
+ align:start position:0%
+paths the rate of change of this flux
+ 
+
+ align:start position:0%
+paths the rate of change of this flux
+makes an addition to the measured
+
+ align:start position:0%
+makes an addition to the measured
+ 
+
+ align:start position:0%
+makes an addition to the measured
+terminal voltage that makes the
+
+ align:start position:0%
+terminal voltage that makes the
+ 
+
+ align:start position:0%
+terminal voltage that makes the
+normalization current I larger than it
+
+ align:start position:0%
+normalization current I larger than it
+ 
+
+ align:start position:0%
+normalization current I larger than it
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+be to see this we can use a loop of wire
+
+ align:start position:0%
+be to see this we can use a loop of wire
+ 
+
+ align:start position:0%
+be to see this we can use a loop of wire
+rather than the terminal voltage to
+
+ align:start position:0%
+rather than the terminal voltage to
+ 
+
+ align:start position:0%
+rather than the terminal voltage to
+measure the flux through the gap between
+
+ align:start position:0%
+measure the flux through the gap between
+ 
+
+ align:start position:0%
+measure the flux through the gap between
+the upper electrode and the left
+
+ align:start position:0%
+the upper electrode and the left
+ 
+
+ align:start position:0%
+the upper electrode and the left
+wall the loop passes along the outer
+
+ align:start position:0%
+wall the loop passes along the outer
+ 
+
+ align:start position:0%
+wall the loop passes along the outer
+edge of the upper Electric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elod and is returned just outside the
+
+ align:start position:0%
+elod and is returned just outside the
+ 
+
+ align:start position:0%
+elod and is returned just outside the
+adjacent conducting
+
+ align:start position:0%
+adjacent conducting
+ 
+
+ align:start position:0%
+adjacent conducting
+wall so arranged it links little
+
+ align:start position:0%
+wall so arranged it links little
+ 
+
+ align:start position:0%
+wall so arranged it links little
+extraneous flux at the
+
+ align:start position:0%
+extraneous flux at the
+ 
+
+ align:start position:0%
+extraneous flux at the
+ends also because it will be connected
+
+ align:start position:0%
+ends also because it will be connected
+ 
+
+ align:start position:0%
+ends also because it will be connected
+to the high impedance of the
+
+ align:start position:0%
+to the high impedance of the
+ 
+
+ align:start position:0%
+to the high impedance of the
+scope it carries a negligible current
+
+ align:start position:0%
+scope it carries a negligible current
+ 
+
+ align:start position:0%
+scope it carries a negligible current
+and so the integral of the electric
+
+ align:start position:0%
+and so the integral of the electric
+ 
+
+ align:start position:0%
+and so the integral of the electric
+field intensity around the loop which is
+
+ align:start position:0%
+field intensity around the loop which is
+ 
+
+ align:start position:0%
+field intensity around the loop which is
+the voltage at the
+
+ align:start position:0%
+the voltage at the
+ 
+
+ align:start position:0%
+the voltage at the
+terminals does not have a part due to
+
+ align:start position:0%
+terminals does not have a part due to
+ 
+
+ align:start position:0%
+terminals does not have a part due to
+the resistance of the
+
+ align:start position:0%
+the resistance of the
+ 
+
+ align:start position:0%
+the resistance of the
+loop the top Trace is the electrode
+
+ align:start position:0%
+loop the top Trace is the electrode
+ 
+
+ align:start position:0%
+loop the top Trace is the electrode
+driving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage here's the terminal voltage of
+
+ align:start position:0%
+voltage here's the terminal voltage of
+ 
+
+ align:start position:0%
+voltage here's the terminal voltage of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loop with the spacing between electrodes
+
+ align:start position:0%
+loop with the spacing between electrodes
+ 
+
+ align:start position:0%
+loop with the spacing between electrodes
+equal to that between the walls the
+
+ align:start position:0%
+equal to that between the walls the
+ 
+
+ align:start position:0%
+equal to that between the walls the
+terminal voltage of the flux Loop is
+
+ align:start position:0%
+terminal voltage of the flux Loop is
+ 
+
+ align:start position:0%
+terminal voltage of the flux Loop is
+about 1.2 mols
+
+ align:start position:0%
+about 1.2 mols
+ 
+
+ align:start position:0%
+about 1.2 mols
+Peak under these same conditions the
+
+ align:start position:0%
+Peak under these same conditions the
+ 
+
+ align:start position:0%
+Peak under these same conditions the
+upper electrode ter voltage was 8.2 Mt
+
+ align:start position:0%
+upper electrode ter voltage was 8.2 Mt
+ 
+
+ align:start position:0%
+upper electrode ter voltage was 8.2 Mt
+Peak about a factor of seven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+larger this data point and others we've
+
+ align:start position:0%
+larger this data point and others we've
+ 
+
+ align:start position:0%
+larger this data point and others we've
+taken using the flux Loop rather than
+
+ align:start position:0%
+taken using the flux Loop rather than
+ 
+
+ align:start position:0%
+taken using the flux Loop rather than
+the upper electrode terminal
+
+ align:start position:0%
+the upper electrode terminal
+ 
+
+ align:start position:0%
+the upper electrode terminal
+voltage not only have the predicted
+
+ align:start position:0%
+voltage not only have the predicted
+ 
+
+ align:start position:0%
+voltage not only have the predicted
+dependence on electrode spacing but more
+
+ align:start position:0%
+dependence on electrode spacing but more
+ 
+
+ align:start position:0%
+dependence on electrode spacing but more
+nearly the predicted absolute magnitude
+
+ align:start position:0%
+nearly the predicted absolute magnitude
+ 
+
+ align:start position:0%
+nearly the predicted absolute magnitude
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the inductive attenuator has
+
+ align:start position:0%
+well the inductive attenuator has
+ 
+
+ align:start position:0%
+well the inductive attenuator has
+Illustrated the lloan nature of free
+
+ align:start position:0%
+Illustrated the lloan nature of free
+ 
+
+ align:start position:0%
+Illustrated the lloan nature of free
+space Magneto quazy static
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fields the magnetic field induced by
+
+ align:start position:0%
+Fields the magnetic field induced by
+ 
+
+ align:start position:0%
+Fields the magnetic field induced by
+applying a voltage to the upper
+
+ align:start position:0%
+applying a voltage to the upper
+ 
+
+ align:start position:0%
+applying a voltage to the upper
+electrode decays essentially
+
+ align:start position:0%
+electrode decays essentially
+ 
+
+ align:start position:0%
+electrode decays essentially
+exponentially into the rectangular
+
+ align:start position:0%
+exponentially into the rectangular
+ 
+
+ align:start position:0%
+exponentially into the rectangular
+region bounded by the essentially
+
+ align:start position:0%
+region bounded by the essentially
+ 
+
+ align:start position:0%
+region bounded by the essentially
+perfectly conducting sidewalls and the
+
+ align:start position:0%
+perfectly conducting sidewalls and the
+ 
+
+ align:start position:0%
+perfectly conducting sidewalls and the
+bottom electrode
\ No newline at end of file
diff --git a/mXkPCaZUXhg.txt b/mXkPCaZUXhg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e7b8ff9c2e44caa95da3727c41ea7b7034bcf14c
--- /dev/null
+++ b/mXkPCaZUXhg.txt
@@ -0,0 +1,13099 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so today we're gonna do some really
+
+ align:start position:0%
+okay so today we're gonna do some really
+ 
+
+ align:start position:0%
+okay so today we're gonna do some really
+cool stuff having to do with
+
+ align:start position:0%
+cool stuff having to do with
+ 
+
+ align:start position:0%
+cool stuff having to do with
+non-deterministic parallel programming
+
+ align:start position:0%
+non-deterministic parallel programming
+ 
+
+ align:start position:0%
+non-deterministic parallel programming
+this is where the course starts to get
+
+ align:start position:0%
+this is where the course starts to get
+ 
+
+ align:start position:0%
+this is where the course starts to get
+hard because non determinism is really
+
+ align:start position:0%
+hard because non determinism is really
+ 
+
+ align:start position:0%
+hard because non determinism is really
+nasty we'll talk about a little bit it's
+
+ align:start position:0%
+nasty we'll talk about a little bit it's
+ 
+
+ align:start position:0%
+nasty we'll talk about a little bit it's
+really nasty parallel computing as you
+
+ align:start position:0%
+really nasty parallel computing as you
+ 
+
+ align:start position:0%
+really nasty parallel computing as you
+know is pretty easy right you know it's
+
+ align:start position:0%
+know is pretty easy right you know it's
+ 
+
+ align:start position:0%
+know is pretty easy right you know it's
+just working span easy stuff right it
+
+ align:start position:0%
+just working span easy stuff right it
+ 
+
+ align:start position:0%
+just working span easy stuff right it
+makes sense can measure these things can
+
+ align:start position:0%
+makes sense can measure these things can
+ 
+
+ align:start position:0%
+makes sense can measure these things can
+learn some skills around them and so
+
+ align:start position:0%
+learn some skills around them and so
+ 
+
+ align:start position:0%
+learn some skills around them and so
+forth but non determinism is is is nasty
+
+ align:start position:0%
+forth but non determinism is is is nasty
+ 
+
+ align:start position:0%
+forth but non determinism is is is nasty
+really nasty so first let's talk about
+
+ align:start position:0%
+really nasty so first let's talk about
+ 
+
+ align:start position:0%
+really nasty so first let's talk about
+what we mean by determinism so we say
+
+ align:start position:0%
+what we mean by determinism so we say
+ 
+
+ align:start position:0%
+what we mean by determinism so we say
+that a program is deterministic on a
+
+ align:start position:0%
+that a program is deterministic on a
+ 
+
+ align:start position:0%
+that a program is deterministic on a
+given input if every memory location is
+
+ align:start position:0%
+given input if every memory location is
+ 
+
+ align:start position:0%
+given input if every memory location is
+updated with the sequence the same
+
+ align:start position:0%
+updated with the sequence the same
+ 
+
+ align:start position:0%
+updated with the sequence the same
+sequence of values in every execution so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the program always behaves the same and
+
+ align:start position:0%
+the program always behaves the same and
+ 
+
+ align:start position:0%
+the program always behaves the same and
+you may end up if it's a parallel
+
+ align:start position:0%
+you may end up if it's a parallel
+ 
+
+ align:start position:0%
+you may end up if it's a parallel
+program having different memory
+
+ align:start position:0%
+program having different memory
+ 
+
+ align:start position:0%
+program having different memory
+locations updated in different orders I
+
+ align:start position:0%
+locations updated in different orders I
+ 
+
+ align:start position:0%
+locations updated in different orders I
+may do a and then B versus updating B
+
+ align:start position:0%
+may do a and then B versus updating B
+ 
+
+ align:start position:0%
+may do a and then B versus updating B
+and then a but if I look at a single
+
+ align:start position:0%
+and then a but if I look at a single
+ 
+
+ align:start position:0%
+and then a but if I look at a single
+memory location a say I'm always
+
+ align:start position:0%
+memory location a say I'm always
+ 
+
+ align:start position:0%
+memory location a say I'm always
+updating a with the same sequence of
+
+ align:start position:0%
+updating a with the same sequence of
+ 
+
+ align:start position:0%
+updating a with the same sequence of
+values okay there are lots of
+
+ align:start position:0%
+values okay there are lots of
+ 
+
+ align:start position:0%
+values okay there are lots of
+definitions of determinism this is not
+
+ align:start position:0%
+definitions of determinism this is not
+ 
+
+ align:start position:0%
+definitions of determinism this is not
+the only one okay there's some where
+
+ align:start position:0%
+the only one okay there's some where
+ 
+
+ align:start position:0%
+the only one okay there's some where
+people say well it's only matters if the
+
+ align:start position:0%
+people say well it's only matters if the
+ 
+
+ align:start position:0%
+people say well it's only matters if the
+output is always the same okay and there
+
+ align:start position:0%
+output is always the same okay and there
+ 
+
+ align:start position:0%
+output is always the same okay and there
+are others where you say not only does
+
+ align:start position:0%
+are others where you say not only does
+ 
+
+ align:start position:0%
+are others where you say not only does
+it have to be the same but every right
+
+ align:start position:0%
+it have to be the same but every right
+ 
+
+ align:start position:0%
+it have to be the same but every right
+to a location has to be in the same
+
+ align:start position:0%
+to a location has to be in the same
+ 
+
+ align:start position:0%
+to a location has to be in the same
+order globally okay that turns out to be
+
+ align:start position:0%
+order globally okay that turns out to be
+ 
+
+ align:start position:0%
+order globally okay that turns out to be
+actually pretty hard because if you have
+
+ align:start position:0%
+actually pretty hard because if you have
+ 
+
+ align:start position:0%
+actually pretty hard because if you have
+parallel computing you're not going to
+
+ align:start position:0%
+parallel computing you're not going to
+ 
+
+ align:start position:0%
+parallel computing you're not going to
+get them all updated the same unless you
+
+ align:start position:0%
+get them all updated the same unless you
+ 
+
+ align:start position:0%
+get them all updated the same unless you
+only have one
+
+ align:start position:0%
+only have one
+ 
+
+ align:start position:0%
+only have one
+you know processor executing
+
+ align:start position:0%
+you know processor executing
+ 
+
+ align:start position:0%
+you know processor executing
+instructions okay and so we'll talk
+
+ align:start position:0%
+instructions okay and so we'll talk
+ 
+
+ align:start position:0%
+instructions okay and so we'll talk
+about this we'll talk a little bit more
+
+ align:start position:0%
+about this we'll talk a little bit more
+ 
+
+ align:start position:0%
+about this we'll talk a little bit more
+about this kind of thing so so why
+
+ align:start position:0%
+about this kind of thing so so why
+ 
+
+ align:start position:0%
+about this kind of thing so so why
+what's the big advantage of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deterministic programs why should we
+
+ align:start position:0%
+deterministic programs why should we
+ 
+
+ align:start position:0%
+deterministic programs why should we
+care whether it's deterministic or
+
+ align:start position:0%
+care whether it's deterministic or
+ 
+
+ align:start position:0%
+care whether it's deterministic or
+non-deterministic sure
+
+ align:start position:0%
+non-deterministic sure
+ 
+
+ align:start position:0%
+non-deterministic sure
+it's repeatable okay so what
+
+ align:start position:0%
+it's repeatable okay so what
+ 
+
+ align:start position:0%
+it's repeatable okay so what
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because sometimes that's what you want
+
+ align:start position:0%
+because sometimes that's what you want
+ 
+
+ align:start position:0%
+because sometimes that's what you want
+okay that doesn't say okay so if I mean
+
+ align:start position:0%
+okay that doesn't say okay so if I mean
+ 
+
+ align:start position:0%
+okay that doesn't say okay so if I mean
+there's a lot of things I might
+
+ align:start position:0%
+there's a lot of things I might
+ 
+
+ align:start position:0%
+there's a lot of things I might
+sometimes want how why is that important
+
+ align:start position:0%
+sometimes want how why is that important
+ 
+
+ align:start position:0%
+sometimes want how why is that important
+to want that yeah yeah makes it easier
+
+ align:start position:0%
+to want that yeah yeah makes it easier
+ 
+
+ align:start position:0%
+to want that yeah yeah makes it easier
+to debug that's probably the number one
+
+ align:start position:0%
+to debug that's probably the number one
+ 
+
+ align:start position:0%
+to debug that's probably the number one
+reason debugging okay if it does the
+
+ align:start position:0%
+reason debugging okay if it does the
+ 
+
+ align:start position:0%
+reason debugging okay if it does the
+same thing every time right then if you
+
+ align:start position:0%
+same thing every time right then if you
+ 
+
+ align:start position:0%
+same thing every time right then if you
+have a bug you can run it again you
+
+ align:start position:0%
+have a bug you can run it again you
+ 
+
+ align:start position:0%
+have a bug you can run it again you
+expect to see the bug again right so
+
+ align:start position:0%
+expect to see the bug again right so
+ 
+
+ align:start position:0%
+expect to see the bug again right so
+every time you run through hey I get the
+
+ align:start position:0%
+every time you run through hey I get the
+ 
+
+ align:start position:0%
+every time you run through hey I get the
+same bug okay but if it's
+
+ align:start position:0%
+same bug okay but if it's
+ 
+
+ align:start position:0%
+same bug okay but if it's
+non-deterministic I get a bug and now I
+
+ align:start position:0%
+non-deterministic I get a bug and now I
+ 
+
+ align:start position:0%
+non-deterministic I get a bug and now I
+go to look for it and the bug is nowhere
+
+ align:start position:0%
+go to look for it and the bug is nowhere
+ 
+
+ align:start position:0%
+go to look for it and the bug is nowhere
+to be found
+
+ align:start position:0%
+to be found
+ 
+
+ align:start position:0%
+to be found
+makes debugging a lot harder there are
+
+ align:start position:0%
+makes debugging a lot harder there are
+ 
+
+ align:start position:0%
+makes debugging a lot harder there are
+other reasons for wanting repeatability
+
+ align:start position:0%
+other reasons for wanting repeatability
+ 
+
+ align:start position:0%
+other reasons for wanting repeatability
+so your answer is actually a broader
+
+ align:start position:0%
+so your answer is actually a broader
+ 
+
+ align:start position:0%
+so your answer is actually a broader
+correct answer but but the the big
+
+ align:start position:0%
+correct answer but but the the big
+ 
+
+ align:start position:0%
+correct answer but but the the big
+advantage is in the specific application
+
+ align:start position:0%
+advantage is in the specific application
+ 
+
+ align:start position:0%
+advantage is in the specific application
+of repeatability to debugging okay so
+
+ align:start position:0%
+of repeatability to debugging okay so
+ 
+
+ align:start position:0%
+of repeatability to debugging okay so
+here's the golden rule of parallel
+
+ align:start position:0%
+here's the golden rule of parallel
+ 
+
+ align:start position:0%
+here's the golden rule of parallel
+programming okay
+
+ align:start position:0%
+programming okay
+ 
+
+ align:start position:0%
+programming okay
+never write non-deterministic parallel
+
+ align:start position:0%
+never write non-deterministic parallel
+ 
+
+ align:start position:0%
+never write non-deterministic parallel
+programs okay they can exhibit anomalous
+
+ align:start position:0%
+programs okay they can exhibit anomalous
+ 
+
+ align:start position:0%
+programs okay they can exhibit anomalous
+behaviors and it's hard to debug them
+
+ align:start position:0%
+behaviors and it's hard to debug them
+ 
+
+ align:start position:0%
+behaviors and it's hard to debug them
+okay so never ever write
+
+ align:start position:0%
+okay so never ever write
+ 
+
+ align:start position:0%
+okay so never ever write
+non-deterministic programs unfortunately
+
+ align:start position:0%
+non-deterministic programs unfortunately
+ 
+
+ align:start position:0%
+non-deterministic programs unfortunately
+this is one of these things that is kind
+
+ align:start position:0%
+this is one of these things that is kind
+ 
+
+ align:start position:0%
+this is one of these things that is kind
+of hard in practice to do so why might
+
+ align:start position:0%
+of hard in practice to do so why might
+ 
+
+ align:start position:0%
+of hard in practice to do so why might
+you want to write a non-deterministic
+
+ align:start position:0%
+you want to write a non-deterministic
+ 
+
+ align:start position:0%
+you want to write a non-deterministic
+program even though even when famous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+masters in the area of performance
+
+ align:start position:0%
+masters in the area of performance
+ 
+
+ align:start position:0%
+masters in the area of performance
+engineering okay with with highly
+
+ align:start position:0%
+engineering okay with with highly
+ 
+
+ align:start position:0%
+engineering okay with with highly
+credentialed you know numerous awards
+
+ align:start position:0%
+credentialed you know numerous awards
+ 
+
+ align:start position:0%
+credentialed you know numerous awards
+and so forth tell you you shouldn't
+
+ align:start position:0%
+and so forth tell you you shouldn't
+ 
+
+ align:start position:0%
+and so forth tell you you shouldn't
+write non-deterministic programs why
+
+ align:start position:0%
+write non-deterministic programs why
+ 
+
+ align:start position:0%
+write non-deterministic programs why
+might you want to do it anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah you might get better
+
+ align:start position:0%
+yeah yeah you might get better
+ 
+
+ align:start position:0%
+yeah yeah you might get better
+performance that's a that's one of the
+
+ align:start position:0%
+performance that's a that's one of the
+ 
+
+ align:start position:0%
+performance that's a that's one of the
+big ones that's one of the big ones and
+
+ align:start position:0%
+big ones that's one of the big ones and
+ 
+
+ align:start position:0%
+big ones that's one of the big ones and
+sometimes you can't
+
+ align:start position:0%
+sometimes you can't
+ 
+
+ align:start position:0%
+sometimes you can't
+okay the nature of the problem is maybe
+
+ align:start position:0%
+okay the nature of the problem is maybe
+ 
+
+ align:start position:0%
+okay the nature of the problem is maybe
+that it's that it's non determinacy you
+
+ align:start position:0%
+that it's that it's non determinacy you
+ 
+
+ align:start position:0%
+that it's that it's non determinacy you
+may have asynchronous inputs coming in
+
+ align:start position:0%
+may have asynchronous inputs coming in
+ 
+
+ align:start position:0%
+may have asynchronous inputs coming in
+and so forth so so this is the Golden
+
+ align:start position:0%
+and so forth so so this is the Golden
+ 
+
+ align:start position:0%
+and so forth so so this is the Golden
+Rule we also have a silver rule silver
+
+ align:start position:0%
+Rule we also have a silver rule silver
+ 
+
+ align:start position:0%
+Rule we also have a silver rule silver
+rule says never write non-deterministic
+
+ align:start position:0%
+rule says never write non-deterministic
+ 
+
+ align:start position:0%
+rule says never write non-deterministic
+parallel programs but if you must always
+
+ align:start position:0%
+parallel programs but if you must always
+ 
+
+ align:start position:0%
+parallel programs but if you must always
+devise a test strategy to manage the non
+
+ align:start position:0%
+devise a test strategy to manage the non
+ 
+
+ align:start position:0%
+devise a test strategy to manage the non
+determinism okay so this gets into you
+
+ align:start position:0%
+determinism okay so this gets into you
+ 
+
+ align:start position:0%
+determinism okay so this gets into you
+better have some way of handling how
+
+ align:start position:0%
+better have some way of handling how
+ 
+
+ align:start position:0%
+better have some way of handling how
+you're gonna tell what's going on if you
+
+ align:start position:0%
+you're gonna tell what's going on if you
+ 
+
+ align:start position:0%
+you're gonna tell what's going on if you
+have a bug okay so what are some of the
+
+ align:start position:0%
+have a bug okay so what are some of the
+ 
+
+ align:start position:0%
+have a bug okay so what are some of the
+typical test strategies that you could
+
+ align:start position:0%
+typical test strategies that you could
+ 
+
+ align:start position:0%
+typical test strategies that you could
+use that would manage the non
+
+ align:start position:0%
+use that would manage the non
+ 
+
+ align:start position:0%
+use that would manage the non
+determinism okay so imagine you've got a
+
+ align:start position:0%
+determinism okay so imagine you've got a
+ 
+
+ align:start position:0%
+determinism okay so imagine you've got a
+parallel program and it's it's got races
+
+ align:start position:0%
+parallel program and it's it's got races
+ 
+
+ align:start position:0%
+parallel program and it's it's got races
+in it and so forth
+
+ align:start position:0%
+in it and so forth
+ 
+
+ align:start position:0%
+in it and so forth
+you know and its operating
+
+ align:start position:0%
+you know and its operating
+ 
+
+ align:start position:0%
+you know and its operating
+non-deterministically what and that's
+
+ align:start position:0%
+non-deterministically what and that's
+ 
+
+ align:start position:0%
+non-deterministically what and that's
+okay if it's everything's going right
+
+ align:start position:0%
+okay if it's everything's going right
+ 
+
+ align:start position:0%
+okay if it's everything's going right
+how would you you find a bug in the
+
+ align:start position:0%
+how would you you find a bug in the
+ 
+
+ align:start position:0%
+how would you you find a bug in the
+program how are you what are you going
+
+ align:start position:0%
+program how are you what are you going
+ 
+
+ align:start position:0%
+program how are you what are you going
+to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what kinds of ideas do you have yeah
+
+ align:start position:0%
+what kinds of ideas do you have yeah
+ 
+
+ align:start position:0%
+what kinds of ideas do you have yeah
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you could turn off the
+
+ align:start position:0%
+yeah you could turn off the
+ 
+
+ align:start position:0%
+yeah you could turn off the
+non-determinism okay you put a switch in
+
+ align:start position:0%
+non-determinism okay you put a switch in
+ 
+
+ align:start position:0%
+non-determinism okay you put a switch in
+there that says well I know the source
+
+ align:start position:0%
+there that says well I know the source
+ 
+
+ align:start position:0%
+there that says well I know the source
+of this non-deterministic behavior let
+
+ align:start position:0%
+of this non-deterministic behavior let
+ 
+
+ align:start position:0%
+of this non-deterministic behavior let
+me do that let me give you an example of
+
+ align:start position:0%
+me do that let me give you an example of
+ 
+
+ align:start position:0%
+me do that let me give you an example of
+that for security reasons these days
+
+ align:start position:0%
+that for security reasons these days
+ 
+
+ align:start position:0%
+that for security reasons these days
+when you allocate memory its allocated
+
+ align:start position:0%
+when you allocate memory its allocated
+ 
+
+ align:start position:0%
+when you allocate memory its allocated
+to different locations on different runs
+
+ align:start position:0%
+to different locations on different runs
+ 
+
+ align:start position:0%
+to different locations on different runs
+of the program its allocated in random
+
+ align:start position:0%
+of the program its allocated in random
+ 
+
+ align:start position:0%
+of the program its allocated in random
+places they want to randomize the
+
+ align:start position:0%
+places they want to randomize the
+ 
+
+ align:start position:0%
+places they want to randomize the
+addresses when you call malloc okay that
+
+ align:start position:0%
+addresses when you call malloc okay that
+ 
+
+ align:start position:0%
+addresses when you call malloc okay that
+means that you can end up with different
+
+ align:start position:0%
+means that you can end up with different
+ 
+
+ align:start position:0%
+means that you can end up with different
+behaviors okay from one to run and that
+
+ align:start position:0%
+behaviors okay from one to run and that
+ 
+
+ align:start position:0%
+behaviors okay from one to run and that
+can compromise your your performance but
+
+ align:start position:0%
+can compromise your your performance but
+ 
+
+ align:start position:0%
+can compromise your your performance but
+there turns out that there is a compiler
+
+ align:start position:0%
+there turns out that there is a compiler
+ 
+
+ align:start position:0%
+there turns out that there is a compiler
+switch and if you run it in debug mode
+
+ align:start position:0%
+switch and if you run it in debug mode
+ 
+
+ align:start position:0%
+switch and if you run it in debug mode
+it'll always deliver the the results of
+
+ align:start position:0%
+it'll always deliver the the results of
+ 
+
+ align:start position:0%
+it'll always deliver the the results of
+malloc in in deterministic locations
+
+ align:start position:0%
+malloc in in deterministic locations
+ 
+
+ align:start position:0%
+malloc in in deterministic locations
+okay where the locations the of the
+
+ align:start position:0%
+okay where the locations the of the
+ 
+
+ align:start position:0%
+okay where the locations the of the
+things your mouth looking are you know
+
+ align:start position:0%
+things your mouth looking are you know
+ 
+
+ align:start position:0%
+things your mouth looking are you know
+are repeatable okay so that's that's
+
+ align:start position:0%
+are repeatable okay so that's that's
+ 
+
+ align:start position:0%
+are repeatable okay so that's that's
+good okay because there's support they
+
+ align:start position:0%
+good okay because there's support they
+ 
+
+ align:start position:0%
+good okay because there's support they
+said yes we have to randomize okay for
+
+ align:start position:0%
+said yes we have to randomize okay for
+ 
+
+ align:start position:0%
+said yes we have to randomize okay for
+security reasons so that people can't
+
+ align:start position:0%
+security reasons so that people can't
+ 
+
+ align:start position:0%
+security reasons so that people can't
+deterministically exploit buffer
+
+ align:start position:0%
+deterministically exploit buffer
+ 
+
+ align:start position:0%
+deterministically exploit buffer
+overflow errors for example but you know
+
+ align:start position:0%
+overflow errors for example but you know
+ 
+
+ align:start position:0%
+overflow errors for example but you know
+I don't want to have to do that every
+
+ align:start position:0%
+I don't want to have to do that every
+ 
+
+ align:start position:0%
+I don't want to have to do that every
+time okay so you know I I don't want to
+
+ align:start position:0%
+time okay so you know I I don't want to
+ 
+
+ align:start position:0%
+time okay so you know I I don't want to
+randomize you know every time I run I
+
+ align:start position:0%
+randomize you know every time I run I
+ 
+
+ align:start position:0%
+randomize you know every time I run I
+won't have the option of making it so
+
+ align:start position:0%
+won't have the option of making it so
+ 
+
+ align:start position:0%
+won't have the option of making it so
+that that randomization is turned off
+
+ align:start position:0%
+that that randomization is turned off
+ 
+
+ align:start position:0%
+that that randomization is turned off
+okay so that's a good one
+
+ align:start position:0%
+okay so that's a good one
+ 
+
+ align:start position:0%
+okay so that's a good one
+what's another one that that can be done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're full of good ideas this is like
+
+ align:start position:0%
+you're full of good ideas this is like
+ 
+
+ align:start position:0%
+you're full of good ideas this is like
+let's try somebody else or not okay
+
+ align:start position:0%
+let's try somebody else or not okay
+ 
+
+ align:start position:0%
+let's try somebody else or not okay
+that's good I like that I like that what
+
+ align:start position:0%
+that's good I like that I like that what
+ 
+
+ align:start position:0%
+that's good I like that I like that what
+are some other ideas what else can you
+
+ align:start position:0%
+are some other ideas what else can you
+ 
+
+ align:start position:0%
+are some other ideas what else can you
+do to handle non determinism okay you
+
+ align:start position:0%
+do to handle non determinism okay you
+ 
+
+ align:start position:0%
+do to handle non determinism okay you
+got a program and it's yeah yeah yeah
+
+ align:start position:0%
+got a program and it's yeah yeah yeah
+ 
+
+ align:start position:0%
+got a program and it's yeah yeah yeah
+yeah if you have random numbers you use
+
+ align:start position:0%
+yeah if you have random numbers you use
+ 
+
+ align:start position:0%
+yeah if you have random numbers you use
+the same seed in some sense that's a
+
+ align:start position:0%
+the same seed in some sense that's a
+ 
+
+ align:start position:0%
+the same seed in some sense that's a
+kind of of same thing if you're turning
+
+ align:start position:0%
+kind of of same thing if you're turning
+ 
+
+ align:start position:0%
+kind of of same thing if you're turning
+off non determinism okay but that's a
+
+ align:start position:0%
+off non determinism okay but that's a
+ 
+
+ align:start position:0%
+off non determinism okay but that's a
+great one you know there are other
+
+ align:start position:0%
+great one you know there are other
+ 
+
+ align:start position:0%
+great one you know there are other
+places for example if you read you know
+
+ align:start position:0%
+places for example if you read you know
+ 
+
+ align:start position:0%
+places for example if you read you know
+if you do get time of day you know for
+
+ align:start position:0%
+if you do get time of day you know for
+ 
+
+ align:start position:0%
+if you do get time of day you know for
+something in your program for something
+
+ align:start position:0%
+something in your program for something
+ 
+
+ align:start position:0%
+something in your program for something
+you could have an option where it'll put
+
+ align:start position:0%
+you could have an option where it'll put
+ 
+
+ align:start position:0%
+you could have an option where it'll put
+in a particular fixed value there so you
+
+ align:start position:0%
+in a particular fixed value there so you
+ 
+
+ align:start position:0%
+in a particular fixed value there so you
+can make sure that it doesn't you know
+
+ align:start position:0%
+can make sure that it doesn't you know
+ 
+
+ align:start position:0%
+can make sure that it doesn't you know
+even a serial program isn't
+
+ align:start position:0%
+even a serial program isn't
+ 
+
+ align:start position:0%
+even a serial program isn't
+non-deterministic okay so that's good
+
+ align:start position:0%
+non-deterministic okay so that's good
+ 
+
+ align:start position:0%
+non-deterministic okay so that's good
+but I also consider that to be that's
+
+ align:start position:0%
+but I also consider that to be that's
+ 
+
+ align:start position:0%
+but I also consider that to be that's
+another great example of turning off non
+
+ align:start position:0%
+another great example of turning off non
+ 
+
+ align:start position:0%
+another great example of turning off non
+determinism okay what other things can
+
+ align:start position:0%
+determinism okay what other things can
+ 
+
+ align:start position:0%
+determinism okay what other things can
+you do yeah
+
+ align:start position:0%
+you do yeah
+ 
+
+ align:start position:0%
+you do yeah
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+ah yep you can do record replay for some
+
+ align:start position:0%
+ah yep you can do record replay for some
+ 
+
+ align:start position:0%
+ah yep you can do record replay for some
+things is that what you're saying is
+
+ align:start position:0%
+things is that what you're saying is
+ 
+
+ align:start position:0%
+things is that what you're saying is
+that what you mean or am i okay so
+
+ align:start position:0%
+that what you mean or am i okay so
+ 
+
+ align:start position:0%
+that what you mean or am i okay so
+record replay says you run it through
+
+ align:start position:0%
+record replay says you run it through
+ 
+
+ align:start position:0%
+record replay says you run it through
+you can run it through with random
+
+ align:start position:0%
+you can run it through with random
+ 
+
+ align:start position:0%
+you can run it through with random
+numbers and then but it's recording
+
+ align:start position:0%
+numbers and then but it's recording
+ 
+
+ align:start position:0%
+numbers and then but it's recording
+those things so that when you when you
+
+ align:start position:0%
+those things so that when you when you
+ 
+
+ align:start position:0%
+those things so that when you when you
+run it again you can instead of using
+
+ align:start position:0%
+run it again you can instead of using
+ 
+
+ align:start position:0%
+run it again you can instead of using
+the random numbers that you you know new
+
+ align:start position:0%
+the random numbers that you you know new
+ 
+
+ align:start position:0%
+the random numbers that you you know new
+random numbers it uses the ones that you
+
+ align:start position:0%
+random numbers it uses the ones that you
+ 
+
+ align:start position:0%
+random numbers it uses the ones that you
+used to use okay so that's a record
+
+ align:start position:0%
+used to use okay so that's a record
+ 
+
+ align:start position:0%
+used to use okay so that's a record
+replay thing is that what you're saying
+
+ align:start position:0%
+replay thing is that what you're saying
+ 
+
+ align:start position:0%
+replay thing is that what you're saying
+are you saying something else yeah okay
+
+ align:start position:0%
+are you saying something else yeah okay
+ 
+
+ align:start position:0%
+are you saying something else yeah okay
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+okay so this so that's using using some
+
+ align:start position:0%
+okay so this so that's using using some
+ 
+
+ align:start position:0%
+okay so this so that's using using some
+tools there's actually a lot of
+
+ align:start position:0%
+tools there's actually a lot of
+ 
+
+ align:start position:0%
+tools there's actually a lot of
+strategies let me just move on in answer
+
+ align:start position:0%
+strategies let me just move on in answer
+ 
+
+ align:start position:0%
+strategies let me just move on in answer
+so another thing you can do is
+
+ align:start position:0%
+so another thing you can do is
+ 
+
+ align:start position:0%
+so another thing you can do is
+encapsulate the non-determinism so
+
+ align:start position:0%
+encapsulate the non-determinism so
+ 
+
+ align:start position:0%
+encapsulate the non-determinism so
+that's actually done in the silk runtime
+
+ align:start position:0%
+that's actually done in the silk runtime
+ 
+
+ align:start position:0%
+that's actually done in the silk runtime
+system already the runtime system is
+
+ align:start position:0%
+system already the runtime system is
+ 
+
+ align:start position:0%
+system already the runtime system is
+using a random scheduling strategy but
+
+ align:start position:0%
+using a random scheduling strategy but
+ 
+
+ align:start position:0%
+using a random scheduling strategy but
+you don't see that it's random in the
+
+ align:start position:0%
+you don't see that it's random in the
+ 
+
+ align:start position:0%
+you don't see that it's random in the
+execution of your code if you don't if
+
+ align:start position:0%
+execution of your code if you don't if
+ 
+
+ align:start position:0%
+execution of your code if you don't if
+you have no race conditions in your code
+
+ align:start position:0%
+you have no race conditions in your code
+ 
+
+ align:start position:0%
+you have no race conditions in your code
+its encapsulated okay so that so that
+
+ align:start position:0%
+its encapsulated okay so that so that
+ 
+
+ align:start position:0%
+its encapsulated okay so that so that
+the you know in the platform so the
+
+ align:start position:0%
+the you know in the platform so the
+ 
+
+ align:start position:0%
+the you know in the platform so the
+platform is going to guarantee you
+
+ align:start position:0%
+platform is going to guarantee you
+ 
+
+ align:start position:0%
+platform is going to guarantee you
+deterministic results even though
+
+ align:start position:0%
+deterministic results even though
+ 
+
+ align:start position:0%
+deterministic results even though
+underneath the covers it's doing
+
+ align:start position:0%
+underneath the covers it's doing
+ 
+
+ align:start position:0%
+underneath the covers it's doing
+non-deterministic things okay you can
+
+ align:start position:0%
+non-deterministic things okay you can
+ 
+
+ align:start position:0%
+non-deterministic things okay you can
+also substitute a deterministic
+
+ align:start position:0%
+also substitute a deterministic
+ 
+
+ align:start position:0%
+also substitute a deterministic
+alternative okay sometimes there's
+
+ align:start position:0%
+alternative okay sometimes there's
+ 
+
+ align:start position:0%
+alternative okay sometimes there's
+there's a way of computing something
+
+ align:start position:0%
+there's a way of computing something
+ 
+
+ align:start position:0%
+there's a way of computing something
+that is non-deterministic but in debug
+
+ align:start position:0%
+that is non-deterministic but in debug
+ 
+
+ align:start position:0%
+that is non-deterministic but in debug
+mode let me not use the
+
+ align:start position:0%
+mode let me not use the
+ 
+
+ align:start position:0%
+mode let me not use the
+non-deterministic one okay and you can
+
+ align:start position:0%
+non-deterministic one okay and you can
+ 
+
+ align:start position:0%
+non-deterministic one okay and you can
+also use analysis tools which can tell
+
+ align:start position:0%
+also use analysis tools which can tell
+ 
+
+ align:start position:0%
+also use analysis tools which can tell
+you things about your program and which
+
+ align:start position:0%
+you things about your program and which
+ 
+
+ align:start position:0%
+you things about your program and which
+you can can control things so there's a
+
+ align:start position:0%
+you can can control things so there's a
+ 
+
+ align:start position:0%
+you can can control things so there's a
+lot of things so whenever you have a
+
+ align:start position:0%
+lot of things so whenever you have a
+ 
+
+ align:start position:0%
+lot of things so whenever you have a
+non-deterministic program you want to
+
+ align:start position:0%
+non-deterministic program you want to
+ 
+
+ align:start position:0%
+non-deterministic program you want to
+find some way of controlling and often
+
+ align:start position:0%
+find some way of controlling and often
+ 
+
+ align:start position:0%
+find some way of controlling and often
+the non determinism is over in this
+
+ align:start position:0%
+the non determinism is over in this
+ 
+
+ align:start position:0%
+the non determinism is over in this
+corner but your bug is over in this
+
+ align:start position:0%
+corner but your bug is over in this
+ 
+
+ align:start position:0%
+corner but your bug is over in this
+corner so if you can turn this thing off
+
+ align:start position:0%
+corner so if you can turn this thing off
+ 
+
+ align:start position:0%
+corner so if you can turn this thing off
+in some way or encapsulate it or you
+
+ align:start position:0%
+in some way or encapsulate it or you
+ 
+
+ align:start position:0%
+in some way or encapsulate it or you
+know otherwise control the non
+
+ align:start position:0%
+know otherwise control the non
+ 
+
+ align:start position:0%
+know otherwise control the non
+determinism over there now you have a
+
+ align:start position:0%
+determinism over there now you have a
+ 
+
+ align:start position:0%
+determinism over there now you have a
+better chance of catching the stuff over
+
+ align:start position:0%
+better chance of catching the stuff over
+ 
+
+ align:start position:0%
+better chance of catching the stuff over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay that's going to be particularly
+
+ align:start position:0%
+okay that's going to be particularly
+ 
+
+ align:start position:0%
+okay that's going to be particularly
+important in project four when we get to
+
+ align:start position:0%
+important in project four when we get to
+ 
+
+ align:start position:0%
+important in project four when we get to
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+because that's going to be actually
+
+ align:start position:0%
+because that's going to be actually
+ 
+
+ align:start position:0%
+because that's going to be actually
+going to be doing non-deterministic
+
+ align:start position:0%
+going to be doing non-deterministic
+ 
+
+ align:start position:0%
+going to be doing non-deterministic
+programming for a game playing program
+
+ align:start position:0%
+programming for a game playing program
+ 
+
+ align:start position:0%
+programming for a game playing program
+and one of the one of the things is that
+
+ align:start position:0%
+and one of the one of the things is that
+ 
+
+ align:start position:0%
+and one of the one of the things is that
+the processors are in this case keeping
+
+ align:start position:0%
+the processors are in this case keeping
+ 
+
+ align:start position:0%
+the processors are in this case keeping
+the game positions together and so the
+
+ align:start position:0%
+the game positions together and so the
+ 
+
+ align:start position:0%
+the game positions together and so the
+if one processor stores something into a
+
+ align:start position:0%
+if one processor stores something into a
+ 
+
+ align:start position:0%
+if one processor stores something into a
+into what's called the transposition
+
+ align:start position:0%
+into what's called the transposition
+ 
+
+ align:start position:0%
+into what's called the transposition
+table which is a essentially a big hash
+
+ align:start position:0%
+table which is a essentially a big hash
+ 
+
+ align:start position:0%
+table which is a essentially a big hash
+table of positions at scene another one
+
+ align:start position:0%
+table of positions at scene another one
+ 
+
+ align:start position:0%
+table of positions at scene another one
+can see that value and change its
+
+ align:start position:0%
+can see that value and change its
+ 
+
+ align:start position:0%
+can see that value and change its
+behavior and so one of the things you
+
+ align:start position:0%
+behavior and so one of the things you
+ 
+
+ align:start position:0%
+behavior and so one of the things you
+want to be able do is turn off
+
+ align:start position:0%
+want to be able do is turn off
+ 
+
+ align:start position:0%
+want to be able do is turn off
+transposition table okay so that so that
+
+ align:start position:0%
+transposition table okay so that so that
+ 
+
+ align:start position:0%
+transposition table okay so that so that
+you don't take advantage that
+
+ align:start position:0%
+you don't take advantage that
+ 
+
+ align:start position:0%
+you don't take advantage that
+performance advantage but now you can
+
+ align:start position:0%
+performance advantage but now you can
+ 
+
+ align:start position:0%
+performance advantage but now you can
+debug the search code or you can debug
+
+ align:start position:0%
+debug the search code or you can debug
+ 
+
+ align:start position:0%
+debug the search code or you can debug
+the evaluation code and so forth you can
+
+ align:start position:0%
+the evaluation code and so forth you can
+ 
+
+ align:start position:0%
+the evaluation code and so forth you can
+also do things like you know unit
+
+ align:start position:0%
+also do things like you know unit
+ 
+
+ align:start position:0%
+also do things like you know unit
+testing so you know whether or not a
+
+ align:start position:0%
+testing so you know whether or not a
+ 
+
+ align:start position:0%
+testing so you know whether or not a
+particular piece is correct that might
+
+ align:start position:0%
+particular piece is correct that might
+ 
+
+ align:start position:0%
+particular piece is correct that might
+have you know so that so that you can
+
+ align:start position:0%
+have you know so that so that you can
+ 
+
+ align:start position:0%
+have you know so that so that you can
+test this thing separately from the rest
+
+ align:start position:0%
+test this thing separately from the rest
+ 
+
+ align:start position:0%
+test this thing separately from the rest
+of your system which may have non
+
+ align:start position:0%
+of your system which may have non
+ 
+
+ align:start position:0%
+of your system which may have non
+determinism and way this is a major
+
+ align:start position:0%
+determinism and way this is a major
+ 
+
+ align:start position:0%
+determinism and way this is a major
+thing so so you never write them but if
+
+ align:start position:0%
+thing so so you never write them but if
+ 
+
+ align:start position:0%
+thing so so you never write them but if
+you have to you always want to have some
+
+ align:start position:0%
+you have to you always want to have some
+ 
+
+ align:start position:0%
+you have to you always want to have some
+test strategy okay and so for the people
+
+ align:start position:0%
+test strategy okay and so for the people
+ 
+
+ align:start position:0%
+test strategy okay and so for the people
+who are not watching this video and who
+
+ align:start position:0%
+who are not watching this video and who
+ 
+
+ align:start position:0%
+who are not watching this video and who
+are you know not in class today they are
+
+ align:start position:0%
+are you know not in class today they are
+ 
+
+ align:start position:0%
+are you know not in class today they are
+going to be sorely hampered by not
+
+ align:start position:0%
+going to be sorely hampered by not
+ 
+
+ align:start position:0%
+going to be sorely hampered by not
+knowing this lesson when they go into
+
+ align:start position:0%
+knowing this lesson when they go into
+ 
+
+ align:start position:0%
+knowing this lesson when they go into
+the fourth project okay so so what we're
+
+ align:start position:0%
+the fourth project okay so so what we're
+ 
+
+ align:start position:0%
+the fourth project okay so so what we're
+gonna do is now we're going to talk
+
+ align:start position:0%
+gonna do is now we're going to talk
+ 
+
+ align:start position:0%
+gonna do is now we're going to talk
+about how to do non-deterministic
+
+ align:start position:0%
+about how to do non-deterministic
+ 
+
+ align:start position:0%
+about how to do non-deterministic
+programming okay so this is you know
+
+ align:start position:0%
+programming okay so this is you know
+ 
+
+ align:start position:0%
+programming okay so this is you know
+there's always there's always some part
+
+ align:start position:0%
+there's always there's always some part
+ 
+
+ align:start position:0%
+there's always there's always some part
+of your code you know which has a skull
+
+ align:start position:0%
+of your code you know which has a skull
+ 
+
+ align:start position:0%
+of your code you know which has a skull
+and crossbones
+
+ align:start position:0%
+and crossbones
+ 
+
+ align:start position:0%
+and crossbones
+like you know you have this abstraction
+
+ align:start position:0%
+like you know you have this abstraction
+ 
+
+ align:start position:0%
+like you know you have this abstraction
+it's beautiful and you can design etc
+
+ align:start position:0%
+it's beautiful and you can design etc
+ 
+
+ align:start position:0%
+it's beautiful and you can design etc
+and then somewhere there's this really
+
+ align:start position:0%
+and then somewhere there's this really
+ 
+
+ align:start position:0%
+and then somewhere there's this really
+ugly thing that nobody should know and
+
+ align:start position:0%
+ugly thing that nobody should know and
+ 
+
+ align:start position:0%
+ugly thing that nobody should know and
+you put the skull and crossbones on that
+
+ align:start position:0%
+you put the skull and crossbones on that
+ 
+
+ align:start position:0%
+you put the skull and crossbones on that
+and only experts go in well anyway
+
+ align:start position:0%
+and only experts go in well anyway
+ 
+
+ align:start position:0%
+and only experts go in well anyway
+that's the that's the barrier we're
+
+ align:start position:0%
+that's the that's the barrier we're
+ 
+
+ align:start position:0%
+that's the that's the barrier we're
+crossing here okay and we're going to
+
+ align:start position:0%
+crossing here okay and we're going to
+ 
+
+ align:start position:0%
+crossing here okay and we're going to
+start out by talking about something
+
+ align:start position:0%
+start out by talking about something
+ 
+
+ align:start position:0%
+start out by talking about something
+that you've probably seen in
+
+ align:start position:0%
+that you've probably seen in
+ 
+
+ align:start position:0%
+that you've probably seen in
+your other classes mutual exclusion and
+
+ align:start position:0%
+your other classes mutual exclusion and
+ 
+
+ align:start position:0%
+your other classes mutual exclusion and
+atomicity so I'm going to use the
+
+ align:start position:0%
+atomicity so I'm going to use the
+ 
+
+ align:start position:0%
+atomicity so I'm going to use the
+example of the hash table so here's a
+
+ align:start position:0%
+example of the hash table so here's a
+ 
+
+ align:start position:0%
+example of the hash table so here's a
+typical hash table it's got collisions
+
+ align:start position:0%
+typical hash table it's got collisions
+ 
+
+ align:start position:0%
+typical hash table it's got collisions
+resolved by chaining so you have a bunch
+
+ align:start position:0%
+resolved by chaining so you have a bunch
+ 
+
+ align:start position:0%
+resolved by chaining so you have a bunch
+of linked lists you hash to a particular
+
+ align:start position:0%
+of linked lists you hash to a particular
+ 
+
+ align:start position:0%
+of linked lists you hash to a particular
+slot in the table and then you chase
+
+ align:start position:0%
+slot in the table and then you chase
+ 
+
+ align:start position:0%
+slot in the table and then you chase
+down the linked list to find the value
+
+ align:start position:0%
+down the linked list to find the value
+ 
+
+ align:start position:0%
+down the linked list to find the value
+and so for example if I'm going to
+
+ align:start position:0%
+and so for example if I'm going to
+ 
+
+ align:start position:0%
+and so for example if I'm going to
+insert X which has a key value of 81 you
+
+ align:start position:0%
+insert X which has a key value of 81 you
+ 
+
+ align:start position:0%
+insert X which has a key value of 81 you
+know what I do is figure out which slot
+
+ align:start position:0%
+know what I do is figure out which slot
+ 
+
+ align:start position:0%
+know what I do is figure out which slot
+I go to by by hashing the key and then
+
+ align:start position:0%
+I go to by by hashing the key and then
+ 
+
+ align:start position:0%
+I go to by by hashing the key and then
+in this case I made it be the last one
+
+ align:start position:0%
+in this case I made it be the last one
+ 
+
+ align:start position:0%
+in this case I made it be the last one
+so the animations could be easier but if
+
+ align:start position:0%
+so the animations could be easier but if
+ 
+
+ align:start position:0%
+so the animations could be easier but if
+it were in the middle and so so now what
+
+ align:start position:0%
+it were in the middle and so so now what
+ 
+
+ align:start position:0%
+it were in the middle and so so now what
+do I do is I make the the pointer of X
+
+ align:start position:0%
+do I do is I make the the pointer of X
+ 
+
+ align:start position:0%
+do I do is I make the the pointer of X
+go to the you know first element of that
+
+ align:start position:0%
+go to the you know first element of that
+ 
+
+ align:start position:0%
+go to the you know first element of that
+list and then I make the slot value now
+
+ align:start position:0%
+list and then I make the slot value now
+ 
+
+ align:start position:0%
+list and then I make the slot value now
+point to X and that effectively in with
+
+ align:start position:0%
+point to X and that effectively in with
+ 
+
+ align:start position:0%
+point to X and that effectively in with
+a constant number of operations inserts
+
+ align:start position:0%
+a constant number of operations inserts
+ 
+
+ align:start position:0%
+a constant number of operations inserts
+X into the hash table and in particular
+
+ align:start position:0%
+X into the hash table and in particular
+ 
+
+ align:start position:0%
+X into the hash table and in particular
+into the linked list in the slot that
+
+ align:start position:0%
+into the linked list in the slot that
+ 
+
+ align:start position:0%
+into the linked list in the slot that
+it's supposed to be okay this is all
+
+ align:start position:0%
+it's supposed to be okay this is all
+ 
+
+ align:start position:0%
+it's supposed to be okay this is all
+familiar right okay so now what happens
+
+ align:start position:0%
+familiar right okay so now what happens
+ 
+
+ align:start position:0%
+familiar right okay so now what happens
+when you have multiple parallel
+
+ align:start position:0%
+when you have multiple parallel
+ 
+
+ align:start position:0%
+when you have multiple parallel
+instructions that are accessing the same
+
+ align:start position:0%
+instructions that are accessing the same
+ 
+
+ align:start position:0%
+instructions that are accessing the same
+the same locations okay so so here we
+
+ align:start position:0%
+the same locations okay so so here we
+ 
+
+ align:start position:0%
+the same locations okay so so here we
+have two threads one inserting X and one
+
+ align:start position:0%
+have two threads one inserting X and one
+ 
+
+ align:start position:0%
+have two threads one inserting X and one
+inserting Y and X goes it does its thing
+
+ align:start position:0%
+inserting Y and X goes it does its thing
+ 
+
+ align:start position:0%
+inserting Y and X goes it does its thing
+it hashes to there and it then sets the
+
+ align:start position:0%
+it hashes to there and it then sets the
+ 
+
+ align:start position:0%
+it hashes to there and it then sets the
+next pointer to be the to add itself
+
+ align:start position:0%
+next pointer to be the to add itself
+ 
+
+ align:start position:0%
+next pointer to be the to add itself
+into the list and then there's this
+
+ align:start position:0%
+into the list and then there's this
+ 
+
+ align:start position:0%
+into the list and then there's this
+other thing going on in parallel which
+
+ align:start position:0%
+other thing going on in parallel which
+ 
+
+ align:start position:0%
+other thing going on in parallel which
+effectively says oh I'm going to hash
+
+ align:start position:0%
+effectively says oh I'm going to hash
+ 
+
+ align:start position:0%
+effectively says oh I'm going to hash
+oh we're going to the same slot it
+
+ align:start position:0%
+oh we're going to the same slot it
+ 
+
+ align:start position:0%
+oh we're going to the same slot it
+doesn't know that somebody's already
+
+ align:start position:0%
+doesn't know that somebody's already
+ 
+
+ align:start position:0%
+doesn't know that somebody's already
+there and so then it decides it's going
+
+ align:start position:0%
+there and so then it decides it's going
+ 
+
+ align:start position:0%
+there and so then it decides it's going
+to put itself in as the first element
+
+ align:start position:0%
+to put itself in as the first element
+ 
+
+ align:start position:0%
+to put itself in as the first element
+of the list and then it sets the value
+
+ align:start position:0%
+of the list and then it sets the value
+ 
+
+ align:start position:0%
+of the list and then it sets the value
+of y that sets the value of the slot to
+
+ align:start position:0%
+of y that sets the value of the slot to
+ 
+
+ align:start position:0%
+of y that sets the value of the slot to
+point to Y and then along comes X
+
+ align:start position:0%
+point to Y and then along comes X
+ 
+
+ align:start position:0%
+point to Y and then along comes X
+finishing off what it's doing and it
+
+ align:start position:0%
+finishing off what it's doing and it
+ 
+
+ align:start position:0%
+finishing off what it's doing and it
+points the value to X and you can see
+
+ align:start position:0%
+points the value to X and you can see
+ 
+
+ align:start position:0%
+points the value to X and you can see
+that we have a race bug here a really
+
+ align:start position:0%
+that we have a race bug here a really
+ 
+
+ align:start position:0%
+that we have a race bug here a really
+nasty one because we've just destroyed
+
+ align:start position:0%
+nasty one because we've just destroyed
+ 
+
+ align:start position:0%
+nasty one because we've just destroyed
+the integrity of our of our system we
+
+ align:start position:0%
+the integrity of our of our system we
+ 
+
+ align:start position:0%
+the integrity of our of our system we
+now have in particular y is sort of
+
+ align:start position:0%
+now have in particular y is sort of
+ 
+
+ align:start position:0%
+now have in particular y is sort of
+floating not in the list when it's
+
+ align:start position:0%
+floating not in the list when it's
+ 
+
+ align:start position:0%
+floating not in the list when it's
+supposed to be in the list right so the
+
+ align:start position:0%
+supposed to be in the list right so the
+ 
+
+ align:start position:0%
+supposed to be in the list right so the
+standard solution to this is to make
+
+ align:start position:0%
+standard solution to this is to make
+ 
+
+ align:start position:0%
+standard solution to this is to make
+some of these instructions be atomic ok
+
+ align:start position:0%
+some of these instructions be atomic ok
+ 
+
+ align:start position:0%
+some of these instructions be atomic ok
+so and what that means is the rest of
+
+ align:start position:0%
+so and what that means is the rest of
+ 
+
+ align:start position:0%
+so and what that means is the rest of
+the system can never view them as being
+
+ align:start position:0%
+the system can never view them as being
+ 
+
+ align:start position:0%
+the system can never view them as being
+partially executed okay so they're
+
+ align:start position:0%
+partially executed okay so they're
+ 
+
+ align:start position:0%
+partially executed okay so they're
+either all have been executed or none of
+
+ align:start position:0%
+either all have been executed or none of
+ 
+
+ align:start position:0%
+either all have been executed or none of
+them have been executed at any point in
+
+ align:start position:0%
+them have been executed at any point in
+ 
+
+ align:start position:0%
+them have been executed at any point in
+time as far as the as far as the rest of
+
+ align:start position:0%
+time as far as the as far as the rest of
+ 
+
+ align:start position:0%
+time as far as the as far as the rest of
+the system is concerned okay and the
+
+ align:start position:0%
+the system is concerned okay and the
+ 
+
+ align:start position:0%
+the system is concerned okay and the
+part of code that is within the atomic
+
+ align:start position:0%
+part of code that is within the atomic
+ 
+
+ align:start position:0%
+part of code that is within the atomic
+regions called the critical section and
+
+ align:start position:0%
+regions called the critical section and
+ 
+
+ align:start position:0%
+regions called the critical section and
+it can typically a critical section of
+
+ align:start position:0%
+it can typically a critical section of
+ 
+
+ align:start position:0%
+it can typically a critical section of
+code is someplace that should not be
+
+ align:start position:0%
+code is someplace that should not be
+ 
+
+ align:start position:0%
+code is someplace that should not be
+being executed by two things at the same
+
+ align:start position:0%
+being executed by two things at the same
+ 
+
+ align:start position:0%
+being executed by two things at the same
+time so the standard solution to
+
+ align:start position:0%
+time so the standard solution to
+ 
+
+ align:start position:0%
+time so the standard solution to
+atomicity is to use what's called a
+
+ align:start position:0%
+atomicity is to use what's called a
+ 
+
+ align:start position:0%
+atomicity is to use what's called a
+mutex lock or a mutual exclusion lock
+
+ align:start position:0%
+mutex lock or a mutual exclusion lock
+ 
+
+ align:start position:0%
+mutex lock or a mutual exclusion lock
+okay and it's basically an object with a
+
+ align:start position:0%
+okay and it's basically an object with a
+ 
+
+ align:start position:0%
+okay and it's basically an object with a
+lock and unlock member functions and an
+
+ align:start position:0%
+lock and unlock member functions and an
+ 
+
+ align:start position:0%
+lock and unlock member functions and an
+attempt by a thread to lock an already
+
+ align:start position:0%
+attempt by a thread to lock an already
+ 
+
+ align:start position:0%
+attempt by a thread to lock an already
+locked mutex causes the thread to block
+
+ align:start position:0%
+locked mutex causes the thread to block
+ 
+
+ align:start position:0%
+locked mutex causes the thread to block
+okay that is wait until the mutex is
+
+ align:start position:0%
+okay that is wait until the mutex is
+ 
+
+ align:start position:0%
+okay that is wait until the mutex is
+unlocked okay so if somebody grabs the
+
+ align:start position:0%
+unlocked okay so if somebody grabs the
+ 
+
+ align:start position:0%
+unlocked okay so if somebody grabs the
+lock somebody else grabs the lock and
+
+ align:start position:0%
+lock somebody else grabs the lock and
+ 
+
+ align:start position:0%
+lock somebody else grabs the lock and
+it's already taken then they have to
+
+ align:start position:0%
+it's already taken then they have to
+ 
+
+ align:start position:0%
+it's already taken then they have to
+wait and they sit there waiting until
+
+ align:start position:0%
+wait and they sit there waiting until
+ 
+
+ align:start position:0%
+wait and they sit there waiting until
+until this guy says yes I'm gonna
+
+ align:start position:0%
+until this guy says yes I'm gonna
+ 
+
+ align:start position:0%
+until this guy says yes I'm gonna
+release it okay so so what we'll do now
+
+ align:start position:0%
+release it okay so so what we'll do now
+ 
+
+ align:start position:0%
+release it okay so so what we'll do now
+is we'll make each straw each slot be a
+
+ align:start position:0%
+is we'll make each straw each slot be a
+ 
+
+ align:start position:0%
+is we'll make each straw each slot be a
+struct with a mutex l and a pointer head
+
+ align:start position:0%
+struct with a mutex l and a pointer head
+ 
+
+ align:start position:0%
+struct with a mutex l and a pointer head
+to the slot context so it's going to be
+
+ align:start position:0%
+to the slot context so it's going to be
+ 
+
+ align:start position:0%
+to the slot context so it's going to be
+the same data structure we had before
+
+ align:start position:0%
+the same data structure we had before
+ 
+
+ align:start position:0%
+the same data structure we had before
+but now I'm gonna have not just the
+
+ align:start position:0%
+but now I'm gonna have not just the
+ 
+
+ align:start position:0%
+but now I'm gonna have not just the
+pointer from the slot but I'll also have
+
+ align:start position:0%
+pointer from the slot but I'll also have
+ 
+
+ align:start position:0%
+pointer from the slot but I'll also have
+I also have a a lock in that position
+
+ align:start position:0%
+I also have a a lock in that position
+ 
+
+ align:start position:0%
+I also have a a lock in that position
+okay and so the idea of in the code now
+
+ align:start position:0%
+okay and so the idea of in the code now
+ 
+
+ align:start position:0%
+okay and so the idea of in the code now
+is that before I access the lock before
+
+ align:start position:0%
+is that before I access the lock before
+ 
+
+ align:start position:0%
+is that before I access the lock before
+I access the list I'm going to lock that
+
+ align:start position:0%
+I access the list I'm going to lock that
+ 
+
+ align:start position:0%
+I access the list I'm going to lock that
+that list in the table by locking the
+
+ align:start position:0%
+that list in the table by locking the
+ 
+
+ align:start position:0%
+that list in the table by locking the
+slot then I'll do the things that I need
+
+ align:start position:0%
+slot then I'll do the things that I need
+ 
+
+ align:start position:0%
+slot then I'll do the things that I need
+to do and then I'll unlock it and now
+
+ align:start position:0%
+to do and then I'll unlock it and now
+ 
+
+ align:start position:0%
+to do and then I'll unlock it and now
+anything else can go on because you know
+
+ align:start position:0%
+anything else can go on because you know
+ 
+
+ align:start position:0%
+anything else can go on because you know
+the what's happening is the reason we're
+
+ align:start position:0%
+the what's happening is the reason we're
+ 
+
+ align:start position:0%
+the what's happening is the reason we're
+getting into trouble is because we got
+
+ align:start position:0%
+getting into trouble is because we got
+ 
+
+ align:start position:0%
+getting into trouble is because we got
+some sort of interleaving of operations
+
+ align:start position:0%
+some sort of interleaving of operations
+ 
+
+ align:start position:0%
+some sort of interleaving of operations
+and our goal is to make sure that it's
+
+ align:start position:0%
+and our goal is to make sure that it's
+ 
+
+ align:start position:0%
+and our goal is to make sure that it's
+either doing this or doing this and
+
+ align:start position:0%
+either doing this or doing this and
+ 
+
+ align:start position:0%
+either doing this or doing this and
+never this okay to make sure that so
+
+ align:start position:0%
+never this okay to make sure that so
+ 
+
+ align:start position:0%
+never this okay to make sure that so
+that each thing each piece of code is
+
+ align:start position:0%
+that each thing each piece of code is
+ 
+
+ align:start position:0%
+that each thing each piece of code is
+restoring the invariant of correctness
+
+ align:start position:0%
+restoring the invariant of correctness
+ 
+
+ align:start position:0%
+restoring the invariant of correctness
+after it executes the pointer swaps them
+
+ align:start position:0%
+after it executes the pointer swaps them
+ 
+
+ align:start position:0%
+after it executes the pointer swaps them
+very in this case is that the elements
+
+ align:start position:0%
+very in this case is that the elements
+ 
+
+ align:start position:0%
+very in this case is that the elements
+are in a list okay and and so you want
+
+ align:start position:0%
+are in a list okay and and so you want
+ 
+
+ align:start position:0%
+are in a list okay and and so you want
+to restore that with each one okay so so
+
+ align:start position:0%
+to restore that with each one okay so so
+ 
+
+ align:start position:0%
+to restore that with each one okay so so
+mutex is this is one way you can use new
+
+ align:start position:0%
+mutex is this is one way you can use new
+ 
+
+ align:start position:0%
+mutex is this is one way you can use new
+mutexes to implement atomicity okay so
+
+ align:start position:0%
+mutexes to implement atomicity okay so
+ 
+
+ align:start position:0%
+mutexes to implement atomicity okay so
+now let's just go back this is this is
+
+ align:start position:0%
+now let's just go back this is this is
+ 
+
+ align:start position:0%
+now let's just go back this is this is
+so who has who has seen you know mutexes
+
+ align:start position:0%
+so who has who has seen you know mutexes
+ 
+
+ align:start position:0%
+so who has who has seen you know mutexes
+before it's at pretty much everybody
+
+ align:start position:0%
+before it's at pretty much everybody
+ 
+
+ align:start position:0%
+before it's at pretty much everybody
+yeah okay good I hope that this is not
+
+ align:start position:0%
+yeah okay good I hope that this is not
+ 
+
+ align:start position:0%
+yeah okay good I hope that this is not
+brand-new for too many of you if it is
+
+ align:start position:0%
+brand-new for too many of you if it is
+ 
+
+ align:start position:0%
+brand-new for too many of you if it is
+brand-new that's great but what I'm
+
+ align:start position:0%
+brand-new that's great but what I'm
+ 
+
+ align:start position:0%
+brand-new that's great but what I'm
+trying to do is make it so let's go back
+
+ align:start position:0%
+trying to do is make it so let's go back
+ 
+
+ align:start position:0%
+trying to do is make it so let's go back
+a little bit and recall in this class
+
+ align:start position:0%
+a little bit and recall in this class
+ 
+
+ align:start position:0%
+a little bit and recall in this class
+our discussion of determinacy races so
+
+ align:start position:0%
+our discussion of determinacy races so
+ 
+
+ align:start position:0%
+our discussion of determinacy races so
+remember that determinacy race occurs
+
+ align:start position:0%
+remember that determinacy race occurs
+ 
+
+ align:start position:0%
+remember that determinacy race occurs
+when you have to logically parallel
+
+ align:start position:0%
+when you have to logically parallel
+ 
+
+ align:start position:0%
+when you have to logically parallel
+instructions that access the same memory
+
+ align:start position:0%
+instructions that access the same memory
+ 
+
+ align:start position:0%
+instructions that access the same memory
+location and at least one of them
+
+ align:start position:0%
+location and at least one of them
+ 
+
+ align:start position:0%
+location and at least one of them
+performs all right okay so mutex locks
+
+ align:start position:0%
+performs all right okay so mutex locks
+ 
+
+ align:start position:0%
+performs all right okay so mutex locks
+can guarantee that critical sections
+
+ align:start position:0%
+can guarantee that critical sections
+ 
+
+ align:start position:0%
+can guarantee that critical sections
+behave atomically but the resulting code
+
+ align:start position:0%
+behave atomically but the resulting code
+ 
+
+ align:start position:0%
+behave atomically but the resulting code
+is inherently non-deterministic because
+
+ align:start position:0%
+is inherently non-deterministic because
+ 
+
+ align:start position:0%
+is inherently non-deterministic because
+you've got a you know we had a race bug
+
+ align:start position:0%
+you've got a you know we had a race bug
+ 
+
+ align:start position:0%
+you've got a you know we had a race bug
+there right we had two things trying to
+
+ align:start position:0%
+there right we had two things trying to
+ 
+
+ align:start position:0%
+there right we had two things trying to
+access the same slot but that may be
+
+ align:start position:0%
+access the same slot but that may be
+ 
+
+ align:start position:0%
+access the same slot but that may be
+what I
+
+ align:start position:0%
+what I
+ 
+
+ align:start position:0%
+what I
+want right I want to have a shared hash
+
+ align:start position:0%
+want right I want to have a shared hash
+ 
+
+ align:start position:0%
+want right I want to have a shared hash
+table maybe okay for these for these
+
+ align:start position:0%
+table maybe okay for these for these
+ 
+
+ align:start position:0%
+table maybe okay for these for these
+things so I want something where there
+
+ align:start position:0%
+things so I want something where there
+ 
+
+ align:start position:0%
+things so I want something where there
+is a race but I just don't want to have
+
+ align:start position:0%
+is a race but I just don't want to have
+ 
+
+ align:start position:0%
+is a race but I just don't want to have
+the anomalies that arise in this case
+
+ align:start position:0%
+the anomalies that arise in this case
+ 
+
+ align:start position:0%
+the anomalies that arise in this case
+you know the race bug caused things and
+
+ align:start position:0%
+you know the race bug caused things and
+ 
+
+ align:start position:0%
+you know the race bug caused things and
+I can solve that with atomicity okay you
+
+ align:start position:0%
+I can solve that with atomicity okay you
+ 
+
+ align:start position:0%
+I can solve that with atomicity okay you
+know if you have no determinacy races it
+
+ align:start position:0%
+know if you have no determinacy races it
+ 
+
+ align:start position:0%
+know if you have no determinacy races it
+means that the program is deterministic
+
+ align:start position:0%
+means that the program is deterministic
+ 
+
+ align:start position:0%
+means that the program is deterministic
+on that input and that it always behaves
+
+ align:start position:0%
+on that input and that it always behaves
+ 
+
+ align:start position:0%
+on that input and that it always behaves
+the same okay and remember also that if
+
+ align:start position:0%
+the same okay and remember also that if
+ 
+
+ align:start position:0%
+the same okay and remember also that if
+a determinacy race exists in an
+
+ align:start position:0%
+a determinacy race exists in an
+ 
+
+ align:start position:0%
+a determinacy race exists in an
+ostensibly deterministic program okay
+
+ align:start position:0%
+ostensibly deterministic program okay
+ 
+
+ align:start position:0%
+ostensibly deterministic program okay
+then it guarantees to find a race now if
+
+ align:start position:0%
+then it guarantees to find a race now if
+ 
+
+ align:start position:0%
+then it guarantees to find a race now if
+you put in mutexes you still have a
+
+ align:start position:0%
+you put in mutexes you still have a
+ 
+
+ align:start position:0%
+you put in mutexes you still have a
+non-deterministic program you still have
+
+ align:start position:0%
+non-deterministic program you still have
+ 
+
+ align:start position:0%
+non-deterministic program you still have
+a race because you have two things that
+
+ align:start position:0%
+a race because you have two things that
+ 
+
+ align:start position:0%
+a race because you have two things that
+are logically parallel that are both
+
+ align:start position:0%
+are logically parallel that are both
+ 
+
+ align:start position:0%
+are logically parallel that are both
+accessing the lock that's a rate that's
+
+ align:start position:0%
+accessing the lock that's a rate that's
+ 
+
+ align:start position:0%
+accessing the lock that's a rate that's
+a determinacy race okay if you have two
+
+ align:start position:0%
+a determinacy race okay if you have two
+ 
+
+ align:start position:0%
+a determinacy race okay if you have two
+things that are in parallel they're both
+
+ align:start position:0%
+things that are in parallel they're both
+ 
+
+ align:start position:0%
+things that are in parallel they're both
+accessing the lock
+
+ align:start position:0%
+accessing the lock
+ 
+
+ align:start position:0%
+accessing the lock
+that's a determinacy race it may be a
+
+ align:start position:0%
+that's a determinacy race it may be a
+ 
+
+ align:start position:0%
+that's a determinacy race it may be a
+safe correct one but it is a determinacy
+
+ align:start position:0%
+safe correct one but it is a determinacy
+ 
+
+ align:start position:0%
+safe correct one but it is a determinacy
+race okay and so any codes that use
+
+ align:start position:0%
+race okay and so any codes that use
+ 
+
+ align:start position:0%
+race okay and so any codes that use
+locks are non-deterministic by intention
+
+ align:start position:0%
+locks are non-deterministic by intention
+ 
+
+ align:start position:0%
+locks are non-deterministic by intention
+and they're going to invalidate the
+
+ align:start position:0%
+and they're going to invalidate the
+ 
+
+ align:start position:0%
+and they're going to invalidate the
+silks and guarantee of finding those
+
+ align:start position:0%
+silks and guarantee of finding those
+ 
+
+ align:start position:0%
+silks and guarantee of finding those
+race bugs okay so you will end up with
+
+ align:start position:0%
+race bugs okay so you will end up with
+ 
+
+ align:start position:0%
+race bugs okay so you will end up with
+races in your code if you're not careful
+
+ align:start position:0%
+races in your code if you're not careful
+ 
+
+ align:start position:0%
+races in your code if you're not careful
+okay and so this is one reason it's
+
+ align:start position:0%
+okay and so this is one reason it's
+ 
+
+ align:start position:0%
+okay and so this is one reason it's
+important to have some way of turning
+
+ align:start position:0%
+important to have some way of turning
+ 
+
+ align:start position:0%
+important to have some way of turning
+off non determinism to detect stuff
+
+ align:start position:0%
+off non determinism to detect stuff
+ 
+
+ align:start position:0%
+off non determinism to detect stuff
+because what you don't want is that
+
+ align:start position:0%
+because what you don't want is that
+ 
+
+ align:start position:0%
+because what you don't want is that
+whole rash of false positives saying oh
+
+ align:start position:0%
+whole rash of false positives saying oh
+ 
+
+ align:start position:0%
+whole rash of false positives saying oh
+you raced on gathering this lock nor do
+
+ align:start position:0%
+you raced on gathering this lock nor do
+ 
+
+ align:start position:0%
+you raced on gathering this lock nor do
+you want to ignore that and then
+
+ align:start position:0%
+you want to ignore that and then
+ 
+
+ align:start position:0%
+you want to ignore that and then
+discover that a race has popped up
+
+ align:start position:0%
+discover that a race has popped up
+ 
+
+ align:start position:0%
+discover that a race has popped up
+somewhere else okay now some people feel
+
+ align:start position:0%
+somewhere else okay now some people feel
+ 
+
+ align:start position:0%
+somewhere else okay now some people feel
+that so this is basically a talking
+
+ align:start position:0%
+that so this is basically a talking
+ 
+
+ align:start position:0%
+that so this is basically a talking
+about having a data race okay and a data
+
+ align:start position:0%
+about having a data race okay and a data
+ 
+
+ align:start position:0%
+about having a data race okay and a data
+race is similar to the definition of
+
+ align:start position:0%
+race is similar to the definition of
+ 
+
+ align:start position:0%
+race is similar to the definition of
+determinacy race okay but it says that
+
+ align:start position:0%
+determinacy race okay but it says that
+ 
+
+ align:start position:0%
+determinacy race okay but it says that
+you have to logically parallel
+
+ align:start position:0%
+you have to logically parallel
+ 
+
+ align:start position:0%
+you have to logically parallel
+instructions and they don't hold locks
+
+ align:start position:0%
+instructions and they don't hold locks
+ 
+
+ align:start position:0%
+instructions and they don't hold locks
+in common
+
+ align:start position:0%
+in common
+ 
+
+ align:start position:0%
+in common
+and then it's the same definition if
+
+ align:start position:0%
+and then it's the same definition if
+ 
+
+ align:start position:0%
+and then it's the same definition if
+they access the same memory location one
+
+ align:start position:0%
+they access the same memory location one
+ 
+
+ align:start position:0%
+they access the same memory location one
+of them performs or right then you have
+
+ align:start position:0%
+of them performs or right then you have
+ 
+
+ align:start position:0%
+of them performs or right then you have
+a then you have a data race bug okay but
+
+ align:start position:0%
+a then you have a data race bug okay but
+ 
+
+ align:start position:0%
+a then you have a data race bug okay but
+if they if they have the locks in common
+
+ align:start position:0%
+if they if they have the locks in common
+ 
+
+ align:start position:0%
+if they if they have the locks in common
+okay if they both have acquired at least
+
+ align:start position:0%
+okay if they both have acquired at least
+ 
+
+ align:start position:0%
+okay if they both have acquired at least
+one lock that's the same then you don't
+
+ align:start position:0%
+one lock that's the same then you don't
+ 
+
+ align:start position:0%
+one lock that's the same then you don't
+have a data race okay because that means
+
+ align:start position:0%
+have a data race okay because that means
+ 
+
+ align:start position:0%
+have a data race okay because that means
+that you've now successfully protected
+
+ align:start position:0%
+that you've now successfully protected
+ 
+
+ align:start position:0%
+that you've now successfully protected
+the atomicity but it is still
+
+ align:start position:0%
+the atomicity but it is still
+ 
+
+ align:start position:0%
+the atomicity but it is still
+non-deterministic and there is a
+
+ align:start position:0%
+non-deterministic and there is a
+ 
+
+ align:start position:0%
+non-deterministic and there is a
+determinacy race just no data race and
+
+ align:start position:0%
+determinacy race just no data race and
+ 
+
+ align:start position:0%
+determinacy race just no data race and
+that's the big distinction between data
+
+ align:start position:0%
+that's the big distinction between data
+ 
+
+ align:start position:0%
+that's the big distinction between data
+races and determinacy races and on quiz
+
+ align:start position:0%
+races and determinacy races and on quiz
+ 
+
+ align:start position:0%
+races and determinacy races and on quiz
+2 you better know the difference between
+
+ align:start position:0%
+2 you better know the difference between
+ 
+
+ align:start position:0%
+2 you better know the difference between
+data races and determinacy races okay
+
+ align:start position:0%
+data races and determinacy races okay
+ 
+
+ align:start position:0%
+data races and determinacy races okay
+because they are different okay so a
+
+ align:start position:0%
+because they are different okay so a
+ 
+
+ align:start position:0%
+because they are different okay so a
+program may have no determinant may have
+
+ align:start position:0%
+program may have no determinant may have
+ 
+
+ align:start position:0%
+program may have no determinant may have
+no data races that doesn't mean that it
+
+ align:start position:0%
+no data races that doesn't mean that it
+ 
+
+ align:start position:0%
+no data races that doesn't mean that it
+doesn't have a determinacy race in fact
+
+ align:start position:0%
+doesn't have a determinacy race in fact
+ 
+
+ align:start position:0%
+doesn't have a determinacy race in fact
+if it's got any locks it probably has a
+
+ align:start position:0%
+if it's got any locks it probably has a
+ 
+
+ align:start position:0%
+if it's got any locks it probably has a
+determinacy race okay okay so so one of
+
+ align:start position:0%
+determinacy race okay okay so so one of
+ 
+
+ align:start position:0%
+determinacy race okay okay so so one of
+the things is if I have no data races
+
+ align:start position:0%
+the things is if I have no data races
+ 
+
+ align:start position:0%
+the things is if I have no data races
+does that mean I have no bugs suppose I
+
+ align:start position:0%
+does that mean I have no bugs suppose I
+ 
+
+ align:start position:0%
+does that mean I have no bugs suppose I
+have no data races in my code does that
+
+ align:start position:0%
+have no data races in my code does that
+ 
+
+ align:start position:0%
+have no data races in my code does that
+mean I have no bugs this is quite an
+
+ align:start position:0%
+mean I have no bugs this is quite an
+ 
+
+ align:start position:0%
+mean I have no bugs this is quite an
+obvious answer just bye-bye quiz
+
+ align:start position:0%
+obvious answer just bye-bye quiz
+ 
+
+ align:start position:0%
+obvious answer just bye-bye quiz
+moonship right so what might happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think about a little bit what might
+
+ align:start position:0%
+think about a little bit what might
+ 
+
+ align:start position:0%
+think about a little bit what might
+happen how could I have no data races
+
+ align:start position:0%
+happen how could I have no data races
+ 
+
+ align:start position:0%
+happen how could I have no data races
+and yet there's still be a bug even
+
+ align:start position:0%
+and yet there's still be a bug even
+ 
+
+ align:start position:0%
+and yet there's still be a bug even
+though and assuming it's a correct piece
+
+ align:start position:0%
+though and assuming it's a correct piece
+ 
+
+ align:start position:0%
+though and assuming it's a correct piece
+of code otherwise okay in other words
+
+ align:start position:0%
+of code otherwise okay in other words
+ 
+
+ align:start position:0%
+of code otherwise okay in other words
+when it runs serially or whatever it's
+
+ align:start position:0%
+when it runs serially or whatever it's
+ 
+
+ align:start position:0%
+when it runs serially or whatever it's
+correct how could I end up having code
+
+ align:start position:0%
+correct how could I end up having code
+ 
+
+ align:start position:0%
+correct how could I end up having code
+no data races but still have a bug
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah but that doesn't mean it's bad
+
+ align:start position:0%
+yeah but that doesn't mean it's bad
+ 
+
+ align:start position:0%
+yeah but that doesn't mean it's bad
+right yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+might still be a different yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh yeah let me give you an example
+
+ align:start position:0%
+okay uh yeah let me give you an example
+ 
+
+ align:start position:0%
+okay uh yeah let me give you an example
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+which is more to the point here is a way
+
+ align:start position:0%
+which is more to the point here is a way
+ 
+
+ align:start position:0%
+which is more to the point here is a way
+of making sure that I have no data race
+
+ align:start position:0%
+of making sure that I have no data race
+ 
+
+ align:start position:0%
+of making sure that I have no data race
+which is I lock before I follow the
+
+ align:start position:0%
+which is I lock before I follow the
+ 
+
+ align:start position:0%
+which is I lock before I follow the
+table slot value and then I unlock then
+
+ align:start position:0%
+table slot value and then I unlock then
+ 
+
+ align:start position:0%
+table slot value and then I unlock then
+I lock again and then I set the value
+
+ align:start position:0%
+I lock again and then I set the value
+ 
+
+ align:start position:0%
+I lock again and then I set the value
+okay so I haven't prevented the
+
+ align:start position:0%
+okay so I haven't prevented the
+ 
+
+ align:start position:0%
+okay so I haven't prevented the
+atomicity right now I've got an atom
+
+ align:start position:0%
+atomicity right now I've got an atom
+ 
+
+ align:start position:0%
+atomicity right now I've got an atom
+isset II violation but I have no data
+
+ align:start position:0%
+isset II violation but I have no data
+ 
+
+ align:start position:0%
+isset II violation but I have no data
+races okay because I never have two
+
+ align:start position:0%
+races okay because I never have two
+ 
+
+ align:start position:0%
+races okay because I never have two
+things that are going to access things
+
+ align:start position:0%
+things that are going to access things
+ 
+
+ align:start position:0%
+things that are going to access things
+at the same time is protected by the
+
+ align:start position:0%
+at the same time is protected by the
+ 
+
+ align:start position:0%
+at the same time is protected by the
+lock okay but it doesn't solve my
+
+ align:start position:0%
+lock okay but it doesn't solve my
+ 
+
+ align:start position:0%
+lock okay but it doesn't solve my
+atomicity so there's a you know there's
+
+ align:start position:0%
+atomicity so there's a you know there's
+ 
+
+ align:start position:0%
+atomicity so there's a you know there's
+you know you can definitely have no data
+
+ align:start position:0%
+you know you can definitely have no data
+ 
+
+ align:start position:0%
+you know you can definitely have no data
+races but that doesn't mean you have no
+
+ align:start position:0%
+races but that doesn't mean you have no
+ 
+
+ align:start position:0%
+races but that doesn't mean you have no
+bugs okay but usually what it happens is
+
+ align:start position:0%
+bugs okay but usually what it happens is
+ 
+
+ align:start position:0%
+bugs okay but usually what it happens is
+if you have no data races then usually
+
+ align:start position:0%
+if you have no data races then usually
+ 
+
+ align:start position:0%
+if you have no data races then usually
+the programmer actually got this code
+
+ align:start position:0%
+the programmer actually got this code
+ 
+
+ align:start position:0%
+the programmer actually got this code
+right okay it's one of these things
+
+ align:start position:0%
+right okay it's one of these things
+ 
+
+ align:start position:0%
+right okay it's one of these things
+we're demonstrating no data races is in
+
+ align:start position:0%
+we're demonstrating no data races is in
+ 
+
+ align:start position:0%
+we're demonstrating no data races is in
+fact you know a very positive thing in
+
+ align:start position:0%
+fact you know a very positive thing in
+ 
+
+ align:start position:0%
+fact you know a very positive thing in
+your code it doesn't mean the program I
+
+ align:start position:0%
+your code it doesn't mean the program I
+ 
+
+ align:start position:0%
+your code it doesn't mean the program I
+did right but most of the time the
+
+ align:start position:0%
+did right but most of the time the
+ 
+
+ align:start position:0%
+did right but most of the time the
+reason they're putting in the in the
+
+ align:start position:0%
+reason they're putting in the in the
+ 
+
+ align:start position:0%
+reason they're putting in the in the
+locks is to provide atomicity for
+
+ align:start position:0%
+locks is to provide atomicity for
+ 
+
+ align:start position:0%
+locks is to provide atomicity for
+something and they usually get it right
+
+ align:start position:0%
+something and they usually get it right
+ 
+
+ align:start position:0%
+something and they usually get it right
+they don't always get it right in fact
+
+ align:start position:0%
+they don't always get it right in fact
+ 
+
+ align:start position:0%
+they don't always get it right in fact
+Java for example had a very famous bug
+
+ align:start position:0%
+Java for example had a very famous bug
+ 
+
+ align:start position:0%
+Java for example had a very famous bug
+early on in the way that it specified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+locking such that you know the you could
+
+ align:start position:0%
+locking such that you know the you could
+ 
+
+ align:start position:0%
+locking such that you know the you could
+look at the length of a string and then
+
+ align:start position:0%
+look at the length of a string and then
+ 
+
+ align:start position:0%
+look at the length of a string and then
+modify it and then you would end up with
+
+ align:start position:0%
+modify it and then you would end up with
+ 
+
+ align:start position:0%
+modify it and then you would end up with
+a race bug because somebody else could
+
+ align:start position:0%
+a race bug because somebody else could
+ 
+
+ align:start position:0%
+a race bug because somebody else could
+swoop in in between so they thought they
+
+ align:start position:0%
+swoop in in between so they thought they
+ 
+
+ align:start position:0%
+swoop in in between so they thought they
+were being providing atomicity and they
+
+ align:start position:0%
+were being providing atomicity and they
+ 
+
+ align:start position:0%
+were being providing atomicity and they
+didn't okay
+
+ align:start position:0%
+didn't okay
+ 
+
+ align:start position:0%
+didn't okay
+so there's there's another set of issues
+
+ align:start position:0%
+so there's there's another set of issues
+ 
+
+ align:start position:0%
+so there's there's another set of issues
+here having to do with benign races now
+
+ align:start position:0%
+here having to do with benign races now
+ 
+
+ align:start position:0%
+here having to do with benign races now
+there's some people who argue that no
+
+ align:start position:0%
+there's some people who argue that no
+ 
+
+ align:start position:0%
+there's some people who argue that no
+races are
+
+ align:start position:0%
+races are
+ 
+
+ align:start position:0%
+races are
+are no determinacy races are benign and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they make academic statements that I
+
+ align:start position:0%
+they make academic statements that I
+ 
+
+ align:start position:0%
+they make academic statements that I
+find quite compelling actually what
+
+ align:start position:0%
+find quite compelling actually what
+ 
+
+ align:start position:0%
+find quite compelling actually what
+they're what they say about about races
+
+ align:start position:0%
+they're what they say about about races
+ 
+
+ align:start position:0%
+they're what they say about about races
+and whether races are benign but
+
+ align:start position:0%
+and whether races are benign but
+ 
+
+ align:start position:0%
+and whether races are benign but
+nevertheless the literature also
+
+ align:start position:0%
+nevertheless the literature also
+ 
+
+ align:start position:0%
+nevertheless the literature also
+continues to use the term benign race
+
+ align:start position:0%
+continues to use the term benign race
+ 
+
+ align:start position:0%
+continues to use the term benign race
+for this kind of example so suppose we
+
+ align:start position:0%
+for this kind of example so suppose we
+ 
+
+ align:start position:0%
+for this kind of example so suppose we
+want to identify what are is the set of
+
+ align:start position:0%
+want to identify what are is the set of
+ 
+
+ align:start position:0%
+want to identify what are is the set of
+digits that perform that occurred in
+
+ align:start position:0%
+digits that perform that occurred in
+ 
+
+ align:start position:0%
+digits that perform that occurred in
+this in in some array so here's an array
+
+ align:start position:0%
+this in in some array so here's an array
+ 
+
+ align:start position:0%
+this in in some array so here's an array
+with a bunch of values in it okay each
+
+ align:start position:0%
+with a bunch of values in it okay each
+ 
+
+ align:start position:0%
+with a bunch of values in it okay each
+one being a digit from zero to nine so I
+
+ align:start position:0%
+one being a digit from zero to nine so I
+ 
+
+ align:start position:0%
+one being a digit from zero to nine so I
+could write a little piece of code that
+
+ align:start position:0%
+could write a little piece of code that
+ 
+
+ align:start position:0%
+could write a little piece of code that
+runs through my digits array of length
+
+ align:start position:0%
+runs through my digits array of length
+ 
+
+ align:start position:0%
+runs through my digits array of length
+10 and sets the number of digits I've
+
+ align:start position:0%
+10 and sets the number of digits I've
+ 
+
+ align:start position:0%
+10 and sets the number of digits I've
+seen so far of each value to be 0 okay
+
+ align:start position:0%
+seen so far of each value to be 0 okay
+ 
+
+ align:start position:0%
+seen so far of each value to be 0 okay
+and now I go through and I'm gonna do
+
+ align:start position:0%
+and now I go through and I'm gonna do
+ 
+
+ align:start position:0%
+and now I go through and I'm gonna do
+this in parallel and I'm going to set
+
+ align:start position:0%
+this in parallel and I'm going to set
+ 
+
+ align:start position:0%
+this in parallel and I'm going to set
+every time I see a value a of I suppose
+
+ align:start position:0%
+every time I see a value a of I suppose
+ 
+
+ align:start position:0%
+every time I see a value a of I suppose
+a of I is 3 I set the location of a 3 to
+
+ align:start position:0%
+a of I is 3 I set the location of a 3 to
+ 
+
+ align:start position:0%
+a of I is 3 I set the location of a 3 to
+be 1 and otherwise and now otherwise
+
+ align:start position:0%
+be 1 and otherwise and now otherwise
+ 
+
+ align:start position:0%
+be 1 and otherwise and now otherwise
+it's zero because that's what I had it
+
+ align:start position:0%
+it's zero because that's what I had it
+ 
+
+ align:start position:0%
+it's zero because that's what I had it
+before so here's the kind of thing I
+
+ align:start position:0%
+before so here's the kind of thing I
+ 
+
+ align:start position:0%
+before so here's the kind of thing I
+have so for example I can have both of
+
+ align:start position:0%
+have so for example I can have both of
+ 
+
+ align:start position:0%
+have so for example I can have both of
+those sixes are in parallel going to
+
+ align:start position:0%
+those sixes are in parallel going to
+ 
+
+ align:start position:0%
+those sixes are in parallel going to
+access the location 6 to set it to 1 but
+
+ align:start position:0%
+access the location 6 to set it to 1 but
+ 
+
+ align:start position:0%
+access the location 6 to set it to 1 but
+they're both setting it to 1 it doesn't
+
+ align:start position:0%
+they're both setting it to 1 it doesn't
+ 
+
+ align:start position:0%
+they're both setting it to 1 it doesn't
+really matter what order they do it in
+
+ align:start position:0%
+really matter what order they do it in
+ 
+
+ align:start position:0%
+really matter what order they do it in
+you're gonna get the same value there 1
+
+ align:start position:0%
+you're gonna get the same value there 1
+ 
+
+ align:start position:0%
+you're gonna get the same value there 1
+ok and so there's a race maybe we don't
+
+ align:start position:0%
+ok and so there's a race maybe we don't
+ 
+
+ align:start position:0%
+ok and so there's a race maybe we don't
+too much care about that race okay
+
+ align:start position:0%
+too much care about that race okay
+ 
+
+ align:start position:0%
+too much care about that race okay
+because they're both setting the same
+
+ align:start position:0%
+because they're both setting the same
+ 
+
+ align:start position:0%
+because they're both setting the same
+value we're not going to get an
+
+ align:start position:0%
+value we're not going to get an
+ 
+
+ align:start position:0%
+value we're not going to get an
+incorrect value well not exactly
+
+ align:start position:0%
+incorrect value well not exactly
+ 
+
+ align:start position:0%
+incorrect value well not exactly
+we might get on some architecture on the
+
+ align:start position:0%
+we might get on some architecture on the
+ 
+
+ align:start position:0%
+we might get on some architecture on the
+Intel architectures you won't get an
+
+ align:start position:0%
+Intel architectures you won't get an
+ 
+
+ align:start position:0%
+Intel architectures you won't get an
+incorrect value on x86 but there are
+
+ align:start position:0%
+incorrect value on x86 but there are
+ 
+
+ align:start position:0%
+incorrect value on x86 but there are
+codes where the elements of the array
+
+ align:start position:0%
+codes where the elements of the array
+ 
+
+ align:start position:0%
+codes where the elements of the array
+values are not set atomically so for
+
+ align:start position:0%
+values are not set atomically so for
+ 
+
+ align:start position:0%
+values are not set atomically so for
+example on the mips architecture
+
+ align:start position:0%
+example on the mips architecture
+ 
+
+ align:start position:0%
+example on the mips architecture
+in order to set a bite to be a
+
+ align:start position:0%
+in order to set a bite to be a
+ 
+
+ align:start position:0%
+in order to set a bite to be a
+particular value you have to you have to
+
+ align:start position:0%
+particular value you have to you have to
+ 
+
+ align:start position:0%
+particular value you have to you have to
+fetch the word mask out set the word and
+
+ align:start position:0%
+fetch the word mask out set the word and
+ 
+
+ align:start position:0%
+fetch the word mask out set the word and
+then store it back in set the the bite
+
+ align:start position:0%
+then store it back in set the the bite
+ 
+
+ align:start position:0%
+then store it back in set the the bite
+and then store it back into the word and
+
+ align:start position:0%
+and then store it back into the word and
+ 
+
+ align:start position:0%
+and then store it back into the word and
+so if there are two guys who are
+
+ align:start position:0%
+so if there are two guys who are
+ 
+
+ align:start position:0%
+so if there are two guys who are
+basically operating on that same word
+
+ align:start position:0%
+basically operating on that same word
+ 
+
+ align:start position:0%
+basically operating on that same word
+location they will have a race even
+
+ align:start position:0%
+location they will have a race even
+ 
+
+ align:start position:0%
+location they will have a race even
+though in the code it looks like they're
+
+ align:start position:0%
+though in the code it looks like they're
+ 
+
+ align:start position:0%
+though in the code it looks like they're
+just setting bites does that make sense
+
+ align:start position:0%
+just setting bites does that make sense
+ 
+
+ align:start position:0%
+just setting bites does that make sense
+okay so nasty nasty bugs okay that's
+
+ align:start position:0%
+okay so nasty nasty bugs okay that's
+ 
+
+ align:start position:0%
+okay so nasty nasty bugs okay that's
+that's why you should never do
+
+ align:start position:0%
+that's why you should never do
+ 
+
+ align:start position:0%
+that's why you should never do
+non-deterministic programming okay
+
+ align:start position:0%
+non-deterministic programming okay
+ 
+
+ align:start position:0%
+non-deterministic programming okay
+unless you have to
+
+ align:start position:0%
+unless you have to
+ 
+
+ align:start position:0%
+unless you have to
+okay so silks and allows you to turn off
+
+ align:start position:0%
+okay so silks and allows you to turn off
+ 
+
+ align:start position:0%
+okay so silks and allows you to turn off
+race detection for intentional races
+
+ align:start position:0%
+race detection for intentional races
+ 
+
+ align:start position:0%
+race detection for intentional races
+okay so if you really meant there to be
+
+ align:start position:0%
+okay so if you really meant there to be
+ 
+
+ align:start position:0%
+okay so if you really meant there to be
+a race as in this case you can turn it
+
+ align:start position:0%
+a race as in this case you can turn it
+ 
+
+ align:start position:0%
+a race as in this case you can turn it
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+this is dangerous but practical turns
+
+ align:start position:0%
+this is dangerous but practical turns
+ 
+
+ align:start position:0%
+this is dangerous but practical turns
+out usually you're not turning it off
+
+ align:start position:0%
+out usually you're not turning it off
+ 
+
+ align:start position:0%
+out usually you're not turning it off
+for because here's what can happen you
+
+ align:start position:0%
+for because here's what can happen you
+ 
+
+ align:start position:0%
+for because here's what can happen you
+can turn it off and yet then there's
+
+ align:start position:0%
+can turn it off and yet then there's
+ 
+
+ align:start position:0%
+can turn it off and yet then there's
+something else which is using that same
+
+ align:start position:0%
+something else which is using that same
+ 
+
+ align:start position:0%
+something else which is using that same
+stuff and now you're running silks and
+
+ align:start position:0%
+stuff and now you're running silks and
+ 
+
+ align:start position:0%
+stuff and now you're running silks and
+without you know having turned it off
+
+ align:start position:0%
+without you know having turned it off
+ 
+
+ align:start position:0%
+without you know having turned it off
+for exactly what your race might be
+
+ align:start position:0%
+for exactly what your race might be
+ 
+
+ align:start position:0%
+for exactly what your race might be
+they're better solutions so in Intel's
+
+ align:start position:0%
+they're better solutions so in Intel's
+ 
+
+ align:start position:0%
+they're better solutions so in Intel's
+silk screen there's the notion of fake
+
+ align:start position:0%
+silk screen there's the notion of fake
+ 
+
+ align:start position:0%
+silk screen there's the notion of fake
+locks we just have not yet implemented
+
+ align:start position:0%
+locks we just have not yet implemented
+ 
+
+ align:start position:0%
+locks we just have not yet implemented
+it in in the open silk compiler so we
+
+ align:start position:0%
+it in in the open silk compiler so we
+ 
+
+ align:start position:0%
+it in in the open silk compiler so we
+will and in silks and we'll eventually
+
+ align:start position:0%
+will and in silks and we'll eventually
+ 
+
+ align:start position:0%
+will and in silks and we'll eventually
+get to doing that and then people who
+
+ align:start position:0%
+get to doing that and then people who
+ 
+
+ align:start position:0%
+get to doing that and then people who
+take this class in the future will have
+
+ align:start position:0%
+take this class in the future will have
+ 
+
+ align:start position:0%
+take this class in the future will have
+an easier time with that okay because
+
+ align:start position:0%
+an easier time with that okay because
+ 
+
+ align:start position:0%
+an easier time with that okay because
+we'll be able to check for that as well
+
+ align:start position:0%
+we'll be able to check for that as well
+ 
+
+ align:start position:0%
+we'll be able to check for that as well
+okay so any questions about these
+
+ align:start position:0%
+okay so any questions about these
+ 
+
+ align:start position:0%
+okay so any questions about these
+notions so you can see the notions of
+
+ align:start position:0%
+notions so you can see the notions of
+ 
+
+ align:start position:0%
+notions so you can see the notions of
+races can get quite hairy and you know
+
+ align:start position:0%
+races can get quite hairy and you know
+ 
+
+ align:start position:0%
+races can get quite hairy and you know
+make it quite difficult to do your
+
+ align:start position:0%
+make it quite difficult to do your
+ 
+
+ align:start position:0%
+make it quite difficult to do your
+debugging and in fact even can confound
+
+ align:start position:0%
+debugging and in fact even can confound
+ 
+
+ align:start position:0%
+debugging and in fact even can confound
+your tools that are supposed to be
+
+ align:start position:0%
+your tools that are supposed to be
+ 
+
+ align:start position:0%
+your tools that are supposed to be
+helping you to get correct code okay
+
+ align:start position:0%
+helping you to get correct code okay
+ 
+
+ align:start position:0%
+helping you to get correct code okay
+all a name of performance okay but we
+
+ align:start position:0%
+all a name of performance okay but we
+ 
+
+ align:start position:0%
+all a name of performance okay but we
+like performance okay any questions
+
+ align:start position:0%
+like performance okay any questions
+ 
+
+ align:start position:0%
+like performance okay any questions
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so how can some architectures cause
+
+ align:start position:0%
+yeah so how can some architectures cause
+ 
+
+ align:start position:0%
+yeah so how can some architectures cause
+some error so here's the thing is that
+
+ align:start position:0%
+some error so here's the thing is that
+ 
+
+ align:start position:0%
+some error so here's the thing is that
+if I have a let's say a byte array it
+
+ align:start position:0%
+if I have a let's say a byte array it
+ 
+
+ align:start position:0%
+if I have a let's say a byte array it
+may be that this is stored int as as a
+
+ align:start position:0%
+may be that this is stored int as as a
+ 
+
+ align:start position:0%
+may be that this is stored int as as a
+set of let's say 4 byte words okay and
+
+ align:start position:0%
+set of let's say 4 byte words okay and
+ 
+
+ align:start position:0%
+set of let's say 4 byte words okay and
+so although you may write that a of 0
+
+ align:start position:0%
+so although you may write that a of 0
+ 
+
+ align:start position:0%
+so although you may write that a of 0
+gets 1 what it does is it says let me
+
+ align:start position:0%
+gets 1 what it does is it says let me
+ 
+
+ align:start position:0%
+gets 1 what it does is it says let me
+fetch these 4 values because there is no
+
+ align:start position:0%
+fetch these 4 values because there is no
+ 
+
+ align:start position:0%
+fetch these 4 values because there is no
+byte set instruction on some
+
+ align:start position:0%
+byte set instruction on some
+ 
+
+ align:start position:0%
+byte set instruction on some
+architectures it can only set in this
+
+ align:start position:0%
+architectures it can only set in this
+ 
+
+ align:start position:0%
+architectures it can only set in this
+case 32-bit words so it fetches the
+
+ align:start position:0%
+case 32-bit words so it fetches the
+ 
+
+ align:start position:0%
+case 32-bit words so it fetches the
+values it then you know into a register
+
+ align:start position:0%
+values it then you know into a register
+ 
+
+ align:start position:0%
+values it then you know into a register
+it then sets the value in the register
+
+ align:start position:0%
+it then sets the value in the register
+ 
+
+ align:start position:0%
+it then sets the value in the register
+ok by masking so it doesn't set the
+
+ align:start position:0%
+ok by masking so it doesn't set the
+ 
+
+ align:start position:0%
+ok by masking so it doesn't set the
+other things here and then it stores it
+
+ align:start position:0%
+other things here and then it stores it
+ 
+
+ align:start position:0%
+other things here and then it stores it
+back right so that it has a 1 here but
+
+ align:start position:0%
+back right so that it has a 1 here but
+ 
+
+ align:start position:0%
+back right so that it has a 1 here but
+what if somebody at the same time is
+
+ align:start position:0%
+what if somebody at the same time is
+ 
+
+ align:start position:0%
+what if somebody at the same time is
+storing into this location they will
+
+ align:start position:0%
+storing into this location they will
+ 
+
+ align:start position:0%
+storing into this location they will
+fetch it into their own register set
+
+ align:start position:0%
+fetch it into their own register set
+ 
+
+ align:start position:0%
+fetch it into their own register set
+their byte mascot etc and now my right
+
+ align:start position:0%
+their byte mascot etc and now my right
+ 
+
+ align:start position:0%
+their byte mascot etc and now my right
+back is going to we're gonna have a lost
+
+ align:start position:0%
+back is going to we're gonna have a lost
+ 
+
+ align:start position:0%
+back is going to we're gonna have a lost
+update in the in the right backs does
+
+ align:start position:0%
+update in the in the right backs does
+ 
+
+ align:start position:0%
+update in the in the right backs does
+that make sense ok good
+
+ align:start position:0%
+that make sense ok good
+ 
+
+ align:start position:0%
+that make sense ok good
+very good question ya know I went
+
+ align:start position:0%
+very good question ya know I went
+ 
+
+ align:start position:0%
+very good question ya know I went
+through that orally a little bit quicker
+
+ align:start position:0%
+through that orally a little bit quicker
+ 
+
+ align:start position:0%
+through that orally a little bit quicker
+than maybe I should have ok great
+
+ align:start position:0%
+than maybe I should have ok great
+ 
+
+ align:start position:0%
+than maybe I should have ok great
+so let's talk a little bit about
+
+ align:start position:0%
+so let's talk a little bit about
+ 
+
+ align:start position:0%
+so let's talk a little bit about
+implementation I always like to take
+
+ align:start position:0%
+implementation I always like to take
+ 
+
+ align:start position:0%
+implementation I always like to take
+things down one level below what you
+
+ align:start position:0%
+things down one level below what you
+ 
+
+ align:start position:0%
+things down one level below what you
+necessarily need to know in order to do
+
+ align:start position:0%
+necessarily need to know in order to do
+ 
+
+ align:start position:0%
+necessarily need to know in order to do
+things but it's helpful to sort of see
+
+ align:start position:0%
+things but it's helpful to sort of see
+ 
+
+ align:start position:0%
+things but it's helpful to sort of see
+how these things are implemented and
+
+ align:start position:0%
+how these things are implemented and
+ 
+
+ align:start position:0%
+how these things are implemented and
+because then that gives you a better
+
+ align:start position:0%
+because then that gives you a better
+ 
+
+ align:start position:0%
+because then that gives you a better
+sense at a higher level what the what
+
+ align:start position:0%
+sense at a higher level what the what
+ 
+
+ align:start position:0%
+sense at a higher level what the what
+your capabilities are and how things are
+
+ align:start position:0%
+your capabilities are and how things are
+ 
+
+ align:start position:0%
+your capabilities are and how things are
+actually working underneath so let's
+
+ align:start position:0%
+actually working underneath so let's
+ 
+
+ align:start position:0%
+actually working underneath so let's
+talk about how in the mutex is so here
+
+ align:start position:0%
+talk about how in the mutex is so here
+ 
+
+ align:start position:0%
+talk about how in the mutex is so here
+first of all to understand there are
+
+ align:start position:0%
+first of all to understand there are
+ 
+
+ align:start position:0%
+first of all to understand there are
+lots of different mutexes if you look at
+
+ align:start position:0%
+lots of different mutexes if you look at
+ 
+
+ align:start position:0%
+lots of different mutexes if you look at
+an operating system they may have a half
+
+ align:start position:0%
+an operating system they may have a half
+ 
+
+ align:start position:0%
+an operating system they may have a half
+a dozen or more different
+
+ align:start position:0%
+a dozen or more different
+ 
+
+ align:start position:0%
+a dozen or more different
+you Texas different locks that can
+
+ align:start position:0%
+you Texas different locks that can
+ 
+
+ align:start position:0%
+you Texas different locks that can
+provide mutual exclusion or parameters
+
+ align:start position:0%
+provide mutual exclusion or parameters
+ 
+
+ align:start position:0%
+provide mutual exclusion or parameters
+that can be set for what kind of mute
+
+ align:start position:0%
+that can be set for what kind of mute
+ 
+
+ align:start position:0%
+that can be set for what kind of mute
+exes so the first basic difference in
+
+ align:start position:0%
+exes so the first basic difference in
+ 
+
+ align:start position:0%
+exes so the first basic difference in
+most things is whether the mutex is
+
+ align:start position:0%
+most things is whether the mutex is
+ 
+
+ align:start position:0%
+most things is whether the mutex is
+yielding or spinning so a yielding mutex
+
+ align:start position:0%
+yielding or spinning so a yielding mutex
+ 
+
+ align:start position:0%
+yielding or spinning so a yielding mutex
+returns control to the operating system
+
+ align:start position:0%
+returns control to the operating system
+ 
+
+ align:start position:0%
+returns control to the operating system
+when it blocks when a program tries to
+
+ align:start position:0%
+when it blocks when a program tries to
+ 
+
+ align:start position:0%
+when it blocks when a program tries to
+get active when it tries to get access
+
+ align:start position:0%
+get active when it tries to get access
+ 
+
+ align:start position:0%
+get active when it tries to get access
+when a thread tries to get access to a
+
+ align:start position:0%
+when a thread tries to get access to a
+ 
+
+ align:start position:0%
+when a thread tries to get access to a
+given low given lock if it is blocked it
+
+ align:start position:0%
+given low given lock if it is blocked it
+ 
+
+ align:start position:0%
+given low given lock if it is blocked it
+doesn't just sit there and keep and
+
+ align:start position:0%
+doesn't just sit there and keep and
+ 
+
+ align:start position:0%
+doesn't just sit there and keep and
+spinning where you're basically spinning
+
+ align:start position:0%
+spinning where you're basically spinning
+ 
+
+ align:start position:0%
+spinning where you're basically spinning
+means I just sit there checking it and
+
+ align:start position:0%
+means I just sit there checking it and
+ 
+
+ align:start position:0%
+means I just sit there checking it and
+checking it and checking it and checking
+
+ align:start position:0%
+checking it and checking it and checking
+ 
+
+ align:start position:0%
+checking it and checking it and checking
+in ok instead what it does is it says oh
+
+ align:start position:0%
+in ok instead what it does is it says oh
+ 
+
+ align:start position:0%
+in ok instead what it does is it says oh
+I'm doing useless work here let me go
+
+ align:start position:0%
+I'm doing useless work here let me go
+ 
+
+ align:start position:0%
+I'm doing useless work here let me go
+and return control of the operating
+
+ align:start position:0%
+and return control of the operating
+ 
+
+ align:start position:0%
+and return control of the operating
+system maybe there's another thread that
+
+ align:start position:0%
+system maybe there's another thread that
+ 
+
+ align:start position:0%
+system maybe there's another thread that
+can run at the same time and therefore
+
+ align:start position:0%
+can run at the same time and therefore
+ 
+
+ align:start position:0%
+can run at the same time and therefore
+I'll give by switching myself out by
+
+ align:start position:0%
+I'll give by switching myself out by
+ 
+
+ align:start position:0%
+I'll give by switching myself out by
+yielding my my scheduling quantum I will
+
+ align:start position:0%
+yielding my my scheduling quantum I will
+ 
+
+ align:start position:0%
+yielding my my scheduling quantum I will
+get better efficiency overall because
+
+ align:start position:0%
+get better efficiency overall because
+ 
+
+ align:start position:0%
+get better efficiency overall because
+somebody some other thread that is
+
+ align:start position:0%
+somebody some other thread that is
+ 
+
+ align:start position:0%
+somebody some other thread that is
+capable of running can run at that point
+
+ align:start position:0%
+capable of running can run at that point
+ 
+
+ align:start position:0%
+capable of running can run at that point
+ok so is that clear the distinction
+
+ align:start position:0%
+ok so is that clear the distinction
+ 
+
+ align:start position:0%
+ok so is that clear the distinction
+between spinning and and yielding ok
+
+ align:start position:0%
+between spinning and and yielding ok
+ 
+
+ align:start position:0%
+between spinning and and yielding ok
+another one is whether the mutex is
+
+ align:start position:0%
+another one is whether the mutex is
+ 
+
+ align:start position:0%
+another one is whether the mutex is
+reentrant or non re-entrant a reentrant
+
+ align:start position:0%
+reentrant or non re-entrant a reentrant
+ 
+
+ align:start position:0%
+reentrant or non re-entrant a reentrant
+mutex allows a thread that is already
+
+ align:start position:0%
+mutex allows a thread that is already
+ 
+
+ align:start position:0%
+mutex allows a thread that is already
+holding a lock to acquire it again ok a
+
+ align:start position:0%
+holding a lock to acquire it again ok a
+ 
+
+ align:start position:0%
+holding a lock to acquire it again ok a
+non reentrant one deadlocks if the
+
+ align:start position:0%
+non reentrant one deadlocks if the
+ 
+
+ align:start position:0%
+non reentrant one deadlocks if the
+thread attempts to require a mutex that
+
+ align:start position:0%
+thread attempts to require a mutex that
+ 
+
+ align:start position:0%
+thread attempts to require a mutex that
+already holds ok so I grab a lock and
+
+ align:start position:0%
+already holds ok so I grab a lock and
+ 
+
+ align:start position:0%
+already holds ok so I grab a lock and
+now I go to a piece of code and it says
+
+ align:start position:0%
+now I go to a piece of code and it says
+ 
+
+ align:start position:0%
+now I go to a piece of code and it says
+grab that lock so very simple I can
+
+ align:start position:0%
+grab that lock so very simple I can
+ 
+
+ align:start position:0%
+grab that lock so very simple I can
+check to see whether I have if I want to
+
+ align:start position:0%
+check to see whether I have if I want to
+ 
+
+ align:start position:0%
+check to see whether I have if I want to
+be reentrant I can check do I have that
+
+ align:start position:0%
+be reentrant I can check do I have that
+ 
+
+ align:start position:0%
+be reentrant I can check do I have that
+lock already and if I do then I don't
+
+ align:start position:0%
+lock already and if I do then I don't
+ 
+
+ align:start position:0%
+lock already and if I do then I don't
+actually have to acquire it I just keep
+
+ align:start position:0%
+actually have to acquire it I just keep
+ 
+
+ align:start position:0%
+actually have to acquire it I just keep
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+but that's extra overhead it's faster
+
+ align:start position:0%
+but that's extra overhead it's faster
+ 
+
+ align:start position:0%
+but that's extra overhead it's faster
+for me to have a non reentrant lock ok
+
+ align:start position:0%
+for me to have a non reentrant lock ok
+ 
+
+ align:start position:0%
+for me to have a non reentrant lock ok
+where I just simply grab the lock and if
+
+ align:start position:0%
+where I just simply grab the lock and if
+ 
+
+ align:start position:0%
+where I just simply grab the lock and if
+somebody's got it
+
+ align:start position:0%
+somebody's got it
+ 
+
+ align:start position:0%
+somebody's got it
+including me then it's a dead lock but
+
+ align:start position:0%
+including me then it's a dead lock but
+ 
+
+ align:start position:0%
+including me then it's a dead lock but
+now if there's the possibility that I
+
+ align:start position:0%
+now if there's the possibility that I
+ 
+
+ align:start position:0%
+now if there's the possibility that I
+could react wire a lock then that might
+
+ align:start position:0%
+could react wire a lock then that might
+ 
+
+ align:start position:0%
+could react wire a lock then that might
+not be safe
+
+ align:start position:0%
+not be safe
+ 
+
+ align:start position:0%
+not be safe
+okay you have to worry about the
+
+ align:start position:0%
+okay you have to worry about the
+ 
+
+ align:start position:0%
+okay you have to worry about the
+programmer has to worry about that now
+
+ align:start position:0%
+programmer has to worry about that now
+ 
+
+ align:start position:0%
+programmer has to worry about that now
+is that clear that one okay
+
+ align:start position:0%
+is that clear that one okay
+ 
+
+ align:start position:0%
+is that clear that one okay
+and then final basic property of mutexes
+
+ align:start position:0%
+and then final basic property of mutexes
+ 
+
+ align:start position:0%
+and then final basic property of mutexes
+is whether they're fair or unfair okay
+
+ align:start position:0%
+is whether they're fair or unfair okay
+ 
+
+ align:start position:0%
+is whether they're fair or unfair okay
+so here's the thing with it's easiest to
+
+ align:start position:0%
+so here's the thing with it's easiest to
+ 
+
+ align:start position:0%
+so here's the thing with it's easiest to
+think about it in the context of
+
+ align:start position:0%
+think about it in the context of
+ 
+
+ align:start position:0%
+think about it in the context of
+spinning
+
+ align:start position:0%
+spinning
+ 
+
+ align:start position:0%
+spinning
+I have several threads that basically
+
+ align:start position:0%
+I have several threads that basically
+ 
+
+ align:start position:0%
+I have several threads that basically
+came to the same lock and we decide
+
+ align:start position:0%
+came to the same lock and we decide
+ 
+
+ align:start position:0%
+came to the same lock and we decide
+they're gonna spin they're just going to
+
+ align:start position:0%
+they're gonna spin they're just going to
+ 
+
+ align:start position:0%
+they're gonna spin they're just going to
+sit there continually checking waiting
+
+ align:start position:0%
+sit there continually checking waiting
+ 
+
+ align:start position:0%
+sit there continually checking waiting
+for that lock to be free okay so when
+
+ align:start position:0%
+for that lock to be free okay so when
+ 
+
+ align:start position:0%
+for that lock to be free okay so when
+finally the guy who has it unlocks it
+
+ align:start position:0%
+finally the guy who has it unlocks it
+ 
+
+ align:start position:0%
+finally the guy who has it unlocks it
+you know maybe I've got half a dozen
+
+ align:start position:0%
+you know maybe I've got half a dozen
+ 
+
+ align:start position:0%
+you know maybe I've got half a dozen
+threads sitting there one of them wins
+
+ align:start position:0%
+threads sitting there one of them wins
+ 
+
+ align:start position:0%
+threads sitting there one of them wins
+okay and which one wins well if they're
+
+ align:start position:0%
+okay and which one wins well if they're
+ 
+
+ align:start position:0%
+okay and which one wins well if they're
+spinning it could be any one of them
+
+ align:start position:0%
+spinning it could be any one of them
+ 
+
+ align:start position:0%
+spinning it could be any one of them
+then it has one and so the issue that
+
+ align:start position:0%
+then it has one and so the issue that
+ 
+
+ align:start position:0%
+then it has one and so the issue that
+can go on is you could have what's
+
+ align:start position:0%
+can go on is you could have what's
+ 
+
+ align:start position:0%
+can go on is you could have what's
+called a starvation problem okay where
+
+ align:start position:0%
+called a starvation problem okay where
+ 
+
+ align:start position:0%
+called a starvation problem okay where
+some guy is sitting there for a really
+
+ align:start position:0%
+some guy is sitting there for a really
+ 
+
+ align:start position:0%
+some guy is sitting there for a really
+long time waiting while everybody else
+
+ align:start position:0%
+long time waiting while everybody else
+ 
+
+ align:start position:0%
+long time waiting while everybody else
+is continually grabbing locks out from
+
+ align:start position:0%
+is continually grabbing locks out from
+ 
+
+ align:start position:0%
+is continually grabbing locks out from
+under his or her nose okay so with a
+
+ align:start position:0%
+under his or her nose okay so with a
+ 
+
+ align:start position:0%
+under his or her nose okay so with a
+fair mutex basically what you do is you
+
+ align:start position:0%
+fair mutex basically what you do is you
+ 
+
+ align:start position:0%
+fair mutex basically what you do is you
+go for the one that's been waiting the
+
+ align:start position:0%
+go for the one that's been waiting the
+ 
+
+ align:start position:0%
+go for the one that's been waiting the
+longest essentially and so therefore you
+
+ align:start position:0%
+longest essentially and so therefore you
+ 
+
+ align:start position:0%
+longest essentially and so therefore you
+never have to wait more than for however
+
+ align:start position:0%
+never have to wait more than for however
+ 
+
+ align:start position:0%
+never have to wait more than for however
+many things were there when you got
+
+ align:start position:0%
+many things were there when you got
+ 
+
+ align:start position:0%
+many things were there when you got
+there before you're able to go question
+
+ align:start position:0%
+there before you're able to go question
+ 
+
+ align:start position:0%
+there before you're able to go question
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+it can be better because you may freeze
+
+ align:start position:0%
+it can be better because you may freeze
+ 
+
+ align:start position:0%
+it can be better because you may freeze
+out or service okay if there's something
+
+ align:start position:0%
+out or service okay if there's something
+ 
+
+ align:start position:0%
+out or service okay if there's something
+that's you know you may never get to do
+
+ align:start position:0%
+that's you know you may never get to do
+ 
+
+ align:start position:0%
+that's you know you may never get to do
+the thing you want to do okay because
+
+ align:start position:0%
+the thing you want to do okay because
+ 
+
+ align:start position:0%
+the thing you want to do okay because
+there's something else always
+
+ align:start position:0%
+there's something else always
+ 
+
+ align:start position:0%
+there's something else always
+interfering with the ability for that
+
+ align:start position:0%
+interfering with the ability for that
+ 
+
+ align:start position:0%
+interfering with the ability for that
+part of the program to make progress
+
+ align:start position:0%
+part of the program to make progress
+ 
+
+ align:start position:0%
+part of the program to make progress
+this tends to be more of an issue in in
+
+ align:start position:0%
+this tends to be more of an issue in in
+ 
+
+ align:start position:0%
+this tends to be more of an issue in in
+concurrent programming where we have
+
+ align:start position:0%
+concurrent programming where we have
+ 
+
+ align:start position:0%
+concurrent programming where we have
+different programs that are trying to
+
+ align:start position:0%
+different programs that are trying to
+ 
+
+ align:start position:0%
+different programs that are trying to
+accomplish different tasks and you want
+
+ align:start position:0%
+accomplish different tasks and you want
+ 
+
+ align:start position:0%
+accomplish different tasks and you want
+to accomplish both tasks okay
+
+ align:start position:0%
+to accomplish both tasks okay
+ 
+
+ align:start position:0%
+to accomplish both tasks okay
+does not come across in parallel
+
+ align:start position:0%
+does not come across in parallel
+ 
+
+ align:start position:0%
+does not come across in parallel
+programming mostly we deal with unfair
+
+ align:start position:0%
+programming mostly we deal with unfair
+ 
+
+ align:start position:0%
+programming mostly we deal with unfair
+often unfair spinning locks because
+
+ align:start position:0%
+often unfair spinning locks because
+ 
+
+ align:start position:0%
+often unfair spinning locks because
+they're the cheapest and we just trust
+
+ align:start position:0%
+they're the cheapest and we just trust
+ 
+
+ align:start position:0%
+they're the cheapest and we just trust
+that a we're not going to do any have
+
+ align:start position:0%
+that a we're not going to do any have
+ 
+
+ align:start position:0%
+that a we're not going to do any have
+any critical regions we write our code
+
+ align:start position:0%
+any critical regions we write our code
+ 
+
+ align:start position:0%
+any critical regions we write our code
+so we don't have critical regions that
+
+ align:start position:0%
+so we don't have critical regions that
+ 
+
+ align:start position:0%
+so we don't have critical regions that
+are really long so nobody ever has to
+
+ align:start position:0%
+are really long so nobody ever has to
+ 
+
+ align:start position:0%
+are really long so nobody ever has to
+wait a very long time but indeed dealing
+
+ align:start position:0%
+wait a very long time but indeed dealing
+ 
+
+ align:start position:0%
+wait a very long time but indeed dealing
+with a contention issue as we talked
+
+ align:start position:0%
+with a contention issue as we talked
+ 
+
+ align:start position:0%
+with a contention issue as we talked
+about last week you know can can make a
+
+ align:start position:0%
+about last week you know can can make a
+ 
+
+ align:start position:0%
+about last week you know can can make a
+difference okay good so here's an
+
+ align:start position:0%
+difference okay good so here's an
+ 
+
+ align:start position:0%
+difference okay good so here's an
+implementation of a simple spinning
+
+ align:start position:0%
+implementation of a simple spinning
+ 
+
+ align:start position:0%
+implementation of a simple spinning
+mutex in assembly language okay
+
+ align:start position:0%
+mutex in assembly language okay
+ 
+
+ align:start position:0%
+mutex in assembly language okay
+so the first thing it does is it checks
+
+ align:start position:0%
+so the first thing it does is it checks
+ 
+
+ align:start position:0%
+so the first thing it does is it checks
+to see if the the mutex is free if it's
+
+ align:start position:0%
+to see if the the mutex is free if it's
+ 
+
+ align:start position:0%
+to see if the the mutex is free if it's
+value is 0 so it compares the value of
+
+ align:start position:0%
+value is 0 so it compares the value of
+ 
+
+ align:start position:0%
+value is 0 so it compares the value of
+the mutex to 0 and if it is 0 it says oh
+
+ align:start position:0%
+the mutex to 0 and if it is 0 it says oh
+ 
+
+ align:start position:0%
+the mutex to 0 and if it is 0 it says oh
+the it's free let me go get it it then
+
+ align:start position:0%
+the it's free let me go get it it then
+ 
+
+ align:start position:0%
+the it's free let me go get it it then
+to get the mutex what it does is it
+
+ align:start position:0%
+to get the mutex what it does is it
+ 
+
+ align:start position:0%
+to get the mutex what it does is it
+moves one into the it basically moves
+
+ align:start position:0%
+moves one into the it basically moves
+ 
+
+ align:start position:0%
+moves one into the it basically moves
+one into a register and then it
+
+ align:start position:0%
+one into a register and then it
+ 
+
+ align:start position:0%
+one into a register and then it
+exchanges the mutex with that register
+
+ align:start position:0%
+exchanges the mutex with that register
+ 
+
+ align:start position:0%
+exchanges the mutex with that register
+EAX ok and then it compares to see
+
+ align:start position:0%
+EAX ok and then it compares to see
+ 
+
+ align:start position:0%
+EAX ok and then it compares to see
+whether or not it actually got the mutex
+
+ align:start position:0%
+whether or not it actually got the mutex
+ 
+
+ align:start position:0%
+whether or not it actually got the mutex
+and if it didn't then it goes back up to
+
+ align:start position:0%
+and if it didn't then it goes back up to
+ 
+
+ align:start position:0%
+and if it didn't then it goes back up to
+the top and starts again ok and then the
+
+ align:start position:0%
+the top and starts again ok and then the
+ 
+
+ align:start position:0%
+the top and starts again ok and then the
+other branch is at the at the top there
+
+ align:start position:0%
+other branch is at the at the top there
+ 
+
+ align:start position:0%
+other branch is at the at the top there
+it does this pause and this apparently
+
+ align:start position:0%
+it does this pause and this apparently
+ 
+
+ align:start position:0%
+it does this pause and this apparently
+is due to a bug in x86 that they end up
+
+ align:start position:0%
+is due to a bug in x86 that they end up
+ 
+
+ align:start position:0%
+is due to a bug in x86 that they end up
+having to put this pause instruction in
+
+ align:start position:0%
+having to put this pause instruction in
+ 
+
+ align:start position:0%
+having to put this pause instruction in
+there and then otherwise you jump to the
+
+ align:start position:0%
+there and then otherwise you jump to the
+ 
+
+ align:start position:0%
+there and then otherwise you jump to the
+where the spin mutex is and and go go
+
+ align:start position:0%
+where the spin mutex is and and go go
+ 
+
+ align:start position:0%
+where the spin mutex is and and go go
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+okay and then once you've done the
+
+ align:start position:0%
+okay and then once you've done the
+ 
+
+ align:start position:0%
+okay and then once you've done the
+critical section when you're done you
+
+ align:start position:0%
+critical section when you're done you
+ 
+
+ align:start position:0%
+critical section when you're done you
+free it by just setting it to zero so
+
+ align:start position:0%
+free it by just setting it to zero so
+ 
+
+ align:start position:0%
+free it by just setting it to zero so
+the question here is so the exchange
+
+ align:start position:0%
+the question here is so the exchange
+ 
+
+ align:start position:0%
+the question here is so the exchange
+instruction is a is a is an atomic
+
+ align:start position:0%
+instruction is a is a is an atomic
+ 
+
+ align:start position:0%
+instruction is a is a is an atomic
+exchange so it takes the register and
+
+ align:start position:0%
+exchange so it takes the register and
+ 
+
+ align:start position:0%
+exchange so it takes the register and
+the memory value and it swaps them and
+
+ align:start position:0%
+the memory value and it swaps them and
+ 
+
+ align:start position:0%
+the memory value and it swaps them and
+you can't have anything come in so one
+
+ align:start position:0%
+you can't have anything come in so one
+ 
+
+ align:start position:0%
+you can't have anything come in so one
+of the things that might have you
+
+ align:start position:0%
+of the things that might have you
+ 
+
+ align:start position:0%
+of the things that might have you
+confused a little bit here is wait a
+
+ align:start position:0%
+confused a little bit here is wait a
+ 
+
+ align:start position:0%
+confused a little bit here is wait a
+second I check to see if the mutex is
+
+ align:start position:0%
+second I check to see if the mutex is
+ 
+
+ align:start position:0%
+second I check to see if the mutex is
+free and then I tried to get it and to
+
+ align:start position:0%
+free and then I tried to get it and to
+ 
+
+ align:start position:0%
+free and then I tried to get it and to
+test if I was successful why why can't I
+
+ align:start position:0%
+test if I was successful why why can't I
+ 
+
+ align:start position:0%
+test if I was successful why why can't I
+just start out by essentially going to
+
+ align:start position:0%
+just start out by essentially going to
+ 
+
+ align:start position:0%
+just start out by essentially going to
+get mutex right I mean why do I need why
+
+ align:start position:0%
+get mutex right I mean why do I need why
+ 
+
+ align:start position:0%
+get mutex right I mean why do I need why
+don't need any of the code between spin
+
+ align:start position:0%
+don't need any of the code between spin
+ 
+
+ align:start position:0%
+don't need any of the code between spin
+mutex and get mutex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so if I just started with getting
+
+ align:start position:0%
+right so if I just started with getting
+ 
+
+ align:start position:0%
+right so if I just started with getting
+new text I would move one in I would
+
+ align:start position:0%
+new text I would move one in I would
+ 
+
+ align:start position:0%
+new text I would move one in I would
+exchange check to see if I could get it
+
+ align:start position:0%
+exchange check to see if I could get it
+ 
+
+ align:start position:0%
+exchange check to see if I could get it
+if I have it fine then I execute the
+
+ align:start position:0%
+if I have it fine then I execute the
+ 
+
+ align:start position:0%
+if I have it fine then I execute the
+internet if not okay I go back and and
+
+ align:start position:0%
+internet if not okay I go back and and
+ 
+
+ align:start position:0%
+internet if not okay I go back and and
+try again so why you know because if
+
+ align:start position:0%
+try again so why you know because if
+ 
+
+ align:start position:0%
+try again so why you know because if
+somebody has it by the way the value
+
+ align:start position:0%
+somebody has it by the way the value
+ 
+
+ align:start position:0%
+somebody has it by the way the value
+that I'm gonna get is going to be one
+
+ align:start position:0%
+that I'm gonna get is going to be one
+ 
+
+ align:start position:0%
+that I'm gonna get is going to be one
+and that's what I swapped in so I
+
+ align:start position:0%
+and that's what I swapped in so I
+ 
+
+ align:start position:0%
+and that's what I swapped in so I
+haven't changed anything I go back and I
+
+ align:start position:0%
+haven't changed anything I go back and I
+ 
+
+ align:start position:0%
+haven't changed anything I go back and I
+check again so so why do I need that
+
+ align:start position:0%
+check again so so why do I need that
+ 
+
+ align:start position:0%
+check again so so why do I need that
+first part yeah yeah maybe it's faster
+
+ align:start position:0%
+first part yeah yeah maybe it's faster
+ 
+
+ align:start position:0%
+first part yeah yeah maybe it's faster
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so indeed it's because it's faster even
+
+ align:start position:0%
+so indeed it's because it's faster even
+ 
+
+ align:start position:0%
+so indeed it's because it's faster even
+though you're executing extra code it's
+
+ align:start position:0%
+though you're executing extra code it's
+ 
+
+ align:start position:0%
+though you're executing extra code it's
+faster tell me why it's faster and this
+
+ align:start position:0%
+faster tell me why it's faster and this
+ 
+
+ align:start position:0%
+faster tell me why it's faster and this
+tape will take you you have to think a
+
+ align:start position:0%
+tape will take you you have to think a
+ 
+
+ align:start position:0%
+tape will take you you have to think a
+little bit about the cache protocols and
+
+ align:start position:0%
+little bit about the cache protocols and
+ 
+
+ align:start position:0%
+little bit about the cache protocols and
+the invalidation issue so why is it
+
+ align:start position:0%
+the invalidation issue so why is it
+ 
+
+ align:start position:0%
+the invalidation issue so why is it
+gonna be faster yeah okay good say more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so so it turns out the exchange
+
+ align:start position:0%
+yeah so so it turns out the exchange
+ 
+
+ align:start position:0%
+yeah so so it turns out the exchange
+operation is like a right and so in
+
+ align:start position:0%
+operation is like a right and so in
+ 
+
+ align:start position:0%
+operation is like a right and so in
+order to do a right what do I need to do
+
+ align:start position:0%
+order to do a right what do I need to do
+ 
+
+ align:start position:0%
+order to do a right what do I need to do
+for the for the cash line that it's on
+
+ align:start position:0%
+for the for the cash line that it's on
+ 
+
+ align:start position:0%
+for the for the cash line that it's on
+to bring it in but what how does it have
+
+ align:start position:0%
+to bring it in but what how does it have
+ 
+
+ align:start position:0%
+to bring it in but what how does it have
+to be brought in remember the cash lines
+
+ align:start position:0%
+to be brought in remember the cash lines
+ 
+
+ align:start position:0%
+to be brought in remember the cash lines
+had let's let's a Matt you have to
+
+ align:start position:0%
+had let's let's a Matt you have to
+ 
+
+ align:start position:0%
+had let's let's a Matt you have to
+invalidate it on the other ones and you
+
+ align:start position:0%
+invalidate it on the other ones and you
+ 
+
+ align:start position:0%
+invalidate it on the other ones and you
+have to hold it in what state
+
+ align:start position:0%
+have to hold it in what state
+ 
+
+ align:start position:0%
+have to hold it in what state
+remember the cash lines have you know if
+
+ align:start position:0%
+remember the cash lines have you know if
+ 
+
+ align:start position:0%
+remember the cash lines have you know if
+we take a look at just a simplified
+
+ align:start position:0%
+we take a look at just a simplified
+ 
+
+ align:start position:0%
+we take a look at just a simplified
+protocol right where the MSI protocol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah you have to have it in the EMA MSI
+
+ align:start position:0%
+yeah you have to have it in the EMA MSI
+ 
+
+ align:start position:0%
+yeah you have to have it in the EMA MSI
+or an ESI you have to bring it in in
+
+ align:start position:0%
+or an ESI you have to bring it in in
+ 
+
+ align:start position:0%
+or an ESI you have to bring it in in
+modified or at least exclusive state
+
+ align:start position:0%
+modified or at least exclusive state
+ 
+
+ align:start position:0%
+modified or at least exclusive state
+right so exclusive is for the Emmy ESI
+
+ align:start position:0%
+right so exclusive is for the Emmy ESI
+ 
+
+ align:start position:0%
+right so exclusive is for the Emmy ESI
+protocol we we mentioned that but we
+
+ align:start position:0%
+protocol we we mentioned that but we
+ 
+
+ align:start position:0%
+protocol we we mentioned that but we
+didn't really do it mostly we just went
+
+ align:start position:0%
+didn't really do it mostly we just went
+ 
+
+ align:start position:0%
+didn't really do it mostly we just went
+but I have to bring it in and modified
+
+ align:start position:0%
+but I have to bring it in and modified
+ 
+
+ align:start position:0%
+but I have to bring it in and modified
+where I guarantee there are no other
+
+ align:start position:0%
+where I guarantee there are no other
+ 
+
+ align:start position:0%
+where I guarantee there are no other
+copies so if I've got two guys that are
+
+ align:start position:0%
+copies so if I've got two guys that are
+ 
+
+ align:start position:0%
+copies so if I've got two guys that are
+polling on this location
+
+ align:start position:0%
+polling on this location
+ 
+
+ align:start position:0%
+polling on this location
+they're both continually invalidating
+
+ align:start position:0%
+they're both continually invalidating
+ 
+
+ align:start position:0%
+they're both continually invalidating
+each other and you create a whole bunch
+
+ align:start position:0%
+each other and you create a whole bunch
+ 
+
+ align:start position:0%
+each other and you create a whole bunch
+of traffic on the memory network that's
+
+ align:start position:0%
+of traffic on the memory network that's
+ 
+
+ align:start position:0%
+of traffic on the memory network that's
+going to slow everything down okay
+
+ align:start position:0%
+going to slow everything down okay
+ 
+
+ align:start position:0%
+going to slow everything down okay
+whereas if I do the first one what state
+
+ align:start position:0%
+whereas if I do the first one what state
+ 
+
+ align:start position:0%
+whereas if I do the first one what state
+do I get it in then you get it in shared
+
+ align:start position:0%
+do I get it in then you get it in shared
+ 
+
+ align:start position:0%
+do I get it in then you get it in shared
+State what does the other guy get it in
+
+ align:start position:0%
+State what does the other guy get it in
+ 
+
+ align:start position:0%
+State what does the other guy get it in
+shared state and now I keep going just
+
+ align:start position:0%
+shared state and now I keep going just
+ 
+
+ align:start position:0%
+shared state and now I keep going just
+having it in spinning in my own local
+
+ align:start position:0%
+having it in spinning in my own local
+ 
+
+ align:start position:0%
+having it in spinning in my own local
+cache not generating any local traffic
+
+ align:start position:0%
+cache not generating any local traffic
+ 
+
+ align:start position:0%
+cache not generating any local traffic
+until the until somebody releases the
+
+ align:start position:0%
+until the until somebody releases the
+ 
+
+ align:start position:0%
+until the until somebody releases the
+Falak in which case it invalidate Sall
+
+ align:start position:0%
+Falak in which case it invalidate Sall
+ 
+
+ align:start position:0%
+Falak in which case it invalidate Sall
+those and now you can actually get it a
+
+ align:start position:0%
+those and now you can actually get it a
+ 
+
+ align:start position:0%
+those and now you can actually get it a
+little bit of a storm after the fact
+
+ align:start position:0%
+little bit of a storm after the fact
+ 
+
+ align:start position:0%
+little bit of a storm after the fact
+there in fact locks where you don't even
+
+ align:start position:0%
+there in fact locks where you don't even
+ 
+
+ align:start position:0%
+there in fact locks where you don't even
+get a storm after the after the fact but
+
+ align:start position:0%
+get a storm after the after the fact but
+ 
+
+ align:start position:0%
+get a storm after the after the fact but
+called mcs locks but but this kind of
+
+ align:start position:0%
+called mcs locks but but this kind of
+ 
+
+ align:start position:0%
+called mcs locks but but this kind of
+lock is for most practical purposes just
+
+ align:start position:0%
+lock is for most practical purposes just
+ 
+
+ align:start position:0%
+lock is for most practical purposes just
+fine okay so so to everybody follow that
+
+ align:start position:0%
+fine okay so so to everybody follow that
+ 
+
+ align:start position:0%
+fine okay so so to everybody follow that
+description of what's going on there so
+
+ align:start position:0%
+description of what's going on there so
+ 
+
+ align:start position:0%
+description of what's going on there so
+that first code for correctness purposes
+
+ align:start position:0%
+that first code for correctness purposes
+ 
+
+ align:start position:0%
+that first code for correctness purposes
+not important for performance it is
+
+ align:start position:0%
+not important for performance it is
+ 
+
+ align:start position:0%
+not important for performance it is
+important okay isn't it great that you
+
+ align:start position:0%
+important okay isn't it great that you
+ 
+
+ align:start position:0%
+important okay isn't it great that you
+guys can read assembly language right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now suppose that this is a spinning
+
+ align:start position:0%
+okay now suppose that this is a spinning
+ 
+
+ align:start position:0%
+okay now suppose that this is a spinning
+mutex suppose that I want to do a
+
+ align:start position:0%
+mutex suppose that I want to do a
+ 
+
+ align:start position:0%
+mutex suppose that I want to do a
+yielding mutex how does this code have
+
+ align:start position:0%
+yielding mutex how does this code have
+ 
+
+ align:start position:0%
+yielding mutex how does this code have
+to change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a spinning one just
+
+ align:start position:0%
+okay so this is a spinning one just
+ 
+
+ align:start position:0%
+okay so this is a spinning one just
+keeps checking instead I want to return
+
+ align:start position:0%
+keeps checking instead I want to return
+ 
+
+ align:start position:0%
+keeps checking instead I want to return
+control of the operating system okay so
+
+ align:start position:0%
+control of the operating system okay so
+ 
+
+ align:start position:0%
+control of the operating system okay so
+how does this code change if I do that
+
+ align:start position:0%
+how does this code change if I do that
+ 
+
+ align:start position:0%
+how does this code change if I do that
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+like that yeah exactly
+
+ align:start position:0%
+like that yeah exactly
+ 
+
+ align:start position:0%
+like that yeah exactly
+okay so instead of doing that that you
+
+ align:start position:0%
+okay so instead of doing that that you
+ 
+
+ align:start position:0%
+okay so instead of doing that that you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+pause instruction which the
+
+ align:start position:0%
+pause instruction which the
+ 
+
+ align:start position:0%
+pause instruction which the
+documentation on this is not very clear
+
+ align:start position:0%
+documentation on this is not very clear
+ 
+
+ align:start position:0%
+documentation on this is not very clear
+I'm love to have the inside scoop on why
+
+ align:start position:0%
+I'm love to have the inside scoop on why
+ 
+
+ align:start position:0%
+I'm love to have the inside scoop on why
+they really had to do the pause there
+
+ align:start position:0%
+they really had to do the pause there
+ 
+
+ align:start position:0%
+they really had to do the pause there
+but in any case you take that no op that
+
+ align:start position:0%
+but in any case you take that no op that
+ 
+
+ align:start position:0%
+but in any case you take that no op that
+they want to have in there and your
+
+ align:start position:0%
+they want to have in there and your
+ 
+
+ align:start position:0%
+they want to have in there and your
+place it with it just a call to the
+
+ align:start position:0%
+place it with it just a call to the
+ 
+
+ align:start position:0%
+place it with it just a call to the
+yield which allows the operating systems
+
+ align:start position:0%
+yield which allows the operating systems
+ 
+
+ align:start position:0%
+yield which allows the operating systems
+to schedule something else and then when
+
+ align:start position:0%
+to schedule something else and then when
+ 
+
+ align:start position:0%
+to schedule something else and then when
+it's your turn again it resumes from
+
+ align:start position:0%
+it's your turn again it resumes from
+ 
+
+ align:start position:0%
+it's your turn again it resumes from
+that point okay so that's the yield so
+
+ align:start position:0%
+that point okay so that's the yield so
+ 
+
+ align:start position:0%
+that point okay so that's the yield so
+so that's the difference in the
+
+ align:start position:0%
+so that's the difference in the
+ 
+
+ align:start position:0%
+so that's the difference in the
+implementation essentially between a
+
+ align:start position:0%
+implementation essentially between a
+ 
+
+ align:start position:0%
+implementation essentially between a
+spinning mutex and a yielding mutex okay
+
+ align:start position:0%
+spinning mutex and a yielding mutex okay
+ 
+
+ align:start position:0%
+spinning mutex and a yielding mutex okay
+now there's another kind of mutex that
+
+ align:start position:0%
+now there's another kind of mutex that
+ 
+
+ align:start position:0%
+now there's another kind of mutex that
+is kind of cool which is called a
+
+ align:start position:0%
+is kind of cool which is called a
+ 
+
+ align:start position:0%
+is kind of cool which is called a
+competitive mutex so think about it this
+
+ align:start position:0%
+competitive mutex so think about it this
+ 
+
+ align:start position:0%
+competitive mutex so think about it this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+I've competing goals one is to I want to
+
+ align:start position:0%
+I've competing goals one is to I want to
+ 
+
+ align:start position:0%
+I've competing goals one is to I want to
+get the mutex as quickly as possible
+
+ align:start position:0%
+get the mutex as quickly as possible
+ 
+
+ align:start position:0%
+get the mutex as quickly as possible
+after it's released right I don't want
+
+ align:start position:0%
+after it's released right I don't want
+ 
+
+ align:start position:0%
+after it's released right I don't want
+if if it's unlocked I don't want to sit
+
+ align:start position:0%
+if if it's unlocked I don't want to sit
+ 
+
+ align:start position:0%
+if if it's unlocked I don't want to sit
+there for a really long time and before
+
+ align:start position:0%
+there for a really long time and before
+ 
+
+ align:start position:0%
+there for a really long time and before
+I actually acquire okay and - yeah but I
+
+ align:start position:0%
+I actually acquire okay and - yeah but I
+ 
+
+ align:start position:0%
+I actually acquire okay and - yeah but I
+don't want to sit there spinning for a
+
+ align:start position:0%
+don't want to sit there spinning for a
+ 
+
+ align:start position:0%
+don't want to sit there spinning for a
+really long time and then you know
+
+ align:start position:0%
+really long time and then you know
+ 
+
+ align:start position:0%
+really long time and then you know
+because as long I'm doing that I'm
+
+ align:start position:0%
+because as long I'm doing that I'm
+ 
+
+ align:start position:0%
+because as long I'm doing that I'm
+taking up cycles and not accomplishing
+
+ align:start position:0%
+taking up cycles and not accomplishing
+ 
+
+ align:start position:0%
+taking up cycles and not accomplishing
+anything let me turn it over to some
+
+ align:start position:0%
+anything let me turn it over to some
+ 
+
+ align:start position:0%
+anything let me turn it over to some
+other thread that can can use the cycles
+
+ align:start position:0%
+other thread that can can use the cycles
+ 
+
+ align:start position:0%
+other thread that can can use the cycles
+more effectively so there at those two
+
+ align:start position:0%
+more effectively so there at those two
+ 
+
+ align:start position:0%
+more effectively so there at those two
+goals how can I get the best of both
+
+ align:start position:0%
+goals how can I get the best of both
+ 
+
+ align:start position:0%
+goals how can I get the best of both
+worlds here something that's close to
+
+ align:start position:0%
+worlds here something that's close to
+ 
+
+ align:start position:0%
+worlds here something that's close to
+the best of both worlds that's not
+
+ align:start position:0%
+the best of both worlds that's not
+ 
+
+ align:start position:0%
+the best of both worlds that's not
+absolutely the best of all flows but
+
+ align:start position:0%
+absolutely the best of all flows but
+ 
+
+ align:start position:0%
+absolutely the best of all flows but
+it's close to the best of both worlds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what strategy could I do so I want to
+
+ align:start position:0%
+what strategy could I do so I want to
+ 
+
+ align:start position:0%
+what strategy could I do so I want to
+claim it very soon so so the point is
+
+ align:start position:0%
+claim it very soon so so the point is
+ 
+
+ align:start position:0%
+claim it very soon so so the point is
+that the spinning mutex achieves goal
+
+ align:start position:0%
+that the spinning mutex achieves goal
+ 
+
+ align:start position:0%
+that the spinning mutex achieves goal
+one and the yielding mutex achieves goal
+
+ align:start position:0%
+one and the yielding mutex achieves goal
+ 
+
+ align:start position:0%
+one and the yielding mutex achieves goal
+two so how can i what can I do to get
+
+ align:start position:0%
+two so how can i what can I do to get
+ 
+
+ align:start position:0%
+two so how can i what can I do to get
+both goals yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+so you're saying use message-passing to
+
+ align:start position:0%
+so you're saying use message-passing to
+ 
+
+ align:start position:0%
+so you're saying use message-passing to
+inform the waiting threads I'm thinking
+
+ align:start position:0%
+inform the waiting threads I'm thinking
+ 
+
+ align:start position:0%
+inform the waiting threads I'm thinking
+something a lot simpler
+
+ align:start position:0%
+something a lot simpler
+ 
+
+ align:start position:0%
+something a lot simpler
+okay in this context so because the
+
+ align:start position:0%
+okay in this context so because the
+ 
+
+ align:start position:0%
+okay in this context so because the
+message passing you're gonna have to go
+
+ align:start position:0%
+message passing you're gonna have to go
+ 
+
+ align:start position:0%
+message passing you're gonna have to go
+through to do message passing properly
+
+ align:start position:0%
+through to do message passing properly
+ 
+
+ align:start position:0%
+through to do message passing properly
+you actually need to use mutex as a
+
+ align:start position:0%
+you actually need to use mutex as a
+ 
+
+ align:start position:0%
+you actually need to use mutex as a
+setter to implement it so you want to be
+
+ align:start position:0%
+setter to implement it so you want to be
+ 
+
+ align:start position:0%
+setter to implement it so you want to be
+a little bit careful you know about
+
+ align:start position:0%
+a little bit careful you know about
+ 
+
+ align:start position:0%
+a little bit careful you know about
+about that but but interesting idea yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using an interrupt how would you do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so typically implement interrupts
+
+ align:start position:0%
+yeah so typically implement interrupts
+ 
+
+ align:start position:0%
+yeah so typically implement interrupts
+you also need to have some mutual
+
+ align:start position:0%
+you also need to have some mutual
+ 
+
+ align:start position:0%
+you also need to have some mutual
+exclusions to do it properly but I mean
+
+ align:start position:0%
+exclusions to do it properly but I mean
+ 
+
+ align:start position:0%
+exclusions to do it properly but I mean
+hardware will support that
+
+ align:start position:0%
+hardware will support that
+ 
+
+ align:start position:0%
+hardware will support that
+that's pretty heavy-handed as well this
+
+ align:start position:0%
+that's pretty heavy-handed as well this
+ 
+
+ align:start position:0%
+that's pretty heavy-handed as well this
+is actually a very simple solution who's
+
+ align:start position:0%
+is actually a very simple solution who's
+ 
+
+ align:start position:0%
+is actually a very simple solution who's
+everybody I'm seeing familiar hands I
+
+ align:start position:0%
+everybody I'm seeing familiar hands I
+ 
+
+ align:start position:0%
+everybody I'm seeing familiar hands I
+want to see so unfamiliar hands who's
+
+ align:start position:0%
+want to see so unfamiliar hands who's
+ 
+
+ align:start position:0%
+want to see so unfamiliar hands who's
+got an unfamiliar hand okay I see you
+
+ align:start position:0%
+got an unfamiliar hand okay I see you
+ 
+
+ align:start position:0%
+got an unfamiliar hand okay I see you
+raised your left hand that time instead
+
+ align:start position:0%
+raised your left hand that time instead
+ 
+
+ align:start position:0%
+raised your left hand that time instead
+of your right hand okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it hard to measure that right how would
+
+ align:start position:0%
+it hard to measure that right how would
+ 
+
+ align:start position:0%
+it hard to measure that right how would
+you write code to measure that yeah
+
+ align:start position:0%
+you write code to measure that yeah
+ 
+
+ align:start position:0%
+you write code to measure that yeah
+mm-hmm yeah good okay good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+why doesn't it have a because if I yield
+
+ align:start position:0%
+why doesn't it have a because if I yield
+ 
+
+ align:start position:0%
+why doesn't it have a because if I yield
+okay so what's the how often does if I
+
+ align:start position:0%
+okay so what's the how often does if I
+ 
+
+ align:start position:0%
+okay so what's the how often does if I
+contact switch how often is it going to
+
+ align:start position:0%
+contact switch how often is it going to
+ 
+
+ align:start position:0%
+contact switch how often is it going to
+be that I how long am I going to have to
+
+ align:start position:0%
+be that I how long am I going to have to
+ 
+
+ align:start position:0%
+be that I how long am I going to have to
+wait typically before I am scheduled
+
+ align:start position:0%
+wait typically before I am scheduled
+ 
+
+ align:start position:0%
+wait typically before I am scheduled
+again okay when when a when a code
+
+ align:start position:0%
+again okay when when a when a code
+ 
+
+ align:start position:0%
+again okay when when a when a code
+yields to the operating system how often
+
+ align:start position:0%
+yields to the operating system how often
+ 
+
+ align:start position:0%
+yields to the operating system how often
+does the operating system normally do
+
+ align:start position:0%
+does the operating system normally do
+ 
+
+ align:start position:0%
+does the operating system normally do
+context switching do you know what's
+
+ align:start position:0%
+context switching do you know what's
+ 
+
+ align:start position:0%
+context switching do you know what's
+that what's the rate at which it
+
+ align:start position:0%
+that what's the rate at which it
+ 
+
+ align:start position:0%
+that what's the rate at which it
+contacts switches for the different
+
+ align:start position:0%
+contacts switches for the different
+ 
+
+ align:start position:0%
+contacts switches for the different
+multiplexing of threads that it does on
+
+ align:start position:0%
+multiplexing of threads that it does on
+ 
+
+ align:start position:0%
+multiplexing of threads that it does on
+to on to the available processors what's
+
+ align:start position:0%
+to on to the available processors what's
+ 
+
+ align:start position:0%
+to on to the available processors what's
+the rate at which it it shifts oh this
+
+ align:start position:0%
+the rate at which it it shifts oh this
+ 
+
+ align:start position:0%
+the rate at which it it shifts oh this
+is what okay that's gonna be on the quiz
+
+ align:start position:0%
+is what okay that's gonna be on the quiz
+ 
+
+ align:start position:0%
+is what okay that's gonna be on the quiz
+okay this is a new numeracy thing yeah
+
+ align:start position:0%
+okay this is a new numeracy thing yeah
+ 
+
+ align:start position:0%
+okay this is a new numeracy thing yeah
+how do you know how frequently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not quite but but your your you're not
+
+ align:start position:0%
+not quite but but your your you're not
+ 
+
+ align:start position:0%
+not quite but but your your you're not
+off by more than an order of magnitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what are the typical rates that
+
+ align:start position:0%
+okay so what are the typical rates that
+ 
+
+ align:start position:0%
+okay so what are the typical rates that
+you that the system does contact
+
+ align:start position:0%
+you that the system does contact
+ 
+
+ align:start position:0%
+you that the system does contact
+switching okay so from human times it's
+
+ align:start position:0%
+switching okay so from human times it's
+ 
+
+ align:start position:0%
+switching okay so from human times it's
+the blink of an eye right so it's
+
+ align:start position:0%
+the blink of an eye right so it's
+ 
+
+ align:start position:0%
+the blink of an eye right so it's
+actually around 10 milliseconds so it
+
+ align:start position:0%
+actually around 10 milliseconds so it
+ 
+
+ align:start position:0%
+actually around 10 milliseconds so it
+would does 100 times a second some of
+
+ align:start position:0%
+would does 100 times a second some of
+ 
+
+ align:start position:0%
+would does 100 times a second some of
+them do some do 60 times a second okay
+
+ align:start position:0%
+them do some do 60 times a second okay
+ 
+
+ align:start position:0%
+them do some do 60 times a second okay
+that's how often it switches okay now
+
+ align:start position:0%
+that's how often it switches okay now
+ 
+
+ align:start position:0%
+that's how often it switches okay now
+let's say it's a hundred times the
+
+ align:start position:0%
+let's say it's a hundred times the
+ 
+
+ align:start position:0%
+let's say it's a hundred times the
+second 10 milliseconds so you're pretty
+
+ align:start position:0%
+second 10 milliseconds so you're pretty
+ 
+
+ align:start position:0%
+second 10 milliseconds so you're pretty
+close okay 10 milliseconds okay how many
+
+ align:start position:0%
+close okay 10 milliseconds okay how many
+ 
+
+ align:start position:0%
+close okay 10 milliseconds okay how many
+orders of magnitude is that from the
+
+ align:start position:0%
+orders of magnitude is that from the
+ 
+
+ align:start position:0%
+orders of magnitude is that from the
+execution of a simple instruction okay
+
+ align:start position:0%
+execution of a simple instruction okay
+ 
+
+ align:start position:0%
+execution of a simple instruction okay
+so we're going at more than a gigahertz
+
+ align:start position:0%
+so we're going at more than a gigahertz
+ 
+
+ align:start position:0%
+so we're going at more than a gigahertz
+right and so a gigahertz is 10 to the
+
+ align:start position:0%
+right and so a gigahertz is 10 to the
+ 
+
+ align:start position:0%
+right and so a gigahertz is 10 to the
+ninth and we're talking ten to the minus
+
+ align:start position:0%
+ninth and we're talking ten to the minus
+ 
+
+ align:start position:0%
+ninth and we're talking ten to the minus
+nine and we're talking ten to the minus
+
+ align:start position:0%
+nine and we're talking ten to the minus
+ 
+
+ align:start position:0%
+nine and we're talking ten to the minus
+two so that's you know 10 million
+
+ align:start position:0%
+two so that's you know 10 million
+ 
+
+ align:start position:0%
+two so that's you know 10 million
+instruction opportunities that we miss
+
+ align:start position:0%
+instruction opportunities that we miss
+ 
+
+ align:start position:0%
+instruction opportunities that we miss
+if we switch out and of course we
+
+ align:start position:0%
+if we switch out and of course we
+ 
+
+ align:start position:0%
+if we switch out and of course we
+probably only switch out for half hour
+
+ align:start position:0%
+probably only switch out for half hour
+ 
+
+ align:start position:0%
+probably only switch out for half hour
+you know where are you along the the
+
+ align:start position:0%
+you know where are you along the the
+ 
+
+ align:start position:0%
+you know where are you along the the
+thing so you're only switching out maybe
+
+ align:start position:0%
+thing so you're only switching out maybe
+ 
+
+ align:start position:0%
+thing so you're only switching out maybe
+for half assuming nothing else is going
+
+ align:start position:0%
+for half assuming nothing else is going
+ 
+
+ align:start position:0%
+for half assuming nothing else is going
+on there but that's that means you're
+
+ align:start position:0%
+on there but that's that means you're
+ 
+
+ align:start position:0%
+on there but that's that means you're
+not grabbing the lock quickly after it's
+
+ align:start position:0%
+not grabbing the lock quickly after it's
+ 
+
+ align:start position:0%
+not grabbing the lock quickly after it's
+released because you've got ten million
+
+ align:start position:0%
+released because you've got ten million
+ 
+
+ align:start position:0%
+released because you've got ten million
+instructions that are going to execute
+
+ align:start position:0%
+instructions that are going to execute
+ 
+
+ align:start position:0%
+instructions that are going to execute
+before you're gonna have a chance to
+
+ align:start position:0%
+before you're gonna have a chance to
+ 
+
+ align:start position:0%
+before you're gonna have a chance to
+come back in and grab it okay
+
+ align:start position:0%
+come back in and grab it okay
+ 
+
+ align:start position:0%
+come back in and grab it okay
+so that's why a yielding one is does not
+
+ align:start position:0%
+so that's why a yielding one is does not
+ 
+
+ align:start position:0%
+so that's why a yielding one is does not
+grab it quickly
+
+ align:start position:0%
+grab it quickly
+ 
+
+ align:start position:0%
+grab it quickly
+okay we're spinning is like we're
+
+ align:start position:0%
+okay we're spinning is like we're
+ 
+
+ align:start position:0%
+okay we're spinning is like we're
+executing this stuff at the rate of
+
+ align:start position:0%
+executing this stuff at the rate of
+ 
+
+ align:start position:0%
+executing this stuff at the rate of
+gigahertz right checking again checking
+
+ align:start position:0%
+gigahertz right checking again checking
+ 
+
+ align:start position:0%
+gigahertz right checking again checking
+and checking again okay so why so what's
+
+ align:start position:0%
+and checking again okay so why so what's
+ 
+
+ align:start position:0%
+and checking again okay so why so what's
+what's the strategy here what can I do
+
+ align:start position:0%
+what's the strategy here what can I do
+ 
+
+ align:start position:0%
+what's the strategy here what can I do
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hey what a good idea okay okay spin for
+
+ align:start position:0%
+hey what a good idea okay okay spin for
+ 
+
+ align:start position:0%
+hey what a good idea okay okay spin for
+a while and then yield okay so the idea
+
+ align:start position:0%
+a while and then yield okay so the idea
+ 
+
+ align:start position:0%
+a while and then yield okay so the idea
+being hey if if the if the lock is
+
+ align:start position:0%
+being hey if if the if the lock is
+ 
+
+ align:start position:0%
+being hey if if the if the lock is
+really soon then I will be able to grab
+
+ align:start position:0%
+really soon then I will be able to grab
+ 
+
+ align:start position:0%
+really soon then I will be able to grab
+it immediately because I'm spinning and
+
+ align:start position:0%
+it immediately because I'm spinning and
+ 
+
+ align:start position:0%
+it immediately because I'm spinning and
+if it takes a long time for the lock to
+
+ align:start position:0%
+if it takes a long time for the lock to
+ 
+
+ align:start position:0%
+if it takes a long time for the lock to
+yield well I will yield eventually so
+
+ align:start position:0%
+yield well I will yield eventually so
+ 
+
+ align:start position:0%
+yield well I will yield eventually so
+yeah but okay how long does spin how
+
+ align:start position:0%
+yeah but okay how long does spin how
+ 
+
+ align:start position:0%
+yeah but okay how long does spin how
+long shall I spin sure
+
+ align:start position:0%
+long shall I spin sure
+ 
+
+ align:start position:0%
+long shall I spin sure
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah basically as long as a context
+
+ align:start position:0%
+yeah basically as long as a context
+ 
+
+ align:start position:0%
+yeah basically as long as a context
+switch takes okay as long as it takes to
+
+ align:start position:0%
+switch takes okay as long as it takes to
+ 
+
+ align:start position:0%
+switch takes okay as long as it takes to
+go out and come back okay and if you do
+
+ align:start position:0%
+go out and come back okay and if you do
+ 
+
+ align:start position:0%
+go out and come back okay and if you do
+that then you never wait more than twice
+
+ align:start position:0%
+that then you never wait more than twice
+ 
+
+ align:start position:0%
+that then you never wait more than twice
+the optimal time okay this is
+
+ align:start position:0%
+the optimal time okay this is
+ 
+
+ align:start position:0%
+the optimal time okay this is
+competitive analysis which the
+
+ align:start position:0%
+competitive analysis which the
+ 
+
+ align:start position:0%
+competitive analysis which the
+theoreticians have gone off there's
+
+ align:start position:0%
+theoreticians have gone off there's
+ 
+
+ align:start position:0%
+theoreticians have gone off there's
+brilliant work in competitive analysis
+
+ align:start position:0%
+brilliant work in competitive analysis
+ 
+
+ align:start position:0%
+brilliant work in competitive analysis
+so the idea here is that if the mutex is
+
+ align:start position:0%
+so the idea here is that if the mutex is
+ 
+
+ align:start position:0%
+so the idea here is that if the mutex is
+released while you're spinning then the
+
+ align:start position:0%
+released while you're spinning then the
+ 
+
+ align:start position:0%
+released while you're spinning then the
+strategy is optimal right because you
+
+ align:start position:0%
+strategy is optimal right because you
+ 
+
+ align:start position:0%
+strategy is optimal right because you
+just sat there spinning and as soon as
+
+ align:start position:0%
+just sat there spinning and as soon as
+ 
+
+ align:start position:0%
+just sat there spinning and as soon as
+was there you got it on the next cycle
+
+ align:start position:0%
+was there you got it on the next cycle
+ 
+
+ align:start position:0%
+was there you got it on the next cycle
+if the mutex is released after the yield
+
+ align:start position:0%
+if the mutex is released after the yield
+ 
+
+ align:start position:0%
+if the mutex is released after the yield
+you've already spun for equal to that so
+
+ align:start position:0%
+you've already spun for equal to that so
+ 
+
+ align:start position:0%
+you've already spun for equal to that so
+you'll come back and get it at within it
+
+ align:start position:0%
+you'll come back and get it at within it
+ 
+
+ align:start position:0%
+you'll come back and get it at within it
+most a factor of two okay this is by the
+
+ align:start position:0%
+most a factor of two okay this is by the
+ 
+
+ align:start position:0%
+most a factor of two okay this is by the
+way that the way this shows up in the
+
+ align:start position:0%
+way that the way this shows up in the
+ 
+
+ align:start position:0%
+way that the way this shows up in the
+Theory literature if you're introduced
+
+ align:start position:0%
+Theory literature if you're introduced
+ 
+
+ align:start position:0%
+Theory literature if you're introduced
+it's called the ski rental problem okay
+
+ align:start position:0%
+it's called the ski rental problem okay
+ 
+
+ align:start position:0%
+it's called the ski rental problem okay
+and here's the idea you're gonna go you
+
+ align:start position:0%
+and here's the idea you're gonna go you
+ 
+
+ align:start position:0%
+and here's the idea you're gonna go you
+know your friends are persuading you to
+
+ align:start position:0%
+know your friends are persuading you to
+ 
+
+ align:start position:0%
+know your friends are persuading you to
+go try skiing okay right snow skiing
+
+ align:start position:0%
+go try skiing okay right snow skiing
+ 
+
+ align:start position:0%
+go try skiing okay right snow skiing
+right right okay and so you say gee
+
+ align:start position:0%
+right right okay and so you say gee
+ 
+
+ align:start position:0%
+right right okay and so you say gee
+should I buy the equipment or should I
+
+ align:start position:0%
+should I buy the equipment or should I
+ 
+
+ align:start position:0%
+should I buy the equipment or should I
+rent after all you may discover it that
+
+ align:start position:0%
+rent after all you may discover it that
+ 
+
+ align:start position:0%
+rent after all you may discover it that
+you rent and then I mean you buy it and
+
+ align:start position:0%
+you rent and then I mean you buy it and
+ 
+
+ align:start position:0%
+you rent and then I mean you buy it and
+then you break your leg and never want
+
+ align:start position:0%
+then you break your leg and never want
+ 
+
+ align:start position:0%
+then you break your leg and never want
+to go back okay well then if you've
+
+ align:start position:0%
+to go back okay well then if you've
+ 
+
+ align:start position:0%
+to go back okay well then if you've
+bought it's been very expensive and if
+
+ align:start position:0%
+bought it's been very expensive and if
+ 
+
+ align:start position:0%
+bought it's been very expensive and if
+you've rented well then then you're
+
+ align:start position:0%
+you've rented well then then you're
+ 
+
+ align:start position:0%
+you've rented well then then you're
+probably better off on the other hand if
+
+ align:start position:0%
+probably better off on the other hand if
+ 
+
+ align:start position:0%
+probably better off on the other hand if
+it turns out you like it
+
+ align:start position:0%
+it turns out you like it
+ 
+
+ align:start position:0%
+it turns out you like it
+you're now accumulating the costs going
+
+ align:start position:0%
+you're now accumulating the costs going
+ 
+
+ align:start position:0%
+you're now accumulating the costs going
+forward okay and so the question is well
+
+ align:start position:0%
+forward okay and so the question is well
+ 
+
+ align:start position:0%
+forward okay and so the question is well
+what's your strategy and the idea is
+
+ align:start position:0%
+what's your strategy and the idea is
+ 
+
+ align:start position:0%
+what's your strategy and the idea is
+well let's look at what renting costs
+
+ align:start position:0%
+well let's look at what renting costs
+ 
+
+ align:start position:0%
+well let's look at what renting costs
+and what buying costs let me rent until
+
+ align:start position:0%
+and what buying costs let me rent until
+ 
+
+ align:start position:0%
+and what buying costs let me rent until
+it's equal to the cost of buying and
+
+ align:start position:0%
+it's equal to the cost of buying and
+ 
+
+ align:start position:0%
+it's equal to the cost of buying and
+then buy and then I'm within a factor of
+
+ align:start position:0%
+then buy and then I'm within a factor of
+ 
+
+ align:start position:0%
+then buy and then I'm within a factor of
+two of having spent the optimal amount
+
+ align:start position:0%
+two of having spent the optimal amount
+ 
+
+ align:start position:0%
+two of having spent the optimal amount
+of of money for because then if I break
+
+ align:start position:0%
+of of money for because then if I break
+ 
+
+ align:start position:0%
+of of money for because then if I break
+my leg after that well at least I you
+
+ align:start position:0%
+my leg after that well at least I you
+ 
+
+ align:start position:0%
+my leg after that well at least I you
+know you know I got you know I I I
+
+ align:start position:0%
+know you know I got you know I I I
+ 
+
+ align:start position:0%
+know you know I got you know I I I
+didn't spend more than a factor of two
+
+ align:start position:0%
+didn't spend more than a factor of two
+ 
+
+ align:start position:0%
+didn't spend more than a factor of two
+and if I get it before it I've spent
+
+ align:start position:0%
+and if I get it before it I've spent
+ 
+
+ align:start position:0%
+and if I get it before it I've spent
+optimally
+
+ align:start position:0%
+optimally
+ 
+
+ align:start position:0%
+optimally
+okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah 10 milliseconds yeah so spin
+
+ align:start position:0%
+yeah yeah 10 milliseconds yeah so spin
+ 
+
+ align:start position:0%
+yeah yeah 10 milliseconds yeah so spin
+for 10 milliseconds okay and then switch
+
+ align:start position:0%
+for 10 milliseconds okay and then switch
+ 
+
+ align:start position:0%
+for 10 milliseconds okay and then switch
+so now the point is that that when you
+
+ align:start position:0%
+so now the point is that that when you
+ 
+
+ align:start position:0%
+so now the point is that that when you
+come back in okay the other job is gonna
+
+ align:start position:0%
+come back in okay the other job is gonna
+ 
+
+ align:start position:0%
+come back in okay the other job is gonna
+run for 10 milliseconds or whatever okay
+
+ align:start position:0%
+run for 10 milliseconds or whatever okay
+ 
+
+ align:start position:0%
+run for 10 milliseconds or whatever okay
+so if you get switched out then if the
+
+ align:start position:0%
+so if you get switched out then if the
+ 
+
+ align:start position:0%
+so if you get switched out then if the
+lock is released you're gonna be done in
+
+ align:start position:0%
+lock is released you're gonna be done in
+ 
+
+ align:start position:0%
+lock is released you're gonna be done in
+20 milliseconds right and so you'll be
+
+ align:start position:0%
+20 milliseconds right and so you'll be
+ 
+
+ align:start position:0%
+20 milliseconds right and so you'll be
+within a factor of 2 and if it happened
+
+ align:start position:0%
+within a factor of 2 and if it happened
+ 
+
+ align:start position:0%
+within a factor of 2 and if it happened
+if they lock out release before then
+
+ align:start position:0%
+if they lock out release before then
+ 
+
+ align:start position:0%
+if they lock out release before then
+you're right there to grab it okay now
+
+ align:start position:0%
+you're right there to grab it okay now
+ 
+
+ align:start position:0%
+you're right there to grab it okay now
+it turns out that there's a really
+
+ align:start position:0%
+it turns out that there's a really
+ 
+
+ align:start position:0%
+it turns out that there's a really
+clever randomized algorithm I love this
+
+ align:start position:0%
+clever randomized algorithm I love this
+ 
+
+ align:start position:0%
+clever randomized algorithm I love this
+rat algorithm okay from 1994 that
+
+ align:start position:0%
+rat algorithm okay from 1994 that
+ 
+
+ align:start position:0%
+rat algorithm okay from 1994 that
+achieves a competitive ratio of e over e
+
+ align:start position:0%
+achieves a competitive ratio of e over e
+ 
+
+ align:start position:0%
+achieves a competitive ratio of e over e
+minus 1 using a randomized strategy and
+
+ align:start position:0%
+minus 1 using a randomized strategy and
+ 
+
+ align:start position:0%
+minus 1 using a randomized strategy and
+I'll encourage you to you know those of
+
+ align:start position:0%
+I'll encourage you to you know those of
+ 
+
+ align:start position:0%
+I'll encourage you to you know those of
+you who have a theoretical bent to go
+
+ align:start position:0%
+you who have a theoretical bent to go
+ 
+
+ align:start position:0%
+you who have a theoretical bent to go
+take a look at that it's very clever
+
+ align:start position:0%
+take a look at that it's very clever
+ 
+
+ align:start position:0%
+take a look at that it's very clever
+ok so basically have some probability of
+
+ align:start position:0%
+ok so basically have some probability of
+ 
+
+ align:start position:0%
+ok so basically have some probability of
+at every step of whether you at that
+
+ align:start position:0%
+at every step of whether you at that
+ 
+
+ align:start position:0%
+at every step of whether you at that
+point decide to yield you know or
+
+ align:start position:0%
+point decide to yield you know or
+ 
+
+ align:start position:0%
+point decide to yield you know or
+continue spinning ok and by using a
+
+ align:start position:0%
+continue spinning ok and by using a
+ 
+
+ align:start position:0%
+continue spinning ok and by using a
+randomized strategy you can actually get
+
+ align:start position:0%
+randomized strategy you can actually get
+ 
+
+ align:start position:0%
+randomized strategy you can actually get
+this to Yi over u minus 1 ok questions
+
+ align:start position:0%
+this to Yi over u minus 1 ok questions
+ 
+
+ align:start position:0%
+this to Yi over u minus 1 ok questions
+about this so this is sort of some of
+
+ align:start position:0%
+about this so this is sort of some of
+ 
+
+ align:start position:0%
+about this so this is sort of some of
+the basics I'm glad we went over some of
+
+ align:start position:0%
+the basics I'm glad we went over some of
+ 
+
+ align:start position:0%
+the basics I'm glad we went over some of
+that because everybody should know these
+
+ align:start position:0%
+that because everybody should know these
+ 
+
+ align:start position:0%
+that because everybody should know these
+basic numbers about what things cost
+
+ align:start position:0%
+basic numbers about what things cost
+ 
+
+ align:start position:0%
+basic numbers about what things cost
+because otherwise you don't know where
+
+ align:start position:0%
+because otherwise you don't know where
+ 
+
+ align:start position:0%
+because otherwise you don't know where
+to spend it so context switching time is
+
+ align:start position:0%
+to spend it so context switching time is
+ 
+
+ align:start position:0%
+to spend it so context switching time is
+on the order of 10 milliseconds how long
+
+ align:start position:0%
+on the order of 10 milliseconds how long
+ 
+
+ align:start position:0%
+on the order of 10 milliseconds how long
+is the disk access compared to you know
+
+ align:start position:0%
+is the disk access compared to you know
+ 
+
+ align:start position:0%
+is the disk access compared to you know
+yeah what's the disk access
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+150 cycles hmm that's an that that would
+
+ align:start position:0%
+150 cycles hmm that's an that that would
+ 
+
+ align:start position:0%
+150 cycles hmm that's an that that would
+be accessing DRAM okay
+
+ align:start position:0%
+be accessing DRAM okay
+ 
+
+ align:start position:0%
+be accessing DRAM okay
+accessing DRAM if you if it wasn't in
+
+ align:start position:0%
+accessing DRAM if you if it wasn't in
+ 
+
+ align:start position:0%
+accessing DRAM if you if it wasn't in
+cache might be 150 cycles okay
+
+ align:start position:0%
+cache might be 150 cycles okay
+ 
+
+ align:start position:0%
+cache might be 150 cycles okay
+so two orders of magnitude or so okay so
+
+ align:start position:0%
+so two orders of magnitude or so okay so
+ 
+
+ align:start position:0%
+so two orders of magnitude or so okay so
+what what about a disk access how long
+
+ align:start position:0%
+what what about a disk access how long
+ 
+
+ align:start position:0%
+what what about a disk access how long
+is that take yeah
+
+ align:start position:0%
+is that take yeah
+ 
+
+ align:start position:0%
+is that take yeah
+yes several milliseconds so ten
+
+ align:start position:0%
+yes several milliseconds so ten
+ 
+
+ align:start position:0%
+yes several milliseconds so ten
+milliseconds that are five milliseconds
+
+ align:start position:0%
+milliseconds that are five milliseconds
+ 
+
+ align:start position:0%
+milliseconds that are five milliseconds
+depend upon how fast your disk is but
+
+ align:start position:0%
+depend upon how fast your disk is but
+ 
+
+ align:start position:0%
+depend upon how fast your disk is but
+once again it's on the order of
+
+ align:start position:0%
+once again it's on the order of
+ 
+
+ align:start position:0%
+once again it's on the order of
+milliseconds so it's helpful to know
+
+ align:start position:0%
+milliseconds so it's helpful to know
+ 
+
+ align:start position:0%
+milliseconds so it's helpful to know
+some of these numbers because otherwise
+
+ align:start position:0%
+some of these numbers because otherwise
+ 
+
+ align:start position:0%
+some of these numbers because otherwise
+you know where are you spending your
+
+ align:start position:0%
+you know where are you spending your
+ 
+
+ align:start position:0%
+you know where are you spending your
+time especially we're sort of doing
+
+ align:start position:0%
+time especially we're sort of doing
+ 
+
+ align:start position:0%
+time especially we're sort of doing
+performance engineering you know in the
+
+ align:start position:0%
+performance engineering you know in the
+ 
+
+ align:start position:0%
+performance engineering you know in the
+small basically looking within the
+
+ align:start position:0%
+small basically looking within the
+ 
+
+ align:start position:0%
+small basically looking within the
+product you know within a multi-core
+
+ align:start position:0%
+product you know within a multi-core
+ 
+
+ align:start position:0%
+product you know within a multi-core
+processor most performance engineering
+
+ align:start position:0%
+processor most performance engineering
+ 
+
+ align:start position:0%
+processor most performance engineering
+is on all the stuff on the outside
+
+ align:start position:0%
+is on all the stuff on the outside
+ 
+
+ align:start position:0%
+is on all the stuff on the outside
+dealing with networking and file systems
+
+ align:start position:0%
+dealing with networking and file systems
+ 
+
+ align:start position:0%
+dealing with networking and file systems
+and stuff where where things are really
+
+ align:start position:0%
+and stuff where where things are really
+ 
+
+ align:start position:0%
+and stuff where where things are really
+costly and where you actually have a lot
+
+ align:start position:0%
+costly and where you actually have a lot
+ 
+
+ align:start position:0%
+costly and where you actually have a lot
+of time you can write fast piece of code
+
+ align:start position:0%
+of time you can write fast piece of code
+ 
+
+ align:start position:0%
+of time you can write fast piece of code
+that can figure out how you should best
+
+ align:start position:0%
+that can figure out how you should best
+ 
+
+ align:start position:0%
+that can figure out how you should best
+deal with these slow parts of your
+
+ align:start position:0%
+deal with these slow parts of your
+ 
+
+ align:start position:0%
+deal with these slow parts of your
+system okay so those are all sort of
+
+ align:start position:0%
+system okay so those are all sort of
+ 
+
+ align:start position:0%
+system okay so those are all sort of
+good numbers to know you'll probably see
+
+ align:start position:0%
+good numbers to know you'll probably see
+ 
+
+ align:start position:0%
+good numbers to know you'll probably see
+some of them on quiz 2 okay okay
+
+ align:start position:0%
+some of them on quiz 2 okay okay
+ 
+
+ align:start position:0%
+some of them on quiz 2 okay okay
+deadlock I mentioned deadlock earlier
+
+ align:start position:0%
+deadlock I mentioned deadlock earlier
+ 
+
+ align:start position:0%
+deadlock I mentioned deadlock earlier
+let's talk about what deadlock is and
+
+ align:start position:0%
+let's talk about what deadlock is and
+ 
+
+ align:start position:0%
+let's talk about what deadlock is and
+understand this once again I expect some
+
+ align:start position:0%
+understand this once again I expect some
+ 
+
+ align:start position:0%
+understand this once again I expect some
+of you have seen this but I still want
+
+ align:start position:0%
+of you have seen this but I still want
+ 
+
+ align:start position:0%
+of you have seen this but I still want
+to go through it because it's hugely
+
+ align:start position:0%
+to go through it because it's hugely
+ 
+
+ align:start position:0%
+to go through it because it's hugely
+important material and this is the issue
+
+ align:start position:0%
+important material and this is the issue
+ 
+
+ align:start position:0%
+important material and this is the issue
+that holding more than one lock at a
+
+ align:start position:0%
+that holding more than one lock at a
+ 
+
+ align:start position:0%
+that holding more than one lock at a
+time can be dangerous okay so imagine
+
+ align:start position:0%
+time can be dangerous okay so imagine
+ 
+
+ align:start position:0%
+time can be dangerous okay so imagine
+that thread one says I'm gonna lock a
+
+ align:start position:0%
+that thread one says I'm gonna lock a
+ 
+
+ align:start position:0%
+that thread one says I'm gonna lock a
+lock B execute the crudo section unlock
+
+ align:start position:0%
+lock B execute the crudo section unlock
+ 
+
+ align:start position:0%
+lock B execute the crudo section unlock
+B unlock a where a and B or mutexes and
+
+ align:start position:0%
+B unlock a where a and B or mutexes and
+ 
+
+ align:start position:0%
+B unlock a where a and B or mutexes and
+thread two does something very similar
+
+ align:start position:0%
+thread two does something very similar
+ 
+
+ align:start position:0%
+thread two does something very similar
+it locks B and locks a then it does the
+
+ align:start position:0%
+it locks B and locks a then it does the
+ 
+
+ align:start position:0%
+it locks B and locks a then it does the
+critical section then it unlocks a and
+
+ align:start position:0%
+critical section then it unlocks a and
+ 
+
+ align:start position:0%
+critical section then it unlocks a and
+then unlocks B okay so what can happen
+
+ align:start position:0%
+then unlocks B okay so what can happen
+ 
+
+ align:start position:0%
+then unlocks B okay so what can happen
+here so we you know thread one locks a
+
+ align:start position:0%
+here so we you know thread one locks a
+ 
+
+ align:start position:0%
+here so we you know thread one locks a
+thread two locks B thread
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one can't go and lock be because thread
+
+ align:start position:0%
+one can't go and lock be because thread
+ 
+
+ align:start position:0%
+one can't go and lock be because thread
+two has it thread two can't go and lock
+
+ align:start position:0%
+two has it thread two can't go and lock
+ 
+
+ align:start position:0%
+two has it thread two can't go and lock
+a because thread one has it so they sit
+
+ align:start position:0%
+a because thread one has it so they sit
+ 
+
+ align:start position:0%
+a because thread one has it so they sit
+there blocked I don't care if they're
+
+ align:start position:0%
+there blocked I don't care if they're
+ 
+
+ align:start position:0%
+there blocked I don't care if they're
+spinning or yielding they're not going
+
+ align:start position:0%
+spinning or yielding they're not going
+ 
+
+ align:start position:0%
+spinning or yielding they're not going
+anywhere okay so this is the ultimate
+
+ align:start position:0%
+anywhere okay so this is the ultimate
+ 
+
+ align:start position:0%
+anywhere okay so this is the ultimate
+loss of performance right it's like it's
+
+ align:start position:0%
+loss of performance right it's like it's
+ 
+
+ align:start position:0%
+loss of performance right it's like it's
+incorrect okay it's like you're stuck
+
+ align:start position:0%
+incorrect okay it's like you're stuck
+ 
+
+ align:start position:0%
+incorrect okay it's like you're stuck
+you've deadlocked okay now there's
+
+ align:start position:0%
+you've deadlocked okay now there's
+ 
+
+ align:start position:0%
+you've deadlocked okay now there's
+there's three basic conditions for
+
+ align:start position:0%
+there's three basic conditions for
+ 
+
+ align:start position:0%
+there's three basic conditions for
+deadlock everybody understands this
+
+ align:start position:0%
+deadlock everybody understands this
+ 
+
+ align:start position:0%
+deadlock everybody understands this
+right there's there any anybody who has
+
+ align:start position:0%
+right there's there any anybody who has
+ 
+
+ align:start position:0%
+right there's there any anybody who has
+a question because just okay it's
+
+ align:start position:0%
+a question because just okay it's
+ 
+
+ align:start position:0%
+a question because just okay it's
+there's three conditions you need for
+
+ align:start position:0%
+there's three conditions you need for
+ 
+
+ align:start position:0%
+there's three conditions you need for
+deadlock the first one is mutual
+
+ align:start position:0%
+deadlock the first one is mutual
+ 
+
+ align:start position:0%
+deadlock the first one is mutual
+exclusion that you're going to have
+
+ align:start position:0%
+exclusion that you're going to have
+ 
+
+ align:start position:0%
+exclusion that you're going to have
+exclusive control over the resources the
+
+ align:start position:0%
+exclusive control over the resources the
+ 
+
+ align:start position:0%
+exclusive control over the resources the
+second is non preemption you don't
+
+ align:start position:0%
+second is non preemption you don't
+ 
+
+ align:start position:0%
+second is non preemption you don't
+release your resources you hold until
+
+ align:start position:0%
+release your resources you hold until
+ 
+
+ align:start position:0%
+release your resources you hold until
+you finish using them okay and and three
+
+ align:start position:0%
+you finish using them okay and and three
+ 
+
+ align:start position:0%
+you finish using them okay and and three
+is circular waiting you have a cycle of
+
+ align:start position:0%
+is circular waiting you have a cycle of
+ 
+
+ align:start position:0%
+is circular waiting you have a cycle of
+threads in which each thread is blocked
+
+ align:start position:0%
+threads in which each thread is blocked
+ 
+
+ align:start position:0%
+threads in which each thread is blocked
+waiting for resources held by the next
+
+ align:start position:0%
+waiting for resources held by the next
+ 
+
+ align:start position:0%
+waiting for resources held by the next
+one in this case the resource is the
+
+ align:start position:0%
+one in this case the resource is the
+ 
+
+ align:start position:0%
+one in this case the resource is the
+lock okay and so if you remove any one
+
+ align:start position:0%
+lock okay and so if you remove any one
+ 
+
+ align:start position:0%
+lock okay and so if you remove any one
+of these constraints okay you can come
+
+ align:start position:0%
+of these constraints okay you can come
+ 
+
+ align:start position:0%
+of these constraints okay you can come
+up with solutions that won't deadlock so
+
+ align:start position:0%
+up with solutions that won't deadlock so
+ 
+
+ align:start position:0%
+up with solutions that won't deadlock so
+for example it could be that when I try
+
+ align:start position:0%
+for example it could be that when I try
+ 
+
+ align:start position:0%
+for example it could be that when I try
+to acquire a lock if somebody else has
+
+ align:start position:0%
+to acquire a lock if somebody else has
+ 
+
+ align:start position:0%
+to acquire a lock if somebody else has
+him I take it away
+
+ align:start position:0%
+him I take it away
+ 
+
+ align:start position:0%
+him I take it away
+okay you know that could be one thing
+
+ align:start position:0%
+okay you know that could be one thing
+ 
+
+ align:start position:0%
+okay you know that could be one thing
+now there may get into other issues
+
+ align:start position:0%
+now there may get into other issues
+ 
+
+ align:start position:0%
+now there may get into other issues
+which is like well but what if he's
+
+ align:start position:0%
+which is like well but what if he's
+ 
+
+ align:start position:0%
+which is like well but what if he's
+actually doing real work okay
+
+ align:start position:0%
+actually doing real work okay
+ 
+
+ align:start position:0%
+actually doing real work okay
+or whatever so all of these things have
+
+ align:start position:0%
+or whatever so all of these things have
+ 
+
+ align:start position:0%
+or whatever so all of these things have
+things or you know I don't insist that
+
+ align:start position:0%
+things or you know I don't insist that
+ 
+
+ align:start position:0%
+things or you know I don't insist that
+it be mutual exclusion except that's the
+
+ align:start position:0%
+it be mutual exclusion except that's the
+ 
+
+ align:start position:0%
+it be mutual exclusion except that's the
+kind of problem that we're trying to
+
+ align:start position:0%
+kind of problem that we're trying to
+ 
+
+ align:start position:0%
+kind of problem that we're trying to
+solve so these are generally the three
+
+ align:start position:0%
+solve so these are generally the three
+ 
+
+ align:start position:0%
+solve so these are generally the three
+things that are necessary in order to in
+
+ align:start position:0%
+things that are necessary in order to in
+ 
+
+ align:start position:0%
+things that are necessary in order to in
+order to have a deadlock situation now
+
+ align:start position:0%
+order to have a deadlock situation now
+ 
+
+ align:start position:0%
+order to have a deadlock situation now
+in any discussion of deadlock you have
+
+ align:start position:0%
+in any discussion of deadlock you have
+ 
+
+ align:start position:0%
+in any discussion of deadlock you have
+to talk about dining philosophers when I
+
+ align:start position:0%
+to talk about dining philosophers when I
+ 
+
+ align:start position:0%
+to talk about dining philosophers when I
+was an undergraduate and I graduated in
+
+ align:start position:0%
+was an undergraduate and I graduated in
+ 
+
+ align:start position:0%
+was an undergraduate and I graduated in
+1975 from Yale humanities school
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I was taught the dining philosophers
+
+ align:start position:0%
+I was taught the dining philosophers
+ 
+
+ align:start position:0%
+I was taught the dining philosophers
+right because after all philosophy is
+
+ align:start position:0%
+right because after all philosophy is
+ 
+
+ align:start position:0%
+right because after all philosophy is
+what you find at humanity schools I mean
+
+ align:start position:0%
+what you find at humanity schools I mean
+ 
+
+ align:start position:0%
+what you find at humanity schools I mean
+we have philosophy department - don't
+
+ align:start position:0%
+we have philosophy department - don't
+ 
+
+ align:start position:0%
+we have philosophy department - don't
+get me wrong but at Yale the humanities
+
+ align:start position:0%
+get me wrong but at Yale the humanities
+ 
+
+ align:start position:0%
+get me wrong but at Yale the humanities
+is huge and so philosophy I guess they
+
+ align:start position:0%
+is huge and so philosophy I guess they
+ 
+
+ align:start position:0%
+is huge and so philosophy I guess they
+thought this was would appeal to the
+
+ align:start position:0%
+thought this was would appeal to the
+ 
+
+ align:start position:0%
+thought this was would appeal to the
+people who were not real techies in the
+
+ align:start position:0%
+people who were not real techies in the
+ 
+
+ align:start position:0%
+people who were not real techies in the
+background I sort of like I was a techie
+
+ align:start position:0%
+background I sort of like I was a techie
+ 
+
+ align:start position:0%
+background I sort of like I was a techie
+in the midst of all these you know
+
+ align:start position:0%
+in the midst of all these you know
+ 
+
+ align:start position:0%
+in the midst of all these you know
+non-technical people dining philosophers
+
+ align:start position:0%
+non-technical people dining philosophers
+ 
+
+ align:start position:0%
+non-technical people dining philosophers
+is a story of deadlock told by Tony
+
+ align:start position:0%
+is a story of deadlock told by Tony
+ 
+
+ align:start position:0%
+is a story of deadlock told by Tony
+Hoare based on an examination question
+
+ align:start position:0%
+Hoare based on an examination question
+ 
+
+ align:start position:0%
+Hoare based on an examination question
+by Edsger Dijkstra okay
+
+ align:start position:0%
+by Edsger Dijkstra okay
+ 
+
+ align:start position:0%
+by Edsger Dijkstra okay
+and it's been embellished too over the
+
+ align:start position:0%
+and it's been embellished too over the
+ 
+
+ align:start position:0%
+and it's been embellished too over the
+years by many many many retailers okay
+
+ align:start position:0%
+years by many many many retailers okay
+ 
+
+ align:start position:0%
+years by many many many retailers okay
+and I like the Chinese version of this
+
+ align:start position:0%
+and I like the Chinese version of this
+ 
+
+ align:start position:0%
+and I like the Chinese version of this
+okay there's versions where they use
+
+ align:start position:0%
+okay there's versions where they use
+ 
+
+ align:start position:0%
+okay there's versions where they use
+Forks but I'm going to this is going to
+
+ align:start position:0%
+Forks but I'm going to this is going to
+ 
+
+ align:start position:0%
+Forks but I'm going to this is going to
+be their dining I'm going to say that
+
+ align:start position:0%
+be their dining I'm going to say that
+ 
+
+ align:start position:0%
+be their dining I'm going to say that
+they are eating noodles with chopsticks
+
+ align:start position:0%
+they are eating noodles with chopsticks
+ 
+
+ align:start position:0%
+they are eating noodles with chopsticks
+and they're in philosophers seated
+
+ align:start position:0%
+and they're in philosophers seated
+ 
+
+ align:start position:0%
+and they're in philosophers seated
+around the table and II and between
+
+ align:start position:0%
+around the table and II and between
+ 
+
+ align:start position:0%
+around the table and II and between
+every plate of noodles there's a
+
+ align:start position:0%
+every plate of noodles there's a
+ 
+
+ align:start position:0%
+every plate of noodles there's a
+chopstick and so in order to eat the
+
+ align:start position:0%
+chopstick and so in order to eat the
+ 
+
+ align:start position:0%
+chopstick and so in order to eat the
+noodles they need two chopsticks okay
+
+ align:start position:0%
+noodles they need two chopsticks okay
+ 
+
+ align:start position:0%
+noodles they need two chopsticks okay
+which to me sounds very natural okay and
+
+ align:start position:0%
+which to me sounds very natural okay and
+ 
+
+ align:start position:0%
+which to me sounds very natural okay and
+so here's the code for philosopher I so
+
+ align:start position:0%
+so here's the code for philosopher I so
+ 
+
+ align:start position:0%
+so here's the code for philosopher I so
+he's a philosopher so he starts by
+
+ align:start position:0%
+he's a philosopher so he starts by
+ 
+
+ align:start position:0%
+he's a philosopher so he starts by
+thinking for a while okay and then he
+
+ align:start position:0%
+thinking for a while okay and then he
+ 
+
+ align:start position:0%
+thinking for a while okay and then he
+gets hungry he or she gets hungry so the
+
+ align:start position:0%
+gets hungry he or she gets hungry so the
+ 
+
+ align:start position:0%
+gets hungry he or she gets hungry so the
+philosopher grabs the chopstick on the
+
+ align:start position:0%
+philosopher grabs the chopstick on the
+ 
+
+ align:start position:0%
+philosopher grabs the chopstick on the
+law right on the Left sorry and then it
+
+ align:start position:0%
+law right on the Left sorry and then it
+ 
+
+ align:start position:0%
+law right on the Left sorry and then it
+grabs the one on the on the right but it
+
+ align:start position:0%
+grabs the one on the on the right but it
+ 
+
+ align:start position:0%
+grabs the one on the on the right but it
+had you know so which is I plus one but
+
+ align:start position:0%
+had you know so which is I plus one but
+ 
+
+ align:start position:0%
+had you know so which is I plus one but
+it has to do that mod in because if it's
+
+ align:start position:0%
+it has to do that mod in because if it's
+ 
+
+ align:start position:0%
+it has to do that mod in because if it's
+the last one you got to go around and
+
+ align:start position:0%
+the last one you got to go around and
+ 
+
+ align:start position:0%
+the last one you got to go around and
+grab the first one then eats and then it
+
+ align:start position:0%
+grab the first one then eats and then it
+ 
+
+ align:start position:0%
+grab the first one then eats and then it
+unlocks the two chopsticks and now they
+
+ align:start position:0%
+unlocks the two chopsticks and now they
+ 
+
+ align:start position:0%
+unlocks the two chopsticks and now they
+can be used by the other dining
+
+ align:start position:0%
+can be used by the other dining
+ 
+
+ align:start position:0%
+can be used by the other dining
+philosophers because they don't think
+
+ align:start position:0%
+philosophers because they don't think
+ 
+
+ align:start position:0%
+philosophers because they don't think
+much about sanitation and
+
+ align:start position:0%
+much about sanitation and
+ 
+
+ align:start position:0%
+much about sanitation and
+and so forth right so they're because
+
+ align:start position:0%
+and so forth right so they're because
+ 
+
+ align:start position:0%
+and so forth right so they're because
+they're they're too busy thinking right
+
+ align:start position:0%
+they're they're too busy thinking right
+ 
+
+ align:start position:0%
+they're they're too busy thinking right
+but but what happens what's wrong with
+
+ align:start position:0%
+but but what happens what's wrong with
+ 
+
+ align:start position:0%
+but but what happens what's wrong with
+this solution what happens what can
+
+ align:start position:0%
+this solution what happens what can
+ 
+
+ align:start position:0%
+this solution what happens what can
+happen for this it's very simple I need
+
+ align:start position:0%
+happen for this it's very simple I need
+ 
+
+ align:start position:0%
+happen for this it's very simple I need
+two chopsticks I grab one I grab the
+
+ align:start position:0%
+two chopsticks I grab one I grab the
+ 
+
+ align:start position:0%
+two chopsticks I grab one I grab the
+other I eat one day what happens yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah they're all it and they grab one to
+
+ align:start position:0%
+yeah they're all it and they grab one to
+ 
+
+ align:start position:0%
+yeah they're all it and they grab one to
+the left and now they go to the right
+
+ align:start position:0%
+the left and now they go to the right
+ 
+
+ align:start position:0%
+the left and now they go to the right
+it's not there and they starve okay you
+
+ align:start position:0%
+it's not there and they starve okay you
+ 
+
+ align:start position:0%
+it's not there and they starve okay you
+know one day they got all the things so
+
+ align:start position:0%
+know one day they got all the things so
+ 
+
+ align:start position:0%
+know one day they got all the things so
+we have the starving philosophers
+
+ align:start position:0%
+we have the starving philosophers
+ 
+
+ align:start position:0%
+we have the starving philosophers
+problem so so be motivated by this
+
+ align:start position:0%
+problem so so be motivated by this
+ 
+
+ align:start position:0%
+problem so so be motivated by this
+problem yeah question yeah so if you are
+
+ align:start position:0%
+problem yeah question yeah so if you are
+ 
+
+ align:start position:0%
+problem yeah question yeah so if you are
+willing to preempt then that would be
+
+ align:start position:0%
+willing to preempt then that would be
+ 
+
+ align:start position:0%
+willing to preempt then that would be
+preemption as I say it's got to be non
+
+ align:start position:0%
+preemption as I say it's got to be non
+ 
+
+ align:start position:0%
+preemption as I say it's got to be non
+pre-emptive in order for deadlock to
+
+ align:start position:0%
+pre-emptive in order for deadlock to
+ 
+
+ align:start position:0%
+pre-emptive in order for deadlock to
+occur in this case yeah but you also
+
+ align:start position:0%
+occur in this case yeah but you also
+ 
+
+ align:start position:0%
+occur in this case yeah but you also
+have to worry in those cases could be oh
+
+ align:start position:0%
+have to worry in those cases could be oh
+ 
+
+ align:start position:0%
+have to worry in those cases could be oh
+well if I couldn't get both let me put
+
+ align:start position:0%
+well if I couldn't get both let me put
+ 
+
+ align:start position:0%
+well if I couldn't get both let me put
+them both down but then you can have a
+
+ align:start position:0%
+them both down but then you can have a
+ 
+
+ align:start position:0%
+them both down but then you can have a
+thing that's called livelock okay so
+
+ align:start position:0%
+thing that's called livelock okay so
+ 
+
+ align:start position:0%
+thing that's called livelock okay so
+they all pick up their left they see the
+
+ align:start position:0%
+they all pick up their left they see the
+ 
+
+ align:start position:0%
+they all pick up their left they see the
+right ones busy so they put it down so
+
+ align:start position:0%
+right ones busy so they put it down so
+ 
+
+ align:start position:0%
+right ones busy so they put it down so
+somebody else can have it they look
+
+ align:start position:0%
+somebody else can have it they look
+ 
+
+ align:start position:0%
+somebody else can have it they look
+around oh okay let me pick out one no no
+
+ align:start position:0%
+around oh okay let me pick out one no no
+ 
+
+ align:start position:0%
+around oh okay let me pick out one no no
+okay okay and so they still starve even
+
+ align:start position:0%
+okay okay and so they still starve even
+ 
+
+ align:start position:0%
+okay okay and so they still starve even
+though they've done that so in that kind
+
+ align:start position:0%
+though they've done that so in that kind
+ 
+
+ align:start position:0%
+though they've done that so in that kind
+of situation you could put in a time
+
+ align:start position:0%
+of situation you could put in a time
+ 
+
+ align:start position:0%
+of situation you could put in a time
+delay you could say let me let everybody
+
+ align:start position:0%
+delay you could say let me let everybody
+ 
+
+ align:start position:0%
+delay you could say let me let everybody
+pick a random number have a randomized
+
+ align:start position:0%
+pick a random number have a randomized
+ 
+
+ align:start position:0%
+pick a random number have a randomized
+scheme so that we're not you know so
+
+ align:start position:0%
+scheme so that we're not you know so
+ 
+
+ align:start position:0%
+scheme so that we're not you know so
+there are other solutions if you don't
+
+ align:start position:0%
+there are other solutions if you don't
+ 
+
+ align:start position:0%
+there are other solutions if you don't
+insist on non preemption I'm going to
+
+ align:start position:0%
+insist on non preemption I'm going to
+ 
+
+ align:start position:0%
+insist on non preemption I'm going to
+give you one where we have non
+
+ align:start position:0%
+give you one where we have non
+ 
+
+ align:start position:0%
+give you one where we have non
+preemption but we still avoid deadlock
+
+ align:start position:0%
+preemption but we still avoid deadlock
+ 
+
+ align:start position:0%
+preemption but we still avoid deadlock
+and it's to go for that cyclic problem
+
+ align:start position:0%
+and it's to go for that cyclic problem
+ 
+
+ align:start position:0%
+and it's to go for that cyclic problem
+so here's the idea
+
+ align:start position:0%
+so here's the idea
+ 
+
+ align:start position:0%
+so here's the idea
+suppose that we can linearly order the
+
+ align:start position:0%
+suppose that we can linearly order the
+ 
+
+ align:start position:0%
+suppose that we can linearly order the
+mutexes okay so I pick some order of the
+
+ align:start position:0%
+mutexes okay so I pick some order of the
+ 
+
+ align:start position:0%
+mutexes okay so I pick some order of the
+mutexes so that whenever a thread holds
+
+ align:start position:0%
+mutexes so that whenever a thread holds
+ 
+
+ align:start position:0%
+mutexes so that whenever a thread holds
+a mutex else of I and attempts to act a
+
+ align:start position:0%
+a mutex else of I and attempts to act a
+ 
+
+ align:start position:0%
+a mutex else of I and attempts to act a
+lock another mutex l sub J we have that
+
+ align:start position:0%
+lock another mutex l sub J we have that
+ 
+
+ align:start position:0%
+lock another mutex l sub J we have that
+in this linear order L sub I comes
+
+ align:start position:0%
+in this linear order L sub I comes
+ 
+
+ align:start position:0%
+in this linear order L sub I comes
+before L sub J then you can't have a
+
+ align:start position:0%
+before L sub J then you can't have a
+ 
+
+ align:start position:0%
+before L sub J then you can't have a
+deadlock okay so in this case for the
+
+ align:start position:0%
+deadlock okay so in this case for the
+ 
+
+ align:start position:0%
+deadlock okay so in this case for the
+dining philosophers it would for example
+
+ align:start position:0%
+dining philosophers it would for example
+ 
+
+ align:start position:0%
+dining philosophers it would for example
+number the number of the chopsticks you
+
+ align:start position:0%
+number the number of the chopsticks you
+ 
+
+ align:start position:0%
+number the number of the chopsticks you
+know from 1 to N and then or 0 to n
+
+ align:start position:0%
+know from 1 to N and then or 0 to n
+ 
+
+ align:start position:0%
+know from 1 to N and then or 0 to n
+minus 1 whatever and then grab the
+
+ align:start position:0%
+minus 1 whatever and then grab the
+ 
+
+ align:start position:0%
+minus 1 whatever and then grab the
+smaller one and then grab the larger one
+
+ align:start position:0%
+smaller one and then grab the larger one
+ 
+
+ align:start position:0%
+smaller one and then grab the larger one
+then then it says then you would never
+
+ align:start position:0%
+then then it says then you would never
+ 
+
+ align:start position:0%
+then then it says then you would never
+have a deadlock
+
+ align:start position:0%
+have a deadlock
+ 
+
+ align:start position:0%
+have a deadlock
+okay and so here's the proof you know I
+
+ align:start position:0%
+okay and so here's the proof you know I
+ 
+
+ align:start position:0%
+okay and so here's the proof you know I
+like proofs okay
+
+ align:start position:0%
+like proofs okay
+ 
+
+ align:start position:0%
+like proofs okay
+proofs are really important so I'm going
+
+ align:start position:0%
+proofs are really important so I'm going
+ 
+
+ align:start position:0%
+proofs are really important so I'm going
+to show you that if you do that you
+
+ align:start position:0%
+to show you that if you do that you
+ 
+
+ align:start position:0%
+to show you that if you do that you
+couldn't have a cycle of waiting so
+
+ align:start position:0%
+couldn't have a cycle of waiting so
+ 
+
+ align:start position:0%
+couldn't have a cycle of waiting so
+suppose you had a cycle of waiting we
+
+ align:start position:0%
+suppose you had a cycle of waiting we
+ 
+
+ align:start position:0%
+suppose you had a cycle of waiting we
+were in a situation where everybody is
+
+ align:start position:0%
+were in a situation where everybody is
+ 
+
+ align:start position:0%
+were in a situation where everybody is
+holding chopsticks and you know one that
+
+ align:start position:0%
+holding chopsticks and you know one that
+ 
+
+ align:start position:0%
+holding chopsticks and you know one that
+one of them is waiting for another one
+
+ align:start position:0%
+one of them is waiting for another one
+ 
+
+ align:start position:0%
+one of them is waiting for another one
+which is waiting for now all the way
+
+ align:start position:0%
+which is waiting for now all the way
+ 
+
+ align:start position:0%
+which is waiting for now all the way
+around to the first one that's what we
+
+ align:start position:0%
+around to the first one that's what we
+ 
+
+ align:start position:0%
+around to the first one that's what we
+need for deadlock to occur so let me
+
+ align:start position:0%
+need for deadlock to occur so let me
+ 
+
+ align:start position:0%
+need for deadlock to occur so let me
+just look at what's the largest mutex on
+
+ align:start position:0%
+just look at what's the largest mutex on
+ 
+
+ align:start position:0%
+just look at what's the largest mutex on
+the cycle let's call that L max okay and
+
+ align:start position:0%
+the cycle let's call that L max okay and
+ 
+
+ align:start position:0%
+the cycle let's call that L max okay and
+suppose that it's waiting on a mutex L
+
+ align:start position:0%
+suppose that it's waiting on a mutex L
+ 
+
+ align:start position:0%
+suppose that it's waiting on a mutex L
+held by the next thread in the cycle
+
+ align:start position:0%
+held by the next thread in the cycle
+ 
+
+ align:start position:0%
+held by the next thread in the cycle
+well then we have a something that's
+
+ align:start position:0%
+well then we have a something that's
+ 
+
+ align:start position:0%
+well then we have a something that's
+bigger than the maximum one okay and so
+
+ align:start position:0%
+bigger than the maximum one okay and so
+ 
+
+ align:start position:0%
+bigger than the maximum one okay and so
+that contradicts the fact that I grabbed
+
+ align:start position:0%
+that contradicts the fact that I grabbed
+ 
+
+ align:start position:0%
+that contradicts the fact that I grabbed
+them whenever I grabbed them I do it in
+
+ align:start position:0%
+them whenever I grabbed them I do it in
+ 
+
+ align:start position:0%
+them whenever I grabbed them I do it in
+order okay so very simple very simple
+
+ align:start position:0%
+order okay so very simple very simple
+ 
+
+ align:start position:0%
+order okay so very simple very simple
+proof that you can't have deadlock if
+
+ align:start position:0%
+proof that you can't have deadlock if
+ 
+
+ align:start position:0%
+proof that you can't have deadlock if
+you grab them according to a linear
+
+ align:start position:0%
+you grab them according to a linear
+ 
+
+ align:start position:0%
+you grab them according to a linear
+order okay and so for this particular
+
+ align:start position:0%
+order okay and so for this particular
+ 
+
+ align:start position:0%
+order okay and so for this particular
+problem what I do is instead of grabbing
+
+ align:start position:0%
+problem what I do is instead of grabbing
+ 
+
+ align:start position:0%
+problem what I do is instead of grabbing
+the one on the left and one on the right
+
+ align:start position:0%
+the one on the left and one on the right
+ 
+
+ align:start position:0%
+the one on the left and one on the right
+as I say you grab the smaller of the two
+
+ align:start position:0%
+as I say you grab the smaller of the two
+ 
+
+ align:start position:0%
+as I say you grab the smaller of the two
+and then grab the larger of the two and
+
+ align:start position:0%
+and then grab the larger of the two and
+ 
+
+ align:start position:0%
+and then grab the larger of the two and
+then you're guaranteed to have no
+
+ align:start position:0%
+then you're guaranteed to have no
+ 
+
+ align:start position:0%
+then you're guaranteed to have no
+deadlock does that make sense now if
+
+ align:start position:0%
+deadlock does that make sense now if
+ 
+
+ align:start position:0%
+deadlock does that make sense now if
+you're going to use locks in silk you
+
+ align:start position:0%
+you're going to use locks in silk you
+ 
+
+ align:start position:0%
+you're going to use locks in silk you
+have to realize that in the operating
+
+ align:start position:0%
+have to realize that in the operating
+ 
+
+ align:start position:0%
+have to realize that in the operating
+sin the runtime system of silk they're
+
+ align:start position:0%
+sin the runtime system of silk they're
+ 
+
+ align:start position:0%
+sin the runtime system of silk they're
+doing they're using locks you can't see
+
+ align:start position:0%
+doing they're using locks you can't see
+ 
+
+ align:start position:0%
+doing they're using locks you can't see
+them they're encapsulated as we talked
+
+ align:start position:0%
+them they're encapsulated as we talked
+ 
+
+ align:start position:0%
+them they're encapsulated as we talked
+about the non determinism in silk is
+
+ align:start position:0%
+about the non determinism in silk is
+ 
+
+ align:start position:0%
+about the non determinism in silk is
+capsulated is still going on underneath
+
+ align:start position:0%
+capsulated is still going on underneath
+ 
+
+ align:start position:0%
+capsulated is still going on underneath
+the color covers and if you start
+
+ align:start position:0%
+the color covers and if you start
+ 
+
+ align:start position:0%
+the color covers and if you start
+introducing your own non determinism
+
+ align:start position:0%
+introducing your own non determinism
+ 
+
+ align:start position:0%
+introducing your own non determinism
+through the use of locks you can run
+
+ align:start position:0%
+through the use of locks you can run
+ 
+
+ align:start position:0%
+through the use of locks you can run
+into trouble if you're not careful and
+
+ align:start position:0%
+into trouble if you're not careful and
+ 
+
+ align:start position:0%
+into trouble if you're not careful and
+let me give you an example okay this is
+
+ align:start position:0%
+let me give you an example okay this is
+ 
+
+ align:start position:0%
+let me give you an example okay this is
+a situation you can deadlock your
+
+ align:start position:0%
+a situation you can deadlock your
+ 
+
+ align:start position:0%
+a situation you can deadlock your
+program in silk okay with just one lock
+
+ align:start position:0%
+program in silk okay with just one lock
+ 
+
+ align:start position:0%
+program in silk okay with just one lock
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here's an example of a code that does
+
+ align:start position:0%
+so here's an example of a code that does
+ 
+
+ align:start position:0%
+so here's an example of a code that does
+that so main spawns off foo and foo
+
+ align:start position:0%
+that so main spawns off foo and foo
+ 
+
+ align:start position:0%
+that so main spawns off foo and foo
+basically locks the lock L and then
+
+ align:start position:0%
+basically locks the lock L and then
+ 
+
+ align:start position:0%
+basically locks the lock L and then
+unlocks it and meanwhile
+
+ align:start position:0%
+unlocks it and meanwhile
+ 
+
+ align:start position:0%
+unlocks it and meanwhile
+after it spawns our food the
+
+ align:start position:0%
+after it spawns our food the
+ 
+
+ align:start position:0%
+after it spawns our food the
+continuation goes and it locks L itself
+
+ align:start position:0%
+continuation goes and it locks L itself
+ 
+
+ align:start position:0%
+continuation goes and it locks L itself
+and then does a sink and then it unlocks
+
+ align:start position:0%
+and then does a sink and then it unlocks
+ 
+
+ align:start position:0%
+and then does a sink and then it unlocks
+it so what happens here we sort of have
+
+ align:start position:0%
+it so what happens here we sort of have
+ 
+
+ align:start position:0%
+it so what happens here we sort of have
+a situation like this where where the
+
+ align:start position:0%
+a situation like this where where the
+ 
+
+ align:start position:0%
+a situation like this where where the
+locking I've done with an open bracket
+
+ align:start position:0%
+locking I've done with an open bracket
+ 
+
+ align:start position:0%
+locking I've done with an open bracket
+and an unlock a release I'm doing with a
+
+ align:start position:0%
+and an unlock a release I'm doing with a
+ 
+
+ align:start position:0%
+and an unlock a release I'm doing with a
+closed bracket so I'm spawning off foo
+
+ align:start position:0%
+closed bracket so I'm spawning off foo
+ 
+
+ align:start position:0%
+closed bracket so I'm spawning off foo
+which is the lower part there and
+
+ align:start position:0%
+which is the lower part there and
+ 
+
+ align:start position:0%
+which is the lower part there and
+locking and unlocking and up above I'm
+
+ align:start position:0%
+locking and unlocking and up above I'm
+ 
+
+ align:start position:0%
+locking and unlocking and up above I'm
+locking and unlocking so what can happen
+
+ align:start position:0%
+locking and unlocking so what can happen
+ 
+
+ align:start position:0%
+locking and unlocking so what can happen
+here I can go and I basically spawn off
+
+ align:start position:0%
+here I can go and I basically spawn off
+ 
+
+ align:start position:0%
+here I can go and I basically spawn off
+the child but then I lock and now the
+
+ align:start position:0%
+the child but then I lock and now the
+ 
+
+ align:start position:0%
+the child but then I lock and now the
+child goes and it says oh I can't you
+
+ align:start position:0%
+child goes and it says oh I can't you
+ 
+
+ align:start position:0%
+child goes and it says oh I can't you
+know foo is going to wait here because
+
+ align:start position:0%
+know foo is going to wait here because
+ 
+
+ align:start position:0%
+know foo is going to wait here because
+it can't grab the lock as it's owned by
+
+ align:start position:0%
+it can't grab the lock as it's owned by
+ 
+
+ align:start position:0%
+it can't grab the lock as it's owned by
+the by main ok and now we get to the
+
+ align:start position:0%
+the by main ok and now we get to the
+ 
+
+ align:start position:0%
+the by main ok and now we get to the
+point where main is has to wait for the
+
+ align:start position:0%
+point where main is has to wait for the
+ 
+
+ align:start position:0%
+point where main is has to wait for the
+sink okay and the child is never going
+
+ align:start position:0%
+sink okay and the child is never going
+ 
+
+ align:start position:0%
+sink okay and the child is never going
+to complete because I hold the resource
+
+ align:start position:0%
+to complete because I hold the resource
+ 
+
+ align:start position:0%
+to complete because I hold the resource
+that the child needs to complete okay so
+
+ align:start position:0%
+that the child needs to complete okay so
+ 
+
+ align:start position:0%
+that the child needs to complete okay so
+don't hold mutexes across silk sinks
+
+ align:start position:0%
+don't hold mutexes across silk sinks
+ 
+
+ align:start position:0%
+don't hold mutexes across silk sinks
+that's the lesson there there are
+
+ align:start position:0%
+that's the lesson there there are
+ 
+
+ align:start position:0%
+that's the lesson there there are
+actually places you can but if you don't
+
+ align:start position:0%
+actually places you can but if you don't
+ 
+
+ align:start position:0%
+actually places you can but if you don't
+hold them across that then you won't run
+
+ align:start position:0%
+hold them across that then you won't run
+ 
+
+ align:start position:0%
+hold them across that then you won't run
+into this particular problem a good
+
+ align:start position:0%
+into this particular problem a good
+ 
+
+ align:start position:0%
+into this particular problem a good
+strategy is only holding mutexes within
+
+ align:start position:0%
+strategy is only holding mutexes within
+ 
+
+ align:start position:0%
+strategy is only holding mutexes within
+strands okay so there's no parallelism
+
+ align:start position:0%
+strands okay so there's no parallelism
+ 
+
+ align:start position:0%
+strands okay so there's no parallelism
+so you you have it bounded and also
+
+ align:start position:0%
+so you you have it bounded and also
+ 
+
+ align:start position:0%
+so you you have it bounded and also
+that's a good idea generally because you
+
+ align:start position:0%
+that's a good idea generally because you
+ 
+
+ align:start position:0%
+that's a good idea generally because you
+want to hold mutex as a short amount of
+
+ align:start position:0%
+want to hold mutex as a short amount of
+ 
+
+ align:start position:0%
+want to hold mutex as a short amount of
+time as you possibly can
+
+ align:start position:0%
+time as you possibly can
+ 
+
+ align:start position:0%
+time as you possibly can
+so for example if you have a big
+
+ align:start position:0%
+so for example if you have a big
+ 
+
+ align:start position:0%
+so for example if you have a big
+calculation and then you want to sign
+
+ align:start position:0%
+calculation and then you want to sign
+ 
+
+ align:start position:0%
+calculation and then you want to sign
+something atomically don't put the big
+
+ align:start position:0%
+something atomically don't put the big
+ 
+
+ align:start position:0%
+something atomically don't put the big
+calculation inside the critical region
+
+ align:start position:0%
+calculation inside the critical region
+ 
+
+ align:start position:0%
+calculation inside the critical region
+move the calculation outside the
+
+ align:start position:0%
+move the calculation outside the
+ 
+
+ align:start position:0%
+move the calculation outside the
+critical region do the calculation you
+
+ align:start position:0%
+critical region do the calculation you
+ 
+
+ align:start position:0%
+critical region do the calculation you
+need to do and then acquire the locks
+
+ align:start position:0%
+need to do and then acquire the locks
+ 
+
+ align:start position:0%
+need to do and then acquire the locks
+just to do the interaction you need to
+
+ align:start position:0%
+just to do the interaction you need to
+ 
+
+ align:start position:0%
+just to do the interaction you need to
+set a value okay so that's and then
+
+ align:start position:0%
+set a value okay so that's and then
+ 
+
+ align:start position:0%
+set a value okay so that's and then
+you'll have a lot faster code okay
+
+ align:start position:0%
+you'll have a lot faster code okay
+ 
+
+ align:start position:0%
+you'll have a lot faster code okay
+because you're not holding up other
+
+ align:start position:0%
+because you're not holding up other
+ 
+
+ align:start position:0%
+because you're not holding up other
+threads for a long time and always try
+
+ align:start position:0%
+threads for a long time and always try
+ 
+
+ align:start position:0%
+threads for a long time and always try
+to avoid non-deterministic programming
+
+ align:start position:0%
+to avoid non-deterministic programming
+ 
+
+ align:start position:0%
+to avoid non-deterministic programming
+but that's not always possible okay I
+
+ align:start position:0%
+but that's not always possible okay I
+ 
+
+ align:start position:0%
+but that's not always possible okay I
+want to so any questions about that then
+
+ align:start position:0%
+want to so any questions about that then
+ 
+
+ align:start position:0%
+want to so any questions about that then
+I want to go on a really interesting
+
+ align:start position:0%
+I want to go on a really interesting
+ 
+
+ align:start position:0%
+I want to go on a really interesting
+topic because it's really
+
+ align:start position:0%
+topic because it's really
+ 
+
+ align:start position:0%
+topic because it's really
+you know recent research level topic and
+
+ align:start position:0%
+you know recent research level topic and
+ 
+
+ align:start position:0%
+you know recent research level topic and
+that's to talk about transactional
+
+ align:start position:0%
+that's to talk about transactional
+ 
+
+ align:start position:0%
+that's to talk about transactional
+memory who's heard this term before
+
+ align:start position:0%
+memory who's heard this term before
+ 
+
+ align:start position:0%
+memory who's heard this term before
+anybody okay so the idea is to have
+
+ align:start position:0%
+anybody okay so the idea is to have
+ 
+
+ align:start position:0%
+anybody okay so the idea is to have
+database transactions that you have
+
+ align:start position:0%
+database transactions that you have
+ 
+
+ align:start position:0%
+database transactions that you have
+things like database transaction or the
+
+ align:start position:0%
+things like database transaction or the
+ 
+
+ align:start position:0%
+things like database transaction or the
+atomicity is happening implicitly you
+
+ align:start position:0%
+atomicity is happening implicitly you
+ 
+
+ align:start position:0%
+atomicity is happening implicitly you
+don't specify locks you just say this is
+
+ align:start position:0%
+don't specify locks you just say this is
+ 
+
+ align:start position:0%
+don't specify locks you just say this is
+a critical region okay don't interrupt
+
+ align:start position:0%
+a critical region okay don't interrupt
+ 
+
+ align:start position:0%
+a critical region okay don't interrupt
+me while I do this critical region the
+
+ align:start position:0%
+me while I do this critical region the
+ 
+
+ align:start position:0%
+me while I do this critical region the
+system works everything out okay here's
+
+ align:start position:0%
+system works everything out okay here's
+ 
+
+ align:start position:0%
+system works everything out okay here's
+a good example of where it might be
+
+ align:start position:0%
+a good example of where it might be
+ 
+
+ align:start position:0%
+a good example of where it might be
+useful suppose we want to do a
+
+ align:start position:0%
+useful suppose we want to do a
+ 
+
+ align:start position:0%
+useful suppose we want to do a
+concurrent graph computation okay and so
+
+ align:start position:0%
+concurrent graph computation okay and so
+ 
+
+ align:start position:0%
+concurrent graph computation okay and so
+you take people involved in parallel and
+
+ align:start position:0%
+you take people involved in parallel and
+ 
+
+ align:start position:0%
+you take people involved in parallel and
+distributed computing and at MIT and you
+
+ align:start position:0%
+distributed computing and at MIT and you
+ 
+
+ align:start position:0%
+distributed computing and at MIT and you
+say okay I want to do Gaussian
+
+ align:start position:0%
+say okay I want to do Gaussian
+ 
+
+ align:start position:0%
+say okay I want to do Gaussian
+elimination on this graph now you guys
+
+ align:start position:0%
+elimination on this graph now you guys
+ 
+
+ align:start position:0%
+elimination on this graph now you guys
+are sure most of you know Gaussian
+
+ align:start position:0%
+are sure most of you know Gaussian
+ 
+
+ align:start position:0%
+are sure most of you know Gaussian
+elimination from the matrix context do
+
+ align:start position:0%
+elimination from the matrix context do
+ 
+
+ align:start position:0%
+elimination from the matrix context do
+you know what it means in a graph
+
+ align:start position:0%
+you know what it means in a graph
+ 
+
+ align:start position:0%
+you know what it means in a graph
+context so if you have a sparse matrix
+
+ align:start position:0%
+context so if you have a sparse matrix
+ 
+
+ align:start position:0%
+context so if you have a sparse matrix
+you actually have a graph and Gaussian
+
+ align:start position:0%
+you actually have a graph and Gaussian
+ 
+
+ align:start position:0%
+you actually have a graph and Gaussian
+elimination is a way of manipulating the
+
+ align:start position:0%
+elimination is a way of manipulating the
+ 
+
+ align:start position:0%
+elimination is a way of manipulating the
+graph and you get exactly the same
+
+ align:start position:0%
+graph and you get exactly the same
+ 
+
+ align:start position:0%
+graph and you get exactly the same
+behavior as you get in the dense one so
+
+ align:start position:0%
+behavior as you get in the dense one so
+ 
+
+ align:start position:0%
+behavior as you get in the dense one so
+I'll show you what it what it is you
+
+ align:start position:0%
+I'll show you what it what it is you
+ 
+
+ align:start position:0%
+I'll show you what it what it is you
+basically pick somebody to eliminate
+
+ align:start position:0%
+basically pick somebody to eliminate
+ 
+
+ align:start position:0%
+basically pick somebody to eliminate
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and now what you do is look at all
+
+ align:start position:0%
+okay and now what you do is look at all
+ 
+
+ align:start position:0%
+okay and now what you do is look at all
+this all the this vertexes neighbors
+
+ align:start position:0%
+this all the this vertexes neighbors
+ 
+
+ align:start position:0%
+this all the this vertexes neighbors
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+those guys and what you do is you
+
+ align:start position:0%
+those guys and what you do is you
+ 
+
+ align:start position:0%
+those guys and what you do is you
+eliminate that vertex bye-bye okay
+
+ align:start position:0%
+eliminate that vertex bye-bye okay
+ 
+
+ align:start position:0%
+eliminate that vertex bye-bye okay
+and you interconnect all the neighbors
+
+ align:start position:0%
+and you interconnect all the neighbors
+ 
+
+ align:start position:0%
+and you interconnect all the neighbors
+with all the edges that don't already
+
+ align:start position:0%
+with all the edges that don't already
+ 
+
+ align:start position:0%
+with all the edges that don't already
+exist and that's Gaussian elimination if
+
+ align:start position:0%
+exist and that's Gaussian elimination if
+ 
+
+ align:start position:0%
+exist and that's Gaussian elimination if
+you think of it in terms of matrix
+
+ align:start position:0%
+you think of it in terms of matrix
+ 
+
+ align:start position:0%
+you think of it in terms of matrix
+fashion the question is if you have a
+
+ align:start position:0%
+fashion the question is if you have a
+ 
+
+ align:start position:0%
+fashion the question is if you have a
+sparse matrix where are you going to get
+
+ align:start position:0%
+sparse matrix where are you going to get
+ 
+
+ align:start position:0%
+sparse matrix where are you going to get
+fill-in what are the places that you
+
+ align:start position:0%
+fill-in what are the places that you
+ 
+
+ align:start position:0%
+fill-in what are the places that you
+need to update when you do a pivot in
+
+ align:start position:0%
+need to update when you do a pivot in
+ 
+
+ align:start position:0%
+need to update when you do a pivot in
+Gaussian elimination in a matrix okay so
+
+ align:start position:0%
+Gaussian elimination in a matrix okay so
+ 
+
+ align:start position:0%
+Gaussian elimination in a matrix okay so
+that's the basic notion of graph of
+
+ align:start position:0%
+that's the basic notion of graph of
+ 
+
+ align:start position:0%
+that's the basic notion of graph of
+doing Gaussian elimination but now we
+
+ align:start position:0%
+doing Gaussian elimination but now we
+ 
+
+ align:start position:0%
+doing Gaussian elimination but now we
+want to deal with the concurrency okay
+
+ align:start position:0%
+want to deal with the concurrency okay
+ 
+
+ align:start position:0%
+want to deal with the concurrency okay
+and the problem occurs is if I want to
+
+ align:start position:0%
+and the problem occurs is if I want to
+ 
+
+ align:start position:0%
+and the problem occurs is if I want to
+eliminate two nodes at the same time
+
+ align:start position:0%
+eliminate two nodes at the same time
+ 
+
+ align:start position:0%
+eliminate two nodes at the same time
+okay because now they're adjacent each
+
+ align:start position:0%
+okay because now they're adjacent each
+ 
+
+ align:start position:0%
+okay because now they're adjacent each
+other and if I just do what i Express
+
+ align:start position:0%
+other and if I just do what i Express
+ 
+
+ align:start position:0%
+other and if I just do what i Express
+there's going to be all kinds of
+
+ align:start position:0%
+there's going to be all kinds of
+ 
+
+ align:start position:0%
+there's going to be all kinds of
+atomicity violations etc by the way the
+
+ align:start position:0%
+atomicity violations etc by the way the
+ 
+
+ align:start position:0%
+atomicity violations etc by the way the
+reason I'm picking these two folks is
+
+ align:start position:0%
+reason I'm picking these two folks is
+ 
+
+ align:start position:0%
+reason I'm picking these two folks is
+because they're going to a better place
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so how do you deal with this and
+
+ align:start position:0%
+okay so so how do you deal with this and
+ 
+
+ align:start position:0%
+okay so so how do you deal with this and
+so in transactional memory what I want
+
+ align:start position:0%
+so in transactional memory what I want
+ 
+
+ align:start position:0%
+so in transactional memory what I want
+to be able to do is just simply say okay
+
+ align:start position:0%
+to be able to do is just simply say okay
+ 
+
+ align:start position:0%
+to be able to do is just simply say okay
+here's the thing that I need to be
+
+ align:start position:0%
+here's the thing that I need to be
+ 
+
+ align:start position:0%
+here's the thing that I need to be
+atomic and so if I look at this code
+
+ align:start position:0%
+atomic and so if I look at this code
+ 
+
+ align:start position:0%
+atomic and so if I look at this code
+it's basically saying you know who are
+
+ align:start position:0%
+it's basically saying you know who are
+ 
+
+ align:start position:0%
+it's basically saying you know who are
+my neighbors and then let me identify
+
+ align:start position:0%
+my neighbors and then let me identify
+ 
+
+ align:start position:0%
+my neighbors and then let me identify
+all of the edges that need to be removed
+
+ align:start position:0%
+all of the edges that need to be removed
+ 
+
+ align:start position:0%
+all of the edges that need to be removed
+the ones that I just showed you they
+
+ align:start position:0%
+the ones that I just showed you they
+ 
+
+ align:start position:0%
+the ones that I just showed you they
+know that we're moved now let me get rid
+
+ align:start position:0%
+know that we're moved now let me get rid
+ 
+
+ align:start position:0%
+know that we're moved now let me get rid
+of the element you know V and now for
+
+ align:start position:0%
+of the element you know V and now for
+ 
+
+ align:start position:0%
+of the element you know V and now for
+all of the neighbors of U let us let us
+
+ align:start position:0%
+all of the neighbors of U let us let us
+ 
+
+ align:start position:0%
+all of the neighbors of U let us let us
+add in the edge between the neighbor and
+
+ align:start position:0%
+add in the edge between the neighbor and
+ 
+
+ align:start position:0%
+add in the edge between the neighbor and
+you know between the pairs of neighbors
+
+ align:start position:0%
+you know between the pairs of neighbors
+ 
+
+ align:start position:0%
+you know between the pairs of neighbors
+okay so that's basically what it's doing
+
+ align:start position:0%
+okay so that's basically what it's doing
+ 
+
+ align:start position:0%
+okay so that's basically what it's doing
+okay and I'd like to just say that's
+
+ align:start position:0%
+okay and I'd like to just say that's
+ 
+
+ align:start position:0%
+okay and I'd like to just say that's
+atomic okay and so the idea is that if I
+
+ align:start position:0%
+atomic okay and so the idea is that if I
+ 
+
+ align:start position:0%
+atomic okay and so the idea is that if I
+express that as a transaction then the
+
+ align:start position:0%
+express that as a transaction then the
+ 
+
+ align:start position:0%
+express that as a transaction then the
+ID
+
+ align:start position:0%
+ID
+ 
+
+ align:start position:0%
+ID
+is that on the transaction commit all
+
+ align:start position:0%
+is that on the transaction commit all
+ 
+
+ align:start position:0%
+is that on the transaction commit all
+the memory updates in the critical
+
+ align:start position:0%
+the memory updates in the critical
+ 
+
+ align:start position:0%
+the memory updates in the critical
+region appear to take it happen at once
+
+ align:start position:0%
+region appear to take it happen at once
+ 
+
+ align:start position:0%
+region appear to take it happen at once
+however in transaction member the idea
+
+ align:start position:0%
+however in transaction member the idea
+ 
+
+ align:start position:0%
+however in transaction member the idea
+is rather than forcing it go forward I
+
+ align:start position:0%
+is rather than forcing it go forward I
+ 
+
+ align:start position:0%
+is rather than forcing it go forward I
+can have the transactions abort okay so
+
+ align:start position:0%
+can have the transactions abort okay so
+ 
+
+ align:start position:0%
+can have the transactions abort okay so
+if I get a conflict I'll abort one and
+
+ align:start position:0%
+if I get a conflict I'll abort one and
+ 
+
+ align:start position:0%
+if I get a conflict I'll abort one and
+restart it and then the restarted
+
+ align:start position:0%
+restart it and then the restarted
+ 
+
+ align:start position:0%
+restart it and then the restarted
+transaction may take a different code
+
+ align:start position:0%
+transaction may take a different code
+ 
+
+ align:start position:0%
+transaction may take a different code
+path because after all I may have
+
+ align:start position:0%
+path because after all I may have
+ 
+
+ align:start position:0%
+path because after all I may have
+restructured the graph underneath and so
+
+ align:start position:0%
+restructured the graph underneath and so
+ 
+
+ align:start position:0%
+restructured the graph underneath and so
+it's may do something different the
+
+ align:start position:0%
+it's may do something different the
+ 
+
+ align:start position:0%
+it's may do something different the
+second time through the first it may
+
+ align:start position:0%
+second time through the first it may
+ 
+
+ align:start position:0%
+second time through the first it may
+also abort again and so forth so when
+
+ align:start position:0%
+also abort again and so forth so when
+ 
+
+ align:start position:0%
+also abort again and so forth so when
+you study transaction transactional
+
+ align:start position:0%
+you study transaction transactional
+ 
+
+ align:start position:0%
+you study transaction transactional
+memory let me just do a couple of -
+
+ align:start position:0%
+memory let me just do a couple of -
+ 
+
+ align:start position:0%
+memory let me just do a couple of -
+there's one is a conflict that's when
+
+ align:start position:0%
+there's one is a conflict that's when
+ 
+
+ align:start position:0%
+there's one is a conflict that's when
+you have two transactions that are you
+
+ align:start position:0%
+you have two transactions that are you
+ 
+
+ align:start position:0%
+you have two transactions that are you
+know they can't both complete one of
+
+ align:start position:0%
+know they can't both complete one of
+ 
+
+ align:start position:0%
+know they can't both complete one of
+them has to be aborted okay and aborting
+
+ align:start position:0%
+them has to be aborted okay and aborting
+ 
+
+ align:start position:0%
+them has to be aborted okay and aborting
+by the way is once again violating the
+
+ align:start position:0%
+by the way is once again violating the
+ 
+
+ align:start position:0%
+by the way is once again violating the
+non you know you know the non
+
+ align:start position:0%
+non you know you know the non
+ 
+
+ align:start position:0%
+non you know you know the non
+pre-emptive nature here we're going to
+
+ align:start position:0%
+pre-emptive nature here we're going to
+ 
+
+ align:start position:0%
+pre-emptive nature here we're going to
+preempt one of them by by keeping all
+
+ align:start position:0%
+preempt one of them by by keeping all
+ 
+
+ align:start position:0%
+preempt one of them by by keeping all
+the states so I can roll a state back
+
+ align:start position:0%
+the states so I can roll a state back
+ 
+
+ align:start position:0%
+the states so I can roll a state back
+and restart it from scratch so
+
+ align:start position:0%
+and restart it from scratch so
+ 
+
+ align:start position:0%
+and restart it from scratch so
+contention resolution is deciding which
+
+ align:start position:0%
+contention resolution is deciding which
+ 
+
+ align:start position:0%
+contention resolution is deciding which
+of the two conflicting transit actions
+
+ align:start position:0%
+of the two conflicting transit actions
+ 
+
+ align:start position:0%
+of the two conflicting transit actions
+to wait or to abort and restart and
+
+ align:start position:0%
+to wait or to abort and restart and
+ 
+
+ align:start position:0%
+to wait or to abort and restart and
+under what conditions you do that so the
+
+ align:start position:0%
+under what conditions you do that so the
+ 
+
+ align:start position:0%
+under what conditions you do that so the
+resolution manager has to figure out
+
+ align:start position:0%
+resolution manager has to figure out
+ 
+
+ align:start position:0%
+resolution manager has to figure out
+what happens in the case of contention
+
+ align:start position:0%
+what happens in the case of contention
+ 
+
+ align:start position:0%
+what happens in the case of contention
+and then forward progress is avoiding
+
+ align:start position:0%
+and then forward progress is avoiding
+ 
+
+ align:start position:0%
+and then forward progress is avoiding
+deadlock of course but also livelock and
+
+ align:start position:0%
+deadlock of course but also livelock and
+ 
+
+ align:start position:0%
+deadlock of course but also livelock and
+starvation you want to make sure that
+
+ align:start position:0%
+starvation you want to make sure that
+ 
+
+ align:start position:0%
+starvation you want to make sure that
+you're going to make because what you
+
+ align:start position:0%
+you're going to make because what you
+ 
+
+ align:start position:0%
+you're going to make because what you
+don't want to have happen for example is
+
+ align:start position:0%
+don't want to have happen for example is
+ 
+
+ align:start position:0%
+don't want to have happen for example is
+that two transactions keep aborting each
+
+ align:start position:0%
+that two transactions keep aborting each
+ 
+
+ align:start position:0%
+that two transactions keep aborting each
+other and you never make forward
+
+ align:start position:0%
+other and you never make forward
+ 
+
+ align:start position:0%
+other and you never make forward
+progress and throughput well you'd like
+
+ align:start position:0%
+progress and throughput well you'd like
+ 
+
+ align:start position:0%
+progress and throughput well you'd like
+to run as many transactions as
+
+ align:start position:0%
+to run as many transactions as
+ 
+
+ align:start position:0%
+to run as many transactions as
+concurrently as possible so I'm going to
+
+ align:start position:0%
+concurrently as possible so I'm going to
+ 
+
+ align:start position:0%
+concurrently as possible so I'm going to
+show you an algorithm for doing this
+
+ align:start position:0%
+show you an algorithm for doing this
+ 
+
+ align:start position:0%
+show you an algorithm for doing this
+it's a really simple algorithm okay it
+
+ align:start position:0%
+it's a really simple algorithm okay it
+ 
+
+ align:start position:0%
+it's a really simple algorithm okay it
+happens to be one that I discovered just
+
+ align:start position:0%
+happens to be one that I discovered just
+ 
+
+ align:start position:0%
+happens to be one that I discovered just
+a couple of years ago okay and I was
+
+ align:start position:0%
+a couple of years ago okay and I was
+ 
+
+ align:start position:0%
+a couple of years ago okay and I was
+surprised that it did not appear in the
+
+ align:start position:0%
+surprised that it did not appear in the
+ 
+
+ align:start position:0%
+surprised that it did not appear in the
+literature and so I wrote a very short
+
+ align:start position:0%
+literature and so I wrote a very short
+ 
+
+ align:start position:0%
+literature and so I wrote a very short
+paper on it because it's because what
+
+ align:start position:0%
+paper on it because it's because what
+ 
+
+ align:start position:0%
+paper on it because it's because what
+happens for a lot of people is they you
+
+ align:start position:0%
+happens for a lot of people is they you
+ 
+
+ align:start position:0%
+happens for a lot of people is they you
+know in if they discover there's a lot
+
+ align:start position:0%
+know in if they discover there's a lot
+ 
+
+ align:start position:0%
+know in if they discover there's a lot
+of aborting they say oh well let's grab
+
+ align:start position:0%
+of aborting they say oh well let's grab
+ 
+
+ align:start position:0%
+of aborting they say oh well let's grab
+a global lock
+
+ align:start position:0%
+a global lock
+ 
+
+ align:start position:0%
+a global lock
+and then if everybody grabs a global
+
+ align:start position:0%
+and then if everybody grabs a global
+ 
+
+ align:start position:0%
+and then if everybody grabs a global
+lock you can do this sort of thing you
+
+ align:start position:0%
+lock you can do this sort of thing you
+ 
+
+ align:start position:0%
+lock you can do this sort of thing you
+can't deadlock with a single lock if if
+
+ align:start position:0%
+can't deadlock with a single lock if if
+ 
+
+ align:start position:0%
+can't deadlock with a single lock if if
+you're not also doing things like you
+
+ align:start position:0%
+you're not also doing things like you
+ 
+
+ align:start position:0%
+you're not also doing things like you
+know silk sync or whatever but but in
+
+ align:start position:0%
+know silk sync or whatever but but in
+ 
+
+ align:start position:0%
+know silk sync or whatever but but in
+any case if you have just a single lock
+
+ align:start position:0%
+any case if you have just a single lock
+ 
+
+ align:start position:0%
+any case if you have just a single lock
+everybody falls back to the single lock
+
+ align:start position:0%
+everybody falls back to the single lock
+ 
+
+ align:start position:0%
+everybody falls back to the single lock
+and then you have no concurrency in your
+
+ align:start position:0%
+and then you have no concurrency in your
+ 
+
+ align:start position:0%
+and then you have no concurrency in your
+program no performance until everybody
+
+ align:start position:0%
+program no performance until everybody
+ 
+
+ align:start position:0%
+program no performance until everybody
+gets through the difficult time so this
+
+ align:start position:0%
+gets through the difficult time so this
+ 
+
+ align:start position:0%
+gets through the difficult time so this
+is an algorithm that doesn't require a
+
+ align:start position:0%
+is an algorithm that doesn't require a
+ 
+
+ align:start position:0%
+is an algorithm that doesn't require a
+global lock okay so it assumes that
+
+ align:start position:0%
+global lock okay so it assumes that
+ 
+
+ align:start position:0%
+global lock okay so it assumes that
+transactional memory system will log the
+
+ align:start position:0%
+transactional memory system will log the
+ 
+
+ align:start position:0%
+transactional memory system will log the
+reads and writes that's typically true
+
+ align:start position:0%
+reads and writes that's typically true
+ 
+
+ align:start position:0%
+reads and writes that's typically true
+of any transaction maybe you log what
+
+ align:start position:0%
+of any transaction maybe you log what
+ 
+
+ align:start position:0%
+of any transaction maybe you log what
+reads and writes you're doing so that
+
+ align:start position:0%
+reads and writes you're doing so that
+ 
+
+ align:start position:0%
+reads and writes you're doing so that
+you can either abort and rollback or you
+
+ align:start position:0%
+you can either abort and rollback or you
+ 
+
+ align:start position:0%
+you can either abort and rollback or you
+can when you abort you or else you
+
+ align:start position:0%
+can when you abort you or else you
+ 
+
+ align:start position:0%
+can when you abort you or else you
+sandbox things and then atomically
+
+ align:start position:0%
+sandbox things and then atomically
+ 
+
+ align:start position:0%
+sandbox things and then atomically
+commit them okay and so we have all the
+
+ align:start position:0%
+commit them okay and so we have all the
+ 
+
+ align:start position:0%
+commit them okay and so we have all the
+mechanisms for boarding and rolling back
+
+ align:start position:0%
+mechanisms for boarding and rolling back
+ 
+
+ align:start position:0%
+mechanisms for boarding and rolling back
+these are all very interesting in their
+
+ align:start position:0%
+these are all very interesting in their
+ 
+
+ align:start position:0%
+these are all very interesting in their
+own right and restarting and this is
+
+ align:start position:0%
+own right and restarting and this is
+ 
+
+ align:start position:0%
+own right and restarting and this is
+going to basically use a lock based
+
+ align:start position:0%
+going to basically use a lock based
+ 
+
+ align:start position:0%
+going to basically use a lock based
+approach that uses two ideas one is the
+
+ align:start position:0%
+approach that uses two ideas one is the
+ 
+
+ align:start position:0%
+approach that uses two ideas one is the
+notion of what's called a final finite
+
+ align:start position:0%
+notion of what's called a final finite
+ 
+
+ align:start position:0%
+notion of what's called a final finite
+ownership array and then another is a
+
+ align:start position:0%
+ownership array and then another is a
+ 
+
+ align:start position:0%
+ownership array and then another is a
+thing called release sort require and
+
+ align:start position:0%
+thing called release sort require and
+ 
+
+ align:start position:0%
+thing called release sort require and
+let me explain those two things and I'll
+
+ align:start position:0%
+let me explain those two things and I'll
+ 
+
+ align:start position:0%
+let me explain those two things and I'll
+show you really quickly how this
+
+ align:start position:0%
+show you really quickly how this
+ 
+
+ align:start position:0%
+show you really quickly how this
+beautiful algorithm works okay so you
+
+ align:start position:0%
+beautiful algorithm works okay so you
+ 
+
+ align:start position:0%
+beautiful algorithm works okay so you
+have an array of anti starvation mutual
+
+ align:start position:0%
+have an array of anti starvation mutual
+ 
+
+ align:start position:0%
+have an array of anti starvation mutual
+exclusion locks so these are ones that
+
+ align:start position:0%
+exclusion locks so these are ones that
+ 
+
+ align:start position:0%
+exclusion locks so these are ones that
+are going to be fair okay so that so
+
+ align:start position:0%
+are going to be fair okay so that so
+ 
+
+ align:start position:0%
+are going to be fair okay so that so
+that you're always going for the oldest
+
+ align:start position:0%
+that you're always going for the oldest
+ 
+
+ align:start position:0%
+that you're always going for the oldest
+one and you can do in a acquire we're
+
+ align:start position:0%
+one and you can do in a acquire we're
+ 
+
+ align:start position:0%
+one and you can do in a acquire we're
+also going to add in a try acquire tell
+
+ align:start position:0%
+also going to add in a try acquire tell
+ 
+
+ align:start position:0%
+also going to add in a try acquire tell
+me whether if I tried to acquire I would
+
+ align:start position:0%
+me whether if I tried to acquire I would
+ 
+
+ align:start position:0%
+me whether if I tried to acquire I would
+get it that is megive it to me if I
+
+ align:start position:0%
+get it that is megive it to me if I
+ 
+
+ align:start position:0%
+get it that is megive it to me if I
+don't get it
+
+ align:start position:0%
+don't get it
+ 
+
+ align:start position:0%
+don't get it
+don't wait just tell me that I didn't
+
+ align:start position:0%
+don't wait just tell me that I didn't
+ 
+
+ align:start position:0%
+don't wait just tell me that I didn't
+get it okay and then release and there's
+
+ align:start position:0%
+get it okay and then release and there's
+ 
+
+ align:start position:0%
+get it okay and then release and there's
+an owner function that map's
+
+ align:start position:0%
+an owner function that map's
+ 
+
+ align:start position:0%
+an owner function that map's
+all of the function H that map's my
+
+ align:start position:0%
+all of the function H that map's my
+ 
+
+ align:start position:0%
+all of the function H that map's my
+universe of memory locations to the
+
+ align:start position:0%
+universe of memory locations to the
+ 
+
+ align:start position:0%
+universe of memory locations to the
+indexes in this finite ownership array
+
+ align:start position:0%
+indexes in this finite ownership array
+ 
+
+ align:start position:0%
+indexes in this finite ownership array
+this lock array okay so the lock has
+
+ align:start position:0%
+this lock array okay so the lock has
+ 
+
+ align:start position:0%
+this lock array okay so the lock has
+length array has length n has n slots in
+
+ align:start position:0%
+length array has length n has n slots in
+ 
+
+ align:start position:0%
+length array has length n has n slots in
+it to lock a location X in the set of
+
+ align:start position:0%
+it to lock a location X in the set of
+ 
+
+ align:start position:0%
+it to lock a location X in the set of
+all possible
+
+ align:start position:0%
+all possible
+ 
+
+ align:start position:0%
+all possible
+you actually require lock of H of X so
+
+ align:start position:0%
+you actually require lock of H of X so
+ 
+
+ align:start position:0%
+you actually require lock of H of X so
+you can think of H as a hash function
+
+ align:start position:0%
+you can think of H as a hash function
+ 
+
+ align:start position:0%
+you can think of H as a hash function
+but doesn't have to be a fair hash
+
+ align:start position:0%
+but doesn't have to be a fair hash
+ 
+
+ align:start position:0%
+but doesn't have to be a fair hash
+function or whatever any function will
+
+ align:start position:0%
+function or whatever any function will
+ 
+
+ align:start position:0%
+function or whatever any function will
+do okay and then there yes there'll be
+
+ align:start position:0%
+do okay and then there yes there'll be
+ 
+
+ align:start position:0%
+do okay and then there yes there'll be
+some advantages to picking some
+
+ align:start position:0%
+some advantages to picking some
+ 
+
+ align:start position:0%
+some advantages to picking some
+functions or another one okay so in
+
+ align:start position:0%
+functions or another one okay so in
+ 
+
+ align:start position:0%
+functions or another one okay so in
+rather than actually locking the
+
+ align:start position:0%
+rather than actually locking the
+ 
+
+ align:start position:0%
+rather than actually locking the
+location or locking the object I lock a
+
+ align:start position:0%
+location or locking the object I lock a
+ 
+
+ align:start position:0%
+location or locking the object I lock a
+location that I that essentially I hash
+
+ align:start position:0%
+location that I that essentially I hash
+ 
+
+ align:start position:0%
+location that I that essentially I hash
+to from that object so if two guys are
+
+ align:start position:0%
+to from that object so if two guys are
+ 
+
+ align:start position:0%
+to from that object so if two guys are
+trying to grab the same location they
+
+ align:start position:0%
+trying to grab the same location they
+ 
+
+ align:start position:0%
+trying to grab the same location they
+will both grab the same lock because
+
+ align:start position:0%
+will both grab the same lock because
+ 
+
+ align:start position:0%
+will both grab the same lock because
+they've got the same hash function but I
+
+ align:start position:0%
+they've got the same hash function but I
+ 
+
+ align:start position:0%
+they've got the same hash function but I
+may have inadvertently where if I were
+
+ align:start position:0%
+may have inadvertently where if I were
+ 
+
+ align:start position:0%
+may have inadvertently where if I were
+locking the objects themselves okay I
+
+ align:start position:0%
+locking the objects themselves okay I
+ 
+
+ align:start position:0%
+locking the objects themselves okay I
+wouldn't have them both trying to
+
+ align:start position:0%
+wouldn't have them both trying to
+ 
+
+ align:start position:0%
+wouldn't have them both trying to
+acquire the same lock that might happen
+
+ align:start position:0%
+acquire the same lock that might happen
+ 
+
+ align:start position:0%
+acquire the same lock that might happen
+in this algorithm okay so here's the
+
+ align:start position:0%
+in this algorithm okay so here's the
+ 
+
+ align:start position:0%
+in this algorithm okay so here's the
+idea it's called the first idea is
+
+ align:start position:0%
+idea it's called the first idea is
+ 
+
+ align:start position:0%
+idea it's called the first idea is
+called a release sort and reacquires so
+
+ align:start position:0%
+called a release sort and reacquires so
+ 
+
+ align:start position:0%
+called a release sort and reacquires so
+that's the ownership array part that I
+
+ align:start position:0%
+that's the ownership array part that I
+ 
+
+ align:start position:0%
+that's the ownership array part that I
+just explained now here's the release
+
+ align:start position:0%
+just explained now here's the release
+ 
+
+ align:start position:0%
+just explained now here's the release
+sort a quat reacquire before you access
+
+ align:start position:0%
+sort a quat reacquire before you access
+ 
+
+ align:start position:0%
+sort a quat reacquire before you access
+a memory location X simply try to grab
+
+ align:start position:0%
+a memory location X simply try to grab
+ 
+
+ align:start position:0%
+a memory location X simply try to grab
+lock of X greedily and if you if you
+
+ align:start position:0%
+lock of X greedily and if you if you
+ 
+
+ align:start position:0%
+lock of X greedily and if you if you
+have a conflict okay so if you don't
+
+ align:start position:0%
+have a conflict okay so if you don't
+ 
+
+ align:start position:0%
+have a conflict okay so if you don't
+have a conflict you get it you just
+
+ align:start position:0%
+have a conflict you get it you just
+ 
+
+ align:start position:0%
+have a conflict you get it you just
+simply try to get it if you can that's
+
+ align:start position:0%
+simply try to get it if you can that's
+ 
+
+ align:start position:0%
+simply try to get it if you can that's
+great if not then what I'm going to do
+
+ align:start position:0%
+great if not then what I'm going to do
+ 
+
+ align:start position:0%
+great if not then what I'm going to do
+is roll back the transaction but don't
+
+ align:start position:0%
+is roll back the transaction but don't
+ 
+
+ align:start position:0%
+is roll back the transaction but don't
+release the locks I hold and then
+
+ align:start position:0%
+release the locks I hold and then
+ 
+
+ align:start position:0%
+release the locks I hold and then
+release all the locks with index is
+
+ align:start position:0%
+release all the locks with index is
+ 
+
+ align:start position:0%
+release all the locks with index is
+greater than H of X and then I'm gonna
+
+ align:start position:0%
+greater than H of X and then I'm gonna
+ 
+
+ align:start position:0%
+greater than H of X and then I'm gonna
+choir the lock that I want and now at
+
+ align:start position:0%
+choir the lock that I want and now at
+ 
+
+ align:start position:0%
+choir the lock that I want and now at
+that point I've released all the bigger
+
+ align:start position:0%
+that point I've released all the bigger
+ 
+
+ align:start position:0%
+that point I've released all the bigger
+locks so I'm acquiring the next lock and
+
+ align:start position:0%
+locks so I'm acquiring the next lock and
+ 
+
+ align:start position:0%
+locks so I'm acquiring the next lock and
+then I acquire the released locks in
+
+ align:start position:0%
+then I acquire the released locks in
+ 
+
+ align:start position:0%
+then I acquire the released locks in
+sorted order so I go through all the
+
+ align:start position:0%
+sorted order so I go through all the
+ 
+
+ align:start position:0%
+sorted order so I go through all the
+locks I release and I really min sorted
+
+ align:start position:0%
+locks I release and I really min sorted
+ 
+
+ align:start position:0%
+locks I release and I really min sorted
+order okay and then I start my
+
+ align:start position:0%
+order okay and then I start my
+ 
+
+ align:start position:0%
+order okay and then I start my
+transaction over again I try again so
+
+ align:start position:0%
+transaction over again I try again so
+ 
+
+ align:start position:0%
+transaction over again I try again so
+what happens each time through this
+
+ align:start position:0%
+what happens each time through this
+ 
+
+ align:start position:0%
+what happens each time through this
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+I'm always whenever trying to acquire a
+
+ align:start position:0%
+I'm always whenever trying to acquire a
+ 
+
+ align:start position:0%
+I'm always whenever trying to acquire a
+lock I'm only holding locks that are
+
+ align:start position:0%
+lock I'm only holding locks that are
+ 
+
+ align:start position:0%
+lock I'm only holding locks that are
+smaller but each time that I restart I
+
+ align:start position:0%
+smaller but each time that I restart I
+ 
+
+ align:start position:0%
+smaller but each time that I restart I
+have one more lock that I didn't used to
+
+ align:start position:0%
+have one more lock that I didn't used to
+ 
+
+ align:start position:0%
+have one more lock that I didn't used to
+have before I restart my transaction
+
+ align:start position:0%
+have before I restart my transaction
+ 
+
+ align:start position:0%
+have before I restart my transaction
+which I've acquired in the order in the
+
+ align:start position:0%
+which I've acquired in the order in the
+ 
+
+ align:start position:0%
+which I've acquired in the order in the
+linear order from you know from the
+
+ align:start position:0%
+linear order from you know from the
+ 
+
+ align:start position:0%
+linear order from you know from the
+in that ownership array from zero to n
+
+ align:start position:0%
+in that ownership array from zero to n
+ 
+
+ align:start position:0%
+in that ownership array from zero to n
+minus one okay and so here's the
+
+ align:start position:0%
+minus one okay and so here's the
+ 
+
+ align:start position:0%
+minus one okay and so here's the
+algorithm I'll let you guys look at it
+
+ align:start position:0%
+algorithm I'll let you guys look at it
+ 
+
+ align:start position:0%
+algorithm I'll let you guys look at it
+in more detail because I see our our
+
+ align:start position:0%
+in more detail because I see our our
+ 
+
+ align:start position:0%
+in more detail because I see our our
+time is up and it's actually fun to take
+
+ align:start position:0%
+time is up and it's actually fun to take
+ 
+
+ align:start position:0%
+time is up and it's actually fun to take
+a look at and we'll put the paper online
+
+ align:start position:0%
+a look at and we'll put the paper online
+ 
+
+ align:start position:0%
+a look at and we'll put the paper online
+there's one other topic that I wanted to
+
+ align:start position:0%
+there's one other topic that I wanted to
+ 
+
+ align:start position:0%
+there's one other topic that I wanted to
+go through here which is which you
+
+ align:start position:0%
+go through here which is which you
+ 
+
+ align:start position:0%
+go through here which is which you
+should know about is this locking
+
+ align:start position:0%
+should know about is this locking
+ 
+
+ align:start position:0%
+should know about is this locking
+anomaly called convoying and this was
+
+ align:start position:0%
+anomaly called convoying and this was
+ 
+
+ align:start position:0%
+anomaly called convoying and this was
+actually a bug that we had performance
+
+ align:start position:0%
+actually a bug that we had performance
+ 
+
+ align:start position:0%
+actually a bug that we had performance
+bug that we had in our original MIT silk
+
+ align:start position:0%
+bug that we had in our original MIT silk
+ 
+
+ align:start position:0%
+bug that we had in our original MIT silk
+so it's kind of a neat one to see and
+
+ align:start position:0%
+so it's kind of a neat one to see and
+ 
+
+ align:start position:0%
+so it's kind of a neat one to see and
+how we resolved it and that's it
\ No newline at end of file
diff --git a/mwL__eKs3fI.txt b/mwL__eKs3fI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..82c555e44424139ccc67956a538d232f3a69a528
--- /dev/null
+++ b/mwL__eKs3fI.txt
@@ -0,0 +1,947 @@
+align:start position:0%
+ 
+devious video we used data in linear
+
+ align:start position:0%
+devious video we used data in linear
+ 
+
+ align:start position:0%
+devious video we used data in linear
+regression to show that if a team scores
+
+ align:start position:0%
+regression to show that if a team scores
+ 
+
+ align:start position:0%
+regression to show that if a team scores
+at least 135 more runs than their
+
+ align:start position:0%
+at least 135 more runs than their
+ 
+
+ align:start position:0%
+at least 135 more runs than their
+opponent throughout the regular season
+
+ align:start position:0%
+opponent throughout the regular season
+ 
+
+ align:start position:0%
+opponent throughout the regular season
+then we predict that that team will win
+
+ align:start position:0%
+then we predict that that team will win
+ 
+
+ align:start position:0%
+then we predict that that team will win
+at least 95 games and make the playoffs
+
+ align:start position:0%
+at least 95 games and make the playoffs
+ 
+
+ align:start position:0%
+at least 95 games and make the playoffs
+this means that we need to know how many
+
+ align:start position:0%
+this means that we need to know how many
+ 
+
+ align:start position:0%
+this means that we need to know how many
+runs a team will score which we will
+
+ align:start position:0%
+runs a team will score which we will
+ 
+
+ align:start position:0%
+runs a team will score which we will
+show can be predicted using batting
+
+ align:start position:0%
+show can be predicted using batting
+ 
+
+ align:start position:0%
+show can be predicted using batting
+statistics and how many runs a team will
+
+ align:start position:0%
+statistics and how many runs a team will
+ 
+
+ align:start position:0%
+statistics and how many runs a team will
+allow which we will show can be
+
+ align:start position:0%
+allow which we will show can be
+ 
+
+ align:start position:0%
+allow which we will show can be
+predicted using fielding and pitching
+
+ align:start position:0%
+predicted using fielding and pitching
+ 
+
+ align:start position:0%
+predicted using fielding and pitching
+statistics let's start by creating a
+
+ align:start position:0%
+statistics let's start by creating a
+ 
+
+ align:start position:0%
+statistics let's start by creating a
+linear regression model to predict run
+
+ align:start position:0%
+linear regression model to predict run
+ 
+
+ align:start position:0%
+linear regression model to predict run
+scored the Oakland A's are interested in
+
+ align:start position:0%
+scored the Oakland A's are interested in
+ 
+
+ align:start position:0%
+scored the Oakland A's are interested in
+answering the question how does a team
+
+ align:start position:0%
+answering the question how does a team
+ 
+
+ align:start position:0%
+answering the question how does a team
+score more runs they discovered that two
+
+ align:start position:0%
+score more runs they discovered that two
+ 
+
+ align:start position:0%
+score more runs they discovered that two
+baseball statistics were significantly
+
+ align:start position:0%
+baseball statistics were significantly
+ 
+
+ align:start position:0%
+baseball statistics were significantly
+more important than anything else
+
+ align:start position:0%
+more important than anything else
+ 
+
+ align:start position:0%
+more important than anything else
+these were on-base percentage or OBP
+
+ align:start position:0%
+these were on-base percentage or OBP
+ 
+
+ align:start position:0%
+these were on-base percentage or OBP
+which is the percentage of time a player
+
+ align:start position:0%
+which is the percentage of time a player
+ 
+
+ align:start position:0%
+which is the percentage of time a player
+gets on base including walks and
+
+ align:start position:0%
+gets on base including walks and
+ 
+
+ align:start position:0%
+gets on base including walks and
+slugging percentage or SLG which
+
+ align:start position:0%
+slugging percentage or SLG which
+ 
+
+ align:start position:0%
+slugging percentage or SLG which
+measures how far a player gets around
+
+ align:start position:0%
+measures how far a player gets around
+ 
+
+ align:start position:0%
+measures how far a player gets around
+the bases on his turn and measures the
+
+ align:start position:0%
+the bases on his turn and measures the
+ 
+
+ align:start position:0%
+the bases on his turn and measures the
+power of a hitter most teams and people
+
+ align:start position:0%
+power of a hitter most teams and people
+ 
+
+ align:start position:0%
+power of a hitter most teams and people
+in baseball focused instead on batting
+
+ align:start position:0%
+in baseball focused instead on batting
+ 
+
+ align:start position:0%
+in baseball focused instead on batting
+average or ba which measures how often a
+
+ align:start position:0%
+average or ba which measures how often a
+ 
+
+ align:start position:0%
+average or ba which measures how often a
+hitter gets on base by hitting the ball
+
+ align:start position:0%
+hitter gets on base by hitting the ball
+ 
+
+ align:start position:0%
+hitter gets on base by hitting the ball
+this focuses on hits instead of walks
+
+ align:start position:0%
+this focuses on hits instead of walks
+ 
+
+ align:start position:0%
+this focuses on hits instead of walks
+the Oakland A's claimed that on-base
+
+ align:start position:0%
+the Oakland A's claimed that on-base
+ 
+
+ align:start position:0%
+the Oakland A's claimed that on-base
+percentage was the most important
+
+ align:start position:0%
+percentage was the most important
+ 
+
+ align:start position:0%
+percentage was the most important
+slugging percentage was important and
+
+ align:start position:0%
+slugging percentage was important and
+ 
+
+ align:start position:0%
+slugging percentage was important and
+batting average was overvalued let's see
+
+ align:start position:0%
+batting average was overvalued let's see
+ 
+
+ align:start position:0%
+batting average was overvalued let's see
+if we can use linear regression in our
+
+ align:start position:0%
+if we can use linear regression in our
+ 
+
+ align:start position:0%
+if we can use linear regression in our
+to verify which baseball statistics are
+
+ align:start position:0%
+to verify which baseball statistics are
+ 
+
+ align:start position:0%
+to verify which baseball statistics are
+more important to predict runs in the
+
+ align:start position:0%
+more important to predict runs in the
+ 
+
+ align:start position:0%
+more important to predict runs in the
+previous video we created our data set
+
+ align:start position:0%
+previous video we created our data set
+ 
+
+ align:start position:0%
+previous video we created our data set
+in our and called it Moneyball let's
+
+ align:start position:0%
+in our and called it Moneyball let's
+ 
+
+ align:start position:0%
+in our and called it Moneyball let's
+take a look at the structure of our data
+
+ align:start position:0%
+take a look at the structure of our data
+ 
+
+ align:start position:0%
+take a look at the structure of our data
+again our dataset includes many
+
+ align:start position:0%
+again our dataset includes many
+ 
+
+ align:start position:0%
+again our dataset includes many
+variables including run scored or RS
+
+ align:start position:0%
+variables including run scored or RS
+ 
+
+ align:start position:0%
+variables including run scored or RS
+on-base percentage OBP slugging
+
+ align:start position:0%
+on-base percentage OBP slugging
+ 
+
+ align:start position:0%
+on-base percentage OBP slugging
+percentage SLG and batting average ba we
+
+ align:start position:0%
+percentage SLG and batting average ba we
+ 
+
+ align:start position:0%
+percentage SLG and batting average ba we
+want to see if we can use linear
+
+ align:start position:0%
+want to see if we can use linear
+ 
+
+ align:start position:0%
+want to see if we can use linear
+regression to predict run scored using
+
+ align:start position:0%
+regression to predict run scored using
+ 
+
+ align:start position:0%
+regression to predict run scored using
+the three hitting statistics on-base
+
+ align:start position:0%
+the three hitting statistics on-base
+ 
+
+ align:start position:0%
+the three hitting statistics on-base
+percentage slugging percentage and
+
+ align:start position:0%
+percentage slugging percentage and
+ 
+
+ align:start position:0%
+percentage slugging percentage and
+batting average so let's build a linear
+
+ align:start position:0%
+batting average so let's build a linear
+ 
+
+ align:start position:0%
+batting average so let's build a linear
+regression equation using the LM
+
+ align:start position:0%
+regression equation using the LM
+ 
+
+ align:start position:0%
+regression equation using the LM
+function to predict run scored using the
+
+ align:start position:0%
+function to predict run scored using the
+ 
+
+ align:start position:0%
+function to predict run scored using the
+independent variables OBP s LG mba our
+
+ align:start position:0%
+independent variables OBP s LG mba our
+ 
+
+ align:start position:0%
+independent variables OBP s LG mba our
+data set is Moneyball if we look at the
+
+ align:start position:0%
+data set is Moneyball if we look at the
+ 
+
+ align:start position:0%
+data set is Moneyball if we look at the
+summary of our regression equation we
+
+ align:start position:0%
+summary of our regression equation we
+ 
+
+ align:start position:0%
+summary of our regression equation we
+can see that all of our independent
+
+ align:start position:0%
+can see that all of our independent
+ 
+
+ align:start position:0%
+can see that all of our independent
+variables are highly significant and our
+
+ align:start position:0%
+variables are highly significant and our
+ 
+
+ align:start position:0%
+variables are highly significant and our
+r-squared is 0.93 if we look at our
+
+ align:start position:0%
+r-squared is 0.93 if we look at our
+ 
+
+ align:start position:0%
+r-squared is 0.93 if we look at our
+coefficients we see that the coefficient
+
+ align:start position:0%
+coefficients we see that the coefficient
+ 
+
+ align:start position:0%
+coefficients we see that the coefficient
+for batting average is negative this
+
+ align:start position:0%
+for batting average is negative this
+ 
+
+ align:start position:0%
+for batting average is negative this
+says that all other things being equal a
+
+ align:start position:0%
+says that all other things being equal a
+ 
+
+ align:start position:0%
+says that all other things being equal a
+team with a higher batting average will
+
+ align:start position:0%
+team with a higher batting average will
+ 
+
+ align:start position:0%
+team with a higher batting average will
+score fewer runs but this is a bit
+
+ align:start position:0%
+score fewer runs but this is a bit
+ 
+
+ align:start position:0%
+score fewer runs but this is a bit
+counterintuitive what's going on here is
+
+ align:start position:0%
+counterintuitive what's going on here is
+ 
+
+ align:start position:0%
+counterintuitive what's going on here is
+a case of multicollinearity these three
+
+ align:start position:0%
+a case of multicollinearity these three
+ 
+
+ align:start position:0%
+a case of multicollinearity these three
+hitting statistics are highly correlated
+
+ align:start position:0%
+hitting statistics are highly correlated
+ 
+
+ align:start position:0%
+hitting statistics are highly correlated
+so it's hard to interpret our model
+
+ align:start position:0%
+so it's hard to interpret our model
+ 
+
+ align:start position:0%
+so it's hard to interpret our model
+let's see if we can remove batting
+
+ align:start position:0%
+let's see if we can remove batting
+ 
+
+ align:start position:0%
+let's see if we can remove batting
+average the variable with the negative
+
+ align:start position:0%
+average the variable with the negative
+ 
+
+ align:start position:0%
+average the variable with the negative
+coefficient and the least significance
+
+ align:start position:0%
+coefficient and the least significance
+ 
+
+ align:start position:0%
+coefficient and the least significance
+to see if we can improve the interpret
+
+ align:start position:0%
+to see if we can improve the interpret
+ 
+
+ align:start position:0%
+to see if we can improve the interpret
+ability of our model so let's rerun our
+
+ align:start position:0%
+ability of our model so let's rerun our
+ 
+
+ align:start position:0%
+ability of our model so let's rerun our
+regression equation without the variable
+
+ align:start position:0%
+regression equation without the variable
+ 
+
+ align:start position:0%
+regression equation without the variable
+ba if we look at the summary of our new
+
+ align:start position:0%
+ba if we look at the summary of our new
+ 
+
+ align:start position:0%
+ba if we look at the summary of our new
+regression equation we can see that our
+
+ align:start position:0%
+regression equation we can see that our
+ 
+
+ align:start position:0%
+regression equation we can see that our
+variables are again highly significant
+
+ align:start position:0%
+variables are again highly significant
+ 
+
+ align:start position:0%
+variables are again highly significant
+the coefficients are all positive as we
+
+ align:start position:0%
+the coefficients are all positive as we
+ 
+
+ align:start position:0%
+the coefficients are all positive as we
+would expect them to be and our R
+
+ align:start position:0%
+would expect them to be and our R
+ 
+
+ align:start position:0%
+would expect them to be and our R
+squared is now 0.92 96 or about the same
+
+ align:start position:0%
+squared is now 0.92 96 or about the same
+ 
+
+ align:start position:0%
+squared is now 0.92 96 or about the same
+as before so this model is simpler with
+
+ align:start position:0%
+as before so this model is simpler with
+ 
+
+ align:start position:0%
+as before so this model is simpler with
+one fewer variable but has about the
+
+ align:start position:0%
+one fewer variable but has about the
+ 
+
+ align:start position:0%
+one fewer variable but has about the
+same predictive ability as a three
+
+ align:start position:0%
+same predictive ability as a three
+ 
+
+ align:start position:0%
+same predictive ability as a three
+variable model you can experiment and
+
+ align:start position:0%
+variable model you can experiment and
+ 
+
+ align:start position:0%
+variable model you can experiment and
+see that if we had taken out on base
+
+ align:start position:0%
+see that if we had taken out on base
+ 
+
+ align:start position:0%
+see that if we had taken out on base
+percentage or slugging percentage
+
+ align:start position:0%
+percentage or slugging percentage
+ 
+
+ align:start position:0%
+percentage or slugging percentage
+instead of batting average our r-squared
+
+ align:start position:0%
+instead of batting average our r-squared
+ 
+
+ align:start position:0%
+instead of batting average our r-squared
+would have gone down more if we look at
+
+ align:start position:0%
+would have gone down more if we look at
+ 
+
+ align:start position:0%
+would have gone down more if we look at
+the coefficients we can see that the
+
+ align:start position:0%
+the coefficients we can see that the
+ 
+
+ align:start position:0%
+the coefficients we can see that the
+coefficient for on-base percentage is
+
+ align:start position:0%
+coefficient for on-base percentage is
+ 
+
+ align:start position:0%
+coefficient for on-base percentage is
+significantly higher than the
+
+ align:start position:0%
+significantly higher than the
+ 
+
+ align:start position:0%
+significantly higher than the
+coefficient for slugging percentage
+
+ align:start position:0%
+coefficient for slugging percentage
+ 
+
+ align:start position:0%
+coefficient for slugging percentage
+since these variables are on
+
+ align:start position:0%
+since these variables are on
+ 
+
+ align:start position:0%
+since these variables are on
+the same scale this tells us that
+
+ align:start position:0%
+the same scale this tells us that
+ 
+
+ align:start position:0%
+the same scale this tells us that
+on-base percentage is worth more than
+
+ align:start position:0%
+on-base percentage is worth more than
+ 
+
+ align:start position:0%
+on-base percentage is worth more than
+slugging percentage
+
+ align:start position:0%
+slugging percentage
+ 
+
+ align:start position:0%
+slugging percentage
+so using linear regression we're able to
+
+ align:start position:0%
+so using linear regression we're able to
+ 
+
+ align:start position:0%
+so using linear regression we're able to
+verify the claims made in Moneyball that
+
+ align:start position:0%
+verify the claims made in Moneyball that
+ 
+
+ align:start position:0%
+verify the claims made in Moneyball that
+batting average is overvalued on-base
+
+ align:start position:0%
+batting average is overvalued on-base
+ 
+
+ align:start position:0%
+batting average is overvalued on-base
+percentage is the most important and
+
+ align:start position:0%
+percentage is the most important and
+ 
+
+ align:start position:0%
+percentage is the most important and
+slugging percentage is important we can
+
+ align:start position:0%
+slugging percentage is important we can
+ 
+
+ align:start position:0%
+slugging percentage is important we can
+create a very similar model to predict
+
+ align:start position:0%
+create a very similar model to predict
+ 
+
+ align:start position:0%
+create a very similar model to predict
+runs Allowed or opponent runs this model
+
+ align:start position:0%
+runs Allowed or opponent runs this model
+ 
+
+ align:start position:0%
+runs Allowed or opponent runs this model
+uses pitching statistics opponent's
+
+ align:start position:0%
+uses pitching statistics opponent's
+ 
+
+ align:start position:0%
+uses pitching statistics opponent's
+on-base percentage or oo BP an opponent
+
+ align:start position:0%
+on-base percentage or oo BP an opponent
+ 
+
+ align:start position:0%
+on-base percentage or oo BP an opponent
+slugging percentage or o SLG these
+
+ align:start position:0%
+slugging percentage or o SLG these
+ 
+
+ align:start position:0%
+slugging percentage or o SLG these
+statistics are computed in the same way
+
+ align:start position:0%
+statistics are computed in the same way
+ 
+
+ align:start position:0%
+statistics are computed in the same way
+as on-base percentage and slugging
+
+ align:start position:0%
+as on-base percentage and slugging
+ 
+
+ align:start position:0%
+as on-base percentage and slugging
+percentage but use the actions of the
+
+ align:start position:0%
+percentage but use the actions of the
+ 
+
+ align:start position:0%
+percentage but use the actions of the
+opposing batters against our team's
+
+ align:start position:0%
+opposing batters against our team's
+ 
+
+ align:start position:0%
+opposing batters against our team's
+pitcher and fielders using our data set
+
+ align:start position:0%
+pitcher and fielders using our data set
+ 
+
+ align:start position:0%
+pitcher and fielders using our data set
+in our we can build a linear regression
+
+ align:start position:0%
+in our we can build a linear regression
+ 
+
+ align:start position:0%
+in our we can build a linear regression
+model to predict runs Allowed using
+
+ align:start position:0%
+model to predict runs Allowed using
+ 
+
+ align:start position:0%
+model to predict runs Allowed using
+opponent's on-base percentage an
+
+ align:start position:0%
+opponent's on-base percentage an
+ 
+
+ align:start position:0%
+opponent's on-base percentage an
+opponent slugging percentage this is
+
+ align:start position:0%
+opponent slugging percentage this is
+ 
+
+ align:start position:0%
+opponent slugging percentage this is
+again a very strong model with an
+
+ align:start position:0%
+again a very strong model with an
+ 
+
+ align:start position:0%
+again a very strong model with an
+r-squared value of 0.9 won and both
+
+ align:start position:0%
+r-squared value of 0.9 won and both
+ 
+
+ align:start position:0%
+r-squared value of 0.9 won and both
+variables are significant in the next
+
+ align:start position:0%
+variables are significant in the next
+ 
+
+ align:start position:0%
+variables are significant in the next
+video we'll show how we can apply these
+
+ align:start position:0%
+video we'll show how we can apply these
+ 
+
+ align:start position:0%
+video we'll show how we can apply these
+models to predict whether or not a team
+
+ align:start position:0%
+models to predict whether or not a team
+ 
+
+ align:start position:0%
+models to predict whether or not a team
+will make the playoffs
\ No newline at end of file
diff --git a/n0seIQ7r8xo.txt b/n0seIQ7r8xo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d4cce1b7565f6f66619f0a9e7dc26d96dc36c049
--- /dev/null
+++ b/n0seIQ7r8xo.txt
@@ -0,0 +1,15803 @@
+align:start position:0%
+ 
+and then on Thursday we'll have these I
+
+ align:start position:0%
+and then on Thursday we'll have these I
+ 
+
+ align:start position:0%
+and then on Thursday we'll have these I
+also want to mention if the towards the
+
+ align:start position:0%
+also want to mention if the towards the
+ 
+
+ align:start position:0%
+also want to mention if the towards the
+end of lecture today we'll have the um
+
+ align:start position:0%
+end of lecture today we'll have the um
+ 
+
+ align:start position:0%
+end of lecture today we'll have the um
+the uh course
+
+ align:start position:0%
+the uh course
+ 
+
+ align:start position:0%
+the uh course
+evaluations for you to fill out okay be
+
+ align:start position:0%
+evaluations for you to fill out okay be
+ 
+
+ align:start position:0%
+evaluations for you to fill out okay be
+before we start the the fal lecture for
+
+ align:start position:0%
+before we start the the fal lecture for
+ 
+
+ align:start position:0%
+before we start the the fal lecture for
+for today I want to for those of you who
+
+ align:start position:0%
+for today I want to for those of you who
+ 
+
+ align:start position:0%
+for today I want to for those of you who
+are here last time uh I wanted to go
+
+ align:start position:0%
+are here last time uh I wanted to go
+ 
+
+ align:start position:0%
+are here last time uh I wanted to go
+over um something that we had talked
+
+ align:start position:0%
+over um something that we had talked
+ 
+
+ align:start position:0%
+over um something that we had talked
+about we didn't have time to go through
+
+ align:start position:0%
+about we didn't have time to go through
+ 
+
+ align:start position:0%
+about we didn't have time to go through
+how you would do these calculations and
+
+ align:start position:0%
+how you would do these calculations and
+ 
+
+ align:start position:0%
+how you would do these calculations and
+uh uh from the last handout which was
+
+ align:start position:0%
+uh uh from the last handout which was
+ 
+
+ align:start position:0%
+uh uh from the last handout which was
+handout 37 or 36
+
+ align:start position:0%
+handout 37 or 36
+ 
+
+ align:start position:0%
+handout 37 or 36
+um on slide 27 there was a question that
+
+ align:start position:0%
+um on slide 27 there was a question that
+ 
+
+ align:start position:0%
+um on slide 27 there was a question that
+a couple of questions that we were
+
+ align:start position:0%
+a couple of questions that we were
+ 
+
+ align:start position:0%
+a couple of questions that we were
+asking and uh I thought we just spend
+
+ align:start position:0%
+asking and uh I thought we just spend
+ 
+
+ align:start position:0%
+asking and uh I thought we just spend
+about 5 minutes before we start the uh
+
+ align:start position:0%
+about 5 minutes before we start the uh
+ 
+
+ align:start position:0%
+about 5 minutes before we start the uh
+today's formal lecture uh going through
+
+ align:start position:0%
+today's formal lecture uh going through
+ 
+
+ align:start position:0%
+today's formal lecture uh going through
+this at least on the board so people
+
+ align:start position:0%
+this at least on the board so people
+ 
+
+ align:start position:0%
+this at least on the board so people
+have an idea of how to make these fact
+
+ align:start position:0%
+have an idea of how to make these fact
+ 
+
+ align:start position:0%
+have an idea of how to make these fact
+of the envelope calculations so the what
+
+ align:start position:0%
+of the envelope calculations so the what
+ 
+
+ align:start position:0%
+of the envelope calculations so the what
+you're being asked to do here is you're
+
+ align:start position:0%
+you're being asked to do here is you're
+ 
+
+ align:start position:0%
+you're being asked to do here is you're
+looking at a silicon mosfet with a uh
+
+ align:start position:0%
+looking at a silicon mosfet with a uh
+ 
+
+ align:start position:0%
+looking at a silicon mosfet with a uh
+these are the source drain extensions
+
+ align:start position:0%
+these are the source drain extensions
+ 
+
+ align:start position:0%
+these are the source drain extensions
+these shallow extensions that have a
+
+ align:start position:0%
+these shallow extensions that have a
+ 
+
+ align:start position:0%
+these shallow extensions that have a
+certain depth XJ these are the Deep
+
+ align:start position:0%
+certain depth XJ these are the Deep
+ 
+
+ align:start position:0%
+certain depth XJ these are the Deep
+source and drain uh um that have been
+
+ align:start position:0%
+source and drain uh um that have been
+ 
+
+ align:start position:0%
+source and drain uh um that have been
+psoc remember the last lecture was all
+
+ align:start position:0%
+psoc remember the last lecture was all
+ 
+
+ align:start position:0%
+psoc remember the last lecture was all
+about psoc so this blue region is
+
+ align:start position:0%
+about psoc so this blue region is
+ 
+
+ align:start position:0%
+about psoc so this blue region is
+supposed to represent a
+
+ align:start position:0%
+supposed to represent a
+ 
+
+ align:start position:0%
+supposed to represent a
+pilici um a suicided region and then
+
+ align:start position:0%
+pilici um a suicided region and then
+ 
+
+ align:start position:0%
+pilici um a suicided region and then
+there's a metal contact and this is
+
+ align:start position:0%
+there's a metal contact and this is
+ 
+
+ align:start position:0%
+there's a metal contact and this is
+highly schematic but imagine this little
+
+ align:start position:0%
+highly schematic but imagine this little
+ 
+
+ align:start position:0%
+highly schematic but imagine this little
+thing coming down here as uh your
+
+ align:start position:0%
+thing coming down here as uh your
+ 
+
+ align:start position:0%
+thing coming down here as uh your
+aluminum metal or whatever uh coming
+
+ align:start position:0%
+aluminum metal or whatever uh coming
+ 
+
+ align:start position:0%
+aluminum metal or whatever uh coming
+down and touching uh the solide and it
+
+ align:start position:0%
+down and touching uh the solide and it
+ 
+
+ align:start position:0%
+down and touching uh the solide and it
+spaced a certain distance the metal
+
+ align:start position:0%
+spaced a certain distance the metal
+ 
+
+ align:start position:0%
+spaced a certain distance the metal
+contact is by by um an insulator um from
+
+ align:start position:0%
+contact is by by um an insulator um from
+ 
+
+ align:start position:0%
+contact is by by um an insulator um from
+from this point here where the soloc
+
+ align:start position:0%
+from this point here where the soloc
+ 
+
+ align:start position:0%
+from this point here where the soloc
+starts and so what we're asked to do is
+
+ align:start position:0%
+starts and so what we're asked to do is
+ 
+
+ align:start position:0%
+starts and so what we're asked to do is
+to calculate separately three resistors
+
+ align:start position:0%
+to calculate separately three resistors
+ 
+
+ align:start position:0%
+to calculate separately three resistors
+that are in this problem there's this
+
+ align:start position:0%
+that are in this problem there's this
+ 
+
+ align:start position:0%
+that are in this problem there's this
+resistor here which represents the
+
+ align:start position:0%
+resistor here which represents the
+ 
+
+ align:start position:0%
+resistor here which represents the
+resistance of the sourc drain extension
+
+ align:start position:0%
+resistance of the sourc drain extension
+ 
+
+ align:start position:0%
+resistance of the sourc drain extension
+as the current flows through the channel
+
+ align:start position:0%
+as the current flows through the channel
+ 
+
+ align:start position:0%
+as the current flows through the channel
+into the extension which is underneath
+
+ align:start position:0%
+into the extension which is underneath
+ 
+
+ align:start position:0%
+into the extension which is underneath
+the spacer and then there's a resistance
+
+ align:start position:0%
+the spacer and then there's a resistance
+ 
+
+ align:start position:0%
+the spacer and then there's a resistance
+associated with this sheet resistance of
+
+ align:start position:0%
+associated with this sheet resistance of
+ 
+
+ align:start position:0%
+associated with this sheet resistance of
+the pilici region because the current
+
+ align:start position:0%
+the pilici region because the current
+ 
+
+ align:start position:0%
+the pilici region because the current
+has to get from this point here to the
+
+ align:start position:0%
+has to get from this point here to the
+ 
+
+ align:start position:0%
+has to get from this point here to the
+point where the metal contact is up here
+
+ align:start position:0%
+point where the metal contact is up here
+ 
+
+ align:start position:0%
+point where the metal contact is up here
+and there then there's the interfacial
+
+ align:start position:0%
+and there then there's the interfacial
+ 
+
+ align:start position:0%
+and there then there's the interfacial
+resistance or the contact resistance
+
+ align:start position:0%
+resistance or the contact resistance
+ 
+
+ align:start position:0%
+resistance or the contact resistance
+associated with this metal contact so
+
+ align:start position:0%
+associated with this metal contact so
+ 
+
+ align:start position:0%
+associated with this metal contact so
+those are the three and uh you know in a
+
+ align:start position:0%
+those are the three and uh you know in a
+ 
+
+ align:start position:0%
+those are the three and uh you know in a
+few minutes here we can just kind of go
+
+ align:start position:0%
+few minutes here we can just kind of go
+ 
+
+ align:start position:0%
+few minutes here we can just kind of go
+through that and I thought it might be
+
+ align:start position:0%
+through that and I thought it might be
+ 
+
+ align:start position:0%
+through that and I thought it might be
+uh useful for us to calculate those so
+
+ align:start position:0%
+uh useful for us to calculate those so
+ 
+
+ align:start position:0%
+uh useful for us to calculate those so
+the first one um what we're really
+
+ align:start position:0%
+the first one um what we're really
+ 
+
+ align:start position:0%
+the first one um what we're really
+trying to we we're asked to to calculate
+
+ align:start position:0%
+trying to we we're asked to to calculate
+ 
+
+ align:start position:0%
+trying to we we're asked to to calculate
+the uh let's figure out the contact
+
+ align:start position:0%
+the uh let's figure out the contact
+ 
+
+ align:start position:0%
+the uh let's figure out the contact
+resistance so you're given the specific
+
+ align:start position:0%
+resistance so you're given the specific
+ 
+
+ align:start position:0%
+resistance so you're given the specific
+contact resistivity which we talked
+
+ align:start position:0%
+contact resistivity which we talked
+ 
+
+ align:start position:0%
+contact resistivity which we talked
+about in the last lecture as 2 and2 * 10
+
+ align:start position:0%
+about in the last lecture as 2 and2 * 10
+ 
+
+ align:start position:0%
+about in the last lecture as 2 and2 * 10
+the uh-
+
+ align:start position:0%
+the uh-
+ 
+
+ align:start position:0%
+the uh-
+7 10 Theus 7 and that has units of
+
+ align:start position:0%
+7 10 Theus 7 and that has units of
+ 
+
+ align:start position:0%
+7 10 Theus 7 and that has units of
+centimet squared
+
+ align:start position:0%
+centimet squared
+ 
+
+ align:start position:0%
+centimet squared
+right it's it's a resistance times an
+
+ align:start position:0%
+right it's it's a resistance times an
+ 
+
+ align:start position:0%
+right it's it's a resistance times an
+area and if I take that if I to get the
+
+ align:start position:0%
+area and if I take that if I to get the
+ 
+
+ align:start position:0%
+area and if I take that if I to get the
+contact resistance R of that contact I
+
+ align:start position:0%
+contact resistance R of that contact I
+ 
+
+ align:start position:0%
+contact resistance R of that contact I
+just have to take that row subs value
+
+ align:start position:0%
+just have to take that row subs value
+ 
+
+ align:start position:0%
+just have to take that row subs value
+and divide it by the area of the
+
+ align:start position:0%
+and divide it by the area of the
+ 
+
+ align:start position:0%
+and divide it by the area of the
+contact UM and you're told that the area
+
+ align:start position:0%
+contact UM and you're told that the area
+ 
+
+ align:start position:0%
+contact UM and you're told that the area
+of the contact in in number one there on
+
+ align:start position:0%
+of the contact in in number one there on
+ 
+
+ align:start position:0%
+of the contact in in number one there on
+the slide is 02 by one uh Square Micron
+
+ align:start position:0%
+the slide is 02 by one uh Square Micron
+ 
+
+ align:start position:0%
+the slide is 02 by one uh Square Micron
+so that's just going to be 2.5 * 10us
+
+ align:start position:0%
+so that's just going to be 2.5 * 10us
+ 
+
+ align:start position:0%
+so that's just going to be 2.5 * 10us
+7th over uh 0.25 so the numbers are easy
+
+ align:start position:0%
+7th over uh 0.25 so the numbers are easy
+ 
+
+ align:start position:0%
+7th over uh 0.25 so the numbers are easy
+um times 10 the minus 8 square cenm
+
+ align:start position:0%
+um times 10 the minus 8 square cenm
+ 
+
+ align:start position:0%
+um times 10 the minus 8 square cenm
+right because uh one micron is 10us 4 uh
+
+ align:start position:0%
+right because uh one micron is 10us 4 uh
+ 
+
+ align:start position:0%
+right because uh one micron is 10us 4 uh
+centimeters and you have to square
+
+ align:start position:0%
+centimeters and you have to square
+ 
+
+ align:start position:0%
+centimeters and you have to square
+that so I end up you just calculate this
+
+ align:start position:0%
+that so I end up you just calculate this
+ 
+
+ align:start position:0%
+that so I end up you just calculate this
+out and you end up with
+
+ align:start position:0%
+out and you end up with
+ 
+
+ align:start position:0%
+out and you end up with
+100 100 ohms for the contact resistance
+
+ align:start position:0%
+100 100 ohms for the contact resistance
+ 
+
+ align:start position:0%
+100 100 ohms for the contact resistance
+that's so that's the resistance between
+
+ align:start position:0%
+that's so that's the resistance between
+ 
+
+ align:start position:0%
+that's so that's the resistance between
+the metal and this contact right here
+
+ align:start position:0%
+the metal and this contact right here
+ 
+
+ align:start position:0%
+the metal and this contact right here
+flowing through this face uh given a
+
+ align:start position:0%
+flowing through this face uh given a
+ 
+
+ align:start position:0%
+flowing through this face uh given a
+contact area of that size uh so that'd
+
+ align:start position:0%
+contact area of that size uh so that'd
+ 
+
+ align:start position:0%
+contact area of that size uh so that'd
+be sort of kind of the state-of-the-art
+
+ align:start position:0%
+be sort of kind of the state-of-the-art
+ 
+
+ align:start position:0%
+be sort of kind of the state-of-the-art
+contact so you have about 100 ohms
+
+ align:start position:0%
+contact so you have about 100 ohms
+ 
+
+ align:start position:0%
+contact so you have about 100 ohms
+associated with
+
+ align:start position:0%
+associated with
+ 
+
+ align:start position:0%
+associated with
+that you also want to calculate the
+
+ align:start position:0%
+that you also want to calculate the
+ 
+
+ align:start position:0%
+that you also want to calculate the
+resistor shown here by this little
+
+ align:start position:0%
+resistor shown here by this little
+ 
+
+ align:start position:0%
+resistor shown here by this little
+resistor here estimate what this
+
+ align:start position:0%
+resistor here estimate what this
+ 
+
+ align:start position:0%
+resistor here estimate what this
+resistor is for the current flowing from
+
+ align:start position:0%
+resistor is for the current flowing from
+ 
+
+ align:start position:0%
+resistor is for the current flowing from
+this point to the point where it get it
+
+ align:start position:0%
+this point to the point where it get it
+ 
+
+ align:start position:0%
+this point to the point where it get it
+just gets into the
+
+ align:start position:0%
+just gets into the
+ 
+
+ align:start position:0%
+just gets into the
+contact well that's going to be
+
+ align:start position:0%
+contact well that's going to be
+ 
+
+ align:start position:0%
+contact well that's going to be
+dominated by the sheet resistance of the
+
+ align:start position:0%
+dominated by the sheet resistance of the
+ 
+
+ align:start position:0%
+dominated by the sheet resistance of the
+pilicide of this blue region right so if
+
+ align:start position:0%
+pilicide of this blue region right so if
+ 
+
+ align:start position:0%
+pilicide of this blue region right so if
+we know the sheet resistance and we
+
+ align:start position:0%
+we know the sheet resistance and we
+ 
+
+ align:start position:0%
+we know the sheet resistance and we
+divide by the thickness we can we can
+
+ align:start position:0%
+divide by the thickness we can we can
+ 
+
+ align:start position:0%
+divide by the thickness we can we can
+calculate for any sheet you can always
+
+ align:start position:0%
+calculate for any sheet you can always
+ 
+
+ align:start position:0%
+calculate for any sheet you can always
+calculate um the the resistance so to
+
+ align:start position:0%
+calculate um the the resistance so to
+ 
+
+ align:start position:0%
+calculate um the the resistance so to
+get the sheet resistance of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pilicide well you're given its
+
+ align:start position:0%
+pilicide well you're given its
+ 
+
+ align:start position:0%
+pilicide well you're given its
+resistivity it's 15 * 10- 6 ohm
+
+ align:start position:0%
+resistivity it's 15 * 10- 6 ohm
+ 
+
+ align:start position:0%
+resistivity it's 15 * 10- 6 ohm
+centimeter so it's just going to be its
+
+ align:start position:0%
+centimeter so it's just going to be its
+ 
+
+ align:start position:0%
+centimeter so it's just going to be its
+resistivity row divided by the thickness
+
+ align:start position:0%
+resistivity row divided by the thickness
+ 
+
+ align:start position:0%
+resistivity row divided by the thickness
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+sheet so that's 15 * 10us 6 ohm
+
+ align:start position:0%
+sheet so that's 15 * 10us 6 ohm
+ 
+
+ align:start position:0%
+sheet so that's 15 * 10us 6 ohm
+centimeter remember that's a resistivity
+
+ align:start position:0%
+centimeter remember that's a resistivity
+ 
+
+ align:start position:0%
+centimeter remember that's a resistivity
+now it's not a specific contact
+
+ align:start position:0%
+now it's not a specific contact
+ 
+
+ align:start position:0%
+now it's not a specific contact
+resistance and you are told the
+
+ align:start position:0%
+resistance and you are told the
+ 
+
+ align:start position:0%
+resistance and you are told the
+thickness of that sheet roughly and I'm
+
+ align:start position:0%
+thickness of that sheet roughly and I'm
+ 
+
+ align:start position:0%
+thickness of that sheet roughly and I'm
+going to ignore the doped region down
+
+ align:start position:0%
+going to ignore the doped region down
+ 
+
+ align:start position:0%
+going to ignore the doped region down
+here because this is a metal it's a
+
+ align:start position:0%
+here because this is a metal it's a
+ 
+
+ align:start position:0%
+here because this is a metal it's a
+silicide it has a much lower resistance
+
+ align:start position:0%
+silicide it has a much lower resistance
+ 
+
+ align:start position:0%
+silicide it has a much lower resistance
+than the Silicon so I'm going to ignore
+
+ align:start position:0%
+than the Silicon so I'm going to ignore
+ 
+
+ align:start position:0%
+than the Silicon so I'm going to ignore
+that we're just going to calculate the
+
+ align:start position:0%
+that we're just going to calculate the
+ 
+
+ align:start position:0%
+that we're just going to calculate the
+resistivity of that metal
+
+ align:start position:0%
+resistivity of that metal
+ 
+
+ align:start position:0%
+resistivity of that metal
+sheet and that thickness is 4 * 10us
+
+ align:start position:0%
+sheet and that thickness is 4 * 10us
+ 
+
+ align:start position:0%
+sheet and that thickness is 4 * 10us
+6 cm so the centimeters go out and you
+
+ align:start position:0%
+6 cm so the centimeters go out and you
+ 
+
+ align:start position:0%
+6 cm so the centimeters go out and you
+end up with a certain resistance about
+
+ align:start position:0%
+end up with a certain resistance about
+ 
+
+ align:start position:0%
+end up with a certain resistance about
+3.75 ohms per square remember that's a
+
+ align:start position:0%
+3.75 ohms per square remember that's a
+ 
+
+ align:start position:0%
+3.75 ohms per square remember that's a
+sheet resistance so that's an ohms per
+
+ align:start position:0%
+sheet resistance so that's an ohms per
+ 
+
+ align:start position:0%
+sheet resistance so that's an ohms per
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+sheet as for a current flowing through a
+
+ align:start position:0%
+sheet as for a current flowing through a
+ 
+
+ align:start position:0%
+sheet as for a current flowing through a
+sheet we talked about this uh that is a
+
+ align:start position:0%
+sheet we talked about this uh that is a
+ 
+
+ align:start position:0%
+sheet we talked about this uh that is a
+square so going in this face coming out
+
+ align:start position:0%
+square so going in this face coming out
+ 
+
+ align:start position:0%
+square so going in this face coming out
+that face where this length and this
+
+ align:start position:0%
+that face where this length and this
+ 
+
+ align:start position:0%
+that face where this length and this
+width are equal that's the definition of
+
+ align:start position:0%
+width are equal that's the definition of
+ 
+
+ align:start position:0%
+width are equal that's the definition of
+the sheet resistance so it's about about
+
+ align:start position:0%
+the sheet resistance so it's about about
+ 
+
+ align:start position:0%
+the sheet resistance so it's about about
+four ohms per square something like
+
+ align:start position:0%
+four ohms per square something like
+ 
+
+ align:start position:0%
+four ohms per square something like
+that then we need to know once you know
+
+ align:start position:0%
+that then we need to know once you know
+ 
+
+ align:start position:0%
+that then we need to know once you know
+the sheet resistance the nice thing
+
+ align:start position:0%
+the sheet resistance the nice thing
+ 
+
+ align:start position:0%
+the sheet resistance the nice thing
+about once you know the sheet resistance
+
+ align:start position:0%
+about once you know the sheet resistance
+ 
+
+ align:start position:0%
+about once you know the sheet resistance
+that tells you the resistance going
+
+ align:start position:0%
+that tells you the resistance going
+ 
+
+ align:start position:0%
+that tells you the resistance going
+through a square you just use geometry
+
+ align:start position:0%
+through a square you just use geometry
+ 
+
+ align:start position:0%
+through a square you just use geometry
+considerations how many squares does the
+
+ align:start position:0%
+considerations how many squares does the
+ 
+
+ align:start position:0%
+considerations how many squares does the
+current go through and flowing from this
+
+ align:start position:0%
+current go through and flowing from this
+ 
+
+ align:start position:0%
+current go through and flowing from this
+point here to the
+
+ align:start position:0%
+point here to the
+ 
+
+ align:start position:0%
+point here to the
+contact well it's a half Micron wall and
+
+ align:start position:0%
+contact well it's a half Micron wall and
+ 
+
+ align:start position:0%
+contact well it's a half Micron wall and
+it's a micron into the page so that's a
+
+ align:start position:0%
+it's a micron into the page so that's a
+ 
+
+ align:start position:0%
+it's a micron into the page so that's a
+half a
+
+ align:start position:0%
+half a
+ 
+
+ align:start position:0%
+half a
+square basically so because it because
+
+ align:start position:0%
+square basically so because it because
+ 
+
+ align:start position:0%
+square basically so because it because
+it it's it looks something like this
+
+ align:start position:0%
+it it's it looks something like this
+ 
+
+ align:start position:0%
+it it's it looks something like this
+it's a half Micron Mo but it goes a
+
+ align:start position:0%
+it's a half Micron Mo but it goes a
+ 
+
+ align:start position:0%
+it's a half Micron Mo but it goes a
+micron into the board into the page so
+
+ align:start position:0%
+micron into the board into the page so
+ 
+
+ align:start position:0%
+micron into the board into the page so
+this is 0 five and this is one so by
+
+ align:start position:0%
+this is 0 five and this is one so by
+ 
+
+ align:start position:0%
+this is 0 five and this is one so by
+definition that's half a square because
+
+ align:start position:0%
+definition that's half a square because
+ 
+
+ align:start position:0%
+definition that's half a square because
+if it were a full Square there'd be two
+
+ align:start position:0%
+if it were a full Square there'd be two
+ 
+
+ align:start position:0%
+if it were a full Square there'd be two
+of these right next to each other so so
+
+ align:start position:0%
+of these right next to each other so so
+ 
+
+ align:start position:0%
+of these right next to each other so so
+then you can just get the resistance of
+
+ align:start position:0%
+then you can just get the resistance of
+ 
+
+ align:start position:0%
+then you can just get the resistance of
+the pilicide
+
+ align:start position:0%
+the pilicide
+ 
+
+ align:start position:0%
+the pilicide
+to be uh 3.8 ohms per square times a
+
+ align:start position:0%
+to be uh 3.8 ohms per square times a
+ 
+
+ align:start position:0%
+to be uh 3.8 ohms per square times a
+half a
+
+ align:start position:0%
+half a
+ 
+
+ align:start position:0%
+half a
+square and you end up with uh about uh
+
+ align:start position:0%
+square and you end up with uh about uh
+ 
+
+ align:start position:0%
+square and you end up with uh about uh
+1.9 ohms very small comparatively
+
+ align:start position:0%
+1.9 ohms very small comparatively
+ 
+
+ align:start position:0%
+1.9 ohms very small comparatively
+speaking couple Waters of magnitude
+
+ align:start position:0%
+speaking couple Waters of magnitude
+ 
+
+ align:start position:0%
+speaking couple Waters of magnitude
+maybe Factor 50 less than than the
+
+ align:start position:0%
+maybe Factor 50 less than than the
+ 
+
+ align:start position:0%
+maybe Factor 50 less than than the
+contact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistance okay so that seems reasonable
+
+ align:start position:0%
+resistance okay so that seems reasonable
+ 
+
+ align:start position:0%
+resistance okay so that seems reasonable
+and then uh because it's a metal and and
+
+ align:start position:0%
+and then uh because it's a metal and and
+ 
+
+ align:start position:0%
+and then uh because it's a metal and and
+and there uh so it has a very low sheet
+
+ align:start position:0%
+and there uh so it has a very low sheet
+ 
+
+ align:start position:0%
+and there uh so it has a very low sheet
+is this so the resistance is
+
+ align:start position:0%
+is this so the resistance is
+ 
+
+ align:start position:0%
+is this so the resistance is
+small so on the final one number three
+
+ align:start position:0%
+small so on the final one number three
+ 
+
+ align:start position:0%
+small so on the final one number three
+which you're
+
+ align:start position:0%
+which you're
+ 
+
+ align:start position:0%
+which you're
+asked now we're going to be
+
+ align:start position:0%
+asked now we're going to be
+ 
+
+ align:start position:0%
+asked now we're going to be
+calculating the source Trin extension
+
+ align:start position:0%
+calculating the source Trin extension
+ 
+
+ align:start position:0%
+calculating the source Trin extension
+resistance so what's the resistance
+
+ align:start position:0%
+resistance so what's the resistance
+ 
+
+ align:start position:0%
+resistance so what's the resistance
+associated with this very thin uh this
+
+ align:start position:0%
+associated with this very thin uh this
+ 
+
+ align:start position:0%
+associated with this very thin uh this
+very shallow Junction depth XJ so this
+
+ align:start position:0%
+very shallow Junction depth XJ so this
+ 
+
+ align:start position:0%
+very shallow Junction depth XJ so this
+little resistor right here so the
+
+ align:start position:0%
+little resistor right here so the
+ 
+
+ align:start position:0%
+little resistor right here so the
+current comes out of the channel has to
+
+ align:start position:0%
+current comes out of the channel has to
+ 
+
+ align:start position:0%
+current comes out of the channel has to
+flow in that sour Trin extension before
+
+ align:start position:0%
+flow in that sour Trin extension before
+ 
+
+ align:start position:0%
+flow in that sour Trin extension before
+it hits the
+
+ align:start position:0%
+it hits the
+ 
+
+ align:start position:0%
+it hits the
+suicide well again that's a very similar
+
+ align:start position:0%
+suicide well again that's a very similar
+ 
+
+ align:start position:0%
+suicide well again that's a very similar
+situation where we just need to C
+
+ align:start position:0%
+situation where we just need to C
+ 
+
+ align:start position:0%
+situation where we just need to C
+calculate a sheet resistance and from
+
+ align:start position:0%
+calculate a sheet resistance and from
+ 
+
+ align:start position:0%
+calculate a sheet resistance and from
+sheet resistance we figure out the
+
+ align:start position:0%
+sheet resistance we figure out the
+ 
+
+ align:start position:0%
+sheet resistance we figure out the
+number of squares from the geometry and
+
+ align:start position:0%
+number of squares from the geometry and
+ 
+
+ align:start position:0%
+number of squares from the geometry and
+we get the resistance so again so for
+
+ align:start position:0%
+we get the resistance so again so for
+ 
+
+ align:start position:0%
+we get the resistance so again so for
+the source drain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extension for that region we're given uh
+
+ align:start position:0%
+extension for that region we're given uh
+ 
+
+ align:start position:0%
+extension for that region we're given uh
+we're told the resistivity row is 5 *
+
+ align:start position:0%
+we're told the resistivity row is 5 *
+ 
+
+ align:start position:0%
+we're told the resistivity row is 5 *
+10us 4 ohm cimer and um we have uh we
+
+ align:start position:0%
+10us 4 ohm cimer and um we have uh we
+ 
+
+ align:start position:0%
+10us 4 ohm cimer and um we have uh we
+know the number of squares and we have a
+
+ align:start position:0%
+know the number of squares and we have a
+ 
+
+ align:start position:0%
+know the number of squares and we have a
+thickness of that region
+
+ align:start position:0%
+thickness of that region
+ 
+
+ align:start position:0%
+thickness of that region
+so I can get the uh sheet
+
+ align:start position:0%
+so I can get the uh sheet
+ 
+
+ align:start position:0%
+so I can get the uh sheet
+resistance again it's just the
+
+ align:start position:0%
+resistance again it's just the
+ 
+
+ align:start position:0%
+resistance again it's just the
+resistivity divided by the thickness of
+
+ align:start position:0%
+resistivity divided by the thickness of
+ 
+
+ align:start position:0%
+resistivity divided by the thickness of
+the region so that's 5 * 10us
+
+ align:start position:0%
+the region so that's 5 * 10us
+ 
+
+ align:start position:0%
+the region so that's 5 * 10us
+4 cimer / by I think it was an easy
+
+ align:start position:0%
+4 cimer / by I think it was an easy
+ 
+
+ align:start position:0%
+4 cimer / by I think it was an easy
+number 500 uh anging so that's 5 * 10us
+
+ align:start position:0%
+number 500 uh anging so that's 5 * 10us
+ 
+
+ align:start position:0%
+number 500 uh anging so that's 5 * 10us
+6 cm and that goes out and we end up
+
+ align:start position:0%
+6 cm and that goes out and we end up
+ 
+
+ align:start position:0%
+6 cm and that goes out and we end up
+with uh about 100 ohms per
+
+ align:start position:0%
+with uh about 100 ohms per
+ 
+
+ align:start position:0%
+with uh about 100 ohms per
+square that's a typical shallow Junction
+
+ align:start position:0%
+square that's a typical shallow Junction
+ 
+
+ align:start position:0%
+square that's a typical shallow Junction
+for a shallow Junction uh shallow being
+
+ align:start position:0%
+for a shallow Junction uh shallow being
+ 
+
+ align:start position:0%
+for a shallow Junction uh shallow being
+500 angstroms or less uh you dop it very
+
+ align:start position:0%
+500 angstroms or less uh you dop it very
+ 
+
+ align:start position:0%
+500 angstroms or less uh you dop it very
+heavily we said this is dope 2 10 the 20
+
+ align:start position:0%
+heavily we said this is dope 2 10 the 20
+ 
+
+ align:start position:0%
+heavily we said this is dope 2 10 the 20
+with r Snick or whatever and it's about
+
+ align:start position:0%
+with r Snick or whatever and it's about
+ 
+
+ align:start position:0%
+with r Snick or whatever and it's about
+100 ohms per
+
+ align:start position:0%
+100 ohms per
+ 
+
+ align:start position:0%
+100 ohms per
+square as the sheet resistance now again
+
+ align:start position:0%
+square as the sheet resistance now again
+ 
+
+ align:start position:0%
+square as the sheet resistance now again
+looking at this how many squares does
+
+ align:start position:0%
+looking at this how many squares does
+ 
+
+ align:start position:0%
+looking at this how many squares does
+this well the distance from this point
+
+ align:start position:0%
+this well the distance from this point
+ 
+
+ align:start position:0%
+this well the distance from this point
+in the channel to the point where it
+
+ align:start position:0%
+in the channel to the point where it
+ 
+
+ align:start position:0%
+in the channel to the point where it
+contacts a suicide that we're told that
+
+ align:start position:0%
+contacts a suicide that we're told that
+ 
+
+ align:start position:0%
+contacts a suicide that we're told that
+space or width is point one microns so
+
+ align:start position:0%
+space or width is point one microns so
+ 
+
+ align:start position:0%
+space or width is point one microns so
+that's 0.1 and into the board is one
+
+ align:start position:0%
+that's 0.1 and into the board is one
+ 
+
+ align:start position:0%
+that's 0.1 and into the board is one
+again so that's a tenth of a square
+
+ align:start position:0%
+again so that's a tenth of a square
+ 
+
+ align:start position:0%
+again so that's a tenth of a square
+so then we can just get the resistance
+
+ align:start position:0%
+so then we can just get the resistance
+ 
+
+ align:start position:0%
+so then we can just get the resistance
+of the source drain
+
+ align:start position:0%
+of the source drain
+ 
+
+ align:start position:0%
+of the source drain
+extension then is just the sheet
+
+ align:start position:0%
+extension then is just the sheet
+ 
+
+ align:start position:0%
+extension then is just the sheet
+resistance times the number of
+
+ align:start position:0%
+resistance times the number of
+ 
+
+ align:start position:0%
+resistance times the number of
+squares so that's 100 ohms per square
+
+ align:start position:0%
+squares so that's 100 ohms per square
+ 
+
+ align:start position:0%
+squares so that's 100 ohms per square
+time 0.1
+
+ align:start position:0%
+time 0.1
+ 
+
+ align:start position:0%
+time 0.1
+squares and then we end up with 10
+
+ align:start position:0%
+squares and then we end up with 10
+ 
+
+ align:start position:0%
+squares and then we end up with 10
+ohms so that resistors roughly I mean
+
+ align:start position:0%
+ohms so that resistors roughly I mean
+ 
+
+ align:start position:0%
+ohms so that resistors roughly I mean
+it's this is a very crude estimate that
+
+ align:start position:0%
+it's this is a very crude estimate that
+ 
+
+ align:start position:0%
+it's this is a very crude estimate that
+that resistor here so this this resistor
+
+ align:start position:0%
+that resistor here so this this resistor
+ 
+
+ align:start position:0%
+that resistor here so this this resistor
+here is about 10 ohms this little sheet
+
+ align:start position:0%
+here is about 10 ohms this little sheet
+ 
+
+ align:start position:0%
+here is about 10 ohms this little sheet
+here represents so about a couple of
+
+ align:start position:0%
+here represents so about a couple of
+ 
+
+ align:start position:0%
+here represents so about a couple of
+ohms the big resistance is is what the
+
+ align:start position:0%
+ohms the big resistance is is what the
+ 
+
+ align:start position:0%
+ohms the big resistance is is what the
+big resistance is the 100 ohms it's the
+
+ align:start position:0%
+big resistance is the 100 ohms it's the
+ 
+
+ align:start position:0%
+big resistance is the 100 ohms it's the
+contact resistance because we have uh a
+
+ align:start position:0%
+contact resistance because we have uh a
+ 
+
+ align:start position:0%
+contact resistance because we have uh a
+finite specific contact resistivity 2
+
+ align:start position:0%
+finite specific contact resistivity 2
+ 
+
+ align:start position:0%
+finite specific contact resistivity 2
+half * 10- 7 ohm cenm squar and we're
+
+ align:start position:0%
+half * 10- 7 ohm cenm squar and we're
+ 
+
+ align:start position:0%
+half * 10- 7 ohm cenm squar and we're
+trying to make contact in a very small
+
+ align:start position:0%
+trying to make contact in a very small
+ 
+
+ align:start position:0%
+trying to make contact in a very small
+area so what's the solution well I can
+
+ align:start position:0%
+area so what's the solution well I can
+ 
+
+ align:start position:0%
+area so what's the solution well I can
+make the area bigger make the devices
+
+ align:start position:0%
+make the area bigger make the devices
+ 
+
+ align:start position:0%
+make the area bigger make the devices
+bigger on the chip I get fewer devices
+
+ align:start position:0%
+bigger on the chip I get fewer devices
+ 
+
+ align:start position:0%
+bigger on the chip I get fewer devices
+that's not good or we have to scale this
+
+ align:start position:0%
+that's not good or we have to scale this
+ 
+
+ align:start position:0%
+that's not good or we have to scale this
+number according to the HRS remember
+
+ align:start position:0%
+number according to the HRS remember
+ 
+
+ align:start position:0%
+number according to the HRS remember
+this number is going to have to go down
+
+ align:start position:0%
+this number is going to have to go down
+ 
+
+ align:start position:0%
+this number is going to have to go down
+in in in 2003 TRS wants this number to
+
+ align:start position:0%
+in in in 2003 TRS wants this number to
+ 
+
+ align:start position:0%
+in in in 2003 TRS wants this number to
+be about 2 * 10us 7 um so it's already
+
+ align:start position:0%
+be about 2 * 10us 7 um so it's already
+ 
+
+ align:start position:0%
+be about 2 * 10us 7 um so it's already
+supposed to be lower than that and over
+
+ align:start position:0%
+supposed to be lower than that and over
+ 
+
+ align:start position:0%
+supposed to be lower than that and over
+the next 10 years it's supposed to be
+
+ align:start position:0%
+the next 10 years it's supposed to be
+ 
+
+ align:start position:0%
+the next 10 years it's supposed to be
+lowered by a factor of three or four um
+
+ align:start position:0%
+lowered by a factor of three or four um
+ 
+
+ align:start position:0%
+lowered by a factor of three or four um
+so that this this number of 100 ohms
+
+ align:start position:0%
+so that this this number of 100 ohms
+ 
+
+ align:start position:0%
+so that this this number of 100 ohms
+gets lower or doesn't certainly does not
+
+ align:start position:0%
+gets lower or doesn't certainly does not
+ 
+
+ align:start position:0%
+gets lower or doesn't certainly does not
+increase as we scale the devices but
+
+ align:start position:0%
+increase as we scale the devices but
+ 
+
+ align:start position:0%
+increase as we scale the devices but
+just kind of gives you a rough idea of
+
+ align:start position:0%
+just kind of gives you a rough idea of
+ 
+
+ align:start position:0%
+just kind of gives you a rough idea of
+what the big contributions are um if you
+
+ align:start position:0%
+what the big contributions are um if you
+ 
+
+ align:start position:0%
+what the big contributions are um if you
+do it right again if if you didn't get
+
+ align:start position:0%
+do it right again if if you didn't get
+ 
+
+ align:start position:0%
+do it right again if if you didn't get
+enough doping in this shallow sour
+
+ align:start position:0%
+enough doping in this shallow sour
+ 
+
+ align:start position:0%
+enough doping in this shallow sour
+strand extension this 10 ohm number
+
+ align:start position:0%
+strand extension this 10 ohm number
+ 
+
+ align:start position:0%
+strand extension this 10 ohm number
+could go up depending on your your
+
+ align:start position:0%
+could go up depending on your your
+ 
+
+ align:start position:0%
+could go up depending on your your
+Junction depth how you scale that and
+
+ align:start position:0%
+Junction depth how you scale that and
+ 
+
+ align:start position:0%
+Junction depth how you scale that and
+and you're you're doping but these are
+
+ align:start position:0%
+and you're you're doping but these are
+ 
+
+ align:start position:0%
+and you're you're doping but these are
+these are simple calculations you can do
+
+ align:start position:0%
+these are simple calculations you can do
+ 
+
+ align:start position:0%
+these are simple calculations you can do
+sort of back of the envelope and and we
+
+ align:start position:0%
+sort of back of the envelope and and we
+ 
+
+ align:start position:0%
+sort of back of the envelope and and we
+didn't get to go through that last time
+
+ align:start position:0%
+didn't get to go through that last time
+ 
+
+ align:start position:0%
+didn't get to go through that last time
+we presented it but this gives you an
+
+ align:start position:0%
+we presented it but this gives you an
+ 
+
+ align:start position:0%
+we presented it but this gives you an
+idea of kind of how those numbers work
+
+ align:start position:0%
+idea of kind of how those numbers work
+ 
+
+ align:start position:0%
+idea of kind of how those numbers work
+out any any questions on that or on the
+
+ align:start position:0%
+out any any questions on that or on the
+ 
+
+ align:start position:0%
+out any any questions on that or on the
+contact we we only spent one lecture on
+
+ align:start position:0%
+contact we we only spent one lecture on
+ 
+
+ align:start position:0%
+contact we we only spent one lecture on
+contact so uh there's a little bit of
+
+ align:start position:0%
+contact so uh there's a little bit of
+ 
+
+ align:start position:0%
+contact so uh there's a little bit of
+this in uh in chapter 11 although I
+
+ align:start position:0%
+this in uh in chapter 11 although I
+ 
+
+ align:start position:0%
+this in uh in chapter 11 although I
+don't think there's some some a specific
+
+ align:start position:0%
+don't think there's some some a specific
+ 
+
+ align:start position:0%
+don't think there's some some a specific
+example of a moset like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay so let's go on then to um
+
+ align:start position:0%
+this okay so let's go on then to um
+ 
+
+ align:start position:0%
+this okay so let's go on then to um
+today's uh actual material which is um
+
+ align:start position:0%
+today's uh actual material which is um
+ 
+
+ align:start position:0%
+today's uh actual material which is um
+going to be um a little bit of a
+
+ align:start position:0%
+going to be um a little bit of a
+ 
+
+ align:start position:0%
+going to be um a little bit of a
+Divergence to a certain extent from the
+
+ align:start position:0%
+Divergence to a certain extent from the
+ 
+
+ align:start position:0%
+Divergence to a certain extent from the
+uh the other lectures this material is
+
+ align:start position:0%
+uh the other lectures this material is
+ 
+
+ align:start position:0%
+uh the other lectures this material is
+not in the text this is all sort of um
+
+ align:start position:0%
+not in the text this is all sort of um
+ 
+
+ align:start position:0%
+not in the text this is all sort of um
+uh more kind of uh upto-date sort of
+
+ align:start position:0%
+uh more kind of uh upto-date sort of
+ 
+
+ align:start position:0%
+uh more kind of uh upto-date sort of
+research material that that's come out
+
+ align:start position:0%
+research material that that's come out
+ 
+
+ align:start position:0%
+research material that that's come out
+and has yet not yet been put into a
+
+ align:start position:0%
+and has yet not yet been put into a
+ 
+
+ align:start position:0%
+and has yet not yet been put into a
+textbook but you have the
+
+ align:start position:0%
+textbook but you have the
+ 
+
+ align:start position:0%
+textbook but you have the
+handouts um so what I want to talk about
+
+ align:start position:0%
+handouts um so what I want to talk about
+ 
+
+ align:start position:0%
+handouts um so what I want to talk about
+well what we've talked about so far for
+
+ align:start position:0%
+well what we've talked about so far for
+ 
+
+ align:start position:0%
+well what we've talked about so far for
+semiconductors is just using pure
+
+ align:start position:0%
+semiconductors is just using pure
+ 
+
+ align:start position:0%
+semiconductors is just using pure
+silicon pure pure silicon Wafers uh and
+
+ align:start position:0%
+silicon pure pure silicon Wafers uh and
+ 
+
+ align:start position:0%
+silicon pure pure silicon Wafers uh and
+pure silicon materials to make uh sea
+
+ align:start position:0%
+pure silicon materials to make uh sea
+ 
+
+ align:start position:0%
+pure silicon materials to make uh sea
+moss to make uh Moss fets um it turns
+
+ align:start position:0%
+moss to make uh Moss fets um it turns
+ 
+
+ align:start position:0%
+moss to make uh Moss fets um it turns
+out if we use epitaxial growth we did
+
+ align:start position:0%
+out if we use epitaxial growth we did
+ 
+
+ align:start position:0%
+out if we use epitaxial growth we did
+spend a little time talking about
+
+ align:start position:0%
+spend a little time talking about
+ 
+
+ align:start position:0%
+spend a little time talking about
+epitaxial growth of silicon by by CBD or
+
+ align:start position:0%
+epitaxial growth of silicon by by CBD or
+ 
+
+ align:start position:0%
+epitaxial growth of silicon by by CBD or
+or some similar technique if we use
+
+ align:start position:0%
+or some similar technique if we use
+ 
+
+ align:start position:0%
+or some similar technique if we use
+epaxal growth you can mix in small
+
+ align:start position:0%
+epaxal growth you can mix in small
+ 
+
+ align:start position:0%
+epaxal growth you can mix in small
+amounts of germanium into the Silicon
+
+ align:start position:0%
+amounts of germanium into the Silicon
+ 
+
+ align:start position:0%
+amounts of germanium into the Silicon
+material and make an alloy called
+
+ align:start position:0%
+material and make an alloy called
+ 
+
+ align:start position:0%
+material and make an alloy called
+silicon germanium or you can mix in even
+
+ align:start position:0%
+silicon germanium or you can mix in even
+ 
+
+ align:start position:0%
+silicon germanium or you can mix in even
+small amount even smaller amounts of
+
+ align:start position:0%
+small amount even smaller amounts of
+ 
+
+ align:start position:0%
+small amount even smaller amounts of
+carbon maybe 1% or so and make an alloy
+
+ align:start position:0%
+carbon maybe 1% or so and make an alloy
+ 
+
+ align:start position:0%
+carbon maybe 1% or so and make an alloy
+of the silicon and car carbon and people
+
+ align:start position:0%
+of the silicon and car carbon and people
+ 
+
+ align:start position:0%
+of the silicon and car carbon and people
+are doing this and some of these Alloys
+
+ align:start position:0%
+are doing this and some of these Alloys
+ 
+
+ align:start position:0%
+are doing this and some of these Alloys
+are used today in modern production
+
+ align:start position:0%
+are used today in modern production
+ 
+
+ align:start position:0%
+are used today in modern production
+devices and Manufacturing so I just
+
+ align:start position:0%
+devices and Manufacturing so I just
+ 
+
+ align:start position:0%
+devices and Manufacturing so I just
+wanted to go through some of the
+
+ align:start position:0%
+wanted to go through some of the
+ 
+
+ align:start position:0%
+wanted to go through some of the
+important material electronic properties
+
+ align:start position:0%
+important material electronic properties
+ 
+
+ align:start position:0%
+important material electronic properties
+of these newer
+
+ align:start position:0%
+of these newer
+ 
+
+ align:start position:0%
+of these newer
+semiconductors uh and how how the layers
+
+ align:start position:0%
+semiconductors uh and how how the layers
+ 
+
+ align:start position:0%
+semiconductors uh and how how the layers
+are processed to a certain extent and
+
+ align:start position:0%
+are processed to a certain extent and
+ 
+
+ align:start position:0%
+are processed to a certain extent and
+and what's some of the issues in
+
+ align:start position:0%
+and what's some of the issues in
+ 
+
+ align:start position:0%
+and what's some of the issues in
+research and development that that
+
+ align:start position:0%
+research and development that that
+ 
+
+ align:start position:0%
+research and development that that
+people are
+
+ align:start position:0%
+people are
+ 
+
+ align:start position:0%
+people are
+considering so here on slide two uh what
+
+ align:start position:0%
+considering so here on slide two uh what
+ 
+
+ align:start position:0%
+considering so here on slide two uh what
+I'm showing are some applications of
+
+ align:start position:0%
+I'm showing are some applications of
+ 
+
+ align:start position:0%
+I'm showing are some applications of
+these Alloys these silicon tranium
+
+ align:start position:0%
+these Alloys these silicon tranium
+ 
+
+ align:start position:0%
+these Alloys these silicon tranium
+Alloys and sort of related material like
+
+ align:start position:0%
+Alloys and sort of related material like
+ 
+
+ align:start position:0%
+Alloys and sort of related material like
+Silicon geranium carbon um the first
+
+ align:start position:0%
+Silicon geranium carbon um the first
+ 
+
+ align:start position:0%
+Silicon geranium carbon um the first
+bullet is for a number of time a number
+
+ align:start position:0%
+bullet is for a number of time a number
+ 
+
+ align:start position:0%
+bullet is for a number of time a number
+of years now maybe the last 10 years
+
+ align:start position:0%
+of years now maybe the last 10 years
+ 
+
+ align:start position:0%
+of years now maybe the last 10 years
+silicon germanium has been used in
+
+ align:start position:0%
+silicon germanium has been used in
+ 
+
+ align:start position:0%
+silicon germanium has been used in
+production as the base layer uh in a a
+
+ align:start position:0%
+production as the base layer uh in a a
+ 
+
+ align:start position:0%
+production as the base layer uh in a a
+heterojunction bipolar transistor in a
+
+ align:start position:0%
+heterojunction bipolar transistor in a
+ 
+
+ align:start position:0%
+heterojunction bipolar transistor in a
+bipolar transistor the base layer being
+
+ align:start position:0%
+bipolar transistor the base layer being
+ 
+
+ align:start position:0%
+bipolar transistor the base layer being
+quite thin we haven't talked much about
+
+ align:start position:0%
+quite thin we haven't talked much about
+ 
+
+ align:start position:0%
+quite thin we haven't talked much about
+bipolars in this class this class is
+
+ align:start position:0%
+bipolars in this class this class is
+ 
+
+ align:start position:0%
+bipolars in this class this class is
+mostly about seos making seos devices
+
+ align:start position:0%
+mostly about seos making seos devices
+ 
+
+ align:start position:0%
+mostly about seos making seos devices
+but um it's a thin layer a couple
+
+ align:start position:0%
+but um it's a thin layer a couple
+ 
+
+ align:start position:0%
+but um it's a thin layer a couple
+hundred Anum maybe 200 to 500 Anum thick
+
+ align:start position:0%
+hundred Anum maybe 200 to 500 Anum thick
+ 
+
+ align:start position:0%
+hundred Anum maybe 200 to 500 Anum thick
+this is used in high frequency analog
+
+ align:start position:0%
+this is used in high frequency analog
+ 
+
+ align:start position:0%
+this is used in high frequency analog
+applications generally
+
+ align:start position:0%
+applications generally
+ 
+
+ align:start position:0%
+applications generally
+telecommunications applications base
+
+ align:start position:0%
+telecommunications applications base
+ 
+
+ align:start position:0%
+telecommunications applications base
+stations and things like that and there
+
+ align:start position:0%
+stations and things like that and there
+ 
+
+ align:start position:0%
+stations and things like that and there
+are a number of companies uh maybe half
+
+ align:start position:0%
+are a number of companies uh maybe half
+ 
+
+ align:start position:0%
+are a number of companies uh maybe half
+a dozen or more that manufacture these
+
+ align:start position:0%
+a dozen or more that manufacture these
+ 
+
+ align:start position:0%
+a dozen or more that manufacture these
+and sell these devices um so this for
+
+ align:start position:0%
+and sell these devices um so this for
+ 
+
+ align:start position:0%
+and sell these devices um so this for
+the purpose of uh you know growing thin
+
+ align:start position:0%
+the purpose of uh you know growing thin
+ 
+
+ align:start position:0%
+the purpose of uh you know growing thin
+films this is something that has been
+
+ align:start position:0%
+films this is something that has been
+ 
+
+ align:start position:0%
+films this is something that has been
+done now in manufacturing for some time
+
+ align:start position:0%
+done now in manufacturing for some time
+ 
+
+ align:start position:0%
+done now in manufacturing for some time
+the second bullet refers to uh a little
+
+ align:start position:0%
+the second bullet refers to uh a little
+ 
+
+ align:start position:0%
+the second bullet refers to uh a little
+more uh more advanced type of material
+
+ align:start position:0%
+more uh more advanced type of material
+ 
+
+ align:start position:0%
+more uh more advanced type of material
+and that's just coming in to production
+
+ align:start position:0%
+and that's just coming in to production
+ 
+
+ align:start position:0%
+and that's just coming in to production
+now and these are um layers of relaxed
+
+ align:start position:0%
+now and these are um layers of relaxed
+ 
+
+ align:start position:0%
+now and these are um layers of relaxed
+silicon ger manum or strain silicon
+
+ align:start position:0%
+silicon ger manum or strain silicon
+ 
+
+ align:start position:0%
+silicon ger manum or strain silicon
+germanium I'll talk about what that
+
+ align:start position:0%
+germanium I'll talk about what that
+ 
+
+ align:start position:0%
+germanium I'll talk about what that
+means in in a little while that are used
+
+ align:start position:0%
+means in in a little while that are used
+ 
+
+ align:start position:0%
+means in in a little while that are used
+to induce strain and silicon so these
+
+ align:start position:0%
+to induce strain and silicon so these
+ 
+
+ align:start position:0%
+to induce strain and silicon so these
+layers are used to uh take silicon
+
+ align:start position:0%
+layers are used to uh take silicon
+ 
+
+ align:start position:0%
+layers are used to uh take silicon
+Channel and to either stretch it or
+
+ align:start position:0%
+Channel and to either stretch it or
+ 
+
+ align:start position:0%
+Channel and to either stretch it or
+compress it
+
+ align:start position:0%
+compress it
+ 
+
+ align:start position:0%
+compress it
+mechanically uh and by stretching and
+
+ align:start position:0%
+mechanically uh and by stretching and
+ 
+
+ align:start position:0%
+mechanically uh and by stretching and
+compressing the lce in the channel you
+
+ align:start position:0%
+compressing the lce in the channel you
+ 
+
+ align:start position:0%
+compressing the lce in the channel you
+can enhance the mobility as it turns out
+
+ align:start position:0%
+can enhance the mobility as it turns out
+ 
+
+ align:start position:0%
+can enhance the mobility as it turns out
+enhancing the mobility means you get a
+
+ align:start position:0%
+enhancing the mobility means you get a
+ 
+
+ align:start position:0%
+enhancing the mobility means you get a
+higher current drive for a given voltage
+
+ align:start position:0%
+higher current drive for a given voltage
+ 
+
+ align:start position:0%
+higher current drive for a given voltage
+so that so the devices will switch
+
+ align:start position:0%
+so that so the devices will switch
+ 
+
+ align:start position:0%
+so that so the devices will switch
+faster so uh for enhancing seamoss um
+
+ align:start position:0%
+faster so uh for enhancing seamoss um
+ 
+
+ align:start position:0%
+faster so uh for enhancing seamoss um
+these some of these materials are now in
+
+ align:start position:0%
+these some of these materials are now in
+ 
+
+ align:start position:0%
+these some of these materials are now in
+production Intel has a new Pentium
+
+ align:start position:0%
+production Intel has a new Pentium
+ 
+
+ align:start position:0%
+production Intel has a new Pentium
+that's uh that's in production using
+
+ align:start position:0%
+that's uh that's in production using
+ 
+
+ align:start position:0%
+that's uh that's in production using
+this this type of technique um these
+
+ align:start position:0%
+this this type of technique um these
+ 
+
+ align:start position:0%
+this this type of technique um these
+materials some sometimes silicon
+
+ align:start position:0%
+materials some sometimes silicon
+ 
+
+ align:start position:0%
+materials some sometimes silicon
+geranium can be used as a boron
+
+ align:start position:0%
+geranium can be used as a boron
+ 
+
+ align:start position:0%
+geranium can be used as a boron
+diffusion barrier uh we spent a lot of
+
+ align:start position:0%
+diffusion barrier uh we spent a lot of
+ 
+
+ align:start position:0%
+diffusion barrier uh we spent a lot of
+time in this class talking about the
+
+ align:start position:0%
+time in this class talking about the
+ 
+
+ align:start position:0%
+time in this class talking about the
+fact that Boron is a fast diffuser in
+
+ align:start position:0%
+fact that Boron is a fast diffuser in
+ 
+
+ align:start position:0%
+fact that Boron is a fast diffuser in
+Silicon that's one of the problems with
+
+ align:start position:0%
+Silicon that's one of the problems with
+ 
+
+ align:start position:0%
+Silicon that's one of the problems with
+making shallow Junctions well it turns
+
+ align:start position:0%
+making shallow Junctions well it turns
+ 
+
+ align:start position:0%
+making shallow Junctions well it turns
+out in silic and geranium for reasons
+
+ align:start position:0%
+out in silic and geranium for reasons
+ 
+
+ align:start position:0%
+out in silic and geranium for reasons
+that are not completely understood the
+
+ align:start position:0%
+that are not completely understood the
+ 
+
+ align:start position:0%
+that are not completely understood the
+more geranium you add the slower the
+
+ align:start position:0%
+more geranium you add the slower the
+ 
+
+ align:start position:0%
+more geranium you add the slower the
+Boron diffusion coefficient so if you
+
+ align:start position:0%
+Boron diffusion coefficient so if you
+ 
+
+ align:start position:0%
+Boron diffusion coefficient so if you
+put in 20% geranium the lattice the
+
+ align:start position:0%
+put in 20% geranium the lattice the
+ 
+
+ align:start position:0%
+put in 20% geranium the lattice the
+Boron diffusivity drops by about about a
+
+ align:start position:0%
+Boron diffusivity drops by about about a
+ 
+
+ align:start position:0%
+Boron diffusivity drops by about about a
+factor of 10 in Silicon geranium so
+
+ align:start position:0%
+factor of 10 in Silicon geranium so
+ 
+
+ align:start position:0%
+factor of 10 in Silicon geranium so
+that's a huge Factor um so people may
+
+ align:start position:0%
+that's a huge Factor um so people may
+ 
+
+ align:start position:0%
+that's a huge Factor um so people may
+want to use silicon geranium just as a
+
+ align:start position:0%
+want to use silicon geranium just as a
+ 
+
+ align:start position:0%
+want to use silicon geranium just as a
+means of slowing down B on diffusion uh
+
+ align:start position:0%
+means of slowing down B on diffusion uh
+ 
+
+ align:start position:0%
+means of slowing down B on diffusion uh
+it's used in micro Machining in Ms
+
+ align:start position:0%
+it's used in micro Machining in Ms
+ 
+
+ align:start position:0%
+it's used in micro Machining in Ms
+technology it happens to be an excellent
+
+ align:start position:0%
+technology it happens to be an excellent
+ 
+
+ align:start position:0%
+technology it happens to be an excellent
+Edge stop so there are uh etches wet
+
+ align:start position:0%
+Edge stop so there are uh etches wet
+ 
+
+ align:start position:0%
+Edge stop so there are uh etches wet
+chemical etches primarily wet maybe a
+
+ align:start position:0%
+chemical etches primarily wet maybe a
+ 
+
+ align:start position:0%
+chemical etches primarily wet maybe a
+few dry that uh etch that will stop on
+
+ align:start position:0%
+few dry that uh etch that will stop on
+ 
+
+ align:start position:0%
+few dry that uh etch that will stop on
+Silicon geranium and and and etch
+
+ align:start position:0%
+Silicon geranium and and and etch
+ 
+
+ align:start position:0%
+Silicon geranium and and and etch
+through a silicon a stop on silic
+
+ align:start position:0%
+through a silicon a stop on silic
+ 
+
+ align:start position:0%
+through a silicon a stop on silic
+tranium and vice versa so it can be used
+
+ align:start position:0%
+tranium and vice versa so it can be used
+ 
+
+ align:start position:0%
+tranium and vice versa so it can be used
+as a sort of an edge stop layer
+
+ align:start position:0%
+as a sort of an edge stop layer
+ 
+
+ align:start position:0%
+as a sort of an edge stop layer
+um some people are advocating using I
+
+ align:start position:0%
+um some people are advocating using I
+ 
+
+ align:start position:0%
+um some people are advocating using I
+don't think it's in production that I
+
+ align:start position:0%
+don't think it's in production that I
+ 
+
+ align:start position:0%
+don't think it's in production that I
+know of but poly Crystal and silicon
+
+ align:start position:0%
+know of but poly Crystal and silicon
+ 
+
+ align:start position:0%
+know of but poly Crystal and silicon
+geranium as the gate material people are
+
+ align:start position:0%
+geranium as the gate material people are
+ 
+
+ align:start position:0%
+geranium as the gate material people are
+we've talked in this class the last few
+
+ align:start position:0%
+we've talked in this class the last few
+ 
+
+ align:start position:0%
+we've talked in this class the last few
+lectures about metal gates before they
+
+ align:start position:0%
+lectures about metal gates before they
+ 
+
+ align:start position:0%
+lectures about metal gates before they
+get to metal gates people were
+
+ align:start position:0%
+get to metal gates people were
+ 
+
+ align:start position:0%
+get to metal gates people were
+advocating using uh poly Crystal and
+
+ align:start position:0%
+advocating using uh poly Crystal and
+ 
+
+ align:start position:0%
+advocating using uh poly Crystal and
+silen geranium instead of polycrystal
+
+ align:start position:0%
+silen geranium instead of polycrystal
+ 
+
+ align:start position:0%
+silen geranium instead of polycrystal
+and silicon uh I don't know if that
+
+ align:start position:0%
+and silicon uh I don't know if that
+ 
+
+ align:start position:0%
+and silicon uh I don't know if that
+again if that really is making it into
+
+ align:start position:0%
+again if that really is making it into
+ 
+
+ align:start position:0%
+again if that really is making it into
+production it so geranium is also used
+
+ align:start position:0%
+production it so geranium is also used
+ 
+
+ align:start position:0%
+production it so geranium is also used
+as an infrared photo detector material
+
+ align:start position:0%
+as an infrared photo detector material
+ 
+
+ align:start position:0%
+as an infrared photo detector material
+uh for integrating photage tectures with
+
+ align:start position:0%
+uh for integrating photage tectures with
+ 
+
+ align:start position:0%
+uh for integrating photage tectures with
+silicon
+
+ align:start position:0%
+silicon
+ 
+
+ align:start position:0%
+silicon
+seamless silicon ium carbon is in
+
+ align:start position:0%
+seamless silicon ium carbon is in
+ 
+
+ align:start position:0%
+seamless silicon ium carbon is in
+production now maybe not silicon carbon
+
+ align:start position:0%
+production now maybe not silicon carbon
+ 
+
+ align:start position:0%
+production now maybe not silicon carbon
+but silicon geranium carbon is in
+
+ align:start position:0%
+but silicon geranium carbon is in
+ 
+
+ align:start position:0%
+but silicon geranium carbon is in
+production with very small amounts of
+
+ align:start position:0%
+production with very small amounts of
+ 
+
+ align:start position:0%
+production with very small amounts of
+carbon maybe a half a percent uh as a
+
+ align:start position:0%
+carbon maybe a half a percent uh as a
+ 
+
+ align:start position:0%
+carbon maybe a half a percent uh as a
+way of suppressing Transit enhanced
+
+ align:start position:0%
+way of suppressing Transit enhanced
+ 
+
+ align:start position:0%
+way of suppressing Transit enhanced
+diffusion uh in in in heterog Junction
+
+ align:start position:0%
+diffusion uh in in in heterog Junction
+ 
+
+ align:start position:0%
+diffusion uh in in in heterog Junction
+bipolar transistors so I think some
+
+ align:start position:0%
+bipolar transistors so I think some
+ 
+
+ align:start position:0%
+bipolar transistors so I think some
+somebody's doing a report on that one
+
+ align:start position:0%
+somebody's doing a report on that one
+ 
+
+ align:start position:0%
+somebody's doing a report on that one
+one of the people signed up for that so
+
+ align:start position:0%
+one of the people signed up for that so
+ 
+
+ align:start position:0%
+one of the people signed up for that so
+that's that's kind of a Hot Topic the
+
+ align:start position:0%
+that's that's kind of a Hot Topic the
+ 
+
+ align:start position:0%
+that's that's kind of a Hot Topic the
+use of carbon to uh completely um suck
+
+ align:start position:0%
+use of carbon to uh completely um suck
+ 
+
+ align:start position:0%
+use of carbon to uh completely um suck
+up all the interstitials and then that
+
+ align:start position:0%
+up all the interstitials and then that
+ 
+
+ align:start position:0%
+up all the interstitials and then that
+that that completely changes the teed
+
+ align:start position:0%
+that that completely changes the teed
+ 
+
+ align:start position:0%
+that that completely changes the teed
+effect so these materials have uh quite
+
+ align:start position:0%
+effect so these materials have uh quite
+ 
+
+ align:start position:0%
+effect so these materials have uh quite
+a bit of of application so on on slide
+
+ align:start position:0%
+a bit of of application so on on slide
+ 
+
+ align:start position:0%
+a bit of of application so on on slide
+three this looks like a long outline but
+
+ align:start position:0%
+three this looks like a long outline but
+ 
+
+ align:start position:0%
+three this looks like a long outline but
+I'm just going to touch on it uh after I
+
+ align:start position:0%
+I'm just going to touch on it uh after I
+ 
+
+ align:start position:0%
+I'm just going to touch on it uh after I
+introduce these M the materials going to
+
+ align:start position:0%
+introduce these M the materials going to
+ 
+
+ align:start position:0%
+introduce these M the materials going to
+touch a little bit on the Moss bits and
+
+ align:start position:0%
+touch a little bit on the Moss bits and
+ 
+
+ align:start position:0%
+touch a little bit on the Moss bits and
+the applications of of strain silicon
+
+ align:start position:0%
+the applications of of strain silicon
+ 
+
+ align:start position:0%
+the applications of of strain silicon
+and strain silicon germanian to se Moss
+
+ align:start position:0%
+and strain silicon germanian to se Moss
+ 
+
+ align:start position:0%
+and strain silicon germanian to se Moss
+uh talk a little bit about how the
+
+ align:start position:0%
+uh talk a little bit about how the
+ 
+
+ align:start position:0%
+uh talk a little bit about how the
+materials are grown and about how the
+
+ align:start position:0%
+materials are grown and about how the
+ 
+
+ align:start position:0%
+materials are grown and about how the
+dope is diffuse in these materials and
+
+ align:start position:0%
+dope is diffuse in these materials and
+ 
+
+ align:start position:0%
+dope is diffuse in these materials and
+um a little bit about some newer
+
+ align:start position:0%
+um a little bit about some newer
+ 
+
+ align:start position:0%
+um a little bit about some newer
+material where we're putting them on
+
+ align:start position:0%
+material where we're putting them on
+ 
+
+ align:start position:0%
+material where we're putting them on
+insulator strain silicon on insulator uh
+
+ align:start position:0%
+insulator strain silicon on insulator uh
+ 
+
+ align:start position:0%
+insulator strain silicon on insulator uh
+is is a very kind of a topic of of
+
+ align:start position:0%
+is is a very kind of a topic of of
+ 
+
+ align:start position:0%
+is is a very kind of a topic of of
+research these
+
+ align:start position:0%
+research these
+ 
+
+ align:start position:0%
+research these
+days well if we go to slide four this is
+
+ align:start position:0%
+days well if we go to slide four this is
+ 
+
+ align:start position:0%
+days well if we go to slide four this is
+more of a motivational slide um what
+
+ align:start position:0%
+more of a motivational slide um what
+ 
+
+ align:start position:0%
+more of a motivational slide um what
+what this show the question we're trying
+
+ align:start position:0%
+what this show the question we're trying
+ 
+
+ align:start position:0%
+what this show the question we're trying
+to ask is if you have a Coss circuit
+
+ align:start position:0%
+to ask is if you have a Coss circuit
+ 
+
+ align:start position:0%
+to ask is if you have a Coss circuit
+maybe inverter or something how quickly
+
+ align:start position:0%
+maybe inverter or something how quickly
+ 
+
+ align:start position:0%
+maybe inverter or something how quickly
+can it switch from one state of the zero
+
+ align:start position:0%
+can it switch from one state of the zero
+ 
+
+ align:start position:0%
+can it switch from one state of the zero
+state to the on state the zero state to
+
+ align:start position:0%
+state to the on state the zero state to
+ 
+
+ align:start position:0%
+state to the on state the zero state to
+to the one state for example um and this
+
+ align:start position:0%
+to the one state for example um and this
+ 
+
+ align:start position:0%
+to the one state for example um and this
+the delay in doing that is something
+
+ align:start position:0%
+the delay in doing that is something
+ 
+
+ align:start position:0%
+the delay in doing that is something
+called the gate delay it's usually
+
+ align:start position:0%
+called the gate delay it's usually
+ 
+
+ align:start position:0%
+called the gate delay it's usually
+measured in PE of seconds and that gate
+
+ align:start position:0%
+measured in PE of seconds and that gate
+ 
+
+ align:start position:0%
+measured in PE of seconds and that gate
+delay is something we want to minimize
+
+ align:start position:0%
+delay is something we want to minimize
+ 
+
+ align:start position:0%
+delay is something we want to minimize
+we want to minimize the switching of
+
+ align:start position:0%
+we want to minimize the switching of
+ 
+
+ align:start position:0%
+we want to minimize the switching of
+each gate in the logic uh sequence so
+
+ align:start position:0%
+each gate in the logic uh sequence so
+ 
+
+ align:start position:0%
+each gate in the logic uh sequence so
+that the overall circuit will will uh
+
+ align:start position:0%
+that the overall circuit will will uh
+ 
+
+ align:start position:0%
+that the overall circuit will will uh
+you know can do computation uh faster so
+
+ align:start position:0%
+you know can do computation uh faster so
+ 
+
+ align:start position:0%
+you know can do computation uh faster so
+the gate delay generally if you've taken
+
+ align:start position:0%
+the gate delay generally if you've taken
+ 
+
+ align:start position:0%
+the gate delay generally if you've taken
+classes like 6012 or you've had some
+
+ align:start position:0%
+classes like 6012 or you've had some
+ 
+
+ align:start position:0%
+classes like 6012 or you've had some
+under other undergraduate classes on
+
+ align:start position:0%
+under other undergraduate classes on
+ 
+
+ align:start position:0%
+under other undergraduate classes on
+seam loss you know as you scale the gate
+
+ align:start position:0%
+seam loss you know as you scale the gate
+ 
+
+ align:start position:0%
+seam loss you know as you scale the gate
+length that's why we're making the gate
+
+ align:start position:0%
+length that's why we're making the gate
+ 
+
+ align:start position:0%
+length that's why we're making the gate
+length shorter and shorter the gate
+
+ align:start position:0%
+length shorter and shorter the gate
+ 
+
+ align:start position:0%
+length shorter and shorter the gate
+delay goes down this is just actually
+
+ align:start position:0%
+delay goes down this is just actually
+ 
+
+ align:start position:0%
+delay goes down this is just actually
+some data showing how it does indeed
+
+ align:start position:0%
+some data showing how it does indeed
+ 
+
+ align:start position:0%
+some data showing how it does indeed
+scale at 0.1 Micron the gate delay is
+
+ align:start position:0%
+scale at 0.1 Micron the gate delay is
+ 
+
+ align:start position:0%
+scale at 0.1 Micron the gate delay is
+down in the five or so uh PC or some
+
+ align:start position:0%
+down in the five or so uh PC or some
+ 
+
+ align:start position:0%
+down in the five or so uh PC or some
+five peos second
+
+ align:start position:0%
+five peos second
+ 
+
+ align:start position:0%
+five peos second
+range well it turns out that the gate
+
+ align:start position:0%
+range well it turns out that the gate
+ 
+
+ align:start position:0%
+range well it turns out that the gate
+delay is inversely proportional to the
+
+ align:start position:0%
+delay is inversely proportional to the
+ 
+
+ align:start position:0%
+delay is inversely proportional to the
+current so if you can pump more current
+
+ align:start position:0%
+current so if you can pump more current
+ 
+
+ align:start position:0%
+current so if you can pump more current
+uh through each device then as one
+
+ align:start position:0%
+uh through each device then as one
+ 
+
+ align:start position:0%
+uh through each device then as one
+device charges the the device after it
+
+ align:start position:0%
+device charges the the device after it
+ 
+
+ align:start position:0%
+device charges the the device after it
+has to charge up a device the more
+
+ align:start position:0%
+has to charge up a device the more
+ 
+
+ align:start position:0%
+has to charge up a device the more
+current going through the more quickly
+
+ align:start position:0%
+current going through the more quickly
+ 
+
+ align:start position:0%
+current going through the more quickly
+it will charge its neighboring device so
+
+ align:start position:0%
+it will charge its neighboring device so
+ 
+
+ align:start position:0%
+it will charge its neighboring device so
+the name of the game and getting higher
+
+ align:start position:0%
+the name of the game and getting higher
+ 
+
+ align:start position:0%
+the name of the game and getting higher
+speed in logic devices at least for
+
+ align:start position:0%
+speed in logic devices at least for
+ 
+
+ align:start position:0%
+speed in logic devices at least for
+digital is at a given voltage to get
+
+ align:start position:0%
+digital is at a given voltage to get
+ 
+
+ align:start position:0%
+digital is at a given voltage to get
+more current more drain current out of
+
+ align:start position:0%
+more current more drain current out of
+ 
+
+ align:start position:0%
+more current more drain current out of
+the device and so you say okay let a
+
+ align:start position:0%
+the device and so you say okay let a
+ 
+
+ align:start position:0%
+the device and so you say okay let a
+give voltage how can I get more drain
+
+ align:start position:0%
+give voltage how can I get more drain
+ 
+
+ align:start position:0%
+give voltage how can I get more drain
+current well this is what the drain
+
+ align:start position:0%
+current well this is what the drain
+ 
+
+ align:start position:0%
+current well this is what the drain
+current looks like there are several uh
+
+ align:start position:0%
+current looks like there are several uh
+ 
+
+ align:start position:0%
+current looks like there are several uh
+physical variables it depends on it
+
+ align:start position:0%
+physical variables it depends on it
+ 
+
+ align:start position:0%
+physical variables it depends on it
+depends on the mobility of the carriers
+
+ align:start position:0%
+depends on the mobility of the carriers
+ 
+
+ align:start position:0%
+depends on the mobility of the carriers
+directly proportional it's inversely
+
+ align:start position:0%
+directly proportional it's inversely
+ 
+
+ align:start position:0%
+directly proportional it's inversely
+proportional to the oxide thickness so
+
+ align:start position:0%
+proportional to the oxide thickness so
+ 
+
+ align:start position:0%
+proportional to the oxide thickness so
+if I make the oxide thinner I get a
+
+ align:start position:0%
+if I make the oxide thinner I get a
+ 
+
+ align:start position:0%
+if I make the oxide thinner I get a
+higher capacitance and the current goes
+
+ align:start position:0%
+higher capacitance and the current goes
+ 
+
+ align:start position:0%
+higher capacitance and the current goes
+up that's why we're talking about gate
+
+ align:start position:0%
+up that's why we're talking about gate
+ 
+
+ align:start position:0%
+up that's why we're talking about gate
+dialectric scaling all the way down to
+
+ align:start position:0%
+dialectric scaling all the way down to
+ 
+
+ align:start position:0%
+dialectric scaling all the way down to
+below 10 angstroms um so that's that's
+
+ align:start position:0%
+below 10 angstroms um so that's that's
+ 
+
+ align:start position:0%
+below 10 angstroms um so that's that's
+where the gate dialectric scaling comes
+
+ align:start position:0%
+where the gate dialectric scaling comes
+ 
+
+ align:start position:0%
+where the gate dialectric scaling comes
+from and if I make the channel length
+
+ align:start position:0%
+from and if I make the channel length
+ 
+
+ align:start position:0%
+from and if I make the channel length
+shorter it does also go up so uh how how
+
+ align:start position:0%
+shorter it does also go up so uh how how
+ 
+
+ align:start position:0%
+shorter it does also go up so uh how how
+do people do conventional scaling to
+
+ align:start position:0%
+do people do conventional scaling to
+ 
+
+ align:start position:0%
+do people do conventional scaling to
+increase ID or speed for logic they they
+
+ align:start position:0%
+increase ID or speed for logic they they
+ 
+
+ align:start position:0%
+increase ID or speed for logic they they
+make the gate length shorter uh they
+
+ align:start position:0%
+make the gate length shorter uh they
+ 
+
+ align:start position:0%
+make the gate length shorter uh they
+reduce the gate oxide thickness the real
+
+ align:start position:0%
+reduce the gate oxide thickness the real
+ 
+
+ align:start position:0%
+reduce the gate oxide thickness the real
+question has been in the last five or 10
+
+ align:start position:0%
+question has been in the last five or 10
+ 
+
+ align:start position:0%
+question has been in the last five or 10
+years what about the mobility is that a
+
+ align:start position:0%
+years what about the mobility is that a
+ 
+
+ align:start position:0%
+years what about the mobility is that a
+variable that we can tweak we're pretty
+
+ align:start position:0%
+variable that we can tweak we're pretty
+ 
+
+ align:start position:0%
+variable that we can tweak we're pretty
+much done with scaling theide because we
+
+ align:start position:0%
+much done with scaling theide because we
+ 
+
+ align:start position:0%
+much done with scaling theide because we
+can't get much thinner only a few atoms
+
+ align:start position:0%
+can't get much thinner only a few atoms
+ 
+
+ align:start position:0%
+can't get much thinner only a few atoms
+thick uh making the the transistor
+
+ align:start position:0%
+thick uh making the the transistor
+ 
+
+ align:start position:0%
+thick uh making the the transistor
+shorter is getting harder and harder log
+
+ align:start position:0%
+shorter is getting harder and harder log
+ 
+
+ align:start position:0%
+shorter is getting harder and harder log
+graphically and for electrostatic
+
+ align:start position:0%
+graphically and for electrostatic
+ 
+
+ align:start position:0%
+graphically and for electrostatic
+reasons don't have too many more
+
+ align:start position:0%
+reasons don't have too many more
+ 
+
+ align:start position:0%
+reasons don't have too many more
+variables in this equation so Mobility
+
+ align:start position:0%
+variables in this equation so Mobility
+ 
+
+ align:start position:0%
+variables in this equation so Mobility
+is the last thing to touch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and that's where these silic and
+
+ align:start position:0%
+uh and that's where these silic and
+ 
+
+ align:start position:0%
+uh and that's where these silic and
+geranium Alloys come in here on page
+
+ align:start position:0%
+geranium Alloys come in here on page
+ 
+
+ align:start position:0%
+geranium Alloys come in here on page
+five uh what I'm showing is some data
+
+ align:start position:0%
+five uh what I'm showing is some data
+ 
+
+ align:start position:0%
+five uh what I'm showing is some data
+some classic data of a literature uh uh
+
+ align:start position:0%
+some classic data of a literature uh uh
+ 
+
+ align:start position:0%
+some classic data of a literature uh uh
+of what the electron Mobility that that
+
+ align:start position:0%
+of what the electron Mobility that that
+ 
+
+ align:start position:0%
+of what the electron Mobility that that
+that number mu is not a single number in
+
+ align:start position:0%
+that number mu is not a single number in
+ 
+
+ align:start position:0%
+that number mu is not a single number in
+a mosfet so this is a plot of the
+
+ align:start position:0%
+a mosfet so this is a plot of the
+ 
+
+ align:start position:0%
+a mosfet so this is a plot of the
+effective electron mobility in a channel
+
+ align:start position:0%
+effective electron mobility in a channel
+ 
+
+ align:start position:0%
+effective electron mobility in a channel
+and again as as this number goes up the
+
+ align:start position:0%
+and again as as this number goes up the
+ 
+
+ align:start position:0%
+and again as as this number goes up the
+current goes up at a given voltage as a
+
+ align:start position:0%
+current goes up at a given voltage as a
+ 
+
+ align:start position:0%
+current goes up at a given voltage as a
+function of the vertical field in the
+
+ align:start position:0%
+function of the vertical field in the
+ 
+
+ align:start position:0%
+function of the vertical field in the
+device the vertical field is induced by
+
+ align:start position:0%
+device the vertical field is induced by
+ 
+
+ align:start position:0%
+device the vertical field is induced by
+the gate so as I put a gate bias on uh
+
+ align:start position:0%
+the gate so as I put a gate bias on uh
+ 
+
+ align:start position:0%
+the gate so as I put a gate bias on uh
+the device as I bias the device uh the
+
+ align:start position:0%
+the device as I bias the device uh the
+ 
+
+ align:start position:0%
+the device as I bias the device uh the
+gate bias I get higher inversion charge
+
+ align:start position:0%
+gate bias I get higher inversion charge
+ 
+
+ align:start position:0%
+gate bias I get higher inversion charge
+density in fact the the mobility
+
+ align:start position:0%
+density in fact the the mobility
+ 
+
+ align:start position:0%
+density in fact the the mobility
+actually goes
+
+ align:start position:0%
+actually goes
+ 
+
+ align:start position:0%
+actually goes
+down uh but so you notice it's a
+
+ align:start position:0%
+down uh but so you notice it's a
+ 
+
+ align:start position:0%
+down uh but so you notice it's a
+function of the vertical effective field
+
+ align:start position:0%
+function of the vertical effective field
+ 
+
+ align:start position:0%
+function of the vertical effective field
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+silicon and that modern mosfets are
+
+ align:start position:0%
+silicon and that modern mosfets are
+ 
+
+ align:start position:0%
+silicon and that modern mosfets are
+operating somewhere in this range right
+
+ align:start position:0%
+operating somewhere in this range right
+ 
+
+ align:start position:0%
+operating somewhere in this range right
+now I can just tell you based on the uh
+
+ align:start position:0%
+now I can just tell you based on the uh
+ 
+
+ align:start position:0%
+now I can just tell you based on the uh
+gate oxide thickness and the typical
+
+ align:start position:0%
+gate oxide thickness and the typical
+ 
+
+ align:start position:0%
+gate oxide thickness and the typical
+voltages one to three volts that you
+
+ align:start position:0%
+voltages one to three volts that you
+ 
+
+ align:start position:0%
+voltages one to three volts that you
+that that mosfets are operating in if
+
+ align:start position:0%
+that that mosfets are operating in if
+ 
+
+ align:start position:0%
+that that mosfets are operating in if
+you calculate it out the effective field
+
+ align:start position:0%
+you calculate it out the effective field
+ 
+
+ align:start position:0%
+you calculate it out the effective field
+in the channel is about a megga volt per
+
+ align:start position:0%
+in the channel is about a megga volt per
+ 
+
+ align:start position:0%
+in the channel is about a megga volt per
+centimeter so modern mosfets these days
+
+ align:start position:0%
+centimeter so modern mosfets these days
+ 
+
+ align:start position:0%
+centimeter so modern mosfets these days
+the electron Mobility is right about on
+
+ align:start position:0%
+the electron Mobility is right about on
+ 
+
+ align:start position:0%
+the electron Mobility is right about on
+this curve somewhere between 200 and 300
+
+ align:start position:0%
+this curve somewhere between 200 and 300
+ 
+
+ align:start position:0%
+this curve somewhere between 200 and 300
+but closer to 200 a number of years ago
+
+ align:start position:0%
+but closer to 200 a number of years ago
+ 
+
+ align:start position:0%
+but closer to 200 a number of years ago
+when we Ed lighter doping so let's say
+
+ align:start position:0%
+when we Ed lighter doping so let's say
+ 
+
+ align:start position:0%
+when we Ed lighter doping so let's say
+you were using much lighter doping like
+
+ align:start position:0%
+you were using much lighter doping like
+ 
+
+ align:start position:0%
+you were using much lighter doping like
+317 and the oxides were thicker the
+
+ align:start position:0%
+317 and the oxides were thicker the
+ 
+
+ align:start position:0%
+317 and the oxides were thicker the
+vertical field was much lower maybe half
+
+ align:start position:0%
+vertical field was much lower maybe half
+ 
+
+ align:start position:0%
+vertical field was much lower maybe half
+a half of what it is today and the
+
+ align:start position:0%
+a half of what it is today and the
+ 
+
+ align:start position:0%
+a half of what it is today and the
+mobility was twice it was like 400 so
+
+ align:start position:0%
+mobility was twice it was like 400 so
+ 
+
+ align:start position:0%
+mobility was twice it was like 400 so
+this is the problem with Mobility as we
+
+ align:start position:0%
+this is the problem with Mobility as we
+ 
+
+ align:start position:0%
+this is the problem with Mobility as we
+March down the itrs we scale that gate
+
+ align:start position:0%
+March down the itrs we scale that gate
+ 
+
+ align:start position:0%
+March down the itrs we scale that gate
+oxide thickness so so we get higher
+
+ align:start position:0%
+oxide thickness so so we get higher
+ 
+
+ align:start position:0%
+oxide thickness so so we get higher
+capacitors that's good uh but we also
+
+ align:start position:0%
+capacitors that's good uh but we also
+ 
+
+ align:start position:0%
+capacitors that's good uh but we also
+increasing the doping in the channel and
+
+ align:start position:0%
+increasing the doping in the channel and
+ 
+
+ align:start position:0%
+increasing the doping in the channel and
+um we're increasing the vertical
+
+ align:start position:0%
+um we're increasing the vertical
+ 
+
+ align:start position:0%
+um we're increasing the vertical
+effective field so we're marching down
+
+ align:start position:0%
+effective field so we're marching down
+ 
+
+ align:start position:0%
+effective field so we're marching down
+this curve and the mobility is going
+
+ align:start position:0%
+this curve and the mobility is going
+ 
+
+ align:start position:0%
+this curve and the mobility is going
+lower and lower and lower with each
+
+ align:start position:0%
+lower and lower and lower with each
+ 
+
+ align:start position:0%
+lower and lower and lower with each
+generation that's bad that takes away
+
+ align:start position:0%
+generation that's bad that takes away
+ 
+
+ align:start position:0%
+generation that's bad that takes away
+from the our current drive to a certain
+
+ align:start position:0%
+from the our current drive to a certain
+ 
+
+ align:start position:0%
+from the our current drive to a certain
+extent um so so that's a problem so what
+
+ align:start position:0%
+extent um so so that's a problem so what
+ 
+
+ align:start position:0%
+extent um so so that's a problem so what
+people have decided to do is okay uh it
+
+ align:start position:0%
+people have decided to do is okay uh it
+ 
+
+ align:start position:0%
+people have decided to do is okay uh it
+turns out if I can change this Mobility
+
+ align:start position:0%
+turns out if I can change this Mobility
+ 
+
+ align:start position:0%
+turns out if I can change this Mobility
+curve in fact I can push the whole curve
+
+ align:start position:0%
+curve in fact I can push the whole curve
+ 
+
+ align:start position:0%
+curve in fact I can push the whole curve
+up quite significantly if I put stress
+
+ align:start position:0%
+up quite significantly if I put stress
+ 
+
+ align:start position:0%
+up quite significantly if I put stress
+on the Silicon
+
+ align:start position:0%
+on the Silicon
+ 
+
+ align:start position:0%
+on the Silicon
+and I'll say a little bit more in in in
+
+ align:start position:0%
+and I'll say a little bit more in in in
+ 
+
+ align:start position:0%
+and I'll say a little bit more in in in
+in the next few slides about how that
+
+ align:start position:0%
+in the next few slides about how that
+ 
+
+ align:start position:0%
+in the next few slides about how that
+works so people have tried a number of
+
+ align:start position:0%
+works so people have tried a number of
+ 
+
+ align:start position:0%
+works so people have tried a number of
+different ways to stress out the devices
+
+ align:start position:0%
+different ways to stress out the devices
+ 
+
+ align:start position:0%
+different ways to stress out the devices
+or to put stress on the Silicon you have
+
+ align:start position:0%
+or to put stress on the Silicon you have
+ 
+
+ align:start position:0%
+or to put stress on the Silicon you have
+to stress it in a certain way and this
+
+ align:start position:0%
+to stress it in a certain way and this
+ 
+
+ align:start position:0%
+to stress it in a certain way and this
+schematic kind of gives you an idea of a
+
+ align:start position:0%
+schematic kind of gives you an idea of a
+ 
+
+ align:start position:0%
+schematic kind of gives you an idea of a
+good way of inducing stress for
+
+ align:start position:0%
+good way of inducing stress for
+ 
+
+ align:start position:0%
+good way of inducing stress for
+electrons if you have a this looks like
+
+ align:start position:0%
+electrons if you have a this looks like
+ 
+
+ align:start position:0%
+electrons if you have a this looks like
+just like a regular n mosfet but you
+
+ align:start position:0%
+just like a regular n mosfet but you
+ 
+
+ align:start position:0%
+just like a regular n mosfet but you
+notice I've highlighted this uh Channel
+
+ align:start position:0%
+notice I've highlighted this uh Channel
+ 
+
+ align:start position:0%
+notice I've highlighted this uh Channel
+region in yellow uh it's called strain
+
+ align:start position:0%
+region in yellow uh it's called strain
+ 
+
+ align:start position:0%
+region in yellow uh it's called strain
+silicon uh classically strain silicon
+
+ align:start position:0%
+silicon uh classically strain silicon
+ 
+
+ align:start position:0%
+silicon uh classically strain silicon
+was generated by um taking taking a
+
+ align:start position:0%
+was generated by um taking taking a
+ 
+
+ align:start position:0%
+was generated by um taking taking a
+wafer of silicon geranium or a very
+
+ align:start position:0%
+wafer of silicon geranium or a very
+ 
+
+ align:start position:0%
+wafer of silicon geranium or a very
+thick layer of silic and geranium uh say
+
+ align:start position:0%
+thick layer of silic and geranium uh say
+ 
+
+ align:start position:0%
+thick layer of silic and geranium uh say
+with 30 or 20 or 30% geranium silicon
+
+ align:start position:0%
+with 30 or 20 or 30% geranium silicon
+ 
+
+ align:start position:0%
+with 30 or 20 or 30% geranium silicon
+geranium has a larger lce parameter than
+
+ align:start position:0%
+geranium has a larger lce parameter than
+ 
+
+ align:start position:0%
+geranium has a larger lce parameter than
+silicon pure geranium is about 4% bigger
+
+ align:start position:0%
+silicon pure geranium is about 4% bigger
+ 
+
+ align:start position:0%
+silicon pure geranium is about 4% bigger
+so this uh 30% layer um is going to be a
+
+ align:start position:0%
+so this uh 30% layer um is going to be a
+ 
+
+ align:start position:0%
+so this uh 30% layer um is going to be a
+little bit larger in its Lattis
+
+ align:start position:0%
+little bit larger in its Lattis
+ 
+
+ align:start position:0%
+little bit larger in its Lattis
+parameter so if it's relaxed it's bigger
+
+ align:start position:0%
+parameter so if it's relaxed it's bigger
+ 
+
+ align:start position:0%
+parameter so if it's relaxed it's bigger
+uh and and if the Silicon layer is thin
+
+ align:start position:0%
+uh and and if the Silicon layer is thin
+ 
+
+ align:start position:0%
+uh and and if the Silicon layer is thin
+when you grow it epot taxi the Silicon
+
+ align:start position:0%
+when you grow it epot taxi the Silicon
+ 
+
+ align:start position:0%
+when you grow it epot taxi the Silicon
+lce will actually stretch in the X and
+
+ align:start position:0%
+lce will actually stretch in the X and
+ 
+
+ align:start position:0%
+lce will actually stretch in the X and
+the Y directions to match that of the
+
+ align:start position:0%
+the Y directions to match that of the
+ 
+
+ align:start position:0%
+the Y directions to match that of the
+substrate as long as it's enough it's
+
+ align:start position:0%
+substrate as long as it's enough it's
+ 
+
+ align:start position:0%
+substrate as long as it's enough it's
+energetically favorable to stretch the
+
+ align:start position:0%
+energetically favorable to stretch the
+ 
+
+ align:start position:0%
+energetically favorable to stretch the
+bonds instead of instead of breaking
+
+ align:start position:0%
+bonds instead of instead of breaking
+ 
+
+ align:start position:0%
+bonds instead of instead of breaking
+them so this silicon is stretched it's
+
+ align:start position:0%
+them so this silicon is stretched it's
+ 
+
+ align:start position:0%
+them so this silicon is stretched it's
+last parameter in the X and Y plane is
+
+ align:start position:0%
+last parameter in the X and Y plane is
+ 
+
+ align:start position:0%
+last parameter in the X and Y plane is
+about 1 and a half% bigger than it would
+
+ align:start position:0%
+about 1 and a half% bigger than it would
+ 
+
+ align:start position:0%
+about 1 and a half% bigger than it would
+be in normal silicon that's a huge
+
+ align:start position:0%
+be in normal silicon that's a huge
+ 
+
+ align:start position:0%
+be in normal silicon that's a huge
+amount for to take a lattice a silic you
+
+ align:start position:0%
+amount for to take a lattice a silic you
+ 
+
+ align:start position:0%
+amount for to take a lattice a silic you
+know to take a crystal lce and stretch
+
+ align:start position:0%
+know to take a crystal lce and stretch
+ 
+
+ align:start position:0%
+know to take a crystal lce and stretch
+it by one and a half percent that's a
+
+ align:start position:0%
+it by one and a half percent that's a
+ 
+
+ align:start position:0%
+it by one and a half percent that's a
+lot uh as a result when you stretch it
+
+ align:start position:0%
+lot uh as a result when you stretch it
+ 
+
+ align:start position:0%
+lot uh as a result when you stretch it
+in the X and Y it actually compresses a
+
+ align:start position:0%
+in the X and Y it actually compresses a
+ 
+
+ align:start position:0%
+in the X and Y it actually compresses a
+little bit in Z so in fact we call this
+
+ align:start position:0%
+little bit in Z so in fact we call this
+ 
+
+ align:start position:0%
+little bit in Z so in fact we call this
+particular uh configuration uniform bi
+
+ align:start position:0%
+particular uh configuration uniform bi
+ 
+
+ align:start position:0%
+particular uh configuration uniform bi
+aial tensil stress it's bi axial because
+
+ align:start position:0%
+aial tensil stress it's bi axial because
+ 
+
+ align:start position:0%
+aial tensil stress it's bi axial because
+it's and it's tensil it's being uh
+
+ align:start position:0%
+it's and it's tensil it's being uh
+ 
+
+ align:start position:0%
+it's and it's tensil it's being uh
+pulled in X and Y so this is sort of the
+
+ align:start position:0%
+pulled in X and Y so this is sort of the
+ 
+
+ align:start position:0%
+pulled in X and Y so this is sort of the
+classic way that people have introduced
+
+ align:start position:0%
+classic way that people have introduced
+ 
+
+ align:start position:0%
+classic way that people have introduced
+strain and made MOS vets and they've
+
+ align:start position:0%
+strain and made MOS vets and they've
+ 
+
+ align:start position:0%
+strain and made MOS vets and they've
+looked at the mobility as a function of
+
+ align:start position:0%
+looked at the mobility as a function of
+ 
+
+ align:start position:0%
+looked at the mobility as a function of
+the amount of the strain there are other
+
+ align:start position:0%
+the amount of the strain there are other
+ 
+
+ align:start position:0%
+the amount of the strain there are other
+methods though for straining uh most of
+
+ align:start position:0%
+methods though for straining uh most of
+ 
+
+ align:start position:0%
+methods though for straining uh most of
+what I'll talk about in this lecture is
+
+ align:start position:0%
+what I'll talk about in this lecture is
+ 
+
+ align:start position:0%
+what I'll talk about in this lecture is
+this epitaxial growth method uh it's the
+
+ align:start position:0%
+this epitaxial growth method uh it's the
+ 
+
+ align:start position:0%
+this epitaxial growth method uh it's the
+easiest one to get a handle on the
+
+ align:start position:0%
+easiest one to get a handle on the
+ 
+
+ align:start position:0%
+easiest one to get a handle on the
+physics but there are other methods
+
+ align:start position:0%
+physics but there are other methods
+ 
+
+ align:start position:0%
+physics but there are other methods
+people have used for example you know
+
+ align:start position:0%
+people have used for example you know
+ 
+
+ align:start position:0%
+people have used for example you know
+when you make a mosset you don't just
+
+ align:start position:0%
+when you make a mosset you don't just
+ 
+
+ align:start position:0%
+when you make a mosset you don't just
+make an individual mosfet on a device
+
+ align:start position:0%
+make an individual mosfet on a device
+ 
+
+ align:start position:0%
+make an individual mosfet on a device
+all around the mosfet you know there's
+
+ align:start position:0%
+all around the mosfet you know there's
+ 
+
+ align:start position:0%
+all around the mosfet you know there's
+something we do something called trench
+
+ align:start position:0%
+something we do something called trench
+ 
+
+ align:start position:0%
+something we do something called trench
+isolation that we talked about in this
+
+ align:start position:0%
+isolation that we talked about in this
+ 
+
+ align:start position:0%
+isolation that we talked about in this
+course we dig out a trench on all the
+
+ align:start position:0%
+course we dig out a trench on all the
+ 
+
+ align:start position:0%
+course we dig out a trench on all the
+way around the moset and we fill it up
+
+ align:start position:0%
+way around the moset and we fill it up
+ 
+
+ align:start position:0%
+way around the moset and we fill it up
+with oxide or something some
+
+ align:start position:0%
+with oxide or something some
+ 
+
+ align:start position:0%
+with oxide or something some
+insulator well uh IBM show back in 97
+
+ align:start position:0%
+insulator well uh IBM show back in 97
+ 
+
+ align:start position:0%
+insulator well uh IBM show back in 97
+depending on how you seal that up you
+
+ align:start position:0%
+depending on how you seal that up you
+ 
+
+ align:start position:0%
+depending on how you seal that up you
+can potentially induce stress either
+
+ align:start position:0%
+can potentially induce stress either
+ 
+
+ align:start position:0%
+can potentially induce stress either
+compressive or tensil depending on what
+
+ align:start position:0%
+compressive or tensil depending on what
+ 
+
+ align:start position:0%
+compressive or tensil depending on what
+material you put in uh because you're
+
+ align:start position:0%
+material you put in uh because you're
+ 
+
+ align:start position:0%
+material you put in uh because you're
+digging a moat around the device and
+
+ align:start position:0%
+digging a moat around the device and
+ 
+
+ align:start position:0%
+digging a moat around the device and
+you're putting some material in it so
+
+ align:start position:0%
+you're putting some material in it so
+ 
+
+ align:start position:0%
+you're putting some material in it so
+you can actually use the STI so-called
+
+ align:start position:0%
+you can actually use the STI so-called
+ 
+
+ align:start position:0%
+you can actually use the STI so-called
+to induce stress um there are other
+
+ align:start position:0%
+to induce stress um there are other
+ 
+
+ align:start position:0%
+to induce stress um there are other
+processes during fabrication uh that uh
+
+ align:start position:0%
+processes during fabrication uh that uh
+ 
+
+ align:start position:0%
+processes during fabrication uh that uh
+Intel is using now um where they
+
+ align:start position:0%
+Intel is using now um where they
+ 
+
+ align:start position:0%
+Intel is using now um where they
+actually dig out to source and drains
+
+ align:start position:0%
+actually dig out to source and drains
+ 
+
+ align:start position:0%
+actually dig out to source and drains
+they cut them out with Ed and they
+
+ align:start position:0%
+they cut them out with Ed and they
+ 
+
+ align:start position:0%
+they cut them out with Ed and they
+fill them back up with silicon geranium
+
+ align:start position:0%
+fill them back up with silicon geranium
+ 
+
+ align:start position:0%
+fill them back up with silicon geranium
+which compresses the channel which helps
+
+ align:start position:0%
+which compresses the channel which helps
+ 
+
+ align:start position:0%
+which compresses the channel which helps
+the whole Mobility so people are are
+
+ align:start position:0%
+the whole Mobility so people are are
+ 
+
+ align:start position:0%
+the whole Mobility so people are are
+doing things like that you can actually
+
+ align:start position:0%
+doing things like that you can actually
+ 
+
+ align:start position:0%
+doing things like that you can actually
+stress the device people take oh on top
+
+ align:start position:0%
+stress the device people take oh on top
+ 
+
+ align:start position:0%
+stress the device people take oh on top
+of the device they put a layer of high
+
+ align:start position:0%
+of the device they put a layer of high
+ 
+
+ align:start position:0%
+of the device they put a layer of high
+stress nitrite and try to induce stress
+
+ align:start position:0%
+stress nitrite and try to induce stress
+ 
+
+ align:start position:0%
+stress nitrite and try to induce stress
+by applying films that are high stress
+
+ align:start position:0%
+by applying films that are high stress
+ 
+
+ align:start position:0%
+by applying films that are high stress
+you can also bend the chip there's a
+
+ align:start position:0%
+you can also bend the chip there's a
+ 
+
+ align:start position:0%
+you can also bend the chip there's a
+small startup company um in the
+
+ align:start position:0%
+small startup company um in the
+ 
+
+ align:start position:0%
+small startup company um in the
+Southeast uh of unit states where
+
+ align:start position:0%
+Southeast uh of unit states where
+ 
+
+ align:start position:0%
+Southeast uh of unit states where
+they're taking chips thinning them and
+
+ align:start position:0%
+they're taking chips thinning them and
+ 
+
+ align:start position:0%
+they're taking chips thinning them and
+actually trying to pin mechanically to
+
+ align:start position:0%
+actually trying to pin mechanically to
+ 
+
+ align:start position:0%
+actually trying to pin mechanically to
+reduce stress it seems a little crazy
+
+ align:start position:0%
+reduce stress it seems a little crazy
+ 
+
+ align:start position:0%
+reduce stress it seems a little crazy
+but may be possible uh but this is
+
+ align:start position:0%
+but may be possible uh but this is
+ 
+
+ align:start position:0%
+but may be possible uh but this is
+epitaxial growth is in some ways the
+
+ align:start position:0%
+epitaxial growth is in some ways the
+ 
+
+ align:start position:0%
+epitaxial growth is in some ways the
+most well-rolled and the physics is a
+
+ align:start position:0%
+most well-rolled and the physics is a
+ 
+
+ align:start position:0%
+most well-rolled and the physics is a
+little bit easier to uh to get a handle
+
+ align:start position:0%
+little bit easier to uh to get a handle
+ 
+
+ align:start position:0%
+little bit easier to uh to get a handle
+on so but let me just mention here on
+
+ align:start position:0%
+on so but let me just mention here on
+ 
+
+ align:start position:0%
+on so but let me just mention here on
+slide seven this is the IBM work in
+
+ align:start position:0%
+slide seven this is the IBM work in
+ 
+
+ align:start position:0%
+slide seven this is the IBM work in
+1997 uh where they talked about if they
+
+ align:start position:0%
+1997 uh where they talked about if they
+ 
+
+ align:start position:0%
+1997 uh where they talked about if they
+in STI you know we' get learned in this
+
+ align:start position:0%
+in STI you know we' get learned in this
+ 
+
+ align:start position:0%
+in STI you know we' get learned in this
+course you fill up the shallow trench
+
+ align:start position:0%
+course you fill up the shallow trench
+ 
+
+ align:start position:0%
+course you fill up the shallow trench
+with with uh with first you oxidize the
+
+ align:start position:0%
+with with uh with first you oxidize the
+ 
+
+ align:start position:0%
+with with uh with first you oxidize the
+liner then you fill it up with lto or
+
+ align:start position:0%
+liner then you fill it up with lto or
+ 
+
+ align:start position:0%
+liner then you fill it up with lto or
+some low temperature oxide what they
+
+ align:start position:0%
+some low temperature oxide what they
+ 
+
+ align:start position:0%
+some low temperature oxide what they
+said was they grew uh an oxide liner for
+
+ align:start position:0%
+said was they grew uh an oxide liner for
+ 
+
+ align:start position:0%
+said was they grew uh an oxide liner for
+in for uh isolation then they filled the
+
+ align:start position:0%
+in for uh isolation then they filled the
+ 
+
+ align:start position:0%
+in for uh isolation then they filled the
+trench with poly poly
+
+ align:start position:0%
+trench with poly poly
+ 
+
+ align:start position:0%
+trench with poly poly
+silicon which they thought would induce
+
+ align:start position:0%
+silicon which they thought would induce
+ 
+
+ align:start position:0%
+silicon which they thought would induce
+a lot of a lot of stress compressive
+
+ align:start position:0%
+a lot of a lot of stress compressive
+ 
+
+ align:start position:0%
+a lot of a lot of stress compressive
+stress pushing in all around the edges
+
+ align:start position:0%
+stress pushing in all around the edges
+ 
+
+ align:start position:0%
+stress pushing in all around the edges
+of the device and then they looked at
+
+ align:start position:0%
+of the device and then they looked at
+ 
+
+ align:start position:0%
+of the device and then they looked at
+the whole Mobility uh and indeed what
+
+ align:start position:0%
+the whole Mobility uh and indeed what
+ 
+
+ align:start position:0%
+the whole Mobility uh and indeed what
+they found um particularly on SOI layers
+
+ align:start position:0%
+they found um particularly on SOI layers
+ 
+
+ align:start position:0%
+they found um particularly on SOI layers
+which are very thin uh when they made
+
+ align:start position:0%
+which are very thin uh when they made
+ 
+
+ align:start position:0%
+which are very thin uh when they made
+the device wi fa small say one micron
+
+ align:start position:0%
+the device wi fa small say one micron
+ 
+
+ align:start position:0%
+the device wi fa small say one micron
+compared to 10 Micron see make the
+
+ align:start position:0%
+compared to 10 Micron see make the
+ 
+
+ align:start position:0%
+compared to 10 Micron see make the
+device width small that brings the
+
+ align:start position:0%
+device width small that brings the
+ 
+
+ align:start position:0%
+device width small that brings the
+shallow trench in closer and closer to
+
+ align:start position:0%
+shallow trench in closer and closer to
+ 
+
+ align:start position:0%
+shallow trench in closer and closer to
+the center of the channel so we can have
+
+ align:start position:0%
+the center of the channel so we can have
+ 
+
+ align:start position:0%
+the center of the channel so we can have
+a bigger effect as it's pushing in and
+
+ align:start position:0%
+a bigger effect as it's pushing in and
+ 
+
+ align:start position:0%
+a bigger effect as it's pushing in and
+they saw that the whole Mobility went up
+
+ align:start position:0%
+they saw that the whole Mobility went up
+ 
+
+ align:start position:0%
+they saw that the whole Mobility went up
+quite a bit a 10 Micron device maybe the
+
+ align:start position:0%
+quite a bit a 10 Micron device maybe the
+ 
+
+ align:start position:0%
+quite a bit a 10 Micron device maybe the
+mobility was here about 100 or 110 and
+
+ align:start position:0%
+mobility was here about 100 or 110 and
+ 
+
+ align:start position:0%
+mobility was here about 100 or 110 and
+went up by about 34% to about 140 uh
+
+ align:start position:0%
+went up by about 34% to about 140 uh
+ 
+
+ align:start position:0%
+went up by about 34% to about 140 uh
+just by doing this now maybe it wasn't
+
+ align:start position:0%
+just by doing this now maybe it wasn't
+ 
+
+ align:start position:0%
+just by doing this now maybe it wasn't
+such a great idea to put that much
+
+ align:start position:0%
+such a great idea to put that much
+ 
+
+ align:start position:0%
+such a great idea to put that much
+stress and use polyc silic it wasn't
+
+ align:start position:0%
+stress and use polyc silic it wasn't
+ 
+
+ align:start position:0%
+stress and use polyc silic it wasn't
+necessarily a practical thing but it
+
+ align:start position:0%
+necessarily a practical thing but it
+ 
+
+ align:start position:0%
+necessarily a practical thing but it
+just kind of shows that you depending on
+
+ align:start position:0%
+just kind of shows that you depending on
+ 
+
+ align:start position:0%
+just kind of shows that you depending on
+how you do your processes how you do
+
+ align:start position:0%
+how you do your processes how you do
+ 
+
+ align:start position:0%
+how you do your processes how you do
+your STI can have a pretty big effect
+
+ align:start position:0%
+your STI can have a pretty big effect
+ 
+
+ align:start position:0%
+your STI can have a pretty big effect
+particularly on the whole
+
+ align:start position:0%
+particularly on the whole
+ 
+
+ align:start position:0%
+particularly on the whole
+Mobility um so this is was an indicator
+
+ align:start position:0%
+Mobility um so this is was an indicator
+ 
+
+ align:start position:0%
+Mobility um so this is was an indicator
+you early on that people need to pay
+
+ align:start position:0%
+you early on that people need to pay
+ 
+
+ align:start position:0%
+you early on that people need to pay
+dramatic attention to exactly what
+
+ align:start position:0%
+dramatic attention to exactly what
+ 
+
+ align:start position:0%
+dramatic attention to exactly what
+thermal budget you use what materials
+
+ align:start position:0%
+thermal budget you use what materials
+ 
+
+ align:start position:0%
+thermal budget you use what materials
+you use in STI in every layer you put on
+
+ align:start position:0%
+you use in STI in every layer you put on
+ 
+
+ align:start position:0%
+you use in STI in every layer you put on
+that device now that the devices are
+
+ align:start position:0%
+that device now that the devices are
+ 
+
+ align:start position:0%
+that device now that the devices are
+small the width of devices say is is
+
+ align:start position:0%
+small the width of devices say is is
+ 
+
+ align:start position:0%
+small the width of devices say is is
+less than a micron now that they're so
+
+ align:start position:0%
+less than a micron now that they're so
+ 
+
+ align:start position:0%
+less than a micron now that they're so
+small Edge effects can have a huge
+
+ align:start position:0%
+small Edge effects can have a huge
+ 
+
+ align:start position:0%
+small Edge effects can have a huge
+impact on the stress in the center of
+
+ align:start position:0%
+impact on the stress in the center of
+ 
+
+ align:start position:0%
+impact on the stress in the center of
+the channel and can end up impacting the
+
+ align:start position:0%
+the channel and can end up impacting the
+ 
+
+ align:start position:0%
+the channel and can end up impacting the
+mobility so I refer to the fact that we
+
+ align:start position:0%
+mobility so I refer to the fact that we
+ 
+
+ align:start position:0%
+mobility so I refer to the fact that we
+have the strain and I guess I should
+
+ align:start position:0%
+have the strain and I guess I should
+ 
+
+ align:start position:0%
+have the strain and I guess I should
+have introduced slide eight a little bit
+
+ align:start position:0%
+have introduced slide eight a little bit
+ 
+
+ align:start position:0%
+have introduced slide eight a little bit
+earlier but this just gives you uh a
+
+ align:start position:0%
+earlier but this just gives you uh a
+ 
+
+ align:start position:0%
+earlier but this just gives you uh a
+picture a ball and stick picture of what
+
+ align:start position:0%
+picture a ball and stick picture of what
+ 
+
+ align:start position:0%
+picture a ball and stick picture of what
+we're talking about so this ball and
+
+ align:start position:0%
+we're talking about so this ball and
+ 
+
+ align:start position:0%
+we're talking about so this ball and
+stick up in the upper left is meant to
+
+ align:start position:0%
+stick up in the upper left is meant to
+ 
+
+ align:start position:0%
+stick up in the upper left is meant to
+represent cubic silicon has a sort of
+
+ align:start position:0%
+represent cubic silicon has a sort of
+ 
+
+ align:start position:0%
+represent cubic silicon has a sort of
+you know it has a l parameter about 5.4
+
+ align:start position:0%
+you know it has a l parameter about 5.4
+ 
+
+ align:start position:0%
+you know it has a l parameter about 5.4
+angstroms it's the diamond cubic
+
+ align:start position:0%
+angstroms it's the diamond cubic
+ 
+
+ align:start position:0%
+angstroms it's the diamond cubic
+structure but nevertheless it has a
+
+ align:start position:0%
+structure but nevertheless it has a
+ 
+
+ align:start position:0%
+structure but nevertheless it has a
+cubic uh symmetry to it X Y and Z in
+
+ align:start position:0%
+cubic uh symmetry to it X Y and Z in
+ 
+
+ align:start position:0%
+cubic uh symmetry to it X Y and Z in
+those three dimensions the lattice
+
+ align:start position:0%
+those three dimensions the lattice
+ 
+
+ align:start position:0%
+those three dimensions the lattice
+constant is parameter is the same
+
+ align:start position:0%
+constant is parameter is the same
+ 
+
+ align:start position:0%
+constant is parameter is the same
+number cubic geranium is larger same
+
+ align:start position:0%
+number cubic geranium is larger same
+ 
+
+ align:start position:0%
+number cubic geranium is larger same
+kind of diamond cubic structure but it's
+
+ align:start position:0%
+kind of diamond cubic structure but it's
+ 
+
+ align:start position:0%
+kind of diamond cubic structure but it's
+larger by about 4% if you make an alloy
+
+ align:start position:0%
+larger by about 4% if you make an alloy
+ 
+
+ align:start position:0%
+larger by about 4% if you make an alloy
+anywhere in between and you have it
+
+ align:start position:0%
+anywhere in between and you have it
+ 
+
+ align:start position:0%
+anywhere in between and you have it
+thick enough that it relaxes it'll have
+
+ align:start position:0%
+thick enough that it relaxes it'll have
+ 
+
+ align:start position:0%
+thick enough that it relaxes it'll have
+pretty much you can use a linear
+
+ align:start position:0%
+pretty much you can use a linear
+ 
+
+ align:start position:0%
+pretty much you can use a linear
+interpolation it's not quite perfect but
+
+ align:start position:0%
+interpolation it's not quite perfect but
+ 
+
+ align:start position:0%
+interpolation it's not quite perfect but
+you can use a linear interpolation uh so
+
+ align:start position:0%
+you can use a linear interpolation uh so
+ 
+
+ align:start position:0%
+you can use a linear interpolation uh so
+at 50% silic and geranium or 50% Gering
+
+ align:start position:0%
+at 50% silic and geranium or 50% Gering
+ 
+
+ align:start position:0%
+at 50% silic and geranium or 50% Gering
+the latest mismatch is about
+
+ align:start position:0%
+the latest mismatch is about
+ 
+
+ align:start position:0%
+the latest mismatch is about
+2% so there are two different types of
+
+ align:start position:0%
+2% so there are two different types of
+ 
+
+ align:start position:0%
+2% so there are two different types of
+silic geranium that people tend to talk
+
+ align:start position:0%
+silic geranium that people tend to talk
+ 
+
+ align:start position:0%
+silic geranium that people tend to talk
+about one is when you start with a
+
+ align:start position:0%
+about one is when you start with a
+ 
+
+ align:start position:0%
+about one is when you start with a
+silicon substrate and you grow a very
+
+ align:start position:0%
+silicon substrate and you grow a very
+ 
+
+ align:start position:0%
+silicon substrate and you grow a very
+thin layer say a few hundred angstrum of
+
+ align:start position:0%
+thin layer say a few hundred angstrum of
+ 
+
+ align:start position:0%
+thin layer say a few hundred angstrum of
+silicon geranium on Silicon what happens
+
+ align:start position:0%
+silicon geranium on Silicon what happens
+ 
+
+ align:start position:0%
+silicon geranium on Silicon what happens
+is you're taking this this this lattice
+
+ align:start position:0%
+is you're taking this this this lattice
+ 
+
+ align:start position:0%
+is you're taking this this this lattice
+here this cubic silicon geranium wants
+
+ align:start position:0%
+here this cubic silicon geranium wants
+ 
+
+ align:start position:0%
+here this cubic silicon geranium wants
+to be cubic uh it's larger it wants to
+
+ align:start position:0%
+to be cubic uh it's larger it wants to
+ 
+
+ align:start position:0%
+to be cubic uh it's larger it wants to
+be larger in equilibrium than silicon
+
+ align:start position:0%
+be larger in equilibrium than silicon
+ 
+
+ align:start position:0%
+be larger in equilibrium than silicon
+and you're squeezing it though it turns
+
+ align:start position:0%
+and you're squeezing it though it turns
+ 
+
+ align:start position:0%
+and you're squeezing it though it turns
+out again if the layer is thin enough
+
+ align:start position:0%
+out again if the layer is thin enough
+ 
+
+ align:start position:0%
+out again if the layer is thin enough
+it's energetically favorable for the
+
+ align:start position:0%
+it's energetically favorable for the
+ 
+
+ align:start position:0%
+it's energetically favorable for the
+inplane L parameter of this material
+
+ align:start position:0%
+inplane L parameter of this material
+ 
+
+ align:start position:0%
+inplane L parameter of this material
+that you're growing to match that of the
+
+ align:start position:0%
+that you're growing to match that of the
+ 
+
+ align:start position:0%
+that you're growing to match that of the
+substrate so the silicon geranium is
+
+ align:start position:0%
+substrate so the silicon geranium is
+ 
+
+ align:start position:0%
+substrate so the silicon geranium is
+kind of squeezed in X and Y and it
+
+ align:start position:0%
+kind of squeezed in X and Y and it
+ 
+
+ align:start position:0%
+kind of squeezed in X and Y and it
+pushes up in
+
+ align:start position:0%
+pushes up in
+ 
+
+ align:start position:0%
+pushes up in
+Z so this layer then is what we call a
+
+ align:start position:0%
+Z so this layer then is what we call a
+ 
+
+ align:start position:0%
+Z so this layer then is what we call a
+strain silicon germanium on relaxed
+
+ align:start position:0%
+strain silicon germanium on relaxed
+ 
+
+ align:start position:0%
+strain silicon germanium on relaxed
+silicon and it's under bi axial
+
+ align:start position:0%
+silicon and it's under bi axial
+ 
+
+ align:start position:0%
+silicon and it's under bi axial
+compression it's being compressed in the
+
+ align:start position:0%
+compression it's being compressed in the
+ 
+
+ align:start position:0%
+compression it's being compressed in the
+XY plane now if you make it thick enough
+
+ align:start position:0%
+XY plane now if you make it thick enough
+ 
+
+ align:start position:0%
+XY plane now if you make it thick enough
+eventually there's too much sored energy
+
+ align:start position:0%
+eventually there's too much sored energy
+ 
+
+ align:start position:0%
+eventually there's too much sored energy
+in those in those stretched bonds and
+
+ align:start position:0%
+in those in those stretched bonds and
+ 
+
+ align:start position:0%
+in those in those stretched bonds and
+the bonds will start breaking and get
+
+ align:start position:0%
+the bonds will start breaking and get
+ 
+
+ align:start position:0%
+the bonds will start breaking and get
+dislocations and it'll relax back to its
+
+ align:start position:0%
+dislocations and it'll relax back to its
+ 
+
+ align:start position:0%
+dislocations and it'll relax back to its
+cubic structure but for thin layers you
+
+ align:start position:0%
+cubic structure but for thin layers you
+ 
+
+ align:start position:0%
+cubic structure but for thin layers you
+can achieve this sort of pseudomorphic
+
+ align:start position:0%
+can achieve this sort of pseudomorphic
+ 
+
+ align:start position:0%
+can achieve this sort of pseudomorphic
+uh structure you can also do kind of the
+
+ align:start position:0%
+uh structure you can also do kind of the
+ 
+
+ align:start position:0%
+uh structure you can also do kind of the
+opposite or the upside down experiment
+
+ align:start position:0%
+opposite or the upside down experiment
+ 
+
+ align:start position:0%
+opposite or the upside down experiment
+you take a wafer of silicon geranium
+
+ align:start position:0%
+you take a wafer of silicon geranium
+ 
+
+ align:start position:0%
+you take a wafer of silicon geranium
+that's very thick that's already relaxed
+
+ align:start position:0%
+that's very thick that's already relaxed
+ 
+
+ align:start position:0%
+that's very thick that's already relaxed
+that has a larger lattice parameter and
+
+ align:start position:0%
+that has a larger lattice parameter and
+ 
+
+ align:start position:0%
+that has a larger lattice parameter and
+I try to stick silicon on it in in in
+
+ align:start position:0%
+I try to stick silicon on it in in in
+ 
+
+ align:start position:0%
+I try to stick silicon on it in in in
+epitaxial growth again if the silicon's
+
+ align:start position:0%
+epitaxial growth again if the silicon's
+ 
+
+ align:start position:0%
+epitaxial growth again if the silicon's
+thin enough it will now stretch in X and
+
+ align:start position:0%
+thin enough it will now stretch in X and
+ 
+
+ align:start position:0%
+thin enough it will now stretch in X and
+Y to match the last parameter of the
+
+ align:start position:0%
+Y to match the last parameter of the
+ 
+
+ align:start position:0%
+Y to match the last parameter of the
+substrate and it will compress in see so
+
+ align:start position:0%
+substrate and it will compress in see so
+ 
+
+ align:start position:0%
+substrate and it will compress in see so
+we call this silicon layer EP layer as
+
+ align:start position:0%
+we call this silicon layer EP layer as
+ 
+
+ align:start position:0%
+we call this silicon layer EP layer as
+being in bi axial tension and again if
+
+ align:start position:0%
+being in bi axial tension and again if
+ 
+
+ align:start position:0%
+being in bi axial tension and again if
+you grow it too large the bogs will no
+
+ align:start position:0%
+you grow it too large the bogs will no
+ 
+
+ align:start position:0%
+you grow it too large the bogs will no
+longer stretch they'll break you'll get
+
+ align:start position:0%
+longer stretch they'll break you'll get
+ 
+
+ align:start position:0%
+longer stretch they'll break you'll get
+dislocations so it can go back instead
+
+ align:start position:0%
+dislocations so it can go back instead
+ 
+
+ align:start position:0%
+dislocations so it can go back instead
+of being stretched it to go back to its
+
+ align:start position:0%
+of being stretched it to go back to its
+ 
+
+ align:start position:0%
+of being stretched it to go back to its
+normaliz parameter that point it be
+
+ align:start position:0%
+normaliz parameter that point it be
+ 
+
+ align:start position:0%
+normaliz parameter that point it be
+relaxed so these this is the type of
+
+ align:start position:0%
+relaxed so these this is the type of
+ 
+
+ align:start position:0%
+relaxed so these this is the type of
+material you'll see a lot in fets and
+
+ align:start position:0%
+material you'll see a lot in fets and
+ 
+
+ align:start position:0%
+material you'll see a lot in fets and
+you see this material in in bipolar
+
+ align:start position:0%
+you see this material in in bipolar
+ 
+
+ align:start position:0%
+you see this material in in bipolar
+transistors and some P channel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mosfets so um what what are some of the
+
+ align:start position:0%
+mosfets so um what what are some of the
+ 
+
+ align:start position:0%
+mosfets so um what what are some of the
+important properties of of this strain I
+
+ align:start position:0%
+important properties of of this strain I
+ 
+
+ align:start position:0%
+important properties of of this strain I
+already mentioned to you for mosfets
+
+ align:start position:0%
+already mentioned to you for mosfets
+ 
+
+ align:start position:0%
+already mentioned to you for mosfets
+when you start stretching the Silicon
+
+ align:start position:0%
+when you start stretching the Silicon
+ 
+
+ align:start position:0%
+when you start stretching the Silicon
+lattice parameter or compressing the
+
+ align:start position:0%
+lattice parameter or compressing the
+ 
+
+ align:start position:0%
+lattice parameter or compressing the
+parameter uh you can improve the
+
+ align:start position:0%
+parameter uh you can improve the
+ 
+
+ align:start position:0%
+parameter uh you can improve the
+mobility but there are other parameters
+
+ align:start position:0%
+mobility but there are other parameters
+ 
+
+ align:start position:0%
+mobility but there are other parameters
+that you change when you introduce
+
+ align:start position:0%
+that you change when you introduce
+ 
+
+ align:start position:0%
+that you change when you introduce
+strain when you put silic and geranium
+
+ align:start position:0%
+strain when you put silic and geranium
+ 
+
+ align:start position:0%
+strain when you put silic and geranium
+in probably one of the most important
+
+ align:start position:0%
+in probably one of the most important
+ 
+
+ align:start position:0%
+in probably one of the most important
+parameters uh you you need to know about
+
+ align:start position:0%
+parameters uh you you need to know about
+ 
+
+ align:start position:0%
+parameters uh you you need to know about
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+bandap so uh there is an energy band Gap
+
+ align:start position:0%
+bandap so uh there is an energy band Gap
+ 
+
+ align:start position:0%
+bandap so uh there is an energy band Gap
+difference between silicon and silicon
+
+ align:start position:0%
+difference between silicon and silicon
+ 
+
+ align:start position:0%
+difference between silicon and silicon
+geranium if this represents the band gap
+
+ align:start position:0%
+geranium if this represents the band gap
+ 
+
+ align:start position:0%
+geranium if this represents the band gap
+of relaxed silicon so EC is the
+
+ align:start position:0%
+of relaxed silicon so EC is the
+ 
+
+ align:start position:0%
+of relaxed silicon so EC is the
+conduction band EV is the veilance band
+
+ align:start position:0%
+conduction band EV is the veilance band
+ 
+
+ align:start position:0%
+conduction band EV is the veilance band
+this is the band gap of strain silicon
+
+ align:start position:0%
+this is the band gap of strain silicon
+ 
+
+ align:start position:0%
+this is the band gap of strain silicon
+geranium you see it's much smaller and
+
+ align:start position:0%
+geranium you see it's much smaller and
+ 
+
+ align:start position:0%
+geranium you see it's much smaller and
+most of the difference occurs in the
+
+ align:start position:0%
+most of the difference occurs in the
+ 
+
+ align:start position:0%
+most of the difference occurs in the
+veence band the veence band energy is is
+
+ align:start position:0%
+veence band the veence band energy is is
+ 
+
+ align:start position:0%
+veence band the veence band energy is is
+is larger so silic geranium has a
+
+ align:start position:0%
+is larger so silic geranium has a
+ 
+
+ align:start position:0%
+is larger so silic geranium has a
+smaller band Gap how much small smaller
+
+ align:start position:0%
+smaller band Gap how much small smaller
+ 
+
+ align:start position:0%
+smaller band Gap how much small smaller
+well you can look on this curve this is
+
+ align:start position:0%
+well you can look on this curve this is
+ 
+
+ align:start position:0%
+well you can look on this curve this is
+the difference between the band gap of
+
+ align:start position:0%
+the difference between the band gap of
+ 
+
+ align:start position:0%
+the difference between the band gap of
+the two as a function of germanium
+
+ align:start position:0%
+the two as a function of germanium
+ 
+
+ align:start position:0%
+the two as a function of germanium
+content so here if I have strain silicon
+
+ align:start position:0%
+content so here if I have strain silicon
+ 
+
+ align:start position:0%
+content so here if I have strain silicon
+geranium you should use this upper curve
+
+ align:start position:0%
+geranium you should use this upper curve
+ 
+
+ align:start position:0%
+geranium you should use this upper curve
+not the one that says unstrained so at
+
+ align:start position:0%
+not the one that says unstrained so at
+ 
+
+ align:start position:0%
+not the one that says unstrained so at
+20% the band Gap shrinks by about 150
+
+ align:start position:0%
+20% the band Gap shrinks by about 150
+ 
+
+ align:start position:0%
+20% the band Gap shrinks by about 150
+molts roughly so and you can read that
+
+ align:start position:0%
+molts roughly so and you can read that
+ 
+
+ align:start position:0%
+molts roughly so and you can read that
+right off the curve here at 50% it's
+
+ align:start position:0%
+right off the curve here at 50% it's
+ 
+
+ align:start position:0%
+right off the curve here at 50% it's
+another number maybe 350 so you have an
+
+ align:start position:0%
+another number maybe 350 so you have an
+ 
+
+ align:start position:0%
+another number maybe 350 so you have an
+idea uh of how it moves all these data
+
+ align:start position:0%
+idea uh of how it moves all these data
+ 
+
+ align:start position:0%
+idea uh of how it moves all these data
+points are are data from the literature
+
+ align:start position:0%
+points are are data from the literature
+ 
+
+ align:start position:0%
+points are are data from the literature
+that people extracted the bandap by
+
+ align:start position:0%
+that people extracted the bandap by
+ 
+
+ align:start position:0%
+that people extracted the bandap by
+various devices dood bipolar transistors
+
+ align:start position:0%
+various devices dood bipolar transistors
+ 
+
+ align:start position:0%
+various devices dood bipolar transistors
+for do and the the solid line is some
+
+ align:start position:0%
+for do and the the solid line is some
+ 
+
+ align:start position:0%
+for do and the the solid line is some
+theory that was published a long time
+
+ align:start position:0%
+theory that was published a long time
+ 
+
+ align:start position:0%
+theory that was published a long time
+ago so uh now the other thing that's if
+
+ align:start position:0%
+ago so uh now the other thing that's if
+ 
+
+ align:start position:0%
+ago so uh now the other thing that's if
+it's strained if it's unstrained if you
+
+ align:start position:0%
+it's strained if it's unstrained if you
+ 
+
+ align:start position:0%
+it's strained if it's unstrained if you
+grow the Silicon geranium so thick that
+
+ align:start position:0%
+grow the Silicon geranium so thick that
+ 
+
+ align:start position:0%
+grow the Silicon geranium so thick that
+it relaxes back so it comes comes back
+
+ align:start position:0%
+it relaxes back so it comes comes back
+ 
+
+ align:start position:0%
+it relaxes back so it comes comes back
+to be this cubic structure then what
+
+ align:start position:0%
+to be this cubic structure then what
+ 
+
+ align:start position:0%
+to be this cubic structure then what
+happens to the band Gap well in fact the
+
+ align:start position:0%
+happens to the band Gap well in fact the
+ 
+
+ align:start position:0%
+happens to the band Gap well in fact the
+band Gap difference is a lot smaller
+
+ align:start position:0%
+band Gap difference is a lot smaller
+ 
+
+ align:start position:0%
+band Gap difference is a lot smaller
+when it's unstrained the band Gap
+
+ align:start position:0%
+when it's unstrained the band Gap
+ 
+
+ align:start position:0%
+when it's unstrained the band Gap
+difference say at 20% is only about 100
+
+ align:start position:0%
+difference say at 20% is only about 100
+ 
+
+ align:start position:0%
+difference say at 20% is only about 100
+molts so a big fraction of this band Gap
+
+ align:start position:0%
+molts so a big fraction of this band Gap
+ 
+
+ align:start position:0%
+molts so a big fraction of this band Gap
+offset this band Gap difference is due
+
+ align:start position:0%
+offset this band Gap difference is due
+ 
+
+ align:start position:0%
+offset this band Gap difference is due
+to the strain it's due to the lce
+
+ align:start position:0%
+to the strain it's due to the lce
+ 
+
+ align:start position:0%
+to the strain it's due to the lce
+parameter change uh a certain fraction
+
+ align:start position:0%
+parameter change uh a certain fraction
+ 
+
+ align:start position:0%
+parameter change uh a certain fraction
+is due to the fact that we're just
+
+ align:start position:0%
+is due to the fact that we're just
+ 
+
+ align:start position:0%
+is due to the fact that we're just
+adding
+
+ align:start position:0%
+adding
+ 
+
+ align:start position:0%
+adding
+germanium um so so you need to know
+
+ align:start position:0%
+germanium um so so you need to know
+ 
+
+ align:start position:0%
+germanium um so so you need to know
+whether the material is unstrained or
+
+ align:start position:0%
+whether the material is unstrained or
+ 
+
+ align:start position:0%
+whether the material is unstrained or
+strained or somewhere in between in
+
+ align:start position:0%
+strained or somewhere in between in
+ 
+
+ align:start position:0%
+strained or somewhere in between in
+order to figure out what the band
+
+ align:start position:0%
+order to figure out what the band
+ 
+
+ align:start position:0%
+order to figure out what the band
+structure looks
+
+ align:start position:0%
+structure looks
+ 
+
+ align:start position:0%
+structure looks
+like and in fact on slide 10 I don't
+
+ align:start position:0%
+like and in fact on slide 10 I don't
+ 
+
+ align:start position:0%
+like and in fact on slide 10 I don't
+have to go through this in great detail
+
+ align:start position:0%
+have to go through this in great detail
+ 
+
+ align:start position:0%
+have to go through this in great detail
+if you haven't had energy Band Theory
+
+ align:start position:0%
+if you haven't had energy Band Theory
+ 
+
+ align:start position:0%
+if you haven't had energy Band Theory
+it's a little tricky but slide 10 gives
+
+ align:start position:0%
+it's a little tricky but slide 10 gives
+ 
+
+ align:start position:0%
+it's a little tricky but slide 10 gives
+you an idea of how the strain does
+
+ align:start position:0%
+you an idea of how the strain does
+ 
+
+ align:start position:0%
+you an idea of how the strain does
+affect the ener bands and the lineup and
+
+ align:start position:0%
+affect the ener bands and the lineup and
+ 
+
+ align:start position:0%
+affect the ener bands and the lineup and
+in fact uh if we look at the case for
+
+ align:start position:0%
+in fact uh if we look at the case for
+ 
+
+ align:start position:0%
+in fact uh if we look at the case for
+strained silicon geranium on Silicon uh
+
+ align:start position:0%
+strained silicon geranium on Silicon uh
+ 
+
+ align:start position:0%
+strained silicon geranium on Silicon uh
+so it'll be remember we said it when we
+
+ align:start position:0%
+so it'll be remember we said it when we
+ 
+
+ align:start position:0%
+so it'll be remember we said it when we
+grow strain silicon geranium is under bi
+
+ align:start position:0%
+grow strain silicon geranium is under bi
+ 
+
+ align:start position:0%
+grow strain silicon geranium is under bi
+axial compression in the X and and Y
+
+ align:start position:0%
+axial compression in the X and and Y
+ 
+
+ align:start position:0%
+axial compression in the X and and Y
+planes being compressed strain silicon
+
+ align:start position:0%
+planes being compressed strain silicon
+ 
+
+ align:start position:0%
+planes being compressed strain silicon
+geranium on silk in the band lineup
+
+ align:start position:0%
+geranium on silk in the band lineup
+ 
+
+ align:start position:0%
+geranium on silk in the band lineup
+looks like this as I mentioned most of
+
+ align:start position:0%
+looks like this as I mentioned most of
+ 
+
+ align:start position:0%
+looks like this as I mentioned most of
+the band offset is in the valance band
+
+ align:start position:0%
+the band offset is in the valance band
+ 
+
+ align:start position:0%
+the band offset is in the valance band
+so the holes will tend to be comined in
+
+ align:start position:0%
+so the holes will tend to be comined in
+ 
+
+ align:start position:0%
+so the holes will tend to be comined in
+the Silicon geranium uh there's very
+
+ align:start position:0%
+the Silicon geranium uh there's very
+ 
+
+ align:start position:0%
+the Silicon geranium uh there's very
+little band offset uh the lowest energy
+
+ align:start position:0%
+little band offset uh the lowest energy
+ 
+
+ align:start position:0%
+little band offset uh the lowest energy
+conduction band is about aligned in
+
+ align:start position:0%
+conduction band is about aligned in
+ 
+
+ align:start position:0%
+conduction band is about aligned in
+strain silicon geranium versus uh versus
+
+ align:start position:0%
+strain silicon geranium versus uh versus
+ 
+
+ align:start position:0%
+strain silicon geranium versus uh versus
+cubic silicon so there's not much
+
+ align:start position:0%
+cubic silicon so there's not much
+ 
+
+ align:start position:0%
+cubic silicon so there's not much
+opportunity for confining electrons so
+
+ align:start position:0%
+opportunity for confining electrons so
+ 
+
+ align:start position:0%
+opportunity for confining electrons so
+this material it turns out is ideal for
+
+ align:start position:0%
+this material it turns out is ideal for
+ 
+
+ align:start position:0%
+this material it turns out is ideal for
+a heter junction bipolar transistor for
+
+ align:start position:0%
+a heter junction bipolar transistor for
+ 
+
+ align:start position:0%
+a heter junction bipolar transistor for
+an npn this material has been in
+
+ align:start position:0%
+an npn this material has been in
+ 
+
+ align:start position:0%
+an npn this material has been in
+production for about 10 years people use
+
+ align:start position:0%
+production for about 10 years people use
+ 
+
+ align:start position:0%
+production for about 10 years people use
+it uh in high-speed RF
+
+ align:start position:0%
+it uh in high-speed RF
+ 
+
+ align:start position:0%
+it uh in high-speed RF
+devices uh so that's kind of a well a
+
+ align:start position:0%
+devices uh so that's kind of a well a
+ 
+
+ align:start position:0%
+devices uh so that's kind of a well a
+more well characterized and well-known
+
+ align:start position:0%
+more well characterized and well-known
+ 
+
+ align:start position:0%
+more well characterized and well-known
+structure where where the Germania
+
+ align:start position:0%
+structure where where the Germania
+ 
+
+ align:start position:0%
+structure where where the Germania
+fraction in a typical hbt you would buy
+
+ align:start position:0%
+fraction in a typical hbt you would buy
+ 
+
+ align:start position:0%
+fraction in a typical hbt you would buy
+off the shelf right now is probably
+
+ align:start position:0%
+off the shelf right now is probably
+ 
+
+ align:start position:0%
+off the shelf right now is probably
+about between 10% and 20% % of the atoms
+
+ align:start position:0%
+about between 10% and 20% % of the atoms
+ 
+
+ align:start position:0%
+about between 10% and 20% % of the atoms
+will be germanium in an
+
+ align:start position:0%
+will be germanium in an
+ 
+
+ align:start position:0%
+will be germanium in an
+hbt on the other hand if you grow the
+
+ align:start position:0%
+hbt on the other hand if you grow the
+ 
+
+ align:start position:0%
+hbt on the other hand if you grow the
+opposite structure so you have relaxed
+
+ align:start position:0%
+opposite structure so you have relaxed
+ 
+
+ align:start position:0%
+opposite structure so you have relaxed
+silicon germanium substrate and you grow
+
+ align:start position:0%
+silicon germanium substrate and you grow
+ 
+
+ align:start position:0%
+silicon germanium substrate and you grow
+a thin layer of silic and remember we
+
+ align:start position:0%
+a thin layer of silic and remember we
+ 
+
+ align:start position:0%
+a thin layer of silic and remember we
+said this was by axial tension the band
+
+ align:start position:0%
+said this was by axial tension the band
+ 
+
+ align:start position:0%
+said this was by axial tension the band
+lineup is quite different in fact you do
+
+ align:start position:0%
+lineup is quite different in fact you do
+ 
+
+ align:start position:0%
+lineup is quite different in fact you do
+get a sizable difference in the
+
+ align:start position:0%
+get a sizable difference in the
+ 
+
+ align:start position:0%
+get a sizable difference in the
+conduction band uh position and in fact
+
+ align:start position:0%
+conduction band uh position and in fact
+ 
+
+ align:start position:0%
+conduction band uh position and in fact
+uh the conduction band is lower the
+
+ align:start position:0%
+uh the conduction band is lower the
+ 
+
+ align:start position:0%
+uh the conduction band is lower the
+energy is lower in strain silicon so the
+
+ align:start position:0%
+energy is lower in strain silicon so the
+ 
+
+ align:start position:0%
+energy is lower in strain silicon so the
+electrons will tend to go into the
+
+ align:start position:0%
+electrons will tend to go into the
+ 
+
+ align:start position:0%
+electrons will tend to go into the
+strain silicon layer so if you make a
+
+ align:start position:0%
+strain silicon layer so if you make a
+ 
+
+ align:start position:0%
+strain silicon layer so if you make a
+fet and you make this as your the
+
+ align:start position:0%
+fet and you make this as your the
+ 
+
+ align:start position:0%
+fet and you make this as your the
+electrons want to go into the strain
+
+ align:start position:0%
+electrons want to go into the strain
+ 
+
+ align:start position:0%
+electrons want to go into the strain
+silicon the holes want to be in the
+
+ align:start position:0%
+silicon the holes want to be in the
+ 
+
+ align:start position:0%
+silicon the holes want to be in the
+Silicon geranium side um so this is
+
+ align:start position:0%
+Silicon geranium side um so this is
+ 
+
+ align:start position:0%
+Silicon geranium side um so this is
+what's called a tight two band alignment
+
+ align:start position:0%
+what's called a tight two band alignment
+ 
+
+ align:start position:0%
+what's called a tight two band alignment
+so you can make lots of interesting
+
+ align:start position:0%
+so you can make lots of interesting
+ 
+
+ align:start position:0%
+so you can make lots of interesting
+devices uh just by taking silic silicon
+
+ align:start position:0%
+devices uh just by taking silic silicon
+ 
+
+ align:start position:0%
+devices uh just by taking silic silicon
+and and straining it on on relaxed
+
+ align:start position:0%
+and and straining it on on relaxed
+ 
+
+ align:start position:0%
+and and straining it on on relaxed
+silicon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geranium the other thing that happens
+
+ align:start position:0%
+geranium the other thing that happens
+ 
+
+ align:start position:0%
+geranium the other thing that happens
+here that's important and we'll talk
+
+ align:start position:0%
+here that's important and we'll talk
+ 
+
+ align:start position:0%
+here that's important and we'll talk
+about when we talk about the mobility
+
+ align:start position:0%
+about when we talk about the mobility
+ 
+
+ align:start position:0%
+about when we talk about the mobility
+enhancement you notice what's happened
+
+ align:start position:0%
+enhancement you notice what's happened
+ 
+
+ align:start position:0%
+enhancement you notice what's happened
+is the conduction band is actually split
+
+ align:start position:0%
+is the conduction band is actually split
+ 
+
+ align:start position:0%
+is the conduction band is actually split
+into two levels originally uh there was
+
+ align:start position:0%
+into two levels originally uh there was
+ 
+
+ align:start position:0%
+into two levels originally uh there was
+only a single uh energy level and that
+
+ align:start position:0%
+only a single uh energy level and that
+ 
+
+ align:start position:0%
+only a single uh energy level and that
+splitting is what truly was responsible
+
+ align:start position:0%
+splitting is what truly was responsible
+ 
+
+ align:start position:0%
+splitting is what truly was responsible
+uh to a large extent for the mobility
+
+ align:start position:0%
+uh to a large extent for the mobility
+ 
+
+ align:start position:0%
+uh to a large extent for the mobility
+Improvement if you really wanted to get
+
+ align:start position:0%
+Improvement if you really wanted to get
+ 
+
+ align:start position:0%
+Improvement if you really wanted to get
+nitty-gritty I won't go through it but
+
+ align:start position:0%
+nitty-gritty I won't go through it but
+ 
+
+ align:start position:0%
+nitty-gritty I won't go through it but
+here on page 11 I've made a reference to
+
+ align:start position:0%
+here on page 11 I've made a reference to
+ 
+
+ align:start position:0%
+here on page 11 I've made a reference to
+a famous paper by Chris vanderwal and
+
+ align:start position:0%
+a famous paper by Chris vanderwal and
+ 
+
+ align:start position:0%
+a famous paper by Chris vanderwal and
+Richard Martin published in the mid
+
+ align:start position:0%
+Richard Martin published in the mid
+ 
+
+ align:start position:0%
+Richard Martin published in the mid
+1980s vanderwall and Martin actually
+
+ align:start position:0%
+1980s vanderwall and Martin actually
+ 
+
+ align:start position:0%
+1980s vanderwall and Martin actually
+theoretically did did a pretty good job
+
+ align:start position:0%
+theoretically did did a pretty good job
+ 
+
+ align:start position:0%
+theoretically did did a pretty good job
+uh of of trying to calculate what the
+
+ align:start position:0%
+uh of of trying to calculate what the
+ 
+
+ align:start position:0%
+uh of of trying to calculate what the
+energy band structure looks like for
+
+ align:start position:0%
+energy band structure looks like for
+ 
+
+ align:start position:0%
+energy band structure looks like for
+strain silicon geranium on cubic silicon
+
+ align:start position:0%
+strain silicon geranium on cubic silicon
+ 
+
+ align:start position:0%
+strain silicon geranium on cubic silicon
+which is we're showing over here and
+
+ align:start position:0%
+which is we're showing over here and
+ 
+
+ align:start position:0%
+which is we're showing over here and
+also for strain silicon geranium on
+
+ align:start position:0%
+also for strain silicon geranium on
+ 
+
+ align:start position:0%
+also for strain silicon geranium on
+cubic geranium so but they have both of
+
+ align:start position:0%
+cubic geranium so but they have both of
+ 
+
+ align:start position:0%
+cubic geranium so but they have both of
+these and and uh I won't go through it
+
+ align:start position:0%
+these and and uh I won't go through it
+ 
+
+ align:start position:0%
+these and and uh I won't go through it
+in any great detail but I if you're
+
+ align:start position:0%
+in any great detail but I if you're
+ 
+
+ align:start position:0%
+in any great detail but I if you're
+interested in the solid state physics
+
+ align:start position:0%
+interested in the solid state physics
+ 
+
+ align:start position:0%
+interested in the solid state physics
+and you end up working in this area this
+
+ align:start position:0%
+and you end up working in this area this
+ 
+
+ align:start position:0%
+and you end up working in this area this
+is a good paper for you to look at um
+
+ align:start position:0%
+is a good paper for you to look at um
+ 
+
+ align:start position:0%
+is a good paper for you to look at um
+again the band Gap would be the
+
+ align:start position:0%
+again the band Gap would be the
+ 
+
+ align:start position:0%
+again the band Gap would be the
+difference uh the the distance between
+
+ align:start position:0%
+difference uh the the distance between
+ 
+
+ align:start position:0%
+difference uh the the distance between
+this point here in the conduction band
+
+ align:start position:0%
+this point here in the conduction band
+ 
+
+ align:start position:0%
+this point here in the conduction band
+and a point here in the veence band so
+
+ align:start position:0%
+and a point here in the veence band so
+ 
+
+ align:start position:0%
+and a point here in the veence band so
+but they actually calculated how the
+
+ align:start position:0%
+but they actually calculated how the
+ 
+
+ align:start position:0%
+but they actually calculated how the
+veence and conduction bands move as you
+
+ align:start position:0%
+veence and conduction bands move as you
+ 
+
+ align:start position:0%
+veence and conduction bands move as you
+add strain and geranium to the
+
+ align:start position:0%
+add strain and geranium to the
+ 
+
+ align:start position:0%
+add strain and geranium to the
+system on slide 12 on also giving you uh
+
+ align:start position:0%
+system on slide 12 on also giving you uh
+ 
+
+ align:start position:0%
+system on slide 12 on also giving you uh
+excuse me a reference for how not only
+
+ align:start position:0%
+excuse me a reference for how not only
+ 
+
+ align:start position:0%
+excuse me a reference for how not only
+has the band Gap changes but people have
+
+ align:start position:0%
+has the band Gap changes but people have
+ 
+
+ align:start position:0%
+has the band Gap changes but people have
+actually made some reference some
+
+ align:start position:0%
+actually made some reference some
+ 
+
+ align:start position:0%
+actually made some reference some
+measurements of the energy band offsets
+
+ align:start position:0%
+measurements of the energy band offsets
+ 
+
+ align:start position:0%
+measurements of the energy band offsets
+when you have strained silicon on
+
+ align:start position:0%
+when you have strained silicon on
+ 
+
+ align:start position:0%
+when you have strained silicon on
+relaxed silicon geranium say for a
+
+ align:start position:0%
+relaxed silicon geranium say for a
+ 
+
+ align:start position:0%
+relaxed silicon geranium say for a
+mosfet this is taken out of Jeff welzer
+
+ align:start position:0%
+mosfet this is taken out of Jeff welzer
+ 
+
+ align:start position:0%
+mosfet this is taken out of Jeff welzer
+thesis from 1994 and and what what you
+
+ align:start position:0%
+thesis from 1994 and and what what you
+ 
+
+ align:start position:0%
+thesis from 1994 and and what what you
+can see here this is the basic structure
+
+ align:start position:0%
+can see here this is the basic structure
+ 
+
+ align:start position:0%
+can see here this is the basic structure
+you have an an oxide you have a thin
+
+ align:start position:0%
+you have an an oxide you have a thin
+ 
+
+ align:start position:0%
+you have an an oxide you have a thin
+layer of strained silicon and you have
+
+ align:start position:0%
+layer of strained silicon and you have
+ 
+
+ align:start position:0%
+layer of strained silicon and you have
+these energy offsets here the energy
+
+ align:start position:0%
+these energy offsets here the energy
+ 
+
+ align:start position:0%
+these energy offsets here the energy
+conduction band energy is a little lower
+
+ align:start position:0%
+conduction band energy is a little lower
+ 
+
+ align:start position:0%
+conduction band energy is a little lower
+and the veence band energy is uh is a
+
+ align:start position:0%
+and the veence band energy is uh is a
+ 
+
+ align:start position:0%
+and the veence band energy is uh is a
+slightly different in strain silicon and
+
+ align:start position:0%
+slightly different in strain silicon and
+ 
+
+ align:start position:0%
+slightly different in strain silicon and
+these numbers Delta EC how different
+
+ align:start position:0%
+these numbers Delta EC how different
+ 
+
+ align:start position:0%
+these numbers Delta EC how different
+they are these these these energy band
+
+ align:start position:0%
+they are these these these energy band
+ 
+
+ align:start position:0%
+they are these these these energy band
+discontinuities were actually measured
+
+ align:start position:0%
+discontinuities were actually measured
+ 
+
+ align:start position:0%
+discontinuities were actually measured
+and Delta EV here as a function of the
+
+ align:start position:0%
+and Delta EV here as a function of the
+ 
+
+ align:start position:0%
+and Delta EV here as a function of the
+geranium fraction in the
+
+ align:start position:0%
+geranium fraction in the
+ 
+
+ align:start position:0%
+geranium fraction in the
+substrate uh the bullets are the
+
+ align:start position:0%
+substrate uh the bullets are the
+ 
+
+ align:start position:0%
+substrate uh the bullets are the
+measurements and the lines are are the
+
+ align:start position:0%
+measurements and the lines are are the
+ 
+
+ align:start position:0%
+measurements and the lines are are the
+uh are the calculations from fand wall
+
+ align:start position:0%
+uh are the calculations from fand wall
+ 
+
+ align:start position:0%
+uh are the calculations from fand wall
+and Martin and indeed you get pretty
+
+ align:start position:0%
+and Martin and indeed you get pretty
+ 
+
+ align:start position:0%
+and Martin and indeed you get pretty
+good agreement so we have a rough idea
+
+ align:start position:0%
+good agreement so we have a rough idea
+ 
+
+ align:start position:0%
+good agreement so we have a rough idea
+now of what these energy band structures
+
+ align:start position:0%
+now of what these energy band structures
+ 
+
+ align:start position:0%
+now of what these energy band structures
+look like when I add strain or when I
+
+ align:start position:0%
+look like when I add strain or when I
+ 
+
+ align:start position:0%
+look like when I add strain or when I
+add uh you know silicon geranium to to
+
+ align:start position:0%
+add uh you know silicon geranium to to
+ 
+
+ align:start position:0%
+add uh you know silicon geranium to to
+the substrate um so that's important for
+
+ align:start position:0%
+the substrate um so that's important for
+ 
+
+ align:start position:0%
+the substrate um so that's important for
+figuring out how all these devices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work I mentioned that um when you
+
+ align:start position:0%
+work I mentioned that um when you
+ 
+
+ align:start position:0%
+work I mentioned that um when you
+squeeze silicon either you stretch it uh
+
+ align:start position:0%
+squeeze silicon either you stretch it uh
+ 
+
+ align:start position:0%
+squeeze silicon either you stretch it uh
+in a bi axial sense um you can improve
+
+ align:start position:0%
+in a bi axial sense um you can improve
+ 
+
+ align:start position:0%
+in a bi axial sense um you can improve
+the mobility and the question is well
+
+ align:start position:0%
+the mobility and the question is well
+ 
+
+ align:start position:0%
+the mobility and the question is well
+why is that I don't want to go into
+
+ align:start position:0%
+why is that I don't want to go into
+ 
+
+ align:start position:0%
+why is that I don't want to go into
+detail in the solid state physics but it
+
+ align:start position:0%
+detail in the solid state physics but it
+ 
+
+ align:start position:0%
+detail in the solid state physics but it
+turns out if you put silicon in bi axial
+
+ align:start position:0%
+turns out if you put silicon in bi axial
+ 
+
+ align:start position:0%
+turns out if you put silicon in bi axial
+tension you break the cubic symmetry of
+
+ align:start position:0%
+tension you break the cubic symmetry of
+ 
+
+ align:start position:0%
+tension you break the cubic symmetry of
+the lattice ordinarily in the lattice
+
+ align:start position:0%
+the lattice ordinarily in the lattice
+ 
+
+ align:start position:0%
+the lattice ordinarily in the lattice
+the X YZ directions are all completely
+
+ align:start position:0%
+the X YZ directions are all completely
+ 
+
+ align:start position:0%
+the X YZ directions are all completely
+symmetric when when silicon is not
+
+ align:start position:0%
+symmetric when when silicon is not
+ 
+
+ align:start position:0%
+symmetric when when silicon is not
+strained when it's strained they
+
+ align:start position:0%
+strained when it's strained they
+ 
+
+ align:start position:0%
+strained when it's strained they
+actually become asymmetric um X and Y
+
+ align:start position:0%
+actually become asymmetric um X and Y
+ 
+
+ align:start position:0%
+actually become asymmetric um X and Y
+last parameters larger than in the Z and
+
+ align:start position:0%
+last parameters larger than in the Z and
+ 
+
+ align:start position:0%
+last parameters larger than in the Z and
+what happens by that breaking of the
+
+ align:start position:0%
+what happens by that breaking of the
+ 
+
+ align:start position:0%
+what happens by that breaking of the
+physical symmetry um is that that um the
+
+ align:start position:0%
+physical symmetry um is that that um the
+ 
+
+ align:start position:0%
+physical symmetry um is that that um the
+six energy of ellipsoids uh ellipsoids
+
+ align:start position:0%
+six energy of ellipsoids uh ellipsoids
+ 
+
+ align:start position:0%
+six energy of ellipsoids uh ellipsoids
+in in constant energy space that are all
+
+ align:start position:0%
+in in constant energy space that are all
+ 
+
+ align:start position:0%
+in in constant energy space that are all
+at the same energy actually split up
+
+ align:start position:0%
+at the same energy actually split up
+ 
+
+ align:start position:0%
+at the same energy actually split up
+when you introduce the strain and two of
+
+ align:start position:0%
+when you introduce the strain and two of
+ 
+
+ align:start position:0%
+when you introduce the strain and two of
+them these two ellipsoids here where the
+
+ align:start position:0%
+them these two ellipsoids here where the
+ 
+
+ align:start position:0%
+them these two ellipsoids here where the
+electrons can be these two uh red ones
+
+ align:start position:0%
+electrons can be these two uh red ones
+ 
+
+ align:start position:0%
+electrons can be these two uh red ones
+the so-called perpendicular valleys
+
+ align:start position:0%
+the so-called perpendicular valleys
+ 
+
+ align:start position:0%
+the so-called perpendicular valleys
+labeled del2 they actually end up being
+
+ align:start position:0%
+labeled del2 they actually end up being
+ 
+
+ align:start position:0%
+labeled del2 they actually end up being
+at a lower energy than these other four
+
+ align:start position:0%
+at a lower energy than these other four
+ 
+
+ align:start position:0%
+at a lower energy than these other four
+so we get this we get this strain
+
+ align:start position:0%
+so we get this we get this strain
+ 
+
+ align:start position:0%
+so we get this we get this strain
+induced splitting uh in bulk silicon all
+
+ align:start position:0%
+induced splitting uh in bulk silicon all
+ 
+
+ align:start position:0%
+induced splitting uh in bulk silicon all
+six of these valleys that that represent
+
+ align:start position:0%
+six of these valleys that that represent
+ 
+
+ align:start position:0%
+six of these valleys that that represent
+states that electrons can occupy all six
+
+ align:start position:0%
+states that electrons can occupy all six
+ 
+
+ align:start position:0%
+states that electrons can occupy all six
+of them are at the same energy level but
+
+ align:start position:0%
+of them are at the same energy level but
+ 
+
+ align:start position:0%
+of them are at the same energy level but
+by group Theory when we break the
+
+ align:start position:0%
+by group Theory when we break the
+ 
+
+ align:start position:0%
+by group Theory when we break the
+Symmetry we break that up into a
+
+ align:start position:0%
+Symmetry we break that up into a
+ 
+
+ align:start position:0%
+Symmetry we break that up into a
+two-fold degenerate uh level which is
+
+ align:start position:0%
+two-fold degenerate uh level which is
+ 
+
+ align:start position:0%
+two-fold degenerate uh level which is
+lower energy and a four-fold degenerate
+
+ align:start position:0%
+lower energy and a four-fold degenerate
+ 
+
+ align:start position:0%
+lower energy and a four-fold degenerate
+level so by breaking this up actually
+
+ align:start position:0%
+level so by breaking this up actually
+ 
+
+ align:start position:0%
+level so by breaking this up actually
+what happens is now most of electrons
+
+ align:start position:0%
+what happens is now most of electrons
+ 
+
+ align:start position:0%
+what happens is now most of electrons
+want to be in these red valleys and the
+
+ align:start position:0%
+want to be in these red valleys and the
+ 
+
+ align:start position:0%
+want to be in these red valleys and the
+scattering between the red and the green
+
+ align:start position:0%
+scattering between the red and the green
+ 
+
+ align:start position:0%
+scattering between the red and the green
+is suppressed because it costs you
+
+ align:start position:0%
+is suppressed because it costs you
+ 
+
+ align:start position:0%
+is suppressed because it costs you
+energy so instead of scattering between
+
+ align:start position:0%
+energy so instead of scattering between
+ 
+
+ align:start position:0%
+energy so instead of scattering between
+all six you can only scatter you know
+
+ align:start position:0%
+all six you can only scatter you know
+ 
+
+ align:start position:0%
+all six you can only scatter you know
+very effectively between these two red
+
+ align:start position:0%
+very effectively between these two red
+ 
+
+ align:start position:0%
+very effectively between these two red
+ones and so the scattering time goes up
+
+ align:start position:0%
+ones and so the scattering time goes up
+ 
+
+ align:start position:0%
+ones and so the scattering time goes up
+and the mobility is directly
+
+ align:start position:0%
+and the mobility is directly
+ 
+
+ align:start position:0%
+and the mobility is directly
+proportional to the scattering time the
+
+ align:start position:0%
+proportional to the scattering time the
+ 
+
+ align:start position:0%
+proportional to the scattering time the
+inplane uh ma uh effective Mass also
+
+ align:start position:0%
+inplane uh ma uh effective Mass also
+ 
+
+ align:start position:0%
+inplane uh ma uh effective Mass also
+goes down so the mobility also goes up
+
+ align:start position:0%
+goes down so the mobility also goes up
+ 
+
+ align:start position:0%
+goes down so the mobility also goes up
+for that reason so just by breaking the
+
+ align:start position:0%
+for that reason so just by breaking the
+ 
+
+ align:start position:0%
+for that reason so just by breaking the
+Symmetry we can change the occupation of
+
+ align:start position:0%
+Symmetry we can change the occupation of
+ 
+
+ align:start position:0%
+Symmetry we can change the occupation of
+the energy bands in Silicon and we can
+
+ align:start position:0%
+the energy bands in Silicon and we can
+ 
+
+ align:start position:0%
+the energy bands in Silicon and we can
+make the mobility higher for electrons
+
+ align:start position:0%
+make the mobility higher for electrons
+ 
+
+ align:start position:0%
+make the mobility higher for electrons
+um in the veence band I'm not going to
+
+ align:start position:0%
+um in the veence band I'm not going to
+ 
+
+ align:start position:0%
+um in the veence band I'm not going to
+go through in great detail but it's it's
+
+ align:start position:0%
+go through in great detail but it's it's
+ 
+
+ align:start position:0%
+go through in great detail but it's it's
+quite a bit more complicated but the
+
+ align:start position:0%
+quite a bit more complicated but the
+ 
+
+ align:start position:0%
+quite a bit more complicated but the
+turn out with strin we also split the
+
+ align:start position:0%
+turn out with strin we also split the
+ 
+
+ align:start position:0%
+turn out with strin we also split the
+genery in the veence band we also
+
+ align:start position:0%
+genery in the veence band we also
+ 
+
+ align:start position:0%
+genery in the veence band we also
+suppress interband scattering it it is a
+
+ align:start position:0%
+suppress interband scattering it it is a
+ 
+
+ align:start position:0%
+suppress interband scattering it it is a
+lot more tricky but uh it is possible to
+
+ align:start position:0%
+lot more tricky but uh it is possible to
+ 
+
+ align:start position:0%
+lot more tricky but uh it is possible to
+also induced uh in improved uh hole
+
+ align:start position:0%
+also induced uh in improved uh hole
+ 
+
+ align:start position:0%
+also induced uh in improved uh hole
+Mobility or pimos Mobility uh by
+
+ align:start position:0%
+Mobility or pimos Mobility uh by
+ 
+
+ align:start position:0%
+Mobility or pimos Mobility uh by
+introducing
+
+ align:start position:0%
+introducing
+ 
+
+ align:start position:0%
+introducing
+strain and in fact here on slide 14 I'll
+
+ align:start position:0%
+strain and in fact here on slide 14 I'll
+ 
+
+ align:start position:0%
+strain and in fact here on slide 14 I'll
+just walk through some of the older data
+
+ align:start position:0%
+just walk through some of the older data
+ 
+
+ align:start position:0%
+just walk through some of the older data
+this was from 1992 by welser these were
+
+ align:start position:0%
+this was from 1992 by welser these were
+ 
+
+ align:start position:0%
+this was from 1992 by welser these were
+the first strain mosfets that were
+
+ align:start position:0%
+the first strain mosfets that were
+ 
+
+ align:start position:0%
+the first strain mosfets that were
+fabricated where uh he made a thin layer
+
+ align:start position:0%
+fabricated where uh he made a thin layer
+ 
+
+ align:start position:0%
+fabricated where uh he made a thin layer
+of strained silicon on relaxed silicon
+
+ align:start position:0%
+of strained silicon on relaxed silicon
+ 
+
+ align:start position:0%
+of strained silicon on relaxed silicon
+Germania and then just implanted it and
+
+ align:start position:0%
+Germania and then just implanted it and
+ 
+
+ align:start position:0%
+Germania and then just implanted it and
+made it made a silicon mosfet with a
+
+ align:start position:0%
+made it made a silicon mosfet with a
+ 
+
+ align:start position:0%
+made it made a silicon mosfet with a
+source and drain was an N mosfet and
+
+ align:start position:0%
+source and drain was an N mosfet and
+ 
+
+ align:start position:0%
+source and drain was an N mosfet and
+this he called the surface Channel
+
+ align:start position:0%
+this he called the surface Channel
+ 
+
+ align:start position:0%
+this he called the surface Channel
+mosfet because the bands aligned so that
+
+ align:start position:0%
+mosfet because the bands aligned so that
+ 
+
+ align:start position:0%
+mosfet because the bands aligned so that
+the electrons wanted to be at the
+
+ align:start position:0%
+the electrons wanted to be at the
+ 
+
+ align:start position:0%
+the electrons wanted to be at the
+surface so the channel is at the surface
+
+ align:start position:0%
+surface so the channel is at the surface
+ 
+
+ align:start position:0%
+surface so the channel is at the surface
+this he called a bur Channel mosfet so
+
+ align:start position:0%
+this he called a bur Channel mosfet so
+ 
+
+ align:start position:0%
+this he called a bur Channel mosfet so
+if you look at the energy band diagram
+
+ align:start position:0%
+if you look at the energy band diagram
+ 
+
+ align:start position:0%
+if you look at the energy band diagram
+here there's a little bit of silicon
+
+ align:start position:0%
+here there's a little bit of silicon
+ 
+
+ align:start position:0%
+here there's a little bit of silicon
+geranium on top and that confines the
+
+ align:start position:0%
+geranium on top and that confines the
+ 
+
+ align:start position:0%
+geranium on top and that confines the
+electrons to be a little bit buried
+
+ align:start position:0%
+electrons to be a little bit buried
+ 
+
+ align:start position:0%
+electrons to be a little bit buried
+below the surface it's like a moss bet
+
+ align:start position:0%
+below the surface it's like a moss bet
+ 
+
+ align:start position:0%
+below the surface it's like a moss bet
+but where the channel is slightly
+
+ align:start position:0%
+but where the channel is slightly
+ 
+
+ align:start position:0%
+but where the channel is slightly
+buried and on on 15 actually measured
+
+ align:start position:0%
+buried and on on 15 actually measured
+ 
+
+ align:start position:0%
+buried and on on 15 actually measured
+some of those mobilities these were the
+
+ align:start position:0%
+some of those mobilities these were the
+ 
+
+ align:start position:0%
+some of those mobilities these were the
+first mobilities measured and if you
+
+ align:start position:0%
+first mobilities measured and if you
+ 
+
+ align:start position:0%
+first mobilities measured and if you
+look at this solid line This is the
+
+ align:start position:0%
+look at this solid line This is the
+ 
+
+ align:start position:0%
+look at this solid line This is the
+mobility measured in a moset that had no
+
+ align:start position:0%
+mobility measured in a moset that had no
+ 
+
+ align:start position:0%
+mobility measured in a moset that had no
+strain and for a surface channel moset
+
+ align:start position:0%
+strain and for a surface channel moset
+ 
+
+ align:start position:0%
+strain and for a surface channel moset
+the mobility that he measured was about
+
+ align:start position:0%
+the mobility that he measured was about
+ 
+
+ align:start position:0%
+the mobility that he measured was about
+um oh I don't know 80% higher about a
+
+ align:start position:0%
+um oh I don't know 80% higher about a
+ 
+
+ align:start position:0%
+um oh I don't know 80% higher about a
+factor of 1.8 Improvement in the surface
+
+ align:start position:0%
+factor of 1.8 Improvement in the surface
+ 
+
+ align:start position:0%
+factor of 1.8 Improvement in the surface
+channel so right off the bat as a
+
+ align:start position:0%
+channel so right off the bat as a
+ 
+
+ align:start position:0%
+channel so right off the bat as a
+function of vertical field you see we
+
+ align:start position:0%
+function of vertical field you see we
+ 
+
+ align:start position:0%
+function of vertical field you see we
+have parameter by changing the strain
+
+ align:start position:0%
+have parameter by changing the strain
+ 
+
+ align:start position:0%
+have parameter by changing the strain
+you can up the mobility by about 80% if
+
+ align:start position:0%
+you can up the mobility by about 80% if
+ 
+
+ align:start position:0%
+you can up the mobility by about 80% if
+you do the berry Channel you can get
+
+ align:start position:0%
+you do the berry Channel you can get
+ 
+
+ align:start position:0%
+you do the berry Channel you can get
+even higher mobilities at at low gate
+
+ align:start position:0%
+even higher mobilities at at low gate
+ 
+
+ align:start position:0%
+even higher mobilities at at low gate
+bias but the mobility seem to go down U
+
+ align:start position:0%
+bias but the mobility seem to go down U
+ 
+
+ align:start position:0%
+bias but the mobility seem to go down U
+at High Gate bias uh for various reasons
+
+ align:start position:0%
+at High Gate bias uh for various reasons
+ 
+
+ align:start position:0%
+at High Gate bias uh for various reasons
+so kind of the the first evidence that
+
+ align:start position:0%
+so kind of the the first evidence that
+ 
+
+ align:start position:0%
+so kind of the the first evidence that
+strain makes a big
+
+ align:start position:0%
+strain makes a big
+ 
+
+ align:start position:0%
+strain makes a big
+difference these are the actual
+
+ align:start position:0%
+difference these are the actual
+ 
+
+ align:start position:0%
+difference these are the actual
+structures that one can grow shown on on
+
+ align:start position:0%
+structures that one can grow shown on on
+ 
+
+ align:start position:0%
+structures that one can grow shown on on
+on slide 16 uh again to make an inoss F
+
+ align:start position:0%
+on slide 16 uh again to make an inoss F
+ 
+
+ align:start position:0%
+on slide 16 uh again to make an inoss F
+you can grow relax silicon geranium with
+
+ align:start position:0%
+you can grow relax silicon geranium with
+ 
+
+ align:start position:0%
+you can grow relax silicon geranium with
+a thin layer of strain silicon and this
+
+ align:start position:0%
+a thin layer of strain silicon and this
+ 
+
+ align:start position:0%
+a thin layer of strain silicon and this
+becomes a high electron Mobility channel
+
+ align:start position:0%
+becomes a high electron Mobility channel
+ 
+
+ align:start position:0%
+becomes a high electron Mobility channel
+it's slightly different structure is
+
+ align:start position:0%
+it's slightly different structure is
+ 
+
+ align:start position:0%
+it's slightly different structure is
+needed for the P Moss very similar but
+
+ align:start position:0%
+needed for the P Moss very similar but
+ 
+
+ align:start position:0%
+needed for the P Moss very similar but
+but with slight variations uh so you can
+
+ align:start position:0%
+but with slight variations uh so you can
+ 
+
+ align:start position:0%
+but with slight variations uh so you can
+make seos uh devices using this type of
+
+ align:start position:0%
+make seos uh devices using this type of
+ 
+
+ align:start position:0%
+make seos uh devices using this type of
+technique and I'll skip through the
+
+ align:start position:0%
+technique and I'll skip through the
+ 
+
+ align:start position:0%
+technique and I'll skip through the
+energy band diagrams for
+
+ align:start position:0%
+energy band diagrams for
+ 
+
+ align:start position:0%
+energy band diagrams for
+now um slide 17 shows some Metrology the
+
+ align:start position:0%
+now um slide 17 shows some Metrology the
+ 
+
+ align:start position:0%
+now um slide 17 shows some Metrology the
+question you may be thinking well how do
+
+ align:start position:0%
+question you may be thinking well how do
+ 
+
+ align:start position:0%
+question you may be thinking well how do
+you really know all right your Mobility
+
+ align:start position:0%
+you really know all right your Mobility
+ 
+
+ align:start position:0%
+you really know all right your Mobility
+went up but how do you really know them
+
+ align:start position:0%
+went up but how do you really know them
+ 
+
+ align:start position:0%
+went up but how do you really know them
+that the layers are strained especially
+
+ align:start position:0%
+that the layers are strained especially
+ 
+
+ align:start position:0%
+that the layers are strained especially
+when they're so thin how do you measure
+
+ align:start position:0%
+when they're so thin how do you measure
+ 
+
+ align:start position:0%
+when they're so thin how do you measure
+strain in a layer that's only 100 Anum
+
+ align:start position:0%
+strain in a layer that's only 100 Anum
+ 
+
+ align:start position:0%
+strain in a layer that's only 100 Anum
+thick you really can't use x-ray
+
+ align:start position:0%
+thick you really can't use x-ray
+ 
+
+ align:start position:0%
+thick you really can't use x-ray
+defraction x-ray defraction on 100
+
+ align:start position:0%
+defraction x-ray defraction on 100
+ 
+
+ align:start position:0%
+defraction x-ray defraction on 100
+anstrom layer going to be really tough
+
+ align:start position:0%
+anstrom layer going to be really tough
+ 
+
+ align:start position:0%
+anstrom layer going to be really tough
+because the layer is very thin so how do
+
+ align:start position:0%
+because the layer is very thin so how do
+ 
+
+ align:start position:0%
+because the layer is very thin so how do
+you measure that reduced that change in
+
+ align:start position:0%
+you measure that reduced that change in
+ 
+
+ align:start position:0%
+you measure that reduced that change in
+the last parameter well it turns out
+
+ align:start position:0%
+the last parameter well it turns out
+ 
+
+ align:start position:0%
+the last parameter well it turns out
+there's a technique called Raman
+
+ align:start position:0%
+there's a technique called Raman
+ 
+
+ align:start position:0%
+there's a technique called Raman
+scattering which is an optical
+
+ align:start position:0%
+scattering which is an optical
+ 
+
+ align:start position:0%
+scattering which is an optical
+interaction there are certain
+
+ align:start position:0%
+interaction there are certain
+ 
+
+ align:start position:0%
+interaction there are certain
+vibrational modes in a lattice that will
+
+ align:start position:0%
+vibrational modes in a lattice that will
+ 
+
+ align:start position:0%
+vibrational modes in a lattice that will
+scatter uh uh scatter photons and the
+
+ align:start position:0%
+scatter uh uh scatter photons and the
+ 
+
+ align:start position:0%
+scatter uh uh scatter photons and the
+ramen effect can be used to measure the
+
+ align:start position:0%
+ramen effect can be used to measure the
+ 
+
+ align:start position:0%
+ramen effect can be used to measure the
+strain or the change in mass parameter
+
+ align:start position:0%
+strain or the change in mass parameter
+ 
+
+ align:start position:0%
+strain or the change in mass parameter
+even a very very thin layer so here's an
+
+ align:start position:0%
+even a very very thin layer so here's an
+ 
+
+ align:start position:0%
+even a very very thin layer so here's an
+example of a mosfet that was made uh a
+
+ align:start position:0%
+example of a mosfet that was made uh a
+ 
+
+ align:start position:0%
+example of a mosfet that was made uh a
+Ramen Spectrum so you're measuring the
+
+ align:start position:0%
+Ramen Spectrum so you're measuring the
+ 
+
+ align:start position:0%
+Ramen Spectrum so you're measuring the
+intensity of the scattered light uh as a
+
+ align:start position:0%
+intensity of the scattered light uh as a
+ 
+
+ align:start position:0%
+intensity of the scattered light uh as a
+f of the
+
+ align:start position:0%
+f of the
+ 
+
+ align:start position:0%
+f of the
+frequency uh in inverse centimeters and
+
+ align:start position:0%
+frequency uh in inverse centimeters and
+ 
+
+ align:start position:0%
+frequency uh in inverse centimeters and
+um there's you see a large Peak here
+
+ align:start position:0%
+um there's you see a large Peak here
+ 
+
+ align:start position:0%
+um there's you see a large Peak here
+associated with relaxed silicon geranium
+
+ align:start position:0%
+associated with relaxed silicon geranium
+ 
+
+ align:start position:0%
+associated with relaxed silicon geranium
+and there's a small Peak here which is
+
+ align:start position:0%
+and there's a small Peak here which is
+ 
+
+ align:start position:0%
+and there's a small Peak here which is
+the thin strained silicon layer now if
+
+ align:start position:0%
+the thin strained silicon layer now if
+ 
+
+ align:start position:0%
+the thin strained silicon layer now if
+that layer were
+
+ align:start position:0%
+that layer were
+ 
+
+ align:start position:0%
+that layer were
+unstrained bulk silicon if you just take
+
+ align:start position:0%
+unstrained bulk silicon if you just take
+ 
+
+ align:start position:0%
+unstrained bulk silicon if you just take
+a wafer of bulk silicon and subject to
+
+ align:start position:0%
+a wafer of bulk silicon and subject to
+ 
+
+ align:start position:0%
+a wafer of bulk silicon and subject to
+Rama scattering you get a line at 521 in
+
+ align:start position:0%
+Rama scattering you get a line at 521 in
+ 
+
+ align:start position:0%
+Rama scattering you get a line at 521 in
+centimeters so it turns out the shift of
+
+ align:start position:0%
+centimeters so it turns out the shift of
+ 
+
+ align:start position:0%
+centimeters so it turns out the shift of
+the sil of the Silicon strain silicon
+
+ align:start position:0%
+the sil of the Silicon strain silicon
+ 
+
+ align:start position:0%
+the sil of the Silicon strain silicon
+Peak the shift between between that Peak
+
+ align:start position:0%
+Peak the shift between between that Peak
+ 
+
+ align:start position:0%
+Peak the shift between between that Peak
+and 521 is a measure of the amount of
+
+ align:start position:0%
+and 521 is a measure of the amount of
+ 
+
+ align:start position:0%
+and 521 is a measure of the amount of
+strength so this is a very nice way you
+
+ align:start position:0%
+strength so this is a very nice way you
+ 
+
+ align:start position:0%
+strength so this is a very nice way you
+can oxidize a wafer strip the oxide a
+
+ align:start position:0%
+can oxidize a wafer strip the oxide a
+ 
+
+ align:start position:0%
+can oxidize a wafer strip the oxide a
+strain silicon you can see if the strain
+
+ align:start position:0%
+strain silicon you can see if the strain
+ 
+
+ align:start position:0%
+strain silicon you can see if the strain
+is still there in fact you can figure
+
+ align:start position:0%
+is still there in fact you can figure
+ 
+
+ align:start position:0%
+is still there in fact you can figure
+out um uh your the relaxed silicon
+
+ align:start position:0%
+out um uh your the relaxed silicon
+ 
+
+ align:start position:0%
+out um uh your the relaxed silicon
+germanium content as well using this so
+
+ align:start position:0%
+germanium content as well using this so
+ 
+
+ align:start position:0%
+germanium content as well using this so
+uh slide 18 just shows you some
+
+ align:start position:0%
+uh slide 18 just shows you some
+ 
+
+ align:start position:0%
+uh slide 18 just shows you some
+measurements that people have made the
+
+ align:start position:0%
+measurements that people have made the
+ 
+
+ align:start position:0%
+measurements that people have made the
+ramen Peak
+
+ align:start position:0%
+ramen Peak
+ 
+
+ align:start position:0%
+ramen Peak
+shift in uh the frequency shift in
+
+ align:start position:0%
+shift in uh the frequency shift in
+ 
+
+ align:start position:0%
+shift in uh the frequency shift in
+inverse centimeter as a function of uh
+
+ align:start position:0%
+inverse centimeter as a function of uh
+ 
+
+ align:start position:0%
+inverse centimeter as a function of uh
+the amount of germanium fraction of the
+
+ align:start position:0%
+the amount of germanium fraction of the
+ 
+
+ align:start position:0%
+the amount of germanium fraction of the
+substrate for strained silicon layers
+
+ align:start position:0%
+substrate for strained silicon layers
+ 
+
+ align:start position:0%
+substrate for strained silicon layers
+you can see it's there's a theoretical
+
+ align:start position:0%
+you can see it's there's a theoretical
+ 
+
+ align:start position:0%
+you can see it's there's a theoretical
+line here and this is some uh the
+
+ align:start position:0%
+line here and this is some uh the
+ 
+
+ align:start position:0%
+line here and this is some uh the
+bullets represent measured points so um
+
+ align:start position:0%
+bullets represent measured points so um
+ 
+
+ align:start position:0%
+bullets represent measured points so um
+using Ramen if you have uh uh you have
+
+ align:start position:0%
+using Ramen if you have uh uh you have
+ 
+
+ align:start position:0%
+using Ramen if you have uh uh you have
+the right kind of ramen set up you can
+
+ align:start position:0%
+the right kind of ramen set up you can
+ 
+
+ align:start position:0%
+the right kind of ramen set up you can
+actually uh get a peak shift so for 20%
+
+ align:start position:0%
+actually uh get a peak shift so for 20%
+ 
+
+ align:start position:0%
+actually uh get a peak shift so for 20%
+geranium here we expect a Ramen Peak
+
+ align:start position:0%
+geranium here we expect a Ramen Peak
+ 
+
+ align:start position:0%
+geranium here we expect a Ramen Peak
+shift of about six uh six to seven uh
+
+ align:start position:0%
+shift of about six uh six to seven uh
+ 
+
+ align:start position:0%
+shift of about six uh six to seven uh
+inverse centimeters that gives you an
+
+ align:start position:0%
+inverse centimeters that gives you an
+ 
+
+ align:start position:0%
+inverse centimeters that gives you an
+idea of uh how you can measure the
+
+ align:start position:0%
+idea of uh how you can measure the
+ 
+
+ align:start position:0%
+idea of uh how you can measure the
+strain in the in the
+
+ align:start position:0%
+strain in the in the
+ 
+
+ align:start position:0%
+strain in the in the
+material slide 19 shows you a material
+
+ align:start position:0%
+material slide 19 shows you a material
+ 
+
+ align:start position:0%
+material slide 19 shows you a material
+that's been oxidized you might be where
+
+ align:start position:0%
+that's been oxidized you might be where
+ 
+
+ align:start position:0%
+that's been oxidized you might be where
+thinking okay fine you can grow these
+
+ align:start position:0%
+thinking okay fine you can grow these
+ 
+
+ align:start position:0%
+thinking okay fine you can grow these
+epitaxial layers they'll be strained
+
+ align:start position:0%
+epitaxial layers they'll be strained
+ 
+
+ align:start position:0%
+epitaxial layers they'll be strained
+what happens if you oxidize the Silicon
+
+ align:start position:0%
+what happens if you oxidize the Silicon
+ 
+
+ align:start position:0%
+what happens if you oxidize the Silicon
+is it going to somehow Relax The Strain
+
+ align:start position:0%
+is it going to somehow Relax The Strain
+ 
+
+ align:start position:0%
+is it going to somehow Relax The Strain
+because of that oxidation process and
+
+ align:start position:0%
+because of that oxidation process and
+ 
+
+ align:start position:0%
+because of that oxidation process and
+the breaking of bonds in the oxidation
+
+ align:start position:0%
+the breaking of bonds in the oxidation
+ 
+
+ align:start position:0%
+the breaking of bonds in the oxidation
+well it turns out it doesn't in fact uh
+
+ align:start position:0%
+well it turns out it doesn't in fact uh
+ 
+
+ align:start position:0%
+well it turns out it doesn't in fact uh
+the as grown Ramen Spectrum here uh this
+
+ align:start position:0%
+the as grown Ramen Spectrum here uh this
+ 
+
+ align:start position:0%
+the as grown Ramen Spectrum here uh this
+is for the epitaxial layer as it was
+
+ align:start position:0%
+is for the epitaxial layer as it was
+ 
+
+ align:start position:0%
+is for the epitaxial layer as it was
+first Grown you do get a strain silicon
+
+ align:start position:0%
+first Grown you do get a strain silicon
+ 
+
+ align:start position:0%
+first Grown you do get a strain silicon
+Peak right here near to 510 if you
+
+ align:start position:0%
+Peak right here near to 510 if you
+ 
+
+ align:start position:0%
+Peak right here near to 510 if you
+oxidize it at 850 for 10 minutes you
+
+ align:start position:0%
+oxidize it at 850 for 10 minutes you
+ 
+
+ align:start position:0%
+oxidize it at 850 for 10 minutes you
+still get that strain silicon peak in
+
+ align:start position:0%
+still get that strain silicon peak in
+ 
+
+ align:start position:0%
+still get that strain silicon peak in
+although the peak is smaller height
+
+ align:start position:0%
+although the peak is smaller height
+ 
+
+ align:start position:0%
+although the peak is smaller height
+because of course the layer is thinner
+
+ align:start position:0%
+because of course the layer is thinner
+ 
+
+ align:start position:0%
+because of course the layer is thinner
+when you oxidize you consume silicon but
+
+ align:start position:0%
+when you oxidize you consume silicon but
+ 
+
+ align:start position:0%
+when you oxidize you consume silicon but
+the the peak position it remains at 510
+
+ align:start position:0%
+the the peak position it remains at 510
+ 
+
+ align:start position:0%
+the the peak position it remains at 510
+it remains at the same point and this
+
+ align:start position:0%
+it remains at the same point and this
+ 
+
+ align:start position:0%
+it remains at the same point and this
+has been verified very many times and of
+
+ align:start position:0%
+has been verified very many times and of
+ 
+
+ align:start position:0%
+has been verified very many times and of
+course in the mosque that you do see the
+
+ align:start position:0%
+course in the mosque that you do see the
+ 
+
+ align:start position:0%
+course in the mosque that you do see the
+enhanced Mobility so there doesn't seem
+
+ align:start position:0%
+enhanced Mobility so there doesn't seem
+ 
+
+ align:start position:0%
+enhanced Mobility so there doesn't seem
+to be any significant strain relaxation
+
+ align:start position:0%
+to be any significant strain relaxation
+ 
+
+ align:start position:0%
+to be any significant strain relaxation
+at least when you oxidize in these type
+
+ align:start position:0%
+at least when you oxidize in these type
+ 
+
+ align:start position:0%
+at least when you oxidize in these type
+of temperatures you're to go up to a
+
+ align:start position:0%
+of temperatures you're to go up to a
+ 
+
+ align:start position:0%
+of temperatures you're to go up to a
+thousand or more then you could start
+
+ align:start position:0%
+thousand or more then you could start
+ 
+
+ align:start position:0%
+thousand or more then you could start
+running into trouble uh when the
+
+ align:start position:0%
+running into trouble uh when the
+ 
+
+ align:start position:0%
+running into trouble uh when the
+geranium starts uh diffusing around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so on slide 20 I'm just sort of
+
+ align:start position:0%
+so on slide 20 I'm just sort of
+ 
+
+ align:start position:0%
+so on slide 20 I'm just sort of
+reviewing for you giving you an idea of
+
+ align:start position:0%
+reviewing for you giving you an idea of
+ 
+
+ align:start position:0%
+reviewing for you giving you an idea of
+some of the early measurements people
+
+ align:start position:0%
+some of the early measurements people
+ 
+
+ align:start position:0%
+some of the early measurements people
+made of how the mobility was enhanced
+
+ align:start position:0%
+made of how the mobility was enhanced
+ 
+
+ align:start position:0%
+made of how the mobility was enhanced
+and the left side is for n mosfets and
+
+ align:start position:0%
+and the left side is for n mosfets and
+ 
+
+ align:start position:0%
+and the left side is for n mosfets and
+you see these this black line This dash
+
+ align:start position:0%
+you see these this black line This dash
+ 
+
+ align:start position:0%
+you see these this black line This dash
+line is for control devices and these
+
+ align:start position:0%
+line is for control devices and these
+ 
+
+ align:start position:0%
+line is for control devices and these
+other lines on top are for 10% geranium
+
+ align:start position:0%
+other lines on top are for 10% geranium
+ 
+
+ align:start position:0%
+other lines on top are for 10% geranium
+in the substrate 20 and 30 you see as
+
+ align:start position:0%
+in the substrate 20 and 30 you see as
+ 
+
+ align:start position:0%
+in the substrate 20 and 30 you see as
+you add more geranium in the substrate
+
+ align:start position:0%
+you add more geranium in the substrate
+ 
+
+ align:start position:0%
+you add more geranium in the substrate
+the whole the electron Mobility curve
+
+ align:start position:0%
+the whole the electron Mobility curve
+ 
+
+ align:start position:0%
+the whole the electron Mobility curve
+all moves up and you get a nice
+
+ align:start position:0%
+all moves up and you get a nice
+ 
+
+ align:start position:0%
+all moves up and you get a nice
+enhancement
+
+ align:start position:0%
+enhancement
+ 
+
+ align:start position:0%
+enhancement
+uh on holes for for the for pmosfets uh
+
+ align:start position:0%
+uh on holes for for the for pmosfets uh
+ 
+
+ align:start position:0%
+uh on holes for for the for pmosfets uh
+there was some enhancement measured
+
+ align:start position:0%
+there was some enhancement measured
+ 
+
+ align:start position:0%
+there was some enhancement measured
+although the enhancement is diminished
+
+ align:start position:0%
+although the enhancement is diminished
+ 
+
+ align:start position:0%
+although the enhancement is diminished
+you see that the enhancement factor is
+
+ align:start position:0%
+you see that the enhancement factor is
+ 
+
+ align:start position:0%
+you see that the enhancement factor is
+actually going down as you go to higher
+
+ align:start position:0%
+actually going down as you go to higher
+ 
+
+ align:start position:0%
+actually going down as you go to higher
+vertical Fields here so that that's
+
+ align:start position:0%
+vertical Fields here so that that's
+ 
+
+ align:start position:0%
+vertical Fields here so that that's
+becomes that's a higher vertical Fields
+
+ align:start position:0%
+becomes that's a higher vertical Fields
+ 
+
+ align:start position:0%
+becomes that's a higher vertical Fields
+is where a lot of modern mosfets operate
+
+ align:start position:0%
+is where a lot of modern mosfets operate
+ 
+
+ align:start position:0%
+is where a lot of modern mosfets operate
+so that's a bit of an issue uh for P
+
+ align:start position:0%
+so that's a bit of an issue uh for P
+ 
+
+ align:start position:0%
+so that's a bit of an issue uh for P
+mosfets for using this
+
+ align:start position:0%
+mosfets for using this
+ 
+
+ align:start position:0%
+mosfets for using this
+technique those are research devices
+
+ align:start position:0%
+technique those are research devices
+ 
+
+ align:start position:0%
+technique those are research devices
+this on slide 21 is some more recent
+
+ align:start position:0%
+this on slide 21 is some more recent
+ 
+
+ align:start position:0%
+this on slide 21 is some more recent
+Publications in a Manu manufacturing
+
+ align:start position:0%
+Publications in a Manu manufacturing
+ 
+
+ align:start position:0%
+Publications in a Manu manufacturing
+style process although it's not in
+
+ align:start position:0%
+style process although it's not in
+ 
+
+ align:start position:0%
+style process although it's not in
+manufacturing the process was a full
+
+ align:start position:0%
+manufacturing the process was a full
+ 
+
+ align:start position:0%
+manufacturing the process was a full
+manufacturing style process that IBM did
+
+ align:start position:0%
+manufacturing style process that IBM did
+ 
+
+ align:start position:0%
+manufacturing style process that IBM did
+it had all the attributes of a real
+
+ align:start position:0%
+it had all the attributes of a real
+ 
+
+ align:start position:0%
+it had all the attributes of a real
+manufactured device it had shallow
+
+ align:start position:0%
+manufactured device it had shallow
+ 
+
+ align:start position:0%
+manufactured device it had shallow
+trench isolation had um it had well uh
+
+ align:start position:0%
+trench isolation had um it had well uh
+ 
+
+ align:start position:0%
+trench isolation had um it had well uh
+implants Halo implants raised Source
+
+ align:start position:0%
+implants Halo implants raised Source
+ 
+
+ align:start position:0%
+implants Halo implants raised Source
+drain by Epi uh and a thin gate oxide so
+
+ align:start position:0%
+drain by Epi uh and a thin gate oxide so
+ 
+
+ align:start position:0%
+drain by Epi uh and a thin gate oxide so
+this is a real uh real device as opposed
+
+ align:start position:0%
+this is a real uh real device as opposed
+ 
+
+ align:start position:0%
+this is a real uh real device as opposed
+to the university style and again you
+
+ align:start position:0%
+to the university style and again you
+ 
+
+ align:start position:0%
+to the university style and again you
+can see the mobility for electrons goes
+
+ align:start position:0%
+can see the mobility for electrons goes
+ 
+
+ align:start position:0%
+can see the mobility for electrons goes
+up with strain about 100% Improvement
+
+ align:start position:0%
+up with strain about 100% Improvement
+ 
+
+ align:start position:0%
+up with strain about 100% Improvement
+that is a factor of two s there is an
+
+ align:start position:0%
+that is a factor of two s there is an
+ 
+
+ align:start position:0%
+that is a factor of two s there is an
+improvement at lowgate bias but here at
+
+ align:start position:0%
+improvement at lowgate bias but here at
+ 
+
+ align:start position:0%
+improvement at lowgate bias but here at
+high effective field or High Gate bias
+
+ align:start position:0%
+high effective field or High Gate bias
+ 
+
+ align:start position:0%
+high effective field or High Gate bias
+the Improvement is is pretty small only
+
+ align:start position:0%
+the Improvement is is pretty small only
+ 
+
+ align:start position:0%
+the Improvement is is pretty small only
+a few percent um so but that just shows
+
+ align:start position:0%
+a few percent um so but that just shows
+ 
+
+ align:start position:0%
+a few percent um so but that just shows
+uh the state-ofthe-art as it exists uh a
+
+ align:start position:0%
+uh the state-ofthe-art as it exists uh a
+ 
+
+ align:start position:0%
+uh the state-ofthe-art as it exists uh a
+couple of years
+
+ align:start position:0%
+couple of years
+ 
+
+ align:start position:0%
+couple of years
+ago and if you working at relatively
+
+ align:start position:0%
+ago and if you working at relatively
+ 
+
+ align:start position:0%
+ago and if you working at relatively
+lowgate bias and you just want to get an
+
+ align:start position:0%
+lowgate bias and you just want to get an
+ 
+
+ align:start position:0%
+lowgate bias and you just want to get an
+idea of how the mobility enhancement
+
+ align:start position:0%
+idea of how the mobility enhancement
+ 
+
+ align:start position:0%
+idea of how the mobility enhancement
+varies with the amount of strain you can
+
+ align:start position:0%
+varies with the amount of strain you can
+ 
+
+ align:start position:0%
+varies with the amount of strain you can
+look at this curve on on page 22 this is
+
+ align:start position:0%
+look at this curve on on page 22 this is
+ 
+
+ align:start position:0%
+look at this curve on on page 22 this is
+the electron Mobility enhancement Factor
+
+ align:start position:0%
+the electron Mobility enhancement Factor
+ 
+
+ align:start position:0%
+the electron Mobility enhancement Factor
+so it's the peak mobility in a strained
+
+ align:start position:0%
+so it's the peak mobility in a strained
+ 
+
+ align:start position:0%
+so it's the peak mobility in a strained
+silicon fet divided the peak mobility in
+
+ align:start position:0%
+silicon fet divided the peak mobility in
+ 
+
+ align:start position:0%
+silicon fet divided the peak mobility in
+an unstrained fet and you see here with
+
+ align:start position:0%
+an unstrained fet and you see here with
+ 
+
+ align:start position:0%
+an unstrained fet and you see here with
+no strain that it's one and then it goes
+
+ align:start position:0%
+no strain that it's one and then it goes
+ 
+
+ align:start position:0%
+no strain that it's one and then it goes
+up to about a factor of 1.8 maybe two
+
+ align:start position:0%
+up to about a factor of 1.8 maybe two
+ 
+
+ align:start position:0%
+up to about a factor of 1.8 maybe two
+something like that there's a lot of
+
+ align:start position:0%
+something like that there's a lot of
+ 
+
+ align:start position:0%
+something like that there's a lot of
+data been published the last 10 or 12
+
+ align:start position:0%
+data been published the last 10 or 12
+ 
+
+ align:start position:0%
+data been published the last 10 or 12
+years and they all seem to agree about
+
+ align:start position:0%
+years and they all seem to agree about
+ 
+
+ align:start position:0%
+years and they all seem to agree about
+this saturating
+
+ align:start position:0%
+this saturating
+ 
+
+ align:start position:0%
+this saturating
+behavior on the right is for pay loss
+
+ align:start position:0%
+behavior on the right is for pay loss
+ 
+
+ align:start position:0%
+behavior on the right is for pay loss
+for whole Mobility the data is does show
+
+ align:start position:0%
+for whole Mobility the data is does show
+ 
+
+ align:start position:0%
+for whole Mobility the data is does show
+an increase especially as you get above
+
+ align:start position:0%
+an increase especially as you get above
+ 
+
+ align:start position:0%
+an increase especially as you get above
+about 30% germanium you can get larger
+
+ align:start position:0%
+about 30% germanium you can get larger
+ 
+
+ align:start position:0%
+about 30% germanium you can get larger
+enhancement factors um and this is the
+
+ align:start position:0%
+enhancement factors um and this is the
+ 
+
+ align:start position:0%
+enhancement factors um and this is the
+theoretical curve the data seems to be a
+
+ align:start position:0%
+theoretical curve the data seems to be a
+ 
+
+ align:start position:0%
+theoretical curve the data seems to be a
+little bit below the theoretic curve but
+
+ align:start position:0%
+little bit below the theoretic curve but
+ 
+
+ align:start position:0%
+little bit below the theoretic curve but
+shows roughly the kind of strain
+
+ align:start position:0%
+shows roughly the kind of strain
+ 
+
+ align:start position:0%
+shows roughly the kind of strain
+dependence you would you expect and so
+
+ align:start position:0%
+dependence you would you expect and so
+ 
+
+ align:start position:0%
+dependence you would you expect and so
+what this is telling you you're
+
+ align:start position:0%
+what this is telling you you're
+ 
+
+ align:start position:0%
+what this is telling you you're
+saturating out you don't really need to
+
+ align:start position:0%
+saturating out you don't really need to
+ 
+
+ align:start position:0%
+saturating out you don't really need to
+put more for electrons more than about
+
+ align:start position:0%
+put more for electrons more than about
+ 
+
+ align:start position:0%
+put more for electrons more than about
+20% geranium in the substrate that's
+
+ align:start position:0%
+20% geranium in the substrate that's
+ 
+
+ align:start position:0%
+20% geranium in the substrate that's
+enough strain so the bands are split
+
+ align:start position:0%
+enough strain so the bands are split
+ 
+
+ align:start position:0%
+enough strain so the bands are split
+enough if you go beyond that you you're
+
+ align:start position:0%
+enough if you go beyond that you you're
+ 
+
+ align:start position:0%
+enough if you go beyond that you you're
+inducing more strain and more splitting
+
+ align:start position:0%
+inducing more strain and more splitting
+ 
+
+ align:start position:0%
+inducing more strain and more splitting
+but the mobility itself is not actually
+
+ align:start position:0%
+but the mobility itself is not actually
+ 
+
+ align:start position:0%
+but the mobility itself is not actually
+improving because something else is
+
+ align:start position:0%
+improving because something else is
+ 
+
+ align:start position:0%
+improving because something else is
+limiting the mobility that gives you a
+
+ align:start position:0%
+limiting the mobility that gives you a
+ 
+
+ align:start position:0%
+limiting the mobility that gives you a
+rough idea of the amount of strain you
+
+ align:start position:0%
+rough idea of the amount of strain you
+ 
+
+ align:start position:0%
+rough idea of the amount of strain you
+need to induce in some of these
+
+ align:start position:0%
+need to induce in some of these
+ 
+
+ align:start position:0%
+need to induce in some of these
+devices uh page 23 is is sort of a
+
+ align:start position:0%
+devices uh page 23 is is sort of a
+ 
+
+ align:start position:0%
+devices uh page 23 is is sort of a
+summary of uh some of the mobility
+
+ align:start position:0%
+summary of uh some of the mobility
+ 
+
+ align:start position:0%
+summary of uh some of the mobility
+enhancements now for
+
+ align:start position:0%
+enhancements now for
+ 
+
+ align:start position:0%
+enhancements now for
+pets uh it's the mobility enhancement
+
+ align:start position:0%
+pets uh it's the mobility enhancement
+ 
+
+ align:start position:0%
+pets uh it's the mobility enhancement
+ratio again this is a number you would
+
+ align:start position:0%
+ratio again this is a number you would
+ 
+
+ align:start position:0%
+ratio again this is a number you would
+like to be large as a function of
+
+ align:start position:0%
+like to be large as a function of
+ 
+
+ align:start position:0%
+like to be large as a function of
+vertical field if you operate the device
+
+ align:start position:0%
+vertical field if you operate the device
+ 
+
+ align:start position:0%
+vertical field if you operate the device
+at very low vertical Fields you can get
+
+ align:start position:0%
+at very low vertical Fields you can get
+ 
+
+ align:start position:0%
+at very low vertical Fields you can get
+large ratios but most mod devices
+
+ align:start position:0%
+large ratios but most mod devices
+ 
+
+ align:start position:0%
+large ratios but most mod devices
+operate over here so the enhancement
+
+ align:start position:0%
+operate over here so the enhancement
+ 
+
+ align:start position:0%
+operate over here so the enhancement
+factor is only about 1.1 or 1.2 it's
+
+ align:start position:0%
+factor is only about 1.1 or 1.2 it's
+ 
+
+ align:start position:0%
+factor is only about 1.1 or 1.2 it's
+approaching one uh that's a problem
+
+ align:start position:0%
+approaching one uh that's a problem
+ 
+
+ align:start position:0%
+approaching one uh that's a problem
+unless you go to very high geranium
+
+ align:start position:0%
+unless you go to very high geranium
+ 
+
+ align:start position:0%
+unless you go to very high geranium
+contents there's some data here with a
+
+ align:start position:0%
+contents there's some data here with a
+ 
+
+ align:start position:0%
+contents there's some data here with a
+40% substrate so that means the strain
+
+ align:start position:0%
+40% substrate so that means the strain
+ 
+
+ align:start position:0%
+40% substrate so that means the strain
+silicon layer is very thin and it's
+
+ align:start position:0%
+silicon layer is very thin and it's
+ 
+
+ align:start position:0%
+silicon layer is very thin and it's
+strained to a 40% substrate here
+
+ align:start position:0%
+strained to a 40% substrate here
+ 
+
+ align:start position:0%
+strained to a 40% substrate here
+Mobility enhan fact there's not a full
+
+ align:start position:0%
+Mobility enhan fact there's not a full
+ 
+
+ align:start position:0%
+Mobility enhan fact there's not a full
+curve available the highest uh um uh
+
+ align:start position:0%
+curve available the highest uh um uh
+ 
+
+ align:start position:0%
+curve available the highest uh um uh
+field these people went to was about 06
+
+ align:start position:0%
+field these people went to was about 06
+ 
+
+ align:start position:0%
+field these people went to was about 06
+but they did get pretty large
+
+ align:start position:0%
+but they did get pretty large
+ 
+
+ align:start position:0%
+but they did get pretty large
+enhancement factors so um it looks like
+
+ align:start position:0%
+enhancement factors so um it looks like
+ 
+
+ align:start position:0%
+enhancement factors so um it looks like
+uh if you're going to use bi axial
+
+ align:start position:0%
+uh if you're going to use bi axial
+ 
+
+ align:start position:0%
+uh if you're going to use bi axial
+tensil strain in the Silicon you need to
+
+ align:start position:0%
+tensil strain in the Silicon you need to
+ 
+
+ align:start position:0%
+tensil strain in the Silicon you need to
+go to very high levels of strain uh uh
+
+ align:start position:0%
+go to very high levels of strain uh uh
+ 
+
+ align:start position:0%
+go to very high levels of strain uh uh
+if you want this to work so that's one
+
+ align:start position:0%
+if you want this to work so that's one
+ 
+
+ align:start position:0%
+if you want this to work so that's one
+big disadvantage uh for the pimos fit in
+
+ align:start position:0%
+big disadvantage uh for the pimos fit in
+ 
+
+ align:start position:0%
+big disadvantage uh for the pimos fit in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technology oh just another um uh um
+
+ align:start position:0%
+technology oh just another um uh um
+ 
+
+ align:start position:0%
+technology oh just another um uh um
+graph on on page 24 to give you an idea
+
+ align:start position:0%
+graph on on page 24 to give you an idea
+ 
+
+ align:start position:0%
+graph on on page 24 to give you an idea
+we talked about about Mobility how about
+
+ align:start position:0%
+we talked about about Mobility how about
+ 
+
+ align:start position:0%
+we talked about about Mobility how about
+things that you uh care about like
+
+ align:start position:0%
+things that you uh care about like
+ 
+
+ align:start position:0%
+things that you uh care about like
+electron velocity or or GM that a lot of
+
+ align:start position:0%
+electron velocity or or GM that a lot of
+ 
+
+ align:start position:0%
+electron velocity or or GM that a lot of
+circuit designers are worried about well
+
+ align:start position:0%
+circuit designers are worried about well
+ 
+
+ align:start position:0%
+circuit designers are worried about well
+indeed that does improve and even as you
+
+ align:start position:0%
+indeed that does improve and even as you
+ 
+
+ align:start position:0%
+indeed that does improve and even as you
+scale devices this is data back from
+
+ align:start position:0%
+scale devices this is data back from
+ 
+
+ align:start position:0%
+scale devices this is data back from
+1998 now it's fairly old but it it still
+
+ align:start position:0%
+1998 now it's fairly old but it it still
+ 
+
+ align:start position:0%
+1998 now it's fairly old but it it still
+uh gives you an idea of if you look at
+
+ align:start position:0%
+uh gives you an idea of if you look at
+ 
+
+ align:start position:0%
+uh gives you an idea of if you look at
+the GM here for an unstrained device
+
+ align:start position:0%
+the GM here for an unstrained device
+ 
+
+ align:start position:0%
+the GM here for an unstrained device
+shown in red as you scale it goes up
+
+ align:start position:0%
+shown in red as you scale it goes up
+ 
+
+ align:start position:0%
+shown in red as you scale it goes up
+like this for a strained n mosfet shown
+
+ align:start position:0%
+like this for a strained n mosfet shown
+ 
+
+ align:start position:0%
+like this for a strained n mosfet shown
+in blue it goes up and this enhancement
+
+ align:start position:0%
+in blue it goes up and this enhancement
+ 
+
+ align:start position:0%
+in blue it goes up and this enhancement
+factor or the the the ratio between
+
+ align:start position:0%
+factor or the the the ratio between
+ 
+
+ align:start position:0%
+factor or the the the ratio between
+these two lines stays about constant in
+
+ align:start position:0%
+these two lines stays about constant in
+ 
+
+ align:start position:0%
+these two lines stays about constant in
+this plot all the way down to about U 90
+
+ align:start position:0%
+this plot all the way down to about U 90
+ 
+
+ align:start position:0%
+this plot all the way down to about U 90
+nanometers or or so was the shortest
+
+ align:start position:0%
+nanometers or or so was the shortest
+ 
+
+ align:start position:0%
+nanometers or or so was the shortest
+devices that were made just just around
+
+ align:start position:0%
+devices that were made just just around
+ 
+
+ align:start position:0%
+devices that were made just just around
+100 nanometers since that time shorter
+
+ align:start position:0%
+100 nanometers since that time shorter
+ 
+
+ align:start position:0%
+100 nanometers since that time shorter
+devices have been made but there so the
+
+ align:start position:0%
+devices have been made but there so the
+ 
+
+ align:start position:0%
+devices have been made but there so the
+the nice thing is that the enhancement
+
+ align:start position:0%
+the nice thing is that the enhancement
+ 
+
+ align:start position:0%
+the nice thing is that the enhancement
+doesn't seem to go away when you go to
+
+ align:start position:0%
+doesn't seem to go away when you go to
+ 
+
+ align:start position:0%
+doesn't seem to go away when you go to
+short channels so that's very important
+
+ align:start position:0%
+short channels so that's very important
+ 
+
+ align:start position:0%
+short channels so that's very important
+for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technology so let me talk a little bit
+
+ align:start position:0%
+technology so let me talk a little bit
+ 
+
+ align:start position:0%
+technology so let me talk a little bit
+but now I want to spend a few minutes on
+
+ align:start position:0%
+but now I want to spend a few minutes on
+ 
+
+ align:start position:0%
+but now I want to spend a few minutes on
+how the material is grown and some of
+
+ align:start position:0%
+how the material is grown and some of
+ 
+
+ align:start position:0%
+how the material is grown and some of
+the issues related to how uh how dopant
+
+ align:start position:0%
+the issues related to how uh how dopant
+ 
+
+ align:start position:0%
+the issues related to how uh how dopant
+diffus in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material slide 26 just shows some
+
+ align:start position:0%
+material slide 26 just shows some
+ 
+
+ align:start position:0%
+material slide 26 just shows some
+typical gas sources that are used uh a
+
+ align:start position:0%
+typical gas sources that are used uh a
+ 
+
+ align:start position:0%
+typical gas sources that are used uh a
+very common way to grow this is by low
+
+ align:start position:0%
+very common way to grow this is by low
+ 
+
+ align:start position:0%
+very common way to grow this is by low
+pressure CBD or sometimes ultra high
+
+ align:start position:0%
+pressure CBD or sometimes ultra high
+ 
+
+ align:start position:0%
+pressure CBD or sometimes ultra high
+vacuum CBD uh depending on the uh uh the
+
+ align:start position:0%
+vacuum CBD uh depending on the uh uh the
+ 
+
+ align:start position:0%
+vacuum CBD uh depending on the uh uh the
+particular uh lab that's doing the work
+
+ align:start position:0%
+particular uh lab that's doing the work
+ 
+
+ align:start position:0%
+particular uh lab that's doing the work
+uh for epitaxial silicon geranium a very
+
+ align:start position:0%
+uh for epitaxial silicon geranium a very
+ 
+
+ align:start position:0%
+uh for epitaxial silicon geranium a very
+common silicon source is siline uh
+
+ align:start position:0%
+common silicon source is siline uh
+ 
+
+ align:start position:0%
+common silicon source is siline uh
+sometimes people use dorosy we've talked
+
+ align:start position:0%
+sometimes people use dorosy we've talked
+ 
+
+ align:start position:0%
+sometimes people use dorosy we've talked
+about dor earlier in the class for
+
+ align:start position:0%
+about dor earlier in the class for
+ 
+
+ align:start position:0%
+about dor earlier in the class for
+germanian people use germine what is
+
+ align:start position:0%
+germanian people use germine what is
+ 
+
+ align:start position:0%
+germanian people use germine what is
+gerine it's the same as siling but you
+
+ align:start position:0%
+gerine it's the same as siling but you
+ 
+
+ align:start position:0%
+gerine it's the same as siling but you
+take out the silicon and you put in a
+
+ align:start position:0%
+take out the silicon and you put in a
+ 
+
+ align:start position:0%
+take out the silicon and you put in a
+germanium atom so it's
+
+ align:start position:0%
+germanium atom so it's
+ 
+
+ align:start position:0%
+germanium atom so it's
+G4 um hydrogen is often used as a cargas
+
+ align:start position:0%
+G4 um hydrogen is often used as a cargas
+ 
+
+ align:start position:0%
+G4 um hydrogen is often used as a cargas
+although not in uhv CBD but in low
+
+ align:start position:0%
+although not in uhv CBD but in low
+ 
+
+ align:start position:0%
+although not in uhv CBD but in low
+pressure CBD and these are common
+
+ align:start position:0%
+pressure CBD and these are common
+ 
+
+ align:start position:0%
+pressure CBD and these are common
+dopants dorine and arcene are used for p
+
+ align:start position:0%
+dopants dorine and arcene are used for p
+ 
+
+ align:start position:0%
+dopants dorine and arcene are used for p
+and end type doping uh sometimes
+
+ align:start position:0%
+and end type doping uh sometimes
+ 
+
+ align:start position:0%
+and end type doping uh sometimes
+phosphine um for silicon geranium in a
+
+ align:start position:0%
+phosphine um for silicon geranium in a
+ 
+
+ align:start position:0%
+phosphine um for silicon geranium in a
+selective process you need to add so if
+
+ align:start position:0%
+selective process you need to add so if
+ 
+
+ align:start position:0%
+selective process you need to add so if
+you want to deposit silicon geranium on
+
+ align:start position:0%
+you want to deposit silicon geranium on
+ 
+
+ align:start position:0%
+you want to deposit silicon geranium on
+a wa for that has oxide on it and little
+
+ align:start position:0%
+a wa for that has oxide on it and little
+ 
+
+ align:start position:0%
+a wa for that has oxide on it and little
+openings in the oxide uh where there's
+
+ align:start position:0%
+openings in the oxide uh where there's
+ 
+
+ align:start position:0%
+openings in the oxide uh where there's
+uh windows that that are that are
+
+ align:start position:0%
+uh windows that that are that are
+ 
+
+ align:start position:0%
+uh windows that that are that are
+patterned so that you can reach down
+
+ align:start position:0%
+patterned so that you can reach down
+ 
+
+ align:start position:0%
+patterned so that you can reach down
+into the Silicon this is called
+
+ align:start position:0%
+into the Silicon this is called
+ 
+
+ align:start position:0%
+into the Silicon this is called
+selective deposition you need to add
+
+ align:start position:0%
+selective deposition you need to add
+ 
+
+ align:start position:0%
+selective deposition you need to add
+hydrogen chloride HCL and this is
+
+ align:start position:0%
+hydrogen chloride HCL and this is
+ 
+
+ align:start position:0%
+hydrogen chloride HCL and this is
+commonly done for both the bipolar and
+
+ align:start position:0%
+commonly done for both the bipolar and
+ 
+
+ align:start position:0%
+commonly done for both the bipolar and
+seamoss
+
+ align:start position:0%
+seamoss
+ 
+
+ align:start position:0%
+seamoss
+applications for silicon geranium carbon
+
+ align:start position:0%
+applications for silicon geranium carbon
+ 
+
+ align:start position:0%
+applications for silicon geranium carbon
+uh you do the same type of thing but you
+
+ align:start position:0%
+uh you do the same type of thing but you
+ 
+
+ align:start position:0%
+uh you do the same type of thing but you
+add one more gas which is called methyl
+
+ align:start position:0%
+add one more gas which is called methyl
+ 
+
+ align:start position:0%
+add one more gas which is called methyl
+siline at that the methyl group The ch3
+
+ align:start position:0%
+siline at that the methyl group The ch3
+ 
+
+ align:start position:0%
+siline at that the methyl group The ch3
+brings in the carbon which is used uh to
+
+ align:start position:0%
+brings in the carbon which is used uh to
+ 
+
+ align:start position:0%
+brings in the carbon which is used uh to
+dope those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+devices uh we talked a little bit about
+
+ align:start position:0%
+devices uh we talked a little bit about
+ 
+
+ align:start position:0%
+devices uh we talked a little bit about
+strain and here on slide uh 27 I'm
+
+ align:start position:0%
+strain and here on slide uh 27 I'm
+ 
+
+ align:start position:0%
+strain and here on slide uh 27 I'm
+showing a little bit of idea what that
+
+ align:start position:0%
+showing a little bit of idea what that
+ 
+
+ align:start position:0%
+showing a little bit of idea what that
+means uh this ball and stick diagram on
+
+ align:start position:0%
+means uh this ball and stick diagram on
+ 
+
+ align:start position:0%
+means uh this ball and stick diagram on
+the lower right was our our pictorial
+
+ align:start position:0%
+the lower right was our our pictorial
+ 
+
+ align:start position:0%
+the lower right was our our pictorial
+picture in our heads when the epil layer
+
+ align:start position:0%
+picture in our heads when the epil layer
+ 
+
+ align:start position:0%
+picture in our heads when the epil layer
+is thin we said the Silicon geranium if
+
+ align:start position:0%
+is thin we said the Silicon geranium if
+ 
+
+ align:start position:0%
+is thin we said the Silicon geranium if
+it's thin enough it will compress in X
+
+ align:start position:0%
+it's thin enough it will compress in X
+ 
+
+ align:start position:0%
+it's thin enough it will compress in X
+and Y it will match the parameter of the
+
+ align:start position:0%
+and Y it will match the parameter of the
+ 
+
+ align:start position:0%
+and Y it will match the parameter of the
+of the thick substrate uh that's only
+
+ align:start position:0%
+of the thick substrate uh that's only
+ 
+
+ align:start position:0%
+of the thick substrate uh that's only
+when it's thin enough and it's
+
+ align:start position:0%
+when it's thin enough and it's
+ 
+
+ align:start position:0%
+when it's thin enough and it's
+energetically favorable to to um bend
+
+ align:start position:0%
+energetically favorable to to um bend
+ 
+
+ align:start position:0%
+energetically favorable to to um bend
+the bonds uh in that case we say it's
+
+ align:start position:0%
+the bonds uh in that case we say it's
+ 
+
+ align:start position:0%
+the bonds uh in that case we say it's
+fully strained if you build up more and
+
+ align:start position:0%
+fully strained if you build up more and
+ 
+
+ align:start position:0%
+fully strained if you build up more and
+more layers you build up more and more
+
+ align:start position:0%
+more layers you build up more and more
+ 
+
+ align:start position:0%
+more layers you build up more and more
+stress at some point it becomes
+
+ align:start position:0%
+stress at some point it becomes
+ 
+
+ align:start position:0%
+stress at some point it becomes
+energetically pable to break bonds so at
+
+ align:start position:0%
+energetically pable to break bonds so at
+ 
+
+ align:start position:0%
+energetically pable to break bonds so at
+this interface bonds are actually broken
+
+ align:start position:0%
+this interface bonds are actually broken
+ 
+
+ align:start position:0%
+this interface bonds are actually broken
+and is represented here by these U
+
+ align:start position:0%
+and is represented here by these U
+ 
+
+ align:start position:0%
+and is represented here by these U
+Misfit dislocations that are going into
+
+ align:start position:0%
+Misfit dislocations that are going into
+ 
+
+ align:start position:0%
+Misfit dislocations that are going into
+the board or into the uh into the um
+
+ align:start position:0%
+the board or into the uh into the um
+ 
+
+ align:start position:0%
+the board or into the uh into the um
+into the board here and so these the
+
+ align:start position:0%
+into the board here and so these the
+ 
+
+ align:start position:0%
+into the board here and so these the
+dislocations uh end up relieving The
+
+ align:start position:0%
+dislocations uh end up relieving The
+ 
+
+ align:start position:0%
+dislocations uh end up relieving The
+Strain in a thick layer uh they have a
+
+ align:start position:0%
+Strain in a thick layer uh they have a
+ 
+
+ align:start position:0%
+Strain in a thick layer uh they have a
+certain spacing and if you have enough
+
+ align:start position:0%
+certain spacing and if you have enough
+ 
+
+ align:start position:0%
+certain spacing and if you have enough
+of them and their spacing is tight
+
+ align:start position:0%
+of them and their spacing is tight
+ 
+
+ align:start position:0%
+of them and their spacing is tight
+enough in fact you'll end up with a
+
+ align:start position:0%
+enough in fact you'll end up with a
+ 
+
+ align:start position:0%
+enough in fact you'll end up with a
+fully relaxed layer the Silicon geranium
+
+ align:start position:0%
+fully relaxed layer the Silicon geranium
+ 
+
+ align:start position:0%
+fully relaxed layer the Silicon geranium
+will have a last parameter that it has
+
+ align:start position:0%
+will have a last parameter that it has
+ 
+
+ align:start position:0%
+will have a last parameter that it has
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+equilibrium and this is a cross-section
+
+ align:start position:0%
+equilibrium and this is a cross-section
+ 
+
+ align:start position:0%
+equilibrium and this is a cross-section
+view in the upper right on and this uh
+
+ align:start position:0%
+view in the upper right on and this uh
+ 
+
+ align:start position:0%
+view in the upper right on and this uh
+transmission electron micrograph is a
+
+ align:start position:0%
+transmission electron micrograph is a
+ 
+
+ align:start position:0%
+transmission electron micrograph is a
+planer view so if you look down through
+
+ align:start position:0%
+planer view so if you look down through
+ 
+
+ align:start position:0%
+planer view so if you look down through
+an epitaxial layer that's been grown to
+
+ align:start position:0%
+an epitaxial layer that's been grown to
+ 
+
+ align:start position:0%
+an epitaxial layer that's been grown to
+be too thick and here is a is a bird's
+
+ align:start position:0%
+be too thick and here is a is a bird's
+ 
+
+ align:start position:0%
+be too thick and here is a is a bird's
+eye view this is a misfit dislocation
+
+ align:start position:0%
+eye view this is a misfit dislocation
+ 
+
+ align:start position:0%
+eye view this is a misfit dislocation
+segment along the interface and there's
+
+ align:start position:0%
+segment along the interface and there's
+ 
+
+ align:start position:0%
+segment along the interface and there's
+a dislocation arm that threads to the
+
+ align:start position:0%
+a dislocation arm that threads to the
+ 
+
+ align:start position:0%
+a dislocation arm that threads to the
+surface and these dark lines end up
+
+ align:start position:0%
+surface and these dark lines end up
+ 
+
+ align:start position:0%
+surface and these dark lines end up
+having uh extra electron defraction
+
+ align:start position:0%
+having uh extra electron defraction
+ 
+
+ align:start position:0%
+having uh extra electron defraction
+contrast in the TM these dark lines
+
+ align:start position:0%
+contrast in the TM these dark lines
+ 
+
+ align:start position:0%
+contrast in the TM these dark lines
+correspond to Misfit dislocations at
+
+ align:start position:0%
+correspond to Misfit dislocations at
+ 
+
+ align:start position:0%
+correspond to Misfit dislocations at
+this interface and they run along the
+
+ align:start position:0%
+this interface and they run along the
+ 
+
+ align:start position:0%
+this interface and they run along the
+easy slip planes in Silicon uh and
+
+ align:start position:0%
+easy slip planes in Silicon uh and
+ 
+
+ align:start position:0%
+easy slip planes in Silicon uh and
+silicon Germania which they run along
+
+ align:start position:0%
+silicon Germania which they run along
+ 
+
+ align:start position:0%
+silicon Germania which they run along
+the 110 Direction so just typically
+
+ align:start position:0%
+the 110 Direction so just typically
+ 
+
+ align:start position:0%
+the 110 Direction so just typically
+parallel and perpendicular to the flat
+
+ align:start position:0%
+parallel and perpendicular to the flat
+ 
+
+ align:start position:0%
+parallel and perpendicular to the flat
+so this filam was grown to be a little
+
+ align:start position:0%
+so this filam was grown to be a little
+ 
+
+ align:start position:0%
+so this filam was grown to be a little
+bit too thick and it started to form
+
+ align:start position:0%
+bit too thick and it started to form
+ 
+
+ align:start position:0%
+bit too thick and it started to form
+dislocations it's snow fully
+
+ align:start position:0%
+dislocations it's snow fully
+ 
+
+ align:start position:0%
+dislocations it's snow fully
+strained uh in fact you may be wondering
+
+ align:start position:0%
+strained uh in fact you may be wondering
+ 
+
+ align:start position:0%
+strained uh in fact you may be wondering
+oh well how thick is too thick uh well
+
+ align:start position:0%
+oh well how thick is too thick uh well
+ 
+
+ align:start position:0%
+oh well how thick is too thick uh well
+there is no one number unfortunately
+
+ align:start position:0%
+there is no one number unfortunately
+ 
+
+ align:start position:0%
+there is no one number unfortunately
+there um for a long time people thought
+
+ align:start position:0%
+there um for a long time people thought
+ 
+
+ align:start position:0%
+there um for a long time people thought
+there was a quote unquote critical
+
+ align:start position:0%
+there was a quote unquote critical
+ 
+
+ align:start position:0%
+there was a quote unquote critical
+thickness so that at a particular
+
+ align:start position:0%
+thickness so that at a particular
+ 
+
+ align:start position:0%
+thickness so that at a particular
+Germania fraction when you go above that
+
+ align:start position:0%
+Germania fraction when you go above that
+ 
+
+ align:start position:0%
+Germania fraction when you go above that
+thickness Bingo you get dislocations
+
+ align:start position:0%
+thickness Bingo you get dislocations
+ 
+
+ align:start position:0%
+thickness Bingo you get dislocations
+doesn't quite happen that way uh in fact
+
+ align:start position:0%
+doesn't quite happen that way uh in fact
+ 
+
+ align:start position:0%
+doesn't quite happen that way uh in fact
+there is a whole metastable
+
+ align:start position:0%
+there is a whole metastable
+ 
+
+ align:start position:0%
+there is a whole metastable
+regime and the critical thickness
+
+ align:start position:0%
+regime and the critical thickness
+ 
+
+ align:start position:0%
+regime and the critical thickness
+depends on the temperature at which
+
+ align:start position:0%
+depends on the temperature at which
+ 
+
+ align:start position:0%
+depends on the temperature at which
+you're doing the growth because it's a
+
+ align:start position:0%
+you're doing the growth because it's a
+ 
+
+ align:start position:0%
+you're doing the growth because it's a
+kinetically li limited process and this
+
+ align:start position:0%
+kinetically li limited process and this
+ 
+
+ align:start position:0%
+kinetically li limited process and this
+is a good paper Derek Hon's paper from
+
+ align:start position:0%
+is a good paper Derek Hon's paper from
+ 
+
+ align:start position:0%
+is a good paper Derek Hon's paper from
+1991 who describes the kinetic model and
+
+ align:start position:0%
+1991 who describes the kinetic model and
+ 
+
+ align:start position:0%
+1991 who describes the kinetic model and
+explains the fact that there's no one
+
+ align:start position:0%
+explains the fact that there's no one
+ 
+
+ align:start position:0%
+explains the fact that there's no one
+critical thickness at a given geranium
+
+ align:start position:0%
+critical thickness at a given geranium
+ 
+
+ align:start position:0%
+critical thickness at a given geranium
+fraction uh what he plotted here was a
+
+ align:start position:0%
+fraction uh what he plotted here was a
+ 
+
+ align:start position:0%
+fraction uh what he plotted here was a
+summary of the critical thickness uh
+
+ align:start position:0%
+summary of the critical thickness uh
+ 
+
+ align:start position:0%
+summary of the critical thickness uh
+above which dislocations form as a
+
+ align:start position:0%
+above which dislocations form as a
+ 
+
+ align:start position:0%
+above which dislocations form as a
+function of geranium fraction of the
+
+ align:start position:0%
+function of geranium fraction of the
+ 
+
+ align:start position:0%
+function of geranium fraction of the
+Silicon geranium layer for different
+
+ align:start position:0%
+Silicon geranium layer for different
+ 
+
+ align:start position:0%
+Silicon geranium layer for different
+growth temperatures so if you're growing
+
+ align:start position:0%
+growth temperatures so if you're growing
+ 
+
+ align:start position:0%
+growth temperatures so if you're growing
+at 900° you're very hot and it's very
+
+ align:start position:0%
+at 900° you're very hot and it's very
+ 
+
+ align:start position:0%
+at 900° you're very hot and it's very
+easy to nucleate dislocations and they
+
+ align:start position:0%
+easy to nucleate dislocations and they
+ 
+
+ align:start position:0%
+easy to nucleate dislocations and they
+travel very rapidly
+
+ align:start position:0%
+travel very rapidly
+ 
+
+ align:start position:0%
+travel very rapidly
+you tend to then get the equilibrium
+
+ align:start position:0%
+you tend to then get the equilibrium
+ 
+
+ align:start position:0%
+you tend to then get the equilibrium
+critical thickness that this this line
+
+ align:start position:0%
+critical thickness that this this line
+ 
+
+ align:start position:0%
+critical thickness that this this line
+here so if you're growing at high
+
+ align:start position:0%
+here so if you're growing at high
+ 
+
+ align:start position:0%
+here so if you're growing at high
+temperature or you kneeling at high
+
+ align:start position:0%
+temperature or you kneeling at high
+ 
+
+ align:start position:0%
+temperature or you kneeling at high
+temperature if you're at 20% the
+
+ align:start position:0%
+temperature if you're at 20% the
+ 
+
+ align:start position:0%
+temperature if you're at 20% the
+equilibrium critical thickness for
+
+ align:start position:0%
+equilibrium critical thickness for
+ 
+
+ align:start position:0%
+equilibrium critical thickness for
+silicon Germania is about 120 angstroms
+
+ align:start position:0%
+silicon Germania is about 120 angstroms
+ 
+
+ align:start position:0%
+silicon Germania is about 120 angstroms
+110 angstrum something like that so that
+
+ align:start position:0%
+110 angstrum something like that so that
+ 
+
+ align:start position:0%
+110 angstrum something like that so that
+says that if you're growing at high
+
+ align:start position:0%
+says that if you're growing at high
+ 
+
+ align:start position:0%
+says that if you're growing at high
+temperature and you grow above about 120
+
+ align:start position:0%
+temperature and you grow above about 120
+ 
+
+ align:start position:0%
+temperature and you grow above about 120
+Anum of 20% silicon geranium it will
+
+ align:start position:0%
+Anum of 20% silicon geranium it will
+ 
+
+ align:start position:0%
+Anum of 20% silicon geranium it will
+start to form
+
+ align:start position:0%
+start to form
+ 
+
+ align:start position:0%
+start to form
+dislocations uh at that point however if
+
+ align:start position:0%
+dislocations uh at that point however if
+ 
+
+ align:start position:0%
+dislocations uh at that point however if
+you are growing that same germanium
+
+ align:start position:0%
+you are growing that same germanium
+ 
+
+ align:start position:0%
+you are growing that same germanium
+fraction at 550 say so you're in a very
+
+ align:start position:0%
+fraction at 550 say so you're in a very
+ 
+
+ align:start position:0%
+fraction at 550 say so you're in a very
+low temperature epitaxial growth you are
+
+ align:start position:0%
+low temperature epitaxial growth you are
+ 
+
+ align:start position:0%
+low temperature epitaxial growth you are
+kinetically suppressing the formation of
+
+ align:start position:0%
+kinetically suppressing the formation of
+ 
+
+ align:start position:0%
+kinetically suppressing the formation of
+dislocations in fact the critical
+
+ align:start position:0%
+dislocations in fact the critical
+ 
+
+ align:start position:0%
+dislocations in fact the critical
+thickness is like this curve here it's
+
+ align:start position:0%
+thickness is like this curve here it's
+ 
+
+ align:start position:0%
+thickness is like this curve here it's
+about 700
+
+ align:start position:0%
+about 700
+ 
+
+ align:start position:0%
+about 700
+an so you can there's a metastable
+
+ align:start position:0%
+an so you can there's a metastable
+ 
+
+ align:start position:0%
+an so you can there's a metastable
+regime if you grow the layers thin
+
+ align:start position:0%
+regime if you grow the layers thin
+ 
+
+ align:start position:0%
+regime if you grow the layers thin
+enough you can keep them strained and
+
+ align:start position:0%
+enough you can keep them strained and
+ 
+
+ align:start position:0%
+enough you can keep them strained and
+they won't form dislocations until a
+
+ align:start position:0%
+they won't form dislocations until a
+ 
+
+ align:start position:0%
+they won't form dislocations until a
+much thicker layer the problem with that
+
+ align:start position:0%
+much thicker layer the problem with that
+ 
+
+ align:start position:0%
+much thicker layer the problem with that
+is you can grow them very thin at high
+
+ align:start position:0%
+is you can grow them very thin at high
+ 
+
+ align:start position:0%
+is you can grow them very thin at high
+temperature very thick and they won't
+
+ align:start position:0%
+temperature very thick and they won't
+ 
+
+ align:start position:0%
+temperature very thick and they won't
+have dislocations but if you go to
+
+ align:start position:0%
+have dislocations but if you go to
+ 
+
+ align:start position:0%
+have dislocations but if you go to
+process them to make a device at a
+
+ align:start position:0%
+process them to make a device at a
+ 
+
+ align:start position:0%
+process them to make a device at a
+higher temperature dislocations can can
+
+ align:start position:0%
+higher temperature dislocations can can
+ 
+
+ align:start position:0%
+higher temperature dislocations can can
+pop in if you're above the equilibrium
+
+ align:start position:0%
+pop in if you're above the equilibrium
+ 
+
+ align:start position:0%
+pop in if you're above the equilibrium
+critical thickness so this region is
+
+ align:start position:0%
+critical thickness so this region is
+ 
+
+ align:start position:0%
+critical thickness so this region is
+called metastable because you can grow
+
+ align:start position:0%
+called metastable because you can grow
+ 
+
+ align:start position:0%
+called metastable because you can grow
+them at low temperatures without
+
+ align:start position:0%
+them at low temperatures without
+ 
+
+ align:start position:0%
+them at low temperatures without
+dislocations but if you were to kneel
+
+ align:start position:0%
+dislocations but if you were to kneel
+ 
+
+ align:start position:0%
+dislocations but if you were to kneel
+them at a higher temperature dislocation
+
+ align:start position:0%
+them at a higher temperature dislocation
+ 
+
+ align:start position:0%
+them at a higher temperature dislocation
+would form and it would start to
+
+ align:start position:0%
+would form and it would start to
+ 
+
+ align:start position:0%
+would form and it would start to
+relax generally this region up here up
+
+ align:start position:0%
+relax generally this region up here up
+ 
+
+ align:start position:0%
+relax generally this region up here up
+in the upper right so it's very thick
+
+ align:start position:0%
+in the upper right so it's very thick
+ 
+
+ align:start position:0%
+in the upper right so it's very thick
+films are almost always relaxed they'll
+
+ align:start position:0%
+films are almost always relaxed they'll
+ 
+
+ align:start position:0%
+films are almost always relaxed they'll
+always have dislocations so but I refer
+
+ align:start position:0%
+always have dislocations so but I refer
+ 
+
+ align:start position:0%
+always have dislocations so but I refer
+you to this 1991 paper for a good
+
+ align:start position:0%
+you to this 1991 paper for a good
+ 
+
+ align:start position:0%
+you to this 1991 paper for a good
+reference on understanding uh uh the
+
+ align:start position:0%
+reference on understanding uh uh the
+ 
+
+ align:start position:0%
+reference on understanding uh uh the
+formation of Misfits um in in strain
+
+ align:start position:0%
+formation of Misfits um in in strain
+ 
+
+ align:start position:0%
+formation of Misfits um in in strain
+silicon tranium layers
+
+ align:start position:0%
+silicon tranium layers
+ 
+
+ align:start position:0%
+silicon tranium layers
+Clyde uh
+
+ align:start position:0%
+Clyde uh
+ 
+
+ align:start position:0%
+Clyde uh
+29 uh it turns out in the early
+
+ align:start position:0%
+29 uh it turns out in the early
+ 
+
+ align:start position:0%
+29 uh it turns out in the early
+1990s uh there was some breakthroughs on
+
+ align:start position:0%
+1990s uh there was some breakthroughs on
+ 
+
+ align:start position:0%
+1990s uh there was some breakthroughs on
+you said well growing strain silicon
+
+ align:start position:0%
+you said well growing strain silicon
+ 
+
+ align:start position:0%
+you said well growing strain silicon
+geranium that's very interesting people
+
+ align:start position:0%
+geranium that's very interesting people
+ 
+
+ align:start position:0%
+geranium that's very interesting people
+want to do that there were actually some
+
+ align:start position:0%
+want to do that there were actually some
+ 
+
+ align:start position:0%
+want to do that there were actually some
+breakthroughs on how to grow relaxed
+
+ align:start position:0%
+breakthroughs on how to grow relaxed
+ 
+
+ align:start position:0%
+breakthroughs on how to grow relaxed
+silicon geran this seems like it should
+
+ align:start position:0%
+silicon geran this seems like it should
+ 
+
+ align:start position:0%
+silicon geran this seems like it should
+be very easy to make the Silicon geran
+
+ align:start position:0%
+be very easy to make the Silicon geran
+ 
+
+ align:start position:0%
+be very easy to make the Silicon geran
+relax you just grow it thick right we
+
+ align:start position:0%
+relax you just grow it thick right we
+ 
+
+ align:start position:0%
+relax you just grow it thick right we
+just saw that paper from Derek hton well
+
+ align:start position:0%
+just saw that paper from Derek hton well
+ 
+
+ align:start position:0%
+just saw that paper from Derek hton well
+if I'm at 30% I just grow it to be uh
+
+ align:start position:0%
+if I'm at 30% I just grow it to be uh
+ 
+
+ align:start position:0%
+if I'm at 30% I just grow it to be uh
+you know three or four microns up here
+
+ align:start position:0%
+you know three or four microns up here
+ 
+
+ align:start position:0%
+you know three or four microns up here
+it'll definitely be above the critical
+
+ align:start position:0%
+it'll definitely be above the critical
+ 
+
+ align:start position:0%
+it'll definitely be above the critical
+thickness it will be relaxed it'll have
+
+ align:start position:0%
+thickness it will be relaxed it'll have
+ 
+
+ align:start position:0%
+thickness it will be relaxed it'll have
+its own lattice parameter the problem
+
+ align:start position:0%
+its own lattice parameter the problem
+ 
+
+ align:start position:0%
+its own lattice parameter the problem
+with that if you just grow it uh right
+
+ align:start position:0%
+with that if you just grow it uh right
+ 
+
+ align:start position:0%
+with that if you just grow it uh right
+off the bat like that a box layer you
+
+ align:start position:0%
+off the bat like that a box layer you
+ 
+
+ align:start position:0%
+off the bat like that a box layer you
+end up with um a huge number of
+
+ align:start position:0%
+end up with um a huge number of
+ 
+
+ align:start position:0%
+end up with um a huge number of
+threading
+
+ align:start position:0%
+threading
+ 
+
+ align:start position:0%
+threading
+dislocations um so if you don't grade
+
+ align:start position:0%
+dislocations um so if you don't grade
+ 
+
+ align:start position:0%
+dislocations um so if you don't grade
+the profile you end up with more than 10
+
+ align:start position:0%
+the profile you end up with more than 10
+ 
+
+ align:start position:0%
+the profile you end up with more than 10
+of the nth maybe 10 of the 10th of these
+
+ align:start position:0%
+of the nth maybe 10 of the 10th of these
+ 
+
+ align:start position:0%
+of the nth maybe 10 of the 10th of these
+threading arms these for every Miss bit
+
+ align:start position:0%
+threading arms these for every Miss bit
+ 
+
+ align:start position:0%
+threading arms these for every Miss bit
+you have an arm that two arms that go up
+
+ align:start position:0%
+you have an arm that two arms that go up
+ 
+
+ align:start position:0%
+you have an arm that two arms that go up
+to the to the surface and you have so
+
+ align:start position:0%
+to the to the surface and you have so
+ 
+
+ align:start position:0%
+to the to the surface and you have so
+many of them that the the layers aren't
+
+ align:start position:0%
+many of them that the the layers aren't
+ 
+
+ align:start position:0%
+many of them that the the layers aren't
+very useful for very many many devices
+
+ align:start position:0%
+very useful for very many many devices
+ 
+
+ align:start position:0%
+very useful for very many many devices
+because there's too many
+
+ align:start position:0%
+because there's too many
+ 
+
+ align:start position:0%
+because there's too many
+defects but in the early 90s there were
+
+ align:start position:0%
+defects but in the early 90s there were
+ 
+
+ align:start position:0%
+defects but in the early 90s there were
+breakthroughs on how to grow these
+
+ align:start position:0%
+breakthroughs on how to grow these
+ 
+
+ align:start position:0%
+breakthroughs on how to grow these
+layers uh how to grow them at high
+
+ align:start position:0%
+layers uh how to grow them at high
+ 
+
+ align:start position:0%
+layers uh how to grow them at high
+enough temperature so the threading arms
+
+ align:start position:0%
+enough temperature so the threading arms
+ 
+
+ align:start position:0%
+enough temperature so the threading arms
+could run to the edge of the wafer and
+
+ align:start position:0%
+could run to the edge of the wafer and
+ 
+
+ align:start position:0%
+could run to the edge of the wafer and
+how to grade the geranium content so you
+
+ align:start position:0%
+how to grade the geranium content so you
+ 
+
+ align:start position:0%
+how to grade the geranium content so you
+start growing it's it's silicon lattice
+
+ align:start position:0%
+start growing it's it's silicon lattice
+ 
+
+ align:start position:0%
+start growing it's it's silicon lattice
+and then you gradually add geranium as
+
+ align:start position:0%
+and then you gradually add geranium as
+ 
+
+ align:start position:0%
+and then you gradually add geranium as
+you go up and you grade it over many
+
+ align:start position:0%
+you go up and you grade it over many
+ 
+
+ align:start position:0%
+you go up and you grade it over many
+microns it turns out when you do that
+
+ align:start position:0%
+microns it turns out when you do that
+ 
+
+ align:start position:0%
+microns it turns out when you do that
+you can relax the Silicon geranium but
+
+ align:start position:0%
+you can relax the Silicon geranium but
+ 
+
+ align:start position:0%
+you can relax the Silicon geranium but
+you can reduce the number of arms that
+
+ align:start position:0%
+you can reduce the number of arms that
+ 
+
+ align:start position:0%
+you can reduce the number of arms that
+thread to the surface all the arms run
+
+ align:start position:0%
+thread to the surface all the arms run
+ 
+
+ align:start position:0%
+thread to the surface all the arms run
+out to the edge of the wafer where you
+
+ align:start position:0%
+out to the edge of the wafer where you
+ 
+
+ align:start position:0%
+out to the edge of the wafer where you
+don't care about them because you're not
+
+ align:start position:0%
+don't care about them because you're not
+ 
+
+ align:start position:0%
+don't care about them because you're not
+going to make any devices at the edge of
+
+ align:start position:0%
+going to make any devices at the edge of
+ 
+
+ align:start position:0%
+going to make any devices at the edge of
+the wafer so the threading dislocation
+
+ align:start position:0%
+the wafer so the threading dislocation
+ 
+
+ align:start position:0%
+the wafer so the threading dislocation
+density can go down from 10 to the 9th
+
+ align:start position:0%
+density can go down from 10 to the 9th
+ 
+
+ align:start position:0%
+density can go down from 10 to the 9th
+to less than 10 the 5ifth if you do the
+
+ align:start position:0%
+to less than 10 the 5ifth if you do the
+ 
+
+ align:start position:0%
+to less than 10 the 5ifth if you do the
+grading right um so the nice thing about
+
+ align:start position:0%
+grading right um so the nice thing about
+ 
+
+ align:start position:0%
+grading right um so the nice thing about
+this is all of a sudden on Silicon
+
+ align:start position:0%
+this is all of a sudden on Silicon
+ 
+
+ align:start position:0%
+this is all of a sudden on Silicon
+substrates in the early 90s people had a
+
+ align:start position:0%
+substrates in the early 90s people had a
+ 
+
+ align:start position:0%
+substrates in the early 90s people had a
+way to take a silicon substrate grow a
+
+ align:start position:0%
+way to take a silicon substrate grow a
+ 
+
+ align:start position:0%
+way to take a silicon substrate grow a
+relaxed silicon germanium layer and had
+
+ align:start position:0%
+relaxed silicon germanium layer and had
+ 
+
+ align:start position:0%
+relaxed silicon germanium layer and had
+it be pretty high quality a reasonable
+
+ align:start position:0%
+it be pretty high quality a reasonable
+ 
+
+ align:start position:0%
+it be pretty high quality a reasonable
+enough high quality that you can make
+
+ align:start position:0%
+enough high quality that you can make
+ 
+
+ align:start position:0%
+enough high quality that you can make
+devices um on it there work there's
+
+ align:start position:0%
+devices um on it there work there's
+ 
+
+ align:start position:0%
+devices um on it there work there's
+still a lot of threading dislocations
+
+ align:start position:0%
+still a lot of threading dislocations
+ 
+
+ align:start position:0%
+still a lot of threading dislocations
+but not enough to screw up other devices
+
+ align:start position:0%
+but not enough to screw up other devices
+ 
+
+ align:start position:0%
+but not enough to screw up other devices
+too badly so that was kind of the
+
+ align:start position:0%
+too badly so that was kind of the
+ 
+
+ align:start position:0%
+too badly so that was kind of the
+Breakthrough that enabled people to make
+
+ align:start position:0%
+Breakthrough that enabled people to make
+ 
+
+ align:start position:0%
+Breakthrough that enabled people to make
+relaxed silicon geranium and then strain
+
+ align:start position:0%
+relaxed silicon geranium and then strain
+ 
+
+ align:start position:0%
+relaxed silicon geranium and then strain
+silicon mosfets on top of
+
+ align:start position:0%
+silicon mosfets on top of
+ 
+
+ align:start position:0%
+silicon mosfets on top of
+it um what are some of the materials
+
+ align:start position:0%
+it um what are some of the materials
+ 
+
+ align:start position:0%
+it um what are some of the materials
+issues if you're growing this uh relaxed
+
+ align:start position:0%
+issues if you're growing this uh relaxed
+ 
+
+ align:start position:0%
+issues if you're growing this uh relaxed
+silicon geranium well I already
+
+ align:start position:0%
+silicon geranium well I already
+ 
+
+ align:start position:0%
+silicon geranium well I already
+mentioned the threading dislocation
+
+ align:start position:0%
+mentioned the threading dislocation
+ 
+
+ align:start position:0%
+mentioned the threading dislocation
+density uh it actually decreases if you
+
+ align:start position:0%
+density uh it actually decreases if you
+ 
+
+ align:start position:0%
+density uh it actually decreases if you
+go to higher growth temperatures because
+
+ align:start position:0%
+go to higher growth temperatures because
+ 
+
+ align:start position:0%
+go to higher growth temperatures because
+the dislocations can move faster uh the
+
+ align:start position:0%
+the dislocations can move faster uh the
+ 
+
+ align:start position:0%
+the dislocations can move faster uh the
+problem though is uh you also tend to
+
+ align:start position:0%
+problem though is uh you also tend to
+ 
+
+ align:start position:0%
+problem though is uh you also tend to
+get um a buried strain field that
+
+ align:start position:0%
+get um a buried strain field that
+ 
+
+ align:start position:0%
+get um a buried strain field that
+creates a cross-hatch in fact if you
+
+ align:start position:0%
+creates a cross-hatch in fact if you
+ 
+
+ align:start position:0%
+creates a cross-hatch in fact if you
+look at this um a plan View Optical
+
+ align:start position:0%
+look at this um a plan View Optical
+ 
+
+ align:start position:0%
+look at this um a plan View Optical
+micrograph of a relaxed silk and
+
+ align:start position:0%
+micrograph of a relaxed silk and
+ 
+
+ align:start position:0%
+micrograph of a relaxed silk and
+geranium layer it looks like a plaid
+
+ align:start position:0%
+geranium layer it looks like a plaid
+ 
+
+ align:start position:0%
+geranium layer it looks like a plaid
+shirt this plaid is that buried strain
+
+ align:start position:0%
+shirt this plaid is that buried strain
+ 
+
+ align:start position:0%
+shirt this plaid is that buried strain
+field causes the surface to undulate
+
+ align:start position:0%
+field causes the surface to undulate
+ 
+
+ align:start position:0%
+field causes the surface to undulate
+ever so slightly maybe 100 anstrom high
+
+ align:start position:0%
+ever so slightly maybe 100 anstrom high
+ 
+
+ align:start position:0%
+ever so slightly maybe 100 anstrom high
+Hills and Valleys very smooth and the
+
+ align:start position:0%
+Hills and Valleys very smooth and the
+ 
+
+ align:start position:0%
+Hills and Valleys very smooth and the
+period of these undulations or the
+
+ align:start position:0%
+period of these undulations or the
+ 
+
+ align:start position:0%
+period of these undulations or the
+spacing is quite large it can be microns
+
+ align:start position:0%
+spacing is quite large it can be microns
+ 
+
+ align:start position:0%
+spacing is quite large it can be microns
+uh so these are these are smooth
+
+ align:start position:0%
+uh so these are these are smooth
+ 
+
+ align:start position:0%
+uh so these are these are smooth
+undulations They Don't Really mess they
+
+ align:start position:0%
+undulations They Don't Really mess they
+ 
+
+ align:start position:0%
+undulations They Don't Really mess they
+don't mess with the electron Mobility
+
+ align:start position:0%
+don't mess with the electron Mobility
+ 
+
+ align:start position:0%
+don't mess with the electron Mobility
+electrons and holes don't care about
+
+ align:start position:0%
+electrons and holes don't care about
+ 
+
+ align:start position:0%
+electrons and holes don't care about
+them they don't it makes the Wafers look
+
+ align:start position:0%
+them they don't it makes the Wafers look
+ 
+
+ align:start position:0%
+them they don't it makes the Wafers look
+ugly
+
+ align:start position:0%
+ugly
+ 
+
+ align:start position:0%
+ugly
+however and it makes lithography a
+
+ align:start position:0%
+however and it makes lithography a
+ 
+
+ align:start position:0%
+however and it makes lithography a
+little difficult because Optical
+
+ align:start position:0%
+little difficult because Optical
+ 
+
+ align:start position:0%
+little difficult because Optical
+machines don't like looking at plaid
+
+ align:start position:0%
+machines don't like looking at plaid
+ 
+
+ align:start position:0%
+machines don't like looking at plaid
+they like things that look smooth so it
+
+ align:start position:0%
+they like things that look smooth so it
+ 
+
+ align:start position:0%
+they like things that look smooth so it
+is a practical problem people have found
+
+ align:start position:0%
+is a practical problem people have found
+ 
+
+ align:start position:0%
+is a practical problem people have found
+a ways around it you can CMP the layer
+
+ align:start position:0%
+a ways around it you can CMP the layer
+ 
+
+ align:start position:0%
+a ways around it you can CMP the layer
+and you can remove all the undulations
+
+ align:start position:0%
+and you can remove all the undulations
+ 
+
+ align:start position:0%
+and you can remove all the undulations
+it's not necessarily a big problem but
+
+ align:start position:0%
+it's not necessarily a big problem but
+ 
+
+ align:start position:0%
+it's not necessarily a big problem but
+it it is an issue if you grow the SL and
+
+ align:start position:0%
+it it is an issue if you grow the SL and
+ 
+
+ align:start position:0%
+it it is an issue if you grow the SL and
+geranium too hot it turns out it doesn't
+
+ align:start position:0%
+geranium too hot it turns out it doesn't
+ 
+
+ align:start position:0%
+geranium too hot it turns out it doesn't
+even grow as a planer film it grows as
+
+ align:start position:0%
+even grow as a planer film it grows as
+ 
+
+ align:start position:0%
+even grow as a planer film it grows as
+big little clumps little mountains or
+
+ align:start position:0%
+big little clumps little mountains or
+ 
+
+ align:start position:0%
+big little clumps little mountains or
+isys uh it doesn't wet the surface
+
+ align:start position:0%
+isys uh it doesn't wet the surface
+ 
+
+ align:start position:0%
+isys uh it doesn't wet the surface
+properly and these films are uh these
+
+ align:start position:0%
+properly and these films are uh these
+ 
+
+ align:start position:0%
+properly and these films are uh these
+this type of growth mode is generally
+
+ align:start position:0%
+this type of growth mode is generally
+ 
+
+ align:start position:0%
+this type of growth mode is generally
+considered uh not very useful because
+
+ align:start position:0%
+considered uh not very useful because
+ 
+
+ align:start position:0%
+considered uh not very useful because
+it's it's not really a smooth film um so
+
+ align:start position:0%
+it's it's not really a smooth film um so
+ 
+
+ align:start position:0%
+it's it's not really a smooth film um so
+you cannot grow silicon germanium at too
+
+ align:start position:0%
+you cannot grow silicon germanium at too
+ 
+
+ align:start position:0%
+you cannot grow silicon germanium at too
+high a temperature for a given geranium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fraction what of these fil these relaxed
+
+ align:start position:0%
+fraction what of these fil these relaxed
+ 
+
+ align:start position:0%
+fraction what of these fil these relaxed
+silicon geranium grad buffer layers look
+
+ align:start position:0%
+silicon geranium grad buffer layers look
+ 
+
+ align:start position:0%
+silicon geranium grad buffer layers look
+like I said well they have very few
+
+ align:start position:0%
+like I said well they have very few
+ 
+
+ align:start position:0%
+like I said well they have very few
+defects that thread to the surface
+
+ align:start position:0%
+defects that thread to the surface
+ 
+
+ align:start position:0%
+defects that thread to the surface
+that's indeed true um these are some
+
+ align:start position:0%
+that's indeed true um these are some
+ 
+
+ align:start position:0%
+that's indeed true um these are some
+cross-section temm micrographs of
+
+ align:start position:0%
+cross-section temm micrographs of
+ 
+
+ align:start position:0%
+cross-section temm micrographs of
+relaxed silicon geranium see at 10% uh
+
+ align:start position:0%
+relaxed silicon geranium see at 10% uh
+ 
+
+ align:start position:0%
+relaxed silicon geranium see at 10% uh
+this is the Silicon substrate this is
+
+ align:start position:0%
+this is the Silicon substrate this is
+ 
+
+ align:start position:0%
+this is the Silicon substrate this is
+the graded layer there're are lots of
+
+ align:start position:0%
+the graded layer there're are lots of
+ 
+
+ align:start position:0%
+the graded layer there're are lots of
+dislocations in the graded layer that's
+
+ align:start position:0%
+dislocations in the graded layer that's
+ 
+
+ align:start position:0%
+dislocations in the graded layer that's
+what you want you want dislocations down
+
+ align:start position:0%
+what you want you want dislocations down
+ 
+
+ align:start position:0%
+what you want you want dislocations down
+in the graded layer because you want to
+
+ align:start position:0%
+in the graded layer because you want to
+ 
+
+ align:start position:0%
+in the graded layer because you want to
+relax the lattice primary you want it to
+
+ align:start position:0%
+relax the lattice primary you want it to
+ 
+
+ align:start position:0%
+relax the lattice primary you want it to
+expand to be its equilibrium parameter
+
+ align:start position:0%
+expand to be its equilibrium parameter
+ 
+
+ align:start position:0%
+expand to be its equilibrium parameter
+but what you see is as you get up to the
+
+ align:start position:0%
+but what you see is as you get up to the
+ 
+
+ align:start position:0%
+but what you see is as you get up to the
+surface um if the grade layer is thick
+
+ align:start position:0%
+surface um if the grade layer is thick
+ 
+
+ align:start position:0%
+surface um if the grade layer is thick
+enough into the box layer there are too
+
+ align:start position:0%
+enough into the box layer there are too
+ 
+
+ align:start position:0%
+enough into the box layer there are too
+many dislocations of visible in
+
+ align:start position:0%
+many dislocations of visible in
+ 
+
+ align:start position:0%
+many dislocations of visible in
+cross-section TM again this is up here
+
+ align:start position:0%
+cross-section TM again this is up here
+ 
+
+ align:start position:0%
+cross-section TM again this is up here
+is where you're going to build your
+
+ align:start position:0%
+is where you're going to build your
+ 
+
+ align:start position:0%
+is where you're going to build your
+device so that's what you care about but
+
+ align:start position:0%
+device so that's what you care about but
+ 
+
+ align:start position:0%
+device so that's what you care about but
+if you compare a 10% to a 20 to a 30%
+
+ align:start position:0%
+if you compare a 10% to a 20 to a 30%
+ 
+
+ align:start position:0%
+if you compare a 10% to a 20 to a 30%
+geranium you see a higher and higher Den
+
+ align:start position:0%
+geranium you see a higher and higher Den
+ 
+
+ align:start position:0%
+geranium you see a higher and higher Den
+it of these buried dislocations of
+
+ align:start position:0%
+it of these buried dislocations of
+ 
+
+ align:start position:0%
+it of these buried dislocations of
+course as you increase the geranium
+
+ align:start position:0%
+course as you increase the geranium
+ 
+
+ align:start position:0%
+course as you increase the geranium
+fraction because you have to relieve
+
+ align:start position:0%
+fraction because you have to relieve
+ 
+
+ align:start position:0%
+fraction because you have to relieve
+more lattice mismatch so that the the uh
+
+ align:start position:0%
+more lattice mismatch so that the the uh
+ 
+
+ align:start position:0%
+more lattice mismatch so that the the uh
+the layers get pretty ugly even though
+
+ align:start position:0%
+the layers get pretty ugly even though
+ 
+
+ align:start position:0%
+the layers get pretty ugly even though
+the device is up on top there's still a
+
+ align:start position:0%
+the device is up on top there's still a
+ 
+
+ align:start position:0%
+the device is up on top there's still a
+lot of integration issues you can
+
+ align:start position:0%
+lot of integration issues you can
+ 
+
+ align:start position:0%
+lot of integration issues you can
+imagine trying to make seamoss circuits
+
+ align:start position:0%
+imagine trying to make seamoss circuits
+ 
+
+ align:start position:0%
+imagine trying to make seamoss circuits
+on a substrate that looks like this all
+
+ align:start position:0%
+on a substrate that looks like this all
+ 
+
+ align:start position:0%
+on a substrate that looks like this all
+these buried dislocations are going to
+
+ align:start position:0%
+these buried dislocations are going to
+ 
+
+ align:start position:0%
+these buried dislocations are going to
+worry and they're going to bother the
+
+ align:start position:0%
+worry and they're going to bother the
+ 
+
+ align:start position:0%
+worry and they're going to bother the
+device Engineers because after all we do
+
+ align:start position:0%
+device Engineers because after all we do
+ 
+
+ align:start position:0%
+device Engineers because after all we do
+have seamoss wells we do have deep
+
+ align:start position:0%
+have seamoss wells we do have deep
+ 
+
+ align:start position:0%
+have seamoss wells we do have deep
+Junctions in some of these um some of
+
+ align:start position:0%
+Junctions in some of these um some of
+ 
+
+ align:start position:0%
+Junctions in some of these um some of
+these structures so this this silicon
+
+ align:start position:0%
+these structures so this this silicon
+ 
+
+ align:start position:0%
+these structures so this this silicon
+geranium can affect our my shallow
+
+ align:start position:0%
+geranium can affect our my shallow
+ 
+
+ align:start position:0%
+geranium can affect our my shallow
+trench isolation fabrication formation
+
+ align:start position:0%
+trench isolation fabrication formation
+ 
+
+ align:start position:0%
+trench isolation fabrication formation
+of silicides and the way doens to fuse
+
+ align:start position:0%
+of silicides and the way doens to fuse
+ 
+
+ align:start position:0%
+of silicides and the way doens to fuse
+so it certainly is an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+issue in fact there's a whole field of
+
+ align:start position:0%
+issue in fact there's a whole field of
+ 
+
+ align:start position:0%
+issue in fact there's a whole field of
+research going on right now which is the
+
+ align:start position:0%
+research going on right now which is the
+ 
+
+ align:start position:0%
+research going on right now which is the
+study of the diffusion of dopin in silic
+
+ align:start position:0%
+study of the diffusion of dopin in silic
+ 
+
+ align:start position:0%
+study of the diffusion of dopin in silic
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+geranium and I'm showing here on um
+
+ align:start position:0%
+geranium and I'm showing here on um
+ 
+
+ align:start position:0%
+geranium and I'm showing here on um
+slide uh on slide 32 this is some data
+
+ align:start position:0%
+slide uh on slide 32 this is some data
+ 
+
+ align:start position:0%
+slide uh on slide 32 this is some data
+for silicon germanium Alloys with 20%
+
+ align:start position:0%
+for silicon germanium Alloys with 20%
+ 
+
+ align:start position:0%
+for silicon germanium Alloys with 20%
+geranium in them and what we're looking
+
+ align:start position:0%
+geranium in them and what we're looking
+ 
+
+ align:start position:0%
+geranium in them and what we're looking
+at is the diffusivity of different dopin
+
+ align:start position:0%
+at is the diffusivity of different dopin
+ 
+
+ align:start position:0%
+at is the diffusivity of different dopin
+so this is the effective equilibrium
+
+ align:start position:0%
+so this is the effective equilibrium
+ 
+
+ align:start position:0%
+so this is the effective equilibrium
+diffusivity so it's the fusion
+
+ align:start position:0%
+diffusivity so it's the fusion
+ 
+
+ align:start position:0%
+diffusivity so it's the fusion
+coefficient in centime squar per second
+
+ align:start position:0%
+coefficient in centime squar per second
+ 
+
+ align:start position:0%
+coefficient in centime squar per second
+as a function of inverse temperature
+
+ align:start position:0%
+as a function of inverse temperature
+ 
+
+ align:start position:0%
+as a function of inverse temperature
+well the usual kind of arous plot and if
+
+ align:start position:0%
+well the usual kind of arous plot and if
+ 
+
+ align:start position:0%
+well the usual kind of arous plot and if
+you look at Boron so so the dash line
+
+ align:start position:0%
+you look at Boron so so the dash line
+ 
+
+ align:start position:0%
+you look at Boron so so the dash line
+here is for diffusion in Silicon and the
+
+ align:start position:0%
+here is for diffusion in Silicon and the
+ 
+
+ align:start position:0%
+here is for diffusion in Silicon and the
+solid is for diffusion in Silicon
+
+ align:start position:0%
+solid is for diffusion in Silicon
+ 
+
+ align:start position:0%
+solid is for diffusion in Silicon
+geranium if you look at Boron here in
+
+ align:start position:0%
+geranium if you look at Boron here in
+ 
+
+ align:start position:0%
+geranium if you look at Boron here in
+fact in 20% silic and geranium the
+
+ align:start position:0%
+fact in 20% silic and geranium the
+ 
+
+ align:start position:0%
+fact in 20% silic and geranium the
+diffusivity is reduced I'd said before
+
+ align:start position:0%
+diffusivity is reduced I'd said before
+ 
+
+ align:start position:0%
+diffusivity is reduced I'd said before
+factor of 10 looks like more like a
+
+ align:start position:0%
+factor of 10 looks like more like a
+ 
+
+ align:start position:0%
+factor of 10 looks like more like a
+factor of six or so but depending on the
+
+ align:start position:0%
+factor of six or so but depending on the
+ 
+
+ align:start position:0%
+factor of six or so but depending on the
+temperature but so the Boron diffusivity
+
+ align:start position:0%
+temperature but so the Boron diffusivity
+ 
+
+ align:start position:0%
+temperature but so the Boron diffusivity
+goes down uh in solanium which is nice
+
+ align:start position:0%
+goes down uh in solanium which is nice
+ 
+
+ align:start position:0%
+goes down uh in solanium which is nice
+because Bor is a fast diffuser in
+
+ align:start position:0%
+because Bor is a fast diffuser in
+ 
+
+ align:start position:0%
+because Bor is a fast diffuser in
+Silicon but if you look at arsenic this
+
+ align:start position:0%
+Silicon but if you look at arsenic this
+ 
+
+ align:start position:0%
+Silicon but if you look at arsenic this
+is arsenic and silicon the dash line
+
+ align:start position:0%
+is arsenic and silicon the dash line
+ 
+
+ align:start position:0%
+is arsenic and silicon the dash line
+Arsenic and silicon geranium is the
+
+ align:start position:0%
+Arsenic and silicon geranium is the
+ 
+
+ align:start position:0%
+Arsenic and silicon geranium is the
+solid line here with the green arrow so
+
+ align:start position:0%
+solid line here with the green arrow so
+ 
+
+ align:start position:0%
+solid line here with the green arrow so
+the ARs and silicon geranium is
+
+ align:start position:0%
+the ARs and silicon geranium is
+ 
+
+ align:start position:0%
+the ARs and silicon geranium is
+diffusing a lot faster in fact arsic and
+
+ align:start position:0%
+diffusing a lot faster in fact arsic and
+ 
+
+ align:start position:0%
+diffusing a lot faster in fact arsic and
+silicon geranium is diffusing at about
+
+ align:start position:0%
+silicon geranium is diffusing at about
+ 
+
+ align:start position:0%
+silicon geranium is diffusing at about
+the same rate as boron in Silicon geran
+
+ align:start position:0%
+the same rate as boron in Silicon geran
+ 
+
+ align:start position:0%
+the same rate as boron in Silicon geran
+at 20% so we've taken the Boron
+
+ align:start position:0%
+at 20% so we've taken the Boron
+ 
+
+ align:start position:0%
+at 20% so we've taken the Boron
+diffusion coefficient goes down arsenic
+
+ align:start position:0%
+diffusion coefficient goes down arsenic
+ 
+
+ align:start position:0%
+diffusion coefficient goes down arsenic
+which is usually very slow and silicon
+
+ align:start position:0%
+which is usually very slow and silicon
+ 
+
+ align:start position:0%
+which is usually very slow and silicon
+now goes up now they diffuse about
+
+ align:start position:0%
+now goes up now they diffuse about
+ 
+
+ align:start position:0%
+now goes up now they diffuse about
+equally which is kind of interesting you
+
+ align:start position:0%
+equally which is kind of interesting you
+ 
+
+ align:start position:0%
+equally which is kind of interesting you
+can might make some interesting device
+
+ align:start position:0%
+can might make some interesting device
+ 
+
+ align:start position:0%
+can might make some interesting device
+structures when you have symmetric
+
+ align:start position:0%
+structures when you have symmetric
+ 
+
+ align:start position:0%
+structures when you have symmetric
+diffusion coefficients between the n and
+
+ align:start position:0%
+diffusion coefficients between the n and
+ 
+
+ align:start position:0%
+diffusion coefficients between the n and
+the P type doping uh unfortunately what
+
+ align:start position:0%
+the P type doping uh unfortunately what
+ 
+
+ align:start position:0%
+the P type doping uh unfortunately what
+it means is that in in silic and
+
+ align:start position:0%
+it means is that in in silic and
+ 
+
+ align:start position:0%
+it means is that in in silic and
+germanian Mos spets we actually are much
+
+ align:start position:0%
+germanian Mos spets we actually are much
+ 
+
+ align:start position:0%
+germanian Mos spets we actually are much
+more worried about the N type dopa
+
+ align:start position:0%
+more worried about the N type dopa
+ 
+
+ align:start position:0%
+more worried about the N type dopa
+diffusion because it's what's going fast
+
+ align:start position:0%
+diffusion because it's what's going fast
+ 
+
+ align:start position:0%
+diffusion because it's what's going fast
+and we're less worried about the ptype
+
+ align:start position:0%
+and we're less worried about the ptype
+ 
+
+ align:start position:0%
+and we're less worried about the ptype
+dopa diffusion the bn's going slower
+
+ align:start position:0%
+dopa diffusion the bn's going slower
+ 
+
+ align:start position:0%
+dopa diffusion the bn's going slower
+phosphorus doesn't help the situation
+
+ align:start position:0%
+phosphorus doesn't help the situation
+ 
+
+ align:start position:0%
+phosphorus doesn't help the situation
+phosphorus is also enhanced maybe about
+
+ align:start position:0%
+phosphorus is also enhanced maybe about
+ 
+
+ align:start position:0%
+phosphorus is also enhanced maybe about
+a factor it two or three depending on
+
+ align:start position:0%
+a factor it two or three depending on
+ 
+
+ align:start position:0%
+a factor it two or three depending on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+temperature um so and this line here
+
+ align:start position:0%
+temperature um so and this line here
+ 
+
+ align:start position:0%
+temperature um so and this line here
+gives you an idea roughly of the the
+
+ align:start position:0%
+gives you an idea roughly of the the
+ 
+
+ align:start position:0%
+gives you an idea roughly of the the
+diffusivity of of germanium well this is
+
+ align:start position:0%
+diffusivity of of germanium well this is
+ 
+
+ align:start position:0%
+diffusivity of of germanium well this is
+at a very low geranium fraction um as a
+
+ align:start position:0%
+at a very low geranium fraction um as a
+ 
+
+ align:start position:0%
+at a very low geranium fraction um as a
+function of temperature it's diffusing
+
+ align:start position:0%
+function of temperature it's diffusing
+ 
+
+ align:start position:0%
+function of temperature it's diffusing
+slower than the dopus at least at this
+
+ align:start position:0%
+slower than the dopus at least at this
+ 
+
+ align:start position:0%
+slower than the dopus at least at this
+geranium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fraction so I mentioned to you that
+
+ align:start position:0%
+fraction so I mentioned to you that
+ 
+
+ align:start position:0%
+fraction so I mentioned to you that
+arsenic moves faster in Silicon geranium
+
+ align:start position:0%
+arsenic moves faster in Silicon geranium
+ 
+
+ align:start position:0%
+arsenic moves faster in Silicon geranium
+this is actually a big problem if you're
+
+ align:start position:0%
+this is actually a big problem if you're
+ 
+
+ align:start position:0%
+this is actually a big problem if you're
+trying to make a strain silicon n mosfet
+
+ align:start position:0%
+trying to make a strain silicon n mosfet
+ 
+
+ align:start position:0%
+trying to make a strain silicon n mosfet
+with silicon germanium in the substrate
+
+ align:start position:0%
+with silicon germanium in the substrate
+ 
+
+ align:start position:0%
+with silicon germanium in the substrate
+let's say you're trying to make uh
+
+ align:start position:0%
+let's say you're trying to make uh
+ 
+
+ align:start position:0%
+let's say you're trying to make uh
+shallow Source drains uh so you do you
+
+ align:start position:0%
+shallow Source drains uh so you do you
+ 
+
+ align:start position:0%
+shallow Source drains uh so you do you
+implant 50 k uh at 3 times 10 15th maybe
+
+ align:start position:0%
+implant 50 k uh at 3 times 10 15th maybe
+ 
+
+ align:start position:0%
+implant 50 k uh at 3 times 10 15th maybe
+a typical sour drain uh implant and you
+
+ align:start position:0%
+a typical sour drain uh implant and you
+ 
+
+ align:start position:0%
+a typical sour drain uh implant and you
+en knal it at a th000
+
+ align:start position:0%
+en knal it at a th000
+ 
+
+ align:start position:0%
+en knal it at a th000
+degrees per various times and the dash
+
+ align:start position:0%
+degrees per various times and the dash
+ 
+
+ align:start position:0%
+degrees per various times and the dash
+lines here are for a silicon substrate
+
+ align:start position:0%
+lines here are for a silicon substrate
+ 
+
+ align:start position:0%
+lines here are for a silicon substrate
+uh and the solid are for silicon
+
+ align:start position:0%
+uh and the solid are for silicon
+ 
+
+ align:start position:0%
+uh and the solid are for silicon
+geranium so if you just look at um say
+
+ align:start position:0%
+geranium so if you just look at um say
+ 
+
+ align:start position:0%
+geranium so if you just look at um say
+this dash line here this red dash line
+
+ align:start position:0%
+this dash line here this red dash line
+ 
+
+ align:start position:0%
+this dash line here this red dash line
+you for the Silicon substrate with this
+
+ align:start position:0%
+you for the Silicon substrate with this
+ 
+
+ align:start position:0%
+you for the Silicon substrate with this
+um 202 anal at a th000 you have a
+
+ align:start position:0%
+um 202 anal at a th000 you have a
+ 
+
+ align:start position:0%
+um 202 anal at a th000 you have a
+junction depth about 500 anstrom that's
+
+ align:start position:0%
+junction depth about 500 anstrom that's
+ 
+
+ align:start position:0%
+junction depth about 500 anstrom that's
+perfect for the Silicon geranium
+
+ align:start position:0%
+perfect for the Silicon geranium
+ 
+
+ align:start position:0%
+perfect for the Silicon geranium
+substrate which is the solid line 202 in
+
+ align:start position:0%
+substrate which is the solid line 202 in
+ 
+
+ align:start position:0%
+substrate which is the solid line 202 in
+Neal your Junction depth is more than
+
+ align:start position:0%
+Neal your Junction depth is more than
+ 
+
+ align:start position:0%
+Neal your Junction depth is more than
+twice that point it's it's like 1,200
+
+ align:start position:0%
+twice that point it's it's like 1,200
+ 
+
+ align:start position:0%
+twice that point it's it's like 1,200
+anrs so uh the RS snck and the Silicon
+
+ align:start position:0%
+anrs so uh the RS snck and the Silicon
+ 
+
+ align:start position:0%
+anrs so uh the RS snck and the Silicon
+Terin is going much more rapidly you see
+
+ align:start position:0%
+Terin is going much more rapidly you see
+ 
+
+ align:start position:0%
+Terin is going much more rapidly you see
+this big big shift uh and uh that that's
+
+ align:start position:0%
+this big big shift uh and uh that that's
+ 
+
+ align:start position:0%
+this big big shift uh and uh that that's
+a problem if you use very short inal
+
+ align:start position:0%
+a problem if you use very short inal
+ 
+
+ align:start position:0%
+a problem if you use very short inal
+times you can minimize that difference
+
+ align:start position:0%
+times you can minimize that difference
+ 
+
+ align:start position:0%
+times you can minimize that difference
+but th degrees 1 second is not enough to
+
+ align:start position:0%
+but th degrees 1 second is not enough to
+ 
+
+ align:start position:0%
+but th degrees 1 second is not enough to
+really repair all the damage and to
+
+ align:start position:0%
+really repair all the damage and to
+ 
+
+ align:start position:0%
+really repair all the damage and to
+activate all the dopent so there's a
+
+ align:start position:0%
+activate all the dopent so there's a
+ 
+
+ align:start position:0%
+activate all the dopent so there's a
+very uh interesting issue here is how do
+
+ align:start position:0%
+very uh interesting issue here is how do
+ 
+
+ align:start position:0%
+very uh interesting issue here is how do
+we optimize the uh a kneeling time for
+
+ align:start position:0%
+we optimize the uh a kneeling time for
+ 
+
+ align:start position:0%
+we optimize the uh a kneeling time for
+uh end typ dopen so we get good
+
+ align:start position:0%
+uh end typ dopen so we get good
+ 
+
+ align:start position:0%
+uh end typ dopen so we get good
+activation in the Silicon geranium but
+
+ align:start position:0%
+activation in the Silicon geranium but
+ 
+
+ align:start position:0%
+activation in the Silicon geranium but
+um we don't uh introduce too much
+
+ align:start position:0%
+um we don't uh introduce too much
+ 
+
+ align:start position:0%
+um we don't uh introduce too much
+diffusion otherwise we can't control uh
+
+ align:start position:0%
+diffusion otherwise we can't control uh
+ 
+
+ align:start position:0%
+diffusion otherwise we can't control uh
+control the device
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fabrication here's another issue on
+
+ align:start position:0%
+fabrication here's another issue on
+ 
+
+ align:start position:0%
+fabrication here's another issue on
+slide 34 I'm not trying to make silicon
+
+ align:start position:0%
+slide 34 I'm not trying to make silicon
+ 
+
+ align:start position:0%
+slide 34 I'm not trying to make silicon
+geranium look difficult but it is a new
+
+ align:start position:0%
+geranium look difficult but it is a new
+ 
+
+ align:start position:0%
+geranium look difficult but it is a new
+material and a lot of things change uh
+
+ align:start position:0%
+material and a lot of things change uh
+ 
+
+ align:start position:0%
+material and a lot of things change uh
+slide 34 shows you that indeed the
+
+ align:start position:0%
+slide 34 shows you that indeed the
+ 
+
+ align:start position:0%
+slide 34 shows you that indeed the
+geranium itself can diffuse we're
+
+ align:start position:0%
+geranium itself can diffuse we're
+ 
+
+ align:start position:0%
+geranium itself can diffuse we're
+talking about taking a silicon geranium
+
+ align:start position:0%
+talking about taking a silicon geranium
+ 
+
+ align:start position:0%
+talking about taking a silicon geranium
+thick layer and putting a thin layer say
+
+ align:start position:0%
+thick layer and putting a thin layer say
+ 
+
+ align:start position:0%
+thick layer and putting a thin layer say
+100 an strims of strained silicon on it
+
+ align:start position:0%
+100 an strims of strained silicon on it
+ 
+
+ align:start position:0%
+100 an strims of strained silicon on it
+that's my channel okay that sounds fine
+
+ align:start position:0%
+that's my channel okay that sounds fine
+ 
+
+ align:start position:0%
+that's my channel okay that sounds fine
+we can grow that epx but now I need to
+
+ align:start position:0%
+we can grow that epx but now I need to
+ 
+
+ align:start position:0%
+we can grow that epx but now I need to
+implant the sourc tray and enal it at a
+
+ align:start position:0%
+implant the sourc tray and enal it at a
+ 
+
+ align:start position:0%
+implant the sourc tray and enal it at a
+thousand what's going to happen to that
+
+ align:start position:0%
+thousand what's going to happen to that
+ 
+
+ align:start position:0%
+thousand what's going to happen to that
+silicon geranium the geranium and
+
+ align:start position:0%
+silicon geranium the geranium and
+ 
+
+ align:start position:0%
+silicon geranium the geranium and
+silicon Germania well it's going to
+
+ align:start position:0%
+silicon Germania well it's going to
+ 
+
+ align:start position:0%
+silicon Germania well it's going to
+diffuse up into the Silicon once we get
+
+ align:start position:0%
+diffuse up into the Silicon once we get
+ 
+
+ align:start position:0%
+diffuse up into the Silicon once we get
+silicon Jill once we get geranium into
+
+ align:start position:0%
+silicon Jill once we get geranium into
+ 
+
+ align:start position:0%
+silicon Jill once we get geranium into
+the channel that's a no no the electrons
+
+ align:start position:0%
+the channel that's a no no the electrons
+ 
+
+ align:start position:0%
+the channel that's a no no the electrons
+don't like geranium in the channel they
+
+ align:start position:0%
+don't like geranium in the channel they
+ 
+
+ align:start position:0%
+don't like geranium in the channel they
+the electrons can be scattered by the
+
+ align:start position:0%
+the electrons can be scattered by the
+ 
+
+ align:start position:0%
+the electrons can be scattered by the
+geranium Mobility goes way down and your
+
+ align:start position:0%
+geranium Mobility goes way down and your
+ 
+
+ align:start position:0%
+geranium Mobility goes way down and your
+device is ruined you lose a lot of your
+
+ align:start position:0%
+device is ruined you lose a lot of your
+ 
+
+ align:start position:0%
+device is ruined you lose a lot of your
+strain too so you have to keep the
+
+ align:start position:0%
+strain too so you have to keep the
+ 
+
+ align:start position:0%
+strain too so you have to keep the
+geranium out of the channel well it
+
+ align:start position:0%
+geranium out of the channel well it
+ 
+
+ align:start position:0%
+geranium out of the channel well it
+doesn't sound too bad but if you just
+
+ align:start position:0%
+doesn't sound too bad but if you just
+ 
+
+ align:start position:0%
+doesn't sound too bad but if you just
+look at some of the diffusion
+
+ align:start position:0%
+look at some of the diffusion
+ 
+
+ align:start position:0%
+look at some of the diffusion
+coefficients uh in fact U these
+
+ align:start position:0%
+coefficients uh in fact U these
+ 
+
+ align:start position:0%
+coefficients uh in fact U these
+different lines these are measured this
+
+ align:start position:0%
+different lines these are measured this
+ 
+
+ align:start position:0%
+different lines these are measured this
+is the geranium self diffusion in silic
+
+ align:start position:0%
+is the geranium self diffusion in silic
+ 
+
+ align:start position:0%
+is the geranium self diffusion in silic
+geranium Alloys uh for different
+
+ align:start position:0%
+geranium Alloys uh for different
+ 
+
+ align:start position:0%
+geranium Alloys uh for different
+geranium content so this is for silicon
+
+ align:start position:0%
+geranium content so this is for silicon
+ 
+
+ align:start position:0%
+geranium content so this is for silicon
+so this will be silicon self- diffusion
+
+ align:start position:0%
+so this will be silicon self- diffusion
+ 
+
+ align:start position:0%
+so this will be silicon self- diffusion
+this is 10%
+
+ align:start position:0%
+this is 10%
+ 
+
+ align:start position:0%
+this is 10%
+geranium 20% 30 40 and 50 so if you just
+
+ align:start position:0%
+geranium 20% 30 40 and 50 so if you just
+ 
+
+ align:start position:0%
+geranium 20% 30 40 and 50 so if you just
+look at a given temperature say at 9 at
+
+ align:start position:0%
+look at a given temperature say at 9 at
+ 
+
+ align:start position:0%
+look at a given temperature say at 9 at
+950 degrees look at what happening to
+
+ align:start position:0%
+950 degrees look at what happening to
+ 
+
+ align:start position:0%
+950 degrees look at what happening to
+the diffusion coefficient in Silicon uh
+
+ align:start position:0%
+the diffusion coefficient in Silicon uh
+ 
+
+ align:start position:0%
+the diffusion coefficient in Silicon uh
+you know pure silicon gerain is
+
+ align:start position:0%
+you know pure silicon gerain is
+ 
+
+ align:start position:0%
+you know pure silicon gerain is
+diffusing very slowly for a low geranium
+
+ align:start position:0%
+diffusing very slowly for a low geranium
+ 
+
+ align:start position:0%
+diffusing very slowly for a low geranium
+content you know here around 10 Theus
+
+ align:start position:0%
+content you know here around 10 Theus
+ 
+
+ align:start position:0%
+content you know here around 10 Theus
+17th cm squ per second but if you go up
+
+ align:start position:0%
+17th cm squ per second but if you go up
+ 
+
+ align:start position:0%
+17th cm squ per second but if you go up
+to a 40% alloy and diffusivity goes up
+
+ align:start position:0%
+to a 40% alloy and diffusivity goes up
+ 
+
+ align:start position:0%
+to a 40% alloy and diffusivity goes up
+by two orders of magnitude so what this
+
+ align:start position:0%
+by two orders of magnitude so what this
+ 
+
+ align:start position:0%
+by two orders of magnitude so what this
+is saying is basically um you get an
+
+ align:start position:0%
+is saying is basically um you get an
+ 
+
+ align:start position:0%
+is saying is basically um you get an
+exponential increase it looks like in
+
+ align:start position:0%
+exponential increase it looks like in
+ 
+
+ align:start position:0%
+exponential increase it looks like in
+the uh geranium diffus diffusion
+
+ align:start position:0%
+the uh geranium diffus diffusion
+ 
+
+ align:start position:0%
+the uh geranium diffus diffusion
+coefficient as you increase the amount
+
+ align:start position:0%
+coefficient as you increase the amount
+ 
+
+ align:start position:0%
+coefficient as you increase the amount
+of geranium in the alloy so it's that's
+
+ align:start position:0%
+of geranium in the alloy so it's that's
+ 
+
+ align:start position:0%
+of geranium in the alloy so it's that's
+a big issue if you want to do strain
+
+ align:start position:0%
+a big issue if you want to do strain
+ 
+
+ align:start position:0%
+a big issue if you want to do strain
+silicon on 20% you're G to have a
+
+ align:start position:0%
+silicon on 20% you're G to have a
+ 
+
+ align:start position:0%
+silicon on 20% you're G to have a
+silicon geranium you have a certain
+
+ align:start position:0%
+silicon geranium you have a certain
+ 
+
+ align:start position:0%
+silicon geranium you have a certain
+diffusion coefficient if you do it on
+
+ align:start position:0%
+diffusion coefficient if you do it on
+ 
+
+ align:start position:0%
+diffusion coefficient if you do it on
+30% all of a sudden your diffusion
+
+ align:start position:0%
+30% all of a sudden your diffusion
+ 
+
+ align:start position:0%
+30% all of a sudden your diffusion
+coefficient factor of five or so higher
+
+ align:start position:0%
+coefficient factor of five or so higher
+ 
+
+ align:start position:0%
+coefficient factor of five or so higher
+uh so that that's a big issue because
+
+ align:start position:0%
+uh so that that's a big issue because
+ 
+
+ align:start position:0%
+uh so that that's a big issue because
+you don't want the geranium diffusing
+
+ align:start position:0%
+you don't want the geranium diffusing
+ 
+
+ align:start position:0%
+you don't want the geranium diffusing
+into the channel so this data is not
+
+ align:start position:0%
+into the channel so this data is not
+ 
+
+ align:start position:0%
+into the channel so this data is not
+exactly inter diffusion data it needs to
+
+ align:start position:0%
+exactly inter diffusion data it needs to
+ 
+
+ align:start position:0%
+exactly inter diffusion data it needs to
+be that whole problem needs to be worked
+
+ align:start position:0%
+be that whole problem needs to be worked
+ 
+
+ align:start position:0%
+be that whole problem needs to be worked
+out but um inter diffusion is definitely
+
+ align:start position:0%
+out but um inter diffusion is definitely
+ 
+
+ align:start position:0%
+out but um inter diffusion is definitely
+observed for like a th000 degrees 10
+
+ align:start position:0%
+observed for like a th000 degrees 10
+ 
+
+ align:start position:0%
+observed for like a th000 degrees 10
+seconds at 20% so that that's a no no so
+
+ align:start position:0%
+seconds at 20% so that that's a no no so
+ 
+
+ align:start position:0%
+seconds at 20% so that that's a no no so
+that's that's going to be a big issue
+
+ align:start position:0%
+that's that's going to be a big issue
+ 
+
+ align:start position:0%
+that's that's going to be a big issue
+and how we're going to activate Source
+
+ align:start position:0%
+and how we're going to activate Source
+ 
+
+ align:start position:0%
+and how we're going to activate Source
+strains in those kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structures that's an interesting
+
+ align:start position:0%
+structures that's an interesting
+ 
+
+ align:start position:0%
+structures that's an interesting
+research uh area um you might be saying
+
+ align:start position:0%
+research uh area um you might be saying
+ 
+
+ align:start position:0%
+research uh area um you might be saying
+well what is the mechanism uh of
+
+ align:start position:0%
+well what is the mechanism uh of
+ 
+
+ align:start position:0%
+well what is the mechanism uh of
+diffusion of germanium in in Silicon
+
+ align:start position:0%
+diffusion of germanium in in Silicon
+ 
+
+ align:start position:0%
+diffusion of germanium in in Silicon
+anyway actually it's not really known
+
+ align:start position:0%
+anyway actually it's not really known
+ 
+
+ align:start position:0%
+anyway actually it's not really known
+and this is a on page 35 an example uh
+
+ align:start position:0%
+and this is a on page 35 an example uh
+ 
+
+ align:start position:0%
+and this is a on page 35 an example uh
+of people are just trying to get a
+
+ align:start position:0%
+of people are just trying to get a
+ 
+
+ align:start position:0%
+of people are just trying to get a
+handle on this this was published about
+
+ align:start position:0%
+handle on this this was published about
+ 
+
+ align:start position:0%
+handle on this this was published about
+about a year and a half ago um and
+
+ align:start position:0%
+about a year and a half ago um and
+ 
+
+ align:start position:0%
+about a year and a half ago um and
+people did uh this particular experiment
+
+ align:start position:0%
+people did uh this particular experiment
+ 
+
+ align:start position:0%
+people did uh this particular experiment
+they did a process where they had
+
+ align:start position:0%
+they did a process where they had
+ 
+
+ align:start position:0%
+they did a process where they had
+strained silicon on relaxed silicon
+
+ align:start position:0%
+strained silicon on relaxed silicon
+ 
+
+ align:start position:0%
+strained silicon on relaxed silicon
+germanian and they did an anal in a
+
+ align:start position:0%
+germanian and they did an anal in a
+ 
+
+ align:start position:0%
+germanian and they did an anal in a
+rapid thermal analer where they put in
+
+ align:start position:0%
+rapid thermal analer where they put in
+ 
+
+ align:start position:0%
+rapid thermal analer where they put in
+ammonia so they're doing rapid thermal
+
+ align:start position:0%
+ammonia so they're doing rapid thermal
+ 
+
+ align:start position:0%
+ammonia so they're doing rapid thermal
+nitridation so what do we know about
+
+ align:start position:0%
+nitridation so what do we know about
+ 
+
+ align:start position:0%
+nitridation so what do we know about
+nitridation well nitridation we believe
+
+ align:start position:0%
+nitridation well nitridation we believe
+ 
+
+ align:start position:0%
+nitridation well nitridation we believe
+injects vacancies right that's when we
+
+ align:start position:0%
+injects vacancies right that's when we
+ 
+
+ align:start position:0%
+injects vacancies right that's when we
+use it so in the samples that were
+
+ align:start position:0%
+use it so in the samples that were
+ 
+
+ align:start position:0%
+use it so in the samples that were
+nitrided the geranium diffused right
+
+ align:start position:0%
+nitrided the geranium diffused right
+ 
+
+ align:start position:0%
+nitrided the geranium diffused right
+through the strain silic all the way to
+
+ align:start position:0%
+through the strain silic all the way to
+ 
+
+ align:start position:0%
+through the strain silic all the way to
+the surface and The Sims profile for the
+
+ align:start position:0%
+the surface and The Sims profile for the
+ 
+
+ align:start position:0%
+the surface and The Sims profile for the
+the blue here shows that geranium went
+
+ align:start position:0%
+the blue here shows that geranium went
+ 
+
+ align:start position:0%
+the blue here shows that geranium went
+right through that that 100 anstrom
+
+ align:start position:0%
+right through that that 100 anstrom
+ 
+
+ align:start position:0%
+right through that that 100 anstrom
+layer it was gone um the red line is for
+
+ align:start position:0%
+layer it was gone um the red line is for
+ 
+
+ align:start position:0%
+layer it was gone um the red line is for
+the geranium that was in NE inner
+
+ align:start position:0%
+the geranium that was in NE inner
+ 
+
+ align:start position:0%
+the geranium that was in NE inner
+ambient it diffused a little bit at this
+
+ align:start position:0%
+ambient it diffused a little bit at this
+ 
+
+ align:start position:0%
+ambient it diffused a little bit at this
+during this rapid thermal knel but uh
+
+ align:start position:0%
+during this rapid thermal knel but uh
+ 
+
+ align:start position:0%
+during this rapid thermal knel but uh
+you can ignore the surface Peak because
+
+ align:start position:0%
+you can ignore the surface Peak because
+ 
+
+ align:start position:0%
+you can ignore the surface Peak because
+that's sort of a Sims artifact but at
+
+ align:start position:0%
+that's sort of a Sims artifact but at
+ 
+
+ align:start position:0%
+that's sort of a Sims artifact but at
+least it didn't go all the way so this
+
+ align:start position:0%
+least it didn't go all the way so this
+ 
+
+ align:start position:0%
+least it didn't go all the way so this
+is a very preliminary result and it has
+
+ align:start position:0%
+is a very preliminary result and it has
+ 
+
+ align:start position:0%
+is a very preliminary result and it has
+to be repeated but it sort of indicates
+
+ align:start position:0%
+to be repeated but it sort of indicates
+ 
+
+ align:start position:0%
+to be repeated but it sort of indicates
+that processes that inject vacancies
+
+ align:start position:0%
+that processes that inject vacancies
+ 
+
+ align:start position:0%
+that processes that inject vacancies
+probably should be avoided if you're
+
+ align:start position:0%
+probably should be avoided if you're
+ 
+
+ align:start position:0%
+probably should be avoided if you're
+trying to control the diffusion of
+
+ align:start position:0%
+trying to control the diffusion of
+ 
+
+ align:start position:0%
+trying to control the diffusion of
+geran uh and so um so there are a lot of
+
+ align:start position:0%
+geran uh and so um so there are a lot of
+ 
+
+ align:start position:0%
+geran uh and so um so there are a lot of
+interest in doing processes to inject
+
+ align:start position:0%
+interest in doing processes to inject
+ 
+
+ align:start position:0%
+interest in doing processes to inject
+intials inject vacancies all the same
+
+ align:start position:0%
+intials inject vacancies all the same
+ 
+
+ align:start position:0%
+intials inject vacancies all the same
+kind of process the uh tests that have
+
+ align:start position:0%
+kind of process the uh tests that have
+ 
+
+ align:start position:0%
+kind of process the uh tests that have
+done in Silicon can now be done in
+
+ align:start position:0%
+done in Silicon can now be done in
+ 
+
+ align:start position:0%
+done in Silicon can now be done in
+strain silicon on Silicon geranium to
+
+ align:start position:0%
+strain silicon on Silicon geranium to
+ 
+
+ align:start position:0%
+strain silicon on Silicon geranium to
+see how the geranium diffuses or even
+
+ align:start position:0%
+see how the geranium diffuses or even
+ 
+
+ align:start position:0%
+see how the geranium diffuses or even
+how the dopin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diffuse I want to say a little bit now
+
+ align:start position:0%
+diffuse I want to say a little bit now
+ 
+
+ align:start position:0%
+diffuse I want to say a little bit now
+about these mod FS on insulator because
+
+ align:start position:0%
+about these mod FS on insulator because
+ 
+
+ align:start position:0%
+about these mod FS on insulator because
+I've talked a little bit about how the
+
+ align:start position:0%
+I've talked a little bit about how the
+ 
+
+ align:start position:0%
+I've talked a little bit about how the
+Silicon geranium is becoming a problem
+
+ align:start position:0%
+Silicon geranium is becoming a problem
+ 
+
+ align:start position:0%
+Silicon geranium is becoming a problem
+how can we get around some of these
+
+ align:start position:0%
+how can we get around some of these
+ 
+
+ align:start position:0%
+how can we get around some of these
+Problem by doing strain silicon on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+insulator well on page 37 I'm showing an
+
+ align:start position:0%
+insulator well on page 37 I'm showing an
+ 
+
+ align:start position:0%
+insulator well on page 37 I'm showing an
+example of a potential thing you might
+
+ align:start position:0%
+example of a potential thing you might
+ 
+
+ align:start position:0%
+example of a potential thing you might
+be thinking of well let's say we could
+
+ align:start position:0%
+be thinking of well let's say we could
+ 
+
+ align:start position:0%
+be thinking of well let's say we could
+get rid of if we go back here let me go
+
+ align:start position:0%
+get rid of if we go back here let me go
+ 
+
+ align:start position:0%
+get rid of if we go back here let me go
+back a few slides and uh I just look at
+
+ align:start position:0%
+back a few slides and uh I just look at
+ 
+
+ align:start position:0%
+back a few slides and uh I just look at
+this on on slide 31 this ugly looking
+
+ align:start position:0%
+this on on slide 31 this ugly looking
+ 
+
+ align:start position:0%
+this on on slide 31 this ugly looking
+thing with all these dislocations and
+
+ align:start position:0%
+thing with all these dislocations and
+ 
+
+ align:start position:0%
+thing with all these dislocations and
+that thick silicon germanium substrate I
+
+ align:start position:0%
+that thick silicon germanium substrate I
+ 
+
+ align:start position:0%
+that thick silicon germanium substrate I
+need them to relax The Strain so I can
+
+ align:start position:0%
+need them to relax The Strain so I can
+ 
+
+ align:start position:0%
+need them to relax The Strain so I can
+grow a thin layer of strain silicon on
+
+ align:start position:0%
+grow a thin layer of strain silicon on
+ 
+
+ align:start position:0%
+grow a thin layer of strain silicon on
+top but I don't really need them once
+
+ align:start position:0%
+top but I don't really need them once
+ 
+
+ align:start position:0%
+top but I don't really need them once
+the strain is relaxed so the idea was
+
+ align:start position:0%
+the strain is relaxed so the idea was
+ 
+
+ align:start position:0%
+the strain is relaxed so the idea was
+what if you could take this layer the
+
+ align:start position:0%
+what if you could take this layer the
+ 
+
+ align:start position:0%
+what if you could take this layer the
+top portion looks pretty good if you
+
+ align:start position:0%
+top portion looks pretty good if you
+ 
+
+ align:start position:0%
+top portion looks pretty good if you
+could take this whole layer and bond it
+
+ align:start position:0%
+could take this whole layer and bond it
+ 
+
+ align:start position:0%
+could take this whole layer and bond it
+to another wafer and then get rid of
+
+ align:start position:0%
+to another wafer and then get rid of
+ 
+
+ align:start position:0%
+to another wafer and then get rid of
+etch away all the dislocated material
+
+ align:start position:0%
+etch away all the dislocated material
+ 
+
+ align:start position:0%
+etch away all the dislocated material
+and you'd have relaxed silicon geranium
+
+ align:start position:0%
+and you'd have relaxed silicon geranium
+ 
+
+ align:start position:0%
+and you'd have relaxed silicon geranium
+on insulator for example and all this
+
+ align:start position:0%
+on insulator for example and all this
+ 
+
+ align:start position:0%
+on insulator for example and all this
+dislocation material would have been
+
+ align:start position:0%
+dislocation material would have been
+ 
+
+ align:start position:0%
+dislocation material would have been
+etched off or maybe removed by a smart
+
+ align:start position:0%
+etched off or maybe removed by a smart
+ 
+
+ align:start position:0%
+etched off or maybe removed by a smart
+cut like process uh I think some of you
+
+ align:start position:0%
+cut like process uh I think some of you
+ 
+
+ align:start position:0%
+cut like process uh I think some of you
+are studying smart cut we talked about a
+
+ align:start position:0%
+are studying smart cut we talked about a
+ 
+
+ align:start position:0%
+are studying smart cut we talked about a
+little bit we talked about SOI formation
+
+ align:start position:0%
+little bit we talked about SOI formation
+ 
+
+ align:start position:0%
+little bit we talked about SOI formation
+so in fact that's what this cartoon on
+
+ align:start position:0%
+so in fact that's what this cartoon on
+ 
+
+ align:start position:0%
+so in fact that's what this cartoon on
+slide 20 37 shows where you might have a
+
+ align:start position:0%
+slide 20 37 shows where you might have a
+ 
+
+ align:start position:0%
+slide 20 37 shows where you might have a
+thin layer of relaxed silic and geranium
+
+ align:start position:0%
+thin layer of relaxed silic and geranium
+ 
+
+ align:start position:0%
+thin layer of relaxed silic and geranium
+that has been generated by growing a
+
+ align:start position:0%
+that has been generated by growing a
+ 
+
+ align:start position:0%
+that has been generated by growing a
+thick layer and bonding it on uh and
+
+ align:start position:0%
+thick layer and bonding it on uh and
+ 
+
+ align:start position:0%
+thick layer and bonding it on uh and
+then you could grow strain silicon on
+
+ align:start position:0%
+then you could grow strain silicon on
+ 
+
+ align:start position:0%
+then you could grow strain silicon on
+top and make your your n moss and your P
+
+ align:start position:0%
+top and make your your n moss and your P
+ 
+
+ align:start position:0%
+top and make your your n moss and your P
+Moss uh that way so this is one idea
+
+ align:start position:0%
+Moss uh that way so this is one idea
+ 
+
+ align:start position:0%
+Moss uh that way so this is one idea
+that people have been pursuing uh to uh
+
+ align:start position:0%
+that people have been pursuing uh to uh
+ 
+
+ align:start position:0%
+that people have been pursuing uh to uh
+to get around some of those dislocation
+
+ align:start position:0%
+to get around some of those dislocation
+ 
+
+ align:start position:0%
+to get around some of those dislocation
+issues in fact on slide 38 if you're
+
+ align:start position:0%
+issues in fact on slide 38 if you're
+ 
+
+ align:start position:0%
+issues in fact on slide 38 if you're
+interested I've listed a number of
+
+ align:start position:0%
+interested I've listed a number of
+ 
+
+ align:start position:0%
+interested I've listed a number of
+different references here on how people
+
+ align:start position:0%
+different references here on how people
+ 
+
+ align:start position:0%
+different references here on how people
+are trying to form relax silicon
+
+ align:start position:0%
+are trying to form relax silicon
+ 
+
+ align:start position:0%
+are trying to form relax silicon
+geranium on insulator it turns out there
+
+ align:start position:0%
+geranium on insulator it turns out there
+ 
+
+ align:start position:0%
+geranium on insulator it turns out there
+are a lot of different processes not
+
+ align:start position:0%
+are a lot of different processes not
+ 
+
+ align:start position:0%
+are a lot of different processes not
+just the bonding process there is a
+
+ align:start position:0%
+just the bonding process there is a
+ 
+
+ align:start position:0%
+just the bonding process there is a
+simox like process where people grow
+
+ align:start position:0%
+simox like process where people grow
+ 
+
+ align:start position:0%
+simox like process where people grow
+silicon geranium on silicon epx and then
+
+ align:start position:0%
+silicon geranium on silicon epx and then
+ 
+
+ align:start position:0%
+silicon geranium on silicon epx and then
+they ion implant the oxygen that's
+
+ align:start position:0%
+they ion implant the oxygen that's
+ 
+
+ align:start position:0%
+they ion implant the oxygen that's
+exactly how SOI is made it's SOI they
+
+ align:start position:0%
+exactly how SOI is made it's SOI they
+ 
+
+ align:start position:0%
+exactly how SOI is made it's SOI they
+ion implant into pure silicon here they
+
+ align:start position:0%
+ion implant into pure silicon here they
+ 
+
+ align:start position:0%
+ion implant into pure silicon here they
+I implant the oxygen into a silicon
+
+ align:start position:0%
+I implant the oxygen into a silicon
+ 
+
+ align:start position:0%
+I implant the oxygen into a silicon
+geranium layer so it's a simox like
+
+ align:start position:0%
+geranium layer so it's a simox like
+ 
+
+ align:start position:0%
+geranium layer so it's a simox like
+process Toshiba has has talked about
+
+ align:start position:0%
+process Toshiba has has talked about
+ 
+
+ align:start position:0%
+process Toshiba has has talked about
+that there's some problems though uh for
+
+ align:start position:0%
+that there's some problems though uh for
+ 
+
+ align:start position:0%
+that there's some problems though uh for
+for high geranium contents of above
+
+ align:start position:0%
+for high geranium contents of above
+ 
+
+ align:start position:0%
+for high geranium contents of above
+about 15% it doesn't work very well um
+
+ align:start position:0%
+about 15% it doesn't work very well um
+ 
+
+ align:start position:0%
+about 15% it doesn't work very well um
+there's another very interesting
+
+ align:start position:0%
+there's another very interesting
+ 
+
+ align:start position:0%
+there's another very interesting
+technique um also came out of Toshiba
+
+ align:start position:0%
+technique um also came out of Toshiba
+ 
+
+ align:start position:0%
+technique um also came out of Toshiba
+called geranium condensation they
+
+ align:start position:0%
+called geranium condensation they
+ 
+
+ align:start position:0%
+called geranium condensation they
+actually start with Ani wafer they start
+
+ align:start position:0%
+actually start with Ani wafer they start
+ 
+
+ align:start position:0%
+actually start with Ani wafer they start
+with a wafer you buy from a commercial
+
+ align:start position:0%
+with a wafer you buy from a commercial
+ 
+
+ align:start position:0%
+with a wafer you buy from a commercial
+vender with a silicon on insulator they
+
+ align:start position:0%
+vender with a silicon on insulator they
+ 
+
+ align:start position:0%
+vender with a silicon on insulator they
+epically grow a thin layer of silicon
+
+ align:start position:0%
+epically grow a thin layer of silicon
+ 
+
+ align:start position:0%
+epically grow a thin layer of silicon
+geranium with a relatively low gerian
+
+ align:start position:0%
+geranium with a relatively low gerian
+ 
+
+ align:start position:0%
+geranium with a relatively low gerian
+content and they oxidize the whole thing
+
+ align:start position:0%
+content and they oxidize the whole thing
+ 
+
+ align:start position:0%
+content and they oxidize the whole thing
+and turns out in the oxidation the geran
+
+ align:start position:0%
+and turns out in the oxidation the geran
+ 
+
+ align:start position:0%
+and turns out in the oxidation the geran
+the snow plow forward into the layer um
+
+ align:start position:0%
+the snow plow forward into the layer um
+ 
+
+ align:start position:0%
+the snow plow forward into the layer um
+and the layer relaxes so they end up
+
+ align:start position:0%
+and the layer relaxes so they end up
+ 
+
+ align:start position:0%
+and the layer relaxes so they end up
+with a higher germanium content after
+
+ align:start position:0%
+with a higher germanium content after
+ 
+
+ align:start position:0%
+with a higher germanium content after
+oxidation and they have the layer
+
+ align:start position:0%
+oxidation and they have the layer
+ 
+
+ align:start position:0%
+oxidation and they have the layer
+originally strain silicon geranium layer
+
+ align:start position:0%
+originally strain silicon geranium layer
+ 
+
+ align:start position:0%
+originally strain silicon geranium layer
+ends up relaxing by form by the
+
+ align:start position:0%
+ends up relaxing by form by the
+ 
+
+ align:start position:0%
+ends up relaxing by form by the
+oxidation process and very high
+
+ align:start position:0%
+oxidation process and very high
+ 
+
+ align:start position:0%
+oxidation process and very high
+temperatures so that seems to be
+
+ align:start position:0%
+temperatures so that seems to be
+ 
+
+ align:start position:0%
+temperatures so that seems to be
+interesting uh there's a very similar
+
+ align:start position:0%
+interesting uh there's a very similar
+ 
+
+ align:start position:0%
+interesting uh there's a very similar
+technique uh called melt solidification
+
+ align:start position:0%
+technique uh called melt solidification
+ 
+
+ align:start position:0%
+technique uh called melt solidification
+by by another group uh and the bond and
+
+ align:start position:0%
+by by another group uh and the bond and
+ 
+
+ align:start position:0%
+by by another group uh and the bond and
+Edge back is what I mentioned before you
+
+ align:start position:0%
+Edge back is what I mentioned before you
+ 
+
+ align:start position:0%
+Edge back is what I mentioned before you
+grow The Strain Sil the relaxed silicon
+
+ align:start position:0%
+grow The Strain Sil the relaxed silicon
+ 
+
+ align:start position:0%
+grow The Strain Sil the relaxed silicon
+geranium Bond it to an oxide wafer and
+
+ align:start position:0%
+geranium Bond it to an oxide wafer and
+ 
+
+ align:start position:0%
+geranium Bond it to an oxide wafer and
+itch it back or smart cut it
+
+ align:start position:0%
+itch it back or smart cut it
+ 
+
+ align:start position:0%
+itch it back or smart cut it
+off um this is just that same process on
+
+ align:start position:0%
+off um this is just that same process on
+ 
+
+ align:start position:0%
+off um this is just that same process on
+slide 39 it won't go in great detail but
+
+ align:start position:0%
+slide 39 it won't go in great detail but
+ 
+
+ align:start position:0%
+slide 39 it won't go in great detail but
+you can imagine by bonding and selective
+
+ align:start position:0%
+you can imagine by bonding and selective
+ 
+
+ align:start position:0%
+you can imagine by bonding and selective
+etching uh you grow your graded silicon
+
+ align:start position:0%
+etching uh you grow your graded silicon
+ 
+
+ align:start position:0%
+etching uh you grow your graded silicon
+germanium relaxed layer you grow your
+
+ align:start position:0%
+germanium relaxed layer you grow your
+ 
+
+ align:start position:0%
+germanium relaxed layer you grow your
+relaxed cap and then uh you um flip it
+
+ align:start position:0%
+relaxed cap and then uh you um flip it
+ 
+
+ align:start position:0%
+relaxed cap and then uh you um flip it
+over and bond it to an oxidized handle
+
+ align:start position:0%
+over and bond it to an oxidized handle
+ 
+
+ align:start position:0%
+over and bond it to an oxidized handle
+wafer just like you would in in a bond
+
+ align:start position:0%
+wafer just like you would in in a bond
+ 
+
+ align:start position:0%
+wafer just like you would in in a bond
+and itch SOI and then you etch
+
+ align:start position:0%
+and itch SOI and then you etch
+ 
+
+ align:start position:0%
+and itch SOI and then you etch
+everything back and you end up with just
+
+ align:start position:0%
+everything back and you end up with just
+ 
+
+ align:start position:0%
+everything back and you end up with just
+relaxed silicon Germania after you've
+
+ align:start position:0%
+relaxed silicon Germania after you've
+ 
+
+ align:start position:0%
+relaxed silicon Germania after you've
+CMP relax silicon geranium on
+
+ align:start position:0%
+CMP relax silicon geranium on
+ 
+
+ align:start position:0%
+CMP relax silicon geranium on
+insulator so that's a technique that's
+
+ align:start position:0%
+insulator so that's a technique that's
+ 
+
+ align:start position:0%
+insulator so that's a technique that's
+uh being pursued to form relax silicon
+
+ align:start position:0%
+uh being pursued to form relax silicon
+ 
+
+ align:start position:0%
+uh being pursued to form relax silicon
+germanium on insulator and then you can
+
+ align:start position:0%
+germanium on insulator and then you can
+ 
+
+ align:start position:0%
+germanium on insulator and then you can
+grow strain silicon
+
+ align:start position:0%
+grow strain silicon
+ 
+
+ align:start position:0%
+grow strain silicon
+afterwards um you can also do bonding uh
+
+ align:start position:0%
+afterwards um you can also do bonding uh
+ 
+
+ align:start position:0%
+afterwards um you can also do bonding uh
+and hydrogen induced delamination or
+
+ align:start position:0%
+and hydrogen induced delamination or
+ 
+
+ align:start position:0%
+and hydrogen induced delamination or
+smart cut uh if you we've studied smart
+
+ align:start position:0%
+smart cut uh if you we've studied smart
+ 
+
+ align:start position:0%
+smart cut uh if you we've studied smart
+cut for silicon here we start with a
+
+ align:start position:0%
+cut for silicon here we start with a
+ 
+
+ align:start position:0%
+cut for silicon here we start with a
+relaxed silicon germanium epilayer we
+
+ align:start position:0%
+relaxed silicon germanium epilayer we
+ 
+
+ align:start position:0%
+relaxed silicon germanium epilayer we
+ion a plant with hydrogen and at the
+
+ align:start position:0%
+ion a plant with hydrogen and at the
+ 
+
+ align:start position:0%
+ion a plant with hydrogen and at the
+peak of the hydrogen bubbles
+
+ align:start position:0%
+peak of the hydrogen bubbles
+ 
+
+ align:start position:0%
+peak of the hydrogen bubbles
+form so after we've done the bonding
+
+ align:start position:0%
+form so after we've done the bonding
+ 
+
+ align:start position:0%
+form so after we've done the bonding
+we heat it up and those bubbles end up
+
+ align:start position:0%
+we heat it up and those bubbles end up
+ 
+
+ align:start position:0%
+we heat it up and those bubbles end up
+cleaving at all you get the delamination
+
+ align:start position:0%
+cleaving at all you get the delamination
+ 
+
+ align:start position:0%
+cleaving at all you get the delamination
+process is exactly analogous to what
+
+ align:start position:0%
+process is exactly analogous to what
+ 
+
+ align:start position:0%
+process is exactly analogous to what
+happens in s SOI Fab and now you have
+
+ align:start position:0%
+happens in s SOI Fab and now you have
+ 
+
+ align:start position:0%
+happens in s SOI Fab and now you have
+silicon geranium on insulator of course
+
+ align:start position:0%
+silicon geranium on insulator of course
+ 
+
+ align:start position:0%
+silicon geranium on insulator of course
+it has to be polished and smoothed but
+
+ align:start position:0%
+it has to be polished and smoothed but
+ 
+
+ align:start position:0%
+it has to be polished and smoothed but
+it it is a way form that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material uh I'll skip through this at
+
+ align:start position:0%
+material uh I'll skip through this at
+ 
+
+ align:start position:0%
+material uh I'll skip through this at
+this point because what basically it
+
+ align:start position:0%
+this point because what basically it
+ 
+
+ align:start position:0%
+this point because what basically it
+shows when you make that and you make a
+
+ align:start position:0%
+shows when you make that and you make a
+ 
+
+ align:start position:0%
+shows when you make that and you make a
+strain silicon mosfet you get the same
+
+ align:start position:0%
+strain silicon mosfet you get the same
+ 
+
+ align:start position:0%
+strain silicon mosfet you get the same
+Mobility that you that people have seen
+
+ align:start position:0%
+Mobility that you that people have seen
+ 
+
+ align:start position:0%
+Mobility that you that people have seen
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+past uh again I'll skip that interest of
+
+ align:start position:0%
+past uh again I'll skip that interest of
+ 
+
+ align:start position:0%
+past uh again I'll skip that interest of
+and and what I want to end up with is
+
+ align:start position:0%
+and and what I want to end up with is
+ 
+
+ align:start position:0%
+and and what I want to end up with is
+there's another approach people thought
+
+ align:start position:0%
+there's another approach people thought
+ 
+
+ align:start position:0%
+there's another approach people thought
+well why don't you just transfer the
+
+ align:start position:0%
+well why don't you just transfer the
+ 
+
+ align:start position:0%
+well why don't you just transfer the
+strain silicon layer itself why do you
+
+ align:start position:0%
+strain silicon layer itself why do you
+ 
+
+ align:start position:0%
+strain silicon layer itself why do you
+even have to transfer once you grow the
+
+ align:start position:0%
+even have to transfer once you grow the
+ 
+
+ align:start position:0%
+even have to transfer once you grow the
+relaxed silicon germanium you can grow
+
+ align:start position:0%
+relaxed silicon germanium you can grow
+ 
+
+ align:start position:0%
+relaxed silicon germanium you can grow
+strain silicon on top of it bond that to
+
+ align:start position:0%
+strain silicon on top of it bond that to
+ 
+
+ align:start position:0%
+strain silicon on top of it bond that to
+oxide and then remove everything except
+
+ align:start position:0%
+oxide and then remove everything except
+ 
+
+ align:start position:0%
+oxide and then remove everything except
+the strain silicon and if the Silicon if
+
+ align:start position:0%
+the strain silicon and if the Silicon if
+ 
+
+ align:start position:0%
+the strain silicon and if the Silicon if
+the strain remains then you have
+
+ align:start position:0%
+the strain remains then you have
+ 
+
+ align:start position:0%
+the strain remains then you have
+strained silicon directly on the
+
+ align:start position:0%
+strained silicon directly on the
+ 
+
+ align:start position:0%
+strained silicon directly on the
+insulator you remove the Silicon
+
+ align:start position:0%
+insulator you remove the Silicon
+ 
+
+ align:start position:0%
+insulator you remove the Silicon
+geranium completely so you don't have to
+
+ align:start position:0%
+geranium completely so you don't have to
+ 
+
+ align:start position:0%
+geranium completely so you don't have to
+worry about silicon geranium diffusion
+
+ align:start position:0%
+worry about silicon geranium diffusion
+ 
+
+ align:start position:0%
+worry about silicon geranium diffusion
+and and diffusion of do silicon
+
+ align:start position:0%
+and and diffusion of do silicon
+ 
+
+ align:start position:0%
+and and diffusion of do silicon
+germanium and all that so this is an
+
+ align:start position:0%
+germanium and all that so this is an
+ 
+
+ align:start position:0%
+germanium and all that so this is an
+ultra thin strain silicon directly an
+
+ align:start position:0%
+ultra thin strain silicon directly an
+ 
+
+ align:start position:0%
+ultra thin strain silicon directly an
+insulator sort of concept this is just a
+
+ align:start position:0%
+insulator sort of concept this is just a
+ 
+
+ align:start position:0%
+insulator sort of concept this is just a
+cartoon um it's actually been
+
+ align:start position:0%
+cartoon um it's actually been
+ 
+
+ align:start position:0%
+cartoon um it's actually been
+demonstrated fairly
+
+ align:start position:0%
+demonstrated fairly
+ 
+
+ align:start position:0%
+demonstrated fairly
+recently uh here at MIT on page 44 in
+
+ align:start position:0%
+recently uh here at MIT on page 44 in
+ 
+
+ align:start position:0%
+recently uh here at MIT on page 44 in
+fact this is the process that was used a
+
+ align:start position:0%
+fact this is the process that was used a
+ 
+
+ align:start position:0%
+fact this is the process that was used a
+very complicated stack of EP layers was
+
+ align:start position:0%
+very complicated stack of EP layers was
+ 
+
+ align:start position:0%
+very complicated stack of EP layers was
+grown but the important thing is the top
+
+ align:start position:0%
+grown but the important thing is the top
+ 
+
+ align:start position:0%
+grown but the important thing is the top
+of the stack was strained silicon and
+
+ align:start position:0%
+of the stack was strained silicon and
+ 
+
+ align:start position:0%
+of the stack was strained silicon and
+that whole stack was bonded to an
+
+ align:start position:0%
+that whole stack was bonded to an
+ 
+
+ align:start position:0%
+that whole stack was bonded to an
+oxidized silicon wafer and then
+
+ align:start position:0%
+oxidized silicon wafer and then
+ 
+
+ align:start position:0%
+oxidized silicon wafer and then
+everything was removed by selective
+
+ align:start position:0%
+everything was removed by selective
+ 
+
+ align:start position:0%
+everything was removed by selective
+etching so when you're done all you have
+
+ align:start position:0%
+etching so when you're done all you have
+ 
+
+ align:start position:0%
+etching so when you're done all you have
+left is strain silicon directly on the
+
+ align:start position:0%
+left is strain silicon directly on the
+ 
+
+ align:start position:0%
+left is strain silicon directly on the
+oxide uh and you use Edge EDG stop
+
+ align:start position:0%
+oxide uh and you use Edge EDG stop
+ 
+
+ align:start position:0%
+oxide uh and you use Edge EDG stop
+layers so you can Edge back the entire
+
+ align:start position:0%
+layers so you can Edge back the entire
+ 
+
+ align:start position:0%
+layers so you can Edge back the entire
+wafer and just leave strained silicon
+
+ align:start position:0%
+wafer and just leave strained silicon
+ 
+
+ align:start position:0%
+wafer and just leave strained silicon
+behind and in fact on page 45 what you
+
+ align:start position:0%
+behind and in fact on page 45 what you
+ 
+
+ align:start position:0%
+behind and in fact on page 45 what you
+see is that uh the strained silicon is
+
+ align:start position:0%
+see is that uh the strained silicon is
+ 
+
+ align:start position:0%
+see is that uh the strained silicon is
+bonded to the oxide um it's low defect
+
+ align:start position:0%
+bonded to the oxide um it's low defect
+ 
+
+ align:start position:0%
+bonded to the oxide um it's low defect
+density material and if you do Ramon
+
+ align:start position:0%
+density material and if you do Ramon
+ 
+
+ align:start position:0%
+density material and if you do Ramon
+scattering The Strain remains even after
+
+ align:start position:0%
+scattering The Strain remains even after
+ 
+
+ align:start position:0%
+scattering The Strain remains even after
+you remove the Silicon geranium and we
+
+ align:start position:0%
+you remove the Silicon geranium and we
+ 
+
+ align:start position:0%
+you remove the Silicon geranium and we
+knal it at high temperatures uh even up
+
+ align:start position:0%
+knal it at high temperatures uh even up
+ 
+
+ align:start position:0%
+knal it at high temperatures uh even up
+to 1,000° the strain doesn't go away so
+
+ align:start position:0%
+to 1,000° the strain doesn't go away so
+ 
+
+ align:start position:0%
+to 1,000° the strain doesn't go away so
+the bond is very strong
+
+ align:start position:0%
+the bond is very strong
+ 
+
+ align:start position:0%
+the bond is very strong
+so now you have strain soen directly on
+
+ align:start position:0%
+so now you have strain soen directly on
+ 
+
+ align:start position:0%
+so now you have strain soen directly on
+insulator looks just like SOI you can
+
+ align:start position:0%
+insulator looks just like SOI you can
+ 
+
+ align:start position:0%
+insulator looks just like SOI you can
+process just like SOI but the strain is
+
+ align:start position:0%
+process just like SOI but the strain is
+ 
+
+ align:start position:0%
+process just like SOI but the strain is
+already built in you don't have any
+
+ align:start position:0%
+already built in you don't have any
+ 
+
+ align:start position:0%
+already built in you don't have any
+geran that you need to worry
+
+ align:start position:0%
+geran that you need to worry
+ 
+
+ align:start position:0%
+geran that you need to worry
+about so I think that's going to be a
+
+ align:start position:0%
+about so I think that's going to be a
+ 
+
+ align:start position:0%
+about so I think that's going to be a
+pretty interesting area for the Future
+
+ align:start position:0%
+pretty interesting area for the Future
+ 
+
+ align:start position:0%
+pretty interesting area for the Future
+these uh just yesterday I read in the
+
+ align:start position:0%
+these uh just yesterday I read in the
+ 
+
+ align:start position:0%
+these uh just yesterday I read in the
+paper that it been announced that a
+
+ align:start position:0%
+paper that it been announced that a
+ 
+
+ align:start position:0%
+paper that it been announced that a
+company called soy is now manufacturing
+
+ align:start position:0%
+company called soy is now manufacturing
+ 
+
+ align:start position:0%
+company called soy is now manufacturing
+300 mm strain silicon directly on
+
+ align:start position:0%
+300 mm strain silicon directly on
+ 
+
+ align:start position:0%
+300 mm strain silicon directly on
+insulator SSD and uh once it becomes
+
+ align:start position:0%
+insulator SSD and uh once it becomes
+ 
+
+ align:start position:0%
+insulator SSD and uh once it becomes
+available 300 millimeter a lot of
+
+ align:start position:0%
+available 300 millimeter a lot of
+ 
+
+ align:start position:0%
+available 300 millimeter a lot of
+companies will be able to use it for
+
+ align:start position:0%
+companies will be able to use it for
+ 
+
+ align:start position:0%
+companies will be able to use it for
+their um for their production so that's
+
+ align:start position:0%
+their um for their production so that's
+ 
+
+ align:start position:0%
+their um for their production so that's
+about all I have to say on that I know I
+
+ align:start position:0%
+about all I have to say on that I know I
+ 
+
+ align:start position:0%
+about all I have to say on that I know I
+need to leave you time I'm glad I see
+
+ align:start position:0%
+need to leave you time I'm glad I see
+ 
+
+ align:start position:0%
+need to leave you time I'm glad I see
+the uh the survey is here I hope you
+
+ align:start position:0%
+the uh the survey is here I hope you
+ 
+
+ align:start position:0%
+the uh the survey is here I hope you
+haven't been waiting outside but uh
+
+ align:start position:0%
+haven't been waiting outside but uh
+ 
+
+ align:start position:0%
+haven't been waiting outside but uh
+please take uh 10 minutes or so and go
+
+ align:start position:0%
+please take uh 10 minutes or so and go
+ 
+
+ align:start position:0%
+please take uh 10 minutes or so and go
+ahead and fill out the class evaluation
+
+ align:start position:0%
+ahead and fill out the class evaluation
+ 
+
+ align:start position:0%
+ahead and fill out the class evaluation
+the course evaluation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+survey
\ No newline at end of file
diff --git a/n25tsUQb3vo.txt b/n25tsUQb3vo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..30fdb25a7f28a744f082350587e54392298efe90
--- /dev/null
+++ b/n25tsUQb3vo.txt
@@ -0,0 +1,16307 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common license. Your support
+
+ align:start position:0%
+a Creative Common license. Your support
+ 
+
+ align:start position:0%
+a Creative Common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh today we're going to dive into cost,
+
+ align:start position:0%
+Uh today we're going to dive into cost,
+ 
+
+ align:start position:0%
+Uh today we're going to dive into cost,
+price, markets, and support mechanisms.
+
+ align:start position:0%
+price, markets, and support mechanisms.
+ 
+
+ align:start position:0%
+price, markets, and support mechanisms.
+The support mechanisms, otherwise known
+
+ align:start position:0%
+The support mechanisms, otherwise known
+ 
+
+ align:start position:0%
+The support mechanisms, otherwise known
+as subsidies, right? Um so uh this is
+
+ align:start position:0%
+as subsidies, right? Um so uh this is
+ 
+
+ align:start position:0%
+as subsidies, right? Um so uh this is
+lecture 18. We're approaching the end of
+
+ align:start position:0%
+lecture 18. We're approaching the end of
+ 
+
+ align:start position:0%
+lecture 18. We're approaching the end of
+our course. Actually, we have about we
+
+ align:start position:0%
+our course. Actually, we have about we
+ 
+
+ align:start position:0%
+our course. Actually, we have about we
+have a handful of lectures left and then
+
+ align:start position:0%
+have a handful of lectures left and then
+ 
+
+ align:start position:0%
+have a handful of lectures left and then
+we um and then we uh go our separate
+
+ align:start position:0%
+we um and then we uh go our separate
+ 
+
+ align:start position:0%
+we um and then we uh go our separate
+ways. the um this particular lecture
+
+ align:start position:0%
+ways. the um this particular lecture
+ 
+
+ align:start position:0%
+ways. the um this particular lecture
+will be followed up not this Thursday
+
+ align:start position:0%
+will be followed up not this Thursday
+ 
+
+ align:start position:0%
+will be followed up not this Thursday
+but the following Thursday. Uh we'll
+
+ align:start position:0%
+but the following Thursday. Uh we'll
+ 
+
+ align:start position:0%
+but the following Thursday. Uh we'll
+have a guest speaker come in and talk
+
+ align:start position:0%
+have a guest speaker come in and talk
+ 
+
+ align:start position:0%
+have a guest speaker come in and talk
+about a cost model that he's developed
+
+ align:start position:0%
+about a cost model that he's developed
+ 
+
+ align:start position:0%
+about a cost model that he's developed
+for PV uh into very high level of
+
+ align:start position:0%
+for PV uh into very high level of
+ 
+
+ align:start position:0%
+for PV uh into very high level of
+detail. So it'll be a lot of fun. Uh and
+
+ align:start position:0%
+detail. So it'll be a lot of fun. Uh and
+ 
+
+ align:start position:0%
+detail. So it'll be a lot of fun. Uh and
+you'll be able to use that cost model to
+
+ align:start position:0%
+you'll be able to use that cost model to
+ 
+
+ align:start position:0%
+you'll be able to use that cost model to
+model your own uh PV uh devices,
+
+ align:start position:0%
+model your own uh PV uh devices,
+ 
+
+ align:start position:0%
+model your own uh PV uh devices,
+apparatus, and so forth. Um next
+
+ align:start position:0%
+apparatus, and so forth. Um next
+ 
+
+ align:start position:0%
+apparatus, and so forth. Um next
+Tuesday, a week from today, we'll be
+
+ align:start position:0%
+Tuesday, a week from today, we'll be
+ 
+
+ align:start position:0%
+Tuesday, a week from today, we'll be
+touring a PV facility. It'll be here on
+
+ align:start position:0%
+touring a PV facility. It'll be here on
+ 
+
+ align:start position:0%
+touring a PV facility. It'll be here on
+campus to make it easy for everybody.
+
+ align:start position:0%
+campus to make it easy for everybody.
+ 
+
+ align:start position:0%
+campus to make it easy for everybody.
+We'll go over to the student center and
+
+ align:start position:0%
+We'll go over to the student center and
+ 
+
+ align:start position:0%
+We'll go over to the student center and
+tour the PB system up on the roof there
+
+ align:start position:0%
+tour the PB system up on the roof there
+ 
+
+ align:start position:0%
+tour the PB system up on the roof there
+as well as the balance of system
+
+ align:start position:0%
+as well as the balance of system
+ 
+
+ align:start position:0%
+as well as the balance of system
+components. So, be able to have a a
+
+ align:start position:0%
+components. So, be able to have a a
+ 
+
+ align:start position:0%
+components. So, be able to have a a
+close-up uh look at at how that works.
+
+ align:start position:0%
+close-up uh look at at how that works.
+ 
+
+ align:start position:0%
+close-up uh look at at how that works.
+Um, but today cost, price, markets, and
+
+ align:start position:0%
+Um, but today cost, price, markets, and
+ 
+
+ align:start position:0%
+Um, but today cost, price, markets, and
+subsidies. We want to talk about those
+
+ align:start position:0%
+subsidies. We want to talk about those
+ 
+
+ align:start position:0%
+subsidies. We want to talk about those
+uh items because at the end of the day,
+
+ align:start position:0%
+uh items because at the end of the day,
+ 
+
+ align:start position:0%
+uh items because at the end of the day,
+PV is a product that is competing
+
+ align:start position:0%
+PV is a product that is competing
+ 
+
+ align:start position:0%
+PV is a product that is competing
+against bulk electricity, right? And if
+
+ align:start position:0%
+against bulk electricity, right? And if
+ 
+
+ align:start position:0%
+against bulk electricity, right? And if
+we can't compete against the bulk
+
+ align:start position:0%
+we can't compete against the bulk
+ 
+
+ align:start position:0%
+we can't compete against the bulk
+electricity, then uh we're our on-grid
+
+ align:start position:0%
+electricity, then uh we're our on-grid
+ 
+
+ align:start position:0%
+electricity, then uh we're our on-grid
+applications are going to be rather
+
+ align:start position:0%
+applications are going to be rather
+ 
+
+ align:start position:0%
+applications are going to be rather
+limited. uh so we want to understand uh
+
+ align:start position:0%
+limited. uh so we want to understand uh
+ 
+
+ align:start position:0%
+limited. uh so we want to understand uh
+how all this works and fits together. Uh
+
+ align:start position:0%
+how all this works and fits together. Uh
+ 
+
+ align:start position:0%
+how all this works and fits together. Uh
+so I'll be providing you several
+
+ align:start position:0%
+so I'll be providing you several
+ 
+
+ align:start position:0%
+so I'll be providing you several
+snapshots and several pieces of the
+
+ align:start position:0%
+snapshots and several pieces of the
+ 
+
+ align:start position:0%
+snapshots and several pieces of the
+puzzle uh with a lot of discussion back
+
+ align:start position:0%
+puzzle uh with a lot of discussion back
+ 
+
+ align:start position:0%
+puzzle uh with a lot of discussion back
+and forth over the course of today's
+
+ align:start position:0%
+and forth over the course of today's
+ 
+
+ align:start position:0%
+and forth over the course of today's
+lecture. So uh first off let's dive into
+
+ align:start position:0%
+lecture. So uh first off let's dive into
+ 
+
+ align:start position:0%
+lecture. So uh first off let's dive into
+PV cost and price. Um what is the
+
+ align:start position:0%
+PV cost and price. Um what is the
+ 
+
+ align:start position:0%
+PV cost and price. Um what is the
+difference between cost and
+
+ align:start position:0%
+difference between cost and
+ 
+
+ align:start position:0%
+difference between cost and
+price? They're used interchangeably in
+
+ align:start position:0%
+price? They're used interchangeably in
+ 
+
+ align:start position:0%
+price? They're used interchangeably in
+in colloquial language but there's a big
+
+ align:start position:0%
+in colloquial language but there's a big
+ 
+
+ align:start position:0%
+in colloquial language but there's a big
+difference. Jessica, cost might be what
+
+ align:start position:0%
+difference. Jessica, cost might be what
+ 
+
+ align:start position:0%
+difference. Jessica, cost might be what
+it cost to manufacture and price is what
+
+ align:start position:0%
+it cost to manufacture and price is what
+ 
+
+ align:start position:0%
+it cost to manufacture and price is what
+it's sold at for the Absolutely. So cost
+
+ align:start position:0%
+it's sold at for the Absolutely. So cost
+ 
+
+ align:start position:0%
+it's sold at for the Absolutely. So cost
+is what it actually costs to make to
+
+ align:start position:0%
+is what it actually costs to make to
+ 
+
+ align:start position:0%
+is what it actually costs to make to
+manufacture and price is what people are
+
+ align:start position:0%
+manufacture and price is what people are
+ 
+
+ align:start position:0%
+manufacture and price is what people are
+willing to pay for it, what the market
+
+ align:start position:0%
+willing to pay for it, what the market
+ 
+
+ align:start position:0%
+willing to pay for it, what the market
+is uh demanding, right? So sometimes
+
+ align:start position:0%
+is uh demanding, right? So sometimes
+ 
+
+ align:start position:0%
+is uh demanding, right? So sometimes
+price can be above cost. That's you're
+
+ align:start position:0%
+price can be above cost. That's you're
+ 
+
+ align:start position:0%
+price can be above cost. That's you're
+hopefully in that situation most of the
+
+ align:start position:0%
+hopefully in that situation most of the
+ 
+
+ align:start position:0%
+hopefully in that situation most of the
+time. And sometimes price can actually
+
+ align:start position:0%
+time. And sometimes price can actually
+ 
+
+ align:start position:0%
+time. And sometimes price can actually
+be below cost. What is an example of
+
+ align:start position:0%
+be below cost. What is an example of
+ 
+
+ align:start position:0%
+be below cost. What is an example of
+when price could be below cost?
+
+ align:start position:0%
+when price could be below cost?
+ 
+
+ align:start position:0%
+when price could be below cost?
+The Amazon Kindle. the Amazon Kindle.
+
+ align:start position:0%
+The Amazon Kindle. the Amazon Kindle.
+ 
+
+ align:start position:0%
+The Amazon Kindle. the Amazon Kindle.
+Why would why would it be doing that? Uh
+
+ align:start position:0%
+Why would why would it be doing that? Uh
+ 
+
+ align:start position:0%
+Why would why would it be doing that? Uh
+because they want to get people to adopt
+
+ align:start position:0%
+because they want to get people to adopt
+ 
+
+ align:start position:0%
+because they want to get people to adopt
+the device and then make money on
+
+ align:start position:0%
+the device and then make money on
+ 
+
+ align:start position:0%
+the device and then make money on
+subscriptions to books or
+
+ align:start position:0%
+subscriptions to books or
+ 
+
+ align:start position:0%
+subscriptions to books or
+a loss leader, right? Something like uh
+
+ align:start position:0%
+a loss leader, right? Something like uh
+ 
+
+ align:start position:0%
+a loss leader, right? Something like uh
+for example, if you buy your razor uh
+
+ align:start position:0%
+for example, if you buy your razor uh
+ 
+
+ align:start position:0%
+for example, if you buy your razor uh
+handle and that's really cheap, but then
+
+ align:start position:0%
+handle and that's really cheap, but then
+ 
+
+ align:start position:0%
+handle and that's really cheap, but then
+they they gouge you on blades. or uh uh
+
+ align:start position:0%
+they they gouge you on blades. or uh uh
+ 
+
+ align:start position:0%
+they they gouge you on blades. or uh uh
+other examples if they include the the
+
+ align:start position:0%
+other examples if they include the the
+ 
+
+ align:start position:0%
+other examples if they include the the
+cheap items in the front of a store. You
+
+ align:start position:0%
+cheap items in the front of a store. You
+ 
+
+ align:start position:0%
+cheap items in the front of a store. You
+walk inside the store and then you're
+
+ align:start position:0%
+walk inside the store and then you're
+ 
+
+ align:start position:0%
+walk inside the store and then you're
+you're bared by all the more expensive
+
+ align:start position:0%
+you're bared by all the more expensive
+ 
+
+ align:start position:0%
+you're bared by all the more expensive
+ones right inside. So loss leading can
+
+ align:start position:0%
+ones right inside. So loss leading can
+ 
+
+ align:start position:0%
+ones right inside. So loss leading can
+be one example of price below cost and
+
+ align:start position:0%
+be one example of price below cost and
+ 
+
+ align:start position:0%
+be one example of price below cost and
+other other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples. What if I start making a gizmo
+
+ align:start position:0%
+examples. What if I start making a gizmo
+ 
+
+ align:start position:0%
+examples. What if I start making a gizmo
+and I pocket an enormous profit and all
+
+ align:start position:0%
+and I pocket an enormous profit and all
+ 
+
+ align:start position:0%
+and I pocket an enormous profit and all
+of you start watching me make that gizmo
+
+ align:start position:0%
+of you start watching me make that gizmo
+ 
+
+ align:start position:0%
+of you start watching me make that gizmo
+and say, "Hey, I I can do that. It's
+
+ align:start position:0%
+and say, "Hey, I I can do that. It's
+ 
+
+ align:start position:0%
+and say, "Hey, I I can do that. It's
+pretty simple. It's not it doesn't take
+
+ align:start position:0%
+pretty simple. It's not it doesn't take
+ 
+
+ align:start position:0%
+pretty simple. It's not it doesn't take
+a rocket scientist to to manufacture
+
+ align:start position:0%
+a rocket scientist to to manufacture
+ 
+
+ align:start position:0%
+a rocket scientist to to manufacture
+that gizmo. I can do it too. And
+
+ align:start position:0%
+that gizmo. I can do it too. And
+ 
+
+ align:start position:0%
+that gizmo. I can do it too. And
+everybody starts manufacturing gizmos.
+
+ align:start position:0%
+everybody starts manufacturing gizmos.
+ 
+
+ align:start position:0%
+everybody starts manufacturing gizmos.
+Um pretty soon we overwhelm the demand
+
+ align:start position:0%
+Um pretty soon we overwhelm the demand
+ 
+
+ align:start position:0%
+Um pretty soon we overwhelm the demand
+at least at that given price point and
+
+ align:start position:0%
+at least at that given price point and
+ 
+
+ align:start position:0%
+at least at that given price point and
+the price is depressed as we enter a
+
+ align:start position:0%
+the price is depressed as we enter a
+ 
+
+ align:start position:0%
+the price is depressed as we enter a
+price war, right? We enter what is
+
+ align:start position:0%
+price war, right? We enter what is
+ 
+
+ align:start position:0%
+price war, right? We enter what is
+called an over supply condition. That's
+
+ align:start position:0%
+called an over supply condition. That's
+ 
+
+ align:start position:0%
+called an over supply condition. That's
+another example where price can fall
+
+ align:start position:0%
+another example where price can fall
+ 
+
+ align:start position:0%
+another example where price can fall
+below cost. And another reason why price
+
+ align:start position:0%
+below cost. And another reason why price
+ 
+
+ align:start position:0%
+below cost. And another reason why price
+can fall below cost is simply uh the
+
+ align:start position:0%
+can fall below cost is simply uh the
+ 
+
+ align:start position:0%
+can fall below cost is simply uh the
+price or the market you're trying to
+
+ align:start position:0%
+price or the market you're trying to
+ 
+
+ align:start position:0%
+price or the market you're trying to
+address simply won't buy your product at
+
+ align:start position:0%
+address simply won't buy your product at
+ 
+
+ align:start position:0%
+address simply won't buy your product at
+that cost. And that's the case with
+
+ align:start position:0%
+that cost. And that's the case with
+ 
+
+ align:start position:0%
+that cost. And that's the case with
+substitution economics. If we're
+
+ align:start position:0%
+substitution economics. If we're
+ 
+
+ align:start position:0%
+substitution economics. If we're
+competing against fossil fuel-based
+
+ align:start position:0%
+competing against fossil fuel-based
+ 
+
+ align:start position:0%
+competing against fossil fuel-based
+electricity, let's say, and we want to
+
+ align:start position:0%
+electricity, let's say, and we want to
+ 
+
+ align:start position:0%
+electricity, let's say, and we want to
+compete against that, we might uh we
+
+ align:start position:0%
+compete against that, we might uh we
+ 
+
+ align:start position:0%
+compete against that, we might uh we
+might not be able to manufacture solar
+
+ align:start position:0%
+might not be able to manufacture solar
+ 
+
+ align:start position:0%
+might not be able to manufacture solar
+panels cheap enough to address certain
+
+ align:start position:0%
+panels cheap enough to address certain
+ 
+
+ align:start position:0%
+panels cheap enough to address certain
+markets. For example, Wyoming, which has
+
+ align:start position:0%
+markets. For example, Wyoming, which has
+ 
+
+ align:start position:0%
+markets. For example, Wyoming, which has
+5 cents per kilowatt hour electricity uh
+
+ align:start position:0%
+5 cents per kilowatt hour electricity uh
+ 
+
+ align:start position:0%
+5 cents per kilowatt hour electricity uh
+due to cheap cheap uh fossil fuel. Um
+
+ align:start position:0%
+due to cheap cheap uh fossil fuel. Um
+ 
+
+ align:start position:0%
+due to cheap cheap uh fossil fuel. Um
+the southeast of the United States as
+
+ align:start position:0%
+the southeast of the United States as
+ 
+
+ align:start position:0%
+the southeast of the United States as
+well, where the TVA, the Tennessee
+
+ align:start position:0%
+well, where the TVA, the Tennessee
+ 
+
+ align:start position:0%
+well, where the TVA, the Tennessee
+Valley Authority, has very low priced
+
+ align:start position:0%
+Valley Authority, has very low priced
+ 
+
+ align:start position:0%
+Valley Authority, has very low priced
+nuclear and coal power. Uh so these are
+
+ align:start position:0%
+nuclear and coal power. Uh so these are
+ 
+
+ align:start position:0%
+nuclear and coal power. Uh so these are
+examples of where price might be be
+
+ align:start position:0%
+examples of where price might be be
+ 
+
+ align:start position:0%
+examples of where price might be be
+below cost. We're going to get more into
+
+ align:start position:0%
+below cost. We're going to get more into
+ 
+
+ align:start position:0%
+below cost. We're going to get more into
+that over the course of today's lecture.
+
+ align:start position:0%
+that over the course of today's lecture.
+ 
+
+ align:start position:0%
+that over the course of today's lecture.
+Uh because there are some very
+
+ align:start position:0%
+Uh because there are some very
+ 
+
+ align:start position:0%
+Uh because there are some very
+interesting geopolitical uh debates
+
+ align:start position:0%
+interesting geopolitical uh debates
+ 
+
+ align:start position:0%
+interesting geopolitical uh debates
+occurring right now. Uh oftentimes the
+
+ align:start position:0%
+occurring right now. Uh oftentimes the
+ 
+
+ align:start position:0%
+occurring right now. Uh oftentimes the
+two sides are very staunch in their
+
+ align:start position:0%
+two sides are very staunch in their
+ 
+
+ align:start position:0%
+two sides are very staunch in their
+positions and there isn't much nuance.
+
+ align:start position:0%
+positions and there isn't much nuance.
+ 
+
+ align:start position:0%
+positions and there isn't much nuance.
+There isn't much shade of gray. There is
+
+ align:start position:0%
+There isn't much shade of gray. There is
+ 
+
+ align:start position:0%
+There isn't much shade of gray. There is
+there aren't many rational arguments
+
+ align:start position:0%
+there aren't many rational arguments
+ 
+
+ align:start position:0%
+there aren't many rational arguments
+presented and instead we're going to be
+
+ align:start position:0%
+presented and instead we're going to be
+ 
+
+ align:start position:0%
+presented and instead we're going to be
+diving into some of that uh discussing
+
+ align:start position:0%
+diving into some of that uh discussing
+ 
+
+ align:start position:0%
+diving into some of that uh discussing
+the nuance over today's lecture. Let's
+
+ align:start position:0%
+the nuance over today's lecture. Let's
+ 
+
+ align:start position:0%
+the nuance over today's lecture. Let's
+dive into cost. Uh first off, this is a
+
+ align:start position:0%
+dive into cost. Uh first off, this is a
+ 
+
+ align:start position:0%
+dive into cost. Uh first off, this is a
+paper that I've presented already in in
+
+ align:start position:0%
+paper that I've presented already in in
+ 
+
+ align:start position:0%
+paper that I've presented already in in
+class. I've also steered some of the
+
+ align:start position:0%
+class. I've also steered some of the
+ 
+
+ align:start position:0%
+class. I've also steered some of the
+project groups toward it. Um this is uh
+
+ align:start position:0%
+project groups toward it. Um this is uh
+ 
+
+ align:start position:0%
+project groups toward it. Um this is uh
+a proceeding back in Whoa, this wasn't
+
+ align:start position:0%
+a proceeding back in Whoa, this wasn't
+ 
+
+ align:start position:0%
+a proceeding back in Whoa, this wasn't
+2009. My apologies. This is 2003. Um
+
+ align:start position:0%
+2009. My apologies. This is 2003. Um
+ 
+
+ align:start position:0%
+2009. My apologies. This is 2003. Um
+this was the uh presented at the third
+
+ align:start position:0%
+this was the uh presented at the third
+ 
+
+ align:start position:0%
+this was the uh presented at the third
+world conference of uh photovoltaic
+
+ align:start position:0%
+world conference of uh photovoltaic
+ 
+
+ align:start position:0%
+world conference of uh photovoltaic
+energy conversion by Tom Surk. Uh
+
+ align:start position:0%
+energy conversion by Tom Surk. Uh
+ 
+
+ align:start position:0%
+energy conversion by Tom Surk. Uh
+presenting a very simple uh uh cost
+
+ align:start position:0%
+presenting a very simple uh uh cost
+ 
+
+ align:start position:0%
+presenting a very simple uh uh cost
+model, if you will, for PV. Uh more
+
+ align:start position:0%
+model, if you will, for PV. Uh more
+ 
+
+ align:start position:0%
+model, if you will, for PV. Uh more
+specifically, the impact of efficiency
+
+ align:start position:0%
+specifically, the impact of efficiency
+ 
+
+ align:start position:0%
+specifically, the impact of efficiency
+on cost. And by no means was this the
+
+ align:start position:0%
+on cost. And by no means was this the
+ 
+
+ align:start position:0%
+on cost. And by no means was this the
+first time that something like this had
+
+ align:start position:0%
+first time that something like this had
+ 
+
+ align:start position:0%
+first time that something like this had
+ever been presented, but it was a nice
+
+ align:start position:0%
+ever been presented, but it was a nice
+ 
+
+ align:start position:0%
+ever been presented, but it was a nice
+uh summary of of the work to date. Um
+
+ align:start position:0%
+uh summary of of the work to date. Um
+ 
+
+ align:start position:0%
+uh summary of of the work to date. Um
+highlighting several uh would say key
+
+ align:start position:0%
+highlighting several uh would say key
+ 
+
+ align:start position:0%
+highlighting several uh would say key
+lever cost levers. Um efficiency, that's
+
+ align:start position:0%
+lever cost levers. Um efficiency, that's
+ 
+
+ align:start position:0%
+lever cost levers. Um efficiency, that's
+the solar conversion efficiency.
+
+ align:start position:0%
+the solar conversion efficiency.
+ 
+
+ align:start position:0%
+the solar conversion efficiency.
+Processing costs, that's the materials
+
+ align:start position:0%
+Processing costs, that's the materials
+ 
+
+ align:start position:0%
+Processing costs, that's the materials
+and and processing costs for the uh u
+
+ align:start position:0%
+and and processing costs for the uh u
+ 
+
+ align:start position:0%
+and and processing costs for the uh u
+for the module in dollars per meter
+
+ align:start position:0%
+for the module in dollars per meter
+ 
+
+ align:start position:0%
+for the module in dollars per meter
+squared. the manufacturing yield. That
+
+ align:start position:0%
+squared. the manufacturing yield. That
+ 
+
+ align:start position:0%
+squared. the manufacturing yield. That
+means uh out of say a hundred cells that
+
+ align:start position:0%
+means uh out of say a hundred cells that
+ 
+
+ align:start position:0%
+means uh out of say a hundred cells that
+enter your manufacturing line, how many
+
+ align:start position:0%
+enter your manufacturing line, how many
+ 
+
+ align:start position:0%
+enter your manufacturing line, how many
+make it through to the other side
+
+ align:start position:0%
+make it through to the other side
+ 
+
+ align:start position:0%
+make it through to the other side
+without breaking? Um and and and or
+
+ align:start position:0%
+without breaking? Um and and and or
+ 
+
+ align:start position:0%
+without breaking? Um and and and or
+being discarded uh due to due to
+
+ align:start position:0%
+being discarded uh due to due to
+ 
+
+ align:start position:0%
+being discarded uh due to due to
+manufacturing defects. Uh capital
+
+ align:start position:0%
+manufacturing defects. Uh capital
+ 
+
+ align:start position:0%
+manufacturing defects. Uh capital
+equipment cost uh that's depreciated
+
+ align:start position:0%
+equipment cost uh that's depreciated
+ 
+
+ align:start position:0%
+equipment cost uh that's depreciated
+over several years, meaning you buy
+
+ align:start position:0%
+over several years, meaning you buy
+ 
+
+ align:start position:0%
+over several years, meaning you buy
+equipment up front, but then uh due to
+
+ align:start position:0%
+equipment up front, but then uh due to
+ 
+
+ align:start position:0%
+equipment up front, but then uh due to
+financial gimmicks, you're allowed to um
+
+ align:start position:0%
+financial gimmicks, you're allowed to um
+ 
+
+ align:start position:0%
+financial gimmicks, you're allowed to um
+uh allow that cost to hit your books
+
+ align:start position:0%
+uh allow that cost to hit your books
+ 
+
+ align:start position:0%
+uh allow that cost to hit your books
+over an extended period of time, not all
+
+ align:start position:0%
+over an extended period of time, not all
+ 
+
+ align:start position:0%
+over an extended period of time, not all
+at once up front. Um overhead and so
+
+ align:start position:0%
+at once up front. Um overhead and so
+ 
+
+ align:start position:0%
+at once up front. Um overhead and so
+forth. overhead being the uh health
+
+ align:start position:0%
+forth. overhead being the uh health
+ 
+
+ align:start position:0%
+forth. overhead being the uh health
+insurance if it is paid to the workers.
+
+ align:start position:0%
+insurance if it is paid to the workers.
+ 
+
+ align:start position:0%
+insurance if it is paid to the workers.
+Um and and uh of course uh R&D and and
+
+ align:start position:0%
+Um and and uh of course uh R&D and and
+ 
+
+ align:start position:0%
+Um and and uh of course uh R&D and and
+um the CEO salary and so forth could be
+
+ align:start position:0%
+um the CEO salary and so forth could be
+ 
+
+ align:start position:0%
+um the CEO salary and so forth could be
+lumped in the uh so this is a very
+
+ align:start position:0%
+lumped in the uh so this is a very
+ 
+
+ align:start position:0%
+lumped in the uh so this is a very
+simple way of of of estimating cost.
+
+ align:start position:0%
+simple way of of of estimating cost.
+ 
+
+ align:start position:0%
+simple way of of of estimating cost.
+It's it's u a linear equation a direct
+
+ align:start position:0%
+It's it's u a linear equation a direct
+ 
+
+ align:start position:0%
+It's it's u a linear equation a direct
+uh uh relationship. What is I would say
+
+ align:start position:0%
+uh uh relationship. What is I would say
+ 
+
+ align:start position:0%
+uh uh relationship. What is I would say
+the economics uh a more sophisticated
+
+ align:start position:0%
+the economics uh a more sophisticated
+ 
+
+ align:start position:0%
+the economics uh a more sophisticated
+way of looking at cost uh other than
+
+ align:start position:0%
+way of looking at cost uh other than
+ 
+
+ align:start position:0%
+way of looking at cost uh other than
+just saying it's the dollars per watt
+
+ align:start position:0%
+just saying it's the dollars per watt
+ 
+
+ align:start position:0%
+just saying it's the dollars per watt
+peak um you would look at it in terms of
+
+ align:start position:0%
+peak um you would look at it in terms of
+ 
+
+ align:start position:0%
+peak um you would look at it in terms of
+cents per kilowatt hour right you would
+
+ align:start position:0%
+cents per kilowatt hour right you would
+ 
+
+ align:start position:0%
+cents per kilowatt hour right you would
+look at it in terms of how much do you
+
+ align:start position:0%
+look at it in terms of how much do you
+ 
+
+ align:start position:0%
+look at it in terms of how much do you
+pay for your electricity coming out of
+
+ align:start position:0%
+pay for your electricity coming out of
+ 
+
+ align:start position:0%
+pay for your electricity coming out of
+the wall or in this case out of the
+
+ align:start position:0%
+the wall or in this case out of the
+ 
+
+ align:start position:0%
+the wall or in this case out of the
+panels what would factor in to what is
+
+ align:start position:0%
+panels what would factor in to what is
+ 
+
+ align:start position:0%
+panels what would factor in to what is
+called the levelized cost of electricity
+
+ align:start position:0%
+called the levelized cost of electricity
+ 
+
+ align:start position:0%
+called the levelized cost of electricity
+when you're actually calculating cents
+
+ align:start position:0%
+when you're actually calculating cents
+ 
+
+ align:start position:0%
+when you're actually calculating cents
+per kilowatt hour how would you convert
+
+ align:start position:0%
+per kilowatt hour how would you convert
+ 
+
+ align:start position:0%
+per kilowatt hour how would you convert
+dollars per watt peak. Okay, I know how
+
+ align:start position:0%
+dollars per watt peak. Okay, I know how
+ 
+
+ align:start position:0%
+dollars per watt peak. Okay, I know how
+many dollars it took to manufacture
+
+ align:start position:0%
+many dollars it took to manufacture
+ 
+
+ align:start position:0%
+many dollars it took to manufacture
+this. I can also uh what would say
+
+ align:start position:0%
+this. I can also uh what would say
+ 
+
+ align:start position:0%
+this. I can also uh what would say
+depreciate my equipment costs over
+
+ align:start position:0%
+depreciate my equipment costs over
+ 
+
+ align:start position:0%
+depreciate my equipment costs over
+several years to manufacture this. Um,
+
+ align:start position:0%
+several years to manufacture this. Um,
+ 
+
+ align:start position:0%
+several years to manufacture this. Um,
+how would I go from dollars per watt
+
+ align:start position:0%
+how would I go from dollars per watt
+ 
+
+ align:start position:0%
+how would I go from dollars per watt
+peak into cents per kilowatt hour? We
+
+ align:start position:0%
+peak into cents per kilowatt hour? We
+ 
+
+ align:start position:0%
+peak into cents per kilowatt hour? We
+all agree that cents per kilowatt hour
+
+ align:start position:0%
+all agree that cents per kilowatt hour
+ 
+
+ align:start position:0%
+all agree that cents per kilowatt hour
+is the metric of importance, right?
+
+ align:start position:0%
+is the metric of importance, right?
+ 
+
+ align:start position:0%
+is the metric of importance, right?
+That's what we pay on our electricity
+
+ align:start position:0%
+That's what we pay on our electricity
+ 
+
+ align:start position:0%
+That's what we pay on our electricity
+bills, or at least some of us do. Um, so
+
+ align:start position:0%
+bills, or at least some of us do. Um, so
+ 
+
+ align:start position:0%
+bills, or at least some of us do. Um, so
+when we pay our electricity bills, we're
+
+ align:start position:0%
+when we pay our electricity bills, we're
+ 
+
+ align:start position:0%
+when we pay our electricity bills, we're
+paying in cents per kilowatt hour from
+
+ align:start position:0%
+paying in cents per kilowatt hour from
+ 
+
+ align:start position:0%
+paying in cents per kilowatt hour from
+the grid. And when we manufacture our
+
+ align:start position:0%
+the grid. And when we manufacture our
+ 
+
+ align:start position:0%
+the grid. And when we manufacture our
+solar panels, we pay in dollars per watt
+
+ align:start position:0%
+solar panels, we pay in dollars per watt
+ 
+
+ align:start position:0%
+solar panels, we pay in dollars per watt
+peak. Let's start simple. Why is dollars
+
+ align:start position:0%
+peak. Let's start simple. Why is dollars
+ 
+
+ align:start position:0%
+peak. Let's start simple. Why is dollars
+per watt peak at all
+
+ align:start position:0%
+per watt peak at all
+ 
+
+ align:start position:0%
+per watt peak at all
+useful? It's so far removed from cents
+
+ align:start position:0%
+useful? It's so far removed from cents
+ 
+
+ align:start position:0%
+useful? It's so far removed from cents
+per kilowatt hour that it it almost
+
+ align:start position:0%
+per kilowatt hour that it it almost
+ 
+
+ align:start position:0%
+per kilowatt hour that it it almost
+seems like an artificial metric. Why why
+
+ align:start position:0%
+seems like an artificial metric. Why why
+ 
+
+ align:start position:0%
+seems like an artificial metric. Why why
+again do we use dollars per watt peak?
+
+ align:start position:0%
+again do we use dollars per watt peak?
+ 
+
+ align:start position:0%
+again do we use dollars per watt peak?
+Jesse, because most um coal based or
+
+ align:start position:0%
+Jesse, because most um coal based or
+ 
+
+ align:start position:0%
+Jesse, because most um coal based or
+most fossil fuel based electricity is
+
+ align:start position:0%
+most fossil fuel based electricity is
+ 
+
+ align:start position:0%
+most fossil fuel based electricity is
+based on a capacity factor which is just
+
+ align:start position:0%
+based on a capacity factor which is just
+ 
+
+ align:start position:0%
+based on a capacity factor which is just
+kilowatt um bas which is measured in
+
+ align:start position:0%
+kilowatt um bas which is measured in
+ 
+
+ align:start position:0%
+kilowatt um bas which is measured in
+kilowatt. That's that's a good way of
+
+ align:start position:0%
+kilowatt. That's that's a good way of
+ 
+
+ align:start position:0%
+kilowatt. That's that's a good way of
+looking at it. Um and then the capacity
+
+ align:start position:0%
+looking at it. Um and then the capacity
+ 
+
+ align:start position:0%
+looking at it. Um and then the capacity
+factor of solar would be based on what?
+
+ align:start position:0%
+factor of solar would be based on what?
+ 
+
+ align:start position:0%
+factor of solar would be based on what?
+on it capacity on on the solar resource
+
+ align:start position:0%
+on it capacity on on the solar resource
+ 
+
+ align:start position:0%
+on it capacity on on the solar resource
+locally, right? Um and and that might
+
+ align:start position:0%
+locally, right? Um and and that might
+ 
+
+ align:start position:0%
+locally, right? Um and and that might
+vary from location to location. Yeah.
+
+ align:start position:0%
+vary from location to location. Yeah.
+ 
+
+ align:start position:0%
+vary from location to location. Yeah.
+Okay. So, what dollars per watt peak
+
+ align:start position:0%
+Okay. So, what dollars per watt peak
+ 
+
+ align:start position:0%
+Okay. So, what dollars per watt peak
+allows you to do is given a rated name
+
+ align:start position:0%
+allows you to do is given a rated name
+ 
+
+ align:start position:0%
+allows you to do is given a rated name
+plate capacity, you can calculate based
+
+ align:start position:0%
+plate capacity, you can calculate based
+ 
+
+ align:start position:0%
+plate capacity, you can calculate based
+on the solar resource locally, how much
+
+ align:start position:0%
+on the solar resource locally, how much
+ 
+
+ align:start position:0%
+on the solar resource locally, how much
+energy will be produced over a certain
+
+ align:start position:0%
+energy will be produced over a certain
+ 
+
+ align:start position:0%
+energy will be produced over a certain
+period of time, right? And then from
+
+ align:start position:0%
+period of time, right? And then from
+ 
+
+ align:start position:0%
+period of time, right? And then from
+that, you can calculate your cents per
+
+ align:start position:0%
+that, you can calculate your cents per
+ 
+
+ align:start position:0%
+that, you can calculate your cents per
+kilowatt hour, right? because now we're
+
+ align:start position:0%
+kilowatt hour, right? because now we're
+ 
+
+ align:start position:0%
+kilowatt hour, right? because now we're
+converting from power uh or rated name
+
+ align:start position:0%
+converting from power uh or rated name
+ 
+
+ align:start position:0%
+converting from power uh or rated name
+plate power into energy which we can use
+
+ align:start position:0%
+plate power into energy which we can use
+ 
+
+ align:start position:0%
+plate power into energy which we can use
+and uh which has economic value. So
+
+ align:start position:0%
+and uh which has economic value. So
+ 
+
+ align:start position:0%
+and uh which has economic value. So
+there there there is a rationale then
+
+ align:start position:0%
+there there there is a rationale then
+ 
+
+ align:start position:0%
+there there there is a rationale then
+for uh giving uh name plate capacity in
+
+ align:start position:0%
+for uh giving uh name plate capacity in
+ 
+
+ align:start position:0%
+for uh giving uh name plate capacity in
+terms of watt peak in other words rating
+
+ align:start position:0%
+terms of watt peak in other words rating
+ 
+
+ align:start position:0%
+terms of watt peak in other words rating
+a factory in terms of megawws per year
+
+ align:start position:0%
+a factory in terms of megawws per year
+ 
+
+ align:start position:0%
+a factory in terms of megawws per year
+or gigawatts per year produced. Uh that
+
+ align:start position:0%
+or gigawatts per year produced. Uh that
+ 
+
+ align:start position:0%
+or gigawatts per year produced. Uh that
+means that each module that goes under
+
+ align:start position:0%
+means that each module that goes under
+ 
+
+ align:start position:0%
+means that each module that goes under
+the cell tester is rated and there's an
+
+ align:start position:0%
+the cell tester is rated and there's an
+ 
+
+ align:start position:0%
+the cell tester is rated and there's an
+estimate uh based on the cumulative
+
+ align:start position:0%
+estimate uh based on the cumulative
+ 
+
+ align:start position:0%
+estimate uh based on the cumulative
+module production what the total watt
+
+ align:start position:0%
+module production what the total watt
+ 
+
+ align:start position:0%
+module production what the total watt
+peak output of that factory was. And
+
+ align:start position:0%
+peak output of that factory was. And
+ 
+
+ align:start position:0%
+peak output of that factory was. And
+then depending on where those modules go
+
+ align:start position:0%
+then depending on where those modules go
+ 
+
+ align:start position:0%
+then depending on where those modules go
+in the world they might produce
+
+ align:start position:0%
+in the world they might produce
+ 
+
+ align:start position:0%
+in the world they might produce
+different amounts of energy. Uh if you
+
+ align:start position:0%
+different amounts of energy. Uh if you
+ 
+
+ align:start position:0%
+different amounts of energy. Uh if you
+take those same modules install them in
+
+ align:start position:0%
+take those same modules install them in
+ 
+
+ align:start position:0%
+take those same modules install them in
+Alaska or Arizona you're going to get
+
+ align:start position:0%
+Alaska or Arizona you're going to get
+ 
+
+ align:start position:0%
+Alaska or Arizona you're going to get
+widely varying energy outputs. Okay. So
+
+ align:start position:0%
+widely varying energy outputs. Okay. So
+ 
+
+ align:start position:0%
+widely varying energy outputs. Okay. So
+then how do we transition? We we we have
+
+ align:start position:0%
+then how do we transition? We we we have
+ 
+
+ align:start position:0%
+then how do we transition? We we we have
+the dollars per watt peak. We have to
+
+ align:start position:0%
+the dollars per watt peak. We have to
+ 
+
+ align:start position:0%
+the dollars per watt peak. We have to
+know the local solar insulation that
+
+ align:start position:0%
+know the local solar insulation that
+ 
+
+ align:start position:0%
+know the local solar insulation that
+would allow us to calculate what the
+
+ align:start position:0%
+would allow us to calculate what the
+ 
+
+ align:start position:0%
+would allow us to calculate what the
+cents per kilowatt hour would be
+
+ align:start position:0%
+cents per kilowatt hour would be
+ 
+
+ align:start position:0%
+cents per kilowatt hour would be
+assuming a certain cost of capital. We
+
+ align:start position:0%
+assuming a certain cost of capital. We
+ 
+
+ align:start position:0%
+assuming a certain cost of capital. We
+have to buy those panels up front,
+
+ align:start position:0%
+have to buy those panels up front,
+ 
+
+ align:start position:0%
+have to buy those panels up front,
+right? You have to buy from me a huge
+
+ align:start position:0%
+right? You have to buy from me a huge
+ 
+
+ align:start position:0%
+right? You have to buy from me a huge
+number of panels which are going to last
+
+ align:start position:0%
+number of panels which are going to last
+ 
+
+ align:start position:0%
+number of panels which are going to last
+for 20 25 years. I'll guarantee it. But
+
+ align:start position:0%
+for 20 25 years. I'll guarantee it. But
+ 
+
+ align:start position:0%
+for 20 25 years. I'll guarantee it. But
+you have to front that money up front.
+
+ align:start position:0%
+you have to front that money up front.
+ 
+
+ align:start position:0%
+you have to front that money up front.
+Which means that you need to loan or
+
+ align:start position:0%
+Which means that you need to loan or
+ 
+
+ align:start position:0%
+Which means that you need to loan or
+lend that money from a bank from a bank
+
+ align:start position:0%
+lend that money from a bank from a bank
+ 
+
+ align:start position:0%
+lend that money from a bank from a bank
+or from a financial institution. Uh and
+
+ align:start position:0%
+or from a financial institution. Uh and
+ 
+
+ align:start position:0%
+or from a financial institution. Uh and
+then you'll be paying a certain amount
+
+ align:start position:0%
+then you'll be paying a certain amount
+ 
+
+ align:start position:0%
+then you'll be paying a certain amount
+of interest every year. And it's the
+
+ align:start position:0%
+of interest every year. And it's the
+ 
+
+ align:start position:0%
+of interest every year. And it's the
+spread. It's the difference between the
+
+ align:start position:0%
+spread. It's the difference between the
+ 
+
+ align:start position:0%
+spread. It's the difference between the
+interest payments and the money saved
+
+ align:start position:0%
+interest payments and the money saved
+ 
+
+ align:start position:0%
+interest payments and the money saved
+that's going to turn your profit. And
+
+ align:start position:0%
+that's going to turn your profit. And
+ 
+
+ align:start position:0%
+that's going to turn your profit. And
+that's what's called the rate of return
+
+ align:start position:0%
+that's what's called the rate of return
+ 
+
+ align:start position:0%
+that's what's called the rate of return
+of your investment. Uh and there's also
+
+ align:start position:0%
+of your investment. Uh and there's also
+ 
+
+ align:start position:0%
+of your investment. Uh and there's also
+a payback period or a monetary payback
+
+ align:start position:0%
+a payback period or a monetary payback
+ 
+
+ align:start position:0%
+a payback period or a monetary payback
+period over which uh you're not going to
+
+ align:start position:0%
+period over which uh you're not going to
+ 
+
+ align:start position:0%
+period over which uh you're not going to
+be making money on on average, but uh
+
+ align:start position:0%
+be making money on on average, but uh
+ 
+
+ align:start position:0%
+be making money on on average, but uh
+after the payback period is finished,
+
+ align:start position:0%
+after the payback period is finished,
+ 
+
+ align:start position:0%
+after the payback period is finished,
+then your solar uh array will be a money
+
+ align:start position:0%
+then your solar uh array will be a money
+ 
+
+ align:start position:0%
+then your solar uh array will be a money
+press. It'll be printing money. And so
+
+ align:start position:0%
+press. It'll be printing money. And so
+ 
+
+ align:start position:0%
+press. It'll be printing money. And so
+over the entire lifetime of the
+
+ align:start position:0%
+over the entire lifetime of the
+ 
+
+ align:start position:0%
+over the entire lifetime of the
+investment, you can calculate an average
+
+ align:start position:0%
+investment, you can calculate an average
+ 
+
+ align:start position:0%
+investment, you can calculate an average
+rate of return. Okay? So um given that
+
+ align:start position:0%
+rate of return. Okay? So um given that
+ 
+
+ align:start position:0%
+rate of return. Okay? So um given that
+uh setup um we're going to be talking
+
+ align:start position:0%
+uh setup um we're going to be talking
+ 
+
+ align:start position:0%
+uh setup um we're going to be talking
+about some incentive mechanisms and um
+
+ align:start position:0%
+about some incentive mechanisms and um
+ 
+
+ align:start position:0%
+about some incentive mechanisms and um
+uh and and today really really simple
+
+ align:start position:0%
+uh and and today really really simple
+ 
+
+ align:start position:0%
+uh and and today really really simple
+cost model uh more on Thursday uh when
+
+ align:start position:0%
+cost model uh more on Thursday uh when
+ 
+
+ align:start position:0%
+cost model uh more on Thursday uh when
+we get back to uh back back to this how
+
+ align:start position:0%
+we get back to uh back back to this how
+ 
+
+ align:start position:0%
+we get back to uh back back to this how
+we calculate uh cost um in a more
+
+ align:start position:0%
+we calculate uh cost um in a more
+ 
+
+ align:start position:0%
+we calculate uh cost um in a more
+sophisticated manner. I I want to
+
+ align:start position:0%
+sophisticated manner. I I want to
+ 
+
+ align:start position:0%
+sophisticated manner. I I want to
+introduce this concept very simply at
+
+ align:start position:0%
+introduce this concept very simply at
+ 
+
+ align:start position:0%
+introduce this concept very simply at
+first just because there are some
+
+ align:start position:0%
+first just because there are some
+ 
+
+ align:start position:0%
+first just because there are some
+parameters here in the sensitivity
+
+ align:start position:0%
+parameters here in the sensitivity
+ 
+
+ align:start position:0%
+parameters here in the sensitivity
+analysis that overwhelm all the others
+
+ align:start position:0%
+analysis that overwhelm all the others
+ 
+
+ align:start position:0%
+analysis that overwhelm all the others
+and they can be very simply seen in an
+
+ align:start position:0%
+and they can be very simply seen in an
+ 
+
+ align:start position:0%
+and they can be very simply seen in an
+equation like that right up there and
+
+ align:start position:0%
+equation like that right up there and
+ 
+
+ align:start position:0%
+equation like that right up there and
+one of them is efficiency. The
+
+ align:start position:0%
+one of them is efficiency. The
+ 
+
+ align:start position:0%
+one of them is efficiency. The
+processing costs also matter quite a
+
+ align:start position:0%
+processing costs also matter quite a
+ 
+
+ align:start position:0%
+processing costs also matter quite a
+bit. Okay. Um inside of processing costs
+
+ align:start position:0%
+bit. Okay. Um inside of processing costs
+ 
+
+ align:start position:0%
+bit. Okay. Um inside of processing costs
+um you also have labor and commodity
+
+ align:start position:0%
+um you also have labor and commodity
+ 
+
+ align:start position:0%
+um you also have labor and commodity
+materials right and those can vary
+
+ align:start position:0%
+materials right and those can vary
+ 
+
+ align:start position:0%
+materials right and those can vary
+significantly from region to region.
+
+ align:start position:0%
+significantly from region to region.
+ 
+
+ align:start position:0%
+significantly from region to region.
+So um there there are a number of uh uh
+
+ align:start position:0%
+So um there there are a number of uh uh
+ 
+
+ align:start position:0%
+So um there there are a number of uh uh
+assessments out there. I'm I'm going to
+
+ align:start position:0%
+assessments out there. I'm I'm going to
+ 
+
+ align:start position:0%
+assessments out there. I'm I'm going to
+be uh leading us into the the current
+
+ align:start position:0%
+be uh leading us into the the current
+ 
+
+ align:start position:0%
+be uh leading us into the the current
+big debate which has exploded in
+
+ align:start position:0%
+big debate which has exploded in
+ 
+
+ align:start position:0%
+big debate which has exploded in
+Washington DC. Uh the case of Celindra
+
+ align:start position:0%
+Washington DC. Uh the case of Celindra
+ 
+
+ align:start position:0%
+Washington DC. Uh the case of Celindra
+and then Solar World filing uh the um uh
+
+ align:start position:0%
+and then Solar World filing uh the um uh
+ 
+
+ align:start position:0%
+and then Solar World filing uh the um uh
+would say the the um complaint with the
+
+ align:start position:0%
+would say the the um complaint with the
+ 
+
+ align:start position:0%
+would say the the um complaint with the
+US commerce uh department. Um, I'll be
+
+ align:start position:0%
+US commerce uh department. Um, I'll be
+ 
+
+ align:start position:0%
+US commerce uh department. Um, I'll be
+I'll be easing us into this whole
+
+ align:start position:0%
+I'll be easing us into this whole
+ 
+
+ align:start position:0%
+I'll be easing us into this whole
+question of US and and and uh and and
+
+ align:start position:0%
+question of US and and and uh and and
+ 
+
+ align:start position:0%
+question of US and and and uh and and
+foreign manufacturing, using that more
+
+ align:start position:0%
+foreign manufacturing, using that more
+ 
+
+ align:start position:0%
+foreign manufacturing, using that more
+as a hook to get us interested in the
+
+ align:start position:0%
+as a hook to get us interested in the
+ 
+
+ align:start position:0%
+as a hook to get us interested in the
+overall topics of the day. Um, and then
+
+ align:start position:0%
+overall topics of the day. Um, and then
+ 
+
+ align:start position:0%
+overall topics of the day. Um, and then
+toward the end, hopefully you'll be able
+
+ align:start position:0%
+toward the end, hopefully you'll be able
+ 
+
+ align:start position:0%
+toward the end, hopefully you'll be able
+to see with more shades of gray uh what
+
+ align:start position:0%
+to see with more shades of gray uh what
+ 
+
+ align:start position:0%
+to see with more shades of gray uh what
+exactly is going on and perhaps
+
+ align:start position:0%
+exactly is going on and perhaps
+ 
+
+ align:start position:0%
+exactly is going on and perhaps
+formulate opinions of your own. So,
+
+ align:start position:0%
+formulate opinions of your own. So,
+ 
+
+ align:start position:0%
+formulate opinions of your own. So,
+where where is PV cost actually at?
+
+ align:start position:0%
+where where is PV cost actually at?
+ 
+
+ align:start position:0%
+where where is PV cost actually at?
+Where where do the current cost numbers
+
+ align:start position:0%
+Where where do the current cost numbers
+ 
+
+ align:start position:0%
+Where where do the current cost numbers
+currently stand? Um, it is extremely
+
+ align:start position:0%
+currently stand? Um, it is extremely
+ 
+
+ align:start position:0%
+currently stand? Um, it is extremely
+difficult to get at true cost. Price,
+
+ align:start position:0%
+difficult to get at true cost. Price,
+ 
+
+ align:start position:0%
+difficult to get at true cost. Price,
+price is easy, right? You go out there,
+
+ align:start position:0%
+price is easy, right? You go out there,
+ 
+
+ align:start position:0%
+price is easy, right? You go out there,
+probe the market, see what people are
+
+ align:start position:0%
+probe the market, see what people are
+ 
+
+ align:start position:0%
+probe the market, see what people are
+willing to sell panels at, maybe send a
+
+ align:start position:0%
+willing to sell panels at, maybe send a
+ 
+
+ align:start position:0%
+willing to sell panels at, maybe send a
+few emails to a few companies saying,
+
+ align:start position:0%
+few emails to a few companies saying,
+ 
+
+ align:start position:0%
+few emails to a few companies saying,
+"Hey, I want to installund hundred of
+
+ align:start position:0%
+"Hey, I want to installund hundred of
+ 
+
+ align:start position:0%
+"Hey, I want to installund hundred of
+your panels, how much you're willing to
+
+ align:start position:0%
+your panels, how much you're willing to
+ 
+
+ align:start position:0%
+your panels, how much you're willing to
+sell them to me." Um, this is what
+
+ align:start position:0%
+sell them to me." Um, this is what
+ 
+
+ align:start position:0%
+sell them to me." Um, this is what
+people do. They probe the market, they
+
+ align:start position:0%
+people do. They probe the market, they
+ 
+
+ align:start position:0%
+people do. They probe the market, they
+test it. So price is fairly easy to
+
+ align:start position:0%
+test it. So price is fairly easy to
+ 
+
+ align:start position:0%
+test it. So price is fairly easy to
+gauge, but manufacturing cost. If I go
+
+ align:start position:0%
+gauge, but manufacturing cost. If I go
+ 
+
+ align:start position:0%
+gauge, but manufacturing cost. If I go
+up to you and say, "Hey, can you tell me
+
+ align:start position:0%
+up to you and say, "Hey, can you tell me
+ 
+
+ align:start position:0%
+up to you and say, "Hey, can you tell me
+how much it costs to manufacture panels
+
+ align:start position:0%
+how much it costs to manufacture panels
+ 
+
+ align:start position:0%
+how much it costs to manufacture panels
+in your factory? Would you be willing to
+
+ align:start position:0%
+in your factory? Would you be willing to
+ 
+
+ align:start position:0%
+in your factory? Would you be willing to
+give me that information?" They'd
+
+ align:start position:0%
+give me that information?" They'd
+ 
+
+ align:start position:0%
+give me that information?" They'd
+probably say, "No." um probably seeing
+
+ align:start position:0%
+probably say, "No." um probably seeing
+ 
+
+ align:start position:0%
+probably say, "No." um probably seeing
+no definitely to me as a professor.
+
+ align:start position:0%
+no definitely to me as a professor.
+ 
+
+ align:start position:0%
+no definitely to me as a professor.
+Maybe you as students they might they
+
+ align:start position:0%
+Maybe you as students they might they
+ 
+
+ align:start position:0%
+Maybe you as students they might they
+might show you a little bit more of how
+
+ align:start position:0%
+might show you a little bit more of how
+ 
+
+ align:start position:0%
+might show you a little bit more of how
+it actually works under the hood since
+
+ align:start position:0%
+it actually works under the hood since
+ 
+
+ align:start position:0%
+it actually works under the hood since
+many people believe in the educational
+
+ align:start position:0%
+many people believe in the educational
+ 
+
+ align:start position:0%
+many people believe in the educational
+mission. But by and large people are
+
+ align:start position:0%
+mission. But by and large people are
+ 
+
+ align:start position:0%
+mission. But by and large people are
+fairly secretive about this because they
+
+ align:start position:0%
+fairly secretive about this because they
+ 
+
+ align:start position:0%
+fairly secretive about this because they
+realize that their stock price is
+
+ align:start position:0%
+realize that their stock price is
+ 
+
+ align:start position:0%
+realize that their stock price is
+heavily dependent on market perception.
+
+ align:start position:0%
+heavily dependent on market perception.
+ 
+
+ align:start position:0%
+heavily dependent on market perception.
+And if I go out there and write an
+
+ align:start position:0%
+And if I go out there and write an
+ 
+
+ align:start position:0%
+And if I go out there and write an
+article and say, "Hey, uh your company
+
+ align:start position:0%
+article and say, "Hey, uh your company
+ 
+
+ align:start position:0%
+article and say, "Hey, uh your company
+uh produces panels at twice the cost of
+
+ align:start position:0%
+uh produces panels at twice the cost of
+ 
+
+ align:start position:0%
+uh produces panels at twice the cost of
+yours, uh investors are going to flee
+
+ align:start position:0%
+yours, uh investors are going to flee
+ 
+
+ align:start position:0%
+yours, uh investors are going to flee
+your company, especially if it comes out
+
+ align:start position:0%
+your company, especially if it comes out
+ 
+
+ align:start position:0%
+your company, especially if it comes out
+of a university like MIT." And so
+
+ align:start position:0%
+of a university like MIT." And so
+ 
+
+ align:start position:0%
+of a university like MIT." And so
+there's a there are big repercussions
+
+ align:start position:0%
+there's a there are big repercussions
+ 
+
+ align:start position:0%
+there's a there are big repercussions
+associated with divulgation of of cost
+
+ align:start position:0%
+associated with divulgation of of cost
+ 
+
+ align:start position:0%
+associated with divulgation of of cost
+numbers and that's why it's very hard to
+
+ align:start position:0%
+numbers and that's why it's very hard to
+ 
+
+ align:start position:0%
+numbers and that's why it's very hard to
+get to the bottom of it. What you find
+
+ align:start position:0%
+get to the bottom of it. What you find
+ 
+
+ align:start position:0%
+get to the bottom of it. What you find
+most often are aggregators. These are
+
+ align:start position:0%
+most often are aggregators. These are
+ 
+
+ align:start position:0%
+most often are aggregators. These are
+consultancies that work with several
+
+ align:start position:0%
+consultancies that work with several
+ 
+
+ align:start position:0%
+consultancies that work with several
+companies. Um they may be for example um
+
+ align:start position:0%
+companies. Um they may be for example um
+ 
+
+ align:start position:0%
+companies. Um they may be for example um
+Photon Consulting across the river uh in
+
+ align:start position:0%
+Photon Consulting across the river uh in
+ 
+
+ align:start position:0%
+Photon Consulting across the river uh in
+in Boston. It might be Green Techch
+
+ align:start position:0%
+in Boston. It might be Green Techch
+ 
+
+ align:start position:0%
+in Boston. It might be Green Techch
+Media uh consulting branch which is
+
+ align:start position:0%
+Media uh consulting branch which is
+ 
+
+ align:start position:0%
+Media uh consulting branch which is
+located here in Cambridge,
+
+ align:start position:0%
+located here in Cambridge,
+ 
+
+ align:start position:0%
+located here in Cambridge,
+Massachusetts. Um there are many
+
+ align:start position:0%
+Massachusetts. Um there are many
+ 
+
+ align:start position:0%
+Massachusetts. Um there are many
+consulting companies and several of them
+
+ align:start position:0%
+consulting companies and several of them
+ 
+
+ align:start position:0%
+consulting companies and several of them
+based here in uh the Boston area. uh and
+
+ align:start position:0%
+based here in uh the Boston area. uh and
+ 
+
+ align:start position:0%
+based here in uh the Boston area. uh and
+these consultant companies work with
+
+ align:start position:0%
+these consultant companies work with
+ 
+
+ align:start position:0%
+these consultant companies work with
+several PV manufacturers and over time
+
+ align:start position:0%
+several PV manufacturers and over time
+ 
+
+ align:start position:0%
+several PV manufacturers and over time
+begin aggregating data and presenting
+
+ align:start position:0%
+begin aggregating data and presenting
+ 
+
+ align:start position:0%
+begin aggregating data and presenting
+market trends, generalized market
+
+ align:start position:0%
+market trends, generalized market
+ 
+
+ align:start position:0%
+market trends, generalized market
+trends, right? Few of them single out
+
+ align:start position:0%
+trends, right? Few of them single out
+ 
+
+ align:start position:0%
+trends, right? Few of them single out
+specific companies, but most of them
+
+ align:start position:0%
+specific companies, but most of them
+ 
+
+ align:start position:0%
+specific companies, but most of them
+just aggregate the data and present
+
+ align:start position:0%
+just aggregate the data and present
+ 
+
+ align:start position:0%
+just aggregate the data and present
+general trends. Uh I've presented to you
+
+ align:start position:0%
+general trends. Uh I've presented to you
+ 
+
+ align:start position:0%
+general trends. Uh I've presented to you
+this uh a few articles as of late. Um
+
+ align:start position:0%
+this uh a few articles as of late. Um
+ 
+
+ align:start position:0%
+this uh a few articles as of late. Um
+these are relatively recent um within
+
+ align:start position:0%
+these are relatively recent um within
+ 
+
+ align:start position:0%
+these are relatively recent um within
+the last three to four years. And
+
+ align:start position:0%
+the last three to four years. And
+ 
+
+ align:start position:0%
+the last three to four years. And
+because there has been so much change
+
+ align:start position:0%
+because there has been so much change
+ 
+
+ align:start position:0%
+because there has been so much change
+over the last 3 to four years within the
+
+ align:start position:0%
+over the last 3 to four years within the
+ 
+
+ align:start position:0%
+over the last 3 to four years within the
+PV market, even an article three years
+
+ align:start position:0%
+PV market, even an article three years
+ 
+
+ align:start position:0%
+PV market, even an article three years
+ago is highly outdated, right? So you'll
+
+ align:start position:0%
+ago is highly outdated, right? So you'll
+ 
+
+ align:start position:0%
+ago is highly outdated, right? So you'll
+want information that's within the last
+
+ align:start position:0%
+want information that's within the last
+ 
+
+ align:start position:0%
+want information that's within the last
+year if you're going to be using uh cost
+
+ align:start position:0%
+year if you're going to be using uh cost
+ 
+
+ align:start position:0%
+year if you're going to be using uh cost
+and price information for your projects,
+
+ align:start position:0%
+and price information for your projects,
+ 
+
+ align:start position:0%
+and price information for your projects,
+even within the last few
+
+ align:start position:0%
+even within the last few
+ 
+
+ align:start position:0%
+even within the last few
+months. And if any of you have any
+
+ align:start position:0%
+months. And if any of you have any
+ 
+
+ align:start position:0%
+months. And if any of you have any
+doubts in that regard, you can come talk
+
+ align:start position:0%
+doubts in that regard, you can come talk
+ 
+
+ align:start position:0%
+doubts in that regard, you can come talk
+to me. So the fully loaded uh module
+
+ align:start position:0%
+to me. So the fully loaded uh module
+ 
+
+ align:start position:0%
+to me. So the fully loaded uh module
+manufacturing cost uh is is shown here.
+
+ align:start position:0%
+manufacturing cost uh is is shown here.
+ 
+
+ align:start position:0%
+manufacturing cost uh is is shown here.
+uh an estimate again an aggregation
+
+ align:start position:0%
+uh an estimate again an aggregation
+ 
+
+ align:start position:0%
+uh an estimate again an aggregation
+based on um access to multiple companies
+
+ align:start position:0%
+based on um access to multiple companies
+ 
+
+ align:start position:0%
+based on um access to multiple companies
+data polyilicon this of course being
+
+ align:start position:0%
+data polyilicon this of course being
+ 
+
+ align:start position:0%
+data polyilicon this of course being
+crystal and silicon technology which
+
+ align:start position:0%
+crystal and silicon technology which
+ 
+
+ align:start position:0%
+crystal and silicon technology which
+accounts for about 90 85% of the current
+
+ align:start position:0%
+accounts for about 90 85% of the current
+ 
+
+ align:start position:0%
+accounts for about 90 85% of the current
+market poly silicon in blue depreciation
+
+ align:start position:0%
+market poly silicon in blue depreciation
+ 
+
+ align:start position:0%
+market poly silicon in blue depreciation
+in red what's depreciation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+the discounting of the capital that we
+
+ align:start position:0%
+the discounting of the capital that we
+ 
+
+ align:start position:0%
+the discounting of the capital that we
+we just talked about exactly exactly so
+
+ align:start position:0%
+we just talked about exactly exactly so
+ 
+
+ align:start position:0%
+we just talked about exactly exactly so
+what that means is I
+
+ align:start position:0%
+what that means is I
+ 
+
+ align:start position:0%
+what that means is I
+I borrow a lot of money to manufacture
+
+ align:start position:0%
+I borrow a lot of money to manufacture
+ 
+
+ align:start position:0%
+I borrow a lot of money to manufacture
+these panels uh to to buy the equipment
+
+ align:start position:0%
+these panels uh to to buy the equipment
+ 
+
+ align:start position:0%
+these panels uh to to buy the equipment
+to buy the factory and set everything
+
+ align:start position:0%
+to buy the factory and set everything
+ 
+
+ align:start position:0%
+to buy the factory and set everything
+up. Um and then I have to pay interest
+
+ align:start position:0%
+up. Um and then I have to pay interest
+ 
+
+ align:start position:0%
+up. Um and then I have to pay interest
+on my loans, right? So and and and I
+
+ align:start position:0%
+on my loans, right? So and and and I
+ 
+
+ align:start position:0%
+on my loans, right? So and and and I
+have to pay interest on uh the loans and
+
+ align:start position:0%
+have to pay interest on uh the loans and
+ 
+
+ align:start position:0%
+have to pay interest on uh the loans and
+I I what I do is I I start writing off
+
+ align:start position:0%
+I I what I do is I I start writing off
+ 
+
+ align:start position:0%
+I I what I do is I I start writing off
+the equipment as a loss uh to the
+
+ align:start position:0%
+the equipment as a loss uh to the
+ 
+
+ align:start position:0%
+the equipment as a loss uh to the
+company. So uh that equipment is going
+
+ align:start position:0%
+company. So uh that equipment is going
+ 
+
+ align:start position:0%
+company. So uh that equipment is going
+to be useful over a certain period of
+
+ align:start position:0%
+to be useful over a certain period of
+ 
+
+ align:start position:0%
+to be useful over a certain period of
+time and then we can assume that it's
+
+ align:start position:0%
+time and then we can assume that it's
+ 
+
+ align:start position:0%
+time and then we can assume that it's
+outdated and that I'll need to buy the
+
+ align:start position:0%
+outdated and that I'll need to buy the
+ 
+
+ align:start position:0%
+outdated and that I'll need to buy the
+next generation of manufacturing
+
+ align:start position:0%
+next generation of manufacturing
+ 
+
+ align:start position:0%
+next generation of manufacturing
+equipment. uh so I can begin writing off
+
+ align:start position:0%
+equipment. uh so I can begin writing off
+ 
+
+ align:start position:0%
+equipment. uh so I can begin writing off
+the value of that equipment over a
+
+ align:start position:0%
+the value of that equipment over a
+ 
+
+ align:start position:0%
+the value of that equipment over a
+certain schedule over a certain period
+
+ align:start position:0%
+certain schedule over a certain period
+ 
+
+ align:start position:0%
+certain schedule over a certain period
+of years five seven depending on the
+
+ align:start position:0%
+of years five seven depending on the
+ 
+
+ align:start position:0%
+of years five seven depending on the
+company depending on the way they're um
+
+ align:start position:0%
+company depending on the way they're um
+ 
+
+ align:start position:0%
+company depending on the way they're um
+I don't want to say cooking their books
+
+ align:start position:0%
+I don't want to say cooking their books
+ 
+
+ align:start position:0%
+I don't want to say cooking their books
+but the way they're uh manipulating the
+
+ align:start position:0%
+but the way they're uh manipulating the
+ 
+
+ align:start position:0%
+but the way they're uh manipulating the
+numbers in the accounting sector so um
+
+ align:start position:0%
+numbers in the accounting sector so um
+ 
+
+ align:start position:0%
+numbers in the accounting sector so um
+the depreciation varies um and it varies
+
+ align:start position:0%
+the depreciation varies um and it varies
+ 
+
+ align:start position:0%
+the depreciation varies um and it varies
+because the interest rate at which you
+
+ align:start position:0%
+because the interest rate at which you
+ 
+
+ align:start position:0%
+because the interest rate at which you
+acquire the
+
+ align:start position:0%
+acquire the
+ 
+
+ align:start position:0%
+acquire the
+loan and the interest rate or the the
+
+ align:start position:0%
+loan and the interest rate or the the
+ 
+
+ align:start position:0%
+loan and the interest rate or the the
+the inflation rate of the uh of the
+
+ align:start position:0%
+the inflation rate of the uh of the
+ 
+
+ align:start position:0%
+the inflation rate of the uh of the
+particular ular currency in question is
+
+ align:start position:0%
+particular ular currency in question is
+ 
+
+ align:start position:0%
+particular ular currency in question is
+different in different regions, right?
+
+ align:start position:0%
+different in different regions, right?
+ 
+
+ align:start position:0%
+different in different regions, right?
+So when you're calculating depreciation,
+
+ align:start position:0%
+So when you're calculating depreciation,
+ 
+
+ align:start position:0%
+So when you're calculating depreciation,
+both of those things matter and that's
+
+ align:start position:0%
+both of those things matter and that's
+ 
+
+ align:start position:0%
+both of those things matter and that's
+why those numbers can vary from place to
+
+ align:start position:0%
+why those numbers can vary from place to
+ 
+
+ align:start position:0%
+why those numbers can vary from place to
+place. Uh materials, materials cost
+
+ align:start position:0%
+place. Uh materials, materials cost
+ 
+
+ align:start position:0%
+place. Uh materials, materials cost
+these are the materials used to
+
+ align:start position:0%
+these are the materials used to
+ 
+
+ align:start position:0%
+these are the materials used to
+manufacture the module, typically called
+
+ align:start position:0%
+manufacture the module, typically called
+ 
+
+ align:start position:0%
+manufacture the module, typically called
+commodity materials. You would look at
+
+ align:start position:0%
+commodity materials. You would look at
+ 
+
+ align:start position:0%
+commodity materials. You would look at
+them as the extruded aluminum
+
+ align:start position:0%
+them as the extruded aluminum
+ 
+
+ align:start position:0%
+them as the extruded aluminum
+components, the glass in the front side,
+
+ align:start position:0%
+components, the glass in the front side,
+ 
+
+ align:start position:0%
+components, the glass in the front side,
+um the encapsulate materials and so
+
+ align:start position:0%
+um the encapsulate materials and so
+ 
+
+ align:start position:0%
+um the encapsulate materials and so
+forth. All the fancy stuff that we saw
+
+ align:start position:0%
+forth. All the fancy stuff that we saw
+ 
+
+ align:start position:0%
+forth. All the fancy stuff that we saw
+when we visited Foundhoffer last
+
+ align:start position:0%
+when we visited Foundhoffer last
+ 
+
+ align:start position:0%
+when we visited Foundhoffer last
+week. Um let's see what else we have.
+
+ align:start position:0%
+week. Um let's see what else we have.
+ 
+
+ align:start position:0%
+week. Um let's see what else we have.
+Labor. Okay, that's pretty
+
+ align:start position:0%
+Labor. Okay, that's pretty
+ 
+
+ align:start position:0%
+Labor. Okay, that's pretty
+straightforward to see. Um, if we're
+
+ align:start position:0%
+straightforward to see. Um, if we're
+ 
+
+ align:start position:0%
+straightforward to see. Um, if we're
+manufacturing in China, we were looking
+
+ align:start position:0%
+manufacturing in China, we were looking
+ 
+
+ align:start position:0%
+manufacturing in China, we were looking
+at a labor rate uh could be could be as
+
+ align:start position:0%
+at a labor rate uh could be could be as
+ 
+
+ align:start position:0%
+at a labor rate uh could be could be as
+low base labor without adding um housing
+
+ align:start position:0%
+low base labor without adding um housing
+ 
+
+ align:start position:0%
+low base labor without adding um housing
+and so forth. The base labor rate could
+
+ align:start position:0%
+and so forth. The base labor rate could
+ 
+
+ align:start position:0%
+and so forth. The base labor rate could
+be as low as $275 an hour in US dollars.
+
+ align:start position:0%
+be as low as $275 an hour in US dollars.
+ 
+
+ align:start position:0%
+be as low as $275 an hour in US dollars.
+Um, and uh in US dollars in the United
+
+ align:start position:0%
+Um, and uh in US dollars in the United
+ 
+
+ align:start position:0%
+Um, and uh in US dollars in the United
+States, we could be looking at labor
+
+ align:start position:0%
+States, we could be looking at labor
+ 
+
+ align:start position:0%
+States, we could be looking at labor
+rates of somewhere in the range of $16
+
+ align:start position:0%
+rates of somewhere in the range of $16
+ 
+
+ align:start position:0%
+rates of somewhere in the range of $16
+an hour, right? Um before you start
+
+ align:start position:0%
+an hour, right? Um before you start
+ 
+
+ align:start position:0%
+an hour, right? Um before you start
+adding in uh social security and
+
+ align:start position:0%
+adding in uh social security and
+ 
+
+ align:start position:0%
+adding in uh social security and
+benefits and so forth. And um there
+
+ align:start position:0%
+benefits and so forth. And um there
+ 
+
+ align:start position:0%
+benefits and so forth. And um there
+might there may be different levels of
+
+ align:start position:0%
+might there may be different levels of
+ 
+
+ align:start position:0%
+might there may be different levels of
+automation in the two different places
+
+ align:start position:0%
+automation in the two different places
+ 
+
+ align:start position:0%
+automation in the two different places
+which shifts costs from labor into uh
+
+ align:start position:0%
+which shifts costs from labor into uh
+ 
+
+ align:start position:0%
+which shifts costs from labor into uh
+capital equipment, right? So if you
+
+ align:start position:0%
+capital equipment, right? So if you
+ 
+
+ align:start position:0%
+capital equipment, right? So if you
+realize that you have a much higher
+
+ align:start position:0%
+realize that you have a much higher
+ 
+
+ align:start position:0%
+realize that you have a much higher
+labor cost, uh you might want to buy
+
+ align:start position:0%
+labor cost, uh you might want to buy
+ 
+
+ align:start position:0%
+labor cost, uh you might want to buy
+more robots to do the manufacturing. Uh
+
+ align:start position:0%
+more robots to do the manufacturing. Uh
+ 
+
+ align:start position:0%
+more robots to do the manufacturing. Uh
+and vice versa, if you're in China and
+
+ align:start position:0%
+and vice versa, if you're in China and
+ 
+
+ align:start position:0%
+and vice versa, if you're in China and
+you realize, oh my goodness, our labor
+
+ align:start position:0%
+you realize, oh my goodness, our labor
+ 
+
+ align:start position:0%
+you realize, oh my goodness, our labor
+rates are increasing uh almost
+
+ align:start position:0%
+rates are increasing uh almost
+ 
+
+ align:start position:0%
+rates are increasing uh almost
+exponentially, definitely super linearly
+
+ align:start position:0%
+exponentially, definitely super linearly
+ 
+
+ align:start position:0%
+exponentially, definitely super linearly
+with time as as as the country takes off
+
+ align:start position:0%
+with time as as as the country takes off
+ 
+
+ align:start position:0%
+with time as as as the country takes off
+and and there's inflation uh labor wage
+
+ align:start position:0%
+and and there's inflation uh labor wage
+ 
+
+ align:start position:0%
+and and there's inflation uh labor wage
+inflation. Um, a company that is trying
+
+ align:start position:0%
+inflation. Um, a company that is trying
+ 
+
+ align:start position:0%
+inflation. Um, a company that is trying
+to project forward five or seven years
+
+ align:start position:0%
+to project forward five or seven years
+ 
+
+ align:start position:0%
+to project forward five or seven years
+might say, "Well, goodness, it doesn't
+
+ align:start position:0%
+might say, "Well, goodness, it doesn't
+ 
+
+ align:start position:0%
+might say, "Well, goodness, it doesn't
+make sense for me to flood my
+
+ align:start position:0%
+make sense for me to flood my
+ 
+
+ align:start position:0%
+make sense for me to flood my
+manufacturing line with people right now
+
+ align:start position:0%
+manufacturing line with people right now
+ 
+
+ align:start position:0%
+manufacturing line with people right now
+because that manufacturing line still
+
+ align:start position:0%
+because that manufacturing line still
+ 
+
+ align:start position:0%
+because that manufacturing line still
+has to make a profit in five years. And
+
+ align:start position:0%
+has to make a profit in five years. And
+ 
+
+ align:start position:0%
+has to make a profit in five years. And
+so, I'm going to buy more robots now.
+
+ align:start position:0%
+so, I'm going to buy more robots now.
+ 
+
+ align:start position:0%
+so, I'm going to buy more robots now.
+Even though I might not need it today, I
+
+ align:start position:0%
+Even though I might not need it today, I
+ 
+
+ align:start position:0%
+Even though I might not need it today, I
+might need it in five years." And so,
+
+ align:start position:0%
+might need it in five years." And so,
+ 
+
+ align:start position:0%
+might need it in five years." And so,
+there's a bit of risk calculation that
+
+ align:start position:0%
+there's a bit of risk calculation that
+ 
+
+ align:start position:0%
+there's a bit of risk calculation that
+gets thrown into this as well, right?
+
+ align:start position:0%
+gets thrown into this as well, right?
+ 
+
+ align:start position:0%
+gets thrown into this as well, right?
+Um, utilities and overhead. Okay, that's
+
+ align:start position:0%
+Um, utilities and overhead. Okay, that's
+ 
+
+ align:start position:0%
+Um, utilities and overhead. Okay, that's
+pretty straightforward. If we're looking
+
+ align:start position:0%
+pretty straightforward. If we're looking
+ 
+
+ align:start position:0%
+pretty straightforward. If we're looking
+at utilities, that means electricity
+
+ align:start position:0%
+at utilities, that means electricity
+ 
+
+ align:start position:0%
+at utilities, that means electricity
+mostly to run uh the lines. uh it could
+
+ align:start position:0%
+mostly to run uh the lines. uh it could
+ 
+
+ align:start position:0%
+mostly to run uh the lines. uh it could
+also be uh water which is is used in the
+
+ align:start position:0%
+also be uh water which is is used in the
+ 
+
+ align:start position:0%
+also be uh water which is is used in the
+manufacturing process. Okay. Um note the
+
+ align:start position:0%
+manufacturing process. Okay. Um note the
+ 
+
+ align:start position:0%
+manufacturing process. Okay. Um note the
+caveats in several of these studies
+
+ align:start position:0%
+caveats in several of these studies
+ 
+
+ align:start position:0%
+caveats in several of these studies
+especially the the one out of Lawrence
+
+ align:start position:0%
+especially the the one out of Lawrence
+ 
+
+ align:start position:0%
+especially the the one out of Lawrence
+Berkeley National Laboratory um
+
+ align:start position:0%
+Berkeley National Laboratory um
+ 
+
+ align:start position:0%
+Berkeley National Laboratory um
+manufacturing cost you can you can do a
+
+ align:start position:0%
+manufacturing cost you can you can do a
+ 
+
+ align:start position:0%
+manufacturing cost you can you can do a
+number of things with that. You can
+
+ align:start position:0%
+number of things with that. You can
+ 
+
+ align:start position:0%
+number of things with that. You can
+assume that you're buying your
+
+ align:start position:0%
+assume that you're buying your
+ 
+
+ align:start position:0%
+assume that you're buying your
+polysilicon. You're buying the
+
+ align:start position:0%
+polysilicon. You're buying the
+ 
+
+ align:start position:0%
+polysilicon. You're buying the
+polysilicon manufacturing cells modules
+
+ align:start position:0%
+polysilicon manufacturing cells modules
+ 
+
+ align:start position:0%
+polysilicon manufacturing cells modules
+and and systems. Or you can assume that
+
+ align:start position:0%
+and and systems. Or you can assume that
+ 
+
+ align:start position:0%
+and and systems. Or you can assume that
+you're buying the cells and the cells
+
+ align:start position:0%
+you're buying the cells and the cells
+ 
+
+ align:start position:0%
+you're buying the cells and the cells
+are commodity products equal in in price
+
+ align:start position:0%
+are commodity products equal in in price
+ 
+
+ align:start position:0%
+are commodity products equal in in price
+throughout the world and that you're
+
+ align:start position:0%
+throughout the world and that you're
+ 
+
+ align:start position:0%
+throughout the world and that you're
+just manufacturing the modules. Right?
+
+ align:start position:0%
+just manufacturing the modules. Right?
+ 
+
+ align:start position:0%
+just manufacturing the modules. Right?
+So you can cut cost in many different
+
+ align:start position:0%
+So you can cut cost in many different
+ 
+
+ align:start position:0%
+So you can cut cost in many different
+ways depending on what assumptions you
+
+ align:start position:0%
+ways depending on what assumptions you
+ 
+
+ align:start position:0%
+ways depending on what assumptions you
+make. The price of the cell on the
+
+ align:start position:0%
+make. The price of the cell on the
+ 
+
+ align:start position:0%
+make. The price of the cell on the
+international market may be very
+
+ align:start position:0%
+international market may be very
+ 
+
+ align:start position:0%
+international market may be very
+different than the cost to manufacture
+
+ align:start position:0%
+different than the cost to manufacture
+ 
+
+ align:start position:0%
+different than the cost to manufacture
+that cell in your particular country.
+
+ align:start position:0%
+that cell in your particular country.
+ 
+
+ align:start position:0%
+that cell in your particular country.
+And and cost is almost one of those
+
+ align:start position:0%
+And and cost is almost one of those
+ 
+
+ align:start position:0%
+And and cost is almost one of those
+things that you can torture until it
+
+ align:start position:0%
+things that you can torture until it
+ 
+
+ align:start position:0%
+things that you can torture until it
+tells you the story you want it to tell,
+
+ align:start position:0%
+tells you the story you want it to tell,
+ 
+
+ align:start position:0%
+tells you the story you want it to tell,
+right? It's it's one of those things
+
+ align:start position:0%
+right? It's it's one of those things
+ 
+
+ align:start position:0%
+right? It's it's one of those things
+where if if you did these numbers a
+
+ align:start position:0%
+where if if you did these numbers a
+ 
+
+ align:start position:0%
+where if if you did these numbers a
+little bit differently and said, "Okay,
+
+ align:start position:0%
+little bit differently and said, "Okay,
+ 
+
+ align:start position:0%
+little bit differently and said, "Okay,
+we're buying cells um and and just
+
+ align:start position:0%
+we're buying cells um and and just
+ 
+
+ align:start position:0%
+we're buying cells um and and just
+making modules and then adding shipment
+
+ align:start position:0%
+making modules and then adding shipment
+ 
+
+ align:start position:0%
+making modules and then adding shipment
+fees, let's say transport fees from
+
+ align:start position:0%
+fees, let's say transport fees from
+ 
+
+ align:start position:0%
+fees, let's say transport fees from
+China to the United States, China and US
+
+ align:start position:0%
+China to the United States, China and US
+ 
+
+ align:start position:0%
+China to the United States, China and US
+might look almost equal."
+
+ align:start position:0%
+might look almost equal."
+ 
+
+ align:start position:0%
+might look almost equal."
+Whereas if you integrate over the entire
+
+ align:start position:0%
+Whereas if you integrate over the entire
+ 
+
+ align:start position:0%
+Whereas if you integrate over the entire
+supply chain and say okay I'm going to
+
+ align:start position:0%
+supply chain and say okay I'm going to
+ 
+
+ align:start position:0%
+supply chain and say okay I'm going to
+be manufacturing my polysilicon then my
+
+ align:start position:0%
+be manufacturing my polysilicon then my
+ 
+
+ align:start position:0%
+be manufacturing my polysilicon then my
+wafers then my cells and finally the
+
+ align:start position:0%
+wafers then my cells and finally the
+ 
+
+ align:start position:0%
+wafers then my cells and finally the
+modules um then you might start seeing
+
+ align:start position:0%
+modules um then you might start seeing
+ 
+
+ align:start position:0%
+modules um then you might start seeing
+some disparity based on these other
+
+ align:start position:0%
+some disparity based on these other
+ 
+
+ align:start position:0%
+some disparity based on these other
+parameters shown here. Point being um be
+
+ align:start position:0%
+parameters shown here. Point being um be
+ 
+
+ align:start position:0%
+parameters shown here. Point being um be
+careful when you see a cost assessment
+
+ align:start position:0%
+careful when you see a cost assessment
+ 
+
+ align:start position:0%
+careful when you see a cost assessment
+probe their base assumptions and try to
+
+ align:start position:0%
+probe their base assumptions and try to
+ 
+
+ align:start position:0%
+probe their base assumptions and try to
+understand what their biases and
+
+ align:start position:0%
+understand what their biases and
+ 
+
+ align:start position:0%
+understand what their biases and
+motivations were for presenting uh that
+
+ align:start position:0%
+motivations were for presenting uh that
+ 
+
+ align:start position:0%
+motivations were for presenting uh that
+particular comparison. um especially
+
+ align:start position:0%
+particular comparison. um especially
+ 
+
+ align:start position:0%
+particular comparison. um especially
+nowadays where you have more and more
+
+ align:start position:0%
+nowadays where you have more and more
+ 
+
+ align:start position:0%
+nowadays where you have more and more
+parties with vested interests in
+
+ align:start position:0%
+parties with vested interests in
+ 
+
+ align:start position:0%
+parties with vested interests in
+presenting one story or
+
+ align:start position:0%
+presenting one story or
+ 
+
+ align:start position:0%
+presenting one story or
+another. We'll get to that in a few
+
+ align:start position:0%
+another. We'll get to that in a few
+ 
+
+ align:start position:0%
+another. We'll get to that in a few
+slides. All right, experience learning
+
+ align:start position:0%
+slides. All right, experience learning
+ 
+
+ align:start position:0%
+slides. All right, experience learning
+curve. Okay, then we're getting into
+
+ align:start position:0%
+curve. Okay, then we're getting into
+ 
+
+ align:start position:0%
+curve. Okay, then we're getting into
+price. Uh we're venturing beyond cost
+
+ align:start position:0%
+price. Uh we're venturing beyond cost
+ 
+
+ align:start position:0%
+price. Uh we're venturing beyond cost
+and into the regime of price which is
+
+ align:start position:0%
+and into the regime of price which is
+ 
+
+ align:start position:0%
+and into the regime of price which is
+definitely more easily measurable and
+
+ align:start position:0%
+definitely more easily measurable and
+ 
+
+ align:start position:0%
+definitely more easily measurable and
+that's why we have some fairly good data
+
+ align:start position:0%
+that's why we have some fairly good data
+ 
+
+ align:start position:0%
+that's why we have some fairly good data
+going back um several decades. And uh
+
+ align:start position:0%
+going back um several decades. And uh
+ 
+
+ align:start position:0%
+going back um several decades. And uh
+you can see here uh this is cumulative
+
+ align:start position:0%
+you can see here uh this is cumulative
+ 
+
+ align:start position:0%
+you can see here uh this is cumulative
+sales in gigawatt peak. That means the
+
+ align:start position:0%
+sales in gigawatt peak. That means the
+ 
+
+ align:start position:0%
+sales in gigawatt peak. That means the
+cumulative number of widgets in this
+
+ align:start position:0%
+cumulative number of widgets in this
+ 
+
+ align:start position:0%
+cumulative number of widgets in this
+case watt peaks produced uh by solar
+
+ align:start position:0%
+case watt peaks produced uh by solar
+ 
+
+ align:start position:0%
+case watt peaks produced uh by solar
+industries worldwide. And this is the
+
+ align:start position:0%
+industries worldwide. And this is the
+ 
+
+ align:start position:0%
+industries worldwide. And this is the
+global average um module selling price
+
+ align:start position:0%
+global average um module selling price
+ 
+
+ align:start position:0%
+global average um module selling price
+not the system the module right so not
+
+ align:start position:0%
+not the system the module right so not
+ 
+
+ align:start position:0%
+not the system the module right so not
+the balance of system installation labor
+
+ align:start position:0%
+the balance of system installation labor
+ 
+
+ align:start position:0%
+the balance of system installation labor
+and so forth but just the manufacturing
+
+ align:start position:0%
+and so forth but just the manufacturing
+ 
+
+ align:start position:0%
+and so forth but just the manufacturing
+of the module. And what we can see here
+
+ align:start position:0%
+of the module. And what we can see here
+ 
+
+ align:start position:0%
+of the module. And what we can see here
+is a general trend over time with a
+
+ align:start position:0%
+is a general trend over time with a
+ 
+
+ align:start position:0%
+is a general trend over time with a
+decreasing price. That's good. Sorry.
+
+ align:start position:0%
+decreasing price. That's good. Sorry.
+ 
+
+ align:start position:0%
+decreasing price. That's good. Sorry.
+Decreasing price with time. That's
+
+ align:start position:0%
+Decreasing price with time. That's
+ 
+
+ align:start position:0%
+Decreasing price with time. That's
+that's excellent. Um what is that
+
+ align:start position:0%
+that's excellent. Um what is that
+ 
+
+ align:start position:0%
+that's excellent. Um what is that
+called? This this uh this curve here
+
+ align:start position:0%
+called? This this uh this curve here
+ 
+
+ align:start position:0%
+called? This this uh this curve here
+plotted in a log log scale where you
+
+ align:start position:0%
+plotted in a log log scale where you
+ 
+
+ align:start position:0%
+plotted in a log log scale where you
+have a line
+
+ align:start position:0%
+have a line
+ 
+
+ align:start position:0%
+have a line
+uh through the cumulative manufacturing
+
+ align:start position:0%
+uh through the cumulative manufacturing
+ 
+
+ align:start position:0%
+uh through the cumulative manufacturing
+production versus versus versus price.
+
+ align:start position:0%
+production versus versus versus price.
+ 
+
+ align:start position:0%
+production versus versus versus price.
+What what is that curve called?
+
+ align:start position:0%
+What what is that curve called?
+ 
+
+ align:start position:0%
+What what is that curve called?
+Experience learning. It's an experience
+
+ align:start position:0%
+Experience learning. It's an experience
+ 
+
+ align:start position:0%
+Experience learning. It's an experience
+learning curve. And you'll get something
+
+ align:start position:0%
+learning curve. And you'll get something
+ 
+
+ align:start position:0%
+learning curve. And you'll get something
+similar for any high-tech product.
+
+ align:start position:0%
+similar for any high-tech product.
+ 
+
+ align:start position:0%
+similar for any high-tech product.
+Computers, toasters, as long as the
+
+ align:start position:0%
+Computers, toasters, as long as the
+ 
+
+ align:start position:0%
+Computers, toasters, as long as the
+product isn't changing significantly
+
+ align:start position:0%
+product isn't changing significantly
+ 
+
+ align:start position:0%
+product isn't changing significantly
+with time. And even sometimes if they
+
+ align:start position:0%
+with time. And even sometimes if they
+ 
+
+ align:start position:0%
+with time. And even sometimes if they
+are uh as it's the case with a solar
+
+ align:start position:0%
+are uh as it's the case with a solar
+ 
+
+ align:start position:0%
+are uh as it's the case with a solar
+panel, solar panels back in the 1960s or
+
+ align:start position:0%
+panel, solar panels back in the 1960s or
+ 
+
+ align:start position:0%
+panel, solar panels back in the 1960s or
+1970s rather look very different than
+
+ align:start position:0%
+1970s rather look very different than
+ 
+
+ align:start position:0%
+1970s rather look very different than
+the solar panels today in terms of the
+
+ align:start position:0%
+the solar panels today in terms of the
+ 
+
+ align:start position:0%
+the solar panels today in terms of the
+materials and the processes used. And
+
+ align:start position:0%
+materials and the processes used. And
+ 
+
+ align:start position:0%
+materials and the processes used. And
+yet it all falls along this very
+
+ align:start position:0%
+yet it all falls along this very
+ 
+
+ align:start position:0%
+yet it all falls along this very
+interesting experience learning curve.
+
+ align:start position:0%
+interesting experience learning curve.
+ 
+
+ align:start position:0%
+interesting experience learning curve.
+So it's extremely tempting to say oh
+
+ align:start position:0%
+So it's extremely tempting to say oh
+ 
+
+ align:start position:0%
+So it's extremely tempting to say oh
+well what what price do we need to reach
+
+ align:start position:0%
+well what what price do we need to reach
+ 
+
+ align:start position:0%
+well what what price do we need to reach
+to be cost competitive or or competitive
+
+ align:start position:0%
+to be cost competitive or or competitive
+ 
+
+ align:start position:0%
+to be cost competitive or or competitive
+let's say with bulk electricity? We need
+
+ align:start position:0%
+let's say with bulk electricity? We need
+ 
+
+ align:start position:0%
+let's say with bulk electricity? We need
+to reach a price of say 50 cents per
+
+ align:start position:0%
+to reach a price of say 50 cents per
+ 
+
+ align:start position:0%
+to reach a price of say 50 cents per
+watt peak. Oh easy. We'll just project
+
+ align:start position:0%
+watt peak. Oh easy. We'll just project
+ 
+
+ align:start position:0%
+watt peak. Oh easy. We'll just project
+forward and we'll see how much
+
+ align:start position:0%
+forward and we'll see how much
+ 
+
+ align:start position:0%
+forward and we'll see how much
+cumulative production is needed. um and
+
+ align:start position:0%
+cumulative production is needed. um and
+ 
+
+ align:start position:0%
+cumulative production is needed. um and
+then we'll subsidize until we get to
+
+ align:start position:0%
+then we'll subsidize until we get to
+ 
+
+ align:start position:0%
+then we'll subsidize until we get to
+that cumulative production and and
+
+ align:start position:0%
+that cumulative production and and
+ 
+
+ align:start position:0%
+that cumulative production and and
+bingo, voila, it'll happen by magic.
+
+ align:start position:0%
+bingo, voila, it'll happen by magic.
+ 
+
+ align:start position:0%
+bingo, voila, it'll happen by magic.
+Well, the reality is that each little
+
+ align:start position:0%
+Well, the reality is that each little
+ 
+
+ align:start position:0%
+Well, the reality is that each little
+bump here along the learning curve was
+
+ align:start position:0%
+bump here along the learning curve was
+ 
+
+ align:start position:0%
+bump here along the learning curve was
+was some if you look closely, you can
+
+ align:start position:0%
+was some if you look closely, you can
+ 
+
+ align:start position:0%
+was some if you look closely, you can
+kind of see these little bumps here.
+
+ align:start position:0%
+kind of see these little bumps here.
+ 
+
+ align:start position:0%
+kind of see these little bumps here.
+There were many traumatic events within
+
+ align:start position:0%
+There were many traumatic events within
+ 
+
+ align:start position:0%
+There were many traumatic events within
+the industry that forced people to uh
+
+ align:start position:0%
+the industry that forced people to uh
+ 
+
+ align:start position:0%
+the industry that forced people to uh
+innovate uh to produce better
+
+ align:start position:0%
+innovate uh to produce better
+ 
+
+ align:start position:0%
+innovate uh to produce better
+technology. um whether it's the
+
+ align:start position:0%
+technology. um whether it's the
+ 
+
+ align:start position:0%
+technology. um whether it's the
+technology itself, something designed
+
+ align:start position:0%
+technology itself, something designed
+ 
+
+ align:start position:0%
+technology itself, something designed
+here in the laboratory at MIT or
+
+ align:start position:0%
+here in the laboratory at MIT or
+ 
+
+ align:start position:0%
+here in the laboratory at MIT or
+Harvard, or whether it's something u uh
+
+ align:start position:0%
+Harvard, or whether it's something u uh
+ 
+
+ align:start position:0%
+Harvard, or whether it's something u uh
+innovated on the manufacturing line
+
+ align:start position:0%
+innovated on the manufacturing line
+ 
+
+ align:start position:0%
+innovated on the manufacturing line
+where they realized, oh, this is a more
+
+ align:start position:0%
+where they realized, oh, this is a more
+ 
+
+ align:start position:0%
+where they realized, oh, this is a more
+efficient way of manufacturing the solar
+
+ align:start position:0%
+efficient way of manufacturing the solar
+ 
+
+ align:start position:0%
+efficient way of manufacturing the solar
+panels. It's cheaper. Um this little
+
+ align:start position:0%
+panels. It's cheaper. Um this little
+ 
+
+ align:start position:0%
+panels. It's cheaper. Um this little
+bump right here, boom. This represents a
+
+ align:start position:0%
+bump right here, boom. This represents a
+ 
+
+ align:start position:0%
+bump right here, boom. This represents a
+period in which prices actually went
+
+ align:start position:0%
+period in which prices actually went
+ 
+
+ align:start position:0%
+period in which prices actually went
+back up year in and year out. What could
+
+ align:start position:0%
+back up year in and year out. What could
+ 
+
+ align:start position:0%
+back up year in and year out. What could
+cause prices to go
+
+ align:start position:0%
+cause prices to go
+ 
+
+ align:start position:0%
+cause prices to go
+up? What are what are some of the
+
+ align:start position:0%
+up? What are what are some of the
+ 
+
+ align:start position:0%
+up? What are what are some of the
+motivations for that? I mean, scale is
+
+ align:start position:0%
+motivations for that? I mean, scale is
+ 
+
+ align:start position:0%
+motivations for that? I mean, scale is
+increasing. The market's growing. It's
+
+ align:start position:0%
+increasing. The market's growing. It's
+ 
+
+ align:start position:0%
+increasing. The market's growing. It's
+not shrinking at all. It's not like the
+
+ align:start position:0%
+not shrinking at all. It's not like the
+ 
+
+ align:start position:0%
+not shrinking at all. It's not like the
+points went back here as they went up.
+
+ align:start position:0%
+points went back here as they went up.
+ 
+
+ align:start position:0%
+points went back here as they went up.
+Um, so the market continued to grow. The
+
+ align:start position:0%
+Um, so the market continued to grow. The
+ 
+
+ align:start position:0%
+Um, so the market continued to grow. The
+manufacturing capacity continued to
+
+ align:start position:0%
+manufacturing capacity continued to
+ 
+
+ align:start position:0%
+manufacturing capacity continued to
+grow, but the price went back up. What
+
+ align:start position:0%
+grow, but the price went back up. What
+ 
+
+ align:start position:0%
+grow, but the price went back up. What
+what could have caused that?
+
+ align:start position:0%
+what could have caused that?
+ 
+
+ align:start position:0%
+what could have caused that?
+Supply. Demand outpaces supply. Exactly.
+
+ align:start position:0%
+Supply. Demand outpaces supply. Exactly.
+ 
+
+ align:start position:0%
+Supply. Demand outpaces supply. Exactly.
+So, uh, in this specific case, what
+
+ align:start position:0%
+So, uh, in this specific case, what
+ 
+
+ align:start position:0%
+So, uh, in this specific case, what
+happened was the polysilicon feed stock,
+
+ align:start position:0%
+happened was the polysilicon feed stock,
+ 
+
+ align:start position:0%
+happened was the polysilicon feed stock,
+which is the input material into this
+
+ align:start position:0%
+which is the input material into this
+ 
+
+ align:start position:0%
+which is the input material into this
+entire process, was in short supply. uh
+
+ align:start position:0%
+entire process, was in short supply. uh
+ 
+
+ align:start position:0%
+entire process, was in short supply. uh
+takes about well in those days it took
+
+ align:start position:0%
+takes about well in those days it took
+ 
+
+ align:start position:0%
+takes about well in those days it took
+about 24 to 36 months to get a new plant
+
+ align:start position:0%
+about 24 to 36 months to get a new plant
+ 
+
+ align:start position:0%
+about 24 to 36 months to get a new plant
+online long lead time billions of
+
+ align:start position:0%
+online long lead time billions of
+ 
+
+ align:start position:0%
+online long lead time billions of
+dollars of investment and so the
+
+ align:start position:0%
+dollars of investment and so the
+ 
+
+ align:start position:0%
+dollars of investment and so the
+polysilicon suppliers didn't really want
+
+ align:start position:0%
+polysilicon suppliers didn't really want
+ 
+
+ align:start position:0%
+polysilicon suppliers didn't really want
+to invest unless they knew photovoltaics
+
+ align:start position:0%
+to invest unless they knew photovoltaics
+ 
+
+ align:start position:0%
+to invest unless they knew photovoltaics
+was for real right and the PV industry
+
+ align:start position:0%
+was for real right and the PV industry
+ 
+
+ align:start position:0%
+was for real right and the PV industry
+had exhausted the uh the elasticity of
+
+ align:start position:0%
+had exhausted the uh the elasticity of
+ 
+
+ align:start position:0%
+had exhausted the uh the elasticity of
+the supply market in the uh in the
+
+ align:start position:0%
+the supply market in the uh in the
+ 
+
+ align:start position:0%
+the supply market in the uh in the
+polysilicon business and polyilicon
+
+ align:start position:0%
+polysilicon business and polyilicon
+ 
+
+ align:start position:0%
+polysilicon business and polyilicon
+suppliers looked at the situation and
+
+ align:start position:0%
+suppliers looked at the situation and
+ 
+
+ align:start position:0%
+suppliers looked at the situation and
+say well let's let prices go up a little
+
+ align:start position:0%
+say well let's let prices go up a little
+ 
+
+ align:start position:0%
+say well let's let prices go up a little
+bit it can't hurt us too bad I mean
+
+ align:start position:0%
+bit it can't hurt us too bad I mean
+ 
+
+ align:start position:0%
+bit it can't hurt us too bad I mean
+let's let's we we've been we've been
+
+ align:start position:0%
+let's let's we we've been we've been
+ 
+
+ align:start position:0%
+let's let's we we've been we've been
+starved for several years because of low
+
+ align:start position:0%
+starved for several years because of low
+ 
+
+ align:start position:0%
+starved for several years because of low
+polysilic feed stock prices. Let's let
+
+ align:start position:0%
+polysilic feed stock prices. Let's let
+ 
+
+ align:start position:0%
+polysilic feed stock prices. Let's let
+this um increased demand kind of push
+
+ align:start position:0%
+this um increased demand kind of push
+ 
+
+ align:start position:0%
+this um increased demand kind of push
+prices up a little bit before we really
+
+ align:start position:0%
+prices up a little bit before we really
+ 
+
+ align:start position:0%
+prices up a little bit before we really
+decide what to do. And by the time they
+
+ align:start position:0%
+decide what to do. And by the time they
+ 
+
+ align:start position:0%
+decide what to do. And by the time they
+decided what to do, um there was a lot
+
+ align:start position:0%
+decided what to do, um there was a lot
+ 
+
+ align:start position:0%
+decided what to do, um there was a lot
+of them getting on the market all at
+
+ align:start position:0%
+of them getting on the market all at
+ 
+
+ align:start position:0%
+of them getting on the market all at
+once, which had this effect. Boom. Now,
+
+ align:start position:0%
+once, which had this effect. Boom. Now,
+ 
+
+ align:start position:0%
+once, which had this effect. Boom. Now,
+um it's not only the polysilicon, but
+
+ align:start position:0%
+um it's not only the polysilicon, but
+ 
+
+ align:start position:0%
+um it's not only the polysilicon, but
+also the uh cell manufacturers, the
+
+ align:start position:0%
+also the uh cell manufacturers, the
+ 
+
+ align:start position:0%
+also the uh cell manufacturers, the
+wafer manufacturers that expanded their
+
+ align:start position:0%
+wafer manufacturers that expanded their
+ 
+
+ align:start position:0%
+wafer manufacturers that expanded their
+capacity during this time between 2007
+
+ align:start position:0%
+capacity during this time between 2007
+ 
+
+ align:start position:0%
+capacity during this time between 2007
+and 2010. Now, today's today's most
+
+ align:start position:0%
+and 2010. Now, today's today's most
+ 
+
+ align:start position:0%
+and 2010. Now, today's today's most
+recent price point, as I saw it on uh on
+
+ align:start position:0%
+recent price point, as I saw it on uh on
+ 
+
+ align:start position:0%
+recent price point, as I saw it on uh on
+on one of our our more trusted websites,
+
+ align:start position:0%
+on one of our our more trusted websites,
+ 
+
+ align:start position:0%
+on one of our our more trusted websites,
+put us down at around uh A13, $15 per
+
+ align:start position:0%
+put us down at around uh A13, $15 per
+ 
+
+ align:start position:0%
+put us down at around uh A13, $15 per
+watt peak. So, we're down here. We're
+
+ align:start position:0%
+watt peak. So, we're down here. We're
+ 
+
+ align:start position:0%
+watt peak. So, we're down here. We're
+well below the historical average trend.
+
+ align:start position:0%
+well below the historical average trend.
+ 
+
+ align:start position:0%
+well below the historical average trend.
+We're in an over supply condition right
+
+ align:start position:0%
+We're in an over supply condition right
+ 
+
+ align:start position:0%
+We're in an over supply condition right
+now. Why did the overupp come about?
+
+ align:start position:0%
+now. Why did the overupp come about?
+ 
+
+ align:start position:0%
+now. Why did the overupp come about?
+Well, partly because of this uh under
+
+ align:start position:0%
+Well, partly because of this uh under
+ 
+
+ align:start position:0%
+Well, partly because of this uh under
+supply condition, many people saw an
+
+ align:start position:0%
+supply condition, many people saw an
+ 
+
+ align:start position:0%
+supply condition, many people saw an
+opportunity and said, "Well, we can
+
+ align:start position:0%
+opportunity and said, "Well, we can
+ 
+
+ align:start position:0%
+opportunity and said, "Well, we can
+address that demand. We can grow in this
+
+ align:start position:0%
+address that demand. We can grow in this
+ 
+
+ align:start position:0%
+address that demand. We can grow in this
+this industry right here." To grow in
+
+ align:start position:0%
+this industry right here." To grow in
+ 
+
+ align:start position:0%
+this industry right here." To grow in
+the industry, you need capital, right?
+
+ align:start position:0%
+the industry, you need capital, right?
+ 
+
+ align:start position:0%
+the industry, you need capital, right?
+You need uh access to finances to
+
+ align:start position:0%
+You need uh access to finances to
+ 
+
+ align:start position:0%
+You need uh access to finances to
+expand. What happened in 2008 in western
+
+ align:start position:0%
+expand. What happened in 2008 in western
+ 
+
+ align:start position:0%
+expand. What happened in 2008 in western
+countries and 2008 was more or less when
+
+ align:start position:0%
+countries and 2008 was more or less when
+ 
+
+ align:start position:0%
+countries and 2008 was more or less when
+it really uh
+
+ align:start position:0%
+it really uh
+ 
+
+ align:start position:0%
+it really uh
+the hit the fan if you will um in in in
+
+ align:start position:0%
+the hit the fan if you will um in in in
+ 
+
+ align:start position:0%
+the hit the fan if you will um in in in
+uh United States in particular. What
+
+ align:start position:0%
+uh United States in particular. What
+ 
+
+ align:start position:0%
+uh United States in particular. What
+what what happened in the capital
+
+ align:start position:0%
+what what happened in the capital
+ 
+
+ align:start position:0%
+what what happened in the capital
+markets
+
+ align:start position:0%
+markets
+ 
+
+ align:start position:0%
+markets
+capital was severely restricted because
+
+ align:start position:0%
+capital was severely restricted because
+ 
+
+ align:start position:0%
+capital was severely restricted because
+we're not providing a lot of loans.
+
+ align:start position:0%
+we're not providing a lot of loans.
+ 
+
+ align:start position:0%
+we're not providing a lot of loans.
+Exactly. We had the financial crisis
+
+ align:start position:0%
+Exactly. We had the financial crisis
+ 
+
+ align:start position:0%
+Exactly. We had the financial crisis
+here in the US. And so in the United
+
+ align:start position:0%
+here in the US. And so in the United
+ 
+
+ align:start position:0%
+here in the US. And so in the United
+States, there was a a pull back um of
+
+ align:start position:0%
+States, there was a a pull back um of
+ 
+
+ align:start position:0%
+States, there was a a pull back um of
+lending. Uh the government stepped in
+
+ align:start position:0%
+lending. Uh the government stepped in
+ 
+
+ align:start position:0%
+lending. Uh the government stepped in
+shortly thereafter realizing that this
+
+ align:start position:0%
+shortly thereafter realizing that this
+ 
+
+ align:start position:0%
+shortly thereafter realizing that this
+was going to be an issue. There was the
+
+ align:start position:0%
+was going to be an issue. There was the
+ 
+
+ align:start position:0%
+was going to be an issue. There was the
+ARRA. Does anybody know what that is?
+
+ align:start position:0%
+ARRA. Does anybody know what that is?
+ 
+
+ align:start position:0%
+ARRA. Does anybody know what that is?
+It's not the American Association of
+
+ align:start position:0%
+It's not the American Association of
+ 
+
+ align:start position:0%
+It's not the American Association of
+Retired People. This is very different.
+
+ align:start position:0%
+Retired People. This is very different.
+ 
+
+ align:start position:0%
+Retired People. This is very different.
+A AR is the American Recovery and
+
+ align:start position:0%
+A AR is the American Recovery and
+ 
+
+ align:start position:0%
+A AR is the American Recovery and
+Reinvestment Act, right? This was the
+
+ align:start position:0%
+Reinvestment Act, right? This was the
+ 
+
+ align:start position:0%
+Reinvestment Act, right? This was the
+stimulus act. And this act um actually
+
+ align:start position:0%
+stimulus act. And this act um actually
+ 
+
+ align:start position:0%
+stimulus act. And this act um actually
+did inject a lot of money into or a lot
+
+ align:start position:0%
+did inject a lot of money into or a lot
+ 
+
+ align:start position:0%
+did inject a lot of money into or a lot
+of capital into renewable energy
+
+ align:start position:0%
+of capital into renewable energy
+ 
+
+ align:start position:0%
+of capital into renewable energy
+projects that began hitting in sometime
+
+ align:start position:0%
+projects that began hitting in sometime
+ 
+
+ align:start position:0%
+projects that began hitting in sometime
+between 2009, let's say the beginning uh
+
+ align:start position:0%
+between 2009, let's say the beginning uh
+ 
+
+ align:start position:0%
+between 2009, let's say the beginning uh
+until 2011. And um so in in this period
+
+ align:start position:0%
+until 2011. And um so in in this period
+ 
+
+ align:start position:0%
+until 2011. And um so in in this period
+right over
+
+ align:start position:0%
+right over
+ 
+
+ align:start position:0%
+right over
+here, anybody hear of the word Celindra?
+
+ align:start position:0%
+here, anybody hear of the word Celindra?
+ 
+
+ align:start position:0%
+here, anybody hear of the word Celindra?
+Yeah, you've heard about it, right? Um
+
+ align:start position:0%
+Yeah, you've heard about it, right? Um
+ 
+
+ align:start position:0%
+Yeah, you've heard about it, right? Um
+Celindra was one of the companies that
+
+ align:start position:0%
+Celindra was one of the companies that
+ 
+
+ align:start position:0%
+Celindra was one of the companies that
+received funding under the ARRA, right?
+
+ align:start position:0%
+received funding under the ARRA, right?
+ 
+
+ align:start position:0%
+received funding under the ARRA, right?
+or ARA uh under the stimulus act. Um so
+
+ align:start position:0%
+or ARA uh under the stimulus act. Um so
+ 
+
+ align:start position:0%
+or ARA uh under the stimulus act. Um so
+a lot of interesting things were
+
+ align:start position:0%
+a lot of interesting things were
+ 
+
+ align:start position:0%
+a lot of interesting things were
+happening during this brief little
+
+ align:start position:0%
+happening during this brief little
+ 
+
+ align:start position:0%
+happening during this brief little
+period right here. During uh the mid
+
+ align:start position:0%
+period right here. During uh the mid
+ 
+
+ align:start position:0%
+period right here. During uh the mid
+2000s uh China was getting a lot of bad
+
+ align:start position:0%
+2000s uh China was getting a lot of bad
+ 
+
+ align:start position:0%
+2000s uh China was getting a lot of bad
+rap um by environmental groups um and
+
+ align:start position:0%
+rap um by environmental groups um and
+ 
+
+ align:start position:0%
+rap um by environmental groups um and
+the United States as well for its
+
+ align:start position:0%
+the United States as well for its
+ 
+
+ align:start position:0%
+the United States as well for its
+growing greenhouse gas emissions. there
+
+ align:start position:0%
+growing greenhouse gas emissions. there
+ 
+
+ align:start position:0%
+growing greenhouse gas emissions. there
+was um a growing concern over greenhouse
+
+ align:start position:0%
+was um a growing concern over greenhouse
+ 
+
+ align:start position:0%
+was um a growing concern over greenhouse
+gases uh culminating in the Copenhagen
+
+ align:start position:0%
+gases uh culminating in the Copenhagen
+ 
+
+ align:start position:0%
+gases uh culminating in the Copenhagen
+uh discussions that uh cu uh countries
+
+ align:start position:0%
+uh discussions that uh cu uh countries
+ 
+
+ align:start position:0%
+uh discussions that uh cu uh countries
+especially developing countries had to
+
+ align:start position:0%
+especially developing countries had to
+ 
+
+ align:start position:0%
+especially developing countries had to
+do more uh to reduce their greenhouse
+
+ align:start position:0%
+do more uh to reduce their greenhouse
+ 
+
+ align:start position:0%
+do more uh to reduce their greenhouse
+gas production and uh this of course
+
+ align:start position:0%
+gas production and uh this of course
+ 
+
+ align:start position:0%
+gas production and uh this of course
+invited a wonderful uh tugof war between
+
+ align:start position:0%
+invited a wonderful uh tugof war between
+ 
+
+ align:start position:0%
+invited a wonderful uh tugof war between
+uh developing countries block the the
+
+ align:start position:0%
+uh developing countries block the the
+ 
+
+ align:start position:0%
+uh developing countries block the the
+most progressive of the developing
+
+ align:start position:0%
+most progressive of the developing
+ 
+
+ align:start position:0%
+most progressive of the developing
+countries let's say um normally
+
+ align:start position:0%
+countries let's say um normally
+ 
+
+ align:start position:0%
+countries let's say um normally
+described as bicko um so Brazil, Russia,
+
+ align:start position:0%
+described as bicko um so Brazil, Russia,
+ 
+
+ align:start position:0%
+described as bicko um so Brazil, Russia,
+India, China and other uh including
+
+ align:start position:0%
+India, China and other uh including
+ 
+
+ align:start position:0%
+India, China and other uh including
+South Africa um and uh the developed
+
+ align:start position:0%
+South Africa um and uh the developed
+ 
+
+ align:start position:0%
+South Africa um and uh the developed
+countries and and you can see
+
+ align:start position:0%
+countries and and you can see
+ 
+
+ align:start position:0%
+countries and and you can see
+perspectives uh from both and it's it's
+
+ align:start position:0%
+perspectives uh from both and it's it's
+ 
+
+ align:start position:0%
+perspectives uh from both and it's it's
+wonderful. Uh the uh sophistication of
+
+ align:start position:0%
+wonderful. Uh the uh sophistication of
+ 
+
+ align:start position:0%
+wonderful. Uh the uh sophistication of
+that debate in terms of polyai arguments
+
+ align:start position:0%
+that debate in terms of polyai arguments
+ 
+
+ align:start position:0%
+that debate in terms of polyai arguments
+was just was beautiful to watch. Um on
+
+ align:start position:0%
+was just was beautiful to watch. Um on
+ 
+
+ align:start position:0%
+was just was beautiful to watch. Um on
+one hand you had the developing
+
+ align:start position:0%
+one hand you had the developing
+ 
+
+ align:start position:0%
+one hand you had the developing
+countries that said well wait a second
+
+ align:start position:0%
+countries that said well wait a second
+ 
+
+ align:start position:0%
+countries that said well wait a second
+you folks in the developed world you
+
+ align:start position:0%
+you folks in the developed world you
+ 
+
+ align:start position:0%
+you folks in the developed world you
+used a lot of fossil fuels and the
+
+ align:start position:0%
+used a lot of fossil fuels and the
+ 
+
+ align:start position:0%
+used a lot of fossil fuels and the
+majority of of of the CO2 emissions that
+
+ align:start position:0%
+majority of of of the CO2 emissions that
+ 
+
+ align:start position:0%
+majority of of of the CO2 emissions that
+have occurred to date were from
+
+ align:start position:0%
+have occurred to date were from
+ 
+
+ align:start position:0%
+have occurred to date were from
+developing or developed countries today.
+
+ align:start position:0%
+developing or developed countries today.
+ 
+
+ align:start position:0%
+developing or developed countries today.
+Um, so it's a bit unfair that you're
+
+ align:start position:0%
+Um, so it's a bit unfair that you're
+ 
+
+ align:start position:0%
+Um, so it's a bit unfair that you're
+asking us to reduce our CO2 intensity.
+
+ align:start position:0%
+asking us to reduce our CO2 intensity.
+ 
+
+ align:start position:0%
+asking us to reduce our CO2 intensity.
+Um, because that might hamper our own
+
+ align:start position:0%
+Um, because that might hamper our own
+ 
+
+ align:start position:0%
+Um, because that might hamper our own
+development. Um, why don't you pay
+
+ align:start position:0%
+development. Um, why don't you pay
+ 
+
+ align:start position:0%
+development. Um, why don't you pay
+reparations, right, for the the CO2 that
+
+ align:start position:0%
+reparations, right, for the the CO2 that
+ 
+
+ align:start position:0%
+reparations, right, for the the CO2 that
+you've already emitted and help us
+
+ align:start position:0%
+you've already emitted and help us
+ 
+
+ align:start position:0%
+you've already emitted and help us
+decrease our CO2 intensity? And so
+
+ align:start position:0%
+decrease our CO2 intensity? And so
+ 
+
+ align:start position:0%
+decrease our CO2 intensity? And so
+there's these these beautiful arguments
+
+ align:start position:0%
+there's these these beautiful arguments
+ 
+
+ align:start position:0%
+there's these these beautiful arguments
+being constructed on both sides of the
+
+ align:start position:0%
+being constructed on both sides of the
+ 
+
+ align:start position:0%
+being constructed on both sides of the
+debate. Um, what China decided to do, so
+
+ align:start position:0%
+debate. Um, what China decided to do, so
+ 
+
+ align:start position:0%
+debate. Um, what China decided to do, so
+in the international spectrum, not much
+
+ align:start position:0%
+in the international spectrum, not much
+ 
+
+ align:start position:0%
+in the international spectrum, not much
+happened. Um and that's fairly um sadly
+
+ align:start position:0%
+happened. Um and that's fairly um sadly
+ 
+
+ align:start position:0%
+happened. Um and that's fairly um sadly
+it's fairly typical of of of of today's
+
+ align:start position:0%
+it's fairly typical of of of of today's
+ 
+
+ align:start position:0%
+it's fairly typical of of of of today's
+um would say the larger the body happens
+
+ align:start position:0%
+um would say the larger the body happens
+ 
+
+ align:start position:0%
+um would say the larger the body happens
+to be whether it's uh the federal
+
+ align:start position:0%
+to be whether it's uh the federal
+ 
+
+ align:start position:0%
+to be whether it's uh the federal
+government or the world um u
+
+ align:start position:0%
+government or the world um u
+ 
+
+ align:start position:0%
+government or the world um u
+institutions it seems that things happen
+
+ align:start position:0%
+institutions it seems that things happen
+ 
+
+ align:start position:0%
+institutions it seems that things happen
+at a much slower pace the larger uh the
+
+ align:start position:0%
+at a much slower pace the larger uh the
+ 
+
+ align:start position:0%
+at a much slower pace the larger uh the
+the entity is but at a smaller entity
+
+ align:start position:0%
+the entity is but at a smaller entity
+ 
+
+ align:start position:0%
+the entity is but at a smaller entity
+right for example a state level which
+
+ align:start position:0%
+right for example a state level which
+ 
+
+ align:start position:0%
+right for example a state level which
+we'll see in a few slides in the United
+
+ align:start position:0%
+we'll see in a few slides in the United
+ 
+
+ align:start position:0%
+we'll see in a few slides in the United
+States a lot's happening right now um
+
+ align:start position:0%
+States a lot's happening right now um
+ 
+
+ align:start position:0%
+States a lot's happening right now um
+and within China's central government a
+
+ align:start position:0%
+and within China's central government a
+ 
+
+ align:start position:0%
+and within China's central government a
+lot happened in response to some of that
+
+ align:start position:0%
+lot happened in response to some of that
+ 
+
+ align:start position:0%
+lot happened in response to some of that
+criticism they said
+
+ align:start position:0%
+criticism they said
+ 
+
+ align:start position:0%
+criticism they said
+There's a point um more a point that uh
+
+ align:start position:0%
+There's a point um more a point that uh
+ 
+
+ align:start position:0%
+There's a point um more a point that uh
+fossil fuel emissions really decreases
+
+ align:start position:0%
+fossil fuel emissions really decreases
+ 
+
+ align:start position:0%
+fossil fuel emissions really decreases
+our quality of life. If you look at some
+
+ align:start position:0%
+our quality of life. If you look at some
+ 
+
+ align:start position:0%
+our quality of life. If you look at some
+of the pollution in our cities, that's
+
+ align:start position:0%
+of the pollution in our cities, that's
+ 
+
+ align:start position:0%
+of the pollution in our cities, that's
+not very becoming um you know, we we can
+
+ align:start position:0%
+not very becoming um you know, we we can
+ 
+
+ align:start position:0%
+not very becoming um you know, we we can
+do better. Um and furthermore, we can
+
+ align:start position:0%
+do better. Um and furthermore, we can
+ 
+
+ align:start position:0%
+do better. Um and furthermore, we can
+create jobs for the people who are
+
+ align:start position:0%
+create jobs for the people who are
+ 
+
+ align:start position:0%
+create jobs for the people who are
+flooding our cities from the countryside
+
+ align:start position:0%
+flooding our cities from the countryside
+ 
+
+ align:start position:0%
+flooding our cities from the countryside
+looking for economic opportunity. We can
+
+ align:start position:0%
+looking for economic opportunity. We can
+ 
+
+ align:start position:0%
+looking for economic opportunity. We can
+create new jobs in this industry. um and
+
+ align:start position:0%
+create new jobs in this industry. um and
+ 
+
+ align:start position:0%
+create new jobs in this industry. um and
+we'll do it by uh making capital
+
+ align:start position:0%
+we'll do it by uh making capital
+ 
+
+ align:start position:0%
+we'll do it by uh making capital
+available uh to this new nassent
+
+ align:start position:0%
+available uh to this new nassent
+ 
+
+ align:start position:0%
+available uh to this new nassent
+industry at a time when it's very
+
+ align:start position:0%
+industry at a time when it's very
+ 
+
+ align:start position:0%
+industry at a time when it's very
+difficult to achieve capital or acquire
+
+ align:start position:0%
+difficult to achieve capital or acquire
+ 
+
+ align:start position:0%
+difficult to achieve capital or acquire
+capital in the west in Europe and the
+
+ align:start position:0%
+capital in the west in Europe and the
+ 
+
+ align:start position:0%
+capital in the west in Europe and the
+United States. And so that began
+
+ align:start position:0%
+United States. And so that began
+ 
+
+ align:start position:0%
+United States. And so that began
+happening really in the in the mid uh
+
+ align:start position:0%
+happening really in the in the mid uh
+ 
+
+ align:start position:0%
+happening really in the in the mid uh
+2000s. And um what we'll see in a few
+
+ align:start position:0%
+2000s. And um what we'll see in a few
+ 
+
+ align:start position:0%
+2000s. And um what we'll see in a few
+slides is the massive growth of the
+
+ align:start position:0%
+slides is the massive growth of the
+ 
+
+ align:start position:0%
+slides is the massive growth of the
+Chinese manufacturing market in response
+
+ align:start position:0%
+Chinese manufacturing market in response
+ 
+
+ align:start position:0%
+Chinese manufacturing market in response
+to this uh the availability of capital
+
+ align:start position:0%
+to this uh the availability of capital
+ 
+
+ align:start position:0%
+to this uh the availability of capital
+in those countries. Let me um go back to
+
+ align:start position:0%
+in those countries. Let me um go back to
+ 
+
+ align:start position:0%
+in those countries. Let me um go back to
+a slide that I presented. I think it was
+
+ align:start position:0%
+a slide that I presented. I think it was
+ 
+
+ align:start position:0%
+a slide that I presented. I think it was
+lecture number one uh where we looked at
+
+ align:start position:0%
+lecture number one uh where we looked at
+ 
+
+ align:start position:0%
+lecture number one uh where we looked at
+the cumulative production of PV as a
+
+ align:start position:0%
+the cumulative production of PV as a
+ 
+
+ align:start position:0%
+the cumulative production of PV as a
+function of year. And if we plot this on
+
+ align:start position:0%
+function of year. And if we plot this on
+ 
+
+ align:start position:0%
+function of year. And if we plot this on
+a log linear plot, we can read the
+
+ align:start position:0%
+a log linear plot, we can read the
+ 
+
+ align:start position:0%
+a log linear plot, we can read the
+growth rate uh off of the slope of that
+
+ align:start position:0%
+growth rate uh off of the slope of that
+ 
+
+ align:start position:0%
+growth rate uh off of the slope of that
+curve. Right? So this uh was somewhere
+
+ align:start position:0%
+curve. Right? So this uh was somewhere
+ 
+
+ align:start position:0%
+curve. Right? So this uh was somewhere
+around 10% uh 40% maybe upwards to 60%
+
+ align:start position:0%
+around 10% uh 40% maybe upwards to 60%
+ 
+
+ align:start position:0%
+around 10% uh 40% maybe upwards to 60%
+if you uh depending on on on how what
+
+ align:start position:0%
+if you uh depending on on on how what
+ 
+
+ align:start position:0%
+if you uh depending on on on how what
+what data points you include in those
+
+ align:start position:0%
+what data points you include in those
+ 
+
+ align:start position:0%
+what data points you include in those
+lines. Interestingly back in 1990 if we
+
+ align:start position:0%
+lines. Interestingly back in 1990 if we
+ 
+
+ align:start position:0%
+lines. Interestingly back in 1990 if we
+look at the uh distribution of different
+
+ align:start position:0%
+look at the uh distribution of different
+ 
+
+ align:start position:0%
+look at the uh distribution of different
+technologies multi- crystallin silicon
+
+ align:start position:0%
+technologies multi- crystallin silicon
+ 
+
+ align:start position:0%
+technologies multi- crystallin silicon
+was a third single crystal and silicon
+
+ align:start position:0%
+was a third single crystal and silicon
+ 
+
+ align:start position:0%
+was a third single crystal and silicon
+about a third and thin film technology
+
+ align:start position:0%
+about a third and thin film technology
+ 
+
+ align:start position:0%
+about a third and thin film technology
+namely pushed by amorphous silicon was
+
+ align:start position:0%
+namely pushed by amorphous silicon was
+ 
+
+ align:start position:0%
+namely pushed by amorphous silicon was
+about a third of all manufacturing
+
+ align:start position:0%
+about a third of all manufacturing
+ 
+
+ align:start position:0%
+about a third of all manufacturing
+production in um as a market evolved.
+
+ align:start position:0%
+production in um as a market evolved.
+ 
+
+ align:start position:0%
+production in um as a market evolved.
+Sorry about this. Um there we go. So
+
+ align:start position:0%
+Sorry about this. Um there we go. So
+ 
+
+ align:start position:0%
+Sorry about this. Um there we go. So
+again the different technologies just to
+
+ align:start position:0%
+again the different technologies just to
+ 
+
+ align:start position:0%
+again the different technologies just to
+situate ourselves uh single crystal
+
+ align:start position:0%
+situate ourselves uh single crystal
+ 
+
+ align:start position:0%
+situate ourselves uh single crystal
+multi crystallin and thin films as a
+
+ align:start position:0%
+multi crystallin and thin films as a
+ 
+
+ align:start position:0%
+multi crystallin and thin films as a
+market evolved uh going into the 2000s
+
+ align:start position:0%
+market evolved uh going into the 2000s
+ 
+
+ align:start position:0%
+market evolved uh going into the 2000s
+we saw this type of breakdown u occur
+
+ align:start position:0%
+we saw this type of breakdown u occur
+ 
+
+ align:start position:0%
+we saw this type of breakdown u occur
+right we have silicon or crystal and
+
+ align:start position:0%
+right we have silicon or crystal and
+ 
+
+ align:start position:0%
+right we have silicon or crystal and
+silicon comprising around 85 to 90% of
+
+ align:start position:0%
+silicon comprising around 85 to 90% of
+ 
+
+ align:start position:0%
+silicon comprising around 85 to 90% of
+the market and thin films um not growing
+
+ align:start position:0%
+the market and thin films um not growing
+ 
+
+ align:start position:0%
+the market and thin films um not growing
+as fast as crystal and silicon it was
+
+ align:start position:0%
+as fast as crystal and silicon it was
+ 
+
+ align:start position:0%
+as fast as crystal and silicon it was
+still growing the market overall is is
+
+ align:start position:0%
+still growing the market overall is is
+ 
+
+ align:start position:0%
+still growing the market overall is is
+is going gang busters but crystal and
+
+ align:start position:0%
+is going gang busters but crystal and
+ 
+
+ align:start position:0%
+is going gang busters but crystal and
+silicon technology was growing faster
+
+ align:start position:0%
+silicon technology was growing faster
+ 
+
+ align:start position:0%
+silicon technology was growing faster
+than the others
+
+ align:start position:0%
+than the others
+ 
+
+ align:start position:0%
+than the others
+And in part this was due to the fact
+
+ align:start position:0%
+And in part this was due to the fact
+ 
+
+ align:start position:0%
+And in part this was due to the fact
+that crystal and silicon technology was
+
+ align:start position:0%
+that crystal and silicon technology was
+ 
+
+ align:start position:0%
+that crystal and silicon technology was
+you know a bit cheaper uh than than than
+
+ align:start position:0%
+you know a bit cheaper uh than than than
+ 
+
+ align:start position:0%
+you know a bit cheaper uh than than than
+films at the time largely driven by the
+
+ align:start position:0%
+films at the time largely driven by the
+ 
+
+ align:start position:0%
+films at the time largely driven by the
+efficiency parameter that we had just
+
+ align:start position:0%
+efficiency parameter that we had just
+ 
+
+ align:start position:0%
+efficiency parameter that we had just
+seen in the previous slides and turnkey
+
+ align:start position:0%
+seen in the previous slides and turnkey
+ 
+
+ align:start position:0%
+seen in the previous slides and turnkey
+equipment was available. So if you had
+
+ align:start position:0%
+equipment was available. So if you had
+ 
+
+ align:start position:0%
+equipment was available. So if you had
+capital someplace in the world anywhere
+
+ align:start position:0%
+capital someplace in the world anywhere
+ 
+
+ align:start position:0%
+capital someplace in the world anywhere
+in the world and the labor and
+
+ align:start position:0%
+in the world and the labor and
+ 
+
+ align:start position:0%
+in the world and the labor and
+commodities uh were such that you could
+
+ align:start position:0%
+commodities uh were such that you could
+ 
+
+ align:start position:0%
+commodities uh were such that you could
+compete in the market and the um the
+
+ align:start position:0%
+compete in the market and the um the
+ 
+
+ align:start position:0%
+compete in the market and the um the
+shipping costs weren't ex extremely uh
+
+ align:start position:0%
+shipping costs weren't ex extremely uh
+ 
+
+ align:start position:0%
+shipping costs weren't ex extremely uh
+prohibitive to to get your product to
+
+ align:start position:0%
+prohibitive to to get your product to
+ 
+
+ align:start position:0%
+prohibitive to to get your product to
+the most interesting markets in the
+
+ align:start position:0%
+the most interesting markets in the
+ 
+
+ align:start position:0%
+the most interesting markets in the
+world. um you could compete because you
+
+ align:start position:0%
+world. um you could compete because you
+ 
+
+ align:start position:0%
+world. um you could compete because you
+could buy turnkey equipment. Even if you
+
+ align:start position:0%
+could buy turnkey equipment. Even if you
+ 
+
+ align:start position:0%
+could buy turnkey equipment. Even if you
+knew nothing about how to manufacture a
+
+ align:start position:0%
+knew nothing about how to manufacture a
+ 
+
+ align:start position:0%
+knew nothing about how to manufacture a
+solar cell, knew nothing about
+
+ align:start position:0%
+solar cell, knew nothing about
+ 
+
+ align:start position:0%
+solar cell, knew nothing about
+semiconductors or solid state physics,
+
+ align:start position:0%
+semiconductors or solid state physics,
+ 
+
+ align:start position:0%
+semiconductors or solid state physics,
+what we had discussed here in this
+
+ align:start position:0%
+what we had discussed here in this
+ 
+
+ align:start position:0%
+what we had discussed here in this
+class, you could still go out and buy a
+
+ align:start position:0%
+class, you could still go out and buy a
+ 
+
+ align:start position:0%
+class, you could still go out and buy a
+turnkey manufacturing line and get
+
+ align:start position:0%
+turnkey manufacturing line and get
+ 
+
+ align:start position:0%
+turnkey manufacturing line and get
+technicians to come in and teach you how
+
+ align:start position:0%
+technicians to come in and teach you how
+ 
+
+ align:start position:0%
+technicians to come in and teach you how
+to manufacture solar cells, right? That
+
+ align:start position:0%
+to manufacture solar cells, right? That
+ 
+
+ align:start position:0%
+to manufacture solar cells, right? That
+was the beauty of of these equipment
+
+ align:start position:0%
+was the beauty of of these equipment
+ 
+
+ align:start position:0%
+was the beauty of of these equipment
+companies. And so, uh the equipment
+
+ align:start position:0%
+companies. And so, uh the equipment
+ 
+
+ align:start position:0%
+companies. And so, uh the equipment
+companies specialized in crystal and
+
+ align:start position:0%
+companies specialized in crystal and
+ 
+
+ align:start position:0%
+companies specialized in crystal and
+silicon technologies. And as such, many
+
+ align:start position:0%
+silicon technologies. And as such, many
+ 
+
+ align:start position:0%
+silicon technologies. And as such, many
+of the turnkey lines that grew up um out
+
+ align:start position:0%
+of the turnkey lines that grew up um out
+ 
+
+ align:start position:0%
+of the turnkey lines that grew up um out
+of the uh out of green field uh
+
+ align:start position:0%
+of the uh out of green field uh
+ 
+
+ align:start position:0%
+of the uh out of green field uh
+factories in um especially in in in in
+
+ align:start position:0%
+factories in um especially in in in in
+ 
+
+ align:start position:0%
+factories in um especially in in in in
+China uh Taiwan and other places around
+
+ align:start position:0%
+China uh Taiwan and other places around
+ 
+
+ align:start position:0%
+China uh Taiwan and other places around
+the world leverage these turnkey
+
+ align:start position:0%
+the world leverage these turnkey
+ 
+
+ align:start position:0%
+the world leverage these turnkey
+manufacturers to a great
+
+ align:start position:0%
+manufacturers to a great
+ 
+
+ align:start position:0%
+manufacturers to a great
+extent. Okay, sorry about this. We'll go
+
+ align:start position:0%
+extent. Okay, sorry about this. We'll go
+ 
+
+ align:start position:0%
+extent. Okay, sorry about this. We'll go
+forward. So price, markets, and
+
+ align:start position:0%
+forward. So price, markets, and
+ 
+
+ align:start position:0%
+forward. So price, markets, and
+subsidies, we're going to be looking at
+
+ align:start position:0%
+subsidies, we're going to be looking at
+ 
+
+ align:start position:0%
+subsidies, we're going to be looking at
+um it's a bit of a hodgepodge in the
+
+ align:start position:0%
+um it's a bit of a hodgepodge in the
+ 
+
+ align:start position:0%
+um it's a bit of a hodgepodge in the
+sense that we're addressing cost, price,
+
+ align:start position:0%
+sense that we're addressing cost, price,
+ 
+
+ align:start position:0%
+sense that we're addressing cost, price,
+and manufacturing all together in one
+
+ align:start position:0%
+and manufacturing all together in one
+ 
+
+ align:start position:0%
+and manufacturing all together in one
+big stew. I think that's useful because
+
+ align:start position:0%
+big stew. I think that's useful because
+ 
+
+ align:start position:0%
+big stew. I think that's useful because
+the three are interrelated, right? A
+
+ align:start position:0%
+the three are interrelated, right? A
+ 
+
+ align:start position:0%
+the three are interrelated, right? A
+price is difficult to set without a
+
+ align:start position:0%
+price is difficult to set without a
+ 
+
+ align:start position:0%
+price is difficult to set without a
+cost. and the manufacturing is part of
+
+ align:start position:0%
+cost. and the manufacturing is part of
+ 
+
+ align:start position:0%
+cost. and the manufacturing is part of
+that that story and can help us tease
+
+ align:start position:0%
+that that story and can help us tease
+ 
+
+ align:start position:0%
+that that story and can help us tease
+apart what exactly is going on right now
+
+ align:start position:0%
+apart what exactly is going on right now
+ 
+
+ align:start position:0%
+apart what exactly is going on right now
+with Celindra with solar world and so
+
+ align:start position:0%
+with Celindra with solar world and so
+ 
+
+ align:start position:0%
+with Celindra with solar world and so
+forth. Okay, so let's start with
+
+ align:start position:0%
+forth. Okay, so let's start with
+ 
+
+ align:start position:0%
+forth. Okay, so let's start with
+customer needs just to acquaint
+
+ align:start position:0%
+customer needs just to acquaint
+ 
+
+ align:start position:0%
+customer needs just to acquaint
+ourselves. If we're talking about price,
+
+ align:start position:0%
+ourselves. If we're talking about price,
+ 
+
+ align:start position:0%
+ourselves. If we're talking about price,
+we can't uh divorce price from a c from
+
+ align:start position:0%
+we can't uh divorce price from a c from
+ 
+
+ align:start position:0%
+we can't uh divorce price from a c from
+our customer. And in terms of what our
+
+ align:start position:0%
+our customer. And in terms of what our
+ 
+
+ align:start position:0%
+our customer. And in terms of what our
+customer needs are, we have on-grid
+
+ align:start position:0%
+customer needs are, we have on-grid
+ 
+
+ align:start position:0%
+customer needs are, we have on-grid
+applications that's represented by for
+
+ align:start position:0%
+applications that's represented by for
+ 
+
+ align:start position:0%
+applications that's represented by for
+example a solar system on my house on
+
+ align:start position:0%
+example a solar system on my house on
+ 
+
+ align:start position:0%
+example a solar system on my house on
+the student center. These are systems
+
+ align:start position:0%
+the student center. These are systems
+ 
+
+ align:start position:0%
+the student center. These are systems
+that are tied to the grid and using the
+
+ align:start position:0%
+that are tied to the grid and using the
+ 
+
+ align:start position:0%
+that are tied to the grid and using the
+grid as a battery to store the the
+
+ align:start position:0%
+grid as a battery to store the the
+ 
+
+ align:start position:0%
+grid as a battery to store the the
+excess energy. um off-grid. This
+
+ align:start position:0%
+excess energy. um off-grid. This
+ 
+
+ align:start position:0%
+excess energy. um off-grid. This
+represents for example the lighting
+
+ align:start position:0%
+represents for example the lighting
+ 
+
+ align:start position:0%
+represents for example the lighting
+Africa project here within our our our
+
+ align:start position:0%
+Africa project here within our our our
+ 
+
+ align:start position:0%
+Africa project here within our our our
+uh our class. Uh these are folks who
+
+ align:start position:0%
+uh our class. Uh these are folks who
+ 
+
+ align:start position:0%
+uh our class. Uh these are folks who
+don't have access to an electrical grid
+
+ align:start position:0%
+don't have access to an electrical grid
+ 
+
+ align:start position:0%
+don't have access to an electrical grid
+and who uh need to have that uh
+
+ align:start position:0%
+and who uh need to have that uh
+ 
+
+ align:start position:0%
+and who uh need to have that uh
+electricity there. So while people on
+
+ align:start position:0%
+electricity there. So while people on
+ 
+
+ align:start position:0%
+electricity there. So while people on
+the grid are worried about cents per
+
+ align:start position:0%
+the grid are worried about cents per
+ 
+
+ align:start position:0%
+the grid are worried about cents per
+kilowatt hour, people off the grid might
+
+ align:start position:0%
+kilowatt hour, people off the grid might
+ 
+
+ align:start position:0%
+kilowatt hour, people off the grid might
+be worried about the dollars per hour of
+
+ align:start position:0%
+be worried about the dollars per hour of
+ 
+
+ align:start position:0%
+be worried about the dollars per hour of
+light, right? That might be their metric
+
+ align:start position:0%
+light, right? That might be their metric
+ 
+
+ align:start position:0%
+light, right? That might be their metric
+of of merit. So from the customer's
+
+ align:start position:0%
+of of merit. So from the customer's
+ 
+
+ align:start position:0%
+of of merit. So from the customer's
+perspective, what is their value? What
+
+ align:start position:0%
+perspective, what is their value? What
+ 
+
+ align:start position:0%
+perspective, what is their value? What
+do they get from the solar uh uh PV
+
+ align:start position:0%
+do they get from the solar uh uh PV
+ 
+
+ align:start position:0%
+do they get from the solar uh uh PV
+system on the roof? These parameters
+
+ align:start position:0%
+system on the roof? These parameters
+ 
+
+ align:start position:0%
+system on the roof? These parameters
+under here, underneath each of the
+
+ align:start position:0%
+under here, underneath each of the
+ 
+
+ align:start position:0%
+under here, underneath each of the
+pictures, represent the value parameter.
+
+ align:start position:0%
+pictures, represent the value parameter.
+ 
+
+ align:start position:0%
+pictures, represent the value parameter.
+And again, it's a it's a very cartoonish
+
+ align:start position:0%
+And again, it's a it's a very cartoonish
+ 
+
+ align:start position:0%
+And again, it's a it's a very cartoonish
+way of thinking about it. It's a lot
+
+ align:start position:0%
+way of thinking about it. It's a lot
+ 
+
+ align:start position:0%
+way of thinking about it. It's a lot
+more complex when you start getting into
+
+ align:start position:0%
+more complex when you start getting into
+ 
+
+ align:start position:0%
+more complex when you start getting into
+the weeds and figure out what the
+
+ align:start position:0%
+the weeds and figure out what the
+ 
+
+ align:start position:0%
+the weeds and figure out what the
+customer actually wants. Reliability
+
+ align:start position:0%
+customer actually wants. Reliability
+ 
+
+ align:start position:0%
+customer actually wants. Reliability
+factors in, access to the product, um,
+
+ align:start position:0%
+factors in, access to the product, um,
+ 
+
+ align:start position:0%
+factors in, access to the product, um,
+repair, uh, reliability and so forth
+
+ align:start position:0%
+repair, uh, reliability and so forth
+ 
+
+ align:start position:0%
+repair, uh, reliability and so forth
+factor in as well. There are many
+
+ align:start position:0%
+factor in as well. There are many
+ 
+
+ align:start position:0%
+factor in as well. There are many
+factors that add into value. But what
+
+ align:start position:0%
+factors that add into value. But what
+ 
+
+ align:start position:0%
+factors that add into value. But what
+I've done or what we've done here is is
+
+ align:start position:0%
+I've done or what we've done here is is
+ 
+
+ align:start position:0%
+I've done or what we've done here is is
+emphasize the biggest levers, if you
+
+ align:start position:0%
+emphasize the biggest levers, if you
+ 
+
+ align:start position:0%
+emphasize the biggest levers, if you
+will, and some of the biggest
+
+ align:start position:0%
+will, and some of the biggest
+ 
+
+ align:start position:0%
+will, and some of the biggest
+differences between different
+
+ align:start position:0%
+differences between different
+ 
+
+ align:start position:0%
+differences between different
+applications of PV. Um, if you're
+
+ align:start position:0%
+applications of PV. Um, if you're
+ 
+
+ align:start position:0%
+applications of PV. Um, if you're
+looking at uh the uh solar panels on top
+
+ align:start position:0%
+looking at uh the uh solar panels on top
+ 
+
+ align:start position:0%
+looking at uh the uh solar panels on top
+of the Toyota Prius, um you might not
+
+ align:start position:0%
+of the Toyota Prius, um you might not
+ 
+
+ align:start position:0%
+of the Toyota Prius, um you might not
+really care about the cents per kilowatt
+
+ align:start position:0%
+really care about the cents per kilowatt
+ 
+
+ align:start position:0%
+really care about the cents per kilowatt
+hour because you're paying $20,000 for
+
+ align:start position:0%
+hour because you're paying $20,000 for
+ 
+
+ align:start position:0%
+hour because you're paying $20,000 for
+your car. Um so what's a few extra
+
+ align:start position:0%
+your car. Um so what's a few extra
+ 
+
+ align:start position:0%
+your car. Um so what's a few extra
+dollars here or there, but you might
+
+ align:start position:0%
+dollars here or there, but you might
+ 
+
+ align:start position:0%
+dollars here or there, but you might
+care about the watts per meter squared,
+
+ align:start position:0%
+care about the watts per meter squared,
+ 
+
+ align:start position:0%
+care about the watts per meter squared,
+which is really an efficiency parameter.
+
+ align:start position:0%
+which is really an efficiency parameter.
+ 
+
+ align:start position:0%
+which is really an efficiency parameter.
+You might want it to satisfy a certain
+
+ align:start position:0%
+You might want it to satisfy a certain
+ 
+
+ align:start position:0%
+You might want it to satisfy a certain
+function that it could not do otherwise
+
+ align:start position:0%
+function that it could not do otherwise
+ 
+
+ align:start position:0%
+function that it could not do otherwise
+if the panel was too low efficiency. If
+
+ align:start position:0%
+if the panel was too low efficiency. If
+ 
+
+ align:start position:0%
+if the panel was too low efficiency. If
+you're sending something into outer
+
+ align:start position:0%
+you're sending something into outer
+ 
+
+ align:start position:0%
+you're sending something into outer
+space, again, you might not care about
+
+ align:start position:0%
+space, again, you might not care about
+ 
+
+ align:start position:0%
+space, again, you might not care about
+the manufacturing cost of the panel
+
+ align:start position:0%
+the manufacturing cost of the panel
+ 
+
+ align:start position:0%
+the manufacturing cost of the panel
+because the shipment costs, in other
+
+ align:start position:0%
+because the shipment costs, in other
+ 
+
+ align:start position:0%
+because the shipment costs, in other
+words, the putting it onto the rocket
+
+ align:start position:0%
+words, the putting it onto the rocket
+ 
+
+ align:start position:0%
+words, the putting it onto the rocket
+and setting up outer space is $10,000
+
+ align:start position:0%
+and setting up outer space is $10,000
+ 
+
+ align:start position:0%
+and setting up outer space is $10,000
+per kilogram, right? You might be more
+
+ align:start position:0%
+per kilogram, right? You might be more
+ 
+
+ align:start position:0%
+per kilogram, right? You might be more
+worried about how much does it weigh?
+
+ align:start position:0%
+worried about how much does it weigh?
+ 
+
+ align:start position:0%
+worried about how much does it weigh?
+What is the specific power of the solar
+
+ align:start position:0%
+What is the specific power of the solar
+ 
+
+ align:start position:0%
+What is the specific power of the solar
+panels? Likewise, if you're installing
+
+ align:start position:0%
+panels? Likewise, if you're installing
+ 
+
+ align:start position:0%
+panels? Likewise, if you're installing
+them on a big box company, for example,
+
+ align:start position:0%
+them on a big box company, for example,
+ 
+
+ align:start position:0%
+them on a big box company, for example,
+Walmart or Kmart, and you have a big
+
+ align:start position:0%
+Walmart or Kmart, and you have a big
+ 
+
+ align:start position:0%
+Walmart or Kmart, and you have a big
+flat roof that isn't very strong, isn't
+
+ align:start position:0%
+flat roof that isn't very strong, isn't
+ 
+
+ align:start position:0%
+flat roof that isn't very strong, isn't
+well reinforced, you might care about
+
+ align:start position:0%
+well reinforced, you might care about
+ 
+
+ align:start position:0%
+well reinforced, you might care about
+that parameter as well, or the grams per
+
+ align:start position:0%
+that parameter as well, or the grams per
+ 
+
+ align:start position:0%
+that parameter as well, or the grams per
+meter squared. Um, sure that factors in
+
+ align:start position:0%
+meter squared. Um, sure that factors in
+ 
+
+ align:start position:0%
+meter squared. Um, sure that factors in
+somewhere. Actually, it doesn't. So, um,
+
+ align:start position:0%
+somewhere. Actually, it doesn't. So, um,
+ 
+
+ align:start position:0%
+somewhere. Actually, it doesn't. So, um,
+there are many other parameters that
+
+ align:start position:0%
+there are many other parameters that
+ 
+
+ align:start position:0%
+there are many other parameters that
+that could matter for a particular
+
+ align:start position:0%
+that could matter for a particular
+ 
+
+ align:start position:0%
+that could matter for a particular
+application. Um, dollars per meter
+
+ align:start position:0%
+application. Um, dollars per meter
+ 
+
+ align:start position:0%
+application. Um, dollars per meter
+squared per aesthetics for a building
+
+ align:start position:0%
+squared per aesthetics for a building
+ 
+
+ align:start position:0%
+squared per aesthetics for a building
+integrated system. Um, I've had
+
+ align:start position:0%
+integrated system. Um, I've had
+ 
+
+ align:start position:0%
+integrated system. Um, I've had
+architects come to me and say, "Can you
+
+ align:start position:0%
+architects come to me and say, "Can you
+ 
+
+ align:start position:0%
+architects come to me and say, "Can you
+make a a yellow solar panel? I'd really
+
+ align:start position:0%
+make a a yellow solar panel? I'd really
+ 
+
+ align:start position:0%
+make a a yellow solar panel? I'd really
+like a yellow solar panel." And here I
+
+ align:start position:0%
+like a yellow solar panel." And here I
+ 
+
+ align:start position:0%
+like a yellow solar panel." And here I
+am thinking of the solar spectrum and
+
+ align:start position:0%
+am thinking of the solar spectrum and
+ 
+
+ align:start position:0%
+am thinking of the solar spectrum and
+seeing the biggest the peak of the solar
+
+ align:start position:0%
+seeing the biggest the peak of the solar
+ 
+
+ align:start position:0%
+seeing the biggest the peak of the solar
+spectrum being reflected away from the
+
+ align:start position:0%
+spectrum being reflected away from the
+ 
+
+ align:start position:0%
+spectrum being reflected away from the
+panel into the the observer's eye and
+
+ align:start position:0%
+panel into the the observer's eye and
+ 
+
+ align:start position:0%
+panel into the the observer's eye and
+thinking, "Well, I can make it kind of
+
+ align:start position:0%
+thinking, "Well, I can make it kind of
+ 
+
+ align:start position:0%
+thinking, "Well, I can make it kind of
+dark
+
+ align:start position:0%
+dark
+ 
+
+ align:start position:0%
+dark
+yellowish." Okay, how much are you
+
+ align:start position:0%
+yellowish." Okay, how much are you
+ 
+
+ align:start position:0%
+yellowish." Okay, how much are you
+willing to pay? Um, and uh, you know,
+
+ align:start position:0%
+willing to pay? Um, and uh, you know,
+ 
+
+ align:start position:0%
+willing to pay? Um, and uh, you know,
+there there are many different
+
+ align:start position:0%
+there there are many different
+ 
+
+ align:start position:0%
+there there are many different
+parameters here that matter for the
+
+ align:start position:0%
+parameters here that matter for the
+ 
+
+ align:start position:0%
+parameters here that matter for the
+customer. Um, this one right here is a
+
+ align:start position:0%
+customer. Um, this one right here is a
+ 
+
+ align:start position:0%
+customer. Um, this one right here is a
+concentrator system. So you have these
+
+ align:start position:0%
+concentrator system. So you have these
+ 
+
+ align:start position:0%
+concentrator system. So you have these
+optics that concentrate the light into a
+
+ align:start position:0%
+optics that concentrate the light into a
+ 
+
+ align:start position:0%
+optics that concentrate the light into a
+small little spot. Um and they're
+
+ align:start position:0%
+small little spot. Um and they're
+ 
+
+ align:start position:0%
+small little spot. Um and they're
+looking at the watts per millimeter
+
+ align:start position:0%
+looking at the watts per millimeter
+ 
+
+ align:start position:0%
+looking at the watts per millimeter
+squared, right? A very small device. How
+
+ align:start position:0%
+squared, right? A very small device. How
+ 
+
+ align:start position:0%
+squared, right? A very small device. How
+much power does it output? Um the cost
+
+ align:start position:0%
+much power does it output? Um the cost
+ 
+
+ align:start position:0%
+much power does it output? Um the cost
+of the actual device is almost
+
+ align:start position:0%
+of the actual device is almost
+ 
+
+ align:start position:0%
+of the actual device is almost
+irrelevant. Um it's the power output
+
+ align:start position:0%
+irrelevant. Um it's the power output
+ 
+
+ align:start position:0%
+irrelevant. Um it's the power output
+that matters because uh the majority of
+
+ align:start position:0%
+that matters because uh the majority of
+ 
+
+ align:start position:0%
+that matters because uh the majority of
+the cost is sunk in and all the
+
+ align:start position:0%
+the cost is sunk in and all the
+ 
+
+ align:start position:0%
+the cost is sunk in and all the
+commodity materials around it. All
+
+ align:start position:0%
+commodity materials around it. All
+ 
+
+ align:start position:0%
+commodity materials around it. All
+right. So we're we're getting into this
+
+ align:start position:0%
+right. So we're we're getting into this
+ 
+
+ align:start position:0%
+right. So we're we're getting into this
+because we're going to focus largely on
+
+ align:start position:0%
+because we're going to focus largely on
+ 
+
+ align:start position:0%
+because we're going to focus largely on
+on-grid applications and I'm going to
+
+ align:start position:0%
+on-grid applications and I'm going to
+ 
+
+ align:start position:0%
+on-grid applications and I'm going to
+explain to you why. If you're in the
+
+ align:start position:0%
+explain to you why. If you're in the
+ 
+
+ align:start position:0%
+explain to you why. If you're in the
+Lighting Africa project, you probably
+
+ align:start position:0%
+Lighting Africa project, you probably
+ 
+
+ align:start position:0%
+Lighting Africa project, you probably
+care mostly about that. Um but the
+
+ align:start position:0%
+care mostly about that. Um but the
+ 
+
+ align:start position:0%
+care mostly about that. Um but the
+on-grid applications currently comprise
+
+ align:start position:0%
+on-grid applications currently comprise
+ 
+
+ align:start position:0%
+on-grid applications currently comprise
+95% of the current market. Substitution
+
+ align:start position:0%
+95% of the current market. Substitution
+ 
+
+ align:start position:0%
+95% of the current market. Substitution
+economics. We're substituting um PV with
+
+ align:start position:0%
+economics. We're substituting um PV with
+ 
+
+ align:start position:0%
+economics. We're substituting um PV with
+uh or we're substituting fossil fuel
+
+ align:start position:0%
+uh or we're substituting fossil fuel
+ 
+
+ align:start position:0%
+uh or we're substituting fossil fuel
+based power. Um on average in the United
+
+ align:start position:0%
+based power. Um on average in the United
+ 
+
+ align:start position:0%
+based power. Um on average in the United
+States somewhere around 600 gram of CO2
+
+ align:start position:0%
+States somewhere around 600 gram of CO2
+ 
+
+ align:start position:0%
+States somewhere around 600 gram of CO2
+per kilowatt hour. Um we're substituting
+
+ align:start position:0%
+per kilowatt hour. Um we're substituting
+ 
+
+ align:start position:0%
+per kilowatt hour. Um we're substituting
+that with PV which is on the order of
+
+ align:start position:0%
+that with PV which is on the order of
+ 
+
+ align:start position:0%
+that with PV which is on the order of
+factor of 5 to 20 lower. Um so what
+
+ align:start position:0%
+factor of 5 to 20 lower. Um so what
+ 
+
+ align:start position:0%
+factor of 5 to 20 lower. Um so what
+types of grid electricity will PV
+
+ align:start position:0%
+types of grid electricity will PV
+ 
+
+ align:start position:0%
+types of grid electricity will PV
+substitute? uh what does this mean for
+
+ align:start position:0%
+substitute? uh what does this mean for
+ 
+
+ align:start position:0%
+substitute? uh what does this mean for
+traditional generation companies also
+
+ align:start position:0%
+traditional generation companies also
+ 
+
+ align:start position:0%
+traditional generation companies also
+called genkos and what is the fair
+
+ align:start position:0%
+called genkos and what is the fair
+ 
+
+ align:start position:0%
+called genkos and what is the fair
+selling price for PV electricity very
+
+ align:start position:0%
+selling price for PV electricity very
+ 
+
+ align:start position:0%
+selling price for PV electricity very
+interesting question so in terms of
+
+ align:start position:0%
+interesting question so in terms of
+ 
+
+ align:start position:0%
+interesting question so in terms of
+markets um this is just a breakdown of
+
+ align:start position:0%
+markets um this is just a breakdown of
+ 
+
+ align:start position:0%
+markets um this is just a breakdown of
+off-grid consumer applications and
+
+ align:start position:0%
+off-grid consumer applications and
+ 
+
+ align:start position:0%
+off-grid consumer applications and
+on-grid when I first got into this
+
+ align:start position:0%
+on-grid when I first got into this
+ 
+
+ align:start position:0%
+on-grid when I first got into this
+somewhere around here um it was broken
+
+ align:start position:0%
+somewhere around here um it was broken
+ 
+
+ align:start position:0%
+somewhere around here um it was broken
+down about 50/50 PV on grid and off-grid
+
+ align:start position:0%
+down about 50/50 PV on grid and off-grid
+ 
+
+ align:start position:0%
+down about 50/50 PV on grid and off-grid
+today um today much further down uh
+
+ align:start position:0%
+today um today much further down uh
+ 
+
+ align:start position:0%
+today um today much further down uh
+off-grid applications probably below 10%
+
+ align:start position:0%
+off-grid applications probably below 10%
+ 
+
+ align:start position:0%
+off-grid applications probably below 10%
+% I don't know the precise numbers for
+
+ align:start position:0%
+% I don't know the precise numbers for
+ 
+
+ align:start position:0%
+% I don't know the precise numbers for
+you but it's it's stayed relatively flat
+
+ align:start position:0%
+you but it's it's stayed relatively flat
+ 
+
+ align:start position:0%
+you but it's it's stayed relatively flat
+compared to the growth rate of the
+
+ align:start position:0%
+compared to the growth rate of the
+ 
+
+ align:start position:0%
+compared to the growth rate of the
+on-grid. Um and the reasons for this
+
+ align:start position:0%
+on-grid. Um and the reasons for this
+ 
+
+ align:start position:0%
+on-grid. Um and the reasons for this
+we'll see in a couple of slides. Um
+
+ align:start position:0%
+we'll see in a couple of slides. Um
+ 
+
+ align:start position:0%
+we'll see in a couple of slides. Um
+these are this is the value of PV
+
+ align:start position:0%
+these are this is the value of PV
+ 
+
+ align:start position:0%
+these are this is the value of PV
+electricity uh per a 2008 report. Um if
+
+ align:start position:0%
+electricity uh per a 2008 report. Um if
+ 
+
+ align:start position:0%
+electricity uh per a 2008 report. Um if
+you look at um what is easily
+
+ align:start position:0%
+you look at um what is easily
+ 
+
+ align:start position:0%
+you look at um what is easily
+monetized easily monetized depending on
+
+ align:start position:0%
+monetized easily monetized depending on
+ 
+
+ align:start position:0%
+monetized easily monetized depending on
+the policy in a particular case um you
+
+ align:start position:0%
+the policy in a particular case um you
+ 
+
+ align:start position:0%
+the policy in a particular case um you
+have uh the cost of fuel uh the cost of
+
+ align:start position:0%
+have uh the cost of fuel uh the cost of
+ 
+
+ align:start position:0%
+have uh the cost of fuel uh the cost of
+of capital typically for a power plant.
+
+ align:start position:0%
+of capital typically for a power plant.
+ 
+
+ align:start position:0%
+of capital typically for a power plant.
+Um the CO2 emissions offset this is if
+
+ align:start position:0%
+Um the CO2 emissions offset this is if
+ 
+
+ align:start position:0%
+Um the CO2 emissions offset this is if
+you have a price of carbon notice how
+
+ align:start position:0%
+you have a price of carbon notice how
+ 
+
+ align:start position:0%
+you have a price of carbon notice how
+small it actually is leading a lot of
+
+ align:start position:0%
+small it actually is leading a lot of
+ 
+
+ align:start position:0%
+small it actually is leading a lot of
+people to conclude that maybe carbon
+
+ align:start position:0%
+people to conclude that maybe carbon
+ 
+
+ align:start position:0%
+people to conclude that maybe carbon
+pricing isn't the biggest lever uh for
+
+ align:start position:0%
+pricing isn't the biggest lever uh for
+ 
+
+ align:start position:0%
+pricing isn't the biggest lever uh for
+bringing PV onto the grid. That's a
+
+ align:start position:0%
+bringing PV onto the grid. That's a
+ 
+
+ align:start position:0%
+bringing PV onto the grid. That's a
+whole another discussion. We can have
+
+ align:start position:0%
+whole another discussion. We can have
+ 
+
+ align:start position:0%
+whole another discussion. We can have
+that later. Uh grid losses. These are
+
+ align:start position:0%
+that later. Uh grid losses. These are
+ 
+
+ align:start position:0%
+that later. Uh grid losses. These are
+the transmission and distribution
+
+ align:start position:0%
+the transmission and distribution
+ 
+
+ align:start position:0%
+the transmission and distribution
+losses. The difference between having
+
+ align:start position:0%
+losses. The difference between having
+ 
+
+ align:start position:0%
+losses. The difference between having
+the PV mounted or distributed power
+
+ align:start position:0%
+the PV mounted or distributed power
+ 
+
+ align:start position:0%
+the PV mounted or distributed power
+generation source mounted right on the
+
+ align:start position:0%
+generation source mounted right on the
+ 
+
+ align:start position:0%
+generation source mounted right on the
+site of use as opposed to a centralized
+
+ align:start position:0%
+site of use as opposed to a centralized
+ 
+
+ align:start position:0%
+site of use as opposed to a centralized
+location that has to distribute
+
+ align:start position:0%
+location that has to distribute
+ 
+
+ align:start position:0%
+location that has to distribute
+it. These are much more difficult to
+
+ align:start position:0%
+it. These are much more difficult to
+ 
+
+ align:start position:0%
+it. These are much more difficult to
+monetize and you can add in here health
+
+ align:start position:0%
+monetize and you can add in here health
+ 
+
+ align:start position:0%
+monetize and you can add in here health
+impacts related to emissions and so
+
+ align:start position:0%
+impacts related to emissions and so
+ 
+
+ align:start position:0%
+impacts related to emissions and so
+forth. Um you're you're looking at uh
+
+ align:start position:0%
+forth. Um you're you're looking at uh
+ 
+
+ align:start position:0%
+forth. Um you're you're looking at uh
+the security the reduced risk of having
+
+ align:start position:0%
+the security the reduced risk of having
+ 
+
+ align:start position:0%
+the security the reduced risk of having
+a product on uh producing electricity at
+
+ align:start position:0%
+a product on uh producing electricity at
+ 
+
+ align:start position:0%
+a product on uh producing electricity at
+a certain known price for 20 years.
+
+ align:start position:0%
+a certain known price for 20 years.
+ 
+
+ align:start position:0%
+a certain known price for 20 years.
+You're also looking at um tax bonuses.
+
+ align:start position:0%
+You're also looking at um tax bonuses.
+ 
+
+ align:start position:0%
+You're also looking at um tax bonuses.
+These are are tricky because uh tax
+
+ align:start position:0%
+These are are tricky because uh tax
+ 
+
+ align:start position:0%
+These are are tricky because uh tax
+policy can change. Um you're looking at
+
+ align:start position:0%
+policy can change. Um you're looking at
+ 
+
+ align:start position:0%
+policy can change. Um you're looking at
+uncertainty in your raw feed stock
+
+ align:start position:0%
+uncertainty in your raw feed stock
+ 
+
+ align:start position:0%
+uncertainty in your raw feed stock
+material, the fuel. Um and the need for
+
+ align:start position:0%
+material, the fuel. Um and the need for
+ 
+
+ align:start position:0%
+material, the fuel. Um and the need for
+backup uh is is something that reduces
+
+ align:start position:0%
+backup uh is is something that reduces
+ 
+
+ align:start position:0%
+backup uh is is something that reduces
+the value of PV electricity. Right? If
+
+ align:start position:0%
+the value of PV electricity. Right? If
+ 
+
+ align:start position:0%
+the value of PV electricity. Right? If
+you at some point in the future will
+
+ align:start position:0%
+you at some point in the future will
+ 
+
+ align:start position:0%
+you at some point in the future will
+need to uh back up PV power with
+
+ align:start position:0%
+need to uh back up PV power with
+ 
+
+ align:start position:0%
+need to uh back up PV power with
+something that is uh more dispatchable
+
+ align:start position:0%
+something that is uh more dispatchable
+ 
+
+ align:start position:0%
+something that is uh more dispatchable
+and is still an uncertainty in the power
+
+ align:start position:0%
+and is still an uncertainty in the power
+ 
+
+ align:start position:0%
+and is still an uncertainty in the power
+grid, uh that's something that is um
+
+ align:start position:0%
+grid, uh that's something that is um
+ 
+
+ align:start position:0%
+grid, uh that's something that is um
+reducing the value of installing the PV
+
+ align:start position:0%
+reducing the value of installing the PV
+ 
+
+ align:start position:0%
+reducing the value of installing the PV
+today. Some might argue that that 1 cent
+
+ align:start position:0%
+today. Some might argue that that 1 cent
+ 
+
+ align:start position:0%
+today. Some might argue that that 1 cent
+negative is actually a drastic
+
+ align:start position:0%
+negative is actually a drastic
+ 
+
+ align:start position:0%
+negative is actually a drastic
+underestimation of the risk associated
+
+ align:start position:0%
+underestimation of the risk associated
+ 
+
+ align:start position:0%
+underestimation of the risk associated
+with backup power needs. But this is um
+
+ align:start position:0%
+with backup power needs. But this is um
+ 
+
+ align:start position:0%
+with backup power needs. But this is um
+this is a a fair look at what uh a value
+
+ align:start position:0%
+this is a a fair look at what uh a value
+ 
+
+ align:start position:0%
+this is a a fair look at what uh a value
+the the so-called true value of PV
+
+ align:start position:0%
+the the so-called true value of PV
+ 
+
+ align:start position:0%
+the the so-called true value of PV
+electricity might be which would lead us
+
+ align:start position:0%
+electricity might be which would lead us
+ 
+
+ align:start position:0%
+electricity might be which would lead us
+into pricing right if we know the value
+
+ align:start position:0%
+into pricing right if we know the value
+ 
+
+ align:start position:0%
+into pricing right if we know the value
+we can uh enter pricing and not many
+
+ align:start position:0%
+we can uh enter pricing and not many
+ 
+
+ align:start position:0%
+we can uh enter pricing and not many
+people can argue with this because this
+
+ align:start position:0%
+people can argue with this because this
+ 
+
+ align:start position:0%
+people can argue with this because this
+is substitution economics right this is
+
+ align:start position:0%
+is substitution economics right this is
+ 
+
+ align:start position:0%
+is substitution economics right this is
+just saying okay how much does it cost
+
+ align:start position:0%
+just saying okay how much does it cost
+ 
+
+ align:start position:0%
+just saying okay how much does it cost
+uh to produce pe uh fossil fuel
+
+ align:start position:0%
+uh to produce pe uh fossil fuel
+ 
+
+ align:start position:0%
+uh to produce pe uh fossil fuel
+electricity and let's substitute that um
+
+ align:start position:0%
+electricity and let's substitute that um
+ 
+
+ align:start position:0%
+electricity and let's substitute that um
+anything over here in the yellow is what
+
+ align:start position:0%
+anything over here in the yellow is what
+ 
+
+ align:start position:0%
+anything over here in the yellow is what
+people might say well gee if we really
+
+ align:start position:0%
+people might say well gee if we really
+ 
+
+ align:start position:0%
+people might say well gee if we really
+look at the true price or the true cost
+
+ align:start position:0%
+look at the true price or the true cost
+ 
+
+ align:start position:0%
+look at the true price or the true cost
+of fossil fuels. This is what it really
+
+ align:start position:0%
+of fossil fuels. This is what it really
+ 
+
+ align:start position:0%
+of fossil fuels. This is what it really
+costs if we take away all of the
+
+ align:start position:0%
+costs if we take away all of the
+ 
+
+ align:start position:0%
+costs if we take away all of the
+subsidies and add in all of the
+
+ align:start position:0%
+subsidies and add in all of the
+ 
+
+ align:start position:0%
+subsidies and add in all of the
+externalities. What's an
+
+ align:start position:0%
+externalities. What's an
+ 
+
+ align:start position:0%
+externalities. What's an
+externality? What does an externality
+
+ align:start position:0%
+externality? What does an externality
+ 
+
+ align:start position:0%
+externality? What does an externality
+mean?
+
+ align:start position:0%
+mean?
+ 
+
+ align:start position:0%
+mean?
+An
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exter that producer is doing. Yeah. So,
+
+ align:start position:0%
+exter that producer is doing. Yeah. So,
+ 
+
+ align:start position:0%
+exter that producer is doing. Yeah. So,
+when the consumer Oh, or let's put it
+
+ align:start position:0%
+when the consumer Oh, or let's put it
+ 
+
+ align:start position:0%
+when the consumer Oh, or let's put it
+this way. when the
+
+ align:start position:0%
+this way. when the
+ 
+
+ align:start position:0%
+this way. when the
+true impact price impact is not factored
+
+ align:start position:0%
+true impact price impact is not factored
+ 
+
+ align:start position:0%
+true impact price impact is not factored
+into the selling price. Let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say let's say that um I sell you a
+
+ align:start position:0%
+say let's say that um I sell you a
+ 
+
+ align:start position:0%
+say let's say that um I sell you a
+miracle drug and it allows you to be
+
+ align:start position:0%
+miracle drug and it allows you to be
+ 
+
+ align:start position:0%
+miracle drug and it allows you to be
+five times more productive than you are
+
+ align:start position:0%
+five times more productive than you are
+ 
+
+ align:start position:0%
+five times more productive than you are
+right now. Um, but then every time
+
+ align:start position:0%
+right now. Um, but then every time
+ 
+
+ align:start position:0%
+right now. Um, but then every time
+you have your your needs, um, down the
+
+ align:start position:0%
+you have your your needs, um, down the
+ 
+
+ align:start position:0%
+you have your your needs, um, down the
+toilet goes a bunch of chemicals that
+
+ align:start position:0%
+toilet goes a bunch of chemicals that
+ 
+
+ align:start position:0%
+toilet goes a bunch of chemicals that
+the power that the water plant now needs
+
+ align:start position:0%
+the power that the water plant now needs
+ 
+
+ align:start position:0%
+the power that the water plant now needs
+to, uh, filter out. And the the water
+
+ align:start position:0%
+to, uh, filter out. And the the water
+ 
+
+ align:start position:0%
+to, uh, filter out. And the the water
+plant begins failing some of its, uh,
+
+ align:start position:0%
+plant begins failing some of its, uh,
+ 
+
+ align:start position:0%
+plant begins failing some of its, uh,
+its standard tests when they measure
+
+ align:start position:0%
+its standard tests when they measure
+ 
+
+ align:start position:0%
+its standard tests when they measure
+water quality. So, they add in some more
+
+ align:start position:0%
+water quality. So, they add in some more
+ 
+
+ align:start position:0%
+water quality. So, they add in some more
+filters into their uh, into their
+
+ align:start position:0%
+filters into their uh, into their
+ 
+
+ align:start position:0%
+filters into their uh, into their
+system. They figure out how to get rid
+
+ align:start position:0%
+system. They figure out how to get rid
+ 
+
+ align:start position:0%
+system. They figure out how to get rid
+of this compound. And now all of the
+
+ align:start position:0%
+of this compound. And now all of the
+ 
+
+ align:start position:0%
+of this compound. And now all of the
+water treatment facilities around the
+
+ align:start position:0%
+water treatment facilities around the
+ 
+
+ align:start position:0%
+water treatment facilities around the
+country begin adding in these new
+
+ align:start position:0%
+country begin adding in these new
+ 
+
+ align:start position:0%
+country begin adding in these new
+filters. And it costs somewhere on the
+
+ align:start position:0%
+filters. And it costs somewhere on the
+ 
+
+ align:start position:0%
+filters. And it costs somewhere on the
+order of a billion dollars. That is an
+
+ align:start position:0%
+order of a billion dollars. That is an
+ 
+
+ align:start position:0%
+order of a billion dollars. That is an
+externality, right? That's something
+
+ align:start position:0%
+externality, right? That's something
+ 
+
+ align:start position:0%
+externality, right? That's something
+that wasn't factored into the price of
+
+ align:start position:0%
+that wasn't factored into the price of
+ 
+
+ align:start position:0%
+that wasn't factored into the price of
+selling you that miracle drug that
+
+ align:start position:0%
+selling you that miracle drug that
+ 
+
+ align:start position:0%
+selling you that miracle drug that
+allowed you to be five times more
+
+ align:start position:0%
+allowed you to be five times more
+ 
+
+ align:start position:0%
+allowed you to be five times more
+productive. It's it's an example of of
+
+ align:start position:0%
+productive. It's it's an example of of
+ 
+
+ align:start position:0%
+productive. It's it's an example of of
+how everybody pays for uh the acts or
+
+ align:start position:0%
+how everybody pays for uh the acts or
+ 
+
+ align:start position:0%
+how everybody pays for uh the acts or
+the the the purchases of a few, right?
+
+ align:start position:0%
+the the the purchases of a few, right?
+ 
+
+ align:start position:0%
+the the the purchases of a few, right?
+And that's the case with uh with energy
+
+ align:start position:0%
+And that's the case with uh with energy
+ 
+
+ align:start position:0%
+And that's the case with uh with energy
+production as well. Um so it's it's um
+
+ align:start position:0%
+production as well. Um so it's it's um
+ 
+
+ align:start position:0%
+production as well. Um so it's it's um
+it's difficult to argue in economic
+
+ align:start position:0%
+it's difficult to argue in economic
+ 
+
+ align:start position:0%
+it's difficult to argue in economic
+terms or it's difficult to put a a
+
+ align:start position:0%
+terms or it's difficult to put a a
+ 
+
+ align:start position:0%
+terms or it's difficult to put a a
+specific price on externalities because
+
+ align:start position:0%
+specific price on externalities because
+ 
+
+ align:start position:0%
+specific price on externalities because
+these could be things like premature
+
+ align:start position:0%
+these could be things like premature
+ 
+
+ align:start position:0%
+these could be things like premature
+deaths and there are statistitians who
+
+ align:start position:0%
+deaths and there are statistitians who
+ 
+
+ align:start position:0%
+deaths and there are statistitians who
+will calculate the number of people who
+
+ align:start position:0%
+will calculate the number of people who
+ 
+
+ align:start position:0%
+will calculate the number of people who
+die prematurely as a result of exposure
+
+ align:start position:0%
+die prematurely as a result of exposure
+ 
+
+ align:start position:0%
+die prematurely as a result of exposure
+to uh mercury or or cadmium or some
+
+ align:start position:0%
+to uh mercury or or cadmium or some
+ 
+
+ align:start position:0%
+to uh mercury or or cadmium or some
+other emission coming off of a fossil
+
+ align:start position:0%
+other emission coming off of a fossil
+ 
+
+ align:start position:0%
+other emission coming off of a fossil
+fuel burning plant. But then how do you
+
+ align:start position:0%
+fuel burning plant. But then how do you
+ 
+
+ align:start position:0%
+fuel burning plant. But then how do you
+monetize that? You have to assign a
+
+ align:start position:0%
+monetize that? You have to assign a
+ 
+
+ align:start position:0%
+monetize that? You have to assign a
+value to a human life and say that a
+
+ align:start position:0%
+value to a human life and say that a
+ 
+
+ align:start position:0%
+value to a human life and say that a
+certain economic value was lost uh both
+
+ align:start position:0%
+certain economic value was lost uh both
+ 
+
+ align:start position:0%
+certain economic value was lost uh both
+in terms of productivity costs but also
+
+ align:start position:0%
+in terms of productivity costs but also
+ 
+
+ align:start position:0%
+in terms of productivity costs but also
+in terms of the investment due to that
+
+ align:start position:0%
+in terms of the investment due to that
+ 
+
+ align:start position:0%
+in terms of the investment due to that
+person dying and and and they do that in
+
+ align:start position:0%
+person dying and and and they do that in
+ 
+
+ align:start position:0%
+person dying and and and they do that in
+in government. There is a value to a
+
+ align:start position:0%
+in government. There is a value to a
+ 
+
+ align:start position:0%
+in government. There is a value to a
+human life and it can vary somewhat from
+
+ align:start position:0%
+human life and it can vary somewhat from
+ 
+
+ align:start position:0%
+human life and it can vary somewhat from
+one or from one group to another. Um but
+
+ align:start position:0%
+one or from one group to another. Um but
+ 
+
+ align:start position:0%
+one or from one group to another. Um but
+it it it's it's very difficult to price
+
+ align:start position:0%
+it it it's it's very difficult to price
+ 
+
+ align:start position:0%
+it it it's it's very difficult to price
+in externalities and that's why often
+
+ align:start position:0%
+in externalities and that's why often
+ 
+
+ align:start position:0%
+in externalities and that's why often
+times these things in uh yellow here are
+
+ align:start position:0%
+times these things in uh yellow here are
+ 
+
+ align:start position:0%
+times these things in uh yellow here are
+are neglected are not considered and for
+
+ align:start position:0%
+are neglected are not considered and for
+ 
+
+ align:start position:0%
+are neglected are not considered and for
+the purposes of today's discussion we're
+
+ align:start position:0%
+the purposes of today's discussion we're
+ 
+
+ align:start position:0%
+the purposes of today's discussion we're
+just going to factor in mostly these
+
+ align:start position:0%
+just going to factor in mostly these
+ 
+
+ align:start position:0%
+just going to factor in mostly these
+parameters right here because we have a
+
+ align:start position:0%
+parameters right here because we have a
+ 
+
+ align:start position:0%
+parameters right here because we have a
+greater hold on them right um so in
+
+ align:start position:0%
+greater hold on them right um so in
+ 
+
+ align:start position:0%
+greater hold on them right um so in
+terms of PV installations worldwide
+
+ align:start position:0%
+terms of PV installations worldwide
+ 
+
+ align:start position:0%
+terms of PV installations worldwide
+cumulative I I want to compare and
+
+ align:start position:0%
+cumulative I I want to compare and
+ 
+
+ align:start position:0%
+cumulative I I want to compare and
+contrast where our customers are versus
+
+ align:start position:0%
+contrast where our customers are versus
+ 
+
+ align:start position:0%
+contrast where our customers are versus
+where our manufacturing is and we'll get
+
+ align:start position:0%
+where our manufacturing is and we'll get
+ 
+
+ align:start position:0%
+where our manufacturing is and we'll get
+to some really interesting interesting
+
+ align:start position:0%
+to some really interesting interesting
+ 
+
+ align:start position:0%
+to some really interesting interesting
+questions um associated with that. So
+
+ align:start position:0%
+questions um associated with that. So
+ 
+
+ align:start position:0%
+questions um associated with that. So
+look at look at that um where would you
+
+ align:start position:0%
+look at look at that um where would you
+ 
+
+ align:start position:0%
+look at look at that um where would you
+expect PV to be installed? You'd expect
+
+ align:start position:0%
+expect PV to be installed? You'd expect
+ 
+
+ align:start position:0%
+expect PV to be installed? You'd expect
+it to be installed in the sunniest
+
+ align:start position:0%
+it to be installed in the sunniest
+ 
+
+ align:start position:0%
+it to be installed in the sunniest
+places. Why? Because the amount of
+
+ align:start position:0%
+places. Why? Because the amount of
+ 
+
+ align:start position:0%
+places. Why? Because the amount of
+energy produced is related uh
+
+ align:start position:0%
+energy produced is related uh
+ 
+
+ align:start position:0%
+energy produced is related uh
+proportional to the amount of uh solar
+
+ align:start position:0%
+proportional to the amount of uh solar
+ 
+
+ align:start position:0%
+proportional to the amount of uh solar
+resource that's available in that spot.
+
+ align:start position:0%
+resource that's available in that spot.
+ 
+
+ align:start position:0%
+resource that's available in that spot.
+But from a customer's point of view,
+
+ align:start position:0%
+But from a customer's point of view,
+ 
+
+ align:start position:0%
+But from a customer's point of view,
+solar resource isn't everything. They're
+
+ align:start position:0%
+solar resource isn't everything. They're
+ 
+
+ align:start position:0%
+solar resource isn't everything. They're
+also looking at the cost of
+
+ align:start position:0%
+also looking at the cost of
+ 
+
+ align:start position:0%
+also looking at the cost of
+displacement. how much what is the price
+
+ align:start position:0%
+displacement. how much what is the price
+ 
+
+ align:start position:0%
+displacement. how much what is the price
+of the electricity I'm paying and how
+
+ align:start position:0%
+of the electricity I'm paying and how
+ 
+
+ align:start position:0%
+of the electricity I'm paying and how
+much of that can I displace with my PV
+
+ align:start position:0%
+much of that can I displace with my PV
+ 
+
+ align:start position:0%
+much of that can I displace with my PV
+electricity right so there there there's
+
+ align:start position:0%
+electricity right so there there there's
+ 
+
+ align:start position:0%
+electricity right so there there there's
+a more sophisticated uh uh uh concern
+
+ align:start position:0%
+a more sophisticated uh uh uh concern
+ 
+
+ align:start position:0%
+a more sophisticated uh uh uh concern
+here and further the price of
+
+ align:start position:0%
+here and further the price of
+ 
+
+ align:start position:0%
+here and further the price of
+electricity might not only be dictated
+
+ align:start position:0%
+electricity might not only be dictated
+ 
+
+ align:start position:0%
+electricity might not only be dictated
+by uh the true cost of production of the
+
+ align:start position:0%
+by uh the true cost of production of the
+ 
+
+ align:start position:0%
+by uh the true cost of production of the
+solar power of of the fossil fuel power
+
+ align:start position:0%
+solar power of of the fossil fuel power
+ 
+
+ align:start position:0%
+solar power of of the fossil fuel power
+plants there may be a few governments
+
+ align:start position:0%
+plants there may be a few governments
+ 
+
+ align:start position:0%
+plants there may be a few governments
+out there that say well look at all
+
+ align:start position:0%
+out there that say well look at all
+ 
+
+ align:start position:0%
+out there that say well look at all
+these externalities we want to begin
+
+ align:start position:0%
+these externalities we want to begin
+ 
+
+ align:start position:0%
+these externalities we want to begin
+factoring those in we want to provide an
+
+ align:start position:0%
+factoring those in we want to provide an
+ 
+
+ align:start position:0%
+factoring those in we want to provide an
+incentive for people to produce PV
+
+ align:start position:0%
+incentive for people to produce PV
+ 
+
+ align:start position:0%
+incentive for people to produce PV
+electricity that's commonly referred to
+
+ align:start position:0%
+electricity that's commonly referred to
+ 
+
+ align:start position:0%
+electricity that's commonly referred to
+as a subsidy. So if we look at the total
+
+ align:start position:0%
+as a subsidy. So if we look at the total
+ 
+
+ align:start position:0%
+as a subsidy. So if we look at the total
+installation, EU is really leading the
+
+ align:start position:0%
+installation, EU is really leading the
+ 
+
+ align:start position:0%
+installation, EU is really leading the
+charge here. And we saw in those
+
+ align:start position:0%
+charge here. And we saw in those
+ 
+
+ align:start position:0%
+charge here. And we saw in those
+installation maps, there's not a heck of
+
+ align:start position:0%
+installation maps, there's not a heck of
+ 
+
+ align:start position:0%
+installation maps, there's not a heck of
+a lot of sun there in the EU, right?
+
+ align:start position:0%
+a lot of sun there in the EU, right?
+ 
+
+ align:start position:0%
+a lot of sun there in the EU, right?
+Germany's has has uh solar radiance
+
+ align:start position:0%
+Germany's has has uh solar radiance
+ 
+
+ align:start position:0%
+Germany's has has uh solar radiance
+similar to what we have here in the
+
+ align:start position:0%
+similar to what we have here in the
+ 
+
+ align:start position:0%
+similar to what we have here in the
+northeast of the country. And we know
+
+ align:start position:0%
+northeast of the country. And we know
+ 
+
+ align:start position:0%
+northeast of the country. And we know
+that most of the PV installed in the
+
+ align:start position:0%
+that most of the PV installed in the
+ 
+
+ align:start position:0%
+that most of the PV installed in the
+United States is going into the
+
+ align:start position:0%
+United States is going into the
+ 
+
+ align:start position:0%
+United States is going into the
+southwest. um Japan, uh rest of world,
+
+ align:start position:0%
+southwest. um Japan, uh rest of world,
+ 
+
+ align:start position:0%
+southwest. um Japan, uh rest of world,
+USA, relatively small fraction up there.
+
+ align:start position:0%
+USA, relatively small fraction up there.
+ 
+
+ align:start position:0%
+USA, relatively small fraction up there.
+And China, tiny tiny little bleep.
+
+ align:start position:0%
+And China, tiny tiny little bleep.
+ 
+
+ align:start position:0%
+And China, tiny tiny little bleep.
+China's the peach one right up there at
+
+ align:start position:0%
+China's the peach one right up there at
+ 
+
+ align:start position:0%
+China's the peach one right up there at
+the little top. So I would say less than
+
+ align:start position:0%
+the little top. So I would say less than
+ 
+
+ align:start position:0%
+the little top. So I would say less than
+5% of total installed uh worldwide.
+
+ align:start position:0%
+5% of total installed uh worldwide.
+ 
+
+ align:start position:0%
+5% of total installed uh worldwide.
+Actually, it's this is 1.5%. You can
+
+ align:start position:0%
+Actually, it's this is 1.5%. You can
+ 
+
+ align:start position:0%
+Actually, it's this is 1.5%. You can
+read it off right here. Do the division.
+
+ align:start position:0%
+read it off right here. Do the division.
+ 
+
+ align:start position:0%
+read it off right here. Do the division.
+Okay. So um we have very interesting
+
+ align:start position:0%
+Okay. So um we have very interesting
+ 
+
+ align:start position:0%
+Okay. So um we have very interesting
+perspective here about our customers. Um
+
+ align:start position:0%
+perspective here about our customers. Um
+ 
+
+ align:start position:0%
+perspective here about our customers. Um
+this is a breakdown again in in terms of
+
+ align:start position:0%
+this is a breakdown again in in terms of
+ 
+
+ align:start position:0%
+this is a breakdown again in in terms of
+customers. Again, a little bit uh better
+
+ align:start position:0%
+customers. Again, a little bit uh better
+ 
+
+ align:start position:0%
+customers. Again, a little bit uh better
+detail. Instead of just seeing EU, we're
+
+ align:start position:0%
+detail. Instead of just seeing EU, we're
+ 
+
+ align:start position:0%
+detail. Instead of just seeing EU, we're
+looking at uh a variety of different um
+
+ align:start position:0%
+looking at uh a variety of different um
+ 
+
+ align:start position:0%
+looking at uh a variety of different um
+uh of customers. And this is new
+
+ align:start position:0%
+uh of customers. And this is new
+ 
+
+ align:start position:0%
+uh of customers. And this is new
+installations worldwide. So if, for
+
+ align:start position:0%
+installations worldwide. So if, for
+ 
+
+ align:start position:0%
+installations worldwide. So if, for
+example, this blue bar goes down, that
+
+ align:start position:0%
+example, this blue bar goes down, that
+ 
+
+ align:start position:0%
+example, this blue bar goes down, that
+just means we installed less PV this
+
+ align:start position:0%
+just means we installed less PV this
+ 
+
+ align:start position:0%
+just means we installed less PV this
+year than we did last year. It doesn't
+
+ align:start position:0%
+year than we did last year. It doesn't
+ 
+
+ align:start position:0%
+year than we did last year. It doesn't
+mean that the total amount on the grid
+
+ align:start position:0%
+mean that the total amount on the grid
+ 
+
+ align:start position:0%
+mean that the total amount on the grid
+went down. It's just new new PV
+
+ align:start position:0%
+went down. It's just new new PV
+ 
+
+ align:start position:0%
+went down. It's just new new PV
+installs. So the blue down here is now
+
+ align:start position:0%
+installs. So the blue down here is now
+ 
+
+ align:start position:0%
+installs. So the blue down here is now
+Germany. Um, we have these countries
+
+ align:start position:0%
+Germany. Um, we have these countries
+ 
+
+ align:start position:0%
+Germany. Um, we have these countries
+that are like flashes in the pan. Italy,
+
+ align:start position:0%
+that are like flashes in the pan. Italy,
+ 
+
+ align:start position:0%
+that are like flashes in the pan. Italy,
+for example, right? Uh, sorry, Spain.
+
+ align:start position:0%
+for example, right? Uh, sorry, Spain.
+ 
+
+ align:start position:0%
+for example, right? Uh, sorry, Spain.
+This one, Spain grew up really quick and
+
+ align:start position:0%
+This one, Spain grew up really quick and
+ 
+
+ align:start position:0%
+This one, Spain grew up really quick and
+then disappeared. Italy grew up really
+
+ align:start position:0%
+then disappeared. Italy grew up really
+ 
+
+ align:start position:0%
+then disappeared. Italy grew up really
+quick and then shrinking. Um, if we
+
+ align:start position:0%
+quick and then shrinking. Um, if we
+ 
+
+ align:start position:0%
+quick and then shrinking. Um, if we
+extended it out to 2011, it'd be back to
+
+ align:start position:0%
+extended it out to 2011, it'd be back to
+ 
+
+ align:start position:0%
+extended it out to 2011, it'd be back to
+a very small amount. Um, we have USA
+
+ align:start position:0%
+a very small amount. Um, we have USA
+ 
+
+ align:start position:0%
+a very small amount. Um, we have USA
+that's consistently growing. That's a
+
+ align:start position:0%
+that's consistently growing. That's a
+ 
+
+ align:start position:0%
+that's consistently growing. That's a
+nice healthy market. And Germany that's
+
+ align:start position:0%
+nice healthy market. And Germany that's
+ 
+
+ align:start position:0%
+nice healthy market. And Germany that's
+uh growing as well. Um, wow, what a what
+
+ align:start position:0%
+uh growing as well. Um, wow, what a what
+ 
+
+ align:start position:0%
+uh growing as well. Um, wow, what a what
+an interesting dynamic. Why did Spain
+
+ align:start position:0%
+an interesting dynamic. Why did Spain
+ 
+
+ align:start position:0%
+an interesting dynamic. Why did Spain
+have this flash in the pan and then
+
+ align:start position:0%
+have this flash in the pan and then
+ 
+
+ align:start position:0%
+have this flash in the pan and then
+shrink suddenly? What did they do
+
+ align:start position:0%
+shrink suddenly? What did they do
+ 
+
+ align:start position:0%
+shrink suddenly? What did they do
+differently than Germany did? We'll
+
+ align:start position:0%
+differently than Germany did? We'll
+ 
+
+ align:start position:0%
+differently than Germany did? We'll
+start asking those questions and
+
+ align:start position:0%
+start asking those questions and
+ 
+
+ align:start position:0%
+start asking those questions and
+answering them in a few slides. Um, if
+
+ align:start position:0%
+answering them in a few slides. Um, if
+ 
+
+ align:start position:0%
+answering them in a few slides. Um, if
+you really want to get detailed
+
+ align:start position:0%
+you really want to get detailed
+ 
+
+ align:start position:0%
+you really want to get detailed
+information about the US, where PV is
+
+ align:start position:0%
+information about the US, where PV is
+ 
+
+ align:start position:0%
+information about the US, where PV is
+installed in the United States, um, one
+
+ align:start position:0%
+installed in the United States, um, one
+ 
+
+ align:start position:0%
+installed in the United States, um, one
+of your MIT colleagues and a bunch of,
+
+ align:start position:0%
+of your MIT colleagues and a bunch of,
+ 
+
+ align:start position:0%
+of your MIT colleagues and a bunch of,
+uh, ENL folks got together, uh, and put
+
+ align:start position:0%
+uh, ENL folks got together, uh, and put
+ 
+
+ align:start position:0%
+uh, ENL folks got together, uh, and put
+up this beautiful,
+
+ align:start position:0%
+up this beautiful,
+ 
+
+ align:start position:0%
+up this beautiful,
+uh, archive, if you will, compendex of
+
+ align:start position:0%
+uh, archive, if you will, compendex of
+ 
+
+ align:start position:0%
+uh, archive, if you will, compendex of
+all as as many PV installations as they
+
+ align:start position:0%
+all as as many PV installations as they
+ 
+
+ align:start position:0%
+all as as many PV installations as they
+possibly could in the United States. So,
+
+ align:start position:0%
+possibly could in the United States. So,
+ 
+
+ align:start position:0%
+possibly could in the United States. So,
+that's the website. Unfortunately, I
+
+ align:start position:0%
+that's the website. Unfortunately, I
+ 
+
+ align:start position:0%
+that's the website. Unfortunately, I
+didn't include it in your slides. Um, so
+
+ align:start position:0%
+didn't include it in your slides. Um, so
+ 
+
+ align:start position:0%
+didn't include it in your slides. Um, so
+you might want to write that down if
+
+ align:start position:0%
+you might want to write that down if
+ 
+
+ align:start position:0%
+you might want to write that down if
+you're uh, curious about it. Um,
+
+ align:start position:0%
+you're uh, curious about it. Um,
+ 
+
+ align:start position:0%
+you're uh, curious about it. Um,
+wonderful resource. Uh, again, ENL, the
+
+ align:start position:0%
+wonderful resource. Uh, again, ENL, the
+ 
+
+ align:start position:0%
+wonderful resource. Uh, again, ENL, the
+National Renewable Energy Laboratory
+
+ align:start position:0%
+National Renewable Energy Laboratory
+ 
+
+ align:start position:0%
+National Renewable Energy Laboratory
+based in Golden, Colorado. And, uh, you
+
+ align:start position:0%
+based in Golden, Colorado. And, uh, you
+ 
+
+ align:start position:0%
+based in Golden, Colorado. And, uh, you
+can see the install distribution
+
+ align:start position:0%
+can see the install distribution
+ 
+
+ align:start position:0%
+can see the install distribution
+throughout the United States. Again, a
+
+ align:start position:0%
+throughout the United States. Again, a
+ 
+
+ align:start position:0%
+throughout the United States. Again, a
+bias toward states that have, uh, high
+
+ align:start position:0%
+bias toward states that have, uh, high
+ 
+
+ align:start position:0%
+bias toward states that have, uh, high
+electricity prices like New York in
+
+ align:start position:0%
+electricity prices like New York in
+ 
+
+ align:start position:0%
+electricity prices like New York in
+Massachusetts and lots of sun, uh, like
+
+ align:start position:0%
+Massachusetts and lots of sun, uh, like
+ 
+
+ align:start position:0%
+Massachusetts and lots of sun, uh, like
+Arizona. The, uh, price of electricity
+
+ align:start position:0%
+Arizona. The, uh, price of electricity
+ 
+
+ align:start position:0%
+Arizona. The, uh, price of electricity
+is rather low in Arizona. It's below 10
+
+ align:start position:0%
+is rather low in Arizona. It's below 10
+ 
+
+ align:start position:0%
+is rather low in Arizona. It's below 10
+cents per kilowatt hour, but, um, the
+
+ align:start position:0%
+cents per kilowatt hour, but, um, the
+ 
+
+ align:start position:0%
+cents per kilowatt hour, but, um, the
+amount of sun available is is very high.
+
+ align:start position:0%
+amount of sun available is is very high.
+ 
+
+ align:start position:0%
+amount of sun available is is very high.
+whereas California has both. Okay, so we
+
+ align:start position:0%
+whereas California has both. Okay, so we
+ 
+
+ align:start position:0%
+whereas California has both. Okay, so we
+talked about the customer. Now here
+
+ align:start position:0%
+talked about the customer. Now here
+ 
+
+ align:start position:0%
+talked about the customer. Now here
+we're talking about the manufacturers.
+
+ align:start position:0%
+we're talking about the manufacturers.
+ 
+
+ align:start position:0%
+we're talking about the manufacturers.
+So we have the customers, the demand,
+
+ align:start position:0%
+So we have the customers, the demand,
+ 
+
+ align:start position:0%
+So we have the customers, the demand,
+the manufacturers, the supply. This um
+
+ align:start position:0%
+the manufacturers, the supply. This um
+ 
+
+ align:start position:0%
+the manufacturers, the supply. This um
+obviously the the uh manufacturers are
+
+ align:start position:0%
+obviously the the uh manufacturers are
+ 
+
+ align:start position:0%
+obviously the the uh manufacturers are
+growing at the same rate as our
+
+ align:start position:0%
+growing at the same rate as our
+ 
+
+ align:start position:0%
+growing at the same rate as our
+customers are installing even faster. Uh
+
+ align:start position:0%
+customers are installing even faster. Uh
+ 
+
+ align:start position:0%
+customers are installing even faster. Uh
+mind you, inventory rates are almost
+
+ align:start position:0%
+mind you, inventory rates are almost
+ 
+
+ align:start position:0%
+mind you, inventory rates are almost
+somewhere between 25 and 50% nowadays.
+
+ align:start position:0%
+somewhere between 25 and 50% nowadays.
+ 
+
+ align:start position:0%
+somewhere between 25 and 50% nowadays.
+So um the production has grown faster
+
+ align:start position:0%
+So um the production has grown faster
+ 
+
+ align:start position:0%
+So um the production has grown faster
+than the the the demand has um at least
+
+ align:start position:0%
+than the the the demand has um at least
+ 
+
+ align:start position:0%
+than the the the demand has um at least
+at current prices. Um what we've done
+
+ align:start position:0%
+at current prices. Um what we've done
+ 
+
+ align:start position:0%
+at current prices. Um what we've done
+right here or what what is done right
+
+ align:start position:0%
+right here or what what is done right
+ 
+
+ align:start position:0%
+right here or what what is done right
+here is is a normalization um by market
+
+ align:start position:0%
+here is is a normalization um by market
+ 
+
+ align:start position:0%
+here is is a normalization um by market
+share just to demonstrate how the market
+
+ align:start position:0%
+share just to demonstrate how the market
+ 
+
+ align:start position:0%
+share just to demonstrate how the market
+dynamics are changing as the industry
+
+ align:start position:0%
+dynamics are changing as the industry
+ 
+
+ align:start position:0%
+dynamics are changing as the industry
+grows. So from 2005 to 2009 this doesn't
+
+ align:start position:0%
+grows. So from 2005 to 2009 this doesn't
+ 
+
+ align:start position:0%
+grows. So from 2005 to 2009 this doesn't
+mean that the industry stayed flat. It
+
+ align:start position:0%
+mean that the industry stayed flat. It
+ 
+
+ align:start position:0%
+mean that the industry stayed flat. It
+continued growing at a breakneck pace
+
+ align:start position:0%
+continued growing at a breakneck pace
+ 
+
+ align:start position:0%
+continued growing at a breakneck pace
+but uh the um the countries which
+
+ align:start position:0%
+but uh the um the countries which
+ 
+
+ align:start position:0%
+but uh the um the countries which
+comprise the manufacturers have changed
+
+ align:start position:0%
+comprise the manufacturers have changed
+ 
+
+ align:start position:0%
+comprise the manufacturers have changed
+significantly. So let's look at Europe
+
+ align:start position:0%
+significantly. So let's look at Europe
+ 
+
+ align:start position:0%
+significantly. So let's look at Europe
+first off. Europe pretty much you know
+
+ align:start position:0%
+first off. Europe pretty much you know
+ 
+
+ align:start position:0%
+first off. Europe pretty much you know
+started really feeling it during the
+
+ align:start position:0%
+started really feeling it during the
+ 
+
+ align:start position:0%
+started really feeling it during the
+financial crisis. uh they couldn't keep
+
+ align:start position:0%
+financial crisis. uh they couldn't keep
+ 
+
+ align:start position:0%
+financial crisis. uh they couldn't keep
+uh expanding um uh in 2008 uh and then
+
+ align:start position:0%
+uh expanding um uh in 2008 uh and then
+ 
+
+ align:start position:0%
+uh expanding um uh in 2008 uh and then
+when prices really started to drop uh
+
+ align:start position:0%
+when prices really started to drop uh
+ 
+
+ align:start position:0%
+when prices really started to drop uh
+2009 as we saw they didn't continue
+
+ align:start position:0%
+2009 as we saw they didn't continue
+ 
+
+ align:start position:0%
+2009 as we saw they didn't continue
+expanding um were a bit uncompetitive um
+
+ align:start position:0%
+expanding um were a bit uncompetitive um
+ 
+
+ align:start position:0%
+expanding um were a bit uncompetitive um
+US shown here in the uh green again
+
+ align:start position:0%
+US shown here in the uh green again
+ 
+
+ align:start position:0%
+US shown here in the uh green again
+dropping uh India uh I guess sort of uh
+
+ align:start position:0%
+dropping uh India uh I guess sort of uh
+ 
+
+ align:start position:0%
+dropping uh India uh I guess sort of uh
+growing now it's definitely on the
+
+ align:start position:0%
+growing now it's definitely on the
+ 
+
+ align:start position:0%
+growing now it's definitely on the
+upswing Japan decreased considerably
+
+ align:start position:0%
+upswing Japan decreased considerably
+ 
+
+ align:start position:0%
+upswing Japan decreased considerably
+considerably
+
+ align:start position:0%
+considerably
+ 
+
+ align:start position:0%
+considerably
+During the 1990s um in the early 2000s,
+
+ align:start position:0%
+During the 1990s um in the early 2000s,
+ 
+
+ align:start position:0%
+During the 1990s um in the early 2000s,
+Japan had the largest solar company in
+
+ align:start position:0%
+Japan had the largest solar company in
+ 
+
+ align:start position:0%
+Japan had the largest solar company in
+the world, Sharp, better known for micro
+
+ align:start position:0%
+the world, Sharp, better known for micro
+ 
+
+ align:start position:0%
+the world, Sharp, better known for micro
+electronics that you might find around
+
+ align:start position:0%
+electronics that you might find around
+ 
+
+ align:start position:0%
+electronics that you might find around
+your house. Um somehow some way did the
+
+ align:start position:0%
+your house. Um somehow some way did the
+ 
+
+ align:start position:0%
+your house. Um somehow some way did the
+executives at Sharp saw this coming, saw
+
+ align:start position:0%
+executives at Sharp saw this coming, saw
+ 
+
+ align:start position:0%
+executives at Sharp saw this coming, saw
+a huge rise in demand coming from Europe
+
+ align:start position:0%
+a huge rise in demand coming from Europe
+ 
+
+ align:start position:0%
+a huge rise in demand coming from Europe
+and ramped up capacity in Japan. And
+
+ align:start position:0%
+and ramped up capacity in Japan. And
+ 
+
+ align:start position:0%
+and ramped up capacity in Japan. And
+when they did that, they were able to
+
+ align:start position:0%
+when they did that, they were able to
+ 
+
+ align:start position:0%
+when they did that, they were able to
+address large portions of that. They
+
+ align:start position:0%
+address large portions of that. They
+ 
+
+ align:start position:0%
+address large portions of that. They
+made a healthy profit for several years
+
+ align:start position:0%
+made a healthy profit for several years
+ 
+
+ align:start position:0%
+made a healthy profit for several years
+and then they just stopped expanding in
+
+ align:start position:0%
+and then they just stopped expanding in
+ 
+
+ align:start position:0%
+and then they just stopped expanding in
+PV. Part of it might have been they saw
+
+ align:start position:0%
+PV. Part of it might have been they saw
+ 
+
+ align:start position:0%
+PV. Part of it might have been they saw
+the market dynamics changing. They saw
+
+ align:start position:0%
+the market dynamics changing. They saw
+ 
+
+ align:start position:0%
+the market dynamics changing. They saw
+um their costs, their manufacturing
+
+ align:start position:0%
+um their costs, their manufacturing
+ 
+
+ align:start position:0%
+um their costs, their manufacturing
+costs relative to for example China.
+
+ align:start position:0%
+costs relative to for example China.
+ 
+
+ align:start position:0%
+costs relative to for example China.
+This is the orange right here. Um and
+
+ align:start position:0%
+This is the orange right here. Um and
+ 
+
+ align:start position:0%
+This is the orange right here. Um and
+Taiwan uh in the uh above China above
+
+ align:start position:0%
+Taiwan uh in the uh above China above
+ 
+
+ align:start position:0%
+Taiwan uh in the uh above China above
+the orange and comprised today this is
+
+ align:start position:0%
+the orange and comprised today this is
+ 
+
+ align:start position:0%
+the orange and comprised today this is
+2009 numbers. If we fast forward to
+
+ align:start position:0%
+2009 numbers. If we fast forward to
+ 
+
+ align:start position:0%
+2009 numbers. If we fast forward to
+today in 2011, China and Taiwan comprise
+
+ align:start position:0%
+today in 2011, China and Taiwan comprise
+ 
+
+ align:start position:0%
+today in 2011, China and Taiwan comprise
+55 to 60% of the PV industry worldwide
+
+ align:start position:0%
+55 to 60% of the PV industry worldwide
+ 
+
+ align:start position:0%
+55 to 60% of the PV industry worldwide
+production, manufacturing,
+
+ align:start position:0%
+production, manufacturing,
+ 
+
+ align:start position:0%
+production, manufacturing,
+production. So what does that mean?
+
+ align:start position:0%
+production. So what does that mean?
+ 
+
+ align:start position:0%
+production. So what does that mean?
+Let's explore together some of the uh
+
+ align:start position:0%
+Let's explore together some of the uh
+ 
+
+ align:start position:0%
+Let's explore together some of the uh
+the interesting um results of that. Um
+
+ align:start position:0%
+the interesting um results of that. Um
+ 
+
+ align:start position:0%
+the interesting um results of that. Um
+let's let's look at some of the good
+
+ align:start position:0%
+let's let's look at some of the good
+ 
+
+ align:start position:0%
+let's let's look at some of the good
+things. Um what are some of the good
+
+ align:start position:0%
+things. Um what are some of the good
+ 
+
+ align:start position:0%
+things. Um what are some of the good
+things about um production going to uh
+
+ align:start position:0%
+things about um production going to uh
+ 
+
+ align:start position:0%
+things about um production going to uh
+China and uh Taiwan from say Europe and
+
+ align:start position:0%
+China and uh Taiwan from say Europe and
+ 
+
+ align:start position:0%
+China and uh Taiwan from say Europe and
+the United States of solar panels? Let's
+
+ align:start position:0%
+the United States of solar panels? Let's
+ 
+
+ align:start position:0%
+the United States of solar panels? Let's
+look at that for a sec. So we'll look at
+
+ align:start position:0%
+look at that for a sec. So we'll look at
+ 
+
+ align:start position:0%
+look at that for a sec. So we'll look at
+the glass half full perspective. What
+
+ align:start position:0%
+the glass half full perspective. What
+ 
+
+ align:start position:0%
+the glass half full perspective. What
+are some of the good things? Yeah. More
+
+ align:start position:0%
+are some of the good things? Yeah. More
+ 
+
+ align:start position:0%
+are some of the good things? Yeah. More
+likely that these developing countries
+
+ align:start position:0%
+likely that these developing countries
+ 
+
+ align:start position:0%
+likely that these developing countries
+will use solar panels. More likely the
+
+ align:start position:0%
+will use solar panels. More likely the
+ 
+
+ align:start position:0%
+will use solar panels. More likely the
+developing countries will use solar
+
+ align:start position:0%
+developing countries will use solar
+ 
+
+ align:start position:0%
+developing countries will use solar
+panels. Well um was that the case over
+
+ align:start position:0%
+panels. Well um was that the case over
+ 
+
+ align:start position:0%
+panels. Well um was that the case over
+here? Not really. Right. It's growing.
+
+ align:start position:0%
+here? Not really. Right. It's growing.
+ 
+
+ align:start position:0%
+here? Not really. Right. It's growing.
+it's going um okay uh I suppose if the
+
+ align:start position:0%
+it's going um okay uh I suppose if the
+ 
+
+ align:start position:0%
+it's going um okay uh I suppose if the
+technology is available there um maybe
+
+ align:start position:0%
+technology is available there um maybe
+ 
+
+ align:start position:0%
+technology is available there um maybe
+the technology quite isn't isn't quite
+
+ align:start position:0%
+the technology quite isn't isn't quite
+ 
+
+ align:start position:0%
+the technology quite isn't isn't quite
+cost competitive with local um
+
+ align:start position:0%
+cost competitive with local um
+ 
+
+ align:start position:0%
+cost competitive with local um
+electricity yet so there isn't that
+
+ align:start position:0%
+electricity yet so there isn't that
+ 
+
+ align:start position:0%
+electricity yet so there isn't that
+demand pull locally um maybe the
+
+ align:start position:0%
+demand pull locally um maybe the
+ 
+
+ align:start position:0%
+demand pull locally um maybe the
+realization is that well goodness we can
+
+ align:start position:0%
+realization is that well goodness we can
+ 
+
+ align:start position:0%
+realization is that well goodness we can
+address this European market they're
+
+ align:start position:0%
+address this European market they're
+ 
+
+ align:start position:0%
+address this European market they're
+willing to pay a lot more for the panels
+
+ align:start position:0%
+willing to pay a lot more for the panels
+ 
+
+ align:start position:0%
+willing to pay a lot more for the panels
+than we are um so we might as well
+
+ align:start position:0%
+than we are um so we might as well
+ 
+
+ align:start position:0%
+than we are um so we might as well
+export right now but at some point in
+
+ align:start position:0%
+export right now but at some point in
+ 
+
+ align:start position:0%
+export right now but at some point in
+the future we might be able to satisfy
+
+ align:start position:0%
+the future we might be able to satisfy
+ 
+
+ align:start position:0%
+the future we might be able to satisfy
+internal demand yeah and there are
+
+ align:start position:0%
+internal demand yeah and there are
+ 
+
+ align:start position:0%
+internal demand yeah and there are
+gigawatt plants PV installs going up in
+
+ align:start position:0%
+gigawatt plants PV installs going up in
+ 
+
+ align:start position:0%
+gigawatt plants PV installs going up in
+China right now. Um in part uh due to
+
+ align:start position:0%
+China right now. Um in part uh due to
+ 
+
+ align:start position:0%
+China right now. Um in part uh due to
+increased electricity demand, in part
+
+ align:start position:0%
+increased electricity demand, in part
+ 
+
+ align:start position:0%
+increased electricity demand, in part
+due to weakening demand elsewhere in the
+
+ align:start position:0%
+due to weakening demand elsewhere in the
+ 
+
+ align:start position:0%
+due to weakening demand elsewhere in the
+world and a very large manufacturing
+
+ align:start position:0%
+world and a very large manufacturing
+ 
+
+ align:start position:0%
+world and a very large manufacturing
+base in China that has to put their
+
+ align:start position:0%
+base in China that has to put their
+ 
+
+ align:start position:0%
+base in China that has to put their
+panels out somewhere, right? U so there
+
+ align:start position:0%
+panels out somewhere, right? U so there
+ 
+
+ align:start position:0%
+panels out somewhere, right? U so there
+is um yes adoption. I'll I'll I'll seed
+
+ align:start position:0%
+is um yes adoption. I'll I'll I'll seed
+ 
+
+ align:start position:0%
+is um yes adoption. I'll I'll I'll seed
+that point. Uh yeah, lower cost for the
+
+ align:start position:0%
+that point. Uh yeah, lower cost for the
+ 
+
+ align:start position:0%
+that point. Uh yeah, lower cost for the
+consumer. Lower lower cost for the
+
+ align:start position:0%
+consumer. Lower lower cost for the
+ 
+
+ align:start position:0%
+consumer. Lower lower cost for the
+consumer. Yes. So in uh in the United
+
+ align:start position:0%
+consumer. Yes. So in uh in the United
+ 
+
+ align:start position:0%
+consumer. Yes. So in uh in the United
+States, if we look at the price of
+
+ align:start position:0%
+States, if we look at the price of
+ 
+
+ align:start position:0%
+States, if we look at the price of
+installing a PV system in the United
+
+ align:start position:0%
+installing a PV system in the United
+ 
+
+ align:start position:0%
+installing a PV system in the United
+States, uh the uh price of installing
+
+ align:start position:0%
+States, uh the uh price of installing
+ 
+
+ align:start position:0%
+States, uh the uh price of installing
+the PV system is around
+
+ align:start position:0%
+the PV system is around
+ 
+
+ align:start position:0%
+the PV system is around
+$520 on your roof uh today. The cost of
+
+ align:start position:0%
+$520 on your roof uh today. The cost of
+ 
+
+ align:start position:0%
+$520 on your roof uh today. The cost of
+buying the module is around $1.3,
+
+ align:start position:0%
+buying the module is around $1.3,
+ 
+
+ align:start position:0%
+buying the module is around $1.3,
+$15 from China, right? And so that means
+
+ align:start position:0%
+$15 from China, right? And so that means
+ 
+
+ align:start position:0%
+$15 from China, right? And so that means
+that 80% of the profit margin right now
+
+ align:start position:0%
+that 80% of the profit margin right now
+ 
+
+ align:start position:0%
+that 80% of the profit margin right now
+is being gobbled up by a US company,
+
+ align:start position:0%
+is being gobbled up by a US company,
+ 
+
+ align:start position:0%
+is being gobbled up by a US company,
+right? Um, the price came down. Let's
+
+ align:start position:0%
+right? Um, the price came down. Let's
+ 
+
+ align:start position:0%
+right? Um, the price came down. Let's
+see. When when I installed the panels on
+
+ align:start position:0%
+see. When when I installed the panels on
+ 
+
+ align:start position:0%
+see. When when I installed the panels on
+my roof, uh, got a little bit of a
+
+ align:start position:0%
+my roof, uh, got a little bit of a
+ 
+
+ align:start position:0%
+my roof, uh, got a little bit of a
+better deal, but I would say the average
+
+ align:start position:0%
+better deal, but I would say the average
+ 
+
+ align:start position:0%
+better deal, but I would say the average
+uh, price for a PV system in 2007 must
+
+ align:start position:0%
+uh, price for a PV system in 2007 must
+ 
+
+ align:start position:0%
+uh, price for a PV system in 2007 must
+have been somewhere around $8, uh, per
+
+ align:start position:0%
+have been somewhere around $8, uh, per
+ 
+
+ align:start position:0%
+have been somewhere around $8, uh, per
+watt peak. And now the price is down at
+
+ align:start position:0%
+watt peak. And now the price is down at
+ 
+
+ align:start position:0%
+watt peak. And now the price is down at
+around 520. That said, in Europe, in
+
+ align:start position:0%
+around 520. That said, in Europe, in
+ 
+
+ align:start position:0%
+around 520. That said, in Europe, in
+Germany, uh, which has 10 times more
+
+ align:start position:0%
+Germany, uh, which has 10 times more
+ 
+
+ align:start position:0%
+Germany, uh, which has 10 times more
+installed PV than than the US does, um,
+
+ align:start position:0%
+installed PV than than the US does, um,
+ 
+
+ align:start position:0%
+installed PV than than the US does, um,
+the price of installing PV system on
+
+ align:start position:0%
+the price of installing PV system on
+ 
+
+ align:start position:0%
+the price of installing PV system on
+your roof, uh, could be below €3 per
+
+ align:start position:0%
+your roof, uh, could be below €3 per
+ 
+
+ align:start position:0%
+your roof, uh, could be below €3 per
+watt peak, right? So, the the price is
+
+ align:start position:0%
+watt peak, right? So, the the price is
+ 
+
+ align:start position:0%
+watt peak, right? So, the the price is
+lower because the profit margin that the
+
+ align:start position:0%
+lower because the profit margin that the
+ 
+
+ align:start position:0%
+lower because the profit margin that the
+installers are getting right now is
+
+ align:start position:0%
+installers are getting right now is
+ 
+
+ align:start position:0%
+installers are getting right now is
+smaller. So, yes, absolutely lower cost
+
+ align:start position:0%
+smaller. So, yes, absolutely lower cost
+ 
+
+ align:start position:0%
+smaller. So, yes, absolutely lower cost
+product in US markets. uh that isn't the
+
+ align:start position:0%
+product in US markets. uh that isn't the
+ 
+
+ align:start position:0%
+product in US markets. uh that isn't the
+whole story about what you're going to
+
+ align:start position:0%
+whole story about what you're going to
+ 
+
+ align:start position:0%
+whole story about what you're going to
+pay because there's still the installer
+
+ align:start position:0%
+pay because there's still the installer
+ 
+
+ align:start position:0%
+pay because there's still the installer
+that's stuck in between the Chinese
+
+ align:start position:0%
+that's stuck in between the Chinese
+ 
+
+ align:start position:0%
+that's stuck in between the Chinese
+manufacturer of the module and you right
+
+ align:start position:0%
+manufacturer of the module and you right
+ 
+
+ align:start position:0%
+manufacturer of the module and you right
+serving as the middle person uh
+
+ align:start position:0%
+serving as the middle person uh
+ 
+
+ align:start position:0%
+serving as the middle person uh
+providing you value still but but still
+
+ align:start position:0%
+providing you value still but but still
+ 
+
+ align:start position:0%
+providing you value still but but still
+um extracting a very large profit right
+
+ align:start position:0%
+um extracting a very large profit right
+ 
+
+ align:start position:0%
+um extracting a very large profit right
+now uh a disproportionately large profit
+
+ align:start position:0%
+now uh a disproportionately large profit
+ 
+
+ align:start position:0%
+now uh a disproportionately large profit
+shall I say um what are some of the
+
+ align:start position:0%
+shall I say um what are some of the
+ 
+
+ align:start position:0%
+shall I say um what are some of the
+other good things
+
+ align:start position:0%
+other good things
+ 
+
+ align:start position:0%
+other good things
+if uh cost in big markets is reduced
+
+ align:start position:0%
+if uh cost in big markets is reduced
+ 
+
+ align:start position:0%
+if uh cost in big markets is reduced
+that lead to more market penetration
+
+ align:start position:0%
+that lead to more market penetration
+ 
+
+ align:start position:0%
+that lead to more market penetration
+then the product is just adopted more
+
+ align:start position:0%
+then the product is just adopted more
+ 
+
+ align:start position:0%
+then the product is just adopted more
+and even a price to go up, it might
+
+ align:start position:0%
+and even a price to go up, it might
+ 
+
+ align:start position:0%
+and even a price to go up, it might
+maintain.
+
+ align:start position:0%
+maintain.
+ 
+
+ align:start position:0%
+maintain.
+Yep. And so what what what you're
+
+ align:start position:0%
+Yep. And so what what what you're
+ 
+
+ align:start position:0%
+Yep. And so what what what you're
+leading to here is is really what the
+
+ align:start position:0%
+leading to here is is really what the
+ 
+
+ align:start position:0%
+leading to here is is really what the
+demand curve of PV looks like. And in
+
+ align:start position:0%
+demand curve of PV looks like. And in
+ 
+
+ align:start position:0%
+demand curve of PV looks like. And in
+the past, uh if you look at uh what
+
+ align:start position:0%
+the past, uh if you look at uh what
+ 
+
+ align:start position:0%
+the past, uh if you look at uh what
+people are willing to pay for PV, uh
+
+ align:start position:0%
+people are willing to pay for PV, uh
+ 
+
+ align:start position:0%
+people are willing to pay for PV, uh
+let's say let's convert it into dollars
+
+ align:start position:0%
+let's say let's convert it into dollars
+ 
+
+ align:start position:0%
+let's say let's convert it into dollars
+per watt peak since that's the universal
+
+ align:start position:0%
+per watt peak since that's the universal
+ 
+
+ align:start position:0%
+per watt peak since that's the universal
+unit of of PV uh cost. Um and this is
+
+ align:start position:0%
+unit of of PV uh cost. Um and this is
+ 
+
+ align:start position:0%
+unit of of PV uh cost. Um and this is
+the uh let's call it total market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size in terms of watt peak um and this
+
+ align:start position:0%
+size in terms of watt peak um and this
+ 
+
+ align:start position:0%
+size in terms of watt peak um and this
+being a very very large number what you
+
+ align:start position:0%
+being a very very large number what you
+ 
+
+ align:start position:0%
+being a very very large number what you
+can do to first order just how how would
+
+ align:start position:0%
+can do to first order just how how would
+ 
+
+ align:start position:0%
+can do to first order just how how would
+we construct the demand curve for the
+
+ align:start position:0%
+we construct the demand curve for the
+ 
+
+ align:start position:0%
+we construct the demand curve for the
+United States for PV how would we go
+
+ align:start position:0%
+United States for PV how would we go
+ 
+
+ align:start position:0%
+United States for PV how would we go
+about doing
+
+ align:start position:0%
+about doing
+ 
+
+ align:start position:0%
+about doing
+that how much are people willing to pay
+
+ align:start position:0%
+that how much are people willing to pay
+ 
+
+ align:start position:0%
+that how much are people willing to pay
+for their PV modules to offset the cost
+
+ align:start position:0%
+for their PV modules to offset the cost
+ 
+
+ align:start position:0%
+for their PV modules to offset the cost
+of electricity well to do it right we
+
+ align:start position:0%
+of electricity well to do it right we
+ 
+
+ align:start position:0%
+of electricity well to do it right we
+need a levelized cost of electricity
+
+ align:start position:0%
+need a levelized cost of electricity
+ 
+
+ align:start position:0%
+need a levelized cost of electricity
+analysis we'd assume We're borrowing
+
+ align:start position:0%
+analysis we'd assume We're borrowing
+ 
+
+ align:start position:0%
+analysis we'd assume We're borrowing
+money from the bank, do those fancy
+
+ align:start position:0%
+money from the bank, do those fancy
+ 
+
+ align:start position:0%
+money from the bank, do those fancy
+economics that involve uh you know
+
+ align:start position:0%
+economics that involve uh you know
+ 
+
+ align:start position:0%
+economics that involve uh you know
+something to the power of something and
+
+ align:start position:0%
+something to the power of something and
+ 
+
+ align:start position:0%
+something to the power of something and
+and that being the interest rate uh and
+
+ align:start position:0%
+and that being the interest rate uh and
+ 
+
+ align:start position:0%
+and that being the interest rate uh and
+then we we calculate it through just a
+
+ align:start position:0%
+then we we calculate it through just a
+ 
+
+ align:start position:0%
+then we we calculate it through just a
+first order hand wavy Mickey Mousey we
+
+ align:start position:0%
+first order hand wavy Mickey Mousey we
+ 
+
+ align:start position:0%
+first order hand wavy Mickey Mousey we
+might take into consideration the
+
+ align:start position:0%
+might take into consideration the
+ 
+
+ align:start position:0%
+might take into consideration the
+manufacturing cost of the module sorry
+
+ align:start position:0%
+manufacturing cost of the module sorry
+ 
+
+ align:start position:0%
+manufacturing cost of the module sorry
+back up one step we might take into
+
+ align:start position:0%
+back up one step we might take into
+ 
+
+ align:start position:0%
+back up one step we might take into
+consideration the cents per kilowatt
+
+ align:start position:0%
+consideration the cents per kilowatt
+ 
+
+ align:start position:0%
+consideration the cents per kilowatt
+hour of the electricity that we're uh
+
+ align:start position:0%
+hour of the electricity that we're uh
+ 
+
+ align:start position:0%
+hour of the electricity that we're uh
+getting from the grid and the insulation
+
+ align:start position:0%
+getting from the grid and the insulation
+ 
+
+ align:start position:0%
+getting from the grid and the insulation
+the solar resource that is available at
+
+ align:start position:0%
+the solar resource that is available at
+ 
+
+ align:start position:0%
+the solar resource that is available at
+that particular location. So we if we
+
+ align:start position:0%
+that particular location. So we if we
+ 
+
+ align:start position:0%
+that particular location. So we if we
+have data granular to the state level of
+
+ align:start position:0%
+have data granular to the state level of
+ 
+
+ align:start position:0%
+have data granular to the state level of
+the price of electricity on average
+
+ align:start position:0%
+the price of electricity on average
+ 
+
+ align:start position:0%
+the price of electricity on average
+throughout the state and the solar
+
+ align:start position:0%
+throughout the state and the solar
+ 
+
+ align:start position:0%
+throughout the state and the solar
+resource availability on average
+
+ align:start position:0%
+resource availability on average
+ 
+
+ align:start position:0%
+resource availability on average
+throughout the state we can immediately
+
+ align:start position:0%
+throughout the state we can immediately
+ 
+
+ align:start position:0%
+throughout the state we can immediately
+comprise 150 markets in the US
+
+ align:start position:0%
+comprise 150 markets in the US
+ 
+
+ align:start position:0%
+comprise 150 markets in the US
+residential commercial industrial right
+
+ align:start position:0%
+residential commercial industrial right
+ 
+
+ align:start position:0%
+residential commercial industrial right
+for 50 states and then we'll have a
+
+ align:start position:0%
+for 50 states and then we'll have a
+ 
+
+ align:start position:0%
+for 50 states and then we'll have a
+demand curve very simple one for how
+
+ align:start position:0%
+demand curve very simple one for how
+ 
+
+ align:start position:0%
+demand curve very simple one for how
+much people are willing to pay for their
+
+ align:start position:0%
+much people are willing to pay for their
+ 
+
+ align:start position:0%
+much people are willing to pay for their
+PV electricity and it looks more or less
+
+ align:start position:0%
+PV electricity and it looks more or less
+ 
+
+ align:start position:0%
+PV electricity and it looks more or less
+like this if you start working it
+
+ align:start position:0%
+like this if you start working it
+ 
+
+ align:start position:0%
+like this if you start working it
+out rough sketch rough sketch this is
+
+ align:start position:0%
+out rough sketch rough sketch this is
+ 
+
+ align:start position:0%
+out rough sketch rough sketch this is
+Hawaii. Those poor critters over there,
+
+ align:start position:0%
+Hawaii. Those poor critters over there,
+ 
+
+ align:start position:0%
+Hawaii. Those poor critters over there,
+although they have beautiful sun and
+
+ align:start position:0%
+although they have beautiful sun and
+ 
+
+ align:start position:0%
+although they have beautiful sun and
+enjoy a wonderful life, they're paying a
+
+ align:start position:0%
+enjoy a wonderful life, they're paying a
+ 
+
+ align:start position:0%
+enjoy a wonderful life, they're paying a
+lot for their energy because they're on
+
+ align:start position:0%
+lot for their energy because they're on
+ 
+
+ align:start position:0%
+lot for their energy because they're on
+a few rocks out there, they have no
+
+ align:start position:0%
+a few rocks out there, they have no
+ 
+
+ align:start position:0%
+a few rocks out there, they have no
+natural resource under the ground to
+
+ align:start position:0%
+natural resource under the ground to
+ 
+
+ align:start position:0%
+natural resource under the ground to
+speak of, except geothermal, I suppose.
+
+ align:start position:0%
+speak of, except geothermal, I suppose.
+ 
+
+ align:start position:0%
+speak of, except geothermal, I suppose.
+Um, but uh they're shipping in a lot of
+
+ align:start position:0%
+Um, but uh they're shipping in a lot of
+ 
+
+ align:start position:0%
+Um, but uh they're shipping in a lot of
+their fuel. That's why if you've ever
+
+ align:start position:0%
+their fuel. That's why if you've ever
+ 
+
+ align:start position:0%
+their fuel. That's why if you've ever
+gone to Hawaii and rented a car, you are
+
+ align:start position:0%
+gone to Hawaii and rented a car, you are
+ 
+
+ align:start position:0%
+gone to Hawaii and rented a car, you are
+surprised at this the sticker shock when
+
+ align:start position:0%
+surprised at this the sticker shock when
+ 
+
+ align:start position:0%
+surprised at this the sticker shock when
+you go up to the gas station and try to
+
+ align:start position:0%
+you go up to the gas station and try to
+ 
+
+ align:start position:0%
+you go up to the gas station and try to
+refuel. Um, their uh price of
+
+ align:start position:0%
+refuel. Um, their uh price of
+ 
+
+ align:start position:0%
+refuel. Um, their uh price of
+electricity is above 30 cents per
+
+ align:start position:0%
+electricity is above 30 cents per
+ 
+
+ align:start position:0%
+electricity is above 30 cents per
+kilowatt hour residential.
+
+ align:start position:0%
+kilowatt hour residential.
+ 
+
+ align:start position:0%
+kilowatt hour residential.
+Um, but it's a very very tiny market.
+
+ align:start position:0%
+Um, but it's a very very tiny market.
+ 
+
+ align:start position:0%
+Um, but it's a very very tiny market.
+So, you're not going to be able to
+
+ align:start position:0%
+So, you're not going to be able to
+ 
+
+ align:start position:0%
+So, you're not going to be able to
+satisfy much demand. You're not going to
+
+ align:start position:0%
+satisfy much demand. You're not going to
+ 
+
+ align:start position:0%
+satisfy much demand. You're not going to
+be a prod produce too many panels there.
+
+ align:start position:0%
+be a prod produce too many panels there.
+ 
+
+ align:start position:0%
+be a prod produce too many panels there.
+You start having interesting thing hap
+
+ align:start position:0%
+You start having interesting thing hap
+ 
+
+ align:start position:0%
+You start having interesting thing hap
+things happen when you start hitting the
+
+ align:start position:0%
+things happen when you start hitting the
+ 
+
+ align:start position:0%
+things happen when you start hitting the
+bigger markets like the tiers four and
+
+ align:start position:0%
+bigger markets like the tiers four and
+ 
+
+ align:start position:0%
+bigger markets like the tiers four and
+five of California, Texas, New York.
+
+ align:start position:0%
+five of California, Texas, New York.
+ 
+
+ align:start position:0%
+five of California, Texas, New York.
+These are big markets that have a lot of
+
+ align:start position:0%
+These are big markets that have a lot of
+ 
+
+ align:start position:0%
+These are big markets that have a lot of
+people in them and they have larger
+
+ align:start position:0%
+people in them and they have larger
+ 
+
+ align:start position:0%
+people in them and they have larger
+electricity prices andor large solar
+
+ align:start position:0%
+electricity prices andor large solar
+ 
+
+ align:start position:0%
+electricity prices andor large solar
+resource uh uh available there. And so
+
+ align:start position:0%
+resource uh uh available there. And so
+ 
+
+ align:start position:0%
+resource uh uh available there. And so
+at some point the demand curve reaches
+
+ align:start position:0%
+at some point the demand curve reaches
+ 
+
+ align:start position:0%
+at some point the demand curve reaches
+these plateaus where if you decrease the
+
+ align:start position:0%
+these plateaus where if you decrease the
+ 
+
+ align:start position:0%
+these plateaus where if you decrease the
+price even a little bit all of a sudden
+
+ align:start position:0%
+price even a little bit all of a sudden
+ 
+
+ align:start position:0%
+price even a little bit all of a sudden
+voom the amount of market that you can
+
+ align:start position:0%
+voom the amount of market that you can
+ 
+
+ align:start position:0%
+voom the amount of market that you can
+address right for this amount of of
+
+ align:start position:0%
+address right for this amount of of
+ 
+
+ align:start position:0%
+address right for this amount of of
+price decrease the amount of market that
+
+ align:start position:0%
+price decrease the amount of market that
+ 
+
+ align:start position:0%
+price decrease the amount of market that
+you can address is huge. And so the
+
+ align:start position:0%
+you can address is huge. And so the
+ 
+
+ align:start position:0%
+you can address is huge. And so the
+slope of this line the slope of the
+
+ align:start position:0%
+slope of this line the slope of the
+ 
+
+ align:start position:0%
+slope of this line the slope of the
+demand curve is indicative of what
+
+ align:start position:0%
+demand curve is indicative of what
+ 
+
+ align:start position:0%
+demand curve is indicative of what
+happens when you reduce your price just
+
+ align:start position:0%
+happens when you reduce your price just
+ 
+
+ align:start position:0%
+happens when you reduce your price just
+a little bit. And so yes, producing
+
+ align:start position:0%
+a little bit. And so yes, producing
+ 
+
+ align:start position:0%
+a little bit. And so yes, producing
+cheaper panels when you start hitting
+
+ align:start position:0%
+cheaper panels when you start hitting
+ 
+
+ align:start position:0%
+cheaper panels when you start hitting
+these plateaus can result in massive
+
+ align:start position:0%
+these plateaus can result in massive
+ 
+
+ align:start position:0%
+these plateaus can result in massive
+massive demand pull or market pull. So
+
+ align:start position:0%
+massive demand pull or market pull. So
+ 
+
+ align:start position:0%
+massive demand pull or market pull. So
+that's another good reason to have cheap
+
+ align:start position:0%
+that's another good reason to have cheap
+ 
+
+ align:start position:0%
+that's another good reason to have cheap
+panels. Let's look at the flip side.
+
+ align:start position:0%
+panels. Let's look at the flip side.
+ 
+
+ align:start position:0%
+panels. Let's look at the flip side.
+What would be um what would be some of
+
+ align:start position:0%
+What would be um what would be some of
+ 
+
+ align:start position:0%
+What would be um what would be some of
+the uh downsides let's say uh to uh
+
+ align:start position:0%
+the uh downsides let's say uh to uh
+ 
+
+ align:start position:0%
+the uh downsides let's say uh to uh
+module manufacturing going into China.
+
+ align:start position:0%
+module manufacturing going into China.
+ 
+
+ align:start position:0%
+module manufacturing going into China.
+This you can assume anything is on the
+
+ align:start position:0%
+This you can assume anything is on the
+ 
+
+ align:start position:0%
+This you can assume anything is on the
+table um CO2 emissions, jobs, etc. Let's
+
+ align:start position:0%
+table um CO2 emissions, jobs, etc. Let's
+ 
+
+ align:start position:0%
+table um CO2 emissions, jobs, etc. Let's
+start teasing into some of those
+
+ align:start position:0%
+start teasing into some of those
+ 
+
+ align:start position:0%
+start teasing into some of those
+questions and and looking at some data.
+
+ align:start position:0%
+questions and and looking at some data.
+ 
+
+ align:start position:0%
+questions and and looking at some data.
+I might flip back and forth during the
+
+ align:start position:0%
+I might flip back and forth during the
+ 
+
+ align:start position:0%
+I might flip back and forth during the
+presentation if we have to address
+
+ align:start position:0%
+presentation if we have to address
+ 
+
+ align:start position:0%
+presentation if we have to address
+specific uh topics. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bad politics if
+
+ align:start position:0%
+bad politics if
+ 
+
+ align:start position:0%
+bad politics if
+American tape manufacturers fail
+
+ align:start position:0%
+American tape manufacturers fail
+ 
+
+ align:start position:0%
+American tape manufacturers fail
+then it reflects poorly on the industry
+
+ align:start position:0%
+then it reflects poorly on the industry
+ 
+
+ align:start position:0%
+then it reflects poorly on the industry
+and American political scene and
+
+ align:start position:0%
+and American political scene and
+ 
+
+ align:start position:0%
+and American political scene and
+decreases support for it. Yep. So um
+
+ align:start position:0%
+decreases support for it. Yep. So um
+ 
+
+ align:start position:0%
+decreases support for it. Yep. So um
+that politics uh in DC uh this is often
+
+ align:start position:0%
+that politics uh in DC uh this is often
+ 
+
+ align:start position:0%
+that politics uh in DC uh this is often
+referred to as the optics of the
+
+ align:start position:0%
+referred to as the optics of the
+ 
+
+ align:start position:0%
+referred to as the optics of the
+situation um how people observe or how
+
+ align:start position:0%
+situation um how people observe or how
+ 
+
+ align:start position:0%
+situation um how people observe or how
+people perceive something. Um the
+
+ align:start position:0%
+people perceive something. Um the
+ 
+
+ align:start position:0%
+people perceive something. Um the
+lititness test is not DC itself. Um I
+
+ align:start position:0%
+lititness test is not DC itself. Um I
+ 
+
+ align:start position:0%
+lititness test is not DC itself. Um I
+was down there on Thursday and everybody
+
+ align:start position:0%
+was down there on Thursday and everybody
+ 
+
+ align:start position:0%
+was down there on Thursday and everybody
+in the solar space was I think it was it
+
+ align:start position:0%
+in the solar space was I think it was it
+ 
+
+ align:start position:0%
+in the solar space was I think it was it
+was Wednesday and Thursday. Yeah. And
+
+ align:start position:0%
+was Wednesday and Thursday. Yeah. And
+ 
+
+ align:start position:0%
+was Wednesday and Thursday. Yeah. And
+everybody in the solar space was
+
+ align:start position:0%
+everybody in the solar space was
+ 
+
+ align:start position:0%
+everybody in the solar space was
+freaking out about uh a particular event
+
+ align:start position:0%
+freaking out about uh a particular event
+ 
+
+ align:start position:0%
+freaking out about uh a particular event
+that was going on in Capitol Hill. I was
+
+ align:start position:0%
+that was going on in Capitol Hill. I was
+ 
+
+ align:start position:0%
+that was going on in Capitol Hill. I was
+telling folks, don't worry. It's not
+
+ align:start position:0%
+telling folks, don't worry. It's not
+ 
+
+ align:start position:0%
+telling folks, don't worry. It's not
+going to I mean in in terms of the rest
+
+ align:start position:0%
+going to I mean in in terms of the rest
+ 
+
+ align:start position:0%
+going to I mean in in terms of the rest
+of the country and the perception of the
+
+ align:start position:0%
+of the country and the perception of the
+ 
+
+ align:start position:0%
+of the country and the perception of the
+rest of the country, it won't be that
+
+ align:start position:0%
+rest of the country, it won't be that
+ 
+
+ align:start position:0%
+rest of the country, it won't be that
+significant. And I'm sure Secretary Chu
+
+ align:start position:0%
+significant. And I'm sure Secretary Chu
+ 
+
+ align:start position:0%
+significant. And I'm sure Secretary Chu
+will do a phenomenal job uh up there in
+
+ align:start position:0%
+will do a phenomenal job uh up there in
+ 
+
+ align:start position:0%
+will do a phenomenal job uh up there in
+in in in front of uh the the
+
+ align:start position:0%
+in in in front of uh the the
+ 
+
+ align:start position:0%
+in in in front of uh the the
+congressional panel. He did phenomenal.
+
+ align:start position:0%
+congressional panel. He did phenomenal.
+ 
+
+ align:start position:0%
+congressional panel. He did phenomenal.
+Um and so people were really really
+
+ align:start position:0%
+Um and so people were really really
+ 
+
+ align:start position:0%
+Um and so people were really really
+worried about something that didn't have
+
+ align:start position:0%
+worried about something that didn't have
+ 
+
+ align:start position:0%
+worried about something that didn't have
+too big of an effect outside. Um granted
+
+ align:start position:0%
+too big of an effect outside. Um granted
+ 
+
+ align:start position:0%
+too big of an effect outside. Um granted
+what people should be worried about is
+
+ align:start position:0%
+what people should be worried about is
+ 
+
+ align:start position:0%
+what people should be worried about is
+the impact for example that this
+
+ align:start position:0%
+the impact for example that this
+ 
+
+ align:start position:0%
+the impact for example that this
+sequestration of discretionary funds
+
+ align:start position:0%
+sequestration of discretionary funds
+ 
+
+ align:start position:0%
+sequestration of discretionary funds
+will have on R&D uh once they start
+
+ align:start position:0%
+will have on R&D uh once they start
+ 
+
+ align:start position:0%
+will have on R&D uh once they start
+kicking in in 2013. Um if you mandate a
+
+ align:start position:0%
+kicking in in 2013. Um if you mandate a
+ 
+
+ align:start position:0%
+kicking in in 2013. Um if you mandate a
+reduced uh funding level for um uh uh
+
+ align:start position:0%
+reduced uh funding level for um uh uh
+ 
+
+ align:start position:0%
+reduced uh funding level for um uh uh
+funding agencies uh you will have an
+
+ align:start position:0%
+funding agencies uh you will have an
+ 
+
+ align:start position:0%
+funding agencies uh you will have an
+impact uh and a long-term one for that
+
+ align:start position:0%
+impact uh and a long-term one for that
+ 
+
+ align:start position:0%
+impact uh and a long-term one for that
+matter.
+
+ align:start position:0%
+matter.
+ 
+
+ align:start position:0%
+matter.
+Um so let's uh let's the optics of the
+
+ align:start position:0%
+Um so let's uh let's the optics of the
+ 
+
+ align:start position:0%
+Um so let's uh let's the optics of the
+situation. Uh there has been a slight
+
+ align:start position:0%
+situation. Uh there has been a slight
+ 
+
+ align:start position:0%
+situation. Uh there has been a slight
+decrease in public support I believe on
+
+ align:start position:0%
+decrease in public support I believe on
+ 
+
+ align:start position:0%
+decrease in public support I believe on
+the order of 5 to 10% um since the
+
+ align:start position:0%
+the order of 5 to 10% um since the
+ 
+
+ align:start position:0%
+the order of 5 to 10% um since the
+beginning of the whole cylinder affair
+
+ align:start position:0%
+beginning of the whole cylinder affair
+ 
+
+ align:start position:0%
+beginning of the whole cylinder affair
+uh support for for solar renewables uh
+
+ align:start position:0%
+uh support for for solar renewables uh
+ 
+
+ align:start position:0%
+uh support for for solar renewables uh
+but the support remains high and still
+
+ align:start position:0%
+but the support remains high and still
+ 
+
+ align:start position:0%
+but the support remains high and still
+continues to be high among uh
+
+ align:start position:0%
+continues to be high among uh
+ 
+
+ align:start position:0%
+continues to be high among uh
+Republicans, Democrats alike. Um
+
+ align:start position:0%
+Republicans, Democrats alike. Um
+ 
+
+ align:start position:0%
+Republicans, Democrats alike. Um
+especially when compared to say
+
+ align:start position:0%
+especially when compared to say
+ 
+
+ align:start position:0%
+especially when compared to say
+congressional approvement uh approval
+
+ align:start position:0%
+congressional approvement uh approval
+ 
+
+ align:start position:0%
+congressional approvement uh approval
+ratings um but let's let's not let's not
+
+ align:start position:0%
+ratings um but let's let's not let's not
+ 
+
+ align:start position:0%
+ratings um but let's let's not let's not
+look look down. Let's compare ourselves
+
+ align:start position:0%
+look look down. Let's compare ourselves
+ 
+
+ align:start position:0%
+look look down. Let's compare ourselves
+to higher. Um what else um what are some
+
+ align:start position:0%
+to higher. Um what else um what are some
+ 
+
+ align:start position:0%
+to higher. Um what else um what are some
+of the potential negatives? Let me let
+
+ align:start position:0%
+of the potential negatives? Let me let
+ 
+
+ align:start position:0%
+of the potential negatives? Let me let
+me start guiding you. Um because there
+
+ align:start position:0%
+me start guiding you. Um because there
+ 
+
+ align:start position:0%
+me start guiding you. Um because there
+you hear so much about bad this jobs
+
+ align:start position:0%
+you hear so much about bad this jobs
+ 
+
+ align:start position:0%
+you hear so much about bad this jobs
+that whatever. Um let me um let me guide
+
+ align:start position:0%
+that whatever. Um let me um let me guide
+ 
+
+ align:start position:0%
+that whatever. Um let me um let me guide
+you into some of the questions that you
+
+ align:start position:0%
+you into some of the questions that you
+ 
+
+ align:start position:0%
+you into some of the questions that you
+might not have thought of.
+
+ align:start position:0%
+might not have thought of.
+ 
+
+ align:start position:0%
+might not have thought of.
+Um there is a colleague of ours in uh
+
+ align:start position:0%
+Um there is a colleague of ours in uh
+ 
+
+ align:start position:0%
+Um there is a colleague of ours in uh
+here at MIT Tim Gatowski's group that is
+
+ align:start position:0%
+here at MIT Tim Gatowski's group that is
+ 
+
+ align:start position:0%
+here at MIT Tim Gatowski's group that is
+looking into matters concerning
+
+ align:start position:0%
+looking into matters concerning
+ 
+
+ align:start position:0%
+looking into matters concerning
+manufacturing of PV and installation of
+
+ align:start position:0%
+manufacturing of PV and installation of
+ 
+
+ align:start position:0%
+manufacturing of PV and installation of
+PV from a CO2 perspective.
+
+ align:start position:0%
+PV from a CO2 perspective.
+ 
+
+ align:start position:0%
+PV from a CO2 perspective.
+So if you manufacture your PV in a
+
+ align:start position:0%
+So if you manufacture your PV in a
+ 
+
+ align:start position:0%
+So if you manufacture your PV in a
+coalrich country that is spewing out
+
+ align:start position:0%
+coalrich country that is spewing out
+ 
+
+ align:start position:0%
+coalrich country that is spewing out
+emissions into the air, um you are going
+
+ align:start position:0%
+emissions into the air, um you are going
+ 
+
+ align:start position:0%
+emissions into the air, um you are going
+to have a greater CO2 intensity per
+
+ align:start position:0%
+to have a greater CO2 intensity per
+ 
+
+ align:start position:0%
+to have a greater CO2 intensity per
+kilowatt hour uh of energy that the
+
+ align:start position:0%
+kilowatt hour uh of energy that the
+ 
+
+ align:start position:0%
+kilowatt hour uh of energy that the
+panels will produce over their lifetime
+
+ align:start position:0%
+panels will produce over their lifetime
+ 
+
+ align:start position:0%
+panels will produce over their lifetime
+than if the panels were produced say in
+
+ align:start position:0%
+than if the panels were produced say in
+ 
+
+ align:start position:0%
+than if the panels were produced say in
+a country that uh fu that has a large
+
+ align:start position:0%
+a country that uh fu that has a large
+ 
+
+ align:start position:0%
+a country that uh fu that has a large
+abundance of hydro power or or uh
+
+ align:start position:0%
+abundance of hydro power or or uh
+ 
+
+ align:start position:0%
+abundance of hydro power or or uh
+geothermal or hey even produces solar
+
+ align:start position:0%
+geothermal or hey even produces solar
+ 
+
+ align:start position:0%
+geothermal or hey even produces solar
+panels using other solar panels. That'd
+
+ align:start position:0%
+panels using other solar panels. That'd
+ 
+
+ align:start position:0%
+panels using other solar panels. That'd
+be nice. Um but in a growth situation
+
+ align:start position:0%
+be nice. Um but in a growth situation
+ 
+
+ align:start position:0%
+be nice. Um but in a growth situation
+where solar is rising or the
+
+ align:start position:0%
+where solar is rising or the
+ 
+
+ align:start position:0%
+where solar is rising or the
+manufacturing capacity is rising at 60%
+
+ align:start position:0%
+manufacturing capacity is rising at 60%
+ 
+
+ align:start position:0%
+manufacturing capacity is rising at 60%
+a year, it's a little bit unfeasible uh
+
+ align:start position:0%
+a year, it's a little bit unfeasible uh
+ 
+
+ align:start position:0%
+a year, it's a little bit unfeasible uh
+to think that solar will power itself
+
+ align:start position:0%
+to think that solar will power itself
+ 
+
+ align:start position:0%
+to think that solar will power itself
+forward. It almost violates one of the
+
+ align:start position:0%
+forward. It almost violates one of the
+ 
+
+ align:start position:0%
+forward. It almost violates one of the
+laws of thermodynamics. Um so we uh we
+
+ align:start position:0%
+laws of thermodynamics. Um so we uh we
+ 
+
+ align:start position:0%
+laws of thermodynamics. Um so we uh we
+look at the CO2 balance, right? Right?
+
+ align:start position:0%
+look at the CO2 balance, right? Right?
+ 
+
+ align:start position:0%
+look at the CO2 balance, right? Right?
+We we think about gee what if um what if
+
+ align:start position:0%
+We we think about gee what if um what if
+ 
+
+ align:start position:0%
+We we think about gee what if um what if
+we were to be smart about where we
+
+ align:start position:0%
+we were to be smart about where we
+ 
+
+ align:start position:0%
+we were to be smart about where we
+manufacture and install
+
+ align:start position:0%
+manufacture and install
+ 
+
+ align:start position:0%
+manufacture and install
+PV then it might make more sense to
+
+ align:start position:0%
+PV then it might make more sense to
+ 
+
+ align:start position:0%
+PV then it might make more sense to
+manufacture PV say in Norway which is
+
+ align:start position:0%
+manufacture PV say in Norway which is
+ 
+
+ align:start position:0%
+manufacture PV say in Norway which is
+based on hydropower and install them in
+
+ align:start position:0%
+based on hydropower and install them in
+ 
+
+ align:start position:0%
+based on hydropower and install them in
+China which is largely running on coal
+
+ align:start position:0%
+China which is largely running on coal
+ 
+
+ align:start position:0%
+China which is largely running on coal
+right so from the CO2 from the global
+
+ align:start position:0%
+right so from the CO2 from the global
+ 
+
+ align:start position:0%
+right so from the CO2 from the global
+carbon perspective um again this these
+
+ align:start position:0%
+carbon perspective um again this these
+ 
+
+ align:start position:0%
+carbon perspective um again this these
+are externalities that aren't being
+
+ align:start position:0%
+are externalities that aren't being
+ 
+
+ align:start position:0%
+are externalities that aren't being
+priced in
+
+ align:start position:0%
+priced in
+ 
+
+ align:start position:0%
+priced in
+okay CO2 and yeah go ahead Please, would
+
+ align:start position:0%
+okay CO2 and yeah go ahead Please, would
+ 
+
+ align:start position:0%
+okay CO2 and yeah go ahead Please, would
+they actually be priced in in Norway
+
+ align:start position:0%
+they actually be priced in in Norway
+ 
+
+ align:start position:0%
+they actually be priced in in Norway
+because they are in the EU emissions
+
+ align:start position:0%
+because they are in the EU emissions
+ 
+
+ align:start position:0%
+because they are in the EU emissions
+trading scheme? I mean, they're not
+
+ align:start position:0%
+trading scheme? I mean, they're not
+ 
+
+ align:start position:0%
+trading scheme? I mean, they're not
+priced in China. Sure. The cost of
+
+ align:start position:0%
+priced in China. Sure. The cost of
+ 
+
+ align:start position:0%
+priced in China. Sure. The cost of
+electricity in Norway doesn't Yeah. So,
+
+ align:start position:0%
+electricity in Norway doesn't Yeah. So,
+ 
+
+ align:start position:0%
+electricity in Norway doesn't Yeah. So,
+so point conceded that in in certain
+
+ align:start position:0%
+so point conceded that in in certain
+ 
+
+ align:start position:0%
+so point conceded that in in certain
+countries, uh, some of the externalities
+
+ align:start position:0%
+countries, uh, some of the externalities
+ 
+
+ align:start position:0%
+countries, uh, some of the externalities
+are factored in, not perhaps at the
+
+ align:start position:0%
+are factored in, not perhaps at the
+ 
+
+ align:start position:0%
+are factored in, not perhaps at the
+levels they should be, but but some are
+
+ align:start position:0%
+levels they should be, but but some are
+ 
+
+ align:start position:0%
+levels they should be, but but some are
+factored in, whereas in other countries
+
+ align:start position:0%
+factored in, whereas in other countries
+ 
+
+ align:start position:0%
+factored in, whereas in other countries
+they're not at all. Um so we have um
+
+ align:start position:0%
+they're not at all. Um so we have um
+ 
+
+ align:start position:0%
+they're not at all. Um so we have um
+what is referred to in some uh in in
+
+ align:start position:0%
+what is referred to in some uh in in
+ 
+
+ align:start position:0%
+what is referred to in some uh in in
+some terms as as an uneven playing field
+
+ align:start position:0%
+some terms as as an uneven playing field
+ 
+
+ align:start position:0%
+some terms as as an uneven playing field
+in the sense that in some places there
+
+ align:start position:0%
+in the sense that in some places there
+ 
+
+ align:start position:0%
+in the sense that in some places there
+are regulations in place that increase
+
+ align:start position:0%
+are regulations in place that increase
+ 
+
+ align:start position:0%
+are regulations in place that increase
+the price of electricity whereas they
+
+ align:start position:0%
+the price of electricity whereas they
+ 
+
+ align:start position:0%
+the price of electricity whereas they
+aren't present in other places and in
+
+ align:start position:0%
+aren't present in other places and in
+ 
+
+ align:start position:0%
+aren't present in other places and in
+some cases they work to your advantage
+
+ align:start position:0%
+some cases they work to your advantage
+ 
+
+ align:start position:0%
+some cases they work to your advantage
+like in Norway for instance or
+
+ align:start position:0%
+like in Norway for instance or
+ 
+
+ align:start position:0%
+like in Norway for instance or
+Switzerland big hydro uh countries. Um
+
+ align:start position:0%
+Switzerland big hydro uh countries. Um
+ 
+
+ align:start position:0%
+Switzerland big hydro uh countries. Um
+what are some other potential
+
+ align:start position:0%
+what are some other potential
+ 
+
+ align:start position:0%
+what are some other potential
+disadvantages? You hear a lot about
+
+ align:start position:0%
+disadvantages? You hear a lot about
+ 
+
+ align:start position:0%
+disadvantages? You hear a lot about
+jobs, right? Jobs moving overseas. Um
+
+ align:start position:0%
+jobs, right? Jobs moving overseas. Um
+ 
+
+ align:start position:0%
+jobs, right? Jobs moving overseas. Um
+let's uh let's start looking at some of
+
+ align:start position:0%
+let's uh let's start looking at some of
+ 
+
+ align:start position:0%
+let's uh let's start looking at some of
+the numbers uh next Thursday when when
+
+ align:start position:0%
+the numbers uh next Thursday when when
+ 
+
+ align:start position:0%
+the numbers uh next Thursday when when
+we have uh Doug coming in here and
+
+ align:start position:0%
+we have uh Doug coming in here and
+ 
+
+ align:start position:0%
+we have uh Doug coming in here and
+talking about the cost model. Um a good
+
+ align:start position:0%
+talking about the cost model. Um a good
+ 
+
+ align:start position:0%
+talking about the cost model. Um a good
+number to keep in mind a good number to
+
+ align:start position:0%
+number to keep in mind a good number to
+ 
+
+ align:start position:0%
+number to keep in mind a good number to
+keep in mind for the manufacturing of
+
+ align:start position:0%
+keep in mind for the manufacturing of
+ 
+
+ align:start position:0%
+keep in mind for the manufacturing of
+modules. Um so back to oopsie back to
+
+ align:start position:0%
+modules. Um so back to oopsie back to
+ 
+
+ align:start position:0%
+modules. Um so back to oopsie back to
+this part right over here. Um for the
+
+ align:start position:0%
+this part right over here. Um for the
+ 
+
+ align:start position:0%
+this part right over here. Um for the
+module itself typical numbers would be
+
+ align:start position:0%
+module itself typical numbers would be
+ 
+
+ align:start position:0%
+module itself typical numbers would be
+two to 12 people depending on what
+
+ align:start position:0%
+two to 12 people depending on what
+ 
+
+ align:start position:0%
+two to 12 people depending on what
+region of the world you're in. two to 12
+
+ align:start position:0%
+region of the world you're in. two to 12
+ 
+
+ align:start position:0%
+region of the world you're in. two to 12
+people per megawatt. So if you have a
+
+ align:start position:0%
+people per megawatt. So if you have a
+ 
+
+ align:start position:0%
+people per megawatt. So if you have a
+total market of say 10 gigawatts, it's
+
+ align:start position:0%
+total market of say 10 gigawatts, it's
+ 
+
+ align:start position:0%
+total market of say 10 gigawatts, it's
+larger than that. We'll do quick math.
+
+ align:start position:0%
+larger than that. We'll do quick math.
+ 
+
+ align:start position:0%
+larger than that. We'll do quick math.
+Um so if it's per megawatt be 20,000
+
+ align:start position:0%
+Um so if it's per megawatt be 20,000
+ 
+
+ align:start position:0%
+Um so if it's per megawatt be 20,000
+people per gig per 10 gigawatts,
+
+ align:start position:0%
+people per gig per 10 gigawatts,
+ 
+
+ align:start position:0%
+people per gig per 10 gigawatts,
+somewhere in that range on the low end
+
+ align:start position:0%
+somewhere in that range on the low end
+ 
+
+ align:start position:0%
+somewhere in that range on the low end
+and on the high end it would be
+
+ align:start position:0%
+and on the high end it would be
+ 
+
+ align:start position:0%
+and on the high end it would be
+somewhere around 200,000 uh people per
+
+ align:start position:0%
+somewhere around 200,000 uh people per
+ 
+
+ align:start position:0%
+somewhere around 200,000 uh people per
+gigawatt on the high end of the labor
+
+ align:start position:0%
+gigawatt on the high end of the labor
+ 
+
+ align:start position:0%
+gigawatt on the high end of the labor
+intensity. So the high end of the labor
+
+ align:start position:0%
+intensity. So the high end of the labor
+ 
+
+ align:start position:0%
+intensity. So the high end of the labor
+intensity represents a company like
+
+ align:start position:0%
+intensity represents a company like
+ 
+
+ align:start position:0%
+intensity represents a company like
+Trina Solar in in China that is
+
+ align:start position:0%
+Trina Solar in in China that is
+ 
+
+ align:start position:0%
+Trina Solar in in China that is
+extremely labor intensive. It's located
+
+ align:start position:0%
+extremely labor intensive. It's located
+ 
+
+ align:start position:0%
+extremely labor intensive. It's located
+in in Changhu. It's on the highspeed
+
+ align:start position:0%
+in in Changhu. It's on the highspeed
+ 
+
+ align:start position:0%
+in in Changhu. It's on the highspeed
+rail between uh Shanghai and and and
+
+ align:start position:0%
+rail between uh Shanghai and and and
+ 
+
+ align:start position:0%
+rail between uh Shanghai and and and
+Nanqing. Um the low end of that scale
+
+ align:start position:0%
+Nanqing. Um the low end of that scale
+ 
+
+ align:start position:0%
+Nanqing. Um the low end of that scale
+would be more representative of say
+
+ align:start position:0%
+would be more representative of say
+ 
+
+ align:start position:0%
+would be more representative of say
+SUNTC which is almost next door in Wooi.
+
+ align:start position:0%
+SUNTC which is almost next door in Wooi.
+ 
+
+ align:start position:0%
+SUNTC which is almost next door in Wooi.
+um which has adopted a different
+
+ align:start position:0%
+um which has adopted a different
+ 
+
+ align:start position:0%
+um which has adopted a different
+approach saying we're going to invest in
+
+ align:start position:0%
+approach saying we're going to invest in
+ 
+
+ align:start position:0%
+approach saying we're going to invest in
+robots because we're uncertain about
+
+ align:start position:0%
+robots because we're uncertain about
+ 
+
+ align:start position:0%
+robots because we're uncertain about
+where the whole labor thing is going to
+
+ align:start position:0%
+where the whole labor thing is going to
+ 
+
+ align:start position:0%
+where the whole labor thing is going to
+go in China where the prices are going
+
+ align:start position:0%
+go in China where the prices are going
+ 
+
+ align:start position:0%
+go in China where the prices are going
+to go or RECC in uh which is a Norwegian
+
+ align:start position:0%
+to go or RECC in uh which is a Norwegian
+ 
+
+ align:start position:0%
+to go or RECC in uh which is a Norwegian
+company but they opened a factory in
+
+ align:start position:0%
+company but they opened a factory in
+ 
+
+ align:start position:0%
+company but they opened a factory in
+Singapore which has very very low uh
+
+ align:start position:0%
+Singapore which has very very low uh
+ 
+
+ align:start position:0%
+Singapore which has very very low uh
+labor uh rates because they invested a
+
+ align:start position:0%
+labor uh rates because they invested a
+ 
+
+ align:start position:0%
+labor uh rates because they invested a
+lot of money in capital equipment in
+
+ align:start position:0%
+lot of money in capital equipment in
+ 
+
+ align:start position:0%
+lot of money in capital equipment in
+robots to move modules around their
+
+ align:start position:0%
+robots to move modules around their
+ 
+
+ align:start position:0%
+robots to move modules around their
+factories. Um US if you can look at
+
+ align:start position:0%
+factories. Um US if you can look at
+ 
+
+ align:start position:0%
+factories. Um US if you can look at
+turnkey manufacturing lines are
+
+ align:start position:0%
+turnkey manufacturing lines are
+ 
+
+ align:start position:0%
+turnkey manufacturing lines are
+typically around 3 3.5 people per
+
+ align:start position:0%
+typically around 3 3.5 people per
+ 
+
+ align:start position:0%
+typically around 3 3.5 people per
+megawatt. Uh those are some good numbers
+
+ align:start position:0%
+megawatt. Uh those are some good numbers
+ 
+
+ align:start position:0%
+megawatt. Uh those are some good numbers
+to keep in mind. So when anybody comes
+
+ align:start position:0%
+to keep in mind. So when anybody comes
+ 
+
+ align:start position:0%
+to keep in mind. So when anybody comes
+to you and says jobs, solar jobs, um
+
+ align:start position:0%
+to you and says jobs, solar jobs, um
+ 
+
+ align:start position:0%
+to you and says jobs, solar jobs, um
+with these sorts of numbers, you can
+
+ align:start position:0%
+with these sorts of numbers, you can
+ 
+
+ align:start position:0%
+with these sorts of numbers, you can
+begin estimating. Okay, let give me a
+
+ align:start position:0%
+begin estimating. Okay, let give me a
+ 
+
+ align:start position:0%
+begin estimating. Okay, let give me a
+number. How big is the solar market
+
+ align:start position:0%
+number. How big is the solar market
+ 
+
+ align:start position:0%
+number. How big is the solar market
+going to grow to? Um what is the level
+
+ align:start position:0%
+going to grow to? Um what is the level
+ 
+
+ align:start position:0%
+going to grow to? Um what is the level
+of automation? What is the labor
+
+ align:start position:0%
+of automation? What is the labor
+ 
+
+ align:start position:0%
+of automation? What is the labor
+intensity of manu manufacturing of the
+
+ align:start position:0%
+intensity of manu manufacturing of the
+ 
+
+ align:start position:0%
+intensity of manu manufacturing of the
+modules? And you can make an estimate on
+
+ align:start position:0%
+modules? And you can make an estimate on
+ 
+
+ align:start position:0%
+modules? And you can make an estimate on
+the total number of jobs, direct jobs,
+
+ align:start position:0%
+the total number of jobs, direct jobs,
+ 
+
+ align:start position:0%
+the total number of jobs, direct jobs,
+direct jobs associated with the module
+
+ align:start position:0%
+direct jobs associated with the module
+ 
+
+ align:start position:0%
+direct jobs associated with the module
+manufacturing. Then there are all the
+
+ align:start position:0%
+manufacturing. Then there are all the
+ 
+
+ align:start position:0%
+manufacturing. Then there are all the
+indirect jobs as well, right? They're
+
+ align:start position:0%
+indirect jobs as well, right? They're
+ 
+
+ align:start position:0%
+indirect jobs as well, right? They're
+all the people supplying the commodity
+
+ align:start position:0%
+all the people supplying the commodity
+ 
+
+ align:start position:0%
+all the people supplying the commodity
+materials into your manufacturing line.
+
+ align:start position:0%
+materials into your manufacturing line.
+ 
+
+ align:start position:0%
+materials into your manufacturing line.
+they're all the people um who are
+
+ align:start position:0%
+they're all the people um who are
+ 
+
+ align:start position:0%
+they're all the people um who are
+working as as administrative assistants
+
+ align:start position:0%
+working as as administrative assistants
+ 
+
+ align:start position:0%
+working as as administrative assistants
+and and R&D staff and so forth. So, uh
+
+ align:start position:0%
+and and R&D staff and so forth. So, uh
+ 
+
+ align:start position:0%
+and and R&D staff and so forth. So, uh
+it's not quite as simple as that, but it
+
+ align:start position:0%
+it's not quite as simple as that, but it
+ 
+
+ align:start position:0%
+it's not quite as simple as that, but it
+gives you a number to really start
+
+ align:start position:0%
+gives you a number to really start
+ 
+
+ align:start position:0%
+gives you a number to really start
+grabbing. Um and that of course doesn't
+
+ align:start position:0%
+grabbing. Um and that of course doesn't
+ 
+
+ align:start position:0%
+grabbing. Um and that of course doesn't
+include all the installations, installer
+
+ align:start position:0%
+include all the installations, installer
+ 
+
+ align:start position:0%
+include all the installations, installer
+jobs,
+
+ align:start position:0%
+jobs,
+ 
+
+ align:start position:0%
+jobs,
+I All right. So, when we're talking
+
+ align:start position:0%
+I All right. So, when we're talking
+ 
+
+ align:start position:0%
+I All right. So, when we're talking
+about grid tide electricity, um I'd like
+
+ align:start position:0%
+about grid tide electricity, um I'd like
+ 
+
+ align:start position:0%
+about grid tide electricity, um I'd like
+to move on to our next few um next few
+
+ align:start position:0%
+to move on to our next few um next few
+ 
+
+ align:start position:0%
+to move on to our next few um next few
+topics here. When we're talking about
+
+ align:start position:0%
+topics here. When we're talking about
+ 
+
+ align:start position:0%
+topics here. When we're talking about
+grid tide electricity, um this is in
+
+ align:start position:0%
+grid tide electricity, um this is in
+ 
+
+ align:start position:0%
+grid tide electricity, um this is in
+German. Sorry about that. Um this is
+
+ align:start position:0%
+German. Sorry about that. Um this is
+ 
+
+ align:start position:0%
+German. Sorry about that. Um this is
+over a period uh v means day of the
+
+ align:start position:0%
+over a period uh v means day of the
+ 
+
+ align:start position:0%
+over a period uh v means day of the
+week. Um and this is basically the uh
+
+ align:start position:0%
+week. Um and this is basically the uh
+ 
+
+ align:start position:0%
+week. Um and this is basically the uh
+the peak um uh power uh in gigawatts uh
+
+ align:start position:0%
+the peak um uh power uh in gigawatts uh
+ 
+
+ align:start position:0%
+the peak um uh power uh in gigawatts uh
+instantaneous at at any given point. So
+
+ align:start position:0%
+instantaneous at at any given point. So
+ 
+
+ align:start position:0%
+instantaneous at at any given point. So
+we have you know morning middle of the
+
+ align:start position:0%
+we have you know morning middle of the
+ 
+
+ align:start position:0%
+we have you know morning middle of the
+day night middle of the day night
+
+ align:start position:0%
+day night middle of the day night
+ 
+
+ align:start position:0%
+day night middle of the day night
+there's a little bump right here during
+
+ align:start position:0%
+there's a little bump right here during
+ 
+
+ align:start position:0%
+there's a little bump right here during
+prime time TV. Um and we have the uh
+
+ align:start position:0%
+prime time TV. Um and we have the uh
+ 
+
+ align:start position:0%
+prime time TV. Um and we have the uh
+output of PV um going from 5 gawatt peak
+
+ align:start position:0%
+output of PV um going from 5 gawatt peak
+ 
+
+ align:start position:0%
+output of PV um going from 5 gawatt peak
+to 30 gawatt peak. you can see uh
+
+ align:start position:0%
+to 30 gawatt peak. you can see uh
+ 
+
+ align:start position:0%
+to 30 gawatt peak. you can see uh
+beginning to eat into uh the profits
+
+ align:start position:0%
+beginning to eat into uh the profits
+ 
+
+ align:start position:0%
+beginning to eat into uh the profits
+essentially the uh peak hours um right
+
+ align:start position:0%
+essentially the uh peak hours um right
+ 
+
+ align:start position:0%
+essentially the uh peak hours um right
+so let me let me differentiate between
+
+ align:start position:0%
+so let me let me differentiate between
+ 
+
+ align:start position:0%
+so let me let me differentiate between
+base load and peak base load power would
+
+ align:start position:0%
+base load and peak base load power would
+ 
+
+ align:start position:0%
+base load and peak base load power would
+be voom right something uh providing a
+
+ align:start position:0%
+be voom right something uh providing a
+ 
+
+ align:start position:0%
+be voom right something uh providing a
+constant power output uh as a function
+
+ align:start position:0%
+constant power output uh as a function
+ 
+
+ align:start position:0%
+constant power output uh as a function
+of time something like a nuclear power
+
+ align:start position:0%
+of time something like a nuclear power
+ 
+
+ align:start position:0%
+of time something like a nuclear power
+plant coal fired power plant peakers
+
+ align:start position:0%
+plant coal fired power plant peakers
+ 
+
+ align:start position:0%
+plant coal fired power plant peakers
+would be natural gas fired power plants
+
+ align:start position:0%
+would be natural gas fired power plants
+ 
+
+ align:start position:0%
+would be natural gas fired power plants
+that receive the calls like Jessica
+
+ align:start position:0%
+that receive the calls like Jessica
+ 
+
+ align:start position:0%
+that receive the calls like Jessica
+you're in charge of the peaker over
+
+ align:start position:0%
+you're in charge of the peaker over
+ 
+
+ align:start position:0%
+you're in charge of the peaker over
+there based on my weather report today
+
+ align:start position:0%
+there based on my weather report today
+ 
+
+ align:start position:0%
+there based on my weather report today
+I'm going to need so many gigawatts
+
+ align:start position:0%
+I'm going to need so many gigawatts
+ 
+
+ align:start position:0%
+I'm going to need so many gigawatts
+tomorrow between the hours of 10 and 12
+
+ align:start position:0%
+tomorrow between the hours of 10 and 12
+ 
+
+ align:start position:0%
+tomorrow between the hours of 10 and 12
+you think you can turn yourself on then
+
+ align:start position:0%
+you think you can turn yourself on then
+ 
+
+ align:start position:0%
+you think you can turn yourself on then
+I'll pay you this amount of yep
+
+ align:start position:0%
+I'll pay you this amount of yep
+ 
+
+ align:start position:0%
+I'll pay you this amount of yep
+Jessica's going to battle sheet yes I
+
+ align:start position:0%
+Jessica's going to battle sheet yes I
+ 
+
+ align:start position:0%
+Jessica's going to battle sheet yes I
+can do that PV on the other hand is
+
+ align:start position:0%
+can do that PV on the other hand is
+ 
+
+ align:start position:0%
+can do that PV on the other hand is
+coming on if the sun's coming on right
+
+ align:start position:0%
+coming on if the sun's coming on right
+ 
+
+ align:start position:0%
+coming on if the sun's coming on right
+and today there isn't a great degree of
+
+ align:start position:0%
+and today there isn't a great degree of
+ 
+
+ align:start position:0%
+and today there isn't a great degree of
+predictability we can see if that's
+
+ align:start position:0%
+predictability we can see if that's
+ 
+
+ align:start position:0%
+predictability we can see if that's
+going to change based on one of our
+
+ align:start position:0%
+going to change based on one of our
+ 
+
+ align:start position:0%
+going to change based on one of our
+class projects here but there wasn't a
+
+ align:start position:0%
+class projects here but there wasn't a
+ 
+
+ align:start position:0%
+class projects here but there wasn't a
+great degree of predictability you can
+
+ align:start position:0%
+great degree of predictability you can
+ 
+
+ align:start position:0%
+great degree of predictability you can
+see here for example um and here varying
+
+ align:start position:0%
+see here for example um and here varying
+ 
+
+ align:start position:0%
+see here for example um and here varying
+amounts of sunlight from one day to the
+
+ align:start position:0%
+amounts of sunlight from one day to the
+ 
+
+ align:start position:0%
+amounts of sunlight from one day to the
+other uh as a result of changing um
+
+ align:start position:0%
+other uh as a result of changing um
+ 
+
+ align:start position:0%
+other uh as a result of changing um
+insulation uh there's of course changing
+
+ align:start position:0%
+insulation uh there's of course changing
+ 
+
+ align:start position:0%
+insulation uh there's of course changing
+demand as a day of the week goes by on
+
+ align:start position:0%
+demand as a day of the week goes by on
+ 
+
+ align:start position:0%
+demand as a day of the week goes by on
+Saturday and Sunday there's less demand
+
+ align:start position:0%
+Saturday and Sunday there's less demand
+ 
+
+ align:start position:0%
+Saturday and Sunday there's less demand
+for electricity
+
+ align:start position:0%
+for electricity
+ 
+
+ align:start position:0%
+for electricity
+So what PV is doing is eating into some
+
+ align:start position:0%
+So what PV is doing is eating into some
+ 
+
+ align:start position:0%
+So what PV is doing is eating into some
+of the highest use periods which is good
+
+ align:start position:0%
+of the highest use periods which is good
+ 
+
+ align:start position:0%
+of the highest use periods which is good
+from the markets perspect from the um uh
+
+ align:start position:0%
+from the markets perspect from the um uh
+ 
+
+ align:start position:0%
+from the markets perspect from the um uh
+shall we say the uh person in charge of
+
+ align:start position:0%
+shall we say the uh person in charge of
+ 
+
+ align:start position:0%
+shall we say the uh person in charge of
+maintaining grid stabilities perspective
+
+ align:start position:0%
+maintaining grid stabilities perspective
+ 
+
+ align:start position:0%
+maintaining grid stabilities perspective
+because they want uh uh power to be
+
+ align:start position:0%
+because they want uh uh power to be
+ 
+
+ align:start position:0%
+because they want uh uh power to be
+produced then they don't want to run out
+
+ align:start position:0%
+produced then they don't want to run out
+ 
+
+ align:start position:0%
+produced then they don't want to run out
+of generation capacity. NPV is avoiding
+
+ align:start position:0%
+of generation capacity. NPV is avoiding
+ 
+
+ align:start position:0%
+of generation capacity. NPV is avoiding
+the situation or at least prolonging the
+
+ align:start position:0%
+the situation or at least prolonging the
+ 
+
+ align:start position:0%
+the situation or at least prolonging the
+situation a few more years until we run
+
+ align:start position:0%
+situation a few more years until we run
+ 
+
+ align:start position:0%
+situation a few more years until we run
+out of power generation capacity on the
+
+ align:start position:0%
+out of power generation capacity on the
+ 
+
+ align:start position:0%
+out of power generation capacity on the
+grid.
+
+ align:start position:0%
+grid.
+ 
+
+ align:start position:0%
+grid.
+um as our population grows and our
+
+ align:start position:0%
+um as our population grows and our
+ 
+
+ align:start position:0%
+um as our population grows and our
+energy intensity grows, we're needing
+
+ align:start position:0%
+energy intensity grows, we're needing
+ 
+
+ align:start position:0%
+energy intensity grows, we're needing
+more and more power, but we're not
+
+ align:start position:0%
+more and more power, but we're not
+ 
+
+ align:start position:0%
+more and more power, but we're not
+building new power plants at that rate,
+
+ align:start position:0%
+building new power plants at that rate,
+ 
+
+ align:start position:0%
+building new power plants at that rate,
+right? Generally in Germany and the
+
+ align:start position:0%
+right? Generally in Germany and the
+ 
+
+ align:start position:0%
+right? Generally in Germany and the
+United States. Um and so PV is helping
+
+ align:start position:0%
+United States. Um and so PV is helping
+ 
+
+ align:start position:0%
+United States. Um and so PV is helping
+to defay some of that deferred
+
+ align:start position:0%
+to defay some of that deferred
+ 
+
+ align:start position:0%
+to defay some of that deferred
+investment in new generation capacity.
+
+ align:start position:0%
+investment in new generation capacity.
+ 
+
+ align:start position:0%
+investment in new generation capacity.
+So that's good. On the bad side,
+
+ align:start position:0%
+So that's good. On the bad side,
+ 
+
+ align:start position:0%
+So that's good. On the bad side,
+somebody who's invested, let's say, um
+
+ align:start position:0%
+somebody who's invested, let's say, um
+ 
+
+ align:start position:0%
+somebody who's invested, let's say, um
+let's say Mary has invested in a a
+
+ align:start position:0%
+let's say Mary has invested in a a
+ 
+
+ align:start position:0%
+let's say Mary has invested in a a
+natural gas generation plant, um she put
+
+ align:start position:0%
+natural gas generation plant, um she put
+ 
+
+ align:start position:0%
+natural gas generation plant, um she put
+the money down for Jessica's plant.
+
+ align:start position:0%
+the money down for Jessica's plant.
+ 
+
+ align:start position:0%
+the money down for Jessica's plant.
+Jessica's running it. And uh and and now
+
+ align:start position:0%
+Jessica's running it. And uh and and now
+ 
+
+ align:start position:0%
+Jessica's running it. And uh and and now
+Mary realizes, well, goodness. Um I
+
+ align:start position:0%
+Mary realizes, well, goodness. Um I
+ 
+
+ align:start position:0%
+Mary realizes, well, goodness. Um I
+thought I was going to get a steady rate
+
+ align:start position:0%
+thought I was going to get a steady rate
+ 
+
+ align:start position:0%
+thought I was going to get a steady rate
+of return over 20 years for my natural
+
+ align:start position:0%
+of return over 20 years for my natural
+ 
+
+ align:start position:0%
+of return over 20 years for my natural
+gas firepower plant. That that rate of
+
+ align:start position:0%
+gas firepower plant. That that rate of
+ 
+
+ align:start position:0%
+gas firepower plant. That that rate of
+return was factored into my economic
+
+ align:start position:0%
+return was factored into my economic
+ 
+
+ align:start position:0%
+return was factored into my economic
+analysis when I borrowed money at a
+
+ align:start position:0%
+analysis when I borrowed money at a
+ 
+
+ align:start position:0%
+analysis when I borrowed money at a
+certain rate from a bank. And now you're
+
+ align:start position:0%
+certain rate from a bank. And now you're
+ 
+
+ align:start position:0%
+certain rate from a bank. And now you're
+telling me that this upstart technology,
+
+ align:start position:0%
+telling me that this upstart technology,
+ 
+
+ align:start position:0%
+telling me that this upstart technology,
+this new PV stuff is coming online and
+
+ align:start position:0%
+this new PV stuff is coming online and
+ 
+
+ align:start position:0%
+this new PV stuff is coming online and
+is going to take away some of my profit.
+
+ align:start position:0%
+is going to take away some of my profit.
+ 
+
+ align:start position:0%
+is going to take away some of my profit.
+That that's that that doesn't work for
+
+ align:start position:0%
+That that's that that doesn't work for
+ 
+
+ align:start position:0%
+That that's that that doesn't work for
+me. Um, as a matter of fact, um, on peak
+
+ align:start position:0%
+me. Um, as a matter of fact, um, on peak
+ 
+
+ align:start position:0%
+me. Um, as a matter of fact, um, on peak
+days in Bavaria, which is the
+
+ align:start position:0%
+days in Bavaria, which is the
+ 
+
+ align:start position:0%
+days in Bavaria, which is the
+southeastern part of Germany today, uh,
+
+ align:start position:0%
+southeastern part of Germany today, uh,
+ 
+
+ align:start position:0%
+southeastern part of Germany today, uh,
+PV can comprise as much as 40% of
+
+ align:start position:0%
+PV can comprise as much as 40% of
+ 
+
+ align:start position:0%
+PV can comprise as much as 40% of
+electricity on the grid, uh, during peak
+
+ align:start position:0%
+electricity on the grid, uh, during peak
+ 
+
+ align:start position:0%
+electricity on the grid, uh, during peak
+hours during the summer. And, and what
+
+ align:start position:0%
+hours during the summer. And, and what
+ 
+
+ align:start position:0%
+hours during the summer. And, and what
+that does sometimes is force
+
+ align:start position:0%
+that does sometimes is force
+ 
+
+ align:start position:0%
+that does sometimes is force
+conventional uh, uh, electricity
+
+ align:start position:0%
+conventional uh, uh, electricity
+ 
+
+ align:start position:0%
+conventional uh, uh, electricity
+producers to either turn off or going
+
+ align:start position:0%
+producers to either turn off or going
+ 
+
+ align:start position:0%
+producers to either turn off or going
+into negative pricing, meaning they
+
+ align:start position:0%
+into negative pricing, meaning they
+ 
+
+ align:start position:0%
+into negative pricing, meaning they
+shunt the power to ground so that they
+
+ align:start position:0%
+shunt the power to ground so that they
+ 
+
+ align:start position:0%
+shunt the power to ground so that they
+don't have to pay to put their
+
+ align:start position:0%
+don't have to pay to put their
+ 
+
+ align:start position:0%
+don't have to pay to put their
+electricity on the grid. So that's uh an
+
+ align:start position:0%
+electricity on the grid. So that's uh an
+ 
+
+ align:start position:0%
+electricity on the grid. So that's uh an
+interesting market dynamic that's
+
+ align:start position:0%
+interesting market dynamic that's
+ 
+
+ align:start position:0%
+interesting market dynamic that's
+evolving as more and more PV electricity
+
+ align:start position:0%
+evolving as more and more PV electricity
+ 
+
+ align:start position:0%
+evolving as more and more PV electricity
+enters the grid uh in these regions um
+
+ align:start position:0%
+enters the grid uh in these regions um
+ 
+
+ align:start position:0%
+enters the grid uh in these regions um
+of high penetration which include uh
+
+ align:start position:0%
+of high penetration which include uh
+ 
+
+ align:start position:0%
+of high penetration which include uh
+California, Hawaii uh the island of Lai
+
+ align:start position:0%
+California, Hawaii uh the island of Lai
+ 
+
+ align:start position:0%
+California, Hawaii uh the island of Lai
+I believe has um up to 40% as well on on
+
+ align:start position:0%
+I believe has um up to 40% as well on on
+ 
+
+ align:start position:0%
+I believe has um up to 40% as well on on
+peak days. Um Bavaria and Germany which
+
+ align:start position:0%
+peak days. Um Bavaria and Germany which
+ 
+
+ align:start position:0%
+peak days. Um Bavaria and Germany which
+is the southeastern part of Germany. Um
+
+ align:start position:0%
+is the southeastern part of Germany. Um
+ 
+
+ align:start position:0%
+is the southeastern part of Germany. Um
+let me um try get to this point right
+
+ align:start position:0%
+let me um try get to this point right
+ 
+
+ align:start position:0%
+let me um try get to this point right
+here is predicting where the market will
+
+ align:start position:0%
+here is predicting where the market will
+ 
+
+ align:start position:0%
+here is predicting where the market will
+go. We talked about the demand curve for
+
+ align:start position:0%
+go. We talked about the demand curve for
+ 
+
+ align:start position:0%
+go. We talked about the demand curve for
+PV and we collapsed um we collapsed both
+
+ align:start position:0%
+PV and we collapsed um we collapsed both
+ 
+
+ align:start position:0%
+PV and we collapsed um we collapsed both
+insulation and price of electricity from
+
+ align:start position:0%
+insulation and price of electricity from
+ 
+
+ align:start position:0%
+insulation and price of electricity from
+the grid into this dollars per watt peak
+
+ align:start position:0%
+the grid into this dollars per watt peak
+ 
+
+ align:start position:0%
+the grid into this dollars per watt peak
+figure which is how much people are
+
+ align:start position:0%
+figure which is how much people are
+ 
+
+ align:start position:0%
+figure which is how much people are
+willing to pay. We can also break it out
+
+ align:start position:0%
+willing to pay. We can also break it out
+ 
+
+ align:start position:0%
+willing to pay. We can also break it out
+into annual solar energy yield. This is
+
+ align:start position:0%
+into annual solar energy yield. This is
+ 
+
+ align:start position:0%
+into annual solar energy yield. This is
+the solar resource available. Um it's
+
+ align:start position:0%
+the solar resource available. Um it's
+ 
+
+ align:start position:0%
+the solar resource available. Um it's
+used it's using the uh units of kilowatt
+
+ align:start position:0%
+used it's using the uh units of kilowatt
+ 
+
+ align:start position:0%
+used it's using the uh units of kilowatt
+hours per kilowatt peak meaning the
+
+ align:start position:0%
+hours per kilowatt peak meaning the
+ 
+
+ align:start position:0%
+hours per kilowatt peak meaning the
+number of kilowatt hours the amount of
+
+ align:start position:0%
+number of kilowatt hours the amount of
+ 
+
+ align:start position:0%
+number of kilowatt hours the amount of
+energy that a unit of rated power
+
+ align:start position:0%
+energy that a unit of rated power
+ 
+
+ align:start position:0%
+energy that a unit of rated power
+kilowatt peak of the solar panel is
+
+ align:start position:0%
+kilowatt peak of the solar panel is
+ 
+
+ align:start position:0%
+kilowatt peak of the solar panel is
+going to produce. So, how much energy
+
+ align:start position:0%
+going to produce. So, how much energy
+ 
+
+ align:start position:0%
+going to produce. So, how much energy
+will a unit of solar panel produce?
+
+ align:start position:0%
+will a unit of solar panel produce?
+ 
+
+ align:start position:0%
+will a unit of solar panel produce?
+That's down here. And of course, larger
+
+ align:start position:0%
+That's down here. And of course, larger
+ 
+
+ align:start position:0%
+That's down here. And of course, larger
+amounts mean more sun, more solar
+
+ align:start position:0%
+amounts mean more sun, more solar
+ 
+
+ align:start position:0%
+amounts mean more sun, more solar
+resource. On the uh on the ordinate, we
+
+ align:start position:0%
+resource. On the uh on the ordinate, we
+ 
+
+ align:start position:0%
+resource. On the uh on the ordinate, we
+have average power price of household.
+
+ align:start position:0%
+have average power price of household.
+ 
+
+ align:start position:0%
+have average power price of household.
+This is um US dollars. It should be uh
+
+ align:start position:0%
+This is um US dollars. It should be uh
+ 
+
+ align:start position:0%
+This is um US dollars. It should be uh
+average electricity price, US dollars
+
+ align:start position:0%
+average electricity price, US dollars
+ 
+
+ align:start position:0%
+average electricity price, US dollars
+per kilowatt hour. Um so, that's how
+
+ align:start position:0%
+per kilowatt hour. Um so, that's how
+ 
+
+ align:start position:0%
+per kilowatt hour. Um so, that's how
+much people are paying for their
+
+ align:start position:0%
+much people are paying for their
+ 
+
+ align:start position:0%
+much people are paying for their
+electricity, what you're displacing. And
+
+ align:start position:0%
+electricity, what you're displacing. And
+ 
+
+ align:start position:0%
+electricity, what you're displacing. And
+you can see that these little bubbles
+
+ align:start position:0%
+you can see that these little bubbles
+ 
+
+ align:start position:0%
+you can see that these little bubbles
+here represent the size of the market.
+
+ align:start position:0%
+here represent the size of the market.
+ 
+
+ align:start position:0%
+here represent the size of the market.
+So as the price of PV electricity comes
+
+ align:start position:0%
+So as the price of PV electricity comes
+ 
+
+ align:start position:0%
+So as the price of PV electricity comes
+down, we are able to address more and
+
+ align:start position:0%
+down, we are able to address more and
+ 
+
+ align:start position:0%
+down, we are able to address more and
+more markets. As the subsidization of PV
+
+ align:start position:0%
+more markets. As the subsidization of PV
+ 
+
+ align:start position:0%
+more markets. As the subsidization of PV
+electricity increases, you move these
+
+ align:start position:0%
+electricity increases, you move these
+ 
+
+ align:start position:0%
+electricity increases, you move these
+little bubbles up. And as the
+
+ align:start position:0%
+little bubbles up. And as the
+ 
+
+ align:start position:0%
+little bubbles up. And as the
+subsidiation comes back down, the market
+
+ align:start position:0%
+subsidiation comes back down, the market
+ 
+
+ align:start position:0%
+subsidiation comes back down, the market
+pull, not not the manufacturing
+
+ align:start position:0%
+pull, not not the manufacturing
+ 
+
+ align:start position:0%
+pull, not not the manufacturing
+subsidies, but the uh the uh use or
+
+ align:start position:0%
+subsidies, but the uh the uh use or
+ 
+
+ align:start position:0%
+subsidies, but the uh the uh use or
+installation subsidies as they come back
+
+ align:start position:0%
+installation subsidies as they come back
+ 
+
+ align:start position:0%
+installation subsidies as they come back
+down, the little bubbles move down um
+
+ align:start position:0%
+down, the little bubbles move down um
+ 
+
+ align:start position:0%
+down, the little bubbles move down um
+and eventually rest at their their their
+
+ align:start position:0%
+and eventually rest at their their their
+ 
+
+ align:start position:0%
+and eventually rest at their their their
+uh so-called true market price without
+
+ align:start position:0%
+uh so-called true market price without
+ 
+
+ align:start position:0%
+uh so-called true market price without
+the externalities factored in. And so
+
+ align:start position:0%
+the externalities factored in. And so
+ 
+
+ align:start position:0%
+the externalities factored in. And so
+you can see how we're beginning to enter
+
+ align:start position:0%
+you can see how we're beginning to enter
+ 
+
+ align:start position:0%
+you can see how we're beginning to enter
+uh a regime where PV is starting to look
+
+ align:start position:0%
+uh a regime where PV is starting to look
+ 
+
+ align:start position:0%
+uh a regime where PV is starting to look
+interesting in a lot of places. And as
+
+ align:start position:0%
+interesting in a lot of places. And as
+ 
+
+ align:start position:0%
+interesting in a lot of places. And as
+we begin addressing these markets or
+
+ align:start position:0%
+we begin addressing these markets or
+ 
+
+ align:start position:0%
+we begin addressing these markets or
+hitting these markets, you can imagine
+
+ align:start position:0%
+hitting these markets, you can imagine
+ 
+
+ align:start position:0%
+hitting these markets, you can imagine
+two Gaussian curves intersecting. one
+
+ align:start position:0%
+two Gaussian curves intersecting. one
+ 
+
+ align:start position:0%
+two Gaussian curves intersecting. one
+being the price of PV electricity, other
+
+ align:start position:0%
+being the price of PV electricity, other
+ 
+
+ align:start position:0%
+being the price of PV electricity, other
+being the price of grid electricity. As
+
+ align:start position:0%
+being the price of grid electricity. As
+ 
+
+ align:start position:0%
+being the price of grid electricity. As
+they oversight and overlap, you expect
+
+ align:start position:0%
+they oversight and overlap, you expect
+ 
+
+ align:start position:0%
+they oversight and overlap, you expect
+an exponential growth and that's what
+
+ align:start position:0%
+an exponential growth and that's what
+ 
+
+ align:start position:0%
+an exponential growth and that's what
+we're seeing in the market today.
+
+ align:start position:0%
+we're seeing in the market today.
+ 
+
+ align:start position:0%
+we're seeing in the market today.
+Question, what is the principle for tier
+
+ align:start position:0%
+Question, what is the principle for tier
+ 
+
+ align:start position:0%
+Question, what is the principle for tier
+four? Yeah. So, California decided to
+
+ align:start position:0%
+four? Yeah. So, California decided to
+ 
+
+ align:start position:0%
+four? Yeah. So, California decided to
+implement um more of a instead of um
+
+ align:start position:0%
+implement um more of a instead of um
+ 
+
+ align:start position:0%
+implement um more of a instead of um
+well, it is uh a little bit um
+
+ align:start position:0%
+well, it is uh a little bit um
+ 
+
+ align:start position:0%
+well, it is uh a little bit um
+regressive in that sense, but it what
+
+ align:start position:0%
+regressive in that sense, but it what
+ 
+
+ align:start position:0%
+regressive in that sense, but it what
+they did is they said let's instead of
+
+ align:start position:0%
+they did is they said let's instead of
+ 
+
+ align:start position:0%
+they did is they said let's instead of
+um instead of paying the same price per
+
+ align:start position:0%
+um instead of paying the same price per
+ 
+
+ align:start position:0%
+um instead of paying the same price per
+electricity, everybody um which actually
+
+ align:start position:0%
+electricity, everybody um which actually
+ 
+
+ align:start position:0%
+electricity, everybody um which actually
+it would be even the opposite way. Um
+
+ align:start position:0%
+it would be even the opposite way. Um
+ 
+
+ align:start position:0%
+it would be even the opposite way. Um
+you know how residential we typically
+
+ align:start position:0%
+you know how residential we typically
+ 
+
+ align:start position:0%
+you know how residential we typically
+pay higher rates in industrial that's
+
+ align:start position:0%
+pay higher rates in industrial that's
+ 
+
+ align:start position:0%
+pay higher rates in industrial that's
+because industrial buys in bulk. They
+
+ align:start position:0%
+because industrial buys in bulk. They
+ 
+
+ align:start position:0%
+because industrial buys in bulk. They
+buy electricity Costco size. we just buy
+
+ align:start position:0%
+buy electricity Costco size. we just buy
+ 
+
+ align:start position:0%
+buy electricity Costco size. we just buy
+it, you know, corner store size and so
+
+ align:start position:0%
+it, you know, corner store size and so
+ 
+
+ align:start position:0%
+it, you know, corner store size and so
+they pay less for the electricity. And
+
+ align:start position:0%
+they pay less for the electricity. And
+ 
+
+ align:start position:0%
+they pay less for the electricity. And
+in California realized this and said,
+
+ align:start position:0%
+in California realized this and said,
+ 
+
+ align:start position:0%
+in California realized this and said,
+well, this is a perverse incentive. What
+
+ align:start position:0%
+well, this is a perverse incentive. What
+ 
+
+ align:start position:0%
+well, this is a perverse incentive. What
+this does is it gives an incentive to
+
+ align:start position:0%
+this does is it gives an incentive to
+ 
+
+ align:start position:0%
+this does is it gives an incentive to
+people to use more electricity because
+
+ align:start position:0%
+people to use more electricity because
+ 
+
+ align:start position:0%
+people to use more electricity because
+if you buy in Costco size, you pay less
+
+ align:start position:0%
+if you buy in Costco size, you pay less
+ 
+
+ align:start position:0%
+if you buy in Costco size, you pay less
+per kilowatt hour than if you buy in the
+
+ align:start position:0%
+per kilowatt hour than if you buy in the
+ 
+
+ align:start position:0%
+per kilowatt hour than if you buy in the
+corner store. Um, instead what we're
+
+ align:start position:0%
+corner store. Um, instead what we're
+ 
+
+ align:start position:0%
+corner store. Um, instead what we're
+going to do is reverse that incentive by
+
+ align:start position:0%
+going to do is reverse that incentive by
+ 
+
+ align:start position:0%
+going to do is reverse that incentive by
+penalizing the people who buy more
+
+ align:start position:0%
+penalizing the people who buy more
+ 
+
+ align:start position:0%
+penalizing the people who buy more
+electricity. So your rate is going to be
+
+ align:start position:0%
+electricity. So your rate is going to be
+ 
+
+ align:start position:0%
+electricity. So your rate is going to be
+higher than if you just bought a small
+
+ align:start position:0%
+higher than if you just bought a small
+ 
+
+ align:start position:0%
+higher than if you just bought a small
+uh amount. So what they did is the
+
+ align:start position:0%
+uh amount. So what they did is the
+ 
+
+ align:start position:0%
+uh amount. So what they did is the
+government bureaucrats got together with
+
+ align:start position:0%
+government bureaucrats got together with
+ 
+
+ align:start position:0%
+government bureaucrats got together with
+some of the scholars and decided these
+
+ align:start position:0%
+some of the scholars and decided these
+ 
+
+ align:start position:0%
+some of the scholars and decided these
+are reasonable amounts for a residential
+
+ align:start position:0%
+are reasonable amounts for a residential
+ 
+
+ align:start position:0%
+are reasonable amounts for a residential
+house to consume. Um this is the next
+
+ align:start position:0%
+house to consume. Um this is the next
+ 
+
+ align:start position:0%
+house to consume. Um this is the next
+tier up. This is the next tier up. This
+
+ align:start position:0%
+tier up. This is the next tier up. This
+ 
+
+ align:start position:0%
+tier up. This is the next tier up. This
+is the next tier up and this is
+
+ align:start position:0%
+is the next tier up and this is
+ 
+
+ align:start position:0%
+is the next tier up and this is
+completely unreasonable. Um and so uh
+
+ align:start position:0%
+completely unreasonable. Um and so uh
+ 
+
+ align:start position:0%
+completely unreasonable. Um and so uh
+what they did is they tiered their
+
+ align:start position:0%
+what they did is they tiered their
+ 
+
+ align:start position:0%
+what they did is they tiered their
+electricity and you have California tier
+
+ align:start position:0%
+electricity and you have California tier
+ 
+
+ align:start position:0%
+electricity and you have California tier
+uh tiers one, two, and three represented
+
+ align:start position:0%
+uh tiers one, two, and three represented
+ 
+
+ align:start position:0%
+uh tiers one, two, and three represented
+by the big bubble and tier four and tier
+
+ align:start position:0%
+by the big bubble and tier four and tier
+ 
+
+ align:start position:0%
+by the big bubble and tier four and tier
+five um as represented at higher
+
+ align:start position:0%
+five um as represented at higher
+ 
+
+ align:start position:0%
+five um as represented at higher
+pricing. So, if you happen to fall into
+
+ align:start position:0%
+pricing. So, if you happen to fall into
+ 
+
+ align:start position:0%
+pricing. So, if you happen to fall into
+the tier five category, you could be
+
+ align:start position:0%
+the tier five category, you could be
+ 
+
+ align:start position:0%
+the tier five category, you could be
+paying upward of 30 cents per kilowatt
+
+ align:start position:0%
+paying upward of 30 cents per kilowatt
+ 
+
+ align:start position:0%
+paying upward of 30 cents per kilowatt
+hour uh for your your electricity. And
+
+ align:start position:0%
+hour uh for your your electricity. And
+ 
+
+ align:start position:0%
+hour uh for your your electricity. And
+it's a way of penalizing you for
+
+ align:start position:0%
+it's a way of penalizing you for
+ 
+
+ align:start position:0%
+it's a way of penalizing you for
+powering u two swimming pools in your
+
+ align:start position:0%
+powering u two swimming pools in your
+ 
+
+ align:start position:0%
+powering u two swimming pools in your
+backyard um along with uh I don't know
+
+ align:start position:0%
+backyard um along with uh I don't know
+ 
+
+ align:start position:0%
+backyard um along with uh I don't know
+something in the range of of 10
+
+ align:start position:0%
+something in the range of of 10
+ 
+
+ align:start position:0%
+something in the range of of 10
+kilowatts of of lighting inside of your
+
+ align:start position:0%
+kilowatts of of lighting inside of your
+ 
+
+ align:start position:0%
+kilowatts of of lighting inside of your
+house. Um whereas if if you're running
+
+ align:start position:0%
+house. Um whereas if if you're running
+ 
+
+ align:start position:0%
+house. Um whereas if if you're running
+on a meager budget, um you might do much
+
+ align:start position:0%
+on a meager budget, um you might do much
+ 
+
+ align:start position:0%
+on a meager budget, um you might do much
+better. Do we have a question over here?
+
+ align:start position:0%
+better. Do we have a question over here?
+ 
+
+ align:start position:0%
+better. Do we have a question over here?
+No. Is it all residential? Um the
+
+ align:start position:0%
+No. Is it all residential? Um the
+ 
+
+ align:start position:0%
+No. Is it all residential? Um the
+California's tier one, two, three, and
+
+ align:start position:0%
+California's tier one, two, three, and
+ 
+
+ align:start position:0%
+California's tier one, two, three, and
+four, and five. That's a great question.
+
+ align:start position:0%
+four, and five. That's a great question.
+ 
+
+ align:start position:0%
+four, and five. That's a great question.
+Um Joe, would you happen to know if if
+
+ align:start position:0%
+Um Joe, would you happen to know if if
+ 
+
+ align:start position:0%
+Um Joe, would you happen to know if if
+if commercial and industrial fall into
+
+ align:start position:0%
+if commercial and industrial fall into
+ 
+
+ align:start position:0%
+if commercial and industrial fall into
+tiers as well or if it's just res? No,
+
+ align:start position:0%
+tiers as well or if it's just res? No,
+ 
+
+ align:start position:0%
+tiers as well or if it's just res? No,
+because that'd be political suicide.
+
+ align:start position:0%
+because that'd be political suicide.
+ 
+
+ align:start position:0%
+because that'd be political suicide.
+Well, even the residential is political
+
+ align:start position:0%
+Well, even the residential is political
+ 
+
+ align:start position:0%
+Well, even the residential is political
+suicide. Yeah. So, the residential
+
+ align:start position:0%
+suicide. Yeah. So, the residential
+ 
+
+ align:start position:0%
+suicide. Yeah. So, the residential
+system is actually kind of a bad one
+
+ align:start position:0%
+system is actually kind of a bad one
+ 
+
+ align:start position:0%
+system is actually kind of a bad one
+because if you have like eight people
+
+ align:start position:0%
+because if you have like eight people
+ 
+
+ align:start position:0%
+because if you have like eight people
+living in a house versus two, it doesn't
+
+ align:start position:0%
+living in a house versus two, it doesn't
+ 
+
+ align:start position:0%
+living in a house versus two, it doesn't
+take that into account. So, it's not a
+
+ align:start position:0%
+take that into account. So, it's not a
+ 
+
+ align:start position:0%
+take that into account. So, it's not a
+per capita thing.
+
+ align:start position:0%
+per capita thing.
+ 
+
+ align:start position:0%
+per capita thing.
+Yeah. So um many many states and
+
+ align:start position:0%
+Yeah. So um many many states and
+ 
+
+ align:start position:0%
+Yeah. So um many many states and
+countries have tried to adjust uh
+
+ align:start position:0%
+countries have tried to adjust uh
+ 
+
+ align:start position:0%
+countries have tried to adjust uh
+incentive mechanisms. Uh I'm not sure
+
+ align:start position:0%
+incentive mechanisms. Uh I'm not sure
+ 
+
+ align:start position:0%
+incentive mechanisms. Uh I'm not sure
+specifically about the commercial res
+
+ align:start position:0%
+specifically about the commercial res
+ 
+
+ align:start position:0%
+specifically about the commercial res
+and industrial. You might want to jot it
+
+ align:start position:0%
+and industrial. You might want to jot it
+ 
+
+ align:start position:0%
+and industrial. You might want to jot it
+down and give a quick Google search
+
+ align:start position:0%
+down and give a quick Google search
+ 
+
+ align:start position:0%
+down and give a quick Google search
+after. Um Germany growing gang busters
+
+ align:start position:0%
+after. Um Germany growing gang busters
+ 
+
+ align:start position:0%
+after. Um Germany growing gang busters
+uh the market versus time. This is
+
+ align:start position:0%
+uh the market versus time. This is
+ 
+
+ align:start position:0%
+uh the market versus time. This is
+installed capacity annual versus year.
+
+ align:start position:0%
+installed capacity annual versus year.
+ 
+
+ align:start position:0%
+installed capacity annual versus year.
+And uh we again subsidy support
+
+ align:start position:0%
+And uh we again subsidy support
+ 
+
+ align:start position:0%
+And uh we again subsidy support
+mechanisms, tax breaks, incentives. Um,
+
+ align:start position:0%
+mechanisms, tax breaks, incentives. Um,
+ 
+
+ align:start position:0%
+mechanisms, tax breaks, incentives. Um,
+what we wanted to to emphasize here was
+
+ align:start position:0%
+what we wanted to to emphasize here was
+ 
+
+ align:start position:0%
+what we wanted to to emphasize here was
+that Germany is not one of the sunnier
+
+ align:start position:0%
+that Germany is not one of the sunnier
+ 
+
+ align:start position:0%
+that Germany is not one of the sunnier
+places in the world. Look at this. It
+
+ align:start position:0%
+places in the world. Look at this. It
+ 
+
+ align:start position:0%
+places in the world. Look at this. It
+has almost half of the modules
+
+ align:start position:0%
+has almost half of the modules
+ 
+
+ align:start position:0%
+has almost half of the modules
+installed. And yet, um, oopsie, go back
+
+ align:start position:0%
+installed. And yet, um, oopsie, go back
+ 
+
+ align:start position:0%
+installed. And yet, um, oopsie, go back
+one. Uh, it has less insulation than
+
+ align:start position:0%
+one. Uh, it has less insulation than
+ 
+
+ align:start position:0%
+one. Uh, it has less insulation than
+even here in the US northeast. Even the
+
+ align:start position:0%
+even here in the US northeast. Even the
+ 
+
+ align:start position:0%
+even here in the US northeast. Even the
+sunniest places in Germany. This is
+
+ align:start position:0%
+sunniest places in Germany. This is
+ 
+
+ align:start position:0%
+sunniest places in Germany. This is
+Bavaria. This is the place that hits 40%
+
+ align:start position:0%
+Bavaria. This is the place that hits 40%
+ 
+
+ align:start position:0%
+Bavaria. This is the place that hits 40%
+of electricity on on peak summer days
+
+ align:start position:0%
+of electricity on on peak summer days
+ 
+
+ align:start position:0%
+of electricity on on peak summer days
+coming from PV. And this is the this is
+
+ align:start position:0%
+coming from PV. And this is the this is
+ 
+
+ align:start position:0%
+coming from PV. And this is the this is
+where we are right up there. Same
+
+ align:start position:0%
+where we are right up there. Same
+ 
+
+ align:start position:0%
+where we are right up there. Same
+scale, right? So something's going on in
+
+ align:start position:0%
+scale, right? So something's going on in
+ 
+
+ align:start position:0%
+scale, right? So something's going on in
+Germany and it's not uh it's not sun. Um
+
+ align:start position:0%
+Germany and it's not uh it's not sun. Um
+ 
+
+ align:start position:0%
+Germany and it's not uh it's not sun. Um
+the uh the German government instituted
+
+ align:start position:0%
+the uh the German government instituted
+ 
+
+ align:start position:0%
+the uh the German government instituted
+a number this little D represents
+
+ align:start position:0%
+a number this little D represents
+ 
+
+ align:start position:0%
+a number this little D represents
+Deutseland Germany uh implemented a
+
+ align:start position:0%
+Deutseland Germany uh implemented a
+ 
+
+ align:start position:0%
+Deutseland Germany uh implemented a
+number of incentive programs to increase
+
+ align:start position:0%
+number of incentive programs to increase
+ 
+
+ align:start position:0%
+number of incentive programs to increase
+the amount of PV uh installed on the
+
+ align:start position:0%
+the amount of PV uh installed on the
+ 
+
+ align:start position:0%
+the amount of PV uh installed on the
+grid under the assumption that if they
+
+ align:start position:0%
+grid under the assumption that if they
+ 
+
+ align:start position:0%
+grid under the assumption that if they
+had a demand pull they would have a
+
+ align:start position:0%
+had a demand pull they would have a
+ 
+
+ align:start position:0%
+had a demand pull they would have a
+supply push, meaning they would start up
+
+ align:start position:0%
+supply push, meaning they would start up
+ 
+
+ align:start position:0%
+supply push, meaning they would start up
+local industries. Um initially didn't
+
+ align:start position:0%
+local industries. Um initially didn't
+ 
+
+ align:start position:0%
+local industries. Um initially didn't
+quite take off as fast as they hoped. So
+
+ align:start position:0%
+quite take off as fast as they hoped. So
+ 
+
+ align:start position:0%
+quite take off as fast as they hoped. So
+they began providing direct
+
+ align:start position:0%
+they began providing direct
+ 
+
+ align:start position:0%
+they began providing direct
+manufacturing support, direct subsidies
+
+ align:start position:0%
+manufacturing support, direct subsidies
+ 
+
+ align:start position:0%
+manufacturing support, direct subsidies
+to install uh PV manufacturing plants to
+
+ align:start position:0%
+to install uh PV manufacturing plants to
+ 
+
+ align:start position:0%
+to install uh PV manufacturing plants to
+the point where they were willing to pay
+
+ align:start position:0%
+the point where they were willing to pay
+ 
+
+ align:start position:0%
+the point where they were willing to pay
+uh 50 euro cents in the euro uh for each
+
+ align:start position:0%
+uh 50 euro cents in the euro uh for each
+ 
+
+ align:start position:0%
+uh 50 euro cents in the euro uh for each
+uh piece of capital equipment that moved
+
+ align:start position:0%
+uh piece of capital equipment that moved
+ 
+
+ align:start position:0%
+uh piece of capital equipment that moved
+in on German soil to produce plants in
+
+ align:start position:0%
+in on German soil to produce plants in
+ 
+
+ align:start position:0%
+in on German soil to produce plants in
+the mid-200s. Uh so that combination of
+
+ align:start position:0%
+the mid-200s. Uh so that combination of
+ 
+
+ align:start position:0%
+the mid-200s. Uh so that combination of
+of of of events left them with booming
+
+ align:start position:0%
+of of of events left them with booming
+ 
+
+ align:start position:0%
+of of of events left them with booming
+market upwards of 100,000 jobs I believe
+
+ align:start position:0%
+market upwards of 100,000 jobs I believe
+ 
+
+ align:start position:0%
+market upwards of 100,000 jobs I believe
+in in Germany related to PV
+
+ align:start position:0%
+in in Germany related to PV
+ 
+
+ align:start position:0%
+in in Germany related to PV
+manufacturing and a lot of PV installed
+
+ align:start position:0%
+manufacturing and a lot of PV installed
+ 
+
+ align:start position:0%
+manufacturing and a lot of PV installed
+on their grid um as a result of the
+
+ align:start position:0%
+on their grid um as a result of the
+ 
+
+ align:start position:0%
+on their grid um as a result of the
+market pull. So really when it comes to
+
+ align:start position:0%
+market pull. So really when it comes to
+ 
+
+ align:start position:0%
+market pull. So really when it comes to
+subsidies and support you have to
+
+ align:start position:0%
+subsidies and support you have to
+ 
+
+ align:start position:0%
+subsidies and support you have to
+decouple what is market pull which means
+
+ align:start position:0%
+decouple what is market pull which means
+ 
+
+ align:start position:0%
+decouple what is market pull which means
+we want PV installed on our grid to
+
+ align:start position:0%
+we want PV installed on our grid to
+ 
+
+ align:start position:0%
+we want PV installed on our grid to
+offset our glo our our country's carbon
+
+ align:start position:0%
+offset our glo our our country's carbon
+ 
+
+ align:start position:0%
+offset our glo our our country's carbon
+emissions um versus manufacturing push
+
+ align:start position:0%
+emissions um versus manufacturing push
+ 
+
+ align:start position:0%
+emissions um versus manufacturing push
+which is to say you want to set up a
+
+ align:start position:0%
+which is to say you want to set up a
+ 
+
+ align:start position:0%
+which is to say you want to set up a
+factory in my country fine come right in
+
+ align:start position:0%
+factory in my country fine come right in
+ 
+
+ align:start position:0%
+factory in my country fine come right in
+I'll provide you the finances I'll
+
+ align:start position:0%
+I'll provide you the finances I'll
+ 
+
+ align:start position:0%
+I'll provide you the finances I'll
+provide you a lower cost of capital on
+
+ align:start position:0%
+provide you a lower cost of capital on
+ 
+
+ align:start position:0%
+provide you a lower cost of capital on
+your loan or um help you uh by providing
+
+ align:start position:0%
+your loan or um help you uh by providing
+ 
+
+ align:start position:0%
+your loan or um help you uh by providing
+a direct grant or loan um and and this
+
+ align:start position:0%
+a direct grant or loan um and and this
+ 
+
+ align:start position:0%
+a direct grant or loan um and and this
+is uh these are two different support
+
+ align:start position:0%
+is uh these are two different support
+ 
+
+ align:start position:0%
+is uh these are two different support
+mechanisms and that's why you see that
+
+ align:start position:0%
+mechanisms and that's why you see that
+ 
+
+ align:start position:0%
+mechanisms and that's why you see that
+dichotomy
+
+ align:start position:0%
+dichotomy
+ 
+
+ align:start position:0%
+dichotomy
+uh between Germany which installs a lot
+
+ align:start position:0%
+uh between Germany which installs a lot
+ 
+
+ align:start position:0%
+uh between Germany which installs a lot
+of PV and has a decent amount of
+
+ align:start position:0%
+of PV and has a decent amount of
+ 
+
+ align:start position:0%
+of PV and has a decent amount of
+manufacturing, the US which has a lot of
+
+ align:start position:0%
+manufacturing, the US which has a lot of
+ 
+
+ align:start position:0%
+manufacturing, the US which has a lot of
+installation but not a whole lot of
+
+ align:start position:0%
+installation but not a whole lot of
+ 
+
+ align:start position:0%
+installation but not a whole lot of
+manufacturing uh traditionally although
+
+ align:start position:0%
+manufacturing uh traditionally although
+ 
+
+ align:start position:0%
+manufacturing uh traditionally although
+that's changed the support has changed
+
+ align:start position:0%
+that's changed the support has changed
+ 
+
+ align:start position:0%
+that's changed the support has changed
+over the last three years and uh China
+
+ align:start position:0%
+over the last three years and uh China
+ 
+
+ align:start position:0%
+over the last three years and uh China
+which has a heck of a lot of
+
+ align:start position:0%
+which has a heck of a lot of
+ 
+
+ align:start position:0%
+which has a heck of a lot of
+manufacturing but not a whole lot of
+
+ align:start position:0%
+manufacturing but not a whole lot of
+ 
+
+ align:start position:0%
+manufacturing but not a whole lot of
+local demand. It's because each country
+
+ align:start position:0%
+local demand. It's because each country
+ 
+
+ align:start position:0%
+local demand. It's because each country
+has adopted a different approach uh
+
+ align:start position:0%
+has adopted a different approach uh
+ 
+
+ align:start position:0%
+has adopted a different approach uh
+based on optimization of different
+
+ align:start position:0%
+based on optimization of different
+ 
+
+ align:start position:0%
+based on optimization of different
+functions. in terms of where um where a
+
+ align:start position:0%
+functions. in terms of where um where a
+ 
+
+ align:start position:0%
+functions. in terms of where um where a
+lot has happened on the state level. Um
+
+ align:start position:0%
+lot has happened on the state level. Um
+ 
+
+ align:start position:0%
+lot has happened on the state level. Um
+the these are RPS renewable portfolio
+
+ align:start position:0%
+the these are RPS renewable portfolio
+ 
+
+ align:start position:0%
+the these are RPS renewable portfolio
+standard policies with solar and
+
+ align:start position:0%
+standard policies with solar and
+ 
+
+ align:start position:0%
+standard policies with solar and
+distributed generation provisions uh
+
+ align:start position:0%
+distributed generation provisions uh
+ 
+
+ align:start position:0%
+distributed generation provisions uh
+distributed throughout the United
+
+ align:start position:0%
+distributed throughout the United
+ 
+
+ align:start position:0%
+distributed throughout the United
+States. And you can see that the states
+
+ align:start position:0%
+States. And you can see that the states
+ 
+
+ align:start position:0%
+States. And you can see that the states
+have picked up where the federal
+
+ align:start position:0%
+have picked up where the federal
+ 
+
+ align:start position:0%
+have picked up where the federal
+government lacked in terms of leadership
+
+ align:start position:0%
+government lacked in terms of leadership
+ 
+
+ align:start position:0%
+government lacked in terms of leadership
+right in terms of getting PV on the
+
+ align:start position:0%
+right in terms of getting PV on the
+ 
+
+ align:start position:0%
+right in terms of getting PV on the
+grid. The states really uh pulled hard
+
+ align:start position:0%
+grid. The states really uh pulled hard
+ 
+
+ align:start position:0%
+grid. The states really uh pulled hard
+in specifically New Jersey. Some really
+
+ align:start position:0%
+in specifically New Jersey. Some really
+ 
+
+ align:start position:0%
+in specifically New Jersey. Some really
+oddball states like New Jersey here
+
+ align:start position:0%
+oddball states like New Jersey here
+ 
+
+ align:start position:0%
+oddball states like New Jersey here
+installing about 5 gawatts of solar. Um,
+
+ align:start position:0%
+installing about 5 gawatts of solar. Um,
+ 
+
+ align:start position:0%
+installing about 5 gawatts of solar. Um,
+California had uh another uh more more
+
+ align:start position:0%
+California had uh another uh more more
+ 
+
+ align:start position:0%
+California had uh another uh more more
+of a market pull mechanism. Um, rebate
+
+ align:start position:0%
+of a market pull mechanism. Um, rebate
+ 
+
+ align:start position:0%
+of a market pull mechanism. Um, rebate
+programs for renewables. This is if you
+
+ align:start position:0%
+programs for renewables. This is if you
+ 
+
+ align:start position:0%
+programs for renewables. This is if you
+install uh solar panels, you might get a
+
+ align:start position:0%
+install uh solar panels, you might get a
+ 
+
+ align:start position:0%
+install uh solar panels, you might get a
+few thousand dollars back uh from the
+
+ align:start position:0%
+few thousand dollars back uh from the
+ 
+
+ align:start position:0%
+few thousand dollars back uh from the
+state government. And um it just gives
+
+ align:start position:0%
+state government. And um it just gives
+ 
+
+ align:start position:0%
+state government. And um it just gives
+you a sense of of how the states have
+
+ align:start position:0%
+you a sense of of how the states have
+ 
+
+ align:start position:0%
+you a sense of of how the states have
+filled in that void uh where the federal
+
+ align:start position:0%
+filled in that void uh where the federal
+ 
+
+ align:start position:0%
+filled in that void uh where the federal
+government didn't uh uh uh step in. And
+
+ align:start position:0%
+government didn't uh uh uh step in. And
+ 
+
+ align:start position:0%
+government didn't uh uh uh step in. And
+this has come in part to our detriment.
+
+ align:start position:0%
+this has come in part to our detriment.
+ 
+
+ align:start position:0%
+this has come in part to our detriment.
+nice because we can allow the the
+
+ align:start position:0%
+nice because we can allow the the
+ 
+
+ align:start position:0%
+nice because we can allow the the
+federalist approach allows individual
+
+ align:start position:0%
+federalist approach allows individual
+ 
+
+ align:start position:0%
+federalist approach allows individual
+states to say, "Hey, we prioritize green
+
+ align:start position:0%
+states to say, "Hey, we prioritize green
+ 
+
+ align:start position:0%
+states to say, "Hey, we prioritize green
+jobs. All right, let's let's support it.
+
+ align:start position:0%
+jobs. All right, let's let's support it.
+ 
+
+ align:start position:0%
+jobs. All right, let's let's support it.
+Let's make it happen." And that's
+
+ align:start position:0%
+Let's make it happen." And that's
+ 
+
+ align:start position:0%
+Let's make it happen." And that's
+certainly Massachusetts take,
+
+ align:start position:0%
+certainly Massachusetts take,
+ 
+
+ align:start position:0%
+certainly Massachusetts take,
+California, uh Texas, certain other
+
+ align:start position:0%
+California, uh Texas, certain other
+ 
+
+ align:start position:0%
+California, uh Texas, certain other
+countries throughout the US, uh certain
+
+ align:start position:0%
+countries throughout the US, uh certain
+ 
+
+ align:start position:0%
+countries throughout the US, uh certain
+other states throughout the US, um
+
+ align:start position:0%
+other states throughout the US, um
+ 
+
+ align:start position:0%
+other states throughout the US, um
+including Mississippi most recently. Um
+
+ align:start position:0%
+including Mississippi most recently. Um
+ 
+
+ align:start position:0%
+including Mississippi most recently. Um
+but the downside of that is that you
+
+ align:start position:0%
+but the downside of that is that you
+ 
+
+ align:start position:0%
+but the downside of that is that you
+have each state doing its own thing,
+
+ align:start position:0%
+have each state doing its own thing,
+ 
+
+ align:start position:0%
+have each state doing its own thing,
+each municipality, each local uh
+
+ align:start position:0%
+each municipality, each local uh
+ 
+
+ align:start position:0%
+each municipality, each local uh
+electric utility grid doing its own
+
+ align:start position:0%
+electric utility grid doing its own
+ 
+
+ align:start position:0%
+electric utility grid doing its own
+thing. And what can happen is uh
+
+ align:start position:0%
+thing. And what can happen is uh
+ 
+
+ align:start position:0%
+thing. And what can happen is uh
+diversification of support mechanisms
+
+ align:start position:0%
+diversification of support mechanisms
+ 
+
+ align:start position:0%
+diversification of support mechanisms
+and incentives to the point now that if
+
+ align:start position:0%
+and incentives to the point now that if
+ 
+
+ align:start position:0%
+and incentives to the point now that if
+you want to install panels on your roof
+
+ align:start position:0%
+you want to install panels on your roof
+ 
+
+ align:start position:0%
+you want to install panels on your roof
+in the United States, there are over
+
+ align:start position:0%
+in the United States, there are over
+ 
+
+ align:start position:0%
+in the United States, there are over
+18,000 ways you could do it within the
+
+ align:start position:0%
+18,000 ways you could do it within the
+ 
+
+ align:start position:0%
+18,000 ways you could do it within the
+US alone, 18,000 unique types of
+
+ align:start position:0%
+US alone, 18,000 unique types of
+ 
+
+ align:start position:0%
+US alone, 18,000 unique types of
+paperwork that you have to fill out uh
+
+ align:start position:0%
+paperwork that you have to fill out uh
+ 
+
+ align:start position:0%
+paperwork that you have to fill out uh
+depending on where you are in the United
+
+ align:start position:0%
+depending on where you are in the United
+ 
+
+ align:start position:0%
+depending on where you are in the United
+States. In Germany, you have one unified
+
+ align:start position:0%
+States. In Germany, you have one unified
+ 
+
+ align:start position:0%
+States. In Germany, you have one unified
+paperwork for the entire country and
+
+ align:start position:0%
+paperwork for the entire country and
+ 
+
+ align:start position:0%
+paperwork for the entire country and
+it's very short. I believe it's two
+
+ align:start position:0%
+it's very short. I believe it's two
+ 
+
+ align:start position:0%
+it's very short. I believe it's two
+pages. And in the United States, you can
+
+ align:start position:0%
+pages. And in the United States, you can
+ 
+
+ align:start position:0%
+pages. And in the United States, you can
+fill out a few reams of paper. Um, one
+
+ align:start position:0%
+fill out a few reams of paper. Um, one
+ 
+
+ align:start position:0%
+fill out a few reams of paper. Um, one
+of our our friends in California once
+
+ align:start position:0%
+of our our friends in California once
+ 
+
+ align:start position:0%
+of our our friends in California once
+estimated it takes about a dollar a watt
+
+ align:start position:0%
+estimated it takes about a dollar a watt
+ 
+
+ align:start position:0%
+estimated it takes about a dollar a watt
+uh to uh fill out paperwork um and to
+
+ align:start position:0%
+uh to uh fill out paperwork um and to
+ 
+
+ align:start position:0%
+uh to uh fill out paperwork um and to
+get certifications and so forth. Maybe
+
+ align:start position:0%
+get certifications and so forth. Maybe
+ 
+
+ align:start position:0%
+get certifications and so forth. Maybe
+it was a little bit of an exaggeration,
+
+ align:start position:0%
+it was a little bit of an exaggeration,
+ 
+
+ align:start position:0%
+it was a little bit of an exaggeration,
+but the price is high. And so recently,
+
+ align:start position:0%
+but the price is high. And so recently,
+ 
+
+ align:start position:0%
+but the price is high. And so recently,
+the DOE has attempted to address this as
+
+ align:start position:0%
+the DOE has attempted to address this as
+ 
+
+ align:start position:0%
+the DOE has attempted to address this as
+well by fostering a race to the top type
+
+ align:start position:0%
+well by fostering a race to the top type
+ 
+
+ align:start position:0%
+well by fostering a race to the top type
+uh incentive mechanism for states to uh
+
+ align:start position:0%
+uh incentive mechanism for states to uh
+ 
+
+ align:start position:0%
+uh incentive mechanism for states to uh
+facilitate in installation. But still in
+
+ align:start position:0%
+facilitate in installation. But still in
+ 
+
+ align:start position:0%
+facilitate in installation. But still in
+in Massachusetts we had remember for the
+
+ align:start position:0%
+in Massachusetts we had remember for the
+ 
+
+ align:start position:0%
+in Massachusetts we had remember for the
+system on my roof we had at least two
+
+ align:start position:0%
+system on my roof we had at least two
+ 
+
+ align:start position:0%
+system on my roof we had at least two
+inspectors come by from different
+
+ align:start position:0%
+inspectors come by from different
+ 
+
+ align:start position:0%
+inspectors come by from different
+agencies that could have been
+
+ align:start position:0%
+agencies that could have been
+ 
+
+ align:start position:0%
+agencies that could have been
+consolidated into one. Right? So while
+
+ align:start position:0%
+consolidated into one. Right? So while
+ 
+
+ align:start position:0%
+consolidated into one. Right? So while
+state independence is good and local
+
+ align:start position:0%
+state independence is good and local
+ 
+
+ align:start position:0%
+state independence is good and local
+utility independence is great from the
+
+ align:start position:0%
+utility independence is great from the
+ 
+
+ align:start position:0%
+utility independence is great from the
+perspective the federal government is
+
+ align:start position:0%
+perspective the federal government is
+ 
+
+ align:start position:0%
+perspective the federal government is
+lacking in terms of moving forward. The
+
+ align:start position:0%
+lacking in terms of moving forward. The
+ 
+
+ align:start position:0%
+lacking in terms of moving forward. The
+states can push forward at their
+
+ align:start position:0%
+states can push forward at their
+ 
+
+ align:start position:0%
+states can push forward at their
+comfortable speed. On the flip on the
+
+ align:start position:0%
+comfortable speed. On the flip on the
+ 
+
+ align:start position:0%
+comfortable speed. On the flip on the
+downside, it makes it very difficult for
+
+ align:start position:0%
+downside, it makes it very difficult for
+ 
+
+ align:start position:0%
+downside, it makes it very difficult for
+an installer company to reduce its uh
+
+ align:start position:0%
+an installer company to reduce its uh
+ 
+
+ align:start position:0%
+an installer company to reduce its uh
+costs because it has to address a
+
+ align:start position:0%
+costs because it has to address a
+ 
+
+ align:start position:0%
+costs because it has to address a
+multitude of local markets uh throughout
+
+ align:start position:0%
+multitude of local markets uh throughout
+ 
+
+ align:start position:0%
+multitude of local markets uh throughout
+the US and that uh adds adds to cost. In
+
+ align:start position:0%
+the US and that uh adds adds to cost. In
+ 
+
+ align:start position:0%
+the US and that uh adds adds to cost. In
+terms of projections, I really hesitate
+
+ align:start position:0%
+terms of projections, I really hesitate
+ 
+
+ align:start position:0%
+terms of projections, I really hesitate
+because in 2006, there were a number of
+
+ align:start position:0%
+because in 2006, there were a number of
+ 
+
+ align:start position:0%
+because in 2006, there were a number of
+projections of where we'd be in
+
+ align:start position:0%
+projections of where we'd be in
+ 
+
+ align:start position:0%
+projections of where we'd be in
+2010. And um and many of them you can
+
+ align:start position:0%
+2010. And um and many of them you can
+ 
+
+ align:start position:0%
+2010. And um and many of them you can
+see the range here going from 4 gawatt
+
+ align:start position:0%
+see the range here going from 4 gawatt
+ 
+
+ align:start position:0%
+see the range here going from 4 gawatt
+up to actually I think uh photon
+
+ align:start position:0%
+up to actually I think uh photon
+ 
+
+ align:start position:0%
+up to actually I think uh photon
+consulting had us close to 30 gigawatts
+
+ align:start position:0%
+consulting had us close to 30 gigawatts
+ 
+
+ align:start position:0%
+consulting had us close to 30 gigawatts
+back in uh in
+
+ align:start position:0%
+back in uh in
+ 
+
+ align:start position:0%
+back in uh in
+2010. Um photon consulting was closer to
+
+ align:start position:0%
+2010. Um photon consulting was closer to
+ 
+
+ align:start position:0%
+2010. Um photon consulting was closer to
+right than than most of the other
+
+ align:start position:0%
+right than than most of the other
+ 
+
+ align:start position:0%
+right than than most of the other
+groups. Interestingly, um the 4 gawatts
+
+ align:start position:0%
+groups. Interestingly, um the 4 gawatts
+ 
+
+ align:start position:0%
+groups. Interestingly, um the 4 gawatts
+was was obviously pretty far off. So
+
+ align:start position:0%
+was was obviously pretty far off. So
+ 
+
+ align:start position:0%
+was was obviously pretty far off. So
+projections are very dangerous because
+
+ align:start position:0%
+projections are very dangerous because
+ 
+
+ align:start position:0%
+projections are very dangerous because
+you could be easily wrong. Right? This
+
+ align:start position:0%
+you could be easily wrong. Right? This
+ 
+
+ align:start position:0%
+you could be easily wrong. Right? This
+is just to just to show you an example.
+
+ align:start position:0%
+is just to just to show you an example.
+ 
+
+ align:start position:0%
+is just to just to show you an example.
+Um these are projections of where the
+
+ align:start position:0%
+Um these are projections of where the
+ 
+
+ align:start position:0%
+Um these are projections of where the
+solar market is going to go. Um from the
+
+ align:start position:0%
+solar market is going to go. Um from the
+ 
+
+ align:start position:0%
+solar market is going to go. Um from the
+EPIA, which is the European Photoex
+
+ align:start position:0%
+EPIA, which is the European Photoex
+ 
+
+ align:start position:0%
+EPIA, which is the European Photoex
+Industry Association, um it's one of the
+
+ align:start position:0%
+Industry Association, um it's one of the
+ 
+
+ align:start position:0%
+Industry Association, um it's one of the
+better sources that I could find with
+
+ align:start position:0%
+better sources that I could find with
+ 
+
+ align:start position:0%
+better sources that I could find with
+the various scenarios giving you an
+
+ align:start position:0%
+the various scenarios giving you an
+ 
+
+ align:start position:0%
+the various scenarios giving you an
+indication, a tornado plot, if you will,
+
+ align:start position:0%
+indication, a tornado plot, if you will,
+ 
+
+ align:start position:0%
+indication, a tornado plot, if you will,
+of where the uh where the um market is
+
+ align:start position:0%
+of where the uh where the um market is
+ 
+
+ align:start position:0%
+of where the uh where the um market is
+is going to head over the future. And
+
+ align:start position:0%
+is going to head over the future. And
+ 
+
+ align:start position:0%
+is going to head over the future. And
+the bottom line is that most likely it
+
+ align:start position:0%
+the bottom line is that most likely it
+ 
+
+ align:start position:0%
+the bottom line is that most likely it
+will continue to grow even though it's
+
+ align:start position:0%
+will continue to grow even though it's
+ 
+
+ align:start position:0%
+will continue to grow even though it's
+going to enter a difficult year,
+
+ align:start position:0%
+going to enter a difficult year,
+ 
+
+ align:start position:0%
+going to enter a difficult year,
+difficult two years as the over supply
+
+ align:start position:0%
+difficult two years as the over supply
+ 
+
+ align:start position:0%
+difficult two years as the over supply
+condition work itself out of the market.
+
+ align:start position:0%
+condition work itself out of the market.
+ 
+
+ align:start position:0%
+condition work itself out of the market.
+Uh we're headed for some pretty massive
+
+ align:start position:0%
+Uh we're headed for some pretty massive
+ 
+
+ align:start position:0%
+Uh we're headed for some pretty massive
+growth. And just keep those numbers in
+
+ align:start position:0%
+growth. And just keep those numbers in
+ 
+
+ align:start position:0%
+growth. And just keep those numbers in
+mind. If if this grows up to be say a
+
+ align:start position:0%
+mind. If if this grows up to be say a
+ 
+
+ align:start position:0%
+mind. If if this grows up to be say a
+100 gawatt uh industry and there's two
+
+ align:start position:0%
+100 gawatt uh industry and there's two
+ 
+
+ align:start position:0%
+100 gawatt uh industry and there's two
+people per megawatt, that's 200,000
+
+ align:start position:0%
+people per megawatt, that's 200,000
+ 
+
+ align:start position:0%
+people per megawatt, that's 200,000
+people employed just in the
+
+ align:start position:0%
+people employed just in the
+ 
+
+ align:start position:0%
+people employed just in the
+manufacturing of modules, right? Um not
+
+ align:start position:0%
+manufacturing of modules, right? Um not
+ 
+
+ align:start position:0%
+manufacturing of modules, right? Um not
+counting all of the other people on top
+
+ align:start position:0%
+counting all of the other people on top
+ 
+
+ align:start position:0%
+counting all of the other people on top
+of that. maybe another order of
+
+ align:start position:0%
+of that. maybe another order of
+ 
+
+ align:start position:0%
+of that. maybe another order of
+magnitude if we use the car industry as
+
+ align:start position:0%
+magnitude if we use the car industry as
+ 
+
+ align:start position:0%
+magnitude if we use the car industry as
+an example. Uh so we could be looking at
+
+ align:start position:0%
+an example. Uh so we could be looking at
+ 
+
+ align:start position:0%
+an example. Uh so we could be looking at
+two million jobs worldwide. Uh right and
+
+ align:start position:0%
+two million jobs worldwide. Uh right and
+ 
+
+ align:start position:0%
+two million jobs worldwide. Uh right and
+uh where they are um who works on them.
+
+ align:start position:0%
+uh where they are um who works on them.
+ 
+
+ align:start position:0%
+uh where they are um who works on them.
+Uh how the value chain is distributed
+
+ align:start position:0%
+Uh how the value chain is distributed
+ 
+
+ align:start position:0%
+Uh how the value chain is distributed
+between R&D uh manufacturing. Um this is
+
+ align:start position:0%
+between R&D uh manufacturing. Um this is
+ 
+
+ align:start position:0%
+between R&D uh manufacturing. Um this is
+all all open. The next decade will
+
+ align:start position:0%
+all all open. The next decade will
+ 
+
+ align:start position:0%
+all all open. The next decade will
+decide that you'll help decide that. So
+
+ align:start position:0%
+decide that you'll help decide that. So
+ 
+
+ align:start position:0%
+decide that you'll help decide that. So
+uh with that message I'd let you go.
\ No newline at end of file
diff --git a/nG47fQ-aiHw.txt b/nG47fQ-aiHw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2b82a64fd0d8d827f706956d78be9c4e976b96b1
--- /dev/null
+++ b/nG47fQ-aiHw.txt
@@ -0,0 +1,7251 @@
+align:start position:0%
+ 
+so I think we can start so welcome to my
+
+ align:start position:0%
+so I think we can start so welcome to my
+ 
+
+ align:start position:0%
+so I think we can start so welcome to my
+lecture today we are going to learn
+
+ align:start position:0%
+lecture today we are going to learn
+ 
+
+ align:start position:0%
+lecture today we are going to learn
+about the switching lws and snubbers so
+
+ align:start position:0%
+about the switching lws and snubbers so
+ 
+
+ align:start position:0%
+about the switching lws and snubbers so
+before that I would like to have a quick
+
+ align:start position:0%
+before that I would like to have a quick
+ 
+
+ align:start position:0%
+before that I would like to have a quick
+review about our devices so one of the
+
+ align:start position:0%
+review about our devices so one of the
+ 
+
+ align:start position:0%
+review about our devices so one of the
+same Power Electronics de is is about
+
+ align:start position:0%
+same Power Electronics de is is about
+ 
+
+ align:start position:0%
+same Power Electronics de is is about
+the circuits and now these circuits play
+
+ align:start position:0%
+the circuits and now these circuits play
+ 
+
+ align:start position:0%
+the circuits and now these circuits play
+with the transistors and the transistors
+
+ align:start position:0%
+with the transistors and the transistors
+ 
+
+ align:start position:0%
+with the transistors and the transistors
+can be a bipolar trans istor or the fuel
+
+ align:start position:0%
+can be a bipolar trans istor or the fuel
+ 
+
+ align:start position:0%
+can be a bipolar trans istor or the fuel
+effect transistors so we use transistors
+
+ align:start position:0%
+effect transistors so we use transistors
+ 
+
+ align:start position:0%
+effect transistors so we use transistors
+as switches which is on and off and
+
+ align:start position:0%
+as switches which is on and off and
+ 
+
+ align:start position:0%
+as switches which is on and off and
+other analog circuits or Advanced analog
+
+ align:start position:0%
+other analog circuits or Advanced analog
+ 
+
+ align:start position:0%
+other analog circuits or Advanced analog
+circuits they use transistors as a
+
+ align:start position:0%
+circuits they use transistors as a
+ 
+
+ align:start position:0%
+circuits they use transistors as a
+current source and for the switches we
+
+ align:start position:0%
+current source and for the switches we
+ 
+
+ align:start position:0%
+current source and for the switches we
+are focusing on there could be ideal
+
+ align:start position:0%
+are focusing on there could be ideal
+ 
+
+ align:start position:0%
+are focusing on there could be ideal
+switches or practical switches for ideal
+
+ align:start position:0%
+switches or practical switches for ideal
+ 
+
+ align:start position:0%
+switches or practical switches for ideal
+switches we we we we assume the switches
+
+ align:start position:0%
+switches we we we we assume the switches
+ 
+
+ align:start position:0%
+switches we we we we assume the switches
+will inst continuously turn on and turn
+
+ align:start position:0%
+will inst continuously turn on and turn
+ 
+
+ align:start position:0%
+will inst continuously turn on and turn
+off and also during the switch on state
+
+ align:start position:0%
+off and also during the switch on state
+ 
+
+ align:start position:0%
+off and also during the switch on state
+there is no voltage drop or the resistor
+
+ align:start position:0%
+there is no voltage drop or the resistor
+ 
+
+ align:start position:0%
+there is no voltage drop or the resistor
+is zero and it can carry both positive
+
+ align:start position:0%
+is zero and it can carry both positive
+ 
+
+ align:start position:0%
+is zero and it can carry both positive
+and negative current and when the switch
+
+ align:start position:0%
+and negative current and when the switch
+ 
+
+ align:start position:0%
+and negative current and when the switch
+is off we said there will be a infinite
+
+ align:start position:0%
+is off we said there will be a infinite
+ 
+
+ align:start position:0%
+is off we said there will be a infinite
+resistor and there is no leakage current
+
+ align:start position:0%
+resistor and there is no leakage current
+ 
+
+ align:start position:0%
+resistor and there is no leakage current
+and it can also block positive voltage
+
+ align:start position:0%
+and it can also block positive voltage
+ 
+
+ align:start position:0%
+and it can also block positive voltage
+and negative voltage and also for
+
+ align:start position:0%
+and negative voltage and also for
+ 
+
+ align:start position:0%
+and negative voltage and also for
+parasitics we assume the ideal switch
+
+ align:start position:0%
+parasitics we assume the ideal switch
+ 
+
+ align:start position:0%
+parasitics we assume the ideal switch
+has no parasitics and because of this
+
+ align:start position:0%
+has no parasitics and because of this
+ 
+
+ align:start position:0%
+has no parasitics and because of this
+characteristics we said that there is no
+
+ align:start position:0%
+characteristics we said that there is no
+ 
+
+ align:start position:0%
+characteristics we said that there is no
+loss if we use the ideal switches
+
+ align:start position:0%
+loss if we use the ideal switches
+ 
+
+ align:start position:0%
+loss if we use the ideal switches
+however for reality mostly we use the
+
+ align:start position:0%
+however for reality mostly we use the
+ 
+
+ align:start position:0%
+however for reality mostly we use the
+Practical switches so at least some
+
+ align:start position:0%
+Practical switches so at least some
+ 
+
+ align:start position:0%
+Practical switches so at least some
+partical switches in the in the Lector
+
+ align:start position:0%
+partical switches in the in the Lector
+ 
+
+ align:start position:0%
+partical switches in the in the Lector
+nodes that is like BJT igbt CER which is
+
+ align:start position:0%
+nodes that is like BJT igbt CER which is
+ 
+
+ align:start position:0%
+nodes that is like BJT igbt CER which is
+also called CSR or a diode or these days
+
+ align:start position:0%
+also called CSR or a diode or these days
+ 
+
+ align:start position:0%
+also called CSR or a diode or these days
+we use mostly about the most fat or the
+
+ align:start position:0%
+we use mostly about the most fat or the
+ 
+
+ align:start position:0%
+we use mostly about the most fat or the
+wide band Gap gum nitride fat and for
+
+ align:start position:0%
+wide band Gap gum nitride fat and for
+ 
+
+ align:start position:0%
+wide band Gap gum nitride fat and for
+this practical switches they need some
+
+ align:start position:0%
+this practical switches they need some
+ 
+
+ align:start position:0%
+this practical switches they need some
+finite time to turn on and turn off and
+
+ align:start position:0%
+finite time to turn on and turn off and
+ 
+
+ align:start position:0%
+finite time to turn on and turn off and
+also when the switch is during its on
+
+ align:start position:0%
+also when the switch is during its on
+ 
+
+ align:start position:0%
+also when the switch is during its on
+state there is a finite voltage drop or
+
+ align:start position:0%
+state there is a finite voltage drop or
+ 
+
+ align:start position:0%
+state there is a finite voltage drop or
+a finite small resistors and the current
+
+ align:start position:0%
+a finite small resistors and the current
+ 
+
+ align:start position:0%
+a finite small resistors and the current
+it can carry has some polarity so let
+
+ align:start position:0%
+it can carry has some polarity so let
+ 
+
+ align:start position:0%
+it can carry has some polarity so let
+say for the BJT it can only carry the
+
+ align:start position:0%
+say for the BJT it can only carry the
+ 
+
+ align:start position:0%
+say for the BJT it can only carry the
+positive current but for most fat it can
+
+ align:start position:0%
+positive current but for most fat it can
+ 
+
+ align:start position:0%
+positive current but for most fat it can
+carry both positive and negative current
+
+ align:start position:0%
+carry both positive and negative current
+ 
+
+ align:start position:0%
+carry both positive and negative current
+and also when the switch is off the off
+
+ align:start position:0%
+and also when the switch is off the off
+ 
+
+ align:start position:0%
+and also when the switch is off the off
+resistor will be very big so there could
+
+ align:start position:0%
+resistor will be very big so there could
+ 
+
+ align:start position:0%
+resistor will be very big so there could
+be some leakage current and also the
+
+ align:start position:0%
+be some leakage current and also the
+ 
+
+ align:start position:0%
+be some leakage current and also the
+blocking voltage also has a polar
+
+ align:start position:0%
+blocking voltage also has a polar
+ 
+
+ align:start position:0%
+blocking voltage also has a polar
+polarity and because of this and also
+
+ align:start position:0%
+polarity and because of this and also
+ 
+
+ align:start position:0%
+polarity and because of this and also
+for parasitics we usually have a
+
+ align:start position:0%
+for parasitics we usually have a
+ 
+
+ align:start position:0%
+for parasitics we usually have a
+parallel capacitance in parallel with
+
+ align:start position:0%
+parallel capacitance in parallel with
+ 
+
+ align:start position:0%
+parallel capacitance in parallel with
+the switch and also some switches will
+
+ align:start position:0%
+the switch and also some switches will
+ 
+
+ align:start position:0%
+the switch and also some switches will
+have a anti parallel dial inside of them
+
+ align:start position:0%
+have a anti parallel dial inside of them
+ 
+
+ align:start position:0%
+have a anti parallel dial inside of them
+and because of this non ideal factors
+
+ align:start position:0%
+and because of this non ideal factors
+ 
+
+ align:start position:0%
+and because of this non ideal factors
+there will be some nonzero losses and
+
+ align:start position:0%
+there will be some nonzero losses and
+ 
+
+ align:start position:0%
+there will be some nonzero losses and
+the losses could be conduction loss
+
+ align:start position:0%
+the losses could be conduction loss
+ 
+
+ align:start position:0%
+the losses could be conduction loss
+during the on state all the switching
+
+ align:start position:0%
+during the on state all the switching
+ 
+
+ align:start position:0%
+during the on state all the switching
+loss when we switch turn on and turn off
+
+ align:start position:0%
+loss when we switch turn on and turn off
+ 
+
+ align:start position:0%
+loss when we switch turn on and turn off
+and also we could have some gting losss
+
+ align:start position:0%
+and also we could have some gting losss
+ 
+
+ align:start position:0%
+and also we could have some gting losss
+and some other losss so this is a quick
+
+ align:start position:0%
+and some other losss so this is a quick
+ 
+
+ align:start position:0%
+and some other losss so this is a quick
+review about our transistor and today we
+
+ align:start position:0%
+review about our transistor and today we
+ 
+
+ align:start position:0%
+review about our transistor and today we
+were focusing on the switching loss and
+
+ align:start position:0%
+were focusing on the switching loss and
+ 
+
+ align:start position:0%
+were focusing on the switching loss and
+the corresponding method to minim to to
+
+ align:start position:0%
+the corresponding method to minim to to
+ 
+
+ align:start position:0%
+the corresponding method to minim to to
+improve with the switching loss that we
+
+ align:start position:0%
+improve with the switching loss that we
+ 
+
+ align:start position:0%
+improve with the switching loss that we
+call it snubbers so let's take the most
+
+ align:start position:0%
+call it snubbers so let's take the most
+ 
+
+ align:start position:0%
+call it snubbers so let's take the most
+basic circuit B converter as an example
+
+ align:start position:0%
+basic circuit B converter as an example
+ 
+
+ align:start position:0%
+basic circuit B converter as an example
+so we have a input voltage source and we
+
+ align:start position:0%
+so we have a input voltage source and we
+ 
+
+ align:start position:0%
+so we have a input voltage source and we
+have we can have a practical switch that
+
+ align:start position:0%
+have we can have a practical switch that
+ 
+
+ align:start position:0%
+have we can have a practical switch that
+is a m fat and we can have a dial
+
+ align:start position:0%
+is a m fat and we can have a dial
+ 
+
+ align:start position:0%
+is a m fat and we can have a dial
+here and usually we will have a low pass
+
+ align:start position:0%
+here and usually we will have a low pass
+ 
+
+ align:start position:0%
+here and usually we will have a low pass
+filter L and
+
+ align:start position:0%
+filter L and
+ 
+
+ align:start position:0%
+filter L and
+c and also a resistor
+
+ align:start position:0%
+c and also a resistor
+ 
+
+ align:start position:0%
+c and also a resistor
+here so if we assume that the current
+
+ align:start position:0%
+here so if we assume that the current
+ 
+
+ align:start position:0%
+here so if we assume that the current
+flows through this inductor is constant
+
+ align:start position:0%
+flows through this inductor is constant
+ 
+
+ align:start position:0%
+flows through this inductor is constant
+which is there is no Ripple here and
+
+ align:start position:0%
+which is there is no Ripple here and
+ 
+
+ align:start position:0%
+which is there is no Ripple here and
+this inductor is pretty big and then we
+
+ align:start position:0%
+this inductor is pretty big and then we
+ 
+
+ align:start position:0%
+this inductor is pretty big and then we
+can model our circuit
+
+ align:start position:0%
+can model our circuit
+ 
+
+ align:start position:0%
+can model our circuit
+as we still have a input voltage source
+
+ align:start position:0%
+as we still have a input voltage source
+ 
+
+ align:start position:0%
+as we still have a input voltage source
+and we have a MOS
+
+ align:start position:0%
+and we have a MOS
+ 
+
+ align:start position:0%
+and we have a MOS
+fat and we have a diod
+
+ align:start position:0%
+fat and we have a diod
+ 
+
+ align:start position:0%
+fat and we have a diod
+here and now our load will be a constant
+
+ align:start position:0%
+here and now our load will be a constant
+ 
+
+ align:start position:0%
+here and now our load will be a constant
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+source so we have already know the
+
+ align:start position:0%
+source so we have already know the
+ 
+
+ align:start position:0%
+source so we have already know the
+switching pattern of the bar converter
+
+ align:start position:0%
+switching pattern of the bar converter
+ 
+
+ align:start position:0%
+switching pattern of the bar converter
+so let's see for a given switching
+
+ align:start position:0%
+so let's see for a given switching
+ 
+
+ align:start position:0%
+so let's see for a given switching
+period that is from zero to
+
+ align:start position:0%
+period that is from zero to
+ 
+
+ align:start position:0%
+period that is from zero to
+TS from zero to DTS which is the duty
+
+ align:start position:0%
+TS from zero to DTS which is the duty
+ 
+
+ align:start position:0%
+TS from zero to DTS which is the duty
+cycle the active switch all the most fat
+
+ align:start position:0%
+cycle the active switch all the most fat
+ 
+
+ align:start position:0%
+cycle the active switch all the most fat
+will turn on this load current so the
+
+ align:start position:0%
+will turn on this load current so the
+ 
+
+ align:start position:0%
+will turn on this load current so the
+switch current will be a square wave
+
+ align:start position:0%
+switch current will be a square wave
+ 
+
+ align:start position:0%
+switch current will be a square wave
+like this so this will be
+
+ align:start position:0%
+like this so this will be
+ 
+
+ align:start position:0%
+like this so this will be
+isw and for the diode when the switch is
+
+ align:start position:0%
+isw and for the diode when the switch is
+ 
+
+ align:start position:0%
+isw and for the diode when the switch is
+off during the DTs to TS this diode will
+
+ align:start position:0%
+off during the DTs to TS this diode will
+ 
+
+ align:start position:0%
+off during the DTs to TS this diode will
+flow through this load current so that
+
+ align:start position:0%
+flow through this load current so that
+ 
+
+ align:start position:0%
+flow through this load current so that
+will be a current waveform like this and
+
+ align:start position:0%
+will be a current waveform like this and
+ 
+
+ align:start position:0%
+will be a current waveform like this and
+this is a dial current so when we
+
+ align:start position:0%
+this is a dial current so when we
+ 
+
+ align:start position:0%
+this is a dial current so when we
+considering the conduction loss so what
+
+ align:start position:0%
+considering the conduction loss so what
+ 
+
+ align:start position:0%
+considering the conduction loss so what
+is the power conduction loss is still a
+
+ align:start position:0%
+is the power conduction loss is still a
+ 
+
+ align:start position:0%
+is the power conduction loss is still a
+power so what is power power is V * I I
+
+ align:start position:0%
+power so what is power power is V * I I
+ 
+
+ align:start position:0%
+power so what is power power is V * I I
+so for the most fat the conduction loss
+
+ align:start position:0%
+so for the most fat the conduction loss
+ 
+
+ align:start position:0%
+so for the most fat the conduction loss
+will be something
+
+ align:start position:0%
+will be something
+ 
+
+ align:start position:0%
+will be something
+like I RMS squ times onate
+
+ align:start position:0%
+like I RMS squ times onate
+ 
+
+ align:start position:0%
+like I RMS squ times onate
+resistance so which I said before for a
+
+ align:start position:0%
+resistance so which I said before for a
+ 
+
+ align:start position:0%
+resistance so which I said before for a
+switch for a practical switch when it's
+
+ align:start position:0%
+switch for a practical switch when it's
+ 
+
+ align:start position:0%
+switch for a practical switch when it's
+during the on state either it can be a
+
+ align:start position:0%
+during the on state either it can be a
+ 
+
+ align:start position:0%
+during the on state either it can be a
+resistor or voltage drop and for for a
+
+ align:start position:0%
+resistor or voltage drop and for for a
+ 
+
+ align:start position:0%
+resistor or voltage drop and for for a
+most fat it will be a RDS on
+
+ align:start position:0%
+most fat it will be a RDS on
+ 
+
+ align:start position:0%
+most fat it will be a RDS on
+resistor and we can calculate the RMS
+
+ align:start position:0%
+resistor and we can calculate the RMS
+ 
+
+ align:start position:0%
+resistor and we can calculate the RMS
+current for the M fat so that will be
+
+ align:start position:0%
+current for the M fat so that will be
+ 
+
+ align:start position:0%
+current for the M fat so that will be
+the duty cycle time the i² time the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rdsr so this will be the IL for its
+
+ align:start position:0%
+rdsr so this will be the IL for its
+ 
+
+ align:start position:0%
+rdsr so this will be the IL for its
+amplitude and for the
+
+ align:start position:0%
+amplitude and for the
+ 
+
+ align:start position:0%
+amplitude and for the
+diode its conduction loss will be the
+
+ align:start position:0%
+diode its conduction loss will be the
+ 
+
+ align:start position:0%
+diode its conduction loss will be the
+average current of the diod times the
+
+ align:start position:0%
+average current of the diod times the
+ 
+
+ align:start position:0%
+average current of the diod times the
+voltage drop so still the P the loss is
+
+ align:start position:0%
+voltage drop so still the P the loss is
+ 
+
+ align:start position:0%
+voltage drop so still the P the loss is
+a power power is V * I just like for the
+
+ align:start position:0%
+a power power is V * I just like for the
+ 
+
+ align:start position:0%
+a power power is V * I just like for the
+most fat the V will be I * the R so will
+
+ align:start position:0%
+most fat the V will be I * the R so will
+ 
+
+ align:start position:0%
+most fat the V will be I * the R so will
+be the i i RMS squ times the RDS s but
+
+ align:start position:0%
+be the i i RMS squ times the RDS s but
+ 
+
+ align:start position:0%
+be the i i RMS squ times the RDS s but
+for the dial it will be the average
+
+ align:start position:0%
+for the dial it will be the average
+ 
+
+ align:start position:0%
+for the dial it will be the average
+current times the voltage
+
+ align:start position:0%
+current times the voltage
+ 
+
+ align:start position:0%
+current times the voltage
+drop so that will be the Y minus D time
+
+ align:start position:0%
+drop so that will be the Y minus D time
+ 
+
+ align:start position:0%
+drop so that will be the Y minus D time
+itimes the voltage drop of the
+
+ align:start position:0%
+itimes the voltage drop of the
+ 
+
+ align:start position:0%
+itimes the voltage drop of the
+dial so I also list like during its on
+
+ align:start position:0%
+dial so I also list like during its on
+ 
+
+ align:start position:0%
+dial so I also list like during its on
+state the most fat looks like the
+
+ align:start position:0%
+state the most fat looks like the
+ 
+
+ align:start position:0%
+state the most fat looks like the
+resistor and during its un State a diod
+
+ align:start position:0%
+resistor and during its un State a diod
+ 
+
+ align:start position:0%
+resistor and during its un State a diod
+likes looks like a voltage drop and for
+
+ align:start position:0%
+likes looks like a voltage drop and for
+ 
+
+ align:start position:0%
+likes looks like a voltage drop and for
+the BJT or igbt or the icr during its un
+
+ align:start position:0%
+the BJT or igbt or the icr during its un
+ 
+
+ align:start position:0%
+the BJT or igbt or the icr during its un
+state it still looks like a voltage drop
+
+ align:start position:0%
+state it still looks like a voltage drop
+ 
+
+ align:start position:0%
+state it still looks like a voltage drop
+so when you calculate the conduction
+
+ align:start position:0%
+so when you calculate the conduction
+ 
+
+ align:start position:0%
+so when you calculate the conduction
+loss for a BJT igbt or a diode or a Sor
+
+ align:start position:0%
+loss for a BJT igbt or a diode or a Sor
+ 
+
+ align:start position:0%
+loss for a BJT igbt or a diode or a Sor
+you use the average current times the
+
+ align:start position:0%
+you use the average current times the
+ 
+
+ align:start position:0%
+you use the average current times the
+voltage drop and when you calculate the
+
+ align:start position:0%
+voltage drop and when you calculate the
+ 
+
+ align:start position:0%
+voltage drop and when you calculate the
+conduction loss for a most fat or Gallum
+
+ align:start position:0%
+conduction loss for a most fat or Gallum
+ 
+
+ align:start position:0%
+conduction loss for a most fat or Gallum
+nitride fat you use the RMS Square Times
+
+ align:start position:0%
+nitride fat you use the RMS Square Times
+ 
+
+ align:start position:0%
+nitride fat you use the RMS Square Times
+the RDS on so this is about the
+
+ align:start position:0%
+the RDS on so this is about the
+ 
+
+ align:start position:0%
+the RDS on so this is about the
+conduction
+
+ align:start position:0%
+conduction
+ 
+
+ align:start position:0%
+conduction
+loss and also today the semiconductor
+
+ align:start position:0%
+loss and also today the semiconductor
+ 
+
+ align:start position:0%
+loss and also today the semiconductor
+loss is a back of envelope so if you do
+
+ align:start position:0%
+loss is a back of envelope so if you do
+ 
+
+ align:start position:0%
+loss is a back of envelope so if you do
+more research we can model this
+
+ align:start position:0%
+more research we can model this
+ 
+
+ align:start position:0%
+more research we can model this
+conduction loss more precisely but
+
+ align:start position:0%
+conduction loss more precisely but
+ 
+
+ align:start position:0%
+conduction loss more precisely but
+generally speaking this is this can be a
+
+ align:start position:0%
+generally speaking this is this can be a
+ 
+
+ align:start position:0%
+generally speaking this is this can be a
+room of sum for a rough calculation and
+
+ align:start position:0%
+room of sum for a rough calculation and
+ 
+
+ align:start position:0%
+room of sum for a rough calculation and
+it is enough good for our
+
+ align:start position:0%
+it is enough good for our
+ 
+
+ align:start position:0%
+it is enough good for our
+design and for the conduction loss and
+
+ align:start position:0%
+design and for the conduction loss and
+ 
+
+ align:start position:0%
+design and for the conduction loss and
+and for the switching loss it is during
+
+ align:start position:0%
+and for the switching loss it is during
+ 
+
+ align:start position:0%
+and for the switching loss it is during
+the it occurs during the turn on and
+
+ align:start position:0%
+the it occurs during the turn on and
+ 
+
+ align:start position:0%
+the it occurs during the turn on and
+turn off and we need to imagine like
+
+ align:start position:0%
+turn off and we need to imagine like
+ 
+
+ align:start position:0%
+turn off and we need to imagine like
+what will be the waveform for the switch
+
+ align:start position:0%
+what will be the waveform for the switch
+ 
+
+ align:start position:0%
+what will be the waveform for the switch
+current and the switch voltage during
+
+ align:start position:0%
+current and the switch voltage during
+ 
+
+ align:start position:0%
+current and the switch voltage during
+the turn on and the turn off here we
+
+ align:start position:0%
+the turn on and the turn off here we
+ 
+
+ align:start position:0%
+the turn on and the turn off here we
+have assumption our assumption is like
+
+ align:start position:0%
+have assumption our assumption is like
+ 
+
+ align:start position:0%
+have assumption our assumption is like
+we assume the
+
+ align:start position:0%
+we assume the
+ 
+
+ align:start position:0%
+we assume the
+vsw and the isw
+
+ align:start position:0%
+vsw and the isw
+ 
+
+ align:start position:0%
+vsw and the isw
+will be linear during the
+
+ align:start position:0%
+will be linear during the
+ 
+
+ align:start position:0%
+will be linear during the
+transient and here we also assume like
+
+ align:start position:0%
+transient and here we also assume like
+ 
+
+ align:start position:0%
+transient and here we also assume like
+our dial is
+
+ align:start position:0%
+our dial is
+ 
+
+ align:start position:0%
+our dial is
+ideal so what do I mean by an ideal dial
+
+ align:start position:0%
+ideal so what do I mean by an ideal dial
+ 
+
+ align:start position:0%
+ideal so what do I mean by an ideal dial
+it is from the characteristics iway
+
+ align:start position:0%
+it is from the characteristics iway
+ 
+
+ align:start position:0%
+it is from the characteristics iway
+curve this is VD this is ID so a dial
+
+ align:start position:0%
+curve this is VD this is ID so a dial
+ 
+
+ align:start position:0%
+curve this is VD this is ID so a dial
+can conduct any amount of current during
+
+ align:start position:0%
+can conduct any amount of current during
+ 
+
+ align:start position:0%
+can conduct any amount of current during
+its un state with a zero voltage drop
+
+ align:start position:0%
+its un state with a zero voltage drop
+ 
+
+ align:start position:0%
+its un state with a zero voltage drop
+and a diode can block any amount of the
+
+ align:start position:0%
+and a diode can block any amount of the
+ 
+
+ align:start position:0%
+and a diode can block any amount of the
+voltage during its off State so this is
+
+ align:start position:0%
+voltage during its off State so this is
+ 
+
+ align:start position:0%
+voltage during its off State so this is
+the ideal diode
+
+ align:start position:0%
+the ideal diode
+ 
+
+ align:start position:0%
+the ideal diode
+and if we notate this term reference as
+
+ align:start position:0%
+and if we notate this term reference as
+ 
+
+ align:start position:0%
+and if we notate this term reference as
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+vsw this is
+
+ align:start position:0%
+vsw this is
+ 
+
+ align:start position:0%
+vsw this is
+isw and this is
+
+ align:start position:0%
+isw and this is
+ 
+
+ align:start position:0%
+isw and this is
+ID and this is
+
+ align:start position:0%
+ID and this is
+ 
+
+ align:start position:0%
+ID and this is
+VD we can simply have the KCl and kvl
+
+ align:start position:0%
+VD we can simply have the KCl and kvl
+ 
+
+ align:start position:0%
+VD we can simply have the KCl and kvl
+equation for this the KCl equation at
+
+ align:start position:0%
+equation for this the KCl equation at
+ 
+
+ align:start position:0%
+equation for this the KCl equation at
+this note will be I is equal to
+
+ align:start position:0%
+this note will be I is equal to
+ 
+
+ align:start position:0%
+this note will be I is equal to
+isw plus the
+
+ align:start position:0%
+isw plus the
+ 
+
+ align:start position:0%
+isw plus the
+ID and for the kvl equation that will be
+
+ align:start position:0%
+ID and for the kvl equation that will be
+ 
+
+ align:start position:0%
+ID and for the kvl equation that will be
+the v
+
+ align:start position:0%
+the v
+ 
+
+ align:start position:0%
+the v
+in is is equal to the
+
+ align:start position:0%
+in is is equal to the
+ 
+
+ align:start position:0%
+in is is equal to the
+vsw minus the
+
+ align:start position:0%
+vsw minus the
+ 
+
+ align:start position:0%
+vsw minus the
+VD so let's imagine what will be the
+
+ align:start position:0%
+VD so let's imagine what will be the
+ 
+
+ align:start position:0%
+VD so let's imagine what will be the
+current and voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+waveform so for turning off I would
+
+ align:start position:0%
+waveform so for turning off I would
+ 
+
+ align:start position:0%
+waveform so for turning off I would
+first say that it will be the voltage
+
+ align:start position:0%
+first say that it will be the voltage
+ 
+
+ align:start position:0%
+first say that it will be the voltage
+increase first and when the voltage
+
+ align:start position:0%
+increase first and when the voltage
+ 
+
+ align:start position:0%
+increase first and when the voltage
+increase to its maximum amplitude for
+
+ align:start position:0%
+increase to its maximum amplitude for
+ 
+
+ align:start position:0%
+increase to its maximum amplitude for
+the back convertor it's V in and then
+
+ align:start position:0%
+the back convertor it's V in and then
+ 
+
+ align:start position:0%
+the back convertor it's V in and then
+the current will
+
+ align:start position:0%
+the current will
+ 
+
+ align:start position:0%
+the current will
+drop why it's like this
+
+ align:start position:0%
+drop why it's like this
+ 
+
+ align:start position:0%
+drop why it's like this
+because from this qcl and kvl equation
+
+ align:start position:0%
+because from this qcl and kvl equation
+ 
+
+ align:start position:0%
+because from this qcl and kvl equation
+the diode cannot turn on or carry
+
+ align:start position:0%
+the diode cannot turn on or carry
+ 
+
+ align:start position:0%
+the diode cannot turn on or carry
+current until it has the zero voltage
+
+ align:start position:0%
+current until it has the zero voltage
+ 
+
+ align:start position:0%
+current until it has the zero voltage
+drop so to have the zero voltage drop
+
+ align:start position:0%
+drop so to have the zero voltage drop
+ 
+
+ align:start position:0%
+drop so to have the zero voltage drop
+you need to have the switch voltage vsw
+
+ align:start position:0%
+you need to have the switch voltage vsw
+ 
+
+ align:start position:0%
+you need to have the switch voltage vsw
+to increase to its maximum and when it's
+
+ align:start position:0%
+to increase to its maximum and when it's
+ 
+
+ align:start position:0%
+to increase to its maximum and when it's
+increase to its maximum which is V then
+
+ align:start position:0%
+increase to its maximum which is V then
+ 
+
+ align:start position:0%
+increase to its maximum which is V then
+the VD can become zero and later the
+
+ align:start position:0%
+the VD can become zero and later the
+ 
+
+ align:start position:0%
+the VD can become zero and later the
+dial can conduct the current then then
+
+ align:start position:0%
+dial can conduct the current then then
+ 
+
+ align:start position:0%
+dial can conduct the current then then
+if the dial conducts the current then
+
+ align:start position:0%
+if the dial conducts the current then
+ 
+
+ align:start position:0%
+if the dial conducts the current then
+the isw will decrease so that is during
+
+ align:start position:0%
+the isw will decrease so that is during
+ 
+
+ align:start position:0%
+the isw will decrease so that is during
+the turn off the switch voltage increase
+
+ align:start position:0%
+the turn off the switch voltage increase
+ 
+
+ align:start position:0%
+the turn off the switch voltage increase
+first and then the current and then then
+
+ align:start position:0%
+first and then the current and then then
+ 
+
+ align:start position:0%
+first and then the current and then then
+the switch current decrease
+
+ align:start position:0%
+the switch current decrease
+ 
+
+ align:start position:0%
+the switch current decrease
+later and similarly during the turn on
+
+ align:start position:0%
+later and similarly during the turn on
+ 
+
+ align:start position:0%
+later and similarly during the turn on
+we can also say that it will be the
+
+ align:start position:0%
+we can also say that it will be the
+ 
+
+ align:start position:0%
+we can also say that it will be the
+switch current increase first and when
+
+ align:start position:0%
+switch current increase first and when
+ 
+
+ align:start position:0%
+switch current increase first and when
+the switch current go to its maximum
+
+ align:start position:0%
+the switch current go to its maximum
+ 
+
+ align:start position:0%
+the switch current go to its maximum
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+I and then the switch voltage will
+
+ align:start position:0%
+I and then the switch voltage will
+ 
+
+ align:start position:0%
+I and then the switch voltage will
+decrease and why is that is also because
+
+ align:start position:0%
+decrease and why is that is also because
+ 
+
+ align:start position:0%
+decrease and why is that is also because
+of the characteristics of this dial
+
+ align:start position:0%
+of the characteristics of this dial
+ 
+
+ align:start position:0%
+of the characteristics of this dial
+because the dial cannot be turned off or
+
+ align:start position:0%
+because the dial cannot be turned off or
+ 
+
+ align:start position:0%
+because the dial cannot be turned off or
+block voltage until it has zero current
+
+ align:start position:0%
+block voltage until it has zero current
+ 
+
+ align:start position:0%
+block voltage until it has zero current
+and to have the dial to have the zero
+
+ align:start position:0%
+and to have the dial to have the zero
+ 
+
+ align:start position:0%
+and to have the dial to have the zero
+current it means the isw should flow
+
+ align:start position:0%
+current it means the isw should flow
+ 
+
+ align:start position:0%
+current it means the isw should flow
+through all the load current and which
+
+ align:start position:0%
+through all the load current and which
+ 
+
+ align:start position:0%
+through all the load current and which
+means the load current should increase
+
+ align:start position:0%
+means the load current should increase
+ 
+
+ align:start position:0%
+means the load current should increase
+first and at this time the load the
+
+ align:start position:0%
+first and at this time the load the
+ 
+
+ align:start position:0%
+first and at this time the load the
+current in the dial will become zero and
+
+ align:start position:0%
+current in the dial will become zero and
+ 
+
+ align:start position:0%
+current in the dial will become zero and
+the dial can be turn off and block the
+
+ align:start position:0%
+the dial can be turn off and block the
+ 
+
+ align:start position:0%
+the dial can be turn off and block the
+voltage and once the dial blocks the
+
+ align:start position:0%
+voltage and once the dial blocks the
+ 
+
+ align:start position:0%
+voltage and once the dial blocks the
+voltage the vsw can decrease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the switching waveforms
+
+ align:start position:0%
+so this is the switching waveforms
+ 
+
+ align:start position:0%
+so this is the switching waveforms
+during the during for the switch during
+
+ align:start position:0%
+during the during for the switch during
+ 
+
+ align:start position:0%
+during the during for the switch during
+the turn on and turn off and usually we
+
+ align:start position:0%
+the turn on and turn off and usually we
+ 
+
+ align:start position:0%
+the turn on and turn off and usually we
+notate this time interval as the
+
+ align:start position:0%
+notate this time interval as the
+ 
+
+ align:start position:0%
+notate this time interval as the
+T4 during this turn off and we have the
+
+ align:start position:0%
+T4 during this turn off and we have the
+ 
+
+ align:start position:0%
+T4 during this turn off and we have the
+this time interval as t r during its
+
+ align:start position:0%
+this time interval as t r during its
+ 
+
+ align:start position:0%
+this time interval as t r during its
+turn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on I mean for ideal switch
+
+ align:start position:0%
+on I mean for ideal switch
+ 
+
+ align:start position:0%
+on I mean for ideal switch
+because this will be zero and this will
+
+ align:start position:0%
+because this will be zero and this will
+ 
+
+ align:start position:0%
+because this will be zero and this will
+be zero the current and voltage will
+
+ align:start position:0%
+be zero the current and voltage will
+ 
+
+ align:start position:0%
+be zero the current and voltage will
+have no overlap so the ideal switch the
+
+ align:start position:0%
+have no overlap so the ideal switch the
+ 
+
+ align:start position:0%
+have no overlap so the ideal switch the
+switching loss will be zero but for
+
+ align:start position:0%
+switching loss will be zero but for
+ 
+
+ align:start position:0%
+switching loss will be zero but for
+practical switch because we have the TF
+
+ align:start position:0%
+practical switch because we have the TF
+ 
+
+ align:start position:0%
+practical switch because we have the TF
+and the TR and the switch current and
+
+ align:start position:0%
+and the TR and the switch current and
+ 
+
+ align:start position:0%
+and the TR and the switch current and
+the switch voltage will have some
+
+ align:start position:0%
+the switch voltage will have some
+ 
+
+ align:start position:0%
+the switch voltage will have some
+overlap so we will have some switching
+
+ align:start position:0%
+overlap so we will have some switching
+ 
+
+ align:start position:0%
+overlap so we will have some switching
+loss and what is loss loss is the kind
+
+ align:start position:0%
+loss and what is loss loss is the kind
+ 
+
+ align:start position:0%
+loss and what is loss loss is the kind
+of power so that will still be the
+
+ align:start position:0%
+of power so that will still be the
+ 
+
+ align:start position:0%
+of power so that will still be the
+voltage times the
+
+ align:start position:0%
+voltage times the
+ 
+
+ align:start position:0%
+voltage times the
+current so if we draw the power loss
+
+ align:start position:0%
+current so if we draw the power loss
+ 
+
+ align:start position:0%
+current so if we draw the power loss
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+curve that will be the P disapate equals
+
+ align:start position:0%
+curve that will be the P disapate equals
+ 
+
+ align:start position:0%
+curve that will be the P disapate equals
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+vsw time
+
+ align:start position:0%
+vsw time
+ 
+
+ align:start position:0%
+vsw time
+isw so during the time interval besides
+
+ align:start position:0%
+isw so during the time interval besides
+ 
+
+ align:start position:0%
+isw so during the time interval besides
+the TR and the TF it will become zero
+
+ align:start position:0%
+the TR and the TF it will become zero
+ 
+
+ align:start position:0%
+the TR and the TF it will become zero
+will become a pretty small number and
+
+ align:start position:0%
+will become a pretty small number and
+ 
+
+ align:start position:0%
+will become a pretty small number and
+during this the loss will be a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triangular and similar for the T TR for
+
+ align:start position:0%
+triangular and similar for the T TR for
+ 
+
+ align:start position:0%
+triangular and similar for the T TR for
+the turn on it will also be a triangular
+
+ align:start position:0%
+the turn on it will also be a triangular
+ 
+
+ align:start position:0%
+the turn on it will also be a triangular
+it is just simply the switch voltage
+
+ align:start position:0%
+it is just simply the switch voltage
+ 
+
+ align:start position:0%
+it is just simply the switch voltage
+times the switch current and we will
+
+ align:start position:0%
+times the switch current and we will
+ 
+
+ align:start position:0%
+times the switch current and we will
+find this will be the switching loss and
+
+ align:start position:0%
+find this will be the switching loss and
+ 
+
+ align:start position:0%
+find this will be the switching loss and
+this part of area which is the power
+
+ align:start position:0%
+this part of area which is the power
+ 
+
+ align:start position:0%
+this part of area which is the power
+integrated by the time will be the
+
+ align:start position:0%
+integrated by the time will be the
+ 
+
+ align:start position:0%
+integrated by the time will be the
+energy so this area will be the turn off
+
+ align:start position:0%
+energy so this area will be the turn off
+ 
+
+ align:start position:0%
+energy so this area will be the turn off
+energy let's say e
+
+ align:start position:0%
+energy let's say e
+ 
+
+ align:start position:0%
+energy let's say e
+off and this area will be the turn on
+
+ align:start position:0%
+off and this area will be the turn on
+ 
+
+ align:start position:0%
+off and this area will be the turn on
+energy let's say the E
+
+ align:start position:0%
+energy let's say the E
+ 
+
+ align:start position:0%
+energy let's say the E
+on so that is like if we switch this
+
+ align:start position:0%
+on so that is like if we switch this
+ 
+
+ align:start position:0%
+on so that is like if we switch this
+device in one period we switch off and
+
+ align:start position:0%
+device in one period we switch off and
+ 
+
+ align:start position:0%
+device in one period we switch off and
+we switch on we will we will lose part
+
+ align:start position:0%
+we switch on we will we will lose part
+ 
+
+ align:start position:0%
+we switch on we will we will lose part
+of this energy and as we said like the
+
+ align:start position:0%
+of this energy and as we said like the
+ 
+
+ align:start position:0%
+of this energy and as we said like the
+switching our power converters they
+
+ align:start position:0%
+switching our power converters they
+ 
+
+ align:start position:0%
+switching our power converters they
+switch frequently there's a switching
+
+ align:start position:0%
+switch frequently there's a switching
+ 
+
+ align:start position:0%
+switch frequently there's a switching
+frequency definition so then when we
+
+ align:start position:0%
+frequency definition so then when we
+ 
+
+ align:start position:0%
+frequency definition so then when we
+think about the switching
+
+ align:start position:0%
+think about the switching
+ 
+
+ align:start position:0%
+think about the switching
+loss that will be this triangular area
+
+ align:start position:0%
+loss that will be this triangular area
+ 
+
+ align:start position:0%
+loss that will be this triangular area
+which will be the half TF times the v
+
+ align:start position:0%
+which will be the half TF times the v
+ 
+
+ align:start position:0%
+which will be the half TF times the v
+in times the I which is the turn off
+
+ align:start position:0%
+in times the I which is the turn off
+ 
+
+ align:start position:0%
+in times the I which is the turn off
+energy plus the turn on energy which is
+
+ align:start position:0%
+energy plus the turn on energy which is
+ 
+
+ align:start position:0%
+energy plus the turn on energy which is
+the time times the peak value V in times
+
+ align:start position:0%
+the time times the peak value V in times
+ 
+
+ align:start position:0%
+the time times the peak value V in times
+I and Times by The switching
+
+ align:start position:0%
+I and Times by The switching
+ 
+
+ align:start position:0%
+I and Times by The switching
+frequency that will be our switching
+
+ align:start position:0%
+frequency that will be our switching
+ 
+
+ align:start position:0%
+frequency that will be our switching
+loss and you can also consider like with
+
+ align:start position:0%
+loss and you can also consider like with
+ 
+
+ align:start position:0%
+loss and you can also consider like with
+times the switching frequency is
+
+ align:start position:0%
+times the switching frequency is
+ 
+
+ align:start position:0%
+times the switching frequency is
+equivalent to divided by the switching
+
+ align:start position:0%
+equivalent to divided by the switching
+ 
+
+ align:start position:0%
+equivalent to divided by the switching
+period And if you divide it by the
+
+ align:start position:0%
+period And if you divide it by the
+ 
+
+ align:start position:0%
+period And if you divide it by the
+switching period that will be an average
+
+ align:start position:0%
+switching period that will be an average
+ 
+
+ align:start position:0%
+switching period that will be an average
+power of it so it's still the same
+
+ align:start position:0%
+power of it so it's still the same
+ 
+
+ align:start position:0%
+power of it so it's still the same
+definition but you can look it in two
+
+ align:start position:0%
+definition but you can look it in two
+ 
+
+ align:start position:0%
+definition but you can look it in two
+aspect and also for the switching loss
+
+ align:start position:0%
+aspect and also for the switching loss
+ 
+
+ align:start position:0%
+aspect and also for the switching loss
+this is kind of killing us in our
+
+ align:start position:0%
+this is kind of killing us in our
+ 
+
+ align:start position:0%
+this is kind of killing us in our
+current converters so to to to decrease
+
+ align:start position:0%
+current converters so to to to decrease
+ 
+
+ align:start position:0%
+current converters so to to to decrease
+the switching loss we can decrease the
+
+ align:start position:0%
+the switching loss we can decrease the
+ 
+
+ align:start position:0%
+the switching loss we can decrease the
+switching frequency but however if we
+
+ align:start position:0%
+switching frequency but however if we
+ 
+
+ align:start position:0%
+switching frequency but however if we
+decreasing the switching frequency our
+
+ align:start position:0%
+decreasing the switching frequency our
+ 
+
+ align:start position:0%
+decreasing the switching frequency our
+passive component like the inductor or
+
+ align:start position:0%
+passive component like the inductor or
+ 
+
+ align:start position:0%
+passive component like the inductor or
+the capacitor will be very big so which
+
+ align:start position:0%
+the capacitor will be very big so which
+ 
+
+ align:start position:0%
+the capacitor will be very big so which
+limits our power density and our valve
+
+ align:start position:0%
+limits our power density and our valve
+ 
+
+ align:start position:0%
+limits our power density and our valve
+volume of our converter so we usually
+
+ align:start position:0%
+volume of our converter so we usually
+ 
+
+ align:start position:0%
+volume of our converter so we usually
+want to increase our switching frequency
+
+ align:start position:0%
+want to increase our switching frequency
+ 
+
+ align:start position:0%
+want to increase our switching frequency
+but the switching loss will limit us
+
+ align:start position:0%
+but the switching loss will limit us
+ 
+
+ align:start position:0%
+but the switching loss will limit us
+like how how large or how fast can we
+
+ align:start position:0%
+like how how large or how fast can we
+ 
+
+ align:start position:0%
+like how how large or how fast can we
+switch so another thing to minim to
+
+ align:start position:0%
+switch so another thing to minim to
+ 
+
+ align:start position:0%
+switch so another thing to minim to
+reduce the switching frequency is like
+
+ align:start position:0%
+reduce the switching frequency is like
+ 
+
+ align:start position:0%
+reduce the switching frequency is like
+can we decrease the TF or the TR or we
+
+ align:start position:0%
+can we decrease the TF or the TR or we
+ 
+
+ align:start position:0%
+can we decrease the TF or the TR or we
+decrease the turn on turn off energy or
+
+ align:start position:0%
+decrease the turn on turn off energy or
+ 
+
+ align:start position:0%
+decrease the turn on turn off energy or
+the turn on turn on energy so that comes
+
+ align:start position:0%
+the turn on turn on energy so that comes
+ 
+
+ align:start position:0%
+the turn on turn on energy so that comes
+with our
+
+ align:start position:0%
+with our
+ 
+
+ align:start position:0%
+with our
+snubber so before that let's have a demo
+
+ align:start position:0%
+snubber so before that let's have a demo
+ 
+
+ align:start position:0%
+snubber so before that let's have a demo
+of the switching lws so Rafa will do a
+
+ align:start position:0%
+of the switching lws so Rafa will do a
+ 
+
+ align:start position:0%
+of the switching lws so Rafa will do a
+demo and before we start the demo do you
+
+ align:start position:0%
+demo and before we start the demo do you
+ 
+
+ align:start position:0%
+demo and before we start the demo do you
+have any
+
+ align:start position:0%
+have any
+ 
+
+ align:start position:0%
+have any
+questions all right so I have a circuit
+
+ align:start position:0%
+questions all right so I have a circuit
+ 
+
+ align:start position:0%
+questions all right so I have a circuit
+here that's designed to help us look at
+
+ align:start position:0%
+here that's designed to help us look at
+ 
+
+ align:start position:0%
+here that's designed to help us look at
+the voltage and the current of a mosfet
+
+ align:start position:0%
+the voltage and the current of a mosfet
+ 
+
+ align:start position:0%
+the voltage and the current of a mosfet
+when we're turning it on or off so here
+
+ align:start position:0%
+when we're turning it on or off so here
+ 
+
+ align:start position:0%
+when we're turning it on or off so here
+you can see two
+
+ align:start position:0%
+you can see two
+ 
+
+ align:start position:0%
+you can see two
+transitions the parle or pink the pink W
+
+ align:start position:0%
+transitions the parle or pink the pink W
+ 
+
+ align:start position:0%
+transitions the parle or pink the pink W
+form is the voltage W form and the
+
+ align:start position:0%
+form is the voltage W form and the
+ 
+
+ align:start position:0%
+form is the voltage W form and the
+yellow W form is the current W form so
+
+ align:start position:0%
+yellow W form is the current W form so
+ 
+
+ align:start position:0%
+yellow W form is the current W form so
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+left the yellow webform Rises and the
+
+ align:start position:0%
+left the yellow webform Rises and the
+ 
+
+ align:start position:0%
+left the yellow webform Rises and the
+voltage is falling which means there's
+
+ align:start position:0%
+voltage is falling which means there's
+ 
+
+ align:start position:0%
+voltage is falling which means there's
+no voltage across the switch and the
+
+ align:start position:0%
+no voltage across the switch and the
+ 
+
+ align:start position:0%
+no voltage across the switch and the
+switch turns on on the right the the
+
+ align:start position:0%
+switch turns on on the right the the
+ 
+
+ align:start position:0%
+switch turns on on the right the the
+current the yellow vform is falling and
+
+ align:start position:0%
+current the yellow vform is falling and
+ 
+
+ align:start position:0%
+current the yellow vform is falling and
+the pink webform is rising again which
+
+ align:start position:0%
+the pink webform is rising again which
+ 
+
+ align:start position:0%
+the pink webform is rising again which
+means the switch is turning off now let
+
+ align:start position:0%
+means the switch is turning off now let
+ 
+
+ align:start position:0%
+means the switch is turning off now let
+me zoom
+
+ align:start position:0%
+me zoom
+ 
+
+ align:start position:0%
+me zoom
+on in one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transition let me zoom in on the turn on
+
+ align:start position:0%
+transition let me zoom in on the turn on
+ 
+
+ align:start position:0%
+transition let me zoom in on the turn on
+transition okay so as you can notice the
+
+ align:start position:0%
+transition okay so as you can notice the
+ 
+
+ align:start position:0%
+transition okay so as you can notice the
+yellow form is rising pretty quickly but
+
+ align:start position:0%
+yellow form is rising pretty quickly but
+ 
+
+ align:start position:0%
+yellow form is rising pretty quickly but
+the pink one which is a voltage War form
+
+ align:start position:0%
+the pink one which is a voltage War form
+ 
+
+ align:start position:0%
+the pink one which is a voltage War form
+takes some time time to completely hit
+
+ align:start position:0%
+takes some time time to completely hit
+ 
+
+ align:start position:0%
+takes some time time to completely hit
+zero which is the rise time and fall
+
+ align:start position:0%
+zero which is the rise time and fall
+ 
+
+ align:start position:0%
+zero which is the rise time and fall
+time Sheen was talking about and what
+
+ align:start position:0%
+time Sheen was talking about and what
+ 
+
+ align:start position:0%
+time Sheen was talking about and what
+will this do this means that there is a
+
+ align:start position:0%
+will this do this means that there is a
+ 
+
+ align:start position:0%
+will this do this means that there is a
+overlap time between the pink and the
+
+ align:start position:0%
+overlap time between the pink and the
+ 
+
+ align:start position:0%
+overlap time between the pink and the
+yellow we form Crossing and that's the
+
+ align:start position:0%
+yellow we form Crossing and that's the
+ 
+
+ align:start position:0%
+yellow we form Crossing and that's the
+overlap time creating the overlap loss
+
+ align:start position:0%
+overlap time creating the overlap loss
+ 
+
+ align:start position:0%
+overlap time creating the overlap loss
+now there's another sort of loss here
+
+ align:start position:0%
+now there's another sort of loss here
+ 
+
+ align:start position:0%
+now there's another sort of loss here
+notice when the switch is turning on the
+
+ align:start position:0%
+notice when the switch is turning on the
+ 
+
+ align:start position:0%
+notice when the switch is turning on the
+voltage is non zero which means if the
+
+ align:start position:0%
+voltage is non zero which means if the
+ 
+
+ align:start position:0%
+voltage is non zero which means if the
+switches capacitance is storing energy
+
+ align:start position:0%
+switches capacitance is storing energy
+ 
+
+ align:start position:0%
+switches capacitance is storing energy
+in it now let me also show you the power
+
+ align:start position:0%
+in it now let me also show you the power
+ 
+
+ align:start position:0%
+in it now let me also show you the power
+lws so you can see like the yellow Curve
+
+ align:start position:0%
+lws so you can see like the yellow Curve
+ 
+
+ align:start position:0%
+lws so you can see like the yellow Curve
+will be the current and the purple Curve
+
+ align:start position:0%
+will be the current and the purple Curve
+ 
+
+ align:start position:0%
+will be the current and the purple Curve
+will be the voltage and you can see that
+
+ align:start position:0%
+will be the voltage and you can see that
+ 
+
+ align:start position:0%
+will be the voltage and you can see that
+for hard switching it is the voltage
+
+ align:start position:0%
+for hard switching it is the voltage
+ 
+
+ align:start position:0%
+for hard switching it is the voltage
+increase first and then the current will
+
+ align:start position:0%
+increase first and then the current will
+ 
+
+ align:start position:0%
+increase first and then the current will
+decrease so which match with our Theory
+
+ align:start position:0%
+decrease so which match with our Theory
+ 
+
+ align:start position:0%
+decrease so which match with our Theory
+and you can also observe that for the
+
+ align:start position:0%
+and you can also observe that for the
+ 
+
+ align:start position:0%
+and you can also observe that for the
+yellow curve which we which is the
+
+ align:start position:0%
+yellow curve which we which is the
+ 
+
+ align:start position:0%
+yellow curve which we which is the
+voltage of sorry the the purple curve
+
+ align:start position:0%
+voltage of sorry the the purple curve
+ 
+
+ align:start position:0%
+voltage of sorry the the purple curve
+which is the voltage and during it onate
+
+ align:start position:0%
+which is the voltage and during it onate
+ 
+
+ align:start position:0%
+which is the voltage and during it onate
+it has a very small value so that will
+
+ align:start position:0%
+it has a very small value so that will
+ 
+
+ align:start position:0%
+it has a very small value so that will
+be the onate voltage drop it could be
+
+ align:start position:0%
+be the onate voltage drop it could be
+ 
+
+ align:start position:0%
+be the onate voltage drop it could be
+the RMS current times the
+
+ align:start position:0%
+the RMS current times the
+ 
+
+ align:start position:0%
+the RMS current times the
+rdsr yeah it's really hard to see but
+
+ align:start position:0%
+rdsr yeah it's really hard to see but
+ 
+
+ align:start position:0%
+rdsr yeah it's really hard to see but
+the purplish waveform the zigzag we form
+
+ align:start position:0%
+the purplish waveform the zigzag we form
+ 
+
+ align:start position:0%
+the purplish waveform the zigzag we form
+is the power loss you can also see that
+
+ align:start position:0%
+is the power loss you can also see that
+ 
+
+ align:start position:0%
+is the power loss you can also see that
+in here in the off State the line is
+
+ align:start position:0%
+in here in the off State the line is
+ 
+
+ align:start position:0%
+in here in the off State the line is
+pretty like almost zero because there's
+
+ align:start position:0%
+pretty like almost zero because there's
+ 
+
+ align:start position:0%
+pretty like almost zero because there's
+no voltage because there's no current in
+
+ align:start position:0%
+no voltage because there's no current in
+ 
+
+ align:start position:0%
+no voltage because there's no current in
+the switch in the other hand whenever
+
+ align:start position:0%
+the switch in the other hand whenever
+ 
+
+ align:start position:0%
+the switch in the other hand whenever
+you're seeing all those reps that's
+
+ align:start position:0%
+you're seeing all those reps that's
+ 
+
+ align:start position:0%
+you're seeing all those reps that's
+because when the switch is on it it acts
+
+ align:start position:0%
+because when the switch is on it it acts
+ 
+
+ align:start position:0%
+because when the switch is on it it acts
+like a resistor so it has some RDS on
+
+ align:start position:0%
+like a resistor so it has some RDS on
+ 
+
+ align:start position:0%
+like a resistor so it has some RDS on
+and nonzero current i sare r which makes
+
+ align:start position:0%
+and nonzero current i sare r which makes
+ 
+
+ align:start position:0%
+and nonzero current i sare r which makes
+the loss so now the mass shows the time
+
+ align:start position:0%
+the loss so now the mass shows the time
+ 
+
+ align:start position:0%
+the loss so now the mass shows the time
+of of the multiple of the voltage and
+
+ align:start position:0%
+of of the multiple of the voltage and
+ 
+
+ align:start position:0%
+of of the multiple of the voltage and
+the current and you can observe there's
+
+ align:start position:0%
+the current and you can observe there's
+ 
+
+ align:start position:0%
+the current and you can observe there's
+a triangular of that yeah so like we
+
+ align:start position:0%
+a triangular of that yeah so like we
+ 
+
+ align:start position:0%
+a triangular of that yeah so like we
+turn on and off our switch how many
+
+ align:start position:0%
+turn on and off our switch how many
+ 
+
+ align:start position:0%
+turn on and off our switch how many
+times 10 million times or 100,000 times
+
+ align:start position:0%
+times 10 million times or 100,000 times
+ 
+
+ align:start position:0%
+times 10 million times or 100,000 times
+per second it can seem trivial for one
+
+ align:start position:0%
+per second it can seem trivial for one
+ 
+
+ align:start position:0%
+per second it can seem trivial for one
+time but if we keep doing it this many
+
+ align:start position:0%
+time but if we keep doing it this many
+ 
+
+ align:start position:0%
+time but if we keep doing it this many
+times we cannot neglect this
+
+ align:start position:0%
+times we cannot neglect this
+ 
+
+ align:start position:0%
+times we cannot neglect this
+anymore thank you so another thing like
+
+ align:start position:0%
+anymore thank you so another thing like
+ 
+
+ align:start position:0%
+anymore thank you so another thing like
+I want to I'm not sure if You observe so
+
+ align:start position:0%
+I want to I'm not sure if You observe so
+ 
+
+ align:start position:0%
+I want to I'm not sure if You observe so
+during the switch turn off we do observe
+
+ align:start position:0%
+during the switch turn off we do observe
+ 
+
+ align:start position:0%
+during the switch turn off we do observe
+like the voltage they have some
+
+ align:start position:0%
+like the voltage they have some
+ 
+
+ align:start position:0%
+like the voltage they have some
+resonance here so this is because like
+
+ align:start position:0%
+resonance here so this is because like
+ 
+
+ align:start position:0%
+resonance here so this is because like
+as I said we want to decrease the TR and
+
+ align:start position:0%
+as I said we want to decrease the TR and
+ 
+
+ align:start position:0%
+as I said we want to decrease the TR and
+the TF but we have some limitations so
+
+ align:start position:0%
+the TF but we have some limitations so
+ 
+
+ align:start position:0%
+the TF but we have some limitations so
+the first limitations will be the
+
+ align:start position:0%
+the first limitations will be the
+ 
+
+ align:start position:0%
+the first limitations will be the
+parasitics so why so the parasitics is
+
+ align:start position:0%
+parasitics so why so the parasitics is
+ 
+
+ align:start position:0%
+parasitics so why so the parasitics is
+some unwanted parameters inside of the
+
+ align:start position:0%
+some unwanted parameters inside of the
+ 
+
+ align:start position:0%
+some unwanted parameters inside of the
+circuit so for example the parasitics
+
+ align:start position:0%
+circuit so for example the parasitics
+ 
+
+ align:start position:0%
+circuit so for example the parasitics
+could come from there maybe a parallel
+
+ align:start position:0%
+could come from there maybe a parallel
+ 
+
+ align:start position:0%
+could come from there maybe a parallel
+capacitance in parallel with the switch
+
+ align:start position:0%
+capacitance in parallel with the switch
+ 
+
+ align:start position:0%
+capacitance in parallel with the switch
+and for the and also there could be some
+
+ align:start position:0%
+and for the and also there could be some
+ 
+
+ align:start position:0%
+and for the and also there could be some
+straight inductance and when the switch
+
+ align:start position:0%
+straight inductance and when the switch
+ 
+
+ align:start position:0%
+straight inductance and when the switch
+is turn off this this parallel
+
+ align:start position:0%
+is turn off this this parallel
+ 
+
+ align:start position:0%
+is turn off this this parallel
+capacitance can resonate with this
+
+ align:start position:0%
+capacitance can resonate with this
+ 
+
+ align:start position:0%
+capacitance can resonate with this
+straight inductance and that will cause
+
+ align:start position:0%
+straight inductance and that will cause
+ 
+
+ align:start position:0%
+straight inductance and that will cause
+overshoot during the switch turn off and
+
+ align:start position:0%
+overshoot during the switch turn off and
+ 
+
+ align:start position:0%
+overshoot during the switch turn off and
+this overshoot can kill the switch so so
+
+ align:start position:0%
+this overshoot can kill the switch so so
+ 
+
+ align:start position:0%
+this overshoot can kill the switch so so
+this is one one one thing like we have
+
+ align:start position:0%
+this is one one one thing like we have
+ 
+
+ align:start position:0%
+this is one one one thing like we have
+the limitation for the TR and the TF and
+
+ align:start position:0%
+the limitation for the TR and the TF and
+ 
+
+ align:start position:0%
+the limitation for the TR and the TF and
+the second is is about the during the
+
+ align:start position:0%
+the second is is about the during the
+ 
+
+ align:start position:0%
+the second is is about the during the
+transient if we have very high if we
+
+ align:start position:0%
+transient if we have very high if we
+ 
+
+ align:start position:0%
+transient if we have very high if we
+have pretty low we have pretty small TF
+
+ align:start position:0%
+have pretty low we have pretty small TF
+ 
+
+ align:start position:0%
+have pretty low we have pretty small TF
+and TR our D DT or the DVT could be very
+
+ align:start position:0%
+and TR our D DT or the DVT could be very
+ 
+
+ align:start position:0%
+and TR our D DT or the DVT could be very
+large so what do I mean by the DT and DV
+
+ align:start position:0%
+large so what do I mean by the DT and DV
+ 
+
+ align:start position:0%
+large so what do I mean by the DT and DV
+DT so that will be the slope for the
+
+ align:start position:0%
+DT so that will be the slope for the
+ 
+
+ align:start position:0%
+DT so that will be the slope for the
+rising voltage or the falling current
+
+ align:start position:0%
+rising voltage or the falling current
+ 
+
+ align:start position:0%
+rising voltage or the falling current
+all the slope for the rising current and
+
+ align:start position:0%
+all the slope for the rising current and
+ 
+
+ align:start position:0%
+all the slope for the rising current and
+the falling voltage and this D DT and a
+
+ align:start position:0%
+the falling voltage and this D DT and a
+ 
+
+ align:start position:0%
+the falling voltage and this D DT and a
+dvdt they can have some carine inductor
+
+ align:start position:0%
+dvdt they can have some carine inductor
+ 
+
+ align:start position:0%
+dvdt they can have some carine inductor
+or caraline capacitor so imagine like if
+
+ align:start position:0%
+or caraline capacitor so imagine like if
+ 
+
+ align:start position:0%
+or caraline capacitor so imagine like if
+we have a caraline inductor which is L
+
+ align:start position:0%
+we have a caraline inductor which is L
+ 
+
+ align:start position:0%
+we have a caraline inductor which is L
+this ldt will cause some voltage and if
+
+ align:start position:0%
+this ldt will cause some voltage and if
+ 
+
+ align:start position:0%
+this ldt will cause some voltage and if
+we have a caring capacitor which is C
+
+ align:start position:0%
+we have a caring capacitor which is C
+ 
+
+ align:start position:0%
+we have a caring capacitor which is C
+this c dvdt will cause some current so
+
+ align:start position:0%
+this c dvdt will cause some current so
+ 
+
+ align:start position:0%
+this c dvdt will cause some current so
+previously if we have our DT or dvdt
+
+ align:start position:0%
+previously if we have our DT or dvdt
+ 
+
+ align:start position:0%
+previously if we have our DT or dvdt
+pretty small and our parasitics pretty
+
+ align:start position:0%
+pretty small and our parasitics pretty
+ 
+
+ align:start position:0%
+pretty small and our parasitics pretty
+small these things will not match our
+
+ align:start position:0%
+small these things will not match our
+ 
+
+ align:start position:0%
+small these things will not match our
+control circuit but either if we have a
+
+ align:start position:0%
+control circuit but either if we have a
+ 
+
+ align:start position:0%
+control circuit but either if we have a
+large inductance or a large capacitor
+
+ align:start position:0%
+large inductance or a large capacitor
+ 
+
+ align:start position:0%
+large inductance or a large capacitor
+together with a large DT or dvdt this
+
+ align:start position:0%
+together with a large DT or dvdt this
+ 
+
+ align:start position:0%
+together with a large DT or dvdt this
+voltage or current they are unexpected
+
+ align:start position:0%
+voltage or current they are unexpected
+ 
+
+ align:start position:0%
+voltage or current they are unexpected
+they can cause some errors for our
+
+ align:start position:0%
+they can cause some errors for our
+ 
+
+ align:start position:0%
+they can cause some errors for our
+control circuit so this is the second
+
+ align:start position:0%
+control circuit so this is the second
+ 
+
+ align:start position:0%
+control circuit so this is the second
+limitation and for the third limitation
+
+ align:start position:0%
+limitation and for the third limitation
+ 
+
+ align:start position:0%
+limitation and for the third limitation
+for the device itself we sometimes have
+
+ align:start position:0%
+for the device itself we sometimes have
+ 
+
+ align:start position:0%
+for the device itself we sometimes have
+the D DT or the
+
+ align:start position:0%
+the D DT or the
+ 
+
+ align:start position:0%
+the D DT or the
+dvdt requirement so the upper the second
+
+ align:start position:0%
+dvdt requirement so the upper the second
+ 
+
+ align:start position:0%
+dvdt requirement so the upper the second
+one is for the Emi issues but for this
+
+ align:start position:0%
+one is for the Emi issues but for this
+ 
+
+ align:start position:0%
+one is for the Emi issues but for this
+this is bad for the device itself it has
+
+ align:start position:0%
+this is bad for the device itself it has
+ 
+
+ align:start position:0%
+this is bad for the device itself it has
+nothing to do with the control circuits
+
+ align:start position:0%
+nothing to do with the control circuits
+ 
+
+ align:start position:0%
+nothing to do with the control circuits
+so so for example if we have a large
+
+ align:start position:0%
+so so for example if we have a large
+ 
+
+ align:start position:0%
+so so for example if we have a large
+current rating device let's say the igbt
+
+ align:start position:0%
+current rating device let's say the igbt
+ 
+
+ align:start position:0%
+current rating device let's say the igbt
+or the sccr if the DT is pretty if the
+
+ align:start position:0%
+or the sccr if the DT is pretty if the
+ 
+
+ align:start position:0%
+or the sccr if the DT is pretty if the
+DT is pretty large so in a short time
+
+ align:start position:0%
+DT is pretty large so in a short time
+ 
+
+ align:start position:0%
+DT is pretty large so in a short time
+the current cannot spread for the
+
+ align:start position:0%
+the current cannot spread for the
+ 
+
+ align:start position:0%
+the current cannot spread for the
+parallel die or the multiple wear bound
+
+ align:start position:0%
+parallel die or the multiple wear bound
+ 
+
+ align:start position:0%
+parallel die or the multiple wear bound
+so maybe one die or maybe one we Bond
+
+ align:start position:0%
+so maybe one die or maybe one we Bond
+ 
+
+ align:start position:0%
+so maybe one die or maybe one we Bond
+will blow up so that will destroy our
+
+ align:start position:0%
+will blow up so that will destroy our
+ 
+
+ align:start position:0%
+will blow up so that will destroy our
+device and for the DT if we have a high
+
+ align:start position:0%
+device and for the DT if we have a high
+ 
+
+ align:start position:0%
+device and for the DT if we have a high
+DT inside of the sirer it can trigger
+
+ align:start position:0%
+DT inside of the sirer it can trigger
+ 
+
+ align:start position:0%
+DT inside of the sirer it can trigger
+the syor back to on so usually we want
+
+ align:start position:0%
+the syor back to on so usually we want
+ 
+
+ align:start position:0%
+the syor back to on so usually we want
+to turn off the device but because of
+
+ align:start position:0%
+to turn off the device but because of
+ 
+
+ align:start position:0%
+to turn off the device but because of
+this High dvdt inside of the CER it can
+
+ align:start position:0%
+this High dvdt inside of the CER it can
+ 
+
+ align:start position:0%
+this High dvdt inside of the CER it can
+Tri trigger the CER back on so this is
+
+ align:start position:0%
+Tri trigger the CER back on so this is
+ 
+
+ align:start position:0%
+Tri trigger the CER back on so this is
+the third limitations for the TR and TF
+
+ align:start position:0%
+the third limitations for the TR and TF
+ 
+
+ align:start position:0%
+the third limitations for the TR and TF
+and usually the fourth one we said every
+
+ align:start position:0%
+and usually the fourth one we said every
+ 
+
+ align:start position:0%
+and usually the fourth one we said every
+device has a safe operating
+
+ align:start position:0%
+device has a safe operating
+ 
+
+ align:start position:0%
+device has a safe operating
+area so let's draw the vi curve of a
+
+ align:start position:0%
+area so let's draw the vi curve of a
+ 
+
+ align:start position:0%
+area so let's draw the vi curve of a
+device if this is V this is I so for
+
+ align:start position:0%
+device if this is V this is I so for
+ 
+
+ align:start position:0%
+device if this is V this is I so for
+normal device we have a maximum current
+
+ align:start position:0%
+normal device we have a maximum current
+ 
+
+ align:start position:0%
+normal device we have a maximum current
+rating and we also have a maximum off
+
+ align:start position:0%
+rating and we also have a maximum off
+ 
+
+ align:start position:0%
+rating and we also have a maximum off
+voltage rating but this is not like a
+
+ align:start position:0%
+voltage rating but this is not like a
+ 
+
+ align:start position:0%
+voltage rating but this is not like a
+square because we also have some power
+
+ align:start position:0%
+square because we also have some power
+ 
+
+ align:start position:0%
+square because we also have some power
+limitation or some Thal limitation so
+
+ align:start position:0%
+limitation or some Thal limitation so
+ 
+
+ align:start position:0%
+limitation or some Thal limitation so
+this this is a safe operating area for a
+
+ align:start position:0%
+this this is a safe operating area for a
+ 
+
+ align:start position:0%
+this this is a safe operating area for a
+device and we cannot have our switch
+
+ align:start position:0%
+device and we cannot have our switch
+ 
+
+ align:start position:0%
+device and we cannot have our switch
+voltage or switch current exceed this
+
+ align:start position:0%
+voltage or switch current exceed this
+ 
+
+ align:start position:0%
+voltage or switch current exceed this
+safe operating area for con for
+
+ align:start position:0%
+safe operating area for con for
+ 
+
+ align:start position:0%
+safe operating area for con for
+statistics operation or for a instaneous
+
+ align:start position:0%
+statistics operation or for a instaneous
+ 
+
+ align:start position:0%
+statistics operation or for a instaneous
+operation and here for the sers we care
+
+ align:start position:0%
+operation and here for the sers we care
+ 
+
+ align:start position:0%
+operation and here for the sers we care
+about the inous operation and the next
+
+ align:start position:0%
+about the inous operation and the next
+ 
+
+ align:start position:0%
+about the inous operation and the next
+lecture when we learn about the thermal
+
+ align:start position:0%
+lecture when we learn about the thermal
+ 
+
+ align:start position:0%
+lecture when we learn about the thermal
+we care about the static operation ation
+
+ align:start position:0%
+we care about the static operation ation
+ 
+
+ align:start position:0%
+we care about the static operation ation
+that is the RMS voltage or the RMS RMS
+
+ align:start position:0%
+that is the RMS voltage or the RMS RMS
+ 
+
+ align:start position:0%
+that is the RMS voltage or the RMS RMS
+current cannot exceed but here we C the
+
+ align:start position:0%
+current cannot exceed but here we C the
+ 
+
+ align:start position:0%
+current cannot exceed but here we C the
+inous one so if we think about this hard
+
+ align:start position:0%
+inous one so if we think about this hard
+ 
+
+ align:start position:0%
+inous one so if we think about this hard
+switching during the turn on and turn
+
+ align:start position:0%
+switching during the turn on and turn
+ 
+
+ align:start position:0%
+switching during the turn on and turn
+off let's say for during the turn
+
+ align:start position:0%
+off let's say for during the turn
+ 
+
+ align:start position:0%
+off let's say for during the turn
+off the the the current will hold
+
+ align:start position:0%
+off the the the current will hold
+ 
+
+ align:start position:0%
+off the the the current will hold
+constant until the voltage increase and
+
+ align:start position:0%
+constant until the voltage increase and
+ 
+
+ align:start position:0%
+constant until the voltage increase and
+then the current will drop and if it's a
+
+ align:start position:0%
+then the current will drop and if it's a
+ 
+
+ align:start position:0%
+then the current will drop and if it's a
+hard switching we can find that our
+
+ align:start position:0%
+hard switching we can find that our
+ 
+
+ align:start position:0%
+hard switching we can find that our
+inous current or voltage will exceed the
+
+ align:start position:0%
+inous current or voltage will exceed the
+ 
+
+ align:start position:0%
+inous current or voltage will exceed the
+safe op operating area and this is not
+
+ align:start position:0%
+safe op operating area and this is not
+ 
+
+ align:start position:0%
+safe op operating area and this is not
+good and this can destroy our device so
+
+ align:start position:0%
+good and this can destroy our device so
+ 
+
+ align:start position:0%
+good and this can destroy our device so
+that's why we want the snubber we want
+
+ align:start position:0%
+that's why we want the snubber we want
+ 
+
+ align:start position:0%
+that's why we want the snubber we want
+the snubber to manipulate with this
+
+ align:start position:0%
+the snubber to manipulate with this
+ 
+
+ align:start position:0%
+the snubber to manipulate with this
+switching locus of the iway curves and
+
+ align:start position:0%
+switching locus of the iway curves and
+ 
+
+ align:start position:0%
+switching locus of the iway curves and
+also for snubbers we want to decrease
+
+ align:start position:0%
+also for snubbers we want to decrease
+ 
+
+ align:start position:0%
+also for snubbers we want to decrease
+this turn off energy or the turn on
+
+ align:start position:0%
+this turn off energy or the turn on
+ 
+
+ align:start position:0%
+this turn off energy or the turn on
+energy of the switches inside of the
+
+ align:start position:0%
+energy of the switches inside of the
+ 
+
+ align:start position:0%
+energy of the switches inside of the
+switches so that's the motivation of our
+
+ align:start position:0%
+switches so that's the motivation of our
+ 
+
+ align:start position:0%
+switches so that's the motivation of our
+snabs so before we start snab do you
+
+ align:start position:0%
+snabs so before we start snab do you
+ 
+
+ align:start position:0%
+snabs so before we start snab do you
+have any
+
+ align:start position:0%
+have any
+ 
+
+ align:start position:0%
+have any
+questions cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for Snappers we have two kind of
+
+ align:start position:0%
+so for Snappers we have two kind of
+ 
+
+ align:start position:0%
+so for Snappers we have two kind of
+motivation one is like we want to
+
+ align:start position:0%
+motivation one is like we want to
+ 
+
+ align:start position:0%
+motivation one is like we want to
+maintain the instantaneous current and
+
+ align:start position:0%
+maintain the instantaneous current and
+ 
+
+ align:start position:0%
+maintain the instantaneous current and
+voltage of the switch in the safe of
+
+ align:start position:0%
+voltage of the switch in the safe of
+ 
+
+ align:start position:0%
+voltage of the switch in the safe of
+operating area that is also like we want
+
+ align:start position:0%
+operating area that is also like we want
+ 
+
+ align:start position:0%
+operating area that is also like we want
+to have low DT or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dvdt and the second motivation will be
+
+ align:start position:0%
+dvdt and the second motivation will be
+ 
+
+ align:start position:0%
+dvdt and the second motivation will be
+like we want to decrease the switching
+
+ align:start position:0%
+like we want to decrease the switching
+ 
+
+ align:start position:0%
+like we want to decrease the switching
+loss inside of the
+
+ align:start position:0%
+loss inside of the
+ 
+
+ align:start position:0%
+loss inside of the
+switches so please have attention what
+
+ align:start position:0%
+switches so please have attention what
+ 
+
+ align:start position:0%
+switches so please have attention what
+do I mean by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inside and now let's think about the
+
+ align:start position:0%
+inside and now let's think about the
+ 
+
+ align:start position:0%
+inside and now let's think about the
+turn off SN first so still we use this
+
+ align:start position:0%
+turn off SN first so still we use this
+ 
+
+ align:start position:0%
+turn off SN first so still we use this
+SP converter as our example we have the
+
+ align:start position:0%
+SP converter as our example we have the
+ 
+
+ align:start position:0%
+SP converter as our example we have the
+input voltage
+
+ align:start position:0%
+input voltage
+ 
+
+ align:start position:0%
+input voltage
+source and we have a MOS
+
+ align:start position:0%
+source and we have a MOS
+ 
+
+ align:start position:0%
+source and we have a MOS
+fat and we have a
+
+ align:start position:0%
+fat and we have a
+ 
+
+ align:start position:0%
+fat and we have a
+diode and this will be our constant load
+
+ align:start position:0%
+diode and this will be our constant load
+ 
+
+ align:start position:0%
+diode and this will be our constant load
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+source so previously at this terminal we
+
+ align:start position:0%
+source so previously at this terminal we
+ 
+
+ align:start position:0%
+source so previously at this terminal we
+said the diod cannot turn on or carry
+
+ align:start position:0%
+said the diod cannot turn on or carry
+ 
+
+ align:start position:0%
+said the diod cannot turn on or carry
+current until its voltage becomes
+
+ align:start position:0%
+current until its voltage becomes
+ 
+
+ align:start position:0%
+current until its voltage becomes
+zero but now we can have a capacitor
+
+ align:start position:0%
+zero but now we can have a capacitor
+ 
+
+ align:start position:0%
+zero but now we can have a capacitor
+that is in parallel with the switch and
+
+ align:start position:0%
+that is in parallel with the switch and
+ 
+
+ align:start position:0%
+that is in parallel with the switch and
+previously at this note we will have the
+
+ align:start position:0%
+previously at this note we will have the
+ 
+
+ align:start position:0%
+previously at this note we will have the
+KCl equation as I
+
+ align:start position:0%
+KCl equation as I
+ 
+
+ align:start position:0%
+KCl equation as I
+L is equal to ID plus the
+
+ align:start position:0%
+L is equal to ID plus the
+ 
+
+ align:start position:0%
+L is equal to ID plus the
+isw but now we have extra term which is
+
+ align:start position:0%
+isw but now we have extra term which is
+ 
+
+ align:start position:0%
+isw but now we have extra term which is
+the IC so the previously the D cannot
+
+ align:start position:0%
+the IC so the previously the D cannot
+ 
+
+ align:start position:0%
+the IC so the previously the D cannot
+conduct the current but now the
+
+ align:start position:0%
+conduct the current but now the
+ 
+
+ align:start position:0%
+conduct the current but now the
+capacitor can flow through the current
+
+ align:start position:0%
+capacitor can flow through the current
+ 
+
+ align:start position:0%
+capacitor can flow through the current
+and now we can have instantaneously the
+
+ align:start position:0%
+and now we can have instantaneously the
+ 
+
+ align:start position:0%
+and now we can have instantaneously the
+small voltage and current during the
+
+ align:start position:0%
+small voltage and current during the
+ 
+
+ align:start position:0%
+small voltage and current during the
+turn off at the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so if we draw the iy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve for the switch current we still
+
+ align:start position:0%
+curve for the switch current we still
+ 
+
+ align:start position:0%
+curve for the switch current we still
+see like it will we still assume that
+
+ align:start position:0%
+see like it will we still assume that
+ 
+
+ align:start position:0%
+see like it will we still assume that
+will be a linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Transitions and when the switch current
+
+ align:start position:0%
+Transitions and when the switch current
+ 
+
+ align:start position:0%
+Transitions and when the switch current
+decrease from the IL
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the capacitor current can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conduct and take and pay attention at at
+
+ align:start position:0%
+conduct and take and pay attention at at
+ 
+
+ align:start position:0%
+conduct and take and pay attention at at
+this time the ID the dial is still in
+
+ align:start position:0%
+this time the ID the dial is still in
+ 
+
+ align:start position:0%
+this time the ID the dial is still in
+the off
+
+ align:start position:0%
+the off
+ 
+
+ align:start position:0%
+the off
+State so when the switch has the linear
+
+ align:start position:0%
+State so when the switch has the linear
+ 
+
+ align:start position:0%
+State so when the switch has the linear
+ramp of the current the capacitor will
+
+ align:start position:0%
+ramp of the current the capacitor will
+ 
+
+ align:start position:0%
+ramp of the current the capacitor will
+similarly have the linear ramp of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current and at this this will be the I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for the capacitor voltage we know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this capacitor current will be c
+
+ align:start position:0%
+that this capacitor current will be c
+ 
+
+ align:start position:0%
+that this capacitor current will be c
+times the
+
+ align:start position:0%
+times the
+ 
+
+ align:start position:0%
+times the
+dvdt and correspondingly the voltage of
+
+ align:start position:0%
+dvdt and correspondingly the voltage of
+ 
+
+ align:start position:0%
+dvdt and correspondingly the voltage of
+a capacitor will be the integral of the
+
+ align:start position:0%
+a capacitor will be the integral of the
+ 
+
+ align:start position:0%
+a capacitor will be the integral of the
+capacitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current and here if we have a linear of
+
+ align:start position:0%
+current and here if we have a linear of
+ 
+
+ align:start position:0%
+current and here if we have a linear of
+the switch of the Capac current we will
+
+ align:start position:0%
+the switch of the Capac current we will
+ 
+
+ align:start position:0%
+the switch of the Capac current we will
+have the
+
+ align:start position:0%
+have the
+ 
+
+ align:start position:0%
+have the
+quadratic of the capacitor voltage and
+
+ align:start position:0%
+quadratic of the capacitor voltage and
+ 
+
+ align:start position:0%
+quadratic of the capacitor voltage and
+that capacitor voltage will be the
+
+ align:start position:0%
+that capacitor voltage will be the
+ 
+
+ align:start position:0%
+that capacitor voltage will be the
+switch voltage at the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time maybe I should change another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+color so if we if we draw it the
+
+ align:start position:0%
+color so if we if we draw it the
+ 
+
+ align:start position:0%
+color so if we if we draw it the
+waveform the this will be the Capac
+
+ align:start position:0%
+waveform the this will be the Capac
+ 
+
+ align:start position:0%
+waveform the this will be the Capac
+current if we draw the capacitor voltage
+
+ align:start position:0%
+current if we draw the capacitor voltage
+ 
+
+ align:start position:0%
+current if we draw the capacitor voltage
+because this is linear the integral of a
+
+ align:start position:0%
+because this is linear the integral of a
+ 
+
+ align:start position:0%
+because this is linear the integral of a
+linear will be
+
+ align:start position:0%
+linear will be
+ 
+
+ align:start position:0%
+linear will be
+quadratic so at this time the switch
+
+ align:start position:0%
+quadratic so at this time the switch
+ 
+
+ align:start position:0%
+quadratic so at this time the switch
+current will be off and after that the
+
+ align:start position:0%
+current will be off and after that the
+ 
+
+ align:start position:0%
+current will be off and after that the
+Capac current will fully conduct the
+
+ align:start position:0%
+Capac current will fully conduct the
+ 
+
+ align:start position:0%
+Capac current will fully conduct the
+load
+
+ align:start position:0%
+load
+ 
+
+ align:start position:0%
+load
+current and when the capacitor current
+
+ align:start position:0%
+current and when the capacitor current
+ 
+
+ align:start position:0%
+current and when the capacitor current
+is a constant the capacitor voltage will
+
+ align:start position:0%
+is a constant the capacitor voltage will
+ 
+
+ align:start position:0%
+is a constant the capacitor voltage will
+become
+
+ align:start position:0%
+become
+ 
+
+ align:start position:0%
+become
+linear but we don't care about this part
+
+ align:start position:0%
+linear but we don't care about this part
+ 
+
+ align:start position:0%
+linear but we don't care about this part
+anymore because we care the switching
+
+ align:start position:0%
+anymore because we care the switching
+ 
+
+ align:start position:0%
+anymore because we care the switching
+loss I mean for for this for this time
+
+ align:start position:0%
+loss I mean for for this for this time
+ 
+
+ align:start position:0%
+loss I mean for for this for this time
+we don't care we only C the switching
+
+ align:start position:0%
+we don't care we only C the switching
+ 
+
+ align:start position:0%
+we don't care we only C the switching
+current and voltage during this time
+
+ align:start position:0%
+current and voltage during this time
+ 
+
+ align:start position:0%
+current and voltage during this time
+interval from zero to
+
+ align:start position:0%
+interval from zero to
+ 
+
+ align:start position:0%
+interval from zero to
+TF so we only C the energy loss during
+
+ align:start position:0%
+TF so we only C the energy loss during
+ 
+
+ align:start position:0%
+TF so we only C the energy loss during
+this so actually we can have a
+
+ align:start position:0%
+this so actually we can have a
+ 
+
+ align:start position:0%
+this so actually we can have a
+calculation about this
+
+ align:start position:0%
+calculation about this
+ 
+
+ align:start position:0%
+calculation about this
+energy so let's see our switch current
+
+ align:start position:0%
+energy so let's see our switch current
+ 
+
+ align:start position:0%
+energy so let's see our switch current
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+i y minus t over
+
+ align:start position:0%
+i y minus t over
+ 
+
+ align:start position:0%
+i y minus t over
+TF and correspondingly our Capac current
+
+ align:start position:0%
+TF and correspondingly our Capac current
+ 
+
+ align:start position:0%
+TF and correspondingly our Capac current
+will be I time the T *
+
+ align:start position:0%
+will be I time the T *
+ 
+
+ align:start position:0%
+will be I time the T *
+TF and correspondingly our capacitor
+
+ align:start position:0%
+TF and correspondingly our capacitor
+ 
+
+ align:start position:0%
+TF and correspondingly our capacitor
+voltage or which is also the switch
+
+ align:start position:0%
+voltage or which is also the switch
+ 
+
+ align:start position:0%
+voltage or which is also the switch
+voltage will be the integral of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this that will be the I times the t/ TF
+
+ align:start position:0%
+this that will be the I times the t/ TF
+ 
+
+ align:start position:0%
+this that will be the I times the t/ TF
+DT so that will be
+
+ align:start position:0%
+DT so that will be
+ 
+
+ align:start position:0%
+DT so that will be
+I TF * c t^ 2 so let me check if I do my
+
+ align:start position:0%
+I TF * c t^ 2 so let me check if I do my
+ 
+
+ align:start position:0%
+I TF * c t^ 2 so let me check if I do my
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+correct oh sorry so I should plug into
+
+ align:start position:0%
+correct oh sorry so I should plug into
+ 
+
+ align:start position:0%
+correct oh sorry so I should plug into
+the switch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current oh sorry my bad this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct so that will be i t^2 c * the TF
+
+ align:start position:0%
+correct so that will be i t^2 c * the TF
+ 
+
+ align:start position:0%
+correct so that will be i t^2 c * the TF
+so that will be the switch voltage
+
+ align:start position:0%
+so that will be the switch voltage
+ 
+
+ align:start position:0%
+so that will be the switch voltage
+expression and similarly if we calculate
+
+ align:start position:0%
+expression and similarly if we calculate
+ 
+
+ align:start position:0%
+expression and similarly if we calculate
+the switching
+
+ align:start position:0%
+the switching
+ 
+
+ align:start position:0%
+the switching
+loss what is loss loss is still a kind
+
+ align:start position:0%
+loss what is loss loss is still a kind
+ 
+
+ align:start position:0%
+loss what is loss loss is still a kind
+of power that will be the V switch times
+
+ align:start position:0%
+of power that will be the V switch times
+ 
+
+ align:start position:0%
+of power that will be the V switch times
+the I
+
+ align:start position:0%
+the I
+ 
+
+ align:start position:0%
+the I
+switch so we have the wi switch as this
+
+ align:start position:0%
+switch so we have the wi switch as this
+ 
+
+ align:start position:0%
+switch so we have the wi switch as this
+that will be I * t^2 over the capacitor
+
+ align:start position:0%
+that will be I * t^2 over the capacitor
+ 
+
+ align:start position:0%
+that will be I * t^2 over the capacitor
+value times the TF times the switch
+
+ align:start position:0%
+value times the TF times the switch
+ 
+
+ align:start position:0%
+value times the TF times the switch
+current which is this expression that
+
+ align:start position:0%
+current which is this expression that
+ 
+
+ align:start position:0%
+current which is this expression that
+will be the i y minus t/
+
+ align:start position:0%
+will be the i y minus t/
+ 
+
+ align:start position:0%
+will be the i y minus t/
+TF so that will be the inous power
+
+ align:start position:0%
+TF so that will be the inous power
+ 
+
+ align:start position:0%
+TF so that will be the inous power
+expression and if we integrate this
+
+ align:start position:0%
+expression and if we integrate this
+ 
+
+ align:start position:0%
+expression and if we integrate this
+inous power we will have the turn off
+
+ align:start position:0%
+inous power we will have the turn off
+ 
+
+ align:start position:0%
+inous power we will have the turn off
+energy that is like we we integrate this
+
+ align:start position:0%
+energy that is like we we integrate this
+ 
+
+ align:start position:0%
+energy that is like we we integrate this
+PSW during the time interval from zero
+
+ align:start position:0%
+PSW during the time interval from zero
+ 
+
+ align:start position:0%
+PSW during the time interval from zero
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+TF and if you do the algebra by yourself
+
+ align:start position:0%
+TF and if you do the algebra by yourself
+ 
+
+ align:start position:0%
+TF and if you do the algebra by yourself
+we will find the results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of which is i s time the tf^ S over the
+
+ align:start position:0%
+of which is i s time the tf^ S over the
+ 
+
+ align:start position:0%
+of which is i s time the tf^ S over the
+24 times the
+
+ align:start position:0%
+24 times the
+ 
+
+ align:start position:0%
+24 times the
+capacitance so do you have any questions
+
+ align:start position:0%
+capacitance so do you have any questions
+ 
+
+ align:start position:0%
+capacitance so do you have any questions
+about this part yeah go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead is that coming from
+
+ align:start position:0%
+ahead is that coming from
+ 
+
+ align:start position:0%
+ahead is that coming from
+that I or yeah so here we have
+
+ align:start position:0%
+that I or yeah so here we have
+ 
+
+ align:start position:0%
+that I or yeah so here we have
+assumption so even if we have a snubber
+
+ align:start position:0%
+assumption so even if we have a snubber
+ 
+
+ align:start position:0%
+assumption so even if we have a snubber
+we still assume the transit for the
+
+ align:start position:0%
+we still assume the transit for the
+ 
+
+ align:start position:0%
+we still assume the transit for the
+switch current is linear and we know
+
+ align:start position:0%
+switch current is linear and we know
+ 
+
+ align:start position:0%
+switch current is linear and we know
+that the current will decrease during
+
+ align:start position:0%
+that the current will decrease during
+ 
+
+ align:start position:0%
+that the current will decrease during
+the turn off so we have assumption like
+
+ align:start position:0%
+the turn off so we have assumption like
+ 
+
+ align:start position:0%
+the turn off so we have assumption like
+this will be a linear current so so
+
+ align:start position:0%
+this will be a linear current so so
+ 
+
+ align:start position:0%
+this will be a linear current so so
+that's why we have it start as a as a
+
+ align:start position:0%
+that's why we have it start as a as a
+ 
+
+ align:start position:0%
+that's why we have it start as a as a
+part and sure and previously because we
+
+ align:start position:0%
+part and sure and previously because we
+ 
+
+ align:start position:0%
+part and sure and previously because we
+don't have a another alternate path for
+
+ align:start position:0%
+don't have a another alternate path for
+ 
+
+ align:start position:0%
+don't have a another alternate path for
+current to flow so we need to wait until
+
+ align:start position:0%
+current to flow so we need to wait until
+ 
+
+ align:start position:0%
+current to flow so we need to wait until
+this ID yeah but ID is still zero at
+
+ align:start position:0%
+this ID yeah but ID is still zero at
+ 
+
+ align:start position:0%
+this ID yeah but ID is still zero at
+this time yeah
+
+ align:start position:0%
+this time yeah
+ 
+
+ align:start position:0%
+this time yeah
+cool so then we can calculate this turn
+
+ align:start position:0%
+cool so then we can calculate this turn
+ 
+
+ align:start position:0%
+cool so then we can calculate this turn
+off energy and what we can observe from
+
+ align:start position:0%
+off energy and what we can observe from
+ 
+
+ align:start position:0%
+off energy and what we can observe from
+this is like we can have a control
+
+ align:start position:0%
+this is like we can have a control
+ 
+
+ align:start position:0%
+this is like we can have a control
+handle which is our capacitance so if we
+
+ align:start position:0%
+handle which is our capacitance so if we
+ 
+
+ align:start position:0%
+handle which is our capacitance so if we
+want to decrease our turn off energy we
+
+ align:start position:0%
+want to decrease our turn off energy we
+ 
+
+ align:start position:0%
+want to decrease our turn off energy we
+can increase our capacitance value so we
+
+ align:start position:0%
+can increase our capacitance value so we
+ 
+
+ align:start position:0%
+can increase our capacitance value so we
+can do this however nothing is free we
+
+ align:start position:0%
+can do this however nothing is free we
+ 
+
+ align:start position:0%
+can do this however nothing is free we
+have to pay for
+
+ align:start position:0%
+have to pay for
+ 
+
+ align:start position:0%
+have to pay for
+something so imagine like if we have a
+
+ align:start position:0%
+something so imagine like if we have a
+ 
+
+ align:start position:0%
+something so imagine like if we have a
+capacitance in parallel with the switch
+
+ align:start position:0%
+capacitance in parallel with the switch
+ 
+
+ align:start position:0%
+capacitance in parallel with the switch
+every time during it when the switch is
+
+ align:start position:0%
+every time during it when the switch is
+ 
+
+ align:start position:0%
+every time during it when the switch is
+off we will store the energy inside of
+
+ align:start position:0%
+off we will store the energy inside of
+ 
+
+ align:start position:0%
+off we will store the energy inside of
+the capacitance that will be half CV
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squ so we we reduce the energy loss in
+
+ align:start position:0%
+squ so we we reduce the energy loss in
+ 
+
+ align:start position:0%
+squ so we we reduce the energy loss in
+the inside of the switch but outside the
+
+ align:start position:0%
+the inside of the switch but outside the
+ 
+
+ align:start position:0%
+the inside of the switch but outside the
+switch we we need to dissipate this part
+
+ align:start position:0%
+switch we we need to dissipate this part
+ 
+
+ align:start position:0%
+switch we we need to dissipate this part
+of energy so that what do I mean by we
+
+ align:start position:0%
+of energy so that what do I mean by we
+ 
+
+ align:start position:0%
+of energy so that what do I mean by we
+decrease the switching loss inside of
+
+ align:start position:0%
+decrease the switching loss inside of
+ 
+
+ align:start position:0%
+decrease the switching loss inside of
+the switches but we also have to pay for
+
+ align:start position:0%
+the switches but we also have to pay for
+ 
+
+ align:start position:0%
+the switches but we also have to pay for
+something that is the energy stored in
+
+ align:start position:0%
+something that is the energy stored in
+ 
+
+ align:start position:0%
+something that is the energy stored in
+this snubber capacitance so during the
+
+ align:start position:0%
+this snubber capacitance so during the
+ 
+
+ align:start position:0%
+this snubber capacitance so during the
+turn on if we do nothing this energy
+
+ align:start position:0%
+turn on if we do nothing this energy
+ 
+
+ align:start position:0%
+turn on if we do nothing this energy
+will be dumped into these switches so it
+
+ align:start position:0%
+will be dumped into these switches so it
+ 
+
+ align:start position:0%
+will be dumped into these switches so it
+will still lost and this part of energy
+
+ align:start position:0%
+will still lost and this part of energy
+ 
+
+ align:start position:0%
+will still lost and this part of energy
+could be very large it can still destroy
+
+ align:start position:0%
+could be very large it can still destroy
+ 
+
+ align:start position:0%
+could be very large it can still destroy
+our devices so this is not not a
+
+ align:start position:0%
+our devices so this is not not a
+ 
+
+ align:start position:0%
+our devices so this is not not a
+practical snubber as
+
+ align:start position:0%
+practical snubber as
+ 
+
+ align:start position:0%
+practical snubber as
+turn off SN so a practical one we need
+
+ align:start position:0%
+turn off SN so a practical one we need
+ 
+
+ align:start position:0%
+turn off SN so a practical one we need
+to do something else so let's still take
+
+ align:start position:0%
+to do something else so let's still take
+ 
+
+ align:start position:0%
+to do something else so let's still take
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+circuit we have the input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage and we have the mostat we have
+
+ align:start position:0%
+voltage and we have the mostat we have
+ 
+
+ align:start position:0%
+voltage and we have the mostat we have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+diod and we have the ideal current
+
+ align:start position:0%
+diod and we have the ideal current
+ 
+
+ align:start position:0%
+diod and we have the ideal current
+source so we kind of use two other
+
+ align:start position:0%
+source so we kind of use two other
+ 
+
+ align:start position:0%
+source so we kind of use two other
+component one is the diode in parallel
+
+ align:start position:0%
+component one is the diode in parallel
+ 
+
+ align:start position:0%
+component one is the diode in parallel
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+resistor and then the in series with
+
+ align:start position:0%
+resistor and then the in series with
+ 
+
+ align:start position:0%
+resistor and then the in series with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+capacitance so during it when we want to
+
+ align:start position:0%
+capacitance so during it when we want to
+ 
+
+ align:start position:0%
+capacitance so during it when we want to
+turn off the switch the current will
+
+ align:start position:0%
+turn off the switch the current will
+ 
+
+ align:start position:0%
+turn off the switch the current will
+still SL through this through this St
+
+ align:start position:0%
+still SL through this through this St
+ 
+
+ align:start position:0%
+still SL through this through this St
+and the capacitance and then when we
+
+ align:start position:0%
+and the capacitance and then when we
+ 
+
+ align:start position:0%
+and the capacitance and then when we
+want to turn on the switch so then
+
+ align:start position:0%
+want to turn on the switch so then
+ 
+
+ align:start position:0%
+want to turn on the switch so then
+because of we are charging this
+
+ align:start position:0%
+because of we are charging this
+ 
+
+ align:start position:0%
+because of we are charging this
+capacitor to the V this will be positive
+
+ align:start position:0%
+capacitor to the V this will be positive
+ 
+
+ align:start position:0%
+capacitor to the V this will be positive
+this will be negative and when we turn
+
+ align:start position:0%
+this will be negative and when we turn
+ 
+
+ align:start position:0%
+this will be negative and when we turn
+on the switch this capacitance will have
+
+ align:start position:0%
+on the switch this capacitance will have
+ 
+
+ align:start position:0%
+on the switch this capacitance will have
+a current pass through this resistor and
+
+ align:start position:0%
+a current pass through this resistor and
+ 
+
+ align:start position:0%
+a current pass through this resistor and
+through this m fat and we and most of
+
+ align:start position:0%
+through this m fat and we and most of
+ 
+
+ align:start position:0%
+through this m fat and we and most of
+the energy we can control we can dump it
+
+ align:start position:0%
+the energy we can control we can dump it
+ 
+
+ align:start position:0%
+the energy we can control we can dump it
+into this resistor instead of this m fat
+
+ align:start position:0%
+into this resistor instead of this m fat
+ 
+
+ align:start position:0%
+into this resistor instead of this m fat
+and also we can use this resistor to
+
+ align:start position:0%
+and also we can use this resistor to
+ 
+
+ align:start position:0%
+and also we can use this resistor to
+limits the current that flows through
+
+ align:start position:0%
+limits the current that flows through
+ 
+
+ align:start position:0%
+limits the current that flows through
+this m fat and in this way we are kind
+
+ align:start position:0%
+this m fat and in this way we are kind
+ 
+
+ align:start position:0%
+this m fat and in this way we are kind
+of solve we are kind of solve this part
+
+ align:start position:0%
+of solve we are kind of solve this part
+ 
+
+ align:start position:0%
+of solve we are kind of solve this part
+of energy that could destroy our device
+
+ align:start position:0%
+of energy that could destroy our device
+ 
+
+ align:start position:0%
+of energy that could destroy our device
+during the turn on but again we are not
+
+ align:start position:0%
+during the turn on but again we are not
+ 
+
+ align:start position:0%
+during the turn on but again we are not
+recover this part of energy this part of
+
+ align:start position:0%
+recover this part of energy this part of
+ 
+
+ align:start position:0%
+recover this part of energy this part of
+energy is still dissipated mostly on
+
+ align:start position:0%
+energy is still dissipated mostly on
+ 
+
+ align:start position:0%
+energy is still dissipated mostly on
+this resistor and the small part of
+
+ align:start position:0%
+this resistor and the small part of
+ 
+
+ align:start position:0%
+this resistor and the small part of
+amount in this fat but we can improve
+
+ align:start position:0%
+amount in this fat but we can improve
+ 
+
+ align:start position:0%
+amount in this fat but we can improve
+this so do you have any questions for a
+
+ align:start position:0%
+this so do you have any questions for a
+ 
+
+ align:start position:0%
+this so do you have any questions for a
+practical turn off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SN okay so then let's go to the turn on
+
+ align:start position:0%
+SN okay so then let's go to the turn on
+ 
+
+ align:start position:0%
+SN okay so then let's go to the turn on
+S so the beauty of the circuit is that
+
+ align:start position:0%
+S so the beauty of the circuit is that
+ 
+
+ align:start position:0%
+S so the beauty of the circuit is that
+sometimes we can have a due Circuit of
+
+ align:start position:0%
+sometimes we can have a due Circuit of
+ 
+
+ align:start position:0%
+sometimes we can have a due Circuit of
+original circuit so a turn on S is the
+
+ align:start position:0%
+original circuit so a turn on S is the
+ 
+
+ align:start position:0%
+original circuit so a turn on S is the
+real the Dual Circuit of the turnoff s
+
+ align:start position:0%
+real the Dual Circuit of the turnoff s
+ 
+
+ align:start position:0%
+real the Dual Circuit of the turnoff s
+so let's draw the back converter again
+
+ align:start position:0%
+so let's draw the back converter again
+ 
+
+ align:start position:0%
+so let's draw the back converter again
+so we have a voltage source
+
+ align:start position:0%
+so we have a voltage source
+ 
+
+ align:start position:0%
+so we have a voltage source
+we have a
+
+ align:start position:0%
+we have a
+ 
+
+ align:start position:0%
+we have a
+transistor and we have a
+
+ align:start position:0%
+transistor and we have a
+ 
+
+ align:start position:0%
+transistor and we have a
+diode and we have the constant current
+
+ align:start position:0%
+diode and we have the constant current
+ 
+
+ align:start position:0%
+diode and we have the constant current
+load Source a load constant current load
+
+ align:start position:0%
+load Source a load constant current load
+ 
+
+ align:start position:0%
+load Source a load constant current load
+and now I insert a inductor in series
+
+ align:start position:0%
+and now I insert a inductor in series
+ 
+
+ align:start position:0%
+and now I insert a inductor in series
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+transistor with with this m fat so
+
+ align:start position:0%
+transistor with with this m fat so
+ 
+
+ align:start position:0%
+transistor with with this m fat so
+previously we have the kvl equation
+
+ align:start position:0%
+previously we have the kvl equation
+ 
+
+ align:start position:0%
+previously we have the kvl equation
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+V is equal to the
+
+ align:start position:0%
+V is equal to the
+ 
+
+ align:start position:0%
+V is equal to the
+vsw minus the
+
+ align:start position:0%
+vsw minus the
+ 
+
+ align:start position:0%
+vsw minus the
+VD and now we have a extra voltage extra
+
+ align:start position:0%
+VD and now we have a extra voltage extra
+ 
+
+ align:start position:0%
+VD and now we have a extra voltage extra
+components that can sustain the voltage
+
+ align:start position:0%
+components that can sustain the voltage
+ 
+
+ align:start position:0%
+components that can sustain the voltage
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+VL so previously we are limited by the
+
+ align:start position:0%
+VL so previously we are limited by the
+ 
+
+ align:start position:0%
+VL so previously we are limited by the
+vi curve of this diode and now we have a
+
+ align:start position:0%
+vi curve of this diode and now we have a
+ 
+
+ align:start position:0%
+vi curve of this diode and now we have a
+second component to sustain this input
+
+ align:start position:0%
+second component to sustain this input
+ 
+
+ align:start position:0%
+second component to sustain this input
+voltage which means like when we turn on
+
+ align:start position:0%
+voltage which means like when we turn on
+ 
+
+ align:start position:0%
+voltage which means like when we turn on
+the switch we can have simultaneously
+
+ align:start position:0%
+the switch we can have simultaneously
+ 
+
+ align:start position:0%
+the switch we can have simultaneously
+small current and voltage at the same
+
+ align:start position:0%
+small current and voltage at the same
+ 
+
+ align:start position:0%
+small current and voltage at the same
+time we don't need to sustain the linear
+
+ align:start position:0%
+time we don't need to sustain the linear
+ 
+
+ align:start position:0%
+time we don't need to sustain the linear
+one during the overlap as a
+
+ align:start position:0%
+one during the overlap as a
+ 
+
+ align:start position:0%
+one during the overlap as a
+triangular so if we draw the
+
+ align:start position:0%
+triangular so if we draw the
+ 
+
+ align:start position:0%
+triangular so if we draw the
+waveform of the turn up
+
+ align:start position:0%
+waveform of the turn up
+ 
+
+ align:start position:0%
+waveform of the turn up
+that is still like we have the input we
+
+ align:start position:0%
+that is still like we have the input we
+ 
+
+ align:start position:0%
+that is still like we have the input we
+have the switch voltage which is I
+
+ align:start position:0%
+have the switch voltage which is I
+ 
+
+ align:start position:0%
+have the switch voltage which is I
+vsw they will have a linear decrease
+
+ align:start position:0%
+vsw they will have a linear decrease
+ 
+
+ align:start position:0%
+vsw they will have a linear decrease
+this is our
+
+ align:start position:0%
+this is our
+ 
+
+ align:start position:0%
+this is our
+assumption and also because we have a
+
+ align:start position:0%
+assumption and also because we have a
+ 
+
+ align:start position:0%
+assumption and also because we have a
+linear decrease of our switch voltage we
+
+ align:start position:0%
+linear decrease of our switch voltage we
+ 
+
+ align:start position:0%
+linear decrease of our switch voltage we
+will have a linear increase of our
+
+ align:start position:0%
+will have a linear increase of our
+ 
+
+ align:start position:0%
+will have a linear increase of our
+inductor
+
+ align:start position:0%
+inductor
+ 
+
+ align:start position:0%
+inductor
+voltage so the inductor voltage will
+
+ align:start position:0%
+voltage so the inductor voltage will
+ 
+
+ align:start position:0%
+voltage so the inductor voltage will
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+linearly and the most basic equation for
+
+ align:start position:0%
+linearly and the most basic equation for
+ 
+
+ align:start position:0%
+linearly and the most basic equation for
+inductor that will be V L is LD
+
+ align:start position:0%
+inductor that will be V L is LD
+ 
+
+ align:start position:0%
+inductor that will be V L is LD
+DT so correspondingly if we want to find
+
+ align:start position:0%
+DT so correspondingly if we want to find
+ 
+
+ align:start position:0%
+DT so correspondingly if we want to find
+the inductor current we can just do the
+
+ align:start position:0%
+the inductor current we can just do the
+ 
+
+ align:start position:0%
+the inductor current we can just do the
+integral which is 1 / L time the v l *
+
+ align:start position:0%
+integral which is 1 / L time the v l *
+ 
+
+ align:start position:0%
+integral which is 1 / L time the v l *
+the DT so if we know that the inductor
+
+ align:start position:0%
+the DT so if we know that the inductor
+ 
+
+ align:start position:0%
+the DT so if we know that the inductor
+voltage will be a linear increase than
+
+ align:start position:0%
+voltage will be a linear increase than
+ 
+
+ align:start position:0%
+voltage will be a linear increase than
+the inductor current and if you pay
+
+ align:start position:0%
+the inductor current and if you pay
+ 
+
+ align:start position:0%
+the inductor current and if you pay
+attention this inductor current will be
+
+ align:start position:0%
+attention this inductor current will be
+ 
+
+ align:start position:0%
+attention this inductor current will be
+same as the switch current because they
+
+ align:start position:0%
+same as the switch current because they
+ 
+
+ align:start position:0%
+same as the switch current because they
+are in
+
+ align:start position:0%
+are in
+ 
+
+ align:start position:0%
+are in
+series and now this switch current will
+
+ align:start position:0%
+series and now this switch current will
+ 
+
+ align:start position:0%
+series and now this switch current will
+increase as
+
+ align:start position:0%
+increase as
+ 
+
+ align:start position:0%
+increase as
+quadratical and during this this is the
+
+ align:start position:0%
+quadratical and during this this is the
+ 
+
+ align:start position:0%
+quadratical and during this this is the
+quadratical of the switch
+
+ align:start position:0%
+quadratical of the switch
+ 
+
+ align:start position:0%
+quadratical of the switch
+current and after this TR the switch is
+
+ align:start position:0%
+current and after this TR the switch is
+ 
+
+ align:start position:0%
+current and after this TR the switch is
+fully on so the inductor
+
+ align:start position:0%
+fully on so the inductor
+ 
+
+ align:start position:0%
+fully on so the inductor
+current sorry the the the switch is
+
+ align:start position:0%
+current sorry the the the switch is
+ 
+
+ align:start position:0%
+current sorry the the the switch is
+fully on this will be zero and this is
+
+ align:start position:0%
+fully on this will be zero and this is
+ 
+
+ align:start position:0%
+fully on this will be zero and this is
+still zero and this VL will fully take
+
+ align:start position:0%
+still zero and this VL will fully take
+ 
+
+ align:start position:0%
+still zero and this VL will fully take
+the input voltage so this will be a
+
+ align:start position:0%
+the input voltage so this will be a
+ 
+
+ align:start position:0%
+the input voltage so this will be a
+constant value and if it's a constant
+
+ align:start position:0%
+constant value and if it's a constant
+ 
+
+ align:start position:0%
+constant value and if it's a constant
+value for inductor voltage then the
+
+ align:start position:0%
+value for inductor voltage then the
+ 
+
+ align:start position:0%
+value for inductor voltage then the
+current will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear but again we don't carear this
+
+ align:start position:0%
+linear but again we don't carear this
+ 
+
+ align:start position:0%
+linear but again we don't carear this
+part for the switches because it is
+
+ align:start position:0%
+part for the switches because it is
+ 
+
+ align:start position:0%
+part for the switches because it is
+after the TR the switch has already
+
+ align:start position:0%
+after the TR the switch has already
+ 
+
+ align:start position:0%
+after the TR the switch has already
+passed the transient and we can still
+
+ align:start position:0%
+passed the transient and we can still
+ 
+
+ align:start position:0%
+passed the transient and we can still
+calculate what will be the ener turn on
+
+ align:start position:0%
+calculate what will be the ener turn on
+ 
+
+ align:start position:0%
+calculate what will be the ener turn on
+energy during this part and compared to
+
+ align:start position:0%
+energy during this part and compared to
+ 
+
+ align:start position:0%
+energy during this part and compared to
+the original hard switching we can see
+
+ align:start position:0%
+the original hard switching we can see
+ 
+
+ align:start position:0%
+the original hard switching we can see
+that we have we have small overlap at
+
+ align:start position:0%
+that we have we have small overlap at
+ 
+
+ align:start position:0%
+that we have we have small overlap at
+the same time for the high voltage and
+
+ align:start position:0%
+the same time for the high voltage and
+ 
+
+ align:start position:0%
+the same time for the high voltage and
+high current so we can improve the turn
+
+ align:start position:0%
+high current so we can improve the turn
+ 
+
+ align:start position:0%
+high current so we can improve the turn
+on energy during this and also the same
+
+ align:start position:0%
+on energy during this and also the same
+ 
+
+ align:start position:0%
+on energy during this and also the same
+problem will be we still store the
+
+ align:start position:0%
+problem will be we still store the
+ 
+
+ align:start position:0%
+problem will be we still store the
+energy that is half l i
+
+ align:start position:0%
+energy that is half l i
+ 
+
+ align:start position:0%
+energy that is half l i
+s in this inductor we need to disapate
+
+ align:start position:0%
+s in this inductor we need to disapate
+ 
+
+ align:start position:0%
+s in this inductor we need to disapate
+this part of energy somewhere and for a
+
+ align:start position:0%
+this part of energy somewhere and for a
+ 
+
+ align:start position:0%
+this part of energy somewhere and for a
+practical use we still have
+
+ align:start position:0%
+practical use we still have
+ 
+
+ align:start position:0%
+practical use we still have
+a resistor in series with a
+
+ align:start position:0%
+a resistor in series with a
+ 
+
+ align:start position:0%
+a resistor in series with a
+diode and during if we want to disapate
+
+ align:start position:0%
+diode and during if we want to disapate
+ 
+
+ align:start position:0%
+diode and during if we want to disapate
+the energy of this inductor we will have
+
+ align:start position:0%
+the energy of this inductor we will have
+ 
+
+ align:start position:0%
+the energy of this inductor we will have
+its current flow like this when the
+
+ align:start position:0%
+its current flow like this when the
+ 
+
+ align:start position:0%
+its current flow like this when the
+switch is turn off so that's the beauty
+
+ align:start position:0%
+switch is turn off so that's the beauty
+ 
+
+ align:start position:0%
+switch is turn off so that's the beauty
+of the circuit so for a for for a
+
+ align:start position:0%
+of the circuit so for a for for a
+ 
+
+ align:start position:0%
+of the circuit so for a for for a
+concept we need a turn off parallel
+
+ align:start position:0%
+concept we need a turn off parallel
+ 
+
+ align:start position:0%
+concept we need a turn off parallel
+capacitors and for the concept we need a
+
+ align:start position:0%
+capacitors and for the concept we need a
+ 
+
+ align:start position:0%
+capacitors and for the concept we need a
+series turn on inductor and for a more
+
+ align:start position:0%
+series turn on inductor and for a more
+ 
+
+ align:start position:0%
+series turn on inductor and for a more
+practical use we need a diod in parallel
+
+ align:start position:0%
+practical use we need a diod in parallel
+ 
+
+ align:start position:0%
+practical use we need a diod in parallel
+with the resistor then in series with
+
+ align:start position:0%
+with the resistor then in series with
+ 
+
+ align:start position:0%
+with the resistor then in series with
+this capacitor and for the Practical
+
+ align:start position:0%
+this capacitor and for the Practical
+ 
+
+ align:start position:0%
+this capacitor and for the Practical
+turnout number we need a DI in series
+
+ align:start position:0%
+turnout number we need a DI in series
+ 
+
+ align:start position:0%
+turnout number we need a DI in series
+with the resistor then in parallel with
+
+ align:start position:0%
+with the resistor then in parallel with
+ 
+
+ align:start position:0%
+with the resistor then in parallel with
+this inductor so this is the fully du of
+
+ align:start position:0%
+this inductor so this is the fully du of
+ 
+
+ align:start position:0%
+this inductor so this is the fully du of
+the circuit so this is a practical one
+
+ align:start position:0%
+the circuit so this is a practical one
+ 
+
+ align:start position:0%
+the circuit so this is a practical one
+of the Practical turn on SN and this is
+
+ align:start position:0%
+of the Practical turn on SN and this is
+ 
+
+ align:start position:0%
+of the Practical turn on SN and this is
+a practical turn off
+
+ align:start position:0%
+a practical turn off
+ 
+
+ align:start position:0%
+a practical turn off
+SN so do you have any
+
+ align:start position:0%
+SN so do you have any
+ 
+
+ align:start position:0%
+SN so do you have any
+questions yeah go ahead would you use
+
+ align:start position:0%
+questions yeah go ahead would you use
+ 
+
+ align:start position:0%
+questions yeah go ahead would you use
+both on yeah that's actually a very good
+
+ align:start position:0%
+both on yeah that's actually a very good
+ 
+
+ align:start position:0%
+both on yeah that's actually a very good
+question so this is only we care about
+
+ align:start position:0%
+question so this is only we care about
+ 
+
+ align:start position:0%
+question so this is only we care about
+the turn off this is what we care about
+
+ align:start position:0%
+the turn off this is what we care about
+ 
+
+ align:start position:0%
+the turn off this is what we care about
+the turn on so we and also again we
+
+ align:start position:0%
+the turn on so we and also again we
+ 
+
+ align:start position:0%
+the turn on so we and also again we
+justay this amount of energy fully so in
+
+ align:start position:0%
+justay this amount of energy fully so in
+ 
+
+ align:start position:0%
+justay this amount of energy fully so in
+the Practical we can design some
+
+ align:start position:0%
+the Practical we can design some
+ 
+
+ align:start position:0%
+the Practical we can design some
+Snappers that can both deal with a turn
+
+ align:start position:0%
+Snappers that can both deal with a turn
+ 
+
+ align:start position:0%
+Snappers that can both deal with a turn
+on and a turn off and we can imagine
+
+ align:start position:0%
+on and a turn off and we can imagine
+ 
+
+ align:start position:0%
+on and a turn off and we can imagine
+like some semiconductor devices we may
+
+ align:start position:0%
+like some semiconductor devices we may
+ 
+
+ align:start position:0%
+like some semiconductor devices we may
+care more about the turn on or we may
+
+ align:start position:0%
+care more about the turn on or we may
+ 
+
+ align:start position:0%
+care more about the turn on or we may
+care about the turn off so we can select
+
+ align:start position:0%
+care about the turn off so we can select
+ 
+
+ align:start position:0%
+care about the turn off so we can select
+a trade off like we want to mitigate the
+
+ align:start position:0%
+a trade off like we want to mitigate the
+ 
+
+ align:start position:0%
+a trade off like we want to mitigate the
+turn on loss more or we want to mitigate
+
+ align:start position:0%
+turn on loss more or we want to mitigate
+ 
+
+ align:start position:0%
+turn on loss more or we want to mitigate
+the turn off loss more and also here we
+
+ align:start position:0%
+the turn off loss more and also here we
+ 
+
+ align:start position:0%
+the turn off loss more and also here we
+are dissipated the energy of the half CV
+
+ align:start position:0%
+are dissipated the energy of the half CV
+ 
+
+ align:start position:0%
+are dissipated the energy of the half CV
+squ and the half Li squar in the
+
+ align:start position:0%
+squ and the half Li squar in the
+ 
+
+ align:start position:0%
+squ and the half Li squar in the
+Practical we can still design some
+
+ align:start position:0%
+Practical we can still design some
+ 
+
+ align:start position:0%
+Practical we can still design some
+recovery circuit we can recycle this
+
+ align:start position:0%
+recovery circuit we can recycle this
+ 
+
+ align:start position:0%
+recovery circuit we can recycle this
+part of energy yeah so what's your
+
+ align:start position:0%
+part of energy yeah so what's your
+ 
+
+ align:start position:0%
+part of energy yeah so what's your
+question um in the we have the right uh
+
+ align:start position:0%
+question um in the we have the right uh
+ 
+
+ align:start position:0%
+question um in the we have the right uh
+can you just mention what BD is doing
+
+ align:start position:0%
+can you just mention what BD is doing
+ 
+
+ align:start position:0%
+can you just mention what BD is doing
+during all that you mean this style yeah
+
+ align:start position:0%
+during all that you mean this style yeah
+ 
+
+ align:start position:0%
+during all that you mean this style yeah
+so after this when the let's see this is
+
+ align:start position:0%
+so after this when the let's see this is
+ 
+
+ align:start position:0%
+so after this when the let's see this is
+the inductor current yeah which also the
+
+ align:start position:0%
+the inductor current yeah which also the
+ 
+
+ align:start position:0%
+the inductor current yeah which also the
+switch current so when the switch
+
+ align:start position:0%
+switch current so when the switch
+ 
+
+ align:start position:0%
+switch current so when the switch
+current is go to the
+
+ align:start position:0%
+current is go to the
+ 
+
+ align:start position:0%
+current is go to the
+IL and also similar
+
+ align:start position:0%
+IL and also similar
+ 
+
+ align:start position:0%
+IL and also similar
+here when the capacitor voltage or the
+
+ align:start position:0%
+here when the capacitor voltage or the
+ 
+
+ align:start position:0%
+here when the capacitor voltage or the
+switch voltage is fully go to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V then the diod will make a roll in here
+
+ align:start position:0%
+V then the diod will make a roll in here
+ 
+
+ align:start position:0%
+V then the diod will make a roll in here
+that will be similar in this
+
+ align:start position:0%
+that will be similar in this
+ 
+
+ align:start position:0%
+that will be similar in this
+case yeah so the diode will play a role
+
+ align:start position:0%
+case yeah so the diode will play a role
+ 
+
+ align:start position:0%
+case yeah so the diode will play a role
+after this time
+
+ align:start position:0%
+after this time
+ 
+
+ align:start position:0%
+after this time
+interval why why is not changing all to
+
+ align:start position:0%
+interval why why is not changing all to
+ 
+
+ align:start position:0%
+interval why why is not changing all to
+the left that time oh that will be the
+
+ align:start position:0%
+the left that time oh that will be the
+ 
+
+ align:start position:0%
+the left that time oh that will be the
+same reason of this because we still
+
+ align:start position:0%
+same reason of this because we still
+ 
+
+ align:start position:0%
+same reason of this because we still
+assume this is the ideal diod so the
+
+ align:start position:0%
+assume this is the ideal diod so the
+ 
+
+ align:start position:0%
+assume this is the ideal diod so the
+diod cannot turn on or carry current
+
+ align:start position:0%
+diod cannot turn on or carry current
+ 
+
+ align:start position:0%
+diod cannot turn on or carry current
+until it has zero voltage drop and
+
+ align:start position:0%
+until it has zero voltage drop and
+ 
+
+ align:start position:0%
+until it has zero voltage drop and
+similarly a dial cannot turn off or
+
+ align:start position:0%
+similarly a dial cannot turn off or
+ 
+
+ align:start position:0%
+similarly a dial cannot turn off or
+block the voltage until the current
+
+ align:start position:0%
+block the voltage until the current
+ 
+
+ align:start position:0%
+block the voltage until the current
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+zero yeah
+
+ align:start position:0%
+zero yeah
+ 
+
+ align:start position:0%
+zero yeah
+cool so do you have any questions about
+
+ align:start position:0%
+cool so do you have any questions about
+ 
+
+ align:start position:0%
+cool so do you have any questions about
+those numers yeah go
+
+ align:start position:0%
+those numers yeah go
+ 
+
+ align:start position:0%
+those numers yeah go
+ahead
+
+ align:start position:0%
+ahead
+ 
+
+ align:start position:0%
+ahead
+fuor res worse yeah that's actually a
+
+ align:start position:0%
+fuor res worse yeah that's actually a
+ 
+
+ align:start position:0%
+fuor res worse yeah that's actually a
+very good question so let's say because
+
+ align:start position:0%
+very good question so let's say because
+ 
+
+ align:start position:0%
+very good question so let's say because
+we have a parallel we have a series
+
+ align:start position:0%
+we have a parallel we have a series
+ 
+
+ align:start position:0%
+we have a parallel we have a series
+inductance here and during some
+
+ align:start position:0%
+inductance here and during some
+ 
+
+ align:start position:0%
+inductance here and during some
+transient we we still have this parallel
+
+ align:start position:0%
+transient we we still have this parallel
+ 
+
+ align:start position:0%
+transient we we still have this parallel
+capacitance and for this di there also
+
+ align:start position:0%
+capacitance and for this di there also
+ 
+
+ align:start position:0%
+capacitance and for this di there also
+could be some parallel capacitors they
+
+ align:start position:0%
+could be some parallel capacitors they
+ 
+
+ align:start position:0%
+could be some parallel capacitors they
+still resonant that is something we
+
+ align:start position:0%
+still resonant that is something we
+ 
+
+ align:start position:0%
+still resonant that is something we
+cannot avoid so in the textbook there's
+
+ align:start position:0%
+cannot avoid so in the textbook there's
+ 
+
+ align:start position:0%
+cannot avoid so in the textbook there's
+a chapter talk about like how we choose
+
+ align:start position:0%
+a chapter talk about like how we choose
+ 
+
+ align:start position:0%
+a chapter talk about like how we choose
+this inductor value and how we choose
+
+ align:start position:0%
+this inductor value and how we choose
+ 
+
+ align:start position:0%
+this inductor value and how we choose
+this resistor value and similarly we
+
+ align:start position:0%
+this resistor value and similarly we
+ 
+
+ align:start position:0%
+this resistor value and similarly we
+still have the parasitic St inductance
+
+ align:start position:0%
+still have the parasitic St inductance
+ 
+
+ align:start position:0%
+still have the parasitic St inductance
+here and during some case this capacitor
+
+ align:start position:0%
+here and during some case this capacitor
+ 
+
+ align:start position:0%
+here and during some case this capacitor
+will still resonant with this so there
+
+ align:start position:0%
+will still resonant with this so there
+ 
+
+ align:start position:0%
+will still resonant with this so there
+are some this is something we cannot
+
+ align:start position:0%
+are some this is something we cannot
+ 
+
+ align:start position:0%
+are some this is something we cannot
+avoid but we can have some circuit or
+
+ align:start position:0%
+avoid but we can have some circuit or
+ 
+
+ align:start position:0%
+avoid but we can have some circuit or
+element like how we choose this
+
+ align:start position:0%
+element like how we choose this
+ 
+
+ align:start position:0%
+element like how we choose this
+capacitance and how we choose this
+
+ align:start position:0%
+capacitance and how we choose this
+ 
+
+ align:start position:0%
+capacitance and how we choose this
+resistor to improve this and also if you
+
+ align:start position:0%
+resistor to improve this and also if you
+ 
+
+ align:start position:0%
+resistor to improve this and also if you
+imagine a second order system so we can
+
+ align:start position:0%
+imagine a second order system so we can
+ 
+
+ align:start position:0%
+imagine a second order system so we can
+have critical damp we can have over damp
+
+ align:start position:0%
+have critical damp we can have over damp
+ 
+
+ align:start position:0%
+have critical damp we can have over damp
+or we can have under damp so we can
+
+ align:start position:0%
+or we can have under damp so we can
+ 
+
+ align:start position:0%
+or we can have under damp so we can
+select purposely put some small resistor
+
+ align:start position:0%
+select purposely put some small resistor
+ 
+
+ align:start position:0%
+select purposely put some small resistor
+to damping that out but this is
+
+ align:start position:0%
+to damping that out but this is
+ 
+
+ align:start position:0%
+to damping that out but this is
+something we need to pay off about that
+
+ align:start position:0%
+something we need to pay off about that
+ 
+
+ align:start position:0%
+something we need to pay off about that
+yeah that's actually a very good
+
+ align:start position:0%
+yeah that's actually a very good
+ 
+
+ align:start position:0%
+yeah that's actually a very good
+question and here I want to still
+
+ align:start position:0%
+question and here I want to still
+ 
+
+ align:start position:0%
+question and here I want to still
+mention about the Snapper is we improve
+
+ align:start position:0%
+mention about the Snapper is we improve
+ 
+
+ align:start position:0%
+mention about the Snapper is we improve
+the switching loss or the turn on and
+
+ align:start position:0%
+the switching loss or the turn on and
+ 
+
+ align:start position:0%
+the switching loss or the turn on and
+turn off energy inside of the switch
+
+ align:start position:0%
+turn off energy inside of the switch
+ 
+
+ align:start position:0%
+turn off energy inside of the switch
+itself but we lose energy
+
+ align:start position:0%
+itself but we lose energy
+ 
+
+ align:start position:0%
+itself but we lose energy
+here and we lose energy here and the
+
+ align:start position:0%
+here and we lose energy here and the
+ 
+
+ align:start position:0%
+here and we lose energy here and the
+total energy we lost may be even more
+
+ align:start position:0%
+total energy we lost may be even more
+ 
+
+ align:start position:0%
+total energy we lost may be even more
+but why we want to do this because we
+
+ align:start position:0%
+but why we want to do this because we
+ 
+
+ align:start position:0%
+but why we want to do this because we
+want to keep the switch every curves
+
+ align:start position:0%
+want to keep the switch every curves
+ 
+
+ align:start position:0%
+want to keep the switch every curves
+inside of the safe operating area we
+
+ align:start position:0%
+inside of the safe operating area we
+ 
+
+ align:start position:0%
+inside of the safe operating area we
+want to have a safe DT or dvdt so that's
+
+ align:start position:0%
+want to have a safe DT or dvdt so that's
+ 
+
+ align:start position:0%
+want to have a safe DT or dvdt so that's
+the motivation and as I said before like
+
+ align:start position:0%
+the motivation and as I said before like
+ 
+
+ align:start position:0%
+the motivation and as I said before like
+for the snubbers we use it for igbt we
+
+ align:start position:0%
+for the snubbers we use it for igbt we
+ 
+
+ align:start position:0%
+for the snubbers we use it for igbt we
+use it for CER we use it for the BJT and
+
+ align:start position:0%
+use it for CER we use it for the BJT and
+ 
+
+ align:start position:0%
+use it for CER we use it for the BJT and
+currently for the most fat we we
+
+ align:start position:0%
+currently for the most fat we we
+ 
+
+ align:start position:0%
+currently for the most fat we we
+generally don't use sber for most fat
+
+ align:start position:0%
+generally don't use sber for most fat
+ 
+
+ align:start position:0%
+generally don't use sber for most fat
+but from this we still introduce this
+
+ align:start position:0%
+but from this we still introduce this
+ 
+
+ align:start position:0%
+but from this we still introduce this
+part of the content because you can
+
+ align:start position:0%
+part of the content because you can
+ 
+
+ align:start position:0%
+part of the content because you can
+learn the beauty of a capacitor you can
+
+ align:start position:0%
+learn the beauty of a capacitor you can
+ 
+
+ align:start position:0%
+learn the beauty of a capacitor you can
+learn the beauty of a diode so the diode
+
+ align:start position:0%
+learn the beauty of a diode so the diode
+ 
+
+ align:start position:0%
+learn the beauty of a diode so the diode
+is only one directional device so you
+
+ align:start position:0%
+is only one directional device so you
+ 
+
+ align:start position:0%
+is only one directional device so you
+can imagine like for future when you
+
+ align:start position:0%
+can imagine like for future when you
+ 
+
+ align:start position:0%
+can imagine like for future when you
+design a circuit how to use the dial to
+
+ align:start position:0%
+design a circuit how to use the dial to
+ 
+
+ align:start position:0%
+design a circuit how to use the dial to
+control your current flow paths
+
+ align:start position:0%
+control your current flow paths
+ 
+
+ align:start position:0%
+control your current flow paths
+yeah so another thing I want to say
+
+ align:start position:0%
+yeah so another thing I want to say
+ 
+
+ align:start position:0%
+yeah so another thing I want to say
+because we still have some time is like
+
+ align:start position:0%
+because we still have some time is like
+ 
+
+ align:start position:0%
+because we still have some time is like
+I want to introduce F The Gate Drive
+
+ align:start position:0%
+I want to introduce F The Gate Drive
+ 
+
+ align:start position:0%
+I want to introduce F The Gate Drive
+as we said before for this TR and TF
+
+ align:start position:0%
+as we said before for this TR and TF
+ 
+
+ align:start position:0%
+as we said before for this TR and TF
+where is that
+
+ align:start position:0%
+where is that
+ 
+
+ align:start position:0%
+where is that
+yeah for this TF or TR what do they
+
+ align:start position:0%
+yeah for this TF or TR what do they
+ 
+
+ align:start position:0%
+yeah for this TF or TR what do they
+depend on they depend on the devices or
+
+ align:start position:0%
+depend on they depend on the devices or
+ 
+
+ align:start position:0%
+depend on they depend on the devices or
+they depend on the drivers so imagine
+
+ align:start position:0%
+they depend on the drivers so imagine
+ 
+
+ align:start position:0%
+they depend on the drivers so imagine
+like we have a huge or a big device it
+
+ align:start position:0%
+like we have a huge or a big device it
+ 
+
+ align:start position:0%
+like we have a huge or a big device it
+may takes longer time to finish the turn
+
+ align:start position:0%
+may takes longer time to finish the turn
+ 
+
+ align:start position:0%
+may takes longer time to finish the turn
+on and the turn off transient but if we
+
+ align:start position:0%
+on and the turn off transient but if we
+ 
+
+ align:start position:0%
+on and the turn off transient but if we
+have a powerful driver maybe we can
+
+ align:start position:0%
+have a powerful driver maybe we can
+ 
+
+ align:start position:0%
+have a powerful driver maybe we can
+reduce that time so I want to introduce
+
+ align:start position:0%
+reduce that time so I want to introduce
+ 
+
+ align:start position:0%
+reduce that time so I want to introduce
+a small bit of the G drive is like
+
+ align:start position:0%
+a small bit of the G drive is like
+ 
+
+ align:start position:0%
+a small bit of the G drive is like
+sometimes when we want to drive M
+
+ align:start position:0%
+sometimes when we want to drive M
+ 
+
+ align:start position:0%
+sometimes when we want to drive M
+fat so this is the voltage source which
+
+ align:start position:0%
+fat so this is the voltage source which
+ 
+
+ align:start position:0%
+fat so this is the voltage source which
+is a Gate Drive which is a gate drive so
+
+ align:start position:0%
+is a Gate Drive which is a gate drive so
+ 
+
+ align:start position:0%
+is a Gate Drive which is a gate drive so
+we can have different
+
+ align:start position:0%
+we can have different
+ 
+
+ align:start position:0%
+we can have different
+path to turn on and turn off of
+
+ align:start position:0%
+path to turn on and turn off of
+ 
+
+ align:start position:0%
+path to turn on and turn off of
+the to turn on and turn off of the most
+
+ align:start position:0%
+the to turn on and turn off of the most
+ 
+
+ align:start position:0%
+the to turn on and turn off of the most
+fat so during the turn on so we can
+
+ align:start position:0%
+fat so during the turn on so we can
+ 
+
+ align:start position:0%
+fat so during the turn on so we can
+select a relatively Bigg resistor to
+
+ align:start position:0%
+select a relatively Bigg resistor to
+ 
+
+ align:start position:0%
+select a relatively Bigg resistor to
+charge this capacitor for turn off we
+
+ align:start position:0%
+charge this capacitor for turn off we
+ 
+
+ align:start position:0%
+charge this capacitor for turn off we
+really want it to be fast so we can have
+
+ align:start position:0%
+really want it to be fast so we can have
+ 
+
+ align:start position:0%
+really want it to be fast so we can have
+a small resistor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so do do you have any further
+
+ align:start position:0%
+here so do do you have any further
+ 
+
+ align:start position:0%
+here so do do you have any further
+questions about today's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lecture yeah we still have some
+
+ align:start position:0%
+lecture yeah we still have some
+ 
+
+ align:start position:0%
+lecture yeah we still have some
+time so if not so that will be end for
+
+ align:start position:0%
+time so if not so that will be end for
+ 
+
+ align:start position:0%
+time so if not so that will be end for
+today's lecture thank you
\ No newline at end of file
diff --git a/oEUo2faDJNA.txt b/oEUo2faDJNA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9afe9ece75181e3519524dd156e446a0746d76c7
--- /dev/null
+++ b/oEUo2faDJNA.txt
@@ -0,0 +1,1979 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so my question is sort of twofold sort
+
+ align:start position:0%
+so my question is sort of twofold sort
+ 
+
+ align:start position:0%
+so my question is sort of twofold sort
+of goes back on it sort of goes back on
+
+ align:start position:0%
+of goes back on it sort of goes back on
+ 
+
+ align:start position:0%
+of goes back on it sort of goes back on
+some of other things we've discussed the
+
+ align:start position:0%
+some of other things we've discussed the
+ 
+
+ align:start position:0%
+some of other things we've discussed the
+recent elections so I've recently been
+
+ align:start position:0%
+recent elections so I've recently been
+ 
+
+ align:start position:0%
+recent elections so I've recently been
+following some of your stuff and there's
+
+ align:start position:0%
+following some of your stuff and there's
+ 
+
+ align:start position:0%
+following some of your stuff and there's
+evidence that suggests that you sort of
+
+ align:start position:0%
+evidence that suggests that you sort of
+ 
+
+ align:start position:0%
+evidence that suggests that you sort of
+predicted rise from the campaign about
+
+ align:start position:0%
+predicted rise from the campaign about
+ 
+
+ align:start position:0%
+predicted rise from the campaign about
+seven years ago and I'm sort of curious
+
+ align:start position:0%
+seven years ago and I'm sort of curious
+ 
+
+ align:start position:0%
+seven years ago and I'm sort of curious
+what what what was so different about
+
+ align:start position:0%
+what what what was so different about
+ 
+
+ align:start position:0%
+what what what was so different about
+this election I presume you've seen the
+
+ align:start position:0%
+this election I presume you've seen the
+ 
+
+ align:start position:0%
+this election I presume you've seen the
+rise of funny presidential candidates
+
+ align:start position:0%
+rise of funny presidential candidates
+ 
+
+ align:start position:0%
+rise of funny presidential candidates
+over the years and I'm sort of curious
+
+ align:start position:0%
+over the years and I'm sort of curious
+ 
+
+ align:start position:0%
+over the years and I'm sort of curious
+to understand what what sort of prompted
+
+ align:start position:0%
+to understand what what sort of prompted
+ 
+
+ align:start position:0%
+to understand what what sort of prompted
+that that speculation he's under my
+
+ align:start position:0%
+that that speculation he's under my
+ 
+
+ align:start position:0%
+that that speculation he's under my
+question sort of it's looking more so
+
+ align:start position:0%
+question sort of it's looking more so
+ 
+
+ align:start position:0%
+question sort of it's looking more so
+into the future so as we discussed
+
+ align:start position:0%
+into the future so as we discussed
+ 
+
+ align:start position:0%
+into the future so as we discussed
+America is probably more polarized and
+
+ align:start position:0%
+America is probably more polarized and
+ 
+
+ align:start position:0%
+America is probably more polarized and
+it's I guess sort of been in the past
+
+ align:start position:0%
+it's I guess sort of been in the past
+ 
+
+ align:start position:0%
+it's I guess sort of been in the past
+and there's sort of this idea that the
+
+ align:start position:0%
+and there's sort of this idea that the
+ 
+
+ align:start position:0%
+and there's sort of this idea that the
+clustering of like-minded Americans is
+
+ align:start position:0%
+clustering of like-minded Americans is
+ 
+
+ align:start position:0%
+clustering of like-minded Americans is
+tearing us apart
+
+ align:start position:0%
+tearing us apart
+ 
+
+ align:start position:0%
+tearing us apart
+so where do you see the future of this
+
+ align:start position:0%
+so where do you see the future of this
+ 
+
+ align:start position:0%
+so where do you see the future of this
+nation going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I mean there are many special
+
+ align:start position:0%
+well I mean there are many special
+ 
+
+ align:start position:0%
+well I mean there are many special
+factors in the United States societies
+
+ align:start position:0%
+factors in the United States societies
+ 
+
+ align:start position:0%
+factors in the United States societies
+are different but notice that what
+
+ align:start position:0%
+are different but notice that what
+ 
+
+ align:start position:0%
+are different but notice that what
+happened in this election what actually
+
+ align:start position:0%
+happened in this election what actually
+ 
+
+ align:start position:0%
+happened in this election what actually
+happened in the 2016 election is that
+
+ align:start position:0%
+happened in the 2016 election is that
+ 
+
+ align:start position:0%
+happened in the 2016 election is that
+the mainstream establishment
+
+ align:start position:0%
+the mainstream establishment
+ 
+
+ align:start position:0%
+the mainstream establishment
+institutions were basically destroyed
+
+ align:start position:0%
+institutions were basically destroyed
+ 
+
+ align:start position:0%
+institutions were basically destroyed
+the two major phenomena in this election
+
+ align:start position:0%
+the two major phenomena in this election
+ 
+
+ align:start position:0%
+the two major phenomena in this election
+where the Sanders campaign among the
+
+ align:start position:0%
+where the Sanders campaign among the
+ 
+
+ align:start position:0%
+where the Sanders campaign among the
+Democrats and the Trump campaign among
+
+ align:start position:0%
+Democrats and the Trump campaign among
+ 
+
+ align:start position:0%
+Democrats and the Trump campaign among
+the Republicans and they were both
+
+ align:start position:0%
+the Republicans and they were both
+ 
+
+ align:start position:0%
+the Republicans and they were both
+anti-establishment and the voters went
+
+ align:start position:0%
+anti-establishment and the voters went
+ 
+
+ align:start position:0%
+anti-establishment and the voters went
+that way the if you take a look at poll
+
+ align:start position:0%
+that way the if you take a look at poll
+ 
+
+ align:start position:0%
+that way the if you take a look at poll
+polling results you can see it I mean
+
+ align:start position:0%
+polling results you can see it I mean
+ 
+
+ align:start position:0%
+polling results you can see it I mean
+anger and contempt for institutions is
+
+ align:start position:0%
+anger and contempt for institutions is
+ 
+
+ align:start position:0%
+anger and contempt for institutions is
+just phenomenal you know you ask people
+
+ align:start position:0%
+just phenomenal you know you ask people
+ 
+
+ align:start position:0%
+just phenomenal you know you ask people
+and polls that they have any what do you
+
+ align:start position:0%
+and polls that they have any what do you
+ 
+
+ align:start position:0%
+and polls that they have any what do you
+think about Congress you know 90 percent
+
+ align:start position:0%
+think about Congress you know 90 percent
+ 
+
+ align:start position:0%
+think about Congress you know 90 percent
+say they have you all thrown out you
+
+ align:start position:0%
+say they have you all thrown out you
+ 
+
+ align:start position:0%
+say they have you all thrown out you
+know in fact about the only institution
+
+ align:start position:0%
+know in fact about the only institution
+ 
+
+ align:start position:0%
+know in fact about the only institution
+that has any respect is the military
+
+ align:start position:0%
+that has any respect is the military
+ 
+
+ align:start position:0%
+that has any respect is the military
+because you're taught you know somehow
+
+ align:start position:0%
+because you're taught you know somehow
+ 
+
+ align:start position:0%
+because you're taught you know somehow
+the military's defending us from those
+
+ align:start position:0%
+the military's defending us from those
+ 
+
+ align:start position:0%
+the military's defending us from those
+one but and the same is true in your
+
+ align:start position:0%
+one but and the same is true in your
+ 
+
+ align:start position:0%
+one but and the same is true in your
+take a look at the French election a
+
+ align:start position:0%
+take a look at the French election a
+ 
+
+ align:start position:0%
+take a look at the French election a
+couple days ago the two candidates were
+
+ align:start position:0%
+couple days ago the two candidates were
+ 
+
+ align:start position:0%
+couple days ago the two candidates were
+Outsiders the political parties barely
+
+ align:start position:0%
+Outsiders the political parties barely
+ 
+
+ align:start position:0%
+Outsiders the political parties barely
+participated knock on the pen are from
+
+ align:start position:0%
+participated knock on the pen are from
+ 
+
+ align:start position:0%
+participated knock on the pen are from
+outside the mainstream that has run
+
+ align:start position:0%
+outside the mainstream that has run
+ 
+
+ align:start position:0%
+outside the mainstream that has run
+Europe for 50 years the center right and
+
+ align:start position:0%
+Europe for 50 years the center right and
+ 
+
+ align:start position:0%
+Europe for 50 years the center right and
+center-left parties are gone same thing
+
+ align:start position:0%
+center-left parties are gone same thing
+ 
+
+ align:start position:0%
+center-left parties are gone same thing
+happened in England with brexit same
+
+ align:start position:0%
+happened in England with brexit same
+ 
+
+ align:start position:0%
+happened in England with brexit same
+things happening in other European
+
+ align:start position:0%
+things happening in other European
+ 
+
+ align:start position:0%
+things happening in other European
+countries we're seeing a phenomenon all
+
+ align:start position:0%
+countries we're seeing a phenomenon all
+ 
+
+ align:start position:0%
+countries we're seeing a phenomenon all
+over the world Western world in which
+
+ align:start position:0%
+over the world Western world in which
+ 
+
+ align:start position:0%
+over the world Western world in which
+the centrist you know center left center
+
+ align:start position:0%
+the centrist you know center left center
+ 
+
+ align:start position:0%
+the centrist you know center left center
+right institutions are under attack
+
+ align:start position:0%
+right institutions are under attack
+ 
+
+ align:start position:0%
+right institutions are under attack
+people are angry about them they hate
+
+ align:start position:0%
+people are angry about them they hate
+ 
+
+ align:start position:0%
+people are angry about them they hate
+them they think they're not working for
+
+ align:start position:0%
+them they think they're not working for
+ 
+
+ align:start position:0%
+them they think they're not working for
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+and they're right that's the effect of
+
+ align:start position:0%
+and they're right that's the effect of
+ 
+
+ align:start position:0%
+and they're right that's the effect of
+the neoliberal programs we're all
+
+ align:start position:0%
+the neoliberal programs we're all
+ 
+
+ align:start position:0%
+the neoliberal programs we're all
+subjected to the same socio-economic
+
+ align:start position:0%
+subjected to the same socio-economic
+ 
+
+ align:start position:0%
+subjected to the same socio-economic
+programs they've had a similar effect
+
+ align:start position:0%
+programs they've had a similar effect
+ 
+
+ align:start position:0%
+programs they've had a similar effect
+everywhere they've led to stagnation
+
+ align:start position:0%
+everywhere they've led to stagnation
+ 
+
+ align:start position:0%
+everywhere they've led to stagnation
+decline undermining of public services
+
+ align:start position:0%
+decline undermining of public services
+ 
+
+ align:start position:0%
+decline undermining of public services
+inability the Reagan slogan into the
+
+ align:start position:0%
+inability the Reagan slogan into the
+ 
+
+ align:start position:0%
+inability the Reagan slogan into the
+state is the problem not the solution
+
+ align:start position:0%
+state is the problem not the solution
+ 
+
+ align:start position:0%
+state is the problem not the solution
+let's turn it over to private tyrannies
+
+ align:start position:0%
+let's turn it over to private tyrannies
+ 
+
+ align:start position:0%
+let's turn it over to private tyrannies
+which make it worse that's happening
+
+ align:start position:0%
+which make it worse that's happening
+ 
+
+ align:start position:0%
+which make it worse that's happening
+bits and pieces that are happening
+
+ align:start position:0%
+bits and pieces that are happening
+ 
+
+ align:start position:0%
+bits and pieces that are happening
+everywhere so it happened in the United
+
+ align:start position:0%
+everywhere so it happened in the United
+ 
+
+ align:start position:0%
+everywhere so it happened in the United
+States and its own particular way but
+
+ align:start position:0%
+States and its own particular way but
+ 
+
+ align:start position:0%
+States and its own particular way but
+but notice that it's two directions
+
+ align:start position:0%
+but notice that it's two directions
+ 
+
+ align:start position:0%
+but notice that it's two directions
+it's Sanders and Trump and I think in
+
+ align:start position:0%
+it's Sanders and Trump and I think in
+ 
+
+ align:start position:0%
+it's Sanders and Trump and I think in
+many ways they were appealing to the
+
+ align:start position:0%
+many ways they were appealing to the
+ 
+
+ align:start position:0%
+many ways they were appealing to the
+same sentiments and they could even
+
+ align:start position:0%
+same sentiments and they could even
+ 
+
+ align:start position:0%
+same sentiments and they could even
+converge you know a lot of the poppy if
+
+ align:start position:0%
+converge you know a lot of the poppy if
+ 
+
+ align:start position:0%
+converge you know a lot of the poppy if
+you if you look at what people believe
+
+ align:start position:0%
+you if you look at what people believe
+ 
+
+ align:start position:0%
+you if you look at what people believe
+the policies that they favor it's a lot
+
+ align:start position:0%
+the policies that they favor it's a lot
+ 
+
+ align:start position:0%
+the policies that they favor it's a lot
+of its shared so for example you know
+
+ align:start position:0%
+of its shared so for example you know
+ 
+
+ align:start position:0%
+of its shared so for example you know
+across the population all the way over
+
+ align:start position:0%
+across the population all the way over
+ 
+
+ align:start position:0%
+across the population all the way over
+to the Tea Party people think there
+
+ align:start position:0%
+to the Tea Party people think there
+ 
+
+ align:start position:0%
+to the Tea Party people think there
+ought to be higher taxes on the rich
+
+ align:start position:0%
+ought to be higher taxes on the rich
+ 
+
+ align:start position:0%
+ought to be higher taxes on the rich
+probably a majority of the population
+
+ align:start position:0%
+probably a majority of the population
+ 
+
+ align:start position:0%
+probably a majority of the population
+thinks they're out of the national
+
+ align:start position:0%
+thinks they're out of the national
+ 
+
+ align:start position:0%
+thinks they're out of the national
+health care no in fact I support for
+
+ align:start position:0%
+health care no in fact I support for
+ 
+
+ align:start position:0%
+health care no in fact I support for
+nationally guaranteed self health care
+
+ align:start position:0%
+nationally guaranteed self health care
+ 
+
+ align:start position:0%
+nationally guaranteed self health care
+has been so high over the years that
+
+ align:start position:0%
+has been so high over the years that
+ 
+
+ align:start position:0%
+has been so high over the years that
+sometimes it's almost hard to believe so
+
+ align:start position:0%
+sometimes it's almost hard to believe so
+ 
+
+ align:start position:0%
+sometimes it's almost hard to believe so
+in the late Reagan years for example
+
+ align:start position:0%
+in the late Reagan years for example
+ 
+
+ align:start position:0%
+in the late Reagan years for example
+about seventy percent of the population
+
+ align:start position:0%
+about seventy percent of the population
+ 
+
+ align:start position:0%
+about seventy percent of the population
+I thought that guaranteed national
+
+ align:start position:0%
+I thought that guaranteed national
+ 
+
+ align:start position:0%
+I thought that guaranteed national
+health care ought to be in the
+
+ align:start position:0%
+health care ought to be in the
+ 
+
+ align:start position:0%
+health care ought to be in the
+Constitution because this is an obvious
+
+ align:start position:0%
+Constitution because this is an obvious
+ 
+
+ align:start position:0%
+Constitution because this is an obvious
+demands about 40% of the population
+
+ align:start position:0%
+demands about 40% of the population
+ 
+
+ align:start position:0%
+demands about 40% of the population
+thought it already was in the
+
+ align:start position:0%
+thought it already was in the
+ 
+
+ align:start position:0%
+thought it already was in the
+Constitution nobody knows what's in the
+
+ align:start position:0%
+Constitution nobody knows what's in the
+ 
+
+ align:start position:0%
+Constitution nobody knows what's in the
+Constitution just everything good must
+
+ align:start position:0%
+Constitution just everything good must
+ 
+
+ align:start position:0%
+Constitution just everything good must
+be in the Constitution since this is so
+
+ align:start position:0%
+be in the Constitution since this is so
+ 
+
+ align:start position:0%
+be in the Constitution since this is so
+obviously good it must be in the
+
+ align:start position:0%
+obviously good it must be in the
+ 
+
+ align:start position:0%
+obviously good it must be in the
+Constitution there's right at the
+
+ align:start position:0%
+Constitution there's right at the
+ 
+
+ align:start position:0%
+Constitution there's right at the
+present of the most recent polls show
+
+ align:start position:0%
+present of the most recent polls show
+ 
+
+ align:start position:0%
+present of the most recent polls show
+someone over fifty percent supporting a
+
+ align:start position:0%
+someone over fifty percent supporting a
+ 
+
+ align:start position:0%
+someone over fifty percent supporting a
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+health care when Obama's Affordable Care
+
+ align:start position:0%
+health care when Obama's Affordable Care
+ 
+
+ align:start position:0%
+health care when Obama's Affordable Care
+Act was being pushed through at first
+
+ align:start position:0%
+Act was being pushed through at first
+ 
+
+ align:start position:0%
+Act was being pushed through at first
+there was one of the proposals one of
+
+ align:start position:0%
+there was one of the proposals one of
+ 
+
+ align:start position:0%
+there was one of the proposals one of
+the parts of it was what was called a
+
+ align:start position:0%
+the parts of it was what was called a
+ 
+
+ align:start position:0%
+the parts of it was what was called a
+public option which means you could
+
+ align:start position:0%
+public option which means you could
+ 
+
+ align:start position:0%
+public option which means you could
+choose if you wanted to be part of a
+
+ align:start position:0%
+choose if you wanted to be part of a
+ 
+
+ align:start position:0%
+choose if you wanted to be part of a
+government health care program about
+
+ align:start position:0%
+government health care program about
+ 
+
+ align:start position:0%
+government health care program about
+two-thirds of the population favored
+
+ align:start position:0%
+two-thirds of the population favored
+ 
+
+ align:start position:0%
+two-thirds of the population favored
+that but it was just thrown out without
+
+ align:start position:0%
+that but it was just thrown out without
+ 
+
+ align:start position:0%
+that but it was just thrown out without
+discussion the and in fact Fito
+
+ align:start position:0%
+discussion the and in fact Fito
+ 
+
+ align:start position:0%
+discussion the and in fact Fito
+case-by-case there's a lot of similarity
+
+ align:start position:0%
+case-by-case there's a lot of similarity
+ 
+
+ align:start position:0%
+case-by-case there's a lot of similarity
+in the attitudes about social political
+
+ align:start position:0%
+in the attitudes about social political
+ 
+
+ align:start position:0%
+in the attitudes about social political
+issues not necessarily cultural issues
+
+ align:start position:0%
+issues not necessarily cultural issues
+ 
+
+ align:start position:0%
+issues not necessarily cultural issues
+but social political issues among parts
+
+ align:start position:0%
+but social political issues among parts
+ 
+
+ align:start position:0%
+but social political issues among parts
+of the population that appear to be
+
+ align:start position:0%
+of the population that appear to be
+ 
+
+ align:start position:0%
+of the population that appear to be
+extremely polarized it's very
+
+ align:start position:0%
+extremely polarized it's very
+ 
+
+ align:start position:0%
+extremely polarized it's very
+interesting in England right now if he
+
+ align:start position:0%
+interesting in England right now if he
+ 
+
+ align:start position:0%
+interesting in England right now if he
+followed the Jeremy Corbyn has kind of a
+
+ align:start position:0%
+followed the Jeremy Corbyn has kind of a
+ 
+
+ align:start position:0%
+followed the Jeremy Corbyn has kind of a
+little bit like Sanders is bitterly
+
+ align:start position:0%
+little bit like Sanders is bitterly
+ 
+
+ align:start position:0%
+little bit like Sanders is bitterly
+attacked by the media I mean just
+
+ align:start position:0%
+attacked by the media I mean just
+ 
+
+ align:start position:0%
+attacked by the media I mean just
+including the liberal media like The
+
+ align:start position:0%
+including the liberal media like The
+ 
+
+ align:start position:0%
+including the liberal media like The
+Guardian and by the parliamentary Labour
+
+ align:start position:0%
+Guardian and by the parliamentary Labour
+ 
+
+ align:start position:0%
+Guardian and by the parliamentary Labour
+Party meaning the you know the guys who
+
+ align:start position:0%
+Party meaning the you know the guys who
+ 
+
+ align:start position:0%
+Party meaning the you know the guys who
+sort of the elites who run the party
+
+ align:start position:0%
+sort of the elites who run the party
+ 
+
+ align:start position:0%
+sort of the elites who run the party
+among they just came out with a I
+
+ align:start position:0%
+among they just came out with a I
+ 
+
+ align:start position:0%
+among they just came out with a I
+happened to be in England a couple days
+
+ align:start position:0%
+happened to be in England a couple days
+ 
+
+ align:start position:0%
+happened to be in England a couple days
+ago as I was reading the British press
+
+ align:start position:0%
+ago as I was reading the British press
+ 
+
+ align:start position:0%
+ago as I was reading the British press
+they they just came out with their the
+
+ align:start position:0%
+they they just came out with their the
+ 
+
+ align:start position:0%
+they they just came out with their the
+Labour Party with their program which
+
+ align:start position:0%
+Labour Party with their program which
+ 
+
+ align:start position:0%
+Labour Party with their program which
+was just lambaste it by the media you
+
+ align:start position:0%
+was just lambaste it by the media you
+ 
+
+ align:start position:0%
+was just lambaste it by the media you
+know crazy lunatic insane it'll destroy
+
+ align:start position:0%
+know crazy lunatic insane it'll destroy
+ 
+
+ align:start position:0%
+know crazy lunatic insane it'll destroy
+the Labour Party at the same time polls
+
+ align:start position:0%
+the Labour Party at the same time polls
+ 
+
+ align:start position:0%
+the Labour Party at the same time polls
+came out asking people it was
+
+ align:start position:0%
+came out asking people it was
+ 
+
+ align:start position:0%
+came out asking people it was
+independent about the the components of
+
+ align:start position:0%
+independent about the the components of
+ 
+
+ align:start position:0%
+independent about the the components of
+the program they were all very popular
+
+ align:start position:0%
+the program they were all very popular
+ 
+
+ align:start position:0%
+the program they were all very popular
+very strong support among the population
+
+ align:start position:0%
+very strong support among the population
+ 
+
+ align:start position:0%
+very strong support among the population
+for the elements of the program but
+
+ align:start position:0%
+for the elements of the program but
+ 
+
+ align:start position:0%
+for the elements of the program but
+attack and on the party that's proposing
+
+ align:start position:0%
+attack and on the party that's proposing
+ 
+
+ align:start position:0%
+attack and on the party that's proposing
+them in a particular on cordovan these
+
+ align:start position:0%
+them in a particular on cordovan these
+ 
+
+ align:start position:0%
+them in a particular on cordovan these
+are you know the serious activism and
+
+ align:start position:0%
+are you know the serious activism and
+ 
+
+ align:start position:0%
+are you know the serious activism and
+organizing could overcome this I mean
+
+ align:start position:0%
+organizing could overcome this I mean
+ 
+
+ align:start position:0%
+organizing could overcome this I mean
+you're fighting a link elements who have
+
+ align:start position:0%
+you're fighting a link elements who have
+ 
+
+ align:start position:0%
+you're fighting a link elements who have
+their own
+
+ align:start position:0%
+their own
+ 
+
+ align:start position:0%
+their own
+image of the way they want society to go
+
+ align:start position:0%
+image of the way they want society to go
+ 
+
+ align:start position:0%
+image of the way they want society to go
+and in fact you know there's quite a lot
+
+ align:start position:0%
+and in fact you know there's quite a lot
+ 
+
+ align:start position:0%
+and in fact you know there's quite a lot
+of interesting things going on a lot of
+
+ align:start position:0%
+of interesting things going on a lot of
+ 
+
+ align:start position:0%
+of interesting things going on a lot of
+it has this stuff that you guys might be
+
+ align:start position:0%
+it has this stuff that you guys might be
+ 
+
+ align:start position:0%
+it has this stuff that you guys might be
+interested in has to do with data are
+
+ align:start position:0%
+interested in has to do with data are
+ 
+
+ align:start position:0%
+interested in has to do with data are
+vestee there's a company called
+
+ align:start position:0%
+vestee there's a company called
+ 
+
+ align:start position:0%
+vestee there's a company called
+Cambridge analytics I think which is run
+
+ align:start position:0%
+Cambridge analytics I think which is run
+ 
+
+ align:start position:0%
+Cambridge analytics I think which is run
+by some ultra-right billionaires Peter
+
+ align:start position:0%
+by some ultra-right billionaires Peter
+ 
+
+ align:start position:0%
+by some ultra-right billionaires Peter
+Thiel the guy who owns PayPal and a
+
+ align:start position:0%
+Thiel the guy who owns PayPal and a
+ 
+
+ align:start position:0%
+Thiel the guy who owns PayPal and a
+bunch of other things Robert Mercer
+
+ align:start position:0%
+bunch of other things Robert Mercer
+ 
+
+ align:start position:0%
+bunch of other things Robert Mercer
+who's a hedge fund manager multi
+
+ align:start position:0%
+who's a hedge fund manager multi
+ 
+
+ align:start position:0%
+who's a hedge fund manager multi
+billionaire a couple of others what
+
+ align:start position:0%
+billionaire a couple of others what
+ 
+
+ align:start position:0%
+billionaire a couple of others what
+they've been doing and this essentially
+
+ align:start position:0%
+they've been doing and this essentially
+ 
+
+ align:start position:0%
+they've been doing and this essentially
+gave the election to Trump is extremely
+
+ align:start position:0%
+gave the election to Trump is extremely
+ 
+
+ align:start position:0%
+gave the election to Trump is extremely
+careful data analysis there's a ton of
+
+ align:start position:0%
+careful data analysis there's a ton of
+ 
+
+ align:start position:0%
+careful data analysis there's a ton of
+data now from Facebook and other things
+
+ align:start position:0%
+data now from Facebook and other things
+ 
+
+ align:start position:0%
+data now from Facebook and other things
+about people's personal preferences and
+
+ align:start position:0%
+about people's personal preferences and
+ 
+
+ align:start position:0%
+about people's personal preferences and
+attitudes and you know feelings and are
+
+ align:start position:0%
+attitudes and you know feelings and are
+ 
+
+ align:start position:0%
+attitudes and you know feelings and are
+you depressed you know all kinds of
+
+ align:start position:0%
+you depressed you know all kinds of
+ 
+
+ align:start position:0%
+you depressed you know all kinds of
+things and what they're doing is looking
+
+ align:start position:0%
+things and what they're doing is looking
+ 
+
+ align:start position:0%
+things and what they're doing is looking
+carefully at this data and analyzing it
+
+ align:start position:0%
+carefully at this data and analyzing it
+ 
+
+ align:start position:0%
+carefully at this data and analyzing it
+to see if you can find small numbers of
+
+ align:start position:0%
+to see if you can find small numbers of
+ 
+
+ align:start position:0%
+to see if you can find small numbers of
+people in particular areas who can be
+
+ align:start position:0%
+people in particular areas who can be
+ 
+
+ align:start position:0%
+people in particular areas who can be
+who are vulnerable to one or another
+
+ align:start position:0%
+who are vulnerable to one or another
+ 
+
+ align:start position:0%
+who are vulnerable to one or another
+form of manipulation and what they're
+
+ align:start position:0%
+form of manipulation and what they're
+ 
+
+ align:start position:0%
+form of manipulation and what they're
+doing is trying to say look if they're
+
+ align:start position:0%
+doing is trying to say look if they're
+ 
+
+ align:start position:0%
+doing is trying to say look if they're
+kind of tend to be liberal try to get
+
+ align:start position:0%
+kind of tend to be liberal try to get
+ 
+
+ align:start position:0%
+kind of tend to be liberal try to get
+them to get so disillusioned that they
+
+ align:start position:0%
+them to get so disillusioned that they
+ 
+
+ align:start position:0%
+them to get so disillusioned that they
+won't vote and if they tend to be say
+
+ align:start position:0%
+won't vote and if they tend to be say
+ 
+
+ align:start position:0%
+won't vote and if they tend to be say
+traditionally conservative maybe
+
+ align:start position:0%
+traditionally conservative maybe
+ 
+
+ align:start position:0%
+traditionally conservative maybe
+religious or whatever I try to get them
+
+ align:start position:0%
+religious or whatever I try to get them
+ 
+
+ align:start position:0%
+religious or whatever I try to get them
+to do you know reach them individually
+
+ align:start position:0%
+to do you know reach them individually
+ 
+
+ align:start position:0%
+to do you know reach them individually
+in ways which will increase the
+
+ align:start position:0%
+in ways which will increase the
+ 
+
+ align:start position:0%
+in ways which will increase the
+probability that they'll vote for the
+
+ align:start position:0%
+probability that they'll vote for the
+ 
+
+ align:start position:0%
+probability that they'll vote for the
+right-wing this has small effects but
+
+ align:start position:0%
+right-wing this has small effects but
+ 
+
+ align:start position:0%
+right-wing this has small effects but
+the elections are won on very small
+
+ align:start position:0%
+the elections are won on very small
+ 
+
+ align:start position:0%
+the elections are won on very small
+effects like Trump's as you know Trump
+
+ align:start position:0%
+effects like Trump's as you know Trump
+ 
+
+ align:start position:0%
+effects like Trump's as you know Trump
+lost the popular vote but by a couple of
+
+ align:start position:0%
+lost the popular vote but by a couple of
+ 
+
+ align:start position:0%
+lost the popular vote but by a couple of
+million but in particular counties that
+
+ align:start position:0%
+million but in particular counties that
+ 
+
+ align:start position:0%
+million but in particular counties that
+made the difference a couple of hundred
+
+ align:start position:0%
+made the difference a couple of hundred
+ 
+
+ align:start position:0%
+made the difference a couple of hundred
+thousand votes shifted the election in
+
+ align:start position:0%
+thousand votes shifted the election in
+ 
+
+ align:start position:0%
+thousand votes shifted the election in
+England brexit was the same
+
+ align:start position:0%
+England brexit was the same
+ 
+
+ align:start position:0%
+England brexit was the same
+tomatoe about maybe 600,000 votes in all
+
+ align:start position:0%
+tomatoe about maybe 600,000 votes in all
+ 
+
+ align:start position:0%
+tomatoe about maybe 600,000 votes in all
+countries this week you know these
+
+ align:start position:0%
+countries this week you know these
+ 
+
+ align:start position:0%
+countries this week you know these
+companies using a lot of complicated
+
+ align:start position:0%
+companies using a lot of complicated
+ 
+
+ align:start position:0%
+companies using a lot of complicated
+data processing and statistics and so on
+
+ align:start position:0%
+data processing and statistics and so on
+ 
+
+ align:start position:0%
+data processing and statistics and so on
+working on ways to try to control the
+
+ align:start position:0%
+working on ways to try to control the
+ 
+
+ align:start position:0%
+working on ways to try to control the
+electoral process I mean this is way
+
+ align:start position:0%
+electoral process I mean this is way
+ 
+
+ align:start position:0%
+electoral process I mean this is way
+more important than any of the nonsense
+
+ align:start position:0%
+more important than any of the nonsense
+ 
+
+ align:start position:0%
+more important than any of the nonsense
+about the Russian hacking that's all
+
+ align:start position:0%
+about the Russian hacking that's all
+ 
+
+ align:start position:0%
+about the Russian hacking that's all
+garbage but this stuff is real and it's
+
+ align:start position:0%
+garbage but this stuff is real and it's
+ 
+
+ align:start position:0%
+garbage but this stuff is real and it's
+that's right in front of our eyes it's
+
+ align:start position:0%
+that's right in front of our eyes it's
+ 
+
+ align:start position:0%
+that's right in front of our eyes it's
+the people we know you know MIT students
+
+ align:start position:0%
+the people we know you know MIT students
+ 
+
+ align:start position:0%
+the people we know you know MIT students
+going off to work in these things and it
+
+ align:start position:0%
+going off to work in these things and it
+ 
+
+ align:start position:0%
+going off to work in these things and it
+has a big effect on controlling formal
+
+ align:start position:0%
+has a big effect on controlling formal
+ 
+
+ align:start position:0%
+has a big effect on controlling formal
+democratic systems they feel this is
+
+ align:start position:0%
+democratic systems they feel this is
+ 
+
+ align:start position:0%
+democratic systems they feel this is
+Steve Bannon this is his image of how
+
+ align:start position:0%
+Steve Bannon this is his image of how
+ 
+
+ align:start position:0%
+Steve Bannon this is his image of how
+you control the world you know these are
+
+ align:start position:0%
+you control the world you know these are
+ 
+
+ align:start position:0%
+you control the world you know these are
+people who are influential they have
+
+ align:start position:0%
+people who are influential they have
+ 
+
+ align:start position:0%
+people who are influential they have
+tons of money they deeply reactionary
+
+ align:start position:0%
+tons of money they deeply reactionary
+ 
+
+ align:start position:0%
+tons of money they deeply reactionary
+and they have a fee they want to use
+
+ align:start position:0%
+and they have a fee they want to use
+ 
+
+ align:start position:0%
+and they have a fee they want to use
+modern data processing
+
+ align:start position:0%
+modern data processing
+ 
+
+ align:start position:0%
+modern data processing
+you know big data statistical analysis
+
+ align:start position:0%
+you know big data statistical analysis
+ 
+
+ align:start position:0%
+you know big data statistical analysis
+and so on to see if you can just find
+
+ align:start position:0%
+and so on to see if you can just find
+ 
+
+ align:start position:0%
+and so on to see if you can just find
+ways of swinging elections by going
+
+ align:start position:0%
+ways of swinging elections by going
+ 
+
+ align:start position:0%
+ways of swinging elections by going
+after individual vulnerabilities using
+
+ align:start position:0%
+after individual vulnerabilities using
+ 
+
+ align:start position:0%
+after individual vulnerabilities using
+the massive data that people provide
+
+ align:start position:0%
+the massive data that people provide
+ 
+
+ align:start position:0%
+the massive data that people provide
+through Google and Facebook and all of
+
+ align:start position:0%
+through Google and Facebook and all of
+ 
+
+ align:start position:0%
+through Google and Facebook and all of
+this stuff I mean Google and the rest of
+
+ align:start position:0%
+this stuff I mean Google and the rest of
+ 
+
+ align:start position:0%
+this stuff I mean Google and the rest of
+music for advertisers so that
+
+ align:start position:0%
+music for advertisers so that
+ 
+
+ align:start position:0%
+music for advertisers so that
+advertisers can go after you
+
+ align:start position:0%
+advertisers can go after you
+ 
+
+ align:start position:0%
+advertisers can go after you
+individually and say you know like you
+
+ align:start position:0%
+individually and say you know like you
+ 
+
+ align:start position:0%
+individually and say you know like you
+know you try to get a book on Amazon and
+
+ align:start position:0%
+know you try to get a book on Amazon and
+ 
+
+ align:start position:0%
+know you try to get a book on Amazon and
+they suggest ten other books you ought
+
+ align:start position:0%
+they suggest ten other books you ought
+ 
+
+ align:start position:0%
+they suggest ten other books you ought
+to buy because they've got so much
+
+ align:start position:0%
+to buy because they've got so much
+ 
+
+ align:start position:0%
+to buy because they've got so much
+information on you that they think may
+
+ align:start position:0%
+information on you that they think may
+ 
+
+ align:start position:0%
+information on you that they think may
+be way back and sort of getting to sell
+
+ align:start position:0%
+be way back and sort of getting to sell
+ 
+
+ align:start position:0%
+be way back and sort of getting to sell
+this one that's going on all the time
+
+ align:start position:0%
+this one that's going on all the time
+ 
+
+ align:start position:0%
+this one that's going on all the time
+but here it's right in the middle of the
+
+ align:start position:0%
+but here it's right in the middle of the
+ 
+
+ align:start position:0%
+but here it's right in the middle of the
+political system and it's really
+
+ align:start position:0%
+political system and it's really
+ 
+
+ align:start position:0%
+political system and it's really
+significant quite unlike the Russian
+
+ align:start position:0%
+significant quite unlike the Russian
+ 
+
+ align:start position:0%
+significant quite unlike the Russian
+hacking story this is real and it's not
+
+ align:start position:0%
+hacking story this is real and it's not
+ 
+
+ align:start position:0%
+hacking story this is real and it's not
+very far from us facts happening right
+
+ align:start position:0%
+very far from us facts happening right
+ 
+
+ align:start position:0%
+very far from us facts happening right
+here you know there are things that can
+
+ align:start position:0%
+here you know there are things that can
+ 
+
+ align:start position:0%
+here you know there are things that can
+be done about that
+
+ align:start position:0%
+be done about that
+ 
+
+ align:start position:0%
+be done about that
+like exposing it for one thing these
+
+ align:start position:0%
+like exposing it for one thing these
+ 
+
+ align:start position:0%
+like exposing it for one thing these
+should be live issues I think among
+
+ align:start position:0%
+should be live issues I think among
+ 
+
+ align:start position:0%
+should be live issues I think among
+students do we want to devote our lives
+
+ align:start position:0%
+students do we want to devote our lives
+ 
+
+ align:start position:0%
+students do we want to devote our lives
+to destroying democracy maybe
\ No newline at end of file
diff --git a/oPb9AWMN2fY.txt b/oPb9AWMN2fY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7ceee78ec35860ed08a92556a6ee026ebb73ac13
--- /dev/null
+++ b/oPb9AWMN2fY.txt
@@ -0,0 +1,3853 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: All right.
+
+Good afternoon, everyone, again.
+
+Today, our session is going
+to be on motion perception
+
+and pursuit eye movements.
+
+Now, I want to remind you that
+to our next class next Monday
+
+is going to be a
+whirlwind review.
+
+And then the next
+Wednesday we are
+
+going to have the
+midterm exam on what
+
+we have covered so
+far in the course.
+
+And as I've mentioned already
+to you a couple of times,
+
+that is going to consist of
+a series of multiple choice
+
+questions in which
+you have to circle
+
+the appropriate choice
+for each question.
+
+Then the following week, which
+is going to be November 28,
+
+is when Chris--
+
+AUDIENCE: October.
+
+PROFESSOR: Huh?
+
+AUDIENCE: October 28.
+
+PROFESSOR: Sorry, October what?
+
+AUDIENCE: 28th.
+
+PROFESSOR: October 28.
+
+Yeah, October 28--
+that's when Chris Brown
+
+is going to start the second
+half of the course on audition.
+
+So that is the general
+plan at this point.
+
+And again, I'm going to send
+around an attendance sheet.
+
+So just put your name on it and
+send it around, please, for me.
+
+Thank you.
+
+All right, so I
+think you're going
+
+to find talking about motion
+perception a lot of fun.
+
+I have several demonstrations.
+
+And it is certainly have
+a very interesting topic.
+
+And I'm going to highlight that
+by first of all telling you
+
+what we are going to cover.
+
+And then we are going to talk
+about the basic mechanisms
+
+of direction selectivity
+in the visual cortex.
+
+So first of all,
+as I've said, we're
+
+going to talk about the neurons
+in the brain that code motion.
+
+I'm going to talk about it
+mostly for in the cortex.
+
+But I would also say a few words
+about direction selective cells
+
+that you find in the retina
+that we had mentioned before.
+
+All right, so we are going
+to then discuss briefly
+
+the possible
+mechanisms that make
+
+it feasible to process motion.
+
+And then we are
+going to look at what
+
+happens when you make various
+brain lesions in determining
+
+how well you can process depth.
+
+Then we're going to talk about
+a very interesting topic, which
+
+is structure for motion.
+
+And then further
+pursuing that, we're
+
+going to talk about
+apparent motion.
+
+And then we are going to talk
+about an interesting temporal
+
+effect which is
+called metacontrast.
+
+And then we are going to talk
+about optokynetic nystagmus,
+
+where we link the visual input
+to the generation of pursuit
+
+eye movements.
+
+Then that is accomplished by
+the so-called accessory optic
+
+system that I will
+describe to you.
+
+And that is also the topic
+that, if you remember,
+
+you will be writing a paper on.
+
+Lastly then, we are
+going to have a summary.
+
+OK, so let's look first
+at the neural responses
+
+to motion in the cortex.
+
+Now, one of the most
+remarkable features
+
+of the visual cortex and
+extra cortical areas,
+
+as I had already mentioned,
+is that the majority
+
+of cells in these areas
+are direction selective,
+
+meaning that they respond to one
+particular direction of motion,
+
+but not to the
+opposite direction.
+
+Now, this is extremely evident
+in the visual cortex, where
+
+the so-called simple cells,
+virtually all of them
+
+are direction selective.
+
+So that's one of the
+major transforms,
+
+if you remember, of
+the input that you
+
+have from the lateral
+geniculate nucleus that
+
+goes to the cortex.
+
+That input is just from single
+cells, on and off single cells,
+
+midget and parasol cells that
+have circular receptive fields
+
+that centers around antagonism.
+
+And when they get
+up to the cortex,
+
+a transformation
+takes place by virtue
+
+of intracortical circuits
+that turns these cells
+
+into direction specific
+ones and cells that
+
+are orientation specific.
+
+So let's look at this first
+by starting with a method
+
+so that you'll understand
+exactly how this is done.
+
+In this case, what
+we are going to do
+
+is we are going to
+have a photo cell.
+
+Let's just look at
+the top one here,
+
+A. You're going to have a
+photo cell that responds both
+
+to a light edge and a dark edge.
+
+And so when this bar moves
+across this photo cell,
+
+it will activate it.
+
+And what they're
+going to do-- we
+
+are going to move it
+across in one direction.
+
+And then we are going
+to move it back across
+
+in the other direction.
+
+And this is shown here.
+
+This is a time scale.
+
+And it shows that when
+this edge goes across,
+
+it activates the photo
+cell, gives it the beep.
+
+And then when the
+trailing edge goes across,
+
+it also does the same thing.
+
+So this is the
+light edge response.
+
+This is the dark edge response.
+
+Now, when you're going
+back the other way,
+
+you're going to have,
+again, the same arrangement.
+
+In the opposite direction,
+the light edge responds first.
+
+And the dark edge
+responds second.
+
+Now we are going to make
+a change so that it mimics
+
+the organization of simple
+cells in the visual cortex.
+
+We're going to put
+two photo cells, one
+
+which responds to the light
+edge and a dark one which
+
+responds to the dark edge.
+
+So now when this bar goes across
+and activates these two photo
+
+cells, what happens is, because
+they are not all centered
+
+exactly in the middle,
+it takes a longer time
+
+to activate the two successive
+[INAUDIBLE] when the bar goes
+
+across this way and
+a short time when
+
+it goes across the other way.
+
+Now, the opposite happens
+when you have a dark bar,
+
+because then the dark
+bar doesn't activate
+
+the light sensitive photo cell.
+
+It activities the dark one.
+
+So it takes a little
+longer to start that.
+
+So that then shows you
+the temporal arrangements
+
+of these responses if
+when the photo cells
+
+are arranged in this fashion.
+
+Everybody understand that?
+
+OK, so now we are going
+to do this for the real.
+
+We are going to look
+at a cortical cell.
+
+And there are several different
+subclasses of simple cells.
+
+And the first
+subclass we can refer
+
+to as an S1, S for simple, OK?
+
+So the simple cell
+there is an example,
+
+very similar arrangement.
+
+Here's the receptive field
+of the cell, undefined.
+
+And you either put a light
+edge across back and forth
+
+or a dark edge back and forth.
+
+This is the light edge response.
+
+This is the dark edge response.
+
+Now, you can readily
+see what happens
+
+here, which is quite remarkable.
+
+The cell responds only
+when the bar moves upward
+
+across the receptive
+field and does not
+
+respond when it moves downward.
+
+So this cell is over
+100% direction selective.
+
+Got it?
+
+All right.
+
+Now, the same thing happens
+to the dark edge, all right?
+
+And so this cell is one that
+responds only to the dark edge,
+
+OK?
+
+In this case, it's
+the trailing edge.
+
+In this case, it's
+the leading edge.
+
+Now, at the bottom
+here, you draw out
+
+what the receptive
+field looks like.
+
+This is in 10th of degrees.
+
+And so this is pretty much
+just the spatial response
+
+of the cell.
+
+And it only responds
+in this direction.
+
+There's nothing drawn
+in the other way.
+
+Now I'm going to show
+you another cell, which
+
+is going to be a
+so-called S2 cell.
+
+Now, this cell is different
+in that it responds
+
+both to the light
+and the dark edges.
+
+And the fact that they're--
+in this case, a light bar,
+
+in this case, a dark bar, the
+fact that they're-- displaced
+
+temporally mean that they're
+side by side for the light
+
+and dark responses
+rather than overlapping.
+
+And that, of course, is the
+definition of a simple cell.
+
+And so if you draw out the
+receptive field of this cell,
+
+once again, the cell is almost
+100% direction selective.
+
+And this is what its
+response looks like in space.
+
+Now we are going to
+look at yet another one.
+
+And this is going
+to be a surprise.
+
+It was certainly a surprise
+when this was discovered,
+
+because it's still
+not understood
+
+why we have these
+kinds of cells.
+
+Here is one-- you
+can look at that--
+
+that responds to a light edge in
+this direction and a dark edge
+
+in this direction, OK?
+
+So both subfields are
+direction selective.
+
+But they're direction selective
+in opposite directions,
+
+as depicted here.
+
+Now why on earth would you have
+cells in the visual cortex that
+
+respond selectively to
+light and dark edges
+
+in opposite directions?
+
+That's something
+you can contemplate.
+
+There is no definitive
+answer to that,
+
+and so I'm not going to
+belabor it any further?
+
+Now what I can do is I can
+provide you with a summary.
+
+I showed you this one,
+this one, and this one.
+
+Now, you don't have
+to worry about those.
+
+But I would like you to
+look at this last one, which
+
+is a complex cell.
+
+In a complex cell, the light
+and dark edge responses
+
+are in the same location,
+space-wise, as shown here.
+
+And this particular complex
+cell that's a real cell
+
+is 100% direction selective.
+
+Now, it's true not
+for all complex cells,
+
+but the majority of
+them that they too
+
+are direction selective.
+
+So I can safely
+tell you that one
+
+of the major transforms that
+happens in the brain in vision
+
+is to convert the signals
+form the retina into direction
+
+selective cells.
+
+And therefore, we
+can only surmise
+
+that to have direction
+selective cells is extremely
+
+important for us to
+be able to process
+
+motion information in the world.
+
+So now we are going
+to move on and look
+
+at extrastriate cortex.
+
+And we already talked
+briefly about MT and MST.
+
+In these two areas, we have
+even an stronger disposition
+
+for cells to be
+direction selective.
+
+And here's an example
+of a cell in MT--
+
+in this direction of
+motion, a vigorous response.
+
+This is a cumulative response.
+
+In the opposite direction, it
+actually has some inhibition,
+
+as you can see here and here.
+
+Then if you recall from MST,
+which is an area yet further
+
+removed from area V1-- it's the
+middle superior temporal area--
+
+what you find is, again,
+very strongly direction
+
+selective cells.
+
+Most of them-- maybe
+not all of them,
+
+but the overwhelming majority of
+them-- are direction selective.
+
+But they have much, much
+larger receptive fields
+
+than cells do in MT.
+
+And as I've mentioned to you
+before, one of the basic rules
+
+is that as you
+progress from the V1
+
+to higher cortical
+areas, the receptive
+
+fields in these progressively
+higher areas become
+
+bigger and bigger and cover more
+and more of the visual space.
+
+So here you can
+see this is shown
+
+in terms of the
+visual field here.
+
+This is way out.
+
+This is 20 degrees
+just from here to here.
+
+The receptive is
+gigantic, actually.
+
+And there's a beautiful,
+very lawful arrangement
+
+and even though many, many cells
+feed into this particular cell
+
+from earlier portions
+of the visual cortex,
+
+they maintain or get a specific
+input from all of the cells
+
+that have this
+direction selectivity.
+
+Now, whether this direction
+selectivity is a product
+
+of the input from the cells,
+which have the same kind
+
+of directions, like many,
+many of these cells--
+
+maybe 20 or 30 or 40
+or 50 of them, OK?--
+
+which have the same
+orientation and direction,
+
+or whether orientation and
+direction selectivity are
+
+created anew in MST is
+something that can be debated.
+
+It is still not 100% certain.
+
+So the only thing we have
+to worry about this time is
+
+to realize-- maybe
+not even worry.
+
+That's too strong a
+term-- is to be aware
+
+that there is
+prevalence of direction
+
+selectivity in both MT and MST.
+
+It's very beautiful and
+very, very specific,
+
+as you can see it
+here, even when
+
+you have a huge receptive field.
+
+So that is the basic story then.
+
+And now we can ask the
+question, how on earth
+
+is direction
+selectivity created?
+
+Now, there are several models
+that have been proposed.
+
+And most of these models-- I'll
+show you a simple one just so
+
+that you have a sense for it--
+most of these models assume,
+
+I believe correctly,
+that you need
+
+to have inhibitory circuits
+that are selective for direction
+
+to produce this specific
+response in these cells.
+
+Now, the amazing
+thing about all this
+
+is that already
+in the retina you
+
+have some cells that
+are direction selective.
+
+And these cells I'll
+talk about a bit more
+
+when we talk about the
+accessory optic system.
+
+These cells in the retina
+are not very numerous.
+
+In the rabbit that has
+approximately 350,000 cells
+
+in each retina-- can you
+imagine a little rabbit?
+
+And it has 350,000 cells.
+
+We have a little
+over a million, OK?
+
+And among those 350,000
+cells, about 7,000
+
+are the so-called
+cells of Dogiel.
+
+And actually, I'll
+come back to that.
+
+And those are direction
+selective cells.
+
+So a very clever experimentalist
+examined these direction
+
+selective cells in the retina,
+a fellow called Nigel Daw.
+
+And he asked the
+question, what can I
+
+do to determine what
+the mechanism is
+
+of direction selectivity?
+
+So he did an experiment
+that sounds simple.
+
+But let me tell you, it's a
+very difficult experiment.
+
+When you put your
+electrode into the retina,
+
+you can't see direction
+selective cells.
+
+So you're on a
+hunting expedition.
+
+So you keep recording from
+cell after cell after cell.
+
+And if indeed only
+7,000 among the 350,000
+
+are direction selective, it
+will take you quite a while
+
+before you manage to record
+from a direction selective cell.
+
+So it's a lot of very hard work.
+
+So anyway, if you do that
+when your hypothesis is
+
+that some sort of inhibitory
+mechanism is involved, then
+
+you can do an
+experiment and say,
+
+well if it's inhibitory
+mechanisms, probably
+
+some sort of
+GABAergic system, we
+
+need to put some agent into the
+retina that blocks inhibition.
+
+We talked about that before,
+that that can happen.
+
+And so in this case,
+what they did-- let
+
+me come to that first.
+
+Let me see.
+
+Here we are.
+
+I'll come back to the
+others in just a minute.
+
+What we have here is
+one of these cells.
+
+And we move in
+this direction here
+
+and in this direction for this.
+
+And you can see that this cell
+is very strongly direction
+
+selective, maybe 100%,
+but maybe 80% or 90%.
+
+Then he injected picrotoxin
+into the eye that blocks GABA.
+
+And lo and behold,
+direction selectivity
+
+is virtually eliminated.
+
+And then when picrotoxin
+got washed out,
+
+there was recovery, all right?
+
+So now, on the basis
+of this finding--
+
+it's a beautiful finding-- it
+was established that indeed,
+
+inhibitory circuits play a
+central role in giving rise
+
+to direction selectivity.
+
+And you can imagine that
+in the course of evolution,
+
+the pressures had to
+be tremendous to create
+
+these direction selective
+cells, because the circuitry is
+
+very complicated.
+
+You have to create these
+inhibitory neurons which
+
+inhibit in a particular
+direction rather than just
+
+randomly.
+
+So that's what was done.
+
+And so I'll show you one
+model that describes this.
+
+You have a bunch of--
+this is for the retina.
+
+You have a bunch
+of receptors here.
+
+And they activate a
+retinal ganglion cell here.
+
+But they also connect with
+an inhibitory interneuron
+
+in one direction,
+in that direction.
+
+So now if you move a bar in
+this direction, as shown here,
+
+you get no response.
+
+But if you move a bar
+across the other way,
+
+you get a vigorous response,
+as shown by the action
+
+potentials here.
+
+So this is a fairly simple
+model of creating direction
+
+selectivity by virtue of
+inhibitory interneurons.
+
+So that then was also
+examined in the cortex.
+
+it was found that there
+too inhibitory interneurons
+
+play a central role when
+direction specificity is
+
+created in a cortical cell.
+
+So that now makes me come
+back to a further analysis
+
+of the basic nature of motion.
+
+Can we logically divide motion
+into several types, or what?
+
+And so it was proposed by a
+wonderful scientist called
+
+Wurtz at the National Institutes
+of Health that he could--
+
+he decided that
+you can distinguish
+
+between planar motion, circular
+motion, and radial motion.
+
+Planar motion is when
+something moves straight.
+
+That's what we've talked
+about so far only.
+
+And of course, you can do that.
+
+In this case, he shows
+four different directions.
+
+But of course,
+there'd be all kinds
+
+of directions that are
+not vertical or horizontal
+
+but are diagonal.
+
+And there are many,
+many cortical cells.
+
+Some of those actually I
+showed you had orientation cell
+
+activity that was at an angle.
+
+So you have a huge number
+of different angles.
+
+And these cells
+hypothetically then
+
+would respond to planar motion.
+
+Then you have another
+type of motion,
+
+which is called circular.
+
+And let me tell you, when you
+see circular motion, obviously,
+
+if you were to be spun around
+or something, you'd see it.
+
+But it's not uncommon
+to see something rotate.
+
+So if you have a spinning wheel
+or if you watch a tire rotating
+
+in motion, that's
+circular motion.
+
+And so the hypothesis
+is that there
+
+should be cells in the brain
+that selectively respond
+
+to circular motion, either
+clockwise or counterclockwise.
+
+And lastly, of course, the
+so-called radial motion--
+
+and you encounter that
+just about every day.
+
+Whenever you drive,
+you see trees.
+
+Or if you're driving
+out in the country,
+
+you see trees going past you, so
+to speak, as you drive forward.
+
+And that would be motion
+which would be outward.
+
+Or if you were to
+back up like this,
+
+then you would get
+this kind of motion
+
+where things would
+come together, OK?
+
+So that kind of motion
+is certainly one
+
+that you need to somehow code.
+
+And so another question
+came up once he came up
+
+with this hypothesis that these
+different kinds of motion--
+
+the question is, are there cells
+in various parts of the brain,
+
+especially in higher
+areas like MST,
+
+that are selective for these
+three basic types of motion?
+
+And so they began
+to do an experiment.
+
+And I'll show you some
+summary data here.
+
+Here is a cell when you
+study planar motion.
+
+And these are the eight
+directions of motion
+
+that were studied--
+sorry, four directions
+
+of motion on the top-- then the
+circular one on the next two,
+
+and the in and out
+motion at the bottom.
+
+This particular cell seems to
+be specific for planar motion
+
+from right to left.
+
+Now here is a cell that is
+selective to circular motion,
+
+OK?
+
+And lastly, here
+is a cell that's
+
+elective to radial motion.
+
+So if you only had
+recorded in your life
+
+from three cells in
+MST, and it happened
+
+to be these three
+cells, you would say,
+
+ah, my hypothesis is right.
+
+There are three
+kinds of cells in MST
+
+that respond selectively to
+these three classes of motion.
+
+So everything is incredibly
+beautiful and logical.
+
+But of course, that's not how
+you do your experiment, is it?
+
+The way you do
+your experiment is
+
+you record from
+MST in this case,
+
+and you record from
+many, many, many cells.
+
+And you test them
+just like this, OK?
+
+And if you do that, you
+realize that this is just
+
+an example of three
+cells that were specific.
+
+It was found that
+40% of the cells
+
+responded to all
+three kinds of motion.
+
+305 responded to
+two types of motion.
+
+And only 20% of
+the cells responded
+
+to one type of motion.
+
+So therefore, these
+cells, as is so often
+
+the case in the visual cortex,
+are not unique and specific
+
+to analysis of one thing.
+
+These cells can tell you
+about all three of those.
+
+And what happens in reality then
+is that when something moves,
+
+you activate thousands
+of cells in MT, MST,
+
+and visual cortex,
+maybe tens of thousands.
+
+And it's some sort of
+complex relative activity
+
+that then eventually gives
+rise to the fact that you say,
+
+oh, yeah I see planar motion.
+
+Oh, yeah, I see a
+circular motion,
+
+or I see in and outward motion.
+
+So it's not a
+specific single cell
+
+that tells you or gives
+you that impression,
+
+but it's the concerted
+activity of thousands
+
+of cells even for the
+simplest of cases.
+
+So that's the way it works.
+
+It's a complex business.
+
+And the idea that was
+popular at one time,
+
+namely that you have feature
+detectors in the brain,
+
+has become downgraded
+progressively
+
+with increasing research.
+
+As I mentioned to
+you before, when
+
+we talked about to
+extrastriate cortex,
+
+the initial idea was when the
+various extrastriate areas
+
+had been discovered, that
+each area specializes
+
+in one particular thing.
+
+And then it turned out
+that that is not the case.
+
+There may be shifts or
+trends, but in each area,
+
+many different
+things are analyzed
+
+and thousands and
+thousands of cells
+
+are active whose relative
+activity is somehow
+
+what gives rise to the
+percept that you have.
+
+All right, so that
+then is the essence
+
+of the layout of the
+responses and the models
+
+that this model that
+[INAUDIBLE] told you about,
+
+or something similar to this.
+
+It may be a bit
+more complicated.
+
+And some people
+have hypothesized
+
+that there are temporal
+delays necessary to produce
+
+this thing.
+
+Yes?
+
+AUDIENCE: Sorry.
+
+There was a 10% missing
+in the breakdown.
+
+PROFESSOR: Sorry.
+
+Are you talking about this?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: Well, that's-- 10%
+of the cells were unclassified
+
+or we're not
+direction selective.
+
+These they could with certainty
+say what the situation was.
+
+And maybe some of
+those cells they
+
+lost while that
+we're recording from
+
+or they didn't have any
+particular direction
+
+selectivity.
+
+And because of that,
+they couldn't come up
+
+with 100%, of course, yeah?
+
+Yes, you had a question.
+
+AUDIENCE: It was
+the same question.
+
+PROFESSOR: What?
+
+AUDIENCE: It was
+the same question.
+
+PROFESSOR: Same question, OK.
+
+Very observant-- good for you.
+
+All right, so now we are
+going to move forward
+
+and we're going to look
+at the effects of lesions
+
+on motion perception.
+
+One of the ready ways you
+can assess to what extent
+
+various higher
+cortical areas play
+
+a role in various
+neural mechanisms
+
+is to either reversibly
+inactivate them
+
+or to remove them by making
+lesions and then determining
+
+what happens.
+
+And if you remember, I
+talked about this a bit.
+
+I told you, for example,
+that the hypothesis that
+
+was made initially about area
+V4 is that it's a color area.
+
+That was a single
+function hypothesis.
+
+And then it turned out that
+when area V4 was removed,
+
+it was found that there was
+only a moderate to mild deficit
+
+in color vision.
+
+But there were all
+kinds of other deficits
+
+that we had discussed
+in previous sessions.
+
+So now we come to
+the question about,
+
+what about motion perception?
+
+When we talk about emotion
+perception, we of course
+
+are dealing with
+temporal things,
+
+because motion involves
+successive activation of cells.
+
+And because of that,
+it's also very important
+
+to study how well we can process
+rapid successive presentations
+
+as, for example, in flicker.
+
+And that brings me, of
+course, to the story--
+
+and we will talk about
+that in a minute--
+
+that in the olden days, when
+movies were first invented,
+
+the rate at which successive
+frames were presented
+
+was 16 Hertz, which was
+fairly close to having
+
+a sensational of
+flicker, all right?
+
+And because of
+that, what happened
+
+when a guy asked a
+girl to go the movies?
+
+How did the guy ask the
+person to go to the movies?
+
+Can anybody remember that?
+
+That's an olden thing.
+
+The guy would say,
+hey, how would you
+
+like to go to the
+flicks tonight?
+
+OK, you've heard that
+expression, go to the flicks,
+
+right?
+
+Well, nowadays we are not
+aware of flicks anymore.
+
+And there are two
+reasons for that.
+
+Anybody know what
+the two reasons are
+
+why no one can see
+clicks in the movies
+
+and you no longer go
+to the flicks anymore
+
+but you go to the
+movies instead?
+
+Yeah?
+
+What are the two reasons?
+
+Anybody know?
+
+OK, well, let me tell you.
+
+The first is that the rate of
+the number of frames per second
+
+had been increased
+to about 24, OK?
+
+But that's still slightly
+below the effusion.
+
+OK?
+
+You can still see some flicker.
+
+So how do you get rid of it?
+
+Well, let me tell you, some
+incredibly clever guy--
+
+some things are
+really, really clever.
+
+I'll tell you what this
+person came up with.
+
+He said, all right,
+what we'll do
+
+is we're going to create
+a shutter which is round.
+
+And it's going to
+have one opening here.
+
+And then we're going to
+have a second opening here.
+
+And then we're going to
+have a third opening here.
+
+So this goes around.
+
+And each frame you're
+going to show three times.
+
+And then as this goes around,
+you go to the next frame,
+
+and you show it three times.
+
+So actually, if seeing frames
+24 hertz, you see it 3 times 24,
+
+OK?
+
+But each frame is
+shown three times.
+
+Now, to be even more clever,
+the way they did this,
+
+they took two of these
+circular shutters.
+
+And one of them moved in
+this direction and the other
+
+in that direction.
+
+They sort of equalized
+from the center
+
+out as the light was
+expose from the projector.
+
+So that then reduced
+the rate of flicker.
+
+So therefore, we can
+next ask the question,
+
+what is the flicker rate
+at which you no longer can
+
+see anything?
+
+I mean, do you want
+to see flicker.
+
+Or do you not want to
+see flicker, and so on?
+
+And so experiments
+were done, hundreds
+
+of experiments in which
+a psychologist studied
+
+flicker rate, varying
+contrast, varying color, doing
+
+this, doing that, and then
+varying the spatial frequency
+
+and generating curves to
+see what they look like.
+
+So that's the process.
+
+And so what we can do
+next is to examine this.
+
+And one way to do
+this, for example,
+
+just to give you
+a sense, you can
+
+have, for example, a
+bunch of random dots,
+
+just like we had for the
+[INAUDIBLE] stereogram.
+
+And this would be done
+with a monkey, for example.
+
+The monkey fixates.
+
+And then you start something
+in motion-- ready?-- like that.
+
+And the monkey sees this and
+has to make a saccade to it.
+
+And when he does so, he gets a
+drop of apple juice for reward.
+
+And then what you can
+very are two things.
+
+You can vary the frequency.
+
+I'm showing another one,
+much higher frequency.
+
+Bang-- the monkey goes
+there and gets rewarded.
+
+Or you can-- and/or,
+actually-- you
+
+can vary the contrast
+of the display, OK?
+
+So once you have a sense of when
+you get fairly close to sort
+
+of the edge of things, then
+you can also vary the contrast.
+
+So now let's ask
+the question, what
+
+happens when you remove area
+MT and when you remove V4, OK?
+
+So think about
+that for a second.
+
+And then I will show you
+the actual data, all right?
+
+OK, here we go.
+
+Here is an example.
+
+This is motion detection.
+
+And here we vary percent
+luminance contrast
+
+at a fixed frequency.
+
+You get the same
+effect the other way.
+
+I'll just show you this one.
+
+And you can see very readily
+that the V4 lesion caused
+
+no deficit at all, but the MT
+lesion produced a huge deficit,
+
+OK?
+
+So clearly this
+establishes the fact
+
+that area MT plays
+a central role
+
+in the processing of
+flicker information
+
+in being able to analyze
+rapid temporal events.
+
+And now we can ask
+the next question.
+
+What happens when you actually
+do just stationary flicker,
+
+all right?
+
+So when you do
+stationary flicker,
+
+you can do that in two ways.
+
+You can do an on
+off flicker, or you
+
+can do a flicker between two
+colors, for example, all right?
+
+And you can see why that
+would be interesting.
+
+Because if you do flicker
+between two colors,
+
+like red and green,
+if area V4 were
+
+important for color processing,
+then a lesion in that area
+
+should mess up that
+kind of flicker.
+
+So that's the way to do it.
+
+So let me show you first of
+all how you do this experiment.
+
+Here we have it.
+
+You have a bunch of LED's.
+
+Why does one have LED's
+instead of just doing
+
+this on a monitor?
+
+Any thoughts?
+
+Yes.
+
+AUDIENCE: The frequency at
+which those [INAUDIBLE].
+
+PROFESSOR: Very good.
+
+The reason you do it is because
+your typical frequency rate
+
+is the alternating current
+rate, meaning 60 Hertz.
+
+Now, nowadays you
+can of course buy
+
+devices that can double
+it or even quadruple it.
+
+But back then it was
+easier to do it this way.
+
+And it still is, because
+you can vary these flicker
+
+rates in small amounts.
+
+Now, each of these
+LED's, actually,
+
+for this particular
+set of experiments,
+
+is one that has both
+red and green in it, OK?
+
+So you can flicker between on
+and off, let's say for green.
+
+Or you can flicker between
+red and green, all right?
+
+So that's what we are
+going to find out.
+
+What happens when you do these
+kinds of flickers, red green
+
+as well as on and off?
+
+And ask the question,
+what happens
+
+when you make, again a V4
+lesion or an MT lesion, OK?
+
+Now think about it
+for a minute, as
+
+to what you would
+expect in terms
+
+of the differences between on
+and off and red green flicker
+
+and possible differences
+in the lesions
+
+that cause a
+deficit in this, OK?
+
+All right, ready?
+
+Here we go.
+
+There is the flicker.
+
+You can see that.
+
+Now, the way that really works
+is that the overall flicker--
+
+I'll show it to you again--
+is done in such a fashion that
+
+the mean illumination level
+is the same so that you cannot
+
+tell the location of the
+flickering LED on the basis
+
+of a lumen exchange.
+
+You can only tell on the basis
+of the fact that it flickers
+
+or it doesn't flicker, OK?
+
+All right, so we are now
+ready for the experiment.
+
+And here it is.
+
+On the right, I'm showing you
+a green on and off flicker.
+
+And you can see that there's
+no deficit at the V4 lesion,
+
+but a gigantic, absolutely
+gigantic deficit at the MT
+
+lesion site.
+
+And then very surprisingly-- to
+some people at least who were
+
+convinced that V4
+is a color area--
+
+when you do that for a red
+green flicker, first of all,
+
+notice that the flicker rate
+that you can detect is much
+
+lower-- OK, this is the ratio of
+the flicker, much lower, OK?--
+
+than it is for the
+on off flicker.
+
+And secondly, again, there's
+no significant deficit
+
+with the V4 lesion.
+
+But there's again a major
+deficit with MT lesion.
+
+So area MT is
+essential for being
+
+able to process both red and
+green flicker as well as on
+
+and off flicker, all right?
+
+So bear that in mind as we
+are going to now progress
+
+to the next stage of the
+experiment-- set of experiments
+
+I should say.
+
+And the next step I'm
+going to talk about
+
+is structure from motion.
+
+And that one is a very important
+attribute that we have.
+
+We can reconstruct structure
+by see nothing but motion.
+
+And I'm going to show
+you an example of that.
+
+OK, let me tell you,
+this here actually
+
+is a scene, a made-up
+scene, that's outside.
+
+And somewhere in here
+we have ladybug hiding.
+
+But the ladybug
+is not in motion.
+
+And you know, ladybugs have
+these spots on their back.
+
+And there's a ladybug here.
+
+And I'm going to tell you that
+there's a monkey watching this,
+
+hoping that he could catch
+the ladybug to have it,
+
+because he loves
+to eat ladybugs.
+
+Are you ready to catch her?
+
+OK, here we go.
+
+Ready?
+
+The ladybug after a while got
+tired of just sitting there
+
+and began to move.
+
+And that's a dead
+giveaway, because you
+
+have all these
+cells in your brain
+
+that selectivity see
+motion and flicker.
+
+Are you ready?
+
+Here we go.
+
+There's the ladybug.
+
+See her?
+
+OK, so the monkey is happily
+eating away the ladybug,
+
+all right?
+
+So here is a good example
+of how incredibly useful
+
+motion information
+is that you have
+
+in these visual cortical areas.
+
+Now, I would bet that if this
+monkey had had his MT removed,
+
+he wouldn't have been able
+to catch that ladybug.
+
+Now, another set of
+experiments carried out,
+
+beautiful experiments,
+were carried out
+
+by a fellow called
+Johanson-- I think
+
+that was in Sweden-- who did a
+very clever set of experiments.
+
+He wanted to analyze how well we
+can process motion information
+
+and derive structure from it.
+
+And what he did was that he
+put little teeny little light
+
+bulbs on about 13 points
+in the human's body.
+
+He put some here on the
+elbows, put some at the hand,
+
+put some at the head, and
+so on down, 13 of them.
+
+And then he turned
+off all the lights,
+
+so the only light was that
+little spot of light that
+
+was on these 13 spots of
+light that were on the person.
+
+And then he took a
+movie to see what
+
+happened when this
+person started to walk.
+
+And he discovered
+something amazing,
+
+that we are incredibly capable
+of reconstructing shape
+
+from minimal motion information.
+
+So are you ready?
+
+OK, here we go.
+
+So there it is.
+
+There are your 13
+little spots of light.
+
+And now I'm going
+to set it in motion.
+
+Ready?
+
+So what do you see?
+
+You see a person walking on
+this very minimal information.
+
+And you can even tell--
+who would say it's a male
+
+and who would say it's a female?
+
+Those of you who say it's
+a male, raise your hands.
+
+OK, it's virtually everybody.
+
+Right, very good.
+
+Now, so what he did which
+I don't have a movie of,
+
+which is quite
+remarkable, is that he
+
+took a couple, a
+male and a female
+
+and had them arranged in
+exactly the same way-- each
+
+had 13 of those bulbs--
+and had them dance.
+
+And when you looked at
+that, you had no trouble
+
+telling which was the male
+and which was the female.
+
+Amazing.
+
+So we are able to reconstruct
+a tremendous amount of form
+
+detail on the basis of
+extremely limited information
+
+about motion.
+
+All right, so that
+then ends that session.
+
+And we're going to go next to
+what is called apparent motion,
+
+all right?
+
+So you're going to have various
+forms of apparent motion
+
+I'm going to tell you about.
+
+And the first one is that if you
+show these two dots, if I flick
+
+them back and forth, you
+have a very strong sense
+
+that the thing is going
+back and forth, right?
+
+You don't see one, two,
+going on and one going off,
+
+because of the right
+temporal succession.
+
+But you see them as just
+jumping back and forth.
+
+So now what we can do--
+we can enlarge on that
+
+and carry out a series of
+experiments on the bases
+
+which can make some inferences
+as to whether areas V4
+
+or MT are contributing to this.
+
+So this is going be fun for you.
+
+And I want you to
+pay close attention.
+
+Now, in this kind of
+experiment when it was done,
+
+first, this stayed
+on all the time.
+
+And these two dots
+came on first.
+
+And then these two
+dots came on second.
+
+Now, if you do that, you can see
+either of two types of motion.
+
+You can either see what
+we call zigzag or seesaw.
+
+Seesaw is going to look
+like that, obviously,
+
+and zigzag like this, OK?
+
+So that's what I'm
+going to show you.
+
+And once I set
+this in motion, you
+
+will see it one
+way or the other.
+
+Then if you see
+it's, say, seesawing,
+
+you can take your finger
+and move it horizontally
+
+back and forth on top, say.
+
+And then in short order you're
+going to be seeing this.
+
+You can reverse the sense
+of motion, all right?
+
+So are you ready for that?
+
+OK, so here we go.
+
+If you see it one
+way or the other,
+
+try to move your finger back and
+forth to change it to see it.
+
+If you see it horizontally
+moving, move it vertically.
+
+If you see it vertically,
+move it horizontally.
+
+And then you can see it shift.
+
+Everybody able to reverse it?
+
+Well, keep doing it.
+
+And you should have no
+trouble reversing it
+
+if you move your
+finger back and forth.
+
+This is a bistable situation.
+
+And people can readily
+see the switch.
+
+OK, most of you
+seeing it switching?
+
+All right.
+
+So now we can ask a
+whole bunch of questions.
+
+And the way to put this
+question in general
+
+is we can ask, is first of
+all, is this something that
+
+happens locally, or does
+it happen everywhere
+
+when you're looking?
+
+So how can you do that?
+
+So let me show you.
+
+What they we do here instead is
+we can put up a bunch of them,
+
+OK?
+
+And they're quite far
+apart from each other.
+
+And depending on
+how close you are,
+
+they may be as far
+as a centimeter
+
+apart in the visual
+cortex for the activation.
+
+So now what we're
+going to do is we're
+
+going to move them back and
+forth just like I did before.
+
+And the question
+that you want to ask
+
+yourself-- am I going
+to see these all
+
+move the same way vertically,
+say, or see all of them
+
+move horizontally, OK?
+
+So here we go.
+
+Are you ready?
+
+Basically, the rule is that
+they all move the same way.
+
+And then they shift.
+
+Again, you can use your
+thumb or your forefinger.
+
+And if you manage
+to make it switch,
+
+they all will switch
+at the same time.
+
+OK, everybody manage that?
+
+All right, so now the rule is
+that even though the activation
+
+is very far apart in
+V1 from here to here,
+
+there's some organizing
+principle that
+
+makes you see everything
+a particular given way.
+
+And they shift.
+
+They all shift.
+
+Now, that's a very
+interesting arrangement.
+
+And you can wonder,
+what is there
+
+that can tell the visual
+cortex how to see it and insist
+
+that you got to see
+it the same way?
+
+Now we can move on.
+
+And you can ask the
+question-- so far,
+
+what I've shown you is
+they're all the same-- sorry.
+
+That's my fault.
+
+They are all the same size.
+
+And they are geometrically
+arranged, OK?
+
+So now what happens if
+instead, we do it differently
+
+and we make them different
+sizes and random locations?
+
+What happens under
+these conditions?
+
+Now think about it for a minute.
+
+And then I'm going
+to show it to you.
+
+And once again, even though
+they're different sizes,
+
+different locations,
+they all go the same way.
+
+And when they shift--
+again, use your forefinger
+
+to try to make it shift.
+
+And when they shift, they all
+shift at the same time, OK?
+
+All right, so now we
+can move on and ask
+
+some interesting
+additional questions.
+
+We can ask the
+question, how important
+
+is color information for you to
+see it go one way or the other?
+
+All right?
+
+OK, so to do that, here we have
+the top two are colored red
+
+and the bottom two
+are colored green.
+
+Now we're going to move
+these back and forth.
+
+And the question is, will you
+see them move horizontally
+
+because of the color
+information or what?
+
+So the question
+is, again, are you
+
+going to see zigzag or seesaw?
+
+OK, are you ready?
+
+And you can readily see if,
+again, you can readily shift it
+
+again with your forefinger,
+that color doesn't seem
+
+to be an important determinant
+of the direction in which
+
+the apparent motion
+will take place.
+
+Everybody follow that?
+
+Well, now think about that.
+
+How can we do this
+experiment to be
+
+more convinced that
+color for some reason
+
+doesn't seem to be important
+in how we see apparent motion?
+
+Well, let me tell
+you how you do it.
+
+Here is an example.
+
+Here we have again four rows
+and four columns, all right?
+
+And the first, one A and C,
+the colors are horizontal.
+
+And in the second one, B
+and D, they are vertical.
+
+So if color plays
+a role, we should
+
+be able to see these, the
+first and the third rows
+
+go in one direction
+and the second
+
+and the fourth row go
+in the other direction.
+
+So let's examine that.
+
+Ready?
+
+And you can see that they're
+all going the same direction
+
+anyway.
+
+When they switch, they
+switch in the same direction,
+
+meaning that indeed you pay no
+attention to the color itself,
+
+OK?
+
+Some mechanism is
+involved in which
+
+the apparent motion
+you see does not
+
+play a significant
+role in color.
+
+Now we can do another
+experiment and see
+
+what happens when
+instead of colors, we
+
+use small shapes,
+X's and O's which
+
+are horizontal in the
+first and the third row
+
+and vertical in the
+second and the fourth row.
+
+Will this succeed in breaking
+up the unity of apparent motion?
+
+So here we go.
+
+Ready?
+
+And you still see
+them all the same way,
+
+meaning that you
+don't pay attention
+
+to the small
+differences in shape.
+
+OK, so now what I
+have shown you so far,
+
+remember, has something to do
+with the midget and the parasol
+
+systems for the test.
+
+The midget system can
+process fine detail.
+
+And the midget system
+can process color.
+
+The parasol system does
+not process fine detail
+
+and does not separately
+process color.
+
+So we'll come to
+that in a minute.
+
+Now let's ask the next question.
+
+What happens if
+you vary the size?
+
+OK, again, the first and
+third row, the size difference
+
+is horizontal.
+
+And the second and fourth
+row, it's vertical.
+
+OK, so let's see what happens.
+
+Here it's a bit unclear, OK?
+
+So as you see, some
+of them go one way.
+
+Some go the other way.
+
+And some of you may see
+it all go the same way,
+
+depending on how far you are.
+
+So let's change the ratio
+so it's much, much bigger.
+
+And if you do it now,
+what you see is dramatic.
+
+You see horizontal motion
+in the first and third rows
+
+and vertical motion in the
+second and fourth rows.
+
+Everybody see that?
+
+OK, so we can enhance
+on this maybe a little
+
+bit by adding these together,
+adding size and color
+
+and shape, quite large
+differences in size and shape
+
+and color.
+
+Then if you do this,
+you will indeed
+
+have fully succeeded in
+breaking up the unity of motion,
+
+with the first and third
+rows going horizontally
+
+and the second and fourth
+rows going vertically.
+
+Now then there's one
+other important factor
+
+that we need to
+consider about this.
+
+And that has to
+do with proximity.
+
+So in this case, what
+we're doing now--
+
+in the first and
+the third rows, we
+
+have the horizontal dots
+closer to each other.
+
+he second and fourth rows, we
+have the vertical dots closer
+
+to each other.
+
+So if you do that, you're
+going to ask the question,
+
+how important is proximity?
+
+And if you do that, you
+don't see much so far.
+
+But now what I'm
+going to do is I'm
+
+going to make the
+difference even greater, OK?
+
+The first and third are
+very close horizontally.
+
+And the second and fourth
+are very close vertically.
+
+If you do that,
+you readily can see
+
+that indeed the first and
+third rows move horizontally
+
+and the second and fourth
+rows move vertically.
+
+So proximity is a
+very important factor.
+
+And so that then brings me
+to an interesting question
+
+that probably none of you
+have given much thought.
+
+But I will make you
+more aware of it.
+
+The fact is that
+when you see movies,
+
+you very often see a car or
+a chariot or something move
+
+forward, but the wheels
+are going backwards.
+
+And you certainly
+do that when you
+
+watch those endless ads
+on television about cars.
+
+And you see the wheels going
+backwards most of the time.
+
+And the car is going forward.
+
+And some of you say,
+well, why would I
+
+buy a car whose wheels
+are going backwards?
+
+So at any rate, let's
+examine that question.
+
+And what I'm going
+to do first is
+
+I'm going to show you a movie.
+
+Ready?
+
+This a famous movie, Ben-Hur.
+
+You've probably seen it.
+
+Look at the wheels
+going backwards.
+
+Can you see that?
+
+Now, of course since I have
+given this a lot of thought,
+
+it drives me nuts when I see
+wheels going backwards when
+
+the chariot or the
+car goes forward.
+
+All right, so now
+the question is,
+
+why do we see wheels going
+backwards in the movies
+
+or on the ads on television,
+whereas when you see it
+
+in the real, you never
+see them going backwards?
+
+Well, remember that when you
+look at a movie or television,
+
+you always see apparent motion.
+
+You never see real
+motion on television,
+
+never see real
+motion in the movies.
+
+You're not aware of
+it, but you don't.
+
+You only see apparent
+motion because you
+
+have successive frames
+in each of which there
+
+is a specific, say, if
+it's wheels, rotation, OK?
+
+So let's look at
+that analyze this.
+
+So I'm going to show you a
+wheel that is rotating slowly.
+
+Are you ready?
+
+it's a very brief.
+
+OK, you can see that wheel
+is going forward, right?
+
+Now I'm going to show you
+the same and arrangement.
+
+But I'm going to
+have it move fast.
+
+Ready?
+
+Ready, go.
+
+That time you saw it
+go backwards, right?
+
+OK, so let's analyze this.
+
+What happens when
+you have slow motion?
+
+Let's imagine that
+the red line is
+
+designating one of the spokes.
+
+Then if it moves
+slowly, the next frame
+
+is going to show that displaced
+only a little bit from the red,
+
+and so on.
+
+And because of that, you're
+going to see forward motion.
+
+But now if what you do instead
+is moving fast, what happens
+
+is that this spoke here
+is going to be closer
+
+to this one in the next frame.
+
+And because of that--
+of course, that's
+
+all of them all the
+way around-- you
+
+will see them go backwards,
+because of the principle
+
+of proximity that I showed
+you with the apparent motion
+
+of the four moving dots.
+
+OK, so that then explains to
+you why you see wheels rotating
+
+backwards in the movies
+and on television.
+
+And it's due to a
+fact of the proximity
+
+of successive
+elements, in this case,
+
+spokes that are rotating as the
+picture is taken with a camera.
+
+All right.
+
+So now I'm going to come
+up and tell you briefly
+
+about another very
+interesting phenomenon that
+
+is closely related to motion.
+
+When two successive
+stimuli are presented,
+
+there can be an interaction
+between them, all right?
+
+And in a famous series of
+experiments back in the 1930s,
+
+they did what is called a
+metacontrast experiment.
+
+First, a disc was
+presented like this.
+
+And then it was
+followed by a ring.
+
+And they shared the
+same contour, OK?
+
+This is it, OK?
+
+So now what you
+could do-- you could
+
+vary the temporal
+interval between them.
+
+So if you present these
+two simultaneously,
+
+since they have
+overlapping contours,
+
+that's all you would see.
+
+But then if you present
+them sequentially-- ready?
+
+Like that, then the
+question is, to what degree
+
+did you see that first one?
+
+So let's look at that.
+
+And I want you to
+pay close attention
+
+to when I present
+this to you, OK?
+
+Are you ready?
+
+You're going to do it
+now so that they're only
+
+60 milliseconds apart, OK?
+
+Here we go.
+
+You barely see the
+first one, right?
+
+You could just
+barely make it out.
+
+But it's not gone.
+
+Some people thought it
+would cause it to be gone.
+
+But that's not the case.
+
+So what you do then
+is the following.
+
+If you fixate on
+the red cross, I'm
+
+going to present the stimuli.
+
+And I want you to tell me
+which of the two stimuli
+
+I present is
+preceded by the disc.
+
+Ready?
+
+Could you tell?
+
+Which one, left or right?
+
+Left, good.
+
+Again, repeat.
+
+AUDIENCE: Right.
+
+PROFESSOR: Oh.
+
+Ready?
+
+AUDIENCE: Left.
+
+Left.
+
+PROFESSOR: OK, very good.
+
+So the fact is that when you
+present two side by side where
+
+one of them is
+preceded by the disk,
+
+you can tell which
+one came first.
+
+So somehow this didn't
+obliterate your ability
+
+to see it.
+
+Now, the other
+interesting fact is
+
+that if now you flicker
+back and forth between them,
+
+at equal rates, you
+see both equally.
+
+So therefore, what happened
+is you did not truly
+
+obliterate the percept.
+
+You just somehow weren't
+too much aware of it
+
+because of the
+temporal offset between
+
+the successive presentations.
+
+Now, you can do this
+slightly differently.
+
+Instead of having two stimuli
+that do not overlap but have
+
+adjacent contours,
+we can overlap them.
+
+So here I'm going to show
+you something and ask you
+
+what you see.
+
+Ready?
+
+What do you see?
+
+A big disk?
+
+OK?
+
+There it is.
+
+Now I show it to you.
+
+As to what I really
+showed you, was first
+
+I presented a dim small disc
+followed by a brighter higher
+
+contrast bigger disc.
+
+And that obliterated the
+perception of the first one.
+
+And that is truly obliterated.
+
+And the interesting experiment
+you can do in this regard--
+
+you can do this interocularly.
+
+In other words, you can
+present one of the stimuli
+
+to the left eye and the
+other to the right eye.
+
+If you do that, you don't
+get a masking effect.
+
+But if you go back and
+do the metacontrast,
+
+you still get the
+same pseudo blockage
+
+without actually
+eliminating it, but sort
+
+of making you less aware
+of the first stimulus.
+
+OK, so now if one
+examines this, the way
+
+to do the experiment
+right is you
+
+vary the temporal offset
+between the two stimuli.
+
+And when this was
+done systematically
+
+with the brightness masking
+that I showed you later,
+
+secondly, what happens is that
+the effect rapidly declines.
+
+It's the biggest
+when the two are just
+
+right next to each other.
+
+By contrast, when you
+do the metacontrast,
+
+the biggest effect is when
+they're about 62 to 100
+
+milliseconds separated,
+because that's
+
+when apparent motion
+is most effective.
+
+And then if you do an experiment
+to see where this happens
+
+for the brightness
+masking, here's
+
+what happens in the retina
+recording from a cell.
+
+This is a dim stimulus,
+a smaller response,
+
+and with a longer latency.
+
+And the mask alone will
+get a much shorter response
+
+and a much more vigorous one.
+
+And then when you systematically
+vary the temporal interval
+
+between the two of
+them, you can see
+
+when the interval becomes short.
+
+The second stimulus
+obliterates the first one
+
+because it's faster and
+it has a bigger response.
+
+So this explains what
+happens, because it happens
+
+in the retina by
+virtue of transmission.
+
+And the rule of the fact that
+the rate at which information
+
+is transmitted from
+the four receptors
+
+to the retinal ganglion
+cells is contrast dependent.
+
+The higher the contrast,
+the faster the response.
+
+All right, so now
+does anybody have
+
+any questions about the
+masking or the metacontrast
+
+that we talked about so far?
+
+All right, in that
+case, we are now
+
+going to move on and talk
+about another important motion
+
+perception effect which links
+one to eye movement generation.
+
+And that falls into
+the category of
+
+so-called optokinetic nystagmus.
+
+So how do you study
+optokinetic nystagmus
+
+at the very basic level?
+
+Well, the way you study it is,
+for example, in the olden days,
+
+you could take a large
+lamp shade like that
+
+and put vertical bars
+on int on the inside,
+
+have a person have
+his head inside.
+
+And then you rotate
+the lamp shape
+
+so that the bars go
+across like that.
+
+Or you can do that
+more simply nowadays.
+
+You just go put a bunch of
+vertical bars on a monitor
+
+and have them drift.
+
+And the person is
+asked to look at it.
+
+So when the person
+does that, what you get
+
+is the so-called
+optokinetic nystagmus.
+
+It has two phases.
+
+It has a fast and a slow phase.
+
+The fast phase is a saccade, a
+resetting saccade, if you will.
+
+So you watch an edge.
+
+You follow it.
+
+And then once it gets
+to the periphery,
+
+you make a saccade back
+and you watch the next one.
+
+And you keep doing it.
+
+And this shows you the
+three different rates.
+
+Now, this is quite an
+interesting mechanism.
+
+And it was determined that
+an important contribution
+
+to executing these kinds
+of eye movements, which
+
+is very important, because
+when you track anything, if you
+
+track a bird of something,
+you keep your eye on it.
+
+And then once it gets past
+you, make this a saccade back
+
+and take the next
+bird and track it.
+
+So that's the mechanism.
+
+And it's been shown that
+several neural mechanisms play
+
+a role in it.
+
+And one of those belongs to
+the so-called accessory optic
+
+system, which has
+those cells of Dogiel
+
+in the retina that
+connect to it.
+
+So we're going to look at that.
+
+Some beautiful work has
+been done about that.
+
+But before I do
+that, let me show you
+
+a very interesting factor.
+
+Here is a typical
+optokinetic nystagmus
+
+induced by a drifting vertical
+set of bars at various rates,
+
+as you can see here.
+
+And this is a rabbit.
+
+And in the rabbit, what you have
+is a left eye and a right eye.
+
+And you can activate them
+separately, as shown here.
+
+Now, a remarkable
+discovery that was made
+
+is that the accessory
+optic system-- that there's
+
+a primary role in
+generating this optokinetic
+
+nystagmus that is
+found initially
+
+in among the cells of Dogiel,
+of which in the rabbit, as I've
+
+said, there are about 7,000
+out of 350,000 in the eye.
+
+And it was found-- which
+was incredibly surprising--
+
+that this system originating
+with the cells of Dogiel,
+
+the cells of Dogiel themselves
+get input only from ON bipolar
+
+cells, OK?
+
+So what can we do to prove
+that this system here indeed
+
+is one that is activated
+by the cells of Dogiel,
+
+since the cells of
+Dogiel in the rabbit
+
+get input only from
+the ON bipolar cells?
+
+Anybody can think
+of an experiment?
+
+What did I tell you about
+the on and off systems
+
+and how they can be manipulated?
+
+Anybody remember?
+
+Now, see you've got
+to remember facts.
+
+And one of the facts was I told
+you about what happens when you
+
+use 2-amino-4-phosphonobutyric
+acid, APB.
+
+Anybody remember that?
+
+If not, you'd better
+study it, because there
+
+are going to be questions on
+that on the exam, of course.
+
+OK, so if you put
+APB into the eye,
+
+you block the ON bipolar cells.
+
+And therefore, if
+only ON bipolar cells
+
+feed into the cells
+of Dogiel, you
+
+would expect that if you
+block those bipolar cells,
+
+you should eliminate the
+optokinetic nystagmus
+
+in the eye that had been
+injected, if it's indeed true
+
+that the cells of
+Dogiel are involved, OK?
+
+So that's a
+beautiful experiment,
+
+because it's a definite one
+if indeed the data come out
+
+the way one had hoped.
+
+And guess what happens?
+
+Here are the data.
+
+The red ones are
+from the eye that
+
+had been injected with APB.
+
+You know, you
+blocked the ON cells.
+
+And hence, you
+blocked the responses
+
+of the cells of
+Dogiel, all right?
+
+So this is a rather nice,
+luckily definitive, experiment.
+
+Now, the curious thing is, if
+you did the same experiment
+
+in a monkey, you
+would get nothing.
+
+Here you do the same
+experiment in a monkey.
+
+Here is your OKN.
+
+And here is when you put in APB.
+
+And still after putting
+in APB, the monkey
+
+still does
+optokinetic nystagmus.
+
+That's because the rabbit
+is a very unusual species.
+
+And god only knows
+why it happened
+
+that only On bipolar cells
+fed into the cells of Dogiel.
+
+In the monkey, you get
+both ON and OFF cells
+
+feeding into the
+cells of Dogiel.
+
+All right, so now another
+interesting factor
+
+that I want to
+mention just briefly
+
+is that it's indeed is true
+that the feedback mechanism is
+
+essential for you to do
+optokinetic nystagmus right.
+
+Here is a monkey in which
+one eye has been immobilized
+
+and the other eye is normal.
+
+So if you look at the
+normal eye and you
+
+move a set of vertical
+bars very slowly,
+
+this is what your
+optokinetic nystagmus
+
+looks like-- just a
+very slow tracking.
+
+But then if you do the same
+thing in the mobilized eye,
+
+and you, of course, record the
+eye movement of the other eye
+
+which is blocked, what you
+get is a tremendously rapid
+
+increase in the
+pursuit movement.
+
+This can be called open loop.
+
+And this can be
+called closed loop.
+
+Now, the mechanism
+involved here is
+
+that your intent is to track.
+
+But when you realize--
+or not you realize,
+
+but the brain realizes.
+
+You're not even aware
+of it-- that you are not
+
+following fast enough to
+keep up with the motion
+
+of the vertical bar,
+you order the eyes
+
+to move faster,
+faster, and faster,
+
+and faster and faster,
+and it practically
+
+runs away like crazy.
+
+And it still-- of course,
+because the eye is
+
+immobilized-- hasn't been able
+to catch up to the moving bar.
+
+So this further highlights the
+importance of this mechanism.
+
+And it has to be a closed
+loop system, obviously,
+
+for it to work properly.
+
+So there's a
+feedback telling you
+
+whether you had correctly
+tracked something.
+
+OK, so now I come to
+the last point today,
+
+which is now the mechanism
+that is involved in the motion
+
+analysis of accessory
+optic system.
+
+I'll talk about
+this only briefly,
+
+because this is going to
+be part of your paper.
+
+All right, now, they
+remarkable discovery
+
+that was made--
+amazing discovery--
+
+was that when people recorded
+from the cells of Dogiel,
+
+they found that these cells
+come in three different types
+
+with three different axes of
+orientation, these three axes.
+
+And when that was
+first found, people
+
+said, what on earth is going on?
+
+Why would we have
+three like that?
+
+I would have thought
+we'd have four,
+
+vertical and horizontal
+at least, or something.
+
+So this was really puzzling.
+
+But then they began to
+do some more experiments.
+
+And they made a truly
+remarkable discovery.
+
+And their discovery
+is shown here
+
+in a summary diagram of
+the accessory optic system.
+
+OK, here are these
+cells of Dogiel
+
+with the three axes of
+direction selectivity.
+
+They respond to rather
+slow motion velocities.
+
+So what happens
+here-- I'm not going
+
+to go into detail, because
+you're going to, as I say,
+
+report on this.
+
+But let me tell you
+about the essence of it.
+
+The cells of Dogiel project into
+the so-called terminal nuclei.
+
+And then they project
+up to the cerebellum.
+
+And from the cerebellum,
+there's a projection down
+
+to the vestibular nuclei.
+
+And then it was found,
+as it was known already,
+
+that the semicircular
+canals come
+
+in three orientations
+which are the same as those
+
+of the orientations of
+the cells of Dogiel.
+
+And so then they feed into
+the ocular motor system
+
+to move the eyes so as to
+keep the eyes in accurate
+
+contact with whatever
+you're intending to look at.
+
+So that is the very essence
+of the accessory optic system.
+
+And I just thought
+this will help you
+
+in putting your paper together.
+
+All right, so now I am
+ready to summarize for you.
+
+First of all, motion
+has been classified
+
+into several different types
+that include planar, circular,
+
+and radial.
+
+And one thing we talked about
+earlier that I mentioned here,
+
+but I didn't mention
+in this presentation--
+
+when we talked about
+depth perception,
+
+we talked about motion parallax.
+
+That's a very important
+aspect of motion analysis.
+
+Then secondly, the
+majority of cells in V1
+
+and most cells in MT are
+directionally selective, OK?
+
+And an addition which
+I mentioned earlier
+
+is that they also show
+velocity selectivity.
+
+Some V1 cells respond
+to different directions
+
+of movement for light and dark
+edges, like the S2 type cell
+
+I showed you.
+
+And some cells are sensitive
+to differential velocities
+
+of movement, which
+I didn't show.
+
+Then the accessory
+optic system that
+
+begins with the retinal ganglion
+cells of the cells of Dogiel
+
+form three axes of
+direction selectivity
+
+that correspond
+to the three axes
+
+of the semicircular canals.
+
+And they are involved in
+generating pursuit eye
+
+movements for image
+stabilization.
+
+Then one of the most important
+tasks of motion analysis
+
+is motion parallax,
+as it provides
+
+information about depth.
+
+Motion cues can provide
+important information
+
+for object recognition,
+often referred
+
+to as structure for motion.
+
+And stationary
+stimuli that flicker
+
+with various temporary signals
+induce apparent motion,
+
+of which I showed you
+a lot of examples.
+
+And then we talked about
+metacontrast masking,
+
+which is a phenomenon
+that occurs
+
+when two stimuli share contours.
+
+And when they're presented with
+an interval which corresponds
+
+to apparent motion, you tend
+not to see the first one.
+
+Lastly, brightness masking
+arises with overlapping stimuli
+
+appearing in rapid succession.
+
+And this does not occur with
+interocular presentation,
+
+proving that it's a
+record of phenomenon.
+
+And it has to do with the fact
+that the velocity with which
+
+a stimulus activates the retinal
+ganglion cells and hence,
+
+of course, the cortex, is much
+much slower with dim stimuli
+
+then with bright ones.
+
+And so bright
+stimulus, in a sense
+
+overtakes the responses
+to a dim and weak stimulus
+
+when the two successive
+presentations are very rapid.
+
+OK, so that's the
+end of it here, OK?
+
+And I'll show you one
+more motion effect.
+
+Ready?
+
+All right, so that is
+the story for today.
+
+And next time,
+you're going to have,
+
+as I said, a rapid
+summary of what
+
+we have covered in the
+first half of this course.
+
+And then the following
+Wednesday, we
+
+are going to have the multiple
+choice exam for the midterms.
+
+OK, thank you kindly.
\ No newline at end of file
diff --git a/oXsC9bjMJA4.txt b/oXsC9bjMJA4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d6136785a42aa9d82ec7247f513f710e9211338d
--- /dev/null
+++ b/oXsC9bjMJA4.txt
@@ -0,0 +1,2672 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+HONG LIU: And let us start.
+
+So let me again start
+by reminding you
+
+what we did before.
+
+So consider, say, we have
+a scalar field in AdS
+
+So let me just summarize
+what we did before.
+
+So consider, say,
+a scalar field,
+
+phi, in AdS and with mass
+times square, so with mass
+
+squared given by m
+squared, then we know,
+
+when you go to the
+boundary of AdS-- so let's
+
+take z goes to 0--
+then phi will have
+
+the following
+asymptotic behavior.
+
+So these are the two independent
+modes of phi [? to ?] infinity.
+
+Of course, there are higher
+order corrections in z.
+
+And this delta is
+given by 1/2 d plus nu.
+
+And nu is given by
+this square divided
+
+by 4 plus m squared r squared.
+
+So this is the behavior.
+
+And so this phi is assumed to
+be dual to some boundary, scalar
+
+operator.
+
+And then all of
+those quantities,
+
+on the gravity side, they
+all have counterparts
+
+on field theory side.
+
+For example, the delta,
+which, essentially,
+
+is a function of mass,
+then, essentially, it's
+
+the scaling dimension of O.
+It's a scaling dimension of O.
+
+And this Ax
+essentially translates
+
+into the source for phi.
+
+Or you can consider the
+momentum space version, say, you
+
+can do Fourier transform,
+Ak, then go to the phi k.
+
+And then we also showed, last
+time, that the 2 nu times Bx
+
+is actually related to the
+expectation value of O.
+
+And again, there's a
+momentum space version of it.
+
+So you can just
+Fourier transform, then
+
+become O k and Bk.
+
+And in particular,
+in the example,
+
+we can see the
+scalar field example.
+
+In particular, in the
+example, you can see that.
+
+So we derived this relation
+from a free scalar field.
+
+but you can actually show this
+relation is actually generally
+
+true at non-linear level.
+
+So if you also include the high
+orders, et cetera, so including
+
+non-linear dependence on
+phi, actually this relation
+
+remains true.
+
+But due to the time, we
+will not go into that.
+
+The proof is actually
+not very difficult.
+
+So you can see that the
+free scalar examples--
+
+so, in the example, we
+can see that actually
+
+the B-- so in momentum
+space, the B is actually
+
+proportional to A. If you
+remember what we did last time.
+
+So in other words,
+this one-point
+
+function-- so B is related
+to the one-point function.
+
+So in other words,
+the one-point function
+
+it's proportional to the source.
+
+So this is the standard story.
+
+Say all x equal to 0
+when phi equal to 0.
+
+So if you don't have the source,
+then this one-point function
+
+is 0.
+
+So you don't have a spontaneous
+expectation value for the O.
+
+And now the fact that
+B is proportional to A,
+
+so this is just reflects that,
+in the presence of the source,
+
+then, of course, the
+expectation value-- so
+
+let me write it in momentum
+space for simplicity.
+
+Then we're no
+longer [INAUDIBLE].
+
+Assume the source is small, then
+you can expand the expectation
+
+value in power series of phi.
+
+So to the 0, so that
+would be phi, and then
+
+phi squared, et cetera.
+
+So at linearized
+level, say we just find
+
+O k is proportional to phi k.
+
+We just find that O k is
+proportional to phi k.
+
+And the proportional
+constant is, in fact,
+
+the two-point function.
+
+So at linear level, so O k would
+be just proportional to phi k,
+
+but the proportional constant
+is just the two-point function.
+
+So the reason is very simple.
+
+First, let me write
+down the definition
+
+of this two-point function.
+
+So GEx in coordinate
+space is defined
+
+to be O x of 0, because
+of translational symmetry,
+
+so I can put the
+other point to be 0.
+
+So this is only the
+function of one variable, x.
+
+And then you can
+Fourier transform,
+
+and then you get GEk.
+
+So this is how we
+define the GEk.
+
+So to see that this
+is true, you need
+
+to remember that
+the GEk is given
+
+from taking the generating
+functional, delta phi k
+
+and delta phi minus k, then
+you set phi equal to 0.
+
+So this is the definition
+of the two-point function.
+
+And then next, you can see
+that the [? one  derivative ?]
+
+of phi minus k-- so you can see
+that this takes 1 derivative
+
+on phi minus k.
+
+That just gives you
+the one-point function
+
+in the presence of phi
+and then delta phi k.
+
+And take phi equal to 0.
+
+So I just evaluated
+this derivative.
+
+So if you take this
+generating functional,
+
+take one derivative, we
+just get one-point function.
+
+And then this is the
+other point function.
+
+Then at the linear
+level-- so if O k
+
+is linear in phi k, of
+course, taking the derivative
+
+is just the same as dividing it.
+
+So this is the same.
+
+So continue over.
+
+This is the same just as to
+the phi k divided by phi k
+
+at the linearized level.
+
+And then so this tells you
+that this pre-factor is just
+
+the two-point function.
+
+And so we can now write a
+two-point function explicitly
+
+in terms of B and A,
+so this is just given,
+
+because this is 2 nu Bk.
+
+So this is just given by that.
+
+So this is just a quick
+summary of what we
+
+did at the end of last lecture.
+
+So that's how you can find
+the two-point function.
+
+So you work out what
+B is, what the A is,
+
+and then the rest of them
+is the two-point function.
+
+And the way we work out the
+B and A is the following.
+
+So at the linearized level, when
+you solve the equation motion
+
+for phi, then you impose
+the boundary conditions
+
+at infinity, A should
+be equal to phi.
+
+But then there's
+another condition
+
+being proposed to make
+sure the phi is actually
+
+regular in the interior.
+
+So the regularity
+condition, there's still
+
+a relation between
+A and B. And then
+
+that leads to this
+two-point function.
+
+Any questions on this?
+
+Is everything clear?
+
+Good.
+
+So now let's consider the
+higher-point functions.
+
+So this is, in principle,
+straightforward to do.
+
+Because, recall, that the
+log CFT phi, this generating
+
+functional, in the
+field theory, is just
+
+given by the classical
+action on the gravity
+
+side, which is the boundary
+condition given by phi.
+
+You're solving the
+classical equation
+
+motion, the initial action.
+
+Then you just, as
+we did earlier,
+
+you just solve the
+equation motion for phi
+
+to the [? linear ?] order.
+
+And then you validated
+the initial action.
+
+Then you can express,
+for example, this SE
+
+in power series of phi.
+
+And then the quotient for
+the power series of this phi
+
+then just gives you
+correlation functions.
+
+So the principle of this
+is straightforward to do.
+
+We know how to solve the
+classical equation motion.
+
+We know how to plug
+back into the action,
+
+and then you are done.
+
+So just to be able
+to be more specific,
+
+let's consider an example.
+
+Let's just consider
+two examples.
+
+Again, let we just
+consider the scalar field.
+
+Now, I add the linear term.
+
+For illustration, let me
+give you two examples.
+
+And so a very important thing is
+that in our set-up, the lambda,
+
+this cubic quotient is
+proportional to kappa.
+
+And then if you translate
+into the field series side,
+
+this is 1/n.
+
+So remember, for anything
+in the gravity action,
+
+you always have the 1
+over kappa squared, 1
+
+over G Newton before
+[INAUDIBLE] action.
+
+And then when we try to
+change phi into canonical
+
+normalized, and then
+you rescale phi.
+
+And the consequence is that
+this cubic term or quartic term,
+
+then they will have quotients
+proportionate to kappa.
+
+And according to this rule, if
+you have a quartic term, then
+
+that will be proportional
+to kappa squared, et cetera.
+
+And so the key is that as
+far as [? phi is ?] order 1,
+
+then you can actually treat
+those higher-order terms
+
+by perturbation because
+the quotient is small.
+
+And of course, you can
+also consider the situation
+
+in which phi is
+large, and then you
+
+have to solve the full
+nonlinear problem.
+
+Then you cannot do a
+perturbative expansion.
+
+You have to do the problem.
+
+So for our purpose,
+if you want to find
+
+the higher-point
+function for phi,
+
+then you need to
+solve this equation.
+
+So box phi is just
+a Laplace operator.
+
+I just save time.
+
+So you need to
+solve this equation.
+
+And with the boundary condition
+still the boundary condition,
+
+the boundary value of capital
+phi to equal to this phi x.
+
+And let me call
+this equation star.
+
+So as I said, because
+this lambda is small,
+
+you can actually try to
+solve this equation just
+
+perturbatively in lambda.
+
+And essentially, you're solving
+it perturbatively in this phi,
+
+because everything, in the end,
+will be expressed in this phi.
+
+So one can solve
+star perturbatively
+
+in phi, which is the
+boundary value of the field.
+
+And say phi c, you can expand it
+as phi 1 plus phi 2, et cetera,
+
+so the classical
+solution expanded.
+
+And this linear in phi.
+
+And this is quadratic
+in phi-- and et cetera.
+
+And then when you plug
+back this into the action,
+
+then you find on
+the initial action
+
+can also be expanded in
+power series of this phi.
+
+So you will have S2 phi plus--
+started with quadratic order--
+
+and 3 phi, et cetera.
+
+And then the quotient here gives
+you the two-point function.
+
+And then quotient here gives
+you the three-point function.
+
+And the quotient here gives a
+four-point function, et cetera.
+
+I hope the procedure is clear.
+
+Any questions regarding this?
+
+So even though this is
+very straightforward
+
+to do, conceptually,
+but in practice
+
+that it not what we would do,
+because this is a very tedious.
+
+It's very tedious.
+
+And our knowledge of
+quantum field theory
+
+gives us something much
+simpler to deal with.
+
+Because this, essentially,
+if you think about it,
+
+is not very different from
+doing a correlation function
+
+calculation, just in the
+flat-space quantum field
+
+theory.
+
+And there, whey you
+calculate the Green function
+
+in flat-space-- in
+flat-space quantum field
+
+theory, what do you do?
+
+Do we try to solve the classical
+equation motion and you iterate
+
+the equation?
+
+What do you do?
+
+AUDIENCE: Draw a diagram.
+
+HONG LIU: Yeah, you
+use Feynman diagrams.
+
+So here, it's exactly
+the same thing.
+
+So here it's much easier if you
+just do the Feynman diagrams.
+
+So let me first remind you
+what we do in the flat-space.
+
+So let's now go to
+the field theory
+
+one, standard, ordinary
+flat-space QFT.
+
+So now let's consider the lambda
+phi cubed theory in flat-space
+
+Just the same theory now
+using the flat-space.
+
+Let me call this star-star.
+
+So essentially, let's
+just consider star-star
+
+in flat-space, now in
+flat Euclidean space.
+
+So if we are given a
+field theory like that,
+
+so how would you calculate the
+following correlation function?
+
+Say, suppose I want to
+calculate phi x1, phi xn.
+
+So now this x1, xn, they're
+just flat-space coordinates.
+
+To distinguish them,
+let me just call y1,
+
+yn, just not to confuse
+about the AdS coordinate.
+
+So in flat-space
+with y, y mu, OK?
+
+In flat-space with
+coordinate y mu.
+
+So now suppose you want to
+calculate the correlation
+
+function for this.
+
+What do you do?
+
+So what do you do?
+
+It's easy.
+
+What you do is that this
+theory has a propagator, G,
+
+[? with ?] [? arrow ?]
+propagator.
+
+And also, this theory
+have a interaction vertex,
+
+which is controlled by lambda.
+
+And then, when you calculate
+such endpoint functions,
+
+you just fix your endpoint.
+
+So now remember, this is
+slightly different than what
+
+you would normally do
+in field theory one,
+
+because, here, we're
+doing coordinate space
+
+rather than momentum space.
+
+In field theory one, you're more
+used to doing momentum space.
+
+So here what you do is that you
+fix y1, y2 y3, extends to yn.
+
+So this is essentially the
+location of your insertion,
+
+of your field insertion.
+
+So essentially, imagine
+there's a source there.
+
+And then you just connect
+all the extended points
+
+by propagators and with these
+kind of interaction vertices.
+
+So for example, you can have
+something like this, et cetera.
+
+And this connects to
+some boundary point,
+
+some other point,
+et cetera-- say y's.
+
+And this also have lines.
+
+We just draw all
+possible diagrams,
+
+and you calculate that diagram.
+
+You calculate those diagrams,
+and they give you this thing.
+
+And essentially, the
+diagrams automatically
+
+give you the
+iteration procedure.
+
+So now, back to
+AdS, essentially, we
+
+can just do exactly
+the same thing.
+
+Just remind yourself
+of the procedure
+
+of calculating this and what
+we are going to do here,
+
+and you easily
+convince yourself.
+
+So it requires a couple
+of minutes' thinking,
+
+but we'll leave it to yourself.
+
+Actually, that procedure is
+no different from just doing
+
+the calculation like this.
+
+Of course, the
+difference is that now we
+
+are in the curved spacetime
+rather than flat spacetime.
+
+But there's another
+major difference.
+
+So here, the source all lies in
+the interior of your spacetime,
+
+where you inserted the operator.
+
+But here, all the source, phi
+x, they lie at the boundary.
+
+That's, essentially,
+the only difference.
+
+So if I just schematically--
+so this is AdS.
+
+This is the boundary.
+
+And essentially, all the points
+are lying on the boundary,
+
+like we have x1, x2.
+
+So let's consider
+four-point function.
+
+Because each one of them is
+labeled by the boundary point.
+
+And then for the four-point
+function, you just connect.
+
+So you can connect
+the diagram like this.
+
+Again, you have
+the vertices, which
+
+is the [? cube ?] of vertices.
+
+But your endpoint is all
+lying on the boundary.
+
+So this structure also
+tells you, actually,
+
+there's two types
+of propagators.
+
+Because one type of propagator
+connects the two bulk points.
+
+And then there's this
+kind of propagator
+
+which connects the bulk point
+into the boundary points.
+
+So this is the difference,
+one major difference,
+
+from the flat-space case.
+
+So here, all the
+propagators are the same.
+
+So here, the difference
+is now, you also
+
+have propagators which come
+from boundary to the bulk.
+
+So in this case, there are
+two kind of propagators.
+
+Here, you have two
+type of propagators.
+
+So one type of propagator
+is what we call
+
+the bulk-to-bulk propagator.
+
+Somehow this is going up and up.
+
+OK, I lost some
+blackboard space.
+
+So this the complete
+analog, this
+
+is the precise counterpart
+of the flat-space propagator.
+
+So this connects two points,
+z, x, z prime, x prime.
+
+So I still use the
+notation that z is the bulk
+
+[INAUDIBLE] direction.
+
+And the x is along the
+boundary direction.
+
+And this bulk-to-bulk will
+satisfy the standard Laplace
+
+equation just as in flat-space.
+
+So this gives you
+the delta function.
+
+Let me just express it, z minus
+z prime delta x minus x prime.
+
+So this is a complete analog
+of the standard flat-space
+
+propagator.
+
+It's just now in
+Anti-de Sitter space.
+
+So this is a counterpart in AdS
+standard flat-space propagator.
+
+So in particular,
+so as a propagator,
+
+this should be normalizable
+in either z or z prime,
+
+so when you take
+them to the boundary.
+
+So more explicitly, for
+example, the z at z prime,
+
+x prime, should scale as z
+prime to the power delta, when
+
+you take z prime goes to 0.
+
+And of course, this
+should also be regular.
+
+We should not have singularities
+as z goes to infinity.
+
+They should also be regular.
+
+So essentially, these
+condition will precisely
+
+define those propagators.
+
+But the idea is we
+also, because the source
+
+lies on the boundary, because
+of this boundary condition,
+
+we also have so-called
+boundary-to-bulk propagators.
+
+Actually, the standard
+in flat-space one,
+
+it propagates the field from
+one point to the other point.
+
+So that's why there's
+a delta function here.
+
+So the standard story,
+there's a delta function here.
+
+And you propagate
+the field starting
+
+from this point to that point.
+
+So this boundary-to-bulk
+propagator normally is written
+
+as k z,x, but the second
+index only has x prime,
+
+because this is when you take
+the boundary point to a bulk
+
+point.
+
+A boundary point, of course,
+there's no z anymore.
+
+So z prime is 0 here.
+
+You don't need to write it.
+
+And this boundary-to-bulk
+propagator,
+
+again, should satisfy
+the Laplace equation.
+
+But now the key point is
+that, on the right-hand side,
+
+because there's no bulk
+source, so the right-hand side
+
+should be 0 rather than
+the delta function.
+
+So that delta function is
+due to the bulk source.
+
+But we have to make
+sure this k have
+
+the right
+non-normalizable boundary
+
+conditions, so you
+have the right boundary
+
+condition to the boundary.
+
+So this when it approach to
+the boundary, as z goes to 0,
+
+should be like z d delta,
+delta x minus x prime.
+
+So the k satisfies the Laplace
+equation without a source.
+
+But when you take this
+propagator to the boundary,
+
+then it should give you the
+non-normalizable boundary
+
+conditions, because you
+should approach a source.
+
+And the delta
+function is put here.
+
+So if you write,
+say, a bulk field,
+
+which is sourced by some
+boundary source, say k z, x,
+
+x prime times phi x
+prime, and then this
+
+will have right
+boundary condition
+
+that the phi x, z goes
+to z d minus delta phi x.
+
+So this boundary-to-bulk
+propagator
+
+does not have a
+source in the bulk
+
+but does have a source
+in the boundary,
+
+non-normalizable
+off in the boundary.
+
+So now with this two
+propagator, then the story
+
+is just actually as
+in the standard way
+
+you obtain the Green functions.
+
+It's just really no different.
+
+So let me just summarize
+what we have discussed.
+
+The boundary
+endpoint function can
+
+be obtained by, essentially,
+endpoint function of the phi
+
+field in the gravity side--
+let me write it here-- just
+
+related to the endpoint
+function of the gravity field
+
+on the gravity side, with
+all these points, x1, xn,
+
+they're lying on the boundary.
+
+This side is treated as
+ordinary field theory.
+
+Then compute this endpoint
+function of your field
+
+but just put the
+field on the boundary.
+
+And then that would just
+give you the AdS correlation
+
+functions.
+
+Yeah, and then you just
+need to distinguish
+
+two types of propagators,
+a bulk-to-bulk propagator
+
+and bulk-to-boundary propagator.
+
+So any questions regarding this?
+
+AUDIENCE: Now, here,
+[INAUDIBLE] d minus delta.
+
+Right there, the G goes to
+[? d ?] phi in the delta.
+
+HONG LIU: Yeah.
+
+AUDIENCE: But why
+aren't they different?
+
+HONG LIU: It's because
+this must have a source.
+
+So the boundary-to-bulk
+propagator--
+
+you propagate the source,
+from the boundary to the bulk,
+
+so that means that field
+must have the right boundary
+
+condition.
+
+So that's the reason for this.
+
+We must have non-normalizable
+boundary conditions.
+
+And that propagator is just the
+standard flat-space propagator.
+
+Of course, it's
+always normalizable.
+
+And in the flat-space,
+when you construct
+
+a propagator, of
+course, it's always
+
+used in a normalizable
+wave function.
+
+AUDIENCE: This is
+that's non-normalizable?
+
+HONG LIU: No, this
+is non-normalizable.
+
+This is designed so that
+you have the right boundary
+
+condition.
+
+So this is designed so
+that you can propagate
+
+just as in flat-space.
+
+If you have phi at
+this point, and then
+
+you can propagate to the
+other point by convolution.
+
+And of course, when you write
+down the bulk field phi,
+
+in general, you only
+construct them out
+
+of the normalizable modes.
+
+Any questions?
+
+Good.
+
+So now let me make some remarks.
+
+So here, this
+procedure of iterating
+
+the classical
+equation of motion,
+
+solving the classical
+equation of motion,
+
+then iterating the
+action, of course,
+
+again, from our experience
+with quantum field theory, that
+
+only gives you the
+tree-level diagrams.
+
+So if I really write
+the bulk path integral,
+
+so Z CFT phi, then, in
+the same classical limit,
+
+it can be written
+as Z gravity, which
+
+is phi with the right
+boundary condition.
+
+And then on the gravity side,
+at semi-classical level,
+
+we can actually write down the
+path integral for this gravity
+
+partition function.
+
+So that's what we
+discussed before.
+
+And then at the leading
+order, in performing this path
+
+integral, of
+course, you just get
+
+what we have been doing so far.
+
+You just evaluate it at
+the classical solutions.
+
+But in principle, you can
+also see the fluctuations.
+
+So this is the
+fluctuations around, say,
+
+the classical solution, phi c.
+
+And then the action
+for the fluctuations
+
+is just given by phi c plus phi.
+
+The minus, of course,
+is the classical action.
+
+So we just expand
+around the phi c.
+
+So if we expand this,
+the leading order
+
+would be quadratic in small phi.
+
+I should now quote small phi.
+
+Maybe let me quote chi, because
+that is the same as that phi.
+
+So this chi is the small
+fluctuations around the phi c.
+
+So if you expanded this
+in chi, the linear order
+
+is 0, because phi c satisfies
+the equation of motion.
+
+So this will start in quadratic
+order and then cubic order, et
+
+cetera.
+
+So you validated the
+quadratic order as a Gaussian.
+
+And then that's the
+one-loop diagram.
+
+And then if you go
+to higher orders,
+
+then it'll give you
+higher-order diagrams.
+
+So if you now include
+the fluctuations,
+
+so the SE phi c, which
+is a classical action.
+
+This encodes only
+tree-level diagrams.
+
+And when you include
+the fluctuations, phi,
+
+the fluctuations, chi, and
+then this corresponding
+
+to include loops.
+
+So again, the whole
+procedure can be captured
+
+by the Feynman diagrams.
+
+So the advantage of
+the Feynman diagram
+
+is actually there's a natural
+generalization to the loop
+
+diagrams.
+
+And then just include
+the loops here.
+
+For example, here, you can
+do something like this.
+
+Now you can also have
+something like this.
+
+So that's, of course,
+one and two, including
+
+the fluctuations, are
+under the saddle point,
+
+are including the fluctuation
+around the saddle point.
+
+Any questions
+regarding this point?
+
+Good.
+
+Yes?
+
+AUDIENCE: So when people draw
+these like so-called Witten
+
+diagrams, where they
+draw up like this circle.
+
+HONG LIU: Right.
+
+AUDIENCE: Is that
+basically what we're doing?
+
+HONG LIU: Yeah.
+
+Yeah, right.
+
+Yeah, so let me just
+explain one thing.
+
+In the Euclidean, I have been
+drawing the ideas like this.
+
+So this is z equal
+to 0, et cetera.
+
+So in the Euclidean signature,
+as you will do in your PSet,
+
+then this z equal
+to infinity, you
+
+can argue is actually
+a single point.
+
+So let me just write
+down the metric.
+
+So the metric is R
+square, z square.
+
+When you go to
+Euclidean signature,
+
+you just have dx squared.
+
+So this is a full
+Euclidean metric.
+
+So there's something
+interesting about the difference
+
+between the Euclidean
+and Lorentzian,
+
+even though, from this
+picture, it's roughly the same.
+
+So if it's equal to
+0, you go to z notch.
+
+And then in the Euclidean
+case, you can actually
+
+show that z equal
+infinity, even though,
+
+[? naively, ?] you still
+have a full Euclidean plane,
+
+but you can argue, actually,
+that the whole thing is
+
+actually a point.
+
+And you can roughly see, when
+you go to z equals infinity,
+
+the overall factor goes to 0.
+
+So essentially, the whole
+space shrinks to a point.
+
+The whole space
+shrinks to a point.
+
+So in Euclidean, if
+it's equal to infinity,
+
+it's essentially a point.
+
+And then topologically, this
+is equivalent to having a disk.
+
+Topologically, the whole
+space is just disk.
+
+And the z equal to infinity
+is one point on the boundary.
+
+And then the other
+is z equal to 0.
+
+And so this is the
+interior of the space.
+
+Yes?
+
+AUDIENCE: So in other words, the
+entire perimeter of the circle
+
+is identi--
+
+HONG LIU: It's the boundary.
+
+AUDIENCE: [INAUDIBLE].
+
+HONG LIU: Yeah, this
+is the boundary.
+
+Essentially, you can imagine,
+each point here is R to d.
+
+Then you add the
+point at infinity,
+
+and then it becomes a sphere.
+
+AUDIENCE: [INAUDIBLE].
+
+HONG LIU: Yeah, it
+becomes a sphere.
+
+And then the whole thing
+becomes like a disk.
+
+So normally, when people
+will draw-- so topologically,
+
+you're creating a
+disk, just like this.
+
+Then people will just
+draw diagrams like this.
+
+Yeah, I draw diagrams like this.
+
+AUDIENCE: If you add a
+single point to the boundary,
+
+that single point is equal to
+infinity to the boundary, which
+
+is z equals 0?
+
+HONG LIU: Sorry?
+
+AUDIENCE: You mean that you
+have a point that [INAUDIBLE].
+
+HONG LIU: Yeah.
+
+Yeah, this point turns
+out, it can actually
+
+lie on the boundary.
+
+AUDIENCE: But then, on the
+boundary, the value of t
+
+is not continuous.
+
+HONG LIU: Hm?
+
+Yeah.
+
+So this is due to the
+coordinate choice.
+
+It's just this coordinate
+becomes singular at that point.
+
+You can rewrite it.
+
+Yeah, the simplest thing is that
+you rewrite these [INAUDIBLE]
+
+coordinates to the coordinate
+which has a parameter that has
+
+a boundary really as a sphere.
+
+And then you will see it.
+
+Because when you write
+the sphere as a plane,
+
+then this one point
+becomes singular.
+
+This is just the standard story.
+
+Just that coordinate
+choice is singular.
+
+Any other questions?
+
+Good.
+
+So this is the first remark.
+
+The secondary
+remark is that this
+
+is a little bit of an
+unusual correlation function.
+
+So this is the bulk
+correlation functions,
+
+but with all points
+lying on the boundary.
+
+So the counterpart or
+just the exact analog
+
+of standard flat-space
+correlation functions in AdS--
+
+you can see the end
+bulk point and look
+
+at its correlation functions.
+
+So this then will be really just
+bring you to the standard QFT
+
+one correlation functions.
+
+Then you have endpoints, z1,
+x1, or in the bulk, z2, x2, et
+
+cetera.
+
+And then you just draw a
+diagram between them, et cetera.
+
+The area propagator
+here would be
+
+just bulk-to-bulk propagator.
+
+There's no boundary-to-bulk
+propagator.
+
+There's no boundary-to-bulk
+propagator just
+
+all bulk-to-bulk propagator.
+
+So this is a complete analog of
+your ordinary flat-space Green
+
+functions.
+
+But we can easily imagine that
+this correlation function must
+
+be related to those
+correlations functions
+
+if you just take those
+points to the boundary.
+
+So it's natural to expect, say,
+those correlations functions,
+
+since they're at
+the boundary, must
+
+be related to those kind
+of standard correlation
+
+functions, in which you would
+take the point to the boundary.
+
+So those, somehow, in the
+end, must be the same.
+
+So if I take those
+points to the boundary,
+
+I should recover that guy.
+
+So indeed, this
+relation is true.
+
+And you will work it out
+yourself in the PSet.
+
+You see, the only
+difference is the following.
+
+When you take those points
+to the boundary, what you get
+
+is the boundary limit.
+
+So now let's imagine you take
+those points to the boundary.
+
+Because here, it's
+all bulk propagator.
+
+So those propagator, which
+connect to the boundary,
+
+would be the boundary limit
+of the bulk propagator.
+
+And then, it just
+boils down to, what
+
+is the relation
+between the boundary
+
+limit of the bulk
+propagator and this boundary
+
+to the bulk propagator?
+
+So the above relation-- let
+me just-- I'd rather just
+
+call it a number.
+
+So this star-star-star
+just boils
+
+down to the relation
+between the k
+
+z, x, x prime, which is our
+boundary-to-bulk propagator,
+
+and limit z prime goes to
+0, G x, z, x prime, z prime.
+
+So you will find
+that these two guys
+
+are proportional to each other.
+
+And once you extract out
+that proportional factor,
+
+then you just relate them.
+
+So this is just another
+way to calculate.
+
+Because this is the bounty
+correlation function.
+
+So this is the boundary
+correlation function.
+
+So this is related to the
+CFT correlation functions.
+
+And then you can also calculate
+the CFT correlation function
+
+just by taking the limit of
+the bulk correlation functions.
+
+So this you will work
+out a little bit.
+
+Yeah, you will work out the
+precise relation in your PSet.
+
+Maybe some of you have
+looked at it already.
+
+So any questions on this?
+
+AUDIENCE: What is the
+advantage of maybe
+
+using another to express it?
+
+HONG LIU: Yeah, just different
+ways of calculating things.
+
+And of course, normally,
+I have many different ways
+
+to calculate things.
+
+Some of them may be
+convenient this way.
+
+So of them may be convenient
+for that purpose, et cetera.
+
+It depends.
+
+Normally, we just
+directly are using
+
+the bulk-to-boundary propagator.
+
+If you just do the calculation,
+the bulk-to boundary propagator
+
+actually is simpler.
+
+But sometimes, for certain
+conceptual questions,
+
+this actually becomes simpler.
+
+So now let's look
+at Wilson loops.
+
+So how do you calculate the
+Wilson loops using gravity?
+
+So in the gauge
+theory-- so I assume
+
+you have already done the
+QFT II and the gauge theory?
+
+In the gauge
+theory, we also know
+
+it's essentially one of the
+most important observables.
+
+The Wilson loop is normally
+defined in the following way.
+
+So now I will
+explain my notation.
+
+So let me also add
+in subscript r here.
+
+So c is a closed path.
+
+So this is defined
+for closed paths.
+
+And A mu is a matrix.
+
+So we can see the
+[INAUDIBLE] in gauge theory.
+
+A mu is a matrix, writing
+the standard away,
+
+in terms of the generator,
+in some representations r.
+
+So this is in some
+representations.
+
+So this is just the
+generators of the gauge
+
+group in some representation,
+which we'll call r.
+
+And P is the path ordering.
+
+So in general, you can choose
+any representations you want.
+
+But often, we choose r, say,
+in fundamental representations.
+
+For example, that's
+normally what we do, in QCD,
+
+in fundamental representation.
+
+But you can choose it to
+be any representation.
+
+So the physical meaning
+of this, so this operator,
+
+by definition, is
+gauge invariant,
+
+because of this trace.
+
+And need the path ordering,
+because you have a matrix here.
+
+And the matrix, at different
+points, don't commute.
+
+So you need to specify ordering.
+
+And so you just specify it
+by the order of the path.
+
+And so the physical
+meaning of the Wilson loop,
+
+so this is essentially the
+phase factor associated
+
+with transporting an
+external particle, in a given
+
+representation, say, in r
+representation, along c.
+
+So you transport the
+particle along some path.
+
+And you come back
+to the same point.
+
+Then you find that that
+phase does not necessarily
+
+go back to 0.
+
+And so this is a
+nontrivial phase.
+
+It essentially tells you there's
+a nontrivial gauge field there.
+
+Yeah, so this provides a
+probe of the gauge fields.
+
+Yes?
+
+AUDIENCE: I know
+that people talk
+
+about-- I know that it's
+somehow and observable.
+
+But is it actually observable ?
+
+Can you actually
+do an experiment
+
+to measure this phase?
+
+HONG LIU: I don't think so.
+
+Ha.
+
+It depends.
+
+Yeah, in some
+situations, you can.
+
+Let me mention something
+else, then the answer
+
+to this question will be seen.
+
+So the simplest case
+would be the W c, just
+
+the single-point function
+of W c, say, in a vacuum.
+
+So this is the
+simplest observable.
+
+But of course, you can also
+consider the generic, say,
+
+a large number, several
+[? routes ?] in some general
+
+state, say, for example,
+[? finite ?] [? telemetry ?],
+
+et cetera.
+
+So these are the
+typical observables.
+
+So now let me emphasize
+this external.
+
+So this external
+is very important.
+
+So normally, by calling
+something external,
+
+we mean that this particle
+has infinite mass.
+
+It's infinitely heavy.
+
+And the reason we want
+it to be infinitely heavy
+
+is because only for
+heavy particles,
+
+in principle, you can
+localize the lower path.
+
+Then you can make mathematical
+sense of the precise path.
+
+Otherwise, if it's a
+fluctuating particle,
+
+then you can not specify a
+path-- yeah, ambiguously.
+
+So when we say, an
+external particle, I always
+
+say a particle which is assumed
+to be infinitely massive.
+
+And also, I've
+introduced terminology.
+
+When this r is in the
+fundamental representation--
+
+yeah, maybe not right here.
+
+When this r is in the
+fundamental representation,
+
+we'll call the corresponding
+particle a quark.
+
+If it is in the
+fundamental representation,
+
+I will call it a quark.
+
+I will often just consider the
+fundamental representation.
+
+In the phase factor, where
+we're corresponding to,
+
+you transport a quark.
+
+So one of the very often used
+loops is a rectangular loop.
+
+So this is along some
+spatial direction,
+
+so this is the time direction.
+
+So let's say the
+spatial direction is L,
+
+and the time direction,
+using the length,
+
+is T. So imagine you
+have a loop like this.
+
+So normally, we can
+see that the T, say,
+
+the length of the loop
+in the time direction,
+
+is much, much
+greater than the L.
+
+So in such a limit,
+then, essentially,
+
+you can ignore the
+contribution from this side,
+
+from these two short sides.
+
+So in the limit, in which
+this T goes to infinity,
+
+to leading order, you can
+ignore the short side.
+
+And then you can
+think of this loop
+
+when it just has a particle--
+so this is a particle moving
+
+forward in time.
+
+This is a particle
+going backward in time.
+
+Then you can consider this as
+a particle and an anti-particle
+
+moving forward in time.
+
+So in this case, we can
+argue, on general grounds,
+
+that this will just,
+to leading order,
+
+will give you something iET.
+
+And this e, it just
+can be interpreted
+
+as a potential energy between a
+single quark and an anti-quark.
+
+So in this example,
+this is the same.
+
+In this case, you may be able
+to measure this Wilson loop,
+
+because if you can
+measure-- experimentally,
+
+you may be able to measure
+this energy between the two
+
+particles.
+
+And then, essentially, you can
+say, I have measured the loop.
+
+And then you can compare with
+the prediction of the loop.
+
+So again, in order to make
+this interpretation make sense,
+
+this particle having infinite
+energy is very important.
+
+And again, only for the
+very heavy particle,
+
+you can really
+localize them, and then
+
+talk about the potential energy
+between these two particles.
+
+Otherwise, if they
+fluctuate a lot,
+
+then it's hard to
+make it precise.
+
+So now the question is how do we
+calculate this quantity in AdS?
+
+When I don't put an index
+here, I just mean that this
+
+the fundamental representation.
+
+The question is how we do that.
+
+So in order to
+answer this question,
+
+we first need to
+understand how to introduce
+
+a fundamental external particle,
+external quark in the N
+
+equals 4 super
+Yang-Mills theory.
+
+So how to introduce a
+fundamental external quark
+
+in the N equals 4 super
+Yang-Mills theory.
+
+So we know, as we
+discussed before,
+
+that everything in the N equals
+4 super Yang-Mills theory, so
+
+all fundamental fields,
+all the fields in the N
+
+equals 4 super
+Yang-Mills theory,
+
+they are in a joint
+representation.
+
+There's nothing in the
+fundamental representation.
+
+Everything is in the
+joint representation.
+
+So first we need to introduce
+a fundamental object,
+
+an object we transform under
+fundamental representation.
+
+After we have done that, then we
+need to translate that quantity
+
+to the gravity side.
+
+And then we understand how
+the gravity description
+
+of such an external particle.
+
+So this is easy to do.
+
+This is easy to do.
+
+So let's first think about
+how to do this in the N
+
+equals 4 super
+Yang-Mills theory.
+
+And then this is a
+very intuitive by using
+
+this [INAUDIBLE] picture.
+
+So we know the N equals
+4 super Yang-Mills
+
+theory comes from low-energy
+theory of N D3-branes.
+
+They come from the low-energy
+theory of N D3-branes.
+
+So how do we introduce
+an external particles?
+
+So now let's imagine,
+consider N plus 1 of them,
+
+and let me separate
+one from the rest.
+
+So this is still N,
+separate one from the rest.
+
+So then there can be open
+string connects between them.
+
+So suppose I separate
+them by some distance, r,
+
+in the transverse
+direction to the D3-brane.
+
+So as we described before, such
+as a separation breaks the SU N
+
+plus 1 symmetry of
+the D3-brane SU N
+
+and then a single
+U1 of this 1-brane.
+
+In particular, such
+an open string--
+
+so let's look at the endpoint.
+
+Then the endpoint of this
+string can only have indices.
+
+Because this is a
+single stream, one
+
+end ending on the other side.
+
+There's only one index.
+
+And here, they can only
+have N possible index.
+
+So such a fundamental
+string transforms
+
+in the fundamental
+representation.
+
+So from the point of view
+of this SU N gauge theory,
+
+this is a quark.
+
+So this endpoint is a quark.
+
+So this is a quark.
+
+And the mass of this
+quark is equal to-- so let
+
+me call the mass capital
+M-- is equal to r,
+
+the length between them divided
+by tension of the string.
+
+So this we have derived before.
+
+So this just gives you
+the mass of the quark.
+
+So when you separate one
+D-brane from the other,
+
+so you have introduced
+this quark, with a mass.
+
+So now let's consider that
+there's no low-energy limit
+
+[INAUDIBLE].
+
+So in the low-energy
+limit of [INAUDIBLE],
+
+so we want to keep this
+quark, so there, of course,
+
+you want to take
+alpha prime go to 0.
+
+But we want to keep this quark
+in the low-energy spectrum,
+
+because we want
+this to remain in N
+
+equals 4 super
+Yang-Mills theory,
+
+because we want to
+introduce this particle.
+
+So in this low-energy limit,
+when we take off a prime,
+
+go to 0 limit, we also want
+to take, at the same time,
+
+r goes to 0 limit, so that this
+mass term, r divided by alpha
+
+prime, will remain finite.
+
+Then that means
+this will remain,
+
+this particle, such kind of
+fundamental representation,
+
+will remain in the N equals
+4 super Yang-Mills theory.
+
+Because other modes are massive.
+
+And then when alpha
+prime goes to 0 limit,
+
+it goes to infinity.
+
+And under those modes,
+we will remain with the N
+
+equals 4 super
+Yang-Mills theory.
+
+So now let's see what
+happens on the gravity side.
+
+So here, you will need to
+fill in some details yourself.
+
+I'll only tell you the answer.
+
+On the gravity side, you
+have this N D3-brane.
+
+They have one brane which
+[? is ?] [? r ?] separated from
+
+this N D3-brane.
+
+And they're separation
+is such that, when
+
+you take off alpha
+prime and go to 0 limit,
+
+their ratio is finite.
+
+Now, in the gravity
+side, you have
+
+to take this so-called
+near-horizon limit,
+
+with taking into account.
+
+So what you find in the
+gravity side is that,
+
+as before, that N D3-brane now
+disappeared into r equal to 0.
+
+Remember, r equal to 0 is that
+infinite proper distance away.
+
+And now we are using
+this r coordinate.
+
+And when we take
+this low limit, we're
+
+using this r coordinate
+rather than this z coordinate.
+
+So in that case, you
+have i equal infinity.
+
+Then the brane, essentially,
+goes to r equal to 0.
+
+which has infinite
+proper distance
+
+away from any finite r.
+
+So now this is an
+exercise for yourself just
+
+to repeat our previous argument.
+
+Then you will find that
+in this regime, when
+
+you take alpha prime
+go to 0, this r finite,
+
+this D3-brane does
+not disappear.
+
+The single D3-brane
+will remain in the AdS.
+
+So the difference, from
+our previous story,
+
+is that, in addition
+to the AdS, now
+
+you have an additional
+D3-brane at some point in S5.
+
+Because D3-brane is in
+some transverse direction,
+
+which now become S5.
+
+So you have a D3-brane,
+which is parallel
+
+to the boundary coordinates,
+but sitting at one point in S5.
+
+And I think this
+picture is reasonable,
+
+but you should check yourself.
+
+Because in this regime, this
+D3-brane does not go away.
+
+And a remarkable thing
+you will check yourself
+
+is that when you take
+the [INAUDIBLE] limit,
+
+in this picture,
+this is flat-space.
+
+Then you have this formula.
+
+And now, when you take this
+limit, this now become AdS.
+
+Now, this AdS at some radius
+r, controlled by this r.
+
+And now you can
+check one nice thing.
+
+In AdS, if you consider a
+string, straight string,
+
+from this D3-brane all
+the way to r equal to 0,
+
+which is this
+string, this string
+
+has exactly the same mass.
+
+So the mass is equal to r
+divided by 2 pi alpha prime--
+
+also in AdS5.
+
+So this is a consistency check.
+
+Because when you take the
+low-energy limits, of course,
+
+you should not change the mass.
+
+The mass of the string
+will not change.
+
+The only question is whether
+it will stay in the spectrum
+
+or will not stay in the
+low-energy spectrum.
+
+The mass will not change.
+
+And you will see that
+when you take that limit,
+
+you find this
+D3-brane remains here.
+
+And this string, which now will
+connect some r to r equal to 0,
+
+which is now just some AdS.
+
+This is just some interior
+or AdS, infinite proper
+
+distance away.
+
+And then you can
+check that, in the AdS
+
+metric, the image of this brane,
+viewed from the boundary time--
+
+you have to this ratio
+factor, et cetera--
+
+remains exactly equal to this.
+
+So this is an important
+self-consistency check,
+
+which I will not do here.
+
+So now, the story
+becomes simple.
+
+Now we generate such a string,
+such a fundamental particle
+
+with such a mass.
+
+But in order to introduce an
+external particle-- in order
+
+to have an external particle
+take a mass to go to infinity,
+
+so that means we need to
+take r goes to infinity.
+
+So that means we
+want to this D3-brane
+
+to lie on the boundary of AdS.
+
+So to summarize, now we want to
+move this D3-brane-- in order
+
+for the external
+particle, we want
+
+to take M goes to
+infinity, then we want
+
+to take r goes to infinity.
+
+So we want this
+D3-brane to actually lie
+
+on the boundary of AdS.
+
+So let us just
+conclude, summarize.
+
+An external quark
+with infinite mass,
+
+in N equals 4 super
+Yang-Mills theory,
+
+is described by a string
+ending on the boundary of AdS.
+
+So this is r equal to infinity.
+
+Because now, we have put in
+this D3-brane to the boundary,
+
+and then we'll, of course,
+run into a string ending
+
+on the boundary of AdS.
+
+A external quark with
+[INAUDIBLE] AdS, of course,
+
+run into a string ending
+at boundary of AdS.
+
+And in particular, the
+location of the string
+
+can be mapped to the
+location of the quark.
+
+So then endpoint of the string
+is the location of the quark.
+
+So now we have found a very
+nice picture that introduces
+
+a fundamental quark, in N equals
+4 super Yang-Mills theory,
+
+because [? what you ?]
+[? need  to ?] [? do with ?]
+
+such a string.
+
+And now, when you
+do a Wilson loop,
+
+then corresponding to transport
+this string around some path,
+
+then endpoint of
+the strings runs
+
+on a path in the field theory.
+
+I thought we would stop here.
\ No newline at end of file
diff --git a/oju-1Ogh1ks.txt b/oju-1Ogh1ks.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c4dd9937633084872520023c36bdd876ce11a4dd
--- /dev/null
+++ b/oju-1Ogh1ks.txt
@@ -0,0 +1,2692 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: The first 2/3 of the
+course were covering sort
+
+of what you need to know to know
+basic microeconomics--
+
+consumer theory and
+producer theory.
+
+And basically you can now, if
+you understand the material,
+
+go forth in the world as a
+qualified micro economist.
+
+What we're going to do for the
+rest of the semester is apply
+
+what we've learned and show you
+how you can use the tools
+
+that we've learned from basic
+consumer and producer theory
+
+to understand a broader
+range of phenomena.
+
+Really, you can think
+of this as--
+
+as I talked in the first
+lecture about we make
+
+simplifying assumptions--
+
+this is sort of as we bend those
+simplifying assumptions,
+
+and consider more and more
+realistic applications of
+
+these models.
+
+And the hint of what the sort of
+stuff you can get to see as
+
+you move on in economics and
+move to our other courses
+
+beyond micro.
+
+So what we're going to start
+with today-- and of course,
+
+unfortunately, since I'm going
+to cover a lot of topics, I'll
+
+give each way too little time.
+
+Including today, which
+is one lecture on
+
+international trade.
+
+You could take several
+courses on it.
+
+We have an excellent undergrad
+course, 14.54 on
+
+international trade.
+
+And I'm going to sort of try to
+shove down your throats in
+
+one lecture the key things
+you need to know about
+
+international trade.
+
+But if you find it interesting
+I urge you to
+
+follow up on this.
+
+So, thinking about this--
+
+a good way to think about
+international trade is to
+
+think about an example.
+
+So let's think about
+Valentine's Day.
+
+Valentine's Day sort
+of presents
+
+an interesting conundrum.
+
+Because Valentine's Day
+happens in the winter.
+
+And yet, the thing you're
+supposed to do is give roses.
+
+Which don't grow in the
+winter in the US.
+
+At least not very conveniently
+in many places.
+
+So you've got this difficult
+issue that basically we're
+
+supposed to represent this
+holiday with something that
+
+doesn't actually come
+that time of year.
+
+So historically what that meant
+it was if you wanted to
+
+get roses for Valentine's Day
+you to buy them from specially
+
+heated greenhouses.
+
+Where they set up largely
+to supply the roses for
+
+Valentine's Day.
+
+There wasn't really a large
+purpose for them otherwise.
+
+However, over the past couple of
+decades, what's happened is
+
+instead-- instead of growing
+these in these specially
+
+heated greenhouses, we've
+started flying them in from
+
+other places, from Colombia.
+
+Where of course, Colombia's on
+the other side of the equator.
+
+So February is a wonderful
+time to
+
+grow roses in Colombia.
+
+And as a result we've started
+flying them in.
+
+And the typical rose you will
+give on Valentine's Day this
+
+year will come from Colombia.
+
+Now the issue is-- is that a
+good thing or a bad thing?
+
+Now on the one hand,
+we get cheap roses.
+
+That's good.
+
+Especially for poor college
+students who want to impress
+
+their valentine by sending
+a dozen roses.
+
+It's good they're cheap.
+
+And roses are way cheaper now
+than they were when I was--
+
+even in dollar terms when I was
+in college giving roses.
+
+Roses are just incredibly
+cheap now compared to
+
+20 or 30 years ago.
+
+On the other hand, a lot
+of rose producers
+
+have lost their jobs.
+
+A lot of people whose
+livelihoods and source of
+
+income was growing these roses
+are now out of jobs.
+
+OK, these are typically people
+who are not high-skilled
+
+people who can go find
+another job easily.
+
+These are people who have been
+really displaced for something
+
+which was a specialized skill
+which they cannot easily use
+
+other places.
+
+And basically this trade-off is
+sort of a microcosm of the
+
+debate we have over
+international trade every day.
+
+A debate that's ongoing.
+
+Obama just came back
+to the G20 summit.
+
+Where there was huge discussions
+of the issues of
+
+international trade.
+
+It's an ongoing debate.
+
+And it's a particularly
+important topic right now in
+
+the US because the US is running
+what's called an
+
+enormous trade deficit.
+
+The trade deficit is the
+difference between how much we
+
+export, that is how much of
+our goods we sell to other
+
+countries, minus how
+much we import.
+
+Which is how much of
+goods from other
+
+countries that we buy.
+
+Currently we export about
+$160 billion worth
+
+of goods every month.
+
+So every month we send out $160
+billion worth of goods
+
+around the world.
+
+We import about $200 billion
+of goods every month.
+
+So that means we have a trade
+deficit that's running about
+
+$40 billion.
+
+Now the question is--
+is that a problem?
+
+Is it a problem that the US is
+systematically buying more
+
+stuff from the rest
+of the world than
+
+they're buying from us?
+
+And the answer is it's not
+necessarily a problem.
+
+And really, it might in fact be
+a natural outcome because
+
+of the principle that we'll
+focus on today--
+
+the principle of comparative
+advantage.
+
+Comparative advantage is saying
+if some other place is
+
+particularly good at producing
+roses in February, then we
+
+shouldn't be that stressed
+about the fact that we're
+
+running a deficit of roses.
+
+That's something which is OK in
+terms of total efficiency.
+
+So to see that, let's focus
+as this rose example in a
+
+particularly simplified way.
+
+Imagine there's two
+countries--
+
+the US and Colombia.
+
+And there's only two goods
+in the world--
+
+roses and computers.
+
+Two countries, two
+good models.
+
+The standard model we work with
+with international trade.
+
+With two country two good models
+you can develop almost
+
+everything you need to know.
+
+There is no need to make
+it more complicated.
+
+Now, as I mentioned it's really
+hard to grow roses in
+
+February in the US.
+
+It's a lot easier in Colombia.
+
+On the other hand, it's much
+easier to produce good
+
+computers in the US than in
+Colombia because we have the
+
+high skilled labor force that
+can produce computers.
+
+So we have a thing where the
+US is relatively bad at
+
+producing roses in February.
+
+Colombia's relatively bad
+at producing computers.
+
+So the key point is that means
+that the opportunity cost--
+
+remember the opportunity cost,
+this key concept we've come
+
+back to a couple times.
+
+The opportunity cost of
+producing a rose in terms of
+
+producing computers is
+relatively high in the US.
+
+That is to produce a rose we
+have to use so many resources.
+
+Those resources can be much more
+effectively deployed to
+
+producing computers.
+
+Likewise, in Colombia, to
+produce a computer would use a
+
+ton of resources that would be
+much more effectively deployed
+
+to produce roses.
+
+As a result we see that Colombia
+has a comparative
+
+advantage in roses.
+
+And the US has a comparative
+advantage in computers.
+
+The point is that if a country
+is relatively good at
+
+something then they have a
+comparative advantage.
+
+And it's all about
+relativities.
+
+Because people are going
+to want both.
+
+But the key thing is who's
+relatively good at producing
+
+one versus the other.
+
+So to see that let's
+go to figure 19-1.
+
+To see how we diagram this,
+let's go to figure 19-1.
+
+Figure 19-1 shows production
+possibility frontiers.
+
+You learned about these
+a while back.
+
+Let me remind you, a production
+possibility
+
+frontier we talked about in
+the context of a firm.
+
+It shows the trade-off between
+the firm's ability to produce
+
+one good versus another good.
+
+So for a firm producing
+two goods a production
+
+possibilities frontier is the
+combination of the two goods
+
+they could produce at a
+given level of inputs.
+
+So we talked about it from the
+context of firms. We can also
+
+talk about this in the
+context of countries.
+
+That says, we can draw a US
+
+production possibility frontier.
+
+Which is given the resources the
+US has, it could produce
+
+up to 2000 computers
+and no roses.
+
+Or 1,000 dozen roses, boxes of
+roses, and no computers.
+
+And let's assume it's
+linear in between.
+
+So the US production possibility
+frontier is given
+
+the resources we have-- and
+this is a very simplified
+
+example-- but just
+bear with me.
+
+Given the resources we have, we
+can produce 2000 computers
+
+and no roses or 1,000 boxes
+of roses and no computers.
+
+Or any combination in between.
+
+That's our production
+possibility frontier.
+
+Columbia has a production
+possibility frontier
+
+illustrated in the
+second panel.
+
+They can produce 1,000 computers
+and no roses.
+
+Or 2000 boxes of roses
+and no computers.
+
+That is, Columbia has
+a comparative
+
+advantage in roses.
+
+Meaning that their production
+possibility frontier is a lot
+
+flatter than ours is.
+
+We have a comparative advantage
+in computers.
+
+Meaning our production
+possibility frontier is a lot
+
+steeper than is Colombia's.
+
+Ignore panel C for the moment.
+
+Now remember what the slope of
+the production possibility
+
+frontier is.
+
+It's the marginal rate of
+technical substitution.
+
+It's the marginal rate at
+which the producer can
+
+substitute one good
+for another.
+
+So basically, for the US, the
+marginal rate of substitution
+
+of roses for computers is -2.
+
+That is you have to give
+up two computers to
+
+get one box of roses.
+
+In Colombia it's -1/2.
+
+You have to give up
+1/2 a computer to
+
+get a box of roses.
+
+So since the marginal rate of
+substitution is so much higher
+
+in the US, we say that Colombia
+has a comparative
+
+advantage in producing roses.
+
+Now let's go further and impose
+tastes on consumers in
+
+each country.
+
+Let's say that tastes are such
+that given these production
+
+possibility frontiers, consumers
+in the US choose
+
+1,000 computers and 500
+boxes of roses.
+
+We choose production
+over love.
+
+Colombia chooses love
+over production.
+
+Given their production
+possibility frontier, this is
+
+not inherently about
+taste necessarily.
+
+Because you have very different
+slopes here.
+
+But given their tastes and their
+production possibility
+
+frontier, they choose
+500 computers and
+
+1,000 boxes of roses.
+
+Now this we call the outcome.
+
+We call this outcome the
+autarchy outcome.
+
+Autarchy.
+
+Which is the word--
+
+I don't know what the hell it
+means, but it basically means
+
+no trading.
+
+Autarchy.
+
+I don't know where
+it comes from.
+
+Must be some Russian
+term or something.
+
+Autarchy.
+
+Which means no trading.
+
+So the no trading outcome is
+consumers in the US consume
+
+1,000 computers and 500
+boxes of roses.
+
+Consumers in Colombia consume
+500 computers and
+
+1,000 boxes of roses.
+
+Now the key point is that both
+the US and Colombia can be
+
+better off if we introduce
+trade.
+
+And how is that?
+
+Well if we introduced trade,
+then each country can
+
+specialize in their comparative
+advantage.
+
+Trade allows for
+specialization.
+
+That is the key advantage
+of trade.
+
+Their comparative advantage
+naturally yields
+
+specialization.
+
+Comparative advantage
+naturally yields
+
+specialization-- it makes
+sense for the US to be a
+
+computer producer and Columbia
+to be a rose producer.
+
+It doesn't make sense the two
+countries to produce both.
+
+But absent international trade
+they have to produce both.
+
+Because consumers want both.
+
+So if we're shut off from the
+world and Columbia's shut off
+
+from the world, then we end up
+as in figures A and B. But
+
+once we introduce trade, then
+we can take advantage of our
+
+relative expertise.
+
+And we get a new production
+possibility frontier which
+
+looks like panel C.
+
+That is, if you want more
+than 2000 computers--
+
+so if you want 2000 computers
+and 2000 roses--
+
+then you simply have the US
+produce just computers and
+
+Colombia produce just roses.
+
+And you can get 2000 of each.
+
+Now you can get 3,000 computers
+and no roses by
+
+having everybody produce
+computers.
+
+Or 3,000 roses and no computers
+by having everybody
+
+produce roses.
+
+So you know production
+possibility frontier has its
+
+sort of wedge point that
+2000-2000 intersection.
+
+You can label that point the
+point of specialization where
+
+those two dashed lines
+hit the solid line.
+
+That's the point of
+specialization, pure
+
+specialization.
+
+That's the point where the US
+does just what it's good at.
+
+And Colombia does just
+what it's good at.
+
+Of course you could have
+other combinations too.
+
+And that's what leads
+to this bent
+
+production possibility frontier.
+
+But the key point is this joint
+production possibility
+
+frontier is further out than
+what any country could have
+
+produced on its own.
+
+We've increased the
+opportunity set.
+
+Specialization has led to a
+larger opportunity set.
+
+A larger opportunity set-- we've
+expanded the opportunity
+
+set for the world by allowing
+countries to specialize.
+
+And the result of that you can
+see in the next figure.
+
+In figure 19-2 which shows
+gains from trade.
+
+So what this figure shows--
+
+this is the same autarchy
+figure from
+
+panels A and B before.
+
+I've just added some
+more labels.
+
+So what we see is, in
+autarchy, we're at
+
+point C- sub US.
+
+With the US producing and
+consuming 1,000 computers and
+
+500 boxes of roses.
+
+If we move to specialization,
+move to international trade,
+
+what happens is the US moves
+to producing 2000
+
+computers at Q-US.
+
+And, likewise, looking at the
+second panel, Colombia moves
+
+to producing 2000 box
+of roses at Q-CO.
+
+And US consumers now increase
+their consumption of both
+
+roses and computers.
+
+As do Colombian consumers.
+
+And you end up with total
+consumption of 2000 computers
+
+and 2000 roses.
+
+So the US consumes 1250
+computers and Colombia
+
+consumes 750.
+
+And the flip for roses.
+
+So we are learning that
+Colombians, even at the same
+
+price, do prefer love
+over production.
+
+But nonetheless, the bottom
+line is, both sets of
+
+consumers are better off.
+
+Both sets of consumers are
+consuming at a higher point
+
+than was possible
+without trade.
+
+It's magic.
+
+The magic is that simply by
+letting them trade we have
+
+made both countries
+better off.
+
+And the magic, the key to the
+magic, is specialization and
+
+comparative advantage.
+
+If the US and Colombia were
+identical in terms of their
+
+production possibility frontiers
+then you should be
+
+able to see that there would
+be no gains from trade.
+
+If they had the same production
+possibility
+
+frontier, if in A and B the
+slopes were the same, then the
+
+joint production possibility
+frontier would be identical to
+
+what's in each country.
+
+There would be no gains
+from trade.
+
+Gains from trade come from the
+fact that these production
+
+possibility frontiers have
+different slopes.
+
+That there's comparative
+advantage in one country and
+
+not another.
+
+Which allows specialization.
+
+So, basically, the key insight
+of international trade-- and
+
+once again I'm doing now in 50
+minutes what you do in 12
+
+lectures when you
+get it right.
+
+But the rough insight is that
+comparative advantage yields
+
+specialization, yields
+gains from trade.
+
+That's sort of the chain
+of logic to be
+
+thinking about this.
+
+Questions about that?
+
+Yeah?
+
+AUDIENCE: If we're going to
+adjust to international
+
+situations?
+
+Or could it be any sort of
+
+specialization between two companies?
+
+PROFESSOR: Any specialization
+between two companies.
+
+So just we learned about
+this originally in
+
+the context of companies.
+
+Same issue.
+
+In the business world they
+have a term for this.
+
+What do they call it?
+
+Synergy.
+
+You all know that word, you've
+got to if you're going to
+
+business school.
+
+Synergy.
+
+Synergy means that somehow you
+put two companies together and
+
+they can produce the
+same stuff better.
+
+Synergy is a fancy
+name for this.
+
+Which is the idea is that
+there may be gains from
+
+specialization even
+within a company.
+
+But if you take the old
+example, take two shoe
+
+companies, both producing left
+and right shoes inefficiently
+
+and they could specialize.
+
+And one could do better
+producing left shoes and one
+
+at right shoes.
+
+You put them together
+and overall you
+
+can have more shoes.
+
+That's actually a pretty
+stupid example,
+
+but you get the point.
+
+That basically the same
+principle can occur whenever
+
+there are gains from trade.
+
+Whenever there's comparative
+advantage of specialization
+
+you make gains from trade.
+
+Good question.
+
+Other questions?
+
+Now, that raises the interesting
+question of-- well
+
+these comparative advantage
+things sound great.
+
+Where can I get one?
+
+Where do comparative advantages
+come from?
+
+And there's really two sources
+of comparative advantages.
+
+Comparative advantage in
+international trade.
+
+So where does comparative
+advantage come from?
+
+One is differences in
+factor endowment.
+
+Differences in factor
+endowment.
+
+What that means, is that
+for example, Canada
+
+has a ton of trees.
+
+Everywhere.
+
+Canada is endowed
+with an enormous
+
+amount of lumber resources.
+
+With that factor very well.
+
+So Canada is an enormous
+exporter of
+
+lumber and paper products.
+
+Because they happen to have the
+main thing you need for
+
+that which is unbelievable
+amounts of trees, everywhere.
+
+So Canada can specialize in
+exporting lumber and paper.
+
+So now that gives them
+a comparative
+
+advantage in that area.
+
+Now let me ask you
+another question.
+
+Why does China export most of
+the world's clothes now?
+
+What?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Cheap labor.
+
+It's not that they have
+cheaper textiles.
+
+It's not that the
+cloth itself--
+
+and I realize that the silkworms
+are in China.
+
+But not like the actual
+production of cloth is that
+
+much cheaper.
+
+It's that clothes
+are primarily a
+
+labor intensive good.
+
+And the labor is cheapest
+in China.
+
+So they have a factor
+endowment.
+
+They have an advantage,
+comparative advantage, in
+
+labor intensive goods.
+
+So China, with international
+trade, will produce a
+
+disproportionate share of
+labor intensive goods.
+
+Because they can specialize
+in labor intensive goods.
+
+And make them cheaper for
+the rest of the world.
+
+So likewise, a sweatshirt that
+you would go and buy today--
+
+especially if you go and buy
+it at a not top end store.
+
+At an Old Navy or even
+at a Costco.
+
+Is literally in dollar terms
+cheaper than what I paid for
+
+that same sweatshirt when
+I was in college
+
+in the early 1980s.
+
+Because they're just
+produced incredibly
+
+cheaply in China now.
+
+We bring them in and
+they're just cheap.
+
+Goods where you can specialize
+in that are going to be--
+
+when you take advantage
+of specialization
+
+will be a lot cheaper.
+
+So that's one reason why you
+see comparative advantage.
+
+The second reason is going to
+be technological leadership.
+
+Technological leadership.
+
+So, for example, Japan has no
+natural comparative advantage
+
+of producing cars.
+
+There's no reason why Japan
+should have a comparative
+
+advantage of producing
+cars over the US.
+
+Except they developed the
+technology to more efficiently
+
+mass produce the modern
+automobile.
+
+As a result of that
+technological leadership they
+
+gave themselves, essentially,
+comparative advantage.
+
+Now, once that technology
+becomes public, the production
+
+shifts elsewhere.
+
+So now China is a major
+producer of cars.
+
+Basically copy-catting the
+technology developed in Japan.
+
+So it does move elsewhere.
+
+Unlike factor endowments--
+
+if the US wanted to compete with
+Canada I guess we could
+
+plant trees and in 50 years
+we would compete.
+
+But factor endowments are kind
+of hard to compete on.
+
+Technology is potentially a
+little bit easier because you
+
+can reverse engineer things.
+
+So once again, the
+
+technology's shifting to China.
+
+So really the answer is in the
+long run everything's going to
+
+be made in China.
+
+Because they've got
+the cheap labor.
+
+And they're adopting
+the technology.
+
+And once again, to quote towards
+our most important
+
+sense of cultural relevance,
+there's the episode of the
+
+Simpsons where Homer says,
+don't worry we're fine.
+
+We're going to rule--
+
+our country's going
+to rule the world.
+
+We're fine in the future.
+
+He goes, wait a second
+we're China, right?
+
+So basically China is doing very
+well because they've got
+
+these factor endowments--
+
+these great factor endowments
+and because they are adopting
+
+technology as well.
+
+What's interesting about this
+is this really leads to some
+
+more interesting
+policy issues.
+
+Once again, factor endowment
+you can't
+
+do a whole lot about.
+
+The interesting policy issues
+are in technological progress.
+
+This is an argument that many
+people make for subsidizing
+
+new technologies.
+
+So you often hear President
+Obama saying, we need to
+
+subsidize green technologies.
+
+This is the wave
+of the future.
+
+The idea, what he's saying
+implicitly is if we get the
+
+technological leadership, we
+can make the green products
+
+that are exported.
+
+Not the color--
+
+I mean environmental stuff--
+that can be exported to the
+
+rest of the world.
+
+And that's the argument
+that he's making.
+
+Question about that?
+
+Now let's talk about where we
+started the lecture, which is
+
+is trade a good thing
+or a bad thing?
+
+I just talked about how trade
+can greatly increase
+
+consumption possibilities.
+
+But why haven't we talked
+about the consumers?
+
+What about overall
+social welfare.
+
+And the answer is that
+trade unambiguously
+
+increases social welfare.
+
+That trade is unambiguously
+a good thing to do.
+
+So to see that let's go to the
+next series of figures.
+
+Start with figure 19-3.
+
+So let's start with the
+market for roses
+
+and imagine we have--
+
+[INAUDIBLE] autarchy is
+sometimes spelled with a K,
+
+sometimes with a CH, I don't
+know what the right way to
+
+spell it is.
+
+But anyway, you have autarchy.
+
+So the US-- imagine the old days
+where we produced all our
+
+roses and we're at some
+equilibrium with some consumer
+
+surplus and producer surplus.
+
+So we produce Q sub A roses
+at a price p sub A.
+
+Now, in figure 19-4 we're
+going to introduce
+
+international trade.
+
+It's a little confusing, so
+let's go through it slowly.
+
+Figure 19-4.
+
+You can find on that figure the
+domestic supply and the
+
+domestic demand.
+
+And they intersect at point A.
+Figure 19-4, domestic supply
+
+and domestic demand intersect
+at A. Which is once again a
+
+quantiy of Q sub A and
+a price of P sub a.
+
+Now let's say that what happens
+is we now allow
+
+imports of roses.
+
+We now trade with Colombia
+for roses.
+
+What that does is that means now
+instead of just drawing on
+
+the domestic supply, we
+can now draw on the
+
+world's supply of roses.
+
+We don't have to just rely
+on domestic supply.
+
+Well, that by definition has
+shifted further out.
+
+And it's shifted further out
+because other countries
+
+countries can produce roses so
+much more cheaply than we can.
+
+So we can rely on the world's
+supply of roses.
+
+Remember my cotton example where
+you first buy from the
+
+cheapest country, then the next
+
+cheapest country, et cetera.
+
+This is what we're saying--
+if the US was the cheapest
+
+producer of roses, this
+wouldn't shift out.
+
+But since the US is not the
+cheapest producer of roses
+
+this shifts out to
+world supply.
+
+And we get to a new
+equilibrium at
+
+quantity C sub t.
+
+That's the new quantity
+of roses we consume.
+
+And a lower price P sub w.
+
+The horizontal line's a little
+distracting, actually.
+
+But basically what you have
+here-- the horizontal line is
+
+just showing the price in
+autarchy and the world price.
+
+But the bottom line is, what
+you get you get is you get
+
+this new equilibrium with
+a quantity C sub t and
+
+a price P sub w.
+
+And in particular, what we're
+seeing is that total domestic
+
+consumption of roses
+has increased.
+
+But domestic production
+has fallen.
+
+Because look, the new price
+intersects the supply
+
+curve at Q sub t.
+
+So what happens is at that new
+lower price P sub w, US rose
+
+producers aren't actually
+producing as much.
+
+So US domestic production falls
+from Q sub a to Q sub t.
+
+But US consumption rises from
+Q sub a to C sub t.
+
+The difference is imports.
+
+Production falls from
+Q sub a to Q sub t.
+
+Consumption rises from
+Q sub a to C sub t.
+
+The difference is imports.
+
+And that's what happens
+when we allow
+
+Colombia to send us roses.
+
+What are the welfare
+implications of that?
+
+Let's go to figure 19-5.
+
+And what you can see is we
+can show you the welfare
+
+implications.
+
+Previously consumer surplus was
+W. Producer surplus was X
+
+plus that other white triangle
+below X. Now what's happened?
+
+Consumer surplus has gone up by
+X, because consumers have
+
+gained that plus z.
+
+So consumers have gained that
+entire trapezoid, X plus Z.
+
+Producers have lost x.
+
+Producers have lost that
+trapezoid, X. So in total
+
+we've gained Z. We've gained
+that entire triangle, Z. Z is
+
+the entire triangle on both
+sides of the dashed line.
+
+So we've gained all of Z.
+Consumers gained X plus Z,
+
+producers lost X. We've gained
+Z. So overall we've increased
+
+welfare in the US.
+
+So basically consumers
+win, producers lose.
+
+And that's the problem.
+
+The political problem we have.
+And I'll come back to this.
+
+What you can see is consumers
+win, producers lose.
+
+But by definition, consumers win
+more than producers lose.
+
+So overall, social surplus
+has gone up.
+
+Now that's the case
+of imports.
+
+Now what about exports?
+
+Well if imports make
+us better, do
+
+exports make us worse?
+
+We just said imports
+make us better.
+
+What about exports?
+
+Well let's look at that
+in figure 19-6.
+
+Now figure 19-6 shows what
+happens with exports.
+
+Once again we start at point A,
+the domestic outcome, point
+
+A. And now we're talking
+about computers.
+
+So now the US is going
+to export computers.
+
+What that means is that the
+supply of computers to people
+
+in the US is going to fall.
+
+why?
+
+Because a bunch of them are
+going to get sent away.
+
+So it used to be US consumers
+got to consume on that
+
+domestic supply--
+
+so US producers used domestic
+supply curve.
+
+And we had domestic demand
+intersecting at A. Well now,
+
+domestic producers are shipping
+a bunch of the
+
+computers to Japan, and
+China, and Colombia.
+
+As a result, the supply
+has shifted in.
+
+Because they don't have
+as many computers
+
+to sell in the US.
+
+That means the price rises.
+
+So because of exports we pay
+more for our computers.
+
+And it sort of makes
+sense, right?
+
+They produce a bunch
+of computers.
+
+If there's been a great demand
+for them elsewhere and we want
+
+them too, we're going to have
+to pay a higher price.
+
+Because we're competing
+with other
+
+people for those computers.
+
+So now that supply curve
+has shifted up.
+
+And now we end up that US
+consumers only want to C sub t
+
+computers at a new higher
+price a P sub w.
+
+But the world is now saying,
+well we are interested in the
+
+total amount of computer
+we want is Q sub t.
+
+So what that world
+price of sub w--
+
+the domestic producers say
+great, at that higher price P
+
+sub w, I'm delighted to produce
+Q sub t computers.
+
+So what I'm going to do is I'm
+going to produce Q sub t, I'm
+
+going to ship Q sub t minus
+C sub t elsewhere.
+
+And US consumers will
+consume C sub t.
+
+So consumers are worse off.
+
+So unlike imports which make
+consumers better off,
+
+consumers are worse off.
+
+So is trade bad?
+
+Well, no.
+
+Trade's not bad.
+
+But the bottom line is, domestic
+producers are going
+
+to gain more than domestic
+consumers lose.
+
+The bottom line is we'll be
+better off from exports.
+
+But in this case, consumers
+lose and producers win.
+
+Society gains either way.
+
+Society gains from imports
+because consumers gain more
+
+than producers lose.
+
+Society gains from exports.
+
+Because producers gain more
+than consumers lose.
+
+So what that means is that any
+form of trade is going to make
+
+the US better off.
+
+But also inevitably
+create losers.
+
+Any form of trade will make
+the US better off but
+
+inevitably create losers.
+
+And the problem is that those
+losers are very loud in the
+
+political process.
+
+And the winners are
+not so loud.
+
+So, for example, if you polled
+US consumers and said, how
+
+much are you saving on
+your sweat shirts?
+
+Because we import textiles
+from China.
+
+They wouldn't know.
+
+I mean they'd say a
+couple bucks what
+
+in fact it's maybe--
+
+they'd say I don't know, 10% of
+the price when it's maybe
+
+more like 50% of the price.
+
+But if you polled US textile
+manufacturers, or guys who
+
+have left the business, and
+said how much did you lose
+
+because of imports of China,
+they'd tell you exactly how
+
+much they lost. They'd tell
+you 10 times as much.
+
+But they know how much they
+lost. And they go to their
+
+politicians and they say, hey
+we're losing jobs here.
+
+And the consumers don't come
+saying, hey I'm getting
+
+cheaper sweatshirts here.
+
+As a result, there's huge
+political backlash against
+
+imports in particular.
+
+So that leads to policies
+which limit imports into
+
+countries like the US.
+
+Like tariffs, which are
+essentially taxes.
+
+Tariffs, which are essentially
+taxes on goods imported into
+
+the US to us.
+
+Which are taxes on goods that
+are imported into the US.
+
+Or quotas, which are limits
+on how much companies
+
+can send to the US.
+
+What I think what you should
+know now is by definition--
+
+since I said free trade
+is good, these things
+
+are going to be bad.
+
+And they're going to be bad--
+
+things like tariffs are going
+to be bad because they're
+
+going to hurt US consumers more
+than they're going to
+
+help US producers.
+
+So to see that let's
+go to figure 19-8.
+
+Let's show what happens
+with a tariff.
+
+This is saying that now we're
+starting the world with trade.
+
+So the world with trade we're
+producing C sub 1, which is
+
+where domestic demand equals
+world supply at
+
+a price P sub w.
+
+That's where we were
+with trade.
+
+Now the US government comes
+in and levies a tariff.
+
+And says that that tariff is
+going to be the difference
+
+between P sub w and P sub t.
+
+So that's the amount
+of the tariff.
+
+They are going to raise the
+price essentially to P sub t.
+
+They're essentially going to
+levy a tax on roses that come
+
+in from Colombia.
+
+What that does is that means
+that consumers now, at that
+
+higher price, only want
+C sub 2 roses.
+
+That's where that intersects
+demand.
+
+So they wanted C sub 1 roses
+without the tariff.
+
+But now with the tariff at that
+higher price intersects
+
+demand at C sub 2, they only
+want C sub 2 roses.
+
+Producers, given that they have
+to pay the tariff, are
+
+only going to produce Q sub 2.
+
+Domestic producers are now going
+to produce Q sub 2 roses
+
+because they get
+a higher price.
+
+So domestic consumers
+are consuming less.
+
+Domestic producers are
+producing more.
+
+Right, because now that
+price is higher.
+
+So now you could reopen those
+heated greenhouses because
+
+it's worth it now.
+
+And we end up with a much
+smaller amount of imports.
+
+So in that sense the
+tariff worked.
+
+So in the sense that the goal
+of the tariff was to reduce
+
+imports, it worked.
+
+Consumers wanted less
+from Colombia.
+
+Producers were happy
+to produce more.
+
+So imports fell.
+
+So in that sense
+tariffs worked.
+
+They've lowered imports.
+
+But what do they
+do to welfare?
+
+Well that's our final
+figure 19-9.
+
+What do they do to welfare?
+
+Well what you can see is
+domestic producers gained a
+
+trapezoid A. Their producer
+surplus, which used to be that
+
+little white triangle below A,
+became that entire triangle
+
+that includes A and the
+white part below it.
+
+So their producer surplus became
+A. They gained A in
+
+producer surplus.
+
+But consumers lost a ton.
+
+They lost the entire trapezoid
+A plus B plus C plus D. They
+
+lost that entire trapezoid
+gone up to higher prices.
+
+And now we have one other
+player which is the
+
+government.
+
+The government made
+some money.
+
+This is a tax.
+
+How much did the government
+make?
+
+Well we taxed all imports
+by the amount P sub
+
+t minus P sub w.
+
+So the government made the
+rectangle C. The government
+
+made C because we got
+to tax all the
+
+important at that tariff.
+
+So on net, society as a whole
+is worse off by B plus D.
+
+Consumers have lost the entire
+A plus B plus C plus D.
+
+Producers got some of that, the
+
+government got some of that.
+
+But some of it's dead
+weight loss.
+
+Trades that would have made
+consumers better off, and
+
+worldwide producers better off
+that are not happening.
+
+So this tariff, it
+had its effect.
+
+It lowered imports.
+
+But at the same time it lowered
+social surplus.
+
+So restrictions on trade
+lower welfare.
+
+And this is why economists
+like free trade.
+
+Because restrictions on
+trade lower welfare.
+
+Are there questions
+about that?
+
+Moreover, this is just what
+we call static analysis.
+
+What else could happen if the
+US government voted a tariff
+
+on roses coming from Colombia?
+
+What else might happen?
+
+Yeah?
+
+AUDIENCE: Colombia might vote
+for a tariff on the U.S.
+
+PROFESSOR: Columbia might vote
+for a tariff against computers
+
+coming from the US.
+
+Which of course would hurt
+Colombian consumers.
+
+But would also hurt
+US producers.
+
+So from the US's prospective,
+that would be even worse.
+
+So think about it--
+
+we put a tariff on Colombian
+roses which hurt us.
+
+Then Colombia puts a tariffs on
+US computers which hurts us
+
+even further-- hurts Colombia
+too, but we don't care about
+
+them, we care about us.
+
+It hurts us even further.
+
+So dynamically restrictions on
+trade can be even worse than
+
+it looks in this diagram.
+
+If they cause a trade war you
+can actually end up with
+
+things being even worse than
+you look at this diagram.
+
+So we talked about why
+economists like free trade--
+
+partly so that the gains
+to consumers exceed
+
+the losses to producers.
+
+But partly it's because free
+trade begets free trade.
+
+And that exports make
+us better off too.
+
+So by allowing free trade not
+only do we increase our
+
+welfare by having more imports,
+we also increased our
+
+welfare by allowing
+more exports.
+
+And in fact, producers as a
+class, if they could all get
+
+together and have a cooperative
+equilibrium, they
+
+might be fine without
+restrictions of trade.
+
+Because the computer producers
+and the rose producers get
+
+together and say, wait a second,
+we can trade, on net
+
+we win from this.
+
+On net we win from free trade.
+
+Let's get together
+and make a deal.
+
+But of course we know that's
+going to be an incredibly hard
+
+cooperative equilibrium
+to enforce.
+
+And that's why you have
+different sets of producers.
+
+You have the rose producers
+lobbying the congressmen.
+
+Then they leave and the computer
+producers walk in his
+
+office and lobby him
+the other way.
+
+So you have producers lobbying
+for different effects
+
+depending if they're
+competing with
+
+imports or they're exporting.
+
+They're going to lobby for and
+against trade restrictions.
+
+Moreover, there's yet another
+thing we've missed.
+
+There's yet another thing
+we've missed.
+
+So we've talked about the
+dead weight loss.
+
+We've talked about trade wars.
+
+But let's say for a second--
+let's think
+
+about a third thing.
+
+Let's say for a second
+we're not just
+
+heartless selfish Americans.
+
+But we actually do care about
+the rest of the world.
+
+Well the third thing we miss
+is allowing trade from
+
+Colombia makes Colombia
+better off too.
+
+So not only have we improved
+our welfare by importing
+
+Colombian roses, we've improved
+their welfare too.
+
+And they're a poor country.
+
+And we should be happy to
+improve their welfare too.
+
+We think about free
+trade in Vietnam.
+
+That is the application
+for child labor.
+
+By allowing the import of
+Vietnamese rice we improved
+
+the lives of the Vietnamese
+children.
+
+So independent of the fact we've
+made our lives better
+
+off we've made these
+other country's
+
+lives better off too.
+
+So there's three reasons why
+we should have free trade.
+
+There's the simple welfare
+gain, there's the dynamic
+
+welfare gain, and there's the
+fact that we might care about
+
+the welfare of other
+countries as well.
+
+And as a result, there's been
+a huge emphasis over time in
+
+trying to increase free trade.
+
+By economists saying this for
+years, things going back to
+
+the early economists.
+
+But we've made a lot of headway
+in the last 20 years.
+
+And in particular, one big
+source of headway was NAFTA--
+
+The North American Free
+Trade Agreement.
+
+Which was passed
+under Clinton.
+
+Which basically demolished trade
+barriers between Canada
+
+the US and Mexico.
+
+There used to be a lot
+of trade barriers.
+
+We would tax Canadian lumber.
+
+They would tax our computers.
+
+We would tax Mexican whatever
+they sent to us.
+
+They would tax our stuff.
+
+It was a mess.
+
+So basically NAFTA said let's
+just get rid of all of it.
+
+Let's have a cooperative
+agreement.
+
+Let's have a cooperative
+agreement whereby we all agree
+
+to get rid of trade barriers and
+thereby making all of us
+
+better off.
+
+And it seems like it would be
+a pretty simple thing to do.
+
+But it was a mess.
+
+And it was very hard.
+
+And it was very hard because now
+you had parties in every
+
+country opposing this.
+
+You had you had the
+Canadian computer
+
+producers getting upset.
+
+You had the Mexican computer
+producers getting upset.
+
+You had the US lumber industry
+getting upset.
+
+And you had huge difficulties
+because you had parties in
+
+every case opposing it.
+
+And the reason free trade
+agreements are so difficult--
+
+now eventually NAFTA did pass.
+
+And has been by most measures
+a huge success.
+
+But ultimately the major
+difficulty here is in another
+
+failure of government policy.
+
+Which is the inability of the
+government to effectively tax
+
+the winners and compensate
+the losers from
+
+international trade.
+
+That is--
+
+if the government could
+work as a perfect--
+
+in the way that I design
+it to work--
+
+what would happen is that we
+would tax sweatshirts and take
+
+the money from taxing
+sweatshirts and send it to
+
+compensate the guys who lost
+jobs in the textile industry.
+
+And if we did that, we can make
+life much better off than
+
+with the tariff.
+
+So if consider two outcomes.
+
+One is we don't import
+Chinese sweatshirts.
+
+The other is that we import them
+but we levy a small tax
+
+on all sweatshirts not just
+Chinese lectures.
+
+Levy a small tax on
+all sweatshirts.
+
+We import Chinese sweatshirts
+but then we levy a tax on all
+
+sweatshirts.
+
+And we use that sweatshirt tax
+money to pay off the guys who
+
+lost their jobs in the
+textile industry.
+
+That would be better for society
+than would not allow
+
+sweatshirts to come in
+in the first place.
+
+So the fundamental failure in
+trade policy ultimately is a
+
+failure is that inability of the
+government to effectively
+
+compensate the losers by
+taxing the winners.
+
+Because just as the losers know
+to go to lobby Congress,
+
+the winners will get pissed
+off if you start taxing
+
+sweatshirts.
+
+Because they don't realize that
+they're saving all this
+
+money from all these imports.
+
+And in fact the typical American
+voter would probably
+
+vote to block Chinese imports
+before they'd vote to have a
+
+tax on their sweatshirts.
+
+So really in some sense when you
+have a very concentrated
+
+set of winners or losers
+competing against a very
+
+concentrated set of losers,
+defeating against a very
+
+diffuse set of winners, that's a
+hard policy to get in place.
+
+Unless you can figure out a way
+to get those winners to
+
+compensate the losers.
+
+And that's the tricky thing.
+
+Are there question about that?
+
+About free trade agreements,
+things like that?
+
+Now what I want to talk about
+for a couple minutes then one
+
+subtlety in these free
+trade agreements.
+
+And why things like
+NAFTA are hard.
+
+And the reason they're
+hard is because this
+
+makes enormous sense.
+
+Free trade agreements make
+enormous sense if it's true
+
+comparative advantage like
+Canada has more trees.
+
+But what if Mexico's source of
+comparative advantage is that
+
+they treat their workers
+like shit.
+
+What if China's source of
+comparative advantage is that
+
+they have incredibly bad
+working conditions?
+
+And they have incredibly bad
+environmental conditions?
+
+China has an incredibly bad
+environmental situation.
+
+It is incredibly dangerous
+just to live in
+
+major Chinese cities.
+
+The working conditions
+are awful.
+
+The wages are terrible.
+
+Nonetheless, the result is
+very, very cheap labor.
+
+Then things get a
+little dicier.
+
+Because if the Chinese labor was
+cheap or Mexican labor was
+
+cheap just because inherently
+that was just
+
+the way life was.
+
+At the same working conditions
+and the same environmental
+
+conditions they were just
+cheaper, then that's great.
+
+That's the comparative
+advantage.
+
+But if they're cheap because
+they exploit their population
+
+and put them in horrible working
+conditions and facing
+
+horrible environmental
+conditions, then the welfare
+
+gets a little trickier.
+
+From the US's prospective it
+doesn't get any trickier.
+
+The US--
+
+our welfare is exactly
+the same.
+
+We get these static and dynamic
+gains from trade.
+
+But from a world perspective,
+now we're maybe not so sure we
+
+want to promote Mexico producing
+more clothes or
+
+China producing more clothes.
+
+Because it could just lead to
+more exploitation of the
+
+population.
+
+So this comes back to when I
+talked about free trade in
+
+Vietnam and child labor.
+
+Which is if free trade actually
+let to an increased
+
+use of child labor in Vietnam we
+might worry that gee maybe
+
+this isn't such a good thing.
+
+So really what it comes down
+to is we have to think not
+
+just about the simple
+dead weight loss
+
+triangles and squares.
+
+We have to think about some
+broader social issues as well.
+
+And once again there is
+a right answer here.
+
+And this is what a lot was
+fought over with NAFTA.
+
+Which is one of the conditions
+for NAFTA was the US actually
+
+lobbied and got significantly
+improved work and
+
+environmental standards
+in Mexico.
+
+This was like an opposite
+of a trade war.
+
+Instead of being a vicious
+cycle, this
+
+was a virtuous cycle.
+
+We actually improved the life
+for workers in Mexico because
+
+Mexico is willing to do that in
+order to get the benefits
+
+of trade with the US.
+
+So just like limiting trade with
+Mexico will hurt us and
+
+hurt Mexico, expanding trade
+with Mexico and then tying it
+
+to improve work conditions and
+environmental conditions can
+
+make both countries really
+much better off.
+
+And so that's where, once again,
+trade becomes very
+
+interesting.
+
+And why it's worth
+studying further.
+
+Because it's not as simple
+as these boxes.
+
+It's thinking about
+where comparative
+
+advantage comes from.
+
+And whether we really want to
+promote trade with countries
+
+that have comparative advantage
+depending on the
+
+source of what that comparative
+advantage is.
+
+And that's sort of
+the free trade
+
+versus fair trade argument.
+
+The bottom line in
+that argument--
+
+the free trade versus fair trade
+argument-- the bottom
+
+line is free trade is
+always a good thing.
+
+But fair trade considerations
+can be used to try to make it
+
+work better than just simply
+unfettered free trade.
+
+And so really both sides have
+a point in this debate.
+
+So let me stop there.
+
+That's international trade.
+
+We're going to come back on
+Wednesday to talk about
+
+uncertainty and whether you
+should play the lottery.
\ No newline at end of file
diff --git a/pCoDwHg5Vh8.txt b/pCoDwHg5Vh8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d65ff5bd580c2b37707be3d6d3c982f84acffd1f
--- /dev/null
+++ b/pCoDwHg5Vh8.txt
@@ -0,0 +1,2259 @@
+align:start position:0%
+ 
+welcome back to 8701
+
+ align:start position:0%
+welcome back to 8701
+ 
+
+ align:start position:0%
+welcome back to 8701
+in this lecture we talk about cp
+
+ align:start position:0%
+in this lecture we talk about cp
+ 
+
+ align:start position:0%
+in this lecture we talk about cp
+symmetry or cp violation
+
+ align:start position:0%
+symmetry or cp violation
+ 
+
+ align:start position:0%
+symmetry or cp violation
+in previous lectures we discussed that
+
+ align:start position:0%
+in previous lectures we discussed that
+ 
+
+ align:start position:0%
+in previous lectures we discussed that
+the weak interaction is not invariant
+
+ align:start position:0%
+the weak interaction is not invariant
+ 
+
+ align:start position:0%
+the weak interaction is not invariant
+under parity and charge conjugation
+
+ align:start position:0%
+under parity and charge conjugation
+ 
+
+ align:start position:0%
+under parity and charge conjugation
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+but now we can ask the question how
+
+ align:start position:0%
+but now we can ask the question how
+ 
+
+ align:start position:0%
+but now we can ask the question how
+about cp
+
+ align:start position:0%
+about cp
+ 
+
+ align:start position:0%
+about cp
+so a transformation which does charge
+
+ align:start position:0%
+so a transformation which does charge
+ 
+
+ align:start position:0%
+so a transformation which does charge
+conjugation and
+
+ align:start position:0%
+conjugation and
+ 
+
+ align:start position:0%
+conjugation and
+parity transformation so the classical
+
+ align:start position:0%
+parity transformation so the classical
+ 
+
+ align:start position:0%
+parity transformation so the classical
+example to show parity violation is
+
+ align:start position:0%
+example to show parity violation is
+ 
+
+ align:start position:0%
+example to show parity violation is
+the decay of a pion so we have here
+
+ align:start position:0%
+the decay of a pion so we have here
+ 
+
+ align:start position:0%
+the decay of a pion so we have here
+this um charged pioneers in zero
+
+ align:start position:0%
+this um charged pioneers in zero
+ 
+
+ align:start position:0%
+this um charged pioneers in zero
+and it decays into a neuron and a
+
+ align:start position:0%
+and it decays into a neuron and a
+ 
+
+ align:start position:0%
+and it decays into a neuron and a
+neutrino an anti-muon and a neutrino
+
+ align:start position:0%
+neutrino an anti-muon and a neutrino
+ 
+
+ align:start position:0%
+neutrino an anti-muon and a neutrino
+and so since the neutrino is left-handed
+
+ align:start position:0%
+and so since the neutrino is left-handed
+ 
+
+ align:start position:0%
+and so since the neutrino is left-handed
+the out of the decay coming
+
+ align:start position:0%
+the out of the decay coming
+ 
+
+ align:start position:0%
+the out of the decay coming
+anti-muron needs to be left-handed as
+
+ align:start position:0%
+anti-muron needs to be left-handed as
+ 
+
+ align:start position:0%
+anti-muron needs to be left-handed as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+so if you do parity transformation of
+
+ align:start position:0%
+so if you do parity transformation of
+ 
+
+ align:start position:0%
+so if you do parity transformation of
+this decay you see that the outcoming
+
+ align:start position:0%
+this decay you see that the outcoming
+ 
+
+ align:start position:0%
+this decay you see that the outcoming
+muon would be right-handed on the other
+
+ align:start position:0%
+muon would be right-handed on the other
+ 
+
+ align:start position:0%
+muon would be right-handed on the other
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+there is no right-handed adrenal and
+
+ align:start position:0%
+there is no right-handed adrenal and
+ 
+
+ align:start position:0%
+there is no right-handed adrenal and
+therefore this decay is not possible
+
+ align:start position:0%
+therefore this decay is not possible
+ 
+
+ align:start position:0%
+therefore this decay is not possible
+so this is not so this mirror symmetry
+
+ align:start position:0%
+so this is not so this mirror symmetry
+ 
+
+ align:start position:0%
+so this is not so this mirror symmetry
+is not realized in nature
+
+ align:start position:0%
+is not realized in nature
+ 
+
+ align:start position:0%
+is not realized in nature
+it's a consequence of the weak
+
+ align:start position:0%
+it's a consequence of the weak
+ 
+
+ align:start position:0%
+it's a consequence of the weak
+interaction so similarly we could do a
+
+ align:start position:0%
+interaction so similarly we could do a
+ 
+
+ align:start position:0%
+interaction so similarly we could do a
+charge transformation
+
+ align:start position:0%
+charge transformation
+ 
+
+ align:start position:0%
+charge transformation
+charge conjugation of this decay so you
+
+ align:start position:0%
+charge conjugation of this decay so you
+ 
+
+ align:start position:0%
+charge conjugation of this decay so you
+turn
+
+ align:start position:0%
+turn
+ 
+
+ align:start position:0%
+turn
+particles into the anti-particles and
+
+ align:start position:0%
+particles into the anti-particles and
+ 
+
+ align:start position:0%
+particles into the anti-particles and
+you find here
+
+ align:start position:0%
+you find here
+ 
+
+ align:start position:0%
+you find here
+this anti-neutrino which is left-handed
+
+ align:start position:0%
+this anti-neutrino which is left-handed
+ 
+
+ align:start position:0%
+this anti-neutrino which is left-handed
+and also those don't exist in nature
+
+ align:start position:0%
+and also those don't exist in nature
+ 
+
+ align:start position:0%
+and also those don't exist in nature
+so parity or charged conjugation doesn't
+
+ align:start position:0%
+so parity or charged conjugation doesn't
+ 
+
+ align:start position:0%
+so parity or charged conjugation doesn't
+really work on those decays those weak
+
+ align:start position:0%
+really work on those decays those weak
+ 
+
+ align:start position:0%
+really work on those decays those weak
+decays but what does work if you apply
+
+ align:start position:0%
+decays but what does work if you apply
+ 
+
+ align:start position:0%
+decays but what does work if you apply
+the parity and charge conjugation
+
+ align:start position:0%
+the parity and charge conjugation
+ 
+
+ align:start position:0%
+the parity and charge conjugation
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+you turn the positively charged
+
+ align:start position:0%
+you turn the positively charged
+ 
+
+ align:start position:0%
+you turn the positively charged
+pion into a negatively charged spine
+
+ align:start position:0%
+pion into a negatively charged spine
+ 
+
+ align:start position:0%
+pion into a negatively charged spine
+the antimural intermediary and the
+
+ align:start position:0%
+the antimural intermediary and the
+ 
+
+ align:start position:0%
+the antimural intermediary and the
+neutrino and an antineutrino
+
+ align:start position:0%
+neutrino and an antineutrino
+ 
+
+ align:start position:0%
+neutrino and an antineutrino
+and you see here that the antineutrino
+
+ align:start position:0%
+and you see here that the antineutrino
+ 
+
+ align:start position:0%
+and you see here that the antineutrino
+is right handed
+
+ align:start position:0%
+is right handed
+ 
+
+ align:start position:0%
+is right handed
+um so is the the muon and so that decay
+
+ align:start position:0%
+um so is the the muon and so that decay
+ 
+
+ align:start position:0%
+um so is the the muon and so that decay
+is actually observed in nature
+
+ align:start position:0%
+is actually observed in nature
+ 
+
+ align:start position:0%
+is actually observed in nature
+good so we saved the day you know it
+
+ align:start position:0%
+good so we saved the day you know it
+ 
+
+ align:start position:0%
+good so we saved the day you know it
+seems like
+
+ align:start position:0%
+seems like
+ 
+
+ align:start position:0%
+seems like
+that cp that the weak interaction is
+
+ align:start position:0%
+that cp that the weak interaction is
+ 
+
+ align:start position:0%
+that cp that the weak interaction is
+invariant
+
+ align:start position:0%
+invariant
+ 
+
+ align:start position:0%
+invariant
+under cp transformation however
+
+ align:start position:0%
+under cp transformation however
+ 
+
+ align:start position:0%
+under cp transformation however
+that's not quite true um
+
+ align:start position:0%
+that's not quite true um
+ 
+
+ align:start position:0%
+that's not quite true um
+german and pace noted that in
+
+ align:start position:0%
+german and pace noted that in
+ 
+
+ align:start position:0%
+german and pace noted that in
+systems of neutral chaons there's an odd
+
+ align:start position:0%
+systems of neutral chaons there's an odd
+ 
+
+ align:start position:0%
+systems of neutral chaons there's an odd
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+and the fact is that a particle a k knot
+
+ align:start position:0%
+and the fact is that a particle a k knot
+ 
+
+ align:start position:0%
+and the fact is that a particle a k knot
+can turn into an anti-particle
+
+ align:start position:0%
+can turn into an anti-particle
+ 
+
+ align:start position:0%
+can turn into an anti-particle
+by changing the strangeness
+
+ align:start position:0%
+by changing the strangeness
+ 
+
+ align:start position:0%
+by changing the strangeness
+and that's possible in these kind of
+
+ align:start position:0%
+and that's possible in these kind of
+ 
+
+ align:start position:0%
+and that's possible in these kind of
+box diagrams which include you know a
+
+ align:start position:0%
+box diagrams which include you know a
+ 
+
+ align:start position:0%
+box diagrams which include you know a
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+with a couple of w's um
+
+ align:start position:0%
+with a couple of w's um
+ 
+
+ align:start position:0%
+with a couple of w's um
+and it's easy to see that you know if
+
+ align:start position:0%
+and it's easy to see that you know if
+ 
+
+ align:start position:0%
+and it's easy to see that you know if
+you could prepare
+
+ align:start position:0%
+you could prepare
+ 
+
+ align:start position:0%
+you could prepare
+prepare uh you know decay on it will
+
+ align:start position:0%
+prepare uh you know decay on it will
+ 
+
+ align:start position:0%
+prepare uh you know decay on it will
+oscillate because those diagrams are
+
+ align:start position:0%
+oscillate because those diagrams are
+ 
+
+ align:start position:0%
+oscillate because those diagrams are
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+into an anti-particle so now what is
+
+ align:start position:0%
+into an anti-particle so now what is
+ 
+
+ align:start position:0%
+into an anti-particle so now what is
+happening now to cp here
+
+ align:start position:0%
+happening now to cp here
+ 
+
+ align:start position:0%
+happening now to cp here
+if i apply cp on a k on i find a minus
+
+ align:start position:0%
+if i apply cp on a k on i find a minus
+ 
+
+ align:start position:0%
+if i apply cp on a k on i find a minus
+sign in an antique
+
+ align:start position:0%
+sign in an antique
+ 
+
+ align:start position:0%
+sign in an antique
+so if you want to analyze this further
+
+ align:start position:0%
+so if you want to analyze this further
+ 
+
+ align:start position:0%
+so if you want to analyze this further
+you might want to find the eigenstates
+
+ align:start position:0%
+you might want to find the eigenstates
+ 
+
+ align:start position:0%
+you might want to find the eigenstates
+to this and so the eigenstates can be
+
+ align:start position:0%
+to this and so the eigenstates can be
+ 
+
+ align:start position:0%
+to this and so the eigenstates can be
+found as k1 and k2 which are up mixtures
+
+ align:start position:0%
+found as k1 and k2 which are up mixtures
+ 
+
+ align:start position:0%
+found as k1 and k2 which are up mixtures
+of the k naught and the on decay knot
+
+ align:start position:0%
+of the k naught and the on decay knot
+ 
+
+ align:start position:0%
+of the k naught and the on decay knot
+you find this symmetric the symmetric
+
+ align:start position:0%
+you find this symmetric the symmetric
+ 
+
+ align:start position:0%
+you find this symmetric the symmetric
+and the antisymmetric
+
+ align:start position:0%
+and the antisymmetric
+ 
+
+ align:start position:0%
+and the antisymmetric
+states good so if you apply cp on the
+
+ align:start position:0%
+states good so if you apply cp on the
+ 
+
+ align:start position:0%
+states good so if you apply cp on the
+eigen
+
+ align:start position:0%
+eigen
+ 
+
+ align:start position:0%
+eigen
+states you find eigenvalues of one and
+
+ align:start position:0%
+states you find eigenvalues of one and
+ 
+
+ align:start position:0%
+states you find eigenvalues of one and
+minus one
+
+ align:start position:0%
+minus one
+ 
+
+ align:start position:0%
+minus one
+it turns out that the lifetime of the k1
+
+ align:start position:0%
+it turns out that the lifetime of the k1
+ 
+
+ align:start position:0%
+it turns out that the lifetime of the k1
+and the k2 those eigenstates
+
+ align:start position:0%
+and the k2 those eigenstates
+ 
+
+ align:start position:0%
+and the k2 those eigenstates
+is very different you know one is 10 to
+
+ align:start position:0%
+is very different you know one is 10 to
+ 
+
+ align:start position:0%
+is very different you know one is 10 to
+the minus 10 and one is 5 times 10 to
+
+ align:start position:0%
+the minus 10 and one is 5 times 10 to
+ 
+
+ align:start position:0%
+the minus 10 and one is 5 times 10 to
+the minus 8.
+
+ align:start position:0%
+the minus 8.
+ 
+
+ align:start position:0%
+the minus 8.
+so the k1 decays much much quicker than
+
+ align:start position:0%
+so the k1 decays much much quicker than
+ 
+
+ align:start position:0%
+so the k1 decays much much quicker than
+the k2
+
+ align:start position:0%
+the k2
+ 
+
+ align:start position:0%
+the k2
+so this then sets the stage to a test of
+
+ align:start position:0%
+so this then sets the stage to a test of
+ 
+
+ align:start position:0%
+so this then sets the stage to a test of
+cp
+
+ align:start position:0%
+cp
+ 
+
+ align:start position:0%
+cp
+violation so what you're going to do is
+
+ align:start position:0%
+violation so what you're going to do is
+ 
+
+ align:start position:0%
+violation so what you're going to do is
+prepare a beam of
+
+ align:start position:0%
+prepare a beam of
+ 
+
+ align:start position:0%
+prepare a beam of
+decay 0s and that's mdk
+
+ align:start position:0%
+decay 0s and that's mdk
+ 
+
+ align:start position:0%
+decay 0s and that's mdk
+um and only after some time you study
+
+ align:start position:0%
+um and only after some time you study
+ 
+
+ align:start position:0%
+um and only after some time you study
+the beam again
+
+ align:start position:0%
+the beam again
+ 
+
+ align:start position:0%
+the beam again
+which then should be made up solely of
+
+ align:start position:0%
+which then should be made up solely of
+ 
+
+ align:start position:0%
+which then should be made up solely of
+k2
+
+ align:start position:0%
+k2
+ 
+
+ align:start position:0%
+k2
+so if you in that beam observe the case
+
+ align:start position:0%
+so if you in that beam observe the case
+ 
+
+ align:start position:0%
+so if you in that beam observe the case
+of the k2 into two pions
+
+ align:start position:0%
+of the k2 into two pions
+ 
+
+ align:start position:0%
+of the k2 into two pions
+you noted that there is an add mixture
+
+ align:start position:0%
+you noted that there is an add mixture
+ 
+
+ align:start position:0%
+you noted that there is an add mixture
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+um which violates cp
+
+ align:start position:0%
+um which violates cp
+ 
+
+ align:start position:0%
+um which violates cp
+so you have an admixture of k1's in in
+
+ align:start position:0%
+so you have an admixture of k1's in in
+ 
+
+ align:start position:0%
+so you have an admixture of k1's in in
+in a beam which should just be of k2s
+
+ align:start position:0%
+in a beam which should just be of k2s
+ 
+
+ align:start position:0%
+in a beam which should just be of k2s
+so that mixture then will violate
+
+ align:start position:0%
+so that mixture then will violate
+ 
+
+ align:start position:0%
+so that mixture then will violate
+cp invariants and exactly that was done
+
+ align:start position:0%
+cp invariants and exactly that was done
+ 
+
+ align:start position:0%
+cp invariants and exactly that was done
+so cronin and fitch picked up this idea
+
+ align:start position:0%
+so cronin and fitch picked up this idea
+ 
+
+ align:start position:0%
+so cronin and fitch picked up this idea
+they have set up an experiment
+
+ align:start position:0%
+they have set up an experiment
+ 
+
+ align:start position:0%
+they have set up an experiment
+in which they produced chaons they had
+
+ align:start position:0%
+in which they produced chaons they had
+ 
+
+ align:start position:0%
+in which they produced chaons they had
+them decay
+
+ align:start position:0%
+them decay
+ 
+
+ align:start position:0%
+them decay
+and then they studied later in the beam
+
+ align:start position:0%
+and then they studied later in the beam
+ 
+
+ align:start position:0%
+and then they studied later in the beam
+whether or not
+
+ align:start position:0%
+whether or not
+ 
+
+ align:start position:0%
+whether or not
+they could find to priority case and
+
+ align:start position:0%
+they could find to priority case and
+ 
+
+ align:start position:0%
+they could find to priority case and
+they did
+
+ align:start position:0%
+they did
+ 
+
+ align:start position:0%
+they did
+indeed observe 42 or 45
+
+ align:start position:0%
+indeed observe 42 or 45
+ 
+
+ align:start position:0%
+indeed observe 42 or 45
+by mdks two pion decays in a total of 22
+
+ align:start position:0%
+by mdks two pion decays in a total of 22
+ 
+
+ align:start position:0%
+by mdks two pion decays in a total of 22
+700 decays so that means that this k
+
+ align:start position:0%
+700 decays so that means that this k
+ 
+
+ align:start position:0%
+700 decays so that means that this k
+long beam the long lift k on beam
+
+ align:start position:0%
+long beam the long lift k on beam
+ 
+
+ align:start position:0%
+long beam the long lift k on beam
+is actually an arc mixture of k2
+
+ align:start position:0%
+is actually an arc mixture of k2
+ 
+
+ align:start position:0%
+is actually an arc mixture of k2
+with a small additional component of k1
+
+ align:start position:0%
+with a small additional component of k1
+ 
+
+ align:start position:0%
+with a small additional component of k1
+so here they observed um
+
+ align:start position:0%
+so here they observed um
+ 
+
+ align:start position:0%
+so here they observed um
+cp violation through the mixture of
+
+ align:start position:0%
+cp violation through the mixture of
+ 
+
+ align:start position:0%
+cp violation through the mixture of
+those states and this epsilon gives you
+
+ align:start position:0%
+those states and this epsilon gives you
+ 
+
+ align:start position:0%
+those states and this epsilon gives you
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+you know size of the strength of the cp
+
+ align:start position:0%
+you know size of the strength of the cp
+ 
+
+ align:start position:0%
+you know size of the strength of the cp
+violation
+
+ align:start position:0%
+violation
+ 
+
+ align:start position:0%
+violation
+um so here's a note of the paper we'll
+
+ align:start position:0%
+um so here's a note of the paper we'll
+ 
+
+ align:start position:0%
+um so here's a note of the paper we'll
+have another discussion of this
+
+ align:start position:0%
+have another discussion of this
+ 
+
+ align:start position:0%
+have another discussion of this
+in class by student presentation um
+
+ align:start position:0%
+in class by student presentation um
+ 
+
+ align:start position:0%
+in class by student presentation um
+croning and fitch here this is croning
+
+ align:start position:0%
+croning and fitch here this is croning
+ 
+
+ align:start position:0%
+croning and fitch here this is croning
+this is fitch it turns out that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know croning is actually a student
+
+ align:start position:0%
+you know croning is actually a student
+ 
+
+ align:start position:0%
+you know croning is actually a student
+or was a student of enrico fermi and
+
+ align:start position:0%
+or was a student of enrico fermi and
+ 
+
+ align:start position:0%
+or was a student of enrico fermi and
+also worked in chicago
+
+ align:start position:0%
+also worked in chicago
+ 
+
+ align:start position:0%
+also worked in chicago
+uh so there's quite an interesting
+
+ align:start position:0%
+uh so there's quite an interesting
+ 
+
+ align:start position:0%
+uh so there's quite an interesting
+family tree here
+
+ align:start position:0%
+family tree here
+ 
+
+ align:start position:0%
+family tree here
+uh to which also um gerry friedman
+
+ align:start position:0%
+uh to which also um gerry friedman
+ 
+
+ align:start position:0%
+uh to which also um gerry friedman
+belongs
+
+ align:start position:0%
+belongs
+ 
+
+ align:start position:0%
+belongs
+gerald friedman is a retired faculty at
+
+ align:start position:0%
+gerald friedman is a retired faculty at
+ 
+
+ align:start position:0%
+gerald friedman is a retired faculty at
+mit
+
+ align:start position:0%
+mit
+ 
+
+ align:start position:0%
+mit
+and discovered that protons are made out
+
+ align:start position:0%
+and discovered that protons are made out
+ 
+
+ align:start position:0%
+and discovered that protons are made out
+of cork so this is a very interesting
+
+ align:start position:0%
+of cork so this is a very interesting
+ 
+
+ align:start position:0%
+of cork so this is a very interesting
+family tree if you have some time you
+
+ align:start position:0%
+family tree if you have some time you
+ 
+
+ align:start position:0%
+family tree if you have some time you
+might want to look into this
+
+ align:start position:0%
+might want to look into this
+ 
+
+ align:start position:0%
+might want to look into this
+so here's the experiment so you take
+
+ align:start position:0%
+so here's the experiment so you take
+ 
+
+ align:start position:0%
+so here's the experiment so you take
+protons you dump them into a beam
+
+ align:start position:0%
+protons you dump them into a beam
+ 
+
+ align:start position:0%
+protons you dump them into a beam
+you try to with this um this magnet
+
+ align:start position:0%
+you try to with this um this magnet
+ 
+
+ align:start position:0%
+you try to with this um this magnet
+filter out the neutral component
+
+ align:start position:0%
+filter out the neutral component
+ 
+
+ align:start position:0%
+filter out the neutral component
+uh get rid of all photons and then let
+
+ align:start position:0%
+uh get rid of all photons and then let
+ 
+
+ align:start position:0%
+uh get rid of all photons and then let
+this beam decay
+
+ align:start position:0%
+this beam decay
+ 
+
+ align:start position:0%
+this beam decay
+uh and look in the spectrometer are for
+
+ align:start position:0%
+uh and look in the spectrometer are for
+ 
+
+ align:start position:0%
+uh and look in the spectrometer are for
+the case of two photons here's a bigger
+
+ align:start position:0%
+the case of two photons here's a bigger
+ 
+
+ align:start position:0%
+the case of two photons here's a bigger
+picture of the same spectrometer
+
+ align:start position:0%
+picture of the same spectrometer
+ 
+
+ align:start position:0%
+picture of the same spectrometer
+so this is basically a blow-up view of
+
+ align:start position:0%
+so this is basically a blow-up view of
+ 
+
+ align:start position:0%
+so this is basically a blow-up view of
+this uh so you have your
+
+ align:start position:0%
+this uh so you have your
+ 
+
+ align:start position:0%
+this uh so you have your
+your kaons and neutral kions coming in
+
+ align:start position:0%
+your kaons and neutral kions coming in
+ 
+
+ align:start position:0%
+your kaons and neutral kions coming in
+the k2's
+
+ align:start position:0%
+the k2's
+ 
+
+ align:start position:0%
+the k2's
+and then you look forward to indicates
+
+ align:start position:0%
+and then you look forward to indicates
+ 
+
+ align:start position:0%
+and then you look forward to indicates
+the instrumentation and how we actually
+
+ align:start position:0%
+the instrumentation and how we actually
+ 
+
+ align:start position:0%
+the instrumentation and how we actually
+would do this
+
+ align:start position:0%
+would do this
+ 
+
+ align:start position:0%
+would do this
+is part of later discussion that we
+
+ align:start position:0%
+is part of later discussion that we
+ 
+
+ align:start position:0%
+is part of later discussion that we
+actually talk about detectors
+
+ align:start position:0%
+actually talk about detectors
+ 
+
+ align:start position:0%
+actually talk about detectors
+in more detail all right
+
+ align:start position:0%
+in more detail all right
+ 
+
+ align:start position:0%
+in more detail all right
+so we just saw that cronin and fitch
+
+ align:start position:0%
+so we just saw that cronin and fitch
+ 
+
+ align:start position:0%
+so we just saw that cronin and fitch
+observed cp violation in mixture of
+
+ align:start position:0%
+observed cp violation in mixture of
+ 
+
+ align:start position:0%
+observed cp violation in mixture of
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+but we can also observe cp violation in
+
+ align:start position:0%
+but we can also observe cp violation in
+ 
+
+ align:start position:0%
+but we can also observe cp violation in
+direct decays
+
+ align:start position:0%
+direct decays
+ 
+
+ align:start position:0%
+direct decays
+and the classical example here is the
+
+ align:start position:0%
+and the classical example here is the
+ 
+
+ align:start position:0%
+and the classical example here is the
+case of the k long
+
+ align:start position:0%
+case of the k long
+ 
+
+ align:start position:0%
+case of the k long
+and semi electronic decay so semi
+
+ align:start position:0%
+and semi electronic decay so semi
+ 
+
+ align:start position:0%
+and semi electronic decay so semi
+electronic here means we have a decay
+
+ align:start position:0%
+electronic here means we have a decay
+ 
+
+ align:start position:0%
+electronic here means we have a decay
+of the k long the neutral particle in a
+
+ align:start position:0%
+of the k long the neutral particle in a
+ 
+
+ align:start position:0%
+of the k long the neutral particle in a
+charged ion
+
+ align:start position:0%
+charged ion
+ 
+
+ align:start position:0%
+charged ion
+an electron an antineutrino or
+
+ align:start position:0%
+an electron an antineutrino or
+ 
+
+ align:start position:0%
+an electron an antineutrino or
+it might very well also decay into
+
+ align:start position:0%
+it might very well also decay into
+ 
+
+ align:start position:0%
+it might very well also decay into
+a pi minus a positron and a neutrino
+
+ align:start position:0%
+a pi minus a positron and a neutrino
+ 
+
+ align:start position:0%
+a pi minus a positron and a neutrino
+and it turns out when you really count
+
+ align:start position:0%
+and it turns out when you really count
+ 
+
+ align:start position:0%
+and it turns out when you really count
+those events
+
+ align:start position:0%
+those events
+ 
+
+ align:start position:0%
+those events
+and perform a precise experiment that
+
+ align:start position:0%
+and perform a precise experiment that
+ 
+
+ align:start position:0%
+and perform a precise experiment that
+the k
+
+ align:start position:0%
+the k
+ 
+
+ align:start position:0%
+the k
+longs prefer the case to positrons over
+
+ align:start position:0%
+longs prefer the case to positrons over
+ 
+
+ align:start position:0%
+longs prefer the case to positrons over
+the case to electrons
+
+ align:start position:0%
+the case to electrons
+ 
+
+ align:start position:0%
+the case to electrons
+and so the fractional amount of this you
+
+ align:start position:0%
+and so the fractional amount of this you
+ 
+
+ align:start position:0%
+and so the fractional amount of this you
+know imbalance
+
+ align:start position:0%
+know imbalance
+ 
+
+ align:start position:0%
+know imbalance
+is 3 times 10 to the minus 3. so this is
+
+ align:start position:0%
+is 3 times 10 to the minus 3. so this is
+ 
+
+ align:start position:0%
+is 3 times 10 to the minus 3. so this is
+a rather small effect again
+
+ align:start position:0%
+a rather small effect again
+ 
+
+ align:start position:0%
+a rather small effect again
+of cp violation here indirect decays
+
+ align:start position:0%
+of cp violation here indirect decays
+ 
+
+ align:start position:0%
+of cp violation here indirect decays
+since then cp violation has also been
+
+ align:start position:0%
+since then cp violation has also been
+ 
+
+ align:start position:0%
+since then cp violation has also been
+shown
+
+ align:start position:0%
+shown
+ 
+
+ align:start position:0%
+shown
+in the decay of b mesons and the program
+
+ align:start position:0%
+in the decay of b mesons and the program
+ 
+
+ align:start position:0%
+in the decay of b mesons and the program
+of studying b mesons is a big part of
+
+ align:start position:0%
+of studying b mesons is a big part of
+ 
+
+ align:start position:0%
+of studying b mesons is a big part of
+the lhc experiment at the lh
+
+ align:start position:0%
+the lhc experiment at the lh
+ 
+
+ align:start position:0%
+the lhc experiment at the lh
+the lhc um there's also experiments in
+
+ align:start position:0%
+the lhc um there's also experiments in
+ 
+
+ align:start position:0%
+the lhc um there's also experiments in
+japan going on right now which study b
+
+ align:start position:0%
+japan going on right now which study b
+ 
+
+ align:start position:0%
+japan going on right now which study b
+maisons
+
+ align:start position:0%
+maisons
+ 
+
+ align:start position:0%
+maisons
+in order to learn further about b
+
+ align:start position:0%
+in order to learn further about b
+ 
+
+ align:start position:0%
+in order to learn further about b
+systems
+
+ align:start position:0%
+systems
+ 
+
+ align:start position:0%
+systems
+tests are also on the way for those who
+
+ align:start position:0%
+tests are also on the way for those who
+ 
+
+ align:start position:0%
+tests are also on the way for those who
+listen to the colloquium on monday
+
+ align:start position:0%
+listen to the colloquium on monday
+ 
+
+ align:start position:0%
+listen to the colloquium on monday
+in the neutrino sector so here we have a
+
+ align:start position:0%
+in the neutrino sector so here we have a
+ 
+
+ align:start position:0%
+in the neutrino sector so here we have a
+completely different part so not
+
+ align:start position:0%
+completely different part so not
+ 
+
+ align:start position:0%
+completely different part so not
+quarks are involved in weak interaction
+
+ align:start position:0%
+quarks are involved in weak interaction
+ 
+
+ align:start position:0%
+quarks are involved in weak interaction
+but neutrinos
+
+ align:start position:0%
+but neutrinos
+ 
+
+ align:start position:0%
+but neutrinos
+and so the question is whether or not in
+
+ align:start position:0%
+and so the question is whether or not in
+ 
+
+ align:start position:0%
+and so the question is whether or not in
+that sector of physics
+
+ align:start position:0%
+that sector of physics
+ 
+
+ align:start position:0%
+that sector of physics
+um that sector of the standard model the
+
+ align:start position:0%
+um that sector of the standard model the
+ 
+
+ align:start position:0%
+um that sector of the standard model the
+scp violation
+
+ align:start position:0%
+scp violation
+ 
+
+ align:start position:0%
+scp violation
+those are aspects we'll discuss later on
+
+ align:start position:0%
+those are aspects we'll discuss later on
+ 
+
+ align:start position:0%
+those are aspects we'll discuss later on
+when we talk about neutrinos
+
+ align:start position:0%
+when we talk about neutrinos
+ 
+
+ align:start position:0%
+when we talk about neutrinos
+specifically
+
+ align:start position:0%
+specifically
+ 
+
+ align:start position:0%
+specifically
+before i close a few more remarks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the meta antimatter
+
+ align:start position:0%
+on the meta antimatter
+ 
+
+ align:start position:0%
+on the meta antimatter
+symmetry so one of the biggest mysteries
+
+ align:start position:0%
+symmetry so one of the biggest mysteries
+ 
+
+ align:start position:0%
+symmetry so one of the biggest mysteries
+in physics i would claim
+
+ align:start position:0%
+in physics i would claim
+ 
+
+ align:start position:0%
+in physics i would claim
+the fact that we are even here to ask
+
+ align:start position:0%
+the fact that we are even here to ask
+ 
+
+ align:start position:0%
+the fact that we are even here to ask
+this question
+
+ align:start position:0%
+this question
+ 
+
+ align:start position:0%
+this question
+um so there is apparently more matter in
+
+ align:start position:0%
+um so there is apparently more matter in
+ 
+
+ align:start position:0%
+um so there is apparently more matter in
+the universe than anti-matter
+
+ align:start position:0%
+the universe than anti-matter
+ 
+
+ align:start position:0%
+the universe than anti-matter
+if you start from a big bang there was
+
+ align:start position:0%
+if you start from a big bang there was
+ 
+
+ align:start position:0%
+if you start from a big bang there was
+this symmetry and now we live in a
+
+ align:start position:0%
+this symmetry and now we live in a
+ 
+
+ align:start position:0%
+this symmetry and now we live in a
+universe which is dominated by meta
+
+ align:start position:0%
+universe which is dominated by meta
+ 
+
+ align:start position:0%
+universe which is dominated by meta
+so how is this possible so in
+
+ align:start position:0%
+so how is this possible so in
+ 
+
+ align:start position:0%
+so how is this possible so in
+1967 sakura proposed
+
+ align:start position:0%
+1967 sakura proposed
+ 
+
+ align:start position:0%
+1967 sakura proposed
+that this is possible in a system where
+
+ align:start position:0%
+that this is possible in a system where
+ 
+
+ align:start position:0%
+that this is possible in a system where
+by your number is violated so this is
+
+ align:start position:0%
+by your number is violated so this is
+ 
+
+ align:start position:0%
+by your number is violated so this is
+almost a trivial statement if you start
+
+ align:start position:0%
+almost a trivial statement if you start
+ 
+
+ align:start position:0%
+almost a trivial statement if you start
+from an equal number of baryons and
+
+ align:start position:0%
+from an equal number of baryons and
+ 
+
+ align:start position:0%
+from an equal number of baryons and
+antibiotics
+
+ align:start position:0%
+antibiotics
+ 
+
+ align:start position:0%
+antibiotics
+the sum is then zero are the barrier
+
+ align:start position:0%
+the sum is then zero are the barrier
+ 
+
+ align:start position:0%
+the sum is then zero are the barrier
+number the zero of this system
+
+ align:start position:0%
+number the zero of this system
+ 
+
+ align:start position:0%
+number the zero of this system
+and you end up in a system which is
+
+ align:start position:0%
+and you end up in a system which is
+ 
+
+ align:start position:0%
+and you end up in a system which is
+dominated by variance then barrier
+
+ align:start position:0%
+dominated by variance then barrier
+ 
+
+ align:start position:0%
+dominated by variance then barrier
+number needs to be violated but
+
+ align:start position:0%
+number needs to be violated but
+ 
+
+ align:start position:0%
+number needs to be violated but
+there's also the need of cp violation in
+
+ align:start position:0%
+there's also the need of cp violation in
+ 
+
+ align:start position:0%
+there's also the need of cp violation in
+this so
+
+ align:start position:0%
+this so
+ 
+
+ align:start position:0%
+this so
+we just saw that this is realized in
+
+ align:start position:0%
+we just saw that this is realized in
+ 
+
+ align:start position:0%
+we just saw that this is realized in
+nature but the amount of cp violation
+
+ align:start position:0%
+nature but the amount of cp violation
+ 
+
+ align:start position:0%
+nature but the amount of cp violation
+you observe in this system i just
+
+ align:start position:0%
+you observe in this system i just
+ 
+
+ align:start position:0%
+you observe in this system i just
+discussed
+
+ align:start position:0%
+discussed
+ 
+
+ align:start position:0%
+discussed
+it's not sufficient to explain the meta
+
+ align:start position:0%
+it's not sufficient to explain the meta
+ 
+
+ align:start position:0%
+it's not sufficient to explain the meta
+antimatter symmetry we observed in
+
+ align:start position:0%
+antimatter symmetry we observed in
+ 
+
+ align:start position:0%
+antimatter symmetry we observed in
+nature so there is more to be found
+
+ align:start position:0%
+nature so there is more to be found
+ 
+
+ align:start position:0%
+nature so there is more to be found
+there's new physics to be
+
+ align:start position:0%
+there's new physics to be
+ 
+
+ align:start position:0%
+there's new physics to be
+looked for um in in cp violation on this
+
+ align:start position:0%
+looked for um in in cp violation on this
+ 
+
+ align:start position:0%
+looked for um in in cp violation on this
+overall question
+
+ align:start position:0%
+overall question
+ 
+
+ align:start position:0%
+overall question
+and there's also need for um
+
+ align:start position:0%
+and there's also need for um
+ 
+
+ align:start position:0%
+and there's also need for um
+interactions to be out of
+
+ align:start position:0%
+interactions to be out of
+ 
+
+ align:start position:0%
+interactions to be out of
+equilibrium meaning that you don't you
+
+ align:start position:0%
+equilibrium meaning that you don't you
+ 
+
+ align:start position:0%
+equilibrium meaning that you don't you
+know revert the processes
+
+ align:start position:0%
+know revert the processes
+ 
+
+ align:start position:0%
+know revert the processes
+as you go forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yet another point of discussion which
+
+ align:start position:0%
+um yet another point of discussion which
+ 
+
+ align:start position:0%
+um yet another point of discussion which
+i will not go into much detail
+
+ align:start position:0%
+i will not go into much detail
+ 
+
+ align:start position:0%
+i will not go into much detail
+in this lecture is that you know our
+
+ align:start position:0%
+in this lecture is that you know our
+ 
+
+ align:start position:0%
+in this lecture is that you know our
+quantum field theory which describes
+
+ align:start position:0%
+quantum field theory which describes
+ 
+
+ align:start position:0%
+quantum field theory which describes
+calls the standard model and describes
+
+ align:start position:0%
+calls the standard model and describes
+ 
+
+ align:start position:0%
+calls the standard model and describes
+the interaction of particles
+
+ align:start position:0%
+the interaction of particles
+ 
+
+ align:start position:0%
+the interaction of particles
+is invariant under cpt transformations
+
+ align:start position:0%
+is invariant under cpt transformations
+ 
+
+ align:start position:0%
+is invariant under cpt transformations
+that means that
+
+ align:start position:0%
+that means that
+ 
+
+ align:start position:0%
+that means that
+if cp is violated time reversal
+
+ align:start position:0%
+if cp is violated time reversal
+ 
+
+ align:start position:0%
+if cp is violated time reversal
+cannot uh be a symmetry so meaning going
+
+ align:start position:0%
+cannot uh be a symmetry so meaning going
+ 
+
+ align:start position:0%
+cannot uh be a symmetry so meaning going
+backwards and forward in time is not
+
+ align:start position:0%
+backwards and forward in time is not
+ 
+
+ align:start position:0%
+backwards and forward in time is not
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+um and you can test this you can uh
+
+ align:start position:0%
+um and you can test this you can uh
+ 
+
+ align:start position:0%
+um and you can test this you can uh
+experiments which test
+
+ align:start position:0%
+experiments which test
+ 
+
+ align:start position:0%
+experiments which test
+that effect that fact you can also
+
+ align:start position:0%
+that effect that fact you can also
+ 
+
+ align:start position:0%
+that effect that fact you can also
+design experiments which test cpt
+
+ align:start position:0%
+design experiments which test cpt
+ 
+
+ align:start position:0%
+design experiments which test cpt
+directly so this is those are all
+
+ align:start position:0%
+directly so this is those are all
+ 
+
+ align:start position:0%
+directly so this is those are all
+interesting questions but we will not go
+
+ align:start position:0%
+interesting questions but we will not go
+ 
+
+ align:start position:0%
+interesting questions but we will not go
+into any of those in this
+
+ align:start position:0%
+into any of those in this
+ 
+
+ align:start position:0%
+into any of those in this
+in this lecture further we will however
+
+ align:start position:0%
+in this lecture further we will however
+ 
+
+ align:start position:0%
+in this lecture further we will however
+come back to understanding
+
+ align:start position:0%
+come back to understanding
+ 
+
+ align:start position:0%
+come back to understanding
+the origin of cp violation in the
+
+ align:start position:0%
+the origin of cp violation in the
+ 
+
+ align:start position:0%
+the origin of cp violation in the
+standard model
+
+ align:start position:0%
+standard model
+ 
+
+ align:start position:0%
+standard model
+and we talk in more detail about
+
+ align:start position:0%
+and we talk in more detail about
+ 
+
+ align:start position:0%
+and we talk in more detail about
+the weakened action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/pIwp65fPyYU.txt b/pIwp65fPyYU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cfabb8fcc73a36ec2ecc6d604959236ecf0a3a6f
--- /dev/null
+++ b/pIwp65fPyYU.txt
@@ -0,0 +1,7971 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, where are we in our grand list of
+
+ align:start position:0%
+So, where are we in our grand list of
+ 
+
+ align:start position:0%
+So, where are we in our grand list of
+our five types of problems? We've done
+
+ align:start position:0%
+our five types of problems? We've done
+ 
+
+ align:start position:0%
+our five types of problems? We've done
+weak acid in water, weak base in water,
+
+ align:start position:0%
+weak acid in water, weak base in water,
+ 
+
+ align:start position:0%
+weak acid in water, weak base in water,
+salt, and buffer. We only have two left.
+
+ align:start position:0%
+salt, and buffer. We only have two left.
+ 
+
+ align:start position:0%
+salt, and buffer. We only have two left.
+And that's what we're going to talk
+
+ align:start position:0%
+And that's what we're going to talk
+ 
+
+ align:start position:0%
+And that's what we're going to talk
+about right now. Strong acids and strong
+
+ align:start position:0%
+about right now. Strong acids and strong
+ 
+
+ align:start position:0%
+about right now. Strong acids and strong
+bases. And we're going to talk about
+
+ align:start position:0%
+bases. And we're going to talk about
+ 
+
+ align:start position:0%
+bases. And we're going to talk about
+them in uh in terms of acid base
+
+ align:start position:0%
+them in uh in terms of acid base
+ 
+
+ align:start position:0%
+them in uh in terms of acid base
+titrations. So, switching to today's
+
+ align:start position:0%
+titrations. So, switching to today's
+ 
+
+ align:start position:0%
+titrations. So, switching to today's
+handout.
+
+ align:start position:0%
+handout.
+ 
+
+ align:start position:0%
+handout.
+So, titrations, how many of you have
+
+ align:start position:0%
+So, titrations, how many of you have
+ 
+
+ align:start position:0%
+So, titrations, how many of you have
+done a titration in a laboratory? And
+
+ align:start position:0%
+done a titration in a laboratory? And
+ 
+
+ align:start position:0%
+done a titration in a laboratory? And
+like, okay, a lot a lot of people. Okay,
+
+ align:start position:0%
+like, okay, a lot a lot of people. Okay,
+ 
+
+ align:start position:0%
+like, okay, a lot a lot of people. Okay,
+if you haven't, I have to say you're not
+
+ align:start position:0%
+if you haven't, I have to say you're not
+ 
+
+ align:start position:0%
+if you haven't, I have to say you're not
+missing anything. It is
+
+ align:start position:0%
+missing anything. It is
+ 
+
+ align:start position:0%
+missing anything. It is
+really, it's like watching paint dry for
+
+ align:start position:0%
+really, it's like watching paint dry for
+ 
+
+ align:start position:0%
+really, it's like watching paint dry for
+most of the time during the titration.
+
+ align:start position:0%
+most of the time during the titration.
+ 
+
+ align:start position:0%
+most of the time during the titration.
+Okay. So here in an acidbased titration
+
+ align:start position:0%
+Okay. So here in an acidbased titration
+ 
+
+ align:start position:0%
+Okay. So here in an acidbased titration
+you have the addition of say a base of
+
+ align:start position:0%
+you have the addition of say a base of
+ 
+
+ align:start position:0%
+you have the addition of say a base of
+um known concentration to an acid of
+
+ align:start position:0%
+um known concentration to an acid of
+ 
+
+ align:start position:0%
+um known concentration to an acid of
+unknown
+
+ align:start position:0%
+unknown
+ 
+
+ align:start position:0%
+unknown
+concentration and you can use this by
+
+ align:start position:0%
+concentration and you can use this by
+ 
+
+ align:start position:0%
+concentration and you can use this by
+figuring out what volume you need um to
+
+ align:start position:0%
+figuring out what volume you need um to
+ 
+
+ align:start position:0%
+figuring out what volume you need um to
+reach the equivalence point. You can
+
+ align:start position:0%
+reach the equivalence point. You can
+ 
+
+ align:start position:0%
+reach the equivalence point. You can
+figure out the concentration of that
+
+ align:start position:0%
+figure out the concentration of that
+ 
+
+ align:start position:0%
+figure out the concentration of that
+acid or base. If you know the
+
+ align:start position:0%
+acid or base. If you know the
+ 
+
+ align:start position:0%
+acid or base. If you know the
+concentration of two things, you can
+
+ align:start position:0%
+concentration of two things, you can
+ 
+
+ align:start position:0%
+concentration of two things, you can
+often use it to figure out a Ka or
+
+ align:start position:0%
+often use it to figure out a Ka or
+ 
+
+ align:start position:0%
+often use it to figure out a Ka or
+calculate a molecular weight. Um but
+
+ align:start position:0%
+calculate a molecular weight. Um but
+ 
+
+ align:start position:0%
+calculate a molecular weight. Um but
+that's the uh the purpose of the
+
+ align:start position:0%
+that's the uh the purpose of the
+ 
+
+ align:start position:0%
+that's the uh the purpose of the
+titration. So let's look at the shape of
+
+ align:start position:0%
+titration. So let's look at the shape of
+ 
+
+ align:start position:0%
+titration. So let's look at the shape of
+these titration curves. So here we have
+
+ align:start position:0%
+these titration curves. So here we have
+ 
+
+ align:start position:0%
+these titration curves. So here we have
+a strong acid with a strong base. So we
+
+ align:start position:0%
+a strong acid with a strong base. So we
+ 
+
+ align:start position:0%
+a strong acid with a strong base. So we
+start out all we have at 0 is the strong
+
+ align:start position:0%
+start out all we have at 0 is the strong
+ 
+
+ align:start position:0%
+start out all we have at 0 is the strong
+acid. So we should have a very low pH
+
+ align:start position:0%
+acid. So we should have a very low pH
+ 
+
+ align:start position:0%
+acid. So we should have a very low pH
+here and then it should change slowly.
+
+ align:start position:0%
+here and then it should change slowly.
+ 
+
+ align:start position:0%
+here and then it should change slowly.
+Then it changes very rapidly and then
+
+ align:start position:0%
+Then it changes very rapidly and then
+ 
+
+ align:start position:0%
+Then it changes very rapidly and then
+changes slowly again. So what is this
+
+ align:start position:0%
+changes slowly again. So what is this
+ 
+
+ align:start position:0%
+changes slowly again. So what is this
+point S? So that point S has many many
+
+ align:start position:0%
+point S? So that point S has many many
+ 
+
+ align:start position:0%
+point S? So that point S has many many
+names which are all equivalent. It's
+
+ align:start position:0%
+names which are all equivalent. It's
+ 
+
+ align:start position:0%
+names which are all equivalent. It's
+called the equivalence point and we had
+
+ align:start position:0%
+called the equivalence point and we had
+ 
+
+ align:start position:0%
+called the equivalence point and we had
+uh the clicker question in the beginning
+
+ align:start position:0%
+uh the clicker question in the beginning
+ 
+
+ align:start position:0%
+uh the clicker question in the beginning
+was uh was mentioning that the S um here
+
+ align:start position:0%
+was uh was mentioning that the S um here
+ 
+
+ align:start position:0%
+was uh was mentioning that the S um here
+really stands for the stokometric point.
+
+ align:start position:0%
+really stands for the stokometric point.
+ 
+
+ align:start position:0%
+really stands for the stokometric point.
+Both of these are the same thing and
+
+ align:start position:0%
+Both of these are the same thing and
+ 
+
+ align:start position:0%
+Both of these are the same thing and
+it's the theoretical volume at which
+
+ align:start position:0%
+it's the theoretical volume at which
+ 
+
+ align:start position:0%
+it's the theoretical volume at which
+that base that you've added the number
+
+ align:start position:0%
+that base that you've added the number
+ 
+
+ align:start position:0%
+that base that you've added the number
+of moles of that base is equal to the
+
+ align:start position:0%
+of moles of that base is equal to the
+ 
+
+ align:start position:0%
+of moles of that base is equal to the
+number of moles of acid you have. So
+
+ align:start position:0%
+number of moles of acid you have. So
+ 
+
+ align:start position:0%
+number of moles of acid you have. So
+it's the the point at which the moles
+
+ align:start position:0%
+it's the the point at which the moles
+ 
+
+ align:start position:0%
+it's the the point at which the moles
+are equal to each other. And so that's
+
+ align:start position:0%
+are equal to each other. And so that's
+ 
+
+ align:start position:0%
+are equal to each other. And so that's
+stokometric one one or equivalence the
+
+ align:start position:0%
+stokometric one one or equivalence the
+ 
+
+ align:start position:0%
+stokometric one one or equivalence the
+moles are equivalent. So all these names
+
+ align:start position:0%
+moles are equivalent. So all these names
+ 
+
+ align:start position:0%
+moles are equivalent. So all these names
+are the same. They all mean the same
+
+ align:start position:0%
+are the same. They all mean the same
+ 
+
+ align:start position:0%
+are the same. They all mean the same
+thing. Don't get tricked if problems say
+
+ align:start position:0%
+thing. Don't get tricked if problems say
+ 
+
+ align:start position:0%
+thing. Don't get tricked if problems say
+one thing or the other. You also might
+
+ align:start position:0%
+one thing or the other. You also might
+ 
+
+ align:start position:0%
+one thing or the other. You also might
+hear endpoint. That's often the result
+
+ align:start position:0%
+hear endpoint. That's often the result
+ 
+
+ align:start position:0%
+hear endpoint. That's often the result
+of the experiment that you do um where
+
+ align:start position:0%
+of the experiment that you do um where
+ 
+
+ align:start position:0%
+of the experiment that you do um where
+you figure out what volume you needed to
+
+ align:start position:0%
+you figure out what volume you needed to
+ 
+
+ align:start position:0%
+you figure out what volume you needed to
+add to have a color change. So the way
+
+ align:start position:0%
+add to have a color change. So the way
+ 
+
+ align:start position:0%
+add to have a color change. So the way
+these work usually is you have this and
+
+ align:start position:0%
+these work usually is you have this and
+ 
+
+ align:start position:0%
+these work usually is you have this and
+you go drip drip drip and you look for a
+
+ align:start position:0%
+you go drip drip drip and you look for a
+ 
+
+ align:start position:0%
+you go drip drip drip and you look for a
+color change and at that point of the
+
+ align:start position:0%
+color change and at that point of the
+ 
+
+ align:start position:0%
+color change and at that point of the
+color change the first little hint of
+
+ align:start position:0%
+color change the first little hint of
+ 
+
+ align:start position:0%
+color change the first little hint of
+the color change is where you want to
+
+ align:start position:0%
+the color change is where you want to
+ 
+
+ align:start position:0%
+the color change is where you want to
+stop and measure the volume. Um but
+
+ align:start position:0%
+stop and measure the volume. Um but
+ 
+
+ align:start position:0%
+stop and measure the volume. Um but
+often you get very frustrated and you go
+
+ align:start position:0%
+often you get very frustrated and you go
+ 
+
+ align:start position:0%
+often you get very frustrated and you go
+from totally clear to you you're very
+
+ align:start position:0%
+from totally clear to you you're very
+ 
+
+ align:start position:0%
+from totally clear to you you're very
+very slow and you're right in here and
+
+ align:start position:0%
+very slow and you're right in here and
+ 
+
+ align:start position:0%
+very slow and you're right in here and
+then you can't stand it anymore and you
+
+ align:start position:0%
+then you can't stand it anymore and you
+ 
+
+ align:start position:0%
+then you can't stand it anymore and you
+jump right up here and you have to do it
+
+ align:start position:0%
+jump right up here and you have to do it
+ 
+
+ align:start position:0%
+jump right up here and you have to do it
+over and over again. But it should be
+
+ align:start position:0%
+over and over again. But it should be
+ 
+
+ align:start position:0%
+over and over again. But it should be
+that the end point should equal the
+
+ align:start position:0%
+that the end point should equal the
+ 
+
+ align:start position:0%
+that the end point should equal the
+equivalence point. So if you're good at
+
+ align:start position:0%
+equivalence point. So if you're good at
+ 
+
+ align:start position:0%
+equivalence point. So if you're good at
+these kinds of problems, you might be
+
+ align:start position:0%
+these kinds of problems, you might be
+ 
+
+ align:start position:0%
+these kinds of problems, you might be
+able to do a quick and dirty estimate
+
+ align:start position:0%
+able to do a quick and dirty estimate
+ 
+
+ align:start position:0%
+able to do a quick and dirty estimate
+what the value is and then figure out
+
+ align:start position:0%
+what the value is and then figure out
+ 
+
+ align:start position:0%
+what the value is and then figure out
+exactly how much you can add before you
+
+ align:start position:0%
+exactly how much you can add before you
+ 
+
+ align:start position:0%
+exactly how much you can add before you
+have to go slow. I.e. you can cheat,
+
+ align:start position:0%
+have to go slow. I.e. you can cheat,
+ 
+
+ align:start position:0%
+have to go slow. I.e. you can cheat,
+which I highly recommend in doing these
+
+ align:start position:0%
+which I highly recommend in doing these
+ 
+
+ align:start position:0%
+which I highly recommend in doing these
+kinds of uh laboratory exercises. So
+
+ align:start position:0%
+kinds of uh laboratory exercises. So
+ 
+
+ align:start position:0%
+kinds of uh laboratory exercises. So
+knowing how to do the math is really
+
+ align:start position:0%
+knowing how to do the math is really
+ 
+
+ align:start position:0%
+knowing how to do the math is really
+valuable of these problems. Okay, so we
+
+ align:start position:0%
+valuable of these problems. Okay, so we
+ 
+
+ align:start position:0%
+valuable of these problems. Okay, so we
+had a strong acid and a strong base.
+
+ align:start position:0%
+had a strong acid and a strong base.
+ 
+
+ align:start position:0%
+had a strong acid and a strong base.
+Here's the same curve for a strong base
+
+ align:start position:0%
+Here's the same curve for a strong base
+ 
+
+ align:start position:0%
+Here's the same curve for a strong base
+with a strong acid where we're adding
+
+ align:start position:0%
+with a strong acid where we're adding
+ 
+
+ align:start position:0%
+with a strong acid where we're adding
+the strong um acid in to the strong
+
+ align:start position:0%
+the strong um acid in to the strong
+ 
+
+ align:start position:0%
+the strong um acid in to the strong
+base. Um again, now we're going to start
+
+ align:start position:0%
+base. Um again, now we're going to start
+ 
+
+ align:start position:0%
+base. Um again, now we're going to start
+in the beginning at point zero before
+
+ align:start position:0%
+in the beginning at point zero before
+ 
+
+ align:start position:0%
+in the beginning at point zero before
+we've added any acid. We have a basic
+
+ align:start position:0%
+we've added any acid. We have a basic
+ 
+
+ align:start position:0%
+we've added any acid. We have a basic
+pH, goes slow, goes fast through point
+
+ align:start position:0%
+pH, goes slow, goes fast through point
+ 
+
+ align:start position:0%
+pH, goes slow, goes fast through point
+S, the equivalence point or stochometric
+
+ align:start position:0%
+S, the equivalence point or stochometric
+ 
+
+ align:start position:0%
+S, the equivalence point or stochometric
+point, and then goes slow again. So, how
+
+ align:start position:0%
+point, and then goes slow again. So, how
+ 
+
+ align:start position:0%
+point, and then goes slow again. So, how
+do you know? Um and the TAs are going to
+
+ align:start position:0%
+do you know? Um and the TAs are going to
+ 
+
+ align:start position:0%
+do you know? Um and the TAs are going to
+come down and uh do a little demo for
+
+ align:start position:0%
+come down and uh do a little demo for
+ 
+
+ align:start position:0%
+come down and uh do a little demo for
+you now about pH indicators. How do you
+
+ align:start position:0%
+you now about pH indicators. How do you
+ 
+
+ align:start position:0%
+you now about pH indicators. How do you
+know? And for those of you who have done
+
+ align:start position:0%
+know? And for those of you who have done
+ 
+
+ align:start position:0%
+know? And for those of you who have done
+um these have done these experiments in
+
+ align:start position:0%
+um these have done these experiments in
+ 
+
+ align:start position:0%
+um these have done these experiments in
+lab again, you have this color change.
+
+ align:start position:0%
+lab again, you have this color change.
+ 
+
+ align:start position:0%
+lab again, you have this color change.
+And usually you're clear, you go a
+
+ align:start position:0%
+And usually you're clear, you go a
+ 
+
+ align:start position:0%
+And usually you're clear, you go a
+little bit more, you have a little bit
+
+ align:start position:0%
+little bit more, you have a little bit
+ 
+
+ align:start position:0%
+little bit more, you have a little bit
+more, and you go to this. But as I was
+
+ align:start position:0%
+more, and you go to this. But as I was
+ 
+
+ align:start position:0%
+more, and you go to this. But as I was
+saying, what happens most of the time is
+
+ align:start position:0%
+saying, what happens most of the time is
+ 
+
+ align:start position:0%
+saying, what happens most of the time is
+you go from this clear all the way to
+
+ align:start position:0%
+you go from this clear all the way to
+ 
+
+ align:start position:0%
+you go from this clear all the way to
+the really dark and you have to start
+
+ align:start position:0%
+the really dark and you have to start
+ 
+
+ align:start position:0%
+the really dark and you have to start
+all over again because you missed uh the
+
+ align:start position:0%
+all over again because you missed uh the
+ 
+
+ align:start position:0%
+all over again because you missed uh the
+end point. So these pH indicators are
+
+ align:start position:0%
+end point. So these pH indicators are
+ 
+
+ align:start position:0%
+end point. So these pH indicators are
+able um to tell you that there's this
+
+ align:start position:0%
+able um to tell you that there's this
+ 
+
+ align:start position:0%
+able um to tell you that there's this
+change in
+
+ align:start position:0%
+change in
+ 
+
+ align:start position:0%
+change in
+pH. So um the TAS are going to show you
+
+ align:start position:0%
+pH. So um the TAS are going to show you
+ 
+
+ align:start position:0%
+pH. So um the TAS are going to show you
+um using a pH indicate. Come on in. Set
+
+ align:start position:0%
+um using a pH indicate. Come on in. Set
+ 
+
+ align:start position:0%
+um using a pH indicate. Come on in. Set
+up. I'm just talking while you set up um
+
+ align:start position:0%
+up. I'm just talking while you set up um
+ 
+
+ align:start position:0%
+up. I'm just talking while you set up um
+over there. You can use the document
+
+ align:start position:0%
+over there. You can use the document
+ 
+
+ align:start position:0%
+over there. You can use the document
+camera if you need it.
+
+ align:start position:0%
+camera if you need it.
+ 
+
+ align:start position:0%
+camera if you need it.
+So um so our demo TAS have uh used
+
+ align:start position:0%
+So um so our demo TAS have uh used
+ 
+
+ align:start position:0%
+So um so our demo TAS have uh used
+created a natural dye from red
+
+ align:start position:0%
+created a natural dye from red
+ 
+
+ align:start position:0%
+created a natural dye from red
+cabbage and this dye when it's in acid
+
+ align:start position:0%
+cabbage and this dye when it's in acid
+ 
+
+ align:start position:0%
+cabbage and this dye when it's in acid
+has a different slightly different
+
+ align:start position:0%
+has a different slightly different
+ 
+
+ align:start position:0%
+has a different slightly different
+structure than in base which causes it
+
+ align:start position:0%
+structure than in base which causes it
+ 
+
+ align:start position:0%
+structure than in base which causes it
+to have these two different colors. So
+
+ align:start position:0%
+to have these two different colors. So
+ 
+
+ align:start position:0%
+to have these two different colors. So
+we can tell which things are acidic and
+
+ align:start position:0%
+we can tell which things are acidic and
+ 
+
+ align:start position:0%
+we can tell which things are acidic and
+which things are basic by the color of
+
+ align:start position:0%
+which things are basic by the color of
+ 
+
+ align:start position:0%
+which things are basic by the color of
+the indicator. And I'm just gonna hand
+
+ align:start position:0%
+the indicator. And I'm just gonna hand
+ 
+
+ align:start position:0%
+the indicator. And I'm just gonna hand
+over a
+
+ align:start position:0%
+over a
+ 
+
+ align:start position:0%
+over a
+mic if it's on.
+
+ align:start position:0%
+mic if it's on.
+ 
+
+ align:start position:0%
+mic if it's on.
+Okay. Is it on? Yes. Yes. Okay. Great.
+
+ align:start position:0%
+Okay. Is it on? Yes. Yes. Okay. Great.
+ 
+
+ align:start position:0%
+Okay. Is it on? Yes. Yes. Okay. Great.
+Okay. So, we've got our solutions here.
+
+ align:start position:0%
+Okay. So, we've got our solutions here.
+ 
+
+ align:start position:0%
+Okay. So, we've got our solutions here.
+Um, this is lemon juice. We've got Did I
+
+ align:start position:0%
+Um, this is lemon juice. We've got Did I
+ 
+
+ align:start position:0%
+Um, this is lemon juice. We've got Did I
+put water in here? Right. Yeah. Water.
+
+ align:start position:0%
+put water in here? Right. Yeah. Water.
+ 
+
+ align:start position:0%
+put water in here? Right. Yeah. Water.
+Vinegar. I think maybe it was vinegar.
+
+ align:start position:0%
+Vinegar. I think maybe it was vinegar.
+ 
+
+ align:start position:0%
+Vinegar. I think maybe it was vinegar.
+Then this is
+
+ align:start position:0%
+Then this is
+ 
+
+ align:start position:0%
+Then this is
+vinegar. All right. Don't do that. Don't
+
+ align:start position:0%
+vinegar. All right. Don't do that. Don't
+ 
+
+ align:start position:0%
+vinegar. All right. Don't do that. Don't
+do that in lab. In the lab, you should
+
+ align:start position:0%
+do that in lab. In the lab, you should
+ 
+
+ align:start position:0%
+do that in lab. In the lab, you should
+always label your containers. Yes. Yes,
+
+ align:start position:0%
+always label your containers. Yes. Yes,
+ 
+
+ align:start position:0%
+always label your containers. Yes. Yes,
+indeed. Okay, so we've got lemon
+
+ align:start position:0%
+indeed. Okay, so we've got lemon
+ 
+
+ align:start position:0%
+indeed. Okay, so we've got lemon
+juice, water, vinegar, and ammonia. Did
+
+ align:start position:0%
+juice, water, vinegar, and ammonia. Did
+ 
+
+ align:start position:0%
+juice, water, vinegar, and ammonia. Did
+you add some water into that? Can you?
+
+ align:start position:0%
+you add some water into that? Can you?
+ 
+
+ align:start position:0%
+you add some water into that? Can you?
+Okay, so we're going to add a little bit
+
+ align:start position:0%
+Okay, so we're going to add a little bit
+ 
+
+ align:start position:0%
+Okay, so we're going to add a little bit
+of the p uh the indicator. The indicator
+
+ align:start position:0%
+of the p uh the indicator. The indicator
+ 
+
+ align:start position:0%
+of the p uh the indicator. The indicator
+came from red cabbage. So, the dye in
+
+ align:start position:0%
+came from red cabbage. So, the dye in
+ 
+
+ align:start position:0%
+came from red cabbage. So, the dye in
+the red cabbage uh it is a molecule that
+
+ align:start position:0%
+the red cabbage uh it is a molecule that
+ 
+
+ align:start position:0%
+the red cabbage uh it is a molecule that
+can be protetonated. And when the
+
+ align:start position:0%
+can be protetonated. And when the
+ 
+
+ align:start position:0%
+can be protetonated. And when the
+molecule gets proteinated, it um it
+
+ align:start position:0%
+molecule gets proteinated, it um it
+ 
+
+ align:start position:0%
+molecule gets proteinated, it um it
+basically its double bonds start moving
+
+ align:start position:0%
+basically its double bonds start moving
+ 
+
+ align:start position:0%
+basically its double bonds start moving
+around. And when you do that, um, it
+
+ align:start position:0%
+around. And when you do that, um, it
+ 
+
+ align:start position:0%
+around. And when you do that, um, it
+absorbs light differently. So, what
+
+ align:start position:0%
+absorbs light differently. So, what
+ 
+
+ align:start position:0%
+absorbs light differently. So, what
+we're going to see when we
+
+ align:start position:0%
+we're going to see when we
+ 
+
+ align:start position:0%
+we're going to see when we
+pour into there is that you'll see this,
+
+ align:start position:0%
+pour into there is that you'll see this,
+ 
+
+ align:start position:0%
+pour into there is that you'll see this,
+which is the, uh, the acid forms a nice
+
+ align:start position:0%
+which is the, uh, the acid forms a nice
+ 
+
+ align:start position:0%
+which is the, uh, the acid forms a nice
+pinkish color. Uh, this was the water,
+
+ align:start position:0%
+pinkish color. Uh, this was the water,
+ 
+
+ align:start position:0%
+pinkish color. Uh, this was the water,
+and when you pour it into the water,
+
+ align:start position:0%
+and when you pour it into the water,
+ 
+
+ align:start position:0%
+and when you pour it into the water,
+nothing really happens. Uh, and you can
+
+ align:start position:0%
+nothing really happens. Uh, and you can
+ 
+
+ align:start position:0%
+nothing really happens. Uh, and you can
+kind of understand that because the
+
+ align:start position:0%
+kind of understand that because the
+ 
+
+ align:start position:0%
+kind of understand that because the
+indicator itself is a water-based
+
+ align:start position:0%
+indicator itself is a water-based
+ 
+
+ align:start position:0%
+indicator itself is a water-based
+solution, so it's going to be purple.
+
+ align:start position:0%
+solution, so it's going to be purple.
+ 
+
+ align:start position:0%
+solution, so it's going to be purple.
+Uh, this was the vinegar and as we did
+
+ align:start position:0%
+Uh, this was the vinegar and as we did
+ 
+
+ align:start position:0%
+Uh, this was the vinegar and as we did
+last time, the vinegar um uh is is uh
+
+ align:start position:0%
+last time, the vinegar um uh is is uh
+ 
+
+ align:start position:0%
+last time, the vinegar um uh is is uh
+acidic and this was the ammonia. Um, and
+
+ align:start position:0%
+acidic and this was the ammonia. Um, and
+ 
+
+ align:start position:0%
+acidic and this was the ammonia. Um, and
+I'm gonna add a little bit of water. Can
+
+ align:start position:0%
+I'm gonna add a little bit of water. Can
+ 
+
+ align:start position:0%
+I'm gonna add a little bit of water. Can
+you add a little bit of water into this?
+
+ align:start position:0%
+you add a little bit of water into this?
+ 
+
+ align:start position:0%
+you add a little bit of water into this?
+You add it. Okay, great. Um, and then
+
+ align:start position:0%
+You add it. Okay, great. Um, and then
+ 
+
+ align:start position:0%
+You add it. Okay, great. Um, and then
+we're going to kind of do a little
+
+ align:start position:0%
+we're going to kind of do a little
+ 
+
+ align:start position:0%
+we're going to kind of do a little
+excursion here. Um, so what this is,
+
+ align:start position:0%
+excursion here. Um, so what this is,
+ 
+
+ align:start position:0%
+excursion here. Um, so what this is,
+this is a piece of Oh, it's cold. Piece
+
+ align:start position:0%
+this is a piece of Oh, it's cold. Piece
+ 
+
+ align:start position:0%
+this is a piece of Oh, it's cold. Piece
+of dry ice, which is just solid CO2. Um,
+
+ align:start position:0%
+of dry ice, which is just solid CO2. Um,
+ 
+
+ align:start position:0%
+of dry ice, which is just solid CO2. Um,
+and what I'm going to do is I'm going to
+
+ align:start position:0%
+and what I'm going to do is I'm going to
+ 
+
+ align:start position:0%
+and what I'm going to do is I'm going to
+drop it into there. So, this is um kind
+
+ align:start position:0%
+drop it into there. So, this is um kind
+ 
+
+ align:start position:0%
+drop it into there. So, this is um kind
+of a bit of a run. Yeah, I'll put it
+
+ align:start position:0%
+of a bit of a run. Yeah, I'll put it
+ 
+
+ align:start position:0%
+of a bit of a run. Yeah, I'll put it
+over here. Um so, this is an interesting
+
+ align:start position:0%
+over here. Um so, this is an interesting
+ 
+
+ align:start position:0%
+over here. Um so, this is an interesting
+demo because um Oh, that's not useful at
+
+ align:start position:0%
+demo because um Oh, that's not useful at
+ 
+
+ align:start position:0%
+demo because um Oh, that's not useful at
+all. Um actually, we can change Can we
+
+ align:start position:0%
+all. Um actually, we can change Can we
+ 
+
+ align:start position:0%
+all. Um actually, we can change Can we
+change that? Oh, maybe not. Oh, well,
+
+ align:start position:0%
+change that? Oh, maybe not. Oh, well,
+ 
+
+ align:start position:0%
+change that? Oh, maybe not. Oh, well,
+it's fine. Oh, man. I think we can do
+
+ align:start position:0%
+it's fine. Oh, man. I think we can do
+ 
+
+ align:start position:0%
+it's fine. Oh, man. I think we can do
+that, but this is beyond Well, well,
+
+ align:start position:0%
+that, but this is beyond Well, well,
+ 
+
+ align:start position:0%
+that, but this is beyond Well, well,
+what I was talking about was basically
+
+ align:start position:0%
+what I was talking about was basically
+ 
+
+ align:start position:0%
+what I was talking about was basically
+um when you drop the CO2 into this uh
+
+ align:start position:0%
+um when you drop the CO2 into this uh
+ 
+
+ align:start position:0%
+um when you drop the CO2 into this uh
+mixture, what's happening is that the
+
+ align:start position:0%
+mixture, what's happening is that the
+ 
+
+ align:start position:0%
+mixture, what's happening is that the
+CO2 actually uh decomposes and it forms
+
+ align:start position:0%
+CO2 actually uh decomposes and it forms
+ 
+
+ align:start position:0%
+CO2 actually uh decomposes and it forms
+something called carbonic acid. And good
+
+ align:start position:0%
+something called carbonic acid. And good
+ 
+
+ align:start position:0%
+something called carbonic acid. And good
+idea.
+
+ align:start position:0%
+idea.
+ 
+
+ align:start position:0%
+idea.
+uh carbonic acid um is is is an acid. So
+
+ align:start position:0%
+uh carbonic acid um is is is an acid. So
+ 
+
+ align:start position:0%
+uh carbonic acid um is is is an acid. So
+it will actually change uh the pH of the
+
+ align:start position:0%
+it will actually change uh the pH of the
+ 
+
+ align:start position:0%
+it will actually change uh the pH of the
+solution as we're talking and what this
+
+ align:start position:0%
+solution as we're talking and what this
+ 
+
+ align:start position:0%
+solution as we're talking and what this
+is relevant for is really for um uh
+
+ align:start position:0%
+is relevant for is really for um uh
+ 
+
+ align:start position:0%
+is relevant for is really for um uh
+global warming. So, we know about uh
+
+ align:start position:0%
+global warming. So, we know about uh
+ 
+
+ align:start position:0%
+global warming. So, we know about uh
+companies when they make I mean it's
+
+ align:start position:0%
+companies when they make I mean it's
+ 
+
+ align:start position:0%
+companies when they make I mean it's
+true when you have companies when they
+
+ align:start position:0%
+true when you have companies when they
+ 
+
+ align:start position:0%
+true when you have companies when they
+make um uh lots of different kinds of uh
+
+ align:start position:0%
+make um uh lots of different kinds of uh
+ 
+
+ align:start position:0%
+make um uh lots of different kinds of uh
+chemical compounds, they'll release CO2
+
+ align:start position:0%
+chemical compounds, they'll release CO2
+ 
+
+ align:start position:0%
+chemical compounds, they'll release CO2
+into the atmosphere. And when the CO2
+
+ align:start position:0%
+into the atmosphere. And when the CO2
+ 
+
+ align:start position:0%
+into the atmosphere. And when the CO2
+gets released, is it working or no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+upside down? That's even cooler. Look at
+
+ align:start position:0%
+upside down? That's even cooler. Look at
+ 
+
+ align:start position:0%
+upside down? That's even cooler. Look at
+that. So when the CO2 gets released into
+
+ align:start position:0%
+that. So when the CO2 gets released into
+ 
+
+ align:start position:0%
+that. So when the CO2 gets released into
+the atmosphere um is basically by
+
+ align:start position:0%
+the atmosphere um is basically by
+ 
+
+ align:start position:0%
+the atmosphere um is basically by
+Latier's principle you add all this CO2
+
+ align:start position:0%
+Latier's principle you add all this CO2
+ 
+
+ align:start position:0%
+Latier's principle you add all this CO2
+it will force the reaction to start
+
+ align:start position:0%
+it will force the reaction to start
+ 
+
+ align:start position:0%
+it will force the reaction to start
+making carbonic acid and that will react
+
+ align:start position:0%
+making carbonic acid and that will react
+ 
+
+ align:start position:0%
+making carbonic acid and that will react
+with the water vapor and start making uh
+
+ align:start position:0%
+with the water vapor and start making uh
+ 
+
+ align:start position:0%
+with the water vapor and start making uh
+the water in the air very acidic. Um wow
+
+ align:start position:0%
+the water in the air very acidic. Um wow
+ 
+
+ align:start position:0%
+the water in the air very acidic. Um wow
+that's that's not useful at all and the
+
+ align:start position:0%
+that's that's not useful at all and the
+ 
+
+ align:start position:0%
+that's that's not useful at all and the
+color is not really changing but uh it
+
+ align:start position:0%
+color is not really changing but uh it
+ 
+
+ align:start position:0%
+color is not really changing but uh it
+was supposed to.
+
+ align:start position:0%
+was supposed to.
+ 
+
+ align:start position:0%
+was supposed to.
+I think we might have added too much
+
+ align:start position:0%
+I think we might have added too much
+ 
+
+ align:start position:0%
+I think we might have added too much
+space but we can keep an Yeah, we can
+
+ align:start position:0%
+space but we can keep an Yeah, we can
+ 
+
+ align:start position:0%
+space but we can keep an Yeah, we can
+keep an eye out and watch the color
+
+ align:start position:0%
+keep an eye out and watch the color
+ 
+
+ align:start position:0%
+keep an eye out and watch the color
+change while it's upside down which is
+
+ align:start position:0%
+change while it's upside down which is
+ 
+
+ align:start position:0%
+change while it's upside down which is
+really useful. really cool. Um, but
+
+ align:start position:0%
+really useful. really cool. Um, but
+ 
+
+ align:start position:0%
+really useful. really cool. Um, but
+anyway, yeah, that's how the indicator
+
+ align:start position:0%
+anyway, yeah, that's how the indicator
+ 
+
+ align:start position:0%
+anyway, yeah, that's how the indicator
+works. And, uh, yeah, that's that, I
+
+ align:start position:0%
+works. And, uh, yeah, that's that, I
+ 
+
+ align:start position:0%
+works. And, uh, yeah, that's that, I
+guess. Okay. All right. Okay. So, we'll
+
+ align:start position:0%
+guess. Okay. All right. Okay. So, we'll
+ 
+
+ align:start position:0%
+guess. Okay. All right. Okay. So, we'll
+we can leave this here. I'll switch the
+
+ align:start position:0%
+we can leave this here. I'll switch the
+ 
+
+ align:start position:0%
+we can leave this here. I'll switch the
+document camera back.
+
+ align:start position:0%
+document camera back.
+ 
+
+ align:start position:0%
+document camera back.
+And, uh,
+
+ align:start position:0%
+And, uh,
+ 
+
+ align:start position:0%
+And, uh,
+yeah, we might add a little more. I
+
+ align:start position:0%
+yeah, we might add a little more. I
+ 
+
+ align:start position:0%
+yeah, we might add a little more. I
+still, it's very, very concentrated
+
+ align:start position:0%
+still, it's very, very concentrated
+ 
+
+ align:start position:0%
+still, it's very, very concentrated
+still. See if we can get a little bit
+
+ align:start position:0%
+still. See if we can get a little bit
+ 
+
+ align:start position:0%
+still. See if we can get a little bit
+more without too much overflow. I think
+
+ align:start position:0%
+more without too much overflow. I think
+ 
+
+ align:start position:0%
+more without too much overflow. I think
+it's changing a little bit, actually.
+
+ align:start position:0%
+it's changing a little bit, actually.
+ 
+
+ align:start position:0%
+it's changing a little bit, actually.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, we'll we'll keep an eye on
+
+ align:start position:0%
+All right, we'll we'll keep an eye on
+ 
+
+ align:start position:0%
+All right, we'll we'll keep an eye on
+it. Okay, so let's go through and do uh
+
+ align:start position:0%
+it. Okay, so let's go through and do uh
+ 
+
+ align:start position:0%
+it. Okay, so let's go through and do uh
+calculate some points on a strong acid
+
+ align:start position:0%
+calculate some points on a strong acid
+ 
+
+ align:start position:0%
+calculate some points on a strong acid
+and base curve so we can check off those
+
+ align:start position:0%
+and base curve so we can check off those
+ 
+
+ align:start position:0%
+and base curve so we can check off those
+two final uh final types of uh pH
+
+ align:start position:0%
+two final uh final types of uh pH
+ 
+
+ align:start position:0%
+two final uh final types of uh pH
+problems.
+
+ align:start position:0%
+problems.
+ 
+
+ align:start position:0%
+problems.
+So here when we're calculating strong
+
+ align:start position:0%
+So here when we're calculating strong
+ 
+
+ align:start position:0%
+So here when we're calculating strong
+acid and strong bases if say we have a
+
+ align:start position:0%
+acid and strong bases if say we have a
+ 
+
+ align:start position:0%
+acid and strong bases if say we have a
+strong base that's u 2.5 molar um NaOH
+
+ align:start position:0%
+strong base that's u 2.5 molar um NaOH
+ 
+
+ align:start position:0%
+strong base that's u 2.5 molar um NaOH
+being titrated with a strong acid HCl at
+
+ align:start position:0%
+being titrated with a strong acid HCl at
+ 
+
+ align:start position:0%
+being titrated with a strong acid HCl at
+34 molar.
+
+ align:start position:0%
+34 molar.
+ 
+
+ align:start position:0%
+34 molar.
+So, first we want to calculate the pH um
+
+ align:start position:0%
+So, first we want to calculate the pH um
+ 
+
+ align:start position:0%
+So, first we want to calculate the pH um
+before the equivalence point when we've
+
+ align:start position:0%
+before the equivalence point when we've
+ 
+
+ align:start position:0%
+before the equivalence point when we've
+just added say five ms of our strong
+
+ align:start position:0%
+just added say five ms of our strong
+ 
+
+ align:start position:0%
+just added say five ms of our strong
+acid um to the solution which was 25 ms
+
+ align:start position:0%
+acid um to the solution which was 25 ms
+ 
+
+ align:start position:0%
+acid um to the solution which was 25 ms
+of our strong
+
+ align:start position:0%
+of our strong
+ 
+
+ align:start position:0%
+of our strong
+base. So, the first thing we're going to
+
+ align:start position:0%
+base. So, the first thing we're going to
+ 
+
+ align:start position:0%
+base. So, the first thing we're going to
+do is calculate how many moles of base
+
+ align:start position:0%
+do is calculate how many moles of base
+ 
+
+ align:start position:0%
+do is calculate how many moles of base
+that is. So, how many did we have in
+
+ align:start position:0%
+that is. So, how many did we have in
+ 
+
+ align:start position:0%
+that is. So, how many did we have in
+here? And since this base is strong, the
+
+ align:start position:0%
+here? And since this base is strong, the
+ 
+
+ align:start position:0%
+here? And since this base is strong, the
+number of moles of sodium hydroxide
+
+ align:start position:0%
+number of moles of sodium hydroxide
+ 
+
+ align:start position:0%
+number of moles of sodium hydroxide
+added equals the amount of hydroxide
+
+ align:start position:0%
+added equals the amount of hydroxide
+ 
+
+ align:start position:0%
+added equals the amount of hydroxide
+formed. That's pretty uh you know that's
+
+ align:start position:0%
+formed. That's pretty uh you know that's
+ 
+
+ align:start position:0%
+formed. That's pretty uh you know that's
+the definition of a strong base and it
+
+ align:start position:0%
+the definition of a strong base and it
+ 
+
+ align:start position:0%
+the definition of a strong base and it
+is hydroxide. So pretty much that's how
+
+ align:start position:0%
+is hydroxide. So pretty much that's how
+ 
+
+ align:start position:0%
+is hydroxide. So pretty much that's how
+much you get. Um so all we have to do is
+
+ align:start position:0%
+much you get. Um so all we have to do is
+ 
+
+ align:start position:0%
+much you get. Um so all we have to do is
+know how to calculate the number of
+
+ align:start position:0%
+know how to calculate the number of
+ 
+
+ align:start position:0%
+know how to calculate the number of
+moles and that is the uh volume that we
+
+ align:start position:0%
+moles and that is the uh volume that we
+ 
+
+ align:start position:0%
+moles and that is the uh volume that we
+had and we're converting that to liters
+
+ align:start position:0%
+had and we're converting that to liters
+ 
+
+ align:start position:0%
+had and we're converting that to liters
+um times our concentration. And so that
+
+ align:start position:0%
+um times our concentration. And so that
+ 
+
+ align:start position:0%
+um times our concentration. And so that
+gives us 6.25 25 * 10us3 moles. All
+
+ align:start position:0%
+gives us 6.25 25 * 10us3 moles. All
+ 
+
+ align:start position:0%
+gives us 6.25 25 * 10us3 moles. All
+right, so we know how many moles of O we
+
+ align:start position:0%
+right, so we know how many moles of O we
+ 
+
+ align:start position:0%
+right, so we know how many moles of O we
+have. Now we need to figure out how many
+
+ align:start position:0%
+have. Now we need to figure out how many
+ 
+
+ align:start position:0%
+have. Now we need to figure out how many
+moles of acid we added when we added um
+
+ align:start position:0%
+moles of acid we added when we added um
+ 
+
+ align:start position:0%
+moles of acid we added when we added um
+5 milliliters of the acid. So it's a
+
+ align:start position:0%
+5 milliliters of the acid. So it's a
+ 
+
+ align:start position:0%
+5 milliliters of the acid. So it's a
+strong acid. So the moles of acid added
+
+ align:start position:0%
+strong acid. So the moles of acid added
+ 
+
+ align:start position:0%
+strong acid. So the moles of acid added
+equal the number of moles of our um
+
+ align:start position:0%
+equal the number of moles of our um
+ 
+
+ align:start position:0%
+equal the number of moles of our um
+hydrronium ions that are formed.
+
+ align:start position:0%
+hydrronium ions that are formed.
+ 
+
+ align:start position:0%
+hydrronium ions that are formed.
+Definition of strong acid. And so we had
+
+ align:start position:0%
+Definition of strong acid. And so we had
+ 
+
+ align:start position:0%
+Definition of strong acid. And so we had
+five milliliters. we convert to liters
+
+ align:start position:0%
+five milliliters. we convert to liters
+ 
+
+ align:start position:0%
+five milliliters. we convert to liters
+times our concentration that gives us
+
+ align:start position:0%
+times our concentration that gives us
+ 
+
+ align:start position:0%
+times our concentration that gives us
+1.7
+
+ align:start position:0%
+1.7
+ 
+
+ align:start position:0%
+1.7
+* 10us3 moles. So now we need to figure
+
+ align:start position:0%
+* 10us3 moles. So now we need to figure
+ 
+
+ align:start position:0%
+* 10us3 moles. So now we need to figure
+out how what the new amount of hydroxide
+
+ align:start position:0%
+out how what the new amount of hydroxide
+ 
+
+ align:start position:0%
+out how what the new amount of hydroxide
+is. So we had um we're going to convert
+
+ align:start position:0%
+is. So we had um we're going to convert
+ 
+
+ align:start position:0%
+is. So we had um we're going to convert
+some of our hydroxide will react with
+
+ align:start position:0%
+some of our hydroxide will react with
+ 
+
+ align:start position:0%
+some of our hydroxide will react with
+the amount of acid added because the
+
+ align:start position:0%
+the amount of acid added because the
+ 
+
+ align:start position:0%
+the amount of acid added because the
+stokometry is one to one. you're going
+
+ align:start position:0%
+stokometry is one to one. you're going
+ 
+
+ align:start position:0%
+stokometry is one to one. you're going
+to react equal numbers of O with
+
+ align:start position:0%
+to react equal numbers of O with
+ 
+
+ align:start position:0%
+to react equal numbers of O with
+H3O+. So we had 6.25* 10 the minus3
+
+ align:start position:0%
+H3O+. So we had 6.25* 10 the minus3
+ 
+
+ align:start position:0%
+H3O+. So we had 6.25* 10 the minus3
+moles. We've added this number of moles
+
+ align:start position:0%
+moles. We've added this number of moles
+ 
+
+ align:start position:0%
+moles. We've added this number of moles
+of acid. So that many moles are going to
+
+ align:start position:0%
+of acid. So that many moles are going to
+ 
+
+ align:start position:0%
+of acid. So that many moles are going to
+are going to be con are going to be uh
+
+ align:start position:0%
+are going to be con are going to be uh
+ 
+
+ align:start position:0%
+are going to be con are going to be uh
+formed into salt and we're left with
+
+ align:start position:0%
+formed into salt and we're left with
+ 
+
+ align:start position:0%
+formed into salt and we're left with
+this minus this or 4.55 * 10us3 moles of
+
+ align:start position:0%
+this minus this or 4.55 * 10us3 moles of
+ 
+
+ align:start position:0%
+this minus this or 4.55 * 10us3 moles of
+O minus left. So at this point this is a
+
+ align:start position:0%
+O minus left. So at this point this is a
+ 
+
+ align:start position:0%
+O minus left. So at this point this is a
+strong base and water problem. All we
+
+ align:start position:0%
+strong base and water problem. All we
+ 
+
+ align:start position:0%
+strong base and water problem. All we
+have is hydroxide ions left in our
+
+ align:start position:0%
+have is hydroxide ions left in our
+ 
+
+ align:start position:0%
+have is hydroxide ions left in our
+solution. Um we've com we've uh
+
+ align:start position:0%
+solution. Um we've com we've uh
+ 
+
+ align:start position:0%
+solution. Um we've com we've uh
+converted all the acid that we added
+
+ align:start position:0%
+converted all the acid that we added
+ 
+
+ align:start position:0%
+converted all the acid that we added
+into a salt because it reacted with the
+
+ align:start position:0%
+into a salt because it reacted with the
+ 
+
+ align:start position:0%
+into a salt because it reacted with the
+base. And so this is strong base now. So
+
+ align:start position:0%
+base. And so this is strong base now. So
+ 
+
+ align:start position:0%
+base. And so this is strong base now. So
+for strong base all we have to do is
+
+ align:start position:0%
+for strong base all we have to do is
+ 
+
+ align:start position:0%
+for strong base all we have to do is
+calculate the marity and then calculate
+
+ align:start position:0%
+calculate the marity and then calculate
+ 
+
+ align:start position:0%
+calculate the marity and then calculate
+p and pH. So for marity we have the
+
+ align:start position:0%
+p and pH. So for marity we have the
+ 
+
+ align:start position:0%
+p and pH. So for marity we have the
+number of moles left 4.55*
+
+ align:start position:0%
+number of moles left 4.55*
+ 
+
+ align:start position:0%
+number of moles left 4.55*
+10us3 in our new volume and this is the
+
+ align:start position:0%
+10us3 in our new volume and this is the
+ 
+
+ align:start position:0%
+10us3 in our new volume and this is the
+part where people forget we had 25 mls
+
+ align:start position:0%
+part where people forget we had 25 mls
+ 
+
+ align:start position:0%
+part where people forget we had 25 mls
+we added five more so our new volume is
+
+ align:start position:0%
+we added five more so our new volume is
+ 
+
+ align:start position:0%
+we added five more so our new volume is
+30 ms um and so we have a new
+
+ align:start position:0%
+30 ms um and so we have a new
+ 
+
+ align:start position:0%
+30 ms um and so we have a new
+concentration and then from that we
+
+ align:start position:0%
+concentration and then from that we
+ 
+
+ align:start position:0%
+concentration and then from that we
+calculate pH. First we do P plugging in
+
+ align:start position:0%
+calculate pH. First we do P plugging in
+ 
+
+ align:start position:0%
+calculate pH. First we do P plugging in
+our hydroxide ion concentration and then
+
+ align:start position:0%
+our hydroxide ion concentration and then
+ 
+
+ align:start position:0%
+our hydroxide ion concentration and then
+calculate pH using the fact that at room
+
+ align:start position:0%
+calculate pH using the fact that at room
+ 
+
+ align:start position:0%
+calculate pH using the fact that at room
+temperature and all these problems are
+
+ align:start position:0%
+temperature and all these problems are
+ 
+
+ align:start position:0%
+temperature and all these problems are
+room temperature um that would be 14
+
+ align:start position:0%
+room temperature um that would be 14
+ 
+
+ align:start position:0%
+room temperature um that would be 14
+minus the p is the pH and we have a
+
+ align:start position:0%
+minus the p is the pH and we have a
+ 
+
+ align:start position:0%
+minus the p is the pH and we have a
+point somewhere around here point B um
+
+ align:start position:0%
+point somewhere around here point B um
+ 
+
+ align:start position:0%
+point somewhere around here point B um
+on our titration curve after we've add 5
+
+ align:start position:0%
+on our titration curve after we've add 5
+ 
+
+ align:start position:0%
+on our titration curve after we've add 5
+mls of strong acid our pH is still
+
+ align:start position:0%
+mls of strong acid our pH is still
+ 
+
+ align:start position:0%
+mls of strong acid our pH is still
+pretty basic 13.18 eight left. So,
+
+ align:start position:0%
+pretty basic 13.18 eight left. So,
+ 
+
+ align:start position:0%
+pretty basic 13.18 eight left. So,
+strong base and water problem. All you
+
+ align:start position:0%
+strong base and water problem. All you
+ 
+
+ align:start position:0%
+strong base and water problem. All you
+have to do is calculate the
+
+ align:start position:0%
+have to do is calculate the
+ 
+
+ align:start position:0%
+have to do is calculate the
+concentration of O minus, then the P,
+
+ align:start position:0%
+concentration of O minus, then the P,
+ 
+
+ align:start position:0%
+concentration of O minus, then the P,
+and then the pH. So, you don't have to
+
+ align:start position:0%
+and then the pH. So, you don't have to
+ 
+
+ align:start position:0%
+and then the pH. So, you don't have to
+have any of these minus and pluses in
+
+ align:start position:0%
+have any of these minus and pluses in
+ 
+
+ align:start position:0%
+have any of these minus and pluses in
+terms of setting up our tables and using
+
+ align:start position:0%
+terms of setting up our tables and using
+ 
+
+ align:start position:0%
+terms of setting up our tables and using
+Ka's and KBs. For a weak base and water
+
+ align:start position:0%
+Ka's and KBs. For a weak base and water
+ 
+
+ align:start position:0%
+Ka's and KBs. For a weak base and water
+problem, it's a concentration of
+
+ align:start position:0%
+problem, it's a concentration of
+ 
+
+ align:start position:0%
+problem, it's a concentration of
+hydroxide ion,
+
+ align:start position:0%
+hydroxide ion,
+ 
+
+ align:start position:0%
+hydroxide ion,
+PH. All right. So, let's move on now and
+
+ align:start position:0%
+PH. All right. So, let's move on now and
+ 
+
+ align:start position:0%
+PH. All right. So, let's move on now and
+think about what how what volume we
+
+ align:start position:0%
+think about what how what volume we
+ 
+
+ align:start position:0%
+think about what how what volume we
+would need to get to the stokometric
+
+ align:start position:0%
+would need to get to the stokometric
+ 
+
+ align:start position:0%
+would need to get to the stokometric
+point. So, you're often asked to
+
+ align:start position:0%
+point. So, you're often asked to
+ 
+
+ align:start position:0%
+point. So, you're often asked to
+calculate the volume of the strong acid
+
+ align:start position:0%
+calculate the volume of the strong acid
+ 
+
+ align:start position:0%
+calculate the volume of the strong acid
+needed to get to the stokometric or the
+
+ align:start position:0%
+needed to get to the stokometric or the
+ 
+
+ align:start position:0%
+needed to get to the stokometric or the
+equivalence point. And to do this, you
+
+ align:start position:0%
+equivalence point. And to do this, you
+ 
+
+ align:start position:0%
+equivalence point. And to do this, you
+need to think about how many moles of O
+
+ align:start position:0%
+need to think about how many moles of O
+ 
+
+ align:start position:0%
+need to think about how many moles of O
+you have because at the equivalence
+
+ align:start position:0%
+you have because at the equivalence
+ 
+
+ align:start position:0%
+you have because at the equivalence
+point, you have equal numbers of moles
+
+ align:start position:0%
+point, you have equal numbers of moles
+ 
+
+ align:start position:0%
+point, you have equal numbers of moles
+of acid. So, we had 6.25* 25 * 10us3
+
+ align:start position:0%
+of acid. So, we had 6.25* 25 * 10us3
+ 
+
+ align:start position:0%
+of acid. So, we had 6.25* 25 * 10us3
+moles of O originally. And at the
+
+ align:start position:0%
+moles of O originally. And at the
+ 
+
+ align:start position:0%
+moles of O originally. And at the
+equivalence point then how many moles of
+
+ align:start position:0%
+equivalence point then how many moles of
+ 
+
+ align:start position:0%
+equivalence point then how many moles of
+acid do we need to
+
+ align:start position:0%
+acid do we need to
+ 
+
+ align:start position:0%
+acid do we need to
+add? We have to add that exact same
+
+ align:start position:0%
+add? We have to add that exact same
+ 
+
+ align:start position:0%
+add? We have to add that exact same
+number by definition. It's the
+
+ align:start position:0%
+number by definition. It's the
+ 
+
+ align:start position:0%
+number by definition. It's the
+equivalence point. It's the stokometric
+
+ align:start position:0%
+equivalence point. It's the stokometric
+ 
+
+ align:start position:0%
+equivalence point. It's the stokometric
+point. So if you know how many moles of
+
+ align:start position:0%
+point. So if you know how many moles of
+ 
+
+ align:start position:0%
+point. So if you know how many moles of
+the base you had, that's going to be
+
+ align:start position:0%
+the base you had, that's going to be
+ 
+
+ align:start position:0%
+the base you had, that's going to be
+equal to the moles of acid you need to
+
+ align:start position:0%
+equal to the moles of acid you need to
+ 
+
+ align:start position:0%
+equal to the moles of acid you need to
+add. So now we want to figure out the
+
+ align:start position:0%
+add. So now we want to figure out the
+ 
+
+ align:start position:0%
+add. So now we want to figure out the
+volume that that's needed. We know the
+
+ align:start position:0%
+volume that that's needed. We know the
+ 
+
+ align:start position:0%
+volume that that's needed. We know the
+number of moles that we need and we know
+
+ align:start position:0%
+number of moles that we need and we know
+ 
+
+ align:start position:0%
+number of moles that we need and we know
+the concentration. So now we just have
+
+ align:start position:0%
+the concentration. So now we just have
+ 
+
+ align:start position:0%
+the concentration. So now we just have
+to calculate the volume. So we have the
+
+ align:start position:0%
+to calculate the volume. So we have the
+ 
+
+ align:start position:0%
+to calculate the volume. So we have the
+moles. We use the concentration of the
+
+ align:start position:0%
+moles. We use the concentration of the
+ 
+
+ align:start position:0%
+moles. We use the concentration of the
+acid to figure out the volume that has
+
+ align:start position:0%
+acid to figure out the volume that has
+ 
+
+ align:start position:0%
+acid to figure out the volume that has
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+added. All right. And what would be the
+
+ align:start position:0%
+added. All right. And what would be the
+ 
+
+ align:start position:0%
+added. All right. And what would be the
+pH at this
+
+ align:start position:0%
+pH at this
+ 
+
+ align:start position:0%
+pH at this
+point? It would be seven.
+
+ align:start position:0%
+point? It would be seven.
+ 
+
+ align:start position:0%
+point? It would be seven.
+So, this is a really fast question to
+
+ align:start position:0%
+So, this is a really fast question to
+ 
+
+ align:start position:0%
+So, this is a really fast question to
+ask on an exam because all you have to
+
+ align:start position:0%
+ask on an exam because all you have to
+ 
+
+ align:start position:0%
+ask on an exam because all you have to
+do is say if it was a weak if it was a
+
+ align:start position:0%
+do is say if it was a weak if it was a
+ 
+
+ align:start position:0%
+do is say if it was a weak if it was a
+strong base and a strong acid, they're
+
+ align:start position:0%
+strong base and a strong acid, they're
+ 
+
+ align:start position:0%
+strong base and a strong acid, they're
+going to form a neutral salt in water.
+
+ align:start position:0%
+going to form a neutral salt in water.
+ 
+
+ align:start position:0%
+going to form a neutral salt in water.
+So, the pH is seven and that's it. No
+
+ align:start position:0%
+So, the pH is seven and that's it. No
+ 
+
+ align:start position:0%
+So, the pH is seven and that's it. No
+calculations needed. You can answer that
+
+ align:start position:0%
+calculations needed. You can answer that
+ 
+
+ align:start position:0%
+calculations needed. You can answer that
+question very quickly. So, strong acid,
+
+ align:start position:0%
+question very quickly. So, strong acid,
+ 
+
+ align:start position:0%
+question very quickly. So, strong acid,
+strong base at the equivalence point,
+
+ align:start position:0%
+strong base at the equivalence point,
+ 
+
+ align:start position:0%
+strong base at the equivalence point,
+equal number of moles, you're going to
+
+ align:start position:0%
+equal number of moles, you're going to
+ 
+
+ align:start position:0%
+equal number of moles, you're going to
+get a salt that's neutral.
+
+ align:start position:0%
+get a salt that's neutral.
+ 
+
+ align:start position:0%
+get a salt that's neutral.
+And the salt here um we have HCl and
+
+ align:start position:0%
+And the salt here um we have HCl and
+ 
+
+ align:start position:0%
+And the salt here um we have HCl and
+NaOH is just NaCl salt. So remember at
+
+ align:start position:0%
+NaOH is just NaCl salt. So remember at
+ 
+
+ align:start position:0%
+NaOH is just NaCl salt. So remember at
+the equivalence point strong acid strong
+
+ align:start position:0%
+the equivalence point strong acid strong
+ 
+
+ align:start position:0%
+the equivalence point strong acid strong
+base the pH is going to be
+
+ align:start position:0%
+base the pH is going to be
+ 
+
+ align:start position:0%
+base the pH is going to be
+seven. All right. So now let's go down
+
+ align:start position:0%
+seven. All right. So now let's go down
+ 
+
+ align:start position:0%
+seven. All right. So now let's go down
+here and try point D. So just beyond the
+
+ align:start position:0%
+here and try point D. So just beyond the
+ 
+
+ align:start position:0%
+here and try point D. So just beyond the
+equivalence point. So here we want to
+
+ align:start position:0%
+equivalence point. So here we want to
+ 
+
+ align:start position:0%
+equivalence point. So here we want to
+calculate the pH after 1 mil of strong
+
+ align:start position:0%
+calculate the pH after 1 mil of strong
+ 
+
+ align:start position:0%
+calculate the pH after 1 mil of strong
+acid has been added after you have
+
+ align:start position:0%
+acid has been added after you have
+ 
+
+ align:start position:0%
+acid has been added after you have
+reached the equivalence point. So you
+
+ align:start position:0%
+reached the equivalence point. So you
+ 
+
+ align:start position:0%
+reached the equivalence point. So you
+went one mil too far in your titration
+
+ align:start position:0%
+went one mil too far in your titration
+ 
+
+ align:start position:0%
+went one mil too far in your titration
+and this is a strong acid and water
+
+ align:start position:0%
+and this is a strong acid and water
+ 
+
+ align:start position:0%
+and this is a strong acid and water
+problem. So our last uh type of problem
+
+ align:start position:0%
+problem. So our last uh type of problem
+ 
+
+ align:start position:0%
+problem. So our last uh type of problem
+here. So first what you want to do is
+
+ align:start position:0%
+here. So first what you want to do is
+ 
+
+ align:start position:0%
+here. So first what you want to do is
+figure out how many moles um u of this
+
+ align:start position:0%
+figure out how many moles um u of this
+ 
+
+ align:start position:0%
+figure out how many moles um u of this
+acid were added due to this one mil
+
+ align:start position:0%
+acid were added due to this one mil
+ 
+
+ align:start position:0%
+acid were added due to this one mil
+extra. And again, it's a strong acid. So
+
+ align:start position:0%
+extra. And again, it's a strong acid. So
+ 
+
+ align:start position:0%
+extra. And again, it's a strong acid. So
+the amount of acid added is going to be
+
+ align:start position:0%
+the amount of acid added is going to be
+ 
+
+ align:start position:0%
+the amount of acid added is going to be
+equal to the hydrononeium ion
+
+ align:start position:0%
+equal to the hydrononeium ion
+ 
+
+ align:start position:0%
+equal to the hydrononeium ion
+concentrations formed. Definition of
+
+ align:start position:0%
+concentrations formed. Definition of
+ 
+
+ align:start position:0%
+concentrations formed. Definition of
+strong acid. So we had a concentration
+
+ align:start position:0%
+strong acid. So we had a concentration
+ 
+
+ align:start position:0%
+strong acid. So we had a concentration
+of.34 of our strong acid. We added 1 mil
+
+ align:start position:0%
+of.34 of our strong acid. We added 1 mil
+ 
+
+ align:start position:0%
+of.34 of our strong acid. We added 1 mil
+extra. So we have 3.4 *
+
+ align:start position:0%
+extra. So we have 3.4 *
+ 
+
+ align:start position:0%
+extra. So we have 3.4 *
+10us4 moles of um
+
+ align:start position:0%
+10us4 moles of um
+ 
+
+ align:start position:0%
+10us4 moles of um
+H3+. Now we need to calculate the marity
+
+ align:start position:0%
+H3+. Now we need to calculate the marity
+ 
+
+ align:start position:0%
+H3+. Now we need to calculate the marity
+of that. And that's a clicker
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the trick here is just to think about
+
+ align:start position:0%
+So the trick here is just to think about
+ 
+
+ align:start position:0%
+So the trick here is just to think about
+what is the volume at this
+
+ align:start position:0%
+what is the volume at this
+ 
+
+ align:start position:0%
+what is the volume at this
+point. And if we look over
+
+ align:start position:0%
+point. And if we look over
+ 
+
+ align:start position:0%
+point. And if we look over
+here, okay, do you want to just can
+
+ align:start position:0%
+here, okay, do you want to just can
+ 
+
+ align:start position:0%
+here, okay, do you want to just can
+bring it out? We're we're trying a
+
+ align:start position:0%
+bring it out? We're we're trying a
+ 
+
+ align:start position:0%
+bring it out? We're we're trying a
+couple of different uh variations of the
+
+ align:start position:0%
+couple of different uh variations of the
+ 
+
+ align:start position:0%
+couple of different uh variations of the
+uh the experiment over here. But
+
+ align:start position:0%
+uh the experiment over here. But
+ 
+
+ align:start position:0%
+uh the experiment over here. But
+uh just uh see if we can we can get it
+
+ align:start position:0%
+uh just uh see if we can we can get it
+ 
+
+ align:start position:0%
+uh just uh see if we can we can get it
+over time, but let's let's uh maybe
+
+ align:start position:0%
+over time, but let's let's uh maybe
+ 
+
+ align:start position:0%
+over time, but let's let's uh maybe
+we'll come back to that at the end.
+
+ align:start position:0%
+we'll come back to that at the end.
+ 
+
+ align:start position:0%
+we'll come back to that at the end.
+We'll just leave it there and see. Okay.
+
+ align:start position:0%
+We'll just leave it there and see. Okay.
+ 
+
+ align:start position:0%
+We'll just leave it there and see. Okay.
+or did you want to say something?
+
+ align:start position:0%
+or did you want to say something?
+ 
+
+ align:start position:0%
+or did you want to say something?
+All right. Why don't you talk about it
+
+ align:start position:0%
+All right. Why don't you talk about it
+ 
+
+ align:start position:0%
+All right. Why don't you talk about it
+briefly and then we'll look at the I
+
+ align:start position:0%
+briefly and then we'll look at the I
+ 
+
+ align:start position:0%
+briefly and then we'll look at the I
+mean, we we we did the experiment again
+
+ align:start position:0%
+mean, we we we did the experiment again
+ 
+
+ align:start position:0%
+mean, we we we did the experiment again
+kind of with a less concentrated
+
+ align:start position:0%
+kind of with a less concentrated
+ 
+
+ align:start position:0%
+kind of with a less concentrated
+solution. Added several pieces of dry
+
+ align:start position:0%
+solution. Added several pieces of dry
+ 
+
+ align:start position:0%
+solution. Added several pieces of dry
+ice and as you can see um the color
+
+ align:start position:0%
+ice and as you can see um the color
+ 
+
+ align:start position:0%
+ice and as you can see um the color
+Yeah, we can put it on the camera or we
+
+ align:start position:0%
+Yeah, we can put it on the camera or we
+ 
+
+ align:start position:0%
+Yeah, we can put it on the camera or we
+can't. It's fine. But the color is
+
+ align:start position:0%
+can't. It's fine. But the color is
+ 
+
+ align:start position:0%
+can't. It's fine. But the color is
+changing um very slowly, which is a lot
+
+ align:start position:0%
+changing um very slowly, which is a lot
+ 
+
+ align:start position:0%
+changing um very slowly, which is a lot
+slower than we expected it to change.
+
+ align:start position:0%
+slower than we expected it to change.
+ 
+
+ align:start position:0%
+slower than we expected it to change.
+But um you dilute the concentration and
+
+ align:start position:0%
+But um you dilute the concentration and
+ 
+
+ align:start position:0%
+But um you dilute the concentration and
+this is turning blue um and it will
+
+ align:start position:0%
+this is turning blue um and it will
+ 
+
+ align:start position:0%
+this is turning blue um and it will
+eventually turn kind of yellowish pink,
+
+ align:start position:0%
+eventually turn kind of yellowish pink,
+ 
+
+ align:start position:0%
+eventually turn kind of yellowish pink,
+which is when it will eventually become
+
+ align:start position:0%
+which is when it will eventually become
+ 
+
+ align:start position:0%
+which is when it will eventually become
+an acid. So we'll just leave that there.
+
+ align:start position:0%
+an acid. So we'll just leave that there.
+ 
+
+ align:start position:0%
+an acid. So we'll just leave that there.
+All right. Well, we'll keep an eye on it
+
+ align:start position:0%
+All right. Well, we'll keep an eye on it
+ 
+
+ align:start position:0%
+All right. Well, we'll keep an eye on it
+for the next few minutes. All right. So
+
+ align:start position:0%
+for the next few minutes. All right. So
+ 
+
+ align:start position:0%
+for the next few minutes. All right. So
+the trick here was to figure out the
+
+ align:start position:0%
+the trick here was to figure out the
+ 
+
+ align:start position:0%
+the trick here was to figure out the
+volume. So you had 25 ms to begin with.
+
+ align:start position:0%
+volume. So you had 25 ms to begin with.
+ 
+
+ align:start position:0%
+volume. So you had 25 ms to begin with.
+You needed 18.4 to get to the
+
+ align:start position:0%
+You needed 18.4 to get to the
+ 
+
+ align:start position:0%
+You needed 18.4 to get to the
+stokometric or the equivalence point.
+
+ align:start position:0%
+stokometric or the equivalence point.
+ 
+
+ align:start position:0%
+stokometric or the equivalence point.
+And then you had to add then you added
+
+ align:start position:0%
+And then you had to add then you added
+ 
+
+ align:start position:0%
+And then you had to add then you added
+one more past the equivalence point. And
+
+ align:start position:0%
+one more past the equivalence point. And
+ 
+
+ align:start position:0%
+one more past the equivalence point. And
+if you remember to add those three
+
+ align:start position:0%
+if you remember to add those three
+ 
+
+ align:start position:0%
+if you remember to add those three
+volumes together, then you will get the
+
+ align:start position:0%
+volumes together, then you will get the
+ 
+
+ align:start position:0%
+volumes together, then you will get the
+right concentration. And when you get
+
+ align:start position:0%
+right concentration. And when you get
+ 
+
+ align:start position:0%
+right concentration. And when you get
+the right concentration, the rest of the
+
+ align:start position:0%
+the right concentration, the rest of the
+ 
+
+ align:start position:0%
+the right concentration, the rest of the
+problem is very easy. Um and I'll just
+
+ align:start position:0%
+problem is very easy. Um and I'll just
+ 
+
+ align:start position:0%
+problem is very easy. Um and I'll just
+mention also uh significant figures
+
+ align:start position:0%
+mention also uh significant figures
+ 
+
+ align:start position:0%
+mention also uh significant figures
+here. We have three here because we had
+
+ align:start position:0%
+here. We have three here because we had
+ 
+
+ align:start position:0%
+here. We have three here because we had
+three there. Um and uh so then you just
+
+ align:start position:0%
+three there. Um and uh so then you just
+ 
+
+ align:start position:0%
+three there. Um and uh so then you just
+take the pH of this. This is the
+
+ align:start position:0%
+take the pH of this. This is the
+ 
+
+ align:start position:0%
+take the pH of this. This is the
+hydrononeium concentration and that will
+
+ align:start position:0%
+hydrononeium concentration and that will
+ 
+
+ align:start position:0%
+hydrononeium concentration and that will
+give your answer and it'll be pH2.116
+
+ align:start position:0%
+give your answer and it'll be pH2.116
+ 
+
+ align:start position:0%
+give your answer and it'll be pH2.116
+um with all of those significant figures
+
+ align:start position:0%
+um with all of those significant figures
+ 
+
+ align:start position:0%
+um with all of those significant figures
+which you can never measure that
+
+ align:start position:0%
+which you can never measure that
+ 
+
+ align:start position:0%
+which you can never measure that
+accurately but nonetheless that's what
+
+ align:start position:0%
+accurately but nonetheless that's what
+ 
+
+ align:start position:0%
+accurately but nonetheless that's what
+the rules would tell us. Um so a strong
+
+ align:start position:0%
+the rules would tell us. Um so a strong
+ 
+
+ align:start position:0%
+the rules would tell us. Um so a strong
+acid in um water problem is just you
+
+ align:start position:0%
+acid in um water problem is just you
+ 
+
+ align:start position:0%
+acid in um water problem is just you
+just calculate the hydrronium ion
+
+ align:start position:0%
+just calculate the hydrronium ion
+ 
+
+ align:start position:0%
+just calculate the hydrronium ion
+concentration and then pH. So this is a
+
+ align:start position:0%
+concentration and then pH. So this is a
+ 
+
+ align:start position:0%
+concentration and then pH. So this is a
+pretty simple part. All right. So if we
+
+ align:start position:0%
+pretty simple part. All right. So if we
+ 
+
+ align:start position:0%
+pretty simple part. All right. So if we
+go back now um to our
+
+ align:start position:0%
+go back now um to our
+ 
+
+ align:start position:0%
+go back now um to our
+uh to our diagram, we've measured a
+
+ align:start position:0%
+uh to our diagram, we've measured a
+ 
+
+ align:start position:0%
+uh to our diagram, we've measured a
+couple parts. We measured point B and uh
+
+ align:start position:0%
+couple parts. We measured point B and uh
+ 
+
+ align:start position:0%
+couple parts. We measured point B and uh
+and so we had a pH of
+
+ align:start position:0%
+and so we had a pH of
+ 
+
+ align:start position:0%
+and so we had a pH of
+13.18. This was like a strong basin
+
+ align:start position:0%
+13.18. This was like a strong basin
+ 
+
+ align:start position:0%
+13.18. This was like a strong basin
+water problem. We measure at point S we
+
+ align:start position:0%
+water problem. We measure at point S we
+ 
+
+ align:start position:0%
+water problem. We measure at point S we
+calculated that we needed 18.4 mills of
+
+ align:start position:0%
+calculated that we needed 18.4 mills of
+ 
+
+ align:start position:0%
+calculated that we needed 18.4 mills of
+strong acid and our pH is seven. And so
+
+ align:start position:0%
+strong acid and our pH is seven. And so
+ 
+
+ align:start position:0%
+strong acid and our pH is seven. And so
+at to the trick to doing this problem
+
+ align:start position:0%
+at to the trick to doing this problem
+ 
+
+ align:start position:0%
+at to the trick to doing this problem
+was just to remember that the moles of
+
+ align:start position:0%
+was just to remember that the moles of
+ 
+
+ align:start position:0%
+was just to remember that the moles of
+strong acid equal the moles of strong
+
+ align:start position:0%
+strong acid equal the moles of strong
+ 
+
+ align:start position:0%
+strong acid equal the moles of strong
+base at this point. And then for point D
+
+ align:start position:0%
+base at this point. And then for point D
+ 
+
+ align:start position:0%
+base at this point. And then for point D
+one mil past the equivalence point the
+
+ align:start position:0%
+one mil past the equivalence point the
+ 
+
+ align:start position:0%
+one mil past the equivalence point the
+pH was
+
+ align:start position:0%
+pH was
+ 
+
+ align:start position:0%
+pH was
+2.116. And this is like a um strong acid
+
+ align:start position:0%
+2.116. And this is like a um strong acid
+ 
+
+ align:start position:0%
+2.116. And this is like a um strong acid
+and water problem. And notice how
+
+ align:start position:0%
+and water problem. And notice how
+ 
+
+ align:start position:0%
+and water problem. And notice how
+dramatic it is. Up here you're at pH7.
+
+ align:start position:0%
+dramatic it is. Up here you're at pH7.
+ 
+
+ align:start position:0%
+dramatic it is. Up here you're at pH7.
+You add one mil too much and you're
+
+ align:start position:0%
+You add one mil too much and you're
+ 
+
+ align:start position:0%
+You add one mil too much and you're
+already at pH2. So this is a very rapid
+
+ align:start position:0%
+already at pH2. So this is a very rapid
+ 
+
+ align:start position:0%
+already at pH2. So this is a very rapid
+change. This is why a lot of these
+
+ align:start position:0%
+change. This is why a lot of these
+ 
+
+ align:start position:0%
+change. This is why a lot of these
+titration experiments are so frustrating
+
+ align:start position:0%
+titration experiments are so frustrating
+ 
+
+ align:start position:0%
+titration experiments are so frustrating
+that you add a little bit too much and
+
+ align:start position:0%
+that you add a little bit too much and
+ 
+
+ align:start position:0%
+that you add a little bit too much and
+you're just way way way beyond the
+
+ align:start position:0%
+you're just way way way beyond the
+ 
+
+ align:start position:0%
+you're just way way way beyond the
+stoometric point. All right. So in one
+
+ align:start position:0%
+stoometric point. All right. So in one
+ 
+
+ align:start position:0%
+stoometric point. All right. So in one
+titration curve here we had three types
+
+ align:start position:0%
+titration curve here we had three types
+ 
+
+ align:start position:0%
+titration curve here we had three types
+of problems. But as we get into weak
+
+ align:start position:0%
+of problems. But as we get into weak
+ 
+
+ align:start position:0%
+of problems. But as we get into weak
+acid and weak base, which we'll do now,
+
+ align:start position:0%
+acid and weak base, which we'll do now,
+ 
+
+ align:start position:0%
+acid and weak base, which we'll do now,
+you'll see that a titration curve is
+
+ align:start position:0%
+you'll see that a titration curve is
+ 
+
+ align:start position:0%
+you'll see that a titration curve is
+actually all five types of problems. So
+
+ align:start position:0%
+actually all five types of problems. So
+ 
+
+ align:start position:0%
+actually all five types of problems. So
+this is why one wants to start problem
+
+ align:start position:0%
+this is why one wants to start problem
+ 
+
+ align:start position:0%
+this is why one wants to start problem
+set seven early.
+
+ align:start position:0%
+set seven early.
+ 
+
+ align:start position:0%
+set seven early.
+Okay, so we've done all of these now and
+
+ align:start position:0%
+Okay, so we've done all of these now and
+ 
+
+ align:start position:0%
+Okay, so we've done all of these now and
+now we can apply all of these types of
+
+ align:start position:0%
+now we can apply all of these types of
+ 
+
+ align:start position:0%
+now we can apply all of these types of
+problems while doing weak acid strong
+
+ align:start position:0%
+problems while doing weak acid strong
+ 
+
+ align:start position:0%
+problems while doing weak acid strong
+base part and we'll just start this and
+
+ align:start position:0%
+base part and we'll just start this and
+ 
+
+ align:start position:0%
+base part and we'll just start this and
+we'll continue it later. But let's go
+
+ align:start position:0%
+we'll continue it later. But let's go
+ 
+
+ align:start position:0%
+we'll continue it later. But let's go
+through the curves um now.
+
+ align:start position:0%
+through the curves um now.
+ 
+
+ align:start position:0%
+through the curves um now.
+So, um, this is in your handout. This is
+
+ align:start position:0%
+So, um, this is in your handout. This is
+ 
+
+ align:start position:0%
+So, um, this is in your handout. This is
+the curve for the weak acid and strong
+
+ align:start position:0%
+the curve for the weak acid and strong
+ 
+
+ align:start position:0%
+the curve for the weak acid and strong
+base. And I just want to remind you what
+
+ align:start position:0%
+base. And I just want to remind you what
+ 
+
+ align:start position:0%
+base. And I just want to remind you what
+we just talked about, which is strong
+
+ align:start position:0%
+we just talked about, which is strong
+ 
+
+ align:start position:0%
+we just talked about, which is strong
+acid and strong base. So, for weak acid
+
+ align:start position:0%
+acid and strong base. So, for weak acid
+ 
+
+ align:start position:0%
+acid and strong base. So, for weak acid
+and strong base, the curves look quite a
+
+ align:start position:0%
+and strong base, the curves look quite a
+ 
+
+ align:start position:0%
+and strong base, the curves look quite a
+bit different. So, here we start at a
+
+ align:start position:0%
+bit different. So, here we start at a
+ 
+
+ align:start position:0%
+bit different. So, here we start at a
+higher pH because it's a weak weak acid.
+
+ align:start position:0%
+higher pH because it's a weak weak acid.
+ 
+
+ align:start position:0%
+higher pH because it's a weak weak acid.
+Here's lower. It's a strong acid. Then
+
+ align:start position:0%
+Here's lower. It's a strong acid. Then
+ 
+
+ align:start position:0%
+Here's lower. It's a strong acid. Then
+we go up. the pH levels
+
+ align:start position:0%
+we go up. the pH levels
+ 
+
+ align:start position:0%
+we go up. the pH levels
+off and this is called the buffering
+
+ align:start position:0%
+off and this is called the buffering
+ 
+
+ align:start position:0%
+off and this is called the buffering
+region. There's no such buffering region
+
+ align:start position:0%
+region. There's no such buffering region
+ 
+
+ align:start position:0%
+region. There's no such buffering region
+with a strong acid strong base because
+
+ align:start position:0%
+with a strong acid strong base because
+ 
+
+ align:start position:0%
+with a strong acid strong base because
+strong acids and stone bases don't form
+
+ align:start position:0%
+strong acids and stone bases don't form
+ 
+
+ align:start position:0%
+strong acids and stone bases don't form
+good buffers. But weak acids and strong
+
+ align:start position:0%
+good buffers. But weak acids and strong
+ 
+
+ align:start position:0%
+good buffers. But weak acids and strong
+bases can generate good buffering region
+
+ align:start position:0%
+bases can generate good buffering region
+ 
+
+ align:start position:0%
+bases can generate good buffering region
+because a strong base can convert some
+
+ align:start position:0%
+because a strong base can convert some
+ 
+
+ align:start position:0%
+because a strong base can convert some
+of the weak acid to its conjugate weak
+
+ align:start position:0%
+of the weak acid to its conjugate weak
+ 
+
+ align:start position:0%
+of the weak acid to its conjugate weak
+base and that creates a buffer in this
+
+ align:start position:0%
+base and that creates a buffer in this
+ 
+
+ align:start position:0%
+base and that creates a buffer in this
+region. Then the pH starts to change
+
+ align:start position:0%
+region. Then the pH starts to change
+ 
+
+ align:start position:0%
+region. Then the pH starts to change
+again. It's constant in the buffering
+
+ align:start position:0%
+again. It's constant in the buffering
+ 
+
+ align:start position:0%
+again. It's constant in the buffering
+region. Starts to change again. You get
+
+ align:start position:0%
+region. Starts to change again. You get
+ 
+
+ align:start position:0%
+region. Starts to change again. You get
+to the equivalence point. The definition
+
+ align:start position:0%
+to the equivalence point. The definition
+ 
+
+ align:start position:0%
+to the equivalence point. The definition
+of equivalence points are the same.
+
+ align:start position:0%
+of equivalence points are the same.
+ 
+
+ align:start position:0%
+of equivalence points are the same.
+Equal number of moles of acids and base
+
+ align:start position:0%
+Equal number of moles of acids and base
+ 
+
+ align:start position:0%
+Equal number of moles of acids and base
+at the equivalence point. But now the
+
+ align:start position:0%
+at the equivalence point. But now the
+ 
+
+ align:start position:0%
+at the equivalence point. But now the
+equivalence point is not at pH7 anymore.
+
+ align:start position:0%
+equivalence point is not at pH7 anymore.
+ 
+
+ align:start position:0%
+equivalence point is not at pH7 anymore.
+It's greater than pH7 because we've
+
+ align:start position:0%
+It's greater than pH7 because we've
+ 
+
+ align:start position:0%
+It's greater than pH7 because we've
+converted our weak acid to its conjugate
+
+ align:start position:0%
+converted our weak acid to its conjugate
+ 
+
+ align:start position:0%
+converted our weak acid to its conjugate
+base. So up here we have conjugate base
+
+ align:start position:0%
+base. So up here we have conjugate base
+ 
+
+ align:start position:0%
+base. So up here we have conjugate base
+which makes it more basic. And so the pH
+
+ align:start position:0%
+which makes it more basic. And so the pH
+ 
+
+ align:start position:0%
+which makes it more basic. And so the pH
+is greater than seven. and then the
+
+ align:start position:0%
+is greater than seven. and then the
+ 
+
+ align:start position:0%
+is greater than seven. and then the
+curve goes up
+
+ align:start position:0%
+curve goes up
+ 
+
+ align:start position:0%
+curve goes up
+again. We also have something that's
+
+ align:start position:0%
+again. We also have something that's
+ 
+
+ align:start position:0%
+again. We also have something that's
+special for a weak uh weak with strong
+
+ align:start position:0%
+special for a weak uh weak with strong
+ 
+
+ align:start position:0%
+special for a weak uh weak with strong
+titration that doesn't exist with strong
+
+ align:start position:0%
+titration that doesn't exist with strong
+ 
+
+ align:start position:0%
+titration that doesn't exist with strong
+strong and that's called the half
+
+ align:start position:0%
+strong and that's called the half
+ 
+
+ align:start position:0%
+strong and that's called the half
+equivalence point. The half equivalence
+
+ align:start position:0%
+equivalence point. The half equivalence
+ 
+
+ align:start position:0%
+equivalence point. The half equivalence
+point is the point where half the volume
+
+ align:start position:0%
+point is the point where half the volume
+ 
+
+ align:start position:0%
+point is the point where half the volume
+and half the number of moles needed to
+
+ align:start position:0%
+and half the number of moles needed to
+ 
+
+ align:start position:0%
+and half the number of moles needed to
+reach the equivalence point have been
+
+ align:start position:0%
+reach the equivalence point have been
+ 
+
+ align:start position:0%
+reach the equivalence point have been
+added. So that's the half equivalence
+
+ align:start position:0%
+added. So that's the half equivalence
+ 
+
+ align:start position:0%
+added. So that's the half equivalence
+point. It's half of the equivalence
+
+ align:start position:0%
+point. It's half of the equivalence
+ 
+
+ align:start position:0%
+point. It's half of the equivalence
+point. All right. So, let's just look at
+
+ align:start position:0%
+point. All right. So, let's just look at
+ 
+
+ align:start position:0%
+point. All right. So, let's just look at
+these a couple of different points here
+
+ align:start position:0%
+these a couple of different points here
+ 
+
+ align:start position:0%
+these a couple of different points here
+um and look at at this um this figure
+
+ align:start position:0%
+um and look at at this um this figure
+ 
+
+ align:start position:0%
+um and look at at this um this figure
+here and we'll end with this. Um so, and
+
+ align:start position:0%
+here and we'll end with this. Um so, and
+ 
+
+ align:start position:0%
+here and we'll end with this. Um so, and
+uh and I'm just going to have my TAS
+
+ align:start position:0%
+uh and I'm just going to have my TAS
+ 
+
+ align:start position:0%
+uh and I'm just going to have my TAS
+come down and just help me with this
+
+ align:start position:0%
+come down and just help me with this
+ 
+
+ align:start position:0%
+come down and just help me with this
+this last part. Um so, let's see if we
+
+ align:start position:0%
+this last part. Um so, let's see if we
+ 
+
+ align:start position:0%
+this last part. Um so, let's see if we
+can get uh two more. Um we already have
+
+ align:start position:0%
+can get uh two more. Um we already have
+ 
+
+ align:start position:0%
+can get uh two more. Um we already have
+someone with a hat. You have a hat. We
+
+ align:start position:0%
+someone with a hat. You have a hat. We
+ 
+
+ align:start position:0%
+someone with a hat. You have a hat. We
+have uh two more TAs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, these are all weak acids
+
+ align:start position:0%
+All right. So, these are all weak acids
+ 
+
+ align:start position:0%
+All right. So, these are all weak acids
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+here. Um, so we have just our weak acids
+
+ align:start position:0%
+here. Um, so we have just our weak acids
+ 
+
+ align:start position:0%
+here. Um, so we have just our weak acids
+and we have four of them. Um, and so the
+
+ align:start position:0%
+and we have four of them. Um, and so the
+ 
+
+ align:start position:0%
+and we have four of them. Um, and so the
+TAs can come other TAs you want to come
+
+ align:start position:0%
+TAs can come other TAs you want to come
+ 
+
+ align:start position:0%
+TAs can come other TAs you want to come
+down can help out. This is volume equals
+
+ align:start position:0%
+down can help out. This is volume equals
+ 
+
+ align:start position:0%
+down can help out. This is volume equals
+zero. So, this is like a weak acid and
+
+ align:start position:0%
+zero. So, this is like a weak acid and
+ 
+
+ align:start position:0%
+zero. So, this is like a weak acid and
+water problem. So, now let's bring our
+
+ align:start position:0%
+water problem. So, now let's bring our
+ 
+
+ align:start position:0%
+water problem. So, now let's bring our
+moles of uh of strong base over here.
+
+ align:start position:0%
+moles of uh of strong base over here.
+ 
+
+ align:start position:0%
+moles of uh of strong base over here.
+So, now Amanda, you're a strong base.
+
+ align:start position:0%
+So, now Amanda, you're a strong base.
+ 
+
+ align:start position:0%
+So, now Amanda, you're a strong base.
+So, you're one. So, you're going to
+
+ align:start position:0%
+So, you're one. So, you're going to
+ 
+
+ align:start position:0%
+So, you're one. So, you're going to
+react just with one um with one of these
+
+ align:start position:0%
+react just with one um with one of these
+ 
+
+ align:start position:0%
+react just with one um with one of these
+uh con of these weak acids and
+
+ align:start position:0%
+uh con of these weak acids and
+ 
+
+ align:start position:0%
+uh con of these weak acids and
+deproinate it and form a conjugate base.
+
+ align:start position:0%
+deproinate it and form a conjugate base.
+ 
+
+ align:start position:0%
+deproinate it and form a conjugate base.
+There we go. And then you can you can go
+
+ align:start position:0%
+There we go. And then you can you can go
+ 
+
+ align:start position:0%
+There we go. And then you can you can go
+off and form your salt in water. All
+
+ align:start position:0%
+off and form your salt in water. All
+ 
+
+ align:start position:0%
+off and form your salt in water. All
+right. So, now we have a buffer
+
+ align:start position:0%
+right. So, now we have a buffer
+ 
+
+ align:start position:0%
+right. So, now we have a buffer
+situation. And we have a buffer
+
+ align:start position:0%
+situation. And we have a buffer
+ 
+
+ align:start position:0%
+situation. And we have a buffer
+situation when we have some conjugate
+
+ align:start position:0%
+situation when we have some conjugate
+ 
+
+ align:start position:0%
+situation when we have some conjugate
+acid and some conjugate base. We have a
+
+ align:start position:0%
+acid and some conjugate base. We have a
+ 
+
+ align:start position:0%
+acid and some conjugate base. We have a
+special type of category of buffer at
+
+ align:start position:0%
+special type of category of buffer at
+ 
+
+ align:start position:0%
+special type of category of buffer at
+the half equivalence point where you
+
+ align:start position:0%
+the half equivalence point where you
+ 
+
+ align:start position:0%
+the half equivalence point where you
+have half the conjugate acid, half the
+
+ align:start position:0%
+have half the conjugate acid, half the
+ 
+
+ align:start position:0%
+have half the conjugate acid, half the
+conjugate. So another mole of strong
+
+ align:start position:0%
+conjugate. So another mole of strong
+ 
+
+ align:start position:0%
+conjugate. So another mole of strong
+base comes in and deproenates one of our
+
+ align:start position:0%
+base comes in and deproenates one of our
+ 
+
+ align:start position:0%
+base comes in and deproenates one of our
+acids. So why don't you be Yeah. And you
+
+ align:start position:0%
+acids. So why don't you be Yeah. And you
+ 
+
+ align:start position:0%
+acids. So why don't you be Yeah. And you
+go off and form form a salt. And so then
+
+ align:start position:0%
+go off and form form a salt. And so then
+ 
+
+ align:start position:0%
+go off and form form a salt. And so then
+we have half the weak acid and half the
+
+ align:start position:0%
+we have half the weak acid and half the
+ 
+
+ align:start position:0%
+we have half the weak acid and half the
+conjugate base. Now as we go on, we're
+
+ align:start position:0%
+conjugate base. Now as we go on, we're
+ 
+
+ align:start position:0%
+conjugate base. Now as we go on, we're
+going to reach the equivalence point.
+
+ align:start position:0%
+going to reach the equivalence point.
+ 
+
+ align:start position:0%
+going to reach the equivalence point.
+And now we've added the amount of strong
+
+ align:start position:0%
+And now we've added the amount of strong
+ 
+
+ align:start position:0%
+And now we've added the amount of strong
+base that will fully deproinate our weak
+
+ align:start position:0%
+base that will fully deproinate our weak
+ 
+
+ align:start position:0%
+base that will fully deproinate our weak
+acid. So why don't we have two more
+
+ align:start position:0%
+acid. So why don't we have two more
+ 
+
+ align:start position:0%
+acid. So why don't we have two more
+strong bases come along and deproinate.
+
+ align:start position:0%
+strong bases come along and deproinate.
+ 
+
+ align:start position:0%
+strong bases come along and deproinate.
+And so now we have only weak bases left.
+
+ align:start position:0%
+And so now we have only weak bases left.
+ 
+
+ align:start position:0%
+And so now we have only weak bases left.
+They're just weak bases left because we
+
+ align:start position:0%
+They're just weak bases left because we
+ 
+
+ align:start position:0%
+They're just weak bases left because we
+added equal numbers of moles of our
+
+ align:start position:0%
+added equal numbers of moles of our
+ 
+
+ align:start position:0%
+added equal numbers of moles of our
+strong base as we had weak acid. So now
+
+ align:start position:0%
+strong base as we had weak acid. So now
+ 
+
+ align:start position:0%
+strong base as we had weak acid. So now
+we have conjugate base. So this is like
+
+ align:start position:0%
+we have conjugate base. So this is like
+ 
+
+ align:start position:0%
+we have conjugate base. So this is like
+a weak base in water problem. And then
+
+ align:start position:0%
+a weak base in water problem. And then
+ 
+
+ align:start position:0%
+a weak base in water problem. And then
+at the end if we add more strong base
+
+ align:start position:0%
+at the end if we add more strong base
+ 
+
+ align:start position:0%
+at the end if we add more strong base
+and a strong base comes over there's
+
+ align:start position:0%
+and a strong base comes over there's
+ 
+
+ align:start position:0%
+and a strong base comes over there's
+nothing to do. He's just strong base in
+
+ align:start position:0%
+nothing to do. He's just strong base in
+ 
+
+ align:start position:0%
+nothing to do. He's just strong base in
+solution. And so this is a strong base
+
+ align:start position:0%
+solution. And so this is a strong base
+ 
+
+ align:start position:0%
+solution. And so this is a strong base
+and water problem. So the point is one
+
+ align:start position:0%
+and water problem. So the point is one
+ 
+
+ align:start position:0%
+and water problem. So the point is one
+titration problem is really five
+
+ align:start position:0%
+titration problem is really five
+ 
+
+ align:start position:0%
+titration problem is really five
+different types of acid base problems.
+
+ align:start position:0%
+different types of acid base problems.
+ 
+
+ align:start position:0%
+different types of acid base problems.
+So start problem set seven early. See
+
+ align:start position:0%
+So start problem set seven early. See
+ 
+
+ align:start position:0%
+So start problem set seven early. See
+you on
+
+ align:start position:0%
+you on
+ 
+
+ align:start position:0%
+you on
+Wednesday. All right. Let's just take 10
+
+ align:start position:0%
+Wednesday. All right. Let's just take 10
+ 
+
+ align:start position:0%
+Wednesday. All right. Let's just take 10
+more seconds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I have a feeling that more people
+
+ align:start position:0%
+Okay, I have a feeling that more people
+ 
+
+ align:start position:0%
+Okay, I have a feeling that more people
+understand how to do this, but it's just
+
+ align:start position:0%
+understand how to do this, but it's just
+ 
+
+ align:start position:0%
+understand how to do this, but it's just
+a matter of thinking about the sort of
+
+ align:start position:0%
+a matter of thinking about the sort of
+ 
+
+ align:start position:0%
+a matter of thinking about the sort of
+the sign of things. Um, so the the trick
+
+ align:start position:0%
+the sign of things. Um, so the the trick
+ 
+
+ align:start position:0%
+the sign of things. Um, so the the trick
+here, you have a pH of four, pKa of
+
+ align:start position:0%
+here, you have a pH of four, pKa of
+ 
+
+ align:start position:0%
+here, you have a pH of four, pKa of
+49. And so obviously it's the
+
+ align:start position:0%
+49. And so obviously it's the
+ 
+
+ align:start position:0%
+49. And so obviously it's the
+difference, but you have to think about
+
+ align:start position:0%
+difference, but you have to think about
+ 
+
+ align:start position:0%
+difference, but you have to think about
+if you're uh if you want the ratio to be
+
+ align:start position:0%
+if you're uh if you want the ratio to be
+ 
+
+ align:start position:0%
+if you're uh if you want the ratio to be
+a minus to a um which expression you're
+
+ align:start position:0%
+a minus to a um which expression you're
+ 
+
+ align:start position:0%
+a minus to a um which expression you're
+going to use here to give you the the
+
+ align:start position:0%
+going to use here to give you the the
+ 
+
+ align:start position:0%
+going to use here to give you the the
+correct uh the correct one. So um just
+
+ align:start position:0%
+correct uh the correct one. So um just
+ 
+
+ align:start position:0%
+correct uh the correct one. So um just
+pay attention to your sign. always show
+
+ align:start position:0%
+pay attention to your sign. always show
+ 
+
+ align:start position:0%
+pay attention to your sign. always show
+lot all your work on an exam. So today
+
+ align:start position:0%
+lot all your work on an exam. So today
+ 
+
+ align:start position:0%
+lot all your work on an exam. So today
+we're going to finish the lecture notes
+
+ align:start position:0%
+we're going to finish the lecture notes
+ 
+
+ align:start position:0%
+we're going to finish the lecture notes
+from last time on titrations, continue
+
+ align:start position:0%
+from last time on titrations, continue
+ 
+
+ align:start position:0%
+from last time on titrations, continue
+with titrations and toward the end of
+
+ align:start position:0%
+with titrations and toward the end of
+ 
+
+ align:start position:0%
+with titrations and toward the end of
+the class we're going to start the next
+
+ align:start position:0%
+the class we're going to start the next
+ 
+
+ align:start position:0%
+the class we're going to start the next
+unit which is oxidation reduction. So we
+
+ align:start position:0%
+unit which is oxidation reduction. So we
+ 
+
+ align:start position:0%
+unit which is oxidation reduction. So we
+want to take out uh lecture note 23 top
+
+ align:start position:0%
+want to take out uh lecture note 23 top
+ 
+
+ align:start position:0%
+want to take out uh lecture note 23 top
+of page four where we had this curve.
+
+ align:start position:0%
+of page four where we had this curve.
+ 
+
+ align:start position:0%
+of page four where we had this curve.
+So, as we were finishing last time, we
+
+ align:start position:0%
+So, as we were finishing last time, we
+ 
+
+ align:start position:0%
+So, as we were finishing last time, we
+saw the curve for a titration of a weak
+
+ align:start position:0%
+saw the curve for a titration of a weak
+ 
+
+ align:start position:0%
+saw the curve for a titration of a weak
+acid with a strong base. And this is the
+
+ align:start position:0%
+acid with a strong base. And this is the
+ 
+
+ align:start position:0%
+acid with a strong base. And this is the
+curve for a weak base that's being
+
+ align:start position:0%
+curve for a weak base that's being
+ 
+
+ align:start position:0%
+curve for a weak base that's being
+titrated with a strong acid. And drawing
+
+ align:start position:0%
+titrated with a strong acid. And drawing
+ 
+
+ align:start position:0%
+titrated with a strong acid. And drawing
+curves on an exam, that's one of my
+
+ align:start position:0%
+curves on an exam, that's one of my
+ 
+
+ align:start position:0%
+curves on an exam, that's one of my
+favorite exam questions. Um, so make
+
+ align:start position:0%
+favorite exam questions. Um, so make
+ 
+
+ align:start position:0%
+favorite exam questions. Um, so make
+sure you know how to draw these types of
+
+ align:start position:0%
+sure you know how to draw these types of
+ 
+
+ align:start position:0%
+sure you know how to draw these types of
+titrations. So, things that you should
+
+ align:start position:0%
+titrations. So, things that you should
+ 
+
+ align:start position:0%
+titrations. So, things that you should
+pay attention to in drawing them. if it
+
+ align:start position:0%
+pay attention to in drawing them. if it
+ 
+
+ align:start position:0%
+pay attention to in drawing them. if it
+is a weak base that's being titrated
+
+ align:start position:0%
+is a weak base that's being titrated
+ 
+
+ align:start position:0%
+is a weak base that's being titrated
+with a strong acid, you would expect
+
+ align:start position:0%
+with a strong acid, you would expect
+ 
+
+ align:start position:0%
+with a strong acid, you would expect
+that before you've added any
+
+ align:start position:0%
+that before you've added any
+ 
+
+ align:start position:0%
+that before you've added any
+acid that you're going to have a basic
+
+ align:start position:0%
+acid that you're going to have a basic
+ 
+
+ align:start position:0%
+acid that you're going to have a basic
+pH. So at 0 here, you would expect a
+
+ align:start position:0%
+pH. So at 0 here, you would expect a
+ 
+
+ align:start position:0%
+pH. So at 0 here, you would expect a
+basic pH.
+
+ align:start position:0%
+basic pH.
+ 
+
+ align:start position:0%
+basic pH.
+So then the pH starts decreasing as
+
+ align:start position:0%
+So then the pH starts decreasing as
+ 
+
+ align:start position:0%
+So then the pH starts decreasing as
+you're titrating in the strong acid and
+
+ align:start position:0%
+you're titrating in the strong acid and
+ 
+
+ align:start position:0%
+you're titrating in the strong acid and
+you go into this region of constant pH
+
+ align:start position:0%
+you go into this region of constant pH
+ 
+
+ align:start position:0%
+you go into this region of constant pH
+um where that's the buffering region. So
+
+ align:start position:0%
+um where that's the buffering region. So
+ 
+
+ align:start position:0%
+um where that's the buffering region. So
+the pH is changing very little. It
+
+ align:start position:0%
+the pH is changing very little. It
+ 
+
+ align:start position:0%
+the pH is changing very little. It
+plateaus. It's flat. So when you're
+
+ align:start position:0%
+plateaus. It's flat. So when you're
+ 
+
+ align:start position:0%
+plateaus. It's flat. So when you're
+drawing a region like this, make sure
+
+ align:start position:0%
+drawing a region like this, make sure
+ 
+
+ align:start position:0%
+drawing a region like this, make sure
+that in the curve it looks kind of flat
+
+ align:start position:0%
+that in the curve it looks kind of flat
+ 
+
+ align:start position:0%
+that in the curve it looks kind of flat
+because the idea of a buffering region
+
+ align:start position:0%
+because the idea of a buffering region
+ 
+
+ align:start position:0%
+because the idea of a buffering region
+is that the pH isn't changing much. Here
+
+ align:start position:0%
+is that the pH isn't changing much. Here
+ 
+
+ align:start position:0%
+is that the pH isn't changing much. Here
+you have the conjugate acid and the
+
+ align:start position:0%
+you have the conjugate acid and the
+ 
+
+ align:start position:0%
+you have the conjugate acid and the
+conjugate conjugate base. So it's a
+
+ align:start position:0%
+conjugate conjugate base. So it's a
+ 
+
+ align:start position:0%
+conjugate conjugate base. So it's a
+buffer-like problem. Then when you get
+
+ align:start position:0%
+buffer-like problem. Then when you get
+ 
+
+ align:start position:0%
+buffer-like problem. Then when you get
+out of that buffering region, the pH
+
+ align:start position:0%
+out of that buffering region, the pH
+ 
+
+ align:start position:0%
+out of that buffering region, the pH
+drops rapidly, which is often one of the
+
+ align:start position:0%
+drops rapidly, which is often one of the
+ 
+
+ align:start position:0%
+drops rapidly, which is often one of the
+funs in doing these titrations in lab.
+
+ align:start position:0%
+funs in doing these titrations in lab.
+ 
+
+ align:start position:0%
+funs in doing these titrations in lab.
+Nothing's changing. Nothing's changing.
+
+ align:start position:0%
+Nothing's changing. Nothing's changing.
+ 
+
+ align:start position:0%
+Nothing's changing. Nothing's changing.
+Nothing changing. And all of a sudden,
+
+ align:start position:0%
+Nothing changing. And all of a sudden,
+ 
+
+ align:start position:0%
+Nothing changing. And all of a sudden,
+you're down here. Um, so at the
+
+ align:start position:0%
+you're down here. Um, so at the
+ 
+
+ align:start position:0%
+you're down here. Um, so at the
+equivalence point here, the equivalence
+
+ align:start position:0%
+equivalence point here, the equivalence
+ 
+
+ align:start position:0%
+equivalence point here, the equivalence
+point is going to be below pH7 because
+
+ align:start position:0%
+point is going to be below pH7 because
+ 
+
+ align:start position:0%
+point is going to be below pH7 because
+at this point you have added the same
+
+ align:start position:0%
+at this point you have added the same
+ 
+
+ align:start position:0%
+at this point you have added the same
+number of moles of acid as the weak
+
+ align:start position:0%
+number of moles of acid as the weak
+ 
+
+ align:start position:0%
+number of moles of acid as the weak
+base. So you've converted all of the
+
+ align:start position:0%
+base. So you've converted all of the
+ 
+
+ align:start position:0%
+base. So you've converted all of the
+weak base to its conjugate acid. So the
+
+ align:start position:0%
+weak base to its conjugate acid. So the
+ 
+
+ align:start position:0%
+weak base to its conjugate acid. So the
+pH is below seven and then it drops off
+
+ align:start position:0%
+pH is below seven and then it drops off
+ 
+
+ align:start position:0%
+pH is below seven and then it drops off
+rapidly. So again in these titration
+
+ align:start position:0%
+rapidly. So again in these titration
+ 
+
+ align:start position:0%
+rapidly. So again in these titration
+problems there really five different
+
+ align:start position:0%
+problems there really five different
+ 
+
+ align:start position:0%
+problems there really five different
+types of problems within them. When you
+
+ align:start position:0%
+types of problems within them. When you
+ 
+
+ align:start position:0%
+types of problems within them. When you
+have the volume of zero it's a weak
+
+ align:start position:0%
+have the volume of zero it's a weak
+ 
+
+ align:start position:0%
+have the volume of zero it's a weak
+basin water problem. In this buffering
+
+ align:start position:0%
+basin water problem. In this buffering
+ 
+
+ align:start position:0%
+basin water problem. In this buffering
+region here it's a buffer problem. And
+
+ align:start position:0%
+region here it's a buffer problem. And
+ 
+
+ align:start position:0%
+region here it's a buffer problem. And
+there's a special kind of buffer problem
+
+ align:start position:0%
+there's a special kind of buffer problem
+ 
+
+ align:start position:0%
+there's a special kind of buffer problem
+at the half equivalence point where the
+
+ align:start position:0%
+at the half equivalence point where the
+ 
+
+ align:start position:0%
+at the half equivalence point where the
+number of moles of the conjugate acid
+
+ align:start position:0%
+number of moles of the conjugate acid
+ 
+
+ align:start position:0%
+number of moles of the conjugate acid
+formed equal the number of moles of
+
+ align:start position:0%
+formed equal the number of moles of
+ 
+
+ align:start position:0%
+formed equal the number of moles of
+base. And then we get to the equivalence
+
+ align:start position:0%
+base. And then we get to the equivalence
+ 
+
+ align:start position:0%
+base. And then we get to the equivalence
+point and now we've converted all the
+
+ align:start position:0%
+point and now we've converted all the
+ 
+
+ align:start position:0%
+point and now we've converted all the
+weak base to its conjugate acid. So this
+
+ align:start position:0%
+weak base to its conjugate acid. So this
+ 
+
+ align:start position:0%
+weak base to its conjugate acid. So this
+is just a weak acid and water problem.
+
+ align:start position:0%
+is just a weak acid and water problem.
+ 
+
+ align:start position:0%
+is just a weak acid and water problem.
+And then down here it's a strong acid
+
+ align:start position:0%
+And then down here it's a strong acid
+ 
+
+ align:start position:0%
+And then down here it's a strong acid
+and water problem. So again, the trick
+
+ align:start position:0%
+and water problem. So again, the trick
+ 
+
+ align:start position:0%
+and water problem. So again, the trick
+in doing these is to recognize where you
+
+ align:start position:0%
+in doing these is to recognize where you
+ 
+
+ align:start position:0%
+in doing these is to recognize where you
+are in the curve and figure out what
+
+ align:start position:0%
+are in the curve and figure out what
+ 
+
+ align:start position:0%
+are in the curve and figure out what
+type of problem it is. Once you figure
+
+ align:start position:0%
+type of problem it is. Once you figure
+ 
+
+ align:start position:0%
+type of problem it is. Once you figure
+out what type of problem it is, it's
+
+ align:start position:0%
+out what type of problem it is, it's
+ 
+
+ align:start position:0%
+out what type of problem it is, it's
+usually not so bad to solve it because
+
+ align:start position:0%
+usually not so bad to solve it because
+ 
+
+ align:start position:0%
+usually not so bad to solve it because
+you can all figure out how to solve
+
+ align:start position:0%
+you can all figure out how to solve
+ 
+
+ align:start position:0%
+you can all figure out how to solve
+these five types of problems. It's
+
+ align:start position:0%
+these five types of problems. It's
+ 
+
+ align:start position:0%
+these five types of problems. It's
+recognizing what type of problem it is
+
+ align:start position:0%
+recognizing what type of problem it is
+ 
+
+ align:start position:0%
+recognizing what type of problem it is
+at various time during the titration.
+
+ align:start position:0%
+at various time during the titration.
+ 
+
+ align:start position:0%
+at various time during the titration.
+And in some of the uh problem set
+
+ align:start position:0%
+And in some of the uh problem set
+ 
+
+ align:start position:0%
+And in some of the uh problem set
+problems, you'll have all of the various
+
+ align:start position:0%
+problems, you'll have all of the various
+ 
+
+ align:start position:0%
+problems, you'll have all of the various
+points to do. But on an exam, you're
+
+ align:start position:0%
+points to do. But on an exam, you're
+ 
+
+ align:start position:0%
+points to do. But on an exam, you're
+going to just be thrown into the middle
+
+ align:start position:0%
+going to just be thrown into the middle
+ 
+
+ align:start position:0%
+going to just be thrown into the middle
+of a titration and have to think about
+
+ align:start position:0%
+of a titration and have to think about
+ 
+
+ align:start position:0%
+of a titration and have to think about
+where it is in the midst of titration.
+
+ align:start position:0%
+where it is in the midst of titration.
+ 
+
+ align:start position:0%
+where it is in the midst of titration.
+What type of problem is it? All right.
+
+ align:start position:0%
+What type of problem is it? All right.
+ 
+
+ align:start position:0%
+What type of problem is it? All right.
+So now we're going to go through and do
+
+ align:start position:0%
+So now we're going to go through and do
+ 
+
+ align:start position:0%
+So now we're going to go through and do
+an example work kind of point by point
+
+ align:start position:0%
+an example work kind of point by point
+ 
+
+ align:start position:0%
+an example work kind of point by point
+for a titration. And the titration we're
+
+ align:start position:0%
+for a titration. And the titration we're
+ 
+
+ align:start position:0%
+for a titration. And the titration we're
+going to do is a weak acid and a strong
+
+ align:start position:0%
+going to do is a weak acid and a strong
+ 
+
+ align:start position:0%
+going to do is a weak acid and a strong
+base. So that's the curve here. So we
+
+ align:start position:0%
+base. So that's the curve here. So we
+ 
+
+ align:start position:0%
+base. So that's the curve here. So we
+start at low pH and then go up. So the
+
+ align:start position:0%
+start at low pH and then go up. So the
+ 
+
+ align:start position:0%
+start at low pH and then go up. So the
+particular problem we're going to work
+
+ align:start position:0%
+particular problem we're going to work
+ 
+
+ align:start position:0%
+particular problem we're going to work
+and we're going to work all these points
+
+ align:start position:0%
+and we're going to work all these points
+ 
+
+ align:start position:0%
+and we're going to work all these points
+and we're going to have a bonus point E
+
+ align:start position:0%
+and we're going to have a bonus point E
+ 
+
+ align:start position:0%
+and we're going to have a bonus point E
+at the end um is formic acid and we have
+
+ align:start position:0%
+at the end um is formic acid and we have
+ 
+
+ align:start position:0%
+at the end um is formic acid and we have
+25 ms of 0.1 molar formic acid and we're
+
+ align:start position:0%
+25 ms of 0.1 molar formic acid and we're
+ 
+
+ align:start position:0%
+25 ms of 0.1 molar formic acid and we're
+titrating with a strong base sodium
+
+ align:start position:0%
+titrating with a strong base sodium
+ 
+
+ align:start position:0%
+titrating with a strong base sodium
+hydroxide 0.15 molar and you're often
+
+ align:start position:0%
+hydroxide 0.15 molar and you're often
+ 
+
+ align:start position:0%
+hydroxide 0.15 molar and you're often
+going to be given the Ka of the
+
+ align:start position:0%
+going to be given the Ka of the
+ 
+
+ align:start position:0%
+going to be given the Ka of the
+acid. So the first point A is volume
+
+ align:start position:0%
+acid. So the first point A is volume
+ 
+
+ align:start position:0%
+acid. So the first point A is volume
+zero. You haven't added any of your
+
+ align:start position:0%
+zero. You haven't added any of your
+ 
+
+ align:start position:0%
+zero. You haven't added any of your
+strong base
+
+ align:start position:0%
+strong base
+ 
+
+ align:start position:0%
+strong base
+yet. So you can write the expression for
+
+ align:start position:0%
+yet. So you can write the expression for
+ 
+
+ align:start position:0%
+yet. So you can write the expression for
+what's going on there. You have your
+
+ align:start position:0%
+what's going on there. You have your
+ 
+
+ align:start position:0%
+what's going on there. You have your
+acid plus water going to hydrronium ion
+
+ align:start position:0%
+acid plus water going to hydrronium ion
+ 
+
+ align:start position:0%
+acid plus water going to hydrronium ion
+concentration and you're forming the
+
+ align:start position:0%
+concentration and you're forming the
+ 
+
+ align:start position:0%
+concentration and you're forming the
+conjugate base of that weak acid. So
+
+ align:start position:0%
+conjugate base of that weak acid. So
+ 
+
+ align:start position:0%
+conjugate base of that weak acid. So
+this is again a weak acid problem. So
+
+ align:start position:0%
+this is again a weak acid problem. So
+ 
+
+ align:start position:0%
+this is again a weak acid problem. So
+you know how to do weak acid problems.
+
+ align:start position:0%
+you know how to do weak acid problems.
+ 
+
+ align:start position:0%
+you know how to do weak acid problems.
+So titrations are just the collection of
+
+ align:start position:0%
+So titrations are just the collection of
+ 
+
+ align:start position:0%
+So titrations are just the collection of
+problems we've already talked about how
+
+ align:start position:0%
+problems we've already talked about how
+ 
+
+ align:start position:0%
+problems we've already talked about how
+to do. So just uh very briefly, we'll go
+
+ align:start position:0%
+to do. So just uh very briefly, we'll go
+ 
+
+ align:start position:0%
+to do. So just uh very briefly, we'll go
+through this pretty fast at this point.
+
+ align:start position:0%
+through this pretty fast at this point.
+ 
+
+ align:start position:0%
+through this pretty fast at this point.
+Um so we have our weak acid in water. We
+
+ align:start position:0%
+Um so we have our weak acid in water. We
+ 
+
+ align:start position:0%
+Um so we have our weak acid in water. We
+had 0.1 molar and uh we had none of the
+
+ align:start position:0%
+had 0.1 molar and uh we had none of the
+ 
+
+ align:start position:0%
+had 0.1 molar and uh we had none of the
+other to begin with. So we're at zero
+
+ align:start position:0%
+other to begin with. So we're at zero
+ 
+
+ align:start position:0%
+other to begin with. So we're at zero
+volume here. So as the equilibrium is
+
+ align:start position:0%
+volume here. So as the equilibrium is
+ 
+
+ align:start position:0%
+volume here. So as the equilibrium is
+reached, we have 0.1 - x and x. So
+
+ align:start position:0%
+reached, we have 0.1 - x and x. So
+ 
+
+ align:start position:0%
+reached, we have 0.1 - x and x. So
+because this is a weak acid in water
+
+ align:start position:0%
+because this is a weak acid in water
+ 
+
+ align:start position:0%
+because this is a weak acid in water
+problem, we can use K a to solve the
+
+ align:start position:0%
+problem, we can use K a to solve the
+ 
+
+ align:start position:0%
+problem, we can use K a to solve the
+problem which is our acid ionization
+
+ align:start position:0%
+problem which is our acid ionization
+ 
+
+ align:start position:0%
+problem which is our acid ionization
+constant. It's 1.77 * 10us4 for this
+
+ align:start position:0%
+constant. It's 1.77 * 10us4 for this
+ 
+
+ align:start position:0%
+constant. It's 1.77 * 10us4 for this
+particular one. We can uh set this up.
+
+ align:start position:0%
+particular one. We can uh set this up.
+ 
+
+ align:start position:0%
+particular one. We can uh set this up.
+It's products over reactants at
+
+ align:start position:0%
+It's products over reactants at
+ 
+
+ align:start position:0%
+It's products over reactants at
+equilibrium. So x^2 over.1
+
+ align:start position:0%
+equilibrium. So x^2 over.1
+ 
+
+ align:start position:0%
+equilibrium. So x^2 over.1
+um 0 - x. Again, water doesn't fit in.
+
+ align:start position:0%
+um 0 - x. Again, water doesn't fit in.
+ 
+
+ align:start position:0%
+um 0 - x. Again, water doesn't fit in.
+That's our solvent. So it's not in our
+
+ align:start position:0%
+That's our solvent. So it's not in our
+ 
+
+ align:start position:0%
+That's our solvent. So it's not in our
+expression. We can solve this with a
+
+ align:start position:0%
+expression. We can solve this with a
+ 
+
+ align:start position:0%
+expression. We can solve this with a
+quadratic or we can assume that X is
+
+ align:start position:0%
+quadratic or we can assume that X is
+ 
+
+ align:start position:0%
+quadratic or we can assume that X is
+small which again is a pretty good
+
+ align:start position:0%
+small which again is a pretty good
+ 
+
+ align:start position:0%
+small which again is a pretty good
+assumption usually for a weak acid
+
+ align:start position:0%
+assumption usually for a weak acid
+ 
+
+ align:start position:0%
+assumption usually for a weak acid
+problem. Um and by assuming X is small
+
+ align:start position:0%
+problem. Um and by assuming X is small
+ 
+
+ align:start position:0%
+problem. Um and by assuming X is small
+that means this minus X drops out. So
+
+ align:start position:0%
+that means this minus X drops out. So
+ 
+
+ align:start position:0%
+that means this minus X drops out. So
+we're saying X is small compared to the
+
+ align:start position:0%
+we're saying X is small compared to the
+ 
+
+ align:start position:0%
+we're saying X is small compared to the
+concentration that we started with and
+
+ align:start position:0%
+concentration that we started with and
+ 
+
+ align:start position:0%
+concentration that we started with and
+then we can solve for X. If we do that
+
+ align:start position:0%
+then we can solve for X. If we do that
+ 
+
+ align:start position:0%
+then we can solve for X. If we do that
+here, we get um
+
+ align:start position:0%
+here, we get um
+ 
+
+ align:start position:0%
+here, we get um
+0.004 uh
+
+ align:start position:0%
+0.004 uh
+ 
+
+ align:start position:0%
+0.004 uh
+21 and that we can check and we find
+
+ align:start position:0%
+21 and that we can check and we find
+ 
+
+ align:start position:0%
+21 and that we can check and we find
+that it is 4.2% of 0.1. So that's under
+
+ align:start position:0%
+that it is 4.2% of 0.1. So that's under
+ 
+
+ align:start position:0%
+that it is 4.2% of 0.1. So that's under
+5%. So that assumption is okay. Again,
+
+ align:start position:0%
+5%. So that assumption is okay. Again,
+ 
+
+ align:start position:0%
+5%. So that assumption is okay. Again,
+we're using the 5% rule. And then we can
+
+ align:start position:0%
+we're using the 5% rule. And then we can
+ 
+
+ align:start position:0%
+we're using the 5% rule. And then we can
+uh solve this. X is our hydrronium ion
+
+ align:start position:0%
+uh solve this. X is our hydrronium ion
+ 
+
+ align:start position:0%
+uh solve this. X is our hydrronium ion
+concentration. So we can plug that in
+
+ align:start position:0%
+concentration. So we can plug that in
+ 
+
+ align:start position:0%
+concentration. So we can plug that in
+and get an answer. But now I want you to
+
+ align:start position:0%
+and get an answer. But now I want you to
+ 
+
+ align:start position:0%
+and get an answer. But now I want you to
+tell me how many sigfigs this has. And
+
+ align:start position:0%
+tell me how many sigfigs this has. And
+ 
+
+ align:start position:0%
+tell me how many sigfigs this has. And
+to do that, you have to figure out how
+
+ align:start position:0%
+to do that, you have to figure out how
+ 
+
+ align:start position:0%
+to do that, you have to figure out how
+many sigfigs were actually in this
+
+ align:start position:0%
+many sigfigs were actually in this
+ 
+
+ align:start position:0%
+many sigfigs were actually in this
+number here. So you have to go back and
+
+ align:start position:0%
+number here. So you have to go back and
+ 
+
+ align:start position:0%
+number here. So you have to go back and
+look at the problem and figure out the
+
+ align:start position:0%
+look at the problem and figure out the
+ 
+
+ align:start position:0%
+look at the problem and figure out the
+total number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sigfigs. See how easy that was to fix.
+
+ align:start position:0%
+sigfigs. See how easy that was to fix.
+ 
+
+ align:start position:0%
+sigfigs. See how easy that was to fix.
+Um so it is two because this had two And
+
+ align:start position:0%
+Um so it is two because this had two And
+ 
+
+ align:start position:0%
+Um so it is two because this had two And
+the concentration was limiting here to
+
+ align:start position:0%
+the concentration was limiting here to
+ 
+
+ align:start position:0%
+the concentration was limiting here to
+two significant figures. So there were
+
+ align:start position:0%
+two significant figures. So there were
+ 
+
+ align:start position:0%
+two significant figures. So there were
+two here, which means there are two
+
+ align:start position:0%
+two here, which means there are two
+ 
+
+ align:start position:0%
+two here, which means there are two
+after the decimal point here. And I have
+
+ align:start position:0%
+after the decimal point here. And I have
+ 
+
+ align:start position:0%
+after the decimal point here. And I have
+to say, I was looking at problem set
+
+ align:start position:0%
+to say, I was looking at problem set
+ 
+
+ align:start position:0%
+to say, I was looking at problem set
+seven. And some of those problems are
+
+ align:start position:0%
+seven. And some of those problems are
+ 
+
+ align:start position:0%
+seven. And some of those problems are
+just like, if you love significant
+
+ align:start position:0%
+just like, if you love significant
+ 
+
+ align:start position:0%
+just like, if you love significant
+figures, they're a joy because you got
+
+ align:start position:0%
+figures, they're a joy because you got
+ 
+
+ align:start position:0%
+figures, they're a joy because you got
+adding and subtracting and then you had
+
+ align:start position:0%
+adding and subtracting and then you had
+ 
+
+ align:start position:0%
+adding and subtracting and then you had
+division and then you have logs. It is
+
+ align:start position:0%
+division and then you have logs. It is
+ 
+
+ align:start position:0%
+division and then you have logs. It is
+the triple whammy of sigfig love. All
+
+ align:start position:0%
+the triple whammy of sigfig love. All
+ 
+
+ align:start position:0%
+the triple whammy of sigfig love. All
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+Um, so two after the decimal
+
+ align:start position:0%
+Um, so two after the decimal
+ 
+
+ align:start position:0%
+Um, so two after the decimal
+point. All right. So we have
+
+ align:start position:0%
+point. All right. So we have
+ 
+
+ align:start position:0%
+point. All right. So we have
+0.1. We have a pH that's acidic. That's
+
+ align:start position:0%
+0.1. We have a pH that's acidic. That's
+ 
+
+ align:start position:0%
+0.1. We have a pH that's acidic. That's
+good because at the beginning all we
+
+ align:start position:0%
+good because at the beginning all we
+ 
+
+ align:start position:0%
+good because at the beginning all we
+have is a weak acid. So we have a pH of
+
+ align:start position:0%
+have is a weak acid. So we have a pH of
+ 
+
+ align:start position:0%
+have is a weak acid. So we have a pH of
+2.38. So that's point A. So now let's
+
+ align:start position:0%
+2.38. So that's point A. So now let's
+ 
+
+ align:start position:0%
+2.38. So that's point A. So now let's
+look at this region here in the
+
+ align:start position:0%
+look at this region here in the
+ 
+
+ align:start position:0%
+look at this region here in the
+buffering region. And again the
+
+ align:start position:0%
+buffering region. And again the
+ 
+
+ align:start position:0%
+buffering region. And again the
+buffering region is when you have added
+
+ align:start position:0%
+buffering region is when you have added
+ 
+
+ align:start position:0%
+buffering region is when you have added
+volumes of your acid that are greater
+
+ align:start position:0%
+volumes of your acid that are greater
+ 
+
+ align:start position:0%
+volumes of your acid that are greater
+than zero but less than the volume
+
+ align:start position:0%
+than zero but less than the volume
+ 
+
+ align:start position:0%
+than zero but less than the volume
+needed to reach equilibrium.
+
+ align:start position:0%
+needed to reach equilibrium.
+ 
+
+ align:start position:0%
+needed to reach equilibrium.
+And so in this particular problem, we're
+
+ align:start position:0%
+And so in this particular problem, we're
+ 
+
+ align:start position:0%
+And so in this particular problem, we're
+going to calculate what happens when
+
+ align:start position:0%
+going to calculate what happens when
+ 
+
+ align:start position:0%
+going to calculate what happens when
+five ms of our strong base are added. So
+
+ align:start position:0%
+five ms of our strong base are added. So
+ 
+
+ align:start position:0%
+five ms of our strong base are added. So
+this is basically point B here. And
+
+ align:start position:0%
+this is basically point B here. And
+ 
+
+ align:start position:0%
+this is basically point B here. And
+because it's a strong base, it's going
+
+ align:start position:0%
+because it's a strong base, it's going
+ 
+
+ align:start position:0%
+because it's a strong base, it's going
+to react with all of our of the same
+
+ align:start position:0%
+to react with all of our of the same
+ 
+
+ align:start position:0%
+to react with all of our of the same
+number of moles of our weak acid. It's
+
+ align:start position:0%
+number of moles of our weak acid. It's
+ 
+
+ align:start position:0%
+number of moles of our weak acid. It's
+much stronger than the conjugate base.
+
+ align:start position:0%
+much stronger than the conjugate base.
+ 
+
+ align:start position:0%
+much stronger than the conjugate base.
+So it's going to react pretty much
+
+ align:start position:0%
+So it's going to react pretty much
+ 
+
+ align:start position:0%
+So it's going to react pretty much
+completely with this. So we can write
+
+ align:start position:0%
+completely with this. So we can write
+ 
+
+ align:start position:0%
+completely with this. So we can write
+out that the weak acid plus um our base
+
+ align:start position:0%
+out that the weak acid plus um our base
+ 
+
+ align:start position:0%
+out that the weak acid plus um our base
+are going to be converted over to the
+
+ align:start position:0%
+are going to be converted over to the
+ 
+
+ align:start position:0%
+are going to be converted over to the
+conjugate uh the conjugate base of this
+
+ align:start position:0%
+conjugate uh the conjugate base of this
+ 
+
+ align:start position:0%
+conjugate uh the conjugate base of this
+weak acid. So we just we can just figure
+
+ align:start position:0%
+weak acid. So we just we can just figure
+ 
+
+ align:start position:0%
+weak acid. So we just we can just figure
+out the moles and then subtract them to
+
+ align:start position:0%
+out the moles and then subtract them to
+ 
+
+ align:start position:0%
+out the moles and then subtract them to
+understand how much is uh is left and
+
+ align:start position:0%
+understand how much is uh is left and
+ 
+
+ align:start position:0%
+understand how much is uh is left and
+how much is being formed. So first then
+
+ align:start position:0%
+how much is being formed. So first then
+ 
+
+ align:start position:0%
+how much is being formed. So first then
+we need to figure out how many moles we
+
+ align:start position:0%
+we need to figure out how many moles we
+ 
+
+ align:start position:0%
+we need to figure out how many moles we
+had initially. So for our acid we had 25
+
+ align:start position:0%
+had initially. So for our acid we had 25
+ 
+
+ align:start position:0%
+had initially. So for our acid we had 25
+ms of 0.10 molar. So we have 2.5 * 10us3
+
+ align:start position:0%
+ms of 0.10 molar. So we have 2.5 * 10us3
+ 
+
+ align:start position:0%
+ms of 0.10 molar. So we have 2.5 * 10us3
+moles for our hydroxide our strong base
+
+ align:start position:0%
+moles for our hydroxide our strong base
+ 
+
+ align:start position:0%
+moles for our hydroxide our strong base
+we've added 5 ms and it was a.15 molar
+
+ align:start position:0%
+we've added 5 ms and it was a.15 molar
+ 
+
+ align:start position:0%
+we've added 5 ms and it was a.15 molar
+solution. So we have 75 * 10us3 moles.
+
+ align:start position:0%
+solution. So we have 75 * 10us3 moles.
+ 
+
+ align:start position:0%
+solution. So we have 75 * 10us3 moles.
+So now there's going to be this
+
+ align:start position:0%
+So now there's going to be this
+ 
+
+ align:start position:0%
+So now there's going to be this
+reaction. So we want to think about what
+
+ align:start position:0%
+reaction. So we want to think about what
+ 
+
+ align:start position:0%
+reaction. So we want to think about what
+happens after you have the reaction of
+
+ align:start position:0%
+happens after you have the reaction of
+ 
+
+ align:start position:0%
+happens after you have the reaction of
+the strong base um with the weak acid.
+
+ align:start position:0%
+the strong base um with the weak acid.
+ 
+
+ align:start position:0%
+the strong base um with the weak acid.
+And so just to emphasize this point, say
+
+ align:start position:0%
+And so just to emphasize this point, say
+ 
+
+ align:start position:0%
+And so just to emphasize this point, say
+we have eight moles of a of our acid
+
+ align:start position:0%
+we have eight moles of a of our acid
+ 
+
+ align:start position:0%
+we have eight moles of a of our acid
+here and we added just one mole of our
+
+ align:start position:0%
+here and we added just one mole of our
+ 
+
+ align:start position:0%
+here and we added just one mole of our
+strong base that will react, pull off,
+
+ align:start position:0%
+strong base that will react, pull off,
+ 
+
+ align:start position:0%
+strong base that will react, pull off,
+deproinate and form water and form the
+
+ align:start position:0%
+deproinate and form water and form the
+ 
+
+ align:start position:0%
+deproinate and form water and form the
+conjugate base. So net we had eight, we
+
+ align:start position:0%
+conjugate base. So net we had eight, we
+ 
+
+ align:start position:0%
+conjugate base. So net we had eight, we
+added one of the strong base. So we have
+
+ align:start position:0%
+added one of the strong base. So we have
+ 
+
+ align:start position:0%
+added one of the strong base. So we have
+seven left and we formed one of the
+
+ align:start position:0%
+seven left and we formed one of the
+ 
+
+ align:start position:0%
+seven left and we formed one of the
+conjugate base. And so I'm just uh
+
+ align:start position:0%
+conjugate base. And so I'm just uh
+ 
+
+ align:start position:0%
+conjugate base. And so I'm just uh
+showing this here because so often on
+
+ align:start position:0%
+showing this here because so often on
+ 
+
+ align:start position:0%
+showing this here because so often on
+exams I see people just plug the initial
+
+ align:start position:0%
+exams I see people just plug the initial
+ 
+
+ align:start position:0%
+exams I see people just plug the initial
+moles into uh the later part and they
+
+ align:start position:0%
+moles into uh the later part and they
+ 
+
+ align:start position:0%
+moles into uh the later part and they
+forget that there's a reaction happening
+
+ align:start position:0%
+forget that there's a reaction happening
+ 
+
+ align:start position:0%
+forget that there's a reaction happening
+and so I was hoping if I would show this
+
+ align:start position:0%
+and so I was hoping if I would show this
+ 
+
+ align:start position:0%
+and so I was hoping if I would show this
+I'm going to get people used to being
+
+ align:start position:0%
+I'm going to get people used to being
+ 
+
+ align:start position:0%
+I'm going to get people used to being
+thinking about okay I'm adding strong
+
+ align:start position:0%
+thinking about okay I'm adding strong
+ 
+
+ align:start position:0%
+thinking about okay I'm adding strong
+base what's happening how much is being
+
+ align:start position:0%
+base what's happening how much is being
+ 
+
+ align:start position:0%
+base what's happening how much is being
+converted and if you're not subtracting
+
+ align:start position:0%
+converted and if you're not subtracting
+ 
+
+ align:start position:0%
+converted and if you're not subtracting
+things there's a problem with the way
+
+ align:start position:0%
+things there's a problem with the way
+ 
+
+ align:start position:0%
+things there's a problem with the way
+you're doing the problem. All right. So
+
+ align:start position:0%
+you're doing the problem. All right. So
+ 
+
+ align:start position:0%
+you're doing the problem. All right. So
+here these are less easy numbers to
+
+ align:start position:0%
+here these are less easy numbers to
+ 
+
+ align:start position:0%
+here these are less easy numbers to
+visualize. Um 2.5 * 10us3 moles how much
+
+ align:start position:0%
+visualize. Um 2.5 * 10us3 moles how much
+ 
+
+ align:start position:0%
+visualize. Um 2.5 * 10us3 moles how much
+we had of our weak acid. We have added a
+
+ align:start position:0%
+we had of our weak acid. We have added a
+ 
+
+ align:start position:0%
+we had of our weak acid. We have added a
+strong base at 75 *
+
+ align:start position:0%
+strong base at 75 *
+ 
+
+ align:start position:0%
+strong base at 75 *
+10us3. So we have 1.75 * 10us3 moles of
+
+ align:start position:0%
+10us3. So we have 1.75 * 10us3 moles of
+ 
+
+ align:start position:0%
+10us3. So we have 1.75 * 10us3 moles of
+our acid left. So we subtract the amount
+
+ align:start position:0%
+our acid left. So we subtract the amount
+ 
+
+ align:start position:0%
+our acid left. So we subtract the amount
+that's converted due to the addition of
+
+ align:start position:0%
+that's converted due to the addition of
+ 
+
+ align:start position:0%
+that's converted due to the addition of
+the base. And so why don't you tell me
+
+ align:start position:0%
+the base. And so why don't you tell me
+ 
+
+ align:start position:0%
+the base. And so why don't you tell me
+how much then we're going to have of our
+
+ align:start position:0%
+how much then we're going to have of our
+ 
+
+ align:start position:0%
+how much then we're going to have of our
+conjugate base being formed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, I kind of tried to fool
+
+ align:start position:0%
+All right. So, I kind of tried to fool
+ 
+
+ align:start position:0%
+All right. So, I kind of tried to fool
+you there, but 75 70% of you um were not
+
+ align:start position:0%
+you there, but 75 70% of you um were not
+ 
+
+ align:start position:0%
+you there, but 75 70% of you um were not
+having it. Okay. So, here it's going to
+
+ align:start position:0%
+having it. Okay. So, here it's going to
+ 
+
+ align:start position:0%
+having it. Okay. So, here it's going to
+be equal to the number of moles of O
+
+ align:start position:0%
+be equal to the number of moles of O
+ 
+
+ align:start position:0%
+be equal to the number of moles of O
+that's added because that's how much is
+
+ align:start position:0%
+that's added because that's how much is
+ 
+
+ align:start position:0%
+that's added because that's how much is
+going to be converted. That's how much
+
+ align:start position:0%
+going to be converted. That's how much
+ 
+
+ align:start position:0%
+going to be converted. That's how much
+of the conjugate acid is converted to
+
+ align:start position:0%
+of the conjugate acid is converted to
+ 
+
+ align:start position:0%
+of the conjugate acid is converted to
+the conjugate
+
+ align:start position:0%
+the conjugate
+ 
+
+ align:start position:0%
+the conjugate
+base. All right. Now, we have moles. We
+
+ align:start position:0%
+base. All right. Now, we have moles. We
+ 
+
+ align:start position:0%
+base. All right. Now, we have moles. We
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+marity. If we're going to use a Ka to
+
+ align:start position:0%
+marity. If we're going to use a Ka to
+ 
+
+ align:start position:0%
+marity. If we're going to use a Ka to
+solve the problem because the expression
+
+ align:start position:0%
+solve the problem because the expression
+ 
+
+ align:start position:0%
+solve the problem because the expression
+for equilibrium constant has marity, not
+
+ align:start position:0%
+for equilibrium constant has marity, not
+ 
+
+ align:start position:0%
+for equilibrium constant has marity, not
+moles. So then in converting to marity,
+
+ align:start position:0%
+moles. So then in converting to marity,
+ 
+
+ align:start position:0%
+moles. So then in converting to marity,
+the thing you have to remember is the
+
+ align:start position:0%
+the thing you have to remember is the
+ 
+
+ align:start position:0%
+the thing you have to remember is the
+volume. So we had 25 mls to start with
+
+ align:start position:0%
+volume. So we had 25 mls to start with
+ 
+
+ align:start position:0%
+volume. So we had 25 mls to start with
+and now we've added five. So we need to
+
+ align:start position:0%
+and now we've added five. So we need to
+ 
+
+ align:start position:0%
+and now we've added five. So we need to
+make sure that we have the correct
+
+ align:start position:0%
+make sure that we have the correct
+ 
+
+ align:start position:0%
+make sure that we have the correct
+number of uh lers in our expression. So
+
+ align:start position:0%
+number of uh lers in our expression. So
+ 
+
+ align:start position:0%
+number of uh lers in our expression. So
+we can calculate 1.75 * 10us3 moles for
+
+ align:start position:0%
+we can calculate 1.75 * 10us3 moles for
+ 
+
+ align:start position:0%
+we can calculate 1.75 * 10us3 moles for
+our weak acid volume concentration of
+
+ align:start position:0%
+our weak acid volume concentration of
+ 
+
+ align:start position:0%
+our weak acid volume concentration of
+weak acid. We have 75 * 10us3 of our
+
+ align:start position:0%
+weak acid. We have 75 * 10us3 of our
+ 
+
+ align:start position:0%
+weak acid. We have 75 * 10us3 of our
+conjugate base and then we have a
+
+ align:start position:0%
+conjugate base and then we have a
+ 
+
+ align:start position:0%
+conjugate base and then we have a
+concentration there. Now there are two
+
+ align:start position:0%
+concentration there. Now there are two
+ 
+
+ align:start position:0%
+concentration there. Now there are two
+ways to solve this problem.
+
+ align:start position:0%
+ways to solve this problem.
+ 
+
+ align:start position:0%
+ways to solve this problem.
+And option one uses Ka. It doesn't
+
+ align:start position:0%
+And option one uses Ka. It doesn't
+ 
+
+ align:start position:0%
+And option one uses Ka. It doesn't
+involve Henderson Hasselbach. Option two
+
+ align:start position:0%
+involve Henderson Hasselbach. Option two
+ 
+
+ align:start position:0%
+involve Henderson Hasselbach. Option two
+will involve Henderson Hasselbach. And
+
+ align:start position:0%
+will involve Henderson Hasselbach. And
+ 
+
+ align:start position:0%
+will involve Henderson Hasselbach. And
+it's okay to use this because this is a
+
+ align:start position:0%
+it's okay to use this because this is a
+ 
+
+ align:start position:0%
+it's okay to use this because this is a
+buffer problem. So option one now for
+
+ align:start position:0%
+buffer problem. So option one now for
+ 
+
+ align:start position:0%
+buffer problem. So option one now for
+calculating point B. So we can set up
+
+ align:start position:0%
+calculating point B. So we can set up
+ 
+
+ align:start position:0%
+calculating point B. So we can set up
+this expression. And always remember
+
+ align:start position:0%
+this expression. And always remember
+ 
+
+ align:start position:0%
+this expression. And always remember
+you're talking about marity here. So
+
+ align:start position:0%
+you're talking about marity here. So
+ 
+
+ align:start position:0%
+you're talking about marity here. So
+don't put in your moles in this
+
+ align:start position:0%
+don't put in your moles in this
+ 
+
+ align:start position:0%
+don't put in your moles in this
+expression. Only put in marity. So
+
+ align:start position:0%
+expression. Only put in marity. So
+ 
+
+ align:start position:0%
+expression. Only put in marity. So
+that's why the volume is really
+
+ align:start position:0%
+that's why the volume is really
+ 
+
+ align:start position:0%
+that's why the volume is really
+important. So we can put in our
+
+ align:start position:0%
+important. So we can put in our
+ 
+
+ align:start position:0%
+important. So we can put in our
+concentration 0583
+
+ align:start position:0%
+concentration 0583
+ 
+
+ align:start position:0%
+concentration 0583
+um and it'll be minus x for equilibrium
+
+ align:start position:0%
+um and it'll be minus x for equilibrium
+ 
+
+ align:start position:0%
+um and it'll be minus x for equilibrium
+plus x for our hydrononeium ion
+
+ align:start position:0%
+plus x for our hydrononeium ion
+ 
+
+ align:start position:0%
+plus x for our hydrononeium ion
+concentration and also our concentration
+
+ align:start position:0%
+concentration and also our concentration
+ 
+
+ align:start position:0%
+concentration and also our concentration
+of the conjugate base.
+
+ align:start position:0%
+of the conjugate base.
+ 
+
+ align:start position:0%
+of the conjugate base.
+0250 plus x. So this is like a buffer
+
+ align:start position:0%
+0250 plus x. So this is like a buffer
+ 
+
+ align:start position:0%
+0250 plus x. So this is like a buffer
+problem using option one. And so we can
+
+ align:start position:0%
+problem using option one. And so we can
+ 
+
+ align:start position:0%
+problem using option one. And so we can
+use Ka plug in our values. Here we have
+
+ align:start position:0%
+use Ka plug in our values. Here we have
+ 
+
+ align:start position:0%
+use Ka plug in our values. Here we have
+our conjugate base concentration at
+
+ align:start position:0%
+our conjugate base concentration at
+ 
+
+ align:start position:0%
+our conjugate base concentration at
+equilibrium times our hydrronium ion x
+
+ align:start position:0%
+equilibrium times our hydrronium ion x
+ 
+
+ align:start position:0%
+equilibrium times our hydrronium ion x
+over uh the equilibrium marity of our
+
+ align:start position:0%
+over uh the equilibrium marity of our
+ 
+
+ align:start position:0%
+over uh the equilibrium marity of our
+weak base. We can again assume x is
+
+ align:start position:0%
+weak base. We can again assume x is
+ 
+
+ align:start position:0%
+weak base. We can again assume x is
+small which drops out the plus x and the
+
+ align:start position:0%
+small which drops out the plus x and the
+ 
+
+ align:start position:0%
+small which drops out the plus x and the
+minus x. We solve for x. We get 4.13 *
+
+ align:start position:0%
+minus x. We solve for x. We get 4.13 *
+ 
+
+ align:start position:0%
+minus x. We solve for x. We get 4.13 *
+10us4. We can check the assumption and
+
+ align:start position:0%
+10us4. We can check the assumption and
+ 
+
+ align:start position:0%
+10us4. We can check the assumption and
+sure enough it's much smaller.
+
+ align:start position:0%
+sure enough it's much smaller.
+ 
+
+ align:start position:0%
+sure enough it's much smaller.
+1.7% 7% of of these two and you really
+
+ align:start position:0%
+1.7% 7% of of these two and you really
+ 
+
+ align:start position:0%
+1.7% 7% of of these two and you really
+only need to check one um the smaller
+
+ align:start position:0%
+only need to check one um the smaller
+ 
+
+ align:start position:0%
+only need to check one um the smaller
+one assumption's okay and we can
+
+ align:start position:0%
+one assumption's okay and we can
+ 
+
+ align:start position:0%
+one assumption's okay and we can
+calculate then by putting in X which is
+
+ align:start position:0%
+calculate then by putting in X which is
+ 
+
+ align:start position:0%
+calculate then by putting in X which is
+hydrronium ion concentration into the
+
+ align:start position:0%
+hydrronium ion concentration into the
+ 
+
+ align:start position:0%
+hydrronium ion concentration into the
+equation pH= minus log of the hydrronium
+
+ align:start position:0%
+equation pH= minus log of the hydrronium
+ 
+
+ align:start position:0%
+equation pH= minus log of the hydrronium
+ion concentration equals the pH
+
+ align:start position:0%
+ion concentration equals the pH
+ 
+
+ align:start position:0%
+ion concentration equals the pH
+3.38. We can also use Henderson
+
+ align:start position:0%
+3.38. We can also use Henderson
+ 
+
+ align:start position:0%
+3.38. We can also use Henderson
+Hustelbach because it's a buffer
+
+ align:start position:0%
+Hustelbach because it's a buffer
+ 
+
+ align:start position:0%
+Hustelbach because it's a buffer
+problem. It's allowed. You were given a
+
+ align:start position:0%
+problem. It's allowed. You were given a
+ 
+
+ align:start position:0%
+problem. It's allowed. You were given a
+Ka. You can calculate pKa minus the log
+
+ align:start position:0%
+Ka. You can calculate pKa minus the log
+ 
+
+ align:start position:0%
+Ka. You can calculate pKa minus the log
+of Ka and put that number in. Put in the
+
+ align:start position:0%
+of Ka and put that number in. Put in the
+ 
+
+ align:start position:0%
+of Ka and put that number in. Put in the
+concentrations that you determined. So
+
+ align:start position:0%
+concentrations that you determined. So
+ 
+
+ align:start position:0%
+concentrations that you determined. So
+you still need to subtract the moles.
+
+ align:start position:0%
+you still need to subtract the moles.
+ 
+
+ align:start position:0%
+you still need to subtract the moles.
+You can't skip that step. Um, but you
+
+ align:start position:0%
+You can't skip that step. Um, but you
+ 
+
+ align:start position:0%
+You can't skip that step. Um, but you
+can skip the volume step because when
+
+ align:start position:0%
+can skip the volume step because when
+ 
+
+ align:start position:0%
+can skip the volume step because when
+you use Henderson Hustelblock, the
+
+ align:start position:0%
+you use Henderson Hustelblock, the
+ 
+
+ align:start position:0%
+you use Henderson Hustelblock, the
+volume would cancel out. If you had
+
+ align:start position:0%
+volume would cancel out. If you had
+ 
+
+ align:start position:0%
+volume would cancel out. If you had
+moles per volume, moles per volume, the
+
+ align:start position:0%
+moles per volume, moles per volume, the
+ 
+
+ align:start position:0%
+moles per volume, moles per volume, the
+volume's the same. So, you can skip the
+
+ align:start position:0%
+volume's the same. So, you can skip the
+ 
+
+ align:start position:0%
+volume's the same. So, you can skip the
+calculating marity step here. That
+
+ align:start position:0%
+calculating marity step here. That
+ 
+
+ align:start position:0%
+calculating marity step here. That
+simplifies the problem and solve and you
+
+ align:start position:0%
+simplifies the problem and solve and you
+ 
+
+ align:start position:0%
+simplifies the problem and solve and you
+should get the exact same number or
+
+ align:start position:0%
+should get the exact same number or
+ 
+
+ align:start position:0%
+should get the exact same number or
+something was wrong. Both of these
+
+ align:start position:0%
+something was wrong. Both of these
+ 
+
+ align:start position:0%
+something was wrong. Both of these
+should work equally well. 3.38.
+
+ align:start position:0%
+should work equally well. 3.38.
+ 
+
+ align:start position:0%
+should work equally well. 3.38.
+But you'll often be asked to check the
+
+ align:start position:0%
+But you'll often be asked to check the
+ 
+
+ align:start position:0%
+But you'll often be asked to check the
+Henderson Hustelbach um assumption. And
+
+ align:start position:0%
+Henderson Hustelbach um assumption. And
+ 
+
+ align:start position:0%
+Henderson Hustelbach um assumption. And
+remember there was an assumption here
+
+ align:start position:0%
+remember there was an assumption here
+ 
+
+ align:start position:0%
+remember there was an assumption here
+because we solved the Henderson
+
+ align:start position:0%
+because we solved the Henderson
+ 
+
+ align:start position:0%
+because we solved the Henderson
+Hustelbach from an equation that use Ka,
+
+ align:start position:0%
+Hustelbach from an equation that use Ka,
+ 
+
+ align:start position:0%
+Hustelbach from an equation that use Ka,
+the equilibrium constant. So really this
+
+ align:start position:0%
+the equilibrium constant. So really this
+ 
+
+ align:start position:0%
+the equilibrium constant. So really this
+expression is at equilibrium, but we're
+
+ align:start position:0%
+expression is at equilibrium, but we're
+ 
+
+ align:start position:0%
+expression is at equilibrium, but we're
+plugging in values that are not at
+
+ align:start position:0%
+plugging in values that are not at
+ 
+
+ align:start position:0%
+plugging in values that are not at
+equilibrium. They're the initial values
+
+ align:start position:0%
+equilibrium. They're the initial values
+ 
+
+ align:start position:0%
+equilibrium. They're the initial values
+that we're putting into this equation.
+
+ align:start position:0%
+that we're putting into this equation.
+ 
+
+ align:start position:0%
+that we're putting into this equation.
+So we still need to check and we're
+
+ align:start position:0%
+So we still need to check and we're
+ 
+
+ align:start position:0%
+So we still need to check and we're
+using the 5% rule. So to check the
+
+ align:start position:0%
+using the 5% rule. So to check the
+ 
+
+ align:start position:0%
+using the 5% rule. So to check the
+Henderson Hustelbach then we have to
+
+ align:start position:0%
+Henderson Hustelbach then we have to
+ 
+
+ align:start position:0%
+Henderson Hustelbach then we have to
+back calculate pH of
+
+ align:start position:0%
+back calculate pH of
+ 
+
+ align:start position:0%
+back calculate pH of
+3.38 equals a hydrronium ion
+
+ align:start position:0%
+3.38 equals a hydrronium ion
+ 
+
+ align:start position:0%
+3.38 equals a hydrronium ion
+concentration of 4.2 *
+
+ align:start position:0%
+concentration of 4.2 *
+ 
+
+ align:start position:0%
+concentration of 4.2 *
+10us4 and then you want to check that
+
+ align:start position:0%
+10us4 and then you want to check that
+ 
+
+ align:start position:0%
+10us4 and then you want to check that
+that number is less than 5% of the
+
+ align:start position:0%
+that number is less than 5% of the
+ 
+
+ align:start position:0%
+that number is less than 5% of the
+smaller number and we checked that
+
+ align:start position:0%
+smaller number and we checked that
+ 
+
+ align:start position:0%
+smaller number and we checked that
+assumption when we looked at um option A
+
+ align:start position:0%
+assumption when we looked at um option A
+ 
+
+ align:start position:0%
+assumption when we looked at um option A
+so it's still good for option B um and
+
+ align:start position:0%
+so it's still good for option B um and
+ 
+
+ align:start position:0%
+so it's still good for option B um and
+we can use the Henderson Hustelbach.
+
+ align:start position:0%
+we can use the Henderson Hustelbach.
+ 
+
+ align:start position:0%
+we can use the Henderson Hustelbach.
+Now, if it was greater than 5%, then you
+
+ align:start position:0%
+Now, if it was greater than 5%, then you
+ 
+
+ align:start position:0%
+Now, if it was greater than 5%, then you
+can only use option one and you must use
+
+ align:start position:0%
+can only use option one and you must use
+ 
+
+ align:start position:0%
+can only use option one and you must use
+the quadratic equation. But this doesn't
+
+ align:start position:0%
+the quadratic equation. But this doesn't
+ 
+
+ align:start position:0%
+the quadratic equation. But this doesn't
+happen very often because a buffer is
+
+ align:start position:0%
+happen very often because a buffer is
+ 
+
+ align:start position:0%
+happen very often because a buffer is
+usually not a very good buffer if X is
+
+ align:start position:0%
+usually not a very good buffer if X is
+ 
+
+ align:start position:0%
+usually not a very good buffer if X is
+not small. A buffer is a good buffer
+
+ align:start position:0%
+not small. A buffer is a good buffer
+ 
+
+ align:start position:0%
+not small. A buffer is a good buffer
+when you have a weak conjugate acid
+
+ align:start position:0%
+when you have a weak conjugate acid
+ 
+
+ align:start position:0%
+when you have a weak conjugate acid
+pair. And when you have weak conjugate
+
+ align:start position:0%
+pair. And when you have weak conjugate
+ 
+
+ align:start position:0%
+pair. And when you have weak conjugate
+acids and bases, then usually X is
+
+ align:start position:0%
+acids and bases, then usually X is
+ 
+
+ align:start position:0%
+acids and bases, then usually X is
+small. It doesn't ionize much in water.
+
+ align:start position:0%
+small. It doesn't ionize much in water.
+ 
+
+ align:start position:0%
+small. It doesn't ionize much in water.
+So most of the time these assumptions
+
+ align:start position:0%
+So most of the time these assumptions
+ 
+
+ align:start position:0%
+So most of the time these assumptions
+hold. But if you're asked to check an
+
+ align:start position:0%
+hold. But if you're asked to check an
+ 
+
+ align:start position:0%
+hold. But if you're asked to check an
+assumption, that's what you need to do.
+
+ align:start position:0%
+assumption, that's what you need to do.
+ 
+
+ align:start position:0%
+assumption, that's what you need to do.
+All right. So we have point B two ways
+
+ align:start position:0%
+All right. So we have point B two ways
+ 
+
+ align:start position:0%
+All right. So we have point B two ways
+and we got the same answer. It's 3.38
+
+ align:start position:0%
+and we got the same answer. It's 3.38
+ 
+
+ align:start position:0%
+and we got the same answer. It's 3.38
+and that's point B and we're in the
+
+ align:start position:0%
+and that's point B and we're in the
+ 
+
+ align:start position:0%
+and that's point B and we're in the
+buffering region there. What about point
+
+ align:start position:0%
+buffering region there. What about point
+ 
+
+ align:start position:0%
+buffering region there. What about point
+C? Point C is the half equivalence
+
+ align:start position:0%
+C? Point C is the half equivalence
+ 
+
+ align:start position:0%
+C? Point C is the half equivalence
+point. So let's think about what the pH
+
+ align:start position:0%
+point. So let's think about what the pH
+ 
+
+ align:start position:0%
+point. So let's think about what the pH
+would be at the half equivalence point.
+
+ align:start position:0%
+would be at the half equivalence point.
+ 
+
+ align:start position:0%
+would be at the half equivalence point.
+So at the half equivalence point, by
+
+ align:start position:0%
+So at the half equivalence point, by
+ 
+
+ align:start position:0%
+So at the half equivalence point, by
+definition, you've added half the number
+
+ align:start position:0%
+definition, you've added half the number
+ 
+
+ align:start position:0%
+definition, you've added half the number
+of moles you need to reach the
+
+ align:start position:0%
+of moles you need to reach the
+ 
+
+ align:start position:0%
+of moles you need to reach the
+equivalence point or half the volume of
+
+ align:start position:0%
+equivalence point or half the volume of
+ 
+
+ align:start position:0%
+equivalence point or half the volume of
+the strong base that you need to reach
+
+ align:start position:0%
+the strong base that you need to reach
+ 
+
+ align:start position:0%
+the strong base that you need to reach
+the equivalence point. And at this
+
+ align:start position:0%
+the equivalence point. And at this
+ 
+
+ align:start position:0%
+the equivalence point. And at this
+point, the number of moles of your weak
+
+ align:start position:0%
+point, the number of moles of your weak
+ 
+
+ align:start position:0%
+point, the number of moles of your weak
+acid equal the number of moles of your
+
+ align:start position:0%
+acid equal the number of moles of your
+ 
+
+ align:start position:0%
+acid equal the number of moles of your
+conjugate base. So when that is true and
+
+ align:start position:0%
+conjugate base. So when that is true and
+ 
+
+ align:start position:0%
+conjugate base. So when that is true and
+we look at the Henderson Hustelbach
+
+ align:start position:0%
+we look at the Henderson Hustelbach
+ 
+
+ align:start position:0%
+we look at the Henderson Hustelbach
+expression, we see that this term
+
+ align:start position:0%
+expression, we see that this term
+ 
+
+ align:start position:0%
+expression, we see that this term
+becomes one.
+
+ align:start position:0%
+becomes one.
+ 
+
+ align:start position:0%
+becomes one.
+And so therefore, pH equals
+
+ align:start position:0%
+And so therefore, pH equals
+ 
+
+ align:start position:0%
+And so therefore, pH equals
+pKa. So if you weren't given the pKa and
+
+ align:start position:0%
+pKa. So if you weren't given the pKa and
+ 
+
+ align:start position:0%
+pKa. So if you weren't given the pKa and
+you were just given the Ka, that's no
+
+ align:start position:0%
+you were just given the Ka, that's no
+ 
+
+ align:start position:0%
+you were just given the Ka, that's no
+problem because you can uh calculate it
+
+ align:start position:0%
+problem because you can uh calculate it
+ 
+
+ align:start position:0%
+problem because you can uh calculate it
+minus log of
+
+ align:start position:0%
+minus log of
+ 
+
+ align:start position:0%
+minus log of
+Ka. And so that's minus log of 1.77*
+
+ align:start position:0%
+Ka. And so that's minus log of 1.77*
+ 
+
+ align:start position:0%
+Ka. And so that's minus log of 1.77*
+10us4 for this problem, which gives us a
+
+ align:start position:0%
+10us4 for this problem, which gives us a
+ 
+
+ align:start position:0%
+10us4 for this problem, which gives us a
+pH of about 3.75.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, if you were just given the pKa,
+
+ align:start position:0%
+So, if you were just given the pKa,
+ 
+
+ align:start position:0%
+So, if you were just given the pKa,
+which is for this 3.75,
+
+ align:start position:0%
+which is for this 3.75,
+ 
+
+ align:start position:0%
+which is for this 3.75,
+um, and it's really not much more
+
+ align:start position:0%
+um, and it's really not much more
+ 
+
+ align:start position:0%
+um, and it's really not much more
+significant than that, honestly. And
+
+ align:start position:0%
+significant than that, honestly. And
+ 
+
+ align:start position:0%
+significant than that, honestly. And
+there actually not a lot of significant
+
+ align:start position:0%
+there actually not a lot of significant
+ 
+
+ align:start position:0%
+there actually not a lot of significant
+figures when it comes to measuring pH,
+
+ align:start position:0%
+figures when it comes to measuring pH,
+ 
+
+ align:start position:0%
+figures when it comes to measuring pH,
+um, or pKa's. Um, if on a test you're
+
+ align:start position:0%
+um, or pKa's. Um, if on a test you're
+ 
+
+ align:start position:0%
+um, or pKa's. Um, if on a test you're
+said, the pKa of this is 3.75. What is
+
+ align:start position:0%
+said, the pKa of this is 3.75. What is
+ 
+
+ align:start position:0%
+said, the pKa of this is 3.75. What is
+the pH at the half equivalence point?
+
+ align:start position:0%
+the pH at the half equivalence point?
+ 
+
+ align:start position:0%
+the pH at the half equivalence point?
+You could write down 3.75 and nothing
+
+ align:start position:0%
+You could write down 3.75 and nothing
+ 
+
+ align:start position:0%
+You could write down 3.75 and nothing
+else. You do not need to prove to me
+
+ align:start position:0%
+else. You do not need to prove to me
+ 
+
+ align:start position:0%
+else. You do not need to prove to me
+that that that this expression here is
+
+ align:start position:0%
+that that that this expression here is
+ 
+
+ align:start position:0%
+that that that this expression here is
+true at the half equivalence point. It's
+
+ align:start position:0%
+true at the half equivalence point. It's
+ 
+
+ align:start position:0%
+true at the half equivalence point. It's
+just a a way to ask a question that
+
+ align:start position:0%
+just a a way to ask a question that
+ 
+
+ align:start position:0%
+just a a way to ask a question that
+tests your knowledge of titrations. So,
+
+ align:start position:0%
+tests your knowledge of titrations. So,
+ 
+
+ align:start position:0%
+tests your knowledge of titrations. So,
+this is a good problem that involves
+
+ align:start position:0%
+this is a good problem that involves
+ 
+
+ align:start position:0%
+this is a good problem that involves
+very little work. So, you should be
+
+ align:start position:0%
+very little work. So, you should be
+ 
+
+ align:start position:0%
+very little work. So, you should be
+extremely excited if I'm asking you
+
+ align:start position:0%
+extremely excited if I'm asking you
+ 
+
+ align:start position:0%
+extremely excited if I'm asking you
+about the pH at a half equivalence point
+
+ align:start position:0%
+about the pH at a half equivalence point
+ 
+
+ align:start position:0%
+about the pH at a half equivalence point
+because that's going to be a real easy
+
+ align:start position:0%
+because that's going to be a real easy
+ 
+
+ align:start position:0%
+because that's going to be a real easy
+problem. Don't spend a lot of time on
+
+ align:start position:0%
+problem. Don't spend a lot of time on
+ 
+
+ align:start position:0%
+problem. Don't spend a lot of time on
+it. All right. So, we got point C
+
+ align:start position:0%
+it. All right. So, we got point C
+ 
+
+ align:start position:0%
+it. All right. So, we got point C
+3.75. Very close. We're sort of in this
+
+ align:start position:0%
+3.75. Very close. We're sort of in this
+ 
+
+ align:start position:0%
+3.75. Very close. We're sort of in this
+uh region where the pH is changing not
+
+ align:start position:0%
+uh region where the pH is changing not
+ 
+
+ align:start position:0%
+uh region where the pH is changing not
+that much. All right, so that's the end
+
+ align:start position:0%
+that much. All right, so that's the end
+ 
+
+ align:start position:0%
+that much. All right, so that's the end
+of that lecture, but the beginning of
+
+ align:start position:0%
+of that lecture, but the beginning of
+ 
+
+ align:start position:0%
+of that lecture, but the beginning of
+the next one starts where we left off.
+
+ align:start position:0%
+the next one starts where we left off.
+ 
+
+ align:start position:0%
+the next one starts where we left off.
+As I said, acid base titration problems
+
+ align:start position:0%
+As I said, acid base titration problems
+ 
+
+ align:start position:0%
+As I said, acid base titration problems
+take a long time. They're in two
+
+ align:start position:0%
+take a long time. They're in two
+ 
+
+ align:start position:0%
+take a long time. They're in two
+handouts. Um, and we're just going to
+
+ align:start position:0%
+handouts. Um, and we're just going to
+ 
+
+ align:start position:0%
+handouts. Um, and we're just going to
+kind of continue now um with the next
+
+ align:start position:0%
+kind of continue now um with the next
+ 
+
+ align:start position:0%
+kind of continue now um with the next
+handout and point S, the equivalence
+
+ align:start position:0%
+handout and point S, the equivalence
+ 
+
+ align:start position:0%
+handout and point S, the equivalence
+point.
\ No newline at end of file
diff --git a/pJdUR2uak2s.txt b/pJdUR2uak2s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b90a26ea9cc18d45e6395eb8ad34c80deaae44b7
--- /dev/null
+++ b/pJdUR2uak2s.txt
@@ -0,0 +1,9115 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on. Come on.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So we have uh you can show the
+
+ align:start position:0%
+Okay. So we have uh you can show the
+ 
+
+ align:start position:0%
+Okay. So we have uh you can show the
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+uh 57% one and three. So this is where
+
+ align:start position:0%
+uh 57% one and three. So this is where
+ 
+
+ align:start position:0%
+uh 57% one and three. So this is where
+we were at the end of last lecture. So
+
+ align:start position:0%
+we were at the end of last lecture. So
+ 
+
+ align:start position:0%
+we were at the end of last lecture. So
+if you didn't get this uh written down
+
+ align:start position:0%
+if you didn't get this uh written down
+ 
+
+ align:start position:0%
+if you didn't get this uh written down
+uh in your notes um you want to uh look
+
+ align:start position:0%
+uh in your notes um you want to uh look
+ 
+
+ align:start position:0%
+uh in your notes um you want to uh look
+at these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definitions. So here in this we have NH3
+
+ align:start position:0%
+definitions. So here in this we have NH3
+ 
+
+ align:start position:0%
+definitions. So here in this we have NH3
+with its lone pair and it is acting as
+
+ align:start position:0%
+with its lone pair and it is acting as
+ 
+
+ align:start position:0%
+with its lone pair and it is acting as
+uh the Lewis base and BF3 is acting as
+
+ align:start position:0%
+uh the Lewis base and BF3 is acting as
+ 
+
+ align:start position:0%
+uh the Lewis base and BF3 is acting as
+the Lewis acid. So a Louisis base
+
+ align:start position:0%
+the Lewis acid. So a Louisis base
+ 
+
+ align:start position:0%
+the Lewis acid. So a Louisis base
+donates its lone pair electrons and the
+
+ align:start position:0%
+donates its lone pair electrons and the
+ 
+
+ align:start position:0%
+donates its lone pair electrons and the
+acid accepts them. So what was the other
+
+ align:start position:0%
+acid accepts them. So what was the other
+ 
+
+ align:start position:0%
+acid accepts them. So what was the other
+definition that we had the Bronstead
+
+ align:start position:0%
+definition that we had the Bronstead
+ 
+
+ align:start position:0%
+definition that we had the Bronstead
+Lowry? Does someone want to tell me um
+
+ align:start position:0%
+Lowry? Does someone want to tell me um
+ 
+
+ align:start position:0%
+Lowry? Does someone want to tell me um
+what that definition was?
+
+ align:start position:0%
+what that definition was?
+ 
+
+ align:start position:0%
+what that definition was?
+Let's can you uh if we have a volunteer
+
+ align:start position:0%
+Let's can you uh if we have a volunteer
+ 
+
+ align:start position:0%
+Let's can you uh if we have a volunteer
+tell us the Bronstead Lowry definition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pull out your notes. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somehat. There you go.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, a Bronstet Lowry uh I'm not sure
+
+ align:start position:0%
+So, a Bronstet Lowry uh I'm not sure
+ 
+
+ align:start position:0%
+So, a Bronstet Lowry uh I'm not sure
+it's on.
+
+ align:start position:0%
+it's on.
+ 
+
+ align:start position:0%
+it's on.
+It is on. Okay. Bronstad Lowry base is
+
+ align:start position:0%
+It is on. Okay. Bronstad Lowry base is
+ 
+
+ align:start position:0%
+It is on. Okay. Bronstad Lowry base is
+something that accepts H+ or H30O plus.
+
+ align:start position:0%
+something that accepts H+ or H30O plus.
+ 
+
+ align:start position:0%
+something that accepts H+ or H30O plus.
+Yeah. So the base um accepts the
+
+ align:start position:0%
+Yeah. So the base um accepts the
+ 
+
+ align:start position:0%
+Yeah. So the base um accepts the
+hydrogen ion or the proton and the acid
+
+ align:start position:0%
+hydrogen ion or the proton and the acid
+ 
+
+ align:start position:0%
+hydrogen ion or the proton and the acid
+donates. So is this definition now
+
+ align:start position:0%
+donates. So is this definition now
+ 
+
+ align:start position:0%
+donates. So is this definition now
+incompatible? Are they completely
+
+ align:start position:0%
+incompatible? Are they completely
+ 
+
+ align:start position:0%
+incompatible? Are they completely
+opposite or could they be sort of uh
+
+ align:start position:0%
+opposite or could they be sort of uh
+ 
+
+ align:start position:0%
+opposite or could they be sort of uh
+work together? Does anyone have an
+
+ align:start position:0%
+work together? Does anyone have an
+ 
+
+ align:start position:0%
+work together? Does anyone have an
+opinion on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that? So how many people think that
+
+ align:start position:0%
+that? So how many people think that
+ 
+
+ align:start position:0%
+that? So how many people think that
+these could be consistent definitions in
+
+ align:start position:0%
+these could be consistent definitions in
+ 
+
+ align:start position:0%
+these could be consistent definitions in
+some way? Okay. Oh, quite a few people
+
+ align:start position:0%
+some way? Okay. Oh, quite a few people
+ 
+
+ align:start position:0%
+some way? Okay. Oh, quite a few people
+um that that uh one could make that
+
+ align:start position:0%
+um that that uh one could make that
+ 
+
+ align:start position:0%
+um that that uh one could make that
+argument. So, if you know now that you
+
+ align:start position:0%
+argument. So, if you know now that you
+ 
+
+ align:start position:0%
+argument. So, if you know now that you
+can make the argument, does someone want
+
+ align:start position:0%
+can make the argument, does someone want
+ 
+
+ align:start position:0%
+can make the argument, does someone want
+to try to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it? We have a
+
+ align:start position:0%
+it? We have a
+ 
+
+ align:start position:0%
+it? We have a
+bag. All right. Um our mic went away,
+
+ align:start position:0%
+bag. All right. Um our mic went away,
+ 
+
+ align:start position:0%
+bag. All right. Um our mic went away,
+but uh can we get up get up over
+
+ align:start position:0%
+but uh can we get up get up over
+ 
+
+ align:start position:0%
+but uh can we get up get up over
+there?
+
+ align:start position:0%
+there?
+ 
+
+ align:start position:0%
+there?
+So, where did our mic runner go? I
+
+ align:start position:0%
+So, where did our mic runner go? I
+ 
+
+ align:start position:0%
+So, where did our mic runner go? I
+should have explained they were needed
+
+ align:start position:0%
+should have explained they were needed
+ 
+
+ align:start position:0%
+should have explained they were needed
+twice. All
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. All right. Who uh said try this?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How far? How far?
+
+ align:start position:0%
+How far? How far?
+ 
+
+ align:start position:0%
+How far? How far?
+How far? Uh all Bronstead Lowry bases
+
+ align:start position:0%
+How far? Uh all Bronstead Lowry bases
+ 
+
+ align:start position:0%
+How far? Uh all Bronstead Lowry bases
+are Lewis bases, but not all Lewis bases
+
+ align:start position:0%
+are Lewis bases, but not all Lewis bases
+ 
+
+ align:start position:0%
+are Lewis bases, but not all Lewis bases
+are Bronstead Lowry bases because um you
+
+ align:start position:0%
+are Bronstead Lowry bases because um you
+ 
+
+ align:start position:0%
+are Bronstead Lowry bases because um you
+can like act as a proxy with no hydrogen
+
+ align:start position:0%
+can like act as a proxy with no hydrogen
+ 
+
+ align:start position:0%
+can like act as a proxy with no hydrogen
+ion if it connects directly. But like if
+
+ align:start position:0%
+ion if it connects directly. But like if
+ 
+
+ align:start position:0%
+ion if it connects directly. But like if
+a hydrogen ion bonds an example H30 to
+
+ align:start position:0%
+a hydrogen ion bonds an example H30 to
+ 
+
+ align:start position:0%
+a hydrogen ion bonds an example H30 to
+the lone pair of an oxygen, then it's
+
+ align:start position:0%
+the lone pair of an oxygen, then it's
+ 
+
+ align:start position:0%
+the lone pair of an oxygen, then it's
+the same thing as a Louis base.
+
+ align:start position:0%
+the same thing as a Louis base.
+ 
+
+ align:start position:0%
+the same thing as a Louis base.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Okay. So, so that's right. The the Lewis
+
+ align:start position:0%
+Okay. So, so that's right. The the Lewis
+ 
+
+ align:start position:0%
+Okay. So, so that's right. The the Lewis
+acid Lewis base definition works um if
+
+ align:start position:0%
+acid Lewis base definition works um if
+ 
+
+ align:start position:0%
+acid Lewis base definition works um if
+you don't have a hydrogen ion involved
+
+ align:start position:0%
+you don't have a hydrogen ion involved
+ 
+
+ align:start position:0%
+you don't have a hydrogen ion involved
+or a proton involved, but the other
+
+ align:start position:0%
+or a proton involved, but the other
+ 
+
+ align:start position:0%
+or a proton involved, but the other
+still still applies. So, remember that
+
+ align:start position:0%
+still still applies. So, remember that
+ 
+
+ align:start position:0%
+still still applies. So, remember that
+when you're accepting
+
+ align:start position:0%
+when you're accepting
+ 
+
+ align:start position:0%
+when you're accepting
+H+, you're taking it without an
+
+ align:start position:0%
+H+, you're taking it without an
+ 
+
+ align:start position:0%
+H+, you're taking it without an
+electron. So, the base is taking H+. So,
+
+ align:start position:0%
+electron. So, the base is taking H+. So,
+ 
+
+ align:start position:0%
+electron. So, the base is taking H+. So,
+it's donating its electrons to form the
+
+ align:start position:0%
+it's donating its electrons to form the
+ 
+
+ align:start position:0%
+it's donating its electrons to form the
+bond. And the acid when it gives up H+,
+
+ align:start position:0%
+bond. And the acid when it gives up H+,
+ 
+
+ align:start position:0%
+bond. And the acid when it gives up H+,
+it's keeping all of the electrons. It's
+
+ align:start position:0%
+it's keeping all of the electrons. It's
+ 
+
+ align:start position:0%
+it's keeping all of the electrons. It's
+accepting the electrons. So, when the
+
+ align:start position:0%
+accepting the electrons. So, when the
+ 
+
+ align:start position:0%
+accepting the electrons. So, when the
+acid gives up H+, it's accepting. And
+
+ align:start position:0%
+acid gives up H+, it's accepting. And
+ 
+
+ align:start position:0%
+acid gives up H+, it's accepting. And
+when the base takes H+, it's using its
+
+ align:start position:0%
+when the base takes H+, it's using its
+ 
+
+ align:start position:0%
+when the base takes H+, it's using its
+electrons. So, the um so the Lewis uh
+
+ align:start position:0%
+electrons. So, the um so the Lewis uh
+ 
+
+ align:start position:0%
+electrons. So, the um so the Lewis uh
+definitions are lone pair or electron
+
+ align:start position:0%
+definitions are lone pair or electron
+ 
+
+ align:start position:0%
+definitions are lone pair or electron
+centric definitions whereas Bronston
+
+ align:start position:0%
+centric definitions whereas Bronston
+ 
+
+ align:start position:0%
+centric definitions whereas Bronston
+Lowry is thinking about the proton. but
+
+ align:start position:0%
+Lowry is thinking about the proton. but
+ 
+
+ align:start position:0%
+Lowry is thinking about the proton. but
+they both kind of work together. So,
+
+ align:start position:0%
+they both kind of work together. So,
+ 
+
+ align:start position:0%
+they both kind of work together. So,
+that's a good review of of the
+
+ align:start position:0%
+that's a good review of of the
+ 
+
+ align:start position:0%
+that's a good review of of the
+definitions we talked about last time.
+
+ align:start position:0%
+definitions we talked about last time.
+ 
+
+ align:start position:0%
+definitions we talked about last time.
+And now I'll try to get my mic back
+
+ align:start position:0%
+And now I'll try to get my mic back
+ 
+
+ align:start position:0%
+And now I'll try to get my mic back
+on. All right.
+
+ align:start position:0%
+on. All right.
+ 
+
+ align:start position:0%
+on. All right.
+So, today we're going to continue
+
+ align:start position:0%
+So, today we're going to continue
+ 
+
+ align:start position:0%
+So, today we're going to continue
+talking about acid base and we're going
+
+ align:start position:0%
+talking about acid base and we're going
+ 
+
+ align:start position:0%
+talking about acid base and we're going
+to continue talking about acid base
+
+ align:start position:0%
+to continue talking about acid base
+ 
+
+ align:start position:0%
+to continue talking about acid base
+quite a bit. So, we have a couple we
+
+ align:start position:0%
+quite a bit. So, we have a couple we
+ 
+
+ align:start position:0%
+quite a bit. So, we have a couple we
+have a number more lectures on acid
+
+ align:start position:0%
+have a number more lectures on acid
+ 
+
+ align:start position:0%
+have a number more lectures on acid
+base. So, we're going to start today
+
+ align:start position:0%
+base. So, we're going to start today
+ 
+
+ align:start position:0%
+base. So, we're going to start today
+with the relationship between pKw, pH,
+
+ align:start position:0%
+with the relationship between pKw, pH,
+ 
+
+ align:start position:0%
+with the relationship between pKw, pH,
+and p. We're going to talk about the
+
+ align:start position:0%
+and p. We're going to talk about the
+ 
+
+ align:start position:0%
+and p. We're going to talk about the
+strengths of acids and bases and then
+
+ align:start position:0%
+strengths of acids and bases and then
+ 
+
+ align:start position:0%
+strengths of acids and bases and then
+we're going to start doing problems
+
+ align:start position:0%
+we're going to start doing problems
+ 
+
+ align:start position:0%
+we're going to start doing problems
+equilibrium acid base problems and we're
+
+ align:start position:0%
+equilibrium acid base problems and we're
+ 
+
+ align:start position:0%
+equilibrium acid base problems and we're
+going to do a bunch of those and
+
+ align:start position:0%
+going to do a bunch of those and
+ 
+
+ align:start position:0%
+going to do a bunch of those and
+students always uh who are doing this
+
+ align:start position:0%
+students always uh who are doing this
+ 
+
+ align:start position:0%
+students always uh who are doing this
+and learning it for the first time are
+
+ align:start position:0%
+and learning it for the first time are
+ 
+
+ align:start position:0%
+and learning it for the first time are
+telling me there is an infinite number
+
+ align:start position:0%
+telling me there is an infinite number
+ 
+
+ align:start position:0%
+telling me there is an infinite number
+of different kinds of problems. It's
+
+ align:start position:0%
+of different kinds of problems. It's
+ 
+
+ align:start position:0%
+of different kinds of problems. It's
+really not true. There are only five
+
+ align:start position:0%
+really not true. There are only five
+ 
+
+ align:start position:0%
+really not true. There are only five
+different types and today hopefully
+
+ align:start position:0%
+different types and today hopefully
+ 
+
+ align:start position:0%
+different types and today hopefully
+we'll get through two of them. So, first
+
+ align:start position:0%
+we'll get through two of them. So, first
+ 
+
+ align:start position:0%
+we'll get through two of them. So, first
+we need to think about water because
+
+ align:start position:0%
+we need to think about water because
+ 
+
+ align:start position:0%
+we need to think about water because
+water is a really important solvent when
+
+ align:start position:0%
+water is a really important solvent when
+ 
+
+ align:start position:0%
+water is a really important solvent when
+we're talking about acid base
+
+ align:start position:0%
+we're talking about acid base
+ 
+
+ align:start position:0%
+we're talking about acid base
+equilibrium. And we mentioned last time
+
+ align:start position:0%
+equilibrium. And we mentioned last time
+ 
+
+ align:start position:0%
+equilibrium. And we mentioned last time
+that water can act as an acid and a
+
+ align:start position:0%
+that water can act as an acid and a
+ 
+
+ align:start position:0%
+that water can act as an acid and a
+base. Does anyone remember what that's
+
+ align:start position:0%
+base. Does anyone remember what that's
+ 
+
+ align:start position:0%
+base. Does anyone remember what that's
+called? Something that can act as an
+
+ align:start position:0%
+called? Something that can act as an
+ 
+
+ align:start position:0%
+called? Something that can act as an
+acid and a
+
+ align:start position:0%
+acid and a
+ 
+
+ align:start position:0%
+acid and a
+base. Amphoteric. So here we have we can
+
+ align:start position:0%
+base. Amphoteric. So here we have we can
+ 
+
+ align:start position:0%
+base. Amphoteric. So here we have we can
+think about two waters going to um
+
+ align:start position:0%
+think about two waters going to um
+ 
+
+ align:start position:0%
+think about two waters going to um
+H3O+ and O. We could also write it out
+
+ align:start position:0%
+H3O+ and O. We could also write it out
+ 
+
+ align:start position:0%
+H3O+ and O. We could also write it out
+instead of just saying two waters. One
+
+ align:start position:0%
+instead of just saying two waters. One
+ 
+
+ align:start position:0%
+instead of just saying two waters. One
+water that's acting as the acid and
+
+ align:start position:0%
+water that's acting as the acid and
+ 
+
+ align:start position:0%
+water that's acting as the acid and
+another water is acting as a base. So
+
+ align:start position:0%
+another water is acting as a base. So
+ 
+
+ align:start position:0%
+another water is acting as a base. So
+the water that's acting as an acid gives
+
+ align:start position:0%
+the water that's acting as an acid gives
+ 
+
+ align:start position:0%
+the water that's acting as an acid gives
+up its hydrogen ion or proton to the
+
+ align:start position:0%
+up its hydrogen ion or proton to the
+ 
+
+ align:start position:0%
+up its hydrogen ion or proton to the
+base. The base accepts it forming a
+
+ align:start position:0%
+base. The base accepts it forming a
+ 
+
+ align:start position:0%
+base. The base accepts it forming a
+conjugate acid. And this water that lost
+
+ align:start position:0%
+conjugate acid. And this water that lost
+ 
+
+ align:start position:0%
+conjugate acid. And this water that lost
+H+ becomes O minus. So water plus water
+
+ align:start position:0%
+H+ becomes O minus. So water plus water
+ 
+
+ align:start position:0%
+H+ becomes O minus. So water plus water
+H2O plus H2O forms an acid and a base.
+
+ align:start position:0%
+H2O plus H2O forms an acid and a base.
+ 
+
+ align:start position:0%
+H2O plus H2O forms an acid and a base.
+So we can ask the question then how much
+
+ align:start position:0%
+So we can ask the question then how much
+ 
+
+ align:start position:0%
+So we can ask the question then how much
+water is in a glass of water or how much
+
+ align:start position:0%
+water is in a glass of water or how much
+ 
+
+ align:start position:0%
+water is in a glass of water or how much
+H2O is actually in this uh water uh
+
+ align:start position:0%
+H2O is actually in this uh water uh
+ 
+
+ align:start position:0%
+H2O is actually in this uh water uh
+container that I have here. So when I'm
+
+ align:start position:0%
+container that I have here. So when I'm
+ 
+
+ align:start position:0%
+container that I have here. So when I'm
+asking that question how much H2O in a
+
+ align:start position:0%
+asking that question how much H2O in a
+ 
+
+ align:start position:0%
+asking that question how much H2O in a
+container of water I am and if I know
+
+ align:start position:0%
+container of water I am and if I know
+ 
+
+ align:start position:0%
+container of water I am and if I know
+the delta G KN of that process I'm
+
+ align:start position:0%
+the delta G KN of that process I'm
+ 
+
+ align:start position:0%
+the delta G KN of that process I'm
+asking about what is the relationship
+
+ align:start position:0%
+asking about what is the relationship
+ 
+
+ align:start position:0%
+asking about what is the relationship
+between our products here our ionized
+
+ align:start position:0%
+between our products here our ionized
+ 
+
+ align:start position:0%
+between our products here our ionized
+acid and our base over here the ionized
+
+ align:start position:0%
+acid and our base over here the ionized
+ 
+
+ align:start position:0%
+acid and our base over here the ionized
+products of water compared to water at
+
+ align:start position:0%
+products of water compared to water at
+ 
+
+ align:start position:0%
+products of water compared to water at
+equilibrium because this container the
+
+ align:start position:0%
+equilibrium because this container the
+ 
+
+ align:start position:0%
+equilibrium because this container the
+water is in equilibrium so if I'm asking
+
+ align:start position:0%
+water is in equilibrium so if I'm asking
+ 
+
+ align:start position:0%
+water is in equilibrium so if I'm asking
+about the ratio of products to reactants
+
+ align:start position:0%
+about the ratio of products to reactants
+ 
+
+ align:start position:0%
+about the ratio of products to reactants
+at equilibrium. What am I asking
+
+ align:start position:0%
+at equilibrium. What am I asking
+ 
+
+ align:start position:0%
+at equilibrium. What am I asking
+about? Just yell it out. I'm asking
+
+ align:start position:0%
+about? Just yell it out. I'm asking
+ 
+
+ align:start position:0%
+about? Just yell it out. I'm asking
+about the equilibrium constant. Exactly.
+
+ align:start position:0%
+about the equilibrium constant. Exactly.
+ 
+
+ align:start position:0%
+about the equilibrium constant. Exactly.
+I'm asking what is K? What is the
+
+ align:start position:0%
+I'm asking what is K? What is the
+ 
+
+ align:start position:0%
+I'm asking what is K? What is the
+equilibrium constant? So, let's just
+
+ align:start position:0%
+equilibrium constant? So, let's just
+ 
+
+ align:start position:0%
+equilibrium constant? So, let's just
+briefly review the relationship. Um,
+
+ align:start position:0%
+briefly review the relationship. Um,
+ 
+
+ align:start position:0%
+briefly review the relationship. Um,
+we're given here a delta G KN and we're
+
+ align:start position:0%
+we're given here a delta G KN and we're
+ 
+
+ align:start position:0%
+we're given here a delta G KN and we're
+asking about K. What is the
+
+ align:start position:0%
+asking about K. What is the
+ 
+
+ align:start position:0%
+asking about K. What is the
+relationship? How do you calculate K if
+
+ align:start position:0%
+relationship? How do you calculate K if
+ 
+
+ align:start position:0%
+relationship? How do you calculate K if
+you know delta G KN?
+
+ align:start position:0%
+you know delta G KN?
+ 
+
+ align:start position:0%
+you know delta G KN?
+And we have some equations that will be
+
+ align:start position:0%
+And we have some equations that will be
+ 
+
+ align:start position:0%
+And we have some equations that will be
+given to you. Sorry, not quite yet.
+
+ align:start position:0%
+given to you. Sorry, not quite yet.
+ 
+
+ align:start position:0%
+given to you. Sorry, not quite yet.
+There's going to be a clicker question
+
+ align:start position:0%
+There's going to be a clicker question
+ 
+
+ align:start position:0%
+There's going to be a clicker question
+coming. Um, we have some equations here.
+
+ align:start position:0%
+coming. Um, we have some equations here.
+ 
+
+ align:start position:0%
+coming. Um, we have some equations here.
+So, we have delta G KN= minus RT natural
+
+ align:start position:0%
+So, we have delta G KN= minus RT natural
+ 
+
+ align:start position:0%
+So, we have delta G KN= minus RT natural
+log of K, which we can rearrange to
+
+ align:start position:0%
+log of K, which we can rearrange to
+ 
+
+ align:start position:0%
+log of K, which we can rearrange to
+solve for K. And let's just have a
+
+ align:start position:0%
+solve for K. And let's just have a
+ 
+
+ align:start position:0%
+solve for K. And let's just have a
+little reminder of what these terms are.
+
+ align:start position:0%
+little reminder of what these terms are.
+ 
+
+ align:start position:0%
+little reminder of what these terms are.
+So, we'll put this up here. T is
+
+ align:start position:0%
+So, we'll put this up here. T is
+ 
+
+ align:start position:0%
+So, we'll put this up here. T is
+temperature. And we're going to be
+
+ align:start position:0%
+temperature. And we're going to be
+ 
+
+ align:start position:0%
+temperature. And we're going to be
+talking about room temperature. This is
+
+ align:start position:0%
+talking about room temperature. This is
+ 
+
+ align:start position:0%
+talking about room temperature. This is
+at room temperature now. And in fact,
+
+ align:start position:0%
+at room temperature now. And in fact,
+ 
+
+ align:start position:0%
+at room temperature now. And in fact,
+almost all acidbased problems are going
+
+ align:start position:0%
+almost all acidbased problems are going
+ 
+
+ align:start position:0%
+almost all acidbased problems are going
+to be at room temperature. There might
+
+ align:start position:0%
+to be at room temperature. There might
+ 
+
+ align:start position:0%
+to be at room temperature. There might
+be a few differences, but we have a lot
+
+ align:start position:0%
+be a few differences, but we have a lot
+ 
+
+ align:start position:0%
+be a few differences, but we have a lot
+at room temperature. We have a constant
+
+ align:start position:0%
+at room temperature. We have a constant
+ 
+
+ align:start position:0%
+at room temperature. We have a constant
+R. And so three um 8.314 jewels per
+
+ align:start position:0%
+R. And so three um 8.314 jewels per
+ 
+
+ align:start position:0%
+R. And so three um 8.314 jewels per
+Kelvin per
+
+ align:start position:0%
+Kelvin per
+ 
+
+ align:start position:0%
+Kelvin per
+mole and delta G. So we were uh we were
+
+ align:start position:0%
+mole and delta G. So we were uh we were
+ 
+
+ align:start position:0%
+mole and delta G. So we were uh we were
+already told the value for delta G here.
+
+ align:start position:0%
+already told the value for delta G here.
+ 
+
+ align:start position:0%
+already told the value for delta G here.
+Now thinking about this room temperature
+
+ align:start position:0%
+Now thinking about this room temperature
+ 
+
+ align:start position:0%
+Now thinking about this room temperature
+this constant and this value for delta G
+
+ align:start position:0%
+this constant and this value for delta G
+ 
+
+ align:start position:0%
+this constant and this value for delta G
+do you expect a large or small value for
+
+ align:start position:0%
+do you expect a large or small value for
+ 
+
+ align:start position:0%
+do you expect a large or small value for
+K if you have this delta G KN value and
+
+ align:start position:0%
+K if you have this delta G KN value and
+ 
+
+ align:start position:0%
+K if you have this delta G KN value and
+that's our clicker question.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, let's just do 10 more
+
+ align:start position:0%
+All right, let's just do 10 more
+ 
+
+ align:start position:0%
+All right, let's just do 10 more
+seconds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yep. So K you would expect to be a small
+
+ align:start position:0%
+Yep. So K you would expect to be a small
+ 
+
+ align:start position:0%
+Yep. So K you would expect to be a small
+value less than one. And you could think
+
+ align:start position:0%
+value less than one. And you could think
+ 
+
+ align:start position:0%
+value less than one. And you could think
+about that mathematically from these
+
+ align:start position:0%
+about that mathematically from these
+ 
+
+ align:start position:0%
+about that mathematically from these
+expressions or you could think about it
+
+ align:start position:0%
+expressions or you could think about it
+ 
+
+ align:start position:0%
+expressions or you could think about it
+in terms of the value uh for delta G. So
+
+ align:start position:0%
+in terms of the value uh for delta G. So
+ 
+
+ align:start position:0%
+in terms of the value uh for delta G. So
+if we solve this and we put in our value
+
+ align:start position:0%
+if we solve this and we put in our value
+ 
+
+ align:start position:0%
+if we solve this and we put in our value
+for delta G KN which is a positive
+
+ align:start position:0%
+for delta G KN which is a positive
+ 
+
+ align:start position:0%
+for delta G KN which is a positive
+value. So the forward direction of the
+
+ align:start position:0%
+value. So the forward direction of the
+ 
+
+ align:start position:0%
+value. So the forward direction of the
+reaction is
+
+ align:start position:0%
+reaction is
+ 
+
+ align:start position:0%
+reaction is
+non-spontaneous. Um so we put in our
+
+ align:start position:0%
+non-spontaneous. Um so we put in our
+ 
+
+ align:start position:0%
+non-spontaneous. Um so we put in our
+positive delta G knot and our other
+
+ align:start position:0%
+positive delta G knot and our other
+ 
+
+ align:start position:0%
+positive delta G knot and our other
+values here. And this is again jewels
+
+ align:start position:0%
+values here. And this is again jewels
+ 
+
+ align:start position:0%
+values here. And this is again jewels
+per Kelvin per mole. Um and we have to
+
+ align:start position:0%
+per Kelvin per mole. Um and we have to
+ 
+
+ align:start position:0%
+per Kelvin per mole. Um and we have to
+make sure that we convert KJ to jewels
+
+ align:start position:0%
+make sure that we convert KJ to jewels
+ 
+
+ align:start position:0%
+make sure that we convert KJ to jewels
+and our units will cancel out. And if we
+
+ align:start position:0%
+and our units will cancel out. And if we
+ 
+
+ align:start position:0%
+and our units will cancel out. And if we
+do that, we get this value for natural
+
+ align:start position:0%
+do that, we get this value for natural
+ 
+
+ align:start position:0%
+do that, we get this value for natural
+log of K and this value for K of 1.0 *
+
+ align:start position:0%
+log of K and this value for K of 1.0 *
+ 
+
+ align:start position:0%
+log of K and this value for K of 1.0 *
+10 the minus14 at room temperature. And
+
+ align:start position:0%
+10 the minus14 at room temperature. And
+ 
+
+ align:start position:0%
+10 the minus14 at room temperature. And
+you will find that you end up memorizing
+
+ align:start position:0%
+you will find that you end up memorizing
+ 
+
+ align:start position:0%
+you will find that you end up memorizing
+this value if you do enough acidbased
+
+ align:start position:0%
+this value if you do enough acidbased
+ 
+
+ align:start position:0%
+this value if you do enough acidbased
+problems. In fact, you might have it
+
+ align:start position:0%
+problems. In fact, you might have it
+ 
+
+ align:start position:0%
+problems. In fact, you might have it
+memorized already. Okay, so this is in
+
+ align:start position:0%
+memorized already. Okay, so this is in
+ 
+
+ align:start position:0%
+memorized already. Okay, so this is in
+fact a small value and that indicates
+
+ align:start position:0%
+fact a small value and that indicates
+ 
+
+ align:start position:0%
+fact a small value and that indicates
+that only a small proportion of water
+
+ align:start position:0%
+that only a small proportion of water
+ 
+
+ align:start position:0%
+that only a small proportion of water
+molecules are ionized. about one
+
+ align:start position:0%
+molecules are ionized. about one
+ 
+
+ align:start position:0%
+molecules are ionized. about one
+molecule in every 200 million are
+
+ align:start position:0%
+molecule in every 200 million are
+ 
+
+ align:start position:0%
+molecule in every 200 million are
+ionized. So it's a very very small
+
+ align:start position:0%
+ionized. So it's a very very small
+ 
+
+ align:start position:0%
+ionized. So it's a very very small
+value. So there is a lot of H2O in a
+
+ align:start position:0%
+value. So there is a lot of H2O in a
+ 
+
+ align:start position:0%
+value. So there is a lot of H2O in a
+glass of water. So in here it's mostly
+
+ align:start position:0%
+glass of water. So in here it's mostly
+ 
+
+ align:start position:0%
+glass of water. So in here it's mostly
+H2O. Very few molecules are ionized in
+
+ align:start position:0%
+H2O. Very few molecules are ionized in
+ 
+
+ align:start position:0%
+H2O. Very few molecules are ionized in
+that. Now part of the reason why you're
+
+ align:start position:0%
+that. Now part of the reason why you're
+ 
+
+ align:start position:0%
+that. Now part of the reason why you're
+likely to have this value of K memorized
+
+ align:start position:0%
+likely to have this value of K memorized
+ 
+
+ align:start position:0%
+likely to have this value of K memorized
+is because it has a special name. This K
+
+ align:start position:0%
+is because it has a special name. This K
+ 
+
+ align:start position:0%
+is because it has a special name. This K
+is called KW for
+
+ align:start position:0%
+is called KW for
+ 
+
+ align:start position:0%
+is called KW for
+water. So that's easy to remember. And
+
+ align:start position:0%
+water. So that's easy to remember. And
+ 
+
+ align:start position:0%
+water. So that's easy to remember. And
+KW the equilibrium constant for water is
+
+ align:start position:0%
+KW the equilibrium constant for water is
+ 
+
+ align:start position:0%
+KW the equilibrium constant for water is
+equal to the hydrronium ion
+
+ align:start position:0%
+equal to the hydrronium ion
+ 
+
+ align:start position:0%
+equal to the hydrronium ion
+concentration times the hydroxide ion
+
+ align:start position:0%
+concentration times the hydroxide ion
+ 
+
+ align:start position:0%
+concentration times the hydroxide ion
+concentration. And since this is an
+
+ align:start position:0%
+concentration. And since this is an
+ 
+
+ align:start position:0%
+concentration. And since this is an
+equilibrium constant, if you're at
+
+ align:start position:0%
+equilibrium constant, if you're at
+ 
+
+ align:start position:0%
+equilibrium constant, if you're at
+constant temperature at room
+
+ align:start position:0%
+constant temperature at room
+ 
+
+ align:start position:0%
+constant temperature at room
+temperature, this will always equal 1.0.
+
+ align:start position:0%
+temperature, this will always equal 1.0.
+ 
+
+ align:start position:0%
+temperature, this will always equal 1.0.
+0 * 10 -14. This product is always going
+
+ align:start position:0%
+0 * 10 -14. This product is always going
+ 
+
+ align:start position:0%
+0 * 10 -14. This product is always going
+to be this at room temperature. And that
+
+ align:start position:0%
+to be this at room temperature. And that
+ 
+
+ align:start position:0%
+to be this at room temperature. And that
+is why it's going to turn out to be
+
+ align:start position:0%
+is why it's going to turn out to be
+ 
+
+ align:start position:0%
+is why it's going to turn out to be
+important because you're going to use
+
+ align:start position:0%
+important because you're going to use
+ 
+
+ align:start position:0%
+important because you're going to use
+that information in solving a lot of
+
+ align:start position:0%
+that information in solving a lot of
+ 
+
+ align:start position:0%
+that information in solving a lot of
+problems. All right. So if this is an
+
+ align:start position:0%
+problems. All right. So if this is an
+ 
+
+ align:start position:0%
+problems. All right. So if this is an
+equilibrium constant, um we want to
+
+ align:start position:0%
+equilibrium constant, um we want to
+ 
+
+ align:start position:0%
+equilibrium constant, um we want to
+think again about expressions for
+
+ align:start position:0%
+think again about expressions for
+ 
+
+ align:start position:0%
+think again about expressions for
+equilibrium. And just make a note that
+
+ align:start position:0%
+equilibrium. And just make a note that
+ 
+
+ align:start position:0%
+equilibrium. And just make a note that
+we did not include water squared on the
+
+ align:start position:0%
+we did not include water squared on the
+ 
+
+ align:start position:0%
+we did not include water squared on the
+bottom of this expression. So, KW equals
+
+ align:start position:0%
+bottom of this expression. So, KW equals
+ 
+
+ align:start position:0%
+bottom of this expression. So, KW equals
+hydrronium ion concentration times
+
+ align:start position:0%
+hydrronium ion concentration times
+ 
+
+ align:start position:0%
+hydrronium ion concentration times
+hydroxide ion concentration. You don't
+
+ align:start position:0%
+hydroxide ion concentration. You don't
+ 
+
+ align:start position:0%
+hydroxide ion concentration. You don't
+put it over water. And the reason for
+
+ align:start position:0%
+put it over water. And the reason for
+ 
+
+ align:start position:0%
+put it over water. And the reason for
+this is because this is a pretty pure
+
+ align:start position:0%
+this is because this is a pretty pure
+ 
+
+ align:start position:0%
+this is because this is a pretty pure
+solvent and you don't include pure
+
+ align:start position:0%
+solvent and you don't include pure
+ 
+
+ align:start position:0%
+solvent and you don't include pure
+solvents um in your equilibrium
+
+ align:start position:0%
+solvents um in your equilibrium
+ 
+
+ align:start position:0%
+solvents um in your equilibrium
+expression. You also don't include
+
+ align:start position:0%
+expression. You also don't include
+ 
+
+ align:start position:0%
+expression. You also don't include
+solids. So, we talked about that when we
+
+ align:start position:0%
+solids. So, we talked about that when we
+ 
+
+ align:start position:0%
+solids. So, we talked about that when we
+were talking about solubility. So, you
+
+ align:start position:0%
+were talking about solubility. So, you
+ 
+
+ align:start position:0%
+were talking about solubility. So, you
+have to remember that um solvents like
+
+ align:start position:0%
+have to remember that um solvents like
+ 
+
+ align:start position:0%
+have to remember that um solvents like
+water is nearly pure. doesn't go in.
+
+ align:start position:0%
+water is nearly pure. doesn't go in.
+ 
+
+ align:start position:0%
+water is nearly pure. doesn't go in.
+Pure other liquids, pure other solids
+
+ align:start position:0%
+Pure other liquids, pure other solids
+ 
+
+ align:start position:0%
+Pure other liquids, pure other solids
+are not included in your equilibrium
+
+ align:start position:0%
+are not included in your equilibrium
+ 
+
+ align:start position:0%
+are not included in your equilibrium
+expression. All right, so we now know
+
+ align:start position:0%
+expression. All right, so we now know
+ 
+
+ align:start position:0%
+expression. All right, so we now know
+about water. We know about um KW. Let's
+
+ align:start position:0%
+about water. We know about um KW. Let's
+ 
+
+ align:start position:0%
+about water. We know about um KW. Let's
+do a few more definitions and then think
+
+ align:start position:0%
+do a few more definitions and then think
+ 
+
+ align:start position:0%
+do a few more definitions and then think
+about how all these terms are related to
+
+ align:start position:0%
+about how all these terms are related to
+ 
+
+ align:start position:0%
+about how all these terms are related to
+each other. So a definition that many
+
+ align:start position:0%
+each other. So a definition that many
+ 
+
+ align:start position:0%
+each other. So a definition that many
+people already know probably if you
+
+ align:start position:0%
+people already know probably if you
+ 
+
+ align:start position:0%
+people already know probably if you
+taken any kind of science before you're
+
+ align:start position:0%
+taken any kind of science before you're
+ 
+
+ align:start position:0%
+taken any kind of science before you're
+probably aware that pH equals minus log
+
+ align:start position:0%
+probably aware that pH equals minus log
+ 
+
+ align:start position:0%
+probably aware that pH equals minus log
+of the hydrronium ion concentration of
+
+ align:start position:0%
+of the hydrronium ion concentration of
+ 
+
+ align:start position:0%
+of the hydrronium ion concentration of
+H3+ if you don't know it it will be on
+
+ align:start position:0%
+H3+ if you don't know it it will be on
+ 
+
+ align:start position:0%
+H3+ if you don't know it it will be on
+your equation sheet so um it doesn't
+
+ align:start position:0%
+your equation sheet so um it doesn't
+ 
+
+ align:start position:0%
+your equation sheet so um it doesn't
+really matter but there it is and
+
+ align:start position:0%
+really matter but there it is and
+ 
+
+ align:start position:0%
+really matter but there it is and
+there's also
+
+ align:start position:0%
+there's also
+ 
+
+ align:start position:0%
+there's also
+P equals minus log of the hydroxide ion
+
+ align:start position:0%
+P equals minus log of the hydroxide ion
+ 
+
+ align:start position:0%
+P equals minus log of the hydroxide ion
+concentration O minus
+
+ align:start position:0%
+concentration O minus
+ 
+
+ align:start position:0%
+concentration O minus
+Now let's think about the relationships
+
+ align:start position:0%
+Now let's think about the relationships
+ 
+
+ align:start position:0%
+Now let's think about the relationships
+of pKw, pH, and
+
+ align:start position:0%
+of pKw, pH, and
+ 
+
+ align:start position:0%
+of pKw, pH, and
+p. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relationships. So I just told you and
+
+ align:start position:0%
+relationships. So I just told you and
+ 
+
+ align:start position:0%
+relationships. So I just told you and
+maybe you've already memorized that KW
+
+ align:start position:0%
+maybe you've already memorized that KW
+ 
+
+ align:start position:0%
+maybe you've already memorized that KW
+is going to be equal to the hydrronium
+
+ align:start position:0%
+is going to be equal to the hydrronium
+ 
+
+ align:start position:0%
+is going to be equal to the hydrronium
+ion concentration times the hydroxide
+
+ align:start position:0%
+ion concentration times the hydroxide
+ 
+
+ align:start position:0%
+ion concentration times the hydroxide
+ion concentration. And that's going to
+
+ align:start position:0%
+ion concentration. And that's going to
+ 
+
+ align:start position:0%
+ion concentration. And that's going to
+be equal to 1.0 * 10us14th at room
+
+ align:start position:0%
+be equal to 1.0 * 10us14th at room
+ 
+
+ align:start position:0%
+be equal to 1.0 * 10us14th at room
+temperature. So now if we take this
+
+ align:start position:0%
+temperature. So now if we take this
+ 
+
+ align:start position:0%
+temperature. So now if we take this
+expression and we take the log of all of
+
+ align:start position:0%
+expression and we take the log of all of
+ 
+
+ align:start position:0%
+expression and we take the log of all of
+these terms and multiply by a negative
+
+ align:start position:0%
+these terms and multiply by a negative
+ 
+
+ align:start position:0%
+these terms and multiply by a negative
+value then we will get this expression.
+
+ align:start position:0%
+value then we will get this expression.
+ 
+
+ align:start position:0%
+value then we will get this expression.
+So minus log of KW is P
+
+ align:start position:0%
+So minus log of KW is P
+ 
+
+ align:start position:0%
+So minus log of KW is P
+KW and minus log of the hydrronium ion
+
+ align:start position:0%
+KW and minus log of the hydrronium ion
+ 
+
+ align:start position:0%
+KW and minus log of the hydrronium ion
+concentration is what?
+
+ align:start position:0%
+concentration is what?
+ 
+
+ align:start position:0%
+concentration is what?
+PH minus log of the hydroxide ion
+
+ align:start position:0%
+PH minus log of the hydroxide ion
+ 
+
+ align:start position:0%
+PH minus log of the hydroxide ion
+concentration is what?
+
+ align:start position:0%
+concentration is what?
+ 
+
+ align:start position:0%
+concentration is what?
+P. So P KW equals PH +
+
+ align:start position:0%
+P. So P KW equals PH +
+ 
+
+ align:start position:0%
+P. So P KW equals PH +
+P. And that is equal to
+
+ align:start position:0%
+P. And that is equal to
+ 
+
+ align:start position:0%
+P. And that is equal to
+14.0 at room temperature. And this is a
+
+ align:start position:0%
+14.0 at room temperature. And this is a
+ 
+
+ align:start position:0%
+14.0 at room temperature. And this is a
+very useful expression. The fact that PH
+
+ align:start position:0%
+very useful expression. The fact that PH
+ 
+
+ align:start position:0%
+very useful expression. The fact that PH
+and P are equal to 14. If you know one
+
+ align:start position:0%
+and P are equal to 14. If you know one
+ 
+
+ align:start position:0%
+and P are equal to 14. If you know one
+of these, then you know the other one by
+
+ align:start position:0%
+of these, then you know the other one by
+ 
+
+ align:start position:0%
+of these, then you know the other one by
+doing a simple
+
+ align:start position:0%
+doing a simple
+ 
+
+ align:start position:0%
+doing a simple
+subtraction. So you will find yourself
+
+ align:start position:0%
+subtraction. So you will find yourself
+ 
+
+ align:start position:0%
+subtraction. So you will find yourself
+using this expression quite often in the
+
+ align:start position:0%
+using this expression quite often in the
+ 
+
+ align:start position:0%
+using this expression quite often in the
+problem sets. And so I'll say that one
+
+ align:start position:0%
+problem sets. And so I'll say that one
+ 
+
+ align:start position:0%
+problem sets. And so I'll say that one
+the problem set that's due on Friday has
+
+ align:start position:0%
+the problem set that's due on Friday has
+ 
+
+ align:start position:0%
+the problem set that's due on Friday has
+just a couple of acidbased problems at
+
+ align:start position:0%
+just a couple of acidbased problems at
+ 
+
+ align:start position:0%
+just a couple of acidbased problems at
+the end. The next problem set will be
+
+ align:start position:0%
+the end. The next problem set will be
+ 
+
+ align:start position:0%
+the end. The next problem set will be
+100% acidbased problems. So there's a
+
+ align:start position:0%
+100% acidbased problems. So there's a
+ 
+
+ align:start position:0%
+100% acidbased problems. So there's a
+lot lot to look forward to.
+
+ align:start position:0%
+lot lot to look forward to.
+ 
+
+ align:start position:0%
+lot lot to look forward to.
+Okay, so let's talk about the strengths
+
+ align:start position:0%
+Okay, so let's talk about the strengths
+ 
+
+ align:start position:0%
+Okay, so let's talk about the strengths
+of acids and
+
+ align:start position:0%
+of acids and
+ 
+
+ align:start position:0%
+of acids and
+bases. So if you have a pH of pure
+
+ align:start position:0%
+bases. So if you have a pH of pure
+ 
+
+ align:start position:0%
+bases. So if you have a pH of pure
+water, it should be equal to minus log *
+
+ align:start position:0%
+water, it should be equal to minus log *
+ 
+
+ align:start position:0%
+water, it should be equal to minus log *
+1 1.0 * 10us 7 or the pH equals 7 which
+
+ align:start position:0%
+1 1.0 * 10us 7 or the pH equals 7 which
+ 
+
+ align:start position:0%
+1 1.0 * 10us 7 or the pH equals 7 which
+is a neutral pH. So if we have a scale
+
+ align:start position:0%
+is a neutral pH. So if we have a scale
+ 
+
+ align:start position:0%
+is a neutral pH. So if we have a scale
+here, pH minus1 to
+
+ align:start position:0%
+here, pH minus1 to
+ 
+
+ align:start position:0%
+here, pH minus1 to
+pH14, 7 is a neutral value.
+
+ align:start position:0%
+pH14, 7 is a neutral value.
+ 
+
+ align:start position:0%
+pH14, 7 is a neutral value.
+If we're talking about things that are
+
+ align:start position:0%
+If we're talking about things that are
+ 
+
+ align:start position:0%
+If we're talking about things that are
+acidic, the pH of an acidic solution is
+
+ align:start position:0%
+acidic, the pH of an acidic solution is
+ 
+
+ align:start position:0%
+acidic, the pH of an acidic solution is
+less than seven. And so this is the
+
+ align:start position:0%
+less than seven. And so this is the
+ 
+
+ align:start position:0%
+less than seven. And so this is the
+acidic part over
+
+ align:start position:0%
+acidic part over
+ 
+
+ align:start position:0%
+acidic part over
+here. And the pH of a basic solution is
+
+ align:start position:0%
+here. And the pH of a basic solution is
+ 
+
+ align:start position:0%
+here. And the pH of a basic solution is
+greater than seven. So that is down in
+
+ align:start position:0%
+greater than seven. So that is down in
+ 
+
+ align:start position:0%
+greater than seven. So that is down in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+part. The EPA defines waste as
+
+ align:start position:0%
+part. The EPA defines waste as
+ 
+
+ align:start position:0%
+part. The EPA defines waste as
+corrosive.
+
+ align:start position:0%
+corrosive.
+ 
+
+ align:start position:0%
+corrosive.
+If the pH is lower than three, so that
+
+ align:start position:0%
+If the pH is lower than three, so that
+ 
+
+ align:start position:0%
+If the pH is lower than three, so that
+would be corrosive or higher than
+
+ align:start position:0%
+would be corrosive or higher than
+ 
+
+ align:start position:0%
+would be corrosive or higher than
+12.5, also corrosive. So living
+
+ align:start position:0%
+12.5, also corrosive. So living
+ 
+
+ align:start position:0%
+12.5, also corrosive. So living
+creatures like to be more in the neutral
+
+ align:start position:0%
+creatures like to be more in the neutral
+ 
+
+ align:start position:0%
+creatures like to be more in the neutral
+range. When you get to things of very
+
+ align:start position:0%
+range. When you get to things of very
+ 
+
+ align:start position:0%
+range. When you get to things of very
+low pH or very um high pH, that is less
+
+ align:start position:0%
+low pH or very um high pH, that is less
+ 
+
+ align:start position:0%
+low pH or very um high pH, that is less
+good. So let's now check out a few phes.
+
+ align:start position:0%
+good. So let's now check out a few phes.
+ 
+
+ align:start position:0%
+good. So let's now check out a few phes.
+And I'd like to have uh five uh TAs come
+
+ align:start position:0%
+And I'd like to have uh five uh TAs come
+ 
+
+ align:start position:0%
+And I'd like to have uh five uh TAs come
+down to help me with this. And I'll just
+
+ align:start position:0%
+down to help me with this. And I'll just
+ 
+
+ align:start position:0%
+down to help me with this. And I'll just
+show you what we're going to do. So,
+
+ align:start position:0%
+show you what we're going to do. So,
+ 
+
+ align:start position:0%
+show you what we're going to do. So,
+we'll have some volunteers. We have pH
+
+ align:start position:0%
+we'll have some volunteers. We have pH
+ 
+
+ align:start position:0%
+we'll have some volunteers. We have pH
+paper. The pH paper has an indicator on.
+
+ align:start position:0%
+paper. The pH paper has an indicator on.
+ 
+
+ align:start position:0%
+paper. The pH paper has an indicator on.
+You put the paper in the solution and
+
+ align:start position:0%
+You put the paper in the solution and
+ 
+
+ align:start position:0%
+You put the paper in the solution and
+then try to see which thing matches
+
+ align:start position:0%
+then try to see which thing matches
+ 
+
+ align:start position:0%
+then try to see which thing matches
+best. So, this is a very quick and dirty
+
+ align:start position:0%
+best. So, this is a very quick and dirty
+ 
+
+ align:start position:0%
+best. So, this is a very quick and dirty
+way to estimate pH. There's pH m meters
+
+ align:start position:0%
+way to estimate pH. There's pH m meters
+ 
+
+ align:start position:0%
+way to estimate pH. There's pH m meters
+and indicator dyes that work better, but
+
+ align:start position:0%
+and indicator dyes that work better, but
+ 
+
+ align:start position:0%
+and indicator dyes that work better, but
+you'll you'll have five people measure
+
+ align:start position:0%
+you'll you'll have five people measure
+ 
+
+ align:start position:0%
+you'll you'll have five people measure
+five things. We have ammonia, a cleaner.
+
+ align:start position:0%
+five things. We have ammonia, a cleaner.
+ 
+
+ align:start position:0%
+five things. We have ammonia, a cleaner.
+We talked about the importance of
+
+ align:start position:0%
+We talked about the importance of
+ 
+
+ align:start position:0%
+We talked about the importance of
+cleaning bathrooms um last lecture. We
+
+ align:start position:0%
+cleaning bathrooms um last lecture. We
+ 
+
+ align:start position:0%
+cleaning bathrooms um last lecture. We
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+soda. We have vinegar, which is often
+
+ align:start position:0%
+soda. We have vinegar, which is often
+ 
+
+ align:start position:0%
+soda. We have vinegar, which is often
+used in salad dressings. Um before I
+
+ align:start position:0%
+used in salad dressings. Um before I
+ 
+
+ align:start position:0%
+used in salad dressings. Um before I
+came here, I just went to a random sink
+
+ align:start position:0%
+came here, I just went to a random sink
+ 
+
+ align:start position:0%
+came here, I just went to a random sink
+and got some MIT water um to measure.
+
+ align:start position:0%
+and got some MIT water um to measure.
+ 
+
+ align:start position:0%
+and got some MIT water um to measure.
+And then this this is special. This is a
+
+ align:start position:0%
+And then this this is special. This is a
+ 
+
+ align:start position:0%
+And then this this is special. This is a
+prescription
+
+ align:start position:0%
+prescription
+ 
+
+ align:start position:0%
+prescription
+medicine. So this is um a solution of of
+
+ align:start position:0%
+medicine. So this is um a solution of of
+ 
+
+ align:start position:0%
+medicine. So this is um a solution of of
+iron to sulfate and this is prescribed
+
+ align:start position:0%
+iron to sulfate and this is prescribed
+ 
+
+ align:start position:0%
+iron to sulfate and this is prescribed
+if you're iron have an iron deficiency
+
+ align:start position:0%
+if you're iron have an iron deficiency
+ 
+
+ align:start position:0%
+if you're iron have an iron deficiency
+and iron deficiency is pretty bad and a
+
+ align:start position:0%
+and iron deficiency is pretty bad and a
+ 
+
+ align:start position:0%
+and iron deficiency is pretty bad and a
+lot of kids have iron deficiencies. It's
+
+ align:start position:0%
+lot of kids have iron deficiencies. It's
+ 
+
+ align:start position:0%
+lot of kids have iron deficiencies. It's
+really common in infants. So my daughter
+
+ align:start position:0%
+really common in infants. So my daughter
+ 
+
+ align:start position:0%
+really common in infants. So my daughter
+had an iron deficiency and this was her
+
+ align:start position:0%
+had an iron deficiency and this was her
+ 
+
+ align:start position:0%
+had an iron deficiency and this was her
+medicine. In fact, this box is
+
+ align:start position:0%
+medicine. In fact, this box is
+ 
+
+ align:start position:0%
+medicine. In fact, this box is
+completely full of this medicine. So,
+
+ align:start position:0%
+completely full of this medicine. So,
+ 
+
+ align:start position:0%
+completely full of this medicine. So,
+um, kids cannot swallow pills very
+
+ align:start position:0%
+um, kids cannot swallow pills very
+ 
+
+ align:start position:0%
+um, kids cannot swallow pills very
+easily. How many of you actually cannot
+
+ align:start position:0%
+easily. How many of you actually cannot
+ 
+
+ align:start position:0%
+easily. How many of you actually cannot
+swallow a pill? A lot of adults are pill
+
+ align:start position:0%
+swallow a pill? A lot of adults are pill
+ 
+
+ align:start position:0%
+swallow a pill? A lot of adults are pill
+challenged. You might maybe how many are
+
+ align:start position:0%
+challenged. You might maybe how many are
+ 
+
+ align:start position:0%
+challenged. You might maybe how many are
+happy swallowing pills? Let's do a more
+
+ align:start position:0%
+happy swallowing pills? Let's do a more
+ 
+
+ align:start position:0%
+happy swallowing pills? Let's do a more
+positive thing. Okay. Um, so swallowing
+
+ align:start position:0%
+positive thing. Okay. Um, so swallowing
+ 
+
+ align:start position:0%
+positive thing. Okay. Um, so swallowing
+pills is not everyone's
+
+ align:start position:0%
+pills is not everyone's
+ 
+
+ align:start position:0%
+pills is not everyone's
+favorite. Um, when you're a kid, it's
+
+ align:start position:0%
+favorite. Um, when you're a kid, it's
+ 
+
+ align:start position:0%
+favorite. Um, when you're a kid, it's
+really impossible to tell someone to
+
+ align:start position:0%
+really impossible to tell someone to
+ 
+
+ align:start position:0%
+really impossible to tell someone to
+like put something in their throat and
+
+ align:start position:0%
+like put something in their throat and
+ 
+
+ align:start position:0%
+like put something in their throat and
+like go back and try to get it down.
+
+ align:start position:0%
+like go back and try to get it down.
+ 
+
+ align:start position:0%
+like go back and try to get it down.
+Like they choke, spit up. It's awful.
+
+ align:start position:0%
+Like they choke, spit up. It's awful.
+ 
+
+ align:start position:0%
+Like they choke, spit up. It's awful.
+So, kids have to take medicine in
+
+ align:start position:0%
+So, kids have to take medicine in
+ 
+
+ align:start position:0%
+So, kids have to take medicine in
+solution. So, this medicine is 300 mg in
+
+ align:start position:0%
+solution. So, this medicine is 300 mg in
+ 
+
+ align:start position:0%
+solution. So, this medicine is 300 mg in
+5 milliliters. It's very concentrated
+
+ align:start position:0%
+5 milliliters. It's very concentrated
+ 
+
+ align:start position:0%
+5 milliliters. It's very concentrated
+because my daughter had a pretty severe
+
+ align:start position:0%
+because my daughter had a pretty severe
+ 
+
+ align:start position:0%
+because my daughter had a pretty severe
+iron deficiency. So when she tried
+
+ align:start position:0%
+iron deficiency. So when she tried
+ 
+
+ align:start position:0%
+iron deficiency. So when she tried
+taking it and I tasted it, it was
+
+ align:start position:0%
+taking it and I tasted it, it was
+ 
+
+ align:start position:0%
+taking it and I tasted it, it was
+horrific beyond belief. And after she
+
+ align:start position:0%
+horrific beyond belief. And after she
+ 
+
+ align:start position:0%
+horrific beyond belief. And after she
+had taken it a couple times, she started
+
+ align:start position:0%
+had taken it a couple times, she started
+ 
+
+ align:start position:0%
+had taken it a couple times, she started
+to have sores on her tongue and in her
+
+ align:start position:0%
+to have sores on her tongue and in her
+ 
+
+ align:start position:0%
+to have sores on her tongue and in her
+mouth. And I, as a chemist, said, "Let's
+
+ align:start position:0%
+mouth. And I, as a chemist, said, "Let's
+ 
+
+ align:start position:0%
+mouth. And I, as a chemist, said, "Let's
+measure the pH." So you will measure the
+
+ align:start position:0%
+measure the pH." So you will measure the
+ 
+
+ align:start position:0%
+measure the pH." So you will measure the
+pH of this prescription medicine for a
+
+ align:start position:0%
+pH of this prescription medicine for a
+ 
+
+ align:start position:0%
+pH of this prescription medicine for a
+fouryear-old and tell me whether the EPA
+
+ align:start position:0%
+fouryear-old and tell me whether the EPA
+ 
+
+ align:start position:0%
+fouryear-old and tell me whether the EPA
+would approve it or not. Anyway, so here
+
+ align:start position:0%
+would approve it or not. Anyway, so here
+ 
+
+ align:start position:0%
+would approve it or not. Anyway, so here
+are the TAs and they're going to come
+
+ align:start position:0%
+are the TAs and they're going to come
+ 
+
+ align:start position:0%
+are the TAs and they're going to come
+around. raise your hand if you're
+
+ align:start position:0%
+around. raise your hand if you're
+ 
+
+ align:start position:0%
+around. raise your hand if you're
+willing to measure a pH. Um, TAS, just
+
+ align:start position:0%
+willing to measure a pH. Um, TAS, just
+ 
+
+ align:start position:0%
+willing to measure a pH. Um, TAS, just
+grab a solution. I should have had you
+
+ align:start position:0%
+grab a solution. I should have had you
+ 
+
+ align:start position:0%
+grab a solution. I should have had you
+pour it, but okay. We're doing it. Um,
+
+ align:start position:0%
+pour it, but okay. We're doing it. Um,
+ 
+
+ align:start position:0%
+pour it, but okay. We're doing it. Um,
+and we'll go around and we'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure and I will tell me what you find
+
+ align:start position:0%
+measure and I will tell me what you find
+ 
+
+ align:start position:0%
+measure and I will tell me what you find
+and I'll write it on the board.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't think so. You are. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, we have pH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Do we have an answer?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Did we get one
+
+ align:start position:0%
+Did we get one
+ 
+
+ align:start position:0%
+Did we get one
+for what? Do you have ammonia is 12?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So almost corrosive but not quite. You
+
+ align:start position:0%
+So almost corrosive but not quite. You
+ 
+
+ align:start position:0%
+So almost corrosive but not quite. You
+can still have uh clean, but if you want
+
+ align:start position:0%
+can still have uh clean, but if you want
+ 
+
+ align:start position:0%
+can still have uh clean, but if you want
+an excuse not to clean, you're like,
+
+ align:start position:0%
+an excuse not to clean, you're like,
+ 
+
+ align:start position:0%
+an excuse not to clean, you're like,
+"Sorry, too close uh to uh too
+
+ align:start position:0%
+"Sorry, too close uh to uh too
+ 
+
+ align:start position:0%
+"Sorry, too close uh to uh too
+corrosive." Do we have another one? MIT
+
+ align:start position:0%
+corrosive." Do we have another one? MIT
+ 
+
+ align:start position:0%
+corrosive." Do we have another one? MIT
+water.
+
+ align:start position:0%
+water.
+ 
+
+ align:start position:0%
+water.
+MIT water is seven.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Awesome. So often actually water that
+
+ align:start position:0%
+Awesome. So often actually water that
+ 
+
+ align:start position:0%
+Awesome. So often actually water that
+you get from a tap is not seven because
+
+ align:start position:0%
+you get from a tap is not seven because
+ 
+
+ align:start position:0%
+you get from a tap is not seven because
+often there are ions that are dissolved
+
+ align:start position:0%
+often there are ions that are dissolved
+ 
+
+ align:start position:0%
+often there are ions that are dissolved
+in it. So, but a little bit around
+
+ align:start position:0%
+in it. So, but a little bit around
+ 
+
+ align:start position:0%
+in it. So, but a little bit around
+seven. Uh, a little bit of ions never
+
+ align:start position:0%
+seven. Uh, a little bit of ions never
+ 
+
+ align:start position:0%
+seven. Uh, a little bit of ions never
+hurt anyone. We have lots of ions in our
+
+ align:start position:0%
+hurt anyone. We have lots of ions in our
+ 
+
+ align:start position:0%
+hurt anyone. We have lots of ions in our
+body. Soda and soda at three and a half.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So soda is definitely getting into our
+
+ align:start position:0%
+So soda is definitely getting into our
+ 
+
+ align:start position:0%
+So soda is definitely getting into our
+corrosive range
+
+ align:start position:0%
+corrosive range
+ 
+
+ align:start position:0%
+corrosive range
+and we have vinegar at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two and that is corrosive. People often
+
+ align:start position:0%
+two and that is corrosive. People often
+ 
+
+ align:start position:0%
+two and that is corrosive. People often
+use pure vinegar to clean out a coffee
+
+ align:start position:0%
+use pure vinegar to clean out a coffee
+ 
+
+ align:start position:0%
+use pure vinegar to clean out a coffee
+pot um because it is pretty corrosive.
+
+ align:start position:0%
+pot um because it is pretty corrosive.
+ 
+
+ align:start position:0%
+pot um because it is pretty corrosive.
+It really does a good job of cleaning
+
+ align:start position:0%
+It really does a good job of cleaning
+ 
+
+ align:start position:0%
+It really does a good job of cleaning
+it. Um when you're having it in salad
+
+ align:start position:0%
+it. Um when you're having it in salad
+ 
+
+ align:start position:0%
+it. Um when you're having it in salad
+dressing, you don't want to have it pure
+
+ align:start position:0%
+dressing, you don't want to have it pure
+ 
+
+ align:start position:0%
+dressing, you don't want to have it pure
+vinegar. that would not be good to
+
+ align:start position:0%
+vinegar. that would not be good to
+ 
+
+ align:start position:0%
+vinegar. that would not be good to
+drink. And what about medicine? The
+
+ align:start position:0%
+drink. And what about medicine? The
+ 
+
+ align:start position:0%
+drink. And what about medicine? The
+medicine is a pH of two. Two. Okay. So,
+
+ align:start position:0%
+medicine is a pH of two. Two. Okay. So,
+ 
+
+ align:start position:0%
+medicine is a pH of two. Two. Okay. So,
+we also have in the corrosive
+
+ align:start position:0%
+we also have in the corrosive
+ 
+
+ align:start position:0%
+we also have in the corrosive
+category, the medicine that my
+
+ align:start position:0%
+category, the medicine that my
+ 
+
+ align:start position:0%
+category, the medicine that my
+four-year-old daughter um was asked to
+
+ align:start position:0%
+four-year-old daughter um was asked to
+ 
+
+ align:start position:0%
+four-year-old daughter um was asked to
+take.
+
+ align:start position:0%
+take.
+ 
+
+ align:start position:0%
+take.
+So when she started getting these soores
+
+ align:start position:0%
+So when she started getting these soores
+ 
+
+ align:start position:0%
+So when she started getting these soores
+in her mouth from taking her medicine, I
+
+ align:start position:0%
+in her mouth from taking her medicine, I
+ 
+
+ align:start position:0%
+in her mouth from taking her medicine, I
+brought some pH paper home and measured
+
+ align:start position:0%
+brought some pH paper home and measured
+ 
+
+ align:start position:0%
+brought some pH paper home and measured
+the pH and discovered that what she was
+
+ align:start position:0%
+the pH and discovered that what she was
+ 
+
+ align:start position:0%
+the pH and discovered that what she was
+taking was corrosive. So um I went to
+
+ align:start position:0%
+taking was corrosive. So um I went to
+ 
+
+ align:start position:0%
+taking was corrosive. So um I went to
+the doctor and said, "Can you prescribe
+
+ align:start position:0%
+the doctor and said, "Can you prescribe
+ 
+
+ align:start position:0%
+the doctor and said, "Can you prescribe
+something different? This medicine is
+
+ align:start position:0%
+something different? This medicine is
+ 
+
+ align:start position:0%
+something different? This medicine is
+corrosive." And the doctor looked at me
+
+ align:start position:0%
+corrosive." And the doctor looked at me
+ 
+
+ align:start position:0%
+corrosive." And the doctor looked at me
+and it's like the pH the pH is like two
+
+ align:start position:0%
+and it's like the pH the pH is like two
+ 
+
+ align:start position:0%
+and it's like the pH the pH is like two
+or lower. Um, and she looked at me and
+
+ align:start position:0%
+or lower. Um, and she looked at me and
+ 
+
+ align:start position:0%
+or lower. Um, and she looked at me and
+she's like, "What do you mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pH?" This is why I spend many lectures
+
+ align:start position:0%
+pH?" This is why I spend many lectures
+ 
+
+ align:start position:0%
+pH?" This is why I spend many lectures
+on pH in this class and acids and bases.
+
+ align:start position:0%
+on pH in this class and acids and bases.
+ 
+
+ align:start position:0%
+on pH in this class and acids and bases.
+Some of you will be doctors and some of
+
+ align:start position:0%
+Some of you will be doctors and some of
+ 
+
+ align:start position:0%
+Some of you will be doctors and some of
+you will not encourage parents to buy
+
+ align:start position:0%
+you will not encourage parents to buy
+ 
+
+ align:start position:0%
+you will not encourage parents to buy
+this much corrosive thing to feed their
+
+ align:start position:0%
+this much corrosive thing to feed their
+ 
+
+ align:start position:0%
+this much corrosive thing to feed their
+child when they're iron deficient. So,
+
+ align:start position:0%
+child when they're iron deficient. So,
+ 
+
+ align:start position:0%
+child when they're iron deficient. So,
+this is what I'm talking about. And for
+
+ align:start position:0%
+this is what I'm talking about. And for
+ 
+
+ align:start position:0%
+this is what I'm talking about. And for
+those of you who are not going to be
+
+ align:start position:0%
+those of you who are not going to be
+ 
+
+ align:start position:0%
+those of you who are not going to be
+doctors, many of you will probably have
+
+ align:start position:0%
+doctors, many of you will probably have
+ 
+
+ align:start position:0%
+doctors, many of you will probably have
+children with an iron deficiency. It's
+
+ align:start position:0%
+children with an iron deficiency. It's
+ 
+
+ align:start position:0%
+children with an iron deficiency. It's
+super common. So you will know um that
+
+ align:start position:0%
+super common. So you will know um that
+ 
+
+ align:start position:0%
+super common. So you will know um that
+you need to measure the pH of the
+
+ align:start position:0%
+you need to measure the pH of the
+ 
+
+ align:start position:0%
+you need to measure the pH of the
+solution before giving it to your child.
+
+ align:start position:0%
+solution before giving it to your child.
+ 
+
+ align:start position:0%
+solution before giving it to your child.
+So what did I do? So what I did was I
+
+ align:start position:0%
+So what did I do? So what I did was I
+ 
+
+ align:start position:0%
+So what did I do? So what I did was I
+bought adult pills, same stuff, iron
+
+ align:start position:0%
+bought adult pills, same stuff, iron
+ 
+
+ align:start position:0%
+bought adult pills, same stuff, iron
+sulfate, and I got made sure that this
+
+ align:start position:0%
+sulfate, and I got made sure that this
+ 
+
+ align:start position:0%
+sulfate, and I got made sure that this
+told me the number of milligrams that
+
+ align:start position:0%
+told me the number of milligrams that
+ 
+
+ align:start position:0%
+told me the number of milligrams that
+were in there. I looked at what was
+
+ align:start position:0%
+were in there. I looked at what was
+ 
+
+ align:start position:0%
+were in there. I looked at what was
+prescribed. So, I got the pills with the
+
+ align:start position:0%
+prescribed. So, I got the pills with the
+ 
+
+ align:start position:0%
+prescribed. So, I got the pills with the
+correct number of milligrams and then I
+
+ align:start position:0%
+correct number of milligrams and then I
+ 
+
+ align:start position:0%
+correct number of milligrams and then I
+crushed them. And that stuff also tastes
+
+ align:start position:0%
+crushed them. And that stuff also tastes
+ 
+
+ align:start position:0%
+crushed them. And that stuff also tastes
+really nasty. But a little tip for the
+
+ align:start position:0%
+really nasty. But a little tip for the
+ 
+
+ align:start position:0%
+really nasty. But a little tip for the
+future, there's one and only one that I
+
+ align:start position:0%
+future, there's one and only one that I
+ 
+
+ align:start position:0%
+future, there's one and only one that I
+discovered taste that can cover the
+
+ align:start position:0%
+discovered taste that can cover the
+ 
+
+ align:start position:0%
+discovered taste that can cover the
+taste of iron 2 sulfate and that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Nutella. So, don't give your child
+
+ align:start position:0%
+Nutella. So, don't give your child
+ 
+
+ align:start position:0%
+Nutella. So, don't give your child
+corrosive medicine. Give them crushed
+
+ align:start position:0%
+corrosive medicine. Give them crushed
+ 
+
+ align:start position:0%
+corrosive medicine. Give them crushed
+pills in
+
+ align:start position:0%
+pills in
+ 
+
+ align:start position:0%
+pills in
+Nutella. PH is important. pH is
+
+ align:start position:0%
+Nutella. PH is important. pH is
+ 
+
+ align:start position:0%
+Nutella. PH is important. pH is
+important.
+
+ align:start position:0%
+important.
+ 
+
+ align:start position:0%
+important.
+Okay. So, let's talk about the strengths
+
+ align:start position:0%
+Okay. So, let's talk about the strengths
+ 
+
+ align:start position:0%
+Okay. So, let's talk about the strengths
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acids. And you might want to reconsider
+
+ align:start position:0%
+acids. And you might want to reconsider
+ 
+
+ align:start position:0%
+acids. And you might want to reconsider
+huge soda consumption, too. I I I don't
+
+ align:start position:0%
+huge soda consumption, too. I I I don't
+ 
+
+ align:start position:0%
+huge soda consumption, too. I I I don't
+really know, but uh that's something you
+
+ align:start position:0%
+really know, but uh that's something you
+ 
+
+ align:start position:0%
+really know, but uh that's something you
+might want to think about. Okay.
+
+ align:start position:0%
+might want to think about. Okay.
+ 
+
+ align:start position:0%
+might want to think about. Okay.
+Strength of acids.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here we have some acetic
+
+ align:start position:0%
+So here we have some acetic
+ 
+
+ align:start position:0%
+So here we have some acetic
+acid CH3 CO aquous dissolved in our
+
+ align:start position:0%
+acid CH3 CO aquous dissolved in our
+ 
+
+ align:start position:0%
+acid CH3 CO aquous dissolved in our
+solvent which is liquid
+
+ align:start position:0%
+solvent which is liquid
+ 
+
+ align:start position:0%
+solvent which is liquid
+water and this is an acid so it will
+
+ align:start position:0%
+water and this is an acid so it will
+ 
+
+ align:start position:0%
+water and this is an acid so it will
+give up a hydrogen ion or a proton to
+
+ align:start position:0%
+give up a hydrogen ion or a proton to
+ 
+
+ align:start position:0%
+give up a hydrogen ion or a proton to
+the water which acts as a base and forms
+
+ align:start position:0%
+the water which acts as a base and forms
+ 
+
+ align:start position:0%
+the water which acts as a base and forms
+hydro forms our hydrronium ions H3O plus
+
+ align:start position:0%
+hydro forms our hydrronium ions H3O plus
+ 
+
+ align:start position:0%
+hydro forms our hydrronium ions H3O plus
+and also the conjugate base of the acid.
+
+ align:start position:0%
+and also the conjugate base of the acid.
+ 
+
+ align:start position:0%
+and also the conjugate base of the acid.
+So it's the acid missing H+. So C H3 C
+
+ align:start position:0%
+So it's the acid missing H+. So C H3 C
+ 
+
+ align:start position:0%
+So it's the acid missing H+. So C H3 C
+minus. So if we're talking about the
+
+ align:start position:0%
+minus. So if we're talking about the
+ 
+
+ align:start position:0%
+minus. So if we're talking about the
+strength of the acid, what we really
+
+ align:start position:0%
+strength of the acid, what we really
+ 
+
+ align:start position:0%
+strength of the acid, what we really
+want to know is how much of that acid
+
+ align:start position:0%
+want to know is how much of that acid
+ 
+
+ align:start position:0%
+want to know is how much of that acid
+forms ions, how much of it ionizes. That
+
+ align:start position:0%
+forms ions, how much of it ionizes. That
+ 
+
+ align:start position:0%
+forms ions, how much of it ionizes. That
+is going to make determine how strong it
+
+ align:start position:0%
+is going to make determine how strong it
+ 
+
+ align:start position:0%
+is going to make determine how strong it
+is because the amount that ionizes is
+
+ align:start position:0%
+is because the amount that ionizes is
+ 
+
+ align:start position:0%
+is because the amount that ionizes is
+equal to the amount of the hydrronium
+
+ align:start position:0%
+equal to the amount of the hydrronium
+ 
+
+ align:start position:0%
+equal to the amount of the hydrronium
+ions you get. and pH equals minus the
+
+ align:start position:0%
+ions you get. and pH equals minus the
+ 
+
+ align:start position:0%
+ions you get. and pH equals minus the
+concentration of hydrronium ions. So the
+
+ align:start position:0%
+concentration of hydrronium ions. So the
+ 
+
+ align:start position:0%
+concentration of hydrronium ions. So the
+pH depends on the extent to which it
+
+ align:start position:0%
+pH depends on the extent to which it
+ 
+
+ align:start position:0%
+pH depends on the extent to which it
+ionizes. And again we're talking about
+
+ align:start position:0%
+ionizes. And again we're talking about
+ 
+
+ align:start position:0%
+ionizes. And again we're talking about
+an at equilibrium. So we're talking
+
+ align:start position:0%
+an at equilibrium. So we're talking
+ 
+
+ align:start position:0%
+an at equilibrium. So we're talking
+about a equilibrium constant. And this
+
+ align:start position:0%
+about a equilibrium constant. And this
+ 
+
+ align:start position:0%
+about a equilibrium constant. And this
+one also gets a fancy name in acids and
+
+ align:start position:0%
+one also gets a fancy name in acids and
+ 
+
+ align:start position:0%
+one also gets a fancy name in acids and
+bases. All the equilibrium constants get
+
+ align:start position:0%
+bases. All the equilibrium constants get
+ 
+
+ align:start position:0%
+bases. All the equilibrium constants get
+their own little names. And this is the
+
+ align:start position:0%
+their own little names. And this is the
+ 
+
+ align:start position:0%
+their own little names. And this is the
+acid ionization constant Ka. So it's the
+
+ align:start position:0%
+acid ionization constant Ka. So it's the
+ 
+
+ align:start position:0%
+acid ionization constant Ka. So it's the
+equilibrium constant for an acid, K a.
+
+ align:start position:0%
+equilibrium constant for an acid, K a.
+ 
+
+ align:start position:0%
+equilibrium constant for an acid, K a.
+So that's at least very easy to
+
+ align:start position:0%
+So that's at least very easy to
+ 
+
+ align:start position:0%
+So that's at least very easy to
+remember. So now based on what you know
+
+ align:start position:0%
+remember. So now based on what you know
+ 
+
+ align:start position:0%
+remember. So now based on what you know
+about equilibrium constants, why don't
+
+ align:start position:0%
+about equilibrium constants, why don't
+ 
+
+ align:start position:0%
+about equilibrium constants, why don't
+you uh tell me the answer to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, 10 more seconds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All
+
+ align:start position:0%
+All
+ 
+
+ align:start position:0%
+All
+right. So, this one is wrong. It's
+
+ align:start position:0%
+right. So, this one is wrong. It's
+ 
+
+ align:start position:0%
+right. So, this one is wrong. It's
+always products over reactants for an
+
+ align:start position:0%
+always products over reactants for an
+ 
+
+ align:start position:0%
+always products over reactants for an
+equilibrium expression. Water is a
+
+ align:start position:0%
+equilibrium expression. Water is a
+ 
+
+ align:start position:0%
+equilibrium expression. Water is a
+solvent and is nearly pure, so it should
+
+ align:start position:0%
+solvent and is nearly pure, so it should
+ 
+
+ align:start position:0%
+solvent and is nearly pure, so it should
+not be there. This should be in the
+
+ align:start position:0%
+not be there. This should be in the
+ 
+
+ align:start position:0%
+not be there. This should be in the
+expression because it's aquous. If it
+
+ align:start position:0%
+expression because it's aquous. If it
+ 
+
+ align:start position:0%
+expression because it's aquous. If it
+were solid, it wouldn't be included, but
+
+ align:start position:0%
+were solid, it wouldn't be included, but
+ 
+
+ align:start position:0%
+were solid, it wouldn't be included, but
+it's aquous, so its concentration is
+
+ align:start position:0%
+it's aquous, so its concentration is
+ 
+
+ align:start position:0%
+it's aquous, so its concentration is
+going to change. So, it is in our
+
+ align:start position:0%
+going to change. So, it is in our
+ 
+
+ align:start position:0%
+going to change. So, it is in our
+expression. Um, see answer to three for
+
+ align:start position:0%
+expression. Um, see answer to three for
+ 
+
+ align:start position:0%
+expression. Um, see answer to three for
+that one. Uh, enough information and
+
+ align:start position:0%
+that one. Uh, enough information and
+ 
+
+ align:start position:0%
+that one. Uh, enough information and
+it's not correct. Okay. So, we can write
+
+ align:start position:0%
+it's not correct. Okay. So, we can write
+ 
+
+ align:start position:0%
+it's not correct. Okay. So, we can write
+the expression for Ka. So, that's equal
+
+ align:start position:0%
+the expression for Ka. So, that's equal
+ 
+
+ align:start position:0%
+the expression for Ka. So, that's equal
+to the products, our hydrononeium
+
+ align:start position:0%
+to the products, our hydrononeium
+ 
+
+ align:start position:0%
+to the products, our hydrononeium
+concentration, our conjugate base over
+
+ align:start position:0%
+concentration, our conjugate base over
+ 
+
+ align:start position:0%
+concentration, our conjugate base over
+our conjugate acid.
+
+ align:start position:0%
+our conjugate acid.
+ 
+
+ align:start position:0%
+our conjugate acid.
+And so we can look at what the value is
+
+ align:start position:0%
+And so we can look at what the value is
+ 
+
+ align:start position:0%
+And so we can look at what the value is
+for this expression and we can look it
+
+ align:start position:0%
+for this expression and we can look it
+ 
+
+ align:start position:0%
+for this expression and we can look it
+up. Um there's lots and lots of tables
+
+ align:start position:0%
+up. Um there's lots and lots of tables
+ 
+
+ align:start position:0%
+up. Um there's lots and lots of tables
+of these in your book and it is 1.76
+
+ align:start position:0%
+of these in your book and it is 1.76
+ 
+
+ align:start position:0%
+of these in your book and it is 1.76
+*
+
+ align:start position:0%
+*
+ 
+
+ align:start position:0%
+*
+10us5 or minus3 I don't have my glasses.
+
+ align:start position:0%
+10us5 or minus3 I don't have my glasses.
+ 
+
+ align:start position:0%
+10us5 or minus3 I don't have my glasses.
+Um whatever it says there I think it's
+
+ align:start position:0%
+Um whatever it says there I think it's
+ 
+
+ align:start position:0%
+Um whatever it says there I think it's
+five. Um at room temperature which is
+
+ align:start position:0%
+five. Um at room temperature which is
+ 
+
+ align:start position:0%
+five. Um at room temperature which is
+small.
+
+ align:start position:0%
+small.
+ 
+
+ align:start position:0%
+small.
+So when a Ka is small, it means that
+
+ align:start position:0%
+So when a Ka is small, it means that
+ 
+
+ align:start position:0%
+So when a Ka is small, it means that
+very little of it is
+
+ align:start position:0%
+very little of it is
+ 
+
+ align:start position:0%
+very little of it is
+ionizing. And so only a small number of
+
+ align:start position:0%
+ionizing. And so only a small number of
+ 
+
+ align:start position:0%
+ionizing. And so only a small number of
+our acid molecules of our acetic acid
+
+ align:start position:0%
+our acid molecules of our acetic acid
+ 
+
+ align:start position:0%
+our acid molecules of our acetic acid
+molecules are donating their proton when
+
+ align:start position:0%
+molecules are donating their proton when
+ 
+
+ align:start position:0%
+molecules are donating their proton when
+they're dissolved in water. So that's
+
+ align:start position:0%
+they're dissolved in water. So that's
+ 
+
+ align:start position:0%
+they're dissolved in water. So that's
+the definition of a weak acid when it
+
+ align:start position:0%
+the definition of a weak acid when it
+ 
+
+ align:start position:0%
+the definition of a weak acid when it
+has a very small Ka. It's not ionizing
+
+ align:start position:0%
+has a very small Ka. It's not ionizing
+ 
+
+ align:start position:0%
+has a very small Ka. It's not ionizing
+very much. Now, in doing these units, a
+
+ align:start position:0%
+very much. Now, in doing these units, a
+ 
+
+ align:start position:0%
+very much. Now, in doing these units, a
+lot of people get hung up on kind of the
+
+ align:start position:0%
+lot of people get hung up on kind of the
+ 
+
+ align:start position:0%
+lot of people get hung up on kind of the
+names of the different acids. Um, and
+
+ align:start position:0%
+names of the different acids. Um, and
+ 
+
+ align:start position:0%
+names of the different acids. Um, and
+and one of the first steps in solving a
+
+ align:start position:0%
+and one of the first steps in solving a
+ 
+
+ align:start position:0%
+and one of the first steps in solving a
+problem is to write the equilibrium
+
+ align:start position:0%
+problem is to write the equilibrium
+ 
+
+ align:start position:0%
+problem is to write the equilibrium
+expression out, but people get hung up
+
+ align:start position:0%
+expression out, but people get hung up
+ 
+
+ align:start position:0%
+expression out, but people get hung up
+with that. So, don't get hung up with
+
+ align:start position:0%
+with that. So, don't get hung up with
+ 
+
+ align:start position:0%
+with that. So, don't get hung up with
+that. You can use generic expressions
+
+ align:start position:0%
+that. You can use generic expressions
+ 
+
+ align:start position:0%
+that. You can use generic expressions
+for acids and water. If you don't want
+
+ align:start position:0%
+for acids and water. If you don't want
+ 
+
+ align:start position:0%
+for acids and water. If you don't want
+to write out the whole name of the acid,
+
+ align:start position:0%
+to write out the whole name of the acid,
+ 
+
+ align:start position:0%
+to write out the whole name of the acid,
+you can always just say HA aquous plus
+
+ align:start position:0%
+you can always just say HA aquous plus
+ 
+
+ align:start position:0%
+you can always just say HA aquous plus
+the solvent water goes to hydrronium ion
+
+ align:start position:0%
+the solvent water goes to hydrronium ion
+ 
+
+ align:start position:0%
+the solvent water goes to hydrronium ion
+ions plus a minus, the conjugate of the
+
+ align:start position:0%
+ions plus a minus, the conjugate of the
+ 
+
+ align:start position:0%
+ions plus a minus, the conjugate of the
+weak acid. So this is an acid in water
+
+ align:start position:0%
+weak acid. So this is an acid in water
+ 
+
+ align:start position:0%
+weak acid. So this is an acid in water
+and the acid is HA here and an acid
+
+ align:start position:0%
+and the acid is HA here and an acid
+ 
+
+ align:start position:0%
+and the acid is HA here and an acid
+expression should be forming
+
+ align:start position:0%
+expression should be forming
+ 
+
+ align:start position:0%
+expression should be forming
+hydrononeium ions. If it's acidic, you
+
+ align:start position:0%
+hydrononeium ions. If it's acidic, you
+ 
+
+ align:start position:0%
+hydrononeium ions. If it's acidic, you
+should have acidic pH and so you need to
+
+ align:start position:0%
+should have acidic pH and so you need to
+ 
+
+ align:start position:0%
+should have acidic pH and so you need to
+have some H3+ around. You can also write
+
+ align:start position:0%
+have some H3+ around. You can also write
+ 
+
+ align:start position:0%
+have some H3+ around. You can also write
+this expression as
+
+ align:start position:0%
+this expression as
+ 
+
+ align:start position:0%
+this expression as
+BH+ plus water. BH+ can give up the H+
+
+ align:start position:0%
+BH+ plus water. BH+ can give up the H+
+ 
+
+ align:start position:0%
+BH+ plus water. BH+ can give up the H+
+and become B and also generate
+
+ align:start position:0%
+and become B and also generate
+ 
+
+ align:start position:0%
+and become B and also generate
+hydrronium ions. So here the acid is
+
+ align:start position:0%
+hydrronium ions. So here the acid is
+ 
+
+ align:start position:0%
+hydrronium ions. So here the acid is
+BHA and often when you're looking at
+
+ align:start position:0%
+BHA and often when you're looking at
+ 
+
+ align:start position:0%
+BHA and often when you're looking at
+these kinds of uh problems a weak acid
+
+ align:start position:0%
+these kinds of uh problems a weak acid
+ 
+
+ align:start position:0%
+these kinds of uh problems a weak acid
+will be HA but sometimes you have a
+
+ align:start position:0%
+will be HA but sometimes you have a
+ 
+
+ align:start position:0%
+will be HA but sometimes you have a
+problem involving the conjugate acid of
+
+ align:start position:0%
+problem involving the conjugate acid of
+ 
+
+ align:start position:0%
+problem involving the conjugate acid of
+a weak base and that's often expressed
+
+ align:start position:0%
+a weak base and that's often expressed
+ 
+
+ align:start position:0%
+a weak base and that's often expressed
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+BH+. So both of these expressions are
+
+ align:start position:0%
+BH+. So both of these expressions are
+ 
+
+ align:start position:0%
+BH+. So both of these expressions are
+valid for an acid in
+
+ align:start position:0%
+valid for an acid in
+ 
+
+ align:start position:0%
+valid for an acid in
+water. So now let's think about strong
+
+ align:start position:0%
+water. So now let's think about strong
+ 
+
+ align:start position:0%
+water. So now let's think about strong
+acids versus weaker acids. And here's
+
+ align:start position:0%
+acids versus weaker acids. And here's
+ 
+
+ align:start position:0%
+acids versus weaker acids. And here's
+our definition in this class. A strong
+
+ align:start position:0%
+our definition in this class. A strong
+ 
+
+ align:start position:0%
+our definition in this class. A strong
+acid has a Ka greater than one. A lot of
+
+ align:start position:0%
+acid has a Ka greater than one. A lot of
+ 
+
+ align:start position:0%
+acid has a Ka greater than one. A lot of
+strong acids have a Ka really, really,
+
+ align:start position:0%
+strong acids have a Ka really, really,
+ 
+
+ align:start position:0%
+strong acids have a Ka really, really,
+really greater than one. And the acid
+
+ align:start position:0%
+really greater than one. And the acid
+ 
+
+ align:start position:0%
+really greater than one. And the acid
+ionizes almost completely. So if you say
+
+ align:start position:0%
+ionizes almost completely. So if you say
+ 
+
+ align:start position:0%
+ionizes almost completely. So if you say
+it's a strong acid in water, whatever
+
+ align:start position:0%
+it's a strong acid in water, whatever
+ 
+
+ align:start position:0%
+it's a strong acid in water, whatever
+concentration of a acid you put in is
+
+ align:start position:0%
+concentration of a acid you put in is
+ 
+
+ align:start position:0%
+concentration of a acid you put in is
+going to be equal to the concentration
+
+ align:start position:0%
+going to be equal to the concentration
+ 
+
+ align:start position:0%
+going to be equal to the concentration
+of hydrronium ions. It basically goes
+
+ align:start position:0%
+of hydrronium ions. It basically goes
+ 
+
+ align:start position:0%
+of hydrronium ions. It basically goes
+straight. You form lots and lots and
+
+ align:start position:0%
+straight. You form lots and lots and
+ 
+
+ align:start position:0%
+straight. You form lots and lots and
+lots of products at equilibrium. A weak
+
+ align:start position:0%
+lots of products at equilibrium. A weak
+ 
+
+ align:start position:0%
+lots of products at equilibrium. A weak
+acid has a Ka of less than one. And a
+
+ align:start position:0%
+acid has a Ka of less than one. And a
+ 
+
+ align:start position:0%
+acid has a Ka of less than one. And a
+weak acid does not form many ionized
+
+ align:start position:0%
+weak acid does not form many ionized
+ 
+
+ align:start position:0%
+weak acid does not form many ionized
+species in solution. Not very much
+
+ align:start position:0%
+species in solution. Not very much
+ 
+
+ align:start position:0%
+species in solution. Not very much
+H3+ is
+
+ align:start position:0%
+H3+ is
+ 
+
+ align:start position:0%
+H3+ is
+formed.
+
+ align:start position:0%
+formed.
+ 
+
+ align:start position:0%
+formed.
+Okay. So what about
+
+ align:start position:0%
+Okay. So what about
+ 
+
+ align:start position:0%
+Okay. So what about
+pKa? PKAs are really important in
+
+ align:start position:0%
+pKa? PKAs are really important in
+ 
+
+ align:start position:0%
+pKa? PKAs are really important in
+organic chemistry and biology in a lot
+
+ align:start position:0%
+organic chemistry and biology in a lot
+ 
+
+ align:start position:0%
+organic chemistry and biology in a lot
+of areas. And every year the organic
+
+ align:start position:0%
+of areas. And every year the organic
+ 
+
+ align:start position:0%
+of areas. And every year the organic
+chemistry faculty in
+
+ align:start position:0%
+chemistry faculty in
+ 
+
+ align:start position:0%
+chemistry faculty in
+512 talk about pKa's and organic and the
+
+ align:start position:0%
+512 talk about pKa's and organic and the
+ 
+
+ align:start position:0%
+512 talk about pKa's and organic and the
+students there say no we never learned
+
+ align:start position:0%
+students there say no we never learned
+ 
+
+ align:start position:0%
+students there say no we never learned
+about that. They're like you took
+
+ align:start position:0%
+about that. They're like you took
+ 
+
+ align:start position:0%
+about that. They're like you took
+freshman chem right it's like a GI or
+
+ align:start position:0%
+freshman chem right it's like a GI or
+ 
+
+ align:start position:0%
+freshman chem right it's like a GI or
+you passed the test you should know
+
+ align:start position:0%
+you passed the test you should know
+ 
+
+ align:start position:0%
+you passed the test you should know
+about PKAs. They're like no. So they
+
+ align:start position:0%
+about PKAs. They're like no. So they
+ 
+
+ align:start position:0%
+about PKAs. They're like no. So they
+contact me and I'm like they did not
+
+ align:start position:0%
+contact me and I'm like they did not
+ 
+
+ align:start position:0%
+contact me and I'm like they did not
+take 511 if they do not know what a PKA
+
+ align:start position:0%
+take 511 if they do not know what a PKA
+ 
+
+ align:start position:0%
+take 511 if they do not know what a PKA
+is. There are other courses that
+
+ align:start position:0%
+is. There are other courses that
+ 
+
+ align:start position:0%
+is. There are other courses that
+sometimes people decide to take that are
+
+ align:start position:0%
+sometimes people decide to take that are
+ 
+
+ align:start position:0%
+sometimes people decide to take that are
+not 511, but in 511, you know about
+
+ align:start position:0%
+not 511, but in 511, you know about
+ 
+
+ align:start position:0%
+not 511, but in 511, you know about
+PKAs. So, what I want you to do is later
+
+ align:start position:0%
+PKAs. So, what I want you to do is later
+ 
+
+ align:start position:0%
+PKAs. So, what I want you to do is later
+in life when you're in a class and pKa's
+
+ align:start position:0%
+in life when you're in a class and pKa's
+ 
+
+ align:start position:0%
+in life when you're in a class and pKa's
+come up and everyone else in the class
+
+ align:start position:0%
+come up and everyone else in the class
+ 
+
+ align:start position:0%
+come up and everyone else in the class
+is like, I don't know. You're like, I
+
+ align:start position:0%
+is like, I don't know. You're like, I
+ 
+
+ align:start position:0%
+is like, I don't know. You're like, I
+took
+
+ align:start position:0%
+took
+ 
+
+ align:start position:0%
+took
+511. I can answer that. That makes me
+
+ align:start position:0%
+511. I can answer that. That makes me
+ 
+
+ align:start position:0%
+511. I can answer that. That makes me
+very happy. Okay, so
+
+ align:start position:0%
+very happy. Okay, so
+ 
+
+ align:start position:0%
+very happy. Okay, so
+pKa's so pKa is minus the log of the Ka.
+
+ align:start position:0%
+pKa's so pKa is minus the log of the Ka.
+ 
+
+ align:start position:0%
+pKa's so pKa is minus the log of the Ka.
+That's easy to remember. We already
+
+ align:start position:0%
+That's easy to remember. We already
+ 
+
+ align:start position:0%
+That's easy to remember. We already
+talked about the relationship of Ka with
+
+ align:start position:0%
+talked about the relationship of Ka with
+ 
+
+ align:start position:0%
+talked about the relationship of Ka with
+strong acids or weak acids. The lower
+
+ align:start position:0%
+strong acids or weak acids. The lower
+ 
+
+ align:start position:0%
+strong acids or weak acids. The lower
+the value of the Ka, the higher the
+
+ align:start position:0%
+the value of the Ka, the higher the
+ 
+
+ align:start position:0%
+the value of the Ka, the higher the
+value of the pKa. That's just out of
+
+ align:start position:0%
+value of the pKa. That's just out of
+ 
+
+ align:start position:0%
+value of the pKa. That's just out of
+that expression. So the higher the pKa
+
+ align:start position:0%
+that expression. So the higher the pKa
+ 
+
+ align:start position:0%
+that expression. So the higher the pKa
+means what about the
+
+ align:start position:0%
+means what about the
+ 
+
+ align:start position:0%
+means what about the
+acid? And think about what you know
+
+ align:start position:0%
+acid? And think about what you know
+ 
+
+ align:start position:0%
+acid? And think about what you know
+about Ka to answer this question.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, 10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds. All
+
+ align:start position:0%
+seconds. All
+ 
+
+ align:start position:0%
+seconds. All
+right. So that is
+
+ align:start position:0%
+right. So that is
+ 
+
+ align:start position:0%
+right. So that is
+correct. So we have a weaker acid. So if
+
+ align:start position:0%
+correct. So we have a weaker acid. So if
+ 
+
+ align:start position:0%
+correct. So we have a weaker acid. So if
+we have a low Ka that means that it is a
+
+ align:start position:0%
+we have a low Ka that means that it is a
+ 
+
+ align:start position:0%
+we have a low Ka that means that it is a
+weak acid and then a higher value of Ka.
+
+ align:start position:0%
+weak acid and then a higher value of Ka.
+ 
+
+ align:start position:0%
+weak acid and then a higher value of Ka.
+So the higher the Ka that's going to
+
+ align:start position:0%
+So the higher the Ka that's going to
+ 
+
+ align:start position:0%
+So the higher the Ka that's going to
+mean um the the lower the value or the
+
+ align:start position:0%
+mean um the the lower the value or the
+ 
+
+ align:start position:0%
+mean um the the lower the value or the
+weaker the
+
+ align:start position:0%
+weaker the
+ 
+
+ align:start position:0%
+weaker the
+acid. So these are just remember the
+
+ align:start position:0%
+acid. So these are just remember the
+ 
+
+ align:start position:0%
+acid. So these are just remember the
+relationship from the equation and think
+
+ align:start position:0%
+relationship from the equation and think
+ 
+
+ align:start position:0%
+relationship from the equation and think
+about it and you can think about the
+
+ align:start position:0%
+about it and you can think about the
+ 
+
+ align:start position:0%
+about it and you can think about the
+value of Ka products over reactants.
+
+ align:start position:0%
+value of Ka products over reactants.
+ 
+
+ align:start position:0%
+value of Ka products over reactants.
+think you might have a lot of products
+
+ align:start position:0%
+think you might have a lot of products
+ 
+
+ align:start position:0%
+think you might have a lot of products
+that means a lot of ionization and a
+
+ align:start position:0%
+that means a lot of ionization and a
+ 
+
+ align:start position:0%
+that means a lot of ionization and a
+stronger acid and fewer products um that
+
+ align:start position:0%
+stronger acid and fewer products um that
+ 
+
+ align:start position:0%
+stronger acid and fewer products um that
+means it's weaker. Okay, so let's look
+
+ align:start position:0%
+means it's weaker. Okay, so let's look
+ 
+
+ align:start position:0%
+means it's weaker. Okay, so let's look
+at some uh tables and I just put the
+
+ align:start position:0%
+at some uh tables and I just put the
+ 
+
+ align:start position:0%
+at some uh tables and I just put the
+values that are with the arrows in your
+
+ align:start position:0%
+values that are with the arrows in your
+ 
+
+ align:start position:0%
+values that are with the arrows in your
+notes. I didn't put the entire table.
+
+ align:start position:0%
+notes. I didn't put the entire table.
+ 
+
+ align:start position:0%
+notes. I didn't put the entire table.
+The tables are in the book and this is
+
+ align:start position:0%
+The tables are in the book and this is
+ 
+
+ align:start position:0%
+The tables are in the book and this is
+like page one of the table. So there's a
+
+ align:start position:0%
+like page one of the table. So there's a
+ 
+
+ align:start position:0%
+like page one of the table. So there's a
+lot of values here. So this has the
+
+ align:start position:0%
+lot of values here. So this has the
+ 
+
+ align:start position:0%
+lot of values here. So this has the
+acid. It tells you what the HA term is,
+
+ align:start position:0%
+acid. It tells you what the HA term is,
+ 
+
+ align:start position:0%
+acid. It tells you what the HA term is,
+what the A minus, so what the weak acid
+
+ align:start position:0%
+what the A minus, so what the weak acid
+ 
+
+ align:start position:0%
+what the A minus, so what the weak acid
+is, what the conjugate base is. It gives
+
+ align:start position:0%
+is, what the conjugate base is. It gives
+ 
+
+ align:start position:0%
+is, what the conjugate base is. It gives
+you the Ka and the pKa. And so you can
+
+ align:start position:0%
+you the Ka and the pKa. And so you can
+ 
+
+ align:start position:0%
+you the Ka and the pKa. And so you can
+see the relationship between um Ka and
+
+ align:start position:0%
+see the relationship between um Ka and
+ 
+
+ align:start position:0%
+see the relationship between um Ka and
+pKa. So up here, HI is at the top of
+
+ align:start position:0%
+pKa. So up here, HI is at the top of
+ 
+
+ align:start position:0%
+pKa. So up here, HI is at the top of
+this table. So that probably means it's
+
+ align:start position:0%
+this table. So that probably means it's
+ 
+
+ align:start position:0%
+this table. So that probably means it's
+the strongest or the weakest. Which do
+
+ align:start position:0%
+the strongest or the weakest. Which do
+ 
+
+ align:start position:0%
+the strongest or the weakest. Which do
+you think? Is this the strongest or the
+
+ align:start position:0%
+you think? Is this the strongest or the
+ 
+
+ align:start position:0%
+you think? Is this the strongest or the
+weakest? You just yell it out.
+
+ align:start position:0%
+weakest? You just yell it out.
+ 
+
+ align:start position:0%
+weakest? You just yell it out.
+It is the strongest. Right. So it has a
+
+ align:start position:0%
+It is the strongest. Right. So it has a
+ 
+
+ align:start position:0%
+It is the strongest. Right. So it has a
+Ka value that is much much much much
+
+ align:start position:0%
+Ka value that is much much much much
+ 
+
+ align:start position:0%
+Ka value that is much much much much
+much much much greater than one and it
+
+ align:start position:0%
+much much much greater than one and it
+ 
+
+ align:start position:0%
+much much much greater than one and it
+has a very very very negative tiny tiny
+
+ align:start position:0%
+has a very very very negative tiny tiny
+ 
+
+ align:start position:0%
+has a very very very negative tiny tiny
+pKa value. So this is a super strong
+
+ align:start position:0%
+pKa value. So this is a super strong
+ 
+
+ align:start position:0%
+pKa value. So this is a super strong
+acid. In fact, do not use that. There's
+
+ align:start position:0%
+acid. In fact, do not use that. There's
+ 
+
+ align:start position:0%
+acid. In fact, do not use that. There's
+no reason really you would ever want to
+
+ align:start position:0%
+no reason really you would ever want to
+ 
+
+ align:start position:0%
+no reason really you would ever want to
+be using it. It is not a good thing to
+
+ align:start position:0%
+be using it. It is not a good thing to
+ 
+
+ align:start position:0%
+be using it. It is not a good thing to
+play with. All right. So HCl um is used
+
+ align:start position:0%
+play with. All right. So HCl um is used
+ 
+
+ align:start position:0%
+play with. All right. So HCl um is used
+more often um in pH things. Um, is this
+
+ align:start position:0%
+more often um in pH things. Um, is this
+ 
+
+ align:start position:0%
+more often um in pH things. Um, is this
+a is this a strong aric acid?
+
+ align:start position:0%
+a is this a strong aric acid?
+ 
+
+ align:start position:0%
+a is this a strong aric acid?
+It's also strong. It's um K or K a is
+
+ align:start position:0%
+It's also strong. It's um K or K a is
+ 
+
+ align:start position:0%
+It's also strong. It's um K or K a is
+also greater than one, but not as strong
+
+ align:start position:0%
+also greater than one, but not as strong
+ 
+
+ align:start position:0%
+also greater than one, but not as strong
+as this. We have 10 to the 7th and that
+
+ align:start position:0%
+as this. We have 10 to the 7th and that
+ 
+
+ align:start position:0%
+as this. We have 10 to the 7th and that
+one. Gosh, I should bring my glasses. 10
+
+ align:start position:0%
+one. Gosh, I should bring my glasses. 10
+ 
+
+ align:start position:0%
+one. Gosh, I should bring my glasses. 10
+to the 11th. That's super strong. That's
+
+ align:start position:0%
+to the 11th. That's super strong. That's
+ 
+
+ align:start position:0%
+to the 11th. That's super strong. That's
+still pretty strong. All right, so let's
+
+ align:start position:0%
+still pretty strong. All right, so let's
+ 
+
+ align:start position:0%
+still pretty strong. All right, so let's
+look down here now. Tell me, is this a
+
+ align:start position:0%
+look down here now. Tell me, is this a
+ 
+
+ align:start position:0%
+look down here now. Tell me, is this a
+strong or weak acid?
+
+ align:start position:0%
+strong or weak acid?
+ 
+
+ align:start position:0%
+strong or weak acid?
+that is a weak acid. the KA is less than
+
+ align:start position:0%
+that is a weak acid. the KA is less than
+ 
+
+ align:start position:0%
+that is a weak acid. the KA is less than
+one here and I think that's like a
+
+ align:start position:0%
+one here and I think that's like a
+ 
+
+ align:start position:0%
+one here and I think that's like a
+minus2 and the pKa value now we're out
+
+ align:start position:0%
+minus2 and the pKa value now we're out
+ 
+
+ align:start position:0%
+minus2 and the pKa value now we're out
+of the negative number so it's on the
+
+ align:start position:0%
+of the negative number so it's on the
+ 
+
+ align:start position:0%
+of the negative number so it's on the
+bigger side and down here is this uh
+
+ align:start position:0%
+bigger side and down here is this uh
+ 
+
+ align:start position:0%
+bigger side and down here is this uh
+strong or
+
+ align:start position:0%
+strong or
+ 
+
+ align:start position:0%
+strong or
+weak also weak and it's even weaker than
+
+ align:start position:0%
+weak also weak and it's even weaker than
+ 
+
+ align:start position:0%
+weak also weak and it's even weaker than
+this one it's like 10 to the minus4 and
+
+ align:start position:0%
+this one it's like 10 to the minus4 and
+ 
+
+ align:start position:0%
+this one it's like 10 to the minus4 and
+pKa value is
+
+ align:start position:0%
+pKa value is
+ 
+
+ align:start position:0%
+pKa value is
+3.75 so you see you can look at the Ka
+
+ align:start position:0%
+3.75 so you see you can look at the Ka
+ 
+
+ align:start position:0%
+3.75 so you see you can look at the Ka
+values vales and think about whether
+
+ align:start position:0%
+values vales and think about whether
+ 
+
+ align:start position:0%
+values vales and think about whether
+it's a strong or weak acid. You can also
+
+ align:start position:0%
+it's a strong or weak acid. You can also
+ 
+
+ align:start position:0%
+it's a strong or weak acid. You can also
+look at the pKa values. This is really
+
+ align:start position:0%
+look at the pKa values. This is really
+ 
+
+ align:start position:0%
+look at the pKa values. This is really
+really small negative value. Um this is
+
+ align:start position:0%
+really small negative value. Um this is
+ 
+
+ align:start position:0%
+really small negative value. Um this is
+a bigger value down here. And this is
+
+ align:start position:0%
+a bigger value down here. And this is
+ 
+
+ align:start position:0%
+a bigger value down here. And this is
+not then the weakest acid. There's a
+
+ align:start position:0%
+not then the weakest acid. There's a
+ 
+
+ align:start position:0%
+not then the weakest acid. There's a
+whole another page of tables um to uh
+
+ align:start position:0%
+whole another page of tables um to uh
+ 
+
+ align:start position:0%
+whole another page of tables um to uh
+for acids. Lots and lots of acids. Okay.
+
+ align:start position:0%
+for acids. Lots and lots of acids. Okay.
+ 
+
+ align:start position:0%
+for acids. Lots and lots of acids. Okay.
+Less ba bases. Um there are there are a
+
+ align:start position:0%
+Less ba bases. Um there are there are a
+ 
+
+ align:start position:0%
+Less ba bases. Um there are there are a
+few and you will see this base quite
+
+ align:start position:0%
+few and you will see this base quite
+ 
+
+ align:start position:0%
+few and you will see this base quite
+often. NH3.
+
+ align:start position:0%
+often. NH3.
+ 
+
+ align:start position:0%
+often. NH3.
+So we have a base in water. The base
+
+ align:start position:0%
+So we have a base in water. The base
+ 
+
+ align:start position:0%
+So we have a base in water. The base
+accepts a hydrogen ion or proton from
+
+ align:start position:0%
+accepts a hydrogen ion or proton from
+ 
+
+ align:start position:0%
+accepts a hydrogen ion or proton from
+the water forming
+
+ align:start position:0%
+the water forming
+ 
+
+ align:start position:0%
+the water forming
+NH4+. And then after water loses its
+
+ align:start position:0%
+NH4+. And then after water loses its
+ 
+
+ align:start position:0%
+NH4+. And then after water loses its
+hydrogen ion, it forms O
+
+ align:start position:0%
+hydrogen ion, it forms O
+ 
+
+ align:start position:0%
+hydrogen ion, it forms O
+minus. So the equilibrium expression or
+
+ align:start position:0%
+minus. So the equilibrium expression or
+ 
+
+ align:start position:0%
+minus. So the equilibrium expression or
+the K for this um base in water problem
+
+ align:start position:0%
+the K for this um base in water problem
+ 
+
+ align:start position:0%
+the K for this um base in water problem
+is called the base ionization constant
+
+ align:start position:0%
+is called the base ionization constant
+ 
+
+ align:start position:0%
+is called the base ionization constant
+or KB. And um we can write that
+
+ align:start position:0%
+or KB. And um we can write that
+ 
+
+ align:start position:0%
+or KB. And um we can write that
+expression here. We have the ammonium
+
+ align:start position:0%
+expression here. We have the ammonium
+ 
+
+ align:start position:0%
+expression here. We have the ammonium
+ion concentration times the hydroxide
+
+ align:start position:0%
+ion concentration times the hydroxide
+ 
+
+ align:start position:0%
+ion concentration times the hydroxide
+ion concentration over the concentration
+
+ align:start position:0%
+ion concentration over the concentration
+ 
+
+ align:start position:0%
+ion concentration over the concentration
+of ammonia. Again, water is not in the
+
+ align:start position:0%
+of ammonia. Again, water is not in the
+ 
+
+ align:start position:0%
+of ammonia. Again, water is not in the
+expression. It stays pretty much pure
+
+ align:start position:0%
+expression. It stays pretty much pure
+ 
+
+ align:start position:0%
+expression. It stays pretty much pure
+throughout this entire thing. It's the
+
+ align:start position:0%
+throughout this entire thing. It's the
+ 
+
+ align:start position:0%
+throughout this entire thing. It's the
+solvent. And so this is our expression
+
+ align:start position:0%
+solvent. And so this is our expression
+ 
+
+ align:start position:0%
+solvent. And so this is our expression
+for KB. And if you're writing an
+
+ align:start position:0%
+for KB. And if you're writing an
+ 
+
+ align:start position:0%
+for KB. And if you're writing an
+expression for KB, you should always
+
+ align:start position:0%
+expression for KB, you should always
+ 
+
+ align:start position:0%
+expression for KB, you should always
+make sure check yourself that you're
+
+ align:start position:0%
+make sure check yourself that you're
+ 
+
+ align:start position:0%
+make sure check yourself that you're
+putting hydroxide ion concentration in
+
+ align:start position:0%
+putting hydroxide ion concentration in
+ 
+
+ align:start position:0%
+putting hydroxide ion concentration in
+there. If it is a base in water, it
+
+ align:start position:0%
+there. If it is a base in water, it
+ 
+
+ align:start position:0%
+there. If it is a base in water, it
+should be forming hydroxide ion
+
+ align:start position:0%
+should be forming hydroxide ion
+ 
+
+ align:start position:0%
+should be forming hydroxide ion
+concentration. If you start writing a KB
+
+ align:start position:0%
+concentration. If you start writing a KB
+ 
+
+ align:start position:0%
+concentration. If you start writing a KB
+and you have hydrronium ion
+
+ align:start position:0%
+and you have hydrronium ion
+ 
+
+ align:start position:0%
+and you have hydrronium ion
+concentration in there, you want to stop
+
+ align:start position:0%
+concentration in there, you want to stop
+ 
+
+ align:start position:0%
+concentration in there, you want to stop
+and rethink what you're doing. Okay. So,
+
+ align:start position:0%
+and rethink what you're doing. Okay. So,
+ 
+
+ align:start position:0%
+and rethink what you're doing. Okay. So,
+in this case, we also have a weak base.
+
+ align:start position:0%
+in this case, we also have a weak base.
+ 
+
+ align:start position:0%
+in this case, we also have a weak base.
+Um 1.8 * 10us 5. It is a small number
+
+ align:start position:0%
+Um 1.8 * 10us 5. It is a small number
+ 
+
+ align:start position:0%
+Um 1.8 * 10us 5. It is a small number
+for KB. It's a small equilibrium number.
+
+ align:start position:0%
+for KB. It's a small equilibrium number.
+ 
+
+ align:start position:0%
+for KB. It's a small equilibrium number.
+So that means you're not a lot of
+
+ align:start position:0%
+So that means you're not a lot of
+ 
+
+ align:start position:0%
+So that means you're not a lot of
+products. Not a lot ionizes when you put
+
+ align:start position:0%
+products. Not a lot ionizes when you put
+ 
+
+ align:start position:0%
+products. Not a lot ionizes when you put
+this weak base in water. So only a tiny
+
+ align:start position:0%
+this weak base in water. So only a tiny
+ 
+
+ align:start position:0%
+this weak base in water. So only a tiny
+amount of NH3 ionizes to NH4 plus and O
+
+ align:start position:0%
+amount of NH3 ionizes to NH4 plus and O
+ 
+
+ align:start position:0%
+amount of NH3 ionizes to NH4 plus and O
+in solution. So this is what they call
+
+ align:start position:0%
+in solution. So this is what they call
+ 
+
+ align:start position:0%
+in solution. So this is what they call
+moderately uh weak base.
+
+ align:start position:0%
+moderately uh weak base.
+ 
+
+ align:start position:0%
+moderately uh weak base.
+So as we saw
+
+ align:start position:0%
+So as we saw
+ 
+
+ align:start position:0%
+So as we saw
+before you can have generic expressions
+
+ align:start position:0%
+before you can have generic expressions
+ 
+
+ align:start position:0%
+before you can have generic expressions
+for a base in water. We can write B
+
+ align:start position:0%
+for a base in water. We can write B
+ 
+
+ align:start position:0%
+for a base in water. We can write B
+aqueous plus water goes to BH+. The base
+
+ align:start position:0%
+aqueous plus water goes to BH+. The base
+ 
+
+ align:start position:0%
+aqueous plus water goes to BH+. The base
+accepts a hydrogen ion or proton and the
+
+ align:start position:0%
+accepts a hydrogen ion or proton and the
+ 
+
+ align:start position:0%
+accepts a hydrogen ion or proton and the
+water loses one forming O minus. We can
+
+ align:start position:0%
+water loses one forming O minus. We can
+ 
+
+ align:start position:0%
+water loses one forming O minus. We can
+also write the expression that often
+
+ align:start position:0%
+also write the expression that often
+ 
+
+ align:start position:0%
+also write the expression that often
+exists from the conjugate of a weak base
+
+ align:start position:0%
+exists from the conjugate of a weak base
+ 
+
+ align:start position:0%
+exists from the conjugate of a weak base
+or conjugate of a weak acid and this is
+
+ align:start position:0%
+or conjugate of a weak acid and this is
+ 
+
+ align:start position:0%
+or conjugate of a weak acid and this is
+a weak base. So a minus plus water goes
+
+ align:start position:0%
+a weak base. So a minus plus water goes
+ 
+
+ align:start position:0%
+a weak base. So a minus plus water goes
+to HA plus hydroxide ion concentration.
+
+ align:start position:0%
+to HA plus hydroxide ion concentration.
+ 
+
+ align:start position:0%
+to HA plus hydroxide ion concentration.
+So either of these are generic
+
+ align:start position:0%
+So either of these are generic
+ 
+
+ align:start position:0%
+So either of these are generic
+expressions that you can write for a
+
+ align:start position:0%
+expressions that you can write for a
+ 
+
+ align:start position:0%
+expressions that you can write for a
+base in
+
+ align:start position:0%
+base in
+ 
+
+ align:start position:0%
+base in
+water. So in terms of the definitions,
+
+ align:start position:0%
+water. So in terms of the definitions,
+ 
+
+ align:start position:0%
+water. So in terms of the definitions,
+it's the same. You would say a strong
+
+ align:start position:0%
+it's the same. You would say a strong
+ 
+
+ align:start position:0%
+it's the same. You would say a strong
+base is something that um ionizes almost
+
+ align:start position:0%
+base is something that um ionizes almost
+ 
+
+ align:start position:0%
+base is something that um ionizes almost
+completely to give O. There aren't a lot
+
+ align:start position:0%
+completely to give O. There aren't a lot
+ 
+
+ align:start position:0%
+completely to give O. There aren't a lot
+of examples of strong bases. Most of the
+
+ align:start position:0%
+of examples of strong bases. Most of the
+ 
+
+ align:start position:0%
+of examples of strong bases. Most of the
+ones you'll see in your class are things
+
+ align:start position:0%
+ones you'll see in your class are things
+ 
+
+ align:start position:0%
+ones you'll see in your class are things
+like um sodium hydroxide. Yes, that is
+
+ align:start position:0%
+like um sodium hydroxide. Yes, that is
+ 
+
+ align:start position:0%
+like um sodium hydroxide. Yes, that is
+hydroxide. That's a strong base. And if
+
+ align:start position:0%
+hydroxide. That's a strong base. And if
+ 
+
+ align:start position:0%
+hydroxide. That's a strong base. And if
+you put it in water, um you should
+
+ align:start position:0%
+you put it in water, um you should
+ 
+
+ align:start position:0%
+you put it in water, um you should
+definitely form a lot of hydroxide. So
+
+ align:start position:0%
+definitely form a lot of hydroxide. So
+ 
+
+ align:start position:0%
+definitely form a lot of hydroxide. So
+um there not a whole lot of examples
+
+ align:start position:0%
+um there not a whole lot of examples
+ 
+
+ align:start position:0%
+um there not a whole lot of examples
+there. So we won't they're not they're
+
+ align:start position:0%
+there. So we won't they're not they're
+ 
+
+ align:start position:0%
+there. So we won't they're not they're
+not all those tables. It's not like it's
+
+ align:start position:0%
+not all those tables. It's not like it's
+ 
+
+ align:start position:0%
+not all those tables. It's not like it's
+not like the acids. All right? But there
+
+ align:start position:0%
+not like the acids. All right? But there
+ 
+
+ align:start position:0%
+not like the acids. All right? But there
+are some terms that you still need to
+
+ align:start position:0%
+are some terms that you still need to
+ 
+
+ align:start position:0%
+are some terms that you still need to
+know. So pKb equals minus log of the KB
+
+ align:start position:0%
+know. So pKb equals minus log of the KB
+ 
+
+ align:start position:0%
+know. So pKb equals minus log of the KB
+And again, the larger the value for KB,
+
+ align:start position:0%
+And again, the larger the value for KB,
+ 
+
+ align:start position:0%
+And again, the larger the value for KB,
+the stronger the base. Again, it tells
+
+ align:start position:0%
+the stronger the base. Again, it tells
+ 
+
+ align:start position:0%
+the stronger the base. Again, it tells
+you you have a lot that have
+
+ align:start position:0%
+you you have a lot that have
+ 
+
+ align:start position:0%
+you you have a lot that have
+ionized. And because of this
+
+ align:start position:0%
+ionized. And because of this
+ 
+
+ align:start position:0%
+ionized. And because of this
+relationship of this equation, the
+
+ align:start position:0%
+relationship of this equation, the
+ 
+
+ align:start position:0%
+relationship of this equation, the
+larger the um pKb, the weaker the base.
+
+ align:start position:0%
+larger the um pKb, the weaker the base.
+ 
+
+ align:start position:0%
+larger the um pKb, the weaker the base.
+Um because if you have a big number
+
+ align:start position:0%
+Um because if you have a big number
+ 
+
+ align:start position:0%
+Um because if you have a big number
+here, you're going to have a small
+
+ align:start position:0%
+here, you're going to have a small
+ 
+
+ align:start position:0%
+here, you're going to have a small
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+there. All right.
+
+ align:start position:0%
+there. All right.
+ 
+
+ align:start position:0%
+there. All right.
+So, now let's talk about conjugate acids
+
+ align:start position:0%
+So, now let's talk about conjugate acids
+ 
+
+ align:start position:0%
+So, now let's talk about conjugate acids
+and their bases. This is super important
+
+ align:start position:0%
+and their bases. This is super important
+ 
+
+ align:start position:0%
+and their bases. This is super important
+for buffers that hopefully we'll get to
+
+ align:start position:0%
+for buffers that hopefully we'll get to
+ 
+
+ align:start position:0%
+for buffers that hopefully we'll get to
+um in class on
+
+ align:start position:0%
+um in class on
+ 
+
+ align:start position:0%
+um in class on
+Friday. So, the stronger the acid, the
+
+ align:start position:0%
+Friday. So, the stronger the acid, the
+ 
+
+ align:start position:0%
+Friday. So, the stronger the acid, the
+weaker its conjugate base. The stronger
+
+ align:start position:0%
+weaker its conjugate base. The stronger
+ 
+
+ align:start position:0%
+weaker its conjugate base. The stronger
+the base, the weaker its conjugate acid.
+
+ align:start position:0%
+the base, the weaker its conjugate acid.
+ 
+
+ align:start position:0%
+the base, the weaker its conjugate acid.
+And here we have HCl, which we
+
+ align:start position:0%
+And here we have HCl, which we
+ 
+
+ align:start position:0%
+And here we have HCl, which we
+determined was a strong acid a little
+
+ align:start position:0%
+determined was a strong acid a little
+ 
+
+ align:start position:0%
+determined was a strong acid a little
+while ago, giving up its hydrogen ion to
+
+ align:start position:0%
+while ago, giving up its hydrogen ion to
+ 
+
+ align:start position:0%
+while ago, giving up its hydrogen ion to
+water, forming hydrronium ion
+
+ align:start position:0%
+water, forming hydrronium ion
+ 
+
+ align:start position:0%
+water, forming hydrronium ion
+concentration, higher hydrononeium ion
+
+ align:start position:0%
+concentration, higher hydrononeium ion
+ 
+
+ align:start position:0%
+concentration, higher hydrononeium ion
+concentration and Cl minus. Cl minus is
+
+ align:start position:0%
+concentration and Cl minus. Cl minus is
+ 
+
+ align:start position:0%
+concentration and Cl minus. Cl minus is
+not a very good conjugate base. It's not
+
+ align:start position:0%
+not a very good conjugate base. It's not
+ 
+
+ align:start position:0%
+not a very good conjugate base. It's not
+a good base. So if we look at this
+
+ align:start position:0%
+a good base. So if we look at this
+ 
+
+ align:start position:0%
+a good base. So if we look at this
+table, when we have a strong acid, its
+
+ align:start position:0%
+table, when we have a strong acid, its
+ 
+
+ align:start position:0%
+table, when we have a strong acid, its
+conjugate is going to be ineffective as
+
+ align:start position:0%
+conjugate is going to be ineffective as
+ 
+
+ align:start position:0%
+conjugate is going to be ineffective as
+a base. you're basically not pushing
+
+ align:start position:0%
+a base. you're basically not pushing
+ 
+
+ align:start position:0%
+a base. you're basically not pushing
+that equilibrium back at all the other
+
+ align:start position:0%
+that equilibrium back at all the other
+ 
+
+ align:start position:0%
+that equilibrium back at all the other
+direction. It's completely ionized and
+
+ align:start position:0%
+direction. It's completely ionized and
+ 
+
+ align:start position:0%
+direction. It's completely ionized and
+it stays that way. But if you have a
+
+ align:start position:0%
+it stays that way. But if you have a
+ 
+
+ align:start position:0%
+it stays that way. But if you have a
+moderately weak acid, you're going to
+
+ align:start position:0%
+moderately weak acid, you're going to
+ 
+
+ align:start position:0%
+moderately weak acid, you're going to
+have a very weak base, a very weak acid,
+
+ align:start position:0%
+have a very weak base, a very weak acid,
+ 
+
+ align:start position:0%
+have a very weak base, a very weak acid,
+you'll have a moderately weak conjugate
+
+ align:start position:0%
+you'll have a moderately weak conjugate
+ 
+
+ align:start position:0%
+you'll have a moderately weak conjugate
+base, a strong base, and you'll have
+
+ align:start position:0%
+base, a strong base, and you'll have
+ 
+
+ align:start position:0%
+base, a strong base, and you'll have
+something that's ineffective as an acid.
+
+ align:start position:0%
+something that's ineffective as an acid.
+ 
+
+ align:start position:0%
+something that's ineffective as an acid.
+So they are inversely related to each
+
+ align:start position:0%
+So they are inversely related to each
+ 
+
+ align:start position:0%
+So they are inversely related to each
+other. So let's think about why this
+
+ align:start position:0%
+other. So let's think about why this
+ 
+
+ align:start position:0%
+other. So let's think about why this
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+true. And this relationship holds. K a
+
+ align:start position:0%
+true. And this relationship holds. K a
+ 
+
+ align:start position:0%
+true. And this relationship holds. K a
+time KB equals K W. And we know that KW
+
+ align:start position:0%
+time KB equals K W. And we know that KW
+ 
+
+ align:start position:0%
+time KB equals K W. And we know that KW
+is 1.0 *
+
+ align:start position:0%
+is 1.0 *
+ 
+
+ align:start position:0%
+is 1.0 *
+10us14th at room
+
+ align:start position:0%
+10us14th at room
+ 
+
+ align:start position:0%
+10us14th at room
+temperature. And if we put logs and then
+
+ align:start position:0%
+temperature. And if we put logs and then
+ 
+
+ align:start position:0%
+temperature. And if we put logs and then
+minus logs by everything, we can derive
+
+ align:start position:0%
+minus logs by everything, we can derive
+ 
+
+ align:start position:0%
+minus logs by everything, we can derive
+this expression, which is the pKa plus
+
+ align:start position:0%
+this expression, which is the pKa plus
+ 
+
+ align:start position:0%
+this expression, which is the pKa plus
+the pKb equals the pKw equals
+
+ align:start position:0%
+the pKb equals the pKw equals
+ 
+
+ align:start position:0%
+the pKb equals the pKw equals
+14.00. So you can't have an acid and its
+
+ align:start position:0%
+14.00. So you can't have an acid and its
+ 
+
+ align:start position:0%
+14.00. So you can't have an acid and its
+conjugate base both be strong. You can't
+
+ align:start position:0%
+conjugate base both be strong. You can't
+ 
+
+ align:start position:0%
+conjugate base both be strong. You can't
+have a base and its conjugate acid both
+
+ align:start position:0%
+have a base and its conjugate acid both
+ 
+
+ align:start position:0%
+have a base and its conjugate acid both
+be strong. The pK's need to add up to
+
+ align:start position:0%
+be strong. The pK's need to add up to
+ 
+
+ align:start position:0%
+be strong. The pK's need to add up to
+14. So, if you have something that's a
+
+ align:start position:0%
+14. So, if you have something that's a
+ 
+
+ align:start position:0%
+14. So, if you have something that's a
+good acid, then its conjugate base is
+
+ align:start position:0%
+good acid, then its conjugate base is
+ 
+
+ align:start position:0%
+good acid, then its conjugate base is
+not going to be particularly good. The
+
+ align:start position:0%
+not going to be particularly good. The
+ 
+
+ align:start position:0%
+not going to be particularly good. The
+pKa A and the pKb must add up to 14. If
+
+ align:start position:0%
+pKa A and the pKb must add up to 14. If
+ 
+
+ align:start position:0%
+pKa A and the pKb must add up to 14. If
+you have something that's a good base,
+
+ align:start position:0%
+you have something that's a good base,
+ 
+
+ align:start position:0%
+you have something that's a good base,
+its conjugate acid is not going to be
+
+ align:start position:0%
+its conjugate acid is not going to be
+ 
+
+ align:start position:0%
+its conjugate acid is not going to be
+that good. So, these are connected to
+
+ align:start position:0%
+that good. So, these are connected to
+ 
+
+ align:start position:0%
+that good. So, these are connected to
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+other. So, we can think about then the
+
+ align:start position:0%
+other. So, we can think about then the
+ 
+
+ align:start position:0%
+other. So, we can think about then the
+strong acids and the strong bases again.
+
+ align:start position:0%
+strong acids and the strong bases again.
+ 
+
+ align:start position:0%
+strong acids and the strong bases again.
+So, we talk about equilibrium, but
+
+ align:start position:0%
+So, we talk about equilibrium, but
+ 
+
+ align:start position:0%
+So, we talk about equilibrium, but
+really this is pushing the equilibrium
+
+ align:start position:0%
+really this is pushing the equilibrium
+ 
+
+ align:start position:0%
+really this is pushing the equilibrium
+pretty much to completion. If it's a
+
+ align:start position:0%
+pretty much to completion. If it's a
+ 
+
+ align:start position:0%
+pretty much to completion. If it's a
+strong acid in water, however much
+
+ align:start position:0%
+strong acid in water, however much
+ 
+
+ align:start position:0%
+strong acid in water, however much
+strong acid you put in is how much
+
+ align:start position:0%
+strong acid you put in is how much
+ 
+
+ align:start position:0%
+strong acid you put in is how much
+hydrronium ion concentration you get
+
+ align:start position:0%
+hydrronium ion concentration you get
+ 
+
+ align:start position:0%
+hydrronium ion concentration you get
+out. A strong base is going to give you
+
+ align:start position:0%
+out. A strong base is going to give you
+ 
+
+ align:start position:0%
+out. A strong base is going to give you
+that amount of hydroxide ion
+
+ align:start position:0%
+that amount of hydroxide ion
+ 
+
+ align:start position:0%
+that amount of hydroxide ion
+concentration. Strong acids and bases
+
+ align:start position:0%
+concentration. Strong acids and bases
+ 
+
+ align:start position:0%
+concentration. Strong acids and bases
+push the equilibrium pretty much
+
+ align:start position:0%
+push the equilibrium pretty much
+ 
+
+ align:start position:0%
+push the equilibrium pretty much
+completely toward ionization. You know,
+
+ align:start position:0%
+completely toward ionization. You know,
+ 
+
+ align:start position:0%
+completely toward ionization. You know,
+we have these numbers of 10 to the 11th,
+
+ align:start position:0%
+we have these numbers of 10 to the 11th,
+ 
+
+ align:start position:0%
+we have these numbers of 10 to the 11th,
+10 to the 7th. These are hugely over
+
+ align:start position:0%
+10 to the 7th. These are hugely over
+ 
+
+ align:start position:0%
+10 to the 7th. These are hugely over
+here. We're forming almost ionizing
+
+ align:start position:0%
+here. We're forming almost ionizing
+ 
+
+ align:start position:0%
+here. We're forming almost ionizing
+completely. Now for weak acids and
+
+ align:start position:0%
+completely. Now for weak acids and
+ 
+
+ align:start position:0%
+completely. Now for weak acids and
+bases, it's very different. Here the
+
+ align:start position:0%
+bases, it's very different. Here the
+ 
+
+ align:start position:0%
+bases, it's very different. Here the
+equilibrium you are going back and
+
+ align:start position:0%
+equilibrium you are going back and
+ 
+
+ align:start position:0%
+equilibrium you are going back and
+forth. You have this dynamic
+
+ align:start position:0%
+forth. You have this dynamic
+ 
+
+ align:start position:0%
+forth. You have this dynamic
+equilibrium. The acid in water is
+
+ align:start position:0%
+equilibrium. The acid in water is
+ 
+
+ align:start position:0%
+equilibrium. The acid in water is
+forming hydrronium ions and and A minus.
+
+ align:start position:0%
+forming hydrronium ions and and A minus.
+ 
+
+ align:start position:0%
+forming hydrronium ions and and A minus.
+But a minus is also a somewhat good weak
+
+ align:start position:0%
+But a minus is also a somewhat good weak
+ 
+
+ align:start position:0%
+But a minus is also a somewhat good weak
+base pushing the equilibrium back the
+
+ align:start position:0%
+base pushing the equilibrium back the
+ 
+
+ align:start position:0%
+base pushing the equilibrium back the
+other way. So in this case we have a
+
+ align:start position:0%
+other way. So in this case we have a
+ 
+
+ align:start position:0%
+other way. So in this case we have a
+back and forth between the forward and
+
+ align:start position:0%
+back and forth between the forward and
+ 
+
+ align:start position:0%
+back and forth between the forward and
+the reverse. So if you have very weak,
+
+ align:start position:0%
+the reverse. So if you have very weak,
+ 
+
+ align:start position:0%
+the reverse. So if you have very weak,
+you have moderate, you have moderate,
+
+ align:start position:0%
+you have moderate, you have moderate,
+ 
+
+ align:start position:0%
+you have moderate, you have moderate,
+you have very weak. And this is what's
+
+ align:start position:0%
+you have very weak. And this is what's
+ 
+
+ align:start position:0%
+you have very weak. And this is what's
+important for forming buffers. And
+
+ align:start position:0%
+important for forming buffers. And
+ 
+
+ align:start position:0%
+important for forming buffers. And
+buffers are really important. Okay,
+
+ align:start position:0%
+buffers are really important. Okay,
+ 
+
+ align:start position:0%
+buffers are really important. Okay,
+let's see if we can uh get to uh one of
+
+ align:start position:0%
+let's see if we can uh get to uh one of
+ 
+
+ align:start position:0%
+let's see if we can uh get to uh one of
+these types of problems because there
+
+ align:start position:0%
+these types of problems because there
+ 
+
+ align:start position:0%
+these types of problems because there
+are five we need to get to in this unit
+
+ align:start position:0%
+are five we need to get to in this unit
+ 
+
+ align:start position:0%
+are five we need to get to in this unit
+and um and there are only five and
+
+ align:start position:0%
+and um and there are only five and
+ 
+
+ align:start position:0%
+and um and there are only five and
+people will say salt and water is
+
+ align:start position:0%
+people will say salt and water is
+ 
+
+ align:start position:0%
+people will say salt and water is
+another but salt and water just breaks
+
+ align:start position:0%
+another but salt and water just breaks
+ 
+
+ align:start position:0%
+another but salt and water just breaks
+down into weak acid and weak bases. So
+
+ align:start position:0%
+down into weak acid and weak bases. So
+ 
+
+ align:start position:0%
+down into weak acid and weak bases. So
+everyone can learn how to do five types
+
+ align:start position:0%
+everyone can learn how to do five types
+ 
+
+ align:start position:0%
+everyone can learn how to do five types
+of problems. So this is very doable.
+
+ align:start position:0%
+of problems. So this is very doable.
+ 
+
+ align:start position:0%
+of problems. So this is very doable.
+All right, so let's just look at
+
+ align:start position:0%
+All right, so let's just look at
+ 
+
+ align:start position:0%
+All right, so let's just look at
+equilibrium of weak acids. And we'll
+
+ align:start position:0%
+equilibrium of weak acids. And we'll
+ 
+
+ align:start position:0%
+equilibrium of weak acids. And we'll
+save weak bases for last time. So a weak
+
+ align:start position:0%
+save weak bases for last time. So a weak
+ 
+
+ align:start position:0%
+save weak bases for last time. So a weak
+acid is vitamin C. And I brought some
+
+ align:start position:0%
+acid is vitamin C. And I brought some
+ 
+
+ align:start position:0%
+acid is vitamin C. And I brought some
+vitamin C here. I tried to do a demo
+
+ align:start position:0%
+vitamin C here. I tried to do a demo
+ 
+
+ align:start position:0%
+vitamin C here. I tried to do a demo
+once and discovered that uh vitamin C is
+
+ align:start position:0%
+once and discovered that uh vitamin C is
+ 
+
+ align:start position:0%
+once and discovered that uh vitamin C is
+it's really coated well. So it does not
+
+ align:start position:0%
+it's really coated well. So it does not
+ 
+
+ align:start position:0%
+it's really coated well. So it does not
+dissolve until it hits the acid of your
+
+ align:start position:0%
+dissolve until it hits the acid of your
+ 
+
+ align:start position:0%
+dissolve until it hits the acid of your
+stomach. So I could not dissolve it. Um
+
+ align:start position:0%
+stomach. So I could not dissolve it. Um
+ 
+
+ align:start position:0%
+stomach. So I could not dissolve it. Um
+so I'll just hold this up right here.
+
+ align:start position:0%
+so I'll just hold this up right here.
+ 
+
+ align:start position:0%
+so I'll just hold this up right here.
+But if we had a uh 500 mgram tablet,
+
+ align:start position:0%
+But if we had a uh 500 mgram tablet,
+ 
+
+ align:start position:0%
+But if we had a uh 500 mgram tablet,
+which I think is what this is, and if I
+
+ align:start position:0%
+which I think is what this is, and if I
+ 
+
+ align:start position:0%
+which I think is what this is, and if I
+had 100 mls of water, and if this wasn't
+
+ align:start position:0%
+had 100 mls of water, and if this wasn't
+ 
+
+ align:start position:0%
+had 100 mls of water, and if this wasn't
+coated, so there's no way you can
+
+ align:start position:0%
+coated, so there's no way you can
+ 
+
+ align:start position:0%
+coated, so there's no way you can
+dissolve it, then I could calculate the
+
+ align:start position:0%
+dissolve it, then I could calculate the
+ 
+
+ align:start position:0%
+dissolve it, then I could calculate the
+pH. So, how am I going to do this? I'm
+
+ align:start position:0%
+pH. So, how am I going to do this? I'm
+ 
+
+ align:start position:0%
+pH. So, how am I going to do this? I'm
+given the Ka. I'm told I'm told the
+
+ align:start position:0%
+given the Ka. I'm told I'm told the
+ 
+
+ align:start position:0%
+given the Ka. I'm told I'm told the
+number of milligrams and I'm told the
+
+ align:start position:0%
+number of milligrams and I'm told the
+ 
+
+ align:start position:0%
+number of milligrams and I'm told the
+volume of water. So, the first thing you
+
+ align:start position:0%
+volume of water. So, the first thing you
+ 
+
+ align:start position:0%
+volume of water. So, the first thing you
+want to do is calculate marity. So you
+
+ align:start position:0%
+want to do is calculate marity. So you
+ 
+
+ align:start position:0%
+want to do is calculate marity. So you
+have you want to convert grams um to
+
+ align:start position:0%
+have you want to convert grams um to
+ 
+
+ align:start position:0%
+have you want to convert grams um to
+moles or milligrams to grams to moles
+
+ align:start position:0%
+moles or milligrams to grams to moles
+ 
+
+ align:start position:0%
+moles or milligrams to grams to moles
+and then you want to use your volume and
+
+ align:start position:0%
+and then you want to use your volume and
+ 
+
+ align:start position:0%
+and then you want to use your volume and
+we have 100 ms but we're going to do
+
+ align:start position:0%
+we have 100 ms but we're going to do
+ 
+
+ align:start position:0%
+we have 100 ms but we're going to do
+marity so we want to convert milliliters
+
+ align:start position:0%
+marity so we want to convert milliliters
+ 
+
+ align:start position:0%
+marity so we want to convert milliliters
+to liters and we can calculate
+
+ align:start position:0%
+to liters and we can calculate
+ 
+
+ align:start position:0%
+to liters and we can calculate
+0.0284 molar moles per liter.
+
+ align:start position:0%
+0.0284 molar moles per liter.
+ 
+
+ align:start position:0%
+0.0284 molar moles per liter.
+Then we can write our expression. And if
+
+ align:start position:0%
+Then we can write our expression. And if
+ 
+
+ align:start position:0%
+Then we can write our expression. And if
+you want to, you can just write HA here
+
+ align:start position:0%
+you want to, you can just write HA here
+ 
+
+ align:start position:0%
+you want to, you can just write HA here
+and A minus. You don't have to write out
+
+ align:start position:0%
+and A minus. You don't have to write out
+ 
+
+ align:start position:0%
+and A minus. You don't have to write out
+the whole thing if you don't want
+
+ align:start position:0%
+the whole thing if you don't want
+ 
+
+ align:start position:0%
+the whole thing if you don't want
+to. All right. So here is the expression
+
+ align:start position:0%
+to. All right. So here is the expression
+ 
+
+ align:start position:0%
+to. All right. So here is the expression
+again. Now just as we saw with chemical
+
+ align:start position:0%
+again. Now just as we saw with chemical
+ 
+
+ align:start position:0%
+again. Now just as we saw with chemical
+equilibrium, we can write this table
+
+ align:start position:0%
+equilibrium, we can write this table
+ 
+
+ align:start position:0%
+equilibrium, we can write this table
+talking about the initial marity. So we
+
+ align:start position:0%
+talking about the initial marity. So we
+ 
+
+ align:start position:0%
+talking about the initial marity. So we
+have a weak acid. We have no hy
+
+ align:start position:0%
+have a weak acid. We have no hy
+ 
+
+ align:start position:0%
+have a weak acid. We have no hy
+hydrronium ion concentration. We have no
+
+ align:start position:0%
+hydrronium ion concentration. We have no
+ 
+
+ align:start position:0%
+hydrronium ion concentration. We have no
+weak conjugate base over here. Um so the
+
+ align:start position:0%
+weak conjugate base over here. Um so the
+ 
+
+ align:start position:0%
+weak conjugate base over here. Um so the
+change then is going to be the constant
+
+ align:start position:0%
+change then is going to be the constant
+ 
+
+ align:start position:0%
+change then is going to be the constant
+the marity that we had and these are
+
+ align:start position:0%
+the marity that we had and these are
+ 
+
+ align:start position:0%
+the marity that we had and these are
+change in marity so don't put don't put
+
+ align:start position:0%
+change in marity so don't put don't put
+ 
+
+ align:start position:0%
+change in marity so don't put don't put
+moles or other things here marity here
+
+ align:start position:0%
+moles or other things here marity here
+ 
+
+ align:start position:0%
+moles or other things here marity here
+min - x that's what you have at
+
+ align:start position:0%
+min - x that's what you have at
+ 
+
+ align:start position:0%
+min - x that's what you have at
+equilibrium plus x plus
+
+ align:start position:0%
+equilibrium plus x plus
+ 
+
+ align:start position:0%
+equilibrium plus x plus
+x so we can write our expression now for
+
+ align:start position:0%
+x so we can write our expression now for
+ 
+
+ align:start position:0%
+x so we can write our expression now for
+Ka we're given the value for Ka and we
+
+ align:start position:0%
+Ka we're given the value for Ka and we
+ 
+
+ align:start position:0%
+Ka we're given the value for Ka and we
+know how to write an expression we have
+
+ align:start position:0%
+know how to write an expression we have
+ 
+
+ align:start position:0%
+know how to write an expression we have
+our hydrronium ion concentration our
+
+ align:start position:0%
+our hydrronium ion concentration our
+ 
+
+ align:start position:0%
+our hydrronium ion concentration our
+conjugate base over here over our
+
+ align:start position:0%
+conjugate base over here over our
+ 
+
+ align:start position:0%
+conjugate base over here over our
+conjugate acid. This is equal to
+
+ align:start position:0%
+conjugate acid. This is equal to
+ 
+
+ align:start position:0%
+conjugate acid. This is equal to
+x^2
+
+ align:start position:0%
+x^2
+ 
+
+ align:start position:0%
+x^2
+0.0284 minus x. Now, if you want to with
+
+ align:start position:0%
+0.0284 minus x. Now, if you want to with
+ 
+
+ align:start position:0%
+0.0284 minus x. Now, if you want to with
+these problems, you can make an
+
+ align:start position:0%
+these problems, you can make an
+ 
+
+ align:start position:0%
+these problems, you can make an
+assumption that x is going to be small
+
+ align:start position:0%
+assumption that x is going to be small
+ 
+
+ align:start position:0%
+assumption that x is going to be small
+and then not have to use the quadratic
+
+ align:start position:0%
+and then not have to use the quadratic
+ 
+
+ align:start position:0%
+and then not have to use the quadratic
+equation, but you do need to check your
+
+ align:start position:0%
+equation, but you do need to check your
+ 
+
+ align:start position:0%
+equation, but you do need to check your
+assumption. But I'll show you how to do
+
+ align:start position:0%
+assumption. But I'll show you how to do
+ 
+
+ align:start position:0%
+assumption. But I'll show you how to do
+it with an assumption. So, we're going
+
+ align:start position:0%
+it with an assumption. So, we're going
+ 
+
+ align:start position:0%
+it with an assumption. So, we're going
+to assume x is small and this value, the
+
+ align:start position:0%
+to assume x is small and this value, the
+ 
+
+ align:start position:0%
+to assume x is small and this value, the
+x will drop out. So we can rewrite this
+
+ align:start position:0%
+x will drop out. So we can rewrite this
+ 
+
+ align:start position:0%
+x will drop out. So we can rewrite this
+expression as x^2 over uh just the
+
+ align:start position:0%
+expression as x^2 over uh just the
+ 
+
+ align:start position:0%
+expression as x^2 over uh just the
+concentration we started with and then
+
+ align:start position:0%
+concentration we started with and then
+ 
+
+ align:start position:0%
+concentration we started with and then
+we can solve for
+
+ align:start position:0%
+we can solve for
+ 
+
+ align:start position:0%
+we can solve for
+x and x in that case is
+
+ align:start position:0%
+x and x in that case is
+ 
+
+ align:start position:0%
+x and x in that case is
+0151 but really two significant figures
+
+ align:start position:0%
+0151 but really two significant figures
+ 
+
+ align:start position:0%
+0151 but really two significant figures
+our ka is just two. Now we can check the
+
+ align:start position:0%
+our ka is just two. Now we can check the
+ 
+
+ align:start position:0%
+our ka is just two. Now we can check the
+assumption and we're going to check the
+
+ align:start position:0%
+assumption and we're going to check the
+ 
+
+ align:start position:0%
+assumption and we're going to check the
+assumption that this is in fact small
+
+ align:start position:0%
+assumption that this is in fact small
+ 
+
+ align:start position:0%
+assumption that this is in fact small
+and if it's less than
+
+ align:start position:0%
+and if it's less than
+ 
+
+ align:start position:0%
+and if it's less than
+5% then we can use
+
+ align:start position:0%
+5% then we can use
+ 
+
+ align:start position:0%
+5% then we can use
+that. So here this is the x we
+
+ align:start position:0%
+that. So here this is the x we
+ 
+
+ align:start position:0%
+that. So here this is the x we
+calculated here is the amount times 100%
+
+ align:start position:0%
+calculated here is the amount times 100%
+ 
+
+ align:start position:0%
+calculated here is the amount times 100%
+gives us
+
+ align:start position:0%
+gives us
+ 
+
+ align:start position:0%
+gives us
+5.3% which is more than five. Five is
+
+ align:start position:0%
+5.3% which is more than five. Five is
+ 
+
+ align:start position:0%
+5.3% which is more than five. Five is
+the magic number for the course. And so
+
+ align:start position:0%
+the magic number for the course. And so
+ 
+
+ align:start position:0%
+the magic number for the course. And so
+then we have to use the quadratic
+
+ align:start position:0%
+then we have to use the quadratic
+ 
+
+ align:start position:0%
+then we have to use the quadratic
+equation. Now, a lot of you probably
+
+ align:start position:0%
+equation. Now, a lot of you probably
+ 
+
+ align:start position:0%
+equation. Now, a lot of you probably
+have calculators that you that can work
+
+ align:start position:0%
+have calculators that you that can work
+ 
+
+ align:start position:0%
+have calculators that you that can work
+the quadratic equation, so you don't
+
+ align:start position:0%
+the quadratic equation, so you don't
+ 
+
+ align:start position:0%
+the quadratic equation, so you don't
+really care. But if you want to check
+
+ align:start position:0%
+really care. But if you want to check
+ 
+
+ align:start position:0%
+really care. But if you want to check
+the assumption, you can. And sometimes
+
+ align:start position:0%
+the assumption, you can. And sometimes
+ 
+
+ align:start position:0%
+the assumption, you can. And sometimes
+we'll need to check it. So, this value,
+
+ align:start position:0%
+we'll need to check it. So, this value,
+ 
+
+ align:start position:0%
+we'll need to check it. So, this value,
+this percent here, is sometimes called
+
+ align:start position:0%
+this percent here, is sometimes called
+ 
+
+ align:start position:0%
+this percent here, is sometimes called
+percent ionization because it's X over
+
+ align:start position:0%
+percent ionization because it's X over
+ 
+
+ align:start position:0%
+percent ionization because it's X over
+the amount you started with. It's the
+
+ align:start position:0%
+the amount you started with. It's the
+ 
+
+ align:start position:0%
+the amount you started with. It's the
+percent that ionized or percent
+
+ align:start position:0%
+percent that ionized or percent
+ 
+
+ align:start position:0%
+percent that ionized or percent
+deproinated. If this is an acid, it's
+
+ align:start position:0%
+deproinated. If this is an acid, it's
+ 
+
+ align:start position:0%
+deproinated. If this is an acid, it's
+the amount of hydrronium, the amount
+
+ align:start position:0%
+the amount of hydrronium, the amount
+ 
+
+ align:start position:0%
+the amount of hydrronium, the amount
+that deproinated over what you started
+
+ align:start position:0%
+that deproinated over what you started
+ 
+
+ align:start position:0%
+that deproinated over what you started
+with. So sometimes you're asked to do
+
+ align:start position:0%
+with. So sometimes you're asked to do
+ 
+
+ align:start position:0%
+with. So sometimes you're asked to do
+this even if you're not checking any
+
+ align:start position:0%
+this even if you're not checking any
+ 
+
+ align:start position:0%
+this even if you're not checking any
+assumptions. All right. So we have to
+
+ align:start position:0%
+assumptions. All right. So we have to
+ 
+
+ align:start position:0%
+assumptions. All right. So we have to
+end with if the clicker question we get
+
+ align:start position:0%
+end with if the clicker question we get
+ 
+
+ align:start position:0%
+end with if the clicker question we get
+here. This is really two significant
+
+ align:start position:0%
+here. This is really two significant
+ 
+
+ align:start position:0%
+here. This is really two significant
+figures. So why don't you tell me how
+
+ align:start position:0%
+figures. So why don't you tell me how
+ 
+
+ align:start position:0%
+figures. So why don't you tell me how
+many significant figures are in your
+
+ align:start position:0%
+many significant figures are in your
+ 
+
+ align:start position:0%
+many significant figures are in your
+answer for pH?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, 10 more seconds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Okay. So, uh let's uh take a look at the
+
+ align:start position:0%
+Okay. So, uh let's uh take a look at the
+ 
+
+ align:start position:0%
+Okay. So, uh let's uh take a look at the
+answer here. So, there's the answer. So,
+
+ align:start position:0%
+answer here. So, there's the answer. So,
+ 
+
+ align:start position:0%
+answer here. So, there's the answer. So,
+this had two significant figures, which
+
+ align:start position:0%
+this had two significant figures, which
+ 
+
+ align:start position:0%
+this had two significant figures, which
+means you get two significant figures
+
+ align:start position:0%
+means you get two significant figures
+ 
+
+ align:start position:0%
+means you get two significant figures
+after the decimal point. So, maybe we'll
+
+ align:start position:0%
+after the decimal point. So, maybe we'll
+ 
+
+ align:start position:0%
+after the decimal point. So, maybe we'll
+have one of these in the clicker
+
+ align:start position:0%
+have one of these in the clicker
+ 
+
+ align:start position:0%
+have one of these in the clicker
+competition on Friday. And we'll do uh
+
+ align:start position:0%
+competition on Friday. And we'll do uh
+ 
+
+ align:start position:0%
+competition on Friday. And we'll do uh
+weak bases uh next time. So again, we've
+
+ align:start position:0%
+weak bases uh next time. So again, we've
+ 
+
+ align:start position:0%
+weak bases uh next time. So again, we've
+been studying acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+base and there are only five types of
+
+ align:start position:0%
+base and there are only five types of
+ 
+
+ align:start position:0%
+base and there are only five types of
+acid base
+
+ align:start position:0%
+acid base
+ 
+
+ align:start position:0%
+acid base
+problems. Weak acid in water, which we
+
+ align:start position:0%
+problems. Weak acid in water, which we
+ 
+
+ align:start position:0%
+problems. Weak acid in water, which we
+already did. Check. Weak base and water,
+
+ align:start position:0%
+already did. Check. Weak base and water,
+ 
+
+ align:start position:0%
+already did. Check. Weak base and water,
+which we're going to do right now. And
+
+ align:start position:0%
+which we're going to do right now. And
+ 
+
+ align:start position:0%
+which we're going to do right now. And
+as soon as we're done doing weak base in
+
+ align:start position:0%
+as soon as we're done doing weak base in
+ 
+
+ align:start position:0%
+as soon as we're done doing weak base in
+water, I'm going to explain to you how
+
+ align:start position:0%
+water, I'm going to explain to you how
+ 
+
+ align:start position:0%
+water, I'm going to explain to you how
+salts in water are just weak acid in
+
+ align:start position:0%
+salts in water are just weak acid in
+ 
+
+ align:start position:0%
+salts in water are just weak acid in
+water or weak base and water problems.
+
+ align:start position:0%
+water or weak base and water problems.
+ 
+
+ align:start position:0%
+water or weak base and water problems.
+So, you already know how to do them as
+
+ align:start position:0%
+So, you already know how to do them as
+ 
+
+ align:start position:0%
+So, you already know how to do them as
+soon as I teach you about weak bases.
+
+ align:start position:0%
+soon as I teach you about weak bases.
+ 
+
+ align:start position:0%
+soon as I teach you about weak bases.
+And then we're going to move on and do
+
+ align:start position:0%
+And then we're going to move on and do
+ 
+
+ align:start position:0%
+And then we're going to move on and do
+buffers. Um, and then next week we're
+
+ align:start position:0%
+buffers. Um, and then next week we're
+ 
+
+ align:start position:0%
+buffers. Um, and then next week we're
+going to do strong acids and strong
+
+ align:start position:0%
+going to do strong acids and strong
+ 
+
+ align:start position:0%
+going to do strong acids and strong
+bases. And then you'll have all
+
+ align:start position:0%
+bases. And then you'll have all
+ 
+
+ align:start position:0%
+bases. And then you'll have all
+five. You already have enough that you
+
+ align:start position:0%
+five. You already have enough that you
+ 
+
+ align:start position:0%
+five. You already have enough that you
+can after today's lecture, you can do I
+
+ align:start position:0%
+can after today's lecture, you can do I
+ 
+
+ align:start position:0%
+can after today's lecture, you can do I
+think all the problem set seven except
+
+ align:start position:0%
+think all the problem set seven except
+ 
+
+ align:start position:0%
+think all the problem set seven except
+for the last two questions I believe or
+
+ align:start position:0%
+for the last two questions I believe or
+ 
+
+ align:start position:0%
+for the last two questions I believe or
+at least a large fraction of problem set
+
+ align:start position:0%
+at least a large fraction of problem set
+ 
+
+ align:start position:0%
+at least a large fraction of problem set
+seven. I will warn you that acid base
+
+ align:start position:0%
+seven. I will warn you that acid base
+ 
+
+ align:start position:0%
+seven. I will warn you that acid base
+problems take a lot of a lot of writing
+
+ align:start position:0%
+problems take a lot of a lot of writing
+ 
+
+ align:start position:0%
+problems take a lot of a lot of writing
+and a lot of time to work. One problem
+
+ align:start position:0%
+and a lot of time to work. One problem
+ 
+
+ align:start position:0%
+and a lot of time to work. One problem
+often has like five or six parts to it
+
+ align:start position:0%
+often has like five or six parts to it
+ 
+
+ align:start position:0%
+often has like five or six parts to it
+and they're all time consuming parts
+
+ align:start position:0%
+and they're all time consuming parts
+ 
+
+ align:start position:0%
+and they're all time consuming parts
+pretty much. So don't leave problem set
+
+ align:start position:0%
+pretty much. So don't leave problem set
+ 
+
+ align:start position:0%
+pretty much. So don't leave problem set
+to the last minute. That would be a
+
+ align:start position:0%
+to the last minute. That would be a
+ 
+
+ align:start position:0%
+to the last minute. That would be a
+mistake on this particular problem set.
+
+ align:start position:0%
+mistake on this particular problem set.
+ 
+
+ align:start position:0%
+mistake on this particular problem set.
+Okay. weak
+
+ align:start position:0%
+Okay. weak
+ 
+
+ align:start position:0%
+Okay. weak
+bases, acid base type problem
+
+ align:start position:0%
+bases, acid base type problem
+ 
+
+ align:start position:0%
+bases, acid base type problem
+too. So in this example, we have ammonia
+
+ align:start position:0%
+too. So in this example, we have ammonia
+ 
+
+ align:start position:0%
+too. So in this example, we have ammonia
+NH ammonia
+
+ align:start position:0%
+NH ammonia
+ 
+
+ align:start position:0%
+NH ammonia
+NH3 in water and we measured the pH of
+
+ align:start position:0%
+NH3 in water and we measured the pH of
+ 
+
+ align:start position:0%
+NH3 in water and we measured the pH of
+some solutions before and saw they were
+
+ align:start position:0%
+some solutions before and saw they were
+ 
+
+ align:start position:0%
+some solutions before and saw they were
+basic. We had a pH of I think 12 last
+
+ align:start position:0%
+basic. We had a pH of I think 12 last
+ 
+
+ align:start position:0%
+basic. We had a pH of I think 12 last
+time. And so this conjugate base goes to
+
+ align:start position:0%
+time. And so this conjugate base goes to
+ 
+
+ align:start position:0%
+time. And so this conjugate base goes to
+a conjugate acid. So the base accepts a
+
+ align:start position:0%
+a conjugate acid. So the base accepts a
+ 
+
+ align:start position:0%
+a conjugate acid. So the base accepts a
+hydrogen ion or proton from water
+
+ align:start position:0%
+hydrogen ion or proton from water
+ 
+
+ align:start position:0%
+hydrogen ion or proton from water
+becomes NH4 plus and the water that lost
+
+ align:start position:0%
+becomes NH4 plus and the water that lost
+ 
+
+ align:start position:0%
+becomes NH4 plus and the water that lost
+its hydrogen ion becomes O minus and
+
+ align:start position:0%
+its hydrogen ion becomes O minus and
+ 
+
+ align:start position:0%
+its hydrogen ion becomes O minus and
+that is a base in water problem because
+
+ align:start position:0%
+that is a base in water problem because
+ 
+
+ align:start position:0%
+that is a base in water problem because
+you're forming hydroxide
+
+ align:start position:0%
+you're forming hydroxide
+ 
+
+ align:start position:0%
+you're forming hydroxide
+ions for a base in water. You're talking
+
+ align:start position:0%
+ions for a base in water. You're talking
+ 
+
+ align:start position:0%
+ions for a base in water. You're talking
+about the equilibrium constant for that
+
+ align:start position:0%
+about the equilibrium constant for that
+ 
+
+ align:start position:0%
+about the equilibrium constant for that
+base in water which has a special name
+
+ align:start position:0%
+base in water which has a special name
+ 
+
+ align:start position:0%
+base in water which has a special name
+KB B for base. Um, and it's uh important
+
+ align:start position:0%
+KB B for base. Um, and it's uh important
+ 
+
+ align:start position:0%
+KB B for base. Um, and it's uh important
+to remember the A's and the B's on the
+
+ align:start position:0%
+to remember the A's and the B's on the
+ 
+
+ align:start position:0%
+to remember the A's and the B's on the
+equilibrium constant because it's always
+
+ align:start position:0%
+equilibrium constant because it's always
+ 
+
+ align:start position:0%
+equilibrium constant because it's always
+checking your work. Um, is this a basin
+
+ align:start position:0%
+checking your work. Um, is this a basin
+ 
+
+ align:start position:0%
+checking your work. Um, is this a basin
+water problem? People sometimes try to
+
+ align:start position:0%
+water problem? People sometimes try to
+ 
+
+ align:start position:0%
+water problem? People sometimes try to
+apply Ka's when they should be doing
+
+ align:start position:0%
+apply Ka's when they should be doing
+ 
+
+ align:start position:0%
+apply Ka's when they should be doing
+KBs. So pay attention to basin water,
+
+ align:start position:0%
+KBs. So pay attention to basin water,
+ 
+
+ align:start position:0%
+KBs. So pay attention to basin water,
+we're thinking about KB. So here, if
+
+ align:start position:0%
+we're thinking about KB. So here, if
+ 
+
+ align:start position:0%
+we're thinking about KB. So here, if
+we're going to calculate the pH of a
+
+ align:start position:0%
+we're going to calculate the pH of a
+ 
+
+ align:start position:0%
+we're going to calculate the pH of a
+solution, we have marity of
+
+ align:start position:0%
+solution, we have marity of
+ 
+
+ align:start position:0%
+solution, we have marity of
+0.15 and room temperature. Pretty much
+
+ align:start position:0%
+0.15 and room temperature. Pretty much
+ 
+
+ align:start position:0%
+0.15 and room temperature. Pretty much
+everything's at room temperature. So
+
+ align:start position:0%
+everything's at room temperature. So
+ 
+
+ align:start position:0%
+everything's at room temperature. So
+whenever you're asked to calculate the
+
+ align:start position:0%
+whenever you're asked to calculate the
+ 
+
+ align:start position:0%
+whenever you're asked to calculate the
+pH of a weak base in water, you want to
+
+ align:start position:0%
+pH of a weak base in water, you want to
+ 
+
+ align:start position:0%
+pH of a weak base in water, you want to
+think about at equilibrium, what's the
+
+ align:start position:0%
+think about at equilibrium, what's the
+ 
+
+ align:start position:0%
+think about at equilibrium, what's the
+condition now? What will be the
+
+ align:start position:0%
+condition now? What will be the
+ 
+
+ align:start position:0%
+condition now? What will be the
+condition? What's the change in what
+
+ align:start position:0%
+condition? What's the change in what
+ 
+
+ align:start position:0%
+condition? What's the change in what
+will be the condition at equilibrium?
+
+ align:start position:0%
+will be the condition at equilibrium?
+ 
+
+ align:start position:0%
+will be the condition at equilibrium?
+And so you can make this table. You can
+
+ align:start position:0%
+And so you can make this table. You can
+ 
+
+ align:start position:0%
+And so you can make this table. You can
+write out the expression again. You can
+
+ align:start position:0%
+write out the expression again. You can
+ 
+
+ align:start position:0%
+write out the expression again. You can
+forget about water. Water's our solvent.
+
+ align:start position:0%
+forget about water. Water's our solvent.
+ 
+
+ align:start position:0%
+forget about water. Water's our solvent.
+It's not going to be showing up. Um, and
+
+ align:start position:0%
+It's not going to be showing up. Um, and
+ 
+
+ align:start position:0%
+It's not going to be showing up. Um, and
+then put in our initial marity 0.15. And
+
+ align:start position:0%
+then put in our initial marity 0.15. And
+ 
+
+ align:start position:0%
+then put in our initial marity 0.15. And
+we put zeros in the other categories.
+
+ align:start position:0%
+we put zeros in the other categories.
+ 
+
+ align:start position:0%
+we put zeros in the other categories.
+And uh Oh, why don't you try the rest?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Is it slowing down?
+
+ align:start position:0%
+Is it slowing down?
+ 
+
+ align:start position:0%
+Is it slowing down?
+Okay. All right. Let's just do 10 more
+
+ align:start position:0%
+Okay. All right. Let's just do 10 more
+ 
+
+ align:start position:0%
+Okay. All right. Let's just do 10 more
+seconds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yep. Excellent. Sam told me everyone
+
+ align:start position:0%
+Yep. Excellent. Sam told me everyone
+ 
+
+ align:start position:0%
+Yep. Excellent. Sam told me everyone
+responded really
+
+ align:start position:0%
+responded really
+ 
+
+ align:start position:0%
+responded really
+quickly. So that is in fact what you're
+
+ align:start position:0%
+quickly. So that is in fact what you're
+ 
+
+ align:start position:0%
+quickly. So that is in fact what you're
+going to do. We'll put that up here as
+
+ align:start position:0%
+going to do. We'll put that up here as
+ 
+
+ align:start position:0%
+going to do. We'll put that up here as
+well. So we lose some of this minus x.
+
+ align:start position:0%
+well. So we lose some of this minus x.
+ 
+
+ align:start position:0%
+well. So we lose some of this minus x.
+So at equilibrium we have 0.15 minus x
+
+ align:start position:0%
+So at equilibrium we have 0.15 minus x
+ 
+
+ align:start position:0%
+So at equilibrium we have 0.15 minus x
+and we get plus x here and plus x
+
+ align:start position:0%
+and we get plus x here and plus x
+ 
+
+ align:start position:0%
+and we get plus x here and plus x
+there. Now we can write our KB for our
+
+ align:start position:0%
+there. Now we can write our KB for our
+ 
+
+ align:start position:0%
+there. Now we can write our KB for our
+base in water. its products, the
+
+ align:start position:0%
+base in water. its products, the
+ 
+
+ align:start position:0%
+base in water. its products, the
+conjugate acid,
+
+ align:start position:0%
+conjugate acid,
+ 
+
+ align:start position:0%
+conjugate acid,
+NH4+ times the concentration of
+
+ align:start position:0%
+NH4+ times the concentration of
+ 
+
+ align:start position:0%
+NH4+ times the concentration of
+hydroxide ions over NH3. Again, water is
+
+ align:start position:0%
+hydroxide ions over NH3. Again, water is
+ 
+
+ align:start position:0%
+hydroxide ions over NH3. Again, water is
+the solvent. It's not in the
+
+ align:start position:0%
+the solvent. It's not in the
+ 
+
+ align:start position:0%
+the solvent. It's not in the
+equation. And then we can write out this
+
+ align:start position:0%
+equation. And then we can write out this
+ 
+
+ align:start position:0%
+equation. And then we can write out this
+is X, that's X. So we have
+
+ align:start position:0%
+is X, that's X. So we have
+ 
+
+ align:start position:0%
+is X, that's X. So we have
+X2. And then the change in the amount of
+
+ align:start position:0%
+X2. And then the change in the amount of
+ 
+
+ align:start position:0%
+X2. And then the change in the amount of
+the weak base when it's in water is 0.15
+
+ align:start position:0%
+the weak base when it's in water is 0.15
+ 
+
+ align:start position:0%
+the weak base when it's in water is 0.15
+- X.
+
+ align:start position:0%
+- X.
+ 
+
+ align:start position:0%
+- X.
+So at this point you can either use the
+
+ align:start position:0%
+So at this point you can either use the
+ 
+
+ align:start position:0%
+So at this point you can either use the
+quadratic equation or you can make an
+
+ align:start position:0%
+quadratic equation or you can make an
+ 
+
+ align:start position:0%
+quadratic equation or you can make an
+assumption that x is going to be small
+
+ align:start position:0%
+assumption that x is going to be small
+ 
+
+ align:start position:0%
+assumption that x is going to be small
+compared to 0.5. We don't want to make
+
+ align:start position:0%
+compared to 0.5. We don't want to make
+ 
+
+ align:start position:0%
+compared to 0.5. We don't want to make
+the assumption up here. We want to get
+
+ align:start position:0%
+the assumption up here. We want to get
+ 
+
+ align:start position:0%
+the assumption up here. We want to get
+to this point before we try the
+
+ align:start position:0%
+to this point before we try the
+ 
+
+ align:start position:0%
+to this point before we try the
+assumption. And you always need to check
+
+ align:start position:0%
+assumption. And you always need to check
+ 
+
+ align:start position:0%
+assumption. And you always need to check
+your assumptions to make sure they are
+
+ align:start position:0%
+your assumptions to make sure they are
+ 
+
+ align:start position:0%
+your assumptions to make sure they are
+correct. Um but if we use the assumption
+
+ align:start position:0%
+correct. Um but if we use the assumption
+ 
+
+ align:start position:0%
+correct. Um but if we use the assumption
+here just to simplify the math and so
+
+ align:start position:0%
+here just to simplify the math and so
+ 
+
+ align:start position:0%
+here just to simplify the math and so
+the assumption is that this x is small.
+
+ align:start position:0%
+the assumption is that this x is small.
+ 
+
+ align:start position:0%
+the assumption is that this x is small.
+So we can drop that x - x out. Um and
+
+ align:start position:0%
+So we can drop that x - x out. Um and
+ 
+
+ align:start position:0%
+So we can drop that x - x out. Um and
+then we can calculate that x is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.00164. And then we can check the
+
+ align:start position:0%
+0.00164. And then we can check the
+ 
+
+ align:start position:0%
+0.00164. And then we can check the
+assumption. And that is another clicker
+
+ align:start position:0%
+assumption. And that is another clicker
+ 
+
+ align:start position:0%
+assumption. And that is another clicker
+question.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, 10 more seconds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All
+
+ align:start position:0%
+All
+ 
+
+ align:start position:0%
+All
+right. It is number one. So here you're
+
+ align:start position:0%
+right. It is number one. So here you're
+ 
+
+ align:start position:0%
+right. It is number one. So here you're
+checking the assumption and the way that
+
+ align:start position:0%
+checking the assumption and the way that
+ 
+
+ align:start position:0%
+checking the assumption and the way that
+you check the assumption is that you put
+
+ align:start position:0%
+you check the assumption is that you put
+ 
+
+ align:start position:0%
+you check the assumption is that you put
+x that you've calculated by simplifying
+
+ align:start position:0%
+x that you've calculated by simplifying
+ 
+
+ align:start position:0%
+x that you've calculated by simplifying
+it divide it by the number that you're
+
+ align:start position:0%
+it divide it by the number that you're
+ 
+
+ align:start position:0%
+it divide it by the number that you're
+asking is it smaller than and then times
+
+ align:start position:0%
+asking is it smaller than and then times
+ 
+
+ align:start position:0%
+asking is it smaller than and then times
+100 because our rule is 5%. So if this
+
+ align:start position:0%
+100 because our rule is 5%. So if this
+ 
+
+ align:start position:0%
+100 because our rule is 5%. So if this
+value is greater than 5% of this value
+
+ align:start position:0%
+value is greater than 5% of this value
+ 
+
+ align:start position:0%
+value is greater than 5% of this value
+you need to use the quadratic. If it's
+
+ align:start position:0%
+you need to use the quadratic. If it's
+ 
+
+ align:start position:0%
+you need to use the quadratic. If it's
+less than 5% then you can go ahead and
+
+ align:start position:0%
+less than 5% then you can go ahead and
+ 
+
+ align:start position:0%
+less than 5% then you can go ahead and
+use your assumption. And so this is the
+
+ align:start position:0%
+use your assumption. And so this is the
+ 
+
+ align:start position:0%
+use your assumption. And so this is the
+assumption we're talking about that this
+
+ align:start position:0%
+assumption we're talking about that this
+ 
+
+ align:start position:0%
+assumption we're talking about that this
+number is under 5%. And for acids and
+
+ align:start position:0%
+number is under 5%. And for acids and
+ 
+
+ align:start position:0%
+number is under 5%. And for acids and
+bases, weak acids and bases, it very
+
+ align:start position:0%
+bases, weak acids and bases, it very
+ 
+
+ align:start position:0%
+bases, weak acids and bases, it very
+often is less than 5%. Um because
+
+ align:start position:0%
+often is less than 5%. Um because
+ 
+
+ align:start position:0%
+often is less than 5%. Um because
+they're weak. So there's not a lot of
+
+ align:start position:0%
+they're weak. So there's not a lot of
+ 
+
+ align:start position:0%
+they're weak. So there's not a lot of
+ionization. And this is often referred
+
+ align:start position:0%
+ionization. And this is often referred
+ 
+
+ align:start position:0%
+ionization. And this is often referred
+to as percentage ionization um as well.
+
+ align:start position:0%
+to as percentage ionization um as well.
+ 
+
+ align:start position:0%
+to as percentage ionization um as well.
+All right. So our checking assumption
+
+ align:start position:0%
+All right. So our checking assumption
+ 
+
+ align:start position:0%
+All right. So our checking assumption
+again that X.00164
+
+ align:start position:0%
+again that X.00164
+ 
+
+ align:start position:0%
+again that X.00164
+0164 divided by 0.15 * 100% is 1% 1.1
+
+ align:start position:0%
+0164 divided by 0.15 * 100% is 1% 1.1
+ 
+
+ align:start position:0%
+0164 divided by 0.15 * 100% is 1% 1.1
+and that's less than five. So the
+
+ align:start position:0%
+and that's less than five. So the
+ 
+
+ align:start position:0%
+and that's less than five. So the
+assumption is
+
+ align:start position:0%
+assumption is
+ 
+
+ align:start position:0%
+assumption is
+okay and then we can calculate
+
+ align:start position:0%
+okay and then we can calculate
+ 
+
+ align:start position:0%
+okay and then we can calculate
+um PO because this is a weak base in
+
+ align:start position:0%
+um PO because this is a weak base in
+ 
+
+ align:start position:0%
+um PO because this is a weak base in
+water. So the X that we calculated is
+
+ align:start position:0%
+water. So the X that we calculated is
+ 
+
+ align:start position:0%
+water. So the X that we calculated is
+the amount of hydroxide ion in solution.
+
+ align:start position:0%
+the amount of hydroxide ion in solution.
+ 
+
+ align:start position:0%
+the amount of hydroxide ion in solution.
+So we calculate PO and we get
+
+ align:start position:0%
+So we calculate PO and we get
+ 
+
+ align:start position:0%
+So we calculate PO and we get
+2.79 and that's two significant figures.
+
+ align:start position:0%
+2.79 and that's two significant figures.
+ 
+
+ align:start position:0%
+2.79 and that's two significant figures.
+Everything we had after the decimal
+
+ align:start position:0%
+Everything we had after the decimal
+ 
+
+ align:start position:0%
+Everything we had after the decimal
+because everything um that we had was
+
+ align:start position:0%
+because everything um that we had was
+ 
+
+ align:start position:0%
+because everything um that we had was
+two significant figures. And so this is
+
+ align:start position:0%
+two significant figures. And so this is
+ 
+
+ align:start position:0%
+two significant figures. And so this is
+two significant figures, two significant
+
+ align:start position:0%
+two significant figures, two significant
+ 
+
+ align:start position:0%
+two significant figures, two significant
+figures after the decimal point. And
+
+ align:start position:0%
+figures after the decimal point. And
+ 
+
+ align:start position:0%
+figures after the decimal point. And
+then you need to calculate pH because
+
+ align:start position:0%
+then you need to calculate pH because
+ 
+
+ align:start position:0%
+then you need to calculate pH because
+the problem asked for pH. So this is
+
+ align:start position:0%
+the problem asked for pH. So this is
+ 
+
+ align:start position:0%
+the problem asked for pH. So this is
+again at room temperature. So we can use
+
+ align:start position:0%
+again at room temperature. So we can use
+ 
+
+ align:start position:0%
+again at room temperature. So we can use
+14 minus
+
+ align:start position:0%
+14 minus
+ 
+
+ align:start position:0%
+14 minus
+2.79 is
+
+ align:start position:0%
+2.79 is
+ 
+
+ align:start position:0%
+2.79 is
+11.21. That's our pH. And don't make the
+
+ align:start position:0%
+11.21. That's our pH. And don't make the
+ 
+
+ align:start position:0%
+11.21. That's our pH. And don't make the
+mistake of stopping here forgetting that
+
+ align:start position:0%
+mistake of stopping here forgetting that
+ 
+
+ align:start position:0%
+mistake of stopping here forgetting that
+X is hydroxide ion instead of hydrronium
+
+ align:start position:0%
+X is hydroxide ion instead of hydrronium
+ 
+
+ align:start position:0%
+X is hydroxide ion instead of hydrronium
+ion and tell me that the pH of my weak
+
+ align:start position:0%
+ion and tell me that the pH of my weak
+ 
+
+ align:start position:0%
+ion and tell me that the pH of my weak
+base in solution is
+
+ align:start position:0%
+base in solution is
+ 
+
+ align:start position:0%
+base in solution is
+pH2. So one of the things that's really
+
+ align:start position:0%
+pH2. So one of the things that's really
+ 
+
+ align:start position:0%
+pH2. So one of the things that's really
+good about this unit is that there's
+
+ align:start position:0%
+good about this unit is that there's
+ 
+
+ align:start position:0%
+good about this unit is that there's
+some good checks that you got the right
+
+ align:start position:0%
+some good checks that you got the right
+ 
+
+ align:start position:0%
+some good checks that you got the right
+answer at the end. If you're talking
+
+ align:start position:0%
+answer at the end. If you're talking
+ 
+
+ align:start position:0%
+answer at the end. If you're talking
+about a base in solution, you should
+
+ align:start position:0%
+about a base in solution, you should
+ 
+
+ align:start position:0%
+about a base in solution, you should
+have a pH above what value? Above seven.
+
+ align:start position:0%
+have a pH above what value? Above seven.
+ 
+
+ align:start position:0%
+have a pH above what value? Above seven.
+So, it should be on the basic side of
+
+ align:start position:0%
+So, it should be on the basic side of
+ 
+
+ align:start position:0%
+So, it should be on the basic side of
+neutral. PH7 is neutral. So, it should
+
+ align:start position:0%
+neutral. PH7 is neutral. So, it should
+ 
+
+ align:start position:0%
+neutral. PH7 is neutral. So, it should
+be above seven. And so, if this was your
+
+ align:start position:0%
+be above seven. And so, if this was your
+ 
+
+ align:start position:0%
+be above seven. And so, if this was your
+answer, that for pH, that wouldn't make
+
+ align:start position:0%
+answer, that for pH, that wouldn't make
+ 
+
+ align:start position:0%
+answer, that for pH, that wouldn't make
+a lot of sense. So, always check at the
+
+ align:start position:0%
+a lot of sense. So, always check at the
+ 
+
+ align:start position:0%
+a lot of sense. So, always check at the
+end. And it's fine if you get to an exam
+
+ align:start position:0%
+end. And it's fine if you get to an exam
+ 
+
+ align:start position:0%
+end. And it's fine if you get to an exam
+and you get to the end and you did
+
+ align:start position:0%
+and you get to the end and you did
+ 
+
+ align:start position:0%
+and you get to the end and you did
+something wrong and you realize that
+
+ align:start position:0%
+something wrong and you realize that
+ 
+
+ align:start position:0%
+something wrong and you realize that
+your answer doesn't make any sense. If
+
+ align:start position:0%
+your answer doesn't make any sense. If
+ 
+
+ align:start position:0%
+your answer doesn't make any sense. If
+you write this answer doesn't make any
+
+ align:start position:0%
+you write this answer doesn't make any
+ 
+
+ align:start position:0%
+you write this answer doesn't make any
+sense, but I don't have time to figure
+
+ align:start position:0%
+sense, but I don't have time to figure
+ 
+
+ align:start position:0%
+sense, but I don't have time to figure
+out what I gave wrong, you will get
+
+ align:start position:0%
+out what I gave wrong, you will get
+ 
+
+ align:start position:0%
+out what I gave wrong, you will get
+points for recognizing that that is not
+
+ align:start position:0%
+points for recognizing that that is not
+ 
+
+ align:start position:0%
+points for recognizing that that is not
+a a valid answer because it's a weak
+
+ align:start position:0%
+a a valid answer because it's a weak
+ 
+
+ align:start position:0%
+a a valid answer because it's a weak
+acid problem and you have a basic pH or
+
+ align:start position:0%
+acid problem and you have a basic pH or
+ 
+
+ align:start position:0%
+acid problem and you have a basic pH or
+vice versa. So, keep that that in mind.
+
+ align:start position:0%
+vice versa. So, keep that that in mind.
+ 
+
+ align:start position:0%
+vice versa. So, keep that that in mind.
+There's lots of partial credit. Grading
+
+ align:start position:0%
+There's lots of partial credit. Grading
+ 
+
+ align:start position:0%
+There's lots of partial credit. Grading
+acidbased problems on exams is a whole
+
+ align:start position:0%
+acidbased problems on exams is a whole
+ 
+
+ align:start position:0%
+acidbased problems on exams is a whole
+new fun adventure that the TAs have no
+
+ align:start position:0%
+new fun adventure that the TAs have no
+ 
+
+ align:start position:0%
+new fun adventure that the TAs have no
+idea what they're what what what is
+
+ align:start position:0%
+idea what they're what what what is
+ 
+
+ align:start position:0%
+idea what they're what what what is
+going to be happening. But I'll be right
+
+ align:start position:0%
+going to be happening. But I'll be right
+ 
+
+ align:start position:0%
+going to be happening. But I'll be right
+with you there for 10 hours of grading
+
+ align:start position:0%
+with you there for 10 hours of grading
+ 
+
+ align:start position:0%
+with you there for 10 hours of grading
+and we'll have a good time. Write
+
+ align:start position:0%
+and we'll have a good time. Write
+ 
+
+ align:start position:0%
+and we'll have a good time. Write
+neatly, please.
\ No newline at end of file
diff --git a/q0PxCQWG3ic.txt b/q0PxCQWG3ic.txt
new file mode 100644
index 0000000000000000000000000000000000000000..97f143e106cd600cbe4fb1dfae4230583a4a00ed
--- /dev/null
+++ b/q0PxCQWG3ic.txt
@@ -0,0 +1,1643 @@
+align:start position:0%
+ 
+So in this recitation we're going to
+
+ align:start position:0%
+So in this recitation we're going to
+ 
+
+ align:start position:0%
+So in this recitation we're going to
+look at step and delta functions
+
+ align:start position:0%
+look at step and delta functions
+ 
+
+ align:start position:0%
+look at step and delta functions
+integration and generalized derivatives.
+
+ align:start position:0%
+integration and generalized derivatives.
+ 
+
+ align:start position:0%
+integration and generalized derivatives.
+So the first part you're asked to
+
+ align:start position:0%
+So the first part you're asked to
+ 
+
+ align:start position:0%
+So the first part you're asked to
+compute the integral from 0 minus to
+
+ align:start position:0%
+compute the integral from 0 minus to
+ 
+
+ align:start position:0%
+compute the integral from 0 minus to
+infinity delta t exponential t ^ 2 dt.
+
+ align:start position:0%
+infinity delta t exponential t ^ 2 dt.
+ 
+
+ align:start position:0%
+infinity delta t exponential t ^ 2 dt.
+The second one is from z minus to
+
+ align:start position:0%
+The second one is from z minus to
+ 
+
+ align:start position:0%
+The second one is from z minus to
+infinity delta t minus 2 exponential of
+
+ align:start position:0%
+infinity delta t minus 2 exponential of
+ 
+
+ align:start position:0%
+infinity delta t minus 2 exponential of
+t ^ 2 sin t cos 2t. The third one is 0
+
+ align:start position:0%
+t ^ 2 sin t cos 2t. The third one is 0
+ 
+
+ align:start position:0%
+t ^ 2 sin t cos 2t. The third one is 0
+plus to infinity delta t exponential of
+
+ align:start position:0%
+plus to infinity delta t exponential of
+ 
+
+ align:start position:0%
+plus to infinity delta t exponential of
+t ^ square dt. So note that it's the
+
+ align:start position:0%
+t ^ square dt. So note that it's the
+ 
+
+ align:start position:0%
+t ^ square dt. So note that it's the
+first is the same as a except that the
+
+ align:start position:0%
+first is the same as a except that the
+ 
+
+ align:start position:0%
+first is the same as a except that the
+bounds of integration changed. The
+
+ align:start position:0%
+bounds of integration changed. The
+ 
+
+ align:start position:0%
+bounds of integration changed. The
+second part we're asked to find the
+
+ align:start position:0%
+second part we're asked to find the
+ 
+
+ align:start position:0%
+second part we're asked to find the
+generalized derivatives of these two
+
+ align:start position:0%
+generalized derivatives of these two
+ 
+
+ align:start position:0%
+generalized derivatives of these two
+functions where u here is just a step
+
+ align:start position:0%
+functions where u here is just a step
+ 
+
+ align:start position:0%
+functions where u here is just a step
+function that you saw before. And uh
+
+ align:start position:0%
+function that you saw before. And uh
+ 
+
+ align:start position:0%
+function that you saw before. And uh
+yeah so it's 3 u t minus 2 u t minus one
+
+ align:start position:0%
+yeah so it's 3 u t minus 2 u t minus one
+ 
+
+ align:start position:0%
+yeah so it's 3 u t minus 2 u t minus one
+and the second one is t² for t negative
+
+ align:start position:0%
+and the second one is t² for t negative
+ 
+
+ align:start position:0%
+and the second one is t² for t negative
+and exponential minus t for t positive.
+
+ align:start position:0%
+and exponential minus t for t positive.
+ 
+
+ align:start position:0%
+and exponential minus t for t positive.
+So, why don't you pause the video and
+
+ align:start position:0%
+So, why don't you pause the video and
+ 
+
+ align:start position:0%
+So, why don't you pause the video and
+work through this example, and I'll be
+
+ align:start position:0%
+work through this example, and I'll be
+ 
+
+ align:start position:0%
+work through this example, and I'll be
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back. Welcome back. So, let's compute
+
+ align:start position:0%
+back. Welcome back. So, let's compute
+ 
+
+ align:start position:0%
+back. Welcome back. So, let's compute
+the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one. 0 minus
+
+ align:start position:0%
+one. 0 minus
+ 
+
+ align:start position:0%
+one. 0 minus
+infinity delta t exponential
+
+ align:start position:0%
+infinity delta t exponential
+ 
+
+ align:start position:0%
+infinity delta t exponential
+t² dt. So just to remind
+
+ align:start position:0%
+t² dt. So just to remind
+ 
+
+ align:start position:0%
+t² dt. So just to remind
+you the delta function is everywhere
+
+ align:start position:0%
+you the delta function is everywhere
+ 
+
+ align:start position:0%
+you the delta function is everywhere
+zero except at the value zero and we're
+
+ align:start position:0%
+zero except at the value zero and we're
+ 
+
+ align:start position:0%
+zero except at the value zero and we're
+represented with an
+
+ align:start position:0%
+represented with an
+ 
+
+ align:start position:0%
+represented with an
+arrow and the integral of the delta
+
+ align:start position:0%
+arrow and the integral of the delta
+ 
+
+ align:start position:0%
+arrow and the integral of the delta
+would be one from minus infinity to plus
+
+ align:start position:0%
+would be one from minus infinity to plus
+ 
+
+ align:start position:0%
+would be one from minus infinity to plus
+infinity. In this in this integral we're
+
+ align:start position:0%
+infinity. In this in this integral we're
+ 
+
+ align:start position:0%
+infinity. In this in this integral we're
+integrating from 0 minus to infinity
+
+ align:start position:0%
+integrating from 0 minus to infinity
+ 
+
+ align:start position:0%
+integrating from 0 minus to infinity
+which means that the zero is included in
+
+ align:start position:0%
+which means that the zero is included in
+ 
+
+ align:start position:0%
+which means that the zero is included in
+our interval from 0 minus to infinity.
+
+ align:start position:0%
+our interval from 0 minus to infinity.
+ 
+
+ align:start position:0%
+our interval from 0 minus to infinity.
+Therefore, this integral is basically
+
+ align:start position:0%
+Therefore, this integral is basically
+ 
+
+ align:start position:0%
+Therefore, this integral is basically
+assigning the value to this function
+
+ align:start position:0%
+assigning the value to this function
+ 
+
+ align:start position:0%
+assigning the value to this function
+exponential t² and the value that it's
+
+ align:start position:0%
+exponential t² and the value that it's
+ 
+
+ align:start position:0%
+exponential t² and the value that it's
+assigning to it is the value would take
+
+ align:start position:0%
+assigning to it is the value would take
+ 
+
+ align:start position:0%
+assigning to it is the value would take
+at t equals to zero where the delta is
+
+ align:start position:0%
+at t equals to zero where the delta is
+ 
+
+ align:start position:0%
+at t equals to zero where the delta is
+non zero. And so really clearly this is
+
+ align:start position:0%
+non zero. And so really clearly this is
+ 
+
+ align:start position:0%
+non zero. And so really clearly this is
+just exponential of
+
+ align:start position:0%
+just exponential of
+ 
+
+ align:start position:0%
+just exponential of
+zero and is give us
+
+ align:start position:0%
+zero and is give us
+ 
+
+ align:start position:0%
+zero and is give us
+one. For the second one
+
+ align:start position:0%
+one. For the second one
+ 
+
+ align:start position:0%
+one. For the second one
+integral goes from 0 minus to infinity
+
+ align:start position:0%
+integral goes from 0 minus to infinity
+ 
+
+ align:start position:0%
+integral goes from 0 minus to infinity
+delta t minus 2 exponential a more
+
+ align:start position:0%
+delta t minus 2 exponential a more
+ 
+
+ align:start position:0%
+delta t minus 2 exponential a more
+complicated function t ^
+
+ align:start position:0%
+complicated function t ^
+ 
+
+ align:start position:0%
+complicated function t ^
+2 sin
+
+ align:start position:0%
+2 sin
+ 
+
+ align:start position:0%
+2 sin
+t cos 2t. So now let's represent this
+
+ align:start position:0%
+t cos 2t. So now let's represent this
+ 
+
+ align:start position:0%
+t cos 2t. So now let's represent this
+delta function here.
+
+ align:start position:0%
+delta function here.
+ 
+
+ align:start position:0%
+delta function here.
+So this is just our zero axis and the
+
+ align:start position:0%
+So this is just our zero axis and the
+ 
+
+ align:start position:0%
+So this is just our zero axis and the
+delta here is zero everywhere except at
+
+ align:start position:0%
+delta here is zero everywhere except at
+ 
+
+ align:start position:0%
+delta here is zero everywhere except at
+two where we would represent it again
+
+ align:start position:0%
+two where we would represent it again
+ 
+
+ align:start position:0%
+two where we would represent it again
+with an arrow and amplitude one. Okay.
+
+ align:start position:0%
+with an arrow and amplitude one. Okay.
+ 
+
+ align:start position:0%
+with an arrow and amplitude one. Okay.
+So this delta is zero everywhere except
+
+ align:start position:0%
+So this delta is zero everywhere except
+ 
+
+ align:start position:0%
+So this delta is zero everywhere except
+at two where it would assign the value
+
+ align:start position:0%
+at two where it would assign the value
+ 
+
+ align:start position:0%
+at two where it would assign the value
+to the function next to it at the value
+
+ align:start position:0%
+to the function next to it at the value
+ 
+
+ align:start position:0%
+to the function next to it at the value
+t equals to two. So really this
+
+ align:start position:0%
+t equals to two. So really this
+ 
+
+ align:start position:0%
+t equals to two. So really this
+integration gives us
+
+ align:start position:0%
+integration gives us
+ 
+
+ align:start position:0%
+integration gives us
+just the value of this function at t =
+
+ align:start position:0%
+just the value of this function at t =
+ 
+
+ align:start position:0%
+just the value of this function at t =
+2. So 4 sin
+
+ align:start position:0%
+2. So 4 sin
+ 
+
+ align:start position:0%
+2. So 4 sin
+2 cos
+
+ align:start position:0%
+2 cos
+ 
+
+ align:start position:0%
+2 cos
+4 and here the key was that again this
+
+ align:start position:0%
+4 and here the key was that again this
+ 
+
+ align:start position:0%
+4 and here the key was that again this
+interval of integration from 0 minus to
+
+ align:start position:0%
+interval of integration from 0 minus to
+ 
+
+ align:start position:0%
+interval of integration from 0 minus to
+infinity and clearly includes the value
+
+ align:start position:0%
+infinity and clearly includes the value
+ 
+
+ align:start position:0%
+infinity and clearly includes the value
+at which delta function is non zero. So
+
+ align:start position:0%
+at which delta function is non zero. So
+ 
+
+ align:start position:0%
+at which delta function is non zero. So
+for the last
+
+ align:start position:0%
+for the last
+ 
+
+ align:start position:0%
+for the last
+one, we return to our first integral
+
+ align:start position:0%
+one, we return to our first integral
+ 
+
+ align:start position:0%
+one, we return to our first integral
+except that now we're changing the
+
+ align:start position:0%
+except that now we're changing the
+ 
+
+ align:start position:0%
+except that now we're changing the
+bounds of integration 0 plus to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity. So now if I do a
+
+ align:start position:0%
+infinity. So now if I do a
+ 
+
+ align:start position:0%
+infinity. So now if I do a
+representation of the delta function
+
+ align:start position:0%
+representation of the delta function
+ 
+
+ align:start position:0%
+representation of the delta function
+that we are dealing with. So delta
+
+ align:start position:0%
+that we are dealing with. So delta
+ 
+
+ align:start position:0%
+that we are dealing with. So delta
+centered at one and the interval of
+
+ align:start position:0%
+centered at one and the interval of
+ 
+
+ align:start position:0%
+centered at one and the interval of
+integration. We have an open interval.
+
+ align:start position:0%
+integration. We have an open interval.
+ 
+
+ align:start position:0%
+integration. We have an open interval.
+Now that does not include the value at
+
+ align:start position:0%
+Now that does not include the value at
+ 
+
+ align:start position:0%
+Now that does not include the value at
+which delta is not equal to zero. So
+
+ align:start position:0%
+which delta is not equal to zero. So
+ 
+
+ align:start position:0%
+which delta is not equal to zero. So
+everywhere this function would just be
+
+ align:start position:0%
+everywhere this function would just be
+ 
+
+ align:start position:0%
+everywhere this function would just be
+assigned its value at it just be
+
+ align:start position:0%
+assigned its value at it just be
+ 
+
+ align:start position:0%
+assigned its value at it just be
+multiplied by the function that is zero.
+
+ align:start position:0%
+multiplied by the function that is zero.
+ 
+
+ align:start position:0%
+multiplied by the function that is zero.
+And so basically it's like multiplying
+
+ align:start position:0%
+And so basically it's like multiplying
+ 
+
+ align:start position:0%
+And so basically it's like multiplying
+this function by zero and it just gives
+
+ align:start position:0%
+this function by zero and it just gives
+ 
+
+ align:start position:0%
+this function by zero and it just gives
+us zero. It's like the delta fell off of
+
+ align:start position:0%
+us zero. It's like the delta fell off of
+ 
+
+ align:start position:0%
+us zero. It's like the delta fell off of
+our interval of integration. So we're
+
+ align:start position:0%
+our interval of integration. So we're
+ 
+
+ align:start position:0%
+our interval of integration. So we're
+just left with a zero
+
+ align:start position:0%
+just left with a zero
+ 
+
+ align:start position:0%
+just left with a zero
+function. So let's move to the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part. The second part asks us to find
+
+ align:start position:0%
+part. The second part asks us to find
+ 
+
+ align:start position:0%
+part. The second part asks us to find
+the generalized
+
+ align:start position:0%
+the generalized
+ 
+
+ align:start position:0%
+the generalized
+derivative 2 f of t equals 3 u
+
+ align:start position:0%
+derivative 2 f of t equals 3 u
+ 
+
+ align:start position:0%
+derivative 2 f of t equals 3 u
+t minus 2 u t minus one.
+
+ align:start position:0%
+t minus 2 u t minus one.
+ 
+
+ align:start position:0%
+t minus 2 u t minus one.
+So just to remind you here of what the U
+
+ align:start position:0%
+So just to remind you here of what the U
+ 
+
+ align:start position:0%
+So just to remind you here of what the U
+of Ts are just want to
+
+ align:start position:0%
+of Ts are just want to
+ 
+
+ align:start position:0%
+of Ts are just want to
+sketch a few
+
+ align:start position:0%
+sketch a few
+ 
+
+ align:start position:0%
+sketch a few
+things. So first
+
+ align:start position:0%
+things. So first
+ 
+
+ align:start position:0%
+things. So first
+uft is just the step function that would
+
+ align:start position:0%
+uft is just the step function that would
+ 
+
+ align:start position:0%
+uft is just the step function that would
+be zero everywhere and would take the
+
+ align:start position:0%
+be zero everywhere and would take the
+ 
+
+ align:start position:0%
+be zero everywhere and would take the
+value one for t larger than zero. So
+
+ align:start position:0%
+value one for t larger than zero. So
+ 
+
+ align:start position:0%
+value one for t larger than zero. So
+this first part here would just be non
+
+ align:start position:0%
+this first part here would just be non
+ 
+
+ align:start position:0%
+this first part here would just be non
+zero for t larger than zero. Instead of
+
+ align:start position:0%
+zero for t larger than zero. Instead of
+ 
+
+ align:start position:0%
+zero for t larger than zero. Instead of
+being assigned value one, it's just be
+
+ align:start position:0%
+being assigned value one, it's just be
+ 
+
+ align:start position:0%
+being assigned value one, it's just be
+assigned value three because we're
+
+ align:start position:0%
+assigned value three because we're
+ 
+
+ align:start position:0%
+assigned value three because we're
+multiplying the u of t by three. So this
+
+ align:start position:0%
+multiplying the u of t by three. So this
+ 
+
+ align:start position:0%
+multiplying the u of t by three. So this
+first part would look like this. The
+
+ align:start position:0%
+first part would look like this. The
+ 
+
+ align:start position:0%
+first part would look like this. The
+second part here would be u shifted to t
+
+ align:start position:0%
+second part here would be u shifted to t
+ 
+
+ align:start position:0%
+second part here would be u shifted to t
+t t t t t t t t t t t t t t t t t t t t
+
+ align:start position:0%
+t t t t t t t t t t t t t t t t t t t t
+ 
+
+ align:start position:0%
+t t t t t t t t t t t t t t t t t t t t
+t t t t t t t t t t t t t t t t t t t t
+
+ align:start position:0%
+t t t t t t t t t t t t t t t t t t t t
+ 
+
+ align:start position:0%
+t t t t t t t t t t t t t t t t t t t t
+t by by minus one, which means that u is
+
+ align:start position:0%
+t by by minus one, which means that u is
+ 
+
+ align:start position:0%
+t by by minus one, which means that u is
+zero everywhere for t less than one. So
+
+ align:start position:0%
+zero everywhere for t less than one. So
+ 
+
+ align:start position:0%
+zero everywhere for t less than one. So
+it would have zero function here. So let
+
+ align:start position:0%
+it would have zero function here. So let
+ 
+
+ align:start position:0%
+it would have zero function here. So let
+me just do
+
+ align:start position:0%
+me just do
+ 
+
+ align:start position:0%
+me just do
+dots but it should be on the same axis
+
+ align:start position:0%
+dots but it should be on the same axis
+ 
+
+ align:start position:0%
+dots but it should be on the same axis
+and one for t larger than one. But here
+
+ align:start position:0%
+and one for t larger than one. But here
+ 
+
+ align:start position:0%
+and one for t larger than one. But here
+we're giving it multiplying it by factor
+
+ align:start position:0%
+we're giving it multiplying it by factor
+ 
+
+ align:start position:0%
+we're giving it multiplying it by factor
+minus two. So really what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have is another
+
+ align:start position:0%
+have is another
+ 
+
+ align:start position:0%
+have is another
+u function that is shifted
+
+ align:start position:0%
+u function that is shifted
+ 
+
+ align:start position:0%
+u function that is shifted
+down 2 minus 2. So the sum of these two
+
+ align:start position:0%
+down 2 minus 2. So the sum of these two
+ 
+
+ align:start position:0%
+down 2 minus 2. So the sum of these two
+contributions is zero for t negative
+
+ align:start position:0%
+contributions is zero for t negative
+ 
+
+ align:start position:0%
+contributions is zero for t negative
+takes the value three for t between 0
+
+ align:start position:0%
+takes the value three for t between 0
+ 
+
+ align:start position:0%
+takes the value three for t between 0
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one and a value one 3 minus 2
+
+ align:start position:0%
+one and a value one 3 minus 2
+ 
+
+ align:start position:0%
+one and a value one 3 minus 2
+for t larger than one. Okay, so clearly
+
+ align:start position:0%
+for t larger than one. Okay, so clearly
+ 
+
+ align:start position:0%
+for t larger than one. Okay, so clearly
+here we have discontinuities at t= to0
+
+ align:start position:0%
+here we have discontinuities at t= to0
+ 
+
+ align:start position:0%
+here we have discontinuities at t= to0
+and t= to 1. So let's just write down
+
+ align:start position:0%
+and t= to 1. So let's just write down
+ 
+
+ align:start position:0%
+and t= to 1. So let's just write down
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+derivative. The generalized derivative
+
+ align:start position:0%
+derivative. The generalized derivative
+ 
+
+ align:start position:0%
+derivative. The generalized derivative
+here would lead us first to compute the
+
+ align:start position:0%
+here would lead us first to compute the
+ 
+
+ align:start position:0%
+here would lead us first to compute the
+derivatives when where the function is
+
+ align:start position:0%
+derivatives when where the function is
+ 
+
+ align:start position:0%
+derivatives when where the function is
+continuous. So from minus infinity to
+
+ align:start position:0%
+continuous. So from minus infinity to
+ 
+
+ align:start position:0%
+continuous. So from minus infinity to
+zero, it's a constant. So derivative
+
+ align:start position:0%
+zero, it's a constant. So derivative
+ 
+
+ align:start position:0%
+zero, it's a constant. So derivative
+would be zero. Between 0 and one, it's
+
+ align:start position:0%
+would be zero. Between 0 and one, it's
+ 
+
+ align:start position:0%
+would be zero. Between 0 and one, it's
+constant. Derivative would be zero. And
+
+ align:start position:0%
+constant. Derivative would be zero. And
+ 
+
+ align:start position:0%
+constant. Derivative would be zero. And
+from one to infinity, it would also give
+
+ align:start position:0%
+from one to infinity, it would also give
+ 
+
+ align:start position:0%
+from one to infinity, it would also give
+us zero. So we would have a zero
+
+ align:start position:0%
+us zero. So we would have a zero
+ 
+
+ align:start position:0%
+us zero. So we would have a zero
+contribution from the the continuous
+
+ align:start position:0%
+contribution from the the continuous
+ 
+
+ align:start position:0%
+contribution from the the continuous
+part of the function if you wish but we
+
+ align:start position:0%
+part of the function if you wish but we
+ 
+
+ align:start position:0%
+part of the function if you wish but we
+still need to account for the
+
+ align:start position:0%
+still need to account for the
+ 
+
+ align:start position:0%
+still need to account for the
+discontinuities. So at zero we have a
+
+ align:start position:0%
+discontinuities. So at zero we have a
+ 
+
+ align:start position:0%
+discontinuities. So at zero we have a
+jump from zero to three and that we
+
+ align:start position:0%
+jump from zero to three and that we
+ 
+
+ align:start position:0%
+jump from zero to three and that we
+learned can be written down as a delta
+
+ align:start position:0%
+learned can be written down as a delta
+ 
+
+ align:start position:0%
+learned can be written down as a delta
+function of magnitude three centered at
+
+ align:start position:0%
+function of magnitude three centered at
+ 
+
+ align:start position:0%
+function of magnitude three centered at
+zero. After that we have another jump.
+
+ align:start position:0%
+zero. After that we have another jump.
+ 
+
+ align:start position:0%
+zero. After that we have another jump.
+Now it's from three to one. So it's a
+
+ align:start position:0%
+Now it's from three to one. So it's a
+ 
+
+ align:start position:0%
+Now it's from three to one. So it's a
+jump of minus2 amplitude centered at
+
+ align:start position:0%
+jump of minus2 amplitude centered at
+ 
+
+ align:start position:0%
+jump of minus2 amplitude centered at
+one. So here we can also do that with
+
+ align:start position:0%
+one. So here we can also do that with
+ 
+
+ align:start position:0%
+one. So here we can also do that with
+delta but we just need also to shift it
+
+ align:start position:0%
+delta but we just need also to shift it
+ 
+
+ align:start position:0%
+delta but we just need also to shift it
+by minus one to to show clearly that the
+
+ align:start position:0%
+by minus one to to show clearly that the
+ 
+
+ align:start position:0%
+by minus one to to show clearly that the
+jump occurs at one and multiply this by
+
+ align:start position:0%
+jump occurs at one and multiply this by
+ 
+
+ align:start position:0%
+jump occurs at one and multiply this by
+minus2 to show the amplitude of the jump
+
+ align:start position:0%
+minus2 to show the amplitude of the jump
+ 
+
+ align:start position:0%
+minus2 to show the amplitude of the jump
+down. Okay. So if we were now to
+
+ align:start position:0%
+down. Okay. So if we were now to
+ 
+
+ align:start position:0%
+down. Okay. So if we were now to
+represent it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fprime basically the regular part zero
+
+ align:start position:0%
+fprime basically the regular part zero
+ 
+
+ align:start position:0%
+fprime basically the regular part zero
+so there's nothing to to write down
+
+ align:start position:0%
+so there's nothing to to write down
+ 
+
+ align:start position:0%
+so there's nothing to to write down
+except just a zero function and the
+
+ align:start position:0%
+except just a zero function and the
+ 
+
+ align:start position:0%
+except just a zero function and the
+discontinuities that I'm just going to
+
+ align:start position:0%
+discontinuities that I'm just going to
+ 
+
+ align:start position:0%
+discontinuities that I'm just going to
+represent on the graph would be the
+
+ align:start position:0%
+represent on the graph would be the
+ 
+
+ align:start position:0%
+represent on the graph would be the
+delta function centered at zero of
+
+ align:start position:0%
+delta function centered at zero of
+ 
+
+ align:start position:0%
+delta function centered at zero of
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+3 and delta function centered around one
+
+ align:start position:0%
+3 and delta function centered around one
+ 
+
+ align:start position:0%
+3 and delta function centered around one
+of magnitude minus
+
+ align:start position:0%
+of magnitude minus
+ 
+
+ align:start position:0%
+of magnitude minus
+2 and the rest would just be the zero
+
+ align:start position:0%
+2 and the rest would just be the zero
+ 
+
+ align:start position:0%
+2 and the rest would just be the zero
+function. So that would be f
+
+ align:start position:0%
+function. So that would be f
+ 
+
+ align:start position:0%
+function. So that would be f
+prime that's f of
+
+ align:start position:0%
+prime that's f of
+ 
+
+ align:start position:0%
+prime that's f of
+t. So for the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one that we were given, it's a function
+
+ align:start position:0%
+one that we were given, it's a function
+ 
+
+ align:start position:0%
+one that we were given, it's a function
+f of
+
+ align:start position:0%
+f of
+ 
+
+ align:start position:0%
+f of
+t that takes the value t² for t negative
+
+ align:start position:0%
+t that takes the value t² for t negative
+ 
+
+ align:start position:0%
+t that takes the value t² for t negative
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+exponential minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t for t positive.
+
+ align:start position:0%
+t for t positive.
+ 
+
+ align:start position:0%
+t for t positive.
+So quick sketch here tells that this
+
+ align:start position:0%
+So quick sketch here tells that this
+ 
+
+ align:start position:0%
+So quick sketch here tells that this
+function looks like this an exponential
+
+ align:start position:0%
+function looks like this an exponential
+ 
+
+ align:start position:0%
+function looks like this an exponential
+minus t for t positive. Okay, taking a
+
+ align:start position:0%
+minus t for t positive. Okay, taking a
+ 
+
+ align:start position:0%
+minus t for t positive. Okay, taking a
+value here one. So clearly there is a
+
+ align:start position:0%
+value here one. So clearly there is a
+ 
+
+ align:start position:0%
+value here one. So clearly there is a
+jump
+
+ align:start position:0%
+jump
+ 
+
+ align:start position:0%
+jump
+here this
+
+ align:start position:0%
+here this
+ 
+
+ align:start position:0%
+here this
+continuity. So how do we go about
+
+ align:start position:0%
+continuity. So how do we go about
+ 
+
+ align:start position:0%
+continuity. So how do we go about
+computing this generalized derivative?
+
+ align:start position:0%
+computing this generalized derivative?
+ 
+
+ align:start position:0%
+computing this generalized derivative?
+So let's look again at the continuous
+
+ align:start position:0%
+So let's look again at the continuous
+ 
+
+ align:start position:0%
+So let's look again at the continuous
+parts. So from minus infinity to zero,
+
+ align:start position:0%
+parts. So from minus infinity to zero,
+ 
+
+ align:start position:0%
+parts. So from minus infinity to zero,
+we're dealing with just a t square. So
+
+ align:start position:0%
+we're dealing with just a t square. So
+ 
+
+ align:start position:0%
+we're dealing with just a t square. So
+the derivative is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2t. For t between 0 and infinity, we're
+
+ align:start position:0%
+2t. For t between 0 and infinity, we're
+ 
+
+ align:start position:0%
+2t. For t between 0 and infinity, we're
+just dealing with exponential minus t.
+
+ align:start position:0%
+just dealing with exponential minus t.
+ 
+
+ align:start position:0%
+just dealing with exponential minus t.
+So that's minus exponential minus
+
+ align:start position:0%
+So that's minus exponential minus
+ 
+
+ align:start position:0%
+So that's minus exponential minus
+t. But we need to account for the
+
+ align:start position:0%
+t. But we need to account for the
+ 
+
+ align:start position:0%
+t. But we need to account for the
+discontinuity, the jump of amplitude one
+
+ align:start position:0%
+discontinuity, the jump of amplitude one
+ 
+
+ align:start position:0%
+discontinuity, the jump of amplitude one
+at zero. So as we saw before, this can
+
+ align:start position:0%
+at zero. So as we saw before, this can
+ 
+
+ align:start position:0%
+at zero. So as we saw before, this can
+just be
+
+ align:start position:0%
+just be
+ 
+
+ align:start position:0%
+just be
+modeled with a delta function. And if we
+
+ align:start position:0%
+modeled with a delta function. And if we
+ 
+
+ align:start position:0%
+modeled with a delta function. And if we
+were to represent this function, then we
+
+ align:start position:0%
+were to represent this function, then we
+ 
+
+ align:start position:0%
+were to represent this function, then we
+would just
+
+ align:start position:0%
+would just
+ 
+
+ align:start position:0%
+would just
+need to add a delta
+
+ align:start position:0%
+need to add a delta
+ 
+
+ align:start position:0%
+need to add a delta
+function of magnitude one here and then
+
+ align:start position:0%
+function of magnitude one here and then
+ 
+
+ align:start position:0%
+function of magnitude one here and then
+just sketch 2t. So for
+
+ align:start position:0%
+just sketch 2t. So for
+ 
+
+ align:start position:0%
+just sketch 2t. So for
+example and then minus exponential minus
+
+ align:start position:0%
+example and then minus exponential minus
+ 
+
+ align:start position:0%
+example and then minus exponential minus
+2t that would give us something like
+
+ align:start position:0%
+2t that would give us something like
+ 
+
+ align:start position:0%
+2t that would give us something like
+that. And that ends the problem for
+
+ align:start position:0%
+that. And that ends the problem for
+ 
+
+ align:start position:0%
+that. And that ends the problem for
+today. And the key points here were just
+
+ align:start position:0%
+today. And the key points here were just
+ 
+
+ align:start position:0%
+today. And the key points here were just
+to learn how to manipulate the the step
+
+ align:start position:0%
+to learn how to manipulate the the step
+ 
+
+ align:start position:0%
+to learn how to manipulate the the step
+function and how to use the delta
+
+ align:start position:0%
+function and how to use the delta
+ 
+
+ align:start position:0%
+function and how to use the delta
+function when you compute your integrals
+
+ align:start position:0%
+function when you compute your integrals
+ 
+
+ align:start position:0%
+function when you compute your integrals
+and be careful with the bounds of
+
+ align:start position:0%
+and be careful with the bounds of
+ 
+
+ align:start position:0%
+and be careful with the bounds of
+integration.
\ No newline at end of file
diff --git a/q785KV5ZIN0.txt b/q785KV5ZIN0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..113928ce1afa343fef8ae09fac41b1d1d0dbe29e
--- /dev/null
+++ b/q785KV5ZIN0.txt
@@ -0,0 +1,1011 @@
+align:start position:0%
+ 
+Now we'd like to talk about angular
+
+ align:start position:0%
+Now we'd like to talk about angular
+ 
+
+ align:start position:0%
+Now we'd like to talk about angular
+velocity. So for a particle traveling in
+
+ align:start position:0%
+velocity. So for a particle traveling in
+ 
+
+ align:start position:0%
+velocity. So for a particle traveling in
+a circle, we've seen that the velocity
+
+ align:start position:0%
+a circle, we've seen that the velocity
+ 
+
+ align:start position:0%
+a circle, we've seen that the velocity
+can be written as r d theta
+
+ align:start position:0%
+can be written as r d theta
+ 
+
+ align:start position:0%
+can be written as r d theta
+dt in the theta hat
+
+ align:start position:0%
+dt in the theta hat
+ 
+
+ align:start position:0%
+dt in the theta hat
+direction. And we've also seen that d
+
+ align:start position:0%
+direction. And we've also seen that d
+ 
+
+ align:start position:0%
+direction. And we've also seen that d
+theta dt can be positive in which case
+
+ align:start position:0%
+theta dt can be positive in which case
+ 
+
+ align:start position:0%
+theta dt can be positive in which case
+theta is increasing. And so the particle
+
+ align:start position:0%
+theta is increasing. And so the particle
+ 
+
+ align:start position:0%
+theta is increasing. And so the particle
+is traveling around the circle in this
+
+ align:start position:0%
+is traveling around the circle in this
+ 
+
+ align:start position:0%
+is traveling around the circle in this
+direction. You can call that the
+
+ align:start position:0%
+direction. You can call that the
+ 
+
+ align:start position:0%
+direction. You can call that the
+counterclockwise direction. We've also
+
+ align:start position:0%
+counterclockwise direction. We've also
+ 
+
+ align:start position:0%
+counterclockwise direction. We've also
+seen that d theta dt can be negative in
+
+ align:start position:0%
+seen that d theta dt can be negative in
+ 
+
+ align:start position:0%
+seen that d theta dt can be negative in
+which case the angle is decreasing. So
+
+ align:start position:0%
+which case the angle is decreasing. So
+ 
+
+ align:start position:0%
+which case the angle is decreasing. So
+the particle is traveling around the
+
+ align:start position:0%
+the particle is traveling around the
+ 
+
+ align:start position:0%
+the particle is traveling around the
+circle in this direction which we could
+
+ align:start position:0%
+circle in this direction which we could
+ 
+
+ align:start position:0%
+circle in this direction which we could
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+clockwise. Let's now look at rotation in
+
+ align:start position:0%
+clockwise. Let's now look at rotation in
+ 
+
+ align:start position:0%
+clockwise. Let's now look at rotation in
+an arbitrary plane. So if I have a plane
+
+ align:start position:0%
+an arbitrary plane. So if I have a plane
+ 
+
+ align:start position:0%
+an arbitrary plane. So if I have a plane
+like this and I have some particle
+
+ align:start position:0%
+like this and I have some particle
+ 
+
+ align:start position:0%
+like this and I have some particle
+traveling in a circle like
+
+ align:start position:0%
+traveling in a circle like
+ 
+
+ align:start position:0%
+traveling in a circle like
+this and I have some observer that's
+
+ align:start position:0%
+this and I have some observer that's
+ 
+
+ align:start position:0%
+this and I have some observer that's
+above the plane looking down on this
+
+ align:start position:0%
+above the plane looking down on this
+ 
+
+ align:start position:0%
+above the plane looking down on this
+plane then it will see the uh this
+
+ align:start position:0%
+plane then it will see the uh this
+ 
+
+ align:start position:0%
+plane then it will see the uh this
+rotation as being in the
+
+ align:start position:0%
+rotation as being in the
+ 
+
+ align:start position:0%
+rotation as being in the
+counterclockwise direction. Whereas if I
+
+ align:start position:0%
+counterclockwise direction. Whereas if I
+ 
+
+ align:start position:0%
+counterclockwise direction. Whereas if I
+have another observer down
+
+ align:start position:0%
+have another observer down
+ 
+
+ align:start position:0%
+have another observer down
+here and they're looking up at this
+
+ align:start position:0%
+here and they're looking up at this
+ 
+
+ align:start position:0%
+here and they're looking up at this
+plane, they'll see the the motion as
+
+ align:start position:0%
+plane, they'll see the the motion as
+ 
+
+ align:start position:0%
+plane, they'll see the the motion as
+being clockwise. And so you can see we
+
+ align:start position:0%
+being clockwise. And so you can see we
+ 
+
+ align:start position:0%
+being clockwise. And so you can see we
+have a need for the more formal
+
+ align:start position:0%
+have a need for the more formal
+ 
+
+ align:start position:0%
+have a need for the more formal
+definition uh for the rotation of this.
+
+ align:start position:0%
+definition uh for the rotation of this.
+ 
+
+ align:start position:0%
+definition uh for the rotation of this.
+And so what we're going to do is use the
+
+ align:start position:0%
+And so what we're going to do is use the
+ 
+
+ align:start position:0%
+And so what we're going to do is use the
+right-h hand rule to define a direction
+
+ align:start position:0%
+right-h hand rule to define a direction
+ 
+
+ align:start position:0%
+right-h hand rule to define a direction
+that tells you both the direction. It
+
+ align:start position:0%
+that tells you both the direction. It
+ 
+
+ align:start position:0%
+that tells you both the direction. It
+defines the plane and it also tells you
+
+ align:start position:0%
+defines the plane and it also tells you
+ 
+
+ align:start position:0%
+defines the plane and it also tells you
+what the positive direction of rotation
+
+ align:start position:0%
+what the positive direction of rotation
+ 
+
+ align:start position:0%
+what the positive direction of rotation
+is for that plane. So the way we'll do
+
+ align:start position:0%
+is for that plane. So the way we'll do
+ 
+
+ align:start position:0%
+is for that plane. So the way we'll do
+this right hand rule is we'll take our
+
+ align:start position:0%
+this right hand rule is we'll take our
+ 
+
+ align:start position:0%
+this right hand rule is we'll take our
+right hand, we'll curl our fingers in
+
+ align:start position:0%
+right hand, we'll curl our fingers in
+ 
+
+ align:start position:0%
+right hand, we'll curl our fingers in
+the direction of the rotation and our
+
+ align:start position:0%
+the direction of the rotation and our
+ 
+
+ align:start position:0%
+the direction of the rotation and our
+thumb will point in the direction of
+
+ align:start position:0%
+thumb will point in the direction of
+ 
+
+ align:start position:0%
+thumb will point in the direction of
+that positive that the the positive
+
+ align:start position:0%
+that positive that the the positive
+ 
+
+ align:start position:0%
+that positive that the the positive
+direction that we're defining. So in
+
+ align:start position:0%
+direction that we're defining. So in
+ 
+
+ align:start position:0%
+direction that we're defining. So in
+this case I'm going to have an arrow
+
+ align:start position:0%
+this case I'm going to have an arrow
+ 
+
+ align:start position:0%
+this case I'm going to have an arrow
+like this. I'll call it n hat to
+
+ align:start position:0%
+like this. I'll call it n hat to
+ 
+
+ align:start position:0%
+like this. I'll call it n hat to
+indicate that it's the normal unit
+
+ align:start position:0%
+indicate that it's the normal unit
+ 
+
+ align:start position:0%
+indicate that it's the normal unit
+vector to that plane.
+
+ align:start position:0%
+vector to that plane.
+ 
+
+ align:start position:0%
+vector to that plane.
+All right, let's come back to this
+
+ align:start position:0%
+All right, let's come back to this
+ 
+
+ align:start position:0%
+All right, let's come back to this
+example now. Uh where the plane of the
+
+ align:start position:0%
+example now. Uh where the plane of the
+ 
+
+ align:start position:0%
+example now. Uh where the plane of the
+motion is this plane of the board. Uh
+
+ align:start position:0%
+motion is this plane of the board. Uh
+ 
+
+ align:start position:0%
+motion is this plane of the board. Uh
+and let's look at our two cases again.
+
+ align:start position:0%
+and let's look at our two cases again.
+ 
+
+ align:start position:0%
+and let's look at our two cases again.
+So in the case of d theta dt positive,
+
+ align:start position:0%
+So in the case of d theta dt positive,
+ 
+
+ align:start position:0%
+So in the case of d theta dt positive,
+our circle looks something like
+
+ align:start position:0%
+our circle looks something like
+ 
+
+ align:start position:0%
+our circle looks something like
+this. Um and you can see that if I use
+
+ align:start position:0%
+this. Um and you can see that if I use
+ 
+
+ align:start position:0%
+this. Um and you can see that if I use
+my right- hand
+
+ align:start position:0%
+my right- hand
+ 
+
+ align:start position:0%
+my right- hand
+rule, the plane the um the vector that
+
+ align:start position:0%
+rule, the plane the um the vector that
+ 
+
+ align:start position:0%
+rule, the plane the um the vector that
+I've defined is out of the board. And
+
+ align:start position:0%
+I've defined is out of the board. And
+ 
+
+ align:start position:0%
+I've defined is out of the board. And
+I'm going to use this symbol a circle
+
+ align:start position:0%
+I'm going to use this symbol a circle
+ 
+
+ align:start position:0%
+I'm going to use this symbol a circle
+with a dot to indicate this direction of
+
+ align:start position:0%
+with a dot to indicate this direction of
+ 
+
+ align:start position:0%
+with a dot to indicate this direction of
+out of the
+
+ align:start position:0%
+out of the
+ 
+
+ align:start position:0%
+out of the
+board. In our other case for d theta dt
+
+ align:start position:0%
+board. In our other case for d theta dt
+ 
+
+ align:start position:0%
+board. In our other case for d theta dt
+uh less than zero, our particle is
+
+ align:start position:0%
+uh less than zero, our particle is
+ 
+
+ align:start position:0%
+uh less than zero, our particle is
+traveling in this
+
+ align:start position:0%
+traveling in this
+ 
+
+ align:start position:0%
+traveling in this
+direction. And so you can see by my
+
+ align:start position:0%
+direction. And so you can see by my
+ 
+
+ align:start position:0%
+direction. And so you can see by my
+right-h hand rule that now the partic
+
+ align:start position:0%
+right-h hand rule that now the partic
+ 
+
+ align:start position:0%
+right-h hand rule that now the partic
+the that direction that I've defined is
+
+ align:start position:0%
+the that direction that I've defined is
+ 
+
+ align:start position:0%
+the that direction that I've defined is
+into the board. And for that I'm going
+
+ align:start position:0%
+into the board. And for that I'm going
+ 
+
+ align:start position:0%
+into the board. And for that I'm going
+to draw this as an x in a circle. So
+
+ align:start position:0%
+to draw this as an x in a circle. So
+ 
+
+ align:start position:0%
+to draw this as an x in a circle. So
+these are symbols that you'll see
+
+ align:start position:0%
+these are symbols that you'll see
+ 
+
+ align:start position:0%
+these are symbols that you'll see
+throughout the rest of the course. the
+
+ align:start position:0%
+throughout the rest of the course. the
+ 
+
+ align:start position:0%
+throughout the rest of the course. the
+in the uh out of the board and into the
+
+ align:start position:0%
+in the uh out of the board and into the
+ 
+
+ align:start position:0%
+in the uh out of the board and into the
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+symbols. Um and so now let's look back
+
+ align:start position:0%
+symbols. Um and so now let's look back
+ 
+
+ align:start position:0%
+symbols. Um and so now let's look back
+at our coordinate system that we've
+
+ align:start position:0%
+at our coordinate system that we've
+ 
+
+ align:start position:0%
+at our coordinate system that we've
+defined. We have an r hat direction and
+
+ align:start position:0%
+defined. We have an r hat direction and
+ 
+
+ align:start position:0%
+defined. We have an r hat direction and
+a theta hat direction. And in this
+
+ align:start position:0%
+a theta hat direction. And in this
+ 
+
+ align:start position:0%
+a theta hat direction. And in this
+coordinate system there's a third d
+
+ align:start position:0%
+coordinate system there's a third d
+ 
+
+ align:start position:0%
+coordinate system there's a third d
+direction that's defined which is the
+
+ align:start position:0%
+direction that's defined which is the
+ 
+
+ align:start position:0%
+direction that's defined which is the
+khat direction which you can see is out
+
+ align:start position:0%
+khat direction which you can see is out
+ 
+
+ align:start position:0%
+khat direction which you can see is out
+of the board. And so um now I'm going to
+
+ align:start position:0%
+of the board. And so um now I'm going to
+ 
+
+ align:start position:0%
+of the board. And so um now I'm going to
+define what we actually call the angular
+
+ align:start position:0%
+define what we actually call the angular
+ 
+
+ align:start position:0%
+define what we actually call the angular
+velocity as omega and I'm going to write
+
+ align:start position:0%
+velocity as omega and I'm going to write
+ 
+
+ align:start position:0%
+velocity as omega and I'm going to write
+that as d theta
+
+ align:start position:0%
+that as d theta
+ 
+
+ align:start position:0%
+that as d theta
+dt now in the k hat direction in this
+
+ align:start position:0%
+dt now in the k hat direction in this
+ 
+
+ align:start position:0%
+dt now in the k hat direction in this
+case. Uh it could be in an arbitrary
+
+ align:start position:0%
+case. Uh it could be in an arbitrary
+ 
+
+ align:start position:0%
+case. Uh it could be in an arbitrary
+nhat direction depending on what your
+
+ align:start position:0%
+nhat direction depending on what your
+ 
+
+ align:start position:0%
+nhat direction depending on what your
+plane of motion is. In this case I'm
+
+ align:start position:0%
+plane of motion is. In this case I'm
+ 
+
+ align:start position:0%
+plane of motion is. In this case I'm
+going to call it in the khat direction.
+
+ align:start position:0%
+going to call it in the khat direction.
+ 
+
+ align:start position:0%
+going to call it in the khat direction.
+And now you can see that um these signs
+
+ align:start position:0%
+And now you can see that um these signs
+ 
+
+ align:start position:0%
+And now you can see that um these signs
+are going to line up with uh these
+
+ align:start position:0%
+are going to line up with uh these
+ 
+
+ align:start position:0%
+are going to line up with uh these
+directions. So omega as d theta dt khat
+
+ align:start position:0%
+directions. So omega as d theta dt khat
+ 
+
+ align:start position:0%
+directions. So omega as d theta dt khat
+when d theta dt is positive khat is in
+
+ align:start position:0%
+when d theta dt is positive khat is in
+ 
+
+ align:start position:0%
+when d theta dt is positive khat is in
+the same direction as this unit normal
+
+ align:start position:0%
+the same direction as this unit normal
+ 
+
+ align:start position:0%
+the same direction as this unit normal
+that we've defined that defines both the
+
+ align:start position:0%
+that we've defined that defines both the
+ 
+
+ align:start position:0%
+that we've defined that defines both the
+plane of the motion and the direction of
+
+ align:start position:0%
+plane of the motion and the direction of
+ 
+
+ align:start position:0%
+plane of the motion and the direction of
+the motion and when d theta dt is
+
+ align:start position:0%
+the motion and when d theta dt is
+ 
+
+ align:start position:0%
+the motion and when d theta dt is
+negative I have that omega is in the
+
+ align:start position:0%
+negative I have that omega is in the
+ 
+
+ align:start position:0%
+negative I have that omega is in the
+negative khat direction which is exactly
+
+ align:start position:0%
+negative khat direction which is exactly
+ 
+
+ align:start position:0%
+negative khat direction which is exactly
+this direction here that we've defined
+
+ align:start position:0%
+this direction here that we've defined
+ 
+
+ align:start position:0%
+this direction here that we've defined
+as being the motion for this plane and
+
+ align:start position:0%
+as being the motion for this plane and
+ 
+
+ align:start position:0%
+as being the motion for this plane and
+so this is how we define angular
+
+ align:start position:0%
+so this is how we define angular
+ 
+
+ align:start position:0%
+so this is how we define angular
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+So we can define the comp d theta dt to
+
+ align:start position:0%
+So we can define the comp d theta dt to
+ 
+
+ align:start position:0%
+So we can define the comp d theta dt to
+be the component of the angular velocity
+
+ align:start position:0%
+be the component of the angular velocity
+ 
+
+ align:start position:0%
+be the component of the angular velocity
+omega z because it's in the khat
+
+ align:start position:0%
+omega z because it's in the khat
+ 
+
+ align:start position:0%
+omega z because it's in the khat
+direction and we can also define the
+
+ align:start position:0%
+direction and we can also define the
+ 
+
+ align:start position:0%
+direction and we can also define the
+angular speed which we write as just
+
+ align:start position:0%
+angular speed which we write as just
+ 
+
+ align:start position:0%
+angular speed which we write as just
+omega as being the absolute value of
+
+ align:start position:0%
+omega as being the absolute value of
+ 
+
+ align:start position:0%
+omega as being the absolute value of
+this angular velocity omega. So that is
+
+ align:start position:0%
+this angular velocity omega. So that is
+ 
+
+ align:start position:0%
+this angular velocity omega. So that is
+in other words it's just the absolute
+
+ align:start position:0%
+in other words it's just the absolute
+ 
+
+ align:start position:0%
+in other words it's just the absolute
+value of d theta
+
+ align:start position:0%
+value of d theta
+ 
+
+ align:start position:0%
+value of d theta
+dt. So when a particle is undergoing
+
+ align:start position:0%
+dt. So when a particle is undergoing
+ 
+
+ align:start position:0%
+dt. So when a particle is undergoing
+circular motion, it has a velocity that
+
+ align:start position:0%
+circular motion, it has a velocity that
+ 
+
+ align:start position:0%
+circular motion, it has a velocity that
+you can describe which is the tangential
+
+ align:start position:0%
+you can describe which is the tangential
+ 
+
+ align:start position:0%
+you can describe which is the tangential
+uh motion around the circle and it's
+
+ align:start position:0%
+uh motion around the circle and it's
+ 
+
+ align:start position:0%
+uh motion around the circle and it's
+also it also has an angular velocity
+
+ align:start position:0%
+also it also has an angular velocity
+ 
+
+ align:start position:0%
+also it also has an angular velocity
+which we define as being in a direction
+
+ align:start position:0%
+which we define as being in a direction
+ 
+
+ align:start position:0%
+which we define as being in a direction
+that's perpendicular to that direction
+
+ align:start position:0%
+that's perpendicular to that direction
+ 
+
+ align:start position:0%
+that's perpendicular to that direction
+of uh rotation and it's defined by the
+
+ align:start position:0%
+of uh rotation and it's defined by the
+ 
+
+ align:start position:0%
+of uh rotation and it's defined by the
+right- hand rule. And now that we have
+
+ align:start position:0%
+right- hand rule. And now that we have
+ 
+
+ align:start position:0%
+right- hand rule. And now that we have
+defined this omega z the angular comp
+
+ align:start position:0%
+defined this omega z the angular comp
+ 
+
+ align:start position:0%
+defined this omega z the angular comp
+the component of the angular velocity we
+
+ align:start position:0%
+the component of the angular velocity we
+ 
+
+ align:start position:0%
+the component of the angular velocity we
+can rewrite the velocity as just being
+
+ align:start position:0%
+can rewrite the velocity as just being
+ 
+
+ align:start position:0%
+can rewrite the velocity as just being
+equal to r * omega z still in that theta
+
+ align:start position:0%
+equal to r * omega z still in that theta
+ 
+
+ align:start position:0%
+equal to r * omega z still in that theta
+hat direction. And so this is another
+
+ align:start position:0%
+hat direction. And so this is another
+ 
+
+ align:start position:0%
+hat direction. And so this is another
+way that we can write the velocity and
+
+ align:start position:0%
+way that we can write the velocity and
+ 
+
+ align:start position:0%
+way that we can write the velocity and
+connect it back to the angular velocity.
\ No newline at end of file
diff --git a/qM-X1L3Sjsc.txt b/qM-X1L3Sjsc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dceaa4652f875af650fcba9fe0274084013b0046
--- /dev/null
+++ b/qM-X1L3Sjsc.txt
@@ -0,0 +1,7971 @@
+align:start position:0%
+ 
+Hi, my name is Bob Metaf and I'm here
+
+ align:start position:0%
+Hi, my name is Bob Metaf and I'm here
+ 
+
+ align:start position:0%
+Hi, my name is Bob Metaf and I'm here
+today to talk about the next big thing,
+
+ align:start position:0%
+today to talk about the next big thing,
+ 
+
+ align:start position:0%
+today to talk about the next big thing,
+the video
+
+ align:start position:0%
+the video
+ 
+
+ align:start position:0%
+the video
+internet. Uh, now I'm not sure what kind
+
+ align:start position:0%
+internet. Uh, now I'm not sure what kind
+ 
+
+ align:start position:0%
+internet. Uh, now I'm not sure what kind
+of video we're talking about and I'm not
+
+ align:start position:0%
+of video we're talking about and I'm not
+ 
+
+ align:start position:0%
+of video we're talking about and I'm not
+sure if it'll actually be the internet
+
+ align:start position:0%
+sure if it'll actually be the internet
+ 
+
+ align:start position:0%
+sure if it'll actually be the internet
+when we're all done, but nonetheless,
+
+ align:start position:0%
+when we're all done, but nonetheless,
+ 
+
+ align:start position:0%
+when we're all done, but nonetheless,
+I'm going to call this the next big
+
+ align:start position:0%
+I'm going to call this the next big
+ 
+
+ align:start position:0%
+I'm going to call this the next big
+thing, the video internet. And one of
+
+ align:start position:0%
+thing, the video internet. And one of
+ 
+
+ align:start position:0%
+thing, the video internet. And one of
+the questions which I hope to get to in
+
+ align:start position:0%
+the questions which I hope to get to in
+ 
+
+ align:start position:0%
+the questions which I hope to get to in
+a few minutes is whether in driving the
+
+ align:start position:0%
+a few minutes is whether in driving the
+ 
+
+ align:start position:0%
+a few minutes is whether in driving the
+proliferation of the video internet uh
+
+ align:start position:0%
+proliferation of the video internet uh
+ 
+
+ align:start position:0%
+proliferation of the video internet uh
+whether that'll be driven by
+
+ align:start position:0%
+whether that'll be driven by
+ 
+
+ align:start position:0%
+whether that'll be driven by
+communication or content or
+
+ align:start position:0%
+communication or content or
+ 
+
+ align:start position:0%
+communication or content or
+commerce. Let's begin with a short
+
+ align:start position:0%
+commerce. Let's begin with a short
+ 
+
+ align:start position:0%
+commerce. Let's begin with a short
+history of
+
+ align:start position:0%
+history of
+ 
+
+ align:start position:0%
+history of
+networking. In the beginning there was
+
+ align:start position:0%
+networking. In the beginning there was
+ 
+
+ align:start position:0%
+networking. In the beginning there was
+mail the US mail say and it's still with
+
+ align:start position:0%
+mail the US mail say and it's still with
+ 
+
+ align:start position:0%
+mail the US mail say and it's still with
+us. And what came later in the 19th
+
+ align:start position:0%
+us. And what came later in the 19th
+ 
+
+ align:start position:0%
+us. And what came later in the 19th
+century was uh TX the uh carrying of
+
+ align:start position:0%
+century was uh TX the uh carrying of
+ 
+
+ align:start position:0%
+century was uh TX the uh carrying of
+mail certain forms of mail
+
+ align:start position:0%
+mail certain forms of mail
+ 
+
+ align:start position:0%
+mail certain forms of mail
+electronically through the TX network.
+
+ align:start position:0%
+electronically through the TX network.
+ 
+
+ align:start position:0%
+electronically through the TX network.
+And then TX was generally overtaken by a
+
+ align:start position:0%
+And then TX was generally overtaken by a
+ 
+
+ align:start position:0%
+And then TX was generally overtaken by a
+new electronic network called the
+
+ align:start position:0%
+new electronic network called the
+ 
+
+ align:start position:0%
+new electronic network called the
+telephone network which of course is
+
+ align:start position:0%
+telephone network which of course is
+ 
+
+ align:start position:0%
+telephone network which of course is
+still with us. uh the telephone being uh
+
+ align:start position:0%
+still with us. uh the telephone being uh
+ 
+
+ align:start position:0%
+still with us. uh the telephone being uh
+as you well know a two-way communication
+
+ align:start position:0%
+as you well know a two-way communication
+ 
+
+ align:start position:0%
+as you well know a two-way communication
+system generally paid for by uh
+
+ align:start position:0%
+system generally paid for by uh
+ 
+
+ align:start position:0%
+system generally paid for by uh
+subscriptions and its principal use
+
+ align:start position:0%
+subscriptions and its principal use
+ 
+
+ align:start position:0%
+subscriptions and its principal use
+being communication among people. The
+
+ align:start position:0%
+being communication among people. The
+ 
+
+ align:start position:0%
+being communication among people. The
+next network after that was a television
+
+ align:start position:0%
+next network after that was a television
+ 
+
+ align:start position:0%
+next network after that was a television
+network which uh arose during my
+
+ align:start position:0%
+network which uh arose during my
+ 
+
+ align:start position:0%
+network which uh arose during my
+lifetime. Uh and television as you know
+
+ align:start position:0%
+lifetime. Uh and television as you know
+ 
+
+ align:start position:0%
+lifetime. Uh and television as you know
+is uh one way and generally
+
+ align:start position:0%
+is uh one way and generally
+ 
+
+ align:start position:0%
+is uh one way and generally
+entertainmentoriented and paid for
+
+ align:start position:0%
+entertainmentoriented and paid for
+ 
+
+ align:start position:0%
+entertainmentoriented and paid for
+through advertising although
+
+ align:start position:0%
+through advertising although
+ 
+
+ align:start position:0%
+through advertising although
+increasingly by subscriptions now with
+
+ align:start position:0%
+increasingly by subscriptions now with
+ 
+
+ align:start position:0%
+increasingly by subscriptions now with
+cable television. And finally the
+
+ align:start position:0%
+cable television. And finally the
+ 
+
+ align:start position:0%
+cable television. And finally the
+current big thing the internet which uh
+
+ align:start position:0%
+current big thing the internet which uh
+ 
+
+ align:start position:0%
+current big thing the internet which uh
+came to us starting in
+
+ align:start position:0%
+came to us starting in
+ 
+
+ align:start position:0%
+came to us starting in
+1969. Now the internet itself has been a
+
+ align:start position:0%
+1969. Now the internet itself has been a
+ 
+
+ align:start position:0%
+1969. Now the internet itself has been a
+series of applications since 1969.
+
+ align:start position:0%
+series of applications since 1969.
+ 
+
+ align:start position:0%
+series of applications since 1969.
+The people who first started building
+
+ align:start position:0%
+The people who first started building
+ 
+
+ align:start position:0%
+The people who first started building
+the internet uh thought that it would be
+
+ align:start position:0%
+the internet uh thought that it would be
+ 
+
+ align:start position:0%
+the internet uh thought that it would be
+used uh with dumb terminals logging into
+
+ align:start position:0%
+used uh with dumb terminals logging into
+ 
+
+ align:start position:0%
+used uh with dumb terminals logging into
+remote computers across the country. And
+
+ align:start position:0%
+remote computers across the country. And
+ 
+
+ align:start position:0%
+remote computers across the country. And
+that was the first application built to
+
+ align:start position:0%
+that was the first application built to
+ 
+
+ align:start position:0%
+that was the first application built to
+run on the early internet. Uh and
+
+ align:start position:0%
+run on the early internet. Uh and
+ 
+
+ align:start position:0%
+run on the early internet. Uh and
+shortly after that it was realized that
+
+ align:start position:0%
+shortly after that it was realized that
+ 
+
+ align:start position:0%
+shortly after that it was realized that
+in order to run remote computer
+
+ align:start position:0%
+in order to run remote computer
+ 
+
+ align:start position:0%
+in order to run remote computer
+applications at large computers across
+
+ align:start position:0%
+applications at large computers across
+ 
+
+ align:start position:0%
+applications at large computers across
+the country, you'd have to transfer your
+
+ align:start position:0%
+the country, you'd have to transfer your
+ 
+
+ align:start position:0%
+the country, you'd have to transfer your
+data there. You'd have to transfer
+
+ align:start position:0%
+data there. You'd have to transfer
+ 
+
+ align:start position:0%
+data there. You'd have to transfer
+files. So the file transfer protocol
+
+ align:start position:0%
+files. So the file transfer protocol
+ 
+
+ align:start position:0%
+files. So the file transfer protocol
+arose. And then shortly after that a
+
+ align:start position:0%
+arose. And then shortly after that a
+ 
+
+ align:start position:0%
+arose. And then shortly after that a
+certain kind of file became very
+
+ align:start position:0%
+certain kind of file became very
+ 
+
+ align:start position:0%
+certain kind of file became very
+important and that file was the
+
+ align:start position:0%
+important and that file was the
+ 
+
+ align:start position:0%
+important and that file was the
+electronic message. And so suddenly in
+
+ align:start position:0%
+electronic message. And so suddenly in
+ 
+
+ align:start position:0%
+electronic message. And so suddenly in
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+1971 we had email and email was pretty
+
+ align:start position:0%
+1971 we had email and email was pretty
+ 
+
+ align:start position:0%
+1971 we had email and email was pretty
+much the major use of the internet for
+
+ align:start position:0%
+much the major use of the internet for
+ 
+
+ align:start position:0%
+much the major use of the internet for
+the next 20 years. And dur now during
+
+ align:start position:0%
+the next 20 years. And dur now during
+ 
+
+ align:start position:0%
+the next 20 years. And dur now during
+that time uh a new kind of structure
+
+ align:start position:0%
+that time uh a new kind of structure
+ 
+
+ align:start position:0%
+that time uh a new kind of structure
+arose called news groups. That is where
+
+ align:start position:0%
+arose called news groups. That is where
+ 
+
+ align:start position:0%
+arose called news groups. That is where
+computers on the net would be used to
+
+ align:start position:0%
+computers on the net would be used to
+ 
+
+ align:start position:0%
+computers on the net would be used to
+collect emails and keep them so that uh
+
+ align:start position:0%
+collect emails and keep them so that uh
+ 
+
+ align:start position:0%
+collect emails and keep them so that uh
+other people might view a conversation
+
+ align:start position:0%
+other people might view a conversation
+ 
+
+ align:start position:0%
+other people might view a conversation
+conducted in email and these would be
+
+ align:start position:0%
+conducted in email and these would be
+ 
+
+ align:start position:0%
+conducted in email and these would be
+categorized by topics. So remote login
+
+ align:start position:0%
+categorized by topics. So remote login
+ 
+
+ align:start position:0%
+categorized by topics. So remote login
+and file transfer and electronic mail
+
+ align:start position:0%
+and file transfer and electronic mail
+ 
+
+ align:start position:0%
+and file transfer and electronic mail
+and news groups were pretty much what
+
+ align:start position:0%
+and news groups were pretty much what
+ 
+
+ align:start position:0%
+and news groups were pretty much what
+the internet was used for until the
+
+ align:start position:0%
+the internet was used for until the
+ 
+
+ align:start position:0%
+the internet was used for until the
+1990s. And uh starting in about 1990 we
+
+ align:start position:0%
+1990s. And uh starting in about 1990 we
+ 
+
+ align:start position:0%
+1990s. And uh starting in about 1990 we
+uh learned about the worldwide web. And
+
+ align:start position:0%
+uh learned about the worldwide web. And
+ 
+
+ align:start position:0%
+uh learned about the worldwide web. And
+the first form of that in the early 90s
+
+ align:start position:0%
+the first form of that in the early 90s
+ 
+
+ align:start position:0%
+the first form of that in the early 90s
+was uh the arrival of web publishing,
+
+ align:start position:0%
+was uh the arrival of web publishing,
+ 
+
+ align:start position:0%
+was uh the arrival of web publishing,
+the use of the internet for publishing
+
+ align:start position:0%
+the use of the internet for publishing
+ 
+
+ align:start position:0%
+the use of the internet for publishing
+information. And
+
+ align:start position:0%
+information. And
+ 
+
+ align:start position:0%
+information. And
+uh a stunning conclusion from that
+
+ align:start position:0%
+uh a stunning conclusion from that
+ 
+
+ align:start position:0%
+uh a stunning conclusion from that
+arrival was the recognition among
+
+ align:start position:0%
+arrival was the recognition among
+ 
+
+ align:start position:0%
+arrival was the recognition among
+journalists, publishers that there's a
+
+ align:start position:0%
+journalists, publishers that there's a
+ 
+
+ align:start position:0%
+journalists, publishers that there's a
+new there was a new kind of content
+
+ align:start position:0%
+new there was a new kind of content
+ 
+
+ align:start position:0%
+new there was a new kind of content
+suddenly. Uh prior to web publishing,
+
+ align:start position:0%
+suddenly. Uh prior to web publishing,
+ 
+
+ align:start position:0%
+suddenly. Uh prior to web publishing,
+generally speaking, there were two kinds
+
+ align:start position:0%
+generally speaking, there were two kinds
+ 
+
+ align:start position:0%
+generally speaking, there were two kinds
+of content. There was editorial and
+
+ align:start position:0%
+of content. There was editorial and
+ 
+
+ align:start position:0%
+of content. There was editorial and
+there was advertising. And the whole
+
+ align:start position:0%
+there was advertising. And the whole
+ 
+
+ align:start position:0%
+there was advertising. And the whole
+publishing industry was uh very careful
+
+ align:start position:0%
+publishing industry was uh very careful
+ 
+
+ align:start position:0%
+publishing industry was uh very careful
+to keep to keep those well some were
+
+ align:start position:0%
+to keep to keep those well some were
+ 
+
+ align:start position:0%
+to keep to keep those well some were
+very careful to keep those separate and
+
+ align:start position:0%
+very careful to keep those separate and
+ 
+
+ align:start position:0%
+very careful to keep those separate and
+how they would be managed. It was called
+
+ align:start position:0%
+how they would be managed. It was called
+ 
+
+ align:start position:0%
+how they would be managed. It was called
+the separation of church and state. But
+
+ align:start position:0%
+the separation of church and state. But
+ 
+
+ align:start position:0%
+the separation of church and state. But
+when we began publishing on the
+
+ align:start position:0%
+when we began publishing on the
+ 
+
+ align:start position:0%
+when we began publishing on the
+internet, we discovered a new kind of
+
+ align:start position:0%
+internet, we discovered a new kind of
+ 
+
+ align:start position:0%
+internet, we discovered a new kind of
+content which I'll call community
+
+ align:start position:0%
+content which I'll call community
+ 
+
+ align:start position:0%
+content which I'll call community
+content. That is content which was not
+
+ align:start position:0%
+content. That is content which was not
+ 
+
+ align:start position:0%
+content. That is content which was not
+produced by the editors of the
+
+ align:start position:0%
+produced by the editors of the
+ 
+
+ align:start position:0%
+produced by the editors of the
+publication and not produced by the
+
+ align:start position:0%
+publication and not produced by the
+ 
+
+ align:start position:0%
+publication and not produced by the
+advertisers of the publication but
+
+ align:start position:0%
+advertisers of the publication but
+ 
+
+ align:start position:0%
+advertisers of the publication but
+produced by the readers of the
+
+ align:start position:0%
+produced by the readers of the
+ 
+
+ align:start position:0%
+produced by the readers of the
+publication. So now on the internet, I
+
+ align:start position:0%
+publication. So now on the internet, I
+ 
+
+ align:start position:0%
+publication. So now on the internet, I
+think there are three kinds of content.
+
+ align:start position:0%
+think there are three kinds of content.
+ 
+
+ align:start position:0%
+think there are three kinds of content.
+They're all important and community
+
+ align:start position:0%
+They're all important and community
+ 
+
+ align:start position:0%
+They're all important and community
+content is the new one. Toward the
+
+ align:start position:0%
+content is the new one. Toward the
+ 
+
+ align:start position:0%
+content is the new one. Toward the
+mid90s, the web then went from
+
+ align:start position:0%
+mid90s, the web then went from
+ 
+
+ align:start position:0%
+mid90s, the web then went from
+publishing into commerce. And what we
+
+ align:start position:0%
+publishing into commerce. And what we
+ 
+
+ align:start position:0%
+publishing into commerce. And what we
+saw there was the the dot bubble, which
+
+ align:start position:0%
+saw there was the the dot bubble, which
+ 
+
+ align:start position:0%
+saw there was the the dot bubble, which
+has only recently burst. Not that web
+
+ align:start position:0%
+has only recently burst. Not that web
+ 
+
+ align:start position:0%
+has only recently burst. Not that web
+commerce is going away, but that there
+
+ align:start position:0%
+commerce is going away, but that there
+ 
+
+ align:start position:0%
+commerce is going away, but that there
+was there's been a recent correction
+
+ align:start position:0%
+was there's been a recent correction
+ 
+
+ align:start position:0%
+was there's been a recent correction
+from which we'll soon recover. So,
+
+ align:start position:0%
+from which we'll soon recover. So,
+ 
+
+ align:start position:0%
+from which we'll soon recover. So,
+what's the next big thing after the.com
+
+ align:start position:0%
+what's the next big thing after the.com
+ 
+
+ align:start position:0%
+what's the next big thing after the.com
+bubble has burst, after uh web commerce?
+
+ align:start position:0%
+bubble has burst, after uh web commerce?
+ 
+
+ align:start position:0%
+bubble has burst, after uh web commerce?
+Uh, and and mind you, email's not going
+
+ align:start position:0%
+Uh, and and mind you, email's not going
+ 
+
+ align:start position:0%
+Uh, and and mind you, email's not going
+away and FTP is not going away and web
+
+ align:start position:0%
+away and FTP is not going away and web
+ 
+
+ align:start position:0%
+away and FTP is not going away and web
+publishing is not going away and web
+
+ align:start position:0%
+publishing is not going away and web
+ 
+
+ align:start position:0%
+publishing is not going away and web
+commerce is not going away. They're all
+
+ align:start position:0%
+commerce is not going away. They're all
+ 
+
+ align:start position:0%
+commerce is not going away. They're all
+with us like the US mail. But what's the
+
+ align:start position:0%
+with us like the US mail. But what's the
+ 
+
+ align:start position:0%
+with us like the US mail. But what's the
+next big thing? The next thing that will
+
+ align:start position:0%
+next big thing? The next thing that will
+ 
+
+ align:start position:0%
+next big thing? The next thing that will
+drive proliferation of the internet and
+
+ align:start position:0%
+drive proliferation of the internet and
+ 
+
+ align:start position:0%
+drive proliferation of the internet and
+electronic networking and I think it's
+
+ align:start position:0%
+electronic networking and I think it's
+ 
+
+ align:start position:0%
+electronic networking and I think it's
+the convergence of the web with the
+
+ align:start position:0%
+the convergence of the web with the
+ 
+
+ align:start position:0%
+the convergence of the web with the
+pre-existing voice and video uh
+
+ align:start position:0%
+pre-existing voice and video uh
+ 
+
+ align:start position:0%
+pre-existing voice and video uh
+networks. the uh convergence of the
+
+ align:start position:0%
+networks. the uh convergence of the
+ 
+
+ align:start position:0%
+networks. the uh convergence of the
+internet, the telephone and the
+
+ align:start position:0%
+internet, the telephone and the
+ 
+
+ align:start position:0%
+internet, the telephone and the
+television
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+networks. So let's talk about
+
+ align:start position:0%
+networks. So let's talk about
+ 
+
+ align:start position:0%
+networks. So let's talk about
+convergence, the convergence of the
+
+ align:start position:0%
+convergence, the convergence of the
+ 
+
+ align:start position:0%
+convergence, the convergence of the
+internet, telephone and television
+
+ align:start position:0%
+internet, telephone and television
+ 
+
+ align:start position:0%
+internet, telephone and television
+networks. This is not an entirely new
+
+ align:start position:0%
+networks. This is not an entirely new
+ 
+
+ align:start position:0%
+networks. This is not an entirely new
+process. It's been going on for some
+
+ align:start position:0%
+process. It's been going on for some
+ 
+
+ align:start position:0%
+process. It's been going on for some
+years. In fact, we have some information
+
+ align:start position:0%
+years. In fact, we have some information
+ 
+
+ align:start position:0%
+years. In fact, we have some information
+which I'm about to share with you about
+
+ align:start position:0%
+which I'm about to share with you about
+ 
+
+ align:start position:0%
+which I'm about to share with you about
+the recent history of convergence. So we
+
+ align:start position:0%
+the recent history of convergence. So we
+ 
+
+ align:start position:0%
+the recent history of convergence. So we
+have these three communities of
+
+ align:start position:0%
+have these three communities of
+ 
+
+ align:start position:0%
+have these three communities of
+interest. We have the internet people,
+
+ align:start position:0%
+interest. We have the internet people,
+ 
+
+ align:start position:0%
+interest. We have the internet people,
+my people. We have the telephone people
+
+ align:start position:0%
+my people. We have the telephone people
+ 
+
+ align:start position:0%
+my people. We have the telephone people
+and we have the television people. All
+
+ align:start position:0%
+and we have the television people. All
+ 
+
+ align:start position:0%
+and we have the television people. All
+of whom saw convergence. The notion that
+
+ align:start position:0%
+of whom saw convergence. The notion that
+ 
+
+ align:start position:0%
+of whom saw convergence. The notion that
+the internet and telephone and
+
+ align:start position:0%
+the internet and telephone and
+ 
+
+ align:start position:0%
+the internet and telephone and
+television networks might converge. And
+
+ align:start position:0%
+television networks might converge. And
+ 
+
+ align:start position:0%
+television networks might converge. And
+they all approached this convergent with
+
+ align:start position:0%
+they all approached this convergent with
+ 
+
+ align:start position:0%
+they all approached this convergent with
+certain goals in mind. And what I'd like
+
+ align:start position:0%
+certain goals in mind. And what I'd like
+ 
+
+ align:start position:0%
+certain goals in mind. And what I'd like
+to now summarize is what I my view of
+
+ align:start position:0%
+to now summarize is what I my view of
+ 
+
+ align:start position:0%
+to now summarize is what I my view of
+what they wanted when they approached
+
+ align:start position:0%
+what they wanted when they approached
+ 
+
+ align:start position:0%
+what they wanted when they approached
+convergence and what recently they got
+
+ align:start position:0%
+convergence and what recently they got
+ 
+
+ align:start position:0%
+convergence and what recently they got
+which was quite different from what they
+
+ align:start position:0%
+which was quite different from what they
+ 
+
+ align:start position:0%
+which was quite different from what they
+wanted. Let's begin with the internet
+
+ align:start position:0%
+wanted. Let's begin with the internet
+ 
+
+ align:start position:0%
+wanted. Let's begin with the internet
+people. The internet people wanted
+
+ align:start position:0%
+people. The internet people wanted
+ 
+
+ align:start position:0%
+people. The internet people wanted
+convergence with the telephone and later
+
+ align:start position:0%
+convergence with the telephone and later
+ 
+
+ align:start position:0%
+convergence with the telephone and later
+television networks because they wanted
+
+ align:start position:0%
+television networks because they wanted
+ 
+
+ align:start position:0%
+television networks because they wanted
+ubiquity. They had built this wonderful
+
+ align:start position:0%
+ubiquity. They had built this wonderful
+ 
+
+ align:start position:0%
+ubiquity. They had built this wonderful
+thing the internet and they believed as
+
+ align:start position:0%
+thing the internet and they believed as
+ 
+
+ align:start position:0%
+thing the internet and they believed as
+I do that we wanted everyone to have it
+
+ align:start position:0%
+I do that we wanted everyone to have it
+ 
+
+ align:start position:0%
+I do that we wanted everyone to have it
+and to use it and and convergence was a
+
+ align:start position:0%
+and to use it and and convergence was a
+ 
+
+ align:start position:0%
+and to use it and and convergence was a
+way of getting there because the
+
+ align:start position:0%
+way of getting there because the
+ 
+
+ align:start position:0%
+way of getting there because the
+telephone network is ubiquitous and the
+
+ align:start position:0%
+telephone network is ubiquitous and the
+ 
+
+ align:start position:0%
+telephone network is ubiquitous and the
+television network is ubiquitous. So if
+
+ align:start position:0%
+television network is ubiquitous. So if
+ 
+
+ align:start position:0%
+television network is ubiquitous. So if
+only the internet could be put on the
+
+ align:start position:0%
+only the internet could be put on the
+ 
+
+ align:start position:0%
+only the internet could be put on the
+telephone and television networks, this
+
+ align:start position:0%
+telephone and television networks, this
+ 
+
+ align:start position:0%
+telephone and television networks, this
+great thing that we internet people
+
+ align:start position:0%
+great thing that we internet people
+ 
+
+ align:start position:0%
+great thing that we internet people
+brought to the world would then be
+
+ align:start position:0%
+brought to the world would then be
+ 
+
+ align:start position:0%
+brought to the world would then be
+available to everyone. What a great
+
+ align:start position:0%
+available to everyone. What a great
+ 
+
+ align:start position:0%
+available to everyone. What a great
+goal. And so we began moving the
+
+ align:start position:0%
+goal. And so we began moving the
+ 
+
+ align:start position:0%
+goal. And so we began moving the
+internet on initially onto the telephone
+
+ align:start position:0%
+internet on initially onto the telephone
+ 
+
+ align:start position:0%
+internet on initially onto the telephone
+network. And in in fact today most
+
+ align:start position:0%
+network. And in in fact today most
+ 
+
+ align:start position:0%
+network. And in in fact today most
+people more than 90% of the people who
+
+ align:start position:0%
+people more than 90% of the people who
+ 
+
+ align:start position:0%
+people more than 90% of the people who
+use the internet use it through a dialup
+
+ align:start position:0%
+use the internet use it through a dialup
+ 
+
+ align:start position:0%
+use the internet use it through a dialup
+telephone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modem. But the internet people got
+
+ align:start position:0%
+modem. But the internet people got
+ 
+
+ align:start position:0%
+modem. But the internet people got
+something different, something
+
+ align:start position:0%
+something different, something
+ 
+
+ align:start position:0%
+something different, something
+unexpected that they didn't quite want.
+
+ align:start position:0%
+unexpected that they didn't quite want.
+ 
+
+ align:start position:0%
+unexpected that they didn't quite want.
+For example, when you let a lot of
+
+ align:start position:0%
+For example, when you let a lot of
+ 
+
+ align:start position:0%
+For example, when you let a lot of
+people onto the network who are not uh
+
+ align:start position:0%
+people onto the network who are not uh
+ 
+
+ align:start position:0%
+people onto the network who are not uh
+university PhDs is you get what's called
+
+ align:start position:0%
+university PhDs is you get what's called
+ 
+
+ align:start position:0%
+university PhDs is you get what's called
+newbies. These are people who weren't um
+
+ align:start position:0%
+newbies. These are people who weren't um
+ 
+
+ align:start position:0%
+newbies. These are people who weren't um
+uh brought up properly in the ways of
+
+ align:start position:0%
+uh brought up properly in the ways of
+ 
+
+ align:start position:0%
+uh brought up properly in the ways of
+the internet and had different interests
+
+ align:start position:0%
+the internet and had different interests
+ 
+
+ align:start position:0%
+the internet and had different interests
+and different values and when they came
+
+ align:start position:0%
+and different values and when they came
+ 
+
+ align:start position:0%
+and different values and when they came
+and they didn't know how to use the
+
+ align:start position:0%
+and they didn't know how to use the
+ 
+
+ align:start position:0%
+and they didn't know how to use the
+internet all that well and this was
+
+ align:start position:0%
+internet all that well and this was
+ 
+
+ align:start position:0%
+internet all that well and this was
+infuriating to the internet
+
+ align:start position:0%
+infuriating to the internet
+ 
+
+ align:start position:0%
+infuriating to the internet
+intelligencia. The second thing they got
+
+ align:start position:0%
+intelligencia. The second thing they got
+ 
+
+ align:start position:0%
+intelligencia. The second thing they got
+was slows. The telephone network was not
+
+ align:start position:0%
+was slows. The telephone network was not
+ 
+
+ align:start position:0%
+was slows. The telephone network was not
+designed to carry high-speed data. It
+
+ align:start position:0%
+designed to carry high-speed data. It
+ 
+
+ align:start position:0%
+designed to carry high-speed data. It
+was designed to carry voice
+
+ align:start position:0%
+was designed to carry voice
+ 
+
+ align:start position:0%
+was designed to carry voice
+communications. And so all these people
+
+ align:start position:0%
+communications. And so all these people
+ 
+
+ align:start position:0%
+communications. And so all these people
+who are accessing the internet through
+
+ align:start position:0%
+who are accessing the internet through
+ 
+
+ align:start position:0%
+who are accessing the internet through
+their dialup telephone modems are doing
+
+ align:start position:0%
+their dialup telephone modems are doing
+ 
+
+ align:start position:0%
+their dialup telephone modems are doing
+so slowly. And this is really painful.
+
+ align:start position:0%
+so slowly. And this is really painful.
+ 
+
+ align:start position:0%
+so slowly. And this is really painful.
+And so we're all in a big rush to uh
+
+ align:start position:0%
+And so we're all in a big rush to uh
+ 
+
+ align:start position:0%
+And so we're all in a big rush to uh
+solve that
+
+ align:start position:0%
+solve that
+ 
+
+ align:start position:0%
+solve that
+problem. The telephone people saw great
+
+ align:start position:0%
+problem. The telephone people saw great
+ 
+
+ align:start position:0%
+problem. The telephone people saw great
+promise in convergence too. And they
+
+ align:start position:0%
+promise in convergence too. And they
+ 
+
+ align:start position:0%
+promise in convergence too. And they
+were kind of interested in convergence
+
+ align:start position:0%
+were kind of interested in convergence
+ 
+
+ align:start position:0%
+were kind of interested in convergence
+because what they heard was the internet
+
+ align:start position:0%
+because what they heard was the internet
+ 
+
+ align:start position:0%
+because what they heard was the internet
+is a worldwide network and people use it
+
+ align:start position:0%
+is a worldwide network and people use it
+ 
+
+ align:start position:0%
+is a worldwide network and people use it
+a lot. So the telephone people said
+
+ align:start position:0%
+a lot. So the telephone people said
+ 
+
+ align:start position:0%
+a lot. So the telephone people said
+we're going to get a lot of longd
+
+ align:start position:0%
+we're going to get a lot of longd
+ 
+
+ align:start position:0%
+we're going to get a lot of longd
+distanceance minutes out of this. People
+
+ align:start position:0%
+distanceance minutes out of this. People
+ 
+
+ align:start position:0%
+distanceance minutes out of this. People
+are going to be dialing into that
+
+ align:start position:0%
+are going to be dialing into that
+ 
+
+ align:start position:0%
+are going to be dialing into that
+internet around the world and we're
+
+ align:start position:0%
+internet around the world and we're
+ 
+
+ align:start position:0%
+internet around the world and we're
+going to bill them minute by minute for
+
+ align:start position:0%
+going to bill them minute by minute for
+ 
+
+ align:start position:0%
+going to bill them minute by minute for
+uh their use of the internet. And what a
+
+ align:start position:0%
+uh their use of the internet. And what a
+ 
+
+ align:start position:0%
+uh their use of the internet. And what a
+great new business opportunity this is.
+
+ align:start position:0%
+great new business opportunity this is.
+ 
+
+ align:start position:0%
+great new business opportunity this is.
+They thought what they got the telephone
+
+ align:start position:0%
+They thought what they got the telephone
+ 
+
+ align:start position:0%
+They thought what they got the telephone
+people they got something completely
+
+ align:start position:0%
+people they got something completely
+ 
+
+ align:start position:0%
+people they got something completely
+different. They got a lot of short
+
+ align:start position:0%
+different. They got a lot of short
+ 
+
+ align:start position:0%
+different. They got a lot of short
+distance hours. That is instead of
+
+ align:start position:0%
+distance hours. That is instead of
+ 
+
+ align:start position:0%
+distance hours. That is instead of
+long-distance minutes they got short
+
+ align:start position:0%
+long-distance minutes they got short
+ 
+
+ align:start position:0%
+long-distance minutes they got short
+distance. And people instead of dialing
+
+ align:start position:0%
+distance. And people instead of dialing
+ 
+
+ align:start position:0%
+distance. And people instead of dialing
+around the world to access the internet
+
+ align:start position:0%
+around the world to access the internet
+ 
+
+ align:start position:0%
+around the world to access the internet
+just dialed an internet access port in
+
+ align:start position:0%
+just dialed an internet access port in
+ 
+
+ align:start position:0%
+just dialed an internet access port in
+their hometown on the same exchange. And
+
+ align:start position:0%
+their hometown on the same exchange. And
+ 
+
+ align:start position:0%
+their hometown on the same exchange. And
+instead of being on there for a minute
+
+ align:start position:0%
+instead of being on there for a minute
+ 
+
+ align:start position:0%
+instead of being on there for a minute
+or two or three, which is how the
+
+ align:start position:0%
+or two or three, which is how the
+ 
+
+ align:start position:0%
+or two or three, which is how the
+telephone network was designed, they
+
+ align:start position:0%
+telephone network was designed, they
+ 
+
+ align:start position:0%
+telephone network was designed, they
+used it for hours, if not 24 hours a
+
+ align:start position:0%
+used it for hours, if not 24 hours a
+ 
+
+ align:start position:0%
+used it for hours, if not 24 hours a
+day. And the telephone companies were
+
+ align:start position:0%
+day. And the telephone companies were
+ 
+
+ align:start position:0%
+day. And the telephone companies were
+technically unprepared to take on this
+
+ align:start position:0%
+technically unprepared to take on this
+ 
+
+ align:start position:0%
+technically unprepared to take on this
+load. And they had no way of billing for
+
+ align:start position:0%
+load. And they had no way of billing for
+ 
+
+ align:start position:0%
+load. And they had no way of billing for
+it because year for years and years and
+
+ align:start position:0%
+it because year for years and years and
+ 
+
+ align:start position:0%
+it because year for years and years and
+years, they've been organized around
+
+ align:start position:0%
+years, they've been organized around
+ 
+
+ align:start position:0%
+years, they've been organized around
+collecting money for long distance, not
+
+ align:start position:0%
+collecting money for long distance, not
+ 
+
+ align:start position:0%
+collecting money for long distance, not
+short
+
+ align:start position:0%
+short
+ 
+
+ align:start position:0%
+short
+distance. So this was a bit of a jolt
+
+ align:start position:0%
+distance. So this was a bit of a jolt
+ 
+
+ align:start position:0%
+distance. So this was a bit of a jolt
+and a surprise and made them angry about
+
+ align:start position:0%
+and a surprise and made them angry about
+ 
+
+ align:start position:0%
+and a surprise and made them angry about
+this convergence. Then something even
+
+ align:start position:0%
+this convergence. Then something even
+ 
+
+ align:start position:0%
+this convergence. Then something even
+worse happened. People started talking
+
+ align:start position:0%
+worse happened. People started talking
+ 
+
+ align:start position:0%
+worse happened. People started talking
+about using the internet to carry voice
+
+ align:start position:0%
+about using the internet to carry voice
+ 
+
+ align:start position:0%
+about using the internet to carry voice
+conversations for free. And the
+
+ align:start position:0%
+conversations for free. And the
+ 
+
+ align:start position:0%
+conversations for free. And the
+telephone companies uh in the United
+
+ align:start position:0%
+telephone companies uh in the United
+ 
+
+ align:start position:0%
+telephone companies uh in the United
+States uh generate about $200 billion a
+
+ align:start position:0%
+States uh generate about $200 billion a
+ 
+
+ align:start position:0%
+States uh generate about $200 billion a
+year in carrying longd distanceance
+
+ align:start position:0%
+year in carrying longd distanceance
+ 
+
+ align:start position:0%
+year in carrying longd distanceance
+telephone conversations. And the thought
+
+ align:start position:0%
+telephone conversations. And the thought
+ 
+
+ align:start position:0%
+telephone conversations. And the thought
+that these conversations might be
+
+ align:start position:0%
+that these conversations might be
+ 
+
+ align:start position:0%
+that these conversations might be
+carried for free over the internet was
+
+ align:start position:0%
+carried for free over the internet was
+ 
+
+ align:start position:0%
+carried for free over the internet was
+quite shocking to them. Now, of course,
+
+ align:start position:0%
+quite shocking to them. Now, of course,
+ 
+
+ align:start position:0%
+quite shocking to them. Now, of course,
+free is a very low price and uh they're
+
+ align:start position:0%
+free is a very low price and uh they're
+ 
+
+ align:start position:0%
+free is a very low price and uh they're
+not likely to be free, but the threat of
+
+ align:start position:0%
+not likely to be free, but the threat of
+ 
+
+ align:start position:0%
+not likely to be free, but the threat of
+voice over the internet has been um very
+
+ align:start position:0%
+voice over the internet has been um very
+ 
+
+ align:start position:0%
+voice over the internet has been um very
+motivating to the telephone companies.
+
+ align:start position:0%
+motivating to the telephone companies.
+ 
+
+ align:start position:0%
+motivating to the telephone companies.
+They're not sure they want to do
+
+ align:start position:0%
+They're not sure they want to do
+ 
+
+ align:start position:0%
+They're not sure they want to do
+convergence all that much
+
+ align:start position:0%
+convergence all that much
+ 
+
+ align:start position:0%
+convergence all that much
+anymore. The television community, the
+
+ align:start position:0%
+anymore. The television community, the
+ 
+
+ align:start position:0%
+anymore. The television community, the
+television networking people also saw
+
+ align:start position:0%
+television networking people also saw
+ 
+
+ align:start position:0%
+television networking people also saw
+promise in convergence. Uh for years and
+
+ align:start position:0%
+promise in convergence. Uh for years and
+ 
+
+ align:start position:0%
+promise in convergence. Uh for years and
+years and years, the telephone industry
+
+ align:start position:0%
+years and years, the telephone industry
+ 
+
+ align:start position:0%
+years and years, the telephone industry
+has been trying to branch out into
+
+ align:start position:0%
+has been trying to branch out into
+ 
+
+ align:start position:0%
+has been trying to branch out into
+interactive television. And there have
+
+ align:start position:0%
+interactive television. And there have
+ 
+
+ align:start position:0%
+interactive television. And there have
+been many trials going back 10 and 20
+
+ align:start position:0%
+been many trials going back 10 and 20
+ 
+
+ align:start position:0%
+been many trials going back 10 and 20
+and 30 years, 40 years perhaps to
+
+ align:start position:0%
+and 30 years, 40 years perhaps to
+ 
+
+ align:start position:0%
+and 30 years, 40 years perhaps to
+develop two-way or interactive
+
+ align:start position:0%
+develop two-way or interactive
+ 
+
+ align:start position:0%
+develop two-way or interactive
+television. And they saw in the internet
+
+ align:start position:0%
+television. And they saw in the internet
+ 
+
+ align:start position:0%
+television. And they saw in the internet
+which is two-way and interactive a
+
+ align:start position:0%
+which is two-way and interactive a
+ 
+
+ align:start position:0%
+which is two-way and interactive a
+chance to finally get at the many um
+
+ align:start position:0%
+chance to finally get at the many um
+ 
+
+ align:start position:0%
+chance to finally get at the many um
+benefits that they saw to interactive
+
+ align:start position:0%
+benefits that they saw to interactive
+ 
+
+ align:start position:0%
+benefits that they saw to interactive
+television. So the television industry
+
+ align:start position:0%
+television. So the television industry
+ 
+
+ align:start position:0%
+television. So the television industry
+began approaching the internet and
+
+ align:start position:0%
+began approaching the internet and
+ 
+
+ align:start position:0%
+began approaching the internet and
+convergence and they got something quite
+
+ align:start position:0%
+convergence and they got something quite
+ 
+
+ align:start position:0%
+convergence and they got something quite
+different from what they were expecting.
+
+ align:start position:0%
+different from what they were expecting.
+ 
+
+ align:start position:0%
+different from what they were expecting.
+On the internet, the tradition is that
+
+ align:start position:0%
+On the internet, the tradition is that
+ 
+
+ align:start position:0%
+On the internet, the tradition is that
+content and carriage are separate. That
+
+ align:start position:0%
+content and carriage are separate. That
+ 
+
+ align:start position:0%
+content and carriage are separate. That
+is, there's the infrastructure of the
+
+ align:start position:0%
+is, there's the infrastructure of the
+ 
+
+ align:start position:0%
+is, there's the infrastructure of the
+network which is owned and operated and
+
+ align:start position:0%
+network which is owned and operated and
+ 
+
+ align:start position:0%
+network which is owned and operated and
+run by one group of people and then
+
+ align:start position:0%
+run by one group of people and then
+ 
+
+ align:start position:0%
+run by one group of people and then
+there's all this content which is
+
+ align:start position:0%
+there's all this content which is
+ 
+
+ align:start position:0%
+there's all this content which is
+carried on it and they're generally not
+
+ align:start position:0%
+carried on it and they're generally not
+ 
+
+ align:start position:0%
+carried on it and they're generally not
+owned by the same people. Well, in the
+
+ align:start position:0%
+owned by the same people. Well, in the
+ 
+
+ align:start position:0%
+owned by the same people. Well, in the
+television world, there's a great
+
+ align:start position:0%
+television world, there's a great
+ 
+
+ align:start position:0%
+television world, there's a great
+overlap between those who own the
+
+ align:start position:0%
+overlap between those who own the
+ 
+
+ align:start position:0%
+overlap between those who own the
+carriage and those who own the content.
+
+ align:start position:0%
+carriage and those who own the content.
+ 
+
+ align:start position:0%
+carriage and those who own the content.
+So, the business model of the television
+
+ align:start position:0%
+So, the business model of the television
+ 
+
+ align:start position:0%
+So, the business model of the television
+industry is different from the
+
+ align:start position:0%
+industry is different from the
+ 
+
+ align:start position:0%
+industry is different from the
+fundamental business model or evolving
+
+ align:start position:0%
+fundamental business model or evolving
+ 
+
+ align:start position:0%
+fundamental business model or evolving
+business models of the internet. So this
+
+ align:start position:0%
+business models of the internet. So this
+ 
+
+ align:start position:0%
+business models of the internet. So this
+was a problem and the television people
+
+ align:start position:0%
+was a problem and the television people
+ 
+
+ align:start position:0%
+was a problem and the television people
+were roundly criticized for linking
+
+ align:start position:0%
+were roundly criticized for linking
+ 
+
+ align:start position:0%
+were roundly criticized for linking
+content and carriage uh in their various
+
+ align:start position:0%
+content and carriage uh in their various
+ 
+
+ align:start position:0%
+content and carriage uh in their various
+schemes for deriving revenue from the
+
+ align:start position:0%
+schemes for deriving revenue from the
+ 
+
+ align:start position:0%
+schemes for deriving revenue from the
+internet.
+
+ align:start position:0%
+internet.
+ 
+
+ align:start position:0%
+internet.
+There was even worse development however
+
+ align:start position:0%
+There was even worse development however
+ 
+
+ align:start position:0%
+There was even worse development however
+for television people because television
+
+ align:start position:0%
+for television people because television
+ 
+
+ align:start position:0%
+for television people because television
+people uh for the most part are used to
+
+ align:start position:0%
+people uh for the most part are used to
+ 
+
+ align:start position:0%
+people uh for the most part are used to
+having five channels or 10 channels or
+
+ align:start position:0%
+having five channels or 10 channels or
+ 
+
+ align:start position:0%
+having five channels or 10 channels or
+20 channels. A restricted number of
+
+ align:start position:0%
+20 channels. A restricted number of
+ 
+
+ align:start position:0%
+20 channels. A restricted number of
+channels in which uh the attention of
+
+ align:start position:0%
+channels in which uh the attention of
+ 
+
+ align:start position:0%
+channels in which uh the attention of
+their viewers is uh channeled and so the
+
+ align:start position:0%
+their viewers is uh channeled and so the
+ 
+
+ align:start position:0%
+their viewers is uh channeled and so the
+competition among these channels is
+
+ align:start position:0%
+competition among these channels is
+ 
+
+ align:start position:0%
+competition among these channels is
+um um under their control pretty much.
+
+ align:start position:0%
+um um under their control pretty much.
+ 
+
+ align:start position:0%
+um um under their control pretty much.
+But on the internet there's not 10
+
+ align:start position:0%
+But on the internet there's not 10
+ 
+
+ align:start position:0%
+But on the internet there's not 10
+channels or 100 channels or even 500
+
+ align:start position:0%
+channels or 100 channels or even 500
+ 
+
+ align:start position:0%
+channels or 100 channels or even 500
+channels. On the internet there's a
+
+ align:start position:0%
+channels. On the internet there's a
+ 
+
+ align:start position:0%
+channels. On the internet there's a
+million channels that is every user of
+
+ align:start position:0%
+million channels that is every user of
+ 
+
+ align:start position:0%
+million channels that is every user of
+the internet can be a generator of
+
+ align:start position:0%
+the internet can be a generator of
+ 
+
+ align:start position:0%
+the internet can be a generator of
+content and the competition among u
+
+ align:start position:0%
+content and the competition among u
+ 
+
+ align:start position:0%
+content and the competition among u
+users of the internet that is providers
+
+ align:start position:0%
+users of the internet that is providers
+ 
+
+ align:start position:0%
+users of the internet that is providers
+of content in the internet the
+
+ align:start position:0%
+of content in the internet the
+ 
+
+ align:start position:0%
+of content in the internet the
+competition among them is much more
+
+ align:start position:0%
+competition among them is much more
+ 
+
+ align:start position:0%
+competition among them is much more
+fierce because the real scarce the real
+
+ align:start position:0%
+fierce because the real scarce the real
+ 
+
+ align:start position:0%
+fierce because the real scarce the real
+scarcity on the internet is not uh
+
+ align:start position:0%
+scarcity on the internet is not uh
+ 
+
+ align:start position:0%
+scarcity on the internet is not uh
+broadcast frequencies and it's not
+
+ align:start position:0%
+broadcast frequencies and it's not
+ 
+
+ align:start position:0%
+broadcast frequencies and it's not
+channels on the network it's the
+
+ align:start position:0%
+channels on the network it's the
+ 
+
+ align:start position:0%
+channels on the network it's the
+attention of readers and so the TV
+
+ align:start position:0%
+attention of readers and so the TV
+ 
+
+ align:start position:0%
+attention of readers and so the TV
+people confronted a business model that
+
+ align:start position:0%
+people confronted a business model that
+ 
+
+ align:start position:0%
+people confronted a business model that
+was alien to their experience but Still
+
+ align:start position:0%
+was alien to their experience but Still
+ 
+
+ align:start position:0%
+was alien to their experience but Still
+TV has been the convergence of the
+
+ align:start position:0%
+TV has been the convergence of the
+ 
+
+ align:start position:0%
+TV has been the convergence of the
+internet and television has been the
+
+ align:start position:0%
+internet and television has been the
+ 
+
+ align:start position:0%
+internet and television has been the
+most effective to date. Although when I
+
+ align:start position:0%
+most effective to date. Although when I
+ 
+
+ align:start position:0%
+most effective to date. Although when I
+say that you have to understand there
+
+ align:start position:0%
+say that you have to understand there
+ 
+
+ align:start position:0%
+say that you have to understand there
+are uh three kinds of television
+
+ align:start position:0%
+are uh three kinds of television
+ 
+
+ align:start position:0%
+are uh three kinds of television
+internet convergence of increasing
+
+ align:start position:0%
+internet convergence of increasing
+ 
+
+ align:start position:0%
+internet convergence of increasing
+importance. Uh the first kind of
+
+ align:start position:0%
+importance. Uh the first kind of
+ 
+
+ align:start position:0%
+importance. Uh the first kind of
+television internet convergence is the
+
+ align:start position:0%
+television internet convergence is the
+ 
+
+ align:start position:0%
+television internet convergence is the
+use of televisions as cheap computer
+
+ align:start position:0%
+use of televisions as cheap computer
+ 
+
+ align:start position:0%
+use of televisions as cheap computer
+monitors. And you saw this with such
+
+ align:start position:0%
+monitors. And you saw this with such
+ 
+
+ align:start position:0%
+monitors. And you saw this with such
+systems as you see this with such
+
+ align:start position:0%
+systems as you see this with such
+ 
+
+ align:start position:0%
+systems as you see this with such
+systems as web TV where really what
+
+ align:start position:0%
+systems as web TV where really what
+ 
+
+ align:start position:0%
+systems as web TV where really what
+you're doing is using the telephone
+
+ align:start position:0%
+you're doing is using the telephone
+ 
+
+ align:start position:0%
+you're doing is using the telephone
+network to connect to the internet but
+
+ align:start position:0%
+network to connect to the internet but
+ 
+
+ align:start position:0%
+network to connect to the internet but
+you're using your television as the
+
+ align:start position:0%
+you're using your television as the
+ 
+
+ align:start position:0%
+you're using your television as the
+monitor because televisions are
+
+ align:start position:0%
+monitor because televisions are
+ 
+
+ align:start position:0%
+monitor because televisions are
+generally cheaper than computer
+
+ align:start position:0%
+generally cheaper than computer
+ 
+
+ align:start position:0%
+generally cheaper than computer
+monitors. Uh this is really lowgrade
+
+ align:start position:0%
+monitors. Uh this is really lowgrade
+ 
+
+ align:start position:0%
+monitors. Uh this is really lowgrade
+convergence between television and the
+
+ align:start position:0%
+convergence between television and the
+ 
+
+ align:start position:0%
+convergence between television and the
+internet and it hardly
+
+ align:start position:0%
+internet and it hardly
+ 
+
+ align:start position:0%
+internet and it hardly
+counts. The second more uh vital
+
+ align:start position:0%
+counts. The second more uh vital
+ 
+
+ align:start position:0%
+counts. The second more uh vital
+convergence is the use of cable modems
+
+ align:start position:0%
+convergence is the use of cable modems
+ 
+
+ align:start position:0%
+convergence is the use of cable modems
+to carry the internet over the
+
+ align:start position:0%
+to carry the internet over the
+ 
+
+ align:start position:0%
+to carry the internet over the
+television network. And it turns out
+
+ align:start position:0%
+television network. And it turns out
+ 
+
+ align:start position:0%
+television network. And it turns out
+that cable modems have been the most
+
+ align:start position:0%
+that cable modems have been the most
+ 
+
+ align:start position:0%
+that cable modems have been the most
+effective the most uh widely deployed
+
+ align:start position:0%
+effective the most uh widely deployed
+ 
+
+ align:start position:0%
+effective the most uh widely deployed
+method of uh delivering internet
+
+ align:start position:0%
+method of uh delivering internet
+ 
+
+ align:start position:0%
+method of uh delivering internet
+services at higher speeds to consumers.
+
+ align:start position:0%
+services at higher speeds to consumers.
+ 
+
+ align:start position:0%
+services at higher speeds to consumers.
+But still cable modems is a is a weaker
+
+ align:start position:0%
+But still cable modems is a is a weaker
+ 
+
+ align:start position:0%
+But still cable modems is a is a weaker
+form of convergence between television
+
+ align:start position:0%
+form of convergence between television
+ 
+
+ align:start position:0%
+form of convergence between television
+and internet. The real convergence is
+
+ align:start position:0%
+and internet. The real convergence is
+ 
+
+ align:start position:0%
+and internet. The real convergence is
+when you can carry television over the
+
+ align:start position:0%
+when you can carry television over the
+ 
+
+ align:start position:0%
+when you can carry television over the
+internet which is I believe the intent
+
+ align:start position:0%
+internet which is I believe the intent
+ 
+
+ align:start position:0%
+internet which is I believe the intent
+of uh what you're watching now. This is
+
+ align:start position:0%
+of uh what you're watching now. This is
+ 
+
+ align:start position:0%
+of uh what you're watching now. This is
+supposed to be coming to you over the
+
+ align:start position:0%
+supposed to be coming to you over the
+ 
+
+ align:start position:0%
+supposed to be coming to you over the
+internet. So that's the convergence that
+
+ align:start position:0%
+internet. So that's the convergence that
+ 
+
+ align:start position:0%
+internet. So that's the convergence that
+I think we're after, the ability to
+
+ align:start position:0%
+I think we're after, the ability to
+ 
+
+ align:start position:0%
+I think we're after, the ability to
+carry uh video over the
+
+ align:start position:0%
+carry uh video over the
+ 
+
+ align:start position:0%
+carry uh video over the
+internet. Trouble is, the standard for
+
+ align:start position:0%
+internet. Trouble is, the standard for
+ 
+
+ align:start position:0%
+internet. Trouble is, the standard for
+carrying video over the internet is what
+
+ align:start position:0%
+carrying video over the internet is what
+ 
+
+ align:start position:0%
+carrying video over the internet is what
+I would call the jerky postage stamp.
+
+ align:start position:0%
+I would call the jerky postage stamp.
+ 
+
+ align:start position:0%
+I would call the jerky postage stamp.
+And you've all seen them when you try to
+
+ align:start position:0%
+And you've all seen them when you try to
+ 
+
+ align:start position:0%
+And you've all seen them when you try to
+watch video. Perhaps you're watching me
+
+ align:start position:0%
+watch video. Perhaps you're watching me
+ 
+
+ align:start position:0%
+watch video. Perhaps you're watching me
+now as a jerky postage stamp. A little
+
+ align:start position:0%
+now as a jerky postage stamp. A little
+ 
+
+ align:start position:0%
+now as a jerky postage stamp. A little
+tiny little square on your screen with
+
+ align:start position:0%
+tiny little square on your screen with
+ 
+
+ align:start position:0%
+tiny little square on your screen with
+me going like this. Of course, you can't
+
+ align:start position:0%
+me going like this. Of course, you can't
+ 
+
+ align:start position:0%
+me going like this. Of course, you can't
+tell that I'm doing this because I
+
+ align:start position:0%
+tell that I'm doing this because I
+ 
+
+ align:start position:0%
+tell that I'm doing this because I
+probably am already doing this in front
+
+ align:start position:0%
+probably am already doing this in front
+ 
+
+ align:start position:0%
+probably am already doing this in front
+of you right
+
+ align:start position:0%
+of you right
+ 
+
+ align:start position:0%
+of you right
+now. So, I'm I claim that convergence
+
+ align:start position:0%
+now. So, I'm I claim that convergence
+ 
+
+ align:start position:0%
+now. So, I'm I claim that convergence
+between television and the internet is
+
+ align:start position:0%
+between television and the internet is
+ 
+
+ align:start position:0%
+between television and the internet is
+the next big thing. But in saying so, u
+
+ align:start position:0%
+the next big thing. But in saying so, u
+ 
+
+ align:start position:0%
+the next big thing. But in saying so, u
+there's some serious uh work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead. There's work ahead in the uh
+
+ align:start position:0%
+ahead. There's work ahead in the uh
+ 
+
+ align:start position:0%
+ahead. There's work ahead in the uh
+proliferation of the video internet. And
+
+ align:start position:0%
+proliferation of the video internet. And
+ 
+
+ align:start position:0%
+proliferation of the video internet. And
+among the work to be done is the
+
+ align:start position:0%
+among the work to be done is the
+ 
+
+ align:start position:0%
+among the work to be done is the
+deployment of what's called broadband to
+
+ align:start position:0%
+deployment of what's called broadband to
+ 
+
+ align:start position:0%
+deployment of what's called broadband to
+homes. Uh, as I mentioned earlier, most
+
+ align:start position:0%
+homes. Uh, as I mentioned earlier, most
+ 
+
+ align:start position:0%
+homes. Uh, as I mentioned earlier, most
+people access the internet through a
+
+ align:start position:0%
+people access the internet through a
+ 
+
+ align:start position:0%
+people access the internet through a
+dialup telephone modem at a pitiful 56
+
+ align:start position:0%
+dialup telephone modem at a pitiful 56
+ 
+
+ align:start position:0%
+dialup telephone modem at a pitiful 56
+kilobits per second or less. But in
+
+ align:start position:0%
+kilobits per second or less. But in
+ 
+
+ align:start position:0%
+kilobits per second or less. But in
+order to put video in the internet,
+
+ align:start position:0%
+order to put video in the internet,
+ 
+
+ align:start position:0%
+order to put video in the internet,
+we're going to have to carry bits quite
+
+ align:start position:0%
+we're going to have to carry bits quite
+ 
+
+ align:start position:0%
+we're going to have to carry bits quite
+a bit faster than that. A funny problem
+
+ align:start position:0%
+a bit faster than that. A funny problem
+ 
+
+ align:start position:0%
+a bit faster than that. A funny problem
+has emerged. Uh, we have lots of
+
+ align:start position:0%
+has emerged. Uh, we have lots of
+ 
+
+ align:start position:0%
+has emerged. Uh, we have lots of
+bandwidth in the long haul on the
+
+ align:start position:0%
+bandwidth in the long haul on the
+ 
+
+ align:start position:0%
+bandwidth in the long haul on the
+internet thanks to uh amazing
+
+ align:start position:0%
+internet thanks to uh amazing
+ 
+
+ align:start position:0%
+internet thanks to uh amazing
+technologies like wave division
+
+ align:start position:0%
+technologies like wave division
+ 
+
+ align:start position:0%
+technologies like wave division
+multiplexing where we're carrying now
+
+ align:start position:0%
+multiplexing where we're carrying now
+ 
+
+ align:start position:0%
+multiplexing where we're carrying now
+approaching a terabit per second on a
+
+ align:start position:0%
+approaching a terabit per second on a
+ 
+
+ align:start position:0%
+approaching a terabit per second on a
+single fiber. We have plenty of
+
+ align:start position:0%
+single fiber. We have plenty of
+ 
+
+ align:start position:0%
+single fiber. We have plenty of
+bandwidth in the long distance and
+
+ align:start position:0%
+bandwidth in the long distance and
+ 
+
+ align:start position:0%
+bandwidth in the long distance and
+thanks to local area networks like my
+
+ align:start position:0%
+thanks to local area networks like my
+ 
+
+ align:start position:0%
+thanks to local area networks like my
+own baby Ethernet, we have plenty of
+
+ align:start position:0%
+own baby Ethernet, we have plenty of
+ 
+
+ align:start position:0%
+own baby Ethernet, we have plenty of
+bandwidth in the local area that is with
+
+ align:start position:0%
+bandwidth in the local area that is with
+ 
+
+ align:start position:0%
+bandwidth in the local area that is with
+inside of buildings. But there's a gap
+
+ align:start position:0%
+inside of buildings. But there's a gap
+ 
+
+ align:start position:0%
+inside of buildings. But there's a gap
+there's a gap between the LAN the local
+
+ align:start position:0%
+there's a gap between the LAN the local
+ 
+
+ align:start position:0%
+there's a gap between the LAN the local
+area network and the WAN the wide area
+
+ align:start position:0%
+area network and the WAN the wide area
+ 
+
+ align:start position:0%
+area network and the WAN the wide area
+network. And that's we'll call that
+
+ align:start position:0%
+network. And that's we'll call that
+ 
+
+ align:start position:0%
+network. And that's we'll call that
+access bandwidth getting from the LAN to
+
+ align:start position:0%
+access bandwidth getting from the LAN to
+ 
+
+ align:start position:0%
+access bandwidth getting from the LAN to
+the WAN. And there is a chasm currently
+
+ align:start position:0%
+the WAN. And there is a chasm currently
+ 
+
+ align:start position:0%
+the WAN. And there is a chasm currently
+bridged for most people by this
+
+ align:start position:0%
+bridged for most people by this
+ 
+
+ align:start position:0%
+bridged for most people by this
+low-speed dialup telephone modem. So
+
+ align:start position:0%
+low-speed dialup telephone modem. So
+ 
+
+ align:start position:0%
+low-speed dialup telephone modem. So
+part of the work is getting that chasm
+
+ align:start position:0%
+part of the work is getting that chasm
+ 
+
+ align:start position:0%
+part of the work is getting that chasm
+bridged and there's a variety of ways of
+
+ align:start position:0%
+bridged and there's a variety of ways of
+ 
+
+ align:start position:0%
+bridged and there's a variety of ways of
+doing it, some better than
+
+ align:start position:0%
+doing it, some better than
+ 
+
+ align:start position:0%
+doing it, some better than
+others. Most of the so-called broadband
+
+ align:start position:0%
+others. Most of the so-called broadband
+ 
+
+ align:start position:0%
+others. Most of the so-called broadband
+uh methods of access u most many of them
+
+ align:start position:0%
+uh methods of access u most many of them
+ 
+
+ align:start position:0%
+uh methods of access u most many of them
+are through an old-fashioned system
+
+ align:start position:0%
+are through an old-fashioned system
+ 
+
+ align:start position:0%
+are through an old-fashioned system
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+ISDN. And believe me, it would do you no
+
+ align:start position:0%
+ISDN. And believe me, it would do you no
+ 
+
+ align:start position:0%
+ISDN. And believe me, it would do you no
+good for me to explain what ISDN
+
+ align:start position:0%
+good for me to explain what ISDN
+ 
+
+ align:start position:0%
+good for me to explain what ISDN
+actually means. Suffice to say, it's a
+
+ align:start position:0%
+actually means. Suffice to say, it's a
+ 
+
+ align:start position:0%
+actually means. Suffice to say, it's a
+way of accessing going from the LAN to
+
+ align:start position:0%
+way of accessing going from the LAN to
+ 
+
+ align:start position:0%
+way of accessing going from the LAN to
+the WAN at up to about 128 kilobits per
+
+ align:start position:0%
+the WAN at up to about 128 kilobits per
+ 
+
+ align:start position:0%
+the WAN at up to about 128 kilobits per
+second, which isn't much faster than 56
+
+ align:start position:0%
+second, which isn't much faster than 56
+ 
+
+ align:start position:0%
+second, which isn't much faster than 56
+kilobits per second. And it's a it's a
+
+ align:start position:0%
+kilobits per second. And it's a it's a
+ 
+
+ align:start position:0%
+kilobits per second. And it's a it's a
+sad comment in our time that most U
+
+ align:start position:0%
+sad comment in our time that most U
+ 
+
+ align:start position:0%
+sad comment in our time that most U
+market analysts include ISDN under the
+
+ align:start position:0%
+market analysts include ISDN under the
+ 
+
+ align:start position:0%
+market analysts include ISDN under the
+rubric broadband when really it's much
+
+ align:start position:0%
+rubric broadband when really it's much
+ 
+
+ align:start position:0%
+rubric broadband when really it's much
+too slow to be considered broadband.
+
+ align:start position:0%
+too slow to be considered broadband.
+ 
+
+ align:start position:0%
+too slow to be considered broadband.
+Uh the next uh method of bridging the
+
+ align:start position:0%
+Uh the next uh method of bridging the
+ 
+
+ align:start position:0%
+Uh the next uh method of bridging the
+bandwidth chasm here is DSL digital
+
+ align:start position:0%
+bandwidth chasm here is DSL digital
+ 
+
+ align:start position:0%
+bandwidth chasm here is DSL digital
+subscriber lines that is using the
+
+ align:start position:0%
+subscriber lines that is using the
+ 
+
+ align:start position:0%
+subscriber lines that is using the
+copper of uh that was installed for the
+
+ align:start position:0%
+copper of uh that was installed for the
+ 
+
+ align:start position:0%
+copper of uh that was installed for the
+telephone network to carry data at high
+
+ align:start position:0%
+telephone network to carry data at high
+ 
+
+ align:start position:0%
+telephone network to carry data at high
+speeds at uh 384 kilobits per second at
+
+ align:start position:0%
+speeds at uh 384 kilobits per second at
+ 
+
+ align:start position:0%
+speeds at uh 384 kilobits per second at
+1.5 megabits per second DSL and DSL is
+
+ align:start position:0%
+1.5 megabits per second DSL and DSL is
+ 
+
+ align:start position:0%
+1.5 megabits per second DSL and DSL is
+being deployed over now as we speak over
+
+ align:start position:0%
+being deployed over now as we speak over
+ 
+
+ align:start position:0%
+being deployed over now as we speak over
+the copper network uh by a variety of
+
+ align:start position:0%
+the copper network uh by a variety of
+ 
+
+ align:start position:0%
+the copper network uh by a variety of
+players including mostly the uh
+
+ align:start position:0%
+players including mostly the uh
+ 
+
+ align:start position:0%
+players including mostly the uh
+telephone uh copper
+
+ align:start position:0%
+telephone uh copper
+ 
+
+ align:start position:0%
+telephone uh copper
+monopolies. Another uh method of
+
+ align:start position:0%
+monopolies. Another uh method of
+ 
+
+ align:start position:0%
+monopolies. Another uh method of
+bridging the chasm is cable modems. As I
+
+ align:start position:0%
+bridging the chasm is cable modems. As I
+ 
+
+ align:start position:0%
+bridging the chasm is cable modems. As I
+mentioned earlier, the use of the cable
+
+ align:start position:0%
+mentioned earlier, the use of the cable
+ 
+
+ align:start position:0%
+mentioned earlier, the use of the cable
+television distribution network which
+
+ align:start position:0%
+television distribution network which
+ 
+
+ align:start position:0%
+television distribution network which
+reaches about 65 million homes in the
+
+ align:start position:0%
+reaches about 65 million homes in the
+ 
+
+ align:start position:0%
+reaches about 65 million homes in the
+United States out of 110 million. Uh and
+
+ align:start position:0%
+United States out of 110 million. Uh and
+ 
+
+ align:start position:0%
+United States out of 110 million. Uh and
+cable modems are the leading method of
+
+ align:start position:0%
+cable modems are the leading method of
+ 
+
+ align:start position:0%
+cable modems are the leading method of
+bridging uh the chasm of local area to
+
+ align:start position:0%
+bridging uh the chasm of local area to
+ 
+
+ align:start position:0%
+bridging uh the chasm of local area to
+wide area. And then there are some other
+
+ align:start position:0%
+wide area. And then there are some other
+ 
+
+ align:start position:0%
+wide area. And then there are some other
+technologies which we hope will come
+
+ align:start position:0%
+technologies which we hope will come
+ 
+
+ align:start position:0%
+technologies which we hope will come
+along to uh add to the alternatives and
+
+ align:start position:0%
+along to uh add to the alternatives and
+ 
+
+ align:start position:0%
+along to uh add to the alternatives and
+create more competition in solving that
+
+ align:start position:0%
+create more competition in solving that
+ 
+
+ align:start position:0%
+create more competition in solving that
+problem. Now in 2001 the cable modems
+
+ align:start position:0%
+problem. Now in 2001 the cable modems
+ 
+
+ align:start position:0%
+problem. Now in 2001 the cable modems
+are winning. That is there are more
+
+ align:start position:0%
+are winning. That is there are more
+ 
+
+ align:start position:0%
+are winning. That is there are more
+homes connected at higher speeds through
+
+ align:start position:0%
+homes connected at higher speeds through
+ 
+
+ align:start position:0%
+homes connected at higher speeds through
+cable modems and through digital
+
+ align:start position:0%
+cable modems and through digital
+ 
+
+ align:start position:0%
+cable modems and through digital
+subscriber lines than through DSL. And
+
+ align:start position:0%
+subscriber lines than through DSL. And
+ 
+
+ align:start position:0%
+subscriber lines than through DSL. And
+that can be explained very simply. The
+
+ align:start position:0%
+that can be explained very simply. The
+ 
+
+ align:start position:0%
+that can be explained very simply. The
+cable monopolies have weaker monopolies
+
+ align:start position:0%
+cable monopolies have weaker monopolies
+ 
+
+ align:start position:0%
+cable monopolies have weaker monopolies
+than the telephone monopolies. The
+
+ align:start position:0%
+than the telephone monopolies. The
+ 
+
+ align:start position:0%
+than the telephone monopolies. The
+telephone companies are huge and they
+
+ align:start position:0%
+telephone companies are huge and they
+ 
+
+ align:start position:0%
+telephone companies are huge and they
+have airtight monopolies on their
+
+ align:start position:0%
+have airtight monopolies on their
+ 
+
+ align:start position:0%
+have airtight monopolies on their
+geographies and so their motivation for
+
+ align:start position:0%
+geographies and so their motivation for
+ 
+
+ align:start position:0%
+geographies and so their motivation for
+installing digital subscriber lines is
+
+ align:start position:0%
+installing digital subscriber lines is
+ 
+
+ align:start position:0%
+installing digital subscriber lines is
+much lower. They have no one pressuring
+
+ align:start position:0%
+much lower. They have no one pressuring
+ 
+
+ align:start position:0%
+much lower. They have no one pressuring
+them to do very few people pressuring to
+
+ align:start position:0%
+them to do very few people pressuring to
+ 
+
+ align:start position:0%
+them to do very few people pressuring to
+do so. An industry did rise up in recent
+
+ align:start position:0%
+do so. An industry did rise up in recent
+ 
+
+ align:start position:0%
+do so. An industry did rise up in recent
+years uh to bring DSL to homes in large
+
+ align:start position:0%
+years uh to bring DSL to homes in large
+ 
+
+ align:start position:0%
+years uh to bring DSL to homes in large
+numbers in competition with the u
+
+ align:start position:0%
+numbers in competition with the u
+ 
+
+ align:start position:0%
+numbers in competition with the u
+entrenched uh incumbent local exchange
+
+ align:start position:0%
+entrenched uh incumbent local exchange
+ 
+
+ align:start position:0%
+entrenched uh incumbent local exchange
+carriers as they're called. But most of
+
+ align:start position:0%
+carriers as they're called. But most of
+ 
+
+ align:start position:0%
+carriers as they're called. But most of
+that competition uh has been throttled
+
+ align:start position:0%
+that competition uh has been throttled
+ 
+
+ align:start position:0%
+that competition uh has been throttled
+through the use of the monopoly power of
+
+ align:start position:0%
+through the use of the monopoly power of
+ 
+
+ align:start position:0%
+through the use of the monopoly power of
+the telephone companies. The u cable
+
+ align:start position:0%
+the telephone companies. The u cable
+ 
+
+ align:start position:0%
+the telephone companies. The u cable
+modems on the other hand are being
+
+ align:start position:0%
+modems on the other hand are being
+ 
+
+ align:start position:0%
+modems on the other hand are being
+proliferated by the uh cable companies
+
+ align:start position:0%
+proliferated by the uh cable companies
+ 
+
+ align:start position:0%
+proliferated by the uh cable companies
+which are themselves monopolies but
+
+ align:start position:0%
+which are themselves monopolies but
+ 
+
+ align:start position:0%
+which are themselves monopolies but
+they're much weaker monopolies. They
+
+ align:start position:0%
+they're much weaker monopolies. They
+ 
+
+ align:start position:0%
+they're much weaker monopolies. They
+they have much more competition uh from
+
+ align:start position:0%
+they have much more competition uh from
+ 
+
+ align:start position:0%
+they have much more competition uh from
+say satellite for example. uh and so
+
+ align:start position:0%
+say satellite for example. uh and so
+ 
+
+ align:start position:0%
+say satellite for example. uh and so
+they and plus they're more
+
+ align:start position:0%
+they and plus they're more
+ 
+
+ align:start position:0%
+they and plus they're more
+entrepreneurial and u energetic and
+
+ align:start position:0%
+entrepreneurial and u energetic and
+ 
+
+ align:start position:0%
+entrepreneurial and u energetic and
+they've been pr proliferating these
+
+ align:start position:0%
+they've been pr proliferating these
+ 
+
+ align:start position:0%
+they've been pr proliferating these
+cable modems and we should be rooting
+
+ align:start position:0%
+cable modems and we should be rooting
+ 
+
+ align:start position:0%
+cable modems and we should be rooting
+them on uh as the only uh way of uh
+
+ align:start position:0%
+them on uh as the only uh way of uh
+ 
+
+ align:start position:0%
+them on uh as the only uh way of uh
+stirring the telephone companies to
+
+ align:start position:0%
+stirring the telephone companies to
+ 
+
+ align:start position:0%
+stirring the telephone companies to
+movement. So we've had this recent bad
+
+ align:start position:0%
+movement. So we've had this recent bad
+ 
+
+ align:start position:0%
+movement. So we've had this recent bad
+news with the bursting of the dotcom
+
+ align:start position:0%
+news with the bursting of the dotcom
+ 
+
+ align:start position:0%
+news with the bursting of the dotcom
+bubble that is the telephone monopolies
+
+ align:start position:0%
+bubble that is the telephone monopolies
+ 
+
+ align:start position:0%
+bubble that is the telephone monopolies
+are more entrenched than ever uh in
+
+ align:start position:0%
+are more entrenched than ever uh in
+ 
+
+ align:start position:0%
+are more entrenched than ever uh in
+providing broadband and they will be
+
+ align:start position:0%
+providing broadband and they will be
+ 
+
+ align:start position:0%
+providing broadband and they will be
+slow to provide broadband but the
+
+ align:start position:0%
+slow to provide broadband but the
+ 
+
+ align:start position:0%
+slow to provide broadband but the
+broadband is being deployed and they are
+
+ align:start position:0%
+broadband is being deployed and they are
+ 
+
+ align:start position:0%
+broadband is being deployed and they are
+they will eventually get around to it
+
+ align:start position:0%
+they will eventually get around to it
+ 
+
+ align:start position:0%
+they will eventually get around to it
+and eventually and and uh broadband will
+
+ align:start position:0%
+and eventually and and uh broadband will
+ 
+
+ align:start position:0%
+and eventually and and uh broadband will
+begin to arrive in uh further and
+
+ align:start position:0%
+begin to arrive in uh further and
+ 
+
+ align:start position:0%
+begin to arrive in uh further and
+further and more and more places at
+
+ align:start position:0%
+further and more and more places at
+ 
+
+ align:start position:0%
+further and more and more places at
+faster and faster speeds and in that
+
+ align:start position:0%
+faster and faster speeds and in that
+ 
+
+ align:start position:0%
+faster and faster speeds and in that
+context we need to judge where to put
+
+ align:start position:0%
+context we need to judge where to put
+ 
+
+ align:start position:0%
+context we need to judge where to put
+video, what applications of video over
+
+ align:start position:0%
+video, what applications of video over
+ 
+
+ align:start position:0%
+video, what applications of video over
+what populations, over what businesses,
+
+ align:start position:0%
+what populations, over what businesses,
+ 
+
+ align:start position:0%
+what populations, over what businesses,
+small, large businesses, homes and so
+
+ align:start position:0%
+small, large businesses, homes and so
+ 
+
+ align:start position:0%
+small, large businesses, homes and so
+on. A very complicated strategy
+
+ align:start position:0%
+on. A very complicated strategy
+ 
+
+ align:start position:0%
+on. A very complicated strategy
+problem. So, one of the problems or
+
+ align:start position:0%
+problem. So, one of the problems or
+ 
+
+ align:start position:0%
+problem. So, one of the problems or
+another of the problems with the
+
+ align:start position:0%
+another of the problems with the
+ 
+
+ align:start position:0%
+another of the problems with the
+proliferation of internet video is the
+
+ align:start position:0%
+proliferation of internet video is the
+ 
+
+ align:start position:0%
+proliferation of internet video is the
+plumbing. And I'm a plumber, an internet
+
+ align:start position:0%
+plumbing. And I'm a plumber, an internet
+ 
+
+ align:start position:0%
+plumbing. And I'm a plumber, an internet
+plumber. So, let me talk a bit about the
+
+ align:start position:0%
+plumber. So, let me talk a bit about the
+ 
+
+ align:start position:0%
+plumber. So, let me talk a bit about the
+problems presented by the internet's
+
+ align:start position:0%
+problems presented by the internet's
+ 
+
+ align:start position:0%
+problems presented by the internet's
+plumbing. The uh term to describe the
+
+ align:start position:0%
+plumbing. The uh term to describe the
+ 
+
+ align:start position:0%
+plumbing. The uh term to describe the
+heart and soul of internet plumbing is
+
+ align:start position:0%
+heart and soul of internet plumbing is
+ 
+
+ align:start position:0%
+heart and soul of internet plumbing is
+TCPIP which is the name of the protocols
+
+ align:start position:0%
+TCPIP which is the name of the protocols
+ 
+
+ align:start position:0%
+TCPIP which is the name of the protocols
+that have been I guess they were
+
+ align:start position:0%
+that have been I guess they were
+ 
+
+ align:start position:0%
+that have been I guess they were
+installed in the internet in 1983. They
+
+ align:start position:0%
+installed in the internet in 1983. They
+ 
+
+ align:start position:0%
+installed in the internet in 1983. They
+were probably invented in
+
+ align:start position:0%
+were probably invented in
+ 
+
+ align:start position:0%
+were probably invented in
+1973. And these uh protocols um present
+
+ align:start position:0%
+1973. And these uh protocols um present
+ 
+
+ align:start position:0%
+1973. And these uh protocols um present
+problems for the carriage of video over
+
+ align:start position:0%
+problems for the carriage of video over
+ 
+
+ align:start position:0%
+problems for the carriage of video over
+the internet. When you try to in today's
+
+ align:start position:0%
+the internet. When you try to in today's
+ 
+
+ align:start position:0%
+the internet. When you try to in today's
+world when you try to carry video over
+
+ align:start position:0%
+world when you try to carry video over
+ 
+
+ align:start position:0%
+world when you try to carry video over
+the internet it's the uh plumbing is
+
+ align:start position:0%
+the internet it's the uh plumbing is
+ 
+
+ align:start position:0%
+the internet it's the uh plumbing is
+slow and it's lossy. that is information
+
+ align:start position:0%
+slow and it's lossy. that is information
+ 
+
+ align:start position:0%
+slow and it's lossy. that is information
+is lost and it's delayed jittery jittery
+
+ align:start position:0%
+is lost and it's delayed jittery jittery
+ 
+
+ align:start position:0%
+is lost and it's delayed jittery jittery
+and delayed when it gets there and these
+
+ align:start position:0%
+and delayed when it gets there and these
+ 
+
+ align:start position:0%
+and delayed when it gets there and these
+present problems for television.
+
+ align:start position:0%
+present problems for television.
+ 
+
+ align:start position:0%
+present problems for television.
+Television is much higher uses many more
+
+ align:start position:0%
+Television is much higher uses many more
+ 
+
+ align:start position:0%
+Television is much higher uses many more
+bits per second than telephone or the
+
+ align:start position:0%
+bits per second than telephone or the
+ 
+
+ align:start position:0%
+bits per second than telephone or the
+web. It relies on uh the data getting
+
+ align:start position:0%
+web. It relies on uh the data getting
+ 
+
+ align:start position:0%
+web. It relies on uh the data getting
+through reliably so that the whole
+
+ align:start position:0%
+through reliably so that the whole
+ 
+
+ align:start position:0%
+through reliably so that the whole
+picture gets painted not just little
+
+ align:start position:0%
+picture gets painted not just little
+ 
+
+ align:start position:0%
+picture gets painted not just little
+corners of the picture and it's uh real
+
+ align:start position:0%
+corners of the picture and it's uh real
+ 
+
+ align:start position:0%
+corners of the picture and it's uh real
+time you know I'm moving in real time
+
+ align:start position:0%
+time you know I'm moving in real time
+ 
+
+ align:start position:0%
+time you know I'm moving in real time
+and uh if the packets are delayed and I
+
+ align:start position:0%
+and uh if the packets are delayed and I
+ 
+
+ align:start position:0%
+and uh if the packets are delayed and I
+stop momentarily that's disruptive to um
+
+ align:start position:0%
+stop momentarily that's disruptive to um
+ 
+
+ align:start position:0%
+stop momentarily that's disruptive to um
+what you expect from video now there
+
+ align:start position:0%
+what you expect from video now there
+ 
+
+ align:start position:0%
+what you expect from video now there
+have been some efforts to solve the
+
+ align:start position:0%
+have been some efforts to solve the
+ 
+
+ align:start position:0%
+have been some efforts to solve the
+problems of the internet as a as
+
+ align:start position:0%
+problems of the internet as a as
+ 
+
+ align:start position:0%
+problems of the internet as a as
+plumbing for video and one of those is
+
+ align:start position:0%
+plumbing for video and one of those is
+ 
+
+ align:start position:0%
+plumbing for video and one of those is
+broadband deployment that I've just
+
+ align:start position:0%
+broadband deployment that I've just
+ 
+
+ align:start position:0%
+broadband deployment that I've just
+touched on that is increasing the speed
+
+ align:start position:0%
+touched on that is increasing the speed
+ 
+
+ align:start position:0%
+touched on that is increasing the speed
+of all the circuits so they can better
+
+ align:start position:0%
+of all the circuits so they can better
+ 
+
+ align:start position:0%
+of all the circuits so they can better
+carry video. But then there are protocol
+
+ align:start position:0%
+carry video. But then there are protocol
+ 
+
+ align:start position:0%
+carry video. But then there are protocol
+problems with the internet. The internet
+
+ align:start position:0%
+problems with the internet. The internet
+ 
+
+ align:start position:0%
+problems with the internet. The internet
+was never designed. It was designed in
+
+ align:start position:0%
+was never designed. It was designed in
+ 
+
+ align:start position:0%
+was never designed. It was designed in
+1973. I know I attended the meetings and
+
+ align:start position:0%
+1973. I know I attended the meetings and
+ 
+
+ align:start position:0%
+1973. I know I attended the meetings and
+it was no one was talking about video in
+
+ align:start position:0%
+it was no one was talking about video in
+ 
+
+ align:start position:0%
+it was no one was talking about video in
+1973 and not even in 1983 when it was
+
+ align:start position:0%
+1973 and not even in 1983 when it was
+ 
+
+ align:start position:0%
+1973 and not even in 1983 when it was
+finally deployed in the worldwide
+
+ align:start position:0%
+finally deployed in the worldwide
+ 
+
+ align:start position:0%
+finally deployed in the worldwide
+internet. But recently as we're trying
+
+ align:start position:0%
+internet. But recently as we're trying
+ 
+
+ align:start position:0%
+internet. But recently as we're trying
+to get video on the internet, there have
+
+ align:start position:0%
+to get video on the internet, there have
+ 
+
+ align:start position:0%
+to get video on the internet, there have
+been various proposals to fix TCPIP.
+
+ align:start position:0%
+been various proposals to fix TCPIP.
+ 
+
+ align:start position:0%
+been various proposals to fix TCPIP.
+Uh um one of those proposals is to
+
+ align:start position:0%
+Uh um one of those proposals is to
+ 
+
+ align:start position:0%
+Uh um one of those proposals is to
+replace TCP with various protocols. The
+
+ align:start position:0%
+replace TCP with various protocols. The
+ 
+
+ align:start position:0%
+replace TCP with various protocols. The
+one that comes to mind is RTP, the real
+
+ align:start position:0%
+one that comes to mind is RTP, the real
+ 
+
+ align:start position:0%
+one that comes to mind is RTP, the real
+time protocol to make up some of the
+
+ align:start position:0%
+time protocol to make up some of the
+ 
+
+ align:start position:0%
+time protocol to make up some of the
+deficiencies of
+
+ align:start position:0%
+deficiencies of
+ 
+
+ align:start position:0%
+deficiencies of
+TCP. Another solution has been the
+
+ align:start position:0%
+TCP. Another solution has been the
+ 
+
+ align:start position:0%
+TCP. Another solution has been the
+development of what's called MLS, multi-
+
+ align:start position:0%
+development of what's called MLS, multi-
+ 
+
+ align:start position:0%
+development of what's called MLS, multi-
+protocol labeling system. Actually, I'm
+
+ align:start position:0%
+protocol labeling system. Actually, I'm
+ 
+
+ align:start position:0%
+protocol labeling system. Actually, I'm
+not sure that's what it means, but
+
+ align:start position:0%
+not sure that's what it means, but
+ 
+
+ align:start position:0%
+not sure that's what it means, but
+that's a lower level fix of the plumbing
+
+ align:start position:0%
+that's a lower level fix of the plumbing
+ 
+
+ align:start position:0%
+that's a lower level fix of the plumbing
+whose purpose is to speed the packets
+
+ align:start position:0%
+whose purpose is to speed the packets
+ 
+
+ align:start position:0%
+whose purpose is to speed the packets
+through the network to reduce the losses
+
+ align:start position:0%
+through the network to reduce the losses
+ 
+
+ align:start position:0%
+through the network to reduce the losses
+uh that they encounter and to get them
+
+ align:start position:0%
+uh that they encounter and to get them
+ 
+
+ align:start position:0%
+uh that they encounter and to get them
+through in a shorter time and and with
+
+ align:start position:0%
+through in a shorter time and and with
+ 
+
+ align:start position:0%
+through in a shorter time and and with
+less uh jitter. While all this is going
+
+ align:start position:0%
+less uh jitter. While all this is going
+ 
+
+ align:start position:0%
+less uh jitter. While all this is going
+on, there have been great advances in
+
+ align:start position:0%
+on, there have been great advances in
+ 
+
+ align:start position:0%
+on, there have been great advances in
+the un the plumbing that underlies
+
+ align:start position:0%
+the un the plumbing that underlies
+ 
+
+ align:start position:0%
+the un the plumbing that underlies
+TCPIP. We've seen the development of
+
+ align:start position:0%
+TCPIP. We've seen the development of
+ 
+
+ align:start position:0%
+TCPIP. We've seen the development of
+wave division multiplexing which is the
+
+ align:start position:0%
+wave division multiplexing which is the
+ 
+
+ align:start position:0%
+wave division multiplexing which is the
+use of optical fibers to carry on
+
+ align:start position:0%
+use of optical fibers to carry on
+ 
+
+ align:start position:0%
+use of optical fibers to carry on
+different colors of light carrying very
+
+ align:start position:0%
+different colors of light carrying very
+ 
+
+ align:start position:0%
+different colors of light carrying very
+high-speed uh data. So you you might
+
+ align:start position:0%
+high-speed uh data. So you you might
+ 
+
+ align:start position:0%
+high-speed uh data. So you you might
+have an optical fiber with a thou a
+
+ align:start position:0%
+have an optical fiber with a thou a
+ 
+
+ align:start position:0%
+have an optical fiber with a thou a
+thousand different not quite we're not
+
+ align:start position:0%
+thousand different not quite we're not
+ 
+
+ align:start position:0%
+thousand different not quite we're not
+there yet but very shortly a thousand
+
+ align:start position:0%
+there yet but very shortly a thousand
+ 
+
+ align:start position:0%
+there yet but very shortly a thousand
+different colors of light each carrying
+
+ align:start position:0%
+different colors of light each carrying
+ 
+
+ align:start position:0%
+different colors of light each carrying
+10 or 20 or 30 or 40 gigabits per
+
+ align:start position:0%
+10 or 20 or 30 or 40 gigabits per
+ 
+
+ align:start position:0%
+10 or 20 or 30 or 40 gigabits per
+second. So we're talking about fibers
+
+ align:start position:0%
+second. So we're talking about fibers
+ 
+
+ align:start position:0%
+second. So we're talking about fibers
+carrying terabits per second and those
+
+ align:start position:0%
+carrying terabits per second and those
+ 
+
+ align:start position:0%
+carrying terabits per second and those
+speeds are very promising uh for
+
+ align:start position:0%
+speeds are very promising uh for
+ 
+
+ align:start position:0%
+speeds are very promising uh for
+carrying video. They for example are
+
+ align:start position:0%
+carrying video. They for example are
+ 
+
+ align:start position:0%
+carrying video. They for example are
+much larger than 1.5 gigabits per second
+
+ align:start position:0%
+much larger than 1.5 gigabits per second
+ 
+
+ align:start position:0%
+much larger than 1.5 gigabits per second
+which is how much how many bits come out
+
+ align:start position:0%
+which is how much how many bits come out
+ 
+
+ align:start position:0%
+which is how much how many bits come out
+of an HD TV highdefinition television
+
+ align:start position:0%
+of an HD TV highdefinition television
+ 
+
+ align:start position:0%
+of an HD TV highdefinition television
+camera.
+
+ align:start position:0%
+camera.
+ 
+
+ align:start position:0%
+camera.
+So underneath it all, underneath TCPIP
+
+ align:start position:0%
+So underneath it all, underneath TCPIP
+ 
+
+ align:start position:0%
+So underneath it all, underneath TCPIP
+is a development of this lambda
+
+ align:start position:0%
+is a development of this lambda
+ 
+
+ align:start position:0%
+is a development of this lambda
+switching network, the ability to carry
+
+ align:start position:0%
+switching network, the ability to carry
+ 
+
+ align:start position:0%
+switching network, the ability to carry
+lambdas, that is wavelengths of light
+
+ align:start position:0%
+lambdas, that is wavelengths of light
+ 
+
+ align:start position:0%
+lambdas, that is wavelengths of light
+over these fibers at very high speed uh
+
+ align:start position:0%
+over these fibers at very high speed uh
+ 
+
+ align:start position:0%
+over these fibers at very high speed uh
+and at very low cost. So, what's likely
+
+ align:start position:0%
+and at very low cost. So, what's likely
+ 
+
+ align:start position:0%
+and at very low cost. So, what's likely
+to happen, and I'm about to say
+
+ align:start position:0%
+to happen, and I'm about to say
+ 
+
+ align:start position:0%
+to happen, and I'm about to say
+something very controversial, what's
+
+ align:start position:0%
+something very controversial, what's
+ 
+
+ align:start position:0%
+something very controversial, what's
+about to happen is that the internet,
+
+ align:start position:0%
+about to happen is that the internet,
+ 
+
+ align:start position:0%
+about to happen is that the internet,
+which is trying to fix the TCP IP
+
+ align:start position:0%
+which is trying to fix the TCP IP
+ 
+
+ align:start position:0%
+which is trying to fix the TCP IP
+plumbing up here to better carry video,
+
+ align:start position:0%
+plumbing up here to better carry video,
+ 
+
+ align:start position:0%
+plumbing up here to better carry video,
+is going to be um overlaid or I guess
+
+ align:start position:0%
+is going to be um overlaid or I guess
+ 
+
+ align:start position:0%
+is going to be um overlaid or I guess
+the right word would be underlaid by a
+
+ align:start position:0%
+the right word would be underlaid by a
+ 
+
+ align:start position:0%
+the right word would be underlaid by a
+lambda switching network, which is not
+
+ align:start position:0%
+lambda switching network, which is not
+ 
+
+ align:start position:0%
+lambda switching network, which is not
+TCPIPbased, and that these two networks
+
+ align:start position:0%
+TCPIPbased, and that these two networks
+ 
+
+ align:start position:0%
+TCPIPbased, and that these two networks
+won't fight it out somehow, but they
+
+ align:start position:0%
+won't fight it out somehow, but they
+ 
+
+ align:start position:0%
+won't fight it out somehow, but they
+will be layered. Now, we see some of
+
+ align:start position:0%
+will be layered. Now, we see some of
+ 
+
+ align:start position:0%
+will be layered. Now, we see some of
+that even today. A I mean there there is
+
+ align:start position:0%
+that even today. A I mean there there is
+ 
+
+ align:start position:0%
+that even today. A I mean there there is
+precedent for this that is on the cable
+
+ align:start position:0%
+precedent for this that is on the cable
+ 
+
+ align:start position:0%
+precedent for this that is on the cable
+networks when you use cable modems the
+
+ align:start position:0%
+networks when you use cable modems the
+ 
+
+ align:start position:0%
+networks when you use cable modems the
+cable modems carry the TCP IP network on
+
+ align:start position:0%
+cable modems carry the TCP IP network on
+ 
+
+ align:start position:0%
+cable modems carry the TCP IP network on
+the same cable that uh television is
+
+ align:start position:0%
+the same cable that uh television is
+ 
+
+ align:start position:0%
+the same cable that uh television is
+carried that is there's already an
+
+ align:start position:0%
+carried that is there's already an
+ 
+
+ align:start position:0%
+carried that is there's already an
+overlay underlay structure in the cable
+
+ align:start position:0%
+overlay underlay structure in the cable
+ 
+
+ align:start position:0%
+overlay underlay structure in the cable
+television network I'm thinking that in
+
+ align:start position:0%
+television network I'm thinking that in
+ 
+
+ align:start position:0%
+television network I'm thinking that in
+order for us to get to widescale
+
+ align:start position:0%
+order for us to get to widescale
+ 
+
+ align:start position:0%
+order for us to get to widescale
+highdefinition video uh on the internet
+
+ align:start position:0%
+highdefinition video uh on the internet
+ 
+
+ align:start position:0%
+highdefinition video uh on the internet
+we're going to have to do a similar
+
+ align:start position:0%
+we're going to have to do a similar
+ 
+
+ align:start position:0%
+we're going to have to do a similar
+thing with the underlying lambda
+
+ align:start position:0%
+thing with the underlying lambda
+ 
+
+ align:start position:0%
+thing with the underlying lambda
+switching network and the overlying TCP
+
+ align:start position:0%
+switching network and the overlying TCP
+ 
+
+ align:start position:0%
+switching network and the overlying TCP
+IP internet
+
+ align:start position:0%
+IP internet
+ 
+
+ align:start position:0%
+IP internet
+network. On top of this plumbing,
+
+ align:start position:0%
+network. On top of this plumbing,
+ 
+
+ align:start position:0%
+network. On top of this plumbing,
+problematic plumbing for the video
+
+ align:start position:0%
+problematic plumbing for the video
+ 
+
+ align:start position:0%
+problematic plumbing for the video
+internet are what you might call the
+
+ align:start position:0%
+internet are what you might call the
+ 
+
+ align:start position:0%
+internet are what you might call the
+applications, video applications. And I
+
+ align:start position:0%
+applications, video applications. And I
+ 
+
+ align:start position:0%
+applications, video applications. And I
+talk about video as if I know what those
+
+ align:start position:0%
+talk about video as if I know what those
+ 
+
+ align:start position:0%
+talk about video as if I know what those
+applications are, but I don't and no one
+
+ align:start position:0%
+applications are, but I don't and no one
+ 
+
+ align:start position:0%
+applications are, but I don't and no one
+does. So, we're talking about various
+
+ align:start position:0%
+does. So, we're talking about various
+ 
+
+ align:start position:0%
+does. So, we're talking about various
+uses of the network that involve moving
+
+ align:start position:0%
+uses of the network that involve moving
+ 
+
+ align:start position:0%
+uses of the network that involve moving
+pictures and sound like you're watching
+
+ align:start position:0%
+pictures and sound like you're watching
+ 
+
+ align:start position:0%
+pictures and sound like you're watching
+now. And and the big question is I mean
+
+ align:start position:0%
+now. And and the big question is I mean
+ 
+
+ align:start position:0%
+now. And and the big question is I mean
+as this as the infrastructure is being
+
+ align:start position:0%
+as this as the infrastructure is being
+ 
+
+ align:start position:0%
+as this as the infrastructure is being
+deployed is what will these applications
+
+ align:start position:0%
+deployed is what will these applications
+ 
+
+ align:start position:0%
+deployed is what will these applications
+be what will drive deployment and how
+
+ align:start position:0%
+be what will drive deployment and how
+ 
+
+ align:start position:0%
+be what will drive deployment and how
+will this video be used uh for actual uh
+
+ align:start position:0%
+will this video be used uh for actual uh
+ 
+
+ align:start position:0%
+will this video be used uh for actual uh
+uh delivering valuable services. So
+
+ align:start position:0%
+uh delivering valuable services. So
+ 
+
+ align:start position:0%
+uh delivering valuable services. So
+there's a growing list of forms of video
+
+ align:start position:0%
+there's a growing list of forms of video
+ 
+
+ align:start position:0%
+there's a growing list of forms of video
+and the big question is will one of
+
+ align:start position:0%
+and the big question is will one of
+ 
+
+ align:start position:0%
+and the big question is will one of
+these forms or yet an undiscovered form
+
+ align:start position:0%
+these forms or yet an undiscovered form
+ 
+
+ align:start position:0%
+these forms or yet an undiscovered form
+of video rise up to be what we call in
+
+ align:start position:0%
+of video rise up to be what we call in
+ 
+
+ align:start position:0%
+of video rise up to be what we call in
+the computer industry as the killer app
+
+ align:start position:0%
+the computer industry as the killer app
+ 
+
+ align:start position:0%
+the computer industry as the killer app
+for the video
+
+ align:start position:0%
+for the video
+ 
+
+ align:start position:0%
+for the video
+internet. One long sought use of uh
+
+ align:start position:0%
+internet. One long sought use of uh
+ 
+
+ align:start position:0%
+internet. One long sought use of uh
+networks for video has is called video
+
+ align:start position:0%
+networks for video has is called video
+ 
+
+ align:start position:0%
+networks for video has is called video
+on demand. It used to be that you'd go
+
+ align:start position:0%
+on demand. It used to be that you'd go
+ 
+
+ align:start position:0%
+on demand. It used to be that you'd go
+to the movies to see a movie and then it
+
+ align:start position:0%
+to the movies to see a movie and then it
+ 
+
+ align:start position:0%
+to the movies to see a movie and then it
+got to be you'd walk down to the video
+
+ align:start position:0%
+got to be you'd walk down to the video
+ 
+
+ align:start position:0%
+got to be you'd walk down to the video
+rental store to get a video or you'd
+
+ align:start position:0%
+rental store to get a video or you'd
+ 
+
+ align:start position:0%
+rental store to get a video or you'd
+watch it on pay-per-view or cable
+
+ align:start position:0%
+watch it on pay-per-view or cable
+ 
+
+ align:start position:0%
+watch it on pay-per-view or cable
+television. There's some not some notion
+
+ align:start position:0%
+television. There's some not some notion
+ 
+
+ align:start position:0%
+television. There's some not some notion
+that people want to see video when they
+
+ align:start position:0%
+that people want to see video when they
+ 
+
+ align:start position:0%
+that people want to see video when they
+want to see it and they don't want to
+
+ align:start position:0%
+want to see it and they don't want to
+ 
+
+ align:start position:0%
+want to see it and they don't want to
+wait. Um, so being able to select a
+
+ align:start position:0%
+wait. Um, so being able to select a
+ 
+
+ align:start position:0%
+wait. Um, so being able to select a
+video and watch it right then when you
+
+ align:start position:0%
+video and watch it right then when you
+ 
+
+ align:start position:0%
+video and watch it right then when you
+want to watch it is called video on
+
+ align:start position:0%
+want to watch it is called video on
+ 
+
+ align:start position:0%
+want to watch it is called video on
+demand. So will we be using the internet
+
+ align:start position:0%
+demand. So will we be using the internet
+ 
+
+ align:start position:0%
+demand. So will we be using the internet
+for video on demand? Will that be the
+
+ align:start position:0%
+for video on demand? Will that be the
+ 
+
+ align:start position:0%
+for video on demand? Will that be the
+killer app? Will millions of people
+
+ align:start position:0%
+killer app? Will millions of people
+ 
+
+ align:start position:0%
+killer app? Will millions of people
+wanting to watch this video right when
+
+ align:start position:0%
+wanting to watch this video right when
+ 
+
+ align:start position:0%
+wanting to watch this video right when
+they want to watch it, will that that
+
+ align:start position:0%
+they want to watch it, will that that
+ 
+
+ align:start position:0%
+they want to watch it, will that that
+demand uh drive the proliferation of the
+
+ align:start position:0%
+demand uh drive the proliferation of the
+ 
+
+ align:start position:0%
+demand uh drive the proliferation of the
+video internet? Uh I don't know. In
+
+ align:start position:0%
+video internet? Uh I don't know. In
+ 
+
+ align:start position:0%
+video internet? Uh I don't know. In
+fact, I have a theory that it won't be.
+
+ align:start position:0%
+fact, I have a theory that it won't be.
+ 
+
+ align:start position:0%
+fact, I have a theory that it won't be.
+Another and let's call it an opposite
+
+ align:start position:0%
+Another and let's call it an opposite
+ 
+
+ align:start position:0%
+Another and let's call it an opposite
+kind of uh use of video would be video
+
+ align:start position:0%
+kind of uh use of video would be video
+ 
+
+ align:start position:0%
+kind of uh use of video would be video
+phone. For for decades, we have been
+
+ align:start position:0%
+phone. For for decades, we have been
+ 
+
+ align:start position:0%
+phone. For for decades, we have been
+trying to get to the video. Right now,
+
+ align:start position:0%
+trying to get to the video. Right now,
+ 
+
+ align:start position:0%
+trying to get to the video. Right now,
+telephone as you well know is just
+
+ align:start position:0%
+telephone as you well know is just
+ 
+
+ align:start position:0%
+telephone as you well know is just
+voice. And wouldn't it be nice to be
+
+ align:start position:0%
+voice. And wouldn't it be nice to be
+ 
+
+ align:start position:0%
+voice. And wouldn't it be nice to be
+able to see the person you're talking
+
+ align:start position:0%
+able to see the person you're talking
+ 
+
+ align:start position:0%
+able to see the person you're talking
+to? I think so. But video phone has been
+
+ align:start position:0%
+to? I think so. But video phone has been
+ 
+
+ align:start position:0%
+to? I think so. But video phone has been
+very hard to achieve. It's either been
+
+ align:start position:0%
+very hard to achieve. It's either been
+ 
+
+ align:start position:0%
+very hard to achieve. It's either been
+too expensive or too crummy or uh can we
+
+ align:start position:0%
+too expensive or too crummy or uh can we
+ 
+
+ align:start position:0%
+too expensive or too crummy or uh can we
+use the internet to finally introduce
+
+ align:start position:0%
+use the internet to finally introduce
+ 
+
+ align:start position:0%
+use the internet to finally introduce
+video phone? Now, this is different from
+
+ align:start position:0%
+video phone? Now, this is different from
+ 
+
+ align:start position:0%
+video phone? Now, this is different from
+video on demand. Video on demand has to
+
+ align:start position:0%
+video on demand. Video on demand has to
+ 
+
+ align:start position:0%
+video on demand. Video on demand has to
+do with the delivery of what they call
+
+ align:start position:0%
+do with the delivery of what they call
+ 
+
+ align:start position:0%
+do with the delivery of what they call
+content. Whereas the video phone is a
+
+ align:start position:0%
+content. Whereas the video phone is a
+ 
+
+ align:start position:0%
+content. Whereas the video phone is a
+deliverer of persontoperson
+
+ align:start position:0%
+deliverer of persontoperson
+ 
+
+ align:start position:0%
+deliverer of persontoperson
+communication. These are not nearly the
+
+ align:start position:0%
+communication. These are not nearly the
+ 
+
+ align:start position:0%
+communication. These are not nearly the
+same but they both involve video. Then
+
+ align:start position:0%
+same but they both involve video. Then
+ 
+
+ align:start position:0%
+same but they both involve video. Then
+there's video conferencing and there is
+
+ align:start position:0%
+there's video conferencing and there is
+ 
+
+ align:start position:0%
+there's video conferencing and there is
+a lot of video conferencing going on in
+
+ align:start position:0%
+a lot of video conferencing going on in
+ 
+
+ align:start position:0%
+a lot of video conferencing going on in
+the world. You know you go to a special
+
+ align:start position:0%
+the world. You know you go to a special
+ 
+
+ align:start position:0%
+the world. You know you go to a special
+room with a television and a camera and
+
+ align:start position:0%
+room with a television and a camera and
+ 
+
+ align:start position:0%
+room with a television and a camera and
+then groups of people can meet at great
+
+ align:start position:0%
+then groups of people can meet at great
+ 
+
+ align:start position:0%
+then groups of people can meet at great
+distances. Perhaps video conferencing
+
+ align:start position:0%
+distances. Perhaps video conferencing
+ 
+
+ align:start position:0%
+distances. Perhaps video conferencing
+moved over onto the video internet will
+
+ align:start position:0%
+moved over onto the video internet will
+ 
+
+ align:start position:0%
+moved over onto the video internet will
+be the killer app. And then there's
+
+ align:start position:0%
+be the killer app. And then there's
+ 
+
+ align:start position:0%
+be the killer app. And then there's
+email. Now email for 20 years and
+
+ align:start position:0%
+email. Now email for 20 years and
+ 
+
+ align:start position:0%
+email. Now email for 20 years and
+probably still is the killer app for the
+
+ align:start position:0%
+probably still is the killer app for the
+ 
+
+ align:start position:0%
+probably still is the killer app for the
+internet. What about video email? What
+
+ align:start position:0%
+internet. What about video email? What
+ 
+
+ align:start position:0%
+internet. What about video email? What
+about instead of typing in your me your
+
+ align:start position:0%
+about instead of typing in your me your
+ 
+
+ align:start position:0%
+about instead of typing in your me your
+short message, what if you just turned
+
+ align:start position:0%
+short message, what if you just turned
+ 
+
+ align:start position:0%
+short message, what if you just turned
+on the camera briefly to send a video uh
+
+ align:start position:0%
+on the camera briefly to send a video uh
+ 
+
+ align:start position:0%
+on the camera briefly to send a video uh
+email? So, that was a very short list
+
+ align:start position:0%
+email? So, that was a very short list
+ 
+
+ align:start position:0%
+email? So, that was a very short list
+and I think there will be many nuances
+
+ align:start position:0%
+and I think there will be many nuances
+ 
+
+ align:start position:0%
+and I think there will be many nuances
+of video and one of those or two of
+
+ align:start position:0%
+of video and one of those or two of
+ 
+
+ align:start position:0%
+of video and one of those or two of
+those will be the killer apps driving
+
+ align:start position:0%
+those will be the killer apps driving
+ 
+
+ align:start position:0%
+those will be the killer apps driving
+the proliferation of the video internet.
+
+ align:start position:0%
+the proliferation of the video internet.
+ 
+
+ align:start position:0%
+the proliferation of the video internet.
+I don't think we know uh what it is.
+
+ align:start position:0%
+I don't think we know uh what it is.
+ 
+
+ align:start position:0%
+I don't think we know uh what it is.
+Now, there are some people already
+
+ align:start position:0%
+Now, there are some people already
+ 
+
+ align:start position:0%
+Now, there are some people already
+starting businesses uh based on internet
+
+ align:start position:0%
+starting businesses uh based on internet
+ 
+
+ align:start position:0%
+starting businesses uh based on internet
+video. I'm on the board of one small
+
+ align:start position:0%
+video. I'm on the board of one small
+ 
+
+ align:start position:0%
+video. I'm on the board of one small
+company called Avastar and based on the
+
+ align:start position:0%
+company called Avastar and based on the
+ 
+
+ align:start position:0%
+company called Avastar and based on the
+state of the infrastructure today
+
+ align:start position:0%
+state of the infrastructure today
+ 
+
+ align:start position:0%
+state of the infrastructure today
+they're focused on delivering in essence
+
+ align:start position:0%
+they're focused on delivering in essence
+ 
+
+ align:start position:0%
+they're focused on delivering in essence
+video conferencing for companies
+
+ align:start position:0%
+video conferencing for companies
+ 
+
+ align:start position:0%
+video conferencing for companies
+enterprises of course they choose
+
+ align:start position:0%
+enterprises of course they choose
+ 
+
+ align:start position:0%
+enterprises of course they choose
+companies because homes don't have
+
+ align:start position:0%
+companies because homes don't have
+ 
+
+ align:start position:0%
+companies because homes don't have
+broadband sufficient to carry video
+
+ align:start position:0%
+broadband sufficient to carry video
+ 
+
+ align:start position:0%
+broadband sufficient to carry video
+whereas big companies do so there's
+
+ align:start position:0%
+whereas big companies do so there's
+ 
+
+ align:start position:0%
+whereas big companies do so there's
+infrastructure there uh Avastar has also
+
+ align:start position:0%
+infrastructure there uh Avastar has also
+ 
+
+ align:start position:0%
+infrastructure there uh Avastar has also
+decided that human beings have seen
+
+ align:start position:0%
+decided that human beings have seen
+ 
+
+ align:start position:0%
+decided that human beings have seen
+enough television that they won't really
+
+ align:start position:0%
+enough television that they won't really
+ 
+
+ align:start position:0%
+enough television that they won't really
+appreciate video until it's at least of
+
+ align:start position:0%
+appreciate video until it's at least of
+ 
+
+ align:start position:0%
+appreciate video until it's at least of
+television quality, not jerky postage
+
+ align:start position:0%
+television quality, not jerky postage
+ 
+
+ align:start position:0%
+television quality, not jerky postage
+stamps. So they their whole system is
+
+ align:start position:0%
+stamps. So they their whole system is
+ 
+
+ align:start position:0%
+stamps. So they their whole system is
+focused around
+
+ align:start position:0%
+focused around
+ 
+
+ align:start position:0%
+focused around
+delivering at least television quality
+
+ align:start position:0%
+delivering at least television quality
+ 
+
+ align:start position:0%
+delivering at least television quality
+if not high definition later uh uh
+
+ align:start position:0%
+if not high definition later uh uh
+ 
+
+ align:start position:0%
+if not high definition later uh uh
+television quality of a certain standard
+
+ align:start position:0%
+television quality of a certain standard
+ 
+
+ align:start position:0%
+television quality of a certain standard
+that is normal television and up not uh
+
+ align:start position:0%
+that is normal television and up not uh
+ 
+
+ align:start position:0%
+that is normal television and up not uh
+something down. But after that it
+
+ align:start position:0%
+something down. But after that it
+ 
+
+ align:start position:0%
+something down. But after that it
+becomes unclear as to what the uh the
+
+ align:start position:0%
+becomes unclear as to what the uh the
+ 
+
+ align:start position:0%
+becomes unclear as to what the uh the
+real applications are. As this little
+
+ align:start position:0%
+real applications are. As this little
+ 
+
+ align:start position:0%
+real applications are. As this little
+company introduces new features, they
+
+ align:start position:0%
+company introduces new features, they
+ 
+
+ align:start position:0%
+company introduces new features, they
+find that some features don't affect
+
+ align:start position:0%
+find that some features don't affect
+ 
+
+ align:start position:0%
+find that some features don't affect
+whether people use their network for
+
+ align:start position:0%
+whether people use their network for
+ 
+
+ align:start position:0%
+whether people use their network for
+desktoes video conferencing and other
+
+ align:start position:0%
+desktoes video conferencing and other
+ 
+
+ align:start position:0%
+desktoes video conferencing and other
+features have a dramatic effect on
+
+ align:start position:0%
+features have a dramatic effect on
+ 
+
+ align:start position:0%
+features have a dramatic effect on
+usage. Uh my my theory is that in in
+
+ align:start position:0%
+usage. Uh my my theory is that in in
+ 
+
+ align:start position:0%
+usage. Uh my my theory is that in in
+this case, this is a communication use
+
+ align:start position:0%
+this case, this is a communication use
+ 
+
+ align:start position:0%
+this case, this is a communication use
+of video. It's the and I've invented a
+
+ align:start position:0%
+of video. It's the and I've invented a
+ 
+
+ align:start position:0%
+of video. It's the and I've invented a
+word for this if you'll excuse me, the
+
+ align:start position:0%
+word for this if you'll excuse me, the
+ 
+
+ align:start position:0%
+word for this if you'll excuse me, the
+consummatability. When you make a video
+
+ align:start position:0%
+consummatability. When you make a video
+ 
+
+ align:start position:0%
+consummatability. When you make a video
+call, what is the probability that you
+
+ align:start position:0%
+call, what is the probability that you
+ 
+
+ align:start position:0%
+call, what is the probability that you
+get the job done?
+
+ align:start position:0%
+get the job done?
+ 
+
+ align:start position:0%
+get the job done?
+uh uh voicemail for example increases
+
+ align:start position:0%
+uh uh voicemail for example increases
+ 
+
+ align:start position:0%
+uh uh voicemail for example increases
+the consummatability of a telephone
+
+ align:start position:0%
+the consummatability of a telephone
+ 
+
+ align:start position:0%
+the consummatability of a telephone
+call. When you call someone it's not and
+
+ align:start position:0%
+call. When you call someone it's not and
+ 
+
+ align:start position:0%
+call. When you call someone it's not and
+you get no answer. You have not
+
+ align:start position:0%
+you get no answer. You have not
+ 
+
+ align:start position:0%
+you get no answer. You have not
+consummated your telephone call. But if
+
+ align:start position:0%
+consummated your telephone call. But if
+ 
+
+ align:start position:0%
+consummated your telephone call. But if
+you get an answering machine, well then
+
+ align:start position:0%
+you get an answering machine, well then
+ 
+
+ align:start position:0%
+you get an answering machine, well then
+you might be able to consummate the
+
+ align:start position:0%
+you might be able to consummate the
+ 
+
+ align:start position:0%
+you might be able to consummate the
+purpose of the call even if they're not
+
+ align:start position:0%
+purpose of the call even if they're not
+ 
+
+ align:start position:0%
+purpose of the call even if they're not
+there. Um I think what we're finding in
+
+ align:start position:0%
+there. Um I think what we're finding in
+ 
+
+ align:start position:0%
+there. Um I think what we're finding in
+the video world is that the
+
+ align:start position:0%
+the video world is that the
+ 
+
+ align:start position:0%
+the video world is that the
+consummatability of video calls is
+
+ align:start position:0%
+consummatability of video calls is
+ 
+
+ align:start position:0%
+consummatability of video calls is
+important. If you try to make a video
+
+ align:start position:0%
+important. If you try to make a video
+ 
+
+ align:start position:0%
+important. If you try to make a video
+call and the person's not there, if you
+
+ align:start position:0%
+call and the person's not there, if you
+ 
+
+ align:start position:0%
+call and the person's not there, if you
+have the opportunity to live a to leave
+
+ align:start position:0%
+have the opportunity to live a to leave
+ 
+
+ align:start position:0%
+have the opportunity to live a to leave
+a video mail instead, that increases the
+
+ align:start position:0%
+a video mail instead, that increases the
+ 
+
+ align:start position:0%
+a video mail instead, that increases the
+consummatability of the call and
+
+ align:start position:0%
+consummatability of the call and
+ 
+
+ align:start position:0%
+consummatability of the call and
+therefore its usage.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the picture I'd like to leave you
+
+ align:start position:0%
+So the picture I'd like to leave you
+ 
+
+ align:start position:0%
+So the picture I'd like to leave you
+with on the um emergence of the video
+
+ align:start position:0%
+with on the um emergence of the video
+ 
+
+ align:start position:0%
+with on the um emergence of the video
+internet is one of a 10 or 20 year
+
+ align:start position:0%
+internet is one of a 10 or 20 year
+ 
+
+ align:start position:0%
+internet is one of a 10 or 20 year
+process unfolding in a unpredictable
+
+ align:start position:0%
+process unfolding in a unpredictable
+ 
+
+ align:start position:0%
+process unfolding in a unpredictable
+ways with a lot of um experimentation
+
+ align:start position:0%
+ways with a lot of um experimentation
+ 
+
+ align:start position:0%
+ways with a lot of um experimentation
+and discovery going on uh in the
+
+ align:start position:0%
+and discovery going on uh in the
+ 
+
+ align:start position:0%
+and discovery going on uh in the
+meantime. And here are some of the
+
+ align:start position:0%
+meantime. And here are some of the
+ 
+
+ align:start position:0%
+meantime. And here are some of the
+phases that I anticipate will occur in
+
+ align:start position:0%
+phases that I anticipate will occur in
+ 
+
+ align:start position:0%
+phases that I anticipate will occur in
+this proliferation.
+
+ align:start position:0%
+this proliferation.
+ 
+
+ align:start position:0%
+this proliferation.
+uh often in the proliferation of a new
+
+ align:start position:0%
+uh often in the proliferation of a new
+ 
+
+ align:start position:0%
+uh often in the proliferation of a new
+technology or a new infrastructure
+
+ align:start position:0%
+technology or a new infrastructure
+ 
+
+ align:start position:0%
+technology or a new infrastructure
+there's an arbitrage factor that is the
+
+ align:start position:0%
+there's an arbitrage factor that is the
+ 
+
+ align:start position:0%
+there's an arbitrage factor that is the
+old way is expensive for artificial
+
+ align:start position:0%
+old way is expensive for artificial
+ 
+
+ align:start position:0%
+old way is expensive for artificial
+reasons for example regulation of the
+
+ align:start position:0%
+reasons for example regulation of the
+ 
+
+ align:start position:0%
+reasons for example regulation of the
+telephone network and the new technology
+
+ align:start position:0%
+telephone network and the new technology
+ 
+
+ align:start position:0%
+telephone network and the new technology
+arrives without the burden of that
+
+ align:start position:0%
+arrives without the burden of that
+ 
+
+ align:start position:0%
+arrives without the burden of that
+regulation and is able to just be
+
+ align:start position:0%
+regulation and is able to just be
+ 
+
+ align:start position:0%
+regulation and is able to just be
+cheaper better faster by version of
+
+ align:start position:0%
+cheaper better faster by version of
+ 
+
+ align:start position:0%
+cheaper better faster by version of
+arbitrage against the tariffs that are
+
+ align:start position:0%
+arbitrage against the tariffs that are
+ 
+
+ align:start position:0%
+arbitrage against the tariffs that are
+not really related to costs or
+
+ align:start position:0%
+not really related to costs or
+ 
+
+ align:start position:0%
+not really related to costs or
+underlying factors the arbitrage phase
+
+ align:start position:0%
+underlying factors the arbitrage phase
+ 
+
+ align:start position:0%
+underlying factors the arbitrage phase
+is frequently followed thereafter by
+
+ align:start position:0%
+is frequently followed thereafter by
+ 
+
+ align:start position:0%
+is frequently followed thereafter by
+actual cost savings that is the old way
+
+ align:start position:0%
+actual cost savings that is the old way
+ 
+
+ align:start position:0%
+actual cost savings that is the old way
+is more expensive than the new way
+
+ align:start position:0%
+is more expensive than the new way
+ 
+
+ align:start position:0%
+is more expensive than the new way
+intrinsically and so the new way begins
+
+ align:start position:0%
+intrinsically and so the new way begins
+ 
+
+ align:start position:0%
+intrinsically and so the new way begins
+to dominate.
+
+ align:start position:0%
+to dominate.
+ 
+
+ align:start position:0%
+to dominate.
+uh the new another phase often the third
+
+ align:start position:0%
+uh the new another phase often the third
+ 
+
+ align:start position:0%
+uh the new another phase often the third
+phase is where the the uh the new
+
+ align:start position:0%
+phase is where the the uh the new
+ 
+
+ align:start position:0%
+phase is where the the uh the new
+technology brings with it new
+
+ align:start position:0%
+technology brings with it new
+ 
+
+ align:start position:0%
+technology brings with it new
+applications that were previously not
+
+ align:start position:0%
+applications that were previously not
+ 
+
+ align:start position:0%
+applications that were previously not
+possible with the old technology and
+
+ align:start position:0%
+possible with the old technology and
+ 
+
+ align:start position:0%
+possible with the old technology and
+that's attractive to people to do
+
+ align:start position:0%
+that's attractive to people to do
+ 
+
+ align:start position:0%
+that's attractive to people to do
+entirely new things not to do the old
+
+ align:start position:0%
+entirely new things not to do the old
+ 
+
+ align:start position:0%
+entirely new things not to do the old
+things better cheaper faster but to do
+
+ align:start position:0%
+things better cheaper faster but to do
+ 
+
+ align:start position:0%
+things better cheaper faster but to do
+new things then after that you begin to
+
+ align:start position:0%
+new things then after that you begin to
+ 
+
+ align:start position:0%
+new things then after that you begin to
+see the convergence of the old and the
+
+ align:start position:0%
+see the convergence of the old and the
+ 
+
+ align:start position:0%
+see the convergence of the old and the
+new the integration of the old and the
+
+ align:start position:0%
+new the integration of the old and the
+ 
+
+ align:start position:0%
+new the integration of the old and the
+new so for example video pure video like
+
+ align:start position:0%
+new so for example video pure video like
+ 
+
+ align:start position:0%
+new so for example video pure video like
+you're watching now is probably not the
+
+ align:start position:0%
+you're watching now is probably not the
+ 
+
+ align:start position:0%
+you're watching now is probably not the
+right answer. Ultimately, it'll probably
+
+ align:start position:0%
+right answer. Ultimately, it'll probably
+ 
+
+ align:start position:0%
+right answer. Ultimately, it'll probably
+be the connection of video with
+
+ align:start position:0%
+be the connection of video with
+ 
+
+ align:start position:0%
+be the connection of video with
+PowerPoint, video with telephone, video
+
+ align:start position:0%
+PowerPoint, video with telephone, video
+ 
+
+ align:start position:0%
+PowerPoint, video with telephone, video
+with conferencing, that is an
+
+ align:start position:0%
+with conferencing, that is an
+ 
+
+ align:start position:0%
+with conferencing, that is an
+integration across applications that
+
+ align:start position:0%
+integration across applications that
+ 
+
+ align:start position:0%
+integration across applications that
+were previously uh separate. And then uh
+
+ align:start position:0%
+were previously uh separate. And then uh
+ 
+
+ align:start position:0%
+were previously uh separate. And then uh
+other factors which pace the
+
+ align:start position:0%
+other factors which pace the
+ 
+
+ align:start position:0%
+other factors which pace the
+proliferation of the infrastructure have
+
+ align:start position:0%
+proliferation of the infrastructure have
+ 
+
+ align:start position:0%
+proliferation of the infrastructure have
+to do with the making of standards.
+
+ align:start position:0%
+to do with the making of standards.
+ 
+
+ align:start position:0%
+to do with the making of standards.
+These technologies uh must be
+
+ align:start position:0%
+These technologies uh must be
+ 
+
+ align:start position:0%
+These technologies uh must be
+standardized over time. that is uh
+
+ align:start position:0%
+standardized over time. that is uh
+ 
+
+ align:start position:0%
+standardized over time. that is uh
+communication and content delivery
+
+ align:start position:0%
+communication and content delivery
+ 
+
+ align:start position:0%
+communication and content delivery
+infrastructures require standardization
+
+ align:start position:0%
+infrastructures require standardization
+ 
+
+ align:start position:0%
+infrastructures require standardization
+because they require vast investments in
+
+ align:start position:0%
+because they require vast investments in
+ 
+
+ align:start position:0%
+because they require vast investments in
+infrastructure and no one is willing to
+
+ align:start position:0%
+infrastructure and no one is willing to
+ 
+
+ align:start position:0%
+infrastructure and no one is willing to
+make infrastructural investments uh
+
+ align:start position:0%
+make infrastructural investments uh
+ 
+
+ align:start position:0%
+make infrastructural investments uh
+without standards. If they are willing
+
+ align:start position:0%
+without standards. If they are willing
+ 
+
+ align:start position:0%
+without standards. If they are willing
+they're unwise because when you invest a
+
+ align:start position:0%
+they're unwise because when you invest a
+ 
+
+ align:start position:0%
+they're unwise because when you invest a
+lot of money you want to be sure to have
+
+ align:start position:0%
+lot of money you want to be sure to have
+ 
+
+ align:start position:0%
+lot of money you want to be sure to have
+standards so that you have multiple
+
+ align:start position:0%
+standards so that you have multiple
+ 
+
+ align:start position:0%
+standards so that you have multiple
+suppliers that you can set against each
+
+ align:start position:0%
+suppliers that you can set against each
+ 
+
+ align:start position:0%
+suppliers that you can set against each
+other in a competitive environment.
+
+ align:start position:0%
+other in a competitive environment.
+ 
+
+ align:start position:0%
+other in a competitive environment.
+A question which arises in this
+
+ align:start position:0%
+A question which arises in this
+ 
+
+ align:start position:0%
+A question which arises in this
+unfolding is as I mentioned the which
+
+ align:start position:0%
+unfolding is as I mentioned the which
+ 
+
+ align:start position:0%
+unfolding is as I mentioned the which
+will be the killer apps and we have
+
+ align:start position:0%
+will be the killer apps and we have
+ 
+
+ align:start position:0%
+will be the killer apps and we have
+these broad categories that we've seen
+
+ align:start position:0%
+these broad categories that we've seen
+ 
+
+ align:start position:0%
+these broad categories that we've seen
+emerge on the prevideo internet we had
+
+ align:start position:0%
+emerge on the prevideo internet we had
+ 
+
+ align:start position:0%
+emerge on the prevideo internet we had
+the emergence as I mentioned of the
+
+ align:start position:0%
+the emergence as I mentioned of the
+ 
+
+ align:start position:0%
+the emergence as I mentioned of the
+publishing web web publishing where that
+
+ align:start position:0%
+publishing web web publishing where that
+ 
+
+ align:start position:0%
+publishing web web publishing where that
+was content delivery in a new way then
+
+ align:start position:0%
+was content delivery in a new way then
+ 
+
+ align:start position:0%
+was content delivery in a new way then
+we had uh uh communication and it's been
+
+ align:start position:0%
+we had uh uh communication and it's been
+ 
+
+ align:start position:0%
+we had uh uh communication and it's been
+in the history of the internet
+
+ align:start position:0%
+in the history of the internet
+ 
+
+ align:start position:0%
+in the history of the internet
+communication has been the more vital
+
+ align:start position:0%
+communication has been the more vital
+ 
+
+ align:start position:0%
+communication has been the more vital
+use rather than delivery of content In
+
+ align:start position:0%
+use rather than delivery of content In
+ 
+
+ align:start position:0%
+use rather than delivery of content In
+the early days of the internet, there
+
+ align:start position:0%
+the early days of the internet, there
+ 
+
+ align:start position:0%
+the early days of the internet, there
+was Compius and Prodigy that were
+
+ align:start position:0%
+was Compius and Prodigy that were
+ 
+
+ align:start position:0%
+was Compius and Prodigy that were
+contentoriented and along came America
+
+ align:start position:0%
+contentoriented and along came America
+ 
+
+ align:start position:0%
+contentoriented and along came America
+Online which was very
+
+ align:start position:0%
+Online which was very
+ 
+
+ align:start position:0%
+Online which was very
+communicationoriented and we know which
+
+ align:start position:0%
+communicationoriented and we know which
+ 
+
+ align:start position:0%
+communicationoriented and we know which
+ones uh one that is communication proved
+
+ align:start position:0%
+ones uh one that is communication proved
+ 
+
+ align:start position:0%
+ones uh one that is communication proved
+to be the more at least in the short
+
+ align:start position:0%
+to be the more at least in the short
+ 
+
+ align:start position:0%
+to be the more at least in the short
+term the more desirable um use the more
+
+ align:start position:0%
+term the more desirable um use the more
+ 
+
+ align:start position:0%
+term the more desirable um use the more
+driving use and then came commerce. So
+
+ align:start position:0%
+driving use and then came commerce. So
+ 
+
+ align:start position:0%
+driving use and then came commerce. So
+we had communication, content,
+
+ align:start position:0%
+we had communication, content,
+ 
+
+ align:start position:0%
+we had communication, content,
+communication and commerce and and we
+
+ align:start position:0%
+communication and commerce and and we
+ 
+
+ align:start position:0%
+communication and commerce and and we
+can wonder and guess whether that same
+
+ align:start position:0%
+can wonder and guess whether that same
+ 
+
+ align:start position:0%
+can wonder and guess whether that same
+evolution will uh recapitulate itself in
+
+ align:start position:0%
+evolution will uh recapitulate itself in
+ 
+
+ align:start position:0%
+evolution will uh recapitulate itself in
+the video internet. Now video has in the
+
+ align:start position:0%
+the video internet. Now video has in the
+ 
+
+ align:start position:0%
+the video internet. Now video has in the
+past been driven by entertainment.
+
+ align:start position:0%
+past been driven by entertainment.
+ 
+
+ align:start position:0%
+past been driven by entertainment.
+Television is mostly uh entertainment
+
+ align:start position:0%
+Television is mostly uh entertainment
+ 
+
+ align:start position:0%
+Television is mostly uh entertainment
+and it's an advertising business model
+
+ align:start position:0%
+and it's an advertising business model
+ 
+
+ align:start position:0%
+and it's an advertising business model
+for the most part although increasingly
+
+ align:start position:0%
+for the most part although increasingly
+ 
+
+ align:start position:0%
+for the most part although increasingly
+there are subscriptions but there it's I
+
+ align:start position:0%
+there are subscriptions but there it's I
+ 
+
+ align:start position:0%
+there are subscriptions but there it's I
+think it's best to think of it as an
+
+ align:start position:0%
+think it's best to think of it as an
+ 
+
+ align:start position:0%
+think it's best to think of it as an
+advertising entertainmentdriven medium.
+
+ align:start position:0%
+advertising entertainmentdriven medium.
+ 
+
+ align:start position:0%
+advertising entertainmentdriven medium.
+How will that be affected by integration
+
+ align:start position:0%
+How will that be affected by integration
+ 
+
+ align:start position:0%
+How will that be affected by integration
+with the internet? Uh I think internet
+
+ align:start position:0%
+with the internet? Uh I think internet
+ 
+
+ align:start position:0%
+with the internet? Uh I think internet
+will uh entertainment will drive uh
+
+ align:start position:0%
+will uh entertainment will drive uh
+ 
+
+ align:start position:0%
+will uh entertainment will drive uh
+adoptance of the adoption of the video
+
+ align:start position:0%
+adoptance of the adoption of the video
+ 
+
+ align:start position:0%
+adoptance of the adoption of the video
+internet. Uh and that has some good uh
+
+ align:start position:0%
+internet. Uh and that has some good uh
+ 
+
+ align:start position:0%
+internet. Uh and that has some good uh
+will have some good uh implications for
+
+ align:start position:0%
+will have some good uh implications for
+ 
+
+ align:start position:0%
+will have some good uh implications for
+education. We we talk about education on
+
+ align:start position:0%
+education. We we talk about education on
+ 
+
+ align:start position:0%
+education. We we talk about education on
+the internet and the use of the internet
+
+ align:start position:0%
+the internet and the use of the internet
+ 
+
+ align:start position:0%
+the internet and the use of the internet
+in education. And I think as video and
+
+ align:start position:0%
+in education. And I think as video and
+ 
+
+ align:start position:0%
+in education. And I think as video and
+entertainment get into the internet,
+
+ align:start position:0%
+entertainment get into the internet,
+ 
+
+ align:start position:0%
+entertainment get into the internet,
+this bodess well for education because
+
+ align:start position:0%
+this bodess well for education because
+ 
+
+ align:start position:0%
+this bodess well for education because
+right now education competes with
+
+ align:start position:0%
+right now education competes with
+ 
+
+ align:start position:0%
+right now education competes with
+entertainment on an uneven footing. The
+
+ align:start position:0%
+entertainment on an uneven footing. The
+ 
+
+ align:start position:0%
+entertainment on an uneven footing. The
+uh entertainment model allows for high
+
+ align:start position:0%
+uh entertainment model allows for high
+ 
+
+ align:start position:0%
+uh entertainment model allows for high
+production values which are attractive
+
+ align:start position:0%
+production values which are attractive
+ 
+
+ align:start position:0%
+production values which are attractive
+to the uh uh to kids whereas the
+
+ align:start position:0%
+to the uh uh to kids whereas the
+ 
+
+ align:start position:0%
+to the uh uh to kids whereas the
+entertainment the education business
+
+ align:start position:0%
+entertainment the education business
+ 
+
+ align:start position:0%
+entertainment the education business
+does not have the same access to
+
+ align:start position:0%
+does not have the same access to
+ 
+
+ align:start position:0%
+does not have the same access to
+production values. So there's kind of a
+
+ align:start position:0%
+production values. So there's kind of a
+ 
+
+ align:start position:0%
+production values. So there's kind of a
+uh I mean thank goodness for the
+
+ align:start position:0%
+uh I mean thank goodness for the
+ 
+
+ align:start position:0%
+uh I mean thank goodness for the
+discovery channel which does have high
+
+ align:start position:0%
+discovery channel which does have high
+ 
+
+ align:start position:0%
+discovery channel which does have high
+production values. So there you see an
+
+ align:start position:0%
+production values. So there you see an
+ 
+
+ align:start position:0%
+production values. So there you see an
+example where if you raise the
+
+ align:start position:0%
+example where if you raise the
+ 
+
+ align:start position:0%
+example where if you raise the
+production values of education it can
+
+ align:start position:0%
+production values of education it can
+ 
+
+ align:start position:0%
+production values of education it can
+then compete on an even footing with uh
+
+ align:start position:0%
+then compete on an even footing with uh
+ 
+
+ align:start position:0%
+then compete on an even footing with uh
+entertainment. So as we get video on the
+
+ align:start position:0%
+entertainment. So as we get video on the
+ 
+
+ align:start position:0%
+entertainment. So as we get video on the
+internet and the general facilities for
+
+ align:start position:0%
+internet and the general facilities for
+ 
+
+ align:start position:0%
+internet and the general facilities for
+increasing production values on the
+
+ align:start position:0%
+increasing production values on the
+ 
+
+ align:start position:0%
+increasing production values on the
+internet and as the infrastructure
+
+ align:start position:0%
+internet and as the infrastructure
+ 
+
+ align:start position:0%
+internet and as the infrastructure
+improves for delivering those production
+
+ align:start position:0%
+improves for delivering those production
+ 
+
+ align:start position:0%
+improves for delivering those production
+values, I think this will have a related
+
+ align:start position:0%
+values, I think this will have a related
+ 
+
+ align:start position:0%
+values, I think this will have a related
+benefit to the use of the internet uh
+
+ align:start position:0%
+benefit to the use of the internet uh
+ 
+
+ align:start position:0%
+benefit to the use of the internet uh
+for education. It's getting to the point
+
+ align:start position:0%
+for education. It's getting to the point
+ 
+
+ align:start position:0%
+for education. It's getting to the point
+now where we can begin to think uh not
+
+ align:start position:0%
+now where we can begin to think uh not
+ 
+
+ align:start position:0%
+now where we can begin to think uh not
+so much of putting the internet in
+
+ align:start position:0%
+so much of putting the internet in
+ 
+
+ align:start position:0%
+so much of putting the internet in
+schools but instead using the internet
+
+ align:start position:0%
+schools but instead using the internet
+ 
+
+ align:start position:0%
+schools but instead using the internet
+instead of schools. That is if as we
+
+ align:start position:0%
+instead of schools. That is if as we
+ 
+
+ align:start position:0%
+instead of schools. That is if as we
+begin to have a very high bandwidth and
+
+ align:start position:0%
+begin to have a very high bandwidth and
+ 
+
+ align:start position:0%
+begin to have a very high bandwidth and
+ubiquitous internet with uh video more
+
+ align:start position:0%
+ubiquitous internet with uh video more
+ 
+
+ align:start position:0%
+ubiquitous internet with uh video more
+and more it can be used for education uh
+
+ align:start position:0%
+and more it can be used for education uh
+ 
+
+ align:start position:0%
+and more it can be used for education uh
+from the home instead of uh busing
+
+ align:start position:0%
+from the home instead of uh busing
+ 
+
+ align:start position:0%
+from the home instead of uh busing
+people off to remote places to be taught
+
+ align:start position:0%
+people off to remote places to be taught
+ 
+
+ align:start position:0%
+people off to remote places to be taught
+with uh chalk on
+
+ align:start position:0%
+with uh chalk on
+ 
+
+ align:start position:0%
+with uh chalk on
+slate. I'd like to close with a short
+
+ align:start position:0%
+slate. I'd like to close with a short
+ 
+
+ align:start position:0%
+slate. I'd like to close with a short
+story of a recent interaction that I had
+
+ align:start position:0%
+story of a recent interaction that I had
+ 
+
+ align:start position:0%
+story of a recent interaction that I had
+with video over the internet. Uh only
+
+ align:start position:0%
+with video over the internet. Uh only
+ 
+
+ align:start position:0%
+with video over the internet. Uh only
+this wasn't just normal video. This was
+
+ align:start position:0%
+this wasn't just normal video. This was
+ 
+
+ align:start position:0%
+this wasn't just normal video. This was
+highdefin television, a coming thing in
+
+ align:start position:0%
+highdefin television, a coming thing in
+ 
+
+ align:start position:0%
+highdefin television, a coming thing in
+video. And this wasn't just the
+
+ align:start position:0%
+video. And this wasn't just the
+ 
+
+ align:start position:0%
+video. And this wasn't just the
+internet. This was internet 2, the new
+
+ align:start position:0%
+internet. This was internet 2, the new
+ 
+
+ align:start position:0%
+internet. This was internet 2, the new
+version of the internet, much higher
+
+ align:start position:0%
+version of the internet, much higher
+ 
+
+ align:start position:0%
+version of the internet, much higher
+speed version of the internet that
+
+ align:start position:0%
+speed version of the internet that
+ 
+
+ align:start position:0%
+speed version of the internet that
+people are working on. And I was asked
+
+ align:start position:0%
+people are working on. And I was asked
+ 
+
+ align:start position:0%
+people are working on. And I was asked
+to do a short video presentation, not
+
+ align:start position:0%
+to do a short video presentation, not
+ 
+
+ align:start position:0%
+to do a short video presentation, not
+unlike this one uh from here at from MIT
+
+ align:start position:0%
+unlike this one uh from here at from MIT
+ 
+
+ align:start position:0%
+unlike this one uh from here at from MIT
+uh to be delivered on a huge screen at a
+
+ align:start position:0%
+uh to be delivered on a huge screen at a
+ 
+
+ align:start position:0%
+uh to be delivered on a huge screen at a
+conference center in uh Las Vegas. Uh in
+
+ align:start position:0%
+conference center in uh Las Vegas. Uh in
+ 
+
+ align:start position:0%
+conference center in uh Las Vegas. Uh in
+fact, it was part of the keynote address
+
+ align:start position:0%
+fact, it was part of the keynote address
+ 
+
+ align:start position:0%
+fact, it was part of the keynote address
+of uh Craig Barrett from Intel. So I
+
+ align:start position:0%
+of uh Craig Barrett from Intel. So I
+ 
+
+ align:start position:0%
+of uh Craig Barrett from Intel. So I
+arrived at this room over here at MIT
+
+ align:start position:0%
+arrived at this room over here at MIT
+ 
+
+ align:start position:0%
+arrived at this room over here at MIT
+across campus where there was a
+
+ align:start position:0%
+across campus where there was a
+ 
+
+ align:start position:0%
+across campus where there was a
+highdefinition camera and out of that
+
+ align:start position:0%
+highdefinition camera and out of that
+ 
+
+ align:start position:0%
+highdefinition camera and out of that
+camera came 1.5 gigabits billion bits
+
+ align:start position:0%
+camera came 1.5 gigabits billion bits
+ 
+
+ align:start position:0%
+camera came 1.5 gigabits billion bits
+per second of video of a much higher
+
+ align:start position:0%
+per second of video of a much higher
+ 
+
+ align:start position:0%
+per second of video of a much higher
+quality version of me that went into
+
+ align:start position:0%
+quality version of me that went into
+ 
+
+ align:start position:0%
+quality version of me that went into
+these boxes. And there were people
+
+ align:start position:0%
+these boxes. And there were people
+ 
+
+ align:start position:0%
+these boxes. And there were people
+sitting around by the boxes running
+
+ align:start position:0%
+sitting around by the boxes running
+ 
+
+ align:start position:0%
+sitting around by the boxes running
+them. And those boxes would take this
+
+ align:start position:0%
+them. And those boxes would take this
+ 
+
+ align:start position:0%
+them. And those boxes would take this
+1.5 Gbits per second and crunch it down,
+
+ align:start position:0%
+1.5 Gbits per second and crunch it down,
+ 
+
+ align:start position:0%
+1.5 Gbits per second and crunch it down,
+compress it down to 20 megabits per
+
+ align:start position:0%
+compress it down to 20 megabits per
+ 
+
+ align:start position:0%
+compress it down to 20 megabits per
+second that was then carried over an e
+
+ align:start position:0%
+second that was then carried over an e
+ 
+
+ align:start position:0%
+second that was then carried over an e
+100 megabit per second Ethernet cable
+
+ align:start position:0%
+100 megabit per second Ethernet cable
+ 
+
+ align:start position:0%
+100 megabit per second Ethernet cable
+into internet 2 there in Cambridge here
+
+ align:start position:0%
+into internet 2 there in Cambridge here
+ 
+
+ align:start position:0%
+into internet 2 there in Cambridge here
+in Cambridge. And then it went several
+
+ align:start position:0%
+in Cambridge. And then it went several
+ 
+
+ align:start position:0%
+in Cambridge. And then it went several
+hops through the southern United States
+
+ align:start position:0%
+hops through the southern United States
+ 
+
+ align:start position:0%
+hops through the southern United States
+uh to arrive in uh Las Vegas at 2.4
+
+ align:start position:0%
+uh to arrive in uh Las Vegas at 2.4
+ 
+
+ align:start position:0%
+uh to arrive in uh Las Vegas at 2.4
+gigabits per second. That is the speed
+
+ align:start position:0%
+gigabits per second. That is the speed
+ 
+
+ align:start position:0%
+gigabits per second. That is the speed
+of the circuits being used.
+
+ align:start position:0%
+of the circuits being used.
+ 
+
+ align:start position:0%
+of the circuits being used.
+Uh so I showed up to uh give this
+
+ align:start position:0%
+Uh so I showed up to uh give this
+ 
+
+ align:start position:0%
+Uh so I showed up to uh give this
+presentation and it was very exciting
+
+ align:start position:0%
+presentation and it was very exciting
+ 
+
+ align:start position:0%
+presentation and it was very exciting
+because this was the latest technology,
+
+ align:start position:0%
+because this was the latest technology,
+ 
+
+ align:start position:0%
+because this was the latest technology,
+the best of video and the best of the
+
+ align:start position:0%
+the best of video and the best of the
+ 
+
+ align:start position:0%
+the best of video and the best of the
+internet assembled uh for this short
+
+ align:start position:0%
+internet assembled uh for this short
+ 
+
+ align:start position:0%
+internet assembled uh for this short
+video presentation. Uh and I delivered
+
+ align:start position:0%
+video presentation. Uh and I delivered
+ 
+
+ align:start position:0%
+video presentation. Uh and I delivered
+the presentation and listened to what
+
+ align:start position:0%
+the presentation and listened to what
+ 
+
+ align:start position:0%
+the presentation and listened to what
+was going on around me. Now,
+
+ align:start position:0%
+was going on around me. Now,
+ 
+
+ align:start position:0%
+was going on around me. Now,
+unfortunately, my presentation fell at a
+
+ align:start position:0%
+unfortunately, my presentation fell at a
+ 
+
+ align:start position:0%
+unfortunately, my presentation fell at a
+time of day when the traffic on internet
+
+ align:start position:0%
+time of day when the traffic on internet
+ 
+
+ align:start position:0%
+time of day when the traffic on internet
+2 was a bit higher than usual. And so,
+
+ align:start position:0%
+2 was a bit higher than usual. And so,
+ 
+
+ align:start position:0%
+2 was a bit higher than usual. And so,
+the um the uh broadcast wasn't getting
+
+ align:start position:0%
+the um the uh broadcast wasn't getting
+ 
+
+ align:start position:0%
+the um the uh broadcast wasn't getting
+through reliably to Las Vegas, there was
+
+ align:start position:0%
+through reliably to Las Vegas, there was
+ 
+
+ align:start position:0%
+through reliably to Las Vegas, there was
+a bit of breaking up as of course in the
+
+ align:start position:0%
+a bit of breaking up as of course in the
+ 
+
+ align:start position:0%
+a bit of breaking up as of course in the
+internet, the way the internet works
+
+ align:start position:0%
+internet, the way the internet works
+ 
+
+ align:start position:0%
+internet, the way the internet works
+using TCP IP. When packets accidentally
+
+ align:start position:0%
+using TCP IP. When packets accidentally
+ 
+
+ align:start position:0%
+using TCP IP. When packets accidentally
+arrive in large numbers at a single
+
+ align:start position:0%
+arrive in large numbers at a single
+ 
+
+ align:start position:0%
+arrive in large numbers at a single
+place, some of them get lost. They're
+
+ align:start position:0%
+place, some of them get lost. They're
+ 
+
+ align:start position:0%
+place, some of them get lost. They're
+thrown away. Uh and this led to breakups
+
+ align:start position:0%
+thrown away. Uh and this led to breakups
+ 
+
+ align:start position:0%
+thrown away. Uh and this led to breakups
+in the video. Uh, fortunately, the video
+
+ align:start position:0%
+in the video. Uh, fortunately, the video
+ 
+
+ align:start position:0%
+in the video. Uh, fortunately, the video
+had been um recorded uh in Las Vegas
+
+ align:start position:0%
+had been um recorded uh in Las Vegas
+ 
+
+ align:start position:0%
+had been um recorded uh in Las Vegas
+just in case the internet didn't work
+
+ align:start position:0%
+just in case the internet didn't work
+ 
+
+ align:start position:0%
+just in case the internet didn't work
+during this particularly busy time of
+
+ align:start position:0%
+during this particularly busy time of
+ 
+
+ align:start position:0%
+during this particularly busy time of
+day. So, I'm thinking, uh-oh, is this
+
+ align:start position:0%
+day. So, I'm thinking, uh-oh, is this
+ 
+
+ align:start position:0%
+day. So, I'm thinking, uh-oh, is this
+good plumbing for the video internet?
+
+ align:start position:0%
+good plumbing for the video internet?
+ 
+
+ align:start position:0%
+good plumbing for the video internet?
+That didn't seem to be good plumbing.
+
+ align:start position:0%
+That didn't seem to be good plumbing.
+ 
+
+ align:start position:0%
+That didn't seem to be good plumbing.
+But there was a worse problem that even
+
+ align:start position:0%
+But there was a worse problem that even
+ 
+
+ align:start position:0%
+But there was a worse problem that even
+when the internet wasn't crowded and
+
+ align:start position:0%
+when the internet wasn't crowded and
+ 
+
+ align:start position:0%
+when the internet wasn't crowded and
+therefore failing to reliably deliver
+
+ align:start position:0%
+therefore failing to reliably deliver
+ 
+
+ align:start position:0%
+therefore failing to reliably deliver
+this video stream, there was another
+
+ align:start position:0%
+this video stream, there was another
+ 
+
+ align:start position:0%
+this video stream, there was another
+problem is that it took time to compress
+
+ align:start position:0%
+problem is that it took time to compress
+ 
+
+ align:start position:0%
+problem is that it took time to compress
+this video from the 1.5 gigs down to the
+
+ align:start position:0%
+this video from the 1.5 gigs down to the
+ 
+
+ align:start position:0%
+this video from the 1.5 gigs down to the
+20 megs. And it took time for it to wind
+
+ align:start position:0%
+20 megs. And it took time for it to wind
+ 
+
+ align:start position:0%
+20 megs. And it took time for it to wind
+its way through the internet routers uh
+
+ align:start position:0%
+its way through the internet routers uh
+ 
+
+ align:start position:0%
+its way through the internet routers uh
+that we've known so well over the last
+
+ align:start position:0%
+that we've known so well over the last
+ 
+
+ align:start position:0%
+that we've known so well over the last
+uh 30 years to get all the way to Las
+
+ align:start position:0%
+uh 30 years to get all the way to Las
+ 
+
+ align:start position:0%
+uh 30 years to get all the way to Las
+Vegas. So that in the end it took 4
+
+ align:start position:0%
+Vegas. So that in the end it took 4
+ 
+
+ align:start position:0%
+Vegas. So that in the end it took 4
+seconds for my picture to to leave
+
+ align:start position:0%
+seconds for my picture to to leave
+ 
+
+ align:start position:0%
+seconds for my picture to to leave
+Cambridge and arrive in Las Vegas. Now
+
+ align:start position:0%
+Cambridge and arrive in Las Vegas. Now
+ 
+
+ align:start position:0%
+Cambridge and arrive in Las Vegas. Now
+it was a pretty picture to be sure, but
+
+ align:start position:0%
+it was a pretty picture to be sure, but
+ 
+
+ align:start position:0%
+it was a pretty picture to be sure, but
+it was not an interactive picture. Craig
+
+ align:start position:0%
+it was not an interactive picture. Craig
+ 
+
+ align:start position:0%
+it was not an interactive picture. Craig
+Barrett in Las Vegas and I could not
+
+ align:start position:0%
+Barrett in Las Vegas and I could not
+ 
+
+ align:start position:0%
+Barrett in Las Vegas and I could not
+really have much of a conversation
+
+ align:start position:0%
+really have much of a conversation
+ 
+
+ align:start position:0%
+really have much of a conversation
+because uh there's a 4se secondond
+
+ align:start position:0%
+because uh there's a 4se secondond
+ 
+
+ align:start position:0%
+because uh there's a 4se secondond
+delay. That would be 4 seconds this way
+
+ align:start position:0%
+delay. That would be 4 seconds this way
+ 
+
+ align:start position:0%
+delay. That would be 4 seconds this way
+and then 4 seconds back. That would be
+
+ align:start position:0%
+and then 4 seconds back. That would be
+ 
+
+ align:start position:0%
+and then 4 seconds back. That would be
+an 8-second roundtrip delay.
+
+ align:start position:0%
+an 8-second roundtrip delay.
+ 
+
+ align:start position:0%
+an 8-second roundtrip delay.
+uh it is generally believed that in
+
+ align:start position:0%
+uh it is generally believed that in
+ 
+
+ align:start position:0%
+uh it is generally believed that in
+order for that to work you need uh
+
+ align:start position:0%
+order for that to work you need uh
+ 
+
+ align:start position:0%
+order for that to work you need uh
+roundtrip delays in the milliseconds in
+
+ align:start position:0%
+roundtrip delays in the milliseconds in
+ 
+
+ align:start position:0%
+roundtrip delays in the milliseconds in
+a 100 milliseconds or 200 milliseconds
+
+ align:start position:0%
+a 100 milliseconds or 200 milliseconds
+ 
+
+ align:start position:0%
+a 100 milliseconds or 200 milliseconds
+not 8 seconds. So I took this little um
+
+ align:start position:0%
+not 8 seconds. So I took this little um
+ 
+
+ align:start position:0%
+not 8 seconds. So I took this little um
+interaction as sort of a progress
+
+ align:start position:0%
+interaction as sort of a progress
+ 
+
+ align:start position:0%
+interaction as sort of a progress
+milestone in the proliferation of
+
+ align:start position:0%
+milestone in the proliferation of
+ 
+
+ align:start position:0%
+milestone in the proliferation of
+internet video and my conclusion which
+
+ align:start position:0%
+internet video and my conclusion which
+ 
+
+ align:start position:0%
+internet video and my conclusion which
+you've you've already heard a bit of is
+
+ align:start position:0%
+you've you've already heard a bit of is
+ 
+
+ align:start position:0%
+you've you've already heard a bit of is
+that the internet is not the right
+
+ align:start position:0%
+that the internet is not the right
+ 
+
+ align:start position:0%
+that the internet is not the right
+plumbing for the video internet. We will
+
+ align:start position:0%
+plumbing for the video internet. We will
+ 
+
+ align:start position:0%
+plumbing for the video internet. We will
+call it the video internet. We will call
+
+ align:start position:0%
+call it the video internet. We will call
+ 
+
+ align:start position:0%
+call it the video internet. We will call
+it the internet but it's not going to be
+
+ align:start position:0%
+it the internet but it's not going to be
+ 
+
+ align:start position:0%
+it the internet but it's not going to be
+the internet we know and love today. I
+
+ align:start position:0%
+the internet we know and love today. I
+ 
+
+ align:start position:0%
+the internet we know and love today. I
+suspect that is the the time-tested TCP
+
+ align:start position:0%
+suspect that is the the time-tested TCP
+ 
+
+ align:start position:0%
+suspect that is the the time-tested TCP
+IP structure of the internet will have
+
+ align:start position:0%
+IP structure of the internet will have
+ 
+
+ align:start position:0%
+IP structure of the internet will have
+to be changed and as I mentioned earlier
+
+ align:start position:0%
+to be changed and as I mentioned earlier
+ 
+
+ align:start position:0%
+to be changed and as I mentioned earlier
+perhaps in this overlay fashion and
+
+ align:start position:0%
+perhaps in this overlay fashion and
+ 
+
+ align:start position:0%
+perhaps in this overlay fashion and
+underlying
+
+ align:start position:0%
+underlying
+ 
+
+ align:start position:0%
+underlying
+um dense wave division optical switch
+
+ align:start position:0%
+um dense wave division optical switch
+ 
+
+ align:start position:0%
+um dense wave division optical switch
+network underlying the TCP IP packet
+
+ align:start position:0%
+network underlying the TCP IP packet
+ 
+
+ align:start position:0%
+network underlying the TCP IP packet
+switch network in order to deliver
+
+ align:start position:0%
+switch network in order to deliver
+ 
+
+ align:start position:0%
+switch network in order to deliver
+highdefinition
+
+ align:start position:0%
+highdefinition
+ 
+
+ align:start position:0%
+highdefinition
+video and I also saw that this uh
+
+ align:start position:0%
+video and I also saw that this uh
+ 
+
+ align:start position:0%
+video and I also saw that this uh
+one-way application was not nearly as it
+
+ align:start position:0%
+one-way application was not nearly as it
+ 
+
+ align:start position:0%
+one-way application was not nearly as it
+would have been much more interesting I
+
+ align:start position:0%
+would have been much more interesting I
+ 
+
+ align:start position:0%
+would have been much more interesting I
+think to the audience uh if Craig
+
+ align:start position:0%
+think to the audience uh if Craig
+ 
+
+ align:start position:0%
+think to the audience uh if Craig
+Barrett and I were to argue about
+
+ align:start position:0%
+Barrett and I were to argue about
+ 
+
+ align:start position:0%
+Barrett and I were to argue about
+something, but we couldn't argue about
+
+ align:start position:0%
+something, but we couldn't argue about
+ 
+
+ align:start position:0%
+something, but we couldn't argue about
+something. Instead, the audience had to
+
+ align:start position:0%
+something. Instead, the audience had to
+ 
+
+ align:start position:0%
+something. Instead, the audience had to
+suffer a steady one-way stream of uh my
+
+ align:start position:0%
+suffer a steady one-way stream of uh my
+ 
+
+ align:start position:0%
+suffer a steady one-way stream of uh my
+words instead of interaction between
+
+ align:start position:0%
+words instead of interaction between
+ 
+
+ align:start position:0%
+words instead of interaction between
+Craig and I. So that the applications
+
+ align:start position:0%
+Craig and I. So that the applications
+ 
+
+ align:start position:0%
+Craig and I. So that the applications
+for video uh as I've mentioned there'll
+
+ align:start position:0%
+for video uh as I've mentioned there'll
+ 
+
+ align:start position:0%
+for video uh as I've mentioned there'll
+be considerable exper exciting
+
+ align:start position:0%
+be considerable exper exciting
+ 
+
+ align:start position:0%
+be considerable exper exciting
+experimentation ahead as to what kind of
+
+ align:start position:0%
+experimentation ahead as to what kind of
+ 
+
+ align:start position:0%
+experimentation ahead as to what kind of
+videobased applications or better yet
+
+ align:start position:0%
+videobased applications or better yet
+ 
+
+ align:start position:0%
+videobased applications or better yet
+where to put video in other applications
+
+ align:start position:0%
+where to put video in other applications
+ 
+
+ align:start position:0%
+where to put video in other applications
+to make them interesting and to compel
+
+ align:start position:0%
+to make them interesting and to compel
+ 
+
+ align:start position:0%
+to make them interesting and to compel
+the the deployment of video
+
+ align:start position:0%
+the the deployment of video
+ 
+
+ align:start position:0%
+the the deployment of video
+infrastructure. So in closing, it's
+
+ align:start position:0%
+infrastructure. So in closing, it's
+ 
+
+ align:start position:0%
+infrastructure. So in closing, it's
+going to take time. That little
+
+ align:start position:0%
+going to take time. That little
+ 
+
+ align:start position:0%
+going to take time. That little
+experiment in between Cambridge and Las
+
+ align:start position:0%
+experiment in between Cambridge and Las
+ 
+
+ align:start position:0%
+experiment in between Cambridge and Las
+Vegas indicated that video the video
+
+ align:start position:0%
+Vegas indicated that video the video
+ 
+
+ align:start position:0%
+Vegas indicated that video the video
+internet is not it may be the next big
+
+ align:start position:0%
+internet is not it may be the next big
+ 
+
+ align:start position:0%
+internet is not it may be the next big
+thing, but it's not going to come
+
+ align:start position:0%
+thing, but it's not going to come
+ 
+
+ align:start position:0%
+thing, but it's not going to come
+tomorrow. It's going to take as I
+
+ align:start position:0%
+tomorrow. It's going to take as I
+ 
+
+ align:start position:0%
+tomorrow. It's going to take as I
+mentioned earlier probably 10 to 20
+
+ align:start position:0%
+mentioned earlier probably 10 to 20
+ 
+
+ align:start position:0%
+mentioned earlier probably 10 to 20
+years and these uh these years will be
+
+ align:start position:0%
+years and these uh these years will be
+ 
+
+ align:start position:0%
+years and these uh these years will be
+very interesting and I I look forward to
+
+ align:start position:0%
+very interesting and I I look forward to
+ 
+
+ align:start position:0%
+very interesting and I I look forward to
+them. Thank you.
\ No newline at end of file
diff --git a/qY5Rr-PTMMc.txt b/qY5Rr-PTMMc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..67adb57787c69e14109b6b99beda9fe8dc23da90
--- /dev/null
+++ b/qY5Rr-PTMMc.txt
@@ -0,0 +1,68 @@
+Let's look at a concrete example.
+
+This graph shows the voltage transfer characteristic
+for a particular device and we're wondering
+
+if we can use this device as a combinational
+inverter.
+
+In other words, can we pick values for the
+voltage thresholds V_OL, V_IL, V_IH and V_OH
+
+so that the shown VTC meets the constraints
+imposed on a combinational device?
+
+An inverter outputs a digital 1 when its input
+is a digital 0 and vice versa.
+
+In fact this device does produce a high output
+voltage when its input voltage is low, so
+
+there's a chance that this will work out.
+
+The lowest output voltage produced by the
+device is 0.5V, so if the device is to produce
+
+a legal digital output of 0, we have to choose
+V_OL to be at least 0.5V.
+
+We want the inverter to produce a valid digital
+0 whenever its input is valid digital 1.
+
+Looking at the VTC, we see that if the input
+is higher than 3V, the output will be less
+
+than or equal to V_OL, so let's set V_IH to
+3V.
+
+We could set it to a higher value than 3V,
+but we'll make it as low as possible to leave
+
+room for a generous high noise margin.
+
+That takes care of two of the four signal
+thresholds, V_OL and V_IH.
+
+The other two thresholds are related to these
+two by the noise margin N as shown by these
+
+two equations.
+
+Can we find a value for N such that V_OUT
+>= V_OH when V_IN <= V_IL?
+
+If we chose N = 0.5V, then the formulas tell
+us that V_IL = 1V and V_OH = 3.5V.
+
+Plotting these thresholds on the graph and
+adding the forbidden regions, we see that
+
+happily the VTC is, in fact, legal!
+
+So we can use this device as a combinational
+inverter if we use the signaling specification
+
+with V_OL = 0.5V, V_IL = 1V, V_IH = 3V and
+V_OH = 3.5V.
+
+We're good to go!
\ No newline at end of file
diff --git a/qgA-JxgtjZg.txt b/qgA-JxgtjZg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4869891a3bb9471d2b6869851e48ceee5f31045a
--- /dev/null
+++ b/qgA-JxgtjZg.txt
@@ -0,0 +1,2906 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+ESTHER DUFLO: So actually
+a lot of themes are
+
+criss-crossing in this
+documentary.
+
+It's pretty well done for
+managing to bring many of
+
+those teams up.
+
+So before we sort of I summarize
+them, I'd like to
+
+have your impression of what are
+the themes that seem to be
+
+important in like how the
+students get educated, the
+
+government's decisions, the
+parent's decision, et cetera?
+
+Yeah, Ben?
+
+AUDIENCE: Cultural
+preservation.
+
+I forget the other one.
+
+It was the Kurds, and who's--
+
+ESTHER DUFLO: Just the rest of
+Turkey, mainstream Turkey.
+
+AUDIENCE: --mainstream Turkey
+and how they're willing to
+
+preserve their culture, and how
+that spill-over effects
+
+[INAUDIBLE] how they operate
+[INAUDIBLE].
+
+ESTHER DUFLO: Right, so one
+issue that is kind of there is
+
+whether the whole education is a
+way to mainstream the Kurds,
+
+which they are suspicious
+about.
+
+That's a good point.
+
+AUDIENCE: Yeah, I was going
+to say infrastructure, so
+
+actually physically getting the
+schools becomes a problem.
+
+The guy mentioned like when it
+snows, it becomes hard for the
+
+children to get to school,
+so they fall behind.
+
+And they have the desire to
+become a boarding school, like
+
+religious schools actually
+in their village.
+
+But because they don't have
+that, it becomes difficult.
+
+ESTHER DUFLO: Right.
+
+So there is a supply
+constraint.
+
+There are no schools in the
+villages and getting to them--
+
+they go by bus, but even that
+is difficult, because
+
+infrastructure is difficult.
+
+AUDIENCE: It can also to be hard
+to find justification for
+
+this education, because although
+some people argue
+
+that there is still value to it,
+even if girls or boys who
+
+get educated just come back to
+the village and live with
+
+their family, but a
+lot of people say,
+
+well, what is the point?
+
+ESTHER DUFLO: So there
+is a question of
+
+the benefits of education.
+
+Yaprak's parents, what do they
+think the benefit of education
+
+is for her?
+
+What do they expect from
+the education?
+
+AUDIENCE: For her to come back
+and contribute to the family.
+
+ESTHER DUFLO: Is it what they
+say, or is it someone
+
+else who says that?
+
+What do the parents say,
+the mom, and then
+
+Yaprak say it also.
+
+AUDIENCE: Her mom said
+that she wanted
+
+her to become a doctor.
+
+ESTHER DUFLO: Her mom says she
+wants her to become a doctor.
+
+She also wants to
+become a doctor.
+
+And in fact there is this
+debate where people are
+
+saying, well, what's the point
+of education if we don't have
+
+a job that will take into
+account this education?
+
+And there's this other guy who
+says, well, even if she
+
+doesn't become a doctor, there
+are these other things.
+
+But it seems to have
+a little bit of a
+
+minority view in this.
+
+You don't see any anyone asking
+her the question, but
+
+she answers, saying,
+yeah, yeah, there
+
+would be some value.
+
+But there's somewhat
+of a debate there.
+
+AUDIENCE: When you're talking
+about supply, there's a lack
+
+of supply of teachers
+over there.
+
+So in particular regions, like
+the eastern region for
+
+example, teachers have
+to go out into those
+
+cultural sort of things.
+
+They're coming from
+different regions
+
+where culture's different.
+
+And then at the same
+time, they may not
+
+particularly be there.
+
+They're passing through.
+
+You mentioned that do we go to
+train or to get experience in
+
+this way and them move on.
+
+So there's not sustainability.
+
+When you think about teaching,
+it's important that teachers
+
+build relationships
+with students and
+
+really pour into them.
+
+But when they're in this like
+transit sort of mindset, it
+
+becomes a little hard
+to do that.
+
+ESTHER DUFLO: Right, so that's
+another supply issue from the
+
+supply side is whether there
+are enough teachers.
+
+And then that kind of interacts
+like it was a
+
+cultural issue.
+
+Who were the teachers?
+
+I think you're making
+two points
+
+that are both important.
+
+One is the point that the
+teachers who are coming to
+
+them may not be as motivated.
+
+They might not be accountable
+to the community.
+
+They might be difficult
+to discipline.
+
+They might not care.
+
+In addition, they might be the
+ones who are trying to teach
+
+in Turk and not and not in
+Kurd, and all of that.
+
+So that brings the cultural
+dimension.
+
+Yup?
+
+AUDIENCE: Another thing I didn't
+realize whether or not
+
+they mentioned in that movie.
+
+But there's a problem if all
+these girls are actually
+
+living in those boarding schools
+for most of the week.
+
+And they're just going
+back for the weekend.
+
+You know, they don't have that
+sort of family [INAUDIBLE]
+
+that's going to actually
+give them more balance.
+
+So even though they'll be
+getting an education, there's
+
+a huge drawback for the fact
+that they don't have their
+
+parents right there and
+telling them what
+
+they have to do.
+
+And nobody really knows
+what that could
+
+cause in the long run.
+
+ESTHER DUFLO: Like you guys,
+far from your families--
+
+yeah, I think this sort of
+comes a little bit in
+
+[INAUDIBLE]
+
+when they have this debate about
+I think they would like
+
+to have the schools
+in their villages.
+
+That don't like to send the
+kids to boarding school.
+
+I think one issue is are the
+kids mature enough to manage
+
+in boarding school?
+
+And the other which
+is in [INAUDIBLE]
+
+of that, are they going
+to become different?
+
+Are they going to absolve these
+values that these guys
+
+are not necessarily
+looking for?
+
+There might also be a slight
+conflict underlying this,
+
+where actually from the point
+of view of the Turkish
+
+government, who is trying
+to make the Kurds
+
+into regular Turks.
+
+It's actually a good
+thing to get them
+
+away from the families.
+
+But from the point of the view
+of the Kurd, that's kind of a
+
+way of following
+the exhibition.
+
+So that's one thing that goes
+with education, which you find
+
+in a lot of places.
+
+For example, there was a big
+education drive in Indonesia
+
+that I'm going to talk
+in a bit, which had
+
+exactly the same idea.
+
+Education is about
+imparting skills.
+
+It's also about imparting
+a world view.
+
+And therefore that creates
+conflict between the different
+
+people who have different
+ideas about what these
+
+worldviews should be.
+
+AUDIENCE: Maybe also that those
+parents talked about the
+
+lack of [INAUDIBLE]
+
+practical things maybe teach
+about agriculture [INAUDIBLE]?
+
+ESTHER DUFLO: Yes, so that goes
+back to what is the value
+
+of education?
+
+What's the benefit
+of education?
+
+So it comes back to well, fine,
+if she graduates and
+
+becomes a doctor,
+that's great.
+
+But if not, what has
+education brought?
+
+Maybe nothing.
+
+People might not necessarily see
+the value of the education
+
+that's imparted as being that
+great, unless you can make it
+
+to being a doctor, which would
+be great, but is a
+
+bit more of a leap.
+
+AUDIENCE: I just have
+a question.
+
+So I figured how many children
+were in the household.
+
+My understanding is that they
+only send one to school, like
+
+the impact that has on the
+children who aren't in school.
+
+I know the mom at least said
+that she wasn't happy as she
+
+would like to be [INAUDIBLE]
+education [INAUDIBLE].
+
+But is that mindset perpetuated
+because you have a
+
+child who's going to school kind
+of puts you in further
+
+[INAUDIBLE] your current
+circumstances, which could
+
+pose another problem.
+
+ESTHER DUFLO: That's an
+interesting question.
+
+For example, the sister
+of this girl, Yaprak.
+
+what's her name?
+
+Was [? Meemet. ?]
+
+She wasn't in school, because
+she was too old to benefit
+
+from the compulsory education.
+
+So on the one hand, she gets
+some indirect benefits,
+
+[INAUDIBLE]
+
+benefits from the fact that
+Yaprak is educated.
+
+On the other hand, she also
+gets like these education
+
+envy, and feels that, oh, it
+would have been great if I
+
+could have been educated
+myself.
+
+So that's an interesting
+point.
+
+AUDIENCE: We kind of spoke about
+this before, but just
+
+the idea of the value of
+education and what are the
+
+returns to it?
+
+So when you're most poor, you're
+just kind of raising
+
+everything higher.
+
+When you think about education,
+the returns are
+
+going to be much farther off.
+
+This was sort of mentioned, but
+you get to a certain point
+
+and you need some education,
+then after a while, it's kind
+
+of like, well, you'll probably
+be more valuable if you just
+
+stayed home and helped
+out around the house.
+
+There's a dichotomy, I guess,
+between the social pressure
+
+for education and the
+home pressure to
+
+help your family out.
+
+We need to eat tomorrow,
+so this is a
+
+little bit more important.
+
+You'll be able to go to school
+when you feel like it, or when
+
+you get a little bit older.
+
+Or maybe you won't need to go
+to school because we need a
+
+survivor now.
+
+ESTHER DUFLO: Right, so there's
+another cost of that
+
+in the cost of getting yourself
+to school, and that
+
+now the government is paying for
+the bus, and is paying for
+
+the school, et cetera.
+
+But there is another cost, which
+is in economic jargon we
+
+call the opportunity cost,
+which is while you're in
+
+school, you're not helping
+out on the house.
+
+And that is something that is
+mentioned in the movie at some
+
+point, where they're saying,
+well, that's kind of one
+
+reason why people are not
+complying to the objectives.
+
+People are feeling that they
+are getting on their house.
+
+And you said it exactly right.
+
+There is a trade off.
+
+Even if you don't bear the
+direct cost of schooling like
+
+is the case here, there is
+a trade off between the
+
+opportunity cost, when you're
+losing the value of the child
+
+work now, and the benefits
+that are far out in the
+
+future, potentially very far out
+in the future if you think
+
+that it's worth getting an
+education, only if you can
+
+become a doctor.
+
+AUDIENCE: I was going to say, if
+the child goes back to the
+
+village, then they just wasted
+their time, essentially, if
+
+they weren't helping out.
+
+ESTHER DUFLO: So that is the
+debate that they have at some
+
+point, which is at least some
+people feel that if you go
+
+back to the village, you
+just wasted your time.
+
+So the only value is
+to being a doctor.
+
+And at the same time they
+realize that it's not super
+
+likely that it happens.
+
+And then in general, if someone
+says that it's easier
+
+for men than for women to get
+jobs outside the village,
+
+there might be the other point
+I made earlier, that they
+
+might not want the girls
+to really leave to
+
+be outside the village.
+
+They might accept for them to
+leave to be a doctor, but they
+
+might be less likely to let them
+leave to man a register
+
+in a supermarket, which maybe is
+a job you could get with a
+
+good education without
+continuing.
+
+And so if you're not going to
+leave the village to take that
+
+job, and they feel that there
+is no value in between, then
+
+you would have no reason to
+pay the opportunity cost.
+
+So that's where kind of this
+debate or tension comes up.
+
+Is any of it valuable?
+
+Or is it only valuable if I
+achieve a sufficient amount to
+
+really get like the lottery
+ticket of having a chance to
+
+become a doctor.
+
+So what does this bring, this
+idea that the benefits of
+
+education may or may not be
+obtained from the first years
+
+of education?
+
+We might be able to obtain
+them only if
+
+we get enough education.
+
+What does that remind you
+of that we have seen?
+
+It's that idea of the S shape.
+
+So the question, and here,
+again, at this level, as usual
+
+it's a question.
+
+Is there S shape in education?
+
+So are the first few years of
+education valuable, because
+
+you learn how to socialize.
+
+That's what they said
+in the movie.
+
+You learn how to socialize.
+
+You learn family planning.
+
+You learn maybe to read the
+instruction in the packet of
+
+fertilizer for when you
+come back to the farm.
+
+So there might be reason to
+think that even the first
+
+years of educations
+would be valuable.
+
+Or is it the case that the first
+year of education are
+
+not really valuable, that the
+only thing that's worth it is
+
+a college education.
+
+And the first year of education,
+all that gives you
+
+is the option value of going to
+high school and college if
+
+you want to.
+
+The latter case is a case where
+there is an S shape.
+
+So unless you get enough
+education, it's not worth it.
+
+At the former case is a case
+where there is no S shape.
+
+And so one empirical question is
+whether it's actually an S
+
+shape or it's actually
+not an S shape.
+
+Another empirical question,
+of course, is the value of
+
+education, whatever the
+shape the overall
+
+level of the benefits.
+
+And the third question is what
+people are thinking?
+
+Because even if it's in fact
+linear, if people think that
+
+it's actually S shape,
+then it's going to
+
+influence their behavior.
+
+And it's going to influence
+the choice
+
+that they are making.
+
+So for example here, they have
+all these discussions about is
+
+it even worth it to send the
+kids to school or not.
+
+And they never question the fact
+that it would be great if
+
+she could become a doctor.
+
+But they might question the
+fact that there might be a
+
+value of anything below
+being a doctor.
+
+Is there anything else that
+comes out of this?
+
+Yeah?
+
+AUDIENCE: I think Ben
+might have talked.
+
+I heard him say something
+about cultural--
+
+but just the idea of the head
+scarves, the preventing of the
+
+girls from going to school,
+and then the idea of Kurds
+
+being assimilated as opposed to
+being integrated in a way
+
+that helps them maintain
+their culture.
+
+Again, that's something
+that would deter me
+
+from going to school.
+
+ESTHER DUFLO: Right, so that's
+kind of the convex combination
+
+of the two points, Ben's point
+and the point about once you
+
+send them to boarding school,
+they're not under your thumb.
+
+You can't check what they are
+doing anymore, which is
+
+reinforcing in Turkey that's
+it's not allowed to wear a
+
+head scarf in school.
+
+So from the beginning, there
+is a conflict there.
+
+Is school aware of
+indoctrinating the kids away
+
+from what you would like, under
+the guise of providing
+
+them with valuable skills
+in the labor market?
+
+And there is certainly some
+amount of that, to be honest,
+
+that's actually said by them.
+
+The only thing we missed
+from the movie--
+
+well, we might have missed a bit
+more-- but the only piece
+
+we missed that I remember and
+is worth pointing out is the
+
+woman with the hair like that
+who speaks with this very posh
+
+English accent, the columnist
+from The Economist.
+
+She has the last word.
+
+And she mentions one thing that
+might be worth pointing
+
+out, which is this is compulsory
+education.
+
+This drive to compulsory
+education was very much of a
+
+top down intervention, was done
+without any consultation,
+
+or anybody, which is done.
+
+And the way the schools are run
+is run in this completely
+
+centralized way, with a
+centralized curriculum, with
+
+the teachers appointed from the
+center, the kids driven to
+
+boarding school, et cetera.
+
+And she says that that's not
+going to work, that people are
+
+not going to accept or not going
+to really be in the mood
+
+or thought to be really groovy
+about the whole education
+
+thing, unless they're
+given some autonomy
+
+in running the schools.
+
+So that's an important point,
+because that's the point that
+
+many people make, that any
+effort at top down education
+
+will meet some resistance
+from the people.
+
+They might still go because
+they have to go, but the
+
+parents won't be very engaged.
+
+The children won't
+be very engaged.
+
+The teachers might not
+be very engaged.
+
+And nothing will happen.
+
+So we keep that in mind.
+
+I'm channeling her, because I
+want to keep that in mind as
+
+we have the discussion.
+
+Because this tension between
+education, board-funded top
+
+down, and education, emerging
+from the bottom up, is one of
+
+the central debates
+in education.
+
+So I think you guys said a
+lot of the things that I
+
+wanted to touch on.
+
+Let me kind of make sure that
+we have everything together.
+
+So the stories of a Kurdish
+girl who goes to boarding
+
+school after education was made
+
+compulsory until grade eight.
+
+So many important themes
+appear in the movie.
+
+I think we mentioned them.
+
+One are all the questions about
+the supply of education,
+
+so that seems to have been a
+constraint before this big
+
+education push from the Turkish
+government and still
+
+is a constraint.
+
+There is no schools in
+the remote villages.
+
+The roads are bad.
+
+Transportation is difficult.
+
+There is a shortage of
+well-trained teachers.
+
+Therefore there is a large class
+size, and the teachers
+
+are moving, what you were saying
+about the teachers
+
+coming from far away not being
+necessarily the best teacher,
+
+most motivated teacher.
+
+For part of the international
+community, these types of
+
+constraint are the only thing
+you have to worry about.
+
+I think you guys have all seen
+a picture of a little African
+
+girl in a village saying, that
+if only she had a school, she
+
+would study until she would
+become a doctor.
+
+So there is a whole branch of
+the international community,
+
+governments, et cetera, for whom
+the only problems with
+
+education are supply problems,
+and if only we could get rid
+
+of the supply problem and make
+sure there are enough
+
+well-trained teachers, then the
+kids would go to school.
+
+They would learn something
+in school.
+
+And they would all
+be very educated.
+
+So the problem is a problem of
+fixing the supply constraint.
+
+But what we see in the movie is
+that these are not the only
+
+constraints.
+
+So the reason why it's relevant
+is that a lot of the
+
+international community, a lot
+of the policy was in aid.
+
+And the policies implemented
+by the government have that
+
+flavor in mind, which is let's
+fix the supply problem.
+
+So for example, a lot of African
+countries have gotten
+
+rid of school fees completely to
+make sure school was free.
+
+You go to a country like Kenya,
+and there is a school
+
+every 25 meters, because every
+community who wants a school
+
+can gets one.
+
+So there is plenty of schools.
+
+In some sense, one could say too
+many schools in that the
+
+class size is actually quite
+small at the top.
+
+And in India, it's
+the same thing.
+
+India is debating a right to
+education, where if you don't
+
+have a school right near your
+village, you can get one.
+
+But what we see in the movie
+is that it's not the supply
+
+constraint, not having a school
+near you, et cetera, is
+
+not the new problem.
+
+In fact, Turkey is not only
+building schools, and building
+
+these boarding schools, and
+having kids travel in
+
+minibuses to go to the school,
+they also made education
+
+compulsory.
+
+And if the only problem was
+supply, then making education
+
+compulsory would not
+be necessary.
+
+You would put the schools there
+and people would be
+
+delighted to go.
+
+And you wouldn't need
+any compulsion.
+
+In fact, Turkey decided that the
+only way that they could
+
+get a fast increasing education
+was to make
+
+education compulsory.
+
+So implicitly, there is the
+argument that, well, maybe
+
+people would not want to
+go to all the schools.
+
+So there must be a demand
+constraint as well.
+
+There must be a lower demand
+for education.
+
+So what constrained them?
+
+We mentioned that.
+
+One is no economic resources.
+
+So they don't have money.
+
+So this in principle, the direct
+cost of education can
+
+be compensated by making
+education free by paying for
+
+books, by paying for
+transportation.
+
+But there is also the need
+for child labor.
+
+It was mentioned in the movie.
+
+The kids who are in school are
+not helping on the farm.
+
+Then there is the need to get
+married, which was mentioned
+
+by Yaprak's sister.
+
+She says, now I need
+to get married.
+
+And you can be married and
+in boarding school.
+
+In principle you could, but it's
+not very frequent that
+
+you would be both married
+and in boarding school.
+
+So this is not a cost effect.
+
+This is something which
+is more about culture.
+
+Maybe the husband wants
+a young wife.
+
+Or there is something different
+than just a strict
+
+opportunity cost effect.
+
+Like, why do they think that
+it's important to get married
+
+early instead of continuing
+schooling?
+
+So these are only important
+because they're mentioned.
+
+And there are the benefits.
+
+Is it useful?
+
+Or is it useful only if you
+get enough education?
+
+If it's useful, do parents
+know that it is useful?
+
+What do they expect
+of education?
+
+Do they expect that education
+is making their child
+
+generally better at
+living their life?
+
+I'll do they see
+education as--
+
+the woman employs a term that
+is interesting-- it's almost
+
+like a foreign currency.
+
+So people see your education
+diploma.
+
+Do you see that as something
+that if you get enough of it,
+
+you can actually sell
+to the market?
+
+What is enough?
+
+Is it a foreign currency that
+you could get a few cents of
+
+and that would be good enough?
+
+Or is it a foreign currency that
+you need a big packet of
+
+to be worthwhile?
+
+And in the movie, what was
+interesting was is that we saw
+
+different people having
+different views about whether
+
+it is a foreign currency, that
+is, you have to take it
+
+elsewhere to benefit from it?
+
+Whereas you could also benefit
+from it just in your general
+
+my life, with having fewer,
+healthier children, being more
+
+socialized?
+
+I think it's again Yaprak
+sister who sees another
+
+advantage of education for girls
+in that it is going to
+
+increase her bargaining power
+within the family.
+
+Since traditionally girls are
+quiet and don't say anything
+
+and men have all the power, and
+if girls get education,
+
+that is going to improve
+their bargaining
+
+power within the family.
+
+And that is something that girls
+may find very attractive
+
+and their future husbands might
+find less attractive.
+
+And here the question
+is what are the
+
+fathers going to think?
+
+Yaprak's father, on the one
+hand, probably he has in mind
+
+the value of keeping the
+girls in their place.
+
+On the other hand, he
+likes his daughter.
+
+So there is probably a conflict
+within him between
+
+the fact that as a man, he
+doesn't want to conflict with
+
+his wife, so we would rather
+the woman being lower down,
+
+but as a father probably likes
+his daughter more than his son
+
+in law, who doesn't
+even exist yet.
+
+So there might be a conflict
+here in his preferences which
+
+might easily lead him to say,
+fine, she should get an
+
+education or no, we want
+to move forward.
+
+And what is interesting in the
+movie is that he clearly sees
+
+himself as a bit of a
+[INAUDIBLE] leader and a
+
+modern character.
+
+So he seemed to have concluded
+this debate from his point of
+
+view to say that OK,
+I'll send her.
+
+AUDIENCE: I have a question.
+
+I'm wondering with that attitude
+if it's sort of like
+
+we'll just indulge the girls for
+a while and let them go to
+
+school, but we know secretly
+that we're still going to take
+
+the power we have and not
+actually concede anything and
+
+respect the fact that
+they [INAUDIBLE].
+
+ESTHER DUFLO: Right, so there
+might be a little bit of that.
+
+So just to repeat the question,
+the question was,
+
+are they just indulging them
+for a little while and then
+
+going to bring them
+back in line?
+
+And then education is more
+like it's not seen as an
+
+investment anymore, but more
+consumption value for the
+
+girl, since the government is
+providing it for free and
+
+she's kind of a bit too
+young to be really
+
+helpful in the farm.
+
+Let's get her get an education,
+but we kind of know
+
+that at the end of the
+day, it's not going
+
+to change her life.
+
+And we certainly maybe hope that
+it's not going to change
+
+her attitude.
+
+What's interesting is that if
+this is what people had in
+
+mind is that that's clearly
+not her view.
+
+So that might be a little bit
+of disconnect here, which
+
+would be in her advantage
+in terms of when
+
+she gets the education.
+
+So here if we're thinking of
+these bargaining power issues
+
+and this potential conflict
+withing the father between his
+
+goal as a husband where he wants
+to keep the power, and
+
+his goal as a father, where he
+would like probably her to
+
+have some power, is that that
+may change with economic goals
+
+in the society and what are the
+opportunities he sees for
+
+her to do something with
+the education.
+
+If the society's completely
+paralyzed, then in a way the
+
+benefits of education are very
+high for her, so he has less
+
+of a reason to want
+to go to it.
+
+AUDIENCE: Just from watching the
+video, it seems like it is
+
+possible for them to combine
+both the cultural values and
+
+the value of education.
+
+Like for instance, clearly it
+is a male-dominated society,
+
+but here we watch the scenes
+where there's a bunch of men,
+
+sitting around, and
+they're talking
+
+the value of education.
+
+It's still the women who
+are serving them tea
+
+or whatever it was.
+
+And they still see the women,
+the girl who is getting the
+
+education, she's still
+helping with the
+
+children and all that.
+
+So it seems like--
+
+ESTHER DUFLO: Yeah, it is
+possible that even with the
+
+education they are still going
+to maintain the differences.
+
+What is interesting is that
+there is a level question and
+
+a slope question, which is it
+is possible that the girls
+
+have so far to go that getting
+an education wouldn't be
+
+sufficient to make them
+become equal.
+
+But that would still go
+in that direction.
+
+And at least some of them seem
+to have the hope that it would
+
+bring it in that direction.
+
+But you're right.
+
+So those are the expected
+benefits of education.
+
+And then there is what worries
+them about the schools.
+
+We've mentioned the culturalized
+assimilation, the
+
+fact that it might be like a
+covert way to assimilate them
+
+to a culture that's not theirs,
+and the fact that
+
+maybe there are no benefits, the
+fact that just if sending
+
+the kids away is not
+a very good thing.
+
+Potentially they are
+worried about them.
+
+So these are the
+demand issues.
+
+So the demand issues are a
+little bit tricky, because
+
+depending on how this thing
+balances out, what are the
+
+benefits they see versus the
+feel they have versus the
+
+immediate cost of not having
+the kids on the farm.
+
+Or the decision of sending the
+kids or not sending the kids
+
+is not obvious, even if
+education is free.
+
+And making education compulsory,
+of course, pushes
+
+them in that direction.
+
+So is benefits of education that
+are touched upon in the
+
+movie are of different kinds.
+
+There is this foreign currency
+idea-- you get a job.
+
+You get a higher wage.
+
+They hope that the girl is
+going to be a doctor.
+
+So the issue is can everybody
+become a doctor?
+
+And probably not.
+
+So even though they don't say
+it in the movie, they must
+
+have in the corner of their mind
+that they're not quite
+
+sure that she's going
+to make it.
+
+They sort of say it, but they're
+not quite sure it's
+
+going to make it.
+
+And that uncertainty and the
+fact that the objective is so
+
+hard certainly has some impact
+in how serious it is to take
+
+the whole thing.
+
+And then there is the
+possibility that just getting
+
+an education would help in
+your job, doing your job
+
+better, even if your job
+is to be a farmer,
+
+coming back to the farm.
+
+And nobody seems to
+really say that.
+
+It's only mentioned in a
+negative way, which is if only
+
+they taught something useful
+like home economics then maybe
+
+we would be able to have some
+benefits of this education.
+
+But that's not what
+they are doing.
+
+And so maybe education is
+useless or is seen as being
+
+useless at the lower level.
+
+Then there are the non-monetary
+dimensions of
+
+getting an education.
+
+Girls will become
+more socialized.
+
+The family planning, they'll
+have more friends and know how
+
+to interact with people in
+the city, et cetera.
+
+And then there is the idea of
+learning things that you can
+
+teach others.
+
+So the one guy who has an
+college education in these
+
+men's discussion, he goes and
+say, well, let them get an
+
+education, come back, and
+teach us some stuff.
+
+And so this is the external
+spill-over value of education,
+
+which is the opposite than the
+one that Ben had mentioned,
+
+which was the education envy.
+
+But it's the idea that if I get
+an education, if there is
+
+some benefits, for example,
+I learn how to read the
+
+instructions on the fertilizer
+package, maybe I learn to use
+
+new technology in agriculture,
+not only it can be useful for
+
+me, but potentially it can
+be useful for others.
+
+So if that is the case, a
+village might decide to focus
+
+on the smartest kids on the
+block and make sure that they
+
+at least get an education so
+that everybody benefits.
+
+So those are kind of the
+benefits of education.
+
+So one empirical question
+is what are the
+
+real benefits of education?
+
+The other empirical question is
+what are people perceive to
+
+be the benefits of education?
+
+Another thing that he touched
+upon in the movie is this top
+
+down versus bottom up.
+
+So here the government is
+trying a big top down
+
+approach, trying to
+do it very fast--
+
+putting all the money from the
+top, making it compulsory,
+
+which is the ultimate top
+down, and instead of
+
+supply-drive policy, has been,
+as I was saying, popular in
+
+many countries.
+
+Many African countries--
+
+Kenya, Uganda, Ghana--
+
+have recently, relatively
+recently, in the last 10 years
+
+or so, have adopted free primary
+education and moving
+
+to free secondary
+education now.
+
+India, as I was saying, has a
+right to education, which
+
+actually allowed people, in
+principle, to sue the
+
+government if they don't
+get a school.
+
+So the supply drives have been
+the main education policy say
+
+in the last three decades.
+
+The Millennium Development
+Goal specified that every
+
+child should get at least a
+basic education, basic goes to
+
+nine years of education.
+
+What is interesting is that
+there is no mention anywhere
+
+that they should actually learn
+
+anything in those schools.
+
+It's sort of assumed that if
+they get nine years of
+
+education they'll get
+something out of it.
+
+But as we'll see, it's a
+pretty big assumption.
+
+And there are certainly some
+clear signs success of these
+
+big supply drives.
+
+Between 1999 and 2006, the
+enrollment rates have
+
+increased, in Sub-Saharan Africa
+from 54% to 70%, in
+
+East and Southeast Asia
+from 75% to 88%.
+
+These are primary
+schools only.
+
+Secondary school enrollments
+have also increased, even
+
+though secondary school is much
+more expensive, much more
+
+difficult to do for
+governments.
+
+So worldwide, there are still
+a bunch of millions of kids
+
+who are not in school, but much
+less in 2006 than they
+
+were in 1999.
+
+So is it all worthwhile?
+
+That's the question that
+Easterly is asking in the
+
+reading for today.
+
+And what is his answer?
+
+His answer is not that graph.
+
+AUDIENCE: I thought education
+in itself, an increase in
+
+education, is not going to cause
+and increase in growth.
+
+ESTHER DUFLO: Right.
+
+He is saying it's useless.
+
+And how does he explain that
+despite the fact that it's
+
+used less people have
+still done it?
+
+Yeah, go ahead.
+
+AUDIENCE: [INAUDIBLE].
+
+ESTHER DUFLO: Go ahead,
+go ahead.
+
+AUDIENCE: I was going to say
+because the increments in the
+
+[INAUDIBLE].
+
+ESTHER DUFLO: Exactly.
+
+So what Easterly is saying is
+that you guys have been fooled
+
+by this graph.
+
+These are countries--
+
+USA, Romania, Paraguay,
+Venezuela.
+
+And these are the average years
+of schooling of the
+
+population.
+
+And this is the log output per
+worker, relative to the US.
+
+So everybody is negative because
+the US is a richer
+
+country in the world.
+
+And what you can see here is
+that there is a pretty strong
+
+correlation between the log
+output per worker and the
+
+years of schooling.
+
+Countries which have
+more years of
+
+schooling are also richer.
+
+So one could conclude from there
+that year of education
+
+increases income.
+
+And people have certainly
+drawn this conclusion.
+
+What is his point about
+this graph?
+
+AUDIENCE: I'm not sure this is
+the point but, it's the idea
+
+of mobility bias.
+
+We have more education, perhaps
+that's because we have
+
+some sort of mobility.
+
+I mean, I don't know
+if this is--
+
+ESTHER DUFLO: This
+is countries.
+
+AUDIENCE: --in the
+national sense.
+
+ESTHER DUFLO: Think of it's like
+he made this argument,
+
+not for a person, but
+for a country.
+
+What's different about these
+countries as well?
+
+AUDIENCE: They also
+have more greed.
+
+Their GDPs are higher, so
+they have some more
+
+opportunity for school.
+
+ESTHER DUFLO: Yes,
+they are more
+
+flourishing for younger people.
+
+We run this graph with
+the number of
+
+football team you have.
+
+You would have a
+lot of zeroes.
+
+It wouldn't be such
+a good graph.
+
+But you would have the same
+relationship that places that
+
+play American football
+are also richer.
+
+And we don't think it's because
+of American football.
+
+Or I mean I don't think so.
+
+You may have a different view.
+
+So that correlation is
+not very informative.
+
+So what he's suggesting
+is to say, so
+
+let's not look in levels.
+
+Let's look in differences.
+
+And I couldn't find such a
+nice looking graph for
+
+differences, but here is one.
+
+Now we have the difference in
+human capital from it's 1990
+
+minus 1965.
+
+It's a difference in the log
+other ideas of education.
+
+And now we put the log
+difference in income.
+
+You could do it in level log,
+except that doesn't matter.
+
+What's relevant in this graph
+is you get a big cloud of
+
+points and a completely
+horizontal line.
+
+So if I can say this graph in
+words, what this is saying is
+
+that the countries which have
+increased the most the average
+
+years of education of their
+labor force, are the countries
+
+which have put more and
+more kids to school
+
+have not become richer.
+
+So you compare in the Easterly
+reading, he had a comparison
+
+between different African
+countries which had made
+
+different levels of progress--
+
+so I think, so for example,
+Ghana versus Madagascar, and
+
+saying that Ghana has increased
+education more,
+
+Madagascar increased education
+more, and Ghana is not going
+
+faster than Madagascar.
+
+Actually, I don't think
+that's true anymore.
+
+I think subsequent to that,
+Ghana has increased quite good
+
+and quite a bit faster
+than Madagascar.
+
+But that's, let's say,
+was the point, were
+
+the keys at the time.
+
+So now we interpret him saying,
+well, when we take the
+
+difference out, now we are at
+least seeing what has been the
+
+effort terms of increasing the
+years of education, versus the
+
+gain in terms of increasing
+the GDP.
+
+And we see no effect.
+
+So the level relationship was
+all coming from this bias In
+
+fact, there's no effect of
+the years of education.
+
+And the bias in the level of
+regression are some form of
+
+the ability by us as USA which
+countries have more education,
+
+because it takes money
+to have teachers.
+
+They can afford it.
+
+Or maybe they choose to be
+educated because when it's
+
+more worthwhile to get an
+education if you can do
+
+something with that education.
+
+So that comes back to this
+argument of what's the point
+
+of getting an education if
+you're going to come back to
+
+the village anyway?
+
+So if education allows you
+to take advantage of the
+
+opportunities that are afforded
+by economic growth,
+
+then you're going to be more
+willing to get an education if
+
+you think that the country
+is going to grow a lot.
+
+So for all these reasons, and
+you would expect more
+
+education in rich countries, not
+because education causes
+
+growth, but because growths
+cause education.
+
+So his conclusion is that
+internationally driven
+
+investment to education were
+a waste, that education is
+
+actually useless.
+
+Now there's a bunch of problems
+with his argument,
+
+because in a sense what he is
+saying is that I don't see any
+
+evidence across country that
+there is a lot of increase in
+
+GDP coming from increasing
+education.
+
+But the issue is we don't
+know why these
+
+countries increase education.
+
+We don't know what would have
+happened if they had not
+
+increased education.
+
+So for example, many of the
+African countries that
+
+increased education the most
+also had severe civil war
+
+subsequently.
+
+It is possible that education
+caused the civil war, but it's
+
+not very likely.
+
+It is more likely that the
+social tension that preexisted
+
+in the country caused
+the civil war.
+
+One possible answer to the
+social tension may have been,
+
+well, let's try and get
+people an education.
+
+Yep?
+
+AUDIENCE: This is interesting
+because I guess in our
+
+standard macro classes, you
+look at a factor of A as a
+
+multiplicative factor that
+increase in GDP.
+
+And typically, maybe I'm
+thinking about it wrong, you
+
+look at that as if you have
+increased education, it could
+
+be worth more innovation.
+
+If you have the technology, you
+still go for the forms or
+
+operating a computer.
+
+And education helps facilitate
+that group.
+
+So I'm a little confused as to
+how you make this conjecture.
+
+ESTHER DUFLO: So that's
+an interesting fact.
+
+I think in a sense, in your
+macro class you may have been
+
+interpreting this graph.
+
+And there is certainly a lot of
+theories for why education
+
+would be good for growth.
+
+So one of them is the
+one you point out.
+
+This is the externality argument
+that we were making
+
+about the movie.
+
+One person who is educated can
+figure out some technology,
+
+and then everybody can
+use the technology.
+
+So they are all these
+spill-overs, which is why we
+
+would get this pretty strong
+relationship between education
+
+and income.
+
+So there a lot of theoretical
+reasons to think that there
+
+could be a macroeconomic
+relationship between education
+
+and income.
+
+And in fact, we see one, which
+is why everybody is happy
+
+thinking education
+is a good thing.
+
+What Easterly is saying is just
+commenting on this graph,
+
+which is he doesn't see
+a relationship.
+
+Because when he does, the
+relationship in differences
+
+now between growth and education
+and growth and
+
+income, he doesn't see the
+relationship anymore.
+
+AUDIENCE: How long is that?
+
+ESTHER DUFLO: That's 1990, 1965,
+just about 30 years.
+
+Yup?
+
+AUDIENCE: I have a question.
+
+In Easterly's paper,
+he mentions the
+
+productivity factor.
+
+And he says that only a small
+percentage of this is
+
+accounted for by [INAUDIBLE]
+capital and by machinery and
+
+other forms of capital.
+
+What is the rest of it?
+
+Like, what is productivity
+in that case?
+
+ESTHER DUFLO: So that's
+an excellent question.
+
+The answer to this question is
+that's what I do what I do and
+
+not macroeconomics.
+
+If you're looking at growth
+across country, and you're
+
+trying to account for the growth
+in an pure accounting
+
+sense, which is to say, so
+imagine that you each country
+
+is a big machine.
+
+Think of a country
+as a machine.
+
+So there is a machine.
+
+There are some people to operate
+the machine, labor.
+
+And there is some human capital
+to think about how to
+
+operate the machine.
+
+And then there is some spunk.
+
+So think of a macroeconomy
+as that.
+
+In letters, we write it as an A
+multiplied by K, that's the
+
+capital, to some power, multiply
+by L to some power,
+
+multiply by human capital
+to some power.
+
+That's your macroeconomic
+model of an income.
+
+We can observe K
+to some extent.
+
+What's the capital
+in the economy?
+
+We can observe L to a pretty
+good extent, how many workers
+
+there are in the economy.
+
+We can observe H to some extent,
+what is the the human
+
+capital, usually measured
+with education.
+
+And the rest spunk is what
+we don't observe.
+
+Now we can say, well, let's
+look at what share of the
+
+level of income of the country,
+differences in income
+
+across country, are what share
+of differences in growth
+
+across country are explained
+by those factors.
+
+And the answer is
+not very much.
+
+So the answer is that we use
+factors such as capital,
+
+labor, and human capital,
+measured in this way.
+
+We don't explain much
+of the gross
+
+differences across country.
+
+This is one of the reasons why,
+which when you look at
+
+growth and you look at the
+differences in human capital,
+
+there's just no relationship.
+
+There's a bit more with
+physical capital.
+
+And the rest is like,
+we don't know.
+
+So technological progress is
+just a fancy term for we have
+
+no clue what the hell is going
+on, which is to me saying that
+
+well, if we have no clue what
+the hell is going on, then it
+
+means that we need to go beyond
+thinking of the economy
+
+as one big machine.
+
+And we need to start to
+understand what is happening.
+
+Look at micro level.
+
+That might start giving us a
+sense of what might actually
+
+be going on.
+
+Because technological progress
+is not just how good is the
+
+chip in your computer.
+
+You think of this as, as I was
+saying, the spunk, how people
+
+interact, all of that.
+
+So in your macro class, you
+either saw this graph and
+
+commented on it, or you may also
+seen a graph where you
+
+have growth on the left hand
+side and level of education.
+
+You do see a strong
+relationship
+
+between growth and level.
+
+These countries which had more
+education in 1965 have grown
+
+faster between '65 and 1990.
+
+But what Easterly objects to
+that is that yes, of course.
+
+Because if you anticipate
+growth, that's how you're
+
+going to decide to
+get education.
+
+Because education becomes
+more worthwhile.
+
+So that does not tell me that
+education is worth anything.
+
+So that's where we are
+with the macro data.
+
+And my bottom line is not that
+your macro class is wrong or
+
+that your macro class
+is right.
+
+My bottom line is we just don't
+know by just looking at
+
+these data.
+
+We don't have enough
+data points.
+
+And anything could
+have happened.
+
+In the countries which were
+about to have wars may have
+
+invested more in education
+perhaps as an attempt to not
+
+have those wars.
+
+Who knows.
+
+So in order to answer the
+question of what's the
+
+benefits of education, we need
+to look at specific examples.
+
+So ideally, I would have liked
+to look, for you, at the
+
+example of Turkey, because we
+just saw it in the movie.
+
+But I don't have it.
+
+So we'll be looking at the
+example of Indonesia.
+
+So if we are looking at the
+effect of supply-driven
+
+expansion, there are some
+arguments where one could see
+
+that it's not going to work.
+
+And these are arguments that
+Easterly is making.
+
+And we kind of all saw
+them in the movie.
+
+There was the point about
+the teacher quality.
+
+If the teachers don't care
+because they've just been spar
+
+shooted by a central government
+to the community
+
+exactly as you were saying, then
+the level of education is
+
+not going to be very good.
+
+If the parents don't care and
+just do it because they have
+
+to do it, then they are not
+going to put pressure on the
+
+teachers to actually deliver.
+
+And they're not going to put
+pressure on the children to
+
+actually learn.
+
+So the | case is the point that
+you were making earlier,
+
+where the children are all alone
+in boarding school, and
+
+nobody's looking after
+what they do.
+
+And potentially, they learn
+nothing, or they might learn
+
+to do all sorts of bad stuff.
+
+So if parents do not think that
+schools are delivering
+
+anything useful, then they
+won't pay attention.
+
+And finally, children,
+if they also don't
+
+care, won't pay attention.
+
+So these are all theoretical
+arguments.
+
+I'm not saying they
+are correct.
+
+But these are the types
+of argument
+
+that Easterly is making.
+
+So how would we know whether
+or not there is
+
+a benefit of education?
+
+So as I was saying, I don't
+you want to interpret the
+
+cross-country evidence.
+
+I think it's very difficult
+to interpret.
+
+So I want to focus on one
+country, and this one company
+
+that did almost the same
+thing that Turkey did.
+
+And fortunately for us, they did
+not a few years ago, but
+
+many years ago.
+
+So now we can look at those
+kids as they are
+
+in the labor market.
+
+And we can see whether it was
+beneficial for them to be sent
+
+to these schools.
+
+So that country is Indonesia.
+
+Indonesia is an oil-producing
+country.
+
+So when there was a big oil
+shock in 1970, starting in
+
+1973, for Indonesia, it was
+actually good news.
+
+Because there were producing
+oil, so they became richer.
+
+And they decided that they were
+going to use this oil
+
+money to build a
+lot of schools.
+
+Basically, all the oil money the
+first few years went into
+
+building tons of schools.
+
+Tons means they build almost
+62,000 schools
+
+all over the country.
+
+But particularly in places
+which had a low education
+
+enrollment.
+
+So it's your ultimate
+top down.
+
+Furthermore, what is interesting
+in relationship
+
+with Turkey is that they had
+exactly the same objective,
+
+which is they wanted the kids
+to learn Bahasa Indonesia.
+
+That's the language for the
+country, even people in the
+
+outlying island and
+stuff like that.
+
+And they wanted everyone to
+learn the state ideology,
+
+which was the Pancasila.
+
+It's kind of halfway between
+an ideology and a religion
+
+that [INAUDIBLE]
+
+was keen on.
+
+So it was entirely pushed
+by public effort.
+
+If it was going to fail, then
+this was going to fail.
+
+And what do we see?
+
+So these graphs are the number
+of schools that were built in
+
+the region.
+
+And this is the difference
+between the education of the
+
+young cohort who benefited from
+the school, and education
+
+of the old guys who
+didn't benefit.
+
+So you see that in general, it's
+always positive, because
+
+education went up over
+time between the
+
+younger and the old.
+
+That makes sense.
+
+But it is also increasing in
+slope, that is, places which
+
+got more schools got more
+years of education.
+
+Maybe that's not surprising,
+because that's almost a
+
+mechanical result of
+putting schools.
+
+But this graph is an
+interesting one.
+
+I'm now looking at the wages of
+people in 1995, difference
+
+between the wages of the
+young, minus the
+
+wages of the old.
+
+Now it's all negative, because
+old people have more
+
+experience and tend to
+make more money.
+
+But what is interesting is
+not the negative thing.
+
+It's the slope again.
+
+The slope is again positive.
+
+So it is saying that compared
+to the old guys, the young
+
+people benefit more in places
+which build more schools.
+
+And it's very difficult to think
+of a story why would
+
+this be the case,
+except that the
+
+benefit is from the education.
+
+So it seems to be the case that
+parachuting more schools
+
+to communities increase
+the years of
+
+education, increase wages.
+
+And that seems to imply that
+education increases wages.
+
+And in fact, if you put two
+and two together, you find
+
+that the effect of education
+on wages is about 8%.
+
+You can use similar experiments
+to look at the
+
+non-monetary effect
+of education.
+
+So Taiwan around the same time,
+little bit before, also
+
+did a top down drive to
+increase education.
+
+What they did is compulsory
+education.
+
+And what you find in 1968, and
+what you'll find is compulsory
+
+education in Taiwan led to
+an increase of education.
+
+That's not surprising but also
+a reduction in infant
+
+mortality in places
+where education
+
+increased more as a result.
+
+So again, these are the
+non-monetary benefits.
+
+Nigeria did the same thing
+as Indonesia for the
+
+same type of reasons.
+
+They used their oil money
+to build schools.
+
+Again, they built more
+schools in some
+
+regions than some others.
+
+And again you can compare the
+changes in infant mortality,
+
+and infertility, and in wages
+in places where they built
+
+more schools and
+in places where
+
+they built fewer schools.
+
+And the more schools they
+built, the higher the
+
+education, the higher the
+wages, the lower the
+
+infertilities, the lower
+the infant mortalities.
+
+So the bottom line, when we do
+look at specific top down
+
+policies is that they actually
+are useful, that it seems to
+
+be that there is a returns to
+education, corresponding to
+
+about 8% increase in wages for
+every extra year that you
+
+spend in school.
+
+So when we look at this thing in
+detail and we answer these
+
+questions, we see yes, there
+is a benefit of education.
+
+What we are going to do next
+is to say, well, is the
+
+benefit as high as
+it could be?
+
+And that's where we are going
+to see the limits of these
+
+kinds of things, having to do
+with the quality of education,
+
+the motivation of the teachers,
+the motivation of
+
+the parents, et cetera, which
+we'll do next time.
\ No newline at end of file
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--- /dev/null
+++ b/r_fWDSikuNQ.txt
@@ -0,0 +1,4175 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: I have
+a tiring day today.
+
+Just 10 minutes ago, I finished
+chairing the first part
+
+of a meeting of the
+COA advisory committee.
+
+And I gave a talk to them.
+
+And right after the
+lecture, I have to go back.
+
+So while they have a lunch
+break, I have to teach.
+
+But that's OK.
+
+That's life on the faculty.
+
+Yes.
+
+We're talking about applications
+of the spontaneous light force.
+
+We have used optical
+block recreations and such
+
+to learn about the spontaneous
+force, the stimulated force,
+
+in general.
+
+And this is our expression for
+the spontaneous light force.
+
+It's pretty much, the
+momentum of photons
+
+is transferred to the atom
+times to scattering rate.
+
+And what we started last class,
+and we want to finish today,
+
+is we want to discuss
+applications of this force
+
+to three situations which are
+of experimental importance.
+
+One can actually say that
+slow beams, more or less,
+
+in the magneto-optical trap
+are the key techniques which
+
+triggered a revolution
+in atomic physics.
+
+This is really the
+enabling technology
+
+into ultracold atom science.
+
+So I discussed with you, in
+the last class, molasses.
+
+And we discussed
+what happens when
+
+we have two
+counterpropagating beams.
+
+Maybe the key figure to
+remember is this one.
+
+When we have to
+counterpropagating beams,
+
+by just adding up the
+spontaneous light force
+
+of the two beams, we get the red
+curve, force versus velocity.
+
+And the expert eye immediately
+sees there is a linear slope.
+
+And that's a viscous force.
+
+This is the viscosity of
+light interacting with atoms.
+
+Of course, you'd better
+pick the detuning correctly.
+
+If you use the wrong
+detuning, everything
+
+is flipped upside down.
+
+And instead of a damping force,
+you have an anti-damping force.
+
+We then discussed
+the cooling limit.
+
+Any cooling limit is the balance
+between heating and cooling.
+
+And by just setting the heating
+rate equal to the cooling rate,
+
+this describes a steady state.
+
+We found the famous
+Doppler limit.
+
+OK.
+
+So that's where I
+want to continue.
+
+But do you have any
+questions about molasses,
+
+the Doppler limit, and what we
+discussed in the last class?
+
+Well, I know we had discussions
+about to take two beams which
+
+form a standing wave, and
+take it apart, and calculate
+
+the force for each beam.
+
+Well, sorry, this is
+what molasses is about.
+
+Molasses is about two beams.
+
+And if you want to treat
+two interfering laser
+
+beams in the full
+generality, there
+
+are a lot of other effects.
+
+Some of them, we
+will be uncovering
+
+in the next few lectures.
+
+But I'm happy now, when
+I discuss beam slowing,
+
+to give you when there
+is only one single laser
+
+beam decelerating atoms.
+
+That is the only
+situation I know
+
+about where you have an
+exact analytic solution.
+
+So I want to present
+it to you know.
+
+Actually, for a number of years,
+I presented the exact solution
+
+with one laser beam before
+I presented molasses,
+
+where I have to
+make approximations.
+
+But I always felt that beam
+slowing is more complicated,
+
+because you have to go
+to a decelerating frame
+
+and have to add
+fictitious forces.
+
+So some of the
+intuition is lost.
+
+So that's why I first
+presented you with molasses,
+
+with two beams, for which I
+need to make approximations.
+
+Because the interference
+pattern between two laser beams
+
+has richness and complexity.
+
+But now I discuss
+beam slowing with you.
+
+So this curve here
+could be the result
+
+of the very early beginnings
+of laser cooling in
+
+the late '70s, early '80s.
+
+And this is when people had an
+atomic beam with a Boltzmann
+
+distribution, and they had one
+laser been counterpropagating.
+
+But the laser beam
+had a fixed frequency.
+
+And what is this
+laser beam doing?
+
+Well, it resonantly
+interacts with the atoms
+
+which just have the
+correct Doppler shift
+
+to be in resonance.
+
+Those atoms are pushed--
+scattered photons-- are pushed
+
+to lower frequencies--
+to lower velocities.
+
+But they are pushed
+out of resonance.
+
+And eventually, the slowing
+becomes slower and slower.
+
+And eventually, things come,
+almost, to a standstill.
+
+So a laser beam which
+has a fixed frequency
+
+would modify the
+velocity distribution
+
+of an atomic beam in that way.
+
+People called it,
+already, cooling.
+
+And I think some
+pioneers in Russia
+
+who did those experiments were
+disappointed that they were not
+
+honored with a Nobel
+Prize in laser cooling.
+
+This was the first cooling.
+
+Because this distribution
+here is considerably narrower
+
+than here.
+
+And temperature is nothing
+else than a measure
+
+of the reach of the
+velocity distribution.
+
+But one can say that
+those experiments did not
+
+trigger a revolution
+in atomic physics.
+
+The revolution came when
+people eventually figured out
+
+how they can narrow down this
+peak from maybe a hundred
+
+or tens of kelvins down
+to a million microkelvin.
+
+So it's clear what is needed.
+
+If you want to do
+more slowing, you
+
+have to make sure
+that you are talking
+
+to the other velocities,
+and that you eventually
+
+sweep many velocities into one
+peak-- clear out the velocity
+
+distribution, collect
+all the atoms,
+
+and put them at a
+monochromatic velocity.
+
+So for that, you can say, well,
+if you use a comb of frequency,
+
+or a broad spectrum
+of frequencies,
+
+you could clean
+out a larger area.
+
+And, indeed, there
+are techniques
+
+like this-- white light slowing
+or diffuse light slowing.
+
+But since those
+techniques are not
+
+anymore of practical importance,
+I don't want to discuss them.
+
+Let me talk about the
+simplest technique-- at least,
+
+conceptionally-- which
+is chirped slowing.
+
+And this works like follows.
+
+You start with a laser
+beam which is initially
+
+in resonance with
+the velocity group.
+
+And as the atoms slow down,
+you change the detuning
+
+of the laser that the
+laser stays in resonance
+
+with the atoms.
+
+So it is a pulsed
+technique where
+
+you have a continuous
+atomic beam.
+
+You start with a laser and
+say, now I start slowing.
+
+And the laser is
+following a group of atoms
+
+as they are decelerated.
+
+So you can say it is like the
+atoms are riding the surf.
+
+The laser is always
+following the atoms
+
+as they change their velocity.
+
+And what is, of course,
+necessary for that to happen
+
+is that the chirp and the
+deceleration of the atoms
+
+are synchronized.
+
+You will see that
+in a moment, when
+
+I put this idea into equations.
+
+There is another technique
+which is used in many labs--
+
+actually, in all my labs
+and Martin Zwierlein's lab.
+
+It's called Zeeman slowing.
+
+And this is discussed
+in your homework.
+
+It is a CW version
+of chirped slowing.
+
+And a lot of you
+know what I mean.
+
+The physics which goes on
+there is almost identical.
+
+But for conceptional
+reasons, it's
+
+easier not to use
+magnetic fields and such.
+
+Let's just keep it simple.
+
+Let's have one laser beam
+talking to a two-level atom.
+
+And the only other ingredient
+is the Doppler shift.
+
+Any questions about--
+so I've surveyed,
+
+for you, beam slowing.
+
+And now I want to give
+you the exact description
+
+for one typical example
+of a slowing technique.
+
+And a lot of the results
+we find in chirped slowing
+
+apply to other
+slowing techniques.
+
+OK.
+
+I know I've taught
+it several times.
+
+And there is the
+conceptional point
+
+that you can only describe
+chirped slowing well
+
+when you go to the decelerating
+frame of the atoms.
+
+You want to describe it in
+the frame of the atoms which
+
+are continuously
+being decelerated.
+
+So the way I can introduce
+it is the following.
+
+I take the maximum-- I take
+the spontaneous light force.
+
+This is exactly
+the expression we
+
+have discussed several times.
+
+And now I'm saying
+we decide that we
+
+want to decelerate atoms
+with a deceleration, a, which
+
+is negative, because
+we slow them down.
+
+Of course, if you pick a too
+large that it would require
+
+more than the maximum
+spontaneous light force,
+
+you will not find a solution.
+
+But let's simply assume we
+want to decelerate atoms
+
+with a deceleration a.
+
+Well, what happens is
+this deceleration, a,
+
+requires a certain force.
+
+If the intensity of the laser
+would provide more force
+
+on resonance then it's
+not going to work.
+
+Because we want to decelerate
+the atoms at this deceleration.
+
+So therefore, the atoms,
+if they are decelerated,
+
+have to be at a detuning,
+delta prime, in such a way
+
+that the spontaneous
+light force is exactly
+
+providing the
+acceleration we decided
+
+we want to have for our atoms.
+
+In other words, this detuning--
+in the frame of the atom,
+
+the atoms are on resonance
+when the light force is exactly
+
+providing the force to give
+you the acceleration a.
+
+But if you have more laser
+power than absolutely necessary,
+
+in the frame of the
+atoms, the atoms
+
+have to be detuned in
+such a way that the force,
+
+with the detuning,
+is exactly providing
+
+the acceleration we want.
+
+So that's the easiest
+way to explain it.
+
+We have to set the stage.
+
+We have to introduce
+this nominal detuning.
+
+OK.
+
+So you can say that this
+detuning is just a definition.
+
+And now we want to describe
+the slowing process.
+
+So we have said we want
+to start with atoms
+
+at an initial velocity-- which
+we'll actually cancel out
+
+in a moment.
+
+But let's do it in
+a systematic way--
+
+and afterwards, we want the
+velocity to decrease, linearly,
+
+in time.
+
+I simply defined this
+parameter, delta prime,
+
+to be a solution
+of this equation.
+
+So this is a well
+defined quantity.
+
+And the laser detuning--
+which, I've broken my laser
+
+to change its detuning
+as a function of time--
+
+is now this nominal detuning
+minus the Doppler shift
+
+due to the velocity
+of the atoms.
+
+I'm really solving the
+problem backwards for you.
+
+I first decide which should
+be the velocity trajectory
+
+of the atoms-- how should
+the atoms slow down.
+
+And then, I define what
+is the detuning which
+
+will result in that.
+
+That's the easier
+way to understand it.
+
+Of course, if you
+pick this detuning,
+
+the atoms will exactly do that.
+
+OK.
+
+But now what we're
+doing is the following.
+
+This is sort of the
+acceleration and the velocity
+
+we want the atom to have.
+
+But there may be some
+atoms in the beam which
+
+do not have this velocity.
+
+They deviate from this
+velocity with v prime.
+
+So the goal of
+cooling would now be
+
+to reduce v prime to 0 to
+make all the atoms follow
+
+the trajectory we have
+designed for them.
+
+OK.
+
+Many words, many definitions.
+
+Now we can simply
+substitute what
+
+we have defined
+into the equation.
+
+And we get a wonderful result.
+
+So we take equation
+one, which was
+
+the equation for
+the light force.
+
+And we put all
+those definitions,
+
+which I went to great lengths
+to explain to you, into it.
+
+And we get this result.
+
+It's just that the detuning has
+been expressed by delta prime,
+
+and the velocity by this
+difference velocity v prime.
+
+It's pure mathematical
+substitution.
+
+But now comes the
+important point
+
+that we want to describe
+everything, now,
+
+in the decelerating frame.
+
+The atoms are meant to
+decelerate with a deceleration
+
+a.
+
+And you know, from
+classical mechanics,
+
+if you describe something
+in a decelerating frame,
+
+you have to add a
+fictitious force.
+
+This fictitious force, since
+the acceleration is constant,
+
+is a constant force.
+
+But I'm expressing it, now,
+by the other parameters.
+
+We've chosen our acceleration.
+
+We've chosen the
+detuning, delta prime,
+
+that-- everything is
+sort of connected.
+
+And this is just a way to
+use the correct-- the most
+
+easiest units, or the
+correct parametrization,
+
+for this constant force.
+
+So I have done-- and the
+important thing for you
+
+is, this equation is exact.
+
+It's exact for an arbitrary
+velocity v prime of the atoms.
+
+So let me just summarize.
+
+I've taken the
+spontaneous light force.
+
+I've given you a
+bunch of definitions,
+
+what delta prime is.
+
+That's how you
+program your laser.
+
+But then, in the
+decelerating frame,
+
+we need a fictitious force.
+
+And this is nothing else than
+a mathematically exact rewrite
+
+of the spontaneous light force
+in the decelerating frame.
+
+But now what happens is--
+we had a decelerating--
+
+we had a light force where,
+because we assume the laser is
+
+counterpropagating,
+there's a minus sign.
+
+The fictitious force
+has a plus sign.
+
+And that means that we
+can-- and if v prime is 0,
+
+the force is 0.
+
+So we can now make a Taylor
+expansion for small v prime.
+
+So we have, again, a viscous
+force, a friction force.
+
+And it turns out that
+this friction coefficient
+
+for beam deceleration is
+exactly 1/2 what we got before,
+
+for molasses.
+
+But it's clear we
+have one laser beam.
+
+Whereas in molasses,
+we had two laser beams.
+
+If you ask, what is
+the heating, well,
+
+if you have one laser beam
+and not two laser beams,
+
+the heating described by the
+momentum diffusion coefficient
+
+is also just 1/2.
+
+One beam heats exactly half
+of what we got for two beams.
+
+And therefore, the
+temperature, which
+
+characterizes the width of
+the velocity distribution
+
+in the frame of the
+decelerating atoms
+
+is exactly the Doppler
+temperature we had before.
+
+Because the two
+factors of 1/2 cancel.
+
+So now I have given
+you-- and I hope
+
+you take some pleasure
+in it-- an example where
+
+the laser cooling for
+a two-level system
+
+is exactly described.
+
+There's only a single beam.
+
+And the Doppler limit
+is the exact solution.
+
+I've not made any
+approximation other
+
+than assuming I have a
+two-level system for which
+
+the spontaneous light force has
+the expression we've derived.
+
+OK.
+
+I know, even with
+my explanation,
+
+you have to read through
+it once or twice.
+
+Because I made a
+few substitutions.
+
+And you really have to
+digest them at your own pace.
+
+So let me give you a summary of
+what we have done graphically.
+
+One laser beam scatters light.
+
+And it is this Lorentzian.
+
+And it's a negative
+Lorentzian because we
+
+have a counterpropagating beam.
+
+We push the atoms into
+the negative direction,
+
+they fly in the
+positive direction.
+
+But by going-- by
+chirping the laser,
+
+by going into the
+decelerating frame,
+
+the force doesn't go to 0.
+
+I had to add an offset.
+
+And this offset is
+the fictitious force
+
+due to the transformation
+of the decelerating frame.
+
+And now you realize
+that this force-- and it
+
+is the correct force in the
+decelerating frame-- has two 0
+
+crossings.
+
+One is a stable point, and
+one is an unstable point.
+
+And the stable point says, if
+an atom happens to be too fast,
+
+it gets a correcting force.
+
+And this is like a lock point.
+
+It has a stable lock point.
+
+All the atoms which did not have
+the correct velocity we wanted
+
+them to have, they are sort of
+sucked into this lock point,
+
+and eventually, will
+pile up at a huge peak
+
+at this nominal velocity.
+
+And the width of
+this peak is simply
+
+described by the Doppler limit.
+
+Before I take your
+questions, let
+
+me show you what happens
+in the two frames.
+
+This is v prime.
+
+This is the velocity in
+the decelerating frame.
+
+And let's say our
+initial velocity is this.
+
+So what happens now is all
+the atoms within the atoms
+
+are decelerated towards
+v prime equals 0.
+
+The friction force puts
+them to v prime equals 0.
+
+But since we are in
+a decelerating frame,
+
+in the absence of the laser,
+the whole Maxwell-Boltzmann
+
+distribution is
+just shifted-- not
+
+because the velocity
+of the atoms
+
+changed-- because we are
+in a decelerating frame
+
+and we are accelerating
+away from the atoms.
+
+And what I just described for
+you is the following-- that,
+
+at v prime equals 0, we
+have our friction force.
+
+And the atomic
+distribution in this frame
+
+is now pushed through.
+
+And everything which goes
+through this resonant region
+
+is sort of collected.
+
+And you have a peak which is
+piling up at v prime equals 0.
+
+Probably, it's easier--
+but mathematically,
+
+I needed the
+decelerating frame--
+
+if you use the
+following picture.
+
+And just think of this beam
+slowing I explained to you.
+
+If you just switched
+on a laser here,
+
+you would just burn a hole
+into the velocity distribution
+
+and pile up the atoms.
+
+But now you sweep.
+
+And when you sweep, you take
+the peak, push it further.
+
+It gets a bigger peak here.
+
+Push it further.
+
+So eventually, what
+you're doing is,
+
+by chirping the laser
+in the correct way
+
+with the correct laser
+power and all that,
+
+you're just pushing
+the atoms all out.
+
+And eventually,
+they are piled up
+
+in a narrow distribution which
+is defined by the time when you
+
+just switch off your laser beam.
+
+So one chirp of the laser,
+from an initial detuning
+
+in the lab frame to a final
+detuning in the lab frame,
+
+will just sweep out the whole
+Maxwell-Boltzmann distribution.
+
+And if you suddenly
+switch off the laser,
+
+you have frozen in a velocity
+distribution which is exactly
+
+described by the Doppler limit.
+
+So what is easier to
+understand-- molasses
+
+with two beams, or beam
+slowing with a single beam?
+
+I think molasses is
+easier, because everything
+
+happens in the lab frame.
+
+But think about it.
+
+It's a nice example for which no
+approximations have to be made.
+
+Questions?
+
+Yes, Nancy.
+
+AUDIENCE: It's not
+really obvious to me
+
+how, in this mathematics,
+we are choosing
+
+a time-dependent
+detuning as opposed
+
+to a time-dependent
+deceleration.
+
+PROFESSOR: The way I
+presented it logically, we
+
+said we want a certain
+acceleration to happen.
+
+And then, we provide our laser
+that k/kv is the Doppler shift.
+
+ka is how the Doppler shift
+changes as a function of time.
+
+And we chirp our laser
+exactly in frequency
+
+with a chirp which is ka.
+
+So in other words, I started
+to define a constant a.
+
+And that would require
+that the laser is now
+
+chirped in a linear way.
+
+I could have started the
+other around and said, hey,
+
+let's assume we chirp the
+laser in a linear way.
+
+And then, we do
+corresponding substitutions.
+
+And the result
+would be the same.
+
+AUDIENCE: No, actually,
+like if we did not
+
+want to have a detuning
+which was time-dependent,
+
+would we have gotten--
+we still have a force.
+
+And that force would
+have been just changing.
+
+PROFESSOR: Well then, it's
+more complicated, yeah.
+
+Then, you have to integrate
+a differential equation.
+
+But what happened
+is the following.
+
+What I've done is, by defining
+the acceleration and then
+
+the chirp, I have the situation
+that, in the reference
+
+frame of the decelerating
+atoms, the detuning is constant.
+
+So usually, you go to
+a decelerating frame
+
+if something else simplifies.
+
+And what simplifies is that,
+in the frame of the atom,
+
+the laser detuning is constant.
+
+So you can also say the frame
+in which the atoms decelerate is
+
+exactly the frame in which
+the chirp has disappeared.
+
+Because the decelerating
+frame compensates
+
+the chirp with a
+linearly varying,
+
+time varying Doppler shift.
+
+OK.
+
+But the physics, I
+think, is really--
+
+the moment you have a force
+which has a 0 crossing,
+
+it's a lock point.
+
+You determine the slope.
+
+And alpha, together with
+the momentum diffusion,
+
+gives you the final temperature.
+
+So I hope you enjoy that it's
+actually the same physics--
+
+exactly the same
+physics-- we discussed,
+
+with some approximation
+for molasses.
+
+OK.
+
+We had a discussion last time
+about, we have the force,
+
+we find exactly what
+happens to the atoms.
+
+But we may have to think
+about it in different ways
+
+to figure out where the
+kinetic energy goes from.
+
+And I think we mentioned it
+already, in the last class,
+
+that what happens is you have
+a red-detuned laser, which is,
+
+the photons are absorbed.
+
+But the atom is scattering
+light in all directions.
+
+And so if you go
+at 90 degrees, you
+
+don't have a linear
+Doppler shift.
+
+If you go forward-backward
+with the same probability--
+
+a symmetric pattern-- the
+Doppler shift averages to 0.
+
+So on average, you emit
+photons which are on resonance.
+
+And therefore, every time
+you scatter a photon,
+
+you radiate away
+the energy which
+
+is equal to the Doppler shift.
+
+That means, initially, when
+the Doppler shift is huge,
+
+each photon transports
+away a lot of energy.
+
+And the slower the atoms
+are, the less a photon
+
+transports away.
+
+But that makes sense.
+
+If you have a huge
+velocity and you
+
+subtract h bar k, the
+momentum of the photon,
+
+the kinetic energy is
+quadratic in velocity.
+
+You know, h bar k, the
+momentum transfer of a photon,
+
+takes out more kinetic
+energy the faster
+
+the velocity of the atoms is.
+
+So everything makes
+sense and is consistent.
+
+OK.
+
+Let's go from the-- we
+started with two beams.
+
+We just discussed one
+beam, chirped slowing.
+
+And let's go now to what most
+of you use in the laboratory--
+
+namely, six beams.
+
+You want to cool in x, y, z.
+
+So you have
+one-dimensional molasses
+
+with two beams times 3.
+
+So in the limit that
+the intensity is low,
+
+you just add up all the forces.
+
+You say each beam has a
+spontaneous light force.
+
+And you add the six
+spontaneous light forces up.
+
+At low intensity-- and you
+have to take my word for it--
+
+you can ignore all the
+interference effect
+
+between the beams.
+
+They can actually lead to
+very interesting effects.
+
+I will give you at least a taste
+of what will happen-- actually,
+
+a pretty good taste-- what
+happens at higher power.
+
+We need the traced atom picture.
+
+And we'll discuss how
+the stimulated force
+
+can be used for cooling.
+
+But if you don't have
+a two-level system,
+
+you have sigma plus
+sigma minus transitions
+
+and the beams interfere, you get
+spatially varying polarizations
+
+of your interference
+patterns, and then you
+
+have much [INAUDIBLE] physics.
+
+But in the simplest case
+of a two-level system,
+
+there is a regime
+at low intensity
+
+where you can simply take the
+equations we got for molasses
+
+and apply them to XYZ.
+
+I put, on the website, a nice
+handout, a review paper by Bill
+
+Phillips, who is discussing 1D
+molasses versus 3D molasses,
+
+and if you enjoy
+it, you can read
+
+how numerical factors
+of 1 or 2 or 3
+
+now appear in the
+friction coefficient,
+
+in the heating
+coefficient, and how
+
+they affect the
+final temperature.
+
+But you got the full [INAUDIBLE]
+concepts and the correct idea
+
+for one dimension molasses.
+
+Now, let me give you
+an outlook for what
+
+we will be doing next week.
+
+Next week, we want to
+understand the following-- what
+
+happens to the
+friction coefficient
+
+when you increase the power?
+
+Well, you remember when
+we have red-detuned light,
+
+then we had one Lorentzian,
+another Lorentzian.
+
+The slope was
+negative, and negative
+
+means positive
+friction, we cool.
+
+And if you put
+more power into it,
+
+the linear slope increases,
+and for low power,
+
+the friction coefficient is
+proportional to the laser
+
+intensity.
+
+But now look what happens.
+
+If you approach saturation,
+then the friction
+
+is not only saturating, it
+suddenly changes the sign,
+
+and this is qualitatively new.
+
+And you should a little
+bit wonder about it.
+
+Wasn't the reason why we
+have cooling that you have
+
+a laser which is red-detuned?
+
+And the photon which is
+spontaneously emitted
+
+is on resonance, and this
+is the energy difference.
+
+But now I'm telling
+you, at high intensity,
+
+it's not the red-detuned
+laser which cools,
+
+it's the blue-detuned laser.
+
+So you should wonder about it.
+
+There is really something
+new to be learned.
+
+So I want to motivate you to
+follow me today and next week
+
+through an alternative
+description
+
+of what light does to atoms
+using the dressed atom picture,
+
+and in the dressed
+atom picture, we
+
+will very naturally
+understand why
+
+now blue-detuned light
+provides cooling.
+
+But right now, for you,
+this should be a mystery,
+
+but it should be something
+where you say, hey,
+
+still something
+qualitative is missing
+
+in our understanding
+of light forces.
+
+OK, I will not be
+able to explain
+
+it [? physically ?] to you.
+
+I first have to introduce
+the dressed atom picture,
+
+and I will do that it
+in 10 minutes or so.
+
+But what I want to do
+here is if I'm telling you
+
+something goes terribly
+wrong and we completely
+
+miss even the sign of the
+force, blue-detuned light is now
+
+cooling, not red-detuned
+light, I at least
+
+want to tell you
+what went wrong.
+
+Because haven't we done
+an almost exact discussion
+
+of light forces?
+
+We used the gradient of d dot e.
+
+We used for d the steady state
+solution of the optical Bloch
+
+equations.
+
+Haven't we done
+everything right?
+
+Well, we did approximations.
+
+And what happens is,
+and this is the reason
+
+for those qualitatively
+different things, that we
+
+should, in order to get
+those effects, not use,
+
+for the dipole moment, for the
+off-diagonal matrix elements
+
+of the density matrix,
+the steady state solution
+
+for optical Bloch vector.
+
+We have to acknowledge that
+it always takes a finite time
+
+to reach steady state.
+
+For instance, if he takes, let's
+say, a spontaneous emission
+
+time, if the atom goes
+through a standing wave,
+
+it goes from high
+intensity to low intensity,
+
+it takes about one
+spontaneous emission time.
+
+When you are highly
+excited, but now you
+
+go through a node of
+the standing wave,
+
+the steady state
+solution is [INAUDIBLE].
+
+At the node of the standing
+wave, there is no light.
+
+The steady state
+solution with no light
+
+is you better go back
+to the ground state,
+
+but that takes
+something on the order
+
+of the spontaneous
+emission time.
+
+So therefore, when I
+am excited because I'm
+
+in the middle of the
+[? pied ?] laser beam
+
+and I go fast into
+the dark region,
+
+I'm still excited because
+I didn't have time
+
+to get rid of my excitation.
+
+In other words, the
+internal degree of freedom,
+
+the population of
+grounded excited state,
+
+will lag behind the
+steady state solution
+
+by a lag time which is a
+spontaneous emission time.
+
+And that would mean if I
+multiply with the velocity,
+
+it's pretty much that there
+is a spacial displacement.
+
+I'm always a certain distance
+away from the steady state
+
+solution.
+
+And actually, this point,
+to introduce the lag time,
+
+we with do it in a
+wonderful, physical way when
+
+we have the dressed
+atom picture,
+
+but it can be done with
+optical Bloch equation.
+
+It's just a real pain because
+the optical Bloch equation
+
+is sort of like a
+matrix the equation.
+
+It's completely
+obscure, how it is done,
+
+but in order that you
+convince yourself,
+
+I posted the original paper
+from Gordon and Ashkin
+
+where this was done.
+
+You read the math.
+
+You understand the
+result, but you
+
+don't understand the derivation,
+the physical picture behind it.
+
+The dressed atom picture will
+give us a lucid explanation
+
+for exactly what a
+lag time does and why
+
+this results in colling.
+
+But anyway, this is the
+physics we have done wrong.
+
+At low power, it's OK.
+
+At high power, we really
+have to take care of effect.
+
+And if we would take care
+of effect-- And as I said,
+
+we don't need the
+dressed atom picture,
+
+we can fully do it within the
+framework of the optical Bloch
+
+equation, but it's messy.
+
+--we would actually get out, and
+you see that in the references,
+
+the result that the friction
+coefficient in a standing wave
+
+at weak power is exactly two
+times the friction coefficient
+
+for a travelling wave, and
+that justifies that we describe
+
+molasses by the spontaneous
+light force of two travelling
+
+waves, completely ignoring
+the standing wave.
+
+But the same treatment of
+the optical Bloch equation
+
+will then, eventually,
+give us the result
+
+that alpha changes
+sign at high intensity.
+
+But as I said, I
+want to describe
+
+that after we have introduced
+the dressed atom picture.
+
+Questions?
+
+OK, we have done molasses
+in one dimension.
+
+We have done beam slowing.
+
+We just did a short
+discussion about molasses
+
+in arbitrary dimensions.
+
+The one technique
+which is missing now
+
+is the magneto-optic trap.
+
+Let me just spend five
+minutes to discuss
+
+the background behind
+the magneto-optic trap
+
+because for many of you,
+I think you were just
+
+born when the magneto-optic
+trap was invented.
+
+Well, I joined
+the field in 1990,
+
+and that was three years
+after the magneto-optic trap
+
+has been invented.
+
+And many people say if there is
+one most singular development
+
+in laser cooling and
+such, it's molasses
+
+and the magneto-optical trap.
+
+So let me tell you why,
+the magneto-optical trap,
+
+you shouldn't take
+it for granted.
+
+It was actually in
+1983 that Ashkin--
+
+Was it Gordon or Ashkin?
+
+I think Ashkin, Art Ashkin.
+
+--that he presented an
+Optical Earnshaw theorem,
+
+and it is nicely described
+in Bill Phillips' Varenna
+
+notes which I have
+posted on the website.
+
+And it's pretty much a proof
+that you cannot build a trap
+
+using the spontaneous
+light force.
+
+So in other words,
+this is a proof
+
+which people took
+as a correct proof
+
+that something like
+the magneto-optic trap
+
+could not exist.
+
+So what this is proof like?
+
+Well, and that
+sort of teaches you
+
+what was the mental concept
+or the mental barrier people
+
+had to break through
+before they invented
+
+the magneto-optic trap.
+
+The proof is the following.
+
+If you think that you
+have beams-- I mean,
+
+a model for the spontaneous
+light force is you have photons
+
+and the photons are
+sand blasting the atom.
+
+Each photon is like
+a grain of sand,
+
+and the atom is in scattering
+descent in all directions.
+
+You can really make this
+completely classical picture
+
+of the spontaneous light force.
+
+Almost.
+
+If you do with that you would
+say the spontaneous light force
+
+is proportional to
+the stream of photons
+
+which is described by
+the Poynting vector.
+
+But now, you have
+in electromagnetism
+
+a continuity equation which says
+the divergence of the Poynting
+
+vector plus the change of energy
+density in a certain volume
+
+has to be 0.
+
+So if you are in
+steady state-- If you
+
+have an arrangement
+of laser beams
+
+and the energy density of
+the electromagnetic field
+
+is at steady state,
+that tells you
+
+that the divergence of the
+Poynting vector has to be 0.
+
+Well, if the divergence
+of the Poynting vector
+
+is 0, using this
+equation that says
+
+the divergence of the
+spontaneous light force
+
+has to be 0.
+
+But if the divergence
+of the force
+
+has to be 0, that means you
+can not have a force which
+
+is inward from all directions
+because such a force,
+
+a trap needs a force
+which is inward.
+
+A trap requires a
+negative divergence.
+
+Do you see the wrong
+assumption in this proof,
+
+or did I convince you that
+the magneto-optic trap is not
+
+possible because this
+proof would say you can not
+
+make a trap out of the
+spontaneous light force?
+
+AUDIENCE: Well, you through out
+the change in energy density,
+
+so that's--
+
+PROFESSOR: But that's
+OK because if you switch
+
+on a laser beam, light
+travels at the speed of light,
+
+and in 10 to the minus 10
+seconds, in picoseconds,
+
+you reach steady state.
+
+And you know when
+you operate the MOT,
+
+you're not switching on and
+off your lasers at picoseconds.
+
+It's not that.
+
+Yes, [INAUDIBLE].
+
+AUDIENCE: --the
+spacial variation of c.
+
+PROFESSOR: Yes, exactly.
+
+The force is not just
+proportional to the Poynting
+
+vector.
+
+This would be true if
+I had grains of sand,
+
+but photons have to fill
+a resonance condition.
+
+You can maybe
+assume I'm an atom,
+
+but I have an spatially varying
+magnetic field around me.
+
+At the one magnetic
+field, I feel the force
+
+of the laser beam
+because I am resonant.
+
+At another magnetic
+field, the laser beam
+
+just goes through me because
+I'm not in resonance.
+
+So therefore, the
+proportionality
+
+between the Poynting
+vector of the laser
+
+beam and the light force
+ignores that the light force
+
+is resonant, that the
+light force depends
+
+on polarization and such.
+
+So the solution
+is the divergence
+
+of-- If the c parameter
+is spatially dependent,
+
+then we can have a divergence,
+and then, we can do trapping.
+
+And it was actually Dave
+Pritchard in '85 or in '86
+
+who wrote a really
+influential paper.
+
+He said the Optical Earnshaw
+theorem can be circumvented.
+
+We can have a spatially
+dependent factor,
+
+and what can be spatially
+dependent is saturation.
+
+If you focus a laser beam,
+you have a spatially varying
+
+saturation parameter.
+
+There can be some
+optical pumping.
+
+There can be light--
+
+So he discussed
+several possibilities
+
+how the Optical Earnshaw
+theorem was circumvented.
+
+At this point in 1986,
+he didn't realize
+
+that it can be done with
+a magnetic field gradient.
+
+When he talked about possible
+ways of circumventing
+
+the Optical Earnshaw theorem,
+Jean Dalibard, who many of who
+
+know, who's a famous
+researcher in our field,
+
+had the idea that applying
+a magnetic field gradient
+
+could work.
+
+But nobody thought,
+at this time,
+
+that it would work
+in three dimensions,
+
+so the fact that it
+works in three dimensions
+
+is almost a miracle.
+
+So when the idea was born,
+all those schemes, and also
+
+the original idea of applying
+a magnetic field gradient,
+
+were conceived as
+one dimension scheme.
+
+Most of the schemes can
+not be easily generalized
+
+to three dimension,
+but the MOT scheme
+
+works as well in three dimension
+as it works in one dimension.
+
+Anyway, so this is
+sort of the background.
+
+Since I was a postdoc
+when there were only two
+
+or three groups who were
+operating a magneto-optic trap,
+
+I put together,
+with my own hands,
+
+the first magneto-optic trap
+which was ever used at MIT.
+
+I mean, it's ancient
+history, so I
+
+wanted to share a little
+bit this history to you.
+
+But let me now simply
+describe to you
+
+how the magneto-optic
+trap works.
+
+Let me describe it
+for an atom which
+
+we are not using in the lab.
+
+We all usually use atoms which
+have hyperfine structure.
+
+But let me just for
+pedagogical simplicity
+
+assume that we have an atom
+which has an s to p transition,
+
+and in the p transition,
+we have the three different
+
+magnetic [? quantum ?] numbers.
+
+So it's a simplified model.
+
+And what we're
+doing right now is
+
+we are applying molasses, two
+beams which act as molasses,
+
+but there is one difference now.
+
+They have different
+polarizations, sigma plus
+
+and sigma minus,
+and in addition, we
+
+apply a linear magnetic
+field gradient.
+
+So what happens now
+is the following.
+
+The linear magnetic
+field gradient
+
+does Zeeman shifts in
+the opposite direction
+
+to the n plus 1 and
+n minus 1 level.
+
+Now, the transition to m minus
+1 is done by sigma plus light.
+
+The transition to m plus 1
+is done by sigma minus light.
+
+So what happens now
+is if you have an atom
+
+and it moves away
+from the origin,
+
+it will eventually come
+closer and closer in resonance
+
+with the sigma plus light,
+but the sigma plus light
+
+comes from the left side so
+the atom will be pushed back.
+
+If the atom moves out hear, it
+moves further and further away,
+
+in resonance, from
+the sigma plus light,
+
+but it moves now, in resonance,
+over the sigma minus light,
+
+and the sigma minus light
+is pushing the atoms back.
+
+So this geometry has an inward
+force from both directions
+
+and therefore, works as a trap.
+
+So let me now describe
+it mathematically
+
+which is very, very simple.
+
+What we have to do is we
+just have, like in molasses,
+
+two laser beams two
+times the expression
+
+for the spontaneous light force.
+
+And you'll remember we
+got the molasses equation
+
+by taking the two laser beams
+and putting in the Doppler
+
+shift which is a
+velocity dependent shift.
+
+Well, all we have to do is,
+for those two laser beams,
+
+we have to put now a spatially
+dependent Zeeman shift which
+
+varies linearly with position.
+
+So therefore, all we have to
+do is we sum up the total force
+
+as the spontaneous
+force for the right
+
+and for the left laser
+beam, and in addition
+
+to the molasses effect, we put
+now in the spatial dependence.
+
+So we don't have to
+do the math again.
+
+We did already a
+Taylor expansion in v,
+
+but let's now just
+do a Taylor expansion
+
+in the blue expression.
+
+And then, we find that there
+is a linearly restoring force
+
+both in velocity space and
+in configuration space which
+
+actually tells you
+something interesting.
+
+The more friction you have, the
+larger is the restoring force.
+
+So the trapping and the
+cooling are really connected,
+
+at least in the simple model
+of the spontaneous light force.
+
+OK, so if we have
+this kind of force,
+
+a linear force in velocity,
+a linear force in position,
+
+this is the equation of
+motion of a damped harmonic
+
+oscillator.
+
+You have a spatial
+force constant, k,
+
+this linear force which
+is linear in displacement.
+
+So this is a damped
+harmonic oscillator.
+
+Usually, you don't
+see atoms sloshing
+
+in your magneto-optic trap
+like in an harmonic oscillator
+
+because if you look through
+the [? typical ?] numbers
+
+and by just doing
+the Taylor expansion
+
+of the spontaneous light
+force, you can immediately
+
+get an alluded expressions
+for those numbers.
+
+In almost all cases,
+the harmonic oscillator
+
+is overdamped.
+
+So that's how the
+magneto-optic trap works.
+
+However, the magneto-optic
+trap is not so simple.
+
+I would actually
+say nobody fully
+
+understands the
+magneto-optic trap
+
+because we have
+multi-level structure.
+
+We don't have just
+one count level.
+
+A sodium and a
+rubidium atom has--
+
+f equals one and f equals two--
+has eight different hyperfine
+
+levels.
+
+So there is not one level
+and we can excite the atoms.
+
+There are eight
+different levels.
+
+And those laser beams to optical
+pumping among those eight
+
+levels, and you have to
+solve a rate equation
+
+for eight different levels.
+
+And the amazing thing
+is it still works.
+
+It still works
+pretty much, at least
+
+qualitatively, as well as
+I just described to you.
+
+So it's a combination of optical
+pumping and Zeeman shifts.
+
+It even works better
+than advertised
+
+because as I will tell
+you in the next few weeks,
+
+you can reach
+temperatures-- Because
+
+of the multi-level
+structure, you
+
+reach temperatures which are
+much colder than the Doppler
+
+limit.
+
+It's called polarization
+gradient cooling.
+
+It's just if you
+have laser beams
+
+and you have atoms with
+hyperfine structure,
+
+they are colder than
+the Doppler limit.
+
+First, nobody understood
+it, and then, Bill Phillips
+
+figured it out.
+
+And that he figured
+out why atoms
+
+get colder that
+was the main point
+
+emphasized by the
+Nobel Committee
+
+when he got the Nobel
+Prize for laser cooling.
+
+Of course, he had already
+invented Zeeman slowing before,
+
+so he had a few other
+things under his belt.
+
+But anyway, the fact
+that the MOT works
+
+even better than advertised
+is another miracle,
+
+and this is related to
+the hyperfine structure.
+
+And finally, the fact that
+you can simply extended it
+
+to three dimension, is-- I said
+the first, the second --maybe
+
+the third miracle.
+
+It also works.
+
+Because when you
+look at the field
+
+of two coils, a so-called
+Anti-Helmholtz field,
+
+there are some directions
+where the magnetic field is not
+
+radially outward.
+
+This is a much more
+complicated magnetic field.
+
+It goes outward
+here, outward here,
+
+but in between the quadrupolar
+field, it sort of curves.
+
+There are some directions
+where the magnetic field is not
+
+radial, and you would say, hey,
+the one dimensional scheme is
+
+[INAUDIBLE] [? set. ?]
+
+Actually, before the
+magneto-optic trap
+
+was demonstrated, Dave
+Pritchard's student,
+
+Eric [? Rob ?] did
+calculations what
+
+happens in these
+diagonal directions which
+
+have no resemblance to
+the one dimension scheme.
+
+The solution is in
+those directions,
+
+the trapping form is
+a little bit weaker,
+
+but the big picture
+is it doesn't matter.
+
+So there was an idea
+conceived in one dimension
+
+for a simple atom structure,
+and this idea worked even better
+
+for real atoms and
+in three dimensions.
+
+OK, in your homework
+assignment, you
+
+will put in some
+numbers which show
+
+what happens if you take
+a vapor, an alkali vapor
+
+at a very low density of 10
+to the 8 per cubic centimeter,
+
+pressure of, typically, 10
+to the minus 8 [? Tor, ?]
+
+and you arrange six
+laser beams around it.
+
+Well, those laser beams have
+a restoring force in velocity.
+
+That means they cool and
+increase the phase space
+
+density over your sample
+by 8 orders of magnitude.
+
+Those laser beams have
+also a restoring force
+
+in the spatial dimension.
+
+Therefore, you get
+a cloud which has
+
+3 orders of magnitude
+higher density.
+
+So the temperature goes down
+by 8 orders of magnitude
+
+which means the phase
+space density is enhanced
+
+by 12 orders of magnitude.
+
+So if you're talking
+about the goal of reaching
+
+Bose-Einstein condensation
+which requires a phase space
+
+density of 1, just
+having a dilute vapor
+
+and these six laser beams with
+a little bit of magnetic field,
+
+increases your
+phase space density
+
+by 15 orders of magnitude.
+
+So this is why molasses and
+the MOT were a real milestone.
+
+Now, with 15 orders
+of magnitude,
+
+you are just 4 or 5
+orders of magnitude
+
+from Bose-Einstein
+condensation, and we
+
+will discuss, in
+a week and a half,
+
+what techniques were
+needed to bridge
+
+the gap between those
+temperatures and densities
+
+and quantum
+degeneracy of gasses.
+
+So that's the story of
+the magneto-optic trap.
+
+I'm also telling
+you that because I'm
+
+proud that a lot of the
+pioneering work in this regard
+
+happened at MIT.
+
+It was Dave Pritchard who
+realized at the Optical
+
+Earnshaw theorem
+can be circumvented,
+
+and it was him, in a
+collaboration with Steve Chu,
+
+that they together realized
+the first magneto-optic trap,
+
+and this was in 1987.
+
+Questions?
+
+OK, I think simple applications
+of the spontaneous light force.
+
+So we have time to talk
+about the dressed atom.
+
+Now, I was waiting
+until this point
+
+to introduce the dressed
+atom picture for you
+
+because the dressed atom picture
+is the natural picture you want
+
+to think about, for instance,
+for the Mollow triplet,
+
+and we had already some
+discussion about it.
+
+But it is also the
+natural picture
+
+you want to think about
+it when you describe
+
+the stimulated light force.
+
+And I mentioned already, it is
+the dressed atom picture which
+
+will help me to give you the
+physical picture behind if you
+
+have strong laser beams,
+why blue-detuned light cools
+
+and not red-detuned light.
+
+So you should be motivated now
+to learn about the dressed atom
+
+picture.
+
+But first, I have
+to say it's not
+
+anything new, what
+I'm teaching you.
+
+It has exactly the
+same physics in it
+
+as the optical Bloch equations.
+
+It's just that the optical
+Bloch equations are
+
+often more complicated,
+and they don't
+
+provide the clear insight.
+
+And the reason is the following.
+
+Often when you describe
+a physical phenomenon,
+
+you can choose one basis set, or
+you can use another basis set.
+
+But if you're in
+the wrong basis,
+
+you get the correct results,
+but in the wrong basis,
+
+you just can't describe
+the physics easily.
+
+So in other words, with
+the dressed atom picture,
+
+I want to introduce dressed
+atom states for you which
+
+are no longer the ground
+state and the excited state.
+
+I want to treat the
+atoms dressed up
+
+by the laser beam,
+which is one mode
+
+of the electromagnetic field.
+
+So the atoms, together
+with this one laser beam,
+
+will be partially excited,
+partially in the ground state.
+
+And this partially
+excited atoms, this
+
+is the dressed atom basis.
+
+But if you think in
+terms of those states,
+
+you have a much easier
+way to formulate
+
+certain physical processes,
+exactly processes
+
+where you have high laser power.
+
+At low laser power,
+the dress states
+
+are identical to
+the naked states
+
+to the ground and
+excited states.
+
+But at high laser power,
+at infinite laser power,
+
+the two dressed states are the
+symmetric and anti-symmetric
+
+equal superposition of
+grounded and excited state.
+
+So that's what we
+want to describe now.
+
+So the difference to the
+Optical Bloch Equation
+
+is that we are
+now really looking
+
+for the combined
+state of the atom
+
+in the electromagnetic field.
+
+So what we want to do is--
+this is sort of our picture
+
+that we have.
+
+This is our Hamiltonian.
+
+We have the atom
+interacting with the vacuum
+
+through spontaneous
+emission with a reservoir
+
+of empty modes.
+
+But now, it also interacts
+with the laser beam.
+
+And you remember when we
+did the master equation,
+
+we looked sort of at this.
+
+We derived a master
+equation for this.
+
+And then we added
+in the unitary time
+
+evolution due to laser beam.
+
+But what we want to
+do now is we want
+
+to first take care of the
+atom and the laser beam
+
+almost exactly in an
+exact diagonalization.
+
+And once we have
+re-diagonalized that,
+
+we have now eigenstates which
+we call the dressed states.
+
+Then we allow not the
+ground and excited state.
+
+We then allow the dressed
+states to emit into the vacuum.
+
+And this is the formulation
+we want to obtain now.
+
+Let me make one
+comment before I go
+
+through a few simple equation,
+and that's the following.
+
+If I want to treat this
+system almost exactly,
+
+I have two choices.
+
+I use a strong laser beam.
+
+So I could, as we have
+discussed several times,
+
+simply use the time dependent
+external electric field.
+
+The laser beam is E0
+times cosine omega t.
+
+And I just introduced
+that in the Hamiltonian.
+
+And you can get
+everything I describe now
+
+for you out of this Hamiltonian.
+
+However, there is
+an alternative way.
+
+And this one is I simply
+assume that the laser beam is
+
+described by the
+fully quantized field.
+
+And I use the fog state.
+
+I just assume N, the number
+of photons, is very big.
+
+And this is, at least
+for that purpose,
+
+a valid description
+of the laser beam.
+
+So what happens is you really
+want to look through that.
+
+I've really learned
+a lot by comparing
+
+the purely classical
+treatment of the laser beam
+
+and the fully quantized
+description of the laser beam.
+
+The results are the same.
+
+They are Absolutely identical.
+
+And what you will see is, by
+a bunch of approximations,
+
+we reduce the total
+Hamiltonian to-- I've
+
+seen it many times--
+a two by two matrix.
+
+And whether you start
+with the classical field
+
+or whether you start with
+the fully quantized field,
+
+if you make the
+right approximation,
+
+you get the same
+two by two matrix.
+
+But there's a difference.
+
+This Hamiltonian is
+time independent.
+
+a dagger a, time
+independent Hamiltonian.
+
+If you take a classical field,
+which is cosine omega lt,
+
+you don't have a time
+independent Hamiltonian.
+
+You have a driven system,
+and your wave function
+
+has an external time dependence.
+
+The laser beam is driving
+the wave function.
+
+So in other words,
+you have two choices
+
+when you want to describe
+how an atom interacts
+
+with a strong laser beam.
+
+You can use the fully quantized
+field, which is conceptionally
+
+a little bit more
+complicated, because we've
+
+quantized the
+electromagnetic field.
+
+But then everything
+is time independent,
+
+and everything I do
+here is really easy.
+
+I can go over it
+now in five minutes,
+
+and you understand everything.
+
+Well, in your
+homework, I've already
+
+asked you at an early homework
+to look at simply the two level
+
+system driven by
+classical field.
+
+And in your next homework,
+number 10, your last homework,
+
+I'm asking you now to
+interpret the solution
+
+with the classical field.
+
+And it's actually a
+little bit a challenge
+
+to take the time
+dependent wave function
+
+and read the physics out of this
+time dependent wave function,
+
+which corresponds to the physics
+we derive in the dressed atom
+
+picture.
+
+But you have two ways.
+
+One is the classical field.
+
+Then the wave function, the
+Hamiltonian, is time dependent.
+
+And the wave function
+is time dependent.
+
+Or here, I start with
+the quantum field
+
+and everything is
+time independent.
+
+But the solutions are identical.
+
+Well, one is a time
+dependent wave function.
+
+One is time independent.
+
+But if you interpret
+the solution
+
+in terms of what happens
+to the physical system,
+
+you will find exactly the same.
+
+So in other words, I decided
+I do the easy part here,
+
+which is a fully quantized part.
+
+And this is probably what
+will get stuck in your head.
+
+But since I think it's an
+important pedagogical exercise,
+
+you have to go
+through the homework
+
+and do the time dependent part.
+
+OK, so we want to
+know exactly-- well
+
+not-- we want to do the
+correct approximations.
+
+And after some
+approximations, exactly
+
+solve what the atom does
+with one laser beam.
+
+So the laser beam is described
+by the standard Hamiltonian
+
+for single mode light.
+
+The atom is described by, well,
+excitation energy omega 0.
+
+And b is the excited state.
+
+So if you don't have any
+light atom interaction,
+
+the eigenstates are just product
+states, an atom in the excited
+
+or the ground state.
+
+And N is the photon number.
+
+[? Collin? ?]
+
+AUDIENCE: You said that
+it's usually easier
+
+to understand physics
+in a dressed atom
+
+picture versus optical
+block equations.
+
+PROFESSOR: Yeah.
+
+AUDIENCE: Can you think
+of-- is that a general rule?
+
+Or is this just like it's only
+applicable in certain areas?
+
+[INAUDIBLE]?
+
+PROFESSOR: You're really
+asking an expert question.
+
+And I talked to Jean Dalibard
+and Claude Cohen-Tannoudji,
+
+who invented the dressed
+atom picture, when
+
+I wanted to understand
+what happens when
+
+we have a blue detuned lattice.
+
+And I used the dressed atom
+picture and I got confused.
+
+So what happened
+is the following.
+
+If you pick your right bases,
+the description is simple.
+
+But simple means
+if all the physics
+
+is your atom is in
+one dressed state
+
+or the other dressed state,
+and it does transitions
+
+between the dressed
+states and that is easy,
+
+and this happens in the
+limit of large detuning.
+
+But if you're in
+the regime where
+
+coherences between the
+dressed states matter.
+
+In other words, the density
+matrix in the dressed state
+
+basis has now off
+diagonal matrix element.
+
+The physics becomes
+complicated again.
+
+So in other words, what
+I'm telling you is you
+
+are the best description
+happens when we have a two level
+
+system, we always need
+a two by two matrix.
+
+But if you pick the description
+where the solution is diagonal,
+
+if you have to deal with
+coherence, using coherence
+
+is coupled to population,
+it's complicated.
+
+And there's some cases-- one is
+the blue detuned lattice, which
+
+I encounter where you have to
+consider the coherences to get
+
+the correct answer.
+
+And usually, also when
+the laser beams are weak
+
+and on resonance, the
+dressed atom picture
+
+is not providing any advantages.
+
+So you want to use the bare
+picture for weak excitations.
+
+And yes, in the resonance
+case, the dressed atom picture,
+
+if you're very
+close to resonance,
+
+the dressed atom picture
+gets more complicated.
+
+But to give you the answer in
+something we have discussed,
+
+you know already that when
+you drive an atom with a laser
+
+beam, you get the
+Mollow triplet.
+
+And the Mollow
+triplet shows you--
+
+I hope we can finish that
+today-- shows you the energy
+
+splitting between the
+dressed energy levels,
+
+between the dressed
+energy levels.
+
+But if the Mollow
+triplet is not resolved
+
+because the generalized
+Rabi frequency is small,
+
+then you're not resolving
+your dressed atom levels.
+
+And then the dressed
+atom level is not
+
+providing a big advantage.
+
+For certain problems,
+the dressed atom picture
+
+will not help you.
+
+But I can reassure
+you, and this is
+
+what I learned from
+Jean Dalibard and Claude
+
+Cohen-Tannoudji,
+if you really look
+
+at the full matrix with the
+off diagonal matrix append
+
+and everything, you will always
+find exactly the same solution.
+
+Anyway, we were
+just writing down
+
+product states of the atoms
+and the eigenfunctions
+
+of the Hamiltonian
+for the light, which
+
+are fog states, number
+states with N, L N plus 1.
+
+But the important thing
+is now the following.
+
+In the limit of small
+detuning, the ground state
+
+with N plus 1 photon is almost
+degenerate with the excited
+
+state with N photons.
+
+And we call these two
+states a manifold.
+
+The manifold E of N. And
+N is the photon number
+
+in the excited state.
+
+So what happens is, if you
+look at all those states,
+
+they are grouped into manifolds.
+
+And the energy separation
+between two manifolds
+
+is, of course, I go from N to N
+plus 1, the energy of a photon.
+
+So now I introduce the
+atom laser coupling
+
+in the usual dipole
+approximation.
+
+And what happens is, this
+dipole approximation,
+
+this dipole light atom coupling
+will couple, of course,
+
+ground and excited state.
+
+And it will, of course,
+have a big effect
+
+when the energy
+splitting is small.
+
+Well, you will see
+that in the next line.
+
+But we have the co and
+counter rotating terms.
+
+This dipole Hamiltonian will
+also couple the ground state
+
+to the excited state
+in the other manifold.
+
+This is the off resonant
+term, which will be neglect.
+
+So here are the
+equations for that.
+
+Our electric field is, of
+course, a plus a dagger.
+
+The dipole operator is that.
+
+And if you take what is in
+front of the electric field
+
+and define this as the
+coupling constant, g,
+
+we have what I just told
+you, that within a manifold,
+
+the ground state
+with N plus 1 photons
+
+is coupled to the excited
+state with N photons.
+
+g is simply the
+coupling constant,
+
+which all parameters have
+been included in that.
+
+But then, because of the matrix
+element of a or a dagger,
+
+we have the square
+root of N plus 1.
+
+OK, so what we are now doing is
+we are going with this coupling
+
+within a manifold, which
+is strong because the two
+
+levels are energetically close.
+
+And we will neglect the
+non-resonant couplings
+
+to the other manifolds.
+
+And that's just another
+way of doing, again,
+
+the rotating wave approximation.
+
+Now, when we describe an atom
+in the laser field and the atom
+
+scatters light, or
+we have a laser beam,
+
+and I have to tell you,
+when we have a laser beam,
+
+we don't provide exactly
+N atom, N photons.
+
+The laser beam is
+in a coherent state.
+
+And there are
+Poissonian fluctuations.
+
+But now, we do the next
+approximation, namely we
+
+say when N is
+large, then delta N
+
+can be neglected
+with regard to N.
+
+Then at least for the
+range of important photon
+
+numbers for the problem, this
+coupling becomes independent
+
+of N. And we simply take the
+average number of photons
+
+in our laser beam and define
+now an electric field, which
+
+is independent of N.
+
+And the product with
+the dipole operator
+
+of the atom, that's what
+we call the Rabi frequency.
+
+So at that point, we introduce
+a classical electric field
+
+through this definition, and
+therefore, the dressed atom
+
+picture.
+
+Also, we start with the fully
+quantized Hamiltonian is now
+
+identical to the classical
+field with this electric field
+
+amplitude.
+
+But what we have gained is
+we could discuss everything
+
+in a time independent picture.
+
+And now, I promised you,
+we'll go back to a two
+
+by two matrix, which you
+have seen many times.
+
+It's a two level system.
+
+We have the detuning.
+
+We are in the rotating frame.
+
+So that means the ground and
+excited state with N and N
+
+minus 1 photons have
+the same energy.
+
+But if we have a detuning,
+there is a difference
+
+whether we excite the
+atom or whether we
+
+put a photon in the laser field.
+
+But you have seen
+that many, many times.
+
+And the coupling
+is now described
+
+by the Rabi frequency.
+
+So that's kind of
+our typical two level
+
+system where the two levels
+[INAUDIBLE] the rotating frame,
+
+everything is time independent.
+
+The two levels are split,
+and they are coupled.
+
+And well, how many times have
+you seen the solution of two
+
+by two matrix?
+
+The solution is that
+the coupling is now
+
+increasing the splitting.
+
+The splitting between
+the two levels
+
+is, again, the generalized
+Rabi frequency,
+
+which you have seen
+many, many times.
+
+But now we want to really
+get the wave function.
+
+We want to get something out
+of the dressed atom picture.
+
+And that's the following.
+
+We started out with the
+bare states-- ground
+
+state with N plus 1, excited
+state with N photons.
+
+And the two by two matrix
+after the diagonalization
+
+is now a linear
+combination of those.
+
+And it's convenient to use
+sine theta, cosine theta,
+
+because then the states are
+automatically normalized.
+
+If I introduce the
+solution is now
+
+that the angle theta is
+given by this equation,
+
+that's just the solution
+for the two by two matrix.
+
+And the physical picture,
+which we have obtained,
+
+is the following.
+
+If this here is the energy
+of the excited state with N
+
+photons, I've just sort of drawn
+this as a reference parallel.
+
+But now I want to draw it
+as a function of the laser
+
+frequency.
+
+Well, the ground state
+with N plus 1 photons
+
+has exactly the same
+energy on resonance.
+
+But if the photon is more
+energetic then this state,
+
+because it has N plus 1
+photons versus n photons
+
+if the photon is more energetic
+than a resonant photon,
+
+this state has higher energy.
+
+And here, it has lower energy.
+
+In other words, we
+have now a level
+
+crossing between
+the two bare states.
+
+But a level crossing
+with interaction
+
+turns into an avoided crossing.
+
+And the solution which
+we have just derived
+
+are the blue curves.
+
+And if I go far
+away from resonance,
+
+this behavior here,
+which is perturbative,
+
+is nothing else than
+the AC Stark shift.
+
+So this is exactly what we
+have discussed at this point.
+
+Now, let's get some
+mileage out of it.
+
+And we will talk
+about light forces.
+
+That's really interesting.
+
+And I hope it's another
+highlight of this course
+
+to describe light forces in
+the dressed atom picture.
+
+But what I want to
+do here is already
+
+in preparation for that.
+
+I want to not yet
+introduce forces, simply
+
+figure out what happens in
+the dressed atom picture
+
+when the atoms scatter light.
+
+And you know already
+the solution.
+
+The solution is
+the Mollow triplet.
+
+And we have discussed with
+the Optical Bloch Equations
+
+that at low laser power,
+the Mollow triplet
+
+has three curves.
+
+It has three broadened curves.
+
+And they have
+different broadening.
+
+And I didn't prove it to
+you, but I mentioned to you,
+
+at low laser power there is--
+perturbative laser power,
+
+we discussed at great length
+that there's a delta function.
+
+And at low laser power,
+the delta function remains.
+
+So this is sort of the
+spectrum we get out of it.
+
+And what I want
+to show you now is
+
+how this spectrum is described
+in the dressed atom picture.
+
+Atom photon interaction
+has a wonderful discussion
+
+of all the details.
+
+I will share with
+you a few highlights.
+
+But we will go much further in
+the description of the Mollow
+
+triplet then we've gone before.
+
+But I will not go into
+all excruciating details.
+
+So let's discuss first.
+
+That's something we
+hadn't done so far.
+
+What are the intensities
+in this Mollow triplet?
+
+So the way how we obtain
+it is the following.
+
+We have the manifold, the
+manifold with N minus 1
+
+and the manifold with N photons.
+
+And this is the detuning.
+
+And if we allow for the
+atom laser coupling,
+
+the splitting here is a
+generalized Rabi frequency.
+
+And well, you immediately see
+that in this picture, if you
+
+allow spontaneous emission from
+the upper manifold to the lower
+
+manifold, you have four
+different combinations.
+
+One is the long photon
+is the blue sideband.
+
+This is the red sideband.
+
+This is the blue sideband.
+
+This is the red sideband.
+
+And those two are the carriers.
+
+But now, we can
+do the following.
+
+I've just written down for
+you the solution of the wave
+
+function with sine
+and cosine theta.
+
+If we want to emit the blue
+sideband, we go from the top
+
+to the bottom.
+
+But that means, since a
+photon in the rotating wave
+
+approximation can only be
+emitted when we go from b to a,
+
+we find that the
+matrix element for that
+
+involves cosine theta
+times sine theta.
+
+However, if you want
+to emit the carrier,
+
+you go from here to there.
+
+Well, we always have to find
+the excited state to begin with.
+
+And we go-- I must
+have made a mistake.
+
+Sorry.
+
+When I went to emit
+the blue side, when
+
+I go from all the way
+up to all the way down,
+
+and I always have to find
+an excited state which
+
+connects to the ground state.
+
+And this gives me a term,
+which is cosine square.
+
+The red detuned sideband
+gives me sine squared.
+
+And if I want to get
+the carrier, this one,
+
+I go from here to here.
+
+I get cosine theta sine theta.
+
+So in other words,
+we can immediately
+
+read off the matrix elements.
+
+And since the intensity,
+Fermi's Golden Rule,
+
+is the matrix
+element squared, we
+
+find immediately that the upper
+lower sideband and the carrier
+
+involve terms cosine to the
+4 theta, sine to the 4 theta,
+
+cosine square sine square.
+
+So we got the matrix element.
+
+And the only thing
+we have to know now
+
+is that the width or the rate
+is given by the matrix element.
+
+The rate is given by the
+matrix element square.
+
+But now, what is the
+intensity of the line?
+
+Well, the upper
+sideband is emitted
+
+by the upper dressed
+state, because you
+
+have to go from the
+upper dressed state
+
+to the lower dressed state to
+get the blue detuned photon.
+
+So therefore, the
+intensity for this sideband
+
+is this rate times
+the population
+
+in the upper dressed state.
+
+So what is missing
+at this point,
+
+and we need that urgently
+for next week, what
+
+is the population in the
+upper and the lower sideband?
+
+Well, we know the
+transition rates
+
+between the upper and
+the lower sidebands--
+
+well, between the upper
+and lower dressed state.
+
+We know we've just
+found here the rate.
+
+What is the rate?
+
+What is the matrix element
+squared when you go from one
+
+is the upper, two is the
+lower state of the manifold.
+
+So we have just
+gotten those rates.
+
+And rate equation says,
+the change of population
+
+in the upper dressed
+state is given
+
+by the departure
+from the upper state
+
+and what arrives
+from the lower state.
+
+So since we are interested
+in the steady state solution,
+
+we can just set the
+left side to zero.
+
+And then, the rate
+equations simply
+
+give us the population
+in terms of the rates.
+
+So in other words, if you
+ask, what is the steady state
+
+solution in the upper
+or lower dressed state,
+
+it's given by a ratio of
+those rate coefficients.
+
+But we just got those
+rate coefficients.
+
+And this gives us another bunch
+of sine and cosine functions.
+
+So in other words,
+we know now what
+
+is the population of
+the dressed states.
+
+I mean, everything is expressed
+by one non-trivial parameter
+
+theta.
+
+And all we get is sine square,
+cosine square, sine to the 4th,
+
+we just get those
+trigonometric functions.
+
+Yes.
+
+I think we can finish that.
+
+Good.
+
+So this is the steady
+state solution.
+
+But now, we can go back
+to the rate equation
+
+and say the time derivative
+of the rate equation
+
+has to relax to
+the steady state.
+
+This is nothing else than
+rewriting the equation above.
+
+But by rewriting the
+equation above in that way,
+
+we find now the
+prefactor in front of-- I
+
+mean, here, what you have is
+the time derivative is given
+
+by the difference
+from steady state.
+
+And this is the
+relaxation coefficient.
+
+And the relaxation coefficient
+is-- that's the solution.
+
+You just have to do the
+substitutions yourself.
+
+The relaxation coefficient,
+how populations
+
+relax to steady
+state, is now given
+
+by the sum of the two rates.
+
+One is going from the
+upper to the lower
+
+and from the lower
+to the upper state.
+
+And each of those rates
+has been expressed
+
+by sine square and
+cosine squares.
+
+I'm not doing it here,
+because it's a little bit more
+
+complicated.
+
+But you can also rewrite for
+the dressed atom picture what
+
+happens-- you can rewrite those
+equations in a way what happens
+
+not to the population, but
+what happens to the coherences,
+
+to the off diagram
+matrix element formulated
+
+in the dressed state basis.
+
+And what you find is, you find
+a correlation time, a relaxation
+
+time, for the coherences.
+
+Remember, for the naked
+state, population's
+
+relaxed with gamma.
+
+Coherence is relaxed
+with gamma over 2.
+
+This is for the Optical
+Bloch Equations.
+
+But now we have reformulated
+the physics in the dressed atom
+
+picture.
+
+And what the solution
+is the following.
+
+This is sort of a
+weak laser power.
+
+But in the most general
+case, what you will find
+
+is that the width
+of the central peak
+
+reflects the relaxation
+time for the population.
+
+And the width for the sidebands
+is the relaxation time
+
+for the coherences in
+the dressed atom picture.
+
+So we had before with the
+Optical Bloch Equations,
+
+I showed you different cases.
+
+We had a three quarter gamma.
+
+I need two more minutes and
+I'm finished with my unit.
+
+So we had weird factors
+of three quarters.
+
+And I showed you how they
+come from the eigenvalues
+
+of the matrix of the
+Optical Bloch Equation.
+
+But now we understand
+them physically,
+
+namely the central
+feature has a peak,
+
+which is the relaxation
+time for the populations
+
+in the dressed atom picture.
+
+And the sidebands
+have a width, which
+
+is the relaxation time
+for the coherences.
+
+They no longer differ
+by a factor of two,
+
+as in the naked bases in which
+we formulated the Optical Bloch
+
+Equations.
+
+By the way, I know
+a lot of you may
+
+be curious about
+the coherent peak.
+
+You can read about it in API.
+
+It's 10 pages about
+correlation function.
+
+But in the end, the rate
+of the delta function
+
+can be, again, described by
+values we have just calculated.
+
+We have just calculated
+steady state populations
+
+and transition rates.
+
+So this rate is nothing else
+than another combination
+
+of sine square and cosine
+squares of this angle theta.
+
+So everything is wonderfully
+and simply described
+
+the full physics of
+that by just this angle
+
+theta in the dressed
+atom picture.
+
+OK So with that, we are done.
+
+And I think I'll discuss the
+last page with you on Monday.
\ No newline at end of file
diff --git a/raP-0nqnF_A.txt b/raP-0nqnF_A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2ea37a52a5d189371e40f0c81e962f20c64352d9
--- /dev/null
+++ b/raP-0nqnF_A.txt
@@ -0,0 +1,3184 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: So last time we
+talked about how to describe
+
+say for the boundary CFT is at
+a finite temperature what would
+
+be its gravity description?
+
+So what we described
+was a thermal theory.
+
+Say a Thermal CFT on
+the flat space, OK?
+
+We show that this is related
+to a black hole with a planar
+
+horizon.
+
+The key is that the horizon
+should have the same topology
+
+as the boundary space.
+
+So in terms of the picture
+this is your boundary,
+
+so this is z equal to 0, and
+then the horizon somewhere say,
+
+at some value of z0.
+
+So horizon has some value
+of z0 and then the horizon
+
+have the same topology
+as the boundary on space.
+
+And then you can do some of
+the [? lamicks, ?] et cetera.
+
+Any questions about that?
+
+Good.
+
+So previously we also
+briefly discussed
+
+that the Ads also allow
+you to put the field
+
+theory on the sphere.
+
+So if you put the field
+theory on the sphere
+
+then that will be due
+to the global Ads.
+
+Now you can ask
+the same question.
+
+What happens if we put the
+boundary theory on the sphere
+
+and then put there the
+finite temperature.
+
+So let us put a
+CFT on the sphere
+
+at the finite temperature.
+
+So the story here is much
+richer for a very simple reason.
+
+For a very simple reason.
+
+So if you have a CFT just on the
+Rd minus 1 so this Rd minus 1,
+
+this euclidean space,
+euclidean flat space
+
+does not have a scale and the
+CFT does not have a scale.
+
+So if you put it at
+a finite temperature
+
+then the temperature
+is the only scale,
+
+and essentially provide
+a unit over the scale.
+
+So the temperature
+is the only scale,
+
+so essentially providing
+an energy unit.
+
+So this means that for CFT on
+the finite temperature, CFT,
+
+on the flat space then
+physics at all temperatures
+
+are the same.
+
+So they are just related
+by a scaling of units.
+
+So in some sense you can see it
+seems that the physics is very
+
+simple whether you
+have like 0.0001 degree
+
+or you have 10,000
+degrees, doesn't matter.
+
+And it's only the relative
+scale that matters.
+
+So the physics at all
+temperatures is the same.
+
+There's no difference
+between the low temperature
+
+and the high temperature,
+and the temperature just
+
+provide the units.
+
+But if you put the
+CFT on the sphere
+
+now the story's different.
+
+So for CFT on the sphere because
+the sphere has a side itself.
+
+OK, so let's take the
+sphere have both sides r.
+
+Again when you put
+the CFT on the sphere
+
+the sides of the sphere does
+not matter because again
+
+the sides of the
+sphere are essentially
+
+provide by the units because the
+theory's getting [? warrant. ?]
+
+So let's just put all
+the sides to be r.
+
+So let's take sides to be r.
+
+And the r can be
+chosen to be the same
+
+as the curvature radius
+in the [? back ?]
+
+just to make formula
+simple, and you
+
+can choose it to be any radius.
+
+And now since the sphere
+already have [? all ?] sides
+
+and now you put it at
+a finite temperature.
+
+Now you have the
+dimensionless number.
+
+Then at the finite
+temperature in the physics
+
+is controlled by a
+dimensionless number, r times t.
+
+So now the temperature
+makes a difference.
+
+Now different
+temperature that r is
+
+is different because now
+you have a relative scale
+
+and if rt is small
+then essentially you're
+
+at the low temperature,
+and then when rt is big
+
+then you have a
+high temperature.
+
+Now there's a
+dimensionless number
+
+to characterize whether
+you're in the low temperature
+
+or in the high temperature.
+
+So the physics essentially
+become much richer because
+
+of the and then you have a
+you have a whole parameter
+
+the physics can depend on.
+
+And so indeed the story
+become rather intricate
+
+whether we can see
+the finite temperature
+
+theory on the sphere
+so now let me just
+
+mention some important features.
+
+So I will walk you not too
+slowly but also not too quickly
+
+about the physics on the sphere.
+
+We cannot afford to do it
+very slowly at this time.
+
+Yeah, but if I do
+it too quickly,
+
+of course you won't
+learn anything.
+
+OK, so let me just point
+out some important features.
+
+So first, when we
+talked about the story
+
+last week-- when we talked
+about the finite temperature
+
+on the flat space-- we
+said, oh, probably there
+
+are two possible descriptions
+for finite temperature
+
+theory from the
+[? back ?] point of view.
+
+So one is that you can
+have a thermal gas.
+
+You have a thermal gas in Ads.
+
+But then we argue
+that for a theory
+
+on the sphere that's
+not allowed because you
+
+encompass singularity because
+the metric becomes singular.
+
+And the one big difference
+for the theory on the sphere
+
+is that actually
+now this is allowed.
+
+So the thermal gas in
+Ads is now allowed.
+
+So now let's go
+through the argument.
+
+So now first let me just write
+down the global Ads metric.
+
+Of course you can write in
+many different coordinates.
+
+So the most
+convenient coordinates
+
+to write global Ads for our
+purpose is the following.
+
+So this is just a pure Ads
+and r goes to 0 to infinite.
+
+So this is like somewhat
+analog of a, say,
+
+sprinkle coordinate
+in flat space.
+
+But the difference
+is of course now
+
+you have nontrivial
+factors which tell
+
+you're in the curve space time.
+
+So now to go to
+the thermal Ads we
+
+do the trick you normally
+do for thermal field theory.
+
+Is that you go to
+euclidean space
+
+and then you put
+the euclidean time
+
+to be periodic in the
+inverse temperature.
+
+Actually, let me write
+down here the analogous
+
+metric on the sphere.
+
+So this is a situation
+we can see that
+
+before for the theory on the
+flat space, on the plane,
+
+and then that would be the
+metric to be on the sphere.
+
+So we've talked about
+last time if you
+
+make tau to be
+periodic then as z
+
+goes to infinity then this
+circle shrink to zero sides.
+
+Because the prefactor goes to 0.
+
+So the tau circle
+will have a sides beta
+
+but the proper densities
+controlled by the prefactor.
+
+And because when z goes to
+infinity then the proper lens
+
+of the circle goes to 0.
+
+So whenever you have a
+circle we shrink to 0
+
+then you have a singular
+behavior, et cetera,
+
+and then the metric's singular.
+
+So you can have [? where ?]
+it is a singular behavior
+
+and so that's why this
+is not the amount.
+
+But now in this case, when you
+do such energy configuration
+
+this becomes well defined.
+
+Because of the proper sides
+of the tau circle so now you
+
+local proper lens local proper
+sides over the tau circle,
+
+it's just given by
+this prefactor 1 plus
+
+r squared divided by 1
+squared by r squared beta.
+
+And since a greater
+equal here so
+
+this is greater equal to beta.
+
+So actually this is
+bounded from below.
+
+So this is a circle [? label ?]
+will become too small.
+
+Essentially the minimal
+side of the circle
+
+is the same as the beta itself.
+
+So this euclidean metric
+is perfectly well defined.
+
+OK, so euclidean
+metric well defined.
+
+So you can trust here that the
+euclidean metric is singular
+
+as z goes to infinity.
+
+If you put the 0 in
+the flat space then
+
+that's not allowed but
+in this case allowed.
+
+So for the serial
+in the sphere--
+
+but still there's an analog
+of a black hole solution.
+
+You can also find
+the black hole.
+
+Again you just write
+down the standards,
+
+sprinkle's metric answers,
+for black hole metric
+
+and then you solve
+Einstein equation,
+
+then you find-- so let me
+just write down the answer.
+
+So you find that this space also
+allows a black hole solution.
+
+Can be written as the following.
+
+So now f just slight
+generalization of this factor.
+
+So the mu is primarily
+related to black hole mass.
+
+And the horizon is that
+i equal to r0 and r
+
+satisfy that this
+factor goes to 0.
+
+So you can also find out what
+is temperature associated
+
+with this black hole.
+
+So here that beta
+can be anything.
+
+There's no constraint
+on the beta.
+
+So here using the standard
+technique to find what
+
+is the Hawking temperature
+for this black hole.
+
+Let me just write
+down the answer.
+
+So this is just 4 pi
+divided by f prime.
+
+You've already add to the
+horizon standard formula
+
+and you just find
+the 0 of this guy,
+
+and then you just
+take the derivative
+
+so you find the beta can
+be written in terms of r0
+
+as follows.
+
+So this is just
+a simple algebra.
+
+So you find that if you
+take the derivative,
+
+we express the
+derivative is r0, then
+
+you find the Hawking temperature
+of the following form.
+
+I'm not doing this
+calculation here.
+
+You can use it to
+check yourself.
+
+Good, any questions so far?
+
+So now it seems like
+we have a problem.
+
+Because we have a
+black hole we also
+
+have a standard thermal Ads.
+
+Then which one is
+the right description
+
+for the field theory at
+the finite temperature?
+
+Seems like we have a choice.
+
+But now if you look
+at this function
+
+the story's even more
+tricky than that.
+
+So this product of this function
+this is a rough behavior
+
+of this function.
+
+So this is the
+inverse temperature
+
+and then this is the
+sides of the horizon.
+
+And the side of the
+horizon essentially
+
+determines your entropy.
+
+So it's really a
+physical thing here
+
+and because of the area over
+the horizon it's the entropy.
+
+The area of the
+horizon is a entropy.
+
+So this r0 it can be considered
+as something standard
+
+for entropy.
+
+So now just to
+get the intrusion,
+
+this is a complicated
+function, it's
+
+because intrusion and
+how this beta depend
+
+on this r0, the horizon side.
+
+Suppose horizon side is
+very small, r0 goes to 0,
+
+then downstairs is finite.
+
+Upstairs goes to 0
+so you just go to 0.
+
+And the r0 is very
+large so the downstairs
+
+proportionate to r0
+square but upstairs only
+
+proportionate to r0 so
+when r0 is very large
+
+we go to 0 as the r0.
+
+And this is a small
+function so there
+
+must be a maximum somewhere.
+
+And because you can easily
+find the maximum just
+
+to take the derivative
+of that function.
+
+Anyway, so that's how the
+beta will depend on r.
+
+But now this plot
+is highly peculiar.
+
+Why?
+
+Can you tell me why?
+
+There's a maximum on
+theta, which means?
+
+That's right.
+
+So there's a beta max.
+
+So that means this is a beta
+max which tells you there's
+
+a minimum temperature.
+
+That means that black
+hole solution only
+
+exist above a certain
+minimal temperature.
+
+And you can easily find out
+what is that minimal temperature
+
+just by taking the
+derivative of this function
+
+and it require to be 0.
+
+Is there any other thing
+peculiar regarding this plot?
+
+AUDIENCE: When r0--
+
+PROFESSOR: Hmm?
+
+AUDIENCE: When r0,
+[INAUDIBLE] black hole.
+
+PROFESSOR: Well, r0 is
+0-- the black hole becomes
+
+smaller and smaller.
+
+It means there's no black hole.
+
+AUDIENCE: But the
+temperature is infinity.
+
+PROFESSOR: Hmm?
+
+AUDIENCE: But the temperature
+there is infinity.
+
+That's weird.
+
+PROFESSOR: No, that's not weird.
+
+No, that's the standard,
+the flat space black hole
+
+behaves that way.
+
+Just look at a Schwarzschild
+black hole in flat space
+
+when the horizon side
+becomes smaller and smaller
+
+the temperature become
+higher and higher.
+
+That's a standard
+feature of flat space.
+
+AUDIENCE: It must
+be the other way.
+
+If you have a huge
+black hole, then why
+
+is it that the beta goes down?
+
+That seems bizarre.
+
+Maybe it can't also
+be standard, right?
+
+[LAUGHTER]
+
+PROFESSOR: Both things you said
+are correct and are important
+
+but there's something
+more elementary
+
+you're not pointing out.
+
+You're pointing out the higher
+order of important things.
+
+But there's one lower order
+important thing that which
+
+is not yet pointed out.
+
+AUDIENCE: There
+are two solutions
+
+of the same temperature.
+
+PROFESSOR: Exactly.
+
+In terms of the temperature
+this is a [INAUDIBLE]
+
+So if you look at
+the given temperature
+
+they're actually two solutions.
+
+So for any given temperature
+there are two solutions.
+
+Say T greater than
+T min so this is
+
+for the beta smaller
+than beta max
+
+means that T greater than T
+min There are two solutions.
+
+And then we have to
+label them so let's
+
+very imaginatively call this
+one the big black hole and then
+
+this one the small black hole.
+
+Because this one have a
+larger size and this one
+
+has a smaller size.
+
+So this corresponding
+to the r0 of those two.
+
+So you have two
+black hole solutions.
+
+One have a larger radius
+than the other one.
+
+So we have big black hole
+and a small black hole.
+
+And now this is
+an important thing
+
+you mentioned that for
+the small black hole
+
+the temperature when
+you decrease the sides
+
+the beta decrease.
+
+That then means the
+temperature increases.
+
+So this as I said
+it's like an entropy.
+
+So if you lower
+the entropy somehow
+
+your temperature increases.
+
+So when you increase
+the temperature
+
+you actually lower the entropy
+for the small black hole.
+
+A small black hole
+you go like this.
+
+Go like this.
+
+When you reduce the sides,
+you reduce the beta,
+
+means you increase
+the temperature.
+
+But this is actually the
+standard Schwarzschild black
+
+hole behavior in flat space.
+
+And this just tells you have
+[? a lack ?] of specific heat.
+
+So this is a situation
+we understand.
+
+This is a situation
+we can come up
+
+with a flat space, a
+Schwarzchild black hole.
+
+And it make sense why it's
+happening here because here
+
+roughly is order r.
+
+Because the r is
+the scale here so
+
+the maximum location where the
+maximum is controlled by the r.
+
+So this region corresponding
+to sides of the black hole
+
+to be much, much smaller
+than Ads curvature radius.
+
+So when something
+is much smaller
+
+than the curvature
+radius what you do see?
+
+Hmm?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah, flat space.
+
+Yeah, it just like even though
+we live in the curved universe
+
+but we actually see flat space
+because of course our scale
+
+is much more than curvature
+radius of universe.
+
+And a similar key thing here
+even though the black hole
+
+have a size much smaller than
+the curvature radius of Ads
+
+they essentially behave
+like flat space black hole.
+
+And so that's exactly what
+you see for the flat space
+
+black hole.
+
+And indeed, in a
+more interesting
+
+is this big black hole,
+the [? interesting ?]
+
+is a big black hole.
+
+And the big black hole when
+r0 increases the temperature
+
+increase.
+
+So this is the right way.
+
+So this is indeed the standard,
+just positive specific heat.
+
+You can check it has
+positive specific heat.
+
+So this is indeed what you'd
+expect from a thermal system.
+
+And so this is indeed what you
+expect from a thermal system.
+
+So now we are encountering
+an even weirder situation.
+
+We not only have so more ideas.
+
+We're not only have black hole.
+
+We actually have
+two black holes.
+
+So what's actually described
+with the field theory
+
+at finite temperature?
+
+So what does this really mean?
+
+Number two is a
+black hole solution.
+
+Now let's look at
+the number three.
+
+So now let's look at
+what are the indications
+
+those solutions.
+
+So first thing you
+can just guess.
+
+So what do you think what these
+three solutions should mean?
+
+If you believe this,
+duality has to be true.
+
+Yes, so that the
+game we play here
+
+is that you believe that
+the duality is always true.
+
+And then whenever you see some
+phenomenon, the gravity side,
+
+you say this, I
+try to integrate.
+
+I try to understand on
+the field theory side.
+
+And it makes sense and then
+we just carry out the guess
+
+and check it, et cetera.
+
+So what would the
+three solution mean?
+
+Three gravity solutions, or
+in principle for example,
+
+for a temperature at here
+we can have three solutions
+
+all have the same temperature.
+
+What would this mean?
+
+So the simplest guess
+is that it tells you
+
+that for CFT and the ST
+minus y at this temperature
+
+there's three possible phases.
+
+There's three possible phases.
+
+It's just like
+water, ice, or vapor.
+
+There's three possible phases.
+
+Now, the interpretation
+is clear.
+
+Then we should just find.
+
+So to decide what is
+the right solution then
+
+we should find what?
+
+That's right, we
+should find the phase,
+
+find the one with the
+lowest free energy.
+
+And then to decide which
+is the right one then
+
+we just need to find the one
+with the lowest free energy.
+
+So now recall that the partition
+function the field theory
+
+side should always be
+identified with the partition
+
+function on the gravity side.
+
+And then this side the
+partition function by definition
+
+is minus beta, the free energy.
+
+[? Seems ?] like
+going more and more.
+
+that's weird.
+
+But on the gravity
+side we write this
+
+by saddle-point approximation.
+
+We integrate over
+all possible field
+
+on the gravity side weighted
+by the euclidean action,
+
+and the leading order in the
+saddle-point approximation
+
+you just evaluate it.
+
+You just evaluate it on
+the classical solutions.
+
+So now you can just equate them.
+
+You just need the
+free energy must
+
+be equal to se to
+the to the [? Ic. ?]
+
+So this is just the same
+principle we discussed before
+
+on how we just apply it.
+
+So now if we believe
+the duality and we
+
+believe with some of
+the [? lamicks ?] then
+
+we should just find the
+solution with now just SE.
+
+So we should calculate the
+euclidean action for all three
+
+solutions and then we find
+the corresponding free energy
+
+for each of them, and then
+the one with the largest, SE,
+
+will correspond to the one
+with lowest free energy.
+
+Then that will be
+the stable solution.
+
+And the other phases presumably
+will be unstable or not stable.
+
+just like in the standard story.
+
+So this conclusion was drawn
+from some of the [? lamrick ?]
+
+itself.
+
+But what will be nice we can
+actually draw this conclusion
+
+without using thermal dynamics.
+
+So we say, so this
+[INAUDIBLE] was
+
+drawn to identify this
+with the free energy
+
+and then we say according
+to the sum of dynamics,
+
+and then we should choose the
+one with the lowest energy.
+
+But will be better
+if you can actually
+
+derive this thing
+from the gravity side,
+
+and you can and for
+a very simple reason.
+
+So this also follows
+from the standard rules
+
+of saddle-point
+approximation as follows.
+
+Oh, I forgot to
+write on this board.
+
+So when you evaluate
+this [? possible ?]
+
+so when you evaluate
+your integral
+
+you're in the saddle-point
+approximation,
+
+so normally you are instructed
+to add the contribution
+
+of all saddle points.
+
+So the fact that you have
+three different solutions
+
+it tells you have three
+separate saddle points.
+
+And then just from
+the standard rule
+
+of the saddle-point
+approximation
+
+you just need to add
+all of them together.
+
+So you add the expression SE,
+you evaluate the thermal Ads.
+
+And the expression,
+SE you evaluate it
+
+as a big black hole,
+and then you add the SE
+
+to the small black
+hole, et cetera.
+
+OK, you add all
+of them together.
+
+And now each action
+is in exponential.
+
+And as I said,
+they are weighted.
+
+All this action are
+weighted by n square.
+
+Because the action is
+always proponent to law
+
+of [? Newton ?] and the law of
+newton is [? proponent ?] to n
+
+square.
+
+So there's a big parameter
+in the exponential.
+
+So the saddle is not just SE
+dominates in the large N limit.
+
+You just add three
+exponentials, which one
+
+is the biggest will dominate.
+
+Because each one of them is
+proponent to n square and n
+
+goes to infinity.
+
+And n goes infinite means it's
+greater than the other guy
+
+by a tiny bit.
+
+in the prefactor of n squared
+they will become predominant.
+
+So we see that the sum of
+the [? lammicks. ?] Sum
+
+of the [? lammicks tells ?] us
+we should define the smallest
+
+free energy and then that
+statement can be essentially
+
+derived if I don't
+know that statement.
+
+I can actually derive that
+rule, say finding the smallest
+
+free energy, just by using
+the standard saddle-point
+
+approximation from
+the gravity side.
+
+So this is a nice
+consistency check.
+
+This a nice consistent
+check that the duality
+
+which we believe to be
+true should be true.
+
+Yes?
+
+AUDIENCE: So the one thing
+I don't totally understand
+
+is that, so say that you
+give me this Euclidean
+
+integral over metrics
+on the gravity side.
+
+So the idea that there's really
+only three contributions--
+
+because we found three solutions
+with a particular temperature--
+
+how do we know that there
+aren't any other solutions?
+
+Like, how do we know there
+aren't any other terms that
+
+were not accounted for?
+
+PROFESSOR: Oh yeah,
+there are three--
+
+so this is a rule of the
+saddle-point approximation,
+
+you find the saddle-point.
+
+So you find the solution
+of the equation of motion
+
+with the right boundary
+conditions and these
+
+are the only ones.
+
+Yeah, and then of
+course, each of them
+
+include the fluctuations.
+
+This is just the standard
+saddle-point approximation.
+
+Any other questions?
+
+So now the task just
+boils down to-- yeah,
+
+let me just emphasize
+here-- yeah,
+
+so now, the task just
+boils down to find
+
+what is the lowest free energy.
+
+OK?
+
+So now it's 3-- no, it's 4.
+
+So now, let's try to decide
+which one is more stable.
+
+So first, let me just emphasize
+SE is proportional to the 1
+
+Newton-- 1/G Newton.
+
+And then it's always
+proportional to N squared.
+
+OK?
+
+Because 1/G Newton is
+proportional to N squared
+
+if you translate from
+the [INAUDIBLE] language.
+
+And now, if you vary the
+free energy for them--
+
+for this-- here let me call
+this-- thermal [? gas and ?]
+
+AdS, I always just call
+it TAdS, OK, Thermal AdS.
+
+I think, yeah, just-- the
+shorthand is just thermal AdS.
+
+So for the thermal AdS,
+this is actually 0.
+
+This is actually 0.
+
+So thermal AdS is the free
+energy-- I should say this way.
+
+SE is actually the
+0 times N squared.
+
+And then you can have
+fluctuations then
+
+that can contribute to the
+order and to the power 0
+
+[? contribution ?].
+
+So the 0 in this-- 0 is simple.
+
+It is because, when we go
+from the [? pure ?] AdS
+
+into the thermal
+AdS, essentially
+
+we just changing the
+global structure.
+
+OK?
+
+We just make the Euclidean
+circle so for the pure AdS,
+
+when you go to Euclidean space,
+the tau have infinite size.
+
+And then when you go
+to the thermal AdS,
+
+we just make the tau
+to be a compact circle.
+
+So you have not changed the--
+the solution is identical.
+
+The solution is identical
+go to the pure AdS.
+
+Just the global structure
+is different in terms
+
+of the periodicity of the
+Euclidean time circle.
+
+So now, if you vary
+the classical action--
+
+so if you're reference
+point is that the pure AdS,
+
+the classical action is 0.
+
+And then, for the
+thermal AdS will be 0.
+
+OK?
+
+Will be the same.
+
+It would be the same--
+the classical action will
+
+be the same as pure AdS, OK?
+
+So [INAUDIBLE] order N
+squared, but then you
+
+can have fluctuations
+which contribute.
+
+And the fluctuations
+is to the-- yeah,
+
+so the fluctuations
+can be interpreted
+
+as the, say, the graviton
+symbol [? and ?] division
+
+from the symbol, graviton gas.
+
+OK?
+
+And so, say, in the
+themal AdS sites
+
+essentially, have a
+thermal gas graviton.
+
+And there, free energy
+is independent of N
+
+because they are
+the fluctuations.
+
+And just as usual,
+whenever you can
+
+see that the fluctuations
+there, they're
+
+independent of a
+coupling constant.
+
+Is this clear?
+
+AUDIENCE: Why is
+the first term 0?
+
+PROFESSOR: Hm?
+
+AUDIENCE: Why is
+the first term 0?
+
+PROFESSOR: The first
+term is 0 because this
+
+has the same classical
+solution as the pure AdS.
+
+AUDIENCE: The pure AdS, then,
+has a nonzero [INAUDIBLE].
+
+PROFESSOR: Yeah.
+
+Yeah, that's a
+very good question.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah.
+
+I will-- yeah.
+
+Wait a few minutes.
+
+I will talk about
+this more precisely.
+
+It's a good question.
+
+AUDIENCE: Oh, OK.
+
+PROFESSOR: Yeah.
+
+Let me just tell you
+the answer first,
+
+and then I will
+say a few things.
+
+Any other questions?
+
+OK.
+
+And then if you calculated
+the Euclidean action
+
+for the big black hole
+and the small black hole,
+
+you find that they are
+always greater than that.
+
+It's always larger than action
+for the small black hole.
+
+And this is some number, nonzero
+number, times order N squared.
+
+So this is always the case.
+
+We also [INAUDIBLE] way for you
+to calculate in a few minutes.
+
+But I will not do this
+explicit calculation here
+
+because it takes some time.
+
+So there is a simple
+way, physical way,
+
+to understand this-- to
+understand why this is true
+
+because this is a free energy.
+
+So this tells that the free
+energy of the big black hole
+
+is always much more-- is always
+smaller than the free energy
+
+of the small black hole.
+
+This is not a precise
+way to understand it,
+
+but it is a heuristic way-- is
+that if you look at these two
+
+solutions-- so these
+two solutions have
+
+the same temperature,
+but the big black hole
+
+have a larger size.
+
+When you have a larger
+size and the entropy
+
+is proportional to the
+area of the horizon--
+
+and the entropy is much
+higher, so the big black hole
+
+has much higher entropy
+than the small black hole.
+
+And so you choose-- you
+would expect that this should
+
+have a smaller free energy.
+
+But, of course, you have
+to do a precise calculation
+
+to really check it because
+their energy is not the same.
+
+Their energy is
+also not the same.
+
+Yeah, but this is a
+heuristic way to understand.
+
+Anyway, so you find
+that the free energy--
+
+so you find the Euclidean
+action, or the [INAUDIBLE],
+
+is always much--
+is always greater
+
+than the small black hole.
+
+And that is good.
+
+That is good because
+that tells you
+
+the small back hole
+is never dominate
+
+because you always find
+something bigger than that.
+
+And the small black hole have
+a [? lack of ?] specific heat.
+
+That's not something you
+want because our Field
+
+Theory definitely have
+quality of specific heat.
+
+Our Field Theory definitely
+has quality of specific heat.
+
+So that tells you
+that this is never--
+
+can be low-- that would
+be a dominate phase.
+
+So now, if you
+calculated a number--
+
+so now if you look at
+the number explicitly--
+
+So what you'd find actually--
+so you also have-- let me just
+
+first tell you the results, OK?
+
+You find there exists
+a temperature, Tc,
+
+which is greater than
+the minimal temperature.
+
+Then, you find that the-- when
+you're smaller than the minimal
+
+temperature--
+
+Yeah.
+
+Right.
+
+OK.
+
+So when your T is smaller
+than the minimal temperature--
+
+oh, no.
+
+No.
+
+T is smaller than Tc.
+
+So you find that there
+exists a Tc, which is greater
+
+than the minimal temperature.
+
+So let me just say this.
+
+So when T is smaller than
+T minimum, of course,
+
+there's only thermal AdS exists.
+
+And, of course, that
+would be the only phase
+
+which can describe the
+Field Theory result.
+
+But, now, there exists another
+temperature [? then, ?]
+
+within T, smaller than--
+greater than T minimum
+
+and smaller than Tc.
+
+Then, you find that the SE big
+black hole is smaller than 0.
+
+And the thermal
+AdS, essentially,
+
+by definition to be 0.
+
+So that means that
+the thermal AdS
+
+will have lower free energy.
+
+So in this range, the
+thermal AdS will dominate.
+
+And when T is greater
+than Tc, then you
+
+find that the big black hole
+now has a positive action
+
+and [INAUDIBLE] dominates.
+
+So if I draw this--
+and then there's a Tc
+
+and there's a T minimum-- so
+this is the temperature axis.
+
+So here, of course, you
+only have a thermal AdS.
+
+But within this
+range, the thermal AdS
+
+dominates over big black hole
+and the small black hole.
+
+And when you're above, then
+the big black hole dominates.
+
+So you actually have
+a transition at Tc.
+
+So below here, it's
+just thermal AdS.
+
+And then you have a
+transition from thermal AdS
+
+to the big black hole at Tc.
+
+So a quick side remark.
+
+How we-- how would
+you find this result?
+
+So this would be the result
+if you calculated the-- so
+
+you just calculate
+the Euclidean action.
+
+You compare them.
+
+That's what you would find.
+
+So any questions about that?
+
+Yes?
+
+AUDIENCE: Do you ever get
+the small black hole phase
+
+at all somehow artificially?
+
+PROFESSOR: Yeah, you can
+always get artificially.
+
+Yeah, artificially, always.
+
+Yeah.
+
+And let me not go into that.
+
+So now, let me just say a few
+remarks, say, in finding SE.
+
+So when you find the
+Euclidean action,
+
+you find it is always divergent.
+
+It's the same thing as
+what we encountered before.
+
+If you calculate
+the whole action,
+
+you have to integrate the--
+over the-- essentially,
+
+the volume of the AdS.
+
+But the volume of
+AdS goes to infinity
+
+at-- near the
+boundary, essentially,
+
+you always get infinity.
+
+So in order to get a
+[? finite ?] answer,
+
+you need renormalization.
+
+So when you do renormalization,
+essentially, you
+
+put the [? cut ?] off and
+then you subtract covariant,
+
+the local counter terms.
+
+You put a cutoff.
+
+And then you subtract covariant
+counter terms at the cutoff.
+
+And then you get
+a finite answer.
+
+Then, you take the
+cutoff to the boundary.
+
+So we will not go
+through this procedure,
+
+but it's something you can do.
+
+But there's an
+alternative shortcut
+
+to not go through these.
+
+Or you can just subtract-- just
+calculate the Euclidean action
+
+for the cutoff, then subtract
+the value of pure AdS.
+
+So if you calculate
+the pure AdS,
+
+you will find the answer
+is also divergent.
+
+You will find the answer
+is also divergent.
+
+And you just subtract it.
+
+And then when you
+do the subtract,
+
+you will find the
+difference is [? finite. ?]
+
+And then you find the
+difference is finite.
+
+And this is a slightly
+simple way to do than that,
+
+but we also not do this
+because, still, you
+
+have to calculate Euclidean
+action [? and such. ?]
+
+So the synchron-- shortcut is
+to assume thermal dynamics.
+
+That's what we did last time.
+
+Because you can find the
+entropy density very easy.
+
+So entropy density--
+did I erase my--
+
+so the entropy density
+is just, essentially,
+
+the area of the horizon.
+
+So the entropy-- right now, it's
+actually the total entropy, not
+
+the entropy density because
+now we are [? almost here. ?]
+
+So the entropy would be--
+and size of the sphere
+
+will be r0 to the power d
+minus 1 times omega d minus 1.
+
+Omega is the volume
+of a unit sphere.
+
+And then divided by 4 pi 4GN.
+
+So this is the
+entropy of the system.
+
+And you can express this
+in terms of the temperature
+
+because r0 is a
+function of temperature.
+
+r0 is a function of temperature.
+
+If you invert this,
+you can imagine r0
+
+is a function of temperature.
+
+So you have-- essentially
+you have entropy
+
+as a function of temperature.
+
+And-- Hm?
+
+AUDIENCE: d minus
+1, what's that?
+
+PROFESSOR:
+[? Formula ?] d minus 1
+
+is the volume of
+the unit sphere.
+
+So you know the entropy.
+
+You can just use the formula
+S equal to minus F minus T
+
+divided by T to--
+so you can also
+
+write this as minus F r0,
+partial r0, partial T,
+
+et cetera.
+
+And then you can
+integrate this equation
+
+to find the-- to find
+F as a function of r0
+
+because we know how the
+r0 depends on T from here.
+
+So you just need to
+integrate this equation.
+
+So this is a simple
+exercise because now
+
+you just need to do an
+integral of some function.
+
+And then you find omega
+d minus 1 divided by 16
+
+pi GN, r0 d minus 2 minus
+r0 d divided by R squared.
+
+You get actually a
+rather simple answer
+
+if you do that integration.
+
+So we have chosen the
+integration constant so
+
+that when r0 equals
+to 0, this is
+
+0 because r0 equal to
+0, if the black hole has
+
+0 size, essentially,
+[? there's ?] no black hole.
+
+And then we have
+chosen the free energy
+
+to be 0 for the
+[? no ?] black hole.
+
+So this free energy,
+again, should
+
+be interpreted as the
+difference with the pure AdS.
+
+So for the black hole-- this
+is the black hole free energy
+
+because, by definition,
+this way, the pure AdS,
+
+you just have 0.
+
+Any questions about this?
+
+So now you see here,
+clearly, this expression.
+
+So now this is a
+free energy now.
+
+This is not the
+Euclidean action.
+
+So they differ by the
+amount [? assigned ?]
+
+in my convention.
+
+So now you see that there
+exists r0, critical r0.
+
+F black hole is greater than
+0 Free energy is greater
+
+than 0 for r0 is smaller than R.
+
+So you can write it as formula d
+minus 1-- so let me just write.
+
+Yeah, you can put the omega--
+the r0 to that [? out ?]
+
+for the overall factor r0.
+
+Yeah, put d minus 2
+out, and this just
+
+becomes 1 minus r0 squared.
+
+So you find that the free
+energy is greater than 0.
+
+But r0 is greater than 1.
+
+That's greater
+than the-- so this
+
+is greater than the
+value of the thermal AdS.
+
+And the black hole
+is smaller than 0.
+
+The free energy [? smaller ?]
+than 0 become great than R.
+
+So the r0 is somewhere here.
+
+So r0 is somewhere here.
+
+It has to exist above
+the-- it's somewhere here.
+
+This is r0.
+
+This is this r0 critical
+[? as you go ?] to R.
+
+This is r0 critical
+[? as you go ?] to R,
+
+somewhere here.
+
+So it's always a big black hole.
+
+And you can find out what is
+this critical temperature.
+
+So the critical temperature is
+just the beta evaluate at r0
+
+equal to R. And then
+you can find out
+
+that this is 2 pi R
+divided by d minus 1.
+
+Just using this formula
+you can find out it's that.
+
+So now I emphasize that
+this is a phase transition.
+
+And this is not only
+a phase transition,
+
+this is actually a first
+order phase transition
+
+for the following reason.
+
+So in our unit, below
+here, the free energy
+
+is 0 times order N squared.
+
+It's 0 times N squared.
+
+But about here-- well,
+actually, above Tc-- at Tc,
+
+the free energy is
+exactly equal to 0.
+
+So [? r0c ?] is
+equal to R at Tc.
+
+There's a free energy.
+
+It's exactly 0.
+
+So at Tc, the-- a big black
+hole and the thermal AdS
+
+have the same free energy.
+
+So they can exist together.
+
+And above here, then the free
+energy of the big black hole
+
+is some negative number times
+order-- times N squared.
+
+So your free energy
+has a huge change.
+
+So essentially, the first
+derivative of free energy,
+
+is discontinuous across
+the phase transition.
+
+So this is actually a first
+order phase transition.
+
+So this is-- yeah, let
+me just emphasize that.
+
+So this is a first
+order phase transition,
+
+with the free energy equal
+to order N to the power 0
+
+when T is smaller than Tc and
+some nonzero number times N
+
+squared.
+
+Well, T greater than Tc.
+
+Any questions?
+
+AUDIENCE: When r0 is equal
+to R, then F is equal to 0.
+
+PROFESSOR: Yeah.
+
+AUDIENCE: Then, why is the-- oh.
+
+PROFESSOR: No, the derivative
+of F should be discontinuous.
+
+No, F is continuous.
+
+No, this is a definition of
+the-- for the phase transition,
+
+the free energy is
+always continuous.
+
+And then the free-- so the
+first derivative here will
+
+be proportional to N squared.
+
+And you can check-- Yeah?
+
+AUDIENCE: So the point is-- OK,
+so just see if I understand.
+
+So the point is that
+it's discontinuous
+
+in the limit of
+large N or something?
+
+I mean--
+
+PROFESSOR: Yeah, that's right.
+
+That's right.
+
+Exactly.
+
+So let me emphasize.
+
+So this is N goes
+to infinity limit.
+
+Is there any other questions?
+
+So we see there's a lot
+of [? rich ?] story when
+
+you go to the sphere.
+
+And, actually, there's
+a phase transition.
+
+And the phase transition
+roughly [? adds to-- ?]
+
+the black hole size
+is the AdS radius.
+
+Exactly the black hole
+size is AdS radius.
+
+And this is, more or less, what
+you expected because that's
+
+where the physics become
+nontrivial because when
+
+the horizon is much, much
+smaller than the black hole
+
+[? size-- ?] than the
+curvature radius, as I said,
+
+just should reduce to the flat
+space black hole and et cetera.
+
+Yeah, because the curvature
+radius is only scale here.
+
+So now, let me make
+another remark.
+
+Now, I erase this.
+
+I think it's OK.
+
+Yeah So you should
+actually check yourself.
+
+So below Tc, the F
+prime is always 0.
+
+When you take the
+derivative, it's
+
+always 0 at order N squared.
+
+Let me, again, write this
+answer, 0 times N squared.
+
+So you should check that
+the first derivative of F
+
+is discontinuous.
+
+AUDIENCE: So F itself
+is not discontinuous?
+
+PROFESSOR: No, F is not
+because the F is 0 precisely
+
+at T equal to Tc.
+
+So F is equal to 0.
+
+And the-- Yeah.
+
+So the reason the first
+derivative is discontinuous
+
+is very clear because
+below Tc, this is 0.
+
+So the first derivative
+is 0 times N squared.
+
+And above Tc, the
+derivative is the derivative
+
+of the free energy of the
+black hole at I equal to r0.
+
+And, clearly, the
+derivative is nonzero.
+
+At I equal to r0, the
+derivative is [? nonzero. ?] OK?
+
+And so you see,
+they're discontinuous.
+
+So since physics only depends on
+the [? dimensionless ?] number,
+
+R times T-- So large R,
+small T-- large R at fixed T
+
+essentially is the same as
+the, say, large T fixed R.
+
+It can only depend
+on the ratio of them.
+
+OK?
+
+It depends on the
+product of them.
+
+So you can either think
+of-- you can either
+
+think you fix the
+temperature, you
+
+increase the size of the sphere.
+
+Or you fix the
+size of the sphere,
+
+you increase the temperature.
+
+[? In ?] fact, the same
+is to increase this guy.
+
+And this is essentially the
+limit going to the flat space.
+
+It's going to the R to the T.
+If you take R go to infinity,
+
+you go to a [? theory ?]
+on R d minus 1.
+
+So we see that the
+theory on R d minus 1
+
+is mapped to the high
+temperature limits
+
+of the theory on the sphere.
+
+So essentially, just
+corresponding to the 1
+
+point for the
+[? theory ?] on the sphere
+
+and this infinite temperature of
+the [? theory ?] on the sphere.
+
+So that's why, as
+we said before,
+
+because there's no scale here,
+the [INAUDIBLE] temperature
+
+from here is essentially
+the same in the flat space.
+
+And in particular, this is
+described by a big black hole.
+
+And this is exactly
+what we see before
+
+because when the black
+hole become very big,
+
+then you can approximate
+it to a plane
+
+because, locally, it's
+like a plane [? anymore. ?]
+
+And the spherical horizon
+is just like a plane.
+
+And then you go to
+the black plane--
+
+you go to the black hole
+with the flat horizon.
+
+AUDIENCE: Why are the phases
+only dependent on R times T?
+
+PROFESSOR: Yeah, because
+this a CFT and this
+
+is only dimensions number.
+
+It can only depend on them
+through this dimensions number.
+
+There is no other scale.
+
+Good?
+
+Other questions?
+
+Yes?
+
+AUDIENCE: So on the
+side of the CFT,
+
+what are the different phases?
+
+I didn't-
+
+PROFESSOR: Sorry?
+
+AUDIENCE: What are the different
+phases on the CFT side?
+
+PROFESSOR: Yeah, that's what
+we are going to explain.
+
+So now, we have to describe
+the black hole story.
+
+Or now, we have described
+the gravity story.
+
+Just by looking at
+the gravity size,
+
+we saw there are
+three possible phases.
+
+At low temperature, you
+get this thermal AdS phase.
+
+At high temperature, you
+get big black hole phase,
+
+and then there is a phase
+transition between them.
+
+And then, also, you have
+unstable small black hole
+
+phase, which never
+appears as a stable phase
+
+at any temperature.
+
+So, now, let's try to see
+whether we can understand this
+
+from the Field Theory side.
+
+What does this mean from
+the Field Theory side?
+
+Why somehow-- if I, for example,
+put [INAUDIBLE] on a sphere,
+
+do I expect such kind
+of phase transition?
+
+Does this make sense?
+
+Oh, by the way,
+I should say this
+
+is the-- so this is called
+a Hawking-Page transition.
+
+So this is called a
+Hawking-Page transition.
+
+So remarkably,
+this was discovered
+
+in 1980-- I think '81
+or '82, almost 20 years
+
+before this AdS/CFT conjecture.
+
+But they already
+figured out that there
+
+is a phase transition.
+
+They were-- so they were
+looking at the black holes
+
+[? and ?] AdS, and they said,
+oh, there's two black holes.
+
+But there's also some AdS.
+
+And then, somehow,
+there's some kind
+
+of phase transition
+between them.
+
+But because they don't
+know the Field Theory,
+
+they don't know this
+should correspond
+
+into some kind of
+Field Theory system.
+
+But they figured out this
+gravity story essentially
+
+in 1981.
+
+Now, let's explain what
+should be the Field Theory
+
+interpretation of
+this-- The Field Theory
+
+explanation of this.
+
+Physical reasons for
+Hawking-Page transition.
+
+So now, I will
+consider a toy example.
+
+So I won't consider--
+so [INAUDIBLE]
+
+on the sphere, that's a
+little bit too complicated.
+
+But I'm going to
+consider toy example.
+
+And you will see,
+from this toy example,
+
+that the physics behind this is
+very simple and actually, also,
+
+[INAUDIBLE].
+
+So let's consider you have N
+squared harmonic oscillator--
+
+free harmonic oscillator.
+
+So let's just
+imagine you can take
+
+them to be different
+frequencies-- [? let's ?] just
+
+even for simplicity-- or
+for the same frequency.
+
+Say, omega-- I have some omega,
+which I just take to be 1.
+
+Doesn't matter.
+
+So just consider N squared
+free harmonic oscillator.
+
+So I claim when N-- when
+N goes infinite limit,
+
+this system have the
+same phase transition--
+
+have exactly the same phase
+transition described there.
+
+So, now, I will explain.
+
+So first, let's
+look just at-- this
+
+is a system we know how
+to solve exactly, so let's
+
+look at the spectrum.
+
+So this is total spectrum, the
+total energy spectrum of this N
+
+squared harmonic oscillators.
+
+So let's call the
+0, the ground state.
+
+So let me normalize the
+energy so that the ground
+
+state have energy 0.
+
+And then you can excite
+one harmonic oscillator,
+
+and then you have state of 1.
+
+Yeah.
+
+Actually-- Yeah,
+have state of 1.
+
+And you can have two harmonic
+, oscillator et cetera.
+
+And then you'll have many
+harmonic oscillators, say,
+
+of all-- then, you're going
+to have almost every harmonic
+
+oscillator excited.
+
+And then you have energy of
+order N squared, et cetera.
+
+So now you have to imagine a
+slightly nontrivial condition.
+
+Now, you have to imagine a
+slightly nontrivial condition,
+
+which this is the
+only thing [? reach ?]
+
+beyond the harmonic oscillator.
+
+Yeah.
+
+Actually, I just realized this.
+
+I slightly oversimplified
+the story a little bit.
+
+Yeah.
+
+Yeah, let me say this way.
+
+Yeah.
+
+Let's consider 2N
+harmonic oscillators.
+
+So let me arrange it
+into two matrix, A and B.
+
+And they are all free.
+it doesn't matter.
+
+For this purpose, it doesn't
+matter how many harmonic-- just
+
+imagine I have arranged
+them into two matrices,
+
+so I have two N squared
+harmonic oscillators.
+
+And then I can excite them.
+
+But, now, I have a condition.
+
+So I have a condition, which
+is analog to the condition
+
+of the gauge invariance.
+
+Instead, I want all
+the states to be
+
+the trace singlet
+created by A and B.
+
+You have A, B, et cetera.
+
+So A have N squared creation
+and annihilation operator,
+
+and B have N squared
+annihilation-- creation
+
+and annihilation operator.
+
+And then you can
+act them-- then,
+
+you can [? accurately ?]
+form the spectrum that it is.
+
+But there's a-- but also I
+need to add a gauge invariance
+
+condition.
+
+It's that the state
+[? acted ?] by A and B
+
+have to be SU(N) singlet.
+
+And SU(N) is the conjugate.
+
+Just imagine A and b
+transformed under some SU(N)
+
+[? join representation. ?]
+And they
+
+have to be the SU(N) singlet.
+
+So equivalent statement say that
+the trace A and B-- the order
+
+state has to be
+created by operators
+
+inside the trace, single trace
+or multiple traces, et cetera.
+
+So is this clear?
+
+AUDIENCE: So one thing.
+
+So A and B are operators?
+
+Or they are--
+
+PROFESSOR: They're operators,
+harmonic oscillators.
+
+AUDIENCE: Oh, I see.
+
+PROFESSOR: Yeah.
+
+Imagine you have two
+matrices under-- and two
+
+harmonic oscillators
+that form two matrices.
+
+And each of them have N
+squared harmonic oscillator.
+
+And if I just say they
+are free, then you
+
+don't even have to think
+about the matrix structure.
+
+AUDIENCE: So the only thing,
+I'm confused about the matrices.
+
+So are the matrices acting on
+some [INAUDIBLE] So in other
+
+words--
+
+PROFESSOR: Yeah.
+
+Let me be a little
+bit more explicit.
+
+[INAUDIBLE] Think about
+the foreign system.
+
+The Lagrangian 1/2 Tr
+A dot squared, Tr 1/2,
+
+Tr B dot squared minus 1/2
+Tr A square 1/2 Tr B squared.
+
+So this is a free
+harmonic oscillator.
+
+So these are two N squared
+free harmonic oscillators
+
+with frequency 1.
+
+So if I don't impose
+this singlet condition,
+
+this is just a purely
+free harmonic oscillator.
+
+But now, I [? require ?]
+all the state--
+
+and so SU(N) transformation--
+[? yeah, you can act them. ?]
+
+But now, I impose the
+condition that they will have--
+
+they should be SU(N) singlets.
+
+So they can [? create ?]
+it by A and B, et cetera.
+
+But they should
+be SU(N) singlet.
+
+Good?
+
+So now one thing
+you can convince
+
+yourself is that because
+of the trace condition--
+
+so if you think about the
+state of energy 1 or 2,
+
+et cetera-- so as far as the
+energy is order N to the power
+
+0, so as far as the energy
+does not scale with N,
+
+you can check yourself the
+density of state-- the way
+
+you can-- the degeneracy
+of those states
+
+will always be of
+order N to the power 0.
+
+So this is a fact.
+
+You can convince yourself.
+
+And when you go to the
+energy of order N squared,
+
+then you can check that
+the density of state
+
+become exponential
+of order N squared.
+
+So the reason for
+this is very simple.
+
+So the reason for this is
+very simple heuristically.
+
+So the reason for
+this is very simple
+
+because if you have a state
+of order 1, which does not
+
+scale with N, means there's
+only order 1 states-- order
+
+1 oscillators are excited.
+
+And then, of course,
+the density of state
+
+will be independent of N. And
+if you do have energy of order
+
+N squared because each
+of-- each oscillator
+
+has a frequency of 1, and then
+you have energy N squared.
+
+And then that means order N
+squared oscillator is excited.
+
+And then you have order Ns--
+if you have order N squared
+
+oscillator excited, then how
+many ways you can choose them
+
+to construct the [? state of ?]
+energy order N square and that
+
+[? exponential ?]
+of order N squared.
+
+So imagine each
+of the states, you
+
+can have N possible oscillator
+to act, say, for each of them
+
+for twice.
+
+Then, you have 2 to
+the order N squared
+
+probabilities of doing that.
+
+So that's where this
+[? exponential ?] order
+
+N squared come out.
+
+So this is a fact.
+
+You should try to
+convince yourself
+
+if it's not obvious to you now.
+
+So the reason I add this
+singlet condition is for here.
+
+If I don't add a
+singlet condition,
+
+then there's some
+kind of independence
+
+here, which I don't want.
+
+There can be [? log ?]
+independence.
+
+Yeah, just-- yeah.
+
+So this makes [? your ?] story
+a little bit [? convenient. ?]
+
+Oh, so now-- yeah.
+
+We're running out of
+time unfortunately.
+
+So now let's consider
+the free energy,
+
+which, roughly, you can
+consider as integrates
+
+of all possible states with
+this weight factor and times
+
+the density of state.
+
+[INAUDIBLE] because
+the free energy
+
+sum of all states,
+minus BH, and the sum
+
+translated into the integral
+with a density of states.
+
+And then that
+translates into that.
+
+So naively-- so we
+always consider--
+
+so our beta is always-- does not
+scale with N. That's order 1.
+
+It's always order 1.
+
+So if you look at here
+naively, only state
+
+of energy of order
+that's not scale N
+
+will contribute significantly
+because of this suppression.
+
+Because of the thermal
+suppression, say,
+
+if you have energy
+of state of order
+
+N squared, then this
+is a huge suppression.
+
+Then, they should
+not contribute.
+
+Then, they should not make
+a visible expression--
+
+a contribution to
+your free energy.
+
+Expect, except when those states
+have a huge density of states.
+
+So except when those states
+have a huge density of states.
+
+So, here, we see those
+states have actually
+
+order N squared
+density of states.
+
+So that means, in here, in that
+integral, you have beta times
+
+order N squared-- something of
+order N squared and then times
+
+something positive
+of order N squared.
+
+When you can see the
+contribution of the state
+
+of energy of order N squared.
+
+So when this factor
+dominate over this factor,
+
+then the entropy will overwhelm
+the thermal suppression.
+
+And then, such
+state will dominate.
+
+And that precisely happens
+when beta becomes small enough.
+
+Because when beta
+becomes small enough,
+
+when you got the high
+temperature, then
+
+beta decrease.
+
+So eventually, this
+will overwhelm this one
+
+because the beta will decrease.
+
+And that's precisely the
+Hawking-Page transition
+
+we'll see.
+
+So at low beta-- at big
+beta or small temperature,
+
+thermal-- this one dominates.
+
+And then, the [? V ?] would
+be of order N to the power 0
+
+because only state of
+order-- energy order zero
+
+will contribute.
+
+But the beta-- when beta
+is sufficiently small, then
+
+the [? log ?] D(E) minus BE
+can become greater than 0.
+
+And then the order N squared
+states will dominate.|
+
+And then you find
+the-- then, you find
+
+the [? partial function ?] will
+be [? exponential ?] of order N
+
+squared.
+
+And that's precisely what we see
+in the Hawking-Page transition.
+
+So I emphasize that
+physics here have
+
+nothing to do with the
+details of the system,
+
+only related to the large N
+and to the density of states.
+
+So if you have interactions,
+if you have more complicated
+
+system, it doesn't matter.
+
+It doesn't matter.
+
+As far as your [INAUDIBLE],
+this phenomenon will happen.
+
+This phenomenon will happen.
+
+And so this is the essence of
+the Hawking-Page transition.
+
+We will stop here.
\ No newline at end of file
diff --git a/rxiAQe0t-ZU.txt b/rxiAQe0t-ZU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a888b08b70b3a335650da6cbf018f3fe348d7d4d
--- /dev/null
+++ b/rxiAQe0t-ZU.txt
@@ -0,0 +1,1145 @@
+Good morning.  Thank you.  So, I want to continue today on the  
+
+theme of neurobiology.  Last time we spoke about the action  
+
+potential mechanism.  Today I'd like to go from action  
+
+potential to the synapse.  But let me briefly remind us what we  
+
+say.  So, I'm going to give section zero a recap here.   
+
+The relevant things that we said last time was there's a membrane  
+
+potential which at rest is about minus 70 millivolts as the membrane  
+
+potential, and that's what we work with.  That membrane potential is  
+
+set up by concentration gradients.  More calcium, more potassium on the  
+
+inside.  More sodium on the outside.  More calcium on the outside.  And  
+
+I'm also going to mention chloride,  there's more chloride on the outside  
+
+at 116 millimolar,  four millimolar on the outside.   
+
+These concentration gradients are set up by various different pumps.   
+
+They're there all the time.  Then we have this resting channel.   
+
+So, here we have transporters.    
+
+We have a resting potassium channel.  It means that it's open all the  
+
+time.  It's not activated by anything.   
+
+That allows potassium to leave.  Potassium leaves until it builds up  
+
+this membrane potential about minus 70.  At that point it is  
+
+electrically unfavorable for more positive charges to go out into the  
+
+more positive environment.  Notwithstanding the greater  
+
+internal concentration.  And we reach an equilibrium  
+
+potential of minus 70.  We then have some voltage-gated  
+
+channels.    
+
+And the voltage-gated channels come in two flavors here.   
+
+We have the voltage-gated sodium channel.  The voltage-gated sodium  
+
+channel opens itself up around minus 70.  Oh, sorry,   
+
+around minus 50.  So, if you can get up to minus 50  
+
+it opens up.  Then your sodium rushes in.  It shifts the membrane  
+
+potential from minus 50 to zero to plus 50.   
+
+The channel shuts.  Somewhere around plus 30 or so  
+
+opens the potassium channel,  the voltage graded potassium channel,   
+
+and allows the potassium to rush out and restore the resting potential.   
+
+The effect of this is that, if this is zero here, we have  
+
+a resting potential.  If we climb up a little bit above it  
+
+we shoot up and then we come back down.  And then a millisecond or so  
+
+later another action potential could go down that same neuron.   
+
+And, last of all, if we look along the length of an axon,   
+
+an action potential here causes charges to migrate over which  
+
+launches an action potential here which causes charges to migrate over  
+
+which etc., etc.  propagates an action potential down  
+
+the length.  It's a beautiful system.   
+
+And then the very last thing was that by insulating this we were able  
+
+to make the conduction velocity go faster by effectively making the  
+
+effective length be shorter there being a whole bunch of electrically  
+
+insulated regions.  So, that's it.  It's a beautiful  
+
+piece of engineering.  How do we know any of this is true?   
+
+ As an interesting side point,   
+
+I might just mention that when this was worked out,   
+
+this was worked out by two folks called Hodgkin and Huxley.   
+
+Hodgkin and Huxley won a Nobel prize for this beautiful work on  
+
+this squid giant axon which is the fastest axon that there is.   
+
+And here we're not talking about the giant squid somebody raised last  
+
+time.  It's an ordinary squid.  It has one big fat axon.  It's  
+
+sufficiently big that you can just like stick a wire in the middle of  
+
+it and all that.  It's a very big axon.   
+
+It's a very, very high diameter axon.   
+
+And they were able to measure these things electrically.   
+
+And on the basis of the electrical measurements they made in different  
+
+kinds of solutions,  they were able to infer the  
+
+existence of sodium channels and potassium channels.   
+
+But this all happened mid 20th century.  And they certainly  
+
+couldn't see any.  They couldn't clone them.   
+
+They couldn't see anything.  And so the notion that there were  
+
+individual molecular channels that swung open, did all this stuff was  
+
+an indirect inference,  maybe kind of a little bit like  
+
+Mendel's inference of a gene or Sturtevant's inference  
+
+of genetic maps.  But more recently people have come  
+
+along with an extraordinary technology, also these people won a  
+
+Nobel prize for this because it was way cool, which is called the Patch  
+
+Clamp.  The patch clamp is the following ridiculously simple  
+
+technology.  Suppose I were to make a glass pipette.   
+
+So, this is a cross-section of a glass pipette.   
+
+So, it goes around like that.  And I could bring it up really  
+
+tight up against the membrane.  And suppose I did it in such a way  
+
+that I could get a really great seal and I just have a teeny patch of  
+
+membrane.  Suppose that teeny patch of membrane had just  
+
+one channel in it.  And now, so this is a pipette,   
+
+suppose I were to rip off that patch of membrane from the cell,   
+
+poor cell, and have a glass pipette with a little patch of membrane on  
+
+its end with a single isolated ion channel.  Now,   
+
+if I measured the current through this channel by putting it in an  
+
+appropriate solution,  maybe I ripped off a resting  
+
+potassium channel, OK?  If I put this in a potassium  
+
+solution and I apply a current,  I apply a voltage difference, I  
+
+should be able to see a current.  And you can actually measure a  
+
+current.  Even more cool,  if I do this and I've ripped off a  
+
+voltage-gated sodium channel,  then it turns out that I ought to be  
+
+able to study its properties by changing the voltage on it and  
+
+measuring the current as a function of the voltage.   
+
+And, well, it turns out that if I do this I'm able to measure in resting  
+
+or in these voltage-gated channels current flows conductivities,   
+
+actually, what I'm really measuring is the conductivity of the channel  
+
+like this, I can see the channel opening and closing and opening and  
+
+closing quantily.  I can measure quantily the  
+
+conductivity.  That's not quantum mechanics.  It's just quanta  
+
+measurements of the conductivity.  What would happen if I had two  
+
+channels that had been ripped off?  Now I'd see it go like this.   
+
+Well, maybe another one opens.  Oops, now one closes.  Now the  
+
+other one closes.  And quite remarkably you can get  
+
+this.  So, you can study single molecule, single molecular channels.   
+
+You want to know how this channel opens and at what voltage it opens?   
+
+Just dial in the voltage and see if it's open.  Do you want to know how  
+
+long it stays open?  Just turn it on and see how long it  
+
+stays open.  It's really cool.  You want to see if any other  
+
+chemicals could affect it,  any ions, any other intracellular or  
+
+extra cellular chemicals?  You can do it.   
+
+So, the ability to study isolated single channels came along with  
+
+patch clamping.  And what it allows is a tremendous  
+
+study of the biophysics of individual channels.   
+
+And, whereas, before people had to look at the total conductivity of an  
+
+entire axon.  Now they're able,  and from that infer the behavior of  
+
+single channels,  now what they can do is study the  
+
+behavior of single channels and synthetically build up a picture of  
+
+the total conductivity of an axon from its individual components and  
+
+see if the components we've identified are sufficient to explain  
+
+the behavior that we see.  Anyway, that's patch clamping.   
+
+Lots of fun.  So, now, what I want to turn now to is signaling  
+
+at the synapse.    
+
+So, we have our cell body here.  It's got its dendrites on it.   
+
+Here's our axon.  We've managed to get an action  
+
+potential started on it and it moves all the way down.   
+
+Now we get here to one of the synaptic terminals.   
+
+The electrical signal makes it all the way to the synaptic terminal,   
+
+but how does it affect the post-synaptic cell?   
+
+ Well, let's get a close-up of that.   
+
+Here we go.  Here's the synaptic terminal.  We've got our action  
+
+potential coming.  Action potential coming.   
+
+And then it gets here.  Action potential's arrived.   
+
+I would like to release chemicals into the synaptic cleft,   
+
+the space between the pre and the post-synaptic cell.   
+
+I'd like to spill out chemicals that are neurotransmitters.   
+
+So, the pre-synaptic cell conveniently has vesicles,   
+
+little membrane-bound vesicles with prepackaged neurotransmitters.   
+
+OK?  These prepackaged neurotransmitters have been  
+
+conveniently synthesized by the cell and they're just sitting there  
+
+waiting to be released in response to an action potential.   
+
+When the action potential comes,  it causes these synaptic vesicles to  
+
+fuse --   
+
+-- with the membrane.  And in fusing the insides become  
+
+continuous with the outsides,  here's a little fusion picture here,   
+
+and the neurotransmitters leak out.  OK?   
+
+How does it do that,  though, mechanistically?   
+
+How in the world does an action potential cause these vesicles to  
+
+fuse with the membrane?  Well, somehow it's got to read out  
+
+electrical activity into some kind of a chemical activity  
+
+intracellularly.  Here's what it does.   
+
+When the electrical signal comes down, remember originally the  
+
+membrane potential is negative,  but when an action potential comes  
+
+by what does it do to the membrane potential?  It reverses it.   
+
+It makes it positive inside briefly.  OK?  So, this is the sign of an  
+
+action potential,  an AP coming down.   
+
+In this membrane we have us another voltage-sensitive channel.   
+
+This voltage sensitive channel is a voltage sensitive calcium channel.   
+
+OK?  Who would like to design a voltage-sensitive calcium channel?   
+
+What should it do?  What would you like to have its opening and closing  
+
+properties be?  When does it open?   
+
+At a positive charge.  So, when you get to a positive  
+
+membrane potential it swings open.  And then what does it do?   
+
+Lets calcium move.  Which way does calcium want to go?   
+
+In because it's more out.  So, what's going to happen is in  
+
+response to the action potential calcium will rush in.   
+
+Now, calcium, you will recall,  was in vanishingly small traces  
+
+inside, 0.1 micromolar we said.  And influx of calcium is a very  
+
+serious matter and it is sensed by variety of proteins.   
+
+In particular,  there is, floating around in the  
+
+cell, a protein here called a calcium-dependent protein kinase.   
+
+ The calcium-dependent protein kinase  
+
+is a protein that is capable of putting a phosphate group.   
+
+Its kinase puts a phosphate group on other proteins.   
+
+So, the calcium-dependent protein kinase over here will go along and  
+
+catalyze the addition of a phosphate group to other proteins.   
+
+So, it will enzymaticly catalyze this.  But it only does so in the  
+
+presence of calcium.  So, when there's calcium in the  
+
+cell, the calcium-dependent kinase is activated and it runs around and  
+
+sticks phosphate groups on specific target proteins.   
+
+You know where one of those target proteins lives?  In the vesicles.   
+
+The vesicles happen to be a target for this.  So,   
+
+the vesicles have a protein on them.  And in one of these extraordinary  
+
+coincidences in molecular biology,  the protein on the synaptic vesicle  
+
+happens to be called,  coincidently, synapsin.   
+
+OK?  It's not actually entirely a coincidence that it's called  
+
+synapsin.  It was named synapsin because it was found on the synaptic  
+
+vesicles, obviously.  And so what happens is when the  
+
+action potential comes down it causes the calcium channel to open  
+
+in response to positive voltage.  Calcium comes in,   
+
+actives at the kinase.  The kinase phosphorilates synapsin.   
+
+And now the phosphorilated form of synapsin likes to bind to something  
+
+in the membrane.  That's it.  How many of you still  
+
+know what a Rube Goldberg machine is?  Good. OK.  This is one of these  
+
+just great, well,  others of you should look it up on  
+
+the Web because they're just great cartoons, the Rube Goldberg cartoons  
+
+about the machine where the rooster crows startling the cat which tugs  
+
+the thing with causes this to flop which causes the eggs to go in the  
+
+pan which causes the thing to cook which causes whatever.   
+
+And I always think about these in terms of great molecular Rube  
+
+Goldberg machines.  So, this is the Rube Goldberg  
+
+machine that gets this synaptic vesicle to fuse there.   
+
+OK?  Good.  Every bit of neurobiology has a molecular  
+
+mechanism to be explained like this.  So, now let's go onto the next  
+
+bit.  How does this signal gets sensed at  
+
+the next cell?  What are we up to?   
+
+Number three.  So, let's look at a specific junction.   
+
+Instead of looking at the junction between two nerve cells,   
+
+let me start with the junction between a nerve cell and a muscle  
+
+cell, the neuromuscular junction.  OK?  So, I've now replaced my  
+
+post-synaptic neuron by a muscle fiber here.  This is  
+
+a muscle fiber.  So, when it spritzes out the stuff  
+
+the neurons that innervate muscle fibers, actually,   
+
+I'm going to expand that a bit,  the neurons that innervate muscle  
+
+fibers, here's the muscle,  and I'll put it at some distance  
+
+here, muscle, spray out a particular transmitter in response  
+
+to the calcium influx.  And that transmitter is called  
+
+acetylcholine,  henceforth ACH.   
+
+Acetylcholine is spritzed out into the synaptic cleft and comes out.   
+
+And what do you think acetylcholine is going to do?   
+
+I've got to send the chemical signal to the next cell.   
+
+I've got to somehow send that signal to the surface.   
+
+It's going to bind to something on the next cell.   
+
+You know the deal,  right?  So, it's going to have to  
+
+bind to a protein on this cell.  And, remarkably, what it binds to  
+
+is called an acetylcholine receptor.  OK?  Very reasonable stuff.  An  
+
+acetylcholine receptor.  The acetylcholine receptor happens  
+
+to be an ion channel,  but it's not a voltage-gated ion  
+
+channel.  It's not an ion channel that opens in response to the  
+
+voltage.  It's an ion channel that opens in response to acetylcholine.   
+
+It's what we'd call a ligand-gated ion channel because it's gated by a  
+
+ligand, acetylcholine.  So, this guy here is a ligand-gated  
+
+ion channel which,  when acetylcholine binds to it,   
+
+swings open.  And what it does is it allows in sodium.   
+
+Bingo.  Now, when sodium comes in what happens?  Action potential.   
+
+But what a second.  This is a muscle.   
+
+ All membranes have the machinery to  
+
+have an action potential?  Nah, liver cells are pretty passive.   
+
+You do this to a liver cell it kind of sits there.   
+
+But muscle cells do have an action potential mechanism.   
+
+They do respond here like a neuron,  an action potential.  And so what  
+
+happens when I open up some sodium channels to the resting potential  
+
+of my muscle?  What was the resting potential of my  
+
+muscle?  About minus 70.  What happens when I open up these  
+
+ligand-gated sodium channels?  Sodium rushes in.  What does it do  
+
+to my membrane potential?  It makes it more positive.   
+
+What does that do?  It triggers an action potential spreading  
+
+throughout the muscle.  And because the muscle has an  
+
+action potential --   
+
+-- all you have to do is manage to get this going in a little patch of  
+
+the muscle and it spreads throughout the muscle fiber.   
+
+One neuromuscular synapse will be sufficient to activate the muscle,   
+
+in principle, because you have this action potential mechanism.   
+
+And then when the action potential fires in the muscle it actually  
+
+causes other channels to open,  including some calcium channels.   
+
+The calcium channels cause calcium to come in.  The calcium causes your  
+
+muscle to contract because of sliding of actins and myosins and  
+
+things like that.  That's how it works.   
+
+That's this Rube Goldberg machine.  All right.  So, let's get ready.   
+
+Let's fire.  Let's send a neuromuscular signal down.   
+
+Contract.  Now here's the problem.  I've got all this acetylcholine  
+
+sitting around in my synapse activating the ligand-gated sodium  
+
+channel causing sodium to come in,  but I would like to relax my muscle,   
+
+please.  What are we going to do about this?   
+
+ I could trigger another channel,   
+
+and maybe it could be a delayed acetylcholine activated yeah,   
+
+dah, dah, dah, dah, dah, dah, that's possible.  I could have it close  
+
+itself.  These are all perfectly reasonable possibilities,   
+
+and we're going to refer them to the engineering committee.   
+
+What else?  You could get rid of the acetylcholine some other way.   
+
+It turns out the latter is the solution here.   
+
+We would like to have some enzyme that chews up the acetylcholine.   
+
+How about acetylcholinesterase?  So, let's put acetylcholinesterase,   
+
+ACHE, acetylcholinesterase in the synaptic cleft.   
+
+Then when I spritz acetylcholine it gets to the other side,   
+
+but very rapidly the acetylcholinesterase is degrading it.   
+
+And so it has a very short time of persistence in the synaptic  
+
+cleft.  OK?  That works.  So,   
+
+that's how I run a neuromuscular junction.  OK?   
+
+So, acetylcholinesterase is very important.  Now,   
+
+again, as with many of the things I've talked about,   
+
+we really know these things are true when we're able to inhibit them in  
+
+different ways.  So, I want to take a moment and  
+
+talk about drugs and toxins.  Because they help us to probe these  
+
+different processes.  Anybody ever have fugu?   
+
+Does anybody know what fugu is?  What's fugu?  It's a blowfish.   
+
+Right.  It's a puffer fish eaten in sushi, and it's an extraordinary  
+
+delicacy.  And why is that?  Right.  Because it's one of the only  
+
+sushis where you really have to worry about improper preparation,   
+
+not just giving you food poisoning or a stomachache or something like  
+
+that, but it's lethal prepared incorrectly.  The reason it's lethal  
+
+incorrectly prepared is because the blowfish has a specific poison  
+
+called tetrodotoxin.  So, if you eat sushi,   
+
+so, in fact, chefs in Japan require a license to prepare fugu  
+
+for customers.  Every once, every couple of years  
+
+some famous actor or personality prepares his or her own fugu and  
+
+dies from it and it's in the papers.  Seriously.  This has happened to  
+
+people.  They're able to do this.  Anyway, tetrodotoxin, tetrodotoxin  
+
+is from puffer fish,  fugu.  Why does this stuff kill you?   
+
+It turns out that what tetrodotoxin does, this wonderful poison from  
+
+this sushi, is that it irreversibly binds, irreversible binding and  
+
+inhibition of voltage-gated sodium channels.   
+
+Why would this be an inadvisable thing to have?   
+
+Suppose you irreversibly bound to and inhibited your sodium channels,   
+
+your voltage-gated sodium channels,  what would you be unable  
+
+to accomplish?  An action potential.   
+
+This is ill-advised to be unable to accomplish an action potential.   
+
+You can imagine that what it leads to then is a paralysis and a very  
+
+serious one, and if it's irreversible this is not a good  
+
+thing.  There are other things.  Has anyone ever fired poison darts  
+
+in South American jungles?  [LAUGHTER]  
+
+Well, if you have,  you would have tipped them with  
+
+qurare.  Qurare is used to make poison darts.  What qurare does is  
+
+it reversibly binds,  still not good, but it's a  
+
+reversible binder to the acetylcholine receptor and it  
+
+prevents it, it blocks the binding of acetylcholine.   
+
+Your acetylcholine receptors,  therefore, cannot respond to your  
+
+acetylcholine.  What will that do?   
+
+A flaccid paralysis because you're unable to move your muscles.   
+
+So, if you were trying to shoot prey in the forest and you send the  
+
+poison dart that has qurare,  it will cause the animal to then  
+
+flop over.  Yes?  Snakes.  Ooh,   
+
+what kind of snakes?  Venomous steak snakes,   
+
+yeah.  [LAUGHTER]  Like bungarus snakes, the really poisonous ones.   
+
+So, it turns out, great question,  that they make something called  
+
+alpha-bungerotoxin.  Venomous snakes,   
+
+next thing on my list,  exactly.  The only improvement they  
+
+make here is that this is an irreversible binder to the  
+
+acetylcholine receptors.  Very impressive stuff.  Different  
+
+stuff.  We'll come back to jellyfish.  But, basically,   
+
+everything you know out there that's noxious is being noxious in some way  
+
+that affects molecular biology.  Not all of it affects the nervous  
+
+system.  Those of you who like to collect mushrooms may wish to avoid  
+
+amanitas mushrooms.  They make amanitas.   
+
+Amanitan is an irreversible binder that affects polymerase,   
+
+RNA polymerase.  Not a good thing to lose either.  So,   
+
+all parts of this course have interesting poisons that will affect  
+
+it but we'll focus on the poisons effecting neurobiology today.   
+
+And then there's a human made thing.  Do you remember the, well, those of  
+
+who have heard of World War I,  nerve gas or, in particular, who  
+
+remember the attack in the Tokyo subways with sarin,   
+
+a particular kind of nerve gas.  Do you know what that stuff does?   
+
+It is a potent inhibitor of the enzyme acetylcholinesterase.   
+
+What would happen if I inhibited your acetylcholinesterase?   
+
+The muscles tense up and I'm unable to relieve them because,   
+
+just like I was doing there,  because my acetylcholine is not  
+
+broken down in the synapse.  So, this is a nice menu of  
+
+interesting poisons and fun facts to know and tell and good things to  
+
+avoid.  There are more drugs and things that we can come back to.   
+
+So, now let's talk about, let's move onto other synapses.   
+
+Let's take a look at nerve-nerve synapses.   
+
+ So, we looked at a nerve muscle  
+
+synapse.  What were the properties of this nerve muscle synapse?   
+
+Well, it had the property that a single neuron innervates a single  
+
+muscle fiber.  All right?  This was a one-to-one single fiber,   
+
+sorry, single neuron, single fiber.   
+
+When we get to nerve-nerve synapses,  they're more complex.  Multiple  
+
+different nerve terminals may synapse upon the same neuron,   
+
+as I indicated last time.  There might be a thousand different  
+
+nerve terminals synapsing on the dendrites of a postsynaptic cell,   
+
+but let's look at one of them for a moment.  Then we'll come back to how  
+
+a thousand can work together.  So, here's one.   
+
+And here's my dendrite that I'm synapsing on here.   
+
+The nerve terminal releases into,  sorry, into the synaptic cleft some  
+
+neurotransmitter.  It turns out there's a wide variety  
+
+of neurotransmitters that get released while the neuromuscular  
+
+junction involves acetylcholine.  One example that might be involved  
+
+here is something called glutamate.  What's glutamate?   
+
+It's an amino acid.  Glutamic acid.  It's the ion of  
+
+glutamic acid.  That actually is a neurotransmitter.   
+
+Ever have monosodium glutamate.  Does anybody get a headache from  
+
+monosodium glutamate?  I do.  That's because it's a  
+
+neurotransmitter.  It messes with brain chemistry.   
+
+So, glutamate.  Glutamate is released.   
+
+And what is does is there is a channel on the post-synaptic cell  
+
+that binds glutamate.  And it, too, is a ligand-gated ion  
+
+channel.  And it could be,  for example, a sodium channel.   
+
+Other neurotransmitters might use other channels.   
+
+What happens if I spritz some glutamate on a dendrite of a cell  
+
+that has a glutamate-activated sodium channel?   
+
+What will happen in that dendrite?  Sodium will rush in causing the  
+
+membrane potential to become depolarized and then positive and  
+
+then causing an action potential?  No.  It turns out that that last  
+
+bit doesn't happen because the dendrites don't have the action  
+
+potential machine.  The action potential machinery is  
+
+interestingly confined to the axon.  It's not found on the dendrites.   
+
+So, when we spritz with glutamate,  what will happen is if this is a  
+
+glutamate-bearing synaptic terminal the membrane potential here will  
+
+become locally positive.  But it is not an explosive  
+
+regenerative action potential because there are no voltage-gated  
+
+sodium channels that are going to open in response to that local  
+
+depolarization.  So, it became a little positive  
+
+over in this corner of the neuron.  Now, if it gets a little positive  
+
+over in this corner of the neuron,  you know, it's going to draw some  
+
+negative charges from over here,  right, to offset that local  
+
+positivity.  But if it's just a local little patch of positive then  
+
+it draws a little bit of negative charge.  But is that going to be  
+
+enough to depolarize over here?  No.  So what do you want to do?   
+
+Have more.  Suppose I have two glutaminergic  
+
+synapses and they fire,  it might be.  Probably not.   
+
+Maybe they have to fire at the same time.  Maybe if I have a hundred out  
+
+of a thousand.  Imagine that I have a hundred  
+
+different glutaminergic synapses that fired simultaneously then what  
+
+will happen?  I'll get positive charges at all of them.   
+
+And maybe that's enough to draw some negative charge away from the axon  
+
+and start an action potential going,  or maybe not.  Maybe you need two  
+
+hundred.  What if they don't fire at exactly the same moment?   
+
+Well, the minute one fires it makes it locally positive,   
+
+but then it starts restoring itself so that if they're separated in time  
+
+they're not as effective as if they happen simultaneously.   
+
+So, we have an extraordinary complex analog integration  
+
+circuit here.  The analogy integration circuit  
+
+depends on the temporal arrival of these signals.   
+
+And what else does it depend on?  The number of the signals.  So,   
+
+let's get this down.  We're going to integrate the  
+
+signals here.    
+
+It'll depend on their timing,  the number, and the geometry,   
+
+because it turns out that doing it at different places in the,   
+
+now, I drew my dendritic tree,  the dendrites as all these little  
+
+hairy spikes coming off the cell body, but the dendrites are vastly  
+
+more complex than that.  Some cells have elaborate dendritic  
+
+trees.  The dendritic tree,   
+
+the dendrites of some neurons,  here's the cell body, can go off in  
+
+all sorts of wonderfully complex patterns.  And it may be more  
+
+effective to hit synapses close to the cell body or synapses on  
+
+different parts of the tree.  And so that the entire shape of  
+
+that dendritic tree can have an effect, and where you're hitting it  
+
+has an effect.  So, whereas the action potential is  
+
+a very simple thing,  which you might say just replace it  
+
+by a wire for our computer modeling studies, goodness,   
+
+nobody has actually succeeded in building a perfect model of the  
+
+integration properties of an dendritic arbor for a single neuron.   
+
+They can get guess and approximations.   
+
+So, there's an amazing integration that's going on here.   
+
+But it turns out that it's more complex than that because,   
+
+you see, I said that we had these,  say, glutamate neurotransmitters  
+
+here that were causing positive charges to rush in.   
+
+It turns out there are other neurotransmitters that activate  
+
+other channels in the membrane.  And, for example, there are some  
+
+neurotransmitters that activate,  like glycine, another amino acid  
+
+activates ligand-gated chloride channels.   
+
+So, glutamate,  one amino acid activates sodium  
+
+channels.  Sodium rushes in.  Glycine activates chloride channels.   
+
+What will chloride do?  It can come in.   
+
+What will it do when it comes in?  Negative.  Oh, my goodness.  So,   
+
+when glycine is spritz on the post-synaptic cell chloride comes in  
+
+and the cell becomes locally more negative.  These are called  
+
+inhibitory synapses.    
+
+By contrast those that admit positive ions excitatory synapses.   
+
+ Neurons can have both inhibitory and  
+
+excitatory synapses on their dendrites.  So,   
+
+the postsynaptic cell will be receiving positive signals,   
+
+positive ions coming in from excitatory synapse and negative  
+
+signals, inhibitory signals with negative ions coming in.   
+
+The integration of charge in the dendritic arbor is an integration  
+
+problem of the timing,  number, geometry and sign,   
+
+positive or negative, of these activation signals.   
+
+That's what's going on.  And what happens is the neuron  
+
+integrates these signals,  positive and negative.  So,   
+
+we'll make this one a glycine neuron,  negative, negative, negative.   
+
+All that integration takes place right over here in the region of the  
+
+cell called the axon hillock,  which is the first place that the  
+
+action potential mechanism is found.  And, of course, that integration is  
+
+nothing more and nothing less than figuring out whether the membrane  
+
+potential gets above minus 50.  If it gets above minus 50 it fires.   
+
+OK?  Yes?    
+
+Does the nucleus participate in the,  in what way would the nucleus  
+
+participate?    
+
+It's an interesting question.  I mean the nucleus does, in a sense.   
+
+The geometry of that cell body there has some effect on the  
+
+electrical properties and all that,  but if you think about the  
+
+timescales.  How often do neurons fire?  At a frequency often of about  
+
+a millisecond.  So, that means everything I've just  
+
+old you, this complex integration problem is occurring within  
+
+a millisecond.  The processes in the nucleus that I  
+
+think about typically of transcription and translation and  
+
+all that are operating several orders of magnitude more slowly than  
+
+that.  You know,  they'll operate, even in the best of  
+
+circumstances,  at seconds, and often at more than  
+
+that, minutes before you could get transcription and translation and  
+
+stuff like that going.  So, the nucleus, I think,   
+
+for the most part, better get its act together by producing stuff and  
+
+getting it out to the periphery,  but probably through the expression  
+
+of the genome can't do much in a relevant millisecond or so.   
+
+But I wouldn't be shocked if some neurobiologist knows better than I  
+
+do that nucleoli do something.  I mean there are many cleaver  
+
+things that are going on.  I'm sure a cell has wasted anything,   
+
+but with respect to the operations we've talked about probably not.   
+
+OK?  But I'm always reluctant to say something never happens in any  
+
+possible way.  All right.  So, now how does all this get stuck  
+
+together?  Well, not only do we have this  
+
+complex integration within the dendritic arbor but,   
+
+of course, the neurons are stuck together into circuits themselves.   
+
+If we had more time I would draw the circuit that you use to  
+
+integrate complex functions in calculus, but not having much time  
+
+I'm going to just go for a much simpler circuit here.   
+
+I'm just going to go back to nerves and muscles.  And here we go.   
+
+Suppose I tap right here below your knee.  What happens?   
+
+There's a reflex.  Let's at least get that going,   
+
+OK?  What happens is when I tap there above your patella,   
+
+here's your kneecap here, there's a sensory neuron.   
+
+The sensory neuron brings out a signal and it goes into the  
+
+spinal column here.  This is a reflex.   
+
+It doesn't need to go up to your brain. You don't need to think a lot  
+
+about it.  And it goes into the spinal column here into the dorsal  
+
+root ganglia.  This is a cross-section.   
+
+The, sorry, sensory neuron comes in here.  And what it does is that  
+
+sensory neuron makes a synapse,  and actually another synapse, and it  
+
+makes a synapse on a motor neuron.  The motor neuron comes back and  
+
+synapses on that very muscle.  It is the simplest possible circuit.   
+
+I sense, I send one sensory signal up into the spinal cord,   
+
+there's an excitatory positive synapse onto a motor neuron,   
+
+this motor neuron fires and contracts my muscle so I go back.   
+
+At the same time,  this guy makes another synapse,   
+
+a positive excitatory synapse on a little cell that is an interneuron,   
+
+that's an intermediate neuron.  That intermediate neuron makes a synapse  
+
+on a second motor neuron,  but this is an inhibitory synapse.   
+
+ That motor neuron sends its process  
+
+out and is affecting the opposite muscle.  So now what happens?   
+
+Let's get this straight.  I hit over here.   
+
+And the signal goes back to my spinal cord.  The sensory neuron  
+
+causes one motor neuron,  directly by firing on it,   
+
+to contract.  It causes an interneuron to fire that inhibits  
+
+the opposite motor neuron.  What happens if you inhibit the  
+
+opposite motor neuron?  You relax the contraction,   
+
+or you at least don't contract the opposite muscle.   
+
+So, what happens is you send a positive signal to the muscle on one  
+
+side and you inhibit the signal to the muscle on the other side.   
+
+It's a very simple circuit.  It's got one sensory neuron.   
+
+Two motor neurons.  One interneuron.  It's got two positive excitatory  
+
+synapses.  It's got one negative inhibitory synapse.   
+
+That's about it.  Presumably,  everything else that goes on in  
+
+daily life is basically the same thing.  This is probably what eating  
+
+lunch is like,  falling in love is like and things  
+
+like that, although the details remain to be worked out for exactly  
+
+how that stuff works.  There is a large collection of,   
+
+I give you the simple examples because obviously we don't know a  
+
+lot of the complex examples.  There is a lot more to this.   
+
+If had time in the course we could go into what's known about more  
+
+circuits.  I joke.  We know about the circuits that  
+
+help you see vision,  that allow you to pick up signals in  
+
+your retina, transmit them back and reconstruct things with positive and  
+
+negative signals that allow you to see a straight line,   
+
+for example, and recognize a straight line.   
+
+And there are patterns of cells that send positive signals and negative  
+
+signals, and when you integrate them you can get a signal if and only if  
+
+there's a straight line at this angle in your visual field.   
+
+And people know about that kind of stuff, but some of the more complex  
+
+stuff we don't know about.  There are lots and lots of  
+
+neurotransmitters,  glutamate, glycine,   
+
+histamine, serotonin.  ATP can be a neurotransmitter.   
+
+Adenosine can be a neurotransmitter.  There are peptide neurotransmitters.   
+
+Endorphins, oxytocins and even gases.  Nitrous oxide is a neurotransmitter.   
+
+And then some of the drugs you may know work by affecting these  
+
+neurotransmitters.  Prozac and the general class of  
+
+selective serotonin reuptake inhibitors.  Prozac effects a  
+
+specific process with a neurotransmitter.   
+
+There's a neurotransmitter serotonin.  After it's fired out,   
+
+instead of acetylcholesterase being in the synapse destroying it or some  
+
+other enzyme destroying it,  it's taken back up by the cells.   
+
+If you could inhibit the process by which you take up your serotonin  
+
+again, the serotonin would last longer in your synapse and you would  
+
+be happier, give or take,  roughly speaking to the extent that  
+
+more serotonin is a good thing.  And that's what Prozac does.   
+
+Actually, it's one of the things Prozac does.  There's good evidence  
+
+now that Prozac does other things,  too, including causing neuronal cell  
+
+growth, but that's a whole other story.   
+
+There are things like cocaine.  Cocaine is a bad thing because it  
+
+inhibits certain sodium transporters and other things.   
+
+And if you go through all of the different psychoactive drugs they're  
+
+affecting different parts of these processes.  So,   
+
+for Friday I've invited a colleague who is a real neurobiologist,   
+
+I'm not a card-carrying neurobiologist,   
+
+to talk about some of the more far out things of learning and memory.   
+
+Andy Chess who's a good friend and a colleague is going to talk about  
+
+learning and memory.  And then have a good time with him,   
+
+and I'll see you subsequently.
\ No newline at end of file
diff --git a/sKYY6o71iNM.txt b/sKYY6o71iNM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb9239b2ad0b58e4fce9228e92b037d25d282a2c
--- /dev/null
+++ b/sKYY6o71iNM.txt
@@ -0,0 +1,595 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+In this week's discussion of video,
+
+ align:start position:0%
+In this week's discussion of video,
+ 
+
+ align:start position:0%
+In this week's discussion of video,
+we're going to show you some interesting
+
+ align:start position:0%
+we're going to show you some interesting
+ 
+
+ align:start position:0%
+we're going to show you some interesting
+examples of other people's work. Now,
+
+ align:start position:0%
+examples of other people's work. Now,
+ 
+
+ align:start position:0%
+examples of other people's work. Now,
+remember that the basics of still
+
+ align:start position:0%
+remember that the basics of still
+ 
+
+ align:start position:0%
+remember that the basics of still
+photography that you've just learned all
+
+ align:start position:0%
+photography that you've just learned all
+ 
+
+ align:start position:0%
+photography that you've just learned all
+these previous weeks apply to making
+
+ align:start position:0%
+these previous weeks apply to making
+ 
+
+ align:start position:0%
+these previous weeks apply to making
+successful videos. For starters, we are
+
+ align:start position:0%
+successful videos. For starters, we are
+ 
+
+ align:start position:0%
+successful videos. For starters, we are
+incredibly lucky to be able to show you
+
+ align:start position:0%
+incredibly lucky to be able to show you
+ 
+
+ align:start position:0%
+incredibly lucky to be able to show you
+some remarkable videos from a project
+
+ align:start position:0%
+some remarkable videos from a project
+ 
+
+ align:start position:0%
+some remarkable videos from a project
+called Beautiful
+
+ align:start position:0%
+called Beautiful
+ 
+
+ align:start position:0%
+called Beautiful
+Chemistry. Here's the website with full
+
+ align:start position:0%
+Chemistry. Here's the website with full
+ 
+
+ align:start position:0%
+Chemistry. Here's the website with full
+credit. Now, I encourage you to see them
+
+ align:start position:0%
+credit. Now, I encourage you to see them
+ 
+
+ align:start position:0%
+credit. Now, I encourage you to see them
+all. I am quite sure they will inspire
+
+ align:start position:0%
+all. I am quite sure they will inspire
+ 
+
+ align:start position:0%
+all. I am quite sure they will inspire
+you to come up with your own amazing
+
+ align:start position:0%
+you to come up with your own amazing
+ 
+
+ align:start position:0%
+you to come up with your own amazing
+videos if your work requires video
+
+ align:start position:0%
+videos if your work requires video
+ 
+
+ align:start position:0%
+videos if your work requires video
+capturing macrolevel phenomena.
+
+ align:start position:0%
+capturing macrolevel phenomena.
+ 
+
+ align:start position:0%
+capturing macrolevel phenomena.
+Scientist Yan Leang, a collaborator of
+
+ align:start position:0%
+Scientist Yan Leang, a collaborator of
+ 
+
+ align:start position:0%
+Scientist Yan Leang, a collaborator of
+mine, is the creator and director of the
+
+ align:start position:0%
+mine, is the creator and director of the
+ 
+
+ align:start position:0%
+mine, is the creator and director of the
+project. We asked him to tell us a
+
+ align:start position:0%
+project. We asked him to tell us a
+ 
+
+ align:start position:0%
+project. We asked him to tell us a
+little about his techniques for three of
+
+ align:start position:0%
+little about his techniques for three of
+ 
+
+ align:start position:0%
+little about his techniques for three of
+the videos. Welcome Leang to our class.
+
+ align:start position:0%
+the videos. Welcome Leang to our class.
+ 
+
+ align:start position:0%
+the videos. Welcome Leang to our class.
+Thank you. It's wonderful being part of
+
+ align:start position:0%
+Thank you. It's wonderful being part of
+ 
+
+ align:start position:0%
+Thank you. It's wonderful being part of
+this course. I'll be happy to talk about
+
+ align:start position:0%
+this course. I'll be happy to talk about
+ 
+
+ align:start position:0%
+this course. I'll be happy to talk about
+how we capture three particular
+
+ align:start position:0%
+how we capture three particular
+ 
+
+ align:start position:0%
+how we capture three particular
+phenomena. In this segment, we are
+
+ align:start position:0%
+phenomena. In this segment, we are
+ 
+
+ align:start position:0%
+phenomena. In this segment, we are
+showing metal displacement reactions. We
+
+ align:start position:0%
+showing metal displacement reactions. We
+ 
+
+ align:start position:0%
+showing metal displacement reactions. We
+dropped zinc metal into different
+
+ align:start position:0%
+dropped zinc metal into different
+ 
+
+ align:start position:0%
+dropped zinc metal into different
+solutions and recorded the emergence of
+
+ align:start position:0%
+solutions and recorded the emergence of
+ 
+
+ align:start position:0%
+solutions and recorded the emergence of
+beautiful structures of other metals
+
+ align:start position:0%
+beautiful structures of other metals
+ 
+
+ align:start position:0%
+beautiful structures of other metals
+such as silver and
+
+ align:start position:0%
+such as silver and
+ 
+
+ align:start position:0%
+such as silver and
+lead. All the reactions were shot in
+
+ align:start position:0%
+lead. All the reactions were shot in
+ 
+
+ align:start position:0%
+lead. All the reactions were shot in
+real time and we sped them up during
+
+ align:start position:0%
+real time and we sped them up during
+ 
+
+ align:start position:0%
+real time and we sped them up during
+editing in Final Cut Pro X. For example,
+
+ align:start position:0%
+editing in Final Cut Pro X. For example,
+ 
+
+ align:start position:0%
+editing in Final Cut Pro X. For example,
+one shot of silver displacement was sped
+
+ align:start position:0%
+one shot of silver displacement was sped
+ 
+
+ align:start position:0%
+one shot of silver displacement was sped
+up 60 times, which means 1 second of our
+
+ align:start position:0%
+up 60 times, which means 1 second of our
+ 
+
+ align:start position:0%
+up 60 times, which means 1 second of our
+video is 1 minute in real time. For
+
+ align:start position:0%
+video is 1 minute in real time. For
+ 
+
+ align:start position:0%
+video is 1 minute in real time. For
+light setup, we use two large LED panels
+
+ align:start position:0%
+light setup, we use two large LED panels
+ 
+
+ align:start position:0%
+light setup, we use two large LED panels
+to light a cubic glass container in
+
+ align:start position:0%
+to light a cubic glass container in
+ 
+
+ align:start position:0%
+to light a cubic glass container in
+which the reactions occurred. Typically,
+
+ align:start position:0%
+which the reactions occurred. Typically,
+ 
+
+ align:start position:0%
+which the reactions occurred. Typically,
+a black clothes or a white plastic board
+
+ align:start position:0%
+a black clothes or a white plastic board
+ 
+
+ align:start position:0%
+a black clothes or a white plastic board
+was placed about 1 ft behind the
+
+ align:start position:0%
+was placed about 1 ft behind the
+ 
+
+ align:start position:0%
+was placed about 1 ft behind the
+container as black or white background.
+
+ align:start position:0%
+container as black or white background.
+ 
+
+ align:start position:0%
+container as black or white background.
+We shot reactions in the front with a
+
+ align:start position:0%
+We shot reactions in the front with a
+ 
+
+ align:start position:0%
+We shot reactions in the front with a
+Panasonic GH4 camera and a 100 mm micro
+
+ align:start position:0%
+Panasonic GH4 camera and a 100 mm micro
+ 
+
+ align:start position:0%
+Panasonic GH4 camera and a 100 mm micro
+lens. Older reactions were shot in a
+
+ align:start position:0%
+lens. Older reactions were shot in a
+ 
+
+ align:start position:0%
+lens. Older reactions were shot in a
+normal lab with fluorescent lights.
+
+ align:start position:0%
+normal lab with fluorescent lights.
+ 
+
+ align:start position:0%
+normal lab with fluorescent lights.
+Because the LED panels were so much
+
+ align:start position:0%
+Because the LED panels were so much
+ 
+
+ align:start position:0%
+Because the LED panels were so much
+brighter than the fluorescent lights, we
+
+ align:start position:0%
+brighter than the fluorescent lights, we
+ 
+
+ align:start position:0%
+brighter than the fluorescent lights, we
+typically left them
+
+ align:start position:0%
+typically left them
+ 
+
+ align:start position:0%
+typically left them
+on. In this segment, we are showing a
+
+ align:start position:0%
+on. In this segment, we are showing a
+ 
+
+ align:start position:0%
+on. In this segment, we are showing a
+few crystallization processes, including
+
+ align:start position:0%
+few crystallization processes, including
+ 
+
+ align:start position:0%
+few crystallization processes, including
+crystallization of copper sulfate,
+
+ align:start position:0%
+crystallization of copper sulfate,
+ 
+
+ align:start position:0%
+crystallization of copper sulfate,
+sodium cell sulfate, and two more. We
+
+ align:start position:0%
+sodium cell sulfate, and two more. We
+ 
+
+ align:start position:0%
+sodium cell sulfate, and two more. We
+chose crystallization processes that are
+
+ align:start position:0%
+chose crystallization processes that are
+ 
+
+ align:start position:0%
+chose crystallization processes that are
+fast enough so that we could suit in
+
+ align:start position:0%
+fast enough so that we could suit in
+ 
+
+ align:start position:0%
+fast enough so that we could suit in
+real time and speed them up in editing.
+
+ align:start position:0%
+real time and speed them up in editing.
+ 
+
+ align:start position:0%
+real time and speed them up in editing.
+We did not select crystallization
+
+ align:start position:0%
+We did not select crystallization
+ 
+
+ align:start position:0%
+We did not select crystallization
+process that could take hours or days to
+
+ align:start position:0%
+process that could take hours or days to
+ 
+
+ align:start position:0%
+process that could take hours or days to
+form large crystals. For those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+templating and exposure have to be
+
+ align:start position:0%
+templating and exposure have to be
+ 
+
+ align:start position:0%
+templating and exposure have to be
+carefully controlled to avoid flicker in
+
+ align:start position:0%
+carefully controlled to avoid flicker in
+ 
+
+ align:start position:0%
+carefully controlled to avoid flicker in
+the final video.
+
+ align:start position:0%
+the final video.
+ 
+
+ align:start position:0%
+the final video.
+Finally, in this segment, we are showing
+
+ align:start position:0%
+Finally, in this segment, we are showing
+ 
+
+ align:start position:0%
+Finally, in this segment, we are showing
+a few bubbling reactions such as zinc
+
+ align:start position:0%
+a few bubbling reactions such as zinc
+ 
+
+ align:start position:0%
+a few bubbling reactions such as zinc
+metal reacts with hydrochloric acid to
+
+ align:start position:0%
+metal reacts with hydrochloric acid to
+ 
+
+ align:start position:0%
+metal reacts with hydrochloric acid to
+form hydrogen bubbles. These reactions
+
+ align:start position:0%
+form hydrogen bubbles. These reactions
+ 
+
+ align:start position:0%
+form hydrogen bubbles. These reactions
+were fast and usually we did not speed
+
+ align:start position:0%
+were fast and usually we did not speed
+ 
+
+ align:start position:0%
+were fast and usually we did not speed
+them up in
+
+ align:start position:0%
+them up in
+ 
+
+ align:start position:0%
+them up in
+editing. Overlet setup work well for
+
+ align:start position:0%
+editing. Overlet setup work well for
+ 
+
+ align:start position:0%
+editing. Overlet setup work well for
+bubbles. The white highlights on the
+
+ align:start position:0%
+bubbles. The white highlights on the
+ 
+
+ align:start position:0%
+bubbles. The white highlights on the
+right and left side of the bubbles are
+
+ align:start position:0%
+right and left side of the bubbles are
+ 
+
+ align:start position:0%
+right and left side of the bubbles are
+the reflection of the two LED panels.
+
+ align:start position:0%
+the reflection of the two LED panels.
+ 
+
+ align:start position:0%
+the reflection of the two LED panels.
+These highlights gave bubbles a very
+
+ align:start position:0%
+These highlights gave bubbles a very
+ 
+
+ align:start position:0%
+These highlights gave bubbles a very
+interesting look.
\ No newline at end of file
diff --git a/spY5kl_EYDU.txt b/spY5kl_EYDU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d65b7613a0a02f3bb4b5908131b55d42d315ed59
--- /dev/null
+++ b/spY5kl_EYDU.txt
@@ -0,0 +1,9099 @@
+align:start position:0%
+ 
+the main topic in this part is really
+
+ align:start position:0%
+the main topic in this part is really
+ 
+
+ align:start position:0%
+the main topic in this part is really
+open economy and uh so we extended the
+
+ align:start position:0%
+open economy and uh so we extended the
+ 
+
+ align:start position:0%
+open economy and uh so we extended the
+eslm mo uh we did not bring in we we
+
+ align:start position:0%
+eslm mo uh we did not bring in we we
+ 
+
+ align:start position:0%
+eslm mo uh we did not bring in we we
+again shut down price changes so we said
+
+ align:start position:0%
+again shut down price changes so we said
+ 
+
+ align:start position:0%
+again shut down price changes so we said
+uh pric is completely fixed no Philips
+
+ align:start position:0%
+uh pric is completely fixed no Philips
+ 
+
+ align:start position:0%
+uh pric is completely fixed no Philips
+curve here so we expanded the eslm model
+
+ align:start position:0%
+curve here so we expanded the eslm model
+ 
+
+ align:start position:0%
+curve here so we expanded the eslm model
+to add this open E economy Dimension and
+
+ align:start position:0%
+to add this open E economy Dimension and
+ 
+
+ align:start position:0%
+to add this open E economy Dimension and
+so we start from the same aggregate
+
+ align:start position:0%
+so we start from the same aggregate
+ 
+
+ align:start position:0%
+so we start from the same aggregate
+demand function that we had in close
+
+ align:start position:0%
+demand function that we had in close
+ 
+
+ align:start position:0%
+demand function that we had in close
+economy consumption plus investment plus
+
+ align:start position:0%
+economy consumption plus investment plus
+ 
+
+ align:start position:0%
+economy consumption plus investment plus
+government expenditure but now we have
+
+ align:start position:0%
+government expenditure but now we have
+ 
+
+ align:start position:0%
+government expenditure but now we have
+to draw a distinction between Demand by
+
+ align:start position:0%
+to draw a distinction between Demand by
+ 
+
+ align:start position:0%
+to draw a distinction between Demand by
+domestic households companies and the
+
+ align:start position:0%
+domestic households companies and the
+ 
+
+ align:start position:0%
+domestic households companies and the
+government and the demand for
+
+ align:start position:0%
+government and the demand for
+ 
+
+ align:start position:0%
+government and the demand for
+domestically produced goods and so Z is
+
+ align:start position:0%
+domestically produced goods and so Z is
+ 
+
+ align:start position:0%
+domestically produced goods and so Z is
+the demand domestically produced Goods
+
+ align:start position:0%
+the demand domestically produced Goods
+ 
+
+ align:start position:0%
+the demand domestically produced Goods
+which is equal to demand plus the demand
+
+ align:start position:0%
+which is equal to demand plus the demand
+ 
+
+ align:start position:0%
+which is equal to demand plus the demand
+that foreigners have for the goods
+
+ align:start position:0%
+that foreigners have for the goods
+ 
+
+ align:start position:0%
+that foreigners have for the goods
+produces at home minus the Imports that
+
+ align:start position:0%
+produces at home minus the Imports that
+ 
+
+ align:start position:0%
+produces at home minus the Imports that
+part of that expenditure that is going
+
+ align:start position:0%
+part of that expenditure that is going
+ 
+
+ align:start position:0%
+part of that expenditure that is going
+to Imports that means Goods produced by
+
+ align:start position:0%
+to Imports that means Goods produced by
+ 
+
+ align:start position:0%
+to Imports that means Goods produced by
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+countries um so the new behavioral
+
+ align:start position:0%
+countries um so the new behavioral
+ 
+
+ align:start position:0%
+countries um so the new behavioral
+functions here where the export function
+
+ align:start position:0%
+functions here where the export function
+ 
+
+ align:start position:0%
+functions here where the export function
+and the import function uh export is
+
+ align:start position:0%
+and the import function uh export is
+ 
+
+ align:start position:0%
+and the import function uh export is
+increasing in foreign output more income
+
+ align:start position:0%
+increasing in foreign output more income
+ 
+
+ align:start position:0%
+increasing in foreign output more income
+abroad will lead to more Imports by them
+
+ align:start position:0%
+abroad will lead to more Imports by them
+ 
+
+ align:start position:0%
+abroad will lead to more Imports by them
+which means more export for home home
+
+ align:start position:0%
+which means more export for home home
+ 
+
+ align:start position:0%
+which means more export for home home
+and the it's decreasing on with respect
+
+ align:start position:0%
+and the it's decreasing on with respect
+ 
+
+ align:start position:0%
+and the it's decreasing on with respect
+to the exchange rate real exchange rate
+
+ align:start position:0%
+to the exchange rate real exchange rate
+ 
+
+ align:start position:0%
+to the exchange rate real exchange rate
+and nominal exchange rate will be the
+
+ align:start position:0%
+and nominal exchange rate will be the
+ 
+
+ align:start position:0%
+and nominal exchange rate will be the
+same here since we have fully sticky
+
+ align:start position:0%
+same here since we have fully sticky
+ 
+
+ align:start position:0%
+same here since we have fully sticky
+prices but
+
+ align:start position:0%
+prices but
+ 
+
+ align:start position:0%
+prices but
+H if if the real exchange it appreciat
+
+ align:start position:0%
+H if if the real exchange it appreciat
+ 
+
+ align:start position:0%
+H if if the real exchange it appreciat
+that means domestic goods are more
+
+ align:start position:0%
+that means domestic goods are more
+ 
+
+ align:start position:0%
+that means domestic goods are more
+expensive it means exports are less
+
+ align:start position:0%
+expensive it means exports are less
+ 
+
+ align:start position:0%
+expensive it means exports are less
+foreigners are going to buy less of our
+
+ align:start position:0%
+foreigners are going to buy less of our
+ 
+
+ align:start position:0%
+foreigners are going to buy less of our
+Goods conversely for imports is like the
+
+ align:start position:0%
+Goods conversely for imports is like the
+ 
+
+ align:start position:0%
+Goods conversely for imports is like the
+exports of the other country means that
+
+ align:start position:0%
+exports of the other country means that
+ 
+
+ align:start position:0%
+exports of the other country means that
+if domestic output goes up then then
+
+ align:start position:0%
+if domestic output goes up then then
+ 
+
+ align:start position:0%
+if domestic output goes up then then
+there will be more purchases of foreign
+
+ align:start position:0%
+there will be more purchases of foreign
+ 
+
+ align:start position:0%
+there will be more purchases of foreign
+foreign er er goods and if the exchange
+
+ align:start position:0%
+foreign er er goods and if the exchange
+ 
+
+ align:start position:0%
+foreign er er goods and if the exchange
+is appreciate means also that foreign
+
+ align:start position:0%
+is appreciate means also that foreign
+ 
+
+ align:start position:0%
+is appreciate means also that foreign
+goods are cheaper for us and therefore
+
+ align:start position:0%
+goods are cheaper for us and therefore
+ 
+
+ align:start position:0%
+goods are cheaper for us and therefore
+we import more okay so positive so those
+
+ align:start position:0%
+we import more okay so positive so those
+ 
+
+ align:start position:0%
+we import more okay so positive so those
+were those were the two new behavioral
+
+ align:start position:0%
+were those were the two new behavioral
+ 
+
+ align:start position:0%
+were those were the two new behavioral
+functions in the in the Goods Market
+
+ align:start position:0%
+functions in the in the Goods Market
+ 
+
+ align:start position:0%
+functions in the in the Goods Market
+expanded to include an open economy and
+
+ align:start position:0%
+expanded to include an open economy and
+ 
+
+ align:start position:0%
+expanded to include an open economy and
+that had implications for the diagram
+
+ align:start position:0%
+that had implications for the diagram
+ 
+
+ align:start position:0%
+that had implications for the diagram
+that we had in lecture three or so to
+
+ align:start position:0%
+that we had in lecture three or so to
+ 
+
+ align:start position:0%
+that we had in lecture three or so to
+determine equilibrium output ER you know
+
+ align:start position:0%
+determine equilibrium output ER you know
+ 
+
+ align:start position:0%
+determine equilibrium output ER you know
+we started from the same demand we had
+
+ align:start position:0%
+we started from the same demand we had
+ 
+
+ align:start position:0%
+we started from the same demand we had
+in close economy then we had to subtract
+
+ align:start position:0%
+in close economy then we had to subtract
+ 
+
+ align:start position:0%
+in close economy then we had to subtract
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+in import and uh and that is shift
+
+ align:start position:0%
+in import and uh and that is shift
+ 
+
+ align:start position:0%
+in import and uh and that is shift
+things down because we are now as part
+
+ align:start position:0%
+things down because we are now as part
+ 
+
+ align:start position:0%
+things down because we are now as part
+of the domestic demand that is going to
+
+ align:start position:0%
+of the domestic demand that is going to
+ 
+
+ align:start position:0%
+of the domestic demand that is going to
+foreign Goods not to domestic Goods but
+
+ align:start position:0%
+foreign Goods not to domestic Goods but
+ 
+
+ align:start position:0%
+foreign Goods not to domestic Goods but
+ER it's also rotates a curve because the
+
+ align:start position:0%
+ER it's also rotates a curve because the
+ 
+
+ align:start position:0%
+ER it's also rotates a curve because the
+higher is domestic income the more are
+
+ align:start position:0%
+higher is domestic income the more are
+ 
+
+ align:start position:0%
+higher is domestic income the more are
+the Imports uh that we do from the rest
+
+ align:start position:0%
+the Imports uh that we do from the rest
+ 
+
+ align:start position:0%
+the Imports uh that we do from the rest
+of the world now to that we have to add
+
+ align:start position:0%
+of the world now to that we have to add
+ 
+
+ align:start position:0%
+of the world now to that we have to add
+the export which are not a function of
+
+ align:start position:0%
+the export which are not a function of
+ 
+
+ align:start position:0%
+the export which are not a function of
+domestic output that's that's a parallel
+
+ align:start position:0%
+domestic output that's that's a parallel
+ 
+
+ align:start position:0%
+domestic output that's that's a parallel
+shift with respect to this curve no we
+
+ align:start position:0%
+shift with respect to this curve no we
+ 
+
+ align:start position:0%
+shift with respect to this curve no we
+go up up and and that gives us the ZZ
+
+ align:start position:0%
+go up up and and that gives us the ZZ
+ 
+
+ align:start position:0%
+go up up and and that gives us the ZZ
+curve which is what we call the demand
+
+ align:start position:0%
+curve which is what we call the demand
+ 
+
+ align:start position:0%
+curve which is what we call the demand
+for domestic Le domestically produced
+
+ align:start position:0%
+for domestic Le domestically produced
+ 
+
+ align:start position:0%
+for domestic Le domestically produced
+Goods now notice that the distance
+
+ align:start position:0%
+Goods now notice that the distance
+ 
+
+ align:start position:0%
+Goods now notice that the distance
+between the demand for domestically
+
+ align:start position:0%
+between the demand for domestically
+ 
+
+ align:start position:0%
+between the demand for domestically
+produced goods and the domestic demand
+
+ align:start position:0%
+produced goods and the domestic demand
+ 
+
+ align:start position:0%
+produced goods and the domestic demand
+for goods is what is the net export so
+
+ align:start position:0%
+for goods is what is the net export so
+ 
+
+ align:start position:0%
+for goods is what is the net export so
+the distance between z z and the D is
+
+ align:start position:0%
+the distance between z z and the D is
+ 
+
+ align:start position:0%
+the distance between z z and the D is
+the net export so in this point here for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example ZZ is higher than DD which means
+
+ align:start position:0%
+example ZZ is higher than DD which means
+ 
+
+ align:start position:0%
+example ZZ is higher than DD which means
+that our exports are greater than our
+
+ align:start position:0%
+that our exports are greater than our
+ 
+
+ align:start position:0%
+that our exports are greater than our
+Imports and that's the reason you have a
+
+ align:start position:0%
+Imports and that's the reason you have a
+ 
+
+ align:start position:0%
+Imports and that's the reason you have a
+trade surplus at this point they're the
+
+ align:start position:0%
+trade surplus at this point they're the
+ 
+
+ align:start position:0%
+trade surplus at this point they're the
+same and that's the reason the trade
+
+ align:start position:0%
+same and that's the reason the trade
+ 
+
+ align:start position:0%
+same and that's the reason the trade
+account is balance and but over here
+
+ align:start position:0%
+account is balance and but over here
+ 
+
+ align:start position:0%
+account is balance and but over here
+Imports exceed exports and that's the
+
+ align:start position:0%
+Imports exceed exports and that's the
+ 
+
+ align:start position:0%
+Imports exceed exports and that's the
+reason we have a trade deficit
+
+ align:start position:0%
+reason we have a trade deficit
+ 
+
+ align:start position:0%
+reason we have a trade deficit
+okay I'm going to go very quickly so you
+
+ align:start position:0%
+okay I'm going to go very quickly so you
+ 
+
+ align:start position:0%
+okay I'm going to go very quickly so you
+you're in charge of stopping me I'm not
+
+ align:start position:0%
+you're in charge of stopping me I'm not
+ 
+
+ align:start position:0%
+you're in charge of stopping me I'm not
+going to ask you question just stop me
+
+ align:start position:0%
+going to ask you question just stop me
+ 
+
+ align:start position:0%
+going to ask you question just stop me
+if there's something that you need
+
+ align:start position:0%
+if there's something that you need
+ 
+
+ align:start position:0%
+if there's something that you need
+clarifications okay for so that's what
+
+ align:start position:0%
+clarifications okay for so that's what
+ 
+
+ align:start position:0%
+clarifications okay for so that's what
+the demand for domestically produced
+
+ align:start position:0%
+the demand for domestically produced
+ 
+
+ align:start position:0%
+the demand for domestically produced
+Goods now we're going to determine
+
+ align:start position:0%
+Goods now we're going to determine
+ 
+
+ align:start position:0%
+Goods now we're going to determine
+equilibrium output in this open e e omic
+
+ align:start position:0%
+equilibrium output in this open e e omic
+ 
+
+ align:start position:0%
+equilibrium output in this open e e omic
+context and that means you know
+
+ align:start position:0%
+context and that means you know
+ 
+
+ align:start position:0%
+context and that means you know
+aggregate demand has to be equal
+
+ align:start position:0%
+aggregate demand has to be equal
+ 
+
+ align:start position:0%
+aggregate demand has to be equal
+aggregate demand for domestically
+
+ align:start position:0%
+aggregate demand for domestically
+ 
+
+ align:start position:0%
+aggregate demand for domestically
+produced good has to be equal to output
+
+ align:start position:0%
+produced good has to be equal to output
+ 
+
+ align:start position:0%
+produced good has to be equal to output
+and that's what we do with the 45 degree
+
+ align:start position:0%
+and that's what we do with the 45 degree
+ 
+
+ align:start position:0%
+and that's what we do with the 45 degree
+line here and so where the 45 degree
+
+ align:start position:0%
+line here and so where the 45 degree
+ 
+
+ align:start position:0%
+line here and so where the 45 degree
+line intersect with this ZZ curve that's
+
+ align:start position:0%
+line intersect with this ZZ curve that's
+ 
+
+ align:start position:0%
+line intersect with this ZZ curve that's
+our equilibrium output now it happens
+
+ align:start position:0%
+our equilibrium output now it happens
+ 
+
+ align:start position:0%
+our equilibrium output now it happens
+that in this example that leads to a
+
+ align:start position:0%
+that in this example that leads to a
+ 
+
+ align:start position:0%
+that in this example that leads to a
+trade deficit but there's nothing here
+
+ align:start position:0%
+trade deficit but there's nothing here
+ 
+
+ align:start position:0%
+trade deficit but there's nothing here
+so we still determine equili output up
+
+ align:start position:0%
+so we still determine equili output up
+ 
+
+ align:start position:0%
+so we still determine equili output up
+here and then we read in this curve
+
+ align:start position:0%
+here and then we read in this curve
+ 
+
+ align:start position:0%
+here and then we read in this curve
+bottom curve what is implication for the
+
+ align:start position:0%
+bottom curve what is implication for the
+ 
+
+ align:start position:0%
+bottom curve what is implication for the
+traes deficit or Surplus
+
+ align:start position:0%
+traes deficit or Surplus
+ 
+
+ align:start position:0%
+traes deficit or Surplus
+okay H but the equilibrium condition
+
+ align:start position:0%
+okay H but the equilibrium condition
+ 
+
+ align:start position:0%
+okay H but the equilibrium condition
+important is that output domestically
+
+ align:start position:0%
+important is that output domestically
+ 
+
+ align:start position:0%
+important is that output domestically
+produc output has to be equal to the
+
+ align:start position:0%
+produc output has to be equal to the
+ 
+
+ align:start position:0%
+produc output has to be equal to the
+demand for domestically produced Goods
+
+ align:start position:0%
+demand for domestically produced Goods
+ 
+
+ align:start position:0%
+demand for domestically produced Goods
+not for total demand it's Dem demand for
+
+ align:start position:0%
+not for total demand it's Dem demand for
+ 
+
+ align:start position:0%
+not for total demand it's Dem demand for
+domestically produced Goods okay because
+
+ align:start position:0%
+domestically produced Goods okay because
+ 
+
+ align:start position:0%
+domestically produced Goods okay because
+this is a can model in which output is
+
+ align:start position:0%
+this is a can model in which output is
+ 
+
+ align:start position:0%
+this is a can model in which output is
+aggregate demand determined but it has
+
+ align:start position:0%
+aggregate demand determined but it has
+ 
+
+ align:start position:0%
+aggregate demand determined but it has
+to be aggregate demand for the things
+
+ align:start position:0%
+to be aggregate demand for the things
+ 
+
+ align:start position:0%
+to be aggregate demand for the things
+you're producing not AG demand for all
+
+ align:start position:0%
+you're producing not AG demand for all
+ 
+
+ align:start position:0%
+you're producing not AG demand for all
+Goods around the world okay good so then
+
+ align:start position:0%
+Goods around the world okay good so then
+ 
+
+ align:start position:0%
+Goods around the world okay good so then
+we did some experiments we said well
+
+ align:start position:0%
+we did some experiments we said well
+ 
+
+ align:start position:0%
+we did some experiments we said well
+suppose what happens in this open
+
+ align:start position:0%
+suppose what happens in this open
+ 
+
+ align:start position:0%
+suppose what happens in this open
+economy context if we increase
+
+ align:start position:0%
+economy context if we increase
+ 
+
+ align:start position:0%
+economy context if we increase
+government expenditure well the curent
+
+ align:start position:0%
+government expenditure well the curent
+ 
+
+ align:start position:0%
+government expenditure well the curent
+will shift up in exactly the same way as
+
+ align:start position:0%
+will shift up in exactly the same way as
+ 
+
+ align:start position:0%
+will shift up in exactly the same way as
+as in the close economy the difference
+
+ align:start position:0%
+as in the close economy the difference
+ 
+
+ align:start position:0%
+as in the close economy the difference
+will be in the multiplier though because
+
+ align:start position:0%
+will be in the multiplier though because
+ 
+
+ align:start position:0%
+will be in the multiplier though because
+as output goes up as a result of the
+
+ align:start position:0%
+as output goes up as a result of the
+ 
+
+ align:start position:0%
+as output goes up as a result of the
+expansionary aggregate demand that also
+
+ align:start position:0%
+expansionary aggregate demand that also
+ 
+
+ align:start position:0%
+expansionary aggregate demand that also
+means that domestic income will go up
+
+ align:start position:0%
+means that domestic income will go up
+ 
+
+ align:start position:0%
+means that domestic income will go up
+and and that means that Imports will go
+
+ align:start position:0%
+and and that means that Imports will go
+ 
+
+ align:start position:0%
+and and that means that Imports will go
+up and that's demand that will go for
+
+ align:start position:0%
+up and that's demand that will go for
+ 
+
+ align:start position:0%
+up and that's demand that will go for
+foreign goods and that's the reason the
+
+ align:start position:0%
+foreign goods and that's the reason the
+ 
+
+ align:start position:0%
+foreign goods and that's the reason the
+z z curve has a lower multiplier it's
+
+ align:start position:0%
+z z curve has a lower multiplier it's
+ 
+
+ align:start position:0%
+z z curve has a lower multiplier it's
+flatter than the DD curve okay still if
+
+ align:start position:0%
+flatter than the DD curve okay still if
+ 
+
+ align:start position:0%
+flatter than the DD curve okay still if
+we start for example with a trade
+
+ align:start position:0%
+we start for example with a trade
+ 
+
+ align:start position:0%
+we start for example with a trade
+balance since Imports are going to
+
+ align:start position:0%
+balance since Imports are going to
+ 
+
+ align:start position:0%
+balance since Imports are going to
+increase as a result of this
+
+ align:start position:0%
+increase as a result of this
+ 
+
+ align:start position:0%
+increase as a result of this
+expansionary fiscal policy we going end
+
+ align:start position:0%
+expansionary fiscal policy we going end
+ 
+
+ align:start position:0%
+expansionary fiscal policy we going end
+up with a trade deficit and that's the
+
+ align:start position:0%
+up with a trade deficit and that's the
+ 
+
+ align:start position:0%
+up with a trade deficit and that's the
+reason the response of output is less
+
+ align:start position:0%
+reason the response of output is less
+ 
+
+ align:start position:0%
+reason the response of output is less
+than close economies because part of
+
+ align:start position:0%
+than close economies because part of
+ 
+
+ align:start position:0%
+than close economies because part of
+that goes to foreign Goods conversely if
+
+ align:start position:0%
+that goes to foreign Goods conversely if
+ 
+
+ align:start position:0%
+that goes to foreign Goods conversely if
+this other country that is doing a
+
+ align:start position:0%
+this other country that is doing a
+ 
+
+ align:start position:0%
+this other country that is doing a
+expansion in fiscal policy or something
+
+ align:start position:0%
+expansion in fiscal policy or something
+ 
+
+ align:start position:0%
+expansion in fiscal policy or something
+that leads to higher output abroad wi
+
+ align:start position:0%
+that leads to higher output abroad wi
+ 
+
+ align:start position:0%
+that leads to higher output abroad wi
+star that's also expansionary for home
+
+ align:start position:0%
+star that's also expansionary for home
+ 
+
+ align:start position:0%
+star that's also expansionary for home
+because exports the export function goes
+
+ align:start position:0%
+because exports the export function goes
+ 
+
+ align:start position:0%
+because exports the export function goes
+up no and that leads to an increase in
+
+ align:start position:0%
+up no and that leads to an increase in
+ 
+
+ align:start position:0%
+up no and that leads to an increase in
+output ER still with lower multiplier
+
+ align:start position:0%
+output ER still with lower multiplier
+ 
+
+ align:start position:0%
+output ER still with lower multiplier
+because part of that increase in
+
+ align:start position:0%
+because part of that increase in
+ 
+
+ align:start position:0%
+because part of that increase in
+domestic output will go will go to
+
+ align:start position:0%
+domestic output will go will go to
+ 
+
+ align:start position:0%
+domestic output will go will go to
+Imports but the in this case unlike the
+
+ align:start position:0%
+Imports but the in this case unlike the
+ 
+
+ align:start position:0%
+Imports but the in this case unlike the
+other ones actually the current the the
+
+ align:start position:0%
+other ones actually the current the the
+ 
+
+ align:start position:0%
+other ones actually the current the the
+trade balance improves because it's been
+
+ align:start position:0%
+trade balance improves because it's been
+ 
+
+ align:start position:0%
+trade balance improves because it's been
+pulled by exports and so we at at impact
+
+ align:start position:0%
+pulled by exports and so we at at impact
+ 
+
+ align:start position:0%
+pulled by exports and so we at at impact
+we get a big increase in export which is
+
+ align:start position:0%
+we get a big increase in export which is
+ 
+
+ align:start position:0%
+we get a big increase in export which is
+the driver of increasable demand for
+
+ align:start position:0%
+the driver of increasable demand for
+ 
+
+ align:start position:0%
+the driver of increasable demand for
+domestically produced Goods and then as
+
+ align:start position:0%
+domestically produced Goods and then as
+ 
+
+ align:start position:0%
+domestically produced Goods and then as
+income goes up we undo some of that but
+
+ align:start position:0%
+income goes up we undo some of that but
+ 
+
+ align:start position:0%
+income goes up we undo some of that but
+you end up with sort of higher high
+
+ align:start position:0%
+you end up with sort of higher high
+ 
+
+ align:start position:0%
+you end up with sort of higher high
+higher better trade deficit better trade
+
+ align:start position:0%
+higher better trade deficit better trade
+ 
+
+ align:start position:0%
+higher better trade deficit better trade
+surpluses than than in the case in which
+
+ align:start position:0%
+surpluses than than in the case in which
+ 
+
+ align:start position:0%
+surpluses than than in the case in which
+you induce the the expansion in agre
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demand uh then the last step there was H
+
+ align:start position:0%
+demand uh then the last step there was H
+ 
+
+ align:start position:0%
+demand uh then the last step there was H
+to look at the role of the exchange rate
+
+ align:start position:0%
+to look at the role of the exchange rate
+ 
+
+ align:start position:0%
+to look at the role of the exchange rate
+and uh where we said is we're going to
+
+ align:start position:0%
+and uh where we said is we're going to
+ 
+
+ align:start position:0%
+and uh where we said is we're going to
+make some assumptions that I promise you
+
+ align:start position:0%
+make some assumptions that I promise you
+ 
+
+ align:start position:0%
+make some assumptions that I promise you
+and and I now read the quiz so I I I I
+
+ align:start position:0%
+and and I now read the quiz so I I I I
+ 
+
+ align:start position:0%
+and and I now read the quiz so I I I I
+guarantee you I honor This Promise H
+
+ align:start position:0%
+guarantee you I honor This Promise H
+ 
+
+ align:start position:0%
+guarantee you I honor This Promise H
+nothing weird will happen meaning if if
+
+ align:start position:0%
+nothing weird will happen meaning if if
+ 
+
+ align:start position:0%
+nothing weird will happen meaning if if
+our Goods gets more expensive that means
+
+ align:start position:0%
+our Goods gets more expensive that means
+ 
+
+ align:start position:0%
+our Goods gets more expensive that means
+that net exports will be worse and and
+
+ align:start position:0%
+that net exports will be worse and and
+ 
+
+ align:start position:0%
+that net exports will be worse and and
+if if H for two reasons for at least for
+
+ align:start position:0%
+if if H for two reasons for at least for
+ 
+
+ align:start position:0%
+if if H for two reasons for at least for
+at least one reason but it could be too
+
+ align:start position:0%
+at least one reason but it could be too
+ 
+
+ align:start position:0%
+at least one reason but it could be too
+if if if the exchange rate goes up then
+
+ align:start position:0%
+if if if the exchange rate goes up then
+ 
+
+ align:start position:0%
+if if if the exchange rate goes up then
+there's going to be less exports at any
+
+ align:start position:0%
+there's going to be less exports at any
+ 
+
+ align:start position:0%
+there's going to be less exports at any
+given level of foreign income that will
+
+ align:start position:0%
+given level of foreign income that will
+ 
+
+ align:start position:0%
+given level of foreign income that will
+worsen the net export and then we were
+
+ align:start position:0%
+worsen the net export and then we were
+ 
+
+ align:start position:0%
+worsen the net export and then we were
+going to tend to import more now that
+
+ align:start position:0%
+going to tend to import more now that
+ 
+
+ align:start position:0%
+going to tend to import more now that
+will be parti should upset for the fact
+
+ align:start position:0%
+will be parti should upset for the fact
+ 
+
+ align:start position:0%
+will be parti should upset for the fact
+that you can buy more with the same
+
+ align:start position:0%
+that you can buy more with the same
+ 
+
+ align:start position:0%
+that you can buy more with the same
+amount of dollars H but we said we're
+
+ align:start position:0%
+amount of dollars H but we said we're
+ 
+
+ align:start position:0%
+amount of dollars H but we said we're
+going to impose conditions such that the
+
+ align:start position:0%
+going to impose conditions such that the
+ 
+
+ align:start position:0%
+going to impose conditions such that the
+positive the negative effect of an
+
+ align:start position:0%
+positive the negative effect of an
+ 
+
+ align:start position:0%
+positive the negative effect of an
+appreciation on that export always
+
+ align:start position:0%
+appreciation on that export always
+ 
+
+ align:start position:0%
+appreciation on that export always
+dominates and again in your quiz you're
+
+ align:start position:0%
+dominates and again in your quiz you're
+ 
+
+ align:start position:0%
+dominates and again in your quiz you're
+going to have a situation like that and
+
+ align:start position:0%
+going to have a situation like that and
+ 
+
+ align:start position:0%
+going to have a situation like that and
+that will be the
+
+ align:start position:0%
+that will be the
+ 
+
+ align:start position:0%
+that will be the
+case so don't think that that we're
+
+ align:start position:0%
+case so don't think that that we're
+ 
+
+ align:start position:0%
+case so don't think that that we're
+trying to trick you anything this will
+
+ align:start position:0%
+trying to trick you anything this will
+ 
+
+ align:start position:0%
+trying to trick you anything this will
+hold okay the the point of this being
+
+ align:start position:0%
+hold okay the the point of this being
+ 
+
+ align:start position:0%
+hold okay the the point of this being
+that you know that that uh
+
+ align:start position:0%
+that you know that that uh
+ 
+
+ align:start position:0%
+that you know that that uh
+depreciating your
+
+ align:start position:0%
+depreciating your
+ 
+
+ align:start position:0%
+depreciating your
+currency you know making your goods less
+
+ align:start position:0%
+currency you know making your goods less
+ 
+
+ align:start position:0%
+currency you know making your goods less
+expensive ER is equivalent to will
+
+ align:start position:0%
+expensive ER is equivalent to will
+ 
+
+ align:start position:0%
+expensive ER is equivalent to will
+produce an a response equivalent to what
+
+ align:start position:0%
+produce an a response equivalent to what
+ 
+
+ align:start position:0%
+produce an a response equivalent to what
+you get here out of an increasing y star
+
+ align:start position:0%
+you get here out of an increasing y star
+ 
+
+ align:start position:0%
+you get here out of an increasing y star
+no because that's export will go
+
+ align:start position:0%
+no because that's export will go
+ 
+
+ align:start position:0%
+no because that's export will go
+up and you're going to get all the shift
+
+ align:start position:0%
+up and you're going to get all the shift
+ 
+
+ align:start position:0%
+up and you're going to get all the shift
+net export function will go up that will
+
+ align:start position:0%
+net export function will go up that will
+ 
+
+ align:start position:0%
+net export function will go up that will
+increase aggregate demand and so on so
+
+ align:start position:0%
+increase aggregate demand and so on so
+ 
+
+ align:start position:0%
+increase aggregate demand and so on so
+that's kind things that countries want
+
+ align:start position:0%
+that's kind things that countries want
+ 
+
+ align:start position:0%
+that's kind things that countries want
+to typically when they're in a recession
+
+ align:start position:0%
+to typically when they're in a recession
+ 
+
+ align:start position:0%
+to typically when they're in a recession
+and so on then that was an introduction
+
+ align:start position:0%
+and so on then that was an introduction
+ 
+
+ align:start position:0%
+and so on then that was an introduction
+to the most important lecture in this
+
+ align:start position:0%
+to the most important lecture in this
+ 
+
+ align:start position:0%
+to the most important lecture in this
+part of
+
+ align:start position:0%
+part of
+ 
+
+ align:start position:0%
+part of
+the course which is the Mandel flaming
+
+ align:start position:0%
+the course which is the Mandel flaming
+ 
+
+ align:start position:0%
+the course which is the Mandel flaming
+model and I I I promise you that you
+
+ align:start position:0%
+model and I I I promise you that you
+ 
+
+ align:start position:0%
+model and I I I promise you that you
+would get 70% at least in the quiz and I
+
+ align:start position:0%
+would get 70% at least in the quiz and I
+ 
+
+ align:start position:0%
+would get 70% at least in the quiz and I
+already read the quiz so I tell you
+
+ align:start position:0%
+already read the quiz so I tell you
+ 
+
+ align:start position:0%
+already read the quiz so I tell you
+there is at least 70% of your points
+
+ align:start position:0%
+there is at least 70% of your points
+ 
+
+ align:start position:0%
+there is at least 70% of your points
+have to do with this model so you better
+
+ align:start position:0%
+have to do with this model so you better
+ 
+
+ align:start position:0%
+have to do with this model so you better
+understand it very well you do every
+
+ align:start position:0%
+understand it very well you do every
+ 
+
+ align:start position:0%
+understand it very well you do every
+single comparative Statics that you can
+
+ align:start position:0%
+single comparative Statics that you can
+ 
+
+ align:start position:0%
+single comparative Statics that you can
+imagine with this Mo and then you'll get
+
+ align:start position:0%
+imagine with this Mo and then you'll get
+ 
+
+ align:start position:0%
+imagine with this Mo and then you'll get
+70% at least I think you get 73 actually
+
+ align:start position:0%
+70% at least I think you get 73 actually
+ 
+
+ align:start position:0%
+70% at least I think you get 73 actually
+but but but that's
+
+ align:start position:0%
+but but but that's
+ 
+
+ align:start position:0%
+but but but that's
+the so what's this well the Mandel
+
+ align:start position:0%
+the so what's this well the Mandel
+ 
+
+ align:start position:0%
+the so what's this well the Mandel
+flaming model is simply what I just
+
+ align:start position:0%
+flaming model is simply what I just
+ 
+
+ align:start position:0%
+flaming model is simply what I just
+showed you is the good market
+
+ align:start position:0%
+showed you is the good market
+ 
+
+ align:start position:0%
+showed you is the good market
+equilibrium no that's the but with an
+
+ align:start position:0%
+equilibrium no that's the but with an
+ 
+
+ align:start position:0%
+equilibrium no that's the but with an
+endogenous exchange rate and uh so we we
+
+ align:start position:0%
+endogenous exchange rate and uh so we we
+ 
+
+ align:start position:0%
+endogenous exchange rate and uh so we we
+rewrote to say since we're assuming
+
+ align:start position:0%
+rewrote to say since we're assuming
+ 
+
+ align:start position:0%
+rewrote to say since we're assuming
+compettive sticky prices we can replace
+
+ align:start position:0%
+compettive sticky prices we can replace
+ 
+
+ align:start position:0%
+compettive sticky prices we can replace
+the real Exchange by the nominal
+
+ align:start position:0%
+the real Exchange by the nominal
+ 
+
+ align:start position:0%
+the real Exchange by the nominal
+exchange rate H but now we're going to
+
+ align:start position:0%
+exchange rate H but now we're going to
+ 
+
+ align:start position:0%
+exchange rate H but now we're going to
+endogenize the exchange rate and and and
+
+ align:start position:0%
+endogenize the exchange rate and and and
+ 
+
+ align:start position:0%
+endogenize the exchange rate and and and
+for that we're going to use the uncover
+
+ align:start position:0%
+for that we're going to use the uncover
+ 
+
+ align:start position:0%
+for that we're going to use the uncover
+in parity condition this a condition you
+
+ align:start position:0%
+in parity condition this a condition you
+ 
+
+ align:start position:0%
+in parity condition this a condition you
+should understand very well as well okay
+
+ align:start position:0%
+should understand very well as well okay
+ 
+
+ align:start position:0%
+should understand very well as well okay
+so that tells you essentially that the
+
+ align:start position:0%
+so that tells you essentially that the
+ 
+
+ align:start position:0%
+so that tells you essentially that the
+expected Return of the two bonds the
+
+ align:start position:0%
+expected Return of the two bonds the
+ 
+
+ align:start position:0%
+expected Return of the two bonds the
+bonds issuing foreign currency and
+
+ align:start position:0%
+bonds issuing foreign currency and
+ 
+
+ align:start position:0%
+bonds issuing foreign currency and
+domestic currency have to be the same
+
+ align:start position:0%
+domestic currency have to be the same
+ 
+
+ align:start position:0%
+domestic currency have to be the same
+the Spector return have to be the same
+
+ align:start position:0%
+the Spector return have to be the same
+ 
+
+ align:start position:0%
+the Spector return have to be the same
+okay and this condition ensures that
+
+ align:start position:0%
+okay and this condition ensures that
+ 
+
+ align:start position:0%
+okay and this condition ensures that
+because if a country for example example
+
+ align:start position:0%
+because if a country for example example
+ 
+
+ align:start position:0%
+because if a country for example example
+if the domestic interest rate is higher
+
+ align:start position:0%
+if the domestic interest rate is higher
+ 
+
+ align:start position:0%
+if the domestic interest rate is higher
+than the international interest rate you
+
+ align:start position:0%
+than the international interest rate you
+ 
+
+ align:start position:0%
+than the international interest rate you
+need to expect a depreciation of the
+
+ align:start position:0%
+need to expect a depreciation of the
+ 
+
+ align:start position:0%
+need to expect a depreciation of the
+current currency otherwise the expected
+
+ align:start position:0%
+current currency otherwise the expected
+ 
+
+ align:start position:0%
+current currency otherwise the expected
+return would not be the same okay and
+
+ align:start position:0%
+return would not be the same okay and
+ 
+
+ align:start position:0%
+return would not be the same okay and
+that's the reason when we add the
+
+ align:start position:0%
+that's the reason when we add the
+ 
+
+ align:start position:0%
+that's the reason when we add the
+assumption that the Spector exchanges is
+
+ align:start position:0%
+assumption that the Spector exchanges is
+ 
+
+ align:start position:0%
+assumption that the Spector exchanges is
+fixed at least temporarily H then an
+
+ align:start position:0%
+fixed at least temporarily H then an
+ 
+
+ align:start position:0%
+fixed at least temporarily H then an
+increase in the interest rate leads to
+
+ align:start position:0%
+increase in the interest rate leads to
+ 
+
+ align:start position:0%
+increase in the interest rate leads to
+an appreciation of the exchange rate why
+
+ align:start position:0%
+an appreciation of the exchange rate why
+ 
+
+ align:start position:0%
+an appreciation of the exchange rate why
+because that if the exchange rate
+
+ align:start position:0%
+because that if the exchange rate
+ 
+
+ align:start position:0%
+because that if the exchange rate
+appreciate but the expected exchange
+
+ align:start position:0%
+appreciate but the expected exchange
+ 
+
+ align:start position:0%
+appreciate but the expected exchange
+rate stays put that that means the
+
+ align:start position:0%
+rate stays put that that means the
+ 
+
+ align:start position:0%
+rate stays put that that means the
+expected appreciation will have to be
+
+ align:start position:0%
+expected appreciation will have to be
+ 
+
+ align:start position:0%
+expected appreciation will have to be
+undone and that means that leads to
+
+ align:start position:0%
+undone and that means that leads to
+ 
+
+ align:start position:0%
+undone and that means that leads to
+unexpected depreciation okay so that's
+
+ align:start position:0%
+unexpected depreciation okay so that's
+ 
+
+ align:start position:0%
+unexpected depreciation okay so that's
+very important okay so here you have
+
+ align:start position:0%
+very important okay so here you have
+ 
+
+ align:start position:0%
+very important okay so here you have
+therefore you need to understand this
+
+ align:start position:0%
+therefore you need to understand this
+ 
+
+ align:start position:0%
+therefore you need to understand this
+know that forgiv expectation of the
+
+ align:start position:0%
+know that forgiv expectation of the
+ 
+
+ align:start position:0%
+know that forgiv expectation of the
+exchange rate and increasing domestic
+
+ align:start position:0%
+exchange rate and increasing domestic
+ 
+
+ align:start position:0%
+exchange rate and increasing domestic
+interest rate appreciates the domestic
+
+ align:start position:0%
+interest rate appreciates the domestic
+ 
+
+ align:start position:0%
+interest rate appreciates the domestic
+currency and and increasing the foreign
+
+ align:start position:0%
+currency and and increasing the foreign
+ 
+
+ align:start position:0%
+currency and and increasing the foreign
+interest rate without us matching it
+
+ align:start position:0%
+interest rate without us matching it
+ 
+
+ align:start position:0%
+interest rate without us matching it
+will lead to a depreciation of the
+
+ align:start position:0%
+will lead to a depreciation of the
+ 
+
+ align:start position:0%
+will lead to a depreciation of the
+current of of the domestic currency okay
+
+ align:start position:0%
+current of of the domestic currency okay
+ 
+
+ align:start position:0%
+current of of the domestic currency okay
+so that's what you have there that's
+
+ align:start position:0%
+so that's what you have there that's
+ 
+
+ align:start position:0%
+so that's what you have there that's
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important now notice that if the
+
+ align:start position:0%
+important now notice that if the
+ 
+
+ align:start position:0%
+important now notice that if the
+expected exchange rate goes
+
+ align:start position:0%
+expected exchange rate goes
+ 
+
+ align:start position:0%
+expected exchange rate goes
+up and the interest rates do not change
+
+ align:start position:0%
+up and the interest rates do not change
+ 
+
+ align:start position:0%
+up and the interest rates do not change
+then the current exchanger has to go up
+
+ align:start position:0%
+then the current exchanger has to go up
+ 
+
+ align:start position:0%
+then the current exchanger has to go up
+because if it didn't then you would have
+
+ align:start position:0%
+because if it didn't then you would have
+ 
+
+ align:start position:0%
+because if it didn't then you would have
+an expected capital gain out of the
+
+ align:start position:0%
+an expected capital gain out of the
+ 
+
+ align:start position:0%
+an expected capital gain out of the
+currency and expected appreciation and
+
+ align:start position:0%
+currency and expected appreciation and
+ 
+
+ align:start position:0%
+currency and expected appreciation and
+that would add to the expected return of
+
+ align:start position:0%
+that would add to the expected return of
+ 
+
+ align:start position:0%
+that would add to the expected return of
+own owning a domestic bones okay
+
+ align:start position:0%
+own owning a domestic bones okay
+ 
+
+ align:start position:0%
+own owning a domestic bones okay
+good so we characterize that interest
+
+ align:start position:0%
+good so we characterize that interest
+ 
+
+ align:start position:0%
+good so we characterize that interest
+parity condition as follows we said well
+
+ align:start position:0%
+parity condition as follows we said well
+ 
+
+ align:start position:0%
+parity condition as follows we said well
+look this this here we're plotting the
+
+ align:start position:0%
+look this this here we're plotting the
+ 
+
+ align:start position:0%
+look this this here we're plotting the
+domestic interest rate here we're
+
+ align:start position:0%
+domestic interest rate here we're
+ 
+
+ align:start position:0%
+domestic interest rate here we're
+putting the current exchange rate and
+
+ align:start position:0%
+putting the current exchange rate and
+ 
+
+ align:start position:0%
+putting the current exchange rate and
+what we're marking in this picture this
+
+ align:start position:0%
+what we're marking in this picture this
+ 
+
+ align:start position:0%
+what we're marking in this picture this
+is the curve that traces the uip the and
+
+ align:start position:0%
+is the curve that traces the uip the and
+ 
+
+ align:start position:0%
+is the curve that traces the uip the and
+cover by the condition and naturally
+
+ align:start position:0%
+cover by the condition and naturally
+ 
+
+ align:start position:0%
+cover by the condition and naturally
+when the domestic interest rate is equal
+
+ align:start position:0%
+when the domestic interest rate is equal
+ 
+
+ align:start position:0%
+when the domestic interest rate is equal
+to International interest rate then it
+
+ align:start position:0%
+to International interest rate then it
+ 
+
+ align:start position:0%
+to International interest rate then it
+has to be the case that the exchange
+
+ align:start position:0%
+has to be the case that the exchange
+ 
+
+ align:start position:0%
+has to be the case that the exchange
+rate is at the same level as the
+
+ align:start position:0%
+rate is at the same level as the
+ 
+
+ align:start position:0%
+rate is at the same level as the
+expected exchange no if that is equal to
+
+ align:start position:0%
+expected exchange no if that is equal to
+ 
+
+ align:start position:0%
+expected exchange no if that is equal to
+that so if we're here then we know that
+
+ align:start position:0%
+that so if we're here then we know that
+ 
+
+ align:start position:0%
+that so if we're here then we know that
+a point in that curve is that in which
+
+ align:start position:0%
+a point in that curve is that in which
+ 
+
+ align:start position:0%
+a point in that curve is that in which
+the exchange rate is equal to the
+
+ align:start position:0%
+the exchange rate is equal to the
+ 
+
+ align:start position:0%
+the exchange rate is equal to the
+expected exchange rate okay that's what
+
+ align:start position:0%
+expected exchange rate okay that's what
+ 
+
+ align:start position:0%
+expected exchange rate okay that's what
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+yeah good so you should understand this
+
+ align:start position:0%
+yeah good so you should understand this
+ 
+
+ align:start position:0%
+yeah good so you should understand this
+curve and and know what moves it here
+
+ align:start position:0%
+curve and and know what moves it here
+ 
+
+ align:start position:0%
+curve and and know what moves it here
+it's very clear what moves it no if
+
+ align:start position:0%
+it's very clear what moves it no if
+ 
+
+ align:start position:0%
+it's very clear what moves it no if
+there are two things that can move this
+
+ align:start position:0%
+there are two things that can move this
+ 
+
+ align:start position:0%
+there are two things that can move this
+this curve here one is a change in I
+
+ align:start position:0%
+this curve here one is a change in I
+ 
+
+ align:start position:0%
+this curve here one is a change in I
+star the other one is a change in
+
+ align:start position:0%
+star the other one is a change in
+ 
+
+ align:start position:0%
+star the other one is a change in
+expected exchange rate if what happens
+
+ align:start position:0%
+expected exchange rate if what happens
+ 
+
+ align:start position:0%
+expected exchange rate if what happens
+if the is star goes
+
+ align:start position:0%
+if the is star goes
+ 
+
+ align:start position:0%
+if the is star goes
+up well you know that the new new the
+
+ align:start position:0%
+up well you know that the new new the
+ 
+
+ align:start position:0%
+up well you know that the new new the
+uip will shift but you do know that the
+
+ align:start position:0%
+uip will shift but you do know that the
+ 
+
+ align:start position:0%
+uip will shift but you do know that the
+next the The Point equivalent to that
+
+ align:start position:0%
+next the The Point equivalent to that
+ 
+
+ align:start position:0%
+next the The Point equivalent to that
+that is one in which exchange rate is
+
+ align:start position:0%
+that is one in which exchange rate is
+ 
+
+ align:start position:0%
+that is one in which exchange rate is
+equal to expected exchange rate we have
+
+ align:start position:0%
+equal to expected exchange rate we have
+ 
+
+ align:start position:0%
+equal to expected exchange rate we have
+to have a higher interest rate domestic
+
+ align:start position:0%
+to have a higher interest rate domestic
+ 
+
+ align:start position:0%
+to have a higher interest rate domestic
+interest rate no because if I'm bringing
+
+ align:start position:0%
+interest rate no because if I'm bringing
+ 
+
+ align:start position:0%
+interest rate no because if I'm bringing
+this up and I want to still look at the
+
+ align:start position:0%
+this up and I want to still look at the
+ 
+
+ align:start position:0%
+this up and I want to still look at the
+point in which e is equal to expected
+
+ align:start position:0%
+point in which e is equal to expected
+ 
+
+ align:start position:0%
+point in which e is equal to expected
+exchange rate then I have to move I up
+
+ align:start position:0%
+exchange rate then I have to move I up
+ 
+
+ align:start position:0%
+exchange rate then I have to move I up
+by the same amount and so I know that
+
+ align:start position:0%
+by the same amount and so I know that
+ 
+
+ align:start position:0%
+by the same amount and so I know that
+this curve when when is Star goes up
+
+ align:start position:0%
+this curve when when is Star goes up
+ 
+
+ align:start position:0%
+this curve when when is Star goes up
+this curve moves up or to the left you
+
+ align:start position:0%
+this curve moves up or to the left you
+ 
+
+ align:start position:0%
+this curve moves up or to the left you
+pick which way you analyze
+
+ align:start position:0%
+pick which way you analyze
+ 
+
+ align:start position:0%
+pick which way you analyze
+okay now what about the expected
+
+ align:start position:0%
+okay now what about the expected
+ 
+
+ align:start position:0%
+okay now what about the expected
+exchange rate well if the expected
+
+ align:start position:0%
+exchange rate well if the expected
+ 
+
+ align:start position:0%
+exchange rate well if the expected
+exchange rate goes
+
+ align:start position:0%
+exchange rate goes
+ 
+
+ align:start position:0%
+exchange rate goes
+up if the spected exchange goes up and
+
+ align:start position:0%
+up if the spected exchange goes up and
+ 
+
+ align:start position:0%
+up if the spected exchange goes up and
+the international interest hasn't gone
+
+ align:start position:0%
+the international interest hasn't gone
+ 
+
+ align:start position:0%
+the international interest hasn't gone
+up H so if this moves to to the spected
+
+ align:start position:0%
+up H so if this moves to to the spected
+ 
+
+ align:start position:0%
+up H so if this moves to to the spected
+exchanger moves to the right then and
+
+ align:start position:0%
+exchanger moves to the right then and
+ 
+
+ align:start position:0%
+exchanger moves to the right then and
+the and the and the domestic interest
+
+ align:start position:0%
+the and the and the domestic interest
+ 
+
+ align:start position:0%
+the and the and the domestic interest
+doesn't go up then that means that the
+
+ align:start position:0%
+doesn't go up then that means that the
+ 
+
+ align:start position:0%
+doesn't go up then that means that the
+current exchanger will have to also go
+
+ align:start position:0%
+current exchanger will have to also go
+ 
+
+ align:start position:0%
+current exchanger will have to also go
+up okay so that means H if this goes up
+
+ align:start position:0%
+up okay so that means H if this goes up
+ 
+
+ align:start position:0%
+up okay so that means H if this goes up
+then at an interest rate equal to the
+
+ align:start position:0%
+then at an interest rate equal to the
+ 
+
+ align:start position:0%
+then at an interest rate equal to the
+the international interest rate so let's
+
+ align:start position:0%
+the international interest rate so let's
+ 
+
+ align:start position:0%
+the international interest rate so let's
+tra look in this direction then we have
+
+ align:start position:0%
+tra look in this direction then we have
+ 
+
+ align:start position:0%
+tra look in this direction then we have
+a point around here okay if if that
+
+ align:start position:0%
+a point around here okay if if that
+ 
+
+ align:start position:0%
+a point around here okay if if that
+wasn't the cas case then you would
+
+ align:start position:0%
+wasn't the cas case then you would
+ 
+
+ align:start position:0%
+wasn't the cas case then you would
+respecting an appreciation and then
+
+ align:start position:0%
+respecting an appreciation and then
+ 
+
+ align:start position:0%
+respecting an appreciation and then
+again would be inconsistent with
+
+ align:start position:0%
+again would be inconsistent with
+ 
+
+ align:start position:0%
+again would be inconsistent with
+h the uip then we put things together so
+
+ align:start position:0%
+h the uip then we put things together so
+ 
+
+ align:start position:0%
+h the uip then we put things together so
+what we did is we replace we use the uip
+
+ align:start position:0%
+what we did is we replace we use the uip
+ 
+
+ align:start position:0%
+what we did is we replace we use the uip
+to replace exchange rate there and now
+
+ align:start position:0%
+to replace exchange rate there and now
+ 
+
+ align:start position:0%
+to replace exchange rate there and now
+we get this expression in the net export
+
+ align:start position:0%
+we get this expression in the net export
+ 
+
+ align:start position:0%
+we get this expression in the net export
+function now we the LM is exactly the
+
+ align:start position:0%
+function now we the LM is exactly the
+ 
+
+ align:start position:0%
+function now we the LM is exactly the
+same as before we we have
+
+ align:start position:0%
+same as before we we have
+ 
+
+ align:start position:0%
+same as before we we have
+a the Central Bank sets the interest
+
+ align:start position:0%
+a the Central Bank sets the interest
+ 
+
+ align:start position:0%
+a the Central Bank sets the interest
+rate here I'm writing it in terms of the
+
+ align:start position:0%
+rate here I'm writing it in terms of the
+ 
+
+ align:start position:0%
+rate here I'm writing it in terms of the
+nominal interest rate I think in the
+
+ align:start position:0%
+nominal interest rate I think in the
+ 
+
+ align:start position:0%
+nominal interest rate I think in the
+quiz we wrote it in terms of the real
+
+ align:start position:0%
+quiz we wrote it in terms of the real
+ 
+
+ align:start position:0%
+quiz we wrote it in terms of the real
+interest rate but it's the same because
+
+ align:start position:0%
+interest rate but it's the same because
+ 
+
+ align:start position:0%
+interest rate but it's the same because
+prices is equal to are fixed so real and
+
+ align:start position:0%
+prices is equal to are fixed so real and
+ 
+
+ align:start position:0%
+prices is equal to are fixed so real and
+nominal interest rate are exactly the
+
+ align:start position:0%
+nominal interest rate are exactly the
+ 
+
+ align:start position:0%
+nominal interest rate are exactly the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+yeah is the xais the expected exchange
+
+ align:start position:0%
+yeah is the xais the expected exchange
+ 
+
+ align:start position:0%
+yeah is the xais the expected exchange
+rate no is the actual exchange rate the
+
+ align:start position:0%
+rate no is the actual exchange rate the
+ 
+
+ align:start position:0%
+rate no is the actual exchange rate the
+spected exchange rate is in this curve
+
+ align:start position:0%
+spected exchange rate is in this curve
+ 
+
+ align:start position:0%
+spected exchange rate is in this curve
+here that is a parameter okay this
+
+ align:start position:0%
+here that is a parameter okay this
+ 
+
+ align:start position:0%
+here that is a parameter okay this
+happens to be a value of the current
+
+ align:start position:0%
+happens to be a value of the current
+ 
+
+ align:start position:0%
+happens to be a value of the current
+exchange equal to the spected exchange
+
+ align:start position:0%
+exchange equal to the spected exchange
+ 
+
+ align:start position:0%
+exchange equal to the spected exchange
+rate which is convenient to plot because
+
+ align:start position:0%
+rate which is convenient to plot because
+ 
+
+ align:start position:0%
+rate which is convenient to plot because
+that's also when the domestic interest
+
+ align:start position:0%
+that's also when the domestic interest
+ 
+
+ align:start position:0%
+that's also when the domestic interest
+rate which is what I'm putting here is
+
+ align:start position:0%
+rate which is what I'm putting here is
+ 
+
+ align:start position:0%
+rate which is what I'm putting here is
+equal to International interest rate
+
+ align:start position:0%
+equal to International interest rate
+ 
+
+ align:start position:0%
+equal to International interest rate
+that's all that I'm saying and then if
+
+ align:start position:0%
+that's all that I'm saying and then if
+ 
+
+ align:start position:0%
+that's all that I'm saying and then if
+you shift this to the
+
+ align:start position:0%
+you shift this to the
+ 
+
+ align:start position:0%
+you shift this to the
+right exchange rate up the expect exate
+
+ align:start position:0%
+right exchange rate up the expect exate
+ 
+
+ align:start position:0%
+right exchange rate up the expect exate
+up then I know that a new point in this
+
+ align:start position:0%
+up then I know that a new point in this
+ 
+
+ align:start position:0%
+up then I know that a new point in this
+curve has to have a higher current
+
+ align:start position:0%
+curve has to have a higher current
+ 
+
+ align:start position:0%
+curve has to have a higher current
+exchange rate so that I know I know that
+
+ align:start position:0%
+exchange rate so that I know I know that
+ 
+
+ align:start position:0%
+exchange rate so that I know I know that
+the equivalent to this point a is going
+
+ align:start position:0%
+the equivalent to this point a is going
+ 
+
+ align:start position:0%
+the equivalent to this point a is going
+to be to the right if you lower the
+
+ align:start position:0%
+to be to the right if you lower the
+ 
+
+ align:start position:0%
+to be to the right if you lower the
+foreign interest rate then what I know
+
+ align:start position:0%
+foreign interest rate then what I know
+ 
+
+ align:start position:0%
+foreign interest rate then what I know
+is that exactly that that the point at
+
+ align:start position:0%
+is that exactly that that the point at
+ 
+
+ align:start position:0%
+is that exactly that that the point at
+which exchange it is equal to expected
+
+ align:start position:0%
+which exchange it is equal to expected
+ 
+
+ align:start position:0%
+which exchange it is equal to expected
+exchange rate has to have a lower
+
+ align:start position:0%
+exchange rate has to have a lower
+ 
+
+ align:start position:0%
+exchange rate has to have a lower
+domestic interest rate so that means
+
+ align:start position:0%
+domestic interest rate so that means
+ 
+
+ align:start position:0%
+domestic interest rate so that means
+that I know that that that this point a
+
+ align:start position:0%
+that I know that that that this point a
+ 
+
+ align:start position:0%
+that I know that that that this point a
+will be around here which is like a
+
+ align:start position:0%
+will be around here which is like a
+ 
+
+ align:start position:0%
+will be around here which is like a
+shift to the right okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway so so as I said I was saying ER
+
+ align:start position:0%
+anyway so so as I said I was saying ER
+ 
+
+ align:start position:0%
+anyway so so as I said I was saying ER
+nominal real interest are the same I
+
+ align:start position:0%
+nominal real interest are the same I
+ 
+
+ align:start position:0%
+nominal real interest are the same I
+think in the in the quiz we wrote are
+
+ align:start position:0%
+think in the in the quiz we wrote are
+ 
+
+ align:start position:0%
+think in the in the quiz we wrote are
+there but it's the same same
+
+ align:start position:0%
+there but it's the same same
+ 
+
+ align:start position:0%
+there but it's the same same
+more so now you see that interest rate
+
+ align:start position:0%
+more so now you see that interest rate
+ 
+
+ align:start position:0%
+more so now you see that interest rate
+have two effects no h one is the
+
+ align:start position:0%
+have two effects no h one is the
+ 
+
+ align:start position:0%
+have two effects no h one is the
+traditional effect affects investment
+
+ align:start position:0%
+traditional effect affects investment
+ 
+
+ align:start position:0%
+traditional effect affects investment
+but it also affects exchange R so H an
+
+ align:start position:0%
+but it also affects exchange R so H an
+ 
+
+ align:start position:0%
+but it also affects exchange R so H an
+increas in the domestic interest rate
+
+ align:start position:0%
+increas in the domestic interest rate
+ 
+
+ align:start position:0%
+increas in the domestic interest rate
+now will will be doubly contractional in
+
+ align:start position:0%
+now will will be doubly contractional in
+ 
+
+ align:start position:0%
+now will will be doubly contractional in
+the sense that we lower domestic
+
+ align:start position:0%
+the sense that we lower domestic
+ 
+
+ align:start position:0%
+the sense that we lower domestic
+investment that reduces aggregate demand
+
+ align:start position:0%
+investment that reduces aggregate demand
+ 
+
+ align:start position:0%
+investment that reduces aggregate demand
+but at the same time it will also
+
+ align:start position:0%
+but at the same time it will also
+ 
+
+ align:start position:0%
+but at the same time it will also
+appreciate the exchange rate and
+
+ align:start position:0%
+appreciate the exchange rate and
+ 
+
+ align:start position:0%
+appreciate the exchange rate and
+therefore it will reduce net exports
+
+ align:start position:0%
+therefore it will reduce net exports
+ 
+
+ align:start position:0%
+therefore it will reduce net exports
+okay we're going to import more and
+
+ align:start position:0%
+okay we're going to import more and
+ 
+
+ align:start position:0%
+okay we're going to import more and
+Export less and that's also going to
+
+ align:start position:0%
+Export less and that's also going to
+ 
+
+ align:start position:0%
+Export less and that's also going to
+reduce aggregate demand so that's that's
+
+ align:start position:0%
+reduce aggregate demand so that's that's
+ 
+
+ align:start position:0%
+reduce aggregate demand so that's that's
+the those are the two effects so that's
+
+ align:start position:0%
+the those are the two effects so that's
+ 
+
+ align:start position:0%
+the those are the two effects so that's
+the contribution of the all this
+
+ align:start position:0%
+the contribution of the all this
+ 
+
+ align:start position:0%
+the contribution of the all this
+exchange rate block to our islm
+
+ align:start position:0%
+exchange rate block to our islm
+ 
+
+ align:start position:0%
+exchange rate block to our islm
+framework Mandel flaming is simply islm
+
+ align:start position:0%
+framework Mandel flaming is simply islm
+ 
+
+ align:start position:0%
+framework Mandel flaming is simply islm
+plus a a you know a uip condition and a
+
+ align:start position:0%
+plus a a you know a uip condition and a
+ 
+
+ align:start position:0%
+plus a a you know a uip condition and a
+net export function that's it
+
+ align:start position:0%
+net export function that's it
+ 
+
+ align:start position:0%
+net export function that's it
+so we put out now the two things
+
+ align:start position:0%
+so we put out now the two things
+ 
+
+ align:start position:0%
+so we put out now the two things
+together sort of a standard is islm now
+
+ align:start position:0%
+together sort of a standard is islm now
+ 
+
+ align:start position:0%
+together sort of a standard is islm now
+with different slope and so on because
+
+ align:start position:0%
+with different slope and so on because
+ 
+
+ align:start position:0%
+with different slope and so on because
+we have this net export function and we
+
+ align:start position:0%
+we have this net export function and we
+ 
+
+ align:start position:0%
+we have this net export function and we
+have more parameter we have y star is
+
+ align:start position:0%
+have more parameter we have y star is
+ 
+
+ align:start position:0%
+have more parameter we have y star is
+star and things like that and then we
+
+ align:start position:0%
+star and things like that and then we
+ 
+
+ align:start position:0%
+star and things like that and then we
+have the uip there and then then we did
+
+ align:start position:0%
+have the uip there and then then we did
+ 
+
+ align:start position:0%
+have the uip there and then then we did
+a few experiments no said suppose that
+
+ align:start position:0%
+a few experiments no said suppose that
+ 
+
+ align:start position:0%
+a few experiments no said suppose that
+now you have an expansionary monetary
+
+ align:start position:0%
+now you have an expansionary monetary
+ 
+
+ align:start position:0%
+now you have an expansionary monetary
+policy okay so an expansion in monetary
+
+ align:start position:0%
+policy okay so an expansion in monetary
+ 
+
+ align:start position:0%
+policy okay so an expansion in monetary
+policy as before with a slightly
+
+ align:start position:0%
+policy as before with a slightly
+ 
+
+ align:start position:0%
+policy as before with a slightly
+different slopes and so on because of
+
+ align:start position:0%
+different slopes and so on because of
+ 
+
+ align:start position:0%
+different slopes and so on because of
+the net export function will lower
+
+ align:start position:0%
+the net export function will lower
+ 
+
+ align:start position:0%
+the net export function will lower
+equilibrium output and it will lower it
+
+ align:start position:0%
+equilibrium output and it will lower it
+ 
+
+ align:start position:0%
+equilibrium output and it will lower it
+for two reasons as I said before will
+
+ align:start position:0%
+for two reasons as I said before will
+ 
+
+ align:start position:0%
+for two reasons as I said before will
+lower it because investment will decline
+
+ align:start position:0%
+lower it because investment will decline
+ 
+
+ align:start position:0%
+lower it because investment will decline
+but also because higher interest rate
+
+ align:start position:0%
+but also because higher interest rate
+ 
+
+ align:start position:0%
+but also because higher interest rate
+means an appreciation of the exchange
+
+ align:start position:0%
+means an appreciation of the exchange
+ 
+
+ align:start position:0%
+means an appreciation of the exchange
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+today because you have to expect a
+
+ align:start position:0%
+today because you have to expect a
+ 
+
+ align:start position:0%
+today because you have to expect a
+depreciation now in the next period and
+
+ align:start position:0%
+depreciation now in the next period and
+ 
+
+ align:start position:0%
+depreciation now in the next period and
+and that that means also less net
+
+ align:start position:0%
+and that that means also less net
+ 
+
+ align:start position:0%
+and that that means also less net
+exports okay so interest rate is
+
+ align:start position:0%
+exports okay so interest rate is
+ 
+
+ align:start position:0%
+exports okay so interest rate is
+contractionary for for two different
+
+ align:start position:0%
+contractionary for for two different
+ 
+
+ align:start position:0%
+contractionary for for two different
+reasons here is that clear
+
+ align:start position:0%
+reasons here is that clear
+ 
+
+ align:start position:0%
+reasons here is that clear
+yeah raise interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate raise interest rate will lower
+
+ align:start position:0%
+rate raise interest rate will lower
+ 
+
+ align:start position:0%
+rate raise interest rate will lower
+aggregate demand for the standard reason
+
+ align:start position:0%
+aggregate demand for the standard reason
+ 
+
+ align:start position:0%
+aggregate demand for the standard reason
+but on top of that we're going to get an
+
+ align:start position:0%
+but on top of that we're going to get an
+ 
+
+ align:start position:0%
+but on top of that we're going to get an
+appreciation of the exchange rate which
+
+ align:start position:0%
+appreciation of the exchange rate which
+ 
+
+ align:start position:0%
+appreciation of the exchange rate which
+also reduces net exports
+
+ align:start position:0%
+also reduces net exports
+ 
+
+ align:start position:0%
+also reduces net exports
+okay what about an increase in go
+
+ align:start position:0%
+okay what about an increase in go
+ 
+
+ align:start position:0%
+okay what about an increase in go
+expenditure well H it's the same as
+
+ align:start position:0%
+expenditure well H it's the same as
+ 
+
+ align:start position:0%
+expenditure well H it's the same as
+before and nothing changes relative to
+
+ align:start position:0%
+before and nothing changes relative to
+ 
+
+ align:start position:0%
+before and nothing changes relative to
+before except for the fact that we have
+
+ align:start position:0%
+before except for the fact that we have
+ 
+
+ align:start position:0%
+before except for the fact that we have
+a lower multiplier but it's still the
+
+ align:start position:0%
+a lower multiplier but it's still the
+ 
+
+ align:start position:0%
+a lower multiplier but it's still the
+case that is expansionary but it doesn't
+
+ align:start position:0%
+case that is expansionary but it doesn't
+ 
+
+ align:start position:0%
+case that is expansionary but it doesn't
+affect the interest rate it doesn't
+
+ align:start position:0%
+affect the interest rate it doesn't
+ 
+
+ align:start position:0%
+affect the interest rate it doesn't
+affect the exchange rate or anything
+
+ align:start position:0%
+affect the exchange rate or anything
+ 
+
+ align:start position:0%
+affect the exchange rate or anything
+like that again it's less expansionary
+
+ align:start position:0%
+like that again it's less expansionary
+ 
+
+ align:start position:0%
+like that again it's less expansionary
+than in closed economy because part of
+
+ align:start position:0%
+than in closed economy because part of
+ 
+
+ align:start position:0%
+than in closed economy because part of
+that energy will go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inputs then I went to this diagram and
+
+ align:start position:0%
+inputs then I went to this diagram and
+ 
+
+ align:start position:0%
+inputs then I went to this diagram and
+and I play with this uh diagram here I
+
+ align:start position:0%
+and I play with this uh diagram here I
+ 
+
+ align:start position:0%
+and I play with this uh diagram here I
+said well suppose that the expected
+
+ align:start position:0%
+said well suppose that the expected
+ 
+
+ align:start position:0%
+said well suppose that the expected
+exchanger goes up then what which curves
+
+ align:start position:0%
+exchanger goes up then what which curves
+ 
+
+ align:start position:0%
+exchanger goes up then what which curves
+change and the first one that changes is
+
+ align:start position:0%
+change and the first one that changes is
+ 
+
+ align:start position:0%
+change and the first one that changes is
+this one no this one moves to the right
+
+ align:start position:0%
+this one no this one moves to the right
+ 
+
+ align:start position:0%
+this one no this one moves to the right
+so you get an appreciation today and
+
+ align:start position:0%
+so you get an appreciation today and
+ 
+
+ align:start position:0%
+so you get an appreciation today and
+that also means that this curve here the
+
+ align:start position:0%
+that also means that this curve here the
+ 
+
+ align:start position:0%
+that also means that this curve here the
+yes will shift to the left okay if the
+
+ align:start position:0%
+yes will shift to the left okay if the
+ 
+
+ align:start position:0%
+yes will shift to the left okay if the
+spected exchanger goes up and you don't
+
+ align:start position:0%
+spected exchanger goes up and you don't
+ 
+
+ align:start position:0%
+spected exchanger goes up and you don't
+change monetary policy that means
+
+ align:start position:0%
+change monetary policy that means
+ 
+
+ align:start position:0%
+change monetary policy that means
+interest rate will go
+
+ align:start position:0%
+interest rate will go
+ 
+
+ align:start position:0%
+interest rate will go
+up sorry and you don't change monetary
+
+ align:start position:0%
+up sorry and you don't change monetary
+ 
+
+ align:start position:0%
+up sorry and you don't change monetary
+policy that means the current exchanger
+
+ align:start position:0%
+policy that means the current exchanger
+ 
+
+ align:start position:0%
+policy that means the current exchanger
+will appreciate that will reduce net
+
+ align:start position:0%
+will appreciate that will reduce net
+ 
+
+ align:start position:0%
+will appreciate that will reduce net
+export and and that's a shift in this
+
+ align:start position:0%
+export and and that's a shift in this
+ 
+
+ align:start position:0%
+export and and that's a shift in this
+space as a shift in the yes to the left
+
+ align:start position:0%
+space as a shift in the yes to the left
+ 
+
+ align:start position:0%
+space as a shift in the yes to the left
+okay this is a parameter these two
+
+ align:start position:0%
+okay this is a parameter these two
+ 
+
+ align:start position:0%
+okay this is a parameter these two
+things are parameters now in the ls
+
+ align:start position:0%
+things are parameters now in the ls
+ 
+
+ align:start position:0%
+things are parameters now in the ls
+diagram okay what about for an output uh
+
+ align:start position:0%
+diagram okay what about for an output uh
+ 
+
+ align:start position:0%
+diagram okay what about for an output uh
+going down well that doesn't affect the
+
+ align:start position:0%
+going down well that doesn't affect the
+ 
+
+ align:start position:0%
+going down well that doesn't affect the
+uip condition but it does affect net
+
+ align:start position:0%
+uip condition but it does affect net
+ 
+
+ align:start position:0%
+uip condition but it does affect net
+export so that moves I to the left okay
+
+ align:start position:0%
+export so that moves I to the left okay
+ 
+
+ align:start position:0%
+export so that moves I to the left okay
+and the last thing we did was an
+
+ align:start position:0%
+and the last thing we did was an
+ 
+
+ align:start position:0%
+and the last thing we did was an
+increase in in in isar and an increase
+
+ align:start position:0%
+increase in in in isar and an increase
+ 
+
+ align:start position:0%
+increase in in in isar and an increase
+in isar what does is know is that at the
+
+ align:start position:0%
+in isar what does is know is that at the
+ 
+
+ align:start position:0%
+in isar what does is know is that at the
+same interest rate then you know that
+
+ align:start position:0%
+same interest rate then you know that
+ 
+
+ align:start position:0%
+same interest rate then you know that
+you need a depreciation of the currency
+
+ align:start position:0%
+you need a depreciation of the currency
+ 
+
+ align:start position:0%
+you need a depreciation of the currency
+today because that will lead to an
+
+ align:start position:0%
+today because that will lead to an
+ 
+
+ align:start position:0%
+today because that will lead to an
+apprec expected appreciation so that
+
+ align:start position:0%
+apprec expected appreciation so that
+ 
+
+ align:start position:0%
+apprec expected appreciation so that
+means that this uip PE curve moves to
+
+ align:start position:0%
+means that this uip PE curve moves to
+ 
+
+ align:start position:0%
+means that this uip PE curve moves to
+the left and the is curve
+
+ align:start position:0%
+the left and the is curve
+ 
+
+ align:start position:0%
+the left and the is curve
+moves to the right that's an increase in
+
+ align:start position:0%
+moves to the right that's an increase in
+ 
+
+ align:start position:0%
+moves to the right that's an increase in
+the interest rate taken as given for an
+
+ align:start position:0%
+the interest rate taken as given for an
+ 
+
+ align:start position:0%
+the interest rate taken as given for an
+output okay if for an output also
+
+ align:start position:0%
+output okay if for an output also
+ 
+
+ align:start position:0%
+output okay if for an output also
+changes then you have to look at the
+
+ align:start position:0%
+changes then you have to look at the
+ 
+
+ align:start position:0%
+changes then you have to look at the
+combination of the two things okay but
+
+ align:start position:0%
+combination of the two things okay but
+ 
+
+ align:start position:0%
+combination of the two things okay but
+um but taking for an output as given
+
+ align:start position:0%
+um but taking for an output as given
+ 
+
+ align:start position:0%
+um but taking for an output as given
+then this Curve will shift to the left
+
+ align:start position:0%
+then this Curve will shift to the left
+ 
+
+ align:start position:0%
+then this Curve will shift to the left
+and that will move the to the right
+
+ align:start position:0%
+and that will move the to the right
+ 
+
+ align:start position:0%
+and that will move the to the right
+because the exchanger will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depreciate you said sometimes countries
+
+ align:start position:0%
+depreciate you said sometimes countries
+ 
+
+ align:start position:0%
+depreciate you said sometimes countries
+choose to fix exchange rates and when
+
+ align:start position:0%
+choose to fix exchange rates and when
+ 
+
+ align:start position:0%
+choose to fix exchange rates and when
+you fix an exchange rate well and if
+
+ align:start position:0%
+you fix an exchange rate well and if
+ 
+
+ align:start position:0%
+you fix an exchange rate well and if
+it's credible exchange rate then the
+
+ align:start position:0%
+it's credible exchange rate then the
+ 
+
+ align:start position:0%
+it's credible exchange rate then the
+spected exchange rate equal to the
+
+ align:start position:0%
+spected exchange rate equal to the
+ 
+
+ align:start position:0%
+spected exchange rate equal to the
+actual exchange rate equal to some
+
+ align:start position:0%
+actual exchange rate equal to some
+ 
+
+ align:start position:0%
+actual exchange rate equal to some
+constant then that implies immediately
+
+ align:start position:0%
+constant then that implies immediately
+ 
+
+ align:start position:0%
+constant then that implies immediately
+that the domestic interest rate has to
+
+ align:start position:0%
+that the domestic interest rate has to
+ 
+
+ align:start position:0%
+that the domestic interest rate has to
+be equal to International interest rate
+
+ align:start position:0%
+be equal to International interest rate
+ 
+
+ align:start position:0%
+be equal to International interest rate
+okay so that if you fix your exchange
+
+ align:start position:0%
+okay so that if you fix your exchange
+ 
+
+ align:start position:0%
+okay so that if you fix your exchange
+rate to someone else then you give up
+
+ align:start position:0%
+rate to someone else then you give up
+ 
+
+ align:start position:0%
+rate to someone else then you give up
+your monetary policy the monetary policy
+
+ align:start position:0%
+your monetary policy the monetary policy
+ 
+
+ align:start position:0%
+your monetary policy the monetary policy
+is run by a different country
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay good okay so that's a very
+
+ align:start position:0%
+okay okay good okay so that's a very
+ 
+
+ align:start position:0%
+okay okay good okay so that's a very
+important lecture play with it please
+
+ align:start position:0%
+important lecture play with it please
+ 
+
+ align:start position:0%
+important lecture play with it please
+well we then we look more carefully at
+
+ align:start position:0%
+well we then we look more carefully at
+ 
+
+ align:start position:0%
+well we then we look more carefully at
+at at
+
+ align:start position:0%
+at at
+ 
+
+ align:start position:0%
+at at
+uh at different exchanger
+
+ align:start position:0%
+uh at different exchanger
+ 
+
+ align:start position:0%
+uh at different exchanger
+regimes ER and and the effectiveness of
+
+ align:start position:0%
+regimes ER and and the effectiveness of
+ 
+
+ align:start position:0%
+regimes ER and and the effectiveness of
+policy within each of this regime the
+
+ align:start position:0%
+policy within each of this regime the
+ 
+
+ align:start position:0%
+policy within each of this regime the
+flexible exchange rate system which is
+
+ align:start position:0%
+flexible exchange rate system which is
+ 
+
+ align:start position:0%
+flexible exchange rate system which is
+the one we were discussing before H you
+
+ align:start position:0%
+the one we were discussing before H you
+ 
+
+ align:start position:0%
+the one we were discussing before H you
+get sort of you know if a country is in
+
+ align:start position:0%
+get sort of you know if a country is in
+ 
+
+ align:start position:0%
+get sort of you know if a country is in
+a recession you can use fiscal policy I
+
+ align:start position:0%
+a recession you can use fiscal policy I
+ 
+
+ align:start position:0%
+a recession you can use fiscal policy I
+showed you that before it works well ER
+
+ align:start position:0%
+showed you that before it works well ER
+ 
+
+ align:start position:0%
+showed you that before it works well ER
+and you can also use expansionary
+
+ align:start position:0%
+and you can also use expansionary
+ 
+
+ align:start position:0%
+and you can also use expansionary
+monetary policy which will be very
+
+ align:start position:0%
+monetary policy which will be very
+ 
+
+ align:start position:0%
+monetary policy which will be very
+successful for two reasons one the
+
+ align:start position:0%
+successful for two reasons one the
+ 
+
+ align:start position:0%
+successful for two reasons one the
+traditional one but the second reason is
+
+ align:start position:0%
+traditional one but the second reason is
+ 
+
+ align:start position:0%
+traditional one but the second reason is
+that it will depreciate your currency
+
+ align:start position:0%
+that it will depreciate your currency
+ 
+
+ align:start position:0%
+that it will depreciate your currency
+okay good now then we say suppose that
+
+ align:start position:0%
+okay good now then we say suppose that
+ 
+
+ align:start position:0%
+okay good now then we say suppose that
+you have a country that that is also in
+
+ align:start position:0%
+you have a country that that is also in
+ 
+
+ align:start position:0%
+you have a country that that is also in
+a recession but you have a a fixed
+
+ align:start position:0%
+a recession but you have a a fixed
+ 
+
+ align:start position:0%
+a recession but you have a a fixed
+exchange rate well then you still can
+
+ align:start position:0%
+exchange rate well then you still can
+ 
+
+ align:start position:0%
+exchange rate well then you still can
+use fiscal policy there's nothing
+
+ align:start position:0%
+use fiscal policy there's nothing
+ 
+
+ align:start position:0%
+use fiscal policy there's nothing
+against that but but you cannot use the
+
+ align:start position:0%
+against that but but you cannot use the
+ 
+
+ align:start position:0%
+against that but but you cannot use the
+expansion in monetary policy okay so
+
+ align:start position:0%
+expansion in monetary policy okay so
+ 
+
+ align:start position:0%
+expansion in monetary policy okay so
+that's a limitation of fixed exchang
+
+ align:start position:0%
+that's a limitation of fixed exchang
+ 
+
+ align:start position:0%
+that's a limitation of fixed exchang
+that you lose an important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tool another problem that can arise with
+
+ align:start position:0%
+tool another problem that can arise with
+ 
+
+ align:start position:0%
+tool another problem that can arise with
+fix fixable exch fixed exchange rates is
+
+ align:start position:0%
+fix fixable exch fixed exchange rates is
+ 
+
+ align:start position:0%
+fix fixable exch fixed exchange rates is
+is speculative attacks on the currency
+
+ align:start position:0%
+is speculative attacks on the currency
+ 
+
+ align:start position:0%
+is speculative attacks on the currency
+sometimes the peg is not credible and
+
+ align:start position:0%
+sometimes the peg is not credible and
+ 
+
+ align:start position:0%
+sometimes the peg is not credible and
+when the peg is not credible you can
+
+ align:start position:0%
+when the peg is not credible you can
+ 
+
+ align:start position:0%
+when the peg is not credible you can
+imagine that you know that suppose that
+
+ align:start position:0%
+imagine that you know that suppose that
+ 
+
+ align:start position:0%
+imagine that you know that suppose that
+people expect your currency to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depreciate depreciate so expected
+
+ align:start position:0%
+depreciate depreciate so expected
+ 
+
+ align:start position:0%
+depreciate depreciate so expected
+exchanger goes down and and suppose that
+
+ align:start position:0%
+exchanger goes down and and suppose that
+ 
+
+ align:start position:0%
+exchanger goes down and and suppose that
+you do want to keep your peg today
+
+ align:start position:0%
+you do want to keep your peg today
+ 
+
+ align:start position:0%
+you do want to keep your peg today
+that's what typically happens somebody
+
+ align:start position:0%
+that's what typically happens somebody
+ 
+
+ align:start position:0%
+that's what typically happens somebody
+speculates against your P But Central
+
+ align:start position:0%
+speculates against your P But Central
+ 
+
+ align:start position:0%
+speculates against your P But Central
+Bank resist that for a while but the
+
+ align:start position:0%
+Bank resist that for a while but the
+ 
+
+ align:start position:0%
+Bank resist that for a while but the
+only way it can resist that short of
+
+ align:start position:0%
+only way it can resist that short of
+ 
+
+ align:start position:0%
+only way it can resist that short of
+closing the capital account and doing
+
+ align:start position:0%
+closing the capital account and doing
+ 
+
+ align:start position:0%
+closing the capital account and doing
+all sort of things there but you haven't
+
+ align:start position:0%
+all sort of things there but you haven't
+ 
+
+ align:start position:0%
+all sort of things there but you haven't
+learned about those so don't worry H the
+
+ align:start position:0%
+learned about those so don't worry H the
+ 
+
+ align:start position:0%
+learned about those so don't worry H the
+only tool you have here to defend a
+
+ align:start position:0%
+only tool you have here to defend a
+ 
+
+ align:start position:0%
+only tool you have here to defend a
+speculative attack on your currency that
+
+ align:start position:0%
+speculative attack on your currency that
+ 
+
+ align:start position:0%
+speculative attack on your currency that
+is for the exchange not to depreciate
+
+ align:start position:0%
+is for the exchange not to depreciate
+ 
+
+ align:start position:0%
+is for the exchange not to depreciate
+today is by raising interest rate so the
+
+ align:start position:0%
+today is by raising interest rate so the
+ 
+
+ align:start position:0%
+today is by raising interest rate so the
+defense of an exchange rate causes a
+
+ align:start position:0%
+defense of an exchange rate causes a
+ 
+
+ align:start position:0%
+defense of an exchange rate causes a
+recession at
+
+ align:start position:0%
+recession at
+ 
+
+ align:start position:0%
+recession at
+home that's another problem that
+
+ align:start position:0%
+home that's another problem that
+ 
+
+ align:start position:0%
+home that's another problem that
+flexible exchange rate
+
+ align:start position:0%
+flexible exchange rate
+ 
+
+ align:start position:0%
+flexible exchange rate
+have and and there are sort of the deal
+
+ align:start position:0%
+have and and there are sort of the deal
+ 
+
+ align:start position:0%
+have and and there are sort of the deal
+seems pretty obvious that you don't want
+
+ align:start position:0%
+seems pretty obvious that you don't want
+ 
+
+ align:start position:0%
+seems pretty obvious that you don't want
+to have a fixed exchange rate and I said
+
+ align:start position:0%
+to have a fixed exchange rate and I said
+ 
+
+ align:start position:0%
+to have a fixed exchange rate and I said
+well be careful because flexible
+
+ align:start position:0%
+well be careful because flexible
+ 
+
+ align:start position:0%
+well be careful because flexible
+exchange rate are also not a panasa you
+
+ align:start position:0%
+exchange rate are also not a panasa you
+ 
+
+ align:start position:0%
+exchange rate are also not a panasa you
+may get lots of volatility in the
+
+ align:start position:0%
+may get lots of volatility in the
+ 
+
+ align:start position:0%
+may get lots of volatility in the
+exchange rate because the role of
+
+ align:start position:0%
+exchange rate because the role of
+ 
+
+ align:start position:0%
+exchange rate because the role of
+expectations is sort of is is very
+
+ align:start position:0%
+expectations is sort of is is very
+ 
+
+ align:start position:0%
+expectations is sort of is is very
+important um anyways this looks
+
+ align:start position:0%
+important um anyways this looks
+ 
+
+ align:start position:0%
+important um anyways this looks
+complicated but it's essentially what we
+
+ align:start position:0%
+complicated but it's essentially what we
+ 
+
+ align:start position:0%
+complicated but it's essentially what we
+did later on when we price equity and
+
+ align:start position:0%
+did later on when we price equity and
+ 
+
+ align:start position:0%
+did later on when we price equity and
+things like that we use sort of the same
+
+ align:start position:0%
+things like that we use sort of the same
+ 
+
+ align:start position:0%
+things like that we use sort of the same
+sort of iterated substitutions of things
+
+ align:start position:0%
+sort of iterated substitutions of things
+ 
+
+ align:start position:0%
+sort of iterated substitutions of things
+this was just meant to say that in a
+
+ align:start position:0%
+this was just meant to say that in a
+ 
+
+ align:start position:0%
+this was just meant to say that in a
+flexible exchange rate really and if
+
+ align:start position:0%
+flexible exchange rate really and if
+ 
+
+ align:start position:0%
+flexible exchange rate really and if
+once you endogenize Spector exchange you
+
+ align:start position:0%
+once you endogenize Spector exchange you
+ 
+
+ align:start position:0%
+once you endogenize Spector exchange you
+don't take it as a constant it gets to
+
+ align:start position:0%
+don't take it as a constant it gets to
+ 
+
+ align:start position:0%
+don't take it as a constant it gets to
+be very complicated because effectively
+
+ align:start position:0%
+be very complicated because effectively
+ 
+
+ align:start position:0%
+be very complicated because effectively
+The Exchange is spin down by the
+
+ align:start position:0%
+The Exchange is spin down by the
+ 
+
+ align:start position:0%
+The Exchange is spin down by the
+expectations of infinite Horizon of
+
+ align:start position:0%
+expectations of infinite Horizon of
+ 
+
+ align:start position:0%
+expectations of infinite Horizon of
+interest rate at home and abroad so so
+
+ align:start position:0%
+interest rate at home and abroad so so
+ 
+
+ align:start position:0%
+interest rate at home and abroad so so
+there's lots of space for creativity and
+
+ align:start position:0%
+there's lots of space for creativity and
+ 
+
+ align:start position:0%
+there's lots of space for creativity and
+moving things around and that's the
+
+ align:start position:0%
+moving things around and that's the
+ 
+
+ align:start position:0%
+moving things around and that's the
+reason exchanges can be very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volatile okay good so anyway so all that
+
+ align:start position:0%
+volatile okay good so anyway so all that
+ 
+
+ align:start position:0%
+volatile okay good so anyway so all that
+that was it for ER Mandel flaming plus
+
+ align:start position:0%
+that was it for ER Mandel flaming plus
+ 
+
+ align:start position:0%
+that was it for ER Mandel flaming plus
+okay any question about that because now
+
+ align:start position:0%
+okay any question about that because now
+ 
+
+ align:start position:0%
+okay any question about that because now
+I'm going to move to the next part okay
+
+ align:start position:0%
+I'm going to move to the next part okay
+ 
+
+ align:start position:0%
+I'm going to move to the next part okay
+so then then uh The Next Step uh was to
+
+ align:start position:0%
+so then then uh The Next Step uh was to
+ 
+
+ align:start position:0%
+so then then uh The Next Step uh was to
+look at the asset prices really and or
+
+ align:start position:0%
+look at the asset prices really and or
+ 
+
+ align:start position:0%
+look at the asset prices really and or
+valuations of Assets in general that
+
+ align:start position:0%
+valuations of Assets in general that
+ 
+
+ align:start position:0%
+valuations of Assets in general that
+that have cash flows in the future or or
+
+ align:start position:0%
+that have cash flows in the future or or
+ 
+
+ align:start position:0%
+that have cash flows in the future or or
+or and exchange it's a little bit like
+
+ align:start position:0%
+or and exchange it's a little bit like
+ 
+
+ align:start position:0%
+or and exchange it's a little bit like
+that by the way but we talk a lot about
+
+ align:start position:0%
+that by the way but we talk a lot about
+ 
+
+ align:start position:0%
+that by the way but we talk a lot about
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+events but the key thing was this no we
+
+ align:start position:0%
+events but the key thing was this no we
+ 
+
+ align:start position:0%
+events but the key thing was this no we
+said okay you know many
+
+ align:start position:0%
+said okay you know many
+ 
+
+ align:start position:0%
+said okay you know many
+things ER many Financial or real assets
+
+ align:start position:0%
+things ER many Financial or real assets
+ 
+
+ align:start position:0%
+things ER many Financial or real assets
+actually or even your human wealth we
+
+ align:start position:0%
+actually or even your human wealth we
+ 
+
+ align:start position:0%
+actually or even your human wealth we
+discuss later on
+
+ align:start position:0%
+discuss later on
+ 
+
+ align:start position:0%
+discuss later on
+you know you you you you you you are
+
+ align:start position:0%
+you know you you you you you you are
+ 
+
+ align:start position:0%
+you know you you you you you you are
+receiving some income today but you're
+
+ align:start position:0%
+receiving some income today but you're
+ 
+
+ align:start position:0%
+receiving some income today but you're
+also expecting to receive income in the
+
+ align:start position:0%
+also expecting to receive income in the
+ 
+
+ align:start position:0%
+also expecting to receive income in the
+future and this part was about how do we
+
+ align:start position:0%
+future and this part was about how do we
+ 
+
+ align:start position:0%
+future and this part was about how do we
+value those things that we receive in
+
+ align:start position:0%
+value those things that we receive in
+ 
+
+ align:start position:0%
+value those things that we receive in
+the future those cash flows that come in
+
+ align:start position:0%
+the future those cash flows that come in
+ 
+
+ align:start position:0%
+the future those cash flows that come in
+the future and so we developed this
+
+ align:start position:0%
+the future and so we developed this
+ 
+
+ align:start position:0%
+the future and so we developed this
+concept
+
+ align:start position:0%
+concept
+ 
+
+ align:start position:0%
+concept
+of expected present discounted value and
+
+ align:start position:0%
+of expected present discounted value and
+ 
+
+ align:start position:0%
+of expected present discounted value and
+we said well very natural way of
+
+ align:start position:0%
+we said well very natural way of
+ 
+
+ align:start position:0%
+we said well very natural way of
+bringing dollars receiving the future to
+
+ align:start position:0%
+bringing dollars receiving the future to
+ 
+
+ align:start position:0%
+bringing dollars receiving the future to
+the present is to discount them by the
+
+ align:start position:0%
+the present is to discount them by the
+ 
+
+ align:start position:0%
+the present is to discount them by the
+interest rate between now and then okay
+
+ align:start position:0%
+interest rate between now and then okay
+ 
+
+ align:start position:0%
+interest rate between now and then okay
+and and the reason the logic behind that
+
+ align:start position:0%
+and and the reason the logic behind that
+ 
+
+ align:start position:0%
+and and the reason the logic behind that
+is because if you give me a dollar today
+
+ align:start position:0%
+is because if you give me a dollar today
+ 
+
+ align:start position:0%
+is because if you give me a dollar today
+I can do a lot more than if you give me
+
+ align:start position:0%
+I can do a lot more than if you give me
+ 
+
+ align:start position:0%
+I can do a lot more than if you give me
+a dollar five years from now because I
+
+ align:start position:0%
+a dollar five years from now because I
+ 
+
+ align:start position:0%
+a dollar five years from now because I
+can invest the dollar today and earn the
+
+ align:start position:0%
+can invest the dollar today and earn the
+ 
+
+ align:start position:0%
+can invest the dollar today and earn the
+interest rate return up to five years
+
+ align:start position:0%
+interest rate return up to five years
+ 
+
+ align:start position:0%
+interest rate return up to five years
+from now so a dollar today is worth a
+
+ align:start position:0%
+from now so a dollar today is worth a
+ 
+
+ align:start position:0%
+from now so a dollar today is worth a
+lot more than five years a dollar five
+
+ align:start position:0%
+lot more than five years a dollar five
+ 
+
+ align:start position:0%
+lot more than five years a dollar five
+years from now therefore a dollar five
+
+ align:start position:0%
+years from now therefore a dollar five
+ 
+
+ align:start position:0%
+years from now therefore a dollar five
+years from now is worth a lot less than
+
+ align:start position:0%
+years from now is worth a lot less than
+ 
+
+ align:start position:0%
+years from now is worth a lot less than
+a dollar today how much less one over
+
+ align:start position:0%
+a dollar today how much less one over
+ 
+
+ align:start position:0%
+a dollar today how much less one over
+one plus the interest rate over that
+
+ align:start position:0%
+one plus the interest rate over that
+ 
+
+ align:start position:0%
+one plus the interest rate over that
+period which is
+
+ align:start position:0%
+period which is
+ 
+
+ align:start position:0%
+period which is
+okay so that's what we did then I show
+
+ align:start position:0%
+okay so that's what we did then I show
+ 
+
+ align:start position:0%
+okay so that's what we did then I show
+you sort of a general a general cash
+
+ align:start position:0%
+you sort of a general a general cash
+ 
+
+ align:start position:0%
+you sort of a general a general cash
+flow this is an asset that gives a cash
+
+ align:start position:0%
+flow this is an asset that gives a cash
+ 
+
+ align:start position:0%
+flow this is an asset that gives a cash
+flow ZT at the beginning of this period
+
+ align:start position:0%
+flow ZT at the beginning of this period
+ 
+
+ align:start position:0%
+flow ZT at the beginning of this period
+ZT plus one at the beginning of the next
+
+ align:start position:0%
+ZT plus one at the beginning of the next
+ 
+
+ align:start position:0%
+ZT plus one at the beginning of the next
+one or at the end of this one something
+
+ align:start position:0%
+one or at the end of this one something
+ 
+
+ align:start position:0%
+one or at the end of this one something
+like that well this one you don't need
+
+ align:start position:0%
+like that well this one you don't need
+ 
+
+ align:start position:0%
+like that well this one you don't need
+to Discount that one you do need to
+
+ align:start position:0%
+to Discount that one you do need to
+ 
+
+ align:start position:0%
+to Discount that one you do need to
+Discount because you're not receiving it
+
+ align:start position:0%
+Discount because you're not receiving it
+ 
+
+ align:start position:0%
+Discount because you're not receiving it
+now you're receiving it a year from now
+
+ align:start position:0%
+now you're receiving it a year from now
+ 
+
+ align:start position:0%
+now you're receiving it a year from now
+this when you need it's two years from
+
+ align:start position:0%
+this when you need it's two years from
+ 
+
+ align:start position:0%
+this when you need it's two years from
+now you need to discount it more because
+
+ align:start position:0%
+now you need to discount it more because
+ 
+
+ align:start position:0%
+now you need to discount it more because
+you know it's two years that you could
+
+ align:start position:0%
+you know it's two years that you could
+ 
+
+ align:start position:0%
+you know it's two years that you could
+be earning interest rate and so on so
+
+ align:start position:0%
+be earning interest rate and so on so
+ 
+
+ align:start position:0%
+be earning interest rate and so on so
+forth okay this formula you need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+understand uh and I said well that's if
+
+ align:start position:0%
+understand uh and I said well that's if
+ 
+
+ align:start position:0%
+understand uh and I said well that's if
+you know the future if you don't know
+
+ align:start position:0%
+you know the future if you don't know
+ 
+
+ align:start position:0%
+you know the future if you don't know
+the future then you just replace the
+
+ align:start position:0%
+the future then you just replace the
+ 
+
+ align:start position:0%
+the future then you just replace the
+things you don't know for the respected
+
+ align:start position:0%
+things you don't know for the respected
+ 
+
+ align:start position:0%
+things you don't know for the respected
+value that's what and that's the
+
+ align:start position:0%
+value that's what and that's the
+ 
+
+ align:start position:0%
+value that's what and that's the
+approximation in real I mean if you were
+
+ align:start position:0%
+approximation in real I mean if you were
+ 
+
+ align:start position:0%
+approximation in real I mean if you were
+to do this formally it's a little more
+
+ align:start position:0%
+to do this formally it's a little more
+ 
+
+ align:start position:0%
+to do this formally it's a little more
+complicated but for this course that's
+
+ align:start position:0%
+complicated but for this course that's
+ 
+
+ align:start position:0%
+complicated but for this course that's
+all that you do
+
+ align:start position:0%
+all that you do
+ 
+
+ align:start position:0%
+all that you do
+okay and then I look at some particular
+
+ align:start position:0%
+okay and then I look at some particular
+ 
+
+ align:start position:0%
+okay and then I look at some particular
+cases this this is a case the same case
+
+ align:start position:0%
+cases this this is a case the same case
+ 
+
+ align:start position:0%
+cases this this is a case the same case
+but in one in which the interest rate is
+
+ align:start position:0%
+but in one in which the interest rate is
+ 
+
+ align:start position:0%
+but in one in which the interest rate is
+constant suppose that you expect the
+
+ align:start position:0%
+constant suppose that you expect the
+ 
+
+ align:start position:0%
+constant suppose that you expect the
+interest rate to be constant then is a
+
+ align:start position:0%
+interest rate to be constant then is a
+ 
+
+ align:start position:0%
+interest rate to be constant then is a
+little simpler expression because rather
+
+ align:start position:0%
+little simpler expression because rather
+ 
+
+ align:start position:0%
+little simpler expression because rather
+than getting these products of one plus
+
+ align:start position:0%
+than getting these products of one plus
+ 
+
+ align:start position:0%
+than getting these products of one plus
+one the interest rates at different
+
+ align:start position:0%
+one the interest rates at different
+ 
+
+ align:start position:0%
+one the interest rates at different
+times H you get just powers of one plus
+
+ align:start position:0%
+times H you get just powers of one plus
+ 
+
+ align:start position:0%
+times H you get just powers of one plus
+I then another one that is simpler
+
+ align:start position:0%
+I then another one that is simpler
+ 
+
+ align:start position:0%
+I then another one that is simpler
+obviously is one in which all these
+
+ align:start position:0%
+obviously is one in which all these
+ 
+
+ align:start position:0%
+obviously is one in which all these
+expected payments are constant and so on
+
+ align:start position:0%
+expected payments are constant and so on
+ 
+
+ align:start position:0%
+expected payments are constant and so on
+and then even simpler if you spec if the
+
+ align:start position:0%
+and then even simpler if you spec if the
+ 
+
+ align:start position:0%
+and then even simpler if you spec if the
+con if the interest rate is constant and
+
+ align:start position:0%
+con if the interest rate is constant and
+ 
+
+ align:start position:0%
+con if the interest rate is constant and
+the payment is constant H you get some
+
+ align:start position:0%
+the payment is constant H you get some
+ 
+
+ align:start position:0%
+the payment is constant H you get some
+simple formulas like that simpler
+
+ align:start position:0%
+simple formulas like that simpler
+ 
+
+ align:start position:0%
+simple formulas like that simpler
+formulas and then cases in which asset
+
+ align:start position:0%
+formulas and then cases in which asset
+ 
+
+ align:start position:0%
+formulas and then cases in which asset
+lives forever of that kind then that's
+
+ align:start position:0%
+lives forever of that kind then that's
+ 
+
+ align:start position:0%
+lives forever of that kind then that's
+value if you don't pay for if you don't
+
+ align:start position:0%
+value if you don't pay for if you don't
+ 
+
+ align:start position:0%
+value if you don't pay for if you don't
+receive the the First Cash Flow now but
+
+ align:start position:0%
+receive the the First Cash Flow now but
+ 
+
+ align:start position:0%
+receive the the First Cash Flow now but
+you receive it at the beginning of next
+
+ align:start position:0%
+you receive it at the beginning of next
+ 
+
+ align:start position:0%
+you receive it at the beginning of next
+year or at the end of this one then it
+
+ align:start position:0%
+year or at the end of this one then it
+ 
+
+ align:start position:0%
+year or at the end of this one then it
+gets even simpler like that and I you're
+
+ align:start position:0%
+gets even simpler like that and I you're
+ 
+
+ align:start position:0%
+gets even simpler like that and I you're
+going to get a question of this kind
+
+ align:start position:0%
+going to get a question of this kind
+ 
+
+ align:start position:0%
+going to get a question of this kind
+okay and which you're going to be asked
+
+ align:start position:0%
+okay and which you're going to be asked
+ 
+
+ align:start position:0%
+okay and which you're going to be asked
+to compare two different assets that
+
+ align:start position:0%
+to compare two different assets that
+ 
+
+ align:start position:0%
+to compare two different assets that
+have a different profiles of cash flows
+
+ align:start position:0%
+have a different profiles of cash flows
+ 
+
+ align:start position:0%
+have a different profiles of cash flows
+and you're going to have to compare
+
+ align:start position:0%
+and you're going to have to compare
+ 
+
+ align:start position:0%
+and you're going to have to compare
+between those two okay then we talk
+
+ align:start position:0%
+between those two okay then we talk
+ 
+
+ align:start position:0%
+between those two okay then we talk
+about bonds and bond yields and
+
+ align:start position:0%
+about bonds and bond yields and
+ 
+
+ align:start position:0%
+about bonds and bond yields and
+essentially we use expected present
+
+ align:start position:0%
+essentially we use expected present
+ 
+
+ align:start position:0%
+essentially we use expected present
+discounted value formula just for bonds
+
+ align:start position:0%
+discounted value formula just for bonds
+ 
+
+ align:start position:0%
+discounted value formula just for bonds
+and bonds bonds have a very particular
+
+ align:start position:0%
+and bonds bonds have a very particular
+ 
+
+ align:start position:0%
+and bonds bonds have a very particular
+form profile of payment typically some
+
+ align:start position:0%
+form profile of payment typically some
+ 
+
+ align:start position:0%
+form profile of payment typically some
+coupons and some final payment which is
+
+ align:start position:0%
+coupons and some final payment which is
+ 
+
+ align:start position:0%
+coupons and some final payment which is
+we call it the face value of the bond or
+
+ align:start position:0%
+we call it the face value of the bond or
+ 
+
+ align:start position:0%
+we call it the face value of the bond or
+something like that and we said a very
+
+ align:start position:0%
+something like that and we said a very
+ 
+
+ align:start position:0%
+something like that and we said a very
+important Concept in bonds is
+
+ align:start position:0%
+important Concept in bonds is
+ 
+
+ align:start position:0%
+important Concept in bonds is
+maturity maturity is the date or the
+
+ align:start position:0%
+maturity maturity is the date or the
+ 
+
+ align:start position:0%
+maturity maturity is the date or the
+number of years till the last payment on
+
+ align:start position:0%
+number of years till the last payment on
+ 
+
+ align:start position:0%
+number of years till the last payment on
+that Bond okay doesn't matter whether
+
+ align:start position:0%
+that Bond okay doesn't matter whether
+ 
+
+ align:start position:0%
+that Bond okay doesn't matter whether
+you receive lots of little coupons along
+
+ align:start position:0%
+you receive lots of little coupons along
+ 
+
+ align:start position:0%
+you receive lots of little coupons along
+the way and one final payment whether
+
+ align:start position:0%
+the way and one final payment whether
+ 
+
+ align:start position:0%
+the way and one final payment whether
+you receive no payment what whatever
+
+ align:start position:0%
+you receive no payment what whatever
+ 
+
+ align:start position:0%
+you receive no payment what whatever
+until the last date that doesn't matter
+
+ align:start position:0%
+until the last date that doesn't matter
+ 
+
+ align:start position:0%
+until the last date that doesn't matter
+the maturity of a bond is the date the
+
+ align:start position:0%
+the maturity of a bond is the date the
+ 
+
+ align:start position:0%
+the maturity of a bond is the date the
+number of years till the last time you
+
+ align:start position:0%
+number of years till the last time you
+ 
+
+ align:start position:0%
+number of years till the last time you
+your last payment
+
+ align:start position:0%
+your last payment
+ 
+
+ align:start position:0%
+your last payment
+okay so we give some examples there a
+
+ align:start position:0%
+okay so we give some examples there a
+ 
+
+ align:start position:0%
+okay so we give some examples there a
+bond that pays nothing now but pays 101
+
+ align:start position:0%
+bond that pays nothing now but pays 101
+ 
+
+ align:start position:0%
+bond that pays nothing now but pays 101
+year from now ER has a has a price is a
+
+ align:start position:0%
+year from now ER has a has a price is a
+ 
+
+ align:start position:0%
+year from now ER has a has a price is a
+pres is discounted value of 100 no one
+
+ align:start position:0%
+pres is discounted value of 100 no one
+ 
+
+ align:start position:0%
+pres is discounted value of 100 no one
+year divided by one plus the one year
+
+ align:start position:0%
+year divided by one plus the one year
+ 
+
+ align:start position:0%
+year divided by one plus the one year
+interest rate at time
+
+ align:start position:0%
+interest rate at time
+ 
+
+ align:start position:0%
+interest rate at time
+T um a bond that pays nothing up to two
+
+ align:start position:0%
+T um a bond that pays nothing up to two
+ 
+
+ align:start position:0%
+T um a bond that pays nothing up to two
+years and then in the second at the end
+
+ align:start position:0%
+years and then in the second at the end
+ 
+
+ align:start position:0%
+years and then in the second at the end
+then after two years pays $100 then
+
+ align:start position:0%
+then after two years pays $100 then
+ 
+
+ align:start position:0%
+then after two years pays $100 then
+that's a value the price of that bond
+
+ align:start position:0%
+that's a value the price of that bond
+ 
+
+ align:start position:0%
+that's a value the price of that bond
+which is 100 discounted by that
+
+ align:start position:0%
+which is 100 discounted by that
+ 
+
+ align:start position:0%
+which is 100 discounted by that
+okay H then we look at Arbitrage which
+
+ align:start position:0%
+okay H then we look at Arbitrage which
+ 
+
+ align:start position:0%
+okay H then we look at Arbitrage which
+is says suppose that you you hold a bond
+
+ align:start position:0%
+is says suppose that you you hold a bond
+ 
+
+ align:start position:0%
+is says suppose that you you hold a bond
+that that you're considering
+
+ align:start position:0%
+that that you're considering
+ 
+
+ align:start position:0%
+that that you're considering
+investing your money for one year but
+
+ align:start position:0%
+investing your money for one year but
+ 
+
+ align:start position:0%
+investing your money for one year but
+you have two options one is to buy a
+
+ align:start position:0%
+you have two options one is to buy a
+ 
+
+ align:start position:0%
+you have two options one is to buy a
+one-year Bond the alternative is to buy
+
+ align:start position:0%
+one-year Bond the alternative is to buy
+ 
+
+ align:start position:0%
+one-year Bond the alternative is to buy
+a two-year Bond now and sell it at the
+
+ align:start position:0%
+a two-year Bond now and sell it at the
+ 
+
+ align:start position:0%
+a two-year Bond now and sell it at the
+end of the year those two strategies
+
+ align:start position:0%
+end of the year those two strategies
+ 
+
+ align:start position:0%
+end of the year those two strategies
+should would give you more or less the
+
+ align:start position:0%
+should would give you more or less the
+ 
+
+ align:start position:0%
+should would give you more or less the
+same return H well you know if you if
+
+ align:start position:0%
+same return H well you know if you if
+ 
+
+ align:start position:0%
+same return H well you know if you if
+you buy a one-year Bond you're going to
+
+ align:start position:0%
+you buy a one-year Bond you're going to
+ 
+
+ align:start position:0%
+you buy a one-year Bond you're going to
+get 1 plus i1t at the end of the year if
+
+ align:start position:0%
+get 1 plus i1t at the end of the year if
+ 
+
+ align:start position:0%
+get 1 plus i1t at the end of the year if
+you go through the two-year Bond
+
+ align:start position:0%
+you go through the two-year Bond
+ 
+
+ align:start position:0%
+you go through the two-year Bond
+strategy then H you're going to pay this
+
+ align:start position:0%
+strategy then H you're going to pay this
+ 
+
+ align:start position:0%
+strategy then H you're going to pay this
+today but you're going to you're going
+
+ align:start position:0%
+today but you're going to you're going
+ 
+
+ align:start position:0%
+today but you're going to you're going
+to H ER rece expect you expect to
+
+ align:start position:0%
+to H ER rece expect you expect to
+ 
+
+ align:start position:0%
+to H ER rece expect you expect to
+receive the price of a oneyear bond one
+
+ align:start position:0%
+receive the price of a oneyear bond one
+ 
+
+ align:start position:0%
+receive the price of a oneyear bond one
+year from now and we said these two
+
+ align:start position:0%
+year from now and we said these two
+ 
+
+ align:start position:0%
+year from now and we said these two
+things have to be equal more or less
+
+ align:start position:0%
+things have to be equal more or less
+ 
+
+ align:start position:0%
+things have to be equal more or less
+equal I mean again we're not adding risk
+
+ align:start position:0%
+equal I mean again we're not adding risk
+ 
+
+ align:start position:0%
+equal I mean again we're not adding risk
+to these things H if there's no risk
+
+ align:start position:0%
+to these things H if there's no risk
+ 
+
+ align:start position:0%
+to these things H if there's no risk
+consideration of agents at risk neutral
+
+ align:start position:0%
+consideration of agents at risk neutral
+ 
+
+ align:start position:0%
+consideration of agents at risk neutral
+then these two things have to be equal H
+
+ align:start position:0%
+then these two things have to be equal H
+ 
+
+ align:start position:0%
+then these two things have to be equal H
+that allows you to solve for the price
+
+ align:start position:0%
+that allows you to solve for the price
+ 
+
+ align:start position:0%
+that allows you to solve for the price
+of a two-year Bond as expected price of
+
+ align:start position:0%
+of a two-year Bond as expected price of
+ 
+
+ align:start position:0%
+of a two-year Bond as expected price of
+a oneyear bond one year from now divided
+
+ align:start position:0%
+a oneyear bond one year from now divided
+ 
+
+ align:start position:0%
+a oneyear bond one year from now divided
+by one plus the interest rate but the
+
+ align:start position:0%
+by one plus the interest rate but the
+ 
+
+ align:start position:0%
+by one plus the interest rate but the
+expected price of one year bond one year
+
+ align:start position:0%
+expected price of one year bond one year
+ 
+
+ align:start position:0%
+expected price of one year bond one year
+from now is going to be like a oneyear
+
+ align:start position:0%
+from now is going to be like a oneyear
+ 
+
+ align:start position:0%
+from now is going to be like a oneyear
+bond but one year from now so it's 100
+
+ align:start position:0%
+bond but one year from now so it's 100
+ 
+
+ align:start position:0%
+bond but one year from now so it's 100
+divided 1 + i1 t + 1 expected value I
+
+ align:start position:0%
+divided 1 + i1 t + 1 expected value I
+ 
+
+ align:start position:0%
+divided 1 + i1 t + 1 expected value I
+can stick that in there and I get EX the
+
+ align:start position:0%
+can stick that in there and I get EX the
+ 
+
+ align:start position:0%
+can stick that in there and I get EX the
+same expression okay so these are two
+
+ align:start position:0%
+same expression okay so these are two
+ 
+
+ align:start position:0%
+same expression okay so these are two
+different ways of pricing a
+
+ align:start position:0%
+different ways of pricing a
+ 
+
+ align:start position:0%
+different ways of pricing a
+bond or any other asset by
+
+ align:start position:0%
+bond or any other asset by
+ 
+
+ align:start position:0%
+bond or any other asset by
+actually and then we Define the yield to
+
+ align:start position:0%
+actually and then we Define the yield to
+ 
+
+ align:start position:0%
+actually and then we Define the yield to
+maturity so that's an important
+
+ align:start position:0%
+maturity so that's an important
+ 
+
+ align:start position:0%
+maturity so that's an important
+concept yield to
+
+ align:start position:0%
+concept yield to
+ 
+
+ align:start position:0%
+concept yield to
+maturity is is is is a is a rate that is
+
+ align:start position:0%
+maturity is is is is a is a rate that is
+ 
+
+ align:start position:0%
+maturity is is is is a is a rate that is
+a constant
+
+ align:start position:0%
+a constant
+ 
+
+ align:start position:0%
+a constant
+rate that gives you Thea exactly the
+
+ align:start position:0%
+rate that gives you Thea exactly the
+ 
+
+ align:start position:0%
+rate that gives you Thea exactly the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+that gives you the current price of the
+
+ align:start position:0%
+that gives you the current price of the
+ 
+
+ align:start position:0%
+that gives you the current price of the
+bond okay so we already determined the
+
+ align:start position:0%
+bond okay so we already determined the
+ 
+
+ align:start position:0%
+bond okay so we already determined the
+the price of a two-year bond is that
+
+ align:start position:0%
+the price of a two-year bond is that
+ 
+
+ align:start position:0%
+the price of a two-year bond is that
+okay and now I'm saying well suppose
+
+ align:start position:0%
+okay and now I'm saying well suppose
+ 
+
+ align:start position:0%
+okay and now I'm saying well suppose
+that let me look for a rate that is the
+
+ align:start position:0%
+that let me look for a rate that is the
+ 
+
+ align:start position:0%
+that let me look for a rate that is the
+same in both
+
+ align:start position:0%
+same in both
+ 
+
+ align:start position:0%
+same in both
+periods that gives me the same price and
+
+ align:start position:0%
+periods that gives me the same price and
+ 
+
+ align:start position:0%
+periods that gives me the same price and
+that's that's the reason I have a
+
+ align:start position:0%
+that's that's the reason I have a
+ 
+
+ align:start position:0%
+that's that's the reason I have a
+subscript two here at time T so what is
+
+ align:start position:0%
+subscript two here at time T so what is
+ 
+
+ align:start position:0%
+subscript two here at time T so what is
+the rate that if I put a constant rate
+
+ align:start position:0%
+the rate that if I put a constant rate
+ 
+
+ align:start position:0%
+the rate that if I put a constant rate
+so I have 1 + I2 T * 1 +
+
+ align:start position:0%
+so I have 1 + I2 T * 1 +
+ 
+
+ align:start position:0%
+so I have 1 + I2 T * 1 +
+i2t gives me exactly the same price as
+
+ align:start position:0%
+i2t gives me exactly the same price as
+ 
+
+ align:start position:0%
+i2t gives me exactly the same price as
+the one we already determined okay and
+
+ align:start position:0%
+the one we already determined okay and
+ 
+
+ align:start position:0%
+the one we already determined okay and
+that's what we call the yield to
+
+ align:start position:0%
+that's what we call the yield to
+ 
+
+ align:start position:0%
+that's what we call the yield to
+maturity or the yield or or the end in
+
+ align:start position:0%
+maturity or the yield or or the end in
+ 
+
+ align:start position:0%
+maturity or the yield or or the end in
+this case would be a two-year rate if
+
+ align:start position:0%
+this case would be a two-year rate if
+ 
+
+ align:start position:0%
+this case would be a two-year rate if
+you hear what is a two-year rate is that
+
+ align:start position:0%
+you hear what is a two-year rate is that
+ 
+
+ align:start position:0%
+you hear what is a two-year rate is that
+okay H so so we know what this price is
+
+ align:start position:0%
+okay H so so we know what this price is
+ 
+
+ align:start position:0%
+okay H so so we know what this price is
+which is equal to that that's this
+
+ align:start position:0%
+which is equal to that that's this
+ 
+
+ align:start position:0%
+which is equal to that that's this
+expression there so the whole trick here
+
+ align:start position:0%
+expression there so the whole trick here
+ 
+
+ align:start position:0%
+expression there so the whole trick here
+is to find the 2-year rate at time T
+
+ align:start position:0%
+is to find the 2-year rate at time T
+ 
+
+ align:start position:0%
+is to find the 2-year rate at time T
+that that gives exactly the same value
+
+ align:start position:0%
+that that gives exactly the same value
+ 
+
+ align:start position:0%
+that that gives exactly the same value
+that means obviously since 100 is equal
+
+ align:start position:0%
+that means obviously since 100 is equal
+ 
+
+ align:start position:0%
+that means obviously since 100 is equal
+to 100 it means to find the i2t that
+
+ align:start position:0%
+to 100 it means to find the i2t that
+ 
+
+ align:start position:0%
+to 100 it means to find the i2t that
+gives you this equal to that which would
+
+ align:start position:0%
+gives you this equal to that which would
+ 
+
+ align:start position:0%
+gives you this equal to that which would
+say is approximate implies that
+
+ align:start position:0%
+say is approximate implies that
+ 
+
+ align:start position:0%
+say is approximate implies that
+approximately the twoyear rate is like
+
+ align:start position:0%
+approximately the twoyear rate is like
+ 
+
+ align:start position:0%
+approximately the twoyear rate is like
+an average of the two rate of the two
+
+ align:start position:0%
+an average of the two rate of the two
+ 
+
+ align:start position:0%
+an average of the two rate of the two
+onee rates okay but this concept you
+
+ align:start position:0%
+onee rates okay but this concept you
+ 
+
+ align:start position:0%
+onee rates okay but this concept you
+should know what it
+
+ align:start position:0%
+should know what it
+ 
+
+ align:start position:0%
+should know what it
+is I said there are two forms of risk in
+
+ align:start position:0%
+is I said there are two forms of risk in
+ 
+
+ align:start position:0%
+is I said there are two forms of risk in
+a bond there one one type of risk is the
+
+ align:start position:0%
+a bond there one one type of risk is the
+ 
+
+ align:start position:0%
+a bond there one one type of risk is the
+fall risk what if the issuer of the bond
+
+ align:start position:0%
+fall risk what if the issuer of the bond
+ 
+
+ align:start position:0%
+fall risk what if the issuer of the bond
+doesn't pay you now there's a huge issue
+
+ align:start position:0%
+doesn't pay you now there's a huge issue
+ 
+
+ align:start position:0%
+doesn't pay you now there's a huge issue
+with the US you know Deb ceiling because
+
+ align:start position:0%
+with the US you know Deb ceiling because
+ 
+
+ align:start position:0%
+with the US you know Deb ceiling because
+if they somehow they don't fix that
+
+ align:start position:0%
+if they somehow they don't fix that
+ 
+
+ align:start position:0%
+if they somehow they don't fix that
+there will be a default on some treasury
+
+ align:start position:0%
+there will be a default on some treasury
+ 
+
+ align:start position:0%
+there will be a default on some treasury
+bonds let's hope that it doesn't happen
+
+ align:start position:0%
+bonds let's hope that it doesn't happen
+ 
+
+ align:start position:0%
+bonds let's hope that it doesn't happen
+but but but that's theault risk is that
+
+ align:start position:0%
+but but but that's theault risk is that
+ 
+
+ align:start position:0%
+but but but that's theault risk is that
+whoever issued the debt at the time in
+
+ align:start position:0%
+whoever issued the debt at the time in
+ 
+
+ align:start position:0%
+whoever issued the debt at the time in
+which he should be paying you a coupon
+
+ align:start position:0%
+which he should be paying you a coupon
+ 
+
+ align:start position:0%
+which he should be paying you a coupon
+or or the principal the face value it
+
+ align:start position:0%
+or or the principal the face value it
+ 
+
+ align:start position:0%
+or or the principal the face value it
+doesn't pay you that's the fall risk
+
+ align:start position:0%
+doesn't pay you that's the fall risk
+ 
+
+ align:start position:0%
+doesn't pay you that's the fall risk
+okay and and and typically US Treasury
+
+ align:start position:0%
+okay and and and typically US Treasury
+ 
+
+ align:start position:0%
+okay and and and typically US Treasury
+bonds don't have the risk so nobody
+
+ align:start position:0%
+bonds don't have the risk so nobody
+ 
+
+ align:start position:0%
+bonds don't have the risk so nobody
+worries about that at this moment
+
+ align:start position:0%
+worries about that at this moment
+ 
+
+ align:start position:0%
+worries about that at this moment
+the default risk price in US bonds for
+
+ align:start position:0%
+the default risk price in US bonds for
+ 
+
+ align:start position:0%
+the default risk price in US bonds for
+one month bonds is higher than that of
+
+ align:start position:0%
+one month bonds is higher than that of
+ 
+
+ align:start position:0%
+one month bonds is higher than that of
+Mexico the bonds in Mexico or Brazil
+
+ align:start position:0%
+Mexico the bonds in Mexico or Brazil
+ 
+
+ align:start position:0%
+Mexico the bonds in Mexico or Brazil
+that tells you that the kind of things
+
+ align:start position:0%
+that tells you that the kind of things
+ 
+
+ align:start position:0%
+that tells you that the kind of things
+we have but in any EV so so this is a
+
+ align:start position:0%
+we have but in any EV so so this is a
+ 
+
+ align:start position:0%
+we have but in any EV so so this is a
+temporary default risk I mean nobody
+
+ align:start position:0%
+temporary default risk I mean nobody
+ 
+
+ align:start position:0%
+temporary default risk I mean nobody
+expects in the US that this will not be
+
+ align:start position:0%
+expects in the US that this will not be
+ 
+
+ align:start position:0%
+expects in the US that this will not be
+eventually repaid but you can cause a
+
+ align:start position:0%
+eventually repaid but you can cause a
+ 
+
+ align:start position:0%
+eventually repaid but you can cause a
+big
+
+ align:start position:0%
+big
+ 
+
+ align:start position:0%
+big
+mess by just ER delaying a a coupon
+
+ align:start position:0%
+mess by just ER delaying a a coupon
+ 
+
+ align:start position:0%
+mess by just ER delaying a a coupon
+payment I mean when when when these
+
+ align:start position:0%
+payment I mean when when when these
+ 
+
+ align:start position:0%
+payment I mean when when when these
+coupons are huge no
+
+ align:start position:0%
+coupons are huge no
+ 
+
+ align:start position:0%
+coupons are huge no
+and so so that's what's leading to all
+
+ align:start position:0%
+and so so that's what's leading to all
+ 
+
+ align:start position:0%
+and so so that's what's leading to all
+this concern but but in any
+
+ align:start position:0%
+this concern but but in any
+ 
+
+ align:start position:0%
+this concern but but in any
+EV that's one type of risk but we didn't
+
+ align:start position:0%
+EV that's one type of risk but we didn't
+ 
+
+ align:start position:0%
+EV that's one type of risk but we didn't
+look at that type of risk a lot the
+
+ align:start position:0%
+look at that type of risk a lot the
+ 
+
+ align:start position:0%
+look at that type of risk a lot the
+corporate bonds have a lot of that risk
+
+ align:start position:0%
+corporate bonds have a lot of that risk
+ 
+
+ align:start position:0%
+corporate bonds have a lot of that risk
+but we didn't look at that kind of risk
+
+ align:start position:0%
+but we didn't look at that kind of risk
+ 
+
+ align:start position:0%
+but we didn't look at that kind of risk
+we look at the another kind of risk
+
+ align:start position:0%
+we look at the another kind of risk
+ 
+
+ align:start position:0%
+we look at the another kind of risk
+which is price risk no if you have a one
+
+ align:start position:0%
+which is price risk no if you have a one
+ 
+
+ align:start position:0%
+which is price risk no if you have a one
+you invest in your oneyear bond there no
+
+ align:start position:0%
+you invest in your oneyear bond there no
+ 
+
+ align:start position:0%
+you invest in your oneyear bond there no
+price risk you're going to get your
+
+ align:start position:0%
+price risk you're going to get your
+ 
+
+ align:start position:0%
+price risk you're going to get your
+coupon your face value of 100 at the end
+
+ align:start position:0%
+coupon your face value of 100 at the end
+ 
+
+ align:start position:0%
+coupon your face value of 100 at the end
+of the year that's it if you go through
+
+ align:start position:0%
+of the year that's it if you go through
+ 
+
+ align:start position:0%
+of the year that's it if you go through
+a two-year strategy there's a risk there
+
+ align:start position:0%
+a two-year strategy there's a risk there
+ 
+
+ align:start position:0%
+a two-year strategy there's a risk there
+because you don't know exactly what the
+
+ align:start position:0%
+because you don't know exactly what the
+ 
+
+ align:start position:0%
+because you don't know exactly what the
+price of the two oneyear Bond will will
+
+ align:start position:0%
+price of the two oneyear Bond will will
+ 
+
+ align:start position:0%
+price of the two oneyear Bond will will
+be one year from now and there's a risk
+
+ align:start position:0%
+be one year from now and there's a risk
+ 
+
+ align:start position:0%
+be one year from now and there's a risk
+there we are not looking at what risk
+
+ align:start position:0%
+there we are not looking at what risk
+ 
+
+ align:start position:0%
+there we are not looking at what risk
+Avers cons investors do and so on but in
+
+ align:start position:0%
+Avers cons investors do and so on but in
+ 
+
+ align:start position:0%
+Avers cons investors do and so on but in
+reality there is such a risk okay and
+
+ align:start position:0%
+reality there is such a risk okay and
+ 
+
+ align:start position:0%
+reality there is such a risk okay and
+just the way we mold that is we said
+
+ align:start position:0%
+just the way we mold that is we said
+ 
+
+ align:start position:0%
+just the way we mold that is we said
+well then if I'm going to go through two
+
+ align:start position:0%
+well then if I'm going to go through two
+ 
+
+ align:start position:0%
+well then if I'm going to go through two
+years through a two-year bone route for
+
+ align:start position:0%
+years through a two-year bone route for
+ 
+
+ align:start position:0%
+years through a two-year bone route for
+a one-year investment then I don't have
+
+ align:start position:0%
+a one-year investment then I don't have
+ 
+
+ align:start position:0%
+a one-year investment then I don't have
+to H set this equal to the return I get
+
+ align:start position:0%
+to H set this equal to the return I get
+ 
+
+ align:start position:0%
+to H set this equal to the return I get
+in the sh Bond the oneyear bond I have
+
+ align:start position:0%
+in the sh Bond the oneyear bond I have
+ 
+
+ align:start position:0%
+in the sh Bond the oneyear bond I have
+to add an extra risk premium and then
+
+ align:start position:0%
+to add an extra risk premium and then
+ 
+
+ align:start position:0%
+to add an extra risk premium and then
+where right to this formula using the
+
+ align:start position:0%
+where right to this formula using the
+ 
+
+ align:start position:0%
+where right to this formula using the
+same steps we said well the one the the
+
+ align:start position:0%
+same steps we said well the one the the
+ 
+
+ align:start position:0%
+same steps we said well the one the the
+the two-year rate is really the average
+
+ align:start position:0%
+the two-year rate is really the average
+ 
+
+ align:start position:0%
+the two-year rate is really the average
+of the one expected onee rates plus a a
+
+ align:start position:0%
+of the one expected onee rates plus a a
+ 
+
+ align:start position:0%
+of the one expected onee rates plus a a
+premium and we call that actually the
+
+ align:start position:0%
+premium and we call that actually the
+ 
+
+ align:start position:0%
+premium and we call that actually the
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+premium you're more likely to face a
+
+ align:start position:0%
+premium you're more likely to face a
+ 
+
+ align:start position:0%
+premium you're more likely to face a
+question about the top of this slide and
+
+ align:start position:0%
+question about the top of this slide and
+ 
+
+ align:start position:0%
+question about the top of this slide and
+the bottom of the slide but I don't
+
+ align:start position:0%
+the bottom of the slide but I don't
+ 
+
+ align:start position:0%
+the bottom of the slide but I don't
+remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fully
+
+ align:start position:0%
+fully
+ 
+
+ align:start position:0%
+fully
+ER stock prices and Present Value well
+
+ align:start position:0%
+ER stock prices and Present Value well
+ 
+
+ align:start position:0%
+ER stock prices and Present Value well
+it's the same sort of idea know the only
+
+ align:start position:0%
+it's the same sort of idea know the only
+ 
+
+ align:start position:0%
+it's the same sort of idea know the only
+difference is
+
+ align:start position:0%
+difference is
+ 
+
+ align:start position:0%
+difference is
+that that that uh equities do not have
+
+ align:start position:0%
+that that that uh equities do not have
+ 
+
+ align:start position:0%
+that that that uh equities do not have
+maturity stocks do not have maturity in
+
+ align:start position:0%
+maturity stocks do not have maturity in
+ 
+
+ align:start position:0%
+maturity stocks do not have maturity in
+principle a company would last forever
+
+ align:start position:0%
+principle a company would last forever
+ 
+
+ align:start position:0%
+principle a company would last forever
+and and and so there's no there's no
+
+ align:start position:0%
+and and and so there's no there's no
+ 
+
+ align:start position:0%
+and and and so there's no there's no
+maturity and there is also the
+
+ align:start position:0%
+maturity and there is also the
+ 
+
+ align:start position:0%
+maturity and there is also the
+commitment of the coupons are a lot
+
+ align:start position:0%
+commitment of the coupons are a lot
+ 
+
+ align:start position:0%
+commitment of the coupons are a lot
+shakier in the sense that you know yeah
+
+ align:start position:0%
+shakier in the sense that you know yeah
+ 
+
+ align:start position:0%
+shakier in the sense that you know yeah
+compan is likely to give dividends they
+
+ align:start position:0%
+compan is likely to give dividends they
+ 
+
+ align:start position:0%
+compan is likely to give dividends they
+may announce a dividend policy but it's
+
+ align:start position:0%
+may announce a dividend policy but it's
+ 
+
+ align:start position:0%
+may announce a dividend policy but it's
+not a
+
+ align:start position:0%
+not a
+ 
+
+ align:start position:0%
+not a
+commitment if you know Regional Banks
+
+ align:start position:0%
+commitment if you know Regional Banks
+ 
+
+ align:start position:0%
+commitment if you know Regional Banks
+now are not giving any dividend because
+
+ align:start position:0%
+now are not giving any dividend because
+ 
+
+ align:start position:0%
+now are not giving any dividend because
+they want to preserve the capital okay
+
+ align:start position:0%
+they want to preserve the capital okay
+ 
+
+ align:start position:0%
+they want to preserve the capital okay
+they could but they're not because they
+
+ align:start position:0%
+they could but they're not because they
+ 
+
+ align:start position:0%
+they could but they're not because they
+want to build Capital just to be more
+
+ align:start position:0%
+want to build Capital just to be more
+ 
+
+ align:start position:0%
+want to build Capital just to be more
+resilient
+
+ align:start position:0%
+resilient
+ 
+
+ align:start position:0%
+resilient
+to any fly bad news okay but anyway so
+
+ align:start position:0%
+to any fly bad news okay but anyway so
+ 
+
+ align:start position:0%
+to any fly bad news okay but anyway so
+Equity that that means that you always
+
+ align:start position:0%
+Equity that that means that you always
+ 
+
+ align:start position:0%
+Equity that that means that you always
+have this future price floating around
+
+ align:start position:0%
+have this future price floating around
+ 
+
+ align:start position:0%
+have this future price floating around
+and you can keep substituting this
+
+ align:start position:0%
+and you can keep substituting this
+ 
+
+ align:start position:0%
+and you can keep substituting this
+multiple times and essentially you get
+
+ align:start position:0%
+multiple times and essentially you get
+ 
+
+ align:start position:0%
+multiple times and essentially you get
+to an expression that says look the the
+
+ align:start position:0%
+to an expression that says look the the
+ 
+
+ align:start position:0%
+to an expression that says look the the
+price of equity is really this the
+
+ align:start position:0%
+price of equity is really this the
+ 
+
+ align:start position:0%
+price of equity is really this the
+spected present discounted value of the
+
+ align:start position:0%
+spected present discounted value of the
+ 
+
+ align:start position:0%
+spected present discounted value of the
+dividends H and that includes lots of
+
+ align:start position:0%
+dividends H and that includes lots of
+ 
+
+ align:start position:0%
+dividends H and that includes lots of
+uncertainty because because you don't
+
+ align:start position:0%
+uncertainty because because you don't
+ 
+
+ align:start position:0%
+uncertainty because because you don't
+know exactly where the interest rate
+
+ align:start position:0%
+know exactly where the interest rate
+ 
+
+ align:start position:0%
+know exactly where the interest rate
+will be in that period and so on and
+
+ align:start position:0%
+will be in that period and so on and
+ 
+
+ align:start position:0%
+will be in that period and so on and
+there's always a a a remaining term out
+
+ align:start position:0%
+there's always a a a remaining term out
+ 
+
+ align:start position:0%
+there's always a a a remaining term out
+there which also causes a lot of trouble
+
+ align:start position:0%
+there which also causes a lot of trouble
+ 
+
+ align:start position:0%
+there which also causes a lot of trouble
+in practice
+
+ align:start position:0%
+in practice
+ 
+
+ align:start position:0%
+in practice
+assets equities move a lot more than
+
+ align:start position:0%
+assets equities move a lot more than
+ 
+
+ align:start position:0%
+assets equities move a lot more than
+than what you can justify with the
+
+ align:start position:0%
+than what you can justify with the
+ 
+
+ align:start position:0%
+than what you can justify with the
+Spector present value of
+
+ align:start position:0%
+Spector present value of
+ 
+
+ align:start position:0%
+Spector present value of
+dividends there's a lot of
+
+ align:start position:0%
+dividends there's a lot of
+ 
+
+ align:start position:0%
+dividends there's a lot of
+volatility ER there are bubbles and all
+
+ align:start position:0%
+volatility ER there are bubbles and all
+ 
+
+ align:start position:0%
+volatility ER there are bubbles and all
+sort of things I told you the story of
+
+ align:start position:0%
+sort of things I told you the story of
+ 
+
+ align:start position:0%
+sort of things I told you the story of
+Newton and and so on so so this formula
+
+ align:start position:0%
+Newton and and so on so so this formula
+ 
+
+ align:start position:0%
+Newton and and so on so so this formula
+for the bonds those formulas are great
+
+ align:start position:0%
+for the bonds those formulas are great
+ 
+
+ align:start position:0%
+for the bonds those formulas are great
+for Equity you're going to be pretty far
+
+ align:start position:0%
+for Equity you're going to be pretty far
+ 
+
+ align:start position:0%
+for Equity you're going to be pretty far
+off actual prices if you use this type
+
+ align:start position:0%
+off actual prices if you use this type
+ 
+
+ align:start position:0%
+off actual prices if you use this type
+of formulas still people call this the
+
+ align:start position:0%
+of formulas still people call this the
+ 
+
+ align:start position:0%
+of formulas still people call this the
+fundamental value of equity and then the
+
+ align:start position:0%
+fundamental value of equity and then the
+ 
+
+ align:start position:0%
+fundamental value of equity and then the
+rest is sort of more speculative but the
+
+ align:start position:0%
+rest is sort of more speculative but the
+ 
+
+ align:start position:0%
+rest is sort of more speculative but the
+point is that the speculative component
+
+ align:start position:0%
+point is that the speculative component
+ 
+
+ align:start position:0%
+point is that the speculative component
+moves at all is is responsible for a
+
+ align:start position:0%
+moves at all is is responsible for a
+ 
+
+ align:start position:0%
+moves at all is is responsible for a
+very large share of the volatility in
+
+ align:start position:0%
+very large share of the volatility in
+ 
+
+ align:start position:0%
+very large share of the volatility in
+asset in equity price in any event I'm
+
+ align:start position:0%
+asset in equity price in any event I'm
+ 
+
+ align:start position:0%
+asset in equity price in any event I'm
+not going to ask you about this kind of
+
+ align:start position:0%
+not going to ask you about this kind of
+ 
+
+ align:start position:0%
+not going to ask you about this kind of
+yeah for that final equation on the SL
+
+ align:start position:0%
+yeah for that final equation on the SL
+ 
+
+ align:start position:0%
+yeah for that final equation on the SL
+uh there's no
+
+ align:start position:0%
+uh there's no
+ 
+
+ align:start position:0%
+uh there's no
+like expression for Q it's here keep
+
+ align:start position:0%
+like expression for Q it's here keep
+ 
+
+ align:start position:0%
+like expression for Q it's here keep
+going forever it doesn't stop yeah it
+
+ align:start position:0%
+going forever it doesn't stop yeah it
+ 
+
+ align:start position:0%
+going forever it doesn't stop yeah it
+just discounted more and more and more
+
+ align:start position:0%
+just discounted more and more and more
+ 
+
+ align:start position:0%
+just discounted more and more and more
+so you would expect it to be less and
+
+ align:start position:0%
+so you would expect it to be less and
+ 
+
+ align:start position:0%
+so you would expect it to be less and
+less important but if the thing is
+
+ align:start position:0%
+less important but if the thing is
+ 
+
+ align:start position:0%
+less important but if the thing is
+blowing up then you know it maybe it may
+
+ align:start position:0%
+blowing up then you know it maybe it may
+ 
+
+ align:start position:0%
+blowing up then you know it maybe it may
+dominate the the the the heavier and
+
+ align:start position:0%
+dominate the the the the heavier and
+ 
+
+ align:start position:0%
+dominate the the the the heavier and
+heavier discounting because it's further
+
+ align:start position:0%
+heavier discounting because it's further
+ 
+
+ align:start position:0%
+heavier discounting because it's further
+further out in the future and that's the
+
+ align:start position:0%
+further out in the future and that's the
+ 
+
+ align:start position:0%
+further out in the future and that's the
+way you create theories of bubbles you
+
+ align:start position:0%
+way you create theories of bubbles you
+ 
+
+ align:start position:0%
+way you create theories of bubbles you
+can even come up with rational bubbles
+
+ align:start position:0%
+can even come up with rational bubbles
+ 
+
+ align:start position:0%
+can even come up with rational bubbles
+into the way but again that's what of
+
+ align:start position:0%
+into the way but again that's what of
+ 
+
+ align:start position:0%
+into the way but again that's what of
+course uh what else ah then we look at
+
+ align:start position:0%
+course uh what else ah then we look at
+ 
+
+ align:start position:0%
+course uh what else ah then we look at
+what is the effect of an expansionary
+
+ align:start position:0%
+what is the effect of an expansionary
+ 
+
+ align:start position:0%
+what is the effect of an expansionary
+monetary policy on asset prices and we
+
+ align:start position:0%
+monetary policy on asset prices and we
+ 
+
+ align:start position:0%
+monetary policy on asset prices and we
+said well obviously it's going to if
+
+ align:start position:0%
+said well obviously it's going to if
+ 
+
+ align:start position:0%
+said well obviously it's going to if
+lower interest rate that's going to
+
+ align:start position:0%
+lower interest rate that's going to
+ 
+
+ align:start position:0%
+lower interest rate that's going to
+increase the value of any asset that
+
+ align:start position:0%
+increase the value of any asset that
+ 
+
+ align:start position:0%
+increase the value of any asset that
+pays in the future returns and so it
+
+ align:start position:0%
+pays in the future returns and so it
+ 
+
+ align:start position:0%
+pays in the future returns and so it
+typically is typically the case that
+
+ align:start position:0%
+typically is typically the case that
+ 
+
+ align:start position:0%
+typically is typically the case that
+that expansion in Monet monetary policy
+
+ align:start position:0%
+that expansion in Monet monetary policy
+ 
+
+ align:start position:0%
+that expansion in Monet monetary policy
+will lead to an appreciation of all
+
+ align:start position:0%
+will lead to an appreciation of all
+ 
+
+ align:start position:0%
+will lead to an appreciation of all
+assets uh most assets but certainly
+
+ align:start position:0%
+assets uh most assets but certainly
+ 
+
+ align:start position:0%
+assets uh most assets but certainly
+bonds will go up directly because that's
+
+ align:start position:0%
+bonds will go up directly because that's
+ 
+
+ align:start position:0%
+bonds will go up directly because that's
+where the interest rate has the maximum
+
+ align:start position:0%
+where the interest rate has the maximum
+ 
+
+ align:start position:0%
+where the interest rate has the maximum
+the clearest effect but it's also the
+
+ align:start position:0%
+the clearest effect but it's also the
+ 
+
+ align:start position:0%
+the clearest effect but it's also the
+case that it tends to be bullish for
+
+ align:start position:0%
+case that it tends to be bullish for
+ 
+
+ align:start position:0%
+case that it tends to be bullish for
+Equity as well no it's that got interest
+
+ align:start position:0%
+Equity as well no it's that got interest
+ 
+
+ align:start position:0%
+Equity as well no it's that got interest
+rate and that a lot of the response of
+
+ align:start position:0%
+rate and that a lot of the response of
+ 
+
+ align:start position:0%
+rate and that a lot of the response of
+equity to news has to do with expected
+
+ align:start position:0%
+equity to news has to do with expected
+ 
+
+ align:start position:0%
+equity to news has to do with expected
+behavior of the FED in the future do you
+
+ align:start position:0%
+behavior of the FED in the future do you
+ 
+
+ align:start position:0%
+behavior of the FED in the future do you
+think that this will lead them to
+
+ align:start position:0%
+think that this will lead them to
+ 
+
+ align:start position:0%
+think that this will lead them to
+increase interest rate or to lower
+
+ align:start position:0%
+increase interest rate or to lower
+ 
+
+ align:start position:0%
+increase interest rate or to lower
+interest rate and things of that kind
+
+ align:start position:0%
+interest rate and things of that kind
+ 
+
+ align:start position:0%
+interest rate and things of that kind
+and again I think that's a little too
+
+ align:start position:0%
+and again I think that's a little too
+ 
+
+ align:start position:0%
+and again I think that's a little too
+complicated for you for
+
+ align:start position:0%
+complicated for you for
+ 
+
+ align:start position:0%
+complicated for you for
+now it said what is the effect of an
+
+ align:start position:0%
+now it said what is the effect of an
+ 
+
+ align:start position:0%
+now it said what is the effect of an
+increase in consumer spending on asset
+
+ align:start position:0%
+increase in consumer spending on asset
+ 
+
+ align:start position:0%
+increase in consumer spending on asset
+prices well that depends I mean it's
+
+ align:start position:0%
+prices well that depends I mean it's
+ 
+
+ align:start position:0%
+prices well that depends I mean it's
+clear that that if consumers become more
+
+ align:start position:0%
+clear that that if consumers become more
+ 
+
+ align:start position:0%
+clear that that if consumers become more
+bullish that's going to tend to lead to
+
+ align:start position:0%
+bullish that's going to tend to lead to
+ 
+
+ align:start position:0%
+bullish that's going to tend to lead to
+more cash flows for the firms so Equity
+
+ align:start position:0%
+more cash flows for the firms so Equity
+ 
+
+ align:start position:0%
+more cash flows for the firms so Equity
+at least will go up bonds no because
+
+ align:start position:0%
+at least will go up bonds no because
+ 
+
+ align:start position:0%
+at least will go up bonds no because
+they don't the coupon is set fixed
+
+ align:start position:0%
+they don't the coupon is set fixed
+ 
+
+ align:start position:0%
+they don't the coupon is set fixed
+doesn't depend on whether the econom is
+
+ align:start position:0%
+doesn't depend on whether the econom is
+ 
+
+ align:start position:0%
+doesn't depend on whether the econom is
+doing better or worse I'm assuming
+
+ align:start position:0%
+doing better or worse I'm assuming
+ 
+
+ align:start position:0%
+doing better or worse I'm assuming
+there's no default risk ER but it
+
+ align:start position:0%
+there's no default risk ER but it
+ 
+
+ align:start position:0%
+there's no default risk ER but it
+depends a lot of what you expect the FED
+
+ align:start position:0%
+depends a lot of what you expect the FED
+ 
+
+ align:start position:0%
+depends a lot of what you expect the FED
+to do if the FED if you think that this
+
+ align:start position:0%
+to do if the FED if you think that this
+ 
+
+ align:start position:0%
+to do if the FED if you think that this
+is going to trigger a Fed hike then it's
+
+ align:start position:0%
+is going to trigger a Fed hike then it's
+ 
+
+ align:start position:0%
+is going to trigger a Fed hike then it's
+bad news for bonds you know because the
+
+ align:start position:0%
+bad news for bonds you know because the
+ 
+
+ align:start position:0%
+bad news for bonds you know because the
+F the bonds do not benefit from the
+
+ align:start position:0%
+F the bonds do not benefit from the
+ 
+
+ align:start position:0%
+F the bonds do not benefit from the
+economic activity and and they get hurt
+
+ align:start position:0%
+economic activity and and they get hurt
+ 
+
+ align:start position:0%
+economic activity and and they get hurt
+by higher interest rate so it depends a
+
+ align:start position:0%
+by higher interest rate so it depends a
+ 
+
+ align:start position:0%
+by higher interest rate so it depends a
+lot on what you anticipate the FED to do
+
+ align:start position:0%
+lot on what you anticipate the FED to do
+ 
+
+ align:start position:0%
+lot on what you anticipate the FED to do
+or not but again I think this is a bit
+
+ align:start position:0%
+or not but again I think this is a bit
+ 
+
+ align:start position:0%
+or not but again I think this is a bit
+more complicated than what you need to
+
+ align:start position:0%
+more complicated than what you need to
+ 
+
+ align:start position:0%
+more complicated than what you need to
+know okay the last step was
+
+ align:start position:0%
+know okay the last step was
+ 
+
+ align:start position:0%
+know okay the last step was
+to H bring expectations into the aslm
+
+ align:start position:0%
+to H bring expectations into the aslm
+ 
+
+ align:start position:0%
+to H bring expectations into the aslm
+model I said the model we discussed
+
+ align:start position:0%
+model I said the model we discussed
+ 
+
+ align:start position:0%
+model I said the model we discussed
+through the course on the aslm except
+
+ align:start position:0%
+through the course on the aslm except
+ 
+
+ align:start position:0%
+through the course on the aslm except
+for the part where we put the exchange
+
+ align:start position:0%
+for the part where we put the exchange
+ 
+
+ align:start position:0%
+for the part where we put the exchange
+rate where we you know we we have to
+
+ align:start position:0%
+rate where we you know we we have to
+ 
+
+ align:start position:0%
+rate where we you know we we have to
+think about the future exchange rates
+
+ align:start position:0%
+think about the future exchange rates
+ 
+
+ align:start position:0%
+think about the future exchange rates
+and things like that it was really
+
+ align:start position:0%
+and things like that it was really
+ 
+
+ align:start position:0%
+and things like that it was really
+overweight the present in reality
+
+ align:start position:0%
+overweight the present in reality
+ 
+
+ align:start position:0%
+overweight the present in reality
+expectations matter a lot for consu
+
+ align:start position:0%
+expectations matter a lot for consu
+ 
+
+ align:start position:0%
+expectations matter a lot for consu
+consumers decisions for firm's decisions
+
+ align:start position:0%
+consumers decisions for firm's decisions
+ 
+
+ align:start position:0%
+consumers decisions for firm's decisions
+and so on probably matters even more
+
+ align:start position:0%
+and so on probably matters even more
+ 
+
+ align:start position:0%
+and so on probably matters even more
+than the future than the present okay
+
+ align:start position:0%
+than the future than the present okay
+ 
+
+ align:start position:0%
+than the future than the present okay
+ER and so so what we did is we expanded
+
+ align:start position:0%
+ER and so so what we did is we expanded
+ 
+
+ align:start position:0%
+ER and so so what we did is we expanded
+H the islm to include expectation we see
+
+ align:start position:0%
+H the islm to include expectation we see
+ 
+
+ align:start position:0%
+H the islm to include expectation we see
+well consumers not only worry about
+
+ align:start position:0%
+well consumers not only worry about
+ 
+
+ align:start position:0%
+well consumers not only worry about
+disposable income this part will show up
+
+ align:start position:0%
+disposable income this part will show up
+ 
+
+ align:start position:0%
+disposable income this part will show up
+in your test so so you should understand
+
+ align:start position:0%
+in your test so so you should understand
+ 
+
+ align:start position:0%
+in your test so so you should understand
+what what the eslm model is and do the
+
+ align:start position:0%
+what what the eslm model is and do the
+ 
+
+ align:start position:0%
+what what the eslm model is and do the
+comparative Statics that correspond to
+
+ align:start position:0%
+comparative Statics that correspond to
+ 
+
+ align:start position:0%
+comparative Statics that correspond to
+this model so what we did here is as
+
+ align:start position:0%
+this model so what we did here is as
+ 
+
+ align:start position:0%
+this model so what we did here is as
+well consumers not only worry about the
+
+ align:start position:0%
+well consumers not only worry about the
+ 
+
+ align:start position:0%
+well consumers not only worry about the
+current disposable income H they also
+
+ align:start position:0%
+current disposable income H they also
+ 
+
+ align:start position:0%
+current disposable income H they also
+worry about the income they receive in
+
+ align:start position:0%
+worry about the income they receive in
+ 
+
+ align:start position:0%
+worry about the income they receive in
+the future through financial asset
+
+ align:start position:0%
+the future through financial asset
+ 
+
+ align:start position:0%
+the future through financial asset
+Financial wealth or through their future
+
+ align:start position:0%
+Financial wealth or through their future
+ 
+
+ align:start position:0%
+Financial wealth or through their future
+labor income that's what we call human
+
+ align:start position:0%
+labor income that's what we call human
+ 
+
+ align:start position:0%
+labor income that's what we call human
+wealth but the point is that
+
+ align:start position:0%
+wealth but the point is that
+ 
+
+ align:start position:0%
+wealth but the point is that
+expectations about the future matter for
+
+ align:start position:0%
+expectations about the future matter for
+ 
+
+ align:start position:0%
+expectations about the future matter for
+consumption in the first part of the
+
+ align:start position:0%
+consumption in the first part of the
+ 
+
+ align:start position:0%
+consumption in the first part of the
+course we we summarize all that in that
+
+ align:start position:0%
+course we we summarize all that in that
+ 
+
+ align:start position:0%
+course we we summarize all that in that
+little parameters c0 which said
+
+ align:start position:0%
+little parameters c0 which said
+ 
+
+ align:start position:0%
+little parameters c0 which said
+consumers can be bullish or not but a
+
+ align:start position:0%
+consumers can be bullish or not but a
+ 
+
+ align:start position:0%
+consumers can be bullish or not but a
+lot of what happens here is what shifts
+
+ align:start position:0%
+lot of what happens here is what shifts
+ 
+
+ align:start position:0%
+lot of what happens here is what shifts
+c0 in the first part of the of the
+
+ align:start position:0%
+c0 in the first part of the of the
+ 
+
+ align:start position:0%
+c0 in the first part of the of the
+course and and this also highlight an
+
+ align:start position:0%
+course and and this also highlight an
+ 
+
+ align:start position:0%
+course and and this also highlight an
+important concept which is typically if
+
+ align:start position:0%
+important concept which is typically if
+ 
+
+ align:start position:0%
+important concept which is typically if
+you expect something to have only a
+
+ align:start position:0%
+you expect something to have only a
+ 
+
+ align:start position:0%
+you expect something to have only a
+temporary transitory consequence it will
+
+ align:start position:0%
+temporary transitory consequence it will
+ 
+
+ align:start position:0%
+temporary transitory consequence it will
+move consumption little relative to when
+
+ align:start position:0%
+move consumption little relative to when
+ 
+
+ align:start position:0%
+move consumption little relative to when
+you expect that change to be permanent
+
+ align:start position:0%
+you expect that change to be permanent
+ 
+
+ align:start position:0%
+you expect that change to be permanent
+so you expect current income to be up
+
+ align:start position:0%
+so you expect current income to be up
+ 
+
+ align:start position:0%
+so you expect current income to be up
+but but future income to go back to a
+
+ align:start position:0%
+but but future income to go back to a
+ 
+
+ align:start position:0%
+but but future income to go back to a
+lower level that's not going to change
+
+ align:start position:0%
+lower level that's not going to change
+ 
+
+ align:start position:0%
+lower level that's not going to change
+current consumption a lot however if you
+
+ align:start position:0%
+current consumption a lot however if you
+ 
+
+ align:start position:0%
+current consumption a lot however if you
+think there's a change that will
+
+ align:start position:0%
+think there's a change that will
+ 
+
+ align:start position:0%
+think there's a change that will
+increase in consumers income permanently
+
+ align:start position:0%
+increase in consumers income permanently
+ 
+
+ align:start position:0%
+increase in consumers income permanently
+up well that will increase not only this
+
+ align:start position:0%
+up well that will increase not only this
+ 
+
+ align:start position:0%
+up well that will increase not only this
+but also wealth human wealth and that
+
+ align:start position:0%
+but also wealth human wealth and that
+ 
+
+ align:start position:0%
+but also wealth human wealth and that
+will lead to a much larger response of
+
+ align:start position:0%
+will lead to a much larger response of
+ 
+
+ align:start position:0%
+will lead to a much larger response of
+consumption
+
+ align:start position:0%
+consumption
+ 
+
+ align:start position:0%
+consumption
+okay we did more or less for the same
+
+ align:start position:0%
+okay we did more or less for the same
+ 
+
+ align:start position:0%
+okay we did more or less for the same
+for investment obviously what matters
+
+ align:start position:0%
+for investment obviously what matters
+ 
+
+ align:start position:0%
+for investment obviously what matters
+for investment is the is future cash
+
+ align:start position:0%
+for investment is the is future cash
+ 
+
+ align:start position:0%
+for investment is the is future cash
+flows and and there we talk about the
+
+ align:start position:0%
+flows and and there we talk about the
+ 
+
+ align:start position:0%
+flows and and there we talk about the
+concept of depreciation but really was
+
+ align:start position:0%
+concept of depreciation but really was
+ 
+
+ align:start position:0%
+concept of depreciation but really was
+this was expected present discounted
+
+ align:start position:0%
+this was expected present discounted
+ 
+
+ align:start position:0%
+this was expected present discounted
+value of the cash flow generated by by
+
+ align:start position:0%
+value of the cash flow generated by by
+ 
+
+ align:start position:0%
+value of the cash flow generated by by
+an extra unit of capital so expected per
+
+ align:start position:0%
+an extra unit of capital so expected per
+ 
+
+ align:start position:0%
+an extra unit of capital so expected per
+Val discounted value
+
+ align:start position:0%
+Val discounted value
+ 
+
+ align:start position:0%
+Val discounted value
+formula so we said you know we we in the
+
+ align:start position:0%
+formula so we said you know we we in the
+ 
+
+ align:start position:0%
+formula so we said you know we we in the
+first part of the course we just look at
+
+ align:start position:0%
+first part of the course we just look at
+ 
+
+ align:start position:0%
+first part of the course we just look at
+an investment function that has output
+
+ align:start position:0%
+an investment function that has output
+ 
+
+ align:start position:0%
+an investment function that has output
+here and then we have an interest rate
+
+ align:start position:0%
+here and then we have an interest rate
+ 
+
+ align:start position:0%
+here and then we have an interest rate
+here where now we have something that's
+
+ align:start position:0%
+here where now we have something that's
+ 
+
+ align:start position:0%
+here where now we have something that's
+more complicated has future output which
+
+ align:start position:0%
+more complicated has future output which
+ 
+
+ align:start position:0%
+more complicated has future output which
+has appr proxim for future cash flows
+
+ align:start position:0%
+has appr proxim for future cash flows
+ 
+
+ align:start position:0%
+has appr proxim for future cash flows
+but also current and future interest
+
+ align:start position:0%
+but also current and future interest
+ 
+
+ align:start position:0%
+but also current and future interest
+rates because those affect the value of
+
+ align:start position:0%
+rates because those affect the value of
+ 
+
+ align:start position:0%
+rates because those affect the value of
+those future cash flows H in terms of
+
+ align:start position:0%
+those future cash flows H in terms of
+ 
+
+ align:start position:0%
+those future cash flows H in terms of
+today's
+
+ align:start position:0%
+today's
+ 
+
+ align:start position:0%
+today's
+dollars and we put all of this together
+
+ align:start position:0%
+dollars and we put all of this together
+ 
+
+ align:start position:0%
+dollars and we put all of this together
+and we ended up with an expanded
+
+ align:start position:0%
+and we ended up with an expanded
+ 
+
+ align:start position:0%
+and we ended up with an expanded
+aggregate demand in which ER you know in
+
+ align:start position:0%
+aggregate demand in which ER you know in
+ 
+
+ align:start position:0%
+aggregate demand in which ER you know in
+which we had the same parameters that we
+
+ align:start position:0%
+which we had the same parameters that we
+ 
+
+ align:start position:0%
+which we had the same parameters that we
+had ER when we did the static
+
+ align:start position:0%
+had ER when we did the static
+ 
+
+ align:start position:0%
+had ER when we did the static
+model without expectations but now we
+
+ align:start position:0%
+model without expectations but now we
+ 
+
+ align:start position:0%
+model without expectations but now we
+get sort of the same things repeated
+
+ align:start position:0%
+get sort of the same things repeated
+ 
+
+ align:start position:0%
+get sort of the same things repeated
+here one year ahead because it it
+
+ align:start position:0%
+here one year ahead because it it
+ 
+
+ align:start position:0%
+here one year ahead because it it
+matters not only for aggregate demand
+
+ align:start position:0%
+matters not only for aggregate demand
+ 
+
+ align:start position:0%
+matters not only for aggregate demand
+not only the income the consumers are
+
+ align:start position:0%
+not only the income the consumers are
+ 
+
+ align:start position:0%
+not only the income the consumers are
+receiving today or the sales that firms
+
+ align:start position:0%
+receiving today or the sales that firms
+ 
+
+ align:start position:0%
+receiving today or the sales that firms
+are making today but also what they
+
+ align:start position:0%
+are making today but also what they
+ 
+
+ align:start position:0%
+are making today but also what they
+expect to have next year here it matters
+
+ align:start position:0%
+expect to have next year here it matters
+ 
+
+ align:start position:0%
+expect to have next year here it matters
+what the taxes they're paying today but
+
+ align:start position:0%
+what the taxes they're paying today but
+ 
+
+ align:start position:0%
+what the taxes they're paying today but
+also what they expect to pay in the
+
+ align:start position:0%
+also what they expect to pay in the
+ 
+
+ align:start position:0%
+also what they expect to pay in the
+future the interest rate matters not
+
+ align:start position:0%
+future the interest rate matters not
+ 
+
+ align:start position:0%
+future the interest rate matters not
+only today but also what they expect the
+
+ align:start position:0%
+only today but also what they expect the
+ 
+
+ align:start position:0%
+only today but also what they expect the
+interest rate to be in the future and so
+
+ align:start position:0%
+interest rate to be in the future and so
+ 
+
+ align:start position:0%
+interest rate to be in the future and so
+on okay so the bottom line is that we if
+
+ align:start position:0%
+on okay so the bottom line is that we if
+ 
+
+ align:start position:0%
+on okay so the bottom line is that we if
+we now look at the slm model I said now
+
+ align:start position:0%
+we now look at the slm model I said now
+ 
+
+ align:start position:0%
+we now look at the slm model I said now
+we have lots of more parameters all
+
+ align:start position:0%
+we have lots of more parameters all
+ 
+
+ align:start position:0%
+we have lots of more parameters all
+these things that happen in the future
+
+ align:start position:0%
+these things that happen in the future
+ 
+
+ align:start position:0%
+these things that happen in the future
+are new
+
+ align:start position:0%
+are new
+ 
+
+ align:start position:0%
+are new
+parameters H I said notice notice that
+
+ align:start position:0%
+parameters H I said notice notice that
+ 
+
+ align:start position:0%
+parameters H I said notice notice that
+also this curve now is a lot steeper
+
+ align:start position:0%
+also this curve now is a lot steeper
+ 
+
+ align:start position:0%
+also this curve now is a lot steeper
+why is that well because if you change
+
+ align:start position:0%
+why is that well because if you change
+ 
+
+ align:start position:0%
+why is that well because if you change
+the interest rate today without without
+
+ align:start position:0%
+the interest rate today without without
+ 
+
+ align:start position:0%
+the interest rate today without without
+changing the interest rate in the future
+
+ align:start position:0%
+changing the interest rate in the future
+ 
+
+ align:start position:0%
+changing the interest rate in the future
+then that has a small effect okay and so
+
+ align:start position:0%
+then that has a small effect okay and so
+ 
+
+ align:start position:0%
+then that has a small effect okay and so
+I said now this is becomes very steep
+
+ align:start position:0%
+I said now this is becomes very steep
+ 
+
+ align:start position:0%
+I said now this is becomes very steep
+but the equivalent to what we did the
+
+ align:start position:0%
+but the equivalent to what we did the
+ 
+
+ align:start position:0%
+but the equivalent to what we did the
+static model is a is a situation where
+
+ align:start position:0%
+static model is a is a situation where
+ 
+
+ align:start position:0%
+static model is a is a situation where
+you cut the interest rate today say the
+
+ align:start position:0%
+you cut the interest rate today say the
+ 
+
+ align:start position:0%
+you cut the interest rate today say the
+Central Bank cuts the interest rate
+
+ align:start position:0%
+Central Bank cuts the interest rate
+ 
+
+ align:start position:0%
+Central Bank cuts the interest rate
+today but it also convinces the public
+
+ align:start position:0%
+today but it also convinces the public
+ 
+
+ align:start position:0%
+today but it also convinces the public
+that they will also keep the interest
+
+ align:start position:0%
+that they will also keep the interest
+ 
+
+ align:start position:0%
+that they will also keep the interest
+rate low in the next period that is not
+
+ align:start position:0%
+rate low in the next period that is not
+ 
+
+ align:start position:0%
+rate low in the next period that is not
+only you move along the SAS but you also
+
+ align:start position:0%
+only you move along the SAS but you also
+ 
+
+ align:start position:0%
+only you move along the SAS but you also
+persuade the public that the interest
+
+ align:start position:0%
+persuade the public that the interest
+ 
+
+ align:start position:0%
+persuade the public that the interest
+rate will be lower in the future that
+
+ align:start position:0%
+rate will be lower in the future that
+ 
+
+ align:start position:0%
+rate will be lower in the future that
+will shift yes to the right and then
+
+ align:start position:0%
+will shift yes to the right and then
+ 
+
+ align:start position:0%
+will shift yes to the right and then
+therefore therefore you're going to get
+
+ align:start position:0%
+therefore therefore you're going to get
+ 
+
+ align:start position:0%
+therefore therefore you're going to get
+a much larger kick out of monetary
+
+ align:start position:0%
+a much larger kick out of monetary
+ 
+
+ align:start position:0%
+a much larger kick out of monetary
+policy and pol monetary policy is a lot
+
+ align:start position:0%
+policy and pol monetary policy is a lot
+ 
+
+ align:start position:0%
+policy and pol monetary policy is a lot
+about forward guidance is that you know
+
+ align:start position:0%
+about forward guidance is that you know
+ 
+
+ align:start position:0%
+about forward guidance is that you know
+you cut interest rate today but you're
+
+ align:start position:0%
+you cut interest rate today but you're
+ 
+
+ align:start position:0%
+you cut interest rate today but you're
+also telling there's always a speech
+
+ align:start position:0%
+also telling there's always a speech
+ 
+
+ align:start position:0%
+also telling there's always a speech
+after they they take the policy action
+
+ align:start position:0%
+after they they take the policy action
+ 
+
+ align:start position:0%
+after they they take the policy action
+which they talk about how they see
+
+ align:start position:0%
+which they talk about how they see
+ 
+
+ align:start position:0%
+which they talk about how they see
+interest rates going in the future and
+
+ align:start position:0%
+interest rates going in the future and
+ 
+
+ align:start position:0%
+interest rates going in the future and
+all of that that's because you want to
+
+ align:start position:0%
+all of that that's because you want to
+ 
+
+ align:start position:0%
+all of that that's because you want to
+have maximum power okay if you if if you
+
+ align:start position:0%
+have maximum power okay if you if if you
+ 
+
+ align:start position:0%
+have maximum power okay if you if if you
+just tell the market I'm going to change
+
+ align:start position:0%
+just tell the market I'm going to change
+ 
+
+ align:start position:0%
+just tell the market I'm going to change
+the interest rate for now and then
+
+ align:start position:0%
+the interest rate for now and then
+ 
+
+ align:start position:0%
+the interest rate for now and then
+nothing else that's going to have a very
+
+ align:start position:0%
+nothing else that's going to have a very
+ 
+
+ align:start position:0%
+nothing else that's going to have a very
+limited impact to have a large impact
+
+ align:start position:0%
+limited impact to have a large impact
+ 
+
+ align:start position:0%
+limited impact to have a large impact
+out of monetary policy you have to
+
+ align:start position:0%
+out of monetary policy you have to
+ 
+
+ align:start position:0%
+out of monetary policy you have to
+convince them that you will also affect
+
+ align:start position:0%
+convince them that you will also affect
+ 
+
+ align:start position:0%
+convince them that you will also affect
+the interest R path in the
+
+ align:start position:0%
+the interest R path in the
+ 
+
+ align:start position:0%
+the interest R path in the
+future same sort of situation here the
+
+ align:start position:0%
+future same sort of situation here the
+ 
+
+ align:start position:0%
+future same sort of situation here the
+other parameters is what happens if for
+
+ align:start position:0%
+other parameters is what happens if for
+ 
+
+ align:start position:0%
+other parameters is what happens if for
+example you expect future output to go
+
+ align:start position:0%
+example you expect future output to go
+ 
+
+ align:start position:0%
+example you expect future output to go
+up H well that's going to shift a yes to
+
+ align:start position:0%
+up H well that's going to shift a yes to
+ 
+
+ align:start position:0%
+up H well that's going to shift a yes to
+the right that's yet another reason why
+
+ align:start position:0%
+the right that's yet another reason why
+ 
+
+ align:start position:0%
+the right that's yet another reason why
+convincing people that you're going to
+
+ align:start position:0%
+convincing people that you're going to
+ 
+
+ align:start position:0%
+convincing people that you're going to
+cut interest rate in the future as well
+
+ align:start position:0%
+cut interest rate in the future as well
+ 
+
+ align:start position:0%
+cut interest rate in the future as well
+they going to keep them low in the
+
+ align:start position:0%
+they going to keep them low in the
+ 
+
+ align:start position:0%
+they going to keep them low in the
+future shift yes even more because if
+
+ align:start position:0%
+future shift yes even more because if
+ 
+
+ align:start position:0%
+future shift yes even more because if
+you're going to keep the interest rate
+
+ align:start position:0%
+you're going to keep the interest rate
+ 
+
+ align:start position:0%
+you're going to keep the interest rate
+low in the future that means probably
+
+ align:start position:0%
+low in the future that means probably
+ 
+
+ align:start position:0%
+low in the future that means probably
+the future output will be higher and
+
+ align:start position:0%
+the future output will be higher and
+ 
+
+ align:start position:0%
+the future output will be higher and
+since future output is higher that
+
+ align:start position:0%
+since future output is higher that
+ 
+
+ align:start position:0%
+since future output is higher that
+increases human wealth and that means
+
+ align:start position:0%
+increases human wealth and that means
+ 
+
+ align:start position:0%
+increases human wealth and that means
+consumption will tend to go up okay but
+
+ align:start position:0%
+consumption will tend to go up okay but
+ 
+
+ align:start position:0%
+consumption will tend to go up okay but
+do play with this and and again the the
+
+ align:start position:0%
+do play with this and and again the the
+ 
+
+ align:start position:0%
+do play with this and and again the the
+it's important to have this distinction
+
+ align:start position:0%
+it's important to have this distinction
+ 
+
+ align:start position:0%
+it's important to have this distinction
+between the impact of temporary things
+
+ align:start position:0%
+between the impact of temporary things
+ 
+
+ align:start position:0%
+between the impact of temporary things
+which is much smaller and and the the
+
+ align:start position:0%
+which is much smaller and and the the
+ 
+
+ align:start position:0%
+which is much smaller and and the the
+impact of permanent things which is
+
+ align:start position:0%
+impact of permanent things which is
+ 
+
+ align:start position:0%
+impact of permanent things which is
+bigger because it affect
+
+ align:start position:0%
+bigger because it affect
+ 
+
+ align:start position:0%
+bigger because it affect
+wealth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oh that's an example okay so
+
+ align:start position:0%
+okay oh that's an example okay so
+ 
+
+ align:start position:0%
+okay oh that's an example okay so
+monetary policy again ER that's just if
+
+ align:start position:0%
+monetary policy again ER that's just if
+ 
+
+ align:start position:0%
+monetary policy again ER that's just if
+if you don't persuade the public that
+
+ align:start position:0%
+if you don't persuade the public that
+ 
+
+ align:start position:0%
+if you don't persuade the public that
+you're going to change the interest rate
+
+ align:start position:0%
+you're going to change the interest rate
+ 
+
+ align:start position:0%
+you're going to change the interest rate
+in the future then it just a movement
+
+ align:start position:0%
+in the future then it just a movement
+ 
+
+ align:start position:0%
+in the future then it just a movement
+along but if you also convince them that
+
+ align:start position:0%
+along but if you also convince them that
+ 
+
+ align:start position:0%
+along but if you also convince them that
+you will remain sort of H lose monetary
+
+ align:start position:0%
+you will remain sort of H lose monetary
+ 
+
+ align:start position:0%
+you will remain sort of H lose monetary
+conditions in next year then that that
+
+ align:start position:0%
+conditions in next year then that that
+ 
+
+ align:start position:0%
+conditions in next year then that that
+effectively shift the yes to the right
+
+ align:start position:0%
+effectively shift the yes to the right
+ 
+
+ align:start position:0%
+effectively shift the yes to the right
+for for a variety of Reon for two
+
+ align:start position:0%
+for for a variety of Reon for two
+ 
+
+ align:start position:0%
+for for a variety of Reon for two
+reasons at least that's much more
+
+ align:start position:0%
+reasons at least that's much more
+ 
+
+ align:start position:0%
+reasons at least that's much more
+expansionary the last thing we did is
+
+ align:start position:0%
+expansionary the last thing we did is
+ 
+
+ align:start position:0%
+expansionary the last thing we did is
+fiscal policy I said well fiscal policy
+
+ align:start position:0%
+fiscal policy I said well fiscal policy
+ 
+
+ align:start position:0%
+fiscal policy I said well fiscal policy
+fiscal policy today is contraction and
+
+ align:start position:0%
+fiscal policy today is contraction and
+ 
+
+ align:start position:0%
+fiscal policy today is contraction and
+there's no doubt of that but it can have
+
+ align:start position:0%
+there's no doubt of that but it can have
+ 
+
+ align:start position:0%
+there's no doubt of that but it can have
+but there are episodes and I show you
+
+ align:start position:0%
+but there are episodes and I show you
+ 
+
+ align:start position:0%
+but there are episodes and I show you
+the Irish episode in which actually may
+
+ align:start position:0%
+the Irish episode in which actually may
+ 
+
+ align:start position:0%
+the Irish episode in which actually may
+end up going the other way around in
+
+ align:start position:0%
+end up going the other way around in
+ 
+
+ align:start position:0%
+end up going the other way around in
+which you cut expenditure today which is
+
+ align:start position:0%
+which you cut expenditure today which is
+ 
+
+ align:start position:0%
+which you cut expenditure today which is
+contractionary but you end up actually
+
+ align:start position:0%
+contractionary but you end up actually
+ 
+
+ align:start position:0%
+contractionary but you end up actually
+having an expansion but for that the
+
+ align:start position:0%
+having an expansion but for that the
+ 
+
+ align:start position:0%
+having an expansion but for that the
+only way that can happen is that if
+
+ align:start position:0%
+only way that can happen is that if
+ 
+
+ align:start position:0%
+only way that can happen is that if
+somehow you affect expectations in a
+
+ align:start position:0%
+somehow you affect expectations in a
+ 
+
+ align:start position:0%
+somehow you affect expectations in a
+very significant way so that's what I
+
+ align:start position:0%
+very significant way so that's what I
+ 
+
+ align:start position:0%
+very significant way so that's what I
+said if if you ever get sort of a a a
+
+ align:start position:0%
+said if if you ever get sort of a a a
+ 
+
+ align:start position:0%
+said if if you ever get sort of a a a
+strange correl response to to a policy
+
+ align:start position:0%
+strange correl response to to a policy
+ 
+
+ align:start position:0%
+strange correl response to to a policy
+announcement is probably because there
+
+ align:start position:0%
+announcement is probably because there
+ 
+
+ align:start position:0%
+announcement is probably because there
+has been a big effect on expectations so
+
+ align:start position:0%
+has been a big effect on expectations so
+ 
+
+ align:start position:0%
+has been a big effect on expectations so
+I show you the case of Ireland because
+
+ align:start position:0%
+I show you the case of Ireland because
+ 
+
+ align:start position:0%
+I show you the case of Ireland because
+there a case that was famous in which
+
+ align:start position:0%
+there a case that was famous in which
+ 
+
+ align:start position:0%
+there a case that was famous in which
+all the people talk about there was a
+
+ align:start position:0%
+all the people talk about there was a
+ 
+
+ align:start position:0%
+all the people talk about there was a
+fiscal deficit as the big drug in the
+
+ align:start position:0%
+fiscal deficit as the big drug in the
+ 
+
+ align:start position:0%
+fiscal deficit as the big drug in the
+economy that there was going to be a big
+
+ align:start position:0%
+economy that there was going to be a big
+ 
+
+ align:start position:0%
+economy that there was going to be a big
+Day of Reckoning and that you and so on
+
+ align:start position:0%
+Day of Reckoning and that you and so on
+ 
+
+ align:start position:0%
+Day of Reckoning and that you and so on
+so forth so once they dealt with it sort
+
+ align:start position:0%
+so forth so once they dealt with it sort
+ 
+
+ align:start position:0%
+so forth so once they dealt with it sort
+of expectations they realize they could
+
+ align:start position:0%
+of expectations they realize they could
+ 
+
+ align:start position:0%
+of expectations they realize they could
+cut interest rates then they could
+
+ align:start position:0%
+cut interest rates then they could
+ 
+
+ align:start position:0%
+cut interest rates then they could
+realiz that that that also that that
+
+ align:start position:0%
+realiz that that that also that that
+ 
+
+ align:start position:0%
+realiz that that that also that that
+this Malay and the economy was going to
+
+ align:start position:0%
+this Malay and the economy was going to
+ 
+
+ align:start position:0%
+this Malay and the economy was going to
+go away so people became optimistic
+
+ align:start position:0%
+go away so people became optimistic
+ 
+
+ align:start position:0%
+go away so people became optimistic
+about the future and so on and they end
+
+ align:start position:0%
+about the future and so on and they end
+ 
+
+ align:start position:0%
+about the future and so on and they end
+up with an expansion okay that shows you
+
+ align:start position:0%
+up with an expansion okay that shows you
+ 
+
+ align:start position:0%
+up with an expansion okay that shows you
+how important expectations are so
+
+ align:start position:0%
+how important expectations are so
+ 
+
+ align:start position:0%
+how important expectations are so
+economic policy in general you the the
+
+ align:start position:0%
+economic policy in general you the the
+ 
+
+ align:start position:0%
+economic policy in general you the the
+direct immediate effect is what we have
+
+ align:start position:0%
+direct immediate effect is what we have
+ 
+
+ align:start position:0%
+direct immediate effect is what we have
+been discussing throughout the course
+
+ align:start position:0%
+been discussing throughout the course
+ 
+
+ align:start position:0%
+been discussing throughout the course
+but a lot of its power and even the sort
+
+ align:start position:0%
+but a lot of its power and even the sort
+ 
+
+ align:start position:0%
+but a lot of its power and even the sort
+of perverse or or or or good synergies
+
+ align:start position:0%
+of perverse or or or or good synergies
+ 
+
+ align:start position:0%
+of perverse or or or or good synergies
+that you get out of them has to do with
+
+ align:start position:0%
+that you get out of them has to do with
+ 
+
+ align:start position:0%
+that you get out of them has to do with
+what you do to with expect patience okay
+
+ align:start position:0%
+what you do to with expect patience okay
+ 
+
+ align:start position:0%
+what you do to with expect patience okay
+good
\ No newline at end of file
diff --git a/tZw_eux9Wno.txt b/tZw_eux9Wno.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d7c7d16b8c98a5098f08c6ba02755f988691e80c
--- /dev/null
+++ b/tZw_eux9Wno.txt
@@ -0,0 +1,1325 @@
+align:start position:0%
+ 
+Hi guys. Um, my name is Nicola and in
+
+ align:start position:0%
+Hi guys. Um, my name is Nicola and in
+ 
+
+ align:start position:0%
+Hi guys. Um, my name is Nicola and in
+this video we're going to work out an
+
+ align:start position:0%
+this video we're going to work out an
+ 
+
+ align:start position:0%
+this video we're going to work out an
+example of an orthogonal projection
+
+ align:start position:0%
+example of an orthogonal projection
+ 
+
+ align:start position:0%
+example of an orthogonal projection
+matrix. Specifically, we are going to
+
+ align:start position:0%
+matrix. Specifically, we are going to
+ 
+
+ align:start position:0%
+matrix. Specifically, we are going to
+compute the projection matrix onto the
+
+ align:start position:0%
+compute the projection matrix onto the
+ 
+
+ align:start position:0%
+compute the projection matrix onto the
+plane given by the equation x + y minus
+
+ align:start position:0%
+plane given by the equation x + y minus
+ 
+
+ align:start position:0%
+plane given by the equation x + y minus
+z equals z. So before we start, uh, let
+
+ align:start position:0%
+z equals z. So before we start, uh, let
+ 
+
+ align:start position:0%
+z equals z. So before we start, uh, let
+me just recall what a projection matrix
+
+ align:start position:0%
+me just recall what a projection matrix
+ 
+
+ align:start position:0%
+me just recall what a projection matrix
+is.
+
+ align:start position:0%
+is.
+ 
+
+ align:start position:0%
+is.
+So you've seen um this sketch here a
+
+ align:start position:0%
+So you've seen um this sketch here a
+ 
+
+ align:start position:0%
+So you've seen um this sketch here a
+million times already. Uh a projection
+
+ align:start position:0%
+million times already. Uh a projection
+ 
+
+ align:start position:0%
+million times already. Uh a projection
+matrix takes any vector in three space.
+
+ align:start position:0%
+matrix takes any vector in three space.
+ 
+
+ align:start position:0%
+matrix takes any vector in three space.
+Well in just in this case we're dealing
+
+ align:start position:0%
+Well in just in this case we're dealing
+ 
+
+ align:start position:0%
+Well in just in this case we're dealing
+with a free space and projects it down
+
+ align:start position:0%
+with a free space and projects it down
+ 
+
+ align:start position:0%
+with a free space and projects it down
+onto the plane um a two dimensional
+
+ align:start position:0%
+onto the plane um a two dimensional
+ 
+
+ align:start position:0%
+onto the plane um a two dimensional
+space subspace of of R3. So I'm g give
+
+ align:start position:0%
+space subspace of of R3. So I'm g give
+ 
+
+ align:start position:0%
+space subspace of of R3. So I'm g give
+you a few moments to uh consider the
+
+ align:start position:0%
+you a few moments to uh consider the
+ 
+
+ align:start position:0%
+you a few moments to uh consider the
+problem for yourselves and then you'll
+
+ align:start position:0%
+problem for yourselves and then you'll
+ 
+
+ align:start position:0%
+problem for yourselves and then you'll
+see my take on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it again. Okay. So in in lecture
+
+ align:start position:0%
+it again. Okay. So in in lecture
+ 
+
+ align:start position:0%
+it again. Okay. So in in lecture
+professor strang derived in meticulous
+
+ align:start position:0%
+professor strang derived in meticulous
+ 
+
+ align:start position:0%
+professor strang derived in meticulous
+detail the formula for the projection
+
+ align:start position:0%
+detail the formula for the projection
+ 
+
+ align:start position:0%
+detail the formula for the projection
+matrix. So uh it was given by the
+
+ align:start position:0%
+matrix. So uh it was given by the
+ 
+
+ align:start position:0%
+matrix. So uh it was given by the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+well slightly complicated expression.
+
+ align:start position:0%
+well slightly complicated expression.
+ 
+
+ align:start position:0%
+well slightly complicated expression.
+It's a * a transpose a
+
+ align:start position:0%
+It's a * a transpose a
+ 
+
+ align:start position:0%
+It's a * a transpose a
+inverse a transpose where a is a matrix
+
+ align:start position:0%
+inverse a transpose where a is a matrix
+ 
+
+ align:start position:0%
+inverse a transpose where a is a matrix
+that somehow encodes the subspace we're
+
+ align:start position:0%
+that somehow encodes the subspace we're
+ 
+
+ align:start position:0%
+that somehow encodes the subspace we're
+projecting
+
+ align:start position:0%
+projecting
+ 
+
+ align:start position:0%
+projecting
+on. Yeah. In particular, A is has as
+
+ align:start position:0%
+on. Yeah. In particular, A is has as
+ 
+
+ align:start position:0%
+on. Yeah. In particular, A is has as
+columns A1, A2. I'm going to denote them
+
+ align:start position:0%
+columns A1, A2. I'm going to denote them
+ 
+
+ align:start position:0%
+columns A1, A2. I'm going to denote them
+a basis for the plane we're projecting
+
+ align:start position:0%
+a basis for the plane we're projecting
+ 
+
+ align:start position:0%
+a basis for the plane we're projecting
+on. Um, so essentially what we need to
+
+ align:start position:0%
+on. Um, so essentially what we need to
+ 
+
+ align:start position:0%
+on. Um, so essentially what we need to
+do is find two such vectors that span
+
+ align:start position:0%
+do is find two such vectors that span
+ 
+
+ align:start position:0%
+do is find two such vectors that span
+the plane and start computing with the
+
+ align:start position:0%
+the plane and start computing with the
+ 
+
+ align:start position:0%
+the plane and start computing with the
+matrix. Um, it's yeah, this is fairly
+
+ align:start position:0%
+matrix. Um, it's yeah, this is fairly
+ 
+
+ align:start position:0%
+matrix. Um, it's yeah, this is fairly
+straightforward.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh one one choice that works for example
+
+ align:start position:0%
+Uh one one choice that works for example
+ 
+
+ align:start position:0%
+Uh one one choice that works for example
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+one zero for the first column
+
+ align:start position:0%
+one zero for the first column
+ 
+
+ align:start position:0%
+one zero for the first column
+and 1 0 1 for the second column.
+
+ align:start position:0%
+and 1 0 1 for the second column.
+ 
+
+ align:start position:0%
+and 1 0 1 for the second column.
+Okay. Uh and let me write out the matrix
+
+ align:start position:0%
+Okay. Uh and let me write out the matrix
+ 
+
+ align:start position:0%
+Okay. Uh and let me write out the matrix
+A.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So in the formula um
+
+ align:start position:0%
+Okay. So in the formula um
+ 
+
+ align:start position:0%
+Okay. So in the formula um
+the I guess the more slightly more
+
+ align:start position:0%
+the I guess the more slightly more
+ 
+
+ align:start position:0%
+the I guess the more slightly more
+complicated uh combination is a
+
+ align:start position:0%
+complicated uh combination is a
+ 
+
+ align:start position:0%
+complicated uh combination is a
+transpose a inverse. So let me compute
+
+ align:start position:0%
+transpose a inverse. So let me compute
+ 
+
+ align:start position:0%
+transpose a inverse. So let me compute
+that first for you. Uh okay. So a
+
+ align:start position:0%
+that first for you. Uh okay. So a
+ 
+
+ align:start position:0%
+that first for you. Uh okay. So a
+transpose a
+
+ align:start position:0%
+transpose a
+ 
+
+ align:start position:0%
+transpose a
+is a 2x two
+
+ align:start position:0%
+is a 2x two
+ 
+
+ align:start position:0%
+is a 2x two
+matrix and it's not so hard to figure
+
+ align:start position:0%
+matrix and it's not so hard to figure
+ 
+
+ align:start position:0%
+matrix and it's not so hard to figure
+out that it's like two and one one two.
+
+ align:start position:0%
+out that it's like two and one one two.
+ 
+
+ align:start position:0%
+out that it's like two and one one two.
+Okay. Now we shall invert
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it using the familiar formula one over
+
+ align:start position:0%
+it using the familiar formula one over
+ 
+
+ align:start position:0%
+it using the familiar formula one over
+the determinant 2 * 2 - 1 is
+
+ align:start position:0%
+the determinant 2 * 2 - 1 is
+ 
+
+ align:start position:0%
+the determinant 2 * 2 - 1 is
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+and so we switch the diagonal
+
+ align:start position:0%
+and so we switch the diagonal
+ 
+
+ align:start position:0%
+and so we switch the diagonal
+entries and we flip the signs of the of
+
+ align:start position:0%
+entries and we flip the signs of the of
+ 
+
+ align:start position:0%
+entries and we flip the signs of the of
+diagonal ones
+
+ align:start position:0%
+diagonal ones
+ 
+
+ align:start position:0%
+diagonal ones
+okay right and
+
+ align:start position:0%
+okay right and
+ 
+
+ align:start position:0%
+okay right and
+therefore projection matrix is given by
+
+ align:start position:0%
+therefore projection matrix is given by
+ 
+
+ align:start position:0%
+therefore projection matrix is given by
+the following uh product of matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is 1/3
+
+ align:start position:0%
+is 1/3
+ 
+
+ align:start position:0%
+is 1/3
+21 2 and
+
+ align:start position:0%
+21 2 and
+ 
+
+ align:start position:0%
+21 2 and
+then transpose of A which
+
+ align:start position:0%
+then transpose of A which
+ 
+
+ align:start position:0%
+then transpose of A which
+is 1 0 1 0 1
+
+ align:start position:0%
+is 1 0 1 0 1
+ 
+
+ align:start position:0%
+is 1 0 1 0 1
+Okay, I'm going to carry out this
+
+ align:start position:0%
+Okay, I'm going to carry out this
+ 
+
+ align:start position:0%
+Okay, I'm going to carry out this
+multiplication in an inhumanly fast
+
+ align:start position:0%
+multiplication in an inhumanly fast
+ 
+
+ align:start position:0%
+multiplication in an inhumanly fast
+fashion.
+
+ align:start position:0%
+fashion.
+ 
+
+ align:start position:0%
+fashion.
+So, I'm just going to write down the
+
+ align:start position:0%
+So, I'm just going to write down the
+ 
+
+ align:start position:0%
+So, I'm just going to write down the
+answer, which is a
+
+ align:start position:0%
+answer, which is a
+ 
+
+ align:start position:0%
+answer, which is a
+third
+
+ align:start position:0%
+third
+ 
+
+ align:start position:0%
+third
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+1 2 2 one one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one. Right. So what you can do now is
+
+ align:start position:0%
+one. Right. So what you can do now is
+ 
+
+ align:start position:0%
+one. Right. So what you can do now is
+well you can check whether this answer
+
+ align:start position:0%
+well you can check whether this answer
+ 
+
+ align:start position:0%
+well you can check whether this answer
+actually makes sense. One thing you can
+
+ align:start position:0%
+actually makes sense. One thing you can
+ 
+
+ align:start position:0%
+actually makes sense. One thing you can
+do is just well a projection matrix is
+
+ align:start position:0%
+do is just well a projection matrix is
+ 
+
+ align:start position:0%
+do is just well a projection matrix is
+supposed to take the normal to the plane
+
+ align:start position:0%
+supposed to take the normal to the plane
+ 
+
+ align:start position:0%
+supposed to take the normal to the plane
+down to zero. So you can just multiply P
+
+ align:start position:0%
+down to zero. So you can just multiply P
+ 
+
+ align:start position:0%
+down to zero. So you can just multiply P
+and the normal vector one one negative
+
+ align:start position:0%
+and the normal vector one one negative
+ 
+
+ align:start position:0%
+and the normal vector one one negative
+one and if you get zero maybe you've
+
+ align:start position:0%
+one and if you get zero maybe you've
+ 
+
+ align:start position:0%
+one and if you get zero maybe you've
+done a good job. Um, another curious
+
+ align:start position:0%
+done a good job. Um, another curious
+ 
+
+ align:start position:0%
+done a good job. Um, another curious
+thing that I would like to point out
+
+ align:start position:0%
+thing that I would like to point out
+ 
+
+ align:start position:0%
+thing that I would like to point out
+here is so you see we had lots of
+
+ align:start position:0%
+here is so you see we had lots of
+ 
+
+ align:start position:0%
+here is so you see we had lots of
+freedom of choosing the matrix A. I mean
+
+ align:start position:0%
+freedom of choosing the matrix A. I mean
+ 
+
+ align:start position:0%
+freedom of choosing the matrix A. I mean
+you could have we could have chosen any
+
+ align:start position:0%
+you could have we could have chosen any
+ 
+
+ align:start position:0%
+you could have we could have chosen any
+two columns that span the subspace that
+
+ align:start position:0%
+two columns that span the subspace that
+ 
+
+ align:start position:0%
+two columns that span the subspace that
+spans the plane. The beautiful thing
+
+ align:start position:0%
+spans the plane. The beautiful thing
+ 
+
+ align:start position:0%
+spans the plane. The beautiful thing
+about it is that in the end we will get
+
+ align:start position:0%
+about it is that in the end we will get
+ 
+
+ align:start position:0%
+about it is that in the end we will get
+the same same
+
+ align:start position:0%
+the same same
+ 
+
+ align:start position:0%
+the same same
+answer. Um,
+
+ align:start position:0%
+answer. Um,
+ 
+
+ align:start position:0%
+answer. Um,
+right. So I hope there will be many of
+
+ align:start position:0%
+right. So I hope there will be many of
+ 
+
+ align:start position:0%
+right. So I hope there will be many of
+you who would say hey there is an easier
+
+ align:start position:0%
+you who would say hey there is an easier
+ 
+
+ align:start position:0%
+you who would say hey there is an easier
+way to do the problem and I'll agree
+
+ align:start position:0%
+way to do the problem and I'll agree
+ 
+
+ align:start position:0%
+way to do the problem and I'll agree
+with these people.
+
+ align:start position:0%
+with these people.
+ 
+
+ align:start position:0%
+with these people.
+So let's
+
+ align:start position:0%
+So let's
+ 
+
+ align:start position:0%
+So let's
+yeah let's see what would be an easier
+
+ align:start position:0%
+yeah let's see what would be an easier
+ 
+
+ align:start position:0%
+yeah let's see what would be an easier
+approach.
+
+ align:start position:0%
+approach.
+ 
+
+ align:start position:0%
+approach.
+Well, let's go back to the sketch here,
+
+ align:start position:0%
+Well, let's go back to the sketch here,
+ 
+
+ align:start position:0%
+Well, let's go back to the sketch here,
+right? And let's make the following
+
+ align:start position:0%
+right? And let's make the following
+ 
+
+ align:start position:0%
+right? And let's make the following
+observation that any vector is a sum of
+
+ align:start position:0%
+observation that any vector is a sum of
+ 
+
+ align:start position:0%
+observation that any vector is a sum of
+two components. One, the first component
+
+ align:start position:0%
+two components. One, the first component
+ 
+
+ align:start position:0%
+two components. One, the first component
+is its projection onto the plane and the
+
+ align:start position:0%
+is its projection onto the plane and the
+ 
+
+ align:start position:0%
+is its projection onto the plane and the
+other component is its projection onto
+
+ align:start position:0%
+other component is its projection onto
+ 
+
+ align:start position:0%
+other component is its projection onto
+the orthogonal complement of the plane.
+
+ align:start position:0%
+the orthogonal complement of the plane.
+ 
+
+ align:start position:0%
+the orthogonal complement of the plane.
+in this case onto the normal vector to
+
+ align:start position:0%
+in this case onto the normal vector to
+ 
+
+ align:start position:0%
+in this case onto the normal vector to
+the plane. So in the language of linear
+
+ align:start position:0%
+the plane. So in the language of linear
+ 
+
+ align:start position:0%
+the plane. So in the language of linear
+algebra this is just B equals to its
+
+ align:start position:0%
+algebra this is just B equals to its
+ 
+
+ align:start position:0%
+algebra this is just B equals to its
+projection onto the plane
+
+ align:start position:0%
+projection onto the plane
+ 
+
+ align:start position:0%
+projection onto the plane
+plus its projection I'm going to call it
+
+ align:start position:0%
+plus its projection I'm going to call it
+ 
+
+ align:start position:0%
+plus its projection I'm going to call it
+PN onto the orthogonal complement of the
+
+ align:start position:0%
+PN onto the orthogonal complement of the
+ 
+
+ align:start position:0%
+PN onto the orthogonal complement of the
+plane. Okay, I'm going
+
+ align:start position:0%
+plane. Okay, I'm going
+ 
+
+ align:start position:0%
+plane. Okay, I'm going
+to suggestively write here the identity
+
+ align:start position:0%
+to suggestively write here the identity
+ 
+
+ align:start position:0%
+to suggestively write here the identity
+matrix so that you can immediately read
+
+ align:start position:0%
+matrix so that you can immediately read
+ 
+
+ align:start position:0%
+matrix so that you can immediately read
+off a matrix equality associated with
+
+ align:start position:0%
+off a matrix equality associated with
+ 
+
+ align:start position:0%
+off a matrix equality associated with
+this um equality here. It's the identity
+
+ align:start position:0%
+this um equality here. It's the identity
+ 
+
+ align:start position:0%
+this um equality here. It's the identity
+equals P +
+
+ align:start position:0%
+equals P +
+ 
+
+ align:start position:0%
+equals P +
+N and therefore the projection matrix is
+
+ align:start position:0%
+N and therefore the projection matrix is
+ 
+
+ align:start position:0%
+N and therefore the projection matrix is
+just the identity minus the projection
+
+ align:start position:0%
+just the identity minus the projection
+ 
+
+ align:start position:0%
+just the identity minus the projection
+matrix onto the normal vector.
+
+ align:start position:0%
+matrix onto the normal vector.
+ 
+
+ align:start position:0%
+matrix onto the normal vector.
+Now this object here PN is much easier
+
+ align:start position:0%
+Now this object here PN is much easier
+ 
+
+ align:start position:0%
+Now this object here PN is much easier
+to compute. Well, for two reasons. First
+
+ align:start position:0%
+to compute. Well, for two reasons. First
+ 
+
+ align:start position:0%
+to compute. Well, for two reasons. First
+one is that well projecting onto a
+
+ align:start position:0%
+one is that well projecting onto a
+ 
+
+ align:start position:0%
+one is that well projecting onto a
+one-dimensional subspace is infinitely
+
+ align:start position:0%
+one-dimensional subspace is infinitely
+ 
+
+ align:start position:0%
+one-dimensional subspace is infinitely
+easier than projecting onto a higher
+
+ align:start position:0%
+easier than projecting onto a higher
+ 
+
+ align:start position:0%
+easier than projecting onto a higher
+dimensional subspace. And second
+
+ align:start position:0%
+dimensional subspace. And second
+ 
+
+ align:start position:0%
+dimensional subspace. And second
+um we already have well immediately we
+
+ align:start position:0%
+um we already have well immediately we
+ 
+
+ align:start position:0%
+um we already have well immediately we
+can read off from the equation of the
+
+ align:start position:0%
+can read off from the equation of the
+ 
+
+ align:start position:0%
+can read off from the equation of the
+plane what the normal vector is. So we
+
+ align:start position:0%
+plane what the normal vector is. So we
+ 
+
+ align:start position:0%
+plane what the normal vector is. So we
+don't have to um
+
+ align:start position:0%
+don't have to um
+ 
+
+ align:start position:0%
+don't have to um
+derive these guy like we don't have to
+
+ align:start position:0%
+derive these guy like we don't have to
+ 
+
+ align:start position:0%
+derive these guy like we don't have to
+do what we did here. Um okay. So
+
+ align:start position:0%
+do what we did here. Um okay. So
+ 
+
+ align:start position:0%
+do what we did here. Um okay. So
+uh essentially PN will be
+
+ align:start position:0%
+uh essentially PN will be
+ 
+
+ align:start position:0%
+uh essentially PN will be
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+N transpose N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse N transpose.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And that's equal to
+
+ align:start position:0%
+And that's equal to
+ 
+
+ align:start position:0%
+And that's equal to
+um one
+
+ align:start position:0%
+um one
+ 
+
+ align:start position:0%
+um one
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and n transpose n inverse. This is
+
+ align:start position:0%
+one and n transpose n inverse. This is
+ 
+
+ align:start position:0%
+one and n transpose n inverse. This is
+just a
+
+ align:start position:0%
+just a
+ 
+
+ align:start position:0%
+just a
+number. It's one over the magnitude of
+
+ align:start position:0%
+number. It's one over the magnitude of
+ 
+
+ align:start position:0%
+number. It's one over the magnitude of
+the normal vector. Uh so that's the
+
+ align:start position:0%
+the normal vector. Uh so that's the
+ 
+
+ align:start position:0%
+the normal vector. Uh so that's the
+magnitude squared. So that's three and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+Okay, I'm going
+
+ align:start position:0%
+Okay, I'm going
+ 
+
+ align:start position:0%
+Okay, I'm going
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write the answer here.
+
+ align:start position:0%
+write the answer here.
+ 
+
+ align:start position:0%
+write the answer here.
+It's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+one one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um one
+
+ align:start position:0%
+um one
+ 
+
+ align:start position:0%
+um one
+one andative one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one right
+
+ align:start position:0%
+one right
+ 
+
+ align:start position:0%
+one right
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+Yeah. In order and in order to get the
+
+ align:start position:0%
+Yeah. In order and in order to get the
+ 
+
+ align:start position:0%
+Yeah. In order and in order to get the
+projection matrix.
+
+ align:start position:0%
+projection matrix.
+ 
+
+ align:start position:0%
+projection matrix.
+Yes.
+
+ align:start position:0%
+Yes.
+ 
+
+ align:start position:0%
+Yes.
+Oh, thank you. Thank you. And in order
+
+ align:start position:0%
+Oh, thank you. Thank you. And in order
+ 
+
+ align:start position:0%
+Oh, thank you. Thank you. And in order
+to get the projection
+
+ align:start position:0%
+to get the projection
+ 
+
+ align:start position:0%
+to get the projection
+matrix, we just subtract from the
+
+ align:start position:0%
+matrix, we just subtract from the
+ 
+
+ align:start position:0%
+matrix, we just subtract from the
+identity this expression. And you can
+
+ align:start position:0%
+identity this expression. And you can
+ 
+
+ align:start position:0%
+identity this expression. And you can
+confirm that it's this answer. We get
+
+ align:start position:0%
+confirm that it's this answer. We get
+ 
+
+ align:start position:0%
+confirm that it's this answer. We get
+the same answer as here. All right. I
+
+ align:start position:0%
+the same answer as here. All right. I
+ 
+
+ align:start position:0%
+the same answer as here. All right. I
+think we're done here.
\ No newline at end of file
diff --git a/tei0bSKTyf0.txt b/tei0bSKTyf0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6b91f4cf29aa9256da0804752165d29fb834c69c
--- /dev/null
+++ b/tei0bSKTyf0.txt
@@ -0,0 +1,267 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Here's another example, not as dramatic
+
+ align:start position:0%
+Here's another example, not as dramatic
+ 
+
+ align:start position:0%
+Here's another example, not as dramatic
+of uh creating a photo illustration out
+
+ align:start position:0%
+of uh creating a photo illustration out
+ 
+
+ align:start position:0%
+of uh creating a photo illustration out
+of photographs, but in this case, this
+
+ align:start position:0%
+of photographs, but in this case, this
+ 
+
+ align:start position:0%
+of photographs, but in this case, this
+is also showing evidence that you are
+
+ align:start position:0%
+is also showing evidence that you are
+ 
+
+ align:start position:0%
+is also showing evidence that you are
+fabricating the pieces in your device.
+
+ align:start position:0%
+fabricating the pieces in your device.
+ 
+
+ align:start position:0%
+fabricating the pieces in your device.
+This particular image is a CAD image
+
+ align:start position:0%
+This particular image is a CAD image
+ 
+
+ align:start position:0%
+This particular image is a CAD image
+used by the researchers to show their
+
+ align:start position:0%
+used by the researchers to show their
+ 
+
+ align:start position:0%
+used by the researchers to show their
+device showing the various fabrications.
+
+ align:start position:0%
+device showing the various fabrications.
+ 
+
+ align:start position:0%
+device showing the various fabrications.
+And this is how they used it in their
+
+ align:start position:0%
+And this is how they used it in their
+ 
+
+ align:start position:0%
+And this is how they used it in their
+patent submission. But this is done in
+
+ align:start position:0%
+patent submission. But this is done in
+ 
+
+ align:start position:0%
+patent submission. But this is done in
+CAD. They also made a picture of their
+
+ align:start position:0%
+CAD. They also made a picture of their
+ 
+
+ align:start position:0%
+CAD. They also made a picture of their
+device, but you really can't see very
+
+ align:start position:0%
+device, but you really can't see very
+ 
+
+ align:start position:0%
+device, but you really can't see very
+much about their very sophisticated
+
+ align:start position:0%
+much about their very sophisticated
+ 
+
+ align:start position:0%
+much about their very sophisticated
+ability to make the various layers. And
+
+ align:start position:0%
+ability to make the various layers. And
+ 
+
+ align:start position:0%
+ability to make the various layers. And
+so what I did was I took that device and
+
+ align:start position:0%
+so what I did was I took that device and
+ 
+
+ align:start position:0%
+so what I did was I took that device and
+separated into the initial pieces that
+
+ align:start position:0%
+separated into the initial pieces that
+ 
+
+ align:start position:0%
+separated into the initial pieces that
+they did fabricate. I laid them out on a
+
+ align:start position:0%
+they did fabricate. I laid them out on a
+ 
+
+ align:start position:0%
+they did fabricate. I laid them out on a
+background and decided to try to use
+
+ align:start position:0%
+background and decided to try to use
+ 
+
+ align:start position:0%
+background and decided to try to use
+these images showing the layering of how
+
+ align:start position:0%
+these images showing the layering of how
+ 
+
+ align:start position:0%
+these images showing the layering of how
+the device is made. So I out of these
+
+ align:start position:0%
+the device is made. So I out of these
+ 
+
+ align:start position:0%
+the device is made. So I out of these
+images I constructed a photo
+
+ align:start position:0%
+images I constructed a photo
+ 
+
+ align:start position:0%
+images I constructed a photo
+illustration of those pieces using
+
+ align:start position:0%
+illustration of those pieces using
+ 
+
+ align:start position:0%
+illustration of those pieces using
+software but these are real images that
+
+ align:start position:0%
+software but these are real images that
+ 
+
+ align:start position:0%
+software but these are real images that
+you've just seen from before. Here's
+
+ align:start position:0%
+you've just seen from before. Here's
+ 
+
+ align:start position:0%
+you've just seen from before. Here's
+another way of showing it making it
+
+ align:start position:0%
+another way of showing it making it
+ 
+
+ align:start position:0%
+another way of showing it making it
+somewhat
+
+ align:start position:0%
+somewhat
+ 
+
+ align:start position:0%
+somewhat
+three-dimensional. But basically this is
+
+ align:start position:0%
+three-dimensional. But basically this is
+ 
+
+ align:start position:0%
+three-dimensional. But basically this is
+a photo illustration of the layers of
+
+ align:start position:0%
+a photo illustration of the layers of
+ 
+
+ align:start position:0%
+a photo illustration of the layers of
+this device. Not only
+
+ align:start position:0%
+this device. Not only
+ 
+
+ align:start position:0%
+this device. Not only
+showing how it works with the right
+
+ align:start position:0%
+showing how it works with the right
+ 
+
+ align:start position:0%
+showing how it works with the right
+labeling, of course, but also showing
+
+ align:start position:0%
+labeling, of course, but also showing
+ 
+
+ align:start position:0%
+labeling, of course, but also showing
+that they did indeed fabricate the
+
+ align:start position:0%
+that they did indeed fabricate the
+ 
+
+ align:start position:0%
+that they did indeed fabricate the
+layers.
\ No newline at end of file
diff --git a/uBRdfsz_YB4.txt b/uBRdfsz_YB4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a5e94cfc0cef914dace393a435a8e27ad1bc1678
--- /dev/null
+++ b/uBRdfsz_YB4.txt
@@ -0,0 +1,787 @@
+PROFESSOR: Good morning.
+
+Come on down.
+
+All right.
+
+So last time, we talked about
+the first couple of steps of
+
+the central dogma.
+
+The central dogma is this name
+given to the statement DNA
+
+goes to DNA by replication.
+
+DNA goes to RNA by the process
+of transcription.
+
+We call it transcription because
+it's such a direct
+
+copying of letter to letter.
+
+RNA goes to protein by a
+process of translation,
+
+because translation is the
+kind of word we would use
+
+between two different
+languages.
+
+And there are two different
+languages--
+
+the languages of nucleotides
+and the
+
+language of amino acids.
+
+For what it's worth, it's name,
+the central dogma, goes
+
+back to Francis Crick, who
+called this the central dogma.
+
+He did it in a kind of a
+light-hearted way, although
+
+others since then have
+criticized it, saying, oh,
+
+this is dogmatic.
+
+Actually, Crick said not
+that DNA goes to
+
+RNA goes to the protein.
+
+He says that all information
+flows from nucleic acids to
+
+proteins and not back again.
+
+Because even then, Crick knew
+that in theory, there was no
+
+reason you couldn't go back from
+RNA to DNA, and as we'll
+
+see today, that happens.
+
+So sometimes people say, oh,
+well, the central dogma was
+
+proved wrong because RNA
+can go back to DNA.
+
+Well, actually, that was even
+anticipated right then at the
+
+very beginning, when they
+realized RNA and DNA were
+
+essentially equivalent
+information.
+
+The key step of converting
+nucleic acid information into
+
+protein information
+is translation.
+
+And that's the last bit
+we have to fill in
+
+and talk about today.
+
+So let me start by just
+reminding you-- because most
+
+of you know it--
+
+how translation works.
+
+So, in translation, you have a
+particular RNA that has been
+
+made by the cell.
+
+Here's my RNA.
+
+It goes five prime
+to three prime.
+
+That's always the way we
+write these things.
+
+And it has some particular
+sequence.
+
+I'll make up a sequence here.
+
+A, U, A, C, G, A, U, G, A, A,
+G, A, G, G, C, C, C, dot dot
+
+dot dot dot, U, A, G, dot dot
+dot dot, three prime.
+
+All right.
+
+Somehow, that's going to be
+translated into a protein.
+
+It's translated according to a
+fantastic look-up up table.
+
+This look-up table is called
+the genetic code.
+
+And the rule, the algorithm--
+
+and it's a fairly simple
+algorithm, well, nothing's
+
+ever really simple in biology,
+but it's close to simple--
+
+is you run along the sequence
+from the beginning.
+
+And you guys could write this.
+
+Anybody who's taken basic
+computer programming.
+
+Run along the sequence and find
+the first occurrence of
+
+A, U, G. Why A, U, G?
+
+Because A, U, G is the
+place you start.
+
+That's how life worked it out,
+and that's what it does.
+
+After that, you parse the
+sequence in triplets.
+
+These triplets get
+the name codons.
+
+And then you keep going
+until you hit one of
+
+three possible triplets.
+
+U, A, G. U, A, A. U, G,
+A. And you stop there.
+
+Any MIT student should be able
+to write an algorithm that
+
+takes a string, finds the first
+occurrence of U, A, G,
+
+breaks it up into triplets
+passed there, keeps going
+
+until you encounter one of
+these three triplets.
+
+What do you do for
+a given triplet?
+
+You look it up against
+the table.
+
+How many triplets are there?
+
+How many three-letter words
+are there with the four
+
+nucleotides?
+
+AUDIENCE: 64.
+
+PROFESSOR: It's 4 to the 3rd--
+
+64 possible words.
+
+I've used up three of them to be
+stop, so there are 4 to the
+
+3rd possible codons.
+
+That's 64.
+
+Three stops.
+
+The other 61 possible codons
+specify an amino acid.
+
+That's it.
+
+There's a look-up table.
+
+The genetic code.
+
+How many amino acids
+are there?
+
+20.
+
+And there are 61 possible
+codons, so that implies there
+
+is some redundancy.
+
+Some codons--
+
+some amino acids are coded
+for by the same codon.
+
+Okay.
+
+That's fine.
+
+And in your book is the genetic
+code that is the
+
+look-up table here.
+
+The genetic code translates
+these codons into amino acids.
+
+Or to stop, in the case of
+the three stop signals.
+
+So for example, this A, U,
+G at the front is always
+
+translated into methionine.
+
+Met.
+
+And if I've got it right,
+this should be a lysine.
+
+Here we go.
+
+Arginine, proline, et cetera--
+you just look it up.
+
+That's it.
+
+That's the order in which
+you make the proteins.
+
+So you send off an order written
+in RNA, you send it
+
+off to the factory, the factory
+sends you back a
+
+protein that is methionine,
+lysine, arginine, proline,
+
+blah, blah, blah, blah, blah.
+
+That's it.
+
+This genetic code is essentially
+universal amongst
+
+all of life.
+
+That's pretty stunning.
+
+What does that tell you?
+
+The fact that all of life uses
+virtually the identical
+
+genetic code?
+
+There's actually a tiny
+difference between prokaryotes
+
+and eukaryotes affecting a
+codon and there's a tiny
+
+difference somewhere else.
+
+But essentially, it's the exact
+same genetic code that
+
+all of life uses.
+
+It's very unlikely that this
+genetic code is the only
+
+possible way you could make
+a genetic code, right?
+
+So the fact that all of life
+uses, essentially, exactly the
+
+same code is pretty strong
+evidence that all currently
+
+existing life descends from
+a common ancestor.
+
+Because if these were evolved
+independently, it's extremely
+
+unlikely that you would have
+gotten exactly the same
+
+genetic code.
+
+So that's an interesting point
+that you can see from just the
+
+fact that everybody uses
+essentially the
+
+same genetic code.
+
+It's a universal genetic code.
+
+All right.
+
+So I've expressed this to you
+in a completely computer
+
+sciencey kind of way.
+
+But, of course, the cell doesn't
+do this by computer
+
+science because cells are
+unable to write C code.
+
+The reason that cells are unable
+to write C code is C
+
+wasn't really developed until
+the last several decades, and
+
+cells, pretty sure, precede the
+development of C code by
+
+Kernighan and Ritchie.
+
+So it's got to be the case that
+it's done some other way.
+
+How is it done?
+
+Well, it's done like this.
+
+And I'll just be very
+schematic and you'll
+
+get it in your book.
+
+There's a big machine.
+
+The big machine here is
+called the ribosome.
+
+It consists, itself, of proteins
+and RNAs, and it's a
+
+huge structure.
+
+The huge structure needs
+to read codons.
+
+And this is a case where
+Francis Crick
+
+drove everybody nuts.
+
+Francis Crick, back in the
+1950s, just sat at his desk
+
+and thought.
+
+He was terrible at doing
+experiments--
+
+nobody really wanted to let
+him do experiments.
+
+Francis was a great thinker.
+
+He thought.
+
+He said, golly, how can this
+sequence be translated into
+
+amino acids?
+
+Well, people at the time had
+all sorts of nutty ideas.
+
+Some of the nutty ideas was that
+the sequence of the RNA
+
+folded up into pockets that
+just fit a proline.
+
+And another pocket that
+just an arginine.
+
+And if you just think about the
+constraints to get that to
+
+work, it's nuts.
+
+That the sequence itself would
+form perfect binding pockets
+
+for the necessary amino acids.
+
+Crick said impossible.
+
+He said the really sensible
+way to do this, if I were
+
+running life, what I
+would do is I would
+
+have an adapter molecule.
+
+The adapter molecule would be
+some kind of a nucleic acid,
+
+and the nucleic acid would kind
+of match the codon on one
+
+end and have the amino acid
+on the other end.
+
+And then there'd be another
+adapter, and the adapter would
+
+have the next amino acid.
+
+And then you would catalyze
+a bond between them.
+
+Therefore, I predict, says
+Francis, there will be small
+
+adapter molecules, probably made
+out of RNAs themselves.
+
+And Francis called this the
+Adapter Hypothesis.
+
+It drove people crazy because,
+of course, he was right.
+
+People found the adapters and
+they would use transfer things
+
+that transfer information--
+
+get called transfer RNAs.
+
+What happens is the ribosome
+has pockets in which these
+
+transfer RNAs basically come
+in, match their sequence,
+
+there's a codon each of these
+transfer RNAs has a matching
+
+anticodon that matches the
+triplet, and it has already
+
+attached to it an amino acid--
+
+the right amino acid
+for that anticodon.
+
+How does that right amino
+acid get attached
+
+to the right tRNA?
+
+There's an enzyme.
+
+The job of that enzyme is to
+attach this amino acid,
+
+proline, to this transfer RNA.
+
+It's a Prolyl-tRNA synthetase.
+
+And its job is to put proline
+on the right tRNAs.
+
+There's another one that puts
+arginine on the right tRNAs.
+
+There's a whole business that's
+set up to get the right
+
+tRNAs, have the right amino
+acids attached to them through
+
+a bunch of enzymes
+floating around.
+
+So then these tRNAs with the
+amino acid attached drop in,
+
+they drop into the next
+position, and a bond--
+
+the peptide bond--
+is catalyzed.
+
+Interesting factoid.
+
+The catalysis, this enzymatic
+catalysis to join together
+
+those amino acids is actually
+carried out not by the
+
+proteins in a ribosome,
+but actually
+
+by RNA in the ribosome.
+
+The RNA is the enzyme.
+
+You know why that's
+kind of cool?
+
+If this bothers you, just forget
+it, but one of the
+
+mysteries about how you ever go
+from DNA to RNA to protein
+
+and all of that is how the whole
+thing ever got started.
+
+How could you possibly have
+gotten protein synthesis
+
+started if the things that were
+needed to make protein
+
+synthesis were proteins?
+
+So this is actually an echo of
+an ancient world 3 billion
+
+years ago, where this was all
+probably carried out by RNAs.
+
+RNA was probably the early
+catalysts for most things, and
+
+we still see evidence of the
+fact that even today your
+
+peptide bonds are catalyzed
+actually by RNA and they're
+
+doing the enzymatic work.
+
+Anyway, it's kind of cool.
+
+If you didn't get that, don't
+worry about it, but
+
+it's kind of cool.
+
+So then what happens after
+you attach the
+
+first two amino acids?
+
+Well, the ribosome chugs down
+here and grabs the next code--
+
+these two shift over.
+
+You can either think about the
+ribosome moving this way or
+
+the RNA moving that way.
+
+The next tRNA drops in, the
+next bond gets made, chugs
+
+over, the next one drops in,
+the next one gets made, and
+
+onward like that until it hits
+a stop codon at which, it
+
+releases it.
+
+The ribosome knows
+to release it.
+
+There's actually a little factor
+that drops in and tells
+
+it to release it there.
+
+And that's how you
+make proteins--
+
+kind of cool.
+
+It works very well.
+
+It chugs along in
+that fashion.
+
+For you computer scientists,
+what you basically have is a
+
+two-tape turing machine--
+
+you're reading one tape and
+writing to the other tape.
+
+There's a nucleic acid
+tape and there's
+
+an amino acid tape.
+
+If you're not a computer
+scientist, forget I said that.
+
+OK.
+
+So it's basically a two-tape
+tape turing machine where the
+
+RNA is coming through here and
+the protein is coming out that
+
+way, but the amino acids
+attach to each other
+
+until it comes off.
+
+In fact, actually, very
+recently, a Nobel Prize was
+
+awarded last year for beautiful,
+beautiful work on
+
+how this actually takes place--
+the molecular details
+
+of the ribosome.
+
+Really gorgeous.
+
+Any questions about that?
+
+Yeah.
+
+AUDIENCE: Is that not
+susceptible to the same error
+
+as replication is?
+
+PROFESSOR: Oh, is that not
+susceptible to the same error?
+
+Does the ribosome ever
+make mistakes?
+
+It does.
+
+What happens if you make
+the wrong protein?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Oh well.
+
+The answer turns out to be "oh
+well" because for any given
+
+DNA, you make lots of RNAs.
+
+For any RNA, you use it
+again and again to
+
+make lots of proteins.
+
+And if the occasional protein is
+not so good, if the quality
+
+control is not perfect, it's
+much less serious than if your
+
+master instructions in the
+DNA were not perfect.
+
+So the cell actually
+devotes a lot less
+
+attention to quality control.
+
+Now.
+
+That's not to say there isn't
+important quality control.
+
+There are quality control
+mechanisms, but it doesn't
+
+have to be as accurate as one
+error in a billion, like you
+
+want to be in copying
+your DNA.
+
+And that's really an important
+point, is the archival copy
+
+has to be really good, but
+little yellow sticky notes--
+
+what you make from it, which
+are basically RNA or the
+
+little yellow sticky notes you
+copied down-- they don't have
+
+to be perfect.
+
+And each copy, the protein
+doesn't have to be--
+
+and if the protein is not
+perfect, there are mechanisms
+
+that take unfolded proteins
+and degrade them.
+
+So it turns out there are ways
+to achieve quality control in
+
+that sense.
+
+It's a great question.
\ No newline at end of file
diff --git a/uDXH6Uu0ghc.txt b/uDXH6Uu0ghc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2f26a1db3454a972fb88ddbb19db6bd6733b8231
--- /dev/null
+++ b/uDXH6Uu0ghc.txt
@@ -0,0 +1,489 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Good morning.
+
+AUDIENCE: Good morning.
+
+PROFESSOR: All right.
+
+So today--
+
+I haven't seen you in a while.
+
+Anyway, today, we're going to
+turn back to our picture,
+
+function gene protein.
+
+We filled in genetics.
+
+We filled in biochemistry.
+
+We've now got the connection
+between gene and protein
+
+through molecular biology.
+
+We know gene encodes protein.
+
+We know central dogma,
+DNA goes to the
+
+RNA goes to the protein.
+
+We know all that in theory.
+
+In fact, people knew this by
+the middle of the 1960s.
+
+People were so excited that they
+understood the idea of
+
+how genes give rise to proteins
+through transcription
+
+and translation, they read the
+genetic code, that they
+
+declared victory.
+
+Some of them said, done with
+the secret of life.
+
+Let's go on and do the brain.
+
+That was actually the thinking
+of a lot of the great
+
+molecular biologists
+in the late 1960s.
+
+Let's go do the brain.
+
+Why did they say such a thing?
+
+Well, because they
+thought they were
+
+done with the problem.
+
+They thought that once you knew
+in principle how a gene
+
+gave rise to a protein,
+you could do it.
+
+But in practice, nobody could
+read a single gene.
+
+Nobody could even identify
+a single gene.
+
+Maybe that's why they went on
+to say, let's go study the
+
+brain, because they actually
+weren't sure what they could
+
+do past that point.
+
+All right.
+
+So wait a second,
+wait a second.
+
+I said nobody could even
+purify a single gene.
+
+Didn't we talk about purifying
+the genetic material?
+
+You're supposed to say
+yes at that point.
+
+Yes, right?
+
+We talked about that.
+
+Avery, McCarty, MacLeod-- we
+purified the genetic material.
+
+We did it by using this
+assay of transforming.
+
+So what do I mean by we can't
+purify a single gene?
+
+What I mean is that we can
+purify the hereditary material
+
+away from everything else, but
+we get all of it together.
+
+We don't get individual genes
+separated from each other.
+
+We get the whole mixture
+of all the genes,
+
+all the genetic material.
+
+As a biochemist, how are we
+going to ever separate the
+
+gene encoding--
+
+oh I don't know, ARG1, our
+favorite gene for arginine
+
+biosynthesis--
+
+from the gene encoding
+ARG2, for example?
+
+What kind of biochemistry
+can we do to
+
+separate these two genes?
+
+Do they have different
+biochemical properties?
+
+What's so different about
+ARG1 and ARG2?
+
+What's their different
+biochemical properties?
+
+They're both DNA.
+
+They have exactly the same
+building blocks, slightly
+
+different order.
+
+You think you have a
+purification procedure, I'm
+
+going to run it over some column
+and separate it by
+
+something that's going to
+separate ARG1 from ARG2?
+
+No.
+
+From the point of view of a
+pure biochemist, they look
+
+exactly the same.
+
+All the different genes have
+the same biochemical
+
+properties.
+
+How in the world would we ever
+purify ARG1 from ARG2, or in
+
+the human, the gene encoding
+hemoglobin from the gene
+
+encoding collagen from the gene
+encoding keratin from the
+
+gene encoding anything else?
+
+Think about it.
+
+That's a tough problem.
+
+There is a brilliant solution
+that arose in the 1970s to how
+
+we could purify the individual
+genes away from each other.
+
+But it's like no other piece
+of biochemistry anybody had
+
+ever seen before.
+
+It has a totally different
+principle behind it.
+
+Because it isn't just
+fractionating things according
+
+to their biochemical
+properties.
+
+It involves something else.
+
+And it's called cloning.
+
+It is called cloning.
+
+Molecular cloning.
+
+You see, the problem is this.
+
+The human genome--
+
+how big is the human genome?
+
+How many bases?
+
+Three billion bases, three
+times 10 to the
+
+ninth bases, right?
+
+How big is a typical
+human gene?
+
+A typical human gene might
+be 30,000 bases.
+
+How big is a typical mutation
+that we might want to find in
+
+a typical gene, like causing
+sickle cell anemia?
+
+One base.
+
+We've got to purify out genes
+that are one part in 10 to the
+
+fifth and mutations that
+are one part in 10 to
+
+the ninth or so.
+
+And how are we going
+to do that?
+
+Well, the trick is this.
+
+I'll give you the quick
+overview, and then we'll spend
+
+today looking at it.
+
+Step one is we cut up our DNA.
+
+We cut DNA at defined sites, and
+we then paste the DNA to
+
+distinct molecules
+called vectors.
+
+These vectors have a cool
+property, that when you take a
+
+vector and you insert in it a
+piece of DNA, that vector is
+
+able to grow in another
+organism.
+
+You then transform the DNA--
+
+that's transfer, we use the
+word transform the DNA--
+
+into something like E. coli,
+where you get your little
+
+vector in there.
+
+It grows within E. coli, and as
+E. coli divides, it makes
+
+copies of itself.
+
+And then you select those
+bacteria that have received,
+
+that have been transformed, grow
+them up on a petri plate
+
+so that you have little
+colonies.
+
+And then you screen
+the colonies.
+
+Now, what do I mean?
+
+We cut the DNA.
+
+We paste the DNA.
+
+We transform the DNA.
+
+We select the bacteria that
+have been successfully
+
+transformed.
+
+And we screen the resulting
+colonies to find what we're
+
+looking for.
+
+Now, notice--
+
+that amazing trick here is when
+we cut up the DNA into
+
+single molecules, lots and lots
+of single molecules, and
+
+we paste them into vectors,
+and we transform them into
+
+bacteria, each one of those
+bacteria gets exactly one
+
+molecule, give or take.
+
+It gets one piece
+of human DNA.
+
+We then spread them out on a
+plate and they grow up, and
+
+each one grows up
+copies for us of
+
+individual pieces of DNA.
+
+That is so cool.
+
+Because we've just accomplished
+biochemical
+
+purification.
+
+It's not based on any different
+properties of the
+
+individual molecules.
+
+It's based on the fact that
+we dilute them, in effect.
+
+They're diluted, and
+one molecule
+
+ends up in each bacteria.
+
+So they're purified
+in that sense.
+
+And then when that bacteria
+grows up, everything it grows
+
+up is a pure copy, a copy of
+that single piece of DNA that
+
+went into it.
+
+That's a different kind
+of purification.
+
+When I'm done-- and we'll go
+through this whole process.
+
+That's the point of today's
+lecture, is to go through the
+
+whole process.
+
+When I'm done, I have
+bacteria spread out.
+
+And right over there, one of
+these guys has ARG1, and one
+
+of these guys has ARG2, and one
+of these guys has ARG10.
+
+Now, admittedly, I don't know
+which one has which, but I've
+
+accomplished the purification.
+
+I'll then have to figure out
+how to screen and find out
+
+which one is which, but I have
+separated the molecules away
+
+from each other by this process
+of cloning, diluting
+
+them in a way--
+
+one molecule per bacteria--
+
+and growing them back up.
+
+I could do this for anything.
+
+I could dilute proteins down
+into test tubes that had one
+
+protein molecule per test tube,
+and I could say I've
+
+accomplished purification.
+
+The problem with it is I have
+no way to replicate those
+
+proteins to get a meaningful
+amount of it.
+
+But when it's DNA, and I've put
+it back into a bacteria, I
+
+have a way to grow it back up.
+
+And that's why this
+trick works--
+
+is because DNA is a molecule
+that can replicate.
+
+No other molecule has
+that cool property.
+
+And so you can pull
+this off for DNA.
+
+All right.
+
+Now we have to dive in to
+understand how this could
+
+possibly work.
\ No newline at end of file
diff --git a/uhjq0UQqkVg.txt b/uhjq0UQqkVg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..593c0a516cc83b0aa4bb39a9ac134b566e3018b3
--- /dev/null
+++ b/uhjq0UQqkVg.txt
@@ -0,0 +1,15803 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license your support
+
+ align:start position:0%
+a creative commons license your support
+ 
+
+ align:start position:0%
+a creative commons license your support
+will help mit opencourseware continue to
+
+ align:start position:0%
+will help mit opencourseware continue to
+ 
+
+ align:start position:0%
+will help mit opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of mit courses
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+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in the last class this is what we did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first we did torque we
+
+ align:start position:0%
+first we did torque we
+ 
+
+ align:start position:0%
+first we did torque we
+we uh define torque
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and torque
+
+ align:start position:0%
+and torque
+ 
+
+ align:start position:0%
+and torque
+of a force on a particle don't look at
+
+ align:start position:0%
+of a force on a particle don't look at
+ 
+
+ align:start position:0%
+of a force on a particle don't look at
+that look at this
+
+ align:start position:0%
+that look at this
+ 
+
+ align:start position:0%
+that look at this
+the torque on a for of a force
+
+ align:start position:0%
+the torque on a for of a force
+ 
+
+ align:start position:0%
+the torque on a for of a force
+on a particle is equal to tau
+
+ align:start position:0%
+on a particle is equal to tau
+ 
+
+ align:start position:0%
+on a particle is equal to tau
+it's a vector little tau
+
+ align:start position:0%
+it's a vector little tau
+ 
+
+ align:start position:0%
+it's a vector little tau
+on the particle p about point q
+
+ align:start position:0%
+on the particle p about point q
+ 
+
+ align:start position:0%
+on the particle p about point q
+is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know this but
+
+ align:start position:0%
+you know this but
+ 
+
+ align:start position:0%
+you know this but
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+the force on the particle p
+
+ align:start position:0%
+the force on the particle p
+ 
+
+ align:start position:0%
+the force on the particle p
+you can pick any q you want
+
+ align:start position:0%
+you can pick any q you want
+ 
+
+ align:start position:0%
+you can pick any q you want
+the second thing we did was angular
+
+ align:start position:0%
+the second thing we did was angular
+ 
+
+ align:start position:0%
+the second thing we did was angular
+momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks aj
+
+ align:start position:0%
+thanks aj
+ 
+
+ align:start position:0%
+thanks aj
+okay the second thing that's just
+
+ align:start position:0%
+okay the second thing that's just
+ 
+
+ align:start position:0%
+okay the second thing that's just
+recreating stuff we did in the last
+
+ align:start position:0%
+recreating stuff we did in the last
+ 
+
+ align:start position:0%
+recreating stuff we did in the last
+class don't worry i just i just want to
+
+ align:start position:0%
+class don't worry i just i just want to
+ 
+
+ align:start position:0%
+class don't worry i just i just want to
+save some insight i want to give you
+
+ align:start position:0%
+save some insight i want to give you
+ 
+
+ align:start position:0%
+save some insight i want to give you
+some context don't worry about it we'll
+
+ align:start position:0%
+some context don't worry about it we'll
+ 
+
+ align:start position:0%
+some context don't worry about it we'll
+get there
+
+ align:start position:0%
+get there
+ 
+
+ align:start position:0%
+get there
+okay angular momentum we defined it as
+
+ align:start position:0%
+okay angular momentum we defined it as
+ 
+
+ align:start position:0%
+okay angular momentum we defined it as
+we called it a with respect to frame a
+
+ align:start position:0%
+we called it a with respect to frame a
+ 
+
+ align:start position:0%
+we called it a with respect to frame a
+h is angle momentum because angular
+
+ align:start position:0%
+h is angle momentum because angular
+ 
+
+ align:start position:0%
+h is angle momentum because angular
+momentum is
+
+ align:start position:0%
+momentum is
+ 
+
+ align:start position:0%
+momentum is
+really angular momentum that's where it
+
+ align:start position:0%
+really angular momentum that's where it
+ 
+
+ align:start position:0%
+really angular momentum that's where it
+comes from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the h is silent
+
+ align:start position:0%
+the h is silent
+ 
+
+ align:start position:0%
+the h is silent
+i'm joking you know that
+
+ align:start position:0%
+i'm joking you know that
+ 
+
+ align:start position:0%
+i'm joking you know that
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to r
+
+ align:start position:0%
+is equal to r
+ 
+
+ align:start position:0%
+is equal to r
+qp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+of p
+
+ align:start position:0%
+of p
+ 
+
+ align:start position:0%
+of p
+right so all this is you know for a
+
+ align:start position:0%
+right so all this is you know for a
+ 
+
+ align:start position:0%
+right so all this is you know for a
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+this is o this is q is the reference
+
+ align:start position:0%
+this is o this is q is the reference
+ 
+
+ align:start position:0%
+this is o this is q is the reference
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+this is a particle p
+
+ align:start position:0%
+this is a particle p
+ 
+
+ align:start position:0%
+this is a particle p
+right and there's a force on it
+
+ align:start position:0%
+right and there's a force on it
+ 
+
+ align:start position:0%
+right and there's a force on it
+right this is for that can this is for
+
+ align:start position:0%
+right this is for that can this is for
+ 
+
+ align:start position:0%
+right this is for that can this is for
+that situation
+
+ align:start position:0%
+that situation
+ 
+
+ align:start position:0%
+that situation
+little p of course is the momentum
+
+ align:start position:0%
+little p of course is the momentum
+ 
+
+ align:start position:0%
+little p of course is the momentum
+linear momentum take the cross product
+
+ align:start position:0%
+linear momentum take the cross product
+ 
+
+ align:start position:0%
+linear momentum take the cross product
+with r to get angular momentum
+
+ align:start position:0%
+with r to get angular momentum
+ 
+
+ align:start position:0%
+with r to get angular momentum
+and then finally we said that
+
+ align:start position:0%
+and then finally we said that
+ 
+
+ align:start position:0%
+and then finally we said that
+torque
+
+ align:start position:0%
+torque
+ 
+
+ align:start position:0%
+torque
+kind of the equivalent of f is equal to
+
+ align:start position:0%
+kind of the equivalent of f is equal to
+ 
+
+ align:start position:0%
+kind of the equivalent of f is equal to
+m a for rotation
+
+ align:start position:0%
+m a for rotation
+ 
+
+ align:start position:0%
+m a for rotation
+is this
+
+ align:start position:0%
+is this
+ 
+
+ align:start position:0%
+is this
+torque
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p over q
+
+ align:start position:0%
+p over q
+ 
+
+ align:start position:0%
+p over q
+sorry p uh let's just pick a q
+
+ align:start position:0%
+sorry p uh let's just pick a q
+ 
+
+ align:start position:0%
+sorry p uh let's just pick a q
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+d by dt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+angular momentum
+
+ align:start position:0%
+angular momentum
+ 
+
+ align:start position:0%
+angular momentum
+right rate of change of angular momentum
+
+ align:start position:0%
+right rate of change of angular momentum
+ 
+
+ align:start position:0%
+right rate of change of angular momentum
+is that strictly correct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that correct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's only true in some special
+
+ align:start position:0%
+so that's only true in some special
+ 
+
+ align:start position:0%
+so that's only true in some special
+cases the real complete formula
+
+ align:start position:0%
+cases the real complete formula
+ 
+
+ align:start position:0%
+cases the real complete formula
+is there's this
+
+ align:start position:0%
+is there's this
+ 
+
+ align:start position:0%
+is there's this
+correction term
+
+ align:start position:0%
+correction term
+ 
+
+ align:start position:0%
+correction term
+which again has no name so i called it
+
+ align:start position:0%
+which again has no name so i called it
+ 
+
+ align:start position:0%
+which again has no name so i called it
+the pesky term which is because i need
+
+ align:start position:0%
+the pesky term which is because i need
+ 
+
+ align:start position:0%
+the pesky term which is because i need
+to refer to it and i need a name for it
+
+ align:start position:0%
+to refer to it and i need a name for it
+ 
+
+ align:start position:0%
+to refer to it and i need a name for it
+is a v
+
+ align:start position:0%
+is a v
+ 
+
+ align:start position:0%
+is a v
+p sorry avq a bigger pattern
+
+ align:start position:0%
+p sorry avq a bigger pattern
+ 
+
+ align:start position:0%
+p sorry avq a bigger pattern
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we call this the pesky term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the three things we did
+
+ align:start position:0%
+okay so that's the three things we did
+ 
+
+ align:start position:0%
+okay so that's the three things we did
+yesterday i mean on in the last class
+
+ align:start position:0%
+yesterday i mean on in the last class
+ 
+
+ align:start position:0%
+yesterday i mean on in the last class
+torque angular momentum
+
+ align:start position:0%
+torque angular momentum
+ 
+
+ align:start position:0%
+torque angular momentum
+and torque related to angular momentum
+
+ align:start position:0%
+and torque related to angular momentum
+ 
+
+ align:start position:0%
+and torque related to angular momentum
+right two definitions these two are
+
+ align:start position:0%
+right two definitions these two are
+ 
+
+ align:start position:0%
+right two definitions these two are
+definitions
+
+ align:start position:0%
+definitions
+ 
+
+ align:start position:0%
+definitions
+and this is a
+
+ align:start position:0%
+and this is a
+ 
+
+ align:start position:0%
+and this is a
+a law which comes from f is equal to m a
+
+ align:start position:0%
+a law which comes from f is equal to m a
+ 
+
+ align:start position:0%
+a law which comes from f is equal to m a
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and then the other thing we did in the
+
+ align:start position:0%
+and then the other thing we did in the
+ 
+
+ align:start position:0%
+and then the other thing we did in the
+last class
+
+ align:start position:0%
+last class
+ 
+
+ align:start position:0%
+last class
+was we started the dumbbell problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+all this was for a single point
+
+ align:start position:0%
+all this was for a single point
+ 
+
+ align:start position:0%
+all this was for a single point
+no rigid body is a single particle right
+
+ align:start position:0%
+no rigid body is a single particle right
+ 
+
+ align:start position:0%
+no rigid body is a single particle right
+which is a point mass
+
+ align:start position:0%
+which is a point mass
+ 
+
+ align:start position:0%
+which is a point mass
+the dumbbell problem
+
+ align:start position:0%
+the dumbbell problem
+ 
+
+ align:start position:0%
+the dumbbell problem
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+two point passes connected with the link
+
+ align:start position:0%
+two point passes connected with the link
+ 
+
+ align:start position:0%
+two point passes connected with the link
+remember that
+
+ align:start position:0%
+remember that
+ 
+
+ align:start position:0%
+remember that
+but i said look a physical ma
+
+ align:start position:0%
+but i said look a physical ma
+ 
+
+ align:start position:0%
+but i said look a physical ma
+assume some unknown forces
+
+ align:start position:0%
+assume some unknown forces
+ 
+
+ align:start position:0%
+assume some unknown forces
+in the link and we'll just solve it like
+
+ align:start position:0%
+in the link and we'll just solve it like
+ 
+
+ align:start position:0%
+in the link and we'll just solve it like
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+two one particles
+
+ align:start position:0%
+two one particles
+ 
+
+ align:start position:0%
+two one particles
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and we should be able to handle two
+
+ align:start position:0%
+and we should be able to handle two
+ 
+
+ align:start position:0%
+and we should be able to handle two
+particles everything that follows in
+
+ align:start position:0%
+particles everything that follows in
+ 
+
+ align:start position:0%
+particles everything that follows in
+this course we should be able to solve
+
+ align:start position:0%
+this course we should be able to solve
+ 
+
+ align:start position:0%
+this course we should be able to solve
+with f is equal to m a
+
+ align:start position:0%
+with f is equal to m a
+ 
+
+ align:start position:0%
+with f is equal to m a
+so we started that we didn't finish it
+
+ align:start position:0%
+so we started that we didn't finish it
+ 
+
+ align:start position:0%
+so we started that we didn't finish it
+so i'm going to finish that today and
+
+ align:start position:0%
+so i'm going to finish that today and
+ 
+
+ align:start position:0%
+so i'm going to finish that today and
+that's what rj has written
+
+ align:start position:0%
+that's what rj has written
+ 
+
+ align:start position:0%
+that's what rj has written
+up for me on the right hand side i'll go
+
+ align:start position:0%
+up for me on the right hand side i'll go
+ 
+
+ align:start position:0%
+up for me on the right hand side i'll go
+finish it right there's a lot of stuff
+
+ align:start position:0%
+finish it right there's a lot of stuff
+ 
+
+ align:start position:0%
+finish it right there's a lot of stuff
+we've already done and he's going to
+
+ align:start position:0%
+we've already done and he's going to
+ 
+
+ align:start position:0%
+we've already done and he's going to
+save me some writing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the next thing we'll do today and
+
+ align:start position:0%
+then the next thing we'll do today and
+ 
+
+ align:start position:0%
+then the next thing we'll do today and
+when you when you're done with the
+
+ align:start position:0%
+when you when you're done with the
+ 
+
+ align:start position:0%
+when you when you're done with the
+dumbbell problem
+
+ align:start position:0%
+dumbbell problem
+ 
+
+ align:start position:0%
+dumbbell problem
+you'll be like well listen i saw the
+
+ align:start position:0%
+you'll be like well listen i saw the
+ 
+
+ align:start position:0%
+you'll be like well listen i saw the
+dumbbell like it was two single
+
+ align:start position:0%
+dumbbell like it was two single
+ 
+
+ align:start position:0%
+dumbbell like it was two single
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+but really i solved a rigid body problem
+
+ align:start position:0%
+but really i solved a rigid body problem
+ 
+
+ align:start position:0%
+but really i solved a rigid body problem
+because it's actually a rigid body right
+
+ align:start position:0%
+because it's actually a rigid body right
+ 
+
+ align:start position:0%
+because it's actually a rigid body right
+and you'll see moment of inertia just
+
+ align:start position:0%
+and you'll see moment of inertia just
+ 
+
+ align:start position:0%
+and you'll see moment of inertia just
+kind of drop out magically
+
+ align:start position:0%
+kind of drop out magically
+ 
+
+ align:start position:0%
+kind of drop out magically
+and then you'll be like huh moment of
+
+ align:start position:0%
+and then you'll be like huh moment of
+ 
+
+ align:start position:0%
+and then you'll be like huh moment of
+inertia is therefore
+
+ align:start position:0%
+inertia is therefore
+ 
+
+ align:start position:0%
+inertia is therefore
+comes naturally when you solve multiple
+
+ align:start position:0%
+comes naturally when you solve multiple
+ 
+
+ align:start position:0%
+comes naturally when you solve multiple
+particle problems right
+
+ align:start position:0%
+particle problems right
+ 
+
+ align:start position:0%
+particle problems right
+so then what we'll do
+
+ align:start position:0%
+so then what we'll do
+ 
+
+ align:start position:0%
+so then what we'll do
+is we will actually formally define
+
+ align:start position:0%
+is we will actually formally define
+ 
+
+ align:start position:0%
+is we will actually formally define
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+moment of inertia and formally introduce
+
+ align:start position:0%
+moment of inertia and formally introduce
+ 
+
+ align:start position:0%
+moment of inertia and formally introduce
+you to torque is equal to i alpha that
+
+ align:start position:0%
+you to torque is equal to i alpha that
+ 
+
+ align:start position:0%
+you to torque is equal to i alpha that
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+it'll actually come out of this you'll
+
+ align:start position:0%
+it'll actually come out of this you'll
+ 
+
+ align:start position:0%
+it'll actually come out of this you'll
+see torque is good i alpha but you'll
+
+ align:start position:0%
+see torque is good i alpha but you'll
+ 
+
+ align:start position:0%
+see torque is good i alpha but you'll
+see it here right so you'll see torque
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to i alpha you'll see that so
+
+ align:start position:0%
+is equal to i alpha you'll see that so
+ 
+
+ align:start position:0%
+is equal to i alpha you'll see that so
+that's kind of what we're going to do
+
+ align:start position:0%
+that's kind of what we're going to do
+ 
+
+ align:start position:0%
+that's kind of what we're going to do
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you remember the dumbbell problem
+
+ align:start position:0%
+so if you remember the dumbbell problem
+ 
+
+ align:start position:0%
+so if you remember the dumbbell problem
+what we had was two number a dumbbell
+
+ align:start position:0%
+what we had was two number a dumbbell
+ 
+
+ align:start position:0%
+what we had was two number a dumbbell
+which is two point masses
+
+ align:start position:0%
+which is two point masses
+ 
+
+ align:start position:0%
+which is two point masses
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and uh we applied two forces f p and f q
+
+ align:start position:0%
+and uh we applied two forces f p and f q
+ 
+
+ align:start position:0%
+and uh we applied two forces f p and f q
+the unequal forces were just to make the
+
+ align:start position:0%
+the unequal forces were just to make the
+ 
+
+ align:start position:0%
+the unequal forces were just to make the
+math easy we made them parallel i don't
+
+ align:start position:0%
+math easy we made them parallel i don't
+ 
+
+ align:start position:0%
+math easy we made them parallel i don't
+care it really doesn't matter which you
+
+ align:start position:0%
+care it really doesn't matter which you
+ 
+
+ align:start position:0%
+care it really doesn't matter which you
+can solve the problem anyway
+
+ align:start position:0%
+can solve the problem anyway
+ 
+
+ align:start position:0%
+can solve the problem anyway
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and we said that the for the reference
+
+ align:start position:0%
+and we said that the for the reference
+ 
+
+ align:start position:0%
+and we said that the for the reference
+frame a is inertial
+
+ align:start position:0%
+frame a is inertial
+ 
+
+ align:start position:0%
+frame a is inertial
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+the origin is o we call the center of
+
+ align:start position:0%
+the origin is o we call the center of
+ 
+
+ align:start position:0%
+the origin is o we call the center of
+the two dumbbells c
+
+ align:start position:0%
+the two dumbbells c
+ 
+
+ align:start position:0%
+the two dumbbells c
+of the two sorry point masses right the
+
+ align:start position:0%
+of the two sorry point masses right the
+ 
+
+ align:start position:0%
+of the two sorry point masses right the
+center of the dumbbell c
+
+ align:start position:0%
+center of the dumbbell c
+ 
+
+ align:start position:0%
+center of the dumbbell c
+this is q and that is p
+
+ align:start position:0%
+this is q and that is p
+ 
+
+ align:start position:0%
+this is q and that is p
+we pick these
+
+ align:start position:0%
+we pick these
+ 
+
+ align:start position:0%
+we pick these
+non-standard coordinates because they
+
+ align:start position:0%
+non-standard coordinates because they
+ 
+
+ align:start position:0%
+non-standard coordinates because they
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+convenient
+
+ align:start position:0%
+convenient
+ 
+
+ align:start position:0%
+convenient
+they're minimal
+
+ align:start position:0%
+they're minimal
+ 
+
+ align:start position:0%
+they're minimal
+right because this thing has three
+
+ align:start position:0%
+right because this thing has three
+ 
+
+ align:start position:0%
+right because this thing has three
+degrees of freedom
+
+ align:start position:0%
+degrees of freedom
+ 
+
+ align:start position:0%
+degrees of freedom
+and now you have
+
+ align:start position:0%
+and now you have
+ 
+
+ align:start position:0%
+and now you have
+you can take these two
+
+ align:start position:0%
+you can take these two
+ 
+
+ align:start position:0%
+you can take these two
+lengths and the and we we picked theta
+
+ align:start position:0%
+lengths and the and we we picked theta
+ 
+
+ align:start position:0%
+lengths and the and we we picked theta
+as the other non-standard coordinate
+
+ align:start position:0%
+as the other non-standard coordinate
+ 
+
+ align:start position:0%
+as the other non-standard coordinate
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+oh you missed bix p and q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are you sure
+
+ align:start position:0%
+are you sure
+ 
+
+ align:start position:0%
+are you sure
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the two forces on it so the two drum
+
+ align:start position:0%
+and the two forces on it so the two drum
+ 
+
+ align:start position:0%
+and the two forces on it so the two drum
+dumbbells sitting on a on a ring
+
+ align:start position:0%
+dumbbells sitting on a on a ring
+ 
+
+ align:start position:0%
+dumbbells sitting on a on a ring
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+think of it that way and you have two
+
+ align:start position:0%
+think of it that way and you have two
+ 
+
+ align:start position:0%
+think of it that way and you have two
+rockets attached to them they both apply
+
+ align:start position:0%
+rockets attached to them they both apply
+ 
+
+ align:start position:0%
+rockets attached to them they both apply
+forces heading that that way
+
+ align:start position:0%
+forces heading that that way
+ 
+
+ align:start position:0%
+forces heading that that way
+and the two forces are constant but they
+
+ align:start position:0%
+and the two forces are constant but they
+ 
+
+ align:start position:0%
+and the two forces are constant but they
+always head that way
+
+ align:start position:0%
+always head that way
+ 
+
+ align:start position:0%
+always head that way
+fp and fq
+
+ align:start position:0%
+fp and fq
+ 
+
+ align:start position:0%
+fp and fq
+and what we're trying to figure out is
+
+ align:start position:0%
+and what we're trying to figure out is
+ 
+
+ align:start position:0%
+and what we're trying to figure out is
+what this dumbbell does
+
+ align:start position:0%
+what this dumbbell does
+ 
+
+ align:start position:0%
+what this dumbbell does
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we'll come to the free body diagrams
+
+ align:start position:0%
+so we'll come to the free body diagrams
+ 
+
+ align:start position:0%
+so we'll come to the free body diagrams
+actually so the first thing you do is
+
+ align:start position:0%
+actually so the first thing you do is
+ 
+
+ align:start position:0%
+actually so the first thing you do is
+you draw a free body diagram
+
+ align:start position:0%
+you draw a free body diagram
+ 
+
+ align:start position:0%
+you draw a free body diagram
+and the free body diagrams are
+
+ align:start position:0%
+and the free body diagrams are
+ 
+
+ align:start position:0%
+and the free body diagrams are
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the u here ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh i see just the unit vector okay all
+
+ align:start position:0%
+oh i see just the unit vector okay all
+ 
+
+ align:start position:0%
+oh i see just the unit vector okay all
+right so essentially what uh what we're
+
+ align:start position:0%
+right so essentially what uh what we're
+ 
+
+ align:start position:0%
+right so essentially what uh what we're
+doing here is well we could have called
+
+ align:start position:0%
+doing here is well we could have called
+ 
+
+ align:start position:0%
+doing here is well we could have called
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+b1 right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we can take each point mass
+
+ align:start position:0%
+okay so we can take each point mass
+ 
+
+ align:start position:0%
+okay so we can take each point mass
+this point mass has only two forces on
+
+ align:start position:0%
+this point mass has only two forces on
+ 
+
+ align:start position:0%
+this point mass has only two forces on
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+one force is this f and the other is a
+
+ align:start position:0%
+one force is this f and the other is a
+ 
+
+ align:start position:0%
+one force is this f and the other is a
+kind of a tension
+
+ align:start position:0%
+kind of a tension
+ 
+
+ align:start position:0%
+kind of a tension
+in the in the rod right we'll come to
+
+ align:start position:0%
+in the in the rod right we'll come to
+ 
+
+ align:start position:0%
+in the in the rod right we'll come to
+that in a second this point mass has the
+
+ align:start position:0%
+that in a second this point mass has the
+ 
+
+ align:start position:0%
+that in a second this point mass has the
+force fp and it has the tension in the
+
+ align:start position:0%
+force fp and it has the tension in the
+ 
+
+ align:start position:0%
+force fp and it has the tension in the
+rod this way right yes
+
+ align:start position:0%
+rod this way right yes
+ 
+
+ align:start position:0%
+rod this way right yes
+why is the tension along the rod anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and why is that why does it have to
+
+ align:start position:0%
+yeah and why is that why does it have to
+ 
+
+ align:start position:0%
+yeah and why is that why does it have to
+be coaxial
+
+ align:start position:0%
+be coaxial
+ 
+
+ align:start position:0%
+be coaxial
+can a rod not apply a sideways force
+
+ align:start position:0%
+can a rod not apply a sideways force
+ 
+
+ align:start position:0%
+can a rod not apply a sideways force
+i mean i can do it right i can pick up a
+
+ align:start position:0%
+i mean i can do it right i can pick up a
+ 
+
+ align:start position:0%
+i mean i can do it right i can pick up a
+stick and wave it
+
+ align:start position:0%
+stick and wave it
+ 
+
+ align:start position:0%
+stick and wave it
+what was that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the reason actually is this
+
+ align:start position:0%
+well the reason actually is this
+ 
+
+ align:start position:0%
+well the reason actually is this
+if you just did a free body diagram on
+
+ align:start position:0%
+if you just did a free body diagram on
+ 
+
+ align:start position:0%
+if you just did a free body diagram on
+the rod and the tensions were not
+
+ align:start position:0%
+the rod and the tensions were not
+ 
+
+ align:start position:0%
+the rod and the tensions were not
+collinear
+
+ align:start position:0%
+collinear
+ 
+
+ align:start position:0%
+collinear
+and they were kind of skewed right that
+
+ align:start position:0%
+and they were kind of skewed right that
+ 
+
+ align:start position:0%
+and they were kind of skewed right that
+they didn't meet there would be a net
+
+ align:start position:0%
+they didn't meet there would be a net
+ 
+
+ align:start position:0%
+they didn't meet there would be a net
+torque on the rod
+
+ align:start position:0%
+torque on the rod
+ 
+
+ align:start position:0%
+torque on the rod
+but you know the mass of the rod is zero
+
+ align:start position:0%
+but you know the mass of the rod is zero
+ 
+
+ align:start position:0%
+but you know the mass of the rod is zero
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the change of momentum the rod is
+
+ align:start position:0%
+so the change of momentum the rod is
+ 
+
+ align:start position:0%
+so the change of momentum the rod is
+going to be zero
+
+ align:start position:0%
+going to be zero
+ 
+
+ align:start position:0%
+going to be zero
+change of angular momentum so the net
+
+ align:start position:0%
+change of angular momentum so the net
+ 
+
+ align:start position:0%
+change of angular momentum so the net
+torque must be zero
+
+ align:start position:0%
+torque must be zero
+ 
+
+ align:start position:0%
+torque must be zero
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+the angular momentum of the torque is
+
+ align:start position:0%
+the angular momentum of the torque is
+ 
+
+ align:start position:0%
+the angular momentum of the torque is
+zero forever more
+
+ align:start position:0%
+zero forever more
+ 
+
+ align:start position:0%
+zero forever more
+so the rate of change of angular
+
+ align:start position:0%
+so the rate of change of angular
+ 
+
+ align:start position:0%
+so the rate of change of angular
+momentum is zero
+
+ align:start position:0%
+momentum is zero
+ 
+
+ align:start position:0%
+momentum is zero
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and torque is equal to
+
+ align:start position:0%
+and torque is equal to
+ 
+
+ align:start position:0%
+and torque is equal to
+i alpha plus you know even if even if
+
+ align:start position:0%
+i alpha plus you know even if even if
+ 
+
+ align:start position:0%
+i alpha plus you know even if even if
+you take all this
+
+ align:start position:0%
+you take all this
+ 
+
+ align:start position:0%
+you take all this
+the right hand side is going to be zero
+
+ align:start position:0%
+the right hand side is going to be zero
+ 
+
+ align:start position:0%
+the right hand side is going to be zero
+so the torque is going to be zero which
+
+ align:start position:0%
+so the torque is going to be zero which
+ 
+
+ align:start position:0%
+so the torque is going to be zero which
+means that the tension forces have to be
+
+ align:start position:0%
+means that the tension forces have to be
+ 
+
+ align:start position:0%
+means that the tension forces have to be
+co-linear if you don't understand this
+
+ align:start position:0%
+co-linear if you don't understand this
+ 
+
+ align:start position:0%
+co-linear if you don't understand this
+i'll explain later it's not a big deal
+
+ align:start position:0%
+i'll explain later it's not a big deal
+ 
+
+ align:start position:0%
+i'll explain later it's not a big deal
+right assume that this is a sort of a
+
+ align:start position:0%
+right assume that this is a sort of a
+ 
+
+ align:start position:0%
+right assume that this is a sort of a
+struct which can only support
+
+ align:start position:0%
+struct which can only support
+ 
+
+ align:start position:0%
+struct which can only support
+compressive attention it can't support
+
+ align:start position:0%
+compressive attention it can't support
+ 
+
+ align:start position:0%
+compressive attention it can't support
+any bending that's the other way to
+
+ align:start position:0%
+any bending that's the other way to
+ 
+
+ align:start position:0%
+any bending that's the other way to
+think about it
+
+ align:start position:0%
+think about it
+ 
+
+ align:start position:0%
+think about it
+so these are the two forces
+
+ align:start position:0%
+so these are the two forces
+ 
+
+ align:start position:0%
+so these are the two forces
+so we've drawn a free body diagram then
+
+ align:start position:0%
+so we've drawn a free body diagram then
+ 
+
+ align:start position:0%
+so we've drawn a free body diagram then
+the next step
+
+ align:start position:0%
+the next step
+ 
+
+ align:start position:0%
+the next step
+is we're going to calculate the
+
+ align:start position:0%
+is we're going to calculate the
+ 
+
+ align:start position:0%
+is we're going to calculate the
+accelerations of points p and q all this
+
+ align:start position:0%
+accelerations of points p and q all this
+ 
+
+ align:start position:0%
+accelerations of points p and q all this
+i did in the last class right the
+
+ align:start position:0%
+i did in the last class right the
+ 
+
+ align:start position:0%
+i did in the last class right the
+acceleration of point p is ap
+
+ align:start position:0%
+acceleration of point p is ap
+ 
+
+ align:start position:0%
+acceleration of point p is ap
+is basically this vector
+
+ align:start position:0%
+is basically this vector
+ 
+
+ align:start position:0%
+is basically this vector
+plus this vector the rate of change of
+
+ align:start position:0%
+plus this vector the rate of change of
+ 
+
+ align:start position:0%
+plus this vector the rate of change of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+right and you can use the ultra super
+
+ align:start position:0%
+right and you can use the ultra super
+ 
+
+ align:start position:0%
+right and you can use the ultra super
+cool magic formula if you want
+
+ align:start position:0%
+cool magic formula if you want
+ 
+
+ align:start position:0%
+cool magic formula if you want
+and what you get is the acceleration of
+
+ align:start position:0%
+and what you get is the acceleration of
+ 
+
+ align:start position:0%
+and what you get is the acceleration of
+point p is acceleration of point
+
+ align:start position:0%
+point p is acceleration of point
+ 
+
+ align:start position:0%
+point p is acceleration of point
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+this what term is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+centripetal term just from magic formula
+
+ align:start position:0%
+centripetal term just from magic formula
+ 
+
+ align:start position:0%
+centripetal term just from magic formula
+plus what is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+euler formula right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is r i'm just writing in my
+
+ align:start position:0%
+this is r i'm just writing in my
+ 
+
+ align:start position:0%
+this is r i'm just writing in my
+handwriting right
+
+ align:start position:0%
+handwriting right
+ 
+
+ align:start position:0%
+handwriting right
+and then a q
+
+ align:start position:0%
+and then a q
+ 
+
+ align:start position:0%
+and then a q
+same thing right so we know the
+
+ align:start position:0%
+same thing right so we know the
+ 
+
+ align:start position:0%
+same thing right so we know the
+accelerations of the two endpoints right
+
+ align:start position:0%
+accelerations of the two endpoints right
+ 
+
+ align:start position:0%
+accelerations of the two endpoints right
+i'm going to stop here because i see
+
+ align:start position:0%
+i'm going to stop here because i see
+ 
+
+ align:start position:0%
+i'm going to stop here because i see
+some quizzical faces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everyone good with this copacetic with
+
+ align:start position:0%
+everyone good with this copacetic with
+ 
+
+ align:start position:0%
+everyone good with this copacetic with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+not a big deal all i'm saying is look
+
+ align:start position:0%
+not a big deal all i'm saying is look
+ 
+
+ align:start position:0%
+not a big deal all i'm saying is look
+the you know this end instead of finding
+
+ align:start position:0%
+the you know this end instead of finding
+ 
+
+ align:start position:0%
+the you know this end instead of finding
+the if i want to find the accelerations
+
+ align:start position:0%
+the if i want to find the accelerations
+ 
+
+ align:start position:0%
+the if i want to find the accelerations
+of the endpoints
+
+ align:start position:0%
+of the endpoints
+ 
+
+ align:start position:0%
+of the endpoints
+in terms of the
+
+ align:start position:0%
+in terms of the
+ 
+
+ align:start position:0%
+in terms of the
+coordinates i picked
+
+ align:start position:0%
+coordinates i picked
+ 
+
+ align:start position:0%
+coordinates i picked
+which are
+
+ align:start position:0%
+which are
+ 
+
+ align:start position:0%
+which are
+the center points kind of x and y
+
+ align:start position:0%
+the center points kind of x and y
+ 
+
+ align:start position:0%
+the center points kind of x and y
+location and the angle of the dumbbell
+
+ align:start position:0%
+location and the angle of the dumbbell
+ 
+
+ align:start position:0%
+location and the angle of the dumbbell
+this is how i would write it andrew
+
+ align:start position:0%
+this is how i would write it andrew
+ 
+
+ align:start position:0%
+this is how i would write it andrew
+everyone good
+
+ align:start position:0%
+everyone good
+ 
+
+ align:start position:0%
+everyone good
+go ahead see i knew
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's talk about the tension here's
+
+ align:start position:0%
+okay let's talk about the tension here's
+ 
+
+ align:start position:0%
+okay let's talk about the tension here's
+why i don't have a place to write let me
+
+ align:start position:0%
+why i don't have a place to write let me
+ 
+
+ align:start position:0%
+why i don't have a place to write let me
+just write it here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's why
+
+ align:start position:0%
+here's why
+ 
+
+ align:start position:0%
+here's why
+this is the rod these are the spheres
+
+ align:start position:0%
+this is the rod these are the spheres
+ 
+
+ align:start position:0%
+this is the rod these are the spheres
+right the point masses i'm saying the
+
+ align:start position:0%
+right the point masses i'm saying the
+ 
+
+ align:start position:0%
+right the point masses i'm saying the
+tension has to be this way if the
+
+ align:start position:0%
+tension has to be this way if the
+ 
+
+ align:start position:0%
+tension has to be this way if the
+tension would ratchet this way
+
+ align:start position:0%
+tension would ratchet this way
+ 
+
+ align:start position:0%
+tension would ratchet this way
+they would still be equal and opposite
+
+ align:start position:0%
+they would still be equal and opposite
+ 
+
+ align:start position:0%
+they would still be equal and opposite
+so they would still
+
+ align:start position:0%
+so they would still
+ 
+
+ align:start position:0%
+so they would still
+satisfy the weak form of newton's law
+
+ align:start position:0%
+satisfy the weak form of newton's law
+ 
+
+ align:start position:0%
+satisfy the weak form of newton's law
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+even without invoking you know newton's
+
+ align:start position:0%
+even without invoking you know newton's
+ 
+
+ align:start position:0%
+even without invoking you know newton's
+strong form right
+
+ align:start position:0%
+strong form right
+ 
+
+ align:start position:0%
+strong form right
+the fact of the matter is if they're
+
+ align:start position:0%
+the fact of the matter is if they're
+ 
+
+ align:start position:0%
+the fact of the matter is if they're
+this way then if you just look at the
+
+ align:start position:0%
+this way then if you just look at the
+ 
+
+ align:start position:0%
+this way then if you just look at the
+rod
+
+ align:start position:0%
+rod
+ 
+
+ align:start position:0%
+rod
+does it have a net torque on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think about it if i take let's say it
+
+ align:start position:0%
+think about it if i take let's say it
+ 
+
+ align:start position:0%
+think about it if i take let's say it
+talks around this point the center of
+
+ align:start position:0%
+talks around this point the center of
+ 
+
+ align:start position:0%
+talks around this point the center of
+mass just the rod
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+do you understand
+
+ align:start position:0%
+do you understand
+ 
+
+ align:start position:0%
+do you understand
+the torque if the rod is massless
+
+ align:start position:0%
+the torque if the rod is massless
+ 
+
+ align:start position:0%
+the torque if the rod is massless
+and it's got two forces creating a
+
+ align:start position:0%
+and it's got two forces creating a
+ 
+
+ align:start position:0%
+and it's got two forces creating a
+torque around it
+
+ align:start position:0%
+torque around it
+ 
+
+ align:start position:0%
+torque around it
+it'll have to accelerate at an infinite
+
+ align:start position:0%
+it'll have to accelerate at an infinite
+ 
+
+ align:start position:0%
+it'll have to accelerate at an infinite
+you know alpha or go to infinity right
+
+ align:start position:0%
+you know alpha or go to infinity right
+ 
+
+ align:start position:0%
+you know alpha or go to infinity right
+at some intuitive level do you
+
+ align:start position:0%
+at some intuitive level do you
+ 
+
+ align:start position:0%
+at some intuitive level do you
+understand what i'm saying
+
+ align:start position:0%
+understand what i'm saying
+ 
+
+ align:start position:0%
+understand what i'm saying
+right a massless rod
+
+ align:start position:0%
+right a massless rod
+ 
+
+ align:start position:0%
+right a massless rod
+therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cannot have
+
+ align:start position:0%
+cannot have
+ 
+
+ align:start position:0%
+cannot have
+uh or the forces on it must be along
+
+ align:start position:0%
+uh or the forces on it must be along
+ 
+
+ align:start position:0%
+uh or the forces on it must be along
+the the line connecting the points they
+
+ align:start position:0%
+the the line connecting the points they
+ 
+
+ align:start position:0%
+the the line connecting the points they
+have to be collinear
+
+ align:start position:0%
+have to be collinear
+ 
+
+ align:start position:0%
+have to be collinear
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+anyone not get this i can say it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and are you okay with that right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway so now i got the accelerations of
+
+ align:start position:0%
+anyway so now i got the accelerations of
+ 
+
+ align:start position:0%
+anyway so now i got the accelerations of
+ap and aq and now i can write newton's
+
+ align:start position:0%
+ap and aq and now i can write newton's
+ 
+
+ align:start position:0%
+ap and aq and now i can write newton's
+laws right
+
+ align:start position:0%
+laws right
+ 
+
+ align:start position:0%
+laws right
+so i can write newton's law for this guy
+
+ align:start position:0%
+so i can write newton's law for this guy
+ 
+
+ align:start position:0%
+so i can write newton's law for this guy
+f q minus t b1
+
+ align:start position:0%
+f q minus t b1
+ 
+
+ align:start position:0%
+f q minus t b1
+right fq minus t
+
+ align:start position:0%
+right fq minus t
+ 
+
+ align:start position:0%
+right fq minus t
+b1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f q minus t b 1 is equal to mass times
+
+ align:start position:0%
+f q minus t b 1 is equal to mass times
+ 
+
+ align:start position:0%
+f q minus t b 1 is equal to mass times
+acceleration of
+
+ align:start position:0%
+acceleration of
+ 
+
+ align:start position:0%
+acceleration of
+point of particle q
+
+ align:start position:0%
+point of particle q
+ 
+
+ align:start position:0%
+point of particle q
+f p plus t b b 1 is mass times
+
+ align:start position:0%
+f p plus t b b 1 is mass times
+ 
+
+ align:start position:0%
+f p plus t b b 1 is mass times
+acceleration of point p
+
+ align:start position:0%
+acceleration of point p
+ 
+
+ align:start position:0%
+acceleration of point p
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+i've done i actually have this is
+
+ align:start position:0%
+i've done i actually have this is
+ 
+
+ align:start position:0%
+i've done i actually have this is
+actually very simple i mean i you know
+
+ align:start position:0%
+actually very simple i mean i you know
+ 
+
+ align:start position:0%
+actually very simple i mean i you know
+sometimes i'm saying things so simply
+
+ align:start position:0%
+sometimes i'm saying things so simply
+ 
+
+ align:start position:0%
+sometimes i'm saying things so simply
+that you might get confused
+
+ align:start position:0%
+that you might get confused
+ 
+
+ align:start position:0%
+that you might get confused
+any questions from anyone you can stop
+
+ align:start position:0%
+any questions from anyone you can stop
+ 
+
+ align:start position:0%
+any questions from anyone you can stop
+me here if you want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first step
+
+ align:start position:0%
+first step
+ 
+
+ align:start position:0%
+first step
+label and draw everything second step
+
+ align:start position:0%
+label and draw everything second step
+ 
+
+ align:start position:0%
+label and draw everything second step
+draw the free body diagram third step
+
+ align:start position:0%
+draw the free body diagram third step
+ 
+
+ align:start position:0%
+draw the free body diagram third step
+figure out the accelerations fourth step
+
+ align:start position:0%
+figure out the accelerations fourth step
+ 
+
+ align:start position:0%
+figure out the accelerations fourth step
+right f is equal to m a
+
+ align:start position:0%
+right f is equal to m a
+ 
+
+ align:start position:0%
+right f is equal to m a
+that's what i just did well that's what
+
+ align:start position:0%
+that's what i just did well that's what
+ 
+
+ align:start position:0%
+that's what i just did well that's what
+rj did
+
+ align:start position:0%
+rj did
+ 
+
+ align:start position:0%
+rj did
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+actually what happens next is
+
+ align:start position:0%
+actually what happens next is
+ 
+
+ align:start position:0%
+actually what happens next is
+look you have
+
+ align:start position:0%
+look you have
+ 
+
+ align:start position:0%
+look you have
+two equations
+
+ align:start position:0%
+two equations
+ 
+
+ align:start position:0%
+two equations
+they're both vector equations
+
+ align:start position:0%
+they're both vector equations
+ 
+
+ align:start position:0%
+they're both vector equations
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and at some level
+
+ align:start position:0%
+and at some level
+ 
+
+ align:start position:0%
+and at some level
+you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three unknowns
+
+ align:start position:0%
+three unknowns
+ 
+
+ align:start position:0%
+three unknowns
+so there's actually four equations right
+
+ align:start position:0%
+so there's actually four equations right
+ 
+
+ align:start position:0%
+so there's actually four equations right
+but you have
+
+ align:start position:0%
+but you have
+ 
+
+ align:start position:0%
+but you have
+how many unknowns what are the unknowns
+
+ align:start position:0%
+how many unknowns what are the unknowns
+ 
+
+ align:start position:0%
+how many unknowns what are the unknowns
+the x location of the rod the y location
+
+ align:start position:0%
+the x location of the rod the y location
+ 
+
+ align:start position:0%
+the x location of the rod the y location
+of center of the rod the angle is there
+
+ align:start position:0%
+of center of the rod the angle is there
+ 
+
+ align:start position:0%
+of center of the rod the angle is there
+any other unknown
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay so let's list them again what
+
+ align:start position:0%
+well okay so let's list them again what
+ 
+
+ align:start position:0%
+well okay so let's list them again what
+are the unknowns
+
+ align:start position:0%
+are the unknowns
+ 
+
+ align:start position:0%
+are the unknowns
+you want to know where the orders x y
+
+ align:start position:0%
+you want to know where the orders x y
+ 
+
+ align:start position:0%
+you want to know where the orders x y
+and angle that's three
+
+ align:start position:0%
+and angle that's three
+ 
+
+ align:start position:0%
+and angle that's three
+i have four equations so there must be
+
+ align:start position:0%
+i have four equations so there must be
+ 
+
+ align:start position:0%
+i have four equations so there must be
+one more unknown right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tension
+
+ align:start position:0%
+tension
+ 
+
+ align:start position:0%
+tension
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if the two rods weren't connected the
+
+ align:start position:0%
+if the two rods weren't connected the
+ 
+
+ align:start position:0%
+if the two rods weren't connected the
+fourth unknown would be like
+
+ align:start position:0%
+fourth unknown would be like
+ 
+
+ align:start position:0%
+fourth unknown would be like
+you know x y x y of the two you know two
+
+ align:start position:0%
+you know x y x y of the two you know two
+ 
+
+ align:start position:0%
+you know x y x y of the two you know two
+bodies
+
+ align:start position:0%
+bodies
+ 
+
+ align:start position:0%
+bodies
+and there wouldn't be a tension so if
+
+ align:start position:0%
+and there wouldn't be a tension so if
+ 
+
+ align:start position:0%
+and there wouldn't be a tension so if
+there's a kinematic constraint
+
+ align:start position:0%
+there's a kinematic constraint
+ 
+
+ align:start position:0%
+there's a kinematic constraint
+one of the
+
+ align:start position:0%
+one of the
+ 
+
+ align:start position:0%
+one of the
+degrees of freedom would go away but an
+
+ align:start position:0%
+degrees of freedom would go away but an
+ 
+
+ align:start position:0%
+degrees of freedom would go away but an
+unknown force replaces it you understand
+
+ align:start position:0%
+unknown force replaces it you understand
+ 
+
+ align:start position:0%
+unknown force replaces it you understand
+it's very important that you get this
+
+ align:start position:0%
+it's very important that you get this
+ 
+
+ align:start position:0%
+it's very important that you get this
+gestalt
+
+ align:start position:0%
+gestalt
+ 
+
+ align:start position:0%
+gestalt
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+four equations four unknowns
+
+ align:start position:0%
+four equations four unknowns
+ 
+
+ align:start position:0%
+four equations four unknowns
+you should be able to solve it
+
+ align:start position:0%
+you should be able to solve it
+ 
+
+ align:start position:0%
+you should be able to solve it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but now let's solve it
+
+ align:start position:0%
+but now let's solve it
+ 
+
+ align:start position:0%
+but now let's solve it
+and i want to show you something
+
+ align:start position:0%
+and i want to show you something
+ 
+
+ align:start position:0%
+and i want to show you something
+interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what do you have what do you do when
+
+ align:start position:0%
+now what do you have what do you do when
+ 
+
+ align:start position:0%
+now what do you have what do you do when
+you have simultaneous equations you
+
+ align:start position:0%
+you have simultaneous equations you
+ 
+
+ align:start position:0%
+you have simultaneous equations you
+subtract them you add them you eliminate
+
+ align:start position:0%
+subtract them you add them you eliminate
+ 
+
+ align:start position:0%
+subtract them you add them you eliminate
+terms right
+
+ align:start position:0%
+terms right
+ 
+
+ align:start position:0%
+terms right
+i'm just going to do them all in vector
+
+ align:start position:0%
+i'm just going to do them all in vector
+ 
+
+ align:start position:0%
+i'm just going to do them all in vector
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+so if i add these two equations
+
+ align:start position:0%
+so if i add these two equations
+ 
+
+ align:start position:0%
+so if i add these two equations
+1 and 2
+
+ align:start position:0%
+1 and 2
+ 
+
+ align:start position:0%
+1 and 2
+this term will cancel out right
+
+ align:start position:0%
+this term will cancel out right
+ 
+
+ align:start position:0%
+this term will cancel out right
+so i'll get f p plus f q
+
+ align:start position:0%
+so i'll get f p plus f q
+ 
+
+ align:start position:0%
+so i'll get f p plus f q
+is equal to the sum of these two guys
+
+ align:start position:0%
+is equal to the sum of these two guys
+ 
+
+ align:start position:0%
+is equal to the sum of these two guys
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+so that's the first equation here
+
+ align:start position:0%
+so that's the first equation here
+ 
+
+ align:start position:0%
+so that's the first equation here
+f p plus f q is equal to 2 m a
+
+ align:start position:0%
+f p plus f q is equal to 2 m a
+ 
+
+ align:start position:0%
+f p plus f q is equal to 2 m a
+acceleration of center of mass
+
+ align:start position:0%
+acceleration of center of mass
+ 
+
+ align:start position:0%
+acceleration of center of mass
+got it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so that's the only little bit of
+
+ align:start position:0%
+yeah so that's the only little bit of
+ 
+
+ align:start position:0%
+yeah so that's the only little bit of
+you know shell game i played here
+
+ align:start position:0%
+you know shell game i played here
+ 
+
+ align:start position:0%
+you know shell game i played here
+m a
+
+ align:start position:0%
+m a
+ 
+
+ align:start position:0%
+m a
+so the definition of the center of mass
+
+ align:start position:0%
+so the definition of the center of mass
+ 
+
+ align:start position:0%
+so the definition of the center of mass
+is the so that's how that's the
+
+ align:start position:0%
+is the so that's how that's the
+ 
+
+ align:start position:0%
+is the so that's how that's the
+definition of the center of mass right
+
+ align:start position:0%
+definition of the center of mass right
+ 
+
+ align:start position:0%
+definition of the center of mass right
+if you take the acceleration of one end
+
+ align:start position:0%
+if you take the acceleration of one end
+ 
+
+ align:start position:0%
+if you take the acceleration of one end
+times the mass of that end
+
+ align:start position:0%
+times the mass of that end
+ 
+
+ align:start position:0%
+times the mass of that end
+plus the acceleration on the other end
+
+ align:start position:0%
+plus the acceleration on the other end
+ 
+
+ align:start position:0%
+plus the acceleration on the other end
+plus the mass of the other end
+
+ align:start position:0%
+plus the mass of the other end
+ 
+
+ align:start position:0%
+plus the mass of the other end
+right what you get
+
+ align:start position:0%
+right what you get
+ 
+
+ align:start position:0%
+right what you get
+is like two times that mass at the
+
+ align:start position:0%
+is like two times that mass at the
+ 
+
+ align:start position:0%
+is like two times that mass at the
+center of mass at the center of mass
+
+ align:start position:0%
+center of mass at the center of mass
+ 
+
+ align:start position:0%
+center of mass at the center of mass
+accelerating with the acceleration
+
+ align:start position:0%
+accelerating with the acceleration
+ 
+
+ align:start position:0%
+accelerating with the acceleration
+center of mass all right
+
+ align:start position:0%
+center of mass all right
+ 
+
+ align:start position:0%
+center of mass all right
+this will become more clear in a minute
+
+ align:start position:0%
+this will become more clear in a minute
+ 
+
+ align:start position:0%
+this will become more clear in a minute
+when i do the actual derivation you'll
+
+ align:start position:0%
+when i do the actual derivation you'll
+ 
+
+ align:start position:0%
+when i do the actual derivation you'll
+see it but essentially when you add maap
+
+ align:start position:0%
+see it but essentially when you add maap
+ 
+
+ align:start position:0%
+see it but essentially when you add maap
+plus maaq
+
+ align:start position:0%
+plus maaq
+ 
+
+ align:start position:0%
+plus maaq
+it's the same as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2m
+
+ align:start position:0%
+2m
+ 
+
+ align:start position:0%
+2m
+times acceleration the central mass is
+
+ align:start position:0%
+times acceleration the central mass is
+ 
+
+ align:start position:0%
+times acceleration the central mass is
+the weighted average that's what the
+
+ align:start position:0%
+the weighted average that's what the
+ 
+
+ align:start position:0%
+the weighted average that's what the
+central mass will do don't worry i'll
+
+ align:start position:0%
+central mass will do don't worry i'll
+ 
+
+ align:start position:0%
+central mass will do don't worry i'll
+nail this in a minute okay so it's a
+
+ align:start position:0%
+nail this in a minute okay so it's a
+ 
+
+ align:start position:0%
+nail this in a minute okay so it's a
+good good catch that was a little bit of
+
+ align:start position:0%
+good good catch that was a little bit of
+ 
+
+ align:start position:0%
+good good catch that was a little bit of
+shell game i played
+
+ align:start position:0%
+shell game i played
+ 
+
+ align:start position:0%
+shell game i played
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+actually rj played it not me i would
+
+ align:start position:0%
+actually rj played it not me i would
+ 
+
+ align:start position:0%
+actually rj played it not me i would
+have you know if i derived it i was
+
+ align:start position:0%
+have you know if i derived it i was
+ 
+
+ align:start position:0%
+have you know if i derived it i was
+shown you you know very carefully but he
+
+ align:start position:0%
+shown you you know very carefully but he
+ 
+
+ align:start position:0%
+shown you you know very carefully but he
+what did you derive it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said again i'm sorry
+
+ align:start position:0%
+said again i'm sorry
+ 
+
+ align:start position:0%
+said again i'm sorry
+yeah actually actually
+
+ align:start position:0%
+yeah actually actually
+ 
+
+ align:start position:0%
+yeah actually actually
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+if you write ap
+
+ align:start position:0%
+if you write ap
+ 
+
+ align:start position:0%
+if you write ap
+and aq in terms of these two terms
+
+ align:start position:0%
+and aq in terms of these two terms
+ 
+
+ align:start position:0%
+and aq in terms of these two terms
+right it'll all cancel out
+
+ align:start position:0%
+right it'll all cancel out
+ 
+
+ align:start position:0%
+right it'll all cancel out
+good catch
+
+ align:start position:0%
+good catch
+ 
+
+ align:start position:0%
+good catch
+all right but it's also the definition
+
+ align:start position:0%
+all right but it's also the definition
+ 
+
+ align:start position:0%
+all right but it's also the definition
+of the center of mass just so you know
+
+ align:start position:0%
+of the center of mass just so you know
+ 
+
+ align:start position:0%
+of the center of mass just so you know
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you just expand this right just
+
+ align:start position:0%
+so if you just expand this right just
+ 
+
+ align:start position:0%
+so if you just expand this right just
+write ap
+
+ align:start position:0%
+write ap
+ 
+
+ align:start position:0%
+write ap
+then see this term will cancel out
+
+ align:start position:0%
+then see this term will cancel out
+ 
+
+ align:start position:0%
+then see this term will cancel out
+this term will remain and this term will
+
+ align:start position:0%
+this term will remain and this term will
+ 
+
+ align:start position:0%
+this term will remain and this term will
+remain right and even this will cancel
+
+ align:start position:0%
+remain right and even this will cancel
+ 
+
+ align:start position:0%
+remain right and even this will cancel
+out so all you'll get is two times this
+
+ align:start position:0%
+out so all you'll get is two times this
+ 
+
+ align:start position:0%
+out so all you'll get is two times this
+okay so you'll get that anyway
+
+ align:start position:0%
+okay so you'll get that anyway
+ 
+
+ align:start position:0%
+okay so you'll get that anyway
+everyone's good with that adding up the
+
+ align:start position:0%
+everyone's good with that adding up the
+ 
+
+ align:start position:0%
+everyone's good with that adding up the
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now so that's the first one take a1 and
+
+ align:start position:0%
+now so that's the first one take a1 and
+ 
+
+ align:start position:0%
+now so that's the first one take a1 and
+a2
+
+ align:start position:0%
+a2
+ 
+
+ align:start position:0%
+a2
+and add up
+
+ align:start position:0%
+and add up
+ 
+
+ align:start position:0%
+and add up
+the second reduction i'm going to do
+
+ align:start position:0%
+the second reduction i'm going to do
+ 
+
+ align:start position:0%
+the second reduction i'm going to do
+is i'm going to take equation multiple
+
+ align:start position:0%
+is i'm going to take equation multiple
+ 
+
+ align:start position:0%
+is i'm going to take equation multiple
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+pre-cross product it with rcp
+
+ align:start position:0%
+pre-cross product it with rcp
+ 
+
+ align:start position:0%
+pre-cross product it with rcp
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+which is basically the moment let me
+
+ align:start position:0%
+which is basically the moment let me
+ 
+
+ align:start position:0%
+which is basically the moment let me
+explain that
+
+ align:start position:0%
+explain that
+ 
+
+ align:start position:0%
+explain that
+so i'm going to take equation one
+
+ align:start position:0%
+so i'm going to take equation one
+ 
+
+ align:start position:0%
+so i'm going to take equation one
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+and go rcp cross this plus rcp cross
+
+ align:start position:0%
+and go rcp cross this plus rcp cross
+ 
+
+ align:start position:0%
+and go rcp cross this plus rcp cross
+this plus rcp across this still a valid
+
+ align:start position:0%
+this plus rcp across this still a valid
+ 
+
+ align:start position:0%
+this plus rcp across this still a valid
+equation right
+
+ align:start position:0%
+equation right
+ 
+
+ align:start position:0%
+equation right
+and i'm going to take equation two and
+
+ align:start position:0%
+and i'm going to take equation two and
+ 
+
+ align:start position:0%
+and i'm going to take equation two and
+go r c q cross this
+
+ align:start position:0%
+go r c q cross this
+ 
+
+ align:start position:0%
+go r c q cross this
+minus r c q cross this is equal to r c q
+
+ align:start position:0%
+minus r c q cross this is equal to r c q
+ 
+
+ align:start position:0%
+minus r c q cross this is equal to r c q
+cross this and add them up
+
+ align:start position:0%
+cross this and add them up
+ 
+
+ align:start position:0%
+cross this and add them up
+get it so it's kind of like taking
+
+ align:start position:0%
+get it so it's kind of like taking
+ 
+
+ align:start position:0%
+get it so it's kind of like taking
+simultaneous equations you know
+
+ align:start position:0%
+simultaneous equations you know
+ 
+
+ align:start position:0%
+simultaneous equations you know
+multiplying all the terms by something
+
+ align:start position:0%
+multiplying all the terms by something
+ 
+
+ align:start position:0%
+multiplying all the terms by something
+and then you know adding it that kind of
+
+ align:start position:0%
+and then you know adding it that kind of
+ 
+
+ align:start position:0%
+and then you know adding it that kind of
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll give you a handwritten version of
+
+ align:start position:0%
+we'll give you a handwritten version of
+ 
+
+ align:start position:0%
+we'll give you a handwritten version of
+this don't worry
+
+ align:start position:0%
+this don't worry
+ 
+
+ align:start position:0%
+this don't worry
+okay you'll see it i wanted to make a
+
+ align:start position:0%
+okay you'll see it i wanted to make a
+ 
+
+ align:start position:0%
+okay you'll see it i wanted to make a
+very simple point
+
+ align:start position:0%
+very simple point
+ 
+
+ align:start position:0%
+very simple point
+which was that if you do that
+
+ align:start position:0%
+which was that if you do that
+ 
+
+ align:start position:0%
+which was that if you do that
+and you do all the math
+
+ align:start position:0%
+and you do all the math
+ 
+
+ align:start position:0%
+and you do all the math
+a lot of terms will cancel out
+
+ align:start position:0%
+a lot of terms will cancel out
+ 
+
+ align:start position:0%
+a lot of terms will cancel out
+and guess what you will end up with
+
+ align:start position:0%
+and guess what you will end up with
+ 
+
+ align:start position:0%
+and guess what you will end up with
+you will end up with rcq cross
+
+ align:start position:0%
+you will end up with rcq cross
+ 
+
+ align:start position:0%
+you will end up with rcq cross
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i just do that now you know cancel all
+
+ align:start position:0%
+i just do that now you know cancel all
+ 
+
+ align:start position:0%
+i just do that now you know cancel all
+our terms will cancel out right i'll end
+
+ align:start position:0%
+our terms will cancel out right i'll end
+ 
+
+ align:start position:0%
+our terms will cancel out right i'll end
+up with rcq cross so you don't have to
+
+ align:start position:0%
+up with rcq cross so you don't have to
+ 
+
+ align:start position:0%
+up with rcq cross so you don't have to
+write this down guys we'll give this to
+
+ align:start position:0%
+write this down guys we'll give this to
+ 
+
+ align:start position:0%
+write this down guys we'll give this to
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+all right i'm trying to make a deeper
+
+ align:start position:0%
+all right i'm trying to make a deeper
+ 
+
+ align:start position:0%
+all right i'm trying to make a deeper
+point here not the map point
+
+ align:start position:0%
+point here not the map point
+ 
+
+ align:start position:0%
+point here not the map point
+all right the math trust me if you check
+
+ align:start position:0%
+all right the math trust me if you check
+ 
+
+ align:start position:0%
+all right the math trust me if you check
+through it it all works out
+
+ align:start position:0%
+through it it all works out
+ 
+
+ align:start position:0%
+through it it all works out
+r c q cross f q minus f p
+
+ align:start position:0%
+r c q cross f q minus f p
+ 
+
+ align:start position:0%
+r c q cross f q minus f p
+you will get is equal to m r squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a alpha b
+
+ align:start position:0%
+a alpha b
+ 
+
+ align:start position:0%
+a alpha b
+okay and i want you to stare at this for
+
+ align:start position:0%
+okay and i want you to stare at this for
+ 
+
+ align:start position:0%
+okay and i want you to stare at this for
+a second because it's really cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's what's really cool about it
+
+ align:start position:0%
+here's what's really cool about it
+ 
+
+ align:start position:0%
+here's what's really cool about it
+and by the way i i eliminate t right if
+
+ align:start position:0%
+and by the way i i eliminate t right if
+ 
+
+ align:start position:0%
+and by the way i i eliminate t right if
+you you can come up with another
+
+ align:start position:0%
+you you can come up with another
+ 
+
+ align:start position:0%
+you you can come up with another
+equation it tells you what t is but
+
+ align:start position:0%
+equation it tells you what t is but
+ 
+
+ align:start position:0%
+equation it tells you what t is but
+essentially i've solved the problem
+
+ align:start position:0%
+essentially i've solved the problem
+ 
+
+ align:start position:0%
+essentially i've solved the problem
+this is saying the sum of forces
+
+ align:start position:0%
+this is saying the sum of forces
+ 
+
+ align:start position:0%
+this is saying the sum of forces
+on the particles
+
+ align:start position:0%
+on the particles
+ 
+
+ align:start position:0%
+on the particles
+if you take if you take the two
+
+ align:start position:0%
+if you take if you take the two
+ 
+
+ align:start position:0%
+if you take if you take the two
+particles and treat them like one
+
+ align:start position:0%
+particles and treat them like one
+ 
+
+ align:start position:0%
+particles and treat them like one
+particle with twice its mass right at
+
+ align:start position:0%
+particle with twice its mass right at
+ 
+
+ align:start position:0%
+particle with twice its mass right at
+the center of mass
+
+ align:start position:0%
+the center of mass
+ 
+
+ align:start position:0%
+the center of mass
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+the sum of forces is equal to
+
+ align:start position:0%
+the sum of forces is equal to
+ 
+
+ align:start position:0%
+the sum of forces is equal to
+m a
+
+ align:start position:0%
+m a
+ 
+
+ align:start position:0%
+m a
+mass of this kind of combined
+
+ align:start position:0%
+mass of this kind of combined
+ 
+
+ align:start position:0%
+mass of this kind of combined
+you know lumped particle
+
+ align:start position:0%
+you know lumped particle
+ 
+
+ align:start position:0%
+you know lumped particle
+times the acceleration center of mass
+
+ align:start position:0%
+times the acceleration center of mass
+ 
+
+ align:start position:0%
+times the acceleration center of mass
+that's inside number one
+
+ align:start position:0%
+that's inside number one
+ 
+
+ align:start position:0%
+that's inside number one
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can anyone interpret this for me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+torque is equal to i alpha do you
+
+ align:start position:0%
+torque is equal to i alpha do you
+ 
+
+ align:start position:0%
+torque is equal to i alpha do you
+understand this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is simply the torque about the
+
+ align:start position:0%
+this is simply the torque about the
+ 
+
+ align:start position:0%
+this is simply the torque about the
+center of mass
+
+ align:start position:0%
+center of mass
+ 
+
+ align:start position:0%
+center of mass
+and in our math
+
+ align:start position:0%
+and in our math
+ 
+
+ align:start position:0%
+and in our math
+out popped
+
+ align:start position:0%
+out popped
+ 
+
+ align:start position:0%
+out popped
+what is actually
+
+ align:start position:0%
+what is actually
+ 
+
+ align:start position:0%
+what is actually
+the moment of inertia
+
+ align:start position:0%
+the moment of inertia
+ 
+
+ align:start position:0%
+the moment of inertia
+although i haven't defined it you
+
+ align:start position:0%
+although i haven't defined it you
+ 
+
+ align:start position:0%
+although i haven't defined it you
+officially yet
+
+ align:start position:0%
+officially yet
+ 
+
+ align:start position:0%
+officially yet
+the moment of inertia
+
+ align:start position:0%
+the moment of inertia
+ 
+
+ align:start position:0%
+the moment of inertia
+of this dumbbell
+
+ align:start position:0%
+of this dumbbell
+ 
+
+ align:start position:0%
+of this dumbbell
+multiplied by alpha
+
+ align:start position:0%
+multiplied by alpha
+ 
+
+ align:start position:0%
+multiplied by alpha
+torque is equal to i alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's a reason we did all this
+
+ align:start position:0%
+and there's a reason we did all this
+ 
+
+ align:start position:0%
+and there's a reason we did all this
+and the reason was to give you a hint
+
+ align:start position:0%
+and the reason was to give you a hint
+ 
+
+ align:start position:0%
+and the reason was to give you a hint
+of what was going to come ahead
+
+ align:start position:0%
+of what was going to come ahead
+ 
+
+ align:start position:0%
+of what was going to come ahead
+so my question to you first is
+
+ align:start position:0%
+so my question to you first is
+ 
+
+ align:start position:0%
+so my question to you first is
+do you understand this
+
+ align:start position:0%
+do you understand this
+ 
+
+ align:start position:0%
+do you understand this
+do you understand what i'm trying to say
+
+ align:start position:0%
+do you understand what i'm trying to say
+ 
+
+ align:start position:0%
+do you understand what i'm trying to say
+can anyone yep levi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't really always understand what
+
+ align:start position:0%
+i don't really always understand what
+ 
+
+ align:start position:0%
+i don't really always understand what
+you are talking about
+
+ align:start position:0%
+you are talking about
+ 
+
+ align:start position:0%
+you are talking about
+uh okay
+
+ align:start position:0%
+uh okay
+ 
+
+ align:start position:0%
+uh okay
+we uh i didn't emphasize it but in the
+
+ align:start position:0%
+we uh i didn't emphasize it but in the
+ 
+
+ align:start position:0%
+we uh i didn't emphasize it but in the
+drawing last last week
+
+ align:start position:0%
+drawing last last week
+ 
+
+ align:start position:0%
+drawing last last week
+we defined
+
+ align:start position:0%
+we defined
+ 
+
+ align:start position:0%
+we defined
+the length of the rod
+
+ align:start position:0%
+the length of the rod
+ 
+
+ align:start position:0%
+the length of the rod
+as 2r
+
+ align:start position:0%
+as 2r
+ 
+
+ align:start position:0%
+as 2r
+there are a lot of r's floating around
+
+ align:start position:0%
+there are a lot of r's floating around
+ 
+
+ align:start position:0%
+there are a lot of r's floating around
+all right r is a position vector but an
+
+ align:start position:0%
+all right r is a position vector but an
+ 
+
+ align:start position:0%
+all right r is a position vector but an
+unsubscripted unvectored r is simply the
+
+ align:start position:0%
+unsubscripted unvectored r is simply the
+ 
+
+ align:start position:0%
+unsubscripted unvectored r is simply the
+length of the uh
+
+ align:start position:0%
+length of the uh
+ 
+
+ align:start position:0%
+length of the uh
+dumbbell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say it again
+
+ align:start position:0%
+say it again
+ 
+
+ align:start position:0%
+say it again
+so they're all
+
+ align:start position:0%
+so they're all
+ 
+
+ align:start position:0%
+so they're all
+unsubscriptive
+
+ align:start position:0%
+unsubscriptive
+ 
+
+ align:start position:0%
+unsubscriptive
+but they're all vectors
+
+ align:start position:0%
+but they're all vectors
+ 
+
+ align:start position:0%
+but they're all vectors
+no no
+
+ align:start position:0%
+no no
+ 
+
+ align:start position:0%
+no no
+which maybe we shouldn't have used r
+
+ align:start position:0%
+which maybe we shouldn't have used r
+ 
+
+ align:start position:0%
+which maybe we shouldn't have used r
+maybe we should have called this l
+
+ align:start position:0%
+maybe we should have called this l
+ 
+
+ align:start position:0%
+maybe we should have called this l
+get it just this length of the dumbbell
+
+ align:start position:0%
+get it just this length of the dumbbell
+ 
+
+ align:start position:0%
+get it just this length of the dumbbell
+then this would have been then this
+
+ align:start position:0%
+then this would have been then this
+ 
+
+ align:start position:0%
+then this would have been then this
+would have been 2 m l squared a alpha b
+
+ align:start position:0%
+would have been 2 m l squared a alpha b
+ 
+
+ align:start position:0%
+would have been 2 m l squared a alpha b
+got it it's just another it's just it's
+
+ align:start position:0%
+got it it's just another it's just it's
+ 
+
+ align:start position:0%
+got it it's just another it's just it's
+just a
+
+ align:start position:0%
+just a
+ 
+
+ align:start position:0%
+just a
+it's the length of the rod
+
+ align:start position:0%
+it's the length of the rod
+ 
+
+ align:start position:0%
+it's the length of the rod
+it's 2r right that's you think of it as
+
+ align:start position:0%
+it's 2r right that's you think of it as
+ 
+
+ align:start position:0%
+it's 2r right that's you think of it as
+2l then this would be m 2 m l squared
+
+ align:start position:0%
+2l then this would be m 2 m l squared
+ 
+
+ align:start position:0%
+2l then this would be m 2 m l squared
+alpha b
+
+ align:start position:0%
+alpha b
+ 
+
+ align:start position:0%
+alpha b
+you understand yeah okay someone else
+
+ align:start position:0%
+you understand yeah okay someone else
+ 
+
+ align:start position:0%
+you understand yeah okay someone else
+had a question here do you have a
+
+ align:start position:0%
+had a question here do you have a
+ 
+
+ align:start position:0%
+had a question here do you have a
+question anybody else
+
+ align:start position:0%
+question anybody else
+ 
+
+ align:start position:0%
+question anybody else
+look here's what i was trying to say
+
+ align:start position:0%
+look here's what i was trying to say
+ 
+
+ align:start position:0%
+look here's what i was trying to say
+you want to send f is equal to m a for
+
+ align:start position:0%
+you want to send f is equal to m a for
+ 
+
+ align:start position:0%
+you want to send f is equal to m a for
+particles right totally get it
+
+ align:start position:0%
+particles right totally get it
+ 
+
+ align:start position:0%
+particles right totally get it
+here's the deal guys
+
+ align:start position:0%
+here's the deal guys
+ 
+
+ align:start position:0%
+here's the deal guys
+if you have multiple particle systems
+
+ align:start position:0%
+if you have multiple particle systems
+ 
+
+ align:start position:0%
+if you have multiple particle systems
+for example a two particle system
+
+ align:start position:0%
+for example a two particle system
+ 
+
+ align:start position:0%
+for example a two particle system
+where the two particles are rigidly
+
+ align:start position:0%
+where the two particles are rigidly
+ 
+
+ align:start position:0%
+where the two particles are rigidly
+attached
+
+ align:start position:0%
+attached
+ 
+
+ align:start position:0%
+attached
+you can apply a physical ma to each
+
+ align:start position:0%
+you can apply a physical ma to each
+ 
+
+ align:start position:0%
+you can apply a physical ma to each
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+and assume an unknown force and just
+
+ align:start position:0%
+and assume an unknown force and just
+ 
+
+ align:start position:0%
+and assume an unknown force and just
+solve it that's completely completely
+
+ align:start position:0%
+solve it that's completely completely
+ 
+
+ align:start position:0%
+solve it that's completely completely
+correct we just did it
+
+ align:start position:0%
+correct we just did it
+ 
+
+ align:start position:0%
+correct we just did it
+completely correct
+
+ align:start position:0%
+completely correct
+ 
+
+ align:start position:0%
+completely correct
+when you do it
+
+ align:start position:0%
+when you do it
+ 
+
+ align:start position:0%
+when you do it
+what you'll find is when you solve all
+
+ align:start position:0%
+what you'll find is when you solve all
+ 
+
+ align:start position:0%
+what you'll find is when you solve all
+the equations
+
+ align:start position:0%
+the equations
+ 
+
+ align:start position:0%
+the equations
+they will reduce to a very interesting
+
+ align:start position:0%
+they will reduce to a very interesting
+ 
+
+ align:start position:0%
+they will reduce to a very interesting
+form which is
+
+ align:start position:0%
+form which is
+ 
+
+ align:start position:0%
+form which is
+f is equal to m a for the center of mass
+
+ align:start position:0%
+f is equal to m a for the center of mass
+ 
+
+ align:start position:0%
+f is equal to m a for the center of mass
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this funky new term that keeps cropping
+
+ align:start position:0%
+this funky new term that keeps cropping
+ 
+
+ align:start position:0%
+this funky new term that keeps cropping
+up which we've kind of already defined
+
+ align:start position:0%
+up which we've kind of already defined
+ 
+
+ align:start position:0%
+up which we've kind of already defined
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+this thing which is actually the torque
+
+ align:start position:0%
+this thing which is actually the torque
+ 
+
+ align:start position:0%
+this thing which is actually the torque
+times i
+
+ align:start position:0%
+times i
+ 
+
+ align:start position:0%
+times i
+this kind of mr squared kind of term 2mr
+
+ align:start position:0%
+this kind of mr squared kind of term 2mr
+ 
+
+ align:start position:0%
+this kind of mr squared kind of term 2mr
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+and this will keep cropping up if you
+
+ align:start position:0%
+and this will keep cropping up if you
+ 
+
+ align:start position:0%
+and this will keep cropping up if you
+have three particles you will get the
+
+ align:start position:0%
+have three particles you will get the
+ 
+
+ align:start position:0%
+have three particles you will get the
+same thing you get four particles you
+
+ align:start position:0%
+same thing you get four particles you
+ 
+
+ align:start position:0%
+same thing you get four particles you
+get the same thing 300 million particles
+
+ align:start position:0%
+get the same thing 300 million particles
+ 
+
+ align:start position:0%
+get the same thing 300 million particles
+a lot of equations you would still end
+
+ align:start position:0%
+a lot of equations you would still end
+ 
+
+ align:start position:0%
+a lot of equations you would still end
+up with the same thing
+
+ align:start position:0%
+up with the same thing
+ 
+
+ align:start position:0%
+up with the same thing
+got it
+
+ align:start position:0%
+got it
+ 
+
+ align:start position:0%
+got it
+so why not we just derive the same thing
+
+ align:start position:0%
+so why not we just derive the same thing
+ 
+
+ align:start position:0%
+so why not we just derive the same thing
+once and for all
+
+ align:start position:0%
+once and for all
+ 
+
+ align:start position:0%
+once and for all
+and we can show that tau is equal to i
+
+ align:start position:0%
+and we can show that tau is equal to i
+ 
+
+ align:start position:0%
+and we can show that tau is equal to i
+alpha around the center of mass and then
+
+ align:start position:0%
+alpha around the center of mass and then
+ 
+
+ align:start position:0%
+alpha around the center of mass and then
+every time we see a rigid body we can
+
+ align:start position:0%
+every time we see a rigid body we can
+ 
+
+ align:start position:0%
+every time we see a rigid body we can
+just use that directly
+
+ align:start position:0%
+just use that directly
+ 
+
+ align:start position:0%
+just use that directly
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+but there's nothing new in here all i'm
+
+ align:start position:0%
+but there's nothing new in here all i'm
+ 
+
+ align:start position:0%
+but there's nothing new in here all i'm
+saying what nothing shocking what i'm
+
+ align:start position:0%
+saying what nothing shocking what i'm
+ 
+
+ align:start position:0%
+saying what nothing shocking what i'm
+doing i'm just going to derive this for
+
+ align:start position:0%
+doing i'm just going to derive this for
+ 
+
+ align:start position:0%
+doing i'm just going to derive this for
+an infinite or any number of particle
+
+ align:start position:0%
+an infinite or any number of particle
+ 
+
+ align:start position:0%
+an infinite or any number of particle
+system i'm going to show that torque is
+
+ align:start position:0%
+system i'm going to show that torque is
+ 
+
+ align:start position:0%
+system i'm going to show that torque is
+a chloride alpha but you can see from a
+
+ align:start position:0%
+a chloride alpha but you can see from a
+ 
+
+ align:start position:0%
+a chloride alpha but you can see from a
+two particle system you can show toxic
+
+ align:start position:0%
+two particle system you can show toxic
+ 
+
+ align:start position:0%
+two particle system you can show toxic
+i-alpha
+
+ align:start position:0%
+i-alpha
+ 
+
+ align:start position:0%
+i-alpha
+get it no yes maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's good
+
+ align:start position:0%
+it's good
+ 
+
+ align:start position:0%
+it's good
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that was the objective of this exercise
+
+ align:start position:0%
+that was the objective of this exercise
+ 
+
+ align:start position:0%
+that was the objective of this exercise
+was to just give you that
+
+ align:start position:0%
+was to just give you that
+ 
+
+ align:start position:0%
+was to just give you that
+taste
+
+ align:start position:0%
+taste
+ 
+
+ align:start position:0%
+taste
+of what uh what we're going to do next
+
+ align:start position:0%
+of what uh what we're going to do next
+ 
+
+ align:start position:0%
+of what uh what we're going to do next
+so what we're going to do next
+
+ align:start position:0%
+so what we're going to do next
+ 
+
+ align:start position:0%
+so what we're going to do next
+is we're going to take
+
+ align:start position:0%
+is we're going to take
+ 
+
+ align:start position:0%
+is we're going to take
+millions of particles
+
+ align:start position:0%
+millions of particles
+ 
+
+ align:start position:0%
+millions of particles
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+do the same thing except we'll do it in
+
+ align:start position:0%
+do the same thing except we'll do it in
+ 
+
+ align:start position:0%
+do the same thing except we'll do it in
+a kind of a generalized format
+
+ align:start position:0%
+a kind of a generalized format
+ 
+
+ align:start position:0%
+a kind of a generalized format
+and that's called a derivation and the
+
+ align:start position:0%
+and that's called a derivation and the
+ 
+
+ align:start position:0%
+and that's called a derivation and the
+output is going to be that same result
+
+ align:start position:0%
+output is going to be that same result
+ 
+
+ align:start position:0%
+output is going to be that same result
+but in a generalized way it's a general
+
+ align:start position:0%
+but in a generalized way it's a general
+ 
+
+ align:start position:0%
+but in a generalized way it's a general
+formula okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh raise it i'm sorry i thought you said
+
+ align:start position:0%
+oh raise it i'm sorry i thought you said
+ 
+
+ align:start position:0%
+oh raise it i'm sorry i thought you said
+erase it i was like what do you want to
+
+ align:start position:0%
+erase it i was like what do you want to
+ 
+
+ align:start position:0%
+erase it i was like what do you want to
+erase it it's only below what do you
+
+ align:start position:0%
+erase it it's only below what do you
+ 
+
+ align:start position:0%
+erase it it's only below what do you
+want me to erase it guys don't seriously
+
+ align:start position:0%
+want me to erase it guys don't seriously
+ 
+
+ align:start position:0%
+want me to erase it guys don't seriously
+i want you to get the point of what i'm
+
+ align:start position:0%
+i want you to get the point of what i'm
+ 
+
+ align:start position:0%
+i want you to get the point of what i'm
+saying right i'll give this to you
+
+ align:start position:0%
+saying right i'll give this to you
+ 
+
+ align:start position:0%
+saying right i'll give this to you
+promise promise you we will scan it and
+
+ align:start position:0%
+promise promise you we will scan it and
+ 
+
+ align:start position:0%
+promise promise you we will scan it and
+post it if it's already written down
+
+ align:start position:0%
+post it if it's already written down
+ 
+
+ align:start position:0%
+post it if it's already written down
+right we'll post it for you on the web
+
+ align:start position:0%
+right we'll post it for you on the web
+ 
+
+ align:start position:0%
+right we'll post it for you on the web
+so you can read it okay
+
+ align:start position:0%
+so you can read it okay
+ 
+
+ align:start position:0%
+so you can read it okay
+writing it down it won't add a lot for
+
+ align:start position:0%
+writing it down it won't add a lot for
+ 
+
+ align:start position:0%
+writing it down it won't add a lot for
+this you should write all the other
+
+ align:start position:0%
+this you should write all the other
+ 
+
+ align:start position:0%
+this you should write all the other
+stuff i doubt i say and do down but not
+
+ align:start position:0%
+stuff i doubt i say and do down but not
+ 
+
+ align:start position:0%
+stuff i doubt i say and do down but not
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but you can stare at it but don't write
+
+ align:start position:0%
+but you can stare at it but don't write
+ 
+
+ align:start position:0%
+but you can stare at it but don't write
+it down because we'll give it to you
+
+ align:start position:0%
+it down because we'll give it to you
+ 
+
+ align:start position:0%
+it down because we'll give it to you
+point i'm making is a very simple one
+
+ align:start position:0%
+point i'm making is a very simple one
+ 
+
+ align:start position:0%
+point i'm making is a very simple one
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+torque is equal to i alpha for rigid
+
+ align:start position:0%
+torque is equal to i alpha for rigid
+ 
+
+ align:start position:0%
+torque is equal to i alpha for rigid
+bodies that's all i'm trying to say okay
+
+ align:start position:0%
+bodies that's all i'm trying to say okay
+ 
+
+ align:start position:0%
+bodies that's all i'm trying to say okay
+and really this is all just boring math
+
+ align:start position:0%
+and really this is all just boring math
+ 
+
+ align:start position:0%
+and really this is all just boring math
+this is the result i want you to see
+
+ align:start position:0%
+this is the result i want you to see
+ 
+
+ align:start position:0%
+this is the result i want you to see
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and i didn't cheat i just did all from
+
+ align:start position:0%
+and i didn't cheat i just did all from
+ 
+
+ align:start position:0%
+and i didn't cheat i just did all from
+my physical dna
+
+ align:start position:0%
+my physical dna
+ 
+
+ align:start position:0%
+my physical dna
+all right so what we're going to do now
+
+ align:start position:0%
+all right so what we're going to do now
+ 
+
+ align:start position:0%
+all right so what we're going to do now
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+we're going to look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiple particles like that in one shot
+
+ align:start position:0%
+multiple particles like that in one shot
+ 
+
+ align:start position:0%
+multiple particles like that in one shot
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+first consider
+
+ align:start position:0%
+first consider
+ 
+
+ align:start position:0%
+first consider
+again a frame of reference a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is point o
+
+ align:start position:0%
+and this is point o
+ 
+
+ align:start position:0%
+and this is point o
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+a particle i
+
+ align:start position:0%
+a particle i
+ 
+
+ align:start position:0%
+a particle i
+a particle j
+
+ align:start position:0%
+a particle j
+ 
+
+ align:start position:0%
+a particle j
+and thousands millions
+
+ align:start position:0%
+and thousands millions
+ 
+
+ align:start position:0%
+and thousands millions
+of other particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+on each particle i or j
+
+ align:start position:0%
+on each particle i or j
+ 
+
+ align:start position:0%
+on each particle i or j
+there is a force
+
+ align:start position:0%
+there is a force
+ 
+
+ align:start position:0%
+there is a force
+which i'm going to write
+
+ align:start position:0%
+which i'm going to write
+ 
+
+ align:start position:0%
+which i'm going to write
+subscript of the superscript i
+
+ align:start position:0%
+subscript of the superscript i
+ 
+
+ align:start position:0%
+subscript of the superscript i
+little f which is the force on i
+
+ align:start position:0%
+little f which is the force on i
+ 
+
+ align:start position:0%
+little f which is the force on i
+and there's a force on j
+
+ align:start position:0%
+and there's a force on j
+ 
+
+ align:start position:0%
+and there's a force on j
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+that's the force on j
+
+ align:start position:0%
+that's the force on j
+ 
+
+ align:start position:0%
+that's the force on j
+okay and each particle has a position
+
+ align:start position:0%
+okay and each particle has a position
+ 
+
+ align:start position:0%
+okay and each particle has a position
+vector o i r o i and r o j
+
+ align:start position:0%
+vector o i r o i and r o j
+ 
+
+ align:start position:0%
+vector o i r o i and r o j
+okay same thing x i'm now going to do it
+
+ align:start position:0%
+okay same thing x i'm now going to do it
+ 
+
+ align:start position:0%
+okay same thing x i'm now going to do it
+in a general way
+
+ align:start position:0%
+in a general way
+ 
+
+ align:start position:0%
+in a general way
+now first you need to tell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how is fi related to
+
+ align:start position:0%
+how is fi related to
+ 
+
+ align:start position:0%
+how is fi related to
+the acceleration of particle i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+actually let's not assume that thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m i ai
+
+ align:start position:0%
+m i ai
+ 
+
+ align:start position:0%
+m i ai
+right that's the acceleration of
+
+ align:start position:0%
+right that's the acceleration of
+ 
+
+ align:start position:0%
+right that's the acceleration of
+particle a
+
+ align:start position:0%
+particle a
+ 
+
+ align:start position:0%
+particle a
+or i right
+
+ align:start position:0%
+or i right
+ 
+
+ align:start position:0%
+or i right
+what is the uh
+
+ align:start position:0%
+what is the uh
+ 
+
+ align:start position:0%
+what is the uh
+torque on particle i let's pick a point
+
+ align:start position:0%
+torque on particle i let's pick a point
+ 
+
+ align:start position:0%
+torque on particle i let's pick a point
+q
+
+ align:start position:0%
+q
+ 
+
+ align:start position:0%
+q
+we'll call this the reference point for
+
+ align:start position:0%
+we'll call this the reference point for
+ 
+
+ align:start position:0%
+we'll call this the reference point for
+torques
+
+ align:start position:0%
+torques
+ 
+
+ align:start position:0%
+torques
+what is the torque on particle i
+
+ align:start position:0%
+what is the torque on particle i
+ 
+
+ align:start position:0%
+what is the torque on particle i
+and how is that related to its motion
+
+ align:start position:0%
+and how is that related to its motion
+ 
+
+ align:start position:0%
+and how is that related to its motion
+anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so that's the definition of torque
+
+ align:start position:0%
+yeah so that's the definition of torque
+ 
+
+ align:start position:0%
+yeah so that's the definition of torque
+what's the angular momentum type thing
+
+ align:start position:0%
+what's the angular momentum type thing
+ 
+
+ align:start position:0%
+what's the angular momentum type thing
+it's just going to be the formula i
+
+ align:start position:0%
+it's just going to be the formula i
+ 
+
+ align:start position:0%
+it's just going to be the formula i
+didn't ask the question clearly it's
+
+ align:start position:0%
+didn't ask the question clearly it's
+ 
+
+ align:start position:0%
+didn't ask the question clearly it's
+just going to be this formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right these are the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are the two
+
+ align:start position:0%
+these are the two
+ 
+
+ align:start position:0%
+these are the two
+statements we can make about those two
+
+ align:start position:0%
+statements we can make about those two
+ 
+
+ align:start position:0%
+statements we can make about those two
+particles right
+
+ align:start position:0%
+particles right
+ 
+
+ align:start position:0%
+particles right
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens when you have multiple
+
+ align:start position:0%
+what happens when you have multiple
+ 
+
+ align:start position:0%
+what happens when you have multiple
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+i j k
+
+ align:start position:0%
+i j k
+ 
+
+ align:start position:0%
+i j k
+1 to in you know 300 million
+
+ align:start position:0%
+1 to in you know 300 million
+ 
+
+ align:start position:0%
+1 to in you know 300 million
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+how do those equations work
+
+ align:start position:0%
+how do those equations work
+ 
+
+ align:start position:0%
+how do those equations work
+look at these two look look what
+
+ align:start position:0%
+look at these two look look what
+ 
+
+ align:start position:0%
+look at these two look look what
+happened here what happens in your
+
+ align:start position:0%
+happened here what happens in your
+ 
+
+ align:start position:0%
+happened here what happens in your
+multiple particles
+
+ align:start position:0%
+multiple particles
+ 
+
+ align:start position:0%
+multiple particles
+anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say it again
+
+ align:start position:0%
+say it again
+ 
+
+ align:start position:0%
+say it again
+oh let's do it that's right this should
+
+ align:start position:0%
+oh let's do it that's right this should
+ 
+
+ align:start position:0%
+oh let's do it that's right this should
+be q is that what you're saying yeah
+
+ align:start position:0%
+be q is that what you're saying yeah
+ 
+
+ align:start position:0%
+be q is that what you're saying yeah
+thank you that should be q
+
+ align:start position:0%
+thank you that should be q
+ 
+
+ align:start position:0%
+thank you that should be q
+reference point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what happens in the multiple points
+
+ align:start position:0%
+now what happens in the multiple points
+ 
+
+ align:start position:0%
+now what happens in the multiple points
+take a guess what's the equation going
+
+ align:start position:0%
+take a guess what's the equation going
+ 
+
+ align:start position:0%
+take a guess what's the equation going
+to look at for multiple points
+
+ align:start position:0%
+to look at for multiple points
+ 
+
+ align:start position:0%
+to look at for multiple points
+anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+say it's going to look the same
+
+ align:start position:0%
+say it's going to look the same
+ 
+
+ align:start position:0%
+say it's going to look the same
+what's now by the way i'm going to call
+
+ align:start position:0%
+what's now by the way i'm going to call
+ 
+
+ align:start position:0%
+what's now by the way i'm going to call
+this entire set of points
+
+ align:start position:0%
+this entire set of points
+ 
+
+ align:start position:0%
+this entire set of points
+all of them i'm going to call them the
+
+ align:start position:0%
+all of them i'm going to call them the
+ 
+
+ align:start position:0%
+all of them i'm going to call them the
+ensemble e so when i say e i'm referring
+
+ align:start position:0%
+ensemble e so when i say e i'm referring
+ 
+
+ align:start position:0%
+ensemble e so when i say e i'm referring
+to the entire set of points because i
+
+ align:start position:0%
+to the entire set of points because i
+ 
+
+ align:start position:0%
+to the entire set of points because i
+need a term for it all right so here's
+
+ align:start position:0%
+need a term for it all right so here's
+ 
+
+ align:start position:0%
+need a term for it all right so here's
+what we're going
+
+ align:start position:0%
+what we're going
+ 
+
+ align:start position:0%
+what we're going
+to end up
+
+ align:start position:0%
+to end up
+ 
+
+ align:start position:0%
+to end up
+the total force on the ensemble the
+
+ align:start position:0%
+the total force on the ensemble the
+ 
+
+ align:start position:0%
+the total force on the ensemble the
+total external force on the ensemble
+
+ align:start position:0%
+total external force on the ensemble
+ 
+
+ align:start position:0%
+total external force on the ensemble
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+the mass of the ensemble where the mass
+
+ align:start position:0%
+the mass of the ensemble where the mass
+ 
+
+ align:start position:0%
+the mass of the ensemble where the mass
+of the ensemble is sigma mi so it's the
+
+ align:start position:0%
+of the ensemble is sigma mi so it's the
+ 
+
+ align:start position:0%
+of the ensemble is sigma mi so it's the
+sum of all the masses
+
+ align:start position:0%
+sum of all the masses
+ 
+
+ align:start position:0%
+sum of all the masses
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+the acceleration
+
+ align:start position:0%
+the acceleration
+ 
+
+ align:start position:0%
+the acceleration
+of the ensemble
+
+ align:start position:0%
+of the ensemble
+ 
+
+ align:start position:0%
+of the ensemble
+that's right the center of mass of the
+
+ align:start position:0%
+that's right the center of mass of the
+ 
+
+ align:start position:0%
+that's right the center of mass of the
+ensemble that's where we're going to end
+
+ align:start position:0%
+ensemble that's where we're going to end
+ 
+
+ align:start position:0%
+ensemble that's where we're going to end
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+the center of mass
+
+ align:start position:0%
+the center of mass
+ 
+
+ align:start position:0%
+the center of mass
+and i'm going to write it like this
+
+ align:start position:0%
+and i'm going to write it like this
+ 
+
+ align:start position:0%
+and i'm going to write it like this
+all right just right now for emphasis
+
+ align:start position:0%
+all right just right now for emphasis
+ 
+
+ align:start position:0%
+all right just right now for emphasis
+i'm going to say the center of mass of
+
+ align:start position:0%
+i'm going to say the center of mass of
+ 
+
+ align:start position:0%
+i'm going to say the center of mass of
+that ensemble
+
+ align:start position:0%
+that ensemble
+ 
+
+ align:start position:0%
+that ensemble
+when i say c subscript e it's the center
+
+ align:start position:0%
+when i say c subscript e it's the center
+ 
+
+ align:start position:0%
+when i say c subscript e it's the center
+of mass of that ensemble
+
+ align:start position:0%
+of mass of that ensemble
+ 
+
+ align:start position:0%
+of mass of that ensemble
+okay after some time i'll get lazy and
+
+ align:start position:0%
+okay after some time i'll get lazy and
+ 
+
+ align:start position:0%
+okay after some time i'll get lazy and
+i'll stop writing the e it'll just be c
+
+ align:start position:0%
+i'll stop writing the e it'll just be c
+ 
+
+ align:start position:0%
+i'll stop writing the e it'll just be c
+when you see a c assume it's the center
+
+ align:start position:0%
+when you see a c assume it's the center
+ 
+
+ align:start position:0%
+when you see a c assume it's the center
+of mass of the ensemble i'll try and
+
+ align:start position:0%
+of mass of the ensemble i'll try and
+ 
+
+ align:start position:0%
+of mass of the ensemble i'll try and
+keep it up as long as i can
+
+ align:start position:0%
+keep it up as long as i can
+ 
+
+ align:start position:0%
+keep it up as long as i can
+and you know what else we're going to
+
+ align:start position:0%
+and you know what else we're going to
+ 
+
+ align:start position:0%
+and you know what else we're going to
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+we're gonna find
+
+ align:start position:0%
+we're gonna find
+ 
+
+ align:start position:0%
+we're gonna find
+the torque
+
+ align:start position:0%
+the torque
+ 
+
+ align:start position:0%
+the torque
+on the ensemble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about point q which is the sum of all
+
+ align:start position:0%
+about point q which is the sum of all
+ 
+
+ align:start position:0%
+about point q which is the sum of all
+the torques about all the points
+
+ align:start position:0%
+the torques about all the points
+ 
+
+ align:start position:0%
+the torques about all the points
+about point q we're gonna find this i'm
+
+ align:start position:0%
+about point q we're gonna find this i'm
+ 
+
+ align:start position:0%
+about point q we're gonna find this i'm
+just giving a heads up is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+it's going to look very similar to what
+
+ align:start position:0%
+it's going to look very similar to what
+ 
+
+ align:start position:0%
+it's going to look very similar to what
+we have there d by dt
+
+ align:start position:0%
+we have there d by dt
+ 
+
+ align:start position:0%
+we have there d by dt
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+when i write a capital
+
+ align:start position:0%
+when i write a capital
+ 
+
+ align:start position:0%
+when i write a capital
+is the total right the total torque not
+
+ align:start position:0%
+is the total right the total torque not
+ 
+
+ align:start position:0%
+is the total right the total torque not
+tau
+
+ align:start position:0%
+tau
+ 
+
+ align:start position:0%
+tau
+the total force not little force it's
+
+ align:start position:0%
+the total force not little force it's
+ 
+
+ align:start position:0%
+the total force not little force it's
+the total angular momentum
+
+ align:start position:0%
+the total angular momentum
+ 
+
+ align:start position:0%
+the total angular momentum
+of the entire ensemble
+
+ align:start position:0%
+of the entire ensemble
+ 
+
+ align:start position:0%
+of the entire ensemble
+about point q
+
+ align:start position:0%
+about point q
+ 
+
+ align:start position:0%
+about point q
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+v q
+
+ align:start position:0%
+v q
+ 
+
+ align:start position:0%
+v q
+cross what's this term going to be
+
+ align:start position:0%
+cross what's this term going to be
+ 
+
+ align:start position:0%
+cross what's this term going to be
+what's the equivalent here going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say it again
+
+ align:start position:0%
+say it again
+ 
+
+ align:start position:0%
+say it again
+yeah capital p what's the reference
+
+ align:start position:0%
+yeah capital p what's the reference
+ 
+
+ align:start position:0%
+yeah capital p what's the reference
+frame
+
+ align:start position:0%
+frame
+ 
+
+ align:start position:0%
+frame
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+and what what is it the angle the linear
+
+ align:start position:0%
+and what what is it the angle the linear
+ 
+
+ align:start position:0%
+and what what is it the angle the linear
+momentum off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the center of mass of the ensemble now
+
+ align:start position:0%
+the center of mass of the ensemble now
+ 
+
+ align:start position:0%
+the center of mass of the ensemble now
+as it turns out in this one case
+
+ align:start position:0%
+as it turns out in this one case
+ 
+
+ align:start position:0%
+as it turns out in this one case
+center of mass of the ons the momentum
+
+ align:start position:0%
+center of mass of the ons the momentum
+ 
+
+ align:start position:0%
+center of mass of the ons the momentum
+of the center of mass of the ensemble is
+
+ align:start position:0%
+of the center of mass of the ensemble is
+ 
+
+ align:start position:0%
+of the center of mass of the ensemble is
+the same as the total momentum of the
+
+ align:start position:0%
+the same as the total momentum of the
+ 
+
+ align:start position:0%
+the same as the total momentum of the
+ensemble
+
+ align:start position:0%
+ensemble
+ 
+
+ align:start position:0%
+ensemble
+got it
+
+ align:start position:0%
+got it
+ 
+
+ align:start position:0%
+got it
+so this is simply going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is what we're gonna do
+
+ align:start position:0%
+so this is what we're gonna do
+ 
+
+ align:start position:0%
+so this is what we're gonna do
+this is what you've seen
+
+ align:start position:0%
+this is what you've seen
+ 
+
+ align:start position:0%
+this is what you've seen
+this is we're gonna go to and then by
+
+ align:start position:0%
+this is we're gonna go to and then by
+ 
+
+ align:start position:0%
+this is we're gonna go to and then by
+the way
+
+ align:start position:0%
+the way
+ 
+
+ align:start position:0%
+the way
+we will show that under certain
+
+ align:start position:0%
+we will show that under certain
+ 
+
+ align:start position:0%
+we will show that under certain
+circumstances
+
+ align:start position:0%
+circumstances
+ 
+
+ align:start position:0%
+circumstances
+this reduces to
+
+ align:start position:0%
+this reduces to
+ 
+
+ align:start position:0%
+this reduces to
+i alpha
+
+ align:start position:0%
+i alpha
+ 
+
+ align:start position:0%
+i alpha
+and really these are the two equations
+
+ align:start position:0%
+and really these are the two equations
+ 
+
+ align:start position:0%
+and really these are the two equations
+we seek these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the roadmap we're going
+
+ align:start position:0%
+okay so that's the roadmap we're going
+ 
+
+ align:start position:0%
+okay so that's the roadmap we're going
+to follow
+
+ align:start position:0%
+to follow
+ 
+
+ align:start position:0%
+to follow
+got it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this equation we're going to turn into
+
+ align:start position:0%
+this equation we're going to turn into
+ 
+
+ align:start position:0%
+this equation we're going to turn into
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+this equation we're going to turn to
+
+ align:start position:0%
+this equation we're going to turn to
+ 
+
+ align:start position:0%
+this equation we're going to turn to
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+under certain circumstances this
+
+ align:start position:0%
+under certain circumstances this
+ 
+
+ align:start position:0%
+under certain circumstances this
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+becomes i alpha
+
+ align:start position:0%
+becomes i alpha
+ 
+
+ align:start position:0%
+becomes i alpha
+and we're done
+
+ align:start position:0%
+and we're done
+ 
+
+ align:start position:0%
+and we're done
+that's what we're going to do now any
+
+ align:start position:0%
+that's what we're going to do now any
+ 
+
+ align:start position:0%
+that's what we're going to do now any
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+i insist on at least one question at
+
+ align:start position:0%
+i insist on at least one question at
+ 
+
+ align:start position:0%
+i insist on at least one question at
+this point
+
+ align:start position:0%
+this point
+ 
+
+ align:start position:0%
+this point
+i'm feeling
+
+ align:start position:0%
+i'm feeling
+ 
+
+ align:start position:0%
+i'm feeling
+unquestioned i need to be questioned
+
+ align:start position:0%
+unquestioned i need to be questioned
+ 
+
+ align:start position:0%
+unquestioned i need to be questioned
+yes thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what we're going to do now so
+
+ align:start position:0%
+that's what we're going to do now so
+ 
+
+ align:start position:0%
+that's what we're going to do now so
+this is that's where we're going to go
+
+ align:start position:0%
+this is that's where we're going to go
+ 
+
+ align:start position:0%
+this is that's where we're going to go
+and what i'm going to do is i'm going to
+
+ align:start position:0%
+and what i'm going to do is i'm going to
+ 
+
+ align:start position:0%
+and what i'm going to do is i'm going to
+take you there
+
+ align:start position:0%
+take you there
+ 
+
+ align:start position:0%
+take you there
+i'm going to show you these results good
+
+ align:start position:0%
+i'm going to show you these results good
+ 
+
+ align:start position:0%
+i'm going to show you these results good
+question okay
+
+ align:start position:0%
+question okay
+ 
+
+ align:start position:0%
+question okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what we're going to do now
+
+ align:start position:0%
+what we're going to do now
+ 
+
+ align:start position:0%
+what we're going to do now
+is derive this
+
+ align:start position:0%
+is derive this
+ 
+
+ align:start position:0%
+is derive this
+derive this then we'll divide this and
+
+ align:start position:0%
+derive this then we'll divide this and
+ 
+
+ align:start position:0%
+derive this then we'll divide this and
+then we'll divide this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's derive this first
+
+ align:start position:0%
+so let's derive this first
+ 
+
+ align:start position:0%
+so let's derive this first
+in order for me to derive that the first
+
+ align:start position:0%
+in order for me to derive that the first
+ 
+
+ align:start position:0%
+in order for me to derive that the first
+thing i need to do i need to do
+
+ align:start position:0%
+thing i need to do i need to do
+ 
+
+ align:start position:0%
+thing i need to do i need to do
+is i need to introduce
+
+ align:start position:0%
+is i need to introduce
+ 
+
+ align:start position:0%
+is i need to introduce
+the concept of a center of mass
+
+ align:start position:0%
+the concept of a center of mass
+ 
+
+ align:start position:0%
+the concept of a center of mass
+officially you've seen it unofficially
+
+ align:start position:0%
+officially you've seen it unofficially
+ 
+
+ align:start position:0%
+officially you've seen it unofficially
+but i need to do it officially
+
+ align:start position:0%
+but i need to do it officially
+ 
+
+ align:start position:0%
+but i need to do it officially
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if i have an ensemble can anyone tell me
+
+ align:start position:0%
+if i have an ensemble can anyone tell me
+ 
+
+ align:start position:0%
+if i have an ensemble can anyone tell me
+the definition
+
+ align:start position:0%
+the definition
+ 
+
+ align:start position:0%
+the definition
+of the center of mass of the ensemble
+
+ align:start position:0%
+of the center of mass of the ensemble
+ 
+
+ align:start position:0%
+of the center of mass of the ensemble
+take a guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll say it in english and let's see if
+
+ align:start position:0%
+i'll say it in english and let's see if
+ 
+
+ align:start position:0%
+i'll say it in english and let's see if
+you can put it in formulae
+
+ align:start position:0%
+you can put it in formulae
+ 
+
+ align:start position:0%
+you can put it in formulae
+it is the weighted average
+
+ align:start position:0%
+it is the weighted average
+ 
+
+ align:start position:0%
+it is the weighted average
+mass weighted average of the position
+
+ align:start position:0%
+mass weighted average of the position
+ 
+
+ align:start position:0%
+mass weighted average of the position
+vectors of all the individual particles
+
+ align:start position:0%
+vectors of all the individual particles
+ 
+
+ align:start position:0%
+vectors of all the individual particles
+right does that make sense in english
+
+ align:start position:0%
+right does that make sense in english
+ 
+
+ align:start position:0%
+right does that make sense in english
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here let me tell you how to do it right
+
+ align:start position:0%
+here let me tell you how to do it right
+ 
+
+ align:start position:0%
+here let me tell you how to do it right
+i'm just going to write it down
+
+ align:start position:0%
+i'm just going to write it down
+ 
+
+ align:start position:0%
+i'm just going to write it down
+and you'll see it's correct
+
+ align:start position:0%
+and you'll see it's correct
+ 
+
+ align:start position:0%
+and you'll see it's correct
+you by the way this you need to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're exactly right by the way but the
+
+ align:start position:0%
+you're exactly right by the way but the
+ 
+
+ align:start position:0%
+you're exactly right by the way but the
+only thing i'll defer with is you don't
+
+ align:start position:0%
+only thing i'll defer with is you don't
+ 
+
+ align:start position:0%
+only thing i'll defer with is you don't
+have to do it separately you can do it
+
+ align:start position:0%
+have to do it separately you can do it
+ 
+
+ align:start position:0%
+have to do it separately you can do it
+in one vector form
+
+ align:start position:0%
+in one vector form
+ 
+
+ align:start position:0%
+in one vector form
+let me explain
+
+ align:start position:0%
+let me explain
+ 
+
+ align:start position:0%
+let me explain
+here look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this forks is the center of mass
+
+ align:start position:0%
+this forks is the center of mass
+ 
+
+ align:start position:0%
+this forks is the center of mass
+take every vector of every particle
+
+ align:start position:0%
+take every vector of every particle
+ 
+
+ align:start position:0%
+take every vector of every particle
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+multiplied by its mass
+
+ align:start position:0%
+multiplied by its mass
+ 
+
+ align:start position:0%
+multiplied by its mass
+add the whole thing up
+
+ align:start position:0%
+add the whole thing up
+ 
+
+ align:start position:0%
+add the whole thing up
+divided by the total mass the vector
+
+ align:start position:0%
+divided by the total mass the vector
+ 
+
+ align:start position:0%
+divided by the total mass the vector
+that comes out it's some sort of mean
+
+ align:start position:0%
+that comes out it's some sort of mean
+ 
+
+ align:start position:0%
+that comes out it's some sort of mean
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+that is the vector of the center of mass
+
+ align:start position:0%
+that is the vector of the center of mass
+ 
+
+ align:start position:0%
+that is the vector of the center of mass
+see what i mean and in fact you were
+
+ align:start position:0%
+see what i mean and in fact you were
+ 
+
+ align:start position:0%
+see what i mean and in fact you were
+right in principle i mean in practice
+
+ align:start position:0%
+right in principle i mean in practice
+ 
+
+ align:start position:0%
+right in principle i mean in practice
+you might do it in in coordinates but
+
+ align:start position:0%
+you might do it in in coordinates but
+ 
+
+ align:start position:0%
+you might do it in in coordinates but
+you can write this way so now here i'm
+
+ align:start position:0%
+you can write this way so now here i'm
+ 
+
+ align:start position:0%
+you can write this way so now here i'm
+going to stop and ask you does anyone
+
+ align:start position:0%
+going to stop and ask you does anyone
+ 
+
+ align:start position:0%
+going to stop and ask you does anyone
+have any questions about this
+
+ align:start position:0%
+have any questions about this
+ 
+
+ align:start position:0%
+have any questions about this
+i've simply written an age-old concept
+
+ align:start position:0%
+i've simply written an age-old concept
+ 
+
+ align:start position:0%
+i've simply written an age-old concept
+things you've seen in high school
+
+ align:start position:0%
+things you've seen in high school
+ 
+
+ align:start position:0%
+things you've seen in high school
+in vector form and do you get it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you twitched
+
+ align:start position:0%
+you twitched
+ 
+
+ align:start position:0%
+you twitched
+was that just doing this or did you have
+
+ align:start position:0%
+was that just doing this or did you have
+ 
+
+ align:start position:0%
+was that just doing this or did you have
+a question
+
+ align:start position:0%
+a question
+ 
+
+ align:start position:0%
+a question
+just kidding anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you understand this
+
+ align:start position:0%
+do you understand this
+ 
+
+ align:start position:0%
+do you understand this
+if you don't if you think i went fast
+
+ align:start position:0%
+if you don't if you think i went fast
+ 
+
+ align:start position:0%
+if you don't if you think i went fast
+and you want me to say this again i'll
+
+ align:start position:0%
+and you want me to say this again i'll
+ 
+
+ align:start position:0%
+and you want me to say this again i'll
+say it again
+
+ align:start position:0%
+say it again
+ 
+
+ align:start position:0%
+say it again
+who wants me to say this again
+
+ align:start position:0%
+who wants me to say this again
+ 
+
+ align:start position:0%
+who wants me to say this again
+anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that is the central mass
+
+ align:start position:0%
+that is the central mass
+ 
+
+ align:start position:0%
+that is the central mass
+it is again take every vector every
+
+ align:start position:0%
+it is again take every vector every
+ 
+
+ align:start position:0%
+it is again take every vector every
+position vector
+
+ align:start position:0%
+position vector
+ 
+
+ align:start position:0%
+position vector
+multiplied by the mass of that particle
+
+ align:start position:0%
+multiplied by the mass of that particle
+ 
+
+ align:start position:0%
+multiplied by the mass of that particle
+add up all this ensemble you know
+
+ align:start position:0%
+add up all this ensemble you know
+ 
+
+ align:start position:0%
+add up all this ensemble you know
+position vectors weighted and divided by
+
+ align:start position:0%
+position vectors weighted and divided by
+ 
+
+ align:start position:0%
+position vectors weighted and divided by
+the total mass boom
+
+ align:start position:0%
+the total mass boom
+ 
+
+ align:start position:0%
+the total mass boom
+it's the average position vector got it
+
+ align:start position:0%
+it's the average position vector got it
+ 
+
+ align:start position:0%
+it's the average position vector got it
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i wanted to find the velocity
+
+ align:start position:0%
+if i wanted to find the velocity
+ 
+
+ align:start position:0%
+if i wanted to find the velocity
+of the center of mass it would be this i
+
+ align:start position:0%
+of the center of mass it would be this i
+ 
+
+ align:start position:0%
+of the center of mass it would be this i
+would write it as this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm only doing this because in the end
+
+ align:start position:0%
+i'm only doing this because in the end
+ 
+
+ align:start position:0%
+i'm only doing this because in the end
+we'll need an acceleration of the center
+
+ align:start position:0%
+we'll need an acceleration of the center
+ 
+
+ align:start position:0%
+we'll need an acceleration of the center
+of mass right so i'm going to take the
+
+ align:start position:0%
+of mass right so i'm going to take the
+ 
+
+ align:start position:0%
+of mass right so i'm going to take the
+first derivative and i'll write it for
+
+ align:start position:0%
+first derivative and i'll write it for
+ 
+
+ align:start position:0%
+first derivative and i'll write it for
+you and you'll see that there's no great
+
+ align:start position:0%
+you and you'll see that there's no great
+ 
+
+ align:start position:0%
+you and you'll see that there's no great
+magic here
+
+ align:start position:0%
+magic here
+ 
+
+ align:start position:0%
+magic here
+it'll come out to be simply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the way we can expand this summation
+
+ align:start position:0%
+by the way we can expand this summation
+ 
+
+ align:start position:0%
+by the way we can expand this summation
+it's i is equal to one
+
+ align:start position:0%
+it's i is equal to one
+ 
+
+ align:start position:0%
+it's i is equal to one
+if there are n particles of summation
+
+ align:start position:0%
+if there are n particles of summation
+ 
+
+ align:start position:0%
+if there are n particles of summation
+the summation i is equal to one through
+
+ align:start position:0%
+the summation i is equal to one through
+ 
+
+ align:start position:0%
+the summation i is equal to one through
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+m i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can anyone tell me what the velocity is
+
+ align:start position:0%
+can anyone tell me what the velocity is
+ 
+
+ align:start position:0%
+can anyone tell me what the velocity is
+going to be at the center of mass
+
+ align:start position:0%
+going to be at the center of mass
+ 
+
+ align:start position:0%
+going to be at the center of mass
+for the position vector to take the the
+
+ align:start position:0%
+for the position vector to take the the
+ 
+
+ align:start position:0%
+for the position vector to take the the
+weighted average of the position vectors
+
+ align:start position:0%
+weighted average of the position vectors
+ 
+
+ align:start position:0%
+weighted average of the position vectors
+for the velocity what do i need to take
+
+ align:start position:0%
+for the velocity what do i need to take
+ 
+
+ align:start position:0%
+for the velocity what do i need to take
+excellent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to replace this ensemble
+
+ align:start position:0%
+i'm going to replace this ensemble
+ 
+
+ align:start position:0%
+i'm going to replace this ensemble
+summation
+
+ align:start position:0%
+summation
+ 
+
+ align:start position:0%
+summation
+with just this term which means the mass
+
+ align:start position:0%
+with just this term which means the mass
+ 
+
+ align:start position:0%
+with just this term which means the mass
+of the ensemble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and finally
+
+ align:start position:0%
+and finally
+ 
+
+ align:start position:0%
+and finally
+if i want the acceleration of the center
+
+ align:start position:0%
+if i want the acceleration of the center
+ 
+
+ align:start position:0%
+if i want the acceleration of the center
+of mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's going to be what the weighted
+
+ align:start position:0%
+it's going to be what the weighted
+ 
+
+ align:start position:0%
+it's going to be what the weighted
+average of the
+
+ align:start position:0%
+average of the
+ 
+
+ align:start position:0%
+average of the
+accelerations of the individual
+
+ align:start position:0%
+accelerations of the individual
+ 
+
+ align:start position:0%
+accelerations of the individual
+particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i'm going to raise this only because
+
+ align:start position:0%
+now i'm going to raise this only because
+ 
+
+ align:start position:0%
+now i'm going to raise this only because
+i need some room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now i've told you what central mass
+
+ align:start position:0%
+so now i've told you what central mass
+ 
+
+ align:start position:0%
+so now i've told you what central mass
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ajay can you publish the handwritten
+
+ align:start position:0%
+ajay can you publish the handwritten
+ 
+
+ align:start position:0%
+ajay can you publish the handwritten
+dumbbell problem if you just scan your
+
+ align:start position:0%
+dumbbell problem if you just scan your
+ 
+
+ align:start position:0%
+dumbbell problem if you just scan your
+notes
+
+ align:start position:0%
+notes
+ 
+
+ align:start position:0%
+notes
+thanks
+
+ align:start position:0%
+thanks
+ 
+
+ align:start position:0%
+thanks
+all right that's the center of mass
+
+ align:start position:0%
+all right that's the center of mass
+ 
+
+ align:start position:0%
+all right that's the center of mass
+stuff okay now you understand center of
+
+ align:start position:0%
+stuff okay now you understand center of
+ 
+
+ align:start position:0%
+stuff okay now you understand center of
+mass
+
+ align:start position:0%
+mass
+ 
+
+ align:start position:0%
+mass
+uh i i remember when someone asked me
+
+ align:start position:0%
+uh i i remember when someone asked me
+ 
+
+ align:start position:0%
+uh i i remember when someone asked me
+you know where that a acceleration c
+
+ align:start position:0%
+you know where that a acceleration c
+ 
+
+ align:start position:0%
+you know where that a acceleration c
+came from
+
+ align:start position:0%
+came from
+ 
+
+ align:start position:0%
+came from
+right there were two ways to do it the
+
+ align:start position:0%
+right there were two ways to do it the
+ 
+
+ align:start position:0%
+right there were two ways to do it the
+ajay way which is to expand it and just
+
+ align:start position:0%
+ajay way which is to expand it and just
+ 
+
+ align:start position:0%
+ajay way which is to expand it and just
+show that it comes out to be that
+
+ align:start position:0%
+show that it comes out to be that
+ 
+
+ align:start position:0%
+show that it comes out to be that
+but my explanation was actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i was kind of alluding to this
+
+ align:start position:0%
+i was kind of alluding to this
+ 
+
+ align:start position:0%
+i was kind of alluding to this
+you understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+let's take this guy
+
+ align:start position:0%
+let's take this guy
+ 
+
+ align:start position:0%
+let's take this guy
+and summit
+
+ align:start position:0%
+and summit
+ 
+
+ align:start position:0%
+and summit
+for the entire ensemble of particles
+
+ align:start position:0%
+for the entire ensemble of particles
+ 
+
+ align:start position:0%
+for the entire ensemble of particles
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's just simply that equation summed
+
+ align:start position:0%
+that's just simply that equation summed
+ 
+
+ align:start position:0%
+that's just simply that equation summed
+up for the entire ensemble of particles
+
+ align:start position:0%
+up for the entire ensemble of particles
+ 
+
+ align:start position:0%
+up for the entire ensemble of particles
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+everyone
+
+ align:start position:0%
+everyone
+ 
+
+ align:start position:0%
+everyone
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you know that's the same thing
+
+ align:start position:0%
+uh you know that's the same thing
+ 
+
+ align:start position:0%
+uh you know that's the same thing
+believe it or not
+
+ align:start position:0%
+believe it or not
+ 
+
+ align:start position:0%
+believe it or not
+in fact that's so think of it that's
+
+ align:start position:0%
+in fact that's so think of it that's
+ 
+
+ align:start position:0%
+in fact that's so think of it that's
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+um i'm glad you're asking that question
+
+ align:start position:0%
+um i'm glad you're asking that question
+ 
+
+ align:start position:0%
+um i'm glad you're asking that question
+because it's good it's important to
+
+ align:start position:0%
+because it's good it's important to
+ 
+
+ align:start position:0%
+because it's good it's important to
+think about it those are not different
+
+ align:start position:0%
+think about it those are not different
+ 
+
+ align:start position:0%
+think about it those are not different
+things they're not incompatible if you
+
+ align:start position:0%
+things they're not incompatible if you
+ 
+
+ align:start position:0%
+things they're not incompatible if you
+remove this it's an individual particle
+
+ align:start position:0%
+remove this it's an individual particle
+ 
+
+ align:start position:0%
+remove this it's an individual particle
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+and then when you sum it you're just
+
+ align:start position:0%
+and then when you sum it you're just
+ 
+
+ align:start position:0%
+and then when you sum it you're just
+saying this individual particle plus
+
+ align:start position:0%
+saying this individual particle plus
+ 
+
+ align:start position:0%
+saying this individual particle plus
+this individual particle plus this
+
+ align:start position:0%
+this individual particle plus this
+ 
+
+ align:start position:0%
+this individual particle plus this
+individual particle a counter is simply
+
+ align:start position:0%
+individual particle a counter is simply
+ 
+
+ align:start position:0%
+individual particle a counter is simply
+saying consider each individual particle
+
+ align:start position:0%
+saying consider each individual particle
+ 
+
+ align:start position:0%
+saying consider each individual particle
+and then do repeat until it's like
+
+ align:start position:0%
+and then do repeat until it's like
+ 
+
+ align:start position:0%
+and then do repeat until it's like
+writing a program
+
+ align:start position:0%
+writing a program
+ 
+
+ align:start position:0%
+writing a program
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+everyone understand this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so where does this lead us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is this written as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the total force on the ensemble
+
+ align:start position:0%
+the total force on the ensemble
+ 
+
+ align:start position:0%
+the total force on the ensemble
+capital f
+
+ align:start position:0%
+capital f
+ 
+
+ align:start position:0%
+capital f
+e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is th
+
+ align:start position:0%
+what is th
+ 
+
+ align:start position:0%
+what is th
+and what is this
+
+ align:start position:0%
+and what is this
+ 
+
+ align:start position:0%
+and what is this
+look up there
+
+ align:start position:0%
+look up there
+ 
+
+ align:start position:0%
+look up there
+what is this right hand side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's correct
+
+ align:start position:0%
+that's correct
+ 
+
+ align:start position:0%
+that's correct
+so we have that first result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so f e is equal to m e times the
+
+ align:start position:0%
+so f e is equal to m e times the
+ 
+
+ align:start position:0%
+so f e is equal to m e times the
+acceleration that's the first result
+
+ align:start position:0%
+acceleration that's the first result
+ 
+
+ align:start position:0%
+acceleration that's the first result
+we've just proved it
+
+ align:start position:0%
+we've just proved it
+ 
+
+ align:start position:0%
+we've just proved it
+it's very simple i just took the
+
+ align:start position:0%
+it's very simple i just took the
+ 
+
+ align:start position:0%
+it's very simple i just took the
+equation of the motion for each
+
+ align:start position:0%
+equation of the motion for each
+ 
+
+ align:start position:0%
+equation of the motion for each
+particular added them up i use
+
+ align:start position:0%
+particular added them up i use
+ 
+
+ align:start position:0%
+particular added them up i use
+the definition of central message is
+
+ align:start position:0%
+the definition of central message is
+ 
+
+ align:start position:0%
+the definition of central message is
+what i get
+
+ align:start position:0%
+what i get
+ 
+
+ align:start position:0%
+what i get
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it's just a nice way to do that once and
+
+ align:start position:0%
+it's just a nice way to do that once and
+ 
+
+ align:start position:0%
+it's just a nice way to do that once and
+for all and we're done
+
+ align:start position:0%
+for all and we're done
+ 
+
+ align:start position:0%
+for all and we're done
+two quick questions for you first
+
+ align:start position:0%
+two quick questions for you first
+ 
+
+ align:start position:0%
+two quick questions for you first
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+does this assume
+
+ align:start position:0%
+does this assume
+ 
+
+ align:start position:0%
+does this assume
+that the particles are connected or
+
+ align:start position:0%
+that the particles are connected or
+ 
+
+ align:start position:0%
+that the particles are connected or
+rigid did i make that assumption
+
+ align:start position:0%
+rigid did i make that assumption
+ 
+
+ align:start position:0%
+rigid did i make that assumption
+anywhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i did not
+
+ align:start position:0%
+i did not
+ 
+
+ align:start position:0%
+i did not
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+that eve in fact i'm assuming these are
+
+ align:start position:0%
+that eve in fact i'm assuming these are
+ 
+
+ align:start position:0%
+that eve in fact i'm assuming these are
+like independent hockey pucks with
+
+ align:start position:0%
+like independent hockey pucks with
+ 
+
+ align:start position:0%
+like independent hockey pucks with
+rockets attached to them
+
+ align:start position:0%
+rockets attached to them
+ 
+
+ align:start position:0%
+rockets attached to them
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are independent hockey pucks with
+
+ align:start position:0%
+these are independent hockey pucks with
+ 
+
+ align:start position:0%
+these are independent hockey pucks with
+rockets attached to them add up the
+
+ align:start position:0%
+rockets attached to them add up the
+ 
+
+ align:start position:0%
+rockets attached to them add up the
+forces of all the rockets
+
+ align:start position:0%
+forces of all the rockets
+ 
+
+ align:start position:0%
+forces of all the rockets
+i take the total mass i find the central
+
+ align:start position:0%
+i take the total mass i find the central
+ 
+
+ align:start position:0%
+i take the total mass i find the central
+mass and i go a physical damage
+
+ align:start position:0%
+mass and i go a physical damage
+ 
+
+ align:start position:0%
+mass and i go a physical damage
+so i made no assumption
+
+ align:start position:0%
+so i made no assumption
+ 
+
+ align:start position:0%
+so i made no assumption
+that the particles are connected now
+
+ align:start position:0%
+that the particles are connected now
+ 
+
+ align:start position:0%
+that the particles are connected now
+here's the tough question
+
+ align:start position:0%
+here's the tough question
+ 
+
+ align:start position:0%
+here's the tough question
+if the particles were rigidly connected
+
+ align:start position:0%
+if the particles were rigidly connected
+ 
+
+ align:start position:0%
+if the particles were rigidly connected
+by massless trucks
+
+ align:start position:0%
+by massless trucks
+ 
+
+ align:start position:0%
+by massless trucks
+would this formula still hold
+
+ align:start position:0%
+would this formula still hold
+ 
+
+ align:start position:0%
+would this formula still hold
+and this is actually a deep question
+
+ align:start position:0%
+and this is actually a deep question
+ 
+
+ align:start position:0%
+and this is actually a deep question
+i won't do this
+
+ align:start position:0%
+i won't do this
+ 
+
+ align:start position:0%
+i won't do this
+in detail right now you'll see the same
+
+ align:start position:0%
+in detail right now you'll see the same
+ 
+
+ align:start position:0%
+in detail right now you'll see the same
+question pop up later so i'll give you
+
+ align:start position:0%
+question pop up later so i'll give you
+ 
+
+ align:start position:0%
+question pop up later so i'll give you
+the verbal answer right now and i'll do
+
+ align:start position:0%
+the verbal answer right now and i'll do
+ 
+
+ align:start position:0%
+the verbal answer right now and i'll do
+it in more detail later so my question
+
+ align:start position:0%
+it in more detail later so my question
+ 
+
+ align:start position:0%
+it in more detail later so my question
+to you
+
+ align:start position:0%
+to you
+ 
+
+ align:start position:0%
+to you
+if the particles are rigidly connected
+
+ align:start position:0%
+if the particles are rigidly connected
+ 
+
+ align:start position:0%
+if the particles are rigidly connected
+by massless struts would the formula
+
+ align:start position:0%
+by massless struts would the formula
+ 
+
+ align:start position:0%
+by massless struts would the formula
+still hold question mark yes or no or
+
+ align:start position:0%
+still hold question mark yes or no or
+ 
+
+ align:start position:0%
+still hold question mark yes or no or
+maybe or only on tuesdays
+
+ align:start position:0%
+maybe or only on tuesdays
+ 
+
+ align:start position:0%
+maybe or only on tuesdays
+yes and why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody yeah go ahead yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right look if it's a rigid if the
+
+ align:start position:0%
+that's right look if it's a rigid if the
+ 
+
+ align:start position:0%
+that's right look if it's a rigid if the
+particles are originally connected
+
+ align:start position:0%
+particles are originally connected
+ 
+
+ align:start position:0%
+particles are originally connected
+there might be internal forces for sure
+
+ align:start position:0%
+there might be internal forces for sure
+ 
+
+ align:start position:0%
+there might be internal forces for sure
+in fact there will be internal forces
+
+ align:start position:0%
+in fact there will be internal forces
+ 
+
+ align:start position:0%
+in fact there will be internal forces
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you know what you give to one particle
+
+ align:start position:0%
+you know what you give to one particle
+ 
+
+ align:start position:0%
+you know what you give to one particle
+you're going to add to the other
+
+ align:start position:0%
+you're going to add to the other
+ 
+
+ align:start position:0%
+you're going to add to the other
+particle get it
+
+ align:start position:0%
+particle get it
+ 
+
+ align:start position:0%
+particle get it
+remember how here it kept showing you
+
+ align:start position:0%
+remember how here it kept showing you
+ 
+
+ align:start position:0%
+remember how here it kept showing you
+know this to this these internal forces
+
+ align:start position:0%
+know this to this these internal forces
+ 
+
+ align:start position:0%
+know this to this these internal forces
+when you add them keep canceling out
+
+ align:start position:0%
+when you add them keep canceling out
+ 
+
+ align:start position:0%
+when you add them keep canceling out
+these two cancelled out
+
+ align:start position:0%
+these two cancelled out
+ 
+
+ align:start position:0%
+these two cancelled out
+so even if it's rigid that holds but the
+
+ align:start position:0%
+so even if it's rigid that holds but the
+ 
+
+ align:start position:0%
+so even if it's rigid that holds but the
+beauty is it also holds if the particles
+
+ align:start position:0%
+beauty is it also holds if the particles
+ 
+
+ align:start position:0%
+beauty is it also holds if the particles
+are unconnected
+
+ align:start position:0%
+are unconnected
+ 
+
+ align:start position:0%
+are unconnected
+so it
+
+ align:start position:0%
+so it
+ 
+
+ align:start position:0%
+so it
+applies to multiple unconnected
+
+ align:start position:0%
+applies to multiple unconnected
+ 
+
+ align:start position:0%
+applies to multiple unconnected
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+and it applies to a rigid body is
+
+ align:start position:0%
+and it applies to a rigid body is
+ 
+
+ align:start position:0%
+and it applies to a rigid body is
+everyone good with this
+
+ align:start position:0%
+everyone good with this
+ 
+
+ align:start position:0%
+everyone good with this
+i'm not going to show you the internal
+
+ align:start position:0%
+i'm not going to show you the internal
+ 
+
+ align:start position:0%
+i'm not going to show you the internal
+forces canceling out it's pretty obvious
+
+ align:start position:0%
+forces canceling out it's pretty obvious
+ 
+
+ align:start position:0%
+forces canceling out it's pretty obvious
+because you've kind of seen it here
+
+ align:start position:0%
+because you've kind of seen it here
+ 
+
+ align:start position:0%
+because you've kind of seen it here
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so we have just derived
+
+ align:start position:0%
+so we have just derived
+ 
+
+ align:start position:0%
+so we have just derived
+this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+now i'm going to derive this guy
+
+ align:start position:0%
+now i'm going to derive this guy
+ 
+
+ align:start position:0%
+now i'm going to derive this guy
+and then i will reduce it to this
+
+ align:start position:0%
+and then i will reduce it to this
+ 
+
+ align:start position:0%
+and then i will reduce it to this
+that's the roadmap for the remaining 35
+
+ align:start position:0%
+that's the roadmap for the remaining 35
+ 
+
+ align:start position:0%
+that's the roadmap for the remaining 35
+minutes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to keep referring to that
+
+ align:start position:0%
+i'm going to keep referring to that
+ 
+
+ align:start position:0%
+i'm going to keep referring to that
+diagram all right that picture there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now now how did i do this
+
+ align:start position:0%
+so now now how did i do this
+ 
+
+ align:start position:0%
+so now now how did i do this
+i just took a summation of the f
+
+ align:start position:0%
+i just took a summation of the f
+ 
+
+ align:start position:0%
+i just took a summation of the f
+physical m equation right
+
+ align:start position:0%
+physical m equation right
+ 
+
+ align:start position:0%
+physical m equation right
+i'm going to do the same thing
+
+ align:start position:0%
+i'm going to do the same thing
+ 
+
+ align:start position:0%
+i'm going to do the same thing
+with that with that tau is tau
+
+ align:start position:0%
+with that with that tau is tau
+ 
+
+ align:start position:0%
+with that with that tau is tau
+is equal to d by d a dt of h plus
+
+ align:start position:0%
+is equal to d by d a dt of h plus
+ 
+
+ align:start position:0%
+is equal to d by d a dt of h plus
+v cross b i'm going to just sum it
+
+ align:start position:0%
+v cross b i'm going to just sum it
+ 
+
+ align:start position:0%
+v cross b i'm going to just sum it
+no great magic right
+
+ align:start position:0%
+no great magic right
+ 
+
+ align:start position:0%
+no great magic right
+and i'm going to add it up and show that
+
+ align:start position:0%
+and i'm going to add it up and show that
+ 
+
+ align:start position:0%
+and i'm going to add it up and show that
+you get the same equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you know the reason we do derivations
+
+ align:start position:0%
+you know the reason we do derivations
+ 
+
+ align:start position:0%
+you know the reason we do derivations
+which are really boring
+
+ align:start position:0%
+which are really boring
+ 
+
+ align:start position:0%
+which are really boring
+no i said the wrong the reason that even
+
+ align:start position:0%
+no i said the wrong the reason that even
+ 
+
+ align:start position:0%
+no i said the wrong the reason that even
+though derivations could be boring we do
+
+ align:start position:0%
+though derivations could be boring we do
+ 
+
+ align:start position:0%
+though derivations could be boring we do
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+is because when you take something like
+
+ align:start position:0%
+is because when you take something like
+ 
+
+ align:start position:0%
+is because when you take something like
+this makes a lot of sense great and i do
+
+ align:start position:0%
+this makes a lot of sense great and i do
+ 
+
+ align:start position:0%
+this makes a lot of sense great and i do
+like to do this but when you generalize
+
+ align:start position:0%
+like to do this but when you generalize
+ 
+
+ align:start position:0%
+like to do this but when you generalize
+them they generalize kinda but they're
+
+ align:start position:0%
+them they generalize kinda but they're
+ 
+
+ align:start position:0%
+them they generalize kinda but they're
+pitfalls
+
+ align:start position:0%
+pitfalls
+ 
+
+ align:start position:0%
+pitfalls
+and the reason to be precise
+
+ align:start position:0%
+and the reason to be precise
+ 
+
+ align:start position:0%
+and the reason to be precise
+is because it's those pitfalls
+
+ align:start position:0%
+is because it's those pitfalls
+ 
+
+ align:start position:0%
+is because it's those pitfalls
+that you need to be aware of
+
+ align:start position:0%
+that you need to be aware of
+ 
+
+ align:start position:0%
+that you need to be aware of
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so when you're a supervisor at nasa
+
+ align:start position:0%
+so when you're a supervisor at nasa
+ 
+
+ align:start position:0%
+so when you're a supervisor at nasa
+right you're the person who's going to
+
+ align:start position:0%
+right you're the person who's going to
+ 
+
+ align:start position:0%
+right you're the person who's going to
+catch the
+
+ align:start position:0%
+catch the
+ 
+
+ align:start position:0%
+catch the
+you know dude you missed a term you know
+
+ align:start position:0%
+you know dude you missed a term you know
+ 
+
+ align:start position:0%
+you know dude you missed a term you know
+you know you're the you're the that's
+
+ align:start position:0%
+you know you're the you're the that's
+ 
+
+ align:start position:0%
+you know you're the you're the that's
+your thing right you're the dude you mr
+
+ align:start position:0%
+your thing right you're the dude you mr
+ 
+
+ align:start position:0%
+your thing right you're the dude you mr
+term people right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that was a terrible movie by the dude
+
+ align:start position:0%
+that was a terrible movie by the dude
+ 
+
+ align:start position:0%
+that was a terrible movie by the dude
+where's my car
+
+ align:start position:0%
+where's my car
+ 
+
+ align:start position:0%
+where's my car
+terrible movie
+
+ align:start position:0%
+terrible movie
+ 
+
+ align:start position:0%
+terrible movie
+i finally saw it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know i was trying to be cool i
+
+ align:start position:0%
+you know i was trying to be cool i
+ 
+
+ align:start position:0%
+you know i was trying to be cool i
+thought yeah i'll see it you know it's
+
+ align:start position:0%
+thought yeah i'll see it you know it's
+ 
+
+ align:start position:0%
+thought yeah i'll see it you know it's
+terrible i'm sorry if you guys liked it
+
+ align:start position:0%
+terrible i'm sorry if you guys liked it
+ 
+
+ align:start position:0%
+terrible i'm sorry if you guys liked it
+i'm not cool okay
+
+ align:start position:0%
+i'm not cool okay
+ 
+
+ align:start position:0%
+i'm not cool okay
+did anyone like it
+
+ align:start position:0%
+did anyone like it
+ 
+
+ align:start position:0%
+did anyone like it
+come on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i had to detox i haven't watched a
+
+ align:start position:0%
+and i had to detox i haven't watched a
+ 
+
+ align:start position:0%
+and i had to detox i haven't watched a
+monty python i was like that's better
+
+ align:start position:0%
+monty python i was like that's better
+ 
+
+ align:start position:0%
+monty python i was like that's better
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i just i know i aged my i just dated
+
+ align:start position:0%
+i just i know i aged my i just dated
+ 
+
+ align:start position:0%
+i just i know i aged my i just dated
+myself but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we know
+
+ align:start position:0%
+okay so we know
+ 
+
+ align:start position:0%
+okay so we know
+that our oh you know i'm just rewriting
+
+ align:start position:0%
+that our oh you know i'm just rewriting
+ 
+
+ align:start position:0%
+that our oh you know i'm just rewriting
+that guy now
+
+ align:start position:0%
+that guy now
+ 
+
+ align:start position:0%
+that guy now
+right the torque
+
+ align:start position:0%
+right the torque
+ 
+
+ align:start position:0%
+right the torque
+i'm actually just writing defining
+
+ align:start position:0%
+i'm actually just writing defining
+ 
+
+ align:start position:0%
+i'm actually just writing defining
+torque
+
+ align:start position:0%
+torque
+ 
+
+ align:start position:0%
+torque
+is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the definition of torque right
+
+ align:start position:0%
+this is the definition of torque right
+ 
+
+ align:start position:0%
+this is the definition of torque right
+that's the total torque on particle i
+
+ align:start position:0%
+that's the total torque on particle i
+ 
+
+ align:start position:0%
+that's the total torque on particle i
+from the external force
+
+ align:start position:0%
+from the external force
+ 
+
+ align:start position:0%
+from the external force
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now what if there's an internal force
+
+ align:start position:0%
+now what if there's an internal force
+ 
+
+ align:start position:0%
+now what if there's an internal force
+what if there's an internal force
+
+ align:start position:0%
+what if there's an internal force
+ 
+
+ align:start position:0%
+what if there's an internal force
+from particle j onto particle i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right what if there's a force like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right if you look at particle i it'll
+
+ align:start position:0%
+right if you look at particle i it'll
+ 
+
+ align:start position:0%
+right if you look at particle i it'll
+have two forces let's write it down
+
+ align:start position:0%
+have two forces let's write it down
+ 
+
+ align:start position:0%
+have two forces let's write it down
+remember i said here i just hand waved
+
+ align:start position:0%
+remember i said here i just hand waved
+ 
+
+ align:start position:0%
+remember i said here i just hand waved
+it in this case let's write it down what
+
+ align:start position:0%
+it in this case let's write it down what
+ 
+
+ align:start position:0%
+it in this case let's write it down what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+you will get another torque which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm going to write it like this
+
+ align:start position:0%
+and i'm going to write it like this
+ 
+
+ align:start position:0%
+and i'm going to write it like this
+force on particle i
+
+ align:start position:0%
+force on particle i
+ 
+
+ align:start position:0%
+force on particle i
+from particle j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and i'll get you know k i mean i'll get
+
+ align:start position:0%
+and i'll get you know k i mean i'll get
+ 
+
+ align:start position:0%
+and i'll get you know k i mean i'll get
+a bunch of these terms
+
+ align:start position:0%
+a bunch of these terms
+ 
+
+ align:start position:0%
+a bunch of these terms
+right from every other particle that
+
+ align:start position:0%
+right from every other particle that
+ 
+
+ align:start position:0%
+right from every other particle that
+wants to you know push in internally in
+
+ align:start position:0%
+wants to you know push in internally in
+ 
+
+ align:start position:0%
+wants to you know push in internally in
+an internal force on this particle
+
+ align:start position:0%
+an internal force on this particle
+ 
+
+ align:start position:0%
+an internal force on this particle
+right so that's the force total force on
+
+ align:start position:0%
+right so that's the force total force on
+ 
+
+ align:start position:0%
+right so that's the force total force on
+this particle
+
+ align:start position:0%
+this particle
+ 
+
+ align:start position:0%
+this particle
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if you look at particle j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+because it's a counter i need to look at
+
+ align:start position:0%
+because it's a counter i need to look at
+ 
+
+ align:start position:0%
+because it's a counter i need to look at
+each particle
+
+ align:start position:0%
+each particle
+ 
+
+ align:start position:0%
+each particle
+i'm going to get
+
+ align:start position:0%
+i'm going to get
+ 
+
+ align:start position:0%
+i'm going to get
+r the torque on it is r o j
+
+ align:start position:0%
+r the torque on it is r o j
+ 
+
+ align:start position:0%
+r the torque on it is r o j
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+oj
+
+ align:start position:0%
+oj
+ 
+
+ align:start position:0%
+oj
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+f what am i going to get here what's the
+
+ align:start position:0%
+f what am i going to get here what's the
+ 
+
+ align:start position:0%
+f what am i going to get here what's the
+equivalent here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot dot
+
+ align:start position:0%
+dot dot
+ 
+
+ align:start position:0%
+dot dot
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now if i add them up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do i get here some of all the
+
+ align:start position:0%
+what do i get here some of all the
+ 
+
+ align:start position:0%
+what do i get here some of all the
+torques
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right by the way why does this cancel
+
+ align:start position:0%
+right by the way why does this cancel
+ 
+
+ align:start position:0%
+right by the way why does this cancel
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+oh sorry sir so sorry we'll come back so
+
+ align:start position:0%
+oh sorry sir so sorry we'll come back so
+ 
+
+ align:start position:0%
+oh sorry sir so sorry we'll come back so
+add them up what do i get here
+
+ align:start position:0%
+add them up what do i get here
+ 
+
+ align:start position:0%
+add them up what do i get here
+you said it right
+
+ align:start position:0%
+you said it right
+ 
+
+ align:start position:0%
+you said it right
+huh talking the entire thing and the
+
+ align:start position:0%
+huh talking the entire thing and the
+ 
+
+ align:start position:0%
+huh talking the entire thing and the
+word the way i'm defining that is
+
+ align:start position:0%
+word the way i'm defining that is
+ 
+
+ align:start position:0%
+word the way i'm defining that is
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+capital t
+
+ align:start position:0%
+capital t
+ 
+
+ align:start position:0%
+capital t
+it's the sum of the torques on the
+
+ align:start position:0%
+it's the sum of the torques on the
+ 
+
+ align:start position:0%
+it's the sum of the torques on the
+individual particles added up about
+
+ align:start position:0%
+individual particles added up about
+ 
+
+ align:start position:0%
+individual particles added up about
+reference point q
+
+ align:start position:0%
+reference point q
+ 
+
+ align:start position:0%
+reference point q
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+excuse me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+torque
+
+ align:start position:0%
+torque
+ 
+
+ align:start position:0%
+torque
+on the ensemble about point q
+
+ align:start position:0%
+on the ensemble about point q
+ 
+
+ align:start position:0%
+on the ensemble about point q
+and i define it as
+
+ align:start position:0%
+and i define it as
+ 
+
+ align:start position:0%
+and i define it as
+sigma
+
+ align:start position:0%
+sigma
+ 
+
+ align:start position:0%
+sigma
+i is equal to 1
+
+ align:start position:0%
+i is equal to 1
+ 
+
+ align:start position:0%
+i is equal to 1
+to n if the ensemble has n points
+
+ align:start position:0%
+to n if the ensemble has n points
+ 
+
+ align:start position:0%
+to n if the ensemble has n points
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+o i
+
+ align:start position:0%
+o i
+ 
+
+ align:start position:0%
+o i
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+and here's the deal
+
+ align:start position:0%
+and here's the deal
+ 
+
+ align:start position:0%
+and here's the deal
+what is f i j what's the relationship
+
+ align:start position:0%
+what is f i j what's the relationship
+ 
+
+ align:start position:0%
+what is f i j what's the relationship
+between fij and fji
+
+ align:start position:0%
+between fij and fji
+ 
+
+ align:start position:0%
+between fij and fji
+so all these terms cancel out
+
+ align:start position:0%
+so all these terms cancel out
+ 
+
+ align:start position:0%
+so all these terms cancel out
+all the internal terms cancel out get it
+
+ align:start position:0%
+all the internal terms cancel out get it
+ 
+
+ align:start position:0%
+all the internal terms cancel out get it
+i mean look here's the deal
+
+ align:start position:0%
+i mean look here's the deal
+ 
+
+ align:start position:0%
+i mean look here's the deal
+if you take
+
+ align:start position:0%
+if you take
+ 
+
+ align:start position:0%
+if you take
+two particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say let's say you're flying a
+
+ align:start position:0%
+let's say let's say you're flying a
+ 
+
+ align:start position:0%
+let's say let's say you're flying a
+plane right let's say launcher or you
+
+ align:start position:0%
+plane right let's say launcher or you
+ 
+
+ align:start position:0%
+plane right let's say launcher or you
+know yeah there's a you're flying a
+
+ align:start position:0%
+know yeah there's a you're flying a
+ 
+
+ align:start position:0%
+know yeah there's a you're flying a
+plane right
+
+ align:start position:0%
+plane right
+ 
+
+ align:start position:0%
+plane right
+now if two kids sitting next to each
+
+ align:start position:0%
+now if two kids sitting next to each
+ 
+
+ align:start position:0%
+now if two kids sitting next to each
+other pushing each other does it make
+
+ align:start position:0%
+other pushing each other does it make
+ 
+
+ align:start position:0%
+other pushing each other does it make
+any difference to the flight of the
+
+ align:start position:0%
+any difference to the flight of the
+ 
+
+ align:start position:0%
+any difference to the flight of the
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it doesn't as long as they're stably you
+
+ align:start position:0%
+it doesn't as long as they're stably you
+ 
+
+ align:start position:0%
+it doesn't as long as they're stably you
+know they're just kind of pushing each
+
+ align:start position:0%
+know they're just kind of pushing each
+ 
+
+ align:start position:0%
+know they're just kind of pushing each
+other in the stable against their chairs
+
+ align:start position:0%
+other in the stable against their chairs
+ 
+
+ align:start position:0%
+other in the stable against their chairs
+their seats it makes no difference to
+
+ align:start position:0%
+their seats it makes no difference to
+ 
+
+ align:start position:0%
+their seats it makes no difference to
+the flight of the plane right it's an
+
+ align:start position:0%
+the flight of the plane right it's an
+ 
+
+ align:start position:0%
+the flight of the plane right it's an
+internal matter
+
+ align:start position:0%
+internal matter
+ 
+
+ align:start position:0%
+internal matter
+and neutron sitting outside doesn't see
+
+ align:start position:0%
+and neutron sitting outside doesn't see
+ 
+
+ align:start position:0%
+and neutron sitting outside doesn't see
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+you understand
+
+ align:start position:0%
+you understand
+ 
+
+ align:start position:0%
+you understand
+so that's the way to think about the
+
+ align:start position:0%
+so that's the way to think about the
+ 
+
+ align:start position:0%
+so that's the way to think about the
+internal forces make no difference they
+
+ align:start position:0%
+internal forces make no difference they
+ 
+
+ align:start position:0%
+internal forces make no difference they
+cancel out they only make a difference
+
+ align:start position:0%
+cancel out they only make a difference
+ 
+
+ align:start position:0%
+cancel out they only make a difference
+by the way
+
+ align:start position:0%
+by the way
+ 
+
+ align:start position:0%
+by the way
+if the kids are moving around
+
+ align:start position:0%
+if the kids are moving around
+ 
+
+ align:start position:0%
+if the kids are moving around
+but if it's static
+
+ align:start position:0%
+but if it's static
+ 
+
+ align:start position:0%
+but if it's static
+which is what happens in a rigid body
+
+ align:start position:0%
+which is what happens in a rigid body
+ 
+
+ align:start position:0%
+which is what happens in a rigid body
+they make no difference
+
+ align:start position:0%
+they make no difference
+ 
+
+ align:start position:0%
+they make no difference
+okay yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how's that that was quick huh
+
+ align:start position:0%
+how's that that was quick huh
+ 
+
+ align:start position:0%
+how's that that was quick huh
+sorry i'm sure written q thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the definition of the
+
+ align:start position:0%
+okay so that's the definition of the
+ 
+
+ align:start position:0%
+okay so that's the definition of the
+total torque on a rigid body
+
+ align:start position:0%
+total torque on a rigid body
+ 
+
+ align:start position:0%
+total torque on a rigid body
+i write it as capital t and it's simply
+
+ align:start position:0%
+i write it as capital t and it's simply
+ 
+
+ align:start position:0%
+i write it as capital t and it's simply
+the sum of all this and i can ignore the
+
+ align:start position:0%
+the sum of all this and i can ignore the
+ 
+
+ align:start position:0%
+the sum of all this and i can ignore the
+internal forces got it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the first result i want
+
+ align:start position:0%
+okay so that's the first result i want
+ 
+
+ align:start position:0%
+okay so that's the first result i want
+to show you in that's in in my trying to
+
+ align:start position:0%
+to show you in that's in in my trying to
+ 
+
+ align:start position:0%
+to show you in that's in in my trying to
+prove that other equation
+
+ align:start position:0%
+prove that other equation
+ 
+
+ align:start position:0%
+prove that other equation
+now let's do the same for
+
+ align:start position:0%
+now let's do the same for
+ 
+
+ align:start position:0%
+now let's do the same for
+angular momentum because the three terms
+
+ align:start position:0%
+angular momentum because the three terms
+ 
+
+ align:start position:0%
+angular momentum because the three terms
+i'm going to sum up the torques i'm
+
+ align:start position:0%
+i'm going to sum up the torques i'm
+ 
+
+ align:start position:0%
+i'm going to sum up the torques i'm
+going to solve the angular momentum and
+
+ align:start position:0%
+going to solve the angular momentum and
+ 
+
+ align:start position:0%
+going to solve the angular momentum and
+i'm going to try and sum up this term
+
+ align:start position:0%
+i'm going to try and sum up this term
+ 
+
+ align:start position:0%
+i'm going to try and sum up this term
+okay yep
+
+ align:start position:0%
+okay yep
+ 
+
+ align:start position:0%
+okay yep
+yeah so i understand like right yeah
+
+ align:start position:0%
+yeah so i understand like right yeah
+ 
+
+ align:start position:0%
+yeah so i understand like right yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+but if you know because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it turns out that that's a quick
+
+ align:start position:0%
+yeah so it turns out that that's a quick
+ 
+
+ align:start position:0%
+yeah so it turns out that that's a quick
+question it's a very deep question it
+
+ align:start position:0%
+question it's a very deep question it
+ 
+
+ align:start position:0%
+question it's a very deep question it
+turns out that even in that case it
+
+ align:start position:0%
+turns out that even in that case it
+ 
+
+ align:start position:0%
+turns out that even in that case it
+becomes goes to zero
+
+ align:start position:0%
+becomes goes to zero
+ 
+
+ align:start position:0%
+becomes goes to zero
+right i won't write it out here but let
+
+ align:start position:0%
+right i won't write it out here but let
+ 
+
+ align:start position:0%
+right i won't write it out here but let
+me explain why first of all if it's a
+
+ align:start position:0%
+me explain why first of all if it's a
+ 
+
+ align:start position:0%
+me explain why first of all if it's a
+continuum
+
+ align:start position:0%
+continuum
+ 
+
+ align:start position:0%
+continuum
+then these two are very close
+
+ align:start position:0%
+then these two are very close
+ 
+
+ align:start position:0%
+then these two are very close
+right so the terms go to zero if they're
+
+ align:start position:0%
+right so the terms go to zero if they're
+ 
+
+ align:start position:0%
+right so the terms go to zero if they're
+you know attached by massless rods then
+
+ align:start position:0%
+you know attached by massless rods then
+ 
+
+ align:start position:0%
+you know attached by massless rods then
+you've got to use that kind of an
+
+ align:start position:0%
+you've got to use that kind of an
+ 
+
+ align:start position:0%
+you've got to use that kind of an
+argument
+
+ align:start position:0%
+argument
+ 
+
+ align:start position:0%
+argument
+and you can show that fij is the
+
+ align:start position:0%
+and you can show that fij is the
+ 
+
+ align:start position:0%
+and you can show that fij is the
+negative of fji
+
+ align:start position:0%
+negative of fji
+ 
+
+ align:start position:0%
+negative of fji
+and you can you know you can expand it
+
+ align:start position:0%
+and you can you know you can expand it
+ 
+
+ align:start position:0%
+and you can you know you can expand it
+all out and write f r i j and kind of
+
+ align:start position:0%
+all out and write f r i j and kind of
+ 
+
+ align:start position:0%
+all out and write f r i j and kind of
+write it out like that you're sure the
+
+ align:start position:0%
+write it out like that you're sure the
+ 
+
+ align:start position:0%
+write it out like that you're sure the
+term still vanishes
+
+ align:start position:0%
+term still vanishes
+ 
+
+ align:start position:0%
+term still vanishes
+okay and if you would like
+
+ align:start position:0%
+okay and if you would like
+ 
+
+ align:start position:0%
+okay and if you would like
+if you're interested in that if you come
+
+ align:start position:0%
+if you're interested in that if you come
+ 
+
+ align:start position:0%
+if you're interested in that if you come
+to uh if you come and see me i can show
+
+ align:start position:0%
+to uh if you come and see me i can show
+ 
+
+ align:start position:0%
+to uh if you come and see me i can show
+you some of the stuff
+
+ align:start position:0%
+you some of the stuff
+ 
+
+ align:start position:0%
+you some of the stuff
+all right so this term these so that
+
+ align:start position:0%
+all right so this term these so that
+ 
+
+ align:start position:0%
+all right so this term these so that
+that sort of body you're talking about
+
+ align:start position:0%
+that sort of body you're talking about
+ 
+
+ align:start position:0%
+that sort of body you're talking about
+which is not a real body a real body is
+
+ align:start position:0%
+which is not a real body a real body is
+ 
+
+ align:start position:0%
+which is not a real body a real body is
+all particles right next to each other
+
+ align:start position:0%
+all particles right next to each other
+ 
+
+ align:start position:0%
+all particles right next to each other
+right even in that sort of a thing these
+
+ align:start position:0%
+right even in that sort of a thing these
+ 
+
+ align:start position:0%
+right even in that sort of a thing these
+terms will cancel out it's very cool
+
+ align:start position:0%
+terms will cancel out it's very cool
+ 
+
+ align:start position:0%
+terms will cancel out it's very cool
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+and in fact aj and i spent banged our
+
+ align:start position:0%
+and in fact aj and i spent banged our
+ 
+
+ align:start position:0%
+and in fact aj and i spent banged our
+heads heads against this
+
+ align:start position:0%
+heads heads against this
+ 
+
+ align:start position:0%
+heads heads against this
+every year we're like ah why does it
+
+ align:start position:0%
+every year we're like ah why does it
+ 
+
+ align:start position:0%
+every year we're like ah why does it
+cancel again and oh yeah finally cancels
+
+ align:start position:0%
+cancel again and oh yeah finally cancels
+ 
+
+ align:start position:0%
+cancel again and oh yeah finally cancels
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+that's a good question it's actually not
+
+ align:start position:0%
+that's a good question it's actually not
+ 
+
+ align:start position:0%
+that's a good question it's actually not
+that obvious
+
+ align:start position:0%
+that obvious
+ 
+
+ align:start position:0%
+that obvious
+you know einstein was giving a speech
+
+ align:start position:0%
+you know einstein was giving a speech
+ 
+
+ align:start position:0%
+you know einstein was giving a speech
+i've forgotten where i think it is in
+
+ align:start position:0%
+i've forgotten where i think it is in
+ 
+
+ align:start position:0%
+i've forgotten where i think it is in
+berlin
+
+ align:start position:0%
+berlin
+ 
+
+ align:start position:0%
+berlin
+in the 50s and uh
+
+ align:start position:0%
+in the 50s and uh
+ 
+
+ align:start position:0%
+in the 50s and uh
+he wrote something you know i'm einstein
+
+ align:start position:0%
+he wrote something you know i'm einstein
+ 
+
+ align:start position:0%
+he wrote something you know i'm einstein
+you know so it's a reasonable comparison
+
+ align:start position:0%
+you know so it's a reasonable comparison
+ 
+
+ align:start position:0%
+you know so it's a reasonable comparison
+anyway so he wrote something or an
+
+ align:start position:0%
+anyway so he wrote something or an
+ 
+
+ align:start position:0%
+anyway so he wrote something or an
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+and he said obviously and he wrote the
+
+ align:start position:0%
+and he said obviously and he wrote the
+ 
+
+ align:start position:0%
+and he said obviously and he wrote the
+next i think the next result was easily
+
+ align:start position:0%
+next i think the next result was easily
+ 
+
+ align:start position:0%
+next i think the next result was easily
+mc square or something very profound
+
+ align:start position:0%
+mc square or something very profound
+ 
+
+ align:start position:0%
+mc square or something very profound
+obviously right and a young physicist on
+
+ align:start position:0%
+obviously right and a young physicist on
+ 
+
+ align:start position:0%
+obviously right and a young physicist on
+the back apparently said professor
+
+ align:start position:0%
+the back apparently said professor
+ 
+
+ align:start position:0%
+the back apparently said professor
+einstein it's not so obvious to me
+
+ align:start position:0%
+einstein it's not so obvious to me
+ 
+
+ align:start position:0%
+einstein it's not so obvious to me
+and all the you know the old bearded you
+
+ align:start position:0%
+and all the you know the old bearded you
+ 
+
+ align:start position:0%
+and all the you know the old bearded you
+know professors kind of turn up at him
+
+ align:start position:0%
+know professors kind of turn up at him
+ 
+
+ align:start position:0%
+know professors kind of turn up at him
+and stare at him right
+
+ align:start position:0%
+and stare at him right
+ 
+
+ align:start position:0%
+and stare at him right
+and the guy's like oh sorry can he sit
+
+ align:start position:0%
+and the guy's like oh sorry can he sit
+ 
+
+ align:start position:0%
+and the guy's like oh sorry can he sit
+down and then einstein goes you know
+
+ align:start position:0%
+down and then einstein goes you know
+ 
+
+ align:start position:0%
+down and then einstein goes you know
+actually you're exactly right and he
+
+ align:start position:0%
+actually you're exactly right and he
+ 
+
+ align:start position:0%
+actually you're exactly right and he
+takes another four blackboards to derive
+
+ align:start position:0%
+takes another four blackboards to derive
+ 
+
+ align:start position:0%
+takes another four blackboards to derive
+that and if i remember correctly the
+
+ align:start position:0%
+that and if i remember correctly the
+ 
+
+ align:start position:0%
+that and if i remember correctly the
+story is that that man
+
+ align:start position:0%
+story is that that man
+ 
+
+ align:start position:0%
+story is that that man
+that kid was leola landau who then won a
+
+ align:start position:0%
+that kid was leola landau who then won a
+ 
+
+ align:start position:0%
+that kid was leola landau who then won a
+nobel prize himself so you might win a
+
+ align:start position:0%
+nobel prize himself so you might win a
+ 
+
+ align:start position:0%
+nobel prize himself so you might win a
+nobel prize like me
+
+ align:start position:0%
+nobel prize like me
+ 
+
+ align:start position:0%
+nobel prize like me
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+this is the uh so let's do the next term
+
+ align:start position:0%
+this is the uh so let's do the next term
+ 
+
+ align:start position:0%
+this is the uh so let's do the next term
+which is a
+
+ align:start position:0%
+which is a
+ 
+
+ align:start position:0%
+which is a
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+i q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+q i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+p i
+
+ align:start position:0%
+p i
+ 
+
+ align:start position:0%
+p i
+and if you write that out
+
+ align:start position:0%
+and if you write that out
+ 
+
+ align:start position:0%
+and if you write that out
+and you sum it up for all the particles
+
+ align:start position:0%
+and you sum it up for all the particles
+ 
+
+ align:start position:0%
+and you sum it up for all the particles
+i'm not going to do it there's no terms
+
+ align:start position:0%
+i'm not going to do it there's no terms
+ 
+
+ align:start position:0%
+i'm not going to do it there's no terms
+to cancel
+
+ align:start position:0%
+to cancel
+ 
+
+ align:start position:0%
+to cancel
+it comes out that the total angular
+
+ align:start position:0%
+it comes out that the total angular
+ 
+
+ align:start position:0%
+it comes out that the total angular
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+of the ensemble about point q you can
+
+ align:start position:0%
+of the ensemble about point q you can
+ 
+
+ align:start position:0%
+of the ensemble about point q you can
+define it simply as
+
+ align:start position:0%
+define it simply as
+ 
+
+ align:start position:0%
+define it simply as
+this summation
+
+ align:start position:0%
+this summation
+ 
+
+ align:start position:0%
+this summation
+which is sigma
+
+ align:start position:0%
+which is sigma
+ 
+
+ align:start position:0%
+which is sigma
+i is equal to 1
+
+ align:start position:0%
+i is equal to 1
+ 
+
+ align:start position:0%
+i is equal to 1
+to n where n is the number of particles
+
+ align:start position:0%
+to n where n is the number of particles
+ 
+
+ align:start position:0%
+to n where n is the number of particles
+in the ensemble
+
+ align:start position:0%
+in the ensemble
+ 
+
+ align:start position:0%
+in the ensemble
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+q i
+
+ align:start position:0%
+q i
+ 
+
+ align:start position:0%
+q i
+cross a
+
+ align:start position:0%
+cross a
+ 
+
+ align:start position:0%
+cross a
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hm
+
+ align:start position:0%
+hm
+ 
+
+ align:start position:0%
+hm
+did i miss something
+
+ align:start position:0%
+did i miss something
+ 
+
+ align:start position:0%
+did i miss something
+eq
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did i miss something is right
+
+ align:start position:0%
+did i miss something is right
+ 
+
+ align:start position:0%
+did i miss something is right
+yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then finally
+
+ align:start position:0%
+okay and then finally
+ 
+
+ align:start position:0%
+okay and then finally
+let's plug this
+
+ align:start position:0%
+let's plug this
+ 
+
+ align:start position:0%
+let's plug this
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+into that equation
+
+ align:start position:0%
+into that equation
+ 
+
+ align:start position:0%
+into that equation
+and into actually that equation
+
+ align:start position:0%
+and into actually that equation
+ 
+
+ align:start position:0%
+and into actually that equation
+so now we can say tau i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point q
+
+ align:start position:0%
+point q
+ 
+
+ align:start position:0%
+point q
+is equal to i'm just recreating that
+
+ align:start position:0%
+is equal to i'm just recreating that
+ 
+
+ align:start position:0%
+is equal to i'm just recreating that
+equation i'm going to add it all up now
+
+ align:start position:0%
+equation i'm going to add it all up now
+ 
+
+ align:start position:0%
+equation i'm going to add it all up now
+that we've done the hard work
+
+ align:start position:0%
+that we've done the hard work
+ 
+
+ align:start position:0%
+that we've done the hard work
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+d by dt
+
+ align:start position:0%
+d by dt
+ 
+
+ align:start position:0%
+d by dt
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+by q
+
+ align:start position:0%
+by q
+ 
+
+ align:start position:0%
+by q
+i'm just rewriting that plus
+
+ align:start position:0%
+i'm just rewriting that plus
+ 
+
+ align:start position:0%
+i'm just rewriting that plus
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+v q
+
+ align:start position:0%
+v q
+ 
+
+ align:start position:0%
+v q
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+repeat
+
+ align:start position:0%
+repeat
+ 
+
+ align:start position:0%
+repeat
+n times
+
+ align:start position:0%
+n times
+ 
+
+ align:start position:0%
+n times
+when you add it up
+
+ align:start position:0%
+when you add it up
+ 
+
+ align:start position:0%
+when you add it up
+we can see that
+
+ align:start position:0%
+we can see that
+ 
+
+ align:start position:0%
+we can see that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+if you add this up use this to get
+
+ align:start position:0%
+if you add this up use this to get
+ 
+
+ align:start position:0%
+if you add this up use this to get
+the total torque on the ensemble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+that's it by definition right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to what is the summations of
+
+ align:start position:0%
+is equal to what is the summations of
+ 
+
+ align:start position:0%
+is equal to what is the summations of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's just
+
+ align:start position:0%
+yeah it's just
+ 
+
+ align:start position:0%
+yeah it's just
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+d by dt
+
+ align:start position:0%
+d by dt
+ 
+
+ align:start position:0%
+d by dt
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+i how about q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah if it's capital here
+
+ align:start position:0%
+yeah if it's capital here
+ 
+
+ align:start position:0%
+yeah if it's capital here
+if it's yeah this is yeah that's right
+
+ align:start position:0%
+if it's yeah this is yeah that's right
+ 
+
+ align:start position:0%
+if it's yeah this is yeah that's right
+and what's that going to
+
+ align:start position:0%
+and what's that going to
+ 
+
+ align:start position:0%
+and what's that going to
+become
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just going to be look it's just
+
+ align:start position:0%
+it's just going to be look it's just
+ 
+
+ align:start position:0%
+it's just going to be look it's just
+good this is constant right and the
+
+ align:start position:0%
+good this is constant right and the
+ 
+
+ align:start position:0%
+good this is constant right and the
+summing this hang up add up all the
+
+ align:start position:0%
+summing this hang up add up all the
+ 
+
+ align:start position:0%
+summing this hang up add up all the
+linear momentum of the individual
+
+ align:start position:0%
+linear momentum of the individual
+ 
+
+ align:start position:0%
+linear momentum of the individual
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+to get the linear momentum of the total
+
+ align:start position:0%
+to get the linear momentum of the total
+ 
+
+ align:start position:0%
+to get the linear momentum of the total
+ensemble
+
+ align:start position:0%
+ensemble
+ 
+
+ align:start position:0%
+ensemble
+so that's going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital p because it's an ensemble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+is that equation
+
+ align:start position:0%
+is that equation
+ 
+
+ align:start position:0%
+is that equation
+got it
+
+ align:start position:0%
+got it
+ 
+
+ align:start position:0%
+got it
+the sum sum sum it's done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the way the same things apply right
+
+ align:start position:0%
+by the way the same things apply right
+ 
+
+ align:start position:0%
+by the way the same things apply right
+so torque is equal to rate of change of
+
+ align:start position:0%
+so torque is equal to rate of change of
+ 
+
+ align:start position:0%
+so torque is equal to rate of change of
+angular momentum of the ensemble what
+
+ align:start position:0%
+angular momentum of the ensemble what
+ 
+
+ align:start position:0%
+angular momentum of the ensemble what
+happens if the reference point is
+
+ align:start position:0%
+happens if the reference point is
+ 
+
+ align:start position:0%
+happens if the reference point is
+stationary
+
+ align:start position:0%
+stationary
+ 
+
+ align:start position:0%
+stationary
+this term goes to zero right
+
+ align:start position:0%
+this term goes to zero right
+ 
+
+ align:start position:0%
+this term goes to zero right
+if the reference point is moving
+
+ align:start position:0%
+if the reference point is moving
+ 
+
+ align:start position:0%
+if the reference point is moving
+parallel
+
+ align:start position:0%
+parallel
+ 
+
+ align:start position:0%
+parallel
+to the center of mass
+
+ align:start position:0%
+to the center of mass
+ 
+
+ align:start position:0%
+to the center of mass
+this term goes to starts with z
+
+ align:start position:0%
+this term goes to starts with z
+ 
+
+ align:start position:0%
+this term goes to starts with z
+zero right same thing right similar
+
+ align:start position:0%
+zero right same thing right similar
+ 
+
+ align:start position:0%
+zero right same thing right similar
+concepts just added it up all right
+
+ align:start position:0%
+concepts just added it up all right
+ 
+
+ align:start position:0%
+concepts just added it up all right
+okay so now we have our second result
+
+ align:start position:0%
+okay so now we have our second result
+ 
+
+ align:start position:0%
+okay so now we have our second result
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+we're going to do the final thing
+
+ align:start position:0%
+we're going to do the final thing
+ 
+
+ align:start position:0%
+we're going to do the final thing
+uh vis-a-vis the dumbbell problem we're
+
+ align:start position:0%
+uh vis-a-vis the dumbbell problem we're
+ 
+
+ align:start position:0%
+uh vis-a-vis the dumbbell problem we're
+going to show that under certain
+
+ align:start position:0%
+going to show that under certain
+ 
+
+ align:start position:0%
+going to show that under certain
+circumstances this reduces to i alpha
+
+ align:start position:0%
+circumstances this reduces to i alpha
+ 
+
+ align:start position:0%
+circumstances this reduces to i alpha
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and everyone remember moment of inertia
+
+ align:start position:0%
+and everyone remember moment of inertia
+ 
+
+ align:start position:0%
+and everyone remember moment of inertia
+what's moment of inertia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+definition what it means any anything
+
+ align:start position:0%
+definition what it means any anything
+ 
+
+ align:start position:0%
+definition what it means any anything
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's hard to just rotate something
+
+ align:start position:0%
+yeah it's hard to just rotate something
+ 
+
+ align:start position:0%
+yeah it's hard to just rotate something
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and the basic insight is
+
+ align:start position:0%
+and the basic insight is
+ 
+
+ align:start position:0%
+and the basic insight is
+a mass that is twice the distance from
+
+ align:start position:0%
+a mass that is twice the distance from
+ 
+
+ align:start position:0%
+a mass that is twice the distance from
+you is four times more difficult to
+
+ align:start position:0%
+you is four times more difficult to
+ 
+
+ align:start position:0%
+you is four times more difficult to
+rotate
+
+ align:start position:0%
+rotate
+ 
+
+ align:start position:0%
+rotate
+square it weights with the square
+
+ align:start position:0%
+square it weights with the square
+ 
+
+ align:start position:0%
+square it weights with the square
+it's integral m r squared d r
+
+ align:start position:0%
+it's integral m r squared d r
+ 
+
+ align:start position:0%
+it's integral m r squared d r
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and that's why we ended up with this mr
+
+ align:start position:0%
+and that's why we ended up with this mr
+ 
+
+ align:start position:0%
+and that's why we ended up with this mr
+squared here
+
+ align:start position:0%
+squared here
+ 
+
+ align:start position:0%
+squared here
+right if the dumbbell is half the length
+
+ align:start position:0%
+right if the dumbbell is half the length
+ 
+
+ align:start position:0%
+right if the dumbbell is half the length
+that equation doesn't change but it'll
+
+ align:start position:0%
+that equation doesn't change but it'll
+ 
+
+ align:start position:0%
+that equation doesn't change but it'll
+it'll it'll rotate four times as fast
+
+ align:start position:0%
+it'll it'll rotate four times as fast
+ 
+
+ align:start position:0%
+it'll it'll rotate four times as fast
+right so now let's do that final thing
+
+ align:start position:0%
+right so now let's do that final thing
+ 
+
+ align:start position:0%
+right so now let's do that final thing
+which is going from here to introducing
+
+ align:start position:0%
+which is going from here to introducing
+ 
+
+ align:start position:0%
+which is going from here to introducing
+the concept of moment of inertia
+
+ align:start position:0%
+the concept of moment of inertia
+ 
+
+ align:start position:0%
+the concept of moment of inertia
+okay and this is where you know here be
+
+ align:start position:0%
+okay and this is where you know here be
+ 
+
+ align:start position:0%
+okay and this is where you know here be
+dragons so you need to be careful
+
+ align:start position:0%
+dragons so you need to be careful
+ 
+
+ align:start position:0%
+dragons so you need to be careful
+because you cannot do that about any
+
+ align:start position:0%
+because you cannot do that about any
+ 
+
+ align:start position:0%
+because you cannot do that about any
+reference point so only some reference
+
+ align:start position:0%
+reference point so only some reference
+ 
+
+ align:start position:0%
+reference point so only some reference
+points are valid
+
+ align:start position:0%
+points are valid
+ 
+
+ align:start position:0%
+points are valid
+and that's the difference between you
+
+ align:start position:0%
+and that's the difference between you
+ 
+
+ align:start position:0%
+and that's the difference between you
+and a harvard student right okay because
+
+ align:start position:0%
+and a harvard student right okay because
+ 
+
+ align:start position:0%
+and a harvard student right okay because
+you know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in order to go from here
+
+ align:start position:0%
+so in order to go from here
+ 
+
+ align:start position:0%
+so in order to go from here
+to i alpha
+
+ align:start position:0%
+to i alpha
+ 
+
+ align:start position:0%
+to i alpha
+what we'll do
+
+ align:start position:0%
+what we'll do
+ 
+
+ align:start position:0%
+what we'll do
+is we will express this guy
+
+ align:start position:0%
+is we will express this guy
+ 
+
+ align:start position:0%
+is we will express this guy
+we'll actually expand this guy
+
+ align:start position:0%
+we'll actually expand this guy
+ 
+
+ align:start position:0%
+we'll actually expand this guy
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what is a
+
+ align:start position:0%
+what is a
+ 
+
+ align:start position:0%
+what is a
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+of the ensemble about point o
+
+ align:start position:0%
+of the ensemble about point o
+ 
+
+ align:start position:0%
+of the ensemble about point o
+it is equal to
+
+ align:start position:0%
+it is equal to
+ 
+
+ align:start position:0%
+it is equal to
+as we said earlier
+
+ align:start position:0%
+as we said earlier
+ 
+
+ align:start position:0%
+as we said earlier
+and there's a lot of math and just a lot
+
+ align:start position:0%
+and there's a lot of math and just a lot
+ 
+
+ align:start position:0%
+and there's a lot of math and just a lot
+of writing here so you'll have to bear
+
+ align:start position:0%
+of writing here so you'll have to bear
+ 
+
+ align:start position:0%
+of writing here so you'll have to bear
+with me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's useful to pay attention all
+
+ align:start position:0%
+but it's useful to pay attention all
+ 
+
+ align:start position:0%
+but it's useful to pay attention all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+even now after all these years i get
+
+ align:start position:0%
+even now after all these years i get
+ 
+
+ align:start position:0%
+even now after all these years i get
+myself confused and i have to go back to
+
+ align:start position:0%
+myself confused and i have to go back to
+ 
+
+ align:start position:0%
+myself confused and i have to go back to
+the derivations to kind of figure out
+
+ align:start position:0%
+the derivations to kind of figure out
+ 
+
+ align:start position:0%
+the derivations to kind of figure out
+because a lot of things go unsaid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh i cross what anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+what's this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+p yeah exactly
+
+ align:start position:0%
+p yeah exactly
+ 
+
+ align:start position:0%
+p yeah exactly
+but i'm going to write it out like this
+
+ align:start position:0%
+but i'm going to write it out like this
+ 
+
+ align:start position:0%
+but i'm going to write it out like this
+i'm going to expand p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now here's a very important thing
+
+ align:start position:0%
+now here's a very important thing
+ 
+
+ align:start position:0%
+now here's a very important thing
+what did we do in the dumbbell
+
+ align:start position:0%
+what did we do in the dumbbell
+ 
+
+ align:start position:0%
+what did we do in the dumbbell
+we took
+
+ align:start position:0%
+we took
+ 
+
+ align:start position:0%
+we took
+if you remember correctly
+
+ align:start position:0%
+if you remember correctly
+ 
+
+ align:start position:0%
+if you remember correctly
+if you remember
+
+ align:start position:0%
+if you remember
+ 
+
+ align:start position:0%
+if you remember
+we expressed the velocities of these
+
+ align:start position:0%
+we expressed the velocities of these
+ 
+
+ align:start position:0%
+we expressed the velocities of these
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+not by themselves but how
+
+ align:start position:0%
+not by themselves but how
+ 
+
+ align:start position:0%
+not by themselves but how
+in terms of
+
+ align:start position:0%
+in terms of
+ 
+
+ align:start position:0%
+in terms of
+the velocity of the center of mass with
+
+ align:start position:0%
+the velocity of the center of mass with
+ 
+
+ align:start position:0%
+the velocity of the center of mass with
+the and the lever arm omega cross r
+
+ align:start position:0%
+the and the lever arm omega cross r
+ 
+
+ align:start position:0%
+the and the lever arm omega cross r
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+right because we're trying to get the
+
+ align:start position:0%
+right because we're trying to get the
+ 
+
+ align:start position:0%
+right because we're trying to get the
+whole rotation thing into it so we're
+
+ align:start position:0%
+whole rotation thing into it so we're
+ 
+
+ align:start position:0%
+whole rotation thing into it so we're
+going to do the same thing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yes that should be q it should both
+
+ align:start position:0%
+uh yes that should be q it should both
+ 
+
+ align:start position:0%
+uh yes that should be q it should both
+be q
+
+ align:start position:0%
+be q
+ 
+
+ align:start position:0%
+be q
+we will let's thank you they should both
+
+ align:start position:0%
+we will let's thank you they should both
+ 
+
+ align:start position:0%
+we will let's thank you they should both
+be q
+
+ align:start position:0%
+be q
+ 
+
+ align:start position:0%
+be q
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now the way we'll do it so how do we
+
+ align:start position:0%
+now the way we'll do it so how do we
+ 
+
+ align:start position:0%
+now the way we'll do it so how do we
+break it up into uh how do we rewrite
+
+ align:start position:0%
+break it up into uh how do we rewrite
+ 
+
+ align:start position:0%
+break it up into uh how do we rewrite
+this anyone
+
+ align:start position:0%
+this anyone
+ 
+
+ align:start position:0%
+this anyone
+just to keep you awake for a boring
+
+ align:start position:0%
+just to keep you awake for a boring
+ 
+
+ align:start position:0%
+just to keep you awake for a boring
+derivation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as i'm writing can anyone figure this
+
+ align:start position:0%
+as i'm writing can anyone figure this
+ 
+
+ align:start position:0%
+as i'm writing can anyone figure this
+out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does this make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so think about what i'm doing
+
+ align:start position:0%
+right so think about what i'm doing
+ 
+
+ align:start position:0%
+right so think about what i'm doing
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+here's the ensemble
+
+ align:start position:0%
+here's the ensemble
+ 
+
+ align:start position:0%
+here's the ensemble
+here's the dumbbell here's the center of
+
+ align:start position:0%
+here's the dumbbell here's the center of
+ 
+
+ align:start position:0%
+here's the dumbbell here's the center of
+the dumbbell
+
+ align:start position:0%
+the dumbbell
+ 
+
+ align:start position:0%
+the dumbbell
+i want to find the end point of the
+
+ align:start position:0%
+i want to find the end point of the
+ 
+
+ align:start position:0%
+i want to find the end point of the
+dumbbell
+
+ align:start position:0%
+dumbbell
+ 
+
+ align:start position:0%
+dumbbell
+velocity the end point
+
+ align:start position:0%
+velocity the end point
+ 
+
+ align:start position:0%
+velocity the end point
+so i find av center of
+
+ align:start position:0%
+so i find av center of
+ 
+
+ align:start position:0%
+so i find av center of
+vc
+
+ align:start position:0%
+vc
+ 
+
+ align:start position:0%
+vc
+plus omega
+
+ align:start position:0%
+plus omega
+ 
+
+ align:start position:0%
+plus omega
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+that distance
+
+ align:start position:0%
+that distance
+ 
+
+ align:start position:0%
+that distance
+that is the magic formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so fundamentally what i'm saying
+
+ align:start position:0%
+yeah so fundamentally what i'm saying
+ 
+
+ align:start position:0%
+yeah so fundamentally what i'm saying
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is i'm assuming
+
+ align:start position:0%
+is i'm assuming
+ 
+
+ align:start position:0%
+is i'm assuming
+this is where i'm doing it
+
+ align:start position:0%
+this is where i'm doing it
+ 
+
+ align:start position:0%
+this is where i'm doing it
+that those particles
+
+ align:start position:0%
+that those particles
+ 
+
+ align:start position:0%
+that those particles
+are a rigid body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+which means that if the ensemble rotates
+
+ align:start position:0%
+which means that if the ensemble rotates
+ 
+
+ align:start position:0%
+which means that if the ensemble rotates
+all the points rotate you know how if
+
+ align:start position:0%
+all the points rotate you know how if
+ 
+
+ align:start position:0%
+all the points rotate you know how if
+you look at the stars
+
+ align:start position:0%
+you look at the stars
+ 
+
+ align:start position:0%
+you look at the stars
+and you kind of do those time
+
+ align:start position:0%
+and you kind of do those time
+ 
+
+ align:start position:0%
+and you kind of do those time
+lapse things they're all in scrap
+
+ align:start position:0%
+lapse things they're all in scrap
+ 
+
+ align:start position:0%
+lapse things they're all in scrap
+circles time lapse photographs right
+
+ align:start position:0%
+circles time lapse photographs right
+ 
+
+ align:start position:0%
+circles time lapse photographs right
+that's kind of what i'm doing here i'm
+
+ align:start position:0%
+that's kind of what i'm doing here i'm
+ 
+
+ align:start position:0%
+that's kind of what i'm doing here i'm
+saying look
+
+ align:start position:0%
+saying look
+ 
+
+ align:start position:0%
+saying look
+whatever the velocity of a particle is
+
+ align:start position:0%
+whatever the velocity of a particle is
+ 
+
+ align:start position:0%
+whatever the velocity of a particle is
+it must be related to all the other
+
+ align:start position:0%
+it must be related to all the other
+ 
+
+ align:start position:0%
+it must be related to all the other
+particles in the following way which is
+
+ align:start position:0%
+particles in the following way which is
+ 
+
+ align:start position:0%
+particles in the following way which is
+they're all center of mass velocity plus
+
+ align:start position:0%
+they're all center of mass velocity plus
+ 
+
+ align:start position:0%
+they're all center of mass velocity plus
+omega cross their distance from the
+
+ align:start position:0%
+omega cross their distance from the
+ 
+
+ align:start position:0%
+omega cross their distance from the
+center of mass
+
+ align:start position:0%
+center of mass
+ 
+
+ align:start position:0%
+center of mass
+as a vector get it
+
+ align:start position:0%
+as a vector get it
+ 
+
+ align:start position:0%
+as a vector get it
+are you okay with this
+
+ align:start position:0%
+are you okay with this
+ 
+
+ align:start position:0%
+are you okay with this
+if you're not you stop me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're saying where is bvi that's yeah
+
+ align:start position:0%
+you're saying where is bvi that's yeah
+ 
+
+ align:start position:0%
+you're saying where is bvi that's yeah
+that makes sense
+
+ align:start position:0%
+that makes sense
+ 
+
+ align:start position:0%
+that makes sense
+bvi zero because it's not moving with
+
+ align:start position:0%
+bvi zero because it's not moving with
+ 
+
+ align:start position:0%
+bvi zero because it's not moving with
+respect to b i'm not writing up the
+
+ align:start position:0%
+respect to b i'm not writing up the
+ 
+
+ align:start position:0%
+respect to b i'm not writing up the
+whole uh
+
+ align:start position:0%
+whole uh
+ 
+
+ align:start position:0%
+whole uh
+formula here all right if you wanted to
+
+ align:start position:0%
+formula here all right if you wanted to
+ 
+
+ align:start position:0%
+formula here all right if you wanted to
+use the entire formula it should be your
+
+ align:start position:0%
+use the entire formula it should be your
+ 
+
+ align:start position:0%
+use the entire formula it should be your
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+it should be a
+
+ align:start position:0%
+it should be a
+ 
+
+ align:start position:0%
+it should be a
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+plus b
+
+ align:start position:0%
+plus b
+ 
+
+ align:start position:0%
+plus b
+v i
+
+ align:start position:0%
+v i
+ 
+
+ align:start position:0%
+v i
+plus a omega p b cross
+
+ align:start position:0%
+plus a omega p b cross
+ 
+
+ align:start position:0%
+plus a omega p b cross
+r right
+
+ align:start position:0%
+r right
+ 
+
+ align:start position:0%
+r right
+b is zero thank you rj that's i think
+
+ align:start position:0%
+b is zero thank you rj that's i think
+ 
+
+ align:start position:0%
+b is zero thank you rj that's i think
+that's where you were going because it's
+
+ align:start position:0%
+that's where you were going because it's
+ 
+
+ align:start position:0%
+that's where you were going because it's
+rigid so if you're sitting on the
+
+ align:start position:0%
+rigid so if you're sitting on the
+ 
+
+ align:start position:0%
+rigid so if you're sitting on the
+ensemble
+
+ align:start position:0%
+ensemble
+ 
+
+ align:start position:0%
+ensemble
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+getting the those particles aren't
+
+ align:start position:0%
+getting the those particles aren't
+ 
+
+ align:start position:0%
+getting the those particles aren't
+moving
+
+ align:start position:0%
+moving
+ 
+
+ align:start position:0%
+moving
+okay is anyone good with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you call the ensemble a framework
+
+ align:start position:0%
+so if you call the ensemble a framework
+ 
+
+ align:start position:0%
+so if you call the ensemble a framework
+reference e
+
+ align:start position:0%
+reference e
+ 
+
+ align:start position:0%
+reference e
+then the kind of the velocity version of
+
+ align:start position:0%
+then the kind of the velocity version of
+ 
+
+ align:start position:0%
+then the kind of the velocity version of
+the super ultra magic formula would be
+
+ align:start position:0%
+the super ultra magic formula would be
+ 
+
+ align:start position:0%
+the super ultra magic formula would be
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+velocity of i
+
+ align:start position:0%
+velocity of i
+ 
+
+ align:start position:0%
+velocity of i
+is equal to a
+
+ align:start position:0%
+is equal to a
+ 
+
+ align:start position:0%
+is equal to a
+velocity of this some reference point c
+
+ align:start position:0%
+velocity of this some reference point c
+ 
+
+ align:start position:0%
+velocity of this some reference point c
+plus b
+
+ align:start position:0%
+plus b
+ 
+
+ align:start position:0%
+plus b
+velocity of i
+
+ align:start position:0%
+velocity of i
+ 
+
+ align:start position:0%
+velocity of i
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+actually we call be right the ensemble i
+
+ align:start position:0%
+actually we call be right the ensemble i
+ 
+
+ align:start position:0%
+actually we call be right the ensemble i
+just use e
+
+ align:start position:0%
+just use e
+ 
+
+ align:start position:0%
+just use e
+omega b
+
+ align:start position:0%
+omega b
+ 
+
+ align:start position:0%
+omega b
+e sorry e
+
+ align:start position:0%
+e sorry e
+ 
+
+ align:start position:0%
+e sorry e
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+c i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you understand
+
+ align:start position:0%
+you understand
+ 
+
+ align:start position:0%
+you understand
+so space shuttle
+
+ align:start position:0%
+so space shuttle
+ 
+
+ align:start position:0%
+so space shuttle
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+a point on the space shuttle space
+
+ align:start position:0%
+a point on the space shuttle space
+ 
+
+ align:start position:0%
+a point on the space shuttle space
+shuttle is e endeavor right
+
+ align:start position:0%
+shuttle is e endeavor right
+ 
+
+ align:start position:0%
+shuttle is e endeavor right
+c is some point on it
+
+ align:start position:0%
+c is some point on it
+ 
+
+ align:start position:0%
+c is some point on it
+we want to find the velocity of a
+
+ align:start position:0%
+we want to find the velocity of a
+ 
+
+ align:start position:0%
+we want to find the velocity of a
+astronaut who's running away from
+
+ align:start position:0%
+astronaut who's running away from
+ 
+
+ align:start position:0%
+astronaut who's running away from
+you know the central space shuttle
+
+ align:start position:0%
+you know the central space shuttle
+ 
+
+ align:start position:0%
+you know the central space shuttle
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+evi velocity
+
+ align:start position:0%
+evi velocity
+ 
+
+ align:start position:0%
+evi velocity
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it doesn't matter this formula holds for
+
+ align:start position:0%
+it doesn't matter this formula holds for
+ 
+
+ align:start position:0%
+it doesn't matter this formula holds for
+any reference point
+
+ align:start position:0%
+any reference point
+ 
+
+ align:start position:0%
+any reference point
+but as it happens i'm going to do
+
+ align:start position:0%
+but as it happens i'm going to do
+ 
+
+ align:start position:0%
+but as it happens i'm going to do
+everything about center of mass of the
+
+ align:start position:0%
+everything about center of mass of the
+ 
+
+ align:start position:0%
+everything about center of mass of the
+space shuttle
+
+ align:start position:0%
+space shuttle
+ 
+
+ align:start position:0%
+space shuttle
+this formula holds right but this term
+
+ align:start position:0%
+this formula holds right but this term
+ 
+
+ align:start position:0%
+this formula holds right but this term
+is going to vanish
+
+ align:start position:0%
+is going to vanish
+ 
+
+ align:start position:0%
+is going to vanish
+because it's a rigid body
+
+ align:start position:0%
+because it's a rigid body
+ 
+
+ align:start position:0%
+because it's a rigid body
+right with respect to central mass on a
+
+ align:start position:0%
+right with respect to central mass on a
+ 
+
+ align:start position:0%
+right with respect to central mass on a
+frame attached to the ensemble
+
+ align:start position:0%
+frame attached to the ensemble
+ 
+
+ align:start position:0%
+frame attached to the ensemble
+the point i isn't moving
+
+ align:start position:0%
+the point i isn't moving
+ 
+
+ align:start position:0%
+the point i isn't moving
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+this term is not zero because the whole
+
+ align:start position:0%
+this term is not zero because the whole
+ 
+
+ align:start position:0%
+this term is not zero because the whole
+ensemble is moving
+
+ align:start position:0%
+ensemble is moving
+ 
+
+ align:start position:0%
+ensemble is moving
+and this term is not zero
+
+ align:start position:0%
+and this term is not zero
+ 
+
+ align:start position:0%
+and this term is not zero
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+just using the super magic formula
+
+ align:start position:0%
+just using the super magic formula
+ 
+
+ align:start position:0%
+just using the super magic formula
+answer your question
+
+ align:start position:0%
+answer your question
+ 
+
+ align:start position:0%
+answer your question
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's rewrite it
+
+ align:start position:0%
+so let's rewrite it
+ 
+
+ align:start position:0%
+so let's rewrite it
+i have one see
+
+ align:start position:0%
+i have one see
+ 
+
+ align:start position:0%
+i have one see
+10 12 minutes
+
+ align:start position:0%
+10 12 minutes
+ 
+
+ align:start position:0%
+10 12 minutes
+i'm going to rewrite this now is equal
+
+ align:start position:0%
+i'm going to rewrite this now is equal
+ 
+
+ align:start position:0%
+i'm going to rewrite this now is equal
+to sigma
+
+ align:start position:0%
+to sigma
+ 
+
+ align:start position:0%
+to sigma
+i is equal to 1
+
+ align:start position:0%
+i is equal to 1
+ 
+
+ align:start position:0%
+i is equal to 1
+through n
+
+ align:start position:0%
+through n
+ 
+
+ align:start position:0%
+through n
+r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry mi
+
+ align:start position:0%
+sorry mi
+ 
+
+ align:start position:0%
+sorry mi
+r q i
+
+ align:start position:0%
+r q i
+ 
+
+ align:start position:0%
+r q i
+just pull the m out
+
+ align:start position:0%
+just pull the m out
+ 
+
+ align:start position:0%
+just pull the m out
+cross can you help me out here folks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just to be clear the c is the center of
+
+ align:start position:0%
+just to be clear the c is the center of
+ 
+
+ align:start position:0%
+just to be clear the c is the center of
+what do i get here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sigma
+
+ align:start position:0%
+sigma
+ 
+
+ align:start position:0%
+sigma
+pi is equal to 1 to n i'm just expanding
+
+ align:start position:0%
+pi is equal to 1 to n i'm just expanding
+ 
+
+ align:start position:0%
+pi is equal to 1 to n i'm just expanding
+it out the two additions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again i'm going to pull the mi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i'll put the mi out
+
+ align:start position:0%
+yeah i'll put the mi out
+ 
+
+ align:start position:0%
+yeah i'll put the mi out
+and i'm going to rewrite this guy again
+
+ align:start position:0%
+and i'm going to rewrite this guy again
+ 
+
+ align:start position:0%
+and i'm going to rewrite this guy again
+in terms of rci
+
+ align:start position:0%
+in terms of rci
+ 
+
+ align:start position:0%
+in terms of rci
+how can i rewrite this guy in terms of
+
+ align:start position:0%
+how can i rewrite this guy in terms of
+ 
+
+ align:start position:0%
+how can i rewrite this guy in terms of
+rci
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody our qi
+
+ align:start position:0%
+anybody our qi
+ 
+
+ align:start position:0%
+anybody our qi
+is equal to rqc plus rci all right
+
+ align:start position:0%
+is equal to rqc plus rci all right
+ 
+
+ align:start position:0%
+is equal to rqc plus rci all right
+basically i'm going to take the vector
+
+ align:start position:0%
+basically i'm going to take the vector
+ 
+
+ align:start position:0%
+basically i'm going to take the vector
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rci our our qi is this vector
+
+ align:start position:0%
+rci our our qi is this vector
+ 
+
+ align:start position:0%
+rci our our qi is this vector
+right the center of mass is some point
+
+ align:start position:0%
+right the center of mass is some point
+ 
+
+ align:start position:0%
+right the center of mass is some point
+here c
+
+ align:start position:0%
+here c
+ 
+
+ align:start position:0%
+here c
+so i'm going to go this way
+
+ align:start position:0%
+so i'm going to go this way
+ 
+
+ align:start position:0%
+so i'm going to go this way
+i want to express everything in terms of
+
+ align:start position:0%
+i want to express everything in terms of
+ 
+
+ align:start position:0%
+i want to express everything in terms of
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+so this is equal to
+
+ align:start position:0%
+so this is equal to
+ 
+
+ align:start position:0%
+so this is equal to
+r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+q c
+
+ align:start position:0%
+q c
+ 
+
+ align:start position:0%
+q c
+plus r
+
+ align:start position:0%
+plus r
+ 
+
+ align:start position:0%
+plus r
+c i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what i just do here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then i have
+
+ align:start position:0%
+and then i have
+ 
+
+ align:start position:0%
+and then i have
+cross this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll just summarize in a second okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's what i did first step
+
+ align:start position:0%
+here's what i did first step
+ 
+
+ align:start position:0%
+here's what i did first step
+i wrote it you know just the definition
+
+ align:start position:0%
+i wrote it you know just the definition
+ 
+
+ align:start position:0%
+i wrote it you know just the definition
+of ahq
+
+ align:start position:0%
+of ahq
+ 
+
+ align:start position:0%
+of ahq
+a h e by e around q
+
+ align:start position:0%
+a h e by e around q
+ 
+
+ align:start position:0%
+a h e by e around q
+then i wrote rewrote this then i
+
+ align:start position:0%
+then i wrote rewrote this then i
+ 
+
+ align:start position:0%
+then i wrote rewrote this then i
+uh rewrote avi in terms of the center of
+
+ align:start position:0%
+uh rewrote avi in terms of the center of
+ 
+
+ align:start position:0%
+uh rewrote avi in terms of the center of
+mass velocity
+
+ align:start position:0%
+mass velocity
+ 
+
+ align:start position:0%
+mass velocity
+and angular
+
+ align:start position:0%
+and angular
+ 
+
+ align:start position:0%
+and angular
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+i took this term out here
+
+ align:start position:0%
+i took this term out here
+ 
+
+ align:start position:0%
+i took this term out here
+and then the remaining that's this term
+
+ align:start position:0%
+and then the remaining that's this term
+ 
+
+ align:start position:0%
+and then the remaining that's this term
+i split it up this way
+
+ align:start position:0%
+i split it up this way
+ 
+
+ align:start position:0%
+i split it up this way
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+drudgery
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it's just it's just drudgery i'm not
+
+ align:start position:0%
+it's just it's just drudgery i'm not
+ 
+
+ align:start position:0%
+it's just it's just drudgery i'm not
+doing anything particularly profound
+
+ align:start position:0%
+doing anything particularly profound
+ 
+
+ align:start position:0%
+doing anything particularly profound
+here just vectors
+
+ align:start position:0%
+here just vectors
+ 
+
+ align:start position:0%
+here just vectors
+express a vector this way that way all
+
+ align:start position:0%
+express a vector this way that way all
+ 
+
+ align:start position:0%
+express a vector this way that way all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and in some ways you can't even see why
+
+ align:start position:0%
+and in some ways you can't even see why
+ 
+
+ align:start position:0%
+and in some ways you can't even see why
+i'm doing it until you get to the end
+
+ align:start position:0%
+i'm doing it until you get to the end
+ 
+
+ align:start position:0%
+i'm doing it until you get to the end
+point you go ah or hopefully you'll go
+
+ align:start position:0%
+point you go ah or hopefully you'll go
+ 
+
+ align:start position:0%
+point you go ah or hopefully you'll go
+ah if you're not sleeping all right
+
+ align:start position:0%
+ah if you're not sleeping all right
+ 
+
+ align:start position:0%
+ah if you're not sleeping all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this rewrites two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this is actually the definition of
+
+ align:start position:0%
+right this is actually the definition of
+ 
+
+ align:start position:0%
+right this is actually the definition of
+center of mass at some level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+plus this rewrites to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a really really ugly term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this term
+
+ align:start position:0%
+this term
+ 
+
+ align:start position:0%
+this term
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+a term which will look ugly for a moment
+
+ align:start position:0%
+a term which will look ugly for a moment
+ 
+
+ align:start position:0%
+a term which will look ugly for a moment
+but is actually very elegant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i just expanded that out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so just so you know from here to here
+
+ align:start position:0%
+so just so you know from here to here
+ 
+
+ align:start position:0%
+so just so you know from here to here
+it's just expanding rewriting there's
+
+ align:start position:0%
+it's just expanding rewriting there's
+ 
+
+ align:start position:0%
+it's just expanding rewriting there's
+nothing profound if you fell asleep and
+
+ align:start position:0%
+nothing profound if you fell asleep and
+ 
+
+ align:start position:0%
+nothing profound if you fell asleep and
+you just woke up it's okay i didn't miss
+
+ align:start position:0%
+you just woke up it's okay i didn't miss
+ 
+
+ align:start position:0%
+you just woke up it's okay i didn't miss
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so that is uh simply rewriting uh
+
+ align:start position:0%
+so that is uh simply rewriting uh
+ 
+
+ align:start position:0%
+so that is uh simply rewriting uh
+the angular momentum of ensemble e about
+
+ align:start position:0%
+the angular momentum of ensemble e about
+ 
+
+ align:start position:0%
+the angular momentum of ensemble e about
+point q in terms of
+
+ align:start position:0%
+point q in terms of
+ 
+
+ align:start position:0%
+point q in terms of
+center of mass distance from centromere
+
+ align:start position:0%
+center of mass distance from centromere
+ 
+
+ align:start position:0%
+center of mass distance from centromere
+stuff like that
+
+ align:start position:0%
+stuff like that
+ 
+
+ align:start position:0%
+stuff like that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+we get to the fun part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is in fact
+
+ align:start position:0%
+this is in fact
+ 
+
+ align:start position:0%
+this is in fact
+nothing more
+
+ align:start position:0%
+nothing more
+ 
+
+ align:start position:0%
+nothing more
+than the distance of the center of mass
+
+ align:start position:0%
+than the distance of the center of mass
+ 
+
+ align:start position:0%
+than the distance of the center of mass
+from point q
+
+ align:start position:0%
+from point q
+ 
+
+ align:start position:0%
+from point q
+cross product with what anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hmm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the angle it's the linear momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's cute sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now this guy
+
+ align:start position:0%
+now this guy
+ 
+
+ align:start position:0%
+now this guy
+i'm not even going to bother to expand
+
+ align:start position:0%
+i'm not even going to bother to expand
+ 
+
+ align:start position:0%
+i'm not even going to bother to expand
+it because it's just a mess and there's
+
+ align:start position:0%
+it because it's just a mess and there's
+ 
+
+ align:start position:0%
+it because it's just a mess and there's
+no saving it right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's this guy this is just no i
+
+ align:start position:0%
+okay that's this guy this is just no i
+ 
+
+ align:start position:0%
+okay that's this guy this is just no i
+can't simplify it even i can't do it
+
+ align:start position:0%
+can't simplify it even i can't do it
+ 
+
+ align:start position:0%
+can't simplify it even i can't do it
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this is very interesting this is called
+
+ align:start position:0%
+this is very interesting this is called
+ 
+
+ align:start position:0%
+this is very interesting this is called
+the vector triple product
+
+ align:start position:0%
+the vector triple product
+ 
+
+ align:start position:0%
+the vector triple product
+here's a beautiful little formula
+
+ align:start position:0%
+here's a beautiful little formula
+ 
+
+ align:start position:0%
+here's a beautiful little formula
+if you have something like this
+
+ align:start position:0%
+if you have something like this
+ 
+
+ align:start position:0%
+if you have something like this
+a vector a across a vector b
+
+ align:start position:0%
+a vector a across a vector b
+ 
+
+ align:start position:0%
+a vector a across a vector b
+across a vector c
+
+ align:start position:0%
+across a vector c
+ 
+
+ align:start position:0%
+across a vector c
+this is called a vector triple product
+
+ align:start position:0%
+this is called a vector triple product
+ 
+
+ align:start position:0%
+this is called a vector triple product
+you can solve you can rewrite this as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did you know that
+
+ align:start position:0%
+did you know that
+ 
+
+ align:start position:0%
+did you know that
+have you seen this before
+
+ align:start position:0%
+have you seen this before
+ 
+
+ align:start position:0%
+have you seen this before
+it's a vector identity you've seen it in
+
+ align:start position:0%
+it's a vector identity you've seen it in
+ 
+
+ align:start position:0%
+it's a vector identity you've seen it in
+map trust me you've forgotten it's
+
+ align:start position:0%
+map trust me you've forgotten it's
+ 
+
+ align:start position:0%
+map trust me you've forgotten it's
+called the vector triple product you can
+
+ align:start position:0%
+called the vector triple product you can
+ 
+
+ align:start position:0%
+called the vector triple product you can
+prove it easily i'm not going to prove
+
+ align:start position:0%
+prove it easily i'm not going to prove
+ 
+
+ align:start position:0%
+prove it easily i'm not going to prove
+it it's a well-known mathematical thing
+
+ align:start position:0%
+it it's a well-known mathematical thing
+ 
+
+ align:start position:0%
+it it's a well-known mathematical thing
+we'll just call call it here
+
+ align:start position:0%
+we'll just call call it here
+ 
+
+ align:start position:0%
+we'll just call call it here
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+with that you can rewrite this
+
+ align:start position:0%
+with that you can rewrite this
+ 
+
+ align:start position:0%
+with that you can rewrite this
+okay that's the vector triple product
+
+ align:start position:0%
+okay that's the vector triple product
+ 
+
+ align:start position:0%
+okay that's the vector triple product
+formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any three vectors so if you rewrite it
+
+ align:start position:0%
+any three vectors so if you rewrite it
+ 
+
+ align:start position:0%
+any three vectors so if you rewrite it
+here's what you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is the mess that we've just
+
+ align:start position:0%
+so this is the mess that we've just
+ 
+
+ align:start position:0%
+so this is the mess that we've just
+inherited and i'm going to clean up the
+
+ align:start position:0%
+inherited and i'm going to clean up the
+ 
+
+ align:start position:0%
+inherited and i'm going to clean up the
+mess
+
+ align:start position:0%
+mess
+ 
+
+ align:start position:0%
+mess
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+first of all
+
+ align:start position:0%
+first of all
+ 
+
+ align:start position:0%
+first of all
+in a tour we're looking at two
+
+ align:start position:0%
+in a tour we're looking at two
+ 
+
+ align:start position:0%
+in a tour we're looking at two
+dimensions by the way this can be
+
+ align:start position:0%
+dimensions by the way this can be
+ 
+
+ align:start position:0%
+dimensions by the way this can be
+generalized to three dimensions
+
+ align:start position:0%
+generalized to three dimensions
+ 
+
+ align:start position:0%
+generalized to three dimensions
+what happens to this term
+
+ align:start position:0%
+what happens to this term
+ 
+
+ align:start position:0%
+what happens to this term
+in two dimensions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+position vector of points i with respect
+
+ align:start position:0%
+position vector of points i with respect
+ 
+
+ align:start position:0%
+position vector of points i with respect
+to the center of mass
+
+ align:start position:0%
+to the center of mass
+ 
+
+ align:start position:0%
+to the center of mass
+dot product with the angular velocity
+
+ align:start position:0%
+dot product with the angular velocity
+ 
+
+ align:start position:0%
+dot product with the angular velocity
+what happens to this term
+
+ align:start position:0%
+what happens to this term
+ 
+
+ align:start position:0%
+what happens to this term
+vanishes why because if this is the
+
+ align:start position:0%
+vanishes why because if this is the
+ 
+
+ align:start position:0%
+vanishes why because if this is the
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+the angular velocity points this way
+
+ align:start position:0%
+the angular velocity points this way
+ 
+
+ align:start position:0%
+the angular velocity points this way
+position vectors are all in the plane
+
+ align:start position:0%
+position vectors are all in the plane
+ 
+
+ align:start position:0%
+position vectors are all in the plane
+right and these days the dot product of
+
+ align:start position:0%
+right and these days the dot product of
+ 
+
+ align:start position:0%
+right and these days the dot product of
+two orthogonal vectors is zero
+
+ align:start position:0%
+two orthogonal vectors is zero
+ 
+
+ align:start position:0%
+two orthogonal vectors is zero
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so this is zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so this is i use the scalar dot cross
+
+ align:start position:0%
+so this is i use the scalar dot cross
+ 
+
+ align:start position:0%
+so this is i use the scalar dot cross
+you know the vector dot uh
+
+ align:start position:0%
+you know the vector dot uh
+ 
+
+ align:start position:0%
+you know the vector dot uh
+triple product rule to write rewrite
+
+ align:start position:0%
+triple product rule to write rewrite
+ 
+
+ align:start position:0%
+triple product rule to write rewrite
+this this is our
+
+ align:start position:0%
+this this is our
+ 
+
+ align:start position:0%
+this this is our
+position vector
+
+ align:start position:0%
+position vector
+ 
+
+ align:start position:0%
+position vector
+of point i from the center of mass
+
+ align:start position:0%
+of point i from the center of mass
+ 
+
+ align:start position:0%
+of point i from the center of mass
+it's in the plane of the blackboard
+
+ align:start position:0%
+it's in the plane of the blackboard
+ 
+
+ align:start position:0%
+it's in the plane of the blackboard
+angular velocity is outwards yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe i wrote it in the wrong order it's
+
+ align:start position:0%
+maybe i wrote it in the wrong order it's
+ 
+
+ align:start position:0%
+maybe i wrote it in the wrong order it's
+fine okay uh it it doesn't matter only
+
+ align:start position:0%
+fine okay uh it it doesn't matter only
+ 
+
+ align:start position:0%
+fine okay uh it it doesn't matter only
+because it goes to zero but it does
+
+ align:start position:0%
+because it goes to zero but it does
+ 
+
+ align:start position:0%
+because it goes to zero but it does
+matter in the sense that i screwed up so
+
+ align:start position:0%
+matter in the sense that i screwed up so
+ 
+
+ align:start position:0%
+matter in the sense that i screwed up so
+in what way did i
+
+ align:start position:0%
+in what way did i
+ 
+
+ align:start position:0%
+in what way did i
+what did i what was the mistake
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have your parentheses and the second
+
+ align:start position:0%
+you have your parentheses and the second
+ 
+
+ align:start position:0%
+you have your parentheses and the second
+part as opposed to the first two
+
+ align:start position:0%
+part as opposed to the first two
+ 
+
+ align:start position:0%
+part as opposed to the first two
+ah good point we'll have to check let me
+
+ align:start position:0%
+ah good point we'll have to check let me
+ 
+
+ align:start position:0%
+ah good point we'll have to check let me
+check okay i don't want to just because
+
+ align:start position:0%
+check okay i don't want to just because
+ 
+
+ align:start position:0%
+check okay i don't want to just because
+i'm running out of time it turns out my
+
+ align:start position:0%
+i'm running out of time it turns out my
+ 
+
+ align:start position:0%
+i'm running out of time it turns out my
+answer is wrong so i've made two
+
+ align:start position:0%
+answer is wrong so i've made two
+ 
+
+ align:start position:0%
+answer is wrong so i've made two
+mistakes and cancelled them out or maybe
+
+ align:start position:0%
+mistakes and cancelled them out or maybe
+ 
+
+ align:start position:0%
+mistakes and cancelled them out or maybe
+it doesn't matter i can just look at
+
+ align:start position:0%
+it doesn't matter i can just look at
+ 
+
+ align:start position:0%
+it doesn't matter i can just look at
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+yeah we'll just confirm that thank you
+
+ align:start position:0%
+yeah we'll just confirm that thank you
+ 
+
+ align:start position:0%
+yeah we'll just confirm that thank you
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the point is this term vanishes
+
+ align:start position:0%
+but the point is this term vanishes
+ 
+
+ align:start position:0%
+but the point is this term vanishes
+anyway because it'll be a dot product
+
+ align:start position:0%
+anyway because it'll be a dot product
+ 
+
+ align:start position:0%
+anyway because it'll be a dot product
+anyone recognize this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m r squared of omega
+
+ align:start position:0%
+m r squared of omega
+ 
+
+ align:start position:0%
+m r squared of omega
+so what is m r squared
+
+ align:start position:0%
+so what is m r squared
+ 
+
+ align:start position:0%
+so what is m r squared
+all right okay so this is i in its
+
+ align:start position:0%
+all right okay so this is i in its
+ 
+
+ align:start position:0%
+all right okay so this is i in its
+primordial form
+
+ align:start position:0%
+primordial form
+ 
+
+ align:start position:0%
+primordial form
+anyone recognize this term
+
+ align:start position:0%
+anyone recognize this term
+ 
+
+ align:start position:0%
+anyone recognize this term
+yeah it's a terrible term this term
+
+ align:start position:0%
+yeah it's a terrible term this term
+ 
+
+ align:start position:0%
+yeah it's a terrible term this term
+whatever right
+
+ align:start position:0%
+whatever right
+ 
+
+ align:start position:0%
+whatever right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the point i want to make is
+
+ align:start position:0%
+the point i want to make is
+ 
+
+ align:start position:0%
+the point i want to make is
+these guys only vanish under certain
+
+ align:start position:0%
+these guys only vanish under certain
+ 
+
+ align:start position:0%
+these guys only vanish under certain
+circumstances and that's the pitfall you
+
+ align:start position:0%
+circumstances and that's the pitfall you
+ 
+
+ align:start position:0%
+circumstances and that's the pitfall you
+need to be aware of
+
+ align:start position:0%
+need to be aware of
+ 
+
+ align:start position:0%
+need to be aware of
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and for example
+
+ align:start position:0%
+and for example
+ 
+
+ align:start position:0%
+and for example
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+q the point about which you're taking
+
+ align:start position:0%
+q the point about which you're taking
+ 
+
+ align:start position:0%
+q the point about which you're taking
+this the angular momentum
+
+ align:start position:0%
+this the angular momentum
+ 
+
+ align:start position:0%
+this the angular momentum
+is equal to is the same as the center of
+
+ align:start position:0%
+is equal to is the same as the center of
+ 
+
+ align:start position:0%
+is equal to is the same as the center of
+mass
+
+ align:start position:0%
+mass
+ 
+
+ align:start position:0%
+mass
+this term vanishes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this term vanishes
+
+ align:start position:0%
+this term vanishes
+ 
+
+ align:start position:0%
+this term vanishes
+get it because this is rqc
+
+ align:start position:0%
+get it because this is rqc
+ 
+
+ align:start position:0%
+get it because this is rqc
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so if q is the center of mass
+
+ align:start position:0%
+so if q is the center of mass
+ 
+
+ align:start position:0%
+so if q is the center of mass
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+what we have just shown is
+
+ align:start position:0%
+what we have just shown is
+ 
+
+ align:start position:0%
+what we have just shown is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+ensemble about point out where the
+
+ align:start position:0%
+ensemble about point out where the
+ 
+
+ align:start position:0%
+ensemble about point out where the
+center of mass
+
+ align:start position:0%
+center of mass
+ 
+
+ align:start position:0%
+center of mass
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+that in fact my friends is the
+
+ align:start position:0%
+that in fact my friends is the
+ 
+
+ align:start position:0%
+that in fact my friends is the
+definition of i
+
+ align:start position:0%
+definition of i
+ 
+
+ align:start position:0%
+definition of i
+that is the definition of i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a omega b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got it
+
+ align:start position:0%
+got it
+ 
+
+ align:start position:0%
+got it
+and then if that holds
+
+ align:start position:0%
+and then if that holds
+ 
+
+ align:start position:0%
+and then if that holds
+and only if that holds can you also say
+
+ align:start position:0%
+and only if that holds can you also say
+ 
+
+ align:start position:0%
+and only if that holds can you also say
+that the total torque on the ensemble
+
+ align:start position:0%
+that the total torque on the ensemble
+ 
+
+ align:start position:0%
+that the total torque on the ensemble
+which is the rate of change of that
+
+ align:start position:0%
+which is the rate of change of that
+ 
+
+ align:start position:0%
+which is the rate of change of that
+about point q
+
+ align:start position:0%
+about point q
+ 
+
+ align:start position:0%
+about point q
+is equal to what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the way in a continuum a summation is
+
+ align:start position:0%
+by the way in a continuum a summation is
+ 
+
+ align:start position:0%
+by the way in a continuum a summation is
+an integral so when you do integrals
+
+ align:start position:0%
+an integral so when you do integrals
+ 
+
+ align:start position:0%
+an integral so when you do integrals
+it's the same thing
+
+ align:start position:0%
+it's the same thing
+ 
+
+ align:start position:0%
+it's the same thing
+but for very tiny particles
+
+ align:start position:0%
+but for very tiny particles
+ 
+
+ align:start position:0%
+but for very tiny particles
+but in a continuum so it would become
+
+ align:start position:0%
+but in a continuum so it would become
+ 
+
+ align:start position:0%
+but in a continuum so it would become
+and this will be done in recitation
+
+ align:start position:0%
+and this will be done in recitation
+ 
+
+ align:start position:0%
+and this will be done in recitation
+it'll become dm you know it's an
+
+ align:start position:0%
+it'll become dm you know it's an
+ 
+
+ align:start position:0%
+it'll become dm you know it's an
+integral right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the definition of of of moment of
+
+ align:start position:0%
+so the definition of of of moment of
+ 
+
+ align:start position:0%
+so the definition of of of moment of
+inertia is this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yes same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i can't answer this question
+
+ align:start position:0%
+if i can't answer this question
+ 
+
+ align:start position:0%
+if i can't answer this question
+i'll answer it i mean if i think about
+
+ align:start position:0%
+i'll answer it i mean if i think about
+ 
+
+ align:start position:0%
+i'll answer it i mean if i think about
+it i'll answer it in class next week
\ No newline at end of file
diff --git a/up3zP2z81SE.txt b/up3zP2z81SE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..91db0762168c02745557d6825677e8bf6d9de8c6
--- /dev/null
+++ b/up3zP2z81SE.txt
@@ -0,0 +1,2775 @@
+SPEAKER: The following content
+is provided under a Creative
+
+Commons License.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: This Wednesday
+will be the first
+
+celebration of learning.
+
+Test 1 on Wednesday, October 7,
+you will write during the
+
+normal class time.
+
+So you'll have 50 minutes.
+
+And we want to have a little
+bit of comfort here, so you
+
+won't be sitting
+cheek to jowl.
+
+So before long I'll have
+the room assignment.
+
+So some of you will
+write in here.
+
+We'll have fewer people than
+seats so that there'll be
+
+vacancies next to each person.
+
+And then some will write in a
+few of the other locations,
+
+probably 26-100 and the gym
+above the Walker Memorial.
+
+And we'll get that out to you.
+
+And next week on the 6th we
+will have no weekly quiz,
+
+because enough celebrating.
+
+No point in testing you on the
+6th and then on the 7th.
+
+There will be, of course,
+the mini-celebration
+
+tomorrow, quiz 3.
+
+And I'll be available for office
+hours later today.
+
+Oh, and the coverage, just to
+remove the mystery, will be
+
+right up to the 7th
+of October.
+
+I've been doing this for over 30
+years and I've learned that
+
+in order to inspire interest on
+the part of the student it
+
+really pays to have the coverage
+of the celebration
+
+extend up to the lecture
+before the celebration.
+
+Now obviously I'm not going to
+drill deep on something I
+
+taught you on October 5, but
+it would be a good idea to
+
+stay awake during all of the
+lectures between now and then.
+
+So last day we talked
+about ionic bonding.
+
+And ionic bonding occurs with
+electrostatic attraction
+
+between ions that have formed
+through electron transfer.
+
+And we saw the energy of the
+ion pair given by this
+
+formula, where we have
+Coulomb's law
+
+with the Born exponent.
+
+And then this is plotted.
+
+This is E at r equals r0, and we
+learned that there were two
+
+terms. The attractive term,
+which is the Coulombic force
+
+here shown.
+
+And then there's a repulsive
+term, which results from
+
+electron-electron interaction
+when the two lines get very,
+
+very close together.
+
+And this is taken
+from your text.
+
+And I think they did a very nice
+job here of illustrating
+
+as you go to high values of r
+they're depicting that you
+
+have the ions separated by
+considerable distance.
+
+And there's a certain
+amount of stored
+
+energy, but not a lot.
+
+And then if you go much, much
+closer than the hard sphere
+
+sum of the ionic radii, I think
+they're depicting here
+
+that there's some squashing
+of the electron clouds.
+
+And you can see that the energy
+has gone way, way up.
+
+So this is an unfavorable
+situation, meaning that the
+
+energy here is greater than 0.
+
+And there's a sweet spot here
+at 236 picometers, which
+
+represents the ideal location.
+
+And that is the sum of the
+radius of the sodium ion and
+
+the radius of the
+chloride ion.
+
+And so you can see how
+energy tracks.
+
+And if you go far, far, far
+away to the point where
+
+they're at infinite separation,
+
+there's no energy stored.
+
+So everything makes sense.
+
+And then we said, well what
+happens if we keep packing
+
+these things?
+
+We rationalized that they would
+continue to do so and
+
+ultimately form a 3-dimensional
+crystal.
+
+And so you can see there's a
+lot of similarity between
+
+what's above and what's
+down here.
+
+This has been written
+for a 1-1 system.
+
+In other words, a cation plus
+1 and an anion minus 1.
+
+But it could be mediated
+by the valences.
+
+And what we have here is
+the structure factor.
+
+This Madelung constant tells us
+how much we get decrease in
+
+the energy of the system
+by going to a
+
+3-dimensional array.
+
+So depending on the atomic
+arrangement we'll have a
+
+different value of Madelung
+constant.
+
+We saw that for sodium chloride
+the value is 1.7476.
+
+And different crystals have
+different things.
+
+And what determines the
+crystal structure?
+
+It's a combination of
+the size of the two
+
+ions and their valence.
+
+So what we saw for sodium
+chloride, this
+
+is a structure type.
+
+So obviously sodium chloride
+is sodium chloride crystal
+
+structure, but there is an
+entire suite of compounds that
+
+have radius ratios and charges
+that end up with a sodium
+
+chloride type crystal
+structure.
+
+And then towards the end we
+started looking at the
+
+Born-Haber Cycle.
+
+And the purpose of the
+Born-Haber Cycle was to give
+
+us a sense of scale of the
+various constituents in the
+
+formation of a crystal.
+
+And what we noted, the takeaway
+message from the
+
+Born-Haber Cycle, is that this
+enthalpy of crystallization,
+
+which is basically this
+term here, is huge.
+
+It's huge.
+
+It was the big component of the
+energy required to form
+
+the crystal.
+
+It's large and it is negative.
+
+So what I want to do today
+is start by talking about
+
+shortcomings of the business
+of ionic bonding.
+
+See, how did we get
+to ionic bonding?
+
+We started with this idea
+of octet stability.
+
+Octet stability was
+the driving idea
+
+behind all of this.
+
+Octet stability, and in the case
+of ionic bonding this was
+
+via electron transfer.
+
+And so that got us a long way,
+but it has its limitations.
+
+So let's put up some new data.
+
+So suppose I look at compounds
+like H2, N2, O2.
+
+Do these things form
+ionic bonds?
+
+How does octet stability
+play here?
+
+And so let's start by
+looking at hydrogen.
+
+So if we took hydrogen and
+started with atomic hydrogen
+
+and added an electron to it,
+then we would form an anion
+
+known as H minus.
+
+And H minus looks pretty good
+because it's isoelectronic
+
+with helium.
+
+So maybe this isn't going
+to be so bad a day.
+
+But if we're going to have
+a bond then we need
+
+to form an H plus.
+
+So let's do that.
+
+So that would be, then, H goes
+to H plus, plus an electron.
+
+And that's really nothing
+more than a proton.
+
+So that doesn't look
+too appealing.
+
+That's probably a high
+energy state.
+
+And besides, in the same
+location at the same time--
+
+in other words, same
+temperature, same conditions--
+
+half of the hydrogens have to
+acquire electrons and half of
+
+the hydrogens have to
+lose electrons.
+
+And that's not going
+to happen.
+
+They're either going to have a
+propensity for electron gain
+
+or a propensity for
+electron loss.
+
+So it looks like ionic bonding
+is not going to help us
+
+explain the formation
+of molecules such as
+
+H2, N2, and so on.
+
+So who came to the rescue
+in this case to get
+
+us out of the conundrum?
+
+G.N.
+
+Lewis.
+
+G.N.
+
+Lewis was actually born in
+Weymouth, Massachusetts and he
+
+finished his PhD at
+Harvard in 1899.
+
+And then, like so many Americans
+of the day, went off
+
+to Europe and he postdoc'd
+in Europe for a while.
+
+And then he came back and
+got a job at MIT.
+
+And he taught at MIT
+from 1905 to 1912.
+
+And then in 1912 he was lured
+to the West Coast where they
+
+were starting to establish the
+chemistry department, the
+
+University of California at
+Berkeley, and he went out to
+
+Berkeley and that's where he
+spent the rest of his career.
+
+And we can speculate
+why he went.
+
+Maybe he was fed up with
+the weather here.
+
+Actually, today is one of those
+few days-- write it
+
+down, because one of the few
+lovely days in Massachusetts.
+
+So G.N.
+
+Lewis, what did he say?
+
+He said, well I've
+got an idea here.
+
+He said, what if hydrogen
+achieved shell filling not by
+
+electron transfer but
+by electron sharing.
+
+So he posited the idea of shell
+
+filling by electron sharing.
+
+This is in contrast to
+electron transfer.
+
+So let's see.
+
+Oh.
+
+There's an image of G.N.
+
+Lewis.
+
+He died, actually, on the job.
+
+He came back to his
+lab one day after
+
+lunch and hit the floor.
+
+So he worked right
+to the very end.
+
+Here's some data taken
+from a lab
+
+notebook and memo, actually.
+
+1902.
+
+And what do you see here?
+
+Well, he developed a notation
+for us, and we still use this
+
+notation to this day:
+Lewis notation.
+
+So here's lithium and he's
+got one electron.
+
+But we know lithium has
+three electrons but
+
+only one valence electron.
+
+And then there's beryllium
+and magnesium--
+
+two electrons.
+
+Aluminum with three.
+
+Here's fluorine chlorine, and
+when they ionize he puts the
+
+eighth electron right here.
+
+And look at this one
+for silicon.
+
+He's got probably some kernel
+inside the atom, thus.
+
+So he's even starting to think
+about concentric shells.
+
+This is 1902.
+
+Remember the Bohr model
+isn't until 1913.
+
+So you can see people
+struggling.
+
+And notice that we have eight
+electrons in a shell--
+
+that's where we're getting
+the octet stability--
+
+and he's using cubes.
+
+Now we know that the cube isn't
+the shape of the shell,
+
+but it's a pretty good device
+to help you keep track of
+
+electron number--
+
+because there's eight
+corners on a cube.
+
+So it's another example of how
+that's not what it is but it's
+
+a really good model and it keeps
+you out of trouble and
+
+allows you to go forward.
+
+So this is going back-- way,
+way back-- for G.N.
+
+Lewis.
+
+Now let's use this idea
+and account for the
+
+formation of H2.
+
+So here's hydrogen, and using
+the Lewis notation we'll put a
+
+dot here for its one electron.
+
+And we'll bring in a second
+hydrogen and we'll use a
+
+cross, or an x, to indicate
+the electron
+
+from the second hydrogen.
+
+And now we're going
+to double count--
+
+in other words, double
+attribute.
+
+These are shared electrons so
+they count for both atoms.
+
+Double count the shared
+electrons.
+
+And when you do so what
+do you come up with?
+
+Well, the element on the left
+has two electrons and,
+
+therefore, is isoelectronic
+with helium.
+
+OK?
+
+Maybe it was a California
+thing.
+
+They were sharing.
+
+And then there was
+sort of another
+
+California concept, like.
+
+So it was like helium.
+
+And then on this side this
+is also sharing.
+
+And it's kind of like helium.
+
+So now we've achieved the
+stability of the filled shell
+
+by sharing the electrons.
+
+OK.
+
+And I think I even have
+another slide of how--
+
+this is the more modern
+version of it.
+
+Electron dot.
+
+So the nucleus and the
+inner-electrons are contained
+
+inside the chemical symbol.
+
+And, actually, this goes
+all the way to
+
+modern quantum mechanics.
+
+Density functional theory does
+the same thing: lumps all of
+
+the inner-shell electrons plus
+the nucleus into one piece,
+
+and then the valence electrons
+are outside.
+
+And so starting in 1902 with
+some little dots and crosses
+
+we go all the way
+to DFT today.
+
+All right.
+
+So let's do another one.
+
+How about nitrogen?
+
+Let's try nitrogen.
+
+So when we going to nitrogen
+we know the valence
+
+electron's 2s2 2p3.
+
+So put nitrogen here.
+
+One, two, three, four, five.
+
+Now these three electrons
+here are
+
+according to the Hund rule.
+
+So it's px, py, pz, and this is
+the 2s2 sitting over here.
+
+And I'll bring in a second
+nitrogen, and there's its 2s2.
+
+2px, 2py, 2pz.
+
+And now what do I have?
+
+Look at the nitrogen
+on the left.
+
+Two, four, six, eight.
+
+So the nitrogen on the left
+feels as though it has access
+
+to eight electrons.
+
+The nitrogen on the right--
+two, four, six, eight-- it
+
+feels as though it has access
+to eight electrons.
+
+So both nitrogens are
+isoelectronic with neon if we
+
+push on this concept of
+electron sharing.
+
+Now there's a second
+thing I want to do.
+
+It's to draw attention to
+two types of orbitals.
+
+So these three orbitals in the
+center consist of electrons
+
+that are shared.
+
+So these are going to be called
+bonding orbitals.
+
+And "bonding" and "blue" both
+begin with a "b", so I'm going
+
+to denote the bonding orbitals,
+or bonding domains,
+
+as distinct from the nonbonding
+domains in red.
+
+Red are nonbonding domains.
+
+Always two electrons
+per orbital.
+
+They like to live in pairs.
+
+That's the way it works.
+
+OK?
+
+And so each one of these
+pairs is a bond.
+
+So I can then write nitrogen
+with three lines through it
+
+indicating I have
+a triple bond.
+
+Three pairs of electrons,
+three bonding
+
+domains, triple bond.
+
+This is all in formation
+according to the concept of
+
+electron sharing.
+
+And Lewis coined a name for
+the type of bond that is
+
+formed in this way.
+
+He said we get bond formation
+involves cooperative use--
+
+sharing, cooperative--
+
+of valence electrons.
+
+So now we can take the "co"
+symbol here and the "valence"
+
+here and come up with the term
+"covalent bond." Covalent
+
+bond, thanks to G.N.
+
+Lewis.
+
+So, again, to make sure we're
+very clear, ionic bond results
+
+from electron transfer, covalent
+bond results from
+
+electron sharing.
+
+Now we can do this-- so let's go
+to heteronuclear molecules.
+
+These are homonuclear.
+
+So let's go to heteronuclear
+molecules.
+
+And so let's see.
+
+I've got some rules
+up here, I think.
+
+Yeah.
+
+Drawing Lewis structures.
+
+So let's go to a heteronuclear
+molecule.
+
+And I'm going to choose as an
+example sulfuryl chloride.
+
+And I don't expect you
+to be able to name
+
+these things on site.
+
+I will always give
+you the name.
+
+I'll say sulfuryl chloride,
+parenthesis, SO2Cl2, blah,
+
+blah, blah.
+
+OK?
+
+So sulfuryl chloride.
+
+I want to put up the Lewis
+
+structure of sulfuryl chloride.
+
+So center the element with the
+lowest average valence
+
+electron energy.
+
+So it turns out that the average
+valence electron
+
+energy stack like this.
+
+Sulfur is the lowest, then
+chlorine, and then oxygen.
+
+This is this ranking of average
+
+valence electron energies.
+
+And you'd be given those data.
+
+So it says put sulfur
+in the center.
+
+So I'll put sulfur
+in the center.
+
+And then what does it say?
+
+We're going to count all
+the valence electrons.
+
+So sulfur over here
+is 3s2 3p4.
+
+So that gives me six
+valence electrons.
+
+And there's two oxygens.
+
+And oxygen lies above sulfur,
+so that's 2s2 2p4.
+
+So that's 2 times 6.
+
+So that's 12.
+
+All right?
+
+Let's put the 6 over here.
+
+And then there's chlorines
+in this compound,
+
+so that's 3s2 3p5.
+
+So that's 5 plus 2 is
+7, 2 times 7 is 14.
+
+And we add this whole
+thing up, we get
+
+there's 32 valence electrons.
+
+And draw a single bond from each
+surrounding atom to the
+
+central atom.
+
+All right.
+
+Again, this is a model.
+
+I'm not saying that this is the
+shape of the molecule, but
+
+it's a way to count.
+
+All I'm doing is trying
+to keep track of
+
+bonds and paired electrons.
+
+So I can put chlorine
+on either side.
+
+And I'll put an oxygen below
+and an oxygen above.
+
+All right.
+
+So that's already two,
+four, six, eight.
+
+So I'm losing eight.
+
+So 32 minus 8 is 24.
+
+And so with the 24 that means
+I've got 12 pairs of
+
+electrons to place.
+
+So let's start putting the
+Lewis structures up.
+
+So chlorine consists
+of one, two, three,
+
+four, five, six, seven.
+
+And I'll do the same thing
+on the other side.
+
+Two, four, six, seven.
+
+And oxygen has six, so that's
+two, four, six.
+
+And then the lower
+one, same thing.
+
+Two, four, six.
+
+And sulfur has six.
+
+I'm going to use
+x's for sulfur.
+
+So I'll put one x with
+the chlorine,
+
+another x with the chlorine.
+
+Two with the oxygen, two
+with the oxygen.
+
+And so now we're in pretty
+good shape, right?
+
+We can identify bonding and
+nonbonding domains.
+
+Here's the bonding.
+
+One, two, three, four.
+
+And then the nonbonding.
+
+Looks like there's 12.
+
+And sure enough, 1, 2, 3, 4,
+5, 6, 7, 8, 9, 10, 11, 12.
+
+The 12 nonbonding domains.
+
+4 bonds.
+
+And we have the Lewis
+structure for
+
+this particular compound.
+
+And one last little piece
+worth pointing out.
+
+Notice that in the bonds to
+the chlorine you have two
+
+electrons, as you need.
+
+One electron comes from the
+chlorine and one electron
+
+comes from sulfur.
+
+But in the bonds between the
+sulfur and the oxygen the
+
+sulfur's so desperate to form
+a bond that it actually
+
+donates both electrons
+to the bond.
+
+And oxygen's happy because it's
+isoelectronic with neon,
+
+and sulfur's happy because it's
+going to be isoelectronic
+
+with argon.
+
+But, you know, it has to
+go to some lengths.
+
+So this is called a dative bond,
+when both electrons come
+
+from the one element.
+
+OK.
+
+Well, this is great.
+
+I'm going to do one more.
+
+How about methane?
+
+CH4.
+
+So I'm going to start
+with carbon.
+
+Carbon's going to go
+with this on there.
+
+And a carbon is 2s2 2p2.
+
+And so I'm going to use
+the box notation now.
+
+See, this is the Lewis
+structure, this is chemical
+
+equation, now we're going
+to a box structure.
+
+We can move fluidly from
+one model to another.
+
+We had cubes up there.
+
+It's all good.
+
+So this is 2s.
+
+And now this is 2px,
+2py, and 2pz.
+
+Now according to this,
+2s2, that gives
+
+me an electron pair.
+
+And now I've got 2p2, which
+according to the Hund rule
+
+goes in like this.
+
+Well I've got a problem here.
+
+How many unpaired electrons?
+
+Two.
+
+Now what's my maximum number
+of bonds I can form by
+
+electron sharing?
+
+It's two according to this.
+
+So the best I can do, best
+possible here, is CH2.
+
+And that's no good.
+
+We know from mass measurements
+it's CH4.
+
+The stoichiometry's CH4.
+
+And besides, what are these
+orbitals going to look like?
+
+These are the p orbitals, so
+they're dumbbell-shaped and
+
+they're orthogonal, right?
+
+They're 90 degrees, which means
+if I formed this thing--
+
+which is called methylene--
+
+if I form methylene I'd end up
+with CH2 looking like this,
+
+which has a dipole moment.
+
+And we know from spectral
+measurements and electrical
+
+properties measurements that
+this thing is symmetric.
+
+So this thing--
+
+electron sharing
+isn't working.
+
+It's not working.
+
+So we need another patch here,
+and that patch comes from none
+
+other than Linus Pauling.
+
+Another American.
+
+You see, it's American science
+today and it's in the 20s.
+
+That's why we have Gershwin
+playing at the beginning.
+
+Celebration of American
+science.
+
+So Pauling was born in
+Portland, Oregon.
+
+He was the son of a pharmacist.
+And he went to
+
+Caltech, got his PhD in 1925.
+
+So the Rhapsody in Blue came out
+in 1924 when he was just
+
+hunkering down to his thesis.
+
+Probably listened to it, got
+some pleasure out of it, as
+
+most people did.
+
+So then he finishes, 1925, at
+Caltech in Pasadena and he
+
+goes to Europe.
+
+Now he chose wisely.
+
+He chose four postdoctoral
+positions.
+
+These are people he
+postdoc'd with.
+
+First with Sommerfeld, then
+with Bohr, then with
+
+Schrodinger, and then
+finally with Bragg.
+
+You'll learn about Bragg.
+
+Bragg got the Nobel Prize
+for X-ray diffraction.
+
+So that's not a bad
+preparatory start.
+
+So he comes back and
+teaches at Caltech.
+
+In fact, I have a picture
+of Linus Pauling.
+
+There he is.
+
+That's a middle-aged Linus
+Pauling, probably around the
+
+time he got the first
+of two Nobel Prizes.
+
+So what did Pauling do?
+
+Pauling said, why don't
+we mix the orbitals?
+
+They're all in the shell n
+equals 2, and what we're
+
+trying to do is to fill
+the n equals 2 shell.
+
+So how about mix?
+
+Let's mix 2s and 2p states
+in order to maximize
+
+the number of bonds.
+
+Remember, when you form a
+bond you decrease the
+
+energy of the system.
+
+Four bonds is a greater
+decrease in
+
+energy than two bonds.
+
+So the system, if it could--
+
+and they're all within
+the same shell.
+
+You notice he didn't say, gee,
+if mixing 2s with 2p is good
+
+let's go get some 1s.
+
+Well 1s is down in n equals
+1, and there's
+
+no way you can mix.
+
+They had to be in
+the same shell.
+
+Mix states in order to
+maximize number of
+
+bonds that can form.
+
+It's all about maximize
+the number of
+
+bonds that can be formed.
+
+And this, of course, is
+by electron sharing.
+
+We're talking about covalent
+bonds here.
+
+OK?
+
+And he termed these mixed
+orbitals "hybrids." Termed the
+
+mixed orbitals as "hybrid
+orbitals." They're
+
+cross-breed--
+
+part s, part p.
+
+So now let's look at the
+energy level diagram--
+
+or the box notation.
+
+Forgive me.
+
+So I'm going to mix s and p.
+
+So I've got a single s and I've
+got three p's, so this is
+
+called sp3.
+
+Each one of these is a mixed
+sp3 hybrid orbital.
+
+And I've got four of them.
+
+And how many electrons
+do I have?
+
+Four.
+
+So now I use the Hund rule
+and in go the electrons.
+
+One, two, three, four.
+
+And now I have the ability
+to form four bonds.
+
+But it gets better.
+
+Here's the next thing.
+
+These are degenerate.
+
+They're all in the same state.
+
+That's why we're using
+the Hund rule.
+
+And so degeneracy in energy
+implies degeneracy in spatial
+
+orientation.
+
+So what does that mean?
+
+It means that if these are four
+bonds equivalent, then
+
+the way those bonds will arrange
+themselves in space is
+
+to be equivalent.
+
+So if I've got a central carbon
+here and I'm going to
+
+put four sticks from the central
+carbon so as to make
+
+the four sticks symmetrically
+disposed in space, that
+
+dictates the architecture
+of the molecule.
+
+And how do I put four sticks
+off of a central point
+
+symmetrically disposed
+in space?
+
+One, two, three, and four.
+
+This is meant to be the corners
+of a tetrahedron.
+
+Each one of these is
+109 degrees apart.
+
+And this describes
+a tetrahedron.
+
+So now I've got carbon in the
+center, and now I've got the
+
+hydrogens at the four corners
+of a tetrahedron.
+
+There is the structure
+of methane.
+
+And each of the hydrogens has
+a shared electron with the
+
+carbon, making it isoelectronic
+with helium.
+
+And the carbon has four of its
+own electrons, four shared
+
+with the four hydrogens
+to make it
+
+isoelectronic with neon.
+
+So everybody's happy.
+
+Shell filling, and
+it's all good.
+
+So now it's symmetric and it
+has no net dipole moment.
+
+Everything squares
+with the data.
+
+Well, good for Pauling.
+
+But he went further.
+
+He went much further.
+
+What Pauling wanted to do was
+to make it quantitative.
+
+And so he wanted to have
+something analogous in
+
+covalent bonding to what we
+have in ionic bonding.
+
+So what Leslie is now rubbing
+off the board there is--
+
+no, keep going.
+
+It's good.
+
+It's OK.
+
+This is a rule of academics:
+You always erase that which
+
+you will refer back to.
+
+We need more boards in here.
+
+How many boards do I
+fill in a period?
+
+9, 18?
+
+Maybe what?
+
+We need about 24 boards.
+
+That's a good lecture.
+
+All right.
+
+So here's what Pauling
+was thinking about.
+
+He was thinking about the
+analogy, for example, if I
+
+want to get the energy of
+magnesium oxide I can use the
+
+formula that Leslie has
+just erased, and
+
+it looks like this.
+
+So if all I need to know is the
+radius of the anion, the
+
+radius of the cation, it's
+charge, and the Madelung
+
+constant and then I just
+plug in, I get the
+
+crystallization energy.
+
+But then suppose instead of
+magnesium oxide I want to go
+
+to magnesium chloride.
+
+I can use the same formula
+only I need
+
+the Madelung constant.
+
+This is the Madelung constant
+for magnesium oxide.
+
+If I have the Madelung
+constant--
+
+forgive me, script M--
+
+for magnesium chloride, and
+I know the ionic radius of
+
+magnesium cation and chloride
+anion, away I go again.
+
+I need this.
+
+I need, of course, the
+Born exponent.
+
+This Born exponent
+and away we go.
+
+The same formula applies.
+
+So I can build with a library
+of basic physical data.
+
+So what did Pauling do?
+
+Pauling said, what if we
+can do the same thing
+
+for covalent bonds?
+
+Is there some kind
+of an analogy?
+
+So he said, let's take a
+look at an arbitrary
+
+heteronuclear compound.
+
+So I'm going to do this with
+HF, hydrogen fluoride.
+
+So, first of all, let's build a
+hydrogen fluoride molecule.
+
+H with its one electron, and
+fluorine with its seven.
+
+So now hydrogen sharing an
+electron with fluorine is
+
+isoelectronic with helium.
+
+It's happy.
+
+And fluorine sharing the
+electron hydrogen is
+
+isoelectronic with neon.
+
+It's happy.
+
+So again we see shell filling
+by electron sharing.
+
+So what Pauling wanted to ask
+is, can I get a measure of the
+
+HF bond energy knowing
+only the bond
+
+energies of H-H and F-F?
+
+So then if I knew all the
+homonuclear bond energies and
+
+then I mixed these to make
+heteronuclear bonds, is there
+
+a path from homonuclear
+bond energy to
+
+heteronuclear bond energy?
+
+So let's look and see what
+the numbers are.
+
+So hydrogen.
+
+The hydrogen bond's
+fairly strong.
+
+It's 435 kilojoules per mole.
+
+That's mole of bonds.
+
+435.
+
+Fluorine-flourine is 160.
+
+And so what do you think
+the value of the
+
+H-F bond should be?
+
+Well when I first look at this
+I say, well it's part H and
+
+it's part F, so it's somewhere
+between 435 and 160.
+
+I don't know if it's the
+arithmetic mean--
+
+you know, add these two and
+divide by two-- or maybe it's
+
+the geometric mean--
+
+multiply them together and
+take the square root--
+
+but it's got to be somewhere
+in between.
+
+What do the data show?
+
+The number's 569, which
+is greater than 435.
+
+So I take a bond of 435 and
+a bond of 160, I put them
+
+together I get 569.
+
+That's very, very strange.
+
+But Pauling was smart.
+
+Pauling said, I have
+an explanation.
+
+He says, suppose when these
+electrons are shared in
+
+between the two atoms, suppose
+they're not shared equally.
+
+Suppose there is a displacement
+of the electrons.
+
+So instead of putting them
+dead center, as I've been
+
+doing up until now, suppose
+the electrons are actually
+
+drawn closer to the fluorine.
+
+So we still have octet
+stability, or in this case
+
+duet stability, but
+the sharing of the
+
+electrons is not equal.
+
+So this is charge
+displacement.
+
+And what does charge
+displacement constitute?
+
+Well, charge displacement
+means stored energy.
+
+And Pauling quantified
+that stored energy.
+
+And so what he did is he said
+that you increase the bond
+
+strength by thinking of it
+as a two-step reaction.
+
+So in the heteronuclear bond
+that is a bond between two
+
+different atoms. So in a
+heteronuclear bond we form by
+
+what-- and this is my coinage,
+you don't see this
+
+anywhere in the book--
+
+two-step, share and then pull.
+
+So share is, as the name
+implies, we share electrons to
+
+achieve octet stability.
+
+But then because we have unequal
+atoms we pull towards
+
+one of the atoms. And which
+one do we pull towards?
+
+Well, we pull towards the one
+that's got a greater appetite
+
+for electrons.
+
+And we've already gone
+through this concept.
+
+Which atoms on the periodic
+table have the highest
+
+appetite for electrons?
+
+The nonmetals.
+
+The weakest appetite
+is the metals.
+
+The metals are good donors, the
+
+nonmetals are good acceptors.
+
+And fluorine's up in the top
+right corner, so fluorine has
+
+a very, very high appetite
+for electrons.
+
+And, indeed, in this bond
+the electrons are
+
+pulled to the right.
+
+And why Pauling got the Nobel
+Prize and Lewis didn't-- it's
+
+my theory-- is that Pauling
+was quantitative.
+
+So he came up with a
+quantitative measure.
+
+He devised a quantitative
+measure for the degree of
+
+unequal sharing, thereby
+allowing us to make these
+
+calculations with
+some accuracy.
+
+And he called that quantity
+electronegativity, and it's
+
+denoted by the Greek
+symbol chi.
+
+OK?
+
+And he devised a whole scale.
+
+How did he get the scale?
+
+He looked at bond energies for
+all sorts of pairs of elements
+
+across the periodic table and
+went through an exercise with
+
+pencil and paper that today we
+would call multivariable
+
+regression analysis.
+
+And came with a set of--
+
+[SLIDE APPEARING]
+
+PROFESSOR: Oh, I'll
+come back to this.
+
+This is the structure
+of methane.
+
+This is the s and p.
+
+Oh, let's take a break.
+
+You can stack.
+
+All right.
+
+So this is what methane
+looks like.
+
+There's the s, there's the p.
+
+And the sp hybrid
+looks like this.
+
+It's sort of an asymmetric
+dumbbell.
+
+And these four things
+stick out.
+
+And then you bond the hydrogens
+
+and there's the methane.
+
+OK.
+
+So here's what the
+
+electronegativity scale looks like.
+
+It looks a lot like the
+scale for average
+
+valence electron energies.
+
+The nonmetals have the highest
+appetite for electrons period,
+
+which means in a bond they're
+going to hog the electrons.
+
+And the nonmetals have the
+weakest appetite, and so
+
+they're going to end up having
+the electrons in a covalent
+
+bond pulled away from them.
+
+So nonmetals have high
+electronegativity, metals have
+
+low electronegativity.
+
+And now here's taken
+from the text.
+
+And you see that the
+electronegativity is periodic.
+
+If you go across a period the
+metal has the lowest value and
+
+the nonmetal has the highest.
+And there's fluorine, number
+
+nine, at a value of about 4.
+
+It's got the most intense
+appetite for electrons.
+
+And then you jump down here to
+sodium, et cetera, et cetera.
+
+Here we are going across the
+lanthanides and whatnot.
+
+And this is taken
+from your text.
+
+There's fluorine, 3.984.
+
+That's the thing.
+
+And down here we have very low
+values of electronegativity.
+
+So with electronegativity
+we are now able to make
+
+calculations.
+
+And this is the Pauling formula
+for calculating the
+
+bond energy in a heteronuclear
+bond starting from homonuclear
+
+bond energy.
+
+So let's continue with the HF.
+
+So if I want to get the
+bond energy of HF
+
+I'm going to take--
+
+and this is the Pauling
+formula--
+
+the geometric mean.
+
+So I take the bond energy of
+hydrogen-hydrogen times the
+
+bond energy of
+
+fluorine-fluorine, and square root.
+
+So that's the geometric
+mean of the two.
+
+And then comes the Pauling
+piece that gets
+
+him the Nobel Prize.
+
+You take the difference in the
+electronegativity between the
+
+two elements squared, and then
+the factor 96.3 gives us the
+
+unit consistency with
+kilojoules per mole.
+
+So the greater the difference
+in electronegativity the
+
+greater the contribution here in
+terms of the deviation from
+
+just the geometric mean of the
+two homonuclear bond energies.
+
+Or put another way, if you have
+a homonuclear atom such
+
+as H2, if it's chi H minus chi
+H is 0, so this second
+
+term goes to 0.
+
+And obviously when fluorine is
+one of the members you're
+
+going to get a very, very
+high number, because
+
+this has the most--
+
+and it doesn't matter which
+order you put them in because
+
+you're taking the square,
+so it's always
+
+going to come out positive.
+
+And I want you to appreciate the
+sense of scale here, so if
+
+we go in here we'll multiply.
+
+This is going to be
+435 times 160.
+
+And I'm going to take the
+square root of this.
+
+And then this is 96.3.
+
+And you look on your
+periodic table
+
+this is 2.2 for hydrogen.
+
+Fluorine is 3.98.
+
+And I know there are different
+tables of electronegativity.
+
+I don't care.
+
+Just whatever you've got
+on your periodic table.
+
+The one in the book is a little
+bit different but it
+
+all comes out in the wash.
+
+So you multiply all this out,
+and we find that the first
+
+term is 264 kilojoules
+per mole and the
+
+second term is 344.
+
+So this second term is even
+greater than the first term.
+
+So the amount of energy in that
+electron displacement is
+
+substantial.
+
+And if you sum the two
+of these you get 608.
+
+Now you might say, well
+wait a minute.
+
+The real number is 569.
+
+But 608 takes you in the right
+direction and accounts for the
+
+contribution of electron
+displacement.
+
+264 is just plain wrong.
+
+So this was an important
+start for Pauling.
+
+And he has labels on these
+two contributions.
+
+This first term, which is just
+the combination of the
+
+homonuclear bond energies, is
+called purely covalent.
+
+It's the purely covalent
+contribution.
+
+And it's what I've been
+referring to as the sharing.
+
+This is what you get
+from sharing.
+
+OK?
+
+And then this second term here
+with the difference in
+
+electronegativity is what you
+get from what I've been
+
+calling the pull on
+the electron pair.
+
+And Pauling called this the
+partial ionic character.
+
+He's not saying that there's
+electron transfer, but it's a
+
+move in that direction.
+
+Partial electronic character.
+
+So what I've done here is I've
+decided I'll make a sort of a
+
+panorama of what we've
+seen up until now.
+
+And so I'm going to make
+something called the electron
+
+sharing meter.
+
+All right.
+
+So if I look at a homonuclear
+system like hydrogen.
+
+So my meter reads neutral.
+
+So the arrow's at 12 o'clock.
+
+The electrons are
+shared equally.
+
+And then if I go to
+HF what do I have?
+
+Well, I know that the fluorine
+is pulling the electrons.
+
+And so we can designate that by
+writing delta minus, delta
+
+plus. delta the physicists
+use.
+
+The lowercase Greek delta
+means little bit of.
+
+All right?
+
+So delta minus means it's
+a little bit negative.
+
+And we've got charge neutrality,
+so if the fluorine
+
+end is a little bit negative
+then the hydrogen end has to
+
+be a little bit positive, which
+means this thing has a
+
+net dipole moment.
+
+It's a dipole.
+
+And the arrow points to
+the negative end.
+
+One way to think about it is I
+put a little slash there and
+
+that starts to look a little
+bit like a plus sign.
+
+You can come up with your
+own way to remember it.
+
+So it's got a little bit
+of a dipole moment.
+
+And people depict dipoles
+usually as ovals, and they'll
+
+put a minus end and
+a plus end.
+
+So it's net neutral but the
+charge is not uniformly
+
+distributed.
+
+OK?
+
+So our sharing meter in this
+case is going to show
+
+something to the right.
+
+We've got electrons that are
+unequally shared, and that
+
+moves over to the right.
+
+And, you know, the dipoles have
+interesting properties.
+
+Oh, there's a plot of
+electronegativity
+
+3-bar in the bar plot.
+
+And actually this is
+an interesting one.
+
+Just parenthetically, you
+see hydrogen here?
+
+Hydrogen's weird.
+
+They put it in the periodic
+table above lithium but it's
+
+not an alkaline metal.
+
+And you can see it just
+doesn't belong there.
+
+And there's a lot of
+conversation about putting it
+
+maybe somewhere centered above
+the p block elements, because
+
+it certainly doesn't belong
+next to helium.
+
+But it probably doesn't belong
+above lithium either.
+
+Anyway, I thought that
+was very interesting.
+
+I can tell from the
+response of the
+
+class, why does he care?
+
+[LAUGHTER]
+
+PROFESSOR: All right.
+
+Now this is really--
+
+I'm going to use an
+adverb here--
+
+this is really important.
+
+All right?
+
+So here's HCl, is a cousin of
+HF, and you see in the upper
+
+frame it's just a bunch of HCl
+molecules just bopping around
+
+any which way.
+
+So there's the delta plus
+and the delta minus.
+
+Now if you take these dipoles
+and you put them in an
+
+electric field they will align
+themselves, and the positive
+
+ends will face the negative
+plate and the negative ends
+
+will face the positive plate.
+
+And there's energy stored when
+the random orientation goes
+
+into an ordered orientation.
+
+This is the principle
+behind a capacitor.
+
+A capacitor is nothing
+more than a whole
+
+bunch of aligned dipoles.
+
+So if you want to invent a
+supercapacitor that we can use
+
+on a car to extend the range
+of the automobile so we can
+
+reduce our dependence on
+imported petroleum, you're
+
+going to look for molecules
+that have a
+
+honking big dipole moment.
+
+That way you get more energy
+per unit electric field.
+
+So, again, a simple idea that
+tells me how to go and invent.
+
+I can go back to my office and
+go and invent something right
+
+now just based on
+this lecture 9.
+
+[LAUGHTER]
+
+PROFESSOR: See, you
+go and invent.
+
+You start the company,
+you make the billion.
+
+Remember good old Professor
+Sadoway at MIT, and
+
+established the fellowship
+for students, and so.
+
+All right.
+
+But you have to know what
+a dipole moment is.
+
+Got to know what a
+dipole moment is.
+
+OK.
+
+So there's the dipole moment.
+
+And then lastly I'm going
+to put sodium chloride.
+
+So what's sodium chloride
+look like?
+
+Well it's Na plus
+and Cl minus.
+
+So the electron has transferred
+completely.
+
+So this isn't even
+sharing at all.
+
+So this is really
+bury the needle.
+
+This is not sharing.
+
+In this instance the sodium
+doesn't even get visitation
+
+rights to the electron.
+
+The electron's gone.
+
+Whereas here hydrogen gets to
+see the electron on Saturdays
+
+kind of thing.
+
+Depends what kind of lawyer
+fluorine had.
+
+That's what it all
+boils down to.
+
+All right.
+
+This is the same thing that
+I just showed you.
+
+But you see, the textbook
+gives you, as the name
+
+implies, dense text.
+
+I gave you the sharing meter.
+
+The sharing meter is far
+more expositive.
+
+All right.
+
+And then, finally, the percent
+ionic character is given by
+
+this formula here.
+
+So this is 1 minus
+the exponential.
+
+So the exp term, this
+exponential of-- what is it--
+
+minus 1/4 times the
+difference in
+
+electronegativities squared.
+
+This notation means e base
+natural logarithms, minus 1/4,
+
+blah, blah, blah.
+
+That's what this thing is.
+
+So if you plug in, multiply by
+100% you get something that
+
+goes from 0 to 100.
+
+So obviously when delta
+chi is 0 you get 0%.
+
+e to the 0 is 1, 1 minus
+1 is 0, and so you
+
+have no ionic character.
+
+And so if you plug in
+the numbers for HF--
+
+so you're going to take this
+difference here, square it--
+
+it ends up giving you 1.8, which
+gives you a value of
+
+about 56% ionic character.
+
+So it's as though the electron
+is sort of half transferred.
+
+But you might also look at
+it from this perspective.
+
+If you take 344--
+
+because this is the partial
+ionic character, which is the
+
+energy of electron displacement
+over the total
+
+energy in the calculation--
+
+that turns out to be 57%.
+
+So this stuff makes sense.
+
+There's a sensible metric
+here at work.
+
+And so this is what Linus
+Pauling got his Nobel Prize
+
+for, and it's the description
+of polar covalency.
+
+And polar covalency is operative
+when you have
+
+heteronuclear bonds, because
+the two different elements
+
+don't share the electron
+equally.
+
+And the Pauling formula allows
+you to calculate that.
+
+And his formative book was
+written in 1937, called The
+
+Nature of the Chemical Bond.
+
+OK.
+
+So turning to the last five
+minutes, I want to bring to
+
+your attention some covalent
+molecules.
+
+Today we're going to
+talk about Freon.
+
+Freon was an invention, it was
+a designer chemical, invented
+
+by Thomas Midgley.
+
+This is me.
+
+I named him "sp3." That's
+his nickname.
+
+Thomas sp3, for the hybridized
+orbital.
+
+So he was working at the
+Dayton engineering
+
+laboratories in Dayton, which
+was owned by General Motors,
+
+and he was working in the 20s
+at a time when there were no
+
+refrigerators in American
+kitchens.
+
+The only refrigerants that were
+used were either toxic or
+
+flammable, things like ammonia,
+methyl chloride,
+
+sulfur dioxide.
+
+And you read about horrible
+accidents.
+
+People making ice cream at some
+plant and the compressor
+
+blows up and two or three
+people are killed.
+
+So it was deemed unsafe in
+the American kitchen.
+
+In the 20s Midgley discovered
+this molecule, which looks
+
+just like methane only we've
+replace the hydrogens with two
+
+chlorines and two fluorines.
+
+So this is called
+dichlorodifluoromethane and
+
+it's a chlorofluorocarbon,
+a CFC.
+
+And this was fantastic stuff.
+
+It it was colorless, odorless,
+tasteless, non-toxic.
+
+It was not just used as a
+refrigerant, it was used in
+
+propellant.
+
+When I was your age all
+of the sprays--
+
+whether it was hair spray,
+shaving cream, any aerosol--
+
+was propelled by Freon-12.
+
+It was fantastic stuff.
+
+Well, it turns out that in
+the upper atmosphere--
+
+you know, you go pss pss pss.
+
+You got people all over the
+world doing this, eventually
+
+this stuff starts
+floating away.
+
+And what turns out in the upper
+atmosphere where we
+
+don't have shielding
+from ultraviolet--
+
+you know how to do this
+calculation, because you can
+
+look up the energy.
+
+And, in fact, it's part of your
+homework, where you look
+
+at the energy differences and
+the electronegativity
+
+differences, you can compute the
+wavelength of light that's
+
+capable of breaking the
+carbon-chlorine bond.
+
+And it turns out to be
+in the ultraviolet.
+
+Once the chlorine is broken you
+have a chlorine radical,
+
+and that chlorine radical goes
+over here and attacks ozone.
+
+[CELL PHONE RINGING]
+
+PROFESSOR: Cell phone--
+
+out.
+
+Just get up and leave
+out of courtesy.
+
+[CELL PHONE STILL RINGING]
+
+[LAUGHTER]
+
+PROFESSOR: Hello?
+
+The first year I was teaching
+3.091 there was a Nobel Prize
+
+awarded to Mario Molina, who was
+a faculty member here in
+
+Earth and Planetary Sciences who
+had worked years earlier
+
+at University of California,
+Irvine, and had speculated on
+
+the mechanism by which ozone
+depletion occurs and linked it
+
+to rising levels of CFCs.
+
+Initially--
+
+that's why it says
+a vindication--
+
+people pooh poohed it,
+said it was crazy.
+
+There wasn't enough of this pss
+pss to cause any trouble.
+
+But then later with the NASA
+program they started taking a
+
+lot of images and they could
+track ozone levels in the
+
+atmosphere and start seeing
+that not only was ozone
+
+changing but there were actually
+pockets where ozone
+
+was being depleted at an
+accelerating rate-- because
+
+obviously the atmosphere isn't
+constant composition and
+
+constant temperature.
+
+Duh.
+
+So anyways, yeah.
+
+There he is.
+
+And this was the paper that was
+
+published in 1974 in Nature.
+
+And this was done before
+computers.
+
+The PC wasn't invented
+and commercialized
+
+until the early 80s.
+
+So this was typeset, and the
+person who typeset it
+
+obviously didn't take 3.091
+because instead of "atom"
+
+hyphen "catalysed" we have
+"atomc-atalysed." But even
+
+ignoring the spelling error in
+a Nobel Prize winning paper--
+
+[LAUGHTER]
+
+PROFESSOR: --the Nobel committee
+overlooked this.
+
+Yeah.
+
+So there it is.
+
+And then they went to
+HFCs and so on.
+
+There's a lot of activity
+in this.
+
+And what happened is when we
+changed from CFCs to HFCs we
+
+had to change the design
+of the compressors.
+
+And what happened was
+everything got
+
+much, much more efficient.
+
+So this was an example of
+necessity for a change that
+
+was driven by concern
+for the environment.
+
+Instead of putting people out
+of work and killing an
+
+industry, gave us much more
+efficient refrigeration.
+
+And the last thing I'll
+show you is this
+
+to draw your attention.
+
+This was in your textbook.
+
+This is the cap at the top of
+the Washington Monument.
+
+The Washington Monument was
+built to celebrate the
+
+American centennial, 1876.
+
+They finished it in 1884.
+
+And this is 100 ounces of
+aluminum, because aluminum was
+
+a precious metal.
+
+It was priced higher
+than silver.
+
+1884.
+
+Two years later Charles Martin
+Hall and Paul Heroult invent
+
+an electrochemical process
+that drives the price of
+
+aluminum down to the point
+that we make beer cans--
+
+I mean soda cans--
+out of it today.
+
+[LAUGHTER]
+
+PROFESSOR: And a good example of
+how chemical innovation can
+
+lead to superior products.
+
+I'll see you on Wednesday.
\ No newline at end of file
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new file mode 100644
index 0000000000000000000000000000000000000000..f77b6fedf07553d02870d140ae9c00b628971550
--- /dev/null
+++ b/usWjdV0-Jg0.txt
@@ -0,0 +1,3870 @@
+PROFESSOR: Today we begin the
+third major part of the class.
+
+We've done paper
+folding, linkage folding,
+
+and now we're going to
+do polyhedron folding.
+
+The very last topic we
+did was hinged dissection,
+
+which is somewhere in the
+middle of all these things.
+
+But with polyhedron
+folding, we're
+
+thinking about a two
+dimensional surface
+
+in 3D, something like
+a cube, and we're
+
+interested in cutting along
+the edges of that shape
+
+or somehow cutting along
+the surface-- that's
+
+a good cutting-- and then
+unfolding into some flat shape.
+
+So this is a standard cross
+unfolding of the cube.
+
+This is the unfolding process,
+and of course the reverse
+
+is the folding process, and
+both of them are interesting.
+
+We're going to start
+thinking about unfolding.
+
+That's one of the most
+practical problems here.
+
+You really want to build some
+3D shape out of sheet material.
+
+What shape do you
+cut out in order
+
+to bend it into that surface?
+
+So you start with the surface.
+
+You need to figure out where
+to cut so that when you unfold,
+
+you get something
+that has no overlap.
+
+If you want to make
+it from one sheet,
+
+it shouldn't have any overlap,
+and ideally just one piece
+
+because then you have to do
+less welding or edge joining
+
+to make that surface.
+
+So today and the
+next couple lectures
+
+will be all about unfolding,
+and then eventually we
+
+will turn to the reverse
+problem, folding problem.
+
+And there are two
+kinds of unfolding.
+
+The one that I just
+drew is an edge
+
+unfolding because it
+only cuts along edges.
+
+Edge unfolding only cut
+along edges of the surface.
+
+This property is nice.
+
+If you're building
+something, you
+
+don't want to have
+visible seems.
+
+You have to be
+bent at the edges,
+
+so it's not such a big
+deal if you're also
+
+fusing along an edge.
+
+But in general, you could
+imagine cutting anywhere
+
+on the surface, and
+this is an example
+
+where the solid red
+lines are cutting
+
+on what you see and the
+dotted red lines were
+
+cutting on the backside.
+
+And when you unfold that thing,
+you get this stoplight polygon,
+
+and this is what we call a
+general unfolding, or just
+
+unfolding.
+
+There you can cut anywhere.
+
+In both cases, we want
+one piece, no overlap,
+
+but you can change where
+you're allowed to cut.
+
+So those are the
+rules of the game,
+
+or two possible
+rules of the game.
+
+And let me tell you what's
+known about these kinds
+
+of unfoldings.
+
+I've mentioned it way
+back in lecture one.
+
+so we can think
+about edge unfolding,
+
+we can think about
+general unfolding,
+
+and we can think about
+them for convex polyhedra--
+
+simple things like the
+cube have no dents--
+
+or general polyhedra,
+non-convex polyhedra.
+
+And status is these
+two corners are open.
+
+This one is solved.
+
+It can always be done.
+
+You can always generally
+unfold a convex polyhedron,
+
+but we don't know about
+general polyhedra.
+
+Edge unfolding of
+convex polyhedra,
+
+we don't know whether
+it's possible,
+
+but for non-convex
+polyhedra, we know
+
+that's too much to hope for.
+
+Not always possible.
+
+Both of these questions
+could go either way,
+
+but we know in various
+generalizations, easy case
+
+of convex polyhedra general
+unfolding, we can do it.
+
+The most restrictive,
+hardest situation
+
+is edge unfolding
+non-convex polyhedra.
+
+That's too much.
+
+But each of these
+things, we don't know.
+
+And these are some of the
+biggest open questions
+
+remaining in geometric folding
+algorithms, this field.
+
+I'm going to talk mostly
+about these three things
+
+today, so this open problem
+and these two results.
+
+And then this topic will
+essentially be next lecture.
+
+Obviously it's not solved, but
+we still have a lot to say.
+
+There are various
+partial results
+
+toward solving both
+of those problems,
+
+I would say more on this one.
+
+This one is five centuries old.
+
+This one is one
+decade old or so.
+
+So I need to set the stage
+a little bit before I
+
+can talk about any
+of these things,
+
+so let me start with a
+little bit of terminology.
+
+We've in some sense talked
+about curvature before.
+
+I don't think I gave
+it this name, though,
+
+in the context of origami.
+
+And I use it almost
+subconsciously
+
+so it's good for
+me to define it.
+
+If you have some vertex
+on your polyhedron.
+
+Let's say we're looking
+at a corner of a cube,
+
+so this has three 90 degree
+angles coming together.
+
+You sum those
+angles, we get 270,
+
+and then you take
+360 minus that sum,
+
+and that is your curvature.
+
+This is going to be 90.
+
+And what I really care about
+is whether the curvature
+
+is positive, 0, or negative.
+
+Positive curvature, which
+is what we got here--
+
+this is plus 90-- is
+like a convex cone.
+
+So if you're thinking about
+convex polyhedra, which
+
+is one of the situations
+we care about,
+
+you'll always get positive or
+0, maybe, curvature vertices,
+
+depending on what
+you're thinking about.
+
+Zero, this is like
+a piece of paper,
+
+so this is what you might call
+flat, but it's locally flat.
+
+It could be drawn
+flat or we know
+
+how to fold pieces of paper.
+
+You never change the curvature.
+
+The sum of the
+instant face angles
+
+will always stay the same, no
+matter how you fold this thing.
+
+Curvature is an invariant.
+
+If you just think locally and
+forget about the actual folding
+
+of the thing, it's kind of flat.
+
+So you can think of this
+as a piece of paper.
+
+We talked about
+these two situations
+
+in the context of Kawasaki's
+theorem way back when.
+
+Kawasaki's theorem
+applied for both
+
+of these for the negative
+curvature case, which
+
+is when you have lots
+of material all joined
+
+at a single point,
+something like this.
+
+Then Kawasaki's theorem
+changed a little bit.
+
+There were some other
+cases that could happen.
+
+So when you have
+tons of material,
+
+this can only happen in
+a non-convex polyhedron.
+
+That's sort of the point.
+
+If you're a convex
+polyhedron, you
+
+know you have to have
+only these two situations.
+
+Where do you get flat vertices?
+
+Well, if you think of
+this point as a vertex
+
+and you add up all the angles
+around it, well, that's 360.
+
+360 minus 360 is 0.
+
+So you have zero curvature on
+all the faces and on the edges.
+
+Also, if you look here,
+you have 180 and other 180.
+
+That adds to 360.
+
+And then at the actual
+vertices, that's
+
+where you have positive
+curvature for a convex
+
+polyhedron.
+
+So just some terminology.
+
+Get used to the idea of positive
+curvature, zero curvature,
+
+and negative curvature.
+
+Then we have the
+idea of a cutting.
+
+So cutting is just,
+what edges do you cut?
+
+It's the red stuff
+in this picture.
+
+What edges do you cut
+in order to unfold?
+
+So this is an unfolding, the
+mapping here, but the red part,
+
+I'll call it cutting.
+
+Sometimes it's also
+called an unfolding,
+
+but that can be a
+little confusing.
+
+The main point here is I want
+to talk about what constraints
+
+cutting must satisfy in order
+to be valid so we can just
+
+get a sense of what
+is happening here.
+
+If you look at these pictures,
+you can see two properties.
+
+One is that the cuttings
+visit all the vertices
+
+of the polyhedron.
+
+So there's this red stuff.
+
+The red stuff is connected.
+
+It's acyclic, so it's actually
+a tree in these pictures,
+
+and it's visiting
+all the corners.
+
+Even back here, it's
+visited on the back.
+
+Is that always true?
+
+Most of those properties
+are mostly true,
+
+but it depends a little bit.
+
+One thing that is
+sure is the cutting
+
+must span all non-zero
+curvature vertices.
+
+But I do have to say
+"non-zero curvature." "Spans"
+
+just means visits.
+
+You have to hit all the
+vertices of non-zero curvature
+
+because anything of
+non-zero curvature
+
+can't be flattened by itself.
+
+It needs to be cut.
+
+At that point, the cutting has
+to have degree at least one.
+
+With zero curvature
+vertices, even if they're not
+
+flat in three dimensions,
+you could flatten them
+
+because we know locally,
+it really is a flat thing.
+
+So there may not be any cuts
+at zero curvature vertices.
+
+Most of the time, we won't
+have to worry about them,
+
+but something to think about.
+
+Everybody else you have to span.
+
+You can say even more.
+
+If you have very
+negative curvature,
+
+if the curvature of a vertex
+is less than some integer,
+
+k times 360 with a minus
+sign in front, then cutting
+
+must have degree strictly
+more than k plus 1.
+
+So if you have
+negative curvature,
+
+you know you have to
+have at least two cuts
+
+for a negative curvature
+vertex because if you
+
+had negative curvature--
+one of these things--
+
+you made a single cut.
+
+Then all that material
+is still there.
+
+If you then flattened it,
+it's going to overlap itself
+
+because you're trying
+to flatten it into 360.
+
+There's more than
+360 material there.
+
+So negative curvature already,
+you need two vertices.
+
+That's the plus 1 here.
+
+And as soon as you get to
+smaller than negative 360,
+
+then you have to have at least
+three cuts and so on, just
+
+to partition up into
+at most 360 groups.
+
+This is useful.
+
+Negative curvature is basically
+really tough to unfold
+
+and we'll use that to make
+counter examples here.
+
+What else?
+
+your polyhedron has no handles,
+then cutting has no cycles.
+
+A handle is something
+of higher genus.
+
+If this is your polyhedron,
+we call this a handle.
+
+You have sort of
+a blob down here
+
+and you have a connection
+from one place to the other.
+
+If you have a
+handle, you can have
+
+a cycle of cuts like this
+that does not disconnect
+
+the surface, but we
+basically never think
+
+about that situation.
+
+Whenever we're thinking of
+something of genus zero,
+
+like a convex polyhedron or a
+regular, non-convex polyhedron,
+
+you really shouldn't have
+a cycle in your cutting
+
+because if you
+had a cycle, you'd
+
+disconnect your
+surface into two parts
+
+normally, if you're like
+a sphere or like a disk.
+
+That's the acyclic
+condition and when it holds.
+
+Some other good things.
+
+If a polyhedron has no
+boundary and no handles,
+
+and the unfolding has
+no holes, then cutting
+
+is a spanning tree.
+
+Spanning tree, it's a concept
+we've used a few times.
+
+It's just a tree.
+
+In this case, it's got
+to visit all the vertices
+
+of non-zero curvature and
+it's a tree, so it's connected
+
+and it's acyclic.
+
+The main new thing here
+is that it's connected.
+
+We've already said
+that it should
+
+be acyclic with no
+handles, we've already
+
+said that it should
+span everybody,
+
+so it's sort of a
+summary theorem,
+
+but we have a whole
+bunch of conditions here.
+
+In particular, this will hold
+if your polyhedron is convex.
+
+So for convex polyhedra,
+you have a spanning tree,
+
+and that's what's going
+on in this picture even
+
+for general unfoldings.
+
+That's the interesting case.
+
+Here, it's maybe more
+obvious, here it's
+
+a little less obvious.
+
+And to sort of see what could go
+wrong here, I have an example.
+
+This is a non-convex polyhedron.
+
+There's a whole
+bunch of views of it
+
+up here, and in
+particular this top view.
+
+What we're doing is slicing
+along just those two
+
+edges and some other
+stuff around the outside,
+
+but in particular, we
+cut those two edges
+
+and there aren't any
+other cuts around there.
+
+A polyhedron is set up so
+that when you open it up,
+
+this works out.
+
+It's nice and flat.
+
+This is extremely rare.
+
+If you perturbed this
+example, it wouldn't hold.
+
+But you can set things up
+so that, in fact, what's
+
+happening is that the total
+curvature-- this vertex has
+
+positive curvature, this has
+negative, this has positive,
+
+and the sum of those
+three curvatures is zero,
+
+and that's what
+allows this to be flat
+
+because the total curvature
+in that little region is zero,
+
+and that's when things
+are allowed to be flat.
+
+So you can cut here and make
+a separate collection of cuts
+
+on the outside, but
+it's disconnected,
+
+so this is kind of weird.
+
+Most of the time, things
+will be connected,
+
+and as long as your
+unfolding has no holes--
+
+and for an unfolding
+to have holes,
+
+you'd have to have
+this weird property
+
+that a bunch of curvatures sum
+to zero like in that picture--
+
+as long as you don't
+have that, you're OK.
+
+Let's get to these theorems.
+
+Actually, one thing
+related to this problem,
+
+general unfolding of
+arbitrary polyhedra,
+
+is you can't be too
+general what you
+
+mean by non-convex polyhedra.
+
+So we have this example.
+
+It's the simplest nasty
+polyhedron there is this.
+
+It has one vertex at the
+top there with a big dot
+
+that has negative curvature.
+
+There's more than 360
+degrees of material
+
+from all these triangles.
+
+And that's sort of
+all that it has.
+
+This is the polyhedron.
+
+This is what we call
+boundary of the polyhedron.
+
+So far, all the polyhedra
+I've done haven't had that,
+
+and you may have
+seen that I assumed
+
+that it wasn't there
+for that last lemma.
+
+This polyhedron can't
+be unfolded at all
+
+in one piece, no overlap.
+
+Why?
+
+Because it has one vertex.
+
+You could think of
+these as vertices,
+
+but they're kind of flat.
+
+Everything's flat
+except that one point.
+
+It has negative curvature.
+
+Negative curvature,
+we said you have
+
+to have at least two
+cuts coming in there.
+
+If you just made one cut, then
+when you flatten this thing,
+
+it'll overlap itself locally.
+
+So there's got to be at least
+two cuts coming in there.
+
+I don't think that
+even matters much.
+
+I mean, there's at
+least one, certainly.
+
+Where could those
+guys go, those cuts?
+
+They have to wander
+around the surface.
+
+If they just stop in
+the middle of nowhere,
+
+then you're sort of doing
+nothing because a cut that just
+
+stops in the middle
+of a flat vertex,
+
+well, you might as well
+not have done that cut,
+
+so you could erase it.
+
+So it's got to go somewhere.
+
+They could go to each other, in
+which case you've made a cycle
+
+and then you've disconnected
+your surface because this
+
+is like a disk, or they
+could go to the boundary.
+
+And if they both
+go to the boundary,
+
+again, you disconnect
+your surface, two pieces.
+
+So this is kind of pathetic,
+but you can't unfold this
+
+with one piece, no overlap.
+
+So when I say, in
+this picture, and I
+
+say that it's open whether
+non-convex polyhedra can
+
+be generally unfolded, I
+mean non-convex polyhedra
+
+without boundary.
+
+I'll even give you
+handles if you want.
+
+I'm not sure that
+it matters too much,
+
+but boundary seems to
+make a big difference.
+
+So what's wrong
+is this polyhedron
+
+is kind of incomplete,
+and as long
+
+as you close it up somehow
+and don't have these boundary
+
+effects, then maybe you can
+generally unfold everything.
+
+That's this question.
+
+That was a little bit on this.
+
+We'll come back to
+it more next lecture.
+
+Next, I want to do this one,
+general unfolding of convex
+
+polyhedra.
+
+This is really the most
+positive news I could give you.
+
+All this unfolding stuff,
+it's the one good result.
+
+We know several good results,
+but in terms of that table,
+
+it's our only good result.
+
+And to do that, there's a bunch
+of solutions to this problem.
+
+They all use the idea
+of shortest paths.
+
+The shortest path is a
+path that's shortest.
+
+So you have some surface,
+you have some points.
+
+You do this all the
+time when you're
+
+flying between two cities.
+
+You follow a shortest
+path on a sphere.
+
+It's not straight
+in three dimensions.
+
+It's the shortest thing subject
+to lying on that surface, what
+
+is the shortest path you can do?
+
+So you're used to
+it on a sphere.
+
+It's a little weirder
+on a polyhedron,
+
+but it's just the same idea.
+
+Take all the possible paths you
+could, find the shortest one.
+
+You fix the two
+endpoints, x and y,
+
+and you get to optimize this.
+
+Whatever is shortest
+is the right thing.
+
+I have some pictures of
+what they look like here.
+
+So these are some
+convex polyhedra.
+
+They're probably random
+points on a sphere,
+
+take the convex hull.
+
+And then we pick some vertex,
+or some point x in the corner
+
+there, and this is
+computing the shortest paths
+
+from x to every other
+vertex on the polyhedron.
+
+So they look very
+straight in this case
+
+because the polyhedron
+is almost a sphere.
+
+They look kind of like great
+circular arcs on a sphere,
+
+but they're not quite.
+
+You can look carefully
+at an edge here,
+
+this does bend a little bit.
+
+It's a bit subtle.
+
+It bends only a little bit
+because the property you want
+
+is if you look at this
+triangle and this triangle
+
+and you unfold
+them-- so right now,
+
+they have some dihedral
+angle between them,
+
+and if you open it out
+so that they're flat,
+
+then this line
+should be straight.
+
+Still the case that shortest
+paths are straight lines,
+
+but only when you unfold.
+
+That's the idea.
+
+So if you look at all
+the triangles are visited
+
+by a path, and you unfold them
+to be a straight thing-- this
+
+is called developing, you
+flatten it out-- then actually,
+
+the shortest path will
+be a straight line,
+
+so that makes it really
+easy to draw these things.
+
+There still might be multiple
+candidates, like to get here,
+
+should I go this way or
+the other way around,
+
+but each of those will
+be locally straight,
+
+and this is a property
+called geodesic.
+
+Shortest paths always
+unfold straight.
+
+And in general, anything
+that unfolds straight,
+
+it might not even be
+shortest, is a geodesic.
+
+These are like locally shortest.
+
+Locally, you can't
+make them any shorter,
+
+but they might have
+made the wrong choice.
+
+They might have gone
+around the wrong way.
+
+Geodesic means going
+straight for a long time.
+
+You could actually
+spiral around and do
+
+all sorts of crazy things.
+
+But shortest paths
+never cross themselves
+
+because if you had the shortest
+path that crossed itself,
+
+that wasn't shortest.
+
+You should have just
+gotten rid of this part
+
+and gone straight
+through the crossing.
+
+That's sort of trivial.
+
+And there's another
+good, fun property
+
+that you may not have
+noticed in those figures,
+
+but they never pass through
+positive curvature vertex.
+
+So if you look at
+these pictures,
+
+they might end at a
+positive curvature vertex
+
+because that's where we told
+the shortest path to go,
+
+but in the middle, they're
+always crossing edges.
+
+This is a convex polyhedron so
+everything's positive curvature
+
+or zero.
+
+In that case, the
+paths can really only
+
+go through zero
+curvature points.
+
+They might start
+and end wherever,
+
+but in between, they
+never hit a corner.
+
+Why?
+
+Because if you have a
+positive curvature vertex--
+
+I'm just going to sketch this
+idea-- if you went up here
+
+in order to go back down
+somewhere like there,
+
+it's always better to
+shortcut a little bit
+
+and not go through the vertex.
+
+It's better to go around
+one way or the other.
+
+I'm just going to wave my
+hands at that, but it's true.
+
+So what?
+
+Shortest paths are going to
+be a really powerful tool
+
+for finding unfoldings.
+
+In particular, I want to
+define the star, that picture,
+
+of all shortest
+paths from one point.
+
+And do I want points here?
+
+I think I want vertices.
+
+That's the picture that we drew.
+
+The interesting thing about all
+the shortest paths, they all
+
+start from the same point,
+they never hit each other.
+
+So not only does a
+shortest path not hit
+
+itself, but if you take many
+shortest paths, or even two
+
+shortest paths from a
+common starting point,
+
+they can't hit each other.
+
+It could be one is
+a subset of another.
+
+For example, if I took
+the shortest path to here
+
+and then I also took the
+shortest path to a point
+
+just beyond it,
+well, one's going
+
+to be a prefix of the other.
+
+Other than that, they will
+never cross each other.
+
+I'm going to just assert
+that, not prove it here.
+
+So really, it does
+look like a star.
+
+In fact, you could fill
+in more shortest paths.
+
+You could take the shortest
+path to here, for example,
+
+and it'll fit in nicely, kind
+of bisect that angle in there.
+
+It's a very simple
+kind of structure.
+
+It's just from a point, you
+have all this stuff going out.
+
+They never hit each
+other except at something
+
+called the cut locus, also
+called the ridge tree.
+
+And these are points with
+non-unique shortest paths to x.
+
+So we're fixing some point, x.
+
+So here's a simpler polyhedron.
+
+It's just a
+square-based pyramid.
+
+We're picking x to be in
+the middle of this face,
+
+and drawn in these black
+lines are the shortest paths
+
+from x to all the vertices.
+
+Here, that's a straight line.
+
+This one, if you unfolded
+it, it would be straight,
+
+and there's some similar
+ones on the back.
+
+And I think this is the back
+in case you want to see.
+
+There's one back face that you
+can't see at all, C, behind B
+
+here, and that's
+what it looks like.
+
+There's no shortest paths there.
+
+Now, there's these dashed lines.
+
+That's the ridge tree.
+
+That's the cut locus.
+
+And these are points on the
+backside with respect to x.
+
+If you're going from x,
+you go around behind to C,
+
+or you could go from x around
+behind to D and then to C.
+
+At some point, those things meet
+and are still of equal length.
+
+So here, if you're
+trying to go to x,
+
+you could go around this way or
+you could go around this way.
+
+They will be the same
+length, and all the points
+
+with that property
+are the dashed lines.
+
+Now, if you're familiar
+with [? Vornar ?] diagrams,
+
+this is the [? Vornar ?]
+diagram of one point, x.
+
+Imagine you plant grass over
+your polyhedron, you light
+
+a fire here, it burns at
+uniform speed in all directions.
+
+Where the fire meets
+itself on the backside,
+
+that is the ridge tree.
+
+That is the
+[? Vornar ?] diagram.
+
+So it's kind of intuitive
+that it's there.
+
+Maybe less obvious
+is that it's a tree
+
+and it's a spanning tree.
+
+It hits all the vertices.
+
+So it's a natural cutting.
+
+That's why it's
+called the cut locus,
+
+and it works really well.
+
+And it's called the
+source unfolding.
+
+Source unfolding goes
+back to the mid '80s.
+
+A bunch of people
+discovered it for
+
+various computational
+geometry applications.
+
+They didn't care about
+unfolding at the time.
+
+And it's kind of obvious after
+you think about it for a while,
+
+trying to solve this
+general unfolding problem.
+
+Once you have this structure,
+cut along the cut locus,
+
+unfold the star of
+shortest paths from x.
+
+So let's do it for this example.
+
+It's the same
+example on the left.
+
+This is the star unfolding.
+
+I've just splayed out
+everything, so at the boundary,
+
+I'm cutting at the dashed part.
+
+That's the cut locus.
+
+Ignore these little
+dashed lines.
+
+Those are just edges, unfolded.
+
+And what's happening is that
+all the shortest paths are all
+
+here.
+
+If I look at any shortest path
+from x on the left diagram,
+
+I can map it to a line
+segment starting from x.
+
+x was a flat vertex.
+
+It has 360 degrees of
+material around it.
+
+I just chose it to be somewhere
+in the middle somewhere.
+
+Doesn't matter other than that.
+
+And now there's 360 degrees of
+material on the flat unfolding.
+
+That's great.
+
+And you pick any
+direction here, you
+
+can map it to a corresponding
+direction over there
+
+on the surface, see where
+that shortest path would
+
+go if you kept going until
+you were no longer shortest.
+
+When you stop being shortest,
+the edge of that place
+
+is the ridge tree, and
+that's where you cut.
+
+You stop your segment there.
+
+So it's actually pretty obvious
+this thing doesn't overlap
+
+because all of
+these shortest paths
+
+are going in different
+directions from x.
+
+What you have is what we call
+a star shaped polygon around x.
+
+Every point on the
+surface is visible from x
+
+because we just sort of
+unrolled it to be right there.
+
+That's the source unfolding.
+
+It's a little hard to
+see the 3D diagrams,
+
+but it's actually really easy
+once you draw those shortest
+
+paths.
+
+So the source unfolding
+is star shaped.
+
+We have another unfolding
+called the star unfolding,
+
+which is not star shaped.
+
+Very confusing.
+
+I mean, what you call one
+doesn't matter too much.
+
+This unfolding was
+mentioned in 1948
+
+by Alexandrov, who
+we'll be hearing
+
+about more in the
+future, but wasn't
+
+improved to
+non-overlap until '92.
+
+So this one is much less
+obvious that it doesn't overlap,
+
+and I'm not going
+to prove it here.
+
+But it goes back to
+this idea of star.
+
+Say, OK, this cut locus
+is nice, but let's
+
+focus on the star
+of shortest paths
+
+from one point to all
+the other vertices.
+
+Instead of keeping those paths
+as the things that you unroll,
+
+what if we cut along them?
+
+It's another natural thing to
+try and it turns out to work.
+
+So here, we cut along the star.
+
+We've already
+proved this result,
+
+every convex polyhedron
+is generally unfoldable.
+
+Just with that picture,
+it's very easy.
+
+But hey, it's fun to have more.
+
+And this is what the
+star unfolding looks
+
+like for the same example.
+
+This is a little less obvious,
+but if you think about it,
+
+the star, the set
+of all shortest
+
+paths to all the vertices,
+is a spanning tree.
+
+It hits all the vertices
+because we told it to,
+
+and it's a tree
+because it's just
+
+all these edges coming
+together at a point.
+
+So it's a natural cutting also.
+
+And magically it works.
+
+How it works is a
+little less obvious.
+
+You see here the ridge tree
+drawn on the unfolding,
+
+and you can see all the
+parts and map the letter E,
+
+this is the bottom square,
+and stays connected.
+
+It's just like you
+reattach everything
+
+around the ridge tree
+and it doesn't overlap.
+
+It's quite difficult, I think,
+to give intuition why this
+
+doesn't overlap, but it doesn't.
+
+I'll wave my hands
+at some point when
+
+we have the necessary
+tools to prove it,
+
+I can mention how it's done.
+
+But we don't have them yet.
+
+We'll get them in a couple
+of lectures, I think.
+
+These results can be extended
+also in various directions.
+
+Let me tell you briefly
+about some extensions.
+
+For a long time, these
+were the two ways
+
+to solve that problem
+and that was sort of it.
+
+It would be nice, for example,
+to have some general family
+
+of unfoldings that includes the
+star unfolding and the source
+
+unfolding and there's
+something in the middle,
+
+but we don't necessarily
+know what that is.
+
+Do you have a question?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: How do you find
+the creases is your question?
+
+You find the creases because
+you know for every point
+
+here where it was
+on the surface,
+
+and if it was on an edge,
+then it's a crease point.
+
+That's the easy way to do it.
+
+I don't know if that's
+a satisfactory answer,
+
+but it can be done.
+
+AUDIENCE: Does it matter
+where you choose x to be?
+
+PROFESSOR: Does it matter
+where you choose x to be?
+
+It will change the unfolding.
+
+It will never overlap,
+but in that sense
+
+there's a whole family
+of star unfoldings,
+
+depending on where you move x.
+
+There's a whole family
+of source unfoldings
+
+depending on where you move x.
+
+AUDIENCE: Does it make it
+more efficient, any choice?
+
+PROFESSOR: I mean,
+some of the unfoldings
+
+might have more cuts,
+some might have less cuts.
+
+You're going to
+get more cuts when
+
+you have-- depends
+how you count.
+
+In some sense, there's only
+n cuts, n shortest paths.
+
+But a shortest path
+might cut over many faces
+
+or it might just
+cut over one face.
+
+Depends where x is.
+
+If you choose x to
+be in a nice place,
+
+maybe you could get
+away with fewer cuts
+
+and have to do less welding, but
+there's no theory about that.
+
+More questions.
+
+AUDIENCE: So it doesn't
+matter where you put x.
+
+If it works at one spot, it
+basically works at every spot.
+
+[INAUDIBLE]?
+
+PROFESSOR: For
+convex polyhedra, it
+
+works no matter where you put x.
+
+For non-convex polyhedra, some
+x's might work, some might not.
+
+Here, let me show you.
+
+Here's more star unfoldings.
+
+Cool.
+
+They're really crazy looking
+and not really star shaped.
+
+There isn't one point
+that can see everything.
+
+They look kind of spiky like a
+star, but it's quite different.
+
+These are random
+points on a sphere,
+
+like take 42 random points on
+a sphere, take the convex hull,
+
+then take a star unfolding.
+
+Here's an example with
+a non-convex polyhedron.
+
+So one thing we hoped for
+for a little while briefly
+
+was that if you only had one
+vertex of negative curvature,
+
+which is this one, maybe if
+you choose x to be right there
+
+and did the star
+unfolding, because that
+
+cuts x into lots of
+little tiny pieces, then
+
+maybe it would unfold about
+overlap, but it doesn't work.
+
+We were destroyed.
+
+In fact, you can
+show neither of them
+
+will work in general for
+a non-convex polyhedra,
+
+so there's no hope of
+solving this problem
+
+with these techniques, at least
+with these exact algorithms.
+
+You might get lucky,
+but most of the time,
+
+I think they won't work.
+
+Currently, x is a point.
+
+You can actually
+let x be-- I guess
+
+I'm not going to
+be safe-- I'm going
+
+to call it a geodesic path.
+
+There's some restrictions
+on when this is allowed,
+
+but the idea is you
+have your surface,
+
+you take some straight
+path on the surface,
+
+and then you take
+shortest paths from there.
+
+And if you just think
+about the source unfolding
+
+where you keep x intact
+and unfold from there,
+
+the picture is
+going to look like,
+
+well, you have
+this straight line
+
+when you unfold that
+thing, and then you
+
+have this nice star
+of stuff around it.
+
+And under some
+simple conditions,
+
+that will work without overlap.
+
+What's more impressive is
+that the star unfolding
+
+works from a source like that.
+
+Again, there are
+some restrictions
+
+on x that I'm not
+going to define here,
+
+but it can be done.
+
+These are two very recent
+papers by O'Rourke and Itoh
+
+and Vilku from the
+last two years.
+
+So that's exciting.
+
+We now have four general methods
+for unfolding convex polyhedra.
+
+Again, these are big families.
+
+You can choose
+any geodesic path.
+
+Maybe some are
+nicer than others.
+
+You can do higher dimensions.
+
+Star unfolding doesn't
+really make sense
+
+in higher dimensions.
+
+I don't think I've
+thought about it much,
+
+but source unfolding
+makes sense.
+
+So you have some four polytopes,
+a little hard to imagine.
+
+You take some point and
+just radiate out from there,
+
+unfold like that until you hit
+yourself, and then you stop,
+
+and that works in any dimension.
+
+Source unfolding works
+in any dimension.
+
+That's fairly recent,
+2003, Miller and Pak.
+
+Another thing you can do
+is continuous blooming.
+
+This is an idea posed by
+Connolly several years
+
+back and then solved
+last year, I guess.
+
+It was presented in Japan.
+
+This is about folded states
+versus folding motions,
+
+an issue we have thought
+about many times in origami.
+
+It was easy for any
+polygonal piece of paper.
+
+We could go from
+unfolded to folded state
+
+by a continuous motion
+without self intersection.
+
+For linkages, it
+was the big deal.
+
+It was all about, can
+we get from a to b?
+
+For convex polyhedra, you can
+do it, continuous blooming.
+
+This is in the middle of an
+algorithm of continuously
+
+blooming the source unfolding.
+
+So here's our point x.
+
+This is the cube, and
+the source unfolding
+
+of a cube for this
+point x in the center
+
+of a face, these four vertical
+lines and then a little x
+
+on the top side.
+
+The algorithm unfolds
+one edge at a time
+
+but in a very specific order.
+
+So it ends up unfolding this
+entire house shape first,
+
+and then it's done
+one edge of this one,
+
+and then it's going to fold
+the other one down and then
+
+unfold one, two for the
+backside, and then one,
+
+two for the left side.
+
+And you can show that
+will not self intersect
+
+as long as you had
+a convex polyhedron.
+
+It's not obvious but it's true.
+
+There are some other
+results that if you
+
+have any unfolding that doesn't
+self intersect at the end,
+
+you can add some cuts and make
+it actually continuously bloom.
+
+It's kind of like
+hinged dissections.
+
+It may not work by
+itself, but you'd
+
+cut the pieces into smaller
+pieces and then it will work.
+
+That's pretty good news,
+and source unfolding just
+
+works as is.
+
+I might talk about that
+some future lecture.
+
+Not known, for example, whether
+the star unfolding continuously
+
+blooms.
+
+That sounds a
+little scary to me.
+
+We don't actually have
+an unfolding of a convex
+
+polyhedron that does
+not continuously bloom.
+
+I think there should be one,
+but that's an open problem.
+
+Is this always possible, or
+is there some crazy collection
+
+of cuts that you cannot escape?
+
+That's that, general
+unfolding of convex polyhedra.
+
+Let's turn to the--
+it's not the last topic.
+
+We still want to
+cover both of these.
+
+Next topic is edge unfolding
+of convex polyhedra.
+
+Now, this problem,
+as I said, goes
+
+back to 1525,
+implicitly at least,
+
+by this guy, Albrecht
+Durer, who was a cool guy.
+
+This is Renaissance time.
+
+He did many different things.
+
+I guess painter is maybe
+his primary profession,
+
+but he did a lot of
+different things.
+
+He studied early perspective,
+all that good stuff.
+
+This is one of
+his famous prints.
+
+It was actually on display
+at the MFA last year,
+
+I got to see it, and it
+has a little polyhedron
+
+thrown in there.
+
+It's a nice polyhedron.
+
+How did he draw them?
+
+Well, he probably built
+models out of some material.
+
+And he was just
+generally interested
+
+in the third dimension
+and understanding
+
+how all these things worked, and
+so he made a lot of unfoldings
+
+in this book.
+
+This is the original title.
+
+Here's a translation.
+
+Titles were a lot
+longer in those days.
+
+The Painter's Manual
+is what I usually
+
+call it, "A Manual of
+Measurement of Lines, Areas,
+
+and Solids by Means
+of Compass and Ruler
+
+Assembled by Albrecht Durer for
+the Use of all Lovers of Art
+
+with Appropriate
+Illustrations Arranged
+
+to be Printed in
+the Year MDXXV."
+
+And I don't even know what the
+subtitle is, but there you go.
+
+If you read German,
+I'm told this
+
+is a challenge because
+of the old script.
+
+So unfoldings like this.
+
+He did mostly Archimedian
+solids in this book.
+
+This book is several
+hundred pages long.
+
+I have a copy.
+
+This is a
+cuboctahedron unfolded.
+
+He is only cutting along edges,
+and he liked this, I presume,
+
+for building models.
+
+Here's a fancy
+one, the snub cube.
+
+This one, I think,
+might have an error.
+
+A couple of them have very small
+errors, but for the most part,
+
+he was the inventor
+of edge unfolding.
+
+Now, he didn't ask, is this
+always possible, but we did.
+
+Mathematicians did in
+1976, I believe, or '85.
+
+'75, G. C. Shephard, geometer.
+
+He was the first one
+to write it in a paper,
+
+does every convex polyhedron
+have an edge unfolding?
+
+So what can I tell you
+about this problem?
+
+It's hard.
+
+Many people have
+thought about it.
+
+I'm not really sure
+that it's possible.
+
+A lot of people do, though.
+
+It's possible for
+a lot of polyhedra.
+
+In fact, every polyhedron
+we've tried to unfold we
+
+have eventually unfolded--
+convex polyhedron.
+
+Simple set of examples are
+the Archimedian solids.
+
+Doesn't take that much effort to
+find unfoldings of all of them.
+
+You can do this with exhaustive
+search or just playing around.
+
+A lot of people have
+done this over the years.
+
+This is all the
+unfoldings of those guys.
+
+There's a lot of
+heuristic software
+
+for actually doing this.
+
+I think the coolest one
+right now is Pepakura.
+
+If you want to build a
+paper model of something,
+
+you have a 3D model
+thrown into Pepakura
+
+and it'll probably give you
+a one piece unfolding, even
+
+for non-convex shapes.
+
+Even though it's
+not always possible,
+
+it'll do edge
+cuttings, it'll try
+
+to do some exhaustive search,
+and usually does pretty well.
+
+Sometimes it'll use
+multiple pieces.
+
+That's the catch.
+
+There's a link in
+the lecture notes.
+
+The most thorough
+mathematical search
+
+is by this guy, Wolfram
+Schlickenrieder,
+
+who wrote the equivalent
+of a master's thesis
+
+in Berlin 13 years ago.
+
+I just wrote to him
+about it yesterday.
+
+I was like, hey,
+this is cool stuff.
+
+Can I show it in my lecture?
+
+He was like, yeah, it lives on.
+
+He had a class of 10
+different algorithms,
+
+around that many,
+possible algorithms
+
+for unfolding all
+convex polyhedra,
+
+and then he came up with
+a dozen different families
+
+of polyhedra.
+
+I don't have the polyhedra
+drawn here, just the unfoldings.
+
+They're generators of
+big classes of polyhedra.
+
+He applied every
+algorithm to every class.
+
+Ideally, you get an algorithm
+that works for all classes
+
+or you find a class that
+foils all algorithms.
+
+Sadly, he found neither.
+
+Every algorithm was
+foiled by some example,
+
+yet every example was
+foiled by some algorithm.
+
+It's really annoying, but here's
+some examples where they fail.
+
+They just barely fail, just a
+couple triangles are messed up.
+
+Little squares are messed up.
+
+I think these are called
+the turtle polyhedra.
+
+It's like a big, flat thing
+and then a dome on top.
+
+So inconclusive, I
+guess, is the answer.
+
+There was one algorithm that
+had a degree of freedom.
+
+You had to choose
+a direction, then
+
+you cut along all the edges
+that are most in that direction.
+
+And there was a conjecture
+on the table from this thesis
+
+that maybe for every
+polyhedron, there
+
+is a direction that
+works, but then
+
+that was destroyed
+four years ago.
+
+Brendan Lucier from Waterloo
+proved that that's not true.
+
+He found a polyhedron
+that doesn't
+
+work from any direction.
+
+So at the moment, we have
+no candidate algorithms,
+
+which makes me worry whether
+this could possibly be true.
+
+We have some more bad examples.
+
+Here are some annoying things,
+like a cube with a corner
+
+cut off.
+
+It's a very local thing, but
+you can mess up really easily.
+
+It's actually quite common
+to mess up, I would say,
+
+even though for things
+like Archimedian,
+
+it's much harder to mess up.
+
+Simplest polyhedron that messes
+up is this sliver tetrahedron.
+
+So the polyhedron
+is drawn at the top.
+
+It's a little hard to
+see, but on the backside,
+
+there's an edge like
+that, if you can imagine.
+
+So it's almost
+flat, so that's why
+
+it's drawn flat, and
+the four corners,
+
+like a tetrahedron
+should have, four faces,
+
+the front two triangles
+and the back two
+
+triangles with the
+line that I drew.
+
+And if you unfold it in a simple
+way, you just cut from a to b,
+
+it unfolds like
+this, no problem.
+
+But if you unfold
+the wrong way, which
+
+is to cut both of
+the diagonal lines,
+
+then you end up with the
+spears that cross each other,
+
+so you really have
+to be careful.
+
+In fact, if you take
+a random polyhedron--
+
+I choose 80 points on a
+sphere, I take the convex hull.
+
+It's a very nice, round
+sphere-like polyhedron.
+
+And I look at all
+the unfoldings--
+
+this is probably not
+all the unfoldings,
+
+but I randomly generate
+unfoldings, and I evaluate,
+
+what is the observed
+probability that I get overlap?
+
+And it's very close to 100%.
+
+The conjecture is that
+as n goes to infinity,
+
+the probability of
+overlap goes to 1.
+
+We don't have a proof of that.
+
+That would be nice to prove.
+
+There's good reason to
+believe that's easy to prove
+
+or that it's true, let's
+say, that there is a proof.
+
+I don't know how to
+actually formalize it.
+
+This is some work
+from the late '80s.
+
+Just because most
+unfoldings fail
+
+doesn't mean there isn't
+one unfolding that works.
+
+If I were to try to prove that
+there is an unfolding that
+
+works, here's my best hope,
+and it ties into some things
+
+that we've seen
+with tensegrities.
+
+If you take a really big
+polyhedron, which is the case
+
+you worry about, and you look
+at a small portion of it,
+
+that portion will be
+almost completely flat.
+
+Locally, this thing
+is mostly flat.
+
+Instead of thinking
+about the big polyhedron,
+
+if we at least wanted to
+get it to work in any patch,
+
+think about the case of
+an almost flat polyhedron.
+
+So it's like a little dome.
+
+It has boundary now.
+
+Makes life a little
+harder, but let's say
+
+it's a nice, convex boundary.
+
+This is a convex dome.
+
+It's actually polyhedral.
+
+Well, let's make it
+super, super flat.
+
+So we have this z-coordinate.
+
+Scale z to squash it
+down into the plane.
+
+What's nice about
+this is then you
+
+can think of your
+convex polyhedron
+
+just as some drawing
+in the plane.
+
+So here maybe is my
+convex polyhedron.
+
+Now, in fact, each
+of these vertices
+
+is lifted a tiny amount,
+some infinitesimal amount,
+
+but you can think
+of it in the plane.
+
+These are convex faces.
+
+We know this thing can be
+lifted to a convex polyhedron.
+
+That lifting is
+a positive stress
+
+on all the edges except
+the boundary edges.
+
+Maybe that stress gives
+you some useful structure.
+
+If there's any hope
+of this working,
+
+that structure better be useful,
+but I don't know how to use it.
+
+But in particular,
+open question.
+
+If I give you a super
+shallow, arbitrarily
+
+shallow, convex polyhedral
+dome, can it be unfolded?
+
+I don't know.
+
+Maybe we'll work on it
+in the problem session.
+
+Haven't thought
+about it for awhile.
+
+That's if you want
+to solve everything.
+
+What if you just want to
+solve some special cases?
+
+That is a special case
+motivated by the general case.
+
+Well, you can solve the
+case of a polyhedron
+
+with at most six vertices.
+
+That's as far as we've gotten.
+
+You can solve some simple
+examples like pyramids
+
+if you take any convex
+polygon, doesn't
+
+have to be irregular
+or anything,
+
+and then you take a point
+and you take the convex hull.
+
+So that's a polyhedron
+and it unfolds.
+
+How does it unfold?
+
+Any suggestions where to cut?
+
+How?
+
+AUDIENCE: From the top?
+
+PROFESSOR: From the top.
+
+Yeah, just cut here.
+
+Here, we're only allowed
+to cut along edges.
+
+This is called the
+volcano unfolding.
+
+What do we have?
+
+Like that, and then there's
+just a bunch of triangles.
+
+What's nice about
+the volcano unfolding
+
+is if you look at these
+perpendicular strips here,
+
+those triangles will fit inside
+those perpendicular strips,
+
+and therefore they won't
+intersect each other
+
+because these strips don't
+intersect each other.
+
+You could probably
+even continuously bloom
+
+this, no problem.
+
+So a very simple example,
+easy to do with volcanoes.
+
+That's the so-called pyramid.
+
+Prism, a little bit more
+interesting, but not by much.
+
+You take some polygon.
+
+Again, doesn't
+have to be regular,
+
+but you take two copies of
+it vertically offset, take
+
+the convex hull.
+
+This one you can
+cut in two ways.
+
+You could do a
+volcano-like thing
+
+where you cut all
+the vertical edges
+
+and then you cut all but
+one of the bottom edges.
+
+Then you'll have basically a
+volcano with little rectangles
+
+hanging off all the sides.
+
+And then there's another copy,
+the bottom copy of this face,
+
+and it just hangs out
+over here, and you
+
+could prove that that
+won't hit anybody
+
+in this very simple situation.
+
+There's another unfolding,
+though, that I mention
+
+because it's useful
+for other things,
+
+and it's so-called
+band unfolding.
+
+Band unfolding, I
+want to keep intact
+
+the radial band around the
+thing, maybe like this.
+
+What do I want to do
+to keep that edge?
+
+Cut, cut.
+
+So I cut on all the
+top edges except one,
+
+I cut on all the bottom
+edges except the same one,
+
+and then I also cut
+this vertical edge.
+
+So what I should get
+is I get my top face,
+
+then I get a
+rectangle, then I get
+
+the band that goes
+around the outside,
+
+and then I get another copy
+of my shape, the bottom side.
+
+This is what we
+call band unfolding.
+
+There's some nice theorems about
+band unfoldings working out.
+
+Let me get to more
+interesting polyhedra.
+
+These are some
+pretty simple cases,
+
+but we don't know very
+much on the positive side.
+
+Prismoid.
+
+Suppose you take a polygon,
+and you basically inset it.
+
+So I want to make a new
+version of the polygon
+
+where all of the angles match,
+so these edges are parallel
+
+to each other.
+
+I think, actually, the
+lengths can change.
+
+And then you take
+the convex hull.
+
+These unfold with the
+volcano unfolding.
+
+It's a little more
+subtle to prove
+
+but it's proved in the textbook.
+
+Edges have to stay parallel.
+
+I think that might
+force something.
+
+I'm not quite sure,
+but the constraints
+
+are that the edges
+have to be parallel
+
+and the angles have to be equal.
+
+Dome.
+
+Dome is actually in
+some ways simpler.
+
+You take some base, and then
+I want a whole bunch of faces
+
+that all touch the base.
+
+So in general, it's going to be
+like a tree of faces, something
+
+like this.
+
+Every face has to touch
+an edge of the base.
+
+These also unfold, and
+also with a volcano.
+
+This is proved also
+in the textbook.
+
+Both results are
+by Joe O'Rourke.
+
+Prismatoid.
+
+This is the coolest
+special case I'm
+
+going to talk about,
+the most interesting.
+
+I take some convex polygon,
+and then in a parallel offset,
+
+I take some other
+convex polygon--
+
+no relation to each
+other except that they're
+
+in parallel planes--
+and then I take
+
+the convex hull,
+something like that.
+
+This one, sadly, is open.
+
+Now, what we do know,
+and this is related
+
+to the band
+unfolding, if you look
+
+at the band around the
+sides of this prismatoid
+
+and just unfold
+that by itself, that
+
+will not self intersect,
+and that's quite nontrivial,
+
+the proof.
+
+But if you just
+unroll the side faces,
+
+they will wander around but
+they won't hit themselves.
+
+The only remaining
+problem is, where
+
+does the top and
+the bottom face go?
+
+I think I have an example
+where that's a little dicey.
+
+Prism.
+
+Prismoid.
+
+That gives you an
+answer to your offset.
+
+So they can be sheared
+away from each other,
+
+but this is a prismoid.
+
+All of the sides are parallel
+and the angles match, a and b.
+
+Here is the volcano
+unfolding of the prismoid,
+
+and here's showing that it's
+not so obvious that it always
+
+works.
+
+If you're not careful where
+you put the top face-- so this
+
+is a on top of b
+in plan-- you could
+
+attach a to any of these faces.
+
+You have to choose
+one that's not
+
+so inside because
+it's overlapping here.
+
+But if you choose
+the outermost one,
+
+it works and you can prove that.
+
+This is the dome.
+
+You can even have
+overhang and they
+
+will unfold, volcano style.
+
+You no longer have those
+nice perpendicular wedges
+
+to say everything is disjoined.
+
+But it still turns out.
+
+Nothing intersects.
+
+Here's the prismatoid
+I wanted to show you.
+
+This one's actually almost flat.
+
+So a is this triangle right on
+top of b, the triangle beneath.
+
+You take the convex
+hull and you get
+
+all those edges on the outside.
+
+And if you're not careful--
+this is more volcano
+
+style unfolding-- but
+you can get overlap.
+
+One thing we do know,
+this is kind of weird.
+
+If you try to go more general,
+and instead of taking a convex
+
+polygon on the top and a
+convex polygon on the bottom,
+
+instead you take a
+smooth convex curve
+
+on the top and a
+smooth convex curve
+
+on the bottom, which is getting
+weird because now there's
+
+infinitely many
+vertices and going
+
+to be infinitely many cuts.
+
+But there is a natural
+notion of unfolding
+
+which sort of takes
+the continuum.
+
+You take all those lines
+that go from one side
+
+to the other, the rule
+lines of the convex shape,
+
+and you just unfold them.
+
+You don't actually preserve
+area when you do this.
+
+It's not a valid unfolding
+in the usual sense,
+
+but it's a natural
+generalization
+
+of unfolding to smooth shapes.
+
+You can prove, well, that part's
+going to work just fine if you
+
+just volcano it, and
+then you can actually
+
+find a place for the top face.
+
+Those are the special
+cases we know,
+
+and even some pretty simple
+cases that we don't know,
+
+although it's almost there.
+
+One more open problem.
+
+Just mention this because
+it's a fun problem.
+
+So again, I want to edge
+unfold all convex polyhedra,
+
+but I allow multiple
+pieces to make
+
+the problem a little easier.
+
+So let's say I have a
+polyhedron with f faces.
+
+I want to know how few
+pieces could I get away with?
+
+The big open problem is, can
+I get away with one piece?
+
+What if you make it easier?
+
+What if I just want, say,
+little o of f pieces?
+
+Smaller than any
+constant times f.
+
+This is open.
+
+What we do know is
+some constant times
+
+f where the constant
+is less than 1.
+
+Best constant I have
+written here is 1/2.
+
+There is a better
+bound, but I think
+
+it's not so easy to
+summarize in this form.
+
+So you can get a
+little less than half
+
+the faces' number of pieces,
+but that's pretty pathetic.
+
+It's a problem that seemed
+like it would be a good idea,
+
+but so far it hasn't seemed to
+make the problem much easier.
+
+What do I mean by pieces?
+
+Well, we're all about
+one piece unfolding,
+
+so now your cutting
+can have cycles in it
+
+and disconnect the surface
+into multiple parts.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Multiple
+connected components.
+
+The tricky part is
+to pair up the faces
+
+so that everybody has a mate.
+
+That's not always possible.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Yeah.
+
+You would hope that one
+third, but-- I mean,
+
+you can do lots of
+little local arguments
+
+and prove this constant,
+but the big question
+
+is, can you get less
+than a constant?
+
+So last topic for today is edge
+unfolding non-convex polyhedra.
+
+Sort of did that
+problem addressed,
+
+and now this is not
+always possible.
+
+So I want to give you a
+polyhedron where you cannot
+
+edge unfold it.
+
+This is actually pretty easy,
+and we did it way back in '98
+
+when we started
+working on folding,
+
+but it's kind of cheating.
+
+This is a box on a box,
+and the only edges here
+
+are the edges of the two boxes.
+
+There's no edges connecting
+the outside of this face
+
+to the inside of that face.
+
+That face here is a donut.
+
+It's a square donut.
+
+So if you're only cutting along
+edges, that face is intact.
+
+Now I ask you, where
+does the top box go?
+
+The top box has five
+square faces, not six.
+
+There's nothing on the bottom.
+
+And somehow, it has to
+be attached to the rest
+
+if I want one piece.
+
+That means that all
+five faces fit in here,
+
+but there's only room
+for one in terms of area
+
+so you're screwed.
+
+But this is cheating because
+what I really wanted to do
+
+was generalize this
+problem, edge unfolding
+
+of convex polyhedra.
+
+Now, I know they're not
+going to look convex,
+
+but that thing is
+really not convex.
+
+It's really not
+convex in the sense
+
+that you have this face that is
+not even topologically a disk.
+
+It has a hole in it.
+
+Convex polyhedra
+don't have that.
+
+So in some sense, this
+is a topological problem,
+
+you might say.
+
+And you might hope that if
+I looked at polyhedra that
+
+are topologically
+convex, maybe those
+
+would unfold by edge cuts.
+
+"Topologically convex"
+means that if you just
+
+move the vertices around but
+preserve the edge structure,
+
+then it becomes a
+convex polyhedron.
+
+In other words, I take a
+convex polyhedron, which
+
+we think maybe has
+an edge unfolding,
+
+and then I just pull
+the vertices around
+
+but preserve all the faces.
+
+Then can you edge unfold those?
+
+And the answer is no.
+
+I have one more example
+before we get there.
+
+This polyhedron, at least
+all the faces are disks.
+
+There's no holes.
+
+So it's a cube with
+little bites taken out
+
+of all the edges, same paper.
+
+And this thing also
+does not unfold.
+
+It's a little less obvious.
+
+What's cheating about
+this example is you
+
+have two faces, like this
+purple one and the yellow one,
+
+that share two different edges.
+
+And for convex polyhedra,
+two faces either
+
+share an edge or a
+vertex or nothing,
+
+but they can't reach
+around and do to joins.
+
+Again, this is not topologically
+convex, but this is.
+
+So this is two views
+of the same thing,
+
+and if I take these spikes and
+I just push that vertex down
+
+to be really close to this
+triangle, this will be convex.
+
+So it's just a convex
+polyhedron that I
+
+pull on four of the points.
+
+Same facial structure.
+
+This has no edge unfolding
+and we're going to prove that.
+
+This example is even
+stronger in that
+
+all the faces are triangles.
+
+So what we're going to
+do is take this thing.
+
+It's kind of appropriate
+for this season.
+
+So I've got a
+tetrahedral spike on top.
+
+Think of that as going
+out of the board.
+
+And then in the plane of
+the board is this triangle,
+
+and then I just add
+in all the edges
+
+to make it a triangulation.
+
+Adding edges is a
+worry because that's
+
+where we're allowed
+to cut, so you really
+
+have to worry about
+all those edges we add.
+
+If we add them in
+that way, I claim,
+
+you take this-- we call
+it the witch's hat--
+
+then you multiply, in some
+sense, by a tetrahedron,
+
+meaning I take four
+copies of this hat,
+
+I put one on each face
+of the tetrahedron,
+
+and you get that example.
+
+Here's one witch's hat and
+they're just joined along edges
+
+to make the tetrahedron.
+
+You could do this
+with bigger polyhedra,
+
+too, like octahedron, anything
+with equilateral triangles,
+
+but tetrahedron is the
+smallest where it works.
+
+Just two of them glued face
+to face would not work,
+
+but this way does work.
+
+Is that true?
+
+Now I've got to think about two
+of them joined face to face.
+
+I don't think it works.
+
+Otherwise, we would
+have done that.
+
+Oh yes, I think I see why.
+
+Why doesn't this work?
+
+I should say it doesn't work
+if the spikes are really tall
+
+and the base is really flat.
+
+I'm going to define
+what "really" means,
+
+but we'll get there.
+
+So here's our witch's hat.
+
+When this spike is really
+tall, these angles, alpha,
+
+are very close to 90,
+a little bit under 90.
+
+This angle in the floor here--
+well, this angle in the floor
+
+is about 60, probably
+actually is exactly 60.
+
+This is an equilateral triangle.
+
+So if this thing is very flat,
+this angle will be almost 300
+
+because it's 360 minus 60.
+
+It'll be a little bit less
+than 300 but almost 300.
+
+These matter.
+
+In particular, the
+total sum of angles
+
+here is 300 plus twice
+90, which is big.
+
+It's bigger than 360.
+
+That's the point.
+
+In fact, 300 plus one
+of these angles, 90,
+
+would be almost 390,
+which is way above 360.
+
+So this has negative curvature,
+and even if you cut out
+
+one of the spike
+triangles, it would still
+
+have negative curvature.
+
+That's going to be bad
+news because let's just
+
+imagine for the moment.
+
+We know unfolding
+things with boundary
+
+is hard, but let's pretend
+for now that you wanted
+
+to unfold a hat in isolation.
+
+You wanted to unfold it into
+one piece without overlap.
+
+Think about what you could do.
+
+I have to cut with
+a spanning forest,
+
+I guess, meaning
+it's acyclic, it's
+
+got to hit all the vertices.
+
+There's only four vertices here.
+
+How could I hit all the
+vertices with a forest?
+
+You may recall from way back
+when that trees have leaves.
+
+Every tree has at
+least two leaves.
+
+Here I might have multiple
+trees, maybe, but unlikely,
+
+and I have to have
+at least to leaves.
+
+Where could those two leaves be?
+
+Could they be at any leaves
+or vertices at degree one?
+
+Could they be at any of
+these three vertices?
+
+No, because they have
+negative curvature.
+
+We know a vertex with
+negative curvature
+
+has to have at least
+two cuts incident to it.
+
+You can't stop at
+these three vertices.
+
+That only leaves one
+vertex and the boundary.
+
+So the only thing
+you can do if you
+
+want to visit all the
+vertices and start somewhere
+
+on the boundary and get
+to the x, get to the peak.
+
+That's all you can do.
+
+You couldn't have multiple
+connections to the boundary
+
+because then you
+would disconnect.
+
+Then there's really
+only two choices
+
+and they're
+reflectionally symmetric.
+
+And we're only allowed
+to go along edges.
+
+It's super constrained.
+
+You can go here, walk
+around, and go up,
+
+or you can walk around
+the other way and go up.
+
+Those are actually slightly
+different because you
+
+have two choices of which
+edge to follow here.
+
+They're both screwed
+because if you
+
+look at this point, the
+white dot, or the white dot
+
+up there, what remains
+here on the outside
+
+is almost 300 degrees
+of material on the base
+
+plus one of the 90 degree
+faces, the back one
+
+that you can't see.
+
+It's easier to see here.
+
+You have the 300
+degrees on the bottom
+
+and then the white face
+is still attached to it,
+
+and that's almost 390.
+
+When you flatten
+that thing, it's
+
+going to overlap
+itself at that point.
+
+Bad news.
+
+So this just says, if I
+look at a hat in isolation,
+
+it can't unfold, but that's
+not what I care about.
+
+I care about four of
+them joined together.
+
+Suppose you had some
+unfolding of the whole thing,
+
+and then I look
+at, well, what cuts
+
+happen within the witch's hat?
+
+I know the witch's hat
+cannot remain in one piece.
+
+Therefore, it must
+be disconnected
+
+into multiple pieces,
+something like this.
+
+Again, the cuts have to visit
+all the vertices somehow,
+
+but we know from the
+perspective of a single hat,
+
+that hat must split
+into two parts.
+
+There are lots of things
+you could consider.
+
+Let's suppose this is
+possible, not even worry
+
+about these kinds of pictures.
+
+Well, I claim we have a problem.
+
+Here's a tetrahedron.
+
+These vertices are all
+the same point, actually.
+
+I've just unfolded
+the tetrahedron
+
+because it's way easier
+to draw in two dimensions.
+
+So if I look at the hat
+that is on this triangle,
+
+this hat gets disconnected
+into two parts.
+
+There's only three
+connection points
+
+to the rest of the world.
+
+So what these pictures
+have to look like is they
+
+connect two of the vertices
+by a collection of cuts.
+
+If you're going to
+cut into two halves,
+
+you've got to have
+a path across,
+
+and there's only three
+vertices to visit.
+
+There's some collection
+of cuts that go from,
+
+let's say, this
+vertex to this vertex.
+
+At this point,
+everything's symmetric.
+
+Maybe it would be more obvious
+if I started the center.
+
+It could be from
+here to there, could
+
+be from here to there or from
+here to there, but at least one
+
+of those things exist,
+and by rotational symmetry
+
+of this diagram,
+say it's that one.
+
+Well, what happens to this face?
+
+Could there be
+something like this?
+
+No, because then this
+would be disconnected
+
+from the rest of the world.
+
+So suddenly, this
+hat is constrained.
+
+Maybe it could look like this.
+
+You have a choice.
+
+It could look like
+that or like that,
+
+but by reflectional
+symmetry, same thing.
+
+So let's say this one.
+
+Remember, x is the
+same everywhere.
+
+Well, that means
+this is impossible
+
+because this edge is
+actually glued to this edge,
+
+and so then this thing
+would be disconnected
+
+from the rest of the world.
+
+So there's a couple
+of possibilities.
+
+It could look like this,
+or it could look like this.
+
+It was one of those
+two for this face.
+
+We've got one face left.
+
+This is impossible because
+this edge glues to this one,
+
+so imagine this thing being
+picked up and moved over here.
+
+So we have a wiggly line
+here and then this stuff,
+
+and so that would
+be disconnected
+
+from the rest of the world,
+so that can't happen.
+
+What about this one?
+
+Is that the harder one?
+
+I don't know.
+
+It's been a while since
+I've used the argument.
+
+If we have this
+together with this,
+
+that's clearly bad because
+that forms a cycle.
+
+No good.
+
+But what if I have this
+together with this one?
+
+It gets hard to see.
+
+It's bad.
+
+It's a cycle.
+
+It starts and ends at x,
+and if you fold it up right,
+
+you'll see there's really
+two sides to that cycle.
+
+It's actually forced,
+so that's bad.
+
+All right, one more
+choice, this one.
+
+If I do this together
+with this one,
+
+that's going to be bad
+because that's a cycle.
+
+We start and end at x.
+
+What if I do this
+one and that one?
+
+Well, that's also
+bad because here's
+
+a cycle that starts
+at x, ends at x.
+
+This and this form the
+inner of the cycle.
+
+All cases are bad,
+so no edge unfolding.
+
+Tragic.
+
+We can think briefly about
+the case-- do I have time?
+
+I have 10 seconds.
+
+About the case where
+there are two triangles.
+
+I guess I should
+draw them like this.
+
+So this point is the
+same as this point.
+
+So if I try to simplify this,
+instead of using four hats,
+
+I just use two hats,
+put one here, one here.
+
+Then I could do something
+like this, I think,
+
+and maybe that's OK if
+there's no cycle formed there.
+
+So we really needed the
+tetrahedron somehow.
+
+I think it does work for
+octahedron and larger also,
+
+but just two triangles
+is not enough.
+
+And that is unfolding.
+
+We did not always edge foldable
+for general polyhedra, even
+
+topologically convex polyhedra.
+
+Next time, we'll talk more
+about general unfolding
+
+of arbitrary polyhedra.
\ No newline at end of file
diff --git a/vPQ9a_xIqRg.txt b/vPQ9a_xIqRg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..30aa4c4b141da857e5cf2df30176eee1251fcc6e
--- /dev/null
+++ b/vPQ9a_xIqRg.txt
@@ -0,0 +1,2851 @@
+The following content is
+provided under a Creative
+
+Commons License.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Let's get started.
+
+Settle down.
+
+Settle down.
+
+Welcome to 3.091.
+
+I'm Donald Sadoway and I'm going
+to be your instructor
+
+this semester.
+
+So what I want to do today
+is to introduce my plans.
+
+I've got plans for you.
+
+Plans for learning.
+
+I want to talk a little bit
+today about those plans,
+
+introduce myself, introduce
+my class curriculum--
+
+the path forward.
+
+So let me begin by saying that
+3.091 is the most important
+
+class you will take at MIT.
+
+It's true.
+
+But, you know, anybody who
+stands in front of you to
+
+lecture should say the same
+thing about his or her class.
+
+If they don't believe that they
+shouldn't be standing in
+
+front of you lecturing.
+
+The difference is when
+I say it, I'm right.
+
+[LAUGHTER]
+
+PROFESSOR: And it's not just
+an opinion, it's because of
+
+the content of 3.091.
+
+3.091 is about chemistry.
+
+It's about the central science,
+but it's not just
+
+about any old chemistry.
+
+This isn't a class that you
+could take anywhere else in
+
+this country.
+
+This is the only place that
+you can take 3.091.
+
+3.091 is solid state
+chemistry.
+
+Now why do we talk about
+solid state chemistry?
+
+Because engineering systems
+are made of solids.
+
+Now I know what you're
+thinking-- oh, he said solid
+
+state, he's going to talk
+about the chemistry that
+
+constitutes his laptop computer
+or the chemistry that
+
+constitutes this
+laser pointer.
+
+And that's true.
+
+We will talk about
+that chemistry.
+
+But we will also talk
+about soft matter.
+
+We as human beings are
+chemical machines.
+
+When this hand changes shape,
+it is a polymer that is
+
+changing conformality.
+
+These eyes are photodetectors,
+band gap of about
+
+two electron volts.
+
+They're not made of
+gallium nitride.
+
+They're made of organic
+compounds.
+
+Inside, what supports us,
+it's a ceramic skeleton.
+
+So solid state chemistry
+describes
+
+life science as well.
+
+Well, what we're going
+to learn in
+
+3.091 is the rudiments.
+
+We're going to learn
+the rudiments.
+
+So what I'm going to do today is
+now go through some of the
+
+basic organization.
+
+So tomorrow you're going
+to meet your recitation
+
+instructors and get to know each
+other and get to know the
+
+recitation instructor.
+
+Today I'll say a few words about
+myself so you know who's
+
+standing in front of you.
+
+I graduated from the University
+of Toronto in
+
+chemical metallurgy, came down
+here in 1977 to spend a year
+
+as a postdoctoral fellow and, I
+guess, I lost track of time.
+
+Now what's my research?
+
+My research is in
+electrochemistry.
+
+Electrochemistry is the most
+important branch of chemistry.
+
+Do you notice some theme in
+my professional life?
+
+See, I have tenure.
+
+So what does that mean?
+
+It means you find your passion
+and pursue it.
+
+You don't waste time on
+trivia, all right?
+
+And that's what I urge
+you to do: Find your
+
+passion and pursue it.
+
+So what's my passion?
+
+My passion is electrochemistry
+in nonaqueous media.
+
+Anything but water.
+
+Let the rest of the world
+work on water.
+
+I work on molten salts, ionic
+liquids, and polymers.
+
+And what's the reason
+for this?
+
+There's an application.
+
+I'm in the School
+of Engineering.
+
+So I'm interested in
+environmentally sound
+
+technologies for metal
+production, all right?
+
+Right now looking at titanium,
+iron recycling as well.
+
+I'm also interested in
+electrochemistry as it applies
+
+to energy storage, energy
+storage for mobile power.
+
+See this gal here?
+
+She's got the cell phone.
+
+She's not even looking
+where she's driving.
+
+[LAUGHTER]
+
+PROFESSOR: So making safe
+batteries out of
+
+earth-abundant, accessible
+materials for portable power,
+
+ultimately to drive the car with
+electrons, electric fuel,
+
+to eliminate this country's
+
+dependence on imported petroleum.
+
+We can do it.
+
+How?
+
+By inventing.
+
+By inventing.
+
+And the way we're going to
+invent is to learn the lessons
+
+in 3.091 that will give us the
+chemistry we need to invent a
+
+battery that can send that car
+250 miles on a single charge,
+
+and put it in a show room for
+the same price as a car with
+
+an internal combustion engine.
+
+The only thing that stands
+between that image and where
+
+we are today is invention, and
+the requisite material is
+
+right here in this class.
+
+We're also looking at
+colossal batteries.
+
+Store the grid.
+
+Enable renewables,
+wind, solar.
+
+And then, lastly, let's never
+forget about dreaming.
+
+So if we want to dream and
+imagine that man will return
+
+to the moon or maybe even go to
+Mars, we're going to have
+
+to be able to produce oxygen.
+
+We'll live like the pioneers,
+produce oxygen from local
+
+resources, produce structural
+metals, and even produce
+
+photovoltaic silicon so they can
+generate their own energy
+
+from local resources.
+
+And so electrochemistry is the
+key enabler for that as well.
+
+So now let's turn to the whole
+underpinning of 3.091.
+
+If we take a look at the
+performance of any engineering
+
+system it's a combination
+of the design and the
+
+construction.
+
+Now the construction is both the
+workmanship and the choice
+
+of materials.
+
+Now how do we choose
+materials?
+
+We choose them on the basis
+of their properties.
+
+So, for example, here's an
+
+application: a beverage container.
+
+This one I'm holding is made
+out of an aluminum alloy.
+
+It's a metal.
+
+When I was your age, they
+had steel beverage cans.
+
+You can take this same beverage
+and contain it in a
+
+glass bottle.
+
+You can contain it in
+a polymer bottle.
+
+Why do we make those
+various choices?
+
+Because they have the right
+mix of properties.
+
+Now how do you determine
+the properties?
+
+Properties obviously are
+determined by the composition.
+
+We wouldn't make this thing
+out of sodium chloride.
+
+It would dissolve.
+
+So composition is important,
+but atomic arrangement is
+
+important as well.
+
+Example is 1/2-inch-thick
+pine board compared to a
+
+1/2-inch-thick piece
+of plywood.
+
+Both pine, but the
+1/2-inch-thick pine board is
+
+one solid pine board.
+
+I can take that pine board and
+I can fracture it if I strike
+
+it along the grain.
+
+But the 1/2-inch-thick plywood,
+I can't do that
+
+because it's 1/8-inch sheet
+pine cross-laminated.
+
+1/8 inch north-south, 1/8 inch
+east-west. If I try to cut
+
+through that board, I can't
+advance the fracture.
+
+Same composition, different
+atomic arrangement.
+
+So the thesis of 3.091 is that
+the electronic structure of
+
+the elements holds the key
+to understanding that
+
+relationship between
+composition, atomic
+
+arrangement, and properties.
+
+And once you have properties
+that's how
+
+you make your selection.
+
+And away we go.
+
+And that's how we got the
+syllabus of 3.091.
+
+So the syllabus has
+two major blocks.
+
+The first block is general
+principles of chemistry-- it's
+
+going to be about the
+first five weeks--
+
+and that's the same stuff that
+you get here, 5.111, 5.112,
+
+the basics of electronic
+structure and bonding.
+
+And then we part company and
+in 3.091 we dig down into
+
+solid state chemistry.
+
+You don't have to take notes.
+
+You can relax.
+
+All this is going to be
+burned to PDF and
+
+posted at the website.
+
+So everything that you see in
+this class that goes up on the
+
+screen is archived for you.
+
+This lecture is being video
+recorded right now and within
+
+an hour will be posted
+at the website.
+
+So in the unlikely event that
+you can't quite come to class,
+
+it is available.
+
+[LAUGHTER]
+
+PROFESSOR: So now what I want to
+do is introduce some of the
+
+operational aspects
+of the class.
+
+And we had some handouts
+going around.
+
+If you didn't get them we
+can get you extras.
+
+But again, this is all posted
+at the website.
+
+So you know who I am.
+
+The key person in this operation
+is my administrative
+
+assistant, Hilary Sheldon, and
+she's just down the hall.
+
+You can roll a penny down
+the hall from here
+
+and get to my office.
+
+So if you tell me you tried
+looking for me, you couldn't
+
+find me, I know you couldn't
+have been trying very hard.
+
+The text is a two-volume set
+consisting of the text
+
+Chemistry: Principles, Patterns,
+and Applications by
+
+Averill and Eldredge, and then
+a second volume that consists
+
+of miscellaneous readings
+taken from other
+
+Prentice Hall texts.
+
+And it's identical in content to
+the blue book that was used
+
+last year and the year before.
+
+So if you get a copy of
+that blue book, you
+
+don't have to buy these.
+
+I don't work for Prentice Hall,
+I'm not trying to sell
+
+books, but we will take the
+homeworks out of the books to
+
+a great extent.
+
+And the page numbering is the
+same, so anything this year or
+
+the last two years
+will be fine.
+
+If you have to buy something,
+you'll have this.
+
+This one will come with a CD
+that will get you into a
+
+mastering chemistry, which
+is a sort of a tutorial,
+
+computerized system to help
+you with certain homework
+
+problems.
+
+The lectures, Monday, Wednesday,
+Friday, here in
+
+this room at 11 o'clock.
+
+The lecture starts at five
+minutes after the hour--
+
+gives you five minutes
+to get in--
+
+and then the lecture
+stops at five
+
+minutes to the next hour--
+
+time for you to leave and then
+for the next class to arrive.
+
+And what I'm going to try
+to do is establish
+
+some plug flow here.
+
+So what I'm going to try is to
+have everybody leave by the
+
+exit to the north here to my
+right, and there's also an
+
+exit over the top back.
+
+So leave to your left and that
+way it'll be easier for the
+
+next class to come in.
+
+And maybe we can persuade the
+people here before us to do
+
+the same and then it'll
+be easy to change.
+
+I don't know why but there's
+this sort of-- everybody has
+
+to charge to this door.
+
+And I just stand here and
+watch people collide.
+
+And I don't know.
+
+Just interesting social
+experiment.
+
+And there are two doors.
+
+I don't understand why people
+do this, but I'm not in the
+
+social sciences.
+
+Recitations.
+
+Recitations will meet Tuesdays
+and Thursdays.
+
+So you'll go to the same hour
+on Tuesday and Thursday.
+
+The section should be
+roughly 20 students.
+
+And that's where the question
+and answer occurs.
+
+Here it's largely I
+talk, you listen.
+
+I've got time for a question
+like, hey, shouldn't that be a
+
+minus sign?
+
+I can take something
+really quick.
+
+But where you get to really
+interact with the instructor
+
+is in recitation.
+
+And I've given a direction to my
+recitation instructors not
+
+to give you a fourth
+and fifth lecture.
+
+You control the content
+of the recitation.
+
+So you have to come
+to the recitation
+
+prepared with questions.
+
+So they're supposed to walk in
+and say, good morning, good
+
+afternoon, what are
+your questions?
+
+And you can say, I didn't
+understand the last five
+
+minutes of the lecture
+yesterday.
+
+Would you do number five
+on the homework?
+
+Would you go over secondary
+bonding?
+
+That's the sort of thing
+that's supposed
+
+to happen in section.
+
+You've been assigned
+by the Registrar.
+
+You are forbidden to change
+your section on your own.
+
+You can't just squat
+in another section.
+
+We do this with the intention
+of trying to keep the
+
+enrollment roughly uniform.
+
+We don't want sections growing
+to 35 because then that limits
+
+your ability to interact.
+
+If you've changed classes or
+you've picked up a UROP, or
+
+what have you, and your
+situation has changed, please
+
+go down the hall and meet with
+my assistant Hilary, who will
+
+then arrange to move you.
+
+And that way we can keep some
+control over the section size.
+
+Again, you may not change
+simply on your own.
+
+And it has to be with cause,
+academic cause.
+
+You can't go in and say, I was
+assigned to the 9:00 am
+
+section and I don't
+do mornings.
+
+That's not going to work.
+
+Homework.
+
+Homework is very
+important here.
+
+Homework is a little bit
+different, though, in 3.091.
+
+You're not going to be
+asked to turn in
+
+homework for grading.
+
+Instead, at the beginning of
+each unit, you will be given
+
+homework with the
+model solutions
+
+right at the beginning.
+
+This is a study aid, and you can
+use the model solutions to
+
+help you understand the
+homework material.
+
+Now since we're not asking you
+to turn anything in and we do
+
+want to stimulate interest in
+the homework, we found a way
+
+to stimulate interest. And that
+is that once a week in
+
+section you will have
+a 10-minute quiz
+
+based on the homework.
+
+That will ensure that
+you've at least
+
+looked at the homework.
+
+And those weekly quizzes will
+be graded, and the aggregate
+
+of all of those quiz scores will
+constitute your homework
+
+grade in the subject.
+
+And you must take
+those quizzes.
+
+If you don't take the quiz--
+
+you got sick or some personal
+emergency came up-- contact
+
+your recitation instructor and
+within a week of the date of
+
+the original quiz arrange
+to take a makeup.
+
+If you don't take the
+makeup, we're going
+
+to give you a zero.
+
+And there's no dropping
+of lowest score.
+
+Somewhere there's this in the
+lore here that, oh, you can
+
+drop the lowest score, the
+lowest two scores.
+
+People come to me with this
+proposal and I say no.
+
+[LAUGHTER]
+
+PROFESSOR: So let's
+get started.
+
+This is homework number one.
+
+It's assigned today.
+
+We're going to save paper--
+just go to the website--
+
+and you'll be tested on
+Tuesday, next Tuesday,
+
+September 15, at the beginning
+of section.
+
+At the beginning of section
+there'll be a 10-minute quiz
+
+based on that homework,
+and you can get the
+
+homework and so on.
+
+By the way, here's what the
+homework looks like.
+
+Chapter 1, Chapter
+3 of Averill.
+
+Averill is the major text.
+
+We just refer to it by the
+author's last name.
+
+So taken from Averill.
+
+By the way, I don't like to
+use this unpleasant term
+
+"test." I like to refer to it as
+a celebration of learning.
+
+[LAUGHTER]
+
+PROFESSOR: So it's
+a celebration.
+
+We're going to start celebrating
+on Tuesday.
+
+There's the website
+by the way.
+
+You probably want to
+bookmark that.
+
+You're probably going
+to go to that a lot.
+
+We're going to keep celebrating,
+and so we will
+
+have some monthly celebrations,
+monthly tests,
+
+and they've already
+been scheduled.
+
+And you will write those tests
+during the normal class time.
+
+But on those days we will
+spread you out a bit.
+
+I like to see some vacancies.
+
+So you will not be sitting
+one next to another.
+
+There'll be at least one human
+vacancy next to every human,
+
+and that way you've got room to
+spread out, keep your eyes
+
+on your own work.
+
+So those are the dates
+and there'll be
+
+more of that in time.
+
+Now when you take the monthly
+test, I allow you to use aids.
+
+So everyone will be given in
+recitation tomorrow a Periodic
+
+Table of the Elements, very
+nice one, laminated one.
+
+So you take that with you to the
+test. In fact, you should
+
+take this with you everywhere.
+
+[LAUGHTER]
+
+PROFESSOR: If I run into you at
+Harvard Square, I want to
+
+see the Periodic Table, because
+every educated person
+
+has the Periodic Table.
+
+You get a table of constants.
+
+So you'll have one of these.
+
+You'll get that tomorrow
+as well.
+
+Paper copy, and on there are all
+the constants so you don't
+
+have to remember that the
+permittivity of vacuum is 8.85
+
+times 10 to the minus
+12 farads per meter.
+
+It's on there.
+
+I urge you to use that when
+you do your homework.
+
+So it's always amusing to me
+during the time of the first
+
+monthly celebration, somebody's
+looking at this as
+
+though it's today's newspaper
+and they're
+
+looking, where is that?
+
+Sort of revealing about the
+intensity with which the
+
+homework has been embraced.
+
+Calculator, something to
+calculate with, and I don't
+
+care if you bring in a graphing
+
+calculator or a mainframe.
+
+I don't care.
+
+[LAUGHTER]
+
+PROFESSOR: And you're allowed
+an aid sheet, an 8 1/2-by-11
+
+sheet of paper.
+
+And you can write on
+the front, you can
+
+write on the back.
+
+You can photoreduce previous
+exams down to micro-dot size.
+
+I don't care what you put on
+it, but with this, you have
+
+then no excuse to say I really
+understood this stuff, but I
+
+couldn't remember a formula.
+
+Actually, many students tell me
+that the act of preparing
+
+the aid sheet organizes the
+subject matter in their minds.
+
+They bring this with them to
+the exam, and they never
+
+consult it, but it just soothes
+the nerves and makes
+
+sure that everybody does well
+on the monthly test.
+
+The weekly test, no.
+
+The weekly test you bring your
+Periodic Table and table of
+
+constants, but no aid sheet.
+
+For the weekly test,
+it's a very
+
+concentrated amount of material.
+
+And I'm not going to test your
+memories, because that doesn't
+
+prove anything to me.
+
+And then, of course, the
+celebration of celebrations is
+
+the final exam.
+
+[LAUGHTER]
+
+PROFESSOR: That's huge.
+
+That's a huge celebration.
+
+It's three hours.
+
+See, these are really
+50 minutes.
+
+This is three full hours.
+
+The time and location will
+be set by the Registrar.
+
+We should know by October 1.
+
+The final exam period is
+December 14 to 18.
+
+And so what I urge you to do
+is as soon as that schedule
+
+comes out and we know when all
+the final exams are going to
+
+be held, then you book your
+passage for the holidays.
+
+Do not get that order
+reversed.
+
+You cannot come to me and
+say, I got a really
+
+good price on a ticket.
+
+I'm going Acapulco on the 15th
+of December, and your exam is
+
+on the 16th of December.
+
+I'll say, you just got
+a zero on the final.
+
+You have to be here for that.
+
+You know why?
+
+I have to be here for that, you
+can be here for that, too.
+
+There are about a quarter of a
+million students in Boston.
+
+It's a great college town, but
+at Christmas time, it's
+
+pandemonium at Logan Airport.
+
+So you want to book your passage
+early, but you can't
+
+do it until you know what your
+final exam obligations are.
+
+Grading.
+
+Freshman, you know, it's
+pass/no record.
+
+Pass/no record.
+
+And so that means that if you
+struggle and things don't go
+
+well, you don't have any
+blemishes on your record.
+
+Unfortunately, some of the
+upperclassmen will tell you as
+
+pass/no record, you
+now, barest pass
+
+imaginable/ no record.
+
+Well, I hate to let you know
+this, but increasingly I am
+
+being asked by medical
+schools, law schools,
+
+scholarship providers to reveal
+the scores on the
+
+freshman year.
+
+So think about that before you
+call Hilary in late November
+
+saying, what do I need
+to get a 50?
+
+I need a 32 on the final?
+
+OK.
+
+But Lord help you, you
+get a 31 you go down.
+
+[LAUGHTER]
+
+PROFESSOR: Upperclassmen get
+the luxury of the entire
+
+alphabet: A, B, C, D, F.
+
+The final grade composition.
+
+1/6 for homework--
+
+that's the aggregates of the
+weekly test scores-- and 1/6
+
+for each of the three tests.
+
+And then the final
+is 2/6, or 1/3.
+
+I didn't want to get into
+transcendental numbers, so I
+
+made it 33 exact, 16.75 exact.
+
+I could have made it 16.77, I
+could have made it 16.81, I
+
+could have made it
+anything I want.
+
+I'm the professor.
+
+But I chose 16.75.
+
+Bottom line here is it's really
+dumb to fail the final.
+
+If you passed the final, you're
+pretty much assured
+
+that we're going
+to be favorably
+
+disposed to passing you.
+
+But you fail the final
+that says two things.
+
+It says, number one, you don't
+have a grasp of the overall
+
+year, but it also sort of
+indicates that you ran out of
+
+steam partway through the
+semester and stopped working.
+
+It's very bad.
+
+You get a lot of good advice
+from upperclassmen, but
+
+sometimes--
+
+I'd ignore that one that says,
+hey, you don't have to do that
+
+well on the final.
+
+Anyway, so you have to
+get a C level as
+
+a freshmen or greater.
+
+And, by the way, we do
+not grade on a curve.
+
+I've seen it in magazines
+this last year that
+
+MIT grades on a curve.
+
+I don't where they
+get that from.
+
+I don't grade on a curve.
+
+Your success does not come at
+the expense of your neighbor.
+
+As far as I'm concerned
+everybody in this
+
+class can get an A.
+
+Again, I'm the professor,
+all right?
+
+So you say, well, how
+do you know that 50
+
+is the right number?
+
+Why isn't it 55?
+
+Why isn't it 75?
+
+Well, I know.
+
+I know.
+
+How do I know?
+
+Because when we grade, we set up
+the point scheme so that if
+
+the student has the mastery of
+the barest level of competency
+
+of the key concept the
+point scheme must
+
+reflect a passing grade--
+
+5 out of 10, 5 out of 9--
+
+and you propagate
+that through.
+
+I don't care how much is
+written, if it doesn't
+
+demonstrate basic mastery of
+the key concept the point
+
+scheme must give 4, 3, 2, 0.
+
+Maybe a 1.
+
+And so that, if you propagate it
+through the whole semester,
+
+means 50 is a pass.
+
+There's some wiggle
+room there.
+
+How do I know 49.7 is a
+fail and 50 is a pass?
+
+That's when I call your
+recitation instructor.
+
+[CELL PHONE RINGING]
+
+PROFESSOR: Let's kill that.
+
+We're going to get to
+that in a second.
+
+Let's call the recitation
+instructor.
+
+And what happens?
+
+I ask the recitation instructor,
+well, what can you
+
+tell me about this young lady?
+
+And, oh, she came to all my
+classes, she tried really
+
+hard, she came to
+office hours.
+
+I don't think the exam is a
+proper reflection of her
+
+understanding.
+
+I'll listen to that and
+maybe we'll promote.
+
+If, on the other hand, I get the
+response, I never saw her,
+
+didn't come to class.
+
+I repeatedly reached out to her,
+ignored my entreaties,
+
+she's going down.
+
+[LAUGHTER]
+
+PROFESSOR: OK.
+
+Website.
+
+This is what the website
+looks like.
+
+There's a number of tabs here.
+
+The readings are there, the
+videos are there archived.
+
+The schedule--
+
+what's going to be coming up.
+
+So, for example, this is
+what's going on today.
+
+It says what the topic is,
+roughly what the readings are.
+
+I know today you didn't come
+to class having read.
+
+And it's OK, we'll
+get through it.
+
+But from now on I urge you
+to do the readings.
+
+A couple of topics I'm required
+to talk about.
+
+My management requires
+me to do so.
+
+Academic honesty.
+
+There's a lot of texts here,
+but in plain English, this
+
+says don't cheat!
+
+You know what this means!
+
+Now I don't want to hear,
+well, in my country, the
+
+custom is--
+
+I don't care what they
+do in your country!
+
+You're in my class, and if
+you cheat in my class you
+
+will pay for it.
+
+Very simple.
+
+Accept information of any
+kind from others--
+
+wrong.
+
+Represent somebody else's work
+as your own-- wrong.
+
+You know this.
+
+It was Juvenal, the Roman
+politician, said men need not
+
+so much be instructed
+as reminded.
+
+I'm not telling you anything
+you don't already know, but
+
+I'm going to say it so no one
+can say, well, nobody told us
+
+it wasn't OK to erase our
+answers and hand them back in
+
+for more points.
+
+I just did.
+
+All right?
+
+So if in the unlikely-- but
+it happens every so often.
+
+Maybe every two, three years.
+
+And people get caught.
+
+You know why they get caught?
+
+Because for the first time in
+your life you're being taught
+
+by people who are as
+smart as you are.
+
+[LAUGHTER]
+
+PROFESSOR: My TAs are
+really smart.
+
+And it never ceases to amaze
+me-- somebody succumbs and
+
+does something dishonest,
+and they get caught!
+
+They get busted!
+
+And what happens then?
+
+Then I get angry.
+
+You know why?
+
+Because we can't settle
+that in my office.
+
+You can't come and
+cry in my office.
+
+I have to take this episode to a
+committee here at MIT called
+
+the Committee on Discipline.
+
+It is staffed by faculty, by
+
+administrators, and by students.
+
+And the case is brought before
+the COD at a hearing and a
+
+punishment is decided.
+
+And it can be anything from
+suspension to expulsion.
+
+And of the three categories,
+faculty, administrators,
+
+students, which category do you
+think is most severe on
+
+infringers?
+
+AUDIENCE: Students.
+
+PROFESSOR: Your peers.
+
+You got it.
+
+You know, because people my age,
+old faculty, they'll be
+
+like, oh, they're just
+kids, whatever.
+
+The students say, no!
+
+Throw them out!
+
+[LAUGHTER]
+
+PROFESSOR: So it's not going to
+be me that's going to expel
+
+you, it's going to
+be your peers.
+
+So don't do it.
+
+And if you're ever in an exam
+and somebody's pressuring you,
+
+just raise your hand and
+ask to be reseated.
+
+For all I know, the guy next to
+you has got a bad case of
+
+B.O., you just want to move.
+
+We will not ask any
+questions, so take
+
+yourself out of the situation.
+
+Conduct yourself
+appropriately.
+
+Classroom behavior.
+
+Now this is the first lecture,
+there's a whole bunch of
+
+violations in here right now.
+
+So I'm going to say it now and
+we'll fix it for next time.
+
+We've got 425 seats here, we've
+probably got 475 people,
+
+and there's only one way we can
+make this system work and
+
+we have to observe certain
+rules of decorum.
+
+And I make the rules.
+
+So if I want to maintain a
+fertile learning environment
+
+I'm going to ask for these
+rules to be observed.
+
+No talking at all.
+
+No talking.
+
+Little conversation here, little
+conversation here--
+
+it disturbs people.
+
+I don't want any
+food or drink.
+
+No food, no drink.
+
+One exception is
+the professor.
+
+[LAUGHTER]
+
+PROFESSOR: Because I do not want
+to have my throat get so
+
+dry that I can't finish talking
+my way through the end
+
+of the class.
+
+Otherwise, no food or drink and
+no disruptive behavior.
+
+No horseplay or anything
+like that.
+
+And wireless communication
+devices must be silenced.
+
+Cell phone goes off, you get
+up, you leave the room.
+
+That's it.
+
+AUDIENCE: Is water OK?
+
+PROFESSOR: If you need water
+because it's some kind of a
+
+health thing, fine.
+
+But I do not want to see a whole
+bunch of people drawing
+
+on water bottles.
+
+Don't need it.
+
+Don't need it.
+
+You can go 50 minutes without
+your little--
+
+whatever.
+
+[LAUGHTER]
+
+PROFESSOR: You know why?
+
+I'll tell you why.
+
+It's not because I'm trying
+to be a control freak.
+
+This is a chemistry class, but
+it's chemistry-centered.
+
+You didn't just come to MIT to
+learn some geeky techno stuff.
+
+You're preparing for a
+professional career, and part
+
+of that is how you behave, how
+to act as a professional.
+
+And you cannot learn behavior
+by doing problem sets.
+
+How do you learn behavior?
+
+You learn behavior
+by observation.
+
+And how does one
+teach behavior?
+
+By modeling.
+
+If you're in some high-level
+committee meeting and all of a
+
+sudden your cell phone goes off
+and you're scrambling and
+
+you can't find the damn thing,
+it's in the bottom of your
+
+briefcase, right?
+
+I can't tell you how
+vulgar that is.
+
+You're in a professional
+setting, you commit
+
+professional suicide.
+
+And I need to tell you that.
+
+If you think it's
+OK you're wrong.
+
+So let's get in the habit.
+
+Disable the damn thing.
+
+What do you need?
+
+You're going to call
+your stockbroker?
+
+What's so important right now?
+
+And on an exam, that thing goes
+off I take the exam in
+
+front of everybody and--
+
+[MAKING RIPPING NOISE]
+
+PROFESSOR: --we introduce a
+defect, it's called a tear.
+
+[LAUGHTER]
+
+PROFESSOR: And then I put a zero
+on it like this, with a
+
+circle around it.
+
+It's called a donut.
+
+[LAUGHTER]
+
+PROFESSOR: All right.
+
+Now let's talk about
+some lighter
+
+things, more upbeat things.
+
+Look, I want you to succeed
+in this class.
+
+Now how are we going
+to succeed?
+
+You go to the listing
+in the bulletin
+
+you'll see this, right?
+
+And you zoom in here
+it says 5-0-7.
+
+What's this mean?
+
+Well the 5 is 5 contact hours.
+
+3 here and 2 with
+your recitation.
+
+The 0 is lab.
+
+There's no lab with
+this class.
+
+So what's the 7?
+
+The 7 is the reading,
+the homework,
+
+preparation, et cetera.
+
+I pledge to you, you give me 7
+hours-- you go to the 5 hours
+
+contact and 7 hours--
+
+you will not just pass this
+class, you will flourish in
+
+this class.
+
+How do I know this?
+
+Because I used to chair the
+committee on admissions and
+
+I've read applications.
+
+I know the quality of individual
+in this room.
+
+You should have seen, there were
+11,000 applications piled
+
+up like this, each dossier like
+this, and they just get
+
+copied down on a four-by-six
+card.
+
+We get here on a Presidents' Day
+weekend and we got stacks
+
+and stacks of the cards.
+
+We're looking at your whole
+academic life is on a
+
+four-by-six card.
+
+And I pick that up
+and I go, yes.
+
+Literally at this speed.
+
+About 45 seconds.
+
+No.
+
+[LAUGHTER]
+
+PROFESSOR: Hell no!
+
+[LAUGHTER]
+
+PROFESSOR: That's how I spent
+Presidents' Day weekend.
+
+And so you got through a very
+grueling selection process.
+
+What's the corollary of that?
+
+Listen carefully to this:
+Everybody in this room has the
+
+intellectual apparatus
+to pass 3.091.
+
+The only people who fail
+3.091 are people who
+
+choose to fail 3.091.
+
+They choose not to come to
+class, they chose not to go to
+
+recitation, they chose not
+to work the homework.
+
+I don't know why they
+make those choices.
+
+But I guarantee you if you give
+me this amount of time,
+
+you'll do well.
+
+It's straightforward.
+
+Number one problem you are going
+to face this fall is not
+
+secondary bonding, it's
+time management.
+
+So I used to call this
+strategies for--
+
+what did I used to call it?
+
+I forgot.
+
+I used to have it something
+like, survival strategies.
+
+But I don't want
+you to survive,
+
+I want you to flourish.
+
+So I call it recipe
+for success.
+
+There are different venues
+for learning.
+
+OK?
+
+So lecture, that's here.
+
+That's my responsibility.
+
+Recitation, that's Tuesdays
+and Thursdays.
+
+That's my staff.
+
+Now reading, that's you.
+
+Homework, that'd be you.
+
+Weekly quizzes is you,
+monthly tests is you,
+
+final exam is you.
+
+[LAUGHTER]
+
+PROFESSOR: What we have
+here is a partnership.
+
+See?
+
+[LAUGHTER]
+
+PROFESSOR: So I'll do my
+part, you do your part.
+
+You know, one of the things
+beyond the basic learning of
+
+the chemistry that we're going
+to attempt here is a
+
+transition.
+
+You are going to change in
+ways you can't imagine.
+
+I want you to think about the
+way you are right now, and I'm
+
+going to ask you to think
+about how you feel about
+
+yourself on the last
+day of class.
+
+You will be amazed, and it's
+not because you know a few
+
+more chemical equations.
+
+And what one of the things that
+I want to see happen and
+
+to help facilitate is the
+transition from student, which
+
+you are as a high school
+graduate, to scholar.
+
+And the difference between a
+student and a scholar is a
+
+scholar takes ownership of
+his or her learning.
+
+So you're going to take
+ownership of it.
+
+You know, is this
+going to be on?
+
+Are we responsible for this?
+
+Go back to high school.
+
+Here you're a scholar.
+
+You say, how can I learn
+more about this?
+
+That's the difference.
+
+So I think we've
+covered enough.
+
+I think we don't want to just
+have the whole day, welcome to
+
+MIT, welcome to MIT.
+
+So what we're going to do is
+we'll get into the lecture,
+
+and in the very brief amount of
+time we have left I'm going
+
+to talk about the beginnings
+of chemistry.
+
+We're going to talk about
+taxonomy, classification,
+
+nomenclature.
+
+And to help introduce this I'm
+going to refer to the writings
+
+of William Shakespeare.
+
+We're going to integrate
+some humanities here.
+
+We're going to read from
+Romeo and Juliet.
+
+Maybe there are people here
+who were admitted on the
+
+strength of the performance
+in Romeo and Juliet.
+
+Maybe one of you was Romeo,
+one of you was Juliet.
+
+Maybe one of you did
+the lighting.
+
+Maybe one of you did
+the set design.
+
+Maybe one of you took
+the tickets.
+
+Somehow you were involved,
+right?
+
+Because we're all involved.
+
+So let's take a look.
+
+Act 2, Scene 2.
+
+Romeo: "But soft, what light
+through yonder window breaks?
+
+It is the east"--
+
+that's the east. East Campus
+is that way, right?
+
+[LAUGHTER]
+
+PROFESSOR: "It is the east, and
+Juliet is the sun." That
+
+has nothing to do with
+nomenclature.
+
+Maybe photon emission, but--
+
+that's a joke.
+
+We'll get to it.
+
+Now Juliet: "O Romeo, Romeo!
+
+Wherefore art thou Romeo?
+
+Deny thy father and
+refuse thy name.
+
+Or, if thou wilt not, be but
+sworn my love, and I'll no
+
+longer be a Capulet."
+See she's a
+
+Capulet, he's a Montague.
+
+You know, the Hatfields
+and the McCoys.
+
+And this is a metaphor.
+
+It's as old as literature.
+
+It's about warring factions,
+two communities that can't
+
+stand each other based
+on prejudice.
+
+And then these two youngsters
+fall in love, and how love
+
+triumphs over hatred,
+and so on.
+
+It's powerful stuff and
+it's written here.
+
+Romeo: "Shall I hear more, or
+shall I speak at this?"
+
+Remember, she's up high, he's
+doing "Shall I hear more,
+
+shall I speak at this?" Fellows,
+the answer to that
+
+question is don't speak.
+
+Don't interrupt her.
+
+All right.
+
+So now she goes, "'Tis but thy
+name that is my enemy.
+
+Thou art thyself, though
+not a Montague.
+
+What's Montague?
+
+It is nor hand, nor foot, nor
+arm, nor face, nor any other
+
+part belonging to a man.
+
+O, be some other name!
+
+What's in a name?
+
+That which we call a rose by any
+other word would smell as
+
+sweet." That's properties,
+right?
+
+"So Romeo would, were he not
+Romeo called, retain that dear
+
+perfection which he owes
+without that title.
+
+Romeo, doff thy name, and for
+that name which is no part of
+
+thee take all myself."
+
+Beautiful writing.
+
+400 years ago and it's
+just fantastic.
+
+Well, that's no good.
+
+That's not the way it
+works in science.
+
+In science we have to agree--
+
+[LAUGHTER]
+
+PROFESSOR: We have to
+agree on the name.
+
+And so this is taken from
+Chapter 1 of the text, and
+
+this is the classification
+of matter.
+
+This is about stuff and the
+different forms of stuff.
+
+Over here we have the simplest
+form of stuff,
+
+which is the element.
+
+And we're going to start here
+in 3.091 and we're going to
+
+work our way all the way through
+this table, starting
+
+with electronic structure and
+how electronic structure
+
+governs stuff.
+
+So let's start with
+a history lesson.
+
+We'll start with a
+history lesson.
+
+And the history lesson
+goes like this.
+
+What are the origins
+of chemistry?
+
+The ancient Egyptian hieroglyphs
+refer to khemeia,
+
+which was a chemical process
+for embalming the dead.
+
+You know the Egyptians were very
+fixated on the afterlife.
+
+And the chemists, the chemists
+were revered in that society--
+
+not like here.
+
+They were revered in that
+society because they knew how
+
+to prepare the body
+for the afterlife.
+
+Embalming is a chemical
+process.
+
+A few years ago I
+was in London.
+
+I toured the British Museum
+and came upon this.
+
+This is 18 inches tall.
+
+It's the mummified cat.
+
+It's a fantastic example
+of mummification.
+
+It's a beautiful-- most people
+go zooming right past it.
+
+They're looking at the
+big dinosaurs and
+
+all that other nonsense.
+
+But this, this is beautiful.
+
+Mummified cat.
+
+And then khemeia expanded to
+other chemical processes:
+
+dying of cloth, glassmaking,
+and metals extraction.
+
+The chemist could take dirt
+and turn it into metal.
+
+Sorcery.
+
+Some things haven't changed.
+
+I'm in that tradition: producing
+metal from dirt.
+
+And they were always looking for
+an overarching theme, to
+
+unite the heavens with
+the simple elements.
+
+So the seven known,
+naked-to-the-eye, astronomical
+
+bodies were associated
+with the seven
+
+known chemical elements.
+
+And you could even talk in
+this priestly language.
+
+So if you wanted to make a
+bronze, which is an alloy of
+
+tin and copper, you could say,
+well let's have the confluence
+
+of Jupiter and Venus.
+
+It's all there.
+
+Mercury.
+
+Why do we call it Mercury?
+
+Mercury's a metal that's liquid
+at room temperature.
+
+It's fast. Because Mercury is
+the planet that moves quickest
+
+around the sun.
+
+Very nice.
+
+So this is what we knew
+2,400 years ago.
+
+We had the seven metals,
+carbon, and silicon.
+
+And the beginning of the shift
+from practice to theory, or
+
+from craft to science, is with
+the work of Democritus.
+
+Democritus, who lived
+around 400 BCE.
+
+Democritus, who was Greek.
+
+He described the physical
+world as consisting of a
+
+combination of void
+plus being.
+
+Void plus being.
+
+These are lofty words.
+
+Listen to this.
+
+Void, being not some
+little equation.
+
+It's big, big ideas.
+
+And how did he describe void?
+
+Void is something that we
+would recognize, in his
+
+language, as akin to what we
+recognize to be vacuum.
+
+And being, he said, was
+comprised of an infinity of
+
+atoms.
+
+He coined the term "atom."
+"Atom" comes from the Greek
+
+tomoi, which is to slice.
+
+And then if you put "a" in front
+of it as in apolitical
+
+or amoral, cannot be sliced:
+indivisible.
+
+The atom cannot be sliced,
+and so to these atoms he
+
+attributed these properties.
+
+They're indivisible
+and eternal.
+
+I mean, this takes you all the
+way to E equals m c squared.
+
+From 400 BCE, and that's all
+he had to work with.
+
+This is brilliant.
+
+Absolutely brilliant.
+
+But to show you that things
+don't always go in a linear
+
+fashion for the better,
+along comes Aristotle.
+
+Aristotle, another Greek, and he
+decided, nah, we don't need
+
+all this carbon, sulfur,
+and so on.
+
+He said, we will have four
+essences that will describe
+
+the earthly world.
+
+Four essences.
+
+And here are the
+four essences.
+
+Earth, water, air, fire.
+
+So those are the Aristotelian
+essences.
+
+And there's actually a
+fifth essence that
+
+describes the heavens.
+
+That's why we say something
+is quintessential.
+
+It's heavenly, it's et cetera.
+
+So these are the
+four essences.
+
+All right?
+
+And then it gets even worse
+because he has compounds, a
+
+combination, so you can take
+fire plus earth and make dry,
+
+earth plus water make cold, air
+plus water make wet, air
+
+plus fire make hot.
+
+This is nuts.
+
+[LAUGHTER]
+
+PROFESSOR: And it dominated
+science for a long, long time.
+
+Because we know really earth
+is an aggregate.
+
+It's an aggregate of different
+minerals which are compounds.
+
+Water, as you know,
+is a compound H2O.
+
+Fire is the product
+of combustion.
+
+It doesn't even belong
+in this set.
+
+And air is a solution.
+
+It's a homogeneous mixture of
+nitrogen, oxygen, argon,
+
+rising levels of carbon dioxide,
+sulfur dioxide.
+
+And if you're next to
+an aluminum smelter,
+
+tetrafluoromethane.
+
+And so on and so forth.
+
+And finally this thing
+was knocked down.
+
+So we can look at this chart
+and go back to this one and
+
+say, now we can make
+the connections.
+
+All right.
+
+Here's the way the elements
+looked at the time of the
+
+American Revolution.
+
+The alchemists gave us arsenic,
+antimony, and bismuth
+
+in the 12th, 13th,
+14th centuries.
+
+In 13th century India, there
+was zinc isolated.
+
+There's a tall zinc pillar
+still standing there.
+
+Platinum is an American metal.
+
+It was unknown to
+the Europeans.
+
+It was discovered when the
+Spanish came to the Americas.
+
+Actually, it's kind of ironic
+because plata is silver, so
+
+platina is sort of like a
+diminutive of silver, which in
+
+point of fact is backwards
+because silver melts at 962
+
+degrees Celsius, platinum
+melts at 1768.
+
+It is nobler than silver.
+
+It has catalytic properties.
+
+It is even fashionable in
+jewelry now if you know how to
+
+work with it, because gold melts
+at 1063 and platinum
+
+melts at 1762.
+
+A lot of jewelers can't
+work with platinum.
+
+It's too high-melting.
+
+It's a fantastic metal.
+
+It's an American metal.
+
+[LAUGHTER]
+
+PROFESSOR: It really is.
+
+I mean it's an American metal.
+
+I didn't make this up.
+
+It's true.
+
+And then we see these
+other elements.
+
+Discovered, discovered,
+discovered, discovered.
+
+Now we see modern science.
+
+So what does it mean,
+discovered 1766?
+
+There was no hydrogen
+before 1766?
+
+They found it?
+
+No.
+
+It means that Cavendish isolated
+it and documented its
+
+properties.
+
+Hence, it was discovered.
+
+Now I've been cheating here.
+
+This is actually lined up in
+a way that we already know,
+
+where the story is going to
+end with this, with the
+
+Periodic Table.
+
+I'm just lying them on the table
+in a way that makes it
+
+possible to anticipate.
+
+But this was the first table of
+elements that is of record,
+
+and this was by John Dalton, the
+English chemist, who put
+
+these in order of atomic mass.
+
+They're organized in ascending
+order of atomic mass.
+
+And he also started a system
+of chemical symbols.
+
+And you can see that iron has
+an "I" with a circle around
+
+it, and zinc has a "Z" with
+a circle around it.
+
+And the Swedish chemist
+Berzelius said, you know I
+
+don't think the French are going
+to like to use "I" with
+
+a circle around it for iron,
+or Germans aren't
+
+going to like that.
+
+We better choose something
+a little bit neutral.
+
+So they chose Latin.
+
+And that's why iron is "Fe" for
+ferrum, and gold is "Au"
+
+for arum, and so on.
+
+But this was the
+first attempt.
+
+John Dalton actually
+was a polymath.
+
+He was also working on vision,
+human vision, and he suffered
+
+from an affliction that is
+present in about 10% of men,
+
+which is red-green
+color blindness.
+
+And he did the original work on
+red-green color blindness.
+
+In fact, in some circles it
+is known as Daltonism.
+
+It's the same man,
+John Dalton.
+
+Other classifications.
+
+Dobereiner in Jena talked
+about triads.
+
+And if you took the atomic mass
+of chlorine, added it to
+
+the atomic massive of iodine
+divided by two, you get
+
+something that's not
+too far off the
+
+atomic mass of bromine.
+
+Newlands was a musician and
+he talked about octaves.
+
+So if you start here, if this
+is a diatonic scale, so this
+
+is C, D, E, F, G, A, B, C.
+
+So potassium lies an octave
+away from sodium.
+
+He was ridiculed.
+
+They said, have you considered
+perhaps putting the elements
+
+in alphabetical order?
+
+They were cruel.
+
+Scientists can be very
+cruel to new ideas.
+
+And, in fact, in your book this
+is some of Newlands work,
+
+and you can see to what extent
+it helps understand things.
+
+But the first proper
+organization came in 1869 with
+
+Mendeleyev, and also 1870 with
+Lothar Meyer in Tuebingen, the
+
+Periodic table as we know it.
+
+And this is the set of
+elements that were
+
+known at the time.
+
+And this is a page from the
+paper in which Mendeleyev
+
+published the Periodic Table.
+
+And here's the smoking
+gun right here.
+
+It's right here where he says,
+in this new system, in this
+
+proposed system, there are very
+many missing elements.
+
+Very many missing elements--
+
+that was the key.
+
+Because he knew that even though
+arsenic has the atomic
+
+mass next highest to that of
+zinc not to put arsenic under
+
+aluminum, not to put
+it under silicon.
+
+It had more in common
+with phosphorus.
+
+So he put it under phosphorus,
+and so did Meyer.
+
+But what Mendeleyev did, which
+was a first, he said, there
+
+are missing elements here.
+
+There is an element that lies
+between silicon and tin, and I
+
+predict what it's
+mass will be.
+
+I predict what it's chemical
+formulation will be, how it
+
+will react with oxygen.
+
+The predictions.
+
+And how did he get this?
+
+Because he used to travel by
+train and he would sit in the
+
+train station on his trunk
+playing solitaire.
+
+And he'd be going down
+one suit, and then
+
+there'd be a gap.
+
+And he'd go down the other suit
+and he could go farther.
+
+And so the concept of, I know
+there should be an eight of
+
+spades here, but I have
+to stop at the nine.
+
+I've got a seven but there's
+something in there--
+
+triggered his imagination and
+led him to have the courage to
+
+say, there are elements there
+and I will predict their
+
+properties.
+
+And when they were discovered
+how close he was is shocking.
+
+Absolutely shocking.
+
+So we'll get to that next day.
+
+But before you go I want
+to leave you with this.
+
+This is the portrait
+of Mendeleyev that
+
+you typically see.
+
+This man on in years,
+disheveled, sort of mad
+
+scientist look.
+
+Don't remember that.
+
+Look at this.
+
+This is Mendeleyev, age 35, when
+he proposed the Periodic
+
+Table of the Elements.
+
+OK.
+
+We'll adjourn.
+
+We'll see you on Friday.
\ No newline at end of file
diff --git a/vPXTDpXwBs0.txt b/vPXTDpXwBs0.txt
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--- /dev/null
+++ b/vPXTDpXwBs0.txt
@@ -0,0 +1,4031 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: All right.
+
+Good afternoon, everyone.
+
+Today, we are going
+to have two topics.
+
+In the first half we are going
+to discuss visual illusions,
+
+and in the second
+half we are going
+
+to talk about prosthetic
+devices for the blind.
+
+What I would like to
+start with is, again,
+
+to send around the
+attendance sheet,
+
+so please put your name to it.
+
+And then, in addition,
+I'm going to send
+
+around some handouts,
+one for each person.
+
+I'm going to hand them
+out in both directions.
+
+Thank you.
+
+The handouts we're
+going to look at,
+
+I'll refer to them
+specifically as we go around.
+
+And I also will show pretty
+much the same handouts, figures
+
+in the handouts, on the screen.
+
+All right.
+
+So for the first half of
+the presentation today
+
+we are going to talk
+about visual illusions.
+
+Now, the main emphasis of
+what I'm going to talk about,
+
+it'll be an attempt
+to convey to you what
+
+kinds of procedures one can use
+to get a better sense of why
+
+we see in illusions what we see.
+
+Some of these approaches
+are strictly behavioral.
+
+And some of them have involved
+experiments carried out
+
+on a more thorough basis using
+electrophysiological procedures
+
+and so on.
+
+But those I'm not going
+to talk too much about.
+
+But I will relate
+what we can figure out
+
+through how the
+visual system works.
+
+Now, because of that, there
+are hundreds of illusions,
+
+and I will emphasize
+those that allow
+
+us to think about why
+we see what we see.
+
+Now, one of these
+illusory effects
+
+is the so-called
+Hermann grid illusion,
+
+and that's the one
+I'm going to start
+
+with because it's a
+fascinating illusion.
+
+If you look at
+this, what you see
+
+is that at the intersections
+you see sort of smudges.
+
+And so the big question arose
+as to why we see these smudges.
+
+Now, does everybody
+see those smudges?
+
+If you look at the
+handouts, I also
+
+show you-- pay attention
+only to the front page,
+
+the one on the left, which
+says the Hermann grid illusion.
+
+So if you look at that
+either on your handout
+
+or you look at it
+on the screen here,
+
+you see these smudges at the
+intersections, not where you're
+
+looking at, but in the
+smudges other than where
+
+you're fixating.
+
+Does everybody
+see those smudges?
+
+OK.
+
+So the question arose why
+we have these smudges.
+
+And back in the
+1960s, an investigator
+
+came up with a
+rather clever idea
+
+of why we see these smudges.
+
+And the person who came
+up with this theory
+
+was a fellow called Baumgartner.
+
+And so what he proposed,
+that this illusory effect
+
+is not directly attributable
+to the center-surround
+
+organization or the receptive
+fields or retinal ganglion
+
+cells.
+
+So what he proposed is that when
+a retinal ganglion cell falls
+
+in the center like this, there's
+more inhibition in the surround
+
+than when it falls along
+not the intersections,
+
+but along the straight lines.
+
+And because of that, there's
+more inhibition here than here,
+
+and that's why we
+see the smudges.
+
+Now, that was a very
+attractive theory.
+
+And in fact, it has appeared and
+still exists in many textbooks
+
+that you read about illusions
+and about vision in general.
+
+Now, OK, so here is
+the exact description
+
+that I just made
+to tell you this.
+
+And of course, you would expect
+that if this is the case,
+
+you should also get the smudges
+if you'd reverse the contrast.
+
+And in fact, that is true.
+
+So here, once again, you see
+the smudges, maybe not quite
+
+as sharp.
+
+But in this case,
+it's whiter smudges,
+
+whereas in the previous
+case, this one,
+
+you have darker smudges.
+
+So that kind of fits
+with that basic idea.
+
+But then, subsequently,
+people began
+
+to play around with various
+conditions to see when you do
+
+and when you don't
+get the smudge effect
+
+and to see whether that
+would fit with this theory.
+
+Now, that's the basic tenet
+in just about everything
+
+that psychologists
+and neuroscientists
+
+working in the visual system do.
+
+They try to critically
+examine various hypotheses.
+
+And doesn't have to
+be just illusions,
+
+it can be a whole
+bunch of other things.
+
+And they do this then by
+systematically manipulating
+
+things in experiments that
+can present these things just
+
+under free viewing
+conditions, as I'm doing it
+
+in terms of these
+handouts, or you
+
+can do it under more
+controlled conditions.
+
+The subjects can look through
+a tachistoscope or something
+
+like that.
+
+All right.
+
+So anyway, let's now look
+at this in a bit more detail
+
+and see what's wrong
+with this theory.
+
+Well, first of all, if
+you look at this figure,
+
+what you can see here that
+you can see the smudges
+
+irrespective of the size
+of the overall display.
+
+Now, that's a problem
+because, of course,
+
+the size of the receptive
+fields in the retina,
+
+in their center-surround
+arrangement, is constant.
+
+So if it were the
+sharp arrangement
+
+that we described about the
+way the center and the surround
+
+are activated by
+the intersections
+
+and the non-intersections in
+the display, that should not
+
+apply to different sizes.
+
+It should only work then
+for a particular size
+
+where you approximate that.
+
+Now, I will elaborate on that
+in more detail in just a minute.
+
+Now, another bug
+that arose here is
+
+that if you now turn this
+display just 45 degrees,
+
+all right, so that it's a
+diamond rather than a square,
+
+the illusory effect has
+declined considerably.
+
+And then to make this
+even more problematic,
+
+and this appears in your
+handout on that backside
+
+of the first page,
+what you can see here
+
+is that when you make
+the lines arranged
+
+in such a fashion at slight
+angles to each other, then
+
+you don't see the
+illusory effect at all.
+
+Whereas here, we also see it
+a little bit less but still
+
+slightly visible.
+
+But here it's not
+visible at all.
+
+And you can compare that even
+better on the handout there.
+
+So the question is,
+why would that be?
+
+Well, we give you
+another example here.
+
+If you make serrated
+edges-- I don't
+
+know if the people in the
+back can see the serrations.
+
+Those of you in front
+can see the serrations.
+
+And when you do that,
+also you fail to see it.
+
+And the problem
+here, of course, is
+
+that if you make these
+slight changes in the angles
+
+of the intersecting lines
+or you make them serrated,
+
+the center-surround
+antagonism should be the same.
+
+And yet such a small change
+causes the illusory effect
+
+to disappear.
+
+So that then, in itself,
+questions the Baumgartner
+
+theory.
+
+Now, there are several other
+factors that enter into this.
+
+This is a very subtle one.
+
+If you look at this side,
+OK, we have different shades
+
+for the lines.
+
+OK?
+
+On this side, we have the
+darkened lines, OK, in front.
+
+And in this case, they
+have them in the back.
+
+And here you see the illusory
+effect, and here you don't.
+
+And once again, how can that
+be if the illusory effect is
+
+due to the center-surround
+antagonism?
+
+Even more dramatic is when
+you do this with colors.
+
+Here you have, again, the
+colored lines in front,
+
+and here you have
+them in the back.
+
+And here you can see
+homonymous shades, all right?
+
+This is darker yellow and so on.
+
+But it's the same color
+but a little bit darker
+
+at the intersections.
+
+So here you get a pretty
+good illusory effect.
+
+But once those white
+lines are in front,
+
+we get very little
+effect at all.
+
+So that then denotes a number
+of problems with the theory.
+
+And then one more fact is that
+when you present the stimuli
+
+at isoluminance, you don't
+get an effect at all.
+
+So that then raised
+some serious questions
+
+about the illusory effect.
+
+And then a
+quantitative study was
+
+undertaken to see just what
+is the layout of the receptive
+
+fields in this display.
+
+And so here what we
+have is a display.
+
+This square here is exactly five
+degrees from your fixation, OK,
+
+and you can calculate the number
+of midget and parasol cells
+
+that are activated
+by that square area.
+
+And you can see in total there
+are more than 360 cells that
+
+are being activated
+in that little region.
+
+And here is a display, in this
+case, of only the ON cells,
+
+and you can double
+that by having the OFF
+
+cells in the same location.
+
+Saying that there's just
+no good correspondence
+
+whatsoever in the
+number of ganglion cells
+
+that are being activated and
+how the center-surround is truly
+
+laid out at a point where
+you get a very good smudge
+
+effect with this illusion.
+
+So this then,
+taken all together,
+
+raises the issue then if indeed
+there's a retina phenomenon,
+
+why is there no fit here?
+
+And so it does look
+like that it's unlikely
+
+that this illusion
+can be explained
+
+by the center-surround
+antagonism theory.
+
+So then another
+theory was advanced
+
+claiming that this doesn't
+take place in the retina,
+
+but instead that it takes
+place in the cortex.
+
+And so another theory
+that was advanced
+
+is saying that this happens
+in the cortex due to the fact
+
+that you have these
+simple cells-- we talked
+
+about those before-- that had
+these elongated inhibitory,
+
+supposedly
+inhibitory, surrounds.
+
+And if one calculates this,
+that can explain the illusion
+
+a little bit better,
+especially since these cells,
+
+even at any given point
+in the visual cortex,
+
+come in several different sizes.
+
+So that's an alternate theory.
+
+But still, further
+research needs
+
+to be done to be able to verify
+whether this theory is more
+
+valid than the center-surround
+theory in the retina, which
+
+certainly is totally wrong.
+
+So I think maybe in
+another 100 years,
+
+they're going to drop the
+Baumgartner theory out
+
+from textbooks and general
+reviews of illusions
+
+and vision.
+
+OK.
+
+So now I want to show you one
+more illusory effect, which
+
+is a variant of the illusion
+that I have just shown you.
+
+And this one is something that
+can drive you nuts, I suppose.
+
+And that appears on the second
+front page, the second sheet,
+
+I should say, of the handout.
+
+You can look at it there,
+or you can look at it here.
+
+And you can see this
+scintillating effect,
+
+and therefore it has been
+called the scintillating grid
+
+illusion.
+
+It was invented by
+fellow called Lingelbach.
+
+All right?
+
+That's a very strong illusory
+effect, very dramatic.
+
+And whether this
+can be explained
+
+by any particular theory
+about the visual cortex
+
+still remains to be settled.
+
+Right now I don't think
+there's a specific theory that
+
+can explain this.
+
+Now, I will now move
+on and talk about yet
+
+another illusory effect,
+or actually a set of them,
+
+that has a much
+better explanation.
+
+This one we don't
+have a handout for.
+
+If you look at
+this display here,
+
+you'll agree that the left and
+right bars here are identical,
+
+right, going in shade
+from light to dark.
+
+All right?
+
+So now what I'm going to
+do here-- what I want to do
+
+is to present these
+two images here.
+
+I want you to fixate
+in the fixation spot,
+
+and we'll count to about,
+I don't know, 20, say.
+
+Keep fixating.
+
+1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
+
+1, 2, 3, 4, 5, 6, 7, 8, 9, 20.
+
+And then I'm going
+to go back here,
+
+and you can see that this side
+is much darker than that one.
+
+Everybody got that effect?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: I'll do it once more.
+
+Pretty dramatic, huh?
+
+OK.
+
+Now I'll tell you
+what I'm going to do.
+
+What I want you to do is to
+look at this with one eye.
+
+OK?
+
+Don't look at it yet.
+
+Wait a while.
+
+Just let your eye get settled.
+
+You're going to look
+at it with one eye.
+
+And then when I switch over,
+I want you to switch eyes.
+
+OK?
+
+All right, ready?
+
+Go ahead now and fixate,
+and we'll count to 20 again.
+
+5, 6, 7, 8, 9, 10.
+
+1, 2, 3, 4, 5, 6, 7, 8, 9, 20.
+
+Switch.
+
+And if you do that, you
+don't have an effect.
+
+OK?
+
+So what does that prove?
+
+Well, that obviously
+proves-- that's why
+
+it's nice to do these little,
+itty-bitty experiments one can
+
+do in minutes-- it proves
+that this is a retinal effect.
+
+And the effect is
+actually due to adaptation
+
+that we have talked about, when
+was it, a couple of times ago.
+
+Now, I want to show
+you yet another effect
+
+that has a similar arrangement.
+
+What I'm going to do here is I'm
+going to put this display on.
+
+And what I'm going
+to do here is I'm
+
+going to turn these
+off successively
+
+as we go around the clock.
+
+OK?
+
+And what I want
+you to do, again,
+
+is to fixate here
+on the cross, OK,
+
+and then I'm going
+to start running it.
+
+And what are you going to see?
+
+A pretty amazing thing
+you're going to see.
+
+What do you see?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah?
+
+You see a green
+spot going around?
+
+Everybody see that?
+
+OK.
+
+So now the big question
+comes up, why on earth
+
+do we see this green spot?
+
+What is the explanation?
+
+Well, this again is
+a retinal effect.
+
+And to test this
+in more detail, we
+
+have to go back to what I
+told you about color vision.
+
+And when I told you
+about color vision--
+
+if you remember we did that
+experiment with Gaussians--
+
+that if you look at the color
+circle, all right, and then
+
+you adapt to a stimulus here,
+which is pretty similar to what
+
+was on the screen,
+then the afterimage
+
+is on the opposite side cutting
+across the color circle.
+
+So the afterimages that
+you see that are in color
+
+can be perfectly explained
+by the color circle.
+
+If you adapt to this,
+this is the afterimage.
+
+You adapt to this,
+this is the afterimage.
+
+It's always straight across
+the center line, center point,
+
+I should say, where you have the
+white center, which perfectly
+
+explains your afterimage.
+
+So what I'll do again, I'll
+show this to you just once more.
+
+OK, here we go, ready?
+
+You can experience it again
+just to sort of get a sense.
+
+It's amazing how
+the green circle
+
+becomes more and more
+and more and more vivid.
+
+Now, one more thing
+I'm going to tell
+
+you is when I turn this
+off-- keep fixating--
+
+and then you're going to see
+a green afterimage, right?
+
+So it proves that, indeed,
+it's the afterimage that
+
+appears over a period of time
+with that rotating circle,
+
+and it's fully explained
+by the color circle.
+
+All right.
+
+So now we're going
+to move on, and you
+
+look at yet another
+illusory effect.
+
+If you look at this display,
+what do you see here?
+
+You see a light square
+and a dark square, right?
+
+Everybody see that?
+
+Now, what if I told you
+that what you're seeing
+
+is a total misconception?
+
+So I'll tell you
+what I'm going to do.
+
+I'm going to leave these two
+squares exactly as they are,
+
+but I'm going to
+change the background.
+
+Ready?
+
+What's the difference here?
+
+The difference is that now the
+background is uniform, right?
+
+And you can see these
+two squares are indeed
+
+identical in contrast, right?
+
+But now if I go back
+to the previous one,
+
+if you look at it
+more carefully you
+
+can see this goes
+from light to dark.
+
+Of course, the projector
+makes this look bluish.
+
+It shouldn't be, but that's OK.
+
+And it's a gradual shift
+in the illumination level
+
+that fools you to think that
+one is light, the other is dark.
+
+And that has to do
+heavily with the fact
+
+that the receptive fields
+of cells in the retina
+
+have center-surround
+organization,
+
+and they're sensitive to
+local contrast differences.
+
+That's their make-up.
+
+And so until I
+point it out to you,
+
+can't even tell that
+this is a gradual shift.
+
+And if it did not
+change in color,
+
+it would be harder to tell.
+
+And it has to do with
+the fact that you're
+
+making local comparisons.
+
+And because of that, to
+make a distant comparison
+
+you are inaccurate about it.
+
+So this illusory effect,
+again, can be readily explained
+
+on the basis of what we know
+about the center-surround
+
+organization of receptive
+fields in the retina.
+
+OK.
+
+Now, if you look at the
+same thing in color, which
+
+doesn't come up too well here
+because of the projector,
+
+but still you can tell that
+these are not the same color,
+
+OK, again because of
+the gradual shift,
+
+color shift, in the background.
+
+But exactly identical they
+are, as they had been before.
+
+So this works not
+only for contrast,
+
+but it also works for color.
+
+Now, some illusory effects don't
+work for color and some do.
+
+All right.
+
+So now yet another
+related effect
+
+that I'm sure some
+of you have seen
+
+before is if you
+look at this circle,
+
+we agree that it's
+uniform in color.
+
+Now, if I cover half of it with
+dark and the other with light,
+
+it still looks pretty the same.
+
+Maybe it's a little
+darker here than here.
+
+But then if I put a partition
+here, as you can see here,
+
+then this side definitely
+looks darker than that side.
+
+OK?
+
+So this, again, looks
+at contrast effects,
+
+and we'll talk about these
+contrasts in just a bit
+
+with more detail.
+
+Next, let me turn to
+another illusory effect
+
+that you can see in many,
+many textbooks, which
+
+is called the
+wallpaper illusion.
+
+If you look at this--
+I'll come to it
+
+in a second in your display,
+where it will appear
+
+on the back of the second
+page-- what you see here,
+
+it looks like that these
+are not parallel lines here.
+
+I shouldn't say
+lines, but parallel
+
+black and white squares.
+
+It looks like that they're going
+like back and forth like that,
+
+OK, and it's quite dramatic.
+
+And so now we can ask the
+question, how can we see this?
+
+What is this due to?
+
+It could be due to the
+way they're aligned.
+
+It could be due to
+the fact that there
+
+is space between
+them, that gray space.
+
+And so one can do
+experiments like the one
+
+you have on your
+next page there.
+
+Let me first-- I will
+prove that, indeed, we
+
+have parallel lines here.
+
+These are fully parallel lines,
+and they go back and forth.
+
+To convince you, you can see
+that the lines are identical,
+
+and yet they do
+not look parallel
+
+at all because of
+this illusory effect.
+
+OK.
+
+So now what we can do is we can
+fiddle around with this a bit.
+
+Now, that's the kind of
+thing you guys would probably
+
+enjoy doing yourselves--
+look at various illusions
+
+and start playing
+around with them.
+
+This is an example.
+
+This is a basic
+wallpaper illusion.
+
+And now you turn this into
+an equal checkerboard, OK?
+
+And if you keep the
+lines in between,
+
+and you get no
+effect whatsoever.
+
+And then here we
+eliminate those gray bars,
+
+and the illusory effect
+is greatly reduced.
+
+So consequently,
+the illusory effect
+
+has to do with both
+the fact that you
+
+have space between the
+alternating black and white
+
+bars, meaning these
+gray lines here,
+
+and that you have them offset.
+
+So when it's not offset,
+you don't get it.
+
+And when you don't have
+the bars, you don't get it.
+
+So these two factors
+play an important role
+
+in giving rise to
+the illusory effect.
+
+Now, what we also can examine
+is what happens at isoluminance.
+
+And in this case, once
+again, what happens
+
+is that the illusory
+effect is still there,
+
+but it is reduced under
+isoluminant conditions.
+
+And this is not the
+isoluminant actually
+
+because of the projector.
+
+But when it's
+perfectly isoluminant,
+
+then the illusory
+effect is largely lost.
+
+All right.
+
+So now we have a variant of this
+illusion which is fascinating.
+
+And this one I will show
+you on the next page, OK?
+
+And if you look at
+just this display,
+
+and you are convinced that we
+have lines that are alternating
+
+that are filtered
+back and forth, right?
+
+Well, is that really true?
+
+Well, it turns out if you
+take a bunch of red lines here
+
+that are perfectly
+parallel, OK, and then you
+
+superimpose those
+on the display,
+
+you can see that actually
+the display is parallel.
+
+OK?
+
+The reason it
+doesn't look parallel
+
+is due to the way these
+individual little pieces
+
+that you're not even
+conscious of are arranged.
+
+So let's look at
+that in more detail.
+
+Let me add here one more thing.
+
+At isoluminance, you get
+practically no effect.
+
+So these illusions, this
+one and the previous one,
+
+heavily depend on
+contrast differences.
+
+OK.
+
+So here we go.
+
+Here's the basic
+illusory effect.
+
+And the way this was constructed
+is shown enlarged on top.
+
+Alternate lines have
+1, 2, 1, 2, 1, 2, 1.
+
+OK?
+
+What you have in the top line,
+and the third, and so on,
+
+you have it in this orientation.
+
+Here you have them reversed.
+
+And that vague cue
+is what somehow
+
+provides the illusory
+effect for you.
+
+Now, if you make all
+the lines similar,
+
+OK, in other words don't
+reverse the alternate lines,
+
+then what you see
+here is actually
+
+the bars are all
+tilted slightly upward.
+
+OK?
+
+And because of that,
+the illusory effect
+
+is not as dramatic as this
+one, but you still have it.
+
+All right?
+
+So what then you
+can do with this
+
+is to enlarge on this
+effect as shown here.
+
+It looks like that you have
+somehow a very unequal set
+
+of lines, as a result
+of which you do not
+
+have a bunch of
+clear-cut squares.
+
+And if you, again, superimpose
+true parallel lines through it,
+
+you see that they are
+actually parallel.
+
+All right.
+
+So that then explains
+that illusory effect
+
+in terms of how we somehow
+integrate information of shape
+
+that we are not even
+aware of to have
+
+a perception of a whole thing.
+
+Now, that's not much
+of an explanation.
+
+It doesn't tell you what
+neurons are involved
+
+or anything like that.
+
+But it gives you
+a general concept
+
+of how that illusory
+effect is created.
+
+Now we come to yet another
+fascinating illusory effect,
+
+and that one is in the next
+few pages in the handout.
+
+So if you take the
+backside of page 3,
+
+you will see this
+illusory effect here.
+
+Does everybody see that?
+
+Now, this illusory effect is
+one which gives you a sense
+
+that you have a whole
+bunch of swirls.
+
+All right?
+
+Does everybody see those swirls?
+
+Instead of seeing 1, 2, 3, 4
+circles, you see some swirls.
+
+And you say what on earth
+is giving us that sensation?
+
+So what you want to do then
+is to look at it analytically.
+
+And what you see
+here is you have
+
+alternating black and white
+squares, first of all.
+
+And you say, well,
+is alternating
+
+black and white squares
+the central point?
+
+But then if you look
+at it more closely,
+
+you can see this is-- I
+don't know how they came up
+
+with this one-- what you see
+here, if you look at each
+
+of these, that there's a
+gradual shift as you go
+
+around the circle in the
+orientation of the square.
+
+So this square
+becomes progressively,
+
+very slowly, more rotated.
+
+OK?
+
+And that goes around
+the clock, and that's
+
+true for every one
+of those circles.
+
+And you can say, well, is it due
+to the black and white squares?
+
+Is it due to the change in
+the orientation of the squares
+
+that you're not even aware of?
+
+Or what?
+
+So what kind of
+experiment do you
+
+do to check this out, to come
+up with some understanding?
+
+What kind of game can you play?
+
+Well, the first
+game you can play,
+
+so you can say,
+well, let's eliminate
+
+these slight changes
+in orientation.
+
+OK?
+
+And so what you can do instead,
+as shown on the next page,
+
+is that you have a
+bunch of circles,
+
+black and white circles,
+which are all the same.
+
+And as you can see
+here, there's no swirls.
+
+You have four
+circles, very clear.
+
+So therefore,
+obviously, the squares,
+
+changing their orientation in
+a subtle fashion going around
+
+in the clock, is very
+important in introducing
+
+this illusory effect.
+
+Well, then you can say,
+OK, but is that all of it?
+
+And so what we can do here,
+as shown on the next page,
+
+is we can maintain
+the orientation shift,
+
+but we can make them all the
+same contrast, as we have here.
+
+And when you do that, you have
+have a rather weak illusory
+
+effect.
+
+There's still a little bit left
+maybe, but it's kind of weak.
+
+And then if you instead
+make it isoluminant,
+
+you get some in-between effect.
+
+So on the basis of
+that, we can conclude
+
+that very important
+in this display
+
+is that you have a gradual
+shift in the orientations
+
+of these squares.
+
+And that, in turn, suggests that
+somehow the way these squares
+
+activate orientation
+selective cells in V1
+
+plays an important
+role in giving rise
+
+to this strange illusory effect.
+
+OK.
+
+So now what we
+are going to do is
+
+to look at yet another
+illusory effect, which
+
+has a different
+source, and that one
+
+is the famous
+Muller-Lyer illusion.
+
+The fact is that
+these two bars here
+
+are identical in size-- do I
+have the picture-- like that.
+
+OK?
+
+But when you put these inducing
+elements, as we will call them,
+
+OK, on there, you'll swear
+that this one is longer
+
+than this one is.
+
+OK?
+
+So now we can ask the question,
+what kind of manipulations
+
+can we undertake to see
+what that is all about?
+
+And let me come back
+to that in a minute.
+
+So what you can
+do here is to make
+
+the inducing elements and
+the bars different in color
+
+or in contrast, and you still
+get a strong illusory effect.
+
+OK?
+
+So making them
+isoluminant or making them
+
+opposite in contrast does
+not eliminate this illusion.
+
+So the theory that
+somebody has come up with
+
+is shown here, which
+I'm not sure I buy,
+
+but that's
+nevertheless a theory,
+
+it claims that the
+brain interprets
+
+these two displays as
+differences in depth,
+
+as if here we had a protruding
+edge in a building inside
+
+or a receding edge
+as shown here.
+
+And that difference that
+we almost unconsciously,
+
+if you will, interpret as
+being in different depths
+
+is what gives rise
+to the illusion
+
+according to this theory.
+
+Of course, there's a
+simpler theory simply saying
+
+that we just integrate these
+two bits of information.
+
+All right.
+
+So now we can ask the question,
+if you have illusory effects
+
+of this sort, is this something
+that really takes place higher
+
+up in the brain, or does it take
+place in the retina where we
+
+cannot separate these
+inducing and testing elements?
+
+Well, the way you
+can do this-- I'm
+
+going to show you
+another illusion which
+
+is similar to this.
+
+Here we have the so-called
+Ebbinghaus illusion.
+
+This is a very similar
+kind of illusion.
+
+This is a test element
+and an inducing element.
+
+The test element here
+are these two circles,
+
+and you swear that
+this one is a smaller
+
+circle than that one is, right?
+
+And we have a bunch
+of small circles,
+
+and here we have bunch
+of large circles.
+
+So now we can ask,
+well, is this something
+
+that takes place in
+the retina or what?
+
+So what kind of
+experiment can you do?
+
+Well, the experiment
+that you can do
+
+is to present these
+displays interocularly.
+
+What does that mean?
+
+What that means is
+that you present this
+
+to the left eye and
+this to the right eye.
+
+And you present
+this device that's
+
+used by psychologists
+for this kind of thing.
+
+It's called a tachistoscope.
+
+You look through it.
+
+It can present things
+separately through the two eyes,
+
+and you can flash
+them on briefly
+
+so you don't get any
+binocular rivalry.
+
+And when you do that, then
+you can systematically
+
+vary the size of
+these to make sure
+
+that you can get a
+quantitative measure of it.
+
+And when you do that, you
+find that the illusory effect
+
+is just as good under
+interocular conditions
+
+as it is under binocular
+viewing conditions.
+
+Because of this
+then-- this has been
+
+done with many
+kinds of illusions
+
+including the Muller-Lyer one.
+
+And when you do that,
+you show, in essence,
+
+that this is an effect
+that takes place
+
+most likely in the
+cortex, certainly
+
+not in the retina or the
+lateral geniculate nucleus.
+
+It takes place someplace
+where the images
+
+from the left and
+two eyes converge.
+
+All right.
+
+So now yet another
+set of illusions
+
+that I want to show you.
+
+I think that these
+illusory effects are done.
+
+You can take this home and enjoy
+it or show it to your friends.
+
+Now I'm going to show
+you a set of just two
+
+kinds of motion illusions.
+
+OK, here's the first one.
+
+I want you to look
+at the screen,
+
+and I'm going to flash
+something on briefly,
+
+and I'm going to
+do it repeatedly.
+
+Ready?
+
+What do you see?
+
+Do you see something moving?
+
+A very brief sense of
+motion that you see.
+
+This twirls a little bit.
+
+And this is called
+the snake illusion,
+
+which is really curious.
+
+This has, again, appeared in
+quite a number of textbooks,
+
+and we do not have a really
+good explanation for it.
+
+But we have another one,
+which I think is related.
+
+OK.
+
+So what I'm going
+to do here, this
+
+is called the
+waterfall illusion.
+
+So what we are
+going to do here is
+
+I'm going to set this in motion.
+
+In this case, I don't
+want you to fixate.
+
+What I want you
+to do is just keep
+
+looking at it in various places.
+
+You can look here, here,
+here, and here, and so on.
+
+OK?
+
+And I'm going to let
+it run for a while,
+
+and then I'm going to stop it.
+
+OK?
+
+And I want you to tell me
+what is your aftereffect.
+
+Ready?
+
+OK.
+
+I'm about to stop it.
+
+Are you ready?
+
+Pay close attention
+to what you're
+
+going to perceive once it stops.
+
+Anybody see what happened?
+
+What did you see?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: You see the water
+running up here, right?
+
+OK.
+
+I'll do it once more so
+you can appreciate it.
+
+Pretty nice, huh?
+
+OK.
+
+So this illusory effect is one
+that also occurs interocularly.
+
+And it has been shown that
+when you record from area MT,
+
+we talked about the fact that
+area MT is a region where cells
+
+respond selectively to
+direction of motion.
+
+Well, people have
+shown that if you,
+
+for an extended period of time,
+a minute maybe or whatever,
+
+you stimulate a cell in MT
+with this kind of a display,
+
+then after you stop it, OK, the
+cells with the opposite sense
+
+of motion will
+discharge some, which
+
+then is attributable to the
+upward sensation that you have.
+
+So it's clear enough
+that this is something
+
+that does take place
+predominantly by virtue
+
+of direction-selective
+cells and, probably,
+
+by direction-selective
+cells in area MT.
+
+All right.
+
+So then what we are
+going to do here
+
+is we're going to look
+at some other limitations
+
+and ambiguities in perception.
+
+And in particular,
+we're going to examine
+
+some figure/ground
+relationships.
+
+The first one I'm going
+to show you is this one.
+
+If you look at these two
+diagonals, OK, a and b,
+
+they certainly look very,
+very different, don't they?
+
+OK?
+
+One looks shorter and
+a different angle.
+
+But now if I eliminate the
+trapezoid in the surround,
+
+you can see that they're
+actually identical.
+
+OK?
+
+I'll show it to you again.
+
+Pretty dramatic.
+
+So that's an interesting
+illusory effect.
+
+And it's clear enough
+that this is something
+
+that takes place in
+higher cortical areas.
+
+Yet another one here that
+I'm going to show you also
+
+has something to do with
+figure/ground relationships,
+
+which has been
+extensively studied,
+
+especially by Gestalt
+psychologists.
+
+And I spoke about this a
+little bit the last time.
+
+What you see here is a bunch
+of vases, so to speak, right?
+
+That's good enough.
+
+So what I'm going
+to do now, I'm going
+
+to show you another
+set of vases.
+
+Are you ready?
+
+There is another set of vases.
+
+Everybody see the vases?
+
+Now, what if I tell
+you that there's
+
+much more to this
+than just vases?
+
+So if you look really
+closely, you're
+
+going to see
+something else there.
+
+What else do you see there?
+
+AUDIENCE: Faces.
+
+PROFESSOR: Oh, OK, two faces,
+two guys facing each other.
+
+Now, if I change the relative
+number of elements in here,
+
+which changes the
+figure/ground relationships,
+
+you get a different effect.
+
+Here you have--
+predominantly you
+
+see the faces rather
+than the vases.
+
+OK?
+
+And that's a cute
+way of putting it.
+
+I see the faces, not the vases.
+
+And then you switch
+it, and you say,
+
+I see the vases, not the faces.
+
+All right?
+
+So that then is a way you
+can play around, again,
+
+with various illusory
+effects by fiddling around
+
+on your computer and
+creating things like that.
+
+OK.
+
+Now, yet another
+strange effect is
+
+where you can have
+difficulty telling what's
+
+what is this kind of a display.
+
+You say, well, what's
+happening here?
+
+Are arrows pointing
+to the right,
+
+or are they pointing
+to the left?
+
+And that reminds one of a
+fellow called Yogi Berra.
+
+How many of you have
+ever heard of Yogi Berra?
+
+Oh, my goodness, very good.
+
+OK.
+
+So he was a famous catcher for
+the New York Yankees, right?
+
+Well, he was a very
+interesting guy,
+
+had all kinds of
+interesting statements.
+
+And one of those many curious
+statements, one of them
+
+is-- it doesn't relate to this.
+
+It just comes into my head.
+
+"It isn't over until it's over."
+
+That's one of his, OK?
+
+This one here
+that's relevant is,
+
+"When you get to a fork
+in the road, take it."
+
+Yeah?
+
+And that's a Yogi Berra quote.
+
+And so what we have
+here is a sign that you
+
+come to a fork in the road, and
+you have to decide to take it.
+
+What are you going to do?
+
+Are you going to go this way,
+or are you going to go that way?
+
+So that's a kind of
+game you can play
+
+with this kind of strange
+effect that you can create
+
+that is confusing your
+ability to organize
+
+your visual percepts.
+
+Another famous one, maybe
+not that famous, actually.
+
+Maybe some of you
+have seen this.
+
+This, again, has appeared many,
+many years ago in The New.
+
+Yorker.
+
+It says, "I'm turning
+into my mother."
+
+Now, keep looking
+at it and tell me,
+
+why do you think that that
+comment is being made?
+
+What we have here, a young woman
+looking at another young woman,
+
+right?
+
+But now if you keep looking
+at this display, look.
+
+This is a nose here,
+and this is a mouth.
+
+You see an old lady now?
+
+OK.
+
+You played around with this, it
+gives you a confusing percept.
+
+And ultimately, you can
+see the young person
+
+looking that way or an old
+lady looking the other way.
+
+I mean looking not
+backwards but across.
+
+And that's why this
+statement says,
+
+"I'm turning into my mother."
+
+So the essence here
+is that playing around
+
+with these kinds of illusory
+effect is a lot of fun,
+
+and we all very much enjoy
+looking at illusions.
+
+And some of us like to
+play around with them
+
+to try to figure out what their
+existence is for the reasons.
+
+Now, I want to
+show you one more,
+
+which I think is very
+appropriate at this time.
+
+This is the famous
+Greek key motif.
+
+Everybody's seen
+this, I presume.
+
+Does everybody know where
+this is displayed, actually,
+
+at several places?
+
+In the Senate.
+
+OK?
+
+Whenever you have a picture
+of the Senate Building,
+
+you will see this.
+
+All right?
+
+Now, that's a little
+bit amusing, actually,
+
+if you think about it.
+
+So this has become
+symbolic of democracy.
+
+And considering just what
+happened most recently,
+
+you could almost
+say that, perhaps,
+
+what's happening here is that
+you cannot tell whether we see
+
+this guy or this guy
+here going around.
+
+OK?
+
+And one of them you could say,
+oh, these are the Democrats.
+
+These are the Republicans.
+
+And you have sort of a conflict
+as to which ones you see.
+
+All right?
+
+And that is, in a way, symbolic
+of what's going on today.
+
+But to educate you
+a little bit, which
+
+I suspect probably most of
+you know already anyway,
+
+this Greek key motif
+actually has its source
+
+in the so-called
+myth of the Labyrinth
+
+that had imprisoned
+the Minotaur.
+
+Who knows who the Minotaur is?
+
+Oh, very good.
+
+Many of you do.
+
+All right.
+
+So the Minotaur
+was a creature that
+
+was half bull and half human.
+
+All right?
+
+And what happened, according to
+this myth-- and let me tell you
+
+it's a myth, and it's
+a bit of risque thing.
+
+There was a king
+called King Minos
+
+whose wife Pasiphae--
+Pasiphae, I'm not sure
+
+how you pronounce it properly--
+is the one who had intercourse
+
+with a bull and
+gave birth-- sorry,
+
+had intercourse with a bull.
+
+And as a result of
+that, gave birth
+
+to the Minotaur, which was a
+half-bull, half-human monster,
+
+if you will.
+
+All right?
+
+And that became so
+threatening and so irritating,
+
+I guess, to King
+Minos that he asked
+
+one of his subjugates, Daedalus,
+to create a maze, a huge maze,
+
+and he put the Minotaur in it.
+
+So it was such a maze
+that the Minotaur just
+
+couldn't get out of it.
+
+All right?
+
+But then things got
+progressively worse,
+
+and King Minos decided
+that he had better
+
+get this Minotaur killed.
+
+And so he asked a person
+whose name is Theseus, OK,
+
+to go into the maze
+and kill the Minotaur.
+
+Now, the king also
+had another offspring
+
+whose name is Ariadne--
+nice name, Ariadne.
+
+And she said to Theseus that
+if you take a ball of thread
+
+and you walk through
+the maze, once you
+
+do what you have to do, you
+can follow the thread back,
+
+and that way you can
+get out of the maze.
+
+So that's what Theseus
+did, and then he
+
+went on and killed the Minotaur.
+
+Now, the story didn't end
+there because somehow,
+
+for reasons I'm not sure I
+know the details anymore,
+
+King Minos had a fall
+out with Daedalus,
+
+and he jailed Daedalus
+and his son Icarus.
+
+And while they
+were in jail, they
+
+tried to figure out
+how they could escape.
+
+And so Daedalus
+fashioned a pair of wings
+
+made out of bird's feathers and
+wax, and then put it on Icarus.
+
+And then Icarus, by
+doing this, he could fly.
+
+OK?
+
+And then he flew and
+escaped from the prison.
+
+But unfortunately, he
+flew fairly high up
+
+where the sun was very hot.
+
+That melted the wax, and
+Icarus, sadly, fell to his death
+
+as a result.
+
+So that's quite the story.
+
+And that's something that
+obviously some of you
+
+already know.
+
+And those of you who
+don't, you will probably
+
+remember, as so many Greek
+myths are just fascinating,
+
+ancient, old stories.
+
+All right.
+
+So then here is actually
+a reconstruction
+
+of the kill of the
+Minotaur by Theseus.
+
+And this is actually a
+sculpture that exists in Greece.
+
+Pretty nice, huh?
+
+OK.
+
+Now, the last confusing image
+that I wanted to show you
+
+is this one that had appeared--
+I think this appeared also
+
+in The New Yorker,
+but I'm not 100% sure.
+
+What you have here
+is a confusion--
+
+do we have three
+or two prongs here?
+
+And the reason I show
+this sometimes in class
+
+is because in our department
+when it was originally
+
+formed by Hans-Lukas
+Teuber, he created
+
+what is called three prongs.
+
+OK?
+
+And then it became sort
+of an issue as to, well,
+
+what are the three prongs?
+
+Are there two prongs?
+
+Are there three prongs?
+
+Who belongs into which prong?
+
+And so somebody came
+up with this picture
+
+that was put up as a joke
+in the department when
+
+the department was still in
+one of the old buildings that
+
+doesn't even exist anymore.
+
+All right.
+
+So that then brings me to the
+end of the illusory effects
+
+that I thought we'd
+talk about briefly.
+
+And I will now move on and
+talk about visual prosthesis.
+
+All right.
+
+Now, as far as
+prosthetics are concerned,
+
+you're going to hear quite a
+bit about that from Chris Brown
+
+because in audition, an auditory
+prosthetic device, the cochlear
+
+implant, has become
+an incredible success.
+
+There are well over 50,000
+people in the country now
+
+who have a prosthetic
+device like that
+
+that enables them to
+hear, to converse.
+
+It's really incredible.
+
+Unfortunately, when it
+comes to visual prostheses,
+
+we have nothing
+comparable at this stage.
+
+It's a much needed device that
+will take many, many, many more
+
+years to create.
+
+But I thought I'd give you
+sort of a crude sense of how
+
+that kind of work
+progresses because there are
+
+many laboratories that
+are trying to come up
+
+with something that will provide
+an ability for people to see.
+
+Now, I can tell you
+that in the world
+
+there are more than 40
+million people who are blind.
+
+In the United States, there are
+more than a million individuals
+
+who are blind.
+
+So because of that--
+that's a huge number--
+
+it, of course, is extremely
+desirable to come up
+
+with some device
+to do this for you.
+
+Now, this is a very,
+very long history,
+
+and people have tried
+all sorts of things.
+
+One of those is to try to induce
+the ability to see something
+
+in the world that you
+normally see with your eye
+
+by putting it through
+some other sense.
+
+Now, a simple example
+of that is Braille.
+
+All right?
+
+Everybody knows what
+Braille is, right?
+
+That's you can use your
+hand to feel something that
+
+has protruding
+elements in it that
+
+can be shown in
+terms of letters.
+
+And so as you get into an
+elevator and you can't see,
+
+you can feel it, and then
+you can push the right button
+
+to get to the right floor.
+
+OK?
+
+Now, that's one way
+it has been done.
+
+Another approach had been
+to present stimulation
+
+to your somatosensory system,
+either by putting something
+
+on your back or putting
+something on your fingertip,
+
+that an image would be converted
+into actually activating
+
+your somatosensory
+system that would
+
+be equivalent to something that
+you would perceive if you could
+
+see.
+
+So that's the basic thing.
+
+And a tremendous
+amount of effort
+
+has been going on to try to
+come up with something to create
+
+a workable prosthetic
+device for the blind.
+
+Now, there's a lot
+of disagreement
+
+as to where such a device
+should be placed in the body
+
+and also a lot of debate
+of what kind of procedures
+
+should be used.
+
+Now, some people
+advocate that it
+
+should be done on the retina.
+
+Some people advocate
+it should be
+
+done in the lateral
+geniculate nucleus.
+
+Actually, some
+work is being done
+
+at Harvard trying to
+come up with something
+
+for the lateral
+geniculate nucleus.
+
+And there's some
+people who think
+
+it would be best to do
+it in the visual cortex.
+
+So let me sort of go into
+this in a bit more detail.
+
+And let me, first of all,
+raise the question of,
+
+what kinds of devices, and
+what kinds of necessities
+
+do we have for converting
+vision into something
+
+that enables blind
+people to see?
+
+Well, first of all,
+it's very important
+
+to be able to see some basic
+patterns, very important to see
+
+motion, and very
+important, often ignored,
+
+is that you got to be
+able to see something
+
+in the third dimension,
+because a person who is blind,
+
+he should be able to
+walk in the world.
+
+And if you're going
+to walk around,
+
+you should be able to see
+where things are in depth.
+
+So those are the
+basic requirements.
+
+You're certainly not required
+to process color information.
+
+So that's not important.
+
+And there are several other
+things that are not important.
+
+But these are the three
+most important ones
+
+that you would like to
+have if you are going
+
+to create a prosthetics
+device for the blind.
+
+Now, then the next
+question is, how are we
+
+going to deal with
+this, and what kinds
+
+of issues and problems
+are we going to deal with?
+
+First of all, the big issue is
+what kind of prosthetic device
+
+should we use.
+
+One of those that
+I've already mentioned
+
+is to try to convert
+visual impressions
+
+into other modalities such
+as your somatosensory system.
+
+All right?
+
+The other is to create some
+sort of stimulating device,
+
+which there are various kinds.
+
+But one of those
+would be, for example,
+
+to put a bunch of
+electrodes into the brain,
+
+or into the retina, or whatever,
+and then selectively stimulate
+
+through this series
+of electrodes
+
+to mimic the visual field.
+
+Now, the other one,
+and it is a big issue,
+
+what brain areas
+should be considered?
+
+And because we're at
+an early stage in this,
+
+I think it is
+desirable for people
+
+to pursue just about any
+area they think might work.
+
+Now, the problem with
+a retinal implant--
+
+there are two problems with it.
+
+One is the retina is extremely
+small, and very confined,
+
+and has these millions of
+receptors and ganglion cells,
+
+and how can you
+selectively activate them?
+
+Now, the biggest
+problem, though,
+
+is that in most blind
+people, the retina
+
+becomes non-functional.
+
+And even worse, it degenerates
+in a relatively short time
+
+so that it no longer is useful
+for electrical stimulation
+
+or for whatever
+kind of stimulation
+
+you wish to engage in.
+
+So because of that,
+some people have
+
+moved on to the lateral
+geniculate nucleus.
+
+That area has some problems
+because it's deep in the brain,
+
+and it's quite small.
+
+OK?
+
+And also, it tends to
+degenerate over time,
+
+although it takes it a lot
+longer than the degeneration
+
+of the retina.
+
+Thirdly, people have considered
+stimulating the visual cortex,
+
+and that's what
+I'm going to talk
+
+about in a bit more
+detail just now.
+
+But the last thing that's very
+important here-- I think it's
+
+the last thing.
+
+Yeah, just let me go back.
+
+Ah, sorry.
+
+The third big issue
+is, can you create
+
+a device that has longevity?
+
+As soon as you put
+something into the brain
+
+and into the eye,
+there's going to be
+
+some sort of adverse
+reaction that
+
+may kill the cells at
+the tip of the electrodes
+
+or something like that.
+
+So all kinds of
+approaches have been
+
+created to try to increase
+the longevity of the device.
+
+Now, I'm going to
+next look at what
+
+happens in the
+visual cortex, which
+
+is a promising, at least I
+think it is, a promising site
+
+where you could electrically
+stimulate and use
+
+that to create a
+visual impression.
+
+All right.
+
+If you do that-- here
+is a monkey brain.
+
+The monkey is very
+well suited for this
+
+because, as I have mentioned
+before, the posterior
+
+part of the cortex-- see, this
+is area V1-- is lissencephalic.
+
+And so it's relatively easy
+to place accurately electrodes
+
+into it.
+
+OK?
+
+So then if what you do
+here-- here, just a reminder,
+
+is the central sulcus.
+
+Here's the lunate sulcus.
+
+And here, of course, is area V1.
+
+If you now take the
+contralateral hemifield,
+
+that projects into this region.
+
+OK?
+
+This is shown out to
+about five degrees.
+
+That will go to
+around here like that.
+
+OK?
+
+So now the next big
+question that, initially,
+
+had been done
+actually in humans,
+
+what do you see when you
+insert a microelectrode
+
+into the brain-- as I say, this
+was done on humans initially--
+
+and you electrically stimulate?
+
+What do you see?
+
+And this work was done by
+Brindley many years ago.
+
+And he discovered that
+when you electrically
+
+stimulate in the human primary
+visual cortex, what you get
+
+is a small, star-like image.
+
+All right?
+
+So that's what he found.
+
+And so that then triggered
+a great deal of research,
+
+including work in
+monkeys, to determine
+
+what could be done to create
+a prosthetic device that
+
+might just work.
+
+So the first step
+then was to try
+
+to determine what
+happens when you
+
+put a microelectrode in here.
+
+This is, by the way, the
+layout of the visual field
+
+in the posterior cortex
+with much more area devoted
+
+to the fovea than into the
+periphery because, of course,
+
+there's a much higher packing
+density of receptor cells
+
+as well as retinal
+ganglion cells in the fovea
+
+representation than further out.
+
+In the cortex, the thickness
+of the gray matter is constant.
+
+It's about roughly
+2 millimeters thick.
+
+And the frequency, spatial
+frequency of the cells,
+
+is pretty constant as well.
+
+So therefore, you need
+to allocate more space
+
+to the incoming huge
+number of retinal ganglion
+
+cells projected
+to the geniculate
+
+and then to the cortex
+than for the periphery.
+
+And that's why
+you have this kind
+
+of a layout of much
+more space allocated
+
+to the central than
+to peripheral vision.
+
+So that's a very
+important factor
+
+in considering how to
+create a prosthetic device.
+
+So now the first step in
+doing this kind of stuff,
+
+if you're going to do serious
+experiments on monkeys,
+
+is to determine,
+what does the monkey
+
+see when you electrically
+stimulate the visual cortex?
+
+And so the experiment
+that's been done here
+
+is one in which a
+monkey has been trained
+
+to make an eye movement to the
+bigger of two visual stimuli
+
+or the brighter of two stimuli.
+
+In this case, we have
+two visual targets.
+
+By the way, one
+of these is going
+
+to appear where the receptive
+field is of the cells
+
+that you're going to stimulate
+in the visual cortex.
+
+So then you may sometimes make
+this one brighter, this one
+
+brighter.
+
+And the monkey makes
+a saccade to it,
+
+and he gets a drop of
+apple juice for reward.
+
+And then you can systematically
+vary the relative size
+
+of the two stimuli to see what
+kind of a function you get.
+
+And the same thing you can do
+for the relative brightness
+
+of it.
+
+And then on some trials
+interspersed with those trials,
+
+you present
+[INAUDIBLE] stimulation
+
+with the visual
+target and see which
+
+one does the monkey go to.
+
+And then you
+systematically vary,
+
+as I said, the brightness or
+the size of those stimuli.
+
+OK?
+
+We vary the contrast in
+this case, and in this case,
+
+we vary the size.
+
+OK?
+
+So that's the basic experiment.
+
+And if you do that
+systematically,
+
+you can tell exactly what
+the size and the contrast
+
+is of the visual
+stimulus created
+
+by electrical stimulation.
+
+If you do that--
+here's an example.
+
+When you present
+two visual stimuli
+
+and you vary the percent
+contrast difference, all right,
+
+of the two stimuli, you can see
+that it crosses over, indeed,
+
+when they're identical.
+
+So that tells you that
+this system works.
+
+It says these are identical.
+
+And the same thing is
+true for the size series.
+
+So this way then, if you
+do the same experiment
+
+with electrical stimulation,
+you can find out
+
+where this 50%
+crossover point is.
+
+This is for contrast,
+and this is for size.
+
+So then you can establish
+this with slightly different
+
+locations in the visual field.
+
+And if you do that
+overall, you come up
+
+with a summary
+statement, which says
+
+that when you use currents
+between 20 and 120 microamps,
+
+OK, at eccentricities between 2
+and 1/2 and 3 and 1/2 degrees,
+
+the contrast of the visual
+percept created in monkeys
+
+is 6% to 12%, and the size
+is between 15 and 20 minutes
+
+of visual angle.
+
+Now, that's quite
+small fortunately.
+
+So it's a local, little
+spot, like a star-like image.
+
+Now, what do we mean
+by 6% to 12% contrast?
+
+So let me tell you
+this, that that's
+
+a useful thing for
+you to memorize.
+
+We talk about percent contrast.
+
+What you do is you
+measure, for example,
+
+in candelas per square
+meter, what the contrast is
+
+of this and what is the
+contest of the background.
+
+Then you subtract one
+from the other, divide it
+
+by the sum of the two,
+and you multiply by 100.
+
+So when you do that, this
+is roughly 8% contrast.
+
+This is roughly 75% contrast.
+
+So it gives you a sense
+of what contrast means.
+
+All right?
+
+So what that means, in essence,
+that the visual stimulus
+
+created by the
+electrical stimulation
+
+is fairly low contrast.
+
+All right.
+
+So now the next
+important factor,
+
+once one knows what
+the visual percept is
+
+that is created by electrical
+stimulation in the monkey,
+
+the next thing is to
+ask the question, well,
+
+what kind of electrode array
+should one put together?
+
+All right.
+
+Well, the big issue
+here has to do
+
+with the so-called
+magnification factor
+
+that I just talked about.
+
+So let's look at
+this analytically.
+
+First of all, I
+already mentioned this.
+
+We have a very high packing
+density of photoreceptors
+
+in the fovea and much
+lower density further out.
+
+And so what you have
+is that this plate
+
+goes through the optic nerve
+up to the visual cortex
+
+to the lateral
+geniculate nucleus.
+
+So that's the basic
+arrangement, meaning
+
+that there are many, many
+more retinal ganglion
+
+cells per unit area that
+impinge on the visual cortex
+
+near the fovea than
+in the periphery.
+
+So then to examine this, here
+we have, again, another picture.
+
+It's the geniculate again.
+
+Here's the fact that the cortex
+is constant in thickness.
+
+And here's the layout of the
+visual field on the posterior
+
+cortex with more area
+allocated to the fovea
+
+than to-- excuse me,
+than to periphery.
+
+All right.
+
+So now I've shown you a
+variant of this before.
+
+If you present an arrow
+across the visual field here,
+
+this is the impression made
+with much more activation
+
+in central vision than
+in peripheral vision.
+
+I mean, you don't have
+to worry about that.
+
+That simply tells you, as
+we had discussed before,
+
+that the images
+created depend heavily
+
+on where you stimulate
+in the visual field.
+
+OK.
+
+So now to look at
+this quantitatively,
+
+so we put a bunch of dots
+up in the visual field.
+
+This is in the
+central four degrees,
+
+and this is the
+actual activation
+
+in the visual cortex.
+
+OK?
+
+Meaning that in the fovea,
+we have two elements here,
+
+this one and this one, here
+and here, that they take up
+
+a lot of space, whereas
+in the periphery,
+
+OK, they're very
+close to each other.
+
+That's due to the so-called
+magnification factor.
+
+And so one of the basic
+rules is that we've
+
+got to be able to stimulate
+the visual cortex taking
+
+into account the
+magnification factor.
+
+So if you have this kind
+of spatial arrangement,
+
+if we then were to put
+a bunch of electrodes
+
+in like this, which we will
+call proportional electrodes,
+
+then if you
+stimulated all those,
+
+you would get a similar
+square with one proviso,
+
+namely that the little dots
+would be smaller in the fovea,
+
+obviously, than
+in the periphery.
+
+So then if you have this kind
+of arrangement, what you can do
+
+is you can take a camera that
+has a fixed number of elements,
+
+and each of those
+elements you hook up
+
+to one of the electrodes.
+
+If you put the word
+"fiat lux" there,
+
+this is what you hypothetically
+would create, like that.
+
+OK?
+
+That's what it would look like.
+
+So in contrast with
+this arrangement,
+
+if we were to use
+an electrode array,
+
+which you can readily buy-- you
+cannot buy proportional arrays.
+
+You have to somehow
+create them yourself.
+
+But if you buy a fixed
+array, which the elements are
+
+equidistant, then if
+you stimulated all those
+
+you would get a butterfly
+image, butterfly image.
+
+I will show a movie
+of that as well.
+
+And that means that if you do
+that same conversion as before,
+
+this is what you would
+see in contrast to this.
+
+So in other words, it's a
+greatly distorted vision
+
+because you didn't take into
+account the magnification
+
+factor.
+
+All right.
+
+So then what you can
+do, actually, you
+
+can also increase the number of
+electrodes in the center here.
+
+OK?
+
+And that would
+mean-- in this case
+
+we have 428 elements-- that you
+can recreate fiat lux pretty
+
+well with this increased
+number of elements,
+
+where with the original set
+you couldn't make anything out.
+
+Now, the alternate
+to this would be
+
+that you could
+take a whole bunch
+
+of equally-spaced electrodes,
+which you can commercially buy,
+
+and put them in.
+
+But then to get the same acuity,
+you would need, in this case,
+
+something like over
+600 electrodes,
+
+whereas in this case you
+would only need about 420.
+
+So because of that,
+obviously we want
+
+to minimize the number of
+things you put into the brain,
+
+it's desirable to use
+a proportional device.
+
+So that's the first big step.
+
+Now, let's assume that you have
+created a proportional device.
+
+The next thing would be to
+see, how do you stimulate these
+
+through a camera?
+
+So what you do then
+is an experiment
+
+in which you take
+a human subject,
+
+and you can put a
+camera on a helmet,
+
+and also, the person
+looks at a monitor.
+
+And otherwise, the
+rest of the world
+
+is excluded by having
+this bezel here.
+
+And then the camera
+looks at something,
+
+and then it can
+display the image here.
+
+Well, one thing it can do, it
+can display the image as it is.
+
+But the other thing that's
+much more important,
+
+it can display that image
+as if electrical stimulation
+
+had taken place.
+
+Now, this becomes
+complicated because you
+
+have to do a lot of conversion
+of the input from the camera
+
+to the computer that's going
+to then drive the electrodes.
+
+Now, the first important
+point, I mentioned this before,
+
+is that if you present a small
+spot-- this is actual real data
+
+here-- you present a small spot
+in the center of a small array
+
+of cells in the visual cortex,
+you get a vigorous response,
+
+whether a light increment
+or light decrement.
+
+But if you use a larger
+spot, you get no response,
+
+meaning that the cortical cells
+look at local differences.
+
+That has a lot to do
+with what we talked about
+
+with the illusions.
+
+And so what you
+have to create is
+
+an algorithm that mimics that.
+
+And so the way
+you do that is you
+
+have these individual elements
+for each of the electrodes.
+
+And if that individual
+element in the computer that
+
+gets the input from the camera,
+if the whole element gets
+
+activated, there's no real
+activation of the electrode.
+
+But if an edge
+appears like here,
+
+here, or here, then the
+electrode is activated.
+
+OK?
+
+So you create local differences
+by this conversion system,
+
+all right, by this
+algorithm that then,
+
+when the camera
+looks at the world,
+
+will respond whenever there's
+an edge, an illumination
+
+difference.
+
+OK.
+
+So now the way this
+looks is like this.
+
+Again, as I've told you,
+whatever is in the fovea,
+
+the dots are smaller and
+further out, but that's OK.
+
+So that's the basic
+activation system.
+
+And so now what we
+are going to do,
+
+having created
+such an algorithm,
+
+we're going to examine
+what the person who
+
+carries this camera on
+his head can actually see.
+
+Now, the way this can be done,
+you can either physically
+
+move the stimuli in the world,
+or the person looks at it
+
+and can slowly move
+his head around.
+
+OK?
+
+So let's first
+look at what would
+
+happen if, instead of
+a proportional display,
+
+we used an equally-spaced
+display like that butterfly
+
+display.
+
+OK?
+
+So what I'm going to
+show you here on the left
+
+is what the camera is viewing.
+
+And here I'm going to
+show you what is actually
+
+perceived by this algorithm, by
+the person, where this image is
+
+converted into what he's
+looking at through that bezel.
+
+OK, you ready?
+
+I mean, you don't see
+a square at all, right?
+
+What you see is, because
+you're not taking into account
+
+the magnification factor,
+you get a huge distortion.
+
+So now let's go move on
+and ask the question,
+
+well, what happens when you are
+using a proportional display?
+
+All right?
+
+And now we get a
+rather nice story.
+
+Again, the visual
+display's on the left,
+
+and the image created
+is on the right.
+
+Ready?
+
+So the rule,
+therefore, is that you
+
+must use a proportional image,
+proportional display, that
+
+can be done either by having it
+truly proportional as you put
+
+it into the visual cortex or by
+having an equally-spaced array,
+
+and the computer computes
+the proportional arrangement.
+
+But the disadvantage
+of the latter
+
+is that you need many,
+many more electrodes.
+
+All right.
+
+Now, what I'm going
+to do is I'm going
+
+to show you whether
+you can read something
+
+when you use a proportional
+display like that.
+
+And in this case, we're going
+to have a bunch of big letters,
+
+and either the letters
+are going to move slowly
+
+across the visual
+field, or your head
+
+is going to move slowly
+with the camera like that
+
+to view that display
+that's up on the wall.
+
+OK?
+
+So if we do that--
+are you ready?
+
+See if you can read it.
+
+OK.
+
+Everybody able to read that one?
+
+OK.
+
+Who remembers what
+"fiat lux" means?
+
+I've only shown it about
+four or five times.
+
+Let there be light.
+
+OK.
+
+So now, just to be [INAUDIBLE]
+attractive about it,
+
+I'm going to show
+you one more display.
+
+And this one is
+a display, again,
+
+a series of letters
+and words, is one
+
+that John F. Kennedy has used in
+a very, very famous statement,
+
+which I think most
+of you will remember.
+
+And eventually, as you
+see the whole thing,
+
+you will be able
+to put it together.
+
+Are you ready?
+
+OK.
+
+Everybody's seen that, right?
+
+People nowadays, because
+of what's going on,
+
+are less inclined
+to take his advice.
+
+All right.
+
+So that is then
+the essence of what
+
+I was going to cover today.
+
+And so let me now provide
+you with a brief summary.
+
+I will start with
+the prosthetics then.
+
+OK?
+
+Research on visual
+prosthetics is in its infancy,
+
+as I've noted.
+
+A great deal of
+basic research is
+
+needed before such a device
+can become effective.
+
+That's very unlike
+what you're going
+
+to hear about the
+auditory system.
+
+The brain area that holds
+considerable promise
+
+for the prosthetic device
+based on electrical stimulation
+
+is area V1.
+
+Now, a prosthetic device for
+electrical stimulation of V1
+
+must take into account
+the magnification factor.
+
+That's absolutely
+essential, and too many
+
+people are ignoring it.
+
+Now, in a different
+color, we're going
+
+to talk about the illusions.
+
+There is no unitary
+explanation for
+
+the great many visual
+illusions extant.
+
+I pointed out to you
+that different illusions
+
+have different sources and
+different explanations.
+
+The most popular theory
+explaining the Hermann grid
+
+illusion based on the
+center/surround organization
+
+of retinal ganglion
+cells is incorrect.
+
+That's a polite way of
+saying it's all wrong.
+
+A more likely theory
+is the one that
+
+assumes that area V1
+cells are involved.
+
+Retinal adaptation processes
+can explain illusions
+
+based on aftereffects,
+and you've
+
+seen quite a few of those.
+
+And many illusions disappear
+under isoluminant conditions.
+
+And lastly, there are no viable
+theories that explain illusions
+
+based on figure/ground
+relationships.
+
+We know what they
+are, but we don't
+
+know how the brain resolves
+figure and ground effects.
+
+So that then is the end of
+what I wanted to cover today.
+
+And next time, we are going
+to talk about eye movement.
+
+And I hope that you
+will enjoy that as well.
\ No newline at end of file
diff --git a/vmE4N0m67AA.txt b/vmE4N0m67AA.txt
new file mode 100644
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--- /dev/null
+++ b/vmE4N0m67AA.txt
@@ -0,0 +1,9931 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
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+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
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+for free
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+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+what I'm going to be talking about some
+
+ align:start position:0%
+what I'm going to be talking about some
+ 
+
+ align:start position:0%
+what I'm going to be talking about some
+of the fundamental work that has been
+
+ align:start position:0%
+of the fundamental work that has been
+ 
+
+ align:start position:0%
+of the fundamental work that has been
+done trying to understand neural basis
+
+ align:start position:0%
+done trying to understand neural basis
+ 
+
+ align:start position:0%
+done trying to understand neural basis
+for for memory and spatial perception
+
+ align:start position:0%
+for for memory and spatial perception
+ 
+
+ align:start position:0%
+for for memory and spatial perception
+and cognition that comes from largely
+
+ align:start position:0%
+and cognition that comes from largely
+ 
+
+ align:start position:0%
+and cognition that comes from largely
+from behavioral and electrophysiological
+
+ align:start position:0%
+from behavioral and electrophysiological
+ 
+
+ align:start position:0%
+from behavioral and electrophysiological
+studies in the brain system that's shown
+
+ align:start position:0%
+studies in the brain system that's shown
+ 
+
+ align:start position:0%
+studies in the brain system that's shown
+here at the hippocampus and as I was
+
+ align:start position:0%
+here at the hippocampus and as I was
+ 
+
+ align:start position:0%
+here at the hippocampus and as I was
+mentioning before we started this year's
+
+ align:start position:0%
+mentioning before we started this year's
+ 
+
+ align:start position:0%
+mentioning before we started this year's
+Nobel Prize was given to John Okeefe who
+
+ align:start position:0%
+Nobel Prize was given to John Okeefe who
+ 
+
+ align:start position:0%
+Nobel Prize was given to John Okeefe who
+discovered the properties of individual
+
+ align:start position:0%
+discovered the properties of individual
+ 
+
+ align:start position:0%
+discovered the properties of individual
+neurons in the hippocampus by applying
+
+ align:start position:0%
+neurons in the hippocampus by applying
+ 
+
+ align:start position:0%
+neurons in the hippocampus by applying
+these methods for recording the
+
+ align:start position:0%
+these methods for recording the
+ 
+
+ align:start position:0%
+these methods for recording the
+discharge of single cells by putting
+
+ align:start position:0%
+discharge of single cells by putting
+ 
+
+ align:start position:0%
+discharge of single cells by putting
+little wires into the brain so called
+
+ align:start position:0%
+little wires into the brain so called
+ 
+
+ align:start position:0%
+little wires into the brain so called
+extracellular recordings you put in a
+
+ align:start position:0%
+extracellular recordings you put in a
+ 
+
+ align:start position:0%
+extracellular recordings you put in a
+wire the tip of the electrode can record
+
+ align:start position:0%
+wire the tip of the electrode can record
+ 
+
+ align:start position:0%
+wire the tip of the electrode can record
+electrical discharges of cells you
+
+ align:start position:0%
+electrical discharges of cells you
+ 
+
+ align:start position:0%
+electrical discharges of cells you
+measure the discharge of cells as
+
+ align:start position:0%
+measure the discharge of cells as
+ 
+
+ align:start position:0%
+measure the discharge of cells as
+animals move around in space and you try
+
+ align:start position:0%
+animals move around in space and you try
+ 
+
+ align:start position:0%
+animals move around in space and you try
+to you know you try to figure out what
+
+ align:start position:0%
+to you know you try to figure out what
+ 
+
+ align:start position:0%
+to you know you try to figure out what
+this part of the brain does now where
+
+ align:start position:0%
+this part of the brain does now where
+ 
+
+ align:start position:0%
+this part of the brain does now where
+the observation part of science comes in
+
+ align:start position:0%
+the observation part of science comes in
+ 
+
+ align:start position:0%
+the observation part of science comes in
+in this case is interesting because it
+
+ align:start position:0%
+in this case is interesting because it
+ 
+
+ align:start position:0%
+in this case is interesting because it
+relates to another aspect of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neuroscience and that is the
+
+ align:start position:0%
+neuroscience and that is the
+ 
+
+ align:start position:0%
+neuroscience and that is the
+relationship between the neurobiology
+
+ align:start position:0%
+relationship between the neurobiology
+ 
+
+ align:start position:0%
+relationship between the neurobiology
+and behavior and this is an approach
+
+ align:start position:0%
+and behavior and this is an approach
+ 
+
+ align:start position:0%
+and behavior and this is an approach
+known as an ERV ecological approach and
+
+ align:start position:0%
+known as an ERV ecological approach and
+ 
+
+ align:start position:0%
+known as an ERV ecological approach and
+as studying the brain systems in the
+
+ align:start position:0%
+as studying the brain systems in the
+ 
+
+ align:start position:0%
+as studying the brain systems in the
+context in which they actually they you
+
+ align:start position:0%
+context in which they actually they you
+ 
+
+ align:start position:0%
+context in which they actually they you
+know they evolved and were used and so
+
+ align:start position:0%
+know they evolved and were used and so
+ 
+
+ align:start position:0%
+know they evolved and were used and so
+that could apply to the use of song as a
+
+ align:start position:0%
+that could apply to the use of song as a
+ 
+
+ align:start position:0%
+that could apply to the use of song as a
+as a mechanism of communication and
+
+ align:start position:0%
+as a mechanism of communication and
+ 
+
+ align:start position:0%
+as a mechanism of communication and
+birds it can come from the you know
+
+ align:start position:0%
+birds it can come from the you know
+ 
+
+ align:start position:0%
+birds it can come from the you know
+finding you know finding prey in the
+
+ align:start position:0%
+finding you know finding prey in the
+ 
+
+ align:start position:0%
+finding you know finding prey in the
+dark when it comes to sound localization
+
+ align:start position:0%
+dark when it comes to sound localization
+ 
+
+ align:start position:0%
+dark when it comes to sound localization
+owls and the case of rodents
+
+ align:start position:0%
+owls and the case of rodents
+ 
+
+ align:start position:0%
+owls and the case of rodents
+o'keefe appreciated the fact that the
+
+ align:start position:0%
+o'keefe appreciated the fact that the
+ 
+
+ align:start position:0%
+o'keefe appreciated the fact that the
+campus and rodents really has a primary
+
+ align:start position:0%
+campus and rodents really has a primary
+ 
+
+ align:start position:0%
+campus and rodents really has a primary
+role in spatial navigation that animals
+
+ align:start position:0%
+role in spatial navigation that animals
+ 
+
+ align:start position:0%
+role in spatial navigation that animals
+that have damaged that the campus have
+
+ align:start position:0%
+that have damaged that the campus have
+ 
+
+ align:start position:0%
+that have damaged that the campus have
+problems with spatial navigation and the
+
+ align:start position:0%
+problems with spatial navigation and the
+ 
+
+ align:start position:0%
+problems with spatial navigation and the
+hippocampus had been studied up to that
+
+ align:start position:0%
+hippocampus had been studied up to that
+ 
+
+ align:start position:0%
+hippocampus had been studied up to that
+point using animals that were head fixed
+
+ align:start position:0%
+point using animals that were head fixed
+ 
+
+ align:start position:0%
+point using animals that were head fixed
+and so you take take a little rat you
+
+ align:start position:0%
+and so you take take a little rat you
+ 
+
+ align:start position:0%
+and so you take take a little rat you
+fix his head and the reason for fixing
+
+ align:start position:0%
+fix his head and the reason for fixing
+ 
+
+ align:start position:0%
+fix his head and the reason for fixing
+its head is for convenience largely so
+
+ align:start position:0%
+its head is for convenience largely so
+ 
+
+ align:start position:0%
+its head is for convenience largely so
+that when you place these little
+
+ align:start position:0%
+that when you place these little
+ 
+
+ align:start position:0%
+that when you place these little
+electrodes into the brain animal doesn't
+
+ align:start position:0%
+electrodes into the brain animal doesn't
+ 
+
+ align:start position:0%
+electrodes into the brain animal doesn't
+move it all moves like probe moves you
+
+ align:start position:0%
+move it all moves like probe moves you
+ 
+
+ align:start position:0%
+move it all moves like probe moves you
+can't get good recordings so you need to
+
+ align:start position:0%
+can't get good recordings so you need to
+ 
+
+ align:start position:0%
+can't get good recordings so you need to
+have you need to keep the preparation
+
+ align:start position:0%
+have you need to keep the preparation
+ 
+
+ align:start position:0%
+have you need to keep the preparation
+fixed so you fix the animals head then
+
+ align:start position:0%
+fixed so you fix the animals head then
+ 
+
+ align:start position:0%
+fixed so you fix the animals head then
+you figure out ways to actually look how
+
+ align:start position:0%
+you figure out ways to actually look how
+ 
+
+ align:start position:0%
+you figure out ways to actually look how
+to study the system given the
+
+ align:start position:0%
+to study the system given the
+ 
+
+ align:start position:0%
+to study the system given the
+constraints of the methodology and that
+
+ align:start position:0%
+constraints of the methodology and that
+ 
+
+ align:start position:0%
+constraints of the methodology and that
+involved largely before John Okeefe and
+
+ align:start position:0%
+involved largely before John Okeefe and
+ 
+
+ align:start position:0%
+involved largely before John Okeefe and
+1970 using the methods of classical
+
+ align:start position:0%
+1970 using the methods of classical
+ 
+
+ align:start position:0%
+1970 using the methods of classical
+conditioning so familiar with basic
+
+ align:start position:0%
+conditioning so familiar with basic
+ 
+
+ align:start position:0%
+conditioning so familiar with basic
+learning theory and you know how do we
+
+ align:start position:0%
+learning theory and you know how do we
+ 
+
+ align:start position:0%
+learning theory and you know how do we
+learn how to do things
+
+ align:start position:0%
+learn how to do things
+ 
+
+ align:start position:0%
+learn how to do things
+most basically chaining together
+
+ align:start position:0%
+most basically chaining together
+ 
+
+ align:start position:0%
+most basically chaining together
+stimulus-response associations you see
+
+ align:start position:0%
+stimulus-response associations you see
+ 
+
+ align:start position:0%
+stimulus-response associations you see
+something you do something you've got
+
+ align:start position:0%
+something you do something you've got
+ 
+
+ align:start position:0%
+something you do something you've got
+rewarded for doing that you're more
+
+ align:start position:0%
+rewarded for doing that you're more
+ 
+
+ align:start position:0%
+rewarded for doing that you're more
+likely to do that again in the future
+
+ align:start position:0%
+likely to do that again in the future
+ 
+
+ align:start position:0%
+likely to do that again in the future
+this is this is basic Pavlovian
+
+ align:start position:0%
+this is this is basic Pavlovian
+ 
+
+ align:start position:0%
+this is this is basic Pavlovian
+conditioning I ring a bell you get food
+
+ align:start position:0%
+conditioning I ring a bell you get food
+ 
+
+ align:start position:0%
+conditioning I ring a bell you get food
+okay you associate that with the food
+
+ align:start position:0%
+okay you associate that with the food
+ 
+
+ align:start position:0%
+okay you associate that with the food
+and so that was the thinking that all of
+
+ align:start position:0%
+and so that was the thinking that all of
+ 
+
+ align:start position:0%
+and so that was the thinking that all of
+cognition can be built up from basic
+
+ align:start position:0%
+cognition can be built up from basic
+ 
+
+ align:start position:0%
+cognition can be built up from basic
+stimulus-response associations but there
+
+ align:start position:0%
+stimulus-response associations but there
+ 
+
+ align:start position:0%
+stimulus-response associations but there
+was this movement around the time that
+
+ align:start position:0%
+was this movement around the time that
+ 
+
+ align:start position:0%
+was this movement around the time that
+O'Keefe was doing this work that that
+
+ align:start position:0%
+O'Keefe was doing this work that that
+ 
+
+ align:start position:0%
+O'Keefe was doing this work that that
+proposed that that was insufficient that
+
+ align:start position:0%
+proposed that that was insufficient that
+ 
+
+ align:start position:0%
+proposed that that was insufficient that
+simple behavioral simple stimulus
+
+ align:start position:0%
+simple behavioral simple stimulus
+ 
+
+ align:start position:0%
+simple behavioral simple stimulus
+responsibility was insufficient that
+
+ align:start position:0%
+responsibility was insufficient that
+ 
+
+ align:start position:0%
+responsibility was insufficient that
+there was some kind of internal
+
+ align:start position:0%
+there was some kind of internal
+ 
+
+ align:start position:0%
+there was some kind of internal
+foundation upon which learning was was
+
+ align:start position:0%
+foundation upon which learning was was
+ 
+
+ align:start position:0%
+foundation upon which learning was was
+applied and this was the so called
+
+ align:start position:0%
+applied and this was the so called
+ 
+
+ align:start position:0%
+applied and this was the so called
+cognitive theory of of learning and
+
+ align:start position:0%
+cognitive theory of of learning and
+ 
+
+ align:start position:0%
+cognitive theory of of learning and
+memory and the hippocampus was posited
+
+ align:start position:0%
+memory and the hippocampus was posited
+ 
+
+ align:start position:0%
+memory and the hippocampus was posited
+to be the site of one property of this
+
+ align:start position:0%
+to be the site of one property of this
+ 
+
+ align:start position:0%
+to be the site of one property of this
+cognitive learning as applied to space
+
+ align:start position:0%
+cognitive learning as applied to space
+ 
+
+ align:start position:0%
+cognitive learning as applied to space
+and the observation was actually a
+
+ align:start position:0%
+and the observation was actually a
+ 
+
+ align:start position:0%
+and the observation was actually a
+fairly simple one if you take a rat ic1
+
+ align:start position:0%
+fairly simple one if you take a rat ic1
+ 
+
+ align:start position:0%
+fairly simple one if you take a rat ic1
+to learn learn something that is it you
+
+ align:start position:0%
+to learn learn something that is it you
+ 
+
+ align:start position:0%
+to learn learn something that is it you
+want to learn to I know you know
+
+ align:start position:0%
+want to learn to I know you know
+ 
+
+ align:start position:0%
+want to learn to I know you know
+associate a associate a you know a cue
+
+ align:start position:0%
+associate a associate a you know a cue
+ 
+
+ align:start position:0%
+associate a associate a you know a cue
+with food or
+
+ align:start position:0%
+with food or
+ 
+
+ align:start position:0%
+with food or
+you know you want to train it to go over
+
+ align:start position:0%
+you know you want to train it to go over
+ 
+
+ align:start position:0%
+you know you want to train it to go over
+and you know press a lever for food you
+
+ align:start position:0%
+and you know press a lever for food you
+ 
+
+ align:start position:0%
+and you know press a lever for food you
+want to learn something and you do this
+
+ align:start position:0%
+want to learn something and you do this
+ 
+
+ align:start position:0%
+want to learn something and you do this
+in an environment that put it in a box
+
+ align:start position:0%
+in an environment that put it in a box
+ 
+
+ align:start position:0%
+in an environment that put it in a box
+well if you take her out you put it in
+
+ align:start position:0%
+well if you take her out you put it in
+ 
+
+ align:start position:0%
+well if you take her out you put it in
+that box let's say the date before and
+
+ align:start position:0%
+that box let's say the date before and
+ 
+
+ align:start position:0%
+that box let's say the date before and
+just let it wander around does nothing
+
+ align:start position:0%
+just let it wander around does nothing
+ 
+
+ align:start position:0%
+just let it wander around does nothing
+it's just explores the space you take it
+
+ align:start position:0%
+it's just explores the space you take it
+ 
+
+ align:start position:0%
+it's just explores the space you take it
+out and now we take two rats one that's
+
+ align:start position:0%
+out and now we take two rats one that's
+ 
+
+ align:start position:0%
+out and now we take two rats one that's
+been in the box before and one that has
+
+ align:start position:0%
+been in the box before and one that has
+ 
+
+ align:start position:0%
+been in the box before and one that has
+not been in the box before and the one
+
+ align:start position:0%
+not been in the box before and the one
+ 
+
+ align:start position:0%
+not been in the box before and the one
+the wrath has been in the box before
+
+ align:start position:0%
+the wrath has been in the box before
+ 
+
+ align:start position:0%
+the wrath has been in the box before
+we'll learn faster then the animal has
+
+ align:start position:0%
+we'll learn faster then the animal has
+ 
+
+ align:start position:0%
+we'll learn faster then the animal has
+not been in the box you say why would
+
+ align:start position:0%
+not been in the box you say why would
+ 
+
+ align:start position:0%
+not been in the box you say why would
+why would just passive exposure to that
+
+ align:start position:0%
+why would just passive exposure to that
+ 
+
+ align:start position:0%
+why would just passive exposure to that
+box enhance its learning and this
+
+ align:start position:0%
+box enhance its learning and this
+ 
+
+ align:start position:0%
+box enhance its learning and this
+phenomenon I was latent learning the
+
+ align:start position:0%
+phenomenon I was latent learning the
+ 
+
+ align:start position:0%
+phenomenon I was latent learning the
+animal had learned something that he
+
+ align:start position:0%
+animal had learned something that he
+ 
+
+ align:start position:0%
+animal had learned something that he
+could then apply to this new learning
+
+ align:start position:0%
+could then apply to this new learning
+ 
+
+ align:start position:0%
+could then apply to this new learning
+even though it was not instructive you
+
+ align:start position:0%
+even though it was not instructive you
+ 
+
+ align:start position:0%
+even though it was not instructive you
+didn't nothing that wasn't rewarded for
+
+ align:start position:0%
+didn't nothing that wasn't rewarded for
+ 
+
+ align:start position:0%
+didn't nothing that wasn't rewarded for
+doing anything it just explored and so
+
+ align:start position:0%
+doing anything it just explored and so
+ 
+
+ align:start position:0%
+doing anything it just explored and so
+this idea that there was some sort of
+
+ align:start position:0%
+this idea that there was some sort of
+ 
+
+ align:start position:0%
+this idea that there was some sort of
+latent capacity to enhance learning was
+
+ align:start position:0%
+latent capacity to enhance learning was
+ 
+
+ align:start position:0%
+latent capacity to enhance learning was
+motivated the study of the hippocampus
+
+ align:start position:0%
+motivated the study of the hippocampus
+ 
+
+ align:start position:0%
+motivated the study of the hippocampus
+in the context of non head fixed
+
+ align:start position:0%
+in the context of non head fixed
+ 
+
+ align:start position:0%
+in the context of non head fixed
+recording and so O'Keefe's real insight
+
+ align:start position:0%
+recording and so O'Keefe's real insight
+ 
+
+ align:start position:0%
+recording and so O'Keefe's real insight
+in fact the paper that was cited for you
+
+ align:start position:0%
+in fact the paper that was cited for you
+ 
+
+ align:start position:0%
+in fact the paper that was cited for you
+know for the Nobel Prize was the paper
+
+ align:start position:0%
+know for the Nobel Prize was the paper
+ 
+
+ align:start position:0%
+know for the Nobel Prize was the paper
+in which he first recorded from these
+
+ align:start position:0%
+in which he first recorded from these
+ 
+
+ align:start position:0%
+in which he first recorded from these
+cells and all he did was just take the
+
+ align:start position:0%
+cells and all he did was just take the
+ 
+
+ align:start position:0%
+cells and all he did was just take the
+animals out of the ear bars so he took
+
+ align:start position:0%
+animals out of the ear bars so he took
+ 
+
+ align:start position:0%
+animals out of the ear bars so he took
+the animal out of yours and just let it
+
+ align:start position:0%
+the animal out of yours and just let it
+ 
+
+ align:start position:0%
+the animal out of yours and just let it
+run around on a tabletop just like this
+
+ align:start position:0%
+run around on a tabletop just like this
+ 
+
+ align:start position:0%
+run around on a tabletop just like this
+actually as a table at the University
+
+ align:start position:0%
+actually as a table at the University
+ 
+
+ align:start position:0%
+actually as a table at the University
+College London about the size where this
+
+ align:start position:0%
+College London about the size where this
+ 
+
+ align:start position:0%
+College London about the size where this
+rat just kind of wandered around and he
+
+ align:start position:0%
+rat just kind of wandered around and he
+ 
+
+ align:start position:0%
+rat just kind of wandered around and he
+made observations oh here's a cell that
+
+ align:start position:0%
+made observations oh here's a cell that
+ 
+
+ align:start position:0%
+made observations oh here's a cell that
+fires when the animal goes over to the
+
+ align:start position:0%
+fires when the animal goes over to the
+ 
+
+ align:start position:0%
+fires when the animal goes over to the
+left-hand side and very descriptive but
+
+ align:start position:0%
+left-hand side and very descriptive but
+ 
+
+ align:start position:0%
+left-hand side and very descriptive but
+the key insight was to study the
+
+ align:start position:0%
+the key insight was to study the
+ 
+
+ align:start position:0%
+the key insight was to study the
+hippocampus when rats are doing what
+
+ align:start position:0%
+hippocampus when rats are doing what
+ 
+
+ align:start position:0%
+hippocampus when rats are doing what
+rats normally do explore in space so it
+
+ align:start position:0%
+rats normally do explore in space so it
+ 
+
+ align:start position:0%
+rats normally do explore in space so it
+was this ethological approach and what
+
+ align:start position:0%
+was this ethological approach and what
+ 
+
+ align:start position:0%
+was this ethological approach and what
+he discovered was that and that these
+
+ align:start position:0%
+he discovered was that and that these
+ 
+
+ align:start position:0%
+he discovered was that and that these
+cells cells in the hippocampus and this
+
+ align:start position:0%
+cells cells in the hippocampus and this
+ 
+
+ align:start position:0%
+cells cells in the hippocampus and this
+is a cross-section the campus is found
+
+ align:start position:0%
+is a cross-section the campus is found
+ 
+
+ align:start position:0%
+is a cross-section the campus is found
+here it's in the medial temporal lobes
+
+ align:start position:0%
+here it's in the medial temporal lobes
+ 
+
+ align:start position:0%
+here it's in the medial temporal lobes
+it's the name hippocampus comes from the
+
+ align:start position:0%
+it's the name hippocampus comes from the
+ 
+
+ align:start position:0%
+it's the name hippocampus comes from the
+Greek for C horror so in humans it sort
+
+ align:start position:0%
+Greek for C horror so in humans it sort
+ 
+
+ align:start position:0%
+Greek for C horror so in humans it sort
+of looks like a seahorse the regions
+
+ align:start position:0%
+of looks like a seahorse the regions
+ 
+
+ align:start position:0%
+of looks like a seahorse the regions
+here the terminology ca these they're
+
+ align:start position:0%
+here the terminology ca these they're
+ 
+
+ align:start position:0%
+here the terminology ca these they're
+these different fields of hippocampus
+
+ align:start position:0%
+these different fields of hippocampus
+ 
+
+ align:start position:0%
+these different fields of hippocampus
+comes from Cornell Montes or Amin's horn
+
+ align:start position:0%
+comes from Cornell Montes or Amin's horn
+ 
+
+ align:start position:0%
+comes from Cornell Montes or Amin's horn
+that's because it looks like a ram's
+
+ align:start position:0%
+that's because it looks like a ram's
+ 
+
+ align:start position:0%
+that's because it looks like a ram's
+horn so if you think about this like
+
+ align:start position:0%
+horn so if you think about this like
+ 
+
+ align:start position:0%
+horn so if you think about this like
+little little ram's horns right here put
+
+ align:start position:0%
+little little ram's horns right here put
+ 
+
+ align:start position:0%
+little little ram's horns right here put
+them anytime
+
+ align:start position:0%
+them anytime
+ 
+
+ align:start position:0%
+them anytime
+the lobes and you move them in there
+
+ align:start position:0%
+the lobes and you move them in there
+ 
+
+ align:start position:0%
+the lobes and you move them in there
+that's where your hippocampus is just
+
+ align:start position:0%
+that's where your hippocampus is just
+ 
+
+ align:start position:0%
+that's where your hippocampus is just
+like this and if you make a
+
+ align:start position:0%
+like this and if you make a
+ 
+
+ align:start position:0%
+like this and if you make a
+cross-section slice through that this is
+
+ align:start position:0%
+cross-section slice through that this is
+ 
+
+ align:start position:0%
+cross-section slice through that this is
+the circuit so information comes in from
+
+ align:start position:0%
+the circuit so information comes in from
+ 
+
+ align:start position:0%
+the circuit so information comes in from
+across the brain converges in the
+
+ align:start position:0%
+across the brain converges in the
+ 
+
+ align:start position:0%
+across the brain converges in the
+primary input to the hippocampus that's
+
+ align:start position:0%
+primary input to the hippocampus that's
+ 
+
+ align:start position:0%
+primary input to the hippocampus that's
+called the internal cortex which is what
+
+ align:start position:0%
+called the internal cortex which is what
+ 
+
+ align:start position:0%
+called the internal cortex which is what
+the other the the other Nobel Prize was
+
+ align:start position:0%
+the other the the other Nobel Prize was
+ 
+
+ align:start position:0%
+the other the the other Nobel Prize was
+awarded to the husband-and-wife team
+
+ align:start position:0%
+awarded to the husband-and-wife team
+ 
+
+ align:start position:0%
+awarded to the husband-and-wife team
+that had identified discovered and
+
+ align:start position:0%
+that had identified discovered and
+ 
+
+ align:start position:0%
+that had identified discovered and
+identified the properties of cells in
+
+ align:start position:0%
+identified the properties of cells in
+ 
+
+ align:start position:0%
+identified the properties of cells in
+the internal cortex these so called grid
+
+ align:start position:0%
+the internal cortex these so called grid
+ 
+
+ align:start position:0%
+the internal cortex these so called grid
+cells that seem to carry information
+
+ align:start position:0%
+cells that seem to carry information
+ 
+
+ align:start position:0%
+cells that seem to carry information
+about actual seemed like Cartesian like
+
+ align:start position:0%
+about actual seemed like Cartesian like
+ 
+
+ align:start position:0%
+about actual seemed like Cartesian like
+spatial information conveyed in the P
+
+ align:start position:0%
+spatial information conveyed in the P
+ 
+
+ align:start position:0%
+spatial information conveyed in the P
+campus so stuff comes in from the rest
+
+ align:start position:0%
+campus so stuff comes in from the rest
+ 
+
+ align:start position:0%
+campus so stuff comes in from the rest
+of the brain converges an internal
+
+ align:start position:0%
+of the brain converges an internal
+ 
+
+ align:start position:0%
+of the brain converges an internal
+cortex and then goes around this little
+
+ align:start position:0%
+cortex and then goes around this little
+ 
+
+ align:start position:0%
+cortex and then goes around this little
+loop from these these three primary
+
+ align:start position:0%
+loop from these these three primary
+ 
+
+ align:start position:0%
+loop from these these three primary
+subfields the dentate gyrus c8 cornrow -
+
+ align:start position:0%
+subfields the dentate gyrus c8 cornrow -
+ 
+
+ align:start position:0%
+subfields the dentate gyrus c8 cornrow -
+3 C a1 cibecue l'm back on again so it
+
+ align:start position:0%
+3 C a1 cibecue l'm back on again so it
+ 
+
+ align:start position:0%
+3 C a1 cibecue l'm back on again so it
+goes through this loop classically it
+
+ align:start position:0%
+goes through this loop classically it
+ 
+
+ align:start position:0%
+goes through this loop classically it
+had been referred to as the Tri synaptic
+
+ align:start position:0%
+had been referred to as the Tri synaptic
+ 
+
+ align:start position:0%
+had been referred to as the Tri synaptic
+loop one synapse dente CA 3 C a1 and
+
+ align:start position:0%
+loop one synapse dente CA 3 C a1 and
+ 
+
+ align:start position:0%
+loop one synapse dente CA 3 C a1 and
+then back out and again recordings in
+
+ align:start position:0%
+then back out and again recordings in
+ 
+
+ align:start position:0%
+then back out and again recordings in
+this part of the hippocampus revealed
+
+ align:start position:0%
+this part of the hippocampus revealed
+ 
+
+ align:start position:0%
+this part of the hippocampus revealed
+the properties at all which I'll mention
+
+ align:start position:0%
+the properties at all which I'll mention
+ 
+
+ align:start position:0%
+the properties at all which I'll mention
+and that is these cells respond to
+
+ align:start position:0%
+and that is these cells respond to
+ 
+
+ align:start position:0%
+and that is these cells respond to
+locations in space but prior to that the
+
+ align:start position:0%
+locations in space but prior to that the
+ 
+
+ align:start position:0%
+locations in space but prior to that the
+selector physiological work in rodents
+
+ align:start position:0%
+selector physiological work in rodents
+ 
+
+ align:start position:0%
+selector physiological work in rodents
+there had been human neuropsychological
+
+ align:start position:0%
+there had been human neuropsychological
+ 
+
+ align:start position:0%
+there had been human neuropsychological
+work in particular the seminal case of
+
+ align:start position:0%
+work in particular the seminal case of
+ 
+
+ align:start position:0%
+work in particular the seminal case of
+the patient HM who had been studied here
+
+ align:start position:0%
+the patient HM who had been studied here
+ 
+
+ align:start position:0%
+the patient HM who had been studied here
+from for many decades before he just
+
+ align:start position:0%
+from for many decades before he just
+ 
+
+ align:start position:0%
+from for many decades before he just
+recently passed away known as HM hen
+
+ align:start position:0%
+recently passed away known as HM hen
+ 
+
+ align:start position:0%
+recently passed away known as HM hen
+neural iesson as he is as he's sort of
+
+ align:start position:0%
+neural iesson as he is as he's sort of
+ 
+
+ align:start position:0%
+neural iesson as he is as he's sort of
+now revealed sort of recently revealed
+
+ align:start position:0%
+now revealed sort of recently revealed
+ 
+
+ align:start position:0%
+now revealed sort of recently revealed
+to be a patient who had undergone
+
+ align:start position:0%
+to be a patient who had undergone
+ 
+
+ align:start position:0%
+to be a patient who had undergone
+bilateral resection and medial temporal
+
+ align:start position:0%
+bilateral resection and medial temporal
+ 
+
+ align:start position:0%
+bilateral resection and medial temporal
+lobes cut out parts of his of the
+
+ align:start position:0%
+lobes cut out parts of his of the
+ 
+
+ align:start position:0%
+lobes cut out parts of his of the
+hippocampus and other associated medial
+
+ align:start position:0%
+hippocampus and other associated medial
+ 
+
+ align:start position:0%
+hippocampus and other associated medial
+temporal lobe structures to treat
+
+ align:start position:0%
+temporal lobe structures to treat
+ 
+
+ align:start position:0%
+temporal lobe structures to treat
+intractable epilepsy he subsequently
+
+ align:start position:0%
+intractable epilepsy he subsequently
+ 
+
+ align:start position:0%
+intractable epilepsy he subsequently
+Billy to form any new memories
+
+ align:start position:0%
+Billy to form any new memories
+ 
+
+ align:start position:0%
+Billy to form any new memories
+so had permanent
+
+ align:start position:0%
+so had permanent
+ 
+
+ align:start position:0%
+so had permanent
+permanent answer and tear great couldn't
+
+ align:start position:0%
+permanent answer and tear great couldn't
+ 
+
+ align:start position:0%
+permanent answer and tear great couldn't
+form any new memories going on going
+
+ align:start position:0%
+form any new memories going on going
+ 
+
+ align:start position:0%
+form any new memories going on going
+forward in the future and lost some of
+
+ align:start position:0%
+forward in the future and lost some of
+ 
+
+ align:start position:0%
+forward in the future and lost some of
+his older memories so you lose memories
+
+ align:start position:0%
+his older memories so you lose memories
+ 
+
+ align:start position:0%
+his older memories so you lose memories
+in humans rodents can't navigate in
+
+ align:start position:0%
+in humans rodents can't navigate in
+ 
+
+ align:start position:0%
+in humans rodents can't navigate in
+space also humans have a spatial deficit
+
+ align:start position:0%
+space also humans have a spatial deficit
+ 
+
+ align:start position:0%
+space also humans have a spatial deficit
+so there's some connection between space
+
+ align:start position:0%
+so there's some connection between space
+ 
+
+ align:start position:0%
+so there's some connection between space
+and memory and the question is what is
+
+ align:start position:0%
+and memory and the question is what is
+ 
+
+ align:start position:0%
+and memory and the question is what is
+that what would were linked spatial
+
+ align:start position:0%
+that what would were linked spatial
+ 
+
+ align:start position:0%
+that what would were linked spatial
+navigation and memory but not just kind
+
+ align:start position:0%
+navigation and memory but not just kind
+ 
+
+ align:start position:0%
+navigation and memory but not just kind
+of any kind of memory what we referred
+
+ align:start position:0%
+of any kind of memory what we referred
+ 
+
+ align:start position:0%
+of any kind of memory what we referred
+to as episodic memory or memory for
+
+ align:start position:0%
+to as episodic memory or memory for
+ 
+
+ align:start position:0%
+to as episodic memory or memory for
+events or experiences and so the working
+
+ align:start position:0%
+events or experiences and so the working
+ 
+
+ align:start position:0%
+events or experiences and so the working
+and hypothesis is that these two things
+
+ align:start position:0%
+and hypothesis is that these two things
+ 
+
+ align:start position:0%
+and hypothesis is that these two things
+are really connected by a need a
+
+ align:start position:0%
+are really connected by a need a
+ 
+
+ align:start position:0%
+are really connected by a need a
+computational imperative to maintain
+
+ align:start position:0%
+computational imperative to maintain
+ 
+
+ align:start position:0%
+computational imperative to maintain
+information about time order and that is
+
+ align:start position:0%
+information about time order and that is
+ 
+
+ align:start position:0%
+information about time order and that is
+if you're going to use experience to
+
+ align:start position:0%
+if you're going to use experience to
+ 
+
+ align:start position:0%
+if you're going to use experience to
+guide future behavior you need to figure
+
+ align:start position:0%
+guide future behavior you need to figure
+ 
+
+ align:start position:0%
+guide future behavior you need to figure
+out what the causal relationships are
+
+ align:start position:0%
+out what the causal relationships are
+ 
+
+ align:start position:0%
+out what the causal relationships are
+between events in the world you know why
+
+ align:start position:0%
+between events in the world you know why
+ 
+
+ align:start position:0%
+between events in the world you know why
+did you know I if I if I see a and B
+
+ align:start position:0%
+did you know I if I if I see a and B
+ 
+
+ align:start position:0%
+did you know I if I if I see a and B
+what I really want to figure out I don't
+
+ align:start position:0%
+what I really want to figure out I don't
+ 
+
+ align:start position:0%
+what I really want to figure out I don't
+just want to record the fact that a and
+
+ align:start position:0%
+just want to record the fact that a and
+ 
+
+ align:start position:0%
+just want to record the fact that a and
+B happen together ultimately I want to
+
+ align:start position:0%
+B happen together ultimately I want to
+ 
+
+ align:start position:0%
+B happen together ultimately I want to
+try to understand the relationship
+
+ align:start position:0%
+try to understand the relationship
+ 
+
+ align:start position:0%
+try to understand the relationship
+between a and B did a cos B or what you
+
+ align:start position:0%
+between a and B did a cos B or what you
+ 
+
+ align:start position:0%
+between a and B did a cos B or what you
+know how might I actually predict B
+
+ align:start position:0%
+know how might I actually predict B
+ 
+
+ align:start position:0%
+know how might I actually predict B
+given a and the way I would do that
+
+ align:start position:0%
+given a and the way I would do that
+ 
+
+ align:start position:0%
+given a and the way I would do that
+would be to construct some kind of
+
+ align:start position:0%
+would be to construct some kind of
+ 
+
+ align:start position:0%
+would be to construct some kind of
+simple internal model a predictive model
+
+ align:start position:0%
+simple internal model a predictive model
+ 
+
+ align:start position:0%
+simple internal model a predictive model
+that's based on experience and so the
+
+ align:start position:0%
+that's based on experience and so the
+ 
+
+ align:start position:0%
+that's based on experience and so the
+idea is hippocampus captures experience
+
+ align:start position:0%
+idea is hippocampus captures experience
+ 
+
+ align:start position:0%
+idea is hippocampus captures experience
+and then some through some process which
+
+ align:start position:0%
+and then some through some process which
+ 
+
+ align:start position:0%
+and then some through some process which
+we will refer to as the process of
+
+ align:start position:0%
+we will refer to as the process of
+ 
+
+ align:start position:0%
+we will refer to as the process of
+consolidation translates experience into
+
+ align:start position:0%
+consolidation translates experience into
+ 
+
+ align:start position:0%
+consolidation translates experience into
+some working model that can predict
+
+ align:start position:0%
+some working model that can predict
+ 
+
+ align:start position:0%
+some working model that can predict
+events and can be used to guide behavior
+
+ align:start position:0%
+events and can be used to guide behavior
+ 
+
+ align:start position:0%
+events and can be used to guide behavior
+and decision-making and critical to that
+
+ align:start position:0%
+and decision-making and critical to that
+ 
+
+ align:start position:0%
+and decision-making and critical to that
+is just the idea of time and in
+
+ align:start position:0%
+is just the idea of time and in
+ 
+
+ align:start position:0%
+is just the idea of time and in
+particular time order so as I mentioned
+
+ align:start position:0%
+particular time order so as I mentioned
+ 
+
+ align:start position:0%
+particular time order so as I mentioned
+the the use of very simple technology in
+
+ align:start position:0%
+the the use of very simple technology in
+ 
+
+ align:start position:0%
+the the use of very simple technology in
+this case extracellular near
+
+ align:start position:0%
+this case extracellular near
+ 
+
+ align:start position:0%
+this case extracellular near
+physiological recording taking a tiny
+
+ align:start position:0%
+physiological recording taking a tiny
+ 
+
+ align:start position:0%
+physiological recording taking a tiny
+wire this wire is actually four small
+
+ align:start position:0%
+wire this wire is actually four small
+ 
+
+ align:start position:0%
+wire this wire is actually four small
+wires each one about 10 microns across
+
+ align:start position:0%
+wires each one about 10 microns across
+ 
+
+ align:start position:0%
+wires each one about 10 microns across
+you twist them together in a little
+
+ align:start position:0%
+you twist them together in a little
+ 
+
+ align:start position:0%
+you twist them together in a little
+bundle the bundle is about 35 microns
+
+ align:start position:0%
+bundle the bundle is about 35 microns
+ 
+
+ align:start position:0%
+bundle the bundle is about 35 microns
+human hair is on the order of about 50
+
+ align:start position:0%
+human hair is on the order of about 50
+ 
+
+ align:start position:0%
+human hair is on the order of about 50
+typically about 50 microns so these are
+
+ align:start position:0%
+typically about 50 microns so these are
+ 
+
+ align:start position:0%
+typically about 50 microns so these are
+little these are wires or electrodes
+
+ align:start position:0%
+little these are wires or electrodes
+ 
+
+ align:start position:0%
+little these are wires or electrodes
+multi contact electrodes about as large
+
+ align:start position:0%
+multi contact electrodes about as large
+ 
+
+ align:start position:0%
+multi contact electrodes about as large
+as a hair human hair we thread these
+
+ align:start position:0%
+as a hair human hair we thread these
+ 
+
+ align:start position:0%
+as a hair human hair we thread these
+things through the little oil rig
+
+ align:start position:0%
+things through the little oil rig
+ 
+
+ align:start position:0%
+things through the little oil rig
+drilling device here which is which I'll
+
+ align:start position:0%
+drilling device here which is which I'll
+ 
+
+ align:start position:0%
+drilling device here which is which I'll
+these little micro manipulators
+
+ align:start position:0%
+these little micro manipulators
+ 
+
+ align:start position:0%
+these little micro manipulators
+allow this wire to be driven down
+
+ align:start position:0%
+allow this wire to be driven down
+ 
+
+ align:start position:0%
+allow this wire to be driven down
+through Sperry small guide cannula and
+
+ align:start position:0%
+through Sperry small guide cannula and
+ 
+
+ align:start position:0%
+through Sperry small guide cannula and
+sew out the bottom will will be a number
+
+ align:start position:0%
+sew out the bottom will will be a number
+ 
+
+ align:start position:0%
+sew out the bottom will will be a number
+of these independent individual
+
+ align:start position:0%
+of these independent individual
+ 
+
+ align:start position:0%
+of these independent individual
+electrodes each controlled by these by
+
+ align:start position:0%
+electrodes each controlled by these by
+ 
+
+ align:start position:0%
+electrodes each controlled by these by
+their own micro manipulator so we can
+
+ align:start position:0%
+their own micro manipulator so we can
+ 
+
+ align:start position:0%
+their own micro manipulator so we can
+send these electrodes down this entire
+
+ align:start position:0%
+send these electrodes down this entire
+ 
+
+ align:start position:0%
+send these electrodes down this entire
+device in this case weighs anywhere from
+
+ align:start position:0%
+device in this case weighs anywhere from
+ 
+
+ align:start position:0%
+device in this case weighs anywhere from
+like 12 to 12 to 20 grams and this can
+
+ align:start position:0%
+like 12 to 12 to 20 grams and this can
+ 
+
+ align:start position:0%
+like 12 to 12 to 20 grams and this can
+be placed on an animal's head
+
+ align:start position:0%
+be placed on an animal's head
+ 
+
+ align:start position:0%
+be placed on an animal's head
+permanently or chronically and that is
+
+ align:start position:0%
+permanently or chronically and that is
+ 
+
+ align:start position:0%
+permanently or chronically and that is
+that it once it goes on doesn't come off
+
+ align:start position:0%
+that it once it goes on doesn't come off
+ 
+
+ align:start position:0%
+that it once it goes on doesn't come off
+so they all have this this little helmet
+
+ align:start position:0%
+so they all have this this little helmet
+ 
+
+ align:start position:0%
+so they all have this this little helmet
+like thing on their head small opening
+
+ align:start position:0%
+like thing on their head small opening
+ 
+
+ align:start position:0%
+like thing on their head small opening
+is made in the in the skull the wires
+
+ align:start position:0%
+is made in the in the skull the wires
+ 
+
+ align:start position:0%
+is made in the in the skull the wires
+are sent through and the whole surgical
+
+ align:start position:0%
+are sent through and the whole surgical
+ 
+
+ align:start position:0%
+are sent through and the whole surgical
+procedure takes maybe 30 to 45 minutes
+
+ align:start position:0%
+procedure takes maybe 30 to 45 minutes
+ 
+
+ align:start position:0%
+procedure takes maybe 30 to 45 minutes
+it's like an outpatient thing probably
+
+ align:start position:0%
+it's like an outpatient thing probably
+ 
+
+ align:start position:0%
+it's like an outpatient thing probably
+take longer to have your wisdom teeth
+
+ align:start position:0%
+take longer to have your wisdom teeth
+ 
+
+ align:start position:0%
+take longer to have your wisdom teeth
+pulled and to have a brain implant
+
+ align:start position:0%
+pulled and to have a brain implant
+ 
+
+ align:start position:0%
+pulled and to have a brain implant
+installed then once this is installed
+
+ align:start position:0%
+installed then once this is installed
+ 
+
+ align:start position:0%
+installed then once this is installed
+these electrodes can be driven down and
+
+ align:start position:0%
+these electrodes can be driven down and
+ 
+
+ align:start position:0%
+these electrodes can be driven down and
+placed permanently it gives you the
+
+ align:start position:0%
+placed permanently it gives you the
+ 
+
+ align:start position:0%
+placed permanently it gives you the
+ability to monitor pattern activity
+
+ align:start position:0%
+ability to monitor pattern activity
+ 
+
+ align:start position:0%
+ability to monitor pattern activity
+across large populations over you know
+
+ align:start position:0%
+across large populations over you know
+ 
+
+ align:start position:0%
+across large populations over you know
+long periods of time days weeks months
+
+ align:start position:0%
+long periods of time days weeks months
+ 
+
+ align:start position:0%
+long periods of time days weeks months
+so you have a kind of tapped into
+
+ align:start position:0%
+so you have a kind of tapped into
+ 
+
+ align:start position:0%
+so you have a kind of tapped into
+activity in this brain area and you can
+
+ align:start position:0%
+activity in this brain area and you can
+ 
+
+ align:start position:0%
+activity in this brain area and you can
+monitor as animals experience learn and
+
+ align:start position:0%
+monitor as animals experience learn and
+ 
+
+ align:start position:0%
+monitor as animals experience learn and
+recall and this is what the raw data
+
+ align:start position:0%
+recall and this is what the raw data
+ 
+
+ align:start position:0%
+recall and this is what the raw data
+looks like this is a cartoon of the
+
+ align:start position:0%
+looks like this is a cartoon of the
+ 
+
+ align:start position:0%
+looks like this is a cartoon of the
+electrode or contacts the idea with the
+
+ align:start position:0%
+electrode or contacts the idea with the
+ 
+
+ align:start position:0%
+electrode or contacts the idea with the
+four contacts is it gives you the
+
+ align:start position:0%
+four contacts is it gives you the
+ 
+
+ align:start position:0%
+four contacts is it gives you the
+ability to triangulate location much as
+
+ align:start position:0%
+ability to triangulate location much as
+ 
+
+ align:start position:0%
+ability to triangulate location much as
+you kind of scare stereoscopically can
+
+ align:start position:0%
+you kind of scare stereoscopically can
+ 
+
+ align:start position:0%
+you kind of scare stereoscopically can
+determine depth these four contacts will
+
+ align:start position:0%
+determine depth these four contacts will
+ 
+
+ align:start position:0%
+determine depth these four contacts will
+give you the ability to triangulate
+
+ align:start position:0%
+give you the ability to triangulate
+ 
+
+ align:start position:0%
+give you the ability to triangulate
+things in three-dimensional space one of
+
+ align:start position:0%
+things in three-dimensional space one of
+ 
+
+ align:start position:0%
+things in three-dimensional space one of
+the properties of this hippocampal
+
+ align:start position:0%
+the properties of this hippocampal
+ 
+
+ align:start position:0%
+the properties of this hippocampal
+circuit and that is so this little
+
+ align:start position:0%
+circuit and that is so this little
+ 
+
+ align:start position:0%
+circuit and that is so this little
+cross-section you think of imagine a
+
+ align:start position:0%
+cross-section you think of imagine a
+ 
+
+ align:start position:0%
+cross-section you think of imagine a
+neuron here and so they're going to be
+
+ align:start position:0%
+neuron here and so they're going to be
+ 
+
+ align:start position:0%
+neuron here and so they're going to be
+you know again neurons distributed
+
+ align:start position:0%
+you know again neurons distributed
+ 
+
+ align:start position:0%
+you know again neurons distributed
+across this you know across the
+
+ align:start position:0%
+across this you know across the
+ 
+
+ align:start position:0%
+across this you know across the
+hippocampus in the rat there are on the
+
+ align:start position:0%
+hippocampus in the rat there are on the
+ 
+
+ align:start position:0%
+hippocampus in the rat there are on the
+order of maybe 200,000 cells in areas C
+
+ align:start position:0%
+order of maybe 200,000 cells in areas C
+ 
+
+ align:start position:0%
+order of maybe 200,000 cells in areas C
+a1 and the entire hippocampus there are
+
+ align:start position:0%
+a1 and the entire hippocampus there are
+ 
+
+ align:start position:0%
+a1 and the entire hippocampus there are
+on the order of me 1 to 2 million cells
+
+ align:start position:0%
+on the order of me 1 to 2 million cells
+ 
+
+ align:start position:0%
+on the order of me 1 to 2 million cells
+and if you drop an electrode anyplace
+
+ align:start position:0%
+and if you drop an electrode anyplace
+ 
+
+ align:start position:0%
+and if you drop an electrode anyplace
+into the campus you will find cells that
+
+ align:start position:0%
+into the campus you will find cells that
+ 
+
+ align:start position:0%
+into the campus you will find cells that
+have this kind of spatial property
+
+ align:start position:0%
+have this kind of spatial property
+ 
+
+ align:start position:0%
+have this kind of spatial property
+and so what that says is that spatial
+
+ align:start position:0%
+and so what that says is that spatial
+ 
+
+ align:start position:0%
+and so what that says is that spatial
+information is distributed not you know
+
+ align:start position:0%
+information is distributed not you know
+ 
+
+ align:start position:0%
+information is distributed not you know
+in a topographic way in other words is
+
+ align:start position:0%
+in a topographic way in other words is
+ 
+
+ align:start position:0%
+in a topographic way in other words is
+not you know one location in space is
+
+ align:start position:0%
+not you know one location in space is
+ 
+
+ align:start position:0%
+not you know one location in space is
+mapped into one location on the brain in
+
+ align:start position:0%
+mapped into one location on the brain in
+ 
+
+ align:start position:0%
+mapped into one location on the brain in
+the in the hippocampus unlike some of
+
+ align:start position:0%
+the in the hippocampus unlike some of
+ 
+
+ align:start position:0%
+the in the hippocampus unlike some of
+the sensory areas that you might that
+
+ align:start position:0%
+the sensory areas that you might that
+ 
+
+ align:start position:0%
+the sensory areas that you might that
+have this kind of topography runs for
+
+ align:start position:0%
+have this kind of topography runs for
+ 
+
+ align:start position:0%
+have this kind of topography runs for
+instance if you record in the in the
+
+ align:start position:0%
+instance if you record in the in the
+ 
+
+ align:start position:0%
+instance if you record in the in the
+visual cortex where there's there would
+
+ align:start position:0%
+visual cortex where there's there would
+ 
+
+ align:start position:0%
+visual cortex where there's there would
+be some correspondence between location
+
+ align:start position:0%
+be some correspondence between location
+ 
+
+ align:start position:0%
+be some correspondence between location
+and visual field and the location of
+
+ align:start position:0%
+and visual field and the location of
+ 
+
+ align:start position:0%
+and visual field and the location of
+cells in the cortex that respond to that
+
+ align:start position:0%
+cells in the cortex that respond to that
+ 
+
+ align:start position:0%
+cells in the cortex that respond to that
+is so called retina topic mapping visual
+
+ align:start position:0%
+is so called retina topic mapping visual
+ 
+
+ align:start position:0%
+is so called retina topic mapping visual
+field mapped onto the anatomy same thing
+
+ align:start position:0%
+field mapped onto the anatomy same thing
+ 
+
+ align:start position:0%
+field mapped onto the anatomy same thing
+with like the somatosensory system as I
+
+ align:start position:0%
+with like the somatosensory system as I
+ 
+
+ align:start position:0%
+with like the somatosensory system as I
+move and you know I touch different
+
+ align:start position:0%
+move and you know I touch different
+ 
+
+ align:start position:0%
+move and you know I touch different
+parts of the body the cells that respond
+
+ align:start position:0%
+parts of the body the cells that respond
+ 
+
+ align:start position:0%
+parts of the body the cells that respond
+to that will be mapped out in a you know
+
+ align:start position:0%
+to that will be mapped out in a you know
+ 
+
+ align:start position:0%
+to that will be mapped out in a you know
+in a sort of largely one-to-one
+
+ align:start position:0%
+in a sort of largely one-to-one
+ 
+
+ align:start position:0%
+in a sort of largely one-to-one
+correspondence between the adjacency of
+
+ align:start position:0%
+correspondence between the adjacency of
+ 
+
+ align:start position:0%
+correspondence between the adjacency of
+stimuli in the input space and jccc of
+
+ align:start position:0%
+stimuli in the input space and jccc of
+ 
+
+ align:start position:0%
+stimuli in the input space and jccc of
+the representation in the neural space
+
+ align:start position:0%
+the representation in the neural space
+ 
+
+ align:start position:0%
+the representation in the neural space
+that does not occur in the campus two
+
+ align:start position:0%
+that does not occur in the campus two
+ 
+
+ align:start position:0%
+that does not occur in the campus two
+cells that are right next to one another
+
+ align:start position:0%
+cells that are right next to one another
+ 
+
+ align:start position:0%
+cells that are right next to one another
+are no more likely to respond to nearby
+
+ align:start position:0%
+are no more likely to respond to nearby
+ 
+
+ align:start position:0%
+are no more likely to respond to nearby
+locations in space than two cells that
+
+ align:start position:0%
+locations in space than two cells that
+ 
+
+ align:start position:0%
+locations in space than two cells that
+are distant from one another so as we'll
+
+ align:start position:0%
+are distant from one another so as we'll
+ 
+
+ align:start position:0%
+are distant from one another so as we'll
+discuss the principle of information
+
+ align:start position:0%
+discuss the principle of information
+ 
+
+ align:start position:0%
+discuss the principle of information
+representation hippocampus appears to be
+
+ align:start position:0%
+representation hippocampus appears to be
+ 
+
+ align:start position:0%
+representation hippocampus appears to be
+one of kind of sparse distributed
+
+ align:start position:0%
+one of kind of sparse distributed
+ 
+
+ align:start position:0%
+one of kind of sparse distributed
+patterning that you have lots of cells
+
+ align:start position:0%
+patterning that you have lots of cells
+ 
+
+ align:start position:0%
+patterning that you have lots of cells
+that will that will kind of respond to
+
+ align:start position:0%
+that will that will kind of respond to
+ 
+
+ align:start position:0%
+that will that will kind of respond to
+different environments and individual
+
+ align:start position:0%
+different environments and individual
+ 
+
+ align:start position:0%
+different environments and individual
+cells don't have a unique relationship
+
+ align:start position:0%
+cells don't have a unique relationship
+ 
+
+ align:start position:0%
+cells don't have a unique relationship
+to locations it's really the pattern
+
+ align:start position:0%
+to locations it's really the pattern
+ 
+
+ align:start position:0%
+to locations it's really the pattern
+across cells that gives you a unique
+
+ align:start position:0%
+across cells that gives you a unique
+ 
+
+ align:start position:0%
+across cells that gives you a unique
+signature or code we're taking advantage
+
+ align:start position:0%
+signature or code we're taking advantage
+ 
+
+ align:start position:0%
+signature or code we're taking advantage
+of the fact that you don't necessarily
+
+ align:start position:0%
+of the fact that you don't necessarily
+ 
+
+ align:start position:0%
+of the fact that you don't necessarily
+have to place the electrodes at at the
+
+ align:start position:0%
+have to place the electrodes at at the
+ 
+
+ align:start position:0%
+have to place the electrodes at at the
+proper place in order to see these get
+
+ align:start position:0%
+proper place in order to see these get
+ 
+
+ align:start position:0%
+proper place in order to see these get
+responses in some location of space
+
+ align:start position:0%
+responses in some location of space
+ 
+
+ align:start position:0%
+responses in some location of space
+anywhere you put these electrodes in the
+
+ align:start position:0%
+anywhere you put these electrodes in the
+ 
+
+ align:start position:0%
+anywhere you put these electrodes in the
+hippocampus you're gonna get a certain
+
+ align:start position:0%
+hippocampus you're gonna get a certain
+ 
+
+ align:start position:0%
+hippocampus you're gonna get a certain
+fraction general about thirty percent of
+
+ align:start position:0%
+fraction general about thirty percent of
+ 
+
+ align:start position:0%
+fraction general about thirty percent of
+the cells will respond in a given
+
+ align:start position:0%
+the cells will respond in a given
+ 
+
+ align:start position:0%
+the cells will respond in a given
+environment and this is what those
+
+ align:start position:0%
+environment and this is what those
+ 
+
+ align:start position:0%
+environment and this is what those
+responses look like I won't go through
+
+ align:start position:0%
+responses look like I won't go through
+ 
+
+ align:start position:0%
+responses look like I won't go through
+the technical details but needless to
+
+ align:start position:0%
+the technical details but needless to
+ 
+
+ align:start position:0%
+the technical details but needless to
+say this just shows how of
+
+ align:start position:0%
+say this just shows how of
+ 
+
+ align:start position:0%
+say this just shows how of
+dance action potentials that are
+
+ align:start position:0%
+dance action potentials that are
+ 
+
+ align:start position:0%
+dance action potentials that are
+detected in here you see a voltage trace
+
+ align:start position:0%
+detected in here you see a voltage trace
+ 
+
+ align:start position:0%
+detected in here you see a voltage trace
+you pick out the amplitude of these of
+
+ align:start position:0%
+you pick out the amplitude of these of
+ 
+
+ align:start position:0%
+you pick out the amplitude of these of
+these little voltage transients
+
+ align:start position:0%
+these little voltage transients
+ 
+
+ align:start position:0%
+these little voltage transients
+generated by action potentials in the
+
+ align:start position:0%
+generated by action potentials in the
+ 
+
+ align:start position:0%
+generated by action potentials in the
+cells you plot the amplitude across
+
+ align:start position:0%
+cells you plot the amplitude across
+ 
+
+ align:start position:0%
+cells you plot the amplitude across
+these different channels in this way
+
+ align:start position:0%
+these different channels in this way
+ 
+
+ align:start position:0%
+these different channels in this way
+each point is an action potential and
+
+ align:start position:0%
+each point is an action potential and
+ 
+
+ align:start position:0%
+each point is an action potential and
+what you see is that the amplitudes will
+
+ align:start position:0%
+what you see is that the amplitudes will
+ 
+
+ align:start position:0%
+what you see is that the amplitudes will
+cluster that in a way that reflect the
+
+ align:start position:0%
+cluster that in a way that reflect the
+ 
+
+ align:start position:0%
+cluster that in a way that reflect the
+relative position or location of cells
+
+ align:start position:0%
+relative position or location of cells
+ 
+
+ align:start position:0%
+relative position or location of cells
+the sources relative to these wires with
+
+ align:start position:0%
+the sources relative to these wires with
+ 
+
+ align:start position:0%
+the sources relative to these wires with
+the bit using the basic principle that
+
+ align:start position:0%
+the bit using the basic principle that
+ 
+
+ align:start position:0%
+the bit using the basic principle that
+if you're closer to a wire the signals
+
+ align:start position:0%
+if you're closer to a wire the signals
+ 
+
+ align:start position:0%
+if you're closer to a wire the signals
+gonna get stronger so amplitude is
+
+ align:start position:0%
+gonna get stronger so amplitude is
+ 
+
+ align:start position:0%
+gonna get stronger so amplitude is
+essentially inversely related to
+
+ align:start position:0%
+essentially inversely related to
+ 
+
+ align:start position:0%
+essentially inversely related to
+distance so with this so here this is
+
+ align:start position:0%
+distance so with this so here this is
+ 
+
+ align:start position:0%
+distance so with this so here this is
+the amplitude of an action potential
+
+ align:start position:0%
+the amplitude of an action potential
+ 
+
+ align:start position:0%
+the amplitude of an action potential
+plot across two channels these points
+
+ align:start position:0%
+plot across two channels these points
+ 
+
+ align:start position:0%
+plot across two channels these points
+are large on channel one small on
+
+ align:start position:0%
+are large on channel one small on
+ 
+
+ align:start position:0%
+are large on channel one small on
+Channel two that means it's close to
+
+ align:start position:0%
+Channel two that means it's close to
+ 
+
+ align:start position:0%
+Channel two that means it's close to
+channel one far from channel two and
+
+ align:start position:0%
+channel one far from channel two and
+ 
+
+ align:start position:0%
+channel one far from channel two and
+then different cells will have different
+
+ align:start position:0%
+then different cells will have different
+ 
+
+ align:start position:0%
+then different cells will have different
+relations this will be large on channel
+
+ align:start position:0%
+relations this will be large on channel
+ 
+
+ align:start position:0%
+relations this will be large on channel
+two small on channel 1 etc so you can
+
+ align:start position:0%
+two small on channel 1 etc so you can
+ 
+
+ align:start position:0%
+two small on channel 1 etc so you can
+figure out where these cells are in
+
+ align:start position:0%
+figure out where these cells are in
+ 
+
+ align:start position:0%
+figure out where these cells are in
+space means you can record lots of pick
+
+ align:start position:0%
+space means you can record lots of pick
+ 
+
+ align:start position:0%
+space means you can record lots of pick
+out lots of cells from in this case
+
+ align:start position:0%
+out lots of cells from in this case
+ 
+
+ align:start position:0%
+out lots of cells from in this case
+maybe 12 to 18 electrodes can give you
+
+ align:start position:0%
+maybe 12 to 18 electrodes can give you
+ 
+
+ align:start position:0%
+maybe 12 to 18 electrodes can give you
+50 to 100 or more cells and then looking
+
+ align:start position:0%
+50 to 100 or more cells and then looking
+ 
+
+ align:start position:0%
+50 to 100 or more cells and then looking
+at the activity of those cells in a
+
+ align:start position:0%
+at the activity of those cells in a
+ 
+
+ align:start position:0%
+at the activity of those cells in a
+simple box this is just a little box one
+
+ align:start position:0%
+simple box this is just a little box one
+ 
+
+ align:start position:0%
+simple box this is just a little box one
+wall removed little salient cues your
+
+ align:start position:0%
+wall removed little salient cues your
+ 
+
+ align:start position:0%
+wall removed little salient cues your
+simple architectural design nice clean
+
+ align:start position:0%
+simple architectural design nice clean
+ 
+
+ align:start position:0%
+simple architectural design nice clean
+simple what you get is kind of clean
+
+ align:start position:0%
+simple what you get is kind of clean
+ 
+
+ align:start position:0%
+simple what you get is kind of clean
+simple mapping of spatial locations into
+
+ align:start position:0%
+simple mapping of spatial locations into
+ 
+
+ align:start position:0%
+simple mapping of spatial locations into
+these neuro responses so each one of
+
+ align:start position:0%
+these neuro responses so each one of
+ 
+
+ align:start position:0%
+these neuro responses so each one of
+these panels represents the activity of
+
+ align:start position:0%
+these panels represents the activity of
+ 
+
+ align:start position:0%
+these panels represents the activity of
+individual cells so this is about 80
+
+ align:start position:0%
+individual cells so this is about 80
+ 
+
+ align:start position:0%
+individual cells so this is about 80
+simultaneous they recorded cells the
+
+ align:start position:0%
+simultaneous they recorded cells the
+ 
+
+ align:start position:0%
+simultaneous they recorded cells the
+color or the heat map indicates the the
+
+ align:start position:0%
+color or the heat map indicates the the
+ 
+
+ align:start position:0%
+color or the heat map indicates the the
+firing rate of these individual cells
+
+ align:start position:0%
+firing rate of these individual cells
+ 
+
+ align:start position:0%
+firing rate of these individual cells
+red indicates high firing rate blue
+
+ align:start position:0%
+red indicates high firing rate blue
+ 
+
+ align:start position:0%
+red indicates high firing rate blue
+indicates no firing so this is a
+
+ align:start position:0%
+indicates no firing so this is a
+ 
+
+ align:start position:0%
+indicates no firing so this is a
+top-down view of that box so this cell
+
+ align:start position:0%
+top-down view of that box so this cell
+ 
+
+ align:start position:0%
+top-down view of that box so this cell
+for instance when the animal is
+
+ align:start position:0%
+for instance when the animal is
+ 
+
+ align:start position:0%
+for instance when the animal is
+wandering around in the box the cell is
+
+ align:start position:0%
+wandering around in the box the cell is
+ 
+
+ align:start position:0%
+wandering around in the box the cell is
+silent and all the blue areas and what
+
+ align:start position:0%
+silent and all the blue areas and what
+ 
+
+ align:start position:0%
+silent and all the blue areas and what
+goes in the lower right-hand corner the
+
+ align:start position:0%
+goes in the lower right-hand corner the
+ 
+
+ align:start position:0%
+goes in the lower right-hand corner the
+cell fires vigorously so silent fires
+
+ align:start position:0%
+cell fires vigorously so silent fires
+ 
+
+ align:start position:0%
+cell fires vigorously so silent fires
+vigorously this one fires on
+
+ align:start position:0%
+vigorously this one fires on
+ 
+
+ align:start position:0%
+vigorously this one fires on
+left-hand wall this one also fires in
+
+ align:start position:0%
+left-hand wall this one also fires in
+ 
+
+ align:start position:0%
+left-hand wall this one also fires in
+the lower right hand side so again this
+
+ align:start position:0%
+the lower right hand side so again this
+ 
+
+ align:start position:0%
+the lower right hand side so again this
+sort of points out this the
+
+ align:start position:0%
+sort of points out this the
+ 
+
+ align:start position:0%
+sort of points out this the
+combinatorial nature of this spatial
+
+ align:start position:0%
+combinatorial nature of this spatial
+ 
+
+ align:start position:0%
+combinatorial nature of this spatial
+representation that is that if the
+
+ align:start position:0%
+representation that is that if the
+ 
+
+ align:start position:0%
+representation that is that if the
+animals in the lower right hand corner
+
+ align:start position:0%
+animals in the lower right hand corner
+ 
+
+ align:start position:0%
+animals in the lower right hand corner
+of this particular box you'll see will
+
+ align:start position:0%
+of this particular box you'll see will
+ 
+
+ align:start position:0%
+of this particular box you'll see will
+get these two cells to fire if I take
+
+ align:start position:0%
+get these two cells to fire if I take
+ 
+
+ align:start position:0%
+get these two cells to fire if I take
+the animal I put it into a different box
+
+ align:start position:0%
+the animal I put it into a different box
+ 
+
+ align:start position:0%
+the animal I put it into a different box
+all of these responses will be scrambled
+
+ align:start position:0%
+all of these responses will be scrambled
+ 
+
+ align:start position:0%
+all of these responses will be scrambled
+up there's nothing that says this cell
+
+ align:start position:0%
+up there's nothing that says this cell
+ 
+
+ align:start position:0%
+up there's nothing that says this cell
+will fire in the lower right hand corner
+
+ align:start position:0%
+will fire in the lower right hand corner
+ 
+
+ align:start position:0%
+will fire in the lower right hand corner
+of another box and certainly even if it
+
+ align:start position:0%
+of another box and certainly even if it
+ 
+
+ align:start position:0%
+of another box and certainly even if it
+does fire in the lower right hand corner
+
+ align:start position:0%
+does fire in the lower right hand corner
+ 
+
+ align:start position:0%
+does fire in the lower right hand corner
+this other cell isn't going to fire
+
+ align:start position:0%
+this other cell isn't going to fire
+ 
+
+ align:start position:0%
+this other cell isn't going to fire
+along with it and at any given location
+
+ align:start position:0%
+along with it and at any given location
+ 
+
+ align:start position:0%
+along with it and at any given location
+they're roughly 1 to 5 percent of the
+
+ align:start position:0%
+they're roughly 1 to 5 percent of the
+ 
+
+ align:start position:0%
+they're roughly 1 to 5 percent of the
+cells that are firing so at any given
+
+ align:start position:0%
+cells that are firing so at any given
+ 
+
+ align:start position:0%
+cells that are firing so at any given
+location they're about maybe 5,000 cells
+
+ align:start position:0%
+location they're about maybe 5,000 cells
+ 
+
+ align:start position:0%
+location they're about maybe 5,000 cells
+in the hippocampus that are active so
+
+ align:start position:0%
+in the hippocampus that are active so
+ 
+
+ align:start position:0%
+in the hippocampus that are active so
+the location the unique location and
+
+ align:start position:0%
+the location the unique location and
+ 
+
+ align:start position:0%
+the location the unique location and
+unique contexts and environments can be
+
+ align:start position:0%
+unique contexts and environments can be
+ 
+
+ align:start position:0%
+unique contexts and environments can be
+conveyed across a pattern of a unique
+
+ align:start position:0%
+conveyed across a pattern of a unique
+ 
+
+ align:start position:0%
+conveyed across a pattern of a unique
+pattern of about 5,000 cells out of 100
+
+ align:start position:0%
+pattern of about 5,000 cells out of 100
+ 
+
+ align:start position:0%
+pattern of about 5,000 cells out of 100
+or 200 thousand cells so there's large
+
+ align:start position:0%
+or 200 thousand cells so there's large
+ 
+
+ align:start position:0%
+or 200 thousand cells so there's large
+combinatorial space and which one can
+
+ align:start position:0%
+combinatorial space and which one can
+ 
+
+ align:start position:0%
+combinatorial space and which one can
+represent uniquely unique locations or
+
+ align:start position:0%
+represent uniquely unique locations or
+ 
+
+ align:start position:0%
+represent uniquely unique locations or
+potentially even unique experiences
+
+ align:start position:0%
+potentially even unique experiences
+ 
+
+ align:start position:0%
+potentially even unique experiences
+within different locations you see that
+
+ align:start position:0%
+within different locations you see that
+ 
+
+ align:start position:0%
+within different locations you see that
+many cells are silent on average about
+
+ align:start position:0%
+many cells are silent on average about
+ 
+
+ align:start position:0%
+many cells are silent on average about
+30 percent of the cells respond in a
+
+ align:start position:0%
+30 percent of the cells respond in a
+ 
+
+ align:start position:0%
+30 percent of the cells respond in a
+given environment these silent cells as
+
+ align:start position:0%
+given environment these silent cells as
+ 
+
+ align:start position:0%
+given environment these silent cells as
+we'll see they can be detected when the
+
+ align:start position:0%
+we'll see they can be detected when the
+ 
+
+ align:start position:0%
+we'll see they can be detected when the
+animals are not in a running around or
+
+ align:start position:0%
+animals are not in a running around or
+ 
+
+ align:start position:0%
+animals are not in a running around or
+experiencing space but when they're
+
+ align:start position:0%
+experiencing space but when they're
+ 
+
+ align:start position:0%
+experiencing space but when they're
+asleep or these other offline states
+
+ align:start position:0%
+asleep or these other offline states
+ 
+
+ align:start position:0%
+asleep or these other offline states
+when the hippocampus is actually
+
+ align:start position:0%
+when the hippocampus is actually
+ 
+
+ align:start position:0%
+when the hippocampus is actually
+evaluating thinking about other stuff
+
+ align:start position:0%
+evaluating thinking about other stuff
+ 
+
+ align:start position:0%
+evaluating thinking about other stuff
+and we'll talk about it about that a bit
+
+ align:start position:0%
+and we'll talk about it about that a bit
+ 
+
+ align:start position:0%
+and we'll talk about it about that a bit
+and then here you can also see a small
+
+ align:start position:0%
+and then here you can also see a small
+ 
+
+ align:start position:0%
+and then here you can also see a small
+number of these cells in this case you
+
+ align:start position:0%
+number of these cells in this case you
+ 
+
+ align:start position:0%
+number of these cells in this case you
+know about five to ten percent of these
+
+ align:start position:0%
+know about five to ten percent of these
+ 
+
+ align:start position:0%
+know about five to ten percent of these
+cells seem to have elevated firing rate
+
+ align:start position:0%
+cells seem to have elevated firing rate
+ 
+
+ align:start position:0%
+cells seem to have elevated firing rate
+across the entire space is there
+
+ align:start position:0%
+across the entire space is there
+ 
+
+ align:start position:0%
+across the entire space is there
+actually a different class of neurons
+
+ align:start position:0%
+actually a different class of neurons
+ 
+
+ align:start position:0%
+actually a different class of neurons
+these are excitatory neurons these are
+
+ align:start position:0%
+these are excitatory neurons these are
+ 
+
+ align:start position:0%
+these are excitatory neurons these are
+inhibitory neurons inhibition the idea
+
+ align:start position:0%
+inhibitory neurons inhibition the idea
+ 
+
+ align:start position:0%
+inhibitory neurons inhibition the idea
+that you have circuits that that can
+
+ align:start position:0%
+that you have circuits that that can
+ 
+
+ align:start position:0%
+that you have circuits that that can
+both excite and inhibit and that this is
+
+ align:start position:0%
+both excite and inhibit and that this is
+ 
+
+ align:start position:0%
+both excite and inhibit and that this is
+used as a because as a circuit property
+
+ align:start position:0%
+used as a because as a circuit property
+ 
+
+ align:start position:0%
+used as a because as a circuit property
+to to sculpt computation is something
+
+ align:start position:0%
+to to sculpt computation is something
+ 
+
+ align:start position:0%
+to to sculpt computation is something
+that will also discuss so this balance
+
+ align:start position:0%
+that will also discuss so this balance
+ 
+
+ align:start position:0%
+that will also discuss so this balance
+between excitation as kind of a circuit
+
+ align:start position:0%
+between excitation as kind of a circuit
+ 
+
+ align:start position:0%
+between excitation as kind of a circuit
+principle that's used inhibitory cells
+
+ align:start position:0%
+principle that's used inhibitory cells
+ 
+
+ align:start position:0%
+principle that's used inhibitory cells
+I can fire all over the place they're
+
+ align:start position:0%
+I can fire all over the place they're
+ 
+
+ align:start position:0%
+I can fire all over the place they're
+not really communicating information
+
+ align:start position:0%
+not really communicating information
+ 
+
+ align:start position:0%
+not really communicating information
+they're really modulating the processing
+
+ align:start position:0%
+they're really modulating the processing
+ 
+
+ align:start position:0%
+they're really modulating the processing
+of information and another property of
+
+ align:start position:0%
+of information and another property of
+ 
+
+ align:start position:0%
+of information and another property of
+these cells that that O'Keefe termed
+
+ align:start position:0%
+these cells that that O'Keefe termed
+ 
+
+ align:start position:0%
+these cells that that O'Keefe termed
+play cells is that when animals are
+
+ align:start position:0%
+play cells is that when animals are
+ 
+
+ align:start position:0%
+play cells is that when animals are
+constrained to move along along these
+
+ align:start position:0%
+constrained to move along along these
+ 
+
+ align:start position:0%
+constrained to move along along these
+limited paths in this case this is a
+
+ align:start position:0%
+limited paths in this case this is a
+ 
+
+ align:start position:0%
+limited paths in this case this is a
+linear track as we refer to it it's like
+
+ align:start position:0%
+linear track as we refer to it it's like
+ 
+
+ align:start position:0%
+linear track as we refer to it it's like
+a little corridor animals moving down
+
+ align:start position:0%
+a little corridor animals moving down
+ 
+
+ align:start position:0%
+a little corridor animals moving down
+this corridor when they move down a
+
+ align:start position:0%
+this corridor when they move down a
+ 
+
+ align:start position:0%
+this corridor when they move down a
+corridor the cells don't only fire where
+
+ align:start position:0%
+corridor the cells don't only fire where
+ 
+
+ align:start position:0%
+corridor the cells don't only fire where
+the animal is but also in the direction
+
+ align:start position:0%
+the animal is but also in the direction
+ 
+
+ align:start position:0%
+the animal is but also in the direction
+of this going and so this is the first
+
+ align:start position:0%
+of this going and so this is the first
+ 
+
+ align:start position:0%
+of this going and so this is the first
+indication these cells are not just
+
+ align:start position:0%
+indication these cells are not just
+ 
+
+ align:start position:0%
+indication these cells are not just
+again it's not just a GPS that's nothing
+
+ align:start position:0%
+again it's not just a GPS that's nothing
+ 
+
+ align:start position:0%
+again it's not just a GPS that's nothing
+that's telling you where you are it's at
+
+ align:start position:0%
+that's telling you where you are it's at
+ 
+
+ align:start position:0%
+that's telling you where you are it's at
+least telling you where you're going
+
+ align:start position:0%
+least telling you where you're going
+ 
+
+ align:start position:0%
+least telling you where you're going
+maybe what you're doing so here if I
+
+ align:start position:0%
+maybe what you're doing so here if I
+ 
+
+ align:start position:0%
+maybe what you're doing so here if I
+look at this yellow cell I can tell that
+
+ align:start position:0%
+look at this yellow cell I can tell that
+ 
+
+ align:start position:0%
+look at this yellow cell I can tell that
+the animal is not only in this location
+
+ align:start position:0%
+the animal is not only in this location
+ 
+
+ align:start position:0%
+the animal is not only in this location
+but it's moving down this this linear
+
+ align:start position:0%
+but it's moving down this this linear
+ 
+
+ align:start position:0%
+but it's moving down this this linear
+track in this direction so there's like
+
+ align:start position:0%
+track in this direction so there's like
+ 
+
+ align:start position:0%
+track in this direction so there's like
+there's going to be a unique sequence
+
+ align:start position:0%
+there's going to be a unique sequence
+ 
+
+ align:start position:0%
+there's going to be a unique sequence
+when the animal walks along this path
+
+ align:start position:0%
+when the animal walks along this path
+ 
+
+ align:start position:0%
+when the animal walks along this path
+yellow cell red cell green cells so the
+
+ align:start position:0%
+yellow cell red cell green cells so the
+ 
+
+ align:start position:0%
+yellow cell red cell green cells so the
+different cells are color coded here so
+
+ align:start position:0%
+different cells are color coded here so
+ 
+
+ align:start position:0%
+different cells are color coded here so
+if you look over time you'll see that
+
+ align:start position:0%
+if you look over time you'll see that
+ 
+
+ align:start position:0%
+if you look over time you'll see that
+there will be a unique sequence of
+
+ align:start position:0%
+there will be a unique sequence of
+ 
+
+ align:start position:0%
+there will be a unique sequence of
+activity in the hippocampus that
+
+ align:start position:0%
+activity in the hippocampus that
+ 
+
+ align:start position:0%
+activity in the hippocampus that
+reflects the animals actual behavior
+
+ align:start position:0%
+reflects the animals actual behavior
+ 
+
+ align:start position:0%
+reflects the animals actual behavior
+experienced in that space so here this
+
+ align:start position:0%
+experienced in that space so here this
+ 
+
+ align:start position:0%
+experienced in that space so here this
+is just a little movie that shows raw
+
+ align:start position:0%
+is just a little movie that shows raw
+ 
+
+ align:start position:0%
+is just a little movie that shows raw
+this is this is what you would actually
+
+ align:start position:0%
+this is this is what you would actually
+ 
+
+ align:start position:0%
+this is this is what you would actually
+see if you're running experiment this
+
+ align:start position:0%
+see if you're running experiment this
+ 
+
+ align:start position:0%
+see if you're running experiment this
+little top-down view the green circle
+
+ align:start position:0%
+little top-down view the green circle
+ 
+
+ align:start position:0%
+little top-down view the green circle
+shows just highlights where the rat
+
+ align:start position:0%
+shows just highlights where the rat
+ 
+
+ align:start position:0%
+shows just highlights where the rat
+actually is the color coding these are
+
+ align:start position:0%
+actually is the color coding these are
+ 
+
+ align:start position:0%
+actually is the color coding these are
+the cells that we're picking up over
+
+ align:start position:0%
+the cells that we're picking up over
+ 
+
+ align:start position:0%
+the cells that we're picking up over
+here this is this is data as it would be
+
+ align:start position:0%
+here this is this is data as it would be
+ 
+
+ align:start position:0%
+here this is this is data as it would be
+coming out of the setup so you see this
+
+ align:start position:0%
+coming out of the setup so you see this
+ 
+
+ align:start position:0%
+coming out of the setup so you see this
+light blue cell fires here the dark blue
+
+ align:start position:0%
+light blue cell fires here the dark blue
+ 
+
+ align:start position:0%
+light blue cell fires here the dark blue
+cell fires here dark blue cell light
+
+ align:start position:0%
+cell fires here dark blue cell light
+ 
+
+ align:start position:0%
+cell fires here dark blue cell light
+blue cell so this is the spatial firing
+
+ align:start position:0%
+blue cell so this is the spatial firing
+ 
+
+ align:start position:0%
+blue cell so this is the spatial firing
+property place cells and now so the
+
+ align:start position:0%
+property place cells and now so the
+ 
+
+ align:start position:0%
+property place cells and now so the
+animal is stopped and one thing even
+
+ align:start position:0%
+animal is stopped and one thing even
+ 
+
+ align:start position:0%
+animal is stopped and one thing even
+notice you so lots of activity and
+
+ align:start position:0%
+notice you so lots of activity and
+ 
+
+ align:start position:0%
+notice you so lots of activity and
+animals stop there there was this big
+
+ align:start position:0%
+animals stop there there was this big
+ 
+
+ align:start position:0%
+animals stop there there was this big
+burst of activity he'll stop again a
+
+ align:start position:0%
+burst of activity he'll stop again a
+ 
+
+ align:start position:0%
+burst of activity he'll stop again a
+little bit later he's moving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he's moving if you listen carefully
+
+ align:start position:0%
+and he's moving if you listen carefully
+ 
+
+ align:start position:0%
+and he's moving if you listen carefully
+you'll hear the business background
+
+ align:start position:0%
+you'll hear the business background
+ 
+
+ align:start position:0%
+you'll hear the business background
+rhythm there's a modulation this kind of
+
+ align:start position:0%
+rhythm there's a modulation this kind of
+ 
+
+ align:start position:0%
+rhythm there's a modulation this kind of
+background modulation activity which is
+
+ align:start position:0%
+background modulation activity which is
+ 
+
+ align:start position:0%
+background modulation activity which is
+associated with locomotion so they're
+
+ align:start position:0%
+associated with locomotion so they're
+ 
+
+ align:start position:0%
+associated with locomotion so they're
+really two modes you're actively engaged
+
+ align:start position:0%
+really two modes you're actively engaged
+ 
+
+ align:start position:0%
+really two modes you're actively engaged
+in where you're taking information in
+
+ align:start position:0%
+in where you're taking information in
+ 
+
+ align:start position:0%
+in where you're taking information in
+you get this rhythm when you're
+
+ align:start position:0%
+you get this rhythm when you're
+ 
+
+ align:start position:0%
+you get this rhythm when you're
+inattentive not engaged not taking
+
+ align:start position:0%
+inattentive not engaged not taking
+ 
+
+ align:start position:0%
+inattentive not engaged not taking
+information in but internally evaluate
+
+ align:start position:0%
+information in but internally evaluate
+ 
+
+ align:start position:0%
+information in but internally evaluate
+it the rhythm goes away and it's
+
+ align:start position:0%
+it the rhythm goes away and it's
+ 
+
+ align:start position:0%
+it the rhythm goes away and it's
+replaced by these sort of bursts of
+
+ align:start position:0%
+replaced by these sort of bursts of
+ 
+
+ align:start position:0%
+replaced by these sort of bursts of
+activity and so these two modes active
+
+ align:start position:0%
+activity and so these two modes active
+ 
+
+ align:start position:0%
+activity and so these two modes active
+attentive you're processing information
+
+ align:start position:0%
+attentive you're processing information
+ 
+
+ align:start position:0%
+attentive you're processing information
+coming in inattentive you're evaluating
+
+ align:start position:0%
+coming in inattentive you're evaluating
+ 
+
+ align:start position:0%
+coming in inattentive you're evaluating
+informations it's Jordan taking you're
+
+ align:start position:0%
+informations it's Jordan taking you're
+ 
+
+ align:start position:0%
+informations it's Jordan taking you're
+thinking about stuff can be reflected in
+
+ align:start position:0%
+thinking about stuff can be reflected in
+ 
+
+ align:start position:0%
+thinking about stuff can be reflected in
+these two characteristic modes which you
+
+ align:start position:0%
+these two characteristic modes which you
+ 
+
+ align:start position:0%
+these two characteristic modes which you
+can literally you can hear I mean here
+
+ align:start position:0%
+can literally you can hear I mean here
+ 
+
+ align:start position:0%
+can literally you can hear I mean here
+the difference between the two obviously
+
+ align:start position:0%
+the difference between the two obviously
+ 
+
+ align:start position:0%
+the difference between the two obviously
+I've been listening these things for a
+
+ align:start position:0%
+I've been listening these things for a
+ 
+
+ align:start position:0%
+I've been listening these things for a
+long time so it's very easy for me to
+
+ align:start position:0%
+long time so it's very easy for me to
+ 
+
+ align:start position:0%
+long time so it's very easy for me to
+pick up you might be harder for you but
+
+ align:start position:0%
+pick up you might be harder for you but
+ 
+
+ align:start position:0%
+pick up you might be harder for you but
+you know you listen to it a little bit
+
+ align:start position:0%
+you know you listen to it a little bit
+ 
+
+ align:start position:0%
+you know you listen to it a little bit
+and it's very easy to distinguish these
+
+ align:start position:0%
+and it's very easy to distinguish these
+ 
+
+ align:start position:0%
+and it's very easy to distinguish these
+two different brain modes so this can be
+
+ align:start position:0%
+two different brain modes so this can be
+ 
+
+ align:start position:0%
+two different brain modes so this can be
+another view of that data it's the same
+
+ align:start position:0%
+another view of that data it's the same
+ 
+
+ align:start position:0%
+another view of that data it's the same
+data only now instead of showing you the
+
+ align:start position:0%
+data only now instead of showing you the
+ 
+
+ align:start position:0%
+data only now instead of showing you the
+raw data whereas the you know where is
+
+ align:start position:0%
+raw data whereas the you know where is
+ 
+
+ align:start position:0%
+raw data whereas the you know where is
+the firing and there's one thing about
+
+ align:start position:0%
+the firing and there's one thing about
+ 
+
+ align:start position:0%
+the firing and there's one thing about
+you know this correlate it that's so
+
+ align:start position:0%
+you know this correlate it that's so
+ 
+
+ align:start position:0%
+you know this correlate it that's so
+compelling I mean that was literally raw
+
+ align:start position:0%
+compelling I mean that was literally raw
+ 
+
+ align:start position:0%
+compelling I mean that was literally raw
+data that's as it was coming out there's
+
+ align:start position:0%
+data that's as it was coming out there's
+ 
+
+ align:start position:0%
+data that's as it was coming out there's
+like there's no processing at all and
+
+ align:start position:0%
+like there's no processing at all and
+ 
+
+ align:start position:0%
+like there's no processing at all and
+you could see the coil you can see the
+
+ align:start position:0%
+you could see the coil you can see the
+ 
+
+ align:start position:0%
+you could see the coil you can see the
+spatial correlate which tells you you
+
+ align:start position:0%
+spatial correlate which tells you you
+ 
+
+ align:start position:0%
+spatial correlate which tells you you
+know this is not something that requires
+
+ align:start position:0%
+know this is not something that requires
+ 
+
+ align:start position:0%
+know this is not something that requires
+you know I have to do you know sort of
+
+ align:start position:0%
+you know I have to do you know sort of
+ 
+
+ align:start position:0%
+you know I have to do you know sort of
+you know multiple multiple regressions
+
+ align:start position:0%
+you know multiple multiple regressions
+ 
+
+ align:start position:0%
+you know multiple multiple regressions
+and you know show you all of the you
+
+ align:start position:0%
+and you know show you all of the you
+ 
+
+ align:start position:0%
+and you know show you all of the you
+know the you know give you some sort of
+
+ align:start position:0%
+know the you know give you some sort of
+ 
+
+ align:start position:0%
+know the you know give you some sort of
+you know statistical confidence that
+
+ align:start position:0%
+you know statistical confidence that
+ 
+
+ align:start position:0%
+you know statistical confidence that
+this is what the peak amp is doing you
+
+ align:start position:0%
+this is what the peak amp is doing you
+ 
+
+ align:start position:0%
+this is what the peak amp is doing you
+can literally see it in individual cells
+
+ align:start position:0%
+can literally see it in individual cells
+ 
+
+ align:start position:0%
+can literally see it in individual cells
+the spatial correlate is extremely
+
+ align:start position:0%
+the spatial correlate is extremely
+ 
+
+ align:start position:0%
+the spatial correlate is extremely
+robust compelling and consistent those
+
+ align:start position:0%
+robust compelling and consistent those
+ 
+
+ align:start position:0%
+robust compelling and consistent those
+cells weren't selected if you record any
+
+ align:start position:0%
+cells weren't selected if you record any
+ 
+
+ align:start position:0%
+cells weren't selected if you record any
+of the cells in the hippocampus they're
+
+ align:start position:0%
+of the cells in the hippocampus they're
+ 
+
+ align:start position:0%
+of the cells in the hippocampus they're
+all doing that the estimate is that over
+
+ align:start position:0%
+all doing that the estimate is that over
+ 
+
+ align:start position:0%
+all doing that the estimate is that over
+95% of the cells that you can record the
+
+ align:start position:0%
+95% of the cells that you can record the
+ 
+
+ align:start position:0%
+95% of the cells that you can record the
+rodent hippocampus will have these
+
+ align:start position:0%
+rodent hippocampus will have these
+ 
+
+ align:start position:0%
+rodent hippocampus will have these
+spatial properties so it's really a
+
+ align:start position:0%
+spatial properties so it's really a
+ 
+
+ align:start position:0%
+spatial properties so it's really a
+fundamental property of of this memory
+
+ align:start position:0%
+fundamental property of of this memory
+ 
+
+ align:start position:0%
+fundamental property of of this memory
+system so it's the same data except now
+
+ align:start position:0%
+system so it's the same data except now
+ 
+
+ align:start position:0%
+system so it's the same data except now
+instead of showing the spiking we're
+
+ align:start position:0%
+instead of showing the spiking we're
+ 
+
+ align:start position:0%
+instead of showing the spiking we're
+going to use this sort of a simple
+
+ align:start position:0%
+going to use this sort of a simple
+ 
+
+ align:start position:0%
+going to use this sort of a simple
+Bayesian estimation algorithm to ask the
+
+ align:start position:0%
+Bayesian estimation algorithm to ask the
+ 
+
+ align:start position:0%
+Bayesian estimation algorithm to ask the
+question okay if if we know which
+
+ align:start position:0%
+question okay if if we know which
+ 
+
+ align:start position:0%
+question okay if if we know which
+cells are firing can we guess the
+
+ align:start position:0%
+cells are firing can we guess the
+ 
+
+ align:start position:0%
+cells are firing can we guess the
+location that the animal would likely be
+
+ align:start position:0%
+location that the animal would likely be
+ 
+
+ align:start position:0%
+location that the animal would likely be
+that is if we know the firing as a
+
+ align:start position:0%
+that is if we know the firing as a
+ 
+
+ align:start position:0%
+that is if we know the firing as a
+function of location we can use so
+
+ align:start position:0%
+function of location we can use so
+ 
+
+ align:start position:0%
+function of location we can use so
+Bayesian inference to guess that
+
+ align:start position:0%
+Bayesian inference to guess that
+ 
+
+ align:start position:0%
+Bayesian inference to guess that
+probably have a location given firing
+
+ align:start position:0%
+probably have a location given firing
+ 
+
+ align:start position:0%
+probably have a location given firing
+and that's we're gonna do here just
+
+ align:start position:0%
+and that's we're gonna do here just
+ 
+
+ align:start position:0%
+and that's we're gonna do here just
+asking if we know which cells are firing
+
+ align:start position:0%
+asking if we know which cells are firing
+ 
+
+ align:start position:0%
+asking if we know which cells are firing
+for instance if the blue cell is firing
+
+ align:start position:0%
+for instance if the blue cell is firing
+ 
+
+ align:start position:0%
+for instance if the blue cell is firing
+you would say all the cell the animals
+
+ align:start position:0%
+you would say all the cell the animals
+ 
+
+ align:start position:0%
+you would say all the cell the animals
+probably over here so recording across
+
+ align:start position:0%
+probably over here so recording across
+ 
+
+ align:start position:0%
+probably over here so recording across
+looking at pattern cross many cells and
+
+ align:start position:0%
+looking at pattern cross many cells and
+ 
+
+ align:start position:0%
+looking at pattern cross many cells and
+they were coming up every hundred
+
+ align:start position:0%
+they were coming up every hundred
+ 
+
+ align:start position:0%
+they were coming up every hundred
+milliseconds we're coming up with a
+
+ align:start position:0%
+milliseconds we're coming up with a
+ 
+
+ align:start position:0%
+milliseconds we're coming up with a
+probability that that pattern could have
+
+ align:start position:0%
+probability that that pattern could have
+ 
+
+ align:start position:0%
+probability that that pattern could have
+occurred if the animal is at any
+
+ align:start position:0%
+occurred if the animal is at any
+ 
+
+ align:start position:0%
+occurred if the animal is at any
+location on this track and the
+
+ align:start position:0%
+location on this track and the
+ 
+
+ align:start position:0%
+location on this track and the
+probability is going to be shown by
+
+ align:start position:0%
+probability is going to be shown by
+ 
+
+ align:start position:0%
+probability is going to be shown by
+triangle big triangle means high
+
+ align:start position:0%
+triangle big triangle means high
+ 
+
+ align:start position:0%
+triangle big triangle means high
+probability and what you'll see is when
+
+ align:start position:0%
+probability and what you'll see is when
+ 
+
+ align:start position:0%
+probability and what you'll see is when
+we do this estimation when the animals
+
+ align:start position:0%
+we do this estimation when the animals
+ 
+
+ align:start position:0%
+we do this estimation when the animals
+moving you see the triangle the triangle
+
+ align:start position:0%
+moving you see the triangle the triangle
+ 
+
+ align:start position:0%
+moving you see the triangle the triangle
+basically the triangles are only signai
+
+ align:start position:0%
+basically the triangles are only signai
+ 
+
+ align:start position:0%
+basically the triangles are only signai
+only you know highly probable when the
+
+ align:start position:0%
+only you know highly probable when the
+ 
+
+ align:start position:0%
+only you know highly probable when the
+animal is actually moving when the
+
+ align:start position:0%
+animal is actually moving when the
+ 
+
+ align:start position:0%
+animal is actually moving when the
+animal and only at the location that the
+
+ align:start position:0%
+animal and only at the location that the
+ 
+
+ align:start position:0%
+animal and only at the location that the
+animal is so hippocampus is centrally a
+
+ align:start position:0%
+animal is so hippocampus is centrally a
+ 
+
+ align:start position:0%
+animal is so hippocampus is centrally a
+couple representations tracking location
+
+ align:start position:0%
+couple representations tracking location
+ 
+
+ align:start position:0%
+couple representations tracking location
+the animal notice when the animal stops
+
+ align:start position:0%
+the animal notice when the animal stops
+ 
+
+ align:start position:0%
+the animal notice when the animal stops
+now if you listen so you heard the
+
+ align:start position:0%
+now if you listen so you heard the
+ 
+
+ align:start position:0%
+now if you listen so you heard the
+bursts and you look at the triangle but
+
+ align:start position:0%
+bursts and you look at the triangle but
+ 
+
+ align:start position:0%
+bursts and you look at the triangle but
+animal stops triangle no longer
+
+ align:start position:0%
+animal stops triangle no longer
+ 
+
+ align:start position:0%
+animal stops triangle no longer
+corresponds where the animal is in fact
+
+ align:start position:0%
+corresponds where the animal is in fact
+ 
+
+ align:start position:0%
+corresponds where the animal is in fact
+you can get the burst you see the
+
+ align:start position:0%
+you can get the burst you see the
+ 
+
+ align:start position:0%
+you can get the burst you see the
+triangle jumping around the track so
+
+ align:start position:0%
+triangle jumping around the track so
+ 
+
+ align:start position:0%
+triangle jumping around the track so
+again to these two modes and the
+
+ align:start position:0%
+again to these two modes and the
+ 
+
+ align:start position:0%
+again to these two modes and the
+representations have these two
+
+ align:start position:0%
+representations have these two
+ 
+
+ align:start position:0%
+representations have these two
+properties moving oscillation track
+
+ align:start position:0%
+properties moving oscillation track
+ 
+
+ align:start position:0%
+properties moving oscillation track
+current location stopping oscillation
+
+ align:start position:0%
+current location stopping oscillation
+ 
+
+ align:start position:0%
+current location stopping oscillation
+goes away representation now it jumps
+
+ align:start position:0%
+goes away representation now it jumps
+ 
+
+ align:start position:0%
+goes away representation now it jumps
+across the track and interestingly these
+
+ align:start position:0%
+across the track and interestingly these
+ 
+
+ align:start position:0%
+across the track and interestingly these
+little bursts like that also occur not
+
+ align:start position:0%
+little bursts like that also occur not
+ 
+
+ align:start position:0%
+little bursts like that also occur not
+just when the animal stops briefly but
+
+ align:start position:0%
+just when the animal stops briefly but
+ 
+
+ align:start position:0%
+just when the animal stops briefly but
+when it actually goes to sleep so here
+
+ align:start position:0%
+when it actually goes to sleep so here
+ 
+
+ align:start position:0%
+when it actually goes to sleep so here
+in the inset this is the animal now it's
+
+ align:start position:0%
+in the inset this is the animal now it's
+ 
+
+ align:start position:0%
+in the inset this is the animal now it's
+been taken off the track altogether it's
+
+ align:start position:0%
+been taken off the track altogether it's
+ 
+
+ align:start position:0%
+been taken off the track altogether it's
+just sitting in a little box somewhere
+
+ align:start position:0%
+just sitting in a little box somewhere
+ 
+
+ align:start position:0%
+just sitting in a little box somewhere
+else it's curled up and it's asleep you
+
+ align:start position:0%
+else it's curled up and it's asleep you
+ 
+
+ align:start position:0%
+else it's curled up and it's asleep you
+get these same bursts and when you
+
+ align:start position:0%
+get these same bursts and when you
+ 
+
+ align:start position:0%
+get these same bursts and when you
+decode activity you find you can decode
+
+ align:start position:0%
+decode activity you find you can decode
+ 
+
+ align:start position:0%
+decode activity you find you can decode
+the position on the track and if you
+
+ align:start position:0%
+the position on the track and if you
+ 
+
+ align:start position:0%
+the position on the track and if you
+look carefully you see that the position
+
+ align:start position:0%
+look carefully you see that the position
+ 
+
+ align:start position:0%
+look carefully you see that the position
+actually follows a sequence of
+
+ align:start position:0%
+actually follows a sequence of
+ 
+
+ align:start position:0%
+actually follows a sequence of
+trajectory along the track and and we'll
+
+ align:start position:0%
+trajectory along the track and and we'll
+ 
+
+ align:start position:0%
+trajectory along the track and and we'll
+go into that a little bit
+
+ align:start position:0%
+go into that a little bit
+ 
+
+ align:start position:0%
+go into that a little bit
+detail so you think of there being these
+
+ align:start position:0%
+detail so you think of there being these
+ 
+
+ align:start position:0%
+detail so you think of there being these
+two states the offline and the online in
+
+ align:start position:0%
+two states the offline and the online in
+ 
+
+ align:start position:0%
+two states the offline and the online in
+the online with animals moving the
+
+ align:start position:0%
+the online with animals moving the
+ 
+
+ align:start position:0%
+the online with animals moving the
+characteristic mode of active activity
+
+ align:start position:0%
+characteristic mode of active activity
+ 
+
+ align:start position:0%
+characteristic mode of active activity
+in the hippocampus there's an
+
+ align:start position:0%
+in the hippocampus there's an
+ 
+
+ align:start position:0%
+in the hippocampus there's an
+oscillatory mode described is the theta
+
+ align:start position:0%
+oscillatory mode described is the theta
+ 
+
+ align:start position:0%
+oscillatory mode described is the theta
+rhythm which is this 10 Hertz
+
+ align:start position:0%
+rhythm which is this 10 Hertz
+ 
+
+ align:start position:0%
+rhythm which is this 10 Hertz
+oscillation when the animal stops and
+
+ align:start position:0%
+oscillation when the animal stops and
+ 
+
+ align:start position:0%
+oscillation when the animal stops and
+becomes quiet Numa mobile within about
+
+ align:start position:0%
+becomes quiet Numa mobile within about
+ 
+
+ align:start position:0%
+becomes quiet Numa mobile within about
+half a second oscillation goes away and
+
+ align:start position:0%
+half a second oscillation goes away and
+ 
+
+ align:start position:0%
+half a second oscillation goes away and
+is replaced by these large transient a
+
+ align:start position:0%
+is replaced by these large transient a
+ 
+
+ align:start position:0%
+is replaced by these large transient a
+periodic events these so-called sharp
+
+ align:start position:0%
+periodic events these so-called sharp
+ 
+
+ align:start position:0%
+periodic events these so-called sharp
+waves because in the the extracellular
+
+ align:start position:0%
+waves because in the the extracellular
+ 
+
+ align:start position:0%
+waves because in the the extracellular
+electrical field that you measure you
+
+ align:start position:0%
+electrical field that you measure you
+ 
+
+ align:start position:0%
+electrical field that you measure you
+see these large deflections and then if
+
+ align:start position:0%
+see these large deflections and then if
+ 
+
+ align:start position:0%
+see these large deflections and then if
+you zoom in I also show you shortly
+
+ align:start position:0%
+you zoom in I also show you shortly
+ 
+
+ align:start position:0%
+you zoom in I also show you shortly
+you can actually see these very high
+
+ align:start position:0%
+you can actually see these very high
+ 
+
+ align:start position:0%
+you can actually see these very high
+frequency oscillations about one to two
+
+ align:start position:0%
+frequency oscillations about one to two
+ 
+
+ align:start position:0%
+frequency oscillations about one to two
+hundred Hertz riding on top of that
+
+ align:start position:0%
+hundred Hertz riding on top of that
+ 
+
+ align:start position:0%
+hundred Hertz riding on top of that
+these are referred to as ripples and
+
+ align:start position:0%
+these are referred to as ripples and
+ 
+
+ align:start position:0%
+these are referred to as ripples and
+this is a term that your GU sake
+
+ align:start position:0%
+this is a term that your GU sake
+ 
+
+ align:start position:0%
+this is a term that your GU sake
+came up with he described this sharp
+
+ align:start position:0%
+came up with he described this sharp
+ 
+
+ align:start position:0%
+came up with he described this sharp
+wave ripple activity it's corresponding
+
+ align:start position:0%
+wave ripple activity it's corresponding
+ 
+
+ align:start position:0%
+wave ripple activity it's corresponding
+to this offline state quiet wakeful and
+
+ align:start position:0%
+to this offline state quiet wakeful and
+ 
+
+ align:start position:0%
+to this offline state quiet wakeful and
+some sleep states so the first thing is
+
+ align:start position:0%
+some sleep states so the first thing is
+ 
+
+ align:start position:0%
+some sleep states so the first thing is
+just is to look at this oscillatory
+
+ align:start position:0%
+just is to look at this oscillatory
+ 
+
+ align:start position:0%
+just is to look at this oscillatory
+state so in the animals actually moving
+
+ align:start position:0%
+state so in the animals actually moving
+ 
+
+ align:start position:0%
+state so in the animals actually moving
+and I've already shown you the spatial
+
+ align:start position:0%
+and I've already shown you the spatial
+ 
+
+ align:start position:0%
+and I've already shown you the spatial
+Coral at these play cells but there's
+
+ align:start position:0%
+Coral at these play cells but there's
+ 
+
+ align:start position:0%
+Coral at these play cells but there's
+another property of these cells that
+
+ align:start position:0%
+another property of these cells that
+ 
+
+ align:start position:0%
+another property of these cells that
+O'Keefe also discovered but this was in
+
+ align:start position:0%
+O'Keefe also discovered but this was in
+ 
+
+ align:start position:0%
+O'Keefe also discovered but this was in
+early 1990s around 1991 and that is he
+
+ align:start position:0%
+early 1990s around 1991 and that is he
+ 
+
+ align:start position:0%
+early 1990s around 1991 and that is he
+noted if you actually look at the
+
+ align:start position:0%
+noted if you actually look at the
+ 
+
+ align:start position:0%
+noted if you actually look at the
+discharge of single spikes with respect
+
+ align:start position:0%
+discharge of single spikes with respect
+ 
+
+ align:start position:0%
+discharge of single spikes with respect
+to this oscillation first of all the
+
+ align:start position:0%
+to this oscillation first of all the
+ 
+
+ align:start position:0%
+to this oscillation first of all the
+spikes are actually phase locked and
+
+ align:start position:0%
+spikes are actually phase locked and
+ 
+
+ align:start position:0%
+spikes are actually phase locked and
+there was here spikes fire when the
+
+ align:start position:0%
+there was here spikes fire when the
+ 
+
+ align:start position:0%
+there was here spikes fire when the
+oscillation this theta rhythm is that
+
+ align:start position:0%
+oscillation this theta rhythm is that
+ 
+
+ align:start position:0%
+oscillation this theta rhythm is that
+its peak so the idea is that oscillation
+
+ align:start position:0%
+its peak so the idea is that oscillation
+ 
+
+ align:start position:0%
+its peak so the idea is that oscillation
+really reflects time varying
+
+ align:start position:0%
+really reflects time varying
+ 
+
+ align:start position:0%
+really reflects time varying
+excitability sometimes where the cells
+
+ align:start position:0%
+excitability sometimes where the cells
+ 
+
+ align:start position:0%
+excitability sometimes where the cells
+likely to fire other times when it's not
+
+ align:start position:0%
+likely to fire other times when it's not
+ 
+
+ align:start position:0%
+likely to fire other times when it's not
+and you can think of this oscillation in
+
+ align:start position:0%
+and you can think of this oscillation in
+ 
+
+ align:start position:0%
+and you can think of this oscillation in
+excitability as being an oscillation in
+
+ align:start position:0%
+excitability as being an oscillation in
+ 
+
+ align:start position:0%
+excitability as being an oscillation in
+relative excitability or inhibition so
+
+ align:start position:0%
+relative excitability or inhibition so
+ 
+
+ align:start position:0%
+relative excitability or inhibition so
+inhibition elevation is high it's low
+
+ align:start position:0%
+inhibition elevation is high it's low
+ 
+
+ align:start position:0%
+inhibition elevation is high it's low
+it's high is low when the inhibition is
+
+ align:start position:0%
+it's high is low when the inhibition is
+ 
+
+ align:start position:0%
+it's high is low when the inhibition is
+low cell fires when it's high cell
+
+ align:start position:0%
+low cell fires when it's high cell
+ 
+
+ align:start position:0%
+low cell fires when it's high cell
+doesn't fire so this is modulation
+
+ align:start position:0%
+doesn't fire so this is modulation
+ 
+
+ align:start position:0%
+doesn't fire so this is modulation
+excitability you see this here but he
+
+ align:start position:0%
+excitability you see this here but he
+ 
+
+ align:start position:0%
+excitability you see this here but he
+noted another thing
+
+ align:start position:0%
+noted another thing
+ 
+
+ align:start position:0%
+noted another thing
+that is if you look at the precise phase
+
+ align:start position:0%
+that is if you look at the precise phase
+ 
+
+ align:start position:0%
+that is if you look at the precise phase
+so here yes cells tend to fire kind of
+
+ align:start position:0%
+so here yes cells tend to fire kind of
+ 
+
+ align:start position:0%
+so here yes cells tend to fire kind of
+at the peak but here this is now over
+
+ align:start position:0%
+at the peak but here this is now over
+ 
+
+ align:start position:0%
+at the peak but here this is now over
+time but animal moving at constant
+
+ align:start position:0%
+time but animal moving at constant
+ 
+
+ align:start position:0%
+time but animal moving at constant
+velocity space and time are
+
+ align:start position:0%
+velocity space and time are
+ 
+
+ align:start position:0%
+velocity space and time are
+interchangeable so as an animal is
+
+ align:start position:0%
+interchangeable so as an animal is
+ 
+
+ align:start position:0%
+interchangeable so as an animal is
+moving through its place field the
+
+ align:start position:0%
+moving through its place field the
+ 
+
+ align:start position:0%
+moving through its place field the
+spikes start to fire earlier and earlier
+
+ align:start position:0%
+spikes start to fire earlier and earlier
+ 
+
+ align:start position:0%
+spikes start to fire earlier and earlier
+that is there's a phase code spatial
+
+ align:start position:0%
+that is there's a phase code spatial
+ 
+
+ align:start position:0%
+that is there's a phase code spatial
+location so you can tell based upon the
+
+ align:start position:0%
+location so you can tell based upon the
+ 
+
+ align:start position:0%
+location so you can tell based upon the
+relative phase whether the animal is
+
+ align:start position:0%
+relative phase whether the animal is
+ 
+
+ align:start position:0%
+relative phase whether the animal is
+just entering the field spikes fire late
+
+ align:start position:0%
+just entering the field spikes fire late
+ 
+
+ align:start position:0%
+just entering the field spikes fire late
+here close to the peak versus further
+
+ align:start position:0%
+here close to the peak versus further
+ 
+
+ align:start position:0%
+here close to the peak versus further
+into the field where they fire a little
+
+ align:start position:0%
+into the field where they fire a little
+ 
+
+ align:start position:0%
+into the field where they fire a little
+bit earlier there's a relationship
+
+ align:start position:0%
+bit earlier there's a relationship
+ 
+
+ align:start position:0%
+bit earlier there's a relationship
+between distance into the field and
+
+ align:start position:0%
+between distance into the field and
+ 
+
+ align:start position:0%
+between distance into the field and
+relative phase what he termed phase
+
+ align:start position:0%
+relative phase what he termed phase
+ 
+
+ align:start position:0%
+relative phase what he termed phase
+procession and this is a representation
+
+ align:start position:0%
+procession and this is a representation
+ 
+
+ align:start position:0%
+procession and this is a representation
+of that this is an actual data this is
+
+ align:start position:0%
+of that this is an actual data this is
+ 
+
+ align:start position:0%
+of that this is an actual data this is
+just a cartoon that illustrates the
+
+ align:start position:0%
+just a cartoon that illustrates the
+ 
+
+ align:start position:0%
+just a cartoon that illustrates the
+basic principle this is the idea that if
+
+ align:start position:0%
+basic principle this is the idea that if
+ 
+
+ align:start position:0%
+basic principle this is the idea that if
+I have a place cell if I look at the
+
+ align:start position:0%
+I have a place cell if I look at the
+ 
+
+ align:start position:0%
+I have a place cell if I look at the
+marginal distribution as a function of
+
+ align:start position:0%
+marginal distribution as a function of
+ 
+
+ align:start position:0%
+marginal distribution as a function of
+location this would be the place field
+
+ align:start position:0%
+location this would be the place field
+ 
+
+ align:start position:0%
+location this would be the place field
+otherwise it just collapse all this this
+
+ align:start position:0%
+otherwise it just collapse all this this
+ 
+
+ align:start position:0%
+otherwise it just collapse all this this
+is the spiking now as a function of
+
+ align:start position:0%
+is the spiking now as a function of
+ 
+
+ align:start position:0%
+is the spiking now as a function of
+position and phase if I just look
+
+ align:start position:0%
+position and phase if I just look
+ 
+
+ align:start position:0%
+position and phase if I just look
+expecting as a function of position
+
+ align:start position:0%
+expecting as a function of position
+ 
+
+ align:start position:0%
+expecting as a function of position
+that's just the density of firing what I
+
+ align:start position:0%
+that's just the density of firing what I
+ 
+
+ align:start position:0%
+that's just the density of firing what I
+would get is a place field not many
+
+ align:start position:0%
+would get is a place field not many
+ 
+
+ align:start position:0%
+would get is a place field not many
+spikes here is the animal as the animal
+
+ align:start position:0%
+spikes here is the animal as the animal
+ 
+
+ align:start position:0%
+spikes here is the animal as the animal
+enters the field lots of spikes here as
+
+ align:start position:0%
+enters the field lots of spikes here as
+ 
+
+ align:start position:0%
+enters the field lots of spikes here as
+you get into this would be the classic
+
+ align:start position:0%
+you get into this would be the classic
+ 
+
+ align:start position:0%
+you get into this would be the classic
+spatial receptive field but now if I
+
+ align:start position:0%
+spatial receptive field but now if I
+ 
+
+ align:start position:0%
+spatial receptive field but now if I
+introduce phase as well now you say oh
+
+ align:start position:0%
+introduce phase as well now you say oh
+ 
+
+ align:start position:0%
+introduce phase as well now you say oh
+wait there's a systematic relationship
+
+ align:start position:0%
+wait there's a systematic relationship
+ 
+
+ align:start position:0%
+wait there's a systematic relationship
+as well between phase and location in
+
+ align:start position:0%
+as well between phase and location in
+ 
+
+ align:start position:0%
+as well between phase and location in
+fact phase is a better predictor of
+
+ align:start position:0%
+fact phase is a better predictor of
+ 
+
+ align:start position:0%
+fact phase is a better predictor of
+relative location than firing rate I
+
+ align:start position:0%
+relative location than firing rate I
+ 
+
+ align:start position:0%
+relative location than firing rate I
+asked when did the spike occur if they
+
+ align:start position:0%
+asked when did the spike occur if they
+ 
+
+ align:start position:0%
+asked when did the spike occur if they
+occurred here late in phase then I know
+
+ align:start position:0%
+occurred here late in phase then I know
+ 
+
+ align:start position:0%
+occurred here late in phase then I know
+the animal is just entering the field
+
+ align:start position:0%
+the animal is just entering the field
+ 
+
+ align:start position:0%
+the animal is just entering the field
+that occurs early in phase I know it's
+
+ align:start position:0%
+that occurs early in phase I know it's
+ 
+
+ align:start position:0%
+that occurs early in phase I know it's
+at the end of its field and that's
+
+ align:start position:0%
+at the end of its field and that's
+ 
+
+ align:start position:0%
+at the end of its field and that's
+interesting and this is a simple model
+
+ align:start position:0%
+interesting and this is a simple model
+ 
+
+ align:start position:0%
+interesting and this is a simple model
+that says well an easy way of explaining
+
+ align:start position:0%
+that says well an easy way of explaining
+ 
+
+ align:start position:0%
+that says well an easy way of explaining
+that is if you just have this
+
+ align:start position:0%
+that is if you just have this
+ 
+
+ align:start position:0%
+that is if you just have this
+excitability model and this was one of
+
+ align:start position:0%
+excitability model and this was one of
+ 
+
+ align:start position:0%
+excitability model and this was one of
+the questions that I guess you asked
+
+ align:start position:0%
+the questions that I guess you asked
+ 
+
+ align:start position:0%
+the questions that I guess you asked
+about the sweeping inhibition so if we
+
+ align:start position:0%
+about the sweeping inhibition so if we
+ 
+
+ align:start position:0%
+about the sweeping inhibition so if we
+just imagine that you have an input
+
+ align:start position:0%
+just imagine that you have an input
+ 
+
+ align:start position:0%
+just imagine that you have an input
+excitatory input shown in blue and then
+
+ align:start position:0%
+excitatory input shown in blue and then
+ 
+
+ align:start position:0%
+excitatory input shown in blue and then
+inhibitory input shown in red where the
+
+ align:start position:0%
+inhibitory input shown in red where the
+ 
+
+ align:start position:0%
+inhibitory input shown in red where the
+inhibition is oscillating and you you
+
+ align:start position:0%
+inhibition is oscillating and you you
+ 
+
+ align:start position:0%
+inhibition is oscillating and you you
+apply a very simple biophysical model
+
+ align:start position:0%
+apply a very simple biophysical model
+ 
+
+ align:start position:0%
+apply a very simple biophysical model
+that says a spike action potential is
+
+ align:start position:0%
+that says a spike action potential is
+ 
+
+ align:start position:0%
+that says a spike action potential is
+going to occur when excitation and blue
+
+ align:start position:0%
+going to occur when excitation and blue
+ 
+
+ align:start position:0%
+going to occur when excitation and blue
+exceeds inhibition and read more
+
+ align:start position:0%
+exceeds inhibition and read more
+ 
+
+ align:start position:0%
+exceeds inhibition and read more
+excitation and emission to get a spike
+
+ align:start position:0%
+excitation and emission to get a spike
+ 
+
+ align:start position:0%
+excitation and emission to get a spike
+so here as in this oscillation anywhere
+
+ align:start position:0%
+so here as in this oscillation anywhere
+ 
+
+ align:start position:0%
+so here as in this oscillation anywhere
+the red trace is higher than the blue
+
+ align:start position:0%
+the red trace is higher than the blue
+ 
+
+ align:start position:0%
+the red trace is higher than the blue
+trace no spiking so in this case when
+
+ align:start position:0%
+trace no spiking so in this case when
+ 
+
+ align:start position:0%
+trace no spiking so in this case when
+excitation is low you have to wait until
+
+ align:start position:0%
+excitation is low you have to wait until
+ 
+
+ align:start position:0%
+excitation is low you have to wait until
+inhibition drops all the way to here to
+
+ align:start position:0%
+inhibition drops all the way to here to
+ 
+
+ align:start position:0%
+inhibition drops all the way to here to
+get a spike this is late phase so we get
+
+ align:start position:0%
+get a spike this is late phase so we get
+ 
+
+ align:start position:0%
+get a spike this is late phase so we get
+citation means you have to wait until
+
+ align:start position:0%
+citation means you have to wait until
+ 
+
+ align:start position:0%
+citation means you have to wait until
+inhibition is low so this is a sweeping
+
+ align:start position:0%
+inhibition is low so this is a sweeping
+ 
+
+ align:start position:0%
+inhibition is low so this is a sweeping
+inhibition you have to wait till it's
+
+ align:start position:0%
+inhibition you have to wait till it's
+ 
+
+ align:start position:0%
+inhibition you have to wait till it's
+low when excitation is strong I don't
+
+ align:start position:0%
+low when excitation is strong I don't
+ 
+
+ align:start position:0%
+low when excitation is strong I don't
+have to wait so long
+
+ align:start position:0%
+have to wait so long
+ 
+
+ align:start position:0%
+have to wait so long
+you can fire earlier so the principle
+
+ align:start position:0%
+you can fire earlier so the principle
+ 
+
+ align:start position:0%
+you can fire earlier so the principle
+here is that there's a relationship
+
+ align:start position:0%
+here is that there's a relationship
+ 
+
+ align:start position:0%
+here is that there's a relationship
+between magnitude and latency stronger
+
+ align:start position:0%
+between magnitude and latency stronger
+ 
+
+ align:start position:0%
+between magnitude and latency stronger
+means earlier that's the biophysical
+
+ align:start position:0%
+means earlier that's the biophysical
+ 
+
+ align:start position:0%
+means earlier that's the biophysical
+principle very simple stronger earlier
+
+ align:start position:0%
+principle very simple stronger earlier
+ 
+
+ align:start position:0%
+principle very simple stronger earlier
+weaker later that will give you this
+
+ align:start position:0%
+weaker later that will give you this
+ 
+
+ align:start position:0%
+weaker later that will give you this
+phase procession property phase
+
+ align:start position:0%
+phase procession property phase
+ 
+
+ align:start position:0%
+phase procession property phase
+procession you might think of as this
+
+ align:start position:0%
+procession you might think of as this
+ 
+
+ align:start position:0%
+procession you might think of as this
+biophysical curiosity but when you think
+
+ align:start position:0%
+biophysical curiosity but when you think
+ 
+
+ align:start position:0%
+biophysical curiosity but when you think
+about how that would apply when you have
+
+ align:start position:0%
+about how that would apply when you have
+ 
+
+ align:start position:0%
+about how that would apply when you have
+more than one place cell in fact I have
+
+ align:start position:0%
+more than one place cell in fact I have
+ 
+
+ align:start position:0%
+more than one place cell in fact I have
+two to play cells here one in blue one
+
+ align:start position:0%
+two to play cells here one in blue one
+ 
+
+ align:start position:0%
+two to play cells here one in blue one
+here in purple where play cell one is to
+
+ align:start position:0%
+here in purple where play cell one is to
+ 
+
+ align:start position:0%
+here in purple where play cell one is to
+the left of play cell two
+
+ align:start position:0%
+the left of play cell two
+ 
+
+ align:start position:0%
+the left of play cell two
+so as the animals going through here
+
+ align:start position:0%
+so as the animals going through here
+ 
+
+ align:start position:0%
+so as the animals going through here
+first the blue cell will fire and then
+
+ align:start position:0%
+first the blue cell will fire and then
+ 
+
+ align:start position:0%
+first the blue cell will fire and then
+the purple cell will fire and if you
+
+ align:start position:0%
+the purple cell will fire and if you
+ 
+
+ align:start position:0%
+the purple cell will fire and if you
+look at the excitement sort of the
+
+ align:start position:0%
+look at the excitement sort of the
+ 
+
+ align:start position:0%
+look at the excitement sort of the
+excitatory Drive shown here is a ramp in
+
+ align:start position:0%
+excitatory Drive shown here is a ramp in
+ 
+
+ align:start position:0%
+excitatory Drive shown here is a ramp in
+blue ramp and purple and now you ask
+
+ align:start position:0%
+blue ramp and purple and now you ask
+ 
+
+ align:start position:0%
+blue ramp and purple and now you ask
+when is the blue cell going to fire and
+
+ align:start position:0%
+when is the blue cell going to fire and
+ 
+
+ align:start position:0%
+when is the blue cell going to fire and
+the purple slug on a fire during each
+
+ align:start position:0%
+the purple slug on a fire during each
+ 
+
+ align:start position:0%
+the purple slug on a fire during each
+one of these oscillatory cycles and the
+
+ align:start position:0%
+one of these oscillatory cycles and the
+ 
+
+ align:start position:0%
+one of these oscillatory cycles and the
+answer will be well because the blue the
+
+ align:start position:0%
+answer will be well because the blue the
+ 
+
+ align:start position:0%
+answer will be well because the blue the
+excitatory drives the blue cell is
+
+ align:start position:0%
+excitatory drives the blue cell is
+ 
+
+ align:start position:0%
+excitatory drives the blue cell is
+higher than the purple cell blue is
+
+ align:start position:0%
+higher than the purple cell blue is
+ 
+
+ align:start position:0%
+higher than the purple cell blue is
+always going to fire before purple in
+
+ align:start position:0%
+always going to fire before purple in
+ 
+
+ align:start position:0%
+always going to fire before purple in
+fact in each and every cycle it will be
+
+ align:start position:0%
+fact in each and every cycle it will be
+ 
+
+ align:start position:0%
+fact in each and every cycle it will be
+blue purple blue purple blue purple so
+
+ align:start position:0%
+blue purple blue purple blue purple so
+ 
+
+ align:start position:0%
+blue purple blue purple blue purple so
+this principle of phase procession or
+
+ align:start position:0%
+this principle of phase procession or
+ 
+
+ align:start position:0%
+this principle of phase procession or
+phase coding for single cells actually
+
+ align:start position:0%
+phase coding for single cells actually
+ 
+
+ align:start position:0%
+phase coding for single cells actually
+gives you sequential encoding across a
+
+ align:start position:0%
+gives you sequential encoding across a
+ 
+
+ align:start position:0%
+gives you sequential encoding across a
+population that you will actually on
+
+ align:start position:0%
+population that you will actually on
+ 
+
+ align:start position:0%
+population that you will actually on
+each and every cycle have a sequence the
+
+ align:start position:0%
+each and every cycle have a sequence the
+ 
+
+ align:start position:0%
+each and every cycle have a sequence the
+code in the hippocampus is not a
+
+ align:start position:0%
+code in the hippocampus is not a
+ 
+
+ align:start position:0%
+code in the hippocampus is not a
+location it's actually a sequence a
+
+ align:start position:0%
+location it's actually a sequence a
+ 
+
+ align:start position:0%
+location it's actually a sequence a
+trajectory and this is just raw data but
+
+ align:start position:0%
+trajectory and this is just raw data but
+ 
+
+ align:start position:0%
+trajectory and this is just raw data but
+I'm gonna quickly go this is just the
+
+ align:start position:0%
+I'm gonna quickly go this is just the
+ 
+
+ align:start position:0%
+I'm gonna quickly go this is just the
+spiking looks like and you can see if
+
+ align:start position:0%
+spiking looks like and you can see if
+ 
+
+ align:start position:0%
+spiking looks like and you can see if
+you look at you see these kind of spike
+
+ align:start position:0%
+you look at you see these kind of spike
+ 
+
+ align:start position:0%
+you look at you see these kind of spike
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+but the property is more clearly
+
+ align:start position:0%
+but the property is more clearly
+ 
+
+ align:start position:0%
+but the property is more clearly
+demonstrated when I do this decoding so
+
+ align:start position:0%
+demonstrated when I do this decoding so
+ 
+
+ align:start position:0%
+demonstrated when I do this decoding so
+what's your what I'm showing you here
+
+ align:start position:0%
+what's your what I'm showing you here
+ 
+
+ align:start position:0%
+what's your what I'm showing you here
+this is again raw data but now instead
+
+ align:start position:0%
+this is again raw data but now instead
+ 
+
+ align:start position:0%
+this is again raw data but now instead
+of showing you the spiking I'm showing
+
+ align:start position:0%
+of showing you the spiking I'm showing
+ 
+
+ align:start position:0%
+of showing you the spiking I'm showing
+you that the result of doing this
+
+ align:start position:0%
+you that the result of doing this
+ 
+
+ align:start position:0%
+you that the result of doing this
+decoding this Bayesian decoding where
+
+ align:start position:0%
+decoding this Bayesian decoding where
+ 
+
+ align:start position:0%
+decoding this Bayesian decoding where
+there's a probability estimate that
+
+ align:start position:0%
+there's a probability estimate that
+ 
+
+ align:start position:0%
+there's a probability estimate that
+given spiking activity in each one of us
+
+ align:start position:0%
+given spiking activity in each one of us
+ 
+
+ align:start position:0%
+given spiking activity in each one of us
+set of successive 20 millisecond windows
+
+ align:start position:0%
+set of successive 20 millisecond windows
+ 
+
+ align:start position:0%
+set of successive 20 millisecond windows
+so I'm walking along now at a fire at a
+
+ align:start position:0%
+so I'm walking along now at a fire at a
+ 
+
+ align:start position:0%
+so I'm walking along now at a fire at a
+finer temporal resolution every 20
+
+ align:start position:0%
+finer temporal resolution every 20
+ 
+
+ align:start position:0%
+finer temporal resolution every 20
+milliseconds I'm doing the same decoding
+
+ align:start position:0%
+milliseconds I'm doing the same decoding
+ 
+
+ align:start position:0%
+milliseconds I'm doing the same decoding
+probability is indicated in greyscale so
+
+ align:start position:0%
+probability is indicated in greyscale so
+ 
+
+ align:start position:0%
+probability is indicated in greyscale so
+you can see here the dark areas this is
+
+ align:start position:0%
+you can see here the dark areas this is
+ 
+
+ align:start position:0%
+you can see here the dark areas this is
+like high probability that this pattern
+
+ align:start position:0%
+like high probability that this pattern
+ 
+
+ align:start position:0%
+like high probability that this pattern
+the animal would have been in this
+
+ align:start position:0%
+the animal would have been in this
+ 
+
+ align:start position:0%
+the animal would have been in this
+location or to get this pattern of
+
+ align:start position:0%
+location or to get this pattern of
+ 
+
+ align:start position:0%
+location or to get this pattern of
+activity in this 20 millisecond bin and
+
+ align:start position:0%
+activity in this 20 millisecond bin and
+ 
+
+ align:start position:0%
+activity in this 20 millisecond bin and
+what you can see here is that the
+
+ align:start position:0%
+what you can see here is that the
+ 
+
+ align:start position:0%
+what you can see here is that the
+probability these Bayesian decoded of
+
+ align:start position:0%
+probability these Bayesian decoded of
+ 
+
+ align:start position:0%
+probability these Bayesian decoded of
+probabilities form short sequences every
+
+ align:start position:0%
+probabilities form short sequences every
+ 
+
+ align:start position:0%
+probabilities form short sequences every
+single theta cycle what we've heard is
+
+ align:start position:0%
+single theta cycle what we've heard is
+ 
+
+ align:start position:0%
+single theta cycle what we've heard is
+theta sequences and the theta sequences
+
+ align:start position:0%
+theta sequences and the theta sequences
+ 
+
+ align:start position:0%
+theta sequences and the theta sequences
+actually move from just behind the
+
+ align:start position:0%
+actually move from just behind the
+ 
+
+ align:start position:0%
+actually move from just behind the
+animal dotted line is where the animal
+
+ align:start position:0%
+animal dotted line is where the animal
+ 
+
+ align:start position:0%
+animal dotted line is where the animal
+actually is estimate goes and just
+
+ align:start position:0%
+actually is estimate goes and just
+ 
+
+ align:start position:0%
+actually is estimate goes and just
+behind the animal just in front of the
+
+ align:start position:0%
+behind the animal just in front of the
+ 
+
+ align:start position:0%
+behind the animal just in front of the
+animal so 10 times a second hippocampus
+
+ align:start position:0%
+animal so 10 times a second hippocampus
+ 
+
+ align:start position:0%
+animal so 10 times a second hippocampus
+is actually expressing a representation
+
+ align:start position:0%
+is actually expressing a representation
+ 
+
+ align:start position:0%
+is actually expressing a representation
+of spatial sequence that goes from
+
+ align:start position:0%
+of spatial sequence that goes from
+ 
+
+ align:start position:0%
+of spatial sequence that goes from
+behind to in front the animal you can
+
+ align:start position:0%
+behind to in front the animal you can
+ 
+
+ align:start position:0%
+behind to in front the animal you can
+think of behind in the front as also
+
+ align:start position:0%
+think of behind in the front as also
+ 
+
+ align:start position:0%
+think of behind in the front as also
+reflecting like recent past in near
+
+ align:start position:0%
+reflecting like recent past in near
+ 
+
+ align:start position:0%
+reflecting like recent past in near
+future so there is this relative
+
+ align:start position:0%
+future so there is this relative
+ 
+
+ align:start position:0%
+future so there is this relative
+predictive differentiation of response
+
+ align:start position:0%
+predictive differentiation of response
+ 
+
+ align:start position:0%
+predictive differentiation of response
+as a function of oscillatory phase so if
+
+ align:start position:0%
+as a function of oscillatory phase so if
+ 
+
+ align:start position:0%
+as a function of oscillatory phase so if
+I want to look at see where did I just
+
+ align:start position:0%
+I want to look at see where did I just
+ 
+
+ align:start position:0%
+I want to look at see where did I just
+come from I just have to look at
+
+ align:start position:0%
+come from I just have to look at
+ 
+
+ align:start position:0%
+come from I just have to look at
+activity here at this slightly earlier
+
+ align:start position:0%
+activity here at this slightly earlier
+ 
+
+ align:start position:0%
+activity here at this slightly earlier
+phase if I want to ask the question gee
+
+ align:start position:0%
+phase if I want to ask the question gee
+ 
+
+ align:start position:0%
+phase if I want to ask the question gee
+where am I likely to go to I simply have
+
+ align:start position:0%
+where am I likely to go to I simply have
+ 
+
+ align:start position:0%
+where am I likely to go to I simply have
+to shift the phase the channel that I
+
+ align:start position:0%
+to shift the phase the channel that I
+ 
+
+ align:start position:0%
+to shift the phase the channel that I
+look at here and I can see where the
+
+ align:start position:0%
+look at here and I can see where the
+ 
+
+ align:start position:0%
+look at here and I can see where the
+likely future location is so you can
+
+ align:start position:0%
+likely future location is so you can
+ 
+
+ align:start position:0%
+likely future location is so you can
+think that there is actually a code not
+
+ align:start position:0%
+think that there is actually a code not
+ 
+
+ align:start position:0%
+think that there is actually a code not
+just a location but of the relative
+
+ align:start position:0%
+just a location but of the relative
+ 
+
+ align:start position:0%
+just a location but of the relative
+causal relationship between locations
+
+ align:start position:0%
+causal relationship between locations
+ 
+
+ align:start position:0%
+causal relationship between locations
+mapped into phase and we'll see that we
+
+ align:start position:0%
+mapped into phase and we'll see that we
+ 
+
+ align:start position:0%
+mapped into phase and we'll see that we
+can experimentally test this idea that
+
+ align:start position:0%
+can experimentally test this idea that
+ 
+
+ align:start position:0%
+can experimentally test this idea that
+that's that's just not a you know like
+
+ align:start position:0%
+that's that's just not a you know like
+ 
+
+ align:start position:0%
+that's that's just not a you know like
+an artifact of our decoding but the
+
+ align:start position:0%
+an artifact of our decoding but the
+ 
+
+ align:start position:0%
+an artifact of our decoding but the
+animals are actually using information
+
+ align:start position:0%
+animals are actually using information
+ 
+
+ align:start position:0%
+animals are actually using information
+at these different phases
+
+ align:start position:0%
+at these different phases
+ 
+
+ align:start position:0%
+at these different phases
+to drive spatial navigation in
+
+ align:start position:0%
+to drive spatial navigation in
+ 
+
+ align:start position:0%
+to drive spatial navigation in
+particular ways by using some of the
+
+ align:start position:0%
+particular ways by using some of the
+ 
+
+ align:start position:0%
+particular ways by using some of the
+tools for manipulating activity in a
+
+ align:start position:0%
+tools for manipulating activity in a
+ 
+
+ align:start position:0%
+tools for manipulating activity in a
+closed this so-called closed loop option
+
+ align:start position:0%
+closed this so-called closed loop option
+ 
+
+ align:start position:0%
+closed this so-called closed loop option
+X so we see we can manipulate activity
+
+ align:start position:0%
+X so we see we can manipulate activity
+ 
+
+ align:start position:0%
+X so we see we can manipulate activity
+specifically manipulate activity became
+
+ align:start position:0%
+specifically manipulate activity became
+ 
+
+ align:start position:0%
+specifically manipulate activity became
+plac tivity different phases and show
+
+ align:start position:0%
+plac tivity different phases and show
+ 
+
+ align:start position:0%
+plac tivity different phases and show
+these different phases actually carry
+
+ align:start position:0%
+these different phases actually carry
+ 
+
+ align:start position:0%
+these different phases actually carry
+different functional consequences so
+
+ align:start position:0%
+different functional consequences so
+ 
+
+ align:start position:0%
+different functional consequences so
+we've got these sequences so i've got
+
+ align:start position:0%
+we've got these sequences so i've got
+ 
+
+ align:start position:0%
+we've got these sequences so i've got
+these sequences captured during these
+
+ align:start position:0%
+these sequences captured during these
+ 
+
+ align:start position:0%
+these sequences captured during these
+oscillations are these things actually
+
+ align:start position:0%
+oscillations are these things actually
+ 
+
+ align:start position:0%
+oscillations are these things actually
+meaningful or some of the indications
+
+ align:start position:0%
+meaningful or some of the indications
+ 
+
+ align:start position:0%
+meaningful or some of the indications
+that these that the a the oscillations
+
+ align:start position:0%
+that these that the a the oscillations
+ 
+
+ align:start position:0%
+that these that the a the oscillations
+and the sequences are meaningful first
+
+ align:start position:0%
+and the sequences are meaningful first
+ 
+
+ align:start position:0%
+and the sequences are meaningful first
+come from the observation that as i as i
+
+ align:start position:0%
+come from the observation that as i as i
+ 
+
+ align:start position:0%
+come from the observation that as i as i
+mentioned actually successful using
+
+ align:start position:0%
+mentioned actually successful using
+ 
+
+ align:start position:0%
+mentioned actually successful using
+memory information that the campus
+
+ align:start position:0%
+memory information that the campus
+ 
+
+ align:start position:0%
+memory information that the campus
+requires that you actually communicate
+
+ align:start position:0%
+requires that you actually communicate
+ 
+
+ align:start position:0%
+requires that you actually communicate
+this to executive structures that can
+
+ align:start position:0%
+this to executive structures that can
+ 
+
+ align:start position:0%
+this to executive structures that can
+guide behavior make decisions that would
+
+ align:start position:0%
+guide behavior make decisions that would
+ 
+
+ align:start position:0%
+guide behavior make decisions that would
+include the prefrontal cortex portions
+
+ align:start position:0%
+include the prefrontal cortex portions
+ 
+
+ align:start position:0%
+include the prefrontal cortex portions
+of prefrontal cortex which form a part
+
+ align:start position:0%
+of prefrontal cortex which form a part
+ 
+
+ align:start position:0%
+of prefrontal cortex which form a part
+of this limbic circuit and for those the
+
+ align:start position:0%
+of this limbic circuit and for those the
+ 
+
+ align:start position:0%
+of this limbic circuit and for those the
+limbic prefrontal cortex which have
+
+ align:start position:0%
+limbic prefrontal cortex which have
+ 
+
+ align:start position:0%
+limbic prefrontal cortex which have
+direct connections from the hippocampus
+
+ align:start position:0%
+direct connections from the hippocampus
+ 
+
+ align:start position:0%
+direct connections from the hippocampus
+these structures are in the hippocampus
+
+ align:start position:0%
+these structures are in the hippocampus
+ 
+
+ align:start position:0%
+these structures are in the hippocampus
+you have deficits and spatial learning
+
+ align:start position:0%
+you have deficits and spatial learning
+ 
+
+ align:start position:0%
+you have deficits and spatial learning
+memory prefrontal cortex you sort of
+
+ align:start position:0%
+memory prefrontal cortex you sort of
+ 
+
+ align:start position:0%
+memory prefrontal cortex you sort of
+think of this as as you know sort of
+
+ align:start position:0%
+think of this as as you know sort of
+ 
+
+ align:start position:0%
+think of this as as you know sort of
+deficits and in working memory and
+
+ align:start position:0%
+deficits and in working memory and
+ 
+
+ align:start position:0%
+deficits and in working memory and
+retrieval executive control
+
+ align:start position:0%
+retrieval executive control
+ 
+
+ align:start position:0%
+retrieval executive control
+decision-making but but you can think of
+
+ align:start position:0%
+decision-making but but you can think of
+ 
+
+ align:start position:0%
+decision-making but but you can think of
+these two things is working together
+
+ align:start position:0%
+these two things is working together
+ 
+
+ align:start position:0%
+these two things is working together
+again hippocampus providing information
+
+ align:start position:0%
+again hippocampus providing information
+ 
+
+ align:start position:0%
+again hippocampus providing information
+that the prefrontal cortex can use in
+
+ align:start position:0%
+that the prefrontal cortex can use in
+ 
+
+ align:start position:0%
+that the prefrontal cortex can use in
+order to direct behavior and
+
+ align:start position:0%
+order to direct behavior and
+ 
+
+ align:start position:0%
+order to direct behavior and
+decision-making and you damage either
+
+ align:start position:0%
+decision-making and you damage either
+ 
+
+ align:start position:0%
+decision-making and you damage either
+one of these things animals rats can't
+
+ align:start position:0%
+one of these things animals rats can't
+ 
+
+ align:start position:0%
+one of these things animals rats can't
+find their way around the space you're
+
+ align:start position:0%
+find their way around the space you're
+ 
+
+ align:start position:0%
+find their way around the space you're
+damaged you either one of these in
+
+ align:start position:0%
+damaged you either one of these in
+ 
+
+ align:start position:0%
+damaged you either one of these in
+humans you're gonna get you're gonna get
+
+ align:start position:0%
+humans you're gonna get you're gonna get
+ 
+
+ align:start position:0%
+humans you're gonna get you're gonna get
+memory deficits and you know dementia is
+
+ align:start position:0%
+memory deficits and you know dementia is
+ 
+
+ align:start position:0%
+memory deficits and you know dementia is
+where you think of dementia as being you
+
+ align:start position:0%
+where you think of dementia as being you
+ 
+
+ align:start position:0%
+where you think of dementia as being you
+know problems of cognition and memory
+
+ align:start position:0%
+know problems of cognition and memory
+ 
+
+ align:start position:0%
+know problems of cognition and memory
+you can get them temporal lobe dementia
+
+ align:start position:0%
+you can get them temporal lobe dementia
+ 
+
+ align:start position:0%
+you can get them temporal lobe dementia
+as frontal lobe dementia they have you
+
+ align:start position:0%
+as frontal lobe dementia they have you
+ 
+
+ align:start position:0%
+as frontal lobe dementia they have you
+know they have they they're they're
+
+ align:start position:0%
+know they have they they're they're
+ 
+
+ align:start position:0%
+know they have they they're they're
+really very closely related and so we
+
+ align:start position:0%
+really very closely related and so we
+ 
+
+ align:start position:0%
+really very closely related and so we
+can look at a simple task this is a
+
+ align:start position:0%
+can look at a simple task this is a
+ 
+
+ align:start position:0%
+can look at a simple task this is a
+simple task testing a so called working
+
+ align:start position:0%
+simple task testing a so called working
+ 
+
+ align:start position:0%
+simple task testing a so called working
+memory just remember what did you do
+
+ align:start position:0%
+memory just remember what did you do
+ 
+
+ align:start position:0%
+memory just remember what did you do
+last in this task it's just a simple
+
+ align:start position:0%
+last in this task it's just a simple
+ 
+
+ align:start position:0%
+last in this task it's just a simple
+alternation where you turn left first
+
+ align:start position:0%
+alternation where you turn left first
+ 
+
+ align:start position:0%
+alternation where you turn left first
+time you turn left
+
+ align:start position:0%
+time you turn left
+ 
+
+ align:start position:0%
+time you turn left
+next time you go right Etha logically
+
+ align:start position:0%
+next time you go right Etha logically
+ 
+
+ align:start position:0%
+next time you go right Etha logically
+it's like look I just got food over here
+
+ align:start position:0%
+it's like look I just got food over here
+ 
+
+ align:start position:0%
+it's like look I just got food over here
+why don't I check out the other place
+
+ align:start position:0%
+why don't I check out the other place
+ 
+
+ align:start position:0%
+why don't I check out the other place
+right I'll check out places where I
+
+ align:start position:0%
+right I'll check out places where I
+ 
+
+ align:start position:0%
+right I'll check out places where I
+didn't get food this is this it's the
+
+ align:start position:0%
+didn't get food this is this it's the
+ 
+
+ align:start position:0%
+didn't get food this is this it's the
+so-called wind shift strategy I got
+
+ align:start position:0%
+so-called wind shift strategy I got
+ 
+
+ align:start position:0%
+so-called wind shift strategy I got
+something here this time and go
+
+ align:start position:0%
+something here this time and go
+ 
+
+ align:start position:0%
+something here this time and go
+someplace else as opposed to like a
+
+ align:start position:0%
+someplace else as opposed to like a
+ 
+
+ align:start position:0%
+someplace else as opposed to like a
+reference memory strategy would be where
+
+ align:start position:0%
+reference memory strategy would be where
+ 
+
+ align:start position:0%
+reference memory strategy would be where
+they for there's a winds day that's
+
+ align:start position:0%
+they for there's a winds day that's
+ 
+
+ align:start position:0%
+they for there's a winds day that's
+really a good spot you know home I love
+
+ align:start position:0%
+really a good spot you know home I love
+ 
+
+ align:start position:0%
+really a good spot you know home I love
+going home because you know I've got my
+
+ align:start position:0%
+going home because you know I've got my
+ 
+
+ align:start position:0%
+going home because you know I've got my
+MIT ve got my microwave I'm gonna stick
+
+ align:start position:0%
+MIT ve got my microwave I'm gonna stick
+ 
+
+ align:start position:0%
+MIT ve got my microwave I'm gonna stick
+with that place Wednesdays you keep
+
+ align:start position:0%
+with that place Wednesdays you keep
+ 
+
+ align:start position:0%
+with that place Wednesdays you keep
+going back to the place that you know
+
+ align:start position:0%
+going back to the place that you know
+ 
+
+ align:start position:0%
+going back to the place that you know
+that rewards you and so you can think of
+
+ align:start position:0%
+that rewards you and so you can think of
+ 
+
+ align:start position:0%
+that rewards you and so you can think of
+both again both these things have you
+
+ align:start position:0%
+both again both these things have you
+ 
+
+ align:start position:0%
+both again both these things have you
+Falacci value home is a good place
+
+ align:start position:0%
+Falacci value home is a good place
+ 
+
+ align:start position:0%
+Falacci value home is a good place
+that's reference place if you're
+
+ align:start position:0%
+that's reference place if you're
+ 
+
+ align:start position:0%
+that's reference place if you're
+foraging wind shift don't go back to the
+
+ align:start position:0%
+foraging wind shift don't go back to the
+ 
+
+ align:start position:0%
+foraging wind shift don't go back to the
+place I just glued it right and so if
+
+ align:start position:0%
+place I just glued it right and so if
+ 
+
+ align:start position:0%
+place I just glued it right and so if
+you again these two these two structures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classically you think of in the
+
+ align:start position:0%
+classically you think of in the
+ 
+
+ align:start position:0%
+classically you think of in the
+prefrontal cortex we think of working
+
+ align:start position:0%
+prefrontal cortex we think of working
+ 
+
+ align:start position:0%
+prefrontal cortex we think of working
+memory cells this is the short-term the
+
+ align:start position:0%
+memory cells this is the short-term the
+ 
+
+ align:start position:0%
+memory cells this is the short-term the
+idea of a short-term memory so
+
+ align:start position:0%
+idea of a short-term memory so
+ 
+
+ align:start position:0%
+idea of a short-term memory so
+prefrontal cortex tippet has been
+
+ align:start position:0%
+prefrontal cortex tippet has been
+ 
+
+ align:start position:0%
+prefrontal cortex tippet has been
+thought of as sub serving working memory
+
+ align:start position:0%
+thought of as sub serving working memory
+ 
+
+ align:start position:0%
+thought of as sub serving working memory
+where working memory is about holding
+
+ align:start position:0%
+where working memory is about holding
+ 
+
+ align:start position:0%
+where working memory is about holding
+information over short delays it's a
+
+ align:start position:0%
+information over short delays it's a
+ 
+
+ align:start position:0%
+information over short delays it's a
+it's a it's kind of a an overlap in
+
+ align:start position:0%
+it's a it's kind of a an overlap in
+ 
+
+ align:start position:0%
+it's a it's kind of a an overlap in
+terminology we're working memory in the
+
+ align:start position:0%
+terminology we're working memory in the
+ 
+
+ align:start position:0%
+terminology we're working memory in the
+prefrontal cortex really thinking about
+
+ align:start position:0%
+prefrontal cortex really thinking about
+ 
+
+ align:start position:0%
+prefrontal cortex really thinking about
+time working memory and hippocampus it's
+
+ align:start position:0%
+time working memory and hippocampus it's
+ 
+
+ align:start position:0%
+time working memory and hippocampus it's
+really thinking about kind of the you
+
+ align:start position:0%
+really thinking about kind of the you
+ 
+
+ align:start position:0%
+really thinking about kind of the you
+know the context in which it's used
+
+ align:start position:0%
+know the context in which it's used
+ 
+
+ align:start position:0%
+know the context in which it's used
+relative such and specific information
+
+ align:start position:0%
+relative such and specific information
+ 
+
+ align:start position:0%
+relative such and specific information
+trial specific information so I'm not
+
+ align:start position:0%
+trial specific information so I'm not
+ 
+
+ align:start position:0%
+trial specific information so I'm not
+gonna go through the details just you
+
+ align:start position:0%
+gonna go through the details just you
+ 
+
+ align:start position:0%
+gonna go through the details just you
+have these two systems and one
+
+ align:start position:0%
+have these two systems and one
+ 
+
+ align:start position:0%
+have these two systems and one
+interesting property in the if you look
+
+ align:start position:0%
+interesting property in the if you look
+ 
+
+ align:start position:0%
+interesting property in the if you look
+at these two systems simultaneously what
+
+ align:start position:0%
+at these two systems simultaneously what
+ 
+
+ align:start position:0%
+at these two systems simultaneously what
+you find is that the same idea about
+
+ align:start position:0%
+you find is that the same idea about
+ 
+
+ align:start position:0%
+you find is that the same idea about
+oscillatory phase governing the firing
+
+ align:start position:0%
+oscillatory phase governing the firing
+ 
+
+ align:start position:0%
+oscillatory phase governing the firing
+of cells in the hippocampus also applies
+
+ align:start position:0%
+of cells in the hippocampus also applies
+ 
+
+ align:start position:0%
+of cells in the hippocampus also applies
+in the prefrontal cortex that has cells
+
+ align:start position:0%
+in the prefrontal cortex that has cells
+ 
+
+ align:start position:0%
+in the prefrontal cortex that has cells
+in the prefrontal cortex like to fire at
+
+ align:start position:0%
+in the prefrontal cortex like to fire at
+ 
+
+ align:start position:0%
+in the prefrontal cortex like to fire at
+certain phase of the hippocampal theta
+
+ align:start position:0%
+certain phase of the hippocampal theta
+ 
+
+ align:start position:0%
+certain phase of the hippocampal theta
+rhythm they care about they're listening
+
+ align:start position:0%
+rhythm they care about they're listening
+ 
+
+ align:start position:0%
+rhythm they care about they're listening
+to this rhythm in the hippocampus and so
+
+ align:start position:0%
+to this rhythm in the hippocampus and so
+ 
+
+ align:start position:0%
+to this rhythm in the hippocampus and so
+we can look at a task this is basically
+
+ align:start position:0%
+we can look at a task this is basically
+ 
+
+ align:start position:0%
+we can look at a task this is basically
+the same kind of task only now there's a
+
+ align:start position:0%
+the same kind of task only now there's a
+ 
+
+ align:start position:0%
+the same kind of task only now there's a
+back-to-back teammates there's gonna be
+
+ align:start position:0%
+back-to-back teammates there's gonna be
+ 
+
+ align:start position:0%
+back-to-back teammates there's gonna be
+two tea mazes and we're just gonna do a
+
+ align:start position:0%
+two tea mazes and we're just gonna do a
+ 
+
+ align:start position:0%
+two tea mazes and we're just gonna do a
+simple variation on that well that
+
+ align:start position:0%
+simple variation on that well that
+ 
+
+ align:start position:0%
+simple variation on that well that
+working memory task
+
+ align:start position:0%
+working memory task
+ 
+
+ align:start position:0%
+working memory task
+in which animals gonna start from one of
+
+ align:start position:0%
+in which animals gonna start from one of
+ 
+
+ align:start position:0%
+in which animals gonna start from one of
+these two arms can walk down this arm
+
+ align:start position:0%
+these two arms can walk down this arm
+ 
+
+ align:start position:0%
+these two arms can walk down this arm
+and then it has to go to the arm that's
+
+ align:start position:0%
+and then it has to go to the arm that's
+ 
+
+ align:start position:0%
+and then it has to go to the arm that's
+on the same side that it started from so
+
+ align:start position:0%
+on the same side that it started from so
+ 
+
+ align:start position:0%
+on the same side that it started from so
+it has to remember where did I start
+
+ align:start position:0%
+it has to remember where did I start
+ 
+
+ align:start position:0%
+it has to remember where did I start
+from oh that's the side I have to go to
+
+ align:start position:0%
+from oh that's the side I have to go to
+ 
+
+ align:start position:0%
+from oh that's the side I have to go to
+then it's going to turn around it's
+
+ align:start position:0%
+then it's going to turn around it's
+ 
+
+ align:start position:0%
+then it's going to turn around it's
+gonna come back run down here and then
+
+ align:start position:0%
+gonna come back run down here and then
+ 
+
+ align:start position:0%
+gonna come back run down here and then
+we're gonna force it into one of these
+
+ align:start position:0%
+we're gonna force it into one of these
+ 
+
+ align:start position:0%
+we're gonna force it into one of these
+arms so there's two back to back tea
+
+ align:start position:0%
+arms so there's two back to back tea
+ 
+
+ align:start position:0%
+arms so there's two back to back tea
+mazes in this direction the animal
+
+ align:start position:0%
+mazes in this direction the animal
+ 
+
+ align:start position:0%
+mazes in this direction the animal
+chooses in this direction we choose in
+
+ align:start position:0%
+chooses in this direction we choose in
+ 
+
+ align:start position:0%
+chooses in this direction we choose in
+this direction there's a working memory
+
+ align:start position:0%
+this direction there's a working memory
+ 
+
+ align:start position:0%
+this direction there's a working memory
+demand has to remember where it came
+
+ align:start position:0%
+demand has to remember where it came
+ 
+
+ align:start position:0%
+demand has to remember where it came
+from in this direction doesn't have to
+
+ align:start position:0%
+from in this direction doesn't have to
+ 
+
+ align:start position:0%
+from in this direction doesn't have to
+remember anything doesn't make any
+
+ align:start position:0%
+remember anything doesn't make any
+ 
+
+ align:start position:0%
+remember anything doesn't make any
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+so behaviorally it's symmetric button
+
+ align:start position:0%
+so behaviorally it's symmetric button
+ 
+
+ align:start position:0%
+so behaviorally it's symmetric button
+cognitively here there's a working
+
+ align:start position:0%
+cognitively here there's a working
+ 
+
+ align:start position:0%
+cognitively here there's a working
+memory demand here it is not and then
+
+ align:start position:0%
+memory demand here it is not and then
+ 
+
+ align:start position:0%
+memory demand here it is not and then
+we're gonna look at all these things
+
+ align:start position:0%
+we're gonna look at all these things
+ 
+
+ align:start position:0%
+we're gonna look at all these things
+oscillation spiking and look the
+
+ align:start position:0%
+oscillation spiking and look the
+ 
+
+ align:start position:0%
+oscillation spiking and look the
+oscillations look at the peak time look
+
+ align:start position:0%
+oscillations look at the peak time look
+ 
+
+ align:start position:0%
+oscillations look at the peak time look
+at the firing with respect to that
+
+ align:start position:0%
+at the firing with respect to that
+ 
+
+ align:start position:0%
+at the firing with respect to that
+firing spiking as a function of this
+
+ align:start position:0%
+firing spiking as a function of this
+ 
+
+ align:start position:0%
+firing spiking as a function of this
+oscillation of both structures and the
+
+ align:start position:0%
+oscillation of both structures and the
+ 
+
+ align:start position:0%
+oscillation of both structures and the
+the bottom line is what you find is that
+
+ align:start position:0%
+the bottom line is what you find is that
+ 
+
+ align:start position:0%
+the bottom line is what you find is that
+this is a measure of this is a measure
+
+ align:start position:0%
+this is a measure of this is a measure
+ 
+
+ align:start position:0%
+this is a measure of this is a measure
+of relative phase locking and as how
+
+ align:start position:0%
+of relative phase locking and as how
+ 
+
+ align:start position:0%
+of relative phase locking and as how
+well how well do prefrontal cells
+
+ align:start position:0%
+well how well do prefrontal cells
+ 
+
+ align:start position:0%
+well how well do prefrontal cells
+actually lock to lock to this theta
+
+ align:start position:0%
+actually lock to lock to this theta
+ 
+
+ align:start position:0%
+actually lock to lock to this theta
+oscillation and what you find is that
+
+ align:start position:0%
+oscillation and what you find is that
+ 
+
+ align:start position:0%
+oscillation and what you find is that
+the degree to which they lock to theta
+
+ align:start position:0%
+the degree to which they lock to theta
+ 
+
+ align:start position:0%
+the degree to which they lock to theta
+rhythm is a function of whether or not
+
+ align:start position:0%
+rhythm is a function of whether or not
+ 
+
+ align:start position:0%
+rhythm is a function of whether or not
+the animal has to choose so the red ones
+
+ align:start position:0%
+the animal has to choose so the red ones
+ 
+
+ align:start position:0%
+the animal has to choose so the red ones
+are when the animals going down the arm
+
+ align:start position:0%
+are when the animals going down the arm
+ 
+
+ align:start position:0%
+are when the animals going down the arm
+and it's got to choose the gray one is
+
+ align:start position:0%
+and it's got to choose the gray one is
+ 
+
+ align:start position:0%
+and it's got to choose the gray one is
+when we when it doesn't have to choose
+
+ align:start position:0%
+when we when it doesn't have to choose
+ 
+
+ align:start position:0%
+when we when it doesn't have to choose
+when we choose then in addition the
+
+ align:start position:0%
+when we choose then in addition the
+ 
+
+ align:start position:0%
+when we choose then in addition the
+solid red is when the animal had to
+
+ align:start position:0%
+solid red is when the animal had to
+ 
+
+ align:start position:0%
+solid red is when the animal had to
+choose and it got it right and the
+
+ align:start position:0%
+choose and it got it right and the
+ 
+
+ align:start position:0%
+choose and it got it right and the
+stipler red is when and had to choose
+
+ align:start position:0%
+stipler red is when and had to choose
+ 
+
+ align:start position:0%
+stipler red is when and had to choose
+and it got it wrong so the degree to
+
+ align:start position:0%
+and it got it wrong so the degree to
+ 
+
+ align:start position:0%
+and it got it wrong so the degree to
+which the prefrontal cortex actually
+
+ align:start position:0%
+which the prefrontal cortex actually
+ 
+
+ align:start position:0%
+which the prefrontal cortex actually
+locks successfully locks to the
+
+ align:start position:0%
+locks successfully locks to the
+ 
+
+ align:start position:0%
+locks successfully locks to the
+hippocampal theta rhythm predicts
+
+ align:start position:0%
+hippocampal theta rhythm predicts
+ 
+
+ align:start position:0%
+hippocampal theta rhythm predicts
+whether the animal actually makes the
+
+ align:start position:0%
+whether the animal actually makes the
+ 
+
+ align:start position:0%
+whether the animal actually makes the
+correct choice or not so it says though
+
+ align:start position:0%
+correct choice or not so it says though
+ 
+
+ align:start position:0%
+correct choice or not so it says though
+this is a channel that is necessary for
+
+ align:start position:0%
+this is a channel that is necessary for
+ 
+
+ align:start position:0%
+this is a channel that is necessary for
+effectively communicating information
+
+ align:start position:0%
+effectively communicating information
+ 
+
+ align:start position:0%
+effectively communicating information
+between the two structures and
+
+ align:start position:0%
+between the two structures and
+ 
+
+ align:start position:0%
+between the two structures and
+that not only is it in the in the
+
+ align:start position:0%
+that not only is it in the in the
+ 
+
+ align:start position:0%
+that not only is it in the in the
+blocking of the spikes spikes in the
+
+ align:start position:0%
+blocking of the spikes spikes in the
+ 
+
+ align:start position:0%
+blocking of the spikes spikes in the
+prefrontal cortex the rhythm neighbor
+
+ align:start position:0%
+prefrontal cortex the rhythm neighbor
+ 
+
+ align:start position:0%
+prefrontal cortex the rhythm neighbor
+campus it also comes in the blocking of
+
+ align:start position:0%
+campus it also comes in the blocking of
+ 
+
+ align:start position:0%
+campus it also comes in the blocking of
+the rhythms themselves so you can think
+
+ align:start position:0%
+the rhythms themselves so you can think
+ 
+
+ align:start position:0%
+the rhythms themselves so you can think
+of there being this is the this is the
+
+ align:start position:0%
+of there being this is the this is the
+ 
+
+ align:start position:0%
+of there being this is the this is the
+theta rhythm that you can detecting the
+
+ align:start position:0%
+theta rhythm that you can detecting the
+ 
+
+ align:start position:0%
+theta rhythm that you can detecting the
+prefrontal cortex and the hippocampus
+
+ align:start position:0%
+prefrontal cortex and the hippocampus
+ 
+
+ align:start position:0%
+prefrontal cortex and the hippocampus
+and what you can see is there two
+
+ align:start position:0%
+and what you can see is there two
+ 
+
+ align:start position:0%
+and what you can see is there two
+conditions one you're the animal is
+
+ align:start position:0%
+conditions one you're the animal is
+ 
+
+ align:start position:0%
+conditions one you're the animal is
+actually choosing it's running down here
+
+ align:start position:0%
+actually choosing it's running down here
+ 
+
+ align:start position:0%
+actually choosing it's running down here
+as making a choice and in about the half
+
+ align:start position:0%
+as making a choice and in about the half
+ 
+
+ align:start position:0%
+as making a choice and in about the half
+second before the animal makes a choice
+
+ align:start position:0%
+second before the animal makes a choice
+ 
+
+ align:start position:0%
+second before the animal makes a choice
+you see these two rhythms actually lock
+
+ align:start position:0%
+you see these two rhythms actually lock
+ 
+
+ align:start position:0%
+you see these two rhythms actually lock
+they become coherent so transient
+
+ align:start position:0%
+they become coherent so transient
+ 
+
+ align:start position:0%
+they become coherent so transient
+coherence is predictive of correct
+
+ align:start position:0%
+coherence is predictive of correct
+ 
+
+ align:start position:0%
+coherence is predictive of correct
+choice behavior you know the thinking is
+
+ align:start position:0%
+choice behavior you know the thinking is
+ 
+
+ align:start position:0%
+choice behavior you know the thinking is
+that the rhythms themselves can be
+
+ align:start position:0%
+that the rhythms themselves can be
+ 
+
+ align:start position:0%
+that the rhythms themselves can be
+generating coordinated through the
+
+ align:start position:0%
+generating coordinated through the
+ 
+
+ align:start position:0%
+generating coordinated through the
+regulation of these local inhibitory
+
+ align:start position:0%
+regulation of these local inhibitory
+ 
+
+ align:start position:0%
+regulation of these local inhibitory
+circuits in fact there's been a lot of
+
+ align:start position:0%
+circuits in fact there's been a lot of
+ 
+
+ align:start position:0%
+circuits in fact there's been a lot of
+interest for instance in the
+
+ align:start position:0%
+interest for instance in the
+ 
+
+ align:start position:0%
+interest for instance in the
+relationship of local inhibitory control
+
+ align:start position:0%
+relationship of local inhibitory control
+ 
+
+ align:start position:0%
+relationship of local inhibitory control
+and neuropsychiatric disease and
+
+ align:start position:0%
+and neuropsychiatric disease and
+ 
+
+ align:start position:0%
+and neuropsychiatric disease and
+disorders so for instance disrupting
+
+ align:start position:0%
+disorders so for instance disrupting
+ 
+
+ align:start position:0%
+disorders so for instance disrupting
+local inhibitory rhythms in particular
+
+ align:start position:0%
+local inhibitory rhythms in particular
+ 
+
+ align:start position:0%
+local inhibitory rhythms in particular
+some like for instance the theta rhythms
+
+ align:start position:0%
+some like for instance the theta rhythms
+ 
+
+ align:start position:0%
+some like for instance the theta rhythms
+in prefrontal cortex can be associated
+
+ align:start position:0%
+in prefrontal cortex can be associated
+ 
+
+ align:start position:0%
+in prefrontal cortex can be associated
+with the sores like schizophrenia for
+
+ align:start position:0%
+with the sores like schizophrenia for
+ 
+
+ align:start position:0%
+with the sores like schizophrenia for
+instance so the inability to effectively
+
+ align:start position:0%
+instance so the inability to effectively
+ 
+
+ align:start position:0%
+instance so the inability to effectively
+impose these modes and then synchronize
+
+ align:start position:0%
+impose these modes and then synchronize
+ 
+
+ align:start position:0%
+impose these modes and then synchronize
+these modes can be seen as can can
+
+ align:start position:0%
+these modes can be seen as can can
+ 
+
+ align:start position:0%
+these modes can be seen as can can
+introduce disruptions in the ability to
+
+ align:start position:0%
+introduce disruptions in the ability to
+ 
+
+ align:start position:0%
+introduce disruptions in the ability to
+communicate or use memory cognitive
+
+ align:start position:0%
+communicate or use memory cognitive
+ 
+
+ align:start position:0%
+communicate or use memory cognitive
+disruption coming through disruption of
+
+ align:start position:0%
+disruption coming through disruption of
+ 
+
+ align:start position:0%
+disruption coming through disruption of
+these oscillations through disruption of
+
+ align:start position:0%
+these oscillations through disruption of
+ 
+
+ align:start position:0%
+these oscillations through disruption of
+inhibition in these local circuits now
+
+ align:start position:0%
+inhibition in these local circuits now
+ 
+
+ align:start position:0%
+inhibition in these local circuits now
+how you actually coordinate these two
+
+ align:start position:0%
+how you actually coordinate these two
+ 
+
+ align:start position:0%
+how you actually coordinate these two
+subjective you know study so we've been
+
+ align:start position:0%
+subjective you know study so we've been
+ 
+
+ align:start position:0%
+subjective you know study so we've been
+looking at the role of like midline
+
+ align:start position:0%
+looking at the role of like midline
+ 
+
+ align:start position:0%
+looking at the role of like midline
+thalamic nuclei and so the thalamus as
+
+ align:start position:0%
+thalamic nuclei and so the thalamus as
+ 
+
+ align:start position:0%
+thalamic nuclei and so the thalamus as
+being a you know set of structures that
+
+ align:start position:0%
+being a you know set of structures that
+ 
+
+ align:start position:0%
+being a you know set of structures that
+have widespread connectivity to all
+
+ align:start position:0%
+have widespread connectivity to all
+ 
+
+ align:start position:0%
+have widespread connectivity to all
+these cortical areas that they have much
+
+ align:start position:0%
+these cortical areas that they have much
+ 
+
+ align:start position:0%
+these cortical areas that they have much
+of their connectivity is inhibitory and
+
+ align:start position:0%
+of their connectivity is inhibitory and
+ 
+
+ align:start position:0%
+of their connectivity is inhibitory and
+so they have the ability to actually
+
+ align:start position:0%
+so they have the ability to actually
+ 
+
+ align:start position:0%
+so they have the ability to actually
+coordinate modulate and coordinate these
+
+ align:start position:0%
+coordinate modulate and coordinate these
+ 
+
+ align:start position:0%
+coordinate modulate and coordinate these
+oscillatory modes like we've even just
+
+ align:start position:0%
+oscillatory modes like we've even just
+ 
+
+ align:start position:0%
+oscillatory modes like we've even just
+recently published on individual cells
+
+ align:start position:0%
+recently published on individual cells
+ 
+
+ align:start position:0%
+recently published on individual cells
+so we've found in some of these midline
+
+ align:start position:0%
+so we've found in some of these midline
+ 
+
+ align:start position:0%
+so we've found in some of these midline
+thalamic nuclei that for instance will
+
+ align:start position:0%
+thalamic nuclei that for instance will
+ 
+
+ align:start position:0%
+thalamic nuclei that for instance will
+branch single cells or branch
+
+ align:start position:0%
+branch single cells or branch
+ 
+
+ align:start position:0%
+branch single cells or branch
+target cells in hippocampus and the
+
+ align:start position:0%
+target cells in hippocampus and the
+ 
+
+ align:start position:0%
+target cells in hippocampus and the
+prefrontal cortex so they would be
+
+ align:start position:0%
+prefrontal cortex so they would be
+ 
+
+ align:start position:0%
+prefrontal cortex so they would be
+ideally positioned to introduce to kind
+
+ align:start position:0%
+ideally positioned to introduce to kind
+ 
+
+ align:start position:0%
+ideally positioned to introduce to kind
+of select and impose this
+
+ align:start position:0%
+of select and impose this
+ 
+
+ align:start position:0%
+of select and impose this
+synchronization there and so that's
+
+ align:start position:0%
+synchronization there and so that's
+ 
+
+ align:start position:0%
+synchronization there and so that's
+that's the way we think about a lot of
+
+ align:start position:0%
+that's the way we think about a lot of
+ 
+
+ align:start position:0%
+that's the way we think about a lot of
+this dynamic connectivity being
+
+ align:start position:0%
+this dynamic connectivity being
+ 
+
+ align:start position:0%
+this dynamic connectivity being
+established presumably through some sort
+
+ align:start position:0%
+established presumably through some sort
+ 
+
+ align:start position:0%
+established presumably through some sort
+of thermic regulation and then you think
+
+ align:start position:0%
+of thermic regulation and then you think
+ 
+
+ align:start position:0%
+of thermic regulation and then you think
+about the thalamus is being regulated by
+
+ align:start position:0%
+about the thalamus is being regulated by
+ 
+
+ align:start position:0%
+about the thalamus is being regulated by
+there's the so called the thalamic
+
+ align:start position:0%
+there's the so called the thalamic
+ 
+
+ align:start position:0%
+there's the so called the thalamic
+reticular nucleus that that regulates
+
+ align:start position:0%
+reticular nucleus that that regulates
+ 
+
+ align:start position:0%
+reticular nucleus that that regulates
+the thalamus and it kind of sets up
+
+ align:start position:0%
+the thalamus and it kind of sets up
+ 
+
+ align:start position:0%
+the thalamus and it kind of sets up
+these modes there's also a lot of
+
+ align:start position:0%
+these modes there's also a lot of
+ 
+
+ align:start position:0%
+these modes there's also a lot of
+interest now in the Philemon particular
+
+ align:start position:0%
+interest now in the Philemon particular
+ 
+
+ align:start position:0%
+interest now in the Philemon particular
+nucleus in disease and disorders a lot
+
+ align:start position:0%
+nucleus in disease and disorders a lot
+ 
+
+ align:start position:0%
+nucleus in disease and disorders a lot
+of that you know sort of the genetic
+
+ align:start position:0%
+of that you know sort of the genetic
+ 
+
+ align:start position:0%
+of that you know sort of the genetic
+screening has identified targets in the
+
+ align:start position:0%
+screening has identified targets in the
+ 
+
+ align:start position:0%
+screening has identified targets in the
+Flemming particular nucleus so you kind
+
+ align:start position:0%
+Flemming particular nucleus so you kind
+ 
+
+ align:start position:0%
+Flemming particular nucleus so you kind
+of think about again it's like the it's
+
+ align:start position:0%
+of think about again it's like the it's
+ 
+
+ align:start position:0%
+of think about again it's like the it's
+like the oscillator and you're you know
+
+ align:start position:0%
+like the oscillator and you're you know
+ 
+
+ align:start position:0%
+like the oscillator and you're you know
+in your computer or your you know your
+
+ align:start position:0%
+in your computer or your you know your
+ 
+
+ align:start position:0%
+in your computer or your you know your
+radio that breaks down you can you can't
+
+ align:start position:0%
+radio that breaks down you can you can't
+ 
+
+ align:start position:0%
+radio that breaks down you can you can't
+the information could be there but you
+
+ align:start position:0%
+the information could be there but you
+ 
+
+ align:start position:0%
+the information could be there but you
+can't tune into it so it's this
+
+ align:start position:0%
+can't tune into it so it's this
+ 
+
+ align:start position:0%
+can't tune into it so it's this
+fundamental tune you got to have the
+
+ align:start position:0%
+fundamental tune you got to have the
+ 
+
+ align:start position:0%
+fundamental tune you got to have the
+modes and you got to be able to lock to
+
+ align:start position:0%
+modes and you got to be able to lock to
+ 
+
+ align:start position:0%
+modes and you got to be able to lock to
+these frequencies and then beyond that
+
+ align:start position:0%
+these frequencies and then beyond that
+ 
+
+ align:start position:0%
+these frequencies and then beyond that
+as we'll see it's not just the
+
+ align:start position:0%
+as we'll see it's not just the
+ 
+
+ align:start position:0%
+as we'll see it's not just the
+frequencies but it's also the precise
+
+ align:start position:0%
+frequencies but it's also the precise
+ 
+
+ align:start position:0%
+frequencies but it's also the precise
+phase within those those oscillatory
+
+ align:start position:0%
+phase within those those oscillatory
+ 
+
+ align:start position:0%
+phase within those those oscillatory
+modes that carry different information
+
+ align:start position:0%
+modes that carry different information
+ 
+
+ align:start position:0%
+modes that carry different information
+that way actually determined by taking
+
+ align:start position:0%
+that way actually determined by taking
+ 
+
+ align:start position:0%
+that way actually determined by taking
+advantage of these techniques
+
+ align:start position:0%
+advantage of these techniques
+ 
+
+ align:start position:0%
+advantage of these techniques
+optogenetic techniques for targeted
+
+ align:start position:0%
+optogenetic techniques for targeted
+ 
+
+ align:start position:0%
+optogenetic techniques for targeted
+manipulation so you infect the HIPAA
+
+ align:start position:0%
+manipulation so you infect the HIPAA
+ 
+
+ align:start position:0%
+manipulation so you infect the HIPAA
+can't inhibitory neurons in the
+
+ align:start position:0%
+can't inhibitory neurons in the
+ 
+
+ align:start position:0%
+can't inhibitory neurons in the
+hippocampus with this optogenetic up
+
+ align:start position:0%
+hippocampus with this optogenetic up
+ 
+
+ align:start position:0%
+hippocampus with this optogenetic up
+genetically encoded and controllable
+
+ align:start position:0%
+genetically encoded and controllable
+ 
+
+ align:start position:0%
+genetically encoded and controllable
+channel so that we can optically excite
+
+ align:start position:0%
+channel so that we can optically excite
+ 
+
+ align:start position:0%
+channel so that we can optically excite
+inhibitory cells so we infect this
+
+ align:start position:0%
+inhibitory cells so we infect this
+ 
+
+ align:start position:0%
+inhibitory cells so we infect this
+excitatory channel into inhibitory cells
+
+ align:start position:0%
+excitatory channel into inhibitory cells
+ 
+
+ align:start position:0%
+excitatory channel into inhibitory cells
+and then we can transiently giving very
+
+ align:start position:0%
+and then we can transiently giving very
+ 
+
+ align:start position:0%
+and then we can transiently giving very
+brief pulses of laser light we can
+
+ align:start position:0%
+brief pulses of laser light we can
+ 
+
+ align:start position:0%
+brief pulses of laser light we can
+activate Drive inhibitory cells and then
+
+ align:start position:0%
+activate Drive inhibitory cells and then
+ 
+
+ align:start position:0%
+activate Drive inhibitory cells and then
+because the local circuit those
+
+ align:start position:0%
+because the local circuit those
+ 
+
+ align:start position:0%
+because the local circuit those
+inhibitory cells will inhibit the
+
+ align:start position:0%
+inhibitory cells will inhibit the
+ 
+
+ align:start position:0%
+inhibitory cells will inhibit the
+excitatory cells so we have about 20-25
+
+ align:start position:0%
+excitatory cells so we have about 20-25
+ 
+
+ align:start position:0%
+excitatory cells so we have about 20-25
+millisecond control and now we can lock
+
+ align:start position:0%
+millisecond control and now we can lock
+ 
+
+ align:start position:0%
+millisecond control and now we can lock
+or control inhibition based upon the
+
+ align:start position:0%
+or control inhibition based upon the
+ 
+
+ align:start position:0%
+or control inhibition based upon the
+phase of this oscillation so the eye
+
+ align:start position:0%
+phase of this oscillation so the eye
+ 
+
+ align:start position:0%
+phase of this oscillation so the eye
+is we're going to selectively disrupt or
+
+ align:start position:0%
+is we're going to selectively disrupt or
+ 
+
+ align:start position:0%
+is we're going to selectively disrupt or
+inactivate the hippocampus at different
+
+ align:start position:0%
+inactivate the hippocampus at different
+ 
+
+ align:start position:0%
+inactivate the hippocampus at different
+phases we're gonna ask do those phases
+
+ align:start position:0%
+phases we're gonna ask do those phases
+ 
+
+ align:start position:0%
+phases we're gonna ask do those phases
+that they differ in terms of their
+
+ align:start position:0%
+that they differ in terms of their
+ 
+
+ align:start position:0%
+that they differ in terms of their
+contribution to behavior and performance
+
+ align:start position:0%
+contribution to behavior and performance
+ 
+
+ align:start position:0%
+contribution to behavior and performance
+so here we're gonna lock inhibition
+
+ align:start position:0%
+so here we're gonna lock inhibition
+ 
+
+ align:start position:0%
+so here we're gonna lock inhibition
+either the peak of the trough of the
+
+ align:start position:0%
+either the peak of the trough of the
+ 
+
+ align:start position:0%
+either the peak of the trough of the
+state oscillation and so in this task
+
+ align:start position:0%
+state oscillation and so in this task
+ 
+
+ align:start position:0%
+state oscillation and so in this task
+and we're gonna do this manipulation
+
+ align:start position:0%
+and we're gonna do this manipulation
+ 
+
+ align:start position:0%
+and we're gonna do this manipulation
+that is selectively inhibit hippocampal
+
+ align:start position:0%
+that is selectively inhibit hippocampal
+ 
+
+ align:start position:0%
+that is selectively inhibit hippocampal
+output at either the peak of the trough
+
+ align:start position:0%
+output at either the peak of the trough
+ 
+
+ align:start position:0%
+output at either the peak of the trough
+the theta rhythm at to behavioral phases
+
+ align:start position:0%
+the theta rhythm at to behavioral phases
+ 
+
+ align:start position:0%
+the theta rhythm at to behavioral phases
+so in this task animals gonna start in
+
+ align:start position:0%
+so in this task animals gonna start in
+ 
+
+ align:start position:0%
+so in this task animals gonna start in
+one of these arms gonna run up and it's
+
+ align:start position:0%
+one of these arms gonna run up and it's
+ 
+
+ align:start position:0%
+one of these arms gonna run up and it's
+gonna choose so we're gonna think about
+
+ align:start position:0%
+gonna choose so we're gonna think about
+ 
+
+ align:start position:0%
+gonna choose so we're gonna think about
+the starting arms as we'll refer to this
+
+ align:start position:0%
+the starting arms as we'll refer to this
+ 
+
+ align:start position:0%
+the starting arms as we'll refer to this
+as the encoding phase is where you have
+
+ align:start position:0%
+as the encoding phase is where you have
+ 
+
+ align:start position:0%
+as the encoding phase is where you have
+to keep track of where you are and then
+
+ align:start position:0%
+to keep track of where you are and then
+ 
+
+ align:start position:0%
+to keep track of where you are and then
+here in the central arm will refer to
+
+ align:start position:0%
+here in the central arm will refer to
+ 
+
+ align:start position:0%
+here in the central arm will refer to
+this as the retrieval phase this is
+
+ align:start position:0%
+this as the retrieval phase this is
+ 
+
+ align:start position:0%
+this as the retrieval phase this is
+where you have to remember oh where did
+
+ align:start position:0%
+where you have to remember oh where did
+ 
+
+ align:start position:0%
+where you have to remember oh where did
+I come from and then use that to decide
+
+ align:start position:0%
+I come from and then use that to decide
+ 
+
+ align:start position:0%
+I come from and then use that to decide
+where you're going to go to and we found
+
+ align:start position:0%
+where you're going to go to and we found
+ 
+
+ align:start position:0%
+where you're going to go to and we found
+was pretty surprising and that is that
+
+ align:start position:0%
+was pretty surprising and that is that
+ 
+
+ align:start position:0%
+was pretty surprising and that is that
+you might think well if you shut off
+
+ align:start position:0%
+you might think well if you shut off
+ 
+
+ align:start position:0%
+you might think well if you shut off
+hippocampal output right you turn off
+
+ align:start position:0%
+hippocampal output right you turn off
+ 
+
+ align:start position:0%
+hippocampal output right you turn off
+the campus you're gonna get an
+
+ align:start position:0%
+the campus you're gonna get an
+ 
+
+ align:start position:0%
+the campus you're gonna get an
+impairment it's just like if you you
+
+ align:start position:0%
+impairment it's just like if you you
+ 
+
+ align:start position:0%
+impairment it's just like if you you
+know the examples that I gave of
+
+ align:start position:0%
+know the examples that I gave of
+ 
+
+ align:start position:0%
+know the examples that I gave of
+suggesting hippocampus prefrontal cortex
+
+ align:start position:0%
+suggesting hippocampus prefrontal cortex
+ 
+
+ align:start position:0%
+suggesting hippocampus prefrontal cortex
+control most of those come from lesion
+
+ align:start position:0%
+control most of those come from lesion
+ 
+
+ align:start position:0%
+control most of those come from lesion
+studies you damage that the campus
+
+ align:start position:0%
+studies you damage that the campus
+ 
+
+ align:start position:0%
+studies you damage that the campus
+animal can't find his way around so if
+
+ align:start position:0%
+animal can't find his way around so if
+ 
+
+ align:start position:0%
+animal can't find his way around so if
+you were to optogenetic aliy lesion or
+
+ align:start position:0%
+you were to optogenetic aliy lesion or
+ 
+
+ align:start position:0%
+you were to optogenetic aliy lesion or
+turn off the epic campus you might
+
+ align:start position:0%
+turn off the epic campus you might
+ 
+
+ align:start position:0%
+turn off the epic campus you might
+imagine okay animals won't be able to
+
+ align:start position:0%
+imagine okay animals won't be able to
+ 
+
+ align:start position:0%
+imagine okay animals won't be able to
+find their way around so you could ask
+
+ align:start position:0%
+find their way around so you could ask
+ 
+
+ align:start position:0%
+find their way around so you could ask
+this experiment is going to identify
+
+ align:start position:0%
+this experiment is going to identify
+ 
+
+ align:start position:0%
+this experiment is going to identify
+which phase and you know which
+
+ align:start position:0%
+which phase and you know which
+ 
+
+ align:start position:0%
+which phase and you know which
+behavioral phase are most effective in
+
+ align:start position:0%
+behavioral phase are most effective in
+ 
+
+ align:start position:0%
+behavioral phase are most effective in
+disrupting performance but what we
+
+ align:start position:0%
+disrupting performance but what we
+ 
+
+ align:start position:0%
+disrupting performance but what we
+actually found was when you selectively
+
+ align:start position:0%
+actually found was when you selectively
+ 
+
+ align:start position:0%
+actually found was when you selectively
+inhibit activity at different phases you
+
+ align:start position:0%
+inhibit activity at different phases you
+ 
+
+ align:start position:0%
+inhibit activity at different phases you
+actually get an enhancement of
+
+ align:start position:0%
+actually get an enhancement of
+ 
+
+ align:start position:0%
+actually get an enhancement of
+performance they get better and it
+
+ align:start position:0%
+performance they get better and it
+ 
+
+ align:start position:0%
+performance they get better and it
+depended not there wasn't just one phase
+
+ align:start position:0%
+depended not there wasn't just one phase
+ 
+
+ align:start position:0%
+depended not there wasn't just one phase
+a good phase in a bad phase but both of
+
+ align:start position:0%
+a good phase in a bad phase but both of
+ 
+
+ align:start position:0%
+a good phase in a bad phase but both of
+the peak and the trough were both
+
+ align:start position:0%
+the peak and the trough were both
+ 
+
+ align:start position:0%
+the peak and the trough were both
+effective in enhancing performance but
+
+ align:start position:0%
+effective in enhancing performance but
+ 
+
+ align:start position:0%
+effective in enhancing performance but
+only when applied at certain behavioral
+
+ align:start position:0%
+only when applied at certain behavioral
+ 
+
+ align:start position:0%
+only when applied at certain behavioral
+phases in fact there was this double
+
+ align:start position:0%
+phases in fact there was this double
+ 
+
+ align:start position:0%
+phases in fact there was this double
+dissociation and that is that trough
+
+ align:start position:0%
+dissociation and that is that trough
+ 
+
+ align:start position:0%
+dissociation and that is that trough
+stimulation when applied here so when
+
+ align:start position:0%
+stimulation when applied here so when
+ 
+
+ align:start position:0%
+stimulation when applied here so when
+you stimulate in the trough
+
+ align:start position:0%
+you stimulate in the trough
+ 
+
+ align:start position:0%
+you stimulate in the trough
+in the retrieval segment animals got
+
+ align:start position:0%
+in the retrieval segment animals got
+ 
+
+ align:start position:0%
+in the retrieval segment animals got
+better when you stimulate at the peak
+
+ align:start position:0%
+better when you stimulate at the peak
+ 
+
+ align:start position:0%
+better when you stimulate at the peak
+and the encoding segment animals got
+
+ align:start position:0%
+and the encoding segment animals got
+ 
+
+ align:start position:0%
+and the encoding segment animals got
+better so it wasn't that the peak is
+
+ align:start position:0%
+better so it wasn't that the peak is
+ 
+
+ align:start position:0%
+better so it wasn't that the peak is
+good or the trough is Goods the peak the
+
+ align:start position:0%
+good or the trough is Goods the peak the
+ 
+
+ align:start position:0%
+good or the trough is Goods the peak the
+peak is good during retrieval and the
+
+ align:start position:0%
+peak is good during retrieval and the
+ 
+
+ align:start position:0%
+peak is good during retrieval and the
+trough is good during encoding so what
+
+ align:start position:0%
+trough is good during encoding so what
+ 
+
+ align:start position:0%
+trough is good during encoding so what
+it says is the peak and the trough have
+
+ align:start position:0%
+it says is the peak and the trough have
+ 
+
+ align:start position:0%
+it says is the peak and the trough have
+two different functions and if you
+
+ align:start position:0%
+two different functions and if you
+ 
+
+ align:start position:0%
+two different functions and if you
+actually think about what I was showing
+
+ align:start position:0%
+actually think about what I was showing
+ 
+
+ align:start position:0%
+actually think about what I was showing
+before these sequences the sequences
+
+ align:start position:0%
+before these sequences the sequences
+ 
+
+ align:start position:0%
+before these sequences the sequences
+that are going from just behind just in
+
+ align:start position:0%
+that are going from just behind just in
+ 
+
+ align:start position:0%
+that are going from just behind just in
+front of the animal what it says is oh
+
+ align:start position:0%
+front of the animal what it says is oh
+ 
+
+ align:start position:0%
+front of the animal what it says is oh
+yeah these different phases peak and
+
+ align:start position:0%
+yeah these different phases peak and
+ 
+
+ align:start position:0%
+yeah these different phases peak and
+trough you can think of as like past and
+
+ align:start position:0%
+trough you can think of as like past and
+ 
+
+ align:start position:0%
+trough you can think of as like past and
+future and so if I'm sitting over here
+
+ align:start position:0%
+future and so if I'm sitting over here
+ 
+
+ align:start position:0%
+future and so if I'm sitting over here
+in this encoding segment you know what
+
+ align:start position:0%
+in this encoding segment you know what
+ 
+
+ align:start position:0%
+in this encoding segment you know what
+I'm really trying to do is I'm just
+
+ align:start position:0%
+I'm really trying to do is I'm just
+ 
+
+ align:start position:0%
+I'm really trying to do is I'm just
+trying to keep track of where am i right
+
+ align:start position:0%
+trying to keep track of where am i right
+ 
+
+ align:start position:0%
+trying to keep track of where am i right
+now now I may simultaneously also be
+
+ align:start position:0%
+now now I may simultaneously also be
+ 
+
+ align:start position:0%
+now now I may simultaneously also be
+thinking about well where am I going to
+
+ align:start position:0%
+thinking about well where am I going to
+ 
+
+ align:start position:0%
+thinking about well where am I going to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+but for this task it's not really
+
+ align:start position:0%
+but for this task it's not really
+ 
+
+ align:start position:0%
+but for this task it's not really
+helpful it's not really useful at this
+
+ align:start position:0%
+helpful it's not really useful at this
+ 
+
+ align:start position:0%
+helpful it's not really useful at this
+point I need to focus on where I am
+
+ align:start position:0%
+point I need to focus on where I am
+ 
+
+ align:start position:0%
+point I need to focus on where I am
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+so you can think of simultaneously
+
+ align:start position:0%
+so you can think of simultaneously
+ 
+
+ align:start position:0%
+so you can think of simultaneously
+they're actually these two channels
+
+ align:start position:0%
+they're actually these two channels
+ 
+
+ align:start position:0%
+they're actually these two channels
+where am i where am i where am I going
+
+ align:start position:0%
+where am i where am i where am I going
+ 
+
+ align:start position:0%
+where am i where am i where am I going
+to go and I can enhance performance by
+
+ align:start position:0%
+to go and I can enhance performance by
+ 
+
+ align:start position:0%
+to go and I can enhance performance by
+shutting off or inhibiting the
+
+ align:start position:0%
+shutting off or inhibiting the
+ 
+
+ align:start position:0%
+shutting off or inhibiting the
+non-relevant one so when I keep I shut
+
+ align:start position:0%
+non-relevant one so when I keep I shut
+ 
+
+ align:start position:0%
+non-relevant one so when I keep I shut
+off the retrieval channel here in the
+
+ align:start position:0%
+off the retrieval channel here in the
+ 
+
+ align:start position:0%
+off the retrieval channel here in the
+encoding I get better it's like focusing
+
+ align:start position:0%
+encoding I get better it's like focusing
+ 
+
+ align:start position:0%
+encoding I get better it's like focusing
+attention it's like you know it's like
+
+ align:start position:0%
+attention it's like you know it's like
+ 
+
+ align:start position:0%
+attention it's like you know it's like
+pay attention to what you're doing now
+
+ align:start position:0%
+pay attention to what you're doing now
+ 
+
+ align:start position:0%
+pay attention to what you're doing now
+stop thinking about stuff
+
+ align:start position:0%
+stop thinking about stuff
+ 
+
+ align:start position:0%
+stop thinking about stuff
+similarly when I'm here in the retrieval
+
+ align:start position:0%
+similarly when I'm here in the retrieval
+ 
+
+ align:start position:0%
+similarly when I'm here in the retrieval
+segment I'm also encoding I'm trying to
+
+ align:start position:0%
+segment I'm also encoding I'm trying to
+ 
+
+ align:start position:0%
+segment I'm also encoding I'm trying to
+keep track of where I am as well as
+
+ align:start position:0%
+keep track of where I am as well as
+ 
+
+ align:start position:0%
+keep track of where I am as well as
+think about where I'm going to thing is
+
+ align:start position:0%
+think about where I'm going to thing is
+ 
+
+ align:start position:0%
+think about where I'm going to thing is
+keeping track of where I am here it's
+
+ align:start position:0%
+keeping track of where I am here it's
+ 
+
+ align:start position:0%
+keeping track of where I am here it's
+not relevant for the task it might be
+
+ align:start position:0%
+not relevant for the task it might be
+ 
+
+ align:start position:0%
+not relevant for the task it might be
+broadly relevant for the animal but it's
+
+ align:start position:0%
+broadly relevant for the animal but it's
+ 
+
+ align:start position:0%
+broadly relevant for the animal but it's
+not relevant this test so when I shut
+
+ align:start position:0%
+not relevant this test so when I shut
+ 
+
+ align:start position:0%
+not relevant this test so when I shut
+off I turn off that encoding channel I'm
+
+ align:start position:0%
+off I turn off that encoding channel I'm
+ 
+
+ align:start position:0%
+off I turn off that encoding channel I'm
+able to enhance the retrieval
+
+ align:start position:0%
+able to enhance the retrieval
+ 
+
+ align:start position:0%
+able to enhance the retrieval
+information that goes out so it says it
+
+ align:start position:0%
+information that goes out so it says it
+ 
+
+ align:start position:0%
+information that goes out so it says it
+doesn't this is not I mean you might
+
+ align:start position:0%
+doesn't this is not I mean you might
+ 
+
+ align:start position:0%
+doesn't this is not I mean you might
+interpret this thing oh so this is how
+
+ align:start position:0%
+interpret this thing oh so this is how
+ 
+
+ align:start position:0%
+interpret this thing oh so this is how
+we can improve memory by selectively
+
+ align:start position:0%
+we can improve memory by selectively
+ 
+
+ align:start position:0%
+we can improve memory by selectively
+shutting off the hippocampus well you
+
+ align:start position:0%
+shutting off the hippocampus well you
+ 
+
+ align:start position:0%
+shutting off the hippocampus well you
+know this is not a strategy for general
+
+ align:start position:0%
+know this is not a strategy for general
+ 
+
+ align:start position:0%
+know this is not a strategy for general
+cognitive enhancement they keep the
+
+ align:start position:0%
+cognitive enhancement they keep the
+ 
+
+ align:start position:0%
+cognitive enhancement they keep the
+campus is working much better when all
+
+ align:start position:0%
+campus is working much better when all
+ 
+
+ align:start position:0%
+campus is working much better when all
+these phases are in operation and that's
+
+ align:start position:0%
+these phases are in operation and that's
+ 
+
+ align:start position:0%
+these phases are in operation and that's
+because the epic campus is not designed
+
+ align:start position:0%
+because the epic campus is not designed
+ 
+
+ align:start position:0%
+because the epic campus is not designed
+to solve this task if the camp is
+
+ align:start position:0%
+to solve this task if the camp is
+ 
+
+ align:start position:0%
+to solve this task if the camp is
+designed to solve the broader task is
+
+ align:start position:0%
+designed to solve the broader task is
+ 
+
+ align:start position:0%
+designed to solve the broader task is
+trying to figure out
+
+ align:start position:0%
+trying to figure out
+ 
+
+ align:start position:0%
+trying to figure out
+this task relevant to all the other
+
+ align:start position:0%
+this task relevant to all the other
+ 
+
+ align:start position:0%
+this task relevant to all the other
+things that I have to do as you're
+
+ align:start position:0%
+things that I have to do as you're
+ 
+
+ align:start position:0%
+things that I have to do as you're
+trying to integrate this information
+
+ align:start position:0%
+trying to integrate this information
+ 
+
+ align:start position:0%
+trying to integrate this information
+into all the other information you have
+
+ align:start position:0%
+into all the other information you have
+ 
+
+ align:start position:0%
+into all the other information you have
+and that requires connecting sort of
+
+ align:start position:0%
+and that requires connecting sort of
+ 
+
+ align:start position:0%
+and that requires connecting sort of
+connecting the encoding and retrieval
+
+ align:start position:0%
+connecting the encoding and retrieval
+ 
+
+ align:start position:0%
+connecting the encoding and retrieval
+you really need to have all those pieces
+
+ align:start position:0%
+you really need to have all those pieces
+ 
+
+ align:start position:0%
+you really need to have all those pieces
+of information available but it does
+
+ align:start position:0%
+of information available but it does
+ 
+
+ align:start position:0%
+of information available but it does
+point out that one can actually
+
+ align:start position:0%
+point out that one can actually
+ 
+
+ align:start position:0%
+point out that one can actually
+dissociate the function of information
+
+ align:start position:0%
+dissociate the function of information
+ 
+
+ align:start position:0%
+dissociate the function of information
+in these two different phases the phase
+
+ align:start position:0%
+in these two different phases the phase
+ 
+
+ align:start position:0%
+in these two different phases the phase
+actually matters and it matters at the
+
+ align:start position:0%
+actually matters and it matters at the
+ 
+
+ align:start position:0%
+actually matters and it matters at the
+level of high level behavior
+
+ align:start position:0%
+level of high level behavior
+ 
+
+ align:start position:0%
+level of high level behavior
+decision-making it's not just a it's not
+
+ align:start position:0%
+decision-making it's not just a it's not
+ 
+
+ align:start position:0%
+decision-making it's not just a it's not
+just a idiosyncrasy or artifact of you
+
+ align:start position:0%
+just a idiosyncrasy or artifact of you
+ 
+
+ align:start position:0%
+just a idiosyncrasy or artifact of you
+know excitability as a function of phase
+
+ align:start position:0%
+know excitability as a function of phase
+ 
+
+ align:start position:0%
+know excitability as a function of phase
+this is really how information is being
+
+ align:start position:0%
+this is really how information is being
+ 
+
+ align:start position:0%
+this is really how information is being
+used
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/w6R6V1Mpz7s.txt b/w6R6V1Mpz7s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d4fdec7ec5bdc865d0bff4da0aaa3a34de5bfe29
--- /dev/null
+++ b/w6R6V1Mpz7s.txt
@@ -0,0 +1,9923 @@
+align:start position:0%
+ 
+okay why don't we get
+
+ align:start position:0%
+okay why don't we get
+ 
+
+ align:start position:0%
+okay why don't we get
+started so um before going back to
+
+ align:start position:0%
+started so um before going back to
+ 
+
+ align:start position:0%
+started so um before going back to
+talking about more kinds of power
+
+ align:start position:0%
+talking about more kinds of power
+ 
+
+ align:start position:0%
+talking about more kinds of power
+electronic circuits I wanted to spend
+
+ align:start position:0%
+electronic circuits I wanted to spend
+ 
+
+ align:start position:0%
+electronic circuits I wanted to spend
+one lecture uh talking about heat
+
+ align:start position:0%
+one lecture uh talking about heat
+ 
+
+ align:start position:0%
+one lecture uh talking about heat
+transfer and sort of how you model and
+
+ align:start position:0%
+transfer and sort of how you model and
+ 
+
+ align:start position:0%
+transfer and sort of how you model and
+design thermal system systems and this
+
+ align:start position:0%
+design thermal system systems and this
+ 
+
+ align:start position:0%
+design thermal system systems and this
+is uh principles of Power Electronics
+
+ align:start position:0%
+is uh principles of Power Electronics
+ 
+
+ align:start position:0%
+is uh principles of Power Electronics
+chapter
+
+ align:start position:0%
+chapter
+ 
+
+ align:start position:0%
+chapter
+25 um now to be clear you can spend an
+
+ align:start position:0%
+25 um now to be clear you can spend an
+ 
+
+ align:start position:0%
+25 um now to be clear you can spend an
+entire course or for that matter
+
+ align:start position:0%
+entire course or for that matter
+ 
+
+ align:start position:0%
+entire course or for that matter
+multiple entire courses studying uh heat
+
+ align:start position:0%
+multiple entire courses studying uh heat
+ 
+
+ align:start position:0%
+multiple entire courses studying uh heat
+transfer and the ways to do that and
+
+ align:start position:0%
+transfer and the ways to do that and
+ 
+
+ align:start position:0%
+transfer and the ways to do that and
+clearly we don't have time to do that
+
+ align:start position:0%
+clearly we don't have time to do that
+ 
+
+ align:start position:0%
+clearly we don't have time to do that
+here so what I'm going to attempt to do
+
+ align:start position:0%
+here so what I'm going to attempt to do
+ 
+
+ align:start position:0%
+here so what I'm going to attempt to do
+in this lecture is give you just enough
+
+ align:start position:0%
+in this lecture is give you just enough
+ 
+
+ align:start position:0%
+in this lecture is give you just enough
+information to be dangerous okay in that
+
+ align:start position:0%
+information to be dangerous okay in that
+ 
+
+ align:start position:0%
+information to be dangerous okay in that
+a lot of the things we need to do as a
+
+ align:start position:0%
+a lot of the things we need to do as a
+ 
+
+ align:start position:0%
+a lot of the things we need to do as a
+Power Electronics designer let us offset
+
+ align:start position:0%
+Power Electronics designer let us offset
+ 
+
+ align:start position:0%
+Power Electronics designer let us offset
+some of the sort of the detailed
+
+ align:start position:0%
+some of the sort of the detailed
+ 
+
+ align:start position:0%
+some of the sort of the detailed
+computational or you know deep
+
+ align:start position:0%
+computational or you know deep
+ 
+
+ align:start position:0%
+computational or you know deep
+analytical modeling onto uh heat sync
+
+ align:start position:0%
+analytical modeling onto uh heat sync
+ 
+
+ align:start position:0%
+analytical modeling onto uh heat sync
+designers and other people and what we
+
+ align:start position:0%
+designers and other people and what we
+ 
+
+ align:start position:0%
+designers and other people and what we
+need to know is enough information about
+
+ align:start position:0%
+need to know is enough information about
+ 
+
+ align:start position:0%
+need to know is enough information about
+how to model these things that we can
+
+ align:start position:0%
+how to model these things that we can
+ 
+
+ align:start position:0%
+how to model these things that we can
+predict things like temperature rises
+
+ align:start position:0%
+predict things like temperature rises
+ 
+
+ align:start position:0%
+predict things like temperature rises
+and select the kind of correct
+
+ align:start position:0%
+and select the kind of correct
+ 
+
+ align:start position:0%
+and select the kind of correct
+components and that's what we're going
+
+ align:start position:0%
+components and that's what we're going
+ 
+
+ align:start position:0%
+components and that's what we're going
+to try to get to
+
+ align:start position:0%
+to try to get to
+ 
+
+ align:start position:0%
+to try to get to
+today okay now if we think about heat
+
+ align:start position:0%
+today okay now if we think about heat
+ 
+
+ align:start position:0%
+today okay now if we think about heat
+transfer there's sort of and and first
+
+ align:start position:0%
+transfer there's sort of and and first
+ 
+
+ align:start position:0%
+transfer there's sort of and and first
+of all why am I obsessed about this it's
+
+ align:start position:0%
+of all why am I obsessed about this it's
+ 
+
+ align:start position:0%
+of all why am I obsessed about this it's
+because you know we're going to despite
+
+ align:start position:0%
+because you know we're going to despite
+ 
+
+ align:start position:0%
+because you know we're going to despite
+our best attempts we're going to
+
+ align:start position:0%
+our best attempts we're going to
+ 
+
+ align:start position:0%
+our best attempts we're going to
+dissipate some power in our devices in
+
+ align:start position:0%
+dissipate some power in our devices in
+ 
+
+ align:start position:0%
+dissipate some power in our devices in
+our components and if I want to make
+
+ align:start position:0%
+our components and if I want to make
+ 
+
+ align:start position:0%
+our components and if I want to make
+something really high power density I've
+
+ align:start position:0%
+something really high power density I've
+ 
+
+ align:start position:0%
+something really high power density I've
+really first of all got to minimize how
+
+ align:start position:0%
+really first of all got to minimize how
+ 
+
+ align:start position:0%
+really first of all got to minimize how
+much heat I
+
+ align:start position:0%
+much heat I
+ 
+
+ align:start position:0%
+much heat I
+dissipate but in the end I've also got
+
+ align:start position:0%
+dissipate but in the end I've also got
+ 
+
+ align:start position:0%
+dissipate but in the end I've also got
+to take whatever heat I dissipate and
+
+ align:start position:0%
+to take whatever heat I dissipate and
+ 
+
+ align:start position:0%
+to take whatever heat I dissipate and
+get it out of the system right and how
+
+ align:start position:0%
+get it out of the system right and how
+ 
+
+ align:start position:0%
+get it out of the system right and how
+good a job I do of getting it away from
+
+ align:start position:0%
+good a job I do of getting it away from
+ 
+
+ align:start position:0%
+good a job I do of getting it away from
+the components and keeping their
+
+ align:start position:0%
+the components and keeping their
+ 
+
+ align:start position:0%
+the components and keeping their
+temperature rise low says a lot about
+
+ align:start position:0%
+temperature rise low says a lot about
+ 
+
+ align:start position:0%
+temperature rise low says a lot about
+you know how high performance power
+
+ align:start position:0%
+you know how high performance power
+ 
+
+ align:start position:0%
+you know how high performance power
+converter I can build okay now so let's
+
+ align:start position:0%
+converter I can build okay now so let's
+ 
+
+ align:start position:0%
+converter I can build okay now so let's
+assume we're going to dissipate a
+
+ align:start position:0%
+assume we're going to dissipate a
+ 
+
+ align:start position:0%
+assume we're going to dissipate a
+certain amount of power and ask how do I
+
+ align:start position:0%
+certain amount of power and ask how do I
+ 
+
+ align:start position:0%
+certain amount of power and ask how do I
+get the heat out of my system okay and
+
+ align:start position:0%
+get the heat out of my system okay and
+ 
+
+ align:start position:0%
+get the heat out of my system okay and
+there's really three fundamental ways uh
+
+ align:start position:0%
+there's really three fundamental ways uh
+ 
+
+ align:start position:0%
+there's really three fundamental ways uh
+you can do that you can do it through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conduction okay conduction is just
+
+ align:start position:0%
+conduction okay conduction is just
+ 
+
+ align:start position:0%
+conduction okay conduction is just
+simply you know if I if I think of uh
+
+ align:start position:0%
+simply you know if I if I think of uh
+ 
+
+ align:start position:0%
+simply you know if I if I think of uh
+heat as being vibrations of particles
+
+ align:start position:0%
+heat as being vibrations of particles
+ 
+
+ align:start position:0%
+heat as being vibrations of particles
+right I can let the heat conduct through
+
+ align:start position:0%
+right I can let the heat conduct through
+ 
+
+ align:start position:0%
+right I can let the heat conduct through
+some heat conductor and be carried away
+
+ align:start position:0%
+some heat conductor and be carried away
+ 
+
+ align:start position:0%
+some heat conductor and be carried away
+so some physical element like a piece of
+
+ align:start position:0%
+so some physical element like a piece of
+ 
+
+ align:start position:0%
+so some physical element like a piece of
+metal will carry heat along it okay I
+
+ align:start position:0%
+metal will carry heat along it okay I
+ 
+
+ align:start position:0%
+metal will carry heat along it okay I
+can do it by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convection right I transfer heat to some
+
+ align:start position:0%
+convection right I transfer heat to some
+ 
+
+ align:start position:0%
+convection right I transfer heat to some
+moving fluid that could be air or water
+
+ align:start position:0%
+moving fluid that could be air or water
+ 
+
+ align:start position:0%
+moving fluid that could be air or water
+and I let the fluid carry the heat
+
+ align:start position:0%
+and I let the fluid carry the heat
+ 
+
+ align:start position:0%
+and I let the fluid carry the heat
+away or I could do it by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radiation right if I make something hot
+
+ align:start position:0%
+radiation right if I make something hot
+ 
+
+ align:start position:0%
+radiation right if I make something hot
+it emits photons at whatever wavelength
+
+ align:start position:0%
+it emits photons at whatever wavelength
+ 
+
+ align:start position:0%
+it emits photons at whatever wavelength
+right it emits electromagnetic radiation
+
+ align:start position:0%
+right it emits electromagnetic radiation
+ 
+
+ align:start position:0%
+right it emits electromagnetic radiation
+that carries the heat away from my
+
+ align:start position:0%
+that carries the heat away from my
+ 
+
+ align:start position:0%
+that carries the heat away from my
+device okay and you know depending upon
+
+ align:start position:0%
+device okay and you know depending upon
+ 
+
+ align:start position:0%
+device okay and you know depending upon
+the application all three of these can
+
+ align:start position:0%
+the application all three of these can
+ 
+
+ align:start position:0%
+the application all three of these can
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+important however um you know
+
+ align:start position:0%
+important however um you know
+ 
+
+ align:start position:0%
+important however um you know
+radiation if I looked at the rate of
+
+ align:start position:0%
+radiation if I looked at the rate of
+ 
+
+ align:start position:0%
+radiation if I looked at the rate of
+heat
+
+ align:start position:0%
+heat
+ 
+
+ align:start position:0%
+heat
+transfer so this is sort of heat power
+
+ align:start position:0%
+transfer so this is sort of heat power
+ 
+
+ align:start position:0%
+transfer so this is sort of heat power
+being transferred tends to be
+
+ align:start position:0%
+being transferred tends to be
+ 
+
+ align:start position:0%
+being transferred tends to be
+proportional to the source thing that's
+
+ align:start position:0%
+proportional to the source thing that's
+ 
+
+ align:start position:0%
+proportional to the source thing that's
+delivering the heat away to the fourth
+
+ align:start position:0%
+delivering the heat away to the fourth
+ 
+
+ align:start position:0%
+delivering the heat away to the fourth
+power minus the environment around it to
+
+ align:start position:0%
+power minus the environment around it to
+ 
+
+ align:start position:0%
+power minus the environment around it to
+the fourth power okay so this High to
+
+ align:start position:0%
+the fourth power okay so this High to
+ 
+
+ align:start position:0%
+the fourth power okay so this High to
+the fourth power means that when things
+
+ align:start position:0%
+the fourth power means that when things
+ 
+
+ align:start position:0%
+the fourth power means that when things
+get really
+
+ align:start position:0%
+get really
+ 
+
+ align:start position:0%
+get really
+hot radiation really dominates heat
+
+ align:start position:0%
+hot radiation really dominates heat
+ 
+
+ align:start position:0%
+hot radiation really dominates heat
+transfer but for most terrestrial
+
+ align:start position:0%
+transfer but for most terrestrial
+ 
+
+ align:start position:0%
+transfer but for most terrestrial
+applications it's not the highest it's
+
+ align:start position:0%
+applications it's not the highest it's
+ 
+
+ align:start position:0%
+applications it's not the highest it's
+not the most important thing right so if
+
+ align:start position:0%
+not the most important thing right so if
+ 
+
+ align:start position:0%
+not the most important thing right so if
+I have an incandescent light bulb and
+
+ align:start position:0%
+I have an incandescent light bulb and
+ 
+
+ align:start position:0%
+I have an incandescent light bulb and
+it's really really hot right then yeah a
+
+ align:start position:0%
+it's really really hot right then yeah a
+ 
+
+ align:start position:0%
+it's really really hot right then yeah a
+large part of the energy may get out of
+
+ align:start position:0%
+large part of the energy may get out of
+ 
+
+ align:start position:0%
+large part of the energy may get out of
+it by just radiating away from it okay
+
+ align:start position:0%
+it by just radiating away from it okay
+ 
+
+ align:start position:0%
+it by just radiating away from it okay
+as black body radiation um if
+
+ align:start position:0%
+as black body radiation um if
+ 
+
+ align:start position:0%
+as black body radiation um if
+I'm in a satellite and there's no way
+
+ align:start position:0%
+I'm in a satellite and there's no way
+ 
+
+ align:start position:0%
+I'm in a satellite and there's no way
+for heat to conduct out of the thing and
+
+ align:start position:0%
+for heat to conduct out of the thing and
+ 
+
+ align:start position:0%
+for heat to conduct out of the thing and
+there's no air or anything out for the
+
+ align:start position:0%
+there's no air or anything out for the
+ 
+
+ align:start position:0%
+there's no air or anything out for the
+heat to go into well then eventually all
+
+ align:start position:0%
+heat to go into well then eventually all
+ 
+
+ align:start position:0%
+heat to go into well then eventually all
+the Heat's going to go away from that
+
+ align:start position:0%
+the Heat's going to go away from that
+ 
+
+ align:start position:0%
+the Heat's going to go away from that
+thing by radiation so in those kind of
+
+ align:start position:0%
+thing by radiation so in those kind of
+ 
+
+ align:start position:0%
+thing by radiation so in those kind of
+applications yeah I really May care very
+
+ align:start position:0%
+applications yeah I really May care very
+ 
+
+ align:start position:0%
+applications yeah I really May care very
+heavily about radiation but in most
+
+ align:start position:0%
+heavily about radiation but in most
+ 
+
+ align:start position:0%
+heavily about radiation but in most
+cases it's only a smallish fraction of
+
+ align:start position:0%
+cases it's only a smallish fraction of
+ 
+
+ align:start position:0%
+cases it's only a smallish fraction of
+the heat I'm getting rid of because we
+
+ align:start position:0%
+the heat I'm getting rid of because we
+ 
+
+ align:start position:0%
+the heat I'm getting rid of because we
+don't you know we don't get crazy high
+
+ align:start position:0%
+don't you know we don't get crazy high
+ 
+
+ align:start position:0%
+don't you know we don't get crazy high
+temperatures we don't have thousands of
+
+ align:start position:0%
+temperatures we don't have thousands of
+ 
+
+ align:start position:0%
+temperatures we don't have thousands of
+degrees Kelvin to to remove the
+
+ align:start position:0%
+degrees Kelvin to to remove the
+ 
+
+ align:start position:0%
+degrees Kelvin to to remove the
+heat okay um so let's go back and look
+
+ align:start position:0%
+heat okay um so let's go back and look
+ 
+
+ align:start position:0%
+heat okay um so let's go back and look
+at convection and conduction I'll start
+
+ align:start position:0%
+at convection and conduction I'll start
+ 
+
+ align:start position:0%
+at convection and conduction I'll start
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+conduction okay suppose I
+
+ align:start position:0%
+conduction okay suppose I
+ 
+
+ align:start position:0%
+conduction okay suppose I
+took
+
+ align:start position:0%
+took
+ 
+
+ align:start position:0%
+took
+um actually I I'll just go over here
+
+ align:start position:0%
+um actually I I'll just go over here
+ 
+
+ align:start position:0%
+um actually I I'll just go over here
+suppose I took
+
+ align:start position:0%
+suppose I took
+ 
+
+ align:start position:0%
+suppose I took
+some PL I I'll keep everything 1D and
+
+ align:start position:0%
+some PL I I'll keep everything 1D and
+ 
+
+ align:start position:0%
+some PL I I'll keep everything 1D and
+I'll get
+
+ align:start position:0%
+I'll get
+ 
+
+ align:start position:0%
+I'll get
+some thing that I'll put at temperature
+
+ align:start position:0%
+some thing that I'll put at temperature
+ 
+
+ align:start position:0%
+some thing that I'll put at temperature
+T1 okay and then I'll have some block of
+
+ align:start position:0%
+T1 okay and then I'll have some block of
+ 
+
+ align:start position:0%
+T1 okay and then I'll have some block of
+material
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay and I will
+
+ align:start position:0%
+okay okay and I will
+ 
+
+ align:start position:0%
+okay okay and I will
+have a second surface that I will keep a
+
+ align:start position:0%
+have a second surface that I will keep a
+ 
+
+ align:start position:0%
+have a second surface that I will keep a
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+T2 right and in between them I have some
+
+ align:start position:0%
+T2 right and in between them I have some
+ 
+
+ align:start position:0%
+T2 right and in between them I have some
+material through which Heat's going to
+
+ align:start position:0%
+material through which Heat's going to
+ 
+
+ align:start position:0%
+material through which Heat's going to
+flow it's going to conduct
+
+ align:start position:0%
+flow it's going to conduct
+ 
+
+ align:start position:0%
+flow it's going to conduct
+okay and this material whatever it
+
+ align:start position:0%
+okay and this material whatever it
+ 
+
+ align:start position:0%
+okay and this material whatever it
+is um might have some cross-sectional
+
+ align:start position:0%
+is um might have some cross-sectional
+ 
+
+ align:start position:0%
+is um might have some cross-sectional
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+a and it might be transferring heat
+
+ align:start position:0%
+a and it might be transferring heat
+ 
+
+ align:start position:0%
+a and it might be transferring heat
+through some length L right and in this
+
+ align:start position:0%
+through some length L right and in this
+ 
+
+ align:start position:0%
+through some length L right and in this
+kind of situation with 1D heat transfer
+
+ align:start position:0%
+kind of situation with 1D heat transfer
+ 
+
+ align:start position:0%
+kind of situation with 1D heat transfer
+you for many materials what you get is
+
+ align:start position:0%
+you for many materials what you get is
+ 
+
+ align:start position:0%
+you for many materials what you get is
+the following relationship
+
+ align:start position:0%
+the following relationship
+ 
+
+ align:start position:0%
+the following relationship
+um Q that's the the amount of heat
+
+ align:start position:0%
+um Q that's the the amount of heat
+ 
+
+ align:start position:0%
+um Q that's the the amount of heat
+transferred is um proportional to the
+
+ align:start position:0%
+transferred is um proportional to the
+ 
+
+ align:start position:0%
+transferred is um proportional to the
+temperature difference T1 minus
+
+ align:start position:0%
+temperature difference T1 minus
+ 
+
+ align:start position:0%
+temperature difference T1 minus
+T2 okay um times the um cross-sectional
+
+ align:start position:0%
+T2 okay um times the um cross-sectional
+ 
+
+ align:start position:0%
+T2 okay um times the um cross-sectional
+area divided by the thermal resistance
+
+ align:start position:0%
+area divided by the thermal resistance
+ 
+
+ align:start position:0%
+area divided by the thermal resistance
+rth and divided by the length right so
+
+ align:start position:0%
+rth and divided by the length right so
+ 
+
+ align:start position:0%
+rth and divided by the length right so
+if I have more cross-sectional area more
+
+ align:start position:0%
+if I have more cross-sectional area more
+ 
+
+ align:start position:0%
+if I have more cross-sectional area more
+heat flows if I have to transfer it
+
+ align:start position:0%
+heat flows if I have to transfer it
+ 
+
+ align:start position:0%
+heat flows if I have to transfer it
+through a thicker piece of material the
+
+ align:start position:0%
+through a thicker piece of material the
+ 
+
+ align:start position:0%
+through a thicker piece of material the
+heat flow goes down and this
+
+ align:start position:0%
+heat flow goes down and this
+ 
+
+ align:start position:0%
+heat flow goes down and this
+proportionality constant is called the
+
+ align:start position:0%
+proportionality constant is called the
+ 
+
+ align:start position:0%
+proportionality constant is called the
+thermal resistivity of the material okay
+
+ align:start position:0%
+thermal resistivity of the material okay
+ 
+
+ align:start position:0%
+thermal resistivity of the material okay
+I could rewrite this as um T1 minus T2
+
+ align:start position:0%
+I could rewrite this as um T1 minus T2
+ 
+
+ align:start position:0%
+I could rewrite this as um T1 minus T2
+divided by rth * L / a that would be
+
+ align:start position:0%
+divided by rth * L / a that would be
+ 
+
+ align:start position:0%
+divided by rth * L / a that would be
+another way to write this okay so this
+
+ align:start position:0%
+another way to write this okay so this
+ 
+
+ align:start position:0%
+another way to write this okay so this
+would reflect how heat this would be
+
+ align:start position:0%
+would reflect how heat this would be
+ 
+
+ align:start position:0%
+would reflect how heat this would be
+reflect conduction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of heat okay in steady state
+
+ align:start position:0%
+of heat okay in steady state
+ 
+
+ align:start position:0%
+of heat okay in steady state
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this relationship and this is sort of
+
+ align:start position:0%
+um this relationship and this is sort of
+ 
+
+ align:start position:0%
+um this relationship and this is sort of
+a bulk relationship right I could create
+
+ align:start position:0%
+a bulk relationship right I could create
+ 
+
+ align:start position:0%
+a bulk relationship right I could create
+an A A an incremental relationship uh
+
+ align:start position:0%
+an A A an incremental relationship uh
+ 
+
+ align:start position:0%
+an A A an incremental relationship uh
+which would be you know Q is equal to
+
+ align:start position:0%
+which would be you know Q is equal to
+ 
+
+ align:start position:0%
+which would be you know Q is equal to
+minus a over row t d D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+TDX okay that would be you know if I
+
+ align:start position:0%
+TDX okay that would be you know if I
+ 
+
+ align:start position:0%
+TDX okay that would be you know if I
+treated everything as a little increment
+
+ align:start position:0%
+treated everything as a little increment
+ 
+
+ align:start position:0%
+treated everything as a little increment
+in space and if I want to start doing 4A
+
+ align:start position:0%
+in space and if I want to start doing 4A
+ 
+
+ align:start position:0%
+in space and if I want to start doing 4A
+heat transfer I get into um these kind
+
+ align:start position:0%
+heat transfer I get into um these kind
+ 
+
+ align:start position:0%
+heat transfer I get into um these kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+um kind of differential equations
+
+ align:start position:0%
+um kind of differential equations
+ 
+
+ align:start position:0%
+um kind of differential equations
+descriptions but for a bulk piece of
+
+ align:start position:0%
+descriptions but for a bulk piece of
+ 
+
+ align:start position:0%
+descriptions but for a bulk piece of
+element we can write it like this okay
+
+ align:start position:0%
+element we can write it like this okay
+ 
+
+ align:start position:0%
+element we can write it like this okay
+this relationship where q q is my heat
+
+ align:start position:0%
+this relationship where q q is my heat
+ 
+
+ align:start position:0%
+this relationship where q q is my heat
+flow right so Q is whatever Heat flowing
+
+ align:start position:0%
+flow right so Q is whatever Heat flowing
+ 
+
+ align:start position:0%
+flow right so Q is whatever Heat flowing
+this way okay sort of suggests circuit
+
+ align:start position:0%
+this way okay sort of suggests circuit
+ 
+
+ align:start position:0%
+this way okay sort of suggests circuit
+analog right where here's my circuit
+
+ align:start position:0%
+analog right where here's my circuit
+ 
+
+ align:start position:0%
+analog right where here's my circuit
+model I have some temperature
+
+ align:start position:0%
+model I have some temperature
+ 
+
+ align:start position:0%
+model I have some temperature
+Source
+
+ align:start position:0%
+Source
+ 
+
+ align:start position:0%
+Source
+T1 and another temperature Source or
+
+ align:start position:0%
+T1 and another temperature Source or
+ 
+
+ align:start position:0%
+T1 and another temperature Source or
+temperature sync T2 right so temperature
+
+ align:start position:0%
+temperature sync T2 right so temperature
+ 
+
+ align:start position:0%
+temperature sync T2 right so temperature
+now it means a voltage source here means
+
+ align:start position:0%
+now it means a voltage source here means
+ 
+
+ align:start position:0%
+now it means a voltage source here means
+constant temperature okay and then
+
+ align:start position:0%
+constant temperature okay and then
+ 
+
+ align:start position:0%
+constant temperature okay and then
+there's between them some thermal
+
+ align:start position:0%
+there's between them some thermal
+ 
+
+ align:start position:0%
+there's between them some thermal
+resistance rth
+
+ align:start position:0%
+resistance rth
+ 
+
+ align:start position:0%
+resistance rth
+which is equal to row T * L over
+
+ align:start position:0%
+which is equal to row T * L over
+ 
+
+ align:start position:0%
+which is equal to row T * L over
+a okay and that has the same form as an
+
+ align:start position:0%
+a okay and that has the same form as an
+ 
+
+ align:start position:0%
+a okay and that has the same form as an
+electrical resistor okay and then my
+
+ align:start position:0%
+electrical resistor okay and then my
+ 
+
+ align:start position:0%
+electrical resistor okay and then my
+heat flow
+
+ align:start position:0%
+heat flow
+ 
+
+ align:start position:0%
+heat flow
+Q is sort of the current flowing around
+
+ align:start position:0%
+Q is sort of the current flowing around
+ 
+
+ align:start position:0%
+Q is sort of the current flowing around
+this Loop and
+
+ align:start position:0%
+this Loop and
+ 
+
+ align:start position:0%
+this Loop and
+here right I have
+
+ align:start position:0%
+here right I have
+ 
+
+ align:start position:0%
+here right I have
+some point to which these temperatures
+
+ align:start position:0%
+some point to which these temperatures
+ 
+
+ align:start position:0%
+some point to which these temperatures
+are referenced ideally speaking this
+
+ align:start position:0%
+are referenced ideally speaking this
+ 
+
+ align:start position:0%
+are referenced ideally speaking this
+should be absolute zero in practice
+
+ align:start position:0%
+should be absolute zero in practice
+ 
+
+ align:start position:0%
+should be absolute zero in practice
+people often just just represent
+
+ align:start position:0%
+people often just just represent
+ 
+
+ align:start position:0%
+people often just just represent
+reference it to ambient and pretend
+
+ align:start position:0%
+reference it to ambient and pretend
+ 
+
+ align:start position:0%
+reference it to ambient and pretend
+ambient is the equivalent of absolute
+
+ align:start position:0%
+ambient is the equivalent of absolute
+ 
+
+ align:start position:0%
+ambient is the equivalent of absolute
+zero it' be kind of like having an
+
+ align:start position:0%
+zero it' be kind of like having an
+ 
+
+ align:start position:0%
+zero it' be kind of like having an
+offset from off absolute zero okay any
+
+ align:start position:0%
+offset from off absolute zero okay any
+ 
+
+ align:start position:0%
+offset from off absolute zero okay any
+questions about that structure you get
+
+ align:start position:0%
+questions about that structure you get
+ 
+
+ align:start position:0%
+questions about that structure you get
+you know if you Analyze This circuit you
+
+ align:start position:0%
+you know if you Analyze This circuit you
+ 
+
+ align:start position:0%
+you know if you Analyze This circuit you
+get exactly this
+
+ align:start position:0%
+get exactly this
+ 
+
+ align:start position:0%
+get exactly this
+relationship Okay the reason this works
+
+ align:start position:0%
+relationship Okay the reason this works
+ 
+
+ align:start position:0%
+relationship Okay the reason this works
+is sort of temperature is conserved
+
+ align:start position:0%
+is sort of temperature is conserved
+ 
+
+ align:start position:0%
+is sort of temperature is conserved
+going around any Loop right if I measure
+
+ align:start position:0%
+going around any Loop right if I measure
+ 
+
+ align:start position:0%
+going around any Loop right if I measure
+temperature differences around a loop I
+
+ align:start position:0%
+temperature differences around a loop I
+ 
+
+ align:start position:0%
+temperature differences around a loop I
+would get zero and you know if I
+
+ align:start position:0%
+would get zero and you know if I
+ 
+
+ align:start position:0%
+would get zero and you know if I
+consider heat inputs and Heat transfers
+
+ align:start position:0%
+consider heat inputs and Heat transfers
+ 
+
+ align:start position:0%
+consider heat inputs and Heat transfers
+conservation of power is sort of the
+
+ align:start position:0%
+conservation of power is sort of the
+ 
+
+ align:start position:0%
+conservation of power is sort of the
+equivalent of KCl in the circuit model
+
+ align:start position:0%
+equivalent of KCl in the circuit model
+ 
+
+ align:start position:0%
+equivalent of KCl in the circuit model
+so I you know I'm showing you a
+
+ align:start position:0%
+so I you know I'm showing you a
+ 
+
+ align:start position:0%
+so I you know I'm showing you a
+simplified circuit model for a very
+
+ align:start position:0%
+simplified circuit model for a very
+ 
+
+ align:start position:0%
+simplified circuit model for a very
+particular kind of heat transfer but you
+
+ align:start position:0%
+particular kind of heat transfer but you
+ 
+
+ align:start position:0%
+particular kind of heat transfer but you
+can use this model to represent heat
+
+ align:start position:0%
+can use this model to represent heat
+ 
+
+ align:start position:0%
+can use this model to represent heat
+transfers in a variety of conditions any
+
+ align:start position:0%
+transfers in a variety of conditions any
+ 
+
+ align:start position:0%
+transfers in a variety of conditions any
+questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so okay so I should say by the way
+
+ align:start position:0%
+that so okay so I should say by the way
+ 
+
+ align:start position:0%
+that so okay so I should say by the way
+Q is in Watts
+
+ align:start position:0%
+Q is in Watts
+ 
+
+ align:start position:0%
+Q is in Watts
+right that's the heat flow in Watts T is
+
+ align:start position:0%
+right that's the heat flow in Watts T is
+ 
+
+ align:start position:0%
+right that's the heat flow in Watts T is
+in kelvin or often people use it in
+
+ align:start position:0%
+in kelvin or often people use it in
+ 
+
+ align:start position:0%
+in kelvin or often people use it in
+degrees
+
+ align:start position:0%
+degrees
+ 
+
+ align:start position:0%
+degrees
+cels and
+
+ align:start position:0%
+cels and
+ 
+
+ align:start position:0%
+cels and
+rth ends up having units of degree C per
+
+ align:start position:0%
+rth ends up having units of degree C per
+ 
+
+ align:start position:0%
+rth ends up having units of degree C per
+watt or kelvin per
+
+ align:start position:0%
+watt or kelvin per
+ 
+
+ align:start position:0%
+watt or kelvin per
+watt
+
+ align:start position:0%
+watt
+ 
+
+ align:start position:0%
+watt
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+um in this regard thermal resistance is
+
+ align:start position:0%
+um in this regard thermal resistance is
+ 
+
+ align:start position:0%
+um in this regard thermal resistance is
+very like regular resistance right
+
+ align:start position:0%
+very like regular resistance right
+ 
+
+ align:start position:0%
+very like regular resistance right
+because if I think about a regular
+
+ align:start position:0%
+because if I think about a regular
+ 
+
+ align:start position:0%
+because if I think about a regular
+resistor right if I make the resistor
+
+ align:start position:0%
+resistor right if I make the resistor
+ 
+
+ align:start position:0%
+resistor right if I make the resistor
+proportionately longer the thermal
+
+ align:start position:0%
+proportionately longer the thermal
+ 
+
+ align:start position:0%
+proportionately longer the thermal
+resistance goes up if I increase the
+
+ align:start position:0%
+resistance goes up if I increase the
+ 
+
+ align:start position:0%
+resistance goes up if I increase the
+cross-sectional area the thermal
+
+ align:start position:0%
+cross-sectional area the thermal
+ 
+
+ align:start position:0%
+cross-sectional area the thermal
+resistance goes down and here all I have
+
+ align:start position:0%
+resistance goes down and here all I have
+ 
+
+ align:start position:0%
+resistance goes down and here all I have
+is thermal resistivity instead of
+
+ align:start position:0%
+is thermal resistivity instead of
+ 
+
+ align:start position:0%
+is thermal resistivity instead of
+electrical resistivity so the form of
+
+ align:start position:0%
+electrical resistivity so the form of
+ 
+
+ align:start position:0%
+electrical resistivity so the form of
+the relationships are exactly the same
+
+ align:start position:0%
+the relationships are exactly the same
+ 
+
+ align:start position:0%
+the relationships are exactly the same
+all right so um you know basically we
+
+ align:start position:0%
+all right so um you know basically we
+ 
+
+ align:start position:0%
+all right so um you know basically we
+can assume all of our devices in steady
+
+ align:start position:0%
+can assume all of our devices in steady
+ 
+
+ align:start position:0%
+can assume all of our devices in steady
+state have some thermal resistances we
+
+ align:start position:0%
+state have some thermal resistances we
+ 
+
+ align:start position:0%
+state have some thermal resistances we
+can put Power into the system if we know
+
+ align:start position:0%
+can put Power into the system if we know
+ 
+
+ align:start position:0%
+can put Power into the system if we know
+some fixed temperatures like some
+
+ align:start position:0%
+some fixed temperatures like some
+ 
+
+ align:start position:0%
+some fixed temperatures like some
+ambient temperatures we can create a
+
+ align:start position:0%
+ambient temperatures we can create a
+ 
+
+ align:start position:0%
+ambient temperatures we can create a
+circuit and then analyze what our heat
+
+ align:start position:0%
+circuit and then analyze what our heat
+ 
+
+ align:start position:0%
+circuit and then analyze what our heat
+flows will look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like this is conduction what might my
+
+ align:start position:0%
+like this is conduction what might my
+ 
+
+ align:start position:0%
+like this is conduction what might my
+other uh means of transferring energy a
+
+ align:start position:0%
+other uh means of transferring energy a
+ 
+
+ align:start position:0%
+other uh means of transferring energy a
+heat energy look like well my my other
+
+ align:start position:0%
+heat energy look like well my my other
+ 
+
+ align:start position:0%
+heat energy look like well my my other
+means of heat transferring energy might
+
+ align:start position:0%
+means of heat transferring energy might
+ 
+
+ align:start position:0%
+means of heat transferring energy might
+be something like this right I've got
+
+ align:start position:0%
+be something like this right I've got
+ 
+
+ align:start position:0%
+be something like this right I've got
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+structure which you know has Heat going
+
+ align:start position:0%
+structure which you know has Heat going
+ 
+
+ align:start position:0%
+structure which you know has Heat going
+into it it and then some fluid going
+
+ align:start position:0%
+into it it and then some fluid going
+ 
+
+ align:start position:0%
+into it it and then some fluid going
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+it you know this could be a flow of air
+
+ align:start position:0%
+it you know this could be a flow of air
+ 
+
+ align:start position:0%
+it you know this could be a flow of air
+or a flow of water or something like
+
+ align:start position:0%
+or a flow of water or something like
+ 
+
+ align:start position:0%
+or a flow of water or something like
+that and what we expect to happen is the
+
+ align:start position:0%
+that and what we expect to happen is the
+ 
+
+ align:start position:0%
+that and what we expect to happen is the
+heat is going to come out of whatever
+
+ align:start position:0%
+heat is going to come out of whatever
+ 
+
+ align:start position:0%
+heat is going to come out of whatever
+the item is up into the air and then the
+
+ align:start position:0%
+the item is up into the air and then the
+ 
+
+ align:start position:0%
+the item is up into the air and then the
+air is going to carry it away okay so
+
+ align:start position:0%
+air is going to carry it away okay so
+ 
+
+ align:start position:0%
+air is going to carry it away okay so
+I'm going to transfer the heat into the
+
+ align:start position:0%
+I'm going to transfer the heat into the
+ 
+
+ align:start position:0%
+I'm going to transfer the heat into the
+moving fluid and the moving fluid kind
+
+ align:start position:0%
+moving fluid and the moving fluid kind
+ 
+
+ align:start position:0%
+moving fluid and the moving fluid kind
+of walks away with it
+
+ align:start position:0%
+of walks away with it
+ 
+
+ align:start position:0%
+of walks away with it
+okay um what does this look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um heat transfer for this case looks
+
+ align:start position:0%
+um heat transfer for this case looks
+ 
+
+ align:start position:0%
+um heat transfer for this case looks
+like Q is the heat transfer is equal to
+
+ align:start position:0%
+like Q is the heat transfer is equal to
+ 
+
+ align:start position:0%
+like Q is the heat transfer is equal to
+ha time the temperature of the
+
+ align:start position:0%
+ha time the temperature of the
+ 
+
+ align:start position:0%
+ha time the temperature of the
+surface minus the temperature of the
+
+ align:start position:0%
+surface minus the temperature of the
+ 
+
+ align:start position:0%
+surface minus the temperature of the
+fluid right so if I have some fluid at T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fluid and I have some you know
+
+ align:start position:0%
+fluid and I have some you know
+ 
+
+ align:start position:0%
+fluid and I have some you know
+temperature at the surface T
+
+ align:start position:0%
+temperature at the surface T
+ 
+
+ align:start position:0%
+temperature at the surface T
+surface right the Heat transfer again
+
+ align:start position:0%
+surface right the Heat transfer again
+ 
+
+ align:start position:0%
+surface right the Heat transfer again
+IDE in some range is going to be
+
+ align:start position:0%
+IDE in some range is going to be
+ 
+
+ align:start position:0%
+IDE in some range is going to be
+proportional to the temperature
+
+ align:start position:0%
+proportional to the temperature
+ 
+
+ align:start position:0%
+proportional to the temperature
+difference between the surface of this
+
+ align:start position:0%
+difference between the surface of this
+ 
+
+ align:start position:0%
+difference between the surface of this
+thing and the fluid that's carrying the
+
+ align:start position:0%
+thing and the fluid that's carrying the
+ 
+
+ align:start position:0%
+thing and the fluid that's carrying the
+heat away and this is the so-called uh
+
+ align:start position:0%
+heat away and this is the so-called uh
+ 
+
+ align:start position:0%
+heat away and this is the so-called uh
+wetted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area right this is the area at the
+
+ align:start position:0%
+area right this is the area at the
+ 
+
+ align:start position:0%
+area right this is the area at the
+interface that the the fluid's flowing
+
+ align:start position:0%
+interface that the the fluid's flowing
+ 
+
+ align:start position:0%
+interface that the the fluid's flowing
+over to grab the Heat and carry it away
+
+ align:start position:0%
+over to grab the Heat and carry it away
+ 
+
+ align:start position:0%
+over to grab the Heat and carry it away
+and then this is the heat transfer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coefficient all right now here's where
+
+ align:start position:0%
+coefficient all right now here's where
+ 
+
+ align:start position:0%
+coefficient all right now here's where
+you know it's right
+
+ align:start position:0%
+you know it's right
+ 
+
+ align:start position:0%
+you know it's right
+here is essentially where I'm burying
+
+ align:start position:0%
+here is essentially where I'm burying
+ 
+
+ align:start position:0%
+here is essentially where I'm burying
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+ugliness okay this is where I'm you know
+
+ align:start position:0%
+ugliness okay this is where I'm you know
+ 
+
+ align:start position:0%
+ugliness okay this is where I'm you know
+massively oversimplifying it and the
+
+ align:start position:0%
+massively oversimplifying it and the
+ 
+
+ align:start position:0%
+massively oversimplifying it and the
+reason you can take whole courses in
+
+ align:start position:0%
+reason you can take whole courses in
+ 
+
+ align:start position:0%
+reason you can take whole courses in
+this TR whole courses in this topic is
+
+ align:start position:0%
+this TR whole courses in this topic is
+ 
+
+ align:start position:0%
+this TR whole courses in this topic is
+because you know what is this heat
+
+ align:start position:0%
+because you know what is this heat
+ 
+
+ align:start position:0%
+because you know what is this heat
+transfer coefficient well it depends
+
+ align:start position:0%
+transfer coefficient well it depends
+ 
+
+ align:start position:0%
+transfer coefficient well it depends
+upon is the flow laminer or turbulent it
+
+ align:start position:0%
+upon is the flow laminer or turbulent it
+ 
+
+ align:start position:0%
+upon is the flow laminer or turbulent it
+depends upon all kinds of stuff right
+
+ align:start position:0%
+depends upon all kinds of stuff right
+ 
+
+ align:start position:0%
+depends upon all kinds of stuff right
+and it can even be a fun function of
+
+ align:start position:0%
+and it can even be a fun function of
+ 
+
+ align:start position:0%
+and it can even be a fun function of
+temperatures in the general case Okay um
+
+ align:start position:0%
+temperatures in the general case Okay um
+ 
+
+ align:start position:0%
+temperatures in the general case Okay um
+so you know I have to tell you I'm
+
+ align:start position:0%
+so you know I have to tell you I'm
+ 
+
+ align:start position:0%
+so you know I have to tell you I'm
+telling you this magic number how you
+
+ align:start position:0%
+telling you this magic number how you
+ 
+
+ align:start position:0%
+telling you this magic number how you
+find that magic number is tricky in a
+
+ align:start position:0%
+find that magic number is tricky in a
+ 
+
+ align:start position:0%
+find that magic number is tricky in a
+lot of cases okay what we're going to
+
+ align:start position:0%
+lot of cases okay what we're going to
+ 
+
+ align:start position:0%
+lot of cases okay what we're going to
+see as designers we often don't have to
+
+ align:start position:0%
+see as designers we often don't have to
+ 
+
+ align:start position:0%
+see as designers we often don't have to
+worry about that okay so in this case I
+
+ align:start position:0%
+worry about that okay so in this case I
+ 
+
+ align:start position:0%
+worry about that okay so in this case I
+could kind of have the same model where
+
+ align:start position:0%
+could kind of have the same model where
+ 
+
+ align:start position:0%
+could kind of have the same model where
+I would just say Okay
+
+ align:start position:0%
+I would just say Okay
+ 
+
+ align:start position:0%
+I would just say Okay
+rth is simply equal to ha inverse right
+
+ align:start position:0%
+rth is simply equal to ha inverse right
+ 
+
+ align:start position:0%
+rth is simply equal to ha inverse right
+if I told you the area through which I
+
+ align:start position:0%
+if I told you the area through which I
+ 
+
+ align:start position:0%
+if I told you the area through which I
+was transferring heat and I knew that
+
+ align:start position:0%
+was transferring heat and I knew that
+ 
+
+ align:start position:0%
+was transferring heat and I knew that
+heat transfer
+
+ align:start position:0%
+heat transfer
+ 
+
+ align:start position:0%
+heat transfer
+coefficient great I've got my answer and
+
+ align:start position:0%
+coefficient great I've got my answer and
+ 
+
+ align:start position:0%
+coefficient great I've got my answer and
+I go my Merry way all right so putting
+
+ align:start position:0%
+I go my Merry way all right so putting
+ 
+
+ align:start position:0%
+I go my Merry way all right so putting
+aside that it's difficult to find this
+
+ align:start position:0%
+aside that it's difficult to find this
+ 
+
+ align:start position:0%
+aside that it's difficult to find this
+number or in some cases this equivalent
+
+ align:start position:0%
+number or in some cases this equivalent
+ 
+
+ align:start position:0%
+number or in some cases this equivalent
+number um you know we have a means of
+
+ align:start position:0%
+number um you know we have a means of
+ 
+
+ align:start position:0%
+number um you know we have a means of
+predicting what it is and I can just
+
+ align:start position:0%
+predicting what it is and I can just
+ 
+
+ align:start position:0%
+predicting what it is and I can just
+model that heat transfer as a thermal
+
+ align:start position:0%
+model that heat transfer as a thermal
+ 
+
+ align:start position:0%
+model that heat transfer as a thermal
+resistor again okay any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so how might we use this
+
+ align:start position:0%
+that so how might we use this
+ 
+
+ align:start position:0%
+that so how might we use this
+okay well in the typical
+
+ align:start position:0%
+okay well in the typical
+ 
+
+ align:start position:0%
+okay well in the typical
+case right um I'm going to dissipate
+
+ align:start position:0%
+case right um I'm going to dissipate
+ 
+
+ align:start position:0%
+case right um I'm going to dissipate
+some power in my
+
+ align:start position:0%
+some power in my
+ 
+
+ align:start position:0%
+some power in my
+device I've got to connect that device
+
+ align:start position:0%
+device I've got to connect that device
+ 
+
+ align:start position:0%
+device I've got to connect that device
+through some heat transfer means and the
+
+ align:start position:0%
+through some heat transfer means and the
+ 
+
+ align:start position:0%
+through some heat transfer means and the
+heat transfer is going to carry it away
+
+ align:start position:0%
+heat transfer is going to carry it away
+ 
+
+ align:start position:0%
+heat transfer is going to carry it away
+okay so here's a typical
+
+ align:start position:0%
+okay so here's a typical
+ 
+
+ align:start position:0%
+okay so here's a typical
+structure um you know maybe I have some
+
+ align:start position:0%
+structure um you know maybe I have some
+ 
+
+ align:start position:0%
+structure um you know maybe I have some
+power device this could be a mosfet okay
+
+ align:start position:0%
+power device this could be a mosfet okay
+ 
+
+ align:start position:0%
+power device this could be a mosfet okay
+and basically somewhere inside this
+
+ align:start position:0%
+and basically somewhere inside this
+ 
+
+ align:start position:0%
+and basically somewhere inside this
+device I'm dissipating a bunch of power
+
+ align:start position:0%
+device I'm dissipating a bunch of power
+ 
+
+ align:start position:0%
+device I'm dissipating a bunch of power
+right so that's a source of heat okay
+
+ align:start position:0%
+right so that's a source of heat okay
+ 
+
+ align:start position:0%
+right so that's a source of heat okay
+and then what I'm going to do is I'm
+
+ align:start position:0%
+and then what I'm going to do is I'm
+ 
+
+ align:start position:0%
+and then what I'm going to do is I'm
+going to say okay I need to connect that
+
+ align:start position:0%
+going to say okay I need to connect that
+ 
+
+ align:start position:0%
+going to say okay I need to connect that
+um down onto a heat sink and here when I
+
+ align:start position:0%
+um down onto a heat sink and here when I
+ 
+
+ align:start position:0%
+um down onto a heat sink and here when I
+connect this device I'm going to have
+
+ align:start position:0%
+connect this device I'm going to have
+ 
+
+ align:start position:0%
+connect this device I'm going to have
+some thermal I'm going to have some
+
+ align:start position:0%
+some thermal I'm going to have some
+ 
+
+ align:start position:0%
+some thermal I'm going to have some
+interface here okay what is that
+
+ align:start position:0%
+interface here okay what is that
+ 
+
+ align:start position:0%
+interface here okay what is that
+interface um I'll talk about that in a
+
+ align:start position:0%
+interface um I'll talk about that in a
+ 
+
+ align:start position:0%
+interface um I'll talk about that in a
+second but that's going to be between
+
+ align:start position:0%
+second but that's going to be between
+ 
+
+ align:start position:0%
+second but that's going to be between
+the device and then maybe a heat sink
+
+ align:start position:0%
+the device and then maybe a heat sink
+ 
+
+ align:start position:0%
+the device and then maybe a heat sink
+okay and maybe this seat sink has a
+
+ align:start position:0%
+okay and maybe this seat sink has a
+ 
+
+ align:start position:0%
+okay and maybe this seat sink has a
+bunch of fins that's help designed to
+
+ align:start position:0%
+bunch of fins that's help designed to
+ 
+
+ align:start position:0%
+bunch of fins that's help designed to
+help me cool this thing and so the
+
+ align:start position:0%
+help me cool this thing and so the
+ 
+
+ align:start position:0%
+help me cool this thing and so the
+Heat's going to come from the device
+
+ align:start position:0%
+Heat's going to come from the device
+ 
+
+ align:start position:0%
+Heat's going to come from the device
+through this interface into the heat
+
+ align:start position:0%
+through this interface into the heat
+ 
+
+ align:start position:0%
+through this interface into the heat
+sink and then maybe the heat sink's
+
+ align:start position:0%
+sink and then maybe the heat sink's
+ 
+
+ align:start position:0%
+sink and then maybe the heat sink's
+transferring it off to uh you know by
+
+ align:start position:0%
+transferring it off to uh you know by
+ 
+
+ align:start position:0%
+transferring it off to uh you know by
+convection past the heat SN out into
+
+ align:start position:0%
+convection past the heat SN out into
+ 
+
+ align:start position:0%
+convection past the heat SN out into
+space around it and and then I forget
+
+ align:start position:0%
+space around it and and then I forget
+ 
+
+ align:start position:0%
+space around it and and then I forget
+about the heat right it's just going out
+
+ align:start position:0%
+about the heat right it's just going out
+ 
+
+ align:start position:0%
+about the heat right it's just going out
+somewhere okay well what is this
+
+ align:start position:0%
+somewhere okay well what is this
+ 
+
+ align:start position:0%
+somewhere okay well what is this
+interface this device here and let me
+
+ align:start position:0%
+interface this device here and let me
+ 
+
+ align:start position:0%
+interface this device here and let me
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+illustrate um you know just as an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example here is a typical
+
+ align:start position:0%
+example here is a typical
+ 
+
+ align:start position:0%
+example here is a typical
+mosfet okay this is in a to220 package
+
+ align:start position:0%
+mosfet okay this is in a to220 package
+ 
+
+ align:start position:0%
+mosfet okay this is in a to220 package
+which is you know maybe the not the most
+
+ align:start position:0%
+which is you know maybe the not the most
+ 
+
+ align:start position:0%
+which is you know maybe the not the most
+modern of packages but they're still
+
+ align:start position:0%
+modern of packages but they're still
+ 
+
+ align:start position:0%
+modern of packages but they're still
+used in a lot of cases and so the device
+
+ align:start position:0%
+used in a lot of cases and so the device
+ 
+
+ align:start position:0%
+used in a lot of cases and so the device
+is inside this plastic package these
+
+ align:start position:0%
+is inside this plastic package these
+ 
+
+ align:start position:0%
+is inside this plastic package these
+leads gate drain and Source are
+
+ align:start position:0%
+leads gate drain and Source are
+ 
+
+ align:start position:0%
+leads gate drain and Source are
+connected to the device and then one
+
+ align:start position:0%
+connected to the device and then one
+ 
+
+ align:start position:0%
+connected to the device and then one
+side of the device is connected down
+
+ align:start position:0%
+side of the device is connected down
+ 
+
+ align:start position:0%
+side of the device is connected down
+onto this pad through which you're going
+
+ align:start position:0%
+onto this pad through which you're going
+ 
+
+ align:start position:0%
+onto this pad through which you're going
+to transfer heat all right so that's
+
+ align:start position:0%
+to transfer heat all right so that's
+ 
+
+ align:start position:0%
+to transfer heat all right so that's
+sort of the case of the device so inside
+
+ align:start position:0%
+sort of the case of the device so inside
+ 
+
+ align:start position:0%
+sort of the case of the device so inside
+this package somewhere I'm dissipating
+
+ align:start position:0%
+this package somewhere I'm dissipating
+ 
+
+ align:start position:0%
+this package somewhere I'm dissipating
+heat and it goes to the case of the
+
+ align:start position:0%
+heat and it goes to the case of the
+ 
+
+ align:start position:0%
+heat and it goes to the case of the
+device then I'm going to mount that case
+
+ align:start position:0%
+device then I'm going to mount that case
+ 
+
+ align:start position:0%
+device then I'm going to mount that case
+of the device down to some heat sink
+
+ align:start position:0%
+of the device down to some heat sink
+ 
+
+ align:start position:0%
+of the device down to some heat sink
+okay but there is
+
+ align:start position:0%
+okay but there is
+ 
+
+ align:start position:0%
+okay but there is
+some interface to the heat sink now in a
+
+ align:start position:0%
+some interface to the heat sink now in a
+ 
+
+ align:start position:0%
+some interface to the heat sink now in a
+practical device it depends on the
+
+ align:start position:0%
+practical device it depends on the
+ 
+
+ align:start position:0%
+practical device it depends on the
+device type in this particular device
+
+ align:start position:0%
+device type in this particular device
+ 
+
+ align:start position:0%
+device type in this particular device
+this is a power mosfet that heat sink
+
+ align:start position:0%
+this is a power mosfet that heat sink
+ 
+
+ align:start position:0%
+this is a power mosfet that heat sink
+that terminal the device through which
+
+ align:start position:0%
+that terminal the device through which
+ 
+
+ align:start position:0%
+that terminal the device through which
+all the Heat's going to go is actually
+
+ align:start position:0%
+all the Heat's going to go is actually
+ 
+
+ align:start position:0%
+all the Heat's going to go is actually
+connected to the drain of the device to
+
+ align:start position:0%
+connected to the drain of the device to
+ 
+
+ align:start position:0%
+connected to the drain of the device to
+the to the high side the top side of the
+
+ align:start position:0%
+the to the high side the top side of the
+ 
+
+ align:start position:0%
+the to the high side the top side of the
+mosfet why because it's a vertical
+
+ align:start position:0%
+mosfet why because it's a vertical
+ 
+
+ align:start position:0%
+mosfet why because it's a vertical
+mosfet and that's the way they could
+
+ align:start position:0%
+mosfet and that's the way they could
+ 
+
+ align:start position:0%
+mosfet and that's the way they could
+connect it okay and so you know if that
+
+ align:start position:0%
+connect it okay and so you know if that
+ 
+
+ align:start position:0%
+connect it okay and so you know if that
+drain is say for a boost converter that
+
+ align:start position:0%
+drain is say for a boost converter that
+ 
+
+ align:start position:0%
+drain is say for a boost converter that
+may be flapping up and down in voltage
+
+ align:start position:0%
+may be flapping up and down in voltage
+ 
+
+ align:start position:0%
+may be flapping up and down in voltage
+so it's kind of unfortunate that you're
+
+ align:start position:0%
+so it's kind of unfortunate that you're
+ 
+
+ align:start position:0%
+so it's kind of unfortunate that you're
+trying to transfer heat out of something
+
+ align:start position:0%
+trying to transfer heat out of something
+ 
+
+ align:start position:0%
+trying to transfer heat out of something
+that's flying around in voltage right so
+
+ align:start position:0%
+that's flying around in voltage right so
+ 
+
+ align:start position:0%
+that's flying around in voltage right so
+in that
+
+ align:start position:0%
+in that
+ 
+
+ align:start position:0%
+in that
+case this thing might be a silicone
+
+ align:start position:0%
+case this thing might be a silicone
+ 
+
+ align:start position:0%
+case this thing might be a silicone
+insulation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pad okay what does that thing do it's
+
+ align:start position:0%
+pad okay what does that thing do it's
+ 
+
+ align:start position:0%
+pad okay what does that thing do it's
+essentially it's electrically insulating
+
+ align:start position:0%
+essentially it's electrically insulating
+ 
+
+ align:start position:0%
+essentially it's electrically insulating
+but reasonably thermally conductive so
+
+ align:start position:0%
+but reasonably thermally conductive so
+ 
+
+ align:start position:0%
+but reasonably thermally conductive so
+it lets heat transfer through but not
+
+ align:start position:0%
+it lets heat transfer through but not
+ 
+
+ align:start position:0%
+it lets heat transfer through but not
+electrons and by the way that's not a
+
+ align:start position:0%
+electrons and by the way that's not a
+ 
+
+ align:start position:0%
+electrons and by the way that's not a
+very common thing right most things that
+
+ align:start position:0%
+very common thing right most things that
+ 
+
+ align:start position:0%
+very common thing right most things that
+are good thermal conductors are also
+
+ align:start position:0%
+are good thermal conductors are also
+ 
+
+ align:start position:0%
+are good thermal conductors are also
+good electrical conductors but you can
+
+ align:start position:0%
+good electrical conductors but you can
+ 
+
+ align:start position:0%
+good electrical conductors but you can
+find some materials that'll help you out
+
+ align:start position:0%
+find some materials that'll help you out
+ 
+
+ align:start position:0%
+find some materials that'll help you out
+there right so this thing might be um
+
+ align:start position:0%
+there right so this thing might be um
+ 
+
+ align:start position:0%
+there right so this thing might be um
+some electrical insulation pad to let
+
+ align:start position:0%
+some electrical insulation pad to let
+ 
+
+ align:start position:0%
+some electrical insulation pad to let
+you connect this thing to a heat sink
+
+ align:start position:0%
+you connect this thing to a heat sink
+ 
+
+ align:start position:0%
+you connect this thing to a heat sink
+thermally but not
+
+ align:start position:0%
+thermally but not
+ 
+
+ align:start position:0%
+thermally but not
+electrically okay uh you can find you
+
+ align:start position:0%
+electrically okay uh you can find you
+ 
+
+ align:start position:0%
+electrically okay uh you can find you
+know a typical brand name for this is
+
+ align:start position:0%
+know a typical brand name for this is
+ 
+
+ align:start position:0%
+know a typical brand name for this is
+like a s
+
+ align:start position:0%
+like a s
+ 
+
+ align:start position:0%
+like a s
+pad that's
+
+ align:start position:0%
+pad that's
+ 
+
+ align:start position:0%
+pad that's
+Bergquist trade name for it there's a
+
+ align:start position:0%
+Bergquist trade name for it there's a
+ 
+
+ align:start position:0%
+Bergquist trade name for it there's a
+lot of companies that make it and they
+
+ align:start position:0%
+lot of companies that make it and they
+ 
+
+ align:start position:0%
+lot of companies that make it and they
+come in varing degrees of quality and
+
+ align:start position:0%
+come in varing degrees of quality and
+ 
+
+ align:start position:0%
+come in varing degrees of quality and
+electrical insulation capability and so
+
+ align:start position:0%
+electrical insulation capability and so
+ 
+
+ align:start position:0%
+electrical insulation capability and so
+forth okay in some applications maybe
+
+ align:start position:0%
+forth okay in some applications maybe
+ 
+
+ align:start position:0%
+forth okay in some applications maybe
+you don't
+
+ align:start position:0%
+you don't
+ 
+
+ align:start position:0%
+you don't
+need electrical insulation right if you
+
+ align:start position:0%
+need electrical insulation right if you
+ 
+
+ align:start position:0%
+need electrical insulation right if you
+happen to have a pack pack AG that was
+
+ align:start position:0%
+happen to have a pack pack AG that was
+ 
+
+ align:start position:0%
+happen to have a pack pack AG that was
+already electrically insulated and they
+
+ align:start position:0%
+already electrically insulated and they
+ 
+
+ align:start position:0%
+already electrically insulated and they
+do make some fets that way or the
+
+ align:start position:0%
+do make some fets that way or the
+ 
+
+ align:start position:0%
+do make some fets that way or the
+package happened to be connected to
+
+ align:start position:0%
+package happened to be connected to
+ 
+
+ align:start position:0%
+package happened to be connected to
+ground maybe you could connect that
+
+ align:start position:0%
+ground maybe you could connect that
+ 
+
+ align:start position:0%
+ground maybe you could connect that
+directly down to the heat sink okay but
+
+ align:start position:0%
+directly down to the heat sink okay but
+ 
+
+ align:start position:0%
+directly down to the heat sink okay but
+often you will have some other interface
+
+ align:start position:0%
+often you will have some other interface
+ 
+
+ align:start position:0%
+often you will have some other interface
+between your device and your heat sink
+
+ align:start position:0%
+between your device and your heat sink
+ 
+
+ align:start position:0%
+between your device and your heat sink
+why because you know if you think about
+
+ align:start position:0%
+why because you know if you think about
+ 
+
+ align:start position:0%
+why because you know if you think about
+surface roughness you know maybe here's
+
+ align:start position:0%
+surface roughness you know maybe here's
+ 
+
+ align:start position:0%
+surface roughness you know maybe here's
+the back package of the device and
+
+ align:start position:0%
+the back package of the device and
+ 
+
+ align:start position:0%
+the back package of the device and
+here's the surface of the heat sink you
+
+ align:start position:0%
+here's the surface of the heat sink you
+ 
+
+ align:start position:0%
+here's the surface of the heat sink you
+know you don't want any air in between
+
+ align:start position:0%
+know you don't want any air in between
+ 
+
+ align:start position:0%
+know you don't want any air in between
+it so in that case what you might do is
+
+ align:start position:0%
+it so in that case what you might do is
+ 
+
+ align:start position:0%
+it so in that case what you might do is
+use thermal grease so this could also be
+
+ align:start position:0%
+use thermal grease so this could also be
+ 
+
+ align:start position:0%
+use thermal grease so this could also be
+uh in instead thermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grease okay why would I use thermal
+
+ align:start position:0%
+grease okay why would I use thermal
+ 
+
+ align:start position:0%
+grease okay why would I use thermal
+grease because thermal grease has a lot
+
+ align:start position:0%
+grease because thermal grease has a lot
+ 
+
+ align:start position:0%
+grease because thermal grease has a lot
+better heat transfer characteristics
+
+ align:start position:0%
+better heat transfer characteristics
+ 
+
+ align:start position:0%
+better heat transfer characteristics
+than air does so you wouldn't want any
+
+ align:start position:0%
+than air does so you wouldn't want any
+ 
+
+ align:start position:0%
+than air does so you wouldn't want any
+scratches or open areas in the back of
+
+ align:start position:0%
+scratches or open areas in the back of
+ 
+
+ align:start position:0%
+scratches or open areas in the back of
+your device kind of limiting heat flow
+
+ align:start position:0%
+your device kind of limiting heat flow
+ 
+
+ align:start position:0%
+your device kind of limiting heat flow
+so you fill that with thermal grease of
+
+ align:start position:0%
+so you fill that with thermal grease of
+ 
+
+ align:start position:0%
+so you fill that with thermal grease of
+course thermal grease has way worse
+
+ align:start position:0%
+course thermal grease has way worse
+ 
+
+ align:start position:0%
+course thermal grease has way worse
+thermal con conductivity than metal so
+
+ align:start position:0%
+thermal con conductivity than metal so
+ 
+
+ align:start position:0%
+thermal con conductivity than metal so
+what you would do is you just put enough
+
+ align:start position:0%
+what you would do is you just put enough
+ 
+
+ align:start position:0%
+what you would do is you just put enough
+thermal grease on it and you sometimes
+
+ align:start position:0%
+thermal grease on it and you sometimes
+ 
+
+ align:start position:0%
+thermal grease on it and you sometimes
+if you've ever mounted say a CPU down to
+
+ align:start position:0%
+if you've ever mounted say a CPU down to
+ 
+
+ align:start position:0%
+if you've ever mounted say a CPU down to
+the CPU Cooler they'll give you this
+
+ align:start position:0%
+the CPU Cooler they'll give you this
+ 
+
+ align:start position:0%
+the CPU Cooler they'll give you this
+material to put in there and the idea is
+
+ align:start position:0%
+material to put in there and the idea is
+ 
+
+ align:start position:0%
+material to put in there and the idea is
+you put it on and then you basically try
+
+ align:start position:0%
+you put it on and then you basically try
+ 
+
+ align:start position:0%
+you put it on and then you basically try
+to squeegee it all off it's just to fill
+
+ align:start position:0%
+to squeegee it all off it's just to fill
+ 
+
+ align:start position:0%
+to squeegee it all off it's just to fill
+in cracks you don't want like a thick
+
+ align:start position:0%
+in cracks you don't want like a thick
+ 
+
+ align:start position:0%
+in cracks you don't want like a thick
+layer of this stuff because it will add
+
+ align:start position:0%
+layer of this stuff because it will add
+ 
+
+ align:start position:0%
+layer of this stuff because it will add
+thermal resistance to this path the sil
+
+ align:start position:0%
+thermal resistance to this path the sil
+ 
+
+ align:start position:0%
+thermal resistance to this path the sil
+pad has thermal resistance so does
+
+ align:start position:0%
+pad has thermal resistance so does
+ 
+
+ align:start position:0%
+pad has thermal resistance so does
+thermal grease so you put as little as
+
+ align:start position:0%
+thermal grease so you put as little as
+ 
+
+ align:start position:0%
+thermal grease so you put as little as
+on as you can get away with it just to
+
+ align:start position:0%
+on as you can get away with it just to
+ 
+
+ align:start position:0%
+on as you can get away with it just to
+make it essentially flat and then Mount
+
+ align:start position:0%
+make it essentially flat and then Mount
+ 
+
+ align:start position:0%
+make it essentially flat and then Mount
+that device down to the heat
+
+ align:start position:0%
+that device down to the heat
+ 
+
+ align:start position:0%
+that device down to the heat
+sink any questions about that so it
+
+ align:start position:0%
+sink any questions about that so it
+ 
+
+ align:start position:0%
+sink any questions about that so it
+depends whether you need electrical
+
+ align:start position:0%
+depends whether you need electrical
+ 
+
+ align:start position:0%
+depends whether you need electrical
+insulation whether you just use thermal
+
+ align:start position:0%
+insulation whether you just use thermal
+ 
+
+ align:start position:0%
+insulation whether you just use thermal
+grease or you use an insulating pad or
+
+ align:start position:0%
+grease or you use an insulating pad or
+ 
+
+ align:start position:0%
+grease or you use an insulating pad or
+you use some kind of non-insulated
+
+ align:start position:0%
+you use some kind of non-insulated
+ 
+
+ align:start position:0%
+you use some kind of non-insulated
+thermal pad that'll you know kind of be
+
+ align:start position:0%
+thermal pad that'll you know kind of be
+ 
+
+ align:start position:0%
+thermal pad that'll you know kind of be
+compliant
+
+ align:start position:0%
+compliant
+ 
+
+ align:start position:0%
+compliant
+okay and that's the physical structure
+
+ align:start position:0%
+okay and that's the physical structure
+ 
+
+ align:start position:0%
+okay and that's the physical structure
+what does this thing look like as a
+
+ align:start position:0%
+what does this thing look like as a
+ 
+
+ align:start position:0%
+what does this thing look like as a
+circuit
+
+ align:start position:0%
+circuit
+ 
+
+ align:start position:0%
+circuit
+model well
+
+ align:start position:0%
+model well
+ 
+
+ align:start position:0%
+model well
+here um
+
+ align:start position:0%
+here um
+ 
+
+ align:start position:0%
+here um
+I will have some P
+
+ align:start position:0%
+I will have some P
+ 
+
+ align:start position:0%
+I will have some P
+disc that's the power I'm dissipating in
+
+ align:start position:0%
+disc that's the power I'm dissipating in
+ 
+
+ align:start position:0%
+disc that's the power I'm dissipating in
+the device right and ideally that power
+
+ align:start position:0%
+the device right and ideally that power
+ 
+
+ align:start position:0%
+the device right and ideally that power
+dissipation is connected to absolute
+
+ align:start position:0%
+dissipation is connected to absolute
+ 
+
+ align:start position:0%
+dissipation is connected to absolute
+zero but maybe I'll just call this T
+
+ align:start position:0%
+zero but maybe I'll just call this T
+ 
+
+ align:start position:0%
+zero but maybe I'll just call this T
+ambient and recognize that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh maybe this is connected to really Z
+
+ align:start position:0%
+oh maybe this is connected to really Z
+ 
+
+ align:start position:0%
+oh maybe this is connected to really Z
+Kelvin okay so I can either treat this
+
+ align:start position:0%
+Kelvin okay so I can either treat this
+ 
+
+ align:start position:0%
+Kelvin okay so I can either treat this
+as zero Kelvin or call it you know
+
+ align:start position:0%
+as zero Kelvin or call it you know
+ 
+
+ align:start position:0%
+as zero Kelvin or call it you know
+whatever my ambient temperature is and
+
+ align:start position:0%
+whatever my ambient temperature is and
+ 
+
+ align:start position:0%
+whatever my ambient temperature is and
+work from there
+
+ align:start position:0%
+work from there
+ 
+
+ align:start position:0%
+work from there
+okay that's the power dissipation and we
+
+ align:start position:0%
+okay that's the power dissipation and we
+ 
+
+ align:start position:0%
+okay that's the power dissipation and we
+often say this temperature is at T
+
+ align:start position:0%
+often say this temperature is at T
+ 
+
+ align:start position:0%
+often say this temperature is at T
+Junction right from so it's either you
+
+ align:start position:0%
+Junction right from so it's either you
+ 
+
+ align:start position:0%
+Junction right from so it's either you
+know this is T Junction to ambient or t
+
+ align:start position:0%
+know this is T Junction to ambient or t
+ 
+
+ align:start position:0%
+know this is T Junction to ambient or t
+Junction absolute depending upon how I
+
+ align:start position:0%
+Junction absolute depending upon how I
+ 
+
+ align:start position:0%
+Junction absolute depending upon how I
+decide to write this The Junction is
+
+ align:start position:0%
+decide to write this The Junction is
+ 
+
+ align:start position:0%
+decide to write this The Junction is
+just my notion of wherever the power is
+
+ align:start position:0%
+just my notion of wherever the power is
+ 
+
+ align:start position:0%
+just my notion of wherever the power is
+being dissipated in the device it may be
+
+ align:start position:0%
+being dissipated in the device it may be
+ 
+
+ align:start position:0%
+being dissipated in the device it may be
+an actual physical semiconductor
+
+ align:start position:0%
+an actual physical semiconductor
+ 
+
+ align:start position:0%
+an actual physical semiconductor
+Junction it may just be you know
+
+ align:start position:0%
+Junction it may just be you know
+ 
+
+ align:start position:0%
+Junction it may just be you know
+wherever in this device is where the
+
+ align:start position:0%
+wherever in this device is where the
+ 
+
+ align:start position:0%
+wherever in this device is where the
+Heat's being
+
+ align:start position:0%
+Heat's being
+ 
+
+ align:start position:0%
+Heat's being
+dissipated
+
+ align:start position:0%
+dissipated
+ 
+
+ align:start position:0%
+dissipated
+okay then I've got to
+
+ align:start position:0%
+okay then I've got to
+ 
+
+ align:start position:0%
+okay then I've got to
+transfer the heat to the surface of the
+
+ align:start position:0%
+transfer the heat to the surface of the
+ 
+
+ align:start position:0%
+transfer the heat to the surface of the
+device right because I said you know the
+
+ align:start position:0%
+device right because I said you know the
+ 
+
+ align:start position:0%
+device right because I said you know the
+Heat's
+
+ align:start position:0%
+Heat's
+ 
+
+ align:start position:0%
+Heat's
+actually uh being dissipated inside and
+
+ align:start position:0%
+actually uh being dissipated inside and
+ 
+
+ align:start position:0%
+actually uh being dissipated inside and
+there's some thermal resistance junct
+
+ align:start position:0%
+there's some thermal resistance junct
+ 
+
+ align:start position:0%
+there's some thermal resistance junct
+between where the Heat's being
+
+ align:start position:0%
+between where the Heat's being
+ 
+
+ align:start position:0%
+between where the Heat's being
+dissipated inside the semiconductor to
+
+ align:start position:0%
+dissipated inside the semiconductor to
+ 
+
+ align:start position:0%
+dissipated inside the semiconductor to
+the actual case so there's going to be
+
+ align:start position:0%
+the actual case so there's going to be
+ 
+
+ align:start position:0%
+the actual case so there's going to be
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+rth Jun
+
+ align:start position:0%
+rth Jun
+ 
+
+ align:start position:0%
+rth Jun
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+right and then there's going to be some
+
+ align:start position:0%
+right and then there's going to be some
+ 
+
+ align:start position:0%
+right and then there's going to be some
+other thermal resistance and so this
+
+ align:start position:0%
+other thermal resistance and so this
+ 
+
+ align:start position:0%
+other thermal resistance and so this
+temperature here would be the T
+
+ align:start position:0%
+temperature here would be the T
+ 
+
+ align:start position:0%
+temperature here would be the T
+case right then there's going to be some
+
+ align:start position:0%
+case right then there's going to be some
+ 
+
+ align:start position:0%
+case right then there's going to be some
+other thermal
+
+ align:start position:0%
+other thermal
+ 
+
+ align:start position:0%
+other thermal
+resistance
+
+ align:start position:0%
+resistance
+ 
+
+ align:start position:0%
+resistance
+rth case to
+
+ align:start position:0%
+rth case to
+ 
+
+ align:start position:0%
+rth case to
+sync okay that depends upon is this
+
+ align:start position:0%
+sync okay that depends upon is this
+ 
+
+ align:start position:0%
+sync okay that depends upon is this
+grease is it a thermal pad you know what
+
+ align:start position:0%
+grease is it a thermal pad you know what
+ 
+
+ align:start position:0%
+grease is it a thermal pad you know what
+is it and that and I care because that's
+
+ align:start position:0%
+is it and that and I care because that's
+ 
+
+ align:start position:0%
+is it and that and I care because that's
+going to contribute to temperature rise
+
+ align:start position:0%
+going to contribute to temperature rise
+ 
+
+ align:start position:0%
+going to contribute to temperature rise
+and then I you know over here I have my
+
+ align:start position:0%
+and then I you know over here I have my
+ 
+
+ align:start position:0%
+and then I you know over here I have my
+heat sink right and that heat sink if I
+
+ align:start position:0%
+heat sink right and that heat sink if I
+ 
+
+ align:start position:0%
+heat sink right and that heat sink if I
+include what's going to transfer off it
+
+ align:start position:0%
+include what's going to transfer off it
+ 
+
+ align:start position:0%
+include what's going to transfer off it
+by conduction and convection right maybe
+
+ align:start position:0%
+by conduction and convection right maybe
+ 
+
+ align:start position:0%
+by conduction and convection right maybe
+I say there is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+rth sync to ambient okay and I connect
+
+ align:start position:0%
+rth sync to ambient okay and I connect
+ 
+
+ align:start position:0%
+rth sync to ambient okay and I connect
+this back to ambient and that's my
+
+ align:start position:0%
+this back to ambient and that's my
+ 
+
+ align:start position:0%
+this back to ambient and that's my
+thermal model and this is T sync right
+
+ align:start position:0%
+thermal model and this is T sync right
+ 
+
+ align:start position:0%
+thermal model and this is T sync right
+so this is my model for the whole thing
+
+ align:start position:0%
+so this is my model for the whole thing
+ 
+
+ align:start position:0%
+so this is my model for the whole thing
+any questions about that and I should
+
+ align:start position:0%
+any questions about that and I should
+ 
+
+ align:start position:0%
+any questions about that and I should
+say this is in thermal steady
+
+ align:start position:0%
+say this is in thermal steady
+ 
+
+ align:start position:0%
+say this is in thermal steady
+state now um fortunately if you get a
+
+ align:start position:0%
+state now um fortunately if you get a
+ 
+
+ align:start position:0%
+state now um fortunately if you get a
+lot of typical devices and you look
+
+ align:start position:0%
+lot of typical devices and you look
+ 
+
+ align:start position:0%
+lot of typical devices and you look
+carefully in the device data sheet here
+
+ align:start position:0%
+carefully in the device data sheet here
+ 
+
+ align:start position:0%
+carefully in the device data sheet here
+we go what they tell me is they've done
+
+ align:start position:0%
+we go what they tell me is they've done
+ 
+
+ align:start position:0%
+we go what they tell me is they've done
+some measurements somebody with a lot of
+
+ align:start position:0%
+some measurements somebody with a lot of
+ 
+
+ align:start position:0%
+some measurements somebody with a lot of
+thermal modeling experiences said done
+
+ align:start position:0%
+thermal modeling experiences said done
+ 
+
+ align:start position:0%
+thermal modeling experiences said done
+some measurements to figure out how hot
+
+ align:start position:0%
+some measurements to figure out how hot
+ 
+
+ align:start position:0%
+some measurements to figure out how hot
+the Junctions are going to get from
+
+ align:start position:0%
+the Junctions are going to get from
+ 
+
+ align:start position:0%
+the Junctions are going to get from
+above the C for a given amount of
+
+ align:start position:0%
+above the C for a given amount of
+ 
+
+ align:start position:0%
+above the C for a given amount of
+dissipation and they give me a thermal
+
+ align:start position:0%
+dissipation and they give me a thermal
+ 
+
+ align:start position:0%
+dissipation and they give me a thermal
+resistance Junction to case and they say
+
+ align:start position:0%
+resistance Junction to case and they say
+ 
+
+ align:start position:0%
+resistance Junction to case and they say
+here it's 2.5 de watt then they tell me
+
+ align:start position:0%
+here it's 2.5 de watt then they tell me
+ 
+
+ align:start position:0%
+here it's 2.5 de watt then they tell me
+oh if you go get you know just the right
+
+ align:start position:0%
+oh if you go get you know just the right
+ 
+
+ align:start position:0%
+oh if you go get you know just the right
+amount of thermal grease you do a really
+
+ align:start position:0%
+amount of thermal grease you do a really
+ 
+
+ align:start position:0%
+amount of thermal grease you do a really
+good job of mounting this down to a heat
+
+ align:start position:0%
+good job of mounting this down to a heat
+ 
+
+ align:start position:0%
+good job of mounting this down to a heat
+sink so we're we're not worrying about
+
+ align:start position:0%
+sink so we're we're not worrying about
+ 
+
+ align:start position:0%
+sink so we're we're not worrying about
+any additional insulation pad here it's
+
+ align:start position:0%
+any additional insulation pad here it's
+ 
+
+ align:start position:0%
+any additional insulation pad here it's
+another half a degree C watt between the
+
+ align:start position:0%
+another half a degree C watt between the
+ 
+
+ align:start position:0%
+another half a degree C watt between the
+case and the sink that's if I don't need
+
+ align:start position:0%
+case and the sink that's if I don't need
+ 
+
+ align:start position:0%
+case and the sink that's if I don't need
+electrical isolation if I do I have to
+
+ align:start position:0%
+electrical isolation if I do I have to
+ 
+
+ align:start position:0%
+electrical isolation if I do I have to
+look up the thermal resistance of my S
+
+ align:start position:0%
+look up the thermal resistance of my S
+ 
+
+ align:start position:0%
+look up the thermal resistance of my S
+pad or whatever else I'm putting in
+
+ align:start position:0%
+pad or whatever else I'm putting in
+ 
+
+ align:start position:0%
+pad or whatever else I'm putting in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and then then I'm you know usually as
+
+ align:start position:0%
+and then then I'm you know usually as
+ 
+
+ align:start position:0%
+and then then I'm you know usually as
+the designer I'm trying to pick this
+
+ align:start position:0%
+the designer I'm trying to pick this
+ 
+
+ align:start position:0%
+the designer I'm trying to pick this
+right but if I went out and picked a
+
+ align:start position:0%
+right but if I went out and picked a
+ 
+
+ align:start position:0%
+right but if I went out and picked a
+particular heat sync I can look up its
+
+ align:start position:0%
+particular heat sync I can look up its
+ 
+
+ align:start position:0%
+particular heat sync I can look up its
+value of rth sync to ambient right so
+
+ align:start position:0%
+value of rth sync to ambient right so
+ 
+
+ align:start position:0%
+value of rth sync to ambient right so
+then I can find um sort of delt T
+
+ align:start position:0%
+then I can find um sort of delt T
+ 
+
+ align:start position:0%
+then I can find um sort of delt T
+Junction to ambient is simply going to
+
+ align:start position:0%
+Junction to ambient is simply going to
+ 
+
+ align:start position:0%
+Junction to ambient is simply going to
+be p
+
+ align:start position:0%
+be p
+ 
+
+ align:start position:0%
+be p
+dis which is this power dissipation
+
+ align:start position:0%
+dis which is this power dissipation
+ 
+
+ align:start position:0%
+dis which is this power dissipation
+times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rth Junction to case plus
+
+ align:start position:0%
+rth Junction to case plus
+ 
+
+ align:start position:0%
+rth Junction to case plus
+rth case to sync plus rth sync to
+
+ align:start position:0%
+rth case to sync plus rth sync to
+ 
+
+ align:start position:0%
+rth case to sync plus rth sync to
+ambient right and then I'm done if in my
+
+ align:start position:0%
+ambient right and then I'm done if in my
+ 
+
+ align:start position:0%
+ambient right and then I'm done if in my
+example you know a typical example uh
+
+ align:start position:0%
+example you know a typical example uh
+ 
+
+ align:start position:0%
+example you know a typical example uh
+numbers that I might use um I said t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ambient T ambient might be
+
+ align:start position:0%
+ambient T ambient might be
+ 
+
+ align:start position:0%
+ambient T ambient might be
+40° C I don't know that's not that's a
+
+ align:start position:0%
+40° C I don't know that's not that's a
+ 
+
+ align:start position:0%
+40° C I don't know that's not that's a
+very that's actually a pretty cool
+
+ align:start position:0%
+very that's actually a pretty cool
+ 
+
+ align:start position:0%
+very that's actually a pretty cool
+ambient temperature you know some
+
+ align:start position:0%
+ambient temperature you know some
+ 
+
+ align:start position:0%
+ambient temperature you know some
+industrial stuff you design they assume
+
+ align:start position:0%
+industrial stuff you design they assume
+ 
+
+ align:start position:0%
+industrial stuff you design they assume
+the ambient is going to be 100° C but
+
+ align:start position:0%
+the ambient is going to be 100° C but
+ 
+
+ align:start position:0%
+the ambient is going to be 100° C but
+you know 40° C is hot but not crazy hot
+
+ align:start position:0%
+you know 40° C is hot but not crazy hot
+ 
+
+ align:start position:0%
+you know 40° C is hot but not crazy hot
+if you're in in a room right um and
+
+ align:start position:0%
+if you're in in a room right um and
+ 
+
+ align:start position:0%
+if you're in in a room right um and
+maybe I would say this kind of device uh
+
+ align:start position:0%
+maybe I would say this kind of device uh
+ 
+
+ align:start position:0%
+maybe I would say this kind of device uh
+P disc might be equal to 10 watts right
+
+ align:start position:0%
+P disc might be equal to 10 watts right
+ 
+
+ align:start position:0%
+P disc might be equal to 10 watts right
+this is something I got from my circuit
+
+ align:start position:0%
+this is something I got from my circuit
+ 
+
+ align:start position:0%
+this is something I got from my circuit
+design right so here I could say okay
+
+ align:start position:0%
+design right so here I could say okay
+ 
+
+ align:start position:0%
+design right so here I could say okay
+that's 10 watts times Junction to case I
+
+ align:start position:0%
+that's 10 watts times Junction to case I
+ 
+
+ align:start position:0%
+that's 10 watts times Junction to case I
+said was 2.5 de C per
+
+ align:start position:0%
+said was 2.5 de C per
+ 
+
+ align:start position:0%
+said was 2.5 de C per
+watt right plus 0.5 degrees C per
+
+ align:start position:0%
+watt right plus 0.5 degrees C per
+ 
+
+ align:start position:0%
+watt right plus 0.5 degrees C per
+watt was the if I just had thermal
+
+ align:start position:0%
+watt was the if I just had thermal
+ 
+
+ align:start position:0%
+watt was the if I just had thermal
+degrees in there and I went out and I
+
+ align:start position:0%
+degrees in there and I went out and I
+ 
+
+ align:start position:0%
+degrees in there and I went out and I
+bought a red Point thermoid km 51 heat
+
+ align:start position:0%
+bought a red Point thermoid km 51 heat
+ 
+
+ align:start position:0%
+bought a red Point thermoid km 51 heat
+sink that's just one of these convection
+
+ align:start position:0%
+sink that's just one of these convection
+ 
+
+ align:start position:0%
+sink that's just one of these convection
+cooled heat sinks to which I might Mount
+
+ align:start position:0%
+cooled heat sinks to which I might Mount
+ 
+
+ align:start position:0%
+cooled heat sinks to which I might Mount
+this device uh that is 4.8 degrees C per
+
+ align:start position:0%
+this device uh that is 4.8 degrees C per
+ 
+
+ align:start position:0%
+this device uh that is 4.8 degrees C per
+watt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right which if I say this is plus T
+
+ align:start position:0%
+right which if I say this is plus T
+ 
+
+ align:start position:0%
+right which if I say this is plus T
+ambient this would be just T Junction
+
+ align:start position:0%
+ambient this would be just T Junction
+ 
+
+ align:start position:0%
+ambient this would be just T Junction
+would be T ambient plus this stuff
+
+ align:start position:0%
+would be T ambient plus this stuff
+ 
+
+ align:start position:0%
+would be T ambient plus this stuff
+right this would give me 118 degre
+
+ align:start position:0%
+right this would give me 118 degre
+ 
+
+ align:start position:0%
+right this would give me 118 degre
+C and maybe I'd be a happy guy right
+
+ align:start position:0%
+C and maybe I'd be a happy guy right
+ 
+
+ align:start position:0%
+C and maybe I'd be a happy guy right
+typical devices that you can buy in
+
+ align:start position:0%
+typical devices that you can buy in
+ 
+
+ align:start position:0%
+typical devices that you can buy in
+plastic
+
+ align:start position:0%
+plastic
+ 
+
+ align:start position:0%
+plastic
+packages 150 to 175 is a maximum
+
+ align:start position:0%
+packages 150 to 175 is a maximum
+ 
+
+ align:start position:0%
+packages 150 to 175 is a maximum
+temperature you're allowed to get the
+
+ align:start position:0%
+temperature you're allowed to get the
+ 
+
+ align:start position:0%
+temperature you're allowed to get the
+junction um
+
+ align:start position:0%
+junction um
+ 
+
+ align:start position:0%
+junction um
+you can get devices that are specially
+
+ align:start position:0%
+you can get devices that are specially
+ 
+
+ align:start position:0%
+you can get devices that are specially
+packaged that'll go higher or if they're
+
+ align:start position:0%
+packaged that'll go higher or if they're
+ 
+
+ align:start position:0%
+packaged that'll go higher or if they're
+they're not going to you know bad stuff
+
+ align:start position:0%
+they're not going to you know bad stuff
+ 
+
+ align:start position:0%
+they're not going to you know bad stuff
+won't happen to the device it's often
+
+ align:start position:0%
+won't happen to the device it's often
+ 
+
+ align:start position:0%
+won't happen to the device it's often
+limited by the packaging but typically
+
+ align:start position:0%
+limited by the packaging but typically
+ 
+
+ align:start position:0%
+limited by the packaging but typically
+150 or 175 is what you can get and this
+
+ align:start position:0%
+150 or 175 is what you can get and this
+ 
+
+ align:start position:0%
+150 or 175 is what you can get and this
+just gives me some
+
+ align:start position:0%
+just gives me some
+ 
+
+ align:start position:0%
+just gives me some
+margin any is that on the the data sheet
+
+ align:start position:0%
+margin any is that on the the data sheet
+ 
+
+ align:start position:0%
+margin any is that on the the data sheet
+uh yes usually a data sheet will tell
+
+ align:start position:0%
+uh yes usually a data sheet will tell
+ 
+
+ align:start position:0%
+uh yes usually a data sheet will tell
+you what the maximum allowable
+
+ align:start position:0%
+you what the maximum allowable
+ 
+
+ align:start position:0%
+you what the maximum allowable
+temperature here we go uh operating and
+
+ align:start position:0%
+temperature here we go uh operating and
+ 
+
+ align:start position:0%
+temperature here we go uh operating and
+storage temperature range uh operating
+
+ align:start position:0%
+storage temperature range uh operating
+ 
+
+ align:start position:0%
+storage temperature range uh operating
+Junction and storage temperature range
+
+ align:start position:0%
+Junction and storage temperature range
+ 
+
+ align:start position:0%
+Junction and storage temperature range
+150° C for this part okay a lot of more
+
+ align:start position:0%
+150° C for this part okay a lot of more
+ 
+
+ align:start position:0%
+150° C for this part okay a lot of more
+modern devices might be 175 okay it just
+
+ align:start position:0%
+modern devices might be 175 okay it just
+ 
+
+ align:start position:0%
+modern devices might be 175 okay it just
+depends what you're buying so what would
+
+ align:start position:0%
+depends what you're buying so what would
+ 
+
+ align:start position:0%
+depends what you're buying so what would
+you be a really job usually what you do
+
+ align:start position:0%
+you be a really job usually what you do
+ 
+
+ align:start position:0%
+you be a really job usually what you do
+is you know all this stuff you know your
+
+ align:start position:0%
+is you know all this stuff you know your
+ 
+
+ align:start position:0%
+is you know all this stuff you know your
+ambient of specification you know your
+
+ align:start position:0%
+ambient of specification you know your
+ 
+
+ align:start position:0%
+ambient of specification you know your
+dissipation because you calculated it
+
+ align:start position:0%
+dissipation because you calculated it
+ 
+
+ align:start position:0%
+dissipation because you calculated it
+you know these things and your job is to
+
+ align:start position:0%
+you know these things and your job is to
+ 
+
+ align:start position:0%
+you know these things and your job is to
+go pick the heat sink or maybe the
+
+ align:start position:0%
+go pick the heat sink or maybe the
+ 
+
+ align:start position:0%
+go pick the heat sink or maybe the
+thermal interface material and you have
+
+ align:start position:0%
+thermal interface material and you have
+ 
+
+ align:start position:0%
+thermal interface material and you have
+to pick this so that this number doesn't
+
+ align:start position:0%
+to pick this so that this number doesn't
+ 
+
+ align:start position:0%
+to pick this so that this number doesn't
+get too high right so I don't know this
+
+ align:start position:0%
+get too high right so I don't know this
+ 
+
+ align:start position:0%
+get too high right so I don't know this
+stuff in advance this is the thing I'm
+
+ align:start position:0%
+stuff in advance this is the thing I'm
+ 
+
+ align:start position:0%
+stuff in advance this is the thing I'm
+choosing as the heat snc designer okay
+
+ align:start position:0%
+choosing as the heat snc designer okay
+ 
+
+ align:start position:0%
+choosing as the heat snc designer okay
+what happens if you can't do it well you
+
+ align:start position:0%
+what happens if you can't do it well you
+ 
+
+ align:start position:0%
+what happens if you can't do it well you
+either got to go reduce your dissipation
+
+ align:start position:0%
+either got to go reduce your dissipation
+ 
+
+ align:start position:0%
+either got to go reduce your dissipation
+or find a better package with a lower
+
+ align:start position:0%
+or find a better package with a lower
+ 
+
+ align:start position:0%
+or find a better package with a lower
+Junction to case or some other
+
+ align:start position:0%
+Junction to case or some other
+ 
+
+ align:start position:0%
+Junction to case or some other
+combination of things right and you're
+
+ align:start position:0%
+combination of things right and you're
+ 
+
+ align:start position:0%
+combination of things right and you're
+often pushed up against the wall if
+
+ align:start position:0%
+often pushed up against the wall if
+ 
+
+ align:start position:0%
+often pushed up against the wall if
+especially if you're trying to go for
+
+ align:start position:0%
+especially if you're trying to go for
+ 
+
+ align:start position:0%
+especially if you're trying to go for
+high power
+
+ align:start position:0%
+high power
+ 
+
+ align:start position:0%
+high power
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+questions so it seems like a a lot to do
+
+ align:start position:0%
+questions so it seems like a a lot to do
+ 
+
+ align:start position:0%
+questions so it seems like a a lot to do
+for like one component in your your
+
+ align:start position:0%
+for like one component in your your
+ 
+
+ align:start position:0%
+for like one component in your your
+system what do you do for like a
+
+ align:start position:0%
+system what do you do for like a
+ 
+
+ align:start position:0%
+system what do you do for like a
+workflow and you have a lot of
+
+ align:start position:0%
+workflow and you have a lot of
+ 
+
+ align:start position:0%
+workflow and you have a lot of
+components in C so if you're a power
+
+ align:start position:0%
+components in C so if you're a power
+ 
+
+ align:start position:0%
+components in C so if you're a power
+converter designer right usually you
+
+ align:start position:0%
+converter designer right usually you
+ 
+
+ align:start position:0%
+converter designer right usually you
+only have a few sources of thermal
+
+ align:start position:0%
+only have a few sources of thermal
+ 
+
+ align:start position:0%
+only have a few sources of thermal
+dissipation that are the most important
+
+ align:start position:0%
+dissipation that are the most important
+ 
+
+ align:start position:0%
+dissipation that are the most important
+right and they're often your power
+
+ align:start position:0%
+right and they're often your power
+ 
+
+ align:start position:0%
+right and they're often your power
+devices at a broader scale right if
+
+ align:start position:0%
+devices at a broader scale right if
+ 
+
+ align:start position:0%
+devices at a broader scale right if
+you're if if you have to consider the
+
+ align:start position:0%
+you're if if you have to consider the
+ 
+
+ align:start position:0%
+you're if if you have to consider the
+whole thermal design well either you get
+
+ align:start position:0%
+whole thermal design well either you get
+ 
+
+ align:start position:0%
+whole thermal design well either you get
+a bigger Network or you start to pull
+
+ align:start position:0%
+a bigger Network or you start to pull
+ 
+
+ align:start position:0%
+a bigger Network or you start to pull
+out you know uh computation like finite
+
+ align:start position:0%
+out you know uh computation like finite
+ 
+
+ align:start position:0%
+out you know uh computation like finite
+element tools or something like that but
+
+ align:start position:0%
+element tools or something like that but
+ 
+
+ align:start position:0%
+element tools or something like that but
+very often for a power converter design
+
+ align:start position:0%
+very often for a power converter design
+ 
+
+ align:start position:0%
+very often for a power converter design
+you know you think you got your you know
+
+ align:start position:0%
+you know you think you got your you know
+ 
+
+ align:start position:0%
+you know you think you got your you know
+in a buck converter you might have your
+
+ align:start position:0%
+in a buck converter you might have your
+ 
+
+ align:start position:0%
+in a buck converter you might have your
+mosfet and your diode as being big
+
+ align:start position:0%
+mosfet and your diode as being big
+ 
+
+ align:start position:0%
+mosfet and your diode as being big
+sources of loss and then maybe your
+
+ align:start position:0%
+sources of loss and then maybe your
+ 
+
+ align:start position:0%
+sources of loss and then maybe your
+inductor is next right and you just
+
+ align:start position:0%
+inductor is next right and you just
+ 
+
+ align:start position:0%
+inductor is next right and you just
+model those into the system and and
+
+ align:start position:0%
+model those into the system and and
+ 
+
+ align:start position:0%
+model those into the system and and
+figure out how you're going to heat sync
+
+ align:start position:0%
+figure out how you're going to heat sync
+ 
+
+ align:start position:0%
+figure out how you're going to heat sync
+it I should say by the way that a very
+
+ align:start position:0%
+it I should say by the way that a very
+ 
+
+ align:start position:0%
+it I should say by the way that a very
+typical thing that you would
+
+ align:start position:0%
+typical thing that you would
+ 
+
+ align:start position:0%
+typical thing that you would
+do is um you know m a very typical thing
+
+ align:start position:0%
+do is um you know m a very typical thing
+ 
+
+ align:start position:0%
+do is um you know m a very typical thing
+to do is I'm showing you one picture
+
+ align:start position:0%
+to do is I'm showing you one picture
+ 
+
+ align:start position:0%
+to do is I'm showing you one picture
+here right but it may be true that you
+
+ align:start position:0%
+here right but it may be true that you
+ 
+
+ align:start position:0%
+here right but it may be true that you
+come up and you um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you might do the following you might
+
+ align:start position:0%
+you might do the following you might
+ 
+
+ align:start position:0%
+you might do the following you might
+have a heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sink and then you know your diode and
+
+ align:start position:0%
+sink and then you know your diode and
+ 
+
+ align:start position:0%
+sink and then you know your diode and
+your mosfet are right next to each other
+
+ align:start position:0%
+your mosfet are right next to each other
+ 
+
+ align:start position:0%
+your mosfet are right next to each other
+and mounted to the same heat sink right
+
+ align:start position:0%
+and mounted to the same heat sink right
+ 
+
+ align:start position:0%
+and mounted to the same heat sink right
+so what would you do you'd say okay
+
+ align:start position:0%
+so what would you do you'd say okay
+ 
+
+ align:start position:0%
+so what would you do you'd say okay
+here's P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fat and here's TJ
+
+ align:start position:0%
+fat and here's TJ
+ 
+
+ align:start position:0%
+fat and here's TJ
+fet right and that would be rth you'd
+
+ align:start position:0%
+fet right and that would be rth you'd
+ 
+
+ align:start position:0%
+fet right and that would be rth you'd
+have Junction to Case Case to s so maybe
+
+ align:start position:0%
+have Junction to Case Case to s so maybe
+ 
+
+ align:start position:0%
+have Junction to Case Case to s so maybe
+that would rth Junction to sync would be
+
+ align:start position:0%
+that would rth Junction to sync would be
+ 
+
+ align:start position:0%
+that would rth Junction to sync would be
+the total and you do the same thing for
+
+ align:start position:0%
+the total and you do the same thing for
+ 
+
+ align:start position:0%
+the total and you do the same thing for
+rth Junction to sync for your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diode right and here's
+
+ align:start position:0%
+diode right and here's
+ 
+
+ align:start position:0%
+diode right and here's
+TJ
+
+ align:start position:0%
+TJ
+ 
+
+ align:start position:0%
+TJ
+diode right and then you go out and get
+
+ align:start position:0%
+diode right and then you go out and get
+ 
+
+ align:start position:0%
+diode right and then you go out and get
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+rth syn to
+
+ align:start position:0%
+rth syn to
+ 
+
+ align:start position:0%
+rth syn to
+ambient and you go calculate what the
+
+ align:start position:0%
+ambient and you go calculate what the
+ 
+
+ align:start position:0%
+ambient and you go calculate what the
+junction temperature of the diode is and
+
+ align:start position:0%
+junction temperature of the diode is and
+ 
+
+ align:start position:0%
+junction temperature of the diode is and
+what the junction temperature of the FED
+
+ align:start position:0%
+what the junction temperature of the FED
+ 
+
+ align:start position:0%
+what the junction temperature of the FED
+is and you'd have to pick these things
+
+ align:start position:0%
+is and you'd have to pick these things
+ 
+
+ align:start position:0%
+is and you'd have to pick these things
+low enough and you can expand out from
+
+ align:start position:0%
+low enough and you can expand out from
+ 
+
+ align:start position:0%
+low enough and you can expand out from
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+that's one way to think about
+
+ align:start position:0%
+that's one way to think about
+ 
+
+ align:start position:0%
+that's one way to think about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um this is the steady state thermal
+
+ align:start position:0%
+um this is the steady state thermal
+ 
+
+ align:start position:0%
+um this is the steady state thermal
+model right this is I plug my converter
+
+ align:start position:0%
+model right this is I plug my converter
+ 
+
+ align:start position:0%
+model right this is I plug my converter
+in I let it run for a long time
+
+ align:start position:0%
+in I let it run for a long time
+ 
+
+ align:start position:0%
+in I let it run for a long time
+everything up to its maximum temperature
+
+ align:start position:0%
+everything up to its maximum temperature
+ 
+
+ align:start position:0%
+everything up to its maximum temperature
+and I find out if it blows up or not
+
+ align:start position:0%
+and I find out if it blows up or not
+ 
+
+ align:start position:0%
+and I find out if it blows up or not
+right did the thing get too hot when
+
+ align:start position:0%
+right did the thing get too hot when
+ 
+
+ align:start position:0%
+right did the thing get too hot when
+everything settled out right but this
+
+ align:start position:0%
+everything settled out right but this
+ 
+
+ align:start position:0%
+everything settled out right but this
+isn't really a transient thermal model
+
+ align:start position:0%
+isn't really a transient thermal model
+ 
+
+ align:start position:0%
+isn't really a transient thermal model
+right I mean if I put my you know if I
+
+ align:start position:0%
+right I mean if I put my you know if I
+ 
+
+ align:start position:0%
+right I mean if I put my you know if I
+put my teac kettle on and I turn on the
+
+ align:start position:0%
+put my teac kettle on and I turn on the
+ 
+
+ align:start position:0%
+put my teac kettle on and I turn on the
+power which is basically dumping heat
+
+ align:start position:0%
+power which is basically dumping heat
+ 
+
+ align:start position:0%
+power which is basically dumping heat
+into the water from my tea kettle it
+
+ align:start position:0%
+into the water from my tea kettle it
+ 
+
+ align:start position:0%
+into the water from my tea kettle it
+doesn't instantly get up to maximum
+
+ align:start position:0%
+doesn't instantly get up to maximum
+ 
+
+ align:start position:0%
+doesn't instantly get up to maximum
+temperature right eventually it'll get
+
+ align:start position:0%
+temperature right eventually it'll get
+ 
+
+ align:start position:0%
+temperature right eventually it'll get
+up to hopefully it's if if I have
+
+ align:start position:0%
+up to hopefully it's if if I have
+ 
+
+ align:start position:0%
+up to hopefully it's if if I have
+pouring enough heat in to get up to
+
+ align:start position:0%
+pouring enough heat in to get up to
+ 
+
+ align:start position:0%
+pouring enough heat in to get up to
+Boiling right but it doesn't do it
+
+ align:start position:0%
+Boiling right but it doesn't do it
+ 
+
+ align:start position:0%
+Boiling right but it doesn't do it
+instantly this model does not tell you
+
+ align:start position:0%
+instantly this model does not tell you
+ 
+
+ align:start position:0%
+instantly this model does not tell you
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+all about instantaneous Behavior or
+
+ align:start position:0%
+all about instantaneous Behavior or
+ 
+
+ align:start position:0%
+all about instantaneous Behavior or
+transient behavior and sometimes that's
+
+ align:start position:0%
+transient behavior and sometimes that's
+ 
+
+ align:start position:0%
+transient behavior and sometimes that's
+quite important right because um we
+
+ align:start position:0%
+quite important right because um we
+ 
+
+ align:start position:0%
+quite important right because um we
+sometimes don't even wait for things to
+
+ align:start position:0%
+sometimes don't even wait for things to
+ 
+
+ align:start position:0%
+sometimes don't even wait for things to
+get to steady state or we want to know
+
+ align:start position:0%
+get to steady state or we want to know
+ 
+
+ align:start position:0%
+get to steady state or we want to know
+how quickly is my Beast going to heat up
+
+ align:start position:0%
+how quickly is my Beast going to heat up
+ 
+
+ align:start position:0%
+how quickly is my Beast going to heat up
+well it turns out you can measure that
+
+ align:start position:0%
+well it turns out you can measure that
+ 
+
+ align:start position:0%
+well it turns out you can measure that
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+well or you can model that as well and
+
+ align:start position:0%
+well or you can model that as well and
+ 
+
+ align:start position:0%
+well or you can model that as well and
+what we do with it is to model things
+
+ align:start position:0%
+what we do with it is to model things
+ 
+
+ align:start position:0%
+what we do with it is to model things
+with a thermal capacity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ence which has Unis Jews per degree C or
+
+ align:start position:0%
+Ence which has Unis Jews per degree C or
+ 
+
+ align:start position:0%
+Ence which has Unis Jews per degree C or
+Jews per
+
+ align:start position:0%
+Jews per
+ 
+
+ align:start position:0%
+Jews per
+Kelvin okay how many jewels do I have to
+
+ align:start position:0%
+Kelvin okay how many jewels do I have to
+ 
+
+ align:start position:0%
+Kelvin okay how many jewels do I have to
+put into this structure to raise it 1
+
+ align:start position:0%
+put into this structure to raise it 1
+ 
+
+ align:start position:0%
+put into this structure to raise it 1
+degree Kelvin just by heating up the
+
+ align:start position:0%
+degree Kelvin just by heating up the
+ 
+
+ align:start position:0%
+degree Kelvin just by heating up the
+mass of this thing right and so if I
+
+ align:start position:0%
+mass of this thing right and so if I
+ 
+
+ align:start position:0%
+mass of this thing right and so if I
+knew the heat capacitance for some
+
+ align:start position:0%
+knew the heat capacitance for some
+ 
+
+ align:start position:0%
+knew the heat capacitance for some
+material per volume or per Mass I can
+
+ align:start position:0%
+material per volume or per Mass I can
+ 
+
+ align:start position:0%
+material per volume or per Mass I can
+multiply that and get the the heat
+
+ align:start position:0%
+multiply that and get the the heat
+ 
+
+ align:start position:0%
+multiply that and get the the heat
+capacitor of the whole thing right so
+
+ align:start position:0%
+capacitor of the whole thing right so
+ 
+
+ align:start position:0%
+capacitor of the whole thing right so
+maybe what I would do is I would say
+
+ align:start position:0%
+maybe what I would do is I would say
+ 
+
+ align:start position:0%
+maybe what I would do is I would say
+Okay suppose I have some surface
+
+ align:start position:0%
+Okay suppose I have some surface
+ 
+
+ align:start position:0%
+Okay suppose I have some surface
+here which I know is going to be at some
+
+ align:start position:0%
+here which I know is going to be at some
+ 
+
+ align:start position:0%
+here which I know is going to be at some
+you know T ambient or t let me call this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T2 I guess I did call it t ambient okay
+
+ align:start position:0%
+T2 I guess I did call it t ambient okay
+ 
+
+ align:start position:0%
+T2 I guess I did call it t ambient okay
+so suppose it's t ambient okay and here
+
+ align:start position:0%
+so suppose it's t ambient okay and here
+ 
+
+ align:start position:0%
+so suppose it's t ambient okay and here
+I have some block of
+
+ align:start position:0%
+I have some block of
+ 
+
+ align:start position:0%
+I have some block of
+material piece of element of my
+
+ align:start position:0%
+material piece of element of my
+ 
+
+ align:start position:0%
+material piece of element of my
+system and let me characterize this by
+
+ align:start position:0%
+system and let me characterize this by
+ 
+
+ align:start position:0%
+system and let me characterize this by
+its average temperature
+
+ align:start position:0%
+its average temperature
+ 
+
+ align:start position:0%
+its average temperature
+T1 and now I'm going to go pour heat
+
+ align:start position:0%
+T1 and now I'm going to go pour heat
+ 
+
+ align:start position:0%
+T1 and now I'm going to go pour heat
+into this thing Q right this is the
+
+ align:start position:0%
+into this thing Q right this is the
+ 
+
+ align:start position:0%
+into this thing Q right this is the
+power dissipation you know maybe it's at
+
+ align:start position:0%
+power dissipation you know maybe it's at
+ 
+
+ align:start position:0%
+power dissipation you know maybe it's at
+this surface this is going in and
+
+ align:start position:0%
+this surface this is going in and
+ 
+
+ align:start position:0%
+this surface this is going in and
+heating this thing up and this thing is
+
+ align:start position:0%
+heating this thing up and this thing is
+ 
+
+ align:start position:0%
+heating this thing up and this thing is
+transferring energy to ground how would
+
+ align:start position:0%
+transferring energy to ground how would
+ 
+
+ align:start position:0%
+transferring energy to ground how would
+I model that well the the steady state
+
+ align:start position:0%
+I model that well the the steady state
+ 
+
+ align:start position:0%
+I model that well the the steady state
+model would be look like this right uh
+
+ align:start position:0%
+model would be look like this right uh
+ 
+
+ align:start position:0%
+model would be look like this right uh
+so this is p disc or this is Q I guess
+
+ align:start position:0%
+so this is p disc or this is Q I guess
+ 
+
+ align:start position:0%
+so this is p disc or this is Q I guess
+what did I call my note I guess I called
+
+ align:start position:0%
+what did I call my note I guess I called
+ 
+
+ align:start position:0%
+what did I call my note I guess I called
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+Q
+
+ align:start position:0%
+Q
+ 
+
+ align:start position:0%
+Q
+okay then I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have some if this is T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ambient right this is
+
+ align:start position:0%
+ambient right this is
+ 
+
+ align:start position:0%
+ambient right this is
+rth and this is T1 right so this is the
+
+ align:start position:0%
+rth and this is T1 right so this is the
+ 
+
+ align:start position:0%
+rth and this is T1 right so this is the
+thermal model in steady state for this
+
+ align:start position:0%
+thermal model in steady state for this
+ 
+
+ align:start position:0%
+thermal model in steady state for this
+thing okay how do I count for the fact
+
+ align:start position:0%
+thing okay how do I count for the fact
+ 
+
+ align:start position:0%
+thing okay how do I count for the fact
+that this thing has some thermal Mass it
+
+ align:start position:0%
+that this thing has some thermal Mass it
+ 
+
+ align:start position:0%
+that this thing has some thermal Mass it
+takes time to heat up well I find find
+
+ align:start position:0%
+takes time to heat up well I find find
+ 
+
+ align:start position:0%
+takes time to heat up well I find find
+out what his thermal capacitance is and
+
+ align:start position:0%
+out what his thermal capacitance is and
+ 
+
+ align:start position:0%
+out what his thermal capacitance is and
+I put it right
+
+ align:start position:0%
+I put it right
+ 
+
+ align:start position:0%
+I put it right
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+cth
+
+ align:start position:0%
+cth
+ 
+
+ align:start position:0%
+cth
+okay now this gives me a model so that
+
+ align:start position:0%
+okay now this gives me a model so that
+ 
+
+ align:start position:0%
+okay now this gives me a model so that
+if some at some time right suppose
+
+ align:start position:0%
+if some at some time right suppose
+ 
+
+ align:start position:0%
+if some at some time right suppose
+here's T right if I come in here and I
+
+ align:start position:0%
+here's T right if I come in here and I
+ 
+
+ align:start position:0%
+here's T right if I come in here and I
+say okay here is Q of
+
+ align:start position:0%
+say okay here is Q of
+ 
+
+ align:start position:0%
+say okay here is Q of
+T it's
+
+ align:start position:0%
+T it's
+ 
+
+ align:start position:0%
+T it's
+steps this is Q of T and at T equals z
+
+ align:start position:0%
+steps this is Q of T and at T equals z
+ 
+
+ align:start position:0%
+steps this is Q of T and at T equals z
+it turns on right what I'm going to get
+
+ align:start position:0%
+it turns on right what I'm going to get
+ 
+
+ align:start position:0%
+it turns on right what I'm going to get
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+T1 with respect to
+
+ align:start position:0%
+T1 with respect to
+ 
+
+ align:start position:0%
+T1 with respect to
+ambient uh that's going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this right it
+
+ align:start position:0%
+this right it
+ 
+
+ align:start position:0%
+this right it
+eventually I'm going to get you know the
+
+ align:start position:0%
+eventually I'm going to get you know the
+ 
+
+ align:start position:0%
+eventually I'm going to get you know the
+final value is going to be uh T1 minus t
+
+ align:start position:0%
+final value is going to be uh T1 minus t
+ 
+
+ align:start position:0%
+final value is going to be uh T1 minus t
+ambient is going to be equal to Q *
+
+ align:start position:0%
+ambient is going to be equal to Q *
+ 
+
+ align:start position:0%
+ambient is going to be equal to Q *
+rth that's its final value and it's
+
+ align:start position:0%
+rth that's its final value and it's
+ 
+
+ align:start position:0%
+rth that's its final value and it's
+going to rise with a time constant
+
+ align:start position:0%
+going to rise with a time constant
+ 
+
+ align:start position:0%
+going to rise with a time constant
+tow that's equal to RH
+
+ align:start position:0%
+tow that's equal to RH
+ 
+
+ align:start position:0%
+tow that's equal to RH
+TH or RH C rth
+
+ align:start position:0%
+TH or RH C rth
+ 
+
+ align:start position:0%
+TH or RH C rth
+cth okay so it you know it'll have a
+
+ align:start position:0%
+cth okay so it you know it'll have a
+ 
+
+ align:start position:0%
+cth okay so it you know it'll have a
+time constant it'll rise up so it won't
+
+ align:start position:0%
+time constant it'll rise up so it won't
+ 
+
+ align:start position:0%
+time constant it'll rise up so it won't
+immediately get hot it'll just rise over
+
+ align:start position:0%
+immediately get hot it'll just rise over
+ 
+
+ align:start position:0%
+immediately get hot it'll just rise over
+time okay now I should
+
+ align:start position:0%
+time okay now I should
+ 
+
+ align:start position:0%
+time okay now I should
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fundamentally a thermal
+
+ align:start position:0%
+fundamentally a thermal
+ 
+
+ align:start position:0%
+fundamentally a thermal
+capacitance should technically always be
+
+ align:start position:0%
+capacitance should technically always be
+ 
+
+ align:start position:0%
+capacitance should technically always be
+referenced to absolute zero
+
+ align:start position:0%
+referenced to absolute zero
+ 
+
+ align:start position:0%
+referenced to absolute zero
+if I'm just dealing with some ambient
+
+ align:start position:0%
+if I'm just dealing with some ambient
+ 
+
+ align:start position:0%
+if I'm just dealing with some ambient
+and I want to call it an offset I can
+
+ align:start position:0%
+and I want to call it an offset I can
+ 
+
+ align:start position:0%
+and I want to call it an offset I can
+reference it to a fixed temperature but
+
+ align:start position:0%
+reference it to a fixed temperature but
+ 
+
+ align:start position:0%
+reference it to a fixed temperature but
+thermal capacitance is in terms of
+
+ align:start position:0%
+thermal capacitance is in terms of
+ 
+
+ align:start position:0%
+thermal capacitance is in terms of
+modeling them heating up I really have
+
+ align:start position:0%
+modeling them heating up I really have
+ 
+
+ align:start position:0%
+modeling them heating up I really have
+to in terms of modeling the physics I
+
+ align:start position:0%
+to in terms of modeling the physics I
+ 
+
+ align:start position:0%
+to in terms of modeling the physics I
+always have to have that thermal
+
+ align:start position:0%
+always have to have that thermal
+ 
+
+ align:start position:0%
+always have to have that thermal
+capacitance to my reference point which
+
+ align:start position:0%
+capacitance to my reference point which
+ 
+
+ align:start position:0%
+capacitance to my reference point which
+would ideally be 0 degrees
+
+ align:start position:0%
+would ideally be 0 degrees
+ 
+
+ align:start position:0%
+would ideally be 0 degrees
+Kelvin okay and I'll come back to that
+
+ align:start position:0%
+Kelvin okay and I'll come back to that
+ 
+
+ align:start position:0%
+Kelvin okay and I'll come back to that
+in a moment any questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+though so in this case where we have
+
+ align:start position:0%
+though so in this case where we have
+ 
+
+ align:start position:0%
+though so in this case where we have
+multiple devices how would we insert the
+
+ align:start position:0%
+multiple devices how would we insert the
+ 
+
+ align:start position:0%
+multiple devices how would we insert the
+thermal capacitances that's right well
+
+ align:start position:0%
+thermal capacitances that's right well
+ 
+
+ align:start position:0%
+thermal capacitances that's right well
+so in this case
+
+ align:start position:0%
+so in this case
+ 
+
+ align:start position:0%
+so in this case
+right if I was talking and you got to
+
+ align:start position:0%
+right if I was talking and you got to
+ 
+
+ align:start position:0%
+right if I was talking and you got to
+say the thermal capacitance of what now
+
+ align:start position:0%
+say the thermal capacitance of what now
+ 
+
+ align:start position:0%
+say the thermal capacitance of what now
+the heat sink the device if I was
+
+ align:start position:0%
+the heat sink the device if I was
+ 
+
+ align:start position:0%
+the heat sink the device if I was
+talking about the thermal capacitance of
+
+ align:start position:0%
+talking about the thermal capacitance of
+ 
+
+ align:start position:0%
+talking about the thermal capacitance of
+the device I would put that right here
+
+ align:start position:0%
+the device I would put that right here
+ 
+
+ align:start position:0%
+the device I would put that right here
+right so this device package might have
+
+ align:start position:0%
+right so this device package might have
+ 
+
+ align:start position:0%
+right so this device package might have
+a thermal capacitance and this device
+
+ align:start position:0%
+a thermal capacitance and this device
+ 
+
+ align:start position:0%
+a thermal capacitance and this device
+might have a thermal capacitance and I
+
+ align:start position:0%
+might have a thermal capacitance and I
+ 
+
+ align:start position:0%
+might have a thermal capacitance and I
+ought to place it to to the reference
+
+ align:start position:0%
+ought to place it to to the reference
+ 
+
+ align:start position:0%
+ought to place it to to the reference
+potential the heat sink might have a
+
+ align:start position:0%
+potential the heat sink might have a
+ 
+
+ align:start position:0%
+potential the heat sink might have a
+thermal capacitance and then I get a
+
+ align:start position:0%
+thermal capacitance and then I get a
+ 
+
+ align:start position:0%
+thermal capacitance and then I get a
+higher order thing right now when I get
+
+ align:start position:0%
+higher order thing right now when I get
+ 
+
+ align:start position:0%
+higher order thing right now when I get
+to T equals infinity and I have some
+
+ align:start position:0%
+to T equals infinity and I have some
+ 
+
+ align:start position:0%
+to T equals infinity and I have some
+step response here it always settles out
+
+ align:start position:0%
+step response here it always settles out
+ 
+
+ align:start position:0%
+step response here it always settles out
+to the same steady state
+
+ align:start position:0%
+to the same steady state
+ 
+
+ align:start position:0%
+to the same steady state
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+OKAY along those
+
+ align:start position:0%
+OKAY along those
+ 
+
+ align:start position:0%
+OKAY along those
+lines what happens if I'm not too happy
+
+ align:start position:0%
+lines what happens if I'm not too happy
+ 
+
+ align:start position:0%
+lines what happens if I'm not too happy
+with the resolution I have here right
+
+ align:start position:0%
+with the resolution I have here right
+ 
+
+ align:start position:0%
+with the resolution I have here right
+I'm basically treating T1 of this whole
+
+ align:start position:0%
+I'm basically treating T1 of this whole
+ 
+
+ align:start position:0%
+I'm basically treating T1 of this whole
+block as being the same thing right but
+
+ align:start position:0%
+block as being the same thing right but
+ 
+
+ align:start position:0%
+block as being the same thing right but
+in reality I recognize you know if the
+
+ align:start position:0%
+in reality I recognize you know if the
+ 
+
+ align:start position:0%
+in reality I recognize you know if the
+Heat's really coming in over here this
+
+ align:start position:0%
+Heat's really coming in over here this
+ 
+
+ align:start position:0%
+Heat's really coming in over here this
+ends hotter this ends it cooler right
+
+ align:start position:0%
+ends hotter this ends it cooler right
+ 
+
+ align:start position:0%
+ends hotter this ends it cooler right
+it's not got spatially it doesn't have
+
+ align:start position:0%
+it's not got spatially it doesn't have
+ 
+
+ align:start position:0%
+it's not got spatially it doesn't have
+the same temperature
+
+ align:start position:0%
+the same temperature
+ 
+
+ align:start position:0%
+the same temperature
+everywhere right and maybe even
+
+ align:start position:0%
+everywhere right and maybe even
+ 
+
+ align:start position:0%
+everywhere right and maybe even
+temporally it doesn't have the same
+
+ align:start position:0%
+temporally it doesn't have the same
+ 
+
+ align:start position:0%
+temporally it doesn't have the same
+temperature everywhere if I'm not happy
+
+ align:start position:0%
+temperature everywhere if I'm not happy
+ 
+
+ align:start position:0%
+temperature everywhere if I'm not happy
+with this model I can break it up into
+
+ align:start position:0%
+with this model I can break it up into
+ 
+
+ align:start position:0%
+with this model I can break it up into
+more lumps right so I can come over and
+
+ align:start position:0%
+more lumps right so I can come over and
+ 
+
+ align:start position:0%
+more lumps right so I can come over and
+say okay um here's my
+
+ align:start position:0%
+say okay um here's my
+ 
+
+ align:start position:0%
+say okay um here's my
+Beast right let me break this up into
+
+ align:start position:0%
+Beast right let me break this up into
+ 
+
+ align:start position:0%
+Beast right let me break this up into
+T1 T2
+
+ align:start position:0%
+T1 T2
+ 
+
+ align:start position:0%
+T1 T2
+here's T ambient right here's Q right
+
+ align:start position:0%
+here's T ambient right here's Q right
+ 
+
+ align:start position:0%
+here's T ambient right here's Q right
+and now I have a different thermal model
+
+ align:start position:0%
+and now I have a different thermal model
+ 
+
+ align:start position:0%
+and now I have a different thermal model
+right I have q coming
+
+ align:start position:0%
+right I have q coming
+ 
+
+ align:start position:0%
+right I have q coming
+in I could say okay
+
+ align:start position:0%
+in I could say okay
+ 
+
+ align:start position:0%
+in I could say okay
+here's
+
+ align:start position:0%
+here's
+ 
+
+ align:start position:0%
+here's
+cth1 for just this
+
+ align:start position:0%
+cth1 for just this
+ 
+
+ align:start position:0%
+cth1 for just this
+region here's
+
+ align:start position:0%
+region here's
+ 
+
+ align:start position:0%
+region here's
+rth 1 to2 which is the thermal
+
+ align:start position:0%
+rth 1 to2 which is the thermal
+ 
+
+ align:start position:0%
+rth 1 to2 which is the thermal
+resistance here here's cth for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+block and here's the thermal
+
+ align:start position:0%
+block and here's the thermal
+ 
+
+ align:start position:0%
+block and here's the thermal
+resistance coming back to ambient here
+
+ align:start position:0%
+resistance coming back to ambient here
+ 
+
+ align:start position:0%
+resistance coming back to ambient here
+and this is going to be
+
+ align:start position:0%
+and this is going to be
+ 
+
+ align:start position:0%
+and this is going to be
+T2 this is going to be T1 right and now
+
+ align:start position:0%
+T2 this is going to be T1 right and now
+ 
+
+ align:start position:0%
+T2 this is going to be T1 right and now
+I have something that's more spatially
+
+ align:start position:0%
+I have something that's more spatially
+ 
+
+ align:start position:0%
+I have something that's more spatially
+accurate right if all things were equal
+
+ align:start position:0%
+accurate right if all things were equal
+ 
+
+ align:start position:0%
+accurate right if all things were equal
+rth cth would be sort of a factor of
+
+ align:start position:0%
+rth cth would be sort of a factor of
+ 
+
+ align:start position:0%
+rth cth would be sort of a factor of
+four smaller I'd get better time
+
+ align:start position:0%
+four smaller I'd get better time
+ 
+
+ align:start position:0%
+four smaller I'd get better time
+resolution and better spatial resolution
+
+ align:start position:0%
+resolution and better spatial resolution
+ 
+
+ align:start position:0%
+resolution and better spatial resolution
+as to how I'm modeling my system if I
+
+ align:start position:0%
+as to how I'm modeling my system if I
+ 
+
+ align:start position:0%
+as to how I'm modeling my system if I
+carry this to an ex
+
+ align:start position:0%
+carry this to an ex
+ 
+
+ align:start position:0%
+carry this to an ex
+I get basically in back to Foria heat
+
+ align:start position:0%
+I get basically in back to Foria heat
+ 
+
+ align:start position:0%
+I get basically in back to Foria heat
+transfer in partial differential
+
+ align:start position:0%
+transfer in partial differential
+ 
+
+ align:start position:0%
+transfer in partial differential
+equations so this is sort of your best
+
+ align:start position:0%
+equations so this is sort of your best
+ 
+
+ align:start position:0%
+equations so this is sort of your best
+lumped model approximation to 4A heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transfer any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay um how do
+
+ align:start position:0%
+okay um how do
+ 
+
+ align:start position:0%
+okay um how do
+people model
+
+ align:start position:0%
+people model
+ 
+
+ align:start position:0%
+people model
+this in you
+
+ align:start position:0%
+this in you
+ 
+
+ align:start position:0%
+this in you
+know you know say the thermal capacity
+
+ align:start position:0%
+know you know say the thermal capacity
+ 
+
+ align:start position:0%
+know you know say the thermal capacity
+aspect sometimes you can look up the
+
+ align:start position:0%
+aspect sometimes you can look up the
+ 
+
+ align:start position:0%
+aspect sometimes you can look up the
+ther like if you have a material you can
+
+ align:start position:0%
+ther like if you have a material you can
+ 
+
+ align:start position:0%
+ther like if you have a material you can
+go look up its heat capacity and then
+
+ align:start position:0%
+go look up its heat capacity and then
+ 
+
+ align:start position:0%
+go look up its heat capacity and then
+multiply by the mass and you get a
+
+ align:start position:0%
+multiply by the mass and you get a
+ 
+
+ align:start position:0%
+multiply by the mass and you get a
+thermal capacitance and you can do do it
+
+ align:start position:0%
+thermal capacitance and you can do do it
+ 
+
+ align:start position:0%
+thermal capacitance and you can do do it
+from fundamentals this way that's not
+
+ align:start position:0%
+from fundamentals this way that's not
+ 
+
+ align:start position:0%
+from fundamentals this way that's not
+always the way they give it to you for a
+
+ align:start position:0%
+always the way they give it to you for a
+ 
+
+ align:start position:0%
+always the way they give it to you for a
+device right because if I think about it
+
+ align:start position:0%
+device right because if I think about it
+ 
+
+ align:start position:0%
+device right because if I think about it
+a device is kind of a complicated thing
+
+ align:start position:0%
+a device is kind of a complicated thing
+ 
+
+ align:start position:0%
+a device is kind of a complicated thing
+right there's the silicon and then maybe
+
+ align:start position:0%
+right there's the silicon and then maybe
+ 
+
+ align:start position:0%
+right there's the silicon and then maybe
+inside there's some header and there's
+
+ align:start position:0%
+inside there's some header and there's
+ 
+
+ align:start position:0%
+inside there's some header and there's
+you know different stuff going on
+
+ align:start position:0%
+you know different stuff going on
+ 
+
+ align:start position:0%
+you know different stuff going on
+sometimes what they will do is they will
+
+ align:start position:0%
+sometimes what they will do is they will
+ 
+
+ align:start position:0%
+sometimes what they will do is they will
+give you a
+
+ align:start position:0%
+give you a
+ 
+
+ align:start position:0%
+give you a
+lumped
+
+ align:start position:0%
+lumped
+ 
+
+ align:start position:0%
+lumped
+model and unfortunately this is often
+
+ align:start position:0%
+model and unfortunately this is often
+ 
+
+ align:start position:0%
+model and unfortunately this is often
+called a uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transient thermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impedance or
+
+ align:start position:0%
+impedance or
+ 
+
+ align:start position:0%
+impedance or
+zth and it's a kind I say unfortunately
+
+ align:start position:0%
+zth and it's a kind I say unfortunately
+ 
+
+ align:start position:0%
+zth and it's a kind I say unfortunately
+because it's not an impedance in the way
+
+ align:start position:0%
+because it's not an impedance in the way
+ 
+
+ align:start position:0%
+because it's not an impedance in the way
+you think about an impedance is a
+
+ align:start position:0%
+you think about an impedance is a
+ 
+
+ align:start position:0%
+you think about an impedance is a
+frequency domain thing right
+
+ align:start position:0%
+frequency domain thing right
+ 
+
+ align:start position:0%
+frequency domain thing right
+but this is just the language that is
+
+ align:start position:0%
+but this is just the language that is
+ 
+
+ align:start position:0%
+but this is just the language that is
+stuck it's unfortunate but that's what
+
+ align:start position:0%
+stuck it's unfortunate but that's what
+ 
+
+ align:start position:0%
+stuck it's unfortunate but that's what
+they call it but it's not an impedance
+
+ align:start position:0%
+they call it but it's not an impedance
+ 
+
+ align:start position:0%
+they call it but it's not an impedance
+at all here is an example this is the
+
+ align:start position:0%
+at all here is an example this is the
+ 
+
+ align:start position:0%
+at all here is an example this is the
+transient they or here they actually
+
+ align:start position:0%
+transient they or here they actually
+ 
+
+ align:start position:0%
+transient they or here they actually
+they they they call it the maximum
+
+ align:start position:0%
+they they they call it the maximum
+ 
+
+ align:start position:0%
+they they they call it the maximum
+effective transient thermal impedance
+
+ align:start position:0%
+effective transient thermal impedance
+ 
+
+ align:start position:0%
+effective transient thermal impedance
+Junction to
+
+ align:start position:0%
+Junction to
+ 
+
+ align:start position:0%
+Junction to
+case so what does this thing mean this
+
+ align:start position:0%
+case so what does this thing mean this
+ 
+
+ align:start position:0%
+case so what does this thing mean this
+thing means if I took the device
+
+ align:start position:0%
+thing means if I took the device
+ 
+
+ align:start position:0%
+thing means if I took the device
+case and I mounted it against a really
+
+ align:start position:0%
+case and I mounted it against a really
+ 
+
+ align:start position:0%
+case and I mounted it against a really
+Mega good heat sink that's just going to
+
+ align:start position:0%
+Mega good heat sink that's just going to
+ 
+
+ align:start position:0%
+Mega good heat sink that's just going to
+hold the temperature exactly at ambient
+
+ align:start position:0%
+hold the temperature exactly at ambient
+ 
+
+ align:start position:0%
+hold the temperature exactly at ambient
+okay a perfect heat
+
+ align:start position:0%
+okay a perfect heat
+ 
+
+ align:start position:0%
+okay a perfect heat
+SN
+
+ align:start position:0%
+SN
+ 
+
+ align:start position:0%
+SN
+then I steep the power into it and when
+
+ align:start position:0%
+then I steep the power into it and when
+ 
+
+ align:start position:0%
+then I steep the power into it and when
+they say a single pulse what this really
+
+ align:start position:0%
+they say a single pulse what this really
+ 
+
+ align:start position:0%
+they say a single pulse what this really
+is is a plot of the step response it's
+
+ align:start position:0%
+is is a plot of the step response it's
+ 
+
+ align:start position:0%
+is is a plot of the step response it's
+basically this plot for the junction
+
+ align:start position:0%
+basically this plot for the junction
+ 
+
+ align:start position:0%
+basically this plot for the junction
+temperature above the case where the
+
+ align:start position:0%
+temperature above the case where the
+ 
+
+ align:start position:0%
+temperature above the case where the
+case is held exactly at constant right
+
+ align:start position:0%
+case is held exactly at constant right
+ 
+
+ align:start position:0%
+case is held exactly at constant right
+so what this is saying is if I put if I
+
+ align:start position:0%
+so what this is saying is if I put if I
+ 
+
+ align:start position:0%
+so what this is saying is if I put if I
+put one pulse into this
+
+ align:start position:0%
+put one pulse into this
+ 
+
+ align:start position:0%
+put one pulse into this
+device um and I waited 10 the minus 4
+
+ align:start position:0%
+device um and I waited 10 the minus 4
+ 
+
+ align:start position:0%
+device um and I waited 10 the minus 4
+seconds I would have a 0.1 degre C per
+
+ align:start position:0%
+seconds I would have a 0.1 degre C per
+ 
+
+ align:start position:0%
+seconds I would have a 0.1 degre C per
+watt of that
+
+ align:start position:0%
+watt of that
+ 
+
+ align:start position:0%
+watt of that
+step rise so if I had a 10 watt step I'd
+
+ align:start position:0%
+step rise so if I had a 10 watt step I'd
+ 
+
+ align:start position:0%
+step rise so if I had a 10 watt step I'd
+have a one degre C rise after uh 100
+
+ align:start position:0%
+have a one degre C rise after uh 100
+ 
+
+ align:start position:0%
+have a one degre C rise after uh 100
+micros seconds after a millisecond I'd
+
+ align:start position:0%
+micros seconds after a millisecond I'd
+ 
+
+ align:start position:0%
+micros seconds after a millisecond I'd
+have um a higher value Etc so this curve
+
+ align:start position:0%
+have um a higher value Etc so this curve
+ 
+
+ align:start position:0%
+have um a higher value Etc so this curve
+oh you can't yeah if you can see my
+
+ align:start position:0%
+oh you can't yeah if you can see my
+ 
+
+ align:start position:0%
+oh you can't yeah if you can see my
+cursor right this curve is really a log
+
+ align:start position:0%
+cursor right this curve is really a log
+ 
+
+ align:start position:0%
+cursor right this curve is really a log
+log plot of the step
+
+ align:start position:0%
+log plot of the step
+ 
+
+ align:start position:0%
+log plot of the step
+response okay if it has one time const
+
+ align:start position:0%
+response okay if it has one time const
+ 
+
+ align:start position:0%
+response okay if it has one time const
+it would look like one thing if it has
+
+ align:start position:0%
+it would look like one thing if it has
+ 
+
+ align:start position:0%
+it would look like one thing if it has
+multiple time constants you know the
+
+ align:start position:0%
+multiple time constants you know the
+ 
+
+ align:start position:0%
+multiple time constants you know the
+shape of this curve changes okay so a
+
+ align:start position:0%
+shape of this curve changes okay so a
+ 
+
+ align:start position:0%
+shape of this curve changes okay so a
+transient thermal impedance what they're
+
+ align:start position:0%
+transient thermal impedance what they're
+ 
+
+ align:start position:0%
+transient thermal impedance what they're
+really telling you is essentially this
+
+ align:start position:0%
+really telling you is essentially this
+ 
+
+ align:start position:0%
+really telling you is essentially this
+step response for the device assuming
+
+ align:start position:0%
+step response for the device assuming
+ 
+
+ align:start position:0%
+step response for the device assuming
+it's against the perfect heat
+
+ align:start position:0%
+it's against the perfect heat
+ 
+
+ align:start position:0%
+it's against the perfect heat
+sink okay what they also sometimes tell
+
+ align:start position:0%
+sink okay what they also sometimes tell
+ 
+
+ align:start position:0%
+sink okay what they also sometimes tell
+you is if I now have little pulses I
+
+ align:start position:0%
+you is if I now have little pulses I
+ 
+
+ align:start position:0%
+you is if I now have little pulses I
+step it up and I step it down and I wait
+
+ align:start position:0%
+step it up and I step it down and I wait
+ 
+
+ align:start position:0%
+step it up and I step it down and I wait
+a while I step it up and I step it down
+
+ align:start position:0%
+a while I step it up and I step it down
+ 
+
+ align:start position:0%
+a while I step it up and I step it down
+and wait a while they will tell you the
+
+ align:start position:0%
+and wait a while they will tell you the
+ 
+
+ align:start position:0%
+and wait a while they will tell you the
+maximum temperature it'll get during the
+
+ align:start position:0%
+maximum temperature it'll get during the
+ 
+
+ align:start position:0%
+maximum temperature it'll get during the
+step for different Duty ratios of pulses
+
+ align:start position:0%
+step for different Duty ratios of pulses
+ 
+
+ align:start position:0%
+step for different Duty ratios of pulses
+all right why do they tell you this
+
+ align:start position:0%
+all right why do they tell you this
+ 
+
+ align:start position:0%
+all right why do they tell you this
+because look if I put 100 watts into
+
+ align:start position:0%
+because look if I put 100 watts into
+ 
+
+ align:start position:0%
+because look if I put 100 watts into
+this device
+
+ align:start position:0%
+this device
+ 
+
+ align:start position:0%
+this device
+continuously and I put the case at 0
+
+ align:start position:0%
+continuously and I put the case at 0
+ 
+
+ align:start position:0%
+continuously and I put the case at 0
+degrees C and I held it there
+
+ align:start position:0%
+degrees C and I held it there
+ 
+
+ align:start position:0%
+degrees C and I held it there
+continuously what this would say is 100
+
+ align:start position:0%
+continuously what this would say is 100
+ 
+
+ align:start position:0%
+continuously what this would say is 100
+time you know 2.5 would give me 250
+
+ align:start position:0%
+time you know 2.5 would give me 250
+ 
+
+ align:start position:0%
+time you know 2.5 would give me 250
+degre C rise right well that' blow the
+
+ align:start position:0%
+degre C rise right well that' blow the
+ 
+
+ align:start position:0%
+degre C rise right well that' blow the
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+up right because this said 150 degre C
+
+ align:start position:0%
+up right because this said 150 degre C
+ 
+
+ align:start position:0%
+up right because this said 150 degre C
+device but if I only did it for a
+
+ align:start position:0%
+device but if I only did it for a
+ 
+
+ align:start position:0%
+device but if I only did it for a
+millisecond this thing would tell me
+
+ align:start position:0%
+millisecond this thing would tell me
+ 
+
+ align:start position:0%
+millisecond this thing would tell me
+that I'd have only 0.1 point2
+
+ align:start position:0%
+that I'd have only 0.1 point2
+ 
+
+ align:start position:0%
+that I'd have only 0.1 point2
+you know I'd be right here on the curve
+
+ align:start position:0%
+you know I'd be right here on the curve
+ 
+
+ align:start position:0%
+you know I'd be right here on the curve
+like3 degrees C per watt and maybe it
+
+ align:start position:0%
+like3 degrees C per watt and maybe it
+ 
+
+ align:start position:0%
+like3 degrees C per watt and maybe it
+would only go up 30°c so I can have a
+
+ align:start position:0%
+would only go up 30°c so I can have a
+ 
+
+ align:start position:0%
+would only go up 30°c so I can have a
+one millisecond pulse that's really big
+
+ align:start position:0%
+one millisecond pulse that's really big
+ 
+
+ align:start position:0%
+one millisecond pulse that's really big
+and it won't kill the device because of
+
+ align:start position:0%
+and it won't kill the device because of
+ 
+
+ align:start position:0%
+and it won't kill the device because of
+the thermal capacitance of the device in
+
+ align:start position:0%
+the thermal capacitance of the device in
+ 
+
+ align:start position:0%
+the thermal capacitance of the device in
+its package okay so thermal transient
+
+ align:start position:0%
+its package okay so thermal transient
+ 
+
+ align:start position:0%
+its package okay so thermal transient
+thermal impedance is a step response
+
+ align:start position:0%
+thermal impedance is a step response
+ 
+
+ align:start position:0%
+thermal impedance is a step response
+plotted on a log log plot
+
+ align:start position:0%
+plotted on a log log plot
+ 
+
+ align:start position:0%
+plotted on a log log plot
+okay the other thing I should tell you
+
+ align:start position:0%
+okay the other thing I should tell you
+ 
+
+ align:start position:0%
+okay the other thing I should tell you
+is that you know you could somehow
+
+ align:start position:0%
+is that you know you could somehow
+ 
+
+ align:start position:0%
+is that you know you could somehow
+extract that model and come up with a
+
+ align:start position:0%
+extract that model and come up with a
+ 
+
+ align:start position:0%
+extract that model and come up with a
+thermal model for the device maybe it's
+
+ align:start position:0%
+thermal model for the device maybe it's
+ 
+
+ align:start position:0%
+thermal model for the device maybe it's
+only one RC that you approximate it with
+
+ align:start position:0%
+only one RC that you approximate it with
+ 
+
+ align:start position:0%
+only one RC that you approximate it with
+okay but in a complicated big you know
+
+ align:start position:0%
+okay but in a complicated big you know
+ 
+
+ align:start position:0%
+okay but in a complicated big you know
+module it might be a more complicated
+
+ align:start position:0%
+module it might be a more complicated
+ 
+
+ align:start position:0%
+module it might be a more complicated
+model because there might be like the
+
+ align:start position:0%
+model because there might be like the
+ 
+
+ align:start position:0%
+model because there might be like the
+thermal capacitance of the Silicon the
+
+ align:start position:0%
+thermal capacitance of the Silicon the
+ 
+
+ align:start position:0%
+thermal capacitance of the Silicon the
+thermal capacitance of the header and so
+
+ align:start position:0%
+thermal capacitance of the header and so
+ 
+
+ align:start position:0%
+thermal capacitance of the header and so
+forth right
+
+ align:start position:0%
+forth right
+ 
+
+ align:start position:0%
+forth right
+um You will often see thermal models
+
+ align:start position:0%
+um You will often see thermal models
+ 
+
+ align:start position:0%
+um You will often see thermal models
+this is called a power form Network you
+
+ align:start position:0%
+this is called a power form Network you
+ 
+
+ align:start position:0%
+this is called a power form Network you
+will often see thermal models in data
+
+ align:start position:0%
+will often see thermal models in data
+ 
+
+ align:start position:0%
+will often see thermal models in data
+sheets or appnotes or something that are
+
+ align:start position:0%
+sheets or appnotes or something that are
+ 
+
+ align:start position:0%
+sheets or appnotes or something that are
+something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that are done like this the
+
+ align:start position:0%
+okay and that are done like this the
+ 
+
+ align:start position:0%
+okay and that are done like this the
+thermal resistances and thermal
+
+ align:start position:0%
+thermal resistances and thermal
+ 
+
+ align:start position:0%
+thermal resistances and thermal
+capacitances that's sort of a a foster
+
+ align:start position:0%
+capacitances that's sort of a a foster
+ 
+
+ align:start position:0%
+capacitances that's sort of a a foster
+form of network that's just wrong
+
+ align:start position:0%
+form of network that's just wrong
+ 
+
+ align:start position:0%
+form of network that's just wrong
+unfortunately you can kind of try to
+
+ align:start position:0%
+unfortunately you can kind of try to
+ 
+
+ align:start position:0%
+unfortunately you can kind of try to
+take this kind of model and map it over
+
+ align:start position:0%
+take this kind of model and map it over
+ 
+
+ align:start position:0%
+take this kind of model and map it over
+to that kind of model but any real
+
+ align:start position:0%
+to that kind of model but any real
+ 
+
+ align:start position:0%
+to that kind of model but any real
+thermal capacitors you're going to
+
+ align:start position:0%
+thermal capacitors you're going to
+ 
+
+ align:start position:0%
+thermal capacitors you're going to
+represent fora heat transfer thermal
+
+ align:start position:0%
+represent fora heat transfer thermal
+ 
+
+ align:start position:0%
+represent fora heat transfer thermal
+capacitances ought to always be down to
+
+ align:start position:0%
+capacitances ought to always be down to
+ 
+
+ align:start position:0%
+capacitances ought to always be down to
+we can use ambient but it should always
+
+ align:start position:0%
+we can use ambient but it should always
+ 
+
+ align:start position:0%
+we can use ambient but it should always
+technically be absolute zero these are
+
+ align:start position:0%
+technically be absolute zero these are
+ 
+
+ align:start position:0%
+technically be absolute zero these are
+me referencing the thermal capacitance
+
+ align:start position:0%
+me referencing the thermal capacitance
+ 
+
+ align:start position:0%
+me referencing the thermal capacitance
+to other places in the thermal path
+
+ align:start position:0%
+to other places in the thermal path
+ 
+
+ align:start position:0%
+to other places in the thermal path
+where the temperature is changing all
+
+ align:start position:0%
+where the temperature is changing all
+ 
+
+ align:start position:0%
+where the temperature is changing all
+right so it's basically just not right
+
+ align:start position:0%
+right so it's basically just not right
+ 
+
+ align:start position:0%
+right so it's basically just not right
+but people do it because it's
+
+ align:start position:0%
+but people do it because it's
+ 
+
+ align:start position:0%
+but people do it because it's
+convenient and I suppose you know if the
+
+ align:start position:0%
+convenient and I suppose you know if the
+ 
+
+ align:start position:0%
+convenient and I suppose you know if the
+thermal capacitance here or the thermal
+
+ align:start position:0%
+thermal capacitance here or the thermal
+ 
+
+ align:start position:0%
+thermal capacitance here or the thermal
+resistance here was super low maybe it's
+
+ align:start position:0%
+resistance here was super low maybe it's
+ 
+
+ align:start position:0%
+resistance here was super low maybe it's
+almost like this was it Earth so they
+
+ align:start position:0%
+almost like this was it Earth so they
+ 
+
+ align:start position:0%
+almost like this was it Earth so they
+can kind of get away with it sometimes
+
+ align:start position:0%
+can kind of get away with it sometimes
+ 
+
+ align:start position:0%
+can kind of get away with it sometimes
+but it's just a warning if you want to
+
+ align:start position:0%
+but it's just a warning if you want to
+ 
+
+ align:start position:0%
+but it's just a warning if you want to
+stick with the physics this is the
+
+ align:start position:0%
+stick with the physics this is the
+ 
+
+ align:start position:0%
+stick with the physics this is the
+correct kind of model to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use so that's just giving you a heads up
+
+ align:start position:0%
+use so that's just giving you a heads up
+ 
+
+ align:start position:0%
+use so that's just giving you a heads up
+I want to just tell you about two more
+
+ align:start position:0%
+I want to just tell you about two more
+ 
+
+ align:start position:0%
+I want to just tell you about two more
+things what I've told you so far is if I
+
+ align:start position:0%
+things what I've told you so far is if I
+ 
+
+ align:start position:0%
+things what I've told you so far is if I
+have like a big package that I'm going
+
+ align:start position:0%
+have like a big package that I'm going
+ 
+
+ align:start position:0%
+have like a big package that I'm going
+to mount it against the heat sink and
+
+ align:start position:0%
+to mount it against the heat sink and
+ 
+
+ align:start position:0%
+to mount it against the heat sink and
+that's a very typical thing you have to
+
+ align:start position:0%
+that's a very typical thing you have to
+ 
+
+ align:start position:0%
+that's a very typical thing you have to
+do in some cases and and in a lot of
+
+ align:start position:0%
+do in some cases and and in a lot of
+ 
+
+ align:start position:0%
+do in some cases and and in a lot of
+designs it doesn't work that way you
+
+ align:start position:0%
+designs it doesn't work that way you
+ 
+
+ align:start position:0%
+designs it doesn't work that way you
+might have something like this here's my
+
+ align:start position:0%
+might have something like this here's my
+ 
+
+ align:start position:0%
+might have something like this here's my
+device that I might Mount instead of
+
+ align:start position:0%
+device that I might Mount instead of
+ 
+
+ align:start position:0%
+device that I might Mount instead of
+mounting my device directly to a heat
+
+ align:start position:0%
+mounting my device directly to a heat
+ 
+
+ align:start position:0%
+mounting my device directly to a heat
+sink right you will often have a circuit
+
+ align:start position:0%
+sink right you will often have a circuit
+ 
+
+ align:start position:0%
+sink right you will often have a circuit
+board here's my circuit board okay and
+
+ align:start position:0%
+board here's my circuit board okay and
+ 
+
+ align:start position:0%
+board here's my circuit board okay and
+I'll have some device and maybe this
+
+ align:start position:0%
+I'll have some device and maybe this
+ 
+
+ align:start position:0%
+I'll have some device and maybe this
+device will have a a heat pad you know
+
+ align:start position:0%
+device will have a a heat pad you know
+ 
+
+ align:start position:0%
+device will have a a heat pad you know
+here's my package it'll have a bunch of
+
+ align:start position:0%
+here's my package it'll have a bunch of
+ 
+
+ align:start position:0%
+here's my package it'll have a bunch of
+electrical connections off the device
+
+ align:start position:0%
+electrical connections off the device
+ 
+
+ align:start position:0%
+electrical connections off the device
+onto the circuit board right so the
+
+ align:start position:0%
+onto the circuit board right so the
+ 
+
+ align:start position:0%
+onto the circuit board right so the
+first thing I do is I mount my device to
+
+ align:start position:0%
+first thing I do is I mount my device to
+ 
+
+ align:start position:0%
+first thing I do is I mount my device to
+the CC circuit
+
+ align:start position:0%
+the CC circuit
+ 
+
+ align:start position:0%
+the CC circuit
+board okay and my electrical connections
+
+ align:start position:0%
+board okay and my electrical connections
+ 
+
+ align:start position:0%
+board okay and my electrical connections
+would come off of that right you know
+
+ align:start position:0%
+would come off of that right you know
+ 
+
+ align:start position:0%
+would come off of that right you know
+I'd run my gate and my source right I'd
+
+ align:start position:0%
+I'd run my gate and my source right I'd
+ 
+
+ align:start position:0%
+I'd run my gate and my source right I'd
+have a bunch of wires on the circuit
+
+ align:start position:0%
+have a bunch of wires on the circuit
+ 
+
+ align:start position:0%
+have a bunch of wires on the circuit
+board going different places so I've
+
+ align:start position:0%
+board going different places so I've
+ 
+
+ align:start position:0%
+board going different places so I've
+made my electrical connection to device
+
+ align:start position:0%
+made my electrical connection to device
+ 
+
+ align:start position:0%
+made my electrical connection to device
+but now I also need to get the heat out
+
+ align:start position:0%
+but now I also need to get the heat out
+ 
+
+ align:start position:0%
+but now I also need to get the heat out
+of it right so what do I do often what
+
+ align:start position:0%
+of it right so what do I do often what
+ 
+
+ align:start position:0%
+of it right so what do I do often what
+you do is you instead of trying to mount
+
+ align:start position:0%
+you do is you instead of trying to mount
+ 
+
+ align:start position:0%
+you do is you instead of trying to mount
+the device directly against the heat
+
+ align:start position:0%
+the device directly against the heat
+ 
+
+ align:start position:0%
+the device directly against the heat
+sink you mount the device to the board
+
+ align:start position:0%
+sink you mount the device to the board
+ 
+
+ align:start position:0%
+sink you mount the device to the board
+carry the heat through the board and
+
+ align:start position:0%
+carry the heat through the board and
+ 
+
+ align:start position:0%
+carry the heat through the board and
+then to a heat sink on the other side so
+
+ align:start position:0%
+then to a heat sink on the other side so
+ 
+
+ align:start position:0%
+then to a heat sink on the other side so
+maybe what I would do
+
+ align:start position:0%
+maybe what I would do
+ 
+
+ align:start position:0%
+maybe what I would do
+is on the other side of the board maybe
+
+ align:start position:0%
+is on the other side of the board maybe
+ 
+
+ align:start position:0%
+is on the other side of the board maybe
+I would put a thermal interface pad
+
+ align:start position:0%
+I would put a thermal interface pad
+ 
+
+ align:start position:0%
+I would put a thermal interface pad
+right and then a heat
+
+ align:start position:0%
+right and then a heat
+ 
+
+ align:start position:0%
+right and then a heat
+sink you know the heat sink's mounted to
+
+ align:start position:0%
+sink you know the heat sink's mounted to
+ 
+
+ align:start position:0%
+sink you know the heat sink's mounted to
+the other side of the
+
+ align:start position:0%
+the other side of the
+ 
+
+ align:start position:0%
+the other side of the
+board okay and I'm going to try to get
+
+ align:start position:0%
+board okay and I'm going to try to get
+ 
+
+ align:start position:0%
+board okay and I'm going to try to get
+heat out of the device through the
+
+ align:start position:0%
+heat out of the device through the
+ 
+
+ align:start position:0%
+heat out of the device through the
+package through the board through the
+
+ align:start position:0%
+package through the board through the
+ 
+
+ align:start position:0%
+package through the board through the
+interface material into the heat
+
+ align:start position:0%
+interface material into the heat
+ 
+
+ align:start position:0%
+interface material into the heat
+sink and this is necessary because you
+
+ align:start position:0%
+sink and this is necessary because you
+ 
+
+ align:start position:0%
+sink and this is necessary because you
+want to connect the device to the board
+
+ align:start position:0%
+want to connect the device to the board
+ 
+
+ align:start position:0%
+want to connect the device to the board
+for the electrical connection is the
+
+ align:start position:0%
+for the electrical connection is the
+ 
+
+ align:start position:0%
+for the electrical connection is the
+most important thing okay so one of the
+
+ align:start position:0%
+most important thing okay so one of the
+ 
+
+ align:start position:0%
+most important thing okay so one of the
+things you often do is you will often
+
+ align:start position:0%
+things you often do is you will often
+ 
+
+ align:start position:0%
+things you often do is you will often
+put thermal vas in the board so what
+
+ align:start position:0%
+put thermal vas in the board so what
+ 
+
+ align:start position:0%
+put thermal vas in the board so what
+you'll do is you go to the board and if
+
+ align:start position:0%
+you'll do is you go to the board and if
+ 
+
+ align:start position:0%
+you'll do is you go to the board and if
+I looked at this from the side you'll
+
+ align:start position:0%
+I looked at this from the side you'll
+ 
+
+ align:start position:0%
+I looked at this from the side you'll
+drill a bunch of holes through the board
+
+ align:start position:0%
+drill a bunch of holes through the board
+ 
+
+ align:start position:0%
+drill a bunch of holes through the board
+you'll put holes in the board like this
+
+ align:start position:0%
+you'll put holes in the board like this
+ 
+
+ align:start position:0%
+you'll put holes in the board like this
+and you'll put what's known as a via
+
+ align:start position:0%
+and you'll put what's known as a via
+ 
+
+ align:start position:0%
+and you'll put what's known as a via
+Farm okay if I looked straight down on
+
+ align:start position:0%
+Farm okay if I looked straight down on
+ 
+
+ align:start position:0%
+Farm okay if I looked straight down on
+top of it you'd see a bunch of holes
+
+ align:start position:0%
+top of it you'd see a bunch of holes
+ 
+
+ align:start position:0%
+top of it you'd see a bunch of holes
+driel in the board like this okay why
+
+ align:start position:0%
+driel in the board like this okay why
+ 
+
+ align:start position:0%
+driel in the board like this okay why
+because those holes will then be played
+
+ align:start position:0%
+because those holes will then be played
+ 
+
+ align:start position:0%
+because those holes will then be played
+with copper which is a good thermal
+
+ align:start position:0%
+with copper which is a good thermal
+ 
+
+ align:start position:0%
+with copper which is a good thermal
+conductor and I it'll help me transfer
+
+ align:start position:0%
+conductor and I it'll help me transfer
+ 
+
+ align:start position:0%
+conductor and I it'll help me transfer
+heat through down through the board to
+
+ align:start position:0%
+heat through down through the board to
+ 
+
+ align:start position:0%
+heat through down through the board to
+the interface material to the heat sink
+
+ align:start position:0%
+the interface material to the heat sink
+ 
+
+ align:start position:0%
+the interface material to the heat sink
+sometimes you fill those holes with
+
+ align:start position:0%
+sometimes you fill those holes with
+ 
+
+ align:start position:0%
+sometimes you fill those holes with
+copper and a fancy board or you fill it
+
+ align:start position:0%
+copper and a fancy board or you fill it
+ 
+
+ align:start position:0%
+copper and a fancy board or you fill it
+with thermally conductive epoxy to help
+
+ align:start position:0%
+with thermally conductive epoxy to help
+ 
+
+ align:start position:0%
+with thermally conductive epoxy to help
+the heat transfer through the board
+
+ align:start position:0%
+the heat transfer through the board
+ 
+
+ align:start position:0%
+the heat transfer through the board
+sometimes you'll try to use a thin board
+
+ align:start position:0%
+sometimes you'll try to use a thin board
+ 
+
+ align:start position:0%
+sometimes you'll try to use a thin board
+so that you have lower thermal
+
+ align:start position:0%
+so that you have lower thermal
+ 
+
+ align:start position:0%
+so that you have lower thermal
+resistance right um this
+
+ align:start position:0%
+resistance right um this
+ 
+
+ align:start position:0%
+resistance right um this
+appnote that uh you'll be provided with
+
+ align:start position:0%
+appnote that uh you'll be provided with
+ 
+
+ align:start position:0%
+appnote that uh you'll be provided with
+in the handouts talks about okay if I
+
+ align:start position:0%
+in the handouts talks about okay if I
+ 
+
+ align:start position:0%
+in the handouts talks about okay if I
+have thermal Vias of a certain length um
+
+ align:start position:0%
+have thermal Vias of a certain length um
+ 
+
+ align:start position:0%
+have thermal Vias of a certain length um
+how many degrees C per watt for a 12 mil
+
+ align:start position:0%
+how many degrees C per watt for a 12 mil
+ 
+
+ align:start position:0%
+how many degrees C per watt for a 12 mil
+via going through a 63 mil board and so
+
+ align:start position:0%
+via going through a 63 mil board and so
+ 
+
+ align:start position:0%
+via going through a 63 mil board and so
+forth you can figure out your thermal
+
+ align:start position:0%
+forth you can figure out your thermal
+ 
+
+ align:start position:0%
+forth you can figure out your thermal
+model transferring your heat through the
+
+ align:start position:0%
+model transferring your heat through the
+ 
+
+ align:start position:0%
+model transferring your heat through the
+circuit
+
+ align:start position:0%
+circuit
+ 
+
+ align:start position:0%
+circuit
+board okay so that's just a heads up
+
+ align:start position:0%
+board okay so that's just a heads up
+ 
+
+ align:start position:0%
+board okay so that's just a heads up
+about how you might do things for PC
+
+ align:start position:0%
+about how you might do things for PC
+ 
+
+ align:start position:0%
+about how you might do things for PC
+board mounted
+
+ align:start position:0%
+board mounted
+ 
+
+ align:start position:0%
+board mounted
+components the last thing I'd like to do
+
+ align:start position:0%
+components the last thing I'd like to do
+ 
+
+ align:start position:0%
+components the last thing I'd like to do
+for you today any questions about
+
+ align:start position:0%
+for you today any questions about
+ 
+
+ align:start position:0%
+for you today any questions about
+that the last thing I wanted to do for
+
+ align:start position:0%
+that the last thing I wanted to do for
+ 
+
+ align:start position:0%
+that the last thing I wanted to do for
+you today is just show you a thermal
+
+ align:start position:0%
+you today is just show you a thermal
+ 
+
+ align:start position:0%
+you today is just show you a thermal
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+example okay so here we go go here's the
+
+ align:start position:0%
+example okay so here we go go here's the
+ 
+
+ align:start position:0%
+example okay so here we go go here's the
+thing I'm going to show you this is for
+
+ align:start position:0%
+thing I'm going to show you this is for
+ 
+
+ align:start position:0%
+thing I'm going to show you this is for
+a particular matching Network design
+
+ align:start position:0%
+a particular matching Network design
+ 
+
+ align:start position:0%
+a particular matching Network design
+that we did and this thing has these
+
+ align:start position:0%
+that we did and this thing has these
+ 
+
+ align:start position:0%
+that we did and this thing has these
+four transistors that are mounted
+
+ align:start position:0%
+four transistors that are mounted
+ 
+
+ align:start position:0%
+four transistors that are mounted
+between the circuit and
+
+ align:start position:0%
+between the circuit and
+ 
+
+ align:start position:0%
+between the circuit and
+ground okay each of these transistors
+
+ align:start position:0%
+ground okay each of these transistors
+ 
+
+ align:start position:0%
+ground okay each of these transistors
+can dissipate like something like 30
+
+ align:start position:0%
+can dissipate like something like 30
+ 
+
+ align:start position:0%
+can dissipate like something like 30
+watts in the worst case high power
+
+ align:start position:0%
+watts in the worst case high power
+ 
+
+ align:start position:0%
+watts in the worst case high power
+design okay so four devices times 30
+
+ align:start position:0%
+design okay so four devices times 30
+ 
+
+ align:start position:0%
+design okay so four devices times 30
+watts is like what's 33 w roughly
+
+ align:start position:0%
+watts is like what's 33 w roughly
+ 
+
+ align:start position:0%
+watts is like what's 33 w roughly
+speaking it's like 140 Watts something
+
+ align:start position:0%
+speaking it's like 140 Watts something
+ 
+
+ align:start position:0%
+speaking it's like 140 Watts something
+like that 13 wats okay that's a lot of
+
+ align:start position:0%
+like that 13 wats okay that's a lot of
+ 
+
+ align:start position:0%
+like that 13 wats okay that's a lot of
+heat to pull out of these little devices
+
+ align:start position:0%
+heat to pull out of these little devices
+ 
+
+ align:start position:0%
+heat to pull out of these little devices
+okay here's the here's the devices okay
+
+ align:start position:0%
+okay here's the here's the devices okay
+ 
+
+ align:start position:0%
+okay here's the here's the devices okay
+these are the package one side of this
+
+ align:start position:0%
+these are the package one side of this
+ 
+
+ align:start position:0%
+these are the package one side of this
+has these electrical connections to the
+
+ align:start position:0%
+has these electrical connections to the
+ 
+
+ align:start position:0%
+has these electrical connections to the
+devices and the other side of this has a
+
+ align:start position:0%
+devices and the other side of this has a
+ 
+
+ align:start position:0%
+devices and the other side of this has a
+big thermal pad out of which the Heat's
+
+ align:start position:0%
+big thermal pad out of which the Heat's
+ 
+
+ align:start position:0%
+big thermal pad out of which the Heat's
+supposed to come so this is a
+
+ align:start position:0%
+supposed to come so this is a
+ 
+
+ align:start position:0%
+supposed to come so this is a
+two-sided device where you you have
+
+ align:start position:0%
+two-sided device where you you have
+ 
+
+ align:start position:0%
+two-sided device where you you have
+electrical connections on one side and a
+
+ align:start position:0%
+electrical connections on one side and a
+ 
+
+ align:start position:0%
+electrical connections on one side and a
+thermal pad for heat transfer on the
+
+ align:start position:0%
+thermal pad for heat transfer on the
+ 
+
+ align:start position:0%
+thermal pad for heat transfer on the
+other side of the device okay so one
+
+ align:start position:0%
+other side of the device okay so one
+ 
+
+ align:start position:0%
+other side of the device okay so one
+side of this device the side that's
+
+ align:start position:0%
+side of this device the side that's
+ 
+
+ align:start position:0%
+side of this device the side that's
+showing flat here is going to be
+
+ align:start position:0%
+showing flat here is going to be
+ 
+
+ align:start position:0%
+showing flat here is going to be
+connected to the circuit board and the
+
+ align:start position:0%
+connected to the circuit board and the
+ 
+
+ align:start position:0%
+connected to the circuit board and the
+other side of the device we're going to
+
+ align:start position:0%
+other side of the device we're going to
+ 
+
+ align:start position:0%
+other side of the device we're going to
+want to connect to the heat sink okay so
+
+ align:start position:0%
+want to connect to the heat sink okay so
+ 
+
+ align:start position:0%
+want to connect to the heat sink okay so
+what do we do uh here you can see one
+
+ align:start position:0%
+what do we do uh here you can see one
+ 
+
+ align:start position:0%
+what do we do uh here you can see one
+side this is the top side of the circuit
+
+ align:start position:0%
+side this is the top side of the circuit
+ 
+
+ align:start position:0%
+side this is the top side of the circuit
+board this is not the side of the
+
+ align:start position:0%
+board this is not the side of the
+ 
+
+ align:start position:0%
+board this is not the side of the
+circuit board where the devices are on
+
+ align:start position:0%
+circuit board where the devices are on
+ 
+
+ align:start position:0%
+circuit board where the devices are on
+the devices are mounted to the bottom
+
+ align:start position:0%
+the devices are mounted to the bottom
+ 
+
+ align:start position:0%
+the devices are mounted to the bottom
+side of the circuit board and part of
+
+ align:start position:0%
+side of the circuit board and part of
+ 
+
+ align:start position:0%
+side of the circuit board and part of
+the bottom side of the circuit board is
+
+ align:start position:0%
+the bottom side of the circuit board is
+ 
+
+ align:start position:0%
+the bottom side of the circuit board is
+this silver ground plane you see here
+
+ align:start position:0%
+this silver ground plane you see here
+ 
+
+ align:start position:0%
+this silver ground plane you see here
+these are the devices the side of the
+
+ align:start position:0%
+these are the devices the side of the
+ 
+
+ align:start position:0%
+these are the devices the side of the
+device you cannot see is what's got the
+
+ align:start position:0%
+device you cannot see is what's got the
+ 
+
+ align:start position:0%
+device you cannot see is what's got the
+electrical connections for the drain and
+
+ align:start position:0%
+electrical connections for the drain and
+ 
+
+ align:start position:0%
+electrical connections for the drain and
+the gate and the source and the drivers
+
+ align:start position:0%
+the gate and the source and the drivers
+ 
+
+ align:start position:0%
+the gate and the source and the drivers
+and the drivers are all on this side of
+
+ align:start position:0%
+and the drivers are all on this side of
+ 
+
+ align:start position:0%
+and the drivers are all on this side of
+the board okay so what's exposed here on
+
+ align:start position:0%
+the board okay so what's exposed here on
+ 
+
+ align:start position:0%
+the board okay so what's exposed here on
+the bottom side of the board is the uh
+
+ align:start position:0%
+the bottom side of the board is the uh
+ 
+
+ align:start position:0%
+the bottom side of the board is the uh
+heat pad through which I'm going to try
+
+ align:start position:0%
+heat pad through which I'm going to try
+ 
+
+ align:start position:0%
+heat pad through which I'm going to try
+to transfer
+
+ align:start position:0%
+to transfer
+ 
+
+ align:start position:0%
+to transfer
+heat so what do we do we created a a
+
+ align:start position:0%
+heat so what do we do we created a a
+ 
+
+ align:start position:0%
+heat so what do we do we created a a
+heat
+
+ align:start position:0%
+heat
+ 
+
+ align:start position:0%
+heat
+spreader okay because we're going to
+
+ align:start position:0%
+spreader okay because we're going to
+ 
+
+ align:start position:0%
+spreader okay because we're going to
+flip this board over and bang down on
+
+ align:start position:0%
+flip this board over and bang down on
+ 
+
+ align:start position:0%
+flip this board over and bang down on
+the heat spreader you notice that the
+
+ align:start position:0%
+the heat spreader you notice that the
+ 
+
+ align:start position:0%
+the heat spreader you notice that the
+heat spreader has some like some area
+
+ align:start position:0%
+heat spreader has some like some area
+ 
+
+ align:start position:0%
+heat spreader has some like some area
+mil out right so if you look at this
+
+ align:start position:0%
+mil out right so if you look at this
+ 
+
+ align:start position:0%
+mil out right so if you look at this
+right there's a space
+
+ align:start position:0%
+right there's a space
+ 
+
+ align:start position:0%
+right there's a space
+for the devices to sit in this space in
+
+ align:start position:0%
+for the devices to sit in this space in
+ 
+
+ align:start position:0%
+for the devices to sit in this space in
+these four spaces for the four devices
+
+ align:start position:0%
+these four spaces for the four devices
+ 
+
+ align:start position:0%
+these four spaces for the four devices
+okay so that the circuit board will sit
+
+ align:start position:0%
+okay so that the circuit board will sit
+ 
+
+ align:start position:0%
+okay so that the circuit board will sit
+flat with the heat spreader and then the
+
+ align:start position:0%
+flat with the heat spreader and then the
+ 
+
+ align:start position:0%
+flat with the heat spreader and then the
+devices will s down and sit flat against
+
+ align:start position:0%
+devices will s down and sit flat against
+ 
+
+ align:start position:0%
+devices will s down and sit flat against
+the Little M out
+
+ align:start position:0%
+the Little M out
+ 
+
+ align:start position:0%
+the Little M out
+area um these little circles here are
+
+ align:start position:0%
+area um these little circles here are
+ 
+
+ align:start position:0%
+area um these little circles here are
+just areas for extra solder to flow out
+
+ align:start position:0%
+just areas for extra solder to flow out
+ 
+
+ align:start position:0%
+just areas for extra solder to flow out
+of the device okay so what we're going
+
+ align:start position:0%
+of the device okay so what we're going
+ 
+
+ align:start position:0%
+of the device okay so what we're going
+to do is we have the device soldered to
+
+ align:start position:0%
+to do is we have the device soldered to
+ 
+
+ align:start position:0%
+to do is we have the device soldered to
+the board and then we're going to solder
+
+ align:start position:0%
+the board and then we're going to solder
+ 
+
+ align:start position:0%
+the board and then we're going to solder
+it to this heat spreader okay how do we
+
+ align:start position:0%
+it to this heat spreader okay how do we
+ 
+
+ align:start position:0%
+it to this heat spreader okay how do we
+make that work well the first thing we
+
+ align:start position:0%
+make that work well the first thing we
+ 
+
+ align:start position:0%
+make that work well the first thing we
+do is we solder the circuit the the all
+
+ align:start position:0%
+do is we solder the circuit the the all
+ 
+
+ align:start position:0%
+do is we solder the circuit the the all
+the chips to the board with high
+
+ align:start position:0%
+the chips to the board with high
+ 
+
+ align:start position:0%
+the chips to the board with high
+temperature solder so then then I I've
+
+ align:start position:0%
+temperature solder so then then I I've
+ 
+
+ align:start position:0%
+temperature solder so then then I I've
+mounted my device to the board now I put
+
+ align:start position:0%
+mounted my device to the board now I put
+ 
+
+ align:start position:0%
+mounted my device to the board now I put
+thermal I put solder ball I put solder
+
+ align:start position:0%
+thermal I put solder ball I put solder
+ 
+
+ align:start position:0%
+thermal I put solder ball I put solder
+paste on it here you can see the dots of
+
+ align:start position:0%
+paste on it here you can see the dots of
+ 
+
+ align:start position:0%
+paste on it here you can see the dots of
+solder paste I flip this thing over
+
+ align:start position:0%
+solder paste I flip this thing over
+ 
+
+ align:start position:0%
+solder paste I flip this thing over
+under this heat sink and then I Reflow
+
+ align:start position:0%
+under this heat sink and then I Reflow
+ 
+
+ align:start position:0%
+under this heat sink and then I Reflow
+it again and this solder is low
+
+ align:start position:0%
+it again and this solder is low
+ 
+
+ align:start position:0%
+it again and this solder is low
+temperature solder so I don't unsolder
+
+ align:start position:0%
+temperature solder so I don't unsolder
+ 
+
+ align:start position:0%
+temperature solder so I don't unsolder
+the the device to the board while I do
+
+ align:start position:0%
+the the device to the board while I do
+ 
+
+ align:start position:0%
+the the device to the board while I do
+solder it to the heat spreader make
+
+ align:start position:0%
+solder it to the heat spreader make
+ 
+
+ align:start position:0%
+solder it to the heat spreader make
+sense everybody okay
+
+ align:start position:0%
+sense everybody okay
+ 
+
+ align:start position:0%
+sense everybody okay
+so we got this hierarchy of temperatures
+
+ align:start position:0%
+so we got this hierarchy of temperatures
+ 
+
+ align:start position:0%
+so we got this hierarchy of temperatures
+of my solder how do I cool this device
+
+ align:start position:0%
+of my solder how do I cool this device
+ 
+
+ align:start position:0%
+of my solder how do I cool this device
+now I got this heat spreader which has
+
+ align:start position:0%
+now I got this heat spreader which has
+ 
+
+ align:start position:0%
+now I got this heat spreader which has
+got like you know really low thermal
+
+ align:start position:0%
+got like you know really low thermal
+ 
+
+ align:start position:0%
+got like you know really low thermal
+resistance now right so I've gone from
+
+ align:start position:0%
+resistance now right so I've gone from
+ 
+
+ align:start position:0%
+resistance now right so I've gone from
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+chip directly to the heat spreader and
+
+ align:start position:0%
+chip directly to the heat spreader and
+ 
+
+ align:start position:0%
+chip directly to the heat spreader and
+by the way I said these um this thermal
+
+ align:start position:0%
+by the way I said these um this thermal
+ 
+
+ align:start position:0%
+by the way I said these um this thermal
+pad on the device is actually Connected
+
+ align:start position:0%
+pad on the device is actually Connected
+ 
+
+ align:start position:0%
+pad on the device is actually Connected
+To Source in this particular device and
+
+ align:start position:0%
+To Source in this particular device and
+ 
+
+ align:start position:0%
+To Source in this particular device and
+source is ground in the particular
+
+ align:start position:0%
+source is ground in the particular
+ 
+
+ align:start position:0%
+source is ground in the particular
+circuit so I can basically make this
+
+ align:start position:0%
+circuit so I can basically make this
+ 
+
+ align:start position:0%
+circuit so I can basically make this
+whole heat spreader and the whole thing
+
+ align:start position:0%
+whole heat spreader and the whole thing
+ 
+
+ align:start position:0%
+whole heat spreader and the whole thing
+electrical ground that's kind kind of
+
+ align:start position:0%
+electrical ground that's kind kind of
+ 
+
+ align:start position:0%
+electrical ground that's kind kind of
+nice here's my so I'm going to connect
+
+ align:start position:0%
+nice here's my so I'm going to connect
+ 
+
+ align:start position:0%
+nice here's my so I'm going to connect
+the heat spreader onto this datatron
+
+ align:start position:0%
+the heat spreader onto this datatron
+ 
+
+ align:start position:0%
+the heat spreader onto this datatron
+copper heat
+
+ align:start position:0%
+copper heat
+ 
+
+ align:start position:0%
+copper heat
+sink okay and here's what you can see
+
+ align:start position:0%
+sink okay and here's what you can see
+ 
+
+ align:start position:0%
+sink okay and here's what you can see
+about the seat sink here's the thermal
+
+ align:start position:0%
+about the seat sink here's the thermal
+ 
+
+ align:start position:0%
+about the seat sink here's the thermal
+resistance to ambient of the heat sink
+
+ align:start position:0%
+resistance to ambient of the heat sink
+ 
+
+ align:start position:0%
+resistance to ambient of the heat sink
+versus air flow so this is where I said
+
+ align:start position:0%
+versus air flow so this is where I said
+ 
+
+ align:start position:0%
+versus air flow so this is where I said
+you know yeah to to to really know this
+
+ align:start position:0%
+you know yeah to to to really know this
+ 
+
+ align:start position:0%
+you know yeah to to to really know this
+heat transfer coefficient is a lot of
+
+ align:start position:0%
+heat transfer coefficient is a lot of
+ 
+
+ align:start position:0%
+heat transfer coefficient is a lot of
+work and to design the heat sink to get
+
+ align:start position:0%
+work and to design the heat sink to get
+ 
+
+ align:start position:0%
+work and to design the heat sink to get
+a low heat transfer Coe or a high heat
+
+ align:start position:0%
+a low heat transfer Coe or a high heat
+ 
+
+ align:start position:0%
+a low heat transfer Coe or a high heat
+transfer coefficient hard but somebody
+
+ align:start position:0%
+transfer coefficient hard but somebody
+ 
+
+ align:start position:0%
+transfer coefficient hard but somebody
+else did did that for me all I got to
+
+ align:start position:0%
+else did did that for me all I got to
+ 
+
+ align:start position:0%
+else did did that for me all I got to
+know is how much air I'm going to blow
+
+ align:start position:0%
+know is how much air I'm going to blow
+ 
+
+ align:start position:0%
+know is how much air I'm going to blow
+across this and I can get down to Crazy
+
+ align:start position:0%
+across this and I can get down to Crazy
+ 
+
+ align:start position:0%
+across this and I can get down to Crazy
+low thermal resistances if this wasn't
+
+ align:start position:0%
+low thermal resistances if this wasn't
+ 
+
+ align:start position:0%
+low thermal resistances if this wasn't
+low enough then I'd have to go to liquid
+
+ align:start position:0%
+low enough then I'd have to go to liquid
+ 
+
+ align:start position:0%
+low enough then I'd have to go to liquid
+cooling and get even lower ones okay but
+
+ align:start position:0%
+cooling and get even lower ones okay but
+ 
+
+ align:start position:0%
+cooling and get even lower ones okay but
+we were able to do it there so all we
+
+ align:start position:0%
+we were able to do it there so all we
+ 
+
+ align:start position:0%
+we were able to do it there so all we
+did was then we basically mounted the
+
+ align:start position:0%
+did was then we basically mounted the
+ 
+
+ align:start position:0%
+did was then we basically mounted the
+device to the heat spreader the heat
+
+ align:start position:0%
+device to the heat spreader the heat
+ 
+
+ align:start position:0%
+device to the heat spreader the heat
+spreader the heat sink and then blew air
+
+ align:start position:0%
+spreader the heat sink and then blew air
+ 
+
+ align:start position:0%
+spreader the heat sink and then blew air
+across it here you can see another view
+
+ align:start position:0%
+across it here you can see another view
+ 
+
+ align:start position:0%
+across it here you can see another view
+of it right here's the heat sink the
+
+ align:start position:0%
+of it right here's the heat sink the
+ 
+
+ align:start position:0%
+of it right here's the heat sink the
+device mounted to it and we're going to
+
+ align:start position:0%
+device mounted to it and we're going to
+ 
+
+ align:start position:0%
+device mounted to it and we're going to
+blow a lot of air to it here's the
+
+ align:start position:0%
+blow a lot of air to it here's the
+ 
+
+ align:start position:0%
+blow a lot of air to it here's the
+actual Beast
+
+ align:start position:0%
+actual Beast
+ 
+
+ align:start position:0%
+actual Beast
+right so you can see here's
+
+ align:start position:0%
+right so you can see here's
+ 
+
+ align:start position:0%
+right so you can see here's
+the the circuit mounted to the heat
+
+ align:start position:0%
+the the circuit mounted to the heat
+ 
+
+ align:start position:0%
+the the circuit mounted to the heat
+spreader the heat sink is now all silver
+
+ align:start position:0%
+spreader the heat sink is now all silver
+ 
+
+ align:start position:0%
+spreader the heat sink is now all silver
+because we silver it's silver colored
+
+ align:start position:0%
+because we silver it's silver colored
+ 
+
+ align:start position:0%
+because we silver it's silver colored
+because we silverplated it okay and here
+
+ align:start position:0%
+because we silverplated it okay and here
+ 
+
+ align:start position:0%
+because we silverplated it okay and here
+you could see the fan blowing air
+
+ align:start position:0%
+you could see the fan blowing air
+ 
+
+ align:start position:0%
+you could see the fan blowing air
+through the fins all right the
+
+ align:start position:0%
+through the fins all right the
+ 
+
+ align:start position:0%
+through the fins all right the
+relativity of that is I said we had like
+
+ align:start position:0%
+relativity of that is I said we had like
+ 
+
+ align:start position:0%
+relativity of that is I said we had like
+um 10 and something watts of heat
+
+ align:start position:0%
+um 10 and something watts of heat
+ 
+
+ align:start position:0%
+um 10 and something watts of heat
+dissipation in the worst case but if you
+
+ align:start position:0%
+dissipation in the worst case but if you
+ 
+
+ align:start position:0%
+dissipation in the worst case but if you
+look at the temperature rises of the
+
+ align:start position:0%
+look at the temperature rises of the
+ 
+
+ align:start position:0%
+look at the temperature rises of the
+thing you know the heat SN surface only
+
+ align:start position:0%
+thing you know the heat SN surface only
+ 
+
+ align:start position:0%
+thing you know the heat SN surface only
+goes up 20c why because we got crazy
+
+ align:start position:0%
+goes up 20c why because we got crazy
+ 
+
+ align:start position:0%
+goes up 20c why because we got crazy
+heat
+
+ align:start position:0%
+heat
+ 
+
+ align:start position:0%
+heat
+flow right so this is the kind of thing
+
+ align:start position:0%
+flow right so this is the kind of thing
+ 
+
+ align:start position:0%
+flow right so this is the kind of thing
+you do and we used exactly these models
+
+ align:start position:0%
+you do and we used exactly these models
+ 
+
+ align:start position:0%
+you do and we used exactly these models
+to essentially figure out what's the
+
+ align:start position:0%
+to essentially figure out what's the
+ 
+
+ align:start position:0%
+to essentially figure out what's the
+thermal resistance from The Junction to
+
+ align:start position:0%
+thermal resistance from The Junction to
+ 
+
+ align:start position:0%
+thermal resistance from The Junction to
+the case then we had the the case going
+
+ align:start position:0%
+the case then we had the the case going
+ 
+
+ align:start position:0%
+the case then we had the the case going
+down to the heat spreader and it was
+
+ align:start position:0%
+down to the heat spreader and it was
+ 
+
+ align:start position:0%
+down to the heat spreader and it was
+soldered so that's pretty low and the
+
+ align:start position:0%
+soldered so that's pretty low and the
+ 
+
+ align:start position:0%
+soldered so that's pretty low and the
+heat spreader to the heat sink and the
+
+ align:start position:0%
+heat spreader to the heat sink and the
+ 
+
+ align:start position:0%
+heat spreader to the heat sink and the
+heat sink to ambient we looked up from
+
+ align:start position:0%
+heat sink to ambient we looked up from
+ 
+
+ align:start position:0%
+heat sink to ambient we looked up from
+the data sheet and boom we have our
+
+ align:start position:0%
+the data sheet and boom we have our
+ 
+
+ align:start position:0%
+the data sheet and boom we have our
+model and we have our nice thing where
+
+ align:start position:0%
+model and we have our nice thing where
+ 
+
+ align:start position:0%
+model and we have our nice thing where
+we can pour lots of dissipated power
+
+ align:start position:0%
+we can pour lots of dissipated power
+ 
+
+ align:start position:0%
+we can pour lots of dissipated power
+into it and still keep it
+
+ align:start position:0%
+into it and still keep it
+ 
+
+ align:start position:0%
+into it and still keep it
+cool okay so I'm out of time are there
+
+ align:start position:0%
+cool okay so I'm out of time are there
+ 
+
+ align:start position:0%
+cool okay so I'm out of time are there
+any final questions uh will these slides
+
+ align:start position:0%
+any final questions uh will these slides
+ 
+
+ align:start position:0%
+any final questions uh will these slides
+be posted uh yeah we can put up these
+
+ align:start position:0%
+be posted uh yeah we can put up these
+ 
+
+ align:start position:0%
+be posted uh yeah we can put up these
+slides yep so this um yeah I'm just what
+
+ align:start position:0%
+slides yep so this um yeah I'm just what
+ 
+
+ align:start position:0%
+slides yep so this um yeah I'm just what
+the device what the it was a uh Gan
+
+ align:start position:0%
+the device what the it was a uh Gan
+ 
+
+ align:start position:0%
+the device what the it was a uh Gan
+system there were four Gan systems Ganon
+
+ align:start position:0%
+system there were four Gan systems Ganon
+ 
+
+ align:start position:0%
+system there were four Gan systems Ganon
+silicon 650 volt
+
+ align:start position:0%
+silicon 650 volt
+ 
+
+ align:start position:0%
+silicon 650 volt
+transistors um so yeah that's sort of a
+
+ align:start position:0%
+transistors um so yeah that's sort of a
+ 
+
+ align:start position:0%
+transistors um so yeah that's sort of a
+lightning introduction to quick and
+
+ align:start position:0%
+lightning introduction to quick and
+ 
+
+ align:start position:0%
+lightning introduction to quick and
+dirty heat sinking
+
+ align:start position:0%
+dirty heat sinking
+ 
+
+ align:start position:0%
+dirty heat sinking
+uh I still encourage you to actually
+
+ align:start position:0%
+uh I still encourage you to actually
+ 
+
+ align:start position:0%
+uh I still encourage you to actually
+take much more sophisticated classes on
+
+ align:start position:0%
+take much more sophisticated classes on
+ 
+
+ align:start position:0%
+take much more sophisticated classes on
+heat transfer I'm not saying this
+
+ align:start position:0%
+heat transfer I'm not saying this
+ 
+
+ align:start position:0%
+heat transfer I'm not saying this
+replaces that but it's enough to get you
+
+ align:start position:0%
+replaces that but it's enough to get you
+ 
+
+ align:start position:0%
+replaces that but it's enough to get you
+to build some pretty cool stuff okay so
+
+ align:start position:0%
+to build some pretty cool stuff okay so
+ 
+
+ align:start position:0%
+to build some pretty cool stuff okay so
+next time we'll go back to talking more
+
+ align:start position:0%
+next time we'll go back to talking more
+ 
+
+ align:start position:0%
+next time we'll go back to talking more
+about circuits have a great day
\ No newline at end of file
diff --git a/wRHJjg9jBjA.txt b/wRHJjg9jBjA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42407b6419f6c9e46b92d8d14ff4abc705a330e1
--- /dev/null
+++ b/wRHJjg9jBjA.txt
@@ -0,0 +1,12727 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discussing
+
+ align:start position:0%
+discussing
+ 
+
+ align:start position:0%
+discussing
+quantitation
+
+ align:start position:0%
+quantitation
+ 
+
+ align:start position:0%
+quantitation
+of the free scalar field Theory
+
+ align:start position:0%
+of the free scalar field Theory
+ 
+
+ align:start position:0%
+of the free scalar field Theory
+and then we showed we showed that the
+
+ align:start position:0%
+and then we showed we showed that the
+ 
+
+ align:start position:0%
+and then we showed we showed that the
+excitations
+
+ align:start position:0%
+excitations
+ 
+
+ align:start position:0%
+excitations
+of that theory essentially give rise to
+
+ align:start position:0%
+of that theory essentially give rise to
+ 
+
+ align:start position:0%
+of that theory essentially give rise to
+um relativistic particles okay
+
+ align:start position:0%
+um relativistic particles okay
+ 
+
+ align:start position:0%
+um relativistic particles okay
+and so we also discussed what is other
+
+ align:start position:0%
+and so we also discussed what is other
+ 
+
+ align:start position:0%
+and so we also discussed what is other
+things say here but structure of the
+
+ align:start position:0%
+things say here but structure of the
+ 
+
+ align:start position:0%
+things say here but structure of the
+healable space
+
+ align:start position:0%
+healable space
+ 
+
+ align:start position:0%
+healable space
+conserved quantities Etc
+
+ align:start position:0%
+conserved quantities Etc
+ 
+
+ align:start position:0%
+conserved quantities Etc
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+at the end we talked about the um
+
+ align:start position:0%
+at the end we talked about the um
+ 
+
+ align:start position:0%
+at the end we talked about the um
+how to understand the
+
+ align:start position:0%
+how to understand the
+ 
+
+ align:start position:0%
+how to understand the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the conserved charges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right the quantum level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so classically
+
+ align:start position:0%
+so classically
+ 
+
+ align:start position:0%
+so classically
+so we we have a say symmetric
+
+ align:start position:0%
+so we we have a say symmetric
+ 
+
+ align:start position:0%
+so we we have a say symmetric
+transformation means that if you
+
+ align:start position:0%
+transformation means that if you
+ 
+
+ align:start position:0%
+transformation means that if you
+take Phi a to some Phi a prime okay if I
+
+ align:start position:0%
+take Phi a to some Phi a prime okay if I
+ 
+
+ align:start position:0%
+take Phi a to some Phi a prime okay if I
+have Prime
+
+ align:start position:0%
+have Prime
+ 
+
+ align:start position:0%
+have Prime
+normally we write it in the infinity
+
+ align:start position:0%
+normally we write it in the infinity
+ 
+
+ align:start position:0%
+normally we write it in the infinity
+decimal way
+
+ align:start position:0%
+decimal way
+ 
+
+ align:start position:0%
+decimal way
+introduce some parameter a some
+
+ align:start position:0%
+introduce some parameter a some
+ 
+
+ align:start position:0%
+introduce some parameter a some
+parameter Epsilon
+
+ align:start position:0%
+parameter Epsilon
+ 
+
+ align:start position:0%
+parameter Epsilon
+and I can also have multiple symmetries
+
+ align:start position:0%
+and I can also have multiple symmetries
+ 
+
+ align:start position:0%
+and I can also have multiple symmetries
+so for each transformation say I have a
+
+ align:start position:0%
+so for each transformation say I have a
+ 
+
+ align:start position:0%
+so for each transformation say I have a
+Epsilon so Alpha labels different
+
+ align:start position:0%
+Epsilon so Alpha labels different
+ 
+
+ align:start position:0%
+Epsilon so Alpha labels different
+transformations
+
+ align:start position:0%
+transformations
+ 
+
+ align:start position:0%
+transformations
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+and then so this is the transformation
+
+ align:start position:0%
+and then so this is the transformation
+ 
+
+ align:start position:0%
+and then so this is the transformation
+which can depend on Phi a also depend on
+
+ align:start position:0%
+which can depend on Phi a also depend on
+ 
+
+ align:start position:0%
+which can depend on Phi a also depend on
+its derivatives Etc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then so if you have a sagio
+
+ align:start position:0%
+and then so if you have a sagio
+ 
+
+ align:start position:0%
+and then so if you have a sagio
+symmetric transformation we discussed
+
+ align:start position:0%
+symmetric transformation we discussed
+ 
+
+ align:start position:0%
+symmetric transformation we discussed
+before then that generates a conserved
+
+ align:start position:0%
+before then that generates a conserved
+ 
+
+ align:start position:0%
+before then that generates a conserved
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+and it is labeled by alpha alpha just
+
+ align:start position:0%
+and it is labeled by alpha alpha just
+ 
+
+ align:start position:0%
+and it is labeled by alpha alpha just
+the loads different conserved currents
+
+ align:start position:0%
+the loads different conserved currents
+ 
+
+ align:start position:0%
+the loads different conserved currents
+and then yeah so so it is conserved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is the classical statement
+
+ align:start position:0%
+so this is the classical statement
+ 
+
+ align:start position:0%
+so this is the classical statement
+oh yeah also lots of theorem tells us
+
+ align:start position:0%
+oh yeah also lots of theorem tells us
+ 
+
+ align:start position:0%
+oh yeah also lots of theorem tells us
+how to write down such a current
+
+ align:start position:0%
+how to write down such a current
+ 
+
+ align:start position:0%
+how to write down such a current
+explicitly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can just write it as
+
+ align:start position:0%
+so we can just write it as
+ 
+
+ align:start position:0%
+so we can just write it as
+the current can be written explicitly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so K mu is the um
+
+ align:start position:0%
+okay so K mu is the um
+ 
+
+ align:start position:0%
+okay so K mu is the um
+the transformation of the lagrangian
+
+ align:start position:0%
+the transformation of the lagrangian
+ 
+
+ align:start position:0%
+the transformation of the lagrangian
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+suppose under this transformation the
+
+ align:start position:0%
+suppose under this transformation the
+ 
+
+ align:start position:0%
+suppose under this transformation the
+LaGrange density transform as
+
+ align:start position:0%
+LaGrange density transform as
+ 
+
+ align:start position:0%
+LaGrange density transform as
+say Alpha partial mu
+
+ align:start position:0%
+say Alpha partial mu
+ 
+
+ align:start position:0%
+say Alpha partial mu
+okay Mu Alpha okay
+
+ align:start position:0%
+okay Mu Alpha okay
+ 
+
+ align:start position:0%
+okay Mu Alpha okay
+so R5 doesn't matter Alpha just label
+
+ align:start position:0%
+so R5 doesn't matter Alpha just label
+ 
+
+ align:start position:0%
+so R5 doesn't matter Alpha just label
+different symmetries the the index
+
+ align:start position:0%
+different symmetries the the index
+ 
+
+ align:start position:0%
+different symmetries the the index
+doesn't matter whether it's up up or
+
+ align:start position:0%
+doesn't matter whether it's up up or
+ 
+
+ align:start position:0%
+doesn't matter whether it's up up or
+down okay
+
+ align:start position:0%
+down okay
+ 
+
+ align:start position:0%
+down okay
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+then the zeros component
+
+ align:start position:0%
+then the zeros component
+ 
+
+ align:start position:0%
+then the zeros component
+of the charge this component of the
+
+ align:start position:0%
+of the charge this component of the
+ 
+
+ align:start position:0%
+of the charge this component of the
+current when you integrate of all space
+
+ align:start position:0%
+current when you integrate of all space
+ 
+
+ align:start position:0%
+current when you integrate of all space
+then give rise to a conserved charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+so now let's discuss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you go to Quantum level so when
+
+ align:start position:0%
+so when you go to Quantum level so when
+ 
+
+ align:start position:0%
+so when you go to Quantum level so when
+you quantize the theory
+
+ align:start position:0%
+you quantize the theory
+ 
+
+ align:start position:0%
+you quantize the theory
+and this just become Quantum operator
+
+ align:start position:0%
+and this just become Quantum operator
+ 
+
+ align:start position:0%
+and this just become Quantum operator
+and yeah the whole current become a
+
+ align:start position:0%
+and yeah the whole current become a
+ 
+
+ align:start position:0%
+and yeah the whole current become a
+Quantum operator
+
+ align:start position:0%
+Quantum operator
+ 
+
+ align:start position:0%
+Quantum operator
+and then Q is also a Quantum operator
+
+ align:start position:0%
+and then Q is also a Quantum operator
+ 
+
+ align:start position:0%
+and then Q is also a Quantum operator
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the quantum level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Quantum level and the null Q Alpha
+
+ align:start position:0%
+and Quantum level and the null Q Alpha
+ 
+
+ align:start position:0%
+and Quantum level and the null Q Alpha
+because it's conserved
+
+ align:start position:0%
+because it's conserved
+ 
+
+ align:start position:0%
+because it's conserved
+so this becomes time independent
+
+ align:start position:0%
+so this becomes time independent
+ 
+
+ align:start position:0%
+so this becomes time independent
+operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+receipt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we see the explicit tree in the case of
+
+ align:start position:0%
+we see the explicit tree in the case of
+ 
+
+ align:start position:0%
+we see the explicit tree in the case of
+the say hamiltonian density hamiltonian
+
+ align:start position:0%
+the say hamiltonian density hamiltonian
+ 
+
+ align:start position:0%
+the say hamiltonian density hamiltonian
+and the momentum okay so we show the
+
+ align:start position:0%
+and the momentum okay so we show the
+ 
+
+ align:start position:0%
+and the momentum okay so we show the
+explicitly they they actually don't
+
+ align:start position:0%
+explicitly they they actually don't
+ 
+
+ align:start position:0%
+explicitly they they actually don't
+depend on time
+
+ align:start position:0%
+depend on time
+ 
+
+ align:start position:0%
+depend on time
+but at the quantum mechanical level
+
+ align:start position:0%
+but at the quantum mechanical level
+ 
+
+ align:start position:0%
+but at the quantum mechanical level
+actually this Q can play a more
+
+ align:start position:0%
+actually this Q can play a more
+ 
+
+ align:start position:0%
+actually this Q can play a more
+important role
+
+ align:start position:0%
+important role
+ 
+
+ align:start position:0%
+important role
+uh can play more importantly in fact it
+
+ align:start position:0%
+uh can play more importantly in fact it
+ 
+
+ align:start position:0%
+uh can play more importantly in fact it
+can be viewed as a generator of
+
+ align:start position:0%
+can be viewed as a generator of
+ 
+
+ align:start position:0%
+can be viewed as a generator of
+symmetries okay so we can show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we will show the following statement
+
+ align:start position:0%
+we will show the following statement
+ 
+
+ align:start position:0%
+we will show the following statement
+that if you consider
+
+ align:start position:0%
+that if you consider
+ 
+
+ align:start position:0%
+that if you consider
+the Epsilon so so consider such a
+
+ align:start position:0%
+the Epsilon so so consider such a
+ 
+
+ align:start position:0%
+the Epsilon so so consider such a
+quantity
+
+ align:start position:0%
+quantity
+ 
+
+ align:start position:0%
+quantity
+yeah uh
+
+ align:start position:0%
+yeah uh
+ 
+
+ align:start position:0%
+yeah uh
+can you see the commutative Q
+
+ align:start position:0%
+can you see the commutative Q
+ 
+
+ align:start position:0%
+can you see the commutative Q
+with 5A
+
+ align:start position:0%
+with 5A
+ 
+
+ align:start position:0%
+with 5A
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's continue over to here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah maybe just let me write it here and
+
+ align:start position:0%
+yeah maybe just let me write it here and
+ 
+
+ align:start position:0%
+yeah maybe just let me write it here and
+that generate minus Epsilon Alpha
+
+ align:start position:0%
+that generate minus Epsilon Alpha
+ 
+
+ align:start position:0%
+that generate minus Epsilon Alpha
+F Alpha a
+
+ align:start position:0%
+F Alpha a
+ 
+
+ align:start position:0%
+F Alpha a
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the commutator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a essentially generate this
+
+ align:start position:0%
+a essentially generate this
+ 
+
+ align:start position:0%
+a essentially generate this
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+okay essentially generate this
+
+ align:start position:0%
+okay essentially generate this
+ 
+
+ align:start position:0%
+okay essentially generate this
+infinitesimal transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so that's why we call the Q Alpha also a
+
+ align:start position:0%
+so that's why we call the Q Alpha also a
+ 
+
+ align:start position:0%
+so that's why we call the Q Alpha also a
+generator of symmetries okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this is the statement that I'm
+
+ align:start position:0%
+so so this is the statement that I'm
+ 
+
+ align:start position:0%
+so so this is the statement that I'm
+going to show very soon okay so before I
+
+ align:start position:0%
+going to show very soon okay so before I
+ 
+
+ align:start position:0%
+going to show very soon okay so before I
+do that you have any questions
+
+ align:start position:0%
+do that you have any questions
+ 
+
+ align:start position:0%
+do that you have any questions
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+current equation how can have been
+
+ align:start position:0%
+current equation how can have been
+ 
+
+ align:start position:0%
+current equation how can have been
+helpful in the upper index like Jay
+
+ align:start position:0%
+helpful in the upper index like Jay
+ 
+
+ align:start position:0%
+helpful in the upper index like Jay
+hasn't happened lower either and it's
+
+ align:start position:0%
+hasn't happened lower either and it's
+ 
+
+ align:start position:0%
+hasn't happened lower either and it's
+not me yeah yeah just offer don't worry
+
+ align:start position:0%
+not me yeah yeah just offer don't worry
+ 
+
+ align:start position:0%
+not me yeah yeah just offer don't worry
+about the location of alpha index Alpha
+
+ align:start position:0%
+about the location of alpha index Alpha
+ 
+
+ align:start position:0%
+about the location of alpha index Alpha
+just label a different current
+
+ align:start position:0%
+just label a different current
+ 
+
+ align:start position:0%
+just label a different current
+and just one yeah it yeah here we don't
+
+ align:start position:0%
+and just one yeah it yeah here we don't
+ 
+
+ align:start position:0%
+and just one yeah it yeah here we don't
+worry about its location yeah I just put
+
+ align:start position:0%
+worry about its location yeah I just put
+ 
+
+ align:start position:0%
+worry about its location yeah I just put
+it up and down just for uh for
+
+ align:start position:0%
+it up and down just for uh for
+ 
+
+ align:start position:0%
+it up and down just for uh for
+convenience
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+yes sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there's some of all of us so let me
+
+ align:start position:0%
+yeah there's some of all of us so let me
+ 
+
+ align:start position:0%
+yeah there's some of all of us so let me
+repeat this indices is sound okay so if
+
+ align:start position:0%
+repeat this indices is sound okay so if
+ 
+
+ align:start position:0%
+repeat this indices is sound okay so if
+you only have one
+
+ align:start position:0%
+you only have one
+ 
+
+ align:start position:0%
+you only have one
+say for example if you have yeah one
+
+ align:start position:0%
+say for example if you have yeah one
+ 
+
+ align:start position:0%
+say for example if you have yeah one
+absolute of course there's no sound but
+
+ align:start position:0%
+absolute of course there's no sound but
+ 
+
+ align:start position:0%
+absolute of course there's no sound but
+if you have two different charges uh and
+
+ align:start position:0%
+if you have two different charges uh and
+ 
+
+ align:start position:0%
+if you have two different charges uh and
+then yeah this is some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so we are going to show this statement
+
+ align:start position:0%
+so we are going to show this statement
+ 
+
+ align:start position:0%
+so we are going to show this statement
+and so this statement is very easy to
+
+ align:start position:0%
+and so this statement is very easy to
+ 
+
+ align:start position:0%
+and so this statement is very easy to
+show in the in the general case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so let me call this equation star
+
+ align:start position:0%
+um so let me call this equation star
+ 
+
+ align:start position:0%
+um so let me call this equation star
+so let's first consider the case
+
+ align:start position:0%
+so let's first consider the case
+ 
+
+ align:start position:0%
+so let's first consider the case
+versus consider the sub case
+
+ align:start position:0%
+versus consider the sub case
+ 
+
+ align:start position:0%
+versus consider the sub case
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's first suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far just this transformation
+
+ align:start position:0%
+far just this transformation
+ 
+
+ align:start position:0%
+far just this transformation
+okay I'll find a
+
+ align:start position:0%
+okay I'll find a
+ 
+
+ align:start position:0%
+okay I'll find a
+does not contain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the time derivative of a okay
+
+ align:start position:0%
+the time derivative of a okay
+ 
+
+ align:start position:0%
+the time derivative of a okay
+and also
+
+ align:start position:0%
+and also
+ 
+
+ align:start position:0%
+and also
+the the zeros component of the K is
+
+ align:start position:0%
+the the zeros component of the K is
+ 
+
+ align:start position:0%
+the the zeros component of the K is
+equal to zero okay
+
+ align:start position:0%
+equal to zero okay
+ 
+
+ align:start position:0%
+equal to zero okay
+so let's consider a a a first special
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a more limited case
+
+ align:start position:0%
+a more limited case
+ 
+
+ align:start position:0%
+a more limited case
+okay so this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the more limited case
+
+ align:start position:0%
+so this is the more limited case
+ 
+
+ align:start position:0%
+so this is the more limited case
+actually covers many many examples okay
+
+ align:start position:0%
+actually covers many many examples okay
+ 
+
+ align:start position:0%
+actually covers many many examples okay
+I actually covers a majority of examples
+
+ align:start position:0%
+I actually covers a majority of examples
+ 
+
+ align:start position:0%
+I actually covers a majority of examples
+for example if you look at the of
+
+ align:start position:0%
+for example if you look at the of
+ 
+
+ align:start position:0%
+for example if you look at the of
+translation symmetry which give rise to
+
+ align:start position:0%
+translation symmetry which give rise to
+ 
+
+ align:start position:0%
+translation symmetry which give rise to
+the stress sensor so so this will so
+
+ align:start position:0%
+the stress sensor so so this will so
+ 
+
+ align:start position:0%
+the stress sensor so so this will so
+this applies to the case I mu
+
+ align:start position:0%
+this applies to the case I mu
+ 
+
+ align:start position:0%
+this applies to the case I mu
+team UI so
+
+ align:start position:0%
+team UI so
+ 
+
+ align:start position:0%
+team UI so
+so this corresponding to the spatial
+
+ align:start position:0%
+so this corresponding to the spatial
+ 
+
+ align:start position:0%
+so this corresponding to the spatial
+so this is the conserved current
+
+ align:start position:0%
+so this is the conserved current
+ 
+
+ align:start position:0%
+so this is the conserved current
+corresponding to the spatial
+
+ align:start position:0%
+corresponding to the spatial
+ 
+
+ align:start position:0%
+corresponding to the spatial
+so this is the current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for spatial translations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for spatial translations
+
+ align:start position:0%
+for spatial translations
+ 
+
+ align:start position:0%
+for spatial translations
+and of course this uh this uh F gets
+
+ align:start position:0%
+and of course this uh this uh F gets
+ 
+
+ align:start position:0%
+and of course this uh this uh F gets
+given by the spatial derivatives
+
+ align:start position:0%
+given by the spatial derivatives
+ 
+
+ align:start position:0%
+given by the spatial derivatives
+and then it does not involve time
+
+ align:start position:0%
+and then it does not involve time
+ 
+
+ align:start position:0%
+and then it does not involve time
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+and in that case the uh K also does not
+
+ align:start position:0%
+and in that case the uh K also does not
+ 
+
+ align:start position:0%
+and in that case the uh K also does not
+involve in a k0 component zero yeah just
+
+ align:start position:0%
+involve in a k0 component zero yeah just
+ 
+
+ align:start position:0%
+involve in a k0 component zero yeah just
+I try to remind myself which you worked
+
+ align:start position:0%
+I try to remind myself which you worked
+ 
+
+ align:start position:0%
+I try to remind myself which you worked
+in your PSAT
+
+ align:start position:0%
+in your PSAT
+ 
+
+ align:start position:0%
+in your PSAT
+and so so for this example
+
+ align:start position:0%
+and so so for this example
+ 
+
+ align:start position:0%
+and so so for this example
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+is the counterpart is the alpha here
+
+ align:start position:0%
+is the counterpart is the alpha here
+ 
+
+ align:start position:0%
+is the counterpart is the alpha here
+okay so for each Direction
+
+ align:start position:0%
+okay so for each Direction
+ 
+
+ align:start position:0%
+okay so for each Direction
+you have a translation and so this uh so
+
+ align:start position:0%
+you have a translation and so this uh so
+ 
+
+ align:start position:0%
+you have a translation and so this uh so
+the alpha of course s i is the alpha
+
+ align:start position:0%
+the alpha of course s i is the alpha
+ 
+
+ align:start position:0%
+the alpha of course s i is the alpha
+here and the MU is the JMU here okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and also
+
+ align:start position:0%
+and and also
+ 
+
+ align:start position:0%
+and and also
+this applies to the case which uh
+
+ align:start position:0%
+this applies to the case which uh
+ 
+
+ align:start position:0%
+this applies to the case which uh
+for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+internal symmetries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now internal symmetries we mean the
+
+ align:start position:0%
+now internal symmetries we mean the
+ 
+
+ align:start position:0%
+now internal symmetries we mean the
+Transformations don't involve space-time
+
+ align:start position:0%
+Transformations don't involve space-time
+ 
+
+ align:start position:0%
+Transformations don't involve space-time
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+okay for example you uh you did in your
+
+ align:start position:0%
+okay for example you uh you did in your
+ 
+
+ align:start position:0%
+okay for example you uh you did in your
+piece that the complex scalar field
+
+ align:start position:0%
+piece that the complex scalar field
+ 
+
+ align:start position:0%
+piece that the complex scalar field
+which you can just rotate the bear face
+
+ align:start position:0%
+which you can just rotate the bear face
+ 
+
+ align:start position:0%
+which you can just rotate the bear face
+and that's called the internal
+
+ align:start position:0%
+and that's called the internal
+ 
+
+ align:start position:0%
+and that's called the internal
+transmission because that transformation
+
+ align:start position:0%
+transmission because that transformation
+ 
+
+ align:start position:0%
+transmission because that transformation
+doesn't does not involve uh um
+
+ align:start position:0%
+doesn't does not involve uh um
+ 
+
+ align:start position:0%
+doesn't does not involve uh um
+space-time coordinates in contrast when
+
+ align:start position:0%
+space-time coordinates in contrast when
+ 
+
+ align:start position:0%
+space-time coordinates in contrast when
+we find the stress sensor we we will do
+
+ align:start position:0%
+we find the stress sensor we we will do
+ 
+
+ align:start position:0%
+we find the stress sensor we we will do
+a space-time translation and that does
+
+ align:start position:0%
+a space-time translation and that does
+ 
+
+ align:start position:0%
+a space-time translation and that does
+involve space-time transform yeah so so
+
+ align:start position:0%
+involve space-time transform yeah so so
+ 
+
+ align:start position:0%
+involve space-time transform yeah so so
+this corresponding to the space-time
+
+ align:start position:0%
+this corresponding to the space-time
+ 
+
+ align:start position:0%
+this corresponding to the space-time
+Transformations space time symmetries
+
+ align:start position:0%
+Transformations space time symmetries
+ 
+
+ align:start position:0%
+Transformations space time symmetries
+and this is the phase is the internal
+
+ align:start position:0%
+and this is the phase is the internal
+ 
+
+ align:start position:0%
+and this is the phase is the internal
+symmetries okay so for all internal
+
+ align:start position:0%
+symmetries okay so for all internal
+ 
+
+ align:start position:0%
+symmetries okay so for all internal
+symmetries
+
+ align:start position:0%
+symmetries
+ 
+
+ align:start position:0%
+symmetries
+you don't the the transmission will not
+
+ align:start position:0%
+you don't the the transmission will not
+ 
+
+ align:start position:0%
+you don't the the transmission will not
+contain the time derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so in this case then then it's easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because in this case then we just have
+
+ align:start position:0%
+because in this case then we just have
+ 
+
+ align:start position:0%
+because in this case then we just have
+the one then the zeros component of J mu
+
+ align:start position:0%
+the one then the zeros component of J mu
+ 
+
+ align:start position:0%
+the one then the zeros component of J mu
+j h is given by
+
+ align:start position:0%
+j h is given by
+ 
+
+ align:start position:0%
+j h is given by
+the first term by definition is just the
+
+ align:start position:0%
+the first term by definition is just the
+ 
+
+ align:start position:0%
+the first term by definition is just the
+canonical momentum
+
+ align:start position:0%
+canonical momentum
+ 
+
+ align:start position:0%
+canonical momentum
+conjugate to the um
+
+ align:start position:0%
+conjugate to the um
+ 
+
+ align:start position:0%
+conjugate to the um
+to the A
+
+ align:start position:0%
+to the A
+ 
+
+ align:start position:0%
+to the A
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the the first Factor part of L
+
+ align:start position:0%
+so the the first Factor part of L
+ 
+
+ align:start position:0%
+so the the first Factor part of L
+partial python view Phi a when you set
+
+ align:start position:0%
+partial python view Phi a when you set
+ 
+
+ align:start position:0%
+partial python view Phi a when you set
+mu equal to zero so that's just the
+
+ align:start position:0%
+mu equal to zero so that's just the
+ 
+
+ align:start position:0%
+mu equal to zero so that's just the
+derivative respect to the time
+
+ align:start position:0%
+derivative respect to the time
+ 
+
+ align:start position:0%
+derivative respect to the time
+derivative of Phi a and that by
+
+ align:start position:0%
+derivative of Phi a and that by
+ 
+
+ align:start position:0%
+derivative of Phi a and that by
+definition is just the
+
+ align:start position:0%
+definition is just the
+ 
+
+ align:start position:0%
+definition is just the
+um the canonical momentum density
+
+ align:start position:0%
+um the canonical momentum density
+ 
+
+ align:start position:0%
+um the canonical momentum density
+conjugate to Phi a
+
+ align:start position:0%
+conjugate to Phi a
+ 
+
+ align:start position:0%
+conjugate to Phi a
+and then then you have
+
+ align:start position:0%
+and then then you have
+ 
+
+ align:start position:0%
+and then then you have
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+Alpha a okay
+
+ align:start position:0%
+Alpha a okay
+ 
+
+ align:start position:0%
+Alpha a okay
+f a alpha
+
+ align:start position:0%
+f a alpha
+ 
+
+ align:start position:0%
+f a alpha
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so let me just make one
+
+ align:start position:0%
+so let me just make one
+ 
+
+ align:start position:0%
+so let me just make one
+comment on this because expression
+
+ align:start position:0%
+comment on this because expression
+ 
+
+ align:start position:0%
+comment on this because expression
+so this expression of course uh
+
+ align:start position:0%
+so this expression of course uh
+ 
+
+ align:start position:0%
+so this expression of course uh
+classically
+
+ align:start position:0%
+classically
+ 
+
+ align:start position:0%
+classically
+you can write whatever way you want
+
+ align:start position:0%
+you can write whatever way you want
+ 
+
+ align:start position:0%
+you can write whatever way you want
+but the quantum mechanical is this a
+
+ align:start position:0%
+but the quantum mechanical is this a
+ 
+
+ align:start position:0%
+but the quantum mechanical is this a
+very important subtlety
+
+ align:start position:0%
+very important subtlety
+ 
+
+ align:start position:0%
+very important subtlety
+because this typically will involve Phi
+
+ align:start position:0%
+because this typically will involve Phi
+ 
+
+ align:start position:0%
+because this typically will involve Phi
+okay and and then this is momentum and
+
+ align:start position:0%
+okay and and then this is momentum and
+ 
+
+ align:start position:0%
+okay and and then this is momentum and
+they don't necessarily compute so this
+
+ align:start position:0%
+they don't necessarily compute so this
+ 
+
+ align:start position:0%
+they don't necessarily compute so this
+is the the field three version of
+
+ align:start position:0%
+is the the field three version of
+ 
+
+ align:start position:0%
+is the the field three version of
+so-called the uh operate ordinary
+
+ align:start position:0%
+so-called the uh operate ordinary
+ 
+
+ align:start position:0%
+so-called the uh operate ordinary
+ambiguity which you Authority in quantum
+
+ align:start position:0%
+ambiguity which you Authority in quantum
+ 
+
+ align:start position:0%
+ambiguity which you Authority in quantum
+mechanics okay in quantum mechanics when
+
+ align:start position:0%
+mechanics okay in quantum mechanics when
+ 
+
+ align:start position:0%
+mechanics okay in quantum mechanics when
+you go from classical book
+
+ align:start position:0%
+you go from classical book
+ 
+
+ align:start position:0%
+you go from classical book
+even it's already in the long right
+
+ align:start position:0%
+even it's already in the long right
+ 
+
+ align:start position:0%
+even it's already in the long right
+basic Quantum mechanism when you go to
+
+ align:start position:0%
+basic Quantum mechanism when you go to
+ 
+
+ align:start position:0%
+basic Quantum mechanism when you go to
+classical mechanics to quantum mechanics
+
+ align:start position:0%
+classical mechanics to quantum mechanics
+ 
+
+ align:start position:0%
+classical mechanics to quantum mechanics
+and then there's an issue how you order
+
+ align:start position:0%
+and then there's an issue how you order
+ 
+
+ align:start position:0%
+and then there's an issue how you order
+uh operators when you have X and the P
+
+ align:start position:0%
+uh operators when you have X and the P
+ 
+
+ align:start position:0%
+uh operators when you have X and the P
+at the same time okay so here you also
+
+ align:start position:0%
+at the same time okay so here you also
+ 
+
+ align:start position:0%
+at the same time okay so here you also
+have potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh operate I'm ordering ambiguity
+
+ align:start position:0%
+uh operate I'm ordering ambiguity
+ 
+
+ align:start position:0%
+uh operate I'm ordering ambiguity
+you have to pay attention
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+often such kind of ambiguities can be
+
+ align:start position:0%
+often such kind of ambiguities can be
+ 
+
+ align:start position:0%
+often such kind of ambiguities can be
+resolved by physical considerations okay
+
+ align:start position:0%
+resolved by physical considerations okay
+ 
+
+ align:start position:0%
+resolved by physical considerations okay
+so we will see some examples
+
+ align:start position:0%
+so we will see some examples
+ 
+
+ align:start position:0%
+so we will see some examples
+in a little bit okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now let's just imagine there's
+
+ align:start position:0%
+so so now let's just imagine there's
+ 
+
+ align:start position:0%
+so so now let's just imagine there's
+some ordering we have chosen
+
+ align:start position:0%
+some ordering we have chosen
+ 
+
+ align:start position:0%
+some ordering we have chosen
+and now let's look at this commentator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so we can just write down the
+
+ align:start position:0%
+okay so so we can just write down the
+ 
+
+ align:start position:0%
+okay so so we can just write down the
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+so this is just integrating mobile or
+
+ align:start position:0%
+so this is just integrating mobile or
+ 
+
+ align:start position:0%
+so this is just integrating mobile or
+spatial movement a special Direction
+
+ align:start position:0%
+spatial movement a special Direction
+ 
+
+ align:start position:0%
+spatial movement a special Direction
+Epsilon Alpha
+
+ align:start position:0%
+Epsilon Alpha
+ 
+
+ align:start position:0%
+Epsilon Alpha
+and then we have Pi a
+
+ align:start position:0%
+and then we have Pi a
+ 
+
+ align:start position:0%
+and then we have Pi a
+f a alpha 5A
+
+ align:start position:0%
+f a alpha 5A
+ 
+
+ align:start position:0%
+f a alpha 5A
+yeah let me just
+
+ align:start position:0%
+yeah let me just
+ 
+
+ align:start position:0%
+yeah let me just
+sorry here let me call 5B because the 5A
+
+ align:start position:0%
+sorry here let me call 5B because the 5A
+ 
+
+ align:start position:0%
+sorry here let me call 5B because the 5A
+now they are different so these two
+
+ align:start position:0%
+now they are different so these two
+ 
+
+ align:start position:0%
+now they are different so these two
+indices are sound okay so so like let me
+
+ align:start position:0%
+indices are sound okay so so like let me
+ 
+
+ align:start position:0%
+indices are sound okay so so like let me
+call them B and then you have five a
+
+ align:start position:0%
+call them B and then you have five a
+ 
+
+ align:start position:0%
+call them B and then you have five a
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+so now you can use a commutation
+
+ align:start position:0%
+so now you can use a commutation
+ 
+
+ align:start position:0%
+so now you can use a commutation
+relation uh between the uh a momentum
+
+ align:start position:0%
+relation uh between the uh a momentum
+ 
+
+ align:start position:0%
+relation uh between the uh a momentum
+density and the Phi Phi so
+
+ align:start position:0%
+density and the Phi Phi so
+ 
+
+ align:start position:0%
+density and the Phi Phi so
+so we discussed in general that the
+
+ align:start position:0%
+so we discussed in general that the
+ 
+
+ align:start position:0%
+so we discussed in general that the
+so we discussed the scalar case but in
+
+ align:start position:0%
+so we discussed the scalar case but in
+ 
+
+ align:start position:0%
+so we discussed the scalar case but in
+general you have this commutation
+
+ align:start position:0%
+general you have this commutation
+ 
+
+ align:start position:0%
+general you have this commutation
+relation
+
+ align:start position:0%
+relation
+ 
+
+ align:start position:0%
+relation
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+which is Delta
+
+ align:start position:0%
+which is Delta
+ 
+
+ align:start position:0%
+which is Delta
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+say if this is the X
+
+ align:start position:0%
+say if this is the X
+ 
+
+ align:start position:0%
+say if this is the X
+and this is X Prime
+
+ align:start position:0%
+and this is X Prime
+ 
+
+ align:start position:0%
+and this is X Prime
+and then this is x minus X Prime okay
+
+ align:start position:0%
+and then this is x minus X Prime okay
+ 
+
+ align:start position:0%
+and then this is x minus X Prime okay
+and Delta a b okay so so each one is
+
+ align:start position:0%
+and Delta a b okay so so each one is
+ 
+
+ align:start position:0%
+and Delta a b okay so so each one is
+only uh have come a canonical conjugate
+
+ align:start position:0%
+only uh have come a canonical conjugate
+ 
+
+ align:start position:0%
+only uh have come a canonical conjugate
+momentum with its own momentum okay if
+
+ align:start position:0%
+momentum with its own momentum okay if
+ 
+
+ align:start position:0%
+momentum with its own momentum okay if
+they have different fields then of
+
+ align:start position:0%
+they have different fields then of
+ 
+
+ align:start position:0%
+they have different fields then of
+course yeah so um yeah you have that and
+
+ align:start position:0%
+course yeah so um yeah you have that and
+ 
+
+ align:start position:0%
+course yeah so um yeah you have that and
+now if you use this okay so so here is X
+
+ align:start position:0%
+now if you use this okay so so here is X
+ 
+
+ align:start position:0%
+now if you use this okay so so here is X
+yeah let me call this Prime and this to
+
+ align:start position:0%
+yeah let me call this Prime and this to
+ 
+
+ align:start position:0%
+yeah let me call this Prime and this to
+be X
+
+ align:start position:0%
+be X
+ 
+
+ align:start position:0%
+be X
+okay sorry uh
+
+ align:start position:0%
+okay sorry uh
+ 
+
+ align:start position:0%
+okay sorry uh
+should I should label more explicitly X
+
+ align:start position:0%
+should I should label more explicitly X
+ 
+
+ align:start position:0%
+should I should label more explicitly X
+here and then here will be X okay
+
+ align:start position:0%
+here and then here will be X okay
+ 
+
+ align:start position:0%
+here and then here will be X okay
+and so so here is X and here will be X
+
+ align:start position:0%
+and so so here is X and here will be X
+ 
+
+ align:start position:0%
+and so so here is X and here will be X
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+sorry I I didn't leave myself enough
+
+ align:start position:0%
+sorry I I didn't leave myself enough
+ 
+
+ align:start position:0%
+sorry I I didn't leave myself enough
+space let me just rewrite it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this gives me D3 X Prime
+
+ align:start position:0%
+so this gives me D3 X Prime
+ 
+
+ align:start position:0%
+so this gives me D3 X Prime
+Epsilon Alpha
+
+ align:start position:0%
+Epsilon Alpha
+ 
+
+ align:start position:0%
+Epsilon Alpha
+then I will have this uh
+
+ align:start position:0%
+then I will have this uh
+ 
+
+ align:start position:0%
+then I will have this uh
+um Pi a
+
+ align:start position:0%
+um Pi a
+ 
+
+ align:start position:0%
+um Pi a
+then X Prime
+
+ align:start position:0%
+then X Prime
+ 
+
+ align:start position:0%
+then X Prime
+F Alpha
+
+ align:start position:0%
+F Alpha
+ 
+
+ align:start position:0%
+F Alpha
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+X Prime
+
+ align:start position:0%
+X Prime
+ 
+
+ align:start position:0%
+X Prime
+and then V is commutated with
+
+ align:start position:0%
+and then V is commutated with
+ 
+
+ align:start position:0%
+and then V is commutated with
+yeah not copy sorry Alpha is down
+
+ align:start position:0%
+yeah not copy sorry Alpha is down
+ 
+
+ align:start position:0%
+yeah not copy sorry Alpha is down
+upstairs
+
+ align:start position:0%
+upstairs
+ 
+
+ align:start position:0%
+upstairs
+B and then five x okay
+
+ align:start position:0%
+B and then five x okay
+ 
+
+ align:start position:0%
+B and then five x okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+yeah so we can evaluate this say for
+
+ align:start position:0%
+yeah so we can evaluate this say for
+ 
+
+ align:start position:0%
+yeah so we can evaluate this say for
+example or Olt equal to zero so I
+
+ align:start position:0%
+example or Olt equal to zero so I
+ 
+
+ align:start position:0%
+example or Olt equal to zero so I
+suppress the T
+
+ align:start position:0%
+suppress the T
+ 
+
+ align:start position:0%
+suppress the T
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+um yeah and now you can just trivially
+
+ align:start position:0%
+um yeah and now you can just trivially
+ 
+
+ align:start position:0%
+um yeah and now you can just trivially
+use this computation relation
+
+ align:start position:0%
+use this computation relation
+ 
+
+ align:start position:0%
+use this computation relation
+and and then this just gives you minus I
+
+ align:start position:0%
+and and then this just gives you minus I
+ 
+
+ align:start position:0%
+and and then this just gives you minus I
+Epsilon Alpha F Alpha a
+
+ align:start position:0%
+Epsilon Alpha F Alpha a
+ 
+
+ align:start position:0%
+Epsilon Alpha F Alpha a
+f a alpha
+
+ align:start position:0%
+f a alpha
+ 
+
+ align:start position:0%
+f a alpha
+X okay evaluate at X okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so that just confirmed a confirms
+
+ align:start position:0%
+so so that just confirmed a confirms
+ 
+
+ align:start position:0%
+so so that just confirmed a confirms
+that expression okay
+
+ align:start position:0%
+that expression okay
+ 
+
+ align:start position:0%
+that expression okay
+for mixed extraction
+
+ align:start position:0%
+for mixed extraction
+ 
+
+ align:start position:0%
+for mixed extraction
+so this is not satisfied
+
+ align:start position:0%
+so this is not satisfied
+ 
+
+ align:start position:0%
+so this is not satisfied
+when you have time translation okay
+
+ align:start position:0%
+when you have time translation okay
+ 
+
+ align:start position:0%
+when you have time translation okay
+so for time translation
+
+ align:start position:0%
+so for time translation
+ 
+
+ align:start position:0%
+so for time translation
+so first any questions on this
+
+ align:start position:0%
+so first any questions on this
+ 
+
+ align:start position:0%
+so first any questions on this
+in this simple case yeah the idea is
+
+ align:start position:0%
+in this simple case yeah the idea is
+ 
+
+ align:start position:0%
+in this simple case yeah the idea is
+very simple it essentially just the
+
+ align:start position:0%
+very simple it essentially just the
+ 
+
+ align:start position:0%
+very simple it essentially just the
+first term proponent to the momentum and
+
+ align:start position:0%
+first term proponent to the momentum and
+ 
+
+ align:start position:0%
+first term proponent to the momentum and
+the momentum uh uh uh uh conjugate to
+
+ align:start position:0%
+the momentum uh uh uh uh conjugate to
+ 
+
+ align:start position:0%
+the momentum uh uh uh uh conjugate to
+this and then you just take that okay
+
+ align:start position:0%
+this and then you just take that okay
+ 
+
+ align:start position:0%
+this and then you just take that okay
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right that's right yeah so so if
+
+ align:start position:0%
+that's right that's right yeah so so if
+ 
+
+ align:start position:0%
+that's right that's right yeah so so if
+there's no partial zero there's no time
+
+ align:start position:0%
+there's no partial zero there's no time
+ 
+
+ align:start position:0%
+there's no partial zero there's no time
+due to here means there's no momentum
+
+ align:start position:0%
+due to here means there's no momentum
+ 
+
+ align:start position:0%
+due to here means there's no momentum
+here right if there's no momentum here
+
+ align:start position:0%
+here right if there's no momentum here
+ 
+
+ align:start position:0%
+here right if there's no momentum here
+then this will commute with this one
+
+ align:start position:0%
+then this will commute with this one
+ 
+
+ align:start position:0%
+then this will commute with this one
+yeah no matter is in here it's always
+
+ align:start position:0%
+yeah no matter is in here it's always
+ 
+
+ align:start position:0%
+yeah no matter is in here it's always
+compute yeah a very good question yeah I
+
+ align:start position:0%
+compute yeah a very good question yeah I
+ 
+
+ align:start position:0%
+compute yeah a very good question yeah I
+forgot to mention this point yeah
+
+ align:start position:0%
+forgot to mention this point yeah
+ 
+
+ align:start position:0%
+forgot to mention this point yeah
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the special case
+
+ align:start position:0%
+the special case
+ 
+
+ align:start position:0%
+the special case
+he said if you have time translation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay when you have time translation
+
+ align:start position:0%
+okay when you have time translation
+ 
+
+ align:start position:0%
+okay when you have time translation
+for example a one example is the
+
+ align:start position:0%
+for example a one example is the
+ 
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah uh the the the hamiltonian density
+
+ align:start position:0%
+yeah uh the the the hamiltonian density
+ 
+
+ align:start position:0%
+yeah uh the the the hamiltonian density
+H is equal to Pi a
+
+ align:start position:0%
+H is equal to Pi a
+ 
+
+ align:start position:0%
+H is equal to Pi a
+part of T by a minus L okay so the L
+
+ align:start position:0%
+part of T by a minus L okay so the L
+ 
+
+ align:start position:0%
+part of T by a minus L okay so the L
+here for the time translation L is the
+
+ align:start position:0%
+here for the time translation L is the
+ 
+
+ align:start position:0%
+here for the time translation L is the
+analog of K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the departure t5a is the F here
+
+ align:start position:0%
+and the departure t5a is the F here
+ 
+
+ align:start position:0%
+and the departure t5a is the F here
+and then here is the pay okay so so here
+
+ align:start position:0%
+and then here is the pay okay so so here
+ 
+
+ align:start position:0%
+and then here is the pay okay so so here
+you also have time derivative okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you also have time divided and so
+
+ align:start position:0%
+here you also have time divided and so
+ 
+
+ align:start position:0%
+here you also have time divided and so
+this by itself is also a pi okay
+
+ align:start position:0%
+this by itself is also a pi okay
+ 
+
+ align:start position:0%
+this by itself is also a pi okay
+and the L
+
+ align:start position:0%
+and the L
+ 
+
+ align:start position:0%
+and the L
+uh may also contain time derivative
+
+ align:start position:0%
+uh may also contain time derivative
+ 
+
+ align:start position:0%
+uh may also contain time derivative
+so so L is the k0 here okay so so in
+
+ align:start position:0%
+so so L is the k0 here okay so so in
+ 
+
+ align:start position:0%
+so so L is the k0 here okay so so in
+this case the k0 is non-zero and which
+
+ align:start position:0%
+this case the k0 is non-zero and which
+ 
+
+ align:start position:0%
+this case the k0 is non-zero and which
+is equal to l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so in this case the conserved charge
+
+ align:start position:0%
+and so in this case the conserved charge
+ 
+
+ align:start position:0%
+and so in this case the conserved charge
+is just h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case you uh um
+
+ align:start position:0%
+so in this case you uh um
+ 
+
+ align:start position:0%
+so in this case you uh um
+our general argument here don't apply
+
+ align:start position:0%
+our general argument here don't apply
+ 
+
+ align:start position:0%
+our general argument here don't apply
+because now you have Pi here also and
+
+ align:start position:0%
+because now you have Pi here also and
+ 
+
+ align:start position:0%
+because now you have Pi here also and
+you may have a Time derivative here also
+
+ align:start position:0%
+you may have a Time derivative here also
+ 
+
+ align:start position:0%
+you may have a Time derivative here also
+okay so the story is more complicated
+
+ align:start position:0%
+okay so the story is more complicated
+ 
+
+ align:start position:0%
+okay so the story is more complicated
+but this case we load trivial is true
+
+ align:start position:0%
+but this case we load trivial is true
+ 
+
+ align:start position:0%
+but this case we load trivial is true
+because it's by definition
+
+ align:start position:0%
+because it's by definition
+ 
+
+ align:start position:0%
+because it's by definition
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+acting on any field
+
+ align:start position:0%
+acting on any field
+ 
+
+ align:start position:0%
+acting on any field
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+is minus i r to T if i a
+
+ align:start position:0%
+is minus i r to T if i a
+ 
+
+ align:start position:0%
+is minus i r to T if i a
+and this is exactly the time translation
+
+ align:start position:0%
+and this is exactly the time translation
+ 
+
+ align:start position:0%
+and this is exactly the time translation
+a transformation of our fields
+
+ align:start position:0%
+a transformation of our fields
+ 
+
+ align:start position:0%
+a transformation of our fields
+okay so so in this special case
+
+ align:start position:0%
+okay so so in this special case
+ 
+
+ align:start position:0%
+okay so so in this special case
+this equation is also satisfied
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so this is just followed from
+
+ align:start position:0%
+okay so so this is just followed from
+ 
+
+ align:start position:0%
+okay so so this is just followed from
+the Heisenberg equation itself okay and
+
+ align:start position:0%
+the Heisenberg equation itself okay and
+ 
+
+ align:start position:0%
+the Heisenberg equation itself okay and
+now you should just understand this
+
+ align:start position:0%
+now you should just understand this
+ 
+
+ align:start position:0%
+now you should just understand this
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the age now can be considered as a
+
+ align:start position:0%
+as the age now can be considered as a
+ 
+
+ align:start position:0%
+as the age now can be considered as a
+symmetry generator for time translation
+
+ align:start position:0%
+symmetry generator for time translation
+ 
+
+ align:start position:0%
+symmetry generator for time translation
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+and when it acts on the field and
+
+ align:start position:0%
+and when it acts on the field and
+ 
+
+ align:start position:0%
+and when it acts on the field and
+generate the time translation okay time
+
+ align:start position:0%
+generate the time translation okay time
+ 
+
+ align:start position:0%
+generate the time translation okay time
+translation just
+
+ align:start position:0%
+translation just
+ 
+
+ align:start position:0%
+translation just
+infinitesimally just to time derivative
+
+ align:start position:0%
+infinitesimally just to time derivative
+ 
+
+ align:start position:0%
+infinitesimally just to time derivative
+one Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so these are infinitesimal
+
+ align:start position:0%
+so these are infinitesimal
+ 
+
+ align:start position:0%
+so these are infinitesimal
+transformations
+
+ align:start position:0%
+transformations
+ 
+
+ align:start position:0%
+transformations
+but now starting from here
+
+ align:start position:0%
+but now starting from here
+ 
+
+ align:start position:0%
+but now starting from here
+you can actually
+
+ align:start position:0%
+you can actually
+ 
+
+ align:start position:0%
+you can actually
+obtain finally Transformations on the
+
+ align:start position:0%
+obtain finally Transformations on the
+ 
+
+ align:start position:0%
+obtain finally Transformations on the
+field also using Q okay so we can
+
+ align:start position:0%
+field also using Q okay so we can
+ 
+
+ align:start position:0%
+field also using Q okay so we can
+generate finally transformations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's consider say U
+
+ align:start position:0%
+so let's consider say U
+ 
+
+ align:start position:0%
+so let's consider say U
+Lambda Alpha so Lambda are just some
+
+ align:start position:0%
+Lambda Alpha so Lambda are just some
+ 
+
+ align:start position:0%
+Lambda Alpha so Lambda are just some
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+let's consider this quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now I now experientiate this Cube
+
+ align:start position:0%
+okay now I now experientiate this Cube
+ 
+
+ align:start position:0%
+okay now I now experientiate this Cube
+so Q is the operator and Lambda is just
+
+ align:start position:0%
+so Q is the operator and Lambda is just
+ 
+
+ align:start position:0%
+so Q is the operator and Lambda is just
+some numbers okay
+
+ align:start position:0%
+some numbers okay
+ 
+
+ align:start position:0%
+some numbers okay
+Lambda is some constant parameters okay
+
+ align:start position:0%
+Lambda is some constant parameters okay
+ 
+
+ align:start position:0%
+Lambda is some constant parameters okay
+and again the alpha is sound yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Heisenberg equation but here how
+
+ align:start position:0%
+the Heisenberg equation but here how
+ 
+
+ align:start position:0%
+the Heisenberg equation but here how
+would you evaluate this commentator not
+
+ align:start position:0%
+would you evaluate this commentator not
+ 
+
+ align:start position:0%
+would you evaluate this commentator not
+knowing the form of you but because he
+
+ align:start position:0%
+knowing the form of you but because he
+ 
+
+ align:start position:0%
+knowing the form of you but because he
+said it can depend on my uh time
+
+ align:start position:0%
+said it can depend on my uh time
+ 
+
+ align:start position:0%
+said it can depend on my uh time
+derivatives as well right yeah yeah yeah
+
+ align:start position:0%
+derivatives as well right yeah yeah yeah
+ 
+
+ align:start position:0%
+derivatives as well right yeah yeah yeah
+here just this General argument on the
+
+ align:start position:0%
+here just this General argument on the
+ 
+
+ align:start position:0%
+here just this General argument on the
+apply anymore so so in this case you
+
+ align:start position:0%
+apply anymore so so in this case you
+ 
+
+ align:start position:0%
+apply anymore so so in this case you
+really have to uh uh you can check the
+
+ align:start position:0%
+really have to uh uh you can check the
+ 
+
+ align:start position:0%
+really have to uh uh you can check the
+explicitly you can just write down the
+
+ align:start position:0%
+explicitly you can just write down the
+ 
+
+ align:start position:0%
+explicitly you can just write down the
+explicit value uh Express form of H and
+
+ align:start position:0%
+explicit value uh Express form of H and
+ 
+
+ align:start position:0%
+explicit value uh Express form of H and
+then then work out explicitly but you
+
+ align:start position:0%
+then then work out explicitly but you
+ 
+
+ align:start position:0%
+then then work out explicitly but you
+don't have to do it because we know this
+
+ align:start position:0%
+don't have to do it because we know this
+ 
+
+ align:start position:0%
+don't have to do it because we know this
+has to be true but just by set of
+
+ align:start position:0%
+has to be true but just by set of
+ 
+
+ align:start position:0%
+has to be true but just by set of
+consistency because we solved the
+
+ align:start position:0%
+consistency because we solved the
+ 
+
+ align:start position:0%
+consistency because we solved the
+Heisenberg equation yeah because the
+
+ align:start position:0%
+Heisenberg equation yeah because the
+ 
+
+ align:start position:0%
+Heisenberg equation yeah because the
+when we quantize it essentially we're
+
+ align:start position:0%
+when we quantize it essentially we're
+ 
+
+ align:start position:0%
+when we quantize it essentially we're
+solving the Heisenberg equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah but you can check it explicitly uh
+
+ align:start position:0%
+yeah but you can check it explicitly uh
+ 
+
+ align:start position:0%
+yeah but you can check it explicitly uh
+yourself that this is true yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so so here so so Lambda Alpha here just
+
+ align:start position:0%
+so so here so so Lambda Alpha here just
+ 
+
+ align:start position:0%
+so so here so so Lambda Alpha here just
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+collection of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite
+
+ align:start position:0%
+finite
+ 
+
+ align:start position:0%
+finite
+transformation parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this can be used to uh uh generate
+
+ align:start position:0%
+so this can be used to uh uh generate
+ 
+
+ align:start position:0%
+so this can be used to uh uh generate
+the finite transformations
+
+ align:start position:0%
+the finite transformations
+ 
+
+ align:start position:0%
+the finite transformations
+okay so if you act you are you lamb the
+
+ align:start position:0%
+okay so if you act you are you lamb the
+ 
+
+ align:start position:0%
+okay so if you act you are you lamb the
+alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Phi
+
+ align:start position:0%
+Phi
+ 
+
+ align:start position:0%
+Phi
+by a
+
+ align:start position:0%
+by a
+ 
+
+ align:start position:0%
+by a
+and you Lambda Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dagger and then you just get five a
+
+ align:start position:0%
+dagger and then you just get five a
+ 
+
+ align:start position:0%
+dagger and then you just get five a
+prime and now this is a finite
+
+ align:start position:0%
+prime and now this is a finite
+ 
+
+ align:start position:0%
+prime and now this is a finite
+transformation of finite symmetric
+
+ align:start position:0%
+transformation of finite symmetric
+ 
+
+ align:start position:0%
+transformation of finite symmetric
+transformation of Phi okay
+
+ align:start position:0%
+transformation of Phi okay
+ 
+
+ align:start position:0%
+transformation of Phi okay
+and when you expand when Lambda Alpha is
+
+ align:start position:0%
+and when you expand when Lambda Alpha is
+ 
+
+ align:start position:0%
+and when you expand when Lambda Alpha is
+infinitesimal
+
+ align:start position:0%
+infinitesimal
+ 
+
+ align:start position:0%
+infinitesimal
+and then you can just expand this
+
+ align:start position:0%
+and then you can just expand this
+ 
+
+ align:start position:0%
+and then you can just expand this
+exponential then the leading term
+
+ align:start position:0%
+exponential then the leading term
+ 
+
+ align:start position:0%
+exponential then the leading term
+becomes this one okay
+
+ align:start position:0%
+becomes this one okay
+ 
+
+ align:start position:0%
+becomes this one okay
+the leading term becomes this one and uh
+
+ align:start position:0%
+the leading term becomes this one and uh
+ 
+
+ align:start position:0%
+the leading term becomes this one and uh
+yeah so so when
+
+ align:start position:0%
+yeah so so when
+ 
+
+ align:start position:0%
+yeah so so when
+Lambda Alpha equal to Epsilon Alpha goes
+
+ align:start position:0%
+Lambda Alpha equal to Epsilon Alpha goes
+ 
+
+ align:start position:0%
+Lambda Alpha equal to Epsilon Alpha goes
+to zero
+
+ align:start position:0%
+to zero
+ 
+
+ align:start position:0%
+to zero
+and these equations this equation star
+
+ align:start position:0%
+and these equations this equation star
+ 
+
+ align:start position:0%
+and these equations this equation star
+and Then star star
+
+ align:start position:0%
+and Then star star
+ 
+
+ align:start position:0%
+and Then star star
+reduces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+as leading non-trivial order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you expand the exponential okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so this can be a tongue in general just
+
+ align:start position:0%
+so this can be a tongue in general just
+ 
+
+ align:start position:0%
+so this can be a tongue in general just
+so the reason this is true
+
+ align:start position:0%
+so the reason this is true
+ 
+
+ align:start position:0%
+so the reason this is true
+without even doing any doing any
+
+ align:start position:0%
+without even doing any doing any
+ 
+
+ align:start position:0%
+without even doing any doing any
+calculation you can just imagine you can
+
+ align:start position:0%
+calculation you can just imagine you can
+ 
+
+ align:start position:0%
+calculation you can just imagine you can
+build this U this in this finite
+
+ align:start position:0%
+build this U this in this finite
+ 
+
+ align:start position:0%
+build this U this in this finite
+transformation by infinite number of
+
+ align:start position:0%
+transformation by infinite number of
+ 
+
+ align:start position:0%
+transformation by infinite number of
+infinitesimal transformations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you build them up and then you
+
+ align:start position:0%
+so when you build them up and then you
+ 
+
+ align:start position:0%
+so when you build them up and then you
+will just generate the finite
+
+ align:start position:0%
+will just generate the finite
+ 
+
+ align:start position:0%
+will just generate the finite
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you already worked out the example in
+
+ align:start position:0%
+so you already worked out the example in
+ 
+
+ align:start position:0%
+so you already worked out the example in
+your preset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you already worked out the example in
+
+ align:start position:0%
+so you already worked out the example in
+ 
+
+ align:start position:0%
+so you already worked out the example in
+your pizza that
+
+ align:start position:0%
+your pizza that
+ 
+
+ align:start position:0%
+your pizza that
+if you can see the HT
+
+ align:start position:0%
+if you can see the HT
+ 
+
+ align:start position:0%
+if you can see the HT
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x i
+
+ align:start position:0%
+x i
+ 
+
+ align:start position:0%
+x i
+acting on five zero
+
+ align:start position:0%
+acting on five zero
+ 
+
+ align:start position:0%
+acting on five zero
+minus i h t
+
+ align:start position:0%
+minus i h t
+ 
+
+ align:start position:0%
+minus i h t
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+ipixi
+
+ align:start position:0%
+ipixi
+ 
+
+ align:start position:0%
+ipixi
+and then this just give you 5 p x i t x
+
+ align:start position:0%
+and then this just give you 5 p x i t x
+ 
+
+ align:start position:0%
+and then this just give you 5 p x i t x
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+just give you five DX
+
+ align:start position:0%
+just give you five DX
+ 
+
+ align:start position:0%
+just give you five DX
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+so this is so so here
+
+ align:start position:0%
+so this is so so here
+ 
+
+ align:start position:0%
+so this is so so here
+HT minus
+
+ align:start position:0%
+HT minus
+ 
+
+ align:start position:0%
+HT minus
+p i x i
+
+ align:start position:0%
+p i x i
+ 
+
+ align:start position:0%
+p i x i
+is our Lambda Alpha to Alpha here okay
+
+ align:start position:0%
+is our Lambda Alpha to Alpha here okay
+ 
+
+ align:start position:0%
+is our Lambda Alpha to Alpha here okay
+so Alpha here runs
+
+ align:start position:0%
+so Alpha here runs
+ 
+
+ align:start position:0%
+so Alpha here runs
+0 and I Direction okay so in the zero
+
+ align:start position:0%
+0 and I Direction okay so in the zero
+ 
+
+ align:start position:0%
+0 and I Direction okay so in the zero
+direction of the T now is just some
+
+ align:start position:0%
+direction of the T now is just some
+ 
+
+ align:start position:0%
+direction of the T now is just some
+parameter
+
+ align:start position:0%
+parameter
+ 
+
+ align:start position:0%
+parameter
+and the uh uh and the Lambda
+
+ align:start position:0%
+and the uh uh and the Lambda
+ 
+
+ align:start position:0%
+and the uh uh and the Lambda
+Alpha equal to T and the minus x i okay
+
+ align:start position:0%
+Alpha equal to T and the minus x i okay
+ 
+
+ align:start position:0%
+Alpha equal to T and the minus x i okay
+and then Q off I just uh
+
+ align:start position:0%
+and then Q off I just uh
+ 
+
+ align:start position:0%
+and then Q off I just uh
+and the Q over here
+
+ align:start position:0%
+and the Q over here
+ 
+
+ align:start position:0%
+and the Q over here
+is equal to yeah TXI let me just two t x
+
+ align:start position:0%
+is equal to yeah TXI let me just two t x
+ 
+
+ align:start position:0%
+is equal to yeah TXI let me just two t x
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+and the Q Alpha here is just h
+
+ align:start position:0%
+and the Q Alpha here is just h
+ 
+
+ align:start position:0%
+and the Q Alpha here is just h
+minus pi
+
+ align:start position:0%
+minus pi
+ 
+
+ align:start position:0%
+minus pi
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so this is just the example of that
+
+ align:start position:0%
+good so this is just the example of that
+ 
+
+ align:start position:0%
+good so this is just the example of that
+okay this is just example of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and also you can consider Lawrence
+
+ align:start position:0%
+and also you can consider Lawrence
+ 
+
+ align:start position:0%
+and also you can consider Lawrence
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+so another example is a low range
+
+ align:start position:0%
+so another example is a low range
+ 
+
+ align:start position:0%
+so another example is a low range
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's consider so so in your P set
+
+ align:start position:0%
+so let's consider so so in your P set
+ 
+
+ align:start position:0%
+so let's consider so so in your P set
+you already
+
+ align:start position:0%
+you already
+ 
+
+ align:start position:0%
+you already
+so in the low range transformation uh uh
+
+ align:start position:0%
+so in the low range transformation uh uh
+ 
+
+ align:start position:0%
+so in the low range transformation uh uh
+the conserved charges
+
+ align:start position:0%
+the conserved charges
+ 
+
+ align:start position:0%
+the conserved charges
+actually there are six of them
+
+ align:start position:0%
+actually there are six of them
+ 
+
+ align:start position:0%
+actually there are six of them
+okay you knew
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going from
+
+ align:start position:0%
+going from
+ 
+
+ align:start position:0%
+going from
+one zero three okay so so they all
+
+ align:start position:0%
+one zero three okay so so they all
+ 
+
+ align:start position:0%
+one zero three okay so so they all
+together six conserved charges
+
+ align:start position:0%
+together six conserved charges
+ 
+
+ align:start position:0%
+together six conserved charges
+associated with an orange transformation
+
+ align:start position:0%
+associated with an orange transformation
+ 
+
+ align:start position:0%
+associated with an orange transformation
+three rotations and three boosts okay
+
+ align:start position:0%
+three rotations and three boosts okay
+ 
+
+ align:start position:0%
+three rotations and three boosts okay
+and then so when you write the final
+
+ align:start position:0%
+and then so when you write the final
+ 
+
+ align:start position:0%
+and then so when you write the final
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+and then you will have six parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you have six parameters and Omega
+
+ align:start position:0%
+okay you have six parameters and Omega
+ 
+
+ align:start position:0%
+okay you have six parameters and Omega
+mu mu
+
+ align:start position:0%
+mu mu
+ 
+
+ align:start position:0%
+mu mu
+and this because mu mu is anti-symmetric
+
+ align:start position:0%
+and this because mu mu is anti-symmetric
+ 
+
+ align:start position:0%
+and this because mu mu is anti-symmetric
+which you worked out in your PSAT
+
+ align:start position:0%
+which you worked out in your PSAT
+ 
+
+ align:start position:0%
+which you worked out in your PSAT
+so this parameter should also be
+
+ align:start position:0%
+so this parameter should also be
+ 
+
+ align:start position:0%
+so this parameter should also be
+anti-symmetric
+
+ align:start position:0%
+anti-symmetric
+ 
+
+ align:start position:0%
+anti-symmetric
+okay and uh so they are finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fahrenheit angles
+
+ align:start position:0%
+Fahrenheit angles
+ 
+
+ align:start position:0%
+Fahrenheit angles
+not definite angios
+
+ align:start position:0%
+not definite angios
+ 
+
+ align:start position:0%
+not definite angios
+finite angles
+
+ align:start position:0%
+finite angles
+ 
+
+ align:start position:0%
+finite angles
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+boost
+
+ align:start position:0%
+boost
+ 
+
+ align:start position:0%
+boost
+okay so so the so so essentially the lab
+
+ align:start position:0%
+okay so so the so so essentially the lab
+ 
+
+ align:start position:0%
+okay so so the so so essentially the lab
+they give the parameters for the finite
+
+ align:start position:0%
+they give the parameters for the finite
+ 
+
+ align:start position:0%
+they give the parameters for the finite
+rotation angles and the Boost
+
+ align:start position:0%
+rotation angles and the Boost
+ 
+
+ align:start position:0%
+rotation angles and the Boost
+and so uh so that generates a low range
+
+ align:start position:0%
+and so uh so that generates a low range
+ 
+
+ align:start position:0%
+and so uh so that generates a low range
+transformation okay they generate the
+
+ align:start position:0%
+transformation okay they generate the
+ 
+
+ align:start position:0%
+transformation okay they generate the
+orange transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so for example you uh say if you act
+
+ align:start position:0%
+and so for example you uh say if you act
+ 
+
+ align:start position:0%
+and so for example you uh say if you act
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+new Lambda
+
+ align:start position:0%
+new Lambda
+ 
+
+ align:start position:0%
+new Lambda
+on 5X
+
+ align:start position:0%
+on 5X
+ 
+
+ align:start position:0%
+on 5X
+and you Lambda you can check
+
+ align:start position:0%
+and you Lambda you can check
+ 
+
+ align:start position:0%
+and you Lambda you can check
+dagger on fire x what you get
+
+ align:start position:0%
+dagger on fire x what you get
+ 
+
+ align:start position:0%
+dagger on fire x what you get
+is Phi Prime X
+
+ align:start position:0%
+is Phi Prime X
+ 
+
+ align:start position:0%
+is Phi Prime X
+and the Phi Prime X is also the same as
+
+ align:start position:0%
+and the Phi Prime X is also the same as
+ 
+
+ align:start position:0%
+and the Phi Prime X is also the same as
+5 Lambda 1 and X okay so so here Lambda
+
+ align:start position:0%
+5 Lambda 1 and X okay so so here Lambda
+ 
+
+ align:start position:0%
+5 Lambda 1 and X okay so so here Lambda
+so here Lambda 1 x is the low range
+
+ align:start position:0%
+so here Lambda 1 x is the low range
+ 
+
+ align:start position:0%
+so here Lambda 1 x is the low range
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so X mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with parameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determined by uh uh or yeah just Omega
+
+ align:start position:0%
+determined by uh uh or yeah just Omega
+ 
+
+ align:start position:0%
+determined by uh uh or yeah just Omega
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so describe the Lambda is the
+
+ align:start position:0%
+so describe the Lambda is the
+ 
+
+ align:start position:0%
+so describe the Lambda is the
+corresponding orange transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this clear
+
+ align:start position:0%
+is this clear
+ 
+
+ align:start position:0%
+is this clear
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+so you assumed like that you can
+
+ align:start position:0%
+so you assumed like that you can
+ 
+
+ align:start position:0%
+so you assumed like that you can
+represent the I guess the operators that
+
+ align:start position:0%
+represent the I guess the operators that
+ 
+
+ align:start position:0%
+represent the I guess the operators that
+perform these Transformations like this
+
+ align:start position:0%
+perform these Transformations like this
+ 
+
+ align:start position:0%
+perform these Transformations like this
+but don't you have to like think about
+
+ align:start position:0%
+but don't you have to like think about
+ 
+
+ align:start position:0%
+but don't you have to like think about
+if it follows the algebra such that you
+
+ align:start position:0%
+if it follows the algebra such that you
+ 
+
+ align:start position:0%
+if it follows the algebra such that you
+can represent it like this or like the
+
+ align:start position:0%
+can represent it like this or like the
+ 
+
+ align:start position:0%
+can represent it like this or like the
+group of Transformations yeah yeah yeah
+
+ align:start position:0%
+group of Transformations yeah yeah yeah
+ 
+
+ align:start position:0%
+group of Transformations yeah yeah yeah
+indeed so so here is not uh here is not
+
+ align:start position:0%
+indeed so so here is not uh here is not
+ 
+
+ align:start position:0%
+indeed so so here is not uh here is not
+say I assume here I'm just directly
+
+ align:start position:0%
+say I assume here I'm just directly
+ 
+
+ align:start position:0%
+say I assume here I'm just directly
+telling you the result uh it's just when
+
+ align:start position:0%
+telling you the result uh it's just when
+ 
+
+ align:start position:0%
+telling you the result uh it's just when
+you uh build yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so if you want to generate the uh uh
+
+ align:start position:0%
+so so if you want to generate the uh uh
+ 
+
+ align:start position:0%
+so so if you want to generate the uh uh
+um yeah I'm just directly already
+
+ align:start position:0%
+um yeah I'm just directly already
+ 
+
+ align:start position:0%
+um yeah I'm just directly already
+directly tell you the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you do the composition of the
+
+ align:start position:0%
+if you do the composition of the
+ 
+
+ align:start position:0%
+if you do the composition of the
+infinitesimal transformation you will
+
+ align:start position:0%
+infinitesimal transformation you will
+ 
+
+ align:start position:0%
+infinitesimal transformation you will
+get that yeah yeah the reason I write
+
+ align:start position:0%
+get that yeah yeah the reason I write
+ 
+
+ align:start position:0%
+get that yeah yeah the reason I write
+down this explicitly uh immediately
+
+ align:start position:0%
+down this explicitly uh immediately
+ 
+
+ align:start position:0%
+down this explicitly uh immediately
+because you should have already seen
+
+ align:start position:0%
+because you should have already seen
+ 
+
+ align:start position:0%
+because you should have already seen
+this in quantum mechanics yeah because
+
+ align:start position:0%
+this in quantum mechanics yeah because
+ 
+
+ align:start position:0%
+this in quantum mechanics yeah because
+that's how you do the angular momentum
+
+ align:start position:0%
+that's how you do the angular momentum
+ 
+
+ align:start position:0%
+that's how you do the angular momentum
+yeah in quantum mechanics when you do
+
+ align:start position:0%
+yeah in quantum mechanics when you do
+ 
+
+ align:start position:0%
+yeah in quantum mechanics when you do
+the angular momentum the way is the same
+
+ align:start position:0%
+the angular momentum the way is the same
+ 
+
+ align:start position:0%
+the angular momentum the way is the same
+thing yeah yeah here we just generalize
+
+ align:start position:0%
+thing yeah yeah here we just generalize
+ 
+
+ align:start position:0%
+thing yeah yeah here we just generalize
+it to to uh to General symmetries yeah
+
+ align:start position:0%
+it to to uh to General symmetries yeah
+ 
+
+ align:start position:0%
+it to to uh to General symmetries yeah
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yes it was kind of some similar question
+
+ align:start position:0%
+yes it was kind of some similar question
+ 
+
+ align:start position:0%
+yes it was kind of some similar question
+but just like
+
+ align:start position:0%
+but just like
+ 
+
+ align:start position:0%
+but just like
+um so like this is like a general
+
+ align:start position:0%
+um so like this is like a general
+ 
+
+ align:start position:0%
+um so like this is like a general
+procedure if you have a symmetry to get
+
+ align:start position:0%
+procedure if you have a symmetry to get
+ 
+
+ align:start position:0%
+procedure if you have a symmetry to get
+the representation on your own space
+
+ align:start position:0%
+the representation on your own space
+ 
+
+ align:start position:0%
+the representation on your own space
+yeah like this yeah like in q1 we
+
+ align:start position:0%
+yeah like this yeah like in q1 we
+ 
+
+ align:start position:0%
+yeah like this yeah like in q1 we
+usually just postulate that there's the
+
+ align:start position:0%
+usually just postulate that there's the
+ 
+
+ align:start position:0%
+usually just postulate that there's the
+inventory operator and then demand that
+
+ align:start position:0%
+inventory operator and then demand that
+ 
+
+ align:start position:0%
+inventory operator and then demand that
+the group holds right yeah so like do we
+
+ align:start position:0%
+the group holds right yeah so like do we
+ 
+
+ align:start position:0%
+the group holds right yeah so like do we
+need to show that those things get this
+
+ align:start position:0%
+need to show that those things get this
+ 
+
+ align:start position:0%
+need to show that those things get this
+this preserves the purple or is that not
+
+ align:start position:0%
+this preserves the purple or is that not
+ 
+
+ align:start position:0%
+this preserves the purple or is that not
+yeah yeah so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I didn't go into that but this is
+
+ align:start position:0%
+yeah I didn't go into that but this is
+ 
+
+ align:start position:0%
+yeah I didn't go into that but this is
+guaranteed essentially that's how you
+
+ align:start position:0%
+guaranteed essentially that's how you
+ 
+
+ align:start position:0%
+guaranteed essentially that's how you
+yeah in the uh this is how you build the
+
+ align:start position:0%
+yeah in the uh this is how you build the
+ 
+
+ align:start position:0%
+yeah in the uh this is how you build the
+algebra because the algebra is also uh
+
+ align:start position:0%
+algebra because the algebra is also uh
+ 
+
+ align:start position:0%
+algebra because the algebra is also uh
+the the finite transformation is also
+
+ align:start position:0%
+the the finite transformation is also
+ 
+
+ align:start position:0%
+the the finite transformation is also
+built up by by Infinity transformations
+
+ align:start position:0%
+built up by by Infinity transformations
+ 
+
+ align:start position:0%
+built up by by Infinity transformations
+and so so you're saying it guaranteed uh
+
+ align:start position:0%
+and so so you're saying it guaranteed uh
+ 
+
+ align:start position:0%
+and so so you're saying it guaranteed uh
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+so there is a theory of lead groups and
+
+ align:start position:0%
+so there is a theory of lead groups and
+ 
+
+ align:start position:0%
+so there is a theory of lead groups and
+the algebra behind this
+
+ align:start position:0%
+the algebra behind this
+ 
+
+ align:start position:0%
+the algebra behind this
+yes I didn't go into that um so so some
+
+ align:start position:0%
+yes I didn't go into that um so so some
+ 
+
+ align:start position:0%
+yes I didn't go into that um so so some
+of you may already sing a little bit of
+
+ align:start position:0%
+of you may already sing a little bit of
+ 
+
+ align:start position:0%
+of you may already sing a little bit of
+this when you talk about angular
+
+ align:start position:0%
+this when you talk about angular
+ 
+
+ align:start position:0%
+this when you talk about angular
+momentum saying quantum mechanics so
+
+ align:start position:0%
+momentum saying quantum mechanics so
+ 
+
+ align:start position:0%
+momentum saying quantum mechanics so
+it's exactly the same story there
+
+ align:start position:0%
+it's exactly the same story there
+ 
+
+ align:start position:0%
+it's exactly the same story there
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correspond to the angular momentum being
+
+ align:start position:0%
+correspond to the angular momentum being
+ 
+
+ align:start position:0%
+correspond to the angular momentum being
+preserved yeah but what is like the
+
+ align:start position:0%
+preserved yeah but what is like the
+ 
+
+ align:start position:0%
+preserved yeah but what is like the
+intuition for like the thing that's
+
+ align:start position:0%
+intuition for like the thing that's
+ 
+
+ align:start position:0%
+intuition for like the thing that's
+preserved in boosts
+
+ align:start position:0%
+preserved in boosts
+ 
+
+ align:start position:0%
+preserved in boosts
+yeah yeah it's a uh yeah indeed there's
+
+ align:start position:0%
+yeah yeah it's a uh yeah indeed there's
+ 
+
+ align:start position:0%
+yeah yeah it's a uh yeah indeed there's
+no worry
+
+ align:start position:0%
+no worry
+ 
+
+ align:start position:0%
+no worry
+intuitive way to think about it also
+
+ align:start position:0%
+intuitive way to think about it also
+ 
+
+ align:start position:0%
+intuitive way to think about it also
+it's not that useful you know you can
+
+ align:start position:0%
+it's not that useful you know you can
+ 
+
+ align:start position:0%
+it's not that useful you know you can
+define a boost charge so so so if you
+
+ align:start position:0%
+define a boost charge so so so if you
+ 
+
+ align:start position:0%
+define a boost charge so so so if you
+can see the the all the spatial
+
+ align:start position:0%
+can see the the all the spatial
+ 
+
+ align:start position:0%
+can see the the all the spatial
+components and if you consider the old
+
+ align:start position:0%
+components and if you consider the old
+ 
+
+ align:start position:0%
+components and if you consider the old
+IJ here then these are the angular
+
+ align:start position:0%
+IJ here then these are the angular
+ 
+
+ align:start position:0%
+IJ here then these are the angular
+momentum operator and this is the your
+
+ align:start position:0%
+momentum operator and this is the your
+ 
+
+ align:start position:0%
+momentum operator and this is the your
+standard algorithm operator which you
+
+ align:start position:0%
+standard algorithm operator which you
+ 
+
+ align:start position:0%
+standard algorithm operator which you
+have seen and if you look at zero I and
+
+ align:start position:0%
+have seen and if you look at zero I and
+ 
+
+ align:start position:0%
+have seen and if you look at zero I and
+then that was sometimes we call Boost
+
+ align:start position:0%
+then that was sometimes we call Boost
+ 
+
+ align:start position:0%
+then that was sometimes we call Boost
+charge it generates the Boost
+
+ align:start position:0%
+charge it generates the Boost
+ 
+
+ align:start position:0%
+charge it generates the Boost
+but in terms of the conserved number
+
+ align:start position:0%
+but in terms of the conserved number
+ 
+
+ align:start position:0%
+but in terms of the conserved number
+yeah we don't have
+
+ align:start position:0%
+yeah we don't have
+ 
+
+ align:start position:0%
+yeah we don't have
+we don't use it in the in the essential
+
+ align:start position:0%
+we don't use it in the in the essential
+ 
+
+ align:start position:0%
+we don't use it in the in the essential
+Way say say say in other contexts yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah it just does not give you
+
+ align:start position:0%
+yeah yeah it just does not give you
+ 
+
+ align:start position:0%
+yeah yeah it just does not give you
+something additional
+
+ align:start position:0%
+something additional
+ 
+
+ align:start position:0%
+something additional
+just a normally when you deal with
+
+ align:start position:0%
+just a normally when you deal with
+ 
+
+ align:start position:0%
+just a normally when you deal with
+physical problems say angular momentum
+
+ align:start position:0%
+physical problems say angular momentum
+ 
+
+ align:start position:0%
+physical problems say angular momentum
+kind of basic momentum calibration
+
+ align:start position:0%
+kind of basic momentum calibration
+ 
+
+ align:start position:0%
+kind of basic momentum calibration
+energy conservations right enough uh
+
+ align:start position:0%
+energy conservations right enough uh
+ 
+
+ align:start position:0%
+energy conservations right enough uh
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you normally don't need to use a
+
+ align:start position:0%
+yeah you normally don't need to use a
+ 
+
+ align:start position:0%
+yeah you normally don't need to use a
+boost charge condemnation yeah to solve
+
+ align:start position:0%
+boost charge condemnation yeah to solve
+ 
+
+ align:start position:0%
+boost charge condemnation yeah to solve
+your problem
+
+ align:start position:0%
+your problem
+ 
+
+ align:start position:0%
+your problem
+yeah so that's why we don't see this
+
+ align:start position:0%
+yeah so that's why we don't see this
+ 
+
+ align:start position:0%
+yeah so that's why we don't see this
+object very often say when you discuss
+
+ align:start position:0%
+object very often say when you discuss
+ 
+
+ align:start position:0%
+object very often say when you discuss
+special relativity or or other things
+
+ align:start position:0%
+special relativity or or other things
+ 
+
+ align:start position:0%
+special relativity or or other things
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but here plays a very important role
+
+ align:start position:0%
+but here plays a very important role
+ 
+
+ align:start position:0%
+but here plays a very important role
+that in Quantum field Theory this is the
+
+ align:start position:0%
+that in Quantum field Theory this is the
+ 
+
+ align:start position:0%
+that in Quantum field Theory this is the
+operator which generates
+
+ align:start position:0%
+operator which generates
+ 
+
+ align:start position:0%
+operator which generates
+the Boost symmetry okay if you want to
+
+ align:start position:0%
+the Boost symmetry okay if you want to
+ 
+
+ align:start position:0%
+the Boost symmetry okay if you want to
+do a boost uh General do a boost in your
+
+ align:start position:0%
+do a boost uh General do a boost in your
+ 
+
+ align:start position:0%
+do a boost uh General do a boost in your
+hearable space that's the operator to do
+
+ align:start position:0%
+hearable space that's the operator to do
+ 
+
+ align:start position:0%
+hearable space that's the operator to do
+it okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+yeah so in your presets
+
+ align:start position:0%
+yeah so in your presets
+ 
+
+ align:start position:0%
+yeah so in your presets
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah another example is the phase
+
+ align:start position:0%
+yeah another example is the phase
+ 
+
+ align:start position:0%
+yeah another example is the phase
+rotation let me just very quickly wrote
+
+ align:start position:0%
+rotation let me just very quickly wrote
+ 
+
+ align:start position:0%
+rotation let me just very quickly wrote
+here and so so another example
+
+ align:start position:0%
+here and so so another example
+ 
+
+ align:start position:0%
+here and so so another example
+is the phase rotation if you have a
+
+ align:start position:0%
+is the phase rotation if you have a
+ 
+
+ align:start position:0%
+is the phase rotation if you have a
+complex scalar field
+
+ align:start position:0%
+complex scalar field
+ 
+
+ align:start position:0%
+complex scalar field
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there we show there's another charge
+
+ align:start position:0%
+so there we show there's another charge
+ 
+
+ align:start position:0%
+so there we show there's another charge
+was running to the face rotation there's
+
+ align:start position:0%
+was running to the face rotation there's
+ 
+
+ align:start position:0%
+was running to the face rotation there's
+another current uh corresponding to you
+
+ align:start position:0%
+another current uh corresponding to you
+ 
+
+ align:start position:0%
+another current uh corresponding to you
+can rotate the face to the field that's
+
+ align:start position:0%
+can rotate the face to the field that's
+ 
+
+ align:start position:0%
+can rotate the face to the field that's
+a symmetry and uh and so so that will
+
+ align:start position:0%
+a symmetry and uh and so so that will
+ 
+
+ align:start position:0%
+a symmetry and uh and so so that will
+generate the charge Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then if you have Alpha Q
+
+ align:start position:0%
+and then if you have Alpha Q
+ 
+
+ align:start position:0%
+and then if you have Alpha Q
+and then when you act down Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you can just check explicitly
+
+ align:start position:0%
+and then you can just check explicitly
+ 
+
+ align:start position:0%
+and then you can just check explicitly
+that we generate the phase rotation in
+
+ align:start position:0%
+that we generate the phase rotation in
+ 
+
+ align:start position:0%
+that we generate the phase rotation in
+Phi okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and we'll generate for this rotation
+
+ align:start position:0%
+and and we'll generate for this rotation
+ 
+
+ align:start position:0%
+and and we'll generate for this rotation
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so let's conclude our discussion of
+
+ align:start position:0%
+yeah so let's conclude our discussion of
+ 
+
+ align:start position:0%
+yeah so let's conclude our discussion of
+the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+over the real scalar field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we can move to a new part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so before we go to new parts of your
+
+ align:start position:0%
+so before we go to new parts of your
+ 
+
+ align:start position:0%
+so before we go to new parts of your
+your last chance to ask questions about
+
+ align:start position:0%
+your last chance to ask questions about
+ 
+
+ align:start position:0%
+your last chance to ask questions about
+this part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's very quickly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's very quickly talk about the
+
+ align:start position:0%
+so let's very quickly talk about the
+ 
+
+ align:start position:0%
+so let's very quickly talk about the
+complex scale field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+um you can see the complex scalar field
+
+ align:start position:0%
+um you can see the complex scalar field
+ 
+
+ align:start position:0%
+um you can see the complex scalar field
+we get something new we get the concept
+
+ align:start position:0%
+we get something new we get the concept
+ 
+
+ align:start position:0%
+we get something new we get the concept
+of anti-particle
+
+ align:start position:0%
+of anti-particle
+ 
+
+ align:start position:0%
+of anti-particle
+okay so now let's consider the following
+
+ align:start position:0%
+okay so now let's consider the following
+ 
+
+ align:start position:0%
+okay so now let's consider the following
+LaGrange intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again we only consider quadratic
+
+ align:start position:0%
+again we only consider quadratic
+ 
+
+ align:start position:0%
+again we only consider quadratic
+the simplest only quadratic uh
+
+ align:start position:0%
+the simplest only quadratic uh
+ 
+
+ align:start position:0%
+the simplest only quadratic uh
+Lagro engine
+
+ align:start position:0%
+Lagro engine
+ 
+
+ align:start position:0%
+Lagro engine
+but now the file is complex okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where it's complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so complex
+
+ align:start position:0%
+so complex
+ 
+
+ align:start position:0%
+so complex
+is also the same as too real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you can decompose
+
+ align:start position:0%
+so you can decompose
+ 
+
+ align:start position:0%
+so you can decompose
+you can decompose Phi into its real path
+
+ align:start position:0%
+you can decompose Phi into its real path
+ 
+
+ align:start position:0%
+you can decompose Phi into its real path
+and imaginary part
+
+ align:start position:0%
+and imaginary part
+ 
+
+ align:start position:0%
+and imaginary part
+and if you plug them in here
+
+ align:start position:0%
+and if you plug them in here
+ 
+
+ align:start position:0%
+and if you plug them in here
+and then you find you just get two
+
+ align:start position:0%
+and then you find you just get two
+ 
+
+ align:start position:0%
+and then you find you just get two
+separate P's and one is the freeze real
+
+ align:start position:0%
+separate P's and one is the freeze real
+ 
+
+ align:start position:0%
+separate P's and one is the freeze real
+scalar field for the real part and the Y
+
+ align:start position:0%
+scalar field for the real part and the Y
+ 
+
+ align:start position:0%
+scalar field for the real part and the Y
+is the free scalar field for the
+
+ align:start position:0%
+is the free scalar field for the
+ 
+
+ align:start position:0%
+is the free scalar field for the
+imaginary part okay because each one
+
+ align:start position:0%
+imaginary part okay because each one
+ 
+
+ align:start position:0%
+imaginary part okay because each one
+yeah if you write five equal to a plus
+
+ align:start position:0%
+yeah if you write five equal to a plus
+ 
+
+ align:start position:0%
+yeah if you write five equal to a plus
+IB and here just become a squared plus b
+
+ align:start position:0%
+IB and here just become a squared plus b
+ 
+
+ align:start position:0%
+IB and here just become a squared plus b
+squared here it's also a plus b plus b
+
+ align:start position:0%
+squared here it's also a plus b plus b
+ 
+
+ align:start position:0%
+squared here it's also a plus b plus b
+squared okay
+
+ align:start position:0%
+squared okay
+ 
+
+ align:start position:0%
+squared okay
+but there's a reason we write the in
+
+ align:start position:0%
+but there's a reason we write the in
+ 
+
+ align:start position:0%
+but there's a reason we write the in
+yeah so essentially we just get two
+
+ align:start position:0%
+yeah so essentially we just get two
+ 
+
+ align:start position:0%
+yeah so essentially we just get two
+copies of our previous Theory
+
+ align:start position:0%
+copies of our previous Theory
+ 
+
+ align:start position:0%
+copies of our previous Theory
+okay we just get two copies of a
+
+ align:start position:0%
+okay we just get two copies of a
+ 
+
+ align:start position:0%
+okay we just get two copies of a
+previously so you say oh then it's
+
+ align:start position:0%
+previously so you say oh then it's
+ 
+
+ align:start position:0%
+previously so you say oh then it's
+trigger why should we just consider this
+
+ align:start position:0%
+trigger why should we just consider this
+ 
+
+ align:start position:0%
+trigger why should we just consider this
+we just get two copies of previously
+
+ align:start position:0%
+we just get two copies of previously
+ 
+
+ align:start position:0%
+we just get two copies of previously
+but the disadvantage
+
+ align:start position:0%
+but the disadvantage
+ 
+
+ align:start position:0%
+but the disadvantage
+but there's some conception something
+
+ align:start position:0%
+but there's some conception something
+ 
+
+ align:start position:0%
+but there's some conception something
+conceptually new when we write in this
+
+ align:start position:0%
+conceptually new when we write in this
+ 
+
+ align:start position:0%
+conceptually new when we write in this
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+uh there's advantage to write in this
+
+ align:start position:0%
+uh there's advantage to write in this
+ 
+
+ align:start position:0%
+uh there's advantage to write in this
+form rather than write as two separate
+
+ align:start position:0%
+form rather than write as two separate
+ 
+
+ align:start position:0%
+form rather than write as two separate
+identical scalar field Theory
+
+ align:start position:0%
+identical scalar field Theory
+ 
+
+ align:start position:0%
+identical scalar field Theory
+it's precisely in this form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this phase symmetry is manifest okay if
+
+ align:start position:0%
+this phase symmetry is manifest okay if
+ 
+
+ align:start position:0%
+this phase symmetry is manifest okay if
+I just write it as a two separate real
+
+ align:start position:0%
+I just write it as a two separate real
+ 
+
+ align:start position:0%
+I just write it as a two separate real
+scalar field and then this face image is
+
+ align:start position:0%
+scalar field and then this face image is
+ 
+
+ align:start position:0%
+scalar field and then this face image is
+not manifest okay
+
+ align:start position:0%
+not manifest okay
+ 
+
+ align:start position:0%
+not manifest okay
+and the cell here in this form there's a
+
+ align:start position:0%
+and the cell here in this form there's a
+ 
+
+ align:start position:0%
+and the cell here in this form there's a
+face image manifest Okay so
+
+ align:start position:0%
+face image manifest Okay so
+ 
+
+ align:start position:0%
+face image manifest Okay so
+so if I goes to
+
+ align:start position:0%
+so if I goes to
+ 
+
+ align:start position:0%
+so if I goes to
+I Alpha Phi
+
+ align:start position:0%
+I Alpha Phi
+ 
+
+ align:start position:0%
+I Alpha Phi
+and so you see this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's a when you write it in
+
+ align:start position:0%
+okay so there's a when you write it in
+ 
+
+ align:start position:0%
+okay so there's a when you write it in
+terms of real and imaginary part this
+
+ align:start position:0%
+terms of real and imaginary part this
+ 
+
+ align:start position:0%
+terms of real and imaginary part this
+corresponding to rotation between the
+
+ align:start position:0%
+corresponding to rotation between the
+ 
+
+ align:start position:0%
+corresponding to rotation between the
+real and imaginary part
+
+ align:start position:0%
+real and imaginary part
+ 
+
+ align:start position:0%
+real and imaginary part
+and uh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and equation motion is the same
+
+ align:start position:0%
+and equation motion is the same
+ 
+
+ align:start position:0%
+and equation motion is the same
+because it's just the
+
+ align:start position:0%
+because it's just the
+ 
+
+ align:start position:0%
+because it's just the
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it's a you can easily Define
+
+ align:start position:0%
+because it's a you can easily Define
+ 
+
+ align:start position:0%
+because it's a you can easily Define
+equation motion is the same
+
+ align:start position:0%
+equation motion is the same
+ 
+
+ align:start position:0%
+equation motion is the same
+okay and uh
+
+ align:start position:0%
+okay and uh
+ 
+
+ align:start position:0%
+okay and uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah because just two copies of your
+
+ align:start position:0%
+yeah because just two copies of your
+ 
+
+ align:start position:0%
+yeah because just two copies of your
+previous theory of course equation
+
+ align:start position:0%
+previous theory of course equation
+ 
+
+ align:start position:0%
+previous theory of course equation
+motion should be the same
+
+ align:start position:0%
+motion should be the same
+ 
+
+ align:start position:0%
+motion should be the same
+and the the LaGrange intensity or the
+
+ align:start position:0%
+and the the LaGrange intensity or the
+ 
+
+ align:start position:0%
+and the the LaGrange intensity or the
+the momentum density for Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then it become
+
+ align:start position:0%
+then it become
+ 
+
+ align:start position:0%
+then it become
+partial zero five star
+
+ align:start position:0%
+partial zero five star
+ 
+
+ align:start position:0%
+partial zero five star
+and the partial zip files star
+
+ align:start position:0%
+and the partial zip files star
+ 
+
+ align:start position:0%
+and the partial zip files star
+partial zero five okay so we treat we
+
+ align:start position:0%
+partial zero five okay so we treat we
+ 
+
+ align:start position:0%
+partial zero five okay so we treat we
+can treat
+
+ align:start position:0%
+can treat
+ 
+
+ align:start position:0%
+can treat
+Phi and the five star as two independent
+
+ align:start position:0%
+Phi and the five star as two independent
+ 
+
+ align:start position:0%
+Phi and the five star as two independent
+Fields okay
+
+ align:start position:0%
+Fields okay
+ 
+
+ align:start position:0%
+Fields okay
+and then and then the canonical momentum
+
+ align:start position:0%
+and then and then the canonical momentum
+ 
+
+ align:start position:0%
+and then and then the canonical momentum
+say say if you take derivative with
+
+ align:start position:0%
+say say if you take derivative with
+ 
+
+ align:start position:0%
+say say if you take derivative with
+partial zero Phi then you get the
+
+ align:start position:0%
+partial zero Phi then you get the
+ 
+
+ align:start position:0%
+partial zero Phi then you get the
+partial zero five star and the vice
+
+ align:start position:0%
+partial zero five star and the vice
+ 
+
+ align:start position:0%
+partial zero five star and the vice
+versa okay so so the complex accounting
+
+ align:start position:0%
+versa okay so so the complex accounting
+ 
+
+ align:start position:0%
+versa okay so so the complex accounting
+momentum like that
+
+ align:start position:0%
+momentum like that
+ 
+
+ align:start position:0%
+momentum like that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can now write down again we can
+
+ align:start position:0%
+so we can now write down again we can
+ 
+
+ align:start position:0%
+so we can now write down again we can
+just write down the most General
+
+ align:start position:0%
+just write down the most General
+ 
+
+ align:start position:0%
+just write down the most General
+Solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the basis of solutions is the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of solutions as before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just have
+
+ align:start position:0%
+we just have
+ 
+
+ align:start position:0%
+we just have
+u k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x equal to minus I Omega k
+
+ align:start position:0%
+x equal to minus I Omega k
+ 
+
+ align:start position:0%
+x equal to minus I Omega k
+t plus ikx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you have UK
+
+ align:start position:0%
+and then you have UK
+ 
+
+ align:start position:0%
+and then you have UK
+X star
+
+ align:start position:0%
+X star
+ 
+
+ align:start position:0%
+X star
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+because it's the same equation so so the
+
+ align:start position:0%
+because it's the same equation so so the
+ 
+
+ align:start position:0%
+because it's the same equation so so the
+so the basis of equation of course is
+
+ align:start position:0%
+so the basis of equation of course is
+ 
+
+ align:start position:0%
+so the basis of equation of course is
+also the same as before yes
+
+ align:start position:0%
+also the same as before yes
+ 
+
+ align:start position:0%
+also the same as before yes
+this is an operator like doesn't it if
+
+ align:start position:0%
+this is an operator like doesn't it if
+ 
+
+ align:start position:0%
+this is an operator like doesn't it if
+it's an observable doesn't it have to be
+
+ align:start position:0%
+it's an observable doesn't it have to be
+ 
+
+ align:start position:0%
+it's an observable doesn't it have to be
+permission
+
+ align:start position:0%
+permission
+ 
+
+ align:start position:0%
+permission
+um no the field
+
+ align:start position:0%
+um no the field
+ 
+
+ align:start position:0%
+um no the field
+um it depends
+
+ align:start position:0%
+um it depends
+ 
+
+ align:start position:0%
+um it depends
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah indeed if it's a something directly
+
+ align:start position:0%
+yeah indeed if it's a something directly
+ 
+
+ align:start position:0%
+yeah indeed if it's a something directly
+observable uh has to be a remission but
+
+ align:start position:0%
+observable uh has to be a remission but
+ 
+
+ align:start position:0%
+observable uh has to be a remission but
+doesn't have two observables for example
+
+ align:start position:0%
+doesn't have two observables for example
+ 
+
+ align:start position:0%
+doesn't have two observables for example
+I can combine them into a real variable
+
+ align:start position:0%
+I can combine them into a real variable
+ 
+
+ align:start position:0%
+I can combine them into a real variable
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah just not necessarily the fight
+
+ align:start position:0%
+yeah just not necessarily the fight
+ 
+
+ align:start position:0%
+yeah just not necessarily the fight
+itself having to be directory of the
+
+ align:start position:0%
+itself having to be directory of the
+ 
+
+ align:start position:0%
+itself having to be directory of the
+it's just a field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah the field itself don't have to
+
+ align:start position:0%
+yeah yeah the field itself don't have to
+ 
+
+ align:start position:0%
+yeah yeah the field itself don't have to
+always be observable by itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+this is not the momentum this is just
+
+ align:start position:0%
+this is not the momentum this is just
+ 
+
+ align:start position:0%
+this is not the momentum this is just
+the canonical momentum for the canonical
+
+ align:start position:0%
+the canonical momentum for the canonical
+ 
+
+ align:start position:0%
+the canonical momentum for the canonical
+organization right
+
+ align:start position:0%
+organization right
+ 
+
+ align:start position:0%
+organization right
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah this is not the space-time momentum
+
+ align:start position:0%
+yeah this is not the space-time momentum
+ 
+
+ align:start position:0%
+yeah this is not the space-time momentum
+field operator the same thing as the
+
+ align:start position:0%
+field operator the same thing as the
+ 
+
+ align:start position:0%
+field operator the same thing as the
+pump as the star yeah here we are
+
+ align:start position:0%
+pump as the star yeah here we are
+ 
+
+ align:start position:0%
+pump as the star yeah here we are
+talking about the uh here we are talking
+
+ align:start position:0%
+talking about the uh here we are talking
+ 
+
+ align:start position:0%
+talking about the uh here we are talking
+about the classical Theory and then when
+
+ align:start position:0%
+about the classical Theory and then when
+ 
+
+ align:start position:0%
+about the classical Theory and then when
+we go to the quantum indeed we will
+
+ align:start position:0%
+we go to the quantum indeed we will
+ 
+
+ align:start position:0%
+we go to the quantum indeed we will
+replace the Star by by dagger yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we can just write down the
+
+ align:start position:0%
+okay so now we can just write down the
+ 
+
+ align:start position:0%
+okay so now we can just write down the
+most General solutions to this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now we can just write down the most
+
+ align:start position:0%
+okay now we can just write down the most
+ 
+
+ align:start position:0%
+okay now we can just write down the most
+General solution to this equation
+
+ align:start position:0%
+General solution to this equation
+ 
+
+ align:start position:0%
+General solution to this equation
+so we just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's one slight difference from
+
+ align:start position:0%
+so there's one slight difference from
+ 
+
+ align:start position:0%
+so there's one slight difference from
+before almost the same identical as
+
+ align:start position:0%
+before almost the same identical as
+ 
+
+ align:start position:0%
+before almost the same identical as
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+except with one difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay UK but here previously we have AK
+
+ align:start position:0%
+okay UK but here previously we have AK
+ 
+
+ align:start position:0%
+okay UK but here previously we have AK
+dagger
+
+ align:start position:0%
+dagger
+ 
+
+ align:start position:0%
+dagger
+okay we have a k star say classically
+
+ align:start position:0%
+okay we have a k star say classically
+ 
+
+ align:start position:0%
+okay we have a k star say classically
+let me just first write classically so
+
+ align:start position:0%
+let me just first write classically so
+ 
+
+ align:start position:0%
+let me just first write classically so
+previously we have this
+
+ align:start position:0%
+previously we have this
+ 
+
+ align:start position:0%
+previously we have this
+okay previously why we have a k star
+
+ align:start position:0%
+okay previously why we have a k star
+ 
+
+ align:start position:0%
+okay previously why we have a k star
+here when we have a real scalar field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's because the field has to be real
+
+ align:start position:0%
+it's because the field has to be real
+ 
+
+ align:start position:0%
+it's because the field has to be real
+and then we have always add to its
+
+ align:start position:0%
+and then we have always add to its
+ 
+
+ align:start position:0%
+and then we have always add to its
+complex conjugate okay but now the
+
+ align:start position:0%
+complex conjugate okay but now the
+ 
+
+ align:start position:0%
+complex conjugate okay but now the
+difference is that now Phi is a complex
+
+ align:start position:0%
+difference is that now Phi is a complex
+ 
+
+ align:start position:0%
+difference is that now Phi is a complex
+okay and the Phi is complex and then we
+
+ align:start position:0%
+okay and the Phi is complex and then we
+ 
+
+ align:start position:0%
+okay and the Phi is complex and then we
+no longer have the real condition the
+
+ align:start position:0%
+no longer have the real condition the
+ 
+
+ align:start position:0%
+no longer have the real condition the
+means here I can choose a ladder
+
+ align:start position:0%
+means here I can choose a ladder
+ 
+
+ align:start position:0%
+means here I can choose a ladder
+arbitrary constant here
+
+ align:start position:0%
+arbitrary constant here
+ 
+
+ align:start position:0%
+arbitrary constant here
+okay so this is the arbitrary constant
+
+ align:start position:0%
+okay so this is the arbitrary constant
+ 
+
+ align:start position:0%
+okay so this is the arbitrary constant
+so by convention let me just pull the
+
+ align:start position:0%
+so by convention let me just pull the
+ 
+
+ align:start position:0%
+so by convention let me just pull the
+star here okay it doesn't matter I just
+
+ align:start position:0%
+star here okay it doesn't matter I just
+ 
+
+ align:start position:0%
+star here okay it doesn't matter I just
+the name you call it okay so now the
+
+ align:start position:0%
+the name you call it okay so now the
+ 
+
+ align:start position:0%
+the name you call it okay so now the
+most General solution
+
+ align:start position:0%
+most General solution
+ 
+
+ align:start position:0%
+most General solution
+now you have two sets you have a which
+
+ align:start position:0%
+now you have two sets you have a which
+ 
+
+ align:start position:0%
+now you have two sets you have a which
+is complex number then you have another
+
+ align:start position:0%
+is complex number then you have another
+ 
+
+ align:start position:0%
+is complex number then you have another
+complex number which is p okay now you
+
+ align:start position:0%
+complex number which is p okay now you
+ 
+
+ align:start position:0%
+complex number which is p okay now you
+have two sets of complex numbers okay
+
+ align:start position:0%
+have two sets of complex numbers okay
+ 
+
+ align:start position:0%
+have two sets of complex numbers okay
+and it makes sense because when you have
+
+ align:start position:0%
+and it makes sense because when you have
+ 
+
+ align:start position:0%
+and it makes sense because when you have
+a complex variable you double the
+
+ align:start position:0%
+a complex variable you double the
+ 
+
+ align:start position:0%
+a complex variable you double the
+decrease freedom and your integration
+
+ align:start position:0%
+decrease freedom and your integration
+ 
+
+ align:start position:0%
+decrease freedom and your integration
+constant also doubled
+
+ align:start position:0%
+constant also doubled
+ 
+
+ align:start position:0%
+constant also doubled
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so b k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now you have two sides of
+
+ align:start position:0%
+okay so now you have two sides of
+ 
+
+ align:start position:0%
+okay so now you have two sides of
+variables okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can get the five star just by
+
+ align:start position:0%
+so you can get the five star just by
+ 
+
+ align:start position:0%
+so you can get the five star just by
+taking the compared conjugate of it
+
+ align:start position:0%
+taking the compared conjugate of it
+ 
+
+ align:start position:0%
+taking the compared conjugate of it
+okay just by takes complex conjugate of
+
+ align:start position:0%
+okay just by takes complex conjugate of
+ 
+
+ align:start position:0%
+okay just by takes complex conjugate of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and then the four sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the full set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integration constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just you have a k
+
+ align:start position:0%
+just you have a k
+ 
+
+ align:start position:0%
+just you have a k
+you have AK star
+
+ align:start position:0%
+you have AK star
+ 
+
+ align:start position:0%
+you have AK star
+you have b k
+
+ align:start position:0%
+you have b k
+ 
+
+ align:start position:0%
+you have b k
+and then her BK stop
+
+ align:start position:0%
+and then her BK stop
+ 
+
+ align:start position:0%
+and then her BK stop
+okay so this is a classical story
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now go to Quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just do exactly as we did before
+
+ align:start position:0%
+we just do exactly as we did before
+ 
+
+ align:start position:0%
+we just do exactly as we did before
+we just promoted all those into
+
+ align:start position:0%
+we just promoted all those into
+ 
+
+ align:start position:0%
+we just promoted all those into
+operating equations
+
+ align:start position:0%
+operating equations
+ 
+
+ align:start position:0%
+operating equations
+okay so so the uh so you just call the
+
+ align:start position:0%
+okay so so the uh so you just call the
+ 
+
+ align:start position:0%
+okay so so the uh so you just call the
+Stacker
+
+ align:start position:0%
+Stacker
+ 
+
+ align:start position:0%
+Stacker
+okay just call this diagram just view
+
+ align:start position:0%
+okay just call this diagram just view
+ 
+
+ align:start position:0%
+okay just call this diagram just view
+every of one of them as operators
+
+ align:start position:0%
+every of one of them as operators
+ 
+
+ align:start position:0%
+every of one of them as operators
+and now and now this just become
+
+ align:start position:0%
+and now and now this just become
+ 
+
+ align:start position:0%
+and now and now this just become
+constant operators
+
+ align:start position:0%
+constant operators
+ 
+
+ align:start position:0%
+constant operators
+and it becomes constant operators
+
+ align:start position:0%
+and it becomes constant operators
+ 
+
+ align:start position:0%
+and it becomes constant operators
+and now here you also just call them to
+
+ align:start position:0%
+and now here you also just call them to
+ 
+
+ align:start position:0%
+and now here you also just call them to
+be diagonal okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+um yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now equal time correlation
+
+ align:start position:0%
+so now equal time correlation
+ 
+
+ align:start position:0%
+so now equal time correlation
+still we have to impose the equal time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+commutation relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have to impose the equal time
+
+ align:start position:0%
+so now we have to impose the equal time
+ 
+
+ align:start position:0%
+so now we have to impose the equal time
+commutation relations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again so these are should be
+
+ align:start position:0%
+again so these are should be
+ 
+
+ align:start position:0%
+again so these are should be
+simple so we should have Phi
+
+ align:start position:0%
+simple so we should have Phi
+ 
+
+ align:start position:0%
+simple so we should have Phi
+daggers they can they consider as
+
+ align:start position:0%
+daggers they can they consider as
+ 
+
+ align:start position:0%
+daggers they can they consider as
+independent operators that you should
+
+ align:start position:0%
+independent operators that you should
+ 
+
+ align:start position:0%
+independent operators that you should
+compute with each other they're all
+
+ align:start position:0%
+compute with each other they're all
+ 
+
+ align:start position:0%
+compute with each other they're all
+field variables
+
+ align:start position:0%
+field variables
+ 
+
+ align:start position:0%
+field variables
+and if I could commute itself
+
+ align:start position:0%
+and if I could commute itself
+ 
+
+ align:start position:0%
+and if I could commute itself
+so this is all evaluated at different
+
+ align:start position:0%
+so this is all evaluated at different
+ 
+
+ align:start position:0%
+so this is all evaluated at different
+spatial yeah just to save time I will
+
+ align:start position:0%
+spatial yeah just to save time I will
+ 
+
+ align:start position:0%
+spatial yeah just to save time I will
+not write this expressive but all this
+
+ align:start position:0%
+not write this expressive but all this
+ 
+
+ align:start position:0%
+not write this expressive but all this
+should be evaluated at the same time but
+
+ align:start position:0%
+should be evaluated at the same time but
+ 
+
+ align:start position:0%
+should be evaluated at the same time but
+different spatial locations okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such as all these equal to zero okay
+
+ align:start position:0%
+such as all these equal to zero okay
+ 
+
+ align:start position:0%
+such as all these equal to zero okay
+except the only thing which is non-zero
+
+ align:start position:0%
+except the only thing which is non-zero
+ 
+
+ align:start position:0%
+except the only thing which is non-zero
+is the five with its own
+
+ align:start position:0%
+is the five with its own
+ 
+
+ align:start position:0%
+is the five with its own
+canonical momentum okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so everything else will be zero the only
+
+ align:start position:0%
+so everything else will be zero the only
+ 
+
+ align:start position:0%
+so everything else will be zero the only
+thing on zero is Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is canonical momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again should be given by I Delta 3
+
+ align:start position:0%
+again should be given by I Delta 3
+ 
+
+ align:start position:0%
+again should be given by I Delta 3
+x minus X Prime
+
+ align:start position:0%
+x minus X Prime
+ 
+
+ align:start position:0%
+x minus X Prime
+and then then the similar scene for the
+
+ align:start position:0%
+and then then the similar scene for the
+ 
+
+ align:start position:0%
+and then then the similar scene for the
+fat diagram okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so again I say a effort okay
+
+ align:start position:0%
+okay so again I say a effort okay
+ 
+
+ align:start position:0%
+okay so again I say a effort okay
+so so uh so that's what you should
+
+ align:start position:0%
+so so uh so that's what you should
+ 
+
+ align:start position:0%
+so so uh so that's what you should
+impose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if you plug those things in
+
+ align:start position:0%
+so now if you plug those things in
+ 
+
+ align:start position:0%
+so now if you plug those things in
+then then you can find the uh a
+
+ align:start position:0%
+then then you can find the uh a
+ 
+
+ align:start position:0%
+then then you can find the uh a
+commutation relation between a and a
+
+ align:start position:0%
+commutation relation between a and a
+ 
+
+ align:start position:0%
+commutation relation between a and a
+dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then again you find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and similarly with speed
+
+ align:start position:0%
+and similarly with speed
+ 
+
+ align:start position:0%
+and similarly with speed
+you just get now two two sides of two
+
+ align:start position:0%
+you just get now two two sides of two
+ 
+
+ align:start position:0%
+you just get now two two sides of two
+infinite family of harmonic oscillators
+
+ align:start position:0%
+infinite family of harmonic oscillators
+ 
+
+ align:start position:0%
+infinite family of harmonic oscillators
+okay previously we have one family and
+
+ align:start position:0%
+okay previously we have one family and
+ 
+
+ align:start position:0%
+okay previously we have one family and
+now you get two two families okay and
+
+ align:start position:0%
+now you get two two families okay and
+ 
+
+ align:start position:0%
+now you get two two families okay and
+and all other commentates vanish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this part is boring you can almost
+
+ align:start position:0%
+so so this part is boring you can almost
+ 
+
+ align:start position:0%
+so so this part is boring you can almost
+guess any gas everything
+
+ align:start position:0%
+guess any gas everything
+ 
+
+ align:start position:0%
+guess any gas everything
+without doing any calculation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when essentially cast everything without
+
+ align:start position:0%
+when essentially cast everything without
+ 
+
+ align:start position:0%
+when essentially cast everything without
+doing any calculation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now again you can write the
+
+ align:start position:0%
+so now again you can write the
+ 
+
+ align:start position:0%
+so now again you can write the
+hamiltonian in terms of AK and B K okay
+
+ align:start position:0%
+hamiltonian in terms of AK and B K okay
+ 
+
+ align:start position:0%
+hamiltonian in terms of AK and B K okay
+just will be as you would guess them to
+
+ align:start position:0%
+just will be as you would guess them to
+ 
+
+ align:start position:0%
+just will be as you would guess them to
+be okay uh uh just the harmonic
+
+ align:start position:0%
+be okay uh uh just the harmonic
+ 
+
+ align:start position:0%
+be okay uh uh just the harmonic
+alternator that corresponding to 8K
+
+ align:start position:0%
+alternator that corresponding to 8K
+ 
+
+ align:start position:0%
+alternator that corresponding to 8K
+harmonic acid corresponding to BK okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and then the uh and then the ground
+
+ align:start position:0%
+so and then the uh and then the ground
+ 
+
+ align:start position:0%
+so and then the uh and then the ground
+state again
+
+ align:start position:0%
+state again
+ 
+
+ align:start position:0%
+state again
+is the op
+
+ align:start position:0%
+is the op
+ 
+
+ align:start position:0%
+is the op
+is the state related by both of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the vacuum state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now you can act
+
+ align:start position:0%
+and now you can act
+ 
+
+ align:start position:0%
+and now you can act
+AK dagger on zero
+
+ align:start position:0%
+AK dagger on zero
+ 
+
+ align:start position:0%
+AK dagger on zero
+and BK diagram 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Etc okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have two kinds of particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have two final particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by AK dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and BK dagger now okay
+
+ align:start position:0%
+and BK dagger now okay
+ 
+
+ align:start position:0%
+and BK dagger now okay
+so now you have two kind of bad
+
+ align:start position:0%
+so now you have two kind of bad
+ 
+
+ align:start position:0%
+so now you have two kind of bad
+respectively
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and both of them have the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unsure condition okay both both
+
+ align:start position:0%
+unsure condition okay both both
+ 
+
+ align:start position:0%
+unsure condition okay both both
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+have the same mass
+
+ align:start position:0%
+have the same mass
+ 
+
+ align:start position:0%
+have the same mass
+they satisfy the P-Square equal to M
+
+ align:start position:0%
+they satisfy the P-Square equal to M
+ 
+
+ align:start position:0%
+they satisfy the P-Square equal to M
+squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus M Square okay
+
+ align:start position:0%
+minus M Square okay
+ 
+
+ align:start position:0%
+minus M Square okay
+so because they all come from the same
+
+ align:start position:0%
+so because they all come from the same
+ 
+
+ align:start position:0%
+so because they all come from the same
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now the question is how do we tell
+
+ align:start position:0%
+so now the question is how do we tell
+ 
+
+ align:start position:0%
+so now the question is how do we tell
+them apart
+
+ align:start position:0%
+them apart
+ 
+
+ align:start position:0%
+them apart
+okay now we have two type of particles
+
+ align:start position:0%
+okay now we have two type of particles
+ 
+
+ align:start position:0%
+okay now we have two type of particles
+they they have the same mass
+
+ align:start position:0%
+they they have the same mass
+ 
+
+ align:start position:0%
+they they have the same mass
+and we
+
+ align:start position:0%
+and we
+ 
+
+ align:start position:0%
+and we
+yeah just by definition they don't have
+
+ align:start position:0%
+yeah just by definition they don't have
+ 
+
+ align:start position:0%
+yeah just by definition they don't have
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+they have same mass they all have the
+
+ align:start position:0%
+they have same mass they all have the
+ 
+
+ align:start position:0%
+they have same mass they all have the
+same spin because they're all spin zero
+
+ align:start position:0%
+same spin because they're all spin zero
+ 
+
+ align:start position:0%
+same spin because they're all spin zero
+scalar particles there's no no
+
+ align:start position:0%
+scalar particles there's no no
+ 
+
+ align:start position:0%
+scalar particles there's no no
+directions okay
+
+ align:start position:0%
+directions okay
+ 
+
+ align:start position:0%
+directions okay
+and uh uh um yeah the question how do we
+
+ align:start position:0%
+and uh uh um yeah the question how do we
+ 
+
+ align:start position:0%
+and uh uh um yeah the question how do we
+tell them apart
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here is this U1 symmet to become
+
+ align:start position:0%
+okay here is this U1 symmet to become
+ 
+
+ align:start position:0%
+okay here is this U1 symmet to become
+useful
+
+ align:start position:0%
+useful
+ 
+
+ align:start position:0%
+useful
+so this UI so so this phase rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this phase rotation is a symmetry
+
+ align:start position:0%
+so this phase rotation is a symmetry
+ 
+
+ align:start position:0%
+so this phase rotation is a symmetry
+and mathematically this is called the U1
+
+ align:start position:0%
+and mathematically this is called the U1
+ 
+
+ align:start position:0%
+and mathematically this is called the U1
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+okay so this is called normally called
+
+ align:start position:0%
+okay so this is called normally called
+ 
+
+ align:start position:0%
+okay so this is called normally called
+the U1 cb3
+
+ align:start position:0%
+the U1 cb3
+ 
+
+ align:start position:0%
+the U1 cb3
+you want just a mathematical term
+
+ align:start position:0%
+you want just a mathematical term
+ 
+
+ align:start position:0%
+you want just a mathematical term
+for for phase rotation okay a
+
+ align:start position:0%
+for for phase rotation okay a
+ 
+
+ align:start position:0%
+for for phase rotation okay a
+mathematically it's a U1 group it's a
+
+ align:start position:0%
+mathematically it's a U1 group it's a
+ 
+
+ align:start position:0%
+mathematically it's a U1 group it's a
+mathematical term for uh for um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so the way we take them apart is by
+
+ align:start position:0%
+so so the way we take them apart is by
+ 
+
+ align:start position:0%
+so so the way we take them apart is by
+looking at their conserved number and
+
+ align:start position:0%
+looking at their conserved number and
+ 
+
+ align:start position:0%
+looking at their conserved number and
+look at their quantum numbers okay if we
+
+ align:start position:0%
+look at their quantum numbers okay if we
+ 
+
+ align:start position:0%
+look at their quantum numbers okay if we
+look at two particles so how do we tell
+
+ align:start position:0%
+look at two particles so how do we tell
+ 
+
+ align:start position:0%
+look at two particles so how do we tell
+them apart we look at the quantum
+
+ align:start position:0%
+them apart we look at the quantum
+ 
+
+ align:start position:0%
+them apart we look at the quantum
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+and they're quantum numbers so far they
+
+ align:start position:0%
+and they're quantum numbers so far they
+ 
+
+ align:start position:0%
+and they're quantum numbers so far they
+look almost the same because their mass
+
+ align:start position:0%
+look almost the same because their mass
+ 
+
+ align:start position:0%
+look almost the same because their mass
+is the same
+
+ align:start position:0%
+is the same
+ 
+
+ align:start position:0%
+is the same
+and by definition their scale of
+
+ align:start position:0%
+and by definition their scale of
+ 
+
+ align:start position:0%
+and by definition their scale of
+particles and so they have zeros their
+
+ align:start position:0%
+particles and so they have zeros their
+ 
+
+ align:start position:0%
+particles and so they have zeros their
+spin zero they don't have spin
+
+ align:start position:0%
+spin zero they don't have spin
+ 
+
+ align:start position:0%
+spin zero they don't have spin
+and so the only other conserved number
+
+ align:start position:0%
+and so the only other conserved number
+ 
+
+ align:start position:0%
+and so the only other conserved number
+uh yeah if you want to talk about
+
+ align:start position:0%
+uh yeah if you want to talk about
+ 
+
+ align:start position:0%
+uh yeah if you want to talk about
+quantum number the quantum number has
+
+ align:start position:0%
+quantum number the quantum number has
+ 
+
+ align:start position:0%
+quantum number the quantum number has
+got to be conserved okay because
+
+ align:start position:0%
+got to be conserved okay because
+ 
+
+ align:start position:0%
+got to be conserved okay because
+otherwise if it changes with time it
+
+ align:start position:0%
+otherwise if it changes with time it
+ 
+
+ align:start position:0%
+otherwise if it changes with time it
+doesn't matter it doesn't make sense to
+
+ align:start position:0%
+doesn't matter it doesn't make sense to
+ 
+
+ align:start position:0%
+doesn't matter it doesn't make sense to
+to use that number to label a particle
+
+ align:start position:0%
+to use that number to label a particle
+ 
+
+ align:start position:0%
+to use that number to label a particle
+but we get one more kind of number uh
+
+ align:start position:0%
+but we get one more kind of number uh
+ 
+
+ align:start position:0%
+but we get one more kind of number uh
+corresponding to the uh to this symmetry
+
+ align:start position:0%
+corresponding to the uh to this symmetry
+ 
+
+ align:start position:0%
+corresponding to the uh to this symmetry
+okay so so this UI symmetry
+
+ align:start position:0%
+okay so so this UI symmetry
+ 
+
+ align:start position:0%
+okay so so this UI symmetry
+it's an also theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah from the law system so this is one
+
+ align:start position:0%
+yeah from the law system so this is one
+ 
+
+ align:start position:0%
+yeah from the law system so this is one
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+so if you work it out
+
+ align:start position:0%
+so if you work it out
+ 
+
+ align:start position:0%
+so if you work it out
+you work out the loss of theorem then
+
+ align:start position:0%
+you work out the loss of theorem then
+ 
+
+ align:start position:0%
+you work out the loss of theorem then
+you find it's the the corresponding
+
+ align:start position:0%
+you find it's the the corresponding
+ 
+
+ align:start position:0%
+you find it's the the corresponding
+conserved charge which you should have
+
+ align:start position:0%
+conserved charge which you should have
+ 
+
+ align:start position:0%
+conserved charge which you should have
+already worked out
+
+ align:start position:0%
+already worked out
+ 
+
+ align:start position:0%
+already worked out
+so let me just write it classically
+
+ align:start position:0%
+so let me just write it classically
+ 
+
+ align:start position:0%
+so let me just write it classically
+so as I just write them as five star
+
+ align:start position:0%
+so as I just write them as five star
+ 
+
+ align:start position:0%
+so as I just write them as five star
+so classically they have the following
+
+ align:start position:0%
+so classically they have the following
+ 
+
+ align:start position:0%
+so classically they have the following
+form okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the quantum level this becomes
+
+ align:start position:0%
+so the quantum level this becomes
+ 
+
+ align:start position:0%
+so the quantum level this becomes
+operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but here there's a operator and a
+
+ align:start position:0%
+but here there's a operator and a
+ 
+
+ align:start position:0%
+but here there's a operator and a
+but now here this operator uh uh uh when
+
+ align:start position:0%
+but now here this operator uh uh uh when
+ 
+
+ align:start position:0%
+but now here this operator uh uh uh when
+we go to the quantum level
+
+ align:start position:0%
+we go to the quantum level
+ 
+
+ align:start position:0%
+we go to the quantum level
+now there's the operator ordering
+
+ align:start position:0%
+now there's the operator ordering
+ 
+
+ align:start position:0%
+now there's the operator ordering
+ambiguity now
+
+ align:start position:0%
+ambiguity now
+ 
+
+ align:start position:0%
+ambiguity now
+you see uh here
+
+ align:start position:0%
+you see uh here
+ 
+
+ align:start position:0%
+you see uh here
+the Phi
+
+ align:start position:0%
+the Phi
+ 
+
+ align:start position:0%
+the Phi
+don't commute with its own a conjugate
+
+ align:start position:0%
+don't commute with its own a conjugate
+ 
+
+ align:start position:0%
+don't commute with its own a conjugate
+momentum okay
+
+ align:start position:0%
+momentum okay
+ 
+
+ align:start position:0%
+momentum okay
+and so here we have five multiplied
+
+ align:start position:0%
+and so here we have five multiplied
+ 
+
+ align:start position:0%
+and so here we have five multiplied
+conjugate momentum
+
+ align:start position:0%
+conjugate momentum
+ 
+
+ align:start position:0%
+conjugate momentum
+and if we change the order
+
+ align:start position:0%
+and if we change the order
+ 
+
+ align:start position:0%
+and if we change the order
+and then we build a result a data
+
+ align:start position:0%
+and then we build a result a data
+ 
+
+ align:start position:0%
+and then we build a result a data
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+can we build without the data function
+
+ align:start position:0%
+can we build without the data function
+ 
+
+ align:start position:0%
+can we build without the data function
+okay and and that will give rise to
+
+ align:start position:0%
+okay and and that will give rise to
+ 
+
+ align:start position:0%
+okay and and that will give rise to
+infinite uh uh yeah so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at Quantum level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different ordering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinite constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can take five uh you can yeah if
+
+ align:start position:0%
+so you can take five uh you can yeah if
+ 
+
+ align:start position:0%
+so you can take five uh you can yeah if
+you change order in them then you get a
+
+ align:start position:0%
+you change order in them then you get a
+ 
+
+ align:start position:0%
+you change order in them then you get a
+Delta function but that function again
+
+ align:start position:0%
+Delta function but that function again
+ 
+
+ align:start position:0%
+Delta function but that function again
+is evaluated
+
+ align:start position:0%
+is evaluated
+ 
+
+ align:start position:0%
+is evaluated
+big because these two is a divided at
+
+ align:start position:0%
+big because these two is a divided at
+ 
+
+ align:start position:0%
+big because these two is a divided at
+the same X and then you get the data
+
+ align:start position:0%
+the same X and then you get the data
+ 
+
+ align:start position:0%
+the same X and then you get the data
+function values at the zero okay so
+
+ align:start position:0%
+function values at the zero okay so
+ 
+
+ align:start position:0%
+function values at the zero okay so
+essentially you get the infinite
+
+ align:start position:0%
+essentially you get the infinite
+ 
+
+ align:start position:0%
+essentially you get the infinite
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we can fix this ambiguity
+
+ align:start position:0%
+but we can fix this ambiguity
+ 
+
+ align:start position:0%
+but we can fix this ambiguity
+okay we can fix this ambiguity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by requiring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your vacuum State your lowest energy
+
+ align:start position:0%
+your vacuum State your lowest energy
+ 
+
+ align:start position:0%
+your vacuum State your lowest energy
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+should have charge zero
+
+ align:start position:0%
+should have charge zero
+ 
+
+ align:start position:0%
+should have charge zero
+okay because it's a bad definition when
+
+ align:start position:0%
+okay because it's a bad definition when
+ 
+
+ align:start position:0%
+okay because it's a bad definition when
+you add lowest energy there's nothing
+
+ align:start position:0%
+you add lowest energy there's nothing
+ 
+
+ align:start position:0%
+you add lowest energy there's nothing
+there okay it's a vacuum
+
+ align:start position:0%
+there okay it's a vacuum
+ 
+
+ align:start position:0%
+there okay it's a vacuum
+by requiring the lowest energy State
+
+ align:start position:0%
+by requiring the lowest energy State
+ 
+
+ align:start position:0%
+by requiring the lowest energy State
+have charge to zero
+
+ align:start position:0%
+have charge to zero
+ 
+
+ align:start position:0%
+have charge to zero
+okay so that uniquely fix whatever or
+
+ align:start position:0%
+okay so that uniquely fix whatever or
+ 
+
+ align:start position:0%
+okay so that uniquely fix whatever or
+infinite
+
+ align:start position:0%
+infinite
+ 
+
+ align:start position:0%
+infinite
+the ordering
+
+ align:start position:0%
+the ordering
+ 
+
+ align:start position:0%
+the ordering
+so so by this equal to zero
+
+ align:start position:0%
+so so by this equal to zero
+ 
+
+ align:start position:0%
+so so by this equal to zero
+and then you can show that the Q
+
+ align:start position:0%
+and then you can show that the Q
+ 
+
+ align:start position:0%
+and then you can show that the Q
+so now you can essentially
+
+ align:start position:0%
+so now you can essentially
+ 
+
+ align:start position:0%
+so now you can essentially
+the queue have the following form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you can already you may be able to
+
+ align:start position:0%
+so you can already you may be able to
+ 
+
+ align:start position:0%
+so you can already you may be able to
+guess the answer
+
+ align:start position:0%
+guess the answer
+ 
+
+ align:start position:0%
+guess the answer
+AK
+
+ align:start position:0%
+AK
+ 
+
+ align:start position:0%
+AK
+a AK
+
+ align:start position:0%
+a AK
+ 
+
+ align:start position:0%
+a AK
+the manners
+
+ align:start position:0%
+the manners
+ 
+
+ align:start position:0%
+the manners
+BK dagger
+
+ align:start position:0%
+BK dagger
+ 
+
+ align:start position:0%
+BK dagger
+UK
+
+ align:start position:0%
+UK
+ 
+
+ align:start position:0%
+UK
+okay that's what you get okay
+
+ align:start position:0%
+okay that's what you get okay
+ 
+
+ align:start position:0%
+okay that's what you get okay
+so you plug those expressions in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you plug those expression like this time
+
+ align:start position:0%
+you plug those expression like this time
+ 
+
+ align:start position:0%
+you plug those expression like this time
+derivative okay time is derivative view
+
+ align:start position:0%
+derivative okay time is derivative view
+ 
+
+ align:start position:0%
+derivative okay time is derivative view
+Pi you just plug those expression in
+
+ align:start position:0%
+Pi you just plug those expression in
+ 
+
+ align:start position:0%
+Pi you just plug those expression in
+and again you will find because this is
+
+ align:start position:0%
+and again you will find because this is
+ 
+
+ align:start position:0%
+and again you will find because this is
+conserved you find all this time
+
+ align:start position:0%
+conserved you find all this time
+ 
+
+ align:start position:0%
+conserved you find all this time
+dependence cancel Etc
+
+ align:start position:0%
+dependence cancel Etc
+ 
+
+ align:start position:0%
+dependence cancel Etc
+and then you get these two expressions
+
+ align:start position:0%
+and then you get these two expressions
+ 
+
+ align:start position:0%
+and then you get these two expressions
+up to some constant
+
+ align:start position:0%
+up to some constant
+ 
+
+ align:start position:0%
+up to some constant
+okay and then and then this condition
+
+ align:start position:0%
+okay and then and then this condition
+ 
+
+ align:start position:0%
+okay and then and then this condition
+requires that that constant must be zero
+
+ align:start position:0%
+requires that that constant must be zero
+ 
+
+ align:start position:0%
+requires that that constant must be zero
+okay yeah when you write in this form
+
+ align:start position:0%
+okay yeah when you write in this form
+ 
+
+ align:start position:0%
+okay yeah when you write in this form
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you see this violates the Q because the
+
+ align:start position:0%
+you see this violates the Q because the
+ 
+
+ align:start position:0%
+you see this violates the Q because the
+a is on the right hand side of a dagger
+
+ align:start position:0%
+a is on the right hand side of a dagger
+ 
+
+ align:start position:0%
+a is on the right hand side of a dagger
+so this automatically allows the vacuum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so essentially this is just occupation
+
+ align:start position:0%
+so essentially this is just occupation
+ 
+
+ align:start position:0%
+so essentially this is just occupation
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+for a and this occupation number for b k
+
+ align:start position:0%
+for a and this occupation number for b k
+ 
+
+ align:start position:0%
+for a and this occupation number for b k
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we essentially get Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially the occupation number
+
+ align:start position:0%
+essentially the occupation number
+ 
+
+ align:start position:0%
+essentially the occupation number
+for a k
+
+ align:start position:0%
+for a k
+ 
+
+ align:start position:0%
+for a k
+and the occupation number for b k
+
+ align:start position:0%
+and the occupation number for b k
+ 
+
+ align:start position:0%
+and the occupation number for b k
+okay so occupation number just write as
+
+ align:start position:0%
+okay so occupation number just write as
+ 
+
+ align:start position:0%
+okay so occupation number just write as
+n okay
+
+ align:start position:0%
+n okay
+ 
+
+ align:start position:0%
+n okay
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you switch them you still get pissing
+
+ align:start position:0%
+if you switch them you still get pissing
+ 
+
+ align:start position:0%
+if you switch them you still get pissing
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+but if you create them you still get the
+
+ align:start position:0%
+but if you create them you still get the
+ 
+
+ align:start position:0%
+but if you create them you still get the
+infinite Constance on fused why this
+
+ align:start position:0%
+infinite Constance on fused why this
+ 
+
+ align:start position:0%
+infinite Constance on fused why this
+is considered effective no the one you
+
+ align:start position:0%
+is considered effective no the one you
+ 
+
+ align:start position:0%
+is considered effective no the one you
+permute them then you no longer rally
+
+ align:start position:0%
+permute them then you no longer rally
+ 
+
+ align:start position:0%
+permute them then you no longer rally
+the vacuum right so that constant will
+
+ align:start position:0%
+the vacuum right so that constant will
+ 
+
+ align:start position:0%
+the vacuum right so that constant will
+cancel
+
+ align:start position:0%
+cancel
+ 
+
+ align:start position:0%
+cancel
+so only this form with a is sitting on
+
+ align:start position:0%
+so only this form with a is sitting on
+ 
+
+ align:start position:0%
+so only this form with a is sitting on
+the right hand side of a dagger this
+
+ align:start position:0%
+the right hand side of a dagger this
+ 
+
+ align:start position:0%
+the right hand side of a dagger this
+will violate the vacuum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I guess like because earlier you
+
+ align:start position:0%
+okay I guess like because earlier you
+ 
+
+ align:start position:0%
+okay I guess like because earlier you
+the line of argument was if you permit
+
+ align:start position:0%
+the line of argument was if you permit
+ 
+
+ align:start position:0%
+the line of argument was if you permit
+them yeah
+
+ align:start position:0%
+them yeah
+ 
+
+ align:start position:0%
+them yeah
+you would get the same thing here right
+
+ align:start position:0%
+you would get the same thing here right
+ 
+
+ align:start position:0%
+you would get the same thing here right
+if you create them you also no no no
+
+ align:start position:0%
+if you create them you also no no no
+ 
+
+ align:start position:0%
+if you create them you also no no no
+no no
+
+ align:start position:0%
+no no
+ 
+
+ align:start position:0%
+no no
+here here there's ambiguity
+
+ align:start position:0%
+here here there's ambiguity
+ 
+
+ align:start position:0%
+here here there's ambiguity
+here I don't know how I should order
+
+ align:start position:0%
+here I don't know how I should order
+ 
+
+ align:start position:0%
+here I don't know how I should order
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+whether I should put 5 to the right of
+
+ align:start position:0%
+whether I should put 5 to the right of
+ 
+
+ align:start position:0%
+whether I should put 5 to the right of
+Pi or put pi to the left to the right of
+
+ align:start position:0%
+Pi or put pi to the left to the right of
+ 
+
+ align:start position:0%
+Pi or put pi to the left to the right of
+five I'm not sure how should I do
+
+ align:start position:0%
+five I'm not sure how should I do
+ 
+
+ align:start position:0%
+five I'm not sure how should I do
+okay here there's no prescription
+
+ align:start position:0%
+okay here there's no prescription
+ 
+
+ align:start position:0%
+okay here there's no prescription
+and uh uh uh uh here there's no
+
+ align:start position:0%
+and uh uh uh uh here there's no
+ 
+
+ align:start position:0%
+and uh uh uh uh here there's no
+prescription but if I impose this
+
+ align:start position:0%
+prescription but if I impose this
+ 
+
+ align:start position:0%
+prescription but if I impose this
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+okay then that 40 then that tells you
+
+ align:start position:0%
+okay then that 40 then that tells you
+ 
+
+ align:start position:0%
+okay then that 40 then that tells you
+when I impose this condition then Q must
+
+ align:start position:0%
+when I impose this condition then Q must
+ 
+
+ align:start position:0%
+when I impose this condition then Q must
+be of this form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay must be of this form of course when
+
+ align:start position:0%
+okay must be of this form of course when
+ 
+
+ align:start position:0%
+okay must be of this form of course when
+you permute them it's the same thing we
+
+ align:start position:0%
+you permute them it's the same thing we
+ 
+
+ align:start position:0%
+you permute them it's the same thing we
+inform you then you don't change the
+
+ align:start position:0%
+inform you then you don't change the
+ 
+
+ align:start position:0%
+inform you then you don't change the
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+you don't change the operator yeah but
+
+ align:start position:0%
+you don't change the operator yeah but
+ 
+
+ align:start position:0%
+you don't change the operator yeah but
+but if you do say let's do this order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you do this order
+
+ align:start position:0%
+if you do this order
+ 
+
+ align:start position:0%
+if you do this order
+what you get is this expression with the
+
+ align:start position:0%
+what you get is this expression with the
+ 
+
+ align:start position:0%
+what you get is this expression with the
+infinite constant
+
+ align:start position:0%
+infinite constant
+ 
+
+ align:start position:0%
+infinite constant
+and then this condition tells you
+
+ align:start position:0%
+and then this condition tells you
+ 
+
+ align:start position:0%
+and then this condition tells you
+somehow you have to change your order
+
+ align:start position:0%
+somehow you have to change your order
+ 
+
+ align:start position:0%
+somehow you have to change your order
+here so that that constant is zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah when you write it in this form when
+
+ align:start position:0%
+yeah when you write it in this form when
+ 
+
+ align:start position:0%
+yeah when you write it in this form when
+you write it in A and B and that
+
+ align:start position:0%
+you write it in A and B and that
+ 
+
+ align:start position:0%
+you write it in A and B and that
+constant has to be zero
+
+ align:start position:0%
+constant has to be zero
+ 
+
+ align:start position:0%
+constant has to be zero
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+the ordering ambiguity how many physical
+
+ align:start position:0%
+the ordering ambiguity how many physical
+ 
+
+ align:start position:0%
+the ordering ambiguity how many physical
+consequences because
+
+ align:start position:0%
+consequences because
+ 
+
+ align:start position:0%
+consequences because
+um besides just things that can be
+
+ align:start position:0%
+um besides just things that can be
+ 
+
+ align:start position:0%
+um besides just things that can be
+subtracted off
+
+ align:start position:0%
+subtracted off
+ 
+
+ align:start position:0%
+subtracted off
+yeah yeah it's it's a
+
+ align:start position:0%
+yeah yeah it's it's a
+ 
+
+ align:start position:0%
+yeah yeah it's it's a
+yeah this is a a good question which
+
+ align:start position:0%
+yeah this is a a good question which
+ 
+
+ align:start position:0%
+yeah this is a a good question which
+it's hard to say so so most of the time
+
+ align:start position:0%
+it's hard to say so so most of the time
+ 
+
+ align:start position:0%
+it's hard to say so so most of the time
+you can fix them
+
+ align:start position:0%
+you can fix them
+ 
+
+ align:start position:0%
+you can fix them
+based on physical environment uh
+
+ align:start position:0%
+based on physical environment uh
+ 
+
+ align:start position:0%
+based on physical environment uh
+benefits yeah as here you can fix it
+
+ align:start position:0%
+benefits yeah as here you can fix it
+ 
+
+ align:start position:0%
+benefits yeah as here you can fix it
+based on physical requirement and then
+
+ align:start position:0%
+based on physical requirement and then
+ 
+
+ align:start position:0%
+based on physical requirement and then
+you don't have to worry about it anymore
+
+ align:start position:0%
+you don't have to worry about it anymore
+ 
+
+ align:start position:0%
+you don't have to worry about it anymore
+but but
+
+ align:start position:0%
+but but
+ 
+
+ align:start position:0%
+but but
+the ordinal ambiguity requires you try
+
+ align:start position:0%
+the ordinal ambiguity requires you try
+ 
+
+ align:start position:0%
+the ordinal ambiguity requires you try
+to find such a physical requirement
+
+ align:start position:0%
+to find such a physical requirement
+ 
+
+ align:start position:0%
+to find such a physical requirement
+yeah yeah because otherwise uh what
+
+ align:start position:0%
+yeah yeah because otherwise uh what
+ 
+
+ align:start position:0%
+yeah yeah because otherwise uh what
+ordering should you use and the process
+
+ align:start position:0%
+ordering should you use and the process
+ 
+
+ align:start position:0%
+ordering should you use and the process
+of finding that requirement by itself is
+
+ align:start position:0%
+of finding that requirement by itself is
+ 
+
+ align:start position:0%
+of finding that requirement by itself is
+understanding the physics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes when you got the infinite energy and
+
+ align:start position:0%
+yes when you got the infinite energy and
+ 
+
+ align:start position:0%
+yes when you got the infinite energy and
+the previous lecture because now
+
+ align:start position:0%
+the previous lecture because now
+ 
+
+ align:start position:0%
+the previous lecture because now
+required the round state to have like
+
+ align:start position:0%
+required the round state to have like
+ 
+
+ align:start position:0%
+required the round state to have like
+zero energy and then get some different
+
+ align:start position:0%
+zero energy and then get some different
+ 
+
+ align:start position:0%
+zero energy and then get some different
+ordering right no in that case uh we
+
+ align:start position:0%
+ordering right no in that case uh we
+ 
+
+ align:start position:0%
+ordering right no in that case uh we
+don't have other ambiguity
+
+ align:start position:0%
+don't have other ambiguity
+ 
+
+ align:start position:0%
+don't have other ambiguity
+so in that case because we just have
+
+ align:start position:0%
+so in that case because we just have
+ 
+
+ align:start position:0%
+so in that case because we just have
+Pi Square
+
+ align:start position:0%
+Pi Square
+ 
+
+ align:start position:0%
+Pi Square
+itself Plus
+
+ align:start position:0%
+itself Plus
+ 
+
+ align:start position:0%
+itself Plus
+5 square and plus 5 squared there's no
+
+ align:start position:0%
+5 square and plus 5 squared there's no
+ 
+
+ align:start position:0%
+5 square and plus 5 squared there's no
+ordering ambiguity here
+
+ align:start position:0%
+ordering ambiguity here
+ 
+
+ align:start position:0%
+ordering ambiguity here
+and so so whatever you get is whatever
+
+ align:start position:0%
+and so so whatever you get is whatever
+ 
+
+ align:start position:0%
+and so so whatever you get is whatever
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+and if you get infinite constant then
+
+ align:start position:0%
+and if you get infinite constant then
+ 
+
+ align:start position:0%
+and if you get infinite constant then
+you get infinite constant now you don't
+
+ align:start position:0%
+you get infinite constant now you don't
+ 
+
+ align:start position:0%
+you get infinite constant now you don't
+have freedom yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clear that they can like how do you know
+
+ align:start position:0%
+clear that they can like how do you know
+ 
+
+ align:start position:0%
+clear that they can like how do you know
+that there's no coupling between the
+
+ align:start position:0%
+that there's no coupling between the
+ 
+
+ align:start position:0%
+that there's no coupling between the
+fields oh how do you represent it and oh
+
+ align:start position:0%
+fields oh how do you represent it and oh
+ 
+
+ align:start position:0%
+fields oh how do you represent it and oh
+oh this is a definition uh you say where
+
+ align:start position:0%
+oh this is a definition uh you say where
+ 
+
+ align:start position:0%
+oh this is a definition uh you say where
+this come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah this is just a definition
+
+ align:start position:0%
+yeah yeah this is just a definition
+ 
+
+ align:start position:0%
+yeah yeah this is just a definition
+off of the this is the same uh
+
+ align:start position:0%
+off of the this is the same uh
+ 
+
+ align:start position:0%
+off of the this is the same uh
+this night have nothing to do with field
+
+ align:start position:0%
+this night have nothing to do with field
+ 
+
+ align:start position:0%
+this night have nothing to do with field
+series only this equation have to do
+
+ align:start position:0%
+series only this equation have to do
+ 
+
+ align:start position:0%
+series only this equation have to do
+with sphere Theory this I have nothing
+
+ align:start position:0%
+with sphere Theory this I have nothing
+ 
+
+ align:start position:0%
+with sphere Theory this I have nothing
+to do with filtering this is just
+
+ align:start position:0%
+to do with filtering this is just
+ 
+
+ align:start position:0%
+to do with filtering this is just
+quantum mechanics that differently
+
+ align:start position:0%
+quantum mechanics that differently
+ 
+
+ align:start position:0%
+quantum mechanics that differently
+different because Freedom they compute
+
+ align:start position:0%
+different because Freedom they compute
+ 
+
+ align:start position:0%
+different because Freedom they compute
+with each other yeah just X One commute
+
+ align:start position:0%
+with each other yeah just X One commute
+ 
+
+ align:start position:0%
+with each other yeah just X One commute
+with x2 in quantum mechanics yeah five
+
+ align:start position:0%
+with x2 in quantum mechanics yeah five
+ 
+
+ align:start position:0%
+with x2 in quantum mechanics yeah five
+here just five and five diagramages it's
+
+ align:start position:0%
+here just five and five diagramages it's
+ 
+
+ align:start position:0%
+here just five and five diagramages it's
+analog of x y and X2 there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um no it's different from that here
+
+ align:start position:0%
+um no it's different from that here
+ 
+
+ align:start position:0%
+um no it's different from that here
+here it just means that the uh here you
+
+ align:start position:0%
+here it just means that the uh here you
+ 
+
+ align:start position:0%
+here it just means that the uh here you
+should view them as the variables in the
+
+ align:start position:0%
+should view them as the variables in the
+ 
+
+ align:start position:0%
+should view them as the variables in the
+configuration space and uh it's just the
+
+ align:start position:0%
+configuration space and uh it's just the
+ 
+
+ align:start position:0%
+configuration space and uh it's just the
+in quantum mechanics the worry was a
+
+ align:start position:0%
+in quantum mechanics the worry was a
+ 
+
+ align:start position:0%
+in quantum mechanics the worry was a
+configuration space they always commute
+
+ align:start position:0%
+configuration space they always commute
+ 
+
+ align:start position:0%
+configuration space they always commute
+with each other
+
+ align:start position:0%
+with each other
+ 
+
+ align:start position:0%
+with each other
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now the key thing is that here is the
+
+ align:start position:0%
+so now the key thing is that here is the
+ 
+
+ align:start position:0%
+so now the key thing is that here is the
+minus sign
+
+ align:start position:0%
+minus sign
+ 
+
+ align:start position:0%
+minus sign
+so that means
+
+ align:start position:0%
+so that means
+ 
+
+ align:start position:0%
+so that means
+when you look at the commutator between
+
+ align:start position:0%
+when you look at the commutator between
+ 
+
+ align:start position:0%
+when you look at the commutator between
+Q and A
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you get the a
+
+ align:start position:0%
+you get the a
+ 
+
+ align:start position:0%
+you get the a
+and if you look at the commutative a we
+
+ align:start position:0%
+and if you look at the commutative a we
+ 
+
+ align:start position:0%
+and if you look at the commutative a we
+speak a
+
+ align:start position:0%
+speak a
+ 
+
+ align:start position:0%
+speak a
+you actually get a minus BK
+
+ align:start position:0%
+you actually get a minus BK
+ 
+
+ align:start position:0%
+you actually get a minus BK
+okay you get
+
+ align:start position:0%
+okay you get
+ 
+
+ align:start position:0%
+okay you get
+yeah let me just do the diagram because
+
+ align:start position:0%
+yeah let me just do the diagram because
+ 
+
+ align:start position:0%
+yeah let me just do the diagram because
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+because this is used to create particle
+
+ align:start position:0%
+because this is used to create particle
+ 
+
+ align:start position:0%
+because this is used to create particle
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you just calculate the commutator
+
+ align:start position:0%
+so if you just calculate the commutator
+ 
+
+ align:start position:0%
+so if you just calculate the commutator
+we just find that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you look at the um
+
+ align:start position:0%
+if you look at the um
+ 
+
+ align:start position:0%
+if you look at the um
+States defined by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one particle State corresponding to a
+
+ align:start position:0%
+one particle State corresponding to a
+ 
+
+ align:start position:0%
+one particle State corresponding to a
+and the one particle State corresponding
+
+ align:start position:0%
+and the one particle State corresponding
+ 
+
+ align:start position:0%
+and the one particle State corresponding
+to B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+then then both are acting vectors of Q
+
+ align:start position:0%
+then then both are acting vectors of Q
+ 
+
+ align:start position:0%
+then then both are acting vectors of Q
+but with ch but here with eigenvalue one
+
+ align:start position:0%
+but with ch but here with eigenvalue one
+ 
+
+ align:start position:0%
+but with ch but here with eigenvalue one
+but this one is eigenvalue minus one
+
+ align:start position:0%
+but this one is eigenvalue minus one
+ 
+
+ align:start position:0%
+but this one is eigenvalue minus one
+okay so it means they actually have
+
+ align:start position:0%
+okay so it means they actually have
+ 
+
+ align:start position:0%
+okay so it means they actually have
+opposite charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+it's okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and oh by the way
+
+ align:start position:0%
+and oh by the way
+ 
+
+ align:start position:0%
+and oh by the way
+so so let me explain a little bit of of
+
+ align:start position:0%
+so so let me explain a little bit of of
+ 
+
+ align:start position:0%
+so so let me explain a little bit of of
+this notation this K does not mean the
+
+ align:start position:0%
+this notation this K does not mean the
+ 
+
+ align:start position:0%
+this notation this K does not mean the
+magnitude of K
+
+ align:start position:0%
+magnitude of K
+ 
+
+ align:start position:0%
+magnitude of K
+so this may okay
+
+ align:start position:0%
+so this may okay
+ 
+
+ align:start position:0%
+so this may okay
+k k means the uh because
+
+ align:start position:0%
+k k means the uh because
+ 
+
+ align:start position:0%
+k k means the uh because
+normally our convention is that the four
+
+ align:start position:0%
+normally our convention is that the four
+ 
+
+ align:start position:0%
+normally our convention is that the four
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+says the X mu we always just write as X
+
+ align:start position:0%
+says the X mu we always just write as X
+ 
+
+ align:start position:0%
+says the X mu we always just write as X
+okay the P mu we just write as q p so
+
+ align:start position:0%
+okay the P mu we just write as q p so
+ 
+
+ align:start position:0%
+okay the P mu we just write as q p so
+here you should view this as a four
+
+ align:start position:0%
+here you should view this as a four
+ 
+
+ align:start position:0%
+here you should view this as a four
+Vector okay so it's a four Vector yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just it's a shorthand notation
+
+ align:start position:0%
+it's just it's a shorthand notation
+ 
+
+ align:start position:0%
+it's just it's a shorthand notation
+so so K and K Bar
+
+ align:start position:0%
+so so K and K Bar
+ 
+
+ align:start position:0%
+so so K and K Bar
+then they have update charge okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have the same mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the same spin zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but of the charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so by using this Q
+
+ align:start position:0%
+so so by using this Q
+ 
+
+ align:start position:0%
+so so by using this Q
+we cannot distinguish these two
+
+ align:start position:0%
+we cannot distinguish these two
+ 
+
+ align:start position:0%
+we cannot distinguish these two
+particles okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so normally we call such a particle
+
+ align:start position:0%
+so so normally we call such a particle
+ 
+
+ align:start position:0%
+so so normally we call such a particle
+because in this case which they
+
+ align:start position:0%
+because in this case which they
+ 
+
+ align:start position:0%
+because in this case which they
+they are all quantum numbers are the
+
+ align:start position:0%
+they are all quantum numbers are the
+ 
+
+ align:start position:0%
+they are all quantum numbers are the
+same except some they have opposite
+
+ align:start position:0%
+same except some they have opposite
+ 
+
+ align:start position:0%
+same except some they have opposite
+charge we call them particle
+
+ align:start position:0%
+charge we call them particle
+ 
+
+ align:start position:0%
+charge we call them particle
+antiparticle okay so this would be
+
+ align:start position:0%
+antiparticle okay so this would be
+ 
+
+ align:start position:0%
+antiparticle okay so this would be
+called a creative particle
+
+ align:start position:0%
+called a creative particle
+ 
+
+ align:start position:0%
+called a creative particle
+so here we say they create anti-particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um so here let me just make a a
+
+ align:start position:0%
+so um so here let me just make a a
+ 
+
+ align:start position:0%
+so um so here let me just make a a
+remark without proving it
+
+ align:start position:0%
+remark without proving it
+ 
+
+ align:start position:0%
+remark without proving it
+so so universities you can show
+
+ align:start position:0%
+so so universities you can show
+ 
+
+ align:start position:0%
+so so universities you can show
+that any particle
+
+ align:start position:0%
+that any particle
+ 
+
+ align:start position:0%
+that any particle
+has anti-particle okay in any Quantum
+
+ align:start position:0%
+has anti-particle okay in any Quantum
+ 
+
+ align:start position:0%
+has anti-particle okay in any Quantum
+field any relativity Quantum field
+
+ align:start position:0%
+field any relativity Quantum field
+ 
+
+ align:start position:0%
+field any relativity Quantum field
+Theory any particle has another particle
+
+ align:start position:0%
+Theory any particle has another particle
+ 
+
+ align:start position:0%
+Theory any particle has another particle
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in the case of the real scalar field
+
+ align:start position:0%
+in the case of the real scalar field
+ 
+
+ align:start position:0%
+in the case of the real scalar field
+you say we only have one particle in
+
+ align:start position:0%
+you say we only have one particle in
+ 
+
+ align:start position:0%
+you say we only have one particle in
+that case the under particle is itself
+
+ align:start position:0%
+that case the under particle is itself
+ 
+
+ align:start position:0%
+that case the under particle is itself
+okay and yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good do you have any questions
+
+ align:start position:0%
+good do you have any questions
+ 
+
+ align:start position:0%
+good do you have any questions
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and served separately
+
+ align:start position:0%
+and served separately
+ 
+
+ align:start position:0%
+and served separately
+um having trouble seeing why
+
+ align:start position:0%
+um having trouble seeing why
+ 
+
+ align:start position:0%
+um having trouble seeing why
+conservation of Q is not trivial
+
+ align:start position:0%
+conservation of Q is not trivial
+ 
+
+ align:start position:0%
+conservation of Q is not trivial
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah the conversation of Q for uh it
+
+ align:start position:0%
+yeah the conversation of Q for uh it
+ 
+
+ align:start position:0%
+yeah the conversation of Q for uh it
+follows from the symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like like the number of a particles
+
+ align:start position:0%
+like like the number of a particles
+ 
+
+ align:start position:0%
+like like the number of a particles
+number of B particles they're kind of
+
+ align:start position:0%
+number of B particles they're kind of
+ 
+
+ align:start position:0%
+number of B particles they're kind of
+separately considered so I just read off
+
+ align:start position:0%
+separately considered so I just read off
+ 
+
+ align:start position:0%
+separately considered so I just read off
+that Q is considered from the very
+
+ align:start position:0%
+that Q is considered from the very
+ 
+
+ align:start position:0%
+that Q is considered from the very
+beginning yeah it's a um
+
+ align:start position:0%
+beginning yeah it's a um
+ 
+
+ align:start position:0%
+beginning yeah it's a um
+no actually the uh the number of a
+
+ align:start position:0%
+no actually the uh the number of a
+ 
+
+ align:start position:0%
+no actually the uh the number of a
+particle and number B particle they're
+
+ align:start position:0%
+particle and number B particle they're
+ 
+
+ align:start position:0%
+particle and number B particle they're
+not a separately conserved they can
+
+ align:start position:0%
+not a separately conserved they can
+ 
+
+ align:start position:0%
+not a separately conserved they can
+actually in principle they can allow it
+
+ align:start position:0%
+actually in principle they can allow it
+ 
+
+ align:start position:0%
+actually in principle they can allow it
+yeah yeah here in freeze it with the
+
+ align:start position:0%
+yeah yeah here in freeze it with the
+ 
+
+ align:start position:0%
+yeah yeah here in freeze it with the
+canal they cannot align it but but if I
+
+ align:start position:0%
+canal they cannot align it but but if I
+ 
+
+ align:start position:0%
+canal they cannot align it but but if I
+can see the slightly more complicated
+
+ align:start position:0%
+can see the slightly more complicated
+ 
+
+ align:start position:0%
+can see the slightly more complicated
+series say if they're allowed to
+
+ align:start position:0%
+series say if they're allowed to
+ 
+
+ align:start position:0%
+series say if they're allowed to
+interact and then they can actually land
+
+ align:start position:0%
+interact and then they can actually land
+ 
+
+ align:start position:0%
+interact and then they can actually land
+it and then disappear and uh so in that
+
+ align:start position:0%
+it and then disappear and uh so in that
+ 
+
+ align:start position:0%
+it and then disappear and uh so in that
+case and but this formula still works
+
+ align:start position:0%
+case and but this formula still works
+ 
+
+ align:start position:0%
+case and but this formula still works
+this image is still there yeah so that's
+
+ align:start position:0%
+this image is still there yeah so that's
+ 
+
+ align:start position:0%
+this image is still there yeah so that's
+why the Symmetry is it's powerful also
+
+ align:start position:0%
+why the Symmetry is it's powerful also
+ 
+
+ align:start position:0%
+why the Symmetry is it's powerful also
+applies to to the case with interactions
+
+ align:start position:0%
+applies to to the case with interactions
+ 
+
+ align:start position:0%
+applies to to the case with interactions
+yeah yeah indeed what you what you said
+
+ align:start position:0%
+yeah yeah indeed what you what you said
+ 
+
+ align:start position:0%
+yeah yeah indeed what you what you said
+is correct uh in the in the free Theory
+
+ align:start position:0%
+is correct uh in the in the free Theory
+ 
+
+ align:start position:0%
+is correct uh in the in the free Theory
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between serbs so they work in there
+
+ align:start position:0%
+between serbs so they work in there
+ 
+
+ align:start position:0%
+between serbs so they work in there
+yeah yeah essentially the property means
+
+ align:start position:0%
+yeah yeah essentially the property means
+ 
+
+ align:start position:0%
+yeah yeah essentially the property means
+they're probably almost identical except
+
+ align:start position:0%
+they're probably almost identical except
+ 
+
+ align:start position:0%
+they're probably almost identical except
+they have already charged
+
+ align:start position:0%
+they have already charged
+ 
+
+ align:start position:0%
+they have already charged
+yeah yeah they have essentially uh uh uh
+
+ align:start position:0%
+yeah yeah they have essentially uh uh uh
+ 
+
+ align:start position:0%
+yeah yeah they have essentially uh uh uh
+uh yeah just like real world we have
+
+ align:start position:0%
+uh yeah just like real world we have
+ 
+
+ align:start position:0%
+uh yeah just like real world we have
+electron we have anti if a matter we
+
+ align:start position:0%
+electron we have anti if a matter we
+ 
+
+ align:start position:0%
+electron we have anti if a matter we
+have antimatter uh uh they have a
+
+ align:start position:0%
+have antimatter uh uh they have a
+ 
+
+ align:start position:0%
+have antimatter uh uh they have a
+essential identical properties and if
+
+ align:start position:0%
+essential identical properties and if
+ 
+
+ align:start position:0%
+essential identical properties and if
+the world is made of anti-matter
+
+ align:start position:0%
+the world is made of anti-matter
+ 
+
+ align:start position:0%
+the world is made of anti-matter
+everything still will behave the same
+
+ align:start position:0%
+everything still will behave the same
+ 
+
+ align:start position:0%
+everything still will behave the same
+and yeah yeah but the except just the
+
+ align:start position:0%
+and yeah yeah but the except just the
+ 
+
+ align:start position:0%
+and yeah yeah but the except just the
+charge is different
+
+ align:start position:0%
+charge is different
+ 
+
+ align:start position:0%
+charge is different
+between the number of anti-particles and
+
+ align:start position:0%
+between the number of anti-particles and
+ 
+
+ align:start position:0%
+between the number of anti-particles and
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+is conserved yeah it's conserved yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+um I guess this is like the electric
+
+ align:start position:0%
+um I guess this is like the electric
+ 
+
+ align:start position:0%
+um I guess this is like the electric
+charge or or is this some other charge I
+
+ align:start position:0%
+charge or or is this some other charge I
+ 
+
+ align:start position:0%
+charge or or is this some other charge I
+think some other charge
+
+ align:start position:0%
+think some other charge
+ 
+
+ align:start position:0%
+think some other charge
+so so in the case uh we will go to when
+
+ align:start position:0%
+so so in the case uh we will go to when
+ 
+
+ align:start position:0%
+so so in the case uh we will go to when
+we talk about electrons so you know the
+
+ align:start position:0%
+we talk about electrons so you know the
+ 
+
+ align:start position:0%
+we talk about electrons so you know the
+electrons involving more complications
+
+ align:start position:0%
+electrons involving more complications
+ 
+
+ align:start position:0%
+electrons involving more complications
+we have to introduce spin particle with
+
+ align:start position:0%
+we have to introduce spin particle with
+ 
+
+ align:start position:0%
+we have to introduce spin particle with
+spin in that case we also have an
+
+ align:start position:0%
+spin in that case we also have an
+ 
+
+ align:start position:0%
+spin in that case we also have an
+electron anti-election and in that case
+
+ align:start position:0%
+electron anti-election and in that case
+ 
+
+ align:start position:0%
+electron anti-election and in that case
+it's a story is parallel and uh yeah
+
+ align:start position:0%
+it's a story is parallel and uh yeah
+ 
+
+ align:start position:0%
+it's a story is parallel and uh yeah
+so this does not necessarily involve
+
+ align:start position:0%
+so this does not necessarily involve
+ 
+
+ align:start position:0%
+so this does not necessarily involve
+yeah or like yes repellent no no no yeah
+
+ align:start position:0%
+yeah or like yes repellent no no no yeah
+ 
+
+ align:start position:0%
+yeah or like yes repellent no no no yeah
+but but this is the analog of that is
+
+ align:start position:0%
+but but this is the analog of that is
+ 
+
+ align:start position:0%
+but but this is the analog of that is
+analog of that so the charge here uh
+
+ align:start position:0%
+analog of that so the charge here uh
+ 
+
+ align:start position:0%
+analog of that so the charge here uh
+they can be some other kind of charge
+
+ align:start position:0%
+they can be some other kind of charge
+ 
+
+ align:start position:0%
+they can be some other kind of charge
+does not have to be uh yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how can you get like something that's
+
+ align:start position:0%
+how can you get like something that's
+ 
+
+ align:start position:0%
+how can you get like something that's
+physical that's conserved from a
+
+ align:start position:0%
+physical that's conserved from a
+ 
+
+ align:start position:0%
+physical that's conserved from a
+symmetry that's not really physical like
+
+ align:start position:0%
+symmetry that's not really physical like
+ 
+
+ align:start position:0%
+symmetry that's not really physical like
+this is not like you can translate in
+
+ align:start position:0%
+this is not like you can translate in
+ 
+
+ align:start position:0%
+this is not like you can translate in
+space or like translating time this is I
+
+ align:start position:0%
+space or like translating time this is I
+ 
+
+ align:start position:0%
+space or like translating time this is I
+don't understand I don't know how to
+
+ align:start position:0%
+don't understand I don't know how to
+ 
+
+ align:start position:0%
+don't understand I don't know how to
+think about it yeah yeah that's why we
+
+ align:start position:0%
+think about it yeah yeah that's why we
+ 
+
+ align:start position:0%
+think about it yeah yeah that's why we
+call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for since we don't have good
+
+ align:start position:0%
+so for since we don't have good
+ 
+
+ align:start position:0%
+so for since we don't have good
+intuition about
+
+ align:start position:0%
+intuition about
+ 
+
+ align:start position:0%
+intuition about
+you just invent the new name for it
+
+ align:start position:0%
+you just invent the new name for it
+ 
+
+ align:start position:0%
+you just invent the new name for it
+and and once you get used to this new
+
+ align:start position:0%
+and and once you get used to this new
+ 
+
+ align:start position:0%
+and and once you get used to this new
+name you say oh I understand it
+
+ align:start position:0%
+name you say oh I understand it
+ 
+
+ align:start position:0%
+name you say oh I understand it
+yeah yeah it it is more or less to
+
+ align:start position:0%
+yeah yeah it it is more or less to
+ 
+
+ align:start position:0%
+yeah yeah it it is more or less to
+getting used to it and indeed at first
+
+ align:start position:0%
+getting used to it and indeed at first
+ 
+
+ align:start position:0%
+getting used to it and indeed at first
+side it's not very intuitive because
+
+ align:start position:0%
+side it's not very intuitive because
+ 
+
+ align:start position:0%
+side it's not very intuitive because
+it's not something you can
+
+ align:start position:0%
+it's not something you can
+ 
+
+ align:start position:0%
+it's not something you can
+yeah from your normal experiences Etc
+
+ align:start position:0%
+yeah from your normal experiences Etc
+ 
+
+ align:start position:0%
+yeah from your normal experiences Etc
+but uh yeah but this is the uh
+
+ align:start position:0%
+but uh yeah but this is the uh
+ 
+
+ align:start position:0%
+but uh yeah but this is the uh
+yeah but this is us
+
+ align:start position:0%
+yeah but this is us
+ 
+
+ align:start position:0%
+yeah but this is us
+as fundamental level is not that
+
+ align:start position:0%
+as fundamental level is not that
+ 
+
+ align:start position:0%
+as fundamental level is not that
+different from energy conservation it's
+
+ align:start position:0%
+different from energy conservation it's
+ 
+
+ align:start position:0%
+different from energy conservation it's
+just some symmetry and then this to some
+
+ align:start position:0%
+just some symmetry and then this to some
+ 
+
+ align:start position:0%
+just some symmetry and then this to some
+conserved quantities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electric charge and like which ones do
+
+ align:start position:0%
+electric charge and like which ones do
+ 
+
+ align:start position:0%
+electric charge and like which ones do
+we call I guess particulines
+
+ align:start position:0%
+we call I guess particulines
+ 
+
+ align:start position:0%
+we call I guess particulines
+does that make sense yeah yeah that's
+
+ align:start position:0%
+does that make sense yeah yeah that's
+ 
+
+ align:start position:0%
+does that make sense yeah yeah that's
+right they can hide they can in
+
+ align:start position:0%
+right they can hide they can in
+ 
+
+ align:start position:0%
+right they can hide they can in
+principle have multiple charges but the
+
+ align:start position:0%
+principle have multiple charges but the
+ 
+
+ align:start position:0%
+principle have multiple charges but the
+particle and the particle they're always
+
+ align:start position:0%
+particle and the particle they're always
+ 
+
+ align:start position:0%
+particle and the particle they're always
+opposite
+
+ align:start position:0%
+opposite
+ 
+
+ align:start position:0%
+opposite
+yeah yeah in terms of charges they're
+
+ align:start position:0%
+yeah yeah in terms of charges they're
+ 
+
+ align:start position:0%
+yeah yeah in terms of charges they're
+always opposite yeah whatever charges
+
+ align:start position:0%
+always opposite yeah whatever charges
+ 
+
+ align:start position:0%
+always opposite yeah whatever charges
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+two different charges that each one can
+
+ align:start position:0%
+two different charges that each one can
+ 
+
+ align:start position:0%
+two different charges that each one can
+have you know instead of four things is
+
+ align:start position:0%
+have you know instead of four things is
+ 
+
+ align:start position:0%
+have you know instead of four things is
+it a different language yeah yeah I
+
+ align:start position:0%
+it a different language yeah yeah I
+ 
+
+ align:start position:0%
+it a different language yeah yeah I
+think yeah uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you can have them but but for
+
+ align:start position:0%
+yeah you can have them but but for
+ 
+
+ align:start position:0%
+yeah you can have them but but for
+particle and particle they're always
+
+ align:start position:0%
+particle and particle they're always
+ 
+
+ align:start position:0%
+particle and particle they're always
+opposite
+
+ align:start position:0%
+opposite
+ 
+
+ align:start position:0%
+opposite
+yeah they can have multiple charges but
+
+ align:start position:0%
+yeah they can have multiple charges but
+ 
+
+ align:start position:0%
+yeah they can have multiple charges but
+they're always opposite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good good
+
+ align:start position:0%
+okay good good
+ 
+
+ align:start position:0%
+okay good good
+so so this concludes our discussion
+
+ align:start position:0%
+so so this concludes our discussion
+ 
+
+ align:start position:0%
+so so this concludes our discussion
+of the complex
+
+ align:start position:0%
+of the complex
+ 
+
+ align:start position:0%
+of the complex
+field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so we have a few minutes
+
+ align:start position:0%
+so we have a few minutes
+ 
+
+ align:start position:0%
+so we have a few minutes
+then it's to uh to the next
+
+ align:start position:0%
+then it's to uh to the next
+ 
+
+ align:start position:0%
+then it's to uh to the next
+topic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's talk about the
+
+ align:start position:0%
+so now let's talk about the
+ 
+
+ align:start position:0%
+so now let's talk about the
+concept called the propagators
+
+ align:start position:0%
+concept called the propagators
+ 
+
+ align:start position:0%
+concept called the propagators
+so so in so again let's recall in our
+
+ align:start position:0%
+so so in so again let's recall in our
+ 
+
+ align:start position:0%
+so so in so again let's recall in our
+activity quantum mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this position Vector plays a hero
+
+ align:start position:0%
+so this position Vector plays a hero
+ 
+
+ align:start position:0%
+so this position Vector plays a hero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is the eigenvector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+X which is the position operator
+
+ align:start position:0%
+X which is the position operator
+ 
+
+ align:start position:0%
+X which is the position operator
+okay so again I will uh yeah let me just
+
+ align:start position:0%
+okay so again I will uh yeah let me just
+ 
+
+ align:start position:0%
+okay so again I will uh yeah let me just
+put a hat here to emphasize this is the
+
+ align:start position:0%
+put a hat here to emphasize this is the
+ 
+
+ align:start position:0%
+put a hat here to emphasize this is the
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+and so so this is the eigenved of X okay
+
+ align:start position:0%
+and so so this is the eigenved of X okay
+ 
+
+ align:start position:0%
+and so so this is the eigenved of X okay
+and because this player key role because
+
+ align:start position:0%
+and because this player key role because
+ 
+
+ align:start position:0%
+and because this player key role because
+we need to use this to define the wave
+
+ align:start position:0%
+we need to use this to define the wave
+ 
+
+ align:start position:0%
+we need to use this to define the wave
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the uh the amplitude of the
+
+ align:start position:0%
+and then the uh the amplitude of the
+ 
+
+ align:start position:0%
+and then the uh the amplitude of the
+wave function the square
+
+ align:start position:0%
+wave function the square
+ 
+
+ align:start position:0%
+wave function the square
+give us the probability of a particle at
+
+ align:start position:0%
+give us the probability of a particle at
+ 
+
+ align:start position:0%
+give us the probability of a particle at
+location X okay so so this is a crucial
+
+ align:start position:0%
+location X okay so so this is a crucial
+ 
+
+ align:start position:0%
+location X okay so so this is a crucial
+uh quantity
+
+ align:start position:0%
+uh quantity
+ 
+
+ align:start position:0%
+uh quantity
+so so this language
+
+ align:start position:0%
+so so this language
+ 
+
+ align:start position:0%
+so so this language
+uh normally we talk about the uh the
+
+ align:start position:0%
+uh normally we talk about the uh the
+ 
+
+ align:start position:0%
+uh normally we talk about the uh the
+shorting a picture you started with
+
+ align:start position:0%
+shorting a picture you started with
+ 
+
+ align:start position:0%
+shorting a picture you started with
+percent X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at t equal to zero
+
+ align:start position:0%
+at t equal to zero
+ 
+
+ align:start position:0%
+at t equal to zero
+and then you try to find
+
+ align:start position:0%
+and then you try to find
+ 
+
+ align:start position:0%
+and then you try to find
+yeah or yeah let me say
+
+ align:start position:0%
+yeah or yeah let me say
+ 
+
+ align:start position:0%
+yeah or yeah let me say
+you start to set X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say t Prime I sum T Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you want to find PSI
+
+ align:start position:0%
+okay you want to find PSI
+ 
+
+ align:start position:0%
+okay you want to find PSI
+X at some t Okay so so this is the
+
+ align:start position:0%
+X at some t Okay so so this is the
+ 
+
+ align:start position:0%
+X at some t Okay so so this is the
+depression of quantum mechanics okay
+
+ align:start position:0%
+depression of quantum mechanics okay
+ 
+
+ align:start position:0%
+depression of quantum mechanics okay
+so if you know the wave function at the
+
+ align:start position:0%
+so if you know the wave function at the
+ 
+
+ align:start position:0%
+so if you know the wave function at the
+initial time and you want to find the
+
+ align:start position:0%
+initial time and you want to find the
+ 
+
+ align:start position:0%
+initial time and you want to find the
+the wave functions on future time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so now let's imagine we consider this
+
+ align:start position:0%
+so now let's imagine we consider this
+ 
+
+ align:start position:0%
+so now let's imagine we consider this
+question Heisenberg picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he showed him a picture there's just
+
+ align:start position:0%
+so he showed him a picture there's just
+ 
+
+ align:start position:0%
+so he showed him a picture there's just
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay they just the one eigenvector
+
+ align:start position:0%
+okay they just the one eigenvector
+ 
+
+ align:start position:0%
+okay they just the one eigenvector
+uh yeah just one set of eigenvectors for
+
+ align:start position:0%
+uh yeah just one set of eigenvectors for
+ 
+
+ align:start position:0%
+uh yeah just one set of eigenvectors for
+X okay for different eigenvalues
+
+ align:start position:0%
+X okay for different eigenvalues
+ 
+
+ align:start position:0%
+X okay for different eigenvalues
+but for for the Heisenberg picture now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your position operator now depend on
+
+ align:start position:0%
+your position operator now depend on
+ 
+
+ align:start position:0%
+your position operator now depend on
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so the position operates at
+
+ align:start position:0%
+okay so the position operates at
+ 
+
+ align:start position:0%
+okay so the position operates at
+different times they are different
+
+ align:start position:0%
+different times they are different
+ 
+
+ align:start position:0%
+different times they are different
+so now if you want to talk about the
+
+ align:start position:0%
+so now if you want to talk about the
+ 
+
+ align:start position:0%
+so now if you want to talk about the
+position eigenvector now you read the
+
+ align:start position:0%
+position eigenvector now you read the
+ 
+
+ align:start position:0%
+position eigenvector now you read the
+label
+
+ align:start position:0%
+label
+ 
+
+ align:start position:0%
+label
+okay so now the position eigenvector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the T label okay
+
+ align:start position:0%
+is the T label okay
+ 
+
+ align:start position:0%
+is the T label okay
+this T does not mean that this exactly
+
+ align:start position:0%
+this T does not mean that this exactly
+ 
+
+ align:start position:0%
+this T does not mean that this exactly
+evolved with time it just this is the
+
+ align:start position:0%
+evolved with time it just this is the
+ 
+
+ align:start position:0%
+evolved with time it just this is the
+label okay this means that this is the
+
+ align:start position:0%
+label okay this means that this is the
+ 
+
+ align:start position:0%
+label okay this means that this is the
+eigenvector of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+position Vector at time t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this just tells you this is the egg
+
+ align:start position:0%
+okay this just tells you this is the egg
+ 
+
+ align:start position:0%
+okay this just tells you this is the egg
+marked at time T okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now the question of this question of
+
+ align:start position:0%
+and now the question of this question of
+ 
+
+ align:start position:0%
+and now the question of this question of
+this the question of quantum mechanics
+
+ align:start position:0%
+this the question of quantum mechanics
+ 
+
+ align:start position:0%
+this the question of quantum mechanics
+then can be reformulated into a
+
+ align:start position:0%
+then can be reformulated into a
+ 
+
+ align:start position:0%
+then can be reformulated into a
+different question
+
+ align:start position:0%
+different question
+ 
+
+ align:start position:0%
+different question
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so in this story the question of
+
+ align:start position:0%
+so so in this story the question of
+ 
+
+ align:start position:0%
+so so in this story the question of
+quantum mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+becomes the following
+
+ align:start position:0%
+becomes the following
+ 
+
+ align:start position:0%
+becomes the following
+what is the value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+you are in the eigen state
+
+ align:start position:0%
+you are in the eigen state
+ 
+
+ align:start position:0%
+you are in the eigen state
+you are you are analog you are the econ
+
+ align:start position:0%
+you are you are analog you are the econ
+ 
+
+ align:start position:0%
+you are you are analog you are the econ
+Vector you are in the position
+
+ align:start position:0%
+Vector you are in the position
+ 
+
+ align:start position:0%
+Vector you are in the position
+eigenvector you are in the position
+
+ align:start position:0%
+eigenvector you are in the position
+ 
+
+ align:start position:0%
+eigenvector you are in the position
+eigenstate
+
+ align:start position:0%
+eigenstate
+ 
+
+ align:start position:0%
+eigenstate
+uh at time T Prime with value X Prime
+
+ align:start position:0%
+uh at time T Prime with value X Prime
+ 
+
+ align:start position:0%
+uh at time T Prime with value X Prime
+and what's the amplitude for you to go
+
+ align:start position:0%
+and what's the amplitude for you to go
+ 
+
+ align:start position:0%
+and what's the amplitude for you to go
+to location X at time T okay
+
+ align:start position:0%
+to location X at time T okay
+ 
+
+ align:start position:0%
+to location X at time T okay
+okay remember this this does not involve
+
+ align:start position:0%
+okay remember this this does not involve
+ 
+
+ align:start position:0%
+okay remember this this does not involve
+time Evolution this just because one is
+
+ align:start position:0%
+time Evolution this just because one is
+ 
+
+ align:start position:0%
+time Evolution this just because one is
+labeling different uh economics at
+
+ align:start position:0%
+labeling different uh economics at
+ 
+
+ align:start position:0%
+labeling different uh economics at
+different time okay
+
+ align:start position:0%
+different time okay
+ 
+
+ align:start position:0%
+different time okay
+so if you know this object this is
+
+ align:start position:0%
+so if you know this object this is
+ 
+
+ align:start position:0%
+so if you know this object this is
+called this will be normally below the G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know gee this is called the
+
+ align:start position:0%
+you know gee this is called the
+ 
+
+ align:start position:0%
+you know gee this is called the
+propagator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is called the propagator
+
+ align:start position:0%
+okay this is called the propagator
+ 
+
+ align:start position:0%
+okay this is called the propagator
+so if you know the propagator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a Quantum system
+
+ align:start position:0%
+of a Quantum system
+ 
+
+ align:start position:0%
+of a Quantum system
+then you have full rollage of that
+
+ align:start position:0%
+then you have full rollage of that
+ 
+
+ align:start position:0%
+then you have full rollage of that
+system so you have to solve the system
+
+ align:start position:0%
+system so you have to solve the system
+ 
+
+ align:start position:0%
+system so you have to solve the system
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+because say let's imagine we want to
+
+ align:start position:0%
+because say let's imagine we want to
+ 
+
+ align:start position:0%
+because say let's imagine we want to
+find PSI TX
+
+ align:start position:0%
+find PSI TX
+ 
+
+ align:start position:0%
+find PSI TX
+wave function at time t
+
+ align:start position:0%
+wave function at time t
+ 
+
+ align:start position:0%
+wave function at time t
+and then by definition
+
+ align:start position:0%
+and then by definition
+ 
+
+ align:start position:0%
+and then by definition
+this is given by this so this is the
+
+ align:start position:0%
+this is given by this so this is the
+ 
+
+ align:start position:0%
+this is given by this so this is the
+Heisenberg picture of a definition okay
+
+ align:start position:0%
+Heisenberg picture of a definition okay
+ 
+
+ align:start position:0%
+Heisenberg picture of a definition okay
+it's the side the overlap with the
+
+ align:start position:0%
+it's the side the overlap with the
+ 
+
+ align:start position:0%
+it's the side the overlap with the
+position Vector at time t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now this is now we can insert the
+
+ align:start position:0%
+and now this is now we can insert the
+ 
+
+ align:start position:0%
+and now this is now we can insert the
+complete set of State
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I just insert the complete side
+
+ align:start position:0%
+okay I just insert the complete side
+ 
+
+ align:start position:0%
+okay I just insert the complete side
+here just this is identity okay
+
+ align:start position:0%
+here just this is identity okay
+ 
+
+ align:start position:0%
+here just this is identity okay
+and then underneath the object is just G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you just get G
+
+ align:start position:0%
+so you just get G
+ 
+
+ align:start position:0%
+so you just get G
+x t
+
+ align:start position:0%
+x t
+ 
+
+ align:start position:0%
+x t
+X Prime P Prime then PSI T Prime X Prime
+
+ align:start position:0%
+X Prime P Prime then PSI T Prime X Prime
+ 
+
+ align:start position:0%
+X Prime P Prime then PSI T Prime X Prime
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you know
+
+ align:start position:0%
+so if you know
+ 
+
+ align:start position:0%
+so if you know
+so yeah so so this just gave you the
+
+ align:start position:0%
+so yeah so so this just gave you the
+ 
+
+ align:start position:0%
+so yeah so so this just gave you the
+wave function at T Prime
+
+ align:start position:0%
+wave function at T Prime
+ 
+
+ align:start position:0%
+wave function at T Prime
+so now if you load this
+
+ align:start position:0%
+so now if you load this
+ 
+
+ align:start position:0%
+so now if you load this
+you're given the initial wave function
+
+ align:start position:0%
+you're given the initial wave function
+ 
+
+ align:start position:0%
+you're given the initial wave function
+if you know the propagator
+
+ align:start position:0%
+if you know the propagator
+ 
+
+ align:start position:0%
+if you know the propagator
+you just need to do an integral okay
+
+ align:start position:0%
+you just need to do an integral okay
+ 
+
+ align:start position:0%
+you just need to do an integral okay
+then you find the wave function here
+
+ align:start position:0%
+then you find the wave function here
+ 
+
+ align:start position:0%
+then you find the wave function here
+so the full range of your quantum
+
+ align:start position:0%
+so the full range of your quantum
+ 
+
+ align:start position:0%
+so the full range of your quantum
+mechanical system essentially is encoded
+
+ align:start position:0%
+mechanical system essentially is encoded
+ 
+
+ align:start position:0%
+mechanical system essentially is encoded
+in this propagator
+
+ align:start position:0%
+in this propagator
+ 
+
+ align:start position:0%
+in this propagator
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+is encoded in this propagator
+
+ align:start position:0%
+is encoded in this propagator
+ 
+
+ align:start position:0%
+is encoded in this propagator
+so um yeah so so now we want to talk
+
+ align:start position:0%
+so um yeah so so now we want to talk
+ 
+
+ align:start position:0%
+so um yeah so so now we want to talk
+about what is the analog of this object
+
+ align:start position:0%
+about what is the analog of this object
+ 
+
+ align:start position:0%
+about what is the analog of this object
+say and you write a b c Quantum field
+
+ align:start position:0%
+say and you write a b c Quantum field
+ 
+
+ align:start position:0%
+say and you write a b c Quantum field
+okay uh in Quantum field how do we
+
+ align:start position:0%
+okay uh in Quantum field how do we
+ 
+
+ align:start position:0%
+okay uh in Quantum field how do we
+Define a propagator and what is the
+
+ align:start position:0%
+Define a propagator and what is the
+ 
+
+ align:start position:0%
+Define a propagator and what is the
+what is the analog of the position eigen
+
+ align:start position:0%
+what is the analog of the position eigen
+ 
+
+ align:start position:0%
+what is the analog of the position eigen
+State say in Quantum field Theory okay
+
+ align:start position:0%
+State say in Quantum field Theory okay
+ 
+
+ align:start position:0%
+State say in Quantum field Theory okay
+and we will discuss next time
\ No newline at end of file
diff --git a/wezQdmwolMU.txt b/wezQdmwolMU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ff3926019c5659448e697852fc6f6980c4b1dd51
--- /dev/null
+++ b/wezQdmwolMU.txt
@@ -0,0 +1,1355 @@
+align:start position:0%
+ 
+Welcome back to recitation. Uh we're
+
+ align:start position:0%
+Welcome back to recitation. Uh we're
+ 
+
+ align:start position:0%
+Welcome back to recitation. Uh we're
+going to practice using some of the some
+
+ align:start position:0%
+going to practice using some of the some
+ 
+
+ align:start position:0%
+going to practice using some of the some
+of the tools you developed recently on
+
+ align:start position:0%
+of the tools you developed recently on
+ 
+
+ align:start position:0%
+of the tools you developed recently on
+taking derivatives of exponential
+
+ align:start position:0%
+taking derivatives of exponential
+ 
+
+ align:start position:0%
+taking derivatives of exponential
+functions and taking derivatives of
+
+ align:start position:0%
+functions and taking derivatives of
+ 
+
+ align:start position:0%
+functions and taking derivatives of
+logarithmic functions. So I have three
+
+ align:start position:0%
+logarithmic functions. So I have three
+ 
+
+ align:start position:0%
+logarithmic functions. So I have three
+uh particular examples that I want us to
+
+ align:start position:0%
+uh particular examples that I want us to
+ 
+
+ align:start position:0%
+uh particular examples that I want us to
+look at and I'd like us to find
+
+ align:start position:0%
+look at and I'd like us to find
+ 
+
+ align:start position:0%
+look at and I'd like us to find
+derivatives of the following functions.
+
+ align:start position:0%
+derivatives of the following functions.
+ 
+
+ align:start position:0%
+derivatives of the following functions.
+The first one is f ofx is equal to x pi
+
+ align:start position:0%
+The first one is f ofx is equal to x pi
+ 
+
+ align:start position:0%
+The first one is f ofx is equal to x pi
+plus p to x. The second function is g
+
+ align:start position:0%
+plus p to x. The second function is g
+ 
+
+ align:start position:0%
+plus p to x. The second function is g
+ofx is equal to natural log of cosine of
+
+ align:start position:0%
+ofx is equal to natural log of cosine of
+ 
+
+ align:start position:0%
+ofx is equal to natural log of cosine of
+x. And the third one is that's an h, not
+
+ align:start position:0%
+x. And the third one is that's an h, not
+ 
+
+ align:start position:0%
+x. And the third one is that's an h, not
+a natural log. h ofx is equal to natural
+
+ align:start position:0%
+a natural log. h ofx is equal to natural
+ 
+
+ align:start position:0%
+a natural log. h ofx is equal to natural
+log of e to x^2. So you have three
+
+ align:start position:0%
+log of e to x^2. So you have three
+ 
+
+ align:start position:0%
+log of e to x^2. So you have three
+functions you want to take the
+
+ align:start position:0%
+functions you want to take the
+ 
+
+ align:start position:0%
+functions you want to take the
+derivative of with respect to x. I'm
+
+ align:start position:0%
+derivative of with respect to x. I'm
+ 
+
+ align:start position:0%
+derivative of with respect to x. I'm
+going to give you a moment to uh to work
+
+ align:start position:0%
+going to give you a moment to uh to work
+ 
+
+ align:start position:0%
+going to give you a moment to uh to work
+on those and figure those out using the
+
+ align:start position:0%
+on those and figure those out using the
+ 
+
+ align:start position:0%
+on those and figure those out using the
+the tools you now have. And then we'll
+
+ align:start position:0%
+the tools you now have. And then we'll
+ 
+
+ align:start position:0%
+the tools you now have. And then we'll
+come back and I will work them out for
+
+ align:start position:0%
+come back and I will work them out for
+ 
+
+ align:start position:0%
+come back and I will work them out for
+you as well.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let's start off with the
+
+ align:start position:0%
+Okay, so let's start off with the
+ 
+
+ align:start position:0%
+Okay, so let's start off with the
+derivative of the first one. Okay, now
+
+ align:start position:0%
+derivative of the first one. Okay, now
+ 
+
+ align:start position:0%
+derivative of the first one. Okay, now
+the reason in particular that I that I
+
+ align:start position:0%
+the reason in particular that I that I
+ 
+
+ align:start position:0%
+the reason in particular that I that I
+did this one might have seemed simple to
+
+ align:start position:0%
+did this one might have seemed simple to
+ 
+
+ align:start position:0%
+did this one might have seemed simple to
+you, but the reason I did this one is
+
+ align:start position:0%
+you, but the reason I did this one is
+ 
+
+ align:start position:0%
+you, but the reason I did this one is
+because of a common mistake that people
+
+ align:start position:0%
+because of a common mistake that people
+ 
+
+ align:start position:0%
+because of a common mistake that people
+make. Okay, so the derivative of x to
+
+ align:start position:0%
+make. Okay, so the derivative of x to
+ 
+
+ align:start position:0%
+make. Okay, so the derivative of x to
+the pi is uh is nice and simple because
+
+ align:start position:0%
+the pi is uh is nice and simple because
+ 
+
+ align:start position:0%
+the pi is uh is nice and simple because
+that is our uh rule we know for uh
+
+ align:start position:0%
+that is our uh rule we know for uh
+ 
+
+ align:start position:0%
+that is our uh rule we know for uh
+powers of x. So we can write this as
+
+ align:start position:0%
+powers of x. So we can write this as
+ 
+
+ align:start position:0%
+powers of x. So we can write this as
+that derivative is pi * x^ minus one.
+
+ align:start position:0%
+that derivative is pi * x^ minus one.
+ 
+
+ align:start position:0%
+that derivative is pi * x^ minus one.
+Okay. But the whole point of this
+
+ align:start position:0%
+Okay. But the whole point of this
+ 
+
+ align:start position:0%
+Okay. But the whole point of this
+problem for me is to make sure that you
+
+ align:start position:0%
+problem for me is to make sure that you
+ 
+
+ align:start position:0%
+problem for me is to make sure that you
+recognize that pi to the x is not a
+
+ align:start position:0%
+recognize that pi to the x is not a
+ 
+
+ align:start position:0%
+recognize that pi to the x is not a
+power of of x rule that needs to be
+
+ align:start position:0%
+power of of x rule that needs to be
+ 
+
+ align:start position:0%
+power of of x rule that needs to be
+applied. It's actually an exponential
+
+ align:start position:0%
+applied. It's actually an exponential
+ 
+
+ align:start position:0%
+applied. It's actually an exponential
+function, right? With base pi. So if you
+
+ align:start position:0%
+function, right? With base pi. So if you
+ 
+
+ align:start position:0%
+function, right? With base pi. So if you
+wrote uh the derivative of this term was
+
+ align:start position:0%
+wrote uh the derivative of this term was
+ 
+
+ align:start position:0%
+wrote uh the derivative of this term was
+x sorry was x * pi to the xus one, you
+
+ align:start position:0%
+x sorry was x * pi to the xus one, you
+ 
+
+ align:start position:0%
+x sorry was x * pi to the xus one, you
+would not be alone in the world. But
+
+ align:start position:0%
+would not be alone in the world. But
+ 
+
+ align:start position:0%
+would not be alone in the world. But
+that is not the correct answer all the
+
+ align:start position:0%
+that is not the correct answer all the
+ 
+
+ align:start position:0%
+that is not the correct answer all the
+same because this is not a a power of x.
+
+ align:start position:0%
+same because this is not a a power of x.
+ 
+
+ align:start position:0%
+same because this is not a a power of x.
+This is x is the power. So this is an
+
+ align:start position:0%
+This is x is the power. So this is an
+ 
+
+ align:start position:0%
+This is x is the power. So this is an
+exponential function. So the derivative
+
+ align:start position:0%
+exponential function. So the derivative
+ 
+
+ align:start position:0%
+exponential function. So the derivative
+of this we need the rule that we have
+
+ align:start position:0%
+of this we need the rule that we have
+ 
+
+ align:start position:0%
+of this we need the rule that we have
+for exponential uh derivatives of
+
+ align:start position:0%
+for exponential uh derivatives of
+ 
+
+ align:start position:0%
+for exponential uh derivatives of
+exponential functions. So that's natural
+
+ align:start position:0%
+exponential functions. So that's natural
+ 
+
+ align:start position:0%
+exponential functions. So that's natural
+log of pi
+
+ align:start position:0%
+log of pi
+ 
+
+ align:start position:0%
+log of pi
+time pi to the x. That's the derivative
+
+ align:start position:0%
+time pi to the x. That's the derivative
+ 
+
+ align:start position:0%
+time pi to the x. That's the derivative
+of pi to the x. Um so that's the answer
+
+ align:start position:0%
+of pi to the x. Um so that's the answer
+ 
+
+ align:start position:0%
+of pi to the x. Um so that's the answer
+to number one. Okay. Number two I did
+
+ align:start position:0%
+to number one. Okay. Number two I did
+ 
+
+ align:start position:0%
+to number one. Okay. Number two I did
+for another reason. I think it's a It's
+
+ align:start position:0%
+for another reason. I think it's a It's
+ 
+
+ align:start position:0%
+for another reason. I think it's a It's
+an interesting function um once you find
+
+ align:start position:0%
+an interesting function um once you find
+ 
+
+ align:start position:0%
+an interesting function um once you find
+out what the derivative is. So this is
+
+ align:start position:0%
+out what the derivative is. So this is
+ 
+
+ align:start position:0%
+out what the derivative is. So this is
+going to require us to do the chain rule
+
+ align:start position:0%
+going to require us to do the chain rule
+ 
+
+ align:start position:0%
+going to require us to do the chain rule
+because we have a function of a
+
+ align:start position:0%
+because we have a function of a
+ 
+
+ align:start position:0%
+because we have a function of a
+function. Um but you have seen many
+
+ align:start position:0%
+function. Um but you have seen many
+ 
+
+ align:start position:0%
+function. Um but you have seen many
+times now when you have natural log of a
+
+ align:start position:0%
+times now when you have natural log of a
+ 
+
+ align:start position:0%
+times now when you have natural log of a
+function its derivative
+
+ align:start position:0%
+function its derivative
+ 
+
+ align:start position:0%
+function its derivative
+uh is going to be one over one over the
+
+ align:start position:0%
+uh is going to be one over one over the
+ 
+
+ align:start position:0%
+uh is going to be one over one over the
+inside function times then the
+
+ align:start position:0%
+inside function times then the
+ 
+
+ align:start position:0%
+inside function times then the
+derivative of the inside function. So
+
+ align:start position:0%
+derivative of the inside function. So
+ 
+
+ align:start position:0%
+derivative of the inside function. So
+again what we do is we take the
+
+ align:start position:0%
+again what we do is we take the
+ 
+
+ align:start position:0%
+again what we do is we take the
+derivative of natural log which is 1
+
+ align:start position:0%
+derivative of natural log which is 1
+ 
+
+ align:start position:0%
+derivative of natural log which is 1
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+cossine x. So we take the derivative of
+
+ align:start position:0%
+cossine x. So we take the derivative of
+ 
+
+ align:start position:0%
+cossine x. So we take the derivative of
+the natural log function evaluate it at
+
+ align:start position:0%
+the natural log function evaluate it at
+ 
+
+ align:start position:0%
+the natural log function evaluate it at
+cosine x and then we take the derivative
+
+ align:start position:0%
+cosine x and then we take the derivative
+ 
+
+ align:start position:0%
+cosine x and then we take the derivative
+of the inside function which is the
+
+ align:start position:0%
+of the inside function which is the
+ 
+
+ align:start position:0%
+of the inside function which is the
+derivative of cosine x. So you get
+
+ align:start position:0%
+derivative of cosine x. So you get
+ 
+
+ align:start position:0%
+derivative of cosine x. So you get
+negative sinx.
+
+ align:start position:0%
+negative sinx.
+ 
+
+ align:start position:0%
+negative sinx.
+So you get this whole thing is negative
+
+ align:start position:0%
+So you get this whole thing is negative
+ 
+
+ align:start position:0%
+So you get this whole thing is negative
+of s over cosine. So this is negative
+
+ align:start position:0%
+of s over cosine. So this is negative
+ 
+
+ align:start position:0%
+of s over cosine. So this is negative
+tangent x.
+
+ align:start position:0%
+tangent x.
+ 
+
+ align:start position:0%
+tangent x.
+So the reason I in particular like this
+
+ align:start position:0%
+So the reason I in particular like this
+ 
+
+ align:start position:0%
+So the reason I in particular like this
+one is that we see oh if I wanted to
+
+ align:start position:0%
+one is that we see oh if I wanted to
+ 
+
+ align:start position:0%
+one is that we see oh if I wanted to
+find a function whose derivative was
+
+ align:start position:0%
+find a function whose derivative was
+ 
+
+ align:start position:0%
+find a function whose derivative was
+tangent x a candidate would be the
+
+ align:start position:0%
+tangent x a candidate would be the
+ 
+
+ align:start position:0%
+tangent x a candidate would be the
+negative of the natural log of cosine of
+
+ align:start position:0%
+negative of the natural log of cosine of
+ 
+
+ align:start position:0%
+negative of the natural log of cosine of
+x that in fact gives us a function whose
+
+ align:start position:0%
+x that in fact gives us a function whose
+ 
+
+ align:start position:0%
+x that in fact gives us a function whose
+derivative is tangent x. So it's
+
+ align:start position:0%
+derivative is tangent x. So it's
+ 
+
+ align:start position:0%
+derivative is tangent x. So it's
+interesting now we see that there are uh
+
+ align:start position:0%
+interesting now we see that there are uh
+ 
+
+ align:start position:0%
+interesting now we see that there are uh
+trigonometric functions that I can take
+
+ align:start position:0%
+trigonometric functions that I can take
+ 
+
+ align:start position:0%
+trigonometric functions that I can take
+a derivative of something that's not
+
+ align:start position:0%
+a derivative of something that's not
+ 
+
+ align:start position:0%
+a derivative of something that's not
+just trigonometric and get something
+
+ align:start position:0%
+just trigonometric and get something
+ 
+
+ align:start position:0%
+just trigonometric and get something
+that's trigonometric. So that's kind of
+
+ align:start position:0%
+that's trigonometric. So that's kind of
+ 
+
+ align:start position:0%
+that's trigonometric. So that's kind of
+a nice thing there. And then the last
+
+ align:start position:0%
+a nice thing there. And then the last
+ 
+
+ align:start position:0%
+a nice thing there. And then the last
+one, example three, I'll work out to the
+
+ align:start position:0%
+one, example three, I'll work out to the
+ 
+
+ align:start position:0%
+one, example three, I'll work out to the
+right. Uh there is a fast way and there
+
+ align:start position:0%
+right. Uh there is a fast way and there
+ 
+
+ align:start position:0%
+right. Uh there is a fast way and there
+is a slow way to do this. So I will do
+
+ align:start position:0%
+is a slow way to do this. So I will do
+ 
+
+ align:start position:0%
+is a slow way to do this. So I will do
+the slow way first and then I'll show
+
+ align:start position:0%
+the slow way first and then I'll show
+ 
+
+ align:start position:0%
+the slow way first and then I'll show
+you why it's good to kind of pull back
+
+ align:start position:0%
+you why it's good to kind of pull back
+ 
+
+ align:start position:0%
+you why it's good to kind of pull back
+from a problem sometimes. See how you
+
+ align:start position:0%
+from a problem sometimes. See how you
+ 
+
+ align:start position:0%
+from a problem sometimes. See how you
+can make it a lot simpler for yourself
+
+ align:start position:0%
+can make it a lot simpler for yourself
+ 
+
+ align:start position:0%
+can make it a lot simpler for yourself
+and then and then solve the problem. So
+
+ align:start position:0%
+and then and then solve the problem. So
+ 
+
+ align:start position:0%
+and then and then solve the problem. So
+I'll even write down this is the slow
+
+ align:start position:0%
+I'll even write down this is the slow
+ 
+
+ align:start position:0%
+I'll even write down this is the slow
+way.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, the slow way would be well I have
+
+ align:start position:0%
+Okay, the slow way would be well I have
+ 
+
+ align:start position:0%
+Okay, the slow way would be well I have
+um I have an a composition of functions
+
+ align:start position:0%
+um I have an a composition of functions
+ 
+
+ align:start position:0%
+um I have an a composition of functions
+here. I have natural log of something
+
+ align:start position:0%
+here. I have natural log of something
+ 
+
+ align:start position:0%
+here. I have natural log of something
+and then I have e to the something else,
+
+ align:start position:0%
+and then I have e to the something else,
+ 
+
+ align:start position:0%
+and then I have e to the something else,
+right? And then that function actually
+
+ align:start position:0%
+right? And then that function actually
+ 
+
+ align:start position:0%
+right? And then that function actually
+is not just e to the x. So I have some
+
+ align:start position:0%
+is not just e to the x. So I have some
+ 
+
+ align:start position:0%
+is not just e to the x. So I have some
+some things I have to I have to use the
+
+ align:start position:0%
+some things I have to I have to use the
+ 
+
+ align:start position:0%
+some things I have to I have to use the
+chain rule here. Okay, so let's use the
+
+ align:start position:0%
+chain rule here. Okay, so let's use the
+ 
+
+ align:start position:0%
+chain rule here. Okay, so let's use the
+chain rule. So I'll work from the
+
+ align:start position:0%
+chain rule. So I'll work from the
+ 
+
+ align:start position:0%
+chain rule. So I'll work from the
+outside in. So the derivative of the
+
+ align:start position:0%
+outside in. So the derivative of the
+ 
+
+ align:start position:0%
+outside in. So the derivative of the
+natural log function the derivative of
+
+ align:start position:0%
+natural log function the derivative of
+ 
+
+ align:start position:0%
+natural log function the derivative of
+natural log of x is 1 /x. So I take the
+
+ align:start position:0%
+natural log of x is 1 /x. So I take the
+ 
+
+ align:start position:0%
+natural log of x is 1 /x. So I take the
+derivative of natural log function. I
+
+ align:start position:0%
+derivative of natural log function. I
+ 
+
+ align:start position:0%
+derivative of natural log function. I
+evaluate it here. So the first part
+
+ align:start position:0%
+evaluate it here. So the first part
+ 
+
+ align:start position:0%
+evaluate it here. So the first part
+gives me 1 over e to x^2.
+
+ align:start position:0%
+gives me 1 over e to x^2.
+ 
+
+ align:start position:0%
+gives me 1 over e to x^2.
+And then I have to take the derivative
+
+ align:start position:0%
+And then I have to take the derivative
+ 
+
+ align:start position:0%
+And then I have to take the derivative
+of the next inside function which the
+
+ align:start position:0%
+of the next inside function which the
+ 
+
+ align:start position:0%
+of the next inside function which the
+next one inside after natural log is e
+
+ align:start position:0%
+next one inside after natural log is e
+ 
+
+ align:start position:0%
+next one inside after natural log is e
+to the x^2. And the derivative of that
+
+ align:start position:0%
+to the x^2. And the derivative of that
+ 
+
+ align:start position:0%
+to the x^2. And the derivative of that
+I'm going to do another chain rule. I
+
+ align:start position:0%
+I'm going to do another chain rule. I
+ 
+
+ align:start position:0%
+I'm going to do another chain rule. I
+get e to the x^2
+
+ align:start position:0%
+get e to the x^2
+ 
+
+ align:start position:0%
+get e to the x^2
+times the derivative of this x^2 which
+
+ align:start position:0%
+times the derivative of this x^2 which
+ 
+
+ align:start position:0%
+times the derivative of this x^2 which
+is 2x.
+
+ align:start position:0%
+is 2x.
+ 
+
+ align:start position:0%
+is 2x.
+Okay. So again this part is the
+
+ align:start position:0%
+Okay. So again this part is the
+ 
+
+ align:start position:0%
+Okay. So again this part is the
+derivative of the natural log evaluated
+
+ align:start position:0%
+derivative of the natural log evaluated
+ 
+
+ align:start position:0%
+derivative of the natural log evaluated
+at e x^2. This part is the derivative of
+
+ align:start position:0%
+at e x^2. This part is the derivative of
+ 
+
+ align:start position:0%
+at e x^2. This part is the derivative of
+e x^2. This one comes just from the
+
+ align:start position:0%
+e x^2. This one comes just from the
+ 
+
+ align:start position:0%
+e x^2. This one comes just from the
+derivative of e to the x is e to the x
+
+ align:start position:0%
+derivative of e to the x is e to the x
+ 
+
+ align:start position:0%
+derivative of e to the x is e to the x
+and then so I evaluated at x^2 and then
+
+ align:start position:0%
+and then so I evaluated at x^2 and then
+ 
+
+ align:start position:0%
+and then so I evaluated at x^2 and then
+this is the derivative of the x squ
+
+ align:start position:0%
+this is the derivative of the x squ
+ 
+
+ align:start position:0%
+this is the derivative of the x squ
+part. So I end up with product of three
+
+ align:start position:0%
+part. So I end up with product of three
+ 
+
+ align:start position:0%
+part. So I end up with product of three
+functions because I have a composition
+
+ align:start position:0%
+functions because I have a composition
+ 
+
+ align:start position:0%
+functions because I have a composition
+of three functions. So I have to do the
+
+ align:start position:0%
+of three functions. So I have to do the
+ 
+
+ align:start position:0%
+of three functions. So I have to do the
+chain rule with three different pieces
+
+ align:start position:0%
+chain rule with three different pieces
+ 
+
+ align:start position:0%
+chain rule with three different pieces
+basically. So, but this simplifies,
+
+ align:start position:0%
+basically. So, but this simplifies,
+ 
+
+ align:start position:0%
+basically. So, but this simplifies,
+right? EX^2 / EX2 is 1. So, I get 2x.
+
+ align:start position:0%
+right? EX^2 / EX2 is 1. So, I get 2x.
+ 
+
+ align:start position:0%
+right? EX^2 / EX2 is 1. So, I get 2x.
+Okay. So, what's the fast way? That's
+
+ align:start position:0%
+Okay. So, what's the fast way? That's
+ 
+
+ align:start position:0%
+Okay. So, what's the fast way? That's
+that's our answer. 2x. But what's the
+
+ align:start position:0%
+that's our answer. 2x. But what's the
+ 
+
+ align:start position:0%
+that's our answer. 2x. But what's the
+fast way?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, the fast way is to recognize that
+
+ align:start position:0%
+Well, the fast way is to recognize that
+ 
+
+ align:start position:0%
+Well, the fast way is to recognize that
+natural log of e to x^2. Let me erase
+
+ align:start position:0%
+natural log of e to x^2. Let me erase
+ 
+
+ align:start position:0%
+natural log of e to x^2. Let me erase
+the y here. e to the x^2 is equal to
+
+ align:start position:0%
+the y here. e to the x^2 is equal to
+ 
+
+ align:start position:0%
+the y here. e to the x^2 is equal to
+x^2.
+
+ align:start position:0%
+x^2.
+ 
+
+ align:start position:0%
+x^2.
+Okay. Why is that? That's because
+
+ align:start position:0%
+Okay. Why is that? That's because
+ 
+
+ align:start position:0%
+Okay. Why is that? That's because
+natural log function is the inverse of
+
+ align:start position:0%
+natural log function is the inverse of
+ 
+
+ align:start position:0%
+natural log function is the inverse of
+the exponential function with base e,
+
+ align:start position:0%
+the exponential function with base e,
+ 
+
+ align:start position:0%
+the exponential function with base e,
+right? This is something you've you've
+
+ align:start position:0%
+right? This is something you've you've
+ 
+
+ align:start position:0%
+right? This is something you've you've
+talked about before. So this means that
+
+ align:start position:0%
+talked about before. So this means that
+ 
+
+ align:start position:0%
+talked about before. So this means that
+if I take natural log of e to anything
+
+ align:start position:0%
+if I take natural log of e to anything
+ 
+
+ align:start position:0%
+if I take natural log of e to anything
+here, I'm going to get I'm going to get
+
+ align:start position:0%
+here, I'm going to get I'm going to get
+ 
+
+ align:start position:0%
+here, I'm going to get I'm going to get
+that thing right there, whatever that
+
+ align:start position:0%
+that thing right there, whatever that
+ 
+
+ align:start position:0%
+that thing right there, whatever that
+function is. So natural log of e to the
+
+ align:start position:0%
+function is. So natural log of e to the
+ 
+
+ align:start position:0%
+function is. So natural log of e to the
+x^2 is x^2. Okay? If if you don't like
+
+ align:start position:0%
+x^2 is x^2. Okay? If if you don't like
+ 
+
+ align:start position:0%
+x^2 is x^2. Okay? If if you don't like
+to talk about it that way, if you don't
+
+ align:start position:0%
+to talk about it that way, if you don't
+ 
+
+ align:start position:0%
+to talk about it that way, if you don't
+like inverse functions, uh you can use
+
+ align:start position:0%
+like inverse functions, uh you can use
+ 
+
+ align:start position:0%
+like inverse functions, uh you can use
+one of the rules of logarithms which
+
+ align:start position:0%
+one of the rules of logarithms which
+ 
+
+ align:start position:0%
+one of the rules of logarithms which
+says that this expression is equal to
+
+ align:start position:0%
+says that this expression is equal to
+ 
+
+ align:start position:0%
+says that this expression is equal to
+x^2 time natural log of e.
+
+ align:start position:0%
+x^2 time natural log of e.
+ 
+
+ align:start position:0%
+x^2 time natural log of e.
+That's another way to think about this
+
+ align:start position:0%
+That's another way to think about this
+ 
+
+ align:start position:0%
+That's another way to think about this
+problem. And then you should remember
+
+ align:start position:0%
+problem. And then you should remember
+ 
+
+ align:start position:0%
+problem. And then you should remember
+that natural log of e is equal to 1. So
+
+ align:start position:0%
+that natural log of e is equal to 1. So
+ 
+
+ align:start position:0%
+that natural log of e is equal to 1. So
+at some point you have to uh you have to
+
+ align:start position:0%
+at some point you have to uh you have to
+ 
+
+ align:start position:0%
+at some point you have to uh you have to
+know uh a little bit about logs and
+
+ align:start position:0%
+know uh a little bit about logs and
+ 
+
+ align:start position:0%
+know uh a little bit about logs and
+exponentials. But the thing to recognize
+
+ align:start position:0%
+exponentials. But the thing to recognize
+ 
+
+ align:start position:0%
+exponentials. But the thing to recognize
+is that h of x is just a fancy way of
+
+ align:start position:0%
+is that h of x is just a fancy way of
+ 
+
+ align:start position:0%
+is that h of x is just a fancy way of
+writing x^2. And so the derivative of
+
+ align:start position:0%
+writing x^2. And so the derivative of
+ 
+
+ align:start position:0%
+writing x^2. And so the derivative of
+x^2
+
+ align:start position:0%
+x^2
+ 
+
+ align:start position:0%
+x^2
+is 2x. So sometimes it's better to see
+
+ align:start position:0%
+is 2x. So sometimes it's better to see
+ 
+
+ align:start position:0%
+is 2x. So sometimes it's better to see
+what can what can be done to make the
+
+ align:start position:0%
+what can what can be done to make the
+ 
+
+ align:start position:0%
+what can what can be done to make the
+problem a little easier. But that is
+
+ align:start position:0%
+problem a little easier. But that is
+ 
+
+ align:start position:0%
+problem a little easier. But that is
+where we will stop with these.
\ No newline at end of file
diff --git a/xZ72LPLHVSY.txt b/xZ72LPLHVSY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d0484d8a2d647abaf77cccb876db1fd133efb3d3
--- /dev/null
+++ b/xZ72LPLHVSY.txt
@@ -0,0 +1,7715 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT opencourseware continue to
+
+ align:start position:0%
+will help MIT opencourseware continue to
+ 
+
+ align:start position:0%
+will help MIT opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is where we ended last time we had
+
+ align:start position:0%
+this is where we ended last time we had
+ 
+
+ align:start position:0%
+this is where we ended last time we had
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+talked about these major types of
+
+ align:start position:0%
+talked about these major types of
+ 
+
+ align:start position:0%
+talked about these major types of
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+of neocortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I've named them according to how I
+
+ align:start position:0%
+and I've named them according to how I
+ 
+
+ align:start position:0%
+and I've named them according to how I
+think it evolved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+location sense object sense
+
+ align:start position:0%
+location sense object sense
+ 
+
+ align:start position:0%
+location sense object sense
+functions of the prefrontally
+
+ align:start position:0%
+functions of the prefrontally
+ 
+
+ align:start position:0%
+functions of the prefrontally
+laborations of motor cortex for planning
+
+ align:start position:0%
+laborations of motor cortex for planning
+ 
+
+ align:start position:0%
+laborations of motor cortex for planning
+and I'm going to go through that a
+
+ align:start position:0%
+and I'm going to go through that a
+ 
+
+ align:start position:0%
+and I'm going to go through that a
+little more and that's basically what
+
+ align:start position:0%
+little more and that's basically what
+ 
+
+ align:start position:0%
+little more and that's basically what
+these questions are about
+
+ align:start position:0%
+these questions are about
+ 
+
+ align:start position:0%
+these questions are about
+we had talked about the campus system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I want you to think about how that
+
+ align:start position:0%
+um I want you to think about how that
+ 
+
+ align:start position:0%
+um I want you to think about how that
+facilitates the ability to anticipate to
+
+ align:start position:0%
+facilitates the ability to anticipate to
+ 
+
+ align:start position:0%
+facilitates the ability to anticipate to
+stimuli that you're about to encounter
+
+ align:start position:0%
+stimuli that you're about to encounter
+ 
+
+ align:start position:0%
+stimuli that you're about to encounter
+any animal is going to encounter how
+
+ align:start position:0%
+any animal is going to encounter how
+ 
+
+ align:start position:0%
+any animal is going to encounter how
+does that location information that is
+
+ align:start position:0%
+does that location information that is
+ 
+
+ align:start position:0%
+does that location information that is
+handled by the campus remember
+
+ align:start position:0%
+handled by the campus remember
+ 
+
+ align:start position:0%
+handled by the campus remember
+how it evolved
+
+ align:start position:0%
+how it evolved
+ 
+
+ align:start position:0%
+how it evolved
+to know where the animal is in the local
+
+ align:start position:0%
+to know where the animal is in the local
+ 
+
+ align:start position:0%
+to know where the animal is in the local
+environment and eventually in many
+
+ align:start position:0%
+environment and eventually in many
+ 
+
+ align:start position:0%
+environment and eventually in many
+different local environments and we
+
+ align:start position:0%
+different local environments and we
+ 
+
+ align:start position:0%
+different local environments and we
+remember them
+
+ align:start position:0%
+remember them
+ 
+
+ align:start position:0%
+remember them
+our prior to Cortex remembers them
+
+ align:start position:0%
+our prior to Cortex remembers them
+ 
+
+ align:start position:0%
+our prior to Cortex remembers them
+so the hippocampus doesn't have to
+
+ align:start position:0%
+so the hippocampus doesn't have to
+ 
+
+ align:start position:0%
+so the hippocampus doesn't have to
+totally relearn it every time
+
+ align:start position:0%
+totally relearn it every time
+ 
+
+ align:start position:0%
+totally relearn it every time
+you go to a different area but because
+
+ align:start position:0%
+you go to a different area but because
+ 
+
+ align:start position:0%
+you go to a different area but because
+every time you turn your head the way
+
+ align:start position:0%
+every time you turn your head the way
+ 
+
+ align:start position:0%
+every time you turn your head the way
+that system works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this information
+
+ align:start position:0%
+this information
+ 
+
+ align:start position:0%
+this information
+is sent from hippocampus
+
+ align:start position:0%
+is sent from hippocampus
+ 
+
+ align:start position:0%
+is sent from hippocampus
+back to the mammary buddies that means
+
+ align:start position:0%
+back to the mammary buddies that means
+ 
+
+ align:start position:0%
+back to the mammary buddies that means
+the hippocampus is getting that
+
+ align:start position:0%
+the hippocampus is getting that
+ 
+
+ align:start position:0%
+the hippocampus is getting that
+information based on where
+
+ align:start position:0%
+information based on where
+ 
+
+ align:start position:0%
+information based on where
+the direction we're looking so it can
+
+ align:start position:0%
+the direction we're looking so it can
+ 
+
+ align:start position:0%
+the direction we're looking so it can
+call up all the relevant memories
+
+ align:start position:0%
+call up all the relevant memories
+ 
+
+ align:start position:0%
+call up all the relevant memories
+the things in front of us
+
+ align:start position:0%
+the things in front of us
+ 
+
+ align:start position:0%
+the things in front of us
+so it's a major factor in what how the
+
+ align:start position:0%
+so it's a major factor in what how the
+ 
+
+ align:start position:0%
+so it's a major factor in what how the
+motivations make us decide to go in One
+
+ align:start position:0%
+motivations make us decide to go in One
+ 
+
+ align:start position:0%
+motivations make us decide to go in One
+Direction or another or in an animal I
+
+ align:start position:0%
+Direction or another or in an animal I
+ 
+
+ align:start position:0%
+Direction or another or in an animal I
+shouldn't say humans primarily but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's for navigating the world and that
+
+ align:start position:0%
+it's for navigating the world and that
+ 
+
+ align:start position:0%
+it's for navigating the world and that
+we know that motivation is a major
+
+ align:start position:0%
+we know that motivation is a major
+ 
+
+ align:start position:0%
+we know that motivation is a major
+factor and people haven't considered
+
+ align:start position:0%
+factor and people haven't considered
+ 
+
+ align:start position:0%
+factor and people haven't considered
+enough you know the role of the
+
+ align:start position:0%
+enough you know the role of the
+ 
+
+ align:start position:0%
+enough you know the role of the
+hippocampus and motivation
+
+ align:start position:0%
+hippocampus and motivation
+ 
+
+ align:start position:0%
+hippocampus and motivation
+and why this whole system for memory
+
+ align:start position:0%
+and why this whole system for memory
+ 
+
+ align:start position:0%
+and why this whole system for memory
+long-term memory evolved within hit the
+
+ align:start position:0%
+long-term memory evolved within hit the
+ 
+
+ align:start position:0%
+long-term memory evolved within hit the
+campus that within the limbic system
+
+ align:start position:0%
+campus that within the limbic system
+ 
+
+ align:start position:0%
+campus that within the limbic system
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+but anyway uh
+
+ align:start position:0%
+but anyway uh
+ 
+
+ align:start position:0%
+but anyway uh
+and you need to contrast that with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the kind of anticipatory activity that
+
+ align:start position:0%
+the kind of anticipatory activity that
+ 
+
+ align:start position:0%
+the kind of anticipatory activity that
+these parietal and temples association
+
+ align:start position:0%
+these parietal and temples association
+ 
+
+ align:start position:0%
+these parietal and temples association
+areas are concern with so we'll be
+
+ align:start position:0%
+areas are concern with so we'll be
+ 
+
+ align:start position:0%
+areas are concern with so we'll be
+talking more about that
+
+ align:start position:0%
+talking more about that
+ 
+
+ align:start position:0%
+talking more about that
+so this is a
+
+ align:start position:0%
+so this is a
+ 
+
+ align:start position:0%
+so this is a
+it's all in the book and it's just a
+
+ align:start position:0%
+it's all in the book and it's just a
+ 
+
+ align:start position:0%
+it's all in the book and it's just a
+different way of looking at it in these
+
+ align:start position:0%
+different way of looking at it in these
+ 
+
+ align:start position:0%
+different way of looking at it in these
+slides where I summarize these major
+
+ align:start position:0%
+slides where I summarize these major
+ 
+
+ align:start position:0%
+slides where I summarize these major
+points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+made I think anticipation ability to
+
+ align:start position:0%
+made I think anticipation ability to
+ 
+
+ align:start position:0%
+made I think anticipation ability to
+anticipate
+
+ align:start position:0%
+anticipate
+ 
+
+ align:start position:0%
+anticipate
+stimuli ability to plan movements and
+
+ align:start position:0%
+stimuli ability to plan movements and
+ 
+
+ align:start position:0%
+stimuli ability to plan movements and
+other kind of anticipation
+
+ align:start position:0%
+other kind of anticipation
+ 
+
+ align:start position:0%
+other kind of anticipation
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or major Innovations of the cortex
+
+ align:start position:0%
+or major Innovations of the cortex
+ 
+
+ align:start position:0%
+or major Innovations of the cortex
+it's not what the tectum does
+
+ align:start position:0%
+it's not what the tectum does
+ 
+
+ align:start position:0%
+it's not what the tectum does
+it's not what subcortical systems do
+
+ align:start position:0%
+it's not what subcortical systems do
+ 
+
+ align:start position:0%
+it's not what subcortical systems do
+this thankful aspect is so important for
+
+ align:start position:0%
+this thankful aspect is so important for
+ 
+
+ align:start position:0%
+this thankful aspect is so important for
+new quotas of course planning you know
+
+ align:start position:0%
+new quotas of course planning you know
+ 
+
+ align:start position:0%
+new quotas of course planning you know
+how important we frontal
+
+ align:start position:0%
+how important we frontal
+ 
+
+ align:start position:0%
+how important we frontal
+areas are
+
+ align:start position:0%
+areas are
+ 
+
+ align:start position:0%
+areas are
+they appear to be evolved well you could
+
+ align:start position:0%
+they appear to be evolved well you could
+ 
+
+ align:start position:0%
+they appear to be evolved well you could
+say that in that associate the
+
+ align:start position:0%
+say that in that associate the
+ 
+
+ align:start position:0%
+say that in that associate the
+multimodal original multimodal cortex
+
+ align:start position:0%
+multimodal original multimodal cortex
+ 
+
+ align:start position:0%
+multimodal original multimodal cortex
+the motor cortex evolve very early
+
+ align:start position:0%
+the motor cortex evolve very early
+ 
+
+ align:start position:0%
+the motor cortex evolve very early
+initially as much sense Justice in
+
+ align:start position:0%
+initially as much sense Justice in
+ 
+
+ align:start position:0%
+initially as much sense Justice in
+another Century here but once it became
+
+ align:start position:0%
+another Century here but once it became
+ 
+
+ align:start position:0%
+another Century here but once it became
+specialized for
+
+ align:start position:0%
+specialized for
+ 
+
+ align:start position:0%
+specialized for
+control of movement
+
+ align:start position:0%
+control of movement
+ 
+
+ align:start position:0%
+control of movement
+then the areas near it became involved
+
+ align:start position:0%
+then the areas near it became involved
+ 
+
+ align:start position:0%
+then the areas near it became involved
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+anticipating movement namely planning it
+
+ align:start position:0%
+anticipating movement namely planning it
+ 
+
+ align:start position:0%
+anticipating movement namely planning it
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is uh
+
+ align:start position:0%
+this is uh
+ 
+
+ align:start position:0%
+this is uh
+mostly Theory but I mentioned here
+
+ align:start position:0%
+mostly Theory but I mentioned here
+ 
+
+ align:start position:0%
+mostly Theory but I mentioned here
+support for it the laboratory studies of
+
+ align:start position:0%
+support for it the laboratory studies of
+ 
+
+ align:start position:0%
+support for it the laboratory studies of
+suck love in Moscow back in the 60s he
+
+ align:start position:0%
+suck love in Moscow back in the 60s he
+ 
+
+ align:start position:0%
+suck love in Moscow back in the 60s he
+made did extensive studies of reactions
+
+ align:start position:0%
+made did extensive studies of reactions
+ 
+
+ align:start position:0%
+made did extensive studies of reactions
+of humans to novelty and he studied
+
+ align:start position:0%
+of humans to novelty and he studied
+ 
+
+ align:start position:0%
+of humans to novelty and he studied
+animals as well
+
+ align:start position:0%
+animals as well
+ 
+
+ align:start position:0%
+animals as well
+and how any kind of unexpected input
+
+ align:start position:0%
+and how any kind of unexpected input
+ 
+
+ align:start position:0%
+and how any kind of unexpected input
+even if it was an unexpected lack of
+
+ align:start position:0%
+even if it was an unexpected lack of
+ 
+
+ align:start position:0%
+even if it was an unexpected lack of
+input it could cause an arousal response
+
+ align:start position:0%
+input it could cause an arousal response
+ 
+
+ align:start position:0%
+input it could cause an arousal response
+that alter the electrical activity of
+
+ align:start position:0%
+that alter the electrical activity of
+ 
+
+ align:start position:0%
+that alter the electrical activity of
+the neocortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when the inputs become familiar then
+
+ align:start position:0%
+and when the inputs become familiar then
+ 
+
+ align:start position:0%
+and when the inputs become familiar then
+you don't get those arousal effects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he CLA he in theoretical terms he
+
+ align:start position:0%
+so he CLA he in theoretical terms he
+ 
+
+ align:start position:0%
+so he CLA he in theoretical terms he
+said this these the
+
+ align:start position:0%
+said this these the
+ 
+
+ align:start position:0%
+said this these the
+there was a central model this is how
+
+ align:start position:0%
+there was a central model this is how
+ 
+
+ align:start position:0%
+there was a central model this is how
+the brain is simulating what's going on
+
+ align:start position:0%
+the brain is simulating what's going on
+ 
+
+ align:start position:0%
+the brain is simulating what's going on
+when you're dreaming all you're doing is
+
+ align:start position:0%
+when you're dreaming all you're doing is
+ 
+
+ align:start position:0%
+when you're dreaming all you're doing is
+using that system
+
+ align:start position:0%
+using that system
+ 
+
+ align:start position:0%
+using that system
+your brain is totally capable of
+
+ align:start position:0%
+your brain is totally capable of
+ 
+
+ align:start position:0%
+your brain is totally capable of
+simulating the environment in incredible
+
+ align:start position:0%
+simulating the environment in incredible
+ 
+
+ align:start position:0%
+simulating the environment in incredible
+detail have you ever had
+
+ align:start position:0%
+detail have you ever had
+ 
+
+ align:start position:0%
+detail have you ever had
+hypnagogic imagery in or visit dreaming
+
+ align:start position:0%
+hypnagogic imagery in or visit dreaming
+ 
+
+ align:start position:0%
+hypnagogic imagery in or visit dreaming
+where you actually
+
+ align:start position:0%
+where you actually
+ 
+
+ align:start position:0%
+where you actually
+don't know for sure that you're dreaming
+
+ align:start position:0%
+don't know for sure that you're dreaming
+ 
+
+ align:start position:0%
+don't know for sure that you're dreaming
+you know you see cartoons of people
+
+ align:start position:0%
+you know you see cartoons of people
+ 
+
+ align:start position:0%
+you know you see cartoons of people
+pinching themselves to see if they're
+
+ align:start position:0%
+pinching themselves to see if they're
+ 
+
+ align:start position:0%
+pinching themselves to see if they're
+asleep have you ever had such vivid
+
+ align:start position:0%
+asleep have you ever had such vivid
+ 
+
+ align:start position:0%
+asleep have you ever had such vivid
+dreams that you couldn't tell
+
+ align:start position:0%
+dreams that you couldn't tell
+ 
+
+ align:start position:0%
+dreams that you couldn't tell
+does everybody had some people don't or
+
+ align:start position:0%
+does everybody had some people don't or
+ 
+
+ align:start position:0%
+does everybody had some people don't or
+at least they don't remember but I've
+
+ align:start position:0%
+at least they don't remember but I've
+ 
+
+ align:start position:0%
+at least they don't remember but I've
+had them and they're really not very
+
+ align:start position:0%
+had them and they're really not very
+ 
+
+ align:start position:0%
+had them and they're really not very
+many and only when I was younger
+
+ align:start position:0%
+many and only when I was younger
+ 
+
+ align:start position:0%
+many and only when I was younger
+most of the time I don't have difficulty
+
+ align:start position:0%
+most of the time I don't have difficulty
+ 
+
+ align:start position:0%
+most of the time I don't have difficulty
+knowing that I'm dreaming
+
+ align:start position:0%
+knowing that I'm dreaming
+ 
+
+ align:start position:0%
+knowing that I'm dreaming
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dreaming that you
+
+ align:start position:0%
+dreaming that you
+ 
+
+ align:start position:0%
+dreaming that you
+have supported by me
+
+ align:start position:0%
+have supported by me
+ 
+
+ align:start position:0%
+have supported by me
+yeah that's an anxiety dream but in
+
+ align:start position:0%
+yeah that's an anxiety dream but in
+ 
+
+ align:start position:0%
+yeah that's an anxiety dream but in
+hypnagogic imagery it's a good question
+
+ align:start position:0%
+hypnagogic imagery it's a good question
+ 
+
+ align:start position:0%
+hypnagogic imagery it's a good question
+I don't know we should look there is a
+
+ align:start position:0%
+I don't know we should look there is a
+ 
+
+ align:start position:0%
+I don't know we should look there is a
+literature on it you can read about it
+
+ align:start position:0%
+literature on it you can read about it
+ 
+
+ align:start position:0%
+literature on it you can read about it
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+do all the senses come to play
+
+ align:start position:0%
+do all the senses come to play
+ 
+
+ align:start position:0%
+do all the senses come to play
+you know I remember when I had an
+
+ align:start position:0%
+you know I remember when I had an
+ 
+
+ align:start position:0%
+you know I remember when I had an
+auditory visual it's not a sensory they
+
+ align:start position:0%
+auditory visual it's not a sensory they
+ 
+
+ align:start position:0%
+auditory visual it's not a sensory they
+were all there I cannot remember any
+
+ align:start position:0%
+were all there I cannot remember any
+ 
+
+ align:start position:0%
+were all there I cannot remember any
+olfactory imagery
+
+ align:start position:0%
+olfactory imagery
+ 
+
+ align:start position:0%
+olfactory imagery
+I'm not saying it's not possible in some
+
+ align:start position:0%
+I'm not saying it's not possible in some
+ 
+
+ align:start position:0%
+I'm not saying it's not possible in some
+people but
+
+ align:start position:0%
+people but
+ 
+
+ align:start position:0%
+people but
+often it's true that some of the
+
+ align:start position:0%
+often it's true that some of the
+ 
+
+ align:start position:0%
+often it's true that some of the
+modalities are missing
+
+ align:start position:0%
+modalities are missing
+ 
+
+ align:start position:0%
+modalities are missing
+and what you asked about emotion
+
+ align:start position:0%
+and what you asked about emotion
+ 
+
+ align:start position:0%
+and what you asked about emotion
+that's a major issue you know in that
+
+ align:start position:0%
+that's a major issue you know in that
+ 
+
+ align:start position:0%
+that's a major issue you know in that
+kind of imagery
+
+ align:start position:0%
+kind of imagery
+ 
+
+ align:start position:0%
+kind of imagery
+because of it involves these
+
+ align:start position:0%
+because of it involves these
+ 
+
+ align:start position:0%
+because of it involves these
+association areas posterior cortex
+
+ align:start position:0%
+association areas posterior cortex
+ 
+
+ align:start position:0%
+association areas posterior cortex
+Generations
+
+ align:start position:0%
+Generations
+ 
+
+ align:start position:0%
+Generations
+images of the world us through the
+
+ align:start position:0%
+images of the world us through the
+ 
+
+ align:start position:0%
+images of the world us through the
+parietal primarily
+
+ align:start position:0%
+parietal primarily
+ 
+
+ align:start position:0%
+parietal primarily
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the connections to emotion could be
+
+ align:start position:0%
+the connections to emotion could be
+ 
+
+ align:start position:0%
+the connections to emotion could be
+missing and it could still generate
+
+ align:start position:0%
+missing and it could still generate
+ 
+
+ align:start position:0%
+missing and it could still generate
+these images
+
+ align:start position:0%
+these images
+ 
+
+ align:start position:0%
+these images
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I have another one I'll I'll do the
+
+ align:start position:0%
+if I have another one I'll I'll do the
+ 
+
+ align:start position:0%
+if I have another one I'll I'll do the
+investigation
+
+ align:start position:0%
+investigation
+ 
+
+ align:start position:0%
+investigation
+anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that same model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can control endogenous generation of
+
+ align:start position:0%
+can control endogenous generation of
+ 
+
+ align:start position:0%
+can control endogenous generation of
+actions this is the way the frontal
+
+ align:start position:0%
+actions this is the way the frontal
+ 
+
+ align:start position:0%
+actions this is the way the frontal
+areas in the posterior areas that do
+
+ align:start position:0%
+areas in the posterior areas that do
+ 
+
+ align:start position:0%
+areas in the posterior areas that do
+this kind of simulation of the world or
+
+ align:start position:0%
+this kind of simulation of the world or
+ 
+
+ align:start position:0%
+this kind of simulation of the world or
+connect
+
+ align:start position:0%
+connect
+ 
+
+ align:start position:0%
+connect
+you can use that model to plan your
+
+ align:start position:0%
+you can use that model to plan your
+ 
+
+ align:start position:0%
+you can use that model to plan your
+actions and we do it all the time
+
+ align:start position:0%
+actions and we do it all the time
+ 
+
+ align:start position:0%
+actions and we do it all the time
+it's a view that became unpopular for a
+
+ align:start position:0%
+it's a view that became unpopular for a
+ 
+
+ align:start position:0%
+it's a view that became unpopular for a
+while although back in the 60s
+
+ align:start position:0%
+while although back in the 60s
+ 
+
+ align:start position:0%
+while although back in the 60s
+Makai developed it
+
+ align:start position:0%
+Makai developed it
+ 
+
+ align:start position:0%
+Makai developed it
+but more recently it's been
+
+ align:start position:0%
+but more recently it's been
+ 
+
+ align:start position:0%
+but more recently it's been
+people have come back to it and they've
+
+ align:start position:0%
+people have come back to it and they've
+ 
+
+ align:start position:0%
+people have come back to it and they've
+updated it there was a whole issue of
+
+ align:start position:0%
+updated it there was a whole issue of
+ 
+
+ align:start position:0%
+updated it there was a whole issue of
+I think the journal several contracts
+
+ align:start position:0%
+I think the journal several contracts
+ 
+
+ align:start position:0%
+I think the journal several contracts
+one of these major journals that talks
+
+ align:start position:0%
+one of these major journals that talks
+ 
+
+ align:start position:0%
+one of these major journals that talks
+about cortex so
+
+ align:start position:0%
+about cortex so
+ 
+
+ align:start position:0%
+about cortex so
+had a whole issue on this
+
+ align:start position:0%
+had a whole issue on this
+ 
+
+ align:start position:0%
+had a whole issue on this
+I think I mentioned it and look I'm
+
+ align:start position:0%
+I think I mentioned it and look I'm
+ 
+
+ align:start position:0%
+I think I mentioned it and look I'm
+remembering right
+
+ align:start position:0%
+remembering right
+ 
+
+ align:start position:0%
+remembering right
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+so now we've not mentioned throughout
+
+ align:start position:0%
+so now we've not mentioned throughout
+ 
+
+ align:start position:0%
+so now we've not mentioned throughout
+them in this actually both this
+
+ align:start position:0%
+them in this actually both this
+ 
+
+ align:start position:0%
+them in this actually both this
+throughout them and the cortex expanded
+
+ align:start position:0%
+throughout them and the cortex expanded
+ 
+
+ align:start position:0%
+throughout them and the cortex expanded
+in evolution including recent evolution
+
+ align:start position:0%
+in evolution including recent evolution
+ 
+
+ align:start position:0%
+in evolution including recent evolution
+they can operate relatively
+
+ align:start position:0%
+they can operate relatively
+ 
+
+ align:start position:0%
+they can operate relatively
+independently and that's because
+
+ align:start position:0%
+independently and that's because
+ 
+
+ align:start position:0%
+independently and that's because
+they don't operate independently in
+
+ align:start position:0%
+they don't operate independently in
+ 
+
+ align:start position:0%
+they don't operate independently in
+humans at all
+
+ align:start position:0%
+humans at all
+ 
+
+ align:start position:0%
+humans at all
+but in animals it's quite possible for
+
+ align:start position:0%
+but in animals it's quite possible for
+ 
+
+ align:start position:0%
+but in animals it's quite possible for
+them to operate independently you can
+
+ align:start position:0%
+them to operate independently you can
+ 
+
+ align:start position:0%
+them to operate independently you can
+have an animal
+
+ align:start position:0%
+have an animal
+ 
+
+ align:start position:0%
+have an animal
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+where much of the cortex is rendered
+
+ align:start position:0%
+where much of the cortex is rendered
+ 
+
+ align:start position:0%
+where much of the cortex is rendered
+non-functional and he can still use his
+
+ align:start position:0%
+non-functional and he can still use his
+ 
+
+ align:start position:0%
+non-functional and he can still use his
+striatal system why is that
+
+ align:start position:0%
+striatal system why is that
+ 
+
+ align:start position:0%
+striatal system why is that
+how is the striatoman getting its inputs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where does it get its input so they
+
+ align:start position:0%
+where does it get its input so they
+ 
+
+ align:start position:0%
+where does it get its input so they
+don't come from the cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember it they come from the older
+
+ align:start position:0%
+remember it they come from the older
+ 
+
+ align:start position:0%
+remember it they come from the older
+parts of the thalamus
+
+ align:start position:0%
+parts of the thalamus
+ 
+
+ align:start position:0%
+parts of the thalamus
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the nuclei we call the intralaminer in
+
+ align:start position:0%
+the nuclei we call the intralaminer in
+ 
+
+ align:start position:0%
+the nuclei we call the intralaminer in
+midline nuclei they're mostly getting
+
+ align:start position:0%
+midline nuclei they're mostly getting
+ 
+
+ align:start position:0%
+midline nuclei they're mostly getting
+multimodal input
+
+ align:start position:0%
+multimodal input
+ 
+
+ align:start position:0%
+multimodal input
+but some of those nuclei are more
+
+ align:start position:0%
+but some of those nuclei are more
+ 
+
+ align:start position:0%
+but some of those nuclei are more
+dominated by
+
+ align:start position:0%
+dominated by
+ 
+
+ align:start position:0%
+dominated by
+the visual areas of the tectum they're
+
+ align:start position:0%
+the visual areas of the tectum they're
+ 
+
+ align:start position:0%
+the visual areas of the tectum they're
+getting a lot of input from the app
+
+ align:start position:0%
+getting a lot of input from the app
+ 
+
+ align:start position:0%
+getting a lot of input from the app
+detecting
+
+ align:start position:0%
+detecting
+ 
+
+ align:start position:0%
+detecting
+the somatosensory system Pathways don't
+
+ align:start position:0%
+the somatosensory system Pathways don't
+ 
+
+ align:start position:0%
+the somatosensory system Pathways don't
+all come through detectives some of them
+
+ align:start position:0%
+all come through detectives some of them
+ 
+
+ align:start position:0%
+all come through detectives some of them
+come directly from the spinal thalamic
+
+ align:start position:0%
+come directly from the spinal thalamic
+ 
+
+ align:start position:0%
+come directly from the spinal thalamic
+trait
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and auditory inputs also reach those and
+
+ align:start position:0%
+and auditory inputs also reach those and
+ 
+
+ align:start position:0%
+and auditory inputs also reach those and
+in addition to the interlaminary midline
+
+ align:start position:0%
+in addition to the interlaminary midline
+ 
+
+ align:start position:0%
+in addition to the interlaminary midline
+nuclei there are
+
+ align:start position:0%
+nuclei there are
+ 
+
+ align:start position:0%
+nuclei there are
+what appear to be older
+
+ align:start position:0%
+what appear to be older
+ 
+
+ align:start position:0%
+what appear to be older
+parts of the thalamus and the posterior
+
+ align:start position:0%
+parts of the thalamus and the posterior
+ 
+
+ align:start position:0%
+parts of the thalamus and the posterior
+Thalamus was a group of nuclei sort of
+
+ align:start position:0%
+Thalamus was a group of nuclei sort of
+ 
+
+ align:start position:0%
+Thalamus was a group of nuclei sort of
+in the interstices between the visuals
+
+ align:start position:0%
+in the interstices between the visuals
+ 
+
+ align:start position:0%
+in the interstices between the visuals
+meta sensory and auditory the main
+
+ align:start position:0%
+meta sensory and auditory the main
+ 
+
+ align:start position:0%
+meta sensory and auditory the main
+nuclei we consider to be involved in
+
+ align:start position:0%
+nuclei we consider to be involved in
+ 
+
+ align:start position:0%
+nuclei we consider to be involved in
+those three senses
+
+ align:start position:0%
+those three senses
+ 
+
+ align:start position:0%
+those three senses
+but outside those nuclei there's the
+
+ align:start position:0%
+but outside those nuclei there's the
+ 
+
+ align:start position:0%
+but outside those nuclei there's the
+posterior group of nuclei it's basically
+
+ align:start position:0%
+posterior group of nuclei it's basically
+ 
+
+ align:start position:0%
+posterior group of nuclei it's basically
+multimodal cells
+
+ align:start position:0%
+multimodal cells
+ 
+
+ align:start position:0%
+multimodal cells
+that project to multimodal cortical
+
+ align:start position:0%
+that project to multimodal cortical
+ 
+
+ align:start position:0%
+that project to multimodal cortical
+areas
+
+ align:start position:0%
+areas
+ 
+
+ align:start position:0%
+areas
+okay well we'll be talking more about
+
+ align:start position:0%
+okay well we'll be talking more about
+ 
+
+ align:start position:0%
+okay well we'll be talking more about
+that in a minute but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how did the cortex expand we've talked
+
+ align:start position:0%
+how did the cortex expand we've talked
+ 
+
+ align:start position:0%
+how did the cortex expand we've talked
+about this before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it expanded by individual areas getting
+
+ align:start position:0%
+it expanded by individual areas getting
+ 
+
+ align:start position:0%
+it expanded by individual areas getting
+a lot bigger
+
+ align:start position:0%
+a lot bigger
+ 
+
+ align:start position:0%
+a lot bigger
+like this dried area especially the
+
+ align:start position:0%
+like this dried area especially the
+ 
+
+ align:start position:0%
+like this dried area especially the
+fobial area got quite large like here in
+
+ align:start position:0%
+fobial area got quite large like here in
+ 
+
+ align:start position:0%
+fobial area got quite large like here in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+in the owl monkey but it also there's
+
+ align:start position:0%
+in the owl monkey but it also there's
+ 
+
+ align:start position:0%
+in the owl monkey but it also there's
+been a multiplication of different
+
+ align:start position:0%
+been a multiplication of different
+ 
+
+ align:start position:0%
+been a multiplication of different
+representations of the same sensory
+
+ align:start position:0%
+representations of the same sensory
+ 
+
+ align:start position:0%
+representations of the same sensory
+surface so in this case the retina and
+
+ align:start position:0%
+surface so in this case the retina and
+ 
+
+ align:start position:0%
+surface so in this case the retina and
+it's represented in
+
+ align:start position:0%
+it's represented in
+ 
+
+ align:start position:0%
+it's represented in
+in different ways and sometimes we don't
+
+ align:start position:0%
+in different ways and sometimes we don't
+ 
+
+ align:start position:0%
+in different ways and sometimes we don't
+understand the functional differences in
+
+ align:start position:0%
+understand the functional differences in
+ 
+
+ align:start position:0%
+understand the functional differences in
+some cases we do understand
+
+ align:start position:0%
+some cases we do understand
+ 
+
+ align:start position:0%
+some cases we do understand
+and that's an area that the functional
+
+ align:start position:0%
+and that's an area that the functional
+ 
+
+ align:start position:0%
+and that's an area that the functional
+Imaging work in recent years has
+
+ align:start position:0%
+Imaging work in recent years has
+ 
+
+ align:start position:0%
+Imaging work in recent years has
+contributed quite a bit to for
+
+ align:start position:0%
+contributed quite a bit to for
+ 
+
+ align:start position:0%
+contributed quite a bit to for
+understands in the human brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what was probably the earliest
+
+ align:start position:0%
+so what was probably the earliest
+ 
+
+ align:start position:0%
+so what was probably the earliest
+parcellation of the pallium
+
+ align:start position:0%
+parcellation of the pallium
+ 
+
+ align:start position:0%
+parcellation of the pallium
+isolation meaning it gets divided into
+
+ align:start position:0%
+isolation meaning it gets divided into
+ 
+
+ align:start position:0%
+isolation meaning it gets divided into
+different parts
+
+ align:start position:0%
+different parts
+ 
+
+ align:start position:0%
+different parts
+how did the pallium get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the whole end brain initially
+
+ align:start position:0%
+the whole end brain initially
+ 
+
+ align:start position:0%
+the whole end brain initially
+grew out of the olfactory system
+
+ align:start position:0%
+grew out of the olfactory system
+ 
+
+ align:start position:0%
+grew out of the olfactory system
+was totally dominated by olfaction
+
+ align:start position:0%
+was totally dominated by olfaction
+ 
+
+ align:start position:0%
+was totally dominated by olfaction
+this View
+
+ align:start position:0%
+this View
+ 
+
+ align:start position:0%
+this View
+is actually a common one
+
+ align:start position:0%
+is actually a common one
+ 
+
+ align:start position:0%
+is actually a common one
+it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+argued by C Judson Herrick for example
+
+ align:start position:0%
+argued by C Judson Herrick for example
+ 
+
+ align:start position:0%
+argued by C Judson Herrick for example
+in the early part of the 20th century
+
+ align:start position:0%
+in the early part of the 20th century
+ 
+
+ align:start position:0%
+in the early part of the 20th century
+uh it was commonly believed but the
+
+ align:start position:0%
+uh it was commonly believed but the
+ 
+
+ align:start position:0%
+uh it was commonly believed but the
+evidence for it wasn't major they didn't
+
+ align:start position:0%
+evidence for it wasn't major they didn't
+ 
+
+ align:start position:0%
+evidence for it wasn't major they didn't
+know about some of the most primitive
+
+ align:start position:0%
+know about some of the most primitive
+ 
+
+ align:start position:0%
+know about some of the most primitive
+vertebrates
+
+ align:start position:0%
+vertebrates
+ 
+
+ align:start position:0%
+vertebrates
+so they used
+
+ align:start position:0%
+so they used
+ 
+
+ align:start position:0%
+so they used
+he used uh the tiger salamander more
+
+ align:start position:0%
+he used uh the tiger salamander more
+ 
+
+ align:start position:0%
+he used uh the tiger salamander more
+than any other animal
+
+ align:start position:0%
+than any other animal
+ 
+
+ align:start position:0%
+than any other animal
+and based a lot of his conclusions on
+
+ align:start position:0%
+and based a lot of his conclusions on
+ 
+
+ align:start position:0%
+and based a lot of his conclusions on
+what he found in the tiger salamander he
+
+ align:start position:0%
+what he found in the tiger salamander he
+ 
+
+ align:start position:0%
+what he found in the tiger salamander he
+also at that time they didn't have the
+
+ align:start position:0%
+also at that time they didn't have the
+ 
+
+ align:start position:0%
+also at that time they didn't have the
+really good experimental tracing methods
+
+ align:start position:0%
+really good experimental tracing methods
+ 
+
+ align:start position:0%
+really good experimental tracing methods
+for looking at connections
+
+ align:start position:0%
+for looking at connections
+ 
+
+ align:start position:0%
+for looking at connections
+but I have the big Advantage now in
+
+ align:start position:0%
+but I have the big Advantage now in
+ 
+
+ align:start position:0%
+but I have the big Advantage now in
+writing about this stuff in that they're
+
+ align:start position:0%
+writing about this stuff in that they're
+ 
+
+ align:start position:0%
+writing about this stuff in that they're
+the techniques are much more sensitive
+
+ align:start position:0%
+the techniques are much more sensitive
+ 
+
+ align:start position:0%
+the techniques are much more sensitive
+and they have been applied in a number
+
+ align:start position:0%
+and they have been applied in a number
+ 
+
+ align:start position:0%
+and they have been applied in a number
+of studies to some of these really
+
+ align:start position:0%
+of studies to some of these really
+ 
+
+ align:start position:0%
+of studies to some of these really
+primitive vertebrates
+
+ align:start position:0%
+primitive vertebrates
+ 
+
+ align:start position:0%
+primitive vertebrates
+and that's why I talked in the olfactory
+
+ align:start position:0%
+and that's why I talked in the olfactory
+ 
+
+ align:start position:0%
+and that's why I talked in the olfactory
+when we talked about olfactory system we
+
+ align:start position:0%
+when we talked about olfactory system we
+ 
+
+ align:start position:0%
+when we talked about olfactory system we
+talked about the
+
+ align:start position:0%
+talked about the
+ 
+
+ align:start position:0%
+talked about the
+the sea lampreys and the hagfish
+
+ align:start position:0%
+the sea lampreys and the hagfish
+ 
+
+ align:start position:0%
+the sea lampreys and the hagfish
+are more specialized so some people
+
+ align:start position:0%
+are more specialized so some people
+ 
+
+ align:start position:0%
+are more specialized so some people
+don't think they're very good model but
+
+ align:start position:0%
+don't think they're very good model but
+ 
+
+ align:start position:0%
+don't think they're very good model but
+in both of those animals
+
+ align:start position:0%
+in both of those animals
+ 
+
+ align:start position:0%
+in both of those animals
+olfaction
+
+ align:start position:0%
+olfaction
+ 
+
+ align:start position:0%
+olfaction
+olfactory projections go to everywhere
+
+ align:start position:0%
+olfactory projections go to everywhere
+ 
+
+ align:start position:0%
+olfactory projections go to everywhere
+in the end
+
+ align:start position:0%
+in the end
+ 
+
+ align:start position:0%
+in the end
+everywhere in fact they even go into the
+
+ align:start position:0%
+everywhere in fact they even go into the
+ 
+
+ align:start position:0%
+everywhere in fact they even go into the
+diencephalon
+
+ align:start position:0%
+diencephalon
+ 
+
+ align:start position:0%
+diencephalon
+directly from the olfactory bulbs
+
+ align:start position:0%
+directly from the olfactory bulbs
+ 
+
+ align:start position:0%
+directly from the olfactory bulbs
+so the earliest parcellation is
+
+ align:start position:0%
+so the earliest parcellation is
+ 
+
+ align:start position:0%
+so the earliest parcellation is
+separation of the olfactory
+
+ align:start position:0%
+separation of the olfactory
+ 
+
+ align:start position:0%
+separation of the olfactory
+inputs from the novel Factory that's the
+
+ align:start position:0%
+inputs from the novel Factory that's the
+ 
+
+ align:start position:0%
+inputs from the novel Factory that's the
+earliest persolation so if you look at
+
+ align:start position:0%
+earliest persolation so if you look at
+ 
+
+ align:start position:0%
+earliest persolation so if you look at
+the gene expression data you know in the
+
+ align:start position:0%
+the gene expression data you know in the
+ 
+
+ align:start position:0%
+the gene expression data you know in the
+sea lamprey
+
+ align:start position:0%
+sea lamprey
+ 
+
+ align:start position:0%
+sea lamprey
+there's it's been a little controversial
+
+ align:start position:0%
+there's it's been a little controversial
+ 
+
+ align:start position:0%
+there's it's been a little controversial
+with some varying results but people
+
+ align:start position:0%
+with some varying results but people
+ 
+
+ align:start position:0%
+with some varying results but people
+that have reviewed it
+
+ align:start position:0%
+that have reviewed it
+ 
+
+ align:start position:0%
+that have reviewed it
+that have gone over all of it and
+
+ align:start position:0%
+that have gone over all of it and
+ 
+
+ align:start position:0%
+that have gone over all of it and
+reviewed it carefully will tell you that
+
+ align:start position:0%
+reviewed it carefully will tell you that
+ 
+
+ align:start position:0%
+reviewed it carefully will tell you that
+there's at least two I mean
+
+ align:start position:0%
+there's at least two I mean
+ 
+
+ align:start position:0%
+there's at least two I mean
+types according to gene expression and
+
+ align:start position:0%
+types according to gene expression and
+ 
+
+ align:start position:0%
+types according to gene expression and
+it corresponds to the non-of-factory
+
+ align:start position:0%
+it corresponds to the non-of-factory
+ 
+
+ align:start position:0%
+it corresponds to the non-of-factory
+areas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-alfactional Factory
+
+ align:start position:0%
+non-alfactional Factory
+ 
+
+ align:start position:0%
+non-alfactional Factory
+okay so that was the earliest
+
+ align:start position:0%
+okay so that was the earliest
+ 
+
+ align:start position:0%
+okay so that was the earliest
+persolation do you know
+
+ align:start position:0%
+persolation do you know
+ 
+
+ align:start position:0%
+persolation do you know
+Italian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know that that olfactory cortex
+
+ align:start position:0%
+and we know that that olfactory cortex
+ 
+
+ align:start position:0%
+and we know that that olfactory cortex
+doesn't get direct olfactory input from
+
+ align:start position:0%
+doesn't get direct olfactory input from
+ 
+
+ align:start position:0%
+doesn't get direct olfactory input from
+the olfactory bulbs right
+
+ align:start position:0%
+the olfactory bulbs right
+ 
+
+ align:start position:0%
+the olfactory bulbs right
+the factory bolts project directly to it
+
+ align:start position:0%
+the factory bolts project directly to it
+ 
+
+ align:start position:0%
+the factory bolts project directly to it
+but the part that the olfactory bulb
+
+ align:start position:0%
+but the part that the olfactory bulb
+ 
+
+ align:start position:0%
+but the part that the olfactory bulb
+doesn't project you
+
+ align:start position:0%
+doesn't project you
+ 
+
+ align:start position:0%
+doesn't project you
+it's dominated by their balance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then I asked about factors that
+
+ align:start position:0%
+so then I asked about factors that
+ 
+
+ align:start position:0%
+so then I asked about factors that
+include thalamic parcellation
+
+ align:start position:0%
+include thalamic parcellation
+ 
+
+ align:start position:0%
+include thalamic parcellation
+so we'll look at that
+
+ align:start position:0%
+so we'll look at that
+ 
+
+ align:start position:0%
+so we'll look at that
+and then I mentioned what you commonly
+
+ align:start position:0%
+and then I mentioned what you commonly
+ 
+
+ align:start position:0%
+and then I mentioned what you commonly
+hear and you'll probably hear it in
+
+ align:start position:0%
+hear and you'll probably hear it in
+ 
+
+ align:start position:0%
+hear and you'll probably hear it in
+medical schools if you take your Anatomy
+
+ align:start position:0%
+medical schools if you take your Anatomy
+ 
+
+ align:start position:0%
+medical schools if you take your Anatomy
+but these multimodal association areas
+
+ align:start position:0%
+but these multimodal association areas
+ 
+
+ align:start position:0%
+but these multimodal association areas
+are the most recent to evolve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I would change that a little bit and say
+
+ align:start position:0%
+I would change that a little bit and say
+ 
+
+ align:start position:0%
+I would change that a little bit and say
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+they were probably the oldest type of
+
+ align:start position:0%
+they were probably the oldest type of
+ 
+
+ align:start position:0%
+they were probably the oldest type of
+Cortex but they're the most recent to
+
+ align:start position:0%
+Cortex but they're the most recent to
+ 
+
+ align:start position:0%
+Cortex but they're the most recent to
+really expand in the human brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because there's evidence that the
+
+ align:start position:0%
+because there's evidence that the
+ 
+
+ align:start position:0%
+because there's evidence that the
+unimodal areas
+
+ align:start position:0%
+unimodal areas
+ 
+
+ align:start position:0%
+unimodal areas
+are specialized evolved out of that
+
+ align:start position:0%
+are specialized evolved out of that
+ 
+
+ align:start position:0%
+are specialized evolved out of that
+multimodal periods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you look at the brains of
+
+ align:start position:0%
+if you look at the brains of
+ 
+
+ align:start position:0%
+if you look at the brains of
+some rodents that are a little more
+
+ align:start position:0%
+some rodents that are a little more
+ 
+
+ align:start position:0%
+some rodents that are a little more
+primitive in their structure like the
+
+ align:start position:0%
+primitive in their structure like the
+ 
+
+ align:start position:0%
+primitive in their structure like the
+Prairie Bowls have been studied well
+
+ align:start position:0%
+Prairie Bowls have been studied well
+ 
+
+ align:start position:0%
+Prairie Bowls have been studied well
+studied
+
+ align:start position:0%
+studied
+ 
+
+ align:start position:0%
+studied
+with this and look at the cortical unit
+
+ align:start position:0%
+with this and look at the cortical unit
+ 
+
+ align:start position:0%
+with this and look at the cortical unit
+recording work you'll find
+
+ align:start position:0%
+recording work you'll find
+ 
+
+ align:start position:0%
+recording work you'll find
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+there's a lot of multimodal input into
+
+ align:start position:0%
+there's a lot of multimodal input into
+ 
+
+ align:start position:0%
+there's a lot of multimodal input into
+areas that used to we used to think were
+
+ align:start position:0%
+areas that used to we used to think were
+ 
+
+ align:start position:0%
+areas that used to we used to think were
+we're unimodal they're multimodal and
+
+ align:start position:0%
+we're unimodal they're multimodal and
+ 
+
+ align:start position:0%
+we're unimodal they're multimodal and
+even in the primary sensory areas
+
+ align:start position:0%
+even in the primary sensory areas
+ 
+
+ align:start position:0%
+even in the primary sensory areas
+there's often more than one modality you
+
+ align:start position:0%
+there's often more than one modality you
+ 
+
+ align:start position:0%
+there's often more than one modality you
+find other modalities going right into
+
+ align:start position:0%
+find other modalities going right into
+ 
+
+ align:start position:0%
+find other modalities going right into
+auditory cortex and visual cortex for
+
+ align:start position:0%
+auditory cortex and visual cortex for
+ 
+
+ align:start position:0%
+auditory cortex and visual cortex for
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of its supporting this View
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is so loud
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a lot of incomplete persolation
+
+ align:start position:0%
+there's a lot of incomplete persolation
+ 
+
+ align:start position:0%
+there's a lot of incomplete persolation
+in fact the some of those those mammals
+
+ align:start position:0%
+in fact the some of those those mammals
+ 
+
+ align:start position:0%
+in fact the some of those those mammals
+you never find complete consolation in
+
+ align:start position:0%
+you never find complete consolation in
+ 
+
+ align:start position:0%
+you never find complete consolation in
+the sensory is and that that is just
+
+ align:start position:0%
+the sensory is and that that is just
+ 
+
+ align:start position:0%
+the sensory is and that that is just
+never taught I don't know why it's not
+
+ align:start position:0%
+never taught I don't know why it's not
+ 
+
+ align:start position:0%
+never taught I don't know why it's not
+taught even heuble and weasel here at
+
+ align:start position:0%
+taught even heuble and weasel here at
+ 
+
+ align:start position:0%
+taught even heuble and weasel here at
+Harvard doing that beautiful work on the
+
+ align:start position:0%
+Harvard doing that beautiful work on the
+ 
+
+ align:start position:0%
+Harvard doing that beautiful work on the
+visual cortex they started with cats
+
+ align:start position:0%
+visual cortex they started with cats
+ 
+
+ align:start position:0%
+visual cortex they started with cats
+they found some auditory inputs into the
+
+ align:start position:0%
+they found some auditory inputs into the
+ 
+
+ align:start position:0%
+they found some auditory inputs into the
+visual cortex of the cad
+
+ align:start position:0%
+visual cortex of the cad
+ 
+
+ align:start position:0%
+visual cortex of the cad
+and you have to look very hard for it in
+
+ align:start position:0%
+and you have to look very hard for it in
+ 
+
+ align:start position:0%
+and you have to look very hard for it in
+their early papers and I asked them
+
+ align:start position:0%
+their early papers and I asked them
+ 
+
+ align:start position:0%
+their early papers and I asked them
+about it one time and they said they
+
+ align:start position:0%
+about it one time and they said they
+ 
+
+ align:start position:0%
+about it one time and they said they
+they Tarson told me yes we did find that
+
+ align:start position:0%
+they Tarson told me yes we did find that
+ 
+
+ align:start position:0%
+they Tarson told me yes we did find that
+and we didn't
+
+ align:start position:0%
+and we didn't
+ 
+
+ align:start position:0%
+and we didn't
+we didn't know what to do with it so we
+
+ align:start position:0%
+we didn't know what to do with it so we
+ 
+
+ align:start position:0%
+we didn't know what to do with it so we
+sort of forgot about it
+
+ align:start position:0%
+sort of forgot about it
+ 
+
+ align:start position:0%
+sort of forgot about it
+they were just working out how the
+
+ align:start position:0%
+they were just working out how the
+ 
+
+ align:start position:0%
+they were just working out how the
+Cascade specification of unit properties
+
+ align:start position:0%
+Cascade specification of unit properties
+ 
+
+ align:start position:0%
+Cascade specification of unit properties
+in the vehicle system
+
+ align:start position:0%
+in the vehicle system
+ 
+
+ align:start position:0%
+in the vehicle system
+because that wasn't on yet so they
+
+ align:start position:0%
+because that wasn't on yet so they
+ 
+
+ align:start position:0%
+because that wasn't on yet so they
+focused on that and so
+
+ align:start position:0%
+focused on that and so
+ 
+
+ align:start position:0%
+focused on that and so
+the auditory input just wasn't important
+
+ align:start position:0%
+the auditory input just wasn't important
+ 
+
+ align:start position:0%
+the auditory input just wasn't important
+to understand the main things the visual
+
+ align:start position:0%
+to understand the main things the visual
+ 
+
+ align:start position:0%
+to understand the main things the visual
+cortex was doing and I'm saying well we
+
+ align:start position:0%
+cortex was doing and I'm saying well we
+ 
+
+ align:start position:0%
+cortex was doing and I'm saying well we
+if we're interested in evolution though
+
+ align:start position:0%
+if we're interested in evolution though
+ 
+
+ align:start position:0%
+if we're interested in evolution though
+we have to pay attention to these kinds
+
+ align:start position:0%
+we have to pay attention to these kinds
+ 
+
+ align:start position:0%
+we have to pay attention to these kinds
+of things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh the synesthesia okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's no yeah there is no evidence for
+
+ align:start position:0%
+there's no yeah there is no evidence for
+ 
+
+ align:start position:0%
+there's no yeah there is no evidence for
+that that I know of
+
+ align:start position:0%
+that that I know of
+ 
+
+ align:start position:0%
+that that I know of
+but now with functional good functional
+
+ align:start position:0%
+but now with functional good functional
+ 
+
+ align:start position:0%
+but now with functional good functional
+Imaging methods it would be possible to
+
+ align:start position:0%
+Imaging methods it would be possible to
+ 
+
+ align:start position:0%
+Imaging methods it would be possible to
+study synesthesia in a way that we
+
+ align:start position:0%
+study synesthesia in a way that we
+ 
+
+ align:start position:0%
+study synesthesia in a way that we
+couldn't before
+
+ align:start position:0%
+couldn't before
+ 
+
+ align:start position:0%
+couldn't before
+you know it's a good question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I will look into that because it's such
+
+ align:start position:0%
+I will look into that because it's such
+ 
+
+ align:start position:0%
+I will look into that because it's such
+an interesting question you know
+
+ align:start position:0%
+an interesting question you know
+ 
+
+ align:start position:0%
+an interesting question you know
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+major differences in the way
+
+ align:start position:0%
+major differences in the way
+ 
+
+ align:start position:0%
+major differences in the way
+in human brain is connected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is just what we're talking about
+
+ align:start position:0%
+so this is just what we're talking about
+ 
+
+ align:start position:0%
+so this is just what we're talking about
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the evidence I talk about this is
+
+ align:start position:0%
+and the evidence I talk about this is
+ 
+
+ align:start position:0%
+and the evidence I talk about this is
+actually from data from hamsters that I
+
+ align:start position:0%
+actually from data from hamsters that I
+ 
+
+ align:start position:0%
+actually from data from hamsters that I
+studied looking at projections from
+
+ align:start position:0%
+studied looking at projections from
+ 
+
+ align:start position:0%
+studied looking at projections from
+inferior colliculus super superficial
+
+ align:start position:0%
+inferior colliculus super superficial
+ 
+
+ align:start position:0%
+inferior colliculus super superficial
+and deep Superior folliculous and from
+
+ align:start position:0%
+and deep Superior folliculous and from
+ 
+
+ align:start position:0%
+and deep Superior folliculous and from
+the pre-tactile area and looking at
+
+ align:start position:0%
+the pre-tactile area and looking at
+ 
+
+ align:start position:0%
+the pre-tactile area and looking at
+where they go and the pattern they form
+
+ align:start position:0%
+where they go and the pattern they form
+ 
+
+ align:start position:0%
+where they go and the pattern they form
+in the valves
+
+ align:start position:0%
+in the valves
+ 
+
+ align:start position:0%
+in the valves
+and uh if you look carefully at this you
+
+ align:start position:0%
+and uh if you look carefully at this you
+ 
+
+ align:start position:0%
+and uh if you look carefully at this you
+see that in the thalamus you have the
+
+ align:start position:0%
+see that in the thalamus you have the
+ 
+
+ align:start position:0%
+see that in the thalamus you have the
+same spatial Arrangement that you have
+
+ align:start position:0%
+same spatial Arrangement that you have
+ 
+
+ align:start position:0%
+same spatial Arrangement that you have
+this here
+
+ align:start position:0%
+this here
+ 
+
+ align:start position:0%
+this here
+the auditory input comes in
+
+ align:start position:0%
+the auditory input comes in
+ 
+
+ align:start position:0%
+the auditory input comes in
+in this more inferior lateral position
+
+ align:start position:0%
+in this more inferior lateral position
+ 
+
+ align:start position:0%
+in this more inferior lateral position
+and that's where it forms its
+
+ align:start position:0%
+and that's where it forms its
+ 
+
+ align:start position:0%
+and that's where it forms its
+connections
+
+ align:start position:0%
+connections
+ 
+
+ align:start position:0%
+connections
+but it's right next to multimodal parts
+
+ align:start position:0%
+but it's right next to multimodal parts
+ 
+
+ align:start position:0%
+but it's right next to multimodal parts
+of the lateral posterior nucleus and
+
+ align:start position:0%
+of the lateral posterior nucleus and
+ 
+
+ align:start position:0%
+of the lateral posterior nucleus and
+then in the more superficial parts of
+
+ align:start position:0%
+then in the more superficial parts of
+ 
+
+ align:start position:0%
+then in the more superficial parts of
+lateral posterior getting inputs
+
+ align:start position:0%
+lateral posterior getting inputs
+ 
+
+ align:start position:0%
+lateral posterior getting inputs
+directly from the spiritual existence
+
+ align:start position:0%
+directly from the spiritual existence
+ 
+
+ align:start position:0%
+directly from the spiritual existence
+visual
+
+ align:start position:0%
+visual
+ 
+
+ align:start position:0%
+visual
+and up in front you have the
+
+ align:start position:0%
+and up in front you have the
+ 
+
+ align:start position:0%
+and up in front you have the
+pre-tactical area and those axons of
+
+ align:start position:0%
+pre-tactical area and those axons of
+ 
+
+ align:start position:0%
+pre-tactical area and those axons of
+course rasterly near the midline and
+
+ align:start position:0%
+course rasterly near the midline and
+ 
+
+ align:start position:0%
+course rasterly near the midline and
+they go right into the roster parts of
+
+ align:start position:0%
+they go right into the roster parts of
+ 
+
+ align:start position:0%
+they go right into the roster parts of
+the lateral nucleus highly neglected
+
+ align:start position:0%
+the lateral nucleus highly neglected
+ 
+
+ align:start position:0%
+the lateral nucleus highly neglected
+that that passage and uh it's only
+
+ align:start position:0%
+that that passage and uh it's only
+ 
+
+ align:start position:0%
+that that passage and uh it's only
+recently that you can find
+
+ align:start position:0%
+recently that you can find
+ 
+
+ align:start position:0%
+recently that you can find
+studies of you know what it might be
+
+ align:start position:0%
+studies of you know what it might be
+ 
+
+ align:start position:0%
+studies of you know what it might be
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+so because I've worked in this area I've
+
+ align:start position:0%
+so because I've worked in this area I've
+ 
+
+ align:start position:0%
+so because I've worked in this area I've
+paid a lot of attention to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think when this picture was reproduced
+
+ align:start position:0%
+I think when this picture was reproduced
+ 
+
+ align:start position:0%
+I think when this picture was reproduced
+in the book they put just L because
+
+ align:start position:0%
+in the book they put just L because
+ 
+
+ align:start position:0%
+in the book they put just L because
+it's usually called lateral the lateral
+
+ align:start position:0%
+it's usually called lateral the lateral
+ 
+
+ align:start position:0%
+it's usually called lateral the lateral
+dorsal nucleus a few older Emperors will
+
+ align:start position:0%
+dorsal nucleus a few older Emperors will
+ 
+
+ align:start position:0%
+dorsal nucleus a few older Emperors will
+call it lateral lateralis and interior
+
+ align:start position:0%
+call it lateral lateralis and interior
+ 
+
+ align:start position:0%
+call it lateral lateralis and interior
+okay and then I my interpretation of
+
+ align:start position:0%
+okay and then I my interpretation of
+ 
+
+ align:start position:0%
+okay and then I my interpretation of
+parcellation is that
+
+ align:start position:0%
+parcellation is that
+ 
+
+ align:start position:0%
+parcellation is that
+this is it shows input from the retina
+
+ align:start position:0%
+this is it shows input from the retina
+ 
+
+ align:start position:0%
+this is it shows input from the retina
+here in the dark blue input from
+
+ align:start position:0%
+here in the dark blue input from
+ 
+
+ align:start position:0%
+here in the dark blue input from
+pre-tectin and
+
+ align:start position:0%
+pre-tectin and
+ 
+
+ align:start position:0%
+pre-tectin and
+inferior caliculous and spiritus coming
+
+ align:start position:0%
+inferior caliculous and spiritus coming
+ 
+
+ align:start position:0%
+inferior caliculous and spiritus coming
+into the thalamus and how initially it's
+
+ align:start position:0%
+into the thalamus and how initially it's
+ 
+
+ align:start position:0%
+into the thalamus and how initially it's
+almost certain this big pectin sending
+
+ align:start position:0%
+almost certain this big pectin sending
+ 
+
+ align:start position:0%
+almost certain this big pectin sending
+projections into what initially was a
+
+ align:start position:0%
+projections into what initially was a
+ 
+
+ align:start position:0%
+projections into what initially was a
+pretty small diencephalon they
+
+ align:start position:0%
+pretty small diencephalon they
+ 
+
+ align:start position:0%
+pretty small diencephalon they
+overlapped a lot and if you look at the
+
+ align:start position:0%
+overlapped a lot and if you look at the
+ 
+
+ align:start position:0%
+overlapped a lot and if you look at the
+brain like at the tiger salamander you
+
+ align:start position:0%
+brain like at the tiger salamander you
+ 
+
+ align:start position:0%
+brain like at the tiger salamander you
+find this these kind of widely branched
+
+ align:start position:0%
+find this these kind of widely branched
+ 
+
+ align:start position:0%
+find this these kind of widely branched
+accents and primitive animals and in
+
+ align:start position:0%
+accents and primitive animals and in
+ 
+
+ align:start position:0%
+accents and primitive animals and in
+development you still see a lot of that
+
+ align:start position:0%
+development you still see a lot of that
+ 
+
+ align:start position:0%
+development you still see a lot of that
+but then as they form
+
+ align:start position:0%
+but then as they form
+ 
+
+ align:start position:0%
+but then as they form
+connections
+
+ align:start position:0%
+connections
+ 
+
+ align:start position:0%
+connections
+as the connections increase in density
+
+ align:start position:0%
+as the connections increase in density
+ 
+
+ align:start position:0%
+as the connections increase in density
+they tended to then segregate from the
+
+ align:start position:0%
+they tended to then segregate from the
+ 
+
+ align:start position:0%
+they tended to then segregate from the
+other axons
+
+ align:start position:0%
+other axons
+ 
+
+ align:start position:0%
+other axons
+and that's what I'm showing through
+
+ align:start position:0%
+and that's what I'm showing through
+ 
+
+ align:start position:0%
+and that's what I'm showing through
+these later stages so here they're
+
+ align:start position:0%
+these later stages so here they're
+ 
+
+ align:start position:0%
+these later stages so here they're
+almost completely segregated
+
+ align:start position:0%
+almost completely segregated
+ 
+
+ align:start position:0%
+almost completely segregated
+inferior calculus going down here
+
+ align:start position:0%
+inferior calculus going down here
+ 
+
+ align:start position:0%
+inferior calculus going down here
+the retina going more
+
+ align:start position:0%
+the retina going more
+ 
+
+ align:start position:0%
+the retina going more
+superficially in the thalamus there the
+
+ align:start position:0%
+superficially in the thalamus there the
+ 
+
+ align:start position:0%
+superficially in the thalamus there the
+eventual part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Spirit eclipseless carrying visual input
+
+ align:start position:0%
+Spirit eclipseless carrying visual input
+ 
+
+ align:start position:0%
+Spirit eclipseless carrying visual input
+information that did overlap
+
+ align:start position:0%
+information that did overlap
+ 
+
+ align:start position:0%
+information that did overlap
+with the genesalid body in the genicular
+
+ align:start position:0%
+with the genesalid body in the genicular
+ 
+
+ align:start position:0%
+with the genesalid body in the genicular
+body but then it went to this
+
+ align:start position:0%
+body but then it went to this
+ 
+
+ align:start position:0%
+body but then it went to this
+took over the rights of the lp and the
+
+ align:start position:0%
+took over the rights of the lp and the
+ 
+
+ align:start position:0%
+took over the rights of the lp and the
+pretextual
+
+ align:start position:0%
+pretextual
+ 
+
+ align:start position:0%
+pretextual
+focusing on that
+
+ align:start position:0%
+focusing on that
+ 
+
+ align:start position:0%
+focusing on that
+just specific sections of the lp so you
+
+ align:start position:0%
+just specific sections of the lp so you
+ 
+
+ align:start position:0%
+just specific sections of the lp so you
+end up with this pattern
+
+ align:start position:0%
+end up with this pattern
+ 
+
+ align:start position:0%
+end up with this pattern
+but that process where you get the
+
+ align:start position:0%
+but that process where you get the
+ 
+
+ align:start position:0%
+but that process where you get the
+segregation is called persolation
+
+ align:start position:0%
+segregation is called persolation
+ 
+
+ align:start position:0%
+segregation is called persolation
+experimentally if in development if we
+
+ align:start position:0%
+experimentally if in development if we
+ 
+
+ align:start position:0%
+experimentally if in development if we
+get got the retina to to send
+
+ align:start position:0%
+get got the retina to to send
+ 
+
+ align:start position:0%
+get got the retina to to send
+projections to the wrong side of the
+
+ align:start position:0%
+projections to the wrong side of the
+ 
+
+ align:start position:0%
+projections to the wrong side of the
+tectum here's what they do
+
+ align:start position:0%
+tectum here's what they do
+ 
+
+ align:start position:0%
+tectum here's what they do
+developmentally they grow in and they
+
+ align:start position:0%
+developmentally they grow in and they
+ 
+
+ align:start position:0%
+developmentally they grow in and they
+just overlap with each other they just
+
+ align:start position:0%
+just overlap with each other they just
+ 
+
+ align:start position:0%
+just overlap with each other they just
+and they're trying but then as they
+
+ align:start position:0%
+and they're trying but then as they
+ 
+
+ align:start position:0%
+and they're trying but then as they
+begin to form connections
+
+ align:start position:0%
+begin to form connections
+ 
+
+ align:start position:0%
+begin to form connections
+the connections of one eye and the
+
+ align:start position:0%
+the connections of one eye and the
+ 
+
+ align:start position:0%
+the connections of one eye and the
+connections of the other eye segregate
+
+ align:start position:0%
+connections of the other eye segregate
+ 
+
+ align:start position:0%
+connections of the other eye segregate
+okay as they get denser they tend to
+
+ align:start position:0%
+okay as they get denser they tend to
+ 
+
+ align:start position:0%
+okay as they get denser they tend to
+terminate in the areas closest to where
+
+ align:start position:0%
+terminate in the areas closest to where
+ 
+
+ align:start position:0%
+terminate in the areas closest to where
+they come it came in because that's
+
+ align:start position:0%
+they come it came in because that's
+ 
+
+ align:start position:0%
+they come it came in because that's
+where they form denser connections first
+
+ align:start position:0%
+where they form denser connections first
+ 
+
+ align:start position:0%
+where they form denser connections first
+you see they got there first that's
+
+ align:start position:0%
+you see they got there first that's
+ 
+
+ align:start position:0%
+you see they got there first that's
+where they form the connections first
+
+ align:start position:0%
+where they form the connections first
+ 
+
+ align:start position:0%
+where they form the connections first
+and then they regret they said they pull
+
+ align:start position:0%
+and then they regret they said they pull
+ 
+
+ align:start position:0%
+and then they regret they said they pull
+away from each other
+
+ align:start position:0%
+away from each other
+ 
+
+ align:start position:0%
+away from each other
+literally
+
+ align:start position:0%
+literally
+ 
+
+ align:start position:0%
+literally
+we don't think they they don't
+
+ align:start position:0%
+we don't think they they don't
+ 
+
+ align:start position:0%
+we don't think they they don't
+necessarily degenerate the part that was
+
+ align:start position:0%
+necessarily degenerate the part that was
+ 
+
+ align:start position:0%
+necessarily degenerate the part that was
+but it withdraws
+
+ align:start position:0%
+but it withdraws
+ 
+
+ align:start position:0%
+but it withdraws
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea here is that multimodal
+
+ align:start position:0%
+so the idea here is that multimodal
+ 
+
+ align:start position:0%
+so the idea here is that multimodal
+convergence was the Primitive state of
+
+ align:start position:0%
+convergence was the Primitive state of
+ 
+
+ align:start position:0%
+convergence was the Primitive state of
+most or all of the thalamus and the
+
+ align:start position:0%
+most or all of the thalamus and the
+ 
+
+ align:start position:0%
+most or all of the thalamus and the
+incarceration occurred
+
+ align:start position:0%
+incarceration occurred
+ 
+
+ align:start position:0%
+incarceration occurred
+and correlated changes occurred within
+
+ align:start position:0%
+and correlated changes occurred within
+ 
+
+ align:start position:0%
+and correlated changes occurred within
+the within the neocortex
+
+ align:start position:0%
+the within the neocortex
+ 
+
+ align:start position:0%
+the within the neocortex
+and getting reports on a member of the
+
+ align:start position:0%
+and getting reports on a member of the
+ 
+
+ align:start position:0%
+and getting reports on a member of the
+family that's in the hospital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wait
+
+ align:start position:0%
+wait
+ 
+
+ align:start position:0%
+wait
+if you look at that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so can you look across widely
+
+ align:start position:0%
+all right so can you look across widely
+ 
+
+ align:start position:0%
+all right so can you look across widely
+different animals like here's the
+
+ align:start position:0%
+different animals like here's the
+ 
+
+ align:start position:0%
+different animals like here's the
+and on the outs this is animals like the
+
+ align:start position:0%
+and on the outs this is animals like the
+ 
+
+ align:start position:0%
+and on the outs this is animals like the
+the salamander or the the Frog you know
+
+ align:start position:0%
+the salamander or the the Frog you know
+ 
+
+ align:start position:0%
+the salamander or the the Frog you know
+they have fewer thalamic areas when you
+
+ align:start position:0%
+they have fewer thalamic areas when you
+ 
+
+ align:start position:0%
+they have fewer thalamic areas when you
+go up to reptiles there's more birds
+
+ align:start position:0%
+go up to reptiles there's more birds
+ 
+
+ align:start position:0%
+go up to reptiles there's more birds
+even more and mammals than most
+
+ align:start position:0%
+even more and mammals than most
+ 
+
+ align:start position:0%
+even more and mammals than most
+if you look in the human compared with
+
+ align:start position:0%
+if you look in the human compared with
+ 
+
+ align:start position:0%
+if you look in the human compared with
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+primates you'll find
+
+ align:start position:0%
+primates you'll find
+ 
+
+ align:start position:0%
+primates you'll find
+the same Aries but you can subdivide the
+
+ align:start position:0%
+the same Aries but you can subdivide the
+ 
+
+ align:start position:0%
+the same Aries but you can subdivide the
+areas more it's like the brain with
+
+ align:start position:0%
+areas more it's like the brain with
+ 
+
+ align:start position:0%
+areas more it's like the brain with
+Evolution becomes more specialized
+
+ align:start position:0%
+Evolution becomes more specialized
+ 
+
+ align:start position:0%
+Evolution becomes more specialized
+there's more persolation
+
+ align:start position:0%
+there's more persolation
+ 
+
+ align:start position:0%
+there's more persolation
+than there is earlier and that's what
+
+ align:start position:0%
+than there is earlier and that's what
+ 
+
+ align:start position:0%
+than there is earlier and that's what
+this comparative data support this is
+
+ align:start position:0%
+this comparative data support this is
+ 
+
+ align:start position:0%
+this comparative data support this is
+just a concept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+based on one that street or published
+
+ align:start position:0%
+based on one that street or published
+ 
+
+ align:start position:0%
+based on one that street or published
+and he after reviewing a lot of this
+
+ align:start position:0%
+and he after reviewing a lot of this
+ 
+
+ align:start position:0%
+and he after reviewing a lot of this
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I talk about these three
+
+ align:start position:0%
+and then I talk about these three
+ 
+
+ align:start position:0%
+and then I talk about these three
+systems separately these are all things
+
+ align:start position:0%
+systems separately these are all things
+ 
+
+ align:start position:0%
+systems separately these are all things
+that we did talk about
+
+ align:start position:0%
+that we did talk about
+ 
+
+ align:start position:0%
+that we did talk about
+when we talked about these systems is
+
+ align:start position:0%
+when we talked about these systems is
+ 
+
+ align:start position:0%
+when we talked about these systems is
+just to remind you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I talked about that segregation
+
+ align:start position:0%
+and then I talked about that segregation
+ 
+
+ align:start position:0%
+and then I talked about that segregation
+within this meta sensory system that led
+
+ align:start position:0%
+within this meta sensory system that led
+ 
+
+ align:start position:0%
+within this meta sensory system that led
+to the revolution of the motor cortex
+
+ align:start position:0%
+to the revolution of the motor cortex
+ 
+
+ align:start position:0%
+to the revolution of the motor cortex
+and this is the picture that I had this
+
+ align:start position:0%
+and this is the picture that I had this
+ 
+
+ align:start position:0%
+and this is the picture that I had this
+was from chapter 15. and it shows how
+
+ align:start position:0%
+was from chapter 15. and it shows how
+ 
+
+ align:start position:0%
+was from chapter 15. and it shows how
+you can Define
+
+ align:start position:0%
+you can Define
+ 
+
+ align:start position:0%
+you can Define
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+somatosensory
+
+ align:start position:0%
+somatosensory
+ 
+
+ align:start position:0%
+somatosensory
+cortex you can Define it in terms of
+
+ align:start position:0%
+cortex you can Define it in terms of
+ 
+
+ align:start position:0%
+cortex you can Define it in terms of
+projections the part that gets input
+
+ align:start position:0%
+projections the part that gets input
+ 
+
+ align:start position:0%
+projections the part that gets input
+from the posterior nucleus
+
+ align:start position:0%
+from the posterior nucleus
+ 
+
+ align:start position:0%
+from the posterior nucleus
+because that's where this sensory come
+
+ align:start position:0%
+because that's where this sensory come
+ 
+
+ align:start position:0%
+because that's where this sensory come
+input comes in from the spinal cord in
+
+ align:start position:0%
+input comes in from the spinal cord in
+ 
+
+ align:start position:0%
+input comes in from the spinal cord in
+the trigeminal system and then anterior
+
+ align:start position:0%
+the trigeminal system and then anterior
+ 
+
+ align:start position:0%
+the trigeminal system and then anterior
+to that the ventral lateral nucleus
+
+ align:start position:0%
+to that the ventral lateral nucleus
+ 
+
+ align:start position:0%
+to that the ventral lateral nucleus
+projects
+
+ align:start position:0%
+projects
+ 
+
+ align:start position:0%
+projects
+what we call them or cortex the primary
+
+ align:start position:0%
+what we call them or cortex the primary
+ 
+
+ align:start position:0%
+what we call them or cortex the primary
+motor cortex the VA anterior just goes
+
+ align:start position:0%
+motor cortex the VA anterior just goes
+ 
+
+ align:start position:0%
+motor cortex the VA anterior just goes
+even more anterior premolar cortex
+
+ align:start position:0%
+even more anterior premolar cortex
+ 
+
+ align:start position:0%
+even more anterior premolar cortex
+and it shows how these the projections
+
+ align:start position:0%
+and it shows how these the projections
+ 
+
+ align:start position:0%
+and it shows how these the projections
+of those two nuclei are completely
+
+ align:start position:0%
+of those two nuclei are completely
+ 
+
+ align:start position:0%
+of those two nuclei are completely
+overlapping in The Virginian across so
+
+ align:start position:0%
+overlapping in The Virginian across so
+ 
+
+ align:start position:0%
+overlapping in The Virginian across so
+if you record from it physiologically
+
+ align:start position:0%
+if you record from it physiologically
+ 
+
+ align:start position:0%
+if you record from it physiologically
+you can't you can't separate them
+
+ align:start position:0%
+you can't you can't separate them
+ 
+
+ align:start position:0%
+you can't you can't separate them
+you study the projections again
+
+ align:start position:0%
+you study the projections again
+ 
+
+ align:start position:0%
+you study the projections again
+and then in this is not the opossum it's
+
+ align:start position:0%
+and then in this is not the opossum it's
+ 
+
+ align:start position:0%
+and then in this is not the opossum it's
+the brushed head possum it's a different
+
+ align:start position:0%
+the brushed head possum it's a different
+ 
+
+ align:start position:0%
+the brushed head possum it's a different
+animal and you find an area that doesn't
+
+ align:start position:0%
+animal and you find an area that doesn't
+ 
+
+ align:start position:0%
+animal and you find an area that doesn't
+overlap for each of these nuclei but
+
+ align:start position:0%
+overlap for each of these nuclei but
+ 
+
+ align:start position:0%
+overlap for each of these nuclei but
+then there's a fairly large area where
+
+ align:start position:0%
+then there's a fairly large area where
+ 
+
+ align:start position:0%
+then there's a fairly large area where
+they overlap if you look at a rat
+
+ align:start position:0%
+they overlap if you look at a rat
+ 
+
+ align:start position:0%
+they overlap if you look at a rat
+there's just an area of the hind limb
+
+ align:start position:0%
+there's just an area of the hind limb
+ 
+
+ align:start position:0%
+there's just an area of the hind limb
+representation where there has not been
+
+ align:start position:0%
+representation where there has not been
+ 
+
+ align:start position:0%
+representation where there has not been
+a complete parcelation
+
+ align:start position:0%
+a complete parcelation
+ 
+
+ align:start position:0%
+a complete parcelation
+but otherwise it's pretty good if you
+
+ align:start position:0%
+but otherwise it's pretty good if you
+ 
+
+ align:start position:0%
+but otherwise it's pretty good if you
+look at a primate
+
+ align:start position:0%
+look at a primate
+ 
+
+ align:start position:0%
+look at a primate
+dialogue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete segregation that's true all the
+
+ align:start position:0%
+complete segregation that's true all the
+ 
+
+ align:start position:0%
+complete segregation that's true all the
+larger climates in fact I think all of
+
+ align:start position:0%
+larger climates in fact I think all of
+ 
+
+ align:start position:0%
+larger climates in fact I think all of
+the primates that I know about are like
+
+ align:start position:0%
+the primates that I know about are like
+ 
+
+ align:start position:0%
+the primates that I know about are like
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the evidence is pretty good for this
+
+ align:start position:0%
+so the evidence is pretty good for this
+ 
+
+ align:start position:0%
+so the evidence is pretty good for this
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+parcellation in this meta sensory system
+
+ align:start position:0%
+parcellation in this meta sensory system
+ 
+
+ align:start position:0%
+parcellation in this meta sensory system
+and how the motor cortex signals out of
+
+ align:start position:0%
+and how the motor cortex signals out of
+ 
+
+ align:start position:0%
+and how the motor cortex signals out of
+it okay whereas for the visual system
+
+ align:start position:0%
+it okay whereas for the visual system
+ 
+
+ align:start position:0%
+it okay whereas for the visual system
+people have looked at widely different
+
+ align:start position:0%
+people have looked at widely different
+ 
+
+ align:start position:0%
+people have looked at widely different
+animals including marsupials you always
+
+ align:start position:0%
+animals including marsupials you always
+ 
+
+ align:start position:0%
+animals including marsupials you always
+see a V1 and a V2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in most of them you see a fern area
+
+ align:start position:0%
+and in most of them you see a fern area
+ 
+
+ align:start position:0%
+and in most of them you see a fern area
+that's always there and Mary we call him
+
+ align:start position:0%
+that's always there and Mary we call him
+ 
+
+ align:start position:0%
+that's always there and Mary we call him
+tea and the monkeys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you'll see varying numbers of
+
+ align:start position:0%
+and then you'll see varying numbers of
+ 
+
+ align:start position:0%
+and then you'll see varying numbers of
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+additional visual areas and some there
+
+ align:start position:0%
+additional visual areas and some there
+ 
+
+ align:start position:0%
+additional visual areas and some there
+are not many at all not much cortex
+
+ align:start position:0%
+are not many at all not much cortex
+ 
+
+ align:start position:0%
+are not many at all not much cortex
+but in the large premise in humans
+
+ align:start position:0%
+but in the large premise in humans
+ 
+
+ align:start position:0%
+but in the large premise in humans
+there's a very large
+
+ align:start position:0%
+there's a very large
+ 
+
+ align:start position:0%
+there's a very large
+so these are the methods of expansion
+
+ align:start position:0%
+so these are the methods of expansion
+ 
+
+ align:start position:0%
+so these are the methods of expansion
+that you talk about these are pictures
+
+ align:start position:0%
+that you talk about these are pictures
+ 
+
+ align:start position:0%
+that you talk about these are pictures
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+primates and here you see in
+
+ align:start position:0%
+primates and here you see in
+ 
+
+ align:start position:0%
+primates and here you see in
+the gray color here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see what Muslim calls the
+
+ align:start position:0%
+you see what Muslim calls the
+ 
+
+ align:start position:0%
+you see what Muslim calls the
+heteromotive here it's the multimodal
+
+ align:start position:0%
+heteromotive here it's the multimodal
+ 
+
+ align:start position:0%
+heteromotive here it's the multimodal
+areas
+
+ align:start position:0%
+areas
+ 
+
+ align:start position:0%
+areas
+and it's typical
+
+ align:start position:0%
+and it's typical
+ 
+
+ align:start position:0%
+and it's typical
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+rat and Hedgehog especially hedgehogs
+
+ align:start position:0%
+rat and Hedgehog especially hedgehogs
+ 
+
+ align:start position:0%
+rat and Hedgehog especially hedgehogs
+see how they picture no multimodal areas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I find it'll be interesting to see how
+
+ align:start position:0%
+I find it'll be interesting to see how
+ 
+
+ align:start position:0%
+I find it'll be interesting to see how
+my colleagues that have published these
+
+ align:start position:0%
+my colleagues that have published these
+ 
+
+ align:start position:0%
+my colleagues that have published these
+kinds of pictures for a long time will
+
+ align:start position:0%
+kinds of pictures for a long time will
+ 
+
+ align:start position:0%
+kinds of pictures for a long time will
+react because I've looked really
+
+ align:start position:0%
+react because I've looked really
+ 
+
+ align:start position:0%
+react because I've looked really
+carefully at that literature and that is
+
+ align:start position:0%
+carefully at that literature and that is
+ 
+
+ align:start position:0%
+carefully at that literature and that is
+not what you find
+
+ align:start position:0%
+not what you find
+ 
+
+ align:start position:0%
+not what you find
+there's a lot of multimodal Cortex and
+
+ align:start position:0%
+there's a lot of multimodal Cortex and
+ 
+
+ align:start position:0%
+there's a lot of multimodal Cortex and
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+so I have this slide multimodal regions
+
+ align:start position:0%
+so I have this slide multimodal regions
+ 
+
+ align:start position:0%
+so I have this slide multimodal regions
+do exist in between the major sensory
+
+ align:start position:0%
+do exist in between the major sensory
+ 
+
+ align:start position:0%
+do exist in between the major sensory
+areas and Hedgehog hamster gold
+
+ align:start position:0%
+areas and Hedgehog hamster gold
+ 
+
+ align:start position:0%
+areas and Hedgehog hamster gold
+it's been thus studied in the cold
+
+ align:start position:0%
+it's been thus studied in the cold
+ 
+
+ align:start position:0%
+it's been thus studied in the cold
+and unimodal and multimodal
+
+ align:start position:0%
+and unimodal and multimodal
+ 
+
+ align:start position:0%
+and unimodal and multimodal
+dissociationaries are not so
+
+ align:start position:0%
+dissociationaries are not so
+ 
+
+ align:start position:0%
+dissociationaries are not so
+distinguishable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because they're all multimodal at least
+
+ align:start position:0%
+because they're all multimodal at least
+ 
+
+ align:start position:0%
+because they're all multimodal at least
+two modalities will go into their series
+
+ align:start position:0%
+two modalities will go into their series
+ 
+
+ align:start position:0%
+two modalities will go into their series
+they might be dominated by one since but
+
+ align:start position:0%
+they might be dominated by one since but
+ 
+
+ align:start position:0%
+they might be dominated by one since but
+they're not really unimodal association
+
+ align:start position:0%
+they're not really unimodal association
+ 
+
+ align:start position:0%
+they're not really unimodal association
+race
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I talk about some multimodal
+
+ align:start position:0%
+and then I talk about some multimodal
+ 
+
+ align:start position:0%
+and then I talk about some multimodal
+inputs even in the primary sensory areas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in that Indie just indicates that
+
+ align:start position:0%
+so in that Indie just indicates that
+ 
+
+ align:start position:0%
+so in that Indie just indicates that
+this parcellation is complete
+
+ align:start position:0%
+this parcellation is complete
+ 
+
+ align:start position:0%
+this parcellation is complete
+maybe in in the large primates in humans
+
+ align:start position:0%
+maybe in in the large primates in humans
+ 
+
+ align:start position:0%
+maybe in in the large primates in humans
+it's about as complete as it can be
+
+ align:start position:0%
+it's about as complete as it can be
+ 
+
+ align:start position:0%
+it's about as complete as it can be
+but not in many animals
+
+ align:start position:0%
+but not in many animals
+ 
+
+ align:start position:0%
+but not in many animals
+so it's a neglected fact that gives
+
+ align:start position:0%
+so it's a neglected fact that gives
+ 
+
+ align:start position:0%
+so it's a neglected fact that gives
+clues about evolution
+
+ align:start position:0%
+clues about evolution
+ 
+
+ align:start position:0%
+clues about evolution
+because of that I paid a lot of
+
+ align:start position:0%
+because of that I paid a lot of
+ 
+
+ align:start position:0%
+because of that I paid a lot of
+attention to it and then I have a little
+
+ align:start position:0%
+attention to it and then I have a little
+ 
+
+ align:start position:0%
+attention to it and then I have a little
+bit about axon trajectories that you
+
+ align:start position:0%
+bit about axon trajectories that you
+ 
+
+ align:start position:0%
+bit about axon trajectories that you
+should realize
+
+ align:start position:0%
+should realize
+ 
+
+ align:start position:0%
+should realize
+that in this is for reptilian cortex but
+
+ align:start position:0%
+that in this is for reptilian cortex but
+ 
+
+ align:start position:0%
+that in this is for reptilian cortex but
+you see the same thing for
+
+ align:start position:0%
+you see the same thing for
+ 
+
+ align:start position:0%
+you see the same thing for
+amphibians
+
+ align:start position:0%
+amphibians
+ 
+
+ align:start position:0%
+amphibians
+and Fishes were in the cortex the axons
+
+ align:start position:0%
+and Fishes were in the cortex the axons
+ 
+
+ align:start position:0%
+and Fishes were in the cortex the axons
+don't come in from below like in this
+
+ align:start position:0%
+don't come in from below like in this
+ 
+
+ align:start position:0%
+don't come in from below like in this
+picture you see here for uh the Hedgehog
+
+ align:start position:0%
+picture you see here for uh the Hedgehog
+ 
+
+ align:start position:0%
+picture you see here for uh the Hedgehog
+the mammal they come in through the
+
+ align:start position:0%
+the mammal they come in through the
+ 
+
+ align:start position:0%
+the mammal they come in through the
+white matter then they go up and
+
+ align:start position:0%
+white matter then they go up and
+ 
+
+ align:start position:0%
+white matter then they go up and
+terminate in the various layers
+
+ align:start position:0%
+terminate in the various layers
+ 
+
+ align:start position:0%
+terminate in the various layers
+including layer one there whereas in
+
+ align:start position:0%
+including layer one there whereas in
+ 
+
+ align:start position:0%
+including layer one there whereas in
+the reptiles and turtles and the
+
+ align:start position:0%
+the reptiles and turtles and the
+ 
+
+ align:start position:0%
+the reptiles and turtles and the
+salamander and other
+
+ align:start position:0%
+salamander and other
+ 
+
+ align:start position:0%
+salamander and other
+amphibians they come in
+
+ align:start position:0%
+amphibians they come in
+ 
+
+ align:start position:0%
+amphibians they come in
+like this they don't come in through a
+
+ align:start position:0%
+like this they don't come in through a
+ 
+
+ align:start position:0%
+like this they don't come in through a
+white matter they travel eventually so
+
+ align:start position:0%
+white matter they travel eventually so
+ 
+
+ align:start position:0%
+white matter they travel eventually so
+if you look
+
+ align:start position:0%
+if you look
+ 
+
+ align:start position:0%
+if you look
+this is the way that this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pictured an almond he used the picture
+
+ align:start position:0%
+pictured an almond he used the picture
+ 
+
+ align:start position:0%
+pictured an almond he used the picture
+here of Pedro Ramon Pedro Pedro romoni
+
+ align:start position:0%
+here of Pedro Ramon Pedro Pedro romoni
+ 
+
+ align:start position:0%
+here of Pedro Ramon Pedro Pedro romoni
+kahal Ramona kahal's brother Santiago
+
+ align:start position:0%
+kahal Ramona kahal's brother Santiago
+ 
+
+ align:start position:0%
+kahal Ramona kahal's brother Santiago
+romanica house brother sorry and this is
+
+ align:start position:0%
+romanica house brother sorry and this is
+ 
+
+ align:start position:0%
+romanica house brother sorry and this is
+from the American
+
+ align:start position:0%
+from the American
+ 
+
+ align:start position:0%
+from the American
+CJ Harry
+
+ align:start position:0%
+CJ Harry
+ 
+
+ align:start position:0%
+CJ Harry
+where he shows a similar level where you
+
+ align:start position:0%
+where he shows a similar level where you
+ 
+
+ align:start position:0%
+where he shows a similar level where you
+see this
+
+ align:start position:0%
+see this
+ 
+
+ align:start position:0%
+see this
+beautifully thick medial pallium
+
+ align:start position:0%
+beautifully thick medial pallium
+ 
+
+ align:start position:0%
+beautifully thick medial pallium
+with this cortex next to it
+
+ align:start position:0%
+with this cortex next to it
+ 
+
+ align:start position:0%
+with this cortex next to it
+because and
+
+ align:start position:0%
+because and
+ 
+
+ align:start position:0%
+because and
+it's a multimodal area
+
+ align:start position:0%
+it's a multimodal area
+ 
+
+ align:start position:0%
+it's a multimodal area
+a dorsal cortex and most animals it's
+
+ align:start position:0%
+a dorsal cortex and most animals it's
+ 
+
+ align:start position:0%
+a dorsal cortex and most animals it's
+called dorsa pallium cortex
+
+ align:start position:0%
+called dorsa pallium cortex
+ 
+
+ align:start position:0%
+called dorsa pallium cortex
+and IT projects heavily into the
+
+ align:start position:0%
+and IT projects heavily into the
+ 
+
+ align:start position:0%
+and IT projects heavily into the
+mediality but it gets multimodal input
+
+ align:start position:0%
+mediality but it gets multimodal input
+ 
+
+ align:start position:0%
+mediality but it gets multimodal input
+from balance but to see how the axons
+
+ align:start position:0%
+from balance but to see how the axons
+ 
+
+ align:start position:0%
+from balance but to see how the axons
+travel here they come out of the letter
+
+ align:start position:0%
+travel here they come out of the letter
+ 
+
+ align:start position:0%
+travel here they come out of the letter
+Corbin Runner when they travel they
+
+ align:start position:0%
+Corbin Runner when they travel they
+ 
+
+ align:start position:0%
+Corbin Runner when they travel they
+don't travel through a white matter at
+
+ align:start position:0%
+don't travel through a white matter at
+ 
+
+ align:start position:0%
+don't travel through a white matter at
+the base not to announce okay so then I
+
+ align:start position:0%
+the base not to announce okay so then I
+ 
+
+ align:start position:0%
+the base not to announce okay so then I
+point out that in the hamster
+
+ align:start position:0%
+point out that in the hamster
+ 
+
+ align:start position:0%
+point out that in the hamster
+and this is true for Hedgehog two there
+
+ align:start position:0%
+and this is true for Hedgehog two there
+ 
+
+ align:start position:0%
+and this is true for Hedgehog two there
+are some neurons in lateral films
+
+ align:start position:0%
+are some neurons in lateral films
+ 
+
+ align:start position:0%
+are some neurons in lateral films
+some of the data indicates they might
+
+ align:start position:0%
+some of the data indicates they might
+ 
+
+ align:start position:0%
+some of the data indicates they might
+all be in the posterior nuclear group
+
+ align:start position:0%
+all be in the posterior nuclear group
+ 
+
+ align:start position:0%
+all be in the posterior nuclear group
+but they're in the lateral Thalamus and
+
+ align:start position:0%
+but they're in the lateral Thalamus and
+ 
+
+ align:start position:0%
+but they're in the lateral Thalamus and
+they have a they have a trajectory
+
+ align:start position:0%
+they have a they have a trajectory
+ 
+
+ align:start position:0%
+they have a they have a trajectory
+that's more like this primitive animals
+
+ align:start position:0%
+that's more like this primitive animals
+ 
+
+ align:start position:0%
+that's more like this primitive animals
+so here's I call it the type 1 axon
+
+ align:start position:0%
+so here's I call it the type 1 axon
+ 
+
+ align:start position:0%
+so here's I call it the type 1 axon
+coming in like from geniculid body and
+
+ align:start position:0%
+coming in like from geniculid body and
+ 
+
+ align:start position:0%
+coming in like from geniculid body and
+arborizing primarily in layer one and
+
+ align:start position:0%
+arborizing primarily in layer one and
+ 
+
+ align:start position:0%
+arborizing primarily in layer one and
+four but they have some branches in the
+
+ align:start position:0%
+four but they have some branches in the
+ 
+
+ align:start position:0%
+four but they have some branches in the
+other layers as well but then you have
+
+ align:start position:0%
+other layers as well but then you have
+ 
+
+ align:start position:0%
+other layers as well but then you have
+this other type
+
+ align:start position:0%
+this other type
+ 
+
+ align:start position:0%
+this other type
+the travel long distances and terminate
+
+ align:start position:0%
+the travel long distances and terminate
+ 
+
+ align:start position:0%
+the travel long distances and terminate
+it's like they ignore the boundaries
+
+ align:start position:0%
+it's like they ignore the boundaries
+ 
+
+ align:start position:0%
+it's like they ignore the boundaries
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+Century between cortical areas
+
+ align:start position:0%
+Century between cortical areas
+ 
+
+ align:start position:0%
+Century between cortical areas
+they go
+
+ align:start position:0%
+they go
+ 
+
+ align:start position:0%
+they go
+even the primary visual cortex
+
+ align:start position:0%
+even the primary visual cortex
+ 
+
+ align:start position:0%
+even the primary visual cortex
+apparently carrying multimodal input
+
+ align:start position:0%
+apparently carrying multimodal input
+ 
+
+ align:start position:0%
+apparently carrying multimodal input
+it's an anatomical
+
+ align:start position:0%
+it's an anatomical
+ 
+
+ align:start position:0%
+it's an anatomical
+now uh
+
+ align:start position:0%
+now uh
+ 
+
+ align:start position:0%
+now uh
+it's an odd fact in neuroanatomy that
+
+ align:start position:0%
+it's an odd fact in neuroanatomy that
+ 
+
+ align:start position:0%
+it's an odd fact in neuroanatomy that
+subjections exist and they've not been
+
+ align:start position:0%
+subjections exist and they've not been
+ 
+
+ align:start position:0%
+subjections exist and they've not been
+studied very well at all
+
+ align:start position:0%
+studied very well at all
+ 
+
+ align:start position:0%
+studied very well at all
+okay but they can account for some of
+
+ align:start position:0%
+okay but they can account for some of
+ 
+
+ align:start position:0%
+okay but they can account for some of
+the physiological results that we've
+
+ align:start position:0%
+the physiological results that we've
+ 
+
+ align:start position:0%
+the physiological results that we've
+been talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I want to talk more specifically now
+
+ align:start position:0%
+so I want to talk more specifically now
+ 
+
+ align:start position:0%
+so I want to talk more specifically now
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+this is now a step from chapter 33.
+
+ align:start position:0%
+this is now a step from chapter 33.
+ 
+
+ align:start position:0%
+this is now a step from chapter 33.
+which we'll talk about next time as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll try to finish chapter 33 next time
+
+ align:start position:0%
+we'll try to finish chapter 33 next time
+ 
+
+ align:start position:0%
+we'll try to finish chapter 33 next time
+and maybe at least get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chapter in the book
+
+ align:start position:0%
+chapter in the book
+ 
+
+ align:start position:0%
+chapter in the book
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I want to say more about cell types and
+
+ align:start position:0%
+I want to say more about cell types and
+ 
+
+ align:start position:0%
+I want to say more about cell types and
+their connections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different regions how we name them
+
+ align:start position:0%
+different regions how we name them
+ 
+
+ align:start position:0%
+different regions how we name them
+there's different ways to talk about
+
+ align:start position:0%
+there's different ways to talk about
+ 
+
+ align:start position:0%
+there's different ways to talk about
+different reasons and then the major
+
+ align:start position:0%
+different reasons and then the major
+ 
+
+ align:start position:0%
+different reasons and then the major
+fiber Roots which we brought up before I
+
+ align:start position:0%
+fiber Roots which we brought up before I
+ 
+
+ align:start position:0%
+fiber Roots which we brought up before I
+want to review them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you you should be able to contrast some
+
+ align:start position:0%
+you you should be able to contrast some
+ 
+
+ align:start position:0%
+you you should be able to contrast some
+of the major neuronal cell types what
+
+ align:start position:0%
+of the major neuronal cell types what
+ 
+
+ align:start position:0%
+of the major neuronal cell types what
+are the two main cell types that you can
+
+ align:start position:0%
+are the two main cell types that you can
+ 
+
+ align:start position:0%
+are the two main cell types that you can
+think of if you just think of structure
+
+ align:start position:0%
+think of if you just think of structure
+ 
+
+ align:start position:0%
+think of if you just think of structure
+and talking about neocortex
+
+ align:start position:0%
+and talking about neocortex
+ 
+
+ align:start position:0%
+and talking about neocortex
+when now they talked about these he just
+
+ align:start position:0%
+when now they talked about these he just
+ 
+
+ align:start position:0%
+when now they talked about these he just
+mainly talked about these two cell types
+
+ align:start position:0%
+mainly talked about these two cell types
+ 
+
+ align:start position:0%
+mainly talked about these two cell types
+the dominant cell type
+
+ align:start position:0%
+the dominant cell type
+ 
+
+ align:start position:0%
+the dominant cell type
+parameter cells
+
+ align:start position:0%
+parameter cells
+ 
+
+ align:start position:0%
+parameter cells
+the apical dendrite going right up
+
+ align:start position:0%
+the apical dendrite going right up
+ 
+
+ align:start position:0%
+the apical dendrite going right up
+towards the surface and arborizing okay
+
+ align:start position:0%
+towards the surface and arborizing okay
+ 
+
+ align:start position:0%
+towards the surface and arborizing okay
+and the other type you can lump them all
+
+ align:start position:0%
+and the other type you can lump them all
+ 
+
+ align:start position:0%
+and the other type you can lump them all
+together and call them skelets there are
+
+ align:start position:0%
+together and call them skelets there are
+ 
+
+ align:start position:0%
+together and call them skelets there are
+other shapes
+
+ align:start position:0%
+other shapes
+ 
+
+ align:start position:0%
+other shapes
+a few Supreme shapes for example
+
+ align:start position:0%
+a few Supreme shapes for example
+ 
+
+ align:start position:0%
+a few Supreme shapes for example
+sort of a bipolar looking neuron
+
+ align:start position:0%
+sort of a bipolar looking neuron
+ 
+
+ align:start position:0%
+sort of a bipolar looking neuron
+but there's other ways to classify them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can use neurotransmitters you can
+
+ align:start position:0%
+you can use neurotransmitters you can
+ 
+
+ align:start position:0%
+you can use neurotransmitters you can
+use whether they're spiny or non-spining
+
+ align:start position:0%
+use whether they're spiny or non-spining
+ 
+
+ align:start position:0%
+use whether they're spiny or non-spining
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+whether they're excitatory or inhibitory
+
+ align:start position:0%
+whether they're excitatory or inhibitory
+ 
+
+ align:start position:0%
+whether they're excitatory or inhibitory
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the criteria vary and the nicest
+
+ align:start position:0%
+so the criteria vary and the nicest
+ 
+
+ align:start position:0%
+so the criteria vary and the nicest
+classification I've seen is in this
+
+ align:start position:0%
+classification I've seen is in this
+ 
+
+ align:start position:0%
+classification I've seen is in this
+picture which I put in the book
+
+ align:start position:0%
+picture which I put in the book
+ 
+
+ align:start position:0%
+picture which I put in the book
+in which they separate these groups
+
+ align:start position:0%
+in which they separate these groups
+ 
+
+ align:start position:0%
+in which they separate these groups
+according to the spiny excitatory
+
+ align:start position:0%
+according to the spiny excitatory
+ 
+
+ align:start position:0%
+according to the spiny excitatory
+neurons of using glutamate as a
+
+ align:start position:0%
+neurons of using glutamate as a
+ 
+
+ align:start position:0%
+neurons of using glutamate as a
+transmitter the non-spiny inhibitory or
+
+ align:start position:0%
+transmitter the non-spiny inhibitory or
+ 
+
+ align:start position:0%
+transmitter the non-spiny inhibitory or
+gabaergic or interneurons
+
+ align:start position:0%
+gabaergic or interneurons
+ 
+
+ align:start position:0%
+gabaergic or interneurons
+and notice that these are most all
+
+ align:start position:0%
+and notice that these are most all
+ 
+
+ align:start position:0%
+and notice that these are most all
+stellate in shape a few of them might
+
+ align:start position:0%
+stellate in shape a few of them might
+ 
+
+ align:start position:0%
+stellate in shape a few of them might
+have a few subconscious and mostly the
+
+ align:start position:0%
+have a few subconscious and mostly the
+ 
+
+ align:start position:0%
+have a few subconscious and mostly the
+star-shaped and cells that don't have an
+
+ align:start position:0%
+star-shaped and cells that don't have an
+ 
+
+ align:start position:0%
+star-shaped and cells that don't have an
+apical dendrite here are the pyramidal
+
+ align:start position:0%
+apical dendrite here are the pyramidal
+ 
+
+ align:start position:0%
+apical dendrite here are the pyramidal
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+with this apical dandruff and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see here
+
+ align:start position:0%
+you see here
+ 
+
+ align:start position:0%
+you see here
+this is one in layer five it's a big
+
+ align:start position:0%
+this is one in layer five it's a big
+ 
+
+ align:start position:0%
+this is one in layer five it's a big
+pyramidal cell
+
+ align:start position:0%
+pyramidal cell
+ 
+
+ align:start position:0%
+pyramidal cell
+the apical dendrite goes right up and
+
+ align:start position:0%
+the apical dendrite goes right up and
+ 
+
+ align:start position:0%
+the apical dendrite goes right up and
+arborizes in layer one
+
+ align:start position:0%
+arborizes in layer one
+ 
+
+ align:start position:0%
+arborizes in layer one
+and usually these pictures lack a lot of
+
+ align:start position:0%
+and usually these pictures lack a lot of
+ 
+
+ align:start position:0%
+and usually these pictures lack a lot of
+the processes that are really there
+
+ align:start position:0%
+the processes that are really there
+ 
+
+ align:start position:0%
+the processes that are really there
+they're pretty complex and it shows an
+
+ align:start position:0%
+they're pretty complex and it shows an
+ 
+
+ align:start position:0%
+they're pretty complex and it shows an
+enlargement here
+
+ align:start position:0%
+enlargement here
+ 
+
+ align:start position:0%
+enlargement here
+you look at higher magnification of a
+
+ align:start position:0%
+you look at higher magnification of a
+ 
+
+ align:start position:0%
+you look at higher magnification of a
+Golgi stain or a cell that's been filled
+
+ align:start position:0%
+Golgi stain or a cell that's been filled
+ 
+
+ align:start position:0%
+Golgi stain or a cell that's been filled
+with hrp or something like that you see
+
+ align:start position:0%
+with hrp or something like that you see
+ 
+
+ align:start position:0%
+with hrp or something like that you see
+the little spines they can take so
+
+ align:start position:0%
+the little spines they can take so
+ 
+
+ align:start position:0%
+the little spines they can take so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+the spines are
+
+ align:start position:0%
+the spines are
+ 
+
+ align:start position:0%
+the spines are
+sites in many of this many of the
+
+ align:start position:0%
+sites in many of this many of the
+ 
+
+ align:start position:0%
+sites in many of this many of the
+synapses are formed in response
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then it shows where they go
+
+ align:start position:0%
+and then it shows where they go
+ 
+
+ align:start position:0%
+and then it shows where they go
+like these big cells in layer five go to
+
+ align:start position:0%
+like these big cells in layer five go to
+ 
+
+ align:start position:0%
+like these big cells in layer five go to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+spinal cord brain stem Thalamus triatum
+
+ align:start position:0%
+spinal cord brain stem Thalamus triatum
+ 
+
+ align:start position:0%
+spinal cord brain stem Thalamus triatum
+and other areas of Cortex
+
+ align:start position:0%
+and other areas of Cortex
+ 
+
+ align:start position:0%
+and other areas of Cortex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the pyramidal cells in layer three and
+
+ align:start position:0%
+the pyramidal cells in layer three and
+ 
+
+ align:start position:0%
+the pyramidal cells in layer three and
+Layer Two are much smaller but they're
+
+ align:start position:0%
+Layer Two are much smaller but they're
+ 
+
+ align:start position:0%
+Layer Two are much smaller but they're
+still pyramidal in shape they go They're
+
+ align:start position:0%
+still pyramidal in shape they go They're
+ 
+
+ align:start position:0%
+still pyramidal in shape they go They're
+transported so there
+
+ align:start position:0%
+transported so there
+ 
+
+ align:start position:0%
+transported so there
+are Association cells of the cortex
+
+ align:start position:0%
+are Association cells of the cortex
+ 
+
+ align:start position:0%
+are Association cells of the cortex
+in our propio cortical cells a term
+
+ align:start position:0%
+in our propio cortical cells a term
+ 
+
+ align:start position:0%
+in our propio cortical cells a term
+that's not usually used but it's an
+
+ align:start position:0%
+that's not usually used but it's an
+ 
+
+ align:start position:0%
+that's not usually used but it's an
+appropriate term and the only excitatory
+
+ align:start position:0%
+appropriate term and the only excitatory
+ 
+
+ align:start position:0%
+appropriate term and the only excitatory
+cell here that's not parameter in shape
+
+ align:start position:0%
+cell here that's not parameter in shape
+ 
+
+ align:start position:0%
+cell here that's not parameter in shape
+is a distillate cell we haven't called
+
+ align:start position:0%
+is a distillate cell we haven't called
+ 
+
+ align:start position:0%
+is a distillate cell we haven't called
+them granulson in layer four they get a
+
+ align:start position:0%
+them granulson in layer four they get a
+ 
+
+ align:start position:0%
+them granulson in layer four they get a
+lot of them a lot a lot of input from
+
+ align:start position:0%
+lot of them a lot a lot of input from
+ 
+
+ align:start position:0%
+lot of them a lot a lot of input from
+the thalamus comes in there and the
+
+ align:start position:0%
+the thalamus comes in there and the
+ 
+
+ align:start position:0%
+the thalamus comes in there and the
+axons simply
+
+ align:start position:0%
+axons simply
+ 
+
+ align:start position:0%
+axons simply
+terminates within the same column
+
+ align:start position:0%
+terminates within the same column
+ 
+
+ align:start position:0%
+terminates within the same column
+carries that information right up to the
+
+ align:start position:0%
+carries that information right up to the
+ 
+
+ align:start position:0%
+carries that information right up to the
+superficial layers which we often call
+
+ align:start position:0%
+superficial layers which we often call
+ 
+
+ align:start position:0%
+superficial layers which we often call
+Association layers layers two and three
+
+ align:start position:0%
+Association layers layers two and three
+ 
+
+ align:start position:0%
+Association layers layers two and three
+because they contain these neurons
+
+ align:start position:0%
+because they contain these neurons
+ 
+
+ align:start position:0%
+because they contain these neurons
+they're getting input
+
+ align:start position:0%
+they're getting input
+ 
+
+ align:start position:0%
+they're getting input
+from these stellates and therefore and
+
+ align:start position:0%
+from these stellates and therefore and
+ 
+
+ align:start position:0%
+from these stellates and therefore and
+they're projecting
+
+ align:start position:0%
+they're projecting
+ 
+
+ align:start position:0%
+they're projecting
+to other areas of Cortex
+
+ align:start position:0%
+to other areas of Cortex
+ 
+
+ align:start position:0%
+to other areas of Cortex
+now they do get other inputs they get
+
+ align:start position:0%
+now they do get other inputs they get
+ 
+
+ align:start position:0%
+now they do get other inputs they get
+some direct information problems too
+
+ align:start position:0%
+some direct information problems too
+ 
+
+ align:start position:0%
+some direct information problems too
+because the thalamus context those
+
+ align:start position:0%
+because the thalamus context those
+ 
+
+ align:start position:0%
+because the thalamus context those
+branches of the
+
+ align:start position:0%
+branches of the
+ 
+
+ align:start position:0%
+branches of the
+of the parameters
+
+ align:start position:0%
+of the parameters
+ 
+
+ align:start position:0%
+of the parameters
+and then you'll see here for the
+
+ align:start position:0%
+and then you'll see here for the
+ 
+
+ align:start position:0%
+and then you'll see here for the
+non-spiny inhibitory inner neurons how
+
+ align:start position:0%
+non-spiny inhibitory inner neurons how
+ 
+
+ align:start position:0%
+non-spiny inhibitory inner neurons how
+many different shapes and look at the
+
+ align:start position:0%
+many different shapes and look at the
+ 
+
+ align:start position:0%
+many different shapes and look at the
+the way the axons
+
+ align:start position:0%
+the way the axons
+ 
+
+ align:start position:0%
+the way the axons
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+you know you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells like
+
+ align:start position:0%
+cells like
+ 
+
+ align:start position:0%
+cells like
+like this that have an axon that
+
+ align:start position:0%
+like this that have an axon that
+ 
+
+ align:start position:0%
+like this that have an axon that
+distributes
+
+ align:start position:0%
+distributes
+ 
+
+ align:start position:0%
+distributes
+all the nearby columns here's one that
+
+ align:start position:0%
+all the nearby columns here's one that
+ 
+
+ align:start position:0%
+all the nearby columns here's one that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+all the the axon distributes up and down
+
+ align:start position:0%
+all the the axon distributes up and down
+ 
+
+ align:start position:0%
+all the the axon distributes up and down
+the same column
+
+ align:start position:0%
+the same column
+ 
+
+ align:start position:0%
+the same column
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but they've all got local accents some
+
+ align:start position:0%
+but they've all got local accents some
+ 
+
+ align:start position:0%
+but they've all got local accents some
+of them covering a number of columns
+
+ align:start position:0%
+of them covering a number of columns
+ 
+
+ align:start position:0%
+of them covering a number of columns
+some of them some of them covering only
+
+ align:start position:0%
+some of them some of them covering only
+ 
+
+ align:start position:0%
+some of them some of them covering only
+one column
+
+ align:start position:0%
+one column
+ 
+
+ align:start position:0%
+one column
+but so two major divisions according to
+
+ align:start position:0%
+but so two major divisions according to
+ 
+
+ align:start position:0%
+but so two major divisions according to
+this classification but if you do it
+
+ align:start position:0%
+this classification but if you do it
+ 
+
+ align:start position:0%
+this classification but if you do it
+just structurally you would say
+
+ align:start position:0%
+just structurally you would say
+ 
+
+ align:start position:0%
+just structurally you would say
+pyramidal and
+
+ align:start position:0%
+pyramidal and
+ 
+
+ align:start position:0%
+pyramidal and
+stellite are the two major types and
+
+ align:start position:0%
+stellite are the two major types and
+ 
+
+ align:start position:0%
+stellite are the two major types and
+that's what here's from now this book he
+
+ align:start position:0%
+that's what here's from now this book he
+ 
+
+ align:start position:0%
+that's what here's from now this book he
+shows the small param to sell and say
+
+ align:start position:0%
+shows the small param to sell and say
+ 
+
+ align:start position:0%
+shows the small param to sell and say
+you're six and then he shows a couple of
+
+ align:start position:0%
+you're six and then he shows a couple of
+ 
+
+ align:start position:0%
+you're six and then he shows a couple of
+stellates and he has a more elaborate
+
+ align:start position:0%
+stellates and he has a more elaborate
+ 
+
+ align:start position:0%
+stellates and he has a more elaborate
+picture of their
+
+ align:start position:0%
+picture of their
+ 
+
+ align:start position:0%
+picture of their
+both the dendrites and the axons
+
+ align:start position:0%
+both the dendrites and the axons
+ 
+
+ align:start position:0%
+both the dendrites and the axons
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+whereas other anatomy books like brodol
+
+ align:start position:0%
+whereas other anatomy books like brodol
+ 
+
+ align:start position:0%
+whereas other anatomy books like brodol
+as a simplified picture in this case
+
+ align:start position:0%
+as a simplified picture in this case
+ 
+
+ align:start position:0%
+as a simplified picture in this case
+interneurons we're showing some of those
+
+ align:start position:0%
+interneurons we're showing some of those
+ 
+
+ align:start position:0%
+interneurons we're showing some of those
+same cells that are in the other picture
+
+ align:start position:0%
+same cells that are in the other picture
+ 
+
+ align:start position:0%
+same cells that are in the other picture
+but he's put the axons in red like they
+
+ align:start position:0%
+but he's put the axons in red like they
+ 
+
+ align:start position:0%
+but he's put the axons in red like they
+did
+
+ align:start position:0%
+did
+ 
+
+ align:start position:0%
+did
+simplified the dendritic tree a little
+
+ align:start position:0%
+simplified the dendritic tree a little
+ 
+
+ align:start position:0%
+simplified the dendritic tree a little
+bit and shows
+
+ align:start position:0%
+bit and shows
+ 
+
+ align:start position:0%
+bit and shows
+indicates how they terminate these are
+
+ align:start position:0%
+indicates how they terminate these are
+ 
+
+ align:start position:0%
+indicates how they terminate these are
+all Gaba agencies
+
+ align:start position:0%
+all Gaba agencies
+ 
+
+ align:start position:0%
+all Gaba agencies
+except this one
+
+ align:start position:0%
+except this one
+ 
+
+ align:start position:0%
+except this one
+probably an excited for yourself and
+
+ align:start position:0%
+probably an excited for yourself and
+ 
+
+ align:start position:0%
+probably an excited for yourself and
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+so this would be the only one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is classified over here because it's
+
+ align:start position:0%
+is classified over here because it's
+ 
+
+ align:start position:0%
+is classified over here because it's
+tiny excitatory so
+
+ align:start position:0%
+tiny excitatory so
+ 
+
+ align:start position:0%
+tiny excitatory so
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I I point out here that not all
+
+ align:start position:0%
+then I I point out here that not all
+ 
+
+ align:start position:0%
+then I I point out here that not all
+local interconnections
+
+ align:start position:0%
+local interconnections
+ 
+
+ align:start position:0%
+local interconnections
+within the neocortex are made by this
+
+ align:start position:0%
+within the neocortex are made by this
+ 
+
+ align:start position:0%
+within the neocortex are made by this
+short acts on internet so I'm talking
+
+ align:start position:0%
+short acts on internet so I'm talking
+ 
+
+ align:start position:0%
+short acts on internet so I'm talking
+about just locally
+
+ align:start position:0%
+about just locally
+ 
+
+ align:start position:0%
+about just locally
+that in the same column or between one
+
+ align:start position:0%
+that in the same column or between one
+ 
+
+ align:start position:0%
+that in the same column or between one
+column in nearby columns they're made by
+
+ align:start position:0%
+column in nearby columns they're made by
+ 
+
+ align:start position:0%
+column in nearby columns they're made by
+by axon collapse
+
+ align:start position:0%
+by axon collapse
+ 
+
+ align:start position:0%
+by axon collapse
+almost all pictures of this that you see
+
+ align:start position:0%
+almost all pictures of this that you see
+ 
+
+ align:start position:0%
+almost all pictures of this that you see
+in textbooks never show this elaborate
+
+ align:start position:0%
+in textbooks never show this elaborate
+ 
+
+ align:start position:0%
+in textbooks never show this elaborate
+collateralization of the axon but the
+
+ align:start position:0%
+collateralization of the axon but the
+ 
+
+ align:start position:0%
+collateralization of the axon but the
+shy Bells were very good anatomists they
+
+ align:start position:0%
+shy Bells were very good anatomists they
+ 
+
+ align:start position:0%
+shy Bells were very good anatomists they
+published some of the best Golgi
+
+ align:start position:0%
+published some of the best Golgi
+ 
+
+ align:start position:0%
+published some of the best Golgi
+pictures and modern anatomical
+
+ align:start position:0%
+pictures and modern anatomical
+ 
+
+ align:start position:0%
+pictures and modern anatomical
+literature
+
+ align:start position:0%
+literature
+ 
+
+ align:start position:0%
+literature
+and this here they're showing
+
+ align:start position:0%
+and this here they're showing
+ 
+
+ align:start position:0%
+and this here they're showing
+that the dendritic spread of
+
+ align:start position:0%
+that the dendritic spread of
+ 
+
+ align:start position:0%
+that the dendritic spread of
+in the cat
+
+ align:start position:0%
+in the cat
+ 
+
+ align:start position:0%
+in the cat
+of neocortical cells averaged around 500
+
+ align:start position:0%
+of neocortical cells averaged around 500
+ 
+
+ align:start position:0%
+of neocortical cells averaged around 500
+microns
+
+ align:start position:0%
+microns
+ 
+
+ align:start position:0%
+microns
+whereas the Axon collaterals
+
+ align:start position:0%
+whereas the Axon collaterals
+ 
+
+ align:start position:0%
+whereas the Axon collaterals
+collaterals of the initial segment of
+
+ align:start position:0%
+collaterals of the initial segment of
+ 
+
+ align:start position:0%
+collaterals of the initial segment of
+the axon in this case the actions are
+
+ align:start position:0%
+the axon in this case the actions are
+ 
+
+ align:start position:0%
+the axon in this case the actions are
+all going out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one to other cortical areas these
+
+ align:start position:0%
+this one to other cortical areas these
+ 
+
+ align:start position:0%
+this one to other cortical areas these
+two are two
+
+ align:start position:0%
+two are two
+ 
+
+ align:start position:0%
+two are two
+to the thalamus and brainstem and spinal
+
+ align:start position:0%
+to the thalamus and brainstem and spinal
+ 
+
+ align:start position:0%
+to the thalamus and brainstem and spinal
+cord
+
+ align:start position:0%
+cord
+ 
+
+ align:start position:0%
+cord
+look how much they covered 3 000 so
+
+ align:start position:0%
+look how much they covered 3 000 so
+ 
+
+ align:start position:0%
+look how much they covered 3 000 so
+three millimeters
+
+ align:start position:0%
+three millimeters
+ 
+
+ align:start position:0%
+three millimeters
+very so huge numbers of local
+
+ align:start position:0%
+very so huge numbers of local
+ 
+
+ align:start position:0%
+very so huge numbers of local
+connections are formed by these accent
+
+ align:start position:0%
+connections are formed by these accent
+ 
+
+ align:start position:0%
+connections are formed by these accent
+collaterals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now we you should be able to answer
+
+ align:start position:0%
+okay now we you should be able to answer
+ 
+
+ align:start position:0%
+okay now we you should be able to answer
+this how have neuroscientists Define
+
+ align:start position:0%
+this how have neuroscientists Define
+ 
+
+ align:start position:0%
+this how have neuroscientists Define
+cortical layers and cortical columns
+
+ align:start position:0%
+cortical layers and cortical columns
+ 
+
+ align:start position:0%
+cortical layers and cortical columns
+divided into anatomical methods
+
+ align:start position:0%
+divided into anatomical methods
+ 
+
+ align:start position:0%
+divided into anatomical methods
+or the missile method and also the Golgi
+
+ align:start position:0%
+or the missile method and also the Golgi
+ 
+
+ align:start position:0%
+or the missile method and also the Golgi
+method if it's so dominated
+
+ align:start position:0%
+method if it's so dominated
+ 
+
+ align:start position:0%
+method if it's so dominated
+also fiber stains
+
+ align:start position:0%
+also fiber stains
+ 
+
+ align:start position:0%
+also fiber stains
+but what about the functional side
+
+ align:start position:0%
+but what about the functional side
+ 
+
+ align:start position:0%
+but what about the functional side
+electrophysiology
+
+ align:start position:0%
+electrophysiology
+ 
+
+ align:start position:0%
+electrophysiology
+our initial definition of columns came
+
+ align:start position:0%
+our initial definition of columns came
+ 
+
+ align:start position:0%
+our initial definition of columns came
+from electrophysiologists putting
+
+ align:start position:0%
+from electrophysiologists putting
+ 
+
+ align:start position:0%
+from electrophysiologists putting
+microelectrines and seeing functional
+
+ align:start position:0%
+microelectrines and seeing functional
+ 
+
+ align:start position:0%
+microelectrines and seeing functional
+differences
+
+ align:start position:0%
+differences
+ 
+
+ align:start position:0%
+differences
+between one Regional cortex and
+
+ align:start position:0%
+between one Regional cortex and
+ 
+
+ align:start position:0%
+between one Regional cortex and
+immediately adjacent like in the visual
+
+ align:start position:0%
+immediately adjacent like in the visual
+ 
+
+ align:start position:0%
+immediately adjacent like in the visual
+cortex you would find that cells here
+
+ align:start position:0%
+cortex you would find that cells here
+ 
+
+ align:start position:0%
+cortex you would find that cells here
+respond to one eye
+
+ align:start position:0%
+respond to one eye
+ 
+
+ align:start position:0%
+respond to one eye
+cells here respond to the next day then
+
+ align:start position:0%
+cells here respond to the next day then
+ 
+
+ align:start position:0%
+cells here respond to the next day then
+back to the first die and the second and
+
+ align:start position:0%
+back to the first die and the second and
+ 
+
+ align:start position:0%
+back to the first die and the second and
+so forth you know so physiological
+
+ align:start position:0%
+so forth you know so physiological
+ 
+
+ align:start position:0%
+so forth you know so physiological
+methods and various anatomical methods
+
+ align:start position:0%
+methods and various anatomical methods
+ 
+
+ align:start position:0%
+methods and various anatomical methods
+there are molecular methods in addition
+
+ align:start position:0%
+there are molecular methods in addition
+ 
+
+ align:start position:0%
+there are molecular methods in addition
+especially for layers
+
+ align:start position:0%
+especially for layers
+ 
+
+ align:start position:0%
+especially for layers
+if you look back in chapter two I had a
+
+ align:start position:0%
+if you look back in chapter two I had a
+ 
+
+ align:start position:0%
+if you look back in chapter two I had a
+picture where they had antibodies that
+
+ align:start position:0%
+picture where they had antibodies that
+ 
+
+ align:start position:0%
+picture where they had antibodies that
+bound to cells in specific laminate
+
+ align:start position:0%
+bound to cells in specific laminate
+ 
+
+ align:start position:0%
+bound to cells in specific laminate
+specific layers of the neocortex so
+
+ align:start position:0%
+specific layers of the neocortex so
+ 
+
+ align:start position:0%
+specific layers of the neocortex so
+that's still one more method
+
+ align:start position:0%
+that's still one more method
+ 
+
+ align:start position:0%
+that's still one more method
+molecular methods used for neuroanatomy
+
+ align:start position:0%
+molecular methods used for neuroanatomy
+ 
+
+ align:start position:0%
+molecular methods used for neuroanatomy
+and this just summarizes these pictures
+
+ align:start position:0%
+and this just summarizes these pictures
+ 
+
+ align:start position:0%
+and this just summarizes these pictures
+I wanted this is the one I used in the
+
+ align:start position:0%
+I wanted this is the one I used in the
+ 
+
+ align:start position:0%
+I wanted this is the one I used in the
+book
+
+ align:start position:0%
+book
+ 
+
+ align:start position:0%
+book
+uh and this is the one that usually you
+
+ align:start position:0%
+uh and this is the one that usually you
+ 
+
+ align:start position:0%
+uh and this is the one that usually you
+see in books
+
+ align:start position:0%
+see in books
+ 
+
+ align:start position:0%
+see in books
+and people will wonder why did I choose
+
+ align:start position:0%
+and people will wonder why did I choose
+ 
+
+ align:start position:0%
+and people will wonder why did I choose
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+by an American neuronatalyst
+
+ align:start position:0%
+by an American neuronatalyst
+ 
+
+ align:start position:0%
+by an American neuronatalyst
+and not the one that's always published
+
+ align:start position:0%
+and not the one that's always published
+ 
+
+ align:start position:0%
+and not the one that's always published
+and that's because I insisted
+
+ align:start position:0%
+and that's because I insisted
+ 
+
+ align:start position:0%
+and that's because I insisted
+with Amy's help
+
+ align:start position:0%
+with Amy's help
+ 
+
+ align:start position:0%
+with Amy's help
+finding the sources
+
+ align:start position:0%
+finding the sources
+ 
+
+ align:start position:0%
+finding the sources
+I didn't want it if I found people cited
+
+ align:start position:0%
+I didn't want it if I found people cited
+ 
+
+ align:start position:0%
+I didn't want it if I found people cited
+a certain Source I found the source
+
+ align:start position:0%
+a certain Source I found the source
+ 
+
+ align:start position:0%
+a certain Source I found the source
+and I found out it was wrong again and
+
+ align:start position:0%
+and I found out it was wrong again and
+ 
+
+ align:start position:0%
+and I found out it was wrong again and
+again and again
+
+ align:start position:0%
+again and again
+ 
+
+ align:start position:0%
+again and again
+because people
+
+ align:start position:0%
+because people
+ 
+
+ align:start position:0%
+because people
+usually aren't that careful in their
+
+ align:start position:0%
+usually aren't that careful in their
+ 
+
+ align:start position:0%
+usually aren't that careful in their
+scholarship I just wanted to point that
+
+ align:start position:0%
+scholarship I just wanted to point that
+ 
+
+ align:start position:0%
+scholarship I just wanted to point that
+out to you you can't believe everything
+
+ align:start position:0%
+out to you you can't believe everything
+ 
+
+ align:start position:0%
+out to you you can't believe everything
+you read
+
+ align:start position:0%
+you read
+ 
+
+ align:start position:0%
+you read
+he's an in science okay especially
+
+ align:start position:0%
+he's an in science okay especially
+ 
+
+ align:start position:0%
+he's an in science okay especially
+scientists aren't always very good
+
+ align:start position:0%
+scientists aren't always very good
+ 
+
+ align:start position:0%
+scientists aren't always very good
+historians
+
+ align:start position:0%
+historians
+ 
+
+ align:start position:0%
+historians
+just thought you might like to know that
+
+ align:start position:0%
+just thought you might like to know that
+ 
+
+ align:start position:0%
+just thought you might like to know that
+and uh we'll have to stop there
+
+ align:start position:0%
+and uh we'll have to stop there
+ 
+
+ align:start position:0%
+and uh we'll have to stop there
+we'll come back and go through a few of
+
+ align:start position:0%
+we'll come back and go through a few of
+ 
+
+ align:start position:0%
+we'll come back and go through a few of
+these things and focus on the pictures
+
+ align:start position:0%
+these things and focus on the pictures
+ 
+
+ align:start position:0%
+these things and focus on the pictures
+make sure you're understanding the
+
+ align:start position:0%
+make sure you're understanding the
+ 
+
+ align:start position:0%
+make sure you're understanding the
+pictures okay they're all posted
+
+ align:start position:0%
+pictures okay they're all posted
+ 
+
+ align:start position:0%
+pictures okay they're all posted
+talks about cortical types cortical
+
+ align:start position:0%
+talks about cortical types cortical
+ 
+
+ align:start position:0%
+talks about cortical types cortical
+columns how you can Define them
+
+ align:start position:0%
+columns how you can Define them
+ 
+
+ align:start position:0%
+columns how you can Define them
+anatomically
+
+ align:start position:0%
+anatomically
+ 
+
+ align:start position:0%
+anatomically
+layers as well and a few of the things
+
+ align:start position:0%
+layers as well and a few of the things
+ 
+
+ align:start position:0%
+layers as well and a few of the things
+that are commonly stated in the case
+
+ align:start position:0%
+that are commonly stated in the case
+ 
+
+ align:start position:0%
+that are commonly stated in the case
+come back there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the next class and I know we can get
+
+ align:start position:0%
+in the next class and I know we can get
+ 
+
+ align:start position:0%
+in the next class and I know we can get
+through these and I hope hopefully we
+
+ align:start position:0%
+through these and I hope hopefully we
+ 
+
+ align:start position:0%
+through these and I hope hopefully we
+can get a little better
+
+ align:start position:0%
+can get a little better
+ 
+
+ align:start position:0%
+can get a little better
+the next chapter as well
\ No newline at end of file
diff --git a/xsP-S7yKaRA.txt b/xsP-S7yKaRA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e5714973501ac9419b2a58a60629c1498368d5f8
--- /dev/null
+++ b/xsP-S7yKaRA.txt
@@ -0,0 +1,5899 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me make a start on the left you
+
+ align:start position:0%
+okay let me make a start on the left you
+ 
+
+ align:start position:0%
+okay let me make a start on the left you
+see the topic for today so we're doing
+
+ align:start position:0%
+see the topic for today so we're doing
+ 
+
+ align:start position:0%
+see the topic for today so we're doing
+pretty well this completes my sort of
+
+ align:start position:0%
+pretty well this completes my sort of
+ 
+
+ align:start position:0%
+pretty well this completes my sort of
+review of the highlights of linear
+
+ align:start position:0%
+review of the highlights of linear
+ 
+
+ align:start position:0%
+review of the highlights of linear
+algebra so that's five lectures and it
+
+ align:start position:0%
+algebra so that's five lectures and it
+ 
+
+ align:start position:0%
+algebra so that's five lectures and it
+I'll follow up on those five points
+
+ align:start position:0%
+I'll follow up on those five points
+ 
+
+ align:start position:0%
+I'll follow up on those five points
+because the neat part is it really ties
+
+ align:start position:0%
+because the neat part is it really ties
+ 
+
+ align:start position:0%
+because the neat part is it really ties
+together the whole subject I can values
+
+ align:start position:0%
+together the whole subject I can values
+ 
+
+ align:start position:0%
+together the whole subject I can values
+energy a transpose a determinants pivots
+
+ align:start position:0%
+energy a transpose a determinants pivots
+ 
+
+ align:start position:0%
+energy a transpose a determinants pivots
+they all come together each one gives a
+
+ align:start position:0%
+they all come together each one gives a
+ 
+
+ align:start position:0%
+they all come together each one gives a
+test for positive definite matrices so
+
+ align:start position:0%
+test for positive definite matrices so
+ 
+
+ align:start position:0%
+test for positive definite matrices so
+all that's where I'm going clear is
+
+ align:start position:0%
+all that's where I'm going clear is
+ 
+
+ align:start position:0%
+all that's where I'm going clear is
+hoping to come in for a little bit of
+
+ align:start position:0%
+hoping to come in for a little bit of
+ 
+
+ align:start position:0%
+hoping to come in for a little bit of
+the class to ask if anybody has started
+
+ align:start position:0%
+the class to ask if anybody has started
+ 
+
+ align:start position:0%
+the class to ask if anybody has started
+on the on the homework and got Julia
+
+ align:start position:0%
+on the on the homework and got Julia
+ 
+
+ align:start position:0%
+on the on the homework and got Julia
+rolling and got a yes from the auto
+
+ align:start position:0%
+rolling and got a yes from the auto
+ 
+
+ align:start position:0%
+rolling and got a yes from the auto
+grader did anybody is anybody like no
+
+ align:start position:0%
+grader did anybody is anybody like no
+ 
+
+ align:start position:0%
+grader did anybody is anybody like no
+you're taking a chance right Julia in
+
+ align:start position:0%
+you're taking a chance right Julia in
+ 
+
+ align:start position:0%
+you're taking a chance right Julia in
+principle works but in practice it's
+
+ align:start position:0%
+principle works but in practice it's
+ 
+
+ align:start position:0%
+principle works but in practice it's
+always an adventure the first time so we
+
+ align:start position:0%
+always an adventure the first time so we
+ 
+
+ align:start position:0%
+always an adventure the first time so we
+chose this lab on convolution because it
+
+ align:start position:0%
+chose this lab on convolution because it
+ 
+
+ align:start position:0%
+chose this lab on convolution because it
+was the first lab last time last year
+
+ align:start position:0%
+was the first lab last time last year
+ 
+
+ align:start position:0%
+was the first lab last time last year
+and it doesn't ask for much mass at all
+
+ align:start position:0%
+and it doesn't ask for much mass at all
+ 
+
+ align:start position:0%
+and it doesn't ask for much mass at all
+really just creating a matrix and
+
+ align:start position:0%
+really just creating a matrix and
+ 
+
+ align:start position:0%
+really just creating a matrix and
+getting the auto grader to say yes
+
+ align:start position:0%
+getting the auto grader to say yes
+ 
+
+ align:start position:0%
+getting the auto grader to say yes
+that's the right matrix so and we'll see
+
+ align:start position:0%
+that's the right matrix so and we'll see
+ 
+
+ align:start position:0%
+that's the right matrix so and we'll see
+that matrix
+
+ align:start position:0%
+that matrix
+ 
+
+ align:start position:0%
+that matrix
+we'll see this idea of convolution
+
+ align:start position:0%
+we'll see this idea of convolution
+ 
+
+ align:start position:0%
+we'll see this idea of convolution
+in the right time at the right time
+
+ align:start position:0%
+in the right time at the right time
+ 
+
+ align:start position:0%
+in the right time at the right time
+which is not that far off its signal
+
+ align:start position:0%
+which is not that far off its signal
+ 
+
+ align:start position:0%
+which is not that far off its signal
+processing and it's early in part three
+
+ align:start position:0%
+processing and it's early in part three
+ 
+
+ align:start position:0%
+processing and it's early in part three
+of the book okay so that if Claire comes
+
+ align:start position:0%
+of the book okay so that if Claire comes
+ 
+
+ align:start position:0%
+of the book okay so that if Claire comes
+in she'll answer questions otherwise I
+
+ align:start position:0%
+in she'll answer questions otherwise I
+ 
+
+ align:start position:0%
+in she'll answer questions otherwise I
+guess it would be emailing questions to
+
+ align:start position:0%
+guess it would be emailing questions to
+ 
+
+ align:start position:0%
+guess it would be emailing questions to
+I realize that the deadline is not on
+
+ align:start position:0%
+I realize that the deadline is not on
+ 
+
+ align:start position:0%
+I realize that the deadline is not on
+top of you so and you've got a whole
+
+ align:start position:0%
+top of you so and you've got a whole
+ 
+
+ align:start position:0%
+top of you so and you've got a whole
+weekend to make Julia fly alright so
+
+ align:start position:0%
+weekend to make Julia fly alright so
+ 
+
+ align:start position:0%
+weekend to make Julia fly alright so
+I'll start on the math then we had
+
+ align:start position:0%
+I'll start on the math then we had
+ 
+
+ align:start position:0%
+I'll start on the math then we had
+symmetric matrix I can values of
+
+ align:start position:0%
+symmetric matrix I can values of
+ 
+
+ align:start position:0%
+symmetric matrix I can values of
+matrices and specially symmetric
+
+ align:start position:0%
+matrices and specially symmetric
+ 
+
+ align:start position:0%
+matrices and specially symmetric
+matrices and those have real eigenvalues
+
+ align:start position:0%
+matrices and those have real eigenvalues
+ 
+
+ align:start position:0%
+matrices and those have real eigenvalues
+and I'll quickly show why and orthogonal
+
+ align:start position:0%
+and I'll quickly show why and orthogonal
+ 
+
+ align:start position:0%
+and I'll quickly show why and orthogonal
+eigenvectors and I'll quickly show why
+
+ align:start position:0%
+eigenvectors and I'll quickly show why
+ 
+
+ align:start position:0%
+eigenvectors and I'll quickly show why
+but I want to move to the new idea
+
+ align:start position:0%
+but I want to move to the new idea
+ 
+
+ align:start position:0%
+but I want to move to the new idea
+positive definite matrices so these are
+
+ align:start position:0%
+positive definite matrices so these are
+ 
+
+ align:start position:0%
+positive definite matrices so these are
+the best of the symmetric matrices there
+
+ align:start position:0%
+the best of the symmetric matrices there
+ 
+
+ align:start position:0%
+the best of the symmetric matrices there
+are symmetric matrices that have
+
+ align:start position:0%
+are symmetric matrices that have
+ 
+
+ align:start position:0%
+are symmetric matrices that have
+positive eigenvalues that's the easy way
+
+ align:start position:0%
+positive eigenvalues that's the easy way
+ 
+
+ align:start position:0%
+positive eigenvalues that's the easy way
+to remember positive definite matrices
+
+ align:start position:0%
+to remember positive definite matrices
+ 
+
+ align:start position:0%
+to remember positive definite matrices
+they have positive eigenvalues but it's
+
+ align:start position:0%
+they have positive eigenvalues but it's
+ 
+
+ align:start position:0%
+they have positive eigenvalues but it's
+certainly not the easy way to test if I
+
+ align:start position:0%
+certainly not the easy way to test if I
+ 
+
+ align:start position:0%
+certainly not the easy way to test if I
+give you a matrix like that well that's
+
+ align:start position:0%
+give you a matrix like that well that's
+ 
+
+ align:start position:0%
+give you a matrix like that well that's
+only two by two we could actually find
+
+ align:start position:0%
+only two by two we could actually find
+ 
+
+ align:start position:0%
+only two by two we could actually find
+the eigenvalues but we would like to
+
+ align:start position:0%
+the eigenvalues but we would like to
+ 
+
+ align:start position:0%
+the eigenvalues but we would like to
+have other tests easier tests which
+
+ align:start position:0%
+have other tests easier tests which
+ 
+
+ align:start position:0%
+have other tests easier tests which
+would be which would be equivalent to a
+
+ align:start position:0%
+would be which would be equivalent to a
+ 
+
+ align:start position:0%
+would be which would be equivalent to a
+positive eigenvalues so these other
+
+ align:start position:0%
+positive eigenvalues so these other
+ 
+
+ align:start position:0%
+positive eigenvalues so these other
+every one of those five tests any one of
+
+ align:start position:0%
+every one of those five tests any one of
+ 
+
+ align:start position:0%
+every one of those five tests any one of
+those five tests is is all you need so
+
+ align:start position:0%
+those five tests is is all you need so
+ 
+
+ align:start position:0%
+those five tests is is all you need so
+let me start with that example and ask
+
+ align:start position:0%
+let me start with that example and ask
+ 
+
+ align:start position:0%
+let me start with that example and ask
+you to look and then I'm gonna discuss
+
+ align:start position:0%
+you to look and then I'm gonna discuss
+ 
+
+ align:start position:0%
+you to look and then I'm gonna discuss
+those five separate points but can you
+
+ align:start position:0%
+those five separate points but can you
+ 
+
+ align:start position:0%
+those five separate points but can you
+see well my question is is that matrix s
+
+ align:start position:0%
+see well my question is is that matrix s
+ 
+
+ align:start position:0%
+see well my question is is that matrix s
+it's obviously symmetric is it positive
+
+ align:start position:0%
+it's obviously symmetric is it positive
+ 
+
+ align:start position:0%
+it's obviously symmetric is it positive
+definite or not okay so you could
+
+ align:start position:0%
+definite or not okay so you could
+ 
+
+ align:start position:0%
+definite or not okay so you could
+compute its eigenvalues since it's two
+
+ align:start position:0%
+compute its eigenvalues since it's two
+ 
+
+ align:start position:0%
+compute its eigenvalues since it's two
+by two its energy I'll come back to that
+
+ align:start position:0%
+by two its energy I'll come back to that
+ 
+
+ align:start position:0%
+by two its energy I'll come back to that
+because that's the most important one
+
+ align:start position:0%
+because that's the most important one
+ 
+
+ align:start position:0%
+because that's the most important one
+number two is really fundamental number
+
+ align:start position:0%
+number two is really fundamental number
+ 
+
+ align:start position:0%
+number two is really fundamental number
+three would ask you to factor that well
+
+ align:start position:0%
+three would ask you to factor that well
+ 
+
+ align:start position:0%
+three would ask you to factor that well
+that's you don't
+
+ align:start position:0%
+that's you don't
+ 
+
+ align:start position:0%
+that's you don't
+to take time with that well what do you
+
+ align:start position:0%
+to take time with that well what do you
+ 
+
+ align:start position:0%
+to take time with that well what do you
+think is it positive definite or not I
+
+ align:start position:0%
+think is it positive definite or not I
+ 
+
+ align:start position:0%
+think is it positive definite or not I
+see a expert in the front row saying no
+
+ align:start position:0%
+see a expert in the front row saying no
+ 
+
+ align:start position:0%
+see a expert in the front row saying no
+and why is it no the answer is no that's
+
+ align:start position:0%
+and why is it no the answer is no that's
+ 
+
+ align:start position:0%
+and why is it no the answer is no that's
+not a positive definite matrix where
+
+ align:start position:0%
+not a positive definite matrix where
+ 
+
+ align:start position:0%
+not a positive definite matrix where
+does it let us down it's got all
+
+ align:start position:0%
+does it let us down it's got all
+ 
+
+ align:start position:0%
+does it let us down it's got all
+positive numbers but that's not what
+
+ align:start position:0%
+positive numbers but that's not what
+ 
+
+ align:start position:0%
+positive numbers but that's not what
+we're asking we're asking positive
+
+ align:start position:0%
+we're asking we're asking positive
+ 
+
+ align:start position:0%
+we're asking we're asking positive
+eigenvalues positive determinants
+
+ align:start position:0%
+eigenvalues positive determinants
+ 
+
+ align:start position:0%
+eigenvalues positive determinants
+positive pivots so how does it let us
+
+ align:start position:0%
+positive pivots so how does it let us
+ 
+
+ align:start position:0%
+positive pivots so how does it let us
+down well which which is the easy test
+
+ align:start position:0%
+down well which which is the easy test
+ 
+
+ align:start position:0%
+down well which which is the easy test
+to see that it fails determinant the
+
+ align:start position:0%
+to see that it fails determinant the
+ 
+
+ align:start position:0%
+to see that it fails determinant the
+determinant is 15-16 so negative and
+
+ align:start position:0%
+determinant is 15-16 so negative and
+ 
+
+ align:start position:0%
+determinant is 15-16 so negative and
+that's what so how's the determinate
+
+ align:start position:0%
+that's what so how's the determinate
+ 
+
+ align:start position:0%
+that's what so how's the determinate
+connected to the eigenvalues everybody
+
+ align:start position:0%
+connected to the eigenvalues everybody
+ 
+
+ align:start position:0%
+connected to the eigenvalues everybody
+yep it's the product so the two
+
+ align:start position:0%
+yep it's the product so the two
+ 
+
+ align:start position:0%
+yep it's the product so the two
+eigenvalues of s they're real of course
+
+ align:start position:0%
+eigenvalues of s they're real of course
+ 
+
+ align:start position:0%
+eigenvalues of s they're real of course
+and they multiply to give the
+
+ align:start position:0%
+and they multiply to give the
+ 
+
+ align:start position:0%
+and they multiply to give the
+determinant which is minus one so one of
+
+ align:start position:0%
+determinant which is minus one so one of
+ 
+
+ align:start position:0%
+determinant which is minus one so one of
+them is negative and one of them is
+
+ align:start position:0%
+them is negative and one of them is
+ 
+
+ align:start position:0%
+them is negative and one of them is
+positive this matrix is an indefinite
+
+ align:start position:0%
+positive this matrix is an indefinite
+ 
+
+ align:start position:0%
+positive this matrix is an indefinite
+matrix indefinite so how could I make it
+
+ align:start position:0%
+matrix indefinite so how could I make it
+ 
+
+ align:start position:0%
+matrix indefinite so how could I make it
+positive definite okay just we can just
+
+ align:start position:0%
+positive definite okay just we can just
+ 
+
+ align:start position:0%
+positive definite okay just we can just
+play with an example and then we see
+
+ align:start position:0%
+play with an example and then we see
+ 
+
+ align:start position:0%
+play with an example and then we see
+these things happening let's see okay
+
+ align:start position:0%
+these things happening let's see okay
+ 
+
+ align:start position:0%
+these things happening let's see okay
+well what shall I put in in place of the
+
+ align:start position:0%
+well what shall I put in in place of the
+ 
+
+ align:start position:0%
+well what shall I put in in place of the
+five for example I could lower the four
+
+ align:start position:0%
+five for example I could lower the four
+ 
+
+ align:start position:0%
+five for example I could lower the four
+or I can up the five or up the three I
+
+ align:start position:0%
+or I can up the five or up the three I
+ 
+
+ align:start position:0%
+or I can up the five or up the three I
+can make the diagonal entries if I add
+
+ align:start position:0%
+can make the diagonal entries if I add
+ 
+
+ align:start position:0%
+can make the diagonal entries if I add
+stuff to the main diagonal I'm making it
+
+ align:start position:0%
+stuff to the main diagonal I'm making it
+ 
+
+ align:start position:0%
+stuff to the main diagonal I'm making it
+more positive so that's sort of
+
+ align:start position:0%
+more positive so that's sort of
+ 
+
+ align:start position:0%
+more positive so that's sort of
+straightforward way so what number in
+
+ align:start position:0%
+straightforward way so what number in
+ 
+
+ align:start position:0%
+straightforward way so what number in
+there would be safe six okay six would
+
+ align:start position:0%
+there would be safe six okay six would
+ 
+
+ align:start position:0%
+there would be safe six okay six would
+be safe if I go up from five to six I've
+
+ align:start position:0%
+be safe if I go up from five to six I've
+ 
+
+ align:start position:0%
+be safe if I go up from five to six I've
+got to do yeah so when I say here
+
+ align:start position:0%
+got to do yeah so when I say here
+ 
+
+ align:start position:0%
+got to do yeah so when I say here
+leading determinants what does that mean
+
+ align:start position:0%
+leading determinants what does that mean
+ 
+
+ align:start position:0%
+leading determinants what does that mean
+that so that's a that word leading means
+
+ align:start position:0%
+that so that's a that word leading means
+ 
+
+ align:start position:0%
+that so that's a that word leading means
+something it means that I take the one
+
+ align:start position:0%
+something it means that I take the one
+ 
+
+ align:start position:0%
+something it means that I take the one
+by one determinant it would have to pass
+
+ align:start position:0%
+by one determinant it would have to pass
+ 
+
+ align:start position:0%
+by one determinant it would have to pass
+that just the determinant itself would
+
+ align:start position:0%
+that just the determinant itself would
+ 
+
+ align:start position:0%
+that just the determinant itself would
+not do it let me give you an example
+
+ align:start position:0%
+not do it let me give you an example
+ 
+
+ align:start position:0%
+not do it let me give you an example
+no.4 let me take minus 3 and minus 6
+
+ align:start position:0%
+no.4 let me take minus 3 and minus 6
+ 
+
+ align:start position:0%
+no.4 let me take minus 3 and minus 6
+that would have the same determinant but
+
+ align:start position:0%
+that would have the same determinant but
+ 
+
+ align:start position:0%
+that would have the same determinant but
+it's write the determinant would still
+
+ align:start position:0%
+it's write the determinant would still
+ 
+
+ align:start position:0%
+it's write the determinant would still
+be 18 minus 16 - but it fails the tests
+
+ align:start position:0%
+be 18 minus 16 - but it fails the tests
+ 
+
+ align:start position:0%
+be 18 minus 16 - but it fails the tests
+on the on the one by one and this passes
+
+ align:start position:0%
+on the on the one by one and this passes
+ 
+
+ align:start position:0%
+on the on the one by one and this passes
+this passes the one by one test and the
+
+ align:start position:0%
+this passes the one by one test and the
+ 
+
+ align:start position:0%
+this passes the one by one test and the
+two by two tests so that's what this
+
+ align:start position:0%
+two by two tests so that's what this
+ 
+
+ align:start position:0%
+two by two tests so that's what this
+means here leading determinants are from
+
+ align:start position:0%
+means here leading determinants are from
+ 
+
+ align:start position:0%
+means here leading determinants are from
+the upper left you have to check end
+
+ align:start position:0%
+the upper left you have to check end
+ 
+
+ align:start position:0%
+the upper left you have to check end
+things because you've got n eigenvalues
+
+ align:start position:0%
+things because you've got n eigenvalues
+ 
+
+ align:start position:0%
+things because you've got n eigenvalues
+and those are the end tests right and
+
+ align:start position:0%
+and those are the end tests right and
+ 
+
+ align:start position:0%
+and those are the end tests right and
+have you noticed the connection to
+
+ align:start position:0%
+have you noticed the connection to
+ 
+
+ align:start position:0%
+have you noticed the connection to
+pivots so let's just remember that small
+
+ align:start position:0%
+pivots so let's just remember that small
+ 
+
+ align:start position:0%
+pivots so let's just remember that small
+item what would be the pivots because we
+
+ align:start position:0%
+item what would be the pivots because we
+ 
+
+ align:start position:0%
+item what would be the pivots because we
+didn't take a long time on elimination
+
+ align:start position:0%
+didn't take a long time on elimination
+ 
+
+ align:start position:0%
+didn't take a long time on elimination
+so what would be the pivots for for that
+
+ align:start position:0%
+so what would be the pivots for for that
+ 
+
+ align:start position:0%
+so what would be the pivots for for that
+matrix 3 4 4 second well what's the
+
+ align:start position:0%
+matrix 3 4 4 second well what's the
+ 
+
+ align:start position:0%
+matrix 3 4 4 second well what's the
+first pivot 3 sitting there the 1 1
+
+ align:start position:0%
+first pivot 3 sitting there the 1 1
+ 
+
+ align:start position:0%
+first pivot 3 sitting there the 1 1
+entry would be the first pivot so the
+
+ align:start position:0%
+entry would be the first pivot so the
+ 
+
+ align:start position:0%
+entry would be the first pivot so the
+pivots will be 3 and what's the second
+
+ align:start position:0%
+pivots will be 3 and what's the second
+ 
+
+ align:start position:0%
+pivots will be 3 and what's the second
+pivot well maybe to see it clearly you
+
+ align:start position:0%
+pivot well maybe to see it clearly you
+ 
+
+ align:start position:0%
+pivot well maybe to see it clearly you
+want me to take that elimination step
+
+ align:start position:0%
+want me to take that elimination step
+ 
+
+ align:start position:0%
+want me to take that elimination step
+why don't I do it just so you'll see it
+
+ align:start position:0%
+why don't I do it just so you'll see it
+ 
+
+ align:start position:0%
+why don't I do it just so you'll see it
+here so elimination would subtract some
+
+ align:start position:0%
+here so elimination would subtract some
+ 
+
+ align:start position:0%
+here so elimination would subtract some
+multiple of Row one from Row two I I
+
+ align:start position:0%
+multiple of Row one from Row two I I
+ 
+
+ align:start position:0%
+multiple of Row one from Row two I I
+would leave Row one alone I would
+
+ align:start position:0%
+would leave Row one alone I would
+ 
+
+ align:start position:0%
+would leave Row one alone I would
+subtract some multiple to get a zero
+
+ align:start position:0%
+subtract some multiple to get a zero
+ 
+
+ align:start position:0%
+subtract some multiple to get a zero
+there and what what's the multiple
+
+ align:start position:0%
+there and what what's the multiple
+ 
+
+ align:start position:0%
+there and what what's the multiple
+what's the multiplier in that was 4/3
+
+ align:start position:0%
+what's the multiplier in that was 4/3
+ 
+
+ align:start position:0%
+what's the multiplier in that was 4/3
+4/3 times Row one away from Row two
+
+ align:start position:0%
+4/3 times Row one away from Row two
+ 
+
+ align:start position:0%
+4/3 times Row one away from Row two
+would produce that 0 but 4/3 times the 4
+
+ align:start position:0%
+would produce that 0 but 4/3 times the 4
+ 
+
+ align:start position:0%
+would produce that 0 but 4/3 times the 4
+that would be 16 thirds and we're
+
+ align:start position:0%
+that would be 16 thirds and we're
+ 
+
+ align:start position:0%
+that would be 16 thirds and we're
+subtracting it from 18 thirds I think
+
+ align:start position:0%
+subtracting it from 18 thirds I think
+ 
+
+ align:start position:0%
+subtracting it from 18 thirds I think
+we've got two thirds left so the pivots
+
+ align:start position:0%
+we've got two thirds left so the pivots
+ 
+
+ align:start position:0%
+we've got two thirds left so the pivots
+which is this in elimination or the 3
+
+ align:start position:0%
+which is this in elimination or the 3
+ 
+
+ align:start position:0%
+which is this in elimination or the 3
+and the 2 thirds and of course they're
+
+ align:start position:0%
+and the 2 thirds and of course they're
+ 
+
+ align:start position:0%
+and the 2 thirds and of course they're
+positive and actually you see the
+
+ align:start position:0%
+positive and actually you see the
+ 
+
+ align:start position:0%
+positive and actually you see the
+immediate connection
+
+ align:start position:0%
+immediate connection
+ 
+
+ align:start position:0%
+immediate connection
+this pivot is the 2 by 2 determinant
+
+ align:start position:0%
+this pivot is the 2 by 2 determinant
+ 
+
+ align:start position:0%
+this pivot is the 2 by 2 determinant
+divided by the 1 by 1 determinant the 2
+
+ align:start position:0%
+divided by the 1 by 1 determinant the 2
+ 
+
+ align:start position:0%
+divided by the 1 by 1 determinant the 2
+by 2 determinant we figured out 18-49 ax
+
+ align:start position:0%
+by 2 determinant we figured out 18-49 ax
+ 
+
+ align:start position:0%
+by 2 determinant we figured out 18-49 ax
+16 was to the 1 by 1 determinant is 3
+
+ align:start position:0%
+16 was to the 1 by 1 determinant is 3
+ 
+
+ align:start position:0%
+16 was to the 1 by 1 determinant is 3
+and sure enough that second pivot is 2/3
+
+ align:start position:0%
+and sure enough that second pivot is 2/3
+ 
+
+ align:start position:0%
+and sure enough that second pivot is 2/3
+this is not so by example I'm
+
+ align:start position:0%
+this is not so by example I'm
+ 
+
+ align:start position:0%
+this is not so by example I'm
+illustrating what these different tests
+
+ align:start position:0%
+illustrating what these different tests
+ 
+
+ align:start position:0%
+illustrating what these different tests
+and again each test is all you need if
+
+ align:start position:0%
+and again each test is all you need if
+ 
+
+ align:start position:0%
+and again each test is all you need if
+it passes one test it passes them all
+
+ align:start position:0%
+it passes one test it passes them all
+ 
+
+ align:start position:0%
+it passes one test it passes them all
+and and we haven't found the eigenvalues
+
+ align:start position:0%
+and and we haven't found the eigenvalues
+ 
+
+ align:start position:0%
+and and we haven't found the eigenvalues
+let me do the energy can I do energy
+
+ align:start position:0%
+let me do the energy can I do energy
+ 
+
+ align:start position:0%
+let me do the energy can I do energy
+here okay so what's this I I'm saying
+
+ align:start position:0%
+here okay so what's this I I'm saying
+ 
+
+ align:start position:0%
+here okay so what's this I I'm saying
+that this is the really the great test
+
+ align:start position:0%
+that this is the really the great test
+ 
+
+ align:start position:0%
+that this is the really the great test
+that for me that's the definition of a
+
+ align:start position:0%
+that for me that's the definition of a
+ 
+
+ align:start position:0%
+that for me that's the definition of a
+positive definite matrix and the word
+
+ align:start position:0%
+positive definite matrix and the word
+ 
+
+ align:start position:0%
+positive definite matrix and the word
+energy comes in because it's quadratics
+
+ align:start position:0%
+energy comes in because it's quadratics
+ 
+
+ align:start position:0%
+energy comes in because it's quadratics
+away kinetic energy or potential energy
+
+ align:start position:0%
+away kinetic energy or potential energy
+ 
+
+ align:start position:0%
+away kinetic energy or potential energy
+so that's the energy in the vector X for
+
+ align:start position:0%
+so that's the energy in the vector X for
+ 
+
+ align:start position:0%
+so that's the energy in the vector X for
+this matrix so let me compute it X
+
+ align:start position:0%
+this matrix so let me compute it X
+ 
+
+ align:start position:0%
+this matrix so let me compute it X
+transpose X so let me put in s here the
+
+ align:start position:0%
+transpose X so let me put in s here the
+ 
+
+ align:start position:0%
+transpose X so let me put in s here the
+original s and let me put in an any
+
+ align:start position:0%
+original s and let me put in an any
+ 
+
+ align:start position:0%
+original s and let me put in an any
+vector X so say X Y or X 1 maybe
+
+ align:start position:0%
+vector X so say X Y or X 1 maybe
+ 
+
+ align:start position:0%
+vector X so say X Y or X 1 maybe
+do you like X X Y is easier so that's
+
+ align:start position:0%
+do you like X X Y is easier so that's
+ 
+
+ align:start position:0%
+do you like X X Y is easier so that's
+that's our vector X transpose this is
+
+ align:start position:0%
+that's our vector X transpose this is
+ 
+
+ align:start position:0%
+that's our vector X transpose this is
+our matrix s and here's our vector X so
+
+ align:start position:0%
+our matrix s and here's our vector X so
+ 
+
+ align:start position:0%
+our matrix s and here's our vector X so
+it's a function of x and y it's a pure
+
+ align:start position:0%
+it's a function of x and y it's a pure
+ 
+
+ align:start position:0%
+it's a function of x and y it's a pure
+quadratic function can you do you know
+
+ align:start position:0%
+quadratic function can you do you know
+ 
+
+ align:start position:0%
+quadratic function can you do you know
+what I get when I multiply that out I
+
+ align:start position:0%
+what I get when I multiply that out I
+ 
+
+ align:start position:0%
+what I get when I multiply that out I
+get I get a very simple important type
+
+ align:start position:0%
+get I get a very simple important type
+ 
+
+ align:start position:0%
+get I get a very simple important type
+of function shall we multiply it out
+
+ align:start position:0%
+of function shall we multiply it out
+ 
+
+ align:start position:0%
+of function shall we multiply it out
+let's see so I multiply that by that
+
+ align:start position:0%
+let's see so I multiply that by that
+ 
+
+ align:start position:0%
+let's see so I multiply that by that
+first so I get 3x plus 4y and 4x plus 6y
+
+ align:start position:0%
+first so I get 3x plus 4y and 4x plus 6y
+ 
+
+ align:start position:0%
+first so I get 3x plus 4y and 4x plus 6y
+it's what I'm getting from the these two
+
+ align:start position:0%
+it's what I'm getting from the these two
+ 
+
+ align:start position:0%
+it's what I'm getting from the these two
+and now I'm hitting that with the X Y
+
+ align:start position:0%
+and now I'm hitting that with the X Y
+ 
+
+ align:start position:0%
+and now I'm hitting that with the X Y
+and now I'm gonna see the energy and
+
+ align:start position:0%
+and now I'm gonna see the energy and
+ 
+
+ align:start position:0%
+and now I'm gonna see the energy and
+you'll see the pattern that's always
+
+ align:start position:0%
+you'll see the pattern that's always
+ 
+
+ align:start position:0%
+you'll see the pattern that's always
+what math is about what's the pattern so
+
+ align:start position:0%
+what math is about what's the pattern so
+ 
+
+ align:start position:0%
+what math is about what's the pattern so
+I have x times 3x 3x squared + iy x 6y
+
+ align:start position:0%
+I have x times 3x 3x squared + iy x 6y
+ 
+
+ align:start position:0%
+I have x times 3x 3x squared + iy x 6y
+that's 6 y square and I have x times 4y
+
+ align:start position:0%
+that's 6 y square and I have x times 4y
+ 
+
+ align:start position:0%
+that's 6 y square and I have x times 4y
+that's 4 XY z-- + iy times 4x that's for
+
+ align:start position:0%
+that's 4 XY z-- + iy times 4x that's for
+ 
+
+ align:start position:0%
+that's 4 XY z-- + iy times 4x that's for
+more XY so I've got all those terms
+
+ align:start position:0%
+more XY so I've got all those terms
+ 
+
+ align:start position:0%
+more XY so I've got all those terms
+every every term in every number in the
+
+ align:start position:0%
+every every term in every number in the
+ 
+
+ align:start position:0%
+every every term in every number in the
+matrix gives me a piece of the energy
+
+ align:start position:0%
+matrix gives me a piece of the energy
+ 
+
+ align:start position:0%
+matrix gives me a piece of the energy
+and you see that the diagonal numbers 3
+
+ align:start position:0%
+and you see that the diagonal numbers 3
+ 
+
+ align:start position:0%
+and you see that the diagonal numbers 3
+& 6 those give me the diagonal pieces 3x
+
+ align:start position:0%
+& 6 those give me the diagonal pieces 3x
+ 
+
+ align:start position:0%
+& 6 those give me the diagonal pieces 3x
+squared + 6 y squared and then the crust
+
+ align:start position:0%
+squared + 6 y squared and then the crust
+ 
+
+ align:start position:0%
+squared + 6 y squared and then the crust
+but I maybe call them the cross terms
+
+ align:start position:0%
+but I maybe call them the cross terms
+ 
+
+ align:start position:0%
+but I maybe call them the cross terms
+those give me 4 XY + 4 XY so really 8 X
+
+ align:start position:0%
+those give me 4 XY + 4 XY so really 8 X
+ 
+
+ align:start position:0%
+those give me 4 XY + 4 XY so really 8 X
+Y so so you could call this thing 8 X Y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's my function that's my
+
+ align:start position:0%
+so that's my function that's my
+ 
+
+ align:start position:0%
+so that's my function that's my
+quadratic that's my energy and I believe
+
+ align:start position:0%
+quadratic that's my energy and I believe
+ 
+
+ align:start position:0%
+quadratic that's my energy and I believe
+that that is greater than 0 let me graph
+
+ align:start position:0%
+that that is greater than 0 let me graph
+ 
+
+ align:start position:0%
+that that is greater than 0 let me graph
+the thing let me graph that energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's a graph of my function f
+
+ align:start position:0%
+okay so here's a graph of my function f
+ 
+
+ align:start position:0%
+okay so here's a graph of my function f
+of x and y here is X and here is y and
+
+ align:start position:0%
+of x and y here is X and here is y and
+ 
+
+ align:start position:0%
+of x and y here is X and here is y and
+of course that's on the graph
+
+ align:start position:0%
+of course that's on the graph
+ 
+
+ align:start position:0%
+of course that's on the graph
+zero zero at x equals zero y equals zero
+
+ align:start position:0%
+zero zero at x equals zero y equals zero
+ 
+
+ align:start position:0%
+zero zero at x equals zero y equals zero
+the function is clearly zero everybody's
+
+ align:start position:0%
+the function is clearly zero everybody's
+ 
+
+ align:start position:0%
+the function is clearly zero everybody's
+got his eye let me write that function
+
+ align:start position:0%
+got his eye let me write that function
+ 
+
+ align:start position:0%
+got his eye let me write that function
+again here 3 x squared 6 y squared 8 X Y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually you can see this is how I think
+
+ align:start position:0%
+actually you can see this is how I think
+ 
+
+ align:start position:0%
+actually you can see this is how I think
+about that that function so 3x squared
+
+ align:start position:0%
+about that that function so 3x squared
+ 
+
+ align:start position:0%
+about that that function so 3x squared
+is obviously carrying me upwards it's
+
+ align:start position:0%
+is obviously carrying me upwards it's
+ 
+
+ align:start position:0%
+is obviously carrying me upwards it's
+not it never goes negative 6y squared
+
+ align:start position:0%
+not it never goes negative 6y squared
+ 
+
+ align:start position:0%
+not it never goes negative 6y squared
+will never go negative 8 X Y can go
+
+ align:start position:0%
+will never go negative 8 X Y can go
+ 
+
+ align:start position:0%
+will never go negative 8 X Y can go
+negative right if x and y have opposite
+
+ align:start position:0%
+negative right if x and y have opposite
+ 
+
+ align:start position:0%
+negative right if x and y have opposite
+signs that that will go negative but the
+
+ align:start position:0%
+signs that that will go negative but the
+ 
+
+ align:start position:0%
+signs that that will go negative but the
+question is do these do these positive
+
+ align:start position:0%
+question is do these do these positive
+ 
+
+ align:start position:0%
+question is do these do these positive
+pieces overwhelm it and make the graph
+
+ align:start position:0%
+pieces overwhelm it and make the graph
+ 
+
+ align:start position:0%
+pieces overwhelm it and make the graph
+go up like a bowl and the answer is yes
+
+ align:start position:0%
+go up like a bowl and the answer is yes
+ 
+
+ align:start position:0%
+go up like a bowl and the answer is yes
+for a positive definite matrix so this
+
+ align:start position:0%
+for a positive definite matrix so this
+ 
+
+ align:start position:0%
+for a positive definite matrix so this
+is a graph of a positive definite matrix
+
+ align:start position:0%
+is a graph of a positive definite matrix
+ 
+
+ align:start position:0%
+is a graph of a positive definite matrix
+of a part of positive energy the energy
+
+ align:start position:0%
+of a part of positive energy the energy
+ 
+
+ align:start position:0%
+of a part of positive energy the energy
+of a positive definite matrix so this is
+
+ align:start position:0%
+of a positive definite matrix so this is
+ 
+
+ align:start position:0%
+of a positive definite matrix so this is
+the energy X transpose F X that I'm
+
+ align:start position:0%
+the energy X transpose F X that I'm
+ 
+
+ align:start position:0%
+the energy X transpose F X that I'm
+graph and there it is
+
+ align:start position:0%
+graph and there it is
+ 
+
+ align:start position:0%
+graph and there it is
+this is important this is important this
+
+ align:start position:0%
+this is important this is important this
+ 
+
+ align:start position:0%
+this is important this is important this
+is the kind of function we like X
+
+ align:start position:0%
+is the kind of function we like X
+ 
+
+ align:start position:0%
+is the kind of function we like X
+transpose X where s is positive definite
+
+ align:start position:0%
+transpose X where s is positive definite
+ 
+
+ align:start position:0%
+transpose X where s is positive definite
+so the function goes up like that this
+
+ align:start position:0%
+so the function goes up like that this
+ 
+
+ align:start position:0%
+so the function goes up like that this
+is what deep learning is about this
+
+ align:start position:0%
+is what deep learning is about this
+ 
+
+ align:start position:0%
+is what deep learning is about this
+could be a loss function that you that
+
+ align:start position:0%
+could be a loss function that you that
+ 
+
+ align:start position:0%
+could be a loss function that you that
+you minimize it could depend on a
+
+ align:start position:0%
+you minimize it could depend on a
+ 
+
+ align:start position:0%
+you minimize it could depend on a
+hundred thousand variables or more and
+
+ align:start position:0%
+hundred thousand variables or more and
+ 
+
+ align:start position:0%
+hundred thousand variables or more and
+it could come from the the error in the
+
+ align:start position:0%
+it could come from the the error in the
+ 
+
+ align:start position:0%
+it could come from the the error in the
+difference between training data and
+
+ align:start position:0%
+difference between training data and
+ 
+
+ align:start position:0%
+difference between training data and
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+and the number you get the loss would be
+
+ align:start position:0%
+and the number you get the loss would be
+ 
+
+ align:start position:0%
+and the number you get the loss would be
+some expression like that well I'll make
+
+ align:start position:0%
+some expression like that well I'll make
+ 
+
+ align:start position:0%
+some expression like that well I'll make
+sense of those words as soon as I can
+
+ align:start position:0%
+sense of those words as soon as I can
+ 
+
+ align:start position:0%
+sense of those words as soon as I can
+what I want to say is deep learning
+
+ align:start position:0%
+what I want to say is deep learning
+ 
+
+ align:start position:0%
+what I want to say is deep learning
+neural Nets machine learning that the
+
+ align:start position:0%
+neural Nets machine learning that the
+ 
+
+ align:start position:0%
+neural Nets machine learning that the
+big computation is to minimize an energy
+
+ align:start position:0%
+big computation is to minimize an energy
+ 
+
+ align:start position:0%
+big computation is to minimize an energy
+is to minimize an energy now of course I
+
+ align:start position:0%
+is to minimize an energy now of course I
+ 
+
+ align:start position:0%
+is to minimize an energy now of course I
+made the minimum easy to find because I
+
+ align:start position:0%
+made the minimum easy to find because I
+ 
+
+ align:start position:0%
+made the minimum easy to find because I
+have pure squares
+
+ align:start position:0%
+have pure squares
+ 
+
+ align:start position:0%
+have pure squares
+well that doesn't happen in practice of
+
+ align:start position:0%
+well that doesn't happen in practice of
+ 
+
+ align:start position:0%
+well that doesn't happen in practice of
+course in practice we have linear terms
+
+ align:start position:0%
+course in practice we have linear terms
+ 
+
+ align:start position:0%
+course in practice we have linear terms
+X transpose B or nonlinear yeah the loss
+
+ align:start position:0%
+X transpose B or nonlinear yeah the loss
+ 
+
+ align:start position:0%
+X transpose B or nonlinear yeah the loss
+function doesn't have to be a thing
+
+ align:start position:0%
+function doesn't have to be a thing
+ 
+
+ align:start position:0%
+function doesn't have to be a thing
+cross-entropy all kinds of things there
+
+ align:start position:0%
+cross-entropy all kinds of things there
+ 
+
+ align:start position:0%
+cross-entropy all kinds of things there
+there's a whole dictionary of possible
+
+ align:start position:0%
+there's a whole dictionary of possible
+ 
+
+ align:start position:0%
+there's a whole dictionary of possible
+loss functions but but this is the model
+
+ align:start position:0%
+loss functions but but this is the model
+ 
+
+ align:start position:0%
+loss functions but but this is the model
+this is the model and I'll make it the
+
+ align:start position:0%
+this is the model and I'll make it the
+ 
+
+ align:start position:0%
+this is the model and I'll make it the
+perfect model by just focusing on that
+
+ align:start position:0%
+perfect model by just focusing on that
+ 
+
+ align:start position:0%
+perfect model by just focusing on that
+on that part well yeah by the way what
+
+ align:start position:0%
+on that part well yeah by the way what
+ 
+
+ align:start position:0%
+on that part well yeah by the way what
+what what would create what would happen
+
+ align:start position:0%
+what what would create what would happen
+ 
+
+ align:start position:0%
+what what would create what would happen
+if that was in there I shouldn't have
+
+ align:start position:0%
+if that was in there I shouldn't have
+ 
+
+ align:start position:0%
+if that was in there I shouldn't have
+exited out so so well so quickly since I
+
+ align:start position:0%
+exited out so so well so quickly since I
+ 
+
+ align:start position:0%
+exited out so so well so quickly since I
+just put it up there let me put it back
+
+ align:start position:0%
+just put it up there let me put it back
+ 
+
+ align:start position:0%
+just put it up there let me put it back
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+I saw it better rather okay
+
+ align:start position:0%
+I saw it better rather okay
+ 
+
+ align:start position:0%
+I saw it better rather okay
+this is the kind of least squares
+
+ align:start position:0%
+this is the kind of least squares
+ 
+
+ align:start position:0%
+this is the kind of least squares
+problem with some data be minimize that
+
+ align:start position:0%
+problem with some data be minimize that
+ 
+
+ align:start position:0%
+problem with some data be minimize that
+so what would be the graph of this guy
+
+ align:start position:0%
+so what would be the graph of this guy
+ 
+
+ align:start position:0%
+so what would be the graph of this guy
+can I just draw the same sort of picture
+
+ align:start position:0%
+can I just draw the same sort of picture
+ 
+
+ align:start position:0%
+can I just draw the same sort of picture
+for that function will it be a bowl yes
+
+ align:start position:0%
+for that function will it be a bowl yes
+ 
+
+ align:start position:0%
+for that function will it be a bowl yes
+if I have this term all that does is
+
+ align:start position:0%
+if I have this term all that does is
+ 
+
+ align:start position:0%
+if I have this term all that does is
+move it off center here at x equals 0
+
+ align:start position:0%
+move it off center here at x equals 0
+ 
+
+ align:start position:0%
+move it off center here at x equals 0
+well I still get 0 sorry I still go
+
+ align:start position:0%
+well I still get 0 sorry I still go
+ 
+
+ align:start position:0%
+well I still get 0 sorry I still go
+through that point if this is the zero
+
+ align:start position:0%
+through that point if this is the zero
+ 
+
+ align:start position:0%
+through that point if this is the zero
+vector I'm still getting 0 but this will
+
+ align:start position:0%
+vector I'm still getting 0 but this will
+ 
+
+ align:start position:0%
+vector I'm still getting 0 but this will
+bring it below that would that would
+
+ align:start position:0%
+bring it below that would that would
+ 
+
+ align:start position:0%
+bring it below that would that would
+produce a bowl like that actually it
+
+ align:start position:0%
+produce a bowl like that actually it
+ 
+
+ align:start position:0%
+produce a bowl like that actually it
+would just be
+
+ align:start position:0%
+would just be
+ 
+
+ align:start position:0%
+would just be
+same Bowl the bowl is would just be
+
+ align:start position:0%
+same Bowl the bowl is would just be
+ 
+
+ align:start position:0%
+same Bowl the bowl is would just be
+shifted I could write that to show how
+
+ align:start position:0%
+shifted I could write that to show how
+ 
+
+ align:start position:0%
+shifted I could write that to show how
+that happens so this is this is now
+
+ align:start position:0%
+that happens so this is this is now
+ 
+
+ align:start position:0%
+that happens so this is this is now
+below zero this is the that's the
+
+ align:start position:0%
+below zero this is the that's the
+ 
+
+ align:start position:0%
+below zero this is the that's the
+solution we're after
+
+ align:start position:0%
+solution we're after
+ 
+
+ align:start position:0%
+solution we're after
+that tells us the weights in the neural
+
+ align:start position:0%
+that tells us the weights in the neural
+ 
+
+ align:start position:0%
+that tells us the weights in the neural
+network I'm just using these words but
+
+ align:start position:0%
+network I'm just using these words but
+ 
+
+ align:start position:0%
+network I'm just using these words but
+will soon have a meaning to them I want
+
+ align:start position:0%
+will soon have a meaning to them I want
+ 
+
+ align:start position:0%
+will soon have a meaning to them I want
+to find that minimum in other words and
+
+ align:start position:0%
+to find that minimum in other words and
+ 
+
+ align:start position:0%
+to find that minimum in other words and
+I want to find it for much more
+
+ align:start position:0%
+I want to find it for much more
+ 
+
+ align:start position:0%
+I want to find it for much more
+complicated functions than that of
+
+ align:start position:0%
+complicated functions than that of
+ 
+
+ align:start position:0%
+complicated functions than that of
+course if I minimize a quadratic that
+
+ align:start position:0%
+course if I minimize a quadratic that
+ 
+
+ align:start position:0%
+course if I minimize a quadratic that
+means setting derivatives to zero I just
+
+ align:start position:0%
+means setting derivatives to zero I just
+ 
+
+ align:start position:0%
+means setting derivatives to zero I just
+have linear equations probably I can I
+
+ align:start position:0%
+have linear equations probably I can I
+ 
+
+ align:start position:0%
+have linear equations probably I can I
+could write everything down for that for
+
+ align:start position:0%
+could write everything down for that for
+ 
+
+ align:start position:0%
+could write everything down for that for
+that thing so let's put in some
+
+ align:start position:0%
+that thing so let's put in some
+ 
+
+ align:start position:0%
+that thing so let's put in some
+nonlinear stuff which which wiggles the
+
+ align:start position:0%
+nonlinear stuff which which wiggles the
+ 
+
+ align:start position:0%
+nonlinear stuff which which wiggles the
+bowl makes it not so easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can I look a month ahead how do you find
+
+ align:start position:0%
+can I look a month ahead how do you find
+ 
+
+ align:start position:0%
+can I look a month ahead how do you find
+so this is a big part of mathematics
+
+ align:start position:0%
+so this is a big part of mathematics
+ 
+
+ align:start position:0%
+so this is a big part of mathematics
+applied math optimization minimization
+
+ align:start position:0%
+applied math optimization minimization
+ 
+
+ align:start position:0%
+applied math optimization minimization
+of a complicated function of a hundred
+
+ align:start position:0%
+of a complicated function of a hundred
+ 
+
+ align:start position:0%
+of a complicated function of a hundred
+thousand variables that's the biggest
+
+ align:start position:0%
+thousand variables that's the biggest
+ 
+
+ align:start position:0%
+thousand variables that's the biggest
+computation that's the reason machine
+
+ align:start position:0%
+computation that's the reason machine
+ 
+
+ align:start position:0%
+computation that's the reason machine
+learning on big problems takes a week on
+
+ align:start position:0%
+learning on big problems takes a week on
+ 
+
+ align:start position:0%
+learning on big problems takes a week on
+a GPU or multiple GPUs because you have
+
+ align:start position:0%
+a GPU or multiple GPUs because you have
+ 
+
+ align:start position:0%
+a GPU or multiple GPUs because you have
+so many unknowns more than 100000 would
+
+ align:start position:0%
+so many unknowns more than 100000 would
+ 
+
+ align:start position:0%
+so many unknowns more than 100000 would
+be quite normal in general let's just
+
+ align:start position:0%
+be quite normal in general let's just
+ 
+
+ align:start position:0%
+be quite normal in general let's just
+have the pleasure of looking ahead for
+
+ align:start position:0%
+have the pleasure of looking ahead for
+ 
+
+ align:start position:0%
+have the pleasure of looking ahead for
+one minute and then I'll come back to
+
+ align:start position:0%
+one minute and then I'll come back to
+ 
+
+ align:start position:0%
+one minute and then I'll come back to
+real life here linear algebra yeah just
+
+ align:start position:0%
+real life here linear algebra yeah just
+ 
+
+ align:start position:0%
+real life here linear algebra yeah just
+I can't resist thinking aloud how do you
+
+ align:start position:0%
+I can't resist thinking aloud how do you
+ 
+
+ align:start position:0%
+I can't resist thinking aloud how do you
+find the minimum by the way these
+
+ align:start position:0%
+find the minimum by the way these
+ 
+
+ align:start position:0%
+find the minimum by the way these
+functions both of them are convex so
+
+ align:start position:0%
+functions both of them are convex so
+ 
+
+ align:start position:0%
+functions both of them are convex so
+that is convex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I want to connect convex functions F
+
+ align:start position:0%
+so I want to connect convex functions F
+ 
+
+ align:start position:0%
+so I want to connect convex functions F
+and what does convex mean it means well
+
+ align:start position:0%
+and what does convex mean it means well
+ 
+
+ align:start position:0%
+and what does convex mean it means well
+that the graph is like that yeah I mean
+
+ align:start position:0%
+that the graph is like that yeah I mean
+ 
+
+ align:start position:0%
+that the graph is like that yeah I mean
+not perfect it could it could but if if
+
+ align:start position:0%
+not perfect it could it could but if if
+ 
+
+ align:start position:0%
+not perfect it could it could but if if
+it's a quadratic then convex means
+
+ align:start position:0%
+it's a quadratic then convex means
+ 
+
+ align:start position:0%
+it's a quadratic then convex means
+positive definite or maybe in the
+
+ align:start position:0%
+positive definite or maybe in the
+ 
+
+ align:start position:0%
+positive definite or maybe in the
+extreme positive semi-definite I'll have
+
+ align:start position:0%
+extreme positive semi-definite I'll have
+ 
+
+ align:start position:0%
+extreme positive semi-definite I'll have
+to mention that yeah but but convex
+
+ align:start position:0%
+to mention that yeah but but convex
+ 
+
+ align:start position:0%
+to mention that yeah but but convex
+means it goes up but it could have
+
+ align:start position:0%
+means it goes up but it could have
+ 
+
+ align:start position:0%
+means it goes up but it could have
+Wiggles it doesn't have to be just
+
+ align:start position:0%
+Wiggles it doesn't have to be just
+ 
+
+ align:start position:0%
+Wiggles it doesn't have to be just
+perfect squares and linear terms but
+
+ align:start position:0%
+perfect squares and linear terms but
+ 
+
+ align:start position:0%
+perfect squares and linear terms but
+general things and for for deep learning
+
+ align:start position:0%
+general things and for for deep learning
+ 
+
+ align:start position:0%
+general things and for for deep learning
+it will include none it'll go far beyond
+
+ align:start position:0%
+it will include none it'll go far beyond
+ 
+
+ align:start position:0%
+it will include none it'll go far beyond
+quadratics but well it may not be convex
+
+ align:start position:0%
+quadratics but well it may not be convex
+ 
+
+ align:start position:0%
+quadratics but well it may not be convex
+I guess that's also true yeah so so deep
+
+ align:start position:0%
+I guess that's also true yeah so so deep
+ 
+
+ align:start position:0%
+I guess that's also true yeah so so deep
+learning has got serious problems
+
+ align:start position:0%
+learning has got serious problems
+ 
+
+ align:start position:0%
+learning has got serious problems
+because those functions they may look
+
+ align:start position:0%
+because those functions they may look
+ 
+
+ align:start position:0%
+because those functions they may look
+like this but then over here they could
+
+ align:start position:0%
+like this but then over here they could
+ 
+
+ align:start position:0%
+like this but then over here they could
+go you know non convex they could dip
+
+ align:start position:0%
+go you know non convex they could dip
+ 
+
+ align:start position:0%
+go you know non convex they could dip
+down a little more and you're looking
+
+ align:start position:0%
+down a little more and you're looking
+ 
+
+ align:start position:0%
+down a little more and you're looking
+for this point or for this point still
+
+ align:start position:0%
+for this point or for this point still
+ 
+
+ align:start position:0%
+for this point or for this point still
+I'm determined to tell you how to find
+
+ align:start position:0%
+I'm determined to tell you how to find
+ 
+
+ align:start position:0%
+I'm determined to tell you how to find
+it so or a start on how you find it so
+
+ align:start position:0%
+it so or a start on how you find it so
+ 
+
+ align:start position:0%
+it so or a start on how you find it so
+you're at some point there right sorry
+
+ align:start position:0%
+you're at some point there right sorry
+ 
+
+ align:start position:0%
+you're at some point there right sorry
+start there somewhere on this surface
+
+ align:start position:0%
+start there somewhere on this surface
+ 
+
+ align:start position:0%
+start there somewhere on this surface
+some X some some vector X is your start
+
+ align:start position:0%
+some X some some vector X is your start
+ 
+
+ align:start position:0%
+some X some some vector X is your start
+x0 starting and we're going to just take
+
+ align:start position:0%
+x0 starting and we're going to just take
+ 
+
+ align:start position:0%
+x0 starting and we're going to just take
+a step hopefully down down the bowl well
+
+ align:start position:0%
+a step hopefully down down the bowl well
+ 
+
+ align:start position:0%
+a step hopefully down down the bowl well
+of course it would be fantastic to take
+
+ align:start position:0%
+of course it would be fantastic to take
+ 
+
+ align:start position:0%
+of course it would be fantastic to take
+to get there in one step but that's not
+
+ align:start position:0%
+to get there in one step but that's not
+ 
+
+ align:start position:0%
+to get there in one step but that's not
+going to happen that that would be
+
+ align:start position:0%
+going to happen that that would be
+ 
+
+ align:start position:0%
+going to happen that that would be
+solving a big linear system very
+
+ align:start position:0%
+solving a big linear system very
+ 
+
+ align:start position:0%
+solving a big linear system very
+expensive and a big nonlinear system so
+
+ align:start position:0%
+expensive and a big nonlinear system so
+ 
+
+ align:start position:0%
+expensive and a big nonlinear system so
+really that's what we're trying to solve
+
+ align:start position:0%
+really that's what we're trying to solve
+ 
+
+ align:start position:0%
+really that's what we're trying to solve
+a big nonlinear system and I should be
+
+ align:start position:0%
+a big nonlinear system and I should be
+ 
+
+ align:start position:0%
+a big nonlinear system and I should be
+like on this picture
+
+ align:start position:0%
+like on this picture
+ 
+
+ align:start position:0%
+like on this picture
+because here we can see where the
+
+ align:start position:0%
+because here we can see where the
+ 
+
+ align:start position:0%
+because here we can see where the
+minimum is but they just shift so what
+
+ align:start position:0%
+minimum is but they just shift so what
+ 
+
+ align:start position:0%
+minimum is but they just shift so what
+would you do if you had a starting point
+
+ align:start position:0%
+would you do if you had a starting point
+ 
+
+ align:start position:0%
+would you do if you had a starting point
+and you wanted to go look for the
+
+ align:start position:0%
+and you wanted to go look for the
+ 
+
+ align:start position:0%
+and you wanted to go look for the
+minimum but what's the natural idea
+
+ align:start position:0%
+minimum but what's the natural idea
+ 
+
+ align:start position:0%
+minimum but what's the natural idea
+compute derivatives
+
+ align:start position:0%
+compute derivatives
+ 
+
+ align:start position:0%
+compute derivatives
+you've got calculus on your side compute
+
+ align:start position:0%
+you've got calculus on your side compute
+ 
+
+ align:start position:0%
+you've got calculus on your side compute
+the first derivatives so the first
+
+ align:start position:0%
+the first derivatives so the first
+ 
+
+ align:start position:0%
+the first derivatives so the first
+derivatives with respect to X so so I
+
+ align:start position:0%
+derivatives with respect to X so so I
+ 
+
+ align:start position:0%
+derivatives with respect to X so so I
+would compute the derivative of F with
+
+ align:start position:0%
+would compute the derivative of F with
+ 
+
+ align:start position:0%
+would compute the derivative of F with
+respect to X and the derivative of F
+
+ align:start position:0%
+respect to X and the derivative of F
+ 
+
+ align:start position:0%
+respect to X and the derivative of F
+with respect to Y and hundred thousand
+
+ align:start position:0%
+with respect to Y and hundred thousand
+ 
+
+ align:start position:0%
+with respect to Y and hundred thousand
+more and that takes a little while and
+
+ align:start position:0%
+more and that takes a little while and
+ 
+
+ align:start position:0%
+more and that takes a little while and
+now I've got the derivatives what do I
+
+ align:start position:0%
+now I've got the derivatives what do I
+ 
+
+ align:start position:0%
+now I've got the derivatives what do I
+do I go that tells me the steepest
+
+ align:start position:0%
+do I go that tells me the steepest
+ 
+
+ align:start position:0%
+do I go that tells me the steepest
+direction that tells me at that point
+
+ align:start position:0%
+direction that tells me at that point
+ 
+
+ align:start position:0%
+direction that tells me at that point
+which way is fastest way down so I would
+
+ align:start position:0%
+which way is fastest way down so I would
+ 
+
+ align:start position:0%
+which way is fastest way down so I would
+follow I would do a gradient descent I
+
+ align:start position:0%
+follow I would do a gradient descent I
+ 
+
+ align:start position:0%
+follow I would do a gradient descent I
+would follow that gradient this is
+
+ align:start position:0%
+would follow that gradient this is
+ 
+
+ align:start position:0%
+would follow that gradient this is
+called the gradient all the first
+
+ align:start position:0%
+called the gradient all the first
+ 
+
+ align:start position:0%
+called the gradient all the first
+derivatives is called the gradient of F
+
+ align:start position:0%
+derivatives is called the gradient of F
+ 
+
+ align:start position:0%
+derivatives is called the gradient of F
+the gradient gradient vector it's a
+
+ align:start position:0%
+the gradient gradient vector it's a
+ 
+
+ align:start position:0%
+the gradient gradient vector it's a
+vector of course because F is a function
+
+ align:start position:0%
+vector of course because F is a function
+ 
+
+ align:start position:0%
+vector of course because F is a function
+of lots of variables I would start down
+
+ align:start position:0%
+of lots of variables I would start down
+ 
+
+ align:start position:0%
+of lots of variables I would start down
+in that direction and how far to go
+
+ align:start position:0%
+in that direction and how far to go
+ 
+
+ align:start position:0%
+in that direction and how far to go
+that's like the million dollar question
+
+ align:start position:0%
+that's like the million dollar question
+ 
+
+ align:start position:0%
+that's like the million dollar question
+in in deep learning as when it is it is
+
+ align:start position:0%
+in in deep learning as when it is it is
+ 
+
+ align:start position:0%
+in in deep learning as when it is it is
+it gonna hit zero nope it's not it's not
+
+ align:start position:0%
+it gonna hit zero nope it's not it's not
+ 
+
+ align:start position:0%
+it gonna hit zero nope it's not it's not
+and so you basically you go down until
+
+ align:start position:0%
+and so you basically you go down until
+ 
+
+ align:start position:0%
+and so you basically you go down until
+it until they go in so you're traveling
+
+ align:start position:0%
+it until they go in so you're traveling
+ 
+
+ align:start position:0%
+it until they go in so you're traveling
+here in the X along the gradient and
+
+ align:start position:0%
+here in the X along the gradient and
+ 
+
+ align:start position:0%
+here in the X along the gradient and
+you're you're not even you're not gonna
+
+ align:start position:0%
+you're you're not even you're not gonna
+ 
+
+ align:start position:0%
+you're you're not even you're not gonna
+hit zero you're right you're all going
+
+ align:start position:0%
+hit zero you're right you're all going
+ 
+
+ align:start position:0%
+hit zero you're right you're all going
+here in some direction and you want to
+
+ align:start position:0%
+here in some direction and you want to
+ 
+
+ align:start position:0%
+here in some direction and you want to
+go so you keep going down this thing
+
+ align:start position:0%
+go so you keep going down this thing
+ 
+
+ align:start position:0%
+go so you keep going down this thing
+until it oh my I'm not Rembrandt here
+
+ align:start position:0%
+until it oh my I'm not Rembrandt here
+ 
+
+ align:start position:0%
+until it oh my I'm not Rembrandt here
+I'm there your path down think of
+
+ align:start position:0%
+I'm there your path down think of
+ 
+
+ align:start position:0%
+I'm there your path down think of
+yourself on a mountain
+
+ align:start position:0%
+yourself on a mountain
+ 
+
+ align:start position:0%
+yourself on a mountain
+you're trying to go downhill so you take
+
+ align:start position:0%
+you're trying to go downhill so you take
+ 
+
+ align:start position:0%
+you're trying to go downhill so you take
+as fast as you can so you take the
+
+ align:start position:0%
+as fast as you can so you take the
+ 
+
+ align:start position:0%
+as fast as you can so you take the
+steepest route down until but but but
+
+ align:start position:0%
+steepest route down until but but but
+ 
+
+ align:start position:0%
+steepest route down until but but but
+you have blinkers on you just once you
+
+ align:start position:0%
+you have blinkers on you just once you
+ 
+
+ align:start position:0%
+you have blinkers on you just once you
+decided on a direction you go in that
+
+ align:start position:0%
+decided on a direction you go in that
+ 
+
+ align:start position:0%
+decided on a direction you go in that
+direction of course yeah so so what will
+
+ align:start position:0%
+direction of course yeah so so what will
+ 
+
+ align:start position:0%
+direction of course yeah so so what will
+happen you'll go down for a while and
+
+ align:start position:0%
+happen you'll go down for a while and
+ 
+
+ align:start position:0%
+happen you'll go down for a while and
+then it will turn up again right when
+
+ align:start position:0%
+then it will turn up again right when
+ 
+
+ align:start position:0%
+then it will turn up again right when
+you get sort of maybe close to the
+
+ align:start position:0%
+you get sort of maybe close to the
+ 
+
+ align:start position:0%
+you get sort of maybe close to the
+bottom or maybe not you you're not going
+
+ align:start position:0%
+bottom or maybe not you you're not going
+ 
+
+ align:start position:0%
+bottom or maybe not you you're not going
+to hit here and it's gonna miss that and
+
+ align:start position:0%
+to hit here and it's gonna miss that and
+ 
+
+ align:start position:0%
+to hit here and it's gonna miss that and
+come up maybe I should draw it over here
+
+ align:start position:0%
+come up maybe I should draw it over here
+ 
+
+ align:start position:0%
+come up maybe I should draw it over here
+whatever so this is it's called a line
+
+ align:start position:0%
+whatever so this is it's called a line
+ 
+
+ align:start position:0%
+whatever so this is it's called a line
+surge to decide how far to go there and
+
+ align:start position:0%
+surge to decide how far to go there and
+ 
+
+ align:start position:0%
+surge to decide how far to go there and
+then say okay stop and you can invest a
+
+ align:start position:0%
+then say okay stop and you can invest a
+ 
+
+ align:start position:0%
+then say okay stop and you can invest a
+lot of time or a little time to decide
+
+ align:start position:0%
+lot of time or a little time to decide
+ 
+
+ align:start position:0%
+lot of time or a little time to decide
+on that first stopping point and now
+
+ align:start position:0%
+on that first stopping point and now
+ 
+
+ align:start position:0%
+on that first stopping point and now
+just tell me what do you do next
+
+ align:start position:0%
+just tell me what do you do next
+ 
+
+ align:start position:0%
+just tell me what do you do next
+so now you're here what what now
+
+ align:start position:0%
+so now you're here what what now
+ 
+
+ align:start position:0%
+so now you're here what what now
+recalculate the gradient find the
+
+ align:start position:0%
+recalculate the gradient find the
+ 
+
+ align:start position:0%
+recalculate the gradient find the
+steepest way down from that point follow
+
+ align:start position:0%
+steepest way down from that point follow
+ 
+
+ align:start position:0%
+steepest way down from that point follow
+it until it turns up or approximately
+
+ align:start position:0%
+it until it turns up or approximately
+ 
+
+ align:start position:0%
+it until it turns up or approximately
+then you're at a new point so this is
+
+ align:start position:0%
+then you're at a new point so this is
+ 
+
+ align:start position:0%
+then you're at a new point so this is
+gradient descent
+
+ align:start position:0%
+gradient descent
+ 
+
+ align:start position:0%
+gradient descent
+that's a gradient descent the big
+
+ align:start position:0%
+that's a gradient descent the big
+ 
+
+ align:start position:0%
+that's a gradient descent the big
+algorithm of deep learning of neural
+
+ align:start position:0%
+algorithm of deep learning of neural
+ 
+
+ align:start position:0%
+algorithm of deep learning of neural
+Nets of machine learning great of
+
+ align:start position:0%
+Nets of machine learning great of
+ 
+
+ align:start position:0%
+Nets of machine learning great of
+optimization you could say notice that
+
+ align:start position:0%
+optimization you could say notice that
+ 
+
+ align:start position:0%
+optimization you could say notice that
+we didn't compute second derivatives if
+
+ align:start position:0%
+we didn't compute second derivatives if
+ 
+
+ align:start position:0%
+we didn't compute second derivatives if
+if we computed second derivatives we
+
+ align:start position:0%
+if we computed second derivatives we
+ 
+
+ align:start position:0%
+if we computed second derivatives we
+could have a fancier formula that could
+
+ align:start position:0%
+could have a fancier formula that could
+ 
+
+ align:start position:0%
+could have a fancier formula that could
+account for the bending the curve here
+
+ align:start position:0%
+account for the bending the curve here
+ 
+
+ align:start position:0%
+account for the bending the curve here
+but to compute second derivatives when
+
+ align:start position:0%
+but to compute second derivatives when
+ 
+
+ align:start position:0%
+but to compute second derivatives when
+you've got hundreds of thousands of
+
+ align:start position:0%
+you've got hundreds of thousands of
+ 
+
+ align:start position:0%
+you've got hundreds of thousands of
+variables is is not a lot of fun so most
+
+ align:start position:0%
+variables is is not a lot of fun so most
+ 
+
+ align:start position:0%
+variables is is not a lot of fun so most
+effectively machine learning is limited
+
+ align:start position:0%
+effectively machine learning is limited
+ 
+
+ align:start position:0%
+effectively machine learning is limited
+to first derivatives the gradient so
+
+ align:start position:0%
+to first derivatives the gradient so
+ 
+
+ align:start position:0%
+to first derivatives the gradient so
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's the general idea but there are
+
+ align:start position:0%
+so that's the general idea but there are
+ 
+
+ align:start position:0%
+so that's the general idea but there are
+lots and lots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decisions and why doesn't that how well
+
+ align:start position:0%
+decisions and why doesn't that how well
+ 
+
+ align:start position:0%
+decisions and why doesn't that how well
+does that work
+
+ align:start position:0%
+does that work
+ 
+
+ align:start position:0%
+does that work
+maybe maybe is a good way to good
+
+ align:start position:0%
+maybe maybe is a good way to good
+ 
+
+ align:start position:0%
+maybe maybe is a good way to good
+question to ask does this work pretty
+
+ align:start position:0%
+question to ask does this work pretty
+ 
+
+ align:start position:0%
+question to ask does this work pretty
+well you know or do we have to add more
+
+ align:start position:0%
+well you know or do we have to add more
+ 
+
+ align:start position:0%
+well you know or do we have to add more
+ideas well it doesn't always work well
+
+ align:start position:0%
+ideas well it doesn't always work well
+ 
+
+ align:start position:0%
+ideas well it doesn't always work well
+let me tell you what the trouble is I
+
+ align:start position:0%
+let me tell you what the trouble is I
+ 
+
+ align:start position:0%
+let me tell you what the trouble is I
+don't so I'm Way off of like this is
+
+ align:start position:0%
+don't so I'm Way off of like this is
+ 
+
+ align:start position:0%
+don't so I'm Way off of like this is
+this is like March or something but
+
+ align:start position:0%
+this is like March or something but
+ 
+
+ align:start position:0%
+this is like March or something but
+anyway I'll finish the sentence so what
+
+ align:start position:0%
+anyway I'll finish the sentence so what
+ 
+
+ align:start position:0%
+anyway I'll finish the sentence so what
+what's the problem with this gradient
+
+ align:start position:0%
+what's the problem with this gradient
+ 
+
+ align:start position:0%
+what's the problem with this gradient
+descent idea it it turns out if you're
+
+ align:start position:0%
+descent idea it it turns out if you're
+ 
+
+ align:start position:0%
+descent idea it it turns out if you're
+going down a narrow Valley I don't know
+
+ align:start position:0%
+going down a narrow Valley I don't know
+ 
+
+ align:start position:0%
+going down a narrow Valley I don't know
+if you can sort of imagine a narrow
+
+ align:start position:0%
+if you can sort of imagine a narrow
+ 
+
+ align:start position:0%
+if you can sort of imagine a narrow
+valley toward the bottom so so here's
+
+ align:start position:0%
+valley toward the bottom so so here's
+ 
+
+ align:start position:0%
+valley toward the bottom so so here's
+here's the here's the bottom here's your
+
+ align:start position:0%
+here's the here's the bottom here's your
+ 
+
+ align:start position:0%
+here's the here's the bottom here's your
+starting point and this is so I mean you
+
+ align:start position:0%
+starting point and this is so I mean you
+ 
+
+ align:start position:0%
+starting point and this is so I mean you
+have to think of this as a bowl so the
+
+ align:start position:0%
+have to think of this as a bowl so the
+ 
+
+ align:start position:0%
+have to think of this as a bowl so the
+yeah the bowl is the were the two
+
+ align:start position:0%
+yeah the bowl is the were the two
+ 
+
+ align:start position:0%
+yeah the bowl is the were the two
+eigenvalues you could say are one and a
+
+ align:start position:0%
+eigenvalues you could say are one and a
+ 
+
+ align:start position:0%
+eigenvalues you could say are one and a
+very small number the bowl is long and
+
+ align:start position:0%
+very small number the bowl is long and
+ 
+
+ align:start position:0%
+very small number the bowl is long and
+thin are you with me
+
+ align:start position:0%
+thin are you with me
+ 
+
+ align:start position:0%
+thin are you with me
+imagine a long thin bowl then what
+
+ align:start position:0%
+imagine a long thin bowl then what
+ 
+
+ align:start position:0%
+imagine a long thin bowl then what
+happens for that case you you take
+
+ align:start position:0%
+happens for that case you you take
+ 
+
+ align:start position:0%
+happens for that case you you take
+steepest descent but you cross the
+
+ align:start position:0%
+steepest descent but you cross the
+ 
+
+ align:start position:0%
+steepest descent but you cross the
+valley and very soon you're climbing
+
+ align:start position:0%
+valley and very soon you're climbing
+ 
+
+ align:start position:0%
+valley and very soon you're climbing
+again so you take very it's very small
+
+ align:start position:0%
+again so you take very it's very small
+ 
+
+ align:start position:0%
+again so you take very it's very small
+steps just staggering back and forth
+
+ align:start position:0%
+steps just staggering back and forth
+ 
+
+ align:start position:0%
+steps just staggering back and forth
+across this and getting slowly but too
+
+ align:start position:0%
+across this and getting slowly but too
+ 
+
+ align:start position:0%
+across this and getting slowly but too
+slowly toward the bottom there so that's
+
+ align:start position:0%
+slowly toward the bottom there so that's
+ 
+
+ align:start position:0%
+slowly toward the bottom there so that's
+why things have got to be improved you
+
+ align:start position:0%
+why things have got to be improved you
+ 
+
+ align:start position:0%
+why things have got to be improved you
+can if you have I can value a very small
+
+ align:start position:0%
+can if you have I can value a very small
+ 
+
+ align:start position:0%
+can if you have I can value a very small
+eigenvalue in a very large eigenvalue
+
+ align:start position:0%
+eigenvalue in a very large eigenvalue
+ 
+
+ align:start position:0%
+eigenvalue in a very large eigenvalue
+those tell you the the shape of the bowl
+
+ align:start position:0%
+those tell you the the shape of the bowl
+ 
+
+ align:start position:0%
+those tell you the the shape of the bowl
+of course and many cases will will be
+
+ align:start position:0%
+of course and many cases will will be
+ 
+
+ align:start position:0%
+of course and many cases will will be
+like that have a small and a large I can
+
+ align:start position:0%
+like that have a small and a large I can
+ 
+
+ align:start position:0%
+like that have a small and a large I can
+value and then you're spending all your
+
+ align:start position:0%
+value and then you're spending all your
+ 
+
+ align:start position:0%
+value and then you're spending all your
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+you're quickly going up the other side
+
+ align:start position:0%
+you're quickly going up the other side
+ 
+
+ align:start position:0%
+you're quickly going up the other side
+down up down up down and you need a new
+
+ align:start position:0%
+down up down up down and you need a new
+ 
+
+ align:start position:0%
+down up down up down and you need a new
+idea okay so that's really so this is
+
+ align:start position:0%
+idea okay so that's really so this is
+ 
+
+ align:start position:0%
+idea okay so that's really so this is
+one major reason why positive-definite
+
+ align:start position:0%
+one major reason why positive-definite
+ 
+
+ align:start position:0%
+one major reason why positive-definite
+is so important because
+
+ align:start position:0%
+is so important because
+ 
+
+ align:start position:0%
+is so important because
+positive-definite gives pictures like
+
+ align:start position:0%
+positive-definite gives pictures like
+ 
+
+ align:start position:0%
+positive-definite gives pictures like
+that but then we have this question of
+
+ align:start position:0%
+that but then we have this question of
+ 
+
+ align:start position:0%
+that but then we have this question of
+are the eigenvalues sort of the same
+
+ align:start position:0%
+are the eigenvalues sort of the same
+ 
+
+ align:start position:0%
+are the eigenvalues sort of the same
+size of course if the eigenvalues are
+
+ align:start position:0%
+size of course if the eigenvalues are
+ 
+
+ align:start position:0%
+size of course if the eigenvalues are
+all equal what's my bowl like suppose we
+
+ align:start position:0%
+all equal what's my bowl like suppose we
+ 
+
+ align:start position:0%
+all equal what's my bowl like suppose we
+suppose all the suppose I have the
+
+ align:start position:0%
+suppose all the suppose I have the
+ 
+
+ align:start position:0%
+suppose all the suppose I have the
+identity so that's x squared plus y
+
+ align:start position:0%
+identity so that's x squared plus y
+ 
+
+ align:start position:0%
+identity so that's x squared plus y
+squared is my function then it's a
+
+ align:start position:0%
+squared is my function then it's a
+ 
+
+ align:start position:0%
+squared is my function then it's a
+perfectly circular Bowl what will happen
+
+ align:start position:0%
+perfectly circular Bowl what will happen
+ 
+
+ align:start position:0%
+perfectly circular Bowl what will happen
+if I can you imagine a perfectly
+
+ align:start position:0%
+if I can you imagine a perfectly
+ 
+
+ align:start position:0%
+if I can you imagine a perfectly
+circular like any any bowl in the
+
+ align:start position:0%
+circular like any any bowl in the
+ 
+
+ align:start position:0%
+circular like any any bowl in the
+kitchen is probably most likely circular
+
+ align:start position:0%
+kitchen is probably most likely circular
+ 
+
+ align:start position:0%
+kitchen is probably most likely circular
+and suppose I do gradient descent there
+
+ align:start position:0%
+and suppose I do gradient descent there
+ 
+
+ align:start position:0%
+and suppose I do gradient descent there
+I start at some point on this perfectly
+
+ align:start position:0%
+I start at some point on this perfectly
+ 
+
+ align:start position:0%
+I start at some point on this perfectly
+circular Bowl I start down and where do
+
+ align:start position:0%
+circular Bowl I start down and where do
+ 
+
+ align:start position:0%
+circular Bowl I start down and where do
+I stop in that case do I hit bottom I do
+
+ align:start position:0%
+I stop in that case do I hit bottom I do
+ 
+
+ align:start position:0%
+I stop in that case do I hit bottom I do
+by symmetry I'm gonna so so if I take x
+
+ align:start position:0%
+by symmetry I'm gonna so so if I take x
+ 
+
+ align:start position:0%
+by symmetry I'm gonna so so if I take x
+squared plus y squared as my function
+
+ align:start position:0%
+squared plus y squared as my function
+ 
+
+ align:start position:0%
+squared plus y squared as my function
+and I start somewhere I figure out the
+
+ align:start position:0%
+and I start somewhere I figure out the
+ 
+
+ align:start position:0%
+and I start somewhere I figure out the
+gradient yeah the answer is I'll go
+
+ align:start position:0%
+gradient yeah the answer is I'll go
+ 
+
+ align:start position:0%
+gradient yeah the answer is I'll go
+right through the center so really it's
+
+ align:start position:0%
+right through the center so really it's
+ 
+
+ align:start position:0%
+right through the center so really it's
+positive positive eigen values positive
+
+ align:start position:0%
+positive positive eigen values positive
+ 
+
+ align:start position:0%
+positive positive eigen values positive
+definite matrices give us a bowl but if
+
+ align:start position:0%
+definite matrices give us a bowl but if
+ 
+
+ align:start position:0%
+definite matrices give us a bowl but if
+the eigenvalues are far apart that's
+
+ align:start position:0%
+the eigenvalues are far apart that's
+ 
+
+ align:start position:0%
+the eigenvalues are far apart that's
+when we have problems ok I'm going back
+
+ align:start position:0%
+when we have problems ok I'm going back
+ 
+
+ align:start position:0%
+when we have problems ok I'm going back
+to my job which is this list because you
+
+ align:start position:0%
+to my job which is this list because you
+ 
+
+ align:start position:0%
+to my job which is this list because you
+really this is so nice
+
+ align:start position:0%
+really this is so nice
+ 
+
+ align:start position:0%
+really this is so nice
+yeah right could you
+
+ align:start position:0%
+yeah right could you
+ 
+
+ align:start position:0%
+yeah right could you
+well the homework that may be going out
+
+ align:start position:0%
+well the homework that may be going out
+ 
+
+ align:start position:0%
+well the homework that may be going out
+this minute for middle of next week
+
+ align:start position:0%
+this minute for middle of next week
+ 
+
+ align:start position:0%
+this minute for middle of next week
+gives you some exercises
+
+ align:start position:0%
+gives you some exercises
+ 
+
+ align:start position:0%
+gives you some exercises
+with this let me do a couple of things a
+
+ align:start position:0%
+with this let me do a couple of things a
+ 
+
+ align:start position:0%
+with this let me do a couple of things a
+couple of exercises here for example
+
+ align:start position:0%
+couple of exercises here for example
+ 
+
+ align:start position:0%
+couple of exercises here for example
+suppose I have a positive different
+
+ align:start position:0%
+suppose I have a positive different
+ 
+
+ align:start position:0%
+suppose I have a positive different
+matrix S and a positive definite matrix
+
+ align:start position:0%
+matrix S and a positive definite matrix
+ 
+
+ align:start position:0%
+matrix S and a positive definite matrix
+T if I add those matrices is a result
+
+ align:start position:0%
+T if I add those matrices is a result
+ 
+
+ align:start position:0%
+T if I add those matrices is a result
+positive definite so there's a perfect
+
+ align:start position:0%
+positive definite so there's a perfect
+ 
+
+ align:start position:0%
+positive definite so there's a perfect
+math question and we hope to answer so
+
+ align:start position:0%
+math question and we hope to answer so
+ 
+
+ align:start position:0%
+math question and we hope to answer so
+SMT positive definite what about s plus
+
+ align:start position:0%
+SMT positive definite what about s plus
+ 
+
+ align:start position:0%
+SMT positive definite what about s plus
+T is that matrix positive definite okay
+
+ align:start position:0%
+T is that matrix positive definite okay
+ 
+
+ align:start position:0%
+T is that matrix positive definite okay
+how do I answer such a question I look
+
+ align:start position:0%
+how do I answer such a question I look
+ 
+
+ align:start position:0%
+how do I answer such a question I look
+at my five tests and I think can I use
+
+ align:start position:0%
+at my five tests and I think can I use
+ 
+
+ align:start position:0%
+at my five tests and I think can I use
+it what which one will be good and the
+
+ align:start position:0%
+it what which one will be good and the
+ 
+
+ align:start position:0%
+it what which one will be good and the
+whoa and one that won't tell me much is
+
+ align:start position:0%
+whoa and one that won't tell me much is
+ 
+
+ align:start position:0%
+whoa and one that won't tell me much is
+the eigenvalues because the eigen values
+
+ align:start position:0%
+the eigenvalues because the eigen values
+ 
+
+ align:start position:0%
+the eigenvalues because the eigen values
+of s plus T are not immediately clear
+
+ align:start position:0%
+of s plus T are not immediately clear
+ 
+
+ align:start position:0%
+of s plus T are not immediately clear
+from the eigenvalues of s and T
+
+ align:start position:0%
+from the eigenvalues of s and T
+ 
+
+ align:start position:0%
+from the eigenvalues of s and T
+separately I don't want to use that test
+
+ align:start position:0%
+separately I don't want to use that test
+ 
+
+ align:start position:0%
+separately I don't want to use that test
+this is my favorite test so I'm going to
+
+ align:start position:0%
+this is my favorite test so I'm going to
+ 
+
+ align:start position:0%
+this is my favorite test so I'm going to
+use that what about the energy in so
+
+ align:start position:0%
+use that what about the energy in so
+ 
+
+ align:start position:0%
+use that what about the energy in so
+look at the energies so I look at X
+
+ align:start position:0%
+look at the energies so I look at X
+ 
+
+ align:start position:0%
+look at the energies so I look at X
+transpose s plus T X and what's my
+
+ align:start position:0%
+transpose s plus T X and what's my
+ 
+
+ align:start position:0%
+transpose s plus T X and what's my
+question in my mind here is that a
+
+ align:start position:0%
+question in my mind here is that a
+ 
+
+ align:start position:0%
+question in my mind here is that a
+positive number or not for every X and
+
+ align:start position:0%
+positive number or not for every X and
+ 
+
+ align:start position:0%
+positive number or not for every X and
+how am I going to answer that question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just separate those two into two pieces
+
+ align:start position:0%
+just separate those two into two pieces
+ 
+
+ align:start position:0%
+just separate those two into two pieces
+right it's there in front of me it's
+
+ align:start position:0%
+right it's there in front of me it's
+ 
+
+ align:start position:0%
+right it's there in front of me it's
+this one what's this one and both of
+
+ align:start position:0%
+this one what's this one and both of
+ 
+
+ align:start position:0%
+this one what's this one and both of
+those are positive so the answer is yes
+
+ align:start position:0%
+those are positive so the answer is yes
+ 
+
+ align:start position:0%
+those are positive so the answer is yes
+it is positive definite yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see how the energy just was right I
+
+ align:start position:0%
+you see how the energy just was right I
+ 
+
+ align:start position:0%
+you see how the energy just was right I
+don't want to compute the pivots or any
+
+ align:start position:0%
+don't want to compute the pivots or any
+ 
+
+ align:start position:0%
+don't want to compute the pivots or any
+determinants that would be like a
+
+ align:start position:0%
+determinants that would be like a
+ 
+
+ align:start position:0%
+determinants that would be like a
+nightmare trying to find determinants
+
+ align:start position:0%
+nightmare trying to find determinants
+ 
+
+ align:start position:0%
+nightmare trying to find determinants
+for s plus T but this one just doesn't
+
+ align:start position:0%
+for s plus T but this one just doesn't
+ 
+
+ align:start position:0%
+for s plus T but this one just doesn't
+immediately what else would be a good
+
+ align:start position:0%
+immediately what else would be a good
+ 
+
+ align:start position:0%
+immediately what else would be a good
+example to start with what about their
+
+ align:start position:0%
+example to start with what about their
+ 
+
+ align:start position:0%
+example to start with what about their
+sin verse is that positive definite yes
+
+ align:start position:0%
+sin verse is that positive definite yes
+ 
+
+ align:start position:0%
+sin verse is that positive definite yes
+positive definite and I want to ask
+
+ align:start position:0%
+positive definite and I want to ask
+ 
+
+ align:start position:0%
+positive definite and I want to ask
+about its inverse so int inverse is a
+
+ align:start position:0%
+about its inverse so int inverse is a
+ 
+
+ align:start position:0%
+about its inverse so int inverse is a
+symmetric matrix and is it positive
+
+ align:start position:0%
+symmetric matrix and is it positive
+ 
+
+ align:start position:0%
+symmetric matrix and is it positive
+definite and the answer yes yes I got
+
+ align:start position:0%
+definite and the answer yes yes I got
+ 
+
+ align:start position:0%
+definite and the answer yes yes I got
+five tests 20% chance of picking the
+
+ align:start position:0%
+five tests 20% chance of picking the
+ 
+
+ align:start position:0%
+five tests 20% chance of picking the
+right one determinants not good the
+
+ align:start position:0%
+right one determinants not good the
+ 
+
+ align:start position:0%
+right one determinants not good the
+first one is great
+
+ align:start position:0%
+first one is great
+ 
+
+ align:start position:0%
+first one is great
+the first one is the good one for this
+
+ align:start position:0%
+the first one is the good one for this
+ 
+
+ align:start position:0%
+the first one is the good one for this
+question because the eigen values so the
+
+ align:start position:0%
+question because the eigen values so the
+ 
+
+ align:start position:0%
+question because the eigen values so the
+answer is yes yes yes this is has eigen
+
+ align:start position:0%
+answer is yes yes yes this is has eigen
+ 
+
+ align:start position:0%
+answer is yes yes yes this is has eigen
+values so what are the eigenvalues of s
+
+ align:start position:0%
+values so what are the eigenvalues of s
+ 
+
+ align:start position:0%
+values so what are the eigenvalues of s
+inverse 1 over lambda so yes okay right
+
+ align:start position:0%
+inverse 1 over lambda so yes okay right
+ 
+
+ align:start position:0%
+inverse 1 over lambda so yes okay right
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+what about yeah let me ask just one more
+
+ align:start position:0%
+what about yeah let me ask just one more
+ 
+
+ align:start position:0%
+what about yeah let me ask just one more
+question of this same sort suppose I
+
+ align:start position:0%
+question of this same sort suppose I
+ 
+
+ align:start position:0%
+question of this same sort suppose I
+have a matrix s and suppose I multiply
+
+ align:start position:0%
+have a matrix s and suppose I multiply
+ 
+
+ align:start position:0%
+have a matrix s and suppose I multiply
+it by another matrix oh well okay
+
+ align:start position:0%
+it by another matrix oh well okay
+ 
+
+ align:start position:0%
+it by another matrix oh well okay
+suppose yeah yep suppose I have suppose
+
+ align:start position:0%
+suppose yeah yep suppose I have suppose
+ 
+
+ align:start position:0%
+suppose yeah yep suppose I have suppose
+I asked you about s times another matrix
+
+ align:start position:0%
+I asked you about s times another matrix
+ 
+
+ align:start position:0%
+I asked you about s times another matrix
+M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would that be positive definite or not
+
+ align:start position:0%
+would that be positive definite or not
+ 
+
+ align:start position:0%
+would that be positive definite or not
+now I'm gonna tell you the answer the
+
+ align:start position:0%
+now I'm gonna tell you the answer the
+ 
+
+ align:start position:0%
+now I'm gonna tell you the answer the
+answer is that the question wasn't any
+
+ align:start position:0%
+answer is that the question wasn't any
+ 
+
+ align:start position:0%
+answer is that the question wasn't any
+good because that matrix is probably not
+
+ align:start position:0%
+good because that matrix is probably not
+ 
+
+ align:start position:0%
+good because that matrix is probably not
+symmetric and I'm only dealing with
+
+ align:start position:0%
+symmetric and I'm only dealing with
+ 
+
+ align:start position:0%
+symmetric and I'm only dealing with
+symmetric matrices matrices have to be
+
+ align:start position:0%
+symmetric matrices matrices have to be
+ 
+
+ align:start position:0%
+symmetric matrices matrices have to be
+symmetric before I can before I know
+
+ align:start position:0%
+symmetric before I can before I know
+ 
+
+ align:start position:0%
+symmetric before I can before I know
+they have real eigenvalues and I can ask
+
+ align:start position:0%
+they have real eigenvalues and I can ask
+ 
+
+ align:start position:0%
+they have real eigenvalues and I can ask
+these questions so that's not good but I
+
+ align:start position:0%
+these questions so that's not good but I
+ 
+
+ align:start position:0%
+these questions so that's not good but I
+could oh let's see well let me hear ya
+
+ align:start position:0%
+could oh let's see well let me hear ya
+ 
+
+ align:start position:0%
+could oh let's see well let me hear ya
+let me let me put it in an orthogonal
+
+ align:start position:0%
+let me let me put it in an orthogonal
+ 
+
+ align:start position:0%
+let me let me put it in an orthogonal
+guy well they're still that's not
+
+ align:start position:0%
+guy well they're still that's not
+ 
+
+ align:start position:0%
+guy well they're still that's not
+symmetric but if I put C its transpose
+
+ align:start position:0%
+symmetric but if I put C its transpose
+ 
+
+ align:start position:0%
+symmetric but if I put C its transpose
+over there then I made it symmetric oh
+
+ align:start position:0%
+over there then I made it symmetric oh
+ 
+
+ align:start position:0%
+over there then I made it symmetric oh
+dear I may be getting myself in trouble
+
+ align:start position:0%
+dear I may be getting myself in trouble
+ 
+
+ align:start position:0%
+dear I may be getting myself in trouble
+here so I'm starting with a positive
+
+ align:start position:0%
+here so I'm starting with a positive
+ 
+
+ align:start position:0%
+here so I'm starting with a positive
+definite s I'm hitting with an
+
+ align:start position:0%
+definite s I'm hitting with an
+ 
+
+ align:start position:0%
+definite s I'm hitting with an
+orthogonal matrix and it's transpose and
+
+ align:start position:0%
+orthogonal matrix and it's transpose and
+ 
+
+ align:start position:0%
+orthogonal matrix and it's transpose and
+I sort of my instinct carried me here
+
+ align:start position:0%
+I sort of my instinct carried me here
+ 
+
+ align:start position:0%
+I sort of my instinct carried me here
+because I know that that's still
+
+ align:start position:0%
+because I know that that's still
+ 
+
+ align:start position:0%
+because I know that that's still
+symmetric right everybody sees that if I
+
+ align:start position:0%
+symmetric right everybody sees that if I
+ 
+
+ align:start position:0%
+symmetric right everybody sees that if I
+transpose this Q transpose will come
+
+ align:start position:0%
+transpose this Q transpose will come
+ 
+
+ align:start position:0%
+transpose this Q transpose will come
+here yes Q will go there it'll be some
+
+ align:start position:0%
+here yes Q will go there it'll be some
+ 
+
+ align:start position:0%
+here yes Q will go there it'll be some
+checks symmetric now is that positive
+
+ align:start position:0%
+checks symmetric now is that positive
+ 
+
+ align:start position:0%
+checks symmetric now is that positive
+definite oh yes we can't answer that can
+
+ align:start position:0%
+definite oh yes we can't answer that can
+ 
+
+ align:start position:0%
+definite oh yes we can't answer that can
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+is that positive definite so remember
+
+ align:start position:0%
+is that positive definite so remember
+ 
+
+ align:start position:0%
+is that positive definite so remember
+that this is an orthogonal matrix so I'm
+
+ align:start position:0%
+that this is an orthogonal matrix so I'm
+ 
+
+ align:start position:0%
+that this is an orthogonal matrix so I'm
+also if you wanted me to write it that
+
+ align:start position:0%
+also if you wanted me to write it that
+ 
+
+ align:start position:0%
+also if you wanted me to write it that
+way I could
+
+ align:start position:0%
+way I could
+ 
+
+ align:start position:0%
+way I could
+and what about positive definiteness of
+
+ align:start position:0%
+and what about positive definiteness of
+ 
+
+ align:start position:0%
+and what about positive definiteness of
+that thing the answer I think is yes do
+
+ align:start position:0%
+that thing the answer I think is yes do
+ 
+
+ align:start position:0%
+that thing the answer I think is yes do
+you agree it is positive definite give
+
+ align:start position:0%
+you agree it is positive definite give
+ 
+
+ align:start position:0%
+you agree it is positive definite give
+me a reason though why is this positive
+
+ align:start position:0%
+me a reason though why is this positive
+ 
+
+ align:start position:0%
+me a reason though why is this positive
+definite big so that word similar so
+
+ align:start position:0%
+definite big so that word similar so
+ 
+
+ align:start position:0%
+definite big so that word similar so
+what this is a similar matrix to S do
+
+ align:start position:0%
+what this is a similar matrix to S do
+ 
+
+ align:start position:0%
+what this is a similar matrix to S do
+you remember what similar means from
+
+ align:start position:0%
+you remember what similar means from
+ 
+
+ align:start position:0%
+you remember what similar means from
+last time it means that some m and its
+
+ align:start position:0%
+last time it means that some m and its
+ 
+
+ align:start position:0%
+last time it means that some m and its
+inverse or here we
+
+ align:start position:0%
+inverse or here we
+ 
+
+ align:start position:0%
+inverse or here we
+they are and so what's the what's the
+
+ align:start position:0%
+they are and so what's the what's the
+ 
+
+ align:start position:0%
+they are and so what's the what's the
+consequence of being similar what do I
+
+ align:start position:0%
+consequence of being similar what do I
+ 
+
+ align:start position:0%
+consequence of being similar what do I
+know about a matrix that's similar to s
+
+ align:start position:0%
+know about a matrix that's similar to s
+ 
+
+ align:start position:0%
+know about a matrix that's similar to s
+it has the same eigenvalues and
+
+ align:start position:0%
+it has the same eigenvalues and
+ 
+
+ align:start position:0%
+it has the same eigenvalues and
+therefore we're good right or I could go
+
+ align:start position:0%
+therefore we're good right or I could go
+ 
+
+ align:start position:0%
+therefore we're good right or I could go
+this way I could energy I like energy so
+
+ align:start position:0%
+this way I could energy I like energy so
+ 
+
+ align:start position:0%
+this way I could energy I like energy so
+let me try that one X transpose Q
+
+ align:start position:0%
+let me try that one X transpose Q
+ 
+
+ align:start position:0%
+let me try that one X transpose Q
+transpose su X that would be the energy
+
+ align:start position:0%
+transpose su X that would be the energy
+ 
+
+ align:start position:0%
+transpose su X that would be the energy
+and what am I trying to show I'm trying
+
+ align:start position:0%
+and what am I trying to show I'm trying
+ 
+
+ align:start position:0%
+and what am I trying to show I'm trying
+to show it's positive so of course my as
+
+ align:start position:0%
+to show it's positive so of course my as
+ 
+
+ align:start position:0%
+to show it's positive so of course my as
+soon as I see that like just waiting for
+
+ align:start position:0%
+soon as I see that like just waiting for
+ 
+
+ align:start position:0%
+soon as I see that like just waiting for
+me to the QX be something called Y maybe
+
+ align:start position:0%
+me to the QX be something called Y maybe
+ 
+
+ align:start position:0%
+me to the QX be something called Y maybe
+and then what will this be my Y
+
+ align:start position:0%
+and then what will this be my Y
+ 
+
+ align:start position:0%
+and then what will this be my Y
+transpose so this this energy would be
+
+ align:start position:0%
+transpose so this this energy would be
+ 
+
+ align:start position:0%
+transpose so this this energy would be
+the same as Y transpose s Y and what do
+
+ align:start position:0%
+the same as Y transpose s Y and what do
+ 
+
+ align:start position:0%
+the same as Y transpose s Y and what do
+I know about that it's positive because
+
+ align:start position:0%
+I know about that it's positive because
+ 
+
+ align:start position:0%
+I know about that it's positive because
+that's an energy in the Y for the Y
+
+ align:start position:0%
+that's an energy in the Y for the Y
+ 
+
+ align:start position:0%
+that's an energy in the Y for the Y
+vector so one way or another we get the
+
+ align:start position:0%
+vector so one way or another we get the
+ 
+
+ align:start position:0%
+vector so one way or another we get the
+answer yes to that question ok ok let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+introduce the idea of semi-definite
+
+ align:start position:0%
+introduce the idea of semi-definite
+ 
+
+ align:start position:0%
+introduce the idea of semi-definite
+semi-definite is the borderline so so
+
+ align:start position:0%
+semi-definite is the borderline so so
+ 
+
+ align:start position:0%
+semi-definite is the borderline so so
+what did we have we had three four four
+
+ align:start position:0%
+what did we have we had three four four
+ 
+
+ align:start position:0%
+what did we have we had three four four
+and then when it was five you told me
+
+ align:start position:0%
+and then when it was five you told me
+ 
+
+ align:start position:0%
+and then when it was five you told me
+indefinite and negative eigenvalue when
+
+ align:start position:0%
+indefinite and negative eigenvalue when
+ 
+
+ align:start position:0%
+indefinite and negative eigenvalue when
+it was six you told me two positive
+
+ align:start position:0%
+it was six you told me two positive
+ 
+
+ align:start position:0%
+it was six you told me two positive
+eigenvalues definite what's the
+
+ align:start position:0%
+eigenvalues definite what's the
+ 
+
+ align:start position:0%
+eigenvalues definite what's the
+borderline
+
+ align:start position:0%
+borderline
+ 
+
+ align:start position:0%
+borderline
+what's the borderline there it's not
+
+ align:start position:0%
+what's the borderline there it's not
+ 
+
+ align:start position:0%
+what's the borderline there it's not
+it's not going to be an integer but it's
+
+ align:start position:0%
+it's not going to be an integer but it's
+ 
+
+ align:start position:0%
+it's not going to be an integer but it's
+well what do I mean what am I looking
+
+ align:start position:0%
+well what do I mean what am I looking
+ 
+
+ align:start position:0%
+well what do I mean what am I looking
+for it the borderline well yeah so tell
+
+ align:start position:0%
+for it the borderline well yeah so tell
+ 
+
+ align:start position:0%
+for it the borderline well yeah so tell
+me again sixteen over three that sounds
+
+ align:start position:0%
+me again sixteen over three that sounds
+ 
+
+ align:start position:0%
+me again sixteen over three that sounds
+right why is that the borderline because
+
+ align:start position:0%
+right why is that the borderline because
+ 
+
+ align:start position:0%
+right why is that the borderline because
+now the determinant is zero its singular
+
+ align:start position:0%
+now the determinant is zero its singular
+ 
+
+ align:start position:0%
+now the determinant is zero its singular
+it has a zero eigenvalue there's a zero
+
+ align:start position:0%
+it has a zero eigenvalue there's a zero
+ 
+
+ align:start position:0%
+it has a zero eigenvalue there's a zero
+eigenvalue so that's what semi definite
+
+ align:start position:0%
+eigenvalue so that's what semi definite
+ 
+
+ align:start position:0%
+eigenvalue so that's what semi definite
+means lambdas are greater equal to zero
+
+ align:start position:0%
+means lambdas are greater equal to zero
+ 
+
+ align:start position:0%
+means lambdas are greater equal to zero
+wait a minute that has a zero eigenvalue
+
+ align:start position:0%
+wait a minute that has a zero eigenvalue
+ 
+
+ align:start position:0%
+wait a minute that has a zero eigenvalue
+because it's determinant is zero how do
+
+ align:start position:0%
+because it's determinant is zero how do
+ 
+
+ align:start position:0%
+because it's determinant is zero how do
+i know that the other eigenvalue is
+
+ align:start position:0%
+i know that the other eigenvalue is
+ 
+
+ align:start position:0%
+i know that the other eigenvalue is
+positive could could the could it be
+
+ align:start position:0%
+positive could could the could it be
+ 
+
+ align:start position:0%
+positive could could the could it be
+that the other right so this is the semi
+
+ align:start position:0%
+that the other right so this is the semi
+ 
+
+ align:start position:0%
+that the other right so this is the semi
+definite case we hope but we better
+
+ align:start position:0%
+definite case we hope but we better
+ 
+
+ align:start position:0%
+definite case we hope but we better
+finish that reasoning how do I know that
+
+ align:start position:0%
+finish that reasoning how do I know that
+ 
+
+ align:start position:0%
+finish that reasoning how do I know that
+the other eigenvalue is positive the
+
+ align:start position:0%
+the other eigenvalue is positive the
+ 
+
+ align:start position:0%
+the other eigenvalue is positive the
+trace because the adding 3 plus 16 over
+
+ align:start position:0%
+trace because the adding 3 plus 16 over
+ 
+
+ align:start position:0%
+trace because the adding 3 plus 16 over
+3 whatever the heck that might give it
+
+ align:start position:0%
+3 whatever the heck that might give it
+ 
+
+ align:start position:0%
+3 whatever the heck that might give it
+certainly gives a positive number and
+
+ align:start position:0%
+certainly gives a positive number and
+ 
+
+ align:start position:0%
+certainly gives a positive number and
+that will be lambda 1 plus lambda 2
+
+ align:start position:0%
+that will be lambda 1 plus lambda 2
+ 
+
+ align:start position:0%
+that will be lambda 1 plus lambda 2
+that's the trace but lambda 2 is 0 we
+
+ align:start position:0%
+that's the trace but lambda 2 is 0 we
+ 
+
+ align:start position:0%
+that's the trace but lambda 2 is 0 we
+know from this it's singular so we know
+
+ align:start position:0%
+know from this it's singular so we know
+ 
+
+ align:start position:0%
+know from this it's singular so we know
+where lambda 2 is 0 so lambda 1 must be
+
+ align:start position:0%
+where lambda 2 is 0 so lambda 1 must be
+ 
+
+ align:start position:0%
+where lambda 2 is 0 so lambda 1 must be
+3 plus 5 5 in a service lambda the
+
+ align:start position:0%
+3 plus 5 5 in a service lambda the
+ 
+
+ align:start position:0%
+3 plus 5 5 in a service lambda the
+lambdas must be 8 Messrs 3 plus 5 and
+
+ align:start position:0%
+lambdas must be 8 Messrs 3 plus 5 and
+ 
+
+ align:start position:0%
+lambdas must be 8 Messrs 3 plus 5 and
+1/3 and so that's a positive
+
+ align:start position:0%
+1/3 and so that's a positive
+ 
+
+ align:start position:0%
+1/3 and so that's a positive
+semi-definite oh if you think of the
+
+ align:start position:0%
+semi-definite oh if you think of the
+ 
+
+ align:start position:0%
+semi-definite oh if you think of the
+positive definite matrices as some clump
+
+ align:start position:0%
+positive definite matrices as some clump
+ 
+
+ align:start position:0%
+positive definite matrices as some clump
+in matrix space then the positive
+
+ align:start position:0%
+in matrix space then the positive
+ 
+
+ align:start position:0%
+in matrix space then the positive
+semi-definite ones are sort of the edge
+
+ align:start position:0%
+semi-definite ones are sort of the edge
+ 
+
+ align:start position:0%
+semi-definite ones are sort of the edge
+of that clump they're the boundary of
+
+ align:start position:0%
+of that clump they're the boundary of
+ 
+
+ align:start position:0%
+of that clump they're the boundary of
+the clump the ones that are not quite
+
+ align:start position:0%
+the clump the ones that are not quite
+ 
+
+ align:start position:0%
+the clump the ones that are not quite
+inside but not outside either there
+
+ align:start position:0%
+inside but not outside either there
+ 
+
+ align:start position:0%
+inside but not outside either there
+they're lying right on the edge of
+
+ align:start position:0%
+they're lying right on the edge of
+ 
+
+ align:start position:0%
+they're lying right on the edge of
+positive definite matrices let me just
+
+ align:start position:0%
+positive definite matrices let me just
+ 
+
+ align:start position:0%
+positive definite matrices let me just
+take a so what about what about a matrix
+
+ align:start position:0%
+take a so what about what about a matrix
+ 
+
+ align:start position:0%
+take a so what about what about a matrix
+of all ones what's the what's the story
+
+ align:start position:0%
+of all ones what's the what's the story
+ 
+
+ align:start position:0%
+of all ones what's the what's the story
+on that one positive definite all the
+
+ align:start position:0%
+on that one positive definite all the
+ 
+
+ align:start position:0%
+on that one positive definite all the
+numbers are positive or positive semi
+
+ align:start position:0%
+numbers are positive or positive semi
+ 
+
+ align:start position:0%
+numbers are positive or positive semi
+definite or indefinite what do you think
+
+ align:start position:0%
+definite or indefinite what do you think
+ 
+
+ align:start position:0%
+definite or indefinite what do you think
+here one more all one's semi definite
+
+ align:start position:0%
+here one more all one's semi definite
+ 
+
+ align:start position:0%
+here one more all one's semi definite
+sounds like a good guess
+
+ align:start position:0%
+sounds like a good guess
+ 
+
+ align:start position:0%
+sounds like a good guess
+you know what the eigenvalues of this
+
+ align:start position:0%
+you know what the eigenvalues of this
+ 
+
+ align:start position:0%
+you know what the eigenvalues of this
+matrix would be 3 0 & 0 why did you say
+
+ align:start position:0%
+matrix would be 3 0 & 0 why did you say
+ 
+
+ align:start position:0%
+matrix would be 3 0 & 0 why did you say
+that because we only have the rank is
+
+ align:start position:0%
+that because we only have the rank is
+ 
+
+ align:start position:0%
+that because we only have the rank is
+yeah introduce that key where the rank
+
+ align:start position:0%
+yeah introduce that key where the rank
+ 
+
+ align:start position:0%
+yeah introduce that key where the rank
+is 1 so there's only one nonzero eigen
+
+ align:start position:0%
+is 1 so there's only one nonzero eigen
+ 
+
+ align:start position:0%
+is 1 so there's only one nonzero eigen
+value and then the trace tells me it's
+
+ align:start position:0%
+value and then the trace tells me it's
+ 
+
+ align:start position:0%
+value and then the trace tells me it's
+that that number is 3 so this is a
+
+ align:start position:0%
+that that number is 3 so this is a
+ 
+
+ align:start position:0%
+that that number is 3 so this is a
+positive positive semi definite matrix
+
+ align:start position:0%
+positive positive semi definite matrix
+ 
+
+ align:start position:0%
+positive positive semi definite matrix
+so so all these all these tests change a
+
+ align:start position:0%
+so so all these all these tests change a
+ 
+
+ align:start position:0%
+so so all these all these tests change a
+little for semi definite the eigenvalue
+
+ align:start position:0%
+little for semi definite the eigenvalue
+ 
+
+ align:start position:0%
+little for semi definite the eigenvalue
+is greater or equal the energies greater
+
+ align:start position:0%
+is greater or equal the energies greater
+ 
+
+ align:start position:0%
+is greater or equal the energies greater
+or equal to 0 the a transpose a but now
+
+ align:start position:0%
+or equal to 0 the a transpose a but now
+ 
+
+ align:start position:0%
+or equal to 0 the a transpose a but now
+I don't require oh I didn't discuss this
+
+ align:start position:0%
+I don't require oh I didn't discuss this
+ 
+
+ align:start position:0%
+I don't require oh I didn't discuss this
+but but semi definite would allow
+
+ align:start position:0%
+but but semi definite would allow
+ 
+
+ align:start position:0%
+but but semi definite would allow
+dependent columns by the way
+
+ align:start position:0%
+dependent columns by the way
+ 
+
+ align:start position:0%
+dependent columns by the way
+you got to do this for me right that
+
+ align:start position:0%
+you got to do this for me right that
+ 
+
+ align:start position:0%
+you got to do this for me right that
+matrix as a transpose times a just to
+
+ align:start position:0%
+matrix as a transpose times a just to
+ 
+
+ align:start position:0%
+matrix as a transpose times a just to
+see that it's semi definite because so
+
+ align:start position:0%
+see that it's semi definite because so
+ 
+
+ align:start position:0%
+see that it's semi definite because so
+write that as a transpose a yeah if it's
+
+ align:start position:0%
+write that as a transpose a yeah if it's
+ 
+
+ align:start position:0%
+write that as a transpose a yeah if it's
+a rank one matrix you know how to what
+
+ align:start position:0%
+a rank one matrix you know how to what
+ 
+
+ align:start position:0%
+a rank one matrix you know how to what
+it must look like a transfer was a how
+
+ align:start position:0%
+it must look like a transfer was a how
+ 
+
+ align:start position:0%
+it must look like a transfer was a how
+many terms am I going to have in in this
+
+ align:start position:0%
+many terms am I going to have in in this
+ 
+
+ align:start position:0%
+many terms am I going to have in in this
+and now I'm thinking back to the very
+
+ align:start position:0%
+and now I'm thinking back to the very
+ 
+
+ align:start position:0%
+and now I'm thinking back to the very
+beginning of this course if I pulled off
+
+ align:start position:0%
+beginning of this course if I pulled off
+ 
+
+ align:start position:0%
+beginning of this course if I pulled off
+the pieces in general this is lambda one
+
+ align:start position:0%
+the pieces in general this is lambda one
+ 
+
+ align:start position:0%
+the pieces in general this is lambda one
+times the first eigenvector times the
+
+ align:start position:0%
+times the first eigenvector times the
+ 
+
+ align:start position:0%
+times the first eigenvector times the
+first eigenvector transpose yeah would
+
+ align:start position:0%
+first eigenvector transpose yeah would
+ 
+
+ align:start position:0%
+first eigenvector transpose yeah would
+just be a vector of three ones yeah so
+
+ align:start position:0%
+just be a vector of three ones yeah so
+ 
+
+ align:start position:0%
+just be a vector of three ones yeah so
+so this would be the usual picture that
+
+ align:start position:0%
+so this would be the usual picture that
+ 
+
+ align:start position:0%
+so this would be the usual picture that
+this is the same as the Q lambda Q
+
+ align:start position:0%
+this is the same as the Q lambda Q
+ 
+
+ align:start position:0%
+this is the same as the Q lambda Q
+transpose this is this is the big big
+
+ align:start position:0%
+transpose this is this is the big big
+ 
+
+ align:start position:0%
+transpose this is this is the big big
+fact for any symmetric matrix and this
+
+ align:start position:0%
+fact for any symmetric matrix and this
+ 
+
+ align:start position:0%
+fact for any symmetric matrix and this
+is symmetric but its rank is only one so
+
+ align:start position:0%
+is symmetric but its rank is only one so
+ 
+
+ align:start position:0%
+is symmetric but its rank is only one so
+that so that lambda two is zero for that
+
+ align:start position:0%
+that so that lambda two is zero for that
+ 
+
+ align:start position:0%
+that so that lambda two is zero for that
+matrix lambda 3 is zero for that matrix
+
+ align:start position:0%
+matrix lambda 3 is zero for that matrix
+ 
+
+ align:start position:0%
+matrix lambda 3 is zero for that matrix
+and and the one eigen vector is the
+
+ align:start position:0%
+and and the one eigen vector is the
+ 
+
+ align:start position:0%
+and and the one eigen vector is the
+vector 1 1 1 and the eigen so this would
+
+ align:start position:0%
+vector 1 1 1 and the eigen so this would
+ 
+
+ align:start position:0%
+vector 1 1 1 and the eigen so this would
+be 3 times 1 1 1 oh I have to do yeah so
+
+ align:start position:0%
+be 3 times 1 1 1 oh I have to do yeah so
+ 
+
+ align:start position:0%
+be 3 times 1 1 1 oh I have to do yeah so
+I was going to do 3 times 1 1 1 times 1
+
+ align:start position:0%
+I was going to do 3 times 1 1 1 times 1
+ 
+
+ align:start position:0%
+I was going to do 3 times 1 1 1 times 1
+1 1 but that gives me 3 3 3 that's not
+
+ align:start position:0%
+1 1 but that gives me 3 3 3 that's not
+ 
+
+ align:start position:0%
+1 1 but that gives me 3 3 3 that's not
+right I have to normalize them that's
+
+ align:start position:0%
+right I have to normalize them that's
+ 
+
+ align:start position:0%
+right I have to normalize them that's
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+yeah so that's a vector of whose length
+
+ align:start position:0%
+yeah so that's a vector of whose length
+ 
+
+ align:start position:0%
+yeah so that's a vector of whose length
+is square root of 3 so I have to divide
+
+ align:start position:0%
+is square root of 3 so I have to divide
+ 
+
+ align:start position:0%
+is square root of 3 so I have to divide
+by that divide by it and then the 3
+
+ align:start position:0%
+by that divide by it and then the 3
+ 
+
+ align:start position:0%
+by that divide by it and then the 3
+cancels the square root of threes and
+
+ align:start position:0%
+cancels the square root of threes and
+ 
+
+ align:start position:0%
+cancels the square root of threes and
+I'm just left with the 1 1 1 1 1 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there is a matrix one of our building
+
+ align:start position:0%
+so there is a matrix one of our building
+ 
+
+ align:start position:0%
+so there is a matrix one of our building
+block type matrices because it only has
+
+ align:start position:0%
+block type matrices because it only has
+ 
+
+ align:start position:0%
+block type matrices because it only has
+one nonzero eigen value it's rank is 1
+
+ align:start position:0%
+one nonzero eigen value it's rank is 1
+ 
+
+ align:start position:0%
+one nonzero eigen value it's rank is 1
+so it could not be positive definite
+
+ align:start position:0%
+so it could not be positive definite
+ 
+
+ align:start position:0%
+so it could not be positive definite
+it's it's singular but it is positive
+
+ align:start position:0%
+it's it's singular but it is positive
+ 
+
+ align:start position:0%
+it's it's singular but it is positive
+semi definite because that eigen value
+
+ align:start position:0%
+semi definite because that eigen value
+ 
+
+ align:start position:0%
+semi definite because that eigen value
+is positive okay
+
+ align:start position:0%
+is positive okay
+ 
+
+ align:start position:0%
+is positive okay
+so you got the idea of positive definite
+
+ align:start position:0%
+so you got the idea of positive definite
+ 
+
+ align:start position:0%
+so you got the idea of positive definite
+matrices again all five of those any one
+
+ align:start position:0%
+matrices again all five of those any one
+ 
+
+ align:start position:0%
+matrices again all five of those any one
+of those five tests is enough to show
+
+ align:start position:0%
+of those five tests is enough to show
+ 
+
+ align:start position:0%
+of those five tests is enough to show
+that it's positive definite and so
+
+ align:start position:0%
+that it's positive definite and so
+ 
+
+ align:start position:0%
+that it's positive definite and so
+what's my goal next week is the singular
+
+ align:start position:0%
+what's my goal next week is the singular
+ 
+
+ align:start position:0%
+what's my goal next week is the singular
+value decomposition and all that that
+
+ align:start position:0%
+value decomposition and all that that
+ 
+
+ align:start position:0%
+value decomposition and all that that
+leads us to that's that's where we're
+
+ align:start position:0%
+leads us to that's that's where we're
+ 
+
+ align:start position:0%
+leads us to that's that's where we're
+there now ready for at the SVD okay have
+
+ align:start position:0%
+there now ready for at the SVD okay have
+ 
+
+ align:start position:0%
+there now ready for at the SVD okay have
+a good weekend and see ya oh I see you
+
+ align:start position:0%
+a good weekend and see ya oh I see you
+ 
+
+ align:start position:0%
+a good weekend and see ya oh I see you
+on Tuesday I guess right not Monday but
+
+ align:start position:0%
+on Tuesday I guess right not Monday but
+ 
+
+ align:start position:0%
+on Tuesday I guess right not Monday but
+Tuesday next week
\ No newline at end of file
diff --git a/xx8fH-r3Luk.txt b/xx8fH-r3Luk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bc0e0bc7d5dfe18b67fab7fdd37c93306e12035b
--- /dev/null
+++ b/xx8fH-r3Luk.txt
@@ -0,0 +1,522 @@
+align:start position:0%
+ 
+Kulom's force law can be the basis for
+
+ align:start position:0%
+Kulom's force law can be the basis for
+ 
+
+ align:start position:0%
+Kulom's force law can be the basis for
+estimating the net charge on an
+
+ align:start position:0%
+estimating the net charge on an
+ 
+
+ align:start position:0%
+estimating the net charge on an
+object. Conservation of charge and
+
+ align:start position:0%
+object. Conservation of charge and
+ 
+
+ align:start position:0%
+object. Conservation of charge and
+Gaus's law are also the basis for the
+
+ align:start position:0%
+Gaus's law are also the basis for the
+ 
+
+ align:start position:0%
+Gaus's law are also the basis for the
+measurement of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge. In this demonstration, the
+
+ align:start position:0%
+charge. In this demonstration, the
+ 
+
+ align:start position:0%
+charge. In this demonstration, the
+particles are air filled
+
+ align:start position:0%
+particles are air filled
+ 
+
+ align:start position:0%
+particles are air filled
+balloons of the variety used at parties.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They can be charged by rubbing them with
+
+ align:start position:0%
+They can be charged by rubbing them with
+ 
+
+ align:start position:0%
+They can be charged by rubbing them with
+a dry cloth.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They repel each other because they've
+
+ align:start position:0%
+They repel each other because they've
+ 
+
+ align:start position:0%
+They repel each other because they've
+been charged to the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polarity. Let's use measurements of the
+
+ align:start position:0%
+polarity. Let's use measurements of the
+ 
+
+ align:start position:0%
+polarity. Let's use measurements of the
+separation distance and the weight of
+
+ align:start position:0%
+separation distance and the weight of
+ 
+
+ align:start position:0%
+separation distance and the weight of
+the balloon to approximate the charge
+
+ align:start position:0%
+the balloon to approximate the charge
+ 
+
+ align:start position:0%
+the balloon to approximate the charge
+that's been left on one of the
+
+ align:start position:0%
+that's been left on one of the
+ 
+
+ align:start position:0%
+that's been left on one of the
+balloons. The threads that have been
+
+ align:start position:0%
+balloons. The threads that have been
+ 
+
+ align:start position:0%
+balloons. The threads that have been
+used to suspend them are tied at a
+
+ align:start position:0%
+used to suspend them are tied at a
+ 
+
+ align:start position:0%
+used to suspend them are tied at a
+common point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The spacing between balloon centers is
+
+ align:start position:0%
+The spacing between balloon centers is
+ 
+
+ align:start position:0%
+The spacing between balloon centers is
+about 50 cm. It's not possible to put
+
+ align:start position:0%
+about 50 cm. It's not possible to put
+ 
+
+ align:start position:0%
+about 50 cm. It's not possible to put
+the meter stick close to the balloons
+
+ align:start position:0%
+the meter stick close to the balloons
+ 
+
+ align:start position:0%
+the meter stick close to the balloons
+without their being attracted to
+
+ align:start position:0%
+without their being attracted to
+ 
+
+ align:start position:0%
+without their being attracted to
+Professor Zan. His body's a good
+
+ align:start position:0%
+Professor Zan. His body's a good
+ 
+
+ align:start position:0%
+Professor Zan. His body's a good
+conductor. The charges on the balloons
+
+ align:start position:0%
+conductor. The charges on the balloons
+ 
+
+ align:start position:0%
+conductor. The charges on the balloons
+induce image charges of opposite
+
+ align:start position:0%
+induce image charges of opposite
+ 
+
+ align:start position:0%
+induce image charges of opposite
+polarity on conducting surfaces to which
+
+ align:start position:0%
+polarity on conducting surfaces to which
+ 
+
+ align:start position:0%
+polarity on conducting surfaces to which
+they're attracted.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This image charge is just that
+
+ align:start position:0%
+This image charge is just that
+ 
+
+ align:start position:0%
+This image charge is just that
+responsible for attracting the balloons
+
+ align:start position:0%
+responsible for attracting the balloons
+ 
+
+ align:start position:0%
+responsible for attracting the balloons
+to any essentially grounded conductor in
+
+ align:start position:0%
+to any essentially grounded conductor in
+ 
+
+ align:start position:0%
+to any essentially grounded conductor in
+its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vicinity. By now, one of our balloons is
+
+ align:start position:0%
+vicinity. By now, one of our balloons is
+ 
+
+ align:start position:0%
+vicinity. By now, one of our balloons is
+broken. But with new balloons and a
+
+ align:start position:0%
+broken. But with new balloons and a
+ 
+
+ align:start position:0%
+broken. But with new balloons and a
+renewed charge, the spacing looks to be
+
+ align:start position:0%
+renewed charge, the spacing looks to be
+ 
+
+ align:start position:0%
+renewed charge, the spacing looks to be
+about what we had before.
+
+ align:start position:0%
+about what we had before.
+ 
+
+ align:start position:0%
+about what we had before.
+Here's what happens when we insert the
+
+ align:start position:0%
+Here's what happens when we insert the
+ 
+
+ align:start position:0%
+Here's what happens when we insert the
+balloon in the Faraday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+cage. Watch the meter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too. Our charge conservation statement
+
+ align:start position:0%
+too. Our charge conservation statement
+ 
+
+ align:start position:0%
+too. Our charge conservation statement
+can be used to see that it makes no
+
+ align:start position:0%
+can be used to see that it makes no
+ 
+
+ align:start position:0%
+can be used to see that it makes no
+difference to the measurement whether
+
+ align:start position:0%
+difference to the measurement whether
+ 
+
+ align:start position:0%
+difference to the measurement whether
+the balloon makes physical and
+
+ align:start position:0%
+the balloon makes physical and
+ 
+
+ align:start position:0%
+the balloon makes physical and
+electrical contact with the inner
+
+ align:start position:0%
+electrical contact with the inner
+ 
+
+ align:start position:0%
+electrical contact with the inner
+box. From the dial settings on the top
+
+ align:start position:0%
+box. From the dial settings on the top
+ 
+
+ align:start position:0%
+box. From the dial settings on the top
+scale, a full scale deflection is a
+
+ align:start position:0%
+scale, a full scale deflection is a
+ 
+
+ align:start position:0%
+scale, a full scale deflection is a
+charge of minus 1,000
+
+ align:start position:0%
+charge of minus 1,000
+ 
+
+ align:start position:0%
+charge of minus 1,000
+nanolms. The measured charge is 220 or
+
+ align:start position:0%
+nanolms. The measured charge is 220 or
+ 
+
+ align:start position:0%
+nanolms. The measured charge is 220 or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nano. Let's see what we get for the
+
+ align:start position:0%
+nano. Let's see what we get for the
+ 
+
+ align:start position:0%
+nano. Let's see what we get for the
+other balloon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The reading is about the same about 220
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nanoculum. When the balloon is removed,
+
+ align:start position:0%
+nanoculum. When the balloon is removed,
+ 
+
+ align:start position:0%
+nanoculum. When the balloon is removed,
+the meter reading almost goes back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero. Apparently, the charge is
+
+ align:start position:0%
+zero. Apparently, the charge is
+ 
+
+ align:start position:0%
+zero. Apparently, the charge is
+essentially removed with the balloon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What happens to the charge on the
+
+ align:start position:0%
+What happens to the charge on the
+ 
+
+ align:start position:0%
+What happens to the charge on the
+balloon if it's broken while in the
+
+ align:start position:0%
+balloon if it's broken while in the
+ 
+
+ align:start position:0%
+balloon if it's broken while in the
+Faraday cage and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+removed? We've used scotch tape to hold
+
+ align:start position:0%
+removed? We've used scotch tape to hold
+ 
+
+ align:start position:0%
+removed? We've used scotch tape to hold
+the balloon together.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Professor Zhan feels that most of the
+
+ align:start position:0%
+Professor Zhan feels that most of the
+ 
+
+ align:start position:0%
+Professor Zhan feels that most of the
+balloon was removed. The charge was not.
\ No newline at end of file
diff --git a/yGvxqV-qpQ8.txt b/yGvxqV-qpQ8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6848b621d87ac6ec9a6b17ed30796b30b72ac75a
--- /dev/null
+++ b/yGvxqV-qpQ8.txt
@@ -0,0 +1,1267 @@
+align:start position:0%
+ 
+Welcome to the second week of our class
+
+ align:start position:0%
+Welcome to the second week of our class
+ 
+
+ align:start position:0%
+Welcome to the second week of our class
+on shaping the future of work. We got
+
+ align:start position:0%
+on shaping the future of work. We got
+ 
+
+ align:start position:0%
+on shaping the future of work. We got
+off to a great start last week with lots
+
+ align:start position:0%
+off to a great start last week with lots
+ 
+
+ align:start position:0%
+off to a great start last week with lots
+of good discussions on the future of
+
+ align:start position:0%
+of good discussions on the future of
+ 
+
+ align:start position:0%
+of good discussions on the future of
+work, on your hopes, your aspirations, a
+
+ align:start position:0%
+work, on your hopes, your aspirations, a
+ 
+
+ align:start position:0%
+work, on your hopes, your aspirations, a
+lot of discussion about the future of
+
+ align:start position:0%
+lot of discussion about the future of
+ 
+
+ align:start position:0%
+lot of discussion about the future of
+technology and how it's going to affect
+
+ align:start position:0%
+technology and how it's going to affect
+ 
+
+ align:start position:0%
+technology and how it's going to affect
+work and some of the worries that many
+
+ align:start position:0%
+work and some of the worries that many
+ 
+
+ align:start position:0%
+work and some of the worries that many
+of you have about this. So, we'll
+
+ align:start position:0%
+of you have about this. So, we'll
+ 
+
+ align:start position:0%
+of you have about this. So, we'll
+continue these discussions. We'll go
+
+ align:start position:0%
+continue these discussions. We'll go
+ 
+
+ align:start position:0%
+continue these discussions. We'll go
+into more depth on technology and work
+
+ align:start position:0%
+into more depth on technology and work
+ 
+
+ align:start position:0%
+into more depth on technology and work
+uh down uh the way in about the fourth
+
+ align:start position:0%
+uh down uh the way in about the fourth
+ 
+
+ align:start position:0%
+uh down uh the way in about the fourth
+week of class. But to give you a
+
+ align:start position:0%
+week of class. But to give you a
+ 
+
+ align:start position:0%
+week of class. But to give you a
+preview, I posted uh a new note on the
+
+ align:start position:0%
+preview, I posted uh a new note on the
+ 
+
+ align:start position:0%
+preview, I posted uh a new note on the
+discussion board about a big new MIT
+
+ align:start position:0%
+discussion board about a big new MIT
+ 
+
+ align:start position:0%
+discussion board about a big new MIT
+project on the future of the technology
+
+ align:start position:0%
+project on the future of the technology
+ 
+
+ align:start position:0%
+project on the future of the technology
+in textiles of all industries. We are
+
+ align:start position:0%
+in textiles of all industries. We are
+ 
+
+ align:start position:0%
+in textiles of all industries. We are
+about to start a big project to see if
+
+ align:start position:0%
+about to start a big project to see if
+ 
+
+ align:start position:0%
+about to start a big project to see if
+we can put some of the ideas of this
+
+ align:start position:0%
+we can put some of the ideas of this
+ 
+
+ align:start position:0%
+we can put some of the ideas of this
+course to work in practice where we
+
+ align:start position:0%
+course to work in practice where we
+ 
+
+ align:start position:0%
+course to work in practice where we
+shape the future of the textile and
+
+ align:start position:0%
+shape the future of the textile and
+ 
+
+ align:start position:0%
+shape the future of the textile and
+fabric industry with high technology
+
+ align:start position:0%
+fabric industry with high technology
+ 
+
+ align:start position:0%
+fabric industry with high technology
+jobs, hopefully good quality jobs with
+
+ align:start position:0%
+jobs, hopefully good quality jobs with
+ 
+
+ align:start position:0%
+jobs, hopefully good quality jobs with
+new training programs. So take a look at
+
+ align:start position:0%
+new training programs. So take a look at
+ 
+
+ align:start position:0%
+new training programs. So take a look at
+that post, see if you have thoughts on
+
+ align:start position:0%
+that post, see if you have thoughts on
+ 
+
+ align:start position:0%
+that post, see if you have thoughts on
+how we can shape the future of work in
+
+ align:start position:0%
+how we can shape the future of work in
+ 
+
+ align:start position:0%
+how we can shape the future of work in
+that particular sector. But this week
+
+ align:start position:0%
+that particular sector. But this week
+ 
+
+ align:start position:0%
+that particular sector. But this week
+we'll do three things. First, the videos
+
+ align:start position:0%
+we'll do three things. First, the videos
+ 
+
+ align:start position:0%
+we'll do three things. First, the videos
+that are posted for this week will give
+
+ align:start position:0%
+that are posted for this week will give
+ 
+
+ align:start position:0%
+that are posted for this week will give
+you a bit of a history of how the social
+
+ align:start position:0%
+you a bit of a history of how the social
+ 
+
+ align:start position:0%
+you a bit of a history of how the social
+contract played out and worked well in
+
+ align:start position:0%
+contract played out and worked well in
+ 
+
+ align:start position:0%
+contract played out and worked well in
+the United States and in fact in some
+
+ align:start position:0%
+the United States and in fact in some
+ 
+
+ align:start position:0%
+the United States and in fact in some
+other countries around the world in the
+
+ align:start position:0%
+other countries around the world in the
+ 
+
+ align:start position:0%
+other countries around the world in the
+past. We do this not to try to repeat
+
+ align:start position:0%
+past. We do this not to try to repeat
+ 
+
+ align:start position:0%
+past. We do this not to try to repeat
+history, but to spring forward on the
+
+ align:start position:0%
+history, but to spring forward on the
+ 
+
+ align:start position:0%
+history, but to spring forward on the
+basis of a good understanding of where
+
+ align:start position:0%
+basis of a good understanding of where
+ 
+
+ align:start position:0%
+basis of a good understanding of where
+we've come from and what we need to do
+
+ align:start position:0%
+we've come from and what we need to do
+ 
+
+ align:start position:0%
+we've come from and what we need to do
+to build a new social contract, a good
+
+ align:start position:0%
+to build a new social contract, a good
+ 
+
+ align:start position:0%
+to build a new social contract, a good
+foundation for building a new social
+
+ align:start position:0%
+foundation for building a new social
+ 
+
+ align:start position:0%
+foundation for building a new social
+contract in the future. Second, this
+
+ align:start position:0%
+contract in the future. Second, this
+ 
+
+ align:start position:0%
+contract in the future. Second, this
+week we're going to introduce some new
+
+ align:start position:0%
+week we're going to introduce some new
+ 
+
+ align:start position:0%
+week we're going to introduce some new
+uh regional discussion facilitators. Our
+
+ align:start position:0%
+uh regional discussion facilitators. Our
+ 
+
+ align:start position:0%
+uh regional discussion facilitators. Our
+M MBAs from the class I'm teaching here
+
+ align:start position:0%
+M MBAs from the class I'm teaching here
+ 
+
+ align:start position:0%
+M MBAs from the class I'm teaching here
+on campus are from all over the world,
+
+ align:start position:0%
+on campus are from all over the world,
+ 
+
+ align:start position:0%
+on campus are from all over the world,
+from China, from South Asia, from
+
+ align:start position:0%
+from China, from South Asia, from
+ 
+
+ align:start position:0%
+from China, from South Asia, from
+Africa, from Northern Europe, from
+
+ align:start position:0%
+Africa, from Northern Europe, from
+ 
+
+ align:start position:0%
+Africa, from Northern Europe, from
+Brazil. They will host discussions about
+
+ align:start position:0%
+Brazil. They will host discussions about
+ 
+
+ align:start position:0%
+Brazil. They will host discussions about
+how the issues we're talking about play
+
+ align:start position:0%
+how the issues we're talking about play
+ 
+
+ align:start position:0%
+how the issues we're talking about play
+out in your regions of the world. And we
+
+ align:start position:0%
+out in your regions of the world. And we
+ 
+
+ align:start position:0%
+out in your regions of the world. And we
+ask those of you who are from those
+
+ align:start position:0%
+ask those of you who are from those
+ 
+
+ align:start position:0%
+ask those of you who are from those
+areas to uh join that conversation.
+
+ align:start position:0%
+areas to uh join that conversation.
+ 
+
+ align:start position:0%
+areas to uh join that conversation.
+We'll even have some new experts from
+
+ align:start position:0%
+We'll even have some new experts from
+ 
+
+ align:start position:0%
+We'll even have some new experts from
+Australia, some colleagues of mine in
+
+ align:start position:0%
+Australia, some colleagues of mine in
+ 
+
+ align:start position:0%
+Australia, some colleagues of mine in
+the universities over there who study
+
+ align:start position:0%
+the universities over there who study
+ 
+
+ align:start position:0%
+the universities over there who study
+and work on these issues. So I think
+
+ align:start position:0%
+and work on these issues. So I think
+ 
+
+ align:start position:0%
+and work on these issues. So I think
+we'll have a full-bodied discussion
+
+ align:start position:0%
+we'll have a full-bodied discussion
+ 
+
+ align:start position:0%
+we'll have a full-bodied discussion
+about how the changing nature of work is
+
+ align:start position:0%
+about how the changing nature of work is
+ 
+
+ align:start position:0%
+about how the changing nature of work is
+playing out in different parts of our
+
+ align:start position:0%
+playing out in different parts of our
+ 
+
+ align:start position:0%
+playing out in different parts of our
+planet.
+
+ align:start position:0%
+planet.
+ 
+
+ align:start position:0%
+planet.
+to get uh things started on your
+
+ align:start position:0%
+to get uh things started on your
+ 
+
+ align:start position:0%
+to get uh things started on your
+personal career process. This week uh
+
+ align:start position:0%
+personal career process. This week uh
+ 
+
+ align:start position:0%
+personal career process. This week uh
+there's an assignment that will take you
+
+ align:start position:0%
+there's an assignment that will take you
+ 
+
+ align:start position:0%
+there's an assignment that will take you
+step by step through a process of
+
+ align:start position:0%
+step by step through a process of
+ 
+
+ align:start position:0%
+step by step through a process of
+identifying the kinds of issues that
+
+ align:start position:0%
+identifying the kinds of issues that
+ 
+
+ align:start position:0%
+identifying the kinds of issues that
+you're interested in. You have some
+
+ align:start position:0%
+you're interested in. You have some
+ 
+
+ align:start position:0%
+you're interested in. You have some
+aptitude toward and then the kind of
+
+ align:start position:0%
+aptitude toward and then the kind of
+ 
+
+ align:start position:0%
+aptitude toward and then the kind of
+educational levels that are available to
+
+ align:start position:0%
+educational levels that are available to
+ 
+
+ align:start position:0%
+educational levels that are available to
+get access to the jobs in fields of
+
+ align:start position:0%
+get access to the jobs in fields of
+ 
+
+ align:start position:0%
+get access to the jobs in fields of
+interest to you. So get started by going
+
+ align:start position:0%
+interest to you. So get started by going
+ 
+
+ align:start position:0%
+interest to you. So get started by going
+to the assignment uh page. Start that
+
+ align:start position:0%
+to the assignment uh page. Start that
+ 
+
+ align:start position:0%
+to the assignment uh page. Start that
+process. It'll carry through over the
+
+ align:start position:0%
+process. It'll carry through over the
+ 
+
+ align:start position:0%
+process. It'll carry through over the
+next several weeks and it's accompanied
+
+ align:start position:0%
+next several weeks and it's accompanied
+ 
+
+ align:start position:0%
+next several weeks and it's accompanied
+by several videos around the role of
+
+ align:start position:0%
+by several videos around the role of
+ 
+
+ align:start position:0%
+by several videos around the role of
+education and its changing role in
+
+ align:start position:0%
+education and its changing role in
+ 
+
+ align:start position:0%
+education and its changing role in
+lifelong learning and a special uh video
+
+ align:start position:0%
+lifelong learning and a special uh video
+ 
+
+ align:start position:0%
+lifelong learning and a special uh video
+by our colleague Lee Dyer who talks
+
+ align:start position:0%
+by our colleague Lee Dyer who talks
+ 
+
+ align:start position:0%
+by our colleague Lee Dyer who talks
+about the skills and competencies needed
+
+ align:start position:0%
+about the skills and competencies needed
+ 
+
+ align:start position:0%
+about the skills and competencies needed
+for jobs of the future. So that's what
+
+ align:start position:0%
+for jobs of the future. So that's what
+ 
+
+ align:start position:0%
+for jobs of the future. So that's what
+we'll do uh this week. But before uh we
+
+ align:start position:0%
+we'll do uh this week. But before uh we
+ 
+
+ align:start position:0%
+we'll do uh this week. But before uh we
+finish here, let's take a look at what
+
+ align:start position:0%
+finish here, let's take a look at what
+ 
+
+ align:start position:0%
+finish here, let's take a look at what
+you told us last week about your goals
+
+ align:start position:0%
+you told us last week about your goals
+ 
+
+ align:start position:0%
+you told us last week about your goals
+and your aspirations for work.
+
+ align:start position:0%
+and your aspirations for work.
+ 
+
+ align:start position:0%
+and your aspirations for work.
+Here's the results of the poll that you
+
+ align:start position:0%
+Here's the results of the poll that you
+ 
+
+ align:start position:0%
+Here's the results of the poll that you
+uh filled in about your top priority for
+
+ align:start position:0%
+uh filled in about your top priority for
+ 
+
+ align:start position:0%
+uh filled in about your top priority for
+your work and your career. Notice that
+
+ align:start position:0%
+your work and your career. Notice that
+ 
+
+ align:start position:0%
+your work and your career. Notice that
+the top item comes out to be having a
+
+ align:start position:0%
+the top item comes out to be having a
+ 
+
+ align:start position:0%
+the top item comes out to be having a
+good work life balance followed very
+
+ align:start position:0%
+good work life balance followed very
+ 
+
+ align:start position:0%
+good work life balance followed very
+closely by having a big impact on
+
+ align:start position:0%
+closely by having a big impact on
+ 
+
+ align:start position:0%
+closely by having a big impact on
+problems that are important to you and
+
+ align:start position:0%
+problems that are important to you and
+ 
+
+ align:start position:0%
+problems that are important to you and
+to society. And then in third place, but
+
+ align:start position:0%
+to society. And then in third place, but
+ 
+
+ align:start position:0%
+to society. And then in third place, but
+not too far behind, is the desire to
+
+ align:start position:0%
+not too far behind, is the desire to
+ 
+
+ align:start position:0%
+not too far behind, is the desire to
+have a good living uh from your work
+
+ align:start position:0%
+have a good living uh from your work
+ 
+
+ align:start position:0%
+have a good living uh from your work
+experiences. These are the same top
+
+ align:start position:0%
+experiences. These are the same top
+ 
+
+ align:start position:0%
+experiences. These are the same top
+three items that your colleagues last
+
+ align:start position:0%
+three items that your colleagues last
+ 
+
+ align:start position:0%
+three items that your colleagues last
+year uh indicated were their top
+
+ align:start position:0%
+year uh indicated were their top
+ 
+
+ align:start position:0%
+year uh indicated were their top
+priorities. Although this year the work
+
+ align:start position:0%
+priorities. Although this year the work
+ 
+
+ align:start position:0%
+priorities. Although this year the work
+life balance became a little bit higher
+
+ align:start position:0%
+life balance became a little bit higher
+ 
+
+ align:start position:0%
+life balance became a little bit higher
+in the ranking. So it's very clear that
+
+ align:start position:0%
+in the ranking. So it's very clear that
+ 
+
+ align:start position:0%
+in the ranking. So it's very clear that
+uh you want many things out of your jobs
+
+ align:start position:0%
+uh you want many things out of your jobs
+ 
+
+ align:start position:0%
+uh you want many things out of your jobs
+and your careers. Unlike your parents as
+
+ align:start position:0%
+and your careers. Unlike your parents as
+ 
+
+ align:start position:0%
+and your careers. Unlike your parents as
+many of you told us who focused over
+
+ align:start position:0%
+many of you told us who focused over
+ 
+
+ align:start position:0%
+many of you told us who focused over
+here on earning a good living and having
+
+ align:start position:0%
+here on earning a good living and having
+ 
+
+ align:start position:0%
+here on earning a good living and having
+a stable job, you want to be able to
+
+ align:start position:0%
+a stable job, you want to be able to
+ 
+
+ align:start position:0%
+a stable job, you want to be able to
+both have a big impact on work. You want
+
+ align:start position:0%
+both have a big impact on work. You want
+ 
+
+ align:start position:0%
+both have a big impact on work. You want
+to have a good work life balance so you
+
+ align:start position:0%
+to have a good work life balance so you
+ 
+
+ align:start position:0%
+to have a good work life balance so you
+can have a good opportunity to raise
+
+ align:start position:0%
+can have a good opportunity to raise
+ 
+
+ align:start position:0%
+can have a good opportunity to raise
+your children and have a be a good
+
+ align:start position:0%
+your children and have a be a good
+ 
+
+ align:start position:0%
+your children and have a be a good
+spouse at home or a partner at home and
+
+ align:start position:0%
+spouse at home or a partner at home and
+ 
+
+ align:start position:0%
+spouse at home or a partner at home and
+also uh earn a good living. So let's uh
+
+ align:start position:0%
+also uh earn a good living. So let's uh
+ 
+
+ align:start position:0%
+also uh earn a good living. So let's uh
+focus on how we do that. Let me give you
+
+ align:start position:0%
+focus on how we do that. Let me give you
+ 
+
+ align:start position:0%
+focus on how we do that. Let me give you
+uh a couple of examples of the rich way
+
+ align:start position:0%
+uh a couple of examples of the rich way
+ 
+
+ align:start position:0%
+uh a couple of examples of the rich way
+in which you embodied these rankings in
+
+ align:start position:0%
+in which you embodied these rankings in
+ 
+
+ align:start position:0%
+in which you embodied these rankings in
+the range of comments in the exercise
+
+ align:start position:0%
+the range of comments in the exercise
+ 
+
+ align:start position:0%
+the range of comments in the exercise
+around comparing your goals with those
+
+ align:start position:0%
+around comparing your goals with those
+ 
+
+ align:start position:0%
+around comparing your goals with those
+of your parents. This one I think
+
+ align:start position:0%
+of your parents. This one I think
+ 
+
+ align:start position:0%
+of your parents. This one I think
+captures the essence of what the poll
+
+ align:start position:0%
+captures the essence of what the poll
+ 
+
+ align:start position:0%
+captures the essence of what the poll
+told us. As one of you said, I dream of
+
+ align:start position:0%
+told us. As one of you said, I dream of
+ 
+
+ align:start position:0%
+told us. As one of you said, I dream of
+a well-balanced work family environment
+
+ align:start position:0%
+a well-balanced work family environment
+ 
+
+ align:start position:0%
+a well-balanced work family environment
+where I can develop my skills, put them
+
+ align:start position:0%
+where I can develop my skills, put them
+ 
+
+ align:start position:0%
+where I can develop my skills, put them
+to service for my community, and as well
+
+ align:start position:0%
+to service for my community, and as well
+ 
+
+ align:start position:0%
+to service for my community, and as well
+get a wage that allows me to have a
+
+ align:start position:0%
+get a wage that allows me to have a
+ 
+
+ align:start position:0%
+get a wage that allows me to have a
+decent life so that I can provide for my
+
+ align:start position:0%
+decent life so that I can provide for my
+ 
+
+ align:start position:0%
+decent life so that I can provide for my
+family and my offspring. or this one. My
+
+ align:start position:0%
+family and my offspring. or this one. My
+ 
+
+ align:start position:0%
+family and my offspring. or this one. My
+dream is to change the world by
+
+ align:start position:0%
+dream is to change the world by
+ 
+
+ align:start position:0%
+dream is to change the world by
+contributing something meaningful to it
+
+ align:start position:0%
+contributing something meaningful to it
+ 
+
+ align:start position:0%
+contributing something meaningful to it
+while maintaining a balanced lifestyle.
+
+ align:start position:0%
+while maintaining a balanced lifestyle.
+ 
+
+ align:start position:0%
+while maintaining a balanced lifestyle.
+I consider myself a global citizen. This
+
+ align:start position:0%
+I consider myself a global citizen. This
+ 
+
+ align:start position:0%
+I consider myself a global citizen. This
+is something that a number of you
+
+ align:start position:0%
+is something that a number of you
+ 
+
+ align:start position:0%
+is something that a number of you
+mentioned that you want to work and live
+
+ align:start position:0%
+mentioned that you want to work and live
+ 
+
+ align:start position:0%
+mentioned that you want to work and live
+in a culturally diverse yet an
+
+ align:start position:0%
+in a culturally diverse yet an
+ 
+
+ align:start position:0%
+in a culturally diverse yet an
+integrated workplace and lifestyle and
+
+ align:start position:0%
+integrated workplace and lifestyle and
+ 
+
+ align:start position:0%
+integrated workplace and lifestyle and
+that uh you want to push your children
+
+ align:start position:0%
+that uh you want to push your children
+ 
+
+ align:start position:0%
+that uh you want to push your children
+to be curious about their world and to
+
+ align:start position:0%
+to be curious about their world and to
+ 
+
+ align:start position:0%
+to be curious about their world and to
+push the limits of what they can do as
+
+ align:start position:0%
+push the limits of what they can do as
+ 
+
+ align:start position:0%
+push the limits of what they can do as
+they grow up. Here's another one that it
+
+ align:start position:0%
+they grow up. Here's another one that it
+ 
+
+ align:start position:0%
+they grow up. Here's another one that it
+says particularly about young
+
+ align:start position:0%
+says particularly about young
+ 
+
+ align:start position:0%
+says particularly about young
+millennials and their interest in
+
+ align:start position:0%
+millennials and their interest in
+ 
+
+ align:start position:0%
+millennials and their interest in
+working with the digital re uh
+
+ align:start position:0%
+working with the digital re uh
+ 
+
+ align:start position:0%
+working with the digital re uh
+revolution. My dream is to be part of
+
+ align:start position:0%
+revolution. My dream is to be part of
+ 
+
+ align:start position:0%
+revolution. My dream is to be part of
+the div digital revolution driven by
+
+ align:start position:0%
+the div digital revolution driven by
+ 
+
+ align:start position:0%
+the div digital revolution driven by
+mill millennials working at innovative
+
+ align:start position:0%
+mill millennials working at innovative
+ 
+
+ align:start position:0%
+mill millennials working at innovative
+companies and to make the world a better
+
+ align:start position:0%
+companies and to make the world a better
+ 
+
+ align:start position:0%
+companies and to make the world a better
+place to live and work. That theme comes
+
+ align:start position:0%
+place to live and work. That theme comes
+ 
+
+ align:start position:0%
+place to live and work. That theme comes
+through again. And then finally, I want
+
+ align:start position:0%
+through again. And then finally, I want
+ 
+
+ align:start position:0%
+through again. And then finally, I want
+to earn a living wage and not have to
+
+ align:start position:0%
+to earn a living wage and not have to
+ 
+
+ align:start position:0%
+to earn a living wage and not have to
+miss my children growing up. This is the
+
+ align:start position:0%
+miss my children growing up. This is the
+ 
+
+ align:start position:0%
+miss my children growing up. This is the
+world of work that you aspire to. This
+
+ align:start position:0%
+world of work that you aspire to. This
+ 
+
+ align:start position:0%
+world of work that you aspire to. This
+is the world of work that we have to
+
+ align:start position:0%
+is the world of work that we have to
+ 
+
+ align:start position:0%
+is the world of work that we have to
+create uh moving forward. So, let's get
+
+ align:start position:0%
+create uh moving forward. So, let's get
+ 
+
+ align:start position:0%
+create uh moving forward. So, let's get
+on with the task. This week we'll focus
+
+ align:start position:0%
+on with the task. This week we'll focus
+ 
+
+ align:start position:0%
+on with the task. This week we'll focus
+on your uh responsibilities to make sure
+
+ align:start position:0%
+on your uh responsibilities to make sure
+ 
+
+ align:start position:0%
+on your uh responsibilities to make sure
+that you are prepared to have the right
+
+ align:start position:0%
+that you are prepared to have the right
+ 
+
+ align:start position:0%
+that you are prepared to have the right
+educational levels to achieve your goals
+
+ align:start position:0%
+educational levels to achieve your goals
+ 
+
+ align:start position:0%
+educational levels to achieve your goals
+and your aspirations. And then we'll
+
+ align:start position:0%
+and your aspirations. And then we'll
+ 
+
+ align:start position:0%
+and your aspirations. And then we'll
+also look at what made the world of work
+
+ align:start position:0%
+also look at what made the world of work
+ 
+
+ align:start position:0%
+also look at what made the world of work
+more effective in some times in the past
+
+ align:start position:0%
+more effective in some times in the past
+ 
+
+ align:start position:0%
+more effective in some times in the past
+in our countries so that we can spring
+
+ align:start position:0%
+in our countries so that we can spring
+ 
+
+ align:start position:0%
+in our countries so that we can spring
+forward to think about how we build a
+
+ align:start position:0%
+forward to think about how we build a
+ 
+
+ align:start position:0%
+forward to think about how we build a
+new foundation for the future of work.
\ No newline at end of file
diff --git a/yL-ZljBRlWQ.txt b/yL-ZljBRlWQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bde8e7ce46f9a68058554ad3b555fc429a3ea1b2
--- /dev/null
+++ b/yL-ZljBRlWQ.txt
@@ -0,0 +1,4011 @@
+align:start position:0%
+ 
+Um, a a very very warm welcome, but I uh
+
+ align:start position:0%
+Um, a a very very warm welcome, but I uh
+ 
+
+ align:start position:0%
+Um, a a very very warm welcome, but I uh
+I'm going to turn it over to our um
+
+ align:start position:0%
+I'm going to turn it over to our um
+ 
+
+ align:start position:0%
+I'm going to turn it over to our um
+hosts here at MIT to do the first
+
+ align:start position:0%
+hosts here at MIT to do the first
+ 
+
+ align:start position:0%
+hosts here at MIT to do the first
+welcome.
+
+ align:start position:0%
+welcome.
+ 
+
+ align:start position:0%
+welcome.
+>> Cool. Um, can we move the slide one?
+
+ align:start position:0%
+>> Cool. Um, can we move the slide one?
+ 
+
+ align:start position:0%
+>> Cool. Um, can we move the slide one?
+>> Oh, I got it. Okay, let's see.
+
+ align:start position:0%
+>> Oh, I got it. Okay, let's see.
+ 
+
+ align:start position:0%
+>> Oh, I got it. Okay, let's see.
+Um, do you want to talk about the flying
+
+ align:start position:0%
+Um, do you want to talk about the flying
+ 
+
+ align:start position:0%
+Um, do you want to talk about the flying
+the plane?
+
+ align:start position:0%
+the plane?
+ 
+
+ align:start position:0%
+the plane?
+>> Oh my gosh, I do. Um, all right. We're
+
+ align:start position:0%
+>> Oh my gosh, I do. Um, all right. We're
+ 
+
+ align:start position:0%
+>> Oh my gosh, I do. Um, all right. We're
+going to get our This is actually the
+
+ align:start position:0%
+going to get our This is actually the
+ 
+
+ align:start position:0%
+going to get our This is actually the
+perfect slide for our little start here,
+
+ align:start position:0%
+perfect slide for our little start here,
+ 
+
+ align:start position:0%
+perfect slide for our little start here,
+which we coordinated and and rehearsed.
+
+ align:start position:0%
+which we coordinated and and rehearsed.
+ 
+
+ align:start position:0%
+which we coordinated and and rehearsed.
+Um, I I love this picture because it uh
+
+ align:start position:0%
+Um, I I love this picture because it uh
+ 
+
+ align:start position:0%
+Um, I I love this picture because it uh
+basically embodies everything that is
+
+ align:start position:0%
+basically embodies everything that is
+ 
+
+ align:start position:0%
+basically embodies everything that is
+the organization heat and and the
+
+ align:start position:0%
+the organization heat and and the
+ 
+
+ align:start position:0%
+the organization heat and and the
+process of um moving forward in
+
+ align:start position:0%
+process of um moving forward in
+ 
+
+ align:start position:0%
+process of um moving forward in
+uncertainty. So we are here today um
+
+ align:start position:0%
+uncertainty. So we are here today um
+ 
+
+ align:start position:0%
+uncertainty. So we are here today um
+with this amazing course which you'll
+
+ align:start position:0%
+with this amazing course which you'll
+ 
+
+ align:start position:0%
+with this amazing course which you'll
+about to hear more about uh building uh
+
+ align:start position:0%
+about to hear more about uh building uh
+ 
+
+ align:start position:0%
+about to hear more about uh building uh
+and fixing the airplane while flying it.
+
+ align:start position:0%
+and fixing the airplane while flying it.
+ 
+
+ align:start position:0%
+and fixing the airplane while flying it.
+Um so I I I really want to know how that
+
+ align:start position:0%
+Um so I I I really want to know how that
+ 
+
+ align:start position:0%
+Um so I I I really want to know how that
+picture came to be but
+
+ align:start position:0%
+picture came to be but
+ 
+
+ align:start position:0%
+picture came to be but
+but it it stands. So it to that end I
+
+ align:start position:0%
+but it it stands. So it to that end I
+ 
+
+ align:start position:0%
+but it it stands. So it to that end I
+want to acknowledge that you know we've
+
+ align:start position:0%
+want to acknowledge that you know we've
+ 
+
+ align:start position:0%
+want to acknowledge that you know we've
+never done this before. Um it's really
+
+ align:start position:0%
+never done this before. Um it's really
+ 
+
+ align:start position:0%
+never done this before. Um it's really
+can't it can't go wrong because of the
+
+ align:start position:0%
+can't it can't go wrong because of the
+ 
+
+ align:start position:0%
+can't it can't go wrong because of the
+people in the room
+
+ align:start position:0%
+people in the room
+ 
+
+ align:start position:0%
+people in the room
+and um we're really excited to see where
+
+ align:start position:0%
+and um we're really excited to see where
+ 
+
+ align:start position:0%
+and um we're really excited to see where
+it does go. Uh and we're also really
+
+ align:start position:0%
+it does go. Uh and we're also really
+ 
+
+ align:start position:0%
+it does go. Uh and we're also really
+excited to learn from it as always. So
+
+ align:start position:0%
+excited to learn from it as always. So
+ 
+
+ align:start position:0%
+excited to learn from it as always. So
+for example, there is a lovely
+
+ align:start position:0%
+for example, there is a lovely
+ 
+
+ align:start position:0%
+for example, there is a lovely
+whiteboard outside during your coffee
+
+ align:start position:0%
+whiteboard outside during your coffee
+ 
+
+ align:start position:0%
+whiteboard outside during your coffee
+breaks that has two sides to it. One
+
+ align:start position:0%
+breaks that has two sides to it. One
+ 
+
+ align:start position:0%
+breaks that has two sides to it. One
+side is who are the people and the ideas
+
+ align:start position:0%
+side is who are the people and the ideas
+ 
+
+ align:start position:0%
+side is who are the people and the ideas
+and the topics that we need to add to
+
+ align:start position:0%
+and the topics that we need to add to
+ 
+
+ align:start position:0%
+and the topics that we need to add to
+this conversation.
+
+ align:start position:0%
+this conversation.
+ 
+
+ align:start position:0%
+this conversation.
+Please please put your ideas there. Um
+
+ align:start position:0%
+Please please put your ideas there. Um
+ 
+
+ align:start position:0%
+Please please put your ideas there. Um
+and the other one is just general
+
+ align:start position:0%
+and the other one is just general
+ 
+
+ align:start position:0%
+and the other one is just general
+feedback. Um thoughts, ideas, learnings,
+
+ align:start position:0%
+feedback. Um thoughts, ideas, learnings,
+ 
+
+ align:start position:0%
+feedback. Um thoughts, ideas, learnings,
+changes, etc. Um please don't hesitate
+
+ align:start position:0%
+changes, etc. Um please don't hesitate
+ 
+
+ align:start position:0%
+changes, etc. Um please don't hesitate
+to give us the gift of feedback. Uh and
+
+ align:start position:0%
+to give us the gift of feedback. Uh and
+ 
+
+ align:start position:0%
+to give us the gift of feedback. Uh and
+now for the part we probably should have
+
+ align:start position:0%
+now for the part we probably should have
+ 
+
+ align:start position:0%
+now for the part we probably should have
+started with. Hi, I'm Zay McAfei. I'm
+
+ align:start position:0%
+started with. Hi, I'm Zay McAfei. I'm
+ 
+
+ align:start position:0%
+started with. Hi, I'm Zay McAfei. I'm
+the executive director of HEAT. And heat
+
+ align:start position:0%
+the executive director of HEAT. And heat
+ 
+
+ align:start position:0%
+the executive director of HEAT. And heat
+is a um is a a nonprofit that has been
+
+ align:start position:0%
+is a um is a a nonprofit that has been
+ 
+
+ align:start position:0%
+is a um is a a nonprofit that has been
+focused on trying to solve climate
+
+ align:start position:0%
+focused on trying to solve climate
+ 
+
+ align:start position:0%
+focused on trying to solve climate
+change for a lot of years uh from a
+
+ align:start position:0%
+change for a lot of years uh from a
+ 
+
+ align:start position:0%
+change for a lot of years uh from a
+community level in the beginning and um
+
+ align:start position:0%
+community level in the beginning and um
+ 
+
+ align:start position:0%
+community level in the beginning and um
+scaling. So
+
+ align:start position:0%
+scaling. So
+ 
+
+ align:start position:0%
+scaling. So
+we um will talk more about the topic of
+
+ align:start position:0%
+we um will talk more about the topic of
+ 
+
+ align:start position:0%
+we um will talk more about the topic of
+geothermal networks in a few minutes but
+
+ align:start position:0%
+geothermal networks in a few minutes but
+ 
+
+ align:start position:0%
+geothermal networks in a few minutes but
+first I want to just um express a lot of
+
+ align:start position:0%
+first I want to just um express a lot of
+ 
+
+ align:start position:0%
+first I want to just um express a lot of
+gratitude to all of you for being
+
+ align:start position:0%
+gratitude to all of you for being
+ 
+
+ align:start position:0%
+gratitude to all of you for being
+present and here and offering yourselves
+
+ align:start position:0%
+present and here and offering yourselves
+ 
+
+ align:start position:0%
+present and here and offering yourselves
+to this conversation and and journey
+
+ align:start position:0%
+to this conversation and and journey
+ 
+
+ align:start position:0%
+to this conversation and and journey
+that might might look a little hazardous
+
+ align:start position:0%
+that might might look a little hazardous
+ 
+
+ align:start position:0%
+that might might look a little hazardous
+at times. Um, and also I want to just um
+
+ align:start position:0%
+at times. Um, and also I want to just um
+ 
+
+ align:start position:0%
+at times. Um, and also I want to just um
+thank MIT the inst the amazing
+
+ align:start position:0%
+thank MIT the inst the amazing
+ 
+
+ align:start position:0%
+thank MIT the inst the amazing
+institution and both Chris and Kurt for
+
+ align:start position:0%
+institution and both Chris and Kurt for
+ 
+
+ align:start position:0%
+institution and both Chris and Kurt for
+being our hosts and I want to turn it
+
+ align:start position:0%
+being our hosts and I want to turn it
+ 
+
+ align:start position:0%
+being our hosts and I want to turn it
+over to them to introduce themselves.
+
+ align:start position:0%
+over to them to introduce themselves.
+ 
+
+ align:start position:0%
+over to them to introduce themselves.
+>> Um, thanks Anab. Uh, so yeah, I'm so
+
+ align:start position:0%
+>> Um, thanks Anab. Uh, so yeah, I'm so
+ 
+
+ align:start position:0%
+>> Um, thanks Anab. Uh, so yeah, I'm so
+excited uh to welcome heat here to MIT.
+
+ align:start position:0%
+excited uh to welcome heat here to MIT.
+ 
+
+ align:start position:0%
+excited uh to welcome heat here to MIT.
+Uh, my name is Chris Rae. I'm the
+
+ align:start position:0%
+Uh, my name is Chris Rae. I'm the
+ 
+
+ align:start position:0%
+Uh, my name is Chris Rae. I'm the
+education program director at uh MIT's
+
+ align:start position:0%
+education program director at uh MIT's
+ 
+
+ align:start position:0%
+education program director at uh MIT's
+environmental solutions initiative. Um
+
+ align:start position:0%
+environmental solutions initiative. Um
+ 
+
+ align:start position:0%
+environmental solutions initiative. Um
+the education program mission is to
+
+ align:start position:0%
+the education program mission is to
+ 
+
+ align:start position:0%
+the education program mission is to
+better understand and expand climate
+
+ align:start position:0%
+better understand and expand climate
+ 
+
+ align:start position:0%
+better understand and expand climate
+education across both uh disciplinary
+
+ align:start position:0%
+education across both uh disciplinary
+ 
+
+ align:start position:0%
+education across both uh disciplinary
+contexts and institutional contexts. And
+
+ align:start position:0%
+contexts and institutional contexts. And
+ 
+
+ align:start position:0%
+contexts and institutional contexts. And
+I'd really like to make sure that our
+
+ align:start position:0%
+I'd really like to make sure that our
+ 
+
+ align:start position:0%
+I'd really like to make sure that our
+education our projects and activities
+
+ align:start position:0%
+education our projects and activities
+ 
+
+ align:start position:0%
+education our projects and activities
+are connecting to real world uh
+
+ align:start position:0%
+are connecting to real world uh
+ 
+
+ align:start position:0%
+are connecting to real world uh
+scenarios. So it's so exciting to be
+
+ align:start position:0%
+scenarios. So it's so exciting to be
+ 
+
+ align:start position:0%
+scenarios. So it's so exciting to be
+working with heat and kind of
+
+ align:start position:0%
+working with heat and kind of
+ 
+
+ align:start position:0%
+working with heat and kind of
+reinvisioning the way that energy can
+
+ align:start position:0%
+reinvisioning the way that energy can
+ 
+
+ align:start position:0%
+reinvisioning the way that energy can
+work. Um this is a part of a few other
+
+ align:start position:0%
+work. Um this is a part of a few other
+ 
+
+ align:start position:0%
+work. Um this is a part of a few other
+collaborations. So uh we started a new
+
+ align:start position:0%
+collaborations. So uh we started a new
+ 
+
+ align:start position:0%
+collaborations. So uh we started a new
+course called environmental justice
+
+ align:start position:0%
+course called environmental justice
+ 
+
+ align:start position:0%
+course called environmental justice
+science and technology and that has a
+
+ align:start position:0%
+science and technology and that has a
+ 
+
+ align:start position:0%
+science and technology and that has a
+massive open online version and heat
+
+ align:start position:0%
+massive open online version and heat
+ 
+
+ align:start position:0%
+massive open online version and heat
+participated with a really interesting
+
+ align:start position:0%
+participated with a really interesting
+ 
+
+ align:start position:0%
+participated with a really interesting
+lecture. Um and then also we're working
+
+ align:start position:0%
+lecture. Um and then also we're working
+ 
+
+ align:start position:0%
+lecture. Um and then also we're working
+on some K through2 curriculum in this uh
+
+ align:start position:0%
+on some K through2 curriculum in this uh
+ 
+
+ align:start position:0%
+on some K through2 curriculum in this uh
+day of climate uh project through open
+
+ align:start position:0%
+day of climate uh project through open
+ 
+
+ align:start position:0%
+day of climate uh project through open
+learning. So it's just really exciting
+
+ align:start position:0%
+learning. So it's just really exciting
+ 
+
+ align:start position:0%
+learning. So it's just really exciting
+to be doing both the K through2 space
+
+ align:start position:0%
+to be doing both the K through2 space
+ 
+
+ align:start position:0%
+to be doing both the K through2 space
+and the higher education space with
+
+ align:start position:0%
+and the higher education space with
+ 
+
+ align:start position:0%
+and the higher education space with
+heat. So again just so excited for heat
+
+ align:start position:0%
+heat. So again just so excited for heat
+ 
+
+ align:start position:0%
+heat. So again just so excited for heat
+to be here. Um thank you so much.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Good morning everyone. Um, my name is
+
+ align:start position:0%
+>> Good morning everyone. Um, my name is
+ 
+
+ align:start position:0%
+>> Good morning everyone. Um, my name is
+Kurt Newton. I'm director of MIT Open
+
+ align:start position:0%
+Kurt Newton. I'm director of MIT Open
+ 
+
+ align:start position:0%
+Kurt Newton. I'm director of MIT Open
+Courseware, another of the co-hosts for
+
+ align:start position:0%
+Courseware, another of the co-hosts for
+ 
+
+ align:start position:0%
+Courseware, another of the co-hosts for
+this event. Um, and we're thrilled to be
+
+ align:start position:0%
+this event. Um, and we're thrilled to be
+ 
+
+ align:start position:0%
+this event. Um, and we're thrilled to be
+participating in this, not just to host,
+
+ align:start position:0%
+participating in this, not just to host,
+ 
+
+ align:start position:0%
+participating in this, not just to host,
+but also because this is all going to
+
+ align:start position:0%
+but also because this is all going to
+ 
+
+ align:start position:0%
+but also because this is all going to
+flow out to the world. We're recording,
+
+ align:start position:0%
+flow out to the world. We're recording,
+ 
+
+ align:start position:0%
+flow out to the world. We're recording,
+as you know, we've got video set up here
+
+ align:start position:0%
+as you know, we've got video set up here
+ 
+
+ align:start position:0%
+as you know, we've got video set up here
+to um to capture and then share back
+
+ align:start position:0%
+to um to capture and then share back
+ 
+
+ align:start position:0%
+to um to capture and then share back
+with the world this important emerging
+
+ align:start position:0%
+with the world this important emerging
+ 
+
+ align:start position:0%
+with the world this important emerging
+knowledge. Um you know we've had the
+
+ align:start position:0%
+knowledge. Um you know we've had the
+ 
+
+ align:start position:0%
+knowledge. Um you know we've had the
+pleasure at open courseware with serving
+
+ align:start position:0%
+pleasure at open courseware with serving
+ 
+
+ align:start position:0%
+pleasure at open courseware with serving
+this broader mission of unlocking and
+
+ align:start position:0%
+this broader mission of unlocking and
+ 
+
+ align:start position:0%
+this broader mission of unlocking and
+empowering people around the world both
+
+ align:start position:0%
+empowering people around the world both
+ 
+
+ align:start position:0%
+empowering people around the world both
+learners and educators for over two
+
+ align:start position:0%
+learners and educators for over two
+ 
+
+ align:start position:0%
+learners and educators for over two
+decades. Um you see a screenshot of you
+
+ align:start position:0%
+decades. Um you see a screenshot of you
+ 
+
+ align:start position:0%
+decades. Um you see a screenshot of you
+know the first engagement that we had
+
+ align:start position:0%
+know the first engagement that we had
+ 
+
+ align:start position:0%
+know the first engagement that we had
+with with heat with Zanb a uh a January
+
+ align:start position:0%
+with with heat with Zanb a uh a January
+ 
+
+ align:start position:0%
+with with heat with Zanb a uh a January
+session workshop that we did uh about
+
+ align:start position:0%
+session workshop that we did uh about
+ 
+
+ align:start position:0%
+session workshop that we did uh about
+gas leaks you know part of the maybe the
+
+ align:start position:0%
+gas leaks you know part of the maybe the
+ 
+
+ align:start position:0%
+gas leaks you know part of the maybe the
+origin story for so what we're getting
+
+ align:start position:0%
+origin story for so what we're getting
+ 
+
+ align:start position:0%
+origin story for so what we're getting
+up to here um and what we do at open
+
+ align:start position:0%
+up to here um and what we do at open
+ 
+
+ align:start position:0%
+up to here um and what we do at open
+courseware is not just sharing this
+
+ align:start position:0%
+courseware is not just sharing this
+ 
+
+ align:start position:0%
+courseware is not just sharing this
+knowledge again but to do so in ways
+
+ align:start position:0%
+knowledge again but to do so in ways
+ 
+
+ align:start position:0%
+knowledge again but to do so in ways
+that um encourage practices of sharing
+
+ align:start position:0%
+that um encourage practices of sharing
+ 
+
+ align:start position:0%
+that um encourage practices of sharing
+and the feedback that gets set up
+
+ align:start position:0%
+and the feedback that gets set up
+ 
+
+ align:start position:0%
+and the feedback that gets set up
+through this through this sort of
+
+ align:start position:0%
+through this through this sort of
+ 
+
+ align:start position:0%
+through this through this sort of
+broader open knowledge ecosystem. So
+
+ align:start position:0%
+broader open knowledge ecosystem. So
+ 
+
+ align:start position:0%
+broader open knowledge ecosystem. So
+heat for instance, you know, putting all
+
+ align:start position:0%
+heat for instance, you know, putting all
+ 
+
+ align:start position:0%
+heat for instance, you know, putting all
+of these resources in an open library
+
+ align:start position:0%
+of these resources in an open library
+ 
+
+ align:start position:0%
+of these resources in an open library
+and gathering together to, you know, in
+
+ align:start position:0%
+and gathering together to, you know, in
+ 
+
+ align:start position:0%
+and gathering together to, you know, in
+a really nimble sort of generative way
+
+ align:start position:0%
+a really nimble sort of generative way
+ 
+
+ align:start position:0%
+a really nimble sort of generative way
+create this knowledge new. I I'm
+
+ align:start position:0%
+create this knowledge new. I I'm
+ 
+
+ align:start position:0%
+create this knowledge new. I I'm
+recalling here at MIT in January 2020,
+
+ align:start position:0%
+recalling here at MIT in January 2020,
+ 
+
+ align:start position:0%
+recalling here at MIT in January 2020,
+just before all kinds of stuff got shut
+
+ align:start position:0%
+just before all kinds of stuff got shut
+ 
+
+ align:start position:0%
+just before all kinds of stuff got shut
+down, we we hosted here some design
+
+ align:start position:0%
+down, we we hosted here some design
+ 
+
+ align:start position:0%
+down, we we hosted here some design
+cherettes to start this process. and
+
+ align:start position:0%
+cherettes to start this process. and
+ 
+
+ align:start position:0%
+cherettes to start this process. and
+just what a what a thrill it is to us to
+
+ align:start position:0%
+just what a what a thrill it is to us to
+ 
+
+ align:start position:0%
+just what a what a thrill it is to us to
+be kind of part of this journey
+
+ align:start position:0%
+be kind of part of this journey
+ 
+
+ align:start position:0%
+be kind of part of this journey
+together. And just to let you know if
+
+ align:start position:0%
+together. And just to let you know if
+ 
+
+ align:start position:0%
+together. And just to let you know if
+you're not familiar with open
+
+ align:start position:0%
+you're not familiar with open
+ 
+
+ align:start position:0%
+you're not familiar with open
+courseware, you know, the the reach of
+
+ align:start position:0%
+courseware, you know, the the reach of
+ 
+
+ align:start position:0%
+courseware, you know, the the reach of
+this content is considerable around the
+
+ align:start position:0%
+this content is considerable around the
+ 
+
+ align:start position:0%
+this content is considerable around the
+world. 70% of our of our visitors come
+
+ align:start position:0%
+world. 70% of our of our visitors come
+ 
+
+ align:start position:0%
+world. 70% of our of our visitors come
+from outside North America. So that the
+
+ align:start position:0%
+from outside North America. So that the
+ 
+
+ align:start position:0%
+from outside North America. So that the
+interest around the world that's
+
+ align:start position:0%
+interest around the world that's
+ 
+
+ align:start position:0%
+interest around the world that's
+developing in these technologies, we
+
+ align:start position:0%
+developing in these technologies, we
+ 
+
+ align:start position:0%
+developing in these technologies, we
+want to plug into that. Our website gets
+
+ align:start position:0%
+want to plug into that. Our website gets
+ 
+
+ align:start position:0%
+want to plug into that. Our website gets
+millions of visits every year. Um and
+
+ align:start position:0%
+millions of visits every year. Um and
+ 
+
+ align:start position:0%
+millions of visits every year. Um and
+our YouTube channel where the videos you
+
+ align:start position:0%
+our YouTube channel where the videos you
+ 
+
+ align:start position:0%
+our YouTube channel where the videos you
+know also live is also a really
+
+ align:start position:0%
+know also live is also a really
+ 
+
+ align:start position:0%
+know also live is also a really
+important point of engagement. Um with
+
+ align:start position:0%
+important point of engagement. Um with
+ 
+
+ align:start position:0%
+important point of engagement. Um with
+over five and a half million subscribers
+
+ align:start position:0%
+over five and a half million subscribers
+ 
+
+ align:start position:0%
+over five and a half million subscribers
+on our YouTube channel it's the it's the
+
+ align:start position:0%
+on our YouTube channel it's the it's the
+ 
+
+ align:start position:0%
+on our YouTube channel it's the it's the
+largest subscriber base of any sort of
+
+ align:start position:0%
+largest subscriber base of any sort of
+ 
+
+ align:start position:0%
+largest subscriber base of any sort of
+educational institution out in the
+
+ align:start position:0%
+educational institution out in the
+ 
+
+ align:start position:0%
+educational institution out in the
+world. So rest assured that that what we
+
+ align:start position:0%
+world. So rest assured that that what we
+ 
+
+ align:start position:0%
+world. So rest assured that that what we
+come up with today you know flowing out
+
+ align:start position:0%
+come up with today you know flowing out
+ 
+
+ align:start position:0%
+come up with today you know flowing out
+to the world is going to reach a lot of
+
+ align:start position:0%
+to the world is going to reach a lot of
+ 
+
+ align:start position:0%
+to the world is going to reach a lot of
+people and it's really going to I think
+
+ align:start position:0%
+people and it's really going to I think
+ 
+
+ align:start position:0%
+people and it's really going to I think
+further the the work that we're all
+
+ align:start position:0%
+further the the work that we're all
+ 
+
+ align:start position:0%
+further the the work that we're all
+trying to get up to. So welcome.
+
+ align:start position:0%
+trying to get up to. So welcome.
+ 
+
+ align:start position:0%
+trying to get up to. So welcome.
+But don't hesitate to talk after that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Thank you. My name is Isabel Varela,
+
+ align:start position:0%
+>> Thank you. My name is Isabel Varela,
+ 
+
+ align:start position:0%
+>> Thank you. My name is Isabel Varela,
+science director at HEAT. And I wanted
+
+ align:start position:0%
+science director at HEAT. And I wanted
+ 
+
+ align:start position:0%
+science director at HEAT. And I wanted
+to briefly share this is the heat team
+
+ align:start position:0%
+to briefly share this is the heat team
+ 
+
+ align:start position:0%
+to briefly share this is the heat team
+that is here to help you. If you have
+
+ align:start position:0%
+that is here to help you. If you have
+ 
+
+ align:start position:0%
+that is here to help you. If you have
+any questions, uh don't hesitate to
+
+ align:start position:0%
+any questions, uh don't hesitate to
+ 
+
+ align:start position:0%
+any questions, uh don't hesitate to
+reach out to us.
+
+ align:start position:0%
+reach out to us.
+ 
+
+ align:start position:0%
+reach out to us.
+We've put together um an incredible
+
+ align:start position:0%
+We've put together um an incredible
+ 
+
+ align:start position:0%
+We've put together um an incredible
+program. HEAT takes the aim to look at
+
+ align:start position:0%
+program. HEAT takes the aim to look at
+ 
+
+ align:start position:0%
+program. HEAT takes the aim to look at
+uh for solving a problem bring identify
+
+ align:start position:0%
+uh for solving a problem bring identify
+ 
+
+ align:start position:0%
+uh for solving a problem bring identify
+all the stakeholders that need to be
+
+ align:start position:0%
+all the stakeholders that need to be
+ 
+
+ align:start position:0%
+all the stakeholders that need to be
+involved to make that change happen and
+
+ align:start position:0%
+involved to make that change happen and
+ 
+
+ align:start position:0%
+involved to make that change happen and
+this two-day course reflects that. As
+
+ align:start position:0%
+this two-day course reflects that. As
+ 
+
+ align:start position:0%
+this two-day course reflects that. As
+you see we have eight sessions for each
+
+ align:start position:0%
+you see we have eight sessions for each
+ 
+
+ align:start position:0%
+you see we have eight sessions for each
+day and they vary from what is the
+
+ align:start position:0%
+day and they vary from what is the
+ 
+
+ align:start position:0%
+day and they vary from what is the
+challenge that we need to solve? What
+
+ align:start position:0%
+challenge that we need to solve? What
+ 
+
+ align:start position:0%
+challenge that we need to solve? What
+are the policies that need to be
+
+ align:start position:0%
+are the policies that need to be
+ 
+
+ align:start position:0%
+are the policies that need to be
+implemented to do that? Um what are the
+
+ align:start position:0%
+implemented to do that? Um what are the
+ 
+
+ align:start position:0%
+implemented to do that? Um what are the
+learnings that we can get from the
+
+ align:start position:0%
+learnings that we can get from the
+ 
+
+ align:start position:0%
+learnings that we can get from the
+geothermal networks that are implemented
+
+ align:start position:0%
+geothermal networks that are implemented
+ 
+
+ align:start position:0%
+geothermal networks that are implemented
+today? what are the design principles
+
+ align:start position:0%
+today? what are the design principles
+ 
+
+ align:start position:0%
+today? what are the design principles
+that should be applied um and learn from
+
+ align:start position:0%
+that should be applied um and learn from
+ 
+
+ align:start position:0%
+that should be applied um and learn from
+case studies.
+
+ align:start position:0%
+case studies.
+ 
+
+ align:start position:0%
+case studies.
+We are excited that you're here and we
+
+ align:start position:0%
+We are excited that you're here and we
+ 
+
+ align:start position:0%
+We are excited that you're here and we
+hope you get uh most out of this course
+
+ align:start position:0%
+hope you get uh most out of this course
+ 
+
+ align:start position:0%
+hope you get uh most out of this course
+and participate your participation makes
+
+ align:start position:0%
+and participate your participation makes
+ 
+
+ align:start position:0%
+and participate your participation makes
+the course more lively
+
+ align:start position:0%
+the course more lively
+ 
+
+ align:start position:0%
+the course more lively
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have an incredible lineup of 28
+
+ align:start position:0%
+we have an incredible lineup of 28
+ 
+
+ align:start position:0%
+we have an incredible lineup of 28
+speakers that are here. Some of them
+
+ align:start position:0%
+speakers that are here. Some of them
+ 
+
+ align:start position:0%
+speakers that are here. Some of them
+have come from uh around the country to
+
+ align:start position:0%
+have come from uh around the country to
+ 
+
+ align:start position:0%
+have come from uh around the country to
+be here in these two days. And we have
+
+ align:start position:0%
+be here in these two days. And we have
+ 
+
+ align:start position:0%
+be here in these two days. And we have
+organizations represented from
+
+ align:start position:0%
+organizations represented from
+ 
+
+ align:start position:0%
+organizations represented from
+universities, gas utilities, regulators,
+
+ align:start position:0%
+universities, gas utilities, regulators,
+ 
+
+ align:start position:0%
+universities, gas utilities, regulators,
+design firms, and community- based
+
+ align:start position:0%
+design firms, and community- based
+ 
+
+ align:start position:0%
+design firms, and community- based
+organizations. So, thank you for all the
+
+ align:start position:0%
+organizations. So, thank you for all the
+ 
+
+ align:start position:0%
+organizations. So, thank you for all the
+speakers uh that are here and making
+
+ align:start position:0%
+speakers uh that are here and making
+ 
+
+ align:start position:0%
+speakers uh that are here and making
+this uh course happen.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+>> just a quick note about the nature of
+
+ align:start position:0%
+>> just a quick note about the nature of
+ 
+
+ align:start position:0%
+>> just a quick note about the nature of
+the recordings that we're going to be
+
+ align:start position:0%
+the recordings that we're going to be
+ 
+
+ align:start position:0%
+the recordings that we're going to be
+doing. So what we'll be sharing with the
+
+ align:start position:0%
+doing. So what we'll be sharing with the
+ 
+
+ align:start position:0%
+doing. So what we'll be sharing with the
+world will be the the talks
+
+ align:start position:0%
+world will be the the talks
+ 
+
+ align:start position:0%
+world will be the the talks
+um and just the videos of the talks.
+
+ align:start position:0%
+um and just the videos of the talks.
+ 
+
+ align:start position:0%
+um and just the videos of the talks.
+There's a really important sort of Q&A
+
+ align:start position:0%
+There's a really important sort of Q&A
+ 
+
+ align:start position:0%
+There's a really important sort of Q&A
+interaction segment that will happen for
+
+ align:start position:0%
+interaction segment that will happen for
+ 
+
+ align:start position:0%
+interaction segment that will happen for
+each each of the sessions and we will
+
+ align:start position:0%
+each each of the sessions and we will
+ 
+
+ align:start position:0%
+each each of the sessions and we will
+not be sharing those straight out with
+
+ align:start position:0%
+not be sharing those straight out with
+ 
+
+ align:start position:0%
+not be sharing those straight out with
+the world. We want to have a you know a
+
+ align:start position:0%
+the world. We want to have a you know a
+ 
+
+ align:start position:0%
+the world. We want to have a you know a
+frank um completely un you know
+
+ align:start position:0%
+frank um completely un you know
+ 
+
+ align:start position:0%
+frank um completely un you know
+unconstrained conversation here in the
+
+ align:start position:0%
+unconstrained conversation here in the
+ 
+
+ align:start position:0%
+unconstrained conversation here in the
+room. Our hope is though that we will be
+
+ align:start position:0%
+room. Our hope is though that we will be
+ 
+
+ align:start position:0%
+room. Our hope is though that we will be
+sharing some kind of notes and takeaways
+
+ align:start position:0%
+sharing some kind of notes and takeaways
+ 
+
+ align:start position:0%
+sharing some kind of notes and takeaways
+some summaries and synthesis from those
+
+ align:start position:0%
+some summaries and synthesis from those
+ 
+
+ align:start position:0%
+some summaries and synthesis from those
+conversations. But rest assured um
+
+ align:start position:0%
+conversations. But rest assured um
+ 
+
+ align:start position:0%
+conversations. But rest assured um
+unless you are a speaker up here. We're
+
+ align:start position:0%
+unless you are a speaker up here. We're
+ 
+
+ align:start position:0%
+unless you are a speaker up here. We're
+not expecting you to show up in these
+
+ align:start position:0%
+not expecting you to show up in these
+ 
+
+ align:start position:0%
+not expecting you to show up in these
+videos that we share on OCW. If you have
+
+ align:start position:0%
+videos that we share on OCW. If you have
+ 
+
+ align:start position:0%
+videos that we share on OCW. If you have
+any concerns or questions about that uh
+
+ align:start position:0%
+any concerns or questions about that uh
+ 
+
+ align:start position:0%
+any concerns or questions about that uh
+please reach out to me, be in touch, but
+
+ align:start position:0%
+please reach out to me, be in touch, but
+ 
+
+ align:start position:0%
+please reach out to me, be in touch, but
+hopefully that's all right. Okay.
+
+ align:start position:0%
+hopefully that's all right. Okay.
+ 
+
+ align:start position:0%
+hopefully that's all right. Okay.
+>> Uh yeah. And um our our format uh is
+
+ align:start position:0%
+>> Uh yeah. And um our our format uh is
+ 
+
+ align:start position:0%
+>> Uh yeah. And um our our format uh is
+that each session is going to have a few
+
+ align:start position:0%
+that each session is going to have a few
+ 
+
+ align:start position:0%
+that each session is going to have a few
+brief presentations. Every single one of
+
+ align:start position:0%
+brief presentations. Every single one of
+ 
+
+ align:start position:0%
+brief presentations. Every single one of
+the speakers could likely speak for
+
+ align:start position:0%
+the speakers could likely speak for
+ 
+
+ align:start position:0%
+the speakers could likely speak for
+hours uh on any one of the topics and um
+
+ align:start position:0%
+hours uh on any one of the topics and um
+ 
+
+ align:start position:0%
+hours uh on any one of the topics and um
+and we're so aware of that. But we also
+
+ align:start position:0%
+and we're so aware of that. But we also
+ 
+
+ align:start position:0%
+and we're so aware of that. But we also
+thought that the most valuable thing
+
+ align:start position:0%
+thought that the most valuable thing
+ 
+
+ align:start position:0%
+thought that the most valuable thing
+here in the room is the interaction
+
+ align:start position:0%
+here in the room is the interaction
+ 
+
+ align:start position:0%
+here in the room is the interaction
+between. Uh so for um many speakers
+
+ align:start position:0%
+between. Uh so for um many speakers
+ 
+
+ align:start position:0%
+between. Uh so for um many speakers
+there will be a longer recorded piece of
+
+ align:start position:0%
+there will be a longer recorded piece of
+ 
+
+ align:start position:0%
+there will be a longer recorded piece of
+content that's attached to the
+
+ align:start position:0%
+content that's attached to the
+ 
+
+ align:start position:0%
+content that's attached to the
+courseware. Um but in the room we're
+
+ align:start position:0%
+courseware. Um but in the room we're
+ 
+
+ align:start position:0%
+courseware. Um but in the room we're
+going to keep the presentations brief so
+
+ align:start position:0%
+going to keep the presentations brief so
+ 
+
+ align:start position:0%
+going to keep the presentations brief so
+that we can get to that part of
+
+ align:start position:0%
+that we can get to that part of
+ 
+
+ align:start position:0%
+that we can get to that part of
+interacting between and talking and
+
+ align:start position:0%
+interacting between and talking and
+ 
+
+ align:start position:0%
+interacting between and talking and
+interacting with all of you. Um, and uh,
+
+ align:start position:0%
+interacting with all of you. Um, and uh,
+ 
+
+ align:start position:0%
+interacting with all of you. Um, and uh,
+we've got a Slido. Um, it's a little app
+
+ align:start position:0%
+we've got a Slido. Um, it's a little app
+ 
+
+ align:start position:0%
+we've got a Slido. Um, it's a little app
+that we'll introduce in a second um, for
+
+ align:start position:0%
+that we'll introduce in a second um, for
+ 
+
+ align:start position:0%
+that we'll introduce in a second um, for
+you to engage so we can kind of get more
+
+ align:start position:0%
+you to engage so we can kind of get more
+ 
+
+ align:start position:0%
+you to engage so we can kind of get more
+voices involved more quickly um, so that
+
+ align:start position:0%
+voices involved more quickly um, so that
+ 
+
+ align:start position:0%
+voices involved more quickly um, so that
+we can get the conversation going. Um,
+
+ align:start position:0%
+we can get the conversation going. Um,
+ 
+
+ align:start position:0%
+we can get the conversation going. Um,
+and then I've said this already, I'm
+
+ align:start position:0%
+and then I've said this already, I'm
+ 
+
+ align:start position:0%
+and then I've said this already, I'm
+going to say it again. You know, this is
+
+ align:start position:0%
+going to say it again. You know, this is
+ 
+
+ align:start position:0%
+going to say it again. You know, this is
+this is our first go at this. Um, I I
+
+ align:start position:0%
+this is our first go at this. Um, I I
+ 
+
+ align:start position:0%
+this is our first go at this. Um, I I
+love that you mentioned the previous um,
+
+ align:start position:0%
+love that you mentioned the previous um,
+ 
+
+ align:start position:0%
+love that you mentioned the previous um,
+wonderful events. The first one was a
+
+ align:start position:0%
+wonderful events. The first one was a
+ 
+
+ align:start position:0%
+wonderful events. The first one was a
+hackathon to design a a a tool to
+
+ align:start position:0%
+hackathon to design a a a tool to
+ 
+
+ align:start position:0%
+hackathon to design a a a tool to
+measure gas leaks. Um and the second one
+
+ align:start position:0%
+measure gas leaks. Um and the second one
+ 
+
+ align:start position:0%
+measure gas leaks. Um and the second one
+was a sharet. And now we're now we're
+
+ align:start position:0%
+was a sharet. And now we're now we're
+ 
+
+ align:start position:0%
+was a sharet. And now we're now we're
+trying um this this content. So uh
+
+ align:start position:0%
+trying um this this content. So uh
+ 
+
+ align:start position:0%
+trying um this this content. So uh
+you you will you will be part of making
+
+ align:start position:0%
+you you will you will be part of making
+ 
+
+ align:start position:0%
+you you will you will be part of making
+it um wonderful today. So please don't
+
+ align:start position:0%
+it um wonderful today. So please don't
+ 
+
+ align:start position:0%
+it um wonderful today. So please don't
+hesitate to participate. All right.
+
+ align:start position:0%
+hesitate to participate. All right.
+ 
+
+ align:start position:0%
+hesitate to participate. All right.
+One last comment for housekeeping. We
+
+ align:start position:0%
+One last comment for housekeeping. We
+ 
+
+ align:start position:0%
+One last comment for housekeeping. We
+have uh breakfast in the morning
+
+ align:start position:0%
+have uh breakfast in the morning
+ 
+
+ align:start position:0%
+have uh breakfast in the morning
+outside. We'll have coffee breaks. We'll
+
+ align:start position:0%
+outside. We'll have coffee breaks. We'll
+ 
+
+ align:start position:0%
+outside. We'll have coffee breaks. We'll
+have lunch outside. Uh food is allowed
+
+ align:start position:0%
+have lunch outside. Uh food is allowed
+ 
+
+ align:start position:0%
+have lunch outside. Uh food is allowed
+to come in here if you want to.
+
+ align:start position:0%
+to come in here if you want to.
+ 
+
+ align:start position:0%
+to come in here if you want to.
+Restrooms are here immediately to the
+
+ align:start position:0%
+Restrooms are here immediately to the
+ 
+
+ align:start position:0%
+Restrooms are here immediately to the
+right and there's another one in the
+
+ align:start position:0%
+right and there's another one in the
+ 
+
+ align:start position:0%
+right and there's another one in the
+hallway uh to the left.
+
+ align:start position:0%
+hallway uh to the left.
+ 
+
+ align:start position:0%
+hallway uh to the left.
+>> Thank you. And Isabelle planned this
+
+ align:start position:0%
+>> Thank you. And Isabelle planned this
+ 
+
+ align:start position:0%
+>> Thank you. And Isabelle planned this
+incredibly. So
+
+ align:start position:0%
+incredibly. So
+ 
+
+ align:start position:0%
+incredibly. So
+>> with the tea. With the tea.
+
+ align:start position:0%
+>> with the tea. With the tea.
+ 
+
+ align:start position:0%
+>> with the tea. With the tea.
+>> Yeah. Yeah. Yeah. With with the tea.
+
+ align:start position:0%
+>> Yeah. Yeah. Yeah. With with the tea.
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Yeah. With with the tea.
+All right. So one of the things that we
+
+ align:start position:0%
+All right. So one of the things that we
+ 
+
+ align:start position:0%
+All right. So one of the things that we
+always do and and I know Kurt is always
+
+ align:start position:0%
+always do and and I know Kurt is always
+ 
+
+ align:start position:0%
+always do and and I know Kurt is always
+in on this. It's open. So, uh, your
+
+ align:start position:0%
+in on this. It's open. So, uh, your
+ 
+
+ align:start position:0%
+in on this. It's open. So, uh, your
+backgrounds here in the room are all
+
+ align:start position:0%
+backgrounds here in the room are all
+ 
+
+ align:start position:0%
+backgrounds here in the room are all
+over the spectrum. We think that's
+
+ align:start position:0%
+over the spectrum. We think that's
+ 
+
+ align:start position:0%
+over the spectrum. We think that's
+beautiful and exciting. And one of the
+
+ align:start position:0%
+beautiful and exciting. And one of the
+ 
+
+ align:start position:0%
+beautiful and exciting. And one of the
+things we're going to try to do is make
+
+ align:start position:0%
+things we're going to try to do is make
+ 
+
+ align:start position:0%
+things we're going to try to do is make
+sure that we move between um,
+
+ align:start position:0%
+sure that we move between um,
+ 
+
+ align:start position:0%
+sure that we move between um,
+introductory and advanced. And we're
+
+ align:start position:0%
+introductory and advanced. And we're
+ 
+
+ align:start position:0%
+introductory and advanced. And we're
+we're it may be a fire hose, but that's
+
+ align:start position:0%
+we're it may be a fire hose, but that's
+ 
+
+ align:start position:0%
+we're it may be a fire hose, but that's
+why we're providing coffee. Um, so I get
+
+ align:start position:0%
+why we're providing coffee. Um, so I get
+ 
+
+ align:start position:0%
+why we're providing coffee. Um, so I get
+to start us off with two quick ideas for
+
+ align:start position:0%
+to start us off with two quick ideas for
+ 
+
+ align:start position:0%
+to start us off with two quick ideas for
+the entire two days and then we have the
+
+ align:start position:0%
+the entire two days and then we have the
+ 
+
+ align:start position:0%
+the entire two days and then we have the
+most amazing panel to get going at a
+
+ align:start position:0%
+most amazing panel to get going at a
+ 
+
+ align:start position:0%
+most amazing panel to get going at a
+very like high scale level of you know
+
+ align:start position:0%
+very like high scale level of you know
+ 
+
+ align:start position:0%
+very like high scale level of you know
+the whole the whole world. Um, so
+
+ align:start position:0%
+the whole the whole world. Um, so
+ 
+
+ align:start position:0%
+the whole the whole world. Um, so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+our our new our new uh tagline at the
+
+ align:start position:0%
+our our new our new uh tagline at the
+ 
+
+ align:start position:0%
+our our new our new uh tagline at the
+moment at HEAT is think thermal
+
+ align:start position:0%
+moment at HEAT is think thermal
+ 
+
+ align:start position:0%
+moment at HEAT is think thermal
+together.
+
+ align:start position:0%
+together.
+ 
+
+ align:start position:0%
+together.
+Um it kind of embodies a lot of the
+
+ align:start position:0%
+Um it kind of embodies a lot of the
+ 
+
+ align:start position:0%
+Um it kind of embodies a lot of the
+pieces that we're we've been learning
+
+ align:start position:0%
+pieces that we're we've been learning
+ 
+
+ align:start position:0%
+pieces that we're we've been learning
+over the past few years as we move
+
+ align:start position:0%
+over the past few years as we move
+ 
+
+ align:start position:0%
+over the past few years as we move
+forward with um networking ground source
+
+ align:start position:0%
+forward with um networking ground source
+ 
+
+ align:start position:0%
+forward with um networking ground source
+heat pumps or geothermal heat pumps. And
+
+ align:start position:0%
+heat pumps or geothermal heat pumps. And
+ 
+
+ align:start position:0%
+heat pumps or geothermal heat pumps. And
+um that idea of getting uh a problem
+
+ align:start position:0%
+um that idea of getting uh a problem
+ 
+
+ align:start position:0%
+um that idea of getting uh a problem
+solved by working together that's that's
+
+ align:start position:0%
+solved by working together that's that's
+ 
+
+ align:start position:0%
+solved by working together that's that's
+always been um there. But the piece
+
+ align:start position:0%
+always been um there. But the piece
+ 
+
+ align:start position:0%
+always been um there. But the piece
+where we realized as we as we spoke
+
+ align:start position:0%
+where we realized as we as we spoke
+ 
+
+ align:start position:0%
+where we realized as we as we spoke
+about geothermal that thermal energy
+
+ align:start position:0%
+about geothermal that thermal energy
+ 
+
+ align:start position:0%
+about geothermal that thermal energy
+itself wasn't always on the table in the
+
+ align:start position:0%
+itself wasn't always on the table in the
+ 
+
+ align:start position:0%
+itself wasn't always on the table in the
+climate solution space that people
+
+ align:start position:0%
+climate solution space that people
+ 
+
+ align:start position:0%
+climate solution space that people
+weren't thinking, they weren't
+
+ align:start position:0%
+weren't thinking, they weren't
+ 
+
+ align:start position:0%
+weren't thinking, they weren't
+measuring, they weren't talking about
+
+ align:start position:0%
+measuring, they weren't talking about
+ 
+
+ align:start position:0%
+measuring, they weren't talking about
+thermal energy. So, I'm going to just
+
+ align:start position:0%
+thermal energy. So, I'm going to just
+ 
+
+ align:start position:0%
+thermal energy. So, I'm going to just
+briefly start by getting us to take a
+
+ align:start position:0%
+briefly start by getting us to take a
+ 
+
+ align:start position:0%
+briefly start by getting us to take a
+moment to put on our thermal energy
+
+ align:start position:0%
+moment to put on our thermal energy
+ 
+
+ align:start position:0%
+moment to put on our thermal energy
+glasses. Um and then I'm going to do a
+
+ align:start position:0%
+glasses. Um and then I'm going to do a
+ 
+
+ align:start position:0%
+glasses. Um and then I'm going to do a
+little bit of housekeeping on language
+
+ align:start position:0%
+little bit of housekeeping on language
+ 
+
+ align:start position:0%
+little bit of housekeeping on language
+so that uh you know terminology and then
+
+ align:start position:0%
+so that uh you know terminology and then
+ 
+
+ align:start position:0%
+so that uh you know terminology and then
+we'll move to our first panel. Um so
+
+ align:start position:0%
+we'll move to our first panel. Um so
+ 
+
+ align:start position:0%
+we'll move to our first panel. Um so
+think thermal. Let's start with that
+
+ align:start position:0%
+think thermal. Let's start with that
+ 
+
+ align:start position:0%
+think thermal. Let's start with that
+part. Uh this is an image. If you use a
+
+ align:start position:0%
+part. Uh this is an image. If you use a
+ 
+
+ align:start position:0%
+part. Uh this is an image. If you use a
+thermal camera which actually we've
+
+ align:start position:0%
+thermal camera which actually we've
+ 
+
+ align:start position:0%
+thermal camera which actually we've
+recently purchased for the sheer fun of
+
+ align:start position:0%
+recently purchased for the sheer fun of
+ 
+
+ align:start position:0%
+recently purchased for the sheer fun of
+it. Um if you use a thermal camera you
+
+ align:start position:0%
+it. Um if you use a thermal camera you
+ 
+
+ align:start position:0%
+it. Um if you use a thermal camera you
+see things differently. um our eyes
+
+ align:start position:0%
+see things differently. um our eyes
+ 
+
+ align:start position:0%
+see things differently. um our eyes
+don't do that which may be why we don't
+
+ align:start position:0%
+don't do that which may be why we don't
+ 
+
+ align:start position:0%
+don't do that which may be why we don't
+we ignore it so often. Um but there is a
+
+ align:start position:0%
+we ignore it so often. Um but there is a
+ 
+
+ align:start position:0%
+we ignore it so often. Um but there is a
+huge amount of thermal energy in our
+
+ align:start position:0%
+huge amount of thermal energy in our
+ 
+
+ align:start position:0%
+huge amount of thermal energy in our
+earth and really if you stop and think
+
+ align:start position:0%
+earth and really if you stop and think
+ 
+
+ align:start position:0%
+earth and really if you stop and think
+about climate change what is climate
+
+ align:start position:0%
+about climate change what is climate
+ 
+
+ align:start position:0%
+about climate change what is climate
+change except a thermal energy
+
+ align:start position:0%
+change except a thermal energy
+ 
+
+ align:start position:0%
+change except a thermal energy
+regulation problem.
+
+ align:start position:0%
+regulation problem.
+ 
+
+ align:start position:0%
+regulation problem.
+And so if that's what it is and we talk
+
+ align:start position:0%
+And so if that's what it is and we talk
+ 
+
+ align:start position:0%
+And so if that's what it is and we talk
+about the rising temperature in air,
+
+ align:start position:0%
+about the rising temperature in air,
+ 
+
+ align:start position:0%
+about the rising temperature in air,
+well the kind of stunning thing is that
+
+ align:start position:0%
+well the kind of stunning thing is that
+ 
+
+ align:start position:0%
+well the kind of stunning thing is that
+uh there are a bunch of papers
+
+ align:start position:0%
+uh there are a bunch of papers
+ 
+
+ align:start position:0%
+uh there are a bunch of papers
+calculating how much thermal energy the
+
+ align:start position:0%
+calculating how much thermal energy the
+ 
+
+ align:start position:0%
+calculating how much thermal energy the
+earth has absorbed since say 1960
+
+ align:start position:0%
+earth has absorbed since say 1960
+ 
+
+ align:start position:0%
+earth has absorbed since say 1960
+um and it's 630
+
+ align:start position:0%
+um and it's 630
+ 
+
+ align:start position:0%
+um and it's 630
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+approximately all of the energy humanity
+
+ align:start position:0%
+approximately all of the energy humanity
+ 
+
+ align:start position:0%
+approximately all of the energy humanity
+uses every year.
+
+ align:start position:0%
+uses every year.
+ 
+
+ align:start position:0%
+uses every year.
+So I I was delighted to learn a new
+
+ align:start position:0%
+So I I was delighted to learn a new
+ 
+
+ align:start position:0%
+So I I was delighted to learn a new
+metric of energy, the zeta jewel. Um
+
+ align:start position:0%
+metric of energy, the zeta jewel. Um
+ 
+
+ align:start position:0%
+metric of energy, the zeta jewel. Um
+apparently humanity uses half a zeta
+
+ align:start position:0%
+apparently humanity uses half a zeta
+ 
+
+ align:start position:0%
+apparently humanity uses half a zeta
+jewel a year. All the energy we use. And
+
+ align:start position:0%
+jewel a year. All the energy we use. And
+ 
+
+ align:start position:0%
+jewel a year. All the energy we use. And
+every year our oceans alone are
+
+ align:start position:0%
+every year our oceans alone are
+ 
+
+ align:start position:0%
+every year our oceans alone are
+absorbing five zeta jewels.
+
+ align:start position:0%
+absorbing five zeta jewels.
+ 
+
+ align:start position:0%
+absorbing five zeta jewels.
+So that's a kind of stunning
+
+ align:start position:0%
+So that's a kind of stunning
+ 
+
+ align:start position:0%
+So that's a kind of stunning
+gut-wrenching challenge.
+
+ align:start position:0%
+gut-wrenching challenge.
+ 
+
+ align:start position:0%
+gut-wrenching challenge.
+But if you start to think about thermal
+
+ align:start position:0%
+But if you start to think about thermal
+ 
+
+ align:start position:0%
+But if you start to think about thermal
+energy, if start to look at it, if you
+
+ align:start position:0%
+energy, if start to look at it, if you
+ 
+
+ align:start position:0%
+energy, if start to look at it, if you
+start to measure it, it's also an
+
+ align:start position:0%
+start to measure it, it's also an
+ 
+
+ align:start position:0%
+start to measure it, it's also an
+extraordinary opportunity. It's a
+
+ align:start position:0%
+extraordinary opportunity. It's a
+ 
+
+ align:start position:0%
+extraordinary opportunity. It's a
+massive amount of energy all around us
+
+ align:start position:0%
+massive amount of energy all around us
+ 
+
+ align:start position:0%
+massive amount of energy all around us
+that we have been ignoring.
+
+ align:start position:0%
+that we have been ignoring.
+ 
+
+ align:start position:0%
+that we have been ignoring.
+And we have the technology to tap it,
+
+ align:start position:0%
+And we have the technology to tap it,
+ 
+
+ align:start position:0%
+And we have the technology to tap it,
+which is what we're here to talk about
+
+ align:start position:0%
+which is what we're here to talk about
+ 
+
+ align:start position:0%
+which is what we're here to talk about
+today.
+
+ align:start position:0%
+today.
+ 
+
+ align:start position:0%
+today.
+Um, a recent report from the IEA had a
+
+ align:start position:0%
+Um, a recent report from the IEA had a
+ 
+
+ align:start position:0%
+Um, a recent report from the IEA had a
+rather stunning statement um that kind
+
+ align:start position:0%
+rather stunning statement um that kind
+ 
+
+ align:start position:0%
+rather stunning statement um that kind
+of defines part of our our two days that
+
+ align:start position:0%
+of defines part of our our two days that
+ 
+
+ align:start position:0%
+of defines part of our our two days that
+the technical potential of geothermal
+
+ align:start position:0%
+the technical potential of geothermal
+ 
+
+ align:start position:0%
+the technical potential of geothermal
+would be more than enough to meet all
+
+ align:start position:0%
+would be more than enough to meet all
+ 
+
+ align:start position:0%
+would be more than enough to meet all
+heat demand. That's all heat demand. And
+
+ align:start position:0%
+heat demand. That's all heat demand. And
+ 
+
+ align:start position:0%
+heat demand. That's all heat demand. And
+they're not even talking about cooling
+
+ align:start position:0%
+they're not even talking about cooling
+ 
+
+ align:start position:0%
+they're not even talking about cooling
+in Africa, China, Europe, Southeast
+
+ align:start position:0%
+in Africa, China, Europe, Southeast
+ 
+
+ align:start position:0%
+in Africa, China, Europe, Southeast
+Asia, and the United States. So, I read
+
+ align:start position:0%
+Asia, and the United States. So, I read
+ 
+
+ align:start position:0%
+Asia, and the United States. So, I read
+that and I thought, well, what about
+
+ align:start position:0%
+that and I thought, well, what about
+ 
+
+ align:start position:0%
+that and I thought, well, what about
+those other places? Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I also want to just add into the
+
+ align:start position:0%
+but I also want to just add into the
+ 
+
+ align:start position:0%
+but I also want to just add into the
+conversation not just that geothermal
+
+ align:start position:0%
+conversation not just that geothermal
+ 
+
+ align:start position:0%
+conversation not just that geothermal
+energy that's in the world all around us
+
+ align:start position:0%
+energy that's in the world all around us
+ 
+
+ align:start position:0%
+energy that's in the world all around us
+um but also
+
+ align:start position:0%
+um but also
+ 
+
+ align:start position:0%
+um but also
+uh the energy we waste all that energy
+
+ align:start position:0%
+uh the energy we waste all that energy
+ 
+
+ align:start position:0%
+uh the energy we waste all that energy
+we do use combust burn etc um the
+
+ align:start position:0%
+we do use combust burn etc um the
+ 
+
+ align:start position:0%
+we do use combust burn etc um the
+majority of it is wasted
+
+ align:start position:0%
+majority of it is wasted
+ 
+
+ align:start position:0%
+majority of it is wasted
+uh and a large large portion of that is
+
+ align:start position:0%
+uh and a large large portion of that is
+ 
+
+ align:start position:0%
+uh and a large large portion of that is
+thermal energy. So that is where we can
+
+ align:start position:0%
+thermal energy. So that is where we can
+ 
+
+ align:start position:0%
+thermal energy. So that is where we can
+think about yet another untapped
+
+ align:start position:0%
+think about yet another untapped
+ 
+
+ align:start position:0%
+think about yet another untapped
+resource all around us. All right. So
+
+ align:start position:0%
+resource all around us. All right. So
+ 
+
+ align:start position:0%
+resource all around us. All right. So
+taking the optimistic part of like wow
+
+ align:start position:0%
+taking the optimistic part of like wow
+ 
+
+ align:start position:0%
+taking the optimistic part of like wow
+there's thermal energy all around us.
+
+ align:start position:0%
+there's thermal energy all around us.
+ 
+
+ align:start position:0%
+there's thermal energy all around us.
+This is really exciting. Um what we're
+
+ align:start position:0%
+This is really exciting. Um what we're
+ 
+
+ align:start position:0%
+This is really exciting. Um what we're
+here to do today for two days is talk
+
+ align:start position:0%
+here to do today for two days is talk
+ 
+
+ align:start position:0%
+here to do today for two days is talk
+about um the technology we uh believe is
+
+ align:start position:0%
+about um the technology we uh believe is
+ 
+
+ align:start position:0%
+about um the technology we uh believe is
+there and ready for us to tap it and
+
+ align:start position:0%
+there and ready for us to tap it and
+ 
+
+ align:start position:0%
+there and ready for us to tap it and
+turn it into a solution. Um talking
+
+ align:start position:0%
+turn it into a solution. Um talking
+ 
+
+ align:start position:0%
+turn it into a solution. Um talking
+about that technology sometimes has some
+
+ align:start position:0%
+about that technology sometimes has some
+ 
+
+ align:start position:0%
+about that technology sometimes has some
+challenges.
+
+ align:start position:0%
+challenges.
+ 
+
+ align:start position:0%
+challenges.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+we we try to bring everyone together.
+
+ align:start position:0%
+we we try to bring everyone together.
+ 
+
+ align:start position:0%
+we we try to bring everyone together.
+Lots of different groups have lots of
+
+ align:start position:0%
+Lots of different groups have lots of
+ 
+
+ align:start position:0%
+Lots of different groups have lots of
+different language. Um this is kind of
+
+ align:start position:0%
+different language. Um this is kind of
+ 
+
+ align:start position:0%
+different language. Um this is kind of
+the heat approach that we've been
+
+ align:start position:0%
+the heat approach that we've been
+ 
+
+ align:start position:0%
+the heat approach that we've been
+talking about uh earlier with many other
+
+ align:start position:0%
+talking about uh earlier with many other
+ 
+
+ align:start position:0%
+talking about uh earlier with many other
+events. Um you're now part of it being
+
+ align:start position:0%
+events. Um you're now part of it being
+ 
+
+ align:start position:0%
+events. Um you're now part of it being
+in the room. Uh so coming together
+
+ align:start position:0%
+in the room. Uh so coming together
+ 
+
+ align:start position:0%
+in the room. Uh so coming together
+around what we mean when we say things
+
+ align:start position:0%
+around what we mean when we say things
+ 
+
+ align:start position:0%
+around what we mean when we say things
+is one way to start get us all on the
+
+ align:start position:0%
+is one way to start get us all on the
+ 
+
+ align:start position:0%
+is one way to start get us all on the
+same page. Um, and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first thing we have is a little
+
+ align:start position:0%
+the first thing we have is a little
+ 
+
+ align:start position:0%
+the first thing we have is a little
+quick intro visual, which many of you
+
+ align:start position:0%
+quick intro visual, which many of you
+ 
+
+ align:start position:0%
+quick intro visual, which many of you
+may have already seen. I apologize if
+
+ align:start position:0%
+may have already seen. I apologize if
+ 
+
+ align:start position:0%
+may have already seen. I apologize if
+you have. Um, explaining the technology
+
+ align:start position:0%
+you have. Um, explaining the technology
+ 
+
+ align:start position:0%
+you have. Um, explaining the technology
+of networking geothermal heat pumps in a
+
+ align:start position:0%
+of networking geothermal heat pumps in a
+ 
+
+ align:start position:0%
+of networking geothermal heat pumps in a
+very basic level. Tomorrow, you're going
+
+ align:start position:0%
+very basic level. Tomorrow, you're going
+ 
+
+ align:start position:0%
+very basic level. Tomorrow, you're going
+to get a very advanced level. For now,
+
+ align:start position:0%
+to get a very advanced level. For now,
+ 
+
+ align:start position:0%
+to get a very advanced level. For now,
+this is right beneath our feet. The
+
+ align:start position:0%
+this is right beneath our feet. The
+ 
+
+ align:start position:0%
+this is right beneath our feet. The
+Earth is soaking up energy from the sun.
+
+ align:start position:0%
+Earth is soaking up energy from the sun.
+ 
+
+ align:start position:0%
+Earth is soaking up energy from the sun.
+And it's been doing this for a long
+
+ align:start position:0%
+And it's been doing this for a long
+ 
+
+ align:start position:0%
+And it's been doing this for a long
+time. Near the surface, the ground warms
+
+ align:start position:0%
+time. Near the surface, the ground warms
+ 
+
+ align:start position:0%
+time. Near the surface, the ground warms
+and cools with the seasons, but lower
+
+ align:start position:0%
+and cools with the seasons, but lower
+ 
+
+ align:start position:0%
+and cools with the seasons, but lower
+down, it stays at a constant
+
+ align:start position:0%
+down, it stays at a constant
+ 
+
+ align:start position:0%
+down, it stays at a constant
+temperature. In Massachusetts, that's
+
+ align:start position:0%
+temperature. In Massachusetts, that's
+ 
+
+ align:start position:0%
+temperature. In Massachusetts, that's
+55° F year round. This store temperature
+
+ align:start position:0%
+55° F year round. This store temperature
+ 
+
+ align:start position:0%
+55° F year round. This store temperature
+is a source of renewable energy. It can
+
+ align:start position:0%
+is a source of renewable energy. It can
+ 
+
+ align:start position:0%
+is a source of renewable energy. It can
+be access to heat or cool a single
+
+ align:start position:0%
+be access to heat or cool a single
+ 
+
+ align:start position:0%
+be access to heat or cool a single
+building without using fossil fuels. But
+
+ align:start position:0%
+building without using fossil fuels. But
+ 
+
+ align:start position:0%
+building without using fossil fuels. But
+did you know we can also connect entire
+
+ align:start position:0%
+did you know we can also connect entire
+ 
+
+ align:start position:0%
+did you know we can also connect entire
+communities to that renewable source in
+
+ align:start position:0%
+communities to that renewable source in
+ 
+
+ align:start position:0%
+communities to that renewable source in
+the ground? How does it work? It starts
+
+ align:start position:0%
+the ground? How does it work? It starts
+ 
+
+ align:start position:0%
+the ground? How does it work? It starts
+with underground pipes in the streets,
+
+ align:start position:0%
+with underground pipes in the streets,
+ 
+
+ align:start position:0%
+with underground pipes in the streets,
+sort of like gas pipes, but filled only
+
+ align:start position:0%
+sort of like gas pipes, but filled only
+ 
+
+ align:start position:0%
+sort of like gas pipes, but filled only
+with water. The water absorbs the ground
+
+ align:start position:0%
+with water. The water absorbs the ground
+ 
+
+ align:start position:0%
+with water. The water absorbs the ground
+temperature of the earth and delivers it
+
+ align:start position:0%
+temperature of the earth and delivers it
+ 
+
+ align:start position:0%
+temperature of the earth and delivers it
+to buildings. Pipes connect buildings
+
+ align:start position:0%
+to buildings. Pipes connect buildings
+ 
+
+ align:start position:0%
+to buildings. Pipes connect buildings
+with different heating needs. So, energy
+
+ align:start position:0%
+with different heating needs. So, energy
+ 
+
+ align:start position:0%
+with different heating needs. So, energy
+is never wasted. Instead, it's exchanged
+
+ align:start position:0%
+is never wasted. Instead, it's exchanged
+ 
+
+ align:start position:0%
+is never wasted. Instead, it's exchanged
+between buildings or stored in the
+
+ align:start position:0%
+between buildings or stored in the
+ 
+
+ align:start position:0%
+between buildings or stored in the
+ground until it's needed. Inside, a heat
+
+ align:start position:0%
+ground until it's needed. Inside, a heat
+ 
+
+ align:start position:0%
+ground until it's needed. Inside, a heat
+pump moves heat in or out according to
+
+ align:start position:0%
+pump moves heat in or out according to
+ 
+
+ align:start position:0%
+pump moves heat in or out according to
+the temperature you want. This system of
+
+ align:start position:0%
+the temperature you want. This system of
+ 
+
+ align:start position:0%
+the temperature you want. This system of
+pipes can connect like Lego blocks.
+
+ align:start position:0%
+pipes can connect like Lego blocks.
+ 
+
+ align:start position:0%
+pipes can connect like Lego blocks.
+gradually moving us all from gas to geo,
+
+ align:start position:0%
+gradually moving us all from gas to geo,
+ 
+
+ align:start position:0%
+gradually moving us all from gas to geo,
+giving us cleaner air, efficient heating
+
+ align:start position:0%
+giving us cleaner air, efficient heating
+ 
+
+ align:start position:0%
+giving us cleaner air, efficient heating
+and cooling, and a healthier planet. The
+
+ align:start position:0%
+and cooling, and a healthier planet. The
+ 
+
+ align:start position:0%
+and cooling, and a healthier planet. The
+idea for this worked geothermal system
+
+ align:start position:0%
+idea for this worked geothermal system
+ 
+
+ align:start position:0%
+idea for this worked geothermal system
+run at a utility scale originated at
+
+ align:start position:0%
+run at a utility scale originated at
+ 
+
+ align:start position:0%
+run at a utility scale originated at
+HEAT, a climate solutions nonprofit.
+
+ align:start position:0%
+HEAT, a climate solutions nonprofit.
+ 
+
+ align:start position:0%
+HEAT, a climate solutions nonprofit.
+Uh, all right, I'm going to really
+
+ align:start position:0%
+Uh, all right, I'm going to really
+ 
+
+ align:start position:0%
+Uh, all right, I'm going to really
+quickly go through language and then get
+
+ align:start position:0%
+quickly go through language and then get
+ 
+
+ align:start position:0%
+quickly go through language and then get
+out of here for so we can start this
+
+ align:start position:0%
+out of here for so we can start this
+ 
+
+ align:start position:0%
+out of here for so we can start this
+amazing panel. Um the word geothermal uh
+
+ align:start position:0%
+amazing panel. Um the word geothermal uh
+ 
+
+ align:start position:0%
+amazing panel. Um the word geothermal uh
+if any of you are thinking about uh you
+
+ align:start position:0%
+if any of you are thinking about uh you
+ 
+
+ align:start position:0%
+if any of you are thinking about uh you
+know Iceland and hot lava that's that's
+
+ align:start position:0%
+know Iceland and hot lava that's that's
+ 
+
+ align:start position:0%
+know Iceland and hot lava that's that's
+the stuff on the left. Um this is our
+
+ align:start position:0%
+the stuff on the left. Um this is our
+ 
+
+ align:start position:0%
+the stuff on the left. Um this is our
+one way to try to clarify that
+
+ align:start position:0%
+one way to try to clarify that
+ 
+
+ align:start position:0%
+one way to try to clarify that
+geothermal is like the last name of a
+
+ align:start position:0%
+geothermal is like the last name of a
+ 
+
+ align:start position:0%
+geothermal is like the last name of a
+family of technologies and energies
+
+ align:start position:0%
+family of technologies and energies
+ 
+
+ align:start position:0%
+family of technologies and energies
+both. Um and that uh the one we are
+
+ align:start position:0%
+both. Um and that uh the one we are
+ 
+
+ align:start position:0%
+both. Um and that uh the one we are
+talking about today is on the right. It
+
+ align:start position:0%
+talking about today is on the right. It
+ 
+
+ align:start position:0%
+talking about today is on the right. It
+isworked
+
+ align:start position:0%
+isworked
+ 
+
+ align:start position:0%
+isworked
+geothermal heat pumps can provide
+
+ align:start position:0%
+geothermal heat pumps can provide
+ 
+
+ align:start position:0%
+geothermal heat pumps can provide
+heating and cooling is what is typically
+
+ align:start position:0%
+heating and cooling is what is typically
+ 
+
+ align:start position:0%
+heating and cooling is what is typically
+called shallow. You'll hear purple hear
+
+ align:start position:0%
+called shallow. You'll hear purple hear
+ 
+
+ align:start position:0%
+called shallow. You'll hear purple hear
+people use the word shallow. Um but for
+
+ align:start position:0%
+people use the word shallow. Um but for
+ 
+
+ align:start position:0%
+people use the word shallow. Um but for
+the usual person uh 1,000 or 1200 feet
+
+ align:start position:0%
+the usual person uh 1,000 or 1200 feet
+ 
+
+ align:start position:0%
+the usual person uh 1,000 or 1200 feet
+isn't doesn't sound shallow but I I
+
+ align:start position:0%
+isn't doesn't sound shallow but I I
+ 
+
+ align:start position:0%
+isn't doesn't sound shallow but I I
+promise that's shallow. Um and then uh
+
+ align:start position:0%
+promise that's shallow. Um and then uh
+ 
+
+ align:start position:0%
+promise that's shallow. Um and then uh
+it is ambient temperature. In other
+
+ align:start position:0%
+it is ambient temperature. In other
+ 
+
+ align:start position:0%
+it is ambient temperature. In other
+words kind of the average temperature of
+
+ align:start position:0%
+words kind of the average temperature of
+ 
+
+ align:start position:0%
+words kind of the average temperature of
+the air and the ground. not super hot in
+
+ align:start position:0%
+the air and the ground. not super hot in
+ 
+
+ align:start position:0%
+the air and the ground. not super hot in
+any way. Um, and uh, one of the things
+
+ align:start position:0%
+any way. Um, and uh, one of the things
+ 
+
+ align:start position:0%
+any way. Um, and uh, one of the things
+that's really critical about this type
+
+ align:start position:0%
+that's really critical about this type
+ 
+
+ align:start position:0%
+that's really critical about this type
+of geothermal energy is that it is
+
+ align:start position:0%
+of geothermal energy is that it is
+ 
+
+ align:start position:0%
+of geothermal energy is that it is
+everywhere.
+
+ align:start position:0%
+everywhere.
+ 
+
+ align:start position:0%
+everywhere.
+Um, you'll hear people talking about the
+
+ align:start position:0%
+Um, you'll hear people talking about the
+ 
+
+ align:start position:0%
+Um, you'll hear people talking about the
+word district and certainly this is a
+
+ align:start position:0%
+word district and certainly this is a
+ 
+
+ align:start position:0%
+word district and certainly this is a
+form of district energy and the
+
+ align:start position:0%
+form of district energy and the
+ 
+
+ align:start position:0%
+form of district energy and the
+traditional naming system goes by
+
+ align:start position:0%
+traditional naming system goes by
+ 
+
+ align:start position:0%
+traditional naming system goes by
+generation. first generation, second
+
+ align:start position:0%
+generation. first generation, second
+ 
+
+ align:start position:0%
+generation. first generation, second
+generation and the type we are
+
+ align:start position:0%
+generation and the type we are
+ 
+
+ align:start position:0%
+generation and the type we are
+discussing today primarily is fifth
+
+ align:start position:0%
+discussing today primarily is fifth
+ 
+
+ align:start position:0%
+discussing today primarily is fifth
+generation. Um and
+
+ align:start position:0%
+generation. Um and
+ 
+
+ align:start position:0%
+generation. Um and
+the next more advanced level of this is
+
+ align:start position:0%
+the next more advanced level of this is
+ 
+
+ align:start position:0%
+the next more advanced level of this is
+okay. So why are we calling it a network
+
+ align:start position:0%
+okay. So why are we calling it a network
+ 
+
+ align:start position:0%
+okay. So why are we calling it a network
+then? And uh our proposal which is not
+
+ align:start position:0%
+then? And uh our proposal which is not
+ 
+
+ align:start position:0%
+then? And uh our proposal which is not
+universal um but there is kind of an
+
+ align:start position:0%
+universal um but there is kind of an
+ 
+
+ align:start position:0%
+universal um but there is kind of an
+emerging nomenclature um is that within
+
+ align:start position:0%
+emerging nomenclature um is that within
+ 
+
+ align:start position:0%
+emerging nomenclature um is that within
+fifth generation um if it has a single
+
+ align:start position:0%
+fifth generation um if it has a single
+ 
+
+ align:start position:0%
+fifth generation um if it has a single
+pipe decentralized and renewable and
+
+ align:start position:0%
+pipe decentralized and renewable and
+ 
+
+ align:start position:0%
+pipe decentralized and renewable and
+combustion free then it is a thermal
+
+ align:start position:0%
+combustion free then it is a thermal
+ 
+
+ align:start position:0%
+combustion free then it is a thermal
+energy network and if that thermal
+
+ align:start position:0%
+energy network and if that thermal
+ 
+
+ align:start position:0%
+energy network and if that thermal
+energy network is tapping geothermal
+
+ align:start position:0%
+energy network is tapping geothermal
+ 
+
+ align:start position:0%
+energy network is tapping geothermal
+energy which changes some of the
+
+ align:start position:0%
+energy which changes some of the
+ 
+
+ align:start position:0%
+energy which changes some of the
+outcomes then you could also call it a
+
+ align:start position:0%
+outcomes then you could also call it a
+ 
+
+ align:start position:0%
+outcomes then you could also call it a
+geothermal energy work. That's what
+
+ align:start position:0%
+geothermal energy work. That's what
+ 
+
+ align:start position:0%
+geothermal energy work. That's what
+we're going to use, but you'll hear
+
+ align:start position:0%
+we're going to use, but you'll hear
+ 
+
+ align:start position:0%
+we're going to use, but you'll hear
+speakers use a lot of different
+
+ align:start position:0%
+speakers use a lot of different
+ 
+
+ align:start position:0%
+speakers use a lot of different
+terminology. I just wanted to give you a
+
+ align:start position:0%
+terminology. I just wanted to give you a
+ 
+
+ align:start position:0%
+terminology. I just wanted to give you a
+a quick lay of the land. Um, and our
+
+ align:start position:0%
+a quick lay of the land. Um, and our
+ 
+
+ align:start position:0%
+a quick lay of the land. Um, and our
+last task before we begin is if you
+
+ align:start position:0%
+last task before we begin is if you
+ 
+
+ align:start position:0%
+last task before we begin is if you
+could please take out your phone. We
+
+ align:start position:0%
+could please take out your phone. We
+ 
+
+ align:start position:0%
+could please take out your phone. We
+have um this QR code you can scan and it
+
+ align:start position:0%
+have um this QR code you can scan and it
+ 
+
+ align:start position:0%
+have um this QR code you can scan and it
+should work pretty easily to get you on
+
+ align:start position:0%
+should work pretty easily to get you on
+ 
+
+ align:start position:0%
+should work pretty easily to get you on
+to Slido. And now you have um your first
+
+ align:start position:0%
+to Slido. And now you have um your first
+ 
+
+ align:start position:0%
+to Slido. And now you have um your first
+quiz.
+
+ align:start position:0%
+quiz.
+ 
+
+ align:start position:0%
+quiz.
+We did say class, right?
+
+ align:start position:0%
+We did say class, right?
+ 
+
+ align:start position:0%
+We did say class, right?
+No, don't don't worry. There's actually
+
+ align:start position:0%
+No, don't don't worry. There's actually
+ 
+
+ align:start position:0%
+No, don't don't worry. There's actually
+no test. Uh but um
+
+ align:start position:0%
+no test. Uh but um
+ 
+
+ align:start position:0%
+no test. Uh but um
+let's see how you do.
+
+ align:start position:0%
+let's see how you do.
+ 
+
+ align:start position:0%
+let's see how you do.
+Yeah, I made it too easy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, if you have any trouble getting on,
+
+ align:start position:0%
+So, if you have any trouble getting on,
+ 
+
+ align:start position:0%
+So, if you have any trouble getting on,
+um, Erica back there is happy to help.
+
+ align:start position:0%
+um, Erica back there is happy to help.
+ 
+
+ align:start position:0%
+um, Erica back there is happy to help.
+>> You can also, you can also open your web
+
+ align:start position:0%
+>> You can also, you can also open your web
+ 
+
+ align:start position:0%
+>> You can also, you can also open your web
+browser and just go to slid.com and type
+
+ align:start position:0%
+browser and just go to slid.com and type
+ 
+
+ align:start position:0%
+browser and just go to slid.com and type
+in.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I like watching them go out and back.
+
+ align:start position:0%
+I like watching them go out and back.
+ 
+
+ align:start position:0%
+I like watching them go out and back.
+That's how I think.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Are we good?
+
+ align:start position:0%
+All right. Are we good?
+ 
+
+ align:start position:0%
+All right. Are we good?
+everyone on slidoh now for the rest of
+
+ align:start position:0%
+everyone on slidoh now for the rest of
+ 
+
+ align:start position:0%
+everyone on slidoh now for the rest of
+the day. Okay. Uh so yes um the the
+
+ align:start position:0%
+the day. Okay. Uh so yes um the the
+ 
+
+ align:start position:0%
+the day. Okay. Uh so yes um the the
+group um the group wisdom is prevailing.
+
+ align:start position:0%
+group um the group wisdom is prevailing.
+ 
+
+ align:start position:0%
+group um the group wisdom is prevailing.
+Uh the type of geothermal energy we're
+
+ align:start position:0%
+Uh the type of geothermal energy we're
+ 
+
+ align:start position:0%
+Uh the type of geothermal energy we're
+discussing today is ambient shallow and
+
+ align:start position:0%
+discussing today is ambient shallow and
+ 
+
+ align:start position:0%
+discussing today is ambient shallow and
+everywhere. Um which is a lovely
+
+ align:start position:0%
+everywhere. Um which is a lovely
+ 
+
+ align:start position:0%
+everywhere. Um which is a lovely
+feature.
+
+ align:start position:0%
+feature.
+ 
+
+ align:start position:0%
+feature.
+Um all right. So, we're going to take a
+
+ align:start position:0%
+Um all right. So, we're going to take a
+ 
+
+ align:start position:0%
+Um all right. So, we're going to take a
+a second and um begin our first uh
+
+ align:start position:0%
+a second and um begin our first uh
+ 
+
+ align:start position:0%
+a second and um begin our first uh
+conversation.
\ No newline at end of file
diff --git a/zHa-n2M7Bj8.txt b/zHa-n2M7Bj8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4d0babe280daf698593b2e79e45fd369ae4c9782
--- /dev/null
+++ b/zHa-n2M7Bj8.txt
@@ -0,0 +1,7011 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+so we saw in Laura's talk this
+
+ align:start position:0%
+so we saw in Laura's talk this
+ 
+
+ align:start position:0%
+so we saw in Laura's talk this
+introduction to both this idea of the
+
+ align:start position:0%
+introduction to both this idea of the
+ 
+
+ align:start position:0%
+introduction to both this idea of the
+child as scientists right all the
+
+ align:start position:0%
+child as scientists right all the
+ 
+
+ align:start position:0%
+child as scientists right all the
+different ways that children's learning
+
+ align:start position:0%
+different ways that children's learning
+ 
+
+ align:start position:0%
+different ways that children's learning
+seems to follow the many different
+
+ align:start position:0%
+seems to follow the many different
+ 
+
+ align:start position:0%
+seems to follow the many different
+practices that scientists use to learn
+
+ align:start position:0%
+practices that scientists use to learn
+ 
+
+ align:start position:0%
+practices that scientists use to learn
+about the world not just the data
+
+ align:start position:0%
+about the world not just the data
+ 
+
+ align:start position:0%
+about the world not just the data
+analysis of in a sense if you know if
+
+ align:start position:0%
+analysis of in a sense if you know if
+ 
+
+ align:start position:0%
+analysis of in a sense if you know if
+well you know as much as you know
+
+ align:start position:0%
+well you know as much as you know
+ 
+
+ align:start position:0%
+well you know as much as you know
+various kinds of statistics on a grand
+
+ align:start position:0%
+various kinds of statistics on a grand
+ 
+
+ align:start position:0%
+various kinds of statistics on a grand
+scale whether it's heavy and learning or
+
+ align:start position:0%
+scale whether it's heavy and learning or
+ 
+
+ align:start position:0%
+scale whether it's heavy and learning or
+backprop are important for learning we
+
+ align:start position:0%
+backprop are important for learning we
+ 
+
+ align:start position:0%
+backprop are important for learning we
+know that that's not all that children
+
+ align:start position:0%
+know that that's not all that children
+ 
+
+ align:start position:0%
+know that that's not all that children
+do just like analyzing patterns and data
+
+ align:start position:0%
+do just like analyzing patterns and data
+ 
+
+ align:start position:0%
+do just like analyzing patterns and data
+is not all that scientists do and then
+
+ align:start position:0%
+is not all that scientists do and then
+ 
+
+ align:start position:0%
+is not all that scientists do and then
+Laura added this other cool dimension
+
+ align:start position:0%
+Laura added this other cool dimension
+ 
+
+ align:start position:0%
+Laura added this other cool dimension
+thinking about the costs and rewards of
+
+ align:start position:0%
+thinking about the costs and rewards of
+ 
+
+ align:start position:0%
+thinking about the costs and rewards of
+information right when is it worth it or
+
+ align:start position:0%
+information right when is it worth it or
+ 
+
+ align:start position:0%
+information right when is it worth it or
+not and you could say maybe she was
+
+ align:start position:0%
+not and you could say maybe she was
+ 
+
+ align:start position:0%
+not and you could say maybe she was
+suggesting that we should develop the
+
+ align:start position:0%
+suggesting that we should develop the
+ 
+
+ align:start position:0%
+suggesting that we should develop the
+metaphor expand it a little bit from
+
+ align:start position:0%
+metaphor expand it a little bit from
+ 
+
+ align:start position:0%
+metaphor expand it a little bit from
+child a scientist maybe like the child
+
+ align:start position:0%
+child a scientist maybe like the child
+ 
+
+ align:start position:0%
+child a scientist maybe like the child
+as labs
+
+ align:start position:0%
+as labs
+ 
+
+ align:start position:0%
+as labs
+sorry lab p.i or maybe even NSF center
+
+ align:start position:0%
+sorry lab p.i or maybe even NSF center
+ 
+
+ align:start position:0%
+sorry lab p.i or maybe even NSF center
+director because as everyone knows but
+
+ align:start position:0%
+director because as everyone knows but
+ 
+
+ align:start position:0%
+director because as everyone knows but
+Tommy certainly can tell you whether
+
+ align:start position:0%
+Tommy certainly can tell you whether
+ 
+
+ align:start position:0%
+Tommy certainly can tell you whether
+you're a lab p.i who's just gotten
+
+ align:start position:0%
+you're a lab p.i who's just gotten
+ 
+
+ align:start position:0%
+you're a lab p.i who's just gotten
+tenure or at the director of an NSF
+
+ align:start position:0%
+tenure or at the director of an NSF
+ 
+
+ align:start position:0%
+tenure or at the director of an NSF
+Center you have to make you know
+
+ align:start position:0%
+Center you have to make you know
+ 
+
+ align:start position:0%
+Center you have to make you know
+hard-nosed pragmatic decisions about
+
+ align:start position:0%
+hard-nosed pragmatic decisions about
+ 
+
+ align:start position:0%
+hard-nosed pragmatic decisions about
+what is achievable given the costs and
+
+ align:start position:0%
+what is achievable given the costs and
+ 
+
+ align:start position:0%
+what is achievable given the costs and
+which research questions are really
+
+ align:start position:0%
+which research questions are really
+ 
+
+ align:start position:0%
+which research questions are really
+worth going after and devoting your time
+
+ align:start position:0%
+worth going after and devoting your time
+ 
+
+ align:start position:0%
+worth going after and devoting your time
+and other resources to and that's that's
+
+ align:start position:0%
+and other resources to and that's that's
+ 
+
+ align:start position:0%
+and other resources to and that's that's
+a very important part of science and
+
+ align:start position:0%
+a very important part of science and
+ 
+
+ align:start position:0%
+a very important part of science and
+it's an important part of intuitive
+
+ align:start position:0%
+it's an important part of intuitive
+ 
+
+ align:start position:0%
+it's an important part of intuitive
+knowledge I want to add another
+
+ align:start position:0%
+knowledge I want to add another
+ 
+
+ align:start position:0%
+knowledge I want to add another
+practical dimension two things a way of
+
+ align:start position:0%
+practical dimension two things a way of
+ 
+
+ align:start position:0%
+practical dimension two things a way of
+bringing out fleshing out this idea of
+
+ align:start position:0%
+bringing out fleshing out this idea of
+ 
+
+ align:start position:0%
+bringing out fleshing out this idea of
+the child as scientist you can think
+
+ align:start position:0%
+the child as scientist you can think
+ 
+
+ align:start position:0%
+the child as scientist you can think
+about all these are these are metaphors
+
+ align:start position:0%
+about all these are these are metaphors
+ 
+
+ align:start position:0%
+about all these are these are metaphors
+but they're things that we can formalize
+
+ align:start position:0%
+but they're things that we can formalize
+ 
+
+ align:start position:0%
+but they're things that we can formalize
+and if our goal is to make computational
+
+ align:start position:0%
+and if our goal is to make computational
+ 
+
+ align:start position:0%
+and if our goal is to make computational
+models of and ultimately to get some
+
+ align:start position:0%
+models of and ultimately to get some
+ 
+
+ align:start position:0%
+models of and ultimately to get some
+kind of theoretical handle on then these
+
+ align:start position:0%
+kind of theoretical handle on then these
+ 
+
+ align:start position:0%
+kind of theoretical handle on then these
+are helping us right by by adding in the
+
+ align:start position:0%
+are helping us right by by adding in the
+ 
+
+ align:start position:0%
+are helping us right by by adding in the
+cost and benefits you bring in utility
+
+ align:start position:0%
+cost and benefits you bring in utility
+ 
+
+ align:start position:0%
+cost and benefits you bring in utility
+calculus and there's not just naive
+
+ align:start position:0%
+calculus and there's not just naive
+ 
+
+ align:start position:0%
+calculus and there's not just naive
+utility calculus there's a formal
+
+ align:start position:0%
+utility calculus there's a formal
+ 
+
+ align:start position:0%
+utility calculus there's a formal
+mathematical utility calculus of these
+
+ align:start position:0%
+mathematical utility calculus of these
+ 
+
+ align:start position:0%
+mathematical utility calculus of these
+kinds of decisions Julianne ha Redinger
+
+ align:start position:0%
+kinds of decisions Julianne ha Redinger
+ 
+
+ align:start position:0%
+kinds of decisions Julianne ha Redinger
+whoo Laura mentioned a lot of the was
+
+ align:start position:0%
+whoo Laura mentioned a lot of the was
+ 
+
+ align:start position:0%
+whoo Laura mentioned a lot of the was
+driving a lot of the work towards the
+
+ align:start position:0%
+driving a lot of the work towards the
+ 
+
+ align:start position:0%
+driving a lot of the work towards the
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+
+ align:start position:0%
+end of the talk has done some really
+ 
+
+ align:start position:0%
+end of the talk has done some really
+interesting actual
+
+ align:start position:0%
+interesting actual
+ 
+
+ align:start position:0%
+interesting actual
+automatical computational models of
+
+ align:start position:0%
+automatical computational models of
+ 
+
+ align:start position:0%
+automatical computational models of
+these issues as has CEO and the other
+
+ align:start position:0%
+these issues as has CEO and the other
+ 
+
+ align:start position:0%
+these issues as has CEO and the other
+students you talked about um so the the
+
+ align:start position:0%
+students you talked about um so the the
+ 
+
+ align:start position:0%
+students you talked about um so the the
+direction I want to push here is what
+
+ align:start position:0%
+direction I want to push here is what
+ 
+
+ align:start position:0%
+direction I want to push here is what
+you might call the child as hacker right
+
+ align:start position:0%
+you might call the child as hacker right
+ 
+
+ align:start position:0%
+you might call the child as hacker right
+this is trying to make the connection
+
+ align:start position:0%
+this is trying to make the connection
+ 
+
+ align:start position:0%
+this is trying to make the connection
+back to this idea of formalizing
+
+ align:start position:0%
+back to this idea of formalizing
+ 
+
+ align:start position:0%
+back to this idea of formalizing
+common-sense knowledge and intuitive
+
+ align:start position:0%
+common-sense knowledge and intuitive
+ 
+
+ align:start position:0%
+common-sense knowledge and intuitive
+theories as probabilistic programs or
+
+ align:start position:0%
+theories as probabilistic programs or
+ 
+
+ align:start position:0%
+theories as probabilistic programs or
+just more generally the idea of a
+
+ align:start position:0%
+just more generally the idea of a
+ 
+
+ align:start position:0%
+just more generally the idea of a
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+
+ align:start position:0%
+program a structured out you know an
+ 
+
+ align:start position:0%
+program a structured out you know an
+algorithm and a date or some combination
+
+ align:start position:0%
+algorithm and a date or some combination
+ 
+
+ align:start position:0%
+algorithm and a date or some combination
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+
+ align:start position:0%
+of algorithms data structures networks
+ 
+
+ align:start position:0%
+of algorithms data structures networks
+of functions that can describe
+
+ align:start position:0%
+of functions that can describe
+ 
+
+ align:start position:0%
+of functions that can describe
+interesting causal processes in the
+
+ align:start position:0%
+interesting causal processes in the
+ 
+
+ align:start position:0%
+interesting causal processes in the
+world like for example your intuitive
+
+ align:start position:0%
+world like for example your intuitive
+ 
+
+ align:start position:0%
+world like for example your intuitive
+physics or your intuitive psychology
+
+ align:start position:0%
+physics or your intuitive psychology
+ 
+
+ align:start position:0%
+physics or your intuitive psychology
+that's an idea that we talked a lot
+
+ align:start position:0%
+that's an idea that we talked a lot
+ 
+
+ align:start position:0%
+that's an idea that we talked a lot
+about last week or whenever it was
+
+ align:start position:0%
+about last week or whenever it was
+ 
+
+ align:start position:0%
+about last week or whenever it was
+earlier in the week or last week and
+
+ align:start position:0%
+earlier in the week or last week and
+ 
+
+ align:start position:0%
+earlier in the week or last week and
+this this idea that if if your knowledge
+
+ align:start position:0%
+this this idea that if if your knowledge
+ 
+
+ align:start position:0%
+this this idea that if if your knowledge
+is something like a program or a set of
+
+ align:start position:0%
+is something like a program or a set of
+ 
+
+ align:start position:0%
+is something like a program or a set of
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+
+ align:start position:0%
+programs that you can say for example
+ 
+
+ align:start position:0%
+programs that you can say for example
+run forward to simulate physics like we
+
+ align:start position:0%
+run forward to simulate physics like we
+ 
+
+ align:start position:0%
+run forward to simulate physics like we
+had last time then learning has to be
+
+ align:start position:0%
+had last time then learning has to be
+ 
+
+ align:start position:0%
+had last time then learning has to be
+something like building a program or
+
+ align:start position:0%
+something like building a program or
+ 
+
+ align:start position:0%
+something like building a program or
+hacking and I think you could make this
+
+ align:start position:0%
+hacking and I think you could make this
+ 
+
+ align:start position:0%
+hacking and I think you could make this
+is again a research program that I wish
+
+ align:start position:0%
+is again a research program that I wish
+ 
+
+ align:start position:0%
+is again a research program that I wish
+I had like Laura talked at the end about
+
+ align:start position:0%
+I had like Laura talked at the end about
+ 
+
+ align:start position:0%
+I had like Laura talked at the end about
+the research for him she wished she had
+
+ align:start position:0%
+the research for him she wished she had
+ 
+
+ align:start position:0%
+the research for him she wished she had
+it's it's it's not really a wit just to
+
+ align:start position:0%
+it's it's it's not really a wit just to
+ 
+
+ align:start position:0%
+it's it's it's not really a wit just to
+wish for her she actually is working
+
+ align:start position:0%
+wish for her she actually is working
+ 
+
+ align:start position:0%
+wish for her she actually is working
+towards that research program and this
+
+ align:start position:0%
+towards that research program and this
+ 
+
+ align:start position:0%
+towards that research program and this
+isn't just an empty wish either it's
+
+ align:start position:0%
+isn't just an empty wish either it's
+ 
+
+ align:start position:0%
+isn't just an empty wish either it's
+something that we're working on which is
+
+ align:start position:0%
+something that we're working on which is
+ 
+
+ align:start position:0%
+something that we're working on which is
+to try to take um just as Laura had that
+
+ align:start position:0%
+to try to take um just as Laura had that
+ 
+
+ align:start position:0%
+to try to take um just as Laura had that
+wonderful list of all the things
+
+ align:start position:0%
+wonderful list of all the things
+ 
+
+ align:start position:0%
+wonderful list of all the things
+scientists do in their practices to
+
+ align:start position:0%
+scientists do in their practices to
+ 
+
+ align:start position:0%
+scientists do in their practices to
+learn about the world I think you could
+
+ align:start position:0%
+learn about the world I think you could
+ 
+
+ align:start position:0%
+learn about the world I think you could
+make a similar list of all the things
+
+ align:start position:0%
+make a similar list of all the things
+ 
+
+ align:start position:0%
+make a similar list of all the things
+that you do when you're programming
+
+ align:start position:0%
+that you do when you're programming
+ 
+
+ align:start position:0%
+that you do when you're programming
+right or hacking it by hacking I don't
+
+ align:start position:0%
+right or hacking it by hacking I don't
+ 
+
+ align:start position:0%
+right or hacking it by hacking I don't
+mean right like breaking into a secure
+
+ align:start position:0%
+mean right like breaking into a secure
+ 
+
+ align:start position:0%
+mean right like breaking into a secure
+system but modifying your code to make
+
+ align:start position:0%
+system but modifying your code to make
+ 
+
+ align:start position:0%
+system but modifying your code to make
+it more awesome either more and I use
+
+ align:start position:0%
+it more awesome either more and I use
+ 
+
+ align:start position:0%
+it more awesome either more and I use
+awesome very deliberately right because
+
+ align:start position:0%
+awesome very deliberately right because
+ 
+
+ align:start position:0%
+awesome very deliberately right because
+awesome is a multi-dimensional term it's
+
+ align:start position:0%
+awesome is a multi-dimensional term it's
+ 
+
+ align:start position:0%
+awesome is a multi-dimensional term it's
+just awesome but it could be it could be
+
+ align:start position:0%
+just awesome but it could be it could be
+ 
+
+ align:start position:0%
+just awesome but it could be it could be
+faster more accurate more efficient more
+
+ align:start position:0%
+faster more accurate more efficient more
+ 
+
+ align:start position:0%
+faster more accurate more efficient more
+elegant more generalizable more easily
+
+ align:start position:0%
+elegant more generalizable more easily
+ 
+
+ align:start position:0%
+elegant more generalizable more easily
+communicated to other people more easily
+
+ align:start position:0%
+communicated to other people more easily
+ 
+
+ align:start position:0%
+communicated to other people more easily
+modularly combined with other code to do
+
+ align:start position:0%
+modularly combined with other code to do
+ 
+
+ align:start position:0%
+modularly combined with other code to do
+something even more awesome right I
+
+ align:start position:0%
+something even more awesome right I
+ 
+
+ align:start position:0%
+something even more awesome right I
+think there's a deep sense in which that
+
+ align:start position:0%
+think there's a deep sense in which that
+ 
+
+ align:start position:0%
+think there's a deep sense in which that
+aesthetic behind hacking and making
+
+ align:start position:0%
+aesthetic behind hacking and making
+ 
+
+ align:start position:0%
+aesthetic behind hacking and making
+awesome code in it both an individual in
+
+ align:start position:0%
+awesome code in it both an individual in
+ 
+
+ align:start position:0%
+awesome code in it both an individual in
+a social setting that's a really
+
+ align:start position:0%
+a social setting that's a really
+ 
+
+ align:start position:0%
+a social setting that's a really
+powerful way to think about many of the
+
+ align:start position:0%
+powerful way to think about many of the
+ 
+
+ align:start position:0%
+powerful way to think about many of the
+cognitive activities behind learning and
+
+ align:start position:0%
+cognitive activities behind learning and
+ 
+
+ align:start position:0%
+cognitive activities behind learning and
+it goes together with the idea of the
+
+ align:start position:0%
+it goes together with the idea of the
+ 
+
+ align:start position:0%
+it goes together with the idea of the
+childís scientist right if the form of
+
+ align:start position:0%
+childís scientist right if the form of
+ 
+
+ align:start position:0%
+childís scientist right if the form of
+your of your code intuitive science our
+
+ align:start position:0%
+your of your code intuitive science our
+ 
+
+ align:start position:0%
+your of your code intuitive science our
+computer programs
+
+ align:start position:0%
+computer programs
+ 
+
+ align:start position:0%
+computer programs
+or something like programs so we've been
+
+ align:start position:0%
+or something like programs so we've been
+ 
+
+ align:start position:0%
+or something like programs so we've been
+working on a few projects where you've
+
+ align:start position:0%
+working on a few projects where you've
+ 
+
+ align:start position:0%
+working on a few projects where you've
+been trying to capture this idea and to
+
+ align:start position:0%
+been trying to capture this idea and to
+ 
+
+ align:start position:0%
+been trying to capture this idea and to
+say well what would it mean to describe
+
+ align:start position:0%
+say well what would it mean to describe
+ 
+
+ align:start position:0%
+say well what would it mean to describe
+computationally this idea of learning as
+
+ align:start position:0%
+computationally this idea of learning as
+ 
+
+ align:start position:0%
+computationally this idea of learning as
+either synthesizing programs or
+
+ align:start position:0%
+either synthesizing programs or
+ 
+
+ align:start position:0%
+either synthesizing programs or
+modifying programs or making the
+
+ align:start position:0%
+modifying programs or making the
+ 
+
+ align:start position:0%
+modifying programs or making the
+program's of making more awesome
+
+ align:start position:0%
+program's of making more awesome
+ 
+
+ align:start position:0%
+program's of making more awesome
+programs in your mind and I'll just show
+
+ align:start position:0%
+programs in your mind and I'll just show
+ 
+
+ align:start position:0%
+programs in your mind and I'll just show
+you a few examples of this I'll show you
+
+ align:start position:0%
+you a few examples of this I'll show you
+ 
+
+ align:start position:0%
+you a few examples of this I'll show you
+our good our successful case studies
+
+ align:start position:0%
+our good our successful case studies
+ 
+
+ align:start position:0%
+our good our successful case studies
+places where we've made this idea work
+
+ align:start position:0%
+places where we've made this idea work
+ 
+
+ align:start position:0%
+places where we've made this idea work
+but the bottom line to foreshadow it is
+
+ align:start position:0%
+but the bottom line to foreshadow it is
+ 
+
+ align:start position:0%
+but the bottom line to foreshadow it is
+that this is really really hard and to
+
+ align:start position:0%
+that this is really really hard and to
+ 
+
+ align:start position:0%
+that this is really really hard and to
+get it to work for the kinds of
+
+ align:start position:0%
+get it to work for the kinds of
+ 
+
+ align:start position:0%
+get it to work for the kinds of
+knowledge that say Laura was talking
+
+ align:start position:0%
+knowledge that say Laura was talking
+ 
+
+ align:start position:0%
+knowledge that say Laura was talking
+about or that Liz was talking about the
+
+ align:start position:0%
+about or that Liz was talking about the
+ 
+
+ align:start position:0%
+about or that Liz was talking about the
+real stuff of children's solid is still
+
+ align:start position:0%
+real stuff of children's solid is still
+ 
+
+ align:start position:0%
+real stuff of children's solid is still
+very very open and that's really we want
+
+ align:start position:0%
+very very open and that's really we want
+ 
+
+ align:start position:0%
+very very open and that's really we want
+to basically build up to engaging why
+
+ align:start position:0%
+to basically build up to engaging why
+ 
+
+ align:start position:0%
+to basically build up to engaging why
+that - why that problem is so hard from
+
+ align:start position:0%
+that - why that problem is so hard from
+ 
+
+ align:start position:0%
+that - why that problem is so hard from
+this to what Tomer and then Laura will
+
+ align:start position:0%
+this to what Tomer and then Laura will
+ 
+
+ align:start position:0%
+this to what Tomer and then Laura will
+talk about later on in the afternoon so
+
+ align:start position:0%
+talk about later on in the afternoon so
+ 
+
+ align:start position:0%
+talk about later on in the afternoon so
+here but here's a few at least early
+
+ align:start position:0%
+here but here's a few at least early
+ 
+
+ align:start position:0%
+here but here's a few at least early
+success stories that we've worked on one
+
+ align:start position:0%
+success stories that we've worked on one
+ 
+
+ align:start position:0%
+success stories that we've worked on one
+goes back to this idea that we presented
+
+ align:start position:0%
+goes back to this idea that we presented
+ 
+
+ align:start position:0%
+goes back to this idea that we presented
+it in my lectures last week and it
+
+ align:start position:0%
+it in my lectures last week and it
+ 
+
+ align:start position:0%
+it in my lectures last week and it
+connects to again something that Laura
+
+ align:start position:0%
+connects to again something that Laura
+ 
+
+ align:start position:0%
+connects to again something that Laura
+was saying here you know a very basic
+
+ align:start position:0%
+was saying here you know a very basic
+ 
+
+ align:start position:0%
+was saying here you know a very basic
+kind of learning is just the problem of
+
+ align:start position:0%
+kind of learning is just the problem of
+ 
+
+ align:start position:0%
+kind of learning is just the problem of
+learning some generalizable concepts at
+
+ align:start position:0%
+learning some generalizable concepts at
+ 
+
+ align:start position:0%
+learning some generalizable concepts at
+all from from very sparse evidence like
+
+ align:start position:0%
+all from from very sparse evidence like
+ 
+
+ align:start position:0%
+all from from very sparse evidence like
+one-shot learning you again something
+
+ align:start position:0%
+one-shot learning you again something
+ 
+
+ align:start position:0%
+one-shot learning you again something
+you heard from Tommy a number of the
+
+ align:start position:0%
+you heard from Tommy a number of the
+ 
+
+ align:start position:0%
+you heard from Tommy a number of the
+other speakers we've all been trying to
+
+ align:start position:0%
+other speakers we've all been trying to
+ 
+
+ align:start position:0%
+other speakers we've all been trying to
+wrap our heads around this how can you
+
+ align:start position:0%
+wrap our heads around this how can you
+ 
+
+ align:start position:0%
+wrap our heads around this how can you
+learn safe any concept at all from very
+
+ align:start position:0%
+learn safe any concept at all from very
+ 
+
+ align:start position:0%
+learn safe any concept at all from very
+very little data maybe just one or a few
+
+ align:start position:0%
+very little data maybe just one or a few
+ 
+
+ align:start position:0%
+very little data maybe just one or a few
+examples so you saw this kind of thing
+
+ align:start position:0%
+examples so you saw this kind of thing
+ 
+
+ align:start position:0%
+examples so you saw this kind of thing
+last time and I briefly mentioned how we
+
+ align:start position:0%
+last time and I briefly mentioned how we
+ 
+
+ align:start position:0%
+last time and I briefly mentioned how we
+had tried to capture this this problem
+
+ align:start position:0%
+had tried to capture this this problem
+ 
+
+ align:start position:0%
+had tried to capture this this problem
+as some something like this by building
+
+ align:start position:0%
+as some something like this by building
+ 
+
+ align:start position:0%
+as some something like this by building
+this tree structured hypothesis space
+
+ align:start position:0%
+this tree structured hypothesis space
+ 
+
+ align:start position:0%
+this tree structured hypothesis space
+and you could think of this as a kind of
+
+ align:start position:0%
+and you could think of this as a kind of
+ 
+
+ align:start position:0%
+and you could think of this as a kind of
+program induction if you think that
+
+ align:start position:0%
+program induction if you think that
+ 
+
+ align:start position:0%
+program induction if you think that
+there's something like an evolutionary
+
+ align:start position:0%
+there's something like an evolutionary
+ 
+
+ align:start position:0%
+there's something like an evolutionary
+program which generated these objects
+
+ align:start position:0%
+program which generated these objects
+ 
+
+ align:start position:0%
+program which generated these objects
+and you're trying to find the kind of
+
+ align:start position:0%
+and you're trying to find the kind of
+ 
+
+ align:start position:0%
+and you're trying to find the kind of
+sub procedure of it that generated just
+
+ align:start position:0%
+sub procedure of it that generated just
+ 
+
+ align:start position:0%
+sub procedure of it that generated just
+these kinds of objects but that's not
+
+ align:start position:0%
+these kinds of objects but that's not
+ 
+
+ align:start position:0%
+these kinds of objects but that's not
+that's not at all how we were able to
+
+ align:start position:0%
+that's not at all how we were able to
+ 
+
+ align:start position:0%
+that's not at all how we were able to
+model this I mean we had a much simpler
+
+ align:start position:0%
+model this I mean we had a much simpler
+ 
+
+ align:start position:0%
+model this I mean we had a much simpler
+model but let me show you briefly some
+
+ align:start position:0%
+model but let me show you briefly some
+ 
+
+ align:start position:0%
+model but let me show you briefly some
+work that we did in our group a couple
+
+ align:start position:0%
+work that we did in our group a couple
+ 
+
+ align:start position:0%
+work that we did in our group a couple
+of years ago it's really just getting
+
+ align:start position:0%
+of years ago it's really just getting
+ 
+
+ align:start position:0%
+of years ago it's really just getting
+out into publication now this is work
+
+ align:start position:0%
+out into publication now this is work
+ 
+
+ align:start position:0%
+out into publication now this is work
+that was mostly done by two people
+
+ align:start position:0%
+that was mostly done by two people
+ 
+
+ align:start position:0%
+that was mostly done by two people
+Russell akuti noff who's now a professor
+
+ align:start position:0%
+Russell akuti noff who's now a professor
+ 
+
+ align:start position:0%
+Russell akuti noff who's now a professor
+at Toronto although about to move to
+
+ align:start position:0%
+at Toronto although about to move to
+ 
+
+ align:start position:0%
+at Toronto although about to move to
+Carnegie Mellon I think and Brendan Lake
+
+ align:start position:0%
+Carnegie Mellon I think and Brendan Lake
+ 
+
+ align:start position:0%
+Carnegie Mellon I think and Brendan Lake
+he's a machine learning person also very
+
+ align:start position:0%
+he's a machine learning person also very
+ 
+
+ align:start position:0%
+he's a machine learning person also very
+well known for deep learning and then
+
+ align:start position:0%
+well known for deep learning and then
+ 
+
+ align:start position:0%
+well known for deep learning and then
+Brendan Lake this is really mostly all
+
+ align:start position:0%
+Brendan Lake this is really mostly all
+ 
+
+ align:start position:0%
+Brendan Lake this is really mostly all
+I'll talk about is Brendan Lakes
+
+ align:start position:0%
+I'll talk about is Brendan Lakes
+ 
+
+ align:start position:0%
+I'll talk about is Brendan Lakes
+work who is now a postdoc at NYU and we
+
+ align:start position:0%
+work who is now a postdoc at NYU and we
+ 
+
+ align:start position:0%
+work who is now a postdoc at NYU and we
+you know again where we think we're
+
+ align:start position:0%
+you know again where we think we're
+ 
+
+ align:start position:0%
+you know again where we think we're
+building up to is trying to learn
+
+ align:start position:0%
+building up to is trying to learn
+ 
+
+ align:start position:0%
+building up to is trying to learn
+something like a the program of an
+
+ align:start position:0%
+something like a the program of an
+ 
+
+ align:start position:0%
+something like a the program of an
+intuitive physics or intuitive
+
+ align:start position:0%
+intuitive physics or intuitive
+ 
+
+ align:start position:0%
+intuitive physics or intuitive
+psychology but here we're just talking
+
+ align:start position:0%
+psychology but here we're just talking
+ 
+
+ align:start position:0%
+psychology but here we're just talking
+about learning object concepts and we've
+
+ align:start position:0%
+about learning object concepts and we've
+ 
+
+ align:start position:0%
+about learning object concepts and we've
+been doing this work with the data set
+
+ align:start position:0%
+been doing this work with the data set
+ 
+
+ align:start position:0%
+been doing this work with the data set
+of handwritten characters the ones you
+
+ align:start position:0%
+of handwritten characters the ones you
+ 
+
+ align:start position:0%
+of handwritten characters the ones you
+see on the right here I'll just put it
+
+ align:start position:0%
+see on the right here I'll just put it
+ 
+
+ align:start position:0%
+see on the right here I'll just put it
+up in contrast or by comparison to say
+
+ align:start position:0%
+up in contrast or by comparison to say
+ 
+
+ align:start position:0%
+up in contrast or by comparison to say
+this other much more famous data set of
+
+ align:start position:0%
+this other much more famous data set of
+ 
+
+ align:start position:0%
+this other much more famous data set of
+Hendrick characters the emne Stata set
+
+ align:start position:0%
+Hendrick characters the emne Stata set
+ 
+
+ align:start position:0%
+Hendrick characters the emne Stata set
+how many people have seen the endless
+
+ align:start position:0%
+how many people have seen the endless
+ 
+
+ align:start position:0%
+how many people have seen the endless
+data set maybe in some of the previous
+
+ align:start position:0%
+data set maybe in some of the previous
+ 
+
+ align:start position:0%
+data set maybe in some of the previous
+talks how people have actually used it
+
+ align:start position:0%
+talks how people have actually used it
+ 
+
+ align:start position:0%
+talks how people have actually used it
+yeah it's a great data set to use it's
+
+ align:start position:0%
+yeah it's a great data set to use it's
+ 
+
+ align:start position:0%
+yeah it's a great data set to use it's
+driven a lot of basic machine learning
+
+ align:start position:0%
+driven a lot of basic machine learning
+ 
+
+ align:start position:0%
+driven a lot of basic machine learning
+research including deep learning Yann
+
+ align:start position:0%
+research including deep learning Yann
+ 
+
+ align:start position:0%
+research including deep learning Yann
+laocoon originally collected this data
+
+ align:start position:0%
+laocoon originally collected this data
+ 
+
+ align:start position:0%
+laocoon originally collected this data
+set and put this out there and geoff
+
+ align:start position:0%
+set and put this out there and geoff
+ 
+
+ align:start position:0%
+set and put this out there and geoff
+hinton did most of the development of
+
+ align:start position:0%
+hinton did most of the development of
+ 
+
+ align:start position:0%
+hinton did most of the development of
+the stuff that now wins object
+
+ align:start position:0%
+the stuff that now wins object
+ 
+
+ align:start position:0%
+the stuff that now wins object
+recognition challenges was done on this
+
+ align:start position:0%
+recognition challenges was done on this
+ 
+
+ align:start position:0%
+recognition challenges was done on this
+data set but not only that also a lot of
+
+ align:start position:0%
+data set but not only that also a lot of
+ 
+
+ align:start position:0%
+data set but not only that also a lot of
+bayesian stuff and probabilistic
+
+ align:start position:0%
+bayesian stuff and probabilistic
+ 
+
+ align:start position:0%
+bayesian stuff and probabilistic
+generative models now the the the thing
+
+ align:start position:0%
+generative models now the the the thing
+ 
+
+ align:start position:0%
+generative models now the the the thing
+about that data set though right is it
+
+ align:start position:0%
+about that data set though right is it
+ 
+
+ align:start position:0%
+about that data set though right is it
+has a very small number of classes just
+
+ align:start position:0%
+has a very small number of classes just
+ 
+
+ align:start position:0%
+has a very small number of classes just
+the digits 0 through 9 and a huge number
+
+ align:start position:0%
+the digits 0 through 9 and a huge number
+ 
+
+ align:start position:0%
+the digits 0 through 9 and a huge number
+of examples about you know roughly
+
+ align:start position:0%
+of examples about you know roughly
+ 
+
+ align:start position:0%
+of examples about you know roughly
+10,000 examples in each class or maybe
+
+ align:start position:0%
+10,000 examples in each class or maybe
+ 
+
+ align:start position:0%
+10,000 examples in each class or maybe
+six thousand examples something like
+
+ align:start position:0%
+six thousand examples something like
+ 
+
+ align:start position:0%
+six thousand examples something like
+that but we wanted to construct a data
+
+ align:start position:0%
+that but we wanted to construct a data
+ 
+
+ align:start position:0%
+that but we wanted to construct a data
+set which was similar in some ways in
+
+ align:start position:0%
+set which was similar in some ways in
+ 
+
+ align:start position:0%
+set which was similar in some ways in
+its complexity and scale but which which
+
+ align:start position:0%
+its complexity and scale but which which
+ 
+
+ align:start position:0%
+its complexity and scale but which which
+where we had many many more concepts and
+
+ align:start position:0%
+where we had many many more concepts and
+ 
+
+ align:start position:0%
+where we had many many more concepts and
+many perhaps many fewer examples so here
+
+ align:start position:0%
+many perhaps many fewer examples so here
+ 
+
+ align:start position:0%
+many perhaps many fewer examples so here
+we we got people to write by hand
+
+ align:start position:0%
+we we got people to write by hand
+ 
+
+ align:start position:0%
+we we got people to write by hand
+characters in 50 different alphabets and
+
+ align:start position:0%
+characters in 50 different alphabets and
+ 
+
+ align:start position:0%
+characters in 50 different alphabets and
+it's a really cool data set so that
+
+ align:start position:0%
+it's a really cool data set so that
+ 
+
+ align:start position:0%
+it's a really cool data set so that
+total data set has on 1623 concepts
+
+ align:start position:0%
+total data set has on 1623 concepts
+ 
+
+ align:start position:0%
+total data set has on 1623 concepts
+drawn which are which are you know you
+
+ align:start position:0%
+drawn which are which are you know you
+ 
+
+ align:start position:0%
+drawn which are which are you know you
+can call them handwritten characters you
+
+ align:start position:0%
+can call them handwritten characters you
+ 
+
+ align:start position:0%
+can call them handwritten characters you
+could just call them simple visual
+
+ align:start position:0%
+could just call them simple visual
+ 
+
+ align:start position:0%
+could just call them simple visual
+concepts and so as sort of a warm-up for
+
+ align:start position:0%
+concepts and so as sort of a warm-up for
+ 
+
+ align:start position:0%
+concepts and so as sort of a warm-up for
+bigger problems of say natural objects
+
+ align:start position:0%
+bigger problems of say natural objects
+ 
+
+ align:start position:0%
+bigger problems of say natural objects
+and there's a there's 20 examples per
+
+ align:start position:0%
+and there's a there's 20 examples per
+ 
+
+ align:start position:0%
+and there's a there's 20 examples per
+class so there's roughly 30,000 total
+
+ align:start position:0%
+class so there's roughly 30,000 total
+ 
+
+ align:start position:0%
+class so there's roughly 30,000 total
+data points in this data set just very
+
+ align:start position:0%
+data points in this data set just very
+ 
+
+ align:start position:0%
+data points in this data set just very
+much like a mist um you can see just
+
+ align:start position:0%
+much like a mist um you can see just
+ 
+
+ align:start position:0%
+much like a mist um you can see just
+just to illustrate here there's many
+
+ align:start position:0%
+just to illustrate here there's many
+ 
+
+ align:start position:0%
+just to illustrate here there's many
+different alphabets that have very
+
+ align:start position:0%
+different alphabets that have very
+ 
+
+ align:start position:0%
+different alphabets that have very
+different forms you can see both the
+
+ align:start position:0%
+different forms you can see both the
+ 
+
+ align:start position:0%
+different forms you can see both the
+similarities and differences within
+
+ align:start position:0%
+similarities and differences within
+ 
+
+ align:start position:0%
+similarities and differences within
+between alphabets here right some of the
+
+ align:start position:0%
+between alphabets here right some of the
+ 
+
+ align:start position:0%
+between alphabets here right some of the
+alphabet so so so so in that sense
+
+ align:start position:0%
+alphabet so so so so in that sense
+ 
+
+ align:start position:0%
+alphabet so so so so in that sense
+there's kind of a hierarchical structure
+
+ align:start position:0%
+there's kind of a hierarchical structure
+ 
+
+ align:start position:0%
+there's kind of a hierarchical structure
+right each one of these is a character
+
+ align:start position:0%
+right each one of these is a character
+ 
+
+ align:start position:0%
+right each one of these is a character
+in an alphabet but there's also the
+
+ align:start position:0%
+in an alphabet but there's also the
+ 
+
+ align:start position:0%
+in an alphabet but there's also the
+higher level concept of a sort of a Sam
+
+ align:start position:0%
+higher level concept of a sort of a Sam
+ 
+
+ align:start position:0%
+higher level concept of a sort of a Sam
+script form as
+
+ align:start position:0%
+script form as
+ 
+
+ align:start position:0%
+script form as
+thing from say Tagalog or Hebrew or
+
+ align:start position:0%
+thing from say Tagalog or Hebrew or
+ 
+
+ align:start position:0%
+thing from say Tagalog or Hebrew or
+Braille right there's some made-up
+
+ align:start position:0%
+Braille right there's some made-up
+ 
+
+ align:start position:0%
+Braille right there's some made-up
+alphabets but you know one of the neat
+
+ align:start position:0%
+alphabets but you know one of the neat
+ 
+
+ align:start position:0%
+alphabets but you know one of the neat
+things about this domain is that you can
+
+ align:start position:0%
+things about this domain is that you can
+ 
+
+ align:start position:0%
+things about this domain is that you can
+make up new concepts and you can make up
+
+ align:start position:0%
+make up new concepts and you can make up
+ 
+
+ align:start position:0%
+make up new concepts and you can make up
+new whole concepts of concepts like
+
+ align:start position:0%
+new whole concepts of concepts like
+ 
+
+ align:start position:0%
+new whole concepts of concepts like
+whole new alphabets
+
+ align:start position:0%
+whole new alphabets
+ 
+
+ align:start position:0%
+whole new alphabets
+you can do one-shot learning in it so we
+
+ align:start position:0%
+you can do one-shot learning in it so we
+ 
+
+ align:start position:0%
+you can do one-shot learning in it so we
+can let's just try this out here for a
+
+ align:start position:0%
+can let's just try this out here for a
+ 
+
+ align:start position:0%
+can let's just try this out here for a
+second you'll remember the tufa demo we
+
+ align:start position:0%
+second you'll remember the tufa demo we
+ 
+
+ align:start position:0%
+second you'll remember the tufa demo we
+can do the same kind of thing here like
+
+ align:start position:0%
+can do the same kind of thing here like
+ 
+
+ align:start position:0%
+can do the same kind of thing here like
+let's take these characters anybody know
+
+ align:start position:0%
+let's take these characters anybody know
+ 
+
+ align:start position:0%
+let's take these characters anybody know
+the alphabet that this is okay that's
+
+ align:start position:0%
+the alphabet that this is okay that's
+ 
+
+ align:start position:0%
+the alphabet that this is okay that's
+good most of you have not seen these
+
+ align:start position:0%
+good most of you have not seen these
+ 
+
+ align:start position:0%
+good most of you have not seen these
+before okay that's good that you know
+
+ align:start position:0%
+before okay that's good that you know
+ 
+
+ align:start position:0%
+before okay that's good that you know
+but let will do this exponent on the
+
+ align:start position:0%
+but let will do this exponent on the
+ 
+
+ align:start position:0%
+but let will do this exponent on the
+rest of you so here's a one example of a
+
+ align:start position:0%
+rest of you so here's a one example of a
+ 
+
+ align:start position:0%
+rest of you so here's a one example of a
+concept call it a tufa if you like and
+
+ align:start position:0%
+concept call it a tufa if you like and
+ 
+
+ align:start position:0%
+concept call it a tufa if you like and
+I'll just run my mouse over these other
+
+ align:start position:0%
+I'll just run my mouse over these other
+ 
+
+ align:start position:0%
+I'll just run my mouse over these other
+ones and you just clap when I get to the
+
+ align:start position:0%
+ones and you just clap when I get to the
+ 
+
+ align:start position:0%
+ones and you just clap when I get to the
+other example of the same class okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay very good yeah people are basically
+
+ align:start position:0%
+okay very good yeah people are basically
+ 
+
+ align:start position:0%
+okay very good yeah people are basically
+perfect at this you just it doesn't take
+
+ align:start position:0%
+perfect at this you just it doesn't take
+ 
+
+ align:start position:0%
+perfect at this you just it doesn't take
+I mean again it's it's very fast and
+
+ align:start position:0%
+I mean again it's it's very fast and
+ 
+
+ align:start position:0%
+I mean again it's it's very fast and
+almost perfect and and just like again
+
+ align:start position:0%
+almost perfect and and just like again
+ 
+
+ align:start position:0%
+almost perfect and and just like again
+you you saw me talk a little about this
+
+ align:start position:0%
+you you saw me talk a little about this
+ 
+
+ align:start position:0%
+you you saw me talk a little about this
+last time just like with natural objects
+
+ align:start position:0%
+last time just like with natural objects
+ 
+
+ align:start position:0%
+last time just like with natural objects
+not only can you learn one of these
+
+ align:start position:0%
+not only can you learn one of these
+ 
+
+ align:start position:0%
+not only can you learn one of these
+concepts from one example and generalize
+
+ align:start position:0%
+concepts from one example and generalize
+ 
+
+ align:start position:0%
+concepts from one example and generalize
+it to others but you can use that
+
+ align:start position:0%
+it to others but you can use that
+ 
+
+ align:start position:0%
+it to others but you can use that
+knowledge in various other ways right so
+
+ align:start position:0%
+knowledge in various other ways right so
+ 
+
+ align:start position:0%
+knowledge in various other ways right so
+you can parse these things into parts we
+
+ align:start position:0%
+you can parse these things into parts we
+ 
+
+ align:start position:0%
+you can parse these things into parts we
+think that's part of what you're doing
+
+ align:start position:0%
+think that's part of what you're doing
+ 
+
+ align:start position:0%
+think that's part of what you're doing
+you can generate new examples so here
+
+ align:start position:0%
+you can generate new examples so here
+ 
+
+ align:start position:0%
+you can generate new examples so here
+are three different people all drawing
+
+ align:start position:0%
+are three different people all drawing
+ 
+
+ align:start position:0%
+are three different people all drawing
+the same character and in fact the whole
+
+ align:start position:0%
+the same character and in fact the whole
+ 
+
+ align:start position:0%
+the same character and in fact the whole
+data set was generated that way you can
+
+ align:start position:0%
+data set was generated that way you can
+ 
+
+ align:start position:0%
+data set was generated that way you can
+also make higher-level generalizations
+
+ align:start position:0%
+also make higher-level generalizations
+ 
+
+ align:start position:0%
+also make higher-level generalizations
+right recombining the parts into totally
+
+ align:start position:0%
+right recombining the parts into totally
+ 
+
+ align:start position:0%
+right recombining the parts into totally
+new concepts the way there's that weird
+
+ align:start position:0%
+new concepts the way there's that weird
+ 
+
+ align:start position:0%
+new concepts the way there's that weird
+kind of like eunice unicycle thing over
+
+ align:start position:0%
+kind of like eunice unicycle thing over
+ 
+
+ align:start position:0%
+kind of like eunice unicycle thing over
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+you know motorcycle here you know you
+
+ align:start position:0%
+you know motorcycle here you know you
+ 
+
+ align:start position:0%
+you know motorcycle here you know you
+can I can show you as you'll see ten
+
+ align:start position:0%
+can I can show you as you'll see ten
+ 
+
+ align:start position:0%
+can I can show you as you'll see ten
+characters in a new alphabet and you can
+
+ align:start position:0%
+characters in a new alphabet and you can
+ 
+
+ align:start position:0%
+characters in a new alphabet and you can
+make up hypothetical if perhaps
+
+ align:start position:0%
+make up hypothetical if perhaps
+ 
+
+ align:start position:0%
+make up hypothetical if perhaps
+incorrect examples in it I mean again
+
+ align:start position:0%
+incorrect examples in it I mean again
+ 
+
+ align:start position:0%
+incorrect examples in it I mean again
+I'm just going to show you a couple of
+
+ align:start position:0%
+I'm just going to show you a couple of
+ 
+
+ align:start position:0%
+I'm just going to show you a couple of
+case studies of where this idea of
+
+ align:start position:0%
+case studies of where this idea of
+ 
+
+ align:start position:0%
+case studies of where this idea of
+learning as program synthesis might work
+
+ align:start position:0%
+learning as program synthesis might work
+ 
+
+ align:start position:0%
+learning as program synthesis might work
+so the idea here is that you know kind
+
+ align:start position:0%
+so the idea here is that you know kind
+ 
+
+ align:start position:0%
+so the idea here is that you know kind
+of as you as you might see these are
+
+ align:start position:0%
+of as you as you might see these are
+ 
+
+ align:start position:0%
+of as you as you might see these are
+three characters down on the bottom and
+
+ align:start position:0%
+three characters down on the bottom and
+ 
+
+ align:start position:0%
+three characters down on the bottom and
+this is just a very schematic diagram of
+
+ align:start position:0%
+this is just a very schematic diagram of
+ 
+
+ align:start position:0%
+this is just a very schematic diagram of
+how our model tries to represent these
+
+ align:start position:0%
+how our model tries to represent these
+ 
+
+ align:start position:0%
+how our model tries to represent these
+as simple kinds of programs think about
+
+ align:start position:0%
+as simple kinds of programs think about
+ 
+
+ align:start position:0%
+as simple kinds of programs think about
+how you would draw say that character
+
+ align:start position:0%
+how you would draw say that character
+ 
+
+ align:start position:0%
+how you would draw say that character
+down at the bottom just try to draw it
+
+ align:start position:0%
+down at the bottom just try to draw it
+ 
+
+ align:start position:0%
+down at the bottom just try to draw it
+in in midair or just for every you know
+
+ align:start position:0%
+in in midair or just for every you know
+ 
+
+ align:start position:0%
+in in midair or just for every you know
+just how would you draw that one in the
+
+ align:start position:0%
+just how would you draw that one in the
+ 
+
+ align:start position:0%
+just how would you draw that one in the
+lower left there are many of you doing
+
+ align:start position:0%
+lower left there are many of you doing
+ 
+
+ align:start position:0%
+lower left there are many of you doing
+something like this is that what you're
+
+ align:start position:0%
+something like this is that what you're
+ 
+
+ align:start position:0%
+something like this is that what you're
+doing okay yeah so basically everyone
+
+ align:start position:0%
+doing okay yeah so basically everyone
+ 
+
+ align:start position:0%
+doing okay yeah so basically everyone
+does that and you can describe that as
+
+ align:start position:0%
+does that and you can describe that as
+ 
+
+ align:start position:0%
+does that and you can describe that as
+sort of having two large parts or two
+
+ align:start position:0%
+sort of having two large parts or two
+ 
+
+ align:start position:0%
+sort of having two large parts or two
+strokes where you pick up your pen
+
+ align:start position:0%
+strokes where you pick up your pen
+ 
+
+ align:start position:0%
+strokes where you pick up your pen
+between strokes and one of the strokes
+
+ align:start position:0%
+between strokes and one of the strokes
+ 
+
+ align:start position:0%
+between strokes and one of the strokes
+has two sub strokes where you stop your
+
+ align:start position:0%
+has two sub strokes where you stop your
+ 
+
+ align:start position:0%
+has two sub strokes where you stop your
+pen and there's a consistent
+
+ align:start position:0%
+pen and there's a consistent
+ 
+
+ align:start position:0%
+pen and there's a consistent
+relationship the second stroke has two
+
+ align:start position:0%
+relationship the second stroke has two
+ 
+
+ align:start position:0%
+relationship the second stroke has two
+begins somewhere on a particular general
+
+ align:start position:0%
+begins somewhere on a particular general
+ 
+
+ align:start position:0%
+begins somewhere on a particular general
+region of the first stroke and basically
+
+ align:start position:0%
+region of the first stroke and basically
+ 
+
+ align:start position:0%
+region of the first stroke and basically
+the model that's the models
+
+ align:start position:0%
+the model that's the models
+ 
+
+ align:start position:0%
+the model that's the models
+representation of concepts parts sub
+
+ align:start position:0%
+representation of concepts parts sub
+ 
+
+ align:start position:0%
+representation of concepts parts sub
+parts and simple relations which you can
+
+ align:start position:0%
+parts and simple relations which you can
+ 
+
+ align:start position:0%
+parts and simple relations which you can
+see you know might scale up arguably to
+
+ align:start position:0%
+see you know might scale up arguably to
+ 
+
+ align:start position:0%
+see you know might scale up arguably to
+more interesting kinds of natural
+
+ align:start position:0%
+more interesting kinds of natural
+ 
+
+ align:start position:0%
+more interesting kinds of natural
+objects and the basic idea is that you
+
+ align:start position:0%
+objects and the basic idea is that you
+ 
+
+ align:start position:0%
+objects and the basic idea is that you
+represent that though as a program it's
+
+ align:start position:0%
+represent that though as a program it's
+ 
+
+ align:start position:0%
+represent that though as a program it's
+a generative program it's kind of like a
+
+ align:start position:0%
+a generative program it's kind of like a
+ 
+
+ align:start position:0%
+a generative program it's kind of like a
+motor program but it's more abstract we
+
+ align:start position:0%
+motor program but it's more abstract we
+ 
+
+ align:start position:0%
+motor program but it's more abstract we
+don't think we think that when you see
+
+ align:start position:0%
+don't think we think that when you see
+ 
+
+ align:start position:0%
+don't think we think that when you see
+these characters and many other concepts
+
+ align:start position:0%
+these characters and many other concepts
+ 
+
+ align:start position:0%
+these characters and many other concepts
+you represent something about
+
+ align:start position:0%
+you represent something about
+ 
+
+ align:start position:0%
+you represent something about
+you might create it but it doesn't mean
+
+ align:start position:0%
+you might create it but it doesn't mean
+ 
+
+ align:start position:0%
+you might create it but it doesn't mean
+it's in your muscles you could use other
+
+ align:start position:0%
+it's in your muscles you could use other
+ 
+
+ align:start position:0%
+it's in your muscles you could use other
+hands you could use your toe or you
+
+ align:start position:0%
+hands you could use your toe or you
+ 
+
+ align:start position:0%
+hands you could use your toe or you
+could even just think about it in your
+
+ align:start position:0%
+could even just think about it in your
+ 
+
+ align:start position:0%
+could even just think about it in your
+imagination so the model basically tries
+
+ align:start position:0%
+imagination so the model basically tries
+ 
+
+ align:start position:0%
+imagination so the model basically tries
+to induce these simple think about them
+
+ align:start position:0%
+to induce these simple think about them
+ 
+
+ align:start position:0%
+to induce these simple think about them
+is like maybe simple hierarchical plans
+
+ align:start position:0%
+is like maybe simple hierarchical plans
+ 
+
+ align:start position:0%
+is like maybe simple hierarchical plans
+simple action programs and it does it by
+
+ align:start position:0%
+simple action programs and it does it by
+ 
+
+ align:start position:0%
+simple action programs and it does it by
+having a program generating program that
+
+ align:start position:0%
+having a program generating program that
+ 
+
+ align:start position:0%
+having a program generating program that
+can itself have parameters that can be
+
+ align:start position:0%
+can itself have parameters that can be
+ 
+
+ align:start position:0%
+can itself have parameters that can be
+learned from data so this right right
+
+ align:start position:0%
+learned from data so this right right
+ 
+
+ align:start position:0%
+learned from data so this right right
+here this is a program called generate
+
+ align:start position:0%
+here this is a program called generate
+ 
+
+ align:start position:0%
+here this is a program called generate
+type and what that does is it's a
+
+ align:start position:0%
+type and what that does is it's a
+ 
+
+ align:start position:0%
+type and what that does is it's a
+program a type means a character concept
+
+ align:start position:0%
+program a type means a character concept
+ 
+
+ align:start position:0%
+program a type means a character concept
+like each of those three things is a
+
+ align:start position:0%
+like each of those three things is a
+ 
+
+ align:start position:0%
+like each of those three things is a
+different type this is a program which
+
+ align:start position:0%
+different type this is a program which
+ 
+
+ align:start position:0%
+different type this is a program which
+generates a program that generates the
+
+ align:start position:0%
+generates a program that generates the
+ 
+
+ align:start position:0%
+generates a program that generates the
+actual character that the second level
+
+ align:start position:0%
+actual character that the second level
+ 
+
+ align:start position:0%
+actual character that the second level
+of program is called generate token
+
+ align:start position:0%
+of program is called generate token
+ 
+
+ align:start position:0%
+of program is called generate token
+that's a program which draws a
+
+ align:start position:0%
+that's a program which draws a
+ 
+
+ align:start position:0%
+that's a program which draws a
+particular instance of a character and
+
+ align:start position:0%
+particular instance of a character and
+ 
+
+ align:start position:0%
+particular instance of a character and
+you can you know just like you can draw
+
+ align:start position:0%
+you can you know just like you can draw
+ 
+
+ align:start position:0%
+you can you know just like you can draw
+many examples of any concept you can
+
+ align:start position:0%
+many examples of any concept you can
+ 
+
+ align:start position:0%
+many examples of any concept you can
+call that function many times generate
+
+ align:start position:0%
+call that function many times generate
+ 
+
+ align:start position:0%
+call that function many times generate
+token generate token generate token so
+
+ align:start position:0%
+token generate token generate token so
+ 
+
+ align:start position:0%
+token generate token generate token so
+your concept of a character is a
+
+ align:start position:0%
+your concept of a character is a
+ 
+
+ align:start position:0%
+your concept of a character is a
+generative function and in order to
+
+ align:start position:0%
+generative function and in order to
+ 
+
+ align:start position:0%
+generative function and in order to
+learn this you have basically a prior on
+
+ align:start position:0%
+learn this you have basically a prior on
+ 
+
+ align:start position:0%
+learn this you have basically a prior on
+those programs that comes from a program
+
+ align:start position:0%
+those programs that comes from a program
+ 
+
+ align:start position:0%
+those programs that comes from a program
+generating program that's the generate
+
+ align:start position:0%
+generating program that's the generate
+ 
+
+ align:start position:0%
+generating program that's the generate
+type program so there's a lot of details
+
+ align:start position:0%
+type program so there's a lot of details
+ 
+
+ align:start position:0%
+type program so there's a lot of details
+behind how this works but basically the
+
+ align:start position:0%
+behind how this works but basically the
+ 
+
+ align:start position:0%
+behind how this works but basically the
+the model does a kind of learning to
+
+ align:start position:0%
+the model does a kind of learning to
+ 
+
+ align:start position:0%
+the model does a kind of learning to
+learn from a held out unsupervised set
+
+ align:start position:0%
+learn from a held out unsupervised set
+ 
+
+ align:start position:0%
+learn from a held out unsupervised set
+and sort of learns the program of the
+
+ align:start position:0%
+and sort of learns the program of the
+ 
+
+ align:start position:0%
+and sort of learns the program of the
+parameters of this program generating
+
+ align:start position:0%
+parameters of this program generating
+ 
+
+ align:start position:0%
+parameters of this program generating
+program which kind of would characterize
+
+ align:start position:0%
+program which kind of would characterize
+ 
+
+ align:start position:0%
+program which kind of would characterize
+how we draw things in general how
+
+ align:start position:0%
+how we draw things in general how
+ 
+
+ align:start position:0%
+how we draw things in general how
+characters what they look like in
+
+ align:start position:0%
+characters what they look like in
+ 
+
+ align:start position:0%
+characters what they look like in
+general and then when you see a new
+
+ align:start position:0%
+general and then when you see a new
+ 
+
+ align:start position:0%
+general and then when you see a new
+character like this one what effectively
+
+ align:start position:0%
+character like this one what effectively
+ 
+
+ align:start position:0%
+character like this one what effectively
+what the model is doing is it's it's
+
+ align:start position:0%
+what the model is doing is it's it's
+ 
+
+ align:start position:0%
+what the model is doing is it's it's
+both kind of parsing this into its parts
+
+ align:start position:0%
+both kind of parsing this into its parts
+ 
+
+ align:start position:0%
+both kind of parsing this into its parts
+and subparts and relations but that
+
+ align:start position:0%
+and subparts and relations but that
+ 
+
+ align:start position:0%
+and subparts and relations but that
+parsing is basically the program
+
+ align:start position:0%
+parsing is basically the program
+ 
+
+ align:start position:0%
+parsing is basically the program
+synthesis it is pretty much the same
+
+ align:start position:0%
+synthesis it is pretty much the same
+ 
+
+ align:start position:0%
+synthesis it is pretty much the same
+thing you're constructing you're looking
+
+ align:start position:0%
+thing you're constructing you're looking
+ 
+
+ align:start position:0%
+thing you're constructing you're looking
+at that output of some program and
+
+ align:start position:0%
+at that output of some program and
+ 
+
+ align:start position:0%
+at that output of some program and
+saying what would be the best simple set
+
+ align:start position:0%
+saying what would be the best simple set
+ 
+
+ align:start position:0%
+saying what would be the best simple set
+of parts and subparts and relations that
+
+ align:start position:0%
+of parts and subparts and relations that
+ 
+
+ align:start position:0%
+of parts and subparts and relations that
+could draw that and then I'm gonna infer
+
+ align:start position:0%
+could draw that and then I'm gonna infer
+ 
+
+ align:start position:0%
+could draw that and then I'm gonna infer
+the most likely one and then use that as
+
+ align:start position:0%
+the most likely one and then use that as
+ 
+
+ align:start position:0%
+the most likely one and then use that as
+a generalizable template or program I
+
+ align:start position:0%
+a generalizable template or program I
+ 
+
+ align:start position:0%
+a generalizable template or program I
+can then generate other characters with
+
+ align:start position:0%
+can then generate other characters with
+ 
+
+ align:start position:0%
+can then generate other characters with
+so here it may be to just illustrate
+
+ align:start position:0%
+so here it may be to just illustrate
+ 
+
+ align:start position:0%
+so here it may be to just illustrate
+really concretely um if you were to see
+
+ align:start position:0%
+really concretely um if you were to see
+ 
+
+ align:start position:0%
+really concretely um if you were to see
+this character here well here's here's
+
+ align:start position:0%
+this character here well here's here's
+ 
+
+ align:start position:0%
+this character here well here's here's
+one instance of one class here's an into
+
+ align:start position:0%
+one instance of one class here's an into
+ 
+
+ align:start position:0%
+one instance of one class here's an into
+another class again I have no idea which
+
+ align:start position:0%
+another class again I have no idea which
+ 
+
+ align:start position:0%
+another class again I have no idea which
+alphabet this is now what about this one
+
+ align:start position:0%
+alphabet this is now what about this one
+ 
+
+ align:start position:0%
+alphabet this is now what about this one
+is it class 1 or class 2 what do you
+
+ align:start position:0%
+is it class 1 or class 2 what do you
+ 
+
+ align:start position:0%
+is it class 1 or class 2 what do you
+think what yeah anybody think it's class
+
+ align:start position:0%
+think what yeah anybody think it's class
+ 
+
+ align:start position:0%
+think what yeah anybody think it's class
+2 okay so how do we know it's class 1
+
+ align:start position:0%
+2 okay so how do we know it's class 1
+ 
+
+ align:start position:0%
+2 okay so how do we know it's class 1
+well at the pixel level it doesn't look
+
+ align:start position:0%
+well at the pixel level it doesn't look
+ 
+
+ align:start position:0%
+well at the pixel level it doesn't look
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+like that right so this is again an
+
+ align:start position:0%
+like that right so this is again an
+ 
+
+ align:start position:0%
+like that right so this is again an
+example some of the issues that Tommy
+
+ align:start position:0%
+example some of the issues that Tommy
+ 
+
+ align:start position:0%
+example some of the issues that Tommy
+was talking about a really severe kind
+
+ align:start position:0%
+was talking about a really severe kind
+ 
+
+ align:start position:0%
+was talking about a really severe kind
+of invariance but it's not just
+
+ align:start position:0%
+of invariance but it's not just
+ 
+
+ align:start position:0%
+of invariance but it's not just
+translation or scale invariance although
+
+ align:start position:0%
+translation or scale invariance although
+ 
+
+ align:start position:0%
+translation or scale invariance although
+it does have some of that but it also
+
+ align:start position:0%
+it does have some of that but it also
+ 
+
+ align:start position:0%
+it does have some of that but it also
+has this kind of interesting with in
+
+ align:start position:0%
+has this kind of interesting with in
+ 
+
+ align:start position:0%
+has this kind of interesting with in
+class invariance right there's it's a
+
+ align:start position:0%
+class invariance right there's it's a
+ 
+
+ align:start position:0%
+class invariance right there's it's a
+rather different shape it's been
+
+ align:start position:0%
+rather different shape it's been
+ 
+
+ align:start position:0%
+rather different shape it's been
+distorted somewhat so a program is a
+
+ align:start position:0%
+distorted somewhat so a program is a
+ 
+
+ align:start position:0%
+distorted somewhat so a program is a
+powerful way to capture that where you
+
+ align:start position:0%
+powerful way to capture that where you
+ 
+
+ align:start position:0%
+powerful way to capture that where you
+can say well if you hear if you you
+
+ align:start position:0%
+can say well if you hear if you you
+ 
+
+ align:start position:0%
+can say well if you hear if you you
+wouldn't do something like the program
+
+ align:start position:0%
+wouldn't do something like the program
+ 
+
+ align:start position:0%
+wouldn't do something like the program
+for generating this which is like one
+
+ align:start position:0%
+for generating this which is like one
+ 
+
+ align:start position:0%
+for generating this which is like one
+stroke like that and then these other
+
+ align:start position:0%
+stroke like that and then these other
+ 
+
+ align:start position:0%
+stroke like that and then these other
+two things that's shown with the red and
+
+ align:start position:0%
+two things that's shown with the red and
+ 
+
+ align:start position:0%
+two things that's shown with the red and
+green and here's a program that you
+
+ align:start position:0%
+green and here's a program that you
+ 
+
+ align:start position:0%
+green and here's a program that you
+might induce to generate that and then
+
+ align:start position:0%
+might induce to generate that and then
+ 
+
+ align:start position:0%
+might induce to generate that and then
+the question is which of these is most
+
+ align:start position:0%
+the question is which of these is most
+ 
+
+ align:start position:0%
+the question is which of these is most
+or which of these two programs simple
+
+ align:start position:0%
+or which of these two programs simple
+ 
+
+ align:start position:0%
+or which of these two programs simple
+motor hierarchical motor programs is
+
+ align:start position:0%
+motor hierarchical motor programs is
+ 
+
+ align:start position:0%
+motor hierarchical motor programs is
+most likely to generate that character
+
+ align:start position:0%
+most likely to generate that character
+ 
+
+ align:start position:0%
+most likely to generate that character
+and it turns out that it's incredibly
+
+ align:start position:0%
+and it turns out that it's incredibly
+ 
+
+ align:start position:0%
+and it turns out that it's incredibly
+unlikely to generate any character from
+
+ align:start position:0%
+unlikely to generate any character from
+ 
+
+ align:start position:0%
+unlikely to generate any character from
+one of these programs but these are the
+
+ align:start position:0%
+one of these programs but these are the
+ 
+
+ align:start position:0%
+one of these programs but these are the
+logs scores the log probabilities so
+
+ align:start position:0%
+logs scores the log probabilities so
+ 
+
+ align:start position:0%
+logs scores the log probabilities so
+this one is like 2 to the negative 758
+
+ align:start position:0%
+this one is like 2 to the negative 758
+ 
+
+ align:start position:0%
+this one is like 2 to the negative 758
+and this one is like 2 to the negative
+
+ align:start position:0%
+and this one is like 2 to the negative
+ 
+
+ align:start position:0%
+and this one is like 2 to the negative
+18 hundred and 80 I don't know if it's
+
+ align:start position:0%
+18 hundred and 80 I don't know if it's
+ 
+
+ align:start position:0%
+18 hundred and 80 I don't know if it's
+base years maybe 2 or 8 but whatever so
+
+ align:start position:0%
+base years maybe 2 or 8 but whatever so
+ 
+
+ align:start position:0%
+base years maybe 2 or 8 but whatever so
+each of these is very small but this one
+
+ align:start position:0%
+each of these is very small but this one
+ 
+
+ align:start position:0%
+each of these is very small but this one
+is like a thousand orders of magnitude
+
+ align:start position:0%
+is like a thousand orders of magnitude
+ 
+
+ align:start position:0%
+is like a thousand orders of magnitude
+more likely than than that one and that
+
+ align:start position:0%
+more likely than than that one and that
+ 
+
+ align:start position:0%
+more likely than than that one and that
+makes sense right it just is easier to
+
+ align:start position:0%
+makes sense right it just is easier to
+ 
+
+ align:start position:0%
+makes sense right it just is easier to
+think of think intuitively about
+
+ align:start position:0%
+think of think intuitively about
+ 
+
+ align:start position:0%
+think of think intuitively about
+generating this shape from that the
+
+ align:start position:0%
+generating this shape from that the
+ 
+
+ align:start position:0%
+generating this shape from that the
+distortion so that's basically what the
+
+ align:start position:0%
+distortion so that's basically what the
+ 
+
+ align:start position:0%
+distortion so that's basically what the
+system does and it's able to do this
+
+ align:start position:0%
+system does and it's able to do this
+ 
+
+ align:start position:0%
+system does and it's able to do this
+remarkable thing that you were able to
+
+ align:start position:0%
+remarkable thing that you were able to
+ 
+
+ align:start position:0%
+remarkable thing that you were able to
+do to this one-shot learning of a
+
+ align:start position:0%
+do to this one-shot learning of a
+ 
+
+ align:start position:0%
+do to this one-shot learning of a
+concept here's just another illustration
+
+ align:start position:0%
+concept here's just another illustration
+ 
+
+ align:start position:0%
+concept here's just another illustration
+of this right we show people at one
+
+ align:start position:0%
+of this right we show people at one
+ 
+
+ align:start position:0%
+of this right we show people at one
+example of a new character in an
+
+ align:start position:0%
+example of a new character in an
+ 
+
+ align:start position:0%
+example of a new character in an
+alphabet they don't know and ask them to
+
+ align:start position:0%
+alphabet they don't know and ask them to
+ 
+
+ align:start position:0%
+alphabet they don't know and ask them to
+pick out the other one everybody see
+
+ align:start position:0%
+pick out the other one everybody see
+ 
+
+ align:start position:0%
+pick out the other one everybody see
+where it is here
+
+ align:start position:0%
+where it is here
+ 
+
+ align:start position:0%
+where it is here
+it's not that easy but it's doable down
+
+ align:start position:0%
+it's not that easy but it's doable down
+ 
+
+ align:start position:0%
+it's not that easy but it's doable down
+here right so people make you know are
+
+ align:start position:0%
+here right so people make you know are
+ 
+
+ align:start position:0%
+here right so people make you know are
+better than 95% correct at this this is
+
+ align:start position:0%
+better than 95% correct at this this is
+ 
+
+ align:start position:0%
+better than 95% correct at this this is
+error rate so people error rates less
+
+ align:start position:0%
+error rate so people error rates less
+ 
+
+ align:start position:0%
+error rate so people error rates less
+than 5% for humans and also for this
+
+ align:start position:0%
+than 5% for humans and also for this
+ 
+
+ align:start position:0%
+than 5% for humans and also for this
+model but for a range of more you know
+
+ align:start position:0%
+model but for a range of more you know
+ 
+
+ align:start position:0%
+model but for a range of more you know
+sort of more standard deep learning
+
+ align:start position:0%
+sort of more standard deep learning
+ 
+
+ align:start position:0%
+sort of more standard deep learning
+models this one here is basically like
+
+ align:start position:0%
+models this one here is basically like
+ 
+
+ align:start position:0%
+models this one here is basically like
+an image net or M this type one so this
+
+ align:start position:0%
+an image net or M this type one so this
+ 
+
+ align:start position:0%
+an image net or M this type one so this
+is the kind of model that was really
+
+ align:start position:0%
+is the kind of model that was really
+ 
+
+ align:start position:0%
+is the kind of model that was really
+sort of massive convolutional classifier
+
+ align:start position:0%
+sort of massive convolutional classifier
+ 
+
+ align:start position:0%
+sort of massive convolutional classifier
+the best deep learning one is actually
+
+ align:start position:0%
+the best deep learning one is actually
+ 
+
+ align:start position:0%
+the best deep learning one is actually
+something for this problem is what's
+
+ align:start position:0%
+something for this problem is what's
+ 
+
+ align:start position:0%
+something for this problem is what's
+called a Siamese continent and that can
+
+ align:start position:0%
+called a Siamese continent and that can
+ 
+
+ align:start position:0%
+called a Siamese continent and that can
+do somewhat better but it's still more
+
+ align:start position:0%
+do somewhat better but it's still more
+ 
+
+ align:start position:0%
+do somewhat better but it's still more
+than twice as bad as people so we think
+
+ align:start position:0%
+than twice as bad as people so we think
+ 
+
+ align:start position:0%
+than twice as bad as people so we think
+this is one place where at least in a
+
+ align:start position:0%
+this is one place where at least in a
+ 
+
+ align:start position:0%
+this is one place where at least in a
+hard classification problem you can see
+
+ align:start position:0%
+hard classification problem you can see
+ 
+
+ align:start position:0%
+hard classification problem you can see
+that deep learning still isn't quite
+
+ align:start position:0%
+that deep learning still isn't quite
+ 
+
+ align:start position:0%
+that deep learning still isn't quite
+there whereas this
+
+ align:start position:0%
+there whereas this
+ 
+
+ align:start position:0%
+there whereas this
+even the best thing this this was a
+
+ align:start position:0%
+even the best thing this this was a
+ 
+
+ align:start position:0%
+even the best thing this this was a
+network that was basically specifically
+
+ align:start position:0%
+network that was basically specifically
+ 
+
+ align:start position:0%
+network that was basically specifically
+worked out by one of Russ to students
+
+ align:start position:0%
+worked out by one of Russ to students
+ 
+
+ align:start position:0%
+worked out by one of Russ to students
+for about a year to solve exactly this
+
+ align:start position:0%
+for about a year to solve exactly this
+ 
+
+ align:start position:0%
+for about a year to solve exactly this
+problem on this data set and that it
+
+ align:start position:0%
+problem on this data set and that it
+ 
+
+ align:start position:0%
+problem on this data set and that it
+substantially improved over a standard
+
+ align:start position:0%
+substantially improved over a standard
+ 
+
+ align:start position:0%
+substantially improved over a standard
+deep learning classifier which
+
+ align:start position:0%
+deep learning classifier which
+ 
+
+ align:start position:0%
+deep learning classifier which
+substantially approved over a different
+
+ align:start position:0%
+substantially approved over a different
+ 
+
+ align:start position:0%
+substantially approved over a different
+deep learning model that Russ and I both
+
+ align:start position:0%
+deep learning model that Russ and I both
+ 
+
+ align:start position:0%
+deep learning model that Russ and I both
+worked on so there was a there's
+
+ align:start position:0%
+worked on so there was a there's
+ 
+
+ align:start position:0%
+worked on so there was a there's
+definitely been some improvement here
+
+ align:start position:0%
+definitely been some improvement here
+ 
+
+ align:start position:0%
+definitely been some improvement here
+and you know never bet against deep
+
+ align:start position:0%
+and you know never bet against deep
+ 
+
+ align:start position:0%
+and you know never bet against deep
+learning I can't guarantee that somebody
+
+ align:start position:0%
+learning I can't guarantee that somebody
+ 
+
+ align:start position:0%
+learning I can't guarantee that somebody
+set spends their PhD they could work out
+
+ align:start position:0%
+set spends their PhD they could work out
+ 
+
+ align:start position:0%
+set spends their PhD they could work out
+something that could do this well um but
+
+ align:start position:0%
+something that could do this well um but
+ 
+
+ align:start position:0%
+something that could do this well um but
+it's still it's it's a it's it's a case
+
+ align:start position:0%
+it's still it's it's a it's it's a case
+ 
+
+ align:start position:0%
+it's still it's it's a it's it's a case
+which still has some room to push where
+
+ align:start position:0%
+which still has some room to push where
+ 
+
+ align:start position:0%
+which still has some room to push where
+for example just a pure pattern
+
+ align:start position:0%
+for example just a pure pattern
+ 
+
+ align:start position:0%
+for example just a pure pattern
+recognition approach might go but maybe
+
+ align:start position:0%
+recognition approach might go but maybe
+ 
+
+ align:start position:0%
+recognition approach might go but maybe
+more interesting right is again going
+
+ align:start position:0%
+more interesting right is again going
+ 
+
+ align:start position:0%
+more interesting right is again going
+back to all the things we use our
+
+ align:start position:0%
+back to all the things we use our
+ 
+
+ align:start position:0%
+back to all the things we use our
+knowledge for kids might use their
+
+ align:start position:0%
+knowledge for kids might use their
+ 
+
+ align:start position:0%
+knowledge for kids might use their
+knowledge for is we don't just classify
+
+ align:start position:0%
+knowledge for is we don't just classify
+ 
+
+ align:start position:0%
+knowledge for is we don't just classify
+the world we understand it we generate
+
+ align:start position:0%
+the world we understand it we generate
+ 
+
+ align:start position:0%
+the world we understand it we generate
+new things we imagine new things so
+
+ align:start position:0%
+new things we imagine new things so
+ 
+
+ align:start position:0%
+new things we imagine new things so
+here's a problem here's a place where
+
+ align:start position:0%
+here's a problem here's a place where
+ 
+
+ align:start position:0%
+here's a problem here's a place where
+you can use your generative program that
+
+ align:start position:0%
+you can use your generative program that
+ 
+
+ align:start position:0%
+you can use your generative program that
+none of these networks do at least by by
+
+ align:start position:0%
+none of these networks do at least by by
+ 
+
+ align:start position:0%
+none of these networks do at least by by
+nature maybe you could think of some way
+
+ align:start position:0%
+nature maybe you could think of some way
+ 
+
+ align:start position:0%
+nature maybe you could think of some way
+to get them to do it and this is to say
+
+ align:start position:0%
+to get them to do it and this is to say
+ 
+
+ align:start position:0%
+to get them to do it and this is to say
+not just classify but to produce imagine
+
+ align:start position:0%
+not just classify but to produce imagine
+ 
+
+ align:start position:0%
+not just classify but to produce imagine
+new examples so here's an illustration
+
+ align:start position:0%
+new examples so here's an illustration
+ 
+
+ align:start position:0%
+new examples so here's an illustration
+of this where we gave people one of
+
+ align:start position:0%
+of this where we gave people one of
+ 
+
+ align:start position:0%
+of this where we gave people one of
+these an example of one of these new
+
+ align:start position:0%
+these an example of one of these new
+ 
+
+ align:start position:0%
+these an example of one of these new
+concepts and then we said draw another
+
+ align:start position:0%
+concepts and then we said draw another
+ 
+
+ align:start position:0%
+concepts and then we said draw another
+example of the same concept don't just
+
+ align:start position:0%
+example of the same concept don't just
+ 
+
+ align:start position:0%
+example of the same concept don't just
+copy it make up another example of the
+
+ align:start position:0%
+copy it make up another example of the
+ 
+
+ align:start position:0%
+copy it make up another example of the
+concept and what you can see here is a
+
+ align:start position:0%
+concept and what you can see here is a
+ 
+
+ align:start position:0%
+concept and what you can see here is a
+set of nine examples that people that
+
+ align:start position:0%
+set of nine examples that people that
+ 
+
+ align:start position:0%
+set of nine examples that people that
+nine different people did in response to
+
+ align:start position:0%
+nine different people did in response to
+ 
+
+ align:start position:0%
+nine different people did in response to
+that query and then you can also see on
+
+ align:start position:0%
+that query and then you can also see on
+ 
+
+ align:start position:0%
+that query and then you can also see on
+the other side nine examples of our
+
+ align:start position:0%
+the other side nine examples of our
+ 
+
+ align:start position:0%
+the other side nine examples of our
+program doing that can anybody tell
+
+ align:start position:0%
+program doing that can anybody tell
+ 
+
+ align:start position:0%
+program doing that can anybody tell
+which is the people and which is the
+
+ align:start position:0%
+which is the people and which is the
+ 
+
+ align:start position:0%
+which is the people and which is the
+program let's try this out so which is
+
+ align:start position:0%
+program let's try this out so which is
+ 
+
+ align:start position:0%
+program let's try this out so which is
+the machine for this character the left
+
+ align:start position:0%
+the machine for this character the left
+ 
+
+ align:start position:0%
+the machine for this character the left
+or the right how many police a the left
+
+ align:start position:0%
+or the right how many police a the left
+ 
+
+ align:start position:0%
+or the right how many police a the left
+raise your hand how people say the right
+
+ align:start position:0%
+raise your hand how people say the right
+ 
+
+ align:start position:0%
+raise your hand how people say the right
+okay about fifty fifty very good how
+
+ align:start position:0%
+okay about fifty fifty very good how
+ 
+
+ align:start position:0%
+okay about fifty fifty very good how
+people say this is the machine for this
+
+ align:start position:0%
+people say this is the machine for this
+ 
+
+ align:start position:0%
+people say this is the machine for this
+one have you'll say this is the machine
+
+ align:start position:0%
+one have you'll say this is the machine
+ 
+
+ align:start position:0%
+one have you'll say this is the machine
+it's maybe slight preference there how
+
+ align:start position:0%
+it's maybe slight preference there how
+ 
+
+ align:start position:0%
+it's maybe slight preference there how
+people say this is the machine how
+
+ align:start position:0%
+people say this is the machine how
+ 
+
+ align:start position:0%
+people say this is the machine how
+people say this is the machine how he'll
+
+ align:start position:0%
+people say this is the machine how he'll
+ 
+
+ align:start position:0%
+people say this is the machine how he'll
+say this is the machine some people
+
+ align:start position:0%
+say this is the machine some people
+ 
+
+ align:start position:0%
+say this is the machine some people
+really like the left how many will say
+
+ align:start position:0%
+really like the left how many will say
+ 
+
+ align:start position:0%
+really like the left how many will say
+that's the machine
+
+ align:start position:0%
+that's the machine
+ 
+
+ align:start position:0%
+that's the machine
+okay basically it's 5050 for all of them
+
+ align:start position:0%
+okay basically it's 5050 for all of them
+ 
+
+ align:start position:0%
+okay basically it's 5050 for all of them
+here's the right answer I don't know you
+
+ align:start position:0%
+here's the right answer I don't know you
+ 
+
+ align:start position:0%
+here's the right answer I don't know you
+could decide if you were right or not I
+
+ align:start position:0%
+could decide if you were right or not I
+ 
+
+ align:start position:0%
+could decide if you were right or not I
+don't know here's another set again I
+
+ align:start position:0%
+don't know here's another set again I
+ 
+
+ align:start position:0%
+don't know here's another set again I
+hope it's clear that it this is not an
+
+ align:start position:0%
+hope it's clear that it this is not an
+ 
+
+ align:start position:0%
+hope it's clear that it this is not an
+easy task and in fact people are
+
+ align:start position:0%
+easy task and in fact people are
+ 
+
+ align:start position:0%
+easy task and in fact people are
+basically a chance we've done a bunch of
+
+ align:start position:0%
+basically a chance we've done a bunch of
+ 
+
+ align:start position:0%
+basically a chance we've done a bunch of
+studies of this and most people just
+
+ align:start position:0%
+studies of this and most people just
+ 
+
+ align:start position:0%
+studies of this and most people just
+can't tell
+
+ align:start position:0%
+can't tell
+ 
+
+ align:start position:0%
+can't tell
+the average people are on average are
+
+ align:start position:0%
+the average people are on average are
+ 
+
+ align:start position:0%
+the average people are on average are
+about 50% correct you basically just
+
+ align:start position:0%
+about 50% correct you basically just
+ 
+
+ align:start position:0%
+about 50% correct you basically just
+can't tell so it's an example of a kind
+
+ align:start position:0%
+can't tell so it's an example of a kind
+ 
+
+ align:start position:0%
+can't tell so it's an example of a kind
+of Turing test that a certain
+
+ align:start position:0%
+of Turing test that a certain
+ 
+
+ align:start position:0%
+of Turing test that a certain
+interesting program learning program is
+
+ align:start position:0%
+interesting program learning program is
+ 
+
+ align:start position:0%
+interesting program learning program is
+solving right at a level that's
+
+ align:start position:0%
+solving right at a level that's
+ 
+
+ align:start position:0%
+solving right at a level that's
+confusable with humans this system is
+
+ align:start position:0%
+confusable with humans this system is
+ 
+
+ align:start position:0%
+confusable with humans this system is
+able to learn simple programs for visual
+
+ align:start position:0%
+able to learn simple programs for visual
+ 
+
+ align:start position:0%
+able to learn simple programs for visual
+concepts and not just classify but use
+
+ align:start position:0%
+concepts and not just classify but use
+ 
+
+ align:start position:0%
+concepts and not just classify but use
+them to create new things you can even
+
+ align:start position:0%
+them to create new things you can even
+ 
+
+ align:start position:0%
+them to create new things you can even
+create new things at this higher level
+
+ align:start position:0%
+create new things at this higher level
+ 
+
+ align:start position:0%
+create new things at this higher level
+that I mentioned so here the task which
+
+ align:start position:0%
+that I mentioned so here the task which
+ 
+
+ align:start position:0%
+that I mentioned so here the task which
+again people and machines are roughly
+
+ align:start position:0%
+again people and machines are roughly
+ 
+
+ align:start position:0%
+again people and machines are roughly
+similar on is to give be given ten
+
+ align:start position:0%
+similar on is to give be given ten
+ 
+
+ align:start position:0%
+similar on is to give be given ten
+examples each of a different concept in
+
+ align:start position:0%
+examples each of a different concept in
+ 
+
+ align:start position:0%
+examples each of a different concept in
+a higher level concept like an alphabet
+
+ align:start position:0%
+a higher level concept like an alphabet
+ 
+
+ align:start position:0%
+a higher level concept like an alphabet
+and then draw new characters in that
+
+ align:start position:0%
+and then draw new characters in that
+ 
+
+ align:start position:0%
+and then draw new characters in that
+alphabet and we give people only a few
+
+ align:start position:0%
+alphabet and we give people only a few
+ 
+
+ align:start position:0%
+alphabet and we give people only a few
+seconds to do this so they don't get all
+
+ align:start position:0%
+seconds to do this so they don't get all
+ 
+
+ align:start position:0%
+seconds to do this so they don't get all
+too artistic but again you know you can
+
+ align:start position:0%
+too artistic but again you know you can
+ 
+
+ align:start position:0%
+too artistic but again you know you can
+see that machine is able to do this
+
+ align:start position:0%
+see that machine is able to do this
+ 
+
+ align:start position:0%
+see that machine is able to do this
+people are also kind of similar okay so
+
+ align:start position:0%
+people are also kind of similar okay so
+ 
+
+ align:start position:0%
+people are also kind of similar okay so
+let me let me say this is that was a
+
+ align:start position:0%
+let me let me say this is that was a
+ 
+
+ align:start position:0%
+let me let me say this is that was a
+success story a place where the idea of
+
+ align:start position:0%
+success story a place where the idea of
+ 
+
+ align:start position:0%
+success story a place where the idea of
+learning as program induction kind of
+
+ align:start position:0%
+learning as program induction kind of
+ 
+
+ align:start position:0%
+learning as program induction kind of
+works what about something more like
+
+ align:start position:0%
+works what about something more like
+ 
+
+ align:start position:0%
+works what about something more like
+what we're really most deeply interested
+
+ align:start position:0%
+what we're really most deeply interested
+ 
+
+ align:start position:0%
+what we're really most deeply interested
+in in children's learning like the
+
+ align:start position:0%
+in in children's learning like the
+ 
+
+ align:start position:0%
+in in children's learning like the
+ability for example to say understand
+
+ align:start position:0%
+ability for example to say understand
+ 
+
+ align:start position:0%
+ability for example to say understand
+goal directed action these cases we've
+
+ align:start position:0%
+goal directed action these cases we've
+ 
+
+ align:start position:0%
+goal directed action these cases we've
+talked a lot about or intuitive physics
+
+ align:start position:0%
+talked a lot about or intuitive physics
+ 
+
+ align:start position:0%
+talked a lot about or intuitive physics
+again cases we've talked about and it's
+
+ align:start position:0%
+again cases we've talked about and it's
+ 
+
+ align:start position:0%
+again cases we've talked about and it's
+part of our research program for the
+
+ align:start position:0%
+part of our research program for the
+ 
+
+ align:start position:0%
+part of our research program for the
+center something we'd love all of all of
+
+ align:start position:0%
+center something we'd love all of all of
+ 
+
+ align:start position:0%
+center something we'd love all of all of
+you guys if you're interested to help
+
+ align:start position:0%
+you guys if you're interested to help
+ 
+
+ align:start position:0%
+you guys if you're interested to help
+work on it's a very big problem is how
+
+ align:start position:0%
+work on it's a very big problem is how
+ 
+
+ align:start position:0%
+work on it's a very big problem is how
+do you characterize the knowledge that
+
+ align:start position:0%
+do you characterize the knowledge that
+ 
+
+ align:start position:0%
+do you characterize the knowledge that
+kids are learning over the first few
+
+ align:start position:0%
+kids are learning over the first few
+ 
+
+ align:start position:0%
+kids are learning over the first few
+years and the learning mechanisms that
+
+ align:start position:0%
+years and the learning mechanisms that
+ 
+
+ align:start position:0%
+years and the learning mechanisms that
+build it which we'd like to think of in
+
+ align:start position:0%
+build it which we'd like to think of in
+ 
+
+ align:start position:0%
+build it which we'd like to think of in
+some similar way like could we say
+
+ align:start position:0%
+some similar way like could we say
+ 
+
+ align:start position:0%
+some similar way like could we say
+there's some you know intuitive physics
+
+ align:start position:0%
+there's some you know intuitive physics
+ 
+
+ align:start position:0%
+there's some you know intuitive physics
+program and intuitive physics program
+
+ align:start position:0%
+program and intuitive physics program
+ 
+
+ align:start position:0%
+program and intuitive physics program
+learning programs that are building out
+
+ align:start position:0%
+learning programs that are building out
+ 
+
+ align:start position:0%
+learning programs that are building out
+knowledge for these kinds of problems
+
+ align:start position:0%
+knowledge for these kinds of problems
+ 
+
+ align:start position:0%
+knowledge for these kinds of problems
+and you know I we don't know how to do
+
+ align:start position:0%
+and you know I we don't know how to do
+ 
+
+ align:start position:0%
+and you know I we don't know how to do
+it but again here are some of the steps
+
+ align:start position:0%
+it but again here are some of the steps
+ 
+
+ align:start position:0%
+it but again here are some of the steps
+we've been starting to take so this is
+
+ align:start position:0%
+we've been starting to take so this is
+ 
+
+ align:start position:0%
+we've been starting to take so this is
+work that Tomer did as part of his PhD
+
+ align:start position:0%
+work that Tomer did as part of his PhD
+ 
+
+ align:start position:0%
+work that Tomer did as part of his PhD
+and it's something that he's continuing
+
+ align:start position:0%
+and it's something that he's continuing
+ 
+
+ align:start position:0%
+and it's something that he's continuing
+to do with Liz and others as as part of
+
+ align:start position:0%
+to do with Liz and others as as part of
+ 
+
+ align:start position:0%
+to do with Liz and others as as part of
+his postdoc so we're showing people
+
+ align:start position:0%
+his postdoc so we're showing people
+ 
+
+ align:start position:0%
+his postdoc so we're showing people
+again it's much like what you saw from
+
+ align:start position:0%
+again it's much like what you saw from
+ 
+
+ align:start position:0%
+again it's much like what you saw from
+me and from Laura we're really
+
+ align:start position:0%
+me and from Laura we're really
+ 
+
+ align:start position:0%
+me and from Laura we're really
+interested in learning from sparse data
+
+ align:start position:0%
+interested in learning from sparse data
+ 
+
+ align:start position:0%
+interested in learning from sparse data
+right because all because that all the
+
+ align:start position:0%
+right because all because that all the
+ 
+
+ align:start position:0%
+right because all because that all the
+data is sparse in a sense but in the lab
+
+ align:start position:0%
+data is sparse in a sense but in the lab
+ 
+
+ align:start position:0%
+data is sparse in a sense but in the lab
+you know you push things to the limit so
+
+ align:start position:0%
+you know you push things to the limit so
+ 
+
+ align:start position:0%
+you know you push things to the limit so
+you study really sparse things like
+
+ align:start position:0%
+you study really sparse things like
+ 
+
+ align:start position:0%
+you study really sparse things like
+one-shot learning of a visual concept or
+
+ align:start position:0%
+one-shot learning of a visual concept or
+ 
+
+ align:start position:0%
+one-shot learning of a visual concept or
+here this is like we've been interested
+
+ align:start position:0%
+here this is like we've been interested
+ 
+
+ align:start position:0%
+here this is like we've been interested
+in what can you learn about the laws of
+
+ align:start position:0%
+in what can you learn about the laws of
+ 
+
+ align:start position:0%
+in what can you learn about the laws of
+physics from just watching the threat
+
+ align:start position:0%
+physics from just watching the threat
+ 
+
+ align:start position:0%
+physics from just watching the threat
+for five seconds so we show people
+
+ align:start position:0%
+for five seconds so we show people
+ 
+
+ align:start position:0%
+for five seconds so we show people
+videos like this
+
+ align:start position:0%
+videos like this
+ 
+
+ align:start position:0%
+videos like this
+think of this as like you're watching
+
+ align:start position:0%
+think of this as like you're watching
+ 
+
+ align:start position:0%
+think of this as like you're watching
+hockey pucks on an air hockey table so
+
+ align:start position:0%
+hockey pucks on an air hockey table so
+ 
+
+ align:start position:0%
+hockey pucks on an air hockey table so
+it's like an overhead view of some
+
+ align:start position:0%
+it's like an overhead view of some
+ 
+
+ align:start position:0%
+it's like an overhead view of some
+things bouncing around and you can see
+
+ align:start position:0%
+things bouncing around and you can see
+ 
+
+ align:start position:0%
+things bouncing around and you can see
+that they're kind of Newtonian in some
+
+ align:start position:0%
+that they're kind of Newtonian in some
+ 
+
+ align:start position:0%
+that they're kind of Newtonian in some
+sense they bounce off of each other
+
+ align:start position:0%
+sense they bounce off of each other
+ 
+
+ align:start position:0%
+sense they bounce off of each other
+looks like there's some inertia you know
+
+ align:start position:0%
+looks like there's some inertia you know
+ 
+
+ align:start position:0%
+looks like there's some inertia you know
+inertial collisions but you might notice
+
+ align:start position:0%
+inertial collisions but you might notice
+ 
+
+ align:start position:0%
+inertial collisions but you might notice
+that there's some other interesting
+
+ align:start position:0%
+that there's some other interesting
+ 
+
+ align:start position:0%
+that there's some other interesting
+things going on that are not just F
+
+ align:start position:0%
+things going on that are not just F
+ 
+
+ align:start position:0%
+things going on that are not just F
+equals MA
+
+ align:start position:0%
+equals MA
+ 
+
+ align:start position:0%
+equals MA
+right like other interesting kinds of
+
+ align:start position:0%
+right like other interesting kinds of
+ 
+
+ align:start position:0%
+right like other interesting kinds of
+forces and I'll show you other ones
+
+ align:start position:0%
+forces and I'll show you other ones
+ 
+
+ align:start position:0%
+forces and I'll show you other ones
+Tomer made a whole awesome set of these
+
+ align:start position:0%
+Tomer made a whole awesome set of these
+ 
+
+ align:start position:0%
+Tomer made a whole awesome set of these
+movies hopefully you saw you've got some
+
+ align:start position:0%
+movies hopefully you saw you've got some
+ 
+
+ align:start position:0%
+movies hopefully you saw you've got some
+idea of what's going on there right like
+
+ align:start position:0%
+idea of what's going on there right like
+ 
+
+ align:start position:0%
+idea of what's going on there right like
+interesting forces of attraction
+
+ align:start position:0%
+interesting forces of attraction
+ 
+
+ align:start position:0%
+interesting forces of attraction
+repulsion different kinds of things so
+
+ align:start position:0%
+repulsion different kinds of things so
+ 
+
+ align:start position:0%
+repulsion different kinds of things so
+here's a each of those can be described
+
+ align:start position:0%
+here's a each of those can be described
+ 
+
+ align:start position:0%
+here's a each of those can be described
+as a program and here's a program
+
+ align:start position:0%
+as a program and here's a program
+ 
+
+ align:start position:0%
+as a program and here's a program
+generating program if you like so the
+
+ align:start position:0%
+generating program if you like so the
+ 
+
+ align:start position:0%
+generating program if you like so the
+same kind of idea where we you know just
+
+ align:start position:0%
+same kind of idea where we you know just
+ 
+
+ align:start position:0%
+same kind of idea where we you know just
+as in that the handwritten character
+
+ align:start position:0%
+as in that the handwritten character
+ 
+
+ align:start position:0%
+as in that the handwritten character
+model I showed you it's not like it's
+
+ align:start position:0%
+model I showed you it's not like it's
+ 
+
+ align:start position:0%
+model I showed you it's not like it's
+learning in a blank slate way from
+
+ align:start position:0%
+learning in a blank slate way from
+ 
+
+ align:start position:0%
+learning in a blank slate way from
+scratch it knows about objects parts and
+
+ align:start position:0%
+scratch it knows about objects parts and
+ 
+
+ align:start position:0%
+scratch it knows about objects parts and
+subparts what it has to learn is in this
+
+ align:start position:0%
+subparts what it has to learn is in this
+ 
+
+ align:start position:0%
+subparts what it has to learn is in this
+domain of Henery characters what are the
+
+ align:start position:0%
+domain of Henery characters what are the
+ 
+
+ align:start position:0%
+domain of Henery characters what are the
+parts and relations like and then for
+
+ align:start position:0%
+parts and relations like and then for
+ 
+
+ align:start position:0%
+parts and relations like and then for
+the particular new thing you're learning
+
+ align:start position:0%
+the particular new thing you're learning
+ 
+
+ align:start position:0%
+the particular new thing you're learning
+like this particular new concept water
+
+ align:start position:0%
+like this particular new concept water
+ 
+
+ align:start position:0%
+like this particular new concept water
+it's particular parts and relations so
+
+ align:start position:0%
+it's particular parts and relations so
+ 
+
+ align:start position:0%
+it's particular parts and relations so
+there's these several levels of learning
+
+ align:start position:0%
+there's these several levels of learning
+ 
+
+ align:start position:0%
+there's these several levels of learning
+where the big picture of objects and
+
+ align:start position:0%
+where the big picture of objects and
+ 
+
+ align:start position:0%
+where the big picture of objects and
+parts is not learned and then the
+
+ align:start position:0%
+parts is not learned and then the
+ 
+
+ align:start position:0%
+parts is not learned and then the
+specifics of for this domain of
+
+ align:start position:0%
+specifics of for this domain of
+ 
+
+ align:start position:0%
+specifics of for this domain of
+handwritten characters how how you know
+
+ align:start position:0%
+handwritten characters how how you know
+ 
+
+ align:start position:0%
+handwritten characters how how you know
+what the idea of what strokes look like
+
+ align:start position:0%
+what the idea of what strokes look like
+ 
+
+ align:start position:0%
+what the idea of what strokes look like
+that's learned from sort of a background
+
+ align:start position:0%
+that's learned from sort of a background
+ 
+
+ align:start position:0%
+that's learned from sort of a background
+set and then your ability to do one-shot
+
+ align:start position:0%
+set and then your ability to do one-shot
+ 
+
+ align:start position:0%
+set and then your ability to do one-shot
+learning or learning from very sparse
+
+ align:start position:0%
+learning or learning from very sparse
+ 
+
+ align:start position:0%
+learning or learning from very sparse
+data of a new concept takes all that
+
+ align:start position:0%
+data of a new concept takes all that
+ 
+
+ align:start position:0%
+data of a new concept takes all that
+prior knowledge some of which is wired
+
+ align:start position:0%
+prior knowledge some of which is wired
+ 
+
+ align:start position:0%
+prior knowledge some of which is wired
+in some of which is previously learned
+
+ align:start position:0%
+in some of which is previously learned
+ 
+
+ align:start position:0%
+in some of which is previously learned
+and brings it to bear to generate a new
+
+ align:start position:0%
+and brings it to bear to generate a new
+ 
+
+ align:start position:0%
+and brings it to bear to generate a new
+program very sparsely so you have the
+
+ align:start position:0%
+program very sparsely so you have the
+ 
+
+ align:start position:0%
+program very sparsely so you have the
+same kind of thing here we're wiring in
+
+ align:start position:0%
+same kind of thing here we're wiring in
+ 
+
+ align:start position:0%
+same kind of thing here we're wiring in
+in a sense F equals I'm a the most
+
+ align:start position:0%
+in a sense F equals I'm a the most
+ 
+
+ align:start position:0%
+in a sense F equals I'm a the most
+general laws of physics but then we're
+
+ align:start position:0%
+general laws of physics but then we're
+ 
+
+ align:start position:0%
+general laws of physics but then we're
+sand and then we're also wiring in sort
+
+ align:start position:0%
+sand and then we're also wiring in sort
+ 
+
+ align:start position:0%
+sand and then we're also wiring in sort
+of the possibility that there could be
+
+ align:start position:0%
+of the possibility that there could be
+ 
+
+ align:start position:0%
+of the possibility that there could be
+kinds of things and forces that they
+
+ align:start position:0%
+kinds of things and forces that they
+ 
+
+ align:start position:0%
+kinds of things and forces that they
+exert on each other as a you know some
+
+ align:start position:0%
+exert on each other as a you know some
+ 
+
+ align:start position:0%
+exert on each other as a you know some
+kinds of things exert other kinds of
+
+ align:start position:0%
+kinds of things exert other kinds of
+ 
+
+ align:start position:0%
+kinds of things exert other kinds of
+forces on others and that there could be
+
+ align:start position:0%
+forces on others and that there could be
+ 
+
+ align:start position:0%
+forces on others and that there could be
+latent properties things like mass and
+
+ align:start position:0%
+latent properties things like mass and
+ 
+
+ align:start position:0%
+latent properties things like mass and
+friction and then what the model is
+
+ align:start position:0%
+friction and then what the model is
+ 
+
+ align:start position:0%
+friction and then what the model is
+trying to do is basically to learn about
+
+ align:start position:0%
+trying to do is basically to learn about
+ 
+
+ align:start position:0%
+trying to do is basically to learn about
+these particular properties what's the
+
+ align:start position:0%
+these particular properties what's the
+ 
+
+ align:start position:0%
+these particular properties what's the
+mass of this kind of object what's the
+
+ align:start position:0%
+mass of this kind of object what's the
+ 
+
+ align:start position:0%
+mass of this kind of object what's the
+friction of this kind of surface which
+
+ align:start position:0%
+friction of this kind of surface which
+ 
+
+ align:start position:0%
+friction of this kind of surface which
+objects exert which kind of forces on
+
+ align:start position:0%
+objects exert which kind of forces on
+ 
+
+ align:start position:0%
+objects exert which kind of forces on
+each other or is there some something
+
+ align:start position:0%
+each other or is there some something
+ 
+
+ align:start position:0%
+each other or is there some something
+like gravity blowing everything to the
+
+ align:start position:0%
+like gravity blowing everything to the
+ 
+
+ align:start position:0%
+like gravity blowing everything to the
+left or the right or down and basic what
+
+ align:start position:0%
+left or the right or down and basic what
+ 
+
+ align:start position:0%
+left or the right or down and basic what
+this is showing here it's the same kind
+
+ align:start position:0%
+this is showing here it's the same kind
+ 
+
+ align:start position:0%
+this is showing here it's the same kind
+of thoughts you saw for me last time
+
+ align:start position:0%
+of thoughts you saw for me last time
+ 
+
+ align:start position:0%
+of thoughts you saw for me last time
+it's a plot of people versus model and
+
+ align:start position:0%
+it's a plot of people versus model and
+ 
+
+ align:start position:0%
+it's a plot of people versus model and
+we're basically on a whole
+
+ align:start position:0%
+we're basically on a whole
+ 
+
+ align:start position:0%
+we're basically on a whole
+different conditions of the sort you saw
+
+ align:start position:0%
+different conditions of the sort you saw
+ 
+
+ align:start position:0%
+different conditions of the sort you saw
+people are judging these different
+
+ align:start position:0%
+people are judging these different
+ 
+
+ align:start position:0%
+people are judging these different
+physical properties and they're making
+
+ align:start position:0%
+physical properties and they're making
+ 
+
+ align:start position:0%
+physical properties and they're making
+great a judgments of how likely it is
+
+ align:start position:0%
+great a judgments of how likely it is
+ 
+
+ align:start position:0%
+great a judgments of how likely it is
+basically to have one of these
+
+ align:start position:0%
+basically to have one of these
+ 
+
+ align:start position:0%
+basically to have one of these
+properties or another and there's the
+
+ align:start position:0%
+properties or another and there's the
+ 
+
+ align:start position:0%
+properties or another and there's the
+model on the x-axis people on the y-axis
+
+ align:start position:0%
+model on the x-axis people on the y-axis
+ 
+
+ align:start position:0%
+model on the x-axis people on the y-axis
+and what you can see is a sort of okay
+
+ align:start position:0%
+and what you can see is a sort of okay
+ 
+
+ align:start position:0%
+and what you can see is a sort of okay
+decent fit we characterized this
+
+ align:start position:0%
+decent fit we characterized this
+ 
+
+ align:start position:0%
+decent fit we characterized this
+experiment as a kind of a mixed success
+
+ align:start position:0%
+experiment as a kind of a mixed success
+ 
+
+ align:start position:0%
+experiment as a kind of a mixed success
+in the sense that I mean it's sort of
+
+ align:start position:0%
+in the sense that I mean it's sort of
+ 
+
+ align:start position:0%
+in the sense that I mean it's sort of
+shocking people can learn anything at
+
+ align:start position:0%
+shocking people can learn anything at
+ 
+
+ align:start position:0%
+shocking people can learn anything at
+all like how much could you learn about
+
+ align:start position:0%
+all like how much could you learn about
+ 
+
+ align:start position:0%
+all like how much could you learn about
+the laws of physics from five seconds of
+
+ align:start position:0%
+the laws of physics from five seconds of
+ 
+
+ align:start position:0%
+the laws of physics from five seconds of
+observation well it's also kind of
+
+ align:start position:0%
+observation well it's also kind of
+ 
+
+ align:start position:0%
+observation well it's also kind of
+shocking that Newton could learn about
+
+ align:start position:0%
+shocking that Newton could learn about
+ 
+
+ align:start position:0%
+shocking that Newton could learn about
+the laws of physics by just looking at
+
+ align:start position:0%
+the laws of physics by just looking at
+ 
+
+ align:start position:0%
+the laws of physics by just looking at
+you know relative you know in the
+
+ align:start position:0%
+you know relative you know in the
+ 
+
+ align:start position:0%
+you know relative you know in the
+history of the universe about five
+
+ align:start position:0%
+history of the universe about five
+ 
+
+ align:start position:0%
+history of the universe about five
+seconds or less worth of data that
+
+ align:start position:0%
+seconds or less worth of data that
+ 
+
+ align:start position:0%
+seconds or less worth of data that
+people had collected for the planets
+
+ align:start position:0%
+people had collected for the planets
+ 
+
+ align:start position:0%
+people had collected for the planets
+going around so you know that's it is
+
+ align:start position:0%
+going around so you know that's it is
+ 
+
+ align:start position:0%
+going around so you know that's it is
+the nature of both science and intuitive
+
+ align:start position:0%
+the nature of both science and intuitive
+ 
+
+ align:start position:0%
+the nature of both science and intuitive
+theory building that you only you know
+
+ align:start position:0%
+theory building that you only you know
+ 
+
+ align:start position:0%
+theory building that you only you know
+you can get so much from so little but
+
+ align:start position:0%
+you can get so much from so little but
+ 
+
+ align:start position:0%
+you can get so much from so little but
+people are not Newton here they're just
+
+ align:start position:0%
+people are not Newton here they're just
+ 
+
+ align:start position:0%
+people are not Newton here they're just
+using intuition they're making quick
+
+ align:start position:0%
+using intuition they're making quick
+ 
+
+ align:start position:0%
+using intuition they're making quick
+responses and they're okay you know
+
+ align:start position:0%
+responses and they're okay you know
+ 
+
+ align:start position:0%
+responses and they're okay you know
+there's a correlation but it's not
+
+ align:start position:0%
+there's a correlation but it's not
+ 
+
+ align:start position:0%
+there's a correlation but it's not
+perfect by any means one of the things
+
+ align:start position:0%
+perfect by any means one of the things
+ 
+
+ align:start position:0%
+perfect by any means one of the things
+that we're working on right now is
+
+ align:start position:0%
+that we're working on right now is
+ 
+
+ align:start position:0%
+that we're working on right now is
+looking at say what happens if you can
+
+ align:start position:0%
+looking at say what happens if you can
+ 
+
+ align:start position:0%
+looking at say what happens if you can
+unlike say Newton go in and actually
+
+ align:start position:0%
+unlike say Newton go in and actually
+ 
+
+ align:start position:0%
+unlike say Newton go in and actually
+intervene and push these planets around
+
+ align:start position:0%
+intervene and push these planets around
+ 
+
+ align:start position:0%
+intervene and push these planets around
+hopefully you'll you'll do better but
+
+ align:start position:0%
+hopefully you'll you'll do better but
+ 
+
+ align:start position:0%
+hopefully you'll you'll do better but
+stay tuned for that the basic thing here
+
+ align:start position:0%
+stay tuned for that the basic thing here
+ 
+
+ align:start position:0%
+stay tuned for that the basic thing here
+though is that people can learn
+
+ align:start position:0%
+though is that people can learn
+ 
+
+ align:start position:0%
+though is that people can learn
+something from this but the way our
+
+ align:start position:0%
+something from this but the way our
+ 
+
+ align:start position:0%
+something from this but the way our
+model works is it's it's not very
+
+ align:start position:0%
+model works is it's it's not very
+ 
+
+ align:start position:0%
+model works is it's it's not very
+satisfying for us as a view of a kind of
+
+ align:start position:0%
+satisfying for us as a view of a kind of
+ 
+
+ align:start position:0%
+satisfying for us as a view of a kind of
+program induction or program
+
+ align:start position:0%
+program induction or program
+ 
+
+ align:start position:0%
+program induction or program
+construction because it we think it just
+
+ align:start position:0%
+construction because it we think it just
+ 
+
+ align:start position:0%
+construction because it we think it just
+knows too much it has basically all the
+
+ align:start position:0%
+knows too much it has basically all the
+ 
+
+ align:start position:0%
+knows too much it has basically all the
+form of the program and it's estimating
+
+ align:start position:0%
+form of the program and it's estimating
+ 
+
+ align:start position:0%
+form of the program and it's estimating
+some parameters it's like you know one
+
+ align:start position:0%
+some parameters it's like you know one
+ 
+
+ align:start position:0%
+some parameters it's like you know one
+of the things you do as a hacker or as a
+
+ align:start position:0%
+of the things you do as a hacker or as a
+ 
+
+ align:start position:0%
+of the things you do as a hacker or as a
+coder is you have your code and you tune
+
+ align:start position:0%
+coder is you have your code and you tune
+ 
+
+ align:start position:0%
+coder is you have your code and you tune
+some parameters or you try to decide if
+
+ align:start position:0%
+some parameters or you try to decide if
+ 
+
+ align:start position:0%
+some parameters or you try to decide if
+this function is the right one to use or
+
+ align:start position:0%
+this function is the right one to use or
+ 
+
+ align:start position:0%
+this function is the right one to use or
+that one but and this is doing that but
+
+ align:start position:0%
+that one but and this is doing that but
+ 
+
+ align:start position:0%
+that one but and this is doing that but
+nowhere is this like actually writing
+
+ align:start position:0%
+nowhere is this like actually writing
+ 
+
+ align:start position:0%
+nowhere is this like actually writing
+new code in a sense and that's just a
+
+ align:start position:0%
+new code in a sense and that's just a
+ 
+
+ align:start position:0%
+new code in a sense and that's just a
+really hard problem that I wanted to
+
+ align:start position:0%
+really hard problem that I wanted to
+ 
+
+ align:start position:0%
+really hard problem that I wanted to
+mostly leave you with and set up going
+
+ align:start position:0%
+mostly leave you with and set up going
+ 
+
+ align:start position:0%
+mostly leave you with and set up going
+you know what we're gonna do for the
+
+ align:start position:0%
+you know what we're gonna do for the
+ 
+
+ align:start position:0%
+you know what we're gonna do for the
+rest of the afternoon like if you wanted
+
+ align:start position:0%
+rest of the afternoon like if you wanted
+ 
+
+ align:start position:0%
+rest of the afternoon like if you wanted
+to not just maybe sort of tune the
+
+ align:start position:0%
+to not just maybe sort of tune the
+ 
+
+ align:start position:0%
+to not just maybe sort of tune the
+parameters and figure out the strength
+
+ align:start position:0%
+parameters and figure out the strength
+ 
+
+ align:start position:0%
+parameters and figure out the strength
+or existence of different forces but
+
+ align:start position:0%
+or existence of different forces but
+ 
+
+ align:start position:0%
+or existence of different forces but
+actually like write the form of laws how
+
+ align:start position:0%
+actually like write the form of laws how
+ 
+
+ align:start position:0%
+actually like write the form of laws how
+do you do this what's the right
+
+ align:start position:0%
+do you do this what's the right
+ 
+
+ align:start position:0%
+do you do this what's the right
+hypothesis phase so you need programs
+
+ align:start position:0%
+hypothesis phase so you need programs
+ 
+
+ align:start position:0%
+hypothesis phase so you need programs
+that that don't just generate programs
+
+ align:start position:0%
+that that don't just generate programs
+ 
+
+ align:start position:0%
+that that don't just generate programs
+would actually write the code of them in
+
+ align:start position:0%
+would actually write the code of them in
+ 
+
+ align:start position:0%
+would actually write the code of them in
+a sense and what's an effective
+
+ align:start position:0%
+a sense and what's an effective
+ 
+
+ align:start position:0%
+a sense and what's an effective
+algorithm for searching the space of
+
+ align:start position:0%
+algorithm for searching the space of
+ 
+
+ align:start position:0%
+algorithm for searching the space of
+these theories it's very very difficult
+
+ align:start position:0%
+these theories it's very very difficult
+ 
+
+ align:start position:0%
+these theories it's very very difficult
+I think Thoma are you gonna show this
+
+ align:start position:0%
+I think Thoma are you gonna show this
+ 
+
+ align:start position:0%
+I think Thoma are you gonna show this
+figure at all yeah so mostly I'll leave
+
+ align:start position:0%
+figure at all yeah so mostly I'll leave
+ 
+
+ align:start position:0%
+figure at all yeah so mostly I'll leave
+this hummer but you know it's it's it's
+
+ align:start position:0%
+this hummer but you know it's it's it's
+ 
+
+ align:start position:0%
+this hummer but you know it's it's it's
+there's a very striking contrast
+
+ align:start position:0%
+there's a very striking contrast
+ 
+
+ align:start position:0%
+there's a very striking contrast
+between the nice optimization landscapes
+
+ align:start position:0%
+between the nice optimization landscapes
+ 
+
+ align:start position:0%
+between the nice optimization landscapes
+for say neural networks or any most any
+
+ align:start position:0%
+for say neural networks or any most any
+ 
+
+ align:start position:0%
+for say neural networks or any most any
+standard scalable machine learning
+
+ align:start position:0%
+standard scalable machine learning
+ 
+
+ align:start position:0%
+standard scalable machine learning
+algorithm whether it's trained by
+
+ align:start position:0%
+algorithm whether it's trained by
+ 
+
+ align:start position:0%
+algorithm whether it's trained by
+gradient descent or convex optimization
+
+ align:start position:0%
+gradient descent or convex optimization
+ 
+
+ align:start position:0%
+gradient descent or convex optimization
+and the kinds of landscapes for
+
+ align:start position:0%
+and the kinds of landscapes for
+ 
+
+ align:start position:0%
+and the kinds of landscapes for
+optimization and search that you have if
+
+ align:start position:0%
+optimization and search that you have if
+ 
+
+ align:start position:0%
+optimization and search that you have if
+you're trying to generate a space of
+
+ align:start position:0%
+you're trying to generate a space of
+ 
+
+ align:start position:0%
+you're trying to generate a space of
+programs if you want to see our early
+
+ align:start position:0%
+programs if you want to see our early
+ 
+
+ align:start position:0%
+programs if you want to see our early
+attempts to try to do something like
+
+ align:start position:0%
+attempts to try to do something like
+ 
+
+ align:start position:0%
+attempts to try to do something like
+learning the form of a program look for
+
+ align:start position:0%
+learning the form of a program look for
+ 
+
+ align:start position:0%
+learning the form of a program look for
+example at stuff that Charles Kemp did
+
+ align:start position:0%
+example at stuff that Charles Kemp did
+ 
+
+ align:start position:0%
+example at stuff that Charles Kemp did
+part of his thesis that was published in
+
+ align:start position:0%
+part of his thesis that was published in
+ 
+
+ align:start position:0%
+part of his thesis that was published in
+PNAS a few years ago where he tried to
+
+ align:start position:0%
+PNAS a few years ago where he tried to
+ 
+
+ align:start position:0%
+PNAS a few years ago where he tried to
+generate or basically have think of um
+
+ align:start position:0%
+generate or basically have think of um
+ 
+
+ align:start position:0%
+generate or basically have think of um
+generative grammars for graphs think
+
+ align:start position:0%
+generative grammars for graphs think
+ 
+
+ align:start position:0%
+generative grammars for graphs think
+about like the problem so Laura
+
+ align:start position:0%
+about like the problem so Laura
+ 
+
+ align:start position:0%
+about like the problem so Laura
+mentioned you know Darwin how to Darwin
+
+ align:start position:0%
+mentioned you know Darwin how to Darwin
+ 
+
+ align:start position:0%
+mentioned you know Darwin how to Darwin
+figure out about something about
+
+ align:start position:0%
+figure out about something about
+ 
+
+ align:start position:0%
+figure out about something about
+evolution without understanding any of
+
+ align:start position:0%
+evolution without understanding any of
+ 
+
+ align:start position:0%
+evolution without understanding any of
+the mechanisms or the more basic problem
+
+ align:start position:0%
+the mechanisms or the more basic problem
+ 
+
+ align:start position:0%
+the mechanisms or the more basic problem
+of figuring out that that species should
+
+ align:start position:0%
+of figuring out that that species should
+ 
+
+ align:start position:0%
+of figuring out that that species should
+be generated by some kind of branching
+
+ align:start position:0%
+be generated by some kind of branching
+ 
+
+ align:start position:0%
+be generated by some kind of branching
+tree process versus other kinds of
+
+ align:start position:0%
+tree process versus other kinds of
+ 
+
+ align:start position:0%
+tree process versus other kinds of
+remember in last last time when I talked
+
+ align:start position:0%
+remember in last last time when I talked
+ 
+
+ align:start position:0%
+remember in last last time when I talked
+I talked about various kinds of
+
+ align:start position:0%
+I talked about various kinds of
+ 
+
+ align:start position:0%
+I talked about various kinds of
+structured probabilistic models tree
+
+ align:start position:0%
+structured probabilistic models tree
+ 
+
+ align:start position:0%
+structured probabilistic models tree
+structures or spaces or chains for
+
+ align:start position:0%
+structures or spaces or chains for
+ 
+
+ align:start position:0%
+structures or spaces or chains for
+threshold reasoning so Charles did some
+
+ align:start position:0%
+threshold reasoning so Charles did some
+ 
+
+ align:start position:0%
+threshold reasoning so Charles did some
+really nice work basically trying to use
+
+ align:start position:0%
+really nice work basically trying to use
+ 
+
+ align:start position:0%
+really nice work basically trying to use
+the idea of a program for generating
+
+ align:start position:0%
+the idea of a program for generating
+ 
+
+ align:start position:0%
+the idea of a program for generating
+graphical models like a there's a graph
+
+ align:start position:0%
+graphical models like a there's a graph
+ 
+
+ align:start position:0%
+graphical models like a there's a graph
+a grammar that grows out graphs and he
+
+ align:start position:0%
+a grammar that grows out graphs and he
+ 
+
+ align:start position:0%
+a grammar that grows out graphs and he
+showed how you could take data in the
+
+ align:start position:0%
+showed how you could take data in the
+ 
+
+ align:start position:0%
+showed how you could take data in the
+drawn from different domains like say
+
+ align:start position:0%
+drawn from different domains like say
+ 
+
+ align:start position:0%
+drawn from different domains like say
+those datasets you saw before of animals
+
+ align:start position:0%
+those datasets you saw before of animals
+ 
+
+ align:start position:0%
+those datasets you saw before of animals
+and their properties we spend you know
+
+ align:start position:0%
+and their properties we spend you know
+ 
+
+ align:start position:0%
+and their properties we spend you know
+an hour on that last time on so charles
+
+ align:start position:0%
+an hour on that last time on so charles
+ 
+
+ align:start position:0%
+an hour on that last time on so charles
+showed how you could induce not only a
+
+ align:start position:0%
+showed how you could induce not only a
+ 
+
+ align:start position:0%
+showed how you could induce not only a
+tree structure but the higher level fact
+
+ align:start position:0%
+tree structure but the higher level fact
+ 
+
+ align:start position:0%
+tree structure but the higher level fact
+that there is a tree structure namely a
+
+ align:start position:0%
+that there is a tree structure namely a
+ 
+
+ align:start position:0%
+that there is a tree structure namely a
+rule that generates trees being the
+
+ align:start position:0%
+rule that generates trees being the
+ 
+
+ align:start position:0%
+rule that generates trees being the
+right abstract principle to say give you
+
+ align:start position:0%
+right abstract principle to say give you
+ 
+
+ align:start position:0%
+right abstract principle to say give you
+the structure of species in biology
+
+ align:start position:0%
+the structure of species in biology
+ 
+
+ align:start position:0%
+the structure of species in biology
+whereas other rules like you know would
+
+ align:start position:0%
+whereas other rules like you know would
+ 
+
+ align:start position:0%
+whereas other rules like you know would
+generate other kinds of structures so
+
+ align:start position:0%
+generate other kinds of structures so
+ 
+
+ align:start position:0%
+generate other kinds of structures so
+for example he took similar data
+
+ align:start position:0%
+for example he took similar data
+ 
+
+ align:start position:0%
+for example he took similar data
+matrices for how Supreme Court judges
+
+ align:start position:0%
+matrices for how Supreme Court judges
+ 
+
+ align:start position:0%
+matrices for how Supreme Court judges
+voted and was able to infer a left-right
+
+ align:start position:0%
+voted and was able to infer a left-right
+ 
+
+ align:start position:0%
+voted and was able to infer a left-right
+liberal-conservative spectrum or data
+
+ align:start position:0%
+liberal-conservative spectrum or data
+ 
+
+ align:start position:0%
+liberal-conservative spectrum or data
+from the the proximities between cities
+
+ align:start position:0%
+from the the proximities between cities
+ 
+
+ align:start position:0%
+from the the proximities between cities
+and figure out a kind of sort of
+
+ align:start position:0%
+and figure out a kind of sort of
+ 
+
+ align:start position:0%
+and figure out a kind of sort of
+cylinder like a latitude and longitude
+
+ align:start position:0%
+cylinder like a latitude and longitude
+ 
+
+ align:start position:0%
+cylinder like a latitude and longitude
+map of of the world just from the
+
+ align:start position:0%
+map of of the world just from the
+ 
+
+ align:start position:0%
+map of of the world just from the
+distances between cities or take faces
+
+ align:start position:0%
+distances between cities or take faces
+ 
+
+ align:start position:0%
+distances between cities or take faces
+and figure out a low dimensional space
+
+ align:start position:0%
+and figure out a low dimensional space
+ 
+
+ align:start position:0%
+and figure out a low dimensional space
+as the right way to think about faces so
+
+ align:start position:0%
+as the right way to think about faces so
+ 
+
+ align:start position:0%
+as the right way to think about faces so
+in some sense this was this was really
+
+ align:start position:0%
+in some sense this was this was really
+ 
+
+ align:start position:0%
+in some sense this was this was really
+cool we were really excited oh hey we
+
+ align:start position:0%
+cool we were really excited oh hey we
+ 
+
+ align:start position:0%
+cool we were really excited oh hey we
+have a way to learn these simple
+
+ align:start position:0%
+have a way to learn these simple
+ 
+
+ align:start position:0%
+have a way to learn these simple
+programs which generate structures
+
+ align:start position:0%
+programs which generate structures
+ 
+
+ align:start position:0%
+programs which generate structures
+which themselves generate the data it's
+
+ align:start position:0%
+which themselves generate the data it's
+ 
+
+ align:start position:0%
+which themselves generate the data it's
+where like that idea of hierarchical
+
+ align:start position:0%
+where like that idea of hierarchical
+ 
+
+ align:start position:0%
+where like that idea of hierarchical
+Bayes meets up with this idea of program
+
+ align:start position:0%
+Bayes meets up with this idea of program
+ 
+
+ align:start position:0%
+Bayes meets up with this idea of program
+induction or learning learning a program
+
+ align:start position:0%
+induction or learning learning a program
+ 
+
+ align:start position:0%
+induction or learning learning a program
+um and it even captured okay this is
+
+ align:start position:0%
+um and it even captured okay this is
+ 
+
+ align:start position:0%
+um and it even captured okay this is
+really the last slide I'll show it
+
+ align:start position:0%
+really the last slide I'll show it
+ 
+
+ align:start position:0%
+really the last slide I'll show it
+really got it even captured something
+
+ align:start position:0%
+really got it even captured something
+ 
+
+ align:start position:0%
+really got it even captured something
+which captured all of our imaginations
+
+ align:start position:0%
+which captured all of our imaginations
+ 
+
+ align:start position:0%
+which captured all of our imaginations
+we use this phrase the blessing of
+
+ align:start position:0%
+we use this phrase the blessing of
+ 
+
+ align:start position:0%
+we use this phrase the blessing of
+abstraction to tie back into one more
+
+ align:start position:0%
+abstraction to tie back into one more
+ 
+
+ align:start position:0%
+abstraction to tie back into one more
+theme of Laura's right which is this
+
+ align:start position:0%
+theme of Laura's right which is this
+ 
+
+ align:start position:0%
+theme of Laura's right which is this
+idea that in when kids are building up
+
+ align:start position:0%
+idea that in when kids are building up
+ 
+
+ align:start position:0%
+idea that in when kids are building up
+abstract concepts there's a sense in
+
+ align:start position:0%
+abstract concepts there's a sense in
+ 
+
+ align:start position:0%
+abstract concepts there's a sense in
+which unlike safes not a lot of maybe
+
+ align:start position:0%
+which unlike safes not a lot of maybe
+ 
+
+ align:start position:0%
+which unlike safes not a lot of maybe
+traditional machine learning methods or
+
+ align:start position:0%
+traditional machine learning methods or
+ 
+
+ align:start position:0%
+traditional machine learning methods or
+a lot of traditional ideas in philosophy
+
+ align:start position:0%
+a lot of traditional ideas in philosophy
+ 
+
+ align:start position:0%
+a lot of traditional ideas in philosophy
+about the origins of abstract knowledge
+
+ align:start position:0%
+about the origins of abstract knowledge
+ 
+
+ align:start position:0%
+about the origins of abstract knowledge
+it's not like you just get the concrete
+
+ align:start position:0%
+it's not like you just get the concrete
+ 
+
+ align:start position:0%
+it's not like you just get the concrete
+stuff first and layer on the more
+
+ align:start position:0%
+stuff first and layer on the more
+ 
+
+ align:start position:0%
+stuff first and layer on the more
+abstract stuff there's a sense often in
+
+ align:start position:0%
+abstract stuff there's a sense often in
+ 
+
+ align:start position:0%
+abstract stuff there's a sense often in
+children's learning as in science in
+
+ align:start position:0%
+children's learning as in science in
+ 
+
+ align:start position:0%
+children's learning as in science in
+which sort of the big picture comes in
+
+ align:start position:0%
+which sort of the big picture comes in
+ 
+
+ align:start position:0%
+which sort of the big picture comes in
+first then the abstract idea comes there
+
+ align:start position:0%
+first then the abstract idea comes there
+ 
+
+ align:start position:0%
+first then the abstract idea comes there
+and then you fill in the details so for
+
+ align:start position:0%
+and then you fill in the details so for
+ 
+
+ align:start position:0%
+and then you fill in the details so for
+example you know Darwin figured out in
+
+ align:start position:0%
+example you know Darwin figured out in
+ 
+
+ align:start position:0%
+example you know Darwin figured out in
+some sense the big picture he figured
+
+ align:start position:0%
+some sense the big picture he figured
+ 
+
+ align:start position:0%
+some sense the big picture he figured
+out the idea that there was some kind of
+
+ align:start position:0%
+out the idea that there was some kind of
+ 
+
+ align:start position:0%
+out the idea that there was some kind of
+branching process that generated species
+
+ align:start position:0%
+branching process that generated species
+ 
+
+ align:start position:0%
+branching process that generated species
+it was random not a nice perfect
+
+ align:start position:0%
+it was random not a nice perfect
+ 
+
+ align:start position:0%
+it was random not a nice perfect
+Linnaean seven-layer hierarchy but some
+
+ align:start position:0%
+Linnaean seven-layer hierarchy but some
+ 
+
+ align:start position:0%
+Linnaean seven-layer hierarchy but some
+kind of random branching process he
+
+ align:start position:0%
+kind of random branching process he
+ 
+
+ align:start position:0%
+kind of random branching process he
+didn't know what the mechanisms were
+
+ align:start position:0%
+didn't know what the mechanisms were
+ 
+
+ align:start position:0%
+didn't know what the mechanisms were
+that gave rise to it and similarly
+
+ align:start position:0%
+that gave rise to it and similarly
+ 
+
+ align:start position:0%
+that gave rise to it and similarly
+Newton right figured out something about
+
+ align:start position:0%
+Newton right figured out something about
+ 
+
+ align:start position:0%
+Newton right figured out something about
+the law of gravitation and everything
+
+ align:start position:0%
+the law of gravitation and everything
+ 
+
+ align:start position:0%
+the law of gravitation and everything
+else in his laws though he didn't know
+
+ align:start position:0%
+else in his laws though he didn't know
+ 
+
+ align:start position:0%
+else in his laws though he didn't know
+the mechanisms that gave rise to gravity
+
+ align:start position:0%
+the mechanisms that gave rise to gravity
+ 
+
+ align:start position:0%
+the mechanisms that gave rise to gravity
+and he didn't even know G he didn't even
+
+ align:start position:0%
+and he didn't even know G he didn't even
+ 
+
+ align:start position:0%
+and he didn't even know G he didn't even
+know the value of the gravitational
+
+ align:start position:0%
+know the value of the gravitational
+ 
+
+ align:start position:0%
+know the value of the gravitational
+constant that couldn't be estimated for
+
+ align:start position:0%
+constant that couldn't be estimated for
+ 
+
+ align:start position:0%
+constant that couldn't be estimated for
+a hundred years later but somehow he was
+
+ align:start position:0%
+a hundred years later but somehow he was
+ 
+
+ align:start position:0%
+a hundred years later but somehow he was
+able to get the abstract form and these
+
+ align:start position:0%
+able to get the abstract form and these
+ 
+
+ align:start position:0%
+able to get the abstract form and these
+nice things that Charles Kemp did were
+
+ align:start position:0%
+nice things that Charles Kemp did were
+ 
+
+ align:start position:0%
+nice things that Charles Kemp did were
+also able to do that so for example from
+
+ align:start position:0%
+also able to do that so for example from
+ 
+
+ align:start position:0%
+also able to do that so for example from
+very little data to figure out that
+
+ align:start position:0%
+very little data to figure out that
+ 
+
+ align:start position:0%
+very little data to figure out that
+animals should be generated by some kind
+
+ align:start position:0%
+animals should be generated by some kind
+ 
+
+ align:start position:0%
+animals should be generated by some kind
+of a tree structure as opposed to say
+
+ align:start position:0%
+of a tree structure as opposed to say
+ 
+
+ align:start position:0%
+of a tree structure as opposed to say
+the simpler model of just a bunch of
+
+ align:start position:0%
+the simpler model of just a bunch of
+ 
+
+ align:start position:0%
+the simpler model of just a bunch of
+flat clusters the the model was able to
+
+ align:start position:0%
+flat clusters the the model was able to
+ 
+
+ align:start position:0%
+flat clusters the the model was able to
+figure that out over here on the right
+
+ align:start position:0%
+figure that out over here on the right
+ 
+
+ align:start position:0%
+figure that out over here on the right
+from just a small fraction of the data
+
+ align:start position:0%
+from just a small fraction of the data
+ 
+
+ align:start position:0%
+from just a small fraction of the data
+and then with all the rest of the data
+
+ align:start position:0%
+and then with all the rest of the data
+ 
+
+ align:start position:0%
+and then with all the rest of the data
+was able to figure out the right tree in
+
+ align:start position:0%
+was able to figure out the right tree in
+ 
+
+ align:start position:0%
+was able to figure out the right tree in
+a sense and we called this the blessing
+
+ align:start position:0%
+a sense and we called this the blessing
+ 
+
+ align:start position:0%
+a sense and we called this the blessing
+of abstraction this idea that you could
+
+ align:start position:0%
+of abstraction this idea that you could
+ 
+
+ align:start position:0%
+of abstraction this idea that you could
+that often in these hierarchical program
+
+ align:start position:0%
+that often in these hierarchical program
+ 
+
+ align:start position:0%
+that often in these hierarchical program
+learning programs you could get the
+
+ align:start position:0%
+learning programs you could get the
+ 
+
+ align:start position:0%
+learning programs you could get the
+high-level idea before you got the
+
+ align:start position:0%
+high-level idea before you got the
+ 
+
+ align:start position:0%
+high-level idea before you got the
+lower-level idea and then fill in the
+
+ align:start position:0%
+lower-level idea and then fill in the
+ 
+
+ align:start position:0%
+lower-level idea and then fill in the
+details and there's at least I still
+
+ align:start position:0%
+details and there's at least I still
+ 
+
+ align:start position:0%
+details and there's at least I still
+think there's something fundamentally
+
+ align:start position:0%
+think there's something fundamentally
+ 
+
+ align:start position:0%
+think there's something fundamentally
+right about this idea of children's
+
+ align:start position:0%
+right about this idea of children's
+ 
+
+ align:start position:0%
+right about this idea of children's
+learning and that in both
+
+ align:start position:0%
+learning and that in both
+ 
+
+ align:start position:0%
+learning and that in both
+representationally and mechanistically
+
+ align:start position:0%
+representationally and mechanistically
+ 
+
+ align:start position:0%
+representationally and mechanistically
+and that this dynamics of sometimes
+
+ align:start position:0%
+and that this dynamics of sometimes
+ 
+
+ align:start position:0%
+and that this dynamics of sometimes
+getting the big picture first and using
+
+ align:start position:0%
+getting the big picture first and using
+ 
+
+ align:start position:0%
+getting the big picture first and using
+that as a constraint to fill in the
+
+ align:start position:0%
+that as a constraint to fill in the
+ 
+
+ align:start position:0%
+that as a constraint to fill in the
+details is fundamentally right but
+
+ align:start position:0%
+details is fundamentally right but
+ 
+
+ align:start position:0%
+details is fundamentally right but
+actually understanding how this
+
+ align:start position:0%
+actually understanding how this
+ 
+
+ align:start position:0%
+actually understanding how this
+you know either algorithmically how to
+
+ align:start position:0%
+you know either algorithmically how to
+ 
+
+ align:start position:0%
+you know either algorithmically how to
+search the space of programs for
+
+ align:start position:0%
+search the space of programs for
+ 
+
+ align:start position:0%
+search the space of programs for
+anything that looks like an intuitive
+
+ align:start position:0%
+anything that looks like an intuitive
+ 
+
+ align:start position:0%
+anything that looks like an intuitive
+causal theory of physics and relate that
+
+ align:start position:0%
+causal theory of physics and relate that
+ 
+
+ align:start position:0%
+causal theory of physics and relate that
+to the dynamics of how children actually
+
+ align:start position:0%
+to the dynamics of how children actually
+ 
+
+ align:start position:0%
+to the dynamics of how children actually
+learn that's the big open question that
+
+ align:start position:0%
+learn that's the big open question that
+ 
+
+ align:start position:0%
+learn that's the big open question that
+I will now hand it over to our our other
+
+ align:start position:0%
+I will now hand it over to our our other
+ 
+
+ align:start position:0%
+I will now hand it over to our our other
+speakers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/zptyZRDiLsQ.txt b/zptyZRDiLsQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dc425c41abb441d226b8e8562bce7150cb5f81fe
--- /dev/null
+++ b/zptyZRDiLsQ.txt
@@ -0,0 +1,835 @@
+align:start position:0%
+ 
+So I developed uh the MOO visualizing
+
+ align:start position:0%
+So I developed uh the MOO visualizing
+ 
+
+ align:start position:0%
+So I developed uh the MOO visualizing
+Japan uh which is uh MITx Harvard X
+
+ align:start position:0%
+Japan uh which is uh MITx Harvard X
+ 
+
+ align:start position:0%
+Japan uh which is uh MITx Harvard X
+joint project with John Daer of MIT Andy
+
+ align:start position:0%
+joint project with John Daer of MIT Andy
+ 
+
+ align:start position:0%
+joint project with John Daer of MIT Andy
+Gordon of Harvard and also Jennifer
+
+ align:start position:0%
+Gordon of Harvard and also Jennifer
+ 
+
+ align:start position:0%
+Gordon of Harvard and also Jennifer
+Weisenfeld of Duke. I incorporated the
+
+ align:start position:0%
+Weisenfeld of Duke. I incorporated the
+ 
+
+ align:start position:0%
+Weisenfeld of Duke. I incorporated the
+MOO material uh into my residential
+
+ align:start position:0%
+MOO material uh into my residential
+ 
+
+ align:start position:0%
+MOO material uh into my residential
+class in 2014 and it changed everything.
+
+ align:start position:0%
+class in 2014 and it changed everything.
+ 
+
+ align:start position:0%
+class in 2014 and it changed everything.
+It changed literally everything and I
+
+ align:start position:0%
+It changed literally everything and I
+ 
+
+ align:start position:0%
+It changed literally everything and I
+continued to to use it right up until my
+
+ align:start position:0%
+continued to to use it right up until my
+ 
+
+ align:start position:0%
+continued to to use it right up until my
+last offering which was fall of 2016.
+
+ align:start position:0%
+last offering which was fall of 2016.
+ 
+
+ align:start position:0%
+last offering which was fall of 2016.
+Uh before 2014 it was a very traditional
+
+ align:start position:0%
+Uh before 2014 it was a very traditional
+ 
+
+ align:start position:0%
+Uh before 2014 it was a very traditional
+class with lectures, powerpoints and
+
+ align:start position:0%
+class with lectures, powerpoints and
+ 
+
+ align:start position:0%
+class with lectures, powerpoints and
+little bit of student discussion.
+
+ align:start position:0%
+little bit of student discussion.
+ 
+
+ align:start position:0%
+little bit of student discussion.
+When I incorporated the MOO material in
+
+ align:start position:0%
+When I incorporated the MOO material in
+ 
+
+ align:start position:0%
+When I incorporated the MOO material in
+2014,
+
+ align:start position:0%
+2014,
+ 
+
+ align:start position:0%
+2014,
+um I didn't anticipate any major
+
+ align:start position:0%
+um I didn't anticipate any major
+ 
+
+ align:start position:0%
+um I didn't anticipate any major
+changes. I simply said, why don't you
+
+ align:start position:0%
+changes. I simply said, why don't you
+ 
+
+ align:start position:0%
+changes. I simply said, why don't you
+look at these video lectures we just
+
+ align:start position:0%
+look at these video lectures we just
+ 
+
+ align:start position:0%
+look at these video lectures we just
+produced and see what you think think
+
+ align:start position:0%
+produced and see what you think think
+ 
+
+ align:start position:0%
+produced and see what you think think
+about them?
+
+ align:start position:0%
+about them?
+ 
+
+ align:start position:0%
+about them?
+Uh and what I realized right away was
+
+ align:start position:0%
+Uh and what I realized right away was
+ 
+
+ align:start position:0%
+Uh and what I realized right away was
+that students would come into class and
+
+ align:start position:0%
+that students would come into class and
+ 
+
+ align:start position:0%
+that students would come into class and
+they would have a lot of knowledge which
+
+ align:start position:0%
+they would have a lot of knowledge which
+ 
+
+ align:start position:0%
+they would have a lot of knowledge which
+was not the case before. So I would ask
+
+ align:start position:0%
+was not the case before. So I would ask
+ 
+
+ align:start position:0%
+was not the case before. So I would ask
+you know so when did Perry come to
+
+ align:start position:0%
+you know so when did Perry come to
+ 
+
+ align:start position:0%
+you know so when did Perry come to
+Japan? 1853. Okay. When did major era
+
+ align:start position:0%
+Japan? 1853. Okay. When did major era
+ 
+
+ align:start position:0%
+Japan? 1853. Okay. When did major era
+begin? 1868. Why did it begin? Blah
+
+ align:start position:0%
+begin? 1868. Why did it begin? Blah
+ 
+
+ align:start position:0%
+begin? 1868. Why did it begin? Blah
+blah. So my goodness. uh you know I had
+
+ align:start position:0%
+blah. So my goodness. uh you know I had
+ 
+
+ align:start position:0%
+blah. So my goodness. uh you know I had
+a whole set of powerpoints which I had
+
+ align:start position:0%
+a whole set of powerpoints which I had
+ 
+
+ align:start position:0%
+a whole set of powerpoints which I had
+created from years of teaching. I did
+
+ align:start position:0%
+created from years of teaching. I did
+ 
+
+ align:start position:0%
+created from years of teaching. I did
+not show a single PowerPoint. I for uh
+
+ align:start position:0%
+not show a single PowerPoint. I for uh
+ 
+
+ align:start position:0%
+not show a single PowerPoint. I for uh
+70 minutes I just asked them questions
+
+ align:start position:0%
+70 minutes I just asked them questions
+ 
+
+ align:start position:0%
+70 minutes I just asked them questions
+just to see if I can find something that
+
+ align:start position:0%
+just to see if I can find something that
+ 
+
+ align:start position:0%
+just to see if I can find something that
+they didn't know. They knew the whole
+
+ align:start position:0%
+they didn't know. They knew the whole
+ 
+
+ align:start position:0%
+they didn't know. They knew the whole
+thing and I said gee this is uh this is
+
+ align:start position:0%
+thing and I said gee this is uh this is
+ 
+
+ align:start position:0%
+thing and I said gee this is uh this is
+different.
+
+ align:start position:0%
+different.
+ 
+
+ align:start position:0%
+different.
+And without realizing it, without I I
+
+ align:start position:0%
+And without realizing it, without I I
+ 
+
+ align:start position:0%
+And without realizing it, without I I
+didn't even know what a flip class was.
+
+ align:start position:0%
+didn't even know what a flip class was.
+ 
+
+ align:start position:0%
+didn't even know what a flip class was.
+I just did a flip class. I did not
+
+ align:start position:0%
+I just did a flip class. I did not
+ 
+
+ align:start position:0%
+I just did a flip class. I did not
+lecture for a single minute. It was just
+
+ align:start position:0%
+lecture for a single minute. It was just
+ 
+
+ align:start position:0%
+lecture for a single minute. It was just
+question answer discussion, you know,
+
+ align:start position:0%
+question answer discussion, you know,
+ 
+
+ align:start position:0%
+question answer discussion, you know,
+posing little deeper questions for
+
+ align:start position:0%
+posing little deeper questions for
+ 
+
+ align:start position:0%
+posing little deeper questions for
+students to discuss.
+
+ align:start position:0%
+students to discuss.
+ 
+
+ align:start position:0%
+students to discuss.
+And uh I was absolutely absolutely
+
+ align:start position:0%
+And uh I was absolutely absolutely
+ 
+
+ align:start position:0%
+And uh I was absolutely absolutely
+stunned that just in this one class the
+
+ align:start position:0%
+stunned that just in this one class the
+ 
+
+ align:start position:0%
+stunned that just in this one class the
+way I teach changed fundamentally.
+
+ align:start position:0%
+way I teach changed fundamentally.
+ 
+
+ align:start position:0%
+way I teach changed fundamentally.
+So by uh having flipped the class uh one
+
+ align:start position:0%
+So by uh having flipped the class uh one
+ 
+
+ align:start position:0%
+So by uh having flipped the class uh one
+very concrete thing that came out of it
+
+ align:start position:0%
+very concrete thing that came out of it
+ 
+
+ align:start position:0%
+very concrete thing that came out of it
+uh this is MIT so one of the students
+
+ align:start position:0%
+uh this is MIT so one of the students
+ 
+
+ align:start position:0%
+uh this is MIT so one of the students
+was actually uh getting some data on
+
+ align:start position:0%
+was actually uh getting some data on
+ 
+
+ align:start position:0%
+was actually uh getting some data on
+this. Um
+
+ align:start position:0%
+this. Um
+ 
+
+ align:start position:0%
+this. Um
+so there were a couple times when I had
+
+ align:start position:0%
+so there were a couple times when I had
+ 
+
+ align:start position:0%
+so there were a couple times when I had
+a traditional lecture uh class because I
+
+ align:start position:0%
+a traditional lecture uh class because I
+ 
+
+ align:start position:0%
+a traditional lecture uh class because I
+had to introduce something and uh this
+
+ align:start position:0%
+had to introduce something and uh this
+ 
+
+ align:start position:0%
+had to introduce something and uh this
+student uh uh timed me and she found
+
+ align:start position:0%
+student uh uh timed me and she found
+ 
+
+ align:start position:0%
+student uh uh timed me and she found
+that I was speaking 80% students 20%.
+
+ align:start position:0%
+that I was speaking 80% students 20%.
+ 
+
+ align:start position:0%
+that I was speaking 80% students 20%.
+Okay, which is for a traditional lecture
+
+ align:start position:0%
+Okay, which is for a traditional lecture
+ 
+
+ align:start position:0%
+Okay, which is for a traditional lecture
+class that's not bad. And then so she
+
+ align:start position:0%
+class that's not bad. And then so she
+ 
+
+ align:start position:0%
+class that's not bad. And then so she
+told me that and I said well look why
+
+ align:start position:0%
+told me that and I said well look why
+ 
+
+ align:start position:0%
+told me that and I said well look why
+don't you uh do the same thing when uh
+
+ align:start position:0%
+don't you uh do the same thing when uh
+ 
+
+ align:start position:0%
+don't you uh do the same thing when uh
+we do the discussion. So she did that
+
+ align:start position:0%
+we do the discussion. So she did that
+ 
+
+ align:start position:0%
+we do the discussion. So she did that
+and she found that it was 5050
+
+ align:start position:0%
+and she found that it was 5050
+ 
+
+ align:start position:0%
+and she found that it was 5050
+and qualitatively it's just completely
+
+ align:start position:0%
+and qualitatively it's just completely
+ 
+
+ align:start position:0%
+and qualitatively it's just completely
+different completely different remember
+
+ align:start position:0%
+different completely different remember
+ 
+
+ align:start position:0%
+different completely different remember
+uh we had uh uh a bunch of visitors from
+
+ align:start position:0%
+uh we had uh uh a bunch of visitors from
+ 
+
+ align:start position:0%
+uh we had uh uh a bunch of visitors from
+Japan
+
+ align:start position:0%
+Japan
+ 
+
+ align:start position:0%
+Japan
+second week of the class and I was doing
+
+ align:start position:0%
+second week of the class and I was doing
+ 
+
+ align:start position:0%
+second week of the class and I was doing
+the you know interactive
+
+ align:start position:0%
+the you know interactive
+ 
+
+ align:start position:0%
+the you know interactive
+uh style and they came up to me and said
+
+ align:start position:0%
+uh style and they came up to me and said
+ 
+
+ align:start position:0%
+uh style and they came up to me and said
+uh so how many months have you been
+
+ align:start position:0%
+uh so how many months have you been
+ 
+
+ align:start position:0%
+uh so how many months have you been
+teaching this class? Two weeks. They're
+
+ align:start position:0%
+teaching this class? Two weeks. They're
+ 
+
+ align:start position:0%
+teaching this class? Two weeks. They're
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's quite remarkable. I mean just the
+
+ align:start position:0%
+it's quite remarkable. I mean just the
+ 
+
+ align:start position:0%
+it's quite remarkable. I mean just the
+sheer amount of knowledge the students
+
+ align:start position:0%
+sheer amount of knowledge the students
+ 
+
+ align:start position:0%
+sheer amount of knowledge the students
+gain from this new way of teaching is it
+
+ align:start position:0%
+gain from this new way of teaching is it
+ 
+
+ align:start position:0%
+gain from this new way of teaching is it
+just it's incomp you cannot compare to
+
+ align:start position:0%
+just it's incomp you cannot compare to
+ 
+
+ align:start position:0%
+just it's incomp you cannot compare to
+the previous one. You know we like to
+
+ align:start position:0%
+the previous one. You know we like to
+ 
+
+ align:start position:0%
+the previous one. You know we like to
+lecture. We all like to lecture. Uh and
+
+ align:start position:0%
+lecture. We all like to lecture. Uh and
+ 
+
+ align:start position:0%
+lecture. We all like to lecture. Uh and
+I miss lecturing.
+
+ align:start position:0%
+I miss lecturing.
+ 
+
+ align:start position:0%
+I miss lecturing.
+A lot of faculty members who flip class
+
+ align:start position:0%
+A lot of faculty members who flip class
+ 
+
+ align:start position:0%
+A lot of faculty members who flip class
+tell me this you know. So in in their
+
+ align:start position:0%
+tell me this you know. So in in their
+ 
+
+ align:start position:0%
+tell me this you know. So in in their
+sort of quiet moment, you know, in the
+
+ align:start position:0%
+sort of quiet moment, you know, in the
+ 
+
+ align:start position:0%
+sort of quiet moment, you know, in the
+corner of their room, you know, they
+
+ align:start position:0%
+corner of their room, you know, they
+ 
+
+ align:start position:0%
+corner of their room, you know, they
+whisper, "I miss lecturing." But we all
+
+ align:start position:0%
+whisper, "I miss lecturing." But we all
+ 
+
+ align:start position:0%
+whisper, "I miss lecturing." But we all
+know that this flipping class makes it
+
+ align:start position:0%
+know that this flipping class makes it
+ 
+
+ align:start position:0%
+know that this flipping class makes it
+so much more effective. What's really
+
+ align:start position:0%
+so much more effective. What's really
+ 
+
+ align:start position:0%
+so much more effective. What's really
+important is to have good material for
+
+ align:start position:0%
+important is to have good material for
+ 
+
+ align:start position:0%
+important is to have good material for
+students to study ahead of class. And I
+
+ align:start position:0%
+students to study ahead of class. And I
+ 
+
+ align:start position:0%
+students to study ahead of class. And I
+strongly recommend video. video is a
+
+ align:start position:0%
+strongly recommend video. video is a
+ 
+
+ align:start position:0%
+strongly recommend video. video is a
+very uh rich source of knowledge and if
+
+ align:start position:0%
+very uh rich source of knowledge and if
+ 
+
+ align:start position:0%
+very uh rich source of knowledge and if
+you combine that with reading you'll be
+
+ align:start position:0%
+you combine that with reading you'll be
+ 
+
+ align:start position:0%
+you combine that with reading you'll be
+amazed at how much students bring into
+
+ align:start position:0%
+amazed at how much students bring into
+ 
+
+ align:start position:0%
+amazed at how much students bring into
+into class and uh as uh uh one of my
+
+ align:start position:0%
+into class and uh as uh uh one of my
+ 
+
+ align:start position:0%
+into class and uh as uh uh one of my
+colleagues Rona Gibson who has flipped
+
+ align:start position:0%
+colleagues Rona Gibson who has flipped
+ 
+
+ align:start position:0%
+colleagues Rona Gibson who has flipped
+uh her materials class has said the
+
+ align:start position:0%
+uh her materials class has said the
+ 
+
+ align:start position:0%
+uh her materials class has said the
+reason why flipped class is so effective
+
+ align:start position:0%
+reason why flipped class is so effective
+ 
+
+ align:start position:0%
+reason why flipped class is so effective
+is that students touch the same material
+
+ align:start position:0%
+is that students touch the same material
+ 
+
+ align:start position:0%
+is that students touch the same material
+several times. Okay. uh once when
+
+ align:start position:0%
+several times. Okay. uh once when
+ 
+
+ align:start position:0%
+several times. Okay. uh once when
+they're viewing it before coming to
+
+ align:start position:0%
+they're viewing it before coming to
+ 
+
+ align:start position:0%
+they're viewing it before coming to
+class and second time when we're
+
+ align:start position:0%
+class and second time when we're
+ 
+
+ align:start position:0%
+class and second time when we're
+discussing discussing it and third time
+
+ align:start position:0%
+discussing discussing it and third time
+ 
+
+ align:start position:0%
+discussing discussing it and third time
+when they do a pet set based on it.
+
+ align:start position:0%
+when they do a pet set based on it.
+ 
+
+ align:start position:0%
+when they do a pet set based on it.
+That's why it's so effective.
+
+ align:start position:0%
+That's why it's so effective.
+ 
+
+ align:start position:0%
+That's why it's so effective.
+Yeah, I think lecturing is going to go
+
+ align:start position:0%
+Yeah, I think lecturing is going to go
+ 
+
+ align:start position:0%
+Yeah, I think lecturing is going to go
+the wayside of uh blackboards.
\ No newline at end of file
diff --git a/zrBZjcsQ_BQ.txt b/zrBZjcsQ_BQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..75575c75de7aab080da7a518c1aafb827be9fe5f
--- /dev/null
+++ b/zrBZjcsQ_BQ.txt
@@ -0,0 +1,1405 @@
+So, when I first came to town,  the Red Sox hadn't won for 42 years.   
+
+Now it's been 86 years, so the whole town all of a sudden changes  
+
+its psychology.  A time for great celebration,   
+
+at least for you Red Sox fans.  At the, after last lecture I had an  
+
+interesting conversation with one of you.  One of you came up to me and  
+
+said very politely,  Professor Weinberg, do you have some  
+
+lecture notes that you have written out what the important points of the  
+
+lecture are that you could give me or that you could give us?   
+
+And I said, you know,  I, I'm not really interested in  
+
+doing that.  And the reason I'm not really interested in doing that is  
+
+that the main function of this course is to enable you to listen to,   
+
+when somebody is talking about conceptually complex things and to  
+
+distil what's being said and to figure out in your own mind what's  
+
+important and what is just another piece of drivel coming out of my  
+
+mouth or Eric Lander's mouth.  In fact, speaking for him,   
+
+if I will allow, can allow myself,  and myself, in the end we don't  
+
+really care that much whether you know the difference between DNA and  
+
+RNA or proteins and phospholipids.  What we're really interested in  
+
+doing is to use this course as a vehicle for pushing you to get your  
+
+brains functioning even better than they already are.   
+
+And, therefore, if you learn in this course how to,   
+
+to think about very complex subjects and figure out what's really going  
+
+on then this course will have more than paid for itself in terms of the  
+
+energy you put into it.  So, that's part of the reason why we  
+
+don't provide you with lecture outlines.  We want you to figure out  
+
+what's important on your own.  Being able to do so will itself be  
+
+a major triumph.  At the end of our discussion last  
+
+time we talked about the cell cycle,  the fact that it has, has four major  
+
+active phases.  G1, S, G2 and mitosis.   
+
+We talked about mitosis.  And we talked about the fact that  
+
+when cells emerge from mitosis,  from M phase in the absence of  
+
+growth stimulatory factors then they go into G zero.   
+
+And if they're provided with growth stimulatory factors then they'll go  
+
+back into the active cell cycle.  And this G zero phase we talked  
+
+about is a quiescence phase,  it's a resting phase.   
+
+In fact, there are two kinds of quiescent cells in our bodies.   
+
+Those that go into quiescence,  non-growth reversibly, and are able  
+
+to reemerge back into the active cell cycle, and those cells which  
+
+have irreversibly retreated from the active cell cycle.   
+
+So, for example, there are many cells in our brain where no matter  
+
+what you do to them they will never be able to go back into the active  
+
+cell cycle.  And they are,  in that sense, considered to be  
+
+post-mitotic.  Post-mitotic meaning that they will  
+
+never again grow.  It's really not clear which of the  
+
+post-mitotic cells,  which tissues in the body harbor,   
+
+harbor post-mitotic cells.  We used to think that most of the  
+
+differentiated cells in our body are post-mitotic.  And when I say  
+
+differentiated,  a topic we will not get into for the  
+
+moment, what I mean is that different cells in different parts  
+
+of the body have become differentiated by becoming very  
+
+specialized to become neurons or becoming liver cells or to becoming  
+
+skin cells and so forth.  And it is probably the case that  
+
+there are many kinds of differentiated cells in the body  
+
+which once they differentiate will no longer enter into the active cell  
+
+cycle.  Now, getting back to this.   
+
+As I also mentioned,  if we look at a Petri dish then and  
+
+we put cells like fibroblast,  connective tissue cells in the  
+
+bottom of the Petri dish,  as I told you last time, if you  
+
+provide those cells with medium which contains all the requisite  
+
+nutrients, these cells will sit here happily for an extended period of  
+
+time but will not proliferate.  However, if you add to their serum,   
+
+add their medium, you add serum to this medium.  Serum usually comes  
+
+from cows, so therefore it's called bovine serum.   
+
+Then the serum,  in addition to the nutrients present  
+
+in the, in the medium will indeed provoke these cells to proliferate,   
+
+and there are agents in the serum,  in fact there are agents which are  
+
+called growth factors which are contained within the serum which are  
+
+responsible for inducing these,  these cells to begin to proliferate.   
+
+Well, it's instructive just for a moment to step back and ask  
+
+ourselves what actually is serum?  How do you get serum?   
+
+And the way you get serum is you take blood and you allow it to clot.   
+
+And when blood clots the platelets in the, in the blood,   
+
+platelets are small cellular fragments, they have an intact  
+
+plasma membrane but they're just,  they're very tiny, they don't have a  
+
+nucleus, and these A,  A nuclear fragments, these platelets,   
+
+when blood is induced to clot the platelets aggregate with one another  
+
+and you form a big clump,  and that, a clot settles to the  
+
+bottom of the test-tube.  But in the context of wounding,   
+
+let's say you make a cut on your skin, what happens is that blood  
+
+rushes into the site of,  of the, the cut or the wound,   
+
+clotting occurs in order to create coagulation.  And why is there  
+
+coagulation?  In order to staunch the bleeding.  In order to prevent  
+
+there to be further hemorrhage,  further loss of blood.  But at the  
+
+same time, as the platelets are aggregating to help form the  
+
+structure of the clot that,  that creates a physical barrier to  
+
+prevent further bleeding,  simultaneously the platelets are  
+
+releasing a lot of growth factors into the medium around them.   
+
+Why are they doing that?  Because what's happening  
+
+simultaneous with stopping the bleeding is that the platelets are,   
+
+are releasing growth factors which are used in order to begin to  
+
+reconstruct and heal the site of wounding.  Consequently,   
+
+what happens is that the platelets release growth factors.   
+
+These growth factors stimulate cells right around the sides of the wound  
+
+which are still viable and have not been destroyed to begin to  
+
+proliferate in order to reconstruct and intact tissue.   
+
+One of the most important of these,  of these, of these factors that they  
+
+release is platelet-derived growth factor.  Remember GF is  
+
+just growth factor.  And platelet-derived growth factor,   
+
+or as it's called in the trade PDGF,  I mentioned it briefly last time, is  
+
+a very potent mitogen.  A mitogen is a growth stimulatory  
+
+agent.  It's an important mitogen for fibroblasts.   
+
+Fibroblasts, as you recall,  are the connective tissue, the  
+
+connective tissue cells that are found throughout the body.   
+
+And, therefore, if you were to,  for example, add platelet-derived  
+
+growth factor,  PDGF to those fibroblasts that were  
+
+sitting there in G zero,  PDGF will stimulate the fibroblasts  
+
+to begin to enter into the active cell cycle, to exit from G zero,   
+
+to enter into G1, and therefore to complete a, a full cell cycle.   
+
+And, by the way,  recall what I said before,   
+
+that after the cells leave the active, leave G zero and move  
+
+throughout the active cell cycle and they have a lot of growth factors,   
+
+they'll go all the way around the active growth cycle to mitosis.   
+
+And when they emerge from mitosis,  once again they'll ask themselves  
+
+the question whether it's a good idea to continue to be in the active  
+
+cell cycle or whether they should exit into G zero,   
+
+perhaps doing so reversibly.  Interestingly, if you look at the  
+
+way that the cell cycle is organized then what you see is the following,   
+
+if I can draw the cell cycle again.  Here's G1.   
+
+Here's S phase.  And here's G2.  And right at,   
+
+at a distinct point toward the end of G1 is something called the  
+
+restriction point,  which is going to be very  
+
+interesting shortly.  And what happens is after cells  
+
+emerge from G,  from mitosis and they move  
+
+throughout the,  the most of G1 they're continually  
+
+assessing their extracellular environment to determine whether or  
+
+not there are enough growth factors around to justify their continuing  
+
+the rest of the cell cycle.  And ultimately they'll reach this  
+
+restriction point,  or as it's sometimes called the R  
+
+point, and here they will make the final go versus no-go decision.   
+
+So, if there have historically been enough growth factors from the  
+
+beginning of G1 all the way to the R point then cells will commit  
+
+themselves essentially irreversibly to going through the entire rest of  
+
+the cell cycle, through M.  Conversely, if cells reach up to  
+
+this R point and they calculate that there are enough,   
+
+there are not enough mitogenic growth factors to justify  
+
+proliferation then they'll jump out of the active cell cycle and go back  
+
+to G zero.  What that means,  in effect, is as follows.  Once the  
+
+cells have passed through the R point and they're over here and they  
+
+are committed to complete the rest of the cell cycle then you can take  
+
+growth factors out of their medium and they don't care because they  
+
+only want to receive these stimulatory signals.   
+
+They only care about in this window of time.  Hereafter,   
+
+they're committed essentially irreversibly to go through the rest  
+
+of the cell cycle.  There are, as it turns out,   
+
+also growth inhibitory factors.  So, here we've been talking about  
+
+mitogens, the growth inhibitory factors.  So, an important growth  
+
+inhibitory factor is, for example, TGF beta.   
+
+And TGF beta works exactly opposite to PDGF because it is a single which  
+
+is present in extracellular space and tells the cell it should stop  
+
+proliferating.  And, therefore,   
+
+TGF beta, if it's present in large amounts in this part of the cell  
+
+cycle, if the cell experiences it in large amounts,   
+
+that will influence the cell not to move through the restriction point.   
+
+Conversely, if it's absent then obviously PDGF can have the,   
+
+the undiluted tensions of the cell.  And, therefore,   
+
+what I'm trying to convey by this is to tell you that cell balances both  
+
+its growth stimulatory and growth inhibitory signals that it's  
+
+receiving from extracellular space,  these decisions are weighed, and  
+
+finally down here the cell with make the, the binary decision to go ahead  
+
+or not to go ahead,  depending on historically how many  
+
+of these factors its recruited in this specific window of time.   
+
+Recall, as we said last time,  that once a growth factor like PDGF  
+
+goes to the plasma membrane it encounters a receptor on the surface  
+
+which let's say we call the PDGF receptor.  And I'll just draw it  
+
+like this for the moment.  It's a transmembrane protein.   
+
+The extracellular domain is on the outside.  And I'm drawing two copies  
+
+of the PDGF receptor here for reasons that will become  
+
+apparent in a moment.  And what happens is that PDGF which,   
+
+for example, can be itself a dimer-,  it can be a dimeric growth factor.   
+
+So, it has two distinct subunits in it.  They're both essentially  
+
+equivalent to one another but it is dimeric.  And this dimeric structure,   
+
+PDGF, allows it to bind to two growth factor receptors  
+
+simultaneously.  Well, why is that interesting?   
+
+It's interesting for the following reason.   
+
+These transmembrane PDGF receptors,  like the ones I've indicated right  
+
+here, they're anchored in the plasma membrane because there's a portion  
+
+of their sequence right in here in the transmembrane domain,   
+
+I'm indicating it here in the orange,  which contains highly hydrophobic  
+
+amino acids.  And those hydrophobic amino acids obviously love to be in  
+
+this hydrophobic environment of the lipid bilayer and their,   
+
+by they don't, they have no effect at all on whether the PDGF receptors  
+
+can move, can traverse in the plane of the plasma membrane.   
+
+So, the PDGF receptors can move across the face of the plasma  
+
+membrane.  These ones can move to the right or the left,   
+
+but they're not going to come in or out because they're anchored in this  
+
+lipid bilayer by this stretch of hydrophobic amino acids.   
+
+Now, what happens interestingly when PDGF, the dimeric receptor  
+
+binds to two of these PDGF receptor molecules, which,   
+
+as I told you, have lateral freedom to translate laterally on the plane  
+
+of a plasma membrane,  what happens is it will bind two of  
+
+these receptors.  And, in so doing,   
+
+it will pull the two receptor molecules next to one another.   
+
+Previously, they were just floating around in the plane of the plasma  
+
+membrane having bound their ligand,  recall that PDGF is considered a  
+
+ligand for the PDGF receptor,  having, it will cause these two  
+
+receptor molecules to now become,  become pulled very close to one  
+
+another.  So, I'll redraw it now like this.   
+
+Now these two receptor molecules look like this,   
+
+they're right, they're cheek by jowl,  they're right next to one another,   
+
+and this has some interesting consequences.  Of great interest  
+
+here is the affect this has on the ability of the PDGF receptor to emit  
+
+signals into the cytoplasm.  Because recall that the end game  
+
+here is always how does the,  how does the intracellular part of  
+
+the cell know that this,  there's been an encounter with the  
+
+growth factor in the extracellular space?   
+
+And this signal-emitting power to PDGF receptor comes from the fact  
+
+that once these two domains are brought together,   
+
+each of these two domains is able to modify the other and change the  
+
+other, i.e., subunit A modifies subunit B, subunit B modifies  
+
+subunit A.  And how is this modification achieved?   
+
+For the follow, it is achieved in the following way.   
+
+That the, this domain,  which I've been calling,   
+
+I've just been writing like this,  as a rectangle, is actually a  
+
+catalytic agent.  It's actually a tyrosine kinase.   
+
+So, it's an enzyme.  And a tyrosine kinase is an enzyme that takes the  
+
+gamma phosphate from ATP,  the high energy phosphate from APT,   
+
+ATP and transfers it to tyrosine amino acids that are present  
+
+on substrates.  So, if here is an amino acid  
+
+sequence in the single letter,  letter code, and if we admit that Y  
+
+is the, is the code for tyrosine then if here's a protein that it  
+
+functions as a substrate for a tyrosine kinase,   
+
+a tyrosine kinase will add a phosphate group to the side chain of  
+
+the tyrosine, which I'm not drawing here, but tyrosine has a hydroxyl  
+
+group in its side chain and,  therefore, it will phosphorilate  
+
+this tyrosine.  That is to say will tetraphosphate  
+
+group do it?  It will phosphorilate this tyrosine.   
+
+So, these two rectangles are,  in fact, tyrosine kinases.  And what  
+
+happens, after the two subunits of the receptor have been brought  
+
+together, is thereafter,  what one finds is that each of these  
+
+receptor subunits becomes multiply phosphorilated.   
+
+And each of these lollipops that I'm indicating here are sites where  
+
+there, a tyrosine residue has become phosphorilated.   
+
+In fact, there's a tail of the PDGF receptor that extends even further  
+
+to the cytoplasm which also acquires a number of different phosphates on  
+
+it.  And, again,  I'd remind us that this  
+
+phosphorylation is really what's often called transphosphorylation  
+
+because each receptor molecule phosphorilates the tyrosine residues  
+
+on the other.  Obviously,  when these two receptor molecules  
+
+are far apart in the plain of the plasma membrane,   
+
+this transphosphorylation cannot occur.   
+
+But once the two tyrosine kinase residues, once the two tyrosine  
+
+kinases have been brought together,  pulled together by the dimerization  
+
+of the receptor,  now this cross-phosphorylation,   
+
+on each phosphorylating the other can occur, and soon the receptors  
+
+are highly phosphorilated.  All of these phosphate groups,   
+
+to repeat myself, being attached to tyrosine residues in their  
+
+cytoplasmic domains.  And this, in turn,   
+
+creates interesting docking sites for a variety of other cytoplasmic  
+
+signaling proteins.  And we'll talk about some today and  
+
+next time, but what I want to leave you with is the following impression.   
+
+That after this phosphorylation actually occurs there are a number  
+
+of molecules in the cytoplasm,  signaling molecules that have  
+
+affinity for binding these phosphotyrosines.   
+
+When I say phosphotyrosine,  obviously, I'm referring to the  
+
+phosphorilated form of tyrosine that's been created by a tyrosine  
+
+kinase enzyme.  So, here's one molecule that can  
+
+bind.  Here's molecule A combined to one of these phosphates,   
+
+another one combined to this phosphate specifically,   
+
+and each of these molecules,  once they're attracted to this  
+
+phosphorilated receptor,  can then emit downstream signals,   
+
+send a variety of signals into the cell that ultimately end up in  
+
+persuading the cell to proliferate.   
+
+And so these effects here of growth factors in the G1 phase of the cell  
+
+cycle are mediated by this transmembrane signaling,   
+
+by the activation of these,  of this PDGF receptor, for example,   
+
+and by the resulting a release of downstream signals into the cell  
+
+which pursued the cell to proliferate or not to proliferate.   
+
+To be sure the,  when platelets clot,   
+
+when platelets aggregate and they release PDGF, they also release  
+
+other kinds of growth factors.  For instance, there's another  
+
+growth factor that's called IGF1,  insulin-like growth factor, and that  
+
+has its own receptor on the surface of cells.  And there are,   
+
+on a cell, hundreds to thousands of these PDGF receptors,   
+
+there are IGF receptors,  there are EGF receptors.   
+
+And a cell often will require several distinct kinds of growth  
+
+factor activations in order to proliferate.  So,   
+
+this is only a minor part of the entire exposure that a cell  
+
+experiences in the G1 phase of the cell cycle.  To elaborate on a point  
+
+that I made last time,  an important biological distinction  
+
+between normal cells and cancer cells is the fact that cancer cells  
+
+require relatively little growth factors or in the medium in order to  
+
+proliferate.  Normal cells have a very strong  
+
+requirement for growth factors in their medium.  And,   
+
+therefore, what we can already imagine is the following kind of  
+
+scenario.  That cancer cells have someone deregulated this signaling  
+
+pathway.  Somehow they have become independent of the stimulation that  
+
+is normally required,  usually required for cells to  
+
+proliferate.  And,  in fact, we know of several  
+
+different ways by which cancer cells can acquire this independence.   
+
+One of the most important ways,  it's, it a really interesting one,   
+
+is here's a cancer cell, which we'll talk about very shortly.   
+
+And what you find in certain kinds of cancer cells is that the cancer  
+
+cells themselves release growth factors into the medium.   
+
+So, there are certain kinds of cancer cells that will release,   
+
+let's say, a growth factor that's like EGF into the medium around it,   
+
+around themselves.  Well, you'll say that's kind of  
+
+amusing.  But so what.  The important part here is that  
+
+these same cancer cells have receptors for TG,   
+
+for EGF on their surface.  So, they're producing a growth  
+
+factor and they can also respond to the same growth factor.   
+
+And, therefore, this EGF,  once it's released, can swim over  
+
+here, activate the receptor and pursued the cell to start  
+
+proliferating.  This is, if you will,   
+
+a positive feedback loop.  But note here importantly that this,   
+
+the growth of this cell is not being controlled by growth factors coming  
+
+from cells elsewhere in the tissue or the body.  Here we're not talking  
+
+about different cells talking to one another.  Here we're talking about a  
+
+monologue where this cell is talking to itself.  This is sometimes called  
+
+autocrine signaling and refers to the fact that certain kinds of  
+
+cancer cells are able to make growth factors to which they can respond.   
+
+In fact, in normal tissues it's rare for a single cell type in a normal  
+
+tissue to be able to make a growth factor and to be able to respond to  
+
+the same growth factor.  Why can it normally not respond to  
+
+that growth factor?  Because it won't make the receptor  
+
+for the growth factor.  For example, epithelial cells like  
+
+the cells in your skin or the cells lining the gut,   
+
+they can release PDGF,  but they don't have a PDGF receptor  
+
+on their surface.  And, therefore,   
+
+even though they release copious amounts of PDGF,   
+
+that will not result in this auto stimulatory proliferation and,   
+
+therefore, you don't have this decontrolled self-proliferation that  
+
+you see often in cancer cells,  this autocrine loop.  In many kinds  
+
+of cancer cells you have another alteration of this growth factor  
+
+signaling pathway.  And here what we see is the  
+
+following.  Instead of there being a small number of growth factor  
+
+receptors on the cell surface,  now there are ten or twenty or fifty  
+
+times more than are normally present on the cell surface.   
+
+In other words,  this growth, the growth factor  
+
+receptors are what is called overexpressed.   
+
+ And, therefore,   
+
+a delicate balance is disrupted because normally,   
+
+let's say, a cell with have on its surface 500 EGF receptors,   
+
+but in many kinds of cancers probably 30% or 40% of all  
+
+carcinomas, carcinomas are the tumors from epithelial tissues,   
+
+you'll find overexpressed EGF receptor.  Well,   
+
+why is that interesting?  It's interesting for the following  
+
+reason.  I told you before that the activation of a receptor depends on  
+
+its ligand to persuading two receptor subunits to come together  
+
+and start firing, as we just discussed.   
+
+But if now all of a sudden the cell contains large amounts of this  
+
+growth being expressed,  of the growth factor receptor being  
+
+expressed on the surface,  ten or a hundred times more than  
+
+normal, then these growth factor receptors are going to be rather  
+
+densely packed on the cell surface.  And now they may just come together  
+
+because they happen to bump into each other very frequently.   
+
+They don't need the growth factor to pull them together just because  
+
+there are so many of them.  So, there's random interactions,   
+
+random bumping together And these two growth factor  
+
+receptors may just bump together and thereby send signals into the cell  
+
+persuading the cell that there's been some kind of growth factor in  
+
+the extracellular domain that's been encountered when,   
+
+in fact, all that's happened is that there are so many of these growth  
+
+factor receptors around that they're constantly bumping into each other,   
+
+and while they've collided with one another they can activate signaling  
+
+and release growth stimulatory signals into the cell.   
+
+There's another kind of,  of alteration of growth factor  
+
+receptors that's also seen in many kinds of human tumors.   
+
+For example, in, in glioblastomas,  which is a brain tumor.  And a  
+
+glioblastoma has the following kind of, of receptor on the surface.   
+
+It has truncated forms of the EGF receptor on the surface where a lot  
+
+of the ectodomain is simply not present.  So, here's the normal EGF  
+
+receptor, here is a truncated EGF receptor where a lot of the  
+
+extracellular domain,  which I'm calling the ectodomain,   
+
+has simply been lopped off.  How has it be lopped off?   
+
+Well, there's been a mutation it the gene which has,   
+
+in effect, deleted segments in coding the N-terminus of the  
+
+receptor protein,  which normally sticks its head out  
+
+of the cell.  And now you have these truncated receptors.   
+
+And such truncated EGF receptors are able to fire constitutively.   
+
+Constitutively implies that these receptors are able to fire in a  
+
+fashion that is no longer regulated by physiologic signals.   
+
+It's a high steady rate.  So now these receptor molecules,   
+
+these truncated receptor molecules flood the cell with growth  
+
+stimulatory signal and,  for reasons that aren't really clear  
+
+to this day, these two,  these receptor, truncated receptor  
+
+molecules can dimerize,  they can come together even if  
+
+there's no extracellular ligand present, even if there's no growth  
+
+factor in the extracellular space.  And we now realize,   
+
+for example, that there are a variety of structurally altered  
+
+receptors that fire constitutively into a cell in many kinds of human  
+
+tumors.  And in each case the cancer cell is deluded into thinking that  
+
+some growth factor has been encountered out here when,   
+
+in fact, there's not at all.  Once again, what we see is a  
+
+situation in which the cell,  the cancer cell is being deluded  
+
+into thinking there's growth factors present, extracellular space.   
+
+None has been present at all.  There have been a variety of drugs  
+
+developed against,  for example, lung cancer.   
+
+And there are a variety of different kinds of lung cancers.   
+
+One is called non-small cell lung carcinoma.  We don't have to deal  
+
+with the subsets of lung cancers.  And it turned out, it turned out  
+
+that one of these drugs,  it's called Iressa, had very mixed  
+
+effects on patients.    
+
+In about 90% of these,  of the class of lung cancers,   
+
+patients that were treated, the drug Iressa, used over the last several  
+
+years, had almost no effect on the tumor treatment and the patients  
+
+continued to, to proceed to their death.  It had,   
+
+it really had no effect.  But in 10%, in fact, there was some  
+
+dramatic responses and tumors shrunk down.   
+
+Now, normally a 10% response rate would be enough to cause a drug  
+
+company to abandon all further development of the drug because it's  
+
+just too low a response and who wants to take a drug where the  
+
+chances of having a good response are as low as 10%?   
+
+It's just not a good situation.  But then some geneticists here in  
+
+Boston, one group at the MGH and another over at the Dana Farber,   
+
+began to look at the lung cancer cells that responded,   
+
+i.e., from tumors of patients that responded and shrank in response to  
+
+the drug and the lung,  and the lung cancer cells of  
+
+patients who didn't.  It turns out that Iressa is an  
+
+inhibitor of the tyrosine kinase of the EGF receptor.   
+
+That's how it was designed.  In other words, this drug, it's a  
+
+low molecular weight drug and it goes into the tyrosine kinase domain,   
+
+that rectangular thing I showed you before very schematically,   
+
+and it shuts down the firing of the receptor.   
+
+That was the motivation behind creating this drug.   
+
+So, Iressa shuts down the EGF receptor and 10% of lung cancer  
+
+patients, their tumor shrank,  the other 90% didn't, weren't  
+
+effected at all.  And what these two groups of  
+
+geneticists found over the last three or four months is that the  
+
+patients whose tumors responded had tumor cells where the EGF receptor  
+
+was mutated and therefore firing in a constitutively active fashion.   
+
+That is to say there were actually structural alterations in the  
+
+receptor.  This is a massive structural alteration of the  
+
+receptor here,  this truncation.   
+
+But, in fact, in certain patients the 10% of patients that responded,   
+
+there were much more subtle changes in the cytoplasmic domain of the  
+
+protein which allowed these receptors to constitutively dimerize,   
+
+once again, in a ligand independent fashion.   
+
+So, these subtle mutations mimic,  in effect, the consequences of  
+
+deleting or truncating the extracellular domain in that in both  
+
+cases one gets a ligand independent receptor.  In those cases where  
+
+these, where the patients had a mutant EGF receptor,   
+
+structurally altered EGF receptor that was firing constitutively,   
+
+there were dramatic responses to the Iressa drug.   
+
+In the 90% of patients where there was no effective response to the  
+
+drug, the EGF receptor was wild-type,  it was present in a wild-type  
+
+configuration.  It might have been slightly  
+
+overexpressed but it wasn't,  but it continued to, to function  
+
+essentially as a normal EGF receptor.  And this represents a major advance  
+
+in cancer therapy because it suggests that one has to begin to  
+
+understand what subsets of patients one should treat with a drug which  
+
+can, on its own,  have quite toxic effects on the  
+
+patient.  And, from now on,   
+
+to state the obvious,  when one gets lung cancer patients  
+
+one will check quickly using various reactions, like the PCR reaction,   
+
+to see whether or not their cancer cells have a mutated EGF receptor.   
+
+And, if they do, they will be candidates for Iressa treatment with  
+
+the expectation that 60%,  80% or even 100% of them will have  
+
+tumors that respond.  And if they don't have a mutated  
+
+EGF receptor then they will not be subjected to a treatment  
+
+by this drug.  This is the beginning of a new era  
+
+of cancer drug treatment.  It's called rational drug design,   
+
+or rational treatment, where you don't just lump all the patients  
+
+with a certain disease together and say let's give them all this drug  
+
+and throw things up in the air and see what happens.   
+
+Here one begins to do a genetic diagnosis of the genomes of the  
+
+patient's cancer cells in order to determine whether or not they have  
+
+certain mutated genes.  In this case we're referring to one  
+
+of these growth factor receptors.  By the way, we're talking about lung  
+
+cancer today, right?  If you are smoking now,   
+
+I always ask the class how many people are smoking,   
+
+and nobody has the, has the moral fortitude to raise their hands.   
+
+But if you are smoking now and you started at this age and you continue.   
+
+And, by the way,  if you start at your age and you  
+
+continue smoke,  stopping smoking is actually a bit  
+
+more difficult,  quite a bit more difficult than  
+
+stopping heroine.  That's pretty interesting,   
+
+right?  So, if you continue to smoke now you will be healthy for a pretty  
+
+long period of time,  probably another 20 or 30 years.   
+
+And for you that sounds like forever, but when you get to be  
+
+about 40 or 50 things are going to start falling apart.   
+
+Soon you won't be able to be very athletic, soon your lungs are going  
+
+to be able, are going to degrade,  and by the time you reach your  
+
+fifties, sixties or seventies what's going to happen is you will,   
+
+on average, have a six to eight year shortened life expectancy.   
+
+Now you say six to eight years is not that much,   
+
+but it really is.  You know, when you get to be 70 and  
+
+you think you're going to die next year or you're going to die in six  
+
+or eight years it makes a big difference.  Six to eight years is  
+
+an enormous difference in life expectancy.  20% of all people who  
+
+died last year in this country,  20% of all deaths came from  
+
+cigarette smoking.  Imagine that.  And when you die from cigarette  
+
+smokes, smoking sometimes you get lung cancer.  There probably were,   
+
+I think, 600,000 people who died from smoking last year.   
+
+Six hundred thousand.  There were 55,000 American soldiers who died in  
+
+Vietnam in the whole war,  there were 220,000 American soldiers  
+
+who died in all of World War II,  and last year in this, and there  
+
+were 3,000, or 2,  00 people who died in the World  
+
+Trade Center.  All right?  Got all those numbers?   
+
+So, last year 600,  00 people died premature deaths  
+
+because they were smoking.  How many people died last year from  
+
+smoking marijuana?  Maybe two or three,   
+
+I don't know.  [APPLAUSE]  Am I urging you to do any kind of smoking?   
+
+I'm not saying marijuana smoking is good for you, but I just want you to  
+
+get these things in mind,  the perspective.   
+
+If you smoke, you know,  in many countries, including this  
+
+one, there isn't much tension by,  given by the government to,   
+
+dissuading people from smoking,  and here's the reason why.  If you  
+
+smoke, and you going to get,  get sick eventually, eventually the  
+
+country is always going to have to pay for your medical costs,   
+
+right?  Sooner or later we all have to pay for the costs of people who  
+
+get sick.  It's all shared in one way or another.   
+
+But it's not such a big problem for a government like the  
+
+American government.  Because if you smoke you're going to  
+
+die early enough that you won't draw on social security.   
+
+And, therefore, the government actually saves money by your smoking,   
+
+because by the time they add up how much they get on the tobacco tax and  
+
+how much they earn by your not living long enough to draw a pension,   
+
+it's much better,  it's much more money than how much  
+
+it's going to cost to take care of you while you're dying from  
+
+emphysema or bladder cancer or lung cancer or heart disease.   
+
+Many more people die from heart attacks due to smoking than die from  
+
+lung cancer, in fact.  So, think about this.   
+
+Think about this.  If you smoke it's probably a good time to stop  
+
+because if you continue at your age,  especially if you're women, which is  
+
+women, for some reason women have a harder time stopping than men,   
+
+they can't say why.  It's probably some physiological thing.   
+
+If you, if you continue now at your age, it will be almost impossible to  
+
+stop.  If you live with smokers ask them to leave.  [LAUGHTER]  
+
+If you live at home with your parents and they smoke tell them  
+
+it's time for them to leave.  Throw them out of the house.   
+
+Smoke, second-hand smoking killed probably between 60,   
+
+00 and 80,000 people last year in this country.  Second-hand smoke.   
+
+And, by the way, if you want to see an interesting phenomenon,   
+
+go to a veterinary hospital because there they with great frequently,   
+
+frequency treat dogs who have lung cancer.  And why do they  
+
+have lung cancer?  Not in 99% of the cases,   
+
+in 100% of the cases these dogs live with owners who smoke.   
+
+An average tobacco smoker goes through six or eight dogs in his or  
+
+her lifetime.  [LAUGHTER]  It's true.  It's absolutely true.   
+
+So if you, if you think the dogs,  if that's a fact for the, for the,   
+
+for the dog owners,  think about what's happening to the  
+
+inside of your lungs.  And so I'm going to take back what  
+
+I said before.  Before I told you that the most  
+
+important thing for you to do in this course is to learn how to think  
+
+clearly and to assess and to distil conceptually complex material,   
+
+there's actually one more thing that's even more important to get  
+
+out of this course,  if you do, and that is to stop  
+
+smoking.  If you do that,  if you do that it'll be vastly more  
+
+important for the rest of your life than anything you learn here.   
+
+So, write that down, vastly more important.  You may think it's  
+
+glamorous, you may think it's exciting, but keep in mind,   
+
+people who stop smoking have vastly greater effects on reducing the  
+
+morbidity and the mortality in this country than anything that cancer  
+
+researchers can do.  Keep that in mind.   
+
+And if you start smoking now and you think that somehow the cancer  
+
+researchers are going to be able to come up with some miracle cure by  
+
+this time you start coughing and start spitting up blood,   
+
+don't be so certain.  They may not be able to save you,   
+
+to pull your fat out of the fire.  So, I don't know whether I,   
+
+I gave this message in a very subtle way or I hit you over the head with  
+
+it.  [LAUGHTER]  But think,  think about that.  Now, now we're  
+
+going to focus on lung cancer,  we're going to focus on cancer  
+
+because it's one of the consequences of cigarette smoking,   
+
+but it's a disease we want to talk about both this time and next time,   
+
+and we want to relate it here to the cell cycle and,   
+
+and how the growth of cell proliferation occurs.   
+
+I told you last time that a human tumor is roughly-speaking about,   
+
+a human body roughly carries three times ten to the thirteenth cells.   
+
+So, that's quite a few cells.  That's how many cells there are in  
+
+the human body,  plus or minus.  A human tumor of one,   
+
+let's say one cubic centimeter is roughly ten to the ninth cells.   
+
+So, a tiny tumor this way already has a billion cells in it.   
+
+And what I want to say is that those billion cells,   
+
+or if the tumor grows larger to ten to a hundred billion cells,   
+
+it's still not that much compared with the overall size of the body.   
+
+But tumors of that size can kill you.  And one, an interesting and  
+
+important thing to realize about all the cancer cells in that tumor mass  
+
+is that they all descend from a single progenitor.   
+
+In other words, if we imagine a situation where here are a whole  
+
+bunch of normal cells and here's the boundary between normalcy up here  
+
+and malignancy,  malignancy obviously refers to  
+
+cancer, we could imagine where there are many cells which independently  
+
+cross the boundary from one to the other and become the progenitors of  
+
+a vast tumor mass.  But that's not what happens.   
+
+What happens, in fact, is that only one cell gets converted or becomes,   
+
+as one says here, it becomes transformed from a normal cell into  
+
+a cancer cell.  And this transformation causes this  
+
+one cell to become the progenitor,  the ancestor of all the cells in the  
+
+tumor mass.  So,  one important realization we have  
+
+about looking at different tumors is that cancers are monoclonal growths,   
+
+i.e., they form clonal populations.  They're monoclonal in the sense that  
+
+they all are genetically derived from a single common ancestor rather  
+
+than being polyclonal.  What else can we say about cancer  
+
+cells or the cells in a tumor?  If you take cells out of Petri dish,   
+
+out of an animal or a human and put them on a Petri dish,   
+
+excuse me, and you put them there,  then what you'll see is following  
+
+interesting behavior.  If you put normal cells in a Petri  
+
+dish they'll grow across the bottom of the Petri dish until they cover  
+
+the entire bottom of the Petri dish.   
+
+So, you can put a hundred cells in and they'll continue to proliferate.   
+
+Let's look at the Petri dish from top down, so you might have a small  
+
+number of cells here and here,  and normal cells will continue to  
+
+proliferate until they begin to touch one another,   
+
+and then they'll stop growing.  And this stopping of growing is,   
+
+is the phenomenon that's called contact inhibition.   
+
+So, a normal cell will indicate contact inhibition.   
+
+And to state, to state the obvious,  this phenomenon or this behavior of  
+
+contact inhibition creates what's called a cell monolayer because if  
+
+the cell stopped growing once they touch each other they're not going  
+
+to be two or three or four layers of cells in the Petri dish.   
+
+So, here we're looking at this Petri dish in cross-section and  
+
+there's a monolayer of normal cells here.   
+
+If you put a cancer cell in the Petri dish, or let's put here a  
+
+cancer cell, we'll seed it amidst normal cells, what will happen is  
+
+that the cancer cell lacks,  has lost contact inhibition,   
+
+and the cancer cell will continue to proliferate even after it's touched  
+
+its neighbors.  So, it has lost cancer,   
+
+it has lost contact inhibition and will start growing on top of,   
+
+the cancer cells will start growing on top of each other because they  
+
+don't mind growing in spite of their having intimate contact with  
+
+neighboring cells.  And, in fact, what you can do is  
+
+the following experiment.  You can put cells in a Petri dish  
+
+like this, a whole bunch of normal cells in a Petri dish,   
+
+and then you can put into them some kind of transforming influence,   
+
+which we'll talk about very shortly,  i.e., you can influence some of  
+
+these cells to become transformed.  And how we do so we'll tell, we'll  
+
+hold in abeyance just for a moment.  So, we'll have this cell. We'll do  
+
+this cell to become transformed and this cell to become transformed.   
+
+And what will happen is that those cells will begin to form a very  
+
+thick clump of cells,  these blue ones, the ones that are  
+
+transformed.  Whereas,  all the other cells will grow until  
+
+they form a monolayer at which point they'll stop proliferating.   
+
+So, the cancer cells keep piling up and the transformed cells,   
+
+transformed by one or another agent,  we won't talk about that yet,   
+
+continue to proliferate long after the normal cells have stopped  
+
+proliferating.  The normal cells having stopped  
+
+proliferating because they're contact inhibited.   
+
+And, therefore, they'll form this clump of cells which we'll call a  
+
+focus.  And if you hold the Petri dish up to the light and you look at  
+
+it and there are some transformed cells present,   
+
+you can see the foci,  they're very thick.  Whereas,   
+
+the thin monolayer of cells will just look pretty transparent.   
+
+But this focus will look highly opaque by virtue of the multiple  
+
+layers of cells that are involved in it.   
+
+Now, in fact, we can begin to ask the question of how and why cells  
+
+like this become transformed and exhibit this behavior.   
+
+In fact, until the 1980s there wasn't really a clear understanding  
+
+about how that happened.  I've already given you some clues  
+
+because I've already told you the fact that certain cancer cells carry  
+
+mutant genes.  What kind of mutant genes?   
+
+Well, I gave you, in anticipation of discussion,   
+
+the fact that certain cancer cells carry mutant genes that specify  
+
+mutant growth factor receptors.  And these mutant growth factor  
+
+receptors, as I indicated,  begin to push the cell the  
+
+proliferate.  And so that already anticipates a conclusion we're about  
+
+to make, which is that the reason why cancer cells behave abnormally  
+
+is that they carry mutant genes.  Now, let's talk about the nature of  
+
+these mutant genes because,  if you look at these mutant genes,   
+
+invariably they are the consequences of what we call somatic mutations.   
+
+By that I mean, I mean the following.  Let's say we all start  
+
+out with a really good set of genes.  And, thank the good Lord, we all do.   
+
+But as we go through life through accidents or through intent we can  
+
+damage these genes.  We can muck them up in different  
+
+ways.  And these genes,  this damage may occur to cells in  
+
+the skin, they may occur to cells in your belly, they may occur to cells  
+
+in the brain, and these are called somatic mutations in contrast to the  
+
+germline mutations that affect one's offspring.  Because,   
+
+as you must realize by now,  the only way you can have mutations  
+
+that affect your descendents is if those mutations strike in the gonads  
+
+and affect the genomes of either sperm or egg.   
+
+But the mutations occurring everywhere else in the body outside  
+
+of the gonads,  because they occur in,   
+
+I think I, this is somatic,  excuse me, because they occur in the  
+
+soma, the soma is defined as the entirety of the body outside of the  
+
+gonads, outside of the germi,  these somatic mutations might affect  
+
+the tissues around them but they will not be transmitted from one  
+
+organismic generation to the next.  And, accordingly,   
+
+we begin to imagine,  in fact, correctly we begin to  
+
+construct this model that one of the most important mechanisms of  
+
+creating a cancer cell is to damage its genome.  So,   
+
+I'll tell you a story now,  which I'm only going to finish on  
+
+Monday.  We have,  let's imagine, a 55-year-old,   
+
+this is a true story, 55-year-old man who's been smoking since he or  
+
+she, he was 15 years old.  So, he's been smoking for 40 years.   
+
+And during those periods of 40 years,  by the way, I'm not saying whether  
+
+I'm for or against smoking,  you understand that.  During that  
+
+period of 40 years this person has been introducing large amounts of  
+
+tobacco smoke compounds into his lungs.  Now, it turns out that these  
+
+compounds, this tobacco smoke compounds are carcinogens.   
+
+You know carcinogen means it causes cancer. But it happens also to be  
+
+the case that a lot of carcinogens,  cancer-causing compounds are also  
+
+mutagens.  That is to say they can mutate DNA.   
+
+So, here we have a scenario that we're going to set up for next time.   
+
+55-year-old man.  Smokes for 40 years.  Dumps a lot of carcinogens  
+
+into his lungs.  The carcinogens which are highly,   
+
+which induce mutations very potently are passed from his lungs into his  
+
+blood and there go from the blood into the kidneys.   
+
+And from the kidneys they are excreted into the urine and then  
+
+they sit around in the bladder for a while. And let's imagine now that  
+
+the urine of this man has all of these highly mutation-active  
+
+carcinogens in his urine,  which, in principle, can begin now  
+
+to strike out and attack the genomes of the cells lining the urinary  
+
+bladder.  In other words,  by, by smoking cigarettes you can  
+
+actually mutate the genomes,  somatic mutation, the genomes of  
+
+cells lining the bladder of the,  the urinary bladder, or, of course,   
+
+to state the obvious, you can also mutate the genomes of the cells  
+
+lining the alveoli in the lungs.  That's why you get lung cancer.   
+
+And a consequence of this can be,  with serious probability, that now  
+
+some of these cells become mutated and that, in turn,   
+
+will lead to a life-threatening tumor.  So, on this very cheerful  
+
+note and your having heard two major take-home lessons, have  
+
+a great weekend.  See you on Monday.  Enjoy  
+
+the parade tomorrow.
\ No newline at end of file